LMFDB - Embedded newform 462.2.y.d.163.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(25,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 24]))

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

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

chi := DirichletCharacter("462.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.y (of order $15$, degree $8$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			163.2
Character	$\chi$	$=$	462.163
Dual form			462.2.y.d.445.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.669131 + 0.743145i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(-1.55422 - 0.330360i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-1.63560 - 2.07962i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})$	\(q+(0.669131 + 0.743145i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(-1.55422 - 0.330360i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-1.63560 - 2.07962i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.669131 + 0.743145i) q^{9} +(-0.794473 - 1.37607i) q^{10} +(3.30493 + 0.278246i) q^{11} +(0.500000 - 0.866025i) q^{12} +(1.65680 - 5.09910i) q^{13} +(0.451027 - 2.60702i) q^{14} +(1.28548 + 0.933958i) q^{15} +(-0.978148 - 0.207912i) q^{16} +(4.88491 - 5.42524i) q^{17} +(-0.104528 + 0.994522i) q^{18} +(-0.0962357 - 0.915621i) q^{19} +(0.491011 - 1.51118i) q^{20} +(0.648339 + 2.56508i) q^{21} +(2.00465 + 2.64223i) q^{22} +(0.477314 - 0.826733i) q^{23} +(0.978148 - 0.207912i) q^{24} +(-2.26126 - 1.00678i) q^{25} +(4.89799 - 2.18072i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(2.23919 - 1.40926i) q^{28} +(-4.30641 - 3.12879i) q^{29} +(0.166090 + 1.58024i) q^{30} +(-2.48375 + 0.527938i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.90603 - 1.59843i) q^{33} +7.30038 q^{34} +(1.85506 + 3.77253i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-9.98723 + 4.44660i) q^{37} +(0.616045 - 0.684187i) q^{38} +(-3.58755 + 3.98438i) q^{39} +(1.45157 - 0.646282i) q^{40} +(2.76970 - 2.01231i) q^{41} +(-1.47241 + 2.19819i) q^{42} +11.0313 q^{43} +(-0.622181 + 3.25774i) q^{44} +(-0.794473 - 1.37607i) q^{45} +(0.933768 - 0.198478i) q^{46} +(0.309679 + 2.94640i) q^{47} +(0.809017 + 0.587785i) q^{48} +(-1.64962 + 6.80285i) q^{49} +(-0.764895 - 2.35411i) q^{50} +(-6.66923 + 2.96933i) q^{51} +(4.89799 + 2.18072i) q^{52} +(10.4648 - 2.22437i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-5.04468 - 1.52427i) q^{55} +(2.54560 + 0.721064i) q^{56} +(-0.284501 + 0.875604i) q^{57} +(-0.556407 - 5.29385i) q^{58} +(-0.449852 + 4.28006i) q^{59} +(-1.06321 + 1.18082i) q^{60} +(-9.88922 - 2.10202i) q^{61} +(-2.05429 - 1.49253i) q^{62} +(0.451027 - 2.60702i) q^{63} +(0.309017 - 0.951057i) q^{64} +(-4.25957 + 7.37780i) q^{65} +(-0.756653 - 3.22916i) q^{66} +(-6.94805 - 12.0344i) q^{67} +(4.88491 + 5.42524i) q^{68} +(-0.772311 + 0.561117i) q^{69} +(-1.56225 + 3.90290i) q^{70} +(2.23899 + 6.89091i) q^{71} +(-0.978148 - 0.207912i) q^{72} +(0.182708 - 1.73835i) q^{73} +(-9.98723 - 4.44660i) q^{74} +(1.65627 + 1.83947i) q^{75} +0.920665 q^{76} +(-4.82690 - 7.32810i) q^{77} -5.36151 q^{78} +(7.03898 + 7.81758i) q^{79} +(1.45157 + 0.646282i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(3.34873 + 0.711795i) q^{82} +(1.40191 + 4.31464i) q^{83} +(-2.61880 + 0.376663i) q^{84} +(-9.38452 + 6.81825i) q^{85} +(7.38138 + 8.19785i) q^{86} +(2.66151 + 4.60987i) q^{87} +(-2.83730 + 1.71748i) q^{88} +(8.07291 - 13.9827i) q^{89} +(0.491011 - 1.51118i) q^{90} +(-13.3140 + 4.89459i) q^{91} +(0.772311 + 0.561117i) q^{92} +(2.48375 + 0.527938i) q^{93} +(-1.98239 + 2.20166i) q^{94} +(-0.152913 + 1.45487i) q^{95} +(0.104528 + 0.994522i) q^{96} +(2.23680 - 6.88417i) q^{97} +(-6.15931 + 3.32609i) q^{98} +(2.00465 + 2.64223i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9}+O(q^{10}) $ 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9	\( 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9} + 12 q^{10} + 2 q^{11} + 20 q^{12} + 10 q^{13} + 5 q^{14} - 6 q^{15} + 5 q^{16} + 5 q^{18} - 13 q^{19} + 6 q^{20} - 2 q^{21} - 4 q^{22} - 20 q^{23} - 5 q^{24} + 12 q^{25} + 10 q^{27} - 3 q^{28} + 12 q^{29} + 3 q^{30} - 10 q^{31} - 20 q^{32} + 8 q^{33} - 13 q^{35} - 10 q^{36} + 3 q^{37} + 2 q^{38} + 5 q^{39} - 3 q^{40} - 44 q^{41} - 3 q^{42} + 36 q^{43} - 3 q^{44} + 12 q^{45} + 11 q^{47} + 10 q^{48} + 33 q^{49} - 4 q^{50} + 26 q^{53} + 20 q^{54} - 20 q^{55} + 8 q^{56} + 4 q^{57} - 6 q^{58} + 4 q^{59} + 3 q^{60} - 23 q^{61} + 5 q^{63} - 10 q^{64} - 50 q^{65} - 7 q^{66} - 108 q^{67} + 20 q^{69} - 86 q^{71} + 5 q^{72} - 35 q^{73} + 3 q^{74} - 2 q^{75} - 44 q^{76} - 37 q^{77} + 20 q^{78} + 3 q^{79} - 3 q^{80} + 5 q^{81} - 28 q^{82} - 88 q^{83} - 5 q^{84} + 96 q^{85} - 13 q^{86} + 6 q^{87} - 8 q^{88} + 6 q^{89} + 6 q^{90} + 40 q^{91} - 20 q^{92} + 10 q^{93} - 24 q^{94} + 36 q^{95} - 5 q^{96} + 60 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9 + 12 * q^10 + 2 * q^11 + 20 * q^12 + 10 * q^13 + 5 * q^14 - 6 * q^15 + 5 * q^16 + 5 * q^18 - 13 * q^19 + 6 * q^20 - 2 * q^21 - 4 * q^22 - 20 * q^23 - 5 * q^24 + 12 * q^25 + 10 * q^27 - 3 * q^28 + 12 * q^29 + 3 * q^30 - 10 * q^31 - 20 * q^32 + 8 * q^33 - 13 * q^35 - 10 * q^36 + 3 * q^37 + 2 * q^38 + 5 * q^39 - 3 * q^40 - 44 * q^41 - 3 * q^42 + 36 * q^43 - 3 * q^44 + 12 * q^45 + 11 * q^47 + 10 * q^48 + 33 * q^49 - 4 * q^50 + 26 * q^53 + 20 * q^54 - 20 * q^55 + 8 * q^56 + 4 * q^57 - 6 * q^58 + 4 * q^59 + 3 * q^60 - 23 * q^61 + 5 * q^63 - 10 * q^64 - 50 * q^65 - 7 * q^66 - 108 * q^67 + 20 * q^69 - 86 * q^71 + 5 * q^72 - 35 * q^73 + 3 * q^74 - 2 * q^75 - 44 * q^76 - 37 * q^77 + 20 * q^78 + 3 * q^79 - 3 * q^80 + 5 * q^81 - 28 * q^82 - 88 * q^83 - 5 * q^84 + 96 * q^85 - 13 * q^86 + 6 * q^87 - 8 * q^88 + 6 * q^89 + 6 * q^90 + 40 * q^91 - 20 * q^92 + 10 * q^93 - 24 * q^94 + 36 * q^95 - 5 * q^96 + 60 * q^97 + 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.669131	+	0.743145i	0.473147	+	0.525483i
$2$	0.669131	+	0.743145i	0.473147	+	0.525483i
$3$	−0.913545	−	0.406737i	−0.527436	−	0.234830i
$3$	−0.913545	−	0.406737i	−0.527436	−	0.234830i
$4$	−0.104528	+	0.994522i	−0.0522642	+	0.497261i
$5$	−1.55422	−	0.330360i	−0.695070	−	0.147742i	−0.153189	−	0.988197i	$-0.548954\pi$
$5$	−1.55422	−	0.330360i	−0.695070	−	0.147742i	−0.541881	+	0.840455i	$0.682288\pi$
$6$	−0.309017	−	0.951057i	−0.126156	−	0.388267i
$7$	−1.63560	−	2.07962i	−0.618199	−	0.786022i
$7$	−1.63560	−	2.07962i	−0.618199	−	0.786022i
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	0.669131	+	0.743145i	0.223044	+	0.247715i
$10$	−0.794473	−	1.37607i	−0.251234	−	0.435151i
$11$	3.30493	+	0.278246i	0.996475	+	0.0838943i
$11$	3.30493	+	0.278246i	0.996475	+	0.0838943i
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	1.65680	−	5.09910i	0.459513	−	1.41424i	−0.406241	−	0.913766i	$-0.633160\pi$
$13$	1.65680	−	5.09910i	0.459513	−	1.41424i	0.865754	−	0.500470i	$-0.166840\pi$
$14$	0.451027	−	2.60702i	0.120542	−	0.696757i
$15$	1.28548	+	0.933958i	0.331910	+	0.241147i
$16$	−0.978148	−	0.207912i	−0.244537	−	0.0519779i
$17$	4.88491	−	5.42524i	1.18476	−	1.31581i	0.246806	−	0.969065i	$-0.420619\pi$
$17$	4.88491	−	5.42524i	1.18476	−	1.31581i	0.937958	−	0.346749i	$-0.112714\pi$
$18$	−0.104528	+	0.994522i	−0.0246376	+	0.234411i
$19$	−0.0962357	−	0.915621i	−0.0220780	−	0.210058i	−0.999999	−	0.00108506i	$-0.999655\pi$
$19$	−0.0962357	−	0.915621i	−0.0220780	−	0.210058i	0.977921	−	0.208973i	$-0.0670121\pi$
$20$	0.491011	−	1.51118i	0.109793	−	0.337909i
$21$	0.648339	+	2.56508i	0.141479	+	0.559747i
$22$	2.00465	+	2.64223i	0.427394	+	0.563325i
$23$	0.477314	−	0.826733i	0.0995269	−	0.172386i	−0.811962	−	0.583710i	$-0.801600\pi$
$23$	0.477314	−	0.826733i	0.0995269	−	0.172386i	0.911489	+	0.411325i	$0.134934\pi$
$24$	0.978148	−	0.207912i	0.199664	−	0.0424398i
$25$	−2.26126	−	1.00678i	−0.452251	−	0.201355i
$26$	4.89799	−	2.18072i	0.960574	−	0.427675i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	2.23919	−	1.40926i	0.423168	−	0.266325i
$29$	−4.30641	−	3.12879i	−0.799680	−	0.581002i	0.111140	−	0.993805i	$-0.464550\pi$
$29$	−4.30641	−	3.12879i	−0.799680	−	0.581002i	−0.910820	+	0.412803i	$0.864550\pi$
$30$	0.166090	+	1.58024i	0.0303237	+	0.288511i
$31$	−2.48375	+	0.527938i	−0.446095	+	0.0948204i	−0.425482	−	0.904967i	$-0.639895\pi$
$31$	−2.48375	+	0.527938i	−0.446095	+	0.0948204i	−0.0206134	+	0.999788i	$0.506562\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−2.90603	−	1.59843i	−0.505875	−	0.278250i
$34$	7.30038			1.25200
$35$	1.85506	+	3.77253i	0.313563	+	0.637673i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	−9.98723	+	4.44660i	−1.64189	+	0.731016i	−0.999378	−	0.0352594i	$-0.988774\pi$
$37$	−9.98723	+	4.44660i	−1.64189	+	0.731016i	−0.642512	+	0.766276i	$0.722108\pi$
$38$	0.616045	−	0.684187i	0.0999357	−	0.110990i
$39$	−3.58755	+	3.98438i	−0.574468	+	0.638011i
$40$	1.45157	−	0.646282i	0.229514	−	0.102186i
$41$	2.76970	−	2.01231i	0.432555	−	0.314270i	−0.350115	−	0.936707i	$-0.613857\pi$
$41$	2.76970	−	2.01231i	0.432555	−	0.314270i	0.782670	+	0.622437i	$0.213857\pi$
$42$	−1.47241	+	2.19819i	−0.227197	+	0.339187i
$43$	11.0313			1.68226			0.841128	−	0.540835i	$-0.181892\pi$
$43$	11.0313			1.68226			0.841128	+	0.540835i	$0.181892\pi$
$44$	−0.622181	+	3.25774i	−0.0937973	+	0.491123i
$45$	−0.794473	−	1.37607i	−0.118433	−	0.205132i
$46$	0.933768	−	0.198478i	0.137677	−	0.0292640i
$47$	0.309679	+	2.94640i	0.0451714	+	0.429777i	0.993614	+	0.112829i	$0.0359913\pi$
$47$	0.309679	+	2.94640i	0.0451714	+	0.429777i	−0.948443	+	0.316948i	$0.897342\pi$
$48$	0.809017	+	0.587785i	0.116772	+	0.0848395i
$49$	−1.64962	+	6.80285i	−0.235660	+	0.971836i
$50$	−0.764895	−	2.35411i	−0.108173	−	0.332921i
$51$	−6.66923	+	2.96933i	−0.933879	+	0.415790i
$52$	4.89799	+	2.18072i	0.679228	+	0.302412i
$53$	10.4648	−	2.22437i	1.43746	−	0.305541i	0.577702	−	0.816248i	$-0.303949\pi$
$53$	10.4648	−	2.22437i	1.43746	−	0.305541i	0.859755	+	0.510707i	$0.170616\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−5.04468	−	1.52427i	−0.680225	−	0.205533i
$56$	2.54560	+	0.721064i	0.340170	+	0.0963563i
$57$	−0.284501	+	0.875604i	−0.0376831	+	0.115977i
$58$	−0.556407	−	5.29385i	−0.0730598	−	0.695117i
$59$	−0.449852	+	4.28006i	−0.0585658	+	0.557216i	0.925417	+	0.378951i	$0.123715\pi$
$59$	−0.449852	+	4.28006i	−0.0585658	+	0.557216i	−0.983982	+	0.178265i	$0.942952\pi$
$60$	−1.06321	+	1.18082i	−0.137260	+	0.152443i
$61$	−9.88922	−	2.10202i	−1.26618	−	0.269136i	−0.474603	−	0.880200i	$-0.657408\pi$
$61$	−9.88922	−	2.10202i	−1.26618	−	0.269136i	−0.791581	+	0.611064i	$0.790742\pi$
$62$	−2.05429	−	1.49253i	−0.260895	−	0.189551i
$63$	0.451027	−	2.60702i	0.0568240	−	0.328454i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−4.25957	+	7.37780i	−0.528335	+	0.915103i
$66$	−0.756653	−	3.22916i	−0.0931375	−	0.397482i
$67$	−6.94805	−	12.0344i	−0.848840	−	1.47023i	−0.882245	−	0.470791i	$-0.843968\pi$
$67$	−6.94805	−	12.0344i	−0.848840	−	1.47023i	0.0334051	−	0.999442i	$-0.489365\pi$
$68$	4.88491	+	5.42524i	0.592382	+	0.657907i
$69$	−0.772311	+	0.561117i	−0.0929753	+	0.0675505i
$70$	−1.56225	+	3.90290i	−0.186725	+	0.466485i
$71$	2.23899	+	6.89091i	0.265719	+	0.817800i	0.991527	+	0.129902i	$0.0414664\pi$
$71$	2.23899	+	6.89091i	0.265719	+	0.817800i	−0.725807	+	0.687898i	$0.758534\pi$
$72$	−0.978148	−	0.207912i	−0.115276	−	0.0245026i
$73$	0.182708	−	1.73835i	0.0213844	−	0.203459i	−0.978613	−	0.205709i	$-0.934050\pi$
$73$	0.182708	−	1.73835i	0.0213844	−	0.203459i	0.999997	+	0.00225091i	$0.000716487\pi$
$74$	−9.98723	−	4.44660i	−1.16099	−	0.516907i
$75$	1.65627	+	1.83947i	0.191249	+	0.212404i
$76$	0.920665			0.105608
$77$	−4.82690	−	7.32810i	−0.550077	−	0.835114i
$78$	−5.36151			−0.607072
$79$	7.03898	+	7.81758i	0.791947	+	0.879546i	0.995026	−	0.0996162i	$-0.0317615\pi$
$79$	7.03898	+	7.81758i	0.791947	+	0.879546i	−0.203079	+	0.979162i	$0.565095\pi$
$80$	1.45157	+	0.646282i	0.162291	+	0.0722565i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	3.34873	+	0.711795i	0.369805	+	0.0786046i
$83$	1.40191	+	4.31464i	0.153880	+	0.473593i	0.998046	−	0.0624890i	$-0.0199038\pi$
$83$	1.40191	+	4.31464i	0.153880	+	0.473593i	−0.844166	+	0.536082i	$0.819904\pi$
$84$	−2.61880	+	0.376663i	−0.285735	+	0.0410973i
$85$	−9.38452	+	6.81825i	−1.01789	+	0.739543i
$86$	7.38138	+	8.19785i	0.795954	+	0.883997i
$87$	2.66151	+	4.60987i	0.285344	+	0.494230i
$88$	−2.83730	+	1.71748i	−0.302457	+	0.183085i
$89$	8.07291	−	13.9827i	0.855727	−	1.48216i	−0.0202423	−	0.999795i	$-0.506444\pi$
$89$	8.07291	−	13.9827i	0.855727	−	1.48216i	0.875969	−	0.482367i	$-0.160223\pi$
$90$	0.491011	−	1.51118i	0.0517571	−	0.159292i
$91$	−13.3140	+	4.89459i	−1.39569	+	0.513092i
$92$	0.772311	+	0.561117i	0.0805190	+	0.0585004i
$93$	2.48375	+	0.527938i	0.257553	+	0.0547446i
$94$	−1.98239	+	2.20166i	−0.204468	+	0.227084i
$95$	−0.152913	+	1.45487i	−0.0156886	+	0.149267i
$96$	0.104528	+	0.994522i	0.0106684	+	0.101503i
$97$	2.23680	−	6.88417i	0.227113	−	0.698982i	−0.770957	−	0.636887i	$-0.780222\pi$
$97$	2.23680	−	6.88417i	0.227113	−	0.698982i	0.998070	−	0.0620948i	$-0.0197781\pi$
$98$	−6.15931	+	3.32609i	−0.622185	+	0.335986i
$99$	2.00465	+	2.64223i	0.201475	+	0.265554i
$100$	1.23763	−	2.14363i	0.123763	−	0.214363i
$101$	−3.40224	+	0.723169i	−0.338536	+	0.0719580i	−0.374043	−	0.927411i	$-0.622029\pi$
$101$	−3.40224	+	0.723169i	−0.338536	+	0.0719580i	0.0355070	+	0.999369i	$0.488695\pi$
$102$	−6.66923	−	2.96933i	−0.660352	−	0.294008i
$103$	−7.69499	+	3.42603i	−0.758210	+	0.337577i	−0.749166	−	0.662382i	$-0.769545\pi$
$103$	−7.69499	+	3.42603i	−0.758210	+	0.337577i	−0.00904390	+	0.999959i	$0.502879\pi$
$104$	1.65680	+	5.09910i	0.162462	+	0.500008i
$105$	−0.160261	−	4.20090i	−0.0156399	−	0.409966i
$106$	8.65538	+	6.28850i	0.840685	+	0.610793i
$107$	1.40459	+	13.3638i	0.135787	+	1.29193i	0.824071	+	0.566487i	$0.191698\pi$
$107$	1.40459	+	13.3638i	0.135787	+	1.29193i	−0.688283	+	0.725442i	$0.741635\pi$
$108$	0.978148	−	0.207912i	0.0941223	−	0.0200063i
$109$	0.102319	+	0.177222i	0.00980040	+	0.0169748i	0.870884	−	0.491489i	$-0.163547\pi$
$109$	0.102319	+	0.177222i	0.00980040	+	0.0169748i	−0.861084	+	0.508463i	$0.830214\pi$
$110$	−2.24279	−	4.76887i	−0.213842	−	0.454694i
$111$	10.9324			1.03766
$112$	1.16748	+	2.37423i	0.110317	+	0.224344i
$113$	7.10517	−	5.16221i	0.668398	−	0.485620i	−0.201090	−	0.979573i	$-0.564449\pi$
$113$	7.10517	−	5.16221i	0.668398	−	0.485620i	0.869489	+	0.493953i	$0.164449\pi$
$114$	−0.841069	+	0.374468i	−0.0787734	+	0.0350722i
$115$	−1.01497	+	1.12724i	−0.0946467	+	0.105116i
$116$	3.56179	−	3.95577i	0.330704	−	0.367284i
$117$	4.89799	−	2.18072i	0.452819	−	0.201608i
$118$	−3.48171	+	2.52961i	−0.320518	+	0.232870i
$119$	−19.2722	−	1.28522i	−1.76668	−	0.117816i
$120$	−1.58895			−0.145050
$121$	10.8452	+	1.83917i	0.985923	+	0.167197i
$122$	−5.05507	−	8.75565i	−0.457665	−	0.792699i
$123$	−3.34873	+	0.711795i	−0.301945	+	0.0641804i
$124$	−0.265423	−	2.52533i	−0.0238357	−	0.226781i
$125$	9.60932	+	6.98158i	0.859483	+	0.624451i
$126$	2.23919	−	1.40926i	0.199483	−	0.125547i
$127$	3.84432	+	11.8316i	0.341128	+	1.04988i	0.963624	+	0.267261i	$0.0861186\pi$
$127$	3.84432	+	11.8316i	0.341128	+	1.04988i	−0.622496	+	0.782623i	$0.713881\pi$
$128$	0.913545	−	0.406737i	0.0807468	−	0.0359508i
$129$	−10.0776	−	4.48683i	−0.887282	−	0.395044i
$130$	−8.33299	+	1.77123i	−0.730851	+	0.155347i
$131$	−0.984283	+	1.70483i	−0.0859972	+	0.148952i	−0.905816	−	0.423672i	$-0.860741\pi$
$131$	−0.984283	+	1.70483i	−0.0859972	+	0.148952i	0.819818	+	0.572623i	$0.194074\pi$
$132$	1.89343	−	2.72303i	0.164802	−	0.237010i
$133$	−1.74674	+	1.69772i	−0.151462	+	0.147211i
$134$	4.29413	−	13.2160i	0.370956	−	1.14169i
$135$	0.166090	+	1.58024i	0.0142948	+	0.136005i
$136$	−0.763097	+	7.26039i	−0.0654351	+	0.622573i
$137$	5.40592	−	6.00389i	0.461859	−	0.512947i	−0.466556	−	0.884492i	$-0.654505\pi$
$137$	5.40592	−	6.00389i	0.461859	−	0.512947i	0.928415	+	0.371545i	$0.121172\pi$
$138$	−0.933768	−	0.198478i	−0.0794876	−	0.0168956i
$139$	−9.83068	−	7.14241i	−0.833827	−	0.605811i	0.0868122	−	0.996225i	$-0.472332\pi$
$139$	−9.83068	−	7.14241i	−0.833827	−	0.605811i	−0.920640	+	0.390414i	$0.872332\pi$
$140$	−3.94577	+	1.45057i	−0.333478	+	0.122595i
$141$	0.915503	−	2.81763i	0.0770993	−	0.237287i
$142$	−3.62276	+	6.27481i	−0.304016	+	0.526571i
$143$	6.89441	−	16.3912i	0.576540	−	1.37070i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	5.65949	+	6.28550i	0.469995	+	0.521983i
$146$	1.41410	−	1.02741i	0.117032	−	0.0850286i
$147$	4.27397	−	5.54375i	0.352511	−	0.457241i
$148$	−3.37829	−	10.3973i	−0.277694	−	0.854654i
$149$	−9.96342	−	2.11779i	−0.816235	−	0.173496i	−0.219168	−	0.975687i	$-0.570334\pi$
$149$	−9.96342	−	2.11779i	−0.816235	−	0.173496i	−0.597067	+	0.802191i	$0.703668\pi$
$150$	−0.258734	+	2.46169i	−0.0211256	+	0.200996i
$151$	−14.2721	−	6.35434i	−1.16145	−	0.517109i	−0.266741	−	0.963768i	$-0.585947\pi$
$151$	−14.2721	−	6.35434i	−1.16145	−	0.517109i	−0.894704	+	0.446659i	$0.852614\pi$
$152$	0.616045	+	0.684187i	0.0499679	+	0.0554949i
$153$	7.30038			0.590201
$154$	2.21601	−	8.49054i	0.178571	−	0.684187i
$155$	4.03471			0.324076
$156$	−3.58755	−	3.98438i	−0.287234	−	0.319006i
$157$	5.16830	+	2.30108i	0.412475	+	0.183646i	0.602474	−	0.798138i	$-0.294182\pi$
$157$	5.16830	+	2.30108i	0.412475	+	0.183646i	−0.189999	+	0.981784i	$0.560848\pi$
$158$	−1.09960	+	10.4620i	−0.0874792	+	0.832309i
$159$	−10.4648	−	2.22437i	−0.829916	−	0.176404i
$160$	0.491011	+	1.51118i	0.0388178	+	0.119469i
$161$	−2.49998	+	0.359573i	−0.197026	+	0.0283383i
$162$	−0.809017	+	0.587785i	−0.0635624	+	0.0461808i
$163$	1.53524	+	1.70506i	0.120249	+	0.133550i	0.800263	−	0.599649i	$-0.204693\pi$
$163$	1.53524	+	1.70506i	0.120249	+	0.133550i	−0.680014	+	0.733199i	$0.738026\pi$
$164$	1.71177	+	2.96488i	0.133667	+	0.231518i
$165$	3.98857	+	3.44435i	0.310509	+	0.268142i
$166$	−2.26834	+	3.92888i	−0.176057	+	0.304940i
$167$	−2.47369	+	7.61325i	−0.191420	+	0.589131i	0.808579	+	0.588387i	$0.200237\pi$
$167$	−2.47369	+	7.61325i	−0.191420	+	0.589131i	−1.00000		0.000743933i	$0.999763\pi$
$168$	−2.03224	−	1.69411i	−0.156790	−	0.130704i
$169$	−12.7386	−	9.25516i	−0.979895	−	0.711935i
$170$	−11.3464	−	2.41176i	−0.870230	−	0.184973i
$171$	0.616045	−	0.684187i	0.0471101	−	0.0523211i
$172$	−1.15308	+	10.9709i	−0.0879219	+	0.836521i
$173$	−1.06165	−	10.1009i	−0.0807155	−	0.767956i	−0.957764	−	0.287555i	$-0.907158\pi$
$173$	−1.06165	−	10.1009i	−0.0807155	−	0.767956i	0.877049	−	0.480402i	$-0.159509\pi$
$174$	−1.64490	+	5.06249i	−0.124700	+	0.383786i
$175$	1.60480	+	6.34923i	0.121312	+	0.479957i
$176$	−3.17486	−	0.959300i	−0.239314	−	0.0723099i
$177$	2.15182	−	3.72706i	0.161740	−	0.280143i
$178$	15.7930	−	3.35690i	1.18374	−	0.251611i
$179$	4.54744	+	2.02465i	0.339892	+	0.151330i	0.569583	−	0.821934i	$-0.307105\pi$
$179$	4.54744	+	2.02465i	0.339892	+	0.151330i	−0.229691	+	0.973264i	$0.573771\pi$
$180$	1.45157	−	0.646282i	0.108194	−	0.0481710i
$181$	2.68243	+	8.25567i	0.199383	+	0.613639i	0.999897	+	0.0143248i	$0.00455989\pi$
$181$	2.68243	+	8.25567i	0.199383	+	0.613639i	−0.800514	+	0.599314i	$0.795440\pi$
$182$	−12.5462	−	6.61915i	−0.929988	−	0.490644i
$183$	8.17928	+	5.94260i	0.604630	+	0.439289i
$184$	0.0997859	+	0.949399i	0.00735631	+	0.0699906i
$185$	16.9914	−	3.61162i	1.24923	−	0.265532i
$186$	1.26962	+	2.19905i	0.0930931	+	0.161242i
$187$	17.6538	−	16.5708i	1.29098	−	1.21178i
$188$	−2.96263			−0.216072
$189$	−1.47241	+	2.19819i	−0.107102	+	0.159894i
$190$	−1.18350	+	0.859863i	−0.0858601	+	0.0623810i
$191$	10.0393	−	4.46978i	0.726418	−	0.323422i	−0.00999931	−	0.999950i	$-0.503183\pi$
$191$	10.0393	−	4.46978i	0.726418	−	0.323422i	0.736417	+	0.676528i	$0.236516\pi$
$192$	−0.669131	+	0.743145i	−0.0482903	+	0.0536319i
$193$	12.8782	−	14.3027i	0.926991	−	1.02953i	−0.0724919	−	0.997369i	$-0.523095\pi$
$193$	12.8782	−	14.3027i	0.926991	−	1.02953i	0.999483	−	0.0321587i	$-0.0102382\pi$
$194$	6.61265	−	2.94414i	0.474760	−	0.211377i
$195$	6.89214	−	5.00743i	0.493556	−	0.358590i
$196$	−6.59315	−	2.35168i	−0.470939	−	0.167977i
$197$	1.58778			0.113125			0.0565624	−	0.998399i	$-0.481986\pi$
$197$	1.58778			0.113125			0.0565624	+	0.998399i	$0.481986\pi$
$198$	−0.622181	+	3.25774i	−0.0442165	+	0.231518i
$199$	10.4564	+	18.1110i	0.741233	+	1.28385i	0.951934	+	0.306302i	$0.0990919\pi$
$199$	10.4564	+	18.1110i	0.741233	+	1.28385i	−0.210701	+	0.977550i	$0.567575\pi$
$200$	2.42116	−	0.514634i	0.171202	−	0.0363901i
$201$	1.45254	+	13.8200i	0.102454	+	0.974786i
$202$	−2.81396	−	2.04446i	−0.197990	−	0.143848i
$203$	0.536879	+	14.0731i	0.0376816	+	0.987741i
$204$	−2.25594	−	6.94307i	−0.157947	−	0.486112i
$205$	−4.96953	+	2.21258i	−0.347087	+	0.154533i
$206$	−7.69499	−	3.42603i	−0.536135	−	0.238703i
$207$	0.933768	−	0.198478i	0.0649013	−	0.0137952i
$208$	−2.68076	+	4.64321i	−0.185877	+	0.321948i
$209$	−0.0632846	−	3.05284i	−0.00437749	−	0.211170i
$210$	3.01464	−	2.93005i	0.208030	−	0.202192i
$211$	1.55872	−	4.79726i	0.107307	−	0.330257i	−0.882958	−	0.469452i	$-0.844451\pi$
$211$	1.55872	−	4.79726i	0.107307	−	0.330257i	0.990265	+	0.139195i	$0.0444515\pi$
$212$	1.11831	+	10.6400i	0.0768060	+	0.730760i
$213$	0.757364	−	7.20584i	0.0518937	−	0.493736i
$214$	−8.99140	+	9.98596i	−0.614639	+	0.682626i
$215$	−17.1451	−	3.64430i	−1.16929	−	0.248539i
$216$	0.809017	+	0.587785i	0.0550466	+	0.0399937i
$217$	5.16033	+	4.30176i	0.350306	+	0.292022i
$218$	−0.0632367	+	0.194623i	−0.00428293	+	0.0131815i
$219$	−0.873963	+	1.51375i	−0.0590569	+	0.102290i
$220$	2.04324	−	4.85771i	0.137755	−	0.327507i
$221$	−19.5705	−	33.8972i	−1.31646	−	2.28017i
$222$	7.31519	+	8.12434i	0.490963	+	0.545270i
$223$	16.2215	−	11.7856i	1.08627	−	0.789221i	0.107504	−	0.994205i	$-0.465714\pi$
$223$	16.2215	−	11.7856i	1.08627	−	0.789221i	0.978765	+	0.204984i	$0.0657141\pi$
$224$	−0.983202	+	2.45628i	−0.0656929	+	0.164117i
$225$	−0.764895	−	2.35411i	−0.0509930	−	0.156940i
$226$	8.59055	+	1.82598i	0.571435	+	0.121462i
$227$	−2.44754	+	23.2867i	−0.162449	+	1.54560i	0.544761	+	0.838592i	$0.316621\pi$
$227$	−2.44754	+	23.2867i	−0.162449	+	1.54560i	−0.707209	+	0.707004i	$0.750046\pi$
$228$	−0.841069	−	0.374468i	−0.0557012	−	0.0247998i
$229$	−5.10334	−	5.66783i	−0.337238	−	0.374541i	0.550543	−	0.834807i	$-0.314421\pi$
$229$	−5.10334	−	5.66783i	−0.337238	−	0.374541i	−0.887781	+	0.460266i	$0.847754\pi$
$230$	−1.51685			−0.100018
$231$	1.42899	+	8.65783i	0.0940208	+	0.569643i
$232$	5.32301			0.349473
$233$	19.4281	+	21.5771i	1.27278	+	1.41356i	0.866006	+	0.500034i	$0.166679\pi$
$233$	19.4281	+	21.5771i	1.27278	+	1.41356i	0.406773	+	0.913529i	$0.366654\pi$
$234$	4.89799	+	2.18072i	0.320191	+	0.142558i
$235$	0.492063	−	4.68167i	0.0320987	−	0.305398i
$236$	−4.20959	−	0.894776i	−0.274021	−	0.0582449i
$237$	−3.25073	−	10.0047i	−0.211158	−	0.649877i
$238$	−11.9405	−	15.1820i	−0.773988	−	0.984103i
$239$	14.7235	−	10.6972i	0.952383	−	0.691947i	0.00101394	−	0.999999i	$-0.499677\pi$
$239$	14.7235	−	10.6972i	0.952383	−	0.691947i	0.951369	+	0.308053i	$0.0996773\pi$
$240$	−1.06321	−	1.18082i	−0.0686300	−	0.0762214i
$241$	12.7360	+	22.0593i	0.820396	+	1.42097i	0.905388	+	0.424586i	$0.139580\pi$
$241$	12.7360	+	22.0593i	0.820396	+	1.42097i	−0.0849918	+	0.996382i	$0.527086\pi$
$242$	5.89006	+	9.29017i	0.378627	+	0.597195i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	3.12421	−	9.61532i	0.200007	−	0.615558i
$245$	4.81127	−	10.0282i	0.307381	−	0.640677i
$246$	−2.76970	−	2.01231i	−0.176590	−	0.128300i
$247$	−4.82829	−	1.02628i	−0.307217	−	0.0653009i
$248$	1.69908	−	1.88702i	0.107892	−	0.119826i
$249$	0.474212	−	4.51182i	0.0300520	−	0.285925i
$250$	1.24156	+	11.8127i	0.0785235	+	0.747101i
$251$	4.43039	−	13.6353i	0.279644	−	0.860655i	−0.708309	−	0.705902i	$-0.750542\pi$
$251$	4.43039	−	13.6353i	0.279644	−	0.860655i	0.987953	−	0.154753i	$-0.0494582\pi$
$252$	2.54560	+	0.721064i	0.160358	+	0.0454228i
$253$	1.80753	−	2.59948i	0.113638	−	0.163428i
$254$	−6.22024	+	10.7738i	−0.390292	+	0.676006i
$255$	11.3464	−	2.41176i	0.710540	−	0.151030i
$256$	0.913545	+	0.406737i	0.0570966	+	0.0254210i
$257$	−25.3671	+	11.2942i	−1.58236	+	0.704511i	−0.994528	−	0.104473i	$-0.966685\pi$
$257$	−25.3671	+	11.2942i	−1.58236	+	0.704511i	−0.587831	+	0.808984i	$0.700018\pi$
$258$	−3.40886	−	10.4914i	−0.212226	−	0.653165i
$259$	25.5823	+	13.4968i	1.58961	+	0.838647i
$260$	−6.89214	−	5.00743i	−0.427432	−	0.310548i
$261$	−0.556407	−	5.29385i	−0.0344407	−	0.327681i
$262$	−1.92555	+	0.409288i	−0.118961	+	0.0252859i
$263$	10.0208	+	17.3565i	0.617908	+	1.07025i	0.989867	+	0.141998i	$0.0453528\pi$
$263$	10.0208	+	17.3565i	0.617908	+	1.07025i	−0.371959	+	0.928249i	$0.621314\pi$
$264$	3.29056	−	0.414969i	0.202520	−	0.0255396i
$265$	−16.9995			−1.04427
$266$	−2.43045	−	0.162081i	−0.149021	−	0.00993783i
$267$	−13.0622	+	9.49028i	−0.799396	+	0.580795i
$268$	12.6947	−	5.65205i	0.775453	−	0.345254i
$269$	−20.1339	+	22.3610i	−1.22759	+	1.36337i	−0.317874	+	0.948133i	$0.602969\pi$
$269$	−20.1339	+	22.3610i	−1.22759	+	1.36337i	−0.909712	+	0.415239i	$0.863698\pi$
$270$	−1.06321	+	1.18082i	−0.0647050	+	0.0718622i
$271$	22.5373	−	10.0343i	1.36905	−	0.609538i	0.415171	−	0.909743i	$-0.363722\pi$
$271$	22.5373	−	10.0343i	1.36905	−	0.609538i	0.953875	+	0.300205i	$0.0970551\pi$
$272$	−5.90613	+	4.29106i	−0.358112	+	0.260183i
$273$	14.1538	+	0.943882i	0.856626	+	0.0571264i
$274$	8.07903			0.488072
$275$	−7.19317	−	3.95651i	−0.433764	−	0.238587i
$276$	−0.477314	−	0.826733i	−0.0287309	−	0.0497635i
$277$	5.80055	−	1.23295i	0.348521	−	0.0740805i	−0.0303250	−	0.999540i	$-0.509654\pi$
$277$	5.80055	−	1.23295i	0.348521	−	0.0740805i	0.378846	+	0.925460i	$0.376321\pi$
$278$	−1.27017	−	12.0848i	−0.0761795	−	0.724799i
$279$	−2.05429	−	1.49253i	−0.122987	−	0.0893553i
$280$	−3.71821	−	1.96166i	−0.222206	−	0.117232i
$281$	2.89489	+	8.90954i	0.172694	+	0.531499i	0.999521	−	0.0309588i	$-0.00985605\pi$
$281$	2.89489	+	8.90954i	0.172694	+	0.531499i	−0.826826	+	0.562457i	$0.809856\pi$
$282$	2.70650	−	1.20501i	0.161170	−	0.0717573i
$283$	−9.25699	−	4.12148i	−0.550271	−	0.244996i	0.112716	−	0.993627i	$-0.464045\pi$
$283$	−9.25699	−	4.12148i	−0.550271	−	0.244996i	−0.662987	+	0.748631i	$0.730712\pi$
$284$	−7.08720	+	1.50643i	−0.420548	+	0.0893902i
$285$	0.731443	−	1.26690i	0.0433269	−	0.0750445i
$286$	16.7943	−	5.84430i	0.993067	−	0.345581i
$287$	−8.71496	−	2.46859i	−0.514428	−	0.145717i
$288$	0.309017	−	0.951057i	0.0182090	−	0.0560415i
$289$	−3.79392	−	36.0967i	−0.223172	−	2.12334i
$290$	−0.884099	+	8.41164i	−0.0519161	+	0.493949i
$291$	−4.84346	+	5.37921i	−0.283929	+	0.315335i
$292$	1.70973	+	0.363414i	0.100054	+	0.0212672i
$293$	−0.556698	−	0.404465i	−0.0325226	−	0.0236291i	0.571405	−	0.820668i	$-0.306398\pi$
$293$	−0.556698	−	0.404465i	−0.0325226	−	0.0236291i	−0.603928	+	0.797039i	$0.706398\pi$
$294$	6.97965	−	0.533313i	0.407062	−	0.0311035i
$295$	2.11313	−	6.50355i	0.123031	−	0.378651i
$296$	5.46619	−	9.46772i	0.317716	−	0.550300i
$297$	−0.756653	−	3.22916i	−0.0439054	−	0.187375i
$298$	−5.09300	−	8.82134i	−0.295030	−	0.511007i
$299$	−3.42478	−	3.80360i	−0.198060	−	0.219968i
$300$	−2.00252	+	1.45492i	−0.115616	+	0.0839997i
$301$	−18.0428	−	22.9409i	−1.03997	−	1.32229i
$302$	−4.82769	−	14.8581i	−0.277802	−	0.854988i
$303$	3.40224	+	0.723169i	0.195454	+	0.0415450i
$304$	−0.0962357	+	0.915621i	−0.00551950	+	0.0525145i
$305$	14.6756	+	6.53401i	0.840324	+	0.374136i
$306$	4.88491	+	5.42524i	0.279252	+	0.310140i
$307$	−18.1230			−1.03433			−0.517167	−	0.855884i	$-0.673013\pi$
$307$	−18.1230			−1.03433			−0.517167	+	0.855884i	$0.673013\pi$
$308$	7.79250	−	4.03447i	0.444019	−	0.229885i
$309$	8.42322			0.479180
$310$	2.69975	+	2.99838i	0.153335	+	0.170296i
$311$	13.7830	+	6.13657i	0.781560	+	0.347973i	0.758426	−	0.651759i	$-0.225969\pi$
$311$	13.7830	+	6.13657i	0.781560	+	0.347973i	0.0231344	+	0.999732i	$0.492635\pi$
$312$	0.560431	−	5.33214i	0.0317281	−	0.301873i
$313$	−0.157732	−	0.0335269i	−0.00891553	−	0.00189505i	0.203452	−	0.979085i	$-0.434784\pi$
$313$	−0.157732	−	0.0335269i	−0.00891553	−	0.00189505i	−0.212367	+	0.977190i	$0.568117\pi$
$314$	1.74824	+	5.38052i	0.0986587	+	0.303640i
$315$	−1.56225	+	3.90290i	−0.0880230	+	0.219903i
$316$	−8.51053	+	6.18326i	−0.478754	+	0.347835i
$317$	5.60114	+	6.22070i	0.314591	+	0.349389i	0.879616	−	0.475685i	$-0.157800\pi$
$317$	5.60114	+	6.22070i	0.314591	+	0.349389i	−0.565024	+	0.825074i	$0.691133\pi$
$318$	−5.34932	−	9.26529i	−0.299975	−	0.519572i
$319$	−13.3618	−	11.5387i	−0.748118	−	0.646042i
$320$	−0.794473	+	1.37607i	−0.0444124	+	0.0769245i
$321$	4.15239	−	12.7798i	0.231764	−	0.713296i
$322$	−1.94003	−	1.61725i	−0.108114	−	0.0901257i
$323$	−5.43757	−	3.95062i	−0.302554	−	0.219819i
$324$	−0.978148	−	0.207912i	−0.0543415	−	0.0115506i
$325$	−8.88010	+	9.86235i	−0.492579	+	0.547065i
$326$	−0.239828	+	2.28181i	−0.0132828	+	0.126378i
$327$	−0.0213905	−	0.203517i	−0.00118290	−	0.0112545i
$328$	−1.05793	+	3.25598i	−0.0584146	+	0.179782i
$329$	5.62088	−	5.46315i	0.309889	−	0.301193i
$330$	0.109221	+	5.26880i	0.00601241	+	0.290038i
$331$	−6.15157	+	10.6548i	−0.338121	+	0.585642i	−0.984079	−	0.177730i	$-0.943125\pi$
$331$	−6.15157	+	10.6548i	−0.338121	+	0.585642i	0.645959	+	0.763373i	$0.276458\pi$
$332$	−4.43754	+	0.943228i	−0.243542	+	0.0517664i
$333$	−9.98723	−	4.44660i	−0.547297	−	0.243672i
$334$	−7.31297	+	3.25594i	−0.400148	+	0.178157i
$335$	6.82314	+	20.9995i	0.372788	+	1.14732i
$336$	−0.100860	−	2.64383i	−0.00550237	−	0.144233i
$337$	7.68703	+	5.58495i	0.418739	+	0.304232i	0.777130	−	0.629340i	$-0.216675\pi$
$337$	7.68703	+	5.58495i	0.418739	+	0.304232i	−0.358391	+	0.933571i	$0.616675\pi$
$338$	−1.64589	−	15.6596i	−0.0895244	−	0.851768i
$339$	−8.59055	+	1.82598i	−0.466575	+	0.0991736i
$340$	−5.79995	−	10.0458i	−0.314547	−	0.544811i
$341$	−8.35553	+	1.05370i	−0.452477	+	0.0570613i
$342$	0.920665			0.0497839
$343$	16.8454	−	7.69616i	0.909569	−	0.415554i
$344$	−8.92451	+	6.48403i	−0.481177	+	0.349596i
$345$	1.38571	−	0.616959i	0.0746043	−	0.0332160i
$346$	6.79604	−	7.54777i	0.365358	−	0.405771i
$347$	−15.0324	+	16.6952i	−0.806982	+	0.896245i	−0.996324	−	0.0856666i	$-0.972698\pi$
$347$	−15.0324	+	16.6952i	−0.806982	+	0.896245i	0.189341	+	0.981911i	$0.439365\pi$
$348$	−4.86282	+	2.16507i	−0.260674	+	0.116060i
$349$	16.0103	−	11.6322i	0.857012	−	0.622656i	−0.0700581	−	0.997543i	$-0.522318\pi$
$349$	16.0103	−	11.6322i	0.857012	−	0.622656i	0.927071	+	0.374887i	$0.122318\pi$
$350$	−3.64458	+	5.44107i	−0.194811	+	0.290837i
$351$	−5.36151			−0.286176
$352$	−1.41150	−	3.00128i	−0.0752331	−	0.159969i
$353$	−4.17589	−	7.23285i	−0.222260	−	0.384966i	0.733234	−	0.679977i	$-0.238010\pi$
$353$	−4.17589	−	7.23285i	−0.222260	−	0.384966i	−0.955494	+	0.295011i	$0.904677\pi$
$354$	4.20959	−	0.894776i	0.223737	−	0.0475568i
$355$	−1.20341	−	11.4497i	−0.0638704	−	0.607686i
$356$	13.0622	+	9.49028i	0.692298	+	0.502984i
$357$	17.0833	+	9.01281i	0.904143	+	0.477008i
$358$	1.53822	+	4.73417i	0.0812977	+	0.250208i
$359$	10.8208	−	4.81774i	0.571102	−	0.254271i	−0.100806	−	0.994906i	$-0.532142\pi$
$359$	10.8208	−	4.81774i	0.571102	−	0.254271i	0.671907	+	0.740635i	$0.265475\pi$
$360$	1.45157	+	0.646282i	0.0765046	+	0.0340621i
$361$	17.7557	−	3.77409i	0.934511	−	0.198636i
$362$	−4.34026	+	7.51755i	−0.228119	+	0.395114i
$363$	−9.15949	−	6.09129i	−0.480748	−	0.319710i
$364$	−3.47608	−	13.7527i	−0.182196	−	0.720839i
$365$	−0.858251	+	2.64142i	−0.0449229	+	0.138258i
$366$	1.05680	+	10.0548i	0.0552397	+	0.525571i
$367$	0.119819	−	1.14000i	0.00625450	−	0.0595076i	−0.990949	−	0.134235i	$-0.957142\pi$
$367$	0.119819	−	1.14000i	0.00625450	−	0.0595076i	0.997204	+	0.0747279i	$0.0238088\pi$
$368$	−0.638771	+	0.709427i	−0.0332983	+	0.0369815i
$369$	3.34873	+	0.711795i	0.174328	+	0.0370546i
$370$	14.0534	+	10.2104i	0.730601	+	0.530813i
$371$	−21.7422	−	18.1247i	−1.12880	−	0.940988i
$372$	−0.784668	+	2.41496i	−0.0406832	+	0.125210i
$373$	2.11528	−	3.66377i	0.109525	−	0.189703i	−0.806053	−	0.591844i	$-0.798400\pi$
$373$	2.11528	−	3.66377i	0.109525	−	0.189703i	0.915578	+	0.402140i	$0.131734\pi$
$374$	24.1273	+	2.03130i	1.24759	+	0.105036i
$375$	−5.93888	−	10.2864i	−0.306683	−	0.531190i
$376$	−1.98239	−	2.20166i	−0.102234	−	0.113542i
$377$	−23.0889	+	16.7750i	−1.18914	+	0.863959i
$378$	−2.61880	+	0.376663i	−0.134697	+	0.0193734i
$379$	−1.67674	−	5.16049i	−0.0861285	−	0.265076i	0.898712	−	0.438540i	$-0.144504\pi$
$379$	−1.67674	−	5.16049i	−0.0861285	−	0.265076i	−0.984840	+	0.173463i	$0.944504\pi$
$380$	−1.43092	−	0.304151i	−0.0734046	−	0.0156026i
$381$	1.30038	−	12.3723i	0.0666207	−	0.633853i
$382$	10.0393	+	4.46978i	0.513655	+	0.228694i
$383$	−14.5943	−	16.2086i	−0.745733	−	0.828221i	0.244205	−	0.969724i	$-0.421473\pi$
$383$	−14.5943	−	16.2086i	−0.745733	−	0.828221i	−0.989938	+	0.141503i	$0.954807\pi$
$384$	−1.00000			−0.0510310
$385$	5.08117	+	12.9841i	0.258961	+	0.661732i
$386$	19.2461			0.979602
$387$	7.38138	+	8.19785i	0.375217	+	0.416720i
$388$	6.61265	+	2.94414i	0.335706	+	0.149466i
$389$	−0.630061	+	5.99463i	−0.0319454	+	0.303940i	0.966870	+	0.255271i	$0.0821646\pi$
$389$	−0.630061	+	5.99463i	−0.0319454	+	0.303940i	−0.998815	+	0.0486690i	$0.984502\pi$
$390$	8.33299	+	1.77123i	0.421957	+	0.0896898i
$391$	−2.15359	−	6.62806i	−0.108912	−	0.335195i
$392$	−2.66404	−	6.47324i	−0.134554	−	0.326948i
$393$	1.59260	−	1.15709i	0.0803362	−	0.0583677i
$394$	1.06243	+	1.17995i	0.0535246	+	0.0594451i
$395$	−8.35752	−	14.4757i	−0.420513	−	0.728349i
$396$	−2.83730	+	1.71748i	−0.142579	+	0.0863069i
$397$	5.78337	−	10.0171i	0.290259	−	0.502743i	−0.683612	−	0.729846i	$-0.739592\pi$
$397$	5.78337	−	10.0171i	0.290259	−	0.502743i	0.973871	+	0.227103i	$0.0729253\pi$
$398$	−6.46240	+	19.8892i	−0.323931	+	0.996956i
$399$	2.28625	−	0.840486i	0.114456	−	0.0420769i
$400$	2.00252	+	1.45492i	0.100126	+	0.0727459i
$401$	−16.2776	−	3.45991i	−0.812865	−	0.172780i	−0.217319	−	0.976101i	$-0.569731\pi$
$401$	−16.2776	−	3.45991i	−0.812865	−	0.172780i	−0.595546	+	0.803321i	$0.703064\pi$
$402$	−9.29831	+	10.3268i	−0.463757	+	0.515055i
$403$	−1.42307	+	13.5396i	−0.0708881	+	0.674455i
$404$	−0.363576	−	3.45920i	−0.0180886	−	0.172101i
$405$	0.491011	−	1.51118i	0.0243985	−	0.0750910i
$406$	−10.0991	+	9.81575i	−0.501212	+	0.487147i
$407$	−34.2444	+	11.9168i	−1.69743	+	0.590694i
$408$	3.65019	−	6.32231i	0.180711	−	0.313001i
$409$	−18.5110	+	3.93463i	−0.915310	+	0.194555i	−0.641406	−	0.767202i	$-0.721648\pi$
$409$	−18.5110	+	3.93463i	−0.915310	+	0.194555i	−0.273904	+	0.961757i	$0.588315\pi$
$410$	−4.96953	−	2.21258i	−0.245427	−	0.109271i
$411$	−7.38056	+	3.28604i	−0.364056	+	0.162088i
$412$	−2.60292	−	8.01095i	−0.128236	−	0.394671i
$413$	9.63666	−	6.06495i	0.474189	−	0.298436i
$414$	0.772311	+	0.561117i	0.0379570	+	0.0275774i
$415$	−0.753497	−	7.16904i	−0.0369877	−	0.351914i
$416$	−5.24435	+	1.11472i	−0.257125	+	0.0546537i
$417$	6.07569	+	10.5234i	0.297528	+	0.515334i
$418$	2.22636	−	2.08978i	0.108895	−	0.102215i
$419$	−15.8657			−0.775088			−0.387544	−	0.921851i	$-0.626677\pi$
$419$	−15.8657			−0.775088			−0.387544	+	0.921851i	$0.626677\pi$
$420$	4.19464	+	0.279730i	0.204677	+	0.0136494i
$421$	−16.3651	+	11.8899i	−0.797587	+	0.579481i	−0.910205	−	0.414158i	$-0.864076\pi$
$421$	−16.3651	+	11.8899i	−0.797587	+	0.579481i	0.112618	+	0.993638i	$0.464076\pi$
$422$	4.60805	−	2.05164i	0.224316	−	0.0998721i
$423$	−1.98239	+	2.20166i	−0.0963870	+	0.107049i
$424$	−7.15879	+	7.95064i	−0.347661	+	0.386117i
$425$	−16.5080	+	7.34985i	−0.800757	+	0.356520i
$426$	5.86176	−	4.25881i	0.284003	−	0.206340i
$427$	11.8034	+	24.0039i	0.571207	+	1.16163i
$428$	−13.4374			−0.649523
$429$	−12.9653	+	12.1699i	−0.625968	+	0.587568i
$430$	−8.76406	−	15.1798i	−0.422641	−	0.732035i
$431$	17.2707	−	3.67100i	0.831900	−	0.176826i	0.227773	−	0.973714i	$-0.426855\pi$
$431$	17.2707	−	3.67100i	0.831900	−	0.176826i	0.604127	+	0.796888i	$0.293522\pi$
$432$	0.104528	+	0.994522i	0.00502913	+	0.0478490i
$433$	10.0160	+	7.27708i	0.481340	+	0.349714i	0.801844	−	0.597533i	$-0.203852\pi$
$433$	10.0160	+	7.27708i	0.481340	+	0.349714i	−0.320504	+	0.947247i	$0.603852\pi$
$434$	0.256108	+	6.71331i	0.0122936	+	0.322249i
$435$	−2.61366	−	8.04402i	−0.125315	−	0.385681i
$436$	−0.186946	+	0.0832339i	−0.00895311	+	0.00398618i
$437$	−0.802909	−	0.357478i	−0.0384083	−	0.0171005i
$438$	−1.70973	+	0.363414i	−0.0816940	+	0.0173646i
$439$	−6.77329	+	11.7317i	−0.323271	+	0.559922i	−0.981161	−	0.193192i	$-0.938116\pi$
$439$	−6.77329	+	11.7317i	−0.323271	+	0.559922i	0.657890	+	0.753114i	$0.271449\pi$
$440$	4.97718	−	1.73202i	0.237278	−	0.0825710i
$441$	−6.15931	+	3.32609i	−0.293301	+	0.158385i
$442$	12.0953	−	37.2254i	0.575313	−	1.77063i
$443$	−1.42126	−	13.5224i	−0.0675259	−	0.642466i	−0.974977	−	0.222308i	$-0.928641\pi$
$443$	−1.42126	−	13.5224i	−0.0675259	−	0.642466i	0.907451	−	0.420159i	$-0.138026\pi$
$444$	−1.14274	+	10.8725i	−0.0542323	+	0.515986i
$445$	−17.1664	+	19.0652i	−0.813767	+	0.903779i
$446$	19.6127	+	4.16880i	0.928687	+	0.197399i
$447$	8.24065	+	5.98718i	0.389770	+	0.283184i
$448$	−2.48326	+	0.912911i	−0.117323	+	0.0431310i
$449$	−10.4483	+	32.1566i	−0.493086	+	1.51756i	0.326833	+	0.945082i	$0.394018\pi$
$449$	−10.4483	+	32.1566i	−0.493086	+	1.51756i	−0.819919	+	0.572480i	$0.805982\pi$
$450$	1.23763	−	2.14363i	0.0583423	−	0.101052i
$451$	9.71360	−	5.87988i	0.457396	−	0.276873i
$452$	4.39124	+	7.60584i	0.206546	+	0.357749i
$453$	10.4537	+	11.6100i	0.491155	+	0.545483i
$454$	−18.9431	+	13.7630i	−0.889046	+	0.645930i
$455$	22.3100	−	3.20885i	1.04591	−	0.150433i
$456$	−0.284501	−	0.875604i	−0.0133230	−	0.0410039i
$457$	7.99177	+	1.69870i	0.373839	+	0.0794620i	0.391000	−	0.920391i	$-0.372129\pi$
$457$	7.99177	+	1.69870i	0.373839	+	0.0794620i	−0.0171605	+	0.999853i	$0.505463\pi$
$458$	0.797220	−	7.58504i	0.0372516	−	0.354426i
$459$	−6.66923	−	2.96933i	−0.311293	−	0.138597i
$460$	−1.01497	−	1.12724i	−0.0473233	−	0.0525579i
$461$	5.08662			0.236907			0.118454	−	0.992960i	$-0.462206\pi$
$461$	5.08662			0.236907			0.118454	+	0.992960i	$0.462206\pi$
$462$	−5.47784	+	6.85517i	−0.254852	+	0.318931i
$463$	−22.8380			−1.06137			−0.530686	−	0.847568i	$-0.678066\pi$
$463$	−22.8380			−1.06137			−0.530686	+	0.847568i	$0.678066\pi$
$464$	3.56179	+	3.95577i	0.165352	+	0.183642i
$465$	−3.68589	−	1.64107i	−0.170929	−	0.0761026i
$466$	−3.03497	+	28.8758i	−0.140592	+	1.33765i
$467$	−11.1450	−	2.36894i	−0.515727	−	0.109621i	−0.0573068	−	0.998357i	$-0.518251\pi$
$467$	−11.1450	−	2.36894i	−0.515727	−	0.109621i	−0.458421	+	0.888735i	$0.651585\pi$
$468$	1.65680	+	5.09910i	0.0765855	+	0.235706i
$469$	−13.6627	+	34.1327i	−0.630883	+	1.57610i
$470$	3.80841	−	2.76697i	0.175669	−	0.127631i
$471$	−3.78555	−	4.20428i	−0.174429	−	0.193723i
$472$	−2.15182	−	3.72706i	−0.0990454	−	0.171552i
$473$	36.4577	+	3.06941i	1.67633	+	0.141132i
$474$	5.25979	−	9.11023i	0.241590	−	0.418447i
$475$	−0.704212	+	2.16734i	−0.0323115	+	0.0994445i
$476$	3.29267	−	19.0323i	0.150919	−	0.872342i
$477$	8.65538	+	6.28850i	0.396303	+	0.287931i
$478$	17.8015	+	3.78383i	0.814223	+	0.173069i
$479$	−13.5311	+	15.0278i	−0.618252	+	0.686638i	−0.968213	−	0.250126i	$-0.919528\pi$
$479$	−13.5311	+	15.0278i	−0.618252	+	0.686638i	0.349961	+	0.936764i	$0.386195\pi$
$480$	0.166090	−	1.58024i	0.00758094	−	0.0721278i
$481$	6.12684	+	58.2930i	0.279360	+	2.65793i
$482$	−7.87126	+	24.2253i	−0.358526	+	1.10343i
$483$	2.43010	+	0.688349i	0.110573	+	0.0313209i
$484$	−2.96272	+	10.5935i	−0.134669	+	0.481523i
$485$	−5.75075	+	9.96058i	−0.261128	+	0.452287i
$486$	0.978148	−	0.207912i	0.0443697	−	0.00943107i
$487$	5.53654	+	2.46503i	0.250885	+	0.111701i	0.528326	−	0.849041i	$-0.322820\pi$
$487$	5.53654	+	2.46503i	0.250885	+	0.111701i	−0.277441	+	0.960743i	$0.589486\pi$
$488$	9.23608	−	4.11217i	0.418098	−	0.186149i
$489$	−0.709003	−	2.18209i	−0.0320622	−	0.0986773i
$490$	10.6718	−	3.13469i	0.482101	−	0.141611i
$491$	−9.11358	−	6.62141i	−0.411290	−	0.298820i	0.362834	−	0.931854i	$-0.381809\pi$
$491$	−9.11358	−	6.62141i	−0.411290	−	0.298820i	−0.774124	+	0.633034i	$0.781809\pi$
$492$	−0.357858	−	3.40479i	−0.0161335	−	0.153500i
$493$	−38.0108	+	8.07945i	−1.71192	+	0.363880i
$494$	−2.46808	−	4.27484i	−0.111044	−	0.192334i
$495$	−2.24279	−	4.76887i	−0.100806	−	0.214345i
$496$	2.53924			0.114015
$497$	10.6684	−	15.9270i	0.478541	−	0.714424i
$498$	3.67025	−	2.66659i	0.164468	−	0.119493i
$499$	−12.3599	+	5.50296i	−0.553303	+	0.246346i	−0.664289	−	0.747476i	$-0.731266\pi$
$499$	−12.3599	+	5.50296i	−0.553303	+	0.246346i	0.110986	+	0.993822i	$0.464599\pi$
$500$	−7.94778	+	8.82690i	−0.355435	+	0.394751i
$501$	5.35642	−	5.94891i	0.239307	−	0.265778i
$502$	13.0975	−	5.83140i	0.584572	−	0.260268i
$503$	5.25061	−	3.81479i	0.234113	−	0.170093i	−0.464544	−	0.885550i	$-0.653782\pi$
$503$	5.25061	−	3.81479i	0.234113	−	0.170093i	0.698657	+	0.715457i	$0.253782\pi$
$504$	1.16748	+	2.37423i	0.0520038	+	0.105757i
$505$	5.52675			0.245937
$506$	3.14126	−	0.396141i	0.139646	−	0.0176106i
$507$	7.87291	+	13.6363i	0.349648	+	0.605608i
$508$	−12.1686	+	2.58652i	−0.539895	+	0.114758i
$509$	0.440618	+	4.19220i	0.0195300	+	0.185816i	0.999938	−	0.0111634i	$-0.00355348\pi$
$509$	0.440618	+	4.19220i	0.0195300	+	0.185816i	−0.980408	+	0.196979i	$0.936887\pi$
$510$	9.38452	+	6.81825i	0.415553	+	0.301917i
$511$	−3.91394	+	2.46328i	−0.173143	+	0.108969i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−0.841069	+	0.374468i	−0.0371341	+	0.0165332i
$514$	−25.3671	−	11.2942i	−1.11890	−	0.498165i
$515$	13.0916	−	2.78270i	0.576883	−	0.122620i
$516$	5.51565	−	9.55338i	0.242813	−	0.420564i
$517$	0.203645	+	9.82382i	0.00895630	+	0.432051i
$518$	7.08789	+	28.0425i	0.311424	+	1.23212i
$519$	−3.13854	+	9.65943i	−0.137767	+	0.424002i
$520$	−0.890494	−	8.47248i	−0.0390507	−	0.371543i
$521$	1.68841	−	16.0641i	0.0739705	−	0.703782i	−0.893201	−	0.449658i	$-0.851546\pi$
$521$	1.68841	−	16.0641i	0.0739705	−	0.703782i	0.967171	−	0.254125i	$-0.0817873\pi$
$522$	3.56179	−	3.95577i	0.155895	−	0.173139i
$523$	40.0653	+	8.51614i	1.75193	+	0.372385i	0.968485	−	0.249073i	$-0.0801257\pi$
$523$	40.0653	+	8.51614i	1.75193	+	0.372385i	0.783448	+	0.621457i	$0.213459\pi$
$524$	−1.59260	−	1.15709i	−0.0695732	−	0.0505479i
$525$	1.11641	−	6.45305i	0.0487239	−	0.281634i
$526$	−6.19318	+	19.0607i	−0.270036	+	0.831084i
$527$	−9.26871	+	16.0539i	−0.403751	+	0.699318i
$528$	2.51020	+	2.16770i	0.109242	+	0.0943369i
$529$	11.0443	+	19.1294i	0.480189	+	0.831711i
$530$	−11.3749	−	12.6331i	−0.494095	−	0.548748i
$531$	−3.48171	+	2.52961i	−0.151093	+	0.109776i
$532$	−1.50584	−	1.91463i	−0.0652865	−	0.0830098i
$533$	−5.67212	−	17.4570i	−0.245687	−	0.756146i
$534$	−15.7930	−	3.35690i	−0.683430	−	0.145267i
$535$	2.23182	−	21.2344i	0.0964901	−	0.918042i
$536$	12.6947	+	5.65205i	0.548328	+	0.244132i
$537$	−3.33080	−	3.69922i	−0.143734	−	0.159633i
$538$	−30.0897			−1.29726
$539$	−7.34475	+	22.0240i	−0.316361	+	0.948639i
$540$	−1.58895			−0.0683773
$541$	−28.6621	−	31.8324i	−1.23228	−	1.36858i	−0.905982	−	0.423316i	$-0.860866\pi$
$541$	−28.6621	−	31.8324i	−1.23228	−	1.36858i	−0.326296	−	0.945268i	$-0.605801\pi$
$542$	22.5373	+	10.0343i	0.968062	+	0.431009i
$543$	0.907361	−	8.63297i	0.0389386	−	0.370476i
$544$	−7.14085	−	1.51783i	−0.306161	−	0.0650766i
$545$	−0.100480	−	0.309245i	−0.00430408	−	0.0132466i
$546$	8.76929	+	11.1499i	0.375291	+	0.477172i
$547$	14.4937	−	10.5303i	0.619706	−	0.450243i	−0.233113	−	0.972450i	$-0.574891\pi$
$547$	14.4937	−	10.5303i	0.619706	−	0.450243i	0.852819	+	0.522207i	$0.174891\pi$
$548$	5.40592	+	6.00389i	0.230930	+	0.256473i
$549$	−5.05507	−	8.75565i	−0.215745	−	0.373682i
$550$	−1.87291	−	7.99299i	−0.0798610	−	0.340822i
$551$	−2.45036	+	4.24414i	−0.104389	+	0.180807i
$552$	0.294996	−	0.907906i	0.0125559	−	0.0386430i
$553$	4.74462	−	27.4248i	0.201762	−	1.16622i
$554$	4.79758	+	3.48565i	0.203830	+	0.148091i
$555$	−16.9914	−	3.61162i	−0.721243	−	0.153305i
$556$	8.13087	−	9.03024i	0.344825	−	0.382968i
$557$	2.80832	−	26.7193i	0.118992	−	1.13213i	−0.758209	−	0.652012i	$-0.773925\pi$
$557$	2.80832	−	26.7193i	0.118992	−	1.13213i	0.877201	−	0.480123i	$-0.159408\pi$
$558$	−0.265423	−	2.52533i	−0.0112362	−	0.106906i
$559$	18.2766	−	56.2497i	0.773019	−	2.37911i
$560$	−1.03017	−	4.07578i	−0.0435328	−	0.172233i
$561$	−22.8676	+	7.95776i	−0.965469	+	0.335977i
$562$	−4.68402	+	8.11296i	−0.197584	+	0.342225i
$563$	−22.7117	+	4.82752i	−0.957183	+	0.203456i	−0.659917	−	0.751339i	$-0.729408\pi$
$563$	−22.7117	+	4.82752i	−0.957183	+	0.203456i	−0.297267	+	0.954794i	$0.596075\pi$
$564$	2.70650	+	1.20501i	0.113964	+	0.0507401i
$565$	−12.7484	+	5.67596i	−0.536329	+	0.238789i
$566$	−3.13128	−	9.63709i	−0.131618	−	0.405077i
$567$	2.23919	−	1.40926i	0.0940372	−	0.0591834i
$568$	−5.86176	−	4.25881i	−0.245954	−	0.178696i
$569$	−1.63451	−	15.5513i	−0.0685221	−	0.651944i	−0.973844	−	0.227218i	$-0.927037\pi$
$569$	−1.63451	−	15.5513i	−0.0685221	−	0.651944i	0.905322	−	0.424726i	$-0.139630\pi$
$570$	1.43092	−	0.304151i	0.0599346	−	0.0127395i
$571$	−1.22196	−	2.11649i	−0.0511373	−	0.0885723i	0.839324	−	0.543632i	$-0.182951\pi$
$571$	−1.22196	−	2.11649i	−0.0511373	−	0.0885723i	−0.890461	+	0.455060i	$0.849618\pi$
$572$	15.5807	+	8.56999i	0.651463	+	0.358329i
$573$	−10.9894			−0.459088
$574$	−3.99693	−	8.12829i	−0.166828	−	0.339268i
$575$	−1.91166	+	1.38891i	−0.0797219	+	0.0579214i
$576$	0.913545	−	0.406737i	0.0380644	−	0.0169474i
$577$	−6.41647	+	7.12622i	−0.267121	+	0.296668i	−0.861751	−	0.507331i	$-0.830632\pi$
$577$	−6.41647	+	7.12622i	−0.267121	+	0.296668i	0.594630	+	0.804000i	$0.297299\pi$
$578$	24.2865	−	26.9728i	1.01018	−	1.12192i
$579$	−17.5822	+	7.82810i	−0.730692	+	0.325325i
$580$	−6.84265	+	4.97147i	−0.284126	+	0.206429i
$581$	6.67983	−	9.97246i	0.277126	−	0.413727i
$582$	−7.23844			−0.300043
$583$	35.2045	−	4.43960i	1.45802	−	0.183869i
$584$	0.873963	+	1.51375i	0.0361648	+	0.0626393i
$585$	−8.33299	+	1.77123i	−0.344527	+	0.0732314i
$586$	−0.0719278	−	0.684347i	−0.00297131	−	0.0282701i
$587$	−5.23199	−	3.80127i	−0.215947	−	0.156895i	0.474553	−	0.880227i	$-0.342610\pi$
$587$	−5.23199	−	3.80127i	−0.215947	−	0.156895i	−0.690501	+	0.723332i	$0.742610\pi$
$588$	5.06663	+	4.83004i	0.208944	+	0.199187i
$589$	0.722417	+	2.22337i	0.0297667	+	0.0916124i
$590$	6.24704	−	2.78136i	0.257187	−	0.114507i
$591$	−1.45051	−	0.645809i	−0.0596661	−	0.0265650i
$592$	10.6935	−	2.27297i	0.439499	−	0.0934185i
$593$	7.01299	−	12.1469i	0.287989	−	0.498812i	−0.685341	−	0.728223i	$-0.740347\pi$
$593$	7.01299	−	12.1469i	0.287989	−	0.498812i	0.973330	+	0.229411i	$0.0736800\pi$
$594$	1.89343	−	2.72303i	0.0776885	−	0.111727i
$595$	29.5287	+	8.36427i	1.21056	+	0.342902i
$596$	3.14765	−	9.68747i	0.128933	−	0.396814i
$597$	−2.18598	−	20.7982i	−0.0894661	−	0.851213i
$598$	0.535003	−	5.09021i	0.0218779	−	0.208154i
$599$	22.8117	−	25.3350i	0.932062	−	1.03516i	−0.0672372	−	0.997737i	$-0.521418\pi$
$599$	22.8117	−	25.3350i	0.932062	−	1.03516i	0.999300	−	0.0374230i	$-0.0119149\pi$
$600$	−2.42116	−	0.514634i	−0.0988436	−	0.0210099i
$601$	13.5834	+	9.86894i	0.554080	+	0.402563i	0.829288	−	0.558822i	$-0.188747\pi$
$601$	13.5834	+	9.86894i	0.554080	+	0.402563i	−0.275208	+	0.961385i	$0.588747\pi$
$602$	4.97541	−	28.7589i	0.202783	−	1.17212i
$603$	4.29413	−	13.2160i	0.174871	−	0.538196i
$604$	7.81137	−	13.5297i	0.317840	−	0.550515i
$605$	−16.2482	−	6.44129i	−0.660583	−	0.261876i
$606$	1.73913	+	3.01225i	0.0706472	+	0.122364i
$607$	−19.7982	−	21.9882i	−0.803585	−	0.892472i	0.192461	−	0.981305i	$-0.438353\pi$
$607$	−19.7982	−	21.9882i	−0.803585	−	0.892472i	−0.996047	+	0.0888327i	$0.971686\pi$
$608$	−0.744834	+	0.541153i	−0.0302070	+	0.0219467i
$609$	5.23360	−	13.0748i	0.212076	−	0.529818i
$610$	4.96419	+	15.2782i	0.200994	+	0.618597i
$611$	15.5371	+	3.30251i	0.628563	+	0.133605i
$612$	−0.763097	+	7.26039i	−0.0308464	+	0.293484i
$613$	9.48455	+	4.22279i	0.383077	+	0.170557i	0.589235	−	0.807962i	$-0.299429\pi$
$613$	9.48455	+	4.22279i	0.383077	+	0.170557i	−0.206158	+	0.978519i	$0.566096\pi$
$614$	−12.1267	−	13.4680i	−0.489392	−	0.543525i
$615$	5.43982			0.219355
$616$	8.21239	+	3.09137i	0.330887	+	0.124555i
$617$	23.4633			0.944597			0.472299	−	0.881439i	$-0.343424\pi$
$617$	23.4633			0.944597			0.472299	+	0.881439i	$0.343424\pi$
$618$	5.63623	+	6.25967i	0.226722	+	0.251801i
$619$	30.3357	+	13.5063i	1.21930	+	0.542866i	0.912566	−	0.408931i	$-0.134098\pi$
$619$	30.3357	+	13.5063i	1.21930	+	0.542866i	0.306731	+	0.951796i	$0.400765\pi$
$620$	−0.421742	+	4.01261i	−0.0169376	+	0.161150i
$621$	−0.933768	−	0.198478i	−0.0374708	−	0.00796467i
$622$	4.66224	+	14.3489i	0.186939	+	0.575339i
$623$	−42.2827	+	6.08153i	−1.69402	+	0.243651i
$624$	4.33755	−	3.15142i	0.173641	−	0.126158i
$625$	−4.34724	−	4.82810i	−0.173890	−	0.193124i
$626$	−0.0806278	−	0.139651i	−0.00322253	−	0.00558159i
$627$	−1.18389	+	2.81465i	−0.0472800	+	0.112406i
$628$	−2.82871	+	4.89946i	−0.112878	+	0.195510i
$629$	−24.6628	+	75.9043i	−0.983371	+	3.02650i
$630$	−3.94577	+	1.45057i	−0.157203	+	0.0577919i
$631$	−25.2444	−	18.3412i	−1.00497	−	0.730150i	−0.0418182	−	0.999125i	$-0.513315\pi$
$631$	−25.2444	−	18.3412i	−1.00497	−	0.730150i	−0.963147	+	0.268975i	$0.913315\pi$
$632$	−10.2897	−	2.18715i	−0.409303	−	0.0870000i
$633$	−3.37519	+	3.74852i	−0.134152	+	0.148990i
$634$	−0.874984	+	8.32492i	−0.0347501	+	0.330625i
$635$	−2.06624	−	19.6589i	−0.0819961	−	0.780141i
$636$	3.30606	−	10.1750i	0.131094	−	0.403465i
$637$	31.9553	+	19.6825i	1.26612	+	0.779850i
$638$	−0.365893	−	17.6507i	−0.0144858	−	0.698796i
$639$	−3.62276	+	6.27481i	−0.143314	+	0.248228i
$640$	−1.55422	+	0.330360i	−0.0614361	+	0.0130586i
$641$	10.7451	+	4.78405i	0.424408	+	0.188958i	0.607815	−	0.794078i	$-0.292046\pi$
$641$	10.7451	+	4.78405i	0.424408	+	0.188958i	−0.183408	+	0.983037i	$0.558713\pi$
$642$	12.2757	−	5.46550i	0.484483	−	0.215706i
$643$	−1.87250	−	5.76295i	−0.0738440	−	0.227269i	0.907321	−	0.420438i	$-0.138123\pi$
$643$	−1.87250	−	5.76295i	−0.0738440	−	0.227269i	−0.981165	+	0.193169i	$0.938123\pi$
$644$	−0.0962839	−	2.52387i	−0.00379412	−	0.0994546i
$645$	14.1805	+	10.3028i	0.558359	+	0.405671i
$646$	−0.702557	−	6.68438i	−0.0276417	−	0.262994i
$647$	19.2697	−	4.09590i	0.757570	−	0.161026i	0.187095	−	0.982342i	$-0.440093\pi$
$647$	19.2697	−	4.09590i	0.757570	−	0.161026i	0.570475	+	0.821315i	$0.306759\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−2.67764	+	14.0201i	−0.105107	+	0.550338i
$650$	−13.2711			−0.520535
$651$	−2.96452	−	6.02875i	−0.116189	−	0.236285i
$652$	−1.85619	+	1.34860i	−0.0726941	+	0.0528154i
$653$	35.4735	−	15.7938i	1.38818	−	0.618060i	0.429640	−	0.903000i	$-0.358641\pi$
$653$	35.4735	−	15.7938i	1.38818	−	0.618060i	0.958545	+	0.284941i	$0.0919739\pi$
$654$	0.136930	−	0.152076i	0.00535438	−	0.00594664i
$655$	2.09300	−	2.32452i	0.0817804	−	0.0908263i
$656$	−3.12756	+	1.39248i	−0.122111	+	0.0543672i
$657$	1.41410	−	1.02741i	0.0551694	−	0.0400829i
$658$	7.82101	+	0.521565i	0.304895	+	0.0203327i
$659$	44.7296			1.74242			0.871209	−	0.490911i	$-0.163336\pi$
$659$	44.7296			1.74242			0.871209	+	0.490911i	$0.163336\pi$
$660$	−3.84240	+	3.60668i	−0.149565	+	0.140390i
$661$	−7.69009	−	13.3196i	−0.299110	−	0.518073i	0.676823	−	0.736146i	$-0.263356\pi$
$661$	−7.69009	−	13.3196i	−0.299110	−	0.518073i	−0.975933	+	0.218073i	$0.930023\pi$
$662$	−12.0343	+	2.55797i	−0.467726	+	0.0994182i
$663$	4.09136	+	38.9267i	0.158895	+	1.51179i
$664$	−3.67025	−	2.66659i	−0.142433	−	0.103484i
$665$	3.27568	−	2.06159i	0.127026	−	0.0799450i
$666$	−3.37829	−	10.3973i	−0.130906	−	0.402888i
$667$	−4.64218	+	2.06683i	−0.179746	+	0.0800281i
$668$	−7.31297	−	3.25594i	−0.282947	−	0.125976i
$669$	−19.6127	+	4.16880i	−0.758270	+	0.161175i
$670$	−11.0401	+	19.1220i	−0.426515	+	0.738746i
$671$	−32.0983	−	9.69866i	−1.23914	−	0.374413i
$672$	1.89726	−	1.84402i	0.0731883	−	0.0711346i
$673$	9.69353	−	29.8336i	0.373658	−	1.15000i	−0.570721	−	0.821144i	$-0.693336\pi$
$673$	9.69353	−	29.8336i	0.373658	−	1.15000i	0.944379	−	0.328858i	$-0.106664\pi$
$674$	0.993197	+	9.44964i	0.0382565	+	0.363986i
$675$	−0.258734	+	2.46169i	−0.00995869	+	0.0947506i
$676$	10.5360	−	11.7014i	0.405231	−	0.450055i
$677$	−33.3987	−	7.09910i	−1.28361	−	0.272841i	−0.484910	−	0.874564i	$-0.661148\pi$
$677$	−33.3987	−	7.09910i	−1.28361	−	0.272841i	−0.798705	+	0.601723i	$0.794481\pi$
$678$	−7.10517	−	5.16221i	−0.272872	−	0.198253i
$679$	−17.9750	+	6.60806i	−0.689816	+	0.253594i
$680$	3.58457	−	11.0322i	0.137462	−	0.423064i
$681$	11.7075	−	20.2780i	0.448633	−	0.777055i
$682$	−6.37399	−	5.50430i	−0.244073	−	0.210771i
$683$	0.870184	+	1.50720i	0.0332967	+	0.0576715i	0.882194	−	0.470887i	$-0.156066\pi$
$683$	0.870184	+	1.50720i	0.0332967	+	0.0576715i	−0.848897	+	0.528559i	$0.822733\pi$
$684$	0.616045	+	0.684187i	0.0235551	+	0.0261606i
$685$	−10.3855	+	7.54548i	−0.396808	+	0.288298i
$686$	16.9912	+	7.36887i	0.648726	+	0.281345i
$687$	2.35682	+	7.25354i	0.0899182	+	0.276740i
$688$	−10.7902	−	2.29354i	−0.411374	−	0.0874402i
$689$	5.99585	−	57.0467i	0.228424	−	2.17330i
$690$	1.38571	+	0.616959i	0.0527532	+	0.0234872i
$691$	9.02508	+	10.0234i	0.343330	+	0.381307i	0.889938	−	0.456082i	$-0.150748\pi$
$691$	9.02508	+	10.0234i	0.343330	+	0.381307i	−0.546607	+	0.837389i	$0.684081\pi$
$692$	10.1565			0.386093
$693$	2.21601	−	8.49054i	0.0841791	−	0.322529i
$694$	−22.4656			−0.852782
$695$	12.9195	+	14.3486i	0.490064	+	0.544272i
$696$	−4.86282	−	2.16507i	−0.184325	−	0.0820666i
$697$	2.61250	−	24.8563i	0.0989554	−	0.941498i
$698$	19.3574	+	4.11454i	0.732688	+	0.155738i
$699$	−8.97227	−	27.6138i	−0.339362	−	1.04445i
$700$	−6.48220	+	0.932336i	−0.245004	+	0.0352390i
$701$	22.2709	−	16.1808i	0.841161	−	0.611139i	−0.0815335	−	0.996671i	$-0.525982\pi$
$701$	22.2709	−	16.1808i	0.841161	−	0.611139i	0.922695	+	0.385531i	$0.125982\pi$
$702$	−3.58755	−	3.98438i	−0.135403	−	0.150381i
$703$	5.03253	+	8.71660i	0.189805	+	0.328753i
$704$	1.28591	−	3.05719i	0.0484645	−	0.115222i
$705$	−2.35373	+	4.07678i	−0.0886466	+	0.153540i
$706$	2.58084	−	7.94301i	0.0971312	−	0.298939i
$707$	7.06863	+	5.89255i	0.265843	+	0.221612i
$708$	3.48171	+	2.52961i	0.130851	+	0.0950687i
$709$	−24.4523	−	5.19749i	−0.918324	−	0.195196i	−0.275581	−	0.961278i	$-0.588870\pi$
$709$	−24.4523	−	5.19749i	−0.918324	−	0.195196i	−0.642743	+	0.766082i	$0.722204\pi$
$710$	7.70353	−	8.55564i	0.289108	−	0.321087i
$711$	−1.09960	+	10.4620i	−0.0412381	+	0.392354i
$712$	1.68770	+	16.0574i	0.0632492	+	0.601775i
$713$	−0.749067	+	2.30539i	−0.0280528	+	0.0863376i
$714$	4.73312	+	18.7261i	0.177133	+	0.700806i
$715$	−16.1304	+	23.1979i	−0.603245	+	0.867553i
$716$	−2.48890	+	4.31090i	−0.0930145	+	0.161106i
$717$	−17.8015	+	3.78383i	−0.664811	+	0.141310i
$718$	10.8208	+	4.81774i	0.403830	+	0.179797i
$719$	−3.60174	+	1.60360i	−0.134322	+	0.0598041i	−0.472797	−	0.881171i	$-0.656756\pi$
$719$	−3.60174	+	1.60360i	−0.134322	+	0.0598041i	0.338475	+	0.940975i	$0.390089\pi$
$720$	0.491011	+	1.51118i	0.0182989	+	0.0563182i
$721$	19.7108	+	10.3990i	0.734067	+	0.387280i
$722$	14.6856	+	10.6697i	0.546541	+	0.397085i
$723$	−2.66254	−	25.3324i	−0.0990210	−	0.942122i
$724$	−8.49083	+	1.80478i	−0.315559	+	0.0670742i
$725$	6.58791	+	11.4106i	0.244669	+	0.423779i
$726$	−1.60219	−	10.8827i	−0.0594627	−	0.403895i
$727$	11.7351			0.435231			0.217615	−	0.976035i	$-0.430172\pi$
$727$	11.7351			0.435231			0.217615	+	0.976035i	$0.430172\pi$
$728$	7.89432	−	11.7856i	0.292583	−	0.436803i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−2.53724	+	1.12965i	−0.0939076	+	0.0418103i
$731$	53.8869	−	59.8474i	1.99308	−	2.21354i
$732$	−6.76501	+	7.51331i	−0.250042	+	0.277700i
$733$	22.2191	−	9.89259i	0.820682	−	0.365391i	0.0469447	−	0.998897i	$-0.485052\pi$
$733$	22.2191	−	9.89259i	0.820682	−	0.365391i	0.773738	+	0.633506i	$0.218385\pi$
$734$	0.927361	−	0.673767i	0.0342295	−	0.0248692i
$735$	−8.47414	+	7.20427i	−0.312573	+	0.265734i
$736$	−0.954629			−0.0351881
$737$	−19.6143	−	41.7061i	−0.722503	−	1.53626i
$738$	1.71177	+	2.96488i	0.0630112	+	0.109139i
$739$	−44.4537	+	9.44893i	−1.63526	+	0.347584i	−0.931749	−	0.363103i	$-0.881717\pi$
$739$	−44.4537	+	9.44893i	−1.63526	+	0.347584i	−0.703507	+	0.710688i	$0.748384\pi$
$740$	1.81576	+	17.2758i	0.0667486	+	0.635071i
$741$	3.99343	+	2.90140i	0.146702	+	0.106586i
$742$	−1.07907	−	28.2854i	−0.0396137	−	1.03839i
$743$	6.19386	+	19.0627i	0.227231	+	0.699344i	0.998057	+	0.0622996i	$0.0198434\pi$
$743$	6.19386	+	19.0627i	0.227231	+	0.699344i	−0.770827	+	0.637045i	$0.780157\pi$
$744$	−2.31971	+	1.03280i	−0.0850447	+	0.0378644i
$745$	14.7857	+	6.58304i	0.541708	+	0.241184i
$746$	4.13811	−	0.879583i	0.151507	−	0.0322038i
$747$	−2.26834	+	3.92888i	−0.0829942	+	0.143750i
$748$	14.6347	+	19.2893i	0.535099	+	0.705285i
$749$	25.4943	−	24.7789i	0.931541	−	0.905401i
$750$	3.67043	−	11.2964i	0.134025	−	0.412487i
$751$	−2.80356	−	26.6741i	−0.102303	−	0.973350i	−0.918458	−	0.395518i	$-0.870565\pi$
$751$	−2.80356	−	26.6741i	−0.102303	−	0.973350i	0.816155	−	0.577833i	$-0.196101\pi$
$752$	0.309679	−	2.94640i	0.0112928	−	0.107444i
$753$	−9.59336	+	10.6545i	−0.349601	+	0.388272i
$754$	−27.9158	−	5.93368i	−1.01663	−	0.216092i
$755$	20.0828	+	14.5910i	0.730887	+	0.531021i
$756$	−2.03224	−	1.69411i	−0.0739117	−	0.0616143i
$757$	−8.70124	+	26.7797i	−0.316252	+	0.973323i	0.658984	+	0.752157i	$0.270986\pi$
$757$	−8.70124	+	26.7797i	−0.316252	+	0.973323i	−0.975236	+	0.221166i	$0.929014\pi$
$758$	2.71303	−	4.69910i	0.0985416	−	0.170679i
$759$	−2.70856	+	1.63956i	−0.0983146	+	0.0595123i
$760$	−0.731443	−	1.26690i	−0.0265322	−	0.0459552i
$761$	20.1586	+	22.3884i	0.730747	+	0.811577i	0.987949	−	0.154781i	$-0.0494671\pi$
$761$	20.1586	+	22.3884i	0.730747	+	0.811577i	−0.257201	+	0.966358i	$0.582800\pi$
$762$	10.0646	−	7.31233i	0.364600	−	0.264898i
$763$	0.201201	−	0.502649i	0.00728396	−	0.0181971i
$764$	3.39590	+	10.4515i	0.122859	+	0.378122i
$765$	−11.3464	−	2.41176i	−0.410231	−	0.0871972i
$766$	2.27985	−	21.6913i	0.0823744	−	0.783740i
$767$	21.0791	+	9.38504i	0.761124	+	0.338874i
$768$	−0.669131	−	0.743145i	−0.0241452	−	0.0268159i
$769$	−18.6598			−0.672889			−0.336445	−	0.941703i	$-0.609225\pi$
$769$	−18.6598			−0.672889			−0.336445	+	0.941703i	$0.609225\pi$
$770$	−6.24911	+	12.4641i	−0.225202	+	0.449176i
$771$	27.7678			1.00003
$772$	12.8782	+	14.3027i	0.463495	+	0.514764i
$773$	16.6683	+	7.42120i	0.599517	+	0.266922i	0.683976	−	0.729505i	$-0.260249\pi$
$773$	16.6683	+	7.42120i	0.599517	+	0.266922i	−0.0844587	+	0.996427i	$0.526916\pi$
$774$	−1.15308	+	10.9709i	−0.0414468	+	0.394340i
$775$	6.14791	+	1.30678i	0.220840	+	0.0469409i
$776$	2.23680	+	6.88417i	0.0802965	+	0.247127i
$777$	−17.8810	−	22.7352i	−0.641478	−	0.815620i
$778$	−4.87647	+	3.54296i	−0.174830	+	0.127021i
$779$	−2.10906	−	2.34235i	−0.0755648	−	0.0839232i
$780$	4.25957	+	7.37780i	0.152517	+	0.264168i
$781$	5.48235	+	23.3970i	0.196174	+	0.837210i
$782$	3.48458	−	6.03546i	0.124608	−	0.215828i
$783$	−1.64490	+	5.06249i	−0.0587840	+	0.180919i
$784$	3.02796	−	6.31121i	0.108142	−	0.225401i
$785$	−7.27251	−	5.28379i	−0.259567	−	0.188586i
$786$	1.92555	+	0.409288i	0.0686821	+	0.0145988i
$787$	24.2963	−	26.9838i	0.866070	−	0.961869i	−0.133504	−	0.991048i	$-0.542623\pi$
$787$	24.2963	−	26.9838i	0.866070	−	0.961869i	0.999574	+	0.0291798i	$0.00928953\pi$
$788$	−0.165968	+	1.57908i	−0.00591238	+	0.0562525i
$789$	−2.09491	−	19.9318i	−0.0745809	−	0.709590i
$790$	5.16523	−	15.8970i	0.183771	−	0.565588i
$791$	−22.3566	−	6.33273i	−0.794911	−	0.225166i
$792$	−3.17486	−	0.959300i	−0.112814	−	0.0340872i
$793$	−27.1028	+	46.9435i	−0.962450	+	1.66701i
$794$	11.3140	−	2.40486i	0.401518	−	0.0853452i
$795$	15.5299	+	6.91434i	0.550787	+	0.245226i
$796$	−19.1047	+	8.50598i	−0.677150	+	0.301487i
$797$	−8.37058	−	25.7620i	−0.296501	−	0.912536i	−0.982713	−	0.185135i	$-0.940728\pi$
$797$	−8.37058	−	25.7620i	−0.296501	−	0.912536i	0.686212	−	0.727402i	$-0.259272\pi$
$798$	2.15440	+	1.13662i	0.0762651	+	0.0402360i
$799$	17.4977	+	12.7128i	0.619024	+	0.449747i
$800$	0.258734	+	2.46169i	0.00914764	+	0.0870340i
$801$	15.7930	−	3.35690i	0.558018	−	0.118610i
$802$	−8.32063	−	14.4118i	−0.293812	−	0.508897i
$803$	1.08753	−	5.69429i	0.0383780	−	0.200947i
$804$	−13.8961			−0.490078
$805$	4.00432	+	0.267038i	0.141134	+	0.00941187i
$806$	−11.0141	+	8.00221i	−0.387955	+	0.281866i
$807$	27.4883	−	12.2386i	0.967633	−	0.430818i
$808$	2.32740	−	2.58484i	0.0818778	−	0.0909345i
$809$	−7.20976	+	8.00725i	−0.253482	+	0.281520i	−0.856433	−	0.516258i	$-0.827325\pi$
$809$	−7.20976	+	8.00725i	−0.253482	+	0.281520i	0.602952	+	0.797778i	$0.293991\pi$
$810$	1.45157	−	0.646282i	0.0510031	−	0.0227080i
$811$	−27.8210	+	20.2131i	−0.976926	+	0.709778i	−0.957019	−	0.290024i	$-0.906337\pi$
$811$	−27.8210	+	20.2131i	−0.976926	+	0.709778i	−0.0199064	+	0.999802i	$0.506337\pi$
$812$	−14.0522	−	0.937105i	−0.493134	−	0.0328859i
$813$	−24.6702			−0.865221
$814$	−31.7699	−	17.4746i	−1.11353	−	0.612485i
$815$	−1.82282	−	3.15722i	−0.0638507	−	0.110593i
$816$	7.14085	−	1.51783i	0.249980	−	0.0531348i
$817$	−1.06160	−	10.1005i	−0.0371408	−	0.353371i
$818$	−15.3103	−	11.1236i	−0.535311	−	0.388926i
$819$	−12.5462	−	6.61915i	−0.438400	−	0.231292i
$820$	−1.68100	−	5.17358i	−0.0587030	−	0.180669i
$821$	−12.8683	+	5.72936i	−0.449108	+	0.199956i	−0.618812	−	0.785539i	$-0.712386\pi$
$821$	−12.8683	+	5.72936i	−0.449108	+	0.199956i	0.169703	+	0.985495i	$0.445719\pi$
$822$	−7.38056	−	3.28604i	−0.257427	−	0.114614i
$823$	22.1876	−	4.71611i	0.773410	−	0.164393i	0.195731	−	0.980658i	$-0.437292\pi$
$823$	22.1876	−	4.71611i	0.773410	−	0.164393i	0.577679	+	0.816264i	$0.303959\pi$
$824$	4.21161	−	7.29472i	0.146718	−	0.254124i
$825$	4.96203	+	6.54018i	0.172756	+	0.227700i
$826$	10.9553	+	3.10320i	0.381184	+	0.107974i
$827$	12.1614	−	37.4289i	0.422892	−	1.30153i	−0.482106	−	0.876113i	$-0.660128\pi$
$827$	12.1614	−	37.4289i	0.422892	−	1.30153i	0.904998	−	0.425416i	$-0.139872\pi$
$828$	0.0997859	+	0.949399i	0.00346780	+	0.0329939i
$829$	−4.62451	+	43.9993i	−0.160616	+	1.52816i	0.556290	+	0.830988i	$0.312224\pi$
$829$	−4.62451	+	43.9993i	−0.160616	+	1.52816i	−0.716906	+	0.697170i	$0.754442\pi$
$830$	4.82345	−	5.35698i	0.167424	−	0.185944i
$831$	−5.80055	−	1.23295i	−0.201219	−	0.0427704i
$832$	−4.33755	−	3.15142i	−0.150378	−	0.109256i
$833$	28.8488	+	42.1809i	0.999553	+	1.46148i
$834$	−3.75499	+	11.5567i	−0.130025	+	0.400174i
$835$	6.35979	−	11.0155i	0.220090	−	0.381206i
$836$	3.04274	+	0.256171i	0.105235	+	0.00885987i
$837$	1.26962	+	2.19905i	0.0438845	+	0.0760102i
$838$	−10.6162	−	11.7905i	−0.366731	−	0.407295i
$839$	−12.7867	+	9.29007i	−0.441445	+	0.320729i	−0.786209	−	0.617961i	$-0.787959\pi$
$839$	−12.7867	+	9.29007i	−0.441445	+	0.320729i	0.344764	+	0.938690i	$0.387959\pi$
$840$	2.59888	+	3.30440i	0.0896699	+	0.114013i
$841$	−0.205655	−	0.632941i	−0.00709155	−	0.0218255i
$842$	−19.7863	−	4.20572i	−0.681883	−	0.144939i
$843$	0.979227	−	9.31673i	0.0337264	−	0.320885i
$844$	4.60805	+	2.05164i	0.158616	+	0.0706202i
$845$	16.7411	+	18.5929i	0.575913	+	0.639616i
$846$	−2.96263			−0.101857
$847$	−13.9136	−	25.5619i	−0.478076	−	0.878318i
$848$	−10.6986			−0.367393
$849$	6.78033	+	7.53032i	0.232700	+	0.258440i
$850$	−16.5080	−	7.34985i	−0.566221	−	0.252098i
$851$	−1.09090	+	10.3792i	−0.0373955	+	0.355794i
$852$	7.08720	+	1.50643i	0.242803	+	0.0516094i
$853$	13.2915	+	40.9071i	0.455093	+	1.40063i	0.871025	+	0.491238i	$0.163455\pi$
$853$	13.2915	+	40.9071i	0.455093	+	1.40063i	−0.415932	+	0.909396i	$0.636545\pi$
$854$	−9.94031	+	24.8334i	−0.340151	+	0.849780i
$855$	−1.18350	+	0.859863i	−0.0404748	+	0.0294067i
$856$	−8.99140	−	9.98596i	−0.307320	−	0.341313i
$857$	−15.8434	−	27.4416i	−0.541201	−	0.937387i	−0.998835	−	0.0482468i	$-0.984637\pi$
$857$	−15.8434	−	27.4416i	−0.541201	−	0.937387i	0.457635	−	0.889140i	$-0.348697\pi$
$858$	−17.7194	−	1.49182i	−0.604932	−	0.0509299i
$859$	−15.2171	+	26.3568i	−0.519202	+	0.899284i	0.480549	+	0.876968i	$0.340437\pi$
$859$	−15.2171	+	26.3568i	−0.519202	+	0.899284i	−0.999751	+	0.0223159i	$0.992896\pi$
$860$	5.41649	−	16.6702i	0.184701	−	0.568450i
$861$	6.95745	+	5.79987i	0.237109	+	0.197659i
$862$	14.2844	+	10.3782i	0.486530	+	0.353485i
$863$	33.8977	+	7.20518i	1.15389	+	0.245267i	0.744839	−	0.667244i	$-0.232526\pi$
$863$	33.8977	+	7.20518i	1.15389	+	0.245267i	0.409052	+	0.912511i	$0.365860\pi$
$864$	−0.669131	+	0.743145i	−0.0227643	+	0.0252823i
$865$	−1.68690	+	16.0498i	−0.0573562	+	0.545708i
$866$	1.29412	+	12.3127i	0.0439758	+	0.418402i
$867$	−11.2159	+	34.5191i	−0.380913	+	1.17233i
$868$	−4.81759	+	4.68241i	−0.163520	+	0.158931i
$869$	21.0881	+	27.7951i	0.715366	+	0.942885i
$870$	4.22899	−	7.32482i	0.143376	−	0.248335i
$871$	−72.8760	+	15.4903i	−2.46931	+	0.524868i
$872$	−0.186946	−	0.0832339i	−0.00633081	−	0.00281866i
$873$	6.61265	−	2.94414i	0.223804	−	0.0996441i
$874$	−0.271593	−	0.835877i	−0.00918677	−	0.0282740i
$875$	−1.19799	−	31.4028i	−0.0404995	−	1.06161i
$876$	−1.41410	−	1.02741i	−0.0477781	−	0.0347128i
$877$	1.19168	+	11.3381i	0.0402403	+	0.382861i	0.996044	+	0.0888568i	$0.0283213\pi$
$877$	1.19168	+	11.3381i	0.0402403	+	0.382861i	−0.955804	+	0.294004i	$0.905012\pi$
$878$	−13.2505	+	2.81649i	−0.447184	+	0.0950520i
$879$	0.344058	+	0.595926i	0.0116048	+	0.0201001i
$880$	4.61753	+	2.53981i	0.155657	+	0.0856171i
$881$	−45.7303			−1.54069			−0.770346	−	0.637626i	$-0.779916\pi$
$881$	−45.7303			−1.54069			−0.770346	+	0.637626i	$0.779916\pi$
$882$	−6.59315	−	2.35168i	−0.222003	−	0.0791850i
$883$	1.35021	−	0.980989i	0.0454383	−	0.0330129i	−0.564834	−	0.825204i	$-0.691060\pi$
$883$	1.35021	−	0.980989i	0.0454383	−	0.0330129i	0.610273	+	0.792191i	$0.291060\pi$
$884$	35.7572	−	15.9201i	1.20264	−	0.535451i
$885$	−4.57567	+	5.08180i	−0.153810	+	0.170823i
$886$	9.09806	−	10.1044i	0.305655	−	0.339465i
$887$	39.0536	−	17.3878i	1.31129	−	0.583825i	0.372412	−	0.928068i	$-0.378531\pi$
$887$	39.0536	−	17.3878i	1.31129	−	0.583825i	0.938881	+	0.344243i	$0.111864\pi$
$888$	−8.84448	+	6.42589i	−0.296801	+	0.215639i
$889$	18.3174	−	27.3465i	0.614347	−	0.917171i
$890$	−25.6548			−0.859952
$891$	−0.622181	+	3.25774i	−0.0208439	+	0.109139i
$892$	10.0254	+	17.3645i	0.335676	+	0.581407i
$893$	2.66799	−	0.567098i	0.0892807	−	0.0189772i
$894$	1.06473	+	10.1302i	0.0356098	+	0.338805i
$895$	−6.39888	−	4.64906i	−0.213891	−	0.155401i
$896$	−2.34005	−	1.23457i	−0.0781757	−	0.0412440i
$897$	1.58163	+	4.86775i	0.0528090	+	0.162529i
$898$	−30.8883	+	13.7523i	−1.03075	+	0.458921i
$899$	12.3479	+	5.49762i	0.411824	+	0.183356i
$900$	2.42116	−	0.514634i	0.0807054	−	0.0171545i
$901$	39.0521	−	67.6402i	1.30101	−	2.25342i
$902$	10.8693	+	3.28420i	0.361907	+	0.109352i
$903$	7.15202	+	28.2962i	0.238004	+	0.941639i
$904$	−2.71393	+	8.35263i	−0.0902641	+	0.277804i
$905$	−1.44175	−	13.7173i	−0.0479253	−	0.455979i
$906$	−1.63302	+	15.5372i	−0.0542535	+	0.516187i
$907$	23.5457	−	26.1502i	0.781823	−	0.868302i	−0.212228	−	0.977220i	$-0.568072\pi$
$907$	23.5457	−	26.1502i	0.781823	−	0.868302i	0.994051	+	0.108918i	$0.0347386\pi$
$908$	−22.9033	−	4.86826i	−0.760074	−	0.161559i
$909$	−2.81396	−	2.04446i	−0.0933333	−	0.0678106i
$910$	17.3129	+	14.4324i	0.573918	+	0.478429i
$911$	5.57732	−	17.1652i	0.184785	−	0.568709i	−0.815160	−	0.579236i	$-0.803351\pi$
$911$	5.57732	−	17.1652i	0.184785	−	0.568709i	0.999945	+	0.0105271i	$0.00335095\pi$
$912$	0.460332	−	0.797319i	0.0152431	−	0.0264019i
$913$	3.43269	+	14.6497i	0.113605	+	0.484833i
$914$	4.08516	+	7.07570i	0.135125	+	0.234043i
$915$	−10.7492	−	11.9382i	−0.355359	−	0.394666i
$916$	6.17023	−	4.48293i	0.203870	−	0.148120i
$917$	5.15529	−	0.741486i	0.170243	−	0.0244860i
$918$	−2.25594	−	6.94307i	−0.0744572	−	0.229156i
$919$	5.36100	+	1.13952i	0.176843	+	0.0375891i	0.295482	−	0.955348i	$-0.404520\pi$
$919$	5.36100	+	1.13952i	0.176843	+	0.0375891i	−0.118639	+	0.992937i	$0.537853\pi$
$920$	0.158554	−	1.50854i	0.00522738	−	0.0497352i
$921$	16.5562	+	7.37129i	0.545545	+	0.242892i
$922$	3.40361	+	3.78009i	0.112092	+	0.124491i
$923$	38.8470			1.27866
$924$	−8.75977	+	0.516174i	−0.288175	+	0.0169809i
$925$	27.0604			0.889741
$926$	−15.2816	−	16.9720i	−0.502185	−	0.557733i
$927$	−7.69499	−	3.42603i	−0.252737	−	0.112526i
$928$	−0.556407	+	5.29385i	−0.0182649	+	0.173779i
$929$	35.8729	+	7.62501i	1.17695	+	0.250169i	0.754551	−	0.656241i	$-0.227855\pi$
$929$	35.8729	+	7.62501i	1.17695	+	0.250169i	0.422399	+	0.906410i	$0.361188\pi$
$930$	−1.24679	−	3.83724i	−0.0408840	−	0.125828i
$931$	6.38759	+	0.855751i	0.209345	+	0.0280461i
$932$	−23.4897	+	17.0663i	−0.769431	+	0.559024i
$933$	−10.0954	−	11.2121i	−0.330508	−	0.367067i
$934$	−5.69697	−	9.86745i	−0.186411	−	0.322873i
$935$	−32.9123	+	19.9227i	−1.07635	+	0.651541i
$936$	−2.68076	+	4.64321i	−0.0876233	+	0.151768i
$937$	−0.608836	+	1.87380i	−0.0198898	+	0.0612145i	−0.960509	−	0.278250i	$-0.910246\pi$
$937$	−0.608836	+	1.87380i	−0.0198898	+	0.0612145i	0.940619	+	0.339464i	$0.110246\pi$
$938$	−34.5077	+	12.6859i	−1.12672	+	0.414210i
$939$	0.130458	+	0.0947836i	0.00425735	+	0.00309315i
$940$	4.60459	+	0.978735i	0.150185	+	0.0319228i
$941$	−37.2878	+	41.4123i	−1.21555	+	1.35000i	−0.296907	+	0.954906i	$0.595955\pi$
$941$	−37.2878	+	41.4123i	−1.21555	+	1.35000i	−0.918640	+	0.395096i	$0.870711\pi$
$942$	0.591360	−	5.62642i	0.0192676	−	0.183319i
$943$	−0.341621	−	3.25031i	−0.0111247	−	0.105845i
$944$	1.32990	−	4.09300i	0.0432844	−	0.133216i
$945$	3.01464	−	2.93005i	0.0980662	−	0.0953144i
$946$	22.1139	+	29.1472i	0.718986	+	0.947657i
$947$	0.193802	−	0.335676i	0.00629773	−	0.0109080i	−0.862859	−	0.505444i	$-0.831329\pi$
$947$	0.193802	−	0.335676i	0.00629773	−	0.0109080i	0.869157	+	0.494536i	$0.164662\pi$
$948$	10.2897	−	2.18715i	0.334194	−	0.0710352i
$949$	−8.56132	−	3.81174i	−0.277912	−	0.123734i
$950$	−2.08186	+	0.926904i	−0.0675444	+	0.0300727i
$951$	−2.58671	−	7.96108i	−0.0838799	−	0.258156i
$952$	16.3470	−	10.2881i	0.529808	−	0.333441i
$953$	28.0734	+	20.3965i	0.909388	+	0.660709i	0.940860	−	0.338796i	$-0.110020\pi$
$953$	28.0734	+	20.3965i	0.909388	+	0.660709i	−0.0314722	+	0.999505i	$0.510020\pi$
$954$	1.11831	+	10.6400i	0.0362067	+	0.344484i
$955$	−17.0799	+	3.63045i	−0.552694	+	0.117479i
$956$	9.09962	+	15.7610i	0.294303	+	0.509747i
$957$	7.51343	+	15.9758i	0.242875	+	0.516426i
$958$	−20.2219			−0.653340
$959$	−21.3277	−	1.42229i	−0.688708	−	0.0459283i
$960$	1.28548	−	0.933958i	0.0414888	−	0.0301434i
$961$	−22.4296	+	9.98630i	−0.723536	+	0.322139i
$962$	−39.2205	+	43.5588i	−1.26452	+	1.40439i
$963$	−8.99140	+	9.98596i	−0.289744	+	0.321793i
$964$	−23.2698	+	10.3604i	−0.749469	+	0.333685i
$965$	−24.7406	+	17.9751i	−0.796427	+	0.578638i
$966$	1.11451	+	2.26651i	0.0358588	+	0.0729238i
$967$	−20.1092			−0.646667			−0.323334	−	0.946285i	$-0.604804\pi$
$967$	−20.1092			−0.646667			−0.323334	+	0.946285i	$0.604804\pi$
$968$	−9.85495	+	4.88671i	−0.316750	+	0.157065i
$969$	3.36060	+	5.82073i	0.107958	+	0.186989i
$970$	−11.2502	+	2.39129i	−0.361221	+	0.0767798i
$971$	3.24995	+	30.9212i	0.104296	+	0.992309i	0.914067	+	0.405563i	$0.132925\pi$
$971$	3.24995	+	30.9212i	0.104296	+	0.992309i	−0.809771	+	0.586746i	$0.800409\pi$
$972$	0.809017	+	0.587785i	0.0259492	+	0.0188532i
$973$	1.22559	+	32.1262i	0.0392906	+	1.02992i
$974$	1.87280	+	5.76388i	0.0600083	+	0.184687i
$975$	12.1238	−	5.39784i	0.388271	−	0.172869i
$976$	9.23608	+	4.11217i	0.295640	+	0.131627i
$977$	−11.3443	+	2.41130i	−0.362935	+	0.0771442i	−0.385770	−	0.922595i	$-0.626064\pi$
$977$	−11.3443	+	2.41130i	−0.362935	+	0.0771442i	0.0228348	+	0.999739i	$0.492731\pi$
$978$	1.14719	−	1.98699i	0.0366831	−	0.0635370i
$979$	30.5711	−	43.9656i	0.977055	−	1.40515i
$980$	9.47032	+	5.83314i	0.302518	+	0.186333i
$981$	−0.0632367	+	0.194623i	−0.00201899	+	0.00621382i
$982$	−1.17751	−	11.2033i	−0.0375760	−	0.357512i
$983$	−3.56640	+	33.9321i	−0.113751	+	1.08227i	0.777540	+	0.628833i	$0.216467\pi$
$983$	−3.56640	+	33.9321i	−0.113751	+	1.08227i	−0.891291	+	0.453432i	$0.850200\pi$
$984$	2.29080	−	2.54419i	0.0730280	−	0.0811058i
$985$	−2.46777	−	0.524540i	−0.0786296	−	0.0167132i
$986$	−31.4384	−	22.8414i	−1.00120	−	0.727417i
$987$	−7.35699	+	2.70462i	−0.234176	+	0.0860890i
$988$	1.52536	−	4.69456i	0.0485281	−	0.149354i
$989$	5.26540	−	9.11993i	0.167430	−	0.289997i
$990$	2.04324	−	4.85771i	0.0649383	−	0.154388i
$991$	−14.0880	−	24.4011i	−0.447520	−	0.775127i	0.550704	−	0.834701i	$-0.314359\pi$
$991$	−14.0880	−	24.4011i	−0.447520	−	0.775127i	−0.998224	+	0.0595734i	$0.981026\pi$
$992$	1.69908	+	1.88702i	0.0539459	+	0.0599130i
$993$	9.95344	−	7.23160i	0.315863	−	0.229488i
$994$	18.9746	−	2.72912i	0.601838	−	0.0865625i
$995$	−10.2684	−	31.6029i	−0.325530	−	1.00188i
$996$	4.43754	+	0.943228i	0.140609	+	0.0298873i
$997$	5.35104	−	50.9117i	0.169469	−	1.61239i	−0.497608	−	0.867402i	$-0.665788\pi$
$997$	5.35104	−	50.9117i	0.169469	−	1.61239i	0.667077	−	0.744989i	$-0.267545\pi$
$998$	−12.3599	−	5.50296i	−0.391244	−	0.174193i
$999$	7.31519	+	8.12434i	0.231442	+	0.257043i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.y.d.163.2	✓	40
7.4	even	3	inner	462.2.y.d.361.4	yes	40
11.5	even	5	inner	462.2.y.d.247.4	yes	40
77.60	even	15	inner	462.2.y.d.445.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.y.d.163.2	✓	40	1.1	even	1	trivial
462.2.y.d.247.4	yes	40	11.5	even	5	inner
462.2.y.d.361.4	yes	40	7.4	even	3	inner
462.2.y.d.445.2	yes	40	77.60	even	15	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.669131 + 0.743145i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(-1.55422 - 0.330360i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-1.63560 - 2.07962i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})\)	\(q+(0.669131 + 0.743145i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(-1.55422 - 0.330360i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-1.63560 - 2.07962i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.669131 + 0.743145i) q^{9} +(-0.794473 - 1.37607i) q^{10} +(3.30493 + 0.278246i) q^{11} +(0.500000 - 0.866025i) q^{12} +(1.65680 - 5.09910i) q^{13} +(0.451027 - 2.60702i) q^{14} +(1.28548 + 0.933958i) q^{15} +(-0.978148 - 0.207912i) q^{16} +(4.88491 - 5.42524i) q^{17} +(-0.104528 + 0.994522i) q^{18} +(-0.0962357 - 0.915621i) q^{19} +(0.491011 - 1.51118i) q^{20} +(0.648339 + 2.56508i) q^{21} +(2.00465 + 2.64223i) q^{22} +(0.477314 - 0.826733i) q^{23} +(0.978148 - 0.207912i) q^{24} +(-2.26126 - 1.00678i) q^{25} +(4.89799 - 2.18072i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(2.23919 - 1.40926i) q^{28} +(-4.30641 - 3.12879i) q^{29} +(0.166090 + 1.58024i) q^{30} +(-2.48375 + 0.527938i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.90603 - 1.59843i) q^{33} +7.30038 q^{34} +(1.85506 + 3.77253i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-9.98723 + 4.44660i) q^{37} +(0.616045 - 0.684187i) q^{38} +(-3.58755 + 3.98438i) q^{39} +(1.45157 - 0.646282i) q^{40} +(2.76970 - 2.01231i) q^{41} +(-1.47241 + 2.19819i) q^{42} +11.0313 q^{43} +(-0.622181 + 3.25774i) q^{44} +(-0.794473 - 1.37607i) q^{45} +(0.933768 - 0.198478i) q^{46} +(0.309679 + 2.94640i) q^{47} +(0.809017 + 0.587785i) q^{48} +(-1.64962 + 6.80285i) q^{49} +(-0.764895 - 2.35411i) q^{50} +(-6.66923 + 2.96933i) q^{51} +(4.89799 + 2.18072i) q^{52} +(10.4648 - 2.22437i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-5.04468 - 1.52427i) q^{55} +(2.54560 + 0.721064i) q^{56} +(-0.284501 + 0.875604i) q^{57} +(-0.556407 - 5.29385i) q^{58} +(-0.449852 + 4.28006i) q^{59} +(-1.06321 + 1.18082i) q^{60} +(-9.88922 - 2.10202i) q^{61} +(-2.05429 - 1.49253i) q^{62} +(0.451027 - 2.60702i) q^{63} +(0.309017 - 0.951057i) q^{64} +(-4.25957 + 7.37780i) q^{65} +(-0.756653 - 3.22916i) q^{66} +(-6.94805 - 12.0344i) q^{67} +(4.88491 + 5.42524i) q^{68} +(-0.772311 + 0.561117i) q^{69} +(-1.56225 + 3.90290i) q^{70} +(2.23899 + 6.89091i) q^{71} +(-0.978148 - 0.207912i) q^{72} +(0.182708 - 1.73835i) q^{73} +(-9.98723 - 4.44660i) q^{74} +(1.65627 + 1.83947i) q^{75} +0.920665 q^{76} +(-4.82690 - 7.32810i) q^{77} -5.36151 q^{78} +(7.03898 + 7.81758i) q^{79} +(1.45157 + 0.646282i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(3.34873 + 0.711795i) q^{82} +(1.40191 + 4.31464i) q^{83} +(-2.61880 + 0.376663i) q^{84} +(-9.38452 + 6.81825i) q^{85} +(7.38138 + 8.19785i) q^{86} +(2.66151 + 4.60987i) q^{87} +(-2.83730 + 1.71748i) q^{88} +(8.07291 - 13.9827i) q^{89} +(0.491011 - 1.51118i) q^{90} +(-13.3140 + 4.89459i) q^{91} +(0.772311 + 0.561117i) q^{92} +(2.48375 + 0.527938i) q^{93} +(-1.98239 + 2.20166i) q^{94} +(-0.152913 + 1.45487i) q^{95} +(0.104528 + 0.994522i) q^{96} +(2.23680 - 6.88417i) q^{97} +(-6.15931 + 3.32609i) q^{98} +(2.00465 + 2.64223i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9}+O(q^{10}) \) 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9	\( 40 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 3 q^{5} + 10 q^{6} - 7 q^{7} - 10 q^{8} + 5 q^{9} + 12 q^{10} + 2 q^{11} + 20 q^{12} + 10 q^{13} + 5 q^{14} - 6 q^{15} + 5 q^{16} + 5 q^{18} - 13 q^{19} + 6 q^{20} - 2 q^{21} - 4 q^{22} - 20 q^{23} - 5 q^{24} + 12 q^{25} + 10 q^{27} - 3 q^{28} + 12 q^{29} + 3 q^{30} - 10 q^{31} - 20 q^{32} + 8 q^{33} - 13 q^{35} - 10 q^{36} + 3 q^{37} + 2 q^{38} + 5 q^{39} - 3 q^{40} - 44 q^{41} - 3 q^{42} + 36 q^{43} - 3 q^{44} + 12 q^{45} + 11 q^{47} + 10 q^{48} + 33 q^{49} - 4 q^{50} + 26 q^{53} + 20 q^{54} - 20 q^{55} + 8 q^{56} + 4 q^{57} - 6 q^{58} + 4 q^{59} + 3 q^{60} - 23 q^{61} + 5 q^{63} - 10 q^{64} - 50 q^{65} - 7 q^{66} - 108 q^{67} + 20 q^{69} - 86 q^{71} + 5 q^{72} - 35 q^{73} + 3 q^{74} - 2 q^{75} - 44 q^{76} - 37 q^{77} + 20 q^{78} + 3 q^{79} - 3 q^{80} + 5 q^{81} - 28 q^{82} - 88 q^{83} - 5 q^{84} + 96 q^{85} - 13 q^{86} + 6 q^{87} - 8 q^{88} + 6 q^{89} + 6 q^{90} + 40 q^{91} - 20 q^{92} + 10 q^{93} - 24 q^{94} + 36 q^{95} - 5 q^{96} + 60 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 3 * q^5 + 10 * q^6 - 7 * q^7 - 10 * q^8 + 5 * q^9 + 12 * q^10 + 2 * q^11 + 20 * q^12 + 10 * q^13 + 5 * q^14 - 6 * q^15 + 5 * q^16 + 5 * q^18 - 13 * q^19 + 6 * q^20 - 2 * q^21 - 4 * q^22 - 20 * q^23 - 5 * q^24 + 12 * q^25 + 10 * q^27 - 3 * q^28 + 12 * q^29 + 3 * q^30 - 10 * q^31 - 20 * q^32 + 8 * q^33 - 13 * q^35 - 10 * q^36 + 3 * q^37 + 2 * q^38 + 5 * q^39 - 3 * q^40 - 44 * q^41 - 3 * q^42 + 36 * q^43 - 3 * q^44 + 12 * q^45 + 11 * q^47 + 10 * q^48 + 33 * q^49 - 4 * q^50 + 26 * q^53 + 20 * q^54 - 20 * q^55 + 8 * q^56 + 4 * q^57 - 6 * q^58 + 4 * q^59 + 3 * q^60 - 23 * q^61 + 5 * q^63 - 10 * q^64 - 50 * q^65 - 7 * q^66 - 108 * q^67 + 20 * q^69 - 86 * q^71 + 5 * q^72 - 35 * q^73 + 3 * q^74 - 2 * q^75 - 44 * q^76 - 37 * q^77 + 20 * q^78 + 3 * q^79 - 3 * q^80 + 5 * q^81 - 28 * q^82 - 88 * q^83 - 5 * q^84 + 96 * q^85 - 13 * q^86 + 6 * q^87 - 8 * q^88 + 6 * q^89 + 6 * q^90 + 40 * q^91 - 20 * q^92 + 10 * q^93 - 24 * q^94 + 36 * q^95 - 5 * q^96 + 60 * q^97 + 2 * q^98 - 4 * q^99

Introduction

L-functions

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