LMFDB - Embedded newform 380.2.be.b.51.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(51,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 5]))

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

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

chi := DirichletCharacter("380.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.be (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			51.15
Character	$\chi$	$=$	380.51
Dual form			380.2.be.b.231.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.03833 + 0.960144i) q^{2} +(0.700287 + 0.254884i) q^{3} +(0.156246 + 1.99389i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(0.482402 + 0.937029i) q^{6} +(3.13008 + 1.80715i) q^{7} +(-1.75219 + 2.22033i) q^{8} +(-1.87270 - 1.57138i) q^{9} +O(q^{10})$	\(q+(1.03833 + 0.960144i) q^{2} +(0.700287 + 0.254884i) q^{3} +(0.156246 + 1.99389i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(0.482402 + 0.937029i) q^{6} +(3.13008 + 1.80715i) q^{7} +(-1.75219 + 2.22033i) q^{8} +(-1.87270 - 1.57138i) q^{9} +(0.765254 - 1.18928i) q^{10} +(4.80721 - 2.77545i) q^{11} +(-0.398792 + 1.43612i) q^{12} +(0.738627 + 2.02936i) q^{13} +(1.51492 + 4.88174i) q^{14} +(0.129408 - 0.733908i) q^{15} +(-3.95117 + 0.623074i) q^{16} +(-4.32858 + 3.63211i) q^{17} +(-0.435721 - 3.42967i) q^{18} +(-4.14647 + 1.34415i) q^{19} +(1.93646 - 0.500107i) q^{20} +(1.73134 + 2.06333i) q^{21} +(7.65629 + 1.73380i) q^{22} +(-1.70362 - 0.300395i) q^{23} +(-1.79296 + 1.10826i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(-1.18154 + 2.81633i) q^{26} +(-2.02875 - 3.51390i) q^{27} +(-3.11419 + 6.52338i) q^{28} +(4.56883 - 5.44492i) q^{29} +(0.839025 - 0.637787i) q^{30} +(0.965893 - 1.67298i) q^{31} +(-4.70085 - 3.14674i) q^{32} +(4.07385 - 0.718329i) q^{33} +(-7.98184 - 0.384743i) q^{34} +(1.23616 - 3.39633i) q^{35} +(2.84055 - 3.97947i) q^{36} -1.13116i q^{37} +(-5.59598 - 2.58554i) q^{38} +1.60940i q^{39} +(2.49086 + 1.34001i) q^{40} +(1.35657 - 3.72715i) q^{41} +(-0.183398 + 3.80474i) q^{42} +(3.38006 - 0.595996i) q^{43} +(6.28504 + 9.15139i) q^{44} +(-1.22232 + 2.11711i) q^{45} +(-1.48050 - 1.94763i) q^{46} +(4.40407 - 5.24857i) q^{47} +(-2.92577 - 0.570759i) q^{48} +(3.03158 + 5.25085i) q^{49} +(-1.30410 - 0.547112i) q^{50} +(-3.95702 + 1.44024i) q^{51} +(-3.93091 + 1.78982i) q^{52} +(-10.3559 - 1.82602i) q^{53} +(1.26734 - 5.59647i) q^{54} +(-3.56805 - 4.25223i) q^{55} +(-9.49693 + 3.78333i) q^{56} +(-3.24632 - 0.115575i) q^{57} +(9.97185 - 1.26687i) q^{58} +(-3.05890 + 2.56673i) q^{59} +(1.48355 + 0.143354i) q^{60} +(-0.439276 + 2.49126i) q^{61} +(2.60921 - 0.809699i) q^{62} +(-3.02197 - 8.30278i) q^{63} +(-1.85970 - 7.78084i) q^{64} +(1.87027 - 1.07980i) q^{65} +(4.91968 + 3.16562i) q^{66} +(4.27487 + 3.58704i) q^{67} +(-7.91835 - 8.06320i) q^{68} +(-1.11646 - 0.644589i) q^{69} +(4.54451 - 2.33961i) q^{70} +(-2.36378 - 13.4057i) q^{71} +(6.77029 - 1.40465i) q^{72} +(-4.86974 - 1.77244i) q^{73} +(1.08608 - 1.17452i) q^{74} -0.745230 q^{75} +(-3.32796 - 8.05758i) q^{76} +20.0626 q^{77} +(-1.54526 + 1.67108i) q^{78} +(-9.33512 - 3.39771i) q^{79} +(1.29972 + 3.78295i) q^{80} +(0.748445 + 4.24464i) q^{81} +(4.98717 - 2.56750i) q^{82} +(15.0376 + 8.68195i) q^{83} +(-3.84353 + 3.77448i) q^{84} +(4.32858 + 3.63211i) q^{85} +(4.08185 + 2.62651i) q^{86} +(4.58731 - 2.64849i) q^{87} +(-2.26073 + 15.5367i) q^{88} +(-0.0513214 - 0.141004i) q^{89} +(-3.30190 + 1.02466i) q^{90} +(-1.35540 + 7.68686i) q^{91} +(0.332769 - 3.44377i) q^{92} +(1.10282 - 0.925373i) q^{93} +(9.61225 - 1.22119i) q^{94} +(2.04376 + 3.85007i) q^{95} +(-2.48989 - 3.40179i) q^{96} +(-2.23563 - 2.66432i) q^{97} +(-1.89380 + 8.36286i) q^{98} +(-13.3637 - 2.35639i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9}+O(q^{10}) $ 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9	$ 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9} + 3 q^{10} - 12 q^{13} - 18 q^{14} + 9 q^{16} + 48 q^{17} - 12 q^{21} - 18 q^{24} - 24 q^{26} + 69 q^{28} - 12 q^{30} - 27 q^{32} + 6 q^{33} - 18 q^{34} - 72 q^{36} - 48 q^{38} - 36 q^{41} - 27 q^{42} - 99 q^{44} + 60 q^{45} + 27 q^{46} - 63 q^{48} + 60 q^{49} + 33 q^{52} - 24 q^{53} + 21 q^{54} - 48 q^{57} + 6 q^{60} - 24 q^{61} + 54 q^{62} + 84 q^{64} - 18 q^{65} - 132 q^{66} + 66 q^{68} - 72 q^{69} + 36 q^{70} - 42 q^{72} + 66 q^{74} + 180 q^{76} + 60 q^{77} + 114 q^{78} + 27 q^{80} - 66 q^{81} + 33 q^{82} - 144 q^{84} - 48 q^{85} + 75 q^{86} + 9 q^{88} - 3 q^{90} - 42 q^{92} - 144 q^{93} + 78 q^{96} + 42 q^{97} - 87 q^{98}+O(q^{100}) $ 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9 + 3 * q^10 - 12 * q^13 - 18 * q^14 + 9 * q^16 + 48 * q^17 - 12 * q^21 - 18 * q^24 - 24 * q^26 + 69 * q^28 - 12 * q^30 - 27 * q^32 + 6 * q^33 - 18 * q^34 - 72 * q^36 - 48 * q^38 - 36 * q^41 - 27 * q^42 - 99 * q^44 + 60 * q^45 + 27 * q^46 - 63 * q^48 + 60 * q^49 + 33 * q^52 - 24 * q^53 + 21 * q^54 - 48 * q^57 + 6 * q^60 - 24 * q^61 + 54 * q^62 + 84 * q^64 - 18 * q^65 - 132 * q^66 + 66 * q^68 - 72 * q^69 + 36 * q^70 - 42 * q^72 + 66 * q^74 + 180 * q^76 + 60 * q^77 + 114 * q^78 + 27 * q^80 - 66 * q^81 + 33 * q^82 - 144 * q^84 - 48 * q^85 + 75 * q^86 + 9 * q^88 - 3 * q^90 - 42 * q^92 - 144 * q^93 + 78 * q^96 + 42 * q^97 - 87 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.03833	+	0.960144i	0.734208	+	0.678925i
$2$	1.03833	+	0.960144i	0.734208	+	0.678925i
$3$	0.700287	+	0.254884i	0.404311	+	0.147157i	0.536167	−	0.844112i	$-0.319872\pi$
$3$	0.700287	+	0.254884i	0.404311	+	0.147157i	−0.131856	+	0.991269i	$0.542094\pi$
$4$	0.156246	+	1.99389i	0.0781230	+	0.996944i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$6$	0.482402	+	0.937029i	0.196940	+	0.382541i
$7$	3.13008	+	1.80715i	1.18306	+	0.683038i	0.956720	−	0.291010i	$-0.0939915\pi$
$7$	3.13008	+	1.80715i	1.18306	+	0.683038i	0.226337	+	0.974049i	$0.427325\pi$
$8$	−1.75219	+	2.22033i	−0.619491	+	0.785004i
$9$	−1.87270	−	1.57138i	−0.624232	−	0.523793i
$10$	0.765254	−	1.18928i	0.241995	−	0.376083i
$11$	4.80721	−	2.77545i	1.44943	−	0.836829i	0.450982	−	0.892533i	$-0.351074\pi$
$11$	4.80721	−	2.77545i	1.44943	−	0.836829i	0.998447	+	0.0557043i	$0.0177404\pi$
$12$	−0.398792	+	1.43612i	−0.115121	+	0.414572i
$13$	0.738627	+	2.02936i	0.204858	+	0.562843i	0.998991	−	0.0449003i	$-0.0142970\pi$
$13$	0.738627	+	2.02936i	0.204858	+	0.562843i	−0.794133	+	0.607744i	$0.792075\pi$
$14$	1.51492	+	4.88174i	0.404879	+	1.30470i
$15$	0.129408	−	0.733908i	0.0334130	−	0.189494i
$16$	−3.95117	+	0.623074i	−0.987794	+	0.155769i
$17$	−4.32858	+	3.63211i	−1.04984	+	0.880917i	−0.993076	−	0.117471i	$-0.962521\pi$
$17$	−4.32858	+	3.63211i	−1.04984	+	0.880917i	−0.0567592	+	0.998388i	$0.518077\pi$
$18$	−0.435721	−	3.42967i	−0.102700	−	0.808380i
$19$	−4.14647	+	1.34415i	−0.951266	+	0.308370i
$19$	−4.14647	+	1.34415i	−0.951266	+	0.308370i
$20$	1.93646	−	0.500107i	0.433007	−	0.111827i
$21$	1.73134	+	2.06333i	0.377809	+	0.450255i
$22$	7.65629	+	1.73380i	1.63233	+	0.369647i
$23$	−1.70362	−	0.300395i	−0.355230	−	0.0626367i	−0.00681452	−	0.999977i	$-0.502169\pi$
$23$	−1.70362	−	0.300395i	−0.355230	−	0.0626367i	−0.348416	+	0.937340i	$0.613280\pi$
$24$	−1.79296	+	1.10826i	−0.365986	+	0.226223i
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$	−1.18154	+	2.81633i	−0.231720	+	0.552328i
$27$	−2.02875	−	3.51390i	−0.390433	−	0.676250i
$28$	−3.11419	+	6.52338i	−0.588527	+	1.23280i
$29$	4.56883	−	5.44492i	0.848410	−	1.01110i	−0.151334	−	0.988483i	$-0.548357\pi$
$29$	4.56883	−	5.44492i	0.848410	−	1.01110i	0.999744	−	0.0226133i	$-0.00719866\pi$
$30$	0.839025	−	0.637787i	0.153184	−	0.116443i
$31$	0.965893	−	1.67298i	0.173480	−	0.300475i	−0.766155	−	0.642656i	$-0.777832\pi$
$31$	0.965893	−	1.67298i	0.173480	−	0.300475i	0.939634	+	0.342181i	$0.111166\pi$
$32$	−4.70085	−	3.14674i	−0.831001	−	0.556271i
$33$	4.07385	−	0.718329i	0.709165	−	0.125045i
$34$	−7.98184	−	0.384743i	−1.36887	−	0.0659830i
$35$	1.23616	−	3.39633i	0.208950	−	0.574085i
$36$	2.84055	−	3.97947i	0.473425	−	0.663245i
$37$		−	1.13116i		−	0.185962i	−0.995668	−	0.0929809i	$-0.970360\pi$
$37$		−	1.13116i		−	0.185962i	0.995668	−	0.0929809i	$-0.0296396\pi$
$38$	−5.59598	−	2.58554i	−0.907788	−	0.419430i
$39$			1.60940i			0.257710i
$40$	2.49086	+	1.34001i	0.393839	+	0.211874i
$41$	1.35657	−	3.72715i	0.211861	−	0.582083i	−0.787556	−	0.616244i	$-0.788654\pi$
$41$	1.35657	−	3.72715i	0.211861	−	0.582083i	0.999416	+	0.0341608i	$0.0108758\pi$
$42$	−0.183398	+	3.80474i	−0.0282989	+	0.587085i
$43$	3.38006	−	0.595996i	0.515455	−	0.0908886i	0.0901312	−	0.995930i	$-0.471271\pi$
$43$	3.38006	−	0.595996i	0.515455	−	0.0908886i	0.425324	+	0.905041i	$0.360160\pi$
$44$	6.28504	+	9.15139i	0.947505	+	1.37962i
$45$	−1.22232	+	2.11711i	−0.182212	+	0.315601i
$46$	−1.48050	−	1.94763i	−0.218287	−	0.287163i
$47$	4.40407	−	5.24857i	0.642400	−	0.765583i	−0.342347	−	0.939574i	$-0.611222\pi$
$47$	4.40407	−	5.24857i	0.642400	−	0.765583i	0.984747	+	0.173991i	$0.0556663\pi$
$48$	−2.92577	−	0.570759i	−0.422298	−	0.0823819i
$49$	3.03158	+	5.25085i	0.433083	+	0.750122i
$50$	−1.30410	−	0.547112i	−0.184427	−	0.0773733i
$51$	−3.95702	+	1.44024i	−0.554093	+	0.201673i
$52$	−3.93091	+	1.78982i	−0.545119	+	0.248203i
$53$	−10.3559	−	1.82602i	−1.42249	−	0.250823i	−0.591138	−	0.806571i	$-0.701321\pi$
$53$	−10.3559	−	1.82602i	−1.42249	−	0.250823i	−0.831351	+	0.555747i	$0.812432\pi$
$54$	1.26734	−	5.59647i	0.172464	−	0.761583i
$55$	−3.56805	−	4.25223i	−0.481115	−	0.573371i
$56$	−9.49693	+	3.78333i	−1.26908	+	0.505568i
$57$	−3.24632	−	0.115575i	−0.429986	−	0.0153083i
$58$	9.97185	−	1.26687i	1.30937	−	0.166348i
$59$	−3.05890	+	2.56673i	−0.398235	+	0.334159i	−0.819811	−	0.572634i	$-0.805922\pi$
$59$	−3.05890	+	2.56673i	−0.398235	+	0.334159i	0.421576	+	0.906793i	$0.361477\pi$
$60$	1.48355	+	0.143354i	0.191525	+	0.0185070i
$61$	−0.439276	+	2.49126i	−0.0562436	+	0.318973i	−0.999930	−	0.0118694i	$-0.996222\pi$
$61$	−0.439276	+	2.49126i	−0.0562436	+	0.318973i	0.943686	+	0.330842i	$0.107333\pi$
$62$	2.60921	−	0.809699i	0.331370	−	0.102832i
$63$	−3.02197	−	8.30278i	−0.380732	−	1.04605i
$64$	−1.85970	−	7.78084i	−0.232462	−	0.972606i
$65$	1.87027	−	1.07980i	0.231978	−	0.133933i
$66$	4.91968	+	3.16562i	0.605571	+	0.389661i
$67$	4.27487	+	3.58704i	0.522258	+	0.438227i	0.865418	−	0.501050i	$-0.167053\pi$
$67$	4.27487	+	3.58704i	0.522258	+	0.438227i	−0.343160	+	0.939277i	$0.611497\pi$
$68$	−7.91835	−	8.06320i	−0.960241	−	0.977807i
$69$	−1.11646	−	0.644589i	−0.134406	−	0.0775994i
$70$	4.54451	−	2.33961i	0.543173	−	0.279637i
$71$	−2.36378	−	13.4057i	−0.280529	−	1.59096i	−0.720831	−	0.693111i	$-0.756239\pi$
$71$	−2.36378	−	13.4057i	−0.280529	−	1.59096i	0.440301	−	0.897850i	$-0.354872\pi$
$72$	6.77029	−	1.40465i	0.797886	−	0.165540i
$73$	−4.86974	−	1.77244i	−0.569959	−	0.207448i	0.0409330	−	0.999162i	$-0.486967\pi$
$73$	−4.86974	−	1.77244i	−0.569959	−	0.207448i	−0.610892	+	0.791714i	$0.709189\pi$
$74$	1.08608	−	1.17452i	0.126254	−	0.136535i
$75$	−0.745230			−0.0860517
$76$	−3.32796	−	8.05758i	−0.381743	−	0.924268i
$77$	20.0626			2.28634
$78$	−1.54526	+	1.67108i	−0.174966	+	0.189213i
$79$	−9.33512	−	3.39771i	−1.05028	−	0.382272i	−0.241514	−	0.970397i	$-0.577644\pi$
$79$	−9.33512	−	3.39771i	−1.05028	−	0.382272i	−0.808770	+	0.588126i	$0.799866\pi$
$80$	1.29972	+	3.78295i	0.145313	+	0.422947i
$81$	0.748445	+	4.24464i	0.0831606	+	0.471627i
$82$	4.98717	−	2.56750i	0.550740	−	0.283532i
$83$	15.0376	+	8.68195i	1.65059	+	0.952968i	0.976830	+	0.214018i	$0.0686550\pi$
$83$	15.0376	+	8.68195i	1.65059	+	0.952968i	0.673760	+	0.738951i	$0.264678\pi$
$84$	−3.84353	+	3.77448i	−0.419364	+	0.411830i
$85$	4.32858	+	3.63211i	0.469501	+	0.393958i
$86$	4.08185	+	2.62651i	0.440158	+	0.283224i
$87$	4.58731	−	2.64849i	0.491812	−	0.283948i
$88$	−2.26073	+	15.5367i	−0.240995	+	1.65622i
$89$	−0.0513214	−	0.141004i	−0.00544006	−	0.0149464i	0.936943	−	0.349483i	$-0.113643\pi$
$89$	−0.0513214	−	0.141004i	−0.00544006	−	0.0149464i	−0.942383	+	0.334536i	$0.891420\pi$
$90$	−3.30190	+	1.02466i	−0.348051	+	0.108008i
$91$	−1.35540	+	7.68686i	−0.142085	+	0.805802i
$92$	0.332769	−	3.44377i	0.0346936	−	0.359038i
$93$	1.10282	−	0.925373i	0.114357	−	0.0959567i
$94$	9.61225	−	1.22119i	0.991428	−	0.125956i
$95$	2.04376	+	3.85007i	0.209685	+	0.395009i
$96$	−2.48989	−	3.40179i	−0.254124	−	0.347194i
$97$	−2.23563	−	2.66432i	−0.226994	−	0.270521i	0.640512	−	0.767948i	$-0.278722\pi$
$97$	−2.23563	−	2.66432i	−0.226994	−	0.270521i	−0.867505	+	0.497428i	$0.834278\pi$
$98$	−1.89380	+	8.36286i	−0.191303	+	0.844776i
$99$	−13.3637	−	2.35639i	−1.34311	−	0.236826i
$100$	−0.828773	−	1.82020i	−0.0828773	−	0.182020i
$101$	−4.77950	+	1.73960i	−0.475578	+	0.173096i	−0.568677	−	0.822561i	$-0.692545\pi$
$101$	−4.77950	+	1.73960i	−0.475578	+	0.173096i	0.0930995	+	0.995657i	$0.470323\pi$
$102$	−5.49151	−	2.30387i	−0.543741	−	0.228117i
$103$	4.73756	+	8.20570i	0.466806	+	0.808532i	0.999281	−	0.0379141i	$-0.0120713\pi$
$103$	4.73756	+	8.20570i	0.466806	+	0.808532i	−0.532475	+	0.846446i	$0.678738\pi$
$104$	−5.80005	−	1.91582i	−0.568742	−	0.187862i
$105$	1.73134	−	2.06333i	0.168961	−	0.201360i
$106$	−8.99954	−	11.8391i	−0.874113	−	1.14992i
$107$	4.23725	−	7.33914i	0.409631	−	0.709501i	−0.585218	−	0.810876i	$-0.698991\pi$
$107$	4.23725	−	7.33914i	0.409631	−	0.709501i	0.994848	+	0.101375i	$0.0323242\pi$
$108$	6.68934	−	4.59413i	0.643682	−	0.442071i
$109$	−15.2428	+	2.68772i	−1.46000	+	0.257437i	−0.846554	−	0.532302i	$-0.821327\pi$
$109$	−15.2428	+	2.68772i	−1.46000	+	0.257437i	−0.613443	+	0.789739i	$0.710216\pi$
$110$	0.377957	−	7.84104i	0.0360368	−	0.747614i
$111$	0.288315	−	0.792138i	0.0273656	−	0.0751864i
$112$	−13.4935	−	5.19010i	−1.27501	−	0.490418i
$113$			10.2927i			0.968253i	0.874998	+	0.484126i	$0.160862\pi$
$113$			10.2927i			0.968253i	−0.874998	+	0.484126i	$0.839138\pi$
$114$	−3.25978	−	3.23694i	−0.305306	−	0.303168i
$115$			1.72991i			0.161315i
$116$	11.5704	+	8.25898i	1.07429	+	0.766827i
$117$	1.80567	−	4.96104i	0.166934	−	0.458648i
$118$	−5.64057	−	0.271889i	−0.519257	−	0.0250294i
$119$	−20.1126	+	3.54639i	−1.84372	+	0.325097i
$120$	1.40277	+	1.57327i	0.128055	+	0.143619i
$121$	9.90621	−	17.1581i	0.900564	−	1.55982i
$122$	−2.84808	+	2.16497i	−0.257853	+	0.196007i
$123$	1.89998	−	2.26431i	0.171315	−	0.204166i
$124$	3.48664	+	1.66449i	0.313110	+	0.149475i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	4.83408	−	11.5225i	0.430654	−	1.02651i
$127$	2.34528	−	0.853611i	0.208110	−	0.0757458i	−0.235862	−	0.971787i	$-0.575791\pi$
$127$	2.34528	−	0.853611i	0.208110	−	0.0757458i	0.443972	+	0.896041i	$0.353569\pi$
$128$	5.53976	−	9.86464i	0.489650	−	0.871919i
$129$	2.51892	+	0.444154i	0.221779	+	0.0391056i
$130$	2.97872	+	0.674542i	0.261251	+	0.0591613i
$131$	11.6522	+	13.8866i	1.01806	+	1.21327i	0.976806	+	0.214126i	$0.0686903\pi$
$131$	11.6522	+	13.8866i	1.01806	+	1.21327i	0.0412524	+	0.999149i	$0.486865\pi$
$132$	2.06879	+	8.01055i	0.180065	+	0.697229i
$133$	−15.4079	−	3.28600i	−1.33603	−	0.284932i
$134$	0.994635	+	7.82901i	0.0859234	+	0.676324i
$135$	−3.10823	+	2.60811i	−0.267514	+	0.224471i
$136$	−0.479995	−	15.9750i	−0.0411593	−	1.36984i
$137$	−1.87775	+	10.6493i	−0.160427	+	0.909828i	0.793228	+	0.608925i	$0.208399\pi$
$137$	−1.87775	+	10.6493i	−0.160427	+	0.909828i	−0.953655	+	0.300903i	$0.902712\pi$
$138$	−0.540353	−	1.74126i	−0.0459979	−	0.148226i
$139$	1.74886	+	4.80494i	0.148336	+	0.407550i	0.991500	−	0.130107i	$-0.0415319\pi$
$139$	1.74886	+	4.80494i	0.148336	+	0.407550i	−0.843164	+	0.537657i	$0.819310\pi$
$140$	6.96505	+	1.93411i	0.588654	+	0.163462i
$141$	4.42189	−	2.55298i	0.372390	−	0.215000i
$142$	10.4170	−	16.1890i	0.874176	−	1.35855i
$143$	9.18312	+	7.70555i	0.767931	+	0.644371i
$144$	8.37844	+	5.04196i	0.698203	+	0.420164i
$145$	−6.15557	−	3.55392i	−0.511192	−	0.295137i
$146$	−3.35458	−	6.51602i	−0.277627	−	0.539270i
$147$	0.784621	+	4.44981i	0.0647144	+	0.367014i
$148$	2.25541	−	0.176740i	0.185394	−	0.0145279i
$149$	−7.37347	−	2.68372i	−0.604058	−	0.219859i	0.0218432	−	0.999761i	$-0.493047\pi$
$149$	−7.37347	−	2.68372i	−0.604058	−	0.219859i	−0.625901	+	0.779902i	$0.715269\pi$
$150$	−0.773792	−	0.715528i	−0.0631799	−	0.0584226i
$151$	−4.85527			−0.395116			−0.197558	−	0.980291i	$-0.563301\pi$
$151$	−4.85527			−0.395116			−0.197558	+	0.980291i	$0.563301\pi$
$152$	4.28093	−	11.5617i	0.347229	−	0.937780i
$153$	13.8135			1.11676
$154$	20.8315	+	19.2630i	1.67865	+	1.55226i
$155$	−1.81529	−	0.660710i	−0.145807	−	0.0530695i
$156$	−3.20896	+	0.251462i	−0.256922	+	0.0201331i
$157$	−0.316208	−	1.79330i	−0.0252361	−	0.143121i	0.969586	−	0.244750i	$-0.0787058\pi$
$157$	−0.316208	−	1.79330i	−0.0252361	−	0.143121i	−0.994822	+	0.101628i	$0.967595\pi$
$158$	−6.43062	−	12.4910i	−0.511593	−	0.993730i
$159$	−6.78666	−	3.91828i	−0.538217	−	0.310740i
$160$	−2.28264	+	5.17586i	−0.180459	+	0.409188i
$161$	−4.78961	−	4.01896i	−0.377475	−	0.316739i
$162$	−3.29834	+	5.12594i	−0.259142	+	0.402732i
$163$	−18.5324	+	10.6997i	−1.45157	+	0.838065i	−0.998571	−	0.0534460i	$-0.982979\pi$
$163$	−18.5324	+	10.6997i	−1.45157	+	0.838065i	−0.453000	+	0.891511i	$0.649646\pi$
$164$	7.64347	+	2.12250i	0.596855	+	0.165739i
$165$	−1.41483	−	3.88722i	−0.110144	−	0.302620i
$166$	7.27800	+	23.4530i	0.564883	+	1.82030i
$167$	3.44088	−	19.5142i	0.266264	−	1.51006i	−0.499149	−	0.866516i	$-0.666354\pi$
$167$	3.44088	−	19.5142i	0.266264	−	1.51006i	0.765413	−	0.643540i	$-0.222535\pi$
$168$	−7.61489	+	0.228802i	−0.587501	+	0.0176525i
$169$	6.38584	−	5.35836i	0.491219	−	0.412181i
$170$	1.00713	+	7.92738i	0.0772436	+	0.608003i
$171$	9.87727	+	3.99849i	0.755333	+	0.305772i
$172$	1.71647	+	6.64634i	0.130880	+	0.506779i
$173$	11.5063	+	13.7127i	0.874810	+	1.04256i	0.998736	+	0.0502666i	$0.0160071\pi$
$173$	11.5063	+	13.7127i	0.874810	+	1.04256i	−0.123926	+	0.992291i	$0.539548\pi$
$174$	7.30606	+	1.65449i	0.553871	+	0.125426i
$175$	−3.55939	−	0.627617i	−0.269065	−	0.0474434i
$176$	−17.2648	+	13.9615i	−1.30139	+	1.05239i
$177$	−2.79633	+	1.01778i	−0.210185	+	0.0765010i
$178$	0.0820962	−	0.195685i	0.00615337	−	0.0146672i
$179$	2.69829	+	4.67358i	0.201680	+	0.349320i	0.949070	−	0.315066i	$-0.102027\pi$
$179$	2.69829	+	4.67358i	0.201680	+	0.349320i	−0.747390	+	0.664386i	$0.768693\pi$
$180$	−4.41227	−	2.10637i	−0.328871	−	0.157000i
$181$	−13.9470	+	16.6214i	−1.03667	+	1.23546i	−0.0653052	+	0.997865i	$0.520802\pi$
$181$	−13.9470	+	16.6214i	−1.03667	+	1.23546i	−0.971365	+	0.237591i	$0.923642\pi$
$182$	−8.78785	+	6.68010i	−0.651399	+	0.495162i
$183$	−0.942601	+	1.63263i	−0.0696790	+	0.120688i
$184$	3.65204	−	3.25625i	0.269232	−	0.240054i
$185$	−1.11398	+	0.196424i	−0.0819012	+	0.0144414i
$186$	2.03358	+	0.0980232i	0.149109	+	0.00718741i
$187$	−10.7277	+	29.4741i	−0.784486	+	2.15536i
$188$	11.1532	+	7.96116i	0.813429	+	0.580627i
$189$		−	14.6650i		−	1.06672i
$190$	−1.57453	+	5.95994i	−0.114228	+	0.432379i
$191$			9.58068i			0.693233i	0.938007	+	0.346617i	$0.112670\pi$
$191$			9.58068i			0.693233i	−0.938007	+	0.346617i	$0.887330\pi$
$192$	0.680889	−	5.92283i	0.0491390	−	0.427443i
$193$	6.62663	−	18.2065i	0.476995	−	1.31053i	−0.435036	−	0.900413i	$-0.643264\pi$
$193$	6.62663	−	18.2065i	0.476995	−	1.31053i	0.912031	−	0.410121i	$-0.134513\pi$
$194$	0.236816	−	4.91296i	0.0170024	−	0.352730i
$195$	1.58495	−	0.279469i	0.113501	−	0.0200132i
$196$	−9.99594	+	6.86506i	−0.713996	+	0.490361i
$197$	2.24985	−	3.89686i	0.160296	−	0.277640i	−0.774679	−	0.632355i	$-0.782089\pi$
$197$	2.24985	−	3.89686i	0.160296	−	0.277640i	0.934975	+	0.354715i	$0.115422\pi$
$198$	−11.6135	−	15.2778i	−0.825332	−	1.08575i
$199$	−8.90869	+	10.6170i	−0.631520	+	0.752617i	−0.983005	−	0.183577i	$-0.941232\pi$
$199$	−8.90869	+	10.6170i	−0.631520	+	0.752617i	0.351485	+	0.936194i	$0.385677\pi$
$200$	0.887119	−	2.68571i	0.0627288	−	0.189908i
$201$	2.07936	+	3.60155i	0.146667	+	0.254034i
$202$	−6.63295	−	2.78274i	−0.466692	−	0.195793i
$203$	24.1406	−	8.78645i	1.69434	−	0.616688i
$204$	−3.48994	−	7.66481i	−0.244344	−	0.536644i
$205$	−3.90609	−	0.688749i	−0.272813	−	0.0481043i
$206$	−2.95952	+	13.0689i	−0.206199	+	0.910556i
$207$	2.71834	+	3.23959i	0.188938	+	0.225167i
$208$	−4.18289	−	7.55814i	−0.290031	−	0.524063i
$209$	−16.2024	+	17.9700i	−1.12074	+	1.24301i
$210$	3.77879	−	0.480075i	0.260761	−	0.0331284i
$211$	−19.8058	+	16.6191i	−1.36349	+	1.14410i	−0.388602	+	0.921406i	$0.627042\pi$
$211$	−19.8058	+	16.6191i	−1.36349	+	1.14410i	−0.974888	+	0.222698i	$0.928514\pi$
$212$	2.02281	−	20.9338i	0.138927	−	1.43774i
$213$	1.76156	−	9.99031i	0.120700	−	0.684525i
$214$	11.4463	−	3.55205i	0.782452	−	0.242813i
$215$	−1.17388	−	3.22522i	−0.0800582	−	0.219958i
$216$	11.3568	+	1.65251i	0.772729	+	0.112439i
$217$	6.04664	−	3.49103i	0.410472	−	0.236986i
$218$	−18.4076	−	11.8446i	−1.24672	−	0.802216i
$219$	−2.95845	−	2.48243i	−0.199913	−	0.167747i
$220$	7.92098	−	7.77867i	0.534032	−	0.524438i
$221$	−10.5681	−	6.10148i	−0.710886	−	0.410430i
$222$	1.05993	−	0.545675i	0.0711380	−	0.0366233i
$223$	1.79519	+	10.1810i	0.120215	+	0.681773i	0.984035	+	0.177973i	$0.0569539\pi$
$223$	1.79519	+	10.1810i	0.120215	+	0.681773i	−0.863821	+	0.503800i	$0.831935\pi$
$224$	−9.02739	−	18.3447i	−0.603168	−	1.22571i
$225$	2.29720	+	0.836114i	0.153147	+	0.0557409i
$226$	−9.88244	+	10.6872i	−0.657370	+	0.710899i
$227$	−11.0042			−0.730377			−0.365189	−	0.930934i	$-0.618995\pi$
$227$	−11.0042			−0.730377			−0.365189	+	0.930934i	$0.618995\pi$
$228$	−0.276782	−	6.49086i	−0.0183303	−	0.429868i
$229$	14.0424			0.927951			0.463976	−	0.885848i	$-0.346423\pi$
$229$	14.0424			0.927951			0.463976	+	0.885848i	$0.346423\pi$
$230$	−1.66096	+	1.79621i	−0.109520	+	0.118438i
$231$	14.0496	+	5.11363i	0.924394	+	0.336452i
$232$	4.08406	+	19.6848i	0.268132	+	1.29237i
$233$	3.13662	+	17.7886i	0.205487	+	1.16537i	0.896672	+	0.442695i	$0.145978\pi$
$233$	3.13662	+	17.7886i	0.205487	+	1.16537i	−0.691186	+	0.722677i	$0.742911\pi$
$234$	6.63819	−	3.41748i	0.433952	−	0.223408i
$235$	−5.93359	−	3.42576i	−0.387065	−	0.223472i
$236$	−5.59570	−	5.69807i	−0.364249	−	0.370913i
$237$	−5.67124	−	4.75874i	−0.368387	−	0.309113i
$238$	−24.2885	−	15.6286i	−1.57439	−	1.01305i
$239$	4.84074	−	2.79480i	0.313121	−	0.180781i	−0.335201	−	0.942147i	$-0.608804\pi$
$239$	4.84074	−	2.79480i	0.313121	−	0.180781i	0.648322	+	0.761366i	$0.275471\pi$
$240$	−0.0540336	+	2.98043i	−0.00348785	+	0.192386i
$241$	7.61440	+	20.9204i	0.490487	+	1.34760i	0.900236	+	0.435403i	$0.143394\pi$
$241$	7.61440	+	20.9204i	0.490487	+	1.34760i	−0.409749	+	0.912198i	$0.634384\pi$
$242$	26.7601	−	8.30428i	1.72020	−	0.533820i
$243$	−2.67150	+	15.1508i	−0.171377	+	0.971925i
$244$	−5.03593	−	0.486618i	−0.322392	−	0.0311525i
$245$	4.64465	−	3.89733i	0.296736	−	0.248991i
$246$	4.14686	−	0.526837i	0.264394	−	0.0335899i
$247$	−5.79047	−	7.42187i	−0.368439	−	0.472242i
$248$	2.02213	+	5.07596i	0.128405	+	0.322324i
$249$	8.31774	+	9.91269i	0.527115	+	0.628191i
$250$	−0.312346	+	1.37929i	−0.0197545	+	0.0872339i
$251$	28.7715	+	5.07319i	1.81604	+	0.320217i	0.975243	−	0.221135i	$-0.0709761\pi$
$251$	28.7715	+	5.07319i	1.81604	+	0.320217i	0.840796	+	0.541352i	$0.182087\pi$
$252$	16.0826	−	7.32274i	1.01311	−	0.461289i
$253$	−9.02342	+	3.28426i	−0.567297	+	0.206479i
$254$	3.25476	+	1.36548i	0.204222	+	0.0856777i
$255$	2.10548	+	3.64681i	0.131851	+	0.228372i
$256$	15.2236	−	4.92375i	0.951472	−	0.307734i
$257$	−11.2402	+	13.3955i	−0.701143	+	0.835590i	−0.992655	−	0.120977i	$-0.961397\pi$
$257$	−11.2402	+	13.3955i	−0.701143	+	0.835590i	0.291512	+	0.956567i	$0.405842\pi$
$258$	2.18902	+	2.87971i	0.136282	+	0.179283i
$259$	2.04418	−	3.54062i	0.127019	−	0.220004i
$260$	2.44522	+	3.56039i	0.151646	+	0.220806i
$261$	−17.1121	+	3.01732i	−1.05921	+	0.186767i
$262$	−1.23430	+	25.6066i	−0.0762553	+	1.58198i
$263$	10.1638	−	27.9249i	0.626728	−	1.72192i	−0.0631590	−	0.998003i	$-0.520118\pi$
$263$	10.1638	−	27.9249i	0.626728	−	1.72192i	0.689887	−	0.723917i	$-0.257660\pi$
$264$	−5.54321	+	10.3039i	−0.341161	+	0.634162i
$265$			10.5156i			0.645970i
$266$	−12.8434	−	18.2057i	−0.787478	−	1.11626i
$267$		−	0.111825i		−	0.00684355i
$268$	−6.48423	+	9.08407i	−0.396087	+	0.554898i
$269$	2.84663	−	7.82105i	0.173562	−	0.476858i	−0.822160	−	0.569256i	$-0.807231\pi$
$269$	2.84663	−	7.82105i	0.173562	−	0.476858i	0.995722	+	0.0923987i	$0.0294534\pi$
$270$	−5.73152	−	0.276273i	−0.348809	−	0.0168134i
$271$	19.1961	−	3.38479i	1.16608	−	0.205611i	0.443095	−	0.896475i	$-0.353881\pi$
$271$	19.1961	−	3.38479i	1.16608	−	0.205611i	0.722985	+	0.690864i	$0.242769\pi$
$272$	14.8399	−	17.0481i	0.899802	−	1.03370i
$273$	−2.90843	+	5.03754i	−0.176026	+	0.304886i
$274$	−12.1746	+	9.25451i	−0.735492	+	0.559085i
$275$	−3.56805	+	4.25223i	−0.215161	+	0.256419i
$276$	1.11079	−	2.32681i	0.0668620	−	0.140058i
$277$	11.4817	+	19.8869i	0.689869	+	1.19489i	0.971880	+	0.235477i	$0.0756651\pi$
$277$	11.4817	+	19.8869i	0.689869	+	1.19489i	−0.282011	+	0.959411i	$0.591002\pi$
$278$	−2.79755	+	6.66826i	−0.167786	+	0.399936i
$279$	−4.43771	+	1.61519i	−0.265678	+	0.0966991i
$280$	5.37497	+	8.69569i	0.321216	+	0.519667i
$281$	−11.9322	−	2.10398i	−0.711818	−	0.125513i	−0.193998	−	0.981002i	$-0.562145\pi$
$281$	−11.9322	−	2.10398i	−0.711818	−	0.125513i	−0.517821	+	0.855489i	$0.673257\pi$
$282$	7.04260	+	1.59482i	0.419381	+	0.0949704i
$283$	−4.25525	−	5.07122i	−0.252949	−	0.301452i	0.624595	−	0.780949i	$-0.285264\pi$
$283$	−4.25525	−	5.07122i	−0.252949	−	0.301452i	−0.877544	+	0.479496i	$0.840819\pi$
$284$	26.3601	−	6.80770i	1.56418	−	0.403963i
$285$	0.449899	+	3.21708i	0.0266497	+	0.190563i
$286$	2.13664	+	16.8180i	0.126342	+	0.994470i
$287$	10.9817	−	9.21473i	0.648229	−	0.543928i
$288$	3.85855	+	13.2797i	0.227367	+	0.782515i
$289$	2.59237	−	14.7021i	0.152492	−	0.864827i
$290$	−2.97922	−	9.60036i	−0.174946	−	0.563753i
$291$	−0.886490	−	2.43561i	−0.0519670	−	0.142778i
$292$	2.77317	−	9.98664i	0.162287	−	0.584424i
$293$	25.4001	−	14.6648i	1.48389	−	0.856725i	0.484060	−	0.875035i	$-0.339162\pi$
$293$	25.4001	−	14.6648i	1.48389	−	0.856725i	0.999832	+	0.0183095i	$0.00582842\pi$
$294$	−3.45776	+	5.37370i	−0.201661	+	0.313401i
$295$	3.05890	+	2.56673i	0.178096	+	0.149441i
$296$	2.51155	+	1.98201i	0.145981	+	0.115202i
$297$	−19.5053	−	11.2614i	−1.13181	−	0.653452i
$298$	−5.07931	−	9.86618i	−0.294237	−	0.571532i
$299$	−0.648733	−	3.67915i	−0.0375172	−	0.212771i
$300$	−0.116439	−	1.48590i	−0.00672262	−	0.0857887i
$301$	11.6569	+	4.24277i	0.671893	+	0.244549i
$302$	−5.04135	−	4.66176i	−0.290097	−	0.268254i
$303$	−3.79042			−0.217754
$304$	15.5459	−	7.89455i	0.891621	−	0.452783i
$305$	2.52969			0.144850
$306$	14.3430	+	13.2630i	0.819934	+	0.758195i
$307$	13.3282	+	4.85108i	0.760682	+	0.276866i	0.693093	−	0.720848i	$-0.256247\pi$
$307$	13.3282	+	4.85108i	0.760682	+	0.276866i	0.0675884	+	0.997713i	$0.478470\pi$
$308$	3.13470	+	40.0025i	0.178616	+	2.27936i
$309$	1.22616	+	6.95387i	0.0697535	+	0.395592i
$310$	−1.25048	−	2.42897i	−0.0710227	−	0.137956i
$311$	−26.0677	−	15.0502i	−1.47816	−	0.853418i	−0.478469	−	0.878105i	$-0.658808\pi$
$311$	−26.0677	−	15.0502i	−1.47816	−	0.853418i	−0.999695	+	0.0246863i	$0.992141\pi$
$312$	−3.57339	−	2.81997i	−0.202303	−	0.159649i
$313$	−15.4049	−	12.9262i	−0.870734	−	0.730633i	0.0935185	−	0.995618i	$-0.470189\pi$
$313$	−15.4049	−	12.9262i	−0.870734	−	0.730633i	−0.964253	+	0.264985i	$0.914633\pi$
$314$	1.39350	−	2.16564i	0.0786400	−	0.122214i
$315$	−7.65188	+	4.41782i	−0.431135	+	0.248916i
$316$	5.31607	−	19.1441i	0.299052	−	1.07694i
$317$	−6.97002	−	19.1500i	−0.391475	−	1.07557i	−0.966328	−	0.257312i	$-0.917163\pi$
$317$	−6.97002	−	19.1500i	−0.391475	−	1.07557i	0.574853	−	0.818257i	$-0.305059\pi$
$318$	−3.28466	−	10.5846i	−0.184195	−	0.593557i
$319$	6.85126	−	38.8554i	0.383597	−	2.17549i
$320$	−7.33970	+	3.18257i	−0.410302	+	0.177911i
$321$	4.83792	−	4.05950i	0.270026	−	0.226579i
$322$	−1.11440	−	8.77172i	−0.0621032	−	0.488829i
$323$	13.0662	−	20.8787i	0.727025	−	1.16172i
$324$	−8.34640	+	2.15552i	−0.463689	+	0.119751i
$325$	−1.38816	−	1.65435i	−0.0770015	−	0.0917668i
$326$	−29.5160	−	6.68401i	−1.63474	−	0.370193i
$327$	−11.3594	−	2.00297i	−0.628177	−	0.110764i
$328$	5.89852	+	9.54269i	0.325691	+	0.526907i
$329$	23.2700	−	8.46960i	1.28292	−	0.466944i
$330$	2.26323	−	5.39465i	0.124587	−	0.296966i
$331$	−4.49490	−	7.78539i	−0.247062	−	0.427924i	0.715647	−	0.698462i	$-0.246132\pi$
$331$	−4.49490	−	7.78539i	−0.247062	−	0.427924i	−0.962709	+	0.270538i	$0.912798\pi$
$332$	−14.9613	+	31.3398i	−0.821107	+	1.71999i
$333$	−1.77748	+	2.11832i	−0.0974056	+	0.116083i
$334$	22.3092	−	16.9584i	1.22071	−	0.927923i
$335$	2.79022	−	4.83281i	0.152446	−	0.264045i
$336$	−8.12643	−	7.07382i	−0.443333	−	0.385908i
$337$	−7.18309	+	1.26657i	−0.391288	+	0.0689946i	−0.365831	−	0.930681i	$-0.619215\pi$
$337$	−7.18309	+	1.26657i	−0.391288	+	0.0689946i	−0.0254570	+	0.999676i	$0.508104\pi$
$338$	11.7754	+	0.567602i	0.640497	+	0.0308735i
$339$	−2.62343	+	7.20782i	−0.142485	+	0.391475i
$340$	−6.56570	+	9.19821i	−0.356075	+	0.498843i
$341$		−	10.7231i		−	0.580691i
$342$	6.41670	+	13.6353i	0.346976	+	0.737315i
$343$		−	3.38601i		−	0.182827i
$344$	−4.59919	+	8.54914i	−0.247972	+	0.460939i
$345$	−0.440925	+	1.21143i	−0.0237386	+	0.0652212i
$346$	−1.21885	+	25.2860i	−0.0655256	+	1.35938i
$347$	−15.4024	+	2.71586i	−0.826845	+	0.145795i	−0.571029	−	0.820930i	$-0.693455\pi$
$347$	−15.4024	+	2.71586i	−0.826845	+	0.145795i	−0.255817	+	0.966725i	$0.582344\pi$
$348$	5.99753	+	8.73277i	0.321501	+	0.468126i
$349$	12.8146	−	22.1956i	0.685952	−	1.18810i	−0.287185	−	0.957875i	$-0.592719\pi$
$349$	12.8146	−	22.1956i	0.685952	−	1.18810i	0.973137	−	0.230228i	$-0.0739473\pi$
$350$	−3.09321	−	4.06920i	−0.165339	−	0.217508i
$351$	5.63248	−	6.71253i	0.300640	−	0.358288i
$352$	−31.3316	−	2.08010i	−1.66998	−	0.110870i
$353$	−3.57065	−	6.18455i	−0.190047	−	0.329171i	0.755219	−	0.655473i	$-0.227531\pi$
$353$	−3.57065	−	6.18455i	−0.190047	−	0.329171i	−0.945265	+	0.326302i	$0.894197\pi$
$354$	−3.88072	−	1.62809i	−0.206258	−	0.0865320i
$355$	−12.7915	+	4.65574i	−0.678905	+	0.247101i
$356$	0.273128	−	0.124361i	0.0144758	−	0.00659109i
$357$	−14.9885	−	2.64287i	−0.793275	−	0.139876i
$358$	−1.68560	+	7.44345i	−0.0890868	+	0.393399i
$359$	−7.80193	−	9.29797i	−0.411770	−	0.490728i	0.519801	−	0.854287i	$-0.326006\pi$
$359$	−7.80193	−	9.29797i	−0.411770	−	0.490728i	−0.931571	+	0.363559i	$0.881562\pi$
$360$	−2.55896	−	6.42352i	−0.134869	−	0.338549i
$361$	15.3865	−	11.1470i	0.809816	−	0.586684i
$362$	−30.4404	+	3.86730i	−1.59991	+	0.203261i
$363$	11.3105	−	9.49063i	0.593647	−	0.498129i
$364$	−15.5385	−	1.50148i	−0.814440	−	0.0786987i
$365$	−0.899891	+	5.10353i	−0.0471024	+	0.267131i
$366$	−2.54629	+	0.790174i	−0.133097	+	0.0413030i
$367$	4.11630	+	11.3094i	0.214869	+	0.590348i	0.999564	−	0.0295345i	$-0.00940248\pi$
$367$	4.11630	+	11.3094i	0.214869	+	0.590348i	−0.784695	+	0.619882i	$0.787180\pi$
$368$	6.91849	+	0.125428i	0.360651	+	0.00653841i
$369$	−8.39721	+	4.84813i	−0.437141	+	0.252384i
$370$	−1.34527	−	0.865626i	−0.0699372	−	0.0450018i
$371$	−29.1148	−	24.4302i	−1.51156	−	1.26835i
$372$	2.01740	+	2.05431i	0.104597	+	0.106511i
$373$	18.4023	+	10.6245i	0.952833	+	0.550118i	0.893960	−	0.448147i	$-0.147916\pi$
$373$	18.4023	+	10.6245i	0.952833	+	0.550118i	0.0588729	+	0.998265i	$0.481249\pi$
$374$	−39.4382	+	20.3036i	−2.03930	+	1.04987i
$375$	0.129408	+	0.733908i	0.00668259	+	0.0378989i
$376$	3.93679	+	18.9749i	0.203024	+	0.978558i
$377$	14.4244	+	5.25004i	0.742893	+	0.270391i
$378$	14.0805	−	15.2271i	0.724225	−	0.783197i
$379$	23.2628			1.19493			0.597466	−	0.801895i	$-0.296174\pi$
$379$	23.2628			1.19493			0.597466	+	0.801895i	$0.296174\pi$
$380$	−7.35728	+	4.67659i	−0.377420	+	0.239904i
$381$	1.85994			0.0952876
$382$	−9.19883	+	9.94788i	−0.470653	+	0.508978i
$383$	−3.33984	−	1.21560i	−0.170658	−	0.0621144i	0.255278	−	0.966868i	$-0.417833\pi$
$383$	−3.33984	−	1.21560i	−0.170658	−	0.0621144i	−0.425936	+	0.904753i	$0.640055\pi$
$384$	6.39376	−	5.49608i	0.326280	−	0.280471i
$385$	−3.48383	−	19.7578i	−0.177553	−	1.00695i
$386$	24.3615	−	12.5418i	1.23997	−	0.638361i
$387$	−7.26637	−	4.19524i	−0.369370	−	0.213256i
$388$	4.96304	−	4.87388i	0.251960	−	0.247434i
$389$	27.6853	+	23.2307i	1.40370	+	1.17784i	0.959428	+	0.281953i	$0.0909823\pi$
$389$	27.6853	+	23.2307i	1.40370	+	1.17784i	0.444273	+	0.895892i	$0.353462\pi$
$390$	1.91403	+	1.23160i	0.0969205	+	0.0623644i
$391$	8.46535	−	4.88747i	0.428111	−	0.247170i
$392$	−16.9705	−	2.46937i	−0.857140	−	0.124722i
$393$	4.62043	+	12.6945i	0.233070	+	0.640355i
$394$	6.07764	−	1.88603i	0.306187	−	0.0950170i
$395$	−1.72506	+	9.78331i	−0.0867972	+	0.492252i
$396$	2.61034	−	27.0140i	0.131175	−	1.35750i
$397$	−14.2018	+	11.9168i	−0.712770	+	0.598085i	−0.925375	−	0.379053i	$-0.876250\pi$
$397$	−14.2018	+	11.9168i	−0.712770	+	0.598085i	0.212605	+	0.977138i	$0.431805\pi$
$398$	−19.4440	+	2.47025i	−0.974637	+	0.123823i
$399$	−9.95238	−	6.22835i	−0.498242	−	0.311808i
$400$	3.49979	−	1.93688i	0.174989	−	0.0968440i
$401$	−5.02035	−	5.98303i	−0.250705	−	0.298778i	0.625985	−	0.779835i	$-0.284697\pi$
$401$	−5.02035	−	5.98303i	−0.250705	−	0.298778i	−0.876689	+	0.481057i	$0.840253\pi$
$402$	−1.29896	+	5.73607i	−0.0647861	+	0.286089i
$403$	4.10851	+	0.724441i	0.204659	+	0.0360870i
$404$	−4.21534	−	9.25798i	−0.209721	−	0.460602i
$405$	4.05019	−	1.47415i	0.201256	−	0.0732511i
$406$	33.5021	+	14.0552i	1.66268	+	0.697549i
$407$	−3.13948	−	5.43774i	−0.155618	−	0.269539i
$408$	3.73563	−	11.3094i	0.184941	−	0.559900i
$409$	−15.6024	+	18.5943i	−0.771491	+	0.919427i	−0.998516	−	0.0544616i	$-0.982656\pi$
$409$	−15.6024	+	18.5943i	−0.771491	+	0.919427i	0.227025	+	0.973889i	$0.427100\pi$
$410$	−3.39450	−	4.46556i	−0.167642	−	0.220538i
$411$	−4.02929	+	6.97893i	−0.198750	+	0.344245i
$412$	−15.6210	+	10.7283i	−0.769592	+	0.528544i
$413$	−14.2131	+	2.50615i	−0.699379	+	0.123319i
$414$	−0.287949	+	5.97375i	−0.0141519	+	0.293594i
$415$	5.93881	−	16.3167i	0.291525	−	0.800957i
$416$	2.91370	−	11.8640i	0.142856	−	0.581680i
$417$			3.81060i			0.186606i
$418$	−34.0771	+	3.10208i	−1.66677	+	0.151728i
$419$		−	23.0187i		−	1.12454i	−0.826955	−	0.562268i	$-0.809929\pi$
$419$		−	23.0187i		−	1.12454i	0.826955	−	0.562268i	$-0.190071\pi$
$420$	4.38456	+	3.12971i	0.213945	+	0.152714i
$421$	−2.31219	+	6.35269i	−0.112689	+	0.309611i	−0.983198	−	0.182542i	$-0.941568\pi$
$421$	−2.31219	+	6.35269i	−0.112689	+	0.309611i	0.870509	+	0.492153i	$0.163790\pi$
$422$	−36.5216	−	1.76043i	−1.77785	−	0.0856964i
$423$	−16.4950	+	2.90851i	−0.802014	+	0.141417i
$424$	22.1998	−	19.7939i	1.07812	−	0.961277i
$425$	2.82528	−	4.89353i	0.137046	−	0.237371i
$426$	11.4212	−	8.68186i	0.553360	−	0.420637i
$427$	−5.87705	+	7.00399i	−0.284410	+	0.338947i
$428$	15.2955	+	7.30190i	0.739334	+	0.352950i
$429$	4.46680	+	7.73673i	0.215659	+	0.373533i
$430$	1.87780	−	4.47593i	0.0905556	−	0.215849i
$431$	13.7815	−	5.01607i	0.663833	−	0.241615i	0.0119427	−	0.999929i	$-0.496198\pi$
$431$	13.7815	−	5.01607i	0.663833	−	0.241615i	0.651890	+	0.758313i	$0.273976\pi$
$432$	10.2054	+	12.6200i	0.491006	+	0.607179i
$433$	−21.8218	−	3.84778i	−1.04869	−	0.184912i	−0.377357	−	0.926068i	$-0.623167\pi$
$433$	−21.8218	−	3.84778i	−1.04869	−	0.184912i	−0.671333	+	0.741156i	$0.734278\pi$
$434$	9.63028	+	2.18082i	0.462268	+	0.104682i
$435$	−3.40483	−	4.05772i	−0.163249	−	0.194553i
$436$	−7.74064	−	29.9725i	−0.370710	−	1.43542i
$437$	7.46781	−	1.04435i	0.357234	−	0.0499582i
$438$	−0.688343	−	5.41811i	−0.0328903	−	0.258887i
$439$	−0.444254	+	0.372774i	−0.0212031	+	0.0177915i	−0.653328	−	0.757075i	$-0.726628\pi$
$439$	−0.444254	+	0.372774i	−0.0212031	+	0.0177915i	0.632125	+	0.774867i	$0.282183\pi$
$440$	15.6932	−	0.471529i	0.748145	−	0.0224792i
$441$	2.57385	−	14.5970i	0.122564	−	0.695096i
$442$	−5.11482	−	16.4822i	−0.243287	−	0.783979i
$443$	7.73454	+	21.2505i	0.367479	+	1.00964i	0.976317	+	0.216346i	$0.0694139\pi$
$443$	7.73454	+	21.2505i	0.367479	+	1.00964i	−0.608838	+	0.793295i	$0.708364\pi$
$444$	1.62448	+	0.451099i	0.0770945	+	0.0214082i
$445$	−0.129950	+	0.0750269i	−0.00616024	+	0.00355662i
$446$	−7.91127	+	12.2949i	−0.374609	+	0.582180i
$447$	−4.47951	−	3.75875i	−0.211873	−	0.177783i
$448$	8.24017	−	27.7154i	0.389311	−	1.30943i
$449$	−36.0930	−	20.8383i	−1.70333	−	0.983420i	−0.942337	−	0.334665i	$-0.891377\pi$
$449$	−36.0930	−	20.8383i	−1.70333	−	0.983420i	−0.760997	−	0.648756i	$-0.775290\pi$
$450$	1.58246	+	3.07381i	0.0745978	+	0.144901i
$451$	−3.82317	−	21.6823i	−0.180026	−	1.02098i
$452$	−20.5224	+	1.60819i	−0.965293	+	0.0756428i
$453$	−3.40008	−	1.23753i	−0.159750	−	0.0581441i
$454$	−11.4260	−	10.5657i	−0.536249	−	0.495871i
$455$	7.80545			0.365925
$456$	5.94478	−	7.00539i	0.278390	−	0.328057i
$457$	25.4193			1.18906			0.594532	−	0.804072i	$-0.297337\pi$
$457$	25.4193			1.18906			0.594532	+	0.804072i	$0.297337\pi$
$458$	14.5807	+	13.4828i	0.681309	+	0.630009i
$459$	21.5445	+	7.84156i	1.00561	+	0.366012i
$460$	−3.44924	+	0.270291i	−0.160822	+	0.0126024i
$461$	3.01886	+	17.1208i	0.140602	+	0.797394i	0.970794	+	0.239916i	$0.0771199\pi$
$461$	3.01886	+	17.1208i	0.140602	+	0.797394i	−0.830192	+	0.557478i	$0.811769\pi$
$462$	9.67823	+	18.7992i	0.450272	+	0.874619i
$463$	3.09853	+	1.78894i	0.144001	+	0.0831389i	0.570269	−	0.821458i	$-0.306839\pi$
$463$	3.09853	+	1.78894i	0.144001	+	0.0831389i	−0.426269	+	0.904597i	$0.640172\pi$
$464$	−14.6597	+	24.3605i	−0.680557	+	1.13091i
$465$	−1.10282	−	0.925373i	−0.0511419	−	0.0429131i
$466$	−13.8228	+	21.4820i	−0.640330	+	0.995136i
$467$	−23.0769	+	13.3234i	−1.06787	+	0.616536i	−0.927599	−	0.373577i	$-0.878131\pi$
$467$	−23.0769	+	13.3234i	−1.06787	+	0.616536i	−0.140272	+	0.990113i	$0.544798\pi$
$468$	10.1739	+	2.82516i	0.470288	+	0.130593i
$469$	6.89834	+	18.9530i	0.318536	+	0.875170i
$470$	−2.87178	−	9.25417i	−0.132466	−	0.426863i
$471$	0.235648	−	1.33642i	0.0108581	−	0.0615792i
$472$	−0.339201	−	11.2891i	−0.0156130	−	0.519625i
$473$	14.5945	−	12.2463i	0.671057	−	0.563084i
$474$	−1.31953	−	10.3863i	−0.0606080	−	0.477060i
$475$	3.43668	−	2.68127i	0.157686	−	0.123025i
$476$	−10.2136	−	39.5481i	−0.468140	−	1.81268i
$477$	16.5240	+	19.6926i	0.756584	+	0.901662i
$478$	7.70968	+	1.74589i	0.352632	+	0.0798551i
$479$	7.76493	+	1.36917i	0.354789	+	0.0625588i	0.348202	−	0.937420i	$-0.386792\pi$
$479$	7.76493	+	1.36917i	0.354789	+	0.0625588i	0.00658655	+	0.999978i	$0.497903\pi$
$480$	−2.91775	+	3.04278i	−0.133176	+	0.138883i
$481$	2.29554	−	0.835507i	0.104667	−	0.0380958i
$482$	−12.1804	+	29.0331i	−0.554800	+	1.32242i
$483$	−2.32974	−	4.03522i	−0.106007	−	0.183609i
$484$	35.7590	+	17.0710i	1.62541	+	0.775954i
$485$	−2.23563	+	2.66432i	−0.101515	+	0.120980i
$486$	−17.3209	+	13.1665i	−0.785690	+	0.597244i
$487$	5.33192	−	9.23515i	0.241612	−	0.418485i	−0.719561	−	0.694429i	$-0.755657\pi$
$487$	5.33192	−	9.23515i	0.241612	−	0.418485i	0.961174	+	0.275944i	$0.0889905\pi$
$488$	−4.76171	−	5.34048i	−0.215553	−	0.241752i
$489$	−15.7052	+	2.76925i	−0.710213	+	0.125230i
$490$	8.56466	+	0.412837i	0.386912	+	0.0186501i
$491$	0.667093	−	1.83282i	0.0301055	−	0.0827142i	−0.923729	−	0.383046i	$-0.874875\pi$
$491$	0.667093	−	1.83282i	0.0301055	−	0.0827142i	0.953835	+	0.300332i	$0.0970974\pi$
$492$	4.81164	+	3.43455i	0.216925	+	0.154842i
$493$			40.1633i			1.80886i
$494$	1.11366	−	13.2660i	0.0501058	−	0.596866i
$495$			13.5699i			0.609921i
$496$	−2.77402	+	7.21204i	−0.124557	+	0.323830i
$497$	16.8273	−	46.2325i	0.754805	−	2.07381i
$498$	−0.881084	+	18.2788i	−0.0394823	+	0.819095i
$499$	27.0765	−	4.77432i	1.21211	−	0.213728i	0.469184	−	0.883100i	$-0.344548\pi$
$499$	27.0765	−	4.77432i	1.21211	−	0.213728i	0.742927	+	0.669372i	$0.233437\pi$
$500$	−1.64863	+	1.13226i	−0.0737292	+	0.0506361i
$501$	7.38346	−	12.7885i	0.329869	−	0.571350i
$502$	25.0032	+	32.8924i	1.11595	+	1.46806i
$503$	24.2098	−	28.8521i	1.07946	−	1.28645i	0.123697	−	0.992320i	$-0.460525\pi$
$503$	24.2098	−	28.8521i	1.07946	−	1.28645i	0.955765	−	0.294132i	$-0.0950305\pi$
$504$	23.7299	+	7.83826i	1.05701	+	0.349144i
$505$	2.54312	+	4.40481i	0.113167	+	0.196011i
$506$	−12.5226	−	5.25365i	−0.556698	−	0.233553i
$507$	5.83768	−	2.12474i	0.259260	−	0.0943631i
$508$	2.06845	+	4.54285i	0.0917724	+	0.201556i
$509$	−35.6303	−	6.28259i	−1.57929	−	0.278471i	−0.685878	−	0.727716i	$-0.740582\pi$
$509$	−35.6303	−	6.28259i	−1.57929	−	0.278471i	−0.893408	+	0.449245i	$0.851693\pi$
$510$	−1.31528	+	5.80815i	−0.0582415	+	0.257189i
$511$	−12.0396	−	14.3482i	−0.532600	−	0.634727i
$512$	20.5345	+	9.50435i	0.907507	+	0.420037i
$513$	13.1354	+	11.8433i	0.579942	+	0.522896i
$514$	−24.5326	+	3.11674i	−1.08209	+	0.137474i
$515$	7.25837	−	6.09049i	0.319842	−	0.268379i
$516$	−0.492022	+	5.09185i	−0.0216600	+	0.224156i
$517$	6.60420	−	37.4543i	0.290452	−	1.64724i
$518$	5.52203	−	1.71362i	0.242624	−	0.0752920i
$519$	4.56259	+	12.5356i	0.200275	+	0.550252i
$520$	−0.879549	+	6.04462i	−0.0385708	+	0.265074i
$521$	15.4717	−	8.93257i	0.677826	−	0.391343i	−0.121209	−	0.992627i	$-0.538677\pi$
$521$	15.4717	−	8.93257i	0.677826	−	0.391343i	0.799036	+	0.601284i	$0.205344\pi$
$522$	−20.6650	−	13.2971i	−0.904482	−	0.581998i
$523$	8.27408	+	6.94278i	0.361800	+	0.303587i	0.805508	−	0.592585i	$-0.201893\pi$
$523$	8.27408	+	6.94278i	0.361800	+	0.303587i	−0.443707	+	0.896172i	$0.646337\pi$
$524$	−25.8676	+	25.4029i	−1.13003	+	1.10973i
$525$	−2.33263	−	1.34674i	−0.101804	−	0.0587766i
$526$	37.3653	−	19.2364i	1.62920	−	0.838747i
$527$	1.89549	+	10.7498i	0.0825688	+	0.468271i
$528$	−15.6489	+	5.37655i	−0.681031	+	0.233984i
$529$	−18.8008	−	6.84294i	−0.817427	−	0.297519i
$530$	−10.0965	+	10.9187i	−0.438565	+	0.474276i
$531$	9.76170			0.423622
$532$	4.14449	−	31.2350i	0.179686	−	1.35421i
$533$	8.56573			0.371023
$534$	0.107368	−	0.116110i	0.00464626	−	0.00502459i
$535$	−7.96343	−	2.89845i	−0.344289	−	0.125311i
$536$	−15.4548	+	3.20644i	−0.667544	+	0.138497i
$537$	0.698360	+	3.96060i	0.0301365	+	0.170912i
$538$	10.4651	−	5.38763i	0.451181	−	0.232277i
$539$	29.1469	+	16.8280i	1.25545	+	0.724833i
$540$	−5.68593	−	5.78995i	−0.244684	−	0.249160i
$541$	−11.9192	−	10.0014i	−0.512445	−	0.429993i	0.349543	−	0.936920i	$-0.386337\pi$
$541$	−11.9192	−	10.0014i	−0.512445	−	0.429993i	−0.861989	+	0.506927i	$0.830781\pi$
$542$	23.1817	+	14.9165i	0.995740	+	0.640719i
$543$	−14.0034	+	8.08487i	−0.600943	+	0.346955i
$544$	31.7773	−	3.45309i	1.36244	−	0.148050i
$545$	5.29378	+	14.5445i	0.226760	+	0.623019i
$546$	−7.85666	+	2.43811i	−0.336234	+	0.104341i
$547$	−4.35150	+	24.6786i	−0.186057	+	1.05518i	0.738533	+	0.674217i	$0.235519\pi$
$547$	−4.35150	+	24.6786i	−0.186057	+	1.05518i	−0.924590	+	0.380964i	$0.875592\pi$
$548$	−21.5268	−	2.08012i	−0.919581	−	0.0888584i
$549$	4.73735	−	3.97510i	0.202185	−	0.169653i
$550$	−7.78755	+	0.989368i	−0.332062	+	0.0421868i
$551$	−11.6257	+	28.7184i	−0.495273	+	1.22345i
$552$	3.38744	−	1.34947i	0.144179	−	0.0574371i
$553$	−23.0795	−	27.5050i	−0.981439	−	1.16963i
$554$	−7.17252	+	31.6732i	−0.304731	+	1.34567i
$555$	−0.830169	−	0.146381i	−0.0352387	−	0.00621354i
$556$	−9.30727	+	4.23778i	−0.394716	+	0.179722i
$557$	−26.5975	+	9.68069i	−1.12697	+	0.410184i	−0.837192	−	0.546909i	$-0.815804\pi$
$557$	−26.5975	+	9.68069i	−1.12697	+	0.410184i	−0.289780	+	0.957093i	$0.593582\pi$
$558$	−6.15861	−	2.58374i	−0.260715	−	0.109378i
$559$	3.70610	+	6.41915i	0.156751	+	0.271501i
$560$	−2.76813	+	14.1897i	−0.116975	+	0.599625i
$561$	−15.0249	+	17.9060i	−0.634353	+	0.755992i
$562$	−10.3695	−	13.6413i	−0.437409	−	0.575423i
$563$	−4.91455	+	8.51226i	−0.207124	+	0.358749i	−0.950807	−	0.309783i	$-0.899744\pi$
$563$	−4.91455	+	8.51226i	−0.207124	+	0.358749i	0.743684	+	0.668532i	$0.233077\pi$
$564$	5.78126	+	8.41786i	0.243435	+	0.354456i
$565$	10.1363	−	1.78730i	0.426437	−	0.0751924i
$566$	0.450752	−	9.35124i	0.0189465	−	0.393062i
$567$	−5.32802	+	14.6386i	−0.223756	+	0.614764i
$568$	33.9068	+	18.2409i	1.42270	+	0.765369i
$569$			5.60285i			0.234884i	0.993080	+	0.117442i	$0.0374694\pi$
$569$			5.60285i			0.234884i	−0.993080	+	0.117442i	$0.962531\pi$
$570$	−2.62171	+	3.77234i	−0.109812	+	0.158006i
$571$		−	8.12514i		−	0.340026i	−0.985442	−	0.170013i	$-0.945619\pi$
$571$		−	8.12514i		−	0.340026i	0.985442	−	0.170013i	$-0.0543810\pi$
$572$	−13.9292	+	19.5141i	−0.582408	+	0.815924i
$573$	−2.44196	+	6.70922i	−0.102014	+	0.280282i
$574$	20.2501	+	0.976101i	0.845221	+	0.0407417i
$575$	1.70362	−	0.300395i	0.0710461	−	0.0125273i
$576$	−8.74401	+	17.4935i	−0.364334	+	0.728894i
$577$	0.722105	−	1.25072i	0.0300616	−	0.0520683i	−0.850603	−	0.525808i	$-0.823763\pi$
$577$	0.722105	−	1.25072i	0.0300616	−	0.0520683i	0.880665	+	0.473740i	$0.157096\pi$
$578$	16.8078	−	12.7765i	0.699113	−	0.531432i
$579$	9.28109	−	11.0608i	0.385709	−	0.459670i
$580$	6.12433	−	12.8288i	0.254299	−	0.532687i
$581$	31.3792	+	54.3503i	1.30183	+	2.25483i
$582$	1.41807	−	3.38012i	0.0587810	−	0.140111i
$583$	−54.8509	+	19.9641i	−2.27169	+	0.826829i
$584$	12.4681	−	7.70676i	0.515932	−	0.318908i
$585$	−5.19922	−	0.916763i	−0.214961	−	0.0379035i
$586$	40.4540	+	9.16096i	1.67114	+	0.378436i
$587$	17.7151	+	21.1120i	0.731178	+	0.871385i	0.995666	−	0.0930046i	$-0.0296471\pi$
$587$	17.7151	+	21.1120i	0.731178	+	0.871385i	−0.264487	+	0.964389i	$0.585203\pi$
$588$	−8.74982	+	2.25971i	−0.360836	+	0.0931889i
$589$	−1.75631	+	8.23526i	−0.0723677	+	0.339328i
$590$	0.711716	+	5.60209i	0.0293009	+	0.230634i
$591$	2.56879	−	2.15547i	0.105666	−	0.0886642i
$592$	0.704798	+	4.46942i	0.0289670	+	0.183692i
$593$	0.910477	−	5.16357i	0.0373888	−	0.212042i	−0.960390	−	0.278660i	$-0.910110\pi$
$593$	0.910477	−	5.16357i	0.0373888	−	0.212042i	0.997779	+	0.0666177i	$0.0212208\pi$
$594$	−9.44031	−	30.4209i	−0.387341	−	1.24818i
$595$	6.98502	+	19.1912i	0.286358	+	0.786762i
$596$	4.19897	−	15.1212i	0.171996	−	0.619388i
$597$	−8.94473	+	5.16424i	−0.366083	+	0.211358i
$598$	2.85892	−	4.44304i	0.116910	−	0.181689i
$599$	9.87889	+	8.28937i	0.403640	+	0.338694i	0.821899	−	0.569634i	$-0.192915\pi$
$599$	9.87889	+	8.28937i	0.403640	+	0.338694i	−0.418258	+	0.908328i	$0.637359\pi$
$600$	1.30578	−	1.65465i	0.0533083	−	0.0675509i
$601$	−19.6928	−	11.3696i	−0.803284	−	0.463776i	0.0413342	−	0.999145i	$-0.486839\pi$
$601$	−19.6928	−	11.3696i	−0.803284	−	0.463776i	−0.844618	+	0.535369i	$0.820173\pi$
$602$	8.03001	+	15.5977i	0.327279	+	0.635715i
$603$	−2.36893	−	13.4349i	−0.0964704	−	0.547111i
$604$	−0.758616	−	9.68085i	−0.0308677	−	0.393908i
$605$	−18.6176	−	6.77624i	−0.756912	−	0.275494i
$606$	−3.93569	−	3.63935i	−0.159877	−	0.147838i
$607$	8.56350			0.347582			0.173791	−	0.984783i	$-0.444398\pi$
$607$	8.56350			0.347582			0.173791	+	0.984783i	$0.444398\pi$
$608$	23.7217	+	6.72922i	0.962041	+	0.272906i
$609$	19.1448			0.775788
$610$	2.62665	+	2.42887i	0.106350	+	0.0983420i
$611$	13.9042	+	5.06072i	0.562504	+	0.204735i
$612$	2.15831	+	27.5427i	0.0872446	+	1.11335i
$613$	1.16281	+	6.59463i	0.0469655	+	0.266355i	0.999244	−	0.0388757i	$-0.0123776\pi$
$613$	1.16281	+	6.59463i	0.0469655	+	0.266355i	−0.952279	+	0.305230i	$0.901267\pi$
$614$	9.18132	+	17.8340i	0.370528	+	0.719723i
$615$	−2.55983	−	1.47792i	−0.103222	−	0.0595955i
$616$	−35.1534	+	44.5455i	−1.41637	+	1.79479i
$617$	4.28993	+	3.59968i	0.172706	+	0.144917i	0.725044	−	0.688703i	$-0.241820\pi$
$617$	4.28993	+	3.59968i	0.172706	+	0.144917i	−0.552338	+	0.833621i	$0.686264\pi$
$618$	−5.40357	+	8.39768i	−0.217363	+	0.337804i
$619$	−14.8132	+	8.55238i	−0.595391	+	0.343749i	−0.767226	−	0.641377i	$-0.778364\pi$
$619$	−14.8132	+	8.55238i	−0.595391	+	0.343749i	0.171835	+	0.985126i	$0.445030\pi$
$620$	1.03375	−	3.72271i	0.0415164	−	0.149508i
$621$	2.40067	+	6.59579i	0.0963357	+	0.264680i
$622$	−12.6164	−	40.6558i	−0.505873	−	1.63015i
$623$	0.0941763	−	0.534100i	0.00377309	−	0.0213983i
$624$	−1.00278	−	6.35902i	−0.0401431	−	0.254564i
$625$	0.766044	−	0.642788i	0.0306418	−	0.0257115i
$626$	−3.58425	−	28.2125i	−0.143256	−	1.12760i
$627$	−15.9266	+	8.45441i	−0.636045	+	0.337637i
$628$	3.52624	−	0.910680i	0.140712	−	0.0363401i
$629$	4.10851	+	4.89633i	0.163817	+	0.195229i
$630$	−12.1869	−	2.75977i	−0.485538	−	0.109952i
$631$	−17.9680	−	3.16824i	−0.715295	−	0.126126i	−0.195855	−	0.980633i	$-0.562748\pi$
$631$	−17.9680	−	3.16824i	−0.715295	−	0.126126i	−0.519440	+	0.854507i	$0.673859\pi$
$632$	23.9009	−	14.7736i	0.950726	−	0.587662i
$633$	−18.1057	+	6.58993i	−0.719637	+	0.261926i
$634$	11.1496	−	26.5761i	0.442806	−	1.05547i
$635$	−1.24790	−	2.16142i	−0.0495213	−	0.0857733i
$636$	6.75222	−	14.1441i	0.267743	−	0.560848i
$637$	−8.41667	+	10.0306i	−0.333481	+	0.397427i
$638$	44.4207	−	33.7664i	1.75863	−	1.33683i
$639$	−16.6388	+	28.8192i	−0.658219	+	1.14007i
$640$	−10.6767	−	3.74262i	−0.422035	−	0.147940i
$641$	25.9233	−	4.57097i	1.02391	−	0.180542i	0.363613	−	0.931550i	$-0.381543\pi$
$641$	25.9233	−	4.57097i	1.02391	−	0.180542i	0.660294	+	0.751008i	$0.270432\pi$
$642$	8.92105	+	0.430016i	0.352086	+	0.0169714i
$643$	−1.51004	+	4.14880i	−0.0595502	+	0.163613i	−0.965900	−	0.258915i	$-0.916635\pi$
$643$	−1.51004	+	4.14880i	−0.0595502	+	0.163613i	0.906350	+	0.422528i	$0.138857\pi$
$644$	7.26500	−	10.1779i	0.286281	−	0.401065i
$645$		−	2.55778i		−	0.100713i
$646$	33.6136	−	9.13349i	1.32251	−	0.359352i
$647$			16.8344i			0.661829i	0.943661	+	0.330915i	$0.107357\pi$
$647$			16.8344i			0.661829i	−0.943661	+	0.330915i	$0.892643\pi$
$648$	−10.7359	−	5.77561i	−0.421746	−	0.226887i
$649$	−7.58100	+	20.8286i	−0.297580	+	0.817595i
$650$	0.147046	−	3.05060i	0.00576762	−	0.119654i
$651$	5.12419	−	0.903532i	0.200833	−	0.0354122i
$652$	−24.2296	−	35.2798i	−0.948904	−	1.38166i
$653$	5.08593	−	8.80909i	0.199028	−	0.344726i	−0.749186	−	0.662360i	$-0.769555\pi$
$653$	5.08593	−	8.80909i	0.199028	−	0.344726i	0.948213	+	0.317634i	$0.102888\pi$
$654$	−9.87164	−	12.9864i	−0.386012	−	0.507809i
$655$	11.6522	−	13.8866i	0.455290	−	0.542593i
$656$	−3.03776	+	15.5719i	−0.118605	+	0.607979i
$657$	6.33437	+	10.9714i	0.247127	+	0.428037i
$658$	32.2940	+	13.5484i	1.25895	+	0.528171i
$659$	11.2384	−	4.09043i	0.437785	−	0.159341i	−0.113719	−	0.993513i	$-0.536276\pi$
$659$	11.2384	−	4.09043i	0.437785	−	0.159341i	0.551504	+	0.834172i	$0.314054\pi$
$660$	7.52961	−	3.42838i	0.293090	−	0.133449i
$661$	0.140025	+	0.0246901i	0.00544633	+	0.000960335i	0.176371	−	0.984324i	$-0.443564\pi$
$661$	0.140025	+	0.0246901i	0.00544633	+	0.000960335i	−0.170924	+	0.985284i	$0.554675\pi$
$662$	2.80793	−	12.3995i	0.109133	−	0.481922i
$663$	−5.84552	−	6.96642i	−0.227021	−	0.270553i
$664$	−45.6254	+	18.1760i	−1.77061	+	0.705364i
$665$	−0.560528	+	15.7444i	−0.0217364	+	0.610541i
$666$	−3.87951	+	0.492871i	−0.150328	+	0.0190984i
$667$	−9.41920	+	7.90364i	−0.364713	+	0.306030i
$668$	39.4468	+	3.81172i	1.52624	+	0.147480i
$669$	−1.33783	+	7.58721i	−0.0517235	+	0.293339i
$670$	7.53736	−	2.33902i	0.291193	−	0.0903642i
$671$	4.80266	+	13.1952i	0.185405	+	0.509395i
$672$	−1.64600	−	15.1475i	−0.0634959	−	0.584327i
$673$	23.5115	−	13.5743i	0.906300	−	0.523253i	0.0270613	−	0.999634i	$-0.491385\pi$
$673$	23.5115	−	13.5743i	0.906300	−	0.523253i	0.879239	+	0.476381i	$0.158052\pi$
$674$	−8.67449	−	5.58169i	−0.334129	−	0.214999i
$675$	3.10823	+	2.60811i	0.119636	+	0.100386i
$676$	11.6817	+	11.8954i	0.449297	+	0.457516i
$677$	−32.3593	−	18.6826i	−1.24367	−	0.718032i	−0.273828	−	0.961779i	$-0.588290\pi$
$677$	−32.3593	−	18.6826i	−1.24367	−	0.718032i	−0.969839	+	0.243747i	$0.921623\pi$
$678$	−9.64453	+	4.96520i	−0.370396	+	0.190687i
$679$	−2.18286	−	12.3796i	−0.0837706	−	0.475087i
$680$	−15.6489	+	3.24673i	−0.600110	+	0.124506i
$681$	−7.70613	−	2.80480i	−0.295299	−	0.107480i
$682$	10.2958	−	11.1341i	0.394245	−	0.426348i
$683$	1.12262			0.0429559			0.0214780	−	0.999769i	$-0.493163\pi$
$683$	1.12262			0.0429559			0.0214780	+	0.999769i	$0.493163\pi$
$684$	−6.42926	+	20.3189i	−0.245829	+	0.776913i
$685$	10.8135			0.413164
$686$	3.25106	−	3.51578i	0.124126	−	0.134233i
$687$	9.83375	+	3.57919i	0.375181	+	0.136555i
$688$	−12.9839	+	4.46092i	−0.495005	+	0.170071i
$689$	−3.94348	−	22.3646i	−0.150234	−	0.852022i
$690$	−1.62097	+	0.834510i	−0.0617093	+	0.0317692i
$691$	5.49375	+	3.17182i	0.208992	+	0.120662i	0.600843	−	0.799367i	$-0.294832\pi$
$691$	5.49375	+	3.17182i	0.208992	+	0.120662i	−0.391851	+	0.920029i	$0.628165\pi$
$692$	−25.5438	+	25.0849i	−0.971029	+	0.953584i
$693$	−37.5712	−	31.5259i	−1.42721	−	1.19757i
$694$	−18.6004	−	11.9686i	−0.706060	−	0.454322i
$695$	4.42826	−	2.55666i	0.167974	−	0.0969795i
$696$	−2.15732	+	14.8260i	−0.0817729	+	0.561977i
$697$	7.66539	+	21.0605i	0.290347	+	0.797723i
$698$	34.6168	−	10.7424i	1.31026	−	0.406606i
$699$	−2.33750	+	13.2566i	−0.0884124	+	0.501411i
$700$	0.695256	−	7.19509i	0.0262782	−	0.271949i
$701$	34.5241	−	28.9691i	1.30396	−	1.09415i	0.314510	−	0.949254i	$-0.398160\pi$
$701$	34.5241	−	28.9691i	1.30396	−	1.09415i	0.989447	−	0.144895i	$-0.0462845\pi$
$702$	12.2934	−	1.56181i	0.463983	−	0.0589466i
$703$	1.52046	+	4.69033i	0.0573451	+	0.176899i
$704$	−30.5353	−	32.2427i	−1.15084	−	1.21519i
$705$	−3.28205	−	3.91139i	−0.123609	−	0.147312i
$706$	2.23056	−	9.84993i	0.0839481	−	0.370707i
$707$	−18.1039	−	3.19221i	−0.680867	−	0.120055i
$708$	−2.46625	−	5.41654i	−0.0926875	−	0.203566i
$709$	32.8147	−	11.9436i	1.23238	−	0.448550i	0.357969	−	0.933733i	$-0.383469\pi$
$709$	32.8147	−	11.9436i	1.23238	−	0.448550i	0.874412	+	0.485183i	$0.161247\pi$
$710$	−17.7520	−	7.44755i	−0.666221	−	0.279501i
$711$	12.1428	+	21.0319i	0.455389	+	0.788758i
$712$	0.403000	+	0.133116i	0.0151031	+	0.00498872i
$713$	−2.14807	+	2.55997i	−0.0804460	+	0.0958718i
$714$	−13.0254	−	17.1353i	−0.487464	−	0.641271i
$715$	5.99386	−	10.3817i	0.224158	−	0.388252i
$716$	−8.89699	+	6.11032i	−0.332496	+	0.228353i
$717$	4.10225	−	0.723338i	0.153201	−	0.0270135i
$718$	0.826445	−	17.1453i	0.0308427	−	0.639857i
$719$	6.02001	−	16.5398i	0.224508	−	0.616832i	−0.775384	−	0.631490i	$-0.782444\pi$
$719$	6.02001	−	16.5398i	0.224508	−	0.616832i	0.999893	+	0.0146581i	$0.00466598\pi$
$720$	3.51047	−	9.12668i	0.130827	−	0.340131i
$721$			34.2459i			1.27539i
$722$	26.6789	+	3.19903i	0.992888	+	0.119056i
$723$			16.5911i			0.617029i
$724$	−35.3203	−	25.2117i	−1.31267	−	0.936985i
$725$	−2.43102	+	6.67918i	−0.0902859	+	0.248059i
$726$	20.8564	+	1.00533i	0.774052	+	0.0373112i
$727$	26.4936	−	4.67154i	0.982594	−	0.173258i	0.340801	−	0.940136i	$-0.389302\pi$
$727$	26.4936	−	4.67154i	0.982594	−	0.173258i	0.641793	+	0.766878i	$0.278191\pi$
$728$	−14.6924	−	16.4782i	−0.544538	−	0.610724i
$729$	0.732678	−	1.26904i	0.0271362	−	0.0470013i
$730$	−5.83451	+	4.43511i	−0.215945	+	0.164151i
$731$	−12.4662	+	14.8566i	−0.461078	+	0.549491i
$732$	−3.40256	−	1.62435i	−0.125762	−	0.0600376i
$733$	−2.60707	−	4.51558i	−0.0962944	−	0.166787i	0.813854	−	0.581070i	$-0.197366\pi$
$733$	−2.60707	−	4.51558i	−0.0962944	−	0.166787i	−0.910148	+	0.414283i	$0.864032\pi$
$734$	−6.58463	+	15.6951i	−0.243043	+	0.579318i
$735$	4.24595	−	1.54540i	0.156614	−	0.0570030i
$736$	7.06322	+	6.77298i	0.260354	+	0.249655i
$737$	30.5059	+	5.37901i	1.12370	+	0.198138i
$738$	−13.3740	−	3.02859i	−0.492302	−	0.111484i
$739$	4.31912	+	5.14733i	0.158881	+	0.189348i	0.839612	−	0.543186i	$-0.182782\pi$
$739$	4.31912	+	5.14733i	0.158881	+	0.189348i	−0.680731	+	0.732534i	$0.738338\pi$
$740$	−0.565702	−	2.19045i	−0.0207956	−	0.0805227i
$741$	−2.16328	−	6.67333i	−0.0794701	−	0.245151i
$742$	−6.77415	−	53.3209i	−0.248687	−	1.95747i
$743$	−4.04617	+	3.39514i	−0.148439	+	0.124556i	−0.713983	−	0.700163i	$-0.753111\pi$
$743$	−4.04617	+	3.39514i	−0.148439	+	0.124556i	0.565544	+	0.824718i	$0.308666\pi$
$744$	0.122291	+	4.07004i	0.00448341	+	0.149215i
$745$	−1.36256	+	7.72747i	−0.0499204	+	0.283113i
$746$	8.90646	+	28.7006i	0.326089	+	1.05080i
$747$	−14.5182	−	39.8884i	−0.531193	−	1.45944i
$748$	−60.4442	−	16.7846i	−2.21006	−	0.613706i
$749$	26.5258	−	15.3147i	0.969233	−	0.559587i
$750$	−0.570290	+	0.886287i	−0.0208240	+	0.0323626i
$751$	−26.2576	−	22.0327i	−0.958153	−	0.803986i	0.0224985	−	0.999747i	$-0.492838\pi$
$751$	−26.2576	−	22.0327i	−0.958153	−	0.803986i	−0.980652	+	0.195761i	$0.937282\pi$
$752$	−14.1310	+	23.4821i	−0.515305	+	0.856304i
$753$	18.8552	+	10.8861i	0.687122	+	0.396710i
$754$	9.93641	+	19.3007i	0.361863	+	0.702891i
$755$	0.843108	+	4.78150i	0.0306838	+	0.174017i
$756$	29.2404	−	2.29135i	1.06346	−	0.0833357i
$757$	−10.5751	−	3.84903i	−0.384360	−	0.139896i	0.142611	−	0.989779i	$-0.454450\pi$
$757$	−10.5751	−	3.84903i	−0.384360	−	0.139896i	−0.526971	+	0.849883i	$0.676672\pi$
$758$	24.1544	+	22.3357i	0.877328	+	0.811268i
$759$	−7.15609			−0.259749
$760$	−12.1295	−	2.20822i	−0.439982	−	0.0801006i
$761$	−46.2801			−1.67765			−0.838825	−	0.544401i	$-0.816757\pi$
$761$	−46.2801			−1.67765			−0.838825	+	0.544401i	$0.816757\pi$
$762$	1.93123	+	1.78581i	0.0699609	+	0.0646931i
$763$	−52.5683	−	19.1333i	−1.90310	−	0.692672i
$764$	−19.1028	+	1.49694i	−0.691115	+	0.0541575i
$765$	−2.39870	−	13.6037i	−0.0867251	−	0.491842i
$766$	−2.30069	−	4.46892i	−0.0831274	−	0.161469i
$767$	−7.46820	−	4.31177i	−0.269661	−	0.155689i
$768$	11.9158	+	0.432198i	0.429976	+	0.0155956i
$769$	13.4142	+	11.2558i	0.483727	+	0.405895i	0.851772	−	0.523913i	$-0.175528\pi$
$769$	13.4142	+	11.2558i	0.483727	+	0.405895i	−0.368045	+	0.929808i	$0.619973\pi$
$770$	15.3530	−	23.8600i	0.553283	−	0.859856i
$771$	−11.2857	+	6.51578i	−0.406443	+	0.234660i
$772$	37.3371	+	10.3681i	1.34379	+	0.373155i
$773$	−10.8028	−	29.6804i	−0.388549	−	1.06753i	−0.967655	−	0.252278i	$-0.918820\pi$
$773$	−10.8028	−	29.6804i	−0.388549	−	1.06753i	0.579106	−	0.815253i	$-0.303402\pi$
$774$	−3.51683	−	11.3328i	−0.126410	−	0.407349i
$775$	−0.335451	+	1.90244i	−0.0120498	+	0.0683376i
$776$	9.83289	−	0.295445i	0.352980	−	0.0106059i
$777$	2.33396	−	1.95842i	0.0837303	−	0.0702581i
$778$	6.44155	+	50.7030i	0.230941	+	1.81779i
$779$	−0.615127	+	17.2780i	−0.0220392	+	0.619047i
$780$	0.804872	+	3.11654i	0.0288190	+	0.111590i
$781$	−48.5700	−	57.8834i	−1.73797	−	2.07123i
$782$	13.4825	+	3.05316i	0.482132	+	0.109181i
$783$	−28.4019	−	5.00802i	−1.01500	−	0.178972i
$784$	−15.2500	−	18.8581i	−0.544642	−	0.673505i
$785$	−1.71115	+	0.622808i	−0.0610736	+	0.0222290i
$786$	−7.39107	+	17.6174i	−0.263631	+	0.628391i
$787$	−3.96723	−	6.87144i	−0.141416	−	0.244940i	0.786614	−	0.617445i	$-0.211832\pi$
$787$	−3.96723	−	6.87144i	−0.141416	−	0.244940i	−0.928030	+	0.372505i	$0.878499\pi$
$788$	8.12144	+	3.87709i	0.289314	+	0.138116i
$789$	14.2352	−	16.9648i	0.506786	−	0.603964i
$790$	−11.1846	+	8.50196i	−0.397929	+	0.302486i
$791$	−18.6004	+	32.2168i	−0.661354	+	1.14550i
$792$	28.6477	−	25.5430i	1.01795	−	0.907632i
$793$	−5.38013	+	0.948661i	−0.191054	+	0.0336880i
$794$	−26.1880	−	1.26232i	−0.929376	−	0.0447981i
$795$	−2.68026	+	7.36396i	−0.0950591	+	0.261173i
$796$	−22.5610	−	16.1041i	−0.799653	−	0.570794i
$797$			9.36708i			0.331799i	0.986143	+	0.165900i	$0.0530527\pi$
$797$			9.36708i			0.331799i	−0.986143	+	0.165900i	$0.946947\pi$
$798$	−4.35371	−	16.0228i	−0.154120	−	0.567201i
$799$			38.7150i			1.36964i
$800$	5.49361	+	1.34918i	0.194228	+	0.0477009i
$801$	−0.125462	+	0.344704i	−0.00443298	+	0.0121795i
$802$	0.531798	−	11.0326i	0.0187784	−	0.389575i
$803$	−28.3292	+	4.99520i	−0.999715	+	0.176277i
$804$	−6.85620	+	4.70873i	−0.241800	+	0.166064i
$805$	−3.12620	+	5.41474i	−0.110184	+	0.190844i
$806$	3.57041	+	4.69697i	0.125762	+	0.165444i
$807$	3.98691	−	4.75142i	0.140346	−	0.167258i
$808$	4.51210	−	13.6601i	0.158735	−	0.480562i
$809$	19.1176	+	33.1127i	0.672140	+	1.16418i	0.977296	+	0.211878i	$0.0679579\pi$
$809$	19.1176	+	33.1127i	0.672140	+	1.16418i	−0.305156	+	0.952302i	$0.598709\pi$
$810$	5.62082	+	2.35812i	0.197496	+	0.0828559i
$811$	10.7238	−	3.90316i	0.376565	−	0.137058i	−0.146802	−	0.989166i	$-0.546898\pi$
$811$	10.7238	−	3.90316i	0.376565	−	0.137058i	0.523367	+	0.852108i	$0.324676\pi$
$812$	21.2911	+	46.7607i	0.747170	+	1.64098i
$813$	14.3055	+	2.52245i	0.501716	+	0.0884661i
$814$	1.96121	−	8.66050i	0.0687402	−	0.303550i
$815$	13.7553	+	16.3929i	0.481826	+	0.574218i
$816$	14.7375	−	8.15614i	0.515915	−	0.285522i
$817$	−13.2142	+	7.01461i	−0.462308	+	0.245410i
$818$	−34.0536	+	4.32634i	−1.19066	+	0.151267i
$819$	14.6172	−	12.2653i	0.510768	−	0.428585i
$820$	0.762977	−	7.89592i	0.0266443	−	0.275738i
$821$	5.57400	−	31.6117i	0.194534	−	1.10326i	−0.718547	−	0.695478i	$-0.755193\pi$
$821$	5.57400	−	31.6117i	0.194534	−	1.10326i	0.913081	−	0.407778i	$-0.133696\pi$
$822$	−10.8845	+	3.37772i	−0.379641	+	0.117811i
$823$	−14.6042	−	40.1247i	−0.509070	−	1.39866i	−0.882198	−	0.470878i	$-0.843937\pi$
$823$	−14.6042	−	40.1247i	−0.509070	−	1.39866i	0.373129	−	0.927780i	$-0.378285\pi$
$824$	−26.5204	−	3.85897i	−0.923882	−	0.134434i
$825$	−3.58248	+	2.06835i	−0.124726	+	0.0720106i
$826$	−17.1641	−	11.0444i	−0.597214	−	0.384283i
$827$	−27.0663	−	22.7113i	−0.941188	−	0.789751i	0.0366034	−	0.999330i	$-0.488346\pi$
$827$	−27.0663	−	22.7113i	−0.941188	−	0.789751i	−0.977792	+	0.209579i	$0.932791\pi$
$828$	−6.03465	+	5.92623i	−0.209718	+	0.205951i
$829$	−7.58942	−	4.38175i	−0.263591	−	0.152185i	0.362380	−	0.932030i	$-0.381964\pi$
$829$	−7.58942	−	4.38175i	−0.263591	−	0.152185i	−0.625972	+	0.779846i	$0.715297\pi$
$830$	21.8328	−	11.2400i	0.757829	−	0.390146i
$831$	2.97164	+	16.8530i	0.103085	+	0.584625i
$832$	14.4165	−	9.52113i	0.499803	−	0.330086i
$833$	−32.1941	−	11.7177i	−1.11546	−	0.405995i
$834$	−3.65872	+	3.95664i	−0.126691	+	0.137007i
$835$	−19.8153			−0.685736
$836$	−38.3616	−	29.4980i	−1.32676	−	1.02021i
$837$	−7.83823			−0.270929
$838$	22.1013	−	23.9009i	0.763475	−	0.825644i
$839$	−16.1378	−	5.87367i	−0.557138	−	0.202782i	0.0480772	−	0.998844i	$-0.484691\pi$
$839$	−16.1378	−	5.87367i	−0.557138	−	0.202782i	−0.605215	+	0.796062i	$0.706913\pi$
$840$	1.54764	+	7.45947i	0.0533986	+	0.257376i
$841$	−3.73714	−	21.1944i	−0.128867	−	0.730841i
$842$	−8.50030	+	4.37613i	−0.292940	+	0.150811i
$843$	−7.81973	−	4.51472i	−0.269326	−	0.155495i
$844$	−36.2311	−	36.8939i	−1.24713	−	1.26994i
$845$	−6.38584	−	5.35836i	−0.219680	−	0.184333i
$846$	−19.9198	−	12.8176i	−0.684856	−	0.440678i
$847$	62.0143	−	35.8040i	2.13084	−	1.23024i
$848$	42.0556	+	0.762446i	1.44420	+	0.0261825i
$849$	−1.68733	−	4.63590i	−0.0579090	−	0.159104i
$850$	7.63206	−	2.36841i	0.261778	−	0.0812357i
$851$	−0.339795	+	1.92708i	−0.0116480	+	0.0660593i
$852$	20.1948	+	1.95141i	0.691862	+	0.0668541i
$853$	9.58758	−	8.04493i	0.328272	−	0.275453i	−0.463723	−	0.885980i	$-0.653487\pi$
$853$	9.58758	−	8.04493i	0.328272	−	0.275453i	0.791996	+	0.610527i	$0.209042\pi$
$854$	−12.8271	+	1.62962i	−0.438936	+	0.0557645i
$855$	2.22258	−	10.4215i	0.0760105	−	0.356409i
$856$	8.87083	+	22.2676i	0.303199	+	0.761091i
$857$	−13.6025	−	16.2108i	−0.464652	−	0.553751i	0.481932	−	0.876209i	$-0.339935\pi$
$857$	−13.6025	−	16.2108i	−0.464652	−	0.553751i	−0.946584	+	0.322458i	$0.895491\pi$
$858$	−2.79037	+	12.3220i	−0.0952618	+	0.420667i
$859$	50.7563	+	8.94970i	1.73178	+	0.305360i	0.948610	−	0.316446i	$-0.102490\pi$
$859$	50.7563	+	8.94970i	1.73178	+	0.305360i	0.783171	+	0.621806i	$0.213601\pi$
$860$	6.24731	−	2.84452i	0.213031	−	0.0969973i
$861$	10.0390	−	3.65390i	0.342129	−	0.124525i
$862$	19.1259	+	8.02394i	0.651430	+	0.273297i
$863$	7.79405	+	13.4997i	0.265313	+	0.459535i	0.967645	−	0.252314i	$-0.0811915\pi$
$863$	7.79405	+	13.4997i	0.265313	+	0.459535i	−0.702333	+	0.711849i	$0.747858\pi$
$864$	−1.52048	+	22.9023i	−0.0517278	+	0.779152i
$865$	11.5063	−	13.7127i	0.391227	−	0.466246i
$866$	−18.9638	−	24.9473i	−0.644415	−	0.847745i
$867$	5.56272	−	9.63491i	0.188920	−	0.327219i
$868$	7.90548	+	11.5109i	0.268329	+	0.390704i
$869$	−54.3061	+	9.57563i	−1.84221	+	0.324831i
$870$	0.360668	−	7.48236i	0.0122278	−	0.253676i
$871$	−4.12187	+	11.3247i	−0.139664	+	0.383724i
$872$	20.7406	−	38.5534i	0.702366	−	1.30558i
$873$			8.50248i			0.287765i
$874$	8.75676	+	6.08580i	0.296202	+	0.205855i
$875$			3.61430i			0.122186i
$876$	4.48744	−	6.28668i	0.151617	−	0.212407i
$877$	−3.47956	+	9.56001i	−0.117496	+	0.322819i	−0.984475	−	0.175528i	$-0.943837\pi$
$877$	−3.47956	+	9.56001i	−0.117496	+	0.322819i	0.866978	+	0.498346i	$0.166059\pi$
$878$	−0.819197	−	0.0394873i	−0.0276466	−	0.00133263i
$879$	21.5252	−	3.79547i	0.726027	−	0.128018i
$880$	16.7474	+	14.5781i	0.564556	+	0.491429i
$881$	−24.2188	+	41.9482i	−0.815952	+	1.41327i	0.0926897	+	0.995695i	$0.470454\pi$
$881$	−24.2188	+	41.9482i	−0.815952	+	1.41327i	−0.908642	+	0.417576i	$0.862880\pi$
$882$	16.6877	−	12.6852i	0.561906	−	0.427134i
$883$	−18.0162	+	21.4708i	−0.606292	+	0.722551i	−0.978649	−	0.205539i	$-0.934105\pi$
$883$	−18.0162	+	21.4708i	−0.606292	+	0.722551i	0.372357	+	0.928090i	$0.378550\pi$
$884$	10.5144	−	22.0249i	0.353639	−	0.740777i
$885$	1.48789	+	2.57711i	0.0500150	+	0.0866286i
$886$	−12.3725	+	29.4912i	−0.415664	+	0.990777i
$887$	−19.5887	+	7.12969i	−0.657723	+	0.239391i	−0.649253	−	0.760573i	$-0.724918\pi$
$887$	−19.5887	+	7.12969i	−0.657723	+	0.239391i	−0.00846977	+	0.999964i	$0.502696\pi$
$888$	1.25362	+	2.02812i	0.0420689	+	0.0680594i
$889$	8.88350	+	1.56640i	0.297943	+	0.0525354i
$890$	−0.206968	−	0.0468687i	−0.00693757	−	0.00157104i
$891$	15.3787	+	18.3276i	0.515207	+	0.613999i
$892$	−20.0193	+	5.17016i	−0.670297	+	0.173110i
$893$	−11.2065	+	27.6828i	−0.375011	+	0.926370i
$894$	−1.04225	−	8.20379i	−0.0348580	−	0.274376i
$895$	4.13402	−	3.46886i	0.138185	−	0.115951i
$896$	35.1667	−	20.8659i	1.17484	−	0.697080i
$897$	0.483455	−	2.74181i	0.0161421	−	0.0915464i
$898$	−17.4686	−	56.2915i	−0.582933	−	1.87847i
$899$	−4.69622	−	12.9028i	−0.156628	−	0.430331i
$900$	−1.30819	+	4.71100i	−0.0436062	+	0.157033i
$901$	51.4586	−	29.7096i	1.71433	−	0.989771i
$902$	16.8484	−	26.1841i	0.560991	−	0.871836i
$903$	7.08177	+	5.94231i	0.235667	+	0.197748i
$904$	−22.8531	−	18.0347i	−0.760082	−	0.599824i
$905$	18.7907	+	10.8488i	0.624624	+	0.360627i
$906$	−2.34219	−	4.54953i	−0.0778140	−	0.151148i
$907$	−3.20954	−	18.2022i	−0.106571	−	0.604394i	−0.990581	−	0.136926i	$-0.956278\pi$
$907$	−3.20954	−	18.2022i	−0.106571	−	0.604394i	0.884010	−	0.467468i	$-0.154834\pi$
$908$	−1.71937	−	21.9412i	−0.0570593	−	0.728145i
$909$	11.6841	+	4.25267i	0.387538	+	0.141052i
$910$	8.10460	+	7.49435i	0.268665	+	0.248435i
$911$	−35.8114			−1.18648			−0.593242	−	0.805024i	$-0.702152\pi$
$911$	−35.8114			−1.18648			−0.593242	+	0.805024i	$0.702152\pi$
$912$	12.8988	−	1.56604i	0.427122	−	0.0518569i
$913$	96.3852			3.18988
$914$	26.3936	+	24.4062i	0.873021	+	0.807285i
$915$	1.77151	+	0.644777i	0.0585643	+	0.0213157i
$916$	2.19408	+	27.9991i	0.0724944	+	0.925115i
$917$	11.3772	+	64.5233i	0.375708	+	2.13075i
$918$	14.8412	+	28.8279i	0.489833	+	0.951463i
$919$	27.5583	+	15.9108i	0.909063	+	0.524848i	0.880130	−	0.474733i	$-0.157455\pi$
$919$	27.5583	+	15.9108i	0.909063	+	0.524848i	0.0289338	+	0.999581i	$0.490789\pi$
$920$	−3.84095	−	3.03111i	−0.126633	−	0.0999329i
$921$	8.09712	+	6.79429i	0.266809	+	0.223880i
$922$	−13.3039	+	20.6755i	−0.438139	+	0.680912i
$923$	25.4590	−	14.6988i	0.837993	−	0.483816i
$924$	−8.00080	+	28.8122i	−0.263207	+	0.947853i
$925$	0.386880	+	1.06294i	0.0127205	+	0.0349494i
$926$	1.49965	+	4.83253i	0.0492815	+	0.158807i
$927$	4.02225	−	22.8113i	0.132108	−	0.749221i
$928$	−38.6111	+	11.2188i	−1.26747	+	0.368276i
$929$	−2.71744	+	2.28021i	−0.0891565	+	0.0748112i	−0.686277	−	0.727341i	$-0.740756\pi$
$929$	−2.71744	+	2.28021i	−0.0891565	+	0.0748112i	0.597120	+	0.802152i	$0.296312\pi$
$930$	−0.256593	−	2.01970i	−0.00841401	−	0.0662287i
$931$	−19.6283	−	17.6976i	−0.643293	−	0.580016i
$932$	−34.9785	+	9.03346i	−1.14576	+	0.295901i
$933$	−14.4188	−	17.1837i	−0.472051	−	0.562569i
$934$	−36.7538	−	8.32305i	−1.20262	−	0.272338i
$935$	30.8892	+	5.44659i	1.01018	+	0.178123i
$936$	7.85126	+	12.7018i	0.256626	+	0.415173i
$937$	−5.99745	+	2.18289i	−0.195928	+	0.0713120i	−0.438121	−	0.898916i	$-0.644356\pi$
$937$	−5.99745	+	2.18289i	−0.195928	+	0.0713120i	0.242192	+	0.970228i	$0.422133\pi$
$938$	−11.0349	+	26.3029i	−0.360303	+	0.858819i
$939$	−7.49314	−	12.9785i	−0.244529	−	0.423537i
$940$	5.90348	−	12.3662i	0.192550	−	0.403340i
$941$	−28.7442	+	34.2560i	−0.937033	+	1.11671i	0.0559472	+	0.998434i	$0.482182\pi$
$941$	−28.7442	+	34.2560i	−0.937033	+	1.11671i	−0.992980	+	0.118279i	$0.962262\pi$
$942$	1.52784	−	1.16139i	0.0497797	−	0.0378401i
$943$	−3.43071	+	5.94216i	−0.111719	+	0.193503i
$944$	10.4870	−	12.0475i	0.341323	−	0.392113i
$945$	−14.4422	+	2.54656i	−0.469806	+	0.0828395i
$946$	26.9121	+	1.29723i	0.874987	+	0.0421765i
$947$	8.19915	−	22.5270i	0.266437	−	0.732028i	−0.732262	−	0.681023i	$-0.761535\pi$
$947$	8.19915	−	22.5270i	0.266437	−	0.732028i	0.998698	−	0.0510051i	$-0.0162425\pi$
$948$	8.60228	−	12.0514i	0.279389	−	0.391410i
$949$		−	11.1916i		−	0.363295i
$950$	6.14281	+	0.515678i	0.199299	+	0.0167308i
$951$		−	15.1870i		−	0.492473i
$952$	27.3668	−	50.8704i	0.886963	−	1.64872i
$953$	−15.4202	+	42.3667i	−0.499510	+	1.37239i	0.392239	+	0.919863i	$0.371701\pi$
$953$	−15.4202	+	42.3667i	−0.499510	+	1.37239i	−0.891749	+	0.452530i	$0.850522\pi$
$954$	−1.75036	+	36.3128i	−0.0566701	+	1.17567i
$955$	9.43512	−	1.66367i	0.305313	−	0.0538350i
$956$	6.32886	+	9.21520i	0.204690	+	0.298041i
$957$	14.7015	−	25.4637i	0.475231	−	0.823124i
$958$	6.74794	+	8.87709i	0.218016	+	0.286806i
$959$	−25.1223	+	29.9396i	−0.811242	+	0.966801i
$960$	−5.95108	+	0.357944i	−0.192070	+	0.0115526i
$961$	13.6341	+	23.6150i	0.439810	+	0.761773i
$962$	3.18572	+	1.33652i	0.102712	+	0.0430910i
$963$	−19.4677	+	7.08565i	−0.627337	+	0.228332i
$964$	−40.5232	+	18.4510i	−1.30516	+	0.594266i
$965$	−19.0806	−	3.36443i	−0.614227	−	0.108305i
$966$	1.45537	−	6.42676i	0.0468257	−	0.206778i
$967$	−3.13399	−	3.73495i	−0.100782	−	0.120108i	0.713296	−	0.700863i	$-0.247202\pi$
$967$	−3.13399	−	3.73495i	−0.100782	−	0.120108i	−0.814078	+	0.580755i	$0.802757\pi$
$968$	20.7390	+	52.0591i	0.666576	+	1.67324i
$969$	14.4718	−	11.2907i	0.464900	−	0.362711i
$970$	−4.87944	+	0.619908i	−0.156669	+	0.0199040i
$971$	10.7015	−	8.97964i	0.343428	−	0.288170i	−0.454717	−	0.890636i	$-0.650259\pi$
$971$	10.7015	−	8.97964i	0.343428	−	0.288170i	0.798145	+	0.602466i	$0.205815\pi$
$972$	−30.6264	−	2.95941i	−0.982343	−	0.0949231i
$973$	−3.20920	+	18.2003i	−0.102882	+	0.583474i
$974$	14.4033	−	4.46970i	0.461513	−	0.143218i
$975$	−0.550447	−	1.51234i	−0.0176284	−	0.0484337i
$976$	0.183418	−	10.1171i	0.00587106	−	0.323841i
$977$	22.3669	−	12.9135i	0.715579	−	0.413140i	−0.0975443	−	0.995231i	$-0.531099\pi$
$977$	22.3669	−	12.9135i	0.715579	−	0.413140i	0.813123	+	0.582091i	$0.197765\pi$
$978$	−18.9660	−	12.2039i	−0.606466	−	0.390236i
$979$	−0.638063	−	0.535399i	−0.0203926	−	0.0171114i
$980$	8.49654	+	8.65197i	0.271412	+	0.276377i
$981$	32.7686	+	18.9190i	1.04622	+	0.604036i
$982$	2.45244	−	1.26256i	0.0782604	−	0.0402900i
$983$	10.6320	+	60.2970i	0.339108	+	1.92318i	0.382144	+	0.924103i	$0.375186\pi$
$983$	10.6320	+	60.2970i	0.339108	+	1.92318i	−0.0430360	+	0.999074i	$0.513703\pi$
$984$	1.69838	+	8.18606i	0.0541425	+	0.260962i
$985$	−4.22834	−	1.53899i	−0.134726	−	0.0490363i
$986$	−38.5625	+	41.7026i	−1.22808	+	1.32808i
$987$	18.4545			0.587412
$988$	13.8936	−	12.7052i	0.442015	−	0.404206i
$989$	−5.93739			−0.188798
$990$	−13.0291	+	14.0900i	−0.414091	+	0.447809i
$991$	−20.6589	−	7.51921i	−0.656251	−	0.238856i	−0.00763382	−	0.999971i	$-0.502430\pi$
$991$	−20.6589	−	7.51921i	−0.656251	−	0.238856i	−0.648617	+	0.761115i	$0.724652\pi$
$992$	−9.80495	+	4.82500i	−0.311307	+	0.153194i
$993$	−1.16335	−	6.59769i	−0.0369178	−	0.209371i
$994$	61.8621	−	31.8479i	1.96215	−	1.01015i
$995$	12.0026	+	6.92973i	0.380509	+	0.219687i
$996$	−18.4652	+	18.1335i	−0.585092	+	0.574580i
$997$	8.75864	+	7.34937i	0.277389	+	0.232757i	0.770859	−	0.637006i	$-0.219827\pi$
$997$	8.75864	+	7.34937i	0.277389	+	0.232757i	−0.493470	+	0.869763i	$0.664272\pi$
$998$	32.6983	+	21.0401i	1.03505	+	0.666011i
$999$	−3.97479	+	2.29485i	−0.125757	+	0.0726057i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.be.b.51.15	yes	120
4.3	odd	2	inner	380.2.be.b.51.14	✓	120
19.3	odd	18	inner	380.2.be.b.231.14	yes	120
76.3	even	18	inner	380.2.be.b.231.15	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.be.b.51.14	✓	120	4.3	odd	2	inner
380.2.be.b.51.15	yes	120	1.1	even	1	trivial
380.2.be.b.231.14	yes	120	19.3	odd	18	inner
380.2.be.b.231.15	yes	120	76.3	even	18	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.03833 + 0.960144i) q^{2} +(0.700287 + 0.254884i) q^{3} +(0.156246 + 1.99389i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(0.482402 + 0.937029i) q^{6} +(3.13008 + 1.80715i) q^{7} +(-1.75219 + 2.22033i) q^{8} +(-1.87270 - 1.57138i) q^{9} +O(q^{10})\)	\(q+(1.03833 + 0.960144i) q^{2} +(0.700287 + 0.254884i) q^{3} +(0.156246 + 1.99389i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(0.482402 + 0.937029i) q^{6} +(3.13008 + 1.80715i) q^{7} +(-1.75219 + 2.22033i) q^{8} +(-1.87270 - 1.57138i) q^{9} +(0.765254 - 1.18928i) q^{10} +(4.80721 - 2.77545i) q^{11} +(-0.398792 + 1.43612i) q^{12} +(0.738627 + 2.02936i) q^{13} +(1.51492 + 4.88174i) q^{14} +(0.129408 - 0.733908i) q^{15} +(-3.95117 + 0.623074i) q^{16} +(-4.32858 + 3.63211i) q^{17} +(-0.435721 - 3.42967i) q^{18} +(-4.14647 + 1.34415i) q^{19} +(1.93646 - 0.500107i) q^{20} +(1.73134 + 2.06333i) q^{21} +(7.65629 + 1.73380i) q^{22} +(-1.70362 - 0.300395i) q^{23} +(-1.79296 + 1.10826i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(-1.18154 + 2.81633i) q^{26} +(-2.02875 - 3.51390i) q^{27} +(-3.11419 + 6.52338i) q^{28} +(4.56883 - 5.44492i) q^{29} +(0.839025 - 0.637787i) q^{30} +(0.965893 - 1.67298i) q^{31} +(-4.70085 - 3.14674i) q^{32} +(4.07385 - 0.718329i) q^{33} +(-7.98184 - 0.384743i) q^{34} +(1.23616 - 3.39633i) q^{35} +(2.84055 - 3.97947i) q^{36} -1.13116i q^{37} +(-5.59598 - 2.58554i) q^{38} +1.60940i q^{39} +(2.49086 + 1.34001i) q^{40} +(1.35657 - 3.72715i) q^{41} +(-0.183398 + 3.80474i) q^{42} +(3.38006 - 0.595996i) q^{43} +(6.28504 + 9.15139i) q^{44} +(-1.22232 + 2.11711i) q^{45} +(-1.48050 - 1.94763i) q^{46} +(4.40407 - 5.24857i) q^{47} +(-2.92577 - 0.570759i) q^{48} +(3.03158 + 5.25085i) q^{49} +(-1.30410 - 0.547112i) q^{50} +(-3.95702 + 1.44024i) q^{51} +(-3.93091 + 1.78982i) q^{52} +(-10.3559 - 1.82602i) q^{53} +(1.26734 - 5.59647i) q^{54} +(-3.56805 - 4.25223i) q^{55} +(-9.49693 + 3.78333i) q^{56} +(-3.24632 - 0.115575i) q^{57} +(9.97185 - 1.26687i) q^{58} +(-3.05890 + 2.56673i) q^{59} +(1.48355 + 0.143354i) q^{60} +(-0.439276 + 2.49126i) q^{61} +(2.60921 - 0.809699i) q^{62} +(-3.02197 - 8.30278i) q^{63} +(-1.85970 - 7.78084i) q^{64} +(1.87027 - 1.07980i) q^{65} +(4.91968 + 3.16562i) q^{66} +(4.27487 + 3.58704i) q^{67} +(-7.91835 - 8.06320i) q^{68} +(-1.11646 - 0.644589i) q^{69} +(4.54451 - 2.33961i) q^{70} +(-2.36378 - 13.4057i) q^{71} +(6.77029 - 1.40465i) q^{72} +(-4.86974 - 1.77244i) q^{73} +(1.08608 - 1.17452i) q^{74} -0.745230 q^{75} +(-3.32796 - 8.05758i) q^{76} +20.0626 q^{77} +(-1.54526 + 1.67108i) q^{78} +(-9.33512 - 3.39771i) q^{79} +(1.29972 + 3.78295i) q^{80} +(0.748445 + 4.24464i) q^{81} +(4.98717 - 2.56750i) q^{82} +(15.0376 + 8.68195i) q^{83} +(-3.84353 + 3.77448i) q^{84} +(4.32858 + 3.63211i) q^{85} +(4.08185 + 2.62651i) q^{86} +(4.58731 - 2.64849i) q^{87} +(-2.26073 + 15.5367i) q^{88} +(-0.0513214 - 0.141004i) q^{89} +(-3.30190 + 1.02466i) q^{90} +(-1.35540 + 7.68686i) q^{91} +(0.332769 - 3.44377i) q^{92} +(1.10282 - 0.925373i) q^{93} +(9.61225 - 1.22119i) q^{94} +(2.04376 + 3.85007i) q^{95} +(-2.48989 - 3.40179i) q^{96} +(-2.23563 - 2.66432i) q^{97} +(-1.89380 + 8.36286i) q^{98} +(-13.3637 - 2.35639i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9}+O(q^{10}) \) 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9	\( 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9} + 3 q^{10} - 12 q^{13} - 18 q^{14} + 9 q^{16} + 48 q^{17} - 12 q^{21} - 18 q^{24} - 24 q^{26} + 69 q^{28} - 12 q^{30} - 27 q^{32} + 6 q^{33} - 18 q^{34} - 72 q^{36} - 48 q^{38} - 36 q^{41} - 27 q^{42} - 99 q^{44} + 60 q^{45} + 27 q^{46} - 63 q^{48} + 60 q^{49} + 33 q^{52} - 24 q^{53} + 21 q^{54} - 48 q^{57} + 6 q^{60} - 24 q^{61} + 54 q^{62} + 84 q^{64} - 18 q^{65} - 132 q^{66} + 66 q^{68} - 72 q^{69} + 36 q^{70} - 42 q^{72} + 66 q^{74} + 180 q^{76} + 60 q^{77} + 114 q^{78} + 27 q^{80} - 66 q^{81} + 33 q^{82} - 144 q^{84} - 48 q^{85} + 75 q^{86} + 9 q^{88} - 3 q^{90} - 42 q^{92} - 144 q^{93} + 78 q^{96} + 42 q^{97} - 87 q^{98}+O(q^{100}) \) 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9 + 3 * q^10 - 12 * q^13 - 18 * q^14 + 9 * q^16 + 48 * q^17 - 12 * q^21 - 18 * q^24 - 24 * q^26 + 69 * q^28 - 12 * q^30 - 27 * q^32 + 6 * q^33 - 18 * q^34 - 72 * q^36 - 48 * q^38 - 36 * q^41 - 27 * q^42 - 99 * q^44 + 60 * q^45 + 27 * q^46 - 63 * q^48 + 60 * q^49 + 33 * q^52 - 24 * q^53 + 21 * q^54 - 48 * q^57 + 6 * q^60 - 24 * q^61 + 54 * q^62 + 84 * q^64 - 18 * q^65 - 132 * q^66 + 66 * q^68 - 72 * q^69 + 36 * q^70 - 42 * q^72 + 66 * q^74 + 180 * q^76 + 60 * q^77 + 114 * q^78 + 27 * q^80 - 66 * q^81 + 33 * q^82 - 144 * q^84 - 48 * q^85 + 75 * q^86 + 9 * q^88 - 3 * q^90 - 42 * q^92 - 144 * q^93 + 78 * q^96 + 42 * q^97 - 87 * q^98

Introduction

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