LMFDB - Embedded newform 336.2.bq.b.109.21

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			109.21
Character	$\chi$	$=$	336.109
Dual form			336.2.bq.b.37.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.762858 + 1.19082i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.836096 + 1.81685i) q^{4} +(2.91110 + 0.780028i) q^{5} +(-1.04507 - 0.952800i) q^{6} +(-2.27882 + 1.34423i) q^{7} +(-2.80136 + 0.390360i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.762858 + 1.19082i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.836096 + 1.81685i) q^{4} +(2.91110 + 0.780028i) q^{5} +(-1.04507 - 0.952800i) q^{6} +(-2.27882 + 1.34423i) q^{7} +(-2.80136 + 0.390360i) q^{8} +(0.866025 - 0.500000i) q^{9} +(1.29189 + 4.06164i) q^{10} +(0.419015 + 1.56378i) q^{11} +(0.337371 - 1.97134i) q^{12} +(0.849595 + 0.849595i) q^{13} +(-3.33916 - 1.68820i) q^{14} -3.01380 q^{15} +(-2.60189 - 3.03812i) q^{16} +(0.359133 - 0.622037i) q^{17} +(1.25606 + 0.649850i) q^{18} +(-1.07745 + 4.02110i) q^{19} +(-3.85115 + 4.63686i) q^{20} +(1.85326 - 1.88823i) q^{21} +(-1.54253 + 1.69191i) q^{22} +(0.760593 - 0.439128i) q^{23} +(2.60487 - 1.10210i) q^{24} +(3.53595 + 2.04148i) q^{25} +(-0.363593 + 1.65983i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.536957 - 5.26419i) q^{28} +(-3.65819 - 3.65819i) q^{29} +(-2.29910 - 3.58888i) q^{30} +(1.57279 - 2.72416i) q^{31} +(1.63298 - 5.41603i) q^{32} +(-0.809474 - 1.40205i) q^{33} +(1.01470 - 0.0468634i) q^{34} +(-7.68243 + 2.13566i) q^{35} +(0.184345 + 1.99149i) q^{36} +(5.29912 + 1.41990i) q^{37} +(-5.61034 + 1.78448i) q^{38} +(-1.04054 - 0.600755i) q^{39} +(-8.45954 - 1.04876i) q^{40} +8.90853i q^{41} +(3.66232 + 0.766443i) q^{42} +(8.88764 - 8.88764i) q^{43} +(-3.19150 - 0.546187i) q^{44} +(2.91110 - 0.780028i) q^{45} +(1.10315 + 0.570735i) q^{46} +(6.46708 + 11.2013i) q^{47} +(3.29955 + 2.26118i) q^{48} +(3.38607 - 6.12654i) q^{49} +(0.266393 + 5.76803i) q^{50} +(-0.185901 + 0.693792i) q^{51} +(-2.25393 + 0.833244i) q^{52} +(-0.337945 - 1.26123i) q^{53} +(-1.38146 - 0.302614i) q^{54} +4.87918i q^{55} +(5.85907 - 4.65524i) q^{56} -4.16295i q^{57} +(1.56556 - 7.14691i) q^{58} +(-2.89714 - 10.8123i) q^{59} +(2.51982 - 5.47561i) q^{60} +(1.71974 - 6.41814i) q^{61} +(4.44380 - 0.205234i) q^{62} +(-1.30140 + 2.30355i) q^{63} +(7.69524 - 2.18708i) q^{64} +(1.81055 + 3.13597i) q^{65} +(1.05207 - 2.03350i) q^{66} +(13.2715 - 3.55609i) q^{67} +(0.829878 + 1.17257i) q^{68} +(-0.621021 + 0.621021i) q^{69} +(-8.40378 - 7.51917i) q^{70} -8.61112i q^{71} +(-2.23087 + 1.73874i) q^{72} +(12.1120 + 6.99286i) q^{73} +(2.35164 + 7.39347i) q^{74} +(-3.94384 - 1.05675i) q^{75} +(-6.40488 - 5.31959i) q^{76} +(-3.05695 - 3.00033i) q^{77} +(-0.0783926 - 1.69738i) q^{78} +(-0.793121 - 1.37373i) q^{79} +(-5.20454 - 10.8738i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-10.6084 + 6.79594i) q^{82} +(2.16744 + 2.16744i) q^{83} +(1.88113 + 4.94584i) q^{84} +(1.53068 - 1.53068i) q^{85} +(17.3636 + 3.80356i) q^{86} +(4.48035 + 2.58673i) q^{87} +(-1.78425 - 4.21715i) q^{88} +(-9.85695 + 5.69091i) q^{89} +(3.14963 + 2.87154i) q^{90} +(-3.07813 - 0.794022i) q^{91} +(0.161902 + 1.74904i) q^{92} +(-0.814138 + 3.03841i) q^{93} +(-8.40527 + 16.2461i) q^{94} +(-6.27314 + 10.8654i) q^{95} +(-0.175567 + 5.65413i) q^{96} +7.16419 q^{97} +(9.87869 - 0.641488i) q^{98} +(1.14477 + 1.14477i) 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 $

$2$	0.762858	+	1.19082i	0.539422	+	0.842036i
$2$	0.762858	+	1.19082i	0.539422	+	0.842036i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	−0.836096	+	1.81685i	−0.418048	+	0.908425i
$5$	2.91110	+	0.780028i	1.30188	+	0.348839i	0.842162	−	0.539224i	$-0.181282\pi$
$5$	2.91110	+	0.780028i	1.30188	+	0.348839i	0.459722	+	0.888063i	$0.347949\pi$
$6$	−1.04507	−	0.952800i	−0.426648	−	0.388979i
$7$	−2.27882	+	1.34423i	−0.861314	+	0.508073i
$7$	−2.27882	+	1.34423i	−0.861314	+	0.508073i
$8$	−2.80136	+	0.390360i	−0.990430	+	0.138013i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	1.29189	+	4.06164i	0.408530	+	1.28440i
$11$	0.419015	+	1.56378i	0.126338	+	0.471498i	0.999884	−	0.0152428i	$-0.00485212\pi$
$11$	0.419015	+	1.56378i	0.126338	+	0.471498i	−0.873546	+	0.486741i	$0.838185\pi$
$12$	0.337371	−	1.97134i	0.0973907	−	0.569077i
$13$	0.849595	+	0.849595i	0.235635	+	0.235635i	0.815040	−	0.579405i	$-0.196715\pi$
$13$	0.849595	+	0.849595i	0.235635	+	0.235635i	−0.579405	+	0.815040i	$0.696715\pi$
$14$	−3.33916	−	1.68820i	−0.892427	−	0.451192i
$15$	−3.01380			−0.778159
$16$	−2.60189	−	3.03812i	−0.650472	−	0.759530i
$17$	0.359133	−	0.622037i	0.0871026	−	0.150866i	−0.819183	−	0.573533i	$-0.805573\pi$
$17$	0.359133	−	0.622037i	0.0871026	−	0.150866i	0.906285	+	0.422667i	$0.138906\pi$
$18$	1.25606	+	0.649850i	0.296057	+	0.153171i
$19$	−1.07745	+	4.02110i	−0.247184	+	0.922503i	0.725089	+	0.688655i	$0.241799\pi$
$19$	−1.07745	+	4.02110i	−0.247184	+	0.922503i	−0.972273	+	0.233848i	$0.924868\pi$
$20$	−3.85115	+	4.63686i	−0.861144	+	1.03683i
$21$	1.85326	−	1.88823i	0.404415	−	0.412046i
$22$	−1.54253	+	1.69191i	−0.328869	+	0.360717i
$23$	0.760593	−	0.439128i	0.158595	−	0.0915646i	−0.418602	−	0.908170i	$-0.637480\pi$
$23$	0.760593	−	0.439128i	0.158595	−	0.0915646i	0.577197	+	0.816605i	$0.304147\pi$
$24$	2.60487	−	1.10210i	0.531718	−	0.224966i
$25$	3.53595	+	2.04148i	0.707190	+	0.408296i
$26$	−0.363593	+	1.65983i	−0.0713065	+	0.325520i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−0.536957	−	5.26419i	−0.101475	−	0.994838i
$29$	−3.65819	−	3.65819i	−0.679308	−	0.679308i	0.280535	−	0.959844i	$-0.409488\pi$
$29$	−3.65819	−	3.65819i	−0.679308	−	0.679308i	−0.959844	+	0.280535i	$0.909488\pi$
$30$	−2.29910	−	3.58888i	−0.419756	−	0.655237i
$31$	1.57279	−	2.72416i	0.282482	−	0.489274i	−0.689513	−	0.724273i	$-0.742176\pi$
$31$	1.57279	−	2.72416i	0.282482	−	0.489274i	0.971995	+	0.234999i	$0.0755089\pi$
$32$	1.63298	−	5.41603i	0.288673	−	0.957428i
$33$	−0.809474	−	1.40205i	−0.140911	−	0.244066i
$34$	1.01470	−	0.0468634i	0.174020	−	0.00803701i
$35$	−7.68243	+	2.13566i	−1.29857	+	0.360992i
$36$	0.184345	+	1.99149i	0.0307241	+	0.331914i
$37$	5.29912	+	1.41990i	0.871170	+	0.233429i	0.666594	−	0.745421i	$-0.267752\pi$
$37$	5.29912	+	1.41990i	0.871170	+	0.233429i	0.204577	+	0.978851i	$0.434418\pi$
$38$	−5.61034	+	1.78448i	−0.910117	+	0.289481i
$39$	−1.04054	−	0.600755i	−0.166619	−	0.0961977i
$40$	−8.45954	−	1.04876i	−1.33757	−	0.165824i
$41$			8.90853i			1.39128i	0.718391	+	0.695640i	$0.244879\pi$
$41$			8.90853i			1.39128i	−0.718391	+	0.695640i	$0.755121\pi$
$42$	3.66232	+	0.766443i	0.565108	+	0.118265i
$43$	8.88764	−	8.88764i	1.35535	−	1.35535i	0.475799	−	0.879554i	$-0.342159\pi$
$43$	8.88764	−	8.88764i	1.35535	−	1.35535i	0.879554	−	0.475799i	$-0.157841\pi$
$44$	−3.19150	−	0.546187i	−0.481136	−	0.0823407i
$45$	2.91110	−	0.780028i	0.433962	−	0.116280i
$46$	1.10315	+	0.570735i	0.162650	+	0.0841503i
$47$	6.46708	+	11.2013i	0.943321	+	1.63388i	0.759078	+	0.651000i	$0.225650\pi$
$47$	6.46708	+	11.2013i	0.943321	+	1.63388i	0.184243	+	0.982881i	$0.441017\pi$
$48$	3.29955	+	2.26118i	0.476250	+	0.326374i
$49$	3.38607	−	6.12654i	0.483724	−	0.875220i
$50$	0.266393	+	5.76803i	0.0376737	+	0.815723i
$51$	−0.185901	+	0.693792i	−0.0260314	+	0.0971503i
$52$	−2.25393	+	0.833244i	−0.312564	+	0.115550i
$53$	−0.337945	−	1.26123i	−0.0464204	−	0.173243i	0.938824	−	0.344398i	$-0.111917\pi$
$53$	−0.337945	−	1.26123i	−0.0464204	−	0.173243i	−0.985244	+	0.171155i	$0.945250\pi$
$54$	−1.38146	−	0.302614i	−0.187993	−	0.0411805i
$55$			4.87918i			0.657908i
$56$	5.85907	−	4.65524i	0.782951	−	0.622083i
$57$		−	4.16295i		−	0.551396i
$58$	1.56556	−	7.14691i	0.205568	−	0.938436i
$59$	−2.89714	−	10.8123i	−0.377175	−	1.40764i	−0.850141	−	0.526555i	$-0.823483\pi$
$59$	−2.89714	−	10.8123i	−0.377175	−	1.40764i	0.472966	−	0.881081i	$-0.343183\pi$
$60$	2.51982	−	5.47561i	0.325308	−	0.706899i
$61$	1.71974	−	6.41814i	0.220190	−	0.821759i	−0.764085	−	0.645115i	$-0.776809\pi$
$61$	1.71974	−	6.41814i	0.220190	−	0.821759i	0.984275	−	0.176644i	$-0.0565240\pi$
$62$	4.44380	−	0.205234i	0.564363	−	0.0260648i
$63$	−1.30140	+	2.30355i	−0.163961	+	0.290220i
$64$	7.69524	−	2.18708i	0.961905	−	0.273385i
$65$	1.81055	+	3.13597i	0.224571	+	0.388969i
$66$	1.05207	−	2.03350i	0.129501	−	0.250307i
$67$	13.2715	−	3.55609i	1.62137	−	0.434446i	0.669970	−	0.742388i	$-0.266307\pi$
$67$	13.2715	−	3.55609i	1.62137	−	0.434446i	0.951405	+	0.307942i	$0.0996404\pi$
$68$	0.829878	+	1.17257i	0.100637	+	0.142195i
$69$	−0.621021	+	0.621021i	−0.0747622	+	0.0747622i
$70$	−8.40378	−	7.51917i	−1.00444	−	0.898713i
$71$		−	8.61112i		−	1.02195i	−0.859595	−	0.510976i	$-0.829284\pi$
$71$		−	8.61112i		−	1.02195i	0.859595	−	0.510976i	$-0.170716\pi$
$72$	−2.23087	+	1.73874i	−0.262910	+	0.204913i
$73$	12.1120	+	6.99286i	1.41760	+	0.818452i	0.996088	−	0.0883702i	$-0.0281658\pi$
$73$	12.1120	+	6.99286i	1.41760	+	0.818452i	0.421513	+	0.906822i	$0.361499\pi$
$74$	2.35164	+	7.39347i	0.273372	+	0.859473i
$75$	−3.94384	−	1.05675i	−0.455395	−	0.122023i
$76$	−6.40488	−	5.31959i	−0.734690	−	0.610199i
$77$	−3.05695	−	3.00033i	−0.348372	−	0.341920i
$78$	−0.0783926	−	1.69738i	−0.00887622	−	0.192191i
$79$	−0.793121	−	1.37373i	−0.0892331	−	0.154556i	0.817954	−	0.575284i	$-0.195108\pi$
$79$	−0.793121	−	1.37373i	−0.0892331	−	0.154556i	−0.907187	+	0.420727i	$0.861775\pi$
$80$	−5.20454	−	10.8738i	−0.581885	−	1.21573i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−10.6084	+	6.79594i	−1.17151	+	0.750487i
$83$	2.16744	+	2.16744i	0.237908	+	0.237908i	0.815983	−	0.578075i	$-0.196196\pi$
$83$	2.16744	+	2.16744i	0.237908	+	0.237908i	−0.578075	+	0.815983i	$0.696196\pi$
$84$	1.88113	+	4.94584i	0.205248	+	0.539635i
$85$	1.53068	−	1.53068i	0.166026	−	0.166026i
$86$	17.3636	+	3.80356i	1.87236	+	0.410148i
$87$	4.48035	+	2.58673i	0.480344	+	0.277326i
$88$	−1.78425	−	4.21715i	−0.190202	−	0.449550i
$89$	−9.85695	+	5.69091i	−1.04483	+	0.603236i	−0.921199	−	0.389092i	$-0.872789\pi$
$89$	−9.85695	+	5.69091i	−1.04483	+	0.603236i	−0.123636	+	0.992328i	$0.539455\pi$
$90$	3.14963	+	2.87154i	0.332000	+	0.302687i
$91$	−3.07813	−	0.794022i	−0.322676	−	0.0832362i
$92$	0.161902	+	1.74904i	0.0168794	+	0.182350i
$93$	−0.814138	+	3.03841i	−0.0844222	+	0.315068i
$94$	−8.40527	+	16.2461i	−0.866937	+	1.67566i
$95$	−6.27314	+	10.8654i	−0.643610	+	1.11477i
$96$	−0.175567	+	5.65413i	−0.0179187	+	0.577072i
$97$	7.16419			0.727413			0.363706	−	0.931514i	$-0.381511\pi$
$97$	7.16419			0.727413			0.363706	+	0.931514i	$0.381511\pi$
$98$	9.87869	−	0.641488i	0.997898	−	0.0648000i
$99$	1.14477	+	1.14477i	0.115054	+	0.115054i
$100$	−6.66545	+	4.71741i	−0.666545	+	0.471741i
$101$	−0.760668	−	2.83885i	−0.0756893	−	0.282476i	0.917699	−	0.397275i	$-0.130044\pi$
$101$	−0.760668	−	2.83885i	−0.0756893	−	0.282476i	−0.993389	+	0.114799i	$0.963378\pi$
$102$	−0.967996	+	0.307890i	−0.0958459	+	0.0304857i
$103$	−16.5105	+	9.53236i	−1.62683	+	0.939251i	−0.641800	+	0.766872i	$0.721812\pi$
$103$	−16.5105	+	9.53236i	−1.62683	+	0.939251i	−0.985031	+	0.172379i	$0.944855\pi$
$104$	−2.71167	−	2.04837i	−0.265901	−	0.200860i
$105$	6.86791	−	4.05125i	0.670239	−	0.395361i
$106$	1.24409	−	1.36457i	0.120837	−	0.132539i
$107$	−8.27513	−	2.21731i	−0.799987	−	0.214356i	−0.164409	−	0.986392i	$-0.552572\pi$
$107$	−8.27513	−	2.21731i	−0.799987	−	0.214356i	−0.635578	+	0.772036i	$0.719238\pi$
$108$	−0.693498	−	1.87592i	−0.0667319	−	0.180510i
$109$	−10.2409	+	2.74405i	−0.980904	+	0.262832i	−0.713425	−	0.700731i	$-0.752857\pi$
$109$	−10.2409	+	2.74405i	−0.980904	+	0.262832i	−0.267479	+	0.963564i	$0.586190\pi$
$110$	−5.81021	+	3.72212i	−0.553982	+	0.354890i
$111$	−5.48605			−0.520713
$112$	10.0132	+	3.42580i	0.946157	+	0.323707i
$113$	−6.69490			−0.629803			−0.314901	−	0.949124i	$-0.601971\pi$
$113$	−6.69490			−0.629803			−0.314901	+	0.949124i	$0.601971\pi$
$114$	4.95731	−	3.17574i	0.464295	−	0.297435i
$115$	2.55670	−	0.685065i	0.238413	−	0.0638826i
$116$	9.70497	−	3.58778i	0.901084	−	0.333117i
$117$	1.16057	+	0.310973i	0.107295	+	0.0287495i
$118$	10.6653	−	11.6982i	0.981823	−	1.07690i
$119$	0.0177622	+	1.90027i	0.00162826	+	0.174198i
$120$	8.44273	−	1.17646i	0.770712	−	0.107396i
$121$	7.25643	−	4.18950i	0.659676	−	0.380864i
$122$	8.95475	−	2.84824i	0.810725	−	0.257867i
$123$	−2.30570	−	8.60498i	−0.207898	−	0.775885i
$124$	3.63438	+	5.13519i	0.326377	+	0.461154i
$125$	−1.95428	−	1.95428i	−0.174796	−	0.174796i
$126$	−3.73590	+	0.207550i	−0.332820	+	0.0184900i
$127$	−18.9470			−1.68127			−0.840637	−	0.541598i	$-0.817819\pi$
$127$	−18.9470			−1.68127			−0.840637	+	0.541598i	$0.817819\pi$
$128$	8.47478	+	7.49520i	0.749072	+	0.662488i
$129$	−6.28451	+	10.8851i	−0.553321	+	0.958379i
$130$	−2.35317	+	4.54833i	−0.206387	+	0.398915i
$131$	3.09457	−	11.5491i	0.270373	−	1.00905i	−0.688505	−	0.725231i	$-0.741733\pi$
$131$	3.09457	−	11.5491i	0.270373	−	1.00905i	0.958879	−	0.283816i	$-0.0916005\pi$
$132$	3.22411	−	0.298444i	0.280623	−	0.0259762i
$133$	−2.94998	−	10.6117i	−0.255796	−	0.920153i
$134$	14.3589	+	13.0912i	1.24042	+	1.13091i
$135$	−2.61002	+	1.50690i	−0.224635	+	0.129693i
$136$	−0.763243	+	1.88274i	−0.0654476	+	0.161444i
$137$	13.3825	+	7.72638i	1.14334	+	0.660109i	0.947256	−	0.320478i	$-0.103843\pi$
$137$	13.3825	+	7.72638i	1.14334	+	0.660109i	0.196086	+	0.980587i	$0.437177\pi$
$138$	−1.21327	−	0.265773i	−0.103281	−	0.0226241i
$139$	−3.53403	+	3.53403i	−0.299753	+	0.299753i	−0.840917	−	0.541164i	$-0.817984\pi$
$139$	−3.53403	+	3.53403i	−0.299753	+	0.299753i	0.541164	+	0.840917i	$0.317984\pi$
$140$	2.54308	−	15.7434i	0.214929	−	1.33056i
$141$	−9.14584	−	9.14584i	−0.770219	−	0.770219i
$142$	10.2543	−	6.56906i	0.860520	−	0.551263i
$143$	−0.972590	+	1.68458i	−0.0813321	+	0.140871i
$144$	−3.77236	−	1.33015i	−0.314363	−	0.110846i
$145$	−7.79587	−	13.5028i	−0.647412	−	1.12135i
$146$	0.912500	+	19.7577i	0.0755190	+	1.63516i
$147$	−1.68503	+	6.79417i	−0.138979	+	0.560373i
$148$	−7.01031	+	8.44054i	−0.576244	+	0.693808i
$149$	−18.8812	−	5.05920i	−1.54681	−	0.414466i	−0.618349	−	0.785903i	$-0.712198\pi$
$149$	−18.8812	−	5.05920i	−1.54681	−	0.414466i	−0.928458	+	0.371438i	$0.878865\pi$
$150$	−1.75019	−	5.50254i	−0.142903	−	0.449281i
$151$	6.31357	+	3.64514i	0.513791	+	0.296637i	0.734391	−	0.678727i	$-0.237468\pi$
$151$	6.31357	+	3.64514i	0.513791	+	0.296637i	−0.220600	+	0.975364i	$0.570801\pi$
$152$	1.44865	−	11.6851i	0.117501	−	0.947790i
$153$		−	0.718266i		−	0.0580684i
$154$	1.24083	−	5.92910i	0.0999891	−	0.477780i
$155$	6.70349	−	6.70349i	0.538437	−	0.538437i
$156$	1.96147	−	1.38821i	0.157043	−	0.111146i
$157$	−7.36066	+	1.97228i	−0.587445	+	0.157405i	−0.540285	−	0.841482i	$-0.681684\pi$
$157$	−7.36066	+	1.97228i	−0.587445	+	0.157405i	−0.0471596	+	0.998887i	$0.515017\pi$
$158$	1.03082	−	1.99242i	0.0820076	−	0.158508i
$159$	0.652860	+	1.13079i	0.0517752	+	0.0896773i
$160$	8.97843	−	14.4928i	0.709807	−	1.14576i
$161$	−1.14297	+	2.02311i	−0.0900783	+	0.159443i
$162$	1.41271	−	0.0652451i	0.110993	−	0.00512614i
$163$	0.170934	−	0.637934i	0.0133886	−	0.0499668i	−0.958908	−	0.283716i	$-0.908433\pi$
$163$	0.170934	−	0.637934i	0.0133886	−	0.0499668i	0.972297	+	0.233749i	$0.0750994\pi$
$164$	−16.1855	−	7.44839i	−1.26387	−	0.581621i
$165$	−1.26282	−	4.71292i	−0.0983107	−	0.366901i
$166$	−0.927580	+	4.23448i	−0.0719942	+	0.328660i
$167$			0.743203i			0.0575108i	0.999586	+	0.0287554i	$0.00915439\pi$
$167$			0.743203i			0.0575108i	−0.999586	+	0.0287554i	$0.990846\pi$
$168$	−4.45456	+	6.01306i	−0.343677	+	0.463918i
$169$		−	11.5564i		−	0.888952i
$170$	2.99045	+	0.655070i	0.229357	+	0.0502416i
$171$	1.07745	+	4.02110i	0.0823947	+	0.307501i
$172$	8.71659	+	23.5784i	0.664634	+	1.79784i
$173$	1.43900	−	5.37042i	0.109405	−	0.408306i	−0.889402	−	0.457125i	$-0.848879\pi$
$173$	1.43900	−	5.37042i	0.109405	−	0.408306i	0.998808	+	0.0488194i	$0.0155459\pi$
$174$	0.337543	+	7.30858i	0.0255891	+	0.554062i
$175$	−10.8020	+	0.100968i	−0.816556	+	0.00763250i
$176$	3.66074	−	5.34181i	0.275938	−	0.402654i
$177$	5.59684	+	9.69401i	0.420684	+	0.728646i
$178$	−14.2963	−	7.39648i	−1.07155	−	0.554390i
$179$	−1.01136	+	0.270994i	−0.0755928	+	0.0202550i	−0.296417	−	0.955059i	$-0.595792\pi$
$179$	−1.01136	+	0.270994i	−0.0755928	+	0.0202550i	0.220824	+	0.975314i	$0.429125\pi$
$180$	−1.01677	+	5.94121i	−0.0757854	+	0.442832i
$181$	−4.00187	+	4.00187i	−0.297457	+	0.297457i	−0.840017	−	0.542560i	$-0.817455\pi$
$181$	−4.00187	+	4.00187i	−0.297457	+	0.297457i	0.542560	+	0.840017i	$0.317455\pi$
$182$	−1.40264	−	4.27122i	−0.103971	−	0.316604i
$183$			6.64455i			0.491179i
$184$	−1.95928	+	1.52706i	−0.144440	+	0.112576i
$185$	14.3187	+	8.26692i	1.05273	+	0.607796i
$186$	−4.23926	+	1.34838i	−0.310838	+	0.0988681i
$187$	1.12321	+	0.300964i	0.0821375	+	0.0220087i
$188$	−25.7582	+	2.38434i	−1.87861	+	0.173896i
$189$	0.660854	−	2.56189i	0.0480701	−	0.186350i
$190$	−17.7242	+	0.818583i	−1.28585	+	0.0593863i
$191$	−7.65362	−	13.2565i	−0.553797	−	0.959204i	−0.997996	−	0.0632761i	$-0.979845\pi$
$191$	−7.65362	−	13.2565i	−0.553797	−	0.959204i	0.444199	−	0.895928i	$-0.353488\pi$
$192$	−6.86697	+	4.10423i	−0.495581	+	0.296197i
$193$	7.56239	−	13.0984i	0.544353	−	0.942846i	−0.454295	−	0.890851i	$-0.650109\pi$
$193$	7.56239	−	13.0984i	0.544353	−	0.942846i	0.998647	−	0.0519949i	$-0.0165579\pi$
$194$	5.46525	+	8.53124i	0.392382	+	0.612508i
$195$	−2.56051	−	2.56051i	−0.183362	−	0.183362i
$196$	8.29993	+	11.2744i	0.592852	+	0.805311i
$197$	−15.4948	+	15.4948i	−1.10396	+	1.10396i	−0.110032	+	0.993928i	$0.535095\pi$
$197$	−15.4948	+	15.4948i	−1.10396	+	1.10396i	−0.993928	+	0.110032i	$0.964905\pi$
$198$	−0.489916	+	2.23651i	−0.0348168	+	0.158942i
$199$	−3.62280	−	2.09163i	−0.256814	−	0.148271i	0.366066	−	0.930589i	$-0.380704\pi$
$199$	−3.62280	−	2.09163i	−0.256814	−	0.148271i	−0.622880	+	0.782317i	$0.714038\pi$
$200$	−10.7024	−	4.33863i	−0.756772	−	0.306787i
$201$	−11.8989	+	6.86985i	−0.839285	+	0.484562i
$202$	2.80027	−	3.07146i	0.197027	−	0.216107i
$203$	13.2538	+	3.41890i	0.930236	+	0.239960i
$204$	−1.10508	−	0.917831i	−0.0773714	−	0.0642610i
$205$	−6.94890	+	25.9337i	−0.485332	+	1.81129i
$206$	−23.9465	−	12.3892i	−1.66843	−	0.863197i
$207$	0.439128	−	0.760593i	0.0305215	−	0.0528649i
$208$	0.370623	−	4.79172i	0.0256981	−	0.332246i
$209$	−6.73959			−0.466188
$210$	10.0635	+	5.08790i	0.694450	+	0.351099i
$211$	4.97004	+	4.97004i	0.342152	+	0.342152i	0.857176	−	0.515024i	$-0.172217\pi$
$211$	4.97004	+	4.97004i	0.342152	+	0.342152i	−0.515024	+	0.857176i	$0.672217\pi$
$212$	2.57402	+	0.440513i	0.176784	+	0.0302545i
$213$	2.22872	+	8.31771i	0.152710	+	0.569920i
$214$	−3.67233	−	11.5457i	−0.251035	−	0.789246i
$215$	32.8055	−	18.9402i	2.23731	−	1.29171i
$216$	1.70483	−	2.25689i	0.115999	−	0.153562i
$217$	0.0777880	+	8.32208i	0.00528059	+	0.564940i
$218$	−11.0800	−	10.1018i	−0.750435	−	0.684178i
$219$	−13.5092	−	3.61977i	−0.912865	−	0.244601i
$220$	−8.86473	−	4.07946i	−0.597660	−	0.275037i
$221$	0.833597	−	0.223362i	0.0560738	−	0.0150249i
$222$	−4.18508	−	6.53289i	−0.280884	−	0.438459i
$223$	12.4184			0.831600			0.415800	−	0.909456i	$-0.363502\pi$
$223$	12.4184			0.831600			0.415800	+	0.909456i	$0.363502\pi$
$224$	3.55914	+	14.5373i	0.237805	+	0.971313i
$225$	4.08296			0.272197
$226$	−5.10725	−	7.97240i	−0.339729	−	0.530316i
$227$	11.8831	−	3.18408i	0.788712	−	0.211335i	0.158090	−	0.987425i	$-0.449466\pi$
$227$	11.8831	−	3.18408i	0.788712	−	0.211335i	0.630622	+	0.776090i	$0.282800\pi$
$228$	7.56345	+	3.48062i	0.500902	+	0.230510i
$229$	18.8504	+	5.05095i	1.24567	+	0.333776i	0.820662	−	0.571414i	$-0.193605\pi$
$229$	18.8504	+	5.05095i	1.24567	+	0.333776i	0.425007	+	0.905190i	$0.360272\pi$
$230$	2.76618	+	2.52195i	0.182397	+	0.166293i
$231$	3.72933	+	2.10690i	0.245372	+	0.138624i
$232$	11.6759	+	8.81989i	0.766561	+	0.579054i
$233$	−25.1653	+	14.5292i	−1.64864	+	0.951841i	−0.671021	+	0.741438i	$0.734144\pi$
$233$	−25.1653	+	14.5292i	−1.64864	+	0.951841i	−0.977615	+	0.210403i	$0.932523\pi$
$234$	0.515036	+	1.61925i	0.0336690	+	0.105854i
$235$	10.0890	+	37.6527i	0.658134	+	2.45619i
$236$	22.0665	+	3.77642i	1.43641	+	0.245824i
$237$	1.12164	+	1.12164i	0.0728585	+	0.0728585i
$238$	−2.24933	+	1.47079i	−0.145802	+	0.0953370i
$239$	−8.59317			−0.555846			−0.277923	−	0.960603i	$-0.589646\pi$
$239$	−8.59317			−0.555846			−0.277923	+	0.960603i	$0.589646\pi$
$240$	7.84155	+	9.15628i	0.506170	+	0.591035i
$241$	2.55254	−	4.42114i	0.164424	−	0.284790i	−0.772027	−	0.635590i	$-0.780757\pi$
$241$	2.55254	−	4.42114i	0.164424	−	0.284790i	0.936451	+	0.350800i	$0.114090\pi$
$242$	10.5246	+	5.44510i	0.676545	+	0.350024i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	10.2229	+	8.49068i	0.654456	+	0.543560i
$245$	14.6361	−	15.1938i	0.935064	−	0.970694i
$246$	8.48805	−	9.31005i	0.541178	−	0.593587i
$247$	−4.33170	+	2.50091i	−0.275620	+	0.159129i
$248$	−3.34256	+	8.24531i	−0.212253	+	0.523578i
$249$	−2.65457	−	1.53261i	−0.168226	−	0.0971255i
$250$	0.836354	−	3.81803i	0.0528957	−	0.241473i
$251$	19.8230	−	19.8230i	1.25122	−	1.25122i	0.296043	−	0.955175i	$-0.404333\pi$
$251$	19.8230	−	19.8230i	1.25122	−	1.25122i	0.955175	−	0.296043i	$-0.0956672\pi$
$252$	−3.09711	−	4.29044i	−0.195100	−	0.270272i
$253$	1.00540	+	1.00540i	0.0632090	+	0.0632090i
$254$	−14.4539	−	22.5624i	−0.906916	−	1.41569i
$255$	−1.08235	+	1.87469i	−0.0677796	+	0.117398i
$256$	−2.46037	+	15.8097i	−0.153773	+	0.988106i
$257$	3.00228	+	5.20011i	0.187277	+	0.324374i	0.944342	−	0.328967i	$-0.106700\pi$
$257$	3.00228	+	5.20011i	0.187277	+	0.324374i	−0.757064	+	0.653340i	$0.773367\pi$
$258$	−17.7564	+	0.820068i	−1.10546	+	0.0510552i
$259$	−13.9844	+	3.88757i	−0.868950	+	0.241562i
$260$	−7.21137	+	0.667531i	−0.447230	+	0.0413985i
$261$	−4.99718	−	1.33899i	−0.309318	−	0.0828814i
$262$	16.1136	−	5.12524i	0.995499	−	0.316638i
$263$	3.76626	+	2.17445i	0.232238	+	0.134083i	0.611604	−	0.791164i	$-0.290525\pi$
$263$	3.76626	+	2.17445i	0.232238	+	0.134083i	−0.379366	+	0.925247i	$0.623858\pi$
$264$	2.81493	+	3.61166i	0.173247	+	0.222282i
$265$		−	3.93517i		−	0.241736i
$266$	10.3862	−	11.6081i	0.636820	−	0.711740i
$267$	8.04817	−	8.04817i	0.492540	−	0.492540i
$268$	−4.63538	+	27.0856i	−0.283151	+	1.65452i
$269$	−3.94085	+	1.05595i	−0.240278	+	0.0643823i	−0.376948	−	0.926234i	$-0.623027\pi$
$269$	−3.94085	+	1.05595i	−0.240278	+	0.0643823i	0.136670	+	0.990617i	$0.456360\pi$
$270$	−3.78552	−	1.95851i	−0.230379	−	0.119191i
$271$	2.74862	+	4.76074i	0.166967	+	0.289195i	0.937352	−	0.348384i	$-0.113269\pi$
$271$	2.74862	+	4.76074i	0.166967	+	0.289195i	−0.770385	+	0.637579i	$0.779936\pi$
$272$	−2.82425	+	0.527380i	−0.171245	+	0.0319771i
$273$	3.17876	−	0.0297124i	0.192387	−	0.00179828i
$274$	1.00822	+	21.8302i	0.0609086	+	1.31881i
$275$	−1.71082	+	6.38487i	−0.103166	+	0.385022i
$276$	−0.609069	−	1.64754i	−0.0366617	−	0.0991700i
$277$	−2.92880	−	10.9304i	−0.175974	−	0.656746i	−0.996384	−	0.0849687i	$-0.972921\pi$
$277$	−2.92880	−	10.9304i	−0.175974	−	0.656746i	0.820409	−	0.571777i	$-0.193746\pi$
$278$	−6.90436	−	1.51243i	−0.414096	−	0.0907093i
$279$		−	3.14559i		−	0.188321i
$280$	20.6876	−	8.98166i	1.23632	−	0.536757i
$281$		−	22.1903i		−	1.32376i	−0.749608	−	0.661882i	$-0.769758\pi$
$281$		−	22.1903i		−	1.32376i	0.749608	−	0.661882i	$-0.230242\pi$
$282$	3.91406	−	17.8680i	0.233079	−	1.06402i
$283$	−1.55575	−	5.80612i	−0.0924795	−	0.345138i	0.904146	−	0.427224i	$-0.140508\pi$
$283$	−1.55575	−	5.80612i	−0.0924795	−	0.345138i	−0.996625	+	0.0820859i	$0.973842\pi$
$284$	15.6451	+	7.19972i	0.928367	+	0.427225i
$285$	3.24721	−	12.1188i	0.192348	−	0.717854i
$286$	−2.74797	+	0.126914i	−0.162491	+	0.00750456i
$287$	−11.9752	−	20.3010i	−0.706871	−	1.19833i
$288$	−1.29381	−	5.50691i	−0.0762386	−	0.324498i
$289$	8.24205	+	14.2756i	0.484826	+	0.839744i
$290$	10.1323	−	19.5842i	0.594989	−	1.15002i
$291$	−6.92007	+	1.85423i	−0.405662	+	0.108697i
$292$	−22.8318	+	16.1590i	−1.33613	+	0.945632i
$293$	−17.1405	+	17.1405i	−1.00136	+	1.00136i	−0.00135937	+	0.999999i	$0.500433\pi$
$293$	−17.1405	+	17.1405i	−1.00136	+	1.00136i	−0.999999	+	0.00135937i	$0.999567\pi$
$294$	−9.37605	+	3.17642i	−0.546822	+	0.185253i
$295$		−	33.7354i		−	1.96415i
$296$	−15.3990	−	1.90907i	−0.895050	−	0.110963i
$297$	−1.40205	−	0.809474i	−0.0813552	−	0.0469704i
$298$	−8.37908	−	26.3435i	−0.485387	−	1.52604i
$299$	1.01928	+	0.273115i	0.0589463	+	0.0157946i
$300$	5.21738	−	6.28182i	0.301225	−	0.362681i
$301$	−8.30630	+	32.2004i	−0.478767	+	1.85600i
$302$	0.475655	+	10.2990i	0.0273709	+	0.592643i
$303$	1.46950	+	2.54524i	0.0844204	+	0.146220i
$304$	15.0200	−	7.18902i	0.861456	−	0.412319i
$305$	10.0127	−	17.3424i	0.573323	−	0.993024i
$306$	0.855325	−	0.547935i	0.0488957	−	0.0313234i
$307$	3.64669	+	3.64669i	0.208128	+	0.208128i	0.803471	−	0.595344i	$-0.202984\pi$
$307$	3.64669	+	3.64669i	0.208128	+	0.208128i	−0.595344	+	0.803471i	$0.702984\pi$
$308$	8.00706	−	3.04546i	0.456244	−	0.173531i
$309$	13.4808	−	13.4808i	0.766895	−	0.766895i
$310$	13.0964	+	2.86883i	0.743828	+	0.162938i
$311$	15.9471	+	9.20705i	0.904276	+	0.522084i	0.878585	−	0.477586i	$-0.158488\pi$
$311$	15.9471	+	9.20705i	0.904276	+	0.522084i	0.0256907	+	0.999670i	$0.491822\pi$
$312$	3.14943	+	1.27675i	0.178301	+	0.0722815i
$313$	−16.2715	+	9.39433i	−0.919717	+	0.530999i	−0.883545	−	0.468347i	$-0.844850\pi$
$313$	−16.2715	+	9.39433i	−0.919717	+	0.530999i	−0.0361721	+	0.999346i	$0.511516\pi$
$314$	−7.96377	−	7.26064i	−0.449422	−	0.409742i
$315$	−5.58535	+	5.69075i	−0.314699	+	0.320637i
$316$	3.15898	−	0.292415i	0.177706	−	0.0164496i
$317$	1.38739	−	5.17780i	0.0779235	−	0.290814i	−0.915957	−	0.401277i	$-0.868567\pi$
$317$	1.38739	−	5.17780i	0.0779235	−	0.290814i	0.993880	+	0.110462i	$0.0352332\pi$
$318$	−0.848523	+	1.64007i	−0.0475828	+	0.0919704i
$319$	4.18778	−	7.25345i	0.234471	−	0.406115i
$320$	24.1076	−	0.364308i	1.34766	−	0.0203654i
$321$	8.56705			0.478166
$322$	−3.28108	+	0.182282i	−0.182847	+	0.0101582i
$323$	2.11432	+	2.11432i	0.117644	+	0.117644i
$324$	1.15539	+	1.63251i	0.0641883	+	0.0906947i
$325$	1.26969	+	4.73856i	0.0704299	+	0.262848i
$326$	0.890061	−	0.283102i	0.0492959	−	0.0156795i
$327$	9.18177	−	5.30110i	0.507753	−	0.293151i
$328$	−3.47753	−	24.9560i	−0.192015	−	1.37797i
$329$	−29.7945	−	16.8325i	−1.64263	−	0.928009i
$330$	4.64888	−	5.09908i	0.255912	−	0.280695i
$331$	−3.16038	−	0.846822i	−0.173710	−	0.0465456i	0.170915	−	0.985286i	$-0.445328\pi$
$331$	−3.16038	−	0.846822i	−0.173710	−	0.0465456i	−0.344626	+	0.938740i	$0.611994\pi$
$332$	−5.75011	+	2.12573i	−0.315578	+	0.116665i
$333$	5.29912	−	1.41990i	0.290390	−	0.0778098i
$334$	−0.885020	+	0.566959i	−0.0484261	+	0.0310226i
$335$	41.4086			2.26239
$336$	−10.5587	−	0.717462i	−0.576022	−	0.0391408i
$337$	−11.5318			−0.628176			−0.314088	−	0.949394i	$-0.601699\pi$
$337$	−11.5318			−0.628176			−0.314088	+	0.949394i	$0.601699\pi$
$338$	13.7615	−	8.81587i	0.748529	−	0.479520i
$339$	6.46677	−	1.73277i	0.351227	−	0.0941110i
$340$	1.50122	+	4.06081i	0.0814151	+	0.220228i
$341$	4.91902	+	1.31805i	0.266380	+	0.0713763i
$342$	−3.96646	+	4.35057i	−0.214481	+	0.235252i
$343$	0.519253	+	18.5130i	0.0280370	+	0.999607i
$344$	−21.4281	+	28.3669i	−1.15533	+	1.52944i
$345$	−2.29227	+	1.32344i	−0.123412	+	0.0712518i
$346$	7.49295	−	2.38328i	0.402823	−	0.128126i
$347$	0.617704	+	2.30530i	0.0331601	+	0.123755i	0.980522	−	0.196410i	$-0.0629283\pi$
$347$	0.617704	+	2.30530i	0.0331601	+	0.123755i	−0.947362	+	0.320165i	$0.896262\pi$
$348$	−8.44570	+	5.97736i	−0.452737	+	0.320420i
$349$	−13.3603	−	13.3603i	−0.715162	−	0.715162i	0.252449	−	0.967610i	$-0.418764\pi$
$349$	−13.3603	−	13.3603i	−0.715162	−	0.715162i	−0.967610	+	0.252449i	$0.918764\pi$
$350$	−8.36065	−	12.7862i	−0.446895	−	0.683452i
$351$	−1.20151			−0.0641318
$352$	9.15374	+	0.284233i	0.487896	+	0.0151497i
$353$	−6.73078	+	11.6581i	−0.358243	+	0.620496i	−0.987667	−	0.156566i	$-0.949957\pi$
$353$	−6.73078	+	11.6581i	−0.358243	+	0.620496i	0.629424	+	0.777062i	$0.283291\pi$
$354$	−7.27421	+	14.0600i	−0.386620	+	0.747279i
$355$	6.71691	−	25.0679i	0.356497	−	1.33046i
$356$	−2.09818	−	22.6668i	−0.111203	−	1.20134i
$357$	−0.508983	−	1.83092i	−0.0269383	−	0.0969028i
$358$	−1.09423	−	0.997620i	−0.0578319	−	0.0527259i
$359$	−14.3623	+	8.29205i	−0.758011	+	0.437638i	−0.828581	−	0.559869i	$-0.810851\pi$
$359$	−14.3623	+	8.29205i	−0.758011	+	0.437638i	0.0705701	+	0.997507i	$0.477518\pi$
$360$	−7.85056	+	3.32152i	−0.413761	+	0.175059i
$361$	1.44615	+	0.834933i	0.0761130	+	0.0439439i
$362$	−7.81836	−	1.71264i	−0.410924	−	0.0900144i
$363$	−5.92485	+	5.92485i	−0.310974	+	0.310974i
$364$	4.01623	−	4.92862i	0.210508	−	0.258330i
$365$	29.8046	+	29.8046i	1.56004	+	1.56004i
$366$	−7.91245	+	5.06885i	−0.413590	+	0.264953i
$367$	13.5299	−	23.4345i	0.706255	−	1.22327i	−0.259982	−	0.965614i	$-0.583717\pi$
$367$	13.5299	−	23.4345i	0.706255	−	1.22327i	0.966237	−	0.257656i	$-0.0829501\pi$
$368$	−3.31310	−	1.16821i	−0.172707	−	0.0608972i
$369$	4.45427	+	7.71502i	0.231880	+	0.401628i
$370$	1.07875	+	23.3575i	0.0560817	+	1.21430i
$371$	2.46551	+	2.41984i	0.128003	+	0.125632i
$372$	−4.83963	−	4.01957i	−0.250923	−	0.208405i
$373$	33.7616	+	9.04640i	1.74811	+	0.468405i	0.984221	−	0.176942i	$-0.0566206\pi$
$373$	33.7616	+	9.04640i	1.74811	+	0.468405i	0.763889	+	0.645347i	$0.223287\pi$
$374$	0.498458	+	1.56714i	0.0257747	+	0.0810346i
$375$	2.39349	+	1.38188i	0.123600	+	0.0713602i
$376$	−22.4892	−	28.8544i	−1.15979	−	1.48805i
$377$		−	6.21596i		−	0.320138i
$378$	3.55488	−	1.16740i	0.182843	−	0.0600445i
$379$	10.5700	−	10.5700i	0.542945	−	0.542945i	−0.381446	−	0.924391i	$-0.624574\pi$
$379$	10.5700	−	10.5700i	0.542945	−	0.542945i	0.924391	+	0.381446i	$0.124574\pi$
$380$	−14.4958	−	20.4819i	−0.743621	−	1.05070i
$381$	18.3014	−	4.90385i	0.937609	−	0.251232i
$382$	9.94741	−	19.2269i	0.508954	−	0.983732i
$383$	6.18092	+	10.7057i	0.315830	+	0.547034i	0.979614	−	0.200891i	$-0.0643836\pi$
$383$	6.18092	+	10.7057i	0.315830	+	0.547034i	−0.663783	+	0.747925i	$0.731050\pi$
$384$	−10.1259	−	5.04637i	−0.516736	−	0.257522i
$385$	−6.55876	−	11.1188i	−0.334265	−	0.566666i
$386$	21.3669	−	0.986818i	1.08755	−	0.0502277i
$387$	3.25310	−	12.1407i	0.165365	−	0.617149i
$388$	−5.98995	+	13.0163i	−0.304093	+	0.660800i
$389$	−6.75986	−	25.2281i	−0.342739	−	1.27912i	−0.895232	−	0.445600i	$-0.852990\pi$
$389$	−6.75986	−	25.2281i	−0.342739	−	1.27912i	0.552493	−	0.833517i	$-0.313676\pi$
$390$	1.09580	−	5.00240i	0.0554877	−	0.253306i
$391$		−	0.630822i		−	0.0319021i
$392$	−7.09404	+	18.4844i	−0.358303	+	0.933605i
$393$			11.9565i			0.603125i
$394$	−30.2719	−	6.63117i	−1.52507	−	0.334074i
$395$	−1.23731	−	4.61771i	−0.0622559	−	0.232342i
$396$	−3.03701	+	1.12274i	−0.152615	+	0.0564196i
$397$	8.32959	−	31.0864i	0.418050	−	1.56018i	−0.360597	−	0.932722i	$-0.617427\pi$
$397$	8.32959	−	31.0864i	0.418050	−	1.56018i	0.778647	−	0.627462i	$-0.215906\pi$
$398$	−0.272937	−	5.90971i	−0.0136811	−	0.296227i
$399$	5.59598	+	9.48662i	0.280149	+	0.474925i
$400$	−2.99787	−	16.0543i	−0.149894	−	0.802717i
$401$	8.76492	+	15.1813i	0.437699	+	0.758117i	0.997512	−	0.0705021i	$-0.0224601\pi$
$401$	8.76492	+	15.1813i	0.437699	+	0.758117i	−0.559812	+	0.828619i	$0.689127\pi$
$402$	−17.2579	−	8.92874i	−0.860747	−	0.445325i
$403$	3.65067	−	0.978195i	0.181853	−	0.0487273i
$404$	5.79376	+	0.991532i	0.288250	+	0.0493306i
$405$	2.13107	−	2.13107i	0.105894	−	0.105894i
$406$	6.03949	+	18.3910i	0.299735	+	0.912731i
$407$			8.88164i			0.440246i
$408$	0.249947	−	2.01613i	0.0123742	−	0.0998133i
$409$	−19.1772	−	11.0720i	−0.948254	−	0.547474i	−0.0557156	−	0.998447i	$-0.517744\pi$
$409$	−19.1772	−	11.0720i	−0.948254	−	0.547474i	−0.892538	+	0.450972i	$0.851077\pi$
$410$	−36.1833	+	11.5088i	−1.78697	+	0.568380i
$411$	−14.9262	−	3.99947i	−0.736256	−	0.197279i
$412$	−3.51448	−	37.9671i	−0.173146	−	1.87051i
$413$	21.1363	+	20.7448i	1.04005	+	1.02078i
$414$	1.24072	−	0.0573020i	0.0609781	−	0.00281624i
$415$	4.61899	+	8.00032i	0.226737	+	0.392720i
$416$	5.98881	−	3.21406i	0.293625	−	0.157582i
$417$	2.49894	−	4.32829i	0.122374	−	0.211957i
$418$	−5.14135	−	8.02563i	−0.251472	−	0.392547i
$419$	6.20462	+	6.20462i	0.303116	+	0.303116i	0.842232	−	0.539116i	$-0.181242\pi$
$419$	6.20462	+	6.20462i	0.303116	+	0.303116i	−0.539116	+	0.842232i	$0.681242\pi$
$420$	1.61828	+	15.8652i	0.0789638	+	0.774142i
$421$	3.74625	−	3.74625i	0.182581	−	0.182581i	−0.609898	−	0.792480i	$-0.708790\pi$
$421$	3.74625	−	3.74625i	0.182581	−	0.182581i	0.792480	+	0.609898i	$0.208790\pi$
$422$	−2.12698	+	9.70986i	−0.103540	+	0.472668i
$423$	11.2013	+	6.46708i	0.544627	+	0.314440i
$424$	1.43904	+	3.40124i	0.0698860	+	0.165179i
$425$	2.53975	−	1.46633i	0.123196	−	0.0711273i
$426$	−8.20468	+	8.99923i	−0.397518	+	0.436014i
$427$	4.70851	+	16.9375i	0.227861	+	0.819665i
$428$	10.9473	−	13.1808i	0.529159	−	0.637117i
$429$	0.503450	−	1.87890i	0.0243068	−	0.0907141i
$430$	47.5803	+	24.6166i	2.29452	+	1.18712i
$431$	−2.20070	+	3.81172i	−0.106004	+	0.183604i	−0.914148	−	0.405381i	$-0.867139\pi$
$431$	−2.20070	+	3.81172i	−0.106004	+	0.183604i	0.808144	+	0.588985i	$0.200472\pi$
$432$	3.98809	+	0.308464i	0.191877	+	0.0148410i
$433$	−30.3709			−1.45953			−0.729766	−	0.683697i	$-0.760371\pi$
$433$	−30.3709			−1.45953			−0.729766	+	0.683697i	$0.760371\pi$
$434$	−9.85075	+	6.44120i	−0.472851	+	0.309187i
$435$	11.0250	+	11.0250i	0.528610	+	0.528610i
$436$	3.57688	−	20.9005i	0.171301	−	1.00095i
$437$	0.946278	+	3.53156i	0.0452666	+	0.168937i
$438$	−5.99508	−	18.8483i	−0.286456	−	0.900608i
$439$	−9.52183	+	5.49743i	−0.454452	+	0.262378i	−0.709709	−	0.704495i	$-0.751173\pi$
$439$	−9.52183	+	5.49743i	−0.454452	+	0.262378i	0.255257	+	0.966873i	$0.417840\pi$
$440$	−1.90463	−	13.6683i	−0.0907999	−	0.651612i
$441$	−0.130849	−	6.99878i	−0.00623091	−	0.333275i
$442$	0.901900	+	0.822270i	0.0428990	+	0.0391114i
$443$	1.66801	+	0.446942i	0.0792496	+	0.0212349i	0.298226	−	0.954495i	$-0.403605\pi$
$443$	1.66801	+	0.446942i	0.0792496	+	0.0212349i	−0.218976	+	0.975730i	$0.570272\pi$
$444$	4.58687	−	9.96734i	0.217683	−	0.473029i
$445$	−33.1337	+	8.87814i	−1.57069	+	0.420864i
$446$	9.47350	+	14.7881i	0.448583	+	0.700237i
$447$	19.5472			0.924553
$448$	−14.5961	+	15.3282i	−0.689603	+	0.724188i
$449$	0.963681			0.0454789			0.0227395	−	0.999741i	$-0.492761\pi$
$449$	0.963681			0.0454789			0.0227395	+	0.999741i	$0.492761\pi$
$450$	3.11472	+	4.86206i	0.146829	+	0.229200i
$451$	−13.9310	+	3.73281i	−0.655986	+	0.175771i
$452$	5.59757	−	12.1636i	0.263288	−	0.572129i
$453$	−7.04187	−	1.88686i	−0.330856	−	0.0886526i
$454$	12.8568	+	11.7217i	0.603400	+	0.550125i
$455$	−8.34140	−	4.71251i	−0.391051	−	0.220926i
$456$	1.62505	+	11.6619i	0.0760998	+	0.546119i
$457$	26.7475	−	15.4427i	1.25120	−	0.722378i	0.279849	−	0.960044i	$-0.409716\pi$
$457$	26.7475	−	15.4427i	1.25120	−	0.722378i	0.971347	+	0.237666i	$0.0763823\pi$
$458$	8.36541	+	26.3005i	0.390890	+	1.22894i
$459$	0.185901	+	0.693792i	0.00867712	+	0.0323834i
$460$	−0.892983	+	5.21791i	−0.0416356	+	0.243286i
$461$	−24.0002	−	24.0002i	−1.11780	−	1.11780i	−0.992064	−	0.125737i	$-0.959870\pi$
$461$	−24.0002	−	24.0002i	−1.11780	−	1.11780i	−0.125737	−	0.992064i	$-0.540130\pi$
$462$	0.336013	+	6.04822i	0.0156327	+	0.281389i
$463$	17.5538			0.815793			0.407896	−	0.913028i	$-0.366262\pi$
$463$	17.5538			0.815793			0.407896	+	0.913028i	$0.366262\pi$
$464$	−1.59583	+	20.6322i	−0.0740844	+	0.957826i
$465$	−4.74008	+	8.21006i	−0.219816	+	0.380732i
$466$	−36.4992	−	18.8836i	−1.69079	−	0.874767i
$467$	3.66465	−	13.6767i	0.169580	−	0.632880i	−0.827832	−	0.560976i	$-0.810426\pi$
$467$	3.66465	−	13.6767i	0.169580	−	0.632880i	0.997412	−	0.0719040i	$-0.0229075\pi$
$468$	−1.53534	+	1.84858i	−0.0709711	+	0.0854504i
$469$	−25.4632	+	25.9437i	−1.17578	+	1.19797i
$470$	−37.1410	+	40.7378i	−1.71319	+	1.87910i
$471$	6.59939	−	3.81016i	0.304084	−	0.175563i
$472$	12.3366	+	29.1581i	0.567838	+	1.34211i
$473$	17.6224	+	10.1743i	0.810279	+	0.467815i
$474$	−0.480019	+	2.19133i	−0.0220480	+	0.100651i
$475$	−12.0188	+	12.0188i	−0.551460	+	0.551460i
$476$	−3.46736	−	1.55654i	−0.158926	−	0.0713438i
$477$	−0.923284	−	0.923284i	−0.0422743	−	0.0422743i
$478$	−6.55537	−	10.2329i	−0.299836	−	0.468042i
$479$	−14.2611	+	24.7010i	−0.651608	+	1.12862i	0.331125	+	0.943587i	$0.392572\pi$
$479$	−14.2611	+	24.7010i	−0.651608	+	1.12862i	−0.982733	+	0.185031i	$0.940761\pi$
$480$	−4.92147	+	16.3228i	−0.224633	+	0.745031i
$481$	3.29577	+	5.70844i	0.150274	+	0.260283i
$482$	7.21200	−	0.333082i	0.328498	−	0.0151715i
$483$	0.580400	−	2.25000i	0.0264091	−	0.102378i
$484$	1.54463	+	16.6867i	0.0702102	+	0.758485i
$485$	20.8557	+	5.58826i	0.947008	+	0.253750i
$486$	−1.34768	+	0.428658i	−0.0611322	+	0.0194443i
$487$	−32.0744	−	18.5182i	−1.45343	−	0.839138i	−0.454755	−	0.890617i	$-0.650273\pi$
$487$	−32.0744	−	18.5182i	−1.45343	−	0.839138i	−0.998674	+	0.0514788i	$0.983607\pi$
$488$	−2.31221	+	18.6508i	−0.104669	+	0.844284i
$489$			0.660438i			0.0298660i
$490$	29.2583	+	5.83821i	1.32175	+	0.263744i
$491$	−26.0278	+	26.0278i	−1.17462	+	1.17462i	−0.193521	+	0.981096i	$0.561991\pi$
$491$	−26.0278	+	26.0278i	−1.17462	+	1.17462i	−0.981096	+	0.193521i	$0.938009\pi$
$492$	17.5617	+	3.00548i	0.791745	+	0.135498i
$493$	−3.58930	+	0.961751i	−0.161654	+	0.0433151i
$494$	−6.28260	−	3.25043i	−0.282668	−	0.146244i
$495$	2.43959	+	4.22549i	0.109651	+	0.189922i
$496$	−12.3686	+	2.30962i	−0.555365	+	0.103705i
$497$	11.5754	+	19.6232i	0.519226	+	0.880222i
$498$	−0.199991	−	4.33027i	−0.00896182	−	0.194044i
$499$	9.64417	−	35.9925i	0.431732	−	1.61125i	−0.317035	−	0.948414i	$-0.602687\pi$
$499$	9.64417	−	35.9925i	0.431732	−	1.61125i	0.748767	−	0.662833i	$-0.230646\pi$
$500$	5.18460	−	1.91667i	0.231862	−	0.0857160i
$501$	−0.192355	−	0.717879i	−0.00859380	−	0.0320725i
$502$	38.7278	+	8.48347i	1.72850	+	0.378636i
$503$			8.33653i			0.371708i	0.982577	+	0.185854i	$0.0595051\pi$
$503$			8.33653i			0.371708i	−0.982577	+	0.185854i	$0.940495\pi$
$504$	2.74648	−	6.96110i	0.122338	−	0.310072i
$505$		−	8.85753i		−	0.394155i
$506$	−0.430272	+	1.96423i	−0.0191279	+	0.0873206i
$507$	2.99101	+	11.1626i	0.132835	+	0.495749i
$508$	15.8415	−	34.4239i	0.702853	−	1.52731i
$509$	−5.44210	+	20.3102i	−0.241217	+	0.900233i	0.734031	+	0.679116i	$0.237637\pi$
$509$	−5.44210	+	20.3102i	−0.241217	+	0.900233i	−0.975247	+	0.221117i	$0.929030\pi$
$510$	−3.05810	+	0.141237i	−0.135415	+	0.00625406i
$511$	−37.0011	+	0.345856i	−1.63683	+	0.0152998i
$512$	−20.7034	+	9.13070i	−0.914969	+	0.403524i
$513$	−2.08147	−	3.60522i	−0.0918993	−	0.159174i
$514$	−3.90207	+	7.54212i	−0.172113	+	0.332668i
$515$	−55.4993	+	14.8710i	−2.44559	+	0.655295i
$516$	−14.5221	−	20.5190i	−0.639301	−	0.903299i
$517$	−14.8066	+	14.8066i	−0.651195	+	0.651195i
$518$	−15.2975	−	13.6873i	−0.672135	−	0.601383i
$519$			5.55987i			0.244051i
$520$	−6.29616	−	8.07821i	−0.276105	−	0.354253i
$521$	−9.75009	−	5.62921i	−0.427159	−	0.246620i	0.270977	−	0.962586i	$-0.412653\pi$
$521$	−9.75009	−	5.62921i	−0.427159	−	0.246620i	−0.698136	+	0.715966i	$0.745987\pi$
$522$	−2.21764	−	6.97219i	−0.0970636	−	0.305164i
$523$	23.4830	+	6.29225i	1.02684	+	0.275141i	0.732650	−	0.680606i	$-0.238283\pi$
$523$	23.4830	+	6.29225i	1.02684	+	0.275141i	0.294191	+	0.955747i	$0.404950\pi$
$524$	18.3956	+	15.2785i	0.803615	+	0.667444i
$525$	10.4078	−	2.89330i	0.454235	−	0.126274i
$526$	0.283745	+	6.14373i	0.0123719	+	0.267880i
$527$	−1.12969	−	1.95667i	−0.0492099	−	0.0852340i
$528$	−2.15344	+	6.10726i	−0.0937164	+	0.265784i
$529$	−11.1143	+	19.2506i	−0.483232	+	0.836982i
$530$	4.68608	−	3.00198i	0.203550	−	0.130398i
$531$	−7.91512	−	7.91512i	−0.343487	−	0.343487i
$532$	21.7464	+	3.51274i	0.942824	+	0.152297i
$533$	−7.56865	+	7.56865i	−0.327835	+	0.327835i
$534$	15.7235	+	3.44430i	0.680423	+	0.149049i
$535$	−22.3602	−	12.9097i	−0.966715	−	0.558133i
$536$	−35.7902	+	15.1426i	−1.54590	+	0.654059i
$537$	0.906764	−	0.523520i	0.0391297	−	0.0225916i
$538$	−4.26375	−	3.88730i	−0.183823	−	0.167593i
$539$	10.9994	+	2.72797i	0.473778	+	0.117502i
$540$	−0.555577	−	6.00193i	−0.0239082	−	0.258282i
$541$	1.92604	−	7.18809i	0.0828071	−	0.309040i	−0.912083	−	0.410006i	$-0.865527\pi$
$541$	1.92604	−	7.18809i	0.0828071	−	0.309040i	0.994890	+	0.100966i	$0.0321932\pi$
$542$	−3.57238	+	6.90487i	−0.153447	+	0.296590i
$543$	2.82975	−	4.90127i	0.121436	−	0.210334i
$544$	−2.78251	−	2.96085i	−0.119299	−	0.126945i
$545$	−31.9528			−1.36871
$546$	2.46032	+	3.76265i	0.105292	+	0.161027i
$547$	−8.28379	−	8.28379i	−0.354189	−	0.354189i	0.507476	−	0.861666i	$-0.330578\pi$
$547$	−8.28379	−	8.28379i	−0.354189	−	0.354189i	−0.861666	+	0.507476i	$0.830578\pi$
$548$	−25.2267	+	17.8540i	−1.07763	+	0.762683i
$549$	−1.71974	−	6.41814i	−0.0733965	−	0.273920i
$550$	−8.90833	+	2.83347i	−0.379852	+	0.120820i
$551$	18.6514	−	10.7684i	0.794578	−	0.458750i
$552$	1.49728	−	1.98213i	0.0637286	−	0.0843649i
$553$	3.65399	+	2.06434i	0.155384	+	0.0877846i
$554$	10.7819	−	11.8260i	0.458079	−	0.502440i
$555$	−15.9705	−	4.27927i	−0.677909	−	0.181645i
$556$	−3.46602	−	9.37560i	−0.146992	−	0.397614i
$557$	23.1622	−	6.20628i	0.981412	−	0.262969i	0.267773	−	0.963482i	$-0.413712\pi$
$557$	23.1622	−	6.20628i	0.981412	−	0.262969i	0.713639	+	0.700513i	$0.247046\pi$
$558$	3.74582	−	2.39964i	0.158573	−	0.101585i
$559$	15.1018			0.638738
$560$	26.4772	+	17.7834i	1.11887	+	0.751486i
$561$	−1.16284			−0.0490950
$562$	26.4246	−	16.9281i	1.11466	−	0.714067i
$563$	15.6214	−	4.18575i	0.658364	−	0.176408i	0.0858565	−	0.996308i	$-0.472637\pi$
$563$	15.6214	−	4.18575i	0.658364	−	0.176408i	0.572508	+	0.819899i	$0.305971\pi$
$564$	24.2634	−	8.96982i	1.02167	−	0.377697i
$565$	−19.4895	−	5.22220i	−0.819931	−	0.219700i
$566$	5.72722	−	6.28186i	0.240733	−	0.264046i
$567$	0.0247292	+	2.64564i	0.00103853	+	0.111106i
$568$	3.36144	+	24.1229i	0.141043	+	1.01217i
$569$	18.8165	−	10.8637i	0.788831	−	0.455432i	−0.0507200	−	0.998713i	$-0.516152\pi$
$569$	18.8165	−	10.8637i	0.788831	−	0.455432i	0.839551	+	0.543281i	$0.182818\pi$
$570$	16.9084	−	5.37805i	0.708215	−	0.225262i
$571$	8.89834	+	33.2091i	0.372384	+	1.38976i	0.857130	+	0.515101i	$0.172246\pi$
$571$	8.89834	+	33.2091i	0.372384	+	1.38976i	−0.484746	+	0.874655i	$0.661088\pi$
$572$	−2.24744	−	3.17552i	−0.0939703	−	0.132775i
$573$	10.8239	+	10.8239i	0.452173	+	0.452173i
$574$	15.0394	−	29.7470i	0.627734	−	1.24162i
$575$	3.58589			0.149542
$576$	5.57073	−	5.74168i	0.232114	−	0.239237i
$577$	12.0977	−	20.9538i	0.503632	−	0.872317i	−0.496359	−	0.868117i	$-0.665330\pi$
$577$	12.0977	−	20.9538i	0.503632	−	0.872317i	0.999991	−	0.00419921i	$-0.00133665\pi$
$578$	−10.7122	+	20.7051i	−0.445568	+	0.861217i
$579$	−3.91458	+	14.6094i	−0.162684	+	0.607146i
$580$	31.0507	−	2.87425i	1.28931	−	0.119347i
$581$	−7.85277	−	2.02567i	−0.325788	−	0.0840389i
$582$	−7.48708	−	6.82604i	−0.310349	−	0.282948i
$583$	1.83069	−	1.05695i	0.0758193	−	0.0437743i
$584$	−36.6598	−	14.8615i	−1.51699	−	0.614973i
$585$	3.13597	+	1.81055i	0.129656	+	0.0748571i
$586$	−33.4870	−	7.33545i	−1.38333	−	0.303025i
$587$	−17.5732	+	17.5732i	−0.725324	+	0.725324i	−0.969685	−	0.244360i	$-0.921422\pi$
$587$	−17.5732	+	17.5732i	−0.725324	+	0.725324i	0.244360	+	0.969685i	$0.421422\pi$
$588$	−10.9351	−	8.74201i	−0.450957	−	0.360515i
$589$	9.25951	+	9.25951i	0.381531	+	0.381531i
$590$	40.1728	−	25.7353i	1.65389	−	1.05951i
$591$	10.9565	−	18.9772i	0.450690	−	0.780618i
$592$	−9.47390	−	19.7938i	−0.389375	−	0.813520i
$593$	−2.18629	−	3.78677i	−0.0897802	−	0.155504i	0.817638	−	0.575733i	$-0.195283\pi$
$593$	−2.18629	−	3.78677i	−0.0897802	−	0.155504i	−0.907418	+	0.420229i	$0.861950\pi$
$594$	−0.105628	−	2.28710i	−0.00433399	−	0.0938408i
$595$	−1.43056	+	5.54574i	−0.0586471	+	0.227353i
$596$	24.9783	−	30.0743i	1.02315	−	1.23189i
$597$	4.04071	+	1.08271i	0.165375	+	0.0443122i
$598$	0.452334	+	1.42212i	0.0184973	+	0.0581549i
$599$	−23.1175	−	13.3469i	−0.944555	−	0.545339i	−0.0531695	−	0.998586i	$-0.516932\pi$
$599$	−23.1175	−	13.3469i	−0.944555	−	0.545339i	−0.891385	+	0.453247i	$0.850266\pi$
$600$	11.4606	+	1.42082i	0.467878	+	0.0580046i
$601$			24.7794i			1.01077i	0.862893	+	0.505387i	$0.168650\pi$
$601$			24.7794i			1.01077i	−0.862893	+	0.505387i	$0.831350\pi$
$602$	−44.6814	+	14.6731i	−1.82108	+	0.598030i
$603$	9.71543	−	9.71543i	0.395643	−	0.395643i
$604$	−11.9014	+	8.42312i	−0.484262	+	0.342732i
$605$	24.3922	−	6.53586i	0.991682	−	0.265720i
$606$	−1.90991	+	3.69156i	−0.0775846	+	0.149960i
$607$	1.75533	+	3.04032i	0.0712466	+	0.123403i	0.899448	−	0.437028i	$-0.143969\pi$
$607$	1.75533	+	3.04032i	0.0712466	+	0.123403i	−0.828201	+	0.560431i	$0.810636\pi$
$608$	20.0189	+	12.4019i	0.811875	+	0.502963i
$609$	−13.6871	+	0.127936i	−0.554629	+	0.00518421i
$610$	28.2899	−	1.30655i	1.14542	−	0.0529008i
$611$	−4.02218	+	15.0110i	−0.162720	+	0.607280i
$612$	1.30498	+	0.600540i	0.0527508	+	0.0242754i
$613$	−4.94958	−	18.4721i	−0.199912	−	0.746081i	−0.990940	−	0.134302i	$-0.957121\pi$
$613$	−4.94958	−	18.4721i	−0.199912	−	0.746081i	0.791029	−	0.611779i	$-0.209546\pi$
$614$	−1.56064	+	7.12446i	−0.0629823	+	0.287520i
$615$		−	26.8485i		−	1.08264i
$616$	9.73483	+	7.21170i	0.392227	+	0.290568i
$617$			6.57778i			0.264811i	0.991196	+	0.132406i	$0.0422702\pi$
$617$			6.57778i			0.264811i	−0.991196	+	0.132406i	$0.957730\pi$
$618$	26.3371	+	5.76924i	1.05943	+	0.232073i
$619$	−2.79202	−	10.4200i	−0.112221	−	0.418814i	0.886843	−	0.462070i	$-0.152893\pi$
$619$	−2.79202	−	10.4200i	−0.112221	−	0.418814i	−0.999064	+	0.0432569i	$0.986227\pi$
$620$	6.57447	+	17.7840i	0.264037	+	0.714222i
$621$	−0.227310	+	0.848331i	−0.00912162	+	0.0340424i
$622$	1.20143	+	26.0137i	0.0481730	+	1.04306i
$623$	14.8123	−	26.2186i	0.593443	−	1.05043i
$624$	0.882195	+	4.72437i	0.0353161	+	0.189126i
$625$	−14.3721	−	24.8932i	−0.574885	−	0.995730i
$626$	−23.5997	−	12.2098i	−0.943235	−	0.488002i
$627$	6.50995	−	1.74434i	0.259982	−	0.0696621i
$628$	2.57088	−	15.0222i	0.102589	−	0.599452i
$629$	2.78632	−	2.78632i	0.111098	−	0.111098i
$630$	−11.0375	−	2.30990i	−0.439743	−	0.0920287i
$631$			29.5564i			1.17662i	0.808635	+	0.588311i	$0.200207\pi$
$631$			29.5564i			1.17662i	−0.808635	+	0.588311i	$0.799793\pi$
$632$	2.75807	+	3.53870i	0.109710	+	0.140762i
$633$	−6.08704	−	3.51435i	−0.241938	−	0.139683i
$634$	7.22420	−	2.29780i	0.286910	−	0.0912573i
$635$	−55.1567	−	14.7792i	−2.18883	−	0.586494i
$636$	−2.60032	+	0.240703i	−0.103110	+	0.00954448i
$637$	8.08187	−	2.32829i	0.320215	−	0.0922503i
$638$	11.8322	−	0.546465i	0.468442	−	0.0216347i
$639$	−4.30556	−	7.45745i	−0.170325	−	0.295012i
$640$	18.8245	+	28.4299i	0.744104	+	1.12379i
$641$	10.1860	−	17.6427i	0.402323	−	0.696845i	−0.591682	−	0.806171i	$-0.701536\pi$
$641$	10.1860	−	17.6427i	0.402323	−	0.696845i	0.994006	+	0.109326i	$0.0348694\pi$
$642$	6.53544	+	10.2018i	0.257933	+	0.402633i
$643$	−15.9874	−	15.9874i	−0.630481	−	0.630481i	0.317708	−	0.948189i	$-0.397087\pi$
$643$	−15.9874	−	15.9874i	−0.630481	−	0.630481i	−0.948189	+	0.317708i	$0.897087\pi$
$644$	−2.72006	−	3.76811i	−0.107185	−	0.148484i
$645$	−26.7855	+	26.7855i	−1.05468	+	1.05468i
$646$	−0.904847	+	4.13070i	−0.0356007	+	0.162520i
$647$	−19.5955	−	11.3135i	−0.770379	−	0.444779i	0.0626307	−	0.998037i	$-0.480051\pi$
$647$	−19.5955	−	11.3135i	−0.770379	−	0.444779i	−0.833010	+	0.553258i	$0.813384\pi$
$648$	−1.06262	+	2.62123i	−0.0417436	+	0.102972i
$649$	15.6941	−	9.06099i	0.616047	−	0.355675i
$650$	−4.67416	+	5.12682i	−0.183336	+	0.201090i
$651$	−2.22905	−	8.01838i	−0.0873634	−	0.314265i
$652$	1.01611	+	0.843935i	0.0397940	+	0.0330510i
$653$	10.8802	−	40.6056i	0.425777	−	1.58902i	−0.336445	−	0.941703i	$-0.609224\pi$
$653$	10.8802	−	40.6056i	0.425777	−	1.58902i	0.762221	−	0.647317i	$-0.224109\pi$
$654$	13.3170	+	6.88984i	0.520737	+	0.269414i
$655$	18.0172	−	31.2067i	0.703990	−	1.21935i
$656$	27.0652	−	23.1790i	1.05672	−	0.904988i
$657$	13.9857			0.545635
$658$	−2.68449	−	48.3207i	−0.104652	−	1.88374i
$659$	−15.4073	−	15.4073i	−0.600181	−	0.600181i	0.340179	−	0.940361i	$-0.389512\pi$
$659$	−15.4073	−	15.4073i	−0.600181	−	0.600181i	−0.940361	+	0.340179i	$0.889512\pi$
$660$	9.61852	+	1.64609i	0.374400	+	0.0640741i
$661$	7.92041	+	29.5594i	0.308068	+	1.14973i	0.930272	+	0.366870i	$0.119571\pi$
$661$	7.92041	+	29.5594i	0.308068	+	1.14973i	−0.622204	+	0.782855i	$0.713763\pi$
$662$	−1.40251	−	4.40945i	−0.0545102	−	0.171378i
$663$	−0.747383	+	0.431502i	−0.0290260	+	0.0167581i
$664$	−6.91787	−	5.22571i	−0.268466	−	0.202797i
$665$	−0.310259	−	33.1929i	−0.0120313	−	1.28716i
$666$	5.73331	+	5.22711i	0.222161	+	0.202546i
$667$	−4.38881	−	1.17598i	−0.169935	−	0.0455340i
$668$	−1.35029	−	0.621389i	−0.0522443	−	0.0240423i
$669$	−11.9953	+	3.21413i	−0.463765	+	0.124265i
$670$	31.5889	+	49.3101i	1.22039	+	1.90502i
$671$	10.7572			0.415276
$672$	−7.20039	−	13.1208i	−0.277761	−	0.506144i
$673$	−8.55608			−0.329813			−0.164906	−	0.986309i	$-0.552732\pi$
$673$	−8.55608			−0.329813			−0.164906	+	0.986309i	$0.552732\pi$
$674$	−8.79711	−	13.7323i	−0.338852	−	0.528947i
$675$	−3.94384	+	1.05675i	−0.151798	+	0.0406742i
$676$	20.9962	+	9.66224i	0.807546	+	0.371625i
$677$	23.0916	+	6.18738i	0.887484	+	0.237800i	0.673633	−	0.739066i	$-0.264733\pi$
$677$	23.0916	+	6.18738i	0.887484	+	0.237800i	0.213850	+	0.976866i	$0.431399\pi$
$678$	6.99664	+	6.37890i	0.268704	+	0.244980i
$679$	−16.3259	+	9.63034i	−0.626531	+	0.369579i
$680$	−3.69047	+	4.88550i	−0.141523	+	0.187350i
$681$	−10.6541	+	6.15117i	−0.408267	+	0.235713i
$682$	2.18296	+	6.86314i	0.0835898	+	0.262803i
$683$	8.06779	+	30.1094i	0.308706	+	1.15210i	0.929708	+	0.368296i	$0.120059\pi$
$683$	8.06779	+	30.1094i	0.308706	+	1.15210i	−0.621003	+	0.783808i	$0.713274\pi$
$684$	−8.20658	−	1.40446i	−0.313787	−	0.0537008i
$685$	32.9310	+	32.9310i	1.25823	+	1.25823i
$686$	−21.6495	+	14.7411i	−0.826581	+	0.562818i
$687$	−19.5154			−0.744558
$688$	−50.1264	−	3.87710i	−1.91105	−	0.147813i
$689$	0.784418	−	1.35865i	0.0298839	−	0.0517605i
$690$	−3.32466	−	1.72008i	−0.126568	−	0.0654823i
$691$	−10.5618	+	39.4172i	−0.401791	+	1.49950i	0.408108	+	0.912933i	$0.366189\pi$
$691$	−10.5618	+	39.4172i	−0.401791	+	1.49950i	−0.809899	+	0.586569i	$0.800478\pi$
$692$	8.55411	+	7.10463i	0.325178	+	0.270078i
$693$	−4.14756	−	1.06989i	−0.157553	−	0.0406417i
$694$	−2.27398	+	2.49419i	−0.0863189	+	0.0946782i
$695$	−13.0446	+	7.53129i	−0.494809	+	0.285678i
$696$	−13.5608	−	5.49741i	−0.514022	−	0.208379i
$697$	5.54144	+	3.19935i	0.209897	+	0.121184i
$698$	5.71769	−	26.1017i	0.216418	−	0.987965i
$699$	20.5474	−	20.5474i	0.777175	−	0.777175i
$700$	8.84809	−	19.7101i	0.334426	−	0.744971i
$701$	10.3426	+	10.3426i	0.390635	+	0.390635i	0.874914	−	0.484279i	$-0.160918\pi$
$701$	10.3426	+	10.3426i	0.390635	+	0.390635i	−0.484279	+	0.874914i	$0.660918\pi$
$702$	−0.916581	−	1.43078i	−0.0345941	−	0.0540013i
$703$	−11.4191	+	19.7784i	−0.430679	+	0.745957i
$704$	6.64453	+	11.1173i	0.250425	+	0.418998i
$705$	−19.4905	−	33.7585i	−0.734053	−	1.27142i
$706$	−19.0172	+	0.878301i	−0.715724	+	0.0330553i
$707$	5.54951	+	5.44672i	0.208711	+	0.204845i
$708$	−22.2920	+	2.06349i	−0.837786	+	0.0775508i
$709$	6.65170	+	1.78232i	0.249810	+	0.0669363i	0.381551	−	0.924348i	$-0.375390\pi$
$709$	6.65170	+	1.78232i	0.249810	+	0.0669363i	−0.131741	+	0.991284i	$0.542057\pi$
$710$	34.9753	−	11.1246i	1.31260	−	0.417498i
$711$	−1.37373	−	0.793121i	−0.0515187	−	0.0297444i
$712$	25.3914	−	19.7901i	0.951582	−	0.741664i
$713$		−	2.76264i		−	0.103461i
$714$	1.79202	−	2.00284i	0.0670645	−	0.0749544i
$715$	−4.14533	+	4.14533i	−0.155026	+	0.155026i
$716$	0.353241	−	2.06407i	0.0132012	−	0.0771380i
$717$	8.30037	−	2.22408i	0.309983	−	0.0830597i
$718$	−20.8307	−	10.7772i	−0.777395	−	0.402201i
$719$	−5.05239	−	8.75099i	−0.188422	−	0.326357i	0.756302	−	0.654223i	$-0.227004\pi$
$719$	−5.05239	−	8.75099i	−0.188422	−	0.326357i	−0.944724	+	0.327866i	$0.893671\pi$
$720$	−9.94418	−	6.81474i	−0.370598	−	0.253970i
$721$	24.8109	−	43.9166i	0.924005	−	1.63554i
$722$	0.108951	+	2.35903i	0.00405472	+	0.0877941i
$723$	−1.32129	+	4.93114i	−0.0491395	+	0.183391i
$724$	−3.92485	−	10.6167i	−0.145866	−	0.394568i
$725$	−5.46704	−	20.4033i	−0.203041	−	0.757759i
$726$	−11.5752	−	2.53560i	−0.429598	−	0.0941050i
$727$		−	10.7637i		−	0.399205i	−0.979877	−	0.199602i	$-0.936035\pi$
$727$		−	10.7637i		−	0.399205i	0.979877	−	0.199602i	$-0.0639651\pi$
$728$	8.93291	+	1.02276i	0.331076	+	0.0379061i
$729$		−	1.00000i		−	0.0370370i
$730$	−12.7552	+	58.2286i	−0.472091	+	2.15514i
$731$	−2.33660	−	8.72029i	−0.0864221	−	0.322532i
$732$	−12.0721	−	5.55548i	−0.446199	−	0.205336i
$733$	6.27926	−	23.4345i	0.231930	−	0.865574i	−0.747579	−	0.664173i	$-0.768784\pi$
$733$	6.27926	−	23.4345i	0.231930	−	0.865574i	0.979509	−	0.201401i	$-0.0645494\pi$
$734$	38.2276	−	1.76552i	1.41101	−	0.0651665i
$735$	−10.2049	+	18.4641i	−0.376414	+	0.681060i
$736$	−1.13630	−	4.83648i	−0.0418845	−	0.178275i
$737$	11.1219	+	19.2637i	0.409681	+	0.709589i
$738$	−5.78921	+	11.1897i	−0.213104	+	0.411898i
$739$	−51.9745	+	13.9265i	−1.91191	+	0.512296i	−0.918868	+	0.394565i	$0.870895\pi$
$739$	−51.9745	+	13.9265i	−1.91191	+	0.512296i	−0.993046	+	0.117731i	$0.962438\pi$
$740$	−26.9916	+	19.1030i	−0.992230	+	0.702242i
$741$	3.53682	−	3.53682i	0.129928	−	0.129928i
$742$	−1.00076	+	4.78196i	−0.0367391	+	0.175551i
$743$			38.1257i			1.39870i	0.714781	+	0.699348i	$0.246526\pi$
$743$			38.1257i			1.39870i	−0.714781	+	0.699348i	$0.753474\pi$
$744$	1.09462	−	8.82948i	0.0401308	−	0.323704i
$745$	−51.0188	−	29.4557i	−1.86918	−	1.07917i
$746$	14.9827	+	47.1051i	0.548556	+	1.72464i
$747$	2.96078	+	0.793340i	0.108329	+	0.0290268i
$748$	−1.48592	+	1.78907i	−0.0543306	+	0.0654151i
$749$	21.8382	−	6.07085i	0.797949	−	0.221824i
$750$	0.180322	+	3.90440i	0.00658445	+	0.142568i
$751$	−16.1750	−	28.0158i	−0.590233	−	1.02231i	−0.994201	−	0.107540i	$-0.965703\pi$
$751$	−16.1750	−	28.0158i	−0.590233	−	1.02231i	0.403968	−	0.914773i	$-0.367631\pi$
$752$	17.2043	−	48.7924i	0.627378	−	1.77927i
$753$	−14.0170	+	24.2781i	−0.510807	+	0.884745i
$754$	7.40208	−	4.74189i	0.269568	−	0.172690i
$755$	15.5361	+	15.5361i	0.565418	+	0.565418i
$756$	4.10203	+	3.34266i	0.149189	+	0.121571i
$757$	16.9081	−	16.9081i	0.614534	−	0.614534i	−0.329590	−	0.944124i	$-0.606911\pi$
$757$	16.9081	−	16.9081i	0.614534	−	0.614534i	0.944124	+	0.329590i	$0.106911\pi$
$758$	20.6504	+	4.52355i	0.750056	+	0.164303i
$759$	−1.23136	−	0.710926i	−0.0446955	−	0.0258050i
$760$	13.3319	−	32.8867i	0.483599	−	1.19292i
$761$	−6.16974	+	3.56210i	−0.223653	+	0.129126i	−0.607641	−	0.794212i	$-0.707884\pi$
$761$	−6.16974	+	3.56210i	−0.223653	+	0.129126i	0.383988	+	0.923338i	$0.374551\pi$
$762$	19.8010	+	18.0527i	0.717313	+	0.653980i
$763$	19.6486	−	20.0194i	0.711328	−	0.724752i
$764$	30.4842	−	2.82181i	1.10288	−	0.102089i
$765$	0.560268	−	2.09095i	0.0202565	−	0.0755984i
$766$	−8.03334	+	15.5273i	−0.290256	+	0.561023i
$767$	6.72465	−	11.6474i	0.242813	−	0.420565i
$768$	−1.71532	−	15.9078i	−0.0618963	−	0.574023i
$769$	7.34431			0.264842			0.132421	−	0.991194i	$-0.457725\pi$
$769$	7.34431			0.264842			0.132421	+	0.991194i	$0.457725\pi$
$770$	8.23705	−	16.2923i	0.296843	−	0.587135i
$771$	−4.24587	−	4.24587i	−0.152911	−	0.152911i
$772$	17.4750	+	24.6913i	0.628940	+	0.888658i
$773$	5.82150	+	21.7261i	0.209385	+	0.781434i	0.988068	+	0.154017i	$0.0492211\pi$
$773$	5.82150	+	21.7261i	0.209385	+	0.781434i	−0.778684	+	0.627417i	$0.784112\pi$
$774$	16.9391	−	5.38781i	0.608863	−	0.193661i
$775$	11.1226	−	6.42166i	0.399537	−	0.230673i
$776$	−20.0695	+	2.79661i	−0.720452	+	0.100392i
$777$	12.5017	−	7.37454i	0.448498	−	0.264560i
$778$	24.8853	−	27.2953i	0.892182	−	0.978582i
$779$	−35.8221	−	9.59850i	−1.28346	−	0.343902i
$780$	6.79288	−	2.51123i	0.243224	−	0.0899163i
$781$	13.4659	−	3.60819i	0.481849	−	0.129111i
$782$	0.751195	−	0.481228i	0.0268627	−	0.0172087i
$783$	5.17346			0.184884
$784$	−27.4234	+	5.65328i	−0.979406	+	0.201903i
$785$	−22.9661			−0.819694
$786$	−14.2380	+	9.12110i	−0.507853	+	0.325339i
$787$	19.0783	−	5.11202i	0.680068	−	0.182224i	0.0977825	−	0.995208i	$-0.468825\pi$
$787$	19.0783	−	5.11202i	0.680068	−	0.182224i	0.582286	+	0.812984i	$0.302158\pi$
$788$	−15.1966	−	41.1069i	−0.541357	−	1.46437i
$789$	−4.20072	−	1.12558i	−0.149550	−	0.0400717i
$790$	4.55496	−	4.99607i	0.162058	−	0.177752i
$791$	15.2565	−	8.99951i	0.542458	−	0.319986i
$792$	−3.65378	−	2.76004i	−0.129831	−	0.0980737i
$793$	6.91390	−	3.99174i	0.245520	−	0.141751i
$794$	43.3726	−	13.7955i	1.53924	−	0.489584i
$795$	1.01850	+	3.80109i	0.0361224	+	0.134811i
$796$	6.82918	−	4.83329i	0.242054	−	0.171311i
$797$	−34.1219	−	34.1219i	−1.20866	−	1.20866i	−0.971461	−	0.237198i	$-0.923771\pi$
$797$	−34.1219	−	34.1219i	−1.20866	−	1.20866i	−0.237198	−	0.971461i	$-0.576229\pi$
$798$	−7.02791	+	13.9007i	−0.248785	+	0.492081i
$799$	9.29018			0.328663
$800$	16.8309	−	15.8171i	0.595060	−	0.559219i
$801$	−5.69091	+	9.85695i	−0.201079	+	0.348278i
$802$	−11.3918	+	22.0186i	−0.402257	+	0.777503i
$803$	−5.86022	+	21.8706i	−0.206803	+	0.771798i
$804$	−2.53284	−	27.3624i	−0.0893263	−	0.964998i
$805$	−4.90537	+	4.99794i	−0.172892	+	0.176154i
$806$	3.94980	+	3.60106i	0.139126	+	0.126842i
$807$	3.53327	−	2.03993i	0.124377	−	0.0718091i
$808$	3.23908	+	7.65571i	0.113950	+	0.269327i
$809$	−0.680586	−	0.392937i	−0.0239281	−	0.0138149i	0.487988	−	0.872850i	$-0.337731\pi$
$809$	−0.680586	−	0.392937i	−0.0239281	−	0.0138149i	−0.511916	+	0.859035i	$0.671064\pi$
$810$	4.16343	+	0.912016i	0.146288	+	0.0320450i
$811$	−18.0555	+	18.0555i	−0.634016	+	0.634016i	−0.949073	−	0.315057i	$-0.897976\pi$
$811$	−18.0555	+	18.0555i	−0.634016	+	0.634016i	0.315057	+	0.949073i	$0.397976\pi$
$812$	−17.2931	+	21.2217i	−0.606869	+	0.744735i
$813$	−3.88713	−	3.88713i	−0.136328	−	0.136328i
$814$	−10.5764	+	6.77543i	−0.370703	+	0.237479i
$815$	0.995212	−	1.72376i	0.0348607	−	0.0603806i
$816$	2.59152	−	1.24038i	0.0907213	−	0.0434219i
$817$	26.1621	+	45.3141i	0.915296	+	1.58534i
$818$	−1.44479	−	31.2830i	−0.0505158	−	1.09378i
$819$	−3.06275	+	0.851422i	−0.107021	+	0.0297511i
$820$	−41.3076	−	34.3081i	−1.44252	−	1.19809i
$821$	51.6465	+	13.8386i	1.80247	+	0.482972i	0.994360	−	0.106054i	$-0.0338215\pi$
$821$	51.6465	+	13.8386i	1.80247	+	0.482972i	0.808115	+	0.589025i	$0.200488\pi$
$822$	−6.62394	−	20.8254i	−0.231036	−	0.726370i
$823$	−6.62943	−	3.82750i	−0.231087	−	0.133418i	0.379986	−	0.924992i	$-0.375929\pi$
$823$	−6.62943	−	3.82750i	−0.231087	−	0.133418i	−0.611074	+	0.791574i	$0.709262\pi$
$824$	42.5309	−	33.1486i	1.48163	−	1.15479i
$825$		−	6.61010i		−	0.230134i
$826$	−8.57932	+	40.9948i	−0.298513	+	1.42639i
$827$	−8.82248	+	8.82248i	−0.306788	+	0.306788i	−0.843662	−	0.536874i	$-0.819605\pi$
$827$	−8.82248	+	8.82248i	−0.306788	+	0.306788i	0.536874	+	0.843662i	$0.319605\pi$
$828$	1.01473	+	1.43376i	0.0352643	+	0.0498266i
$829$	25.3301	−	6.78718i	0.879750	−	0.235728i	0.209451	−	0.977819i	$-0.432832\pi$
$829$	25.3301	−	6.78718i	0.879750	−	0.235728i	0.670299	+	0.742091i	$0.266166\pi$
$830$	−6.00329	+	11.6035i	−0.208377	+	0.402763i
$831$	5.65800	+	9.79995i	0.196274	+	0.339957i
$832$	8.39597	+	4.67971i	0.291078	+	0.162240i
$833$	−2.59489	−	4.30651i	−0.0899075	−	0.149212i
$834$	7.06054	−	0.326087i	0.244487	−	0.0112915i
$835$	−0.579719	+	2.16354i	−0.0200620	+	0.0748724i
$836$	5.63495	−	12.2448i	0.194889	−	0.423496i
$837$	0.814138	+	3.03841i	0.0281407	+	0.105023i
$838$	−2.65533	+	12.1218i	−0.0917270	+	0.418741i
$839$		−	27.0281i		−	0.933115i	−0.884491	−	0.466558i	$-0.845494\pi$
$839$		−	27.0281i		−	0.933115i	0.884491	−	0.466558i	$-0.154506\pi$
$840$	−17.6580	+	14.0300i	−0.609260	+	0.484079i
$841$		−	2.23533i		−	0.0770802i
$842$	7.31896	+	1.60325i	0.252228	+	0.0552515i
$843$	5.74328	+	21.4342i	0.197809	+	0.738233i
$844$	−13.1853	+	4.87439i	−0.453855	+	0.167783i
$845$	9.01429	−	33.6418i	0.310101	−	1.15731i
$846$	0.843892	+	18.2722i	0.0290136	+	0.628211i
$847$	−10.9045	+	19.3015i	−0.374682	+	0.663207i
$848$	−2.95247	+	4.30830i	−0.101388	+	0.147947i
$849$	3.00547	+	5.20563i	0.103147	+	0.178657i
$850$	3.68360	+	1.90578i	0.126346	+	0.0653679i
$851$	4.65399	−	1.24703i	0.159537	−	0.0427477i
$852$	−16.9754	−	2.90515i	−0.581569	−	0.0995286i
$853$	−11.4721	+	11.4721i	−0.392799	+	0.392799i	−0.875684	−	0.482885i	$-0.839589\pi$
$853$	−11.4721	+	11.4721i	−0.392799	+	0.392799i	0.482885	+	0.875684i	$0.339589\pi$
$854$	−16.5776	+	18.5279i	−0.567274	+	0.634012i
$855$			12.5463i			0.429073i
$856$	24.0472	+	2.98122i	0.821916	+	0.101896i
$857$	3.79383	+	2.19037i	0.129595	+	0.0748215i	0.563396	−	0.826187i	$-0.309495\pi$
$857$	3.79383	+	2.19037i	0.129595	+	0.0748215i	−0.433801	+	0.901009i	$0.642828\pi$
$858$	2.62149	−	0.833816i	0.0894962	−	0.0284660i
$859$	42.8956	+	11.4938i	1.46358	+	0.392165i	0.900724	−	0.434391i	$-0.143036\pi$
$859$	42.8956	+	11.4938i	1.46358	+	0.392165i	0.562855	+	0.826556i	$0.309703\pi$
$860$	6.98306	+	75.4384i	0.238120	+	2.57243i
$861$	16.8214	+	16.5098i	0.573271	+	0.562654i
$862$	−6.21789	+	0.287170i	−0.211782	+	0.00978105i
$863$	7.50593	+	13.0007i	0.255505	+	0.442547i	0.965033	−	0.262130i	$-0.0844250\pi$
$863$	7.50593	+	13.0007i	0.255505	+	0.442547i	−0.709528	+	0.704678i	$0.751092\pi$
$864$	2.67502	+	4.98440i	0.0910060	+	0.169573i
$865$	8.37815	−	14.5114i	0.284866	−	0.493402i
$866$	−23.1687	−	36.1662i	−0.787303	−	1.22898i
$867$	−11.6560	−	11.6560i	−0.395859	−	0.395859i
$868$	−15.1850	−	6.81673i	−0.515413	−	0.231375i
$869$	1.81588	−	1.81588i	0.0615995	−	0.0615995i
$870$	−4.71828	+	21.5393i	−0.159965	+	0.730252i
$871$	14.2967	+	8.25418i	0.484424	+	0.279682i
$872$	27.6174	−	11.6847i	0.935243	−	0.395695i
$873$	6.20437	−	3.58209i	0.209986	−	0.121235i
$874$	−3.48357	+	3.82092i	−0.117833	+	0.129245i
$875$	7.08047	+	1.82645i	0.239363	+	0.0617452i
$876$	17.8715	−	21.5177i	0.603823	−	0.727014i
$877$	−7.80834	+	29.1411i	−0.263669	+	0.984025i	0.699391	+	0.714739i	$0.253455\pi$
$877$	−7.80834	+	29.1411i	−0.263669	+	0.984025i	−0.963060	+	0.269286i	$0.913212\pi$
$878$	−13.8102	−	7.14501i	−0.466073	−	0.241132i
$879$	12.1202	−	20.9927i	0.408803	−	0.708067i
$880$	14.8235	−	12.6951i	0.499701	−	0.427951i
$881$	18.9574			0.638691			0.319345	−	0.947638i	$-0.396537\pi$
$881$	18.9574			0.638691			0.319345	+	0.947638i	$0.396537\pi$
$882$	8.23445	−	5.49489i	0.277268	−	0.185023i
$883$	37.0679	+	37.0679i	1.24743	+	1.24743i	0.956849	+	0.290584i	$0.0938497\pi$
$883$	37.0679	+	37.0679i	1.24743	+	1.24743i	0.290584	+	0.956849i	$0.406150\pi$
$884$	−0.291153	+	1.70127i	−0.00979252	+	0.0572200i
$885$	8.73137	+	32.5859i	0.293502	+	1.09536i
$886$	0.740229	+	2.32725i	0.0248685	+	0.0781856i
$887$	−30.9413	+	17.8640i	−1.03891	+	0.599814i	−0.919524	−	0.393034i	$-0.871425\pi$
$887$	−30.9413	+	17.8640i	−1.03891	+	0.599814i	−0.119384	+	0.992848i	$0.538092\pi$
$888$	15.3684	−	2.14154i	0.515730	−	0.0718652i
$889$	43.1769	−	25.4692i	1.44811	−	0.854210i
$890$	−35.8485	−	32.6834i	−1.20165	−	1.09555i
$891$	1.56378	+	0.419015i	0.0523887	+	0.0140375i
$892$	−10.3830	+	22.5624i	−0.347649	+	0.755446i
$893$	−52.0096	+	13.9359i	−1.74043	+	0.466348i
$894$	14.9118	+	23.2772i	0.498724	+	0.778507i
$895$	−3.15557			−0.105479
$896$	−29.3878	−	5.68814i	−0.981779	−	0.190028i
$897$	−1.05523			−0.0352332
$898$	0.735151	+	1.14757i	0.0245323	+	0.0382949i
$899$	−15.7191	+	4.21191i	−0.524260	+	0.140475i
$900$	−3.41375	+	7.41813i	−0.113792	+	0.247271i
$901$	−0.905899	−	0.242735i	−0.0301799	−	0.00808667i
$902$	−15.0725	−	13.7417i	−0.501859	−	0.457549i
$903$	−0.310822	−	33.2531i	−0.0103435	−	1.10659i
$904$	18.7548	−	2.61342i	0.623776	−	0.0869210i
$905$	−14.7714	+	8.52828i	−0.491019	+	0.283490i
$906$	−3.12503	−	9.82500i	−0.103822	−	0.326414i
$907$	0.699341	+	2.60997i	0.0232212	+	0.0866628i	0.976564	−	0.215227i	$-0.0690492\pi$
$907$	0.699341	+	2.60997i	0.0232212	+	0.0866628i	−0.953343	+	0.301890i	$0.902383\pi$
$908$	−4.15046	+	24.2521i	−0.137738	+	0.804834i
$909$	−2.07818	−	2.07818i	−0.0689290	−	0.0689290i
$910$	−0.751560	−	13.5281i	−0.0249140	−	0.448451i
$911$	15.6126			0.517268			0.258634	−	0.965975i	$-0.416728\pi$
$911$	15.6126			0.517268			0.258634	+	0.965975i	$0.416728\pi$
$912$	−12.6475	+	10.8315i	−0.418802	+	0.358667i
$913$	−2.48122	+	4.29760i	−0.0821165	+	0.142230i
$914$	38.7940	+	20.0709i	1.28319	+	0.663885i
$915$	−5.18293	+	19.3430i	−0.171342	+	0.639459i
$916$	−24.9376	+	30.0253i	−0.823960	+	0.992063i
$917$	8.47269	+	30.4781i	0.279793	+	1.00648i
$918$	−0.684364	+	0.750639i	−0.0225874	+	0.0247748i
$919$	12.9455	−	7.47409i	0.427033	−	0.246548i	−0.271049	−	0.962566i	$-0.587371\pi$
$919$	12.9455	−	7.47409i	0.427033	−	0.246548i	0.698082	+	0.716018i	$0.254037\pi$
$920$	−6.89480	+	2.91714i	−0.227315	+	0.0961754i
$921$	−4.46627	−	2.57860i	−0.147169	−	0.0849678i
$922$	10.2711	−	46.8886i	0.338262	−	1.54419i
$923$	7.31597	−	7.31597i	0.240808	−	0.240808i
$924$	−6.94600	+	5.01406i	−0.228507	+	0.164951i
$925$	15.8387	+	15.8387i	0.520774	+	0.520774i
$926$	13.3910	+	20.9034i	0.440057	+	0.686927i
$927$	−9.53236	+	16.5105i	−0.313084	+	0.542277i
$928$	−25.7866	+	13.8391i	−0.846487	+	0.454291i
$929$	17.2628	+	29.9000i	0.566374	+	0.980989i	0.996920	+	0.0784203i	$0.0249876\pi$
$929$	17.2628	+	29.9000i	0.566374	+	0.980989i	−0.430546	+	0.902569i	$0.641679\pi$
$930$	−13.3927	+	0.618534i	−0.439164	+	0.0202825i
$931$	20.9871	+	20.2168i	0.687825	+	0.662578i
$932$	−5.35677	−	57.8695i	−0.175467	−	1.89558i
$933$	−17.7866	−	4.76592i	−0.582309	−	0.156029i
$934$	19.0820	−	6.06942i	0.624383	−	0.198597i
$935$	3.03503	+	1.75227i	0.0992560	+	0.0573055i
$936$	−3.37256	−	0.418109i	−0.110236	−	0.0136663i
$937$			20.9451i			0.684245i	0.939655	+	0.342123i	$0.111146\pi$
$937$			20.9451i			0.684245i	−0.939655	+	0.342123i	$0.888854\pi$
$938$	−50.3191	−	10.5307i	−1.64298	−	0.343839i
$939$	13.2856	−	13.2856i	0.433559	−	0.433559i
$940$	−76.8447	−	13.1510i	−2.50640	−	0.428940i
$941$	−7.72198	+	2.06910i	−0.251729	+	0.0674507i	−0.382477	−	0.923965i	$-0.624929\pi$
$941$	−7.72198	+	2.06910i	−0.251729	+	0.0674507i	0.130748	+	0.991416i	$0.458262\pi$
$942$	9.57160	+	4.95206i	0.311860	+	0.161347i
$943$	3.91199	+	6.77577i	0.127392	+	0.220649i
$944$	−25.3109	+	36.9341i	−0.823801	+	1.20210i
$945$	3.92216	−	6.94243i	0.127588	−	0.225837i
$946$	1.32765	+	28.7466i	0.0431655	+	0.934633i
$947$	6.01244	−	22.4387i	0.195378	−	0.729161i	−0.796791	−	0.604256i	$-0.793471\pi$
$947$	6.01244	−	22.4387i	0.195378	−	0.729161i	0.992169	−	0.124905i	$-0.0398628\pi$
$948$	−2.97566	+	1.10006i	−0.0966448	+	0.0357281i
$949$	4.34919	+	16.2314i	0.141181	+	0.526893i
$950$	−23.4808	−	5.14357i	−0.761819	−	0.166879i
$951$			5.36046i			0.173825i
$952$	−0.791548	−	5.31641i	−0.0256542	−	0.172306i
$953$		−	30.0696i		−	0.974050i	−0.873388	−	0.487025i	$-0.838082\pi$
$953$		−	30.0696i		−	0.974050i	0.873388	−	0.487025i	$-0.161918\pi$
$954$	0.395129	−	1.80380i	0.0127928	−	0.0584001i
$955$	−11.9401	−	44.5610i	−0.386372	−	1.44196i
$956$	7.18472	−	15.6125i	0.232370	−	0.504944i
$957$	−2.16775	+	8.09017i	−0.0700735	+	0.261518i
$958$	−40.2936	+	1.86094i	−1.30183	+	0.0601242i
$959$	−40.8824	+	0.382134i	−1.32016	+	0.0123398i
$960$	−23.1919	+	6.59140i	−0.748514	+	0.212737i
$961$	10.5526	+	18.2777i	0.340408	+	0.589603i
$962$	−4.28351	+	8.27940i	−0.138106	+	0.266938i
$963$	−8.27513	+	2.21731i	−0.266662	+	0.0714520i
$964$	5.89837	+	8.33409i	0.189974	+	0.268423i
$965$	32.2320	−	32.2320i	1.03759	−	1.03759i
$966$	3.12210	−	1.02528i	0.100452	−	0.0329877i
$967$		−	10.4038i		−	0.334564i	−0.985909	−	0.167282i	$-0.946501\pi$
$967$		−	10.4038i		−	0.334564i	0.985909	−	0.167282i	$-0.0534990\pi$
$968$	−18.6925	+	14.5689i	−0.600799	+	0.468263i
$969$	−2.58951	−	1.49505i	−0.0831870	−	0.0480280i
$970$	9.25531	+	29.0984i	0.297170	+	0.934292i
$971$	−40.1643	−	10.7620i	−1.28893	−	0.345369i	−0.451679	−	0.892181i	$-0.649175\pi$
$971$	−40.1643	−	10.7620i	−1.28893	−	0.345369i	−0.837256	+	0.546811i	$0.815841\pi$
$972$	−1.53854	−	1.27784i	−0.0493488	−	0.0409868i
$973$	3.30287	−	12.8040i	0.105885	−	0.410478i
$974$	−2.41644	−	52.3215i	−0.0774277	−	1.67649i
$975$	−2.45286	−	4.24847i	−0.0785543	−	0.136060i
$976$	−23.9737	+	11.4745i	−0.767378	+	0.367290i
$977$	15.0608	−	26.0860i	0.481837	−	0.834566i	−0.517946	−	0.855413i	$-0.673303\pi$
$977$	15.0608	−	26.0860i	0.481837	−	0.834566i	0.999783	+	0.0208477i	$0.00663651\pi$
$978$	−0.786461	+	0.503820i	−0.0251483	+	0.0161104i
$979$	−13.0296	−	13.0296i	−0.416427	−	0.416427i
$980$	15.3676	+	39.2950i	0.490901	+	1.25523i
$981$	−7.49688	+	7.49688i	−0.239357	+	0.239357i
$982$	−50.8498	−	11.1389i	−1.62268	−	0.355455i
$983$	24.0587	+	13.8903i	0.767354	+	0.443032i	0.831930	−	0.554881i	$-0.187236\pi$
$983$	24.0587	+	13.8903i	0.767354	+	0.443032i	−0.0645756	+	0.997913i	$0.520569\pi$
$984$	9.81813	+	23.2056i	0.312991	+	0.739768i
$985$	−57.1934	+	33.0206i	−1.82233	+	1.05212i
$986$	−3.88340	−	3.54053i	−0.123673	−	0.112753i
$987$	33.1359	+	8.54760i	1.05473	+	0.272073i
$988$	−0.922059	−	9.96105i	−0.0293346	−	0.316903i
$989$	2.85706	−	10.6627i	0.0908492	−	0.339054i
$990$	−3.17073	+	6.12856i	−0.100772	+	0.194778i
$991$	13.1203	−	22.7250i	0.416779	−	0.721882i	−0.578835	−	0.815445i	$-0.696492\pi$
$991$	13.1203	−	22.7250i	0.416779	−	0.721882i	0.995613	+	0.0935631i	$0.0298257\pi$
$992$	−12.1858	−	12.9668i	−0.386899	−	0.411696i
$993$	3.27187			0.103830
$994$	−14.5373	+	28.7539i	−0.461096	+	0.912018i
$995$	−8.91483	−	8.91483i	−0.282619	−	0.282619i
$996$	5.00400	−	3.54154i	0.158558	−	0.112218i
$997$	−10.9186	−	40.7490i	−0.345797	−	1.29053i	−0.891678	−	0.452670i	$-0.850472\pi$
$997$	−10.9186	−	40.7490i	−0.345797	−	1.29053i	0.545881	−	0.837863i	$-0.316195\pi$
$998$	50.2177	−	15.9727i	1.58961	−	0.505608i
$999$	−4.75106	+	2.74303i	−0.150317	+	0.0867855i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bq.b.109.21	yes	120
7.2	even	3	inner	336.2.bq.b.205.20	yes	120
16.5	even	4	inner	336.2.bq.b.277.20	yes	120
112.37	even	12	inner	336.2.bq.b.37.21	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bq.b.37.21	✓	120	112.37	even	12	inner
336.2.bq.b.109.21	yes	120	1.1	even	1	trivial
336.2.bq.b.205.20	yes	120	7.2	even	3	inner
336.2.bq.b.277.20	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)

\(f(q)\)	\(=\)	\(q+(0.762858 + 1.19082i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.836096 + 1.81685i) q^{4} +(2.91110 + 0.780028i) q^{5} +(-1.04507 - 0.952800i) q^{6} +(-2.27882 + 1.34423i) q^{7} +(-2.80136 + 0.390360i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.762858 + 1.19082i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.836096 + 1.81685i) q^{4} +(2.91110 + 0.780028i) q^{5} +(-1.04507 - 0.952800i) q^{6} +(-2.27882 + 1.34423i) q^{7} +(-2.80136 + 0.390360i) q^{8} +(0.866025 - 0.500000i) q^{9} +(1.29189 + 4.06164i) q^{10} +(0.419015 + 1.56378i) q^{11} +(0.337371 - 1.97134i) q^{12} +(0.849595 + 0.849595i) q^{13} +(-3.33916 - 1.68820i) q^{14} -3.01380 q^{15} +(-2.60189 - 3.03812i) q^{16} +(0.359133 - 0.622037i) q^{17} +(1.25606 + 0.649850i) q^{18} +(-1.07745 + 4.02110i) q^{19} +(-3.85115 + 4.63686i) q^{20} +(1.85326 - 1.88823i) q^{21} +(-1.54253 + 1.69191i) q^{22} +(0.760593 - 0.439128i) q^{23} +(2.60487 - 1.10210i) q^{24} +(3.53595 + 2.04148i) q^{25} +(-0.363593 + 1.65983i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.536957 - 5.26419i) q^{28} +(-3.65819 - 3.65819i) q^{29} +(-2.29910 - 3.58888i) q^{30} +(1.57279 - 2.72416i) q^{31} +(1.63298 - 5.41603i) q^{32} +(-0.809474 - 1.40205i) q^{33} +(1.01470 - 0.0468634i) q^{34} +(-7.68243 + 2.13566i) q^{35} +(0.184345 + 1.99149i) q^{36} +(5.29912 + 1.41990i) q^{37} +(-5.61034 + 1.78448i) q^{38} +(-1.04054 - 0.600755i) q^{39} +(-8.45954 - 1.04876i) q^{40} +8.90853i q^{41} +(3.66232 + 0.766443i) q^{42} +(8.88764 - 8.88764i) q^{43} +(-3.19150 - 0.546187i) q^{44} +(2.91110 - 0.780028i) q^{45} +(1.10315 + 0.570735i) q^{46} +(6.46708 + 11.2013i) q^{47} +(3.29955 + 2.26118i) q^{48} +(3.38607 - 6.12654i) q^{49} +(0.266393 + 5.76803i) q^{50} +(-0.185901 + 0.693792i) q^{51} +(-2.25393 + 0.833244i) q^{52} +(-0.337945 - 1.26123i) q^{53} +(-1.38146 - 0.302614i) q^{54} +4.87918i q^{55} +(5.85907 - 4.65524i) q^{56} -4.16295i q^{57} +(1.56556 - 7.14691i) q^{58} +(-2.89714 - 10.8123i) q^{59} +(2.51982 - 5.47561i) q^{60} +(1.71974 - 6.41814i) q^{61} +(4.44380 - 0.205234i) q^{62} +(-1.30140 + 2.30355i) q^{63} +(7.69524 - 2.18708i) q^{64} +(1.81055 + 3.13597i) q^{65} +(1.05207 - 2.03350i) q^{66} +(13.2715 - 3.55609i) q^{67} +(0.829878 + 1.17257i) q^{68} +(-0.621021 + 0.621021i) q^{69} +(-8.40378 - 7.51917i) q^{70} -8.61112i q^{71} +(-2.23087 + 1.73874i) q^{72} +(12.1120 + 6.99286i) q^{73} +(2.35164 + 7.39347i) q^{74} +(-3.94384 - 1.05675i) q^{75} +(-6.40488 - 5.31959i) q^{76} +(-3.05695 - 3.00033i) q^{77} +(-0.0783926 - 1.69738i) q^{78} +(-0.793121 - 1.37373i) q^{79} +(-5.20454 - 10.8738i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-10.6084 + 6.79594i) q^{82} +(2.16744 + 2.16744i) q^{83} +(1.88113 + 4.94584i) q^{84} +(1.53068 - 1.53068i) q^{85} +(17.3636 + 3.80356i) q^{86} +(4.48035 + 2.58673i) q^{87} +(-1.78425 - 4.21715i) q^{88} +(-9.85695 + 5.69091i) q^{89} +(3.14963 + 2.87154i) q^{90} +(-3.07813 - 0.794022i) q^{91} +(0.161902 + 1.74904i) q^{92} +(-0.814138 + 3.03841i) q^{93} +(-8.40527 + 16.2461i) q^{94} +(-6.27314 + 10.8654i) q^{95} +(-0.175567 + 5.65413i) q^{96} +7.16419 q^{97} +(9.87869 - 0.641488i) q^{98} +(1.14477 + 1.14477i) 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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