LMFDB - Embedded newform 336.2.bu.a.11.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(11,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 6, 8]))

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

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

chi := DirichletCharacter("336.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bu (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$60$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.19
Character	$\chi$	$=$	336.11
Dual form			336.2.bu.a.275.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.860221 + 1.12251i) q^{2} +(-1.55800 + 0.756720i) q^{3} +(-0.520041 - 1.93121i) q^{4} +(1.89562 + 0.507929i) q^{5} +(0.490803 - 2.39982i) q^{6} +(-0.588039 + 2.57958i) q^{7} +(2.61514 + 1.07751i) q^{8} +(1.85475 - 2.35795i) q^{9} +O(q^{10})$	\(q+(-0.860221 + 1.12251i) q^{2} +(-1.55800 + 0.756720i) q^{3} +(-0.520041 - 1.93121i) q^{4} +(1.89562 + 0.507929i) q^{5} +(0.490803 - 2.39982i) q^{6} +(-0.588039 + 2.57958i) q^{7} +(2.61514 + 1.07751i) q^{8} +(1.85475 - 2.35795i) q^{9} +(-2.20080 + 1.69091i) q^{10} +(3.31034 - 0.887003i) q^{11} +(2.27161 + 2.61530i) q^{12} +(-1.24592 + 1.24592i) q^{13} +(-2.38975 - 2.87908i) q^{14} +(-3.33774 + 0.643097i) q^{15} +(-3.45912 + 2.00861i) q^{16} +(2.11957 + 1.22374i) q^{17} +(1.05132 + 4.11032i) q^{18} +(-1.67532 + 6.25236i) q^{19} +(-0.00488227 - 3.92497i) q^{20} +(-1.03585 - 4.46397i) q^{21} +(-1.85196 + 4.47890i) q^{22} +(-4.58309 + 2.64605i) q^{23} +(-4.88978 + 0.300159i) q^{24} +(-0.994755 - 0.574322i) q^{25} +(-0.326788 - 2.47033i) q^{26} +(-1.10540 + 5.07721i) q^{27} +(5.28750 - 0.205860i) q^{28} +(2.18387 + 2.18387i) q^{29} +(2.14931 - 4.29984i) q^{30} +(-3.90197 - 2.25280i) q^{31} +(0.720923 - 5.61073i) q^{32} +(-4.48631 + 3.88696i) q^{33} +(-3.19695 + 1.32655i) q^{34} +(-2.42494 + 4.59121i) q^{35} +(-5.51822 - 2.35567i) q^{36} +(0.744575 - 2.77879i) q^{37} +(-5.57718 - 7.25897i) q^{38} +(0.998338 - 2.88397i) q^{39} +(4.41000 + 3.37086i) q^{40} -0.732552 q^{41} +(5.90189 + 2.67725i) q^{42} +(-1.81305 + 1.81305i) q^{43} +(-3.43450 - 5.93167i) q^{44} +(4.71356 - 3.52768i) q^{45} +(0.972262 - 7.42073i) q^{46} +(3.40795 + 5.90274i) q^{47} +(3.86936 - 5.74701i) q^{48} +(-6.30842 - 3.03378i) q^{49} +(1.50039 - 0.622575i) q^{50} +(-4.22833 - 0.302661i) q^{51} +(3.05407 + 1.75821i) q^{52} +(3.50544 + 13.0825i) q^{53} +(-4.74832 - 5.60834i) q^{54} +6.72567 q^{55} +(-4.31734 + 6.11233i) q^{56} +(-2.12114 - 11.0089i) q^{57} +(-4.33001 + 0.572796i) q^{58} +(10.6669 - 2.85820i) q^{59} +(2.97771 + 6.11142i) q^{60} +(3.30849 + 0.886508i) q^{61} +(5.88534 - 2.44208i) q^{62} +(4.99183 + 6.17103i) q^{63} +(5.67792 + 5.63571i) q^{64} +(-2.99464 + 1.72895i) q^{65} +(-0.503917 - 8.37955i) q^{66} +(10.1457 - 2.71854i) q^{67} +(1.26102 - 4.72972i) q^{68} +(5.13815 - 7.59066i) q^{69} +(-3.06767 - 6.67146i) q^{70} -15.3599i q^{71} +(7.39115 - 4.16784i) q^{72} +(9.63710 + 5.56398i) q^{73} +(2.47871 + 3.22616i) q^{74} +(1.98443 + 0.142044i) q^{75} +(12.9458 - 0.0161033i) q^{76} +(0.341482 + 9.06087i) q^{77} +(2.37848 + 3.60149i) q^{78} +(-8.49086 + 4.90220i) q^{79} +(-7.57739 + 2.05057i) q^{80} +(-2.11982 - 8.74679i) q^{81} +(0.630156 - 0.822294i) q^{82} +(-6.91319 + 6.91319i) q^{83} +(-8.08216 + 4.32189i) q^{84} +(3.39633 + 3.39633i) q^{85} +(-0.475537 - 3.59478i) q^{86} +(-5.05504 - 1.74989i) q^{87} +(9.61277 + 1.24730i) q^{88} +(-1.33285 - 2.30856i) q^{89} +(-0.0948594 + 8.32559i) q^{90} +(-2.48130 - 3.94661i) q^{91} +(7.49345 + 7.47483i) q^{92} +(7.78402 + 0.557175i) q^{93} +(-9.55745 - 1.25222i) q^{94} +(-6.35151 + 11.0011i) q^{95} +(3.12255 + 9.28707i) q^{96} -4.12061 q^{97} +(8.83207 - 4.47152i) q^{98} +(4.04835 - 9.45077i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 16 q^{7}+O(q^{10}) $ 240 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 16 * q^7	$ 240 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 16 q^{7} - 4 q^{10} - 2 q^{12} - 16 q^{13} - 20 q^{16} + 16 q^{18} - 4 q^{19} + 2 q^{21} - 40 q^{22} - 22 q^{24} - 8 q^{27} - 4 q^{28} - 26 q^{30} - 4 q^{33} + 16 q^{36} - 4 q^{37} - 4 q^{39} + 8 q^{40} - 18 q^{42} - 16 q^{43} + 18 q^{45} - 20 q^{46} - 88 q^{48} - 16 q^{49} + 6 q^{51} + 8 q^{52} + 14 q^{54} - 32 q^{55} - 36 q^{58} - 42 q^{60} - 4 q^{61} - 64 q^{64} - 30 q^{66} - 36 q^{67} - 20 q^{69} + 116 q^{70} - 46 q^{72} - 24 q^{75} - 112 q^{76} - 92 q^{78} - 4 q^{81} - 32 q^{82} + 44 q^{84} - 56 q^{85} - 4 q^{87} - 20 q^{88} + 28 q^{90} - 40 q^{91} - 14 q^{93} + 72 q^{94} + 36 q^{96} - 32 q^{97} + 28 q^{99}+O(q^{100}) $ 240 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 16 * q^7 - 4 * q^10 - 2 * q^12 - 16 * q^13 - 20 * q^16 + 16 * q^18 - 4 * q^19 + 2 * q^21 - 40 * q^22 - 22 * q^24 - 8 * q^27 - 4 * q^28 - 26 * q^30 - 4 * q^33 + 16 * q^36 - 4 * q^37 - 4 * q^39 + 8 * q^40 - 18 * q^42 - 16 * q^43 + 18 * q^45 - 20 * q^46 - 88 * q^48 - 16 * q^49 + 6 * q^51 + 8 * q^52 + 14 * q^54 - 32 * q^55 - 36 * q^58 - 42 * q^60 - 4 * q^61 - 64 * q^64 - 30 * q^66 - 36 * q^67 - 20 * q^69 + 116 * q^70 - 46 * q^72 - 24 * q^75 - 112 * q^76 - 92 * q^78 - 4 * q^81 - 32 * q^82 + 44 * q^84 - 56 * q^85 - 4 * q^87 - 20 * q^88 + 28 * q^90 - 40 * q^91 - 14 * q^93 + 72 * q^94 + 36 * q^96 - 32 * q^97 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.860221	+	1.12251i	−0.608268	+	0.793732i
$2$	−0.860221	+	1.12251i	−0.608268	+	0.793732i
$3$	−1.55800	+	0.756720i	−0.899514	+	0.436893i
$3$	−1.55800	+	0.756720i	−0.899514	+	0.436893i
$4$	−0.520041	−	1.93121i	−0.260020	−	0.965603i
$5$	1.89562	+	0.507929i	0.847746	+	0.227153i	0.656440	−	0.754378i	$-0.272061\pi$
$5$	1.89562	+	0.507929i	0.847746	+	0.227153i	0.191305	+	0.981531i	$0.438728\pi$
$6$	0.490803	−	2.39982i	0.200370	−	0.979720i
$7$	−0.588039	+	2.57958i	−0.222258	+	0.974988i
$7$	−0.588039	+	2.57958i	−0.222258	+	0.974988i
$8$	2.61514	+	1.07751i	0.924592	+	0.380959i
$9$	1.85475	−	2.35795i	0.618250	−	0.785982i
$10$	−2.20080	+	1.69091i	−0.695955	+	0.534713i
$11$	3.31034	−	0.887003i	0.998105	−	0.267442i	0.277454	−	0.960739i	$-0.410509\pi$
$11$	3.31034	−	0.887003i	0.998105	−	0.267442i	0.720652	+	0.693297i	$0.243843\pi$
$12$	2.27161	+	2.61530i	0.655757	+	0.754972i
$13$	−1.24592	+	1.24592i	−0.345557	+	0.345557i	−0.858452	−	0.512894i	$-0.828573\pi$
$13$	−1.24592	+	1.24592i	−0.345557	+	0.345557i	0.512894	+	0.858452i	$0.328573\pi$
$14$	−2.38975	−	2.87908i	−0.638687	−	0.769467i
$15$	−3.33774	+	0.643097i	−0.861800	+	0.166047i
$16$	−3.45912	+	2.00861i	−0.864779	+	0.502153i
$17$	2.11957	+	1.22374i	0.514072	+	0.296799i	0.734506	−	0.678602i	$-0.237414\pi$
$17$	2.11957	+	1.22374i	0.514072	+	0.296799i	−0.220434	+	0.975402i	$0.570747\pi$
$18$	1.05132	+	4.11032i	0.247797	+	0.968812i
$19$	−1.67532	+	6.25236i	−0.384344	+	1.43439i	0.454855	+	0.890566i	$0.349691\pi$
$19$	−1.67532	+	6.25236i	−0.384344	+	1.43439i	−0.839199	+	0.543825i	$0.816976\pi$
$20$	−0.00488227	−	3.92497i	−0.00109171	−	0.877650i
$21$	−1.03585	−	4.46397i	−0.226041	−	0.974118i
$22$	−1.85196	+	4.47890i	−0.394839	+	0.954904i
$23$	−4.58309	+	2.64605i	−0.955640	+	0.551739i	−0.894828	−	0.446410i	$-0.852702\pi$
$23$	−4.58309	+	2.64605i	−0.955640	+	0.551739i	−0.0608114	+	0.998149i	$0.519369\pi$
$24$	−4.88978	+	0.300159i	−0.998121	+	0.0612697i
$25$	−0.994755	−	0.574322i	−0.198951	−	0.114864i
$26$	−0.326788	−	2.47033i	−0.0640884	−	0.484471i
$27$	−1.10540	+	5.07721i	−0.212734	+	0.977110i
$28$	5.28750	−	0.205860i	0.999243	−	0.0389038i
$29$	2.18387	+	2.18387i	0.405534	+	0.405534i	0.880178	−	0.474644i	$-0.157423\pi$
$29$	2.18387	+	2.18387i	0.405534	+	0.405534i	−0.474644	+	0.880178i	$0.657423\pi$
$30$	2.14931	−	4.29984i	0.392409	−	0.785039i
$31$	−3.90197	−	2.25280i	−0.700814	−	0.404615i	0.106836	−	0.994277i	$-0.465928\pi$
$31$	−3.90197	−	2.25280i	−0.700814	−	0.404615i	−0.807651	+	0.589661i	$0.799261\pi$
$32$	0.720923	−	5.61073i	0.127442	−	0.991846i
$33$	−4.48631	+	3.88696i	−0.780966	+	0.676632i
$34$	−3.19695	+	1.32655i	−0.548273	+	0.227502i
$35$	−2.42494	+	4.59121i	−0.409889	+	0.776055i
$36$	−5.51822	−	2.35567i	−0.919704	−	0.392612i
$37$	0.744575	−	2.77879i	0.122407	−	0.456830i	−0.877327	−	0.479894i	$-0.840675\pi$
$37$	0.744575	−	2.77879i	0.122407	−	0.456830i	0.999734	+	0.0230633i	$0.00734192\pi$
$38$	−5.57718	−	7.25897i	−0.904737	−	1.17756i
$39$	0.998338	−	2.88397i	0.159862	−	0.461805i
$40$	4.41000	+	3.37086i	0.697283	+	0.532980i
$41$	−0.732552			−0.114405			−0.0572027	−	0.998363i	$-0.518218\pi$
$41$	−0.732552			−0.114405			−0.0572027	+	0.998363i	$0.518218\pi$
$42$	5.90189	+	2.67725i	0.910682	+	0.413108i
$43$	−1.81305	+	1.81305i	−0.276488	+	0.276488i	−0.831705	−	0.555218i	$-0.812635\pi$
$43$	−1.81305	+	1.81305i	−0.276488	+	0.276488i	0.555218	+	0.831705i	$0.312635\pi$
$44$	−3.43450	−	5.93167i	−0.517770	−	0.894234i
$45$	4.71356	−	3.52768i	0.702656	−	0.525876i
$46$	0.972262	−	7.42073i	0.143352	−	1.09413i
$47$	3.40795	+	5.90274i	0.497101	+	0.861003i	0.999994	−	0.00334478i	$-0.00106468\pi$
$47$	3.40795	+	5.90274i	0.497101	+	0.861003i	−0.502894	+	0.864348i	$0.667731\pi$
$48$	3.86936	−	5.74701i	0.558493	−	0.829509i
$49$	−6.30842	−	3.03378i	−0.901203	−	0.433397i
$50$	1.50039	−	0.622575i	0.212187	−	0.0880454i
$51$	−4.22833	−	0.302661i	−0.592084	−	0.0423810i
$52$	3.05407	+	1.75821i	0.423523	+	0.243819i
$53$	3.50544	+	13.0825i	0.481509	+	1.79701i	0.595293	+	0.803509i	$0.297036\pi$
$53$	3.50544	+	13.0825i	0.481509	+	1.79701i	−0.113784	+	0.993505i	$0.536297\pi$
$54$	−4.74832	−	5.60834i	−0.646164	−	0.763199i
$55$	6.72567			0.906890
$56$	−4.31734	+	6.11233i	−0.576928	+	0.816795i
$57$	−2.12114	−	11.0089i	−0.280952	−	1.45817i
$58$	−4.33001	+	0.572796i	−0.568558	+	0.0752118i
$59$	10.6669	−	2.85820i	1.38872	−	0.372106i	0.514437	−	0.857528i	$-0.328001\pi$
$59$	10.6669	−	2.85820i	1.38872	−	0.372106i	0.874280	+	0.485422i	$0.161334\pi$
$60$	2.97771	+	6.11142i	0.384421	+	0.788981i
$61$	3.30849	+	0.886508i	0.423609	+	0.113506i	0.464325	−	0.885665i	$-0.346297\pi$
$61$	3.30849	+	0.886508i	0.423609	+	0.113506i	−0.0407155	+	0.999171i	$0.512964\pi$
$62$	5.88534	−	2.44208i	0.747439	−	0.310144i
$63$	4.99183	+	6.17103i	0.628912	+	0.777476i
$64$	5.67792	+	5.63571i	0.709741	+	0.704463i
$65$	−2.99464	+	1.72895i	−0.371439	+	0.214450i
$66$	−0.503917	−	8.37955i	−0.0620279	−	1.03145i
$67$	10.1457	−	2.71854i	1.23950	−	0.332123i	0.421228	−	0.906955i	$-0.361599\pi$
$67$	10.1457	−	2.71854i	1.23950	−	0.332123i	0.818271	+	0.574832i	$0.194933\pi$
$68$	1.26102	−	4.72972i	0.152921	−	0.573563i
$69$	5.13815	−	7.59066i	0.618560	−	0.913809i
$70$	−3.06767	−	6.67146i	−0.366657	−	0.797392i
$71$		−	15.3599i		−	1.82288i	−0.411430	−	0.911441i	$-0.634970\pi$
$71$		−	15.3599i		−	1.82288i	0.411430	−	0.911441i	$-0.365030\pi$
$72$	7.39115	−	4.16784i	0.871055	−	0.491185i
$73$	9.63710	+	5.56398i	1.12794	+	0.651215i	0.943415	−	0.331614i	$-0.107593\pi$
$73$	9.63710	+	5.56398i	1.12794	+	0.651215i	0.184522	+	0.982828i	$0.440926\pi$
$74$	2.47871	+	3.22616i	0.288144	+	0.375034i
$75$	1.98443	+	0.142044i	0.229143	+	0.0164019i
$76$	12.9458	−	0.0161033i	1.48499	−	0.00184718i
$77$	0.341482	+	9.06087i	0.0389155	+	1.03258i
$78$	2.37848	+	3.60149i	0.269310	+	0.407789i
$79$	−8.49086	+	4.90220i	−0.955296	+	0.551541i	−0.894722	−	0.446623i	$-0.852626\pi$
$79$	−8.49086	+	4.90220i	−0.955296	+	0.551541i	−0.0605741	+	0.998164i	$0.519293\pi$
$80$	−7.57739	+	2.05057i	−0.847178	+	0.229261i
$81$	−2.11982	−	8.74679i	−0.235535	−	0.971866i
$82$	0.630156	−	0.822294i	0.0695891	−	0.0908072i
$83$	−6.91319	+	6.91319i	−0.758821	+	0.758821i	−0.976108	−	0.217287i	$-0.930279\pi$
$83$	−6.91319	+	6.91319i	−0.758821	+	0.758821i	0.217287	+	0.976108i	$0.430279\pi$
$84$	−8.08216	+	4.32189i	−0.881836	+	0.471556i
$85$	3.39633	+	3.39633i	0.368383	+	0.368383i
$86$	−0.475537	−	3.59478i	−0.0512785	−	0.387636i
$87$	−5.05504	−	1.74989i	−0.541958	−	0.187608i
$88$	9.61277	+	1.24730i	1.02472	+	0.132963i
$89$	−1.33285	−	2.30856i	−0.141282	−	0.244707i	0.786698	−	0.617338i	$-0.211789\pi$
$89$	−1.33285	−	2.30856i	−0.141282	−	0.244707i	−0.927979	+	0.372631i	$0.878456\pi$
$90$	−0.0948594	+	8.32559i	−0.00999906	+	0.877594i
$91$	−2.48130	−	3.94661i	−0.260111	−	0.413717i
$92$	7.49345	+	7.47483i	0.781246	+	0.779305i
$93$	7.78402	+	0.557175i	0.807165	+	0.0577763i
$94$	−9.55745	−	1.25222i	−0.985776	−	0.129156i
$95$	−6.35151	+	11.0011i	−0.651652	+	1.12869i
$96$	3.12255	+	9.28707i	0.318694	+	0.947858i
$97$	−4.12061			−0.418385			−0.209192	−	0.977875i	$-0.567083\pi$
$97$	−4.12061			−0.418385			−0.209192	+	0.977875i	$0.567083\pi$
$98$	8.83207	−	4.47152i	0.892174	−	0.451692i
$99$	4.04835	−	9.45077i	0.406874	−	0.949838i
$100$	−0.591821	+	2.21975i	−0.0591821	+	0.221975i
$101$	1.65980	+	6.19447i	0.165157	+	0.616373i	0.998020	+	0.0628945i	$0.0200332\pi$
$101$	1.65980	+	6.19447i	0.165157	+	0.616373i	−0.832864	+	0.553478i	$0.813300\pi$
$102$	3.97703	−	4.48597i	0.393785	−	0.444177i
$103$	−4.02151	−	6.96545i	−0.396251	−	0.686326i	0.597009	−	0.802234i	$-0.296356\pi$
$103$	−4.02151	−	6.96545i	−0.396251	−	0.686326i	−0.993260	+	0.115908i	$0.963022\pi$
$104$	−4.60077	+	1.91577i	−0.451143	+	0.187856i
$105$	0.303803	−	8.98811i	0.0296481	−	0.877150i
$106$	−17.7006	−	7.31893i	−1.71923	−	0.710877i
$107$	3.48623	−	13.0108i	0.337027	−	1.25780i	−0.564629	−	0.825345i	$-0.690981\pi$
$107$	3.48623	−	13.0108i	0.337027	−	1.25780i	0.901655	−	0.432455i	$-0.142353\pi$
$108$	10.3800	−	0.505604i	0.998816	−	0.0486518i
$109$	0.241401	+	0.900920i	0.0231220	+	0.0862925i	0.976523	−	0.215414i	$-0.0691102\pi$
$109$	0.241401	+	0.900920i	0.0231220	+	0.0862925i	−0.953401	+	0.301707i	$0.902444\pi$
$110$	−5.78556	+	7.54961i	−0.551632	+	0.719827i
$111$	0.942718	+	4.89280i	0.0894788	+	0.464404i
$112$	−3.14727	−	10.1042i	−0.297389	−	0.954756i
$113$		−	19.1515i		−	1.80162i	−0.434215	−	0.900809i	$-0.642974\pi$
$113$		−	19.1515i		−	1.80162i	0.434215	−	0.900809i	$-0.357026\pi$
$114$	14.1823	+	7.08913i	1.32829	+	0.663958i
$115$	−10.0318	+	2.68801i	−0.935468	+	0.250658i
$116$	3.08180	−	5.35319i	0.286138	−	0.497031i
$117$	0.626945	+	5.24870i	0.0579611	+	0.485242i
$118$	−5.96758	+	14.4324i	−0.549360	+	1.32861i
$119$	−4.40311	+	4.74799i	−0.403632	+	0.435248i
$120$	−9.42160	−	1.91467i	−0.860071	−	0.174785i
$121$	0.645306	−	0.372567i	0.0586642	−	0.0338698i
$122$	−3.84115	+	2.95121i	−0.347761	+	0.267190i
$123$	1.14132	−	0.554337i	0.102909	−	0.0499829i
$124$	−2.32144	+	8.70706i	−0.208472	+	0.781917i
$125$	−8.53240	−	8.53240i	−0.763161	−	0.763161i
$126$	−11.2211	+	0.294919i	−0.999655	+	0.0262735i
$127$		−	6.57134i		−	0.583112i	−0.956554	−	0.291556i	$-0.905827\pi$
$127$		−	6.57134i		−	0.583112i	0.956554	−	0.291556i	$-0.0941730\pi$
$128$	−11.2104	+	1.52556i	−0.990867	+	0.134841i
$129$	1.45277	−	4.19671i	0.127909	−	0.369500i
$130$	0.635286	−	4.84878i	0.0557183	−	0.425266i
$131$	13.9434	+	3.73611i	1.21824	+	0.326426i	0.809989	−	0.586445i	$-0.199473\pi$
$131$	13.9434	+	3.73611i	1.21824	+	0.326426i	0.408249	+	0.912871i	$0.366140\pi$
$132$	9.83958	+	6.64261i	0.856425	+	0.578165i
$133$	−15.1433	−	7.99824i	−1.31309	−	0.693535i
$134$	−5.67599	+	13.7272i	−0.490331	+	1.18585i
$135$	−4.67428	+	9.06299i	−0.402298	+	0.780018i
$136$	4.22439	+	5.48411i	0.362238	+	0.470259i
$137$	6.46380	−	11.1956i	0.552239	−	0.956507i	−0.445873	−	0.895096i	$-0.647107\pi$
$137$	6.46380	−	11.1956i	0.552239	−	0.956507i	0.998113	−	0.0614105i	$-0.0195599\pi$
$138$	4.10063	+	12.2972i	0.349069	+	1.04681i
$139$	10.9284	−	10.9284i	0.926938	−	0.926938i	−0.0705686	−	0.997507i	$-0.522481\pi$
$139$	10.9284	−	10.9284i	0.926938	−	0.926938i	0.997507	+	0.0705686i	$0.0224814\pi$
$140$	10.1276	+	2.29544i	0.855941	+	0.194000i
$141$	−9.77632	−	6.61763i	−0.823315	−	0.557305i
$142$	17.2416	+	13.2129i	1.44688	+	1.10880i
$143$	−3.01930	+	5.22957i	−0.252486	+	0.437319i
$144$	−1.67959	+	11.8819i	−0.139966	+	0.990156i
$145$	3.03052	+	5.24902i	0.251671	+	0.435907i
$146$	−14.5356	+	6.03145i	−1.20298	+	0.499166i
$147$	12.1243	−	0.0470677i	0.999992	−	0.00388208i
$148$	−5.75363	+	0.00715693i	−0.472945	+	0.000588296i
$149$	0.339954	+	0.0910904i	0.0278501	+	0.00746242i	0.272717	−	0.962094i	$-0.412078\pi$
$149$	0.339954	+	0.0910904i	0.0278501	+	0.00746242i	−0.244867	+	0.969557i	$0.578744\pi$
$150$	−1.86650	+	2.10535i	−0.152399	+	0.171901i
$151$	5.54321	−	9.60112i	0.451100	−	0.781328i	−0.547355	−	0.836901i	$-0.684365\pi$
$151$	5.54321	−	9.60112i	0.451100	−	0.781328i	0.998455	+	0.0555727i	$0.0176985\pi$
$152$	−11.1182	+	14.5456i	−0.901805	+	1.17981i
$153$	6.81678	−	2.72811i	0.551104	−	0.220555i
$154$	−10.4646	−	7.41103i	−0.843264	−	0.597198i
$155$	−6.25237	−	6.25237i	−0.502203	−	0.502203i
$156$	−6.08872	−	0.428214i	−0.487488	−	0.0342846i
$157$	−0.0748535	−	0.279357i	−0.00597396	−	0.0222951i	0.962875	−	0.269949i	$-0.0870070\pi$
$157$	−0.0748535	−	0.279357i	−0.00597396	−	0.0222951i	−0.968848	+	0.247654i	$0.920340\pi$
$158$	1.80126	−	13.7480i	0.143301	−	1.09373i
$159$	−15.3612	−	17.7299i	−1.21823	−	1.40607i
$160$	4.21645	−	10.2696i	0.333339	−	0.811884i
$161$	−4.13064	−	13.3784i	−0.325540	−	1.05437i
$162$	11.6418	+	5.14467i	0.914669	+	0.404203i
$163$	0.101851	−	0.380114i	0.00797760	−	0.0297728i	−0.961822	−	0.273675i	$-0.911761\pi$
$163$	0.101851	−	0.380114i	0.00797760	−	0.0297728i	0.969800	+	0.243902i	$0.0784275\pi$
$164$	0.380957	+	1.41471i	0.0297477	+	0.110470i
$165$	−10.4786	+	5.08945i	−0.815760	+	0.396213i
$166$	−1.81323	−	13.7070i	−0.140734	−	1.06387i
$167$			10.3910i			0.804078i	0.915623	+	0.402039i	$0.131698\pi$
$167$			10.3910i			0.804078i	−0.915623	+	0.402039i	$0.868302\pi$
$168$	2.10110	−	12.7901i	0.162103	−	0.986774i
$169$			9.89535i			0.761180i
$170$	−6.73399	+	0.890807i	−0.516473	+	0.0683218i
$171$	11.6354	+	15.5469i	0.889785	+	1.18890i
$172$	4.44424	+	2.55851i	0.338870	+	0.195085i
$173$	−1.00455	+	3.74904i	−0.0763748	+	0.285034i	−0.993542	−	0.113469i	$-0.963804\pi$
$173$	−1.00455	+	3.74904i	−0.0763748	+	0.285034i	0.917167	+	0.398504i	$0.130470\pi$
$174$	6.31272	−	4.16902i	0.478566	−	0.316053i
$175$	2.06646	−	2.22832i	0.156210	−	0.168445i
$176$	−9.66921	+	9.71744i	−0.728844	+	0.732479i
$177$	−14.4563	+	12.5250i	−1.08660	+	0.941434i
$178$	3.73792	+	0.489741i	0.280169	+	0.0367076i
$179$	−5.88276	−	21.9547i	−0.439698	−	1.64097i	−0.729568	−	0.683909i	$-0.760279\pi$
$179$	−5.88276	−	21.9547i	−0.439698	−	1.64097i	0.289870	−	0.957066i	$-0.406388\pi$
$180$	−9.26392	−	7.26832i	−0.690492	−	0.541749i
$181$	16.5183	+	16.5183i	1.22780	+	1.22780i	0.964795	+	0.263004i	$0.0847133\pi$
$181$	16.5183	+	16.5183i	1.22780	+	1.22780i	0.263004	+	0.964795i	$0.415287\pi$
$182$	6.56456	+	0.609675i	0.486598	+	0.0451921i
$183$	−5.82548	+	1.12242i	−0.430632	+	0.0829718i
$184$	−14.8366	+	1.98144i	−1.09377	+	0.146074i
$185$	2.82286	−	4.88933i	0.207541	−	0.359471i
$186$	−7.32141	+	8.25832i	−0.536832	+	0.605529i
$187$	8.10197	+	2.17092i	0.592474	+	0.158753i
$188$	9.62714	−	9.65112i	0.702131	−	0.703880i
$189$	−12.4470	−	5.83706i	−0.905389	−	0.424584i
$190$	−6.88515	−	16.5930i	−0.499501	−	1.20378i
$191$	9.04314	+	15.6632i	0.654339	+	1.13335i	0.982059	+	0.188573i	$0.0603863\pi$
$191$	9.04314	+	15.6632i	0.654339	+	1.13335i	−0.327720	+	0.944775i	$0.606280\pi$
$192$	−13.1109	−	4.48385i	−0.946196	−	0.323594i
$193$	−2.59979	+	4.50296i	−0.187137	+	0.324130i	−0.944294	−	0.329102i	$-0.893254\pi$
$193$	−2.59979	+	4.50296i	−0.187137	+	0.324130i	0.757158	+	0.653232i	$0.226587\pi$
$194$	3.54464	−	4.62541i	0.254490	−	0.332085i
$195$	3.35732	−	4.95982i	0.240423	−	0.355180i
$196$	−2.57822	+	13.7606i	−0.184159	+	0.982897i
$197$	−0.177149	+	0.177149i	−0.0126213	+	0.0126213i	−0.713389	−	0.700768i	$-0.752841\pi$
$197$	−0.177149	+	0.177149i	−0.0126213	+	0.0126213i	0.700768	+	0.713389i	$0.252841\pi$
$198$	7.12608	+	12.6740i	0.506429	+	0.900705i
$199$	−12.5483	+	21.7342i	−0.889523	+	1.54070i	−0.0490825	+	0.998795i	$0.515630\pi$
$199$	−12.5483	+	21.7342i	−0.889523	+	1.54070i	−0.840440	+	0.541904i	$0.817704\pi$
$200$	−1.98258	−	2.57380i	−0.140190	−	0.181995i
$201$	−13.7499	+	11.9130i	−0.969844	+	0.840277i
$202$	−8.38113	−	3.46547i	−0.589694	−	0.243830i
$203$	−6.91764	+	4.34925i	−0.485523	+	0.305257i
$204$	1.61440	+	8.32317i	0.113031	+	0.582738i
$205$	−1.38864	−	0.372084i	−0.0969867	−	0.0259875i
$206$	11.2781	+	1.47766i	0.785786	+	0.102953i
$207$	−2.26124	+	15.7144i	−0.157167	+	1.09223i
$208$	1.80722	−	6.81237i	0.125308	−	0.472353i
$209$			22.1835i			1.53446i
$210$	9.82788	+	8.07278i	0.678188	+	0.557075i
$211$	−7.10682	−	7.10682i	−0.489254	−	0.489254i	0.418817	−	0.908071i	$-0.362445\pi$
$211$	−7.10682	−	7.10682i	−0.489254	−	0.489254i	−0.908071	+	0.418817i	$0.862445\pi$
$212$	23.4420	−	13.5731i	1.61000	−	0.932206i
$213$	11.6231	+	23.9307i	0.796404	+	1.63971i
$214$	11.6058	+	15.1055i	0.793354	+	1.03259i
$215$	−4.35775	+	2.51595i	−0.297196	+	0.171586i
$216$	−8.36155	+	12.0865i	−0.568931	+	0.822385i
$217$	8.10578	−	8.74069i	0.550257	−	0.593357i
$218$	−1.21895	−	0.504016i	−0.0825574	−	0.0341363i
$219$	−19.2250	−	1.37611i	−1.29911	−	0.0929891i
$220$	−3.49762	−	12.9887i	−0.235810	−	0.875696i
$221$	−4.16551	+	1.11614i	−0.280202	+	0.0750800i
$222$	−6.30314	−	3.15068i	−0.423039	−	0.211460i
$223$		−	19.6334i		−	1.31475i	−0.753562	−	0.657376i	$-0.771666\pi$
$223$		−	19.6334i		−	1.31475i	0.753562	−	0.657376i	$-0.228334\pi$
$224$	14.0494	+	5.15900i	0.938713	+	0.344700i
$225$	−3.19924	+	1.28036i	−0.213283	+	0.0853570i
$226$	21.4976	+	16.4745i	1.43000	+	1.09587i
$227$	−1.34545	−	5.02130i	−0.0893009	−	0.333275i	0.906793	−	0.421576i	$-0.138523\pi$
$227$	−1.34545	−	5.02130i	−0.0893009	−	0.333275i	−0.996094	+	0.0883008i	$0.971856\pi$
$228$	−20.1575	+	9.82147i	−1.33496	+	0.650443i
$229$	1.03121	−	3.84854i	0.0681445	−	0.254319i	−0.923447	−	0.383726i	$-0.874641\pi$
$229$	1.03121	−	3.84854i	0.0681445	−	0.254319i	0.991592	+	0.129407i	$0.0413074\pi$
$230$	5.61224	−	13.5730i	0.370060	−	0.894978i
$231$	−7.38857	−	13.8585i	−0.486132	−	0.911819i
$232$	3.35797	+	8.06426i	0.220461	+	0.529445i
$233$	4.53605	+	7.85667i	0.297166	+	0.514707i	0.975487	−	0.220059i	$-0.0706251\pi$
$233$	4.53605	+	7.85667i	0.297166	+	0.514707i	−0.678320	+	0.734766i	$0.737292\pi$
$234$	−6.43101	−	3.81129i	−0.420408	−	0.249152i
$235$	3.46199	+	12.9203i	0.225836	+	0.842830i
$236$	−11.0670	−	19.1137i	−0.720401	−	1.24419i
$237$	9.51919	−	14.0628i	0.618338	−	0.913480i
$238$	−1.54201	−	9.02684i	−0.0999534	−	0.585123i
$239$	16.5696			1.07180			0.535898	−	0.844283i	$-0.319973\pi$
$239$	16.5696			1.07180			0.535898	+	0.844283i	$0.319973\pi$
$240$	10.2539	−	8.92877i	0.661886	−	0.576349i
$241$	3.89314	−	6.74311i	0.250779	−	0.434362i	−0.712962	−	0.701203i	$-0.752647\pi$
$241$	3.89314	−	6.74311i	0.250779	−	0.434362i	0.963740	+	0.266841i	$0.0859800\pi$
$242$	−0.136896	+	1.04485i	−0.00880001	+	0.0671655i
$243$	9.92156	+	12.0234i	0.636468	+	0.771303i
$244$	−0.00852121	−	6.85040i	−0.000545514	−	0.438552i
$245$	−10.4174	−	8.95512i	−0.665543	−	0.572122i
$246$	−0.359539	+	1.75799i	−0.0229234	+	0.112085i
$247$	−5.70265	−	9.87729i	−0.362851	−	0.628477i
$248$	−7.77677	−	10.0958i	−0.493825	−	0.641086i
$249$	5.53942	−	16.0021i	0.351047	−	1.01409i
$250$	16.9174	−	2.23793i	1.06995	−	0.141539i
$251$	−7.46594	−	7.46594i	−0.471246	−	0.471246i	0.431072	−	0.902318i	$-0.358136\pi$
$251$	−7.46594	−	7.46594i	−0.471246	−	0.471246i	−0.902318	+	0.431072i	$0.858136\pi$
$252$	9.32157	−	12.8494i	0.587204	−	0.809439i
$253$	−12.8245	+	12.8245i	−0.806271	+	0.806271i
$254$	7.37637	+	5.65280i	0.462835	+	0.354689i
$255$	−7.86156	−	2.72142i	−0.492310	−	0.170422i
$256$	7.93096	−	13.8960i	0.495685	−	0.868502i
$257$	16.1135	−	9.30311i	1.00513	−	0.580312i	0.0953675	−	0.995442i	$-0.469597\pi$
$257$	16.1135	−	9.30311i	1.00513	−	0.580312i	0.909762	+	0.415130i	$0.136264\pi$
$258$	3.46114	+	5.24084i	0.215481	+	0.326280i
$259$	6.73026	+	3.55472i	0.418198	+	0.220880i
$260$	4.89630	+	4.88413i	0.303656	+	0.302901i
$261$	9.19996	−	1.09891i	0.569463	−	0.0680211i
$262$	−16.1882	+	12.4376i	−1.00011	+	0.768400i
$263$	13.0416	+	7.52960i	0.804182	+	0.464295i	0.844932	−	0.534874i	$-0.179641\pi$
$263$	13.0416	+	7.52960i	0.804182	+	0.464295i	−0.0407491	+	0.999169i	$0.512974\pi$
$264$	−15.9206	+	5.33088i	−0.979844	+	0.328093i
$265$			26.5799i			1.63279i
$266$	22.0046	−	10.1182i	1.34919	−	0.620386i
$267$	3.82351	+	2.58815i	0.233995	+	0.158392i
$268$	−10.5263	−	18.1798i	−0.642994	−	1.11051i
$269$	16.3794	−	4.38884i	0.998669	−	0.267592i	0.277781	−	0.960644i	$-0.410401\pi$
$269$	16.3794	−	4.38884i	0.998669	−	0.267592i	0.720888	+	0.693052i	$0.243734\pi$
$270$	−6.15235	−	13.0431i	−0.374420	−	0.793776i
$271$	24.2361	−	13.9927i	1.47224	−	0.849997i	0.472726	−	0.881210i	$-0.343270\pi$
$271$	24.2361	−	13.9927i	1.47224	−	0.849997i	0.999513	+	0.0312122i	$0.00993676\pi$
$272$	−9.78985	+	0.0243552i	−0.593597	+	0.00147675i
$273$	6.85236	+	4.27117i	0.414724	+	0.258503i
$274$	7.00687	+	16.8864i	0.423300	+	1.02014i
$275$	−3.80240	−	1.01885i	−0.229294	−	0.0614390i
$276$	−17.3312	−	5.97537i	−1.04321	−	0.359675i
$277$	−3.59680	+	0.963759i	−0.216111	+	0.0579067i	−0.365250	−	0.930910i	$-0.619016\pi$
$277$	−3.59680	+	0.963759i	−0.216111	+	0.0579067i	0.149139	+	0.988816i	$0.452350\pi$
$278$	2.86637	+	21.6681i	0.171914	+	1.29957i
$279$	−12.5492	+	5.02225i	−0.751298	+	0.300674i
$280$	−11.2886	+	9.39374i	−0.674626	+	0.561384i
$281$	4.68363			0.279402			0.139701	−	0.990194i	$-0.455386\pi$
$281$	4.68363			0.279402			0.139701	+	0.990194i	$0.455386\pi$
$282$	15.8381	−	5.28136i	0.943146	−	0.314501i
$283$	−7.27154	−	27.1377i	−0.432248	−	1.61317i	−0.747568	−	0.664186i	$-0.768778\pi$
$283$	−7.27154	−	27.1377i	−0.432248	−	1.61317i	0.315320	−	0.948985i	$-0.397888\pi$
$284$	−29.6631	+	7.98776i	−1.76018	+	0.473987i
$285$	1.57089	−	21.9461i	0.0930515	−	1.29998i
$286$	−3.27297	−	7.88777i	−0.193535	−	0.466413i
$287$	0.430769	−	1.88967i	0.0254275	−	0.111544i
$288$	−11.8927	−	12.1064i	−0.700782	−	0.713376i
$289$	−5.50494	−	9.53484i	−0.323820	−	0.560873i
$290$	−8.49898	−	1.11353i	−0.499077	−	0.0653890i
$291$	6.41993	−	3.11815i	0.376343	−	0.182789i
$292$	5.73351	−	21.5047i	0.335528	−	1.25847i
$293$	−14.7778	+	14.7778i	−0.863327	+	0.863327i	−0.991723	−	0.128396i	$-0.959017\pi$
$293$	−14.7778	+	14.7778i	−0.863327	+	0.863327i	0.128396	+	0.991723i	$0.459017\pi$
$294$	−10.3767	+	13.6501i	−0.605182	+	0.796087i
$295$	21.6722			1.26180
$296$	4.94136	−	6.46464i	0.287210	−	0.375750i
$297$	0.844257	+	17.7878i	0.0489887	+	1.03215i
$298$	−0.394685	+	0.303243i	−0.0228635	+	0.0175664i
$299$	2.41341	−	9.00695i	0.139571	−	0.520885i
$300$	−0.757669	−	3.90622i	−0.0437440	−	0.225526i
$301$	−3.61076	−	5.74305i	−0.208121	−	0.331024i
$302$	6.00893	+	14.4814i	0.345775	+	0.833309i
$303$	−7.27346	−	8.39500i	−0.417849	−	0.482280i
$304$	−6.76346	−	24.9927i	−0.387911	−	1.43343i
$305$	5.82135	+	3.36096i	0.333330	+	0.192448i
$306$	−2.80161	+	9.99865i	−0.160157	+	0.571585i
$307$	−19.2951	−	19.2951i	−1.10123	−	1.10123i	−0.994262	−	0.106970i	$-0.965885\pi$
$307$	−19.2951	−	19.2951i	−1.10123	−	1.10123i	−0.106970	−	0.994262i	$-0.534115\pi$
$308$	17.3208	−	5.37149i	0.986945	−	0.306069i
$309$	11.5364	+	7.80904i	0.656284	+	0.444241i
$310$	12.3968	−	1.63991i	0.704088	−	0.0931405i
$311$	−1.26521	−	0.730471i	−0.0717437	−	0.0414212i	0.463699	−	0.885993i	$-0.346522\pi$
$311$	−1.26521	−	0.730471i	−0.0717437	−	0.0414212i	−0.535443	+	0.844572i	$0.679855\pi$
$312$	5.71831	−	6.46627i	0.323736	−	0.366080i
$313$	−13.3922	+	7.73199i	−0.756971	+	0.437038i	−0.828207	−	0.560422i	$-0.810639\pi$
$313$	−13.3922	+	7.73199i	−0.756971	+	0.437038i	0.0712359	+	0.997459i	$0.477306\pi$
$314$	0.377971	+	0.156285i	0.0213301	+	0.00881969i
$315$	6.32816	+	14.2334i	0.356552	+	0.801961i
$316$	13.8828	+	13.8483i	0.780966	+	0.779025i
$317$	−2.43392	+	9.08351i	−0.136703	+	0.510181i	0.863283	+	0.504721i	$0.168405\pi$
$317$	−2.43392	+	9.08351i	−0.136703	+	0.510181i	−0.999985	+	0.00545986i	$0.998262\pi$
$318$	33.1160	−	1.99148i	1.85705	−	0.111677i
$319$	9.16643	+	5.29224i	0.513222	+	0.296309i
$320$	7.90063	+	13.5671i	0.441659	+	0.758425i
$321$	4.41397	+	22.9090i	0.246364	+	1.27865i
$322$	18.5706	+	6.87170i	1.03490	+	0.382945i
$323$	−11.2022	+	11.2022i	−0.623307	+	0.623307i
$324$	−15.7895	+	8.64249i	−0.877193	+	0.480138i
$325$	1.95495	−	0.523828i	0.108441	−	0.0290567i
$326$	0.339066	+	0.441310i	0.0187791	+	0.0244419i
$327$	−1.05785	−	1.22096i	−0.0584991	−	0.0675194i
$328$	−1.91573	−	0.789335i	−0.105778	−	0.0435838i
$329$	−17.2306	+	5.32002i	−0.949952	+	0.293302i
$330$	3.30098	−	16.1404i	0.181713	−	0.888498i
$331$	12.4974	+	3.34866i	0.686918	+	0.184059i	0.585364	−	0.810771i	$-0.300952\pi$
$331$	12.4974	+	3.34866i	0.686918	+	0.184059i	0.101554	+	0.994830i	$0.467618\pi$
$332$	16.9459	+	9.75566i	0.930029	+	0.535411i
$333$	−5.17124	−	6.90962i	−0.283382	−	0.378645i
$334$	−11.6639	−	8.93853i	−0.638222	−	0.489095i
$335$	20.6133			1.12622
$336$	12.5495	+	13.3608i	0.684632	+	0.728889i
$337$	28.1461			1.53322			0.766609	−	0.642114i	$-0.221942\pi$
$337$	28.1461			1.53322			0.766609	+	0.642114i	$0.221942\pi$
$338$	−11.1076	−	8.51218i	−0.604173	−	0.463002i
$339$	14.4923	+	29.8381i	0.787114	+	1.62058i
$340$	4.79278	−	8.32523i	0.259925	−	0.451499i
$341$	−14.9151	−	3.99649i	−0.807698	−	0.216422i
$342$	−27.4605	−	0.312877i	−1.48489	−	0.0169185i
$343$	11.5355	−	14.4891i	0.622857	−	0.782336i
$344$	−6.69497	+	2.78779i	−0.360969	+	0.150308i
$345$	13.5955	−	11.7792i	0.731956	−	0.634170i
$346$	−3.34419	−	4.35262i	−0.179785	−	0.233998i
$347$	30.1331	−	8.07414i	1.61763	−	0.433443i	0.667326	−	0.744766i	$-0.267439\pi$
$347$	30.1331	−	8.07414i	1.61763	−	0.433443i	0.950304	+	0.311323i	$0.100772\pi$
$348$	−0.750577	+	10.6723i	−0.0402352	+	0.572098i
$349$	−20.8698	+	20.8698i	−1.11713	+	1.11713i	−0.124974	+	0.992160i	$0.539885\pi$
$349$	−20.8698	+	20.8698i	−1.11713	+	1.11713i	−0.992160	+	0.124974i	$0.960115\pi$
$350$	0.723692	+	4.23647i	0.0386830	+	0.226449i
$351$	−4.94858	−	7.70307i	−0.264136	−	0.411159i
$352$	−2.59023	−	19.2129i	−0.138060	−	1.02405i
$353$	−8.98892	−	5.18975i	−0.478432	−	0.276223i	0.241331	−	0.970443i	$-0.422416\pi$
$353$	−8.98892	−	5.18975i	−0.478432	−	0.276223i	−0.719763	+	0.694220i	$0.755749\pi$
$354$	−1.62378	−	27.0015i	−0.0863027	−	1.43511i
$355$	7.80173	−	29.1165i	0.414073	−	1.54534i
$356$	−3.76517	+	3.77455i	−0.199554	+	0.200051i
$357$	3.26716	−	10.7293i	0.172916	−	0.567855i
$358$	29.7048	+	12.2825i	1.56995	+	0.649150i
$359$	3.65172	−	2.10832i	0.192730	−	0.111273i	−0.400530	−	0.916284i	$-0.631174\pi$
$359$	3.65172	−	2.10832i	0.192730	−	0.111273i	0.593260	+	0.805011i	$0.297841\pi$
$360$	16.1278	−	4.14645i	0.850007	−	0.218537i
$361$	−19.8309	−	11.4494i	−1.04373	−	0.602598i
$362$	−32.7514	+	4.33252i	−1.72137	+	0.227712i
$363$	−0.723459	+	1.06878i	−0.0379718	+	0.0560963i
$364$	−6.33133	+	6.84431i	−0.331852	+	0.358739i
$365$	15.4421	+	15.4421i	0.808278	+	0.808278i
$366$	3.75128	−	7.50467i	0.196082	−	0.392275i
$367$	−1.56216	−	0.901915i	−0.0815442	−	0.0470796i	0.458673	−	0.888605i	$-0.348325\pi$
$367$	−1.56216	−	0.901915i	−0.0815442	−	0.0470796i	−0.540218	+	0.841525i	$0.681658\pi$
$368$	10.5385	−	18.3586i	0.549360	−	0.957009i
$369$	−1.35870	+	1.72732i	−0.0707311	+	0.0899206i
$370$	3.06003	+	7.37458i	0.159083	+	0.383386i
$371$	−35.8085	+	1.34954i	−1.85909	+	0.0700645i
$372$	−2.97199	−	15.3223i	−0.154090	−	0.794425i
$373$	−1.44026	+	5.37513i	−0.0745739	+	0.278314i	−0.993136	−	0.116962i	$-0.962684\pi$
$373$	−1.44026	+	5.37513i	−0.0745739	+	0.278314i	0.918562	+	0.395276i	$0.129351\pi$
$374$	−9.40634	+	7.22704i	−0.486390	+	0.373701i
$375$	19.7501	+	6.83687i	1.01989	+	0.353054i
$376$	2.55198	+	19.1086i	0.131608	+	0.985452i
$377$	−5.44186			−0.280270
$378$	17.2593	−	8.95072i	0.887724	−	0.460375i
$379$	−7.56705	+	7.56705i	−0.388693	+	0.388693i	−0.874221	−	0.485528i	$-0.838627\pi$
$379$	−7.56705	+	7.56705i	−0.388693	+	0.388693i	0.485528	+	0.874221i	$0.338627\pi$
$380$	24.5485	+	6.54504i	1.25931	+	0.335753i
$381$	4.97267	+	10.2382i	0.254758	+	0.524517i
$382$	−25.3611	−	3.32281i	−1.29759	−	0.170010i
$383$	−7.00285	−	12.1293i	−0.357829	−	0.619778i	0.629769	−	0.776782i	$-0.283150\pi$
$383$	−7.00285	−	12.1293i	−0.357829	−	0.619778i	−0.987598	+	0.157005i	$0.949816\pi$
$384$	16.3114	−	10.8599i	0.832387	−	0.554194i
$385$	−3.95496	+	17.3494i	−0.201563	+	0.884207i
$386$	−2.81821	−	6.79182i	−0.143443	−	0.345694i
$387$	0.912322	+	7.63783i	0.0463759	+	0.388253i
$388$	2.14289	+	7.95775i	0.108789	+	0.403994i
$389$	−3.06662	−	11.4448i	−0.155484	−	0.580273i	−0.999063	−	0.0432692i	$-0.986223\pi$
$389$	−3.06662	−	11.4448i	−0.155484	−	0.580273i	0.843580	−	0.537004i	$-0.180444\pi$
$390$	2.67939	+	8.03515i	0.135676	+	0.406876i
$391$	−12.9522			−0.655023
$392$	−13.2285	−	14.7312i	−0.668138	−	0.744037i
$393$	−24.5510	+	4.73035i	−1.23843	+	0.238615i
$394$	−0.0464636	−	0.351238i	−0.00234080	−	0.0176951i
$395$	−18.5854	+	4.97994i	−0.935132	+	0.250568i
$396$	−20.3567	−	2.90340i	−1.02296	−	0.145902i
$397$	14.5926	+	3.91009i	0.732384	+	0.196242i	0.605690	−	0.795700i	$-0.292897\pi$
$397$	14.5926	+	3.91009i	0.732384	+	0.196242i	0.126693	+	0.991942i	$0.459564\pi$
$398$	−13.6025	−	32.7817i	−0.681833	−	1.64320i
$399$	29.6457	+	1.00204i	1.48414	+	0.0501648i
$400$	4.59456	−	0.0114304i	0.229728	−	0.000571518i
$401$	6.98532	−	4.03297i	0.348830	−	0.201397i	−0.315340	−	0.948979i	$-0.602119\pi$
$401$	6.98532	−	4.03297i	0.348830	−	0.201397i	0.664170	+	0.747582i	$0.268785\pi$
$402$	−1.54444	−	25.6822i	−0.0770295	−	1.28091i
$403$	7.66838	−	2.05474i	0.381989	−	0.102354i
$404$	11.0996	−	6.42680i	0.552227	−	0.319745i
$405$	0.424393	−	17.6573i	0.0210882	−	0.877398i
$406$	1.06864	−	11.5064i	0.0530358	−	0.571054i
$407$		−	9.85919i		−	0.488702i
$408$	−10.7315	−	5.34758i	−0.531291	−	0.264745i
$409$	−19.0155	−	10.9786i	−0.940257	−	0.542858i	−0.0502162	−	0.998738i	$-0.515991\pi$
$409$	−19.0155	−	10.9786i	−0.940257	−	0.542858i	−0.890041	+	0.455881i	$0.849324\pi$
$410$	1.61220	−	1.23868i	0.0796210	−	0.0611741i
$411$	−1.59866	+	22.3341i	−0.0788561	+	1.10166i
$412$	−11.3604	+	11.3887i	−0.559686	+	0.561080i
$413$	1.10036	+	29.1969i	0.0541452	+	1.43669i
$414$	−15.6944	−	16.0561i	−0.771336	−	0.789116i
$415$	−16.6162	+	9.59335i	−0.815656	+	0.470919i
$416$	6.09233	+	7.88876i	0.298701	+	0.386778i
$417$	−8.75677	+	25.2963i	−0.428821	+	1.23877i
$418$	−24.9011	−	19.0827i	−1.21795	−	0.933364i
$419$	−3.16748	+	3.16748i	−0.154742	+	0.154742i	−0.780232	−	0.625490i	$-0.784899\pi$
$419$	−3.16748	+	3.16748i	−0.154742	+	0.154742i	0.625490	+	0.780232i	$0.284899\pi$
$420$	−17.5159	+	4.08748i	−0.854688	+	0.199449i
$421$	−6.33297	−	6.33297i	−0.308650	−	0.308650i	0.535736	−	0.844386i	$-0.320034\pi$
$421$	−6.33297	−	6.33297i	−0.308650	−	0.308650i	−0.844386	+	0.535736i	$0.820034\pi$
$422$	14.0909	−	1.86402i	0.685934	−	0.0907389i
$423$	20.2392	+	2.91234i	0.984065	+	0.141603i
$424$	−4.92934	+	37.9896i	−0.239390	+	1.84494i
$425$	−1.40564	−	2.43463i	−0.0681834	−	0.118097i
$426$	−36.8609	−	7.53868i	−1.78592	−	0.365250i
$427$	−4.23234	+	8.01321i	−0.204817	+	0.387786i
$428$	−26.9395	+	0.0335100i	−1.30217	+	0.00161977i
$429$	0.746748	−	10.4325i	0.0360533	−	0.503684i
$430$	0.924459	−	7.05587i	0.0445814	−	0.340264i
$431$	−10.6306	+	18.4128i	−0.512059	+	0.886912i	0.487843	+	0.872931i	$0.337784\pi$
$431$	−10.6306	+	18.4128i	−0.512059	+	0.886912i	−0.999902	+	0.0139809i	$0.995550\pi$
$432$	−6.37445	−	19.7830i	−0.306691	−	0.951809i
$433$	−17.1216			−0.822811			−0.411406	−	0.911452i	$-0.634962\pi$
$433$	−17.1216			−0.822811			−0.411406	+	0.911452i	$0.634962\pi$
$434$	2.83871	+	16.6177i	0.136263	+	0.797676i
$435$	−8.69361	−	5.88473i	−0.416827	−	0.282151i
$436$	1.61432	−	0.934710i	0.0773121	−	0.0447645i
$437$	−8.86593	−	33.0881i	−0.424115	−	1.58282i
$438$	18.0824	−	20.3964i	0.864013	−	0.974579i
$439$	−2.88712	−	5.00064i	−0.137795	−	0.238667i	0.788867	−	0.614564i	$-0.210668\pi$
$439$	−2.88712	−	5.00064i	−0.137795	−	0.238667i	−0.926662	+	0.375897i	$0.877335\pi$
$440$	17.5886	+	7.24701i	0.838503	+	0.345488i
$441$	−18.8540	+	9.24801i	−0.897811	+	0.440381i
$442$	2.33038	−	5.63594i	0.110845	−	0.268074i
$443$	−6.01618	+	22.4527i	−0.285837	+	1.06676i	0.662388	+	0.749161i	$0.269543\pi$
$443$	−6.01618	+	22.4527i	−0.285837	+	1.06676i	−0.948225	+	0.317598i	$0.897124\pi$
$444$	8.95875	−	4.36504i	0.425164	−	0.207155i
$445$	−1.35398	−	5.05314i	−0.0641850	−	0.239542i
$446$	22.0387	+	16.8891i	1.04356	+	0.799722i
$447$	−0.598580	+	0.115331i	−0.0283118	+	0.00545497i
$448$	−17.8766	+	11.3326i	−0.844588	+	0.535416i
$449$		−	30.1615i		−	1.42341i	−0.702479	−	0.711705i	$-0.747923\pi$
$449$		−	30.1615i		−	1.42341i	0.702479	−	0.711705i	$-0.252077\pi$
$450$	1.31485	−	4.69256i	0.0619825	−	0.221209i
$451$	−2.42500	+	0.649776i	−0.114189	+	0.0305968i
$452$	−36.9854	+	9.95954i	−1.73965	+	0.468458i
$453$	−1.37098	+	19.1532i	−0.0644140	+	0.899897i
$454$	6.79383	+	2.80915i	0.318850	+	0.131840i
$455$	−2.69900	−	8.74158i	−0.126531	−	0.409812i
$456$	6.31521	−	31.0755i	0.295737	−	1.45524i
$457$	24.4586	−	14.1212i	1.14412	−	0.660560i	0.196676	−	0.980469i	$-0.436985\pi$
$457$	24.4586	−	14.1212i	1.14412	−	0.660560i	0.947449	+	0.319908i	$0.103652\pi$
$458$	3.43294	+	4.46814i	0.160411	+	0.208782i
$459$	−8.55614	+	9.40880i	−0.399366	+	0.439165i
$460$	10.4080	+	17.9756i	0.485277	+	0.838115i
$461$	−2.97002	−	2.97002i	−0.138328	−	0.138328i	0.634552	−	0.772880i	$-0.281184\pi$
$461$	−2.97002	−	2.97002i	−0.138328	−	0.138328i	−0.772880	+	0.634552i	$0.781184\pi$
$462$	21.9120	+	3.62761i	1.01944	+	0.168772i
$463$			9.40459i			0.437068i	0.975829	+	0.218534i	$0.0701275\pi$
$463$			9.40459i			0.437068i	−0.975829	+	0.218534i	$0.929873\pi$
$464$	−11.9408	−	3.16770i	−0.554337	−	0.147057i
$465$	14.4725	+	5.00992i	0.671147	+	0.232330i
$466$	−12.7212	−	1.66672i	−0.589296	−	0.0772095i
$467$	21.5797	+	5.78225i	0.998588	+	0.267571i	0.720854	−	0.693087i	$-0.243750\pi$
$467$	21.5797	+	5.78225i	0.998588	+	0.267571i	0.277734	+	0.960658i	$0.410417\pi$
$468$	9.81028	−	3.94030i	0.453480	−	0.182140i
$469$	1.04660	+	27.7703i	0.0483273	+	1.28231i
$470$	−17.4812	−	7.22823i	−0.806349	−	0.333413i
$471$	0.328017	+	0.378596i	0.0151142	+	0.0174448i
$472$	30.9753	+	4.01919i	1.42575	+	0.184998i
$473$	−4.39364	+	7.61000i	−0.202020	+	0.349908i
$474$	7.59703	+	22.7825i	0.348943	+	1.04644i
$475$	5.25740	−	5.25740i	0.241226	−	0.241226i
$476$	11.4591	+	6.03416i	0.525229	+	0.276575i
$477$	37.3494	+	15.9991i	1.71011	+	0.732546i
$478$	−14.2535	+	18.5994i	−0.651939	+	0.850718i
$479$	19.8768	−	34.4276i	0.908192	−	1.57304i	0.0916188	−	0.995794i	$-0.470796\pi$
$479$	19.8768	−	34.4276i	0.908192	−	1.57304i	0.816574	−	0.577241i	$-0.195871\pi$
$480$	1.20199	+	19.1908i	0.0548630	+	0.875934i
$481$	2.53448	+	4.38985i	0.115562	+	0.200160i
$482$	4.22023	+	10.1706i	0.192226	+	0.463259i
$483$	16.5593	+	17.7178i	0.753472	+	0.806190i
$484$	−1.05509	−	1.05247i	−0.0479586	−	0.0478395i
$485$	−7.81110	−	2.09298i	−0.354684	−	0.0950372i
$486$	−22.0311	+	0.794209i	−0.999351	+	0.0360261i
$487$	−15.7290	+	27.2435i	−0.712751	+	1.23452i	0.251070	+	0.967969i	$0.419218\pi$
$487$	−15.7290	+	27.2435i	−0.712751	+	1.23452i	−0.963821	+	0.266552i	$0.914116\pi$
$488$	7.69695	+	5.88329i	0.348425	+	0.266324i
$489$	0.128955	+	0.669292i	0.00583156	+	0.0302664i
$490$	19.0134	−	3.99022i	0.858940	−	0.180260i
$491$	9.43926	+	9.43926i	0.425988	+	0.425988i	0.887259	−	0.461271i	$-0.152607\pi$
$491$	9.43926	+	9.43926i	0.425988	+	0.425988i	−0.461271	+	0.887259i	$0.652607\pi$
$492$	−1.66407	−	1.91584i	−0.0750221	−	0.0863729i
$493$	1.95639	+	7.30133i	0.0881112	+	0.328836i
$494$	15.9929	+	2.09538i	0.719553	+	0.0942757i
$495$	12.4744	−	15.8588i	0.560684	−	0.712799i
$496$	18.0224	−	0.0448361i	0.809228	−	0.00201320i
$497$	39.6220	+	9.03221i	1.77729	+	0.405150i
$498$	13.1974	+	19.9834i	0.591388	+	0.895477i
$499$	−9.30738	+	34.7356i	−0.416655	+	1.55498i	0.364841	+	0.931070i	$0.381123\pi$
$499$	−9.30738	+	34.7356i	−0.416655	+	1.55498i	−0.781497	+	0.623909i	$0.785543\pi$
$500$	−12.0406	+	20.9150i	−0.538473	+	0.935348i
$501$	−7.86306	−	16.1892i	−0.351296	−	0.723279i
$502$	14.8029	−	1.95821i	0.660687	−	0.0873992i
$503$		−	10.9960i		−	0.490289i	−0.969487	−	0.245144i	$-0.921165\pi$
$503$		−	10.9960i		−	0.490289i	0.969487	−	0.245144i	$-0.0788354\pi$
$504$	6.40498	+	21.5169i	0.285300	+	0.958438i
$505$			12.5854i			0.560043i
$506$	−3.36369	−	25.4275i	−0.149534	−	1.13039i
$507$	−7.48801	−	15.4170i	−0.332554	−	0.684692i
$508$	−12.6906	+	3.41737i	−0.563055	+	0.151621i
$509$	4.95207	−	18.4814i	0.219497	−	0.819173i	−0.765038	−	0.643985i	$-0.777280\pi$
$509$	4.95207	−	18.4814i	0.219497	−	0.819173i	0.984535	−	0.175188i	$-0.0560533\pi$
$510$	9.81748	−	6.48363i	0.434725	−	0.287100i
$511$	−20.0197	+	21.5878i	−0.885619	+	0.954987i
$512$	8.77602	+	20.8562i	0.387849	+	0.921723i
$513$	−29.8927	−	15.4173i	−1.31979	−	0.680690i
$514$	−3.41833	+	26.0902i	−0.150776	+	1.15079i
$515$	−4.08528	−	15.2465i	−0.180019	−	0.671840i
$516$	−8.86021	−	0.623131i	−0.390049	−	0.0274318i
$517$	16.5172	+	16.5172i	0.726427	+	0.726427i
$518$	−9.77971	+	4.49691i	−0.429696	+	0.197583i
$519$	−1.27188	−	6.60119i	−0.0558293	−	0.289760i
$520$	−9.69437	+	1.29469i	−0.425126	+	0.0567761i
$521$	−9.58929	+	16.6091i	−0.420114	+	0.727660i	−0.995950	−	0.0899058i	$-0.971343\pi$
$521$	−9.58929	+	16.6091i	−0.420114	+	0.727660i	0.575836	+	0.817565i	$0.304677\pi$
$522$	−6.68045	+	11.2723i	−0.292396	+	0.493376i
$523$	−20.2893	−	5.43650i	−0.887189	−	0.237722i	−0.213683	−	0.976903i	$-0.568546\pi$
$523$	−20.2893	−	5.43650i	−0.887189	−	0.237722i	−0.673506	+	0.739181i	$0.735213\pi$
$524$	−0.0359119	−	28.8705i	−0.00156882	−	1.26121i
$525$	−1.53334	+	5.03547i	−0.0669204	+	0.219766i
$526$	−19.6707	+	8.16221i	−0.857684	+	0.355889i
$527$	−5.51367	−	9.54996i	−0.240179	−	0.416003i
$528$	7.71127	−	22.4567i	0.335590	−	0.977302i
$529$	2.50312	−	4.33554i	0.108831	−	0.188502i
$530$	−29.8360	−	22.8645i	−1.29600	−	0.993172i
$531$	13.0450	−	30.4533i	0.566105	−	1.32156i
$532$	−7.57112	+	33.4042i	−0.328250	+	1.44826i
$533$	0.912704	−	0.912704i	0.0395336	−	0.0395336i
$534$	−6.19428	+	2.06554i	−0.268053	+	0.0893846i
$535$	13.2171	−	22.8927i	0.571426	−	0.989738i
$536$	29.4618	+	3.82281i	1.27256	+	0.165120i
$537$	25.7790	+	29.7540i	1.11244	+	1.28398i
$538$	−9.16338	+	22.1613i	−0.395061	+	0.955443i
$539$	−23.5740	−	4.44726i	−1.01540	−	0.191557i
$540$	19.9333	+	4.31387i	0.857793	+	0.185639i
$541$	7.71786	+	2.06799i	0.331817	+	0.0889100i	0.420881	−	0.907116i	$-0.361721\pi$
$541$	7.71786	+	2.06799i	0.331817	+	0.0889100i	−0.0890643	+	0.996026i	$0.528388\pi$
$542$	−5.14148	+	39.2420i	−0.220846	+	1.68559i
$543$	−38.2354	−	13.2359i	−1.64084	−	0.568005i
$544$	8.39410	−	11.0101i	0.359894	−	0.472055i
$545$			1.83041i			0.0784063i
$546$	−10.6890	+	4.01766i	−0.457445	+	0.171940i
$547$	15.7816	+	15.7816i	0.674771	+	0.674771i	0.958812	−	0.284041i	$-0.0916751\pi$
$547$	15.7816	+	15.7816i	0.674771	+	0.674771i	−0.284041	+	0.958812i	$0.591675\pi$
$548$	−24.9825	−	6.66074i	−1.06720	−	0.284533i
$549$	8.22676	−	6.15700i	0.351110	−	0.262774i
$550$	4.41457	−	3.39179i	0.188238	−	0.144626i
$551$	−17.3130	+	9.99566i	−0.737558	+	0.425829i
$552$	21.6160	−	14.3142i	0.920039	−	0.609254i
$553$	−7.65264	−	24.7855i	−0.325423	−	1.05399i
$554$	2.01221	−	4.86647i	0.0854908	−	0.206757i
$555$	−0.698164	+	9.75371i	−0.0296354	+	0.414022i
$556$	−26.7883	−	15.4218i	−1.13608	−	0.654032i
$557$	−40.5461	+	10.8643i	−1.71799	+	0.460335i	−0.977361	−	0.211578i	$-0.932140\pi$
$557$	−40.5461	+	10.8643i	−1.71799	+	0.460335i	−0.740631	+	0.671912i	$0.765473\pi$
$558$	5.15754	−	18.4067i	0.218336	−	0.779220i
$559$		−	4.51785i		−	0.191085i
$560$	−0.833809	−	20.7523i	−0.0352348	−	0.876943i
$561$	−14.2657	+	2.74863i	−0.602297	+	0.116047i
$562$	−4.02896	+	5.25740i	−0.169951	+	0.221770i
$563$	−1.36765	−	5.10416i	−0.0576398	−	0.215115i	0.931099	−	0.364767i	$-0.118851\pi$
$563$	−1.36765	−	5.10416i	−0.0576398	−	0.215115i	−0.988739	+	0.149652i	$0.952185\pi$
$564$	−7.69592	+	22.3215i	−0.324057	+	0.939906i
$565$	9.72759	−	36.3039i	0.409243	−	1.52731i
$566$	36.7174	+	15.1821i	1.54335	+	0.638151i
$567$	23.8095	−	0.324768i	0.999907	−	0.0136390i
$568$	16.5505	−	40.1683i	0.694444	−	1.68542i
$569$	3.56688	+	6.17802i	0.149531	+	0.258996i	0.931054	−	0.364880i	$-0.118890\pi$
$569$	3.56688	+	6.17802i	0.149531	+	0.258996i	−0.781523	+	0.623876i	$0.785557\pi$
$570$	23.2834	+	20.6419i	0.975233	+	0.864592i
$571$	2.11408	+	7.88984i	0.0884714	+	0.330180i	0.995949	−	0.0899210i	$-0.0286615\pi$
$571$	2.11408	+	7.88984i	0.0884714	+	0.330180i	−0.907478	+	0.420101i	$0.861995\pi$
$572$	11.6695	+	3.11129i	0.487928	+	0.130090i
$573$	−25.9419	−	17.5602i	−1.08374	−	0.733586i
$574$	1.75061	+	2.10908i	0.0730692	+	0.0880312i
$575$	6.07873			0.253501
$576$	23.8198	−	2.93542i	0.992492	−	0.122309i
$577$	−4.76214	+	8.24826i	−0.198250	+	0.343380i	−0.947961	−	0.318386i	$-0.896859\pi$
$577$	−4.76214	+	8.24826i	−0.198250	+	0.343380i	0.749711	+	0.661766i	$0.230193\pi$
$578$	15.4384	+	2.02273i	0.642152	+	0.0841346i
$579$	0.642993	−	8.98294i	0.0267219	−	0.373318i
$580$	8.56095	−	8.58227i	0.355474	−	0.356359i
$581$	−13.7679	−	21.8983i	−0.571188	−	0.908496i
$582$	−2.02241	+	9.88871i	−0.0838316	+	0.409900i
$583$	23.2084	+	40.1981i	0.961193	+	1.66483i
$584$	19.2071	+	24.9347i	0.794795	+	1.03181i
$585$	−1.47752	+	10.2680i	−0.0610878	+	0.424528i
$586$	−3.87600	−	29.3003i	−0.160116	−	1.21038i
$587$	−10.0973	−	10.0973i	−0.416760	−	0.416760i	0.467325	−	0.884085i	$-0.345218\pi$
$587$	−10.0973	−	10.0973i	−0.416760	−	0.416760i	−0.884085	+	0.467325i	$0.845218\pi$
$588$	−6.39601	−	23.3900i	−0.263767	−	0.964586i
$589$	20.6224	−	20.6224i	0.849730	−	0.849730i
$590$	−18.6429	+	24.3272i	−0.767515	+	1.00153i
$591$	0.141947	−	0.410051i	0.00583890	−	0.0168673i
$592$	3.00594	+	11.1077i	0.123543	+	0.456524i
$593$	−12.8416	+	7.41409i	−0.527341	+	0.304460i	−0.739933	−	0.672681i	$-0.765143\pi$
$593$	−12.8416	+	7.41409i	−0.527341	+	0.304460i	0.212592	+	0.977141i	$0.431809\pi$
$594$	−20.6932	−	14.3538i	−0.849051	−	0.588942i
$595$	−10.7583	+	6.76391i	−0.441045	+	0.277293i
$596$	−0.000875570	−	0.703892i	−3.58648e−5	−	0.0288325i
$597$	3.10350	−	43.3575i	0.127018	−	1.77451i
$598$	8.03430	+	10.4570i	0.328547	+	0.427620i
$599$	10.0525	+	5.80379i	0.410732	+	0.237136i	0.691104	−	0.722755i	$-0.257125\pi$
$599$	10.0525	+	5.80379i	0.410732	+	0.237136i	−0.280372	+	0.959891i	$0.590458\pi$
$600$	5.03652	+	2.50972i	0.205615	+	0.102459i
$601$			9.90149i			0.403890i	0.979397	+	0.201945i	$0.0647262\pi$
$601$			9.90149i			0.403890i	−0.979397	+	0.201945i	$0.935274\pi$
$602$	9.55265	+	0.887190i	0.389337	+	0.0361592i
$603$	12.4076	−	28.9653i	0.505277	−	1.17956i
$604$	−21.4244	−	5.71211i	−0.871748	−	0.232422i
$605$	1.41249	−	0.378476i	0.0574259	−	0.0153872i
$606$	15.6802	−	0.942954i	0.636965	−	0.0383049i
$607$	−24.4385	+	14.1095i	−0.991926	+	0.572689i	−0.905849	−	0.423600i	$-0.860766\pi$
$607$	−24.4385	+	14.1095i	−0.991926	+	0.572689i	−0.0860766	+	0.996289i	$0.527433\pi$
$608$	33.8725	+	13.9072i	1.37371	+	0.564012i
$609$	7.48655	−	12.0109i	0.303370	−	0.486705i
$610$	−8.78035	+	3.64334i	−0.355506	+	0.147514i
$611$	−11.6004	−	3.10832i	−0.469303	−	0.125749i
$612$	−8.81355	−	11.7459i	−0.356267	−	0.474799i
$613$	−21.1897	+	5.67776i	−0.855844	+	0.229323i	−0.659957	−	0.751304i	$-0.729425\pi$
$613$	−21.1897	+	5.67776i	−0.855844	+	0.229323i	−0.195887	+	0.980626i	$0.562759\pi$
$614$	38.2570	−	5.06084i	1.54393	−	0.204239i
$615$	2.44507	−	0.471102i	0.0985946	−	0.0189967i
$616$	−8.87019	+	24.0634i	−0.357390	+	0.969542i
$617$	7.39953			0.297894			0.148947	−	0.988845i	$-0.452412\pi$
$617$	7.39953			0.297894			0.148947	+	0.988845i	$0.452412\pi$
$618$	−18.6896	+	6.23220i	−0.751804	+	0.250696i
$619$	2.17438	+	8.11488i	0.0873956	+	0.326165i	0.995757	−	0.0920212i	$-0.0293327\pi$
$619$	2.17438	+	8.11488i	0.0873956	+	0.326165i	−0.908361	+	0.418186i	$0.862666\pi$
$620$	−8.82314	+	15.3261i	−0.354346	+	0.615512i
$621$	−8.36840	−	26.1942i	−0.335812	−	1.05114i
$622$	1.90832	−	0.791843i	0.0765167	−	0.0317500i
$623$	6.73887	−	2.08066i	0.269987	−	0.0833598i
$624$	2.33941	+	11.9813i	0.0936514	+	0.479634i
$625$	−8.96870	−	15.5342i	−0.358748	−	0.621370i
$626$	2.84104	−	21.6840i	0.113551	−	0.866668i
$627$	−16.7867	−	34.5619i	−0.670396	−	1.38027i
$628$	−0.500570	+	0.289835i	−0.0199749	+	0.0115657i
$629$	4.97869	−	4.97869i	0.198513	−	0.198513i
$630$	−21.4207	−	5.14047i	−0.853421	−	0.204801i
$631$	−4.73110			−0.188342			−0.0941710	−	0.995556i	$-0.530020\pi$
$631$	−4.73110			−0.188342			−0.0941710	+	0.995556i	$0.530020\pi$
$632$	−27.4870	+	3.67092i	−1.09337	+	0.146021i
$633$	16.4503	+	5.69457i	0.653842	+	0.226339i
$634$	−8.10259	−	10.5459i	−0.321795	−	0.418832i
$635$	3.33778	−	12.4567i	0.132456	−	0.494331i
$636$	−26.2516	+	38.8860i	−1.04094	+	1.54193i
$637$	11.6397	−	4.07995i	0.461181	−	0.161654i
$638$	−13.8257	+	5.73688i	−0.547366	+	0.227125i
$639$	−36.2178	−	28.4887i	−1.43275	−	1.12700i
$640$	−22.0255	−	2.80221i	−0.870633	−	0.110767i
$641$	27.1117	+	15.6529i	1.07085	+	0.618253i	0.928413	−	0.371551i	$-0.121174\pi$
$641$	27.1117	+	15.6529i	1.07085	+	0.618253i	0.142434	+	0.989804i	$0.454507\pi$
$642$	−29.5124	−	14.7520i	−1.16476	−	0.582217i
$643$	1.09104	+	1.09104i	0.0430263	+	0.0430263i	0.728293	−	0.685266i	$-0.240314\pi$
$643$	1.09104	+	1.09104i	0.0430263	+	0.0430263i	−0.685266	+	0.728293i	$0.740314\pi$
$644$	−23.6883	+	14.9344i	−0.933451	+	0.588499i
$645$	4.88552	−	7.21746i	0.192367	−	0.284187i
$646$	−2.93817	−	22.2109i	−0.115601	−	0.873876i
$647$	−9.39022	−	5.42144i	−0.369168	−	0.213139i	0.303927	−	0.952695i	$-0.401702\pi$
$647$	−9.39022	−	5.42144i	−0.369168	−	0.213139i	−0.673095	+	0.739556i	$0.735035\pi$
$648$	3.88118	−	25.1582i	0.152467	−	0.988309i
$649$	32.7760	−	18.9232i	1.28657	−	0.742801i
$650$	−1.09369	+	2.64505i	−0.0428980	+	0.103747i
$651$	−6.01458	+	19.7518i	−0.235730	+	0.774135i
$652$	−0.787045		0.000979004i	−0.0308231		3.83408e-5i
$653$	4.25789	−	15.8907i	0.166624	−	0.621850i	−0.831203	−	0.555969i	$-0.812347\pi$
$653$	4.25789	−	15.8907i	0.166624	−	0.621850i	0.997827	−	0.0658813i	$-0.0209859\pi$
$654$	2.28052	−	0.137143i	0.0891754	−	0.00536270i
$655$	24.5336	+	14.1645i	0.958607	+	0.553452i
$656$	2.53398	−	1.47141i	0.0989354	−	0.0574490i
$657$	30.9940	−	12.4040i	1.20919	−	0.483925i
$658$	8.85034	−	23.9178i	0.345022	−	0.932414i
$659$	−8.20739	+	8.20739i	−0.319714	+	0.319714i	−0.848657	−	0.528943i	$-0.822589\pi$
$659$	−8.20739	+	8.20739i	−0.319714	+	0.319714i	0.528943	+	0.848657i	$0.322589\pi$
$660$	15.2781	+	17.5897i	0.594699	+	0.684677i
$661$	10.5655	−	2.83102i	0.410951	−	0.110114i	−0.0474197	−	0.998875i	$-0.515100\pi$
$661$	10.5655	−	2.83102i	0.410951	−	0.110114i	0.458371	+	0.888761i	$0.348433\pi$
$662$	−14.5094	+	11.1478i	−0.563924	+	0.433271i
$663$	5.64527	−	4.89108i	0.219244	−	0.189954i
$664$	−25.5280	+	10.6299i	−0.990680	+	0.412520i
$665$	−24.6433	−	22.8533i	−0.955628	−	0.886213i
$666$	12.2045	+	0.139055i	0.472915	+	0.00538826i
$667$	−15.7875	−	4.23024i	−0.611293	−	0.163795i
$668$	20.0671	−	5.40373i	0.776420	−	0.209077i
$669$	14.8570	+	30.5890i	0.574406	+	1.18264i
$670$	−17.7320	+	23.1385i	−0.685045	+	0.893919i
$671$	11.7386			0.453163
$672$	−25.7929	+	2.59370i	−0.994982	+	0.100054i
$673$	−2.32156			−0.0894898			−0.0447449	−	0.998998i	$-0.514247\pi$
$673$	−2.32156			−0.0894898			−0.0447449	+	0.998998i	$0.514247\pi$
$674$	−24.2119	+	31.5942i	−0.932607	+	1.21696i
$675$	4.01556	−	4.41573i	0.154559	−	0.169961i
$676$	19.1100	−	5.14598i	0.734998	−	0.197922i
$677$	2.48582	+	0.666073i	0.0955377	+	0.0255992i	0.306271	−	0.951944i	$-0.400919\pi$
$677$	2.48582	+	0.666073i	0.0955377	+	0.0255992i	−0.210734	+	0.977544i	$0.567585\pi$
$678$	−45.9600	−	9.39961i	−1.76508	−	0.360990i
$679$	2.42308	−	10.6294i	0.0929893	−	0.407920i
$680$	5.22228	+	12.5415i	0.200265	+	0.480943i
$681$	5.89594	+	6.80507i	0.225933	+	0.260771i
$682$	17.3164	−	13.3044i	0.663077	−	0.509453i
$683$	−46.8719	+	12.5593i	−1.79350	+	0.480568i	−0.992933	−	0.118673i	$-0.962136\pi$
$683$	−46.8719	+	12.5593i	−1.79350	+	0.480568i	−0.800569	+	0.599240i	$0.795469\pi$
$684$	23.9733	−	30.5554i	0.916642	−	1.16832i
$685$	17.9395	−	17.9395i	0.685432	−	0.685432i
$686$	6.34102	+	25.4124i	0.242101	+	0.970251i
$687$	1.30564	+	6.77638i	0.0498131	+	0.258535i
$688$	2.62984	−	9.91327i	0.100262	−	0.377940i
$689$	−20.6673	−	11.9323i	−0.787360	−	0.454583i
$690$	1.52709	+	25.3937i	0.0581353	+	0.966722i
$691$	−9.18598	+	34.2826i	−0.349451	+	1.30417i	0.537874	+	0.843025i	$0.319228\pi$
$691$	−9.18598	+	34.2826i	−0.349451	+	1.30417i	−0.887325	+	0.461144i	$0.847439\pi$
$692$	7.76258	−	0.00965586i	0.295089	−	0.000367061i
$693$	21.9984	+	16.0004i	0.835650	+	0.607806i
$694$	−16.8578	+	40.7702i	−0.639915	+	1.54761i
$695$	26.2670	−	15.1653i	0.996365	−	0.575251i
$696$	−11.3341	−	10.0231i	−0.429619	−	0.379925i
$697$	−1.55270	−	0.896450i	−0.0588126	−	0.0339555i
$698$	−5.47384	−	41.3791i	−0.207188	−	1.56622i
$699$	−13.0125	−	8.80819i	−0.492177	−	0.333156i
$700$	−5.37799	−	2.83195i	−0.203269	−	0.107038i
$701$	−12.6710	−	12.6710i	−0.478578	−	0.478578i	0.426099	−	0.904677i	$-0.359888\pi$
$701$	−12.6710	−	12.6710i	−0.478578	−	0.478578i	−0.904677	+	0.426099i	$0.859888\pi$
$702$	12.9036	+	1.07153i	0.487015	+	0.0404421i
$703$	16.1266	+	9.31070i	0.608227	+	0.351160i
$704$	23.7948	+	13.6198i	0.896799	+	0.513314i
$705$	−15.1709	−	17.5102i	−0.571368	−	0.659471i
$706$	13.5580	−	5.62578i	0.510261	−	0.211729i
$707$	−16.9551	+	0.638998i	−0.637663	+	0.0240320i
$708$	31.7062	+	21.4045i	1.19159	+	0.804432i
$709$	12.1046	−	45.1749i	0.454597	−	1.69658i	−0.234674	−	0.972074i	$-0.575402\pi$
$709$	12.1046	−	45.1749i	0.454597	−	1.69658i	0.689270	−	0.724504i	$-0.257931\pi$
$710$	25.9722	+	33.8041i	0.974719	+	1.26864i
$711$	−4.18929	+	29.1133i	−0.157111	+	1.09184i
$712$	−0.998077	−	7.47337i	−0.0374045	−	0.280076i
$713$	23.8441			0.892968
$714$	9.23324	+	12.8970i	0.345545	+	0.482657i
$715$	−8.37968	+	8.37968i	−0.313382	+	0.313382i
$716$	−39.3399	+	22.7782i	−1.47020	+	0.851260i
$717$	−25.8154	+	12.5385i	−0.964095	+	0.468260i
$718$	−0.774681	+	5.91270i	−0.0289108	+	0.220660i
$719$	−9.39860	−	16.2789i	−0.350509	−	0.607099i	0.635830	−	0.771829i	$-0.280658\pi$
$719$	−9.39860	−	16.2789i	−0.350509	−	0.607099i	−0.986339	+	0.164730i	$0.947325\pi$
$720$	−9.21901	+	21.6704i	−0.343572	+	0.807607i
$721$	20.3327	−	6.27782i	0.757230	−	0.233798i
$722$	29.9109	−	12.4113i	1.11317	−	0.461901i
$723$	−0.962871	+	13.4518i	−0.0358095	+	0.500278i
$724$	23.3101	−	40.4905i	0.866314	−	1.50482i
$725$	−0.918169	−	3.42665i	−0.0340999	−	0.127263i
$726$	−0.577375	−	1.73147i	−0.0214284	−	0.0642609i
$727$	−25.8310			−0.958018			−0.479009	−	0.877810i	$-0.659004\pi$
$727$	−25.8310			−0.958018			−0.479009	+	0.877810i	$0.659004\pi$
$728$	−2.23643	−	12.9946i	−0.0828877	−	0.481611i
$729$	−24.5562	−	11.2247i	−0.909488	−	0.415729i
$730$	−30.6175	+	4.05025i	−1.13321	+	0.149906i
$731$	−6.06159	+	1.62420i	−0.224196	+	0.0600731i
$732$	5.19712	+	10.6665i	0.192091	+	0.394245i
$733$	−22.4173	−	6.00670i	−0.828002	−	0.221863i	−0.180160	−	0.983637i	$-0.557662\pi$
$733$	−22.4173	−	6.00670i	−0.828002	−	0.221863i	−0.647842	+	0.761775i	$0.724328\pi$
$734$	2.35621	−	0.977691i	0.0869693	−	0.0360872i
$735$	23.0069	+	6.06904i	0.848621	+	0.223860i
$736$	11.5422	+	27.6221i	0.425451	+	1.01816i
$737$	31.1745	−	17.9986i	1.14833	−	0.662987i
$738$	−0.770143	−	3.01102i	−0.0283494	−	0.110837i
$739$	29.0087	−	7.77286i	1.06710	−	0.285929i	0.317801	−	0.948158i	$-0.397056\pi$
$739$	29.0087	−	7.77286i	1.06710	−	0.285929i	0.749302	+	0.662228i	$0.230389\pi$
$740$	−10.9103	−	2.90887i	−0.401071	−	0.106932i
$741$	16.3591	+	11.0735i	0.600967	+	0.406796i
$742$	29.2884	−	41.3562i	1.07521	−	1.51823i
$743$		−	12.9790i		−	0.476152i	−0.971246	−	0.238076i	$-0.923483\pi$
$743$		−	12.9790i		−	0.476152i	0.971246	−	0.238076i	$-0.0765168\pi$
$744$	19.7560	+	9.84449i	0.724288	+	0.360916i
$745$	0.598155	+	0.345345i	0.0219147	+	0.0126525i
$746$	−4.79467	−	6.24050i	−0.175545	−	0.228481i
$747$	3.47870	+	29.1232i	0.127279	+	1.06556i
$748$	−0.0208671	−	16.7755i	−0.000762975	−	0.613374i
$749$	31.5123	+	16.6438i	1.15143	+	0.608153i
$750$	−24.6639	+	16.2885i	−0.900599	+	0.594770i
$751$	5.49327	−	3.17154i	0.200452	−	0.115731i	−0.396414	−	0.918072i	$-0.629746\pi$
$751$	5.49327	−	3.17154i	0.200452	−	0.115731i	0.596866	+	0.802341i	$0.296412\pi$
$752$	−23.6448	−	13.5730i	−0.862237	−	0.494957i
$753$	17.2816	+	5.98233i	0.629776	+	0.218008i
$754$	4.68120	−	6.10852i	0.170479	−	0.222459i
$755$	15.3845	−	15.3845i	0.559899	−	0.559899i
$756$	−4.79960	+	27.0733i	−0.174560	+	0.984647i
$757$	−13.9650	−	13.9650i	−0.507565	−	0.507565i	0.406213	−	0.913778i	$-0.366849\pi$
$757$	−13.9650	−	13.9650i	−0.507565	−	0.507565i	−0.913778	+	0.406213i	$0.866849\pi$
$758$	−1.98473	−	15.0034i	−0.0720886	−	0.544948i
$759$	10.2761	−	29.6852i	0.372998	−	1.07751i
$760$	−28.4640	+	21.9257i	−1.03250	+	0.795329i
$761$	22.5861	+	39.1202i	0.818744	+	1.41811i	0.906608	+	0.421974i	$0.138663\pi$
$761$	22.5861	+	39.1202i	0.818744	+	1.41811i	−0.0878640	+	0.996132i	$0.528004\pi$
$762$	−15.7700	−	3.22524i	−0.571287	−	0.116838i
$763$	−2.46594	+	0.0929355i	−0.0892732	+	0.00336449i
$764$	25.5460	−	25.6097i	0.924223	−	0.926525i
$765$	14.3077	−	1.70902i	0.517295	−	0.0617898i
$766$	19.6392	+	2.57312i	0.709593	+	0.0929708i
$767$	−9.72910	+	16.8513i	−0.351297	+	0.608465i
$768$	−1.84104	+	27.6516i	−0.0664329	+	0.997791i
$769$	17.7051			0.638461			0.319231	−	0.947677i	$-0.396576\pi$
$769$	17.7051			0.638461			0.319231	+	0.947677i	$0.396576\pi$
$770$	−16.0727	−	19.3638i	−0.579218	−	0.697822i
$771$	−18.0650	+	26.6876i	−0.650594	+	0.961132i
$772$	10.0481	+	2.67900i	0.361640	+	0.0964193i
$773$	−8.29780	−	30.9678i	−0.298451	−	1.11384i	−0.938438	−	0.345449i	$-0.887727\pi$
$773$	−8.29780	−	30.9678i	−0.298451	−	1.11384i	0.639986	−	0.768386i	$-0.278940\pi$
$774$	−9.35831	−	5.54613i	−0.336377	−	0.199352i
$775$	2.58767	+	4.48197i	0.0929518	+	0.160997i
$776$	−10.7760	−	4.44002i	−0.386835	−	0.159387i
$777$	−13.1757	−	0.445346i	−0.472676	−	0.0159767i
$778$	15.4848	+	6.40273i	0.555157	+	0.229549i
$779$	1.22726	−	4.58018i	0.0439710	−	0.164102i
$780$	−11.3244	−	3.90437i	−0.405478	−	0.139799i
$781$	−13.6243	−	50.8465i	−0.487515	−	1.81943i
$782$	11.1418	−	14.5390i	0.398430	−	0.519913i
$783$	−13.5020	+	8.67391i	−0.482522	+	0.309980i
$784$	27.9152	−	2.17697i	0.996973	−	0.0777488i
$785$		−	0.567575i		−	0.0202576i
$786$	15.8094	−	31.6278i	0.563904	−	1.12813i
$787$	−7.85189	+	2.10391i	−0.279890	+	0.0749962i	−0.396033	−	0.918236i	$-0.629613\pi$
$787$	−7.85189	+	2.10391i	−0.279890	+	0.0749962i	0.116143	+	0.993232i	$0.462947\pi$
$788$	0.434236	+	0.249987i	0.0154690	+	0.00890541i
$789$	−26.0167	−	1.86226i	−0.926220	−	0.0662982i
$790$	10.3975	−	25.1461i	0.369927	−	0.894657i
$791$	49.4027	+	11.2618i	1.75656	+	0.400424i
$792$	20.7703	−	20.3530i	0.738042	−	0.723211i
$793$	−5.22665	+	3.01761i	−0.185604	+	0.107158i
$794$	−16.9420	+	13.0168i	−0.601249	+	0.461949i
$795$	−20.1135	−	41.4115i	−0.713353	−	1.46871i
$796$	48.4989	+	12.9306i	1.71900	+	0.458313i
$797$	0.0162831	+	0.0162831i	0.000576777	+	0.000576777i	0.707395	−	0.706818i	$-0.249870\pi$
$797$	0.0162831	+	0.0162831i	0.000576777	+	0.000576777i	−0.706818	+	0.707395i	$0.749870\pi$
$798$	−26.6267	+	32.4155i	−0.942574	+	1.14750i
$799$			16.6817i			0.590157i
$800$	−3.93951	+	5.16726i	−0.139283	+	0.182690i
$801$	−7.91555	−	1.13902i	−0.279682	−	0.0402451i
$802$	−1.48187	+	11.3103i	−0.0523268	+	0.399381i
$803$	36.8373	+	9.87054i	1.29996	+	0.348324i
$804$	30.1569	+	20.3587i	1.06355	+	0.717996i
$805$	−1.03484	−	27.4584i	−0.0364733	−	0.967781i
$806$	−4.29004	+	10.3753i	−0.151110	+	0.365455i
$807$	−22.1980	+	19.2324i	−0.781407	+	0.677014i
$808$	−2.33401	+	17.9879i	−0.0821103	+	0.632811i
$809$	24.8563	−	43.0523i	0.873900	−	1.51364i	0.0159693	−	0.999872i	$-0.494917\pi$
$809$	24.8563	−	43.0523i	0.873900	−	1.51364i	0.857930	−	0.513766i	$-0.171750\pi$
$810$	19.4553	+	15.6655i	0.683591	+	0.550431i
$811$	13.1752	−	13.1752i	0.462643	−	0.462643i	−0.436878	−	0.899521i	$-0.643916\pi$
$811$	13.1752	−	13.1752i	0.462643	−	0.462643i	0.899521	+	0.436878i	$0.143916\pi$
$812$	11.9968	+	11.0976i	0.421003	+	0.389450i
$813$	−27.1714	+	40.1407i	−0.952941	+	1.40779i
$814$	11.0670	+	8.48108i	0.387898	+	0.297262i
$815$	0.386142	−	0.668817i	0.0135260	−	0.0234276i
$816$	15.2342	−	7.44613i	0.533304	−	0.260667i
$817$	−8.29842	−	14.3733i	−0.290325	−	0.502858i
$818$	28.6811	−	11.9010i	1.00281	−	0.416109i
$819$	−13.9081	−	1.46919i	−0.485988	−	0.0513375i
$820$	0.00357651	+	2.87525i	0.000124897	+	0.100408i
$821$	31.0487	+	8.31948i	1.08361	+	0.290352i	0.756073	−	0.654487i	$-0.227116\pi$
$821$	31.0487	+	8.31948i	1.08361	+	0.290352i	0.327535	+	0.944839i	$0.393782\pi$
$822$	−23.6950	−	21.0068i	−0.826457	−	0.732695i
$823$	4.72835	−	8.18974i	0.164820	−	0.285476i	−0.771771	−	0.635900i	$-0.780629\pi$
$823$	4.72835	−	8.18974i	0.164820	−	0.285476i	0.936591	+	0.350424i	$0.113962\pi$
$824$	−3.01143	−	22.5489i	−0.104908	−	0.785527i
$825$	6.69514	−	1.28998i	0.233095	−	0.0449115i
$826$	−33.7203	−	23.8806i	−1.17328	−	0.830913i
$827$	0.304866	+	0.304866i	0.0106012	+	0.0106012i	0.712388	−	0.701786i	$-0.247614\pi$
$827$	0.304866	+	0.304866i	0.0106012	+	0.0106012i	−0.701786	+	0.712388i	$0.747614\pi$
$828$	31.5237	−	3.80522i	1.09553	−	0.132240i
$829$	−1.68599	−	6.29218i	−0.0585567	−	0.218537i	0.930447	−	0.366426i	$-0.119419\pi$
$829$	−1.68599	−	6.29218i	−0.0585567	−	0.218537i	−0.989004	+	0.147889i	$0.952752\pi$
$830$	3.52498	−	26.9042i	0.122354	−	0.933857i
$831$	4.87453	−	4.22331i	0.169095	−	0.146505i
$832$	−14.0959	+	0.0526019i	−0.488688	+	0.00182364i
$833$	−9.65861	−	14.1502i	−0.334651	−	0.490274i
$834$	−20.8625	−	31.5900i	−0.722410	−	1.09387i
$835$	−5.27788	+	19.6973i	−0.182649	+	0.681654i
$836$	42.8409	−	11.5363i	1.48168	−	0.398992i
$837$	15.7512	−	17.3209i	0.544441	−	0.598697i
$838$	−0.830784	−	6.28025i	−0.0286990	−	0.216948i
$839$			40.4563i			1.39671i	0.715753	+	0.698354i	$0.246084\pi$
$839$			40.4563i			1.39671i	−0.715753	+	0.698354i	$0.753916\pi$
$840$	10.4793	−	23.1778i	0.361571	−	0.799711i
$841$		−	19.4615i		−	0.671085i
$842$	12.5566	−	1.66105i	0.432727	−	0.0572435i
$843$	−7.29711	+	3.54420i	−0.251326	+	0.122069i
$844$	−10.0289	+	17.4206i	−0.345209	+	0.599641i
$845$	−5.02613	+	18.7578i	−0.172904	+	0.645287i
$846$	−20.6793	+	20.2134i	−0.710970	+	0.694951i
$847$	0.581601	+	1.88370i	0.0199840	+	0.0647247i
$848$	−38.4033	−	38.2127i	−1.31877	−	1.31223i
$849$	31.8648	+	36.7782i	1.09360	+	1.26222i
$850$	3.94205	+	0.516487i	0.135211	+	0.0177153i
$851$	3.94036	+	14.7056i	0.135074	+	0.504102i
$852$	40.1707	−	34.8916i	1.37623	−	1.19537i
$853$	−14.8945	−	14.8945i	−0.509978	−	0.509978i	0.404542	−	0.914520i	$-0.367431\pi$
$853$	−14.8945	−	14.8945i	−0.509978	−	0.509978i	−0.914520	+	0.404542i	$0.867431\pi$
$854$	−5.35413	−	11.6440i	−0.183215	−	0.398448i
$855$	14.1596	+	35.3809i	0.484249	+	1.21000i
$856$	23.1363	−	30.2686i	0.790782	−	1.03456i
$857$	−6.11483	+	10.5912i	−0.208878	+	0.361788i	−0.951362	−	0.308077i	$-0.900315\pi$
$857$	−6.11483	+	10.5912i	−0.208878	+	0.361788i	0.742483	+	0.669865i	$0.233648\pi$
$858$	11.0681	+	9.81244i	0.377860	+	0.334991i
$859$	−47.6122	−	12.7577i	−1.62451	−	0.435286i	−0.672187	−	0.740381i	$-0.734645\pi$
$859$	−47.6122	−	12.7577i	−1.62451	−	0.435286i	−0.952322	+	0.305096i	$0.901312\pi$
$860$	7.12502	+	7.10732i	0.242961	+	0.242358i
$861$	0.758814	+	3.27009i	0.0258603	+	0.111444i
$862$	−11.5238	−	27.7720i	−0.392501	−	0.945918i
$863$	7.08824	+	12.2772i	0.241286	+	0.417920i	0.961081	−	0.276267i	$-0.0890973\pi$
$863$	7.08824	+	12.2772i	0.241286	+	0.417920i	−0.719795	+	0.694187i	$0.755764\pi$
$864$	27.6900	+	9.86237i	0.942031	+	0.335525i
$865$	−3.80850	+	6.59651i	−0.129493	+	0.224288i
$866$	14.7284	−	19.2191i	0.500490	−	0.653092i
$867$	15.7919	+	10.6896i	0.536322	+	0.363038i
$868$	−21.0954	−	11.1084i	−0.716025	−	0.377045i
$869$	−23.7594	+	23.7594i	−0.805982	+	0.805982i
$870$	14.0841	−	4.69646i	0.477495	−	0.159225i
$871$	−9.25372	+	16.0279i	−0.313550	+	0.543085i
$872$	−0.339457	+	2.61615i	−0.0114955	+	0.0885939i
$873$	−7.64270	+	9.71618i	−0.258666	+	0.328843i
$874$	44.7682	+	18.5110i	1.51431	+	0.626144i
$875$	27.0274	−	16.9926i	0.913691	−	0.574454i
$876$	7.34023	+	37.8431i	0.248003	+	1.27860i
$877$	6.59730	+	1.76774i	0.222775	+	0.0596924i	0.368480	−	0.929636i	$-0.379878\pi$
$877$	6.59730	+	1.76774i	0.222775	+	0.0596924i	−0.145705	+	0.989328i	$0.546545\pi$
$878$	8.09681	+	1.06084i	0.273254	+	0.0358017i
$879$	11.8412	−	34.2065i	0.399393	−	1.15376i
$880$	−23.2649	+	13.5093i	−0.784259	+	0.455397i
$881$		−	2.25083i		−	0.0758325i	−0.999281	−	0.0379163i	$-0.987928\pi$
$881$		−	2.25083i		−	0.0758325i	0.999281	−	0.0379163i	$-0.0120720\pi$
$882$	5.83768	−	29.1191i	0.196565	−	0.980491i
$883$	18.2593	+	18.2593i	0.614475	+	0.614475i	0.944109	−	0.329634i	$-0.106925\pi$
$883$	18.2593	+	18.2593i	0.614475	+	0.614475i	−0.329634	+	0.944109i	$0.606925\pi$
$884$	4.32174	+	7.46402i	0.145356	+	0.251042i
$885$	−33.7653	+	16.3998i	−1.13501	+	0.551273i
$886$	−20.0280	−	26.0675i	−0.672855	−	0.875754i
$887$	−40.8557	+	23.5881i	−1.37180	+	0.792010i	−0.991155	−	0.132711i	$-0.957632\pi$
$887$	−40.8557	+	23.5881i	−1.37180	+	0.792010i	−0.380646	+	0.924721i	$0.624298\pi$
$888$	−2.80672	+	13.8112i	−0.0941875	+	0.463472i
$889$	16.9513	+	3.86421i	0.568527	+	0.129601i
$890$	6.83690	+	2.82696i	0.229173	+	0.0947598i
$891$	−14.7757	−	27.0746i	−0.495006	−	0.907033i
$892$	−37.9162	+	10.2102i	−1.26953	+	0.341863i
$893$	−42.6155	+	11.4188i	−1.42607	+	0.382115i
$894$	0.385451	−	0.771119i	0.0128914	−	0.0257901i
$895$		−	44.6058i		−	1.49101i
$896$	2.65686	−	29.8151i	0.0887593	−	0.996053i
$897$	3.05565	+	15.8591i	0.102025	+	0.529521i
$898$	33.8565	+	25.9456i	1.12981	+	0.865814i
$899$	−3.60156	−	13.4412i	−0.120119	−	0.448289i
$900$	4.13637	+	5.51256i	0.137879	+	0.183752i
$901$	−8.57945	+	32.0190i	−0.285823	+	1.06671i
$902$	1.35666	−	3.28103i	0.0451717	−	0.109246i
$903$	9.97145	+	6.21535i	0.331829	+	0.206834i
$904$	20.6360	−	50.0838i	0.686343	−	1.66576i
$905$	22.9223	+	39.7026i	0.761963	+	1.31976i
$906$	−20.3203	−	18.0149i	−0.675096	−	0.598506i
$907$	8.63597	+	32.2299i	0.286753	+	1.07018i	0.947549	+	0.319610i	$0.103552\pi$
$907$	8.63597	+	32.2299i	0.286753	+	1.07018i	−0.660797	+	0.750565i	$0.729781\pi$
$908$	−8.99748	+	5.20963i	−0.298592	+	0.172888i
$909$	17.6847	+	7.57546i	0.586566	+	0.251262i
$910$	12.1342	+	4.49004i	0.402246	+	0.148843i
$911$	26.1321			0.865797			0.432898	−	0.901443i	$-0.357491\pi$
$911$	26.1321			0.865797			0.432898	+	0.901443i	$0.357491\pi$
$912$	29.4500	+	33.8207i	0.975186	+	1.11991i
$913$	−16.7530	+	29.0170i	−0.554443	+	0.960324i
$914$	−5.18868	+	39.6022i	−0.171626	+	1.30993i
$915$	−11.6130	−	0.831250i	−0.383914	−	0.0274803i
$916$	−7.96860	+	0.00991213i	−0.263290	+	0.000327506i
$917$	−17.8368	+	33.7710i	−0.589024	+	1.11522i
$918$	−3.20127	−	17.6980i	−0.105658	−	0.584120i
$919$	−11.0037	−	19.0590i	−0.362978	−	0.628697i	0.625471	−	0.780247i	$-0.284907\pi$
$919$	−11.0037	−	19.0590i	−0.362978	−	0.628697i	−0.988450	+	0.151550i	$0.951573\pi$
$920$	−29.1309	−	3.77987i	−0.960417	−	0.124619i
$921$	44.6629	+	15.4609i	1.47169	+	0.509453i
$922$	5.88874	−	0.778993i	0.193935	−	0.0256548i
$923$	19.1373	+	19.1373i	0.629910	+	0.629910i
$924$	−22.9212	+	21.4758i	−0.754051	+	0.706503i
$925$	−2.33659	+	2.33659i	−0.0768266	+	0.0768266i
$926$	−10.5567	−	8.09002i	−0.346915	−	0.265855i
$927$	−23.8830	−	3.43667i	−0.784422	−	0.112875i
$928$	13.8275	−	10.6787i	0.453909	−	0.350545i
$929$	−33.6269	+	19.4145i	−1.10326	+	0.636969i	−0.937076	−	0.349125i	$-0.886479\pi$
$929$	−33.6269	+	19.4145i	−1.10326	+	0.636969i	−0.166187	+	0.986094i	$0.553145\pi$
$930$	−18.0732	+	11.9359i	−0.592645	+	0.391392i
$931$	29.5369	−	34.3600i	0.968033	−	1.12610i
$932$	12.8139	−	12.8458i	0.419734	−	0.420779i
$933$	2.52397	+	0.180664i	0.0826310	+	0.00591467i
$934$	−25.0539	+	19.2493i	−0.819788	+	0.629856i
$935$	14.2556	+	8.23045i	0.466206	+	0.269164i
$936$	−4.01600	+	14.4016i	−0.131267	+	0.470732i
$937$			2.57526i			0.0841301i	0.999115	+	0.0420650i	$0.0133937\pi$
$937$			2.57526i			0.0841301i	−0.999115	+	0.0420650i	$0.986606\pi$
$938$	−32.0726	−	22.7138i	−1.04721	−	0.741631i
$939$	15.0141	−	22.1806i	0.489968	−	0.723837i
$940$	23.1515	−	13.4049i	0.755117	−	0.437220i
$941$	39.5073	−	10.5860i	1.28790	−	0.345092i	0.451039	−	0.892504i	$-0.351054\pi$
$941$	39.5073	−	10.5860i	1.28790	−	0.345092i	0.836863	+	0.547412i	$0.184387\pi$
$942$	−0.707144	+	0.0425252i	−0.0230400	+	0.00138555i
$943$	3.35735	−	1.93837i	0.109330	−	0.0631219i
$944$	−31.1572	+	31.3126i	−1.01408	+	1.01914i
$945$	−20.6300	−	17.3870i	−0.671094	−	0.565600i
$946$	−4.76278	−	11.4782i	−0.154851	−	0.373187i
$947$	24.6056	+	6.59306i	0.799576	+	0.214246i	0.635398	−	0.772185i	$-0.280836\pi$
$947$	24.6056	+	6.59306i	0.799576	+	0.214246i	0.164178	+	0.986431i	$0.447503\pi$
$948$	−32.1086	−	11.0703i	−1.04284	−	0.359546i
$949$	−18.9394	+	5.07479i	−0.614799	+	0.164735i
$950$	1.37894	+	10.4240i	0.0447387	+	0.338199i
$951$	−3.08162	−	15.9939i	−0.0999285	−	0.518639i
$952$	−16.6308	+	7.67226i	−0.539007	+	0.248659i
$953$	−27.6526			−0.895755			−0.447878	−	0.894095i	$-0.647820\pi$
$953$	−27.6526			−0.895755			−0.447878	+	0.894095i	$0.647820\pi$
$954$	−50.0878	+	28.1623i	−1.62165	+	0.911787i
$955$	9.18655	+	34.2847i	0.297270	+	1.10943i
$956$	−8.61684	−	31.9992i	−0.278689	−	1.03493i
$957$	−18.2861	−	1.30891i	−0.591105	−	0.0423109i
$958$	21.5468	+	51.9271i	0.696144	+	1.67769i
$959$	25.0790	+	23.2573i	0.809843	+	0.751018i
$960$	−22.5757	−	15.1591i	−0.728628	−	0.489256i
$961$	−5.34976	−	9.26606i	−0.172573	−	0.298905i
$962$	−7.10784	−	0.931268i	−0.229166	−	0.0300253i
$963$	−24.2127	−	32.3521i	−0.780242	−	1.04253i
$964$	−15.0469	−	4.01176i	−0.484629	−	0.129210i
$965$	−7.21538	+	7.21538i	−0.232271	+	0.232271i
$966$	−34.1330	+	3.34662i	−1.09821	+	0.107676i
$967$	−55.5843			−1.78747			−0.893736	−	0.448594i	$-0.851925\pi$
$967$	−55.5843			−1.78747			−0.893736	+	0.448594i	$0.851925\pi$
$968$	2.08901	−	0.278990i	0.0671434	−	0.00896708i
$969$	8.97613	−	25.9300i	0.288355	−	0.832991i
$970$	9.06865	−	6.96759i	0.291177	−	0.223716i
$971$	−3.35634	+	12.5260i	−0.107710	+	0.401979i	−0.998639	−	0.0521645i	$-0.983388\pi$
$971$	−3.35634	+	12.5260i	−0.107710	+	0.401979i	0.890929	+	0.454143i	$0.150055\pi$
$972$	18.0601	−	25.4132i	0.579278	−	0.815130i
$973$	21.7644	+	34.6171i	0.697734	+	1.10977i
$974$	−17.0505	−	41.0914i	−0.546335	−	1.31665i
$975$	−2.64943	+	2.29548i	−0.0848497	+	0.0735141i
$976$	−13.2251	+	3.57895i	−0.423326	+	0.114559i
$977$	34.4997	+	19.9184i	1.10374	+	0.637247i	0.937202	−	0.348787i	$-0.113406\pi$
$977$	34.4997	+	19.9184i	1.10374	+	0.637247i	0.166543	+	0.986034i	$0.446740\pi$
$978$	−0.862214	−	0.430985i	−0.0275706	−	0.0137814i
$979$	−6.45988	−	6.45988i	−0.206459	−	0.206459i
$980$	−11.8767	+	24.7752i	−0.379388	+	0.791414i
$981$	2.57206	+	1.10177i	0.0821195	+	0.0351768i
$982$	−18.7155	+	2.47578i	−0.597235	+	0.0790053i
$983$	10.5524	+	6.09244i	0.336570	+	0.194319i	0.658754	−	0.752358i	$-0.271084\pi$
$983$	10.5524	+	6.09244i	0.336570	+	0.194319i	−0.322184	+	0.946677i	$0.604417\pi$
$984$	3.58201	−	0.219882i	0.114190	−	0.00700959i
$985$	−0.425786	+	0.245828i	−0.0135667	+	0.00783272i
$986$	−9.87872	−	4.08470i	−0.314602	−	0.130083i
$987$	22.8195	−	21.3273i	0.726354	−	0.678857i
$988$	−16.1095	+	16.1496i	−0.512510	+	0.513787i
$989$	3.51195	−	13.1068i	0.111674	−	0.416772i
$990$	7.07081	+	27.6447i	0.224725	+	0.878606i
$991$	5.95919	+	3.44054i	0.189300	+	0.109292i	0.591655	−	0.806191i	$-0.298475\pi$
$991$	5.95919	+	3.44054i	0.189300	+	0.109292i	−0.402355	+	0.915484i	$0.631808\pi$
$992$	−15.4529	+	20.2688i	−0.490630	+	0.643535i
$993$	−22.0050	+	4.23979i	−0.698306	+	0.134546i
$994$	−44.2224	+	36.7062i	−1.40265	+	1.16425i
$995$	−34.8262	+	34.8262i	−1.10406	+	1.10406i
$996$	−33.7841	−	2.37601i	−1.07049	−	0.0752867i
$997$	15.9162	−	4.26474i	0.504073	−	0.135066i	0.00218309	−	0.999998i	$-0.499305\pi$
$997$	15.9162	−	4.26474i	0.504073	−	0.135066i	0.501889	+	0.864932i	$0.332638\pi$
$998$	−30.9845	−	40.3279i	−0.980798	−	1.27656i
$999$	13.2855	+	6.85204i	0.420333	+	0.216789i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bu.a.11.19	✓	240
3.2	odd	2	inner	336.2.bu.a.11.42	yes	240
7.2	even	3	inner	336.2.bu.a.107.59	yes	240
16.3	odd	4	inner	336.2.bu.a.179.2	yes	240
21.2	odd	6	inner	336.2.bu.a.107.2	yes	240
48.35	even	4	inner	336.2.bu.a.179.59	yes	240
112.51	odd	12	inner	336.2.bu.a.275.42	yes	240
336.275	even	12	inner	336.2.bu.a.275.19	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bu.a.11.19	✓	240	1.1	even	1	trivial
336.2.bu.a.11.42	yes	240	3.2	odd	2	inner
336.2.bu.a.107.2	yes	240	21.2	odd	6	inner
336.2.bu.a.107.59	yes	240	7.2	even	3	inner
336.2.bu.a.179.2	yes	240	16.3	odd	4	inner
336.2.bu.a.179.59	yes	240	48.35	even	4	inner
336.2.bu.a.275.19	yes	240	336.275	even	12	inner
336.2.bu.a.275.42	yes	240	112.51	odd	12	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.860221 + 1.12251i) q^{2} +(-1.55800 + 0.756720i) q^{3} +(-0.520041 - 1.93121i) q^{4} +(1.89562 + 0.507929i) q^{5} +(0.490803 - 2.39982i) q^{6} +(-0.588039 + 2.57958i) q^{7} +(2.61514 + 1.07751i) q^{8} +(1.85475 - 2.35795i) q^{9} +O(q^{10})\)	\(q+(-0.860221 + 1.12251i) q^{2} +(-1.55800 + 0.756720i) q^{3} +(-0.520041 - 1.93121i) q^{4} +(1.89562 + 0.507929i) q^{5} +(0.490803 - 2.39982i) q^{6} +(-0.588039 + 2.57958i) q^{7} +(2.61514 + 1.07751i) q^{8} +(1.85475 - 2.35795i) q^{9} +(-2.20080 + 1.69091i) q^{10} +(3.31034 - 0.887003i) q^{11} +(2.27161 + 2.61530i) q^{12} +(-1.24592 + 1.24592i) q^{13} +(-2.38975 - 2.87908i) q^{14} +(-3.33774 + 0.643097i) q^{15} +(-3.45912 + 2.00861i) q^{16} +(2.11957 + 1.22374i) q^{17} +(1.05132 + 4.11032i) q^{18} +(-1.67532 + 6.25236i) q^{19} +(-0.00488227 - 3.92497i) q^{20} +(-1.03585 - 4.46397i) q^{21} +(-1.85196 + 4.47890i) q^{22} +(-4.58309 + 2.64605i) q^{23} +(-4.88978 + 0.300159i) q^{24} +(-0.994755 - 0.574322i) q^{25} +(-0.326788 - 2.47033i) q^{26} +(-1.10540 + 5.07721i) q^{27} +(5.28750 - 0.205860i) q^{28} +(2.18387 + 2.18387i) q^{29} +(2.14931 - 4.29984i) q^{30} +(-3.90197 - 2.25280i) q^{31} +(0.720923 - 5.61073i) q^{32} +(-4.48631 + 3.88696i) q^{33} +(-3.19695 + 1.32655i) q^{34} +(-2.42494 + 4.59121i) q^{35} +(-5.51822 - 2.35567i) q^{36} +(0.744575 - 2.77879i) q^{37} +(-5.57718 - 7.25897i) q^{38} +(0.998338 - 2.88397i) q^{39} +(4.41000 + 3.37086i) q^{40} -0.732552 q^{41} +(5.90189 + 2.67725i) q^{42} +(-1.81305 + 1.81305i) q^{43} +(-3.43450 - 5.93167i) q^{44} +(4.71356 - 3.52768i) q^{45} +(0.972262 - 7.42073i) q^{46} +(3.40795 + 5.90274i) q^{47} +(3.86936 - 5.74701i) q^{48} +(-6.30842 - 3.03378i) q^{49} +(1.50039 - 0.622575i) q^{50} +(-4.22833 - 0.302661i) q^{51} +(3.05407 + 1.75821i) q^{52} +(3.50544 + 13.0825i) q^{53} +(-4.74832 - 5.60834i) q^{54} +6.72567 q^{55} +(-4.31734 + 6.11233i) q^{56} +(-2.12114 - 11.0089i) q^{57} +(-4.33001 + 0.572796i) q^{58} +(10.6669 - 2.85820i) q^{59} +(2.97771 + 6.11142i) q^{60} +(3.30849 + 0.886508i) q^{61} +(5.88534 - 2.44208i) q^{62} +(4.99183 + 6.17103i) q^{63} +(5.67792 + 5.63571i) q^{64} +(-2.99464 + 1.72895i) q^{65} +(-0.503917 - 8.37955i) q^{66} +(10.1457 - 2.71854i) q^{67} +(1.26102 - 4.72972i) q^{68} +(5.13815 - 7.59066i) q^{69} +(-3.06767 - 6.67146i) q^{70} -15.3599i q^{71} +(7.39115 - 4.16784i) q^{72} +(9.63710 + 5.56398i) q^{73} +(2.47871 + 3.22616i) q^{74} +(1.98443 + 0.142044i) q^{75} +(12.9458 - 0.0161033i) q^{76} +(0.341482 + 9.06087i) q^{77} +(2.37848 + 3.60149i) q^{78} +(-8.49086 + 4.90220i) q^{79} +(-7.57739 + 2.05057i) q^{80} +(-2.11982 - 8.74679i) q^{81} +(0.630156 - 0.822294i) q^{82} +(-6.91319 + 6.91319i) q^{83} +(-8.08216 + 4.32189i) q^{84} +(3.39633 + 3.39633i) q^{85} +(-0.475537 - 3.59478i) q^{86} +(-5.05504 - 1.74989i) q^{87} +(9.61277 + 1.24730i) q^{88} +(-1.33285 - 2.30856i) q^{89} +(-0.0948594 + 8.32559i) q^{90} +(-2.48130 - 3.94661i) q^{91} +(7.49345 + 7.47483i) q^{92} +(7.78402 + 0.557175i) q^{93} +(-9.55745 - 1.25222i) q^{94} +(-6.35151 + 11.0011i) q^{95} +(3.12255 + 9.28707i) q^{96} -4.12061 q^{97} +(8.83207 - 4.47152i) q^{98} +(4.04835 - 9.45077i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 16 q^{7}+O(q^{10}) \) 240 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 16 * q^7	\( 240 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 16 q^{7} - 4 q^{10} - 2 q^{12} - 16 q^{13} - 20 q^{16} + 16 q^{18} - 4 q^{19} + 2 q^{21} - 40 q^{22} - 22 q^{24} - 8 q^{27} - 4 q^{28} - 26 q^{30} - 4 q^{33} + 16 q^{36} - 4 q^{37} - 4 q^{39} + 8 q^{40} - 18 q^{42} - 16 q^{43} + 18 q^{45} - 20 q^{46} - 88 q^{48} - 16 q^{49} + 6 q^{51} + 8 q^{52} + 14 q^{54} - 32 q^{55} - 36 q^{58} - 42 q^{60} - 4 q^{61} - 64 q^{64} - 30 q^{66} - 36 q^{67} - 20 q^{69} + 116 q^{70} - 46 q^{72} - 24 q^{75} - 112 q^{76} - 92 q^{78} - 4 q^{81} - 32 q^{82} + 44 q^{84} - 56 q^{85} - 4 q^{87} - 20 q^{88} + 28 q^{90} - 40 q^{91} - 14 q^{93} + 72 q^{94} + 36 q^{96} - 32 q^{97} + 28 q^{99}+O(q^{100}) \) 240 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 16 * q^7 - 4 * q^10 - 2 * q^12 - 16 * q^13 - 20 * q^16 + 16 * q^18 - 4 * q^19 + 2 * q^21 - 40 * q^22 - 22 * q^24 - 8 * q^27 - 4 * q^28 - 26 * q^30 - 4 * q^33 + 16 * q^36 - 4 * q^37 - 4 * q^39 + 8 * q^40 - 18 * q^42 - 16 * q^43 + 18 * q^45 - 20 * q^46 - 88 * q^48 - 16 * q^49 + 6 * q^51 + 8 * q^52 + 14 * q^54 - 32 * q^55 - 36 * q^58 - 42 * q^60 - 4 * q^61 - 64 * q^64 - 30 * q^66 - 36 * q^67 - 20 * q^69 + 116 * q^70 - 46 * q^72 - 24 * q^75 - 112 * q^76 - 92 * q^78 - 4 * q^81 - 32 * q^82 + 44 * q^84 - 56 * q^85 - 4 * q^87 - 20 * q^88 + 28 * q^90 - 40 * q^91 - 14 * q^93 + 72 * q^94 + 36 * q^96 - 32 * q^97 + 28 * q^99

Introduction

L-functions

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