LMFDB - Embedded newform 336.2.bq.b.109.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(37,336)]

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([0, 3, 0, 4]))

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

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

chi := DirichletCharacter("336.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bq (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:	$120$
Relative dimension:	$30$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			109.27
Character	$\chi$	$=$	336.109
Dual form			336.2.bq.b.37.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30340 - 0.548764i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.39772 - 1.43052i) q^{4} +(-2.53593 - 0.679499i) q^{5} +(-1.11696 + 0.867411i) q^{6} +(2.36624 - 1.18360i) q^{7} +(1.03677 - 2.63156i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(1.30340 - 0.548764i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.39772 - 1.43052i) q^{4} +(-2.53593 - 0.679499i) q^{5} +(-1.11696 + 0.867411i) q^{6} +(2.36624 - 1.18360i) q^{7} +(1.03677 - 2.63156i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-3.67822 + 0.505963i) q^{10} +(-1.08897 - 4.06411i) q^{11} +(-0.979844 + 1.74353i) q^{12} +(0.464324 + 0.464324i) q^{13} +(2.43464 - 2.84122i) q^{14} +2.62538 q^{15} +(-0.0927784 - 3.99892i) q^{16} +(3.46273 - 5.99763i) q^{17} +(0.854398 - 1.12694i) q^{18} +(-1.88917 + 7.05048i) q^{19} +(-4.51654 + 2.67795i) q^{20} +(-1.97927 + 1.75570i) q^{21} +(-3.64961 - 4.69958i) q^{22} +(-0.678671 + 0.391831i) q^{23} +(-0.320344 + 2.81023i) q^{24} +(1.63907 + 0.946318i) q^{25} +(0.860005 + 0.350397i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.61416 - 5.03929i) q^{28} +(2.64771 + 2.64771i) q^{29} +(3.42193 - 1.44072i) q^{30} +(-1.15237 + 1.99596i) q^{31} +(-2.31539 - 5.16129i) q^{32} +(2.10374 + 3.64378i) q^{33} +(1.22205 - 9.71755i) q^{34} +(-6.80486 + 1.39367i) q^{35} +(0.495198 - 1.93773i) q^{36} +(9.13580 + 2.44793i) q^{37} +(1.40670 + 10.2263i) q^{38} +(-0.568678 - 0.328327i) q^{39} +(-4.41731 + 5.96896i) q^{40} +4.12076i q^{41} +(-1.61632 + 3.37454i) q^{42} +(-5.75866 + 5.75866i) q^{43} +(-7.33586 - 4.12267i) q^{44} +(-2.53593 + 0.679499i) q^{45} +(-0.669559 + 0.883144i) q^{46} +(3.59896 + 6.23358i) q^{47} +(1.12461 + 3.83865i) q^{48} +(4.19817 - 5.60138i) q^{49} +(2.65568 + 0.333970i) q^{50} +(-1.79244 + 6.68949i) q^{51} +(1.31322 - 0.0152318i) q^{52} +(1.61173 + 6.01507i) q^{53} +(-0.533610 + 1.30968i) q^{54} +11.0462i q^{55} +(-0.661482 - 7.45402i) q^{56} -7.29919i q^{57} +(4.90400 + 1.99806i) q^{58} +(-0.932495 - 3.48012i) q^{59} +(3.66954 - 3.75566i) q^{60} +(3.02345 - 11.2837i) q^{61} +(-0.406688 + 3.23391i) q^{62} +(1.45742 - 2.20815i) q^{63} +(-5.85022 - 5.45664i) q^{64} +(-0.861983 - 1.49300i) q^{65} +(4.74159 + 3.59485i) q^{66} +(3.24140 - 0.868530i) q^{67} +(-3.73981 - 13.3365i) q^{68} +(0.554133 - 0.554133i) q^{69} +(-8.10468 + 5.55078i) q^{70} +8.86981i q^{71} +(-0.417912 - 2.79738i) q^{72} +(-2.81769 - 1.62680i) q^{73} +(13.2510 - 1.82276i) q^{74} +(-1.82815 - 0.489850i) q^{75} +(7.44533 + 12.5571i) q^{76} +(-7.38706 - 8.32773i) q^{77} +(-0.921391 - 0.115872i) q^{78} +(4.01043 + 6.94626i) q^{79} +(-2.48199 + 10.2040i) q^{80} +(0.500000 - 0.866025i) q^{81} +(2.26133 + 5.37102i) q^{82} +(-11.1462 - 11.1462i) q^{83} +(-0.254894 + 5.28536i) q^{84} +(-12.8566 + 12.8566i) q^{85} +(-4.34570 + 10.6660i) q^{86} +(-3.24277 - 1.87221i) q^{87} +(-11.8240 - 1.34784i) q^{88} +(1.40108 - 0.808914i) q^{89} +(-2.93245 + 2.27729i) q^{90} +(1.64828 + 0.549126i) q^{91} +(-0.388068 + 1.51852i) q^{92} +(0.596508 - 2.22620i) q^{93} +(8.11166 + 6.14988i) q^{94} +(9.58158 - 16.5958i) q^{95} +(3.57234 + 4.38616i) q^{96} +9.91317 q^{97} +(2.39807 - 9.60465i) q^{98} +(-2.97513 - 2.97513i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8}+O(q^{10}) $ 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8	$ 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8} - 8 q^{10} + 4 q^{11} + 8 q^{13} + 32 q^{14} + 8 q^{15} + 12 q^{16} - 16 q^{17} - 4 q^{18} - 8 q^{19} - 64 q^{20} + 12 q^{21} + 24 q^{22} - 8 q^{24} - 8 q^{26} - 8 q^{28} - 64 q^{29} - 52 q^{31} - 4 q^{33} + 32 q^{34} - 8 q^{35} + 24 q^{37} - 40 q^{38} - 60 q^{40} + 24 q^{42} - 32 q^{43} - 12 q^{44} - 8 q^{45} + 4 q^{46} - 8 q^{47} + 32 q^{48} + 20 q^{49} - 16 q^{50} - 8 q^{51} - 16 q^{52} + 4 q^{54} - 104 q^{56} + 4 q^{58} + 52 q^{59} - 16 q^{60} + 4 q^{61} - 144 q^{62} + 8 q^{63} - 64 q^{64} + 24 q^{65} + 24 q^{66} + 12 q^{68} + 24 q^{69} - 48 q^{70} + 4 q^{72} + 16 q^{74} + 16 q^{75} - 8 q^{76} + 8 q^{77} - 56 q^{78} + 28 q^{79} + 68 q^{80} + 60 q^{81} + 28 q^{82} + 8 q^{83} + 24 q^{84} - 80 q^{85} + 36 q^{86} + 40 q^{88} + 8 q^{90} + 36 q^{91} - 184 q^{92} + 4 q^{93} + 60 q^{94} - 16 q^{95} + 36 q^{96} + 24 q^{97} + 124 q^{98} - 8 q^{99}+O(q^{100}) $ 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8 - 8 * q^10 + 4 * q^11 + 8 * q^13 + 32 * q^14 + 8 * q^15 + 12 * q^16 - 16 * q^17 - 4 * q^18 - 8 * q^19 - 64 * q^20 + 12 * q^21 + 24 * q^22 - 8 * q^24 - 8 * q^26 - 8 * q^28 - 64 * q^29 - 52 * q^31 - 4 * q^33 + 32 * q^34 - 8 * q^35 + 24 * q^37 - 40 * q^38 - 60 * q^40 + 24 * q^42 - 32 * q^43 - 12 * q^44 - 8 * q^45 + 4 * q^46 - 8 * q^47 + 32 * q^48 + 20 * q^49 - 16 * q^50 - 8 * q^51 - 16 * q^52 + 4 * q^54 - 104 * q^56 + 4 * q^58 + 52 * q^59 - 16 * q^60 + 4 * q^61 - 144 * q^62 + 8 * q^63 - 64 * q^64 + 24 * q^65 + 24 * q^66 + 12 * q^68 + 24 * q^69 - 48 * q^70 + 4 * q^72 + 16 * q^74 + 16 * q^75 - 8 * q^76 + 8 * q^77 - 56 * q^78 + 28 * q^79 + 68 * q^80 + 60 * q^81 + 28 * q^82 + 8 * q^83 + 24 * q^84 - 80 * q^85 + 36 * q^86 + 40 * q^88 + 8 * q^90 + 36 * q^91 - 184 * q^92 + 4 * q^93 + 60 * q^94 - 16 * q^95 + 36 * q^96 + 24 * q^97 + 124 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.30340	−	0.548764i	0.921645	−	0.388035i
$2$	1.30340	−	0.548764i	0.921645	−	0.388035i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	1.39772	−	1.43052i	0.698858	−	0.715260i
$5$	−2.53593	−	0.679499i	−1.13410	−	0.303881i	−0.357524	−	0.933904i	$-0.616379\pi$
$5$	−2.53593	−	0.679499i	−1.13410	−	0.303881i	−0.776577	+	0.630023i	$0.783046\pi$
$6$	−1.11696	+	0.867411i	−0.455997	+	0.354119i
$7$	2.36624	−	1.18360i	0.894354	−	0.447360i
$7$	2.36624	−	1.18360i	0.894354	−	0.447360i
$8$	1.03677	−	2.63156i	0.366553	−	0.930397i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	−3.67822	+	0.505963i	−1.16315	+	0.160000i
$11$	−1.08897	−	4.06411i	−0.328338	−	1.22537i	−0.910913	−	0.412597i	$-0.864622\pi$
$11$	−1.08897	−	4.06411i	−0.328338	−	1.22537i	0.582576	−	0.812777i	$-0.302045\pi$
$12$	−0.979844	+	1.74353i	−0.282857	+	0.503314i
$13$	0.464324	+	0.464324i	0.128780	+	0.128780i	0.768559	−	0.639779i	$-0.220974\pi$
$13$	0.464324	+	0.464324i	0.128780	+	0.128780i	−0.639779	+	0.768559i	$0.720974\pi$
$14$	2.43464	−	2.84122i	0.650685	−	0.759347i
$15$	2.62538			0.677871
$16$	−0.0927784	−	3.99892i	−0.0231946	−	0.999731i
$17$	3.46273	−	5.99763i	0.839836	−	1.45464i	−0.0501952	−	0.998739i	$-0.515984\pi$
$17$	3.46273	−	5.99763i	0.839836	−	1.45464i	0.890031	−	0.455899i	$-0.150682\pi$
$18$	0.854398	−	1.12694i	0.201383	−	0.265623i
$19$	−1.88917	+	7.05048i	−0.433405	+	1.61749i	0.311449	+	0.950263i	$0.399186\pi$
$19$	−1.88917	+	7.05048i	−0.433405	+	1.61749i	−0.744854	+	0.667227i	$0.767481\pi$
$20$	−4.51654	+	2.67795i	−1.00993	+	0.598807i
$21$	−1.97927	+	1.75570i	−0.431912	+	0.383125i
$22$	−3.64961	−	4.69958i	−0.778099	−	1.00195i
$23$	−0.678671	+	0.391831i	−0.141513	+	0.0817024i	−0.569085	−	0.822279i	$-0.692702\pi$
$23$	−0.678671	+	0.391831i	−0.141513	+	0.0817024i	0.427572	+	0.903981i	$0.359369\pi$
$24$	−0.320344	+	2.81023i	−0.0653899	+	0.573635i
$25$	1.63907	+	0.946318i	0.327814	+	0.189264i
$26$	0.860005	+	0.350397i	0.168661	+	0.0687185i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	1.61416	−	5.03929i	0.305048	−	0.952337i
$29$	2.64771	+	2.64771i	0.491667	+	0.491667i	0.908831	−	0.417164i	$-0.136976\pi$
$29$	2.64771	+	2.64771i	0.491667	+	0.491667i	−0.417164	+	0.908831i	$0.636976\pi$
$30$	3.42193	−	1.44072i	0.624756	−	0.263037i
$31$	−1.15237	+	1.99596i	−0.206971	+	0.358484i	−0.950759	−	0.309931i	$-0.899694\pi$
$31$	−1.15237	+	1.99596i	−0.206971	+	0.358484i	0.743788	+	0.668416i	$0.233027\pi$
$32$	−2.31539	−	5.16129i	−0.409307	−	0.912397i
$33$	2.10374	+	3.64378i	0.366213	+	0.634300i
$34$	1.22205	−	9.71755i	0.209580	−	1.66655i
$35$	−6.80486	+	1.39367i	−1.15023	+	0.235574i
$36$	0.495198	−	1.93773i	0.0825329	−	0.322954i
$37$	9.13580	+	2.44793i	1.50192	+	0.402437i	0.913741	−	0.406297i	$-0.133180\pi$
$37$	9.13580	+	2.44793i	1.50192	+	0.402437i	0.588175	+	0.808734i	$0.299847\pi$
$38$	1.40670	+	10.2263i	0.228197	+	1.65893i
$39$	−0.568678	−	0.328327i	−0.0910614	−	0.0525743i
$40$	−4.41731	+	5.96896i	−0.698438	+	0.943775i
$41$			4.12076i			0.643555i	0.946815	+	0.321778i	$0.104280\pi$
$41$			4.12076i			0.643555i	−0.946815	+	0.321778i	$0.895720\pi$
$42$	−1.61632	+	3.37454i	−0.249404	+	0.520702i
$43$	−5.75866	+	5.75866i	−0.878187	+	0.878187i	−0.993347	−	0.115160i	$-0.963262\pi$
$43$	−5.75866	+	5.75866i	−0.878187	+	0.878187i	0.115160	+	0.993347i	$0.463262\pi$
$44$	−7.33586	−	4.12267i	−1.10592	−	0.621515i
$45$	−2.53593	+	0.679499i	−0.378033	+	0.101294i
$46$	−0.669559	+	0.883144i	−0.0987211	+	0.130212i
$47$	3.59896	+	6.23358i	0.524962	+	0.909261i	0.999577	+	0.0290678i	$0.00925386\pi$
$47$	3.59896	+	6.23358i	0.524962	+	0.909261i	−0.474615	+	0.880193i	$0.657413\pi$
$48$	1.12461	+	3.83865i	0.162324	+	0.554062i
$49$	4.19817	−	5.60138i	0.599738	−	0.800197i
$50$	2.65568	+	0.333970i	0.375569	+	0.0472306i
$51$	−1.79244	+	6.68949i	−0.250992	+	0.936715i
$52$	1.31322	−	0.0152318i	0.182111	−	0.00211227i
$53$	1.61173	+	6.01507i	0.221389	+	0.826234i	0.983819	+	0.179164i	$0.0573392\pi$
$53$	1.61173	+	6.01507i	0.221389	+	0.826234i	−0.762431	+	0.647070i	$0.775994\pi$
$54$	−0.533610	+	1.30968i	−0.0726151	+	0.178225i
$55$			11.0462i			1.48947i
$56$	−0.661482	−	7.45402i	−0.0883943	−	0.996086i
$57$		−	7.29919i		−	0.966801i
$58$	4.90400	+	1.99806i	0.643927	+	0.262359i
$59$	−0.932495	−	3.48012i	−0.121401	−	0.453073i	0.878285	−	0.478137i	$-0.158688\pi$
$59$	−0.932495	−	3.48012i	−0.121401	−	0.453073i	−0.999686	+	0.0250639i	$0.992021\pi$
$60$	3.66954	−	3.75566i	0.473736	−	0.484854i
$61$	3.02345	−	11.2837i	0.387112	−	1.44472i	−0.447697	−	0.894185i	$-0.647756\pi$
$61$	3.02345	−	11.2837i	0.387112	−	1.44472i	0.834810	−	0.550538i	$-0.185578\pi$
$62$	−0.406688	+	3.23391i	−0.0516494	+	0.410707i
$63$	1.45742	−	2.20815i	0.183618	−	0.278201i
$64$	−5.85022	−	5.45664i	−0.731278	−	0.682080i
$65$	−0.861983	−	1.49300i	−0.106916	−	0.185184i
$66$	4.74159	+	3.59485i	0.583649	+	0.442496i
$67$	3.24140	−	0.868530i	0.396000	−	0.106108i	−0.0553232	−	0.998468i	$-0.517619\pi$
$67$	3.24140	−	0.868530i	0.396000	−	0.106108i	0.451323	+	0.892361i	$0.350952\pi$
$68$	−3.73981	−	13.3365i	−0.453519	−	1.61729i
$69$	0.554133	−	0.554133i	0.0667098	−	0.0667098i
$70$	−8.10468	+	5.55078i	−0.968694	+	0.663445i
$71$			8.86981i			1.05265i	0.850283	+	0.526326i	$0.176431\pi$
$71$			8.86981i			1.05265i	−0.850283	+	0.526326i	$0.823569\pi$
$72$	−0.417912	−	2.79738i	−0.0492514	−	0.329675i
$73$	−2.81769	−	1.62680i	−0.329786	−	0.190402i	0.325960	−	0.945384i	$-0.394312\pi$
$73$	−2.81769	−	1.62680i	−0.329786	−	0.190402i	−0.655746	+	0.754982i	$0.727646\pi$
$74$	13.2510	−	1.82276i	1.54039	−	0.211891i
$75$	−1.82815	−	0.489850i	−0.211096	−	0.0565631i
$76$	7.44533	+	12.5571i	0.854038	+	1.44039i
$77$	−7.38706	−	8.32773i	−0.841834	−	0.949033i
$78$	−0.921391	−	0.115872i	−0.104327	−	0.0131199i
$79$	4.01043	+	6.94626i	0.451208	+	0.781515i	0.998461	−	0.0554517i	$-0.0176599\pi$
$79$	4.01043	+	6.94626i	0.451208	+	0.781515i	−0.547253	+	0.836967i	$0.684327\pi$
$80$	−2.48199	+	10.2040i	−0.277495	+	1.14084i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	2.26133	+	5.37102i	0.249722	+	0.593129i
$83$	−11.1462	−	11.1462i	−1.22345	−	1.22345i	−0.966397	−	0.257054i	$-0.917248\pi$
$83$	−11.1462	−	11.1462i	−1.22345	−	1.22345i	−0.257054	−	0.966397i	$-0.582752\pi$
$84$	−0.254894	+	5.28536i	−0.0278112	+	0.576680i
$85$	−12.8566	+	12.8566i	−1.39450	+	1.39450i
$86$	−4.34570	+	10.6660i	−0.468609	+	1.15014i
$87$	−3.24277	−	1.87221i	−0.347661	−	0.200722i
$88$	−11.8240	−	1.34784i	−1.26044	−	0.143680i
$89$	1.40108	−	0.808914i	0.148514	−	0.0857447i	−0.423902	−	0.905708i	$-0.639340\pi$
$89$	1.40108	−	0.808914i	0.148514	−	0.0857447i	0.572416	+	0.819964i	$0.306006\pi$
$90$	−2.93245	+	2.27729i	−0.309107	+	0.240047i
$91$	1.64828	+	0.549126i	0.172786	+	0.0575640i
$92$	−0.388068	+	1.51852i	−0.0404588	+	0.158317i
$93$	0.596508	−	2.22620i	0.0618550	−	0.230846i
$94$	8.11166	+	6.14988i	0.836653	+	0.634312i
$95$	9.58158	−	16.5958i	0.983050	−	1.70269i
$96$	3.57234	+	4.38616i	0.364600	+	0.447661i
$97$	9.91317			1.00653			0.503265	−	0.864132i	$-0.332132\pi$
$97$	9.91317			1.00653			0.503265	+	0.864132i	$0.332132\pi$
$98$	2.39807	−	9.60465i	0.242241	−	0.970216i
$99$	−2.97513	−	2.97513i	−0.299012	−	0.299012i
$100$	3.64469	−	1.02204i	0.364469	−	0.102204i
$101$	0.0271867	+	0.101462i	0.00270518	+	0.0100959i	0.967265	−	0.253768i	$-0.0816698\pi$
$101$	0.0271867	+	0.101462i	0.00270518	+	0.0100959i	−0.964560	+	0.263863i	$0.915003\pi$
$102$	1.33467	+	9.70272i	0.132153	+	0.960713i
$103$	−7.27193	+	4.19845i	−0.716524	+	0.413685i	−0.813472	−	0.581604i	$-0.802425\pi$
$103$	−7.27193	+	4.19845i	−0.716524	+	0.413685i	0.0969479	+	0.995289i	$0.469092\pi$
$104$	1.70329	−	0.740500i	0.167022	−	0.0726120i
$105$	6.21228	−	3.10741i	0.606257	−	0.303252i
$106$	5.40159	+	6.95560i	0.524649	+	0.675587i
$107$	16.2050	+	4.34210i	1.56659	+	0.419767i	0.934743	−	0.355325i	$-0.115630\pi$
$107$	16.2050	+	4.34210i	1.56659	+	0.419767i	0.631849	+	0.775092i	$0.282296\pi$
$108$	0.0231962	+	1.99987i	0.00223205	+	0.192437i
$109$	8.50180	−	2.27805i	0.814325	−	0.218198i	0.172461	−	0.985016i	$-0.444828\pi$
$109$	8.50180	−	2.27805i	0.814325	−	0.218198i	0.641864	+	0.766819i	$0.278161\pi$
$110$	6.06177	+	14.3977i	0.577967	+	1.37276i
$111$	−9.45808			−0.897721
$112$	−4.95268	−	9.35259i	−0.467984	−	0.883737i
$113$	−13.2271			−1.24430			−0.622150	−	0.782898i	$-0.713741\pi$
$113$	−13.2271			−1.24430			−0.622150	+	0.782898i	$0.713741\pi$
$114$	−4.00553	−	9.51378i	−0.375152	−	0.891047i
$115$	1.98731	−	0.532498i	0.185317	−	0.0496557i
$116$	7.48835	−	0.0868563i	0.695276	−	0.00806441i
$117$	0.634278	+	0.169954i	0.0586391	+	0.0157123i
$118$	−3.12518	−	4.02428i	−0.287696	−	0.370465i
$119$	1.09484	−	18.2903i	0.100363	−	1.67667i
$120$	2.72192	−	6.90885i	0.248476	−	0.630689i
$121$	−5.80481	+	3.35141i	−0.527710	+	0.304674i
$122$	−2.25129	−	16.3663i	−0.203823	−	1.48173i
$123$	−1.06653	−	3.98035i	−0.0961660	−	0.358896i
$124$	1.24458	+	4.43826i	0.111766	+	0.398568i
$125$	5.76859	+	5.76859i	0.515958	+	0.515958i
$126$	0.687853	−	3.67789i	0.0612788	−	0.327652i
$127$	−7.95678			−0.706050			−0.353025	−	0.935614i	$-0.614847\pi$
$127$	−7.95678			−0.706050			−0.353025	+	0.935614i	$0.614847\pi$
$128$	−10.6196	−	3.90181i	−0.938649	−	0.344874i
$129$	4.07198	−	7.05288i	0.358518	−	0.620972i
$130$	−1.94281	−	1.47295i	−0.170396	−	0.129187i
$131$	1.41987	−	5.29904i	0.124055	−	0.462979i	−0.875749	−	0.482766i	$-0.839632\pi$
$131$	1.41987	−	5.29904i	0.124055	−	0.462979i	0.999804	+	0.0197871i	$0.00629883\pi$
$132$	8.15292	+	2.08353i	0.709621	+	0.181348i
$133$	3.87474	+	18.9191i	0.335983	+	1.64050i
$134$	3.74823	−	2.91081i	0.323798	−	0.251455i
$135$	2.27365	−	1.31269i	0.195685	−	0.112979i
$136$	−12.1931	−	15.3305i	−1.04555	−	1.31458i
$137$	3.53866	+	2.04305i	0.302328	+	0.174549i	0.643488	−	0.765456i	$-0.277486\pi$
$137$	3.53866	+	2.04305i	0.302328	+	0.174549i	−0.341160	+	0.940005i	$0.610820\pi$
$138$	0.418170	−	1.02635i	0.0355970	−	0.0873684i
$139$	8.94517	−	8.94517i	0.758720	−	0.758720i	−0.217370	−	0.976089i	$-0.569748\pi$
$139$	8.94517	−	8.94517i	0.758720	−	0.758720i	0.976089	+	0.217370i	$0.0697477\pi$
$140$	−7.51759	+	11.6825i	−0.635352	+	0.987348i
$141$	−5.08970	−	5.08970i	−0.428630	−	0.428630i
$142$	4.86743	+	11.5609i	0.408466	+	0.970172i
$143$	1.38143	−	2.39270i	0.115521	−	0.200087i
$144$	−2.07981	−	3.41678i	−0.173318	−	0.284732i
$145$	−4.91528	−	8.51351i	−0.408192	−	0.707009i
$146$	−4.56531	−	0.574121i	−0.377828	−	0.0475146i
$147$	−2.60537	+	6.49708i	−0.214888	+	0.535870i
$148$	16.2711	−	9.64744i	1.33747	−	0.793014i
$149$	−12.0319	−	3.22393i	−0.985688	−	0.264114i	−0.270250	−	0.962790i	$-0.587106\pi$
$149$	−12.0319	−	3.22393i	−0.985688	−	0.264114i	−0.715438	+	0.698676i	$0.753773\pi$
$150$	−2.65162	+	0.364749i	−0.216504	+	0.0297816i
$151$	11.6130	+	6.70479i	0.945055	+	0.545628i	0.891541	−	0.452939i	$-0.149625\pi$
$151$	11.6130	+	6.70479i	0.945055	+	0.545628i	0.0535139	+	0.998567i	$0.482958\pi$
$152$	16.5951	+	12.2812i	1.34604	+	0.996135i
$153$		−	6.92547i		−	0.559891i
$154$	−14.1983	−	6.80063i	−1.14413	−	0.548010i
$155$	4.27856	−	4.27856i	0.343663	−	0.343663i
$156$	−1.26453	+	0.354599i	−0.101243	+	0.0283906i
$157$	−10.6845	+	2.86290i	−0.852715	+	0.228484i	−0.658599	−	0.752494i	$-0.728851\pi$
$157$	−10.6845	+	2.86290i	−0.852715	+	0.228484i	−0.194116	+	0.980979i	$0.562184\pi$
$158$	9.03906	+	6.85300i	0.719109	+	0.545195i
$159$	−3.11363	−	5.39297i	−0.246927	−	0.427690i
$160$	2.36457	+	14.6620i	0.186936	+	1.15913i
$161$	−1.14213	+	1.73044i	−0.0900121	+	0.136378i
$162$	0.176458	−	1.40316i	0.0138638	−	0.110243i
$163$	2.60813	−	9.73368i	0.204285	−	0.762400i	−0.785382	−	0.619012i	$-0.787533\pi$
$163$	2.60813	−	9.73368i	0.204285	−	0.762400i	0.989666	−	0.143389i	$-0.0457999\pi$
$164$	5.89484	+	5.75966i	0.460310	+	0.449754i
$165$	−2.85897	−	10.6698i	−0.222571	−	0.830646i
$166$	−20.6446	−	8.41133i	−1.60233	−	0.652846i
$167$			6.22443i			0.481661i	0.970567	+	0.240830i	$0.0774197\pi$
$167$			6.22443i			0.481661i	−0.970567	+	0.240830i	$0.922580\pi$
$168$	2.56819	+	7.02883i	0.198140	+	0.542286i
$169$		−	12.5688i		−	0.966831i
$170$	−9.70210	+	23.8126i	−0.744117	+	1.82634i
$171$	1.88917	+	7.05048i	0.144468	+	0.539163i
$172$	0.188909	+	16.2868i	0.0144042	+	1.24186i
$173$	−4.39934	+	16.4186i	−0.334476	+	1.24828i	0.569960	+	0.821672i	$0.306959\pi$
$173$	−4.39934	+	16.4186i	−0.334476	+	1.24828i	−0.904436	+	0.426609i	$0.859708\pi$
$174$	−5.25404	−	0.660733i	−0.398308	−	0.0500901i
$175$	4.99850	+	0.299204i	0.377851	+	0.0226177i
$176$	−16.1510	+	4.73178i	−1.21743	+	0.356672i
$177$	1.80144	+	3.12019i	0.135405	+	0.234528i
$178$	1.38227	−	1.82320i	0.103605	−	0.136655i
$179$	−21.2576	+	5.69595i	−1.58887	+	0.425735i	−0.941656	−	0.336576i	$-0.890731\pi$
$179$	−21.2576	+	5.69595i	−1.58887	+	0.425735i	−0.647210	+	0.762312i	$0.724064\pi$
$180$	−2.57247	+	4.57744i	−0.191740	+	0.341182i
$181$	12.4906	−	12.4906i	0.928416	−	0.928416i	−0.0691873	−	0.997604i	$-0.522041\pi$
$181$	12.4906	−	12.4906i	0.928416	−	0.928416i	0.997604	+	0.0691873i	$0.0220406\pi$
$182$	2.44971	−	0.188783i	0.181584	−	0.0139935i
$183$			11.6817i			0.863536i
$184$	0.327502	+	2.19220i	0.0241438	+	0.161611i
$185$	−21.5043	−	12.4155i	−1.58103	−	0.912808i
$186$	−0.444168	−	3.22898i	−0.0325679	−	0.236760i
$187$	−28.1458	−	7.54165i	−2.05823	−	0.551500i
$188$	13.9476	+	3.56439i	1.01723	+	0.259960i
$189$	−0.836249	+	2.51012i	−0.0608282	+	0.182584i
$190$	3.38149	−	26.8890i	0.245319	−	1.95073i
$191$	−1.03851	−	1.79876i	−0.0751442	−	0.130154i	0.826005	−	0.563663i	$-0.190608\pi$
$191$	−1.03851	−	1.79876i	−0.0751442	−	0.130154i	−0.901149	+	0.433510i	$0.857275\pi$
$192$	7.06316	+	3.75656i	0.509740	+	0.271106i
$193$	−7.61822	+	13.1952i	−0.548372	+	0.949808i	0.450015	+	0.893021i	$0.351419\pi$
$193$	−7.61822	+	13.1952i	−0.548372	+	0.949808i	−0.998386	+	0.0567865i	$0.981915\pi$
$194$	12.9209	−	5.43999i	0.927663	−	0.390569i
$195$	1.21903	+	1.21903i	0.0872964	+	0.0872964i
$196$	−2.14504	−	13.8347i	−0.153217	−	0.988193i
$197$	−1.16831	+	1.16831i	−0.0832388	+	0.0832388i	−0.747500	−	0.664261i	$-0.768746\pi$
$197$	−1.16831	+	1.16831i	−0.0832388	+	0.0832388i	0.664261	+	0.747500i	$0.268746\pi$
$198$	−5.51044	−	2.24515i	−0.391610	−	0.159556i
$199$	−2.32369	−	1.34158i	−0.164722	−	0.0951022i	0.415373	−	0.909651i	$-0.363651\pi$
$199$	−2.32369	−	1.34158i	−0.164722	−	0.0951022i	−0.580095	+	0.814549i	$0.696984\pi$
$200$	4.18963	−	3.33220i	0.296252	−	0.235622i
$201$	−2.90616	+	1.67787i	−0.204985	+	0.118348i
$202$	0.0911139	+	0.117327i	0.00641075	+	0.00825509i
$203$	9.39895	+	3.13127i	0.659677	+	0.219772i
$204$	7.06412	+	11.9141i	0.494587	+	0.834156i
$205$	2.80006	−	10.4500i	0.195564	−	0.729856i
$206$	−7.17429	+	9.46284i	−0.499856	+	0.659307i
$207$	−0.391831	+	0.678671i	−0.0272341	+	0.0471709i
$208$	1.81372	−	1.89988i	0.125759	−	0.131733i
$209$	30.7111			2.12433
$210$	6.39187	−	7.45929i	0.441081	−	0.514740i
$211$	−18.1472	−	18.1472i	−1.24930	−	1.24930i	−0.956028	−	0.293276i	$-0.905255\pi$
$211$	−18.1472	−	18.1472i	−1.24930	−	1.24930i	−0.293276	−	0.956028i	$-0.594745\pi$
$212$	10.8574	+	6.10174i	0.745691	+	0.419070i
$213$	−2.29567	−	8.56757i	−0.157297	−	0.587041i
$214$	23.5044	−	3.23318i	1.60673	−	0.221016i
$215$	18.5165	−	10.6905i	1.26282	−	0.729087i
$216$	1.12769	+	2.59390i	0.0767294	+	0.176493i
$217$	−0.364351	+	6.08685i	−0.0247338	+	0.413202i
$218$	9.83115	−	7.63470i	0.665850	−	0.517087i
$219$	3.14273	+	0.842091i	0.212366	+	0.0569033i
$220$	15.8019	+	15.4395i	1.06536	+	1.04093i
$221$	4.39267	−	1.17701i	0.295483	−	0.0791745i
$222$	−12.3277	+	5.19025i	−0.827380	+	0.348347i
$223$	12.4307			0.832419			0.416210	−	0.909269i	$-0.363358\pi$
$223$	12.4307			0.832419			0.416210	+	0.909269i	$0.363358\pi$
$224$	−11.5877	−	9.47234i	−0.774236	−	0.632898i
$225$	1.89264			0.126176
$226$	−17.2402	+	7.25855i	−1.14680	+	0.482832i
$227$	−1.87211	+	0.501630i	−0.124256	+	0.0332944i	−0.320411	−	0.947279i	$-0.603821\pi$
$227$	−1.87211	+	0.501630i	−0.124256	+	0.0332944i	0.196155	+	0.980573i	$0.437154\pi$
$228$	−10.4416	−	10.2022i	−0.691515	−	0.675657i
$229$	20.2051	+	5.41395i	1.33519	+	0.357764i	0.854649	−	0.519207i	$-0.173773\pi$
$229$	20.2051	+	5.41395i	1.33519	+	0.357764i	0.480544	+	0.876971i	$0.340439\pi$
$230$	2.29805	−	1.78462i	0.151529	−	0.117675i
$231$	9.29073	+	6.13206i	0.611285	+	0.403460i
$232$	9.71267	−	4.22255i	0.637668	−	0.277224i
$233$	4.10382	−	2.36934i	0.268850	−	0.155221i	−0.359515	−	0.933139i	$-0.617058\pi$
$233$	4.10382	−	2.36934i	0.268850	−	0.155221i	0.628365	+	0.777919i	$0.283724\pi$
$234$	0.919985	−	0.126550i	0.0601413	−	0.00827284i
$235$	−4.89098	−	18.2534i	−0.319052	−	1.19072i
$236$	−6.28175	−	3.53027i	−0.408907	−	0.229801i
$237$	−5.67160	−	5.67160i	−0.368410	−	0.368410i
$238$	−8.61006	−	24.4405i	−0.558107	−	1.58424i
$239$	−19.8840			−1.28619			−0.643093	−	0.765788i	$-0.722349\pi$
$239$	−19.8840			−1.28619			−0.643093	+	0.765788i	$0.722349\pi$
$240$	−0.243579	−	10.4987i	−0.0157229	−	0.677689i
$241$	2.80489	−	4.85821i	0.180679	−	0.312945i	−0.761433	−	0.648243i	$-0.775504\pi$
$241$	2.80489	−	4.85821i	0.180679	−	0.312945i	0.942112	+	0.335299i	$0.108837\pi$
$242$	−5.72687	+	7.55371i	−0.368137	+	0.485571i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	−11.9156	−	20.0964i	−0.762817	−	1.28654i
$245$	−14.4524	+	11.3520i	−0.923328	+	0.725254i
$246$	−3.57440	−	4.60273i	−0.227895	−	0.293459i
$247$	−4.15089	+	2.39652i	−0.264115	+	0.152487i
$248$	4.05774	+	5.10187i	0.257667	+	0.323969i
$249$	13.6512	+	7.88153i	0.865110	+	0.499472i
$250$	10.6844	+	4.35320i	0.675740	+	0.275321i
$251$	−3.61413	+	3.61413i	−0.228122	+	0.228122i	−0.811908	−	0.583786i	$-0.801571\pi$
$251$	−3.61413	+	3.61413i	−0.228122	+	0.228122i	0.583786	+	0.811908i	$0.301571\pi$
$252$	−1.12174	−	5.17124i	−0.0706632	−	0.325757i
$253$	2.33150	+	2.33150i	0.146580	+	0.146580i
$254$	−10.3709	+	4.36639i	−0.650727	+	0.273972i
$255$	9.09100	−	15.7461i	0.569301	−	0.986058i
$256$	−15.9828	+	0.742027i	−0.998924	+	0.0463767i
$257$	−2.25333	−	3.90288i	−0.140559	−	0.243455i	0.787148	−	0.616764i	$-0.211557\pi$
$257$	−2.25333	−	3.90288i	−0.140559	−	0.243455i	−0.927707	+	0.373309i	$0.878223\pi$
$258$	1.43707	−	11.4273i	0.0894679	−	0.711433i
$259$	24.5149	−	5.02078i	1.52328	−	0.311976i
$260$	−3.34057	−	0.853704i	−0.207174	−	0.0529445i
$261$	3.61684	+	0.969129i	0.223877	+	0.0599876i
$262$	−1.05725	−	7.68595i	−0.0653174	−	0.474840i
$263$	11.0249	+	6.36525i	0.679827	+	0.392498i	0.799790	−	0.600280i	$-0.204944\pi$
$263$	11.0249	+	6.36525i	0.679827	+	0.392498i	−0.119963	+	0.992778i	$0.538278\pi$
$264$	11.7699	−	1.75835i	0.724388	−	0.108219i
$265$		−	16.3489i		−	1.00431i
$266$	15.4325	+	22.5329i	0.946226	+	1.38158i
$267$	−1.14398	+	1.14398i	−0.0700102	+	0.0700102i
$268$	3.28810	−	5.85084i	0.200853	−	0.357397i
$269$	−6.97083	+	1.86783i	−0.425019	+	0.113884i	−0.464987	−	0.885317i	$-0.653941\pi$
$269$	−6.97083	+	1.86783i	−0.425019	+	0.113884i	0.0399681	+	0.999201i	$0.487274\pi$
$270$	2.24312	−	2.95866i	0.136512	−	0.180058i
$271$	4.42119	+	7.65773i	0.268568	+	0.465174i	0.968492	−	0.249043i	$-0.0801162\pi$
$271$	4.42119	+	7.65773i	0.268568	+	0.465174i	−0.699924	+	0.714217i	$0.746783\pi$
$272$	−24.3053	−	13.2908i	−1.47373	−	0.805870i
$273$	−1.73424	−	0.103809i	−0.104961	−	0.00628282i
$274$	5.73345	+	0.721023i	0.346371	+	0.0435586i
$275$	2.06103	−	7.69188i	0.124285	−	0.463838i
$276$	−0.0181779	−	1.56722i	−0.00109418	−	0.0943355i
$277$	0.587001	+	2.19072i	0.0352694	+	0.131627i	0.981316	−	0.192404i	$-0.0616284\pi$
$277$	0.587001	+	2.19072i	0.0352694	+	0.131627i	−0.946046	+	0.324031i	$0.894962\pi$
$278$	6.75037	−	16.5680i	0.404860	−	0.993680i
$279$			2.30473i			0.137981i
$280$	−3.38753	+	19.3523i	−0.202444	+	1.15652i
$281$			26.8434i			1.60134i	0.599104	+	0.800671i	$0.295524\pi$
$281$			26.8434i			1.60134i	−0.599104	+	0.800671i	$0.704476\pi$
$282$	−9.42697	−	3.84088i	−0.561368	−	0.228721i
$283$	6.35418	+	23.7141i	0.377717	+	1.40966i	0.849334	+	0.527855i	$0.177004\pi$
$283$	6.35418	+	23.7141i	0.377717	+	1.40966i	−0.471617	+	0.881803i	$0.656330\pi$
$284$	12.6884	+	12.3975i	0.752920	+	0.735655i
$285$	−4.95979	+	18.5102i	−0.293793	+	1.09645i
$286$	0.487526	−	3.87673i	0.0288280	−	0.229236i
$287$	4.87735	+	9.75071i	0.287901	+	0.575566i
$288$	−4.58584	−	3.31212i	−0.270223	−	0.195168i
$289$	−15.4810	−	26.8139i	−0.910649	−	1.57729i
$290$	−11.0785	−	8.39921i	−0.650552	−	0.493218i
$291$	−9.57539	+	2.56572i	−0.561319	+	0.150405i
$292$	−6.26550	+	1.75697i	−0.366661	+	0.102819i
$293$	−5.99973	+	5.99973i	−0.350508	+	0.350508i	−0.860299	−	0.509790i	$-0.829723\pi$
$293$	−5.99973	+	5.99973i	−0.350508	+	0.350508i	0.509790	+	0.860299i	$0.329723\pi$
$294$	0.169512	+	9.89804i	0.00988613	+	0.577266i
$295$			9.45895i			0.550722i
$296$	15.9136	−	21.5035i	0.924958	−	1.24986i
$297$	3.64378	+	2.10374i	0.211433	+	0.122071i
$298$	−17.4515	+	2.40057i	−1.01094	+	0.139062i
$299$	−0.497060	−	0.133187i	−0.0287457	−	0.00770239i
$300$	−3.25597	+	1.93053i	−0.187984	+	0.111459i
$301$	−6.81039	+	20.4423i	−0.392544	+	1.17828i
$302$	18.8158	+	2.36622i	1.08273	+	0.136161i
$303$	−0.0525206	−	0.0909684i	−0.00301723	−	0.00522600i
$304$	28.3696	+	6.90051i	1.62711	+	0.395771i
$305$	−15.3345	+	26.5601i	−0.878049	+	1.52083i
$306$	−3.80045	−	9.02667i	−0.217257	−	0.516020i
$307$	1.10116	+	1.10116i	0.0628466	+	0.0628466i	0.737832	−	0.674985i	$-0.235850\pi$
$307$	1.10116	+	1.10116i	0.0628466	+	0.0628466i	−0.674985	+	0.737832i	$0.735850\pi$
$308$	−22.2380	−	1.07246i	−1.26713	−	0.0611090i
$309$	5.93750	−	5.93750i	0.337773	−	0.337773i
$310$	3.22877	−	7.92461i	0.183382	−	0.450088i
$311$	2.45268	+	1.41606i	0.139079	+	0.0802972i	0.567925	−	0.823080i	$-0.307746\pi$
$311$	2.45268	+	1.41606i	0.139079	+	0.0802972i	−0.428846	+	0.903378i	$0.641080\pi$
$312$	−1.45360	+	1.15611i	−0.0822939	+	0.0654520i
$313$	−28.9516	+	16.7152i	−1.63644	+	0.944798i	−0.654393	+	0.756154i	$0.727076\pi$
$313$	−28.9516	+	16.7152i	−1.63644	+	0.944798i	−0.982045	+	0.188644i	$0.939591\pi$
$314$	−12.3551	+	9.59477i	−0.697240	+	0.541464i
$315$	−5.19635	+	4.60939i	−0.292781	+	0.259710i
$316$	15.5422	+	3.97191i	0.874317	+	0.223437i
$317$	−7.27507	+	27.1509i	−0.408609	+	1.52495i	0.388693	+	0.921367i	$0.372927\pi$
$317$	−7.27507	+	27.1509i	−0.408609	+	1.52495i	−0.797302	+	0.603581i	$0.793740\pi$
$318$	−7.01778	−	5.32056i	−0.393537	−	0.298362i
$319$	7.87729	−	13.6439i	0.441043	−	0.763910i
$320$	11.1279	+	17.8129i	0.622071	+	0.995769i
$321$	−16.7766			−0.936379
$322$	−0.539044	+	2.88222i	−0.0300397	+	0.160620i
$323$	35.7444	+	35.7444i	1.98887	+	1.98887i
$324$	−0.540009	−	1.92572i	−0.0300005	−	0.106984i
$325$	0.321662	+	1.20046i	0.0178426	+	0.0665895i
$326$	−1.94205	−	14.1181i	−0.107560	−	0.781932i
$327$	−7.62250	+	4.40086i	−0.421525	+	0.243368i
$328$	10.8440	+	4.27228i	0.598762	+	0.235897i
$329$	15.8941	+	10.4904i	0.876269	+	0.578354i
$330$	−9.58161	−	12.3382i	−0.527450	−	0.679195i
$331$	4.95940	+	1.32887i	0.272593	+	0.0730412i	0.392526	−	0.919741i	$-0.371601\pi$
$331$	4.95940	+	1.32887i	0.272593	+	0.0730412i	−0.119933	+	0.992782i	$0.538268\pi$
$332$	−31.5240	+	0.365642i	−1.73010	+	0.0200672i
$333$	9.13580	−	2.44793i	0.500639	−	0.134146i
$334$	3.41574	+	8.11293i	0.186901	+	0.443920i
$335$	−8.81011			−0.481348
$336$	7.20455	+	7.75206i	0.393040	+	0.422910i
$337$	15.9075			0.866539			0.433270	−	0.901264i	$-0.357360\pi$
$337$	15.9075			0.866539			0.433270	+	0.901264i	$0.357360\pi$
$338$	−6.89731	−	16.3822i	−0.375164	−	0.891075i
$339$	12.7764	−	3.42342i	0.693918	−	0.185935i
$340$	0.421753	+	36.3616i	0.0228727	+	1.97198i
$341$	9.36667	+	2.50979i	0.507234	+	0.135913i
$342$	6.33139	+	8.15290i	0.342363	+	0.440858i
$343$	3.30405	−	18.2232i	0.178402	−	0.983958i
$344$	9.18386	+	21.1246i	0.495160	+	1.13896i
$345$	−1.78177	+	1.02871i	−0.0959274	+	0.0553837i
$346$	3.27581	+	23.8142i	0.176108	+	1.28026i
$347$	1.66234	+	6.20393i	0.0892390	+	0.333044i	0.996083	−	0.0884217i	$-0.0281823\pi$
$347$	1.66234	+	6.20393i	0.0892390	+	0.333044i	−0.906844	+	0.421466i	$0.861516\pi$
$348$	−7.21071	+	2.02202i	−0.386535	+	0.108392i
$349$	−3.02973	−	3.02973i	−0.162178	−	0.162178i	0.621353	−	0.783531i	$-0.286583\pi$
$349$	−3.02973	−	3.02973i	−0.162178	−	0.162178i	−0.783531	+	0.621353i	$0.786583\pi$
$350$	6.67925	−	2.35301i	0.357021	−	0.125774i
$351$	−0.656653			−0.0350496
$352$	−18.4546	+	15.0305i	−0.983636	+	0.801129i
$353$	10.5565	−	18.2845i	0.561868	−	0.973184i	−0.435465	−	0.900205i	$-0.643416\pi$
$353$	10.5565	−	18.2845i	0.561868	−	0.973184i	0.997334	−	0.0729786i	$-0.0232505\pi$
$354$	4.06025	+	3.07830i	0.215800	+	0.163610i
$355$	6.02703	−	22.4932i	0.319881	−	1.19381i
$356$	0.801144	−	3.13490i	0.0424605	−	0.166150i
$357$	3.67635	+	17.9505i	0.194573	+	0.950039i
$358$	−24.5815	+	19.0895i	−1.29917	+	1.00891i
$359$	6.17347	−	3.56425i	0.325823	−	0.188114i	−0.328162	−	0.944621i	$-0.606429\pi$
$359$	6.17347	−	3.56425i	0.325823	−	0.188114i	0.653985	+	0.756507i	$0.273096\pi$
$360$	−0.841025	+	7.37792i	−0.0443259	+	0.388851i
$361$	−29.6858	−	17.1391i	−1.56241	−	0.902057i
$362$	9.42586	−	23.1346i	0.495412	−	1.21593i
$363$	4.73961	−	4.73961i	0.248765	−	0.248765i
$364$	3.08936	−	1.59037i	0.161926	−	0.0833581i
$365$	6.04005	+	6.04005i	0.316151	+	0.316151i
$366$	6.41049	+	15.2260i	0.335082	+	0.795873i
$367$	−17.8522	+	30.9210i	−0.931878	+	1.61406i	−0.151770	+	0.988416i	$0.548497\pi$
$367$	−17.8522	+	30.9210i	−0.931878	+	1.61406i	−0.780108	+	0.625645i	$0.784836\pi$
$368$	1.62987	+	2.67760i	0.0849628	+	0.139580i
$369$	2.06038	+	3.56869i	0.107259	+	0.185778i
$370$	−34.8420	−	4.38164i	−1.81135	−	0.227790i
$371$	10.9332	+	12.3254i	0.567624	+	0.639905i
$372$	−2.35087	−	3.96491i	−0.121887	−	0.205571i
$373$	−15.5327	−	4.16197i	−0.804252	−	0.215499i	−0.166802	−	0.985990i	$-0.553344\pi$
$373$	−15.5327	−	4.16197i	−0.804252	−	0.215499i	−0.637450	+	0.770492i	$0.720011\pi$
$374$	−40.8239	+	5.61561i	−2.11095	+	0.290376i
$375$	−7.06505	−	4.07901i	−0.364838	−	0.210639i
$376$	20.1353	−	3.00810i	1.03840	−	0.155131i
$377$			2.45879i			0.126634i
$378$	0.287493	+	3.73060i	0.0147870	+	0.191881i
$379$	−7.17765	+	7.17765i	−0.368691	+	0.368691i	−0.867000	−	0.498308i	$-0.833955\pi$
$379$	−7.17765	+	7.17765i	−0.368691	+	0.368691i	0.498308	+	0.867000i	$0.333955\pi$
$380$	−10.3483	−	36.9029i	−0.530856	−	1.89308i
$381$	7.68566	−	2.05937i	0.393748	−	0.105504i
$382$	−2.34070	−	1.77461i	−0.119760	−	0.0907968i
$383$	−10.0727	−	17.4464i	−0.514691	−	0.891472i	−0.999855	−	0.0170481i	$-0.994573\pi$
$383$	−10.0727	−	17.4464i	−0.514691	−	0.891472i	0.485163	−	0.874424i	$-0.338760\pi$
$384$	11.2676	+	1.02030i	0.574998	+	0.0520671i
$385$	13.0744	+	26.1380i	0.666331	+	1.33212i
$386$	−2.68859	+	21.3792i	−0.136846	+	1.08817i
$387$	−2.10781	+	7.86647i	−0.107146	+	0.399875i
$388$	13.8558	−	14.1810i	0.703422	−	0.719931i
$389$	−5.70092	−	21.2761i	−0.289048	−	1.07874i	−0.945830	−	0.324662i	$-0.894750\pi$
$389$	−5.70092	−	21.2761i	−0.289048	−	1.07874i	0.656782	−	0.754080i	$-0.271917\pi$
$390$	2.25784	+	0.919926i	0.114330	+	0.0465823i
$391$			5.42723i			0.274467i
$392$	−10.3878	−	16.8551i	−0.524665	−	0.851309i
$393$			5.48597i			0.276730i
$394$	−0.881653	+	2.16391i	−0.0444171	+	0.109016i
$395$	−5.45016	−	20.3403i	−0.274227	−	1.02343i
$396$	−8.41438	+	0.0975972i	−0.422838	+	0.00490444i
$397$	−0.0418980	+	0.156365i	−0.00210280	+	0.00784775i	−0.966969	−	0.254893i	$-0.917960\pi$
$397$	−0.0418980	+	0.156365i	−0.00210280	+	0.00784775i	0.964866	+	0.262741i	$0.0846264\pi$
$398$	−3.76491	−	0.473465i	−0.188718	−	0.0237326i
$399$	−8.63935	−	17.2716i	−0.432508	−	0.864662i
$400$	3.63219	−	6.64232i	0.181609	−	0.332116i
$401$	11.3526	+	19.6632i	0.566920	+	0.981934i	0.996868	+	0.0790803i	$0.0251984\pi$
$401$	11.3526	+	19.6632i	0.566920	+	0.981934i	−0.429949	+	0.902853i	$0.641468\pi$
$402$	−2.86714	+	3.78174i	−0.143000	+	0.188616i
$403$	−1.46184	+	0.391699i	−0.0728195	+	0.0195119i
$404$	0.183143	+	0.102924i	0.00911170	+	0.00512067i
$405$	−1.85643	+	1.85643i	−0.0922466	+	0.0922466i
$406$	13.9689	−	1.07650i	0.693267	−	0.0534256i
$407$		−	39.7946i		−	1.97254i
$408$	15.7454	+	11.6524i	0.779515	+	0.576878i
$409$	−5.01248	−	2.89396i	−0.247851	−	0.143097i	0.370929	−	0.928661i	$-0.379039\pi$
$409$	−5.01248	−	2.89396i	−0.247851	−	0.143097i	−0.618780	+	0.785564i	$0.712373\pi$
$410$	−2.08496	−	15.1571i	−0.102969	−	0.748554i
$411$	−3.94687	−	1.05756i	−0.194685	−	0.0521656i
$412$	−4.15812	+	16.2709i	−0.204856	+	0.801609i
$413$	−6.32559	−	7.13109i	−0.311262	−	0.350898i
$414$	−0.138283	+	1.09960i	−0.00679625	+	0.0540426i
$415$	20.6920	+	35.8397i	1.01573	+	1.75930i
$416$	1.32142	−	3.47160i	0.0647880	−	0.170209i
$417$	−6.32519	+	10.9556i	−0.309746	+	0.536496i
$418$	40.0290	−	16.8532i	1.95788	−	0.824315i
$419$	−10.2098	−	10.2098i	−0.498783	−	0.498783i	0.412276	−	0.911059i	$-0.364734\pi$
$419$	−10.2098	−	10.2098i	−0.498783	−	0.498783i	−0.911059	+	0.412276i	$0.864734\pi$
$420$	4.23779	−	13.2301i	0.206783	−	0.645562i
$421$	10.9230	−	10.9230i	0.532353	−	0.532353i	−0.388919	−	0.921272i	$-0.627151\pi$
$421$	10.9230	−	10.9230i	0.532353	−	0.532353i	0.921272	+	0.388919i	$0.127151\pi$
$422$	−33.6116	−	13.6946i	−1.63619	−	0.666641i
$423$	6.23358	+	3.59896i	0.303087	+	0.174987i
$424$	17.5000	+	1.99486i	0.849876	+	0.0968792i
$425$	11.3513	−	6.55370i	0.550621	−	0.317901i
$426$	−7.69376	−	9.90722i	−0.372764	−	0.480006i
$427$	−6.20118	−	30.2784i	−0.300096	−	1.46527i
$428$	28.8614	−	17.1125i	1.39507	−	0.827163i
$429$	−0.715078	+	2.66871i	−0.0345243	+	0.128846i
$430$	18.2679	−	24.0953i	0.880957	−	1.16198i
$431$	4.76577	−	8.25455i	0.229559	−	0.397608i	−0.728118	−	0.685451i	$-0.759605\pi$
$431$	4.76577	−	8.25455i	0.229559	−	0.397608i	0.957677	+	0.287843i	$0.0929383\pi$
$432$	2.89327	+	2.76206i	0.139203	+	0.132890i
$433$	−15.9767			−0.767793			−0.383896	−	0.923376i	$-0.625418\pi$
$433$	−15.9767			−0.767793			−0.383896	+	0.923376i	$0.625418\pi$
$434$	2.86535	+	8.13356i	0.137541	+	0.390423i
$435$	6.95125	+	6.95125i	0.333287	+	0.333287i
$436$	8.62431	−	15.3461i	0.413029	−	0.734943i
$437$	−1.48047	−	5.52519i	−0.0708205	−	0.264306i
$438$	4.55835	−	0.627032i	0.217806	−	0.0299607i
$439$	−20.0489	+	11.5752i	−0.956879	+	0.552455i	−0.895211	−	0.445642i	$-0.852975\pi$
$439$	−20.0489	+	11.5752i	−0.956879	+	0.552455i	−0.0616682	+	0.998097i	$0.519642\pi$
$440$	29.0688	+	11.4524i	1.38580	+	0.545971i
$441$	0.835030	−	6.95002i	0.0397633	−	0.330953i
$442$	5.07952	−	3.94466i	0.241608	−	0.187628i
$443$	31.7276	+	8.50138i	1.50742	+	0.403913i	0.915579	−	0.402139i	$-0.131733\pi$
$443$	31.7276	+	8.50138i	1.50742	+	0.403913i	0.591845	+	0.806052i	$0.298400\pi$
$444$	−13.2197	+	13.5300i	−0.627379	+	0.642104i
$445$	−4.10269	+	1.09931i	−0.194486	+	0.0521124i
$446$	16.2022	−	6.82150i	0.767195	−	0.323007i
$447$	12.4563			0.589162
$448$	−20.3015	−	5.98737i	−0.959156	−	0.282876i
$449$	−6.22058			−0.293567			−0.146784	−	0.989169i	$-0.546892\pi$
$449$	−6.22058			−0.293567			−0.146784	+	0.989169i	$0.546892\pi$
$450$	2.46687	−	1.03861i	0.116289	−	0.0489606i
$451$	16.7472	−	4.48741i	0.788596	−	0.211304i
$452$	−18.4877	+	18.9216i	−0.869589	+	0.889998i
$453$	−12.9527	−	3.47065i	−0.608569	−	0.163066i
$454$	−2.16484	+	1.68117i	−0.101601	+	0.0789013i
$455$	−3.80678	−	2.51254i	−0.178464	−	0.117790i
$456$	−19.2083	−	7.56757i	−0.899509	−	0.354384i
$457$	−15.1163	+	8.72741i	−0.707112	+	0.408251i	−0.809991	−	0.586443i	$-0.800528\pi$
$457$	−15.1163	+	8.72741i	−0.707112	+	0.408251i	0.102879	+	0.994694i	$0.467195\pi$
$458$	29.3064	−	4.03129i	1.36940	−	0.188370i
$459$	1.79244	+	6.68949i	0.0836641	+	0.312238i
$460$	2.01594	−	3.58717i	0.0939939	−	0.167253i
$461$	−9.58175	−	9.58175i	−0.446267	−	0.446267i	0.447845	−	0.894111i	$-0.352192\pi$
$461$	−9.58175	−	9.58175i	−0.446267	−	0.446267i	−0.894111	+	0.447845i	$0.852192\pi$
$462$	15.4746	+	2.89412i	0.719944	+	0.134647i
$463$	−11.0103			−0.511691			−0.255845	−	0.966718i	$-0.582354\pi$
$463$	−11.0103			−0.511691			−0.255845	+	0.966718i	$0.582354\pi$
$464$	10.3423	−	10.8336i	0.480131	−	0.502939i
$465$	−3.02540	+	5.24015i	−0.140300	+	0.243006i
$466$	4.04872	−	5.34023i	0.187553	−	0.247381i
$467$	1.39029	−	5.18864i	0.0643351	−	0.240102i	−0.926269	−	0.376863i	$-0.877003\pi$
$467$	1.39029	−	5.18864i	0.0643351	−	0.240102i	0.990604	+	0.136761i	$0.0436694\pi$
$468$	1.12966	−	0.669800i	0.0522188	−	0.0309615i
$469$	6.64192	−	5.89168i	0.306695	−	0.272052i
$470$	−16.3917	−	21.1075i	−0.756093	−	0.973617i
$471$	9.57945	−	5.53070i	0.441398	−	0.254841i
$472$	−10.1249	−	1.15416i	−0.466038	−	0.0531246i
$473$	29.6748	+	17.1328i	1.36445	+	0.787765i
$474$	−10.5047	−	4.28001i	−0.482499	−	0.196587i
$475$	−9.76848	+	9.76848i	−0.448209	+	0.448209i
$476$	−24.6344	−	27.1309i	−1.12912	−	1.24354i
$477$	4.40334	+	4.40334i	0.201615	+	0.201615i
$478$	−25.9168	+	10.9116i	−1.18541	+	0.499085i
$479$	15.8571	−	27.4653i	0.724529	−	1.25492i	−0.234639	−	0.972083i	$-0.575391\pi$
$479$	15.8571	−	27.4653i	0.724529	−	1.25492i	0.959168	−	0.282838i	$-0.0912759\pi$
$480$	−6.07879	−	13.5504i	−0.277458	−	0.618487i
$481$	3.10534	+	5.37860i	0.141591	+	0.245243i
$482$	0.989888	−	7.87142i	0.0450882	−	0.358533i
$483$	0.655337	−	1.96708i	0.0298188	−	0.0895054i
$484$	−3.31922	+	12.9882i	−0.150874	+	0.590374i
$485$	−25.1391	−	6.73599i	−1.14151	−	0.305866i
$486$	0.192720	+	1.40102i	0.00874195	+	0.0635516i
$487$	−23.6810	−	13.6722i	−1.07309	−	0.619547i	−0.144064	−	0.989568i	$-0.546017\pi$
$487$	−23.6810	−	13.6722i	−1.07309	−	0.619547i	−0.929023	+	0.370022i	$0.879350\pi$
$488$	−26.5590	−	19.6549i	−1.20227	−	0.889736i
$489$			10.0770i			0.455700i
$490$	−12.6077	+	22.7272i	−0.569556	+	1.02671i
$491$	−20.8500	+	20.8500i	−0.940948	+	0.940948i	−0.998351	−	0.0574027i	$-0.981718\pi$
$491$	−20.8500	+	20.8500i	−0.940948	+	0.940948i	0.0574027	+	0.998351i	$0.481718\pi$
$492$	−7.18469	−	4.03771i	−0.323911	−	0.182034i
$493$	25.0483	−	6.71167i	1.12812	−	0.302278i
$494$	−4.09516	+	5.40149i	−0.184250	+	0.243024i
$495$	5.52311	+	9.56631i	0.248245	+	0.429974i
$496$	8.08859	+	4.42304i	0.363188	+	0.198600i
$497$	10.4983	+	20.9881i	0.470915	+	0.941444i
$498$	22.1181	+	2.78151i	0.991137	+	0.124643i
$499$	3.22141	−	12.0225i	0.144210	−	0.538200i	−0.855579	−	0.517672i	$-0.826799\pi$
$499$	3.22141	−	12.0225i	0.144210	−	0.538200i	0.999789	−	0.0205278i	$-0.00653466\pi$
$500$	16.3149	−	0.189235i	0.729626	−	0.00846283i
$501$	−1.61100	−	6.01234i	−0.0719742	−	0.268611i
$502$	−2.72736	+	6.69397i	−0.121728	+	0.298766i
$503$			16.2397i			0.724090i	0.932161	+	0.362045i	$0.117921\pi$
$503$			16.2397i			0.724090i	−0.932161	+	0.362045i	$0.882079\pi$
$504$	−4.29987	−	6.12463i	−0.191531	−	0.272813i
$505$		−	0.275774i		−	0.0122718i
$506$	4.31832	+	1.75944i	0.191973	+	0.0782166i
$507$	3.25305	+	12.1405i	0.144473	+	0.539180i
$508$	−11.1213	+	11.3823i	−0.493429	+	0.505009i
$509$	10.1757	−	37.9760i	0.451028	−	1.68326i	−0.248483	−	0.968636i	$-0.579932\pi$
$509$	10.1757	−	37.9760i	0.451028	−	1.68326i	0.699510	−	0.714622i	$-0.253401\pi$
$510$	3.20836	−	25.5123i	0.142068	−	1.12970i
$511$	−8.59281	−	0.514355i	−0.380124	−	0.0227537i
$512$	−20.4248	+	9.73794i	−0.902657	+	0.430360i
$513$	−3.64959	−	6.32128i	−0.161134	−	0.279091i
$514$	−5.07876	−	3.85048i	−0.224014	−	0.169837i
$515$	21.2939	−	5.70568i	0.938321	−	0.251422i
$516$	−4.39782	−	15.6830i	−0.193603	−	0.690405i
$517$	21.4148	−	21.4148i	0.941820	−	0.941820i
$518$	29.1975	−	19.9970i	1.28286	−	0.878616i
$519$		−	16.9978i		−	0.746119i
$520$	−4.82259	+	0.720466i	−0.211485	+	0.0315945i
$521$	−0.721359	−	0.416477i	−0.0316033	−	0.0182462i	0.484115	−	0.875004i	$-0.339142\pi$
$521$	−0.721359	−	0.416477i	−0.0316033	−	0.0182462i	−0.515718	+	0.856758i	$0.672475\pi$
$522$	5.24602	−	0.721626i	0.229612	−	0.0315847i
$523$	19.1948	+	5.14324i	0.839331	+	0.224898i	0.652780	−	0.757547i	$-0.273602\pi$
$523$	19.1948	+	5.14324i	0.839331	+	0.224898i	0.186551	+	0.982445i	$0.440269\pi$
$524$	−5.59580	−	9.43771i	−0.244454	−	0.412288i
$525$	−4.90562	+	1.00470i	−0.214099	+	0.0438486i
$526$	17.8630	+	2.24640i	0.778862	+	0.0979475i
$527$	7.98067	+	13.8229i	0.347643	+	0.602136i
$528$	14.3760	−	8.75074i	0.625635	−	0.380827i
$529$	−11.1929	+	19.3867i	−0.486649	+	0.842902i
$530$	−8.97171	−	21.3093i	−0.389706	−	0.925615i
$531$	−2.54762	−	2.54762i	−0.110557	−	0.110557i
$532$	32.4800	+	20.9007i	1.40819	+	0.906159i
$533$	−1.91337	+	1.91337i	−0.0828773	+	0.0828773i
$534$	−0.863289	+	2.11884i	−0.0373582	+	0.0916910i
$535$	−38.1441	−	22.0225i	−1.64911	−	0.952116i
$536$	1.07499	−	9.43040i	0.0464325	−	0.407331i
$537$	19.0590	−	11.0037i	0.822458	−	0.474846i
$538$	−8.06080	+	6.25987i	−0.347526	+	0.269882i
$539$	−27.3363	−	10.9620i	−1.17746	−	0.472168i
$540$	1.30008	−	5.08727i	0.0559467	−	0.218921i
$541$	9.84979	−	36.7599i	0.423475	−	1.58043i	−0.343754	−	0.939060i	$-0.611699\pi$
$541$	9.84979	−	36.7599i	0.423475	−	1.58043i	0.767230	−	0.641372i	$-0.221635\pi$
$542$	9.96488	+	7.55491i	0.428028	+	0.324511i
$543$	−8.83216	+	15.2978i	−0.379024	+	0.656490i
$544$	−38.9731	−	3.98532i	−1.67096	−	0.170869i
$545$	−23.1079			−0.989832
$546$	−2.31738	+	0.816382i	−0.0991745	+	0.0349379i
$547$	13.3312	+	13.3312i	0.570002	+	0.570002i	0.932129	−	0.362127i	$-0.117949\pi$
$547$	13.3312	+	13.3312i	0.570002	+	0.570002i	−0.362127	+	0.932129i	$0.617949\pi$
$548$	7.86867	−	2.20653i	0.336133	−	0.0942583i
$549$	−3.02345	−	11.2837i	−0.129037	−	0.481574i
$550$	−1.53467	−	11.1566i	−0.0654385	−	0.475720i
$551$	−23.6696	+	13.6656i	−1.00836	+	0.582176i
$552$	−0.883726	−	2.03274i	−0.0376139	−	0.0865192i
$553$	17.7112	+	11.6898i	0.753159	+	0.497099i
$554$	1.96728	+	2.53326i	0.0835819	+	0.107628i
$555$	23.9850	+	6.42675i	1.01811	+	0.272801i
$556$	−0.293440	−	25.2991i	−0.0124446	−	1.07292i
$557$	−2.89338	+	0.775280i	−0.122597	+	0.0328496i	−0.319596	−	0.947554i	$-0.603547\pi$
$557$	−2.89338	+	0.775280i	−0.122597	+	0.0328496i	0.196999	+	0.980404i	$0.436880\pi$
$558$	1.26475	+	3.00399i	0.0535413	+	0.127169i
$559$	−5.34776			−0.226186
$560$	6.20454	+	27.0828i	0.262190	+	1.14446i
$561$	29.1387			1.23024
$562$	14.7307	+	34.9877i	0.621376	+	1.47587i
$563$	−12.8042	+	3.43086i	−0.539631	+	0.144594i	−0.518332	−	0.855179i	$-0.673447\pi$
$563$	−12.8042	+	3.43086i	−0.539631	+	0.144594i	−0.0212989	+	0.999773i	$0.506780\pi$
$564$	−14.3949	+	0.166964i	−0.606133	+	0.00703045i
$565$	33.5429	+	8.98780i	1.41116	+	0.378119i
$566$	21.2955	+	27.4221i	0.895117	+	1.15264i
$567$	0.158088	−	2.64102i	0.00663908	−	0.110913i
$568$	23.3414	+	9.19594i	0.979385	+	0.385853i
$569$	−1.63427	+	0.943548i	−0.0685123	+	0.0395556i	−0.533865	−	0.845570i	$-0.679261\pi$
$569$	−1.63427	+	0.943548i	−0.0685123	+	0.0395556i	0.465353	+	0.885125i	$0.345928\pi$
$570$	3.69312	+	26.8480i	0.154688	+	1.12454i
$571$	2.39453	+	8.93652i	0.100208	+	0.373982i	0.997758	−	0.0669322i	$-0.0213211\pi$
$571$	2.39453	+	8.93652i	0.100208	+	0.373982i	−0.897549	+	0.440914i	$0.854654\pi$
$572$	−1.49196	−	5.32047i	−0.0623821	−	0.222460i
$573$	1.46868	+	1.46868i	0.0613550	+	0.0613550i
$574$	11.7080	+	10.0326i	0.488682	+	0.418752i
$575$	−1.48319			−0.0618532
$576$	−7.79476	−	1.80048i	−0.324782	−	0.0750199i
$577$	0.830887	−	1.43914i	0.0345903	−	0.0599121i	−0.848212	−	0.529657i	$-0.822321\pi$
$577$	0.830887	−	1.43914i	0.0345903	−	0.0599121i	0.882802	+	0.469745i	$0.155654\pi$
$578$	−34.8926	−	26.4539i	−1.45134	−	1.10034i
$579$	3.94348	−	14.7173i	0.163886	−	0.611629i
$580$	−19.0489	−	4.86807i	−0.790963	−	0.202135i
$581$	−39.5671	−	13.1818i	−1.64152	−	0.546875i
$582$	−11.0726	+	8.59879i	−0.458975	+	0.356431i
$583$	22.6907	−	13.1005i	0.939755	−	0.542568i
$584$	−7.20231	+	5.72832i	−0.298034	+	0.237039i
$585$	−1.49300	−	0.861983i	−0.0617279	−	0.0356386i
$586$	−4.52763	+	11.1125i	−0.187035	+	0.459053i
$587$	−23.5964	+	23.5964i	−0.973929	+	0.973929i	−0.999669	−	0.0257400i	$-0.991806\pi$
$587$	−23.5964	+	23.5964i	−0.973929	+	0.973929i	0.0257400	+	0.999669i	$0.491806\pi$
$588$	5.65263	+	12.8081i	0.233111	+	0.528198i
$589$	−11.8954	−	11.8954i	−0.490142	−	0.490142i
$590$	5.19073	+	12.3288i	0.213699	+	0.507570i
$591$	0.826121	−	1.43088i	0.0339821	−	0.0588587i
$592$	8.94148	−	36.7605i	0.367493	−	1.51085i
$593$	−22.9723	−	39.7892i	−0.943359	−	1.63395i	−0.759004	−	0.651086i	$-0.774314\pi$
$593$	−22.9723	−	39.7892i	−0.943359	−	1.63395i	−0.184355	−	0.982860i	$-0.559020\pi$
$594$	5.90376	+	0.742441i	0.242234	+	0.0304627i
$595$	−15.2047	+	45.6390i	−0.623331	+	1.87101i
$596$	−21.4290	+	12.7057i	−0.877766	+	0.520445i
$597$	2.59174	+	0.694454i	0.106073	+	0.0284221i
$598$	−0.720957	+	0.0991725i	−0.0294821	+	0.00405547i
$599$	−16.6882	−	9.63496i	−0.681863	−	0.393674i	0.118694	−	0.992931i	$-0.462129\pi$
$599$	−16.6882	−	9.63496i	−0.681863	−	0.393674i	−0.800557	+	0.599257i	$0.795463\pi$
$600$	−3.18444	+	4.30302i	−0.130004	+	0.175670i
$601$			11.6641i			0.475791i	0.971291	+	0.237895i	$0.0764575\pi$
$601$			11.6641i			0.475791i	−0.971291	+	0.237895i	$0.923542\pi$
$602$	2.34133	+	30.3819i	0.0954256	+	1.23827i
$603$	2.37287	−	2.37287i	0.0966306	−	0.0966306i
$604$	25.8231	−	7.24129i	1.05073	−	0.294644i
$605$	16.9978	−	4.55456i	0.691061	−	0.185169i
$606$	−0.118376	−	0.0897470i	−0.00480869	−	0.00364572i
$607$	−12.6403	−	21.8936i	−0.513053	−	0.888633i	−0.999885	−	0.0151381i	$-0.995181\pi$
$607$	−12.6403	−	21.8936i	−0.513053	−	0.888633i	0.486833	−	0.873495i	$-0.338152\pi$
$608$	40.7637	−	6.57406i	1.65319	−	0.266613i
$609$	−9.88912	−	0.591950i	−0.400727	−	0.0239870i
$610$	−5.41177	+	43.0335i	−0.219116	+	1.74237i
$611$	−1.22332	+	4.56548i	−0.0494901	+	0.184700i
$612$	−9.90702	−	9.67984i	−0.400468	−	0.391284i
$613$	−8.35333	−	31.1751i	−0.337388	−	1.25915i	−0.901257	−	0.433285i	$-0.857354\pi$
$613$	−8.35333	−	31.1751i	−0.337388	−	1.25915i	0.563869	−	0.825864i	$-0.309312\pi$
$614$	2.03953	+	0.830979i	0.0823089	+	0.0335356i
$615$			10.8186i			0.436248i
$616$	−29.5736	+	10.8056i	−1.19155	+	0.435369i
$617$		−	30.8976i		−	1.24389i	−0.783061	−	0.621944i	$-0.786343\pi$
$617$		−	30.8976i		−	1.24389i	0.783061	−	0.621944i	$-0.213657\pi$
$618$	4.48067	−	10.9972i	0.180239	−	0.442374i
$619$	−6.35015	−	23.6991i	−0.255234	−	0.952546i	−0.967960	−	0.251104i	$-0.919206\pi$
$619$	−6.35015	−	23.6991i	−0.255234	−	0.952546i	0.712726	−	0.701442i	$-0.247460\pi$
$620$	−0.140355	−	12.1008i	−0.00563681	−	0.485980i
$621$	0.202827	−	0.756959i	0.00813915	−	0.0303757i
$622$	3.97391	+	0.499748i	0.159339	+	0.0200381i
$623$	2.35785	−	3.57240i	0.0944654	−	0.143125i
$624$	−1.26019	+	2.30456i	−0.0504481	+	0.0922564i
$625$	−15.4406	−	26.7438i	−0.617622	−	1.06975i
$626$	−28.5628	+	37.6742i	−1.14160	+	1.50576i
$627$	−29.6647	+	7.94863i	−1.18469	+	0.317438i
$628$	−10.8384	+	19.2859i	−0.432501	+	0.769591i
$629$	46.3166	−	46.3166i	1.84676	−	1.84676i
$630$	−4.24346	+	8.85945i	−0.169064	+	0.352969i
$631$		−	42.8629i		−	1.70635i	−0.521628	−	0.853173i	$-0.674675\pi$
$631$		−	42.8629i		−	1.70635i	0.521628	−	0.853173i	$-0.325325\pi$
$632$	22.4374	−	3.35201i	0.892511	−	0.133336i
$633$	22.2257	+	12.8320i	0.883391	+	0.510026i
$634$	5.41711	+	39.3809i	0.215141	+	1.56401i
$635$	20.1778	+	5.40662i	0.800731	+	0.214555i
$636$	−12.0667	−	3.08372i	−0.478477	−	0.122278i
$637$	4.55016	−	0.651544i	0.180284	−	0.0258151i
$638$	2.78002	−	22.1062i	0.110062	−	0.875193i
$639$	4.43490	+	7.68148i	0.175442	+	0.303875i
$640$	24.2792	+	17.1107i	0.959721	+	0.676360i
$641$	−15.8523	+	27.4570i	−0.626130	+	1.08449i	0.362192	+	0.932104i	$0.382029\pi$
$641$	−15.8523	+	27.4570i	−0.626130	+	1.08449i	−0.988321	+	0.152385i	$0.951305\pi$
$642$	−21.8667	+	9.20639i	−0.863008	+	0.363347i
$643$	10.9317	+	10.9317i	0.431104	+	0.431104i	0.889004	−	0.457900i	$-0.151398\pi$
$643$	10.9317	+	10.9317i	0.431104	+	0.431104i	−0.457900	+	0.889004i	$0.651398\pi$
$644$	0.879068	+	4.05250i	0.0346401	+	0.159691i
$645$	−15.1187	+	15.1187i	−0.595297	+	0.595297i
$646$	66.2047	+	26.9741i	2.60479	+	1.06128i
$647$	10.6314	+	6.13802i	0.417962	+	0.241311i	0.694205	−	0.719777i	$-0.255756\pi$
$647$	10.6314	+	6.13802i	0.417962	+	0.241311i	−0.276243	+	0.961088i	$0.589089\pi$
$648$	−1.76061	−	2.21365i	−0.0691634	−	0.0869603i
$649$	−13.1281	+	7.57952i	−0.515323	+	0.297522i
$650$	1.07802	+	1.38816i	0.0422836	+	0.0544483i
$651$	−1.22346	−	5.97375i	−0.0479511	−	0.234130i
$652$	−10.2788	−	17.3359i	−0.402549	−	0.678926i
$653$	4.45807	−	16.6378i	0.174458	−	0.651086i	−0.822185	−	0.569220i	$-0.807245\pi$
$653$	4.45807	−	16.6378i	0.174458	−	0.651086i	0.996643	−	0.0818660i	$-0.0260879\pi$
$654$	−7.52016	+	9.91904i	−0.294062	+	0.387865i
$655$	−7.20138	+	12.4732i	−0.281381	+	0.487367i
$656$	16.4786	−	0.382318i	0.643382	−	0.0149270i
$657$	−3.25359			−0.126935
$658$	26.4731	+	4.95111i	1.03203	+	0.193014i
$659$	23.2582	+	23.2582i	0.906010	+	0.906010i	0.995947	−	0.0899379i	$-0.0286668\pi$
$659$	23.2582	+	23.2582i	0.906010	+	0.906010i	−0.0899379	+	0.995947i	$0.528667\pi$
$660$	−19.2595	−	10.8236i	−0.749673	−	0.421307i
$661$	2.60071	+	9.70597i	0.101156	+	0.377519i	0.997881	−	0.0650697i	$-0.0207270\pi$
$661$	2.60071	+	9.70597i	0.101156	+	0.377519i	−0.896725	+	0.442588i	$0.854060\pi$
$662$	7.19333	−	0.989492i	0.279577	−	0.0384577i
$663$	−3.93836	+	2.27381i	−0.152953	+	0.0883077i
$664$	−40.8878	+	17.7758i	−1.58675	+	0.689835i
$665$	3.02947	−	50.6104i	0.117478	−	1.96259i
$666$	10.5643	−	8.20404i	0.409358	−	0.317900i
$667$	−2.83438	−	0.759470i	−0.109748	−	0.0294068i
$668$	8.90417	+	8.69998i	0.344513	+	0.336612i
$669$	−12.0071	+	3.21729i	−0.464221	+	0.124388i
$670$	−11.4831	+	4.83467i	−0.443631	+	0.186780i
$671$	−49.1504			−1.89743
$672$	13.6445	+	6.15046i	0.526347	+	0.237259i
$673$	−9.60036			−0.370067			−0.185033	−	0.982732i	$-0.559239\pi$
$673$	−9.60036			−0.370067			−0.185033	+	0.982732i	$0.559239\pi$
$674$	20.7339	−	8.72949i	0.798641	−	0.336247i
$675$	−1.82815	+	0.489850i	−0.0703654	+	0.0188544i
$676$	−17.9799	−	17.5676i	−0.691536	−	0.675678i
$677$	23.5924	+	6.32156i	0.906729	+	0.242957i	0.681904	−	0.731442i	$-0.261152\pi$
$677$	23.5924	+	6.32156i	0.906729	+	0.242957i	0.224825	+	0.974399i	$0.427819\pi$
$678$	14.7741	−	11.4733i	0.567397	−	0.440630i
$679$	23.4569	−	11.7333i	0.900194	−	0.450281i
$680$	20.5036	+	47.1623i	0.786278	+	1.80859i
$681$	1.67849	−	0.969075i	0.0643198	−	0.0371350i
$682$	13.5858	−	1.86882i	0.520228	−	0.0715609i
$683$	−10.3945	−	38.7928i	−0.397734	−	1.48436i	−0.817073	−	0.576534i	$-0.804405\pi$
$683$	−10.3945	−	38.7928i	−0.397734	−	1.48436i	0.419339	−	0.907830i	$-0.362262\pi$
$684$	12.7264	+	7.15207i	0.486605	+	0.273466i
$685$	−7.58554	−	7.58554i	−0.289829	−	0.289829i
$686$	−5.69370	−	25.5652i	−0.217386	−	0.976086i
$687$	−20.9179			−0.798067
$688$	23.5627	+	22.4941i	0.898320	+	0.857581i
$689$	−2.04458	+	3.54131i	−0.0778921	+	0.134913i
$690$	−1.75785	+	2.31859i	−0.0669202	+	0.0882673i
$691$	9.22738	−	34.4370i	0.351026	−	1.31005i	−0.534386	−	0.845240i	$-0.679457\pi$
$691$	9.22738	−	34.4370i	0.351026	−	1.31005i	0.885412	−	0.464806i	$-0.153876\pi$
$692$	17.3381	+	29.2419i	0.659095	+	1.11161i
$693$	−10.5612	−	3.51849i	−0.401189	−	0.133657i
$694$	5.57119	+	7.17399i	0.211479	+	0.272321i
$695$	−28.7625	+	16.6061i	−1.09103	+	0.629904i
$696$	−8.28885	+	6.59249i	−0.314188	+	0.249888i
$697$	24.7148	+	14.2691i	0.936141	+	0.540481i
$698$	−5.61157	−	2.28635i	−0.212401	−	0.0865397i
$699$	−3.35075	+	3.35075i	−0.126737	+	0.126737i
$700$	7.41450	−	6.73225i	0.280242	−	0.254455i
$701$	6.04749	+	6.04749i	0.228411	+	0.228411i	0.812028	−	0.583618i	$-0.198363\pi$
$701$	6.04749	+	6.04749i	0.228411	+	0.228411i	−0.583618	+	0.812028i	$0.698363\pi$
$702$	−0.855884	+	0.360348i	−0.0323032	+	0.0136004i
$703$	−34.5181	+	59.7872i	−1.30188	+	2.25492i
$704$	−15.8056	+	29.7181i	−0.595697	+	1.12004i
$705$	9.44865	+	16.3655i	0.355857	+	0.616362i
$706$	3.72557	−	29.6251i	0.140214	−	1.11495i
$707$	0.184421	+	0.207905i	0.00693587	+	0.00781908i
$708$	6.98140	+	1.78414i	0.262377	+	0.0670521i
$709$	−10.9946	−	2.94600i	−0.412912	−	0.110639i	0.0463818	−	0.998924i	$-0.485231\pi$
$709$	−10.9946	−	2.94600i	−0.412912	−	0.110639i	−0.459294	+	0.888284i	$0.651898\pi$
$710$	−4.48780	−	32.6251i	−0.168424	−	1.22440i
$711$	6.94626	+	4.01043i	0.260505	+	0.150403i
$712$	−0.676110	−	4.52568i	−0.0253383	−	0.169607i
$713$		−	1.80613i		−	0.0676401i
$714$	14.6423	+	21.3792i	0.547976	+	0.800097i
$715$	−5.12903	+	5.12903i	−0.191815	+	0.191815i
$716$	−21.5639	+	38.3707i	−0.805880	+	1.43398i
$717$	19.2064	−	5.14635i	0.717278	−	0.192194i
$718$	6.09058	−	8.03343i	0.227298	−	0.299805i
$719$	16.7990	+	29.0968i	0.626499	+	1.08513i	0.988249	+	0.152852i	$0.0488459\pi$
$719$	16.7990	+	29.0968i	0.626499	+	1.08513i	−0.361750	+	0.932275i	$0.617821\pi$
$720$	2.95254	+	10.0779i	0.110035	+	0.375582i
$721$	−12.2378	+	18.5416i	−0.455760	+	0.690525i
$722$	−48.0978	−	6.04865i	−1.79001	−	0.225107i
$723$	−1.45192	+	5.41862i	−0.0539973	+	0.201521i
$724$	−0.409744	−	35.3263i	−0.0152280	−	1.31289i
$725$	1.83421	+	6.84536i	0.0681208	+	0.254230i
$726$	3.57669	−	8.77854i	0.132743	−	0.325802i
$727$			8.60124i			0.319002i	0.987198	+	0.159501i	$0.0509886\pi$
$727$			8.60124i			0.319002i	−0.987198	+	0.159501i	$0.949011\pi$
$728$	3.15394	−	3.76822i	0.116893	−	0.139660i
$729$		−	1.00000i		−	0.0370370i
$730$	11.1872	+	4.55806i	0.414056	+	0.168701i
$731$	14.5976	+	54.4790i	0.539912	+	2.01498i
$732$	16.7109	+	16.3277i	0.617653	+	0.603489i
$733$	−4.51590	+	16.8536i	−0.166799	+	0.622500i	0.831005	+	0.556264i	$0.187766\pi$
$733$	−4.51590	+	16.8536i	−0.166799	+	0.622500i	−0.997804	+	0.0662362i	$0.978901\pi$
$734$	−6.30033	+	50.0991i	−0.232549	+	1.84919i
$735$	11.0218	−	14.7058i	0.406545	−	0.542430i
$736$	3.59375	+	2.59558i	0.132467	+	0.0956743i
$737$	−7.05959	−	12.2276i	−0.260043	−	0.450408i
$738$	4.64387	+	3.52077i	0.170943	+	0.129601i
$739$	−32.1172	+	8.60578i	−1.18145	+	0.316569i	−0.795502	−	0.605951i	$-0.792793\pi$
$739$	−32.1172	+	8.60578i	−1.18145	+	0.316569i	−0.385949	+	0.922520i	$0.626126\pi$
$740$	−47.8176	+	13.4090i	−1.75781	+	0.492925i
$741$	3.38919	−	3.38919i	0.124505	−	0.124505i
$742$	21.0141	+	10.0653i	0.771453	+	0.369507i
$743$		−	5.27029i		−	0.193348i	−0.995316	−	0.0966741i	$-0.969180\pi$
$743$		−	5.27029i		−	0.193348i	0.995316	−	0.0966741i	$-0.0308205\pi$
$744$	−5.23994	−	3.87780i	−0.192105	−	0.142167i
$745$	28.3212	+	16.3513i	1.03761	+	0.599064i
$746$	−22.5293	+	3.09906i	−0.824856	+	0.113465i
$747$	−15.2259	−	4.07978i	−0.557088	−	0.149271i
$748$	−50.1284	+	29.7221i	−1.83287	+	1.08675i
$749$	43.4841	−	8.90579i	1.58887	−	0.325410i
$750$	−11.4470	−	1.43955i	−0.417986	−	0.0525648i
$751$	−23.2297	−	40.2351i	−0.847666	−	1.46820i	−0.883286	−	0.468834i	$-0.844674\pi$
$751$	−23.2297	−	40.2351i	−0.847666	−	1.46820i	0.0356206	−	0.999365i	$-0.488659\pi$
$752$	24.5937	−	14.9703i	0.896840	−	0.545911i
$753$	2.55557	−	4.42639i	0.0931303	−	0.161306i
$754$	1.34930	+	3.20479i	0.0491384	+	0.116712i
$755$	−24.8939	−	24.8939i	−0.905982	−	0.905982i
$756$	2.42194	+	4.70470i	0.0880849	+	0.171108i
$757$	−31.9203	+	31.9203i	−1.16016	+	1.16016i	−0.175724	+	0.984440i	$0.556226\pi$
$757$	−31.9203	+	31.9203i	−1.16016	+	1.16016i	−0.984440	+	0.175724i	$0.943774\pi$
$758$	−5.41654	+	13.2942i	−0.196737	+	0.482868i
$759$	−2.85549	−	1.64862i	−0.103648	−	0.0598410i
$760$	−33.7389	−	42.4205i	−1.22384	−	1.53875i
$761$	12.3398	−	7.12441i	0.447319	−	0.258260i	−0.259378	−	0.965776i	$-0.583518\pi$
$761$	12.3398	−	7.12441i	0.447319	−	0.258260i	0.706697	+	0.707516i	$0.250184\pi$
$762$	8.88740	−	6.90179i	0.321956	−	0.250026i
$763$	17.4210	−	15.4532i	0.630682	−	0.559442i
$764$	−4.02471	−	1.02854i	−0.145609	−	0.0372112i
$765$	−4.70585	+	17.5625i	−0.170140	+	0.634972i
$766$	−22.7028	−	17.2122i	−0.820285	−	0.621902i
$767$	1.18292	−	2.04888i	0.0427129	−	0.0739809i
$768$	15.2461	−	4.85339i	0.550147	−	0.175132i
$769$	5.56732			0.200763			0.100381	−	0.994949i	$-0.467994\pi$
$769$	5.56732			0.200763			0.100381	+	0.994949i	$0.467994\pi$
$770$	31.3847	+	26.8936i	1.13103	+	0.969178i
$771$	3.18669	+	3.18669i	0.114766	+	0.114766i
$772$	8.22782	+	29.3411i	0.296126	+	1.05601i
$773$	6.12004	+	22.8403i	0.220122	+	0.821508i	0.984300	+	0.176503i	$0.0564784\pi$
$773$	6.12004	+	22.8403i	0.220122	+	0.821508i	−0.764178	+	0.645006i	$0.776855\pi$
$774$	1.56950	+	11.4099i	0.0564147	+	0.410119i
$775$	−3.77762	+	2.18101i	−0.135696	+	0.0783442i
$776$	10.2777	−	26.0871i	0.368947	−	0.936473i
$777$	−22.3801	+	11.1946i	−0.802880	+	0.401604i
$778$	−19.1062	−	24.6029i	−0.684989	−	0.882056i
$779$	−29.0534	−	7.78482i	−1.04094	−	0.278920i
$780$	3.44770	−	0.0399894i	0.123447	−	0.00143185i
$781$	36.0478	−	9.65899i	1.28989	−	0.345626i
$782$	2.97827	+	7.07386i	0.106503	+	0.252961i
$783$	−3.74443			−0.133815
$784$	−22.7890	−	16.2685i	−0.813892	−	0.581016i
$785$	29.0404			1.03650
$786$	3.01050	+	7.15042i	0.107381	+	0.255047i
$787$	30.5705	−	8.19135i	1.08972	−	0.291990i	0.331149	−	0.943578i	$-0.392564\pi$
$787$	30.5705	−	8.19135i	1.08972	−	0.291990i	0.758573	+	0.651588i	$0.225897\pi$
$788$	0.0383257	+	3.30426i	0.00136530	+	0.117710i
$789$	−12.2967	−	3.29490i	−0.437775	−	0.117301i
$790$	−18.2658	−	23.5207i	−0.649867	−	0.836830i
$791$	−31.2984	+	15.6556i	−1.11284	+	0.556650i
$792$	−10.9138	+	4.74472i	−0.387804	+	0.168596i
$793$	6.64313	−	3.83541i	0.235904	−	0.136199i
$794$	0.0311978	+	0.226799i	0.00110717	+	0.00804880i
$795$	4.23142	+	15.7919i	0.150073	+	0.560080i
$796$	−5.16702	+	1.44893i	−0.183140	+	0.0513560i
$797$	15.9413	+	15.9413i	0.564670	+	0.564670i	0.930630	−	0.365960i	$-0.119259\pi$
$797$	15.9413	+	15.9413i	0.564670	+	0.564670i	−0.365960	+	0.930630i	$0.619259\pi$
$798$	−20.7386	−	17.7709i	−0.734138	−	0.629083i
$799$	49.8489			1.76353
$800$	1.08913	−	10.6508i	0.0385067	−	0.376564i
$801$	0.808914	−	1.40108i	0.0285816	−	0.0495047i
$802$	25.5874	+	19.3992i	0.903523	+	0.685010i
$803$	−3.54308	+	13.2229i	−0.125032	+	0.466627i
$804$	−1.66175	+	6.50250i	−0.0586056	+	0.229326i
$805$	4.07218	−	3.61220i	0.143525	−	0.127313i
$806$	−1.69042	+	1.31275i	−0.0595424	+	0.0462396i
$807$	6.24988	−	3.60837i	0.220006	−	0.127021i
$808$	0.295190	+	0.0336493i	0.0103847	+	0.00118378i
$809$	35.5172	+	20.5059i	1.24872	+	0.720948i	0.970854	−	0.239672i	$-0.0770398\pi$
$809$	35.5172	+	20.5059i	1.24872	+	0.720948i	0.277865	+	0.960620i	$0.410373\pi$
$810$	−1.40093	+	3.43841i	−0.0492237	+	0.120813i
$811$	4.33071	−	4.33071i	0.152072	−	0.152072i	−0.626971	−	0.779043i	$-0.715705\pi$
$811$	4.33071	−	4.33071i	0.152072	−	0.152072i	0.779043	+	0.626971i	$0.215705\pi$
$812$	17.6164	−	9.06876i	0.618215	−	0.318251i
$813$	−6.25251	−	6.25251i	−0.219285	−	0.219285i
$814$	−21.8378	−	51.8684i	−0.765416	−	1.81799i
$815$	−13.2281	+	22.9117i	−0.463358	+	0.802560i
$816$	26.9170	+	6.54720i	0.942285	+	0.229198i
$817$	−29.7222	−	51.4803i	−1.03985	−	1.80107i
$818$	−8.12138	−	1.02132i	−0.283958	−	0.0357097i
$819$	1.70201	−	0.348582i	0.0594731	−	0.0121804i
$820$	−11.0352	−	18.6116i	−0.385365	−	0.649946i
$821$	46.8699	+	12.5588i	1.63577	+	0.438304i	0.955580	−	0.294731i	$-0.0952302\pi$
$821$	46.8699	+	12.5588i	1.63577	+	0.438304i	0.680191	+	0.733035i	$0.261897\pi$
$822$	−5.72471	+	0.787472i	−0.199672	+	0.0274662i
$823$	7.74752	+	4.47303i	0.270062	+	0.155920i	0.628916	−	0.777474i	$-0.283499\pi$
$823$	7.74752	+	4.47303i	0.270062	+	0.155920i	−0.358854	+	0.933394i	$0.616832\pi$
$824$	3.50916	+	23.4893i	0.122248	+	0.818290i
$825$			7.96322i			0.277244i
$826$	−12.1581	−	5.82342i	−0.423033	−	0.202623i
$827$	0.273915	−	0.273915i	0.00952495	−	0.00952495i	−0.702328	−	0.711853i	$-0.747856\pi$
$827$	0.273915	−	0.273915i	0.00952495	−	0.00952495i	0.711853	+	0.702328i	$0.247856\pi$
$828$	0.423185	+	1.50911i	0.0147067	+	0.0524453i
$829$	−30.8073	+	8.25478i	−1.06998	+	0.286700i	−0.750485	−	0.660887i	$-0.770180\pi$
$829$	−30.8073	+	8.25478i	−1.06998	+	0.286700i	−0.319495	+	0.947588i	$0.603513\pi$
$830$	46.6376	+	35.3585i	1.61881	+	1.22731i
$831$	−1.13400	−	1.96414i	−0.0393380	−	0.0681353i
$832$	−0.182749	−	5.25005i	−0.00633569	−	0.182013i
$833$	−19.0578	−	44.5751i	−0.660315	−	1.54444i
$834$	−2.23226	+	17.7505i	−0.0772968	+	0.614651i
$835$	4.22949	−	15.7847i	0.146368	−	0.546252i
$836$	42.9254	−	43.9329i	1.48461	−	1.51945i
$837$	−0.596508	−	2.22620i	−0.0206183	−	0.0769487i
$838$	−18.9103	−	7.70473i	−0.653246	−	0.266156i
$839$			5.85513i			0.202142i	0.994879	+	0.101071i	$0.0322269\pi$
$839$			5.85513i			0.202142i	−0.994879	+	0.101071i	$0.967773\pi$
$840$	−1.73664	−	19.5697i	−0.0599199	−	0.675218i
$841$		−	14.9793i		−	0.516526i
$842$	8.24290	−	20.2312i	0.284069	−	0.697212i
$843$	−6.94758	−	25.9287i	−0.239287	−	0.893033i
$844$	−51.3245	+	0.595306i	−1.76666	+	0.0204913i
$845$	−8.54049	+	31.8736i	−0.293802	+	1.09648i
$846$	10.0998	+	1.27013i	0.347240	+	0.0436679i
$847$	−9.76883	+	14.8008i	−0.335661	+	0.508562i
$848$	23.9043	−	7.00327i	0.820876	−	0.240493i
$849$	−12.2753	−	21.2615i	−0.421289	−	0.729693i
$850$	11.1989	−	14.7713i	0.384120	−	0.506652i
$851$	−7.15938	+	1.91835i	−0.245420	+	0.0657602i
$852$	−15.4648	−	8.69103i	−0.529815	−	0.297750i
$853$	−31.5114	+	31.5114i	−1.07893	+	1.07893i	−0.0823232	+	0.996606i	$0.526234\pi$
$853$	−31.5114	+	31.5114i	−1.07893	+	1.07893i	−0.996606	+	0.0823232i	$0.973766\pi$
$854$	−24.6983	−	36.0619i	−0.845159	−	1.23401i
$855$		−	19.1632i		−	0.655367i
$856$	28.2273	−	38.1426i	0.964789	−	1.30369i
$857$	−0.567936	−	0.327898i	−0.0194003	−	0.0112008i	0.490268	−	0.871571i	$-0.336899\pi$
$857$	−0.567936	−	0.327898i	−0.0194003	−	0.0112008i	−0.509669	+	0.860371i	$0.670232\pi$
$858$	0.532456	+	3.87081i	0.0181778	+	0.132147i
$859$	26.5018	+	7.10113i	0.904229	+	0.242287i	0.680832	−	0.732440i	$-0.261619\pi$
$859$	26.5018	+	7.10113i	0.904229	+	0.242287i	0.223397	+	0.974727i	$0.428285\pi$
$860$	10.5878	−	41.4306i	0.361042	−	1.41277i
$861$	−7.23483	−	8.15611i	−0.246562	−	0.277960i
$862$	1.68191	−	13.3743i	0.0572862	−	0.455530i
$863$	6.87722	+	11.9117i	0.234103	+	0.405479i	0.959012	−	0.283366i	$-0.0914512\pi$
$863$	6.87722	+	11.9117i	0.234103	+	0.405479i	−0.724908	+	0.688845i	$0.758118\pi$
$864$	5.28682	+	2.01236i	0.179861	+	0.0684617i
$865$	22.3128	−	38.6469i	0.758659	−	1.31404i
$866$	−20.8241	+	8.76745i	−0.707632	+	0.297930i
$867$	21.8935	+	21.8935i	0.743542	+	0.743542i
$868$	8.19811	+	9.02890i	0.278262	+	0.306461i
$869$	23.8631	−	23.8631i	0.809500	−	0.809500i
$870$	12.8749	+	5.24568i	0.436499	+	0.177845i
$871$	1.90834	+	1.10178i	0.0646616	+	0.0373324i
$872$	2.81957	−	24.7348i	0.0954828	−	0.837626i
$873$	8.58506	−	4.95659i	0.290560	−	0.167755i
$874$	−4.96167	−	6.38912i	−0.167831	−	0.216115i
$875$	20.4776	+	6.82213i	0.692269	+	0.230630i
$876$	5.59727	−	3.31873i	0.189114	−	0.112130i
$877$	−7.24393	+	27.0347i	−0.244610	+	0.912898i	0.728969	+	0.684547i	$0.240000\pi$
$877$	−7.24393	+	27.0347i	−0.244610	+	0.912898i	−0.973579	+	0.228351i	$0.926667\pi$
$878$	−19.7797	+	26.0892i	−0.667531	+	0.880469i
$879$	4.24245	−	7.34814i	0.143094	−	0.247847i
$880$	44.1730	−	1.02485i	1.48907	−	0.0345477i
$881$	14.8419			0.500037			0.250018	−	0.968241i	$-0.419563\pi$
$881$	14.8419			0.500037			0.250018	+	0.968241i	$0.419563\pi$
$882$	−2.72554	−	9.51690i	−0.0917736	−	0.320451i
$883$	−17.8378	−	17.8378i	−0.600288	−	0.600288i	0.340101	−	0.940389i	$-0.389539\pi$
$883$	−17.8378	−	17.8378i	−0.600288	−	0.600288i	−0.940389	+	0.340101i	$0.889539\pi$
$884$	4.45597	−	7.92894i	0.149870	−	0.266679i
$885$	−2.44816	−	9.13665i	−0.0822939	−	0.307125i
$886$	46.0191	−	6.33024i	1.54604	−	0.212668i
$887$	−32.4569	+	18.7390i	−1.08980	+	0.629195i	−0.933523	−	0.358519i	$-0.883282\pi$
$887$	−32.4569	+	18.7390i	−1.08980	+	0.629195i	−0.156275	+	0.987714i	$0.549949\pi$
$888$	−9.80584	+	24.8895i	−0.329062	+	0.835237i
$889$	−18.8276	+	9.41767i	−0.631458	+	0.315858i
$890$	−4.74419	+	3.68425i	−0.159026	+	0.123496i
$891$	−4.06411	−	1.08897i	−0.136153	−	0.0364820i
$892$	17.3745	−	17.7823i	0.581743	−	0.595396i
$893$	−50.7487	+	13.5981i	−1.69824	+	0.455043i
$894$	16.2356	−	6.83556i	0.542998	−	0.228615i
$895$	57.7780			1.93131
$896$	−29.7467	+	3.33679i	−0.993767	+	0.111474i
$897$	0.514594			0.0171818
$898$	−8.10792	+	3.41363i	−0.270565	+	0.113914i
$899$	−8.33584	+	2.23358i	−0.278016	+	0.0744941i
$900$	2.64537	−	2.70746i	0.0881790	−	0.0902485i
$901$	41.6572	+	11.1620i	1.38780	+	0.371860i
$902$	19.3658	−	15.0392i	0.644812	−	0.500750i
$903$	1.28747	−	21.5084i	0.0428442	−	0.715755i
$904$	−13.7134	+	34.8079i	−0.456102	+	1.15769i
$905$	−40.1625	+	23.1878i	−1.33505	+	0.770789i
$906$	−18.7871	+	2.58429i	−0.624159	+	0.0858574i
$907$	−3.59543	−	13.4183i	−0.119384	−	0.445548i	0.880193	−	0.474615i	$-0.157413\pi$
$907$	−3.59543	−	13.4183i	−0.119384	−	0.445548i	−0.999577	+	0.0290677i	$0.990746\pi$
$908$	−1.89909	+	3.37923i	−0.0630234	+	0.112144i
$909$	0.0742754	+	0.0742754i	0.00246356	+	0.00246356i
$910$	−6.34056	−	1.18583i	−0.210187	−	0.0393100i
$911$	27.3120			0.904887			0.452443	−	0.891793i	$-0.350553\pi$
$911$	27.3120			0.904887			0.452443	+	0.891793i	$0.350553\pi$
$912$	−29.1889	+	0.677207i	−0.966541	+	0.0224246i
$913$	−33.1613	+	57.4371i	−1.09748	+	1.90089i
$914$	−14.9134	+	19.6706i	−0.493290	+	0.650646i
$915$	7.93770	−	29.6239i	0.262412	−	0.979336i
$916$	35.9858	−	21.3367i	1.18900	−	0.704984i
$917$	−2.91220	−	14.2193i	−0.0961694	−	0.469564i
$918$	6.00722	+	7.73547i	0.198268	+	0.255308i
$919$	−9.64081	+	5.56612i	−0.318021	+	0.183609i	−0.650510	−	0.759498i	$-0.725445\pi$
$919$	−9.64081	+	5.56612i	−0.318021	+	0.183609i	0.332489	+	0.943107i	$0.392112\pi$
$920$	0.659080	−	5.78180i	0.0217292	−	0.190620i
$921$	−1.34864	−	0.778638i	−0.0444392	−	0.0256570i
$922$	−17.7470	−	7.23076i	−0.584466	−	0.238132i
$923$	−4.11846	+	4.11846i	−0.135561	+	0.135561i
$924$	21.7578	−	4.71970i	0.715780	−	0.155267i
$925$	12.6577	+	12.6577i	0.416183	+	0.416183i
$926$	−14.3508	+	6.04204i	−0.471597	+	0.198554i
$927$	−4.19845	+	7.27193i	−0.137895	+	0.238841i
$928$	7.53512	−	19.7961i	0.247352	−	0.649839i
$929$	−13.7390	−	23.7966i	−0.450762	−	0.780742i	0.547672	−	0.836693i	$-0.315514\pi$
$929$	−13.7390	−	23.7966i	−0.450762	−	0.780742i	−0.998434	+	0.0559509i	$0.982181\pi$
$930$	−1.06771	+	8.49026i	−0.0350116	+	0.278406i
$931$	31.5613	+	40.1810i	1.03438	+	1.31688i
$932$	2.34658	−	9.18226i	0.0768649	−	0.300775i
$933$	−2.73561	−	0.733005i	−0.0895599	−	0.0239975i
$934$	−1.03523	−	7.52583i	−0.0338737	−	0.246253i
$935$	66.2512	+	38.2501i	2.16664	+	1.25091i
$936$	1.10485	−	1.49294i	0.0361130	−	0.0487982i
$937$			8.93110i			0.291766i	0.989302	+	0.145883i	$0.0466023\pi$
$937$			8.93110i			0.291766i	−0.989302	+	0.145883i	$0.953398\pi$
$938$	5.42396	−	11.3241i	0.177099	−	0.369744i
$939$	23.6388	−	23.6388i	0.771425	−	0.771425i
$940$	−32.9480	−	18.5164i	−1.07465	−	0.603939i
$941$	−19.5728	+	5.24451i	−0.638054	+	0.170966i	−0.563322	−	0.826237i	$-0.690477\pi$
$941$	−19.5728	+	5.24451i	−0.638054	+	0.170966i	−0.0747324	+	0.997204i	$0.523810\pi$
$942$	9.45083	−	12.4656i	0.307925	−	0.406151i
$943$	−1.61464	−	2.79664i	−0.0525800	−	0.0910713i
$944$	−13.8302	+	4.05186i	−0.450135	+	0.131877i
$945$	3.82629	−	5.79724i	0.124469	−	0.188584i
$946$	48.0801	+	6.04642i	1.56322	+	0.196586i
$947$	−1.84928	+	6.90159i	−0.0600934	+	0.224272i	−0.989441	−	0.144933i	$-0.953703\pi$
$947$	−1.84928	+	6.90159i	−0.0600934	+	0.224272i	0.929348	+	0.369205i	$0.120370\pi$
$948$	−16.0406	+	0.186053i	−0.520975	+	0.00604272i
$949$	−0.552962	−	2.06368i	−0.0179499	−	0.0669900i
$950$	−7.37167	+	18.0928i	−0.239169	+	0.587010i
$951$		−	28.1087i		−	0.911487i
$952$	−46.9970	−	21.8440i	−1.52318	−	0.707967i
$953$			5.26703i			0.170616i	0.996355	+	0.0853079i	$0.0271874\pi$
$953$			5.26703i			0.170616i	−0.996355	+	0.0853079i	$0.972813\pi$
$954$	8.15571	+	3.32293i	0.264051	+	0.107584i
$955$	1.41134	+	5.26719i	0.0456699	+	0.170442i
$956$	−27.7921	+	28.4444i	−0.898862	+	0.919958i
$957$	−4.07758	+	15.2177i	−0.131810	+	0.491920i
$958$	5.59621	−	44.5001i	0.180805	−	1.43773i
$959$	10.7915	+	0.645964i	0.348475	+	0.0208593i
$960$	−15.3591	−	14.3258i	−0.495712	−	0.462362i
$961$	12.8441	+	22.2466i	0.414326	+	0.717634i
$962$	6.99909	+	5.30639i	0.225660	+	0.171085i
$963$	16.2050	−	4.34210i	0.522197	−	0.139922i
$964$	−3.02933	−	10.8028i	−0.0975681	−	0.347936i
$965$	28.2853	−	28.2853i	0.910537	−	0.910537i
$966$	−0.225297	−	2.92353i	−0.00724882	−	0.0940629i
$967$			47.5346i			1.52861i	0.644855	+	0.764305i	$0.276918\pi$
$967$			47.5346i			1.52861i	−0.644855	+	0.764305i	$0.723082\pi$
$968$	2.80119	+	18.7503i	0.0900336	+	0.602659i
$969$	−43.7778	−	25.2751i	−1.40635	−	0.811955i
$970$	−36.4628	+	5.01570i	−1.17075	+	0.161045i
$971$	13.1033	+	3.51103i	0.420506	+	0.112674i	0.462866	−	0.886428i	$-0.346821\pi$
$971$	13.1033	+	3.51103i	0.420506	+	0.112674i	−0.0423600	+	0.999102i	$0.513488\pi$
$972$	1.02002	+	1.72034i	0.0327172	+	0.0551798i
$973$	10.5789	−	31.7540i	0.339143	−	1.01798i
$974$	−38.3686	−	4.82513i	−1.22941	−	0.154607i
$975$	−0.621403	−	1.07630i	−0.0199008	−	0.0344692i
$976$	−45.4030	−	11.0436i	−1.45331	−	0.353499i
$977$	−29.7388	+	51.5090i	−0.951427	+	1.64792i	−0.209087	+	0.977897i	$0.567049\pi$
$977$	−29.7388	+	51.5090i	−0.951427	+	1.64792i	−0.742340	+	0.670023i	$0.766284\pi$
$978$	5.52992	+	13.1344i	0.176827	+	0.419993i
$979$	−4.81325	−	4.81325i	−0.153832	−	0.153832i
$980$	−3.96100	+	36.5413i	−0.126530	+	1.16727i
$981$	6.22375	−	6.22375i	0.198709	−	0.198709i
$982$	−15.7342	+	38.6177i	−0.502100	+	1.23234i
$983$	−4.41483	−	2.54890i	−0.140811	−	0.0812974i	0.427939	−	0.903807i	$-0.359240\pi$
$983$	−4.41483	−	2.54890i	−0.140811	−	0.0812974i	−0.568751	+	0.822510i	$0.692573\pi$
$984$	−11.5803	−	1.32006i	−0.369166	−	0.0420820i
$985$	3.75662	−	2.16889i	0.119696	−	0.0691064i
$986$	28.9649	−	22.4936i	0.922430	−	0.716342i
$987$	−18.0676	−	6.01925i	−0.575099	−	0.191595i
$988$	−2.37350	+	9.28759i	−0.0755111	+	0.295478i
$989$	1.65181	−	6.16466i	0.0525246	−	0.196025i
$990$	12.4485	+	9.43787i	0.395639	+	0.299955i
$991$	25.4492	−	44.0792i	0.808419	−	1.40022i	−0.105539	−	0.994415i	$-0.533657\pi$
$991$	25.4492	−	44.0792i	0.808419	−	1.40022i	0.913958	−	0.405808i	$-0.133010\pi$
$992$	12.9699	+	1.32628i	0.411795	+	0.0421093i
$993$	−5.13435			−0.162934
$994$	25.2011	+	21.5948i	0.799329	+	0.684945i
$995$	4.98109	+	4.98109i	0.157911	+	0.157911i
$996$	30.3552	−	8.51220i	0.961842	−	0.269719i
$997$	0.0766483	+	0.286055i	0.00242748	+	0.00905946i	0.967129	−	0.254286i	$-0.0818406\pi$
$997$	0.0766483	+	0.286055i	0.00242748	+	0.00905946i	−0.964701	+	0.263346i	$0.915174\pi$
$998$	−2.39870	−	17.4379i	−0.0759297	−	0.551988i
$999$	−8.19093	+	4.72904i	−0.259150	+	0.149620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bq.b.109.27	yes	120
7.2	even	3	inner	336.2.bq.b.205.6	yes	120
16.5	even	4	inner	336.2.bq.b.277.6	yes	120
112.37	even	12	inner	336.2.bq.b.37.27	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bq.b.37.27	✓	120	112.37	even	12	inner
336.2.bq.b.109.27	yes	120	1.1	even	1	trivial
336.2.bq.b.205.6	yes	120	7.2	even	3	inner
336.2.bq.b.277.6	yes	120	16.5	even	4	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.bq (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30340 - 0.548764i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.39772 - 1.43052i) q^{4} +(-2.53593 - 0.679499i) q^{5} +(-1.11696 + 0.867411i) q^{6} +(2.36624 - 1.18360i) q^{7} +(1.03677 - 2.63156i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(1.30340 - 0.548764i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.39772 - 1.43052i) q^{4} +(-2.53593 - 0.679499i) q^{5} +(-1.11696 + 0.867411i) q^{6} +(2.36624 - 1.18360i) q^{7} +(1.03677 - 2.63156i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-3.67822 + 0.505963i) q^{10} +(-1.08897 - 4.06411i) q^{11} +(-0.979844 + 1.74353i) q^{12} +(0.464324 + 0.464324i) q^{13} +(2.43464 - 2.84122i) q^{14} +2.62538 q^{15} +(-0.0927784 - 3.99892i) q^{16} +(3.46273 - 5.99763i) q^{17} +(0.854398 - 1.12694i) q^{18} +(-1.88917 + 7.05048i) q^{19} +(-4.51654 + 2.67795i) q^{20} +(-1.97927 + 1.75570i) q^{21} +(-3.64961 - 4.69958i) q^{22} +(-0.678671 + 0.391831i) q^{23} +(-0.320344 + 2.81023i) q^{24} +(1.63907 + 0.946318i) q^{25} +(0.860005 + 0.350397i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.61416 - 5.03929i) q^{28} +(2.64771 + 2.64771i) q^{29} +(3.42193 - 1.44072i) q^{30} +(-1.15237 + 1.99596i) q^{31} +(-2.31539 - 5.16129i) q^{32} +(2.10374 + 3.64378i) q^{33} +(1.22205 - 9.71755i) q^{34} +(-6.80486 + 1.39367i) q^{35} +(0.495198 - 1.93773i) q^{36} +(9.13580 + 2.44793i) q^{37} +(1.40670 + 10.2263i) q^{38} +(-0.568678 - 0.328327i) q^{39} +(-4.41731 + 5.96896i) q^{40} +4.12076i q^{41} +(-1.61632 + 3.37454i) q^{42} +(-5.75866 + 5.75866i) q^{43} +(-7.33586 - 4.12267i) q^{44} +(-2.53593 + 0.679499i) q^{45} +(-0.669559 + 0.883144i) q^{46} +(3.59896 + 6.23358i) q^{47} +(1.12461 + 3.83865i) q^{48} +(4.19817 - 5.60138i) q^{49} +(2.65568 + 0.333970i) q^{50} +(-1.79244 + 6.68949i) q^{51} +(1.31322 - 0.0152318i) q^{52} +(1.61173 + 6.01507i) q^{53} +(-0.533610 + 1.30968i) q^{54} +11.0462i q^{55} +(-0.661482 - 7.45402i) q^{56} -7.29919i q^{57} +(4.90400 + 1.99806i) q^{58} +(-0.932495 - 3.48012i) q^{59} +(3.66954 - 3.75566i) q^{60} +(3.02345 - 11.2837i) q^{61} +(-0.406688 + 3.23391i) q^{62} +(1.45742 - 2.20815i) q^{63} +(-5.85022 - 5.45664i) q^{64} +(-0.861983 - 1.49300i) q^{65} +(4.74159 + 3.59485i) q^{66} +(3.24140 - 0.868530i) q^{67} +(-3.73981 - 13.3365i) q^{68} +(0.554133 - 0.554133i) q^{69} +(-8.10468 + 5.55078i) q^{70} +8.86981i q^{71} +(-0.417912 - 2.79738i) q^{72} +(-2.81769 - 1.62680i) q^{73} +(13.2510 - 1.82276i) q^{74} +(-1.82815 - 0.489850i) q^{75} +(7.44533 + 12.5571i) q^{76} +(-7.38706 - 8.32773i) q^{77} +(-0.921391 - 0.115872i) q^{78} +(4.01043 + 6.94626i) q^{79} +(-2.48199 + 10.2040i) q^{80} +(0.500000 - 0.866025i) q^{81} +(2.26133 + 5.37102i) q^{82} +(-11.1462 - 11.1462i) q^{83} +(-0.254894 + 5.28536i) q^{84} +(-12.8566 + 12.8566i) q^{85} +(-4.34570 + 10.6660i) q^{86} +(-3.24277 - 1.87221i) q^{87} +(-11.8240 - 1.34784i) q^{88} +(1.40108 - 0.808914i) q^{89} +(-2.93245 + 2.27729i) q^{90} +(1.64828 + 0.549126i) q^{91} +(-0.388068 + 1.51852i) q^{92} +(0.596508 - 2.22620i) q^{93} +(8.11166 + 6.14988i) q^{94} +(9.58158 - 16.5958i) q^{95} +(3.57234 + 4.38616i) q^{96} +9.91317 q^{97} +(2.39807 - 9.60465i) q^{98} +(-2.97513 - 2.97513i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8}+O(q^{10}) \) 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8	\( 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8} - 8 q^{10} + 4 q^{11} + 8 q^{13} + 32 q^{14} + 8 q^{15} + 12 q^{16} - 16 q^{17} - 4 q^{18} - 8 q^{19} - 64 q^{20} + 12 q^{21} + 24 q^{22} - 8 q^{24} - 8 q^{26} - 8 q^{28} - 64 q^{29} - 52 q^{31} - 4 q^{33} + 32 q^{34} - 8 q^{35} + 24 q^{37} - 40 q^{38} - 60 q^{40} + 24 q^{42} - 32 q^{43} - 12 q^{44} - 8 q^{45} + 4 q^{46} - 8 q^{47} + 32 q^{48} + 20 q^{49} - 16 q^{50} - 8 q^{51} - 16 q^{52} + 4 q^{54} - 104 q^{56} + 4 q^{58} + 52 q^{59} - 16 q^{60} + 4 q^{61} - 144 q^{62} + 8 q^{63} - 64 q^{64} + 24 q^{65} + 24 q^{66} + 12 q^{68} + 24 q^{69} - 48 q^{70} + 4 q^{72} + 16 q^{74} + 16 q^{75} - 8 q^{76} + 8 q^{77} - 56 q^{78} + 28 q^{79} + 68 q^{80} + 60 q^{81} + 28 q^{82} + 8 q^{83} + 24 q^{84} - 80 q^{85} + 36 q^{86} + 40 q^{88} + 8 q^{90} + 36 q^{91} - 184 q^{92} + 4 q^{93} + 60 q^{94} - 16 q^{95} + 36 q^{96} + 24 q^{97} + 124 q^{98} - 8 q^{99}+O(q^{100}) \) 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8 - 8 * q^10 + 4 * q^11 + 8 * q^13 + 32 * q^14 + 8 * q^15 + 12 * q^16 - 16 * q^17 - 4 * q^18 - 8 * q^19 - 64 * q^20 + 12 * q^21 + 24 * q^22 - 8 * q^24 - 8 * q^26 - 8 * q^28 - 64 * q^29 - 52 * q^31 - 4 * q^33 + 32 * q^34 - 8 * q^35 + 24 * q^37 - 40 * q^38 - 60 * q^40 + 24 * q^42 - 32 * q^43 - 12 * q^44 - 8 * q^45 + 4 * q^46 - 8 * q^47 + 32 * q^48 + 20 * q^49 - 16 * q^50 - 8 * q^51 - 16 * q^52 + 4 * q^54 - 104 * q^56 + 4 * q^58 + 52 * q^59 - 16 * q^60 + 4 * q^61 - 144 * q^62 + 8 * q^63 - 64 * q^64 + 24 * q^65 + 24 * q^66 + 12 * q^68 + 24 * q^69 - 48 * q^70 + 4 * q^72 + 16 * q^74 + 16 * q^75 - 8 * q^76 + 8 * q^77 - 56 * q^78 + 28 * q^79 + 68 * q^80 + 60 * q^81 + 28 * q^82 + 8 * q^83 + 24 * q^84 - 80 * q^85 + 36 * q^86 + 40 * q^88 + 8 * q^90 + 36 * q^91 - 184 * q^92 + 4 * q^93 + 60 * q^94 - 16 * q^95 + 36 * q^96 + 24 * q^97 + 124 * q^98 - 8 * q^99

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