LMFDB - Embedded newform 189.2.bd.a.47.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(47,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 15]))

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

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

chi := DirichletCharacter("189.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.bd (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			47.14
Character	$\chi$	$=$	189.47
Dual form			189.2.bd.a.185.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.882178 + 0.155552i) q^{2} +(1.65967 - 0.495491i) q^{3} +(-1.12534 - 0.409592i) q^{4} +(0.123522 + 0.0449584i) q^{5} +(1.54119 - 0.178947i) q^{6} +(1.69913 - 2.02805i) q^{7} +(-2.48059 - 1.43217i) q^{8} +(2.50898 - 1.64470i) q^{9} +O(q^{10})$	\(q+(0.882178 + 0.155552i) q^{2} +(1.65967 - 0.495491i) q^{3} +(-1.12534 - 0.409592i) q^{4} +(0.123522 + 0.0449584i) q^{5} +(1.54119 - 0.178947i) q^{6} +(1.69913 - 2.02805i) q^{7} +(-2.48059 - 1.43217i) q^{8} +(2.50898 - 1.64470i) q^{9} +(0.101975 + 0.0588754i) q^{10} +(1.37059 + 3.76567i) q^{11} +(-2.07064 - 0.122187i) q^{12} +(-1.02604 + 2.81901i) q^{13} +(1.81440 - 1.52479i) q^{14} +(0.227282 + 0.0134118i) q^{15} +(-0.130766 - 0.109725i) q^{16} +(-0.172311 + 0.298451i) q^{17} +(2.46920 - 1.06064i) q^{18} +(-4.24215 + 2.44921i) q^{19} +(-0.120590 - 0.101187i) q^{20} +(1.81510 - 4.20778i) q^{21} +(0.623349 + 3.53519i) q^{22} +(-6.27733 + 1.10686i) q^{23} +(-4.82657 - 1.14781i) q^{24} +(-3.81699 - 3.20283i) q^{25} +(-1.34365 + 2.32726i) q^{26} +(3.34913 - 3.97282i) q^{27} +(-2.74277 + 1.58630i) q^{28} +(2.29851 + 6.31510i) q^{29} +(0.198417 + 0.0471857i) q^{30} +(2.98538 - 8.20227i) q^{31} +(3.58403 + 4.27128i) q^{32} +(4.14058 + 5.57063i) q^{33} +(-0.198433 + 0.236483i) q^{34} +(0.301058 - 0.174119i) q^{35} +(-3.49712 + 0.823195i) q^{36} -7.28599 q^{37} +(-4.12331 + 1.50076i) q^{38} +(-0.306081 + 5.18700i) q^{39} +(-0.242020 - 0.288428i) q^{40} +(9.04416 + 3.29180i) q^{41} +(2.25577 - 3.42967i) q^{42} +(0.350643 - 1.98860i) q^{43} -4.79906i q^{44} +(0.383858 - 0.0903572i) q^{45} -5.70989 q^{46} +(4.17641 - 1.52009i) q^{47} +(-0.271395 - 0.117314i) q^{48} +(-1.22594 - 6.89181i) q^{49} +(-2.86905 - 3.41920i) q^{50} +(-0.138098 + 0.580706i) q^{51} +(2.30929 - 2.75210i) q^{52} +(-5.49931 + 3.17503i) q^{53} +(3.57251 - 2.98377i) q^{54} +0.526764i q^{55} +(-7.11934 + 2.59731i) q^{56} +(-5.82699 + 6.16681i) q^{57} +(1.04537 + 5.92857i) q^{58} +(0.136314 - 0.114381i) q^{59} +(-0.250277 - 0.108186i) q^{60} +(-1.59759 - 4.38933i) q^{61} +(3.90952 - 6.77148i) q^{62} +(0.927544 - 7.88287i) q^{63} +(2.66805 + 4.62120i) q^{64} +(-0.253476 + 0.302081i) q^{65} +(2.78620 + 5.55836i) q^{66} +(2.00174 + 11.3525i) q^{67} +(0.316152 - 0.265283i) q^{68} +(-9.86983 + 4.94738i) q^{69} +(0.292671 - 0.106774i) q^{70} +(0.373587 - 0.215690i) q^{71} +(-8.57923 + 0.486542i) q^{72} -1.52364i q^{73} +(-6.42754 - 1.13335i) q^{74} +(-7.92189 - 3.42435i) q^{75} +(5.77706 - 1.01865i) q^{76} +(9.96576 + 3.61872i) q^{77} +(-1.07687 + 4.52825i) q^{78} +(0.410757 - 2.32952i) q^{79} +(-0.0112194 - 0.0194325i) q^{80} +(3.58993 - 8.25302i) q^{81} +(7.46651 + 4.31079i) q^{82} +(6.81615 - 2.48087i) q^{83} +(-3.76609 + 3.99175i) q^{84} +(-0.0347021 + 0.0291185i) q^{85} +(0.618659 - 1.69975i) q^{86} +(6.94383 + 9.34206i) q^{87} +(1.99320 - 11.3040i) q^{88} +(-7.70903 - 13.3524i) q^{89} +(0.352686 - 0.0200014i) q^{90} +(3.97372 + 6.87070i) q^{91} +(7.51752 + 1.32554i) q^{92} +(0.890584 - 15.0923i) q^{93} +(3.92079 - 0.691340i) q^{94} +(-0.634113 + 0.111811i) q^{95} +(8.06467 + 5.31304i) q^{96} +(12.2061 + 2.15226i) q^{97} +(-0.00946529 - 6.27050i) q^{98} +(9.63217 + 7.19377i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.882178	+	0.155552i	0.623794	+	0.109992i	0.476606	−	0.879117i	$-0.341867\pi$
$2$	0.882178	+	0.155552i	0.623794	+	0.109992i	0.147188	+	0.989109i	$0.452978\pi$
$3$	1.65967	−	0.495491i	0.958208	−	0.286072i
$3$	1.65967	−	0.495491i	0.958208	−	0.286072i
$4$	−1.12534	−	0.409592i	−0.562672	−	0.204796i
$5$	0.123522	+	0.0449584i	0.0552408	+	0.0201060i	0.369493	−	0.929234i	$-0.379531\pi$
$5$	0.123522	+	0.0449584i	0.0552408	+	0.0201060i	−0.314252	+	0.949340i	$0.601754\pi$
$6$	1.54119	−	0.178947i	0.629190	−	0.0730549i
$7$	1.69913	−	2.02805i	0.642209	−	0.766529i
$7$	1.69913	−	2.02805i	0.642209	−	0.766529i
$8$	−2.48059	−	1.43217i	−0.877021	−	0.506348i
$9$	2.50898	−	1.64470i	0.836326	−	0.548233i
$10$	0.101975	+	0.0588754i	0.0322474	+	0.0186180i
$11$	1.37059	+	3.76567i	0.413249	+	1.13539i	0.955453	+	0.295145i	$0.0953679\pi$
$11$	1.37059	+	3.76567i	0.413249	+	1.13539i	−0.542204	+	0.840247i	$0.682410\pi$
$12$	−2.07064	−	0.122187i	−0.597743	−	0.0352724i
$13$	−1.02604	+	2.81901i	−0.284571	+	0.781852i	0.712231	+	0.701945i	$0.247685\pi$
$13$	−1.02604	+	2.81901i	−0.284571	+	0.781852i	−0.996802	+	0.0799075i	$0.974538\pi$
$14$	1.81440	−	1.52479i	0.484918	−	0.407519i
$15$	0.227282	+	0.0134118i	0.0586840	+	0.00346290i
$16$	−0.130766	−	0.109725i	−0.0326914	−	0.0274313i
$17$	−0.172311	+	0.298451i	−0.0417914	+	0.0723849i	−0.886165	−	0.463371i	$-0.846640\pi$
$17$	−0.172311	+	0.298451i	−0.0417914	+	0.0723849i	0.844373	+	0.535756i	$0.179973\pi$
$18$	2.46920	−	1.06064i	0.581996	−	0.249995i
$19$	−4.24215	+	2.44921i	−0.973216	+	0.561887i	−0.900215	−	0.435445i	$-0.856591\pi$
$19$	−4.24215	+	2.44921i	−0.973216	+	0.561887i	−0.0730010	+	0.997332i	$0.523258\pi$
$20$	−0.120590	−	0.101187i	−0.0269649	−	0.0226262i
$21$	1.81510	−	4.20778i	0.396088	−	0.918213i
$22$	0.623349	+	3.53519i	0.132898	+	0.753704i
$23$	−6.27733	+	1.10686i	−1.30891	+	0.230797i	−0.784214	−	0.620491i	$-0.786934\pi$
$23$	−6.27733	+	1.10686i	−1.30891	+	0.230797i	−0.524700	+	0.851287i	$0.675822\pi$
$24$	−4.82657	−	1.14781i	−0.985220	−	0.234296i
$25$	−3.81699	−	3.20283i	−0.763397	−	0.640566i
$26$	−1.34365	+	2.32726i	−0.263511	+	0.456414i
$27$	3.34913	−	3.97282i	0.644540	−	0.764570i
$28$	−2.74277	+	1.58630i	−0.518335	+	0.299783i
$29$	2.29851	+	6.31510i	0.426822	+	1.17268i	0.947731	+	0.319072i	$0.103371\pi$
$29$	2.29851	+	6.31510i	0.426822	+	1.17268i	−0.520908	+	0.853613i	$0.674407\pi$
$30$	0.198417	+	0.0471857i	0.0362258	+	0.00861489i
$31$	2.98538	−	8.20227i	0.536191	−	1.47317i	−0.315397	−	0.948960i	$-0.602138\pi$
$31$	2.98538	−	8.20227i	0.536191	−	1.47317i	0.851588	−	0.524212i	$-0.175640\pi$
$32$	3.58403	+	4.27128i	0.633573	+	0.755063i
$33$	4.14058	+	5.57063i	0.720782	+	0.969723i
$34$	−0.198433	+	0.236483i	−0.0340310	+	0.0405565i
$35$	0.301058	−	0.174119i	0.0508880	−	0.0294315i
$36$	−3.49712	+	0.823195i	−0.582853	+	0.137199i
$37$	−7.28599			−1.19781			−0.598905	−	0.800820i	$-0.704397\pi$
$37$	−7.28599			−1.19781			−0.598905	+	0.800820i	$0.704397\pi$
$38$	−4.12331	+	1.50076i	−0.668889	+	0.243456i
$39$	−0.306081	+	5.18700i	−0.0490123	+	0.830585i
$40$	−0.242020	−	0.288428i	−0.0382667	−	0.0456045i
$41$	9.04416	+	3.29180i	1.41246	+	0.514094i	0.931851	−	0.362841i	$-0.118193\pi$
$41$	9.04416	+	3.29180i	1.41246	+	0.514094i	0.480609	+	0.876935i	$0.340415\pi$
$42$	2.25577	−	3.42967i	0.348073	−	0.529209i
$43$	0.350643	−	1.98860i	0.0534726	−	0.303258i	−0.946328	−	0.323207i	$-0.895239\pi$
$43$	0.350643	−	1.98860i	0.0534726	−	0.303258i	0.999801	+	0.0199486i	$0.00635026\pi$
$44$		−	4.79906i		−	0.723485i
$45$	0.383858	−	0.0903572i	0.0572221	−	0.0134697i
$46$	−5.70989			−0.841878
$47$	4.17641	−	1.52009i	0.609192	−	0.221728i	−0.0189578	−	0.999820i	$-0.506035\pi$
$47$	4.17641	−	1.52009i	0.609192	−	0.221728i	0.628150	+	0.778093i	$0.283813\pi$
$48$	−0.271395	−	0.117314i	−0.0391725	−	0.0169328i
$49$	−1.22594	−	6.89181i	−0.175135	−	0.984545i
$50$	−2.86905	−	3.41920i	−0.405745	−	0.483549i
$51$	−0.138098	+	0.580706i	−0.0193376	+	0.0813152i
$52$	2.30929	−	2.75210i	0.320240	−	0.381648i
$53$	−5.49931	+	3.17503i	−0.755388	+	0.436123i	−0.827637	−	0.561263i	$-0.810316\pi$
$53$	−5.49931	+	3.17503i	−0.755388	+	0.436123i	0.0722494	+	0.997387i	$0.476982\pi$
$54$	3.57251	−	2.98377i	0.486157	−	0.406040i
$55$			0.526764i			0.0710288i
$56$	−7.11934	+	2.59731i	−0.951361	+	0.347081i
$57$	−5.82699	+	6.16681i	−0.771804	+	0.816814i
$58$	1.04537	+	5.92857i	0.137263	+	0.778460i
$59$	0.136314	−	0.114381i	0.0177466	−	0.0148912i	−0.633871	−	0.773439i	$-0.718535\pi$
$59$	0.136314	−	0.114381i	0.0177466	−	0.0148912i	0.651618	+	0.758547i	$0.274091\pi$
$60$	−0.250277	−	0.108186i	−0.0323107	−	0.0139667i
$61$	−1.59759	−	4.38933i	−0.204550	−	0.561996i	0.794420	−	0.607369i	$-0.207775\pi$
$61$	−1.59759	−	4.38933i	−0.204550	−	0.561996i	−0.998970	+	0.0453721i	$0.985553\pi$
$62$	3.90952	−	6.77148i	0.496509	−	0.859979i
$63$	0.927544	−	7.88287i	0.116860	−	0.993148i
$64$	2.66805	+	4.62120i	0.333506	+	0.577649i
$65$	−0.253476	+	0.302081i	−0.0314399	+	0.0374686i
$66$	2.78620	+	5.55836i	0.342958	+	0.684187i
$67$	2.00174	+	11.3525i	0.244552	+	1.38692i	0.821531	+	0.570164i	$0.193120\pi$
$67$	2.00174	+	11.3525i	0.244552	+	1.38692i	−0.576979	+	0.816759i	$0.695769\pi$
$68$	0.316152	−	0.265283i	0.0383390	−	0.0321702i
$69$	−9.86983	+	4.94738i	−1.18819	+	0.595595i
$70$	0.292671	−	0.106774i	0.0349809	−	0.0127619i
$71$	0.373587	−	0.215690i	0.0443366	−	0.0255977i	−0.477668	−	0.878540i	$-0.658518\pi$
$71$	0.373587	−	0.215690i	0.0443366	−	0.0255977i	0.522004	+	0.852943i	$0.325184\pi$
$72$	−8.57923	+	0.486542i	−1.01107	+	0.0573395i
$73$		−	1.52364i		−	0.178329i	−0.996017	−	0.0891645i	$-0.971580\pi$
$73$		−	1.52364i		−	0.178329i	0.996017	−	0.0891645i	$-0.0284197\pi$
$74$	−6.42754	−	1.13335i	−0.747186	−	0.131749i
$75$	−7.92189	−	3.42435i	−0.914741	−	0.395409i
$76$	5.77706	−	1.01865i	0.662674	−	0.116847i
$77$	9.96576	+	3.61872i	1.13570	+	0.412392i
$78$	−1.07687	+	4.52825i	−0.121931	+	0.512723i
$79$	0.410757	−	2.32952i	0.0462138	−	0.262091i	−0.952943	−	0.303150i	$-0.901962\pi$
$79$	0.410757	−	2.32952i	0.0462138	−	0.262091i	0.999157	+	0.0410582i	$0.0130729\pi$
$80$	−0.0112194	−	0.0194325i	−0.00125436	−	0.00217262i
$81$	3.58993	−	8.25302i	0.398882	−	0.917002i
$82$	7.46651	+	4.31079i	0.824538	+	0.476047i
$83$	6.81615	−	2.48087i	0.748169	−	0.272311i	0.0603341	−	0.998178i	$-0.480783\pi$
$83$	6.81615	−	2.48087i	0.748169	−	0.272311i	0.687835	+	0.725867i	$0.258561\pi$
$84$	−3.76609	+	3.99175i	−0.410914	+	0.435536i
$85$	−0.0347021	+	0.0291185i	−0.00376397	+	0.00315834i
$86$	0.618659	−	1.69975i	0.0667117	−	0.183289i
$87$	6.94383	+	9.34206i	0.744456	+	1.00157i
$88$	1.99320	−	11.3040i	0.212476	−	1.20501i
$89$	−7.70903	−	13.3524i	−0.817156	−	1.41536i	−0.907770	−	0.419469i	$-0.862216\pi$
$89$	−7.70903	−	13.3524i	−0.817156	−	1.41536i	0.0906137	−	0.995886i	$-0.471117\pi$
$90$	0.352686	−	0.0200014i	0.0371764	−	0.00210833i
$91$	3.97372	+	6.87070i	0.416559	+	0.720245i
$92$	7.51752	+	1.32554i	0.783756	+	0.138197i
$93$	0.890584	−	15.0923i	0.0923493	−	1.56499i
$94$	3.92079	−	0.691340i	0.404398	−	0.0713063i
$95$	−0.634113	+	0.111811i	−0.0650586	+	0.0114716i
$96$	8.06467	+	5.31304i	0.823097	+	0.542260i
$97$	12.2061	+	2.15226i	1.23934	+	0.218529i	0.754634	−	0.656147i	$-0.227815\pi$
$97$	12.2061	+	2.15226i	1.23934	+	0.218529i	0.484708	+	0.874676i	$0.338926\pi$
$98$	−0.00946529	−	6.27050i	−0.000956138	−	0.633416i
$99$	9.63217	+	7.19377i	0.968070	+	0.723001i
$100$	2.98357	+	5.16769i	0.298357	+	0.516769i
$101$	−0.655418	+	3.71706i	−0.0652165	+	0.369861i	0.934680	+	0.355490i	$0.115686\pi$
$101$	−0.655418	+	3.71706i	−0.0652165	+	0.369861i	−0.999897	+	0.0143715i	$0.995425\pi$
$102$	−0.212157	+	0.490805i	−0.0210067	+	0.0485969i
$103$	3.42363	−	9.40634i	0.337340	−	0.926835i	−0.648806	−	0.760954i	$-0.724731\pi$
$103$	3.42363	−	9.40634i	0.337340	−	0.926835i	0.986146	−	0.165881i	$-0.0530466\pi$
$104$	6.58247	−	5.52335i	0.645464	−	0.541609i
$105$	0.413381	−	0.438150i	0.0403418	−	0.0427591i
$106$	−5.34525	+	1.94551i	−0.519176	+	0.188965i
$107$	4.00378	+	2.31158i	0.387060	+	0.223469i	0.680885	−	0.732390i	$-0.261595\pi$
$107$	4.00378	+	2.31158i	0.387060	+	0.223469i	−0.293826	+	0.955859i	$0.594928\pi$
$108$	−5.39616	+	3.09902i	−0.519246	+	0.298203i
$109$	−5.95833	−	10.3201i	−0.570704	−	0.988489i	−0.996494	−	0.0836667i	$-0.973337\pi$
$109$	−5.95833	−	10.3201i	−0.570704	−	0.988489i	0.425789	−	0.904822i	$-0.359996\pi$
$110$	−0.0819390	+	0.464699i	−0.00781258	+	0.0443073i
$111$	−12.0923	+	3.61014i	−1.14775	+	0.342660i
$112$	−0.444715	+	0.0787614i	−0.0420216	+	0.00744225i
$113$	−3.00669	+	0.530160i	−0.282846	+	0.0498733i	−0.313271	−	0.949664i	$-0.601425\pi$
$113$	−3.00669	+	0.530160i	−0.282846	+	0.0498733i	0.0304256	+	0.999537i	$0.490314\pi$
$114$	−6.09970	+	4.53382i	−0.571289	+	0.424632i
$115$	−0.825153	−	0.145497i	−0.0769459	−	0.0135676i
$116$		−	8.04811i		−	0.747248i
$117$	2.06212	+	8.76035i	0.190643	+	0.809894i
$118$	0.138046	−	0.0797007i	0.0127081	−	0.00733704i
$119$	0.312494	+	0.856559i	0.0286463	+	0.0785206i
$120$	−0.544586	−	0.358775i	−0.0497136	−	0.0327516i
$121$	−3.87525	+	3.25172i	−0.352296	+	0.295611i
$122$	−0.726587	−	4.12068i	−0.0657821	−	0.373069i
$123$	16.6413	+	0.981994i	1.50050	+	0.0885434i
$124$	−6.71917	+	8.00759i	−0.603399	+	0.719103i
$125$	−0.656113	−	1.13642i	−0.0586845	−	0.101645i
$126$	2.04445	−	6.80981i	0.182134	−	0.606666i
$127$	4.57273	−	7.92020i	0.405764	−	0.702804i	−0.588646	−	0.808391i	$-0.700339\pi$
$127$	4.57273	−	7.92020i	0.405764	−	0.702804i	0.994410	+	0.105587i	$0.0336720\pi$
$128$	−2.17919	−	5.98727i	−0.192615	−	0.529205i
$129$	−0.403381	−	3.47414i	−0.0355157	−	0.305881i
$130$	−0.270600	+	0.227061i	−0.0237332	+	0.0199145i
$131$	−0.968114	−	5.49045i	−0.0845845	−	0.479703i	−0.997445	−	0.0714321i	$-0.977243\pi$
$131$	−0.968114	−	5.49045i	−0.0845845	−	0.479703i	0.912861	−	0.408271i	$-0.133868\pi$
$132$	−2.37789	−	7.96483i	−0.206969	−	0.693249i
$133$	−2.24084	+	12.7648i	−0.194306	+	1.10685i
$134$			10.3263i			0.892052i
$135$	0.592304	−	0.340161i	0.0509774	−	0.0292764i
$136$	0.854863	−	0.493555i	0.0733039	−	0.0423220i
$137$	−9.29828	+	11.0813i	−0.794406	+	0.946736i	−0.999488	−	0.0320091i	$-0.989809\pi$
$137$	−9.29828	+	11.0813i	−0.794406	+	0.946736i	0.205082	+	0.978745i	$0.434254\pi$
$138$	−9.47651	+	2.82920i	−0.806694	+	0.240838i
$139$	8.80185	+	10.4896i	0.746563	+	0.889720i	0.996919	−	0.0784343i	$-0.0249921\pi$
$139$	8.80185	+	10.4896i	0.746563	+	0.889720i	−0.250356	+	0.968154i	$0.580548\pi$
$140$	−0.410111	+	0.0726329i	−0.0346607	+	0.00613860i
$141$	6.17825	−	4.59221i	0.520302	−	0.386734i
$142$	0.363121	−	0.132165i	0.0304724	−	0.0110911i
$143$	−12.0217			−1.00531
$144$	−0.508553	−	0.0602285i	−0.0423794	−	0.00501904i
$145$			0.883393i			0.0733618i
$146$	0.237005	−	1.34412i	0.0196147	−	0.111241i
$147$	−5.44948	−	10.8307i	−0.449466	−	0.893298i
$148$	8.19925	+	2.98428i	0.673974	+	0.245306i
$149$	−10.4655	−	12.4723i	−0.857370	−	1.02177i	−0.999490	−	0.0319247i	$-0.989836\pi$
$149$	−10.4655	−	12.4723i	−0.857370	−	1.02177i	0.142120	−	0.989849i	$-0.454608\pi$
$150$	−6.45585	−	4.25314i	−0.527118	−	0.347268i
$151$	3.98643	−	1.45094i	0.324411	−	0.118076i	−0.174681	−	0.984625i	$-0.555889\pi$
$151$	3.98643	−	1.45094i	0.324411	−	0.118076i	0.499092	+	0.866549i	$0.333667\pi$
$152$	14.0307			1.13804
$153$	0.0585380	+	1.03220i	0.00473252	+	0.0834488i
$154$	8.22867	+	4.74255i	0.663085	+	0.382165i
$155$	0.737523	−	0.878945i	0.0592393	−	0.0705986i
$156$	2.46900	−	5.71179i	0.197678	−	0.457310i
$157$	2.94110	+	3.50506i	0.234725	+	0.279734i	0.870530	−	0.492115i	$-0.163776\pi$
$157$	2.94110	+	3.50506i	0.234725	+	0.279734i	−0.635805	+	0.771850i	$0.719332\pi$
$158$	0.724721	−	1.99116i	0.0576557	−	0.158408i
$159$	−7.55381	+	7.99434i	−0.599056	+	0.633992i
$160$	0.250677	+	0.688731i	0.0198178	+	0.0544489i
$161$	−8.42121	+	14.6114i	−0.663684	+	1.15154i
$162$	4.45073	−	6.72221i	0.349682	−	0.528147i
$163$	−4.14531	+	7.17988i	−0.324686	+	0.562372i	−0.981449	−	0.191725i	$-0.938592\pi$
$163$	−4.14531	+	7.17988i	−0.324686	+	0.562372i	0.656763	+	0.754097i	$0.271925\pi$
$164$	−8.82950	−	7.40883i	−0.689468	−	0.578532i
$165$	0.261007	+	0.874251i	0.0203193	+	0.0680604i
$166$	6.39896	−	1.12831i	0.496655	−	0.0875737i
$167$	−0.761050	−	4.31613i	−0.0588919	−	0.333992i	0.941100	−	0.338130i	$-0.109794\pi$
$167$	−0.761050	−	4.31613i	−0.0588919	−	0.333992i	−0.999991	+	0.00413722i	$0.998683\pi$
$168$	−10.5288	+	7.83824i	−0.812312	+	0.604733i
$169$	3.06452	+	2.57143i	0.235732	+	0.197803i
$170$	−0.0351428	+	0.0202897i	−0.00269533	+	0.00155615i
$171$	−6.61525	+	13.1221i	−0.505881	+	1.00347i
$172$	−1.20911	+	2.09423i	−0.0921935	+	0.159684i
$173$	−12.7106	−	10.6655i	−0.966373	−	0.810883i	0.0156052	−	0.999878i	$-0.495032\pi$
$173$	−12.7106	−	10.6655i	−0.966373	−	0.810883i	−0.981978	+	0.188995i	$0.939477\pi$
$174$	4.67252	+	9.32148i	0.354223	+	0.706659i
$175$	−12.9810	+	2.29901i	−0.981274	+	0.173789i
$176$	0.233963	−	0.642808i	0.0176356	−	0.0484535i
$177$	0.169561	−	0.257377i	0.0127450	−	0.0193457i
$178$	−4.72374	−	12.9784i	−0.354059	−	0.972770i
$179$	9.01384	+	5.20414i	0.673726	+	0.388976i	0.797487	−	0.603336i	$-0.206162\pi$
$179$	9.01384	+	5.20414i	0.673726	+	0.388976i	−0.123761	+	0.992312i	$0.539496\pi$
$180$	−0.468982	−	0.0555420i	−0.0349558	−	0.00413985i
$181$	−14.3465	−	8.28296i	−1.06637	−	0.615668i	−0.139181	−	0.990267i	$-0.544447\pi$
$181$	−14.3465	−	8.28296i	−1.06637	−	0.615668i	−0.927187	+	0.374599i	$0.877780\pi$
$182$	2.43677	+	6.67929i	0.180626	+	0.495102i
$183$	−4.82633	−	6.49323i	−0.356773	−	0.479994i
$184$	17.1567	+	6.24452i	1.26481	+	0.460352i
$185$	−0.899982	−	0.327567i	−0.0661680	−	0.0240832i
$186$	3.13328	−	13.1755i	0.229743	−	0.966076i
$187$	−1.36003	−	0.239811i	−0.0994555	−	0.0175367i
$188$	−5.32251			−0.388184
$189$	−2.36648	−	13.5425i	−0.172136	−	0.985073i
$190$	−0.576792			−0.0418449
$191$	10.2170	+	1.80153i	0.739274	+	0.130354i	0.530589	−	0.847629i	$-0.321971\pi$
$191$	10.2170	+	1.80153i	0.739274	+	0.130354i	0.208685	+	0.977983i	$0.433082\pi$
$192$	6.71783	+	6.34764i	0.484818	+	0.458102i
$193$	−17.1323	−	6.23566i	−1.23321	−	0.448853i	−0.358516	−	0.933524i	$-0.616717\pi$
$193$	−17.1323	−	6.23566i	−1.23321	−	0.448853i	−0.874696	+	0.484671i	$0.838939\pi$
$194$	10.4332	+	3.79736i	0.749057	+	0.272635i
$195$	−0.271007	+	0.626949i	−0.0194072	+	0.0448968i
$196$	−1.44322	+	8.25780i	−0.103087	+	0.589843i
$197$	−18.9850	−	10.9610i	−1.35263	−	0.780941i	−0.364012	−	0.931394i	$-0.618593\pi$
$197$	−18.9850	−	10.9610i	−1.35263	−	0.780941i	−0.988617	+	0.150454i	$0.951927\pi$
$198$	7.37828	+	7.84448i	0.524352	+	0.557483i
$199$	6.28334	+	3.62769i	0.445414	+	0.257160i	0.705891	−	0.708320i	$-0.250547\pi$
$199$	6.28334	+	3.62769i	0.445414	+	0.257160i	−0.260477	+	0.965480i	$0.583880\pi$
$200$	4.88138	+	13.4115i	0.345166	+	0.948334i
$201$	8.94726	+	17.8494i	0.631091	+	1.25900i
$202$	−1.15639	+	3.17715i	−0.0813633	+	0.223544i
$203$	16.7128	+	6.06867i	1.17301	+	0.425937i
$204$	0.393261	−	0.596931i	0.0275337	−	0.0417935i
$205$	0.969161	+	0.813222i	0.0676891	+	0.0567979i
$206$	4.48342	−	7.76552i	0.312375	−	0.541049i
$207$	−13.9292	+	13.1014i	−0.968148	+	0.910611i
$208$	0.443487	−	0.256047i	0.0307503	−	0.0177537i
$209$	−15.0372	−	12.6177i	−1.04014	−	0.872783i
$210$	0.432830	−	0.322224i	0.0298681	−	0.0222356i
$211$	0.796078	+	4.51478i	0.0548043	+	0.310810i	0.999871	−	0.0160673i	$-0.00511459\pi$
$211$	0.796078	+	4.51478i	0.0548043	+	0.310810i	−0.945067	+	0.326878i	$0.894003\pi$
$212$	7.48908	−	1.32053i	0.514352	−	0.0906942i
$213$	0.513156	−	0.543082i	0.0351609	−	0.0372114i
$214$	3.17247	+	2.66202i	0.216866	+	0.181972i
$215$	0.132716	−	0.229871i	0.00905118	−	0.0156771i
$216$	−13.9976	+	5.05843i	−0.952414	+	0.344182i
$217$	−11.5620	−	19.9912i	−0.784883	−	1.35709i
$218$	−3.65099	−	10.0310i	−0.247276	−	0.679386i
$219$	−0.754952	−	2.52874i	−0.0510149	−	0.170876i
$220$	0.215758	−	0.592790i	0.0145464	−	0.0399659i
$221$	−0.664538	−	0.791966i	−0.0447017	−	0.0532734i
$222$	−11.2291	+	1.30381i	−0.753650	+	0.0875059i
$223$	−15.1586	+	18.0653i	−1.01510	+	1.20974i	−0.0374904	+	0.999297i	$0.511936\pi$
$223$	−15.1586	+	18.0653i	−1.01510	+	1.20974i	−0.977605	+	0.210447i	$0.932508\pi$
$224$	14.7521	−	0.0111341i	0.985664	−	0.000743927i
$225$	−14.8444	−	1.75804i	−0.989628	−	0.117203i
$226$	−2.73490			−0.181923
$227$	−2.30126	+	0.837591i	−0.152740	+	0.0555929i	−0.417259	−	0.908788i	$-0.637009\pi$
$227$	−2.30126	+	0.837591i	−0.152740	+	0.0555929i	0.264519	+	0.964381i	$0.414787\pi$
$228$	9.08325	−	4.55310i	0.601553	−	0.301536i
$229$	0.168408	+	0.200701i	0.0111287	+	0.0132627i	0.771580	−	0.636132i	$-0.219467\pi$
$229$	0.168408	+	0.200701i	0.0111287	+	0.0132627i	−0.760451	+	0.649395i	$0.775022\pi$
$230$	−0.705299	−	0.256708i	−0.0465060	−	0.0169268i
$231$	18.3329	+	1.06793i	1.20621	+	0.0702644i
$232$	3.34263	−	18.9570i	0.219455	−	1.24459i
$233$			29.0321i			1.90195i	0.309260	+	0.950977i	$0.399919\pi$
$233$			29.0321i			1.90195i	−0.309260	+	0.950977i	$0.600081\pi$
$234$	0.456469	+	8.04895i	0.0298403	+	0.526176i
$235$	0.584220			0.0381103
$236$	−0.200250	+	0.0728851i	−0.0130352	+	0.00474442i
$237$	−0.472537	−	4.06975i	−0.0306945	−	0.264359i
$238$	0.142436	+	0.804246i	0.00923277	+	0.0521315i
$239$	1.21344	+	1.44612i	0.0784911	+	0.0935420i	0.803861	−	0.594817i	$-0.202776\pi$
$239$	1.21344	+	1.44612i	0.0784911	+	0.0935420i	−0.725370	+	0.688359i	$0.758331\pi$
$240$	−0.0282491	−	0.0266924i	−0.00182347	−	0.00172299i
$241$	11.7834	−	14.0430i	0.759038	−	0.904586i	−0.238749	−	0.971081i	$-0.576737\pi$
$241$	11.7834	−	14.0430i	0.759038	−	0.904586i	0.997787	+	0.0664953i	$0.0211818\pi$
$242$	−3.92447	+	2.26580i	−0.252275	+	0.145651i
$243$	1.86879	−	15.4760i	0.119883	−	0.992788i
$244$			5.59387i			0.358111i
$245$	0.158414	−	0.906409i	0.0101207	−	0.0579083i
$246$	14.5279	+	3.45488i	0.926263	+	0.220275i
$247$	−2.55174	−	14.4716i	−0.162363	−	0.920808i
$248$	−19.1525	+	16.0709i	−1.21619	+	1.02050i
$249$	10.0833	−	7.49476i	0.639001	−	0.474961i
$250$	−0.402036	−	1.10458i	−0.0254270	−	0.0698600i
$251$	−3.29266	+	5.70305i	−0.207831	+	0.359973i	−0.951031	−	0.309096i	$-0.899974\pi$
$251$	−3.29266	+	5.70305i	−0.207831	+	0.359973i	0.743200	+	0.669069i	$0.233307\pi$
$252$	−4.27257	+	8.49103i	−0.269146	+	0.534885i
$253$	−12.7717	−	22.1213i	−0.802952	−	1.39075i
$254$	5.26596	−	6.27573i	0.330416	−	0.393774i
$255$	−0.0431659	+	0.0655215i	−0.00270315	+	0.00410312i
$256$	−2.84431	−	16.1309i	−0.177769	−	1.00818i
$257$	−22.1780	+	18.6096i	−1.38343	+	1.16083i	−0.415503	+	0.909592i	$0.636394\pi$
$257$	−22.1780	+	18.6096i	−1.38343	+	1.16083i	−0.967924	+	0.251242i	$0.919161\pi$
$258$	0.184555	−	3.12756i	0.0114899	−	0.194713i
$259$	−12.3798	+	14.7763i	−0.769244	+	0.918156i
$260$	0.408978	−	0.236124i	0.0253638	−	0.0146438i
$261$	16.1533	+	12.0641i	0.999866	+	0.746748i
$262$		−	4.99414i		−	0.308539i
$263$	22.8663	+	4.03194i	1.41000	+	0.248620i	0.826244	−	0.563312i	$-0.190473\pi$
$263$	22.8663	+	4.03194i	1.41000	+	0.248620i	0.583751	+	0.811932i	$0.301584\pi$
$264$	−2.29298	−	19.7485i	−0.141123	−	1.21543i
$265$	−0.822031	+	0.144946i	−0.0504970	+	0.00890398i
$266$	−3.96241	+	10.9122i	−0.242951	+	0.669073i
$267$	−19.4104	−	18.3408i	−1.18790	−	1.12244i
$268$	2.39722	−	13.5953i	0.146434	−	0.830466i
$269$	4.60903	+	7.98308i	0.281018	+	0.486737i	0.971636	−	0.236483i	$-0.0759947\pi$
$269$	4.60903	+	7.98308i	0.281018	+	0.486737i	−0.690618	+	0.723220i	$0.742661\pi$
$270$	0.575430	−	0.207948i	0.0350196	−	0.0126553i
$271$	25.5138	+	14.7304i	1.54985	+	0.894807i	0.998152	+	0.0607643i	$0.0193538\pi$
$271$	25.5138	+	14.7304i	1.54985	+	0.894807i	0.551700	+	0.834043i	$0.313980\pi$
$272$	0.0552799	−	0.0201202i	0.00335183	−	0.00121997i
$273$	9.99941	+	9.43412i	0.605192	+	0.570979i
$274$	−9.92644	+	8.32927i	−0.599678	+	0.503190i
$275$	6.82927	−	18.7633i	0.411821	−	1.13147i
$276$	13.1334	−	1.52491i	0.790535	−	0.0917887i
$277$	0.528964	−	2.99991i	0.0317824	−	0.180247i	−0.964784	−	0.263043i	$-0.915274\pi$
$277$	0.528964	−	2.99991i	0.0317824	−	0.180247i	0.996567	+	0.0827961i	$0.0263850\pi$
$278$	6.13312	+	10.6229i	0.367840	+	0.637117i
$279$	−6.00001	−	25.4894i	−0.359211	−	1.52601i
$280$	−0.996168		0.000751855i	−0.0595324		4.49319e-5i
$281$	24.6845	+	4.35255i	1.47256	+	0.259651i	0.851599	−	0.524194i	$-0.175633\pi$
$281$	24.6845	+	4.35255i	1.47256	+	0.259651i	0.620956	+	0.783845i	$0.286744\pi$
$282$	6.16464	−	3.09011i	0.367099	−	0.184013i
$283$	10.9985	−	1.93934i	0.653794	−	0.115282i	0.163095	−	0.986610i	$-0.447852\pi$
$283$	10.9985	−	1.93934i	0.653794	−	0.115282i	0.490700	+	0.871329i	$0.336741\pi$
$284$	−0.508758	+	0.0897078i	−0.0301893	+	0.00532318i
$285$	−0.997013	+	0.499766i	−0.0590580	+	0.0296036i
$286$	−10.6053	−	1.87000i	−0.627105	−	0.110575i
$287$	22.0431	−	12.7488i	1.30116	−	0.752537i
$288$	16.0172	+	4.82190i	0.943824	+	0.284133i
$289$	8.44062	+	14.6196i	0.496507	+	0.859975i
$290$	−0.137413	+	0.779309i	−0.00806918	+	0.0457626i
$291$	21.3245	−	2.47597i	1.25006	−	0.145144i
$292$	−0.624072	+	1.71462i	−0.0365211	+	0.100341i
$293$	−3.69754	+	3.10260i	−0.216012	+	0.181256i	−0.744373	−	0.667764i	$-0.767251\pi$
$293$	−3.69754	+	3.10260i	−0.216012	+	0.181256i	0.528360	+	0.849020i	$0.322807\pi$
$294$	−3.12269	−	10.4022i	−0.182119	−	0.606671i
$295$	0.0219803	−	0.00800016i	0.00127974	−	0.000465787i
$296$	18.0735	+	10.4348i	1.05050	+	0.606508i
$297$	19.5506	+	7.16659i	1.13444	+	0.415848i
$298$	−7.29237	−	12.6308i	−0.422436	−	0.731680i
$299$	3.32051	−	18.8315i	0.192030	−	1.08906i
$300$	7.51227	+	7.09831i	0.433721	+	0.409821i
$301$	−3.43718	−	4.08999i	−0.198116	−	0.235743i
$302$	3.74243	−	0.659892i	0.215353	−	0.0379725i
$303$	0.753995	+	6.49383i	0.0433159	+	0.373061i
$304$	0.823467	+	0.145200i	0.0472291	+	0.00832776i
$305$		−	0.614005i		−	0.0351578i
$306$	−0.108920	+	0.919693i	−0.00622656	+	0.0525754i
$307$	17.7257	−	10.2339i	1.01166	−	0.584082i	0.0999825	−	0.994989i	$-0.468121\pi$
$307$	17.7257	−	10.2339i	1.01166	−	0.584082i	0.911677	+	0.410907i	$0.134788\pi$
$308$	−9.73271	−	8.15420i	−0.554573	−	0.464629i
$309$	1.02132	−	17.3078i	0.0581008	−	0.984604i
$310$	0.787347	−	0.660663i	0.0447183	−	0.0375231i
$311$	−2.56159	−	14.5275i	−0.145255	−	0.823780i	−0.967162	−	0.254160i	$-0.918201\pi$
$311$	−2.56159	−	14.5275i	−0.145255	−	0.823780i	0.821908	−	0.569621i	$-0.192910\pi$
$312$	8.18792	−	12.4285i	0.463550	−	0.703623i
$313$	−7.62965	+	9.09266i	−0.431253	+	0.513947i	−0.937283	−	0.348568i	$-0.886668\pi$
$313$	−7.62965	+	9.09266i	−0.431253	+	0.513947i	0.506030	+	0.862516i	$0.331112\pi$
$314$	2.04935	+	3.54958i	0.115652	+	0.200314i
$315$	0.468974	−	0.932009i	0.0264237	−	0.0525128i
$316$	−1.41639	+	2.45327i	−0.0796784	+	0.138007i
$317$	7.00153	+	19.2365i	0.393245	+	1.08043i	0.965511	+	0.260364i	$0.0838425\pi$
$317$	7.00153	+	19.2365i	0.393245	+	1.08043i	−0.572265	+	0.820068i	$0.693935\pi$
$318$	−7.90734	+	5.87742i	−0.443421	+	0.329589i
$319$	−20.6303	+	17.3108i	−1.15507	+	0.969221i
$320$	0.121802	+	0.690772i	0.00680892	+	0.0386153i
$321$	7.79030	+	1.85262i	0.434812	+	0.103403i
$322$	−9.70183	+	11.5799i	−0.540662	+	0.645324i
$323$		−	1.68810i		−	0.0939282i
$324$	−7.42028	+	7.81708i	−0.412238	+	0.434282i
$325$	12.9452	−	7.47390i	0.718069	−	0.414577i
$326$	−4.77374	+	5.68912i	−0.264393	+	0.315091i
$327$	−15.0024	−	14.1757i	−0.829632	−	0.783916i
$328$	−17.7204	−	21.1184i	−0.978447	−	1.16607i
$329$	4.01343	−	11.0528i	0.221268	−	0.609359i
$330$	0.0942630	+	0.811845i	0.00518900	+	0.0446906i
$331$	12.9346	−	4.70781i	0.710950	−	0.258765i	0.0388711	−	0.999244i	$-0.487624\pi$
$331$	12.9346	−	4.70781i	0.710950	−	0.258765i	0.672079	+	0.740480i	$0.265402\pi$
$332$	−8.68666			−0.476742
$333$	−18.2804	+	11.9833i	−1.00176	+	0.656678i
$334$		−	3.92598i		−	0.214820i
$335$	−0.263129	+	1.49228i	−0.0143762	+	0.0815317i
$336$	−0.699053	+	0.351070i	−0.0381365	+	0.0191524i
$337$	−11.8712	−	4.32077i	−0.646667	−	0.235367i	−0.00219742	−	0.999998i	$-0.500699\pi$
$337$	−11.8712	−	4.32077i	−0.646667	−	0.235367i	−0.644469	+	0.764630i	$0.722922\pi$
$338$	2.30346	+	2.74515i	0.125292	+	0.149317i
$339$	−4.72741	+	2.36968i	−0.256758	+	0.128703i
$340$	0.0509785	−	0.0185546i	0.00276469	−	0.00100627i
$341$	34.9788			1.89421
$342$	−7.87699	+	10.5470i	−0.425939	+	0.570315i
$343$	−16.0599	−	9.22379i	−0.867155	−	0.498038i
$344$	−3.71780	+	4.43071i	−0.200451	+	0.238888i
$345$	−1.44157	+	0.167380i	−0.0776115	+	0.00901144i
$346$	−9.55401	−	11.3860i	−0.513627	−	0.612117i
$347$	−6.19856	+	17.0304i	−0.332756	+	0.914240i	0.654635	+	0.755945i	$0.272822\pi$
$347$	−6.19856	+	17.0304i	−0.332756	+	0.914240i	−0.987392	+	0.158296i	$0.949400\pi$
$348$	−3.98777	−	13.3572i	−0.213767	−	0.716019i
$349$	6.17471	+	16.9649i	0.330525	+	0.908109i	0.987975	+	0.154612i	$0.0494127\pi$
$349$	6.17471	+	16.9649i	0.330525	+	0.908109i	−0.657450	+	0.753498i	$0.728365\pi$
$350$	−11.8092	+	0.00891295i	−0.631228	+	0.000476417i
$351$	7.76310	+	13.5175i	0.414364	+	0.721510i
$352$	−11.1720	+	19.3505i	−0.595469	+	1.03138i
$353$	11.9752	+	10.0484i	0.637378	+	0.534824i	0.903212	−	0.429195i	$-0.141203\pi$
$353$	11.9752	+	10.0484i	0.637378	+	0.534824i	−0.265834	+	0.964019i	$0.585647\pi$
$354$	0.189619	−	0.200677i	0.0100781	−	0.0106659i
$355$	0.0558434	−	0.00984669i	0.00296386	−	0.000522608i
$356$	3.20627	+	18.1836i	0.169932	+	0.963731i
$357$	0.943053	+	1.26676i	0.0499117	+	0.0670442i
$358$	7.14229	+	5.99309i	0.377482	+	0.316745i
$359$	−8.75879	+	5.05689i	−0.462271	+	0.266892i	−0.712999	−	0.701165i	$-0.752663\pi$
$359$	−8.75879	+	5.05689i	−0.462271	+	0.266892i	0.250728	+	0.968058i	$0.419330\pi$
$360$	−1.08160	−	0.325610i	−0.0570053	−	0.0171611i
$361$	2.49723	−	4.32533i	0.131433	−	0.227649i
$362$	−11.3677	−	9.53867i	−0.597475	−	0.501341i
$363$	−4.82042	+	7.31693i	−0.253007	+	0.384039i
$364$	−1.65762	−	9.35950i	−0.0868828	−	0.490571i
$365$	0.0685006	−	0.188204i	0.00358549	−	0.00985105i
$366$	−3.24765	−	6.47893i	−0.169757	−	0.338659i
$367$	9.52935	+	26.1817i	0.497428	+	1.36667i	0.893752	+	0.448561i	$0.148063\pi$
$367$	9.52935	+	26.1817i	0.497428	+	1.36667i	−0.396324	+	0.918111i	$0.629714\pi$
$368$	0.942309	+	0.544043i	0.0491213	+	0.0283602i
$369$	28.1056	−	6.61585i	1.46312	−	0.344407i
$370$	−0.742991	−	0.428966i	−0.0386262	−	0.0223009i
$371$	−2.90492	+	16.5476i	−0.150816	+	0.859110i
$372$	−7.18388	+	16.6192i	−0.372467	+	0.861666i
$373$	−18.5415	−	6.74854i	−0.960040	−	0.349426i	−0.185991	−	0.982551i	$-0.559549\pi$
$373$	−18.5415	−	6.74854i	−0.960040	−	0.349426i	−0.774049	+	0.633126i	$0.781772\pi$
$374$	−1.16249	−	0.423111i	−0.0601108	−	0.0218786i
$375$	−1.65201	−	1.56098i	−0.0853096	−	0.0806086i
$376$	−12.5370	−	2.21061i	−0.646545	−	0.114003i
$377$	−20.1607			−1.03833
$378$	0.0189068	−	12.3150i	0.000972463	−	0.633416i
$379$	3.29633			0.169321			0.0846605	−	0.996410i	$-0.473019\pi$
$379$	3.29633			0.169321			0.0846605	+	0.996410i	$0.473019\pi$
$380$	0.759392	+	0.133901i	0.0389560	+	0.00686899i
$381$	3.66481	−	15.4106i	0.187754	−	0.789511i
$382$	8.73295	+	3.17853i	0.446817	+	0.162628i
$383$	−28.9959	−	10.5537i	−1.48162	−	0.539267i	−0.530393	−	0.847752i	$-0.677956\pi$
$383$	−28.9959	−	10.5537i	−1.48162	−	0.539267i	−0.951229	+	0.308485i	$0.900178\pi$
$384$	−6.58336	−	8.85709i	−0.335956	−	0.451987i
$385$	1.06830	+	0.895038i	0.0544457	+	0.0456154i
$386$	−14.1438	−	8.16592i	−0.719900	−	0.415635i
$387$	−2.39088	−	5.56604i	−0.121535	−	0.282938i
$388$	−12.8545	−	7.42156i	−0.652589	−	0.376773i
$389$	−4.59734	−	12.6311i	−0.233094	−	0.640421i	0.766905	−	0.641761i	$-0.221796\pi$
$389$	−4.59734	−	12.6311i	−0.233094	−	0.640421i	−0.999999	+	0.00133967i	$0.999574\pi$
$390$	−0.336600	+	0.510925i	−0.0170444	+	0.0258717i
$391$	0.751306	−	2.06420i	0.0379952	−	0.104391i
$392$	−6.82918	+	18.8515i	−0.344926	+	0.952145i
$393$	−4.32721	−	8.63262i	−0.218279	−	0.435458i
$394$	−15.0432	−	12.6227i	−0.757864	−	0.635924i
$395$	0.155469	−	0.269280i	0.00782250	−	0.0135490i
$396$	−7.89300	−	12.0407i	−0.396638	−	0.605069i
$397$	28.0188	−	16.1766i	1.40622	−	0.811882i	0.411200	−	0.911545i	$-0.365110\pi$
$397$	28.0188	−	16.1766i	1.40622	−	0.811882i	0.995021	+	0.0996625i	$0.0317763\pi$
$398$	4.97873	+	4.17765i	0.249561	+	0.209407i
$399$	2.60579	+	22.2956i	0.130453	+	1.11618i
$400$	0.147699	+	0.837640i	0.00738493	+	0.0418820i
$401$	−37.5651	+	6.62375i	−1.87591	+	0.330774i	−0.990879	−	0.134753i	$-0.956976\pi$
$401$	−37.5651	+	6.62375i	−1.87591	+	0.330774i	−0.885034	+	0.465527i	$0.845865\pi$
$402$	5.11657	+	17.1381i	0.255191	+	0.854772i
$403$	20.0592	+	16.8316i	0.999218	+	0.838444i
$404$	2.26005	−	3.91452i	0.112442	−	0.194754i
$405$	0.814480	−	0.858034i	0.0404718	−	0.0426361i
$406$	13.7996	+	7.95334i	0.684864	+	0.394718i
$407$	−9.98612	−	27.4366i	−0.494993	−	1.35998i
$408$	1.17423	−	1.24271i	0.0581333	−	0.0615235i
$409$	−7.75021	+	21.2935i	−0.383223	+	1.05290i	0.586768	+	0.809755i	$0.300400\pi$
$409$	−7.75021	+	21.2935i	−0.383223	+	1.05290i	−0.969991	+	0.243142i	$0.921822\pi$
$410$	0.728474	+	0.868161i	0.0359768	+	0.0428754i
$411$	−9.94137	+	22.9984i	−0.490371	+	1.13443i
$412$	−7.70552	+	9.18309i	−0.379624	+	0.452418i
$413$	−0.000355335	−	0.470800i	−1.74849e−5	−	0.0231666i
$414$	−14.3260	+	9.39105i	−0.704084	+	0.461545i
$415$	0.953482			0.0468046
$416$	−15.7181	+	5.72093i	−0.770644	+	0.280492i
$417$	19.8057	+	13.0481i	0.969887	+	0.638966i
$418$	−11.3027	−	13.4701i	−0.552835	−	0.658843i
$419$	−1.24840	−	0.454379i	−0.0609881	−	0.0221979i	0.311346	−	0.950297i	$-0.399220\pi$
$419$	−1.24840	−	0.454379i	−0.0609881	−	0.0221979i	−0.372334	+	0.928099i	$0.621442\pi$
$420$	−0.644658	+	0.323753i	−0.0314561	+	0.0157975i
$421$	−0.798906	+	4.53082i	−0.0389363	+	0.220819i	−0.998067	−	0.0621441i	$-0.980206\pi$
$421$	−0.798906	+	4.53082i	−0.0389363	+	0.220819i	0.959131	+	0.282963i	$0.0913173\pi$
$422$			4.10667i			0.199910i
$423$	7.97843	−	10.6828i	0.387924	−	0.519415i
$424$	18.1887			0.883321
$425$	1.61359	−	0.587300i	0.0782708	−	0.0284882i
$426$	0.537172	−	0.399273i	0.0260261	−	0.0193448i
$427$	−11.6163	−	4.21805i	−0.562151	−	0.204126i
$428$	−3.55882	−	4.24124i	−0.172022	−	0.205008i
$429$	−19.9520	+	5.95666i	−0.963294	+	0.287590i
$430$	0.152836	−	0.182143i	0.00737042	−	0.00878373i
$431$	−15.3689	+	8.87327i	−0.740296	+	0.427410i	−0.822177	−	0.569232i	$-0.807241\pi$
$431$	−15.3689	+	8.87327i	−0.740296	+	0.427410i	0.0818808	+	0.996642i	$0.473907\pi$
$432$	−0.873870	+	0.152024i	−0.0420441	+	0.00731427i
$433$			1.22234i			0.0587418i	0.999569	+	0.0293709i	$0.00935038\pi$
$433$			1.22234i			0.0587418i	−0.999569	+	0.0293709i	$0.990650\pi$
$434$	−7.09011	−	19.4343i	−0.340336	−	0.932875i
$435$	0.437713	+	1.46614i	0.0209867	+	0.0702958i
$436$	2.47813	+	14.0542i	0.118681	+	0.673073i
$437$	23.9184	−	20.0700i	1.14417	−	0.960076i
$438$	−0.272652	−	2.34823i	−0.0130278	−	0.112203i
$439$	1.66599	+	4.57728i	0.0795135	+	0.218461i	0.973079	−	0.230471i	$-0.0740266\pi$
$439$	1.66599	+	4.57728i	0.0795135	+	0.218461i	−0.893566	+	0.448932i	$0.851804\pi$
$440$	0.754414	−	1.30668i	0.0359653	−	0.0622937i
$441$	−14.4108	−	15.2751i	−0.686229	−	0.727385i
$442$	−0.463049	−	0.802024i	−0.0220250	−	0.0381484i
$443$	14.9512	−	17.8181i	0.710353	−	0.846565i	−0.283303	−	0.959030i	$-0.591430\pi$
$443$	14.9512	−	17.8181i	0.710353	−	0.846565i	0.993656	+	0.112465i	$0.0358747\pi$
$444$	15.0867	+	0.890255i	0.715983	+	0.0422497i
$445$	−0.351933	−	1.99591i	−0.0166832	−	0.0946152i
$446$	−16.1827	+	13.5789i	−0.766272	+	0.642979i
$447$	−23.5492	−	15.5143i	−1.11384	−	0.733803i
$448$	13.9053	+	2.44107i	0.656966	+	0.115330i
$449$	19.9333	−	11.5085i	0.940710	−	0.543119i	0.0505273	−	0.998723i	$-0.483910\pi$
$449$	19.9333	−	11.5085i	0.940710	−	0.543119i	0.890183	+	0.455603i	$0.150576\pi$
$450$	−12.8220	−	3.85998i	−0.604433	−	0.181961i
$451$			38.5690i			1.81614i
$452$	3.60071	+	0.634902i	0.169363	+	0.0298633i
$453$	5.89721	−	4.38332i	0.277075	−	0.205946i
$454$	−2.16041	+	0.380939i	−0.101393	+	0.0178783i
$455$	0.181947	+	1.02734i	0.00852979	+	0.0481623i
$456$	23.2863	−	6.95209i	1.09048	−	0.325561i
$457$	4.61926	−	26.1971i	0.216080	−	1.22545i	−0.662943	−	0.748670i	$-0.730693\pi$
$457$	4.61926	−	26.1971i	0.216080	−	1.22545i	0.879023	−	0.476780i	$-0.158196\pi$
$458$	0.117346	+	0.203250i	0.00548323	+	0.00949724i
$459$	0.608602	+	1.68411i	0.0284071	+	0.0786075i
$460$	0.868987	+	0.501710i	0.0405167	+	0.0233923i
$461$	25.7975	−	9.38952i	1.20151	−	0.437314i	0.337758	−	0.941233i	$-0.390331\pi$
$461$	25.7975	−	9.38952i	1.20151	−	0.437314i	0.863751	+	0.503919i	$0.168109\pi$
$462$	16.0067	+	3.79381i	0.744700	+	0.176504i
$463$	2.44473	−	2.05137i	0.113616	−	0.0953355i	−0.584210	−	0.811603i	$-0.698595\pi$
$463$	2.44473	−	2.05137i	0.113616	−	0.0953355i	0.697826	+	0.716267i	$0.254151\pi$
$464$	0.392361	−	1.07800i	0.0182149	−	0.0500450i
$465$	0.788531	−	1.82419i	0.0365673	−	0.0845948i
$466$	−4.51599	+	25.6115i	−0.209199	+	1.18643i
$467$	8.45133	+	14.6381i	0.391081	+	0.677372i	0.992592	−	0.121492i	$-0.0387679\pi$
$467$	8.45133	+	14.6381i	0.391081	+	0.677372i	−0.601512	+	0.798864i	$0.705435\pi$
$468$	1.26757	−	10.7030i	0.0585935	−	0.494748i
$469$	26.4245	+	15.2296i	1.22017	+	0.703238i
$470$	0.515386	+	0.0908765i	0.0237730	+	0.00419182i
$471$	6.61796	+	4.35994i	0.304940	+	0.200896i
$472$	−0.501953	+	0.0885079i	−0.0231043	+	0.00407391i
$473$	7.96898	−	1.40515i	0.366414	−	0.0646087i
$474$	0.216195	−	3.66374i	0.00993017	−	0.168281i
$475$	24.0366	+	4.23831i	1.10288	+	0.194467i
$476$	−0.000824122	−	1.09192i	−3.77736e−5	−	0.0500480i
$477$	−8.57568	+	17.0108i	−0.392653	+	0.778870i
$478$	0.845525	+	1.46449i	0.0386734	+	0.0669843i
$479$	6.55126	−	37.1540i	0.299335	−	1.69761i	−0.349707	−	0.936859i	$-0.613719\pi$
$479$	6.55126	−	37.1540i	0.299335	−	1.69761i	0.649042	−	0.760753i	$-0.275170\pi$
$480$	0.757301	+	1.01885i	0.0345659	+	0.0465041i
$481$	7.47568	−	20.5393i	0.340862	−	0.936510i
$482$	12.5795	−	10.5554i	0.572980	−	0.480787i
$483$	−6.73656	+	28.4227i	−0.306524	+	1.29328i
$484$	5.69287	−	2.07204i	0.258767	−	0.0941835i
$485$	1.41096	+	0.814620i	0.0640685	+	0.0369900i
$486$	4.05593	−	13.3619i	0.183981	−	0.606109i
$487$	−9.18231	−	15.9042i	−0.416090	−	0.720689i	0.579452	−	0.815006i	$-0.303267\pi$
$487$	−9.18231	−	15.9042i	−0.416090	−	0.720689i	−0.995542	+	0.0943172i	$0.969933\pi$
$488$	−2.32331	+	13.1761i	−0.105171	+	0.596456i
$489$	−3.32225	+	13.9702i	−0.150238	+	0.631753i
$490$	0.280743	−	0.774972i	0.0126827	−	0.0350097i
$491$	−17.9717	+	3.16890i	−0.811053	+	0.143011i	−0.563769	−	0.825933i	$-0.690649\pi$
$491$	−17.9717	+	3.16890i	−0.811053	+	0.143011i	−0.247284	+	0.968943i	$0.579538\pi$
$492$	−18.3250	−	7.92124i	−0.826155	−	0.357117i
$493$	−2.28080	−	0.402167i	−0.102722	−	0.0181127i
$494$		−	13.1635i		−	0.592253i
$495$	0.866367	+	1.32164i	0.0389403	+	0.0594032i
$496$	−1.29038	+	0.745003i	−0.0579399	+	0.0334516i
$497$	0.197341	−	1.12414i	0.00885194	−	0.0504244i
$498$	10.0611	−	5.04324i	0.450847	−	0.225993i
$499$	28.6729	−	24.0594i	1.28358	−	1.07705i	0.290836	−	0.956773i	$-0.406067\pi$
$499$	28.6729	−	24.0594i	1.28358	−	1.07705i	0.992741	−	0.120276i	$-0.0383778\pi$
$500$	0.272884	+	1.54760i	0.0122037	+	0.0692109i
$501$	−3.40169	−	6.78624i	−0.151976	−	0.303187i
$502$	−3.79183	+	4.51892i	−0.169238	+	0.201689i
$503$	−8.72136	−	15.1058i	−0.388866	−	0.673536i	0.603431	−	0.797415i	$-0.293800\pi$
$503$	−8.72136	−	15.1058i	−0.388866	−	0.673536i	−0.992297	+	0.123879i	$0.960466\pi$
$504$	−13.5905	+	18.2258i	−0.605367	+	0.811840i
$505$	−0.248072	+	0.429673i	−0.0110391	+	0.0191202i
$506$	−7.82593	−	21.5016i	−0.347905	−	0.955861i
$507$	6.36019	+	2.74928i	0.282466	+	0.122100i
$508$	−8.38995	+	7.04000i	−0.372244	+	0.312350i
$509$	4.84714	+	27.4895i	0.214846	+	1.21845i	0.881174	+	0.472792i	$0.156754\pi$
$509$	4.84714	+	27.4895i	0.214846	+	1.21845i	−0.666328	+	0.745659i	$0.732135\pi$
$510$	−0.0482719	+	0.0510871i	−0.00213752	+	0.00226217i
$511$	−3.09002	−	2.58886i	−0.136694	−	0.114525i
$512$		−	1.92969i		−	0.0852812i
$513$	−4.47724	+	25.0560i	−0.197675	+	1.10625i
$514$	−22.4597	+	12.9671i	−0.990655	+	0.571955i
$515$	0.845789	−	1.00797i	0.0372699	−	0.0444166i
$516$	−0.969038	+	4.07483i	−0.0426595	+	0.179384i
$517$	11.4483	+	13.6436i	0.503496	+	0.600043i
$518$	−13.2197	+	11.1096i	−0.580839	+	0.488130i
$519$	−26.3801	−	11.4031i	−1.15796	−	0.500543i
$520$	1.06140	−	0.386319i	0.0465456	−	0.0169412i
$521$	6.26889			0.274645			0.137323	−	0.990526i	$-0.456150\pi$
$521$	6.26889			0.274645			0.137323	+	0.990526i	$0.456150\pi$
$522$	12.3735	+	13.1553i	0.541574	+	0.575794i
$523$			6.16606i			0.269623i	0.990871	+	0.134811i	$0.0430429\pi$
$523$			6.16606i			0.269623i	−0.990871	+	0.134811i	$0.956957\pi$
$524$	−1.15938	+	6.57518i	−0.0506478	+	0.287238i
$525$	−20.4050	+	10.2476i	−0.890548	+	0.447241i
$526$	19.5450	+	7.11378i	0.852200	+	0.310176i
$527$	1.93356	+	2.30433i	0.0842272	+	0.100378i
$528$	0.0697947	−	1.18277i	0.00303742	−	0.0514736i
$529$	16.5668	−	6.02982i	0.720295	−	0.262166i
$530$	−0.747724			−0.0324791
$531$	0.153887	−	0.511176i	0.00667812	−	0.0221832i
$532$	7.75007	−	13.4470i	0.336008	−	0.582999i
$533$	−18.5593	+	22.1181i	−0.803890	+	0.958039i
$534$	−14.2705	−	19.1992i	−0.617545	−	0.830830i
$535$	0.390631	+	0.465536i	0.0168884	+	0.0201269i
$536$	11.2931	−	31.0276i	0.487789	−	1.34019i
$537$	17.5386	+	4.17086i	0.756845	+	0.179986i
$538$	2.82420	+	7.75944i	0.121760	+	0.334533i
$539$	24.2720	−	14.0623i	1.04547	−	0.605708i
$540$	−0.805873	+	0.140195i	−0.0346792	+	0.00603304i
$541$	−10.3506	+	17.9278i	−0.445008	+	0.770777i	−0.998053	−	0.0623747i	$-0.980133\pi$
$541$	−10.3506	+	17.9278i	−0.445008	+	0.770777i	0.553045	+	0.833152i	$0.313466\pi$
$542$	20.2163	+	16.9635i	0.868366	+	0.728646i
$543$	−27.9145	−	6.63838i	−1.19793	−	0.284880i
$544$	−1.89233	+	0.333669i	−0.0811331	+	0.0143060i
$545$	−0.272010	−	1.54264i	−0.0116516	−	0.0660796i
$546$	7.35376	+	9.87799i	0.314712	+	0.422739i
$547$	−12.9704	−	10.8834i	−0.554573	−	0.465342i	0.321913	−	0.946769i	$-0.395674\pi$
$547$	−12.9704	−	10.8834i	−0.554573	−	0.465342i	−0.876486	+	0.481427i	$0.840118\pi$
$548$	15.0026	−	8.66173i	0.640877	−	0.370011i
$549$	−11.2274	−	8.38519i	−0.479175	−	0.357871i
$550$	8.94329	−	15.4902i	0.381343	−	0.660506i
$551$	−25.2176	−	21.1601i	−1.07431	−	0.901450i
$552$	31.5685	+	1.86283i	1.34364	+	0.0792875i
$553$	−4.02644	−	4.79118i	−0.171222	−	0.203742i
$554$	0.933281	−	2.56417i	0.0396513	−	0.108941i
$555$	−1.65598	−	0.0977180i	−0.0702922	−	0.00414790i
$556$	−5.60864	−	15.4096i	−0.237859	−	0.653514i
$557$	−37.1778	−	21.4646i	−1.57528	−	0.909486i	−0.995505	−	0.0947060i	$-0.969809\pi$
$557$	−37.1778	−	21.4646i	−1.57528	−	0.909486i	−0.579770	−	0.814780i	$-0.696858\pi$
$558$	−1.32816	−	23.4195i	−0.0562253	−	0.991425i
$559$	5.24610	+	3.02883i	0.221886	+	0.128106i
$560$	−0.0584732	−	0.0102649i	−0.00247094	−	0.000433772i
$561$	−2.37602	+	0.275879i	−0.100316	+	0.0116476i
$562$	21.0991	+	7.67944i	0.890011	+	0.323938i
$563$	2.55016	+	0.928183i	0.107477	+	0.0391183i	0.395199	−	0.918596i	$-0.370676\pi$
$563$	2.55016	+	0.928183i	0.107477	+	0.0391183i	−0.287722	+	0.957714i	$0.592898\pi$
$564$	−8.83359	+	2.63726i	−0.371961	+	0.111049i
$565$	−0.395228	−	0.0696894i	−0.0166274	−	0.00293186i
$566$	10.0043			0.420513
$567$	−10.6378	−	21.3035i	−0.446744	−	0.894662i
$568$	−1.23562			−0.0518454
$569$	32.7153	+	5.76860i	1.37150	+	0.241832i	0.810381	−	0.585904i	$-0.199260\pi$
$569$	32.7153	+	5.76860i	1.37150	+	0.241832i	0.561118	+	0.827736i	$0.310371\pi$
$570$	−0.957282	+	0.285795i	−0.0400961	+	0.0119707i
$571$	−2.04644	−	0.744844i	−0.0856409	−	0.0311708i	0.298844	−	0.954302i	$-0.403399\pi$
$571$	−2.04644	−	0.744844i	−0.0856409	−	0.0311708i	−0.384485	+	0.923131i	$0.625621\pi$
$572$	13.5286	+	4.92400i	0.565658	+	0.205883i
$573$	17.8494	−	2.07248i	0.745669	−	0.0865793i
$574$	21.4290	−	7.81785i	0.894430	−	0.326311i
$575$	27.5056	+	15.8803i	1.14706	+	0.662256i
$576$	14.2945	+	7.20634i	0.595606	+	0.300264i
$577$	−29.6400	−	17.1127i	−1.23393	−	0.712410i	−0.266083	−	0.963950i	$-0.585729\pi$
$577$	−29.6400	−	17.1127i	−1.23393	−	0.712410i	−0.967847	+	0.251541i	$0.919063\pi$
$578$	5.17202	+	14.2100i	0.215128	+	0.591059i
$579$	−31.5236	−	1.86019i	−1.31008	−	0.0773068i
$580$	0.361830	−	0.994121i	0.0150242	−	0.0412786i
$581$	6.55016	−	18.0388i	0.271747	−	0.748375i
$582$	19.1971	+	1.13281i	0.795746	+	0.0469564i
$583$	−19.4934	−	16.3569i	−0.807334	−	0.677434i
$584$	−2.18212	+	3.77953i	−0.0902966	+	0.156398i
$585$	−0.139134	+	1.17481i	−0.00575247	+	0.0485723i
$586$	−3.74450	+	2.16189i	−0.154684	+	0.0893067i
$587$	−10.2925	−	8.63644i	−0.424817	−	0.356464i	0.405175	−	0.914239i	$-0.367211\pi$
$587$	−10.2925	−	8.63644i	−0.424817	−	0.356464i	−0.829992	+	0.557775i	$0.811655\pi$
$588$	1.69640	+	14.4203i	0.0699582	+	0.594682i
$589$	7.42462	+	42.1071i	0.305926	+	1.73499i
$590$	0.0206349	−	0.00363850i	0.000849527	−	0.000149794i
$591$	−36.9399	−	8.78471i	−1.51951	−	0.361355i
$592$	0.952757	+	0.799458i	0.0391581	+	0.0328575i
$593$	−1.95066	+	3.37864i	−0.0801039	+	0.138744i	−0.903294	−	0.429021i	$-0.858859\pi$
$593$	−1.95066	+	3.37864i	−0.0801039	+	0.138744i	0.823190	+	0.567765i	$0.192192\pi$
$594$	16.1324	+	9.36334i	0.661918	+	0.384183i
$595$	9.04589e−5		0.119853i	3.70846e−6		0.00491351i
$596$	6.66876	+	18.3223i	0.273163	+	0.750510i
$597$	12.2257	+	2.90741i	0.500365	+	0.118992i
$598$	5.85855	−	16.0962i	0.239574	−	0.658224i
$599$	−5.98259	−	7.12977i	−0.244442	−	0.291315i	0.629848	−	0.776718i	$-0.283117\pi$
$599$	−5.98259	−	7.12977i	−0.244442	−	0.291315i	−0.874290	+	0.485404i	$0.838673\pi$
$600$	14.7467	+	19.8399i	0.602032	+	0.809960i
$601$	20.1709	−	24.0388i	0.822789	−	0.980561i	−0.177205	−	0.984174i	$-0.556705\pi$
$601$	20.1709	−	24.0388i	0.822789	−	0.980561i	0.999993	+	0.00361252i	$0.00114990\pi$
$602$	−2.39599	−	4.14276i	−0.0976534	−	0.168846i
$603$	23.6937	+	25.1908i	0.964882	+	1.02585i
$604$	−5.08040			−0.206718
$605$	−0.624873	+	0.227435i	−0.0254047	+	0.00924655i
$606$	−0.344968	+	5.84599i	−0.0140134	+	0.237477i
$607$	−4.60295	−	5.48559i	−0.186828	−	0.222653i	0.664498	−	0.747290i	$-0.268645\pi$
$607$	−4.60295	−	5.48559i	−0.186828	−	0.222653i	−0.851326	+	0.524637i	$0.824201\pi$
$608$	−25.6653	−	9.34139i	−1.04086	−	0.378843i
$609$	30.7446	+	1.79093i	1.24583	+	0.0725722i
$610$	0.0955096	−	0.541662i	0.00386707	−	0.0219312i
$611$			13.3330i			0.539395i
$612$	0.356907	−	1.18556i	0.0144271	−	0.0479235i
$613$	34.8506			1.40760			0.703801	−	0.710397i	$-0.251485\pi$
$613$	34.8506			1.40760			0.703801	+	0.710397i	$0.251485\pi$
$614$	17.2291	−	6.27089i	0.695311	−	0.253073i
$615$	2.01143	+	0.869467i	0.0811086	+	0.0350603i
$616$	−19.5383	−	23.2492i	−0.787222	−	0.936737i
$617$	4.32090	+	5.14944i	0.173953	+	0.207309i	0.845976	−	0.533222i	$-0.179019\pi$
$617$	4.32090	+	5.14944i	0.173953	+	0.207309i	−0.672023	+	0.740530i	$0.734574\pi$
$618$	3.59324	−	15.1097i	0.144541	−	0.607799i
$619$	−22.1515	+	26.3991i	−0.890343	+	1.06107i	0.107420	+	0.994214i	$0.465741\pi$
$619$	−22.1515	+	26.3991i	−0.890343	+	1.06107i	−0.997763	+	0.0668555i	$0.978703\pi$
$620$	−1.18998	+	0.687033i	−0.0477906	+	0.0275919i
$621$	−16.6262	+	28.6458i	−0.667187	+	1.14951i
$622$		−	13.2143i		−	0.529846i
$623$	−40.1780	−	7.05320i	−1.60970	−	0.282580i
$624$	0.609170	−	0.644696i	0.0243863	−	0.0258085i
$625$	4.29625	+	24.3652i	0.171850	+	0.974610i
$626$	−8.14508	+	6.83454i	−0.325543	+	0.273163i
$627$	−31.2086	−	13.4903i	−1.24635	−	0.538752i
$628$	−1.87410	−	5.14905i	−0.0747848	−	0.205469i
$629$	1.25545	−	2.17451i	0.0500582	−	0.0867033i
$630$	0.558694	−	0.749248i	0.0222589	−	0.0298508i
$631$	13.2483	+	22.9468i	0.527407	+	0.913496i	0.999490	+	0.0319417i	$0.0101691\pi$
$631$	13.2483	+	22.9468i	0.527407	+	0.913496i	−0.472083	+	0.881554i	$0.656498\pi$
$632$	−4.35518	+	5.19031i	−0.173240	+	0.206459i
$633$	3.55826	+	7.09858i	0.141428	+	0.282143i
$634$	3.18432	+	18.0592i	0.126465	+	0.717221i
$635$	0.920914	−	0.772739i	0.0365454	−	0.0306652i
$636$	11.7751	−	5.90240i	0.466911	−	0.234046i
$637$	20.6859	+	3.61530i	0.819607	+	0.143243i
$638$	−20.8923	+	12.0622i	−0.827133	+	0.477546i
$639$	0.582575	−	1.15560i	0.0230463	−	0.0457148i
$640$		−	0.837534i		−	0.0331064i
$641$	−2.34586	−	0.413639i	−0.0926561	−	0.0163378i	0.127128	−	0.991886i	$-0.459424\pi$
$641$	−2.34586	−	0.413639i	−0.0926561	−	0.0163378i	−0.219784	+	0.975549i	$0.570535\pi$
$642$	6.58425	+	2.84613i	0.259860	+	0.112328i
$643$	−9.49012	+	1.67336i	−0.374254	+	0.0659911i	−0.357612	−	0.933870i	$-0.616409\pi$
$643$	−9.49012	+	1.67336i	−0.374254	+	0.0659911i	−0.0166424	+	0.999862i	$0.505298\pi$
$644$	15.4615	−	12.9936i	0.609267	−	0.512020i
$645$	0.106365	−	0.447269i	0.00418814	−	0.0176112i
$646$	0.262586	−	1.48920i	0.0103313	−	0.0585918i
$647$	1.16581	+	2.01925i	0.0458328	+	0.0793847i	0.888032	−	0.459782i	$-0.152073\pi$
$647$	1.16581	+	2.01925i	0.0458328	+	0.0793847i	−0.842199	+	0.539167i	$0.818739\pi$
$648$	−20.7249	+	15.3310i	−0.814150	+	0.602257i
$649$	0.617553	+	0.356545i	0.0242411	+	0.0139956i
$650$	12.5825	−	4.57966i	0.493527	−	0.179629i
$651$	−29.0946	−	27.4498i	−1.14031	−	1.07584i
$652$	7.60572	−	6.38196i	0.297863	−	0.249937i
$653$	6.57680	−	18.0696i	0.257370	−	0.707119i	−0.741957	−	0.670447i	$-0.766102\pi$
$653$	6.57680	−	18.0696i	0.257370	−	0.707119i	0.999327	−	0.0366714i	$-0.0116755\pi$
$654$	−11.0297	−	14.8391i	−0.431295	−	0.580254i
$655$	0.127258	−	0.721718i	0.00497239	−	0.0281998i
$656$	−0.821470	−	1.42283i	−0.0320730	−	0.0555521i
$657$	−2.50594	−	3.82279i	−0.0977658	−	0.149141i
$658$	5.25984	−	9.12621i	0.205050	−	0.355777i
$659$	38.6246	+	6.81055i	1.50460	+	0.265301i	0.864360	−	0.502874i	$-0.167724\pi$
$659$	38.6246	+	6.81055i	1.50460	+	0.265301i	0.640239	+	0.768176i	$0.278835\pi$
$660$	0.0643638	−	1.09074i	0.00250536	−	0.0424570i
$661$	−34.0284	+	6.00013i	−1.32355	+	0.233378i	−0.790374	−	0.612624i	$-0.790114\pi$
$661$	−34.0284	+	6.00013i	−1.32355	+	0.233378i	−0.533179	+	0.846003i	$0.679003\pi$
$662$	12.1429	−	2.14112i	0.471948	−	0.0832172i
$663$	−1.49532	−	0.985125i	−0.0580735	−	0.0382591i
$664$	−20.4611	−	3.60784i	−0.794044	−	0.140011i
$665$	−0.850679	+	1.47599i	−0.0329879	+	0.0572365i
$666$	−17.9906	+	7.72782i	−0.697120	+	0.299447i
$667$	−21.4184	−	37.0978i	−0.829325	−	1.43643i
$668$	−0.911408	+	5.16885i	−0.0352634	+	0.199989i
$669$	−16.2070	+	37.4934i	−0.626599	+	1.44958i
$670$	−0.464252	+	1.27552i	−0.0179356	+	0.0492777i
$671$	14.3391	−	12.0320i	0.553556	−	0.464489i
$672$	24.4780	−	7.32800i	0.944259	−	0.282684i
$673$	13.9024	−	5.06006i	0.535898	−	0.195051i	−0.0598720	−	0.998206i	$-0.519069\pi$
$673$	13.9024	−	5.06006i	0.535898	−	0.195051i	0.595770	+	0.803155i	$0.296847\pi$
$674$	−9.80042	−	5.65828i	−0.377498	−	0.217949i
$675$	−25.5079	+	4.43752i	−0.981798	+	0.170800i
$676$	−2.39540	−	4.14895i	−0.0921307	−	0.159575i
$677$	−3.25288	+	18.4480i	−0.125018	+	0.709015i	0.856278	+	0.516514i	$0.172771\pi$
$677$	−3.25288	+	18.4480i	−0.125018	+	0.709015i	−0.981297	+	0.192500i	$0.938340\pi$
$678$	−4.53902	+	1.35512i	−0.174320	+	0.0520430i
$679$	25.1046	−	21.0976i	0.963426	−	0.809650i
$680$	0.127784	−	0.0225318i	0.00490030	−	0.000864055i
$681$	−3.40431	+	2.53038i	−0.130453	+	0.0969642i
$682$	30.8575	+	5.44101i	1.18159	+	0.208347i
$683$		−	22.2418i		−	0.851057i	−0.904945	−	0.425529i	$-0.860088\pi$
$683$		−	22.2418i		−	0.851057i	0.904945	−	0.425529i	$-0.139912\pi$
$684$	12.8191	−	12.0573i	0.490152	−	0.461022i
$685$	−1.64674	+	0.950746i	−0.0629187	+	0.0363261i
$686$	−12.7329	−	10.6352i	−0.486146	−	0.406053i
$687$	0.378946	+	0.249651i	0.0144577	+	0.00952479i
$688$	−0.264051	+	0.221565i	−0.0100669	+	0.00844710i
$689$	−3.30794	−	18.7603i	−0.126023	−	0.714710i
$690$	−1.29776	−	0.0765798i	−0.0494048	−	0.00291534i
$691$	−1.75750	+	2.09450i	−0.0668583	+	0.0796786i	−0.798437	−	0.602078i	$-0.794339\pi$
$691$	−1.75750	+	2.09450i	−0.0668583	+	0.0796786i	0.731579	+	0.681757i	$0.238784\pi$
$692$	9.93535	+	17.2085i	0.377685	+	0.654170i
$693$	30.9556	−	7.31137i	1.17590	−	0.277736i
$694$	−8.11734	+	14.0597i	−0.308130	+	0.533697i
$695$	0.615627	+	1.69142i	0.0233521	+	0.0641593i
$696$	−3.84538	−	33.1185i	−0.145759	−	1.25535i
$697$	−2.54084	+	2.13202i	−0.0962414	+	0.0807561i
$698$	2.80828	+	15.9265i	0.106295	+	0.602828i
$699$	14.3851	+	48.1835i	0.544096	+	1.82247i
$700$	15.5498	+	2.72975i	0.587726	+	0.103175i
$701$		−	7.89910i		−	0.298345i	−0.988811	−	0.149173i	$-0.952339\pi$
$701$		−	7.89910i		−	0.298345i	0.988811	−	0.149173i	$-0.0476610\pi$
$702$	4.74577	+	13.1324i	0.179117	+	0.495650i
$703$	30.9083	−	17.8449i	1.16573	−	0.673033i
$704$	−13.7451	+	16.3808i	−0.518038	+	0.617373i
$705$	0.969610	−	0.289476i	0.0365176	−	0.0109023i
$706$	9.00125	+	10.7273i	0.338766	+	0.403726i
$707$	6.42473	+	7.64497i	0.241627	+	0.287519i
$708$	−0.296234	+	0.220187i	−0.0111332	+	0.00827514i
$709$	−32.6400	+	11.8800i	−1.22582	+	0.446163i	−0.872165	−	0.489212i	$-0.837284\pi$
$709$	−32.6400	+	11.8800i	−1.22582	+	0.446163i	−0.353657	+	0.935375i	$0.615062\pi$
$710$	0.0507954			0.00190632
$711$	−2.80078	−	6.52028i	−0.105037	−	0.244530i
$712$			44.1625i			1.65506i
$713$	−9.66145	+	54.7928i	−0.361824	+	2.05201i
$714$	0.634893	+	1.26420i	0.0237603	+	0.0473116i
$715$	−1.48495	−	0.540478i	−0.0555340	−	0.0202127i
$716$	−8.01209	−	9.54844i	−0.299426	−	0.356842i
$717$	2.73045	+	1.79883i	0.101971	+	0.0671787i
$718$	−8.51341	+	3.09863i	−0.317718	+	0.115640i
$719$	−2.89130			−0.107827			−0.0539137	−	0.998546i	$-0.517170\pi$
$719$	−2.89130			−0.107827			−0.0539137	+	0.998546i	$0.517170\pi$
$720$	−0.0601098	−	0.0303033i	−0.00224016	−	0.00112934i
$721$	−13.2593	−	22.9258i	−0.493803	−	0.853803i
$722$	2.87581	−	3.42726i	0.107027	−	0.127549i
$723$	12.5984	−	29.1452i	0.468540	−	1.08392i
$724$	12.7521	+	15.1974i	0.473929	+	0.564807i
$725$	11.4528	−	31.4664i	0.425347	−	1.16863i
$726$	−5.39063	+	5.70500i	−0.200065	+	0.211733i
$727$	−8.56203	−	23.5240i	−0.317548	−	0.872456i	−0.991076	−	0.133295i	$-0.957444\pi$
$727$	−8.56203	−	23.5240i	−0.317548	−	0.872456i	0.673528	−	0.739161i	$-0.264778\pi$
$728$	−0.0171587	−	22.7344i	−0.000635945	−	0.842593i
$729$	−4.56667	−	26.6110i	−0.169136	−	0.985593i
$730$	0.0897052	−	0.155374i	0.00332014	−	0.00575065i
$731$	0.533078	+	0.447306i	0.0197166	+	0.0165442i
$732$	2.77171	+	9.28395i	0.102445	+	0.343145i
$733$	17.9624	−	3.16725i	0.663455	−	0.116985i	0.168228	−	0.985748i	$-0.446196\pi$
$733$	17.9624	−	3.16725i	0.663455	−	0.116985i	0.495228	+	0.868763i	$0.335085\pi$
$734$	4.33397	+	24.5792i	0.159970	+	0.907234i
$735$	−0.186203	−	1.58283i	−0.00686821	−	0.0583835i
$736$	−27.2259	−	22.8452i	−1.00356	−	0.842086i
$737$	−40.0060	+	23.0975i	−1.47364	+	0.850806i
$738$	25.8233	−	1.46448i	0.950567	−	0.0539082i
$739$	−11.8748	+	20.5677i	−0.436821	+	0.756595i	−0.997442	−	0.0714767i	$-0.977229\pi$
$739$	−11.8748	+	20.5677i	−0.436821	+	0.756595i	0.560622	+	0.828072i	$0.310562\pi$
$740$	0.878621	+	0.737251i	0.0322988	+	0.0271019i
$741$	−11.4056	−	22.7537i	−0.418995	−	0.835878i
$742$	−5.13666	+	14.1461i	−0.188573	+	0.519319i
$743$	3.47920	−	9.55903i	0.127640	−	0.350687i	−0.859369	−	0.511357i	$-0.829143\pi$
$743$	3.47920	−	9.55903i	0.127640	−	0.350687i	0.987008	+	0.160670i	$0.0513654\pi$
$744$	−23.8238	+	36.1622i	−0.873424	+	1.32577i
$745$	−0.731990	−	2.01113i	−0.0268180	−	0.0736820i
$746$	−15.3071	−	8.83756i	−0.560433	−	0.323566i
$747$	13.0213	−	17.4350i	0.476423	−	0.637912i
$748$	1.43228	+	0.826928i	0.0523694	+	0.0302355i
$749$	11.4909	−	4.19218i	0.419869	−	0.153179i
$750$	−1.21456	−	1.63403i	−0.0443493	−	0.0596665i
$751$	13.1156	+	4.77368i	0.478594	+	0.174194i	0.570041	−	0.821616i	$-0.306927\pi$
$751$	13.1156	+	4.77368i	0.478594	+	0.174194i	−0.0914474	+	0.995810i	$0.529149\pi$
$752$	−0.712923	−	0.259483i	−0.0259976	−	0.00946236i
$753$	−2.63890	+	11.0966i	−0.0961668	+	0.404384i
$754$	−17.7853	−	3.13603i	−0.647702	−	0.114207i
$755$	0.557645			0.0202948
$756$	−2.88380	+	16.2093i	−0.104883	+	0.589526i
$757$	−23.1271			−0.840570			−0.420285	−	0.907392i	$-0.638070\pi$
$757$	−23.1271			−0.840570			−0.420285	+	0.907392i	$0.638070\pi$
$758$	2.90795	+	0.512750i	0.105621	+	0.0186239i
$759$	−32.1577	−	30.3857i	−1.16725	−	1.10293i
$760$	1.73311	+	0.630799i	0.0628663	+	0.0228815i
$761$	15.7985	+	5.75019i	0.572696	+	0.208444i	0.612102	−	0.790779i	$-0.290324\pi$
$761$	15.7985	+	5.75019i	0.572696	+	0.208444i	−0.0394059	+	0.999223i	$0.512547\pi$
$762$	5.63017	−	13.0248i	0.203959	−	0.471841i
$763$	−31.0536	−	5.45143i	−1.12422	−	0.197355i
$764$	−10.7597	−	6.21212i	−0.389273	−	0.224747i
$765$	−0.0391756	+	0.130132i	−0.00141640	+	0.00470493i
$766$	−23.9379	−	13.8206i	−0.864912	−	0.499357i
$767$	0.182579	+	0.501631i	0.00659253	+	0.0181128i
$768$	−12.7133	−	25.3625i	−0.458752	−	0.915191i
$769$	5.01510	−	13.7789i	0.180849	−	0.496879i	−0.815832	−	0.578290i	$-0.803720\pi$
$769$	5.01510	−	13.7789i	0.180849	−	0.496879i	0.996681	+	0.0814109i	$0.0259426\pi$
$770$	0.803207	+	0.955758i	0.0289456	+	0.0344431i
$771$	−27.5872	+	41.8747i	−0.993530	+	1.50808i
$772$	16.7257	+	14.0345i	0.601971	+	0.505114i
$773$	−24.0914	+	41.7276i	−0.866508	+	1.50084i	−0.000966739		1.00000i	$0.500308\pi$
$773$	−24.0914	+	41.7276i	−0.866508	+	1.50084i	−0.865542	+	0.500837i	$0.833026\pi$
$774$	−1.24338	−	5.28214i	−0.0446923	−	0.189863i
$775$	−37.6657	+	21.7463i	−1.35299	+	0.781149i
$776$	−27.1959	−	22.8201i	−0.976276	−	0.819193i
$777$	−13.2248	+	30.6578i	−0.474438	+	1.09984i
$778$	−2.09088	−	11.8580i	−0.0749617	−	0.425129i
$779$	−46.4290	+	8.18669i	−1.66349	+	0.293318i
$780$	0.561770	−	0.594531i	0.0201146	−	0.0212876i
$781$	1.32425	+	1.11118i	0.0473855	+	0.0397611i
$782$	0.983875	−	1.70412i	0.0351833	−	0.0609393i
$783$	32.7868	+	12.0185i	1.17170	+	0.429506i
$784$	−0.595895	+	1.03573i	−0.0212820	+	0.0369903i
$785$	0.205709	+	0.565180i	0.00734206	+	0.0201722i
$786$	−2.47455	−	8.28861i	−0.0882644	−	0.295645i
$787$	−8.62005	+	23.6834i	−0.307272	+	0.844222i	0.685915	+	0.727682i	$0.259402\pi$
$787$	−8.62005	+	23.6834i	−0.307272	+	0.844222i	−0.993186	+	0.116539i	$0.962820\pi$
$788$	16.8752	+	20.1110i	0.601153	+	0.716426i
$789$	39.9482	−	4.63836i	1.42219	−	0.165130i
$790$	0.179038	−	0.213370i	0.00636990	−	0.00759135i
$791$	−4.03355	+	6.99851i	−0.143417	+	0.248838i
$792$	−13.5908	−	31.6397i	−0.482927	−	1.12427i
$793$	14.0127			0.497607
$794$	27.2338	−	9.91231i	0.966493	−	0.351775i
$795$	−1.29248	+	0.647871i	−0.0458394	+	0.0229776i
$796$	−5.58505	−	6.65600i	−0.197957	−	0.235916i
$797$	48.1785	+	17.5355i	1.70657	+	0.621140i	0.996546	−	0.0830393i	$-0.0264627\pi$
$797$	48.1785	+	17.5355i	1.70657	+	0.621140i	0.710022	+	0.704179i	$0.248685\pi$
$798$	−1.16935	+	20.0740i	−0.0413946	+	0.710612i
$799$	−0.265968	+	1.50838i	−0.00940927	+	0.0533626i
$800$		−	27.7825i		−	0.982258i
$801$	−41.3025	−	20.8219i	−1.45935	−	0.735707i
$802$	−34.1694			−1.20657
$803$	5.73754	−	2.08829i	0.202473	−	0.0736943i
$804$	−2.75777	−	23.7515i	−0.0972591	−	0.837650i
$805$	−1.69711	+	1.42623i	−0.0598154	+	0.0502680i
$806$	15.0776	+	17.9687i	0.531084	+	0.632922i
$807$	11.6050	+	10.9655i	0.408515	+	0.386004i
$808$	6.94928	−	8.28183i	0.244475	−	0.291354i
$809$	17.0109	−	9.82125i	0.598072	−	0.345297i	−0.170211	−	0.985408i	$-0.554445\pi$
$809$	17.0109	−	9.82125i	0.598072	−	0.345297i	0.768283	+	0.640111i	$0.221112\pi$
$810$	0.851985	−	0.630245i	0.0299357	−	0.0221445i
$811$		−	18.4996i		−	0.649608i	−0.945781	−	0.324804i	$-0.894702\pi$
$811$		−	18.4996i		−	0.649608i	0.945781	−	0.324804i	$-0.105298\pi$
$812$	−16.3219	−	13.6748i	−0.572788	−	0.479890i
$813$	49.6431	+	11.8057i	1.74106	+	0.414043i
$814$	−4.54171	−	25.7573i	−0.159187	−	0.902794i
$815$	−0.834834	+	0.700509i	−0.0292430	+	0.0245378i
$816$	0.0817767	−	0.0607835i	0.00286276	−	0.00212785i
$817$	3.38300	+	9.29472i	0.118356	+	0.325181i
$818$	−10.1493	+	17.5791i	−0.354862	+	0.614639i
$819$	21.2702	+	10.7029i	0.743241	+	0.373988i
$820$	−0.757550	−	1.31212i	−0.0264548	−	0.0458211i
$821$	−20.3450	+	24.2462i	−0.710046	+	0.846200i	−0.993623	−	0.112750i	$-0.964034\pi$
$821$	−20.3450	+	24.2462i	−0.710046	+	0.846200i	0.283578	+	0.958949i	$0.408479\pi$
$822$	−12.3475	+	18.7423i	−0.430668	+	0.653712i
$823$	4.89359	+	27.7529i	0.170580	+	0.967407i	0.943123	+	0.332444i	$0.107873\pi$
$823$	4.89359	+	27.7529i	0.170580	+	0.967407i	−0.772543	+	0.634963i	$0.781016\pi$
$824$	−21.9641	+	18.4301i	−0.765155	+	0.642042i
$825$	2.03727	−	34.5246i	0.0709288	−	1.20199i
$826$	0.0729203	−	0.415384i	0.00253722	−	0.0144531i
$827$	−26.8439	+	15.4983i	−0.933454	+	0.538930i	−0.887902	−	0.460032i	$-0.847838\pi$
$827$	−26.8439	+	15.4983i	−0.933454	+	0.538930i	−0.0455515	+	0.998962i	$0.514505\pi$
$828$	21.0414	−	9.03830i	0.731239	−	0.314103i
$829$			9.62164i			0.334173i	0.985942	+	0.167087i	$0.0534360\pi$
$829$			9.62164i			0.334173i	−0.985942	+	0.167087i	$0.946564\pi$
$830$	0.841141	+	0.148316i	0.0291964	+	0.00514812i
$831$	−0.608523	−	5.24094i	−0.0211094	−	0.181806i
$832$	−15.7647	+	2.77974i	−0.546543	+	0.0963702i
$833$	2.26811	+	0.821649i	0.0785853	+	0.0284684i
$834$	15.4425	+	14.5915i	0.534729	+	0.505262i
$835$	0.100040	−	0.567354i	0.00346202	−	0.0196341i
$836$	11.7539	+	20.3583i	0.406517	+	0.704107i
$837$	−22.5878	−	39.3309i	−0.780747	−	1.35947i
$838$	−1.03063	−	0.595033i	−0.0356024	−	0.0205551i
$839$	−46.3318	+	16.8634i	−1.59955	+	0.582189i	−0.979335	−	0.202242i	$-0.935177\pi$
$839$	−46.3318	+	16.8634i	−1.59955	+	0.582189i	−0.620216	+	0.784431i	$0.712955\pi$
$840$	−1.65293	+	0.494840i	−0.0570316	+	0.0170736i
$841$	−12.3820	+	10.3898i	−0.426967	+	0.358268i
$842$	−1.40955	+	3.87272i	−0.0485764	+	0.133463i
$843$	43.1247	−	5.00719i	1.48529	−	0.172457i
$844$	0.953356	−	5.40675i	0.0328159	−	0.186108i
$845$	0.262928	+	0.455405i	0.00904501	+	0.0156664i
$846$	8.70012	−	8.18307i	0.299116	−	0.281340i
$847$	0.0101017	+	13.3843i	0.000347100	+	0.459889i
$848$	1.06750	+	0.188229i	0.0366581	+	0.00646382i
$849$	17.2929	−	8.66832i	0.593492	−	0.297496i
$850$	1.51483	−	0.267106i	0.0519583	−	0.00916165i
$851$	45.7366	−	8.06459i	1.56783	−	0.276451i
$852$	−0.799919	+	0.400970i	−0.0274048	+	0.0137370i
$853$	−15.1514	−	2.67160i	−0.518774	−	0.0914738i	−0.0918701	−	0.995771i	$-0.529284\pi$
$853$	−15.1514	−	2.67160i	−0.518774	−	0.0914738i	−0.426903	+	0.904297i	$0.640396\pi$
$854$	−9.59149	−	5.52800i	−0.328214	−	0.189164i
$855$	−1.40708	+	1.32346i	−0.0481211	+	0.0452612i
$856$	−6.62115	−	11.4682i	−0.226306	−	0.391974i
$857$	−0.535318	+	3.03594i	−0.0182861	+	0.103706i	−0.992585	−	0.121554i	$-0.961212\pi$
$857$	−0.535318	+	3.03594i	−0.0182861	+	0.103706i	0.974299	+	0.225260i	$0.0723232\pi$
$858$	−18.5278	+	2.15126i	−0.632529	+	0.0734427i
$859$	10.7003	−	29.3988i	0.365089	−	1.00307i	−0.612115	−	0.790769i	$-0.709681\pi$
$859$	10.7003	−	29.3988i	0.365089	−	1.00307i	0.977204	−	0.212305i	$-0.0680969\pi$
$860$	−0.243505	+	0.204325i	−0.00830345	+	0.00696742i
$861$	30.2673	−	32.0809i	1.03151	−	1.09331i
$862$	−14.9384	+	5.43713i	−0.508804	+	0.185189i
$863$	5.09715	+	2.94284i	0.173509	+	0.100176i	0.584239	−	0.811581i	$-0.301393\pi$
$863$	5.09715	+	2.94284i	0.173509	+	0.100176i	−0.410730	+	0.911757i	$0.634726\pi$
$864$	28.9724	+	0.0663474i	0.985662	+	0.00225718i
$865$	−1.09054	−	1.88888i	−0.0370796	−	0.0642238i
$866$	−0.190137	+	1.07832i	−0.00646110	+	0.0366427i
$867$	21.2525	+	20.0814i	0.721772	+	0.681999i
$868$	4.82305	+	27.2327i	0.163705	+	0.924338i
$869$	9.33518	−	1.64604i	0.316674	−	0.0558382i
$870$	0.158081	+	1.36148i	0.00535944	+	0.0461585i
$871$	−34.0565	−	6.00508i	−1.15396	−	0.203474i
$872$			34.1333i			1.15590i
$873$	34.1647	−	14.6754i	1.15630	−	0.496686i
$874$	24.2222	−	13.9847i	0.819329	−	0.473040i
$875$	−3.41953	−	0.600295i	−0.115601	−	0.0202937i
$876$	−0.186170	+	3.15492i	−0.00629010	+	0.106595i
$877$	11.4737	−	9.62761i	0.387441	−	0.325101i	−0.428175	−	0.903696i	$-0.640843\pi$
$877$	11.4737	−	9.62761i	0.387441	−	0.325101i	0.815615	+	0.578595i	$0.196399\pi$
$878$	0.757698	+	4.29712i	0.0255711	+	0.145021i
$879$	−4.59936	+	6.98137i	−0.155133	+	0.235476i
$880$	0.0577993	−	0.0688825i	0.00194841	−	0.00232203i
$881$	−11.8885	−	20.5915i	−0.400533	−	0.693744i	0.593257	−	0.805013i	$-0.297842\pi$
$881$	−11.8885	−	20.5915i	−0.400533	−	0.693744i	−0.993790	+	0.111269i	$0.964508\pi$
$882$	−10.3368	−	15.7170i	−0.348059	−	0.529218i
$883$	−11.3387	+	19.6392i	−0.381578	+	0.660913i	−0.991288	−	0.131712i	$-0.957953\pi$
$883$	−11.3387	+	19.6392i	−0.381578	+	0.660913i	0.609710	+	0.792625i	$0.291286\pi$
$884$	0.423451	+	1.16342i	0.0142422	+	0.0391302i
$885$	0.0325159	−	0.0241686i	0.00109301	−	0.000812419i
$886$	15.9612	−	13.3931i	0.536229	−	0.449949i
$887$	−2.00574	−	11.3751i	−0.0673461	−	0.381939i	−0.999787	−	0.0206173i	$-0.993437\pi$
$887$	−2.00574	−	11.3751i	−0.0673461	−	0.381939i	0.932441	−	0.361321i	$-0.117674\pi$
$888$	35.1664	+	8.36294i	1.18011	+	0.280642i
$889$	−8.29289	−	22.7311i	−0.278135	−	0.762378i
$890$		−	1.81549i		−	0.0608554i
$891$	35.9985	+	2.20698i	1.20599	+	0.0739367i
$892$	24.4581	−	14.1209i	0.818917	−	0.472802i
$893$	−13.9939	+	16.6773i	−0.468289	+	0.558086i
$894$	−18.3613	−	17.3495i	−0.614094	−	0.580255i
$895$	0.879440	+	1.04808i	0.0293964	+	0.0350333i
$896$	−15.8452	−	5.75363i	−0.529350	−	0.192215i
$897$	−3.81992	−	32.8993i	−0.127544	−	1.09848i
$898$	19.3749	−	7.05188i	0.646548	−	0.235324i
$899$	58.6601			1.95642
$900$	15.9850	+	8.05855i	0.532834	+	0.268618i
$901$		−	2.18836i		−	0.0729049i
$902$	−5.99948	+	34.0247i	−0.199761	+	1.13290i
$903$	−7.73112	−	5.08493i	−0.257275	−	0.169216i
$904$	8.21764	+	2.99098i	0.273315	+	0.0994784i
$905$	−1.39972	−	1.66813i	−0.0465284	−	0.0554504i
$906$	5.88422	−	2.94954i	0.195490	−	0.0979920i
$907$	21.0307	−	7.65453i	0.698312	−	0.254165i	0.0316218	−	0.999500i	$-0.489933\pi$
$907$	21.0307	−	7.65453i	0.698312	−	0.254165i	0.666690	+	0.745335i	$0.267711\pi$
$908$	2.93278			0.0973278
$909$	4.46901	+	10.4040i	0.148228	+	0.345078i
$910$	0.000705383		0.934595i	2.33832e−5		0.0309815i
$911$	−29.6477	+	35.3327i	−0.982271	+	1.17063i	0.00306421	+	0.999995i	$0.499025\pi$
$911$	−29.6477	+	35.3327i	−0.982271	+	1.17063i	−0.985335	+	0.170630i	$0.945420\pi$
$912$	1.43863	−	0.167038i	0.0476376	−	0.00553118i
$913$	18.6843	+	22.2671i	0.618360	+	0.736933i
$914$	8.15002	−	22.3920i	0.269579	−	0.740661i
$915$	−0.304234	−	1.01904i	−0.0100577	−	0.0336885i
$916$	−0.107311	−	0.294836i	−0.00354567	−	0.00974165i
$917$	−12.7798	−	7.36558i	−0.422027	−	0.243233i
$918$	0.274929	+	1.58035i	0.00907400	+	0.0521594i
$919$	−8.95419	+	15.5091i	−0.295371	+	0.511598i	−0.975071	−	0.221892i	$-0.928777\pi$
$919$	−8.95419	+	15.5091i	−0.295371	+	0.511598i	0.679700	+	0.733490i	$0.262110\pi$
$920$	1.83849	+	1.54268i	0.0606132	+	0.0508605i
$921$	24.3479	−	25.7678i	0.802291	−	0.849079i
$922$	24.2185	−	4.27038i	0.797595	−	0.140637i
$923$	0.224720	+	1.27445i	0.00739674	+	0.0419490i
$924$	−20.1934	−	8.71078i	−0.664313	−	0.286564i
$925$	27.8105	+	23.3358i	0.914404	+	0.767276i
$926$	2.47578	−	1.42939i	0.0813593	−	0.0469728i
$927$	−6.88079	−	29.2311i	−0.225995	−	0.960077i
$928$	−18.7356	+	32.4511i	−0.615027	+	1.06526i
$929$	−22.5691	−	18.9378i	−0.740469	−	0.621328i	0.192494	−	0.981298i	$-0.438342\pi$
$929$	−22.5691	−	18.9378i	−0.740469	−	0.621328i	−0.932964	+	0.359970i	$0.882787\pi$
$930$	0.979381	−	1.48660i	0.0321152	−	0.0487476i
$931$	22.0801	+	26.2335i	0.723646	+	0.859769i
$932$	11.8913	−	32.6711i	0.389513	−	1.07018i
$933$	−11.4496	−	22.8416i	−0.374845	−	0.747800i
$934$	5.17859	+	14.2281i	0.169449	+	0.465556i
$935$	−0.157213	−	0.0907669i	−0.00514141	−	0.00296840i
$936$	7.43102	−	24.6841i	0.242891	−	0.806826i
$937$	−42.6087	−	24.6001i	−1.39196	−	0.803651i	−0.398432	−	0.917198i	$-0.630446\pi$
$937$	−42.6087	−	24.6001i	−1.39196	−	0.803651i	−0.993533	+	0.113547i	$0.963779\pi$
$938$	20.9421	+	17.5456i	0.683784	+	0.572884i
$939$	−8.15733	+	18.8712i	−0.266204	+	0.615838i
$940$	−0.657449	−	0.239292i	−0.0214436	−	0.00780484i
$941$	13.3216	+	4.84865i	0.434271	+	0.158062i	0.549899	−	0.835231i	$-0.314666\pi$
$941$	13.3216	+	4.84865i	0.434271	+	0.158062i	−0.115629	+	0.993293i	$0.536888\pi$
$942$	5.16002	+	4.87568i	0.168123	+	0.158858i
$943$	−60.4167	−	10.6531i	−1.96744	−	0.346913i
$944$	−0.0303757			−0.000988646
$945$	0.316537	−	1.77920i	0.0102970	−	0.0578772i
$946$	7.24863			0.235673
$947$	−15.7766	−	2.78184i	−0.512671	−	0.0903978i	−0.0886730	−	0.996061i	$-0.528263\pi$
$947$	−15.7766	−	2.78184i	−0.512671	−	0.0903978i	−0.423998	+	0.905663i	$0.639374\pi$
$948$	−1.13517	+	4.77341i	−0.0368686	+	0.155033i
$949$	4.29517	+	1.56331i	0.139427	+	0.0507473i
$950$	20.5453	+	7.47788i	0.666578	+	0.242614i
$951$	21.1517	+	28.4570i	0.685892	+	0.922783i
$952$	0.451567	−	2.57231i	0.0146354	−	0.0833692i
$953$	38.0570	+	21.9722i	1.23279	+	0.711750i	0.967610	−	0.252450i	$-0.0812363\pi$
$953$	38.0570	+	21.9722i	1.23279	+	0.711750i	0.265177	+	0.964200i	$0.414570\pi$
$954$	−10.2113	+	13.6726i	−0.330604	+	0.442666i
$955$	1.18103	+	0.681868i	0.0382172	+	0.0220647i
$956$	−0.773220	−	2.12440i	−0.0250077	−	0.0687081i
$957$	−25.6619	+	38.9523i	−0.829533	+	1.25915i
$958$	11.5588	−	31.7574i	0.373446	−	1.02604i
$959$	6.67435	+	37.6858i	0.215526	+	1.21694i
$960$	0.544421	+	1.08610i	0.0175711	+	0.0350537i
$961$	−34.6174	−	29.0474i	−1.11669	−	0.937014i
$962$	9.78980	−	16.9564i	0.315636	−	0.546697i
$963$	13.8472	−	0.785300i	0.446221	−	0.0253059i
$964$	−19.0123	+	10.9768i	−0.612345	+	0.353537i
$965$	−1.83588	−	1.54049i	−0.0590990	−	0.0495900i
$966$	−10.3640	+	24.0260i	−0.333457	+	0.773023i
$967$	−5.36073	−	30.4022i	−0.172389	−	0.977669i	−0.941114	−	0.338089i	$-0.890219\pi$
$967$	−5.36073	−	30.4022i	−0.172389	−	0.977669i	0.768725	−	0.639580i	$-0.220892\pi$
$968$	14.2699	−	2.51617i	0.458653	−	0.0808729i
$969$	−0.836437	−	2.80168i	−0.0268702	−	0.0900028i
$970$	1.11800	+	0.938117i	0.0358970	+	0.0301211i
$971$	26.8436	−	46.4945i	0.861453	−	1.49208i	−0.00907360	−	0.999959i	$-0.502888\pi$
$971$	26.8436	−	46.4945i	0.861453	−	1.49208i	0.870527	−	0.492121i	$-0.163778\pi$
$972$	−8.44189	+	16.6504i	−0.270774	+	0.534063i
$973$	36.2289	−	0.0273437i	1.16145	−	0.000876598i
$974$	−5.62650	−	15.4587i	−0.180285	−	0.495328i
$975$	17.7814	−	18.8184i	0.569461	−	0.602671i
$976$	−0.272712	+	0.749269i	−0.00872929	+	0.0239835i
$977$	−16.1755	−	19.2773i	−0.517502	−	0.616734i	0.442487	−	0.896775i	$-0.354096\pi$
$977$	−16.1755	−	19.2773i	−0.517502	−	0.616734i	−0.959988	+	0.280041i	$0.909652\pi$
$978$	−5.10390	+	11.8074i	−0.163205	+	0.377559i
$979$	39.7149	−	47.3304i	1.26929	−	1.51269i
$980$	−0.549528	+	0.955137i	−0.0175540	+	0.0305107i
$981$	−31.9228	−	16.0933i	−1.01922	−	0.513820i
$982$	−16.3472			−0.521660
$983$	24.6937	−	8.98779i	0.787608	−	0.286666i	0.0832668	−	0.996527i	$-0.473465\pi$
$983$	24.6937	−	8.98779i	0.787608	−	0.286666i	0.704341	+	0.709861i	$0.251242\pi$
$984$	−39.8739	−	26.2691i	−1.27113	−	0.837429i
$985$	−1.85229	−	2.20747i	−0.0590187	−	0.0703358i
$986$	−1.94951	−	0.709565i	−0.0620852	−	0.0225972i
$987$	1.18441	−	20.3325i	0.0377002	−	0.647191i
$988$	−3.05588	+	17.3307i	−0.0972204	+	0.551364i
$989$			12.8712i			0.409280i
$990$	0.558707	+	1.30068i	0.0177569	+	0.0413385i
$991$	36.0925			1.14652			0.573258	−	0.819375i	$-0.305679\pi$
$991$	36.0925			1.14652			0.573258	+	0.819375i	$0.305679\pi$
$992$	45.7339	−	16.6458i	1.45205	−	0.528504i
$993$	19.1344	−	14.2224i	0.607213	−	0.451333i
$994$	0.348951	−	0.960991i	0.0110680	−	0.0304808i
$995$	0.613037	+	0.730589i	0.0194346	+	0.0231612i
$996$	−14.4169	+	4.30416i	−0.456818	+	0.136383i
$997$	−8.13561	+	9.69564i	−0.257657	+	0.307064i	−0.879330	−	0.476213i	$-0.842009\pi$
$997$	−8.13561	+	9.69564i	−0.257657	+	0.307064i	0.621673	+	0.783277i	$0.286453\pi$
$998$	29.0371	−	16.7646i	0.919153	−	0.530673i
$999$	−24.4017	+	28.9460i	−0.772036	+	0.915810i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.bd.a.47.14	yes	132
3.2	odd	2		567.2.bd.a.467.9		132
7.3	odd	6		189.2.ba.a.101.9	✓	132
21.17	even	6		567.2.ba.a.143.14		132
27.4	even	9		567.2.ba.a.341.14		132
27.23	odd	18		189.2.ba.a.131.9	yes	132
189.31	odd	18		567.2.bd.a.17.9		132
189.185	even	18	inner	189.2.bd.a.185.14	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.9	✓	132	7.3	odd	6
189.2.ba.a.131.9	yes	132	27.23	odd	18
189.2.bd.a.47.14	yes	132	1.1	even	1	trivial
189.2.bd.a.185.14	yes	132	189.185	even	18	inner
567.2.ba.a.143.14		132	21.17	even	6
567.2.ba.a.341.14		132	27.4	even	9
567.2.bd.a.17.9		132	189.31	odd	18
567.2.bd.a.467.9		132	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.bd (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.882178 + 0.155552i) q^{2} +(1.65967 - 0.495491i) q^{3} +(-1.12534 - 0.409592i) q^{4} +(0.123522 + 0.0449584i) q^{5} +(1.54119 - 0.178947i) q^{6} +(1.69913 - 2.02805i) q^{7} +(-2.48059 - 1.43217i) q^{8} +(2.50898 - 1.64470i) q^{9} +O(q^{10})\)	\(q+(0.882178 + 0.155552i) q^{2} +(1.65967 - 0.495491i) q^{3} +(-1.12534 - 0.409592i) q^{4} +(0.123522 + 0.0449584i) q^{5} +(1.54119 - 0.178947i) q^{6} +(1.69913 - 2.02805i) q^{7} +(-2.48059 - 1.43217i) q^{8} +(2.50898 - 1.64470i) q^{9} +(0.101975 + 0.0588754i) q^{10} +(1.37059 + 3.76567i) q^{11} +(-2.07064 - 0.122187i) q^{12} +(-1.02604 + 2.81901i) q^{13} +(1.81440 - 1.52479i) q^{14} +(0.227282 + 0.0134118i) q^{15} +(-0.130766 - 0.109725i) q^{16} +(-0.172311 + 0.298451i) q^{17} +(2.46920 - 1.06064i) q^{18} +(-4.24215 + 2.44921i) q^{19} +(-0.120590 - 0.101187i) q^{20} +(1.81510 - 4.20778i) q^{21} +(0.623349 + 3.53519i) q^{22} +(-6.27733 + 1.10686i) q^{23} +(-4.82657 - 1.14781i) q^{24} +(-3.81699 - 3.20283i) q^{25} +(-1.34365 + 2.32726i) q^{26} +(3.34913 - 3.97282i) q^{27} +(-2.74277 + 1.58630i) q^{28} +(2.29851 + 6.31510i) q^{29} +(0.198417 + 0.0471857i) q^{30} +(2.98538 - 8.20227i) q^{31} +(3.58403 + 4.27128i) q^{32} +(4.14058 + 5.57063i) q^{33} +(-0.198433 + 0.236483i) q^{34} +(0.301058 - 0.174119i) q^{35} +(-3.49712 + 0.823195i) q^{36} -7.28599 q^{37} +(-4.12331 + 1.50076i) q^{38} +(-0.306081 + 5.18700i) q^{39} +(-0.242020 - 0.288428i) q^{40} +(9.04416 + 3.29180i) q^{41} +(2.25577 - 3.42967i) q^{42} +(0.350643 - 1.98860i) q^{43} -4.79906i q^{44} +(0.383858 - 0.0903572i) q^{45} -5.70989 q^{46} +(4.17641 - 1.52009i) q^{47} +(-0.271395 - 0.117314i) q^{48} +(-1.22594 - 6.89181i) q^{49} +(-2.86905 - 3.41920i) q^{50} +(-0.138098 + 0.580706i) q^{51} +(2.30929 - 2.75210i) q^{52} +(-5.49931 + 3.17503i) q^{53} +(3.57251 - 2.98377i) q^{54} +0.526764i q^{55} +(-7.11934 + 2.59731i) q^{56} +(-5.82699 + 6.16681i) q^{57} +(1.04537 + 5.92857i) q^{58} +(0.136314 - 0.114381i) q^{59} +(-0.250277 - 0.108186i) q^{60} +(-1.59759 - 4.38933i) q^{61} +(3.90952 - 6.77148i) q^{62} +(0.927544 - 7.88287i) q^{63} +(2.66805 + 4.62120i) q^{64} +(-0.253476 + 0.302081i) q^{65} +(2.78620 + 5.55836i) q^{66} +(2.00174 + 11.3525i) q^{67} +(0.316152 - 0.265283i) q^{68} +(-9.86983 + 4.94738i) q^{69} +(0.292671 - 0.106774i) q^{70} +(0.373587 - 0.215690i) q^{71} +(-8.57923 + 0.486542i) q^{72} -1.52364i q^{73} +(-6.42754 - 1.13335i) q^{74} +(-7.92189 - 3.42435i) q^{75} +(5.77706 - 1.01865i) q^{76} +(9.96576 + 3.61872i) q^{77} +(-1.07687 + 4.52825i) q^{78} +(0.410757 - 2.32952i) q^{79} +(-0.0112194 - 0.0194325i) q^{80} +(3.58993 - 8.25302i) q^{81} +(7.46651 + 4.31079i) q^{82} +(6.81615 - 2.48087i) q^{83} +(-3.76609 + 3.99175i) q^{84} +(-0.0347021 + 0.0291185i) q^{85} +(0.618659 - 1.69975i) q^{86} +(6.94383 + 9.34206i) q^{87} +(1.99320 - 11.3040i) q^{88} +(-7.70903 - 13.3524i) q^{89} +(0.352686 - 0.0200014i) q^{90} +(3.97372 + 6.87070i) q^{91} +(7.51752 + 1.32554i) q^{92} +(0.890584 - 15.0923i) q^{93} +(3.92079 - 0.691340i) q^{94} +(-0.634113 + 0.111811i) q^{95} +(8.06467 + 5.31304i) q^{96} +(12.2061 + 2.15226i) q^{97} +(-0.00946529 - 6.27050i) q^{98} +(9.63217 + 7.19377i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

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