LMFDB - Embedded newform 342.2.w.b.175.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(43,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([12, 16]))

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

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

chi := DirichletCharacter("342.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.w (of order $9$, 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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			175.9
Character	$\chi$	$=$	342.175
Dual form			342.2.w.b.43.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(1.30976 - 1.13337i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.578952 - 3.28340i) q^{5} +(1.34359 + 1.09305i) q^{6} -2.91689 q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.430928 - 2.96889i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(1.30976 - 1.13337i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.578952 - 3.28340i) q^{5} +(1.34359 + 1.09305i) q^{6} -2.91689 q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.430928 - 2.96889i) q^{9} +(3.13299 - 1.14031i) q^{10} +(0.596372 - 1.03295i) q^{11} +(-0.843132 + 1.51299i) q^{12} +(0.00363472 + 0.00304989i) q^{13} +(-0.506512 - 2.87257i) q^{14} +(-4.47961 - 3.64429i) q^{15} +(0.766044 - 0.642788i) q^{16} +(3.56643 + 1.29807i) q^{17} +(2.99861 - 0.0911612i) q^{18} +(0.214150 - 4.35364i) q^{19} +(1.66703 + 2.88738i) q^{20} +(-3.82041 + 3.30592i) q^{21} +(1.12081 + 0.407943i) q^{22} +(-0.425303 + 0.154798i) q^{23} +(-1.63641 - 0.567596i) q^{24} +(-5.74708 + 2.09177i) q^{25} +(-0.00237239 + 0.00410911i) q^{26} +(-2.80045 - 4.37693i) q^{27} +(2.74098 - 0.997634i) q^{28} +(5.14205 + 4.31469i) q^{29} +(2.81105 - 5.04438i) q^{30} +(0.792748 + 1.37308i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-0.389612 - 2.02882i) q^{33} +(-0.659049 + 3.73765i) q^{34} +(1.68874 + 9.57731i) q^{35} +(0.610480 + 2.93723i) q^{36} -5.39716 q^{37} +(4.32468 - 0.545104i) q^{38} +(0.00821726 - 0.000124878i) q^{39} +(-2.55403 + 2.14309i) q^{40} +(9.45663 + 3.44193i) q^{41} +(-3.91911 - 3.18830i) q^{42} +(4.99284 + 1.81724i) q^{43} +(-0.207118 + 1.17462i) q^{44} +(-9.99754 + 0.303936i) q^{45} +(-0.226299 - 0.391961i) q^{46} +(-3.64941 - 3.06222i) q^{47} +(0.274814 - 1.71011i) q^{48} +1.50823 q^{49} +(-3.05796 - 5.29654i) q^{50} +(6.14236 - 2.34194i) q^{51} +(-0.00445864 - 0.00162281i) q^{52} +(10.6725 + 8.95526i) q^{53} +(3.82414 - 3.51795i) q^{54} +(-3.73685 - 1.36010i) q^{55} +(1.45844 + 2.52610i) q^{56} +(-4.65381 - 5.94492i) q^{57} +(-3.35623 + 5.81316i) q^{58} +(7.64958 - 6.41876i) q^{59} +(5.45588 + 1.89240i) q^{60} +(0.968146 - 5.49063i) q^{61} +(-1.21456 + 1.01914i) q^{62} +(-1.25697 + 8.65991i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.00790969 - 0.0137000i) q^{65} +(1.93035 - 0.735995i) q^{66} +(-2.40707 + 13.6512i) q^{67} -3.79531 q^{68} +(-0.381600 + 0.684774i) q^{69} +(-9.13856 + 3.32617i) q^{70} +(-10.5032 + 8.81326i) q^{71} +(-2.78660 + 1.11125i) q^{72} +(-2.14772 - 12.1803i) q^{73} +(-0.937208 - 5.31517i) q^{74} +(-5.15653 + 9.25330i) q^{75} +(1.28780 + 4.16432i) q^{76} +(-1.73955 + 3.01299i) q^{77} +(0.00154989 + 0.00807074i) q^{78} +(0.846615 - 0.710395i) q^{79} +(-2.55403 - 2.14309i) q^{80} +(-8.62860 - 2.55875i) q^{81} +(-1.74752 + 9.91065i) q^{82} -5.80965 q^{83} +(2.45932 - 4.41321i) q^{84} +(2.19731 - 12.4615i) q^{85} +(-0.922639 + 5.23255i) q^{86} +(11.6250 - 0.176665i) q^{87} -1.19274 q^{88} +(2.76306 - 15.6701i) q^{89} +(-2.03537 - 9.79288i) q^{90} +(-0.0106021 - 0.00889618i) q^{91} +(0.346710 - 0.290924i) q^{92} +(2.59452 + 0.899921i) q^{93} +(2.38198 - 4.12572i) q^{94} +(-14.4187 + 1.81741i) q^{95} +(1.73185 - 0.0263190i) q^{96} +(2.26795 + 12.8622i) q^{97} +(0.261901 + 1.48531i) q^{98} +(-2.80971 - 2.21569i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 3 q^{3} - 3 q^{6} + 24 q^{7} - 33 q^{8} - 3 q^{9}+O(q^{10}) $ 66 * q - 3 * q^3 - 3 * q^6 + 24 * q^7 - 33 * q^8 - 3 * q^9	$ 66 q - 3 q^{3} - 3 q^{6} + 24 q^{7} - 33 q^{8} - 3 q^{9} - 3 q^{13} - 3 q^{14} - 30 q^{15} + 9 q^{17} + 6 q^{18} - 21 q^{19} + 6 q^{22} - 12 q^{23} + 6 q^{24} + 6 q^{25} + 30 q^{27} - 3 q^{28} + 9 q^{29} + 18 q^{33} - 18 q^{34} - 18 q^{35} - 3 q^{36} + 6 q^{37} + 6 q^{38} + 12 q^{39} + 6 q^{41} + 6 q^{43} - 12 q^{44} - 18 q^{45} - 18 q^{47} - 3 q^{48} + 114 q^{49} - 63 q^{50} - 63 q^{51} - 3 q^{52} - 24 q^{53} + 18 q^{54} + 36 q^{55} - 12 q^{56} - 60 q^{57} - 18 q^{58} + 78 q^{59} - 3 q^{60} - 21 q^{62} - 27 q^{63} - 33 q^{64} - 12 q^{65} + 45 q^{66} - 3 q^{67} + 12 q^{68} - 24 q^{69} - 18 q^{70} - 24 q^{71} - 3 q^{72} - 15 q^{73} - 3 q^{74} + 15 q^{78} + 12 q^{79} - 87 q^{81} + 6 q^{82} - 24 q^{83} - 15 q^{84} + 72 q^{85} - 3 q^{86} + 66 q^{87} + 9 q^{89} - 6 q^{90} + 27 q^{91} + 6 q^{92} - 45 q^{93} - 6 q^{94} - 30 q^{95} + 87 q^{97} + 24 q^{98} - 96 q^{99}+O(q^{100}) $ 66 * q - 3 * q^3 - 3 * q^6 + 24 * q^7 - 33 * q^8 - 3 * q^9 - 3 * q^13 - 3 * q^14 - 30 * q^15 + 9 * q^17 + 6 * q^18 - 21 * q^19 + 6 * q^22 - 12 * q^23 + 6 * q^24 + 6 * q^25 + 30 * q^27 - 3 * q^28 + 9 * q^29 + 18 * q^33 - 18 * q^34 - 18 * q^35 - 3 * q^36 + 6 * q^37 + 6 * q^38 + 12 * q^39 + 6 * q^41 + 6 * q^43 - 12 * q^44 - 18 * q^45 - 18 * q^47 - 3 * q^48 + 114 * q^49 - 63 * q^50 - 63 * q^51 - 3 * q^52 - 24 * q^53 + 18 * q^54 + 36 * q^55 - 12 * q^56 - 60 * q^57 - 18 * q^58 + 78 * q^59 - 3 * q^60 - 21 * q^62 - 27 * q^63 - 33 * q^64 - 12 * q^65 + 45 * q^66 - 3 * q^67 + 12 * q^68 - 24 * q^69 - 18 * q^70 - 24 * q^71 - 3 * q^72 - 15 * q^73 - 3 * q^74 + 15 * q^78 + 12 * q^79 - 87 * q^81 + 6 * q^82 - 24 * q^83 - 15 * q^84 + 72 * q^85 - 3 * q^86 + 66 * q^87 + 9 * q^89 - 6 * q^90 + 27 * q^91 + 6 * q^92 - 45 * q^93 - 6 * q^94 - 30 * q^95 + 87 * q^97 + 24 * q^98 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	1.30976	−	1.13337i	0.756189	−	0.654354i
$3$	1.30976	−	1.13337i	0.756189	−	0.654354i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−0.578952	−	3.28340i	−0.258915	−	1.46838i	−0.785819	−	0.618457i	$-0.787758\pi$
$5$	−0.578952	−	3.28340i	−0.258915	−	1.46838i	0.526903	−	0.849925i	$-0.323353\pi$
$6$	1.34359	+	1.09305i	0.548519	+	0.446236i
$7$	−2.91689			−1.10248			−0.551240	−	0.834347i	$-0.685845\pi$
$7$	−2.91689			−1.10248			−0.551240	+	0.834347i	$0.685845\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	0.430928	−	2.96889i	0.143643	−	0.989630i
$10$	3.13299	−	1.14031i	0.990737	−	0.360599i
$11$	0.596372	−	1.03295i	0.179813	−	0.311445i	−0.762003	−	0.647573i	$-0.775784\pi$
$11$	0.596372	−	1.03295i	0.179813	−	0.311445i	0.941816	+	0.336128i	$0.109117\pi$
$12$	−0.843132	+	1.51299i	−0.243391	+	0.436762i
$13$	0.00363472	+	0.00304989i	0.00100809	+	0.000845887i	0.643292	−	0.765621i	$-0.277568\pi$
$13$	0.00363472	+	0.00304989i	0.00100809	+	0.000845887i	−0.642283	+	0.766467i	$0.722013\pi$
$14$	−0.506512	−	2.87257i	−0.135371	−	0.767727i
$15$	−4.47961	−	3.64429i	−1.15663	−	0.940952i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	3.56643	+	1.29807i	0.864986	+	0.314829i	0.736135	−	0.676835i	$-0.236649\pi$
$17$	3.56643	+	1.29807i	0.864986	+	0.314829i	0.128851	+	0.991664i	$0.458871\pi$
$18$	2.99861	−	0.0911612i	0.706780	−	0.0214869i
$19$	0.214150	−	4.35364i	0.0491294	−	0.998792i
$19$	0.214150	−	4.35364i	0.0491294	−	0.998792i
$20$	1.66703	+	2.88738i	0.372759	+	0.645637i
$21$	−3.82041	+	3.30592i	−0.833682	+	0.721411i
$22$	1.12081	+	0.407943i	0.238958	+	0.0869737i
$23$	−0.425303	+	0.154798i	−0.0886818	+	0.0322775i	−0.385980	−	0.922507i	$-0.626137\pi$
$23$	−0.425303	+	0.154798i	−0.0886818	+	0.0322775i	0.297298	+	0.954785i	$0.403914\pi$
$24$	−1.63641	−	0.567596i	−0.334031	−	0.115860i
$25$	−5.74708	+	2.09177i	−1.14942	+	0.418353i
$26$	−0.00237239	+	0.00410911i	−0.000465265	+	0.000805862i
$27$	−2.80045	−	4.37693i	−0.538947	−	0.842340i
$28$	2.74098	−	0.997634i	0.517996	−	0.188535i
$29$	5.14205	+	4.31469i	0.954854	+	0.801218i	0.980108	−	0.198464i	$-0.0635951\pi$
$29$	5.14205	+	4.31469i	0.954854	+	0.801218i	−0.0252544	+	0.999681i	$0.508040\pi$
$30$	2.81105	−	5.04438i	0.513225	−	0.920973i
$31$	0.792748	+	1.37308i	0.142382	+	0.246612i	0.928393	−	0.371600i	$-0.121191\pi$
$31$	0.792748	+	1.37308i	0.142382	+	0.246612i	−0.786011	+	0.618212i	$0.787857\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	−0.389612	−	2.02882i	−0.0678228	−	0.353173i
$34$	−0.659049	+	3.73765i	−0.113026	+	0.641002i
$35$	1.68874	+	9.57731i	0.285449	+	1.61886i
$36$	0.610480	+	2.93723i	0.101747	+	0.489538i
$37$	−5.39716			−0.887288			−0.443644	−	0.896203i	$-0.646315\pi$
$37$	−5.39716			−0.887288			−0.443644	+	0.896203i	$0.646315\pi$
$38$	4.32468	−	0.545104i	0.701556	−	0.0884276i
$39$	0.00821726		0.000124878i	0.00131582		1.99965e-5i
$40$	−2.55403	+	2.14309i	−0.403828	+	0.338852i
$41$	9.45663	+	3.44193i	1.47688	+	0.537540i	0.949959	−	0.312376i	$-0.101125\pi$
$41$	9.45663	+	3.44193i	1.47688	+	0.537540i	0.526919	+	0.849915i	$0.323347\pi$
$42$	−3.91911	−	3.18830i	−0.604731	−	0.491966i
$43$	4.99284	+	1.81724i	0.761401	+	0.277127i	0.693395	−	0.720558i	$-0.256114\pi$
$43$	4.99284	+	1.81724i	0.761401	+	0.277127i	0.0680058	+	0.997685i	$0.478336\pi$
$44$	−0.207118	+	1.17462i	−0.0312242	+	0.177081i
$45$	−9.99754	+	0.303936i	−1.49035	+	0.0453082i
$46$	−0.226299	−	0.391961i	−0.0333660	−	0.0577915i
$47$	−3.64941	−	3.06222i	−0.532321	−	0.446671i	0.336581	−	0.941655i	$-0.390729\pi$
$47$	−3.64941	−	3.06222i	−0.532321	−	0.446671i	−0.868902	+	0.494984i	$0.835174\pi$
$48$	0.274814	−	1.71011i	0.0396659	−	0.246833i
$49$	1.50823			0.215461
$50$	−3.05796	−	5.29654i	−0.432461	−	0.749044i
$51$	6.14236	−	2.34194i	0.860102	−	0.327937i
$52$	−0.00445864	−	0.00162281i	−0.000618302	−	0.000225044i
$53$	10.6725	+	8.95526i	1.46598	+	1.23010i	0.919775	+	0.392446i	$0.128371\pi$
$53$	10.6725	+	8.95526i	1.46598	+	1.23010i	0.546201	+	0.837654i	$0.316074\pi$
$54$	3.82414	−	3.51795i	0.520399	−	0.478732i
$55$	−3.73685	−	1.36010i	−0.503877	−	0.183396i
$56$	1.45844	+	2.52610i	0.194893	+	0.337564i
$57$	−4.65381	−	5.94492i	−0.616412	−	0.787424i
$58$	−3.35623	+	5.81316i	−0.440695	+	0.763306i
$59$	7.64958	−	6.41876i	0.995891	−	0.835652i	0.00948114	−	0.999955i	$-0.496982\pi$
$59$	7.64958	−	6.41876i	0.995891	−	0.835652i	0.986410	+	0.164303i	$0.0525376\pi$
$60$	5.45588	+	1.89240i	0.704351	+	0.244307i
$61$	0.968146	−	5.49063i	0.123958	−	0.703003i	−0.857963	−	0.513712i	$-0.828270\pi$
$61$	0.968146	−	5.49063i	0.123958	−	0.703003i	0.981921	−	0.189291i	$-0.0606189\pi$
$62$	−1.21456	+	1.01914i	−0.154249	+	0.129430i
$63$	−1.25697	+	8.65991i	−0.158363	+	1.09105i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.00790969	−	0.0137000i	0.000981076	−	0.00169927i
$66$	1.93035	−	0.735995i	0.237609	−	0.0905947i
$67$	−2.40707	+	13.6512i	−0.294071	+	1.66776i	0.376886	+	0.926260i	$0.376995\pi$
$67$	−2.40707	+	13.6512i	−0.294071	+	1.66776i	−0.670956	+	0.741497i	$0.734116\pi$
$68$	−3.79531			−0.460249
$69$	−0.381600	+	0.684774i	−0.0459392	+	0.0824371i
$70$	−9.13856	+	3.32617i	−1.09227	+	0.397553i
$71$	−10.5032	+	8.81326i	−1.24650	+	1.04594i	−0.249517	+	0.968370i	$0.580272\pi$
$71$	−10.5032	+	8.81326i	−1.24650	+	1.04594i	−0.996987	+	0.0775709i	$0.975284\pi$
$72$	−2.78660	+	1.11125i	−0.328404	+	0.130962i
$73$	−2.14772	−	12.1803i	−0.251371	−	1.42560i	−0.805219	−	0.592978i	$-0.797952\pi$
$73$	−2.14772	−	12.1803i	−0.251371	−	1.42560i	0.553848	−	0.832618i	$-0.313159\pi$
$74$	−0.937208	−	5.31517i	−0.108948	−	0.617876i
$75$	−5.15653	+	9.25330i	−0.595425	+	1.06848i
$76$	1.28780	+	4.16432i	0.147720	+	0.477681i
$77$	−1.73955	+	3.01299i	−0.198240	+	0.343362i
$78$	0.00154989	+	0.00807074i	0.000175491	+	0.000913831i
$79$	0.846615	−	0.710395i	0.0952517	−	0.0799256i	−0.593918	−	0.804525i	$-0.702420\pi$
$79$	0.846615	−	0.710395i	0.0952517	−	0.0799256i	0.689170	+	0.724600i	$0.257975\pi$
$80$	−2.55403	−	2.14309i	−0.285550	−	0.239605i
$81$	−8.62860	−	2.55875i	−0.958734	−	0.284306i
$82$	−1.74752	+	9.91065i	−0.192981	+	1.09445i
$83$	−5.80965			−0.637692			−0.318846	−	0.947807i	$-0.603295\pi$
$83$	−5.80965			−0.637692			−0.318846	+	0.947807i	$0.603295\pi$
$84$	2.45932	−	4.41321i	0.268334	−	0.481521i
$85$	2.19731	−	12.4615i	0.238331	−	1.35164i
$86$	−0.922639	+	5.23255i	−0.0994907	+	0.564240i
$87$	11.6250	−	0.176665i	1.24633	−	0.0189405i
$88$	−1.19274			−0.127147
$89$	2.76306	−	15.6701i	0.292884	−	1.66103i	−0.382798	−	0.923832i	$-0.625039\pi$
$89$	2.76306	−	15.6701i	0.292884	−	1.66103i	0.675681	−	0.737194i	$-0.263850\pi$
$90$	−2.03537	−	9.79288i	−0.214547	−	1.03226i
$91$	−0.0106021	−	0.00889618i	−0.00111140	−	0.000932573i
$92$	0.346710	−	0.290924i	0.0361470	−	0.0303310i
$93$	2.59452	+	0.899921i	0.269039	+	0.0933174i
$94$	2.38198	−	4.12572i	0.245683	−	0.425535i
$95$	−14.4187	+	1.81741i	−1.47933	+	0.186462i
$96$	1.73185	−	0.0263190i	0.176756	−	0.00268617i
$97$	2.26795	+	12.8622i	0.230276	+	1.30596i	0.852338	+	0.522991i	$0.175184\pi$
$97$	2.26795	+	12.8622i	0.230276	+	1.30596i	−0.622062	+	0.782968i	$0.713705\pi$
$98$	0.261901	+	1.48531i	0.0264560	+	0.150039i
$99$	−2.80971	−	2.21569i	−0.282387	−	0.222685i
$100$	4.68506	−	3.93124i	0.468506	−	0.393124i
$101$	0.548448	−	0.199619i	0.0545727	−	0.0198628i	−0.314590	−	0.949228i	$-0.601867\pi$
$101$	0.548448	−	0.199619i	0.0545727	−	0.0198628i	0.369162	+	0.929365i	$0.379645\pi$
$102$	3.37297	+	5.64237i	0.333973	+	0.558678i
$103$	−4.62935			−0.456143			−0.228072	−	0.973644i	$-0.573242\pi$
$103$	−4.62935			−0.456143			−0.228072	+	0.973644i	$0.573242\pi$
$104$	0.000823924	−	0.00467270i	8.07924e−5	−	0.000458196i
$105$	13.0665	+	10.6300i	1.27516	+	1.03738i
$106$	−6.96596	+	12.0654i	−0.676594	+	1.17189i
$107$	6.59028	−	11.4147i	0.637107	−	1.10350i	−0.348958	−	0.937138i	$-0.613464\pi$
$107$	6.59028	−	11.4147i	0.637107	−	1.10350i	0.986065	−	0.166363i	$-0.0532022\pi$
$108$	4.12856	+	3.15515i	0.397271	+	0.303605i
$109$	−7.27648	+	6.10569i	−0.696960	+	0.584819i	−0.920907	−	0.389782i	$-0.872550\pi$
$109$	−7.27648	+	6.10569i	−0.696960	+	0.584819i	0.223947	+	0.974601i	$0.428106\pi$
$110$	0.690543	−	3.91626i	0.0658406	−	0.373401i
$111$	−7.06897	+	6.11700i	−0.670957	+	0.580600i
$112$	−2.23446	+	1.87494i	−0.211137	+	0.177165i
$113$	2.53769	−	4.39541i	0.238726	−	0.413485i	−0.721623	−	0.692286i	$-0.756604\pi$
$113$	2.53769	−	4.39541i	0.238726	−	0.413485i	0.960349	+	0.278801i	$0.0899370\pi$
$114$	5.04647	−	5.61543i	0.472646	−	0.525934i
$115$	0.754493	+	1.30682i	0.0703568	+	0.121862i
$116$	−6.30765	−	2.29580i	−0.585651	−	0.213159i
$117$	0.0106211	−	0.00947679i	0.000981920	−	0.000876130i
$118$	7.64958	+	6.41876i	0.704201	+	0.590895i
$119$	−10.4029	−	3.78633i	−0.953629	−	0.347093i
$120$	−0.916243	+	5.70160i	−0.0836412	+	0.520483i
$121$	4.78868	+	8.29424i	0.435335	+	0.754022i
$122$	5.57533			0.504767
$123$	16.2869	−	6.20980i	1.46854	−	0.559919i
$124$	−1.21456	−	1.01914i	−0.109071	−	0.0915212i
$125$	1.86026	+	3.22207i	0.166387	+	0.288191i
$126$	−8.74662	+	0.265907i	−0.779211	+	0.0236889i
$127$	0.137775	−	0.781361i	0.0122256	−	0.0693346i	−0.978085	−	0.208208i	$-0.933237\pi$
$127$	0.137775	−	0.781361i	0.0122256	−	0.0693346i	0.990310	+	0.138873i	$0.0443481\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	8.59902	−	3.27860i	0.757102	−	0.288665i
$130$	0.0148654	+	0.00541055i	0.00130378	+	0.000474536i
$131$	−11.6303	+	9.75899i	−1.01614	+	0.852647i	−0.989138	−	0.146988i	$-0.953042\pi$
$131$	−11.6303	+	9.75899i	−1.01614	+	0.852647i	−0.0270067	+	0.999635i	$0.508598\pi$
$132$	1.06001	+	1.77321i	0.0922624	+	0.154339i
$133$	−0.624651	+	12.6991i	−0.0541641	+	1.10115i
$134$	−13.8618			−1.19747
$135$	−12.7499	+	11.7290i	−1.09733	+	1.00947i
$136$	−0.659049	−	3.73765i	−0.0565130	−	0.320501i
$137$	0.908803	−	5.15408i	0.0776443	−	0.440343i	−0.921059	−	0.389424i	$-0.872674\pi$
$137$	0.908803	−	5.15408i	0.0776443	−	0.440343i	0.998703	−	0.0509184i	$-0.0162148\pi$
$138$	−0.740635	−	0.256893i	−0.0630471	−	0.0218682i
$139$	−0.494806	−	0.415191i	−0.0419689	−	0.0352161i	0.621562	−	0.783365i	$-0.286498\pi$
$139$	−0.494806	−	0.415191i	−0.0419689	−	0.0352161i	−0.663531	+	0.748149i	$0.730943\pi$
$140$	−4.86253	−	8.42215i	−0.410959	−	0.711801i
$141$	−8.25048	+	0.125383i	−0.694816	+	0.0105591i
$142$	−10.5032	−	8.81326i	−0.881412	−	0.739592i
$143$	0.00531802	−	0.00193560i	0.000444715	−	0.000161863i
$144$	−1.57826	−	2.55130i	−0.131521	−	0.212608i
$145$	11.1899	−	19.3814i	0.929267	−	1.60954i
$146$	11.6223	−	4.23017i	0.961869	−	0.350092i
$147$	1.97541	−	1.70938i	0.162929	−	0.140988i
$148$	5.07168	−	1.84594i	0.416889	−	0.151735i
$149$	20.7013	+	7.53465i	1.69592	+	0.617263i	0.995350	−	0.0963255i	$-0.0307090\pi$
$149$	20.7013	+	7.53465i	1.69592	+	0.617263i	0.700565	+	0.713588i	$0.252931\pi$
$150$	−10.0081	−	3.47137i	−0.817161	−	0.283436i
$151$	−8.93629	−	15.4781i	−0.727225	−	1.25959i	−0.958052	−	0.286596i	$-0.907476\pi$
$151$	−8.93629	−	15.4781i	−0.727225	−	1.25959i	0.230826	−	0.972995i	$-0.425857\pi$
$152$	−3.87743	+	1.99136i	−0.314501	+	0.161520i
$153$	5.39071	−	10.0290i	0.435813	−	0.810793i
$154$	−3.26929	−	1.18992i	−0.263447	−	0.0958867i
$155$	4.04941	−	3.39786i	0.325256	−	0.272922i
$156$	−0.00767899	+	0.00292782i	−0.000614811	+	0.000234413i
$157$	1.97473	+	11.1992i	0.157601	+	0.893797i	0.956370	+	0.292159i	$0.0943738\pi$
$157$	1.97473	+	11.1992i	0.157601	+	0.893797i	−0.798769	+	0.601638i	$0.794515\pi$
$158$	0.846615	+	0.710395i	0.0673531	+	0.0565160i
$159$	24.1280	−	0.366674i	1.91347	−	0.0290792i
$160$	1.66703	−	2.88738i	0.131790	−	0.228267i
$161$	1.24056	−	0.451527i	0.0977698	−	0.0355853i
$162$	1.02154	−	8.94184i	0.0802597	−	0.702537i
$163$	3.68962	+	6.39061i	0.288993	+	0.500551i	0.973570	−	0.228390i	$-0.0733461\pi$
$163$	3.68962	+	6.39061i	0.288993	+	0.500551i	−0.684576	+	0.728941i	$0.740013\pi$
$164$	−10.0635			−0.785830
$165$	−6.43588	+	2.45385i	−0.501032	+	0.191032i
$166$	−1.00883	−	5.72139i	−0.0783008	−	0.444066i
$167$	5.04558	−	1.83644i	0.390439	−	0.142108i	−0.139339	−	0.990245i	$-0.544498\pi$
$167$	5.04558	−	1.83644i	0.390439	−	0.142108i	0.529777	+	0.848137i	$0.322275\pi$
$168$	4.77322	+	1.65561i	0.368262	+	0.127733i
$169$	−2.25742	−	12.8025i	−0.173648	−	0.984806i
$170$	12.6538			0.970501
$171$	−12.8332	−	2.51189i	−0.981378	−	0.192089i
$172$	−5.31327			−0.405133
$173$	−0.533469	−	3.02545i	−0.0405589	−	0.230021i	0.957790	−	0.287470i	$-0.0928143\pi$
$173$	−0.533469	−	3.02545i	−0.0405589	−	0.230021i	−0.998348	+	0.0574495i	$0.981703\pi$
$174$	2.19264	+	11.4177i	0.166224	+	0.865574i
$175$	16.7636	−	6.10145i	1.26721	−	0.461226i
$176$	−0.207118	−	1.17462i	−0.0156121	−	0.0885407i
$177$	2.74424	−	17.0769i	0.206270	−	1.28358i
$178$	15.9118			1.19264
$179$	2.39582	+	4.14968i	0.179072	+	0.310161i	0.941563	−	0.336837i	$-0.109357\pi$
$179$	2.39582	+	4.14968i	0.179072	+	0.310161i	−0.762491	+	0.646999i	$0.776024\pi$
$180$	9.29067	−	3.70497i	0.692485	−	0.276152i
$181$	21.4978	−	7.82456i	1.59792	−	0.581595i	0.618919	−	0.785455i	$-0.287571\pi$
$181$	21.4978	−	7.82456i	1.59792	−	0.581595i	0.979000	+	0.203860i	$0.0653489\pi$
$182$	0.00692000	−	0.0119858i	0.000512945	−	0.000888446i
$183$	−4.95490	−	8.28866i	−0.366277	−	0.612716i
$184$	0.346710	+	0.290924i	0.0255598	+	0.0214472i
$185$	3.12470	+	17.7211i	0.229733	+	1.30288i
$186$	−0.435716	+	2.71137i	−0.0319482	+	0.198807i
$187$	3.46776	−	2.90980i	0.253588	−	0.212785i
$188$	4.47667	+	1.62937i	0.326494	+	0.118834i
$189$	8.16859	+	12.7670i	0.594178	+	0.928662i
$190$	−4.29358	−	13.8841i	−0.311489	−	1.00726i
$191$	0.386012	+	0.668592i	0.0279308	+	0.0483776i	0.879653	−	0.475616i	$-0.157775\pi$
$191$	0.386012	+	0.668592i	0.0279308	+	0.0483776i	−0.851722	+	0.523994i	$0.824442\pi$
$192$	0.326652	+	1.70097i	0.0235741	+	0.122757i
$193$	12.4483	+	4.53082i	0.896050	+	0.326135i	0.748669	−	0.662944i	$-0.230693\pi$
$193$	12.4483	+	4.53082i	0.896050	+	0.326135i	0.147381	+	0.989080i	$0.452916\pi$
$194$	−12.2730	+	4.46700i	−0.881148	+	0.320712i
$195$	−0.00516743	−	0.0269083i	−0.000370047	−	0.00192694i
$196$	−1.41727	+	0.515843i	−0.101233	+	0.0368460i
$197$	5.88953	−	10.2010i	0.419612	−	0.726789i	−0.576288	−	0.817246i	$-0.695500\pi$
$197$	5.88953	−	10.2010i	0.419612	−	0.726789i	0.995900	+	0.0904573i	$0.0288329\pi$
$198$	1.69413	−	3.15178i	0.120396	−	0.223987i
$199$	19.2688	−	7.01326i	1.36593	−	0.497157i	0.448045	−	0.894011i	$-0.352120\pi$
$199$	19.2688	−	7.01326i	1.36593	−	0.497157i	0.917882	+	0.396855i	$0.129898\pi$
$200$	4.68506	+	3.93124i	0.331284	+	0.277980i
$201$	12.3192	+	20.6078i	0.868930	+	1.45356i
$202$	0.291823	+	0.505453i	0.0205326	+	0.0355635i
$203$	−14.9988	−	12.5855i	−1.05271	−	0.883326i
$204$	−4.97094	+	4.30151i	−0.348035	+	0.301166i
$205$	5.82631	−	33.0426i	0.406927	−	2.30780i
$206$	−0.803878	−	4.55902i	−0.0560088	−	0.317642i
$207$	0.276302	+	1.32938i	0.0192043	+	0.0923985i
$208$	0.00474479			0.000328992
$209$	−4.36936	−	2.81759i	−0.302235	−	0.194897i
$210$	−8.19951	+	14.7139i	−0.565820	+	1.01535i
$211$	−3.44121	+	2.88752i	−0.236903	+	0.198785i	−0.753508	−	0.657439i	$-0.771640\pi$
$211$	−3.44121	+	2.88752i	−0.236903	+	0.198785i	0.516605	+	0.856224i	$0.327195\pi$
$212$	−13.0917	−	4.76500i	−0.899143	−	0.327261i
$213$	−3.76797	+	23.4473i	−0.258177	+	1.60658i
$214$	12.3857	+	4.50802i	0.846668	+	0.308162i
$215$	3.07613	−	17.4456i	0.209790	−	1.18978i
$216$	−2.39030	+	4.61372i	−0.162640	+	0.313924i
$217$	−2.31235	−	4.00512i	−0.156973	−	0.271885i
$218$	−7.27648	−	6.10569i	−0.492825	−	0.413530i
$219$	−16.6178	−	13.5191i	−1.12293	−	0.913534i
$220$	3.97668			0.268107
$221$	0.00900398	+	0.0155953i	0.000605673	+	0.00104906i
$222$	−7.25159	−	5.89937i	−0.486695	−	0.395940i
$223$	−23.9587	−	8.72026i	−1.60439	−	0.583952i	−0.624073	−	0.781366i	$-0.714523\pi$
$223$	−23.9587	−	8.72026i	−1.60439	−	0.583952i	−0.980320	+	0.197414i	$0.936746\pi$
$224$	−2.23446	−	1.87494i	−0.149296	−	0.125275i
$225$	3.73365	+	17.9638i	0.248910	+	1.19759i
$226$	4.76930	+	1.73588i	0.317249	+	0.115469i
$227$	11.3329	+	19.6292i	0.752192	+	1.30283i	0.946758	+	0.321945i	$0.104337\pi$
$227$	11.3329	+	19.6292i	0.752192	+	1.30283i	−0.194567	+	0.980889i	$0.562330\pi$
$228$	6.40643	+	3.99470i	0.424276	+	0.264555i
$229$	−8.71577	+	15.0961i	−0.575954	+	0.997582i	0.419983	+	0.907532i	$0.362036\pi$
$229$	−8.71577	+	15.0961i	−0.575954	+	0.997582i	−0.995937	+	0.0900497i	$0.971297\pi$
$230$	−1.15595	+	0.969957i	−0.0762211	+	0.0639571i
$231$	1.13646	+	5.91785i	0.0747733	+	0.389366i
$232$	1.16561	−	6.61049i	0.0765259	−	0.434000i
$233$	−6.88576	+	5.77784i	−0.451101	+	0.378519i	−0.839844	−	0.542827i	$-0.817354\pi$
$233$	−6.88576	+	5.77784i	−0.451101	+	0.378519i	0.388743	+	0.921346i	$0.372909\pi$
$234$	0.0111771	+	0.00881410i	0.000730673	+	0.000576196i
$235$	−7.94166	+	13.7554i	−0.518057	+	0.897301i
$236$	−4.99291	+	8.64798i	−0.325011	+	0.562935i
$237$	0.303718	−	1.88998i	0.0197286	−	0.122767i
$238$	1.92237	−	10.9023i	0.124609	−	0.706692i
$239$	−2.89804			−0.187458			−0.0937292	−	0.995598i	$-0.529879\pi$
$239$	−2.89804			−0.187458			−0.0937292	+	0.995598i	$0.529879\pi$
$240$	−5.77408	+	0.0877490i	−0.372716	+	0.00566417i
$241$	−10.5203	+	3.82906i	−0.677669	+	0.246651i	−0.657846	−	0.753152i	$-0.728532\pi$
$241$	−10.5203	+	3.82906i	−0.677669	+	0.246651i	−0.0198226	+	0.999804i	$0.506310\pi$
$242$	−7.33668	+	6.15621i	−0.471620	+	0.395736i
$243$	−14.2014	+	6.42809i	−0.911020	+	0.412362i
$244$	0.968146	+	5.49063i	0.0619792	+	0.351502i
$245$	−0.873191	−	4.95211i	−0.0557861	−	0.316379i
$246$	8.94365	+	14.9611i	0.570226	+	0.953887i
$247$	0.0140565	−	0.0151711i	0.000894393	−	0.000965314i
$248$	0.792748	−	1.37308i	0.0503395	−	0.0871906i
$249$	−7.60923	+	6.58450i	−0.482215	+	0.417276i
$250$	−2.85009	+	2.39151i	−0.180255	+	0.151252i
$251$	−0.254833	−	0.213830i	−0.0160849	−	0.0134968i	0.634710	−	0.772751i	$-0.281120\pi$
$251$	−0.254833	−	0.213830i	−0.0160849	−	0.0134968i	−0.650795	+	0.759254i	$0.725564\pi$
$252$	−1.78070	−	8.56756i	−0.112174	−	0.539706i
$253$	−0.0937412	+	0.531633i	−0.00589346	+	0.0334235i
$254$	0.793415			0.0497833
$255$	−11.2456	−	18.8120i	−0.704230	−	1.17805i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−1.38025	+	7.82779i	−0.0860976	+	0.488284i	0.911017	+	0.412369i	$0.135299\pi$
$257$	−1.38025	+	7.82779i	−0.0860976	+	0.488284i	−0.997114	+	0.0759145i	$0.975812\pi$
$258$	4.72200	+	7.89906i	0.293979	+	0.491774i
$259$	15.7429			0.978217
$260$	−0.00274701	+	0.0155790i	−0.000170362	+	0.000966171i
$261$	15.0257	−	13.4068i	0.930066	−	0.829863i
$262$	−11.6303	−	9.75899i	−0.718523	−	0.602912i
$263$	−21.0892	+	17.6959i	−1.30041	+	1.09118i	−0.310341	+	0.950625i	$0.600443\pi$
$263$	−21.0892	+	17.6959i	−1.30041	+	1.09118i	−0.990073	+	0.140552i	$0.955112\pi$
$264$	−1.56221	+	1.35183i	−0.0961471	+	0.0831991i
$265$	23.2249	−	40.2267i	1.42669	−	2.47110i
$266$	−12.6146	+	1.59001i	−0.773451	+	0.0974896i
$267$	−14.1411	−	23.6556i	−0.865423	−	1.44770i
$268$	−2.40707	−	13.6512i	−0.147035	−	0.833878i
$269$	−0.863147	−	4.89515i	−0.0526270	−	0.298463i	0.947122	−	0.320874i	$-0.103977\pi$
$269$	−0.863147	−	4.89515i	−0.0526270	−	0.298463i	−0.999749	+	0.0224116i	$0.992866\pi$
$270$	−13.7648	−	10.5195i	−0.837701	−	0.640194i
$271$	−8.90460	+	7.47184i	−0.540916	+	0.453882i	−0.871851	−	0.489771i	$-0.837080\pi$
$271$	−8.90460	+	7.47184i	−0.540916	+	0.453882i	0.330935	+	0.943653i	$0.392636\pi$
$272$	3.56643	−	1.29807i	0.216246	−	0.0787073i
$273$	−0.0239688		0.000364255i	−0.00145066		2.20457e-5i
$274$	5.23359			0.316173
$275$	−1.26672	+	7.18390i	−0.0763859	+	0.433206i
$276$	0.124380	−	0.773992i	0.00748680	−	0.0465889i
$277$	−12.4033	+	21.4832i	−0.745242	+	1.29080i	0.204839	+	0.978796i	$0.434333\pi$
$277$	−12.4033	+	21.4832i	−0.745242	+	1.29080i	−0.950081	+	0.312002i	$0.899000\pi$
$278$	0.322961	−	0.559386i	0.0193699	−	0.0335497i
$279$	4.41814	−	1.76188i	0.264507	−	0.105481i
$280$	7.44983	−	6.25115i	0.445212	−	0.373577i
$281$	−0.0960820	+	0.544908i	−0.00573177	+	0.0325065i	−0.987540	−	0.157371i	$-0.949698\pi$
$281$	−0.0960820	+	0.544908i	−0.00573177	+	0.0325065i	0.981808	+	0.189878i	$0.0608092\pi$
$282$	−1.55616	−	8.10337i	−0.0926679	−	0.482548i
$283$	−14.1922	+	11.9086i	−0.843637	+	0.707895i	−0.958379	−	0.285500i	$-0.907840\pi$
$283$	−14.1922	+	11.9086i	−0.843637	+	0.707895i	0.114742	+	0.993395i	$0.463396\pi$
$284$	6.85550	−	11.8741i	0.406799	−	0.704596i
$285$	−16.8252	+	18.7222i	−0.996640	+	1.10900i
$286$	0.00282966	+	0.00490112i	0.000167321	+	0.000289809i
$287$	−27.5839	−	10.0397i	−1.62823	−	0.592626i
$288$	2.23847	−	1.99731i	0.131903	−	0.117692i
$289$	−1.98834	−	1.66841i	−0.116961	−	0.0981420i
$290$	21.0301	+	7.65431i	1.23493	+	0.449477i
$291$	17.5481	+	14.2759i	1.02869	+	0.836869i
$292$	6.18410	+	10.7112i	0.361897	+	0.626824i
$293$	2.74176			0.160175			0.0800877	−	0.996788i	$-0.474480\pi$
$293$	2.74176			0.160175			0.0800877	+	0.996788i	$0.474480\pi$
$294$	2.02644	+	1.64857i	0.118184	+	0.0961464i
$295$	−25.5041	−	21.4005i	−1.48491	−	1.24599i
$296$	2.69858	+	4.67408i	0.156852	+	0.271675i
$297$	−6.19125	+	0.282440i	−0.359253	+	0.0163888i
$298$	−3.82544	+	21.6952i	−0.221602	+	1.25677i
$299$	−0.00201797		0.000734482i	−0.000116702		4.24762e-5i
$300$	1.68074	−	10.4589i	0.0970374	−	0.603844i
$301$	−14.5635	−	5.30070i	−0.839429	−	0.305527i
$302$	13.6912	−	11.4883i	0.787840	−	0.661076i
$303$	0.492091	−	0.883049i	0.0282699	−	0.0507299i
$304$	−2.63441	−	3.47273i	−0.151094	−	0.199175i
$305$	−18.5885			−1.06437
$306$	10.8127	+	3.56730i	0.618120	+	0.203929i
$307$	3.13719	+	17.7919i	0.179049	+	1.01544i	0.933366	+	0.358927i	$0.116857\pi$
$307$	3.13719	+	17.7919i	0.179049	+	1.01544i	−0.754317	+	0.656511i	$0.772032\pi$
$308$	0.604140	−	3.42625i	0.0344240	−	0.195228i
$309$	−6.06332	+	5.24678i	−0.344930	+	0.298479i
$310$	4.04941	+	3.39786i	0.229991	+	0.192985i
$311$	11.3350	+	19.6328i	0.642749	+	1.11327i	0.984817	+	0.173598i	$0.0555393\pi$
$311$	11.3350	+	19.6328i	0.642749	+	1.11327i	−0.342068	+	0.939675i	$0.611127\pi$
$312$	−0.00421678	−	0.00705392i	−0.000238728	−	0.000399350i
$313$	24.7587	+	20.7750i	1.39945	+	1.17428i	0.961344	+	0.275350i	$0.0887938\pi$
$313$	24.7587	+	20.7750i	1.39945	+	1.17428i	0.438103	+	0.898925i	$0.355651\pi$
$314$	−10.6862	+	3.88946i	−0.603057	+	0.219495i
$315$	29.1617	−	0.886548i	1.64308	−	0.0499513i
$316$	−0.552589	+	0.957112i	−0.0310856	+	0.0538418i
$317$	−11.7148	+	4.26383i	−0.657968	+	0.239481i	−0.649359	−	0.760482i	$-0.724963\pi$
$317$	−11.7148	+	4.26383i	−0.657968	+	0.239481i	−0.00860901	+	0.999963i	$0.502740\pi$
$318$	4.55089	+	23.6978i	0.255201	+	1.32890i
$319$	7.52342	−	2.73830i	0.421231	−	0.153315i
$320$	3.13299	+	1.14031i	0.175139	+	0.0637455i
$321$	−4.30546	−	22.4197i	−0.240307	−	1.25135i
$322$	0.660088	+	1.14331i	0.0367853	+	0.0637140i
$323$	6.41509	−	15.2489i	0.356945	−	0.848474i
$324$	8.98338	−	0.546715i	0.499077	−	0.0303730i
$325$	−0.0272687	−	0.00992499i	−0.00151259	−	0.000550539i
$326$	−5.65283	+	4.74329i	−0.313081	+	0.262706i
$327$	−2.61039	+	16.2439i	−0.144355	+	0.898292i
$328$	−1.74752	−	9.91065i	−0.0964904	−	0.547224i
$329$	10.6449	+	8.93215i	0.586873	+	0.492445i
$330$	−3.53415	−	5.91199i	−0.194548	−	0.325445i
$331$	−5.87890	+	10.1826i	−0.323133	+	0.559684i	−0.981133	−	0.193335i	$-0.938070\pi$
$331$	−5.87890	+	10.1826i	−0.323133	+	0.559684i	0.657999	+	0.753018i	$0.271403\pi$
$332$	5.45928	−	1.98702i	0.299617	−	0.109052i
$333$	−2.32579	+	16.0236i	−0.127452	+	0.878087i
$334$	2.68470	+	4.65003i	0.146900	+	0.254438i
$335$	46.2159			2.52504
$336$	−0.801600	+	4.98820i	−0.0437309	+	0.272128i
$337$	2.38880	+	13.5475i	0.130126	+	0.737981i	0.978130	+	0.207992i	$0.0666929\pi$
$337$	2.38880	+	13.5475i	0.130126	+	0.737981i	−0.848004	+	0.529989i	$0.822196\pi$
$338$	12.2160	−	4.44625i	0.664462	−	0.241844i
$339$	−1.65788	−	8.63306i	−0.0900438	−	0.468884i
$340$	2.19731	+	12.4615i	0.119166	+	0.675822i
$341$	1.89109			0.102408
$342$	0.245271	−	13.0744i	0.0132627	−	0.706982i
$343$	16.0189			0.864938
$344$	−0.922639	−	5.23255i	−0.0497454	−	0.282120i
$345$	2.46932	+	0.856494i	0.132944	+	0.0461121i
$346$	2.88685	−	1.05073i	0.155198	−	0.0564875i
$347$	−5.47495	−	31.0500i	−0.293911	−	1.66685i	−0.671597	−	0.740917i	$-0.734391\pi$
$347$	−5.47495	−	31.0500i	−0.293911	−	1.66685i	0.377686	−	0.925934i	$-0.376720\pi$
$348$	−10.8635	+	4.14199i	−0.582344	+	0.222034i
$349$	−12.7017			−0.679907			−0.339953	−	0.940442i	$-0.610411\pi$
$349$	−12.7017			−0.679907			−0.339953	+	0.940442i	$0.610411\pi$
$350$	8.91972	+	15.4494i	0.476779	+	0.825805i
$351$	0.00317030	−	0.0244500i	0.000169218	−	0.00130504i
$352$	1.12081	−	0.407943i	0.0597396	−	0.0217434i
$353$	0.199421	−	0.345407i	0.0106141	−	0.0183842i	−0.860670	−	0.509164i	$-0.829955\pi$
$353$	0.199421	−	0.345407i	0.0106141	−	0.0183842i	0.871284	+	0.490780i	$0.163288\pi$
$354$	17.2940	−	0.262817i	0.919163	−	0.0139686i
$355$	35.0183	+	29.3839i	1.85858	+	1.55953i
$356$	2.76306	+	15.6701i	0.146442	+	0.830513i
$357$	−17.9166	+	6.83116i	−0.948245	+	0.361543i
$358$	−3.67061	+	3.08000i	−0.193998	+	0.162783i
$359$	0.137417	+	0.0500158i	0.00725261	+	0.00263974i	0.345644	−	0.938366i	$-0.387661\pi$
$359$	0.137417	+	0.0500158i	0.00725261	+	0.00263974i	−0.338391	+	0.941005i	$0.609883\pi$
$360$	5.26199	+	8.50616i	0.277331	+	0.448314i
$361$	−18.9083	−	1.86466i	−0.995173	−	0.0981401i
$362$	11.4387	+	19.8125i	0.601207	+	1.04132i
$363$	15.6725	+	5.43607i	0.822592	+	0.285320i
$364$	0.0130054	+	0.00473356i	0.000681666	+	0.000248106i
$365$	−38.7494	+	14.1036i	−2.02824	+	0.738217i
$366$	7.30233	−	6.31893i	0.381699	−	0.330296i
$367$	7.01907	−	2.55473i	0.366392	−	0.133356i	−0.152262	−	0.988340i	$-0.548656\pi$
$367$	7.01907	−	2.55473i	0.366392	−	0.133356i	0.518654	+	0.854984i	$0.326433\pi$
$368$	−0.226299	+	0.391961i	−0.0117966	+	0.0204324i
$369$	14.2938	−	26.5925i	0.744108	−	1.38435i
$370$	−16.9092	+	6.15446i	−0.879070	+	0.319955i
$371$	−31.1304	−	26.1215i	−1.61621	−	1.35616i
$372$	−2.74584	+	0.0417287i	−0.142365	+	0.00216353i
$373$	−16.7100	−	28.9426i	−0.865212	−	1.49859i	−0.866836	−	0.498593i	$-0.833850\pi$
$373$	−16.7100	−	28.9426i	−0.865212	−	1.49859i	0.00162407	−	0.999999i	$-0.499483\pi$
$374$	3.46776	+	2.90980i	0.179314	+	0.150462i
$375$	6.08830	+	2.11176i	0.314398	+	0.109051i
$376$	−0.827254	+	4.69159i	−0.0426624	+	0.241950i
$377$	0.00553056	+	0.0313654i	0.000284838	+	0.00161540i
$378$	−11.1546	+	10.2615i	−0.573729	+	0.527793i
$379$	−8.42698			−0.432865			−0.216432	−	0.976298i	$-0.569442\pi$
$379$	−8.42698			−0.432865			−0.216432	+	0.976298i	$0.569442\pi$
$380$	12.9276	−	6.63930i	0.663171	−	0.340589i
$381$	−0.705122	−	1.17954i	−0.0361245	−	0.0604299i
$382$	−0.591404	+	0.496247i	−0.0302589	+	0.0253902i
$383$	−2.04843	−	0.745569i	−0.104670	−	0.0380968i	0.289154	−	0.957283i	$-0.406626\pi$
$383$	−2.04843	−	0.745569i	−0.104670	−	0.0380968i	−0.393824	+	0.919186i	$0.628848\pi$
$384$	−1.61841	+	0.617060i	−0.0825889	+	0.0314892i
$385$	10.9000	+	3.96727i	0.555514	+	0.202191i
$386$	−2.30036	+	13.0460i	−0.117085	+	0.664022i
$387$	7.54675	−	14.0401i	0.383623	−	0.713697i
$388$	−6.53031	−	11.3108i	−0.331526	−	0.574220i
$389$	−20.7690	−	17.4272i	−1.05303	−	0.883595i	−0.0596192	−	0.998221i	$-0.518989\pi$
$389$	−20.7690	−	17.4272i	−1.05303	−	0.883595i	−0.993409	+	0.114626i	$0.963433\pi$
$390$	0.0256022	−	0.00976150i	0.00129642	−	0.000494293i
$391$	−1.71775			−0.0868704
$392$	−0.754113	−	1.30616i	−0.0380884	−	0.0659711i
$393$	−4.17230	+	25.9634i	−0.210465	+	1.30968i
$394$	11.0687	+	4.02868i	0.557633	+	0.202962i
$395$	−2.82266	−	2.36849i	−0.142023	−	0.119172i
$396$	3.39808	+	1.12109i	0.170760	+	0.0563368i
$397$	−12.9327	−	4.70713i	−0.649075	−	0.236244i	−0.00356245	−	0.999994i	$-0.501134\pi$
$397$	−12.9327	−	4.70713i	−0.649075	−	0.236244i	−0.645513	+	0.763750i	$0.723356\pi$
$398$	10.2527	+	17.7582i	0.513921	+	0.890138i
$399$	13.5746	+	17.3406i	0.679582	+	0.868118i
$400$	−3.05796	+	5.29654i	−0.152898	+	0.264827i
$401$	15.6974	−	13.1717i	0.783891	−	0.657763i	−0.160334	−	0.987063i	$-0.551257\pi$
$401$	15.6974	−	13.1717i	0.783891	−	0.657763i	0.944225	+	0.329300i	$0.106813\pi$
$402$	−18.1556	+	15.7106i	−0.905517	+	0.783572i
$403$	−0.00130633	+	0.00740855i	−6.50728e−5	+	0.000369046i
$404$	−0.447099	+	0.375161i	−0.0222440	+	0.0186650i
$405$	−3.40587	+	29.8126i	−0.169239	+	1.48140i
$406$	9.78975	−	16.9563i	0.485857	−	0.841529i
$407$	−3.21872	+	5.57499i	−0.159546	+	0.276342i
$408$	−5.09935	−	4.14847i	−0.252456	−	0.205380i
$409$	2.97363	−	16.8643i	0.147037	−	0.833887i	−0.818672	−	0.574261i	$-0.805290\pi$
$409$	2.97363	−	16.8643i	0.147037	−	0.833887i	0.965709	−	0.259626i	$-0.0835994\pi$
$410$	33.5524			1.65703
$411$	−4.65119	−	7.78060i	−0.229426	−	0.383789i
$412$	4.35016	−	1.58333i	0.214317	−	0.0780051i
$413$	−22.3130	+	18.7228i	−1.09795	+	0.921289i
$414$	−1.26121	+	0.502949i	−0.0619850	+	0.0247186i
$415$	3.36351	+	19.0754i	0.165108	+	0.936375i
$416$	0.000823924		0.00467270i	4.03962e−5		0.000229098i
$417$	−1.11864	+	0.0170000i	−0.0547801	+	0.000832496i
$418$	2.01606	−	4.79225i	0.0986085	−	0.234397i
$419$	6.67781	−	11.5663i	0.326232	−	0.565051i	−0.655529	−	0.755170i	$-0.727554\pi$
$419$	6.67781	−	11.5663i	0.326232	−	0.565051i	0.981761	+	0.190120i	$0.0608875\pi$
$420$	−15.9142	−	5.51990i	−0.776532	−	0.269344i
$421$	16.1519	−	13.5531i	0.787198	−	0.660537i	−0.157852	−	0.987463i	$-0.550457\pi$
$421$	16.1519	−	13.5531i	0.787198	−	0.660537i	0.945050	+	0.326925i	$0.106013\pi$
$422$	−3.44121	−	2.88752i	−0.167516	−	0.140562i
$423$	−10.6640	+	9.51510i	−0.518502	+	0.462640i
$424$	2.41925	−	13.7203i	0.117489	−	0.666315i
$425$	−23.2118			−1.12594
$426$	−23.7454	+	0.360860i	−1.15047	+	0.0174837i
$427$	−2.82397	+	16.0155i	−0.136662	+	0.775046i
$428$	−2.28878	+	12.9803i	−0.110632	+	0.627428i
$429$	0.00477156	−	0.00856248i	0.000230373	−	0.000413400i
$430$	17.7147			0.854280
$431$	5.22624	−	29.6395i	0.251739	−	1.42768i	−0.552567	−	0.833468i	$-0.686352\pi$
$431$	5.22624	−	29.6395i	0.251739	−	1.42768i	0.804306	−	0.594215i	$-0.202537\pi$
$432$	−4.95870	−	1.55282i	−0.238576	−	0.0747103i
$433$	3.02083	+	2.53477i	0.145172	+	0.121814i	0.712481	−	0.701691i	$-0.247571\pi$
$433$	3.02083	+	2.53477i	0.145172	+	0.121814i	−0.567310	+	0.823505i	$0.692016\pi$
$434$	3.54273	−	2.97271i	0.170057	−	0.142694i
$435$	−7.31038	−	38.0672i	−0.350506	−	1.82518i
$436$	4.74938	−	8.22617i	0.227454	−	0.393962i
$437$	0.582854	+	1.88476i	0.0278817	+	0.0901605i
$438$	10.4280	−	18.7129i	0.498271	−	0.894138i
$439$	−0.866293	−	4.91299i	−0.0413459	−	0.234484i	0.957131	−	0.289655i	$-0.0935407\pi$
$439$	−0.866293	−	4.91299i	−0.0413459	−	0.234484i	−0.998477	+	0.0551710i	$0.982430\pi$
$440$	0.690543	+	3.91626i	0.0329203	+	0.186700i
$441$	0.649936	−	4.47775i	0.0309493	−	0.213226i
$442$	−0.0137949	+	0.0115753i	−0.000656156	+	0.000550580i
$443$	−31.6466	+	11.5184i	−1.50357	+	0.547256i	−0.956983	−	0.290144i	$-0.906297\pi$
$443$	−31.6466	+	11.5184i	−1.50357	+	0.547256i	−0.546591	+	0.837400i	$0.684075\pi$
$444$	4.55052	−	8.16584i	0.215958	−	0.387533i
$445$	−53.0509			−2.51485
$446$	4.42739	−	25.1090i	0.209643	−	1.18894i
$447$	35.6532	−	13.5937i	1.68634	−	0.642961i
$448$	1.45844	−	2.52610i	0.0689050	−	0.119347i
$449$	4.40160	−	7.62379i	0.207724	−	0.359789i	−0.743273	−	0.668988i	$-0.766728\pi$
$449$	4.40160	−	7.62379i	0.207724	−	0.359789i	0.950997	+	0.309199i	$0.100061\pi$
$450$	−17.0426	+	6.79631i	−0.803396	+	0.320381i
$451$	9.19501	−	7.71553i	0.432976	−	0.363310i
$452$	−0.881330	+	4.99827i	−0.0414543	+	0.235099i
$453$	−29.2469	−	10.1444i	−1.37414	−	0.476626i
$454$	−17.3630	+	14.5693i	−0.814887	+	0.683772i
$455$	−0.0230717	+	0.0399613i	−0.00108162	+	0.00187341i
$456$	−2.82154	+	7.00278i	−0.132131	+	0.327935i
$457$	3.26252	+	5.65086i	0.152614	+	0.264336i	0.932188	−	0.361975i	$-0.117897\pi$
$457$	3.26252	+	5.65086i	0.152614	+	0.264336i	−0.779573	+	0.626311i	$0.784564\pi$
$458$	−16.3803	−	5.96193i	−0.765400	−	0.278583i
$459$	−4.30603	−	19.2452i	−0.200988	−	0.898288i
$460$	−1.15595	−	0.969957i	−0.0538965	−	0.0452245i
$461$	4.47969	+	1.63047i	0.208640	+	0.0759387i	0.444226	−	0.895915i	$-0.353479\pi$
$461$	4.47969	+	1.63047i	0.208640	+	0.0759387i	−0.235586	+	0.971853i	$0.575701\pi$
$462$	−5.63060	+	2.14681i	−0.261959	+	0.0998788i
$463$	3.25430	+	5.63660i	0.151240	+	0.261955i	0.931684	−	0.363271i	$-0.118340\pi$
$463$	3.25430	+	5.63660i	0.151240	+	0.261955i	−0.780444	+	0.625226i	$0.785007\pi$
$464$	6.71246			0.311618
$465$	1.45270	−	9.03986i	0.0673673	−	0.419213i
$466$	−6.88576	−	5.77784i	−0.318977	−	0.267653i
$467$	19.2717	+	33.3795i	0.891787	+	1.54462i	0.837732	+	0.546082i	$0.183881\pi$
$467$	19.2717	+	33.3795i	0.891787	+	1.54462i	0.0540552	+	0.998538i	$0.482785\pi$
$468$	−0.00673930	+	0.0125379i	−0.000311524	+	0.000579564i
$469$	7.02115	−	39.8189i	0.324207	−	1.83867i
$470$	−14.9254	−	5.43242i	−0.688459	−	0.250579i
$471$	15.2793	+	12.4302i	0.704035	+	0.572753i
$472$	−9.38360	−	3.41535i	−0.431915	−	0.157204i
$473$	4.85471	−	4.07358i	0.223220	−	0.187304i
$474$	1.91400	−	0.0290872i	0.0879131	−	0.00133602i
$475$	7.87605	+	25.4686i	0.361378	+	1.16858i
$476$	11.0705			0.507415
$477$	31.1862	−	27.8263i	1.42792	−	1.27408i
$478$	−0.503239	−	2.85401i	−0.0230176	−	0.130539i
$479$	−2.59483	+	14.7160i	−0.118561	+	0.672393i	0.866364	+	0.499413i	$0.166451\pi$
$479$	−2.59483	+	14.7160i	−0.118561	+	0.672393i	−0.984925	+	0.172980i	$0.944660\pi$
$480$	−1.08908	−	5.67113i	−0.0497092	−	0.258850i
$481$	−0.0196172	−	0.0164608i	−0.000894466	−	0.000750546i
$482$	−5.59771	−	9.69552i	−0.254969	−	0.441619i
$483$	1.11308	−	1.99741i	0.0506471	−	0.0908853i
$484$	−7.33668	−	6.15621i	−0.333486	−	0.279828i
$485$	40.9187	−	14.8932i	1.85802	−	0.676266i
$486$	−8.79648	−	12.8694i	−0.399016	−	0.583769i
$487$	−18.4094	+	31.8860i	−0.834209	+	1.44489i	0.0604631	+	0.998170i	$0.480742\pi$
$487$	−18.4094	+	31.8860i	−0.834209	+	1.44489i	−0.894672	+	0.446723i	$0.852591\pi$
$488$	−5.23910	+	1.90688i	−0.237163	+	0.0863202i
$489$	12.0755	+	4.18843i	0.546071	+	0.189407i
$490$	4.72525	−	1.71985i	0.213465	−	0.0776949i
$491$	21.3289	+	7.76309i	0.962561	+	0.350343i	0.775036	−	0.631916i	$-0.217731\pi$
$491$	21.3289	+	7.76309i	0.962561	+	0.350343i	0.187524	+	0.982260i	$0.439954\pi$
$492$	−13.1808	+	11.4058i	−0.594236	+	0.514211i
$493$	12.7380	+	22.0628i	0.573689	+	0.993658i
$494$	0.0173815	+	0.0112085i	0.000782031	+	0.000504294i
$495$	−5.64831	+	10.5082i	−0.253873	+	0.472308i
$496$	1.48988	+	0.542271i	0.0668975	+	0.0243487i
$497$	30.6367	−	25.7073i	1.37425	−	1.15313i
$498$	−7.80580	−	6.35024i	−0.349786	−	0.284561i
$499$	0.791028	+	4.48614i	0.0354113	+	0.200827i	0.997381	−	0.0723295i	$-0.0230433\pi$
$499$	0.791028	+	4.48614i	0.0354113	+	0.200827i	−0.961970	+	0.273157i	$0.911932\pi$
$500$	−2.85009	−	2.39151i	−0.127460	−	0.106951i
$501$	4.52711	−	8.12382i	0.202256	−	0.362946i
$502$	0.166330	−	0.288092i	0.00742368	−	0.0128582i
$503$	19.9153	−	7.24858i	0.887979	−	0.323198i	0.142554	−	0.989787i	$-0.454469\pi$
$503$	19.9153	−	7.24858i	0.887979	−	0.323198i	0.745425	+	0.666589i	$0.232246\pi$
$504$	8.12819	−	3.24139i	0.362058	−	0.144383i
$505$	−0.972955	−	1.68521i	−0.0432959	−	0.0749907i
$506$	−0.539834			−0.0239985
$507$	−17.4667	−	14.2096i	−0.775722	−	0.631072i
$508$	0.137775	+	0.781361i	0.00611278	+	0.0346673i
$509$	−35.9995	+	13.1028i	−1.59565	+	0.580769i	−0.978531	−	0.206100i	$-0.933923\pi$
$509$	−35.9995	+	13.1028i	−1.59565	+	0.580769i	−0.617120	+	0.786869i	$0.711701\pi$
$510$	16.5734	−	14.3415i	0.733882	−	0.635051i
$511$	6.26464	+	35.5285i	0.277131	+	1.57169i
$512$	1.00000			0.0441942
$513$	−19.6553	+	11.2548i	−0.867801	+	0.496912i
$514$	−7.94854			−0.350595
$515$	2.68017	+	15.2000i	0.118103	+	0.669793i
$516$	−6.95909	+	6.02192i	−0.306357	+	0.265100i
$517$	−5.33952	+	1.94343i	−0.234832	+	0.0854718i
$518$	2.73373	+	15.5037i	0.120113	+	0.681195i
$519$	−4.12768	−	3.35799i	−0.181185	−	0.147399i
$520$	−0.0158194			−0.000693726
$521$	15.2411	+	26.3984i	0.667725	+	1.15653i	0.978539	+	0.206062i	$0.0660649\pi$
$521$	15.2411	+	26.3984i	0.667725	+	1.15653i	−0.310814	+	0.950471i	$0.600602\pi$
$522$	15.8123	+	12.4693i	0.692088	+	0.545768i
$523$	3.70294	−	1.34776i	0.161918	−	0.0589334i	−0.259789	−	0.965665i	$-0.583653\pi$
$523$	3.70294	−	1.34776i	0.161918	−	0.0589334i	0.421708	+	0.906732i	$0.361431\pi$
$524$	7.59115	−	13.1483i	0.331621	−	0.574384i
$525$	15.0410	−	26.9908i	0.656443	−	1.17798i
$526$	−21.0892	−	17.6959i	−0.919532	−	0.771579i
$527$	1.04492	+	5.92603i	0.0455174	+	0.258142i
$528$	−1.60256	−	1.30373i	−0.0697426	−	0.0567376i
$529$	−17.4621	+	14.6524i	−0.759222	+	0.637063i
$530$	43.6485	+	15.8868i	1.89597	+	0.690076i
$531$	−15.7602	−	25.4768i	−0.683933	−	1.10560i
$532$	−3.75635	−	12.1469i	−0.162859	−	0.526633i
$533$	0.0238747	+	0.0413522i	0.00103413	+	0.00179116i
$534$	20.8406	−	18.0340i	0.901862	−	0.780409i
$535$	−41.2945	−	15.0300i	−1.78532	−	0.649803i
$536$	13.0258	−	4.74100i	0.562629	−	0.204780i
$537$	7.84107	+	2.71971i	0.338367	+	0.117364i
$538$	4.67090	−	1.70007i	0.201377	−	0.0732951i
$539$	0.899464	−	1.55792i	0.0387427	−	0.0671043i
$540$	7.96940	−	15.3824i	0.342948	−	0.661953i
$541$	18.6170	−	6.77605i	0.800409	−	0.291325i	0.0907531	−	0.995873i	$-0.471073\pi$
$541$	18.6170	−	6.77605i	0.800409	−	0.291325i	0.709656	+	0.704548i	$0.248850\pi$
$542$	−8.90460	−	7.47184i	−0.382485	−	0.320943i
$543$	19.2887	−	34.6133i	0.827759	−	1.48540i
$544$	1.89766	+	3.28684i	0.0813614	+	0.140922i
$545$	24.2602	+	20.3567i	1.03919	+	0.871985i
$546$	−0.00452086	−	0.0235414i	−0.000193475	−	0.00100748i
$547$	−5.43428	+	30.8194i	−0.232353	+	1.31774i	0.615763	+	0.787931i	$0.288848\pi$
$547$	−5.43428	+	30.8194i	−0.232353	+	1.31774i	−0.848117	+	0.529810i	$0.822263\pi$
$548$	0.908803	+	5.15408i	0.0388221	+	0.220171i
$549$	−15.8839	−	5.24038i	−0.677907	−	0.223654i
$550$	−7.29473			−0.311048
$551$	19.8857	−	21.4626i	0.847161	−	0.914338i
$552$	0.783832	−	0.0119119i	0.0333621	−	0.000507005i
$553$	−2.46948	+	2.07214i	−0.105013	+	0.0881164i
$554$	−23.3106	−	8.48436i	−0.990372	−	0.360466i
$555$	24.1772	+	19.6688i	1.02626	+	0.834895i
$556$	0.606969	+	0.220919i	0.0257412	+	0.00936904i
$557$	5.73662	−	32.5340i	0.243068	−	1.37851i	−0.581868	−	0.813283i	$-0.697678\pi$
$557$	5.73662	−	32.5340i	0.243068	−	1.37851i	0.824936	−	0.565226i	$-0.191211\pi$
$558$	2.50232	+	4.04507i	0.105931	+	0.171241i
$559$	0.0126052	+	0.0218328i	0.000533142	+	0.000923428i
$560$	7.44983	+	6.25115i	0.314813	+	0.264159i
$561$	1.24404	−	7.74140i	0.0525233	−	0.326842i
$562$	−0.553314			−0.0233401
$563$	−12.6500	−	21.9104i	−0.533133	−	0.923413i	−0.999251	−	0.0386908i	$-0.987681\pi$
$563$	−12.6500	−	21.9104i	−0.533133	−	0.923413i	0.466118	−	0.884722i	$-0.345652\pi$
$564$	7.71003	−	2.93965i	0.324651	−	0.123782i
$565$	−15.9011	−	5.78752i	−0.668964	−	0.243483i
$566$	−14.1922	−	11.9086i	−0.596541	−	0.500557i
$567$	25.1687	+	7.46359i	1.05698	+	0.313441i
$568$	12.8841	+	4.68944i	0.540606	+	0.196764i
$569$	−18.3705	−	31.8186i	−0.770131	−	1.33391i	−0.937491	−	0.348011i	$-0.886857\pi$
$569$	−18.3705	−	31.8186i	−0.770131	−	1.33391i	0.167359	−	0.985896i	$-0.446476\pi$
$570$	−21.3594	−	13.3185i	−0.894647	−	0.557852i
$571$	−0.900166	+	1.55913i	−0.0376708	+	0.0652477i	−0.884246	−	0.467021i	$-0.845327\pi$
$571$	−0.900166	+	1.55913i	−0.0376708	+	0.0652477i	0.846575	+	0.532269i	$0.178660\pi$
$572$	−0.00433529	+	0.00363774i	−0.000181268	+	0.000152102i
$573$	1.26335	+	0.438197i	0.0527770	+	0.0183060i
$574$	5.09730	−	28.9082i	0.212757	−	1.20661i
$575$	2.12045	−	1.77927i	0.0884289	−	0.0742006i
$576$	2.35567	+	1.85764i	0.0981529	+	0.0774016i
$577$	−13.9845	+	24.2219i	−0.582184	+	1.00837i	0.413036	+	0.910715i	$0.364468\pi$
$577$	−13.9845	+	24.2219i	−0.582184	+	1.00837i	−0.995220	+	0.0976575i	$0.968865\pi$
$578$	1.29780	−	2.24785i	0.0539812	−	0.0934982i
$579$	21.4394	−	8.17433i	0.890991	−	0.339713i
$580$	−3.88620	+	22.0397i	−0.161366	+	0.915150i
$581$	16.9461			0.703042
$582$	−11.0118	+	19.7605i	−0.456455	+	0.819101i
$583$	15.6151	−	5.68342i	0.646711	−	0.235383i
$584$	−9.47459	+	7.95012i	−0.392061	+	0.328978i
$585$	−0.0372652	−	0.0293867i	−0.00154073	−	0.00121499i
$586$	0.476102	+	2.70011i	0.0196676	+	0.111540i
$587$	−1.12508	−	6.38063i	−0.0464369	−	0.263357i	0.952746	−	0.303767i	$-0.0982445\pi$
$587$	−1.12508	−	6.38063i	−0.0464369	−	0.263357i	−0.999183	+	0.0404106i	$0.987133\pi$
$588$	−1.27163	+	2.28192i	−0.0524413	+	0.0941050i
$589$	6.14765	−	3.15729i	0.253310	−	0.130094i
$590$	16.6466	−	28.8328i	0.685331	−	1.18703i
$591$	−3.84765	−	20.0358i	−0.158271	−	0.824164i
$592$	−4.13447	+	3.46923i	−0.169926	+	0.142584i
$593$	−3.59634	−	3.01769i	−0.147684	−	0.123922i	0.565952	−	0.824438i	$-0.308509\pi$
$593$	−3.59634	−	3.01769i	−0.147684	−	0.123922i	−0.713636	+	0.700516i	$0.752953\pi$
$594$	−1.35325	−	6.04814i	−0.0555244	−	0.248158i
$595$	−6.40929	+	36.3489i	−0.262755	+	1.49016i
$596$	−22.0298			−0.902378
$597$	17.2888	−	31.0244i	0.707582	−	1.26974i
$598$	0.000372906	−	0.00211486i	1.52493e−5	−	8.64829e-5i
$599$	2.51750	−	14.2774i	0.102862	−	0.583360i	−0.889191	−	0.457537i	$-0.848732\pi$
$599$	2.51750	−	14.2774i	0.102862	−	0.583360i	0.992053	−	0.125823i	$-0.0401572\pi$
$600$	10.5919	−	0.160965i	0.432411	−	0.00657136i
$601$	−22.3298			−0.910851			−0.455425	−	0.890274i	$-0.650513\pi$
$601$	−22.3298			−0.910851			−0.455425	+	0.890274i	$0.650513\pi$
$602$	2.69123	−	15.2627i	0.109686	−	0.622063i
$603$	39.4916	+	13.0290i	1.60822	+	0.530582i
$604$	13.6912	+	11.4883i	0.557087	+	0.467451i
$605$	24.4609	−	20.5251i	0.994477	−	0.834465i
$606$	0.955085	+	0.331276i	0.0387977	+	0.0134572i
$607$	16.9491	−	29.3568i	0.687945	−	1.19156i	−0.284557	−	0.958659i	$-0.591846\pi$
$607$	16.9491	−	29.3568i	0.687945	−	1.19156i	0.972502	−	0.232896i	$-0.0748202\pi$
$608$	2.96251	−	3.19743i	0.120146	−	0.129673i
$609$	−33.9088	+	0.515313i	−1.37405	+	0.0208815i
$610$	−3.22785	−	18.3061i	−0.130692	−	0.741190i
$611$	−0.00392515	−	0.0222606i	−0.000158794	−	0.000900568i
$612$	−1.63551	+	11.2679i	−0.0661114	+	0.455476i
$613$	−20.5059	+	17.2065i	−0.828226	+	0.694964i	−0.954883	−	0.296983i	$-0.904020\pi$
$613$	−20.5059	+	17.2065i	−0.828226	+	0.694964i	0.126657	+	0.991947i	$0.459575\pi$
$614$	−16.9768	+	6.17906i	−0.685129	+	0.249367i
$615$	−29.8186	−	49.8812i	−1.20240	−	2.01141i
$616$	3.47910			0.140177
$617$	−5.44787	+	30.8964i	−0.219323	+	1.24384i	0.653922	+	0.756562i	$0.273123\pi$
$617$	−5.44787	+	30.8964i	−0.219323	+	1.24384i	−0.873245	+	0.487281i	$0.837989\pi$
$618$	−6.21996	−	5.06011i	−0.250203	−	0.203548i
$619$	9.33293	−	16.1651i	0.375122	−	0.649731i	−0.615223	−	0.788353i	$-0.710934\pi$
$619$	9.33293	−	16.1651i	0.375122	−	0.649731i	0.990345	+	0.138622i	$0.0442674\pi$
$620$	−2.64306	+	4.57792i	−0.106148	+	0.183854i
$621$	1.86858	+	1.42802i	0.0749834	+	0.0573043i
$622$	−17.3662	+	14.5720i	−0.696322	+	0.584284i
$623$	−8.05953	+	45.7079i	−0.322898	+	1.83125i
$624$	0.00621452	−	0.00537762i	0.000248780	−	0.000215277i
$625$	−13.9230	+	11.6828i	−0.556919	+	0.467310i
$626$	−16.1601	+	27.9901i	−0.645888	+	1.11871i
$627$	−8.91619	+	1.26176i	−0.356078	+	0.0503897i
$628$	−5.68601	−	9.84845i	−0.226896	−	0.392996i
$629$	−19.2486	−	7.00592i	−0.767492	−	0.279344i
$630$	5.93695	+	28.5647i	0.236534	+	1.13805i
$631$	13.0727	+	10.9693i	0.520416	+	0.436681i	0.864777	−	0.502157i	$-0.167460\pi$
$631$	13.0727	+	10.9693i	0.520416	+	0.436681i	−0.344361	+	0.938837i	$0.611904\pi$
$632$	−1.03853	−	0.377993i	−0.0413104	−	0.0150358i
$633$	−1.23451	+	7.68213i	−0.0490675	+	0.305337i
$634$	−6.23331	−	10.7964i	−0.247556	−	0.428780i
$635$	−2.64529			−0.104975
$636$	−22.5475	+	8.59682i	−0.894066	+	0.340886i
$637$	0.00548197	+	0.00459992i	0.000217204	+	0.000182256i
$638$	4.00313	+	6.93362i	0.158485	+	0.274505i
$639$	21.6394	+	34.9808i	0.856043	+	1.38382i
$640$	−0.578952	+	3.28340i	−0.0228851	+	0.129788i
$641$	17.9972	+	6.55045i	0.710848	+	0.258727i	0.672035	−	0.740519i	$-0.265420\pi$
$641$	17.9972	+	6.55045i	0.710848	+	0.258727i	0.0388124	+	0.999247i	$0.487643\pi$
$642$	21.3315	−	8.13319i	0.841887	−	0.320992i
$643$	−30.8450	−	11.2267i	−1.21641	−	0.442737i	−0.347487	−	0.937685i	$-0.612965\pi$
$643$	−30.8450	−	11.2267i	−1.21641	−	0.442737i	−0.868923	+	0.494948i	$0.835187\pi$
$644$	−1.01131	+	0.848593i	−0.0398513	+	0.0334393i
$645$	−15.7434	−	26.3359i	−0.619896	−	1.03697i
$646$	16.1312	+	3.66968i	0.634676	+	0.144382i
$647$	8.93880			0.351420			0.175710	−	0.984442i	$-0.443778\pi$
$647$	8.93880			0.351420			0.175710	+	0.984442i	$0.443778\pi$
$648$	2.09836	+	8.75197i	0.0824312	+	0.343810i
$649$	−2.06824	−	11.7296i	−0.0811857	−	0.460427i
$650$	0.00503905	−	0.0285779i	0.000197648	−	0.00112092i
$651$	−7.56792	−	2.62497i	−0.296610	−	0.102881i
$652$	−5.65283	−	4.74329i	−0.221382	−	0.185761i
$653$	11.6104	+	20.1098i	0.454351	+	0.786958i	0.998651	−	0.0519323i	$-0.0165380\pi$
$653$	11.6104	+	20.1098i	0.454351	+	0.786958i	−0.544300	+	0.838891i	$0.683205\pi$
$654$	−16.4504	+	0.249998i	−0.643263	+	0.00977570i
$655$	38.7761	+	32.5370i	1.51511	+	1.27133i
$656$	9.45663	−	3.44193i	0.369219	−	0.134385i
$657$	−37.0875	+	1.12750i	−1.44692	+	0.0439880i
$658$	−6.94798	+	12.0342i	−0.270860	+	0.469144i
$659$	4.02124	−	1.46361i	0.156645	−	0.0570142i	−0.262507	−	0.964930i	$-0.584549\pi$
$659$	4.02124	−	1.46361i	0.156645	−	0.0570142i	0.419153	+	0.907916i	$0.362327\pi$
$660$	5.20848	−	4.50706i	0.202740	−	0.175437i
$661$	−9.57327	+	3.48439i	−0.372357	+	0.135527i	−0.521419	−	0.853301i	$-0.674597\pi$
$661$	−9.57327	+	3.48439i	−0.372357	+	0.135527i	0.149062	+	0.988828i	$0.452375\pi$
$662$	−11.0487	−	4.02140i	−0.429420	−	0.156296i
$663$	0.0294684	+	0.0102212i	0.00114446	+	0.000396960i
$664$	2.90482	+	5.03130i	0.112729	+	0.195252i
$665$	42.0578	−	5.30117i	1.63093	−	0.205571i
$666$	−16.1840	+	0.492012i	−0.627118	+	0.0190651i
$667$	−2.85483	−	1.03907i	−0.110539	−	0.0402331i
$668$	−4.11319	+	3.45138i	−0.159144	+	0.133538i
$669$	−41.2634	+	15.7328i	−1.59534	+	0.608263i
$670$	8.02530	+	45.5138i	0.310045	+	1.75835i
$671$	−5.09416	−	4.27450i	−0.196658	−	0.165015i
$672$	−5.05161	+	0.0767696i	−0.194870	+	0.00296145i
$673$	−3.81479	+	6.60741i	−0.147049	+	0.254697i	−0.930136	−	0.367216i	$-0.880311\pi$
$673$	−3.81479	+	6.60741i	−0.147049	+	0.254697i	0.783086	+	0.621913i	$0.213644\pi$
$674$	−12.9269	+	4.70501i	−0.497926	+	0.181230i
$675$	25.2499	+	19.2967i	0.971870	+	0.742729i
$676$	6.49999	+	11.2583i	0.250000	+	0.433012i
$677$	14.5346			0.558608			0.279304	−	0.960203i	$-0.409896\pi$
$677$	14.5346			0.558608			0.279304	+	0.960203i	$0.409896\pi$
$678$	8.21402	−	3.13181i	0.315458	−	0.120276i
$679$	−6.61536	−	37.5176i	−0.253874	−	1.43979i
$680$	−11.8907	+	4.32785i	−0.455986	+	0.165965i
$681$	37.0906	+	12.8650i	1.42131	+	0.492989i
$682$	0.328385	+	1.86236i	0.0125745	+	0.0713135i
$683$	−47.9091			−1.83319			−0.916595	−	0.399818i	$-0.869073\pi$
$683$	−47.9091			−1.83319			−0.916595	+	0.399818i	$0.869073\pi$
$684$	12.9184	−	2.02880i	0.493946	−	0.0775731i
$685$	−17.4491			−0.666694
$686$	2.78165	+	15.7755i	0.106204	+	0.602312i
$687$	5.69404	+	29.6505i	0.217241	+	1.13124i
$688$	4.99284	−	1.81724i	0.190350	−	0.0692818i
$689$	0.0114788	+	0.0650997i	0.000437309	+	0.00248010i
$690$	−0.414690	+	2.58053i	−0.0157870	+	0.0982392i
$691$	34.6910			1.31971			0.659854	−	0.751394i	$-0.270618\pi$
$691$	34.6910			1.31971			0.659854	+	0.751394i	$0.270618\pi$
$692$	1.53606	+	2.66054i	0.0583923	+	0.101138i
$693$	8.19561	+	6.46291i	0.311326	+	0.245506i
$694$	29.6275	−	10.7835i	1.12465	−	0.409338i
$695$	−1.07677	+	1.86502i	−0.0408442	+	0.0707443i
$696$	−5.96549	−	9.97920i	−0.226121	−	0.378261i
$697$	29.2585	+	24.5508i	1.10825	+	0.929928i
$698$	−2.20563	−	12.5087i	−0.0834843	−	0.473463i
$699$	−2.47022	+	15.3717i	−0.0934324	+	0.581411i
$700$	−13.6658	+	11.4670i	−0.516519	+	0.433411i
$701$	25.7976	+	9.38956i	0.974362	+	0.354639i	0.779646	−	0.626221i	$-0.215399\pi$
$701$	25.7976	+	9.38956i	0.974362	+	0.354639i	0.194716	+	0.980860i	$0.437621\pi$
$702$	0.0246290	−	0.00112356i	0.000929563	−	4.24059e-5i
$703$	−1.15580	+	23.4973i	−0.0435919	+	0.886217i
$704$	0.596372	+	1.03295i	0.0224766	+	0.0389307i
$705$	5.18832	+	27.0171i	0.195403	+	1.01752i
$706$	0.374789	+	0.136412i	0.0141054	+	0.00513393i
$707$	−1.59976	+	0.582266i	−0.0601652	+	0.0218984i
$708$	3.26189	+	16.9856i	0.122589	+	0.638357i
$709$	30.7697	−	11.1992i	1.15558	−	0.420596i	0.308063	−	0.951366i	$-0.400319\pi$
$709$	30.7697	−	11.1992i	1.15558	−	0.420596i	0.847516	+	0.530770i	$0.178097\pi$
$710$	−22.8566	+	39.5888i	−0.857793	+	1.48574i
$711$	−1.74425	−	2.81964i	−0.0654146	−	0.105745i
$712$	−14.9522	+	5.44216i	−0.560358	+	0.203954i
$713$	−0.549707	−	0.461259i	−0.0205867	−	0.0172743i
$714$	−9.83856	−	16.4581i	−0.368199	−	0.615931i
$715$	−0.00943424	−	0.0163406i	−0.000352821	−	0.000611103i
$716$	−3.67061	−	3.08000i	−0.137177	−	0.115105i
$717$	−3.79573	+	3.28456i	−0.141754	+	0.122664i
$718$	−0.0253937	+	0.144015i	−0.000947685	+	0.00537459i
$719$	4.69452	+	26.6239i	0.175076	+	0.992905i	0.938056	+	0.346483i	$0.112624\pi$
$719$	4.69452	+	26.6239i	0.175076	+	0.992905i	−0.762980	+	0.646422i	$0.776265\pi$
$720$	−7.46320	+	6.65913i	−0.278137	+	0.248171i
$721$	13.5033			0.502889
$722$	−1.44705	−	18.9448i	−0.0538538	−	0.705053i
$723$	−9.43922	+	16.9385i	−0.351048	+	0.629950i
$724$	−17.5252	+	14.7054i	−0.651318	+	0.546520i
$725$	−38.5771	−	14.0409i	−1.43272	−	0.521466i
$726$	−2.63199	+	16.3783i	−0.0976823	+	0.607857i
$727$	−12.1957	−	4.43889i	−0.452315	−	0.164629i	0.105809	−	0.994386i	$-0.466257\pi$
$727$	−12.1957	−	4.43889i	−0.452315	−	0.164629i	−0.558125	+	0.829757i	$0.688479\pi$
$728$	−0.00240329	+	0.0136297i	−8.90719e−5	+	0.000505152i
$729$	−11.3150	+	24.5147i	−0.419072	+	0.907953i
$730$	−20.6181	−	35.7116i	−0.763111	−	1.32175i
$731$	15.4477	+	12.9621i	0.571353	+	0.479422i
$732$	7.49097	+	6.09412i	0.276874	+	0.225245i
$733$	−43.1082			−1.59224			−0.796118	−	0.605141i	$-0.793117\pi$
$733$	−43.1082			−1.59224			−0.796118	+	0.605141i	$0.793117\pi$
$734$	3.73477	+	6.46881i	0.137853	+	0.238768i
$735$	−6.75626	−	5.49641i	−0.249208	−	0.202738i
$736$	−0.425303	−	0.154798i	−0.0156769	−	0.00570591i
$737$	12.6654	+	10.6276i	0.466537	+	0.391471i
$738$	28.6706	+	9.45895i	1.05538	+	0.348189i
$739$	3.68686	+	1.34191i	0.135623	+	0.0493629i	0.408940	−	0.912561i	$-0.365898\pi$
$739$	3.68686	+	1.34191i	0.135623	+	0.0493629i	−0.273317	+	0.961924i	$0.588121\pi$
$740$	−8.99722	−	15.5836i	−0.330744	−	0.572866i
$741$	0.00121605	−	0.0358017i	4.46729e−5	−	0.00131521i
$742$	20.3189	−	35.1934i	0.745931	−	1.29199i
$743$	7.25650	−	6.08892i	0.266215	−	0.223381i	−0.499902	−	0.866082i	$-0.666631\pi$
$743$	7.25650	−	6.08892i	0.266215	−	0.223381i	0.766117	+	0.642701i	$0.222186\pi$
$744$	−0.517905	−	2.69688i	−0.0189873	−	0.0988724i
$745$	12.7542	−	72.3328i	0.467279	−	2.65007i
$746$	25.6012	−	21.4820i	0.937328	−	0.786512i
$747$	−2.50354	+	17.2482i	−0.0915997	+	0.631079i
$748$	−2.26342	+	3.92036i	−0.0827589	+	0.143343i
$749$	−19.2231	+	33.2954i	−0.702397	+	1.21659i
$750$	−1.02245	+	6.36251i	−0.0373346	+	0.232326i
$751$	2.94905	−	16.7249i	0.107612	−	0.610301i	−0.882532	−	0.470252i	$-0.844163\pi$
$751$	2.94905	−	16.7249i	0.107612	−	0.610301i	0.990145	−	0.140049i	$-0.0447259\pi$
$752$	−4.76397			−0.173724
$753$	−0.576118	+	0.00875529i	−0.0209949	+	0.000319061i
$754$	−0.0299285	+	0.0108931i	−0.00108993	+	0.000396702i
$755$	−45.6472	+	38.3025i	−1.66127	+	1.39397i
$756$	−12.0425	−	9.20323i	−0.437983	−	0.334718i
$757$	5.16185	+	29.2743i	0.187611	+	1.06399i	0.922555	+	0.385866i	$0.126097\pi$
$757$	5.16185	+	29.2743i	0.187611	+	1.06399i	−0.734944	+	0.678128i	$0.762792\pi$
$758$	−1.46333	−	8.29896i	−0.0531505	−	0.301432i
$759$	0.479760	+	0.802553i	0.0174142	+	0.0291308i
$760$	8.78328	+	11.5783i	0.318603	+	0.419988i
$761$	−3.93591	+	6.81720i	−0.142677	+	0.247123i	−0.928504	−	0.371323i	$-0.878904\pi$
$761$	−3.93591	+	6.81720i	−0.142677	+	0.247123i	0.785827	+	0.618446i	$0.212238\pi$
$762$	1.03918	−	0.899236i	0.0376456	−	0.0325759i
$763$	21.2247	−	17.8096i	0.768384	−	0.644751i
$764$	−0.591404	−	0.496247i	−0.0213962	−	0.0179536i
$765$	−36.0501	−	11.8936i	−1.30339	−	0.430013i
$766$	0.378535	−	2.14678i	0.0136770	−	0.0775664i
$767$	0.0473806			0.00171081
$768$	−0.888718	−	1.48667i	−0.0320689	−	0.0536455i
$769$	5.49724	−	31.1764i	0.198236	−	1.12425i	−0.709499	−	0.704706i	$-0.751079\pi$
$769$	5.49724	−	31.1764i	0.198236	−	1.12425i	0.907735	−	0.419544i	$-0.137810\pi$
$770$	−2.01423	+	11.4233i	−0.0725880	+	0.411667i
$771$	7.06402	+	11.8168i	0.254404	+	0.425573i
$772$	−13.2472			−0.476778
$773$	−4.45384	+	25.2590i	−0.160194	+	0.908503i	0.793689	+	0.608324i	$0.208158\pi$
$773$	−4.45384	+	25.2590i	−0.160194	+	0.908503i	−0.953883	+	0.300179i	$0.902953\pi$
$774$	15.1373	+	4.99406i	0.544098	+	0.179508i
$775$	−7.42815	−	6.23295i	−0.266827	−	0.223894i
$776$	10.0050	−	8.39521i	0.359159	−	0.301370i
$777$	20.6194	−	17.8426i	0.739717	−	0.640100i
$778$	13.5560	−	23.4796i	0.486005	−	0.841786i
$779$	17.0101	−	40.4336i	0.609449	−	1.44869i
$780$	0.0140590	+	0.0235182i	0.000503392	+	0.000842085i
$781$	2.83979	+	16.1053i	0.101616	+	0.576292i
$782$	−0.298284	−	1.69165i	−0.0106666	−	0.0604934i
$783$	4.48503	−	34.5894i	0.160282	−	1.23613i
$784$	1.15537	−	0.969469i	0.0412631	−	0.0346239i
$785$	35.6284	−	12.9677i	1.27163	−	0.462836i
$786$	−26.2935	+	0.399583i	−0.937857	+	0.0142526i
$787$	36.9797			1.31819			0.659093	−	0.752062i	$-0.270940\pi$
$787$	36.9797			1.31819			0.659093	+	0.752062i	$0.270940\pi$
$788$	−2.04541	+	11.6001i	−0.0728648	+	0.413237i
$789$	−7.56561	+	47.0793i	−0.269343	+	1.67607i
$790$	1.84236	−	3.19106i	0.0655483	−	0.113533i
$791$	−7.40215	+	12.8209i	−0.263190	+	0.455859i
$792$	−0.513987	+	3.54113i	−0.0182637	+	0.125828i
$793$	0.0202648	−	0.0170041i	0.000719623	−	0.000603835i
$794$	2.38987	−	13.5536i	0.0848134	−	0.481000i
$795$	−15.1729	−	79.0096i	−0.538127	−	2.80218i
$796$	−15.7080	+	13.1806i	−0.556757	+	0.467174i
$797$	−9.70272	+	16.8056i	−0.343688	+	0.595285i	−0.985115	−	0.171899i	$-0.945010\pi$
$797$	−9.70272	+	16.8056i	−0.343688	+	0.595285i	0.641426	+	0.767185i	$0.278343\pi$
$798$	−14.7200	+	16.3796i	−0.521082	+	0.579831i
$799$	−9.04038	−	15.6584i	−0.319826	−	0.553954i
$800$	−5.74708	−	2.09177i	−0.203190	−	0.0739551i
$801$	−45.3321	−	14.9559i	−1.60173	−	0.528440i
$802$	15.6974	+	13.1717i	0.554295	+	0.465109i
$803$	−13.8624	−	5.04552i	−0.489195	−	0.178052i
$804$	−18.6246	−	15.1516i	−0.656838	−	0.534356i
$805$	−2.20077	−	3.81185i	−0.0775669	−	0.134350i
$806$	−0.00752284			−0.000264981
$807$	−6.67855	−	5.43319i	−0.235096	−	0.191257i
$808$	−0.447099	−	0.375161i	−0.0157289	−	0.0131981i
$809$	−7.84113	−	13.5812i	−0.275679	−	0.477491i	0.694627	−	0.719370i	$-0.255569\pi$
$809$	−7.84113	−	13.5812i	−0.275679	−	0.477491i	−0.970306	+	0.241879i	$0.922236\pi$
$810$	−29.9511	+	1.82278i	−1.05237	+	0.0640458i
$811$	9.30340	−	52.7622i	0.326687	−	1.85273i	−0.170861	−	0.985295i	$-0.554655\pi$
$811$	9.30340	−	52.7622i	0.326687	−	1.85273i	0.497547	−	0.867437i	$-0.334234\pi$
$812$	18.3987	+	6.69658i	0.645668	+	0.235004i
$813$	−3.19447	+	19.8785i	−0.112035	+	0.697171i
$814$	−6.04922	−	2.20173i	−0.212025	−	0.0771707i
$815$	18.8468	−	15.8144i	0.660176	−	0.553953i
$816$	3.19995	−	5.74226i	0.112021	−	0.201019i
$817$	8.98084	−	21.3478i	0.314200	−	0.746866i
$818$	17.1245			0.598743
$819$	−0.0309805	+	0.0276427i	−0.00108255	+	0.000965915i
$820$	5.82631	+	33.0426i	0.203464	+	1.15390i
$821$	0.261204	−	1.48136i	0.00911609	−	0.0516999i	−0.979910	−	0.199438i	$-0.936088\pi$
$821$	0.261204	−	1.48136i	0.00911609	−	0.0516999i	0.989026	+	0.147738i	$0.0471994\pi$
$822$	6.85473	−	5.93161i	0.239086	−	0.206889i
$823$	0.0600817	+	0.0504145i	0.00209432	+	0.00175734i	0.643834	−	0.765165i	$-0.277343\pi$
$823$	0.0600817	+	0.0504145i	0.00209432	+	0.00175734i	−0.641740	+	0.766922i	$0.721787\pi$
$824$	2.31467	+	4.00913i	0.0806355	+	0.139665i
$825$	6.48296	+	10.8448i	0.225708	+	0.377569i
$826$	−22.3130	−	18.7228i	−0.776367	−	0.651450i
$827$	−6.03363	+	2.19606i	−0.209810	+	0.0763646i	−0.444787	−	0.895636i	$-0.646721\pi$
$827$	−6.03363	+	2.19606i	−0.209810	+	0.0763646i	0.234977	+	0.972001i	$0.424498\pi$
$828$	−0.714315	−	1.15471i	−0.0248242	−	0.0401290i
$829$	−4.80294	+	8.31894i	−0.166813	+	0.288929i	−0.937298	−	0.348530i	$-0.886681\pi$
$829$	−4.80294	+	8.31894i	−0.166813	+	0.288929i	0.770485	+	0.637459i	$0.220014\pi$
$830$	−18.2015	+	6.62482i	−0.631785	+	0.229951i
$831$	8.10313	+	42.1953i	0.281094	+	1.46374i
$832$	−0.00445864	+	0.00162281i	−0.000154576	+	5.62609e-5i
$833$	5.37898	+	1.95779i	0.186371	+	0.0678333i
$834$	−0.210992	−	1.09870i	−0.00730605	−	0.0380447i
$835$	−8.95093	−	15.5035i	−0.309760	−	0.536519i
$836$	5.06953	+	1.15326i	0.175333	+	0.0398864i
$837$	3.78982	−	7.31504i	0.130995	−	0.252845i
$838$	12.5502	+	4.56789i	0.433538	+	0.157795i
$839$	2.54023	−	2.13151i	0.0876986	−	0.0735879i	−0.597884	−	0.801582i	$-0.703992\pi$
$839$	2.54023	−	2.13151i	0.0876986	−	0.0735879i	0.685583	+	0.727994i	$0.259547\pi$
$840$	2.67258	−	16.6309i	0.0922127	−	0.573821i
$841$	2.78830	+	15.8132i	0.0961482	+	0.545284i
$842$	16.1519	+	13.5531i	0.556633	+	0.467070i
$843$	0.491740	+	0.822594i	0.0169364	+	0.0283316i
$844$	2.24609	−	3.89034i	0.0773136	−	0.133911i
$845$	−40.7287	+	14.8241i	−1.40111	+	0.509963i
$846$	−11.2223	−	8.84973i	−0.385832	−	0.304260i
$847$	−13.9680	−	24.1933i	−0.479947	−	0.831293i
$848$	13.9319			0.478424
$849$	−5.09135	+	31.6825i	−0.174735	+	1.08734i
$850$	−4.03069	−	22.8592i	−0.138252	−	0.784063i
$851$	2.29543	−	0.835468i	0.0786863	−	0.0286395i
$852$	−4.47872	−	23.3220i	−0.153439	−	0.798998i
$853$	2.38515	+	13.5269i	0.0816661	+	0.463152i	0.998026	+	0.0627968i	$0.0200020\pi$
$853$	2.38515	+	13.5269i	0.0816661	+	0.463152i	−0.916360	+	0.400355i	$0.868887\pi$
$854$	−16.2626			−0.556495
$855$	−0.817747	+	43.5907i	−0.0279663	+	1.49077i
$856$	−13.1806			−0.450502
$857$	7.48686	+	42.4601i	0.255746	+	1.45041i	0.794150	+	0.607721i	$0.207916\pi$
$857$	7.48686	+	42.4601i	0.255746	+	1.45041i	−0.538404	+	0.842687i	$0.680973\pi$
$858$	0.00926096	+	0.00321221i	0.000316164	+	0.000109663i
$859$	42.6546	−	15.5250i	1.45536	−	0.529706i	0.511274	−	0.859418i	$-0.329174\pi$
$859$	42.6546	−	15.5250i	1.45536	−	0.529706i	0.944082	+	0.329711i	$0.106951\pi$
$860$	3.07613	+	17.4456i	0.104895	+	0.594890i
$861$	−47.5070	+	18.1133i	−1.61903	+	0.617299i
$862$	30.0967			1.02510
$863$	−14.6271	−	25.3348i	−0.497911	−	0.862408i	0.502086	−	0.864818i	$-0.332566\pi$
$863$	−14.6271	−	25.3348i	−0.497911	−	0.862408i	−0.999997	+	0.00241001i	$0.999233\pi$
$864$	0.668164	−	5.15301i	0.0227314	−	0.175309i
$865$	−9.62492	+	3.50318i	−0.327257	+	0.119112i
$866$	−1.97170	+	3.41509i	−0.0670013	+	0.116050i
$867$	−4.49518	+	0.0683134i	−0.152664	+	0.00232005i
$868$	3.54273	+	2.97271i	0.120248	+	0.100900i
$869$	−0.228902	−	1.29817i	−0.00776497	−	0.0440374i
$870$	36.2195	−	13.8096i	1.22795	−	0.468190i
$871$	−0.0503836	+	0.0422769i	−0.00170718	+	0.00143250i
$872$	8.92592	+	3.24877i	0.302270	+	0.110017i
$873$	39.1638	−	1.19062i	1.32549	−	0.0402964i
$874$	−1.75492	+	0.901284i	−0.0593610	+	0.0304864i
$875$	−5.42617	−	9.39841i	−0.183438	−	0.317724i
$876$	20.2394	+	7.02014i	0.683827	+	0.237189i
$877$	43.9243	+	15.9872i	1.48322	+	0.539848i	0.951655	−	0.307170i	$-0.0993819\pi$
$877$	43.9243	+	15.9872i	1.48322	+	0.539848i	0.531565	+	0.847017i	$0.321604\pi$
$878$	4.68792	−	1.70626i	0.158210	−	0.0575836i
$879$	3.59104	−	3.10744i	0.121123	−	0.104811i
$880$	−3.73685	+	1.36010i	−0.125969	+	0.0458491i
$881$	−8.37670	+	14.5089i	−0.282218	+	0.488817i	−0.971931	−	0.235267i	$-0.924404\pi$
$881$	−8.37670	+	14.5089i	−0.282218	+	0.488817i	0.689712	+	0.724083i	$0.257737\pi$
$882$	4.52259	−	0.137492i	0.152283	−	0.00462958i
$883$	−49.7464	+	18.1062i	−1.67410	+	0.609322i	−0.992482	−	0.122387i	$-0.960945\pi$
$883$	−49.7464	+	18.1062i	−1.67410	+	0.609322i	−0.681617	+	0.731710i	$0.738723\pi$
$884$	−0.0137949	−	0.0115753i	−0.000463973	−	0.000389319i
$885$	−57.6590	+	0.876246i	−1.93819	+	0.0294547i
$886$	−16.8388	−	29.1656i	−0.565710	−	0.979838i
$887$	−7.02751	−	5.89678i	−0.235961	−	0.197995i	0.517138	−	0.855902i	$-0.326997\pi$
$887$	−7.02751	−	5.89678i	−0.235961	−	0.197995i	−0.753099	+	0.657907i	$0.771442\pi$
$888$	8.83197	+	3.06341i	0.296381	+	0.102801i
$889$	−0.401874	+	2.27914i	−0.0134784	+	0.0764400i
$890$	−9.21219	−	52.2449i	−0.308793	−	1.75125i
$891$	−7.78892	+	7.38692i	−0.260939	+	0.247471i
$892$	25.4963			0.853680
$893$	−14.1133	+	15.2324i	−0.472284	+	0.509734i
$894$	19.5783	+	32.7511i	0.654797	+	1.09536i
$895$	12.2380	−	10.2689i	0.409071	−	0.343251i
$896$	2.74098	+	0.997634i	0.0915696	+	0.0333286i
$897$	−0.00347550	+	0.00132512i	−0.000116043	+	4.42446e-5i
$898$	8.27230	+	3.01087i	0.276050	+	0.100474i
$899$	−1.84806	+	10.4809i	−0.0616364	+	0.349557i
$900$	−9.65248	−	15.6035i	−0.321749	−	0.520117i
$901$	26.4380	+	45.7920i	0.880777	+	1.52555i
$902$	9.19501	+	7.71553i	0.306160	+	0.256899i
$903$	−25.0824	+	9.56331i	−0.834689	+	0.318247i
$904$	−5.07538			−0.168805
$905$	−38.1374	−	66.0559i	−1.26773	−	2.19577i
$906$	4.91163	−	30.5641i	0.163178	−	1.01542i
$907$	−36.4214	−	13.2563i	−1.20935	−	0.440168i	−0.342873	−	0.939382i	$-0.611400\pi$
$907$	−36.4214	−	13.2563i	−1.20935	−	0.440168i	−0.866479	+	0.499214i	$0.833622\pi$
$908$	−17.3630	−	14.5693i	−0.576212	−	0.483499i
$909$	−0.356305	−	1.71430i	−0.0118179	−	0.0568599i
$910$	−0.0433605	−	0.0157819i	−0.00143739	−	0.000523166i
$911$	4.84623	+	8.39392i	0.160563	+	0.278103i	0.935071	−	0.354461i	$-0.115336\pi$
$911$	4.84623	+	8.39392i	0.160563	+	0.278103i	−0.774508	+	0.632564i	$0.782002\pi$
$912$	−7.38635	−	1.56266i	−0.244586	−	0.0517448i
$913$	−3.46471	+	6.00106i	−0.114665	+	0.198606i
$914$	−4.99848	+	4.19422i	−0.165335	+	0.138733i
$915$	−24.3464	+	21.0677i	−0.804866	+	0.696476i
$916$	3.02695	−	17.1667i	0.100013	−	0.567204i
$917$	33.9243	−	28.4659i	1.12028	−	0.940026i
$918$	18.2051	−	7.58251i	0.600857	−	0.250260i
$919$	16.6169	−	28.7813i	0.548141	−	0.949407i	−0.450261	−	0.892897i	$-0.648669\pi$
$919$	16.6169	−	28.7813i	0.548141	−	0.949407i	0.998402	−	0.0565105i	$-0.0179974\pi$
$920$	0.754493	−	1.30682i	0.0248749	−	0.0430846i
$921$	24.2738	+	19.7475i	0.799850	+	0.650701i
$922$	−0.827813	+	4.69476i	−0.0272626	+	0.154614i
$923$	−0.0650558			−0.00214134
$924$	−3.09194	−	5.17227i	−0.101717	−	0.170155i
$925$	31.0179	−	11.2896i	1.01986	−	0.371200i
$926$	−4.98587	+	4.18364i	−0.163846	+	0.137483i
$927$	−1.99491	+	13.7440i	−0.0655216	+	0.451413i
$928$	1.16561	+	6.61049i	0.0382629	+	0.217000i
$929$	−1.75849	−	9.97289i	−0.0576942	−	0.327200i	0.942277	−	0.334835i	$-0.108681\pi$
$929$	−1.75849	−	9.97289i	−0.0576942	−	0.327200i	−0.999971	+	0.00763536i	$0.997570\pi$
$930$	9.15478	−	0.139126i	0.300197	−	0.00456211i
$931$	0.322987	−	6.56626i	0.0105855	−	0.215201i
$932$	4.49436	−	7.78446i	0.147218	−	0.254989i
$933$	37.0974	+	12.8674i	1.21451	+	0.421260i
$934$	−29.5259	+	24.7752i	−0.966118	+	0.810669i
$935$	−11.5617	−	9.70142i	−0.378108	−	0.317270i
$936$	−0.0135177	−	0.00445974i	−0.000441839	−	0.000145771i
$937$	−0.595231	+	3.37572i	−0.0194453	+	0.110280i	−0.992986	−	0.118236i	$-0.962276\pi$
$937$	−0.595231	+	3.37572i	−0.0194453	+	0.110280i	0.973540	+	0.228516i	$0.0733873\pi$
$938$	40.4332			1.32019
$939$	55.9738	−	0.850637i	1.82664	−	0.0277595i
$940$	2.75811	−	15.6420i	0.0899596	−	0.510187i
$941$	−5.92410	+	33.5972i	−0.193120	+	1.09524i	0.721951	+	0.691945i	$0.243246\pi$
$941$	−5.92410	+	33.5972i	−0.193120	+	1.09524i	−0.915071	+	0.403294i	$0.867865\pi$
$942$	−9.58811	+	17.2057i	−0.312398	+	0.560592i
$943$	−4.55474			−0.148323
$944$	1.73402	−	9.83412i	0.0564375	−	0.320073i
$945$	37.1900	−	34.2123i	1.20979	−	1.11293i
$946$	4.85471	+	4.07358i	0.157840	+	0.132444i
$947$	−23.5453	+	19.7569i	−0.765121	+	0.642013i	−0.939454	−	0.342674i	$-0.888667\pi$
$947$	−23.5453	+	19.7569i	−0.765121	+	0.642013i	0.174334	+	0.984687i	$0.444223\pi$
$948$	0.361008	+	1.87987i	0.0117250	+	0.0610555i
$949$	0.0293422	−	0.0508222i	0.000952489	−	0.00164976i
$950$	−23.7141	+	12.1790i	−0.769386	+	0.395138i
$951$	−10.5110	+	18.8618i	−0.340843	+	0.611636i
$952$	1.92237	+	10.9023i	0.0623044	+	0.353346i
$953$	1.12962	+	6.40639i	0.0365920	+	0.207523i	0.997622	−	0.0689200i	$-0.0219553\pi$
$953$	1.12962	+	6.40639i	0.0365920	+	0.207523i	−0.961030	+	0.276443i	$0.910844\pi$
$954$	32.8190	+	25.8805i	1.06255	+	0.837911i
$955$	1.97177	−	1.65451i	0.0638051	−	0.0535388i
$956$	2.72326	−	0.991187i	0.0880767	−	0.0320573i
$957$	6.75034	−	12.1134i	0.218207	−	0.391569i
$958$	−14.9431			−0.482788
$959$	−2.65087	+	15.0339i	−0.0856012	+	0.485469i
$960$	5.39585	−	2.05731i	0.174150	−	0.0663994i
$961$	14.2431	−	24.6698i	0.459455	−	0.795799i
$962$	0.0128042	−	0.0221775i	0.000412824	−	0.000715032i
$963$	−31.0490	−	24.4847i	−1.00054	−	0.789009i
$964$	8.57619	−	7.19628i	0.276220	−	0.231776i
$965$	7.66951	−	43.4960i	0.246890	−	1.40018i
$966$	2.16035	+	0.749327i	0.0695081	+	0.0241092i
$967$	3.06826	−	2.57458i	0.0986686	−	0.0827928i	−0.592119	−	0.805851i	$-0.701708\pi$
$967$	3.06826	−	2.57458i	0.0986686	−	0.0827928i	0.690788	+	0.723058i	$0.257264\pi$
$968$	4.78868	−	8.29424i	0.153914	−	0.266587i
$969$	−8.88054	−	27.2431i	−0.285284	−	0.875175i
$970$	21.7724	+	37.7109i	0.699070	+	1.21082i
$971$	−8.24839	−	3.00217i	−0.264704	−	0.0963442i	0.206259	−	0.978497i	$-0.433871\pi$
$971$	−8.24839	−	3.00217i	−0.264704	−	0.0963442i	−0.470963	+	0.882153i	$0.656093\pi$
$972$	11.1464	−	10.8976i	0.357521	−	0.349540i
$973$	1.44329	+	1.21107i	0.0462698	+	0.0388250i
$974$	−34.5983	−	12.5928i	−1.10860	−	0.403498i
$975$	−0.0469641	+	0.0179063i	−0.00150405	+	0.000573460i
$976$	−2.78767	−	4.82838i	−0.0892310	−	0.154553i
$977$	33.6134			1.07539			0.537693	−	0.843141i	$-0.319296\pi$
$977$	33.6134			1.07539			0.537693	+	0.843141i	$0.319296\pi$
$978$	−2.02792	+	12.6193i	−0.0648456	+	0.403521i
$979$	−14.5386	−	12.1993i	−0.464655	−	0.389891i
$980$	2.51425	+	4.35481i	0.0803148	+	0.139109i
$981$	14.9915	+	24.2342i	0.478641	+	0.773737i
$982$	−3.94143	+	22.3529i	−0.125776	+	0.713311i
$983$	20.2667	+	7.37647i	0.646407	+	0.235273i	0.644357	−	0.764725i	$-0.277125\pi$
$983$	20.2667	+	7.37647i	0.646407	+	0.235273i	0.00205007	+	0.999998i	$0.499347\pi$
$984$	−13.5213	−	11.0000i	−0.431043	−	0.350666i
$985$	−36.9036	−	13.4318i	−1.17585	−	0.427974i
$986$	−19.5157	+	16.3756i	−0.621506	+	0.521505i
$987$	24.0657	−	0.365728i	0.766020	−	0.0116412i
$988$	−0.00801995	+	0.0190638i	−0.000255149	+	0.000606499i
$989$	−2.40477			−0.0764674
$990$	−11.3294	−	3.73777i	−0.360071	−	0.118794i
$991$	−5.50106	−	31.1980i	−0.174747	−	0.991038i	−0.938436	−	0.345454i	$-0.887725\pi$
$991$	−5.50106	−	31.1980i	−0.174747	−	0.991038i	0.763689	−	0.645584i	$-0.223386\pi$
$992$	−0.275318	+	1.56141i	−0.00874137	+	0.0495748i
$993$	3.84071	+	19.9997i	0.121881	+	0.634670i
$994$	30.6367	+	25.7073i	0.971738	+	0.815385i
$995$	−34.1830	−	59.2068i	−1.08368	−	1.87698i
$996$	4.89830	−	8.78992i	0.155209	−	0.278519i
$997$	−9.08451	−	7.62281i	−0.287709	−	0.241417i	0.487497	−	0.873124i	$-0.337910\pi$
$997$	−9.08451	−	7.62281i	−0.287709	−	0.241417i	−0.775207	+	0.631708i	$0.782354\pi$
$998$	−4.28063	+	1.55802i	−0.135501	+	0.0493183i
$999$	15.1145	+	23.6230i	0.478201	+	0.747398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.w.b.175.9	yes	66
9.7	even	3		342.2.v.b.61.2	✓	66
19.5	even	9		342.2.v.b.157.2	yes	66
171.43	even	9	inner	342.2.w.b.43.9	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.v.b.61.2	✓	66	9.7	even	3
342.2.v.b.157.2	yes	66	19.5	even	9
342.2.w.b.43.9	yes	66	171.43	even	9	inner
342.2.w.b.175.9	yes	66	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(1.30976 - 1.13337i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.578952 - 3.28340i) q^{5} +(1.34359 + 1.09305i) q^{6} -2.91689 q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.430928 - 2.96889i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(1.30976 - 1.13337i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.578952 - 3.28340i) q^{5} +(1.34359 + 1.09305i) q^{6} -2.91689 q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.430928 - 2.96889i) q^{9} +(3.13299 - 1.14031i) q^{10} +(0.596372 - 1.03295i) q^{11} +(-0.843132 + 1.51299i) q^{12} +(0.00363472 + 0.00304989i) q^{13} +(-0.506512 - 2.87257i) q^{14} +(-4.47961 - 3.64429i) q^{15} +(0.766044 - 0.642788i) q^{16} +(3.56643 + 1.29807i) q^{17} +(2.99861 - 0.0911612i) q^{18} +(0.214150 - 4.35364i) q^{19} +(1.66703 + 2.88738i) q^{20} +(-3.82041 + 3.30592i) q^{21} +(1.12081 + 0.407943i) q^{22} +(-0.425303 + 0.154798i) q^{23} +(-1.63641 - 0.567596i) q^{24} +(-5.74708 + 2.09177i) q^{25} +(-0.00237239 + 0.00410911i) q^{26} +(-2.80045 - 4.37693i) q^{27} +(2.74098 - 0.997634i) q^{28} +(5.14205 + 4.31469i) q^{29} +(2.81105 - 5.04438i) q^{30} +(0.792748 + 1.37308i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-0.389612 - 2.02882i) q^{33} +(-0.659049 + 3.73765i) q^{34} +(1.68874 + 9.57731i) q^{35} +(0.610480 + 2.93723i) q^{36} -5.39716 q^{37} +(4.32468 - 0.545104i) q^{38} +(0.00821726 - 0.000124878i) q^{39} +(-2.55403 + 2.14309i) q^{40} +(9.45663 + 3.44193i) q^{41} +(-3.91911 - 3.18830i) q^{42} +(4.99284 + 1.81724i) q^{43} +(-0.207118 + 1.17462i) q^{44} +(-9.99754 + 0.303936i) q^{45} +(-0.226299 - 0.391961i) q^{46} +(-3.64941 - 3.06222i) q^{47} +(0.274814 - 1.71011i) q^{48} +1.50823 q^{49} +(-3.05796 - 5.29654i) q^{50} +(6.14236 - 2.34194i) q^{51} +(-0.00445864 - 0.00162281i) q^{52} +(10.6725 + 8.95526i) q^{53} +(3.82414 - 3.51795i) q^{54} +(-3.73685 - 1.36010i) q^{55} +(1.45844 + 2.52610i) q^{56} +(-4.65381 - 5.94492i) q^{57} +(-3.35623 + 5.81316i) q^{58} +(7.64958 - 6.41876i) q^{59} +(5.45588 + 1.89240i) q^{60} +(0.968146 - 5.49063i) q^{61} +(-1.21456 + 1.01914i) q^{62} +(-1.25697 + 8.65991i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.00790969 - 0.0137000i) q^{65} +(1.93035 - 0.735995i) q^{66} +(-2.40707 + 13.6512i) q^{67} -3.79531 q^{68} +(-0.381600 + 0.684774i) q^{69} +(-9.13856 + 3.32617i) q^{70} +(-10.5032 + 8.81326i) q^{71} +(-2.78660 + 1.11125i) q^{72} +(-2.14772 - 12.1803i) q^{73} +(-0.937208 - 5.31517i) q^{74} +(-5.15653 + 9.25330i) q^{75} +(1.28780 + 4.16432i) q^{76} +(-1.73955 + 3.01299i) q^{77} +(0.00154989 + 0.00807074i) q^{78} +(0.846615 - 0.710395i) q^{79} +(-2.55403 - 2.14309i) q^{80} +(-8.62860 - 2.55875i) q^{81} +(-1.74752 + 9.91065i) q^{82} -5.80965 q^{83} +(2.45932 - 4.41321i) q^{84} +(2.19731 - 12.4615i) q^{85} +(-0.922639 + 5.23255i) q^{86} +(11.6250 - 0.176665i) q^{87} -1.19274 q^{88} +(2.76306 - 15.6701i) q^{89} +(-2.03537 - 9.79288i) q^{90} +(-0.0106021 - 0.00889618i) q^{91} +(0.346710 - 0.290924i) q^{92} +(2.59452 + 0.899921i) q^{93} +(2.38198 - 4.12572i) q^{94} +(-14.4187 + 1.81741i) q^{95} +(1.73185 - 0.0263190i) q^{96} +(2.26795 + 12.8622i) q^{97} +(0.261901 + 1.48531i) q^{98} +(-2.80971 - 2.21569i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 3 q^{3} - 3 q^{6} + 24 q^{7} - 33 q^{8} - 3 q^{9}+O(q^{10}) \) 66 * q - 3 * q^3 - 3 * q^6 + 24 * q^7 - 33 * q^8 - 3 * q^9	\( 66 q - 3 q^{3} - 3 q^{6} + 24 q^{7} - 33 q^{8} - 3 q^{9} - 3 q^{13} - 3 q^{14} - 30 q^{15} + 9 q^{17} + 6 q^{18} - 21 q^{19} + 6 q^{22} - 12 q^{23} + 6 q^{24} + 6 q^{25} + 30 q^{27} - 3 q^{28} + 9 q^{29} + 18 q^{33} - 18 q^{34} - 18 q^{35} - 3 q^{36} + 6 q^{37} + 6 q^{38} + 12 q^{39} + 6 q^{41} + 6 q^{43} - 12 q^{44} - 18 q^{45} - 18 q^{47} - 3 q^{48} + 114 q^{49} - 63 q^{50} - 63 q^{51} - 3 q^{52} - 24 q^{53} + 18 q^{54} + 36 q^{55} - 12 q^{56} - 60 q^{57} - 18 q^{58} + 78 q^{59} - 3 q^{60} - 21 q^{62} - 27 q^{63} - 33 q^{64} - 12 q^{65} + 45 q^{66} - 3 q^{67} + 12 q^{68} - 24 q^{69} - 18 q^{70} - 24 q^{71} - 3 q^{72} - 15 q^{73} - 3 q^{74} + 15 q^{78} + 12 q^{79} - 87 q^{81} + 6 q^{82} - 24 q^{83} - 15 q^{84} + 72 q^{85} - 3 q^{86} + 66 q^{87} + 9 q^{89} - 6 q^{90} + 27 q^{91} + 6 q^{92} - 45 q^{93} - 6 q^{94} - 30 q^{95} + 87 q^{97} + 24 q^{98} - 96 q^{99}+O(q^{100}) \) 66 * q - 3 * q^3 - 3 * q^6 + 24 * q^7 - 33 * q^8 - 3 * q^9 - 3 * q^13 - 3 * q^14 - 30 * q^15 + 9 * q^17 + 6 * q^18 - 21 * q^19 + 6 * q^22 - 12 * q^23 + 6 * q^24 + 6 * q^25 + 30 * q^27 - 3 * q^28 + 9 * q^29 + 18 * q^33 - 18 * q^34 - 18 * q^35 - 3 * q^36 + 6 * q^37 + 6 * q^38 + 12 * q^39 + 6 * q^41 + 6 * q^43 - 12 * q^44 - 18 * q^45 - 18 * q^47 - 3 * q^48 + 114 * q^49 - 63 * q^50 - 63 * q^51 - 3 * q^52 - 24 * q^53 + 18 * q^54 + 36 * q^55 - 12 * q^56 - 60 * q^57 - 18 * q^58 + 78 * q^59 - 3 * q^60 - 21 * q^62 - 27 * q^63 - 33 * q^64 - 12 * q^65 + 45 * q^66 - 3 * q^67 + 12 * q^68 - 24 * q^69 - 18 * q^70 - 24 * q^71 - 3 * q^72 - 15 * q^73 - 3 * q^74 + 15 * q^78 + 12 * q^79 - 87 * q^81 + 6 * q^82 - 24 * q^83 - 15 * q^84 + 72 * q^85 - 3 * q^86 + 66 * q^87 + 9 * q^89 - 6 * q^90 + 27 * q^91 + 6 * q^92 - 45 * q^93 - 6 * q^94 - 30 * q^95 + 87 * q^97 + 24 * q^98 - 96 * q^99

Introduction

L-functions

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