LMFDB - Embedded newform 490.2.w.a.397.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(3,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(84))

chi = DirichletCharacter(H, H._module([63, 2]))

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

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

chi := DirichletCharacter("490.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.w (of order $84$, degree $24$, 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:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$28$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			397.20
Character	$\chi$	$=$	490.397
Dual form			490.2.w.a.353.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.804598 + 0.593820i) q^{2} +(-0.000114150 - 0.000603296i) q^{3} +(0.294755 + 0.955573i) q^{4} +(-0.873857 - 2.05825i) q^{5} +(0.000266405 - 0.000553195i) q^{6} +(-0.846959 - 2.50652i) q^{7} +(-0.330279 + 0.943883i) q^{8} +(2.79262 - 1.09602i) q^{9} +O(q^{10})$	\(q+(0.804598 + 0.593820i) q^{2} +(-0.000114150 - 0.000603296i) q^{3} +(0.294755 + 0.955573i) q^{4} +(-0.873857 - 2.05825i) q^{5} +(0.000266405 - 0.000553195i) q^{6} +(-0.846959 - 2.50652i) q^{7} +(-0.330279 + 0.943883i) q^{8} +(2.79262 - 1.09602i) q^{9} +(0.519124 - 2.17497i) q^{10} +(0.156322 - 0.398301i) q^{11} +(0.000542847 - 0.000286903i) q^{12} +(-0.0674675 + 0.598790i) q^{13} +(0.806963 - 2.51968i) q^{14} +(-0.00114198 + 0.000762143i) q^{15} +(-0.826239 + 0.563320i) q^{16} +(0.0657864 - 1.75818i) q^{17} +(2.89778 + 0.776457i) q^{18} +(3.69043 - 6.39202i) q^{19} +(1.70923 - 1.44171i) q^{20} +(-0.00141550 + 0.000797086i) q^{21} +(0.362295 - 0.227645i) q^{22} +(0.287027 - 0.0107398i) q^{23} +(0.000607143 + 9.15120e-5i) q^{24} +(-3.47275 + 3.59723i) q^{25} +(-0.409858 + 0.441722i) q^{26} +(-0.00196001 - 0.00311933i) q^{27} +(2.14552 - 1.54814i) q^{28} +(1.89914 - 0.433466i) q^{29} +(-0.00137141 - 6.49127e-5i) q^{30} +(1.61357 - 0.931593i) q^{31} +(-0.999301 - 0.0373912i) q^{32} +(-0.000258137 - 4.88422e-5i) q^{33} +(1.09697 - 1.37556i) q^{34} +(-4.41892 + 3.93359i) q^{35} +(1.87047 + 2.34549i) q^{36} +(3.11213 + 5.88844i) q^{37} +(6.76502 - 2.95155i) q^{38} +(0.000368949 - 2.76489e-5i) q^{39} +(2.23136 - 0.145024i) q^{40} +(1.46758 + 3.04746i) q^{41} +(-0.00161223 - 0.000199216i) q^{42} +(0.496324 - 0.173671i) q^{43} +(0.426682 + 0.0319754i) q^{44} +(-4.69624 - 4.79013i) q^{45} +(0.237319 + 0.161801i) q^{46} +(-3.23788 + 4.38717i) q^{47} +(0.000434164 + 0.000434164i) q^{48} +(-5.56532 + 4.24584i) q^{49} +(-4.93027 + 0.832132i) q^{50} +(-0.00106821 + 0.000161007i) q^{51} +(-0.592074 + 0.112026i) q^{52} +(-5.13676 + 9.71923i) q^{53} +(0.000275306 - 0.00367370i) q^{54} +(-0.956403 + 0.0263100i) q^{55} +(2.64560 + 0.0284221i) q^{56} +(-0.00427754 - 0.00149678i) q^{57} +(1.78544 + 0.778981i) q^{58} +(-0.483509 - 6.45198i) q^{59} +(-0.00106489 - 0.000866600i) q^{60} +(-1.55283 + 5.03415i) q^{61} +(1.85147 + 0.208611i) q^{62} +(-5.11244 - 6.07148i) q^{63} +(-0.781831 - 0.623490i) q^{64} +(1.29141 - 0.384393i) q^{65} +(-0.000178693 - 0.000192586i) q^{66} +(2.70758 - 10.1048i) q^{67} +(1.69946 - 0.455368i) q^{68} +(-3.92433e-5 - 0.000171936i) q^{69} +(-5.89130 + 0.540916i) q^{70} +(-2.33883 + 10.2471i) q^{71} +(0.112174 + 2.99790i) q^{72} +(-5.85225 - 7.92952i) q^{73} +(-0.992661 + 6.58588i) q^{74} +(0.00256661 + 0.00168447i) q^{75} +(7.19581 + 1.64240i) q^{76} +(-1.13075 - 0.0544793i) q^{77} +(0.000313274 + 0.000196843i) q^{78} +(5.95803 + 3.43987i) q^{79} +(1.88147 + 1.20834i) q^{80} +(6.59746 - 6.12155i) q^{81} +(-0.628831 + 3.32345i) q^{82} +(1.30600 - 0.147151i) q^{83} +(-0.00117890 - 0.00111766i) q^{84} +(-3.67625 + 1.40099i) q^{85} +(0.502471 + 0.154992i) q^{86} +(-0.000478295 - 0.00109626i) q^{87} +(0.324320 + 0.279100i) q^{88} +(-1.25191 - 3.18982i) q^{89} +(-0.934105 - 6.64285i) q^{90} +(1.55802 - 0.338042i) q^{91} +(0.0948653 + 0.271109i) q^{92} +(-0.000746215 - 0.000867118i) q^{93} +(-5.21038 + 1.60719i) q^{94} +(-16.3812 - 2.01010i) q^{95} +(9.15120e-5 + 0.000607143i) q^{96} +(-0.360693 + 0.360693i) q^{97} +(-6.99911 + 0.111396i) q^{98} -1.28364i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q + 12 q^{5} - 28 q^{6} - 8 q^{7}+O(q^{10}) $ 672 * q + 12 * q^5 - 28 * q^6 - 8 * q^7	$ 672 q + 12 q^{5} - 28 q^{6} - 8 q^{7} + 12 q^{10} + 4 q^{11} - 44 q^{15} - 56 q^{16} + 8 q^{17} + 28 q^{21} + 20 q^{22} + 4 q^{23} - 4 q^{25} + 16 q^{26} - 4 q^{28} - 12 q^{30} - 24 q^{31} - 48 q^{33} - 8 q^{35} + 92 q^{36} - 12 q^{37} - 24 q^{38} - 112 q^{41} + 76 q^{42} + 24 q^{43} - 100 q^{45} - 160 q^{46} + 72 q^{47} + 32 q^{50} - 208 q^{51} + 160 q^{53} - 84 q^{55} - 52 q^{56} - 92 q^{57} + 128 q^{58} - 212 q^{61} + 36 q^{63} - 16 q^{67} + 36 q^{68} - 16 q^{70} - 16 q^{71} + 12 q^{73} + 132 q^{75} - 16 q^{77} + 80 q^{78} + 12 q^{80} - 36 q^{81} + 48 q^{82} - 308 q^{83} - 40 q^{85} - 4 q^{86} + 52 q^{87} - 4 q^{88} + 84 q^{90} - 124 q^{91} - 8 q^{92} - 536 q^{93} - 28 q^{95} - 12 q^{96} - 40 q^{98}+O(q^{100}) $ 672 * q + 12 * q^5 - 28 * q^6 - 8 * q^7 + 12 * q^10 + 4 * q^11 - 44 * q^15 - 56 * q^16 + 8 * q^17 + 28 * q^21 + 20 * q^22 + 4 * q^23 - 4 * q^25 + 16 * q^26 - 4 * q^28 - 12 * q^30 - 24 * q^31 - 48 * q^33 - 8 * q^35 + 92 * q^36 - 12 * q^37 - 24 * q^38 - 112 * q^41 + 76 * q^42 + 24 * q^43 - 100 * q^45 - 160 * q^46 + 72 * q^47 + 32 * q^50 - 208 * q^51 + 160 * q^53 - 84 * q^55 - 52 * q^56 - 92 * q^57 + 128 * q^58 - 212 * q^61 + 36 * q^63 - 16 * q^67 + 36 * q^68 - 16 * q^70 - 16 * q^71 + 12 * q^73 + 132 * q^75 - 16 * q^77 + 80 * q^78 + 12 * q^80 - 36 * q^81 + 48 * q^82 - 308 * q^83 - 40 * q^85 - 4 * q^86 + 52 * q^87 - 4 * q^88 + 84 * q^90 - 124 * q^91 - 8 * q^92 - 536 * q^93 - 28 * q^95 - 12 * q^96 - 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.804598	+	0.593820i	0.568937	+	0.419894i
$2$	0.804598	+	0.593820i	0.568937	+	0.419894i
$3$	−0.000114150	0	0.000603296i	−6.59044e−5	0	0.000348313i	0.982534	−	0.186086i	$-0.0595802\pi$
$3$	−0.000114150	0	0.000603296i	−6.59044e−5	0	0.000348313i	−0.982599	+	0.185737i	$0.940533\pi$
$4$	0.294755	+	0.955573i	0.147378	+	0.477786i
$5$	−0.873857	−	2.05825i	−0.390801	−	0.920475i
$5$	−0.873857	−	2.05825i	−0.390801	−	0.920475i
$6$	0.000266405	0	0.000553195i	0.000108759	0	0.000225841i
$7$	−0.846959	−	2.50652i	−0.320120	−	0.947377i
$7$	−0.846959	−	2.50652i	−0.320120	−	0.947377i
$8$	−0.330279	+	0.943883i	−0.116771	+	0.333713i
$9$	2.79262	−	1.09602i	0.930874	−	0.365341i
$10$	0.519124	−	2.17497i	0.164161	−	0.687787i
$11$	0.156322	−	0.398301i	0.0471327	−	0.120092i	−0.905369	−	0.424626i	$-0.860406\pi$
$11$	0.156322	−	0.398301i	0.0471327	−	0.120092i	0.952501	+	0.304534i	$0.0985007\pi$
$12$	0.000542847	0	0.000286903i	0.000156707	0	8.28218e-5i
$13$	−0.0674675	+	0.598790i	−0.0187121	+	0.166075i	−0.999593	−	0.0285356i	$-0.990916\pi$
$13$	−0.0674675	+	0.598790i	−0.0187121	+	0.166075i	0.980881	+	0.194610i	$0.0623442\pi$
$14$	0.806963	−	2.51968i	0.215670	−	0.673414i
$15$	−0.00114198		0.000762143i	−0.000294858		0.000196785i
$16$	−0.826239	+	0.563320i	−0.206560	+	0.140830i
$17$	0.0657864	−	1.75818i	0.0159555	−	0.426421i	−0.968313	−	0.249741i	$-0.919655\pi$
$17$	0.0657864	−	1.75818i	0.0159555	−	0.426421i	0.984268	−	0.176680i	$-0.0565358\pi$
$18$	2.89778	+	0.776457i	0.683013	+	0.183013i
$19$	3.69043	−	6.39202i	0.846643	−	1.46643i	−0.0375434	−	0.999295i	$-0.511953\pi$
$19$	3.69043	−	6.39202i	0.846643	−	1.46643i	0.884187	−	0.467134i	$-0.154713\pi$
$20$	1.70923	−	1.44171i	0.382195	−	0.322377i
$21$	−0.00141550		0.000797086i	−0.000308887		0.000173938i
$22$	0.362295	−	0.227645i	0.0772416	−	0.0485341i
$23$	0.287027	−	0.0107398i	0.0598492	−	0.00223940i	−0.00744982	−	0.999972i	$-0.502371\pi$
$23$	0.287027	−	0.0107398i	0.0598492	−	0.00223940i	0.0672990	+	0.997733i	$0.478562\pi$
$24$	0.000607143	0	9.15120e-5i	0.000123932	0	1.86798e-5i
$25$	−3.47275	+	3.59723i	−0.694549	+	0.719445i
$26$	−0.409858	+	0.441722i	−0.0803798	+	0.0866288i
$27$	−0.00196001	−	0.00311933i	−0.000377204	−	0.000600316i
$28$	2.14552	−	1.54814i	0.405465	−	0.292571i
$29$	1.89914	−	0.433466i	0.352661	−	0.0804926i	−0.0425205	−	0.999096i	$-0.513539\pi$
$29$	1.89914	−	0.433466i	0.352661	−	0.0804926i	0.395182	+	0.918603i	$0.370682\pi$
$30$	−0.00137141		6.49127e-5i	−0.000250384		1.18514e-5i
$31$	1.61357	−	0.931593i	0.289805	−	0.167319i	−0.348049	−	0.937476i	$-0.613156\pi$
$31$	1.61357	−	0.931593i	0.289805	−	0.167319i	0.637854	+	0.770157i	$0.279822\pi$
$32$	−0.999301	−	0.0373912i	−0.176653	−	0.00660989i
$33$	−0.000258137	0	4.88422e-5i	−4.49360e−5	0	8.50234e-6i
$34$	1.09697	−	1.37556i	0.188129	−	0.235907i
$35$	−4.41892	+	3.93359i	−0.746934	+	0.664899i
$36$	1.87047	+	2.34549i	0.311745	+	0.390916i
$37$	3.11213	+	5.88844i	0.511632	+	0.968054i	0.995666	+	0.0930051i	$0.0296473\pi$
$37$	3.11213	+	5.88844i	0.511632	+	0.968054i	−0.484034	+	0.875049i	$0.660829\pi$
$38$	6.76502	−	2.95155i	1.09743	−	0.478804i
$39$	0.000368949	0	2.76489e-5i	5.90792e−5	0	4.42737e-6i
$40$	2.23136	−	0.145024i	0.352809	−	0.0229303i
$41$	1.46758	+	3.04746i	0.229197	+	0.475933i	0.983573	−	0.180510i	$-0.0577747\pi$
$41$	1.46758	+	3.04746i	0.229197	+	0.475933i	−0.754376	+	0.656443i	$0.772060\pi$
$42$	−0.00161223		0.000199216i	−0.000248773		3.07398e-5i
$43$	0.496324	−	0.173671i	0.0756887	−	0.0264846i	−0.292169	−	0.956367i	$-0.594377\pi$
$43$	0.496324	−	0.173671i	0.0756887	−	0.0264846i	0.367858	+	0.929882i	$0.380091\pi$
$44$	0.426682	+	0.0319754i	0.0643247	+	0.00482047i
$45$	−4.69624	−	4.79013i	−0.700074	−	0.714071i
$46$	0.237319	+	0.161801i	0.0349907	+	0.0238563i
$47$	−3.23788	+	4.38717i	−0.472293	+	0.639934i	−0.974387	−	0.224879i	$-0.927801\pi$
$47$	−3.23788	+	4.38717i	−0.472293	+	0.639934i	0.502094	+	0.864813i	$0.332563\pi$
$48$	0.000434164	0	0.000434164i	6.26662e−5	0	6.26662e-5i
$49$	−5.56532	+	4.24584i	−0.795046	+	0.606549i
$50$	−4.93027	+	0.832132i	−0.697245	+	0.117681i
$51$	−0.00106821		0.000161007i	−0.000149580		2.25455e-5i
$52$	−0.592074	+	0.112026i	−0.0821059	+	0.0155353i
$53$	−5.13676	+	9.71923i	−0.705588	+	1.33504i	0.226928	+	0.973911i	$0.427132\pi$
$53$	−5.13676	+	9.71923i	−0.705588	+	1.33504i	−0.932517	+	0.361127i	$0.882392\pi$
$54$	0.000275306	−	0.00367370i	3.74644e−5	−	0.000499927i
$55$	−0.956403	+	0.0263100i	−0.128961	+	0.00354764i
$56$	2.64560	+	0.0284221i	0.353533	+	0.00379806i
$57$	−0.00427754	−	0.00149678i	−0.000566574	−	0.000198253i
$58$	1.78544	+	0.778981i	0.234440	+	0.102285i
$59$	−0.483509	−	6.45198i	−0.0629475	−	0.839977i	−0.935921	−	0.352209i	$-0.885431\pi$
$59$	−0.483509	−	6.45198i	−0.0629475	−	0.839977i	0.872974	−	0.487767i	$-0.162189\pi$
$60$	−0.00106489		0.000866600i	−0.000137476		0.000111878i
$61$	−1.55283	+	5.03415i	−0.198819	+	0.644557i	0.800177	+	0.599764i	$0.204739\pi$
$61$	−1.55283	+	5.03415i	−0.198819	+	0.644557i	−0.998996	+	0.0447927i	$0.985737\pi$
$62$	1.85147	+	0.208611i	0.235137	+	0.0264936i
$63$	−5.11244	−	6.07148i	−0.644107	−	0.764935i
$64$	−0.781831	−	0.623490i	−0.0977289	−	0.0779362i
$65$	1.29141	−	0.384393i	0.160180	−	0.0476780i
$66$	−0.000178693	0	0.000192586i	−2.19956e−5	0	2.37056e-5i
$67$	2.70758	−	10.1048i	0.330783	−	1.23450i	−0.577586	−	0.816330i	$-0.696005\pi$
$67$	2.70758	−	10.1048i	0.330783	−	1.23450i	0.908369	−	0.418170i	$-0.137328\pi$
$68$	1.69946	−	0.455368i	0.206090	−	0.0552215i
$69$	−3.92433e−5	0	0.000171936i	−4.72434e−6	0	2.06987e-5i
$70$	−5.89130	+	0.540916i	−0.704145	+	0.0646519i
$71$	−2.33883	+	10.2471i	−0.277569	+	1.21611i	0.623289	+	0.781992i	$0.285796\pi$
$71$	−2.33883	+	10.2471i	−0.277569	+	1.21611i	−0.900857	+	0.434116i	$0.857061\pi$
$72$	0.112174	+	2.99790i	0.0132198	+	0.353306i
$73$	−5.85225	−	7.92952i	−0.684955	−	0.928081i	0.314823	−	0.949150i	$-0.398055\pi$
$73$	−5.85225	−	7.92952i	−0.684955	−	0.928081i	−0.999778	+	0.0210697i	$0.993293\pi$
$74$	−0.992661	+	6.58588i	−0.115395	+	0.765593i
$75$	0.00256661	+	0.00168447i	0.000296366	+	0.000194506i
$76$	7.19581	+	1.64240i	0.825416	+	0.188396i
$77$	−1.13075	−	0.0544793i	−0.128861	−	0.00620850i
$78$	0.000313274	0	0.000196843i	3.54713e−5	0	2.22881e-5i
$79$	5.95803	+	3.43987i	0.670330	+	0.387015i	0.796202	−	0.605031i	$-0.206839\pi$
$79$	5.95803	+	3.43987i	0.670330	+	0.387015i	−0.125871	+	0.992047i	$0.540173\pi$
$80$	1.88147	+	1.20834i	0.210354	+	0.135097i
$81$	6.59746	−	6.12155i	0.733052	−	0.680172i
$82$	−0.628831	+	3.32345i	−0.0694428	+	0.367014i
$83$	1.30600	−	0.147151i	0.143353	−	0.0161519i	−0.0399966	−	0.999200i	$-0.512735\pi$
$83$	1.30600	−	0.147151i	0.143353	−	0.0161519i	0.183349	+	0.983048i	$0.441306\pi$
$84$	−0.00117890	−	0.00111766i	−0.000128628	−	0.000121947i
$85$	−3.67625	+	1.40099i	−0.398745	+	0.151959i
$86$	0.502471	+	0.154992i	0.0541828	+	0.0167132i
$87$	−0.000478295	−	0.00109626i	−5.12786e−5	−	0.000117532i
$88$	0.324320	+	0.279100i	0.0345726	+	0.0297521i
$89$	−1.25191	−	3.18982i	−0.132702	−	0.338120i	0.849042	−	0.528325i	$-0.177180\pi$
$89$	−1.25191	−	3.18982i	−0.132702	−	0.338120i	−0.981744	+	0.190205i	$0.939085\pi$
$90$	−0.934105	−	6.64285i	−0.0984633	−	0.700218i
$91$	1.55802	−	0.338042i	0.163325	−	0.0354364i
$92$	0.0948653	+	0.271109i	0.00989039	+	0.0282651i
$93$	−0.000746215	0	0.000867118i	−7.73789e−5	0	8.99159e-5i
$94$	−5.21038	+	1.60719i	−0.537409	+	0.165769i
$95$	−16.3812	−	2.01010i	−1.68068	−	0.206232i
$96$	9.15120e−5	0	0.000607143i	9.33991e−6	0	6.19662e-5i
$97$	−0.360693	+	0.360693i	−0.0366228	+	0.0366228i	−0.725181	−	0.688558i	$-0.758244\pi$
$97$	−0.360693	+	0.360693i	−0.0366228	+	0.0366228i	0.688558	+	0.725181i	$0.258244\pi$
$98$	−6.99911	+	0.111396i	−0.707017	+	0.0112527i
$99$		−	1.28364i		−	0.129010i
$100$	−4.46102	−	2.25816i	−0.446102	−	0.225816i
$101$	2.48765	−	3.64871i	0.247530	−	0.363060i	−0.682285	−	0.731086i	$-0.739014\pi$
$101$	2.48765	−	3.64871i	0.247530	−	0.363060i	0.929816	+	0.368026i	$0.119966\pi$
$102$	−0.000955090	0	0.000504780i	−9.45680e−5	0	4.99806e-5i
$103$	−8.43974	+	7.26298i	−0.831592	+	0.715643i	−0.961179	−	0.275925i	$-0.911016\pi$
$103$	−8.43974	+	7.26298i	−0.831592	+	0.715643i	0.129587	+	0.991568i	$0.458635\pi$
$104$	−0.542905	−	0.261449i	−0.0532362	−	0.0256372i
$105$	0.00287754	+	0.00221690i	0.000280819	+	0.000216347i
$106$	−9.90450	+	4.76976i	−0.962010	+	0.463280i
$107$	−1.20343	+	2.75829i	−0.116340	+	0.266654i	−0.964983	−	0.262312i	$-0.915515\pi$
$107$	−1.20343	+	2.75829i	−0.116340	+	0.266654i	0.848643	+	0.528965i	$0.177420\pi$
$108$	0.00240303	−	0.00279237i	0.000231232	−	0.000268696i
$109$	3.11924	+	1.22421i	0.298769	+	0.117258i	0.509991	−	0.860180i	$-0.329649\pi$
$109$	3.11924	+	1.22421i	0.298769	+	0.117258i	−0.211221	+	0.977438i	$0.567744\pi$
$110$	−0.785143	−	0.546763i	−0.0748605	−	0.0521318i
$111$	0.00319723	−	0.00254970i	0.000303467	−	0.000242007i
$112$	2.11177	+	1.59388i	0.199543	+	0.150607i
$113$	1.08071	+	9.59157i	0.101665	+	0.902299i	0.936229	+	0.351389i	$0.114291\pi$
$113$	1.08071	+	9.59157i	0.101665	+	0.902299i	−0.834565	+	0.550910i	$0.814281\pi$
$114$	−0.00255288	−	0.00374439i	−0.000239100	−	0.000350695i
$115$	−0.272926	−	0.581386i	−0.0254504	−	0.0542146i
$116$	0.973989	+	1.68700i	0.0904326	+	0.156634i
$117$	0.467877	+	1.74614i	0.0432552	+	0.161431i
$118$	3.44229	−	5.47837i	0.316888	−	0.504325i
$119$	−4.46263	+	1.32421i	−0.409089	+	0.121390i
$120$	−0.000342202	−	0.00132962i	−3.12386e−5	−	0.000121377i
$121$	7.92936	+	7.35737i	0.720851	+	0.668852i
$122$	−4.23878	+	3.12836i	−0.383761	+	0.283229i
$123$	0.00167100	−	0.00123325i	0.000150669	−	0.000111198i
$124$	1.36581	+	1.26729i	0.122654	+	0.113806i
$125$	10.4387	+	4.00430i	0.933662	+	0.358156i
$126$	−0.508090	−	7.92097i	−0.0452642	−	0.705656i
$127$	5.76642	−	9.17720i	0.511687	−	0.814345i	−0.486553	−	0.873651i	$-0.661746\pi$
$127$	5.76642	−	9.17720i	0.511687	−	0.814345i	0.998240	+	0.0593060i	$0.0188888\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	−0.000161430	0	0.000279606i	−1.42132e−5	0	2.46179e-5i
$130$	1.26733	+	0.457586i	0.111152	+	0.0401330i
$131$	8.40761	+	12.3317i	0.734577	+	1.07743i	0.993754	+	0.111596i	$0.0355963\pi$
$131$	8.40761	+	12.3317i	0.734577	+	1.07743i	−0.259177	+	0.965830i	$0.583451\pi$
$132$	−2.94150e−5	0	0.000261066i	−2.56025e−6	0	2.27228e-5i
$133$	−19.1474	−	3.83638i	−1.66029	−	0.332657i
$134$	8.17895	−	6.52250i	0.706554	−	0.563458i
$135$	−0.00470759	+	0.00676003i	−0.000405165	+	0.000581811i
$136$	1.63779	+	0.642784i	0.140439	+	0.0551183i
$137$	−8.87231	+	10.3098i	−0.758013	+	0.880827i	−0.995900	−	0.0904659i	$-0.971164\pi$
$137$	−8.87231	+	10.3098i	−0.758013	+	0.880827i	0.237887	+	0.971293i	$0.423545\pi$
$138$	7.05241e−5	0	0.000161643i	6.00341e−6	0	1.37600e-5i
$139$	17.2511	−	8.30769i	1.46322	−	0.704649i	0.478385	−	0.878150i	$-0.341222\pi$
$139$	17.2511	−	8.30769i	1.46322	−	0.704649i	0.984834	+	0.173501i	$0.0555081\pi$
$140$	−5.06133	−	3.06315i	−0.427761	−	0.258884i
$141$	0.00301636	+	0.00145260i	0.000254024	+	0.000122331i
$142$	−7.96676	+	6.85595i	−0.668556	+	0.575339i
$143$	0.227952	+	0.120476i	0.0190623	+	0.0100747i
$144$	−1.68996	+	2.47872i	−0.140830	+	0.206560i
$145$	−2.55176	−	3.53011i	−0.211912	−	0.293159i
$146$		−	9.85526i		−	0.815627i
$147$	0.00319678	+	0.00287288i	0.000263666	+	0.000236951i
$148$	−4.70952	+	4.70952i	−0.387120	+	0.387120i
$149$	−0.431980	−	2.86600i	−0.0353892	−	0.234792i	0.964143	−	0.265384i	$-0.0854988\pi$
$149$	−0.431980	−	2.86600i	−0.0353892	−	0.234792i	−0.999532	+	0.0305922i	$0.990261\pi$
$150$	0.00106481	+	0.00287943i	8.69415e−5	+	0.000235104i
$151$	−15.6662	+	4.83238i	−1.27490	+	0.393253i	−0.857035	−	0.515258i	$-0.827696\pi$
$151$	−15.6662	+	4.83238i	−1.27490	+	0.393253i	−0.417861	+	0.908511i	$0.637220\pi$
$152$	4.81444	+	5.59449i	0.390503	+	0.453773i
$153$	−1.74329	−	4.98203i	−0.140936	−	0.402773i
$154$	−0.877447	−	0.715295i	−0.0707067	−	0.0576401i
$155$	−3.32747	−	2.50704i	−0.267269	−	0.201370i
$156$	0.000135170	0	0.000344408i	1.08223e−5	0	2.75747e-5i
$157$	8.23166	+	7.08391i	0.656958	+	0.565358i	0.916332	−	0.400419i	$-0.131135\pi$
$157$	8.23166	+	7.08391i	0.656958	+	0.565358i	−0.259375	+	0.965777i	$0.583516\pi$
$158$	2.75115	+	6.30571i	0.218870	+	0.501655i
$159$	0.00644993	+	0.00198954i	0.000511513	+	0.000157781i
$160$	0.796286	+	2.08948i	0.0629519	+	0.165188i
$161$	−0.270019	−	0.710343i	−0.0212805	−	0.0559829i
$162$	8.94341	−	1.00768i	0.702660	−	0.0791708i
$163$	3.44954	−	18.2313i	0.270189	−	1.42798i	−0.539927	−	0.841712i	$-0.681548\pi$
$163$	3.44954	−	18.2313i	0.270189	−	1.42798i	0.810116	−	0.586270i	$-0.199404\pi$
$164$	−2.47949	+	2.30063i	−0.193616	+	0.179649i
$165$	0.000125046	0	0.000573991i	9.73482e−6	0	4.46852e-5i
$166$	1.13819	+	0.657134i	0.0883406	+	0.0510035i
$167$	−10.1637	−	6.38630i	−0.786494	−	0.494187i	0.0779251	−	0.996959i	$-0.475170\pi$
$167$	−10.1637	−	6.38630i	−0.786494	−	0.494187i	−0.864419	+	0.502773i	$0.832313\pi$
$168$	−0.000284848	−	0.00159932i	−2.19765e−5	−	0.000123391i
$169$	12.3201	+	2.81197i	0.947697	+	0.216306i
$170$	−3.78984	−	1.05580i	−0.290667	−	0.0809758i
$171$	3.30018	−	21.8953i	0.252371	−	1.67437i
$172$	0.312250	+	0.423083i	0.0238088	+	0.0322598i
$173$	0.881266	+	23.5523i	0.0670014	+	1.79065i	0.477342	+	0.878717i	$0.341600\pi$
$173$	0.881266	+	23.5523i	0.0670014	+	1.79065i	−0.410341	+	0.911932i	$0.634590\pi$
$174$	0.000266148	−	0.00116607i	2.01767e−5	−	8.83997e-5i
$175$	11.9578	+	5.65782i	0.903925	+	0.427691i
$176$	0.0952119	+	0.417151i	0.00717687	+	0.0314439i
$177$	−0.00383726	+	0.00102819i	−0.000288426	+	7.72836e-5i
$178$	0.886893	−	3.30993i	0.0664754	−	0.248090i
$179$	−16.6570	−	17.9520i	−1.24500	−	1.34179i	−0.917904	−	0.396804i	$-0.870119\pi$
$179$	−16.6570	−	17.9520i	−1.24500	−	1.34179i	−0.327099	−	0.944990i	$-0.606071\pi$
$180$	3.19308	−	5.89951i	0.237998	−	0.439724i
$181$	14.3920	+	11.4773i	1.06975	+	0.853098i	0.989623	−	0.143687i	$-0.0458958\pi$
$181$	14.3920	+	11.4773i	1.06975	+	0.853098i	0.0801274	+	0.996785i	$0.474467\pi$
$182$	1.45432	+	0.653199i	0.107801	+	0.0484183i
$183$	0.00321434		0.000362169i	0.000237611		2.67723e-5i
$184$	−0.0846618	+	0.274467i	−0.00624135	+	0.0202340i
$185$	9.40030	−	11.5512i	0.691124	−	0.849261i
$186$	−8.54910e−5	−	0.00114080i	−6.26851e−6	−	8.36474e-5i
$187$	−0.690000	−	0.301044i	−0.0504578	−	0.0220145i
$188$	−5.14664	−	1.80089i	−0.375357	−	0.131343i
$189$	−0.00615864	+	0.00755475i	−0.000447975	+	0.000549527i
$190$	−11.9867	−	11.3448i	−0.869605	−	0.823041i
$191$	−0.440891	+	5.88328i	−0.0319017	+	0.425699i	0.958272	+	0.285857i	$0.0922784\pi$
$191$	−0.440891	+	5.88328i	−0.0319017	+	0.425699i	−0.990174	+	0.139842i	$0.955341\pi$
$192$	−0.000286903	0	0.000542847i	−2.07055e−5	0	3.91766e-5i
$193$	−14.3205	+	2.70959i	−1.03081	+	0.195040i	−0.673688	−	0.739016i	$-0.735291\pi$
$193$	−14.3205	+	2.70959i	−1.03081	+	0.195040i	−0.357125	+	0.934057i	$0.616243\pi$
$194$	−0.504399	+	0.0760260i	−0.0362138	+	0.00545835i
$195$	−0.000379317	0	0.000735227i	−2.71635e−5	0	5.26507e-5i
$196$	−5.69762	−	4.06659i	−0.406973	−	0.290470i
$197$	16.9406	+	16.9406i	1.20697	+	1.20697i	0.972004	+	0.234964i	$0.0754973\pi$
$197$	16.9406	+	16.9406i	1.20697	+	1.20697i	0.234964	+	0.972004i	$0.424503\pi$
$198$	0.762248	−	1.03281i	0.0541706	−	0.0733986i
$199$	12.0394	+	8.20830i	0.853448	+	0.581871i	0.909099	−	0.416579i	$-0.136771\pi$
$199$	12.0394	+	8.20830i	0.853448	+	0.581871i	−0.0556515	+	0.998450i	$0.517724\pi$
$200$	−2.24839	−	4.46596i	−0.158985	−	0.315791i
$201$	−0.00640527		0.000480008i	−0.000451793		3.38572e-5i
$202$	4.16823	−	1.45853i	0.293276	−	0.102622i
$203$	−2.69499	−	4.39311i	−0.189151	−	0.308336i
$204$	−0.000468715	0	0.000973296i	−3.28166e−5	0	6.81444e-5i
$205$	4.98996	−	5.68368i	0.348514	−	0.396965i
$206$	−11.1035	+	0.832092i	−0.773617	+	0.0579746i
$207$	0.789786	−	0.344580i	0.0548939	−	0.0239500i
$208$	−0.281566	−	0.532750i	−0.0195231	−	0.0369395i
$209$	−1.96905	−	2.46911i	−0.136202	−	0.170792i
$210$	0.000998824		0.00349245i	6.89254e−5		0.000241002i
$211$	−1.52899	+	1.91730i	−0.105260	+	0.131992i	−0.831671	−	0.555268i	$-0.812616\pi$
$211$	−1.52899	+	1.91730i	−0.105260	+	0.131992i	0.726411	+	0.687261i	$0.241187\pi$
$212$	−10.8015	−	2.04376i	−0.741851	−	0.140366i
$213$	0.00644902		0.000241305i	0.000441879		1.65340e-5i
$214$	−2.60620	+	1.50469i	−0.178156	+	0.102859i
$215$	−0.791174	−	0.869792i	−0.0539576	−	0.0593193i
$216$	0.00359164		0.000819768i	0.000244380		5.57781e-5i
$217$	−3.70169	−	3.25542i	−0.251287	−	0.220992i
$218$	1.78277	+	2.83727i	0.120745	+	0.192164i
$219$	−0.00411582	+	0.00443580i	−0.000278121	+	0.000299743i
$220$	−0.307046	−	0.906158i	−0.0207010	−	0.0610932i
$221$	1.04834	+	0.158012i	0.0705191	+	0.0106290i
$222$	0.00408655		0.000152908i	0.000274271		1.02625e-5i
$223$	2.15022	−	1.35107i	0.143989	−	0.0904743i	−0.458111	−	0.888895i	$-0.651474\pi$
$223$	2.15022	−	1.35107i	0.143989	−	0.0904743i	0.602100	+	0.798421i	$0.294331\pi$
$224$	0.752645	+	2.53644i	0.0502882	+	0.169473i
$225$	−5.75542	+	13.8519i	−0.383695	+	0.923460i
$226$	−4.82613	+	8.35910i	−0.321029	+	0.556039i
$227$	−6.93333	−	1.85778i	−0.460181	−	0.123305i	0.0212782	−	0.999774i	$-0.493226\pi$
$227$	−6.93333	−	1.85778i	−0.460181	−	0.123305i	−0.481459	+	0.876468i	$0.659893\pi$
$228$	0.000169451	−	0.00452869i	1.12222e−5	−	0.000299920i
$229$	21.7334	−	14.8176i	1.43618	−	0.979174i	0.439464	−	0.898260i	$-0.355169\pi$
$229$	21.7334	−	14.8176i	1.43618	−	0.979174i	0.996721	−	0.0809137i	$-0.0257838\pi$
$230$	0.125644	−	0.629851i	0.00828470	−	0.0415311i
$231$	9.62075e−5	0	0.000688395i	6.32999e−6	0	4.52931e-5i
$232$	−0.218104	+	1.93573i	−0.0143193	+	0.127087i
$233$	15.9414	−	8.42525i	1.04435	−	0.551957i	0.145114	−	0.989415i	$-0.453645\pi$
$233$	15.9414	−	8.42525i	1.04435	−	0.551957i	0.899239	+	0.437458i	$0.144121\pi$
$234$	−0.660441	+	1.68278i	−0.0431744	+	0.110006i
$235$	11.8593	+	2.83059i	0.773616	+	0.184647i
$236$	6.02282	−	2.36378i	0.392052	−	0.153869i
$237$	0.00139515	−	0.00398712i	9.06249e−5	−	0.000258991i
$238$	−4.37697	−	1.58455i	−0.283717	−	0.102711i
$239$	4.80039	−	9.96811i	0.310511	−	0.644784i	−0.686058	−	0.727547i	$-0.740660\pi$
$239$	4.80039	−	9.96811i	0.310511	−	0.644784i	0.996569	+	0.0827634i	$0.0263746\pi$
$240$	0.000514219	−	0.00127301i	3.31927e−5	−	8.21726e-5i
$241$	−0.351891	−	1.14080i	−0.0226673	−	0.0734855i	0.943533	−	0.331280i	$-0.107480\pi$
$241$	−0.351891	−	1.14080i	−0.0226673	−	0.0734855i	−0.966200	+	0.257794i	$0.917004\pi$
$242$	2.01099	+	10.6283i	0.129271	+	0.683216i
$243$	−0.0133386	−	0.00984436i	−0.000855674	−	0.000631516i
$244$	−5.26820			−0.337262
$245$	13.6023	+	7.74454i	0.869018	+	0.494780i
$246$	0.00207681			0.000132412
$247$	3.57849	+	2.64105i	0.227694	+	0.168046i
$248$	0.346388	+	1.83070i	0.0219957	+	0.116250i
$249$	−0.000237856	0	0.000771110i	−1.50735e−5	0	4.88671e-5i
$250$	6.02108	+	9.42054i	0.380807	+	0.595807i
$251$	−2.02839	+	4.21199i	−0.128031	+	0.265858i	−0.955124	−	0.296206i	$-0.904278\pi$
$251$	−2.02839	+	4.21199i	−0.128031	+	0.265858i	0.827093	+	0.562064i	$0.189993\pi$
$252$	4.29483	−	6.67491i	0.270549	−	0.420480i
$253$	0.0405908	−	0.116002i	0.00255192	−	0.00729297i
$254$	10.0893	−	3.95974i	0.633056	−	0.248456i
$255$	0.00126486	+	0.00205794i	7.92084e−5	+	0.000128873i
$256$	0.365341	−	0.930874i	0.0228338	−	0.0581796i
$257$	−20.8065	+	10.9966i	−1.29787	+	0.685946i	−0.966284	−	0.257478i	$-0.917109\pi$
$257$	−20.8065	+	10.9966i	−1.29787	+	0.685946i	−0.331589	+	0.943424i	$0.607585\pi$
$258$	3.61490e−5	0	0.000320831i	2.25054e−6	0	1.99741e-5i
$259$	12.1237	−	12.7879i	0.753329	−	0.794602i
$260$	0.747966	+	1.12074i	0.0463869	+	0.0695053i
$261$	4.82849	−	3.29201i	0.298876	−	0.203770i
$262$	−0.558068	+	14.9147i	−0.0344775	+	0.921431i
$263$	4.47899	+	1.20014i	0.276186	+	0.0740039i	0.394254	−	0.919002i	$-0.371003\pi$
$263$	4.47899	+	1.20014i	0.276186	+	0.0740039i	−0.118067	+	0.993006i	$0.537670\pi$
$264$	0.000131359	0	0.000227520i	8.08457e−6	0	1.40029e-5i
$265$	24.4933	+	2.07950i	1.50461	+	0.127742i
$266$	−13.1278	−	14.4568i	−0.804918	−	0.886406i
$267$	−0.00178150	+	0.00111939i	−0.000109026	+	6.85056e-5i
$268$	10.4540	−	0.391160i	0.638577	−	0.0238939i
$269$	−27.7433	−	4.18163i	−1.69154	−	0.254959i	−0.768552	−	0.639787i	$-0.779023\pi$
$269$	−27.7433	−	4.18163i	−1.69154	−	0.254959i	−0.922988	+	0.384828i	$0.874261\pi$
$270$	−0.00780196	+	0.00264364i	−0.000474812	+	0.000160887i
$271$	−1.13657	+	1.22494i	−0.0690419	+	0.0744095i	−0.766628	−	0.642091i	$-0.778067\pi$
$271$	−1.13657	+	1.22494i	−0.0690419	+	0.0744095i	0.697586	+	0.716501i	$0.254257\pi$
$272$	0.936061	+	1.48973i	0.0567571	+	0.0903283i
$273$	−0.000381788	0	0.000901363i	−2.31068e−5	0	5.45530e-5i
$274$	−13.2608	+	3.02670i	−0.801116	+	0.182849i
$275$	0.889913	+	1.94552i	0.0536637	+	0.117319i
$276$	0.000152730	0	8.81789e-5i	9.19329e−6	0	5.30775e-6i
$277$	22.2648	+	0.833092i	1.33777	+	0.0500556i	0.696662	−	0.717399i	$-0.254668\pi$
$277$	22.2648	+	0.833092i	1.33777	+	0.0500556i	0.641103	+	0.767455i	$0.278477\pi$
$278$	18.8135	+	3.55970i	1.12836	+	0.213497i
$279$	3.48503	−	4.37009i	0.208643	−	0.261631i
$280$	−2.25338	−	5.47013i	−0.134665	−	0.326903i
$281$	5.05842	+	6.34306i	0.301760	+	0.378395i	0.909474	−	0.415761i	$-0.136485\pi$
$281$	5.05842	+	6.34306i	0.301760	+	0.378395i	−0.607714	+	0.794156i	$0.707913\pi$
$282$	0.00156437	+	0.00295994i	9.31571e−5	+	0.000176262i
$283$	23.3195	−	10.1742i	1.38620	−	0.604793i	0.431432	−	0.902146i	$-0.358009\pi$
$283$	23.3195	−	10.1742i	1.38620	−	0.604793i	0.954768	+	0.297353i	$0.0961038\pi$
$284$	−10.4812	+	0.785460i	−0.621947	+	0.0466085i
$285$	0.000657228		0.0101122i	3.89308e−5		0.000598995i
$286$	0.111869	+	0.232297i	0.00661492	+	0.0137360i
$287$	6.39554	−	6.25959i	0.377517	−	0.369492i
$288$	−2.83165	+	0.990837i	−0.166857	+	0.0583856i
$289$	13.8656	+	1.03908i	0.815624	+	0.0611226i
$290$	0.0431111	−	4.35560i	0.00253157	−	0.255770i
$291$	0.000258778	0	0.000176432i	1.51698e−5	0	1.03426e-5i
$292$	5.85225	−	7.92952i	0.342477	−	0.464040i
$293$	−6.31038	−	6.31038i	−0.368656	−	0.368656i	0.498331	−	0.866987i	$-0.333947\pi$
$293$	−6.31038	−	6.31038i	−0.368656	−	0.368656i	−0.866987	+	0.498331i	$0.833947\pi$
$294$	0.000866152		0.00420982i	5.05150e−5		0.000245522i
$295$	−12.8572	+	6.63329i	−0.748578	+	0.386205i
$296$	−6.58588	+	0.992661i	−0.382796	+	0.0576973i
$297$	−0.00154882		0.000293053i	−8.98719e−5		1.70047e-5i
$298$	1.35432	−	2.56250i	0.0784536	−	0.148441i
$299$	−0.0129341	+	0.172593i	−0.000747998	+	0.00998133i
$300$	−0.000853116		0.00294909i	−4.92547e−5		0.000170266i
$301$	−0.855677	−	1.09696i	−0.0493204	−	0.0632274i
$302$	−15.4745	−	5.41478i	−0.890460	−	0.311585i
$303$	−0.00248522	−	0.00108429i	−0.000142772	−	6.22908e-5i
$304$	0.551573	+	7.36023i	0.0316349	+	0.422138i
$305$	11.7185	−	1.20302i	0.670997	−	0.0688850i
$306$	1.55578	−	5.04373i	0.0889382	−	0.288331i
$307$	−25.3695	−	2.85846i	−1.44792	−	0.163141i	−0.647262	−	0.762268i	$-0.724086\pi$
$307$	−25.3695	−	2.85846i	−1.44792	−	0.163141i	−0.800654	+	0.599127i	$0.795515\pi$
$308$	−0.281235	−	1.09657i	−0.0160248	−	0.0624829i
$309$	0.00534512	+	0.00426259i	0.000304073	+	0.000242491i
$310$	−1.18855	−	3.99308i	−0.0675051	−	0.226792i
$311$	−13.0564	−	14.0715i	−0.740363	−	0.797922i	0.244794	−	0.969575i	$-0.421280\pi$
$311$	−13.0564	−	14.0715i	−0.740363	−	0.797922i	−0.985157	+	0.171653i	$0.945089\pi$
$312$	−9.57589e−5	0	0.000357377i	−5.42128e−6	0	2.02325e-5i
$313$	−12.1475	+	3.25490i	−0.686614	+	0.183978i	−0.585227	−	0.810869i	$-0.698995\pi$
$313$	−12.1475	+	3.25490i	−0.686614	+	0.183978i	−0.101387	+	0.994847i	$0.532328\pi$
$314$	2.41660	+	10.5878i	0.136377	+	0.597505i
$315$	−8.02906	+	15.8283i	−0.452386	+	0.891822i
$316$	−1.53089	+	6.70725i	−0.0861190	+	0.377312i
$317$	−0.396267	−	10.5905i	−0.0222566	−	0.594819i	−0.965146	−	0.261713i	$-0.915713\pi$
$317$	−0.396267	−	10.5905i	−0.0222566	−	0.594819i	0.942889	−	0.333106i	$-0.108097\pi$
$318$	0.00400817	+	0.00543088i	0.000224767	+	0.000304549i
$319$	0.124226	−	0.824189i	0.00695535	−	0.0461457i
$320$	−0.600086	+	2.15404i	−0.0335458	+	0.120415i
$321$	0.00180143		0.000411166i	0.000100546		2.29490e-5i
$322$	0.204559	−	0.731883i	0.0113996	−	0.0407863i
$323$	−10.9955	−	6.90894i	−0.611807	−	0.384424i
$324$	7.79423	+	4.50000i	0.433013	+	0.250000i
$325$	−1.91969	−	2.32214i	−0.106485	−	0.128809i
$326$	13.6016	−	12.6204i	0.753322	−	0.698980i
$327$	0.000382502	−	0.00202157i	2.11524e−5	−	0.000111793i
$328$	−3.36115	+	0.378711i	−0.185589	+	0.0209108i
$329$	13.7389	+	4.40006i	0.757449	+	0.242583i
$330$	−0.000240236	0	0.000536087i	−1.32246e−5	0	2.95106e-5i
$331$	9.65091	+	2.97691i	0.530462	+	0.163626i	0.548404	−	0.836213i	$-0.315235\pi$
$331$	9.65091	+	2.97691i	0.530462	+	0.163626i	−0.0179427	+	0.999839i	$0.505712\pi$
$332$	0.525565	+	1.20461i	0.0288441	+	0.0661114i
$333$	15.1449	+	13.0332i	0.829934	+	0.714216i
$334$	−4.38541	−	11.1738i	−0.239959	−	0.611405i
$335$	−23.1642	+	3.25731i	−1.26560	+	0.177966i
$336$	0.000720523	−	0.00145596i	3.93078e−5	−	7.94292e-5i
$337$	1.37358	+	3.92547i	0.0748238	+	0.213834i	0.975220	−	0.221236i	$-0.0710092\pi$
$337$	1.37358	+	3.92547i	0.0748238	+	0.213834i	−0.900396	+	0.435070i	$0.856723\pi$
$338$	8.24289	+	9.57841i	0.448354	+	0.520997i
$339$	0.00566320	−	0.00174686i	0.000307583	−	9.48767e-5i
$340$	−2.42234	−	3.09997i	−0.131370	−	0.168120i
$341$	−0.118819	−	0.788313i	−0.00643441	−	0.0426895i
$342$	15.6572	−	15.6572i	0.846643	−	0.846643i
$343$	15.3559	+	10.3536i	0.829141	+	0.559040i
$344$			0.525832i			0.0283509i
$345$	−0.000319594	0	0.000231020i	−1.72064e−5	0	1.24377e-5i
$346$	−13.2768	+	19.4735i	−0.713764	+	1.04690i
$347$	−28.6173	−	15.1247i	−1.53626	−	0.811935i	−0.536762	−	0.843734i	$-0.680353\pi$
$347$	−28.6173	−	15.1247i	−1.53626	−	0.811935i	−0.999494	+	0.0317986i	$0.989876\pi$
$348$	0.000906580	0	0.000780175i	4.85978e−5	0	4.18218e-5i
$349$	−14.7670	−	7.11141i	−0.790459	−	0.380665i	−0.00532088	−	0.999986i	$-0.501694\pi$
$349$	−14.7670	−	7.11141i	−0.790459	−	0.380665i	−0.785138	+	0.619321i	$0.787408\pi$
$350$	6.26149	+	11.6531i	0.334691	+	0.622882i
$351$	0.00200006		0.000963180i	0.000106756		5.14107e-5i
$352$	−0.171105	+	0.392177i	−0.00911994	+	0.0209031i
$353$	−7.53365	+	8.75427i	−0.400976	+	0.465943i	−0.921768	−	0.387741i	$-0.873256\pi$
$353$	−7.53365	+	8.75427i	−0.400976	+	0.465943i	0.520792	+	0.853683i	$0.325637\pi$
$354$	−0.00369802	−	0.00145136i	−0.000196547	−	7.71391e-5i
$355$	23.1349	−	4.14061i	1.22787	−	0.219761i
$356$	2.67910	−	2.13651i	0.141992	−	0.113235i
$357$	0.00130830	+	0.00254113i	6.92425e−5	+	0.000134491i
$358$	−2.74194	−	24.3354i	−0.144916	−	1.28616i
$359$	5.14280	+	7.54311i	0.271427	+	0.398110i	0.937616	−	0.347673i	$-0.113028\pi$
$359$	5.14280	+	7.54311i	0.271427	+	0.398110i	−0.666189	+	0.745783i	$0.732076\pi$
$360$	6.07239	−	2.85062i	0.320043	−	0.150241i
$361$	−17.7386	−	30.7241i	−0.933609	−	1.61706i
$362$	4.76436	+	17.7808i	0.250409	+	0.934541i
$363$	0.00353354	−	0.00562360i	0.000185463	−	0.000295162i
$364$	0.782259	+	1.38917i	0.0410015	+	0.0728121i
$365$	−11.2069	+	18.9746i	−0.586594	+	0.993178i
$366$	0.00237119	+	0.00220014i	0.000123944	+	0.000115003i
$367$	22.6372	−	16.7070i	1.18165	−	0.872098i	0.187733	−	0.982220i	$-0.439886\pi$
$367$	22.6372	−	16.7070i	1.18165	−	0.872098i	0.993918	+	0.110122i	$0.0351241\pi$
$368$	−0.231103	+	0.170562i	−0.0120471	+	0.00889113i
$369$	7.43847	+	6.90189i	0.387231	+	0.359298i
$370$	14.4228	−	3.71198i	0.749805	−	0.192976i
$371$	28.7121	+	4.64363i	1.49066	+	0.241085i
$372$	0.000608643	0	0.000968650i	3.15567e−5	0	5.02222e-5i
$373$	−5.96815	−	22.2734i	−0.309019	−	1.15327i	−0.929430	−	0.368998i	$-0.879701\pi$
$373$	−5.96815	−	22.2734i	−0.309019	−	1.15327i	0.620411	−	0.784277i	$-0.286966\pi$
$374$	−0.376406	−	0.651955i	−0.0194635	−	0.0337118i
$375$	0.00122421	−	0.00675469i	6.32180e−5	−	0.000348811i
$376$	−3.07157	−	4.50517i	−0.158404	−	0.232336i
$377$	0.131425	+	1.16643i	0.00676874	+	0.0600742i
$378$	−0.00944139	+	0.00242141i	−0.000485613	+	0.000124544i
$379$	−8.97023	+	7.15352i	−0.460770	+	0.367452i	−0.826191	−	0.563391i	$-0.809497\pi$
$379$	−8.97023	+	7.15352i	−0.460770	+	0.367452i	0.365421	+	0.930842i	$0.380925\pi$
$380$	−2.90766	−	16.2460i	−0.149160	−	0.833400i
$381$	−0.00619481	−	0.00243128i	−0.000317370	−	0.000124558i
$382$	−3.84835	+	4.47186i	−0.196899	+	0.228800i
$383$	−4.07294	+	9.33528i	−0.208118	+	0.477011i	−0.989046	−	0.147610i	$-0.952842\pi$
$383$	−4.07294	+	9.33528i	−0.208118	+	0.477011i	0.780928	+	0.624621i	$0.214747\pi$
$384$	−0.000553195	0	0.000266405i	−2.82301e−5	0	1.35949e-5i
$385$	0.875981	+	2.37496i	0.0446441	+	0.121039i
$386$	−13.1313	−	6.32368i	−0.668363	−	0.321867i
$387$	1.19570	−	1.02898i	0.0607807	−	0.0523060i
$388$	−0.450984	−	0.238352i	−0.0228953	−	0.0121005i
$389$	1.62340	−	2.38109i	0.0823098	−	0.120726i	−0.782876	−	0.622178i	$-0.786248\pi$
$389$	1.62340	−	2.38109i	0.0823098	−	0.120726i	0.865186	+	0.501452i	$0.167200\pi$
$390$	0.000131395	0	0.000816808i	6.65343e−6	0	4.13607e-5i
$391$		−	0.505350i		−	0.0255567i
$392$	−2.16947	−	6.65533i	−0.109575	−	0.336145i
$393$	0.00647994	−	0.00647994i	0.000326870	−	0.000326870i
$394$	3.57070	+	23.6900i	0.179889	+	1.19349i
$395$	1.87363	−	15.2690i	0.0942724	−	0.768268i
$396$	1.22661	−	0.378358i	0.0616393	−	0.0190132i
$397$	−18.8484	−	21.9022i	−0.945974	−	1.09924i	−0.994943	−	0.100441i	$-0.967975\pi$
$397$	−18.8484	−	21.9022i	−0.945974	−	1.09924i	0.0489694	−	0.998800i	$-0.484406\pi$
$398$	4.81259	+	13.7536i	0.241233	+	0.689405i
$399$	−0.000128805		0.0119895i	−6.44831e−6		0.000600224i
$400$	0.842929	−	4.92843i	0.0421464	−	0.246422i
$401$	−4.91089	−	12.5127i	−0.245238	−	0.624856i	0.754259	−	0.656577i	$-0.227996\pi$
$401$	−4.91089	−	12.5127i	−0.245238	−	0.624856i	−0.999497	+	0.0317211i	$0.989901\pi$
$402$	−0.00486862	−	0.00418979i	−0.000242825	−	0.000208968i
$403$	0.448966	+	1.02904i	0.0223646	+	0.0512602i
$404$	4.21985	+	1.30165i	0.209946	+	0.0647596i
$405$	−18.3649	−	8.22984i	−0.912559	−	0.408944i
$406$	0.440338	−	5.13502i	0.0218536	−	0.254847i
$407$	2.83187	−	0.319075i	0.140370	−	0.0158159i
$408$	0.000200836	−	0.00106144i	9.94287e−6	−	5.25493e-5i
$409$	−15.0142	+	13.9312i	−0.742406	+	0.688852i	−0.957723	−	0.287692i	$-0.907112\pi$
$409$	−15.0142	+	13.9312i	−0.742406	+	0.688852i	0.215317	+	0.976544i	$0.430922\pi$
$410$	7.38999	−	1.60994i	0.364966	−	0.0795090i
$411$	0.00723265	+	0.00417577i	0.000356760	+	0.000205976i
$412$	−9.42796	−	5.92398i	−0.464482	−	0.291854i
$413$	−15.7625	+	6.67649i	−0.775624	+	0.328529i
$414$	0.840078	+	0.191742i	0.0412876	+	0.00942363i
$415$	−1.44413	−	2.55949i	−0.0708898	−	0.125640i
$416$	0.0898098	−	0.595849i	0.00440329	−	0.0292139i
$417$	−0.00698121	−	0.00945920i	−0.000341871	−	0.000463219i
$418$	−0.118086	−	3.15590i	−0.00577576	−	0.154360i
$419$	−2.95014	+	12.9254i	−0.144124	+	0.631448i	0.850328	+	0.526253i	$0.176404\pi$
$419$	−2.95014	+	12.9254i	−0.144124	+	0.631448i	−0.994452	+	0.105195i	$0.966453\pi$
$420$	−0.00127024	+	0.00340314i	−6.19813e−5	+	0.000166056i
$421$	−7.12232	−	31.2049i	−0.347121	−	1.52084i	−0.783683	−	0.621161i	$-0.786661\pi$
$421$	−7.12232	−	31.2049i	−0.347121	−	1.52084i	0.436562	−	0.899674i	$-0.356196\pi$
$422$	−2.36876	+	0.634706i	−0.115309	+	0.0308970i
$423$	−4.23373	+	15.8005i	−0.205851	+	0.768246i
$424$	−7.47725	−	8.05856i	−0.363127	−	0.391358i
$425$	6.09610	+	6.34235i	0.295704	+	0.307649i
$426$	0.00504557	+	0.00402371i	0.000244459	+	0.000194949i
$427$	13.9334	−	0.371513i	0.674284	−	0.0179788i
$428$	−2.99046	−	0.336944i	−0.144549	−	0.0162868i
$429$	4.66621e−5	0	0.000151275i	2.25287e−6	0	7.30362e-6i
$430$	−0.120077	−	1.16965i	−0.00579062	−	0.0564054i
$431$	0.0907812	+	1.21139i	0.00437278	+	0.0583506i	0.998963	−	0.0455228i	$-0.0144954\pi$
$431$	0.0907812	+	1.21139i	0.00437278	+	0.0583506i	−0.994591	+	0.103873i	$0.966876\pi$
$432$	0.00337662	+	0.00147320i	0.000162458	+	7.08795e-5i
$433$	−12.6073	−	4.41149i	−0.605869	−	0.212003i	0.00987212	−	0.999951i	$-0.496858\pi$
$433$	−12.6073	−	4.41149i	−0.605869	−	0.212003i	−0.615741	+	0.787949i	$0.711143\pi$
$434$	−1.04523	−	4.81744i	−0.0501727	−	0.231245i
$435$	−0.00183842	+	0.00194243i	−8.81454e−5	+	9.31322e-5i
$436$	−0.250411	+	3.34151i	−0.0119925	+	0.160029i
$437$	0.990604	−	1.87431i	0.0473870	−	0.0896606i
$438$	−0.00594564	+	0.00112498i	−0.000284094	+	5.37535e-5i
$439$	−27.4665	+	4.13990i	−1.31090	+	0.197587i	−0.767046	−	0.641592i	$-0.778274\pi$
$439$	−27.4665	+	4.13990i	−1.31090	+	0.197587i	−0.543856	+	0.839178i	$0.683036\pi$
$440$	0.291046	−	0.911423i	0.0138751	−	0.0434504i
$441$	−10.8883	+	17.9568i	−0.518490	+	0.855083i
$442$	0.749662	+	0.749662i	0.0356578	+	0.0356578i
$443$	−4.15172	+	5.62538i	−0.197254	+	0.267270i	−0.892050	−	0.451938i	$-0.850733\pi$
$443$	−4.15172	+	5.62538i	−0.197254	+	0.267270i	0.694795	+	0.719207i	$0.255495\pi$
$444$	0.00337883	+	0.00230365i	0.000160352	+	0.000109326i
$445$	−5.47143	+	5.36418i	−0.259371	+	0.254287i
$446$	2.53235	+	0.189773i	0.119910	+	0.00898604i
$447$	−0.00167974		0.000587766i	−7.94489e−5		2.78004e-5i
$448$	−0.900613	+	2.48775i	−0.0425500	+	0.117535i
$449$	10.3905	+	21.5760i	0.490357	+	1.01824i	0.988511	+	0.151148i	$0.0482969\pi$
$449$	10.3905	+	21.5760i	0.490357	+	1.01824i	−0.498155	+	0.867088i	$0.665989\pi$
$450$	−12.8563	+	7.72752i	−0.606054	+	0.364279i
$451$	1.44322	−	0.108154i	0.0679585	−	0.00509279i
$452$	−8.84690	+	3.85986i	−0.416123	+	0.181553i
$453$	0.00470365	+	0.00889974i	0.000220997	+	0.000418146i
$454$	−4.47535	−	5.61192i	−0.210039	−	0.263380i
$455$	−2.05726	−	2.91140i	−0.0964460	−	0.136488i
$456$	0.00282556	−	0.00354315i	0.000132319	−	0.000165923i
$457$	26.7575	+	5.06279i	1.25166	+	0.236827i	0.769153	−	0.639064i	$-0.220678\pi$
$457$	26.7575	+	5.06279i	1.25166	+	0.236827i	0.482508	+	0.875891i	$0.339726\pi$
$458$	26.2856	+	0.983539i	1.22825	+	0.0459578i
$459$	−0.00561329	+	0.00324083i	−0.000262006	+	0.000151269i
$460$	0.475111	−	0.432167i	0.0221522	−	0.0201499i
$461$	−28.4565	+	6.49502i	−1.32535	+	0.302503i	−0.825890	−	0.563832i	$-0.809327\pi$
$461$	−28.4565	+	6.49502i	−1.32535	+	0.302503i	−0.499463	+	0.866335i	$0.666469\pi$
$462$	−0.000331375	0	0.000611011i	−1.54169e−5	0	2.84268e-5i
$463$	−13.1972	−	21.0032i	−0.613325	−	0.976101i	−0.998579	−	0.0532904i	$-0.983029\pi$
$463$	−13.1972	−	21.0032i	−0.613325	−	0.976101i	0.385254	−	0.922810i	$-0.374114\pi$
$464$	−1.32496	+	1.42797i	−0.0615098	+	0.0662918i
$465$	−0.00113266	+	0.00229363i	−5.25256e−5	+	0.000106365i
$466$	17.8295	+	2.68736i	0.825934	+	0.124490i
$467$	−11.7954	+	0.441352i	−0.545825	+	0.0204233i	−0.308882	−	0.951100i	$-0.599955\pi$
$467$	−11.7954	+	0.441352i	−0.545825	+	0.0204233i	−0.236943	+	0.971524i	$0.576145\pi$
$468$	−1.53066	+	0.961774i	−0.0707546	+	0.0444580i
$469$	−27.6212	+	1.77175i	−1.27543	+	0.0818120i
$470$	7.86111	+	9.31978i	0.362606	+	0.429889i
$471$	0.00333406	−	0.00577475i	0.000153625	−	0.000266087i
$472$	6.24961	+	1.67458i	0.287662	+	0.0770787i
$473$	0.00841272	−	0.224835i	0.000386817	−	0.0103379i
$474$	0.00349017	−	0.00237955i	0.000160309	−	0.000109297i
$475$	10.1776	+	35.4732i	0.466980	+	1.62762i
$476$	−2.58076	−	3.87405i	−0.118289	−	0.177567i
$477$	−3.69253	+	32.7721i	−0.169069	+	1.50053i
$478$	9.78165	−	5.16975i	0.447402	−	0.236459i
$479$	−12.2022	+	31.0908i	−0.557534	+	1.42057i	0.322913	+	0.946429i	$0.395338\pi$
$479$	−12.2022	+	31.0908i	−0.557534	+	1.42057i	−0.880447	+	0.474145i	$0.842757\pi$
$480$	0.00116968		0.000718910i	5.33883e−5		3.28136e-5i
$481$	−3.73591	+	1.46624i	−0.170343	+	0.0668547i
$482$	0.394301	−	1.12685i	0.0179599	−	0.0513265i
$483$	−0.000397725	0	0.000243987i	−1.80971e−5	0	1.11018e-5i
$484$	−4.69329	+	9.74571i	−0.213331	+	0.442987i
$485$	1.05759	+	0.427200i	0.0480226	+	0.0193982i
$486$	−0.00488645	−	0.0158415i	−0.000221654	−	0.000718585i
$487$	0.380233	+	2.00958i	0.0172300	+	0.0910628i	0.990126	−	0.140180i	$-0.0447683\pi$
$487$	0.380233	+	2.00958i	0.0172300	+	0.0910628i	−0.972896	+	0.231243i	$0.925721\pi$
$488$	−4.23878	−	3.12836i	−0.191881	−	0.141614i
$489$	−0.0113926			−0.000515192
$490$	6.34551	+	14.3085i	0.286661	+	0.646394i
$491$	37.0496			1.67202			0.836012	−	0.548711i	$-0.184881\pi$
$491$	37.0496			1.67202			0.836012	+	0.548711i	$0.184881\pi$
$492$	0.00167100	+	0.00123325i	7.53343e−5	+	5.55992e-5i
$493$	−0.637173	−	3.36754i	−0.0286968	−	0.151666i
$494$	1.31094	+	4.24996i	0.0589820	+	0.191215i
$495$	−2.64204	+	1.12171i	−0.118751	+	0.0504173i
$496$	−0.808406	+	1.67867i	−0.0362985	+	0.0753747i
$497$	27.6655	−	2.81653i	1.24097	−	0.126339i
$498$	0.000266522	0	0.000761677i	1.19431e−5	0	3.41316e-5i
$499$	−32.6628	+	12.8192i	−1.46219	+	0.573867i	−0.957243	−	0.289284i	$-0.906583\pi$
$499$	−32.6628	+	12.8192i	−1.46219	+	0.573867i	−0.504946	+	0.863151i	$0.668488\pi$
$500$	−0.749555	+	11.1552i	−0.0335211	+	0.498875i
$501$	−0.00269264	+	0.00686074i	−0.000120298	+	0.000306515i
$502$	−4.13320	+	2.18446i	−0.184474	+	0.0974972i
$503$	−4.17521	+	37.0560i	−0.186163	+	1.65225i	0.459172	+	0.888347i	$0.348146\pi$
$503$	−4.17521	+	37.0560i	−0.186163	+	1.65225i	−0.645336	+	0.763899i	$0.723283\pi$
$504$	7.41931	−	2.82026i	0.330482	−	0.125625i
$505$	−9.68379	−	1.93174i	−0.430923	−	0.0859612i
$506$	0.101543	−	0.0692312i	0.00451416	−	0.00307770i
$507$	0.000290121	−	0.00775364i	1.28847e−5	−	0.000344351i
$508$	10.4692	+	2.80521i	0.464494	+	0.124461i
$509$	9.70042	−	16.8016i	0.429964	−	0.744719i	−0.566906	−	0.823783i	$-0.691860\pi$
$509$	9.70042	−	16.8016i	0.429964	−	0.744719i	0.996870	+	0.0790636i	$0.0251930\pi$
$510$	−0.000204348		0.00240691i	−9.04869e−6		0.000106580i
$511$	−14.9189	+	21.3848i	−0.659974	+	0.946008i
$512$	0.846724	−	0.532032i	0.0374203	−	0.0235127i
$513$	−0.0271721	+	0.00101671i	−0.00119968	+	4.48888e-5i
$514$	−23.2708	−	3.50751i	−1.02643	−	0.154710i
$515$	22.3241	+	11.0242i	0.983718	+	0.485786i
$516$	0.000219601	0	0.000236674i	9.66740e−6	0	1.04190e-5i
$517$	1.24126	+	1.97546i	0.0545906	+	0.0868805i
$518$	17.3484	−	3.08984i	0.762245	−	0.135760i
$519$	0.0141084	−	0.00322016i	0.000619291	−	0.000141349i
$520$	−0.0637052	+	1.34590i	−0.00279366	+	0.0590217i
$521$	−27.5810	+	15.9239i	−1.20835	+	0.697639i	−0.962398	−	0.271644i	$-0.912433\pi$
$521$	−27.5810	+	15.9239i	−1.20835	+	0.697639i	−0.245949	+	0.969283i	$0.579099\pi$
$522$	5.83985	+	0.218512i	0.255603	+	0.00956400i
$523$	−30.3239	−	5.73759i	−1.32597	−	0.250887i	−0.525774	−	0.850624i	$-0.676224\pi$
$523$	−30.3239	−	5.73759i	−1.32597	−	0.250887i	−0.800197	+	0.599737i	$0.795272\pi$
$524$	−9.30565	+	11.6689i	−0.406519	+	0.509759i
$525$	0.00204836	−	0.00785994i	8.93978e−5	−	0.000343036i
$526$	2.89112	+	3.62535i	0.126059	+	0.158073i
$527$	−1.53176	−	2.89822i	−0.0667243	−	0.126249i
$528$	0.000240797	0	0.000105059i	1.04793e−5	0	4.57209e-6i
$529$	−22.8534	+	1.71263i	−0.993627	+	0.0744620i
$530$	18.4724	+	16.2178i	0.802392	+	0.704456i
$531$	−8.42178	−	17.4880i	−0.365474	−	0.758915i
$532$	−1.97785	−	19.4275i	−0.0857506	−	0.842289i
$533$	−1.92380	+	0.673167i	−0.0833291	+	0.0291581i
$534$	−0.00209811		0.000157231i	−9.07940e−5		6.80407e-6i
$535$	6.72885	+	0.0666013i	0.290914	+	0.00287942i
$536$	8.64351	+	5.89305i	0.373343	+	0.254541i
$537$	−0.00892897	+	0.0120983i	−0.000385313	+	0.000522081i
$538$	−19.8391	−	19.8391i	−0.855324	−	0.855324i
$539$	0.821143	+	2.88039i	0.0353691	+	0.124067i
$540$	−0.00784729	−	0.00250589i	−0.000337693	−	0.000107836i
$541$	−35.4550	+	5.34398i	−1.52433	+	0.229756i	−0.857121	−	0.515115i	$-0.827749\pi$
$541$	−35.4550	+	5.34398i	−1.52433	+	0.229756i	−0.667209	+	0.744870i	$0.732511\pi$
$542$	−1.64188	+	0.310660i	−0.0705246	+	0.0133440i
$543$	0.00528134	−	0.00999278i	0.000226644	−	0.000428831i
$544$	−0.131481	+	1.75449i	−0.00563719	+	0.0752231i
$545$	−0.206044	−	7.48996i	−0.00882594	−	0.320835i
$546$	0.000228062	0	0.000951948i	9.76015e−6	0	4.07396e-5i
$547$	−3.85566	−	1.34915i	−0.164856	−	0.0576856i	0.246589	−	0.969120i	$-0.420690\pi$
$547$	−3.85566	−	1.34915i	−0.164856	−	0.0576856i	−0.411445	+	0.911434i	$0.634976\pi$
$548$	−12.4669	−	5.43927i	−0.532561	−	0.232354i
$549$	1.18108	+	15.7604i	0.0504072	+	0.672638i
$550$	−0.439268	+	2.09381i	−0.0187305	+	0.0892804i
$551$	4.23792	−	13.7390i	0.180542	−	0.585301i
$552$	0.000175249	0	1.97458e-5i	7.45909e−6	0	8.40438e-7i
$553$	3.57591	−	17.8474i	0.152063	−	0.758947i
$554$	17.4195	+	13.8916i	0.740085	+	0.590198i
$555$	−0.00804184	−	0.00435260i	−0.000341357	−	0.000184758i
$556$	13.0235	+	14.0359i	0.552317	+	0.595257i
$557$	−1.40886	+	5.25794i	−0.0596953	+	0.222786i	−0.989329	−	0.145699i	$-0.953457\pi$
$557$	−1.40886	+	5.25794i	−0.0596953	+	0.222786i	0.929634	+	0.368485i	$0.120124\pi$
$558$	5.39910	−	1.44668i	0.228562	−	0.0612430i
$559$	0.0705069	+	0.308911i	0.00298213	+	0.0130655i
$560$	1.43521	−	5.73935i	0.0606487	−	0.242532i
$561$	−0.000102855	0	0.000450638i	−4.34255e−6	0	1.90260e-5i
$562$	0.303358	+	8.10741i	0.0127964	+	0.341990i
$563$	23.3239	+	31.6027i	0.982983	+	1.33189i	0.943035	+	0.332693i	$0.107957\pi$
$563$	23.3239	+	31.6027i	0.982983	+	1.33189i	0.0399480	+	0.999202i	$0.487281\pi$
$564$	−0.000498980		0.00331052i	−2.10109e−5		0.000139398i
$565$	18.7974	−	10.6060i	0.790813	−	0.446199i
$566$	24.8044	+	5.66145i	1.04261	+	0.237969i
$567$	−20.9316	−	11.3520i	−0.879044	−	0.476739i
$568$	−8.89960	−	5.59199i	−0.373419	−	0.234635i
$569$	−1.30076	−	0.750993i	−0.0545306	−	0.0314833i	0.472487	−	0.881338i	$-0.343356\pi$
$569$	−1.30076	−	0.750993i	−0.0545306	−	0.0314833i	−0.527017	+	0.849854i	$0.676690\pi$
$570$	−0.00547602	+	0.00852653i	−0.000229365	+	0.000357137i
$571$	24.2195	−	22.4724i	1.01355	−	0.940441i	0.0153230	−	0.999883i	$-0.495122\pi$
$571$	24.2195	−	22.4724i	1.01355	−	0.940441i	0.998232	+	0.0594412i	$0.0189319\pi$
$572$	−0.0479337	+	0.253336i	−0.00200421	+	0.0105925i
$573$	0.00359969		0.000405587i	0.000150379		1.69437e-5i
$574$	8.86291	−	1.23865i	0.369931	−	0.0517001i
$575$	−0.958138	+	1.06980i	−0.0399571	+	0.0446136i
$576$	−2.86672	−	0.884265i	−0.119447	−	0.0368444i
$577$	1.36393	+	3.12617i	0.0567813	+	0.130144i	0.942640	−	0.333811i	$-0.108335\pi$
$577$	1.36393	+	3.12617i	0.0567813	+	0.130144i	−0.885859	+	0.463955i	$0.846430\pi$
$578$	10.5392	+	9.06972i	0.438373	+	0.377251i
$579$	0.00326937	+	0.00833021i	0.000135870	+	0.000346192i
$580$	2.62113	−	3.47891i	0.108837	−	0.144454i
$581$	−1.47497	−	3.14890i	−0.0611920	−	0.130638i
$582$	0.000103443	0	0.000295624i	4.28786e−6	0	1.22540e-5i
$583$	3.06819	+	3.56530i	0.127071	+	0.147660i
$584$	9.41742	−	2.90489i	0.389696	−	0.120205i
$585$	3.18513	−	2.48888i	0.131689	−	0.102903i
$586$	−1.33009	−	8.82455i	−0.0549454	−	0.364539i
$587$	23.2903	−	23.2903i	0.961292	−	0.961292i	−0.0379866	−	0.999278i	$-0.512094\pi$
$587$	23.2903	−	23.2903i	0.961292	−	0.961292i	0.999278	+	0.0379866i	$0.0120944\pi$
$588$	−0.00180297	+	0.00390155i	−7.43534e−5	+	0.000160897i
$589$		−	13.7519i		−	0.566638i
$590$	−14.2839	−	2.29776i	−0.588059	−	0.0945972i
$591$	0.00828644	−	0.0121540i	0.000340859	−	0.000499948i
$592$	−5.88844	−	3.11213i	−0.242014	−	0.127908i
$593$	−2.01548	+	1.73446i	−0.0827660	+	0.0712259i	−0.692698	−	0.721228i	$-0.743578\pi$
$593$	−2.01548	+	1.73446i	−0.0827660	+	0.0712259i	0.609931	+	0.792454i	$0.291197\pi$
$594$	−0.00142020		0.000683933i	−5.82716e−5		2.80621e-5i
$595$	6.62525	+	8.02802i	0.271609	+	0.329117i
$596$	2.61134	−	1.25756i	0.106965	−	0.0515116i
$597$	0.00357775	−	0.00820028i	0.000146427	−	0.000335615i
$598$	−0.112896	+	0.131188i	−0.00461667	+	0.00536467i
$599$	−43.4923	−	17.0695i	−1.77705	−	0.697440i	−0.997466	−	0.0711406i	$-0.977336\pi$
$599$	−43.4923	−	17.0695i	−1.77705	−	0.697440i	−0.779582	−	0.626300i	$-0.784569\pi$
$600$	−0.00243764	+	0.00186623i	−9.95163e−5	+	7.61886e-5i
$601$	−27.2469	+	21.7287i	−1.11142	+	0.886332i	−0.994282	−	0.106783i	$-0.965945\pi$
$601$	−27.2469	+	21.7287i	−1.11142	+	0.886332i	−0.117142	+	0.993115i	$0.537373\pi$
$602$	−0.0370816	−	1.39073i	−0.00151133	−	0.0566817i
$603$	−3.51387	−	31.1865i	−0.143096	−	1.27001i
$604$	−9.23538	−	13.5458i	−0.375782	−	0.551171i
$605$	8.21415	−	22.7499i	0.333953	−	0.924914i
$606$	−0.00135573	−	0.00234819i	−5.50727e−5	−	9.53887e-5i
$607$	−6.62788	−	24.7356i	−0.269017	−	1.00399i	−0.959745	−	0.280871i	$-0.909377\pi$
$607$	−6.62788	−	24.7356i	−0.269017	−	1.00399i	0.690728	−	0.723114i	$-0.257290\pi$
$608$	−3.92686	+	6.24956i	−0.159255	+	0.253453i
$609$	−0.00234271	+	0.00212735i	−9.49316e−5	+	8.62045e-5i
$610$	10.1430	+	5.99071i	0.410679	+	0.242557i
$611$	−2.40854	−	2.23480i	−0.0974392	−	0.0904103i
$612$	4.24685	−	3.13432i	0.171669	−	0.126697i
$613$	19.5339	−	14.4167i	0.788968	−	0.582285i	−0.123067	−	0.992398i	$-0.539273\pi$
$613$	19.5339	−	14.4167i	0.788968	−	0.582285i	0.912034	+	0.410114i	$0.134511\pi$
$614$	−18.7149	−	17.3649i	−0.755270	−	0.700788i
$615$	−0.00399854	−	0.00236163i	−0.000161237	−	9.52303e-5i
$616$	0.424885	−	1.04930i	0.0171191	−	0.0422775i
$617$	25.6948	−	40.8930i	1.03443	−	1.64629i	0.318789	−	0.947826i	$-0.396724\pi$
$617$	25.6948	−	40.8930i	1.03443	−	1.64629i	0.715644	−	0.698465i	$-0.246133\pi$
$618$	0.00176946	+	0.00660372i	7.11781e−5	+	0.000265640i
$619$	20.9999	+	36.3729i	0.844057	+	1.46195i	0.886438	+	0.462848i	$0.153173\pi$
$619$	20.9999	+	36.3729i	0.844057	+	1.46195i	−0.0423804	+	0.999102i	$0.513494\pi$
$620$	1.41487	−	3.91861i	0.0568224	−	0.157375i
$621$	−0.000596076	0	0.000874282i	−2.39197e−5	0	3.50837e-5i
$622$	−2.14925	−	19.0751i	−0.0861769	−	0.764841i
$623$	−6.93504	+	5.83959i	−0.277846	+	0.233958i
$624$	−0.000289265	0	0.000230681i	−1.15799e−5	0	9.23464e-6i
$625$	−0.880059	−	24.9845i	−0.0352024	−	0.999380i
$626$	−11.7066	−	4.59452i	−0.467891	−	0.183634i
$627$	−0.00126484	+	0.00146977i	−5.05128e−5	+	5.86970e-5i
$628$	−4.34287	+	9.95397i	−0.173299	+	0.397206i
$629$	10.5577	−	5.08430i	0.420962	−	0.202724i
$630$	−15.8593	+	7.96757i	−0.631850	+	0.317436i
$631$	9.97654	+	4.80445i	0.397160	+	0.191262i	0.621794	−	0.783181i	$-0.286404\pi$
$631$	9.97654	+	4.80445i	0.397160	+	0.191262i	−0.224634	+	0.974443i	$0.572119\pi$
$632$	−5.21465	+	4.48757i	−0.207427	+	0.178506i
$633$	0.00133123		0.000703578i	5.29118e−5		2.79647e-5i
$634$	5.96999	−	8.75637i	0.237099	−	0.347760i
$635$	−23.9280	−	3.84914i	−0.949552	−	0.152748i
$636$			0.00674981i			0.000267647i
$637$	−2.16689	−	3.61892i	−0.0858554	−	0.143387i
$638$	0.589372	−	0.589372i	0.0233335	−	0.0233335i
$639$	4.69958	+	31.1797i	0.185913	+	1.23345i
$640$	−1.76194	+	1.37679i	−0.0696468	+	0.0544226i
$641$	−37.4413	+	11.5491i	−1.47884	+	0.456163i	−0.926129	−	0.377208i	$-0.876884\pi$
$641$	−37.4413	+	11.5491i	−1.47884	+	0.456163i	−0.552714	+	0.833371i	$0.686408\pi$
$642$	0.00120527	+	0.00140055i	4.75683e−5	+	5.52753e-5i
$643$	7.32710	+	20.9396i	0.288953	+	0.825779i	0.993262	+	0.115886i	$0.0369709\pi$
$643$	7.32710	+	20.9396i	0.288953	+	0.825779i	−0.704310	+	0.709893i	$0.748743\pi$
$644$	0.599195	−	0.467400i	0.0236116	−	0.0184182i
$645$	−0.000434430	0	0.000576599i	−1.71057e−5	0	2.27036e-5i
$646$	−4.74430	−	12.0883i	−0.186662	−	0.475607i
$647$	−19.4961	−	16.7778i	−0.766472	−	0.659602i	0.179534	−	0.983752i	$-0.442541\pi$
$647$	−19.4961	−	16.7778i	−0.766472	−	0.659602i	−0.946006	+	0.324150i	$0.894922\pi$
$648$	3.59903	+	8.24906i	0.141383	+	0.324054i
$649$	−2.64541	−	0.816002i	−0.103842	−	0.0320309i
$650$	−0.165640	−	3.00834i	−0.00649694	−	0.117997i
$651$	−0.00154144	+	0.00260482i	−6.04137e−5	+	0.000102091i
$652$	18.4381	−	2.07747i	0.722090	−	0.0813600i
$653$	6.17766	−	32.6497i	0.241750	−	1.27768i	−0.625663	−	0.780094i	$-0.715171\pi$
$653$	6.17766	−	32.6497i	0.241750	−	1.27768i	0.867413	−	0.497588i	$-0.165781\pi$
$654$	0.00150821	−	0.00139942i	5.89757e−5	−	5.47215e-5i
$655$	18.0346	−	28.0811i	0.704671	−	1.09722i
$656$	−2.92926	−	1.69121i	−0.114369	−	0.0660307i
$657$	−25.0341	−	15.7299i	−0.976672	−	0.613684i
$658$	8.44143	+	11.6987i	0.329081	+	0.456063i
$659$	9.88980	+	2.25728i	0.385252	+	0.0879312i	0.410760	−	0.911743i	$-0.365263\pi$
$659$	9.88980	+	2.25728i	0.385252	+	0.0879312i	−0.0255084	+	0.999675i	$0.508120\pi$
$660$	−0.000511633	0	0.000288677i	−1.99153e−5	0	1.12368e-5i
$661$	2.34071	−	15.5296i	0.0910429	−	0.604031i	−0.896059	−	0.443936i	$-0.853582\pi$
$661$	2.34071	−	15.5296i	0.0910429	−	0.604031i	0.987102	−	0.160095i	$-0.0511800\pi$
$662$	5.99735	+	8.12612i	0.233094	+	0.315831i
$663$	−2.43399e−5	0	0.000650498i	−9.45283e−7	0	2.52632e-5i
$664$	−0.292452	+	1.28132i	−0.0113493	+	0.0497247i
$665$	8.83587	+	42.7625i	0.342640	+	1.65826i
$666$	4.44615	+	19.4798i	0.172285	+	0.754828i
$667$	0.540448	−	0.144813i	0.0209262	−	0.00560717i
$668$	3.10676	−	11.5946i	0.120204	−	0.448608i
$669$	−0.00106054	−	0.00114299i	−4.10029e−5	−	4.41907e-5i
$670$	−20.5721	−	11.1346i	−0.794771	−	0.430166i
$671$	1.76236	+	1.40544i	0.0680353	+	0.0542564i
$672$	0.00144431		0.000743602i	5.57155e−5		2.86851e-5i
$673$	32.5764	+	3.67048i	1.25573	+	0.141487i	0.714648	−	0.699485i	$-0.246587\pi$
$673$	32.5764	+	3.67048i	1.25573	+	0.141487i	0.541080	+	0.840971i	$0.318016\pi$
$674$	−1.22584	+	3.97409i	−0.0472177	+	0.153076i
$675$	0.0180276	+	0.00378207i	0.000693881	+	0.000145572i
$676$	0.944357	+	12.6016i	0.0363214	+	0.484675i
$677$	15.8636	+	6.92120i	0.609686	+	0.266003i	0.681969	−	0.731381i	$-0.261124\pi$
$677$	15.8636	+	6.92120i	0.609686	+	0.266003i	−0.0722833	+	0.997384i	$0.523029\pi$
$678$	0.00559392	+	0.00195740i	0.000214833	+	7.51734e-5i
$679$	1.20958	+	0.598593i	0.0464193	+	0.0229719i
$680$	−0.108185	−	3.93267i	−0.00414870	−	0.150811i
$681$	−0.000329353		0.00439492i	−1.26209e−5		0.000168414i
$682$	0.372515	−	0.704832i	0.0142643	−	0.0269894i
$683$	44.7107	−	8.45971i	1.71081	−	0.323702i	0.763930	−	0.645299i	$-0.223267\pi$
$683$	44.7107	−	8.45971i	1.71081	−	0.323702i	0.946876	+	0.321597i	$0.104220\pi$
$684$	21.8953	−	3.30018i	0.837187	−	0.126186i
$685$	28.9733	+	9.25209i	1.10701	+	0.353504i
$686$	6.20718	+	17.4491i	0.236991	+	0.666210i
$687$	−0.0114203	−	0.0114203i	−0.000435710	−	0.000435710i
$688$	−0.312250	+	0.423083i	−0.0119044	+	0.0161299i
$689$	−5.47321	−	3.73157i	−0.208513	−	0.142162i
$690$	−0.000394329	0	3.90302e-6i	−1.50118e−5	0	1.48585e-7i
$691$	18.1885	+	1.36304i	0.691922	+	0.0518524i	0.416050	−	0.909342i	$-0.363414\pi$
$691$	18.1885	+	1.36304i	0.691922	+	0.0518524i	0.275873	+	0.961194i	$0.411033\pi$
$692$	−22.2462	+	7.78428i	−0.845674	+	0.295914i
$693$	−3.21746	+	1.08719i	−0.122221	+	0.0412988i
$694$	−14.0441	−	29.1628i	−0.533105	−	1.10700i
$695$	−32.1743	−	28.2472i	−1.22044	−	1.07148i
$696$	0.00119272		8.93817e-5i	4.52098e−5		3.38800e-6i
$697$	5.45452	−	2.37978i	0.206605	−	0.0901406i
$698$	−7.65859	−	14.4908i	−0.289882	−	0.548483i
$699$	−0.00690263	−	0.00865562i	−0.000261081	−	0.000327386i
$700$	−1.88184	+	13.0942i	−0.0711267	+	0.494915i
$701$	8.07214	−	10.1221i	0.304880	−	0.382308i	−0.605663	−	0.795721i	$-0.707092\pi$
$701$	8.07214	−	10.1221i	0.304880	−	0.382308i	0.910543	+	0.413413i	$0.135664\pi$
$702$	0.00218120		0.000412706i	8.23242e−5		1.55766e-5i
$703$	49.1241	+	1.83810i	1.85275	+	0.0693251i
$704$	−0.370554	+	0.213939i	−0.0139658	+	0.00806314i
$705$	0.000353944	−	0.00747779i	1.33303e−5	−	0.000281630i
$706$	−11.2600	+	2.57003i	−0.423776	+	0.0967242i
$707$	−11.2525	−	3.14504i	−0.423194	−	0.118281i
$708$	−0.00211357	−	0.00336372i	−7.94327e−5	−	0.000126416i
$709$	−7.86271	+	8.47398i	−0.295290	+	0.318247i	−0.863218	−	0.504831i	$-0.831555\pi$
$709$	−7.86271	+	8.47398i	−0.295290	+	0.318247i	0.567928	+	0.823078i	$0.307745\pi$
$710$	21.0730	+	10.4064i	0.790857	+	0.390546i
$711$	20.4087	+	3.07611i	0.765385	+	0.115363i
$712$	3.42430	−	0.128128i	0.128331	−	0.00480180i
$713$	0.453132	−	0.284722i	0.0169699	−	0.0106629i
$714$	−0.000456321		0.00282148i	−1.70774e−5		0.000105591i
$715$	0.0487719	−	0.574460i	0.00182397	−	0.0214836i
$716$	12.2447	−	21.2084i	0.457605	−	0.792596i
$717$	−0.00656169	−	0.00175820i	−0.000245051	−	6.56612e-5i
$718$	−0.341361	+	9.12307i	−0.0127395	+	0.340470i
$719$	−37.4072	+	25.5038i	−1.39505	+	0.951131i	−0.395588	+	0.918428i	$0.629459\pi$
$719$	−37.4072	+	25.5038i	−1.39505	+	0.951131i	−0.999465	+	0.0327034i	$0.989588\pi$
$720$	6.57859	+	1.31231i	0.245170	+	0.0489068i
$721$	25.3529	+	15.0030i	0.944193	+	0.558739i
$722$	3.97218	−	35.2541i	0.147829	−	1.31202i
$723$	−0.000648074	0	0.000342517i	−2.41021e−5	0	1.27383e-5i
$724$	−6.72523	+	17.1356i	−0.249941	+	0.636840i
$725$	−5.03595	+	8.33695i	−0.187031	+	0.309626i
$726$	0.00618249	−	0.00242645i	0.000229454	−	9.00539e-5i
$727$	3.43131	−	9.80611i	0.127260	−	0.363688i	−0.862571	−	0.505936i	$-0.831147\pi$
$727$	3.43131	−	9.80611i	0.127260	−	0.363688i	0.989831	+	0.142248i	$0.0454329\pi$
$728$	−0.195511	+	1.58224i	−0.00724611	+	0.0586418i
$729$	11.7149	−	24.3261i	0.433883	−	0.900968i
$730$	−20.2846	+	8.61209i	−0.750765	+	0.318748i
$731$	−0.272694	−	0.884051i	−0.0100859	−	0.0326978i
$732$	0.000601364		0.00317829i	2.22271e−5		0.000117473i
$733$	28.3736	+	20.9407i	1.04800	+	0.773461i	0.974625	−	0.223843i	$-0.0718604\pi$
$733$	28.3736	+	20.9407i	1.04800	+	0.773461i	0.0733772	+	0.997304i	$0.476622\pi$
$734$	28.1348			1.03847
$735$	0.00311955	−	0.00909025i	0.000115066	−	0.000335299i
$736$	−0.287228			−0.0105873
$737$	−3.60150	−	2.65803i	−0.132663	−	0.0979098i
$738$	1.88649	+	9.97036i	0.0694428	+	0.367014i
$739$	−0.629881	−	2.04202i	−0.0231706	−	0.0751171i	0.943249	−	0.332086i	$-0.107752\pi$
$739$	−0.629881	−	2.04202i	−0.0231706	−	0.0751171i	−0.966420	+	0.256969i	$0.917276\pi$
$740$	13.8088	+	5.57790i	0.507621	+	0.205048i
$741$	0.00118485	−	0.00246037i	4.35266e−5	−	9.03838e-5i
$742$	20.3442	+	20.7861i	0.746859	+	0.763081i
$743$	6.27304	−	17.9273i	0.230135	−	0.657689i	−0.769679	−	0.638431i	$-0.779584\pi$
$743$	6.27304	−	17.9273i	0.230135	−	0.657689i	0.999815	−	0.0192582i	$-0.00613046\pi$
$744$	0.00106492		0.000417949i	3.90418e−5		1.53228e-5i
$745$	−5.52144	+	3.39360i	−0.202290	+	0.124332i
$746$	8.42445	−	21.4652i	0.308441	−	0.785895i
$747$	3.48589	−	1.84235i	0.127542	−	0.0674080i
$748$	0.0842883	−	0.748079i	0.00308188	−	0.0273525i
$749$	7.93296	+	0.680266i	0.289864	+	0.0248564i
$750$	0.00499607	−	0.00470785i	0.000182431	−	0.000171906i
$751$	−44.2170	+	30.1467i	−1.61350	+	1.10007i	−0.685127	+	0.728423i	$0.740253\pi$
$751$	−44.2170	+	30.1467i	−1.61350	+	1.10007i	−0.928375	+	0.371644i	$0.878794\pi$
$752$	0.203880	−	5.44881i	0.00743474	−	0.198698i
$753$	0.00277262		0.000742920i	0.000101040		2.70735e-5i
$754$	−0.586906	+	1.01655i	−0.0213738	+	0.0370206i
$755$	23.6362	+	28.0220i	0.860211	+	1.01983i
$756$	−0.00903441	−	0.00365823i	−0.000328578	−	0.000133048i
$757$	7.70996	−	4.84449i	0.280223	−	0.176076i	−0.384586	−	0.923089i	$-0.625656\pi$
$757$	7.70996	−	4.84449i	0.280223	−	0.176076i	0.664809	+	0.747013i	$0.268513\pi$
$758$	−11.4653	+	0.429002i	−0.416440	+	0.0155821i
$759$	−7.46169e−5	0	1.12467e-5i	−2.70842e−6	0	4.08229e-7i
$760$	7.30769	−	14.7981i	0.265078	−	0.536783i
$761$	32.8198	−	35.3714i	1.18972	−	1.28221i	0.239404	−	0.970920i	$-0.423048\pi$
$761$	32.8198	−	35.3714i	1.18972	−	1.28221i	0.950315	−	0.311291i	$-0.100761\pi$
$762$	−0.00354058	−	0.00563481i	−0.000128262	−	0.000204128i
$763$	0.426648	−	8.85532i	0.0154457	−	0.320584i
$764$	−5.75186	+	1.31282i	−0.208095	+	0.0474963i
$765$	−8.73085	+	7.94169i	−0.315665	+	0.287132i
$766$	−8.82056	+	5.09255i	−0.318700	+	0.184001i
$767$	3.89601	+	0.145778i	0.140677	+	0.00526375i
$768$	−0.000603296	0	0.000114150i	−2.17696e−5	0	4.11903e-6i
$769$	5.94638	−	7.45653i	0.214432	−	0.268889i	−0.662969	−	0.748647i	$-0.730704\pi$
$769$	5.94638	−	7.45653i	0.214432	−	0.268889i	0.877401	+	0.479758i	$0.159275\pi$
$770$	−0.705490	+	2.43107i	−0.0254241	+	0.0876095i
$771$	0.00900924	+	0.0112972i	0.000324460	+	0.000406860i
$772$	−6.81025	−	12.8856i	−0.245106	−	0.463764i
$773$	23.0519	−	10.0574i	0.829119	−	0.361741i	0.0579091	−	0.998322i	$-0.481557\pi$
$773$	23.0519	−	10.0574i	0.829119	−	0.361741i	0.771210	+	0.636581i	$0.219652\pi$
$774$	1.57308	−	0.117886i	0.0565433	−	0.00423734i
$775$	−2.25236	+	9.03955i	−0.0809071	+	0.324710i
$776$	−0.221323	−	0.459581i	−0.00794502	−	0.0164980i
$777$	−0.00909881	−	0.00585443i	−0.000326418	−	0.000210027i
$778$	2.72013	−	0.951814i	0.0975213	−	0.0341242i
$779$	24.8954	+	1.86565i	0.891970	+	0.0668439i
$780$	0.000590757	0	0.000579177i	2.11525e−5	0	2.07379e-5i
$781$	3.71582	+	2.53340i	0.132962	+	0.0906523i
$782$	0.300087	−	0.406604i	0.0107311	−	0.0145401i
$783$	−0.00507445	−	0.00507445i	−0.000181346	−	0.000181346i
$784$	2.20652	−	6.64314i	0.0788041	−	0.237255i
$785$	7.38714	−	23.1331i	0.263658	−	0.825655i
$786$	0.00906167	−	0.00136583i	0.000323219	−	4.87174e-5i
$787$	−27.2495	+	5.15589i	−0.971341	+	0.183788i	−0.647283	−	0.762250i	$-0.724095\pi$
$787$	−27.2495	+	5.15589i	−0.971341	+	0.183788i	−0.324058	+	0.946037i	$0.605047\pi$
$788$	−11.1947	+	21.1813i	−0.398793	+	0.754553i
$789$	0.000212765	−	0.00283915i	7.57464e−6	−	0.000101077i
$790$	10.5746	−	11.1728i	0.376227	−	0.397512i
$791$	23.1262	−	10.8325i	0.822272	−	0.385159i
$792$	1.21160	+	0.423958i	0.0430524	+	0.0150647i
$793$	−2.90963	−	1.26946i	−0.103324	−	0.0450799i
$794$	−2.15939	−	28.8150i	−0.0766338	−	1.02261i
$795$	−0.00154136	−	0.0150141i	−5.46663e−5	−	0.000532496i
$796$	−4.29496	+	13.9239i	−0.152231	+	0.493521i
$797$	−19.2532	−	2.16931i	−0.681983	−	0.0768410i	−0.235825	−	0.971795i	$-0.575779\pi$
$797$	−19.2532	−	2.16931i	−0.681983	−	0.0768410i	−0.446158	+	0.894954i	$0.647208\pi$
$798$	−0.00722322	+	0.00957021i	−0.000255699	+	0.000338782i
$799$	7.50041	+	5.98138i	0.265345	+	0.211606i
$800$	3.60482	−	3.46486i	0.127450	−	0.122501i
$801$	−6.99223	−	7.53583i	−0.247058	−	0.266265i
$802$	3.47903	−	12.9839i	0.122849	−	0.458478i
$803$	−4.07317	+	1.09140i	−0.143739	+	0.0385148i
$804$	−0.00142930	−	0.00626218i	−5.04076e−5	−	0.000220850i
$805$	−1.22610	+	1.17650i	−0.0432144	+	0.0414663i
$806$	−0.249828	+	1.09457i	−0.00879982	+	0.0385545i
$807$	0.000644132		0.0172148i	2.26745e−5		0.000605989i
$808$	2.62234	+	3.55314i	0.0922535	+	0.124999i
$809$	2.50499	−	16.6195i	0.0880706	−	0.584310i	−0.900651	−	0.434544i	$-0.856910\pi$
$809$	2.50499	−	16.6195i	0.0880706	−	0.584310i	0.988721	−	0.149767i	$-0.0478522\pi$
$810$	−9.88931	−	17.5272i	−0.347475	−	0.615841i
$811$	18.1627	+	4.14553i	0.637780	+	0.145569i	0.529171	−	0.848515i	$-0.322503\pi$
$811$	18.1627	+	4.14553i	0.637780	+	0.145569i	0.108609	+	0.994084i	$0.465360\pi$
$812$	3.40357	−	3.87015i	0.119442	−	0.135816i
$813$	0.000868739	0	0.000545865i	3.04680e−5	0	1.91443e-5i
$814$	2.46799	+	1.42489i	0.0865028	+	0.0499424i
$815$	−40.5388	+	8.83152i	−1.42001	+	0.309354i
$816$	0.000791899	0	0.000734775i	2.77220e−5	0	2.57223e-5i
$817$	0.721540	−	3.81343i	0.0252435	−	0.133415i
$818$	−20.3530	+	2.29324i	−0.711627	+	0.0801811i
$819$	3.98047	−	2.65165i	0.139089	−	0.0926563i
$820$	6.90198	+	3.09298i	0.241028	+	0.108011i
$821$	10.9572	+	3.37985i	0.382409	+	0.117958i	0.479999	−	0.877269i	$-0.340637\pi$
$821$	10.9572	+	3.37985i	0.382409	+	0.117958i	−0.0975895	+	0.995227i	$0.531113\pi$
$822$	0.00333972	+	0.00765471i	0.000116486	+	0.000266989i
$823$	6.25353	+	5.38160i	0.217984	+	0.187591i	0.754501	−	0.656299i	$-0.227879\pi$
$823$	6.25353	+	5.38160i	0.217984	+	0.187591i	−0.536516	+	0.843890i	$0.680260\pi$
$824$	−4.06794	−	10.3649i	−0.141713	−	0.361080i
$825$	0.00107214		0.000758962i	3.73272e−5		2.64237e-5i
$826$	−16.6471	−	3.98822i	−0.579228	−	0.138768i
$827$	0.0405693	+	0.115941i	0.00141073	+	0.00403165i	0.944587	−	0.328262i	$-0.106463\pi$
$827$	0.0405693	+	0.115941i	0.00141073	+	0.00403165i	−0.943176	+	0.332294i	$0.892177\pi$
$828$	0.562065	+	0.653131i	0.0195331	+	0.0226979i
$829$	21.5631	−	6.65133i	0.748917	−	0.231010i	0.103277	−	0.994653i	$-0.467067\pi$
$829$	21.5631	−	6.65133i	0.748917	−	0.231010i	0.645639	+	0.763642i	$0.276591\pi$
$830$	0.357928	−	2.91691i	0.0124238	−	0.101248i
$831$	−0.00203893	−	0.0135274i	−7.07296e−5	−	0.000469260i
$832$	0.426088	−	0.426088i	0.0147719	−	0.0147719i
$833$	7.09883	+	10.0641i	0.245960	+	0.348702i
$834$		−	0.0117564i		−	0.000407092i
$835$	−4.26291	+	26.5002i	−0.147524	+	0.917077i
$836$	1.77903	−	2.60935i	0.0615290	−	0.0902464i
$837$	−0.00606855	−	0.00320732i	−0.000209760	−	0.000110861i
$838$	−10.0491	+	8.64791i	−0.347139	+	0.298737i
$839$	36.3394	+	17.5001i	1.25458	+	0.604172i	0.938735	−	0.344641i	$-0.111999\pi$
$839$	36.3394	+	17.5001i	1.25458	+	0.604172i	0.315840	+	0.948812i	$0.397714\pi$
$840$	−0.00304289	+	0.00198387i	−0.000104990	+	6.84499e-5i
$841$	−22.7093	+	10.9362i	−0.783078	+	0.377110i
$842$	12.7995	−	29.3368i	0.441100	−	1.01101i
$843$	0.00324933	−	0.00377579i	0.000111913	−	0.000130045i
$844$	−2.28280	−	0.895932i	−0.0785771	−	0.0308392i
$845$	−4.97825	−	27.8150i	−0.171257	−	0.956864i
$846$	−12.7891	+	10.1990i	−0.439698	+	0.350647i
$847$	11.7256	−	26.1065i	0.402896	−	0.897031i
$848$	−1.23084	−	10.9240i	−0.0422674	−	0.375133i
$849$	−0.00879996	−	0.0129072i	−0.000302014	−	0.000442973i
$850$	1.13869	+	8.72303i	0.0390568	+	0.299198i
$851$	0.956506	+	1.65672i	0.0327886	+	0.0567915i
$852$	0.00167030	+	0.00623363i	5.72234e−5	+	0.000213561i
$853$	−14.4896	+	23.0601i	−0.496115	+	0.789563i	−0.997117	−	0.0758835i	$-0.975822\pi$
$853$	−14.4896	+	23.0601i	−0.496115	+	0.789563i	0.501001	+	0.865446i	$0.332965\pi$
$854$	11.4314	+	7.97501i	0.391174	+	0.272899i
$855$	−47.9497	+	12.3408i	−1.63985	+	0.422045i
$856$	−2.20603	−	2.04690i	−0.0754006	−	0.0699616i
$857$	−40.3617	+	29.7883i	−1.37873	+	1.01755i	−0.383145	+	0.923688i	$0.625159\pi$
$857$	−40.3617	+	29.7883i	−1.37873	+	1.01755i	−0.995585	+	0.0938607i	$0.970079\pi$
$858$	0.000127374	0	9.40066e-5i	4.34849e−6	0	3.20933e-6i
$859$	−27.9256	−	25.9112i	−0.952809	−	0.884078i	0.0405449	−	0.999178i	$-0.487091\pi$
$859$	−27.9256	−	25.9112i	−0.952809	−	0.884078i	−0.993354	+	0.115100i	$0.963281\pi$
$860$	0.597947	−	1.01240i	0.0203898	−	0.0345226i
$861$	−0.00450644	−	0.00314388i	−0.000153579	−	0.000107143i
$862$	−0.646306	+	1.02859i	−0.0220133	+	0.0350339i
$863$	−7.27826	−	27.1628i	−0.247755	−	0.924633i	−0.971979	−	0.235069i	$-0.924469\pi$
$863$	−7.27826	−	27.1628i	−0.247755	−	0.924633i	0.724224	−	0.689565i	$-0.242198\pi$
$864$	0.00184200	+	0.00319044i	6.26662e−5	+	0.000108541i
$865$	47.7063	−	22.3952i	1.62206	−	0.761461i
$866$	−7.52419	−	11.0360i	−0.255682	−	0.375017i
$867$	−0.000955881	−	0.00848368i	−3.24634e−5	−	0.000288121i
$868$	2.01970	−	4.49678i	0.0685532	−	0.152631i
$869$	2.30147	−	1.83536i	0.0780720	−	0.0622604i
$870$	−0.00263264		0.000471182i	−8.92548e−5		1.59746e-5i
$871$	5.86799	+	2.30302i	0.198829	+	0.0780348i
$872$	−2.18574	+	2.53987i	−0.0740184	+	0.0860109i
$873$	−0.611951	+	1.40261i	−0.0207114	+	0.0474710i
$874$	1.91004	−	0.919828i	0.0646082	−	0.0311137i
$875$	1.19577	−	29.5562i	0.0404244	−	0.999183i
$876$	−0.00545189	−	0.00262549i	−0.000184202	−	8.87071e-5i
$877$	−10.5681	+	9.09455i	−0.356858	+	0.307101i	−0.812386	−	0.583120i	$-0.801832\pi$
$877$	−10.5681	+	9.09455i	−0.356858	+	0.307101i	0.455528	+	0.890222i	$0.349451\pi$
$878$	−24.5578	−	12.9792i	−0.828786	−	0.438026i
$879$	−0.00308670	+	0.00452736i	−0.000104112	+	0.000152704i
$880$	0.775397	−	0.560500i	0.0261386	−	0.0188944i
$881$		−	47.7143i		−	1.60754i	−0.594943	−	0.803768i	$-0.702825\pi$
$881$		−	47.7143i		−	1.60754i	0.594943	−	0.803768i	$-0.297175\pi$
$882$	−19.4238	+	7.98228i	−0.654033	+	0.268777i
$883$	27.2362	−	27.2362i	0.916571	−	0.916571i	−0.0802072	−	0.996778i	$-0.525558\pi$
$883$	27.2362	−	27.2362i	0.916571	−	0.916571i	0.996778	+	0.0802072i	$0.0255582\pi$
$884$	0.158012	+	1.04834i	0.00531452	+	0.0352595i
$885$	0.00546949	+	0.00699954i	0.000183855	+	0.000235287i
$886$	−6.68093	+	2.06079i	−0.224450	+	0.0692337i
$887$	−8.85973	−	10.2952i	−0.297481	−	0.345679i	0.589262	−	0.807942i	$-0.299419\pi$
$887$	−8.85973	−	10.2952i	−0.297481	−	0.345679i	−0.886743	+	0.462263i	$0.847038\pi$
$888$	0.00135065	+	0.00385992i	4.53247e−5	+	0.000129531i
$889$	−27.8868	−	6.68095i	−0.935293	−	0.224072i
$890$	−7.58766	+	1.06696i	−0.254339	+	0.0357647i
$891$	−1.40689	−	3.58471i	−0.0471327	−	0.120092i
$892$	1.92483	+	1.65645i	0.0644482	+	0.0554621i
$893$	16.0937	+	36.8871i	0.538554	+	1.23438i
$894$	−0.00170054		0.000524547i	−5.68746e−5		1.75435e-5i
$895$	−22.3937	+	49.9717i	−0.748540	+	1.67037i
$896$	−2.20191	+	1.46684i	−0.0735605	+	0.0490035i
$897$	0.000105601	0	1.18984e-5i	3.52593e−6	0	3.97277e-7i
$898$	−4.45213	+	23.5301i	−0.148570	+	0.785210i
$899$	2.66057	−	2.46865i	0.0887351	−	0.0823341i
$900$	−14.9329	−	1.41681i	−0.497765	−	0.0472269i
$901$	16.7502	+	9.67073i	0.558030	+	0.322179i
$902$	1.22543	+	0.769992i	0.0408025	+	0.0256379i
$903$	−0.000564114	0	0.000641444i	−1.87725e−5	0	2.13459e-5i
$904$	−9.41026	−	2.14783i	−0.312981	−	0.0714358i
$905$	11.0464	−	39.6518i	0.367196	−	1.31807i
$906$	−0.00150030	+	0.00995383i	−4.98441e−5	+	0.000330694i
$907$	24.9466	+	33.8015i	0.828339	+	1.12236i	0.990758	+	0.135638i	$0.0433084\pi$
$907$	24.9466	+	33.8015i	0.828339	+	1.12236i	−0.162419	+	0.986722i	$0.551930\pi$
$908$	−0.268391	−	7.17289i	−0.00890686	−	0.238041i
$909$	2.94799	−	12.9160i	0.0977786	−	0.428396i
$910$	0.0735755	−	3.56415i	0.00243900	−	0.118150i
$911$	−6.43998	−	28.2154i	−0.213366	−	0.934817i	−0.962261	−	0.272129i	$-0.912272\pi$
$911$	−6.43998	−	28.2154i	−0.213366	−	0.934817i	0.748895	−	0.662689i	$-0.230585\pi$
$912$	0.00437744	−	0.00117293i	0.000144951	−	3.88396e-5i
$913$	0.145546	−	0.543185i	0.00481687	−	0.0179768i
$914$	18.5226	+	19.9626i	0.612674	+	0.660305i
$915$	−0.00206344	−	0.00693238i	−6.82153e−5	−	0.000229177i
$916$	20.5653	+	16.4003i	0.679498	+	0.541881i
$917$	23.7888	−	31.5183i	0.785576	−	1.04083i
$918$	−0.00644091		0.000725716i	−0.000212582		2.39522e-5i
$919$	−13.2388	+	42.9190i	−0.436706	+	1.41577i	0.423535	+	0.905880i	$0.360789\pi$
$919$	−13.2388	+	42.9190i	−0.436706	+	1.41577i	−0.860241	+	0.509887i	$0.829687\pi$
$920$	0.638902	−	0.0655901i	0.0210640	−	0.00216244i
$921$	0.00117143	+	0.0156316i	3.85999e−5	+	0.000515080i
$922$	−26.7529	−	11.6722i	−0.881061	−	0.384403i
$923$	−5.97807	−	2.09182i	−0.196771	−	0.0688530i
$924$	−0.000629454	0	0.000294841i	−2.07075e−5	0	9.69957e-6i
$925$	−31.9897	−	9.25403i	−1.05182	−	0.304271i
$926$	1.85370	−	24.7359i	0.0609163	−	0.812871i
$927$	−15.6086	+	29.5329i	−0.512653	+	0.969988i
$928$	−1.91402	+	0.362152i	−0.0628307	+	0.0118882i
$929$	−19.2732	+	2.90497i	−0.632335	+	0.0953091i	−0.457386	−	0.889268i	$-0.651214\pi$
$929$	−19.2732	+	2.90497i	−0.632335	+	0.0953091i	−0.174949	+	0.984578i	$0.555976\pi$
$930$	−0.00227334	+	0.00117286i	−7.45456e−5	+	3.84595e-5i
$931$	6.60106	+	51.2426i	0.216341	+	1.67941i
$932$	12.7497	+	12.7497i	0.417632	+	0.417632i
$933$	−0.00699889	+	0.00948317i	−0.000229134	+	0.000310465i
$934$	−9.75262	−	6.64923i	−0.319116	−	0.217569i
$935$	−0.0166607	+	1.68326i	−0.000544862	+	0.0550484i
$936$	−1.80268	−	0.135092i	−0.0589225	−	0.00441563i
$937$	−19.0443	+	6.66389i	−0.622150	+	0.217700i	−0.622902	−	0.782300i	$-0.714046\pi$
$937$	−19.0443	+	6.66389i	−0.622150	+	0.217700i	0.000751841		1.00000i	$0.499761\pi$
$938$	−23.2760	−	14.9765i	−0.759989	−	0.488999i
$939$	0.00335030	+	0.00695697i	0.000109333	+	0.000227032i
$940$	0.790761	+	12.1668i	0.0257918	+	0.396836i
$941$	33.4947	−	2.51008i	1.09190	−	0.0818263i	0.483413	−	0.875393i	$-0.339397\pi$
$941$	33.4947	−	2.51008i	1.09190	−	0.0818263i	0.608484	+	0.793566i	$0.291778\pi$
$942$	0.00611174	−	0.00266652i	0.000199131	−	8.68801e-5i
$943$	0.453963	+	0.858940i	0.0147831	+	0.0279709i
$944$	4.03403	+	5.05851i	0.131296	+	0.164640i
$945$	0.0209313	+	0.00607422i	0.000680895	+	0.000197594i
$946$	0.140280	−	0.175906i	0.00456090	−	0.00571919i
$947$	41.7381	+	7.89727i	1.35631	+	0.256627i	0.812685	−	0.582704i	$-0.198005\pi$
$947$	41.7381	+	7.89727i	1.35631	+	0.256627i	0.543621	+	0.839331i	$0.317053\pi$
$948$	0.00422121		0.000157946i	0.000137098		5.12986e-6i
$949$	5.14296	−	2.96929i	0.166948	−	0.0963872i
$950$	−12.8758	+	34.5853i	−0.417747	+	1.12209i
$951$	−0.00634395	+	0.00144796i	−0.000205717	+	4.69535e-5i
$952$	0.224015	−	4.64956i	0.00726038	−	0.150693i
$953$	−1.39666	−	2.22276i	−0.0452421	−	0.0720024i	0.823337	−	0.567552i	$-0.192109\pi$
$953$	−1.39666	−	2.22276i	−0.0452421	−	0.0720024i	−0.868580	+	0.495550i	$0.834967\pi$
$954$	−22.4318	+	24.1757i	−0.726255	+	0.782716i
$955$	12.4945	−	4.23368i	0.404313	−	0.136999i
$956$	10.9402	+	1.64897i	0.353831	+	0.0533315i
$957$	−0.000511410	0	1.91356e-5i	−1.65315e−5	0	6.18567e-7i
$958$	−28.2802	+	17.7696i	−0.913692	+	0.574111i
$959$	33.3563	+	13.5067i	1.07713	+	0.436153i
$960$	0.00136803		0.000116146i	4.41528e−5		3.74860e-6i
$961$	−13.7643	+	23.8404i	−0.444009	+	0.769046i
$962$	−3.87659	−	1.03873i	−0.124986	−	0.0334899i
$963$	−0.337573	+	9.02183i	−0.0108781	+	0.290724i
$964$	0.986398	−	0.672515i	0.0317697	−	0.0216602i
$965$	18.0911	+	27.1073i	0.582372	+	0.872616i
$966$	−0.000464893	0	3.98654e-5i	−1.49577e−5	0	1.28265e-6i
$967$	−3.88717	+	34.4996i	−0.125003	+	1.10943i	0.761971	+	0.647611i	$0.224232\pi$
$967$	−3.88717	+	34.4996i	−0.125003	+	1.10943i	−0.886974	+	0.461820i	$0.847197\pi$
$968$	−9.56341	+	5.05441i	−0.307379	+	0.162455i
$969$	−0.00291300	+	0.00742221i	−9.35791e−5	+	0.000238436i
$970$	0.597253	+	0.971742i	0.0191766	+	0.0312008i
$971$	12.3871	−	4.86159i	0.397522	−	0.156016i	−0.158155	−	0.987414i	$-0.550554\pi$
$971$	12.3871	−	4.86159i	0.397522	−	0.156016i	0.555677	+	0.831398i	$0.312459\pi$
$972$	0.00547537	−	0.0156477i	0.000175623	−	0.000501900i
$973$	−35.4344	−	36.2040i	−1.13597	−	1.16065i
$974$	−0.887395	+	1.84269i	−0.0284340	+	0.0590438i
$975$	−0.00118181	+	0.00142321i	−3.78482e−5	+	4.55793e-5i
$976$	−1.55283	−	5.03415i	−0.0497049	−	0.161139i
$977$	9.28435	+	49.0690i	0.297033	+	1.56986i	0.739554	+	0.673098i	$0.235037\pi$
$977$	9.28435	+	49.0690i	0.297033	+	1.56986i	−0.442521	+	0.896758i	$0.645916\pi$
$978$	−0.00916647	−	0.00676516i	−0.000293111	−	0.000216326i
$979$	−1.46621			−0.0468602
$980$	−3.39112	+	15.2807i	−0.108325	+	0.488125i
$981$	10.0526			0.320956
$982$	29.8100	+	22.0008i	0.951276	+	0.702074i
$983$	0.845189	+	4.46693i	0.0269573	+	0.142473i	0.993459	−	0.114186i	$-0.0364259\pi$
$983$	0.845189	+	4.46693i	0.0269573	+	0.142473i	−0.966502	+	0.256659i	$0.917378\pi$
$984$	0.000612150		0.00198454i	1.95146e−5		6.32649e-5i
$985$	20.0643	−	49.6716i	0.639300	−	1.58267i
$986$	1.48705	−	3.08788i	0.0473572	−	0.0983382i
$987$	0.00108625	−	0.00879088i	3.45758e−5	−	0.000279817i
$988$	−1.46893	+	4.19797i	−0.0467330	+	0.133555i
$989$	0.140593	−	0.0551787i	0.00447060	−	0.00175458i
$990$	−2.79187	−	0.666366i	−0.0887315	−	0.0211785i
$991$	1.13725	−	2.89766i	0.0361259	−	0.0920473i	−0.911672	−	0.410918i	$-0.865208\pi$
$991$	1.13725	−	2.89766i	0.0361259	−	0.0920473i	0.947798	+	0.318871i	$0.103304\pi$
$992$	−1.64727	+	0.870609i	−0.0523009	+	0.0276419i
$993$	0.000694310	−	0.00616217i	2.20333e−5	−	0.000195551i
$994$	23.9321	+	14.1622i	0.759081	+	0.449197i
$995$	6.37401	−	31.9528i	0.202070	−	1.01297i
$996$	0.000666742	0	0.000454577i	2.11265e−5	0	1.44038e-5i
$997$	−0.936280	+	25.0226i	−0.0296523	+	0.792474i	0.902561	+	0.430563i	$0.141685\pi$
$997$	−0.936280	+	25.0226i	−0.0296523	+	0.792474i	−0.932213	+	0.361911i	$0.882125\pi$
$998$	−33.8928	−	9.08154i	−1.07286	−	0.287471i
$999$	0.0122682	−	0.0212492i	0.000388149	−	0.000672294i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.w.a.397.20	yes	672
5.3	odd	4	inner	490.2.w.a.103.23	✓	672
49.10	odd	42	inner	490.2.w.a.157.23	yes	672
245.108	even	84	inner	490.2.w.a.353.20	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.2.w.a.103.23	✓	672	5.3	odd	4	inner
490.2.w.a.157.23	yes	672	49.10	odd	42	inner
490.2.w.a.353.20	yes	672	245.108	even	84	inner
490.2.w.a.397.20	yes	672	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.w (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.804598 + 0.593820i) q^{2} +(-0.000114150 - 0.000603296i) q^{3} +(0.294755 + 0.955573i) q^{4} +(-0.873857 - 2.05825i) q^{5} +(0.000266405 - 0.000553195i) q^{6} +(-0.846959 - 2.50652i) q^{7} +(-0.330279 + 0.943883i) q^{8} +(2.79262 - 1.09602i) q^{9} +O(q^{10})\)	\(q+(0.804598 + 0.593820i) q^{2} +(-0.000114150 - 0.000603296i) q^{3} +(0.294755 + 0.955573i) q^{4} +(-0.873857 - 2.05825i) q^{5} +(0.000266405 - 0.000553195i) q^{6} +(-0.846959 - 2.50652i) q^{7} +(-0.330279 + 0.943883i) q^{8} +(2.79262 - 1.09602i) q^{9} +(0.519124 - 2.17497i) q^{10} +(0.156322 - 0.398301i) q^{11} +(0.000542847 - 0.000286903i) q^{12} +(-0.0674675 + 0.598790i) q^{13} +(0.806963 - 2.51968i) q^{14} +(-0.00114198 + 0.000762143i) q^{15} +(-0.826239 + 0.563320i) q^{16} +(0.0657864 - 1.75818i) q^{17} +(2.89778 + 0.776457i) q^{18} +(3.69043 - 6.39202i) q^{19} +(1.70923 - 1.44171i) q^{20} +(-0.00141550 + 0.000797086i) q^{21} +(0.362295 - 0.227645i) q^{22} +(0.287027 - 0.0107398i) q^{23} +(0.000607143 + 9.15120e-5i) q^{24} +(-3.47275 + 3.59723i) q^{25} +(-0.409858 + 0.441722i) q^{26} +(-0.00196001 - 0.00311933i) q^{27} +(2.14552 - 1.54814i) q^{28} +(1.89914 - 0.433466i) q^{29} +(-0.00137141 - 6.49127e-5i) q^{30} +(1.61357 - 0.931593i) q^{31} +(-0.999301 - 0.0373912i) q^{32} +(-0.000258137 - 4.88422e-5i) q^{33} +(1.09697 - 1.37556i) q^{34} +(-4.41892 + 3.93359i) q^{35} +(1.87047 + 2.34549i) q^{36} +(3.11213 + 5.88844i) q^{37} +(6.76502 - 2.95155i) q^{38} +(0.000368949 - 2.76489e-5i) q^{39} +(2.23136 - 0.145024i) q^{40} +(1.46758 + 3.04746i) q^{41} +(-0.00161223 - 0.000199216i) q^{42} +(0.496324 - 0.173671i) q^{43} +(0.426682 + 0.0319754i) q^{44} +(-4.69624 - 4.79013i) q^{45} +(0.237319 + 0.161801i) q^{46} +(-3.23788 + 4.38717i) q^{47} +(0.000434164 + 0.000434164i) q^{48} +(-5.56532 + 4.24584i) q^{49} +(-4.93027 + 0.832132i) q^{50} +(-0.00106821 + 0.000161007i) q^{51} +(-0.592074 + 0.112026i) q^{52} +(-5.13676 + 9.71923i) q^{53} +(0.000275306 - 0.00367370i) q^{54} +(-0.956403 + 0.0263100i) q^{55} +(2.64560 + 0.0284221i) q^{56} +(-0.00427754 - 0.00149678i) q^{57} +(1.78544 + 0.778981i) q^{58} +(-0.483509 - 6.45198i) q^{59} +(-0.00106489 - 0.000866600i) q^{60} +(-1.55283 + 5.03415i) q^{61} +(1.85147 + 0.208611i) q^{62} +(-5.11244 - 6.07148i) q^{63} +(-0.781831 - 0.623490i) q^{64} +(1.29141 - 0.384393i) q^{65} +(-0.000178693 - 0.000192586i) q^{66} +(2.70758 - 10.1048i) q^{67} +(1.69946 - 0.455368i) q^{68} +(-3.92433e-5 - 0.000171936i) q^{69} +(-5.89130 + 0.540916i) q^{70} +(-2.33883 + 10.2471i) q^{71} +(0.112174 + 2.99790i) q^{72} +(-5.85225 - 7.92952i) q^{73} +(-0.992661 + 6.58588i) q^{74} +(0.00256661 + 0.00168447i) q^{75} +(7.19581 + 1.64240i) q^{76} +(-1.13075 - 0.0544793i) q^{77} +(0.000313274 + 0.000196843i) q^{78} +(5.95803 + 3.43987i) q^{79} +(1.88147 + 1.20834i) q^{80} +(6.59746 - 6.12155i) q^{81} +(-0.628831 + 3.32345i) q^{82} +(1.30600 - 0.147151i) q^{83} +(-0.00117890 - 0.00111766i) q^{84} +(-3.67625 + 1.40099i) q^{85} +(0.502471 + 0.154992i) q^{86} +(-0.000478295 - 0.00109626i) q^{87} +(0.324320 + 0.279100i) q^{88} +(-1.25191 - 3.18982i) q^{89} +(-0.934105 - 6.64285i) q^{90} +(1.55802 - 0.338042i) q^{91} +(0.0948653 + 0.271109i) q^{92} +(-0.000746215 - 0.000867118i) q^{93} +(-5.21038 + 1.60719i) q^{94} +(-16.3812 - 2.01010i) q^{95} +(9.15120e-5 + 0.000607143i) q^{96} +(-0.360693 + 0.360693i) q^{97} +(-6.99911 + 0.111396i) q^{98} -1.28364i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q + 12 q^{5} - 28 q^{6} - 8 q^{7}+O(q^{10}) \) 672 * q + 12 * q^5 - 28 * q^6 - 8 * q^7	\( 672 q + 12 q^{5} - 28 q^{6} - 8 q^{7} + 12 q^{10} + 4 q^{11} - 44 q^{15} - 56 q^{16} + 8 q^{17} + 28 q^{21} + 20 q^{22} + 4 q^{23} - 4 q^{25} + 16 q^{26} - 4 q^{28} - 12 q^{30} - 24 q^{31} - 48 q^{33} - 8 q^{35} + 92 q^{36} - 12 q^{37} - 24 q^{38} - 112 q^{41} + 76 q^{42} + 24 q^{43} - 100 q^{45} - 160 q^{46} + 72 q^{47} + 32 q^{50} - 208 q^{51} + 160 q^{53} - 84 q^{55} - 52 q^{56} - 92 q^{57} + 128 q^{58} - 212 q^{61} + 36 q^{63} - 16 q^{67} + 36 q^{68} - 16 q^{70} - 16 q^{71} + 12 q^{73} + 132 q^{75} - 16 q^{77} + 80 q^{78} + 12 q^{80} - 36 q^{81} + 48 q^{82} - 308 q^{83} - 40 q^{85} - 4 q^{86} + 52 q^{87} - 4 q^{88} + 84 q^{90} - 124 q^{91} - 8 q^{92} - 536 q^{93} - 28 q^{95} - 12 q^{96} - 40 q^{98}+O(q^{100}) \) 672 * q + 12 * q^5 - 28 * q^6 - 8 * q^7 + 12 * q^10 + 4 * q^11 - 44 * q^15 - 56 * q^16 + 8 * q^17 + 28 * q^21 + 20 * q^22 + 4 * q^23 - 4 * q^25 + 16 * q^26 - 4 * q^28 - 12 * q^30 - 24 * q^31 - 48 * q^33 - 8 * q^35 + 92 * q^36 - 12 * q^37 - 24 * q^38 - 112 * q^41 + 76 * q^42 + 24 * q^43 - 100 * q^45 - 160 * q^46 + 72 * q^47 + 32 * q^50 - 208 * q^51 + 160 * q^53 - 84 * q^55 - 52 * q^56 - 92 * q^57 + 128 * q^58 - 212 * q^61 + 36 * q^63 - 16 * q^67 + 36 * q^68 - 16 * q^70 - 16 * q^71 + 12 * q^73 + 132 * q^75 - 16 * q^77 + 80 * q^78 + 12 * q^80 - 36 * q^81 + 48 * q^82 - 308 * q^83 - 40 * q^85 - 4 * q^86 + 52 * q^87 - 4 * q^88 + 84 * q^90 - 124 * q^91 - 8 * q^92 - 536 * q^93 - 28 * q^95 - 12 * q^96 - 40 * q^98

Introduction

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