LMFDB - Embedded newform 804.2.w.a.59.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(59,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 12]))

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

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

chi := DirichletCharacter("804.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.w (of order $22$, degree $10$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$1320$
Relative dimension:	$132$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			59.20
Character	$\chi$	$=$	804.59
Dual form			804.2.w.a.695.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23455 - 0.689841i) q^{2} +(-1.66550 - 0.475496i) q^{3} +(1.04824 + 1.70329i) q^{4} +(0.120449 - 0.187422i) q^{5} +(1.72814 + 1.73596i) q^{6} +(4.49296 + 0.645990i) q^{7} +(-0.119106 - 2.82592i) q^{8} +(2.54781 + 1.58388i) q^{9} +O(q^{10})$	\(q+(-1.23455 - 0.689841i) q^{2} +(-1.66550 - 0.475496i) q^{3} +(1.04824 + 1.70329i) q^{4} +(0.120449 - 0.187422i) q^{5} +(1.72814 + 1.73596i) q^{6} +(4.49296 + 0.645990i) q^{7} +(-0.119106 - 2.82592i) q^{8} +(2.54781 + 1.58388i) q^{9} +(-0.277992 + 0.148292i) q^{10} +(-0.272005 - 0.174807i) q^{11} +(-0.935939 - 3.33527i) q^{12} +(-0.331439 - 0.725750i) q^{13} +(-5.10116 - 3.89694i) q^{14} +(-0.289726 + 0.254879i) q^{15} +(-1.80239 + 3.57091i) q^{16} +(1.85128 + 6.30487i) q^{17} +(-2.05278 - 3.71297i) q^{18} +(2.00286 - 0.287967i) q^{19} +(0.445493 + 0.00869627i) q^{20} +(-7.17588 - 3.21228i) q^{21} +(0.215215 + 0.403448i) q^{22} +(-3.33370 - 3.84729i) q^{23} +(-1.14534 + 4.76321i) q^{24} +(2.05646 + 4.50301i) q^{25} +(-0.0914736 + 1.12462i) q^{26} +(-3.49026 - 3.84943i) q^{27} +(3.60939 + 8.32996i) q^{28} +8.68024i q^{29} +(0.533509 - 0.114797i) q^{30} +(-8.98860 - 4.10496i) q^{31} +(4.68851 - 3.16511i) q^{32} +(0.369905 + 0.420479i) q^{33} +(2.06386 - 9.06077i) q^{34} +(0.662245 - 0.764271i) q^{35} +(-0.0270965 + 5.99994i) q^{36} -0.764418 q^{37} +(-2.67128 - 1.02614i) q^{38} +(0.206922 + 1.36634i) q^{39} +(-0.543986 - 0.318055i) q^{40} +(1.03056 + 3.50975i) q^{41} +(6.64303 + 8.91595i) q^{42} +(1.19672 + 4.07567i) q^{43} +(0.0126209 - 0.646542i) q^{44} +(0.603734 - 0.286739i) q^{45} +(1.46160 + 7.04940i) q^{46} +(7.80706 + 9.00982i) q^{47} +(4.69984 - 5.09033i) q^{48} +(13.0529 + 3.83269i) q^{49} +(0.567559 - 6.97783i) q^{50} +(-0.0853706 - 11.3811i) q^{51} +(0.888736 - 1.32530i) q^{52} +(2.83045 - 9.63962i) q^{53} +(1.65341 + 7.16004i) q^{54} +(-0.0655253 + 0.0299244i) q^{55} +(1.29038 - 12.7737i) q^{56} +(-3.47269 - 0.472739i) q^{57} +(5.98798 - 10.7162i) q^{58} +(2.25299 - 4.93336i) q^{59} +(-0.737836 - 0.226314i) q^{60} +(4.58457 - 2.94632i) q^{61} +(8.26513 + 11.2685i) q^{62} +(10.4240 + 8.76217i) q^{63} +(-7.97163 + 0.673167i) q^{64} +(-0.175943 - 0.0252968i) q^{65} +(-0.166604 - 0.774279i) q^{66} +(7.72593 - 2.70369i) q^{67} +(-8.79844 + 9.76226i) q^{68} +(3.72292 + 7.99284i) q^{69} +(-1.34480 + 0.486689i) q^{70} +(6.42349 + 1.88611i) q^{71} +(4.17246 - 7.38855i) q^{72} +(3.67908 - 2.36440i) q^{73} +(0.943714 + 0.527327i) q^{74} +(-1.28387 - 8.47762i) q^{75} +(2.58996 + 3.10959i) q^{76} +(-1.10918 - 0.961113i) q^{77} +(0.687100 - 1.82956i) q^{78} +(-7.51095 + 3.43014i) q^{79} +(0.452171 + 0.767920i) q^{80} +(3.98265 + 8.07084i) q^{81} +(1.14890 - 5.04389i) q^{82} +(-3.13010 - 2.01159i) q^{83} +(-2.05058 - 15.5898i) q^{84} +(1.40466 + 0.412444i) q^{85} +(1.33414 - 5.85717i) q^{86} +(4.12742 - 14.4570i) q^{87} +(-0.461593 + 0.789484i) q^{88} +(2.60242 + 2.25501i) q^{89} +(-0.943146 - 0.0624868i) q^{90} +(-1.02031 - 3.47487i) q^{91} +(3.05854 - 9.71113i) q^{92} +(13.0187 + 11.1109i) q^{93} +(-3.42287 - 16.5087i) q^{94} +(0.187270 - 0.410065i) q^{95} +(-9.31372 + 3.04214i) q^{96} -2.29020 q^{97} +(-13.4706 - 13.7361i) q^{98} +(-0.416143 - 0.876198i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1320 q - 18 q^{4} - 5 q^{6} - 22 q^{9}+O(q^{10}) $ 1320 * q - 18 * q^4 - 5 * q^6 - 22 * q^9	$ 1320 q - 18 q^{4} - 5 q^{6} - 22 q^{9} - 26 q^{10} - 15 q^{12} - 44 q^{13} - 34 q^{16} - 13 q^{18} - 66 q^{21} + 74 q^{22} + 13 q^{24} + 80 q^{25} - 110 q^{28} - 36 q^{30} - 22 q^{33} - 54 q^{34} - 37 q^{36} - 72 q^{37} - 22 q^{40} + q^{42} - 154 q^{45} - 82 q^{46} + 11 q^{48} + 96 q^{49} - 14 q^{52} - 138 q^{54} - 6 q^{57} + 74 q^{58} + 3 q^{60} - 28 q^{61} - 6 q^{64} - 4 q^{66} - 38 q^{69} - 18 q^{70} - 145 q^{72} + 96 q^{73} + 14 q^{76} - 51 q^{78} - 38 q^{81} - 74 q^{82} - 41 q^{84} - 76 q^{85} + 6 q^{88} - 5 q^{90} + 78 q^{93} - 22 q^{94} + 184 q^{96} - 128 q^{97}+O(q^{100}) $ 1320 * q - 18 * q^4 - 5 * q^6 - 22 * q^9 - 26 * q^10 - 15 * q^12 - 44 * q^13 - 34 * q^16 - 13 * q^18 - 66 * q^21 + 74 * q^22 + 13 * q^24 + 80 * q^25 - 110 * q^28 - 36 * q^30 - 22 * q^33 - 54 * q^34 - 37 * q^36 - 72 * q^37 - 22 * q^40 + q^42 - 154 * q^45 - 82 * q^46 + 11 * q^48 + 96 * q^49 - 14 * q^52 - 138 * q^54 - 6 * q^57 + 74 * q^58 + 3 * q^60 - 28 * q^61 - 6 * q^64 - 4 * q^66 - 38 * q^69 - 18 * q^70 - 145 * q^72 + 96 * q^73 + 14 * q^76 - 51 * q^78 - 38 * q^81 - 74 * q^82 - 41 * q^84 - 76 * q^85 + 6 * q^88 - 5 * q^90 + 78 * q^93 - 22 * q^94 + 184 * q^96 - 128 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{6}{11}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.23455	−	0.689841i	−0.872960	−	0.487791i
$2$	−1.23455	−	0.689841i	−0.872960	−	0.487791i
$3$	−1.66550	−	0.475496i	−0.961579	−	0.274528i
$3$	−1.66550	−	0.475496i	−0.961579	−	0.274528i
$4$	1.04824	+	1.70329i	0.524119	+	0.851645i
$5$	0.120449	−	0.187422i	0.0538664	−	0.0838177i	−0.813276	−	0.581878i	$-0.802318\pi$
$5$	0.120449	−	0.187422i	0.0538664	−	0.0838177i	0.867142	+	0.498061i	$0.165954\pi$
$6$	1.72814	+	1.73596i	0.705508	+	0.708702i
$7$	4.49296	+	0.645990i	1.69818	+	0.244161i	0.922232	−	0.386637i	$-0.126363\pi$
$7$	4.49296	+	0.645990i	1.69818	+	0.244161i	0.775947	+	0.630798i	$0.217272\pi$
$8$	−0.119106	−	2.82592i	−0.0421103	−	0.999113i
$9$	2.54781	+	1.58388i	0.849269	+	0.527960i
$10$	−0.277992	+	0.148292i	−0.0879087	+	0.0468940i
$11$	−0.272005	−	0.174807i	−0.0820126	−	0.0527063i	0.498992	−	0.866607i	$-0.333704\pi$
$11$	−0.272005	−	0.174807i	−0.0820126	−	0.0527063i	−0.581004	+	0.813900i	$0.697340\pi$
$12$	−0.935939	−	3.33527i	−0.270182	−	0.962809i
$13$	−0.331439	−	0.725750i	−0.0919247	−	0.201287i	0.858085	−	0.513508i	$-0.171654\pi$
$13$	−0.331439	−	0.725750i	−0.0919247	−	0.201287i	−0.950009	+	0.312221i	$0.898927\pi$
$14$	−5.10116	−	3.89694i	−1.36334	−	1.04150i
$15$	−0.289726	+	0.254879i	−0.0748070	+	0.0658095i
$16$	−1.80239	+	3.57091i	−0.450598	+	0.892727i
$17$	1.85128	+	6.30487i	0.449000	+	1.52915i	0.804197	+	0.594363i	$0.202596\pi$
$17$	1.85128	+	6.30487i	0.449000	+	1.52915i	−0.355196	+	0.934792i	$0.615586\pi$
$18$	−2.05278	−	3.71297i	−0.483844	−	0.875154i
$19$	2.00286	−	0.287967i	0.459487	−	0.0660643i	0.0913152	−	0.995822i	$-0.470893\pi$
$19$	2.00286	−	0.287967i	0.459487	−	0.0660643i	0.368172	+	0.929758i	$0.379984\pi$
$20$	0.445493	+	0.00869627i	0.0996153	+	0.00194454i
$21$	−7.17588	−	3.21228i	−1.56590	−	0.700977i
$22$	0.215215	+	0.403448i	0.0458840	+	0.0860155i
$23$	−3.33370	−	3.84729i	−0.695124	−	0.802216i	0.292961	−	0.956124i	$-0.405359\pi$
$23$	−3.33370	−	3.84729i	−0.695124	−	0.802216i	−0.988085	+	0.153909i	$0.950814\pi$
$24$	−1.14534	+	4.76321i	−0.233792	+	0.972287i
$25$	2.05646	+	4.50301i	0.411291	+	0.900602i
$26$	−0.0914736	+	1.12462i	−0.0179394	+	0.220556i
$27$	−3.49026	−	3.84943i	−0.671700	−	0.740823i
$28$	3.60939	+	8.32996i	0.682110	+	1.57422i
$29$			8.68024i			1.61188i	0.591998	+	0.805940i	$0.298340\pi$
$29$			8.68024i			1.61188i	−0.591998	+	0.805940i	$0.701660\pi$
$30$	0.533509	−	0.114797i	0.0974049	−	0.0209589i
$31$	−8.98860	−	4.10496i	−1.61440	−	0.737272i	−0.615688	−	0.787990i	$-0.711122\pi$
$31$	−8.98860	−	4.10496i	−1.61440	−	0.737272i	−0.998713	+	0.0507182i	$0.983849\pi$
$32$	4.68851	−	3.16511i	0.828819	−	0.559517i
$33$	0.369905	+	0.420479i	0.0643922	+	0.0731960i
$34$	2.06386	−	9.06077i	0.353949	−	1.55391i
$35$	0.662245	−	0.764271i	0.111940	−	0.129185i
$36$	−0.0270965	+	5.99994i	−0.00451609	+	0.999990i
$37$	−0.764418			−0.125670			−0.0628348	−	0.998024i	$-0.520014\pi$
$37$	−0.764418			−0.125670			−0.0628348	+	0.998024i	$0.520014\pi$
$38$	−2.67128	−	1.02614i	−0.433340	−	0.166462i
$39$	0.206922	+	1.36634i	0.0331340	+	0.218789i
$40$	−0.543986	−	0.318055i	−0.0860117	−	0.0502890i
$41$	1.03056	+	3.50975i	0.160946	+	0.548131i	0.999992	+	0.00407054i	$0.00129570\pi$
$41$	1.03056	+	3.50975i	0.160946	+	0.548131i	−0.839046	+	0.544061i	$0.816886\pi$
$42$	6.64303	+	8.91595i	1.02504	+	1.37576i
$43$	1.19672	+	4.07567i	0.182499	+	0.621533i	0.999022	+	0.0442205i	$0.0140804\pi$
$43$	1.19672	+	4.07567i	0.182499	+	0.621533i	−0.816523	+	0.577313i	$0.804101\pi$
$44$	0.0126209	−	0.646542i	0.00190267	−	0.0974699i
$45$	0.603734	−	0.286739i	0.0899994	−	0.0427445i
$46$	1.46160	+	7.04940i	0.215502	+	1.03938i
$47$	7.80706	+	9.00982i	1.13878	+	1.31422i	0.942705	+	0.333628i	$0.108273\pi$
$47$	7.80706	+	9.00982i	1.13878	+	1.31422i	0.196071	+	0.980590i	$0.437182\pi$
$48$	4.69984	−	5.09033i	0.678364	−	0.734726i
$49$	13.0529	+	3.83269i	1.86470	+	0.547527i
$50$	0.567559	−	6.97783i	0.0802650	−	0.986814i
$51$	−0.0853706	−	11.3811i	−0.0119543	−	1.59367i
$52$	0.888736	−	1.32530i	0.123246	−	0.183786i
$53$	2.83045	−	9.63962i	0.388792	−	1.32410i	−0.500093	−	0.865972i	$-0.666701\pi$
$53$	2.83045	−	9.63962i	0.388792	−	1.32410i	0.888885	−	0.458131i	$-0.151481\pi$
$54$	1.65341	+	7.16004i	0.225000	+	0.974359i
$55$	−0.0655253	+	0.0299244i	−0.00883544	+	0.00403501i
$56$	1.29038	−	12.7737i	0.172434	−	1.70695i
$57$	−3.47269	−	0.472739i	−0.459970	−	0.0626158i
$58$	5.98798	−	10.7162i	0.786261	−	1.40711i
$59$	2.25299	−	4.93336i	0.293314	−	0.642268i	−0.704403	−	0.709800i	$-0.748785\pi$
$59$	2.25299	−	4.93336i	0.293314	−	0.642268i	0.997717	+	0.0675320i	$0.0215125\pi$
$60$	−0.737836	−	0.226314i	−0.0952542	−	0.0292170i
$61$	4.58457	−	2.94632i	0.586994	−	0.377238i	−0.213174	−	0.977014i	$-0.568380\pi$
$61$	4.58457	−	2.94632i	0.586994	−	0.377238i	0.800168	+	0.599776i	$0.204744\pi$
$62$	8.26513	+	11.2685i	1.04967	+	1.43110i
$63$	10.4240	+	8.76217i	1.31330	+	1.10393i
$64$	−7.97163	+	0.673167i	−0.996453	+	0.0841459i
$65$	−0.175943	−	0.0252968i	−0.0218231	−	0.00313768i
$66$	−0.166604	−	0.774279i	−0.0205075	−	0.0953071i
$67$	7.72593	−	2.70369i	0.943873	−	0.330308i
$67$	7.72593	−	2.70369i	0.943873	−	0.330308i
$68$	−8.79844	+	9.76226i	−1.06697	+	1.18385i
$69$	3.72292	+	7.99284i	0.448186	+	0.962225i
$70$	−1.34480	+	0.486689i	−0.160734	+	0.0581705i
$71$	6.42349	+	1.88611i	0.762328	+	0.223840i	0.639712	−	0.768614i	$-0.279053\pi$
$71$	6.42349	+	1.88611i	0.762328	+	0.223840i	0.122616	+	0.992454i	$0.460872\pi$
$72$	4.17246	−	7.38855i	0.491729	−	0.870748i
$73$	3.67908	−	2.36440i	0.430604	−	0.276732i	−0.307333	−	0.951602i	$-0.599437\pi$
$73$	3.67908	−	2.36440i	0.430604	−	0.276732i	0.737937	+	0.674870i	$0.235800\pi$
$74$	0.943714	+	0.527327i	0.109705	+	0.0613005i
$75$	−1.28387	−	8.47762i	−0.148249	−	0.978911i
$76$	2.58996	+	3.10959i	0.297089	+	0.356694i
$77$	−1.10918	−	0.961113i	−0.126403	−	0.109529i
$78$	0.687100	−	1.82956i	0.0777988	−	0.207157i
$79$	−7.51095	+	3.43014i	−0.845048	+	0.385921i	−0.790404	−	0.612585i	$-0.790130\pi$
$79$	−7.51095	+	3.43014i	−0.845048	+	0.385921i	−0.0546437	+	0.998506i	$0.517402\pi$
$80$	0.452171	+	0.767920i	0.0505542	+	0.0858560i
$81$	3.98265	+	8.07084i	0.442516	+	0.896760i
$82$	1.14890	−	5.04389i	0.126874	−	0.557005i
$83$	−3.13010	−	2.01159i	−0.343573	−	0.220801i	0.357462	−	0.933928i	$-0.383642\pi$
$83$	−3.13010	−	2.01159i	−0.343573	−	0.220801i	−0.701035	+	0.713127i	$0.747278\pi$
$84$	−2.05058	−	15.5898i	−0.223737	−	1.70099i
$85$	1.40466	+	0.412444i	0.152356	+	0.0447358i
$86$	1.33414	−	5.85717i	0.143864	−	0.631595i
$87$	4.12742	−	14.4570i	0.442505	−	1.54995i
$88$	−0.461593	+	0.789484i	−0.0492059	+	0.0841593i
$89$	2.60242	+	2.25501i	0.275856	+	0.239030i	0.781790	−	0.623542i	$-0.214307\pi$
$89$	2.60242	+	2.25501i	0.275856	+	0.239030i	−0.505935	+	0.862572i	$0.668852\pi$
$90$	−0.943146	−	0.0624868i	−0.0994163	−	0.00658669i
$91$	−1.02031	−	3.47487i	−0.106958	−	0.364266i
$92$	3.05854	−	9.71113i	0.318875	−	1.01246i
$93$	13.0187	+	11.1109i	1.34997	+	1.15214i
$94$	−3.42287	−	16.5087i	−0.353042	−	1.70275i
$95$	0.187270	−	0.410065i	0.0192135	−	0.0420718i
$96$	−9.31372	+	3.04214i	−0.950578	+	0.310487i
$97$	−2.29020			−0.232535			−0.116267	−	0.993218i	$-0.537093\pi$
$97$	−2.29020			−0.232535			−0.116267	+	0.993218i	$0.537093\pi$
$98$	−13.4706	−	13.7361i	−1.36073	−	1.38756i
$99$	−0.416143	−	0.876198i	−0.0418239	−	0.0880612i
$100$	−5.51428	+	8.22297i	−0.551428	+	0.822297i
$101$	−18.0181	+	2.59061i	−1.79287	+	0.257776i	−0.956779	−	0.290816i	$-0.906073\pi$
$101$	−18.0181	+	2.59061i	−1.79287	+	0.257776i	−0.836090	+	0.548592i	$0.815164\pi$
$102$	−7.74573	+	14.1094i	−0.766941	+	1.39704i
$103$	14.5736	+	6.65556i	1.43598	+	0.655792i	0.973048	−	0.230601i	$-0.0740691\pi$
$103$	14.5736	+	6.65556i	1.43598	+	0.655792i	0.462935	+	0.886392i	$0.346796\pi$
$104$	−2.01143	+	1.02306i	−0.197237	+	0.100319i
$105$	−1.46638	+	0.958002i	−0.143104	+	0.0934914i
$106$	−10.1441	+	9.94805i	−0.985286	+	0.966240i
$107$	1.07990	−	0.694008i	0.104398	−	0.0670923i	−0.487400	−	0.873179i	$-0.662055\pi$
$107$	1.07990	−	0.694008i	0.104398	−	0.0670923i	0.591798	+	0.806086i	$0.298418\pi$
$108$	2.89807	−	9.98004i	0.278867	−	0.960330i
$109$	0.323762	+	0.708940i	0.0310108	+	0.0679042i	0.924504	−	0.381173i	$-0.124480\pi$
$109$	0.323762	+	0.708940i	0.0310108	+	0.0679042i	−0.893493	+	0.449078i	$0.851753\pi$
$110$	0.101538	+	0.00825881i	0.00968123	+	0.000787447i
$111$	1.27314	+	0.363477i	0.120841	+	0.0344998i
$112$	−10.4048	+	14.8796i	−0.983166	+	1.40599i
$113$	5.43985	+	8.46457i	0.511738	+	0.796280i	0.996944	−	0.0781198i	$-0.0248917\pi$
$113$	5.43985	+	8.46457i	0.511738	+	0.796280i	−0.485206	+	0.874400i	$0.661255\pi$
$114$	3.96111	+	2.97923i	0.370992	+	0.279030i
$115$	−1.12261	+	0.161407i	−0.104684	+	0.0150512i
$116$	−14.7850	+	9.09896i	−1.37275	+	0.844817i
$117$	0.305058	−	2.37403i	0.0282027	−	0.219479i
$118$	−6.18466	+	4.53628i	−0.569344	+	0.417599i
$119$	4.24483	+	29.5234i	0.389123	+	2.70641i
$120$	0.754776	+	0.788385i	0.0689013	+	0.0719694i
$121$	−4.52614	−	9.91086i	−0.411467	−	0.900987i
$122$	−7.69238	+	0.474766i	−0.696435	+	0.0429833i
$123$	−0.0475236	−	6.33553i	−0.00428506	−	0.571256i
$124$	−2.43027	−	19.6132i	−0.218244	−	1.76131i
$125$	2.19427	+	0.315488i	0.196261	+	0.0282181i
$126$	−6.82450	−	18.0083i	−0.607975	−	1.60430i
$127$	19.3587	+	2.78336i	1.71781	+	0.246984i	0.929638	−	0.368474i	$-0.120119\pi$
$127$	19.3587	+	2.78336i	1.71781	+	0.246984i	0.788170	+	0.615457i	$0.211029\pi$
$128$	10.3058	+	4.66810i	0.910910	+	0.412605i
$129$	−0.0551863	−	7.35707i	−0.00485888	−	0.647754i
$130$	0.199760	+	0.152603i	0.0175201	+	0.0133842i
$131$	−3.82786	−	4.41758i	−0.334442	−	0.385966i	0.563474	−	0.826134i	$-0.309464\pi$
$131$	−3.82786	−	4.41758i	−0.334442	−	0.385966i	−0.897916	+	0.440168i	$0.854919\pi$
$132$	−0.328448	+	1.07082i	−0.0285878	+	0.0932027i
$133$	9.18478			0.796422
$134$	−11.4032	−	1.99182i	−0.985085	−	0.172067i
$135$	−1.14187	+	0.190492i	−0.0982761	+	0.0163949i
$136$	17.5965	−	5.98250i	1.50889	−	0.512995i
$137$	0.0403263	−	0.0349429i	0.00344530	−	0.00298537i	−0.653136	−	0.757240i	$-0.726547\pi$
$137$	0.0403263	−	0.0349429i	0.00344530	−	0.00298537i	0.656582	+	0.754255i	$0.272002\pi$
$138$	0.917655	−	12.4358i	0.0781160	−	1.05861i
$139$	−5.70869	+	8.88290i	−0.484205	+	0.753438i	−0.994293	−	0.106685i	$-0.965976\pi$
$139$	−5.70869	+	8.88290i	−0.484205	+	0.753438i	0.510088	+	0.860122i	$0.329613\pi$
$140$	1.99597	+	0.326856i	0.168690	+	0.0276244i
$141$	−8.71855	−	18.7181i	−0.734235	−	1.57635i
$142$	−6.62902	−	6.75969i	−0.556295	−	0.567260i
$143$	−0.0367131	+	0.255345i	−0.00307011	+	0.0213531i
$144$	−10.2480	+	6.24321i	−0.854003	+	0.520268i
$145$	1.62687	+	1.04552i	0.135104	+	0.0868261i
$146$	−6.17308	+	0.380996i	−0.510888	+	0.0315315i
$147$	−19.9173	−	12.5900i	−1.64275	−	1.03840i
$148$	−0.801292	−	1.30203i	−0.0658658	−	0.107026i
$149$	8.50150	−	1.22233i	0.696470	−	0.100137i	0.215019	−	0.976610i	$-0.431019\pi$
$149$	8.50150	−	1.22233i	0.696470	−	0.100137i	0.481452	+	0.876473i	$0.340110\pi$
$150$	−4.26320	+	11.3517i	−0.348089	+	0.926865i
$151$	−3.83046	−	13.0453i	−0.311718	−	1.06161i	−0.955153	−	0.296114i	$-0.904309\pi$
$151$	−3.83046	−	13.0453i	−0.311718	−	1.06161i	0.643435	−	0.765501i	$-0.277509\pi$
$152$	−1.05232	−	5.62561i	−0.0853548	−	0.456298i
$153$	−5.26946	+	18.9958i	−0.426010	+	1.53572i
$154$	0.706330	+	1.95170i	0.0569177	+	0.157273i
$155$	−1.85203	+	1.19022i	−0.148758	+	0.0956012i
$156$	−2.11037	+	1.78470i	−0.168965	+	0.142890i
$157$	12.9832	+	14.9834i	1.03617	+	1.19580i	0.980331	+	0.197363i	$0.0632377\pi$
$157$	12.9832	+	14.9834i	1.03617	+	1.19580i	0.0558382	+	0.998440i	$0.482217\pi$
$158$	11.6389	+	0.946680i	0.925942	+	0.0753138i
$159$	−9.29772	+	14.7090i	−0.737357	+	1.16650i
$160$	−0.0284859	−	1.25996i	−0.00225201	−	0.0996088i
$161$	−12.4929	−	19.4393i	−0.984575	−	1.53203i
$162$	0.650812	−	12.7113i	0.0511326	−	0.998692i
$163$			5.58581i			0.437515i	0.975779	+	0.218757i	$0.0702003\pi$
$163$			5.58581i			0.437515i	−0.975779	+	0.218757i	$0.929800\pi$
$164$	−4.89786	+	5.43439i	−0.382458	+	0.424355i
$165$	0.123362	−	0.0186822i	0.00960369	−	0.00145441i
$166$	2.47659	+	4.64269i	0.192221	+	0.360343i
$167$	0.609840	+	4.24153i	0.0471908	+	0.328219i	0.999718	+	0.0237645i	$0.00756519\pi$
$167$	0.609840	+	4.24153i	0.0471908	+	0.328219i	−0.952527	+	0.304455i	$0.901526\pi$
$168$	−8.22296	+	20.6610i	−0.634415	+	1.59403i
$169$	8.09633	−	9.34366i	0.622794	−	0.718743i
$170$	−1.44960	−	1.47817i	−0.111179	−	0.113371i
$171$	5.55900	+	2.43860i	0.425108	+	0.186484i
$172$	−5.68759	+	6.31064i	−0.433675	+	0.481181i
$173$	−16.0817	−	7.34426i	−1.22267	−	0.558374i	−0.303723	−	0.952760i	$-0.598230\pi$
$173$	−16.0817	−	7.34426i	−1.22267	−	0.558374i	−0.918945	+	0.394386i	$0.870957\pi$
$174$	−15.0685	+	15.0006i	−1.14234	+	1.13719i
$175$	6.33067	+	21.5603i	0.478554	+	1.62981i
$176$	1.11448	−	0.656234i	0.0840070	−	0.0494655i
$177$	−6.09815	+	7.14524i	−0.458365	+	0.537069i
$178$	−1.65722	−	4.57918i	−0.124214	−	0.343224i
$179$	7.03836	−	8.12270i	0.526072	−	0.607119i	−0.429069	−	0.903272i	$-0.641158\pi$
$179$	7.03836	−	8.12270i	0.526072	−	0.607119i	0.955141	+	0.296152i	$0.0957036\pi$
$180$	1.12126	+	0.727764i	0.0835736	+	0.0542443i
$181$	0.371542	+	0.428782i	0.0276165	+	0.0318711i	0.769390	−	0.638780i	$-0.220560\pi$
$181$	0.371542	+	0.428782i	0.0276165	+	0.0318711i	−0.741773	+	0.670651i	$0.766015\pi$
$182$	−1.13748	+	4.99377i	−0.0843155	+	0.370163i
$183$	−9.03658	+	2.72717i	−0.668003	+	0.201598i
$184$	−10.4751	+	9.87899i	−0.772232	+	0.728289i
$185$	−0.0920733	+	0.143269i	−0.00676936	+	0.0105333i
$186$	−8.40749	−	22.6978i	−0.616467	−	1.66428i
$187$	0.598578	−	2.03857i	0.0437724	−	0.149075i
$188$	−7.16268	+	22.7421i	−0.522392	+	1.65864i
$189$	−13.1949	−	19.5500i	−0.959787	−	1.42205i
$190$	−0.514075	+	0.377060i	−0.0372949	+	0.0273548i
$191$	−6.18749	+	7.14075i	−0.447711	+	0.516686i	−0.934078	−	0.357068i	$-0.883776\pi$
$191$	−6.18749	+	7.14075i	−0.447711	+	0.516686i	0.486367	+	0.873755i	$0.338322\pi$
$192$	13.5969	+	2.66931i	0.981269	+	0.192641i
$193$	−5.94676	+	13.0216i	−0.428057	+	0.937314i	0.565581	+	0.824693i	$0.308652\pi$
$193$	−5.94676	+	13.0216i	−0.428057	+	0.937314i	−0.993638	+	0.112622i	$0.964075\pi$
$194$	2.82737	+	1.57987i	0.202994	+	0.113428i
$195$	0.281005	+	0.125792i	0.0201232	+	0.00900816i
$196$	7.15441	+	26.2505i	0.511029	+	1.87504i
$197$	1.11752	−	3.80592i	0.0796198	−	0.271160i	−0.910056	−	0.414486i	$-0.863961\pi$
$197$	1.11752	−	3.80592i	0.0796198	−	0.271160i	0.989676	+	0.143326i	$0.0457796\pi$
$198$	−0.0906869	+	1.36878i	−0.00644484	+	0.0972753i
$199$	−24.4645	−	3.51746i	−1.73424	−	0.249346i	−0.798489	−	0.602009i	$-0.794367\pi$
$199$	−24.4645	−	3.51746i	−1.73424	−	0.249346i	−0.935750	+	0.352663i	$0.885276\pi$
$200$	12.4802	−	6.34771i	0.882484	−	0.448851i
$201$	−14.1532	+	0.829358i	−0.998288	+	0.0584984i
$202$	24.0314	+	9.23139i	1.69084	+	0.649518i
$203$	−5.60735	+	39.0000i	−0.393559	+	2.73726i
$204$	19.2957	−	12.0755i	1.35097	−	0.845452i
$205$	0.781934	+	0.229597i	0.0546127	+	0.0160357i
$206$	−13.4006	−	18.2701i	−0.933667	−	1.27294i
$207$	−2.39997	−	15.0823i	−0.166810	−	1.04829i
$208$	3.18897	+	0.124548i	0.221115	+	0.00863587i
$209$	−0.595126	−	0.271785i	−0.0411657	−	0.0187998i
$210$	2.47119	−	0.171135i	0.170528	−	0.0118095i
$211$	−4.67313	−	4.04929i	−0.321712	−	0.278765i	0.479000	−	0.877815i	$-0.341000\pi$
$211$	−4.67313	−	4.04929i	−0.321712	−	0.278765i	−0.800711	+	0.599050i	$0.795545\pi$
$212$	19.3860	−	5.28355i	1.33144	−	0.362875i
$213$	−9.80152	−	6.19566i	−0.671589	−	0.424520i
$214$	−1.81194	+	0.111831i	−0.123862	+	0.00764464i
$215$	0.908013	+	0.266617i	0.0619260	+	0.0181831i
$216$	−10.4625	+	10.3217i	−0.711881	+	0.702301i
$217$	−37.7337	−	24.2500i	−2.56153	−	1.64619i
$218$	0.0893548	−	1.09857i	0.00605187	−	0.0744044i
$219$	−7.25179	+	2.18853i	−0.490030	+	0.147887i
$220$	−0.119656	−	0.0802407i	−0.00806722	−	0.00540983i
$221$	3.96217	−	3.43324i	0.266525	−	0.230945i
$222$	−1.32102	−	1.32700i	−0.0886609	−	0.0890622i
$223$	−11.1790	−	9.68665i	−0.748600	−	0.648666i	0.194603	−	0.980882i	$-0.437658\pi$
$223$	−11.1790	−	9.68665i	−0.748600	−	0.648666i	−0.943203	+	0.332216i	$0.892204\pi$
$224$	23.1099	−	11.1920i	1.54410	−	0.747795i
$225$	−1.89277	+	14.7300i	−0.126185	+	0.981999i
$226$	−0.876570	−	14.2026i	−0.0583085	−	0.944742i
$227$	4.14320	−	1.21655i	0.274994	−	0.0807454i	−0.141328	−	0.989963i	$-0.545137\pi$
$227$	4.14320	−	1.21655i	0.274994	−	0.0807454i	0.416322	+	0.909217i	$0.363319\pi$
$228$	−2.83500	−	6.41055i	−0.187753	−	0.424549i
$229$	6.33663	−	13.8753i	0.418737	−	0.916905i	−0.576285	−	0.817249i	$-0.695498\pi$
$229$	6.33663	−	13.8753i	0.418737	−	0.916905i	0.995022	−	0.0996567i	$-0.0317745\pi$
$230$	1.49726	+	0.575156i	0.0987265	+	0.0379246i
$231$	1.39034	+	2.12815i	0.0914780	+	0.140022i
$232$	24.5296	−	1.03387i	1.61045	−	0.0678767i
$233$	7.09997	+	6.15216i	0.465135	+	0.403042i	0.855650	−	0.517555i	$-0.173158\pi$
$233$	7.09997	+	6.15216i	0.465135	+	0.403042i	−0.390515	+	0.920596i	$0.627703\pi$
$234$	−2.01432	+	2.72042i	−0.131680	+	0.177840i
$235$	2.62899	−	0.377992i	0.171496	−	0.0246575i
$236$	10.7646	−	1.33384i	0.700716	−	0.0868257i
$237$	14.1405	−	2.14148i	0.918527	−	0.139104i
$238$	15.1260	−	39.3765i	0.980474	−	2.55240i
$239$	−8.83992			−0.571807			−0.285904	−	0.958258i	$-0.592294\pi$
$239$	−8.83992			−0.571807			−0.285904	+	0.958258i	$0.592294\pi$
$240$	−0.387950	−	1.49398i	−0.0250421	−	0.0964359i
$241$	−6.38638	+	4.10428i	−0.411383	+	0.264380i	−0.729923	−	0.683530i	$-0.760444\pi$
$241$	−6.38638	+	4.10428i	−0.411383	+	0.264380i	0.318540	+	0.947909i	$0.396808\pi$
$242$	−1.24916	+	15.3578i	−0.0802993	+	0.987236i
$243$	−2.79547	−	15.3358i	−0.179329	−	0.983789i
$244$	9.82416	+	4.72040i	0.628927	+	0.302192i
$245$	2.29054	−	1.98476i	0.146337	−	0.126802i
$246$	−4.31184	+	7.85433i	−0.274913	+	0.500774i
$247$	−0.872818	−	1.35813i	−0.0555361	−	0.0864158i
$248$	−10.5297	+	25.8900i	−0.668635	+	1.64402i
$249$	4.25669	+	4.83867i	0.269757	+	0.306638i
$250$	−2.49130	−	1.90318i	−0.157564	−	0.120368i
$251$	12.3638	−	3.63035i	0.780398	−	0.229145i	0.132815	−	0.991141i	$-0.457598\pi$
$251$	12.3638	−	3.63035i	0.780398	−	0.229145i	0.647582	+	0.761995i	$0.275780\pi$
$252$	−3.99764	+	26.9400i	−0.251828	+	1.69706i
$253$	0.234249	+	1.62924i	0.0147271	+	0.102429i
$254$	−21.9793	−	16.7906i	−1.37910	−	1.05354i
$255$	−2.14334	−	1.35483i	−0.134221	−	0.0848430i
$256$	−9.50277	−	12.8724i	−0.593923	−	0.804522i
$257$	9.18112	−	14.2861i	0.572703	−	0.891143i	−0.427213	−	0.904151i	$-0.640504\pi$
$257$	9.18112	−	14.2861i	0.572703	−	0.891143i	0.999915	+	0.0130085i	$0.00414086\pi$
$258$	−5.00708	+	9.12076i	−0.311727	+	0.567834i
$259$	−3.43450	−	0.493806i	−0.213409	−	0.0306836i
$260$	−0.141343	−	0.326199i	−0.00876569	−	0.0202300i
$261$	−13.7485	+	22.1156i	−0.851008	+	1.36892i
$262$	1.67826	+	8.09435i	0.103683	+	0.500071i
$263$	−12.9044	−	8.29317i	−0.795721	−	0.511379i	0.0784957	−	0.996914i	$-0.474988\pi$
$263$	−12.9044	−	8.29317i	−0.795721	−	0.511379i	−0.874217	+	0.485535i	$0.838625\pi$
$264$	1.14418	−	1.09540i	0.0704195	−	0.0674174i
$265$	−1.46575	−	1.69157i	−0.0900405	−	0.103912i
$266$	−11.3391	−	6.33604i	−0.695245	−	0.388488i
$267$	−3.26209	−	4.99316i	−0.199637	−	0.305577i
$268$	12.7038	+	10.3254i	0.776007	+	0.630724i
$269$		−	21.3642i		−	1.30260i	−0.758821	−	0.651299i	$-0.774224\pi$
$269$		−	21.3642i		−	1.30260i	0.758821	−	0.651299i	$-0.225776\pi$
$270$	1.54110	+	0.552534i	0.0937884	+	0.0336261i
$271$	12.4042	−	10.7483i	0.753501	−	0.652912i	−0.190937	−	0.981602i	$-0.561153\pi$
$271$	12.4042	−	10.7483i	0.753501	−	0.652912i	0.944438	+	0.328690i	$0.106607\pi$
$272$	−25.8508	−	4.75311i	−1.56744	−	0.288199i
$273$	0.0470513	+	6.27257i	0.00284767	+	0.379633i
$274$	−0.0738899	+	0.0153201i	−0.00446385	+	0.000925523i
$275$	0.227791	−	1.58432i	0.0137363	−	0.0955383i
$276$	−9.71162	+	14.7196i	−0.584571	+	0.886016i
$277$	0.142728	−	0.992693i	0.00857567	−	0.0596451i	−0.985084	−	0.172073i	$-0.944954\pi$
$277$	0.142728	−	0.992693i	0.00857567	−	0.0596451i	0.993660	+	0.112428i	$0.0358627\pi$
$278$	13.1755	−	7.02831i	0.790212	−	0.421530i
$279$	−16.3995	−	24.6955i	−0.981811	−	1.47848i
$280$	−2.23864	−	1.78042i	−0.133785	−	0.106400i
$281$	29.6056	−	13.5204i	1.76612	−	0.806562i	0.783393	−	0.621527i	$-0.213487\pi$
$281$	29.6056	−	13.5204i	1.76612	−	0.806562i	0.982732	−	0.185035i	$-0.0592400\pi$
$282$	−2.14902	+	29.1229i	−0.127972	+	1.73424i
$283$	−13.6334	+	1.96019i	−0.810424	+	0.116521i	−0.535055	−	0.844817i	$-0.679709\pi$
$283$	−13.6334	+	1.96019i	−0.810424	+	0.116521i	−0.275369	+	0.961339i	$0.588800\pi$
$284$	3.52076	+	12.9182i	0.208919	+	0.766552i
$285$	−0.506884	+	0.593919i	−0.0300252	+	0.0351807i
$286$	0.221472	−	0.289911i	0.0130959	−	0.0171428i
$287$	2.36298	+	16.4349i	0.139482	+	0.970122i
$288$	16.9586	−	0.638055i	0.999293	−	0.0375978i
$289$	−22.0228	+	14.1532i	−1.29546	+	0.832542i
$290$	−1.28721	−	2.41303i	−0.0755874	−	0.141698i
$291$	3.81434	+	1.08898i	0.223601	+	0.0638372i
$292$	7.88382	+	3.78808i	0.461365	+	0.221681i
$293$	20.1686	−	9.21071i	1.17826	−	0.538096i	0.272616	−	0.962123i	$-0.412111\pi$
$293$	20.1686	−	9.21071i	1.17826	−	0.538096i	0.905649	+	0.424028i	$0.139384\pi$
$294$	15.9039	+	29.2827i	0.927532	+	1.70780i
$295$	−0.653250	−	1.01648i	−0.0380337	−	0.0591816i
$296$	0.0910467	+	2.16018i	0.00529198	+	0.125558i
$297$	0.276460	+	1.65718i	0.0160418	+	0.0961596i
$298$	−11.3388	−	4.35565i	−0.656837	−	0.252316i
$299$	−1.68726	+	3.69457i	−0.0975765	+	0.213663i
$300$	13.0940	−	11.0734i	0.755984	−	0.639322i
$301$	2.74399	+	19.0849i	0.158161	+	1.10003i
$302$	−4.27031	+	18.7476i	−0.245729	+	1.07880i
$303$	31.2411	+	4.25286i	1.79475	+	0.244320i
$304$	−2.58163	+	7.67105i	−0.148067	+	0.439965i
$305$		−	1.21413i		−	0.0695209i
$306$	19.6095	−	19.8162i	1.12100	−	1.13282i
$307$	0.0286299	+	0.0130748i	0.00163399	+	0.000746220i	0.416232	−	0.909259i	$-0.363350\pi$
$307$	0.0286299	+	0.0130748i	0.00163399	+	0.000746220i	−0.414598	+	0.910005i	$0.636078\pi$
$308$	0.474365	−	2.89674i	0.0270295	−	0.165057i
$309$	−21.1078	−	18.0146i	−1.20078	−	1.02481i
$310$	3.10749	−	0.191791i	0.176494	−	0.0108930i
$311$	−3.70211	+	1.08704i	−0.209927	+	0.0616402i	−0.385005	−	0.922914i	$-0.625800\pi$
$311$	−3.70211	+	1.08704i	−0.209927	+	0.0616402i	0.175078	+	0.984555i	$0.443982\pi$
$312$	3.83651	−	0.747483i	0.217200	−	0.0423179i
$313$	13.3462	−	15.4023i	0.754371	−	0.870590i	−0.240614	−	0.970621i	$-0.577349\pi$
$313$	13.3462	−	15.4023i	0.754371	−	0.870590i	0.994984	+	0.100031i	$0.0318942\pi$
$314$	−5.69225	−	27.4541i	−0.321232	−	1.54932i
$315$	2.89779	−	0.898299i	0.163272	−	0.0506134i
$316$	−13.7158	−	9.19773i	−0.771573	−	0.517413i
$317$	−2.68931	+	9.15893i	−0.151046	+	0.514417i	−0.999899	−	0.0142128i	$-0.995476\pi$
$317$	−2.68931	+	9.15893i	−0.151046	+	0.514417i	0.848853	+	0.528630i	$0.177294\pi$
$318$	21.6254	−	11.7450i	1.21269	−	0.658628i
$319$	1.51737	−	2.36107i	0.0849562	−	0.132194i
$320$	−0.834007	+	1.57514i	−0.0466224	+	0.0880531i
$321$	−2.12857	+	0.642386i	−0.118805	+	0.0358545i
$322$	2.01308	+	32.6169i	0.112185	+	1.81767i
$323$	5.52344	+	12.0946i	0.307332	+	0.672964i
$324$	−9.57222	+	15.2438i	−0.531790	+	0.846876i
$325$	2.58647	−	2.98495i	0.143472	−	0.165575i
$326$	3.85332	−	6.89598i	0.213416	−	0.381933i
$327$	−0.202129	−	1.33469i	−0.0111778	−	0.0738085i
$328$	9.79553	−	3.33030i	0.540868	−	0.183885i
$329$	29.2565	+	45.5241i	1.61296	+	2.50982i
$330$	−0.165184	−	0.0620358i	−0.00909309	−	0.00341496i
$331$	−4.16044	+	14.1692i	−0.228679	+	0.778808i	0.762582	+	0.646891i	$0.223931\pi$
$331$	−4.16044	+	14.1692i	−0.228679	+	0.778808i	−0.991261	+	0.131917i	$0.957887\pi$
$332$	0.145235	−	7.44010i	0.00797079	−	0.408328i
$333$	−1.94759	−	1.21075i	−0.106727	−	0.0663485i
$334$	2.17310	−	5.65708i	0.118907	−	0.309542i
$335$	0.423849	−	1.77367i	0.0231573	−	0.0969058i
$336$	24.4045	−	19.8346i	1.33138	−	1.08207i
$337$	3.41073	−	23.7222i	0.185794	−	1.29223i	−0.656958	−	0.753927i	$-0.728157\pi$
$337$	3.41073	−	23.7222i	0.185794	−	1.29223i	0.842753	−	0.538301i	$-0.180934\pi$
$338$	−16.4410	+	5.95006i	−0.894271	+	0.323640i
$339$	−5.03523	−	16.6844i	−0.273476	−	0.906173i
$340$	0.769902	+	2.82487i	0.0417538	+	0.153200i
$341$	1.72737	+	2.68784i	0.0935423	+	0.145555i
$342$	−5.18063	−	6.84541i	−0.280136	−	0.370157i
$343$	27.2677	+	12.4527i	1.47232	+	0.672384i
$344$	11.3750	−	3.86728i	0.613297	−	0.208510i
$345$	1.94646	+	0.264972i	0.104794	+	0.0142656i
$346$	14.7873	+	20.1607i	0.794971	+	1.08384i
$347$	5.17544	+	11.3326i	0.277832	+	0.608368i	0.996181	−	0.0873159i	$-0.0278289\pi$
$347$	5.17544	+	11.3326i	0.277832	+	0.608368i	−0.718349	+	0.695683i	$0.755102\pi$
$348$	28.9509	−	8.12417i	1.55193	−	0.435501i
$349$	−27.8853	−	8.18787i	−1.49267	−	0.438287i	−0.569276	−	0.822146i	$-0.692777\pi$
$349$	−27.8853	−	8.18787i	−1.49267	−	0.438287i	−0.923392	+	0.383859i	$0.874595\pi$
$350$	7.05763	−	30.9845i	0.377246	−	1.65619i
$351$	−1.63692	+	3.80891i	−0.0873722	+	0.203304i
$352$	−1.82858	+	0.0413415i	−0.0974636	+	0.00220351i
$353$	−3.11801	+	10.6190i	−0.165955	+	0.565191i	0.833956	+	0.551831i	$0.186071\pi$
$353$	−3.11801	+	10.6190i	−0.165955	+	0.565191i	−0.999911	+	0.0133595i	$0.995747\pi$
$354$	12.4576	−	4.61442i	0.662112	−	0.245253i
$355$	1.12720	−	0.976725i	0.0598256	−	0.0518392i
$356$	−1.11298	+	6.79646i	−0.0589877	+	0.360211i
$357$	6.96848	−	51.1898i	0.368811	−	2.70925i
$358$	−14.2926	+	5.17255i	−0.755387	+	0.273378i
$359$	20.6341	−	6.05871i	1.08903	−	0.319767i	0.312542	−	0.949904i	$-0.398820\pi$
$359$	20.6341	−	6.05871i	1.08903	−	0.319767i	0.776484	+	0.630137i	$0.217001\pi$
$360$	−0.882209	−	1.67195i	−0.0464965	−	0.0881196i
$361$	−14.3019	+	4.19940i	−0.752729	+	0.221021i
$362$	−0.162896	−	0.785659i	−0.00856164	−	0.0412933i
$363$	2.82573	+	18.6587i	0.148312	+	0.979329i
$364$	4.84918	−	5.38039i	0.254166	−	0.282009i
$365$		−	0.974330i		−	0.0509988i
$366$	13.0374	+	2.86697i	0.681478	+	0.149859i
$367$	−14.3202	−	12.4085i	−0.747507	−	0.647719i	0.195419	−	0.980720i	$-0.437393\pi$
$367$	−14.3202	−	12.4085i	−0.747507	−	0.647719i	−0.942926	+	0.333001i	$0.891939\pi$
$368$	19.7470	−	4.97000i	1.02938	−	0.259079i
$369$	−2.93337	+	10.5745i	−0.152705	+	0.550484i
$370$	0.212502	−	0.113357i	0.0110474	−	0.00589314i
$371$	18.9442	−	41.4820i	0.983533	−	2.15364i
$372$	−5.27836	+	33.8214i	−0.273670	+	1.75356i
$373$	−15.6775			−0.811752			−0.405876	−	0.913928i	$-0.633033\pi$
$373$	−15.6775			−0.811752			−0.405876	+	0.913928i	$0.633033\pi$
$374$	−2.14527	+	2.10380i	−0.110929	+	0.108785i
$375$	−3.50455	−	1.56881i	−0.180974	−	0.0810131i
$376$	24.5312	−	23.1352i	1.26510	−	1.19311i
$377$	6.29969	−	2.87697i	0.324450	−	0.148171i
$378$	2.80338	+	33.2379i	0.144190	+	1.70957i
$379$	−20.7918	+	18.0162i	−1.06800	+	0.925428i	−0.997399	−	0.0720763i	$-0.977038\pi$
$379$	−20.7918	+	18.0162i	−1.06800	+	0.925428i	−0.0706021	+	0.997505i	$0.522492\pi$
$380$	0.894764	−	0.110870i	0.0459004	−	0.00568752i
$381$	−30.9185	−	13.8407i	−1.58401	−	0.709080i
$382$	12.5648	−	4.54724i	0.642869	−	0.232657i
$383$	−0.734618	−	5.10938i	−0.0375372	−	0.261077i	0.962407	−	0.271610i	$-0.0875562\pi$
$383$	−0.734618	−	5.10938i	−0.0375372	−	0.261077i	−0.999945	+	0.0105333i	$0.996647\pi$
$384$	−14.9446	−	12.6751i	−0.762640	−	0.646823i
$385$	−0.313734	+	0.0921205i	−0.0159893	+	0.00469490i
$386$	16.3244	−	11.9735i	0.830891	−	0.609436i
$387$	−3.40634	+	12.2795i	−0.173154	+	0.624201i
$388$	−2.40068	−	3.90088i	−0.121876	−	0.198037i
$389$	−18.5593	+	8.47576i	−0.940995	+	0.429738i	−0.826026	−	0.563631i	$-0.809404\pi$
$389$	−18.5593	+	8.47576i	−0.940995	+	0.429738i	−0.114968	+	0.993369i	$0.536677\pi$
$390$	−0.260139	−	0.349146i	−0.0131727	−	0.0176797i
$391$	18.0851	−	28.1409i	0.914601	−	1.42315i
$392$	9.27618	−	37.3430i	0.468518	−	1.88611i
$393$	4.27477	+	9.17763i	0.215634	+	0.462950i
$394$	−4.00511	+	3.92769i	−0.201775	+	0.197874i
$395$	−0.261802	+	1.82087i	−0.0131727	+	0.0916181i
$396$	1.05620	−	1.62728i	0.0530761	−	0.0817737i
$397$	−8.80962	−	5.66160i	−0.442142	−	0.284148i	0.300568	−	0.953760i	$-0.402824\pi$
$397$	−8.80962	−	5.66160i	−0.442142	−	0.284148i	−0.742710	+	0.669613i	$0.766460\pi$
$398$	27.7762	+	21.2191i	1.39229	+	1.06362i
$399$	−15.2973	−	4.36732i	−0.765823	−	0.218640i
$400$	−19.7864	−	0.772776i	−0.989319	−	0.0386388i
$401$		−	12.4053i		−	0.619492i	−0.950819	−	0.309746i	$-0.899756\pi$
$401$		−	12.4053i		−	0.619492i	0.950819	−	0.309746i	$-0.100244\pi$
$402$	18.0450	+	8.73955i	0.900000	+	0.435889i
$403$			7.88402i			0.392731i
$404$	−23.2998	−	27.9745i	−1.15921	−	1.39178i
$405$	1.99236	+	0.225688i	0.0990011	+	0.0112145i
$406$	33.8263	−	44.2793i	1.67877	−	2.19755i
$407$	0.207925	+	0.133626i	0.0103065	+	0.00662357i
$408$	−32.1518	+	1.59680i	−1.59175	+	0.0790534i
$409$	2.00832	−	13.9682i	0.0993052	−	0.690683i	−0.877971	−	0.478714i	$-0.841103\pi$
$409$	2.00832	−	13.9682i	0.0993052	−	0.690683i	0.977276	−	0.211969i	$-0.0679877\pi$
$410$	−0.806954	−	0.822859i	−0.0398526	−	0.0406381i
$411$	−0.0837787	+	0.0390226i	−0.00413250	+	0.00192484i
$412$	3.94031	+	31.7997i	0.194125	+	1.56666i
$413$	13.3095	−	20.7100i	0.654917	−	1.01907i
$414$	−7.44153	+	20.2755i	−0.365731	+	0.996488i
$415$	−0.754034	+	0.344356i	−0.0370141	+	0.0169038i
$416$	−3.85103	−	2.35364i	−0.188812	−	0.115397i
$417$	13.7316	−	12.0800i	0.672441	−	0.591562i
$418$	0.547226	+	0.746075i	0.0267657	+	0.0364917i
$419$	−11.5135	+	3.38065i	−0.562469	+	0.165156i	−0.550593	−	0.834774i	$-0.685598\pi$
$419$	−11.5135	+	3.38065i	−0.562469	+	0.165156i	−0.0118757	+	0.999929i	$0.503780\pi$
$420$	−3.16887	−	1.49345i	−0.154625	−	0.0728730i
$421$	5.53493	+	38.4963i	0.269756	+	1.87619i	0.450662	+	0.892694i	$0.351188\pi$
$421$	5.53493	+	38.4963i	0.269756	+	1.87619i	−0.180906	+	0.983500i	$0.557903\pi$
$422$	2.97586	+	8.22278i	0.144863	+	0.400279i
$423$	5.62040	+	35.3207i	0.273273	+	1.71735i
$424$	−27.5779	−	6.85048i	−1.33930	−	0.332689i
$425$	−24.5838	+	21.3020i	−1.19249	+	1.03330i
$426$	7.82646	+	14.4104i	0.379193	+	0.698184i
$427$	22.5016	−	10.2761i	1.08893	−	0.497296i
$428$	2.31409	+	1.11189i	0.111856	+	0.0537453i
$429$	0.182562	−	0.407822i	0.00881416	−	0.0196898i
$430$	−0.937067	−	0.955537i	−0.0451894	−	0.0460801i
$431$	−17.5882			−0.847192			−0.423596	−	0.905851i	$-0.639232\pi$
$431$	−17.5882			−0.847192			−0.423596	+	0.905851i	$0.639232\pi$
$432$	20.0368	−	5.52520i	0.964020	−	0.265831i
$433$	5.61708	−	12.2997i	0.269940	−	0.591085i	−0.725312	−	0.688420i	$-0.758305\pi$
$433$	5.61708	−	12.2997i	0.269940	−	0.591085i	0.995252	+	0.0973350i	$0.0310318\pi$
$434$	29.8556	+	55.9681i	1.43311	+	2.68655i
$435$	−2.21241	−	2.51489i	−0.106077	−	0.120580i
$436$	−0.868151	+	1.29460i	−0.0415769	+	0.0620001i
$437$	−7.78482	−	6.74558i	−0.372398	−	0.322685i
$438$	10.4625	+	2.30072i	0.499915	+	0.109933i
$439$			12.4896i			0.596094i	0.954551	+	0.298047i	$0.0963352\pi$
$439$			12.4896i			0.596094i	−0.954551	+	0.298047i	$0.903665\pi$
$440$	0.0923684	+	0.181605i	0.00440349	+	0.00865768i
$441$	27.1858	+	30.4392i	1.29456	+	1.44949i
$442$	−7.25990	+	1.50525i	−0.345318	+	0.0715973i
$443$	22.3359	−	6.55841i	1.06121	−	0.311599i	0.295872	−	0.955228i	$-0.404390\pi$
$443$	22.3359	−	6.55841i	1.06121	−	0.311599i	0.765338	+	0.643628i	$0.222572\pi$
$444$	0.715448	+	2.54954i	0.0339537	+	0.120996i
$445$	0.736096	−	0.216137i	0.0348943	−	0.0102459i
$446$	7.11879	+	19.6704i	0.337085	+	0.931420i
$447$	−14.7405	−	2.00663i	−0.697202	−	0.0949103i
$448$	−36.2511	−	2.12508i	−1.71270	−	0.100401i
$449$	5.81761	−	5.04099i	0.274550	−	0.237899i	−0.506692	−	0.862127i	$-0.669132\pi$
$449$	5.81761	−	5.04099i	0.274550	−	0.237899i	0.781242	+	0.624228i	$0.214586\pi$
$450$	12.4981	−	16.8792i	0.589165	−	0.795694i
$451$	0.333213	−	1.13482i	0.0156904	−	0.0534365i
$452$	−8.71536	+	18.1385i	−0.409936	+	0.853165i
$453$	0.176640	+	23.5484i	0.00829925	+	1.10640i
$454$	−5.95422	−	1.35625i	−0.279445	−	0.0636520i
$455$	−0.774164	−	0.227315i	−0.0362934	−	0.0106567i
$456$	−0.922304	+	9.86986i	−0.0431908	+	0.462198i
$457$	14.1277	+	30.9353i	0.660864	+	1.44709i	0.881715	+	0.471783i	$0.156389\pi$
$457$	14.1277	+	30.9353i	0.660864	+	1.44709i	−0.220851	+	0.975308i	$0.570883\pi$
$458$	−17.3947	+	12.7585i	−0.812799	+	0.596166i
$459$	17.8087	−	29.1320i	0.831240	−	1.35976i
$460$	−1.45168	−	1.74293i	−0.0676850	−	0.0812647i
$461$	3.64124	+	1.66290i	0.169590	+	0.0774490i	0.498401	−	0.866947i	$-0.333921\pi$
$461$	3.64124	+	1.66290i	0.169590	+	0.0774490i	−0.328811	+	0.944396i	$0.606648\pi$
$462$	−0.248368	−	3.58643i	−0.0115551	−	0.166856i
$463$	−14.9077	−	23.1969i	−0.692820	−	1.07805i	−0.992289	−	0.123943i	$-0.960446\pi$
$463$	−14.9077	−	23.1969i	−0.692820	−	1.07805i	0.299469	−	0.954106i	$-0.403190\pi$
$464$	−30.9963	−	15.6452i	−1.43897	−	0.726310i
$465$	3.65050	−	1.10169i	0.169288	−	0.0510898i
$466$	−4.52127	−	12.4930i	−0.209444	−	0.578728i
$467$	3.10387	−	21.5879i	0.143630	−	0.998968i	−0.782739	−	0.622350i	$-0.786178\pi$
$467$	3.10387	−	21.5879i	0.143630	−	0.998968i	0.926369	−	0.376618i	$-0.122913\pi$
$468$	4.36344	−	1.96895i	0.201700	−	0.0910147i
$469$	36.4589	−	7.15669i	1.68351	−	0.330465i
$470$	−3.50638	−	1.34693i	−0.161737	−	0.0621295i
$471$	−14.4990	−	31.1283i	−0.668078	−	1.43432i
$472$	−14.2096	−	5.77917i	−0.654050	−	0.266008i
$473$	0.386940	−	1.31780i	0.0177915	−	0.0605923i
$474$	−18.9345	−	7.11095i	−0.869691	−	0.326617i
$475$	5.41551	+	8.42670i	0.248481	+	0.386643i
$476$	−45.8374	+	38.1778i	−2.10095	+	1.74987i
$477$	22.4794	−	20.0768i	1.02926	−	0.919253i
$478$	10.9133	+	6.09814i	0.499165	+	0.278923i
$479$	−14.7724	+	17.0483i	−0.674970	+	0.778956i	−0.985145	−	0.171723i	$-0.945067\pi$
$479$	−14.7724	+	17.0483i	−0.674970	+	0.778956i	0.310176	+	0.950679i	$0.399612\pi$
$480$	−0.551664	+	2.11202i	−0.0251799	+	0.0964000i
$481$	0.253358	+	0.554777i	0.0115521	+	0.0252956i
$482$	10.7156	−	0.661357i	0.488083	−	0.0301240i
$483$	11.5636	+	38.3165i	0.526163	+	1.74346i
$484$	12.1366	−	18.0983i	0.551663	−	0.822648i
$485$	−0.275852	+	0.429234i	−0.0125258	+	0.0194905i
$486$	−7.12809	+	20.8612i	−0.323337	+	0.946284i
$487$	1.77266	−	6.03714i	0.0803271	−	0.273569i	−0.909529	−	0.415640i	$-0.863558\pi$
$487$	1.77266	−	6.03714i	0.0803271	−	0.273569i	0.989857	+	0.142071i	$0.0453760\pi$
$488$	−8.87211	−	12.6047i	−0.401622	−	0.570587i
$489$	2.65603	−	9.30319i	0.120110	−	0.420705i
$490$	−4.19696	+	0.870187i	−0.189600	+	0.0393110i
$491$	−16.2282	+	18.7284i	−0.732369	+	0.845199i	−0.992736	−	0.120311i	$-0.961611\pi$
$491$	−16.2282	+	18.7284i	−0.732369	+	0.845199i	0.260367	+	0.965510i	$0.416156\pi$
$492$	10.7414	−	6.72209i	0.484261	−	0.303055i
$493$	−54.7277	+	16.0695i	−2.46481	+	0.723735i
$494$	0.140645	+	2.27879i	0.00632790	+	0.102528i
$495$	−0.214343	−	0.0275426i	−0.00963399	−	0.00123795i
$496$	30.8594	−	24.6987i	1.38563	−	1.10901i
$497$	27.6421	+	12.6237i	1.23992	+	0.566251i
$498$	−1.91720	−	8.91003i	−0.0859116	−	0.399268i
$499$		−	7.38702i		−	0.330688i	−0.986236	−	0.165344i	$-0.947126\pi$
$499$		−	7.38702i		−	0.330688i	0.986236	−	0.165344i	$-0.0528735\pi$
$500$	1.76275	+	4.06818i	0.0788325	+	0.181935i
$501$	1.00114	−	7.35426i	0.0447276	−	0.328564i
$502$	−17.7682	−	4.04722i	−0.793031	−	0.180636i
$503$	1.17907	+	8.20059i	0.0525720	+	0.365646i	0.999077	+	0.0429569i	$0.0136778\pi$
$503$	1.17907	+	8.20059i	0.0525720	+	0.365646i	−0.946505	+	0.322689i	$0.895413\pi$
$504$	23.5196	−	30.5011i	1.04765	−	1.35863i
$505$	−1.68472	+	3.68903i	−0.0749692	+	0.164160i
$506$	0.834721	−	2.17297i	0.0371079	−	0.0966003i
$507$	−17.9273	+	11.7121i	−0.796181	+	0.520154i
$508$	15.5517	+	35.8911i	0.689994	+	1.59241i
$509$	−0.301723	−	0.469490i	−0.0133736	−	0.0208098i	0.834502	−	0.551004i	$-0.185755\pi$
$509$	−0.301723	−	0.469490i	−0.0133736	−	0.0208098i	−0.847876	+	0.530195i	$0.822119\pi$
$510$	1.71145	+	3.15118i	0.0757842	+	0.139537i
$511$	18.0573	−	8.24651i	0.798810	−	0.364804i
$512$	2.85178	+	22.4470i	0.126032	+	0.992026i
$513$	−8.09900	−	6.70478i	−0.357579	−	0.296023i
$514$	−21.1897	+	11.3034i	−0.934638	+	0.498573i
$515$	3.00278	−	1.92977i	0.132318	−	0.0850357i
$516$	12.4734	−	7.80597i	0.549110	−	0.343639i
$517$	−0.548578	−	3.81544i	−0.0241264	−	0.167803i
$518$	3.89942	+	2.97889i	0.171331	+	0.130885i
$519$	23.2920	+	19.8787i	1.02240	+	0.872577i
$520$	−0.0505308	+	0.500214i	−0.00221592	+	0.0219358i
$521$	−20.3459	+	2.92529i	−0.891368	+	0.128159i	−0.572756	−	0.819726i	$-0.694126\pi$
$521$	−20.3459	+	2.92529i	−0.891368	+	0.128159i	−0.318612	+	0.947885i	$0.603217\pi$
$522$	32.2294	−	17.8186i	1.41064	−	0.779898i
$523$	−26.0600	+	11.9012i	−1.13952	+	0.520403i	−0.893590	−	0.448883i	$-0.851822\pi$
$523$	−26.0600	+	11.9012i	−1.13952	+	0.520403i	−0.245934	+	0.969287i	$0.579095\pi$
$524$	3.51192	−	11.1506i	0.153419	−	0.487118i
$525$	−0.291936	−	38.9190i	−0.0127411	−	1.69856i
$526$	10.2102	+	19.1404i	0.445187	+	0.834560i
$527$	9.24083	−	64.2714i	0.402537	−	2.79970i
$528$	−2.16821	+	0.563030i	−0.0943590	+	0.0245027i
$529$	−0.414875	+	2.88552i	−0.0180380	+	0.125457i
$530$	0.642634	+	3.09947i	0.0279143	+	0.134632i
$531$	13.5540	−	9.00078i	0.588195	−	0.390601i
$532$	9.62784	+	15.6443i	0.417420	+	0.678268i
$533$	2.20564	−	1.91120i	0.0955368	−	0.0827831i
$534$	0.582732	+	8.41464i	0.0252173	+	0.364137i
$535$		−	0.285989i		−	0.0123644i
$536$	−8.56061	−	21.5108i	−0.369762	−	0.929126i
$537$	−15.5847	+	10.1817i	−0.672531	+	0.439372i
$538$	−14.7379	+	26.3752i	−0.635396	+	1.13712i
$539$	−2.88048	−	3.32425i	−0.124071	−	0.143186i
$540$	−1.52141	−	1.74525i	−0.0654710	−	0.0751035i
$541$	24.0933	+	15.4838i	1.03585	+	0.665701i	0.943957	−	0.330068i	$-0.107072\pi$
$541$	24.0933	+	15.4838i	1.03585	+	0.665701i	0.0918937	+	0.995769i	$0.470708\pi$
$542$	−22.7282	+	4.71241i	−0.976262	+	0.202415i
$543$	−0.414921	−	0.890806i	−0.0178059	−	0.0382281i
$544$	28.6353	+	23.7009i	1.22773	+	1.01617i
$545$	0.171868	+	0.0247109i	0.00736201	+	0.00105850i
$546$	4.26899	−	7.77628i	0.182696	−	0.332794i
$547$	−15.3759	+	23.9253i	−0.657424	+	1.02297i	0.339187	+	0.940719i	$0.389848\pi$
$547$	−15.3759	+	23.9253i	−0.657424	+	1.02297i	−0.996611	+	0.0822533i	$0.973788\pi$
$548$	0.101789	+	0.0320588i	0.00434823	+	0.00136948i
$549$	16.3472	−	0.245259i	0.697682	−	0.0104674i
$550$	−1.37415	+	1.79879i	−0.0585940	+	0.0767007i
$551$	2.49963	+	17.3853i	0.106488	+	0.740638i
$552$	22.1437	−	11.4726i	0.942498	−	0.488308i
$553$	−35.9622	+	10.5595i	−1.52927	+	0.449034i
$554$	−0.861005	+	1.12707i	−0.0365806	+	0.0478847i
$555$	0.221472	−	0.194834i	0.00940097	−	0.00827026i
$556$	−21.1142	−	0.412161i	−0.895442	−	0.0174795i
$557$	−1.44645	−	2.25071i	−0.0612879	−	0.0953658i	0.809257	−	0.587455i	$-0.199870\pi$
$557$	−1.44645	−	2.25071i	−0.0612879	−	0.0953658i	−0.870545	+	0.492089i	$0.836234\pi$
$558$	3.21003	+	41.8009i	0.135891	+	1.76957i
$559$	2.56127	−	2.21936i	0.108330	−	0.0938688i
$560$	1.53552	+	3.74233i	0.0648874	+	0.158142i
$561$	−1.96627	+	3.11063i	−0.0830158	+	0.131331i
$562$	−45.8767	−	3.73150i	−1.93519	−	0.157404i
$563$	−28.4935	+	18.3117i	−1.20086	+	0.771745i	−0.979104	−	0.203358i	$-0.934815\pi$
$563$	−28.4935	+	18.3117i	−1.20086	+	0.771745i	−0.221754	+	0.975103i	$0.571178\pi$
$564$	22.7433	−	34.4713i	0.957664	−	1.45150i
$565$	2.24167			0.0943078
$566$	18.1834	+	6.98495i	0.764306	+	0.293599i
$567$	12.6802	+	38.8347i	0.532518	+	1.63091i
$568$	4.56491	−	18.3769i	0.191539	−	0.771078i
$569$	1.70419	−	0.245026i	0.0714436	−	0.0102720i	−0.106500	−	0.994313i	$-0.533965\pi$
$569$	1.70419	−	0.245026i	0.0714436	−	0.0102720i	0.177944	+	0.984041i	$0.443055\pi$
$570$	1.03548	−	0.383554i	0.0433717	−	0.0160653i
$571$	16.8805	+	14.6270i	0.706425	+	0.612121i	0.932151	−	0.362070i	$-0.117930\pi$
$571$	16.8805	+	14.6270i	0.706425	+	0.612121i	−0.225726	+	0.974191i	$0.572475\pi$
$572$	−0.473411	+	0.205130i	−0.0197943	+	0.00857691i
$573$	13.7007	−	8.95082i	0.572355	−	0.373926i
$574$	8.42025	−	21.9198i	0.351454	−	0.914916i
$575$	10.4688	−	22.9235i	0.436579	−	0.955974i
$576$	−21.3764	−	10.9110i	−0.890683	−	0.454625i
$577$	−21.0840	+	6.19082i	−0.877738	+	0.257727i	−0.689403	−	0.724378i	$-0.742127\pi$
$577$	−21.0840	+	6.19082i	−0.877738	+	0.257727i	−0.188335	+	0.982105i	$0.560309\pi$
$578$	36.9518	−	2.28063i	1.53699	−	0.0948616i
$579$	16.0961	−	18.8599i	0.668930	−	0.783789i
$580$	−0.0754857	+	3.86699i	−0.00313437	+	0.160568i
$581$	−12.7639	−	11.0600i	−0.529538	−	0.458847i
$582$	−3.95778	−	3.97569i	−0.164055	−	0.164798i
$583$	−2.45497	+	2.12724i	−0.101674	+	0.0881013i
$584$	−7.11981	−	10.1152i	−0.294620	−	0.418569i
$585$	−0.408202	−	0.343124i	−0.0168771	−	0.0141864i
$586$	−31.2532	−	2.54206i	−1.29106	−	0.105011i
$587$	21.3600	+	13.7272i	0.881622	+	0.566584i	0.901287	−	0.433223i	$-0.142624\pi$
$587$	21.3600	+	13.7272i	0.881622	+	0.566584i	−0.0196650	+	0.999807i	$0.506260\pi$
$588$	0.566299	−	47.1222i	0.0233538	−	1.94329i
$589$	−19.1850	−	5.63322i	−0.790504	−	0.232113i
$590$	0.105264	+	1.70553i	0.00433364	+	0.0702156i
$591$	−3.67093	+	5.80739i	−0.151002	+	0.238884i
$592$	1.37778	−	2.72967i	0.0566265	−	0.112189i
$593$	−25.3181	−	21.9383i	−1.03969	−	0.900898i	−0.0445158	−	0.999009i	$-0.514175\pi$
$593$	−25.3181	−	21.9383i	−1.03969	−	0.900898i	−0.995175	+	0.0981110i	$0.968720\pi$
$594$	0.801890	−	2.23659i	0.0329020	−	0.0917686i
$595$	6.04462	+	2.76049i	0.247805	+	0.113169i
$596$	10.9936	+	13.1992i	0.450315	+	0.540661i
$597$	39.0731	+	17.4911i	1.59916	+	0.715862i
$598$	4.63168	−	3.39721i	0.189403	−	0.138922i
$599$	−6.34358	−	1.86264i	−0.259192	−	0.0761056i	0.149555	−	0.988753i	$-0.452216\pi$
$599$	−6.34358	−	1.86264i	−0.259192	−	0.0761056i	−0.408747	+	0.912648i	$0.634034\pi$
$600$	−23.8041	+	4.63786i	−0.971800	+	0.189340i
$601$	−3.16910	+	22.0416i	−0.129270	+	0.899094i	0.817212	+	0.576337i	$0.195519\pi$
$601$	−3.16910	+	22.0416i	−0.129270	+	0.899094i	−0.946482	+	0.322756i	$0.895391\pi$
$602$	9.77793	−	25.4542i	0.398519	−	1.03744i
$603$	23.9665	+	5.34847i	0.975992	+	0.217807i
$604$	18.2048	−	20.1990i	0.740741	−	0.821886i
$605$	−2.40268	−	0.345453i	−0.0976829	−	0.0140447i
$606$	−35.6349	−	26.8017i	−1.44757	−	1.08875i
$607$	−1.63069	+	5.55360i	−0.0661875	+	0.225414i	−0.985944	−	0.167075i	$-0.946568\pi$
$607$	−1.63069	+	5.55360i	−0.0661875	+	0.225414i	0.919757	+	0.392489i	$0.128386\pi$
$608$	8.47896	−	7.68940i	0.343867	−	0.311846i
$609$	27.8834	−	62.2883i	1.12989	−	2.52405i
$610$	−0.837557	+	1.49891i	−0.0339117	+	0.0606890i
$611$	3.95132	−	8.65218i	0.159853	−	0.350030i
$612$	−37.8790	+	10.9367i	−1.53117	+	0.442090i
$613$	27.8714	−	32.1653i	1.12571	−	1.29914i	0.176576	−	0.984287i	$-0.443498\pi$
$613$	27.8714	−	32.1653i	1.12571	−	1.29914i	0.949139	−	0.314857i	$-0.101957\pi$
$614$	−0.0263255	−	0.0358916i	−0.00106241	−	0.00144847i
$615$	−1.19314	−	0.754200i	−0.0481121	−	0.0304123i
$616$	−2.58392	+	3.24894i	−0.104109	+	0.130903i
$617$	6.50129	−	22.1414i	0.261732	−	0.891377i	−0.718833	−	0.695183i	$-0.755323\pi$
$617$	6.50129	−	22.1414i	0.261732	−	0.891377i	0.980565	−	0.196194i	$-0.0628584\pi$
$618$	13.6315	+	36.8009i	0.548338	+	1.48035i
$619$	−8.95241	+	13.9302i	−0.359828	+	0.559903i	−0.973220	−	0.229876i	$-0.926168\pi$
$619$	−8.95241	+	13.9302i	−0.359828	+	0.559903i	0.613392	+	0.789778i	$0.289804\pi$
$620$	−3.96866	−	1.90690i	−0.159385	−	0.0765828i
$621$	−3.17442	+	26.2609i	−0.127385	+	1.05381i
$622$	5.32033	+	1.21186i	0.213326	+	0.0485912i
$623$	10.2358	+	11.8128i	0.410090	+	0.473270i
$624$	−5.25202	−	1.72378i	−0.210249	−	0.0690063i
$625$	−15.8856	+	18.3329i	−0.635423	+	0.733317i
$626$	−27.1017	+	9.80821i	−1.08320	+	0.392015i
$627$	0.861952	+	0.735639i	0.0344230	+	0.0293786i
$628$	−11.9116	+	37.8202i	−0.475323	+	1.50919i
$629$	−1.41515	−	4.81955i	−0.0564257	−	0.192168i
$630$	−4.19715	−	0.890014i	−0.167219	−	0.0354590i
$631$	−8.61239	−	3.93315i	−0.342854	−	0.156576i	0.236544	−	0.971621i	$-0.423985\pi$
$631$	−8.61239	−	3.93315i	−0.342854	−	0.156576i	−0.579398	+	0.815045i	$0.696712\pi$
$632$	10.5879	+	20.8168i	0.421163	+	0.828047i
$633$	5.85770	+	8.96617i	0.232823	+	0.356373i
$634$	9.63830	−	9.45199i	0.382786	−	0.375386i
$635$	2.85340	−	3.29300i	0.113234	−	0.130679i
$636$	−34.7998	−	0.418213i	−1.37990	−	0.0165832i
$637$	−1.54468	−	10.7435i	−0.0612024	−	0.425672i
$638$	−3.50203	+	1.86812i	−0.138647	+	0.0739595i
$639$	13.3785	+	14.9795i	0.529244	+	0.592579i
$640$	2.11622	−	1.36926i	0.0836510	−	0.0541248i
$641$		−	8.45775i		−	0.334061i	−0.985952	−	0.167031i	$-0.946582\pi$
$641$		−	8.45775i		−	0.334061i	0.985952	−	0.167031i	$-0.0534178\pi$
$642$	3.07098	+	0.675316i	0.121202	+	0.0266526i
$643$	−10.7989	−	16.8035i	−0.425869	−	0.662665i	0.560322	−	0.828275i	$-0.310677\pi$
$643$	−10.7989	−	16.8035i	−0.425869	−	0.662665i	−0.986191	+	0.165610i	$0.947041\pi$
$644$	20.0152	−	41.6559i	0.788710	−	1.64147i
$645$	−1.38552	−	0.875808i	−0.0545550	−	0.0344849i
$646$	1.52441	−	18.7418i	0.0599771	−	0.737385i
$647$	−12.3492	−	14.2518i	−0.485499	−	0.560295i	0.459159	−	0.888354i	$-0.348151\pi$
$647$	−12.3492	−	14.2518i	−0.485499	−	0.560295i	−0.944657	+	0.328059i	$0.893605\pi$
$648$	22.3332	−	12.2159i	0.877330	−	0.479887i
$649$	−1.47521	+	0.948059i	−0.0579070	+	0.0372146i
$650$	−5.25227	+	1.90082i	−0.206011	+	0.0745563i
$651$	51.3148	+	58.3306i	2.01119	+	2.28616i
$652$	−9.51426	+	5.85526i	−0.372607	+	0.229310i
$653$	9.18454	+	31.2797i	0.359419	+	1.22407i	0.918655	+	0.395060i	$0.129276\pi$
$653$	9.18454	+	31.2797i	0.359419	+	1.22407i	−0.559237	+	0.829008i	$0.688906\pi$
$654$	−0.671185	+	1.78718i	−0.0262454	+	0.0698843i
$655$	−1.28901	+	0.185332i	−0.0503659	+	0.00724153i
$656$	−14.3905	−	2.64593i	−0.561853	−	0.103306i
$657$	13.1185	−	0.196818i	0.511802	−	0.00767861i
$658$	−4.71435	−	76.3842i	−0.183785	−	2.97777i
$659$	−21.8217	−	14.0240i	−0.850053	−	0.546296i	0.0415380	−	0.999137i	$-0.486774\pi$
$659$	−21.8217	−	14.0240i	−0.850053	−	0.546296i	−0.891591	+	0.452841i	$0.850411\pi$
$660$	0.161134	+	0.190537i	0.00627212	+	0.00741665i
$661$	6.09662	−	42.4029i	0.237131	−	1.64928i	−0.428895	−	0.903354i	$-0.641097\pi$
$661$	6.09662	−	42.4029i	0.237131	−	1.64928i	0.666026	−	0.745928i	$-0.267994\pi$
$662$	14.9108	−	14.6225i	0.579523	−	0.568321i
$663$	−8.23151	+	3.83408i	−0.319685	+	0.148904i
$664$	−5.31178	+	9.08500i	−0.206137	+	0.352566i
$665$	1.10630	−	1.72143i	0.0429003	−	0.0667542i
$666$	1.56918	+	2.83826i	0.0608045	+	0.109980i
$667$	33.3954	−	28.9373i	1.29308	−	1.12046i
$668$	−6.58530	+	5.48487i	−0.254793	+	0.212216i
$669$	14.0127	+	21.4487i	0.541762	+	0.829255i
$670$	−1.74681	+	1.89730i	−0.0674852	+	0.0732989i
$671$	−1.76206			−0.0680236
$672$	−43.8114	+	7.65162i	−1.69006	+	0.295168i
$673$	9.66171	+	11.1502i	0.372432	+	0.429809i	0.910766	−	0.412922i	$-0.135492\pi$
$673$	9.66171	+	11.1502i	0.372432	+	0.429809i	−0.538335	+	0.842731i	$0.680946\pi$
$674$	−20.5752	+	26.9334i	−0.792529	+	1.03743i
$675$	10.1565	−	23.6328i	0.390923	−	0.909629i
$676$	24.4018	+	3.99601i	0.938532	+	0.153693i
$677$	−27.9650	−	4.02077i	−1.07478	−	0.154531i	−0.417878	−	0.908503i	$-0.637226\pi$
$677$	−27.9650	−	4.02077i	−1.07478	−	0.154531i	−0.656906	+	0.753973i	$0.728135\pi$
$678$	−5.29334	+	24.0713i	−0.203290	+	0.924452i
$679$	−10.2898	−	1.47945i	−0.394886	−	0.0567760i
$680$	0.998230	−	4.01857i	0.0382804	−	0.154105i
$681$	−7.47898	+	0.0561007i	−0.286595	+	0.00214978i
$682$	−0.278346	−	4.50989i	−0.0106584	−	0.172692i
$683$	11.4308	+	25.0300i	0.437389	+	0.957748i	0.992070	+	0.125685i	$0.0401129\pi$
$683$	11.4308	+	25.0300i	0.437389	+	0.957748i	−0.554681	+	0.832063i	$0.687160\pi$
$684$	1.67352	+	12.0248i	0.0639885	+	0.459781i
$685$	−0.00169182	−	0.0117669i	−6.46411e−5	−	0.000449589i
$686$	−25.0730	−	34.1839i	−0.957290	−	1.30515i
$687$	−17.1513	+	20.0963i	−0.654364	+	0.766722i
$688$	−16.7108	−	3.07256i	−0.637093	−	0.117140i
$689$	−7.93408	+	1.14075i	−0.302264	+	0.0434590i
$690$	−2.22021	−	1.66987i	−0.0845220	−	0.0635707i
$691$	−4.40448	−	6.85350i	−0.167554	−	0.260719i	0.747315	−	0.664470i	$-0.231343\pi$
$691$	−4.40448	−	6.85350i	−0.167554	−	0.260719i	−0.914869	+	0.403751i	$0.867706\pi$
$692$	−4.34804	−	35.0903i	−0.165288	−	1.33393i
$693$	−1.30370	−	4.20554i	−0.0495234	−	0.159755i
$694$	1.42836	−	17.5610i	0.0542200	−	0.666605i
$695$	0.977246	+	2.13987i	0.0370690	+	0.0811699i
$696$	−41.3458	−	9.94183i	−1.56721	−	0.376844i
$697$	−20.2207	+	12.9950i	−0.765913	+	0.492222i
$698$	28.7776	+	29.3448i	1.08925	+	1.11072i
$699$	−8.89971	−	13.6225i	−0.336618	−	0.515249i
$700$	−30.0874	+	33.3833i	−1.13720	+	1.26177i
$701$	−22.5952	−	10.3189i	−0.853410	−	0.389739i	−0.0598324	−	0.998208i	$-0.519057\pi$
$701$	−22.5952	−	10.3189i	−0.853410	−	0.389739i	−0.793577	+	0.608469i	$0.791784\pi$
$702$	4.64840	−	3.57308i	0.175443	−	0.134857i
$703$	−1.53102	+	0.220128i	−0.0577435	+	0.00830227i
$704$	2.28600	+	1.21039i	0.0861567	+	0.0456183i
$705$	−4.55833	−	0.620527i	−0.171677	−	0.0233704i
$706$	11.1748	−	10.9587i	0.420567	−	0.412438i
$707$	−82.6282			−3.10755
$708$	−18.5627	−	2.89700i	−0.697630	−	0.108876i
$709$	15.0544	−	32.9644i	0.565378	−	1.23801i	−0.383844	−	0.923398i	$-0.625400\pi$
$709$	15.0544	−	32.9644i	0.565378	−	1.23801i	0.949222	−	0.314608i	$-0.101873\pi$
$710$	−2.06537	+	0.428228i	−0.0775120	+	0.0160711i
$711$	−24.5694	−	3.15712i	−0.921424	−	0.118401i
$712$	6.06250	−	7.62280i	0.227202	−	0.285677i
$713$	14.1723	+	48.2665i	0.530757	+	1.80759i
$714$	−43.9158	+	58.3893i	−1.64351	+	2.18517i
$715$	0.0434353	+	0.0376369i	0.00162439	+	0.00140754i
$716$	21.2132	+	3.47384i	0.792775	+	0.129824i
$717$	14.7229	+	4.20335i	0.549838	+	0.156977i
$718$	−29.6534	−	6.75444i	−1.10666	−	0.252073i
$719$	24.2104	+	7.10881i	0.902895	+	0.265114i	0.700047	−	0.714096i	$-0.253162\pi$
$719$	24.2104	+	7.10881i	0.902895	+	0.265114i	0.202848	+	0.979210i	$0.434980\pi$
$720$	−0.0642484	+	2.67270i	−0.00239440	+	0.0996055i
$721$	61.1794	+	39.3176i	2.27844	+	1.46426i
$722$	20.5533	+	4.68162i	0.764915	+	0.174232i
$723$	12.5881	−	3.79899i	0.468157	−	0.141286i
$724$	−0.340876	+	1.08231i	−0.0126686	+	0.0402237i
$725$	−39.0872	+	17.8505i	−1.45166	+	0.662952i
$726$	9.38305	−	24.9845i	0.348238	−	0.927261i
$727$	−20.9521	−	18.1551i	−0.777071	−	0.673336i	0.173156	−	0.984894i	$-0.444604\pi$
$727$	−20.9521	−	18.1551i	−0.777071	−	0.673336i	−0.950227	+	0.311558i	$0.899149\pi$
$728$	−9.69818	+	3.29720i	−0.359439	+	0.122203i
$729$	−2.63623	+	26.8710i	−0.0976380	+	0.995222i
$730$	−0.672133	+	1.20286i	−0.0248768	+	0.0445199i
$731$	−23.4811	+	15.0904i	−0.868479	+	0.558137i
$732$	−14.1176	−	12.5332i	−0.521803	−	0.463240i
$733$	41.3342	+	12.1368i	1.52671	+	0.448283i	0.934043	−	0.357162i	$-0.116256\pi$
$733$	41.3342	+	12.1368i	1.52671	+	0.448283i	0.592670	+	0.805445i	$0.298074\pi$
$734$	9.11911	+	25.1976i	0.336593	+	0.930060i
$735$	−4.75865	+	2.21649i	−0.175526	+	0.0817565i
$736$	−27.8072	−	7.48654i	−1.02499	−	0.275957i
$737$	−2.57412	−	0.615130i	−0.0948188	−	0.0226586i
$738$	10.9161	−	11.0312i	0.401827	−	0.406062i
$739$	−1.30032	−	0.186958i	−0.0478331	−	0.00687736i	0.118357	−	0.992971i	$-0.462237\pi$
$739$	−1.30032	−	0.186958i	−0.0478331	−	0.00687736i	−0.166190	+	0.986094i	$0.553146\pi$
$740$	−0.340543	−	0.00664758i	−0.0125186	−	0.000244370i
$741$	0.807896	+	2.67699i	0.0296788	+	0.0983418i
$742$	−52.0035	+	38.1432i	−1.90911	+	1.40028i
$743$	11.4880	−	7.38286i	0.421452	−	0.270851i	−0.312679	−	0.949859i	$-0.601226\pi$
$743$	11.4880	−	7.38286i	0.421452	−	0.270851i	0.734131	+	0.679008i	$0.237590\pi$
$744$	29.8478	−	38.1131i	1.09427	−	1.39729i
$745$	0.794904	−	1.74060i	0.0291230	−	0.0637706i
$746$	19.3547	+	10.8150i	0.708627	+	0.395965i
$747$	−4.78877	−	10.0829i	−0.175212	−	0.368912i
$748$	4.09973	−	1.11736i	0.149901	−	0.0408546i
$749$	5.30026	−	2.42055i	0.193667	−	0.0884448i
$750$	3.24432	+	4.35436i	0.118466	+	0.158999i
$751$	−0.125217	+	0.426450i	−0.00456924	+	0.0155614i	−0.961746	−	0.273943i	$-0.911672\pi$
$751$	−0.125217	+	0.426450i	−0.00456924	+	0.0155614i	0.957177	+	0.289504i	$0.0934903\pi$
$752$	−46.2446	+	11.6390i	−1.68637	+	0.424432i
$753$	−22.3182	+	0.167412i	−0.813321	+	0.00610082i
$754$	−9.76194	−	0.794012i	−0.355509	−	0.0289162i
$755$	−2.90636	−	0.853384i	−0.105773	−	0.0310578i
$756$	19.4679	−	42.9678i	0.708042	−	1.56272i
$757$	−28.2803	−	32.6372i	−1.02786	−	1.18622i	−0.982311	−	0.187257i	$-0.940040\pi$
$757$	−28.2803	−	32.6372i	−1.02786	−	1.18622i	−0.0455539	−	0.998962i	$-0.514505\pi$
$758$	38.0968	−	7.89888i	1.38374	−	0.286900i
$759$	0.384552	−	2.82488i	0.0139584	−	0.102537i
$760$	−1.18112	−	0.480370i	−0.0428436	−	0.0174248i
$761$	−6.29096	−	21.4250i	−0.228047	−	0.776657i	−0.991422	−	0.130701i	$-0.958277\pi$
$761$	−6.29096	−	21.4250i	−0.228047	−	0.776657i	0.763375	−	0.645956i	$-0.223541\pi$
$762$	28.6227	+	38.4159i	1.03689	+	1.39166i
$763$	0.996682	+	3.39439i	0.0360823	+	0.122885i
$764$	−18.6487	−	3.05389i	−0.674687	−	0.110486i
$765$	2.92553	+	3.27563i	0.105773	+	0.118431i
$766$	−2.61774	+	6.81457i	−0.0945826	+	0.246220i
$767$	−4.32711			−0.156243
$768$	9.70615	+	25.9575i	0.350240	+	0.936660i
$769$	10.1650	−	11.7310i	0.366558	−	0.423030i	−0.542268	−	0.840205i	$-0.682434\pi$
$769$	10.1650	−	11.7310i	0.366558	−	0.423030i	0.908826	+	0.417175i	$0.136980\pi$
$770$	0.450869	+	0.102699i	0.0162482	+	0.00370101i
$771$	−22.0842	+	19.4280i	−0.795342	+	0.699682i
$772$	−28.4132	+	3.52067i	−1.02261	+	0.126712i
$773$	−41.3891	−	18.9018i	−1.48866	−	0.679850i	−0.505541	−	0.862802i	$-0.668707\pi$
$773$	−41.3891	−	18.9018i	−1.48866	−	0.679850i	−0.983122	+	0.182953i	$0.941434\pi$
$774$	12.6762	−	12.8098i	0.455637	−	0.460440i
$775$		−	48.9174i		−	1.75717i
$776$	0.272776	+	6.47192i	0.00979210	+	0.232328i
$777$	5.48537	+	2.45553i	0.196787	+	0.0880915i
$778$	28.7594	+	2.33922i	1.03107	+	0.0838650i
$779$	3.07475	+	6.73277i	0.110164	+	0.241226i
$780$	0.0803003	+	0.610494i	0.00287521	+	0.0218592i
$781$	−1.41752	−	1.63590i	−0.0507227	−	0.0585372i
$782$	−41.7397	+	22.2656i	−1.49261	+	0.796217i
$783$	33.4140	−	30.2962i	1.19412	−	1.08270i
$784$	−37.2127	+	39.7028i	−1.32902	+	1.41796i
$785$	4.37202	−	0.628601i	0.156044	−	0.0224357i
$786$	1.05368	−	14.2792i	0.0375835	−	0.509322i
$787$	−3.36181	−	11.4493i	−0.119836	−	0.408123i	0.877625	−	0.479349i	$-0.159127\pi$
$787$	−3.36181	−	11.4493i	−0.119836	−	0.408123i	−0.997460	+	0.0712258i	$0.977309\pi$
$788$	7.65400	−	2.08605i	0.272663	−	0.0743125i
$789$	17.5490	+	19.9483i	0.624761	+	0.710179i
$790$	1.57932	−	2.06736i	0.0561898	−	0.0735534i
$791$	18.9730	+	41.5451i	0.674602	+	1.47717i
$792$	−2.42650	+	1.28035i	−0.0862218	+	0.0454951i
$793$	−3.65780	−	2.35072i	−0.129892	−	0.0834767i
$794$	6.97033	+	13.0668i	0.247368	+	0.463723i
$795$	1.63688	+	3.51427i	0.0580543	+	0.124638i
$796$	−19.6533	−	45.3572i	−0.696594	−	1.60764i
$797$	−25.2635	−	3.63234i	−0.894879	−	0.128664i	−0.320495	−	0.947250i	$-0.603849\pi$
$797$	−25.2635	−	3.63234i	−0.894879	−	0.128664i	−0.574384	+	0.818586i	$0.694758\pi$
$798$	15.8725	+	15.9444i	0.561882	+	0.564425i
$799$	−42.3527	+	65.9021i	−1.49833	+	2.33145i
$800$	23.8942	+	14.6035i	0.844788	+	0.516311i
$801$	3.05880	+	9.86724i	0.108077	+	0.348642i
$802$	−8.55770	+	15.3150i	−0.302183	+	0.540792i
$803$	−1.41404			−0.0499005
$804$	−16.2485	−	23.2376i	−0.573042	−	0.819526i
$805$	−5.14810			−0.181447
$806$	5.43872	−	9.73324i	0.191571	−	0.342839i
$807$	−10.1586	+	35.5822i	−0.357599	+	1.25255i
$808$	9.46692	+	50.6092i	0.333045	+	1.78042i
$809$	−17.4288	+	27.1197i	−0.612763	+	0.953478i	0.386747	+	0.922186i	$0.373599\pi$
$809$	−17.4288	+	27.1197i	−0.612763	+	0.953478i	−0.999510	+	0.0312921i	$0.990038\pi$
$810$	−2.30398	−	1.65303i	−0.0809537	−	0.0580817i
$811$	−45.3877	−	6.52577i	−1.59378	−	0.229151i	−0.712474	−	0.701699i	$-0.752425\pi$
$811$	−45.3877	−	6.52577i	−1.59378	−	0.229151i	−0.881305	+	0.472548i	$0.843334\pi$
$812$	−72.3061	+	31.3303i	−2.53745	+	1.09948i
$813$	−25.7700	+	12.0032i	−0.903794	+	0.420970i
$814$	−0.164514	−	0.308403i	−0.00576623	−	0.0108095i
$815$	1.04690	+	0.672805i	0.0366715	+	0.0235673i
$816$	40.7946	+	20.2083i	1.42810	+	0.707431i
$817$	3.57053	+	7.81836i	0.124917	+	0.273530i
$818$	−12.1152	+	15.8590i	−0.423599	+	0.554499i
$819$	2.90422	−	10.4694i	0.101482	−	0.365829i
$820$	0.428584	+	1.57253i	0.0149668	+	0.0549152i
$821$	−5.35311	−	18.2310i	−0.186825	−	0.636267i	−0.998629	−	0.0523376i	$-0.983333\pi$
$821$	−5.35311	−	18.2310i	−0.186825	−	0.636267i	0.811805	−	0.583929i	$-0.198485\pi$
$822$	0.130349	+	0.00961860i	0.00454643	+	0.000335487i
$823$	29.1504	−	4.19119i	1.01612	−	0.146096i	0.385922	−	0.922531i	$-0.373883\pi$
$823$	29.1504	−	4.19119i	1.01612	−	0.146096i	0.630197	+	0.776436i	$0.282974\pi$
$824$	17.0723	−	41.9766i	0.594740	−	1.46233i
$825$	−1.13273	+	2.53038i	−0.0394365	+	0.0880966i
$826$	−30.7178	+	16.3861i	−1.06881	+	0.570145i
$827$	−8.60130	−	9.92643i	−0.299097	−	0.345176i	0.586231	−	0.810144i	$-0.300611\pi$
$827$	−8.60130	−	9.92643i	−0.299097	−	0.345176i	−0.885327	+	0.464968i	$0.846066\pi$
$828$	23.1738	−	19.8977i	0.805347	−	0.691494i
$829$	−1.42420	−	3.11856i	−0.0494645	−	0.108312i	0.883286	−	0.468834i	$-0.155326\pi$
$829$	−1.42420	−	3.11856i	−0.0494645	−	0.108312i	−0.932751	+	0.360522i	$0.882599\pi$
$830$	1.16844	+	0.0950384i	0.0405573	+	0.00329883i
$831$	−0.709735	+	1.58547i	−0.0246204	+	0.0549992i
$832$	3.13066	+	5.56230i	0.108536	+	0.192838i
$833$			89.3924i			3.09726i
$834$	−25.2857	+	5.44080i	−0.875573	+	0.188400i
$835$	0.868411	+	0.396590i	0.0300526	+	0.0137246i
$836$	−0.160905	−	1.29857i	−0.00556503	−	0.0449119i
$837$	15.5708	+	48.9283i	0.538205	+	1.69121i
$838$	16.5461	+	3.76886i	0.571575	+	0.130193i
$839$	−6.88523	+	7.94598i	−0.237705	+	0.274326i	−0.862051	−	0.506822i	$-0.830820\pi$
$839$	−6.88523	+	7.94598i	−0.237705	+	0.274326i	0.624346	+	0.781148i	$0.285366\pi$
$840$	2.88189	+	4.02976i	0.0994346	+	0.139040i
$841$	−46.3465			−1.59816
$842$	19.7232	−	51.3439i	0.679705	−	1.76943i
$843$	−55.7372	+	8.44100i	−1.91969	+	0.290723i
$844$	1.99856	−	12.2043i	0.0687933	−	0.420090i
$845$	−0.776015	−	2.64286i	−0.0266957	−	0.0909173i
$846$	17.4270	−	47.4825i	0.599153	−	1.63248i
$847$	−13.9334	−	47.4529i	−0.478758	−	1.63050i
$848$	29.3206	+	27.4816i	1.00687	+	0.943723i
$849$	23.6386	+	3.21793i	0.811275	+	0.110439i
$850$	45.0450	−	9.33950i	1.54503	−	0.320342i
$851$	2.54834	+	2.94094i	0.0873559	+	0.100814i
$852$	0.278682	−	23.1894i	0.00954748	−	0.794454i
$853$	−22.4075	−	6.57944i	−0.767218	−	0.225276i	−0.125373	−	0.992110i	$-0.540013\pi$
$853$	−22.4075	−	6.57944i	−0.767218	−	0.225276i	−0.641845	+	0.766834i	$0.721831\pi$
$854$	−34.8682	−	2.83610i	−1.19317	−	0.0970492i
$855$	1.12662	−	0.748153i	0.0385297	−	0.0255863i
$856$	−2.08983	−	2.96904i	−0.0714290	−	0.101480i
$857$	−1.09811	+	3.73982i	−0.0375108	+	0.127750i	−0.976120	−	0.217233i	$-0.930297\pi$
$857$	−1.09811	+	3.73982i	−0.0375108	+	0.127750i	0.938609	+	0.344983i	$0.112115\pi$
$858$	−0.506714	+	0.377539i	−0.0172989	+	0.0128890i
$859$	45.5543	−	20.8039i	1.55429	−	0.709821i	0.561257	−	0.827642i	$-0.310318\pi$
$859$	45.5543	−	20.8039i	1.55429	−	0.709821i	0.993035	+	0.117820i	$0.0375907\pi$
$860$	0.497689	+	1.82609i	0.0169711	+	0.0622691i
$861$	3.87917	−	28.4960i	0.132202	−	0.971141i
$862$	21.7135	+	12.1330i	0.739565	+	0.413253i
$863$	15.5114	−	33.9653i	0.528016	−	1.15619i	−0.438299	−	0.898829i	$-0.644419\pi$
$863$	15.5114	−	33.9653i	0.528016	−	1.15619i	0.966315	−	0.257364i	$-0.0828538\pi$
$864$	−28.5479	−	7.00104i	−0.971221	−	0.238180i
$865$	−3.31350	+	2.12945i	−0.112662	+	0.0724036i
$866$	−15.4194	+	11.3097i	−0.523973	+	0.384320i
$867$	43.4089	−	13.1005i	1.47424	−	0.444915i
$868$	1.75082	−	89.6911i	0.0594267	−	3.04431i
$869$	2.64263	+	0.379952i	0.0896450	+	0.0128890i
$870$	0.996462	+	4.63098i	0.0337832	+	0.157005i
$871$	−4.52288	−	4.71099i	−0.153252	−	0.159626i
$872$	1.96484	−	0.999364i	0.0665380	−	0.0338427i
$873$	−5.83499	−	3.62740i	−0.197485	−	0.122769i
$874$	4.95738	+	13.6981i	0.167686	+	0.463344i
$875$	9.65495	+	2.83495i	0.326397	+	0.0958388i
$876$	−11.3293	−	10.0578i	−0.382782	−	0.339821i
$877$	32.2776	−	20.7435i	1.08994	−	0.700460i	0.133105	−	0.991102i	$-0.457505\pi$
$877$	32.2776	−	20.7435i	1.08994	−	0.700460i	0.956832	+	0.290642i	$0.0938690\pi$
$878$	8.61581	−	15.4190i	0.290769	−	0.520366i
$879$	−37.9706	+	5.75037i	−1.28072	+	0.193955i
$880$	0.0112450	−	0.287920i	0.000379069	−	0.00970580i
$881$	30.3565	+	26.3040i	1.02274	+	0.886206i	0.993553	−	0.113368i	$-0.0361641\pi$
$881$	30.3565	+	26.3040i	1.02274	+	0.886206i	0.0291828	+	0.999574i	$0.490710\pi$
$882$	−12.5641	−	56.3327i	−0.423056	−	1.89682i
$883$	44.1869	−	20.1795i	1.48701	−	0.679094i	0.504177	−	0.863600i	$-0.331796\pi$
$883$	44.1869	−	20.1795i	1.48701	−	0.679094i	0.982831	+	0.184507i	$0.0590687\pi$
$884$	10.0011	+	3.14987i	0.336374	+	0.105942i
$885$	0.604660	+	2.00356i	0.0203254	+	0.0673490i
$886$	−32.0991	−	7.31151i	−1.07839	−	0.245635i
$887$	−30.9845	−	19.9126i	−1.04036	−	0.668598i	−0.0952834	−	0.995450i	$-0.530376\pi$
$887$	−30.9845	−	19.9126i	−1.04036	−	0.668598i	−0.945075	+	0.326852i	$0.894012\pi$
$888$	0.875519	−	3.64109i	0.0293805	−	0.122187i
$889$	85.1799	+	25.0111i	2.85684	+	0.838845i
$890$	−1.05785	−	0.240957i	−0.0354592	−	0.00807688i
$891$	0.327540	−	2.89150i	0.0109730	−	0.0968690i
$892$	4.78092	−	29.1950i	0.160077	−	0.977520i
$893$	18.2310	+	15.7972i	0.610076	+	0.528634i
$894$	16.8137	+	12.6459i	0.562333	+	0.422942i
$895$	−0.674611	−	2.29751i	−0.0225498	−	0.0767974i
$896$	43.2879	+	27.6310i	1.44615	+	0.923087i
$897$	4.56689	−	5.35105i	0.152484	−	0.178666i
$898$	−10.6596	+	2.21014i	−0.355716	+	0.0737532i
$899$	35.6320	−	78.0232i	1.18839	−	2.60222i
$900$	−27.0735	+	12.2166i	−0.902450	+	0.407220i
$901$	66.0164			2.19933
$902$	−1.19421	+	1.17113i	−0.0397629	+	0.0389943i
$903$	4.50465	−	33.0907i	0.149905	−	1.10119i
$904$	23.2723	−	16.3808i	0.774024	−	0.544816i
$905$	0.125115	−	0.0179888i	0.00415897	−	0.000597969i
$906$	16.0266	−	29.1936i	0.532448	−	0.969893i
$907$	−34.8741	−	15.9265i	−1.15798	−	0.528830i	−0.258591	−	0.965987i	$-0.583258\pi$
$907$	−34.8741	−	15.9265i	−1.15798	−	0.528830i	−0.899385	+	0.437157i	$0.855985\pi$
$908$	6.41520	+	5.78183i	0.212896	+	0.191877i
$909$	−50.0099	−	21.9381i	−1.65872	−	0.727642i
$910$	0.798934	+	0.814682i	0.0264844	+	0.0270064i
$911$	27.1214	−	17.4299i	0.898572	−	0.577477i	−0.00779426	−	0.999970i	$-0.502481\pi$
$911$	27.1214	−	17.4299i	0.898572	−	0.577477i	0.906367	+	0.422492i	$0.138845\pi$
$912$	7.94727	−	11.5486i	0.263160	−	0.382413i
$913$	0.499762	+	1.09433i	0.0165397	+	0.0362169i
$914$	3.89908	−	47.9370i	0.128970	−	1.58562i
$915$	−0.577313	+	2.02214i	−0.0190854	+	0.0668498i
$916$	30.2760	−	3.75149i	1.00035	−	0.123953i
$917$	−14.3447	−	22.3208i	−0.473704	−	0.737097i
$918$	−42.0822	+	23.6797i	−1.38892	+	0.781548i
$919$	−13.6396	+	1.96108i	−0.449928	+	0.0646899i	−0.363555	−	0.931573i	$-0.618437\pi$
$919$	−13.6396	+	1.96108i	−0.449928	+	0.0646899i	−0.0863738	+	0.996263i	$0.527528\pi$
$920$	0.589831	+	3.15317i	0.0194461	+	0.103957i
$921$	−0.0414662	−	0.0353896i	−0.00136636	−	0.00116613i
$922$	−3.34817	−	4.56482i	−0.110266	−	0.150334i
$923$	−0.760153	−	5.28698i	−0.0250207	−	0.174023i
$924$	−2.16744	+	4.59897i	−0.0713036	+	0.151295i
$925$	−1.57199	−	3.44218i	−0.0516868	−	0.113178i
$926$	2.40221	+	38.9217i	0.0789414	+	1.27905i
$927$	26.5892	+	40.0400i	0.873305	+	1.31509i
$928$	27.4739	+	40.6973i	0.901875	+	1.33596i
$929$	19.5814	+	2.81538i	0.642446	+	0.0923697i	0.455835	−	0.890064i	$-0.349341\pi$
$929$	19.5814	+	2.81538i	0.642446	+	0.0923697i	0.186610	+	0.982434i	$0.440250\pi$
$930$	−5.26673	−	1.15817i	−0.172703	−	0.0379779i
$931$	27.2469	+	3.91751i	0.892980	+	0.128391i
$932$	−3.03645	+	18.5422i	−0.0994622	+	0.607372i
$933$	6.68276	−	0.0501281i	0.218784	−	0.00164112i
$934$	−18.7241	+	24.5102i	−0.612671	+	0.801998i
$935$	−0.309975	−	0.357730i	−0.0101373	−	0.0116990i
$936$	−6.74515	−	0.579309i	−0.220472	−	0.0189353i
$937$	13.6408			0.445627			0.222813	−	0.974861i	$-0.428476\pi$
$937$	13.6408			0.445627			0.222813	+	0.974861i	$0.428476\pi$
$938$	−49.9474	−	16.3155i	−1.63084	−	0.532721i
$939$	−29.5518	+	19.3066i	−0.964388	+	0.630046i
$940$	3.39964	+	4.08171i	0.110884	+	0.133131i
$941$	−19.7304	+	17.0965i	−0.643194	+	0.557331i	−0.914208	−	0.405244i	$-0.867186\pi$
$941$	−19.7304	+	17.0965i	−0.643194	+	0.557331i	0.271014	+	0.962575i	$0.412641\pi$
$942$	−3.57383	+	48.4315i	−0.116442	+	1.57798i
$943$	10.0675	−	15.6653i	0.327842	−	0.510132i
$944$	13.5558	+	16.9371i	0.441203	+	0.551254i
$945$	−5.25341	+	0.118237i	−0.170893	+	0.00384625i
$946$	−1.38677	+	1.35996i	−0.0450877	+	0.0442162i
$947$	−0.840929	+	5.84879i	−0.0273265	+	0.190060i	−0.998912	−	0.0466273i	$-0.985153\pi$
$947$	−0.840929	+	5.84879i	−0.0273265	+	0.190060i	0.971586	+	0.236688i	$0.0760618\pi$
$948$	18.4702	+	21.8406i	0.599885	+	0.709351i
$949$	−2.93536	−	1.88644i	−0.0952857	−	0.0612364i
$950$	−0.872647	−	14.1390i	−0.0283124	−	0.458731i
$951$	8.83408	−	13.9755i	0.286465	−	0.453186i
$952$	82.9252	−	15.5119i	2.68762	−	0.502745i
$953$	18.1245	−	2.60592i	0.587112	−	0.0844139i	0.157644	−	0.987496i	$-0.449610\pi$
$953$	18.1245	−	2.60592i	0.587112	−	0.0844139i	0.429468	+	0.903082i	$0.358701\pi$
$954$	−41.6018	+	9.27862i	−1.34691	+	0.300407i
$955$	0.593057	+	2.01977i	0.0191909	+	0.0653581i
$956$	−9.26635	−	15.0570i	−0.299695	−	0.486977i
$957$	−3.64986	+	3.21087i	−0.117983	+	0.103793i
$958$	29.9980	−	10.8564i	0.969190	−	0.350754i
$959$	0.203757	−	0.130947i	0.00657966	−	0.00422849i
$960$	2.13801	−	2.22684i	0.0690041	−	0.0718709i
$961$	43.6436	+	50.3674i	1.40786	+	1.62476i
$962$	0.0699240	−	0.859678i	0.00225444	−	0.0277171i
$963$	3.85060	−	0.0577708i	0.124084	−	0.00186164i
$964$	−13.6852	−	6.57559i	−0.440771	−	0.211786i
$965$	1.72425	+	2.68299i	0.0555056	+	0.0863685i
$966$	12.1564	−	55.2807i	0.391125	−	1.77863i
$967$			18.7808i			0.603949i	0.953316	+	0.301975i	$0.0976458\pi$
$967$			18.7808i			0.603949i	−0.953316	+	0.301975i	$0.902354\pi$
$968$	−27.4682	+	13.9709i	−0.882861	+	0.449043i
$969$	−3.44836	−	22.7701i	−0.110777	−	0.731479i
$970$	0.636657	−	0.339618i	0.0204418	−	0.0109045i
$971$	4.29623	+	29.8809i	0.137873	+	0.958925i	0.934882	+	0.354958i	$0.115505\pi$
$971$	4.29623	+	29.8809i	0.137873	+	0.958925i	−0.797010	+	0.603967i	$0.793586\pi$
$972$	23.1909	−	20.8370i	0.743849	−	0.668348i
$973$	−31.3872	+	36.2228i	−1.00623	+	1.16125i
$974$	−6.35311	+	6.23031i	−0.203567	+	0.199632i
$975$	−5.72711	+	3.74159i	−0.183414	+	0.119827i
$976$	2.25786	+	21.6815i	0.0722723	+	0.694008i
$977$	−12.1342	−	5.54148i	−0.388206	−	0.177288i	0.211744	−	0.977325i	$-0.432086\pi$
$977$	−12.1342	−	5.54148i	−0.388206	−	0.177288i	−0.599950	+	0.800037i	$0.704813\pi$
$978$	−9.69673	+	9.65304i	−0.310067	+	0.308670i
$979$	−0.313679	−	1.06829i	−0.0100252	−	0.0341428i
$980$	5.78166	+	1.82095i	0.184688	+	0.0581680i
$981$	−0.297993	+	2.31904i	−0.00951417	+	0.0740414i
$982$	32.9542	−	11.9262i	1.05161	−	0.380582i
$983$	9.51645	−	10.9826i	0.303528	−	0.350289i	−0.583411	−	0.812177i	$-0.698282\pi$
$983$	9.51645	−	10.9826i	0.303528	−	0.350289i	0.886938	+	0.461888i	$0.152828\pi$
$984$	−17.8980	+	0.888897i	−0.570569	+	0.0283370i
$985$	−0.578709	−	0.667865i	−0.0184392	−	0.0212800i
$986$	78.6497	+	17.9148i	2.50472	+	0.570523i
$987$	−27.0804	−	89.7319i	−0.861978	−	2.85620i
$988$	1.39837	−	2.91031i	0.0444881	−	0.0925892i
$989$	11.6908	−	18.1912i	0.371745	−	0.578446i
$990$	0.245617	+	0.181865i	0.00780623	+	0.00578005i
$991$	1.14364	−	3.89488i	0.0363289	−	0.123725i	−0.939332	−	0.343009i	$-0.888554\pi$
$991$	1.14364	−	3.89488i	0.0363289	−	0.123725i	0.975661	+	0.219284i	$0.0703721\pi$
$992$	−55.1358	+	9.20378i	−1.75056	+	0.292220i
$993$	13.6666	−	21.6205i	0.433697	−	0.686107i
$994$	−25.4172	−	34.6533i	−0.806186	−	1.09914i
$995$	−3.60596	+	4.16150i	−0.114317	+	0.131929i
$996$	−3.77962	+	12.3225i	−0.119762	+	0.390452i
$997$	−8.04624	+	17.6188i	−0.254827	+	0.557993i	−0.993203	−	0.116396i	$-0.962866\pi$
$997$	−8.04624	+	17.6188i	−0.254827	+	0.557993i	0.738376	+	0.674389i	$0.235593\pi$
$998$	−5.09587	+	9.11966i	−0.161307	+	0.288678i
$999$	2.66801	+	2.94257i	0.0844122	+	0.0930989i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.w.a.59.20	yes	1320
3.2	odd	2	inner	804.2.w.a.59.113	yes	1320
4.3	odd	2	inner	804.2.w.a.59.9	✓	1320
12.11	even	2	inner	804.2.w.a.59.124	yes	1320
67.25	even	11	inner	804.2.w.a.695.124	yes	1320
201.92	odd	22	inner	804.2.w.a.695.9	yes	1320
268.159	odd	22	inner	804.2.w.a.695.113	yes	1320
804.695	even	22	inner	804.2.w.a.695.20	yes	1320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.w.a.59.9	✓	1320	4.3	odd	2	inner
804.2.w.a.59.20	yes	1320	1.1	even	1	trivial
804.2.w.a.59.113	yes	1320	3.2	odd	2	inner
804.2.w.a.59.124	yes	1320	12.11	even	2	inner
804.2.w.a.695.9	yes	1320	201.92	odd	22	inner
804.2.w.a.695.20	yes	1320	804.695	even	22	inner
804.2.w.a.695.113	yes	1320	268.159	odd	22	inner
804.2.w.a.695.124	yes	1320	67.25	even	11	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.w (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23455 - 0.689841i) q^{2} +(-1.66550 - 0.475496i) q^{3} +(1.04824 + 1.70329i) q^{4} +(0.120449 - 0.187422i) q^{5} +(1.72814 + 1.73596i) q^{6} +(4.49296 + 0.645990i) q^{7} +(-0.119106 - 2.82592i) q^{8} +(2.54781 + 1.58388i) q^{9} +O(q^{10})\)	\(q+(-1.23455 - 0.689841i) q^{2} +(-1.66550 - 0.475496i) q^{3} +(1.04824 + 1.70329i) q^{4} +(0.120449 - 0.187422i) q^{5} +(1.72814 + 1.73596i) q^{6} +(4.49296 + 0.645990i) q^{7} +(-0.119106 - 2.82592i) q^{8} +(2.54781 + 1.58388i) q^{9} +(-0.277992 + 0.148292i) q^{10} +(-0.272005 - 0.174807i) q^{11} +(-0.935939 - 3.33527i) q^{12} +(-0.331439 - 0.725750i) q^{13} +(-5.10116 - 3.89694i) q^{14} +(-0.289726 + 0.254879i) q^{15} +(-1.80239 + 3.57091i) q^{16} +(1.85128 + 6.30487i) q^{17} +(-2.05278 - 3.71297i) q^{18} +(2.00286 - 0.287967i) q^{19} +(0.445493 + 0.00869627i) q^{20} +(-7.17588 - 3.21228i) q^{21} +(0.215215 + 0.403448i) q^{22} +(-3.33370 - 3.84729i) q^{23} +(-1.14534 + 4.76321i) q^{24} +(2.05646 + 4.50301i) q^{25} +(-0.0914736 + 1.12462i) q^{26} +(-3.49026 - 3.84943i) q^{27} +(3.60939 + 8.32996i) q^{28} +8.68024i q^{29} +(0.533509 - 0.114797i) q^{30} +(-8.98860 - 4.10496i) q^{31} +(4.68851 - 3.16511i) q^{32} +(0.369905 + 0.420479i) q^{33} +(2.06386 - 9.06077i) q^{34} +(0.662245 - 0.764271i) q^{35} +(-0.0270965 + 5.99994i) q^{36} -0.764418 q^{37} +(-2.67128 - 1.02614i) q^{38} +(0.206922 + 1.36634i) q^{39} +(-0.543986 - 0.318055i) q^{40} +(1.03056 + 3.50975i) q^{41} +(6.64303 + 8.91595i) q^{42} +(1.19672 + 4.07567i) q^{43} +(0.0126209 - 0.646542i) q^{44} +(0.603734 - 0.286739i) q^{45} +(1.46160 + 7.04940i) q^{46} +(7.80706 + 9.00982i) q^{47} +(4.69984 - 5.09033i) q^{48} +(13.0529 + 3.83269i) q^{49} +(0.567559 - 6.97783i) q^{50} +(-0.0853706 - 11.3811i) q^{51} +(0.888736 - 1.32530i) q^{52} +(2.83045 - 9.63962i) q^{53} +(1.65341 + 7.16004i) q^{54} +(-0.0655253 + 0.0299244i) q^{55} +(1.29038 - 12.7737i) q^{56} +(-3.47269 - 0.472739i) q^{57} +(5.98798 - 10.7162i) q^{58} +(2.25299 - 4.93336i) q^{59} +(-0.737836 - 0.226314i) q^{60} +(4.58457 - 2.94632i) q^{61} +(8.26513 + 11.2685i) q^{62} +(10.4240 + 8.76217i) q^{63} +(-7.97163 + 0.673167i) q^{64} +(-0.175943 - 0.0252968i) q^{65} +(-0.166604 - 0.774279i) q^{66} +(7.72593 - 2.70369i) q^{67} +(-8.79844 + 9.76226i) q^{68} +(3.72292 + 7.99284i) q^{69} +(-1.34480 + 0.486689i) q^{70} +(6.42349 + 1.88611i) q^{71} +(4.17246 - 7.38855i) q^{72} +(3.67908 - 2.36440i) q^{73} +(0.943714 + 0.527327i) q^{74} +(-1.28387 - 8.47762i) q^{75} +(2.58996 + 3.10959i) q^{76} +(-1.10918 - 0.961113i) q^{77} +(0.687100 - 1.82956i) q^{78} +(-7.51095 + 3.43014i) q^{79} +(0.452171 + 0.767920i) q^{80} +(3.98265 + 8.07084i) q^{81} +(1.14890 - 5.04389i) q^{82} +(-3.13010 - 2.01159i) q^{83} +(-2.05058 - 15.5898i) q^{84} +(1.40466 + 0.412444i) q^{85} +(1.33414 - 5.85717i) q^{86} +(4.12742 - 14.4570i) q^{87} +(-0.461593 + 0.789484i) q^{88} +(2.60242 + 2.25501i) q^{89} +(-0.943146 - 0.0624868i) q^{90} +(-1.02031 - 3.47487i) q^{91} +(3.05854 - 9.71113i) q^{92} +(13.0187 + 11.1109i) q^{93} +(-3.42287 - 16.5087i) q^{94} +(0.187270 - 0.410065i) q^{95} +(-9.31372 + 3.04214i) q^{96} -2.29020 q^{97} +(-13.4706 - 13.7361i) q^{98} +(-0.416143 - 0.876198i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1320 q - 18 q^{4} - 5 q^{6} - 22 q^{9}+O(q^{10}) \) 1320 * q - 18 * q^4 - 5 * q^6 - 22 * q^9	\( 1320 q - 18 q^{4} - 5 q^{6} - 22 q^{9} - 26 q^{10} - 15 q^{12} - 44 q^{13} - 34 q^{16} - 13 q^{18} - 66 q^{21} + 74 q^{22} + 13 q^{24} + 80 q^{25} - 110 q^{28} - 36 q^{30} - 22 q^{33} - 54 q^{34} - 37 q^{36} - 72 q^{37} - 22 q^{40} + q^{42} - 154 q^{45} - 82 q^{46} + 11 q^{48} + 96 q^{49} - 14 q^{52} - 138 q^{54} - 6 q^{57} + 74 q^{58} + 3 q^{60} - 28 q^{61} - 6 q^{64} - 4 q^{66} - 38 q^{69} - 18 q^{70} - 145 q^{72} + 96 q^{73} + 14 q^{76} - 51 q^{78} - 38 q^{81} - 74 q^{82} - 41 q^{84} - 76 q^{85} + 6 q^{88} - 5 q^{90} + 78 q^{93} - 22 q^{94} + 184 q^{96} - 128 q^{97}+O(q^{100}) \) 1320 * q - 18 * q^4 - 5 * q^6 - 22 * q^9 - 26 * q^10 - 15 * q^12 - 44 * q^13 - 34 * q^16 - 13 * q^18 - 66 * q^21 + 74 * q^22 + 13 * q^24 + 80 * q^25 - 110 * q^28 - 36 * q^30 - 22 * q^33 - 54 * q^34 - 37 * q^36 - 72 * q^37 - 22 * q^40 + q^42 - 154 * q^45 - 82 * q^46 + 11 * q^48 + 96 * q^49 - 14 * q^52 - 138 * q^54 - 6 * q^57 + 74 * q^58 + 3 * q^60 - 28 * q^61 - 6 * q^64 - 4 * q^66 - 38 * q^69 - 18 * q^70 - 145 * q^72 + 96 * q^73 + 14 * q^76 - 51 * q^78 - 38 * q^81 - 74 * q^82 - 41 * q^84 - 76 * q^85 + 6 * q^88 - 5 * q^90 + 78 * q^93 - 22 * q^94 + 184 * q^96 - 128 * q^97

Introduction

L-functions

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