LMFDB - Embedded newform 546.2.bq.c.419.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(419,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

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

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

chi := DirichletCharacter("546.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bq (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			419.1
Character	$\chi$	$=$	546.419
Dual form			546.2.bq.c.503.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-1.73204 - 0.00466741i) q^{3} +(0.500000 - 0.866025i) q^{4} +0.915374 q^{5} +(1.50233 - 0.861980i) q^{6} +(-2.64454 + 0.0800636i) q^{7} +1.00000i q^{8} +(2.99996 + 0.0161683i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.73204 - 0.00466741i) q^{3} +(0.500000 - 0.866025i) q^{4} +0.915374 q^{5} +(1.50233 - 0.861980i) q^{6} +(-2.64454 + 0.0800636i) q^{7} +1.00000i q^{8} +(2.99996 + 0.0161683i) q^{9} +(-0.792737 + 0.457687i) q^{10} +(1.18022 - 0.681403i) q^{11} +(-0.870064 + 1.49766i) q^{12} +(-1.88939 + 3.07087i) q^{13} +(2.25021 - 1.39161i) q^{14} +(-1.58547 - 0.00427243i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.15494 - 3.73246i) q^{17} +(-2.60612 + 1.48598i) q^{18} +(-2.79445 - 1.61337i) q^{19} +(0.457687 - 0.792737i) q^{20} +(4.58083 - 0.126331i) q^{21} +(-0.681403 + 1.18022i) q^{22} +(-0.854610 + 0.493409i) q^{23} +(0.00466741 - 1.73204i) q^{24} -4.16209 q^{25} +(0.100823 - 3.60414i) q^{26} +(-5.19598 - 0.0420063i) q^{27} +(-1.25293 + 2.33027i) q^{28} +(7.51934 - 4.34129i) q^{29} +(1.37519 - 0.789034i) q^{30} -9.44703i q^{31} +(0.866025 + 0.500000i) q^{32} +(-2.04738 + 1.17471i) q^{33} +4.30988i q^{34} +(-2.42074 + 0.0732882i) q^{35} +(1.51398 - 2.58995i) q^{36} +(0.142310 + 0.246487i) q^{37} +3.22675 q^{38} +(3.28683 - 5.31006i) q^{39} +0.915374i q^{40} +(-1.15899 - 2.00743i) q^{41} +(-3.90395 + 2.39982i) q^{42} +(3.88259 - 6.72485i) q^{43} -1.36281i q^{44} +(2.74608 + 0.0148001i) q^{45} +(0.493409 - 0.854610i) q^{46} -2.48166 q^{47} +(0.861980 + 1.50233i) q^{48} +(6.98718 - 0.423463i) q^{49} +(3.60448 - 2.08105i) q^{50} +(-3.74987 + 6.45473i) q^{51} +(1.71476 + 3.17169i) q^{52} -13.3842i q^{53} +(4.52086 - 2.56161i) q^{54} +(1.08035 - 0.623738i) q^{55} +(-0.0800636 - 2.64454i) q^{56} +(4.83258 + 2.80748i) q^{57} +(-4.34129 + 7.51934i) q^{58} +(3.96711 - 6.87124i) q^{59} +(-0.796434 + 1.37092i) q^{60} +(-0.626160 - 0.361514i) q^{61} +(4.72352 + 8.18137i) q^{62} +(-7.93480 + 0.197430i) q^{63} -1.00000 q^{64} +(-1.72949 + 2.81099i) q^{65} +(1.18573 - 2.04102i) q^{66} +(2.24163 + 3.88262i) q^{67} +(-2.15494 - 3.73246i) q^{68} +(1.48252 - 0.850618i) q^{69} +(2.05978 - 1.27384i) q^{70} +(-10.1544 - 5.86266i) q^{71} +(-0.0161683 + 2.99996i) q^{72} -4.69308i q^{73} +(-0.246487 - 0.142310i) q^{74} +(7.20893 + 0.0194262i) q^{75} +(-2.79445 + 1.61337i) q^{76} +(-3.06659 + 1.89649i) q^{77} +(-0.191452 + 6.24206i) q^{78} -2.91429 q^{79} +(-0.457687 - 0.792737i) q^{80} +(8.99948 + 0.0970086i) q^{81} +(2.00743 + 1.15899i) q^{82} -2.84354 q^{83} +(2.18101 - 4.03028i) q^{84} +(1.97257 - 3.41660i) q^{85} +7.76519i q^{86} +(-13.0441 + 7.48422i) q^{87} +(0.681403 + 1.18022i) q^{88} +(2.13411 + 3.69640i) q^{89} +(-2.38558 + 1.36022i) q^{90} +(4.75069 - 8.27230i) q^{91} +0.986818i q^{92} +(-0.0440932 + 16.3627i) q^{93} +(2.14918 - 1.24083i) q^{94} +(-2.55796 - 1.47684i) q^{95} +(-1.49766 - 0.870064i) q^{96} +(5.76613 + 3.32908i) q^{97} +(-5.83934 + 3.86032i) q^{98} +(3.55164 - 2.02510i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} + 16 q^{7} + 16 q^{9}+O(q^{10}) $ 64 * q + 32 * q^4 + 16 * q^7 + 16 * q^9	$ 64 q + 32 q^{4} + 16 q^{7} + 16 q^{9} - 12 q^{15} - 32 q^{16} - 24 q^{18} + 16 q^{21} - 16 q^{28} + 8 q^{30} - 16 q^{36} - 48 q^{39} + 20 q^{42} - 8 q^{43} + 8 q^{46} + 8 q^{49} - 8 q^{51} + 8 q^{57} + 16 q^{58} - 24 q^{60} + 32 q^{63} - 64 q^{64} + 24 q^{67} + 48 q^{70} - 12 q^{72} - 12 q^{78} + 96 q^{79} + 68 q^{81} + 8 q^{84} - 112 q^{85} - 16 q^{91} - 56 q^{93}+O(q^{100}) $ 64 * q + 32 * q^4 + 16 * q^7 + 16 * q^9 - 12 * q^15 - 32 * q^16 - 24 * q^18 + 16 * q^21 - 16 * q^28 + 8 * q^30 - 16 * q^36 - 48 * q^39 + 20 * q^42 - 8 * q^43 + 8 * q^46 + 8 * q^49 - 8 * q^51 + 8 * q^57 + 16 * q^58 - 24 * q^60 + 32 * q^63 - 64 * q^64 + 24 * q^67 + 48 * q^70 - 12 * q^72 - 12 * q^78 + 96 * q^79 + 68 * q^81 + 8 * q^84 - 112 * q^85 - 16 * q^91 - 56 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.73204	−	0.00466741i	−0.999996	−	0.00269473i
$3$	−1.73204	−	0.00466741i	−0.999996	−	0.00269473i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.915374			0.409368			0.204684	−	0.978828i	$-0.434383\pi$
$5$	0.915374			0.409368			0.204684	+	0.978828i	$0.434383\pi$
$6$	1.50233	−	0.861980i	0.613323	−	0.351902i
$7$	−2.64454	+	0.0800636i	−0.999542	+	0.0302612i
$7$	−2.64454	+	0.0800636i	−0.999542	+	0.0302612i
$8$			1.00000i			0.353553i
$9$	2.99996	+	0.0161683i	0.999985	+	0.00538944i
$10$	−0.792737	+	0.457687i	−0.250685	+	0.144733i
$11$	1.18022	−	0.681403i	0.355851	−	0.205451i	−0.311408	−	0.950276i	$-0.600801\pi$
$11$	1.18022	−	0.681403i	0.355851	−	0.205451i	0.667259	+	0.744826i	$0.267467\pi$
$12$	−0.870064	+	1.49766i	−0.251166	+	0.432337i
$13$	−1.88939	+	3.07087i	−0.524021	+	0.851705i
$13$	−1.88939	+	3.07087i	−0.524021	+	0.851705i
$14$	2.25021	−	1.39161i	0.601393	−	0.371923i
$15$	−1.58547	−	0.00427243i	−0.409366	−	0.00110314i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.15494	−	3.73246i	0.522649	−	0.905255i	−0.477004	−	0.878901i	$-0.658277\pi$
$17$	2.15494	−	3.73246i	0.522649	−	0.905255i	0.999653	−	0.0263535i	$-0.00838955\pi$
$18$	−2.60612	+	1.48598i	−0.614269	+	0.350248i
$19$	−2.79445	−	1.61337i	−0.641090	−	0.370134i	0.143944	−	0.989586i	$-0.454021\pi$
$19$	−2.79445	−	1.61337i	−0.641090	−	0.370134i	−0.785034	+	0.619452i	$0.787355\pi$
$20$	0.457687	−	0.792737i	0.102342	−	0.177261i
$21$	4.58083	−	0.126331i	0.999620	−	0.0275676i
$22$	−0.681403	+	1.18022i	−0.145276	+	0.251625i
$23$	−0.854610	+	0.493409i	−0.178198	+	0.102883i	−0.586446	−	0.809988i	$-0.699473\pi$
$23$	−0.854610	+	0.493409i	−0.178198	+	0.102883i	0.408248	+	0.912871i	$0.366140\pi$
$24$	0.00466741	−	1.73204i	0.000952731	−	0.353552i
$25$	−4.16209			−0.832418
$26$	0.100823	−	3.60414i	0.0197731	−	0.706830i
$27$	−5.19598	−	0.0420063i	−0.999967	−	0.00808412i
$28$	−1.25293	+	2.33027i	−0.236782	+	0.440380i
$29$	7.51934	−	4.34129i	1.39631	−	0.806158i	0.402303	−	0.915507i	$-0.368210\pi$
$29$	7.51934	−	4.34129i	1.39631	−	0.806158i	0.994003	+	0.109349i	$0.0348766\pi$
$30$	1.37519	−	0.789034i	0.251075	−	0.144057i
$31$		−	9.44703i		−	1.69674i	−0.529406	−	0.848369i	$-0.677585\pi$
$31$		−	9.44703i		−	1.69674i	0.529406	−	0.848369i	$-0.322415\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−2.04738	+	1.17471i	−0.356403	+	0.204491i
$34$			4.30988i			0.739137i
$35$	−2.42074	+	0.0732882i	−0.409180	+	0.0123880i
$36$	1.51398	−	2.58995i	0.252330	−	0.431659i
$37$	0.142310	+	0.246487i	0.0233955	+	0.0405223i	0.877486	−	0.479602i	$-0.159219\pi$
$37$	0.142310	+	0.246487i	0.0233955	+	0.0405223i	−0.854091	+	0.520124i	$0.825886\pi$
$38$	3.22675			0.523448
$39$	3.28683	−	5.31006i	0.526315	−	0.850290i
$40$			0.915374i			0.144733i
$41$	−1.15899	−	2.00743i	−0.181004	−	0.313508i	0.761219	−	0.648495i	$-0.224601\pi$
$41$	−1.15899	−	2.00743i	−0.181004	−	0.313508i	−0.942223	+	0.334987i	$0.891268\pi$
$42$	−3.90395	+	2.39982i	−0.602393	+	0.370301i
$43$	3.88259	−	6.72485i	0.592090	−	1.02553i	−0.401860	−	0.915701i	$-0.631636\pi$
$43$	3.88259	−	6.72485i	0.592090	−	1.02553i	0.993950	−	0.109829i	$-0.0350304\pi$
$44$		−	1.36281i		−	0.205451i
$45$	2.74608	+	0.0148001i	0.409362	+	0.00220626i
$46$	0.493409	−	0.854610i	0.0727492	−	0.126005i
$47$	−2.48166			−0.361987			−0.180993	−	0.983484i	$-0.557931\pi$
$47$	−2.48166			−0.361987			−0.180993	+	0.983484i	$0.557931\pi$
$48$	0.861980	+	1.50233i	0.124416	+	0.216842i
$49$	6.98718	−	0.423463i	0.998169	−	0.0604947i
$50$	3.60448	−	2.08105i	0.509750	−	0.294304i
$51$	−3.74987	+	6.45473i	−0.525087	+	0.903843i
$52$	1.71476	+	3.17169i	0.237794	+	0.439834i
$53$		−	13.3842i		−	1.83847i	−0.393713	−	0.919234i	$-0.628810\pi$
$53$		−	13.3842i		−	1.83847i	0.393713	−	0.919234i	$-0.371190\pi$
$54$	4.52086	−	2.56161i	0.615211	−	0.348591i
$55$	1.08035	−	0.623738i	0.145674	−	0.0841049i
$56$	−0.0800636	−	2.64454i	−0.0106990	−	0.353391i
$57$	4.83258	+	2.80748i	0.640090	+	0.371860i
$58$	−4.34129	+	7.51934i	−0.570040	+	0.987338i
$59$	3.96711	−	6.87124i	0.516474	−	0.894560i	−0.483343	−	0.875431i	$-0.660578\pi$
$59$	3.96711	−	6.87124i	0.516474	−	0.894560i	0.999817	−	0.0191284i	$-0.00608913\pi$
$60$	−0.796434	+	1.37092i	−0.102819	+	0.176985i
$61$	−0.626160	−	0.361514i	−0.0801716	−	0.0462871i	0.459378	−	0.888241i	$-0.348072\pi$
$61$	−0.626160	−	0.361514i	−0.0801716	−	0.0462871i	−0.539550	+	0.841954i	$0.681406\pi$
$62$	4.72352	+	8.18137i	0.599887	+	1.03904i
$63$	−7.93480	+	0.197430i	−0.999691	+	0.0248738i
$64$	−1.00000			−0.125000
$65$	−1.72949	+	2.81099i	−0.214517	+	0.348661i
$66$	1.18573	−	2.04102i	0.145953	−	0.251232i
$67$	2.24163	+	3.88262i	0.273859	+	0.474338i	0.969847	−	0.243716i	$-0.0783665\pi$
$67$	2.24163	+	3.88262i	0.273859	+	0.474338i	−0.695988	+	0.718054i	$0.745033\pi$
$68$	−2.15494	−	3.73246i	−0.261325	−	0.452627i
$69$	1.48252	−	0.850618i	0.178475	−	0.102402i
$70$	2.05978	−	1.27384i	0.246191	−	0.152253i
$71$	−10.1544	−	5.86266i	−1.20511	−	0.695770i	−0.243422	−	0.969920i	$-0.578270\pi$
$71$	−10.1544	−	5.86266i	−1.20511	−	0.695770i	−0.961687	+	0.274151i	$0.911603\pi$
$72$	−0.0161683	+	2.99996i	−0.00190546	+	0.353548i
$73$		−	4.69308i		−	0.549284i	−0.961547	−	0.274642i	$-0.911441\pi$
$73$		−	4.69308i		−	0.549284i	0.961547	−	0.274642i	$-0.0885593\pi$
$74$	−0.246487	−	0.142310i	−0.0286536	−	0.0165431i
$75$	7.20893	+	0.0194262i	0.832415	+	0.00224314i
$76$	−2.79445	+	1.61337i	−0.320545	+	0.185067i
$77$	−3.06659	+	1.89649i	−0.349471	+	0.216125i
$78$	−0.191452	+	6.24206i	−0.0216777	+	0.706774i
$79$	−2.91429			−0.327883			−0.163941	−	0.986470i	$-0.552421\pi$
$79$	−2.91429			−0.327883			−0.163941	+	0.986470i	$0.552421\pi$
$80$	−0.457687	−	0.792737i	−0.0511710	−	0.0886307i
$81$	8.99948	+	0.0970086i	0.999942	+	0.0107787i
$82$	2.00743	+	1.15899i	0.221684	+	0.127989i
$83$	−2.84354			−0.312119			−0.156060	−	0.987748i	$-0.549879\pi$
$83$	−2.84354			−0.312119			−0.156060	+	0.987748i	$0.549879\pi$
$84$	2.18101	−	4.03028i	0.237968	−	0.439740i
$85$	1.97257	−	3.41660i	0.213956	−	0.370582i
$86$			7.76519i			0.837342i
$87$	−13.0441	+	7.48422i	−1.39847	+	0.802392i
$88$	0.681403	+	1.18022i	0.0726378	+	0.125812i
$89$	2.13411	+	3.69640i	0.226216	+	0.391817i	0.956683	−	0.291130i	$-0.0940312\pi$
$89$	2.13411	+	3.69640i	0.226216	+	0.391817i	−0.730468	+	0.682947i	$0.760698\pi$
$90$	−2.38558	+	1.36022i	−0.251462	+	0.143380i
$91$	4.75069	−	8.27230i	0.498008	−	0.867173i
$92$			0.986818i			0.102883i
$93$	−0.0440932	+	16.3627i	−0.00457225	+	1.69673i
$94$	2.14918	−	1.24083i	0.221671	−	0.127982i
$95$	−2.55796	−	1.47684i	−0.262442	−	0.151521i
$96$	−1.49766	−	0.870064i	−0.152854	−	0.0888006i
$97$	5.76613	+	3.32908i	0.585462	+	0.338017i	0.763301	−	0.646043i	$-0.223577\pi$
$97$	5.76613	+	3.32908i	0.585462	+	0.338017i	−0.177839	+	0.984060i	$0.556911\pi$
$98$	−5.83934	+	3.86032i	−0.589863	+	0.389951i
$99$	3.55164	−	2.02510i	0.356953	−	0.203530i
$100$	−2.08105	+	3.60448i	−0.208105	+	0.360448i
$101$	6.23732	+	10.8034i	0.620636	+	1.07497i	0.989367	+	0.145438i	$0.0464590\pi$
$101$	6.23732	+	10.8034i	0.620636	+	1.07497i	−0.368731	+	0.929536i	$0.620208\pi$
$102$	0.0201160	−	7.46490i	0.00199178	−	0.739135i
$103$			14.7630i			1.45464i	0.686296	+	0.727322i	$0.259235\pi$
$103$			14.7630i			1.45464i	−0.686296	+	0.727322i	$0.740765\pi$
$104$	−3.07087	−	1.88939i	−0.301123	−	0.185270i
$105$	4.19318	−	0.115640i	0.409212	−	0.0112853i
$106$	6.69212	+	11.5911i	0.649996	+	1.12583i
$107$	−8.64105	+	4.98891i	−0.835361	+	0.482296i	−0.855685	−	0.517497i	$-0.826864\pi$
$107$	−8.64105	+	4.98891i	−0.835361	+	0.482296i	0.0203235	+	0.999793i	$0.493530\pi$
$108$	−2.63437	+	4.47885i	−0.253492	+	0.430978i
$109$	−15.6942			−1.50323			−0.751617	−	0.659600i	$-0.770726\pi$
$109$	−15.6942			−1.50323			−0.751617	+	0.659600i	$0.770726\pi$
$110$	−0.623738	+	1.08035i	−0.0594711	+	0.103007i
$111$	−0.245336	−	0.427591i	−0.0232863	−	0.0405852i
$112$	1.39161	+	2.25021i	0.131494	+	0.212625i
$113$	−3.82295	−	2.20718i	−0.359633	−	0.207634i	0.309287	−	0.950969i	$-0.399910\pi$
$113$	−3.82295	−	2.20718i	−0.359633	−	0.207634i	−0.668920	+	0.743335i	$0.733243\pi$
$114$	−5.58887	−	0.0150606i	−0.523446	−	0.00141055i
$115$	−0.782287	+	0.451654i	−0.0729487	+	0.0421169i
$116$		−	8.68259i		−	0.806158i
$117$	−5.71773	+	9.18192i	−0.528604	+	0.848869i
$118$			7.93423i			0.730405i
$119$	−5.39998	+	10.0432i	−0.495016	+	0.920656i
$120$	0.00427243	−	1.58547i	0.000390017	−	0.144733i
$121$	−4.57138	+	7.91786i	−0.415580	+	0.719806i
$122$	0.723027			0.0654598
$123$	1.99805	+	3.48237i	0.180159	+	0.313995i
$124$	−8.18137	−	4.72352i	−0.734709	−	0.424184i
$125$	−8.38674			−0.750133
$126$	6.77302	−	4.13838i	0.603389	−	0.368676i
$127$	−8.86383	−	15.3526i	−0.786538	−	1.36232i	−0.928076	−	0.372390i	$-0.878538\pi$
$127$	−8.86383	−	15.3526i	−0.786538	−	1.36232i	0.141539	−	0.989933i	$-0.454795\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−6.75621	+	11.6296i	−0.594852	+	1.02393i
$130$	0.0922910	−	3.29914i	0.00809445	−	0.289353i
$131$	6.87137			0.600354			0.300177	−	0.953884i	$-0.402954\pi$
$131$	6.87137			0.600354			0.300177	+	0.953884i	$0.402954\pi$
$132$	−0.00636077	+	2.36044i	−0.000553634	+	0.205450i
$133$	7.51920	+	4.04290i	0.651997	+	0.350564i
$134$	−3.88262	−	2.24163i	−0.335407	−	0.193648i
$135$	−4.75627	−	0.0384515i	−0.409354	−	0.00330938i
$136$	3.73246	+	2.15494i	0.320056	+	0.184784i
$137$	10.0411	+	5.79723i	0.857869	+	0.495291i	0.863298	−	0.504694i	$-0.168395\pi$
$137$	10.0411	+	5.79723i	0.857869	+	0.495291i	−0.00542924	+	0.999985i	$0.501728\pi$
$138$	−0.858595	+	1.47792i	−0.0730885	+	0.125809i
$139$	3.50046	+	2.02099i	0.296905	+	0.171418i	0.641052	−	0.767498i	$-0.278498\pi$
$139$	3.50046	+	2.02099i	0.296905	+	0.171418i	−0.344147	+	0.938916i	$0.611832\pi$
$140$	−1.14690	+	2.13307i	−0.0969309	+	0.180277i
$141$	4.29834	+	0.0115829i	0.361986	+	0.000975457i
$142$	11.7253			0.983967
$143$	−0.137403	+	4.91174i	−0.0114902	+	0.410741i
$144$	−1.48598	−	2.60612i	−0.123831	−	0.217177i
$145$	6.88301	−	3.97391i	0.571603	−	0.330015i
$146$	2.34654	+	4.06433i	0.194201	+	0.336366i
$147$	−12.1041	+	0.700845i	−0.998328	+	0.0578047i
$148$	0.284619			0.0233955
$149$	−13.0094	−	7.51098i	−1.06577	−	0.615323i	−0.138748	−	0.990328i	$-0.544308\pi$
$149$	−13.0094	−	7.51098i	−1.06577	−	0.615323i	−0.927023	+	0.375005i	$0.877641\pi$
$150$	−6.25283	+	3.58764i	−0.510541	+	0.292930i
$151$	−3.29806			−0.268392			−0.134196	−	0.990955i	$-0.542845\pi$
$151$	−3.29806			−0.268392			−0.134196	+	0.990955i	$0.542845\pi$
$152$	1.61337	−	2.79445i	0.130862	−	0.226660i
$153$	6.52507	−	11.1624i	0.527520	−	0.902425i
$154$	1.70750	−	3.17571i	0.137595	−	0.255906i
$155$		−	8.64757i		−	0.694589i
$156$	−2.95523	−	5.50151i	−0.236608	−	0.440473i
$157$			4.29690i			0.342930i	0.985190	+	0.171465i	$0.0548501\pi$
$157$			4.29690i			0.342930i	−0.985190	+	0.171465i	$0.945150\pi$
$158$	2.52385	−	1.45714i	0.200786	−	0.115924i
$159$	−0.0624698	+	23.1821i	−0.00495417	+	1.83846i
$160$	0.792737	+	0.457687i	0.0626714	+	0.0361833i
$161$	2.22054	−	1.37326i	0.175003	−	0.108228i
$162$	−7.84228	+	4.41573i	−0.616148	+	0.346932i
$163$	5.87295	−	10.1723i	0.460005	−	0.796752i	−0.538955	−	0.842334i	$-0.681181\pi$
$163$	5.87295	−	10.1723i	0.460005	−	0.796752i	0.998961	+	0.0455820i	$0.0145142\pi$
$164$	−2.31798			−0.181004
$165$	−1.87412	+	1.07530i	−0.145900	+	0.0837120i
$166$	2.46258	−	1.42177i	0.191133	−	0.110351i
$167$	10.3463	+	17.9202i	0.800617	+	1.38671i	0.919210	+	0.393767i	$0.128828\pi$
$167$	10.3463	+	17.9202i	0.800617	+	1.38671i	−0.118593	+	0.992943i	$0.537838\pi$
$168$	0.126331	+	4.58083i	0.00974662	+	0.353419i
$169$	−5.86044	−	11.6041i	−0.450803	−	0.892623i
$170$			3.94515i			0.302579i
$171$	−8.35713	−	4.88524i	−0.639086	−	0.373583i
$172$	−3.88259	−	6.72485i	−0.296045	−	0.512765i
$173$	8.00405	−	13.8634i	0.608537	−	1.05402i	−0.382945	−	0.923771i	$-0.625090\pi$
$173$	8.00405	−	13.8634i	0.608537	−	1.05402i	0.991482	−	0.130245i	$-0.0415765\pi$
$174$	7.55441	−	13.0036i	0.572698	−	0.985798i
$175$	11.0068	−	0.333232i	0.832037	−	0.0251900i
$176$	−1.18022	−	0.681403i	−0.0889628	−	0.0513627i
$177$	−6.90329	+	11.8828i	−0.518883	+	0.893165i
$178$	−3.69640	−	2.13411i	−0.277057	−	0.159959i
$179$	22.9156	−	13.2303i	1.71279	−	0.988879i	0.782035	−	0.623235i	$-0.214182\pi$
$179$	22.9156	−	13.2303i	1.71279	−	0.988879i	0.930754	−	0.365645i	$-0.119152\pi$
$180$	1.38586	−	2.37078i	0.103296	−	0.176707i
$181$		−	14.0391i		−	1.04352i	−0.853094	−	0.521758i	$-0.825276\pi$
$181$		−	14.0391i		−	1.04352i	0.853094	−	0.521758i	$-0.174724\pi$
$182$	0.0219295	+	9.53937i	0.00162553	+	0.707105i
$183$	1.08285	+	0.629080i	0.0800466	+	0.0465030i
$184$	−0.493409	−	0.854610i	−0.0363746	−	0.0630027i
$185$	0.130266	+	0.225628i	0.00957738	+	0.0165885i
$186$	−8.14316	−	14.1925i	−0.597085	−	1.04065i
$187$		−	5.87352i		−	0.429514i
$188$	−1.24083	+	2.14918i	−0.0904967	+	0.156745i
$189$	13.7443	−	0.304922i	0.999754	−	0.0221798i
$190$	2.95368			0.214283
$191$	10.4404	+	6.02776i	0.755440	+	0.436153i	0.827656	−	0.561236i	$-0.189674\pi$
$191$	10.4404	+	6.02776i	0.755440	+	0.436153i	−0.0722162	+	0.997389i	$0.523007\pi$
$192$	1.73204	+	0.00466741i	0.125000	+	0.000336841i
$193$	−7.49194	−	12.9764i	−0.539282	−	0.934063i	−0.998943	−	0.0459691i	$-0.985362\pi$
$193$	−7.49194	−	12.9764i	−0.539282	−	0.934063i	0.459661	−	0.888094i	$-0.347971\pi$
$194$	−6.65816			−0.478028
$195$	3.00868	−	4.86069i	0.215456	−	0.348081i
$196$	3.12686	−	6.26281i	0.223347	−	0.447343i
$197$	−1.79067	+	1.03384i	−0.127580	+	0.0736583i	−0.562432	−	0.826844i	$-0.690134\pi$
$197$	−1.79067	+	1.03384i	−0.127580	+	0.0736583i	0.434852	+	0.900502i	$0.356801\pi$
$198$	−2.06326	+	3.52960i	−0.146630	+	0.250838i
$199$	−2.38680	−	1.37802i	−0.169196	−	0.0976853i	0.413011	−	0.910726i	$-0.364477\pi$
$199$	−2.38680	−	1.37802i	−0.169196	−	0.0976853i	−0.582207	+	0.813041i	$0.697811\pi$
$200$		−	4.16209i		−	0.294304i
$201$	−3.86448	−	6.73533i	−0.272580	−	0.475074i
$202$	−10.8034	−	6.23732i	−0.760121	−	0.438856i
$203$	−19.5376	+	12.0827i	−1.37127	+	0.848043i
$204$	3.71503	+	6.47485i	0.260104	+	0.453330i
$205$	−1.06091	−	1.83755i	−0.0740972	−	0.128340i
$206$	−7.38152	−	12.7852i	−0.514295	−	0.890784i
$207$	−2.57177	+	1.46639i	−0.178750	+	0.101921i
$208$	3.60414	+	0.100823i	0.249902	+	0.00699084i
$209$	−4.39743			−0.304177
$210$	−3.57358	+	2.19674i	−0.246600	+	0.151589i
$211$	8.77344	+	15.1960i	0.603988	+	1.04614i	0.992210	+	0.124573i	$0.0397560\pi$
$211$	8.77344	+	15.1960i	0.603988	+	1.04614i	−0.388222	+	0.921566i	$0.626911\pi$
$212$	−11.5911	−	6.69212i	−0.796080	−	0.459617i
$213$	17.5606	+	10.2018i	1.20323	+	0.699015i
$214$	4.98891	−	8.64105i	0.341035	−	0.590690i
$215$	3.55403	−	6.15575i	0.242383	−	0.419819i
$216$	0.0420063	−	5.19598i	0.00285817	−	0.353542i
$217$	0.756364	+	24.9831i	0.0513453	+	1.69596i
$218$	13.5916	−	7.84711i	0.920539	−	0.531474i
$219$	−0.0219046	+	8.12863i	−0.00148017	+	0.549282i
$220$		−	1.24748i		−	0.0841049i
$221$	7.39038	+	13.6696i	0.497131	+	0.919516i
$222$	0.426263	+	0.247637i	0.0286089	+	0.0166203i
$223$	−23.7939	+	13.7374i	−1.59335	+	0.919923i	−0.600628	+	0.799529i	$0.705083\pi$
$223$	−23.7939	+	13.7374i	−1.59335	+	0.919923i	−0.992726	+	0.120395i	$0.961584\pi$
$224$	−2.33027	−	1.25293i	−0.155698	−	0.0837151i
$225$	−12.4861	−	0.0672940i	−0.832406	−	0.00448627i
$226$	4.41436			0.293639
$227$	−6.73547	+	11.6662i	−0.447049	+	0.774312i	−0.998192	−	0.0600989i	$-0.980858\pi$
$227$	−6.73547	+	11.6662i	−0.447049	+	0.774312i	0.551143	+	0.834411i	$0.314192\pi$
$228$	4.84764	−	2.78139i	0.321043	−	0.184202i
$229$			9.18057i			0.606669i	0.952884	+	0.303334i	$0.0980999\pi$
$229$			9.18057i			0.606669i	−0.952884	+	0.303334i	$0.901900\pi$
$230$	0.451654	−	0.782287i	0.0297812	−	0.0515825i
$231$	5.32033	−	3.27049i	0.350052	−	0.215183i
$232$	4.34129	+	7.51934i	0.285020	+	0.493669i
$233$			8.17061i			0.535275i	0.963520	+	0.267637i	$0.0862429\pi$
$233$			8.17061i			0.535275i	−0.963520	+	0.267637i	$0.913757\pi$
$234$	0.360738	−	10.8106i	0.0235822	−	0.706713i
$235$	−2.27164			−0.148186
$236$	−3.96711	−	6.87124i	−0.258237	−	0.447280i
$237$	5.04768	+	0.0136022i	0.327882	+	0.000883556i
$238$	−0.345064	−	11.3976i	−0.0223672	−	0.738799i
$239$			4.24199i			0.274391i	0.990544	+	0.137196i	$0.0438089\pi$
$239$			4.24199i			0.274391i	−0.990544	+	0.137196i	$0.956191\pi$
$240$	0.789034	+	1.37519i	0.0509319	+	0.0887683i
$241$	13.7546	+	7.94124i	0.886013	+	0.511540i	0.872636	−	0.488370i	$-0.162409\pi$
$241$	13.7546	+	7.94124i	0.886013	+	0.511540i	0.0133770	+	0.999911i	$0.495742\pi$
$242$		−	9.14276i		−	0.587719i
$243$	−15.5870	−	0.210027i	−0.999909	−	0.0134733i
$244$	−0.626160	+	0.361514i	−0.0400858	+	0.0231435i
$245$	6.39588	−	0.387627i	0.408618	−	0.0247646i
$246$	−3.47155	−	2.01679i	−0.221338	−	0.128586i
$247$	10.2342	−	5.53309i	0.651190	−	0.352062i
$248$	9.44703			0.599887
$249$	4.92514	+	0.0132720i	0.312118	+	0.000841077i
$250$	7.26313	−	4.19337i	0.459361	−	0.265212i
$251$	7.83280	−	13.5668i	0.494402	−	0.856329i	−0.505578	−	0.862781i	$-0.668721\pi$
$251$	7.83280	−	13.5668i	0.494402	−	0.856329i	0.999979	+	0.00645237i	$0.00205387\pi$
$252$	−3.79642	+	6.97045i	−0.239152	+	0.439097i
$253$	−0.672421	+	1.16467i	−0.0422747	+	0.0732220i
$254$	15.3526	+	8.86383i	0.963308	+	0.556166i
$255$	−3.43253	+	5.90849i	−0.214953	+	0.370004i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.32533	−	12.6878i	−0.456941	−	0.791446i	0.541856	−	0.840471i	$-0.317722\pi$
$257$	−7.32533	−	12.6878i	−0.456941	−	0.791446i	−0.998798	+	0.0490255i	$0.984388\pi$
$258$	0.0362433	−	13.4497i	0.00225641	−	0.837339i
$259$	−0.396078	−	0.640452i	−0.0246111	−	0.0397957i
$260$	1.56964	+	2.90328i	0.0973451	+	0.180054i
$261$	22.6279	−	12.9021i	1.40063	−	0.798621i
$262$	−5.95078	+	3.43568i	−0.367640	+	0.212257i
$263$	24.4433	−	14.1123i	1.50724	−	0.870203i	0.507272	−	0.861786i	$-0.330654\pi$
$263$	24.4433	−	14.1123i	1.50724	−	0.870203i	0.999965	−	0.00841706i	$-0.00267926\pi$
$264$	−1.17471	−	2.04738i	−0.0722985	−	0.126008i
$265$		−	12.2516i		−	0.752609i
$266$	−8.53327	+	0.258345i	−0.523208	+	0.0158402i
$267$	−3.67913	−	6.41228i	−0.225159	−	0.392425i
$268$	4.48326			0.273859
$269$	15.7419	−	27.2657i	0.959799	−	1.66242i	0.236816	−	0.971554i	$-0.423896\pi$
$269$	15.7419	−	27.2657i	0.959799	−	1.66242i	0.722983	−	0.690866i	$-0.242771\pi$
$270$	4.13827	−	2.34483i	0.251847	−	0.142702i
$271$	−5.95739	+	3.43950i	−0.361886	+	0.208935i	−0.669908	−	0.742444i	$-0.733666\pi$
$271$	−5.95739	+	3.43950i	−0.361886	+	0.208935i	0.308022	+	0.951379i	$0.400333\pi$
$272$	−4.30988			−0.261325
$273$	−8.26702	+	14.3058i	−0.500343	+	0.865827i
$274$	−11.5945			−0.700447
$275$	−4.91220	+	2.83606i	−0.296217	+	0.171021i
$276$	0.00460589	−	1.70921i	0.000277242	−	0.102883i
$277$	−4.86529	+	8.42693i	−0.292327	+	0.506325i	−0.974359	−	0.224997i	$-0.927763\pi$
$277$	−4.86529	+	8.42693i	−0.292327	+	0.506325i	0.682033	+	0.731322i	$0.261096\pi$
$278$	−4.04198			−0.242422
$279$	0.152743	−	28.3407i	0.00914447	−	1.69671i
$280$	−0.0732882	−	2.42074i	−0.00437981	−	0.144667i
$281$			28.8380i			1.72033i	0.510013	+	0.860167i	$0.329641\pi$
$281$			28.8380i			1.72033i	−0.510013	+	0.860167i	$0.670359\pi$
$282$	−3.72826	+	2.13914i	−0.222015	+	0.127384i
$283$	17.4739	−	10.0886i	1.03872	−	0.599703i	0.119247	−	0.992865i	$-0.461952\pi$
$283$	17.4739	−	10.0886i	1.03872	−	0.599703i	0.919469	+	0.393162i	$0.128619\pi$
$284$	−10.1544	+	5.86266i	−0.602554	+	0.347885i
$285$	4.42361	+	2.56989i	0.262032	+	0.152227i
$286$	−2.33688	−	4.32240i	−0.138182	−	0.255589i
$287$	3.22572	+	5.21594i	0.190408	+	0.307887i
$288$	2.58995	+	1.51398i	0.152615	+	0.0892122i
$289$	−0.787512	−	1.36401i	−0.0463242	−	0.0802359i
$290$	−3.97391	+	6.88301i	−0.233356	+	0.404184i
$291$	−9.97166	−	5.79303i	−0.584549	−	0.339593i
$292$	−4.06433	−	2.34654i	−0.237847	−	0.137321i
$293$	1.91542	−	3.31760i	0.111900	−	0.193816i	−0.804636	−	0.593768i	$-0.797640\pi$
$293$	1.91542	−	3.31760i	0.111900	−	0.193816i	0.916536	+	0.399952i	$0.130973\pi$
$294$	10.1320	−	6.65899i	0.590911	−	0.388360i
$295$	3.63139	−	6.28976i	0.211428	−	0.366204i
$296$	−0.246487	+	0.142310i	−0.0143268	+	0.00827157i
$297$	−6.16105	+	3.49098i	−0.357500	+	0.202567i
$298$	15.0220			0.870198
$299$	0.0994942	−	3.55663i	0.00575390	−	0.205685i
$300$	3.62129	−	6.23340i	0.209075	−	0.359886i
$301$	−9.72926	+	18.0950i	−0.560785	+	1.04298i
$302$	2.85620	−	1.64903i	0.164356	−	0.0948910i
$303$	−10.7529	−	18.7410i	−0.617737	−	1.07664i
$304$			3.22675i			0.185067i
$305$	−0.573171	−	0.330920i	−0.0328197	−	0.0189484i
$306$	−0.0696835	+	12.9294i	−0.00398354	+	0.739127i
$307$			2.01412i			0.114952i	0.998347	+	0.0574759i	$0.0183052\pi$
$307$			2.01412i			0.114952i	−0.998347	+	0.0574759i	$0.981695\pi$
$308$	0.109111	+	3.60399i	0.00621719	+	0.205357i
$309$	0.0689051	−	25.5702i	0.00391988	−	1.45464i
$310$	4.32378	+	7.48901i	0.245574	+	0.425347i
$311$	−15.7934			−0.895559			−0.447780	−	0.894144i	$-0.647785\pi$
$311$	−15.7934			−0.895559			−0.447780	+	0.894144i	$0.647785\pi$
$312$	5.31006	+	3.28683i	0.300623	+	0.186080i
$313$		−	4.05670i		−	0.229299i	−0.993406	−	0.114649i	$-0.963426\pi$
$313$		−	4.05670i		−	0.229299i	0.993406	−	0.114649i	$-0.0365744\pi$
$314$	−2.14845	−	3.72123i	−0.121244	−	0.210001i
$315$	−7.26331	+	0.180722i	−0.409241	+	0.0101825i
$316$	−1.45714	+	2.52385i	−0.0819707	+	0.141977i
$317$		−	10.0133i		−	0.562404i	−0.959649	−	0.281202i	$-0.909267\pi$
$317$		−	10.0133i		−	0.562404i	0.959649	−	0.281202i	$-0.0907330\pi$
$318$	−11.5370	−	20.1075i	−0.646960	−	1.12757i
$319$	5.91634	−	10.2474i	0.331251	−	0.573744i
$320$	−0.915374			−0.0511710
$321$	14.9900	−	8.60068i	0.836658	−	0.480043i
$322$	−1.23642	+	2.29955i	−0.0689028	+	0.128149i
$323$	−12.0437	+	6.95344i	−0.670130	+	0.386900i
$324$	4.58375	−	7.74527i	0.254653	−	0.430293i
$325$	7.86380	−	12.7812i	0.436205	−	0.708975i
$326$			11.7459i			0.650546i
$327$	27.1831	+	0.0732514i	1.50323	+	0.00405081i
$328$	2.00743	−	1.15899i	0.110842	−	0.0639946i
$329$	6.56284	−	0.198690i	0.361821	−	0.0109542i
$330$	1.08539	−	1.86830i	0.0597485	−	0.102846i
$331$	−5.32803	+	9.22842i	−0.292855	+	0.507240i	−0.974484	−	0.224459i	$-0.927939\pi$
$331$	−5.32803	+	9.22842i	−0.292855	+	0.507240i	0.681629	+	0.731698i	$0.261272\pi$
$332$	−1.42177	+	2.46258i	−0.0780298	+	0.135152i
$333$	0.422937	+	0.741752i	0.0231768	+	0.0406478i
$334$	−17.9202	−	10.3463i	−0.980552	−	0.566122i
$335$	2.05193	+	3.55405i	0.112109	+	0.194178i
$336$	−2.39982	−	3.90395i	−0.130921	−	0.212978i
$337$	−4.72510			−0.257392			−0.128696	−	0.991684i	$-0.541079\pi$
$337$	−4.72510			−0.257392			−0.128696	+	0.991684i	$0.541079\pi$
$338$	10.8773	+	7.11923i	0.591649	+	0.387235i
$339$	6.61122	+	3.84078i	0.359072	+	0.208602i
$340$	−1.97257	−	3.41660i	−0.106978	−	0.185291i
$341$	−6.43724	−	11.1496i	−0.348596	−	0.603786i
$342$	9.68011	+	0.0521711i	0.523440	+	0.00282109i
$343$	−18.4440	+	1.67928i	−0.995881	+	0.0906728i
$344$	6.72485	+	3.88259i	0.362580	+	0.209335i
$345$	1.35706	−	0.778633i	0.0730619	−	0.0419202i
$346$			16.0081i			0.860601i
$347$	−19.3558	−	11.1751i	−1.03907	−	0.599908i	−0.119502	−	0.992834i	$-0.538130\pi$
$347$	−19.3558	−	11.1751i	−1.03907	−	0.599908i	−0.919570	+	0.392926i	$0.871463\pi$
$348$	−0.0405252	+	15.0386i	−0.00217238	+	0.806155i
$349$	−8.28832	+	4.78526i	−0.443663	+	0.256149i	−0.705150	−	0.709058i	$-0.749121\pi$
$349$	−8.28832	+	4.78526i	−0.443663	+	0.256149i	0.261487	+	0.965207i	$0.415787\pi$
$350$	−9.36556	+	5.79199i	−0.500610	+	0.309595i
$351$	9.94621	−	15.8768i	0.530890	−	0.847441i
$352$	1.36281			0.0726378
$353$	−13.1453	−	22.7684i	−0.699655	−	1.21184i	−0.968586	−	0.248678i	$-0.920004\pi$
$353$	−13.1453	−	22.7684i	−0.699655	−	1.21184i	0.268932	−	0.963159i	$-0.413329\pi$
$354$	0.0370323	−	13.7424i	0.00196824	−	0.730402i
$355$	−9.29510	−	5.36653i	−0.493333	−	0.284826i
$356$	4.26823			0.226216
$357$	9.39989	−	17.3700i	0.497495	−	0.919319i
$358$	−13.2303	+	22.9156i	−0.699243	+	1.21113i
$359$			25.7142i			1.35714i	0.734535	+	0.678571i	$0.237400\pi$
$359$			25.7142i			1.35714i	−0.734535	+	0.678571i	$0.762600\pi$
$360$	−0.0148001	+	2.74608i	−0.000780032	+	0.144731i
$361$	−4.29404	−	7.43750i	−0.226002	−	0.391448i
$362$	7.01953	+	12.1582i	0.368938	+	0.639020i
$363$	7.95479	−	13.6928i	0.417518	−	0.718683i
$364$	−4.78867	−	8.25037i	−0.250995	−	0.432437i
$365$		−	4.29593i		−	0.224859i
$366$	−1.25232	−	0.00337467i	−0.0654596	−	0.000176397i
$367$	−20.6101	+	11.8992i	−1.07584	+	0.621134i	−0.929770	−	0.368140i	$-0.879995\pi$
$367$	−20.6101	+	11.8992i	−1.07584	+	0.621134i	−0.146066	+	0.989275i	$0.546661\pi$
$368$	0.854610	+	0.493409i	0.0445496	+	0.0257207i
$369$	−3.44447	−	6.04095i	−0.179312	−	0.314479i
$370$	−0.225628	−	0.130266i	−0.0117298	−	0.00677223i
$371$	1.07159	+	35.3952i	0.0556342	+	1.83763i
$372$	14.1485	+	8.21953i	0.733563	+	0.426163i
$373$	1.65972	−	2.87471i	0.0859368	−	0.148847i	−0.819853	−	0.572574i	$-0.805945\pi$
$373$	1.65972	−	2.87471i	0.0859368	−	0.148847i	0.905790	+	0.423727i	$0.139278\pi$
$374$	2.93676	+	5.08662i	0.151856	+	0.263023i
$375$	14.5262	+	0.0391444i	0.750130	+	0.00202141i
$376$		−	2.48166i		−	0.127982i
$377$	−0.875407	+	31.2933i	−0.0450857	+	1.61169i
$378$	−11.7505	+	7.13624i	−0.604380	+	0.367049i
$379$	−18.1029	−	31.3551i	−0.929882	−	1.61060i	−0.783515	−	0.621373i	$-0.786575\pi$
$379$	−18.1029	−	31.3551i	−0.929882	−	1.61060i	−0.146367	−	0.989230i	$-0.546758\pi$
$380$	−2.55796	+	1.47684i	−0.131221	+	0.0757604i
$381$	15.2809	+	26.6328i	0.782864	+	1.36444i
$382$	−12.0555			−0.616814
$383$	12.0936	−	20.9467i	0.617954	−	1.07033i	−0.371904	−	0.928271i	$-0.621295\pi$
$383$	12.0936	−	20.9467i	0.617954	−	1.07033i	0.989858	−	0.142057i	$-0.0453717\pi$
$384$	−1.50233	+	0.861980i	−0.0766654	+	0.0439877i
$385$	−2.80708	+	1.73600i	−0.143062	+	0.0884746i
$386$	12.9764	+	7.49194i	0.660483	+	0.381330i
$387$	11.7563	−	20.1115i	0.597609	−	1.02232i
$388$	5.76613	−	3.32908i	0.292731	−	0.169008i
$389$			14.1010i			0.714948i	0.933923	+	0.357474i	$0.116362\pi$
$389$			14.1010i			0.714948i	−0.933923	+	0.357474i	$0.883638\pi$
$390$	−0.175251	+	5.71382i	−0.00887416	+	0.289331i
$391$			4.25306i			0.215087i
$392$	0.423463	+	6.98718i	0.0213881	+	0.352906i
$393$	−11.9015	−	0.0320715i	−0.600352	−	0.00161779i
$394$	1.03384	−	1.79067i	0.0520843	−	0.0902127i
$395$	−2.66766			−0.134225
$396$	0.0220343	−	4.08836i	0.00110726	−	0.205448i
$397$	26.1497	+	15.0975i	1.31241	+	0.757723i	0.982496	−	0.186286i	$-0.0596451\pi$
$397$	26.1497	+	15.0975i	1.31241	+	0.757723i	0.329919	+	0.944009i	$0.392978\pi$
$398$	2.75604			0.138148
$399$	−13.0047	−	7.03758i	−0.651050	−	0.352320i
$400$	2.08105	+	3.60448i	0.104052	+	0.180224i
$401$	−4.17185	+	2.40862i	−0.208332	+	0.120281i	−0.600536	−	0.799598i	$-0.705046\pi$
$401$	−4.17185	+	2.40862i	−0.208332	+	0.120281i	0.392204	+	0.919878i	$0.371713\pi$
$402$	6.71441	+	3.90073i	0.334884	+	0.194551i
$403$	29.0106	+	17.8491i	1.44512	+	0.889127i
$404$	12.4746			0.620636
$405$	8.23789	+	0.0887991i	0.409344	+	0.00441246i
$406$	10.8787	−	20.2328i	0.539901	−	1.00414i
$407$	0.335914	+	0.193940i	0.0166507	+	0.00961326i
$408$	−6.45473	−	3.74987i	−0.319557	−	0.185646i
$409$	−3.57104	−	2.06174i	−0.176577	−	0.101946i	0.409107	−	0.912487i	$-0.365840\pi$
$409$	−3.57104	−	2.06174i	−0.176577	−	0.101946i	−0.585683	+	0.810540i	$0.699174\pi$
$410$	1.83755	+	1.06091i	0.0907501	+	0.0523946i
$411$	−17.3646	−	10.0879i	−0.856531	−	0.497601i
$412$	12.7852	+	7.38152i	0.629880	+	0.363661i
$413$	−9.94105	+	18.4889i	−0.489167	+	0.909779i
$414$	1.49402	−	2.55581i	0.0734272	−	0.125611i
$415$	−2.60290			−0.127772
$416$	−3.17169	+	1.71476i	−0.155505	+	0.0840728i
$417$	−6.05351	−	3.51678i	−0.296442	−	0.172218i
$418$	3.80829	−	2.19872i	0.186269	−	0.107543i
$419$	1.27199	+	2.20315i	0.0621408	+	0.107631i	0.895422	−	0.445218i	$-0.146874\pi$
$419$	1.27199	+	2.20315i	0.0621408	+	0.107631i	−0.833281	+	0.552849i	$0.813541\pi$
$420$	1.99644	−	3.68922i	0.0974163	−	0.180015i
$421$	−6.51258			−0.317404			−0.158702	−	0.987327i	$-0.550731\pi$
$421$	−6.51258			−0.317404			−0.158702	+	0.987327i	$0.550731\pi$
$422$	−15.1960	−	8.77344i	−0.739732	−	0.427084i
$423$	−7.44486	−	0.0401242i	−0.361982	−	0.00195091i
$424$	13.3842			0.649996
$425$	−8.96905	+	15.5348i	−0.435063	+	0.753551i
$426$	−20.3088	−	0.0547269i	−0.983964	−	0.00265153i
$427$	1.68485	+	0.905905i	0.0815356	+	0.0438398i
$428$			9.97782i			0.482296i
$429$	0.260912	−	8.50672i	0.0125970	−	0.410708i
$430$			7.10805i			0.342781i
$431$	−9.07179	+	5.23760i	−0.436973	+	0.252286i	−0.702313	−	0.711869i	$-0.747849\pi$
$431$	−9.07179	+	5.23760i	−0.436973	+	0.252286i	0.265340	+	0.964155i	$0.414516\pi$
$432$	2.56161	+	4.52086i	0.123246	+	0.217510i
$433$	−24.4831	−	14.1353i	−1.17658	−	0.679301i	−0.221362	−	0.975192i	$-0.571050\pi$
$433$	−24.4831	−	14.1353i	−1.17658	−	0.679301i	−0.955222	+	0.295891i	$0.904384\pi$
$434$	−13.1466	−	21.2578i	−0.631055	−	1.02041i
$435$	−11.9402	+	6.85086i	−0.572490	+	0.328473i
$436$	−7.84711	+	13.5916i	−0.375809	+	0.650920i
$437$	3.18422			0.152322
$438$	−4.04534	−	7.05055i	−0.193294	−	0.336888i
$439$	−16.4096	+	9.47410i	−0.783188	+	0.452174i	−0.837559	−	0.546347i	$-0.816018\pi$
$439$	−16.4096	+	9.47410i	−0.783188	+	0.452174i	0.0543708	+	0.998521i	$0.482685\pi$
$440$	0.623738	+	1.08035i	0.0297356	+	0.0515035i
$441$	20.9681	−	1.15740i	0.998480	−	0.0551142i
$442$	−13.2351	−	8.14302i	−0.629527	−	0.387324i
$443$		−	15.0200i		−	0.713624i	−0.934176	−	0.356812i	$-0.883864\pi$
$443$		−	15.0200i		−	0.713624i	0.934176	−	0.356812i	$-0.116136\pi$
$444$	−0.492973	−	0.00132843i	−0.0233955	−	6.30447e-5i
$445$	1.95351	+	3.38358i	0.0926054	+	0.160397i
$446$	13.7374	−	23.7939i	0.650484	−	1.12667i
$447$	22.4978	+	13.0701i	1.06411	+	0.618193i
$448$	2.64454	−	0.0800636i	0.124943	−	0.00378265i
$449$	5.83706	+	3.37003i	0.275468	+	0.159041i	0.631370	−	0.775482i	$-0.282493\pi$
$449$	5.83706	+	3.37003i	0.275468	+	0.159041i	−0.355902	+	0.934523i	$0.615826\pi$
$450$	10.8469	−	6.18477i	0.511329	−	0.291553i
$451$	−2.73574	−	1.57948i	−0.128821	−	0.0743748i
$452$	−3.82295	+	2.20718i	−0.179816	+	0.103817i
$453$	5.71238	+	0.0153934i	0.268391	+	0.000723245i
$454$		−	13.4709i		−	0.632223i
$455$	4.34866	−	7.57225i	0.203868	−	0.354992i
$456$	−2.80748	+	4.83258i	−0.131472	+	0.226306i
$457$	7.04998	+	12.2109i	0.329784	+	0.571203i	0.982469	−	0.186426i	$-0.0596906\pi$
$457$	7.04998	+	12.2109i	0.329784	+	0.571203i	−0.652685	+	0.757630i	$0.726357\pi$
$458$	−4.59028	−	7.95060i	−0.214490	−	0.371507i
$459$	−11.3538	+	19.3033i	−0.529950	+	0.901000i
$460$			0.903308i			0.0421169i
$461$	−16.6186	+	28.7843i	−0.774007	+	1.34062i	0.161344	+	0.986898i	$0.448417\pi$
$461$	−16.6186	+	28.7843i	−0.774007	+	1.34062i	−0.935351	+	0.353721i	$0.884916\pi$
$462$	−2.97229	+	5.49249i	−0.138284	+	0.255534i
$463$	23.4863			1.09150			0.545750	−	0.837948i	$-0.316245\pi$
$463$	23.4863			1.09150			0.545750	+	0.837948i	$0.316245\pi$
$464$	−7.51934	−	4.34129i	−0.349077	−	0.201539i
$465$	−0.0403618	+	14.9780i	−0.00187173	+	0.694587i
$466$	−4.08531	−	7.07596i	−0.189248	−	0.327787i
$467$	5.45764			0.252550			0.126275	−	0.991995i	$-0.459698\pi$
$467$	5.45764			0.252550			0.126275	+	0.991995i	$0.459698\pi$
$468$	5.09291	+	9.54266i	0.235420	+	0.441109i
$469$	−6.23894	−	10.0883i	−0.288088	−	0.465833i
$470$	1.96730	−	1.13582i	0.0907449	−	0.0523916i
$471$	0.0200554	−	7.44242i	0.000924104	−	0.342929i
$472$	6.87124	+	3.96711i	0.316275	+	0.182601i
$473$		−	10.5824i		−	0.486581i
$474$	−4.37822	+	2.51206i	−0.201098	+	0.115383i
$475$	11.6307	+	6.71501i	0.533655	+	0.308106i
$476$	5.99765	+	9.69811i	0.274902	+	0.444512i
$477$	0.216401	−	40.1521i	0.00990831	−	1.83844i
$478$	−2.12099	−	3.67367i	−0.0970120	−	0.168030i
$479$	9.44233	+	16.3546i	0.431431	+	0.747260i	0.996997	−	0.0774427i	$-0.0246755\pi$
$479$	9.44233	+	16.3546i	0.431431	+	0.747260i	−0.565566	+	0.824703i	$0.691342\pi$
$480$	−1.37092	−	0.796434i	−0.0625736	−	0.0363521i
$481$	−1.02581	−	0.0286962i	−0.0467728	−	0.00130844i
$482$	−15.8825			−0.723427
$483$	−3.85249	+	2.36819i	−0.175294	+	0.107756i
$484$	4.57138	+	7.91786i	0.207790	+	0.359903i
$485$	5.27817	+	3.04735i	0.239669	+	0.138373i
$486$	13.6038	−	7.61163i	0.617080	−	0.345271i
$487$	−11.7815	+	20.4062i	−0.533873	+	0.924695i	0.465344	+	0.885130i	$0.345931\pi$
$487$	−11.7815	+	20.4062i	−0.533873	+	0.924695i	−0.999217	+	0.0395649i	$0.987403\pi$
$488$	0.361514	−	0.626160i	0.0163650	−	0.0283449i
$489$	−10.2197	+	17.5914i	−0.462151	+	0.795510i
$490$	−5.34518	+	3.53364i	−0.241471	+	0.159633i
$491$	10.7815	−	6.22472i	0.486564	−	0.280918i	−0.236584	−	0.971611i	$-0.576028\pi$
$491$	10.7815	−	6.22472i	0.486564	−	0.280918i	0.723148	+	0.690693i	$0.242695\pi$
$492$	4.01485	+	0.0108190i	0.181003	+	0.000487757i
$493$		−	37.4209i		−	1.68535i
$494$	−6.09658	+	9.90892i	−0.274298	+	0.445823i
$495$	3.25108	−	1.85372i	0.146125	−	0.0833185i
$496$	−8.18137	+	4.72352i	−0.367354	+	0.212092i
$497$	27.3232	+	14.6910i	1.22561	+	0.658983i
$498$	−4.27193	+	2.45108i	−0.191430	+	0.109835i
$499$	24.4985			1.09670			0.548351	−	0.836248i	$-0.315256\pi$
$499$	24.4985			1.09670			0.548351	+	0.836248i	$0.315256\pi$
$500$	−4.19337	+	7.26313i	−0.187533	+	0.324817i
$501$	−17.8365	−	31.0869i	−0.796878	−	1.38886i
$502$			15.6656i			0.699190i
$503$	−7.67158	+	13.2876i	−0.342059	+	0.592464i	−0.984815	−	0.173607i	$-0.944458\pi$
$503$	−7.67158	+	13.2876i	−0.342059	+	0.592464i	0.642756	+	0.766071i	$0.277791\pi$
$504$	−0.197430	−	7.93480i	−0.00879421	−	0.353444i
$505$	5.70948	+	9.88911i	0.254068	+	0.440060i
$506$		−	1.34484i		−	0.0597855i
$507$	10.0964	+	20.1262i	0.448396	+	0.893835i
$508$	−17.7277			−0.786538
$509$	−15.1511	−	26.2425i	−0.671562	−	1.16318i	−0.977461	−	0.211116i	$-0.932290\pi$
$509$	−15.1511	−	26.2425i	−0.671562	−	1.16318i	0.305899	−	0.952064i	$-0.401043\pi$
$510$	0.0184136	−	6.83317i	0.000815369	−	0.302578i
$511$	0.375745	+	12.4110i	0.0166220	+	0.549032i
$512$		−	1.00000i		−	0.0441942i
$513$	14.4521	+	8.50045i	0.638077	+	0.375304i
$514$	12.6878	+	7.32533i	0.559637	+	0.323106i
$515$			13.5137i			0.595485i
$516$	6.69344	+	11.6659i	0.294662	+	0.513561i
$517$	−2.92891	+	1.69101i	−0.128813	+	0.0743705i
$518$	0.663239	+	0.356609i	0.0291411	+	0.0156685i
$519$	−13.9281	+	23.9747i	−0.611375	+	1.05237i
$520$	−2.81099	−	1.72949i	−0.123270	−	0.0758434i
$521$	−29.3421			−1.28550			−0.642749	−	0.766077i	$-0.722206\pi$
$521$	−29.3421			−1.28550			−0.642749	+	0.766077i	$0.722206\pi$
$522$	−13.1453	+	22.4875i	−0.575353	+	0.984251i
$523$	16.2568	−	9.38587i	0.710860	−	0.410415i	−0.100519	−	0.994935i	$-0.532050\pi$
$523$	16.2568	−	9.38587i	0.710860	−	0.410415i	0.811379	+	0.584520i	$0.198717\pi$
$524$	3.43568	−	5.95078i	0.150089	−	0.259961i
$525$	−19.0658	+	0.525799i	−0.832102	+	0.0229478i
$526$	−14.1123	+	24.4433i	−0.615327	+	1.06578i
$527$	−35.2607	−	20.3578i	−1.53598	−	0.886798i
$528$	2.04102	+	1.18573i	0.0888240	+	0.0516022i
$529$	−11.0131	+	19.0752i	−0.478830	+	0.829358i
$530$	6.12579	+	10.6102i	0.266087	+	0.460877i
$531$	12.0123	−	20.5493i	0.521288	−	0.891763i
$532$	7.26085	−	4.49037i	0.314798	−	0.194682i
$533$	8.35433	+	0.233706i	0.361866	+	0.0101230i
$534$	6.39236	+	3.71363i	0.276624	+	0.160705i
$535$	−7.90979	+	4.56672i	−0.341970	+	0.197436i
$536$	−3.88262	+	2.24163i	−0.167704	+	0.0968238i
$537$	−39.7525	+	22.8085i	−1.71545	+	0.984260i
$538$			31.4837i			1.35736i
$539$	7.95789	−	5.26087i	0.342771	−	0.226602i
$540$	−2.41143	+	4.09982i	−0.103772	+	0.176428i
$541$	5.29317			0.227571			0.113786	−	0.993505i	$-0.463702\pi$
$541$	5.29317			0.227571			0.113786	+	0.993505i	$0.463702\pi$
$542$	3.43950	−	5.95739i	0.147739	−	0.255892i
$543$	−0.0655261	+	24.3163i	−0.00281199	+	1.04351i
$544$	3.73246	−	2.15494i	0.160028	−	0.0923922i
$545$	−14.3661			−0.615376
$546$	0.00654121	−	16.5227i	0.000279938	−	0.707107i
$547$	27.6938			1.18410			0.592051	−	0.805901i	$-0.298319\pi$
$547$	27.6938			1.18410			0.592051	+	0.805901i	$0.298319\pi$
$548$	10.0411	−	5.79723i	0.428934	−	0.247645i
$549$	−1.87261	−	1.09465i	−0.0799209	−	0.0467185i
$550$	2.83606	−	4.91220i	0.120930	−	0.209457i
$551$	−28.0165			−1.19354
$552$	0.850618	+	1.48252i	0.0362047	+	0.0631004i
$553$	7.70695	−	0.233328i	0.327733	−	0.00992213i
$554$		−	9.73057i		−	0.413413i
$555$	−0.224574	−	0.391406i	−0.00953264	−	0.0166143i
$556$	3.50046	−	2.02099i	0.148452	−	0.0857091i
$557$	−20.6301	+	11.9108i	−0.874124	+	0.504675i	−0.868716	−	0.495310i	$-0.835055\pi$
$557$	−20.6301	+	11.9108i	−0.874124	+	0.504675i	−0.00540719	+	0.999985i	$0.501721\pi$
$558$	14.0381	+	24.6201i	0.594279	+	1.04225i
$559$	13.3154	+	24.6288i	0.563181	+	1.04169i
$560$	1.27384	+	2.05978i	0.0538296	+	0.0870416i
$561$	−0.0274141	+	10.1732i	−0.00115743	+	0.429513i
$562$	−14.4190	−	24.9745i	−0.608230	−	1.05349i
$563$	−0.150013	+	0.259830i	−0.00632229	+	0.0109505i	−0.869169	−	0.494515i	$-0.835346\pi$
$563$	−0.150013	+	0.259830i	−0.00632229	+	0.0109505i	0.862847	+	0.505465i	$0.168679\pi$
$564$	2.15920	−	3.71668i	0.0909188	−	0.156500i
$565$	−3.49943	−	2.02040i	−0.147222	−	0.0849987i
$566$	−10.0886	+	17.4739i	−0.424054	+	0.734483i
$567$	−23.8072	+	0.463988i	−0.999810	+	0.0194857i
$568$	5.86266	−	10.1544i	0.245992	−	0.426070i
$569$	16.3735	−	9.45324i	0.686412	−	0.396300i	−0.115854	−	0.993266i	$-0.536961\pi$
$569$	16.3735	−	9.45324i	0.686412	−	0.396300i	0.802267	+	0.596966i	$0.203627\pi$
$570$	−5.11591	−	0.0137861i	−0.214282	−	0.000577434i
$571$	44.5322			1.86361			0.931807	−	0.362955i	$-0.118232\pi$
$571$	44.5322			1.86361			0.931807	+	0.362955i	$0.118232\pi$
$572$	4.18499	+	2.57487i	0.174983	+	0.107661i
$573$	−18.0551	−	10.4891i	−0.754262	−	0.438188i
$574$	−5.40152	−	2.90428i	−0.225455	−	0.121222i
$575$	3.55696	−	2.05361i	0.148336	−	0.0856416i
$576$	−2.99996	−	0.0161683i	−0.124998	−	0.000673680i
$577$		−	12.1372i		−	0.505278i	−0.967561	−	0.252639i	$-0.918702\pi$
$577$		−	12.1372i		−	0.505278i	0.967561	−	0.252639i	$-0.0812985\pi$
$578$	1.36401	+	0.787512i	0.0567354	+	0.0327562i
$579$	12.9158	+	22.5107i	0.536763	+	0.935513i
$580$		−	7.94781i		−	0.330015i
$581$	7.51986	−	0.227664i	0.311976	−	0.00944510i
$582$	11.5322	+	0.0310764i	0.478026	+	0.00128816i
$583$	−9.12006	−	15.7964i	−0.377714	−	0.654220i
$584$	4.69308			0.194201
$585$	−5.23386	+	8.40489i	−0.216393	+	0.347499i
$586$			3.83084i			0.158250i
$587$	3.40595	+	5.89927i	0.140578	+	0.243489i	0.927715	−	0.373290i	$-0.121770\pi$
$587$	3.40595	+	5.89927i	0.140578	+	0.243489i	−0.787136	+	0.616779i	$0.788437\pi$
$588$	−5.44509	+	10.8329i	−0.224552	+	0.446740i
$589$	−15.2416	+	26.3992i	−0.628019	+	1.08776i
$590$			7.26278i			0.299004i
$591$	3.10635	−	1.78231i	0.127778	−	0.0733143i
$592$	0.142310	−	0.246487i	0.00584889	−	0.0101306i
$593$	8.27070			0.339637			0.169819	−	0.985475i	$-0.445682\pi$
$593$	8.27070			0.339637			0.169819	+	0.985475i	$0.445682\pi$
$594$	3.59013	−	6.10380i	0.147305	−	0.250442i
$595$	−4.94300	+	9.19326i	−0.202643	+	0.376887i
$596$	−13.0094	+	7.51098i	−0.532885	+	0.307662i
$597$	4.12762	+	2.39793i	0.168932	+	0.0981409i
$598$	1.69215	+	3.12988i	0.0691972	+	0.127990i
$599$			5.44458i			0.222459i	0.993795	+	0.111230i	$0.0354789\pi$
$599$			5.44458i			0.222459i	−0.993795	+	0.111230i	$0.964521\pi$
$600$	−0.0194262	+	7.20893i	−0.000793071	+	0.294303i
$601$	5.98996	−	3.45830i	0.244336	−	0.141067i	−0.372832	−	0.927899i	$-0.621613\pi$
$601$	5.98996	−	3.45830i	0.244336	−	0.141067i	0.617168	+	0.786832i	$0.288280\pi$
$602$	−0.621709	−	20.5354i	−0.0253390	−	0.836958i
$603$	6.66202	+	11.6839i	0.271299	+	0.475807i
$604$	−1.64903	+	2.85620i	−0.0670980	+	0.116217i
$605$	−4.18452	+	7.24781i	−0.170125	+	0.294665i
$606$	18.6828	+	10.8537i	0.758936	+	0.440903i
$607$	−1.24644	−	0.719635i	−0.0505916	−	0.0292091i	0.474491	−	0.880260i	$-0.342632\pi$
$607$	−1.24644	−	0.719635i	−0.0505916	−	0.0292091i	−0.525082	+	0.851051i	$0.675966\pi$
$608$	−1.61337	−	2.79445i	−0.0654310	−	0.113330i
$609$	33.8964	−	20.8367i	1.37355	−	0.844344i
$610$	0.661840			0.0267971
$611$	4.68881	−	7.62084i	0.189689	−	0.308306i
$612$	−6.40437	−	11.2321i	−0.258881	−	0.454029i
$613$	−2.01464	−	3.48946i	−0.0813707	−	0.140938i	0.822468	−	0.568811i	$-0.192596\pi$
$613$	−2.01464	−	3.48946i	−0.0813707	−	0.140938i	−0.903839	+	0.427873i	$0.859263\pi$
$614$	−1.00706	−	1.74428i	−0.0406416	−	0.0703933i
$615$	1.82897	+	3.18767i	0.0737511	+	0.128539i
$616$	−1.89649	−	3.06659i	−0.0764118	−	0.123557i
$617$	−37.4159	−	21.6021i	−1.50631	−	0.869667i	−0.999973	−	0.00733051i	$-0.997667\pi$
$617$	−37.4159	−	21.6021i	−1.50631	−	0.869667i	−0.506335	−	0.862337i	$-0.669000\pi$
$618$	12.7254	+	22.1789i	0.511892	+	0.892167i
$619$		−	46.1557i		−	1.85515i	−0.373633	−	0.927577i	$-0.621888\pi$
$619$		−	46.1557i		−	1.85515i	0.373633	−	0.927577i	$-0.378112\pi$
$620$	−7.48901	−	4.32378i	−0.300766	−	0.173647i
$621$	4.46126	−	2.52785i	0.179024	−	0.101439i
$622$	13.6774	−	7.89668i	0.548416	−	0.316628i
$623$	−5.93970	−	9.60440i	−0.237969	−	0.384792i
$624$	−6.24206	−	0.191452i	−0.249882	−	0.00766423i
$625$	13.1335			0.525338
$626$	2.02835	+	3.51321i	0.0810693	+	0.140416i
$627$	7.61655	+	0.0205246i	0.304176	+	0.000819675i
$628$	3.72123	+	2.14845i	0.148493	+	0.0857325i
$629$	1.22667			0.0489106
$630$	6.19985	−	3.78816i	0.247008	−	0.150924i
$631$	−7.10333	+	12.3033i	−0.282779	+	0.489787i	−0.972068	−	0.234699i	$-0.924590\pi$
$631$	−7.10333	+	12.3033i	−0.282779	+	0.489787i	0.689289	+	0.724486i	$0.257923\pi$
$632$		−	2.91429i		−	0.115924i
$633$	−15.1251	−	26.3612i	−0.601167	−	1.04776i
$634$	5.00666	+	8.67178i	0.198840	+	0.344400i
$635$	−8.11372	−	14.0534i	−0.321983	−	0.557691i
$636$	20.0451	+	11.6452i	0.794838	+	0.461760i
$637$	−11.9011	+	22.2568i	−0.471538	+	0.881846i
$638$			11.8327i			0.468460i
$639$	−30.3680	−	17.7519i	−1.20134	−	0.702255i
$640$	0.792737	−	0.457687i	0.0313357	−	0.0180917i
$641$	0.880679	+	0.508460i	0.0347847	+	0.0200830i	0.517292	−	0.855809i	$-0.326940\pi$
$641$	0.880679	+	0.508460i	0.0347847	+	0.0200830i	−0.482507	+	0.875892i	$0.660274\pi$
$642$	−8.68134	+	14.9434i	−0.342625	+	0.589769i
$643$	4.33665	+	2.50376i	0.171021	+	0.0987388i	0.583067	−	0.812424i	$-0.301852\pi$
$643$	4.33665	+	2.50376i	0.171021	+	0.0987388i	−0.412046	+	0.911163i	$0.635186\pi$
$644$	−0.0790083	−	2.60968i	−0.00311336	−	0.102836i
$645$	−6.18446	+	10.6455i	−0.243513	+	0.419164i
$646$	6.95344	−	12.0437i	0.273580	−	0.473854i
$647$	9.95259	+	17.2384i	0.391277	+	0.677711i	0.992618	−	0.121281i	$-0.0387002\pi$
$647$	9.95259	+	17.2384i	0.391277	+	0.677711i	−0.601342	+	0.798992i	$0.705367\pi$
$648$	−0.0970086	+	8.99948i	−0.00381086	+	0.353533i
$649$		−	10.8128i		−	0.424440i
$650$	−0.419636	+	15.0008i	−0.0164595	+	0.588378i
$651$	−1.19345	−	43.2753i	−0.0467750	−	1.69609i
$652$	−5.87295	−	10.1723i	−0.230003	−	0.398376i
$653$	30.2897	−	17.4877i	1.18533	−	0.684348i	0.228086	−	0.973641i	$-0.426753\pi$
$653$	30.2897	−	17.4877i	1.18533	−	0.684348i	0.957241	+	0.289293i	$0.0934201\pi$
$654$	−23.5779	+	13.5281i	−0.921968	+	0.528991i
$655$	6.28987			0.245766
$656$	−1.15899	+	2.00743i	−0.0452510	+	0.0783770i
$657$	0.0758793	−	14.0790i	0.00296033	−	0.549276i
$658$	−5.58424	+	3.45349i	−0.217696	+	0.134631i
$659$	16.6794	+	9.62985i	0.649737	+	0.375126i	0.788355	−	0.615220i	$-0.210933\pi$
$659$	16.6794	+	9.62985i	0.649737	+	0.375126i	−0.138619	+	0.990346i	$0.544266\pi$
$660$	−0.00582249	+	2.16069i	−0.000226640	+	0.0841046i
$661$	−12.5659	+	7.25495i	−0.488758	+	0.282185i	−0.724059	−	0.689738i	$-0.757726\pi$
$661$	−12.5659	+	7.25495i	−0.488758	+	0.282185i	0.235301	+	0.971923i	$0.424392\pi$
$662$		−	10.6561i		−	0.414159i
$663$	−12.7367	−	23.7108i	−0.494651	−	0.920852i
$664$		−	2.84354i		−	0.110351i
$665$	6.88288	+	3.70077i	0.266907	+	0.143510i
$666$	−0.737150	−	0.430908i	−0.0285640	−	0.0166973i
$667$	−4.28407	+	7.42022i	−0.165880	+	0.287312i
$668$	20.6925			0.800617
$669$	41.2761	−	23.6827i	1.59583	−	0.915626i
$670$	−3.55405	−	2.05193i	−0.137305	−	0.0792730i
$671$	−0.985346			−0.0380388
$672$	4.03028	+	2.18101i	0.155472	+	0.0841343i
$673$	−16.4670	−	28.5217i	−0.634757	−	1.09943i	−0.986567	−	0.163359i	$-0.947767\pi$
$673$	−16.4670	−	28.5217i	−0.634757	−	1.09943i	0.351810	−	0.936071i	$-0.385566\pi$
$674$	4.09205	−	2.36255i	0.157620	−	0.0910020i
$675$	21.6262	+	0.174834i	0.832391	+	0.00672936i
$676$	−12.9797	−	0.726763i	−0.499218	−	0.0279524i
$677$	36.0196			1.38434			0.692172	−	0.721732i	$-0.256654\pi$
$677$	36.0196			1.38434			0.692172	+	0.721732i	$0.256654\pi$
$678$	−7.64587	−	0.0206036i	−0.293638	−	0.000791278i
$679$	−15.5153	−	8.34222i	−0.595423	−	0.320145i
$680$	3.41660	+	1.97257i	0.131021	+	0.0756447i
$681$	11.7206	−	20.1749i	0.449134	−	0.773104i
$682$	11.1496	+	6.43724i	0.426941	+	0.246495i
$683$	−4.16387	−	2.40401i	−0.159326	−	0.0919870i	0.418217	−	0.908347i	$-0.362655\pi$
$683$	−4.16387	−	2.40401i	−0.159326	−	0.0919870i	−0.577543	+	0.816360i	$0.695988\pi$
$684$	−8.40930	+	4.79487i	−0.321538	+	0.183337i
$685$	9.19136	+	5.30663i	0.351184	+	0.202756i
$686$	15.1333	−	10.6763i	0.577792	−	0.407623i
$687$	0.0428495	−	15.9011i	0.00163481	−	0.606667i
$688$	−7.76519			−0.296045
$689$	41.1012	+	25.2880i	1.56583	+	0.963396i
$690$	−0.785936	+	1.35285i	−0.0299201	+	0.0515021i
$691$	24.4565	−	14.1200i	0.930369	−	0.537149i	0.0434405	−	0.999056i	$-0.486168\pi$
$691$	24.4565	−	14.1200i	0.930369	−	0.537149i	0.886928	+	0.461907i	$0.152835\pi$
$692$	−8.00405	−	13.8634i	−0.304268	−	0.527008i
$693$	−9.23031	+	5.63981i	−0.350631	+	0.214238i
$694$	22.3501			0.848399
$695$	3.20423	+	1.84996i	0.121543	+	0.0701730i
$696$	−7.48422	−	13.0441i	−0.283688	−	0.494435i
$697$	−9.99021			−0.378406
$698$	4.78526	−	8.28832i	0.181125	−	0.313717i
$699$	0.0381356	−	14.1519i	0.00144242	−	0.535273i
$700$	5.21482	−	9.69880i	0.197102	−	0.366580i
$701$		−	18.1806i		−	0.686671i	−0.939213	−	0.343335i	$-0.888443\pi$
$701$		−	18.1806i		−	0.686671i	0.939213	−	0.343335i	$-0.111557\pi$
$702$	−0.675273	+	18.7228i	−0.0254865	+	0.706647i
$703$		−	0.918394i		−	0.0346379i
$704$	−1.18022	+	0.681403i	−0.0444814	+	0.0256813i
$705$	3.93459	+	0.0106027i	0.148185	+	0.000399321i
$706$	22.7684	+	13.1453i	0.856898	+	0.494731i
$707$	−17.3598	−	28.0705i	−0.652882	−	1.05570i
$708$	6.83915	+	11.9198i	0.257031	+	0.447974i
$709$	8.24816	−	14.2862i	0.309766	−	0.536531i	−0.668545	−	0.743672i	$-0.733083\pi$
$709$	8.24816	−	14.2862i	0.309766	−	0.536531i	0.978311	+	0.207141i	$0.0664159\pi$
$710$	10.7331			0.402804
$711$	−8.74274	−	0.0471192i	−0.327878	−	0.00176711i
$712$	−3.69640	+	2.13411i	−0.138528	+	0.0799793i
$713$	4.66125	+	8.07353i	0.174565	+	0.302356i
$714$	0.544469	+	19.7428i	0.0203762	+	0.738857i
$715$	−0.125775	+	4.49608i	−0.00470371	+	0.168144i
$716$		−	26.4606i		−	0.988879i
$717$	0.0197991	−	7.34731i	0.000739411	−	0.274390i
$718$	−12.8571	−	22.2691i	−0.479822	−	0.831076i
$719$	26.0158	−	45.0606i	0.970224	−	1.68048i	0.275353	−	0.961343i	$-0.411205\pi$
$719$	26.0158	−	45.0606i	0.970224	−	1.68048i	0.694871	−	0.719134i	$-0.255461\pi$
$720$	−1.36022	−	2.38558i	−0.0506925	−	0.0889052i
$721$	−1.18198	−	39.0414i	−0.0440193	−	1.45398i
$722$	7.43750	+	4.29404i	0.276795	+	0.159808i
$723$	−23.7866	−	13.8188i	−0.884632	−	0.513926i
$724$	−12.1582	−	7.01953i	−0.451856	−	0.260879i
$725$	−31.2962	+	18.0689i	−1.16231	+	0.671060i
$726$	−0.0426730	+	15.8357i	−0.00158374	+	0.587717i
$727$			16.4042i			0.608396i	0.952609	+	0.304198i	$0.0983885\pi$
$727$			16.4042i			0.608396i	−0.952609	+	0.304198i	$0.901611\pi$
$728$	8.27230	+	4.75069i	0.306592	+	0.176072i
$729$	26.9965	+	0.436528i	0.999869	+	0.0161677i
$730$	2.14796	+	3.72038i	0.0794997	+	0.137697i
$731$	−16.7335	−	28.9833i	−0.618911	−	1.07198i
$732$	1.08622	−	0.623235i	0.0401480	−	0.0230354i
$733$			25.9877i			0.959878i	0.877302	+	0.479939i	$0.159341\pi$
$733$			25.9877i			0.959878i	−0.877302	+	0.479939i	$0.840659\pi$
$734$	11.8992	−	20.6101i	0.439208	−	0.760731i
$735$	−11.0798	+	0.641535i	−0.408683	+	0.0236634i
$736$	−0.986818			−0.0363746
$737$	5.29126	+	3.05491i	0.194906	+	0.112529i
$738$	6.00347	+	3.50938i	0.220991	+	0.129182i
$739$	7.13119	+	12.3516i	0.262325	+	0.454360i	0.966859	−	0.255310i	$-0.0821774\pi$
$739$	7.13119	+	12.3516i	0.262325	+	0.454360i	−0.704534	+	0.709670i	$0.748844\pi$
$740$	0.260533			0.00957738
$741$	−17.7520	+	9.53578i	−0.652136	+	0.350306i
$742$	−18.6256	−	30.1173i	−0.683767	−	1.10564i
$743$	−32.5718	+	18.8053i	−1.19494	+	0.689901i	−0.959424	−	0.281968i	$-0.909013\pi$
$743$	−32.5718	+	18.8053i	−1.19494	+	0.689901i	−0.235520	+	0.971869i	$0.575679\pi$
$744$	−16.3627	−	0.0440932i	−0.599885	−	0.00161654i
$745$	−11.9085	−	6.87535i	−0.436292	−	0.251893i
$746$			3.31943i			0.121533i
$747$	−8.53050	−	0.0459753i	−0.312115	−	0.00168215i
$748$	−5.08662	−	2.93676i	−0.185985	−	0.107379i
$749$	22.4522	−	13.8852i	0.820384	−	0.507354i
$750$	−12.5996	+	7.22920i	−0.460074	+	0.263973i
$751$	−20.3619	−	35.2679i	−0.743018	−	1.28694i	−0.951115	−	0.308837i	$-0.900060\pi$
$751$	−20.3619	−	35.2679i	−0.743018	−	1.28694i	0.208097	−	0.978108i	$-0.433273\pi$
$752$	1.24083	+	2.14918i	0.0452484	+	0.0783725i
$753$	−13.6301	+	23.4617i	−0.496707	+	0.854993i
$754$	−14.8885	−	27.5385i	−0.542207	−	1.00289i
$755$	−3.01896			−0.109871
$756$	6.60810	−	12.0554i	0.240334	−	0.438451i
$757$	11.6971	+	20.2600i	0.425138	+	0.736361i	0.996433	−	0.0843838i	$-0.0268922\pi$
$757$	11.6971	+	20.2600i	0.425138	+	0.736361i	−0.571295	+	0.820745i	$0.693559\pi$
$758$	31.3551	+	18.1029i	1.13887	+	0.657526i
$759$	1.17010	−	2.01412i	0.0424719	−	0.0731078i
$760$	1.47684	−	2.55796i	0.0535707	−	0.0927871i
$761$	14.4425	−	25.0152i	0.523540	−	0.906799i	−0.476084	−	0.879400i	$-0.657944\pi$
$761$	14.4425	−	25.0152i	0.523540	−	0.906799i	0.999625	−	0.0273989i	$-0.00872242\pi$
$762$	−26.5500	−	15.4242i	−0.961806	−	0.558760i
$763$	41.5040	−	1.25654i	1.50255	−	0.0454897i
$764$	10.4404	−	6.02776i	0.377720	−	0.218077i
$765$	5.97288	−	10.2178i	0.215950	−	0.369424i
$766$			24.1872i			0.873919i
$767$	13.6053	+	25.1649i	0.491257	+	0.908652i
$768$	0.870064	−	1.49766i	0.0313957	−	0.0540422i
$769$	−19.8564	+	11.4641i	−0.716040	+	0.413406i	−0.813294	−	0.581854i	$-0.802328\pi$
$769$	−19.8564	+	11.4641i	−0.716040	+	0.413406i	0.0972532	+	0.995260i	$0.468994\pi$
$770$	1.56300	−	2.90696i	0.0563268	−	0.104760i
$771$	12.6286	+	22.0101i	0.454807	+	0.792674i
$772$	−14.9839			−0.539282
$773$	10.4412	−	18.0847i	0.375544	−	0.650462i	−0.614864	−	0.788633i	$-0.710789\pi$
$773$	10.4412	−	18.0847i	0.375544	−	0.650462i	0.990408	+	0.138171i	$0.0441225\pi$
$774$	−0.125550	+	23.2952i	−0.00451281	+	0.837330i
$775$			39.3194i			1.41240i
$776$	−3.32908	+	5.76613i	−0.119507	+	0.206992i
$777$	0.683035	+	1.11114i	0.0245038	+	0.0398619i
$778$	−7.05049	−	12.2118i	−0.252772	−	0.437815i
$779$			7.47955i			0.267983i
$780$	−2.70514	−	5.03594i	−0.0968595	−	0.180316i
$781$	−15.9793			−0.571786
$782$	−2.12653	−	3.68326i	−0.0760446	−	0.131713i
$783$	−39.2527	+	22.2414i	−1.40278	+	0.794844i
$784$	−3.86032	−	5.83934i	−0.137869	−	0.208548i
$785$			3.93327i			0.140384i
$786$	10.3230	−	5.92298i	0.368211	−	0.211266i
$787$	10.6246	+	6.13410i	0.378725	+	0.218657i	0.677263	−	0.735741i	$-0.263166\pi$
$787$	10.6246	+	6.13410i	0.378725	+	0.218657i	−0.298538	+	0.954398i	$0.596499\pi$
$788$			2.06769i			0.0736583i
$789$	−42.4027	+	24.3291i	−1.50958	+	0.866138i
$790$	2.31026	−	1.33383i	0.0821955	−	0.0474556i
$791$	10.2867	+	5.53090i	0.365751	+	0.196656i
$792$	2.02510	+	3.55164i	0.0719587	+	0.126202i
$793$	2.29322	−	1.23981i	0.0814346	−	0.0440271i
$794$	−30.1950			−1.07158
$795$	−0.0571832	+	21.2203i	−0.00202808	+	0.752606i
$796$	−2.38680	+	1.37802i	−0.0845979	+	0.0488426i
$797$	−11.0516	+	19.1419i	−0.391467	+	0.678040i	−0.992643	−	0.121076i	$-0.961365\pi$
$797$	−11.0516	+	19.1419i	−0.391467	+	0.678040i	0.601177	+	0.799116i	$0.294699\pi$
$798$	14.7812	−	0.407637i	0.523249	−	0.0144302i
$799$	−5.34782	+	9.26269i	−0.189192	+	0.327690i
$800$	−3.60448	−	2.08105i	−0.127437	−	0.0735761i
$801$	6.34249	+	11.1235i	0.224101	+	0.393031i
$802$	2.40862	−	4.17185i	0.0850512	−	0.147313i
$803$	−3.19788	−	5.53889i	−0.112851	−	0.195463i
$804$	−7.76521	−	0.0209252i	−0.273858	−	0.000737976i
$805$	2.03263	−	1.25705i	0.0716408	−	0.0443052i
$806$	−34.0484	−	0.952481i	−1.19931	−	0.0335497i
$807$	−27.3929	+	47.1520i	−0.964275	+	1.65983i
$808$	−10.8034	+	6.23732i	−0.380061	+	0.219428i
$809$	−38.7955	+	22.3986i	−1.36398	+	0.787493i	−0.990151	−	0.140006i	$-0.955288\pi$
$809$	−38.7955	+	22.3986i	−1.36398	+	0.787493i	−0.373827	+	0.927499i	$0.621955\pi$
$810$	−7.17862	+	4.04204i	−0.252231	+	0.142023i
$811$		−	8.02108i		−	0.281658i	−0.990034	−	0.140829i	$-0.955023\pi$
$811$		−	8.02108i		−	0.281658i	0.990034	−	0.140829i	$-0.0449768\pi$
$812$	0.695159	+	22.9614i	0.0243953	+	0.805789i
$813$	10.3345	−	5.92956i	0.362447	−	0.207959i
$814$	−0.387880			−0.0135952
$815$	5.37595	−	9.31142i	0.188311	−	0.326165i
$816$	7.46490	+	0.0201160i	0.261324	+	0.000704199i
$817$	−21.6994	+	12.5282i	−0.759166	+	0.438305i
$818$	4.12348			0.144174
$819$	14.3856	−	24.7397i	0.502674	−	0.864476i
$820$	−2.12182			−0.0740972
$821$	37.7036	−	21.7682i	1.31586	−	0.759715i	0.332804	−	0.942996i	$-0.392005\pi$
$821$	37.7036	−	21.7682i	1.31586	−	0.759715i	0.983060	+	0.183281i	$0.0586719\pi$
$822$	20.0821	+	0.0541161i	0.700444	+	0.00188752i
$823$	7.09465	−	12.2883i	0.247304	−	0.428343i	−0.715473	−	0.698640i	$-0.753789\pi$
$823$	7.09465	−	12.2883i	0.247304	−	0.428343i	0.962777	+	0.270297i	$0.0871220\pi$
$824$	−14.7630			−0.514295
$825$	8.52139	−	4.88926i	0.296677	−	0.170222i
$826$	−0.635243	−	20.9824i	−0.0221029	−	0.730070i
$827$		−	41.1184i		−	1.42983i	−0.699213	−	0.714913i	$-0.746466\pi$
$827$		−	41.1184i		−	1.42983i	0.699213	−	0.714913i	$-0.253534\pi$
$828$	−0.0159552	+	2.96041i	−0.000554482	+	0.102881i
$829$	−23.5068	+	13.5717i	−0.816425	+	0.471363i	−0.849182	−	0.528100i	$-0.822905\pi$
$829$	−23.5068	+	13.5717i	−0.816425	+	0.471363i	0.0327571	+	0.999463i	$0.489571\pi$
$830$	2.25418	−	1.30145i	0.0782437	−	0.0451740i
$831$	8.46623	−	14.5731i	0.293690	−	0.505535i
$832$	1.88939	−	3.07087i	0.0655027	−	0.106463i
$833$	13.4764	−	26.9919i	0.466929	−	0.935214i
$834$	7.00089	+	0.0188656i	0.242421	+	0.000653262i
$835$	9.47069	+	16.4037i	0.327747	+	0.567674i
$836$	−2.19872	+	3.80829i	−0.0760442	+	0.131712i
$837$	−0.396835	+	49.0866i	−0.0137166	+	1.69668i
$838$	−2.20315	−	1.27199i	−0.0761066	−	0.0439402i
$839$	8.84854	−	15.3261i	0.305486	−	0.529117i	−0.671884	−	0.740657i	$-0.734515\pi$
$839$	8.84854	−	15.3261i	0.305486	−	0.529117i	0.977369	+	0.211540i	$0.0678479\pi$
$840$	0.115640	+	4.19318i	0.00398995	+	0.144678i
$841$	23.1936	−	40.1726i	0.799781	−	1.38526i
$842$	5.64006	−	3.25629i	0.194369	−	0.112219i
$843$	0.134599	−	49.9488i	0.00463584	−	1.72033i
$844$	17.5469			0.603988
$845$	−5.36449	−	10.6221i	−0.184544	−	0.365411i
$846$	6.46750	−	3.68768i	0.222357	−	0.126785i
$847$	11.4553	−	21.3051i	0.393608	−	0.732052i
$848$	−11.5911	+	6.69212i	−0.398040	+	0.229808i
$849$	−30.3127	+	17.3923i	−1.04033	+	0.596902i
$850$		−	17.9381i		−	0.615271i
$851$	−0.243238	−	0.140434i	−0.00833810	−	0.00481400i
$852$	17.6153	−	10.1070i	0.603490	−	0.346260i
$853$		−	27.0976i		−	0.927804i	−0.885887	−	0.463902i	$-0.846449\pi$
$853$		−	27.0976i		−	0.927804i	0.885887	−	0.463902i	$-0.153551\pi$
$854$	−1.91207	+	0.0578882i	−0.0654298	+	0.00198089i
$855$	−7.64990	−	4.47182i	−0.261621	−	0.152933i
$856$	−4.98891	−	8.64105i	−0.170517	−	0.295345i
$857$	−32.2317			−1.10101			−0.550507	−	0.834830i	$-0.685566\pi$
$857$	−32.2317			−1.10101			−0.550507	+	0.834830i	$0.685566\pi$
$858$	4.02740	+	7.49749i	0.137493	+	0.255960i
$859$			40.1486i			1.36985i	0.728613	+	0.684926i	$0.240165\pi$
$859$			40.1486i			1.36985i	−0.728613	+	0.684926i	$0.759835\pi$
$860$	−3.55403	−	6.15575i	−0.121191	−	0.209909i
$861$	−5.56275	−	9.04929i	−0.189578	−	0.308399i
$862$	5.23760	−	9.07179i	0.178393	−	0.308986i
$863$		−	26.2785i		−	0.894531i	−0.894401	−	0.447266i	$-0.852398\pi$
$863$		−	26.2785i		−	0.894531i	0.894401	−	0.447266i	$-0.147602\pi$
$864$	−4.47885	−	2.63437i	−0.152374	−	0.0896231i
$865$	7.32670	−	12.6902i	0.249115	−	0.431480i
$866$	28.2707			0.960676
$867$	1.35764	+	2.36620i	0.0461078	+	0.0803605i
$868$	22.0141	+	11.8365i	0.747209	+	0.401757i
$869$	−3.43951	+	1.98580i	−0.116677	+	0.0673638i
$870$	6.91511	−	11.9031i	0.234444	−	0.403554i
$871$	−16.1583	−	0.452017i	−0.547504	−	0.0153160i
$872$		−	15.6942i		−	0.531474i
$873$	17.2443	+	10.0803i	0.583632	+	0.341167i
$874$	−2.75761	+	1.59211i	−0.0932776	+	0.0538538i
$875$	22.1791	−	0.671473i	0.749789	−	0.0226999i
$876$	7.02865	+	4.08328i	0.237476	+	0.137961i
$877$	−8.35029	+	14.4631i	−0.281969	+	0.488385i	−0.971870	−	0.235519i	$-0.924321\pi$
$877$	−8.35029	+	14.4631i	−0.281969	+	0.488385i	0.689901	+	0.723904i	$0.257654\pi$
$878$	9.47410	−	16.4096i	0.319735	−	0.553798i
$879$	−3.33308	+	5.73730i	−0.112422	+	0.193514i
$880$	−1.08035	−	0.623738i	−0.0364185	−	0.0210262i
$881$	−2.41558	−	4.18392i	−0.0813831	−	0.140960i	0.822461	−	0.568821i	$-0.192600\pi$
$881$	−2.41558	−	4.18392i	−0.0813831	−	0.140960i	−0.903844	+	0.427862i	$0.859267\pi$
$882$	−17.5802	+	11.4864i	−0.591956	+	0.386766i
$883$	−9.59290			−0.322827			−0.161413	−	0.986887i	$-0.551605\pi$
$883$	−9.59290			−0.322827			−0.161413	+	0.986887i	$0.551605\pi$
$884$	15.5334	+	0.434536i	0.522445	+	0.0146150i
$885$	−6.31909	+	10.8772i	−0.212414	+	0.365633i
$886$	7.51002	+	13.0077i	0.252304	+	0.437003i
$887$	18.4327	+	31.9264i	0.618911	+	1.07199i	0.989685	+	0.143262i	$0.0457591\pi$
$887$	18.4327	+	31.9264i	0.618911	+	1.07199i	−0.370774	+	0.928723i	$0.620908\pi$
$888$	0.427591	−	0.245336i	0.0143490	−	0.00823294i
$889$	24.6699	+	39.8909i	0.827403	+	1.33790i
$890$	−3.38358	−	1.95351i	−0.113418	−	0.0654819i
$891$	10.6875	−	6.01778i	0.358045	−	0.201603i
$892$			27.4748i			0.919923i
$893$	6.93486	+	4.00384i	0.232066	+	0.133983i
$894$	−26.0187	−	0.0701136i	−0.870195	−	0.00234495i
$895$	20.9763	−	12.1107i	0.701161	−	0.404815i
$896$	−2.25021	+	1.39161i	−0.0751741	+	0.0464903i
$897$	−0.188929	+	6.15978i	−0.00630815	+	0.205669i
$898$	−6.74005			−0.224918
$899$	−41.0123	−	71.0355i	−1.36784	−	2.36917i
$900$	−6.30132	+	10.7796i	−0.210044	+	0.359321i
$901$	−49.9562	−	28.8422i	−1.66428	−	0.960873i
$902$	3.15896			0.105182
$903$	16.9360	−	31.2959i	0.563594	−	1.04146i
$904$	2.20718	−	3.82295i	0.0734097	−	0.127149i
$905$		−	12.8510i		−	0.427182i
$906$	−4.95477	+	2.84286i	−0.164611	+	0.0944477i
$907$	17.5222	+	30.3493i	0.581815	+	1.00773i	0.995264	+	0.0972056i	$0.0309904\pi$
$907$	17.5222	+	30.3493i	0.581815	+	1.00773i	−0.413450	+	0.910527i	$0.635676\pi$
$908$	6.73547	+	11.6662i	0.223525	+	0.387156i
$909$	18.5370	+	32.5104i	0.614834	+	1.07830i
$910$	0.0200737	+	8.73209i	0.000665438	+	0.289466i
$911$			27.4974i			0.911031i	0.890228	+	0.455515i	$0.150545\pi$
$911$			27.4974i			0.911031i	−0.890228	+	0.455515i	$0.849455\pi$
$912$	0.0150606	−	5.58887i	0.000498705	−	0.185066i
$913$	−3.35602	+	1.93760i	−0.111068	+	0.0641251i
$914$	−12.2109	−	7.04998i	−0.403902	−	0.233193i
$915$	0.991212	+	0.575844i	0.0327685	+	0.0190368i
$916$	7.95060	+	4.59028i	0.262695	+	0.151667i
$917$	−18.1716	+	0.550147i	−0.600079	+	0.0181674i
$918$	0.181042	−	22.3940i	0.00597527	−	0.739113i
$919$	−19.5303	+	33.8274i	−0.644244	+	1.11586i	0.340232	+	0.940342i	$0.389494\pi$
$919$	−19.5303	+	33.8274i	−0.644244	+	1.11586i	−0.984476	+	0.175521i	$0.943839\pi$
$920$	−0.451654	−	0.782287i	−0.0148906	−	0.0257913i
$921$	0.00940071	−	3.48854i	0.000309764	−	0.114951i
$922$		−	33.2373i		−	1.09461i
$923$	37.1891	−	20.1061i	1.22409	−	0.661799i
$924$	−0.172164	−	6.24279i	−0.00566378	−	0.205373i
$925$	−0.592305	−	1.02590i	−0.0194749	−	0.0337315i
$926$	−20.3397	+	11.7432i	−0.668405	+	0.385904i
$927$	−0.238694	+	44.2885i	−0.00783973	+	1.45462i
$928$	8.68259			0.285020
$929$	0.161744	−	0.280148i	0.00530663	−	0.00919136i	−0.863360	−	0.504589i	$-0.831644\pi$
$929$	0.161744	−	0.280148i	0.00530663	−	0.00919136i	0.868667	+	0.495397i	$0.164978\pi$
$930$	−7.45403	−	12.9915i	−0.244427	−	0.426008i
$931$	−20.2085	−	10.0896i	−0.662307	−	0.330673i
$932$	7.07596	+	4.08531i	0.231781	+	0.133819i
$933$	27.3548	+	0.0737141i	0.895556	+	0.00241329i
$934$	−4.72646	+	2.72882i	−0.154654	+	0.0892898i
$935$		−	5.37647i		−	0.175829i
$936$	−9.18192	−	5.71773i	−0.300120	−	0.186890i
$937$		−	12.1500i		−	0.396922i	−0.980109	−	0.198461i	$-0.936406\pi$
$937$		−	12.1500i		−	0.396922i	0.980109	−	0.198461i	$-0.0635943\pi$
$938$	10.4472	+	5.61723i	0.341114	+	0.183409i
$939$	−0.0189343	+	7.02639i	−0.000617898	+	0.229298i
$940$	−1.13582	+	1.96730i	−0.0370464	+	0.0641663i
$941$	47.3214			1.54263			0.771317	−	0.636451i	$-0.219598\pi$
$941$	47.3214			1.54263			0.771317	+	0.636451i	$0.219598\pi$
$942$	3.70384	+	6.45536i	0.120678	+	0.210327i
$943$	1.98097	+	1.14371i	0.0645093	+	0.0372444i
$944$	−7.93423			−0.258237
$945$	12.5812	−	0.279118i	0.409267	−	0.00907970i
$946$	5.29122	+	9.16467i	0.172032	+	0.297969i
$947$	−3.20978	+	1.85317i	−0.104304	+	0.0602199i	−0.551245	−	0.834344i	$-0.685847\pi$
$947$	−3.20978	+	1.85317i	−0.104304	+	0.0602199i	0.446941	+	0.894564i	$0.352514\pi$
$948$	2.53562	−	4.36461i	0.0823530	−	0.141756i
$949$	14.4118	+	8.86705i	0.467828	+	0.287837i
$950$	−13.4300			−0.435727
$951$	−0.0467362	+	17.3435i	−0.00151553	+	0.562402i
$952$	−10.0432	−	5.39998i	−0.325501	−	0.175014i
$953$	−8.84176	−	5.10479i	−0.286413	−	0.165361i	0.349910	−	0.936783i	$-0.386212\pi$
$953$	−8.84176	−	5.10479i	−0.286413	−	0.165361i	−0.636323	+	0.771423i	$0.719545\pi$
$954$	19.8887	+	34.8810i	0.643919	+	1.12931i
$955$	9.55686	+	5.51765i	0.309253	+	0.178547i
$956$	3.67367	+	2.12099i	0.118815	+	0.0685979i
$957$	−10.2952	+	17.7213i	−0.332796	+	0.572849i
$958$	−16.3546	−	9.44233i	−0.528393	−	0.305068i
$959$	−27.0182	−	14.5271i	−0.872464	−	0.469104i
$960$	1.58547	+	0.00427243i	0.0511708	+	0.000137892i
$961$	−58.2465			−1.87892
$962$	0.902723	−	0.488052i	0.0291050	−	0.0157354i
$963$	−26.0034	+	14.8268i	−0.837949	+	0.477787i
$964$	13.7546	−	7.94124i	0.443007	−	0.255770i
$965$	−6.85793	−	11.8783i	−0.220765	−	0.382375i
$966$	2.15226	−	3.97716i	0.0692479	−	0.127963i
$967$	60.5201			1.94620			0.973098	−	0.230391i	$-0.0740006\pi$
$967$	60.5201			1.94620			0.973098	+	0.230391i	$0.0740006\pi$
$968$	−7.91786	−	4.57138i	−0.254490	−	0.146930i
$969$	20.8927	−	11.9875i	0.671171	−	0.385093i
$970$	−6.09470			−0.195689
$971$	−4.25649	+	7.37246i	−0.136597	+	0.236593i	−0.926207	−	0.377017i	$-0.876950\pi$
$971$	−4.25649	+	7.37246i	−0.136597	+	0.236593i	0.789609	+	0.613610i	$0.210283\pi$
$972$	−7.97541	+	13.3938i	−0.255811	+	0.429605i
$973$	−9.41890	−	5.06433i	−0.301956	−	0.162355i
$974$		−	23.5631i		−	0.755010i
$975$	−13.6801	+	22.1009i	−0.438114	+	0.707797i
$976$			0.723027i			0.0231435i
$977$	9.62617	−	5.55767i	0.307968	−	0.177806i	−0.338049	−	0.941129i	$-0.609767\pi$
$977$	9.62617	−	5.55767i	0.307968	−	0.177806i	0.646017	+	0.763323i	$0.276434\pi$
$978$	0.0548230	−	20.3444i	0.00175305	−	0.650543i
$979$	5.03747	+	2.90838i	0.160998	+	0.0929523i
$980$	2.86225	−	5.73281i	0.0914311	−	0.183128i
$981$	−47.0820	−	0.253749i	−1.50321	−	0.00810160i
$982$	−6.22472	+	10.7815i	−0.198639	+	0.344053i
$983$	38.5291			1.22889			0.614444	−	0.788960i	$-0.289380\pi$
$983$	38.5291			1.22889			0.614444	+	0.788960i	$0.289380\pi$
$984$	−3.48237	+	1.99805i	−0.111014	+	0.0636957i
$985$	−1.63913	+	0.946354i	−0.0522271	+	0.0301533i
$986$	18.7104	+	32.4074i	0.595861	+	1.03206i
$987$	−11.3681	+	0.313509i	−0.361849	+	0.00997911i
$988$	0.325331	−	11.6297i	0.0103502	−	0.369989i
$989$			7.66283i			0.243664i
$990$	−1.88866	+	3.23091i	−0.0600254	+	0.102685i
$991$	19.8325	+	34.3509i	0.630001	+	1.09119i	0.987551	+	0.157299i	$0.0502788\pi$
$991$	19.8325	+	34.3509i	0.630001	+	1.09119i	−0.357550	+	0.933894i	$0.616388\pi$
$992$	4.72352	−	8.18137i	0.149972	−	0.259759i
$993$	9.27145	−	15.9592i	0.294221	−	0.506449i
$994$	−31.0081	+	0.938772i	−0.983517	+	0.0297760i
$995$	−2.18482	−	1.26140i	−0.0692633	−	0.0399892i
$996$	2.47406	−	4.25866i	0.0783937	−	0.134941i
$997$	16.5309	+	9.54409i	0.523537	+	0.302264i	0.738381	−	0.674384i	$-0.235591\pi$
$997$	16.5309	+	9.54409i	0.523537	+	0.302264i	−0.214843	+	0.976649i	$0.568924\pi$
$998$	−21.2163	+	12.2492i	−0.671591	+	0.387743i
$999$	−0.729084	−	1.28672i	−0.0230672	−	0.0407101i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bq.c.419.1	✓	64
3.2	odd	2	inner	546.2.bq.c.419.22	yes	64
7.6	odd	2	inner	546.2.bq.c.419.16	yes	64
13.9	even	3	inner	546.2.bq.c.503.27	yes	64
21.20	even	2	inner	546.2.bq.c.419.27	yes	64
39.35	odd	6	inner	546.2.bq.c.503.16	yes	64
91.48	odd	6	inner	546.2.bq.c.503.22	yes	64
273.230	even	6	inner	546.2.bq.c.503.1	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bq.c.419.1	✓	64	1.1	even	1	trivial
546.2.bq.c.419.16	yes	64	7.6	odd	2	inner
546.2.bq.c.419.22	yes	64	3.2	odd	2	inner
546.2.bq.c.419.27	yes	64	21.20	even	2	inner
546.2.bq.c.503.1	yes	64	273.230	even	6	inner
546.2.bq.c.503.16	yes	64	39.35	odd	6	inner
546.2.bq.c.503.22	yes	64	91.48	odd	6	inner
546.2.bq.c.503.27	yes	64	13.9	even	3	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bq (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.73204 - 0.00466741i) q^{3} +(0.500000 - 0.866025i) q^{4} +0.915374 q^{5} +(1.50233 - 0.861980i) q^{6} +(-2.64454 + 0.0800636i) q^{7} +1.00000i q^{8} +(2.99996 + 0.0161683i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.73204 - 0.00466741i) q^{3} +(0.500000 - 0.866025i) q^{4} +0.915374 q^{5} +(1.50233 - 0.861980i) q^{6} +(-2.64454 + 0.0800636i) q^{7} +1.00000i q^{8} +(2.99996 + 0.0161683i) q^{9} +(-0.792737 + 0.457687i) q^{10} +(1.18022 - 0.681403i) q^{11} +(-0.870064 + 1.49766i) q^{12} +(-1.88939 + 3.07087i) q^{13} +(2.25021 - 1.39161i) q^{14} +(-1.58547 - 0.00427243i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.15494 - 3.73246i) q^{17} +(-2.60612 + 1.48598i) q^{18} +(-2.79445 - 1.61337i) q^{19} +(0.457687 - 0.792737i) q^{20} +(4.58083 - 0.126331i) q^{21} +(-0.681403 + 1.18022i) q^{22} +(-0.854610 + 0.493409i) q^{23} +(0.00466741 - 1.73204i) q^{24} -4.16209 q^{25} +(0.100823 - 3.60414i) q^{26} +(-5.19598 - 0.0420063i) q^{27} +(-1.25293 + 2.33027i) q^{28} +(7.51934 - 4.34129i) q^{29} +(1.37519 - 0.789034i) q^{30} -9.44703i q^{31} +(0.866025 + 0.500000i) q^{32} +(-2.04738 + 1.17471i) q^{33} +4.30988i q^{34} +(-2.42074 + 0.0732882i) q^{35} +(1.51398 - 2.58995i) q^{36} +(0.142310 + 0.246487i) q^{37} +3.22675 q^{38} +(3.28683 - 5.31006i) q^{39} +0.915374i q^{40} +(-1.15899 - 2.00743i) q^{41} +(-3.90395 + 2.39982i) q^{42} +(3.88259 - 6.72485i) q^{43} -1.36281i q^{44} +(2.74608 + 0.0148001i) q^{45} +(0.493409 - 0.854610i) q^{46} -2.48166 q^{47} +(0.861980 + 1.50233i) q^{48} +(6.98718 - 0.423463i) q^{49} +(3.60448 - 2.08105i) q^{50} +(-3.74987 + 6.45473i) q^{51} +(1.71476 + 3.17169i) q^{52} -13.3842i q^{53} +(4.52086 - 2.56161i) q^{54} +(1.08035 - 0.623738i) q^{55} +(-0.0800636 - 2.64454i) q^{56} +(4.83258 + 2.80748i) q^{57} +(-4.34129 + 7.51934i) q^{58} +(3.96711 - 6.87124i) q^{59} +(-0.796434 + 1.37092i) q^{60} +(-0.626160 - 0.361514i) q^{61} +(4.72352 + 8.18137i) q^{62} +(-7.93480 + 0.197430i) q^{63} -1.00000 q^{64} +(-1.72949 + 2.81099i) q^{65} +(1.18573 - 2.04102i) q^{66} +(2.24163 + 3.88262i) q^{67} +(-2.15494 - 3.73246i) q^{68} +(1.48252 - 0.850618i) q^{69} +(2.05978 - 1.27384i) q^{70} +(-10.1544 - 5.86266i) q^{71} +(-0.0161683 + 2.99996i) q^{72} -4.69308i q^{73} +(-0.246487 - 0.142310i) q^{74} +(7.20893 + 0.0194262i) q^{75} +(-2.79445 + 1.61337i) q^{76} +(-3.06659 + 1.89649i) q^{77} +(-0.191452 + 6.24206i) q^{78} -2.91429 q^{79} +(-0.457687 - 0.792737i) q^{80} +(8.99948 + 0.0970086i) q^{81} +(2.00743 + 1.15899i) q^{82} -2.84354 q^{83} +(2.18101 - 4.03028i) q^{84} +(1.97257 - 3.41660i) q^{85} +7.76519i q^{86} +(-13.0441 + 7.48422i) q^{87} +(0.681403 + 1.18022i) q^{88} +(2.13411 + 3.69640i) q^{89} +(-2.38558 + 1.36022i) q^{90} +(4.75069 - 8.27230i) q^{91} +0.986818i q^{92} +(-0.0440932 + 16.3627i) q^{93} +(2.14918 - 1.24083i) q^{94} +(-2.55796 - 1.47684i) q^{95} +(-1.49766 - 0.870064i) q^{96} +(5.76613 + 3.32908i) q^{97} +(-5.83934 + 3.86032i) q^{98} +(3.55164 - 2.02510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} + 16 q^{7} + 16 q^{9}+O(q^{10}) \) 64 * q + 32 * q^4 + 16 * q^7 + 16 * q^9	\( 64 q + 32 q^{4} + 16 q^{7} + 16 q^{9} - 12 q^{15} - 32 q^{16} - 24 q^{18} + 16 q^{21} - 16 q^{28} + 8 q^{30} - 16 q^{36} - 48 q^{39} + 20 q^{42} - 8 q^{43} + 8 q^{46} + 8 q^{49} - 8 q^{51} + 8 q^{57} + 16 q^{58} - 24 q^{60} + 32 q^{63} - 64 q^{64} + 24 q^{67} + 48 q^{70} - 12 q^{72} - 12 q^{78} + 96 q^{79} + 68 q^{81} + 8 q^{84} - 112 q^{85} - 16 q^{91} - 56 q^{93}+O(q^{100}) \) 64 * q + 32 * q^4 + 16 * q^7 + 16 * q^9 - 12 * q^15 - 32 * q^16 - 24 * q^18 + 16 * q^21 - 16 * q^28 + 8 * q^30 - 16 * q^36 - 48 * q^39 + 20 * q^42 - 8 * q^43 + 8 * q^46 + 8 * q^49 - 8 * q^51 + 8 * q^57 + 16 * q^58 - 24 * q^60 + 32 * q^63 - 64 * q^64 + 24 * q^67 + 48 * q^70 - 12 * q^72 - 12 * q^78 + 96 * q^79 + 68 * q^81 + 8 * q^84 - 112 * q^85 - 16 * q^91 - 56 * q^93

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