LMFDB - Embedded newform 572.2.e.b.131.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(131,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("572.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.e (of order $2$, degree $1$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.16
Character	$\chi$	$=$	572.131
Dual form			572.2.e.b.131.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16339 + 0.804061i) q^{2} -0.360913i q^{3} +(0.706971 - 1.87088i) q^{4} +2.06255 q^{5} +(0.290196 + 0.419884i) q^{6} +0.974044 q^{7} +(0.681817 + 2.74502i) q^{8} +2.86974 q^{9} +O(q^{10})$	\(q+(-1.16339 + 0.804061i) q^{2} -0.360913i q^{3} +(0.706971 - 1.87088i) q^{4} +2.06255 q^{5} +(0.290196 + 0.419884i) q^{6} +0.974044 q^{7} +(0.681817 + 2.74502i) q^{8} +2.86974 q^{9} +(-2.39956 + 1.65842i) q^{10} +(-2.02900 + 2.62357i) q^{11} +(-0.675224 - 0.255155i) q^{12} +1.00000i q^{13} +(-1.13320 + 0.783191i) q^{14} -0.744400i q^{15} +(-3.00039 - 2.64531i) q^{16} -0.873790i q^{17} +(-3.33864 + 2.30745i) q^{18} +4.74647 q^{19} +(1.45816 - 3.85878i) q^{20} -0.351545i q^{21} +(0.251015 - 4.68369i) q^{22} +0.532905i q^{23} +(0.990712 - 0.246076i) q^{24} -0.745888 q^{25} +(-0.804061 - 1.16339i) q^{26} -2.11846i q^{27} +(0.688621 - 1.82232i) q^{28} +1.58668i q^{29} +(0.598544 + 0.866031i) q^{30} -4.02061i q^{31} +(5.61762 + 0.665049i) q^{32} +(0.946881 + 0.732293i) q^{33} +(0.702581 + 1.01656i) q^{34} +2.00901 q^{35} +(2.02882 - 5.36894i) q^{36} +6.80331 q^{37} +(-5.52201 + 3.81645i) q^{38} +0.360913 q^{39} +(1.40628 + 5.66174i) q^{40} -2.36738i q^{41} +(0.282664 + 0.408985i) q^{42} +6.30053 q^{43} +(3.47395 + 5.65081i) q^{44} +5.91899 q^{45} +(-0.428488 - 0.619979i) q^{46} +11.5058i q^{47} +(-0.954728 + 1.08288i) q^{48} -6.05124 q^{49} +(0.867762 - 0.599740i) q^{50} -0.315362 q^{51} +(1.87088 + 0.706971i) q^{52} +1.67504 q^{53} +(1.70338 + 2.46461i) q^{54} +(-4.18492 + 5.41125i) q^{55} +(0.664120 + 2.67377i) q^{56} -1.71306i q^{57} +(-1.27578 - 1.84593i) q^{58} +2.68550i q^{59} +(-1.39268 - 0.526269i) q^{60} -7.81490i q^{61} +(3.23281 + 4.67755i) q^{62} +2.79526 q^{63} +(-7.07025 + 3.74320i) q^{64} +2.06255i q^{65} +(-1.69040 - 0.0905944i) q^{66} -2.29762i q^{67} +(-1.63476 - 0.617744i) q^{68} +0.192332 q^{69} +(-2.33728 + 1.61537i) q^{70} -0.963290i q^{71} +(1.95664 + 7.87749i) q^{72} +3.90723i q^{73} +(-7.91493 + 5.47028i) q^{74} +0.269201i q^{75} +(3.35561 - 8.88008i) q^{76} +(-1.97634 + 2.55548i) q^{77} +(-0.419884 + 0.290196i) q^{78} -3.55476 q^{79} +(-6.18844 - 5.45609i) q^{80} +7.84465 q^{81} +(1.90352 + 2.75420i) q^{82} +5.37513 q^{83} +(-0.657698 - 0.248532i) q^{84} -1.80224i q^{85} +(-7.33000 + 5.06601i) q^{86} +0.572651 q^{87} +(-8.58517 - 3.78085i) q^{88} +12.4029 q^{89} +(-6.88611 + 4.75923i) q^{90} +0.974044i q^{91} +(0.997002 + 0.376748i) q^{92} -1.45109 q^{93} +(-9.25136 - 13.3858i) q^{94} +9.78983 q^{95} +(0.240025 - 2.02747i) q^{96} -4.78545 q^{97} +(7.03997 - 4.86557i) q^{98} +(-5.82272 + 7.52898i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9}+O(q^{10}) $ 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9	$ 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9} - 8 q^{12} - 34 q^{14} + 26 q^{16} + 14 q^{20} - 8 q^{22} + 76 q^{25} + 2 q^{26} - 16 q^{33} + 32 q^{34} - 24 q^{36} - 32 q^{37} - 30 q^{38} + 54 q^{42} + 10 q^{44} + 12 q^{45} + 34 q^{48} - 36 q^{49} - 32 q^{53} - 36 q^{56} + 62 q^{58} + 4 q^{60} - 18 q^{64} - 30 q^{66} - 24 q^{69} - 30 q^{70} + 88 q^{77} - 10 q^{78} - 46 q^{80} + 64 q^{81} - 46 q^{82} + 98 q^{86} + 16 q^{88} + 24 q^{89} + 84 q^{92} + 8 q^{93} - 88 q^{97}+O(q^{100}) $ 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9 - 8 * q^12 - 34 * q^14 + 26 * q^16 + 14 * q^20 - 8 * q^22 + 76 * q^25 + 2 * q^26 - 16 * q^33 + 32 * q^34 - 24 * q^36 - 32 * q^37 - 30 * q^38 + 54 * q^42 + 10 * q^44 + 12 * q^45 + 34 * q^48 - 36 * q^49 - 32 * q^53 - 36 * q^56 + 62 * q^58 + 4 * q^60 - 18 * q^64 - 30 * q^66 - 24 * q^69 - 30 * q^70 + 88 * q^77 - 10 * q^78 - 46 * q^80 + 64 * q^81 - 46 * q^82 + 98 * q^86 + 16 * q^88 + 24 * q^89 + 84 * q^92 + 8 * q^93 - 88 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.16339	+	0.804061i	−0.822644	+	0.568557i
$2$	−1.16339	+	0.804061i	−0.822644	+	0.568557i
$3$		−	0.360913i		−	0.208373i	−0.994558	−	0.104187i	$-0.966776\pi$
$3$		−	0.360913i		−	0.208373i	0.994558	−	0.104187i	$-0.0332239\pi$
$4$	0.706971	−	1.87088i	0.353485	−	0.935440i
$5$	2.06255			0.922400			0.461200	−	0.887296i	$-0.347419\pi$
$5$	2.06255			0.922400			0.461200	+	0.887296i	$0.347419\pi$
$6$	0.290196	+	0.419884i	0.118472	+	0.171417i
$7$	0.974044			0.368154			0.184077	−	0.982912i	$-0.441070\pi$
$7$	0.974044			0.368154			0.184077	+	0.982912i	$0.441070\pi$
$8$	0.681817	+	2.74502i	0.241059	+	0.970511i
$9$	2.86974			0.956581
$10$	−2.39956	+	1.65842i	−0.758807	+	0.524437i
$11$	−2.02900	+	2.62357i	−0.611768	+	0.791038i
$11$	−2.02900	+	2.62357i	−0.611768	+	0.791038i
$12$	−0.675224	−	0.255155i	−0.194920	−	0.0736568i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	−1.13320	+	0.783191i	−0.302860	+	0.209317i
$15$		−	0.744400i		−	0.192203i
$16$	−3.00039	−	2.64531i	−0.750096	−	0.661329i
$17$		−	0.873790i		−	0.211925i	−0.994370	−	0.105963i	$-0.966208\pi$
$17$		−	0.873790i		−	0.211925i	0.994370	−	0.105963i	$-0.0337924\pi$
$18$	−3.33864	+	2.30745i	−0.786925	+	0.543871i
$19$	4.74647			1.08891			0.544457	−	0.838789i	$-0.316736\pi$
$19$	4.74647			1.08891			0.544457	+	0.838789i	$0.316736\pi$
$20$	1.45816	−	3.85878i	0.326055	−	0.862850i
$21$		−	0.351545i		−	0.0767134i
$22$	0.251015	−	4.68369i	0.0535165	−	0.998567i
$23$			0.532905i			0.111118i	0.998455	+	0.0555592i	$0.0176942\pi$
$23$			0.532905i			0.111118i	−0.998455	+	0.0555592i	$0.982306\pi$
$24$	0.990712	−	0.246076i	0.202228	−	0.0502301i
$25$	−0.745888			−0.149178
$26$	−0.804061	−	1.16339i	−0.157689	−	0.228160i
$27$		−	2.11846i		−	0.407699i
$28$	0.688621	−	1.82232i	0.130137	−	0.344386i
$29$			1.58668i			0.294638i	0.989089	+	0.147319i	$0.0470644\pi$
$29$			1.58668i			0.294638i	−0.989089	+	0.147319i	$0.952936\pi$
$30$	0.598544	+	0.866031i	0.109279	+	0.158115i
$31$		−	4.02061i		−	0.722122i	−0.932542	−	0.361061i	$-0.882415\pi$
$31$		−	4.02061i		−	0.722122i	0.932542	−	0.361061i	$-0.117585\pi$
$32$	5.61762	+	0.665049i	0.993065	+	0.117565i
$33$	0.946881	+	0.732293i	0.164831	+	0.127476i
$34$	0.702581	+	1.01656i	0.120492	+	0.174339i
$35$	2.00901			0.339585
$36$	2.02882	−	5.36894i	0.338137	−	0.894824i
$37$	6.80331			1.11846			0.559228	−	0.829014i	$-0.311097\pi$
$37$	6.80331			1.11846			0.559228	+	0.829014i	$0.311097\pi$
$38$	−5.52201	+	3.81645i	−0.895789	+	0.619110i
$39$	0.360913			0.0577923
$40$	1.40628	+	5.66174i	0.222353	+	0.895199i
$41$		−	2.36738i		−	0.369723i	−0.982765	−	0.184862i	$-0.940816\pi$
$41$		−	2.36738i		−	0.369723i	0.982765	−	0.184862i	$-0.0591837\pi$
$42$	0.282664	+	0.408985i	0.0436160	+	0.0631078i
$43$	6.30053			0.960822			0.480411	−	0.877043i	$-0.340488\pi$
$43$	6.30053			0.960822			0.480411	+	0.877043i	$0.340488\pi$
$44$	3.47395	+	5.65081i	0.523717	+	0.851892i
$45$	5.91899			0.882350
$46$	−0.428488	−	0.619979i	−0.0631772	−	0.0914109i
$47$			11.5058i			1.67829i	0.543906	+	0.839146i	$0.316945\pi$
$47$			11.5058i			1.67829i	−0.543906	+	0.839146i	$0.683055\pi$
$48$	−0.954728	+	1.08288i	−0.137803	+	0.156300i
$49$	−6.05124			−0.864463
$50$	0.867762	−	0.599740i	0.122720	−	0.0848160i
$51$	−0.315362			−0.0441595
$52$	1.87088	+	0.706971i	0.259444	+	0.0980392i
$53$	1.67504			0.230085			0.115042	−	0.993361i	$-0.463300\pi$
$53$	1.67504			0.230085			0.115042	+	0.993361i	$0.463300\pi$
$54$	1.70338	+	2.46461i	0.231800	+	0.335391i
$55$	−4.18492	+	5.41125i	−0.564295	+	0.729653i
$56$	0.664120	+	2.67377i	0.0887468	+	0.357297i
$57$		−	1.71306i		−	0.226900i
$58$	−1.27578	−	1.84593i	−0.167519	−	0.242382i
$59$			2.68550i			0.349622i	0.984602	+	0.174811i	$0.0559315\pi$
$59$			2.68550i			0.349622i	−0.984602	+	0.174811i	$0.944069\pi$
$60$	−1.39268	−	0.526269i	−0.179795	−	0.0679411i
$61$		−	7.81490i		−	1.00059i	−0.865854	−	0.500297i	$-0.833224\pi$
$61$		−	7.81490i		−	1.00059i	0.865854	−	0.500297i	$-0.166776\pi$
$62$	3.23281	+	4.67755i	0.410568	+	0.594049i
$63$	2.79526			0.352169
$64$	−7.07025	+	3.74320i	−0.883781	+	0.467900i
$65$			2.06255i			0.255828i
$66$	−1.69040	−	0.0905944i	−0.208074	−	0.0111514i
$67$		−	2.29762i		−	0.280699i	−0.990102	−	0.140349i	$-0.955177\pi$
$67$		−	2.29762i		−	0.280699i	0.990102	−	0.140349i	$-0.0448226\pi$
$68$	−1.63476	−	0.617744i	−0.198243	−	0.0749125i
$69$	0.192332			0.0231541
$70$	−2.33728	+	1.61537i	−0.279358	+	0.193074i
$71$		−	0.963290i		−	0.114322i	−0.998365	−	0.0571608i	$-0.981795\pi$
$71$		−	0.963290i		−	0.114322i	0.998365	−	0.0571608i	$-0.0182048\pi$
$72$	1.95664	+	7.87749i	0.230592	+	0.928372i
$73$			3.90723i			0.457307i	0.973508	+	0.228654i	$0.0734323\pi$
$73$			3.90723i			0.457307i	−0.973508	+	0.228654i	$0.926568\pi$
$74$	−7.91493	+	5.47028i	−0.920092	+	0.635907i
$75$			0.269201i			0.0310846i
$76$	3.35561	−	8.88008i	0.384915	−	1.01861i
$77$	−1.97634	+	2.55548i	−0.225225	+	0.291224i
$78$	−0.419884	+	0.290196i	−0.0475425	+	0.0328582i
$79$	−3.55476			−0.399942			−0.199971	−	0.979802i	$-0.564085\pi$
$79$	−3.55476			−0.399942			−0.199971	+	0.979802i	$0.564085\pi$
$80$	−6.18844	−	5.45609i	−0.691889	−	0.610010i
$81$	7.84465			0.871627
$82$	1.90352	+	2.75420i	0.210209	+	0.304150i
$83$	5.37513			0.589997			0.294998	−	0.955498i	$-0.404681\pi$
$83$	5.37513			0.589997			0.294998	+	0.955498i	$0.404681\pi$
$84$	−0.657698	−	0.248532i	−0.0717608	−	0.0271171i
$85$		−	1.80224i		−	0.195480i
$86$	−7.33000	+	5.06601i	−0.790414	+	0.546282i
$87$	0.572651			0.0613947
$88$	−8.58517	−	3.78085i	−0.915182	−	0.403040i
$89$	12.4029			1.31470			0.657352	−	0.753584i	$-0.271677\pi$
$89$	12.4029			1.31470			0.657352	+	0.753584i	$0.271677\pi$
$90$	−6.88611	+	4.75923i	−0.725860	+	0.501667i
$91$			0.974044i			0.102108i
$92$	0.997002	+	0.376748i	0.103945	+	0.0392787i
$93$	−1.45109			−0.150471
$94$	−9.25136	−	13.3858i	−0.954205	−	1.38064i
$95$	9.78983			1.00442
$96$	0.240025	−	2.02747i	0.0244974	−	0.206928i
$97$	−4.78545			−0.485889			−0.242944	−	0.970040i	$-0.578113\pi$
$97$	−4.78545			−0.485889			−0.242944	+	0.970040i	$0.578113\pi$
$98$	7.03997	−	4.86557i	0.711145	−	0.491496i
$99$	−5.82272	+	7.52898i	−0.585205	+	0.756691i
$100$	−0.527321	+	1.39547i	−0.0527321	+	0.139547i
$101$		−	3.57635i		−	0.355860i	−0.984043	−	0.177930i	$-0.943060\pi$
$101$		−	3.57635i		−	0.355860i	0.984043	−	0.177930i	$-0.0569401\pi$
$102$	0.366890	−	0.253570i	0.0363276	−	0.0251072i
$103$			2.30083i			0.226708i	0.993555	+	0.113354i	$0.0361594\pi$
$103$			2.30083i			0.226708i	−0.993555	+	0.113354i	$0.963841\pi$
$104$	−2.74502	+	0.681817i	−0.269171	+	0.0668577i
$105$		−	0.725079i		−	0.0707605i
$106$	−1.94873	+	1.34684i	−0.189278	+	0.130816i
$107$	−9.15799			−0.885336			−0.442668	−	0.896686i	$-0.645968\pi$
$107$	−9.15799			−0.885336			−0.442668	+	0.896686i	$0.645968\pi$
$108$	−3.96339	−	1.49769i	−0.381378	−	0.144115i
$109$		−	16.9273i		−	1.62134i	−0.585505	−	0.810669i	$-0.699104\pi$
$109$		−	16.9273i		−	1.62134i	0.585505	−	0.810669i	$-0.300896\pi$
$110$	0.517730	−	9.66035i	0.0493637	−	0.921078i
$111$		−	2.45540i		−	0.233056i
$112$	−2.92251	−	2.57665i	−0.276151	−	0.243471i
$113$	−12.5109			−1.17693			−0.588464	−	0.808524i	$-0.700267\pi$
$113$	−12.5109			−1.17693			−0.588464	+	0.808524i	$0.700267\pi$
$114$	1.37741	+	1.99296i	0.129006	+	0.186658i
$115$			1.09914i			0.102496i
$116$	2.96848	+	1.12173i	0.275616	+	0.104150i
$117$			2.86974i			0.265308i
$118$	−2.15931	−	3.12429i	−0.198780	−	0.287614i
$119$		−	0.851110i		−	0.0780212i
$120$	2.04339	−	0.507545i	0.186535	−	0.0463323i
$121$	−2.76629	−	10.6465i	−0.251481	−	0.967862i
$122$	6.28366	+	9.09180i	0.568895	+	0.823133i
$123$	−0.854418			−0.0770403
$124$	−7.52207	−	2.84245i	−0.675502	−	0.255260i
$125$	−11.8512			−1.06000
$126$	−3.25198	+	2.24756i	−0.289710	+	0.200228i
$127$	−1.19449			−0.105994			−0.0529968	−	0.998595i	$-0.516877\pi$
$127$	−1.19449			−0.105994			−0.0529968	+	0.998595i	$0.516877\pi$
$128$	5.21572	−	10.0397i	0.461009	−	0.887395i
$129$		−	2.27394i		−	0.200209i
$130$	−1.65842	−	2.39956i	−0.145453	−	0.210455i
$131$	11.0740			0.967543			0.483771	−	0.875194i	$-0.339267\pi$
$131$	11.0740			0.967543			0.483771	+	0.875194i	$0.339267\pi$
$132$	2.03945	−	1.25379i	0.177511	−	0.109129i
$133$	4.62327			0.400888
$134$	1.84743	+	2.67303i	0.159593	+	0.230915i
$135$		−	4.36944i		−	0.376061i
$136$	2.39857	−	0.595765i	0.205676	−	0.0510865i
$137$	−0.942084			−0.0804877			−0.0402438	−	0.999190i	$-0.512813\pi$
$137$	−0.942084			−0.0804877			−0.0402438	+	0.999190i	$0.512813\pi$
$138$	−0.223758	+	0.154647i	−0.0190476	+	0.0131644i
$139$	−14.1951			−1.20401			−0.602005	−	0.798492i	$-0.705631\pi$
$139$	−14.1951			−1.20401			−0.602005	+	0.798492i	$0.705631\pi$
$140$	1.42031	−	3.75863i	0.120038	−	0.317662i
$141$	4.15259			0.349711
$142$	0.774544	+	1.12069i	0.0649983	+	0.0940459i
$143$	−2.62357	−	2.02900i	−0.219394	−	0.169674i
$144$	−8.61033	−	7.59137i	−0.717528	−	0.632614i
$145$			3.27260i			0.271774i
$146$	−3.14166	−	4.54565i	−0.260005	−	0.376201i
$147$			2.18397i			0.180131i
$148$	4.80974	−	12.7282i	0.395358	−	1.04625i
$149$		−	16.8747i		−	1.38243i	−0.722651	−	0.691213i	$-0.757077\pi$
$149$		−	16.8747i		−	1.38243i	0.722651	−	0.691213i	$-0.242923\pi$
$150$	−0.216454	−	0.313186i	−0.0176734	−	0.0255715i
$151$	−8.41190			−0.684551			−0.342275	−	0.939600i	$-0.611198\pi$
$151$	−8.41190			−0.684551			−0.342275	+	0.939600i	$0.611198\pi$
$152$	3.23622	+	13.0291i	0.262492	+	1.05680i
$153$		−	2.50755i		−	0.202724i
$154$	0.244499	−	4.56213i	0.0197023	−	0.367627i
$155$		−	8.29270i		−	0.666086i
$156$	0.255155	−	0.675224i	0.0204287	−	0.0540612i
$157$	−18.4077			−1.46909			−0.734547	−	0.678557i	$-0.762605\pi$
$157$	−18.4077			−1.46909			−0.734547	+	0.678557i	$0.762605\pi$
$158$	4.13559	−	2.85825i	0.329010	−	0.227390i
$159$		−	0.604544i		−	0.0479435i
$160$	11.5866	+	1.37170i	0.916004	+	0.108442i
$161$			0.519073i			0.0409087i
$162$	−9.12641	+	6.30758i	−0.717039	+	0.495570i
$163$		−	18.2947i		−	1.43295i	−0.697614	−	0.716474i	$-0.745755\pi$
$163$		−	18.2947i		−	1.43295i	0.697614	−	0.716474i	$-0.254245\pi$
$164$	−4.42909	−	1.67367i	−0.345854	−	0.130692i
$165$	1.95299	+	1.51039i	0.152040	+	0.117584i
$166$	−6.25339	+	4.32193i	−0.485357	+	0.335447i
$167$	−17.9160			−1.38638			−0.693192	−	0.720753i	$-0.743796\pi$
$167$	−17.9160			−1.38638			−0.693192	+	0.720753i	$0.743796\pi$
$168$	0.964997	−	0.239689i	0.0744511	−	0.0184924i
$169$	−1.00000			−0.0769231
$170$	1.44911	+	2.09671i	0.111142	+	0.160810i
$171$	13.6211			1.04163
$172$	4.45429	−	11.7875i	0.339636	−	0.898791i
$173$			21.2058i			1.61225i	0.591747	+	0.806124i	$0.298439\pi$
$173$			21.2058i			1.61225i	−0.591747	+	0.806124i	$0.701561\pi$
$174$	−0.666219	+	0.460447i	−0.0505059	+	0.0349064i
$175$	−0.726528			−0.0549204
$176$	13.0280	−	2.50438i	0.982020	−	0.188775i
$177$	0.969231			0.0728518
$178$	−14.4294	+	9.97268i	−1.08153	+	0.747484i
$179$		−	11.8957i		−	0.889127i	−0.895747	−	0.444564i	$-0.853359\pi$
$179$		−	11.8957i		−	0.889127i	0.895747	−	0.444564i	$-0.146641\pi$
$180$	4.18455	−	11.0737i	0.311898	−	0.825386i
$181$	−6.35411			−0.472297			−0.236148	−	0.971717i	$-0.575885\pi$
$181$	−6.35411			−0.472297			−0.236148	+	0.971717i	$0.575885\pi$
$182$	−0.783191	−	1.13320i	−0.0580540	−	0.0839982i
$183$	−2.82049			−0.208497
$184$	−1.46283	+	0.363344i	−0.107842	+	0.0267861i
$185$	14.0322			1.03167
$186$	1.68819	−	1.16676i	0.123784	−	0.0855512i
$187$	2.29245	+	1.77292i	0.167641	+	0.129649i
$188$	21.5260	+	8.13426i	1.56994	+	0.593252i
$189$		−	2.06348i		−	0.150096i
$190$	−11.3894	+	7.87162i	−0.826276	+	0.571068i
$191$			6.85869i			0.496278i	0.968724	+	0.248139i	$0.0798189\pi$
$191$			6.85869i			0.496278i	−0.968724	+	0.248139i	$0.920181\pi$
$192$	1.35097	+	2.55174i	0.0974978	+	0.184156i
$193$			8.00695i			0.576353i	0.957577	+	0.288177i	$0.0930490\pi$
$193$			8.00695i			0.576353i	−0.957577	+	0.288177i	$0.906951\pi$
$194$	5.56736	−	3.84779i	0.399713	−	0.276255i
$195$	0.744400			0.0533076
$196$	−4.27805	+	11.3211i	−0.305575	+	0.808653i
$197$			24.4809i			1.74419i	0.489334	+	0.872096i	$0.337240\pi$
$197$			24.4809i			1.74419i	−0.489334	+	0.872096i	$0.662760\pi$
$198$	0.720347	−	13.4410i	0.0511929	−	0.955210i
$199$			7.09886i			0.503225i	0.967828	+	0.251612i	$0.0809608\pi$
$199$			7.09886i			0.503225i	−0.967828	+	0.251612i	$0.919039\pi$
$200$	−0.508559	−	2.04748i	−0.0359606	−	0.144778i
$201$	−0.829240			−0.0584900
$202$	2.87561	+	4.16071i	0.202327	+	0.292746i
$203$			1.54549i			0.108472i
$204$	−0.222952	+	0.590005i	−0.0156097	+	0.0413086i
$205$		−	4.88284i		−	0.341033i
$206$	−1.85001	−	2.67677i	−0.128896	−	0.186500i
$207$			1.52930i			0.106294i
$208$	2.64531	−	3.00039i	0.183420	−	0.208039i
$209$	−9.63060	+	12.4527i	−0.666163	+	0.861373i
$210$	0.583008	+	0.843552i	0.0402314	+	0.0582106i
$211$	−20.0543			−1.38059			−0.690297	−	0.723526i	$-0.742520\pi$
$211$	−20.0543			−1.38059			−0.690297	+	0.723526i	$0.742520\pi$
$212$	1.18421	−	3.13380i	0.0813316	−	0.215230i
$213$	−0.347664			−0.0238215
$214$	10.6543	−	7.36358i	0.728316	−	0.503364i
$215$	12.9952			0.886263
$216$	5.81522	−	1.44441i	0.395676	−	0.0982793i
$217$		−	3.91625i		−	0.265852i
$218$	13.6106	+	19.6931i	0.921824	+	1.33378i
$219$	1.41017			0.0952905
$220$	7.16519	+	11.6551i	0.483077	+	0.785785i
$221$	0.873790			0.0587775
$222$	1.97429	+	2.85660i	0.132506	+	0.191722i
$223$		−	5.52485i		−	0.369972i	−0.982741	−	0.184986i	$-0.940776\pi$
$223$		−	5.52485i		−	0.369972i	0.982741	−	0.184986i	$-0.0592239\pi$
$224$	5.47181	+	0.647787i	0.365601	+	0.0432821i
$225$	−2.14051			−0.142700
$226$	14.5551	−	10.0595i	0.968192	−	0.669150i
$227$	18.2777			1.21313			0.606567	−	0.795032i	$-0.292546\pi$
$227$	18.2777			1.21313			0.606567	+	0.795032i	$0.292546\pi$
$228$	−3.20493	−	1.21108i	−0.212252	−	0.0802060i
$229$	−9.17524			−0.606317			−0.303158	−	0.952940i	$-0.598041\pi$
$229$	−9.17524			−0.606317			−0.303158	+	0.952940i	$0.598041\pi$
$230$	−0.883779	−	1.27874i	−0.0582746	−	0.0843174i
$231$	0.922304	+	0.713286i	0.0606832	+	0.0469308i
$232$	−4.35545	+	1.08182i	−0.285950	+	0.0710251i
$233$			18.6287i			1.22040i	0.792246	+	0.610202i	$0.208912\pi$
$233$			18.6287i			1.22040i	−0.792246	+	0.610202i	$0.791088\pi$
$234$	−2.30745	−	3.33864i	−0.150843	−	0.218254i
$235$			23.7313i			1.54806i
$236$	5.02425	+	1.89857i	0.327051	+	0.123586i
$237$			1.28296i			0.0833371i
$238$	0.684345	+	0.990177i	0.0443595	+	0.0641836i
$239$	−17.0242			−1.10120			−0.550601	−	0.834768i	$-0.685602\pi$
$239$	−17.0242			−1.10120			−0.550601	+	0.834768i	$0.685602\pi$
$240$	−1.96917	+	2.23349i	−0.127110	+	0.144171i
$241$		−	2.17287i		−	0.139967i	−0.997548	−	0.0699834i	$-0.977705\pi$
$241$		−	2.17287i		−	0.139967i	0.997548	−	0.0699834i	$-0.0222946\pi$
$242$	11.7787	+	10.1618i	0.757164	+	0.653224i
$243$		−	9.18663i		−	0.589322i
$244$	−14.6207	−	5.52490i	−0.935996	−	0.353696i
$245$	−12.4810			−0.797381
$246$	0.994025	−	0.687005i	0.0633767	−	0.0438018i
$247$			4.74647i			0.302011i
$248$	11.0366	−	2.74132i	0.700827	−	0.174074i
$249$		−	1.93995i		−	0.122939i
$250$	13.7876	−	9.52908i	0.872004	−	0.602672i
$251$		−	25.7348i		−	1.62437i	−0.583401	−	0.812184i	$-0.698278\pi$
$251$		−	25.7348i		−	1.62437i	0.583401	−	0.812184i	$-0.301722\pi$
$252$	1.97616	−	5.22959i	0.124487	−	0.329433i
$253$	−1.39812	−	1.08127i	−0.0878988	−	0.0679786i
$254$	1.38966	−	0.960442i	0.0871950	−	0.0602635i
$255$	−0.650450			−0.0407328
$256$	2.00462	+	15.8739i	0.125289	+	0.992120i
$257$	−7.96516			−0.496853			−0.248427	−	0.968651i	$-0.579913\pi$
$257$	−7.96516			−0.496853			−0.248427	+	0.968651i	$0.579913\pi$
$258$	1.82839	+	2.64549i	0.113831	+	0.164701i
$259$	6.62672			0.411764
$260$	3.85878	+	1.45816i	0.239312	+	0.0904314i
$261$			4.55335i			0.281845i
$262$	−12.8835	+	8.90420i	−0.795943	+	0.550104i
$263$	−9.44705			−0.582530			−0.291265	−	0.956642i	$-0.594076\pi$
$263$	−9.44705			−0.582530			−0.291265	+	0.956642i	$0.594076\pi$
$264$	−1.36456	+	3.09850i	−0.0839827	+	0.190699i
$265$	3.45486			0.212230
$266$	−5.37868	+	3.71739i	−0.329788	+	0.227928i
$267$		−	4.47636i		−	0.273949i
$268$	−4.29857	−	1.62435i	−0.262577	−	0.0992229i
$269$	−30.1242			−1.83671			−0.918353	−	0.395762i	$-0.870480\pi$
$269$	−30.1242			−1.83671			−0.918353	+	0.395762i	$0.870480\pi$
$270$	3.51330	+	5.08338i	0.213812	+	0.309365i
$271$	7.75412			0.471029			0.235515	−	0.971871i	$-0.424322\pi$
$271$	7.75412			0.471029			0.235515	+	0.971871i	$0.424322\pi$
$272$	−2.31145	+	2.62171i	−0.140152	+	0.158964i
$273$	0.351545			0.0212765
$274$	1.09601	−	0.757493i	0.0662127	−	0.0457619i
$275$	1.51341	−	1.95689i	0.0912620	−	0.118005i
$276$	0.135973	−	0.359831i	0.00818463	−	0.0216593i
$277$			18.6536i			1.12079i	0.828227	+	0.560393i	$0.189350\pi$
$277$			18.6536i			1.12079i	−0.828227	+	0.560393i	$0.810650\pi$
$278$	16.5145	−	11.4137i	0.990471	−	0.684549i
$279$		−	11.5381i		−	0.690768i
$280$	1.36978	+	5.51478i	0.0818601	+	0.329571i
$281$			26.5577i			1.58430i	0.610328	+	0.792149i	$0.291038\pi$
$281$			26.5577i			1.58430i	−0.610328	+	0.792149i	$0.708962\pi$
$282$	−4.83109	+	3.33893i	−0.287687	+	0.198831i
$283$	1.63031			0.0969119			0.0484559	−	0.998825i	$-0.484570\pi$
$283$	1.63031			0.0969119			0.0484559	+	0.998825i	$0.484570\pi$
$284$	−1.80220	−	0.681018i	−0.106941	−	0.0404110i
$285$		−	3.53327i		−	0.209293i
$286$	4.68369	+	0.251015i	0.276953	+	0.0148428i
$287$		−	2.30594i		−	0.136115i
$288$	16.1211	+	1.90852i	0.949947	+	0.112461i
$289$	16.2365			0.955088
$290$	−2.63137	−	3.80732i	−0.154519	−	0.223574i
$291$			1.72713i			0.101246i
$292$	7.30996	+	2.76230i	0.427783	+	0.161651i
$293$			5.25511i			0.307007i	0.988148	+	0.153503i	$0.0490556\pi$
$293$			5.25511i			0.307007i	−0.988148	+	0.153503i	$0.950944\pi$
$294$	−1.75604	−	2.54082i	−0.102415	−	0.148183i
$295$			5.53898i			0.322492i
$296$	4.63861	+	18.6752i	0.269614	+	1.08547i
$297$	5.55795	+	4.29837i	0.322505	+	0.249417i
$298$	13.5683	+	19.6319i	0.785989	+	1.13724i
$299$	−0.532905			−0.0308187
$300$	0.503642	+	0.190317i	0.0290778	+	0.0109879i
$301$	6.13700			0.353731
$302$	9.78635	−	6.76368i	0.563141	−	0.389206i
$303$	−1.29075			−0.0741517
$304$	−14.2412	−	12.5559i	−0.816791	−	0.720131i
$305$		−	16.1186i		−	0.922949i
$306$	2.01623	+	2.91727i	0.115260	+	0.166769i
$307$	12.3881			0.707027			0.353513	−	0.935430i	$-0.384987\pi$
$307$	12.3881			0.707027			0.353513	+	0.935430i	$0.384987\pi$
$308$	3.38378	+	5.50414i	0.192809	+	0.313628i
$309$	0.830400			0.0472398
$310$	6.66784	+	9.64767i	0.378708	+	0.547951i
$311$			12.0778i			0.684868i	0.939542	+	0.342434i	$0.111251\pi$
$311$			12.0778i			0.684868i	−0.939542	+	0.342434i	$0.888749\pi$
$312$	0.246076	+	0.990712i	0.0139313	+	0.0560880i
$313$	−7.87567			−0.445159			−0.222580	−	0.974915i	$-0.571448\pi$
$313$	−7.87567			−0.445159			−0.222580	+	0.974915i	$0.571448\pi$
$314$	21.4154	−	14.8009i	1.20854	−	0.835264i
$315$	5.76535			0.324841
$316$	−2.51311	+	6.65053i	−0.141374	+	0.374122i
$317$	12.7076			0.713728			0.356864	−	0.934156i	$-0.383846\pi$
$317$	12.7076			0.713728			0.356864	+	0.934156i	$0.383846\pi$
$318$	0.486090	+	0.703323i	0.0272586	+	0.0394404i
$319$	−4.16276	−	3.21937i	−0.233070	−	0.180250i
$320$	−14.5827	+	7.72054i	−0.815200	+	0.431591i
$321$			3.30523i			0.184480i
$322$	−0.417367	−	0.603887i	−0.0232589	−	0.0336533i
$323$		−	4.14742i		−	0.230769i
$324$	5.54593	−	14.6764i	0.308107	−	0.815355i
$325$		−	0.745888i		−	0.0413744i
$326$	14.7100	+	21.2839i	0.814713	+	1.17881i
$327$	−6.10927			−0.337843
$328$	6.49851	−	1.61412i	0.358820	−	0.0891250i
$329$			11.2071i			0.617870i
$330$	−3.48654	−	0.186855i	−0.191928	−	0.0102861i
$331$		−	23.4172i		−	1.28712i	−0.765394	−	0.643562i	$-0.777456\pi$
$331$		−	23.4172i		−	1.28712i	0.765394	−	0.643562i	$-0.222544\pi$
$332$	3.80006	−	10.0562i	0.208555	−	0.551907i
$333$	19.5237			1.06989
$334$	20.8434	−	14.4056i	1.14050	−	0.788238i
$335$		−	4.73895i		−	0.258917i
$336$	−0.929947	+	1.05477i	−0.0507328	+	0.0575424i
$337$		−	27.5631i		−	1.50146i	−0.660609	−	0.750730i	$-0.729702\pi$
$337$		−	27.5631i		−	1.50146i	0.660609	−	0.750730i	$-0.270298\pi$
$338$	1.16339	−	0.804061i	0.0632803	−	0.0437352i
$339$			4.51535i			0.245240i
$340$	−3.37177	−	1.27413i	−0.182860	−	0.0690993i
$341$	10.5484	+	8.15782i	0.571226	+	0.441771i
$342$	−15.8468	+	10.9522i	−0.856894	+	0.592229i
$343$	−12.7125			−0.686410
$344$	4.29581	+	17.2951i	0.231615	+	0.932488i
$345$	0.396695			0.0213573
$346$	−17.0508	−	24.6707i	−0.916655	−	1.32631i
$347$	34.1294			1.83216			0.916081	−	0.400992i	$-0.131335\pi$
$347$	34.1294			1.83216			0.916081	+	0.400992i	$0.131335\pi$
$348$	0.404848	−	1.07136i	0.0217021	−	0.0574310i
$349$			8.58781i			0.459695i	0.973227	+	0.229848i	$0.0738228\pi$
$349$			8.58781i			0.459695i	−0.973227	+	0.229848i	$0.926177\pi$
$350$	0.845238	−	0.584173i	0.0451799	−	0.0312254i
$351$	2.11846			0.113075
$352$	−13.1430	+	13.3889i	−0.700523	+	0.713629i
$353$	15.0402			0.800508			0.400254	−	0.916404i	$-0.368922\pi$
$353$	15.0402			0.800508			0.400254	+	0.916404i	$0.368922\pi$
$354$	−1.12760	+	0.779321i	−0.0599311	+	0.0414204i
$355$		−	1.98683i		−	0.105450i
$356$	8.76848	−	23.2043i	0.464728	−	1.22983i
$357$	−0.307177			−0.0162575
$358$	9.56488	+	13.8394i	0.505520	+	0.731435i
$359$	−32.4547			−1.71289			−0.856447	−	0.516236i	$-0.827333\pi$
$359$	−32.4547			−1.71289			−0.856447	+	0.516236i	$0.827333\pi$
$360$	4.03567	+	16.2477i	0.212698	+	0.856330i
$361$	3.52897			0.185735
$362$	7.39233	−	5.10909i	0.388532	−	0.268528i
$363$	−3.84245	+	0.998390i	−0.201676	+	0.0524019i
$364$	1.82232	+	0.688621i	0.0955155	+	0.0360935i
$365$			8.05886i			0.421820i
$366$	3.28135	−	2.26785i	0.171519	−	0.118542i
$367$			32.4862i			1.69577i	0.530182	+	0.847884i	$0.322124\pi$
$367$			32.4862i			1.69577i	−0.530182	+	0.847884i	$0.677876\pi$
$368$	1.40970	−	1.59892i	0.0734858	−	0.0833495i
$369$		−	6.79378i		−	0.353670i
$370$	−16.3249	+	11.2827i	−0.848693	+	0.586561i
$371$	1.63157			0.0847066
$372$	−1.02588	+	2.71481i	−0.0531892	+	0.140756i
$373$		−	16.7364i		−	0.866577i	−0.901255	−	0.433289i	$-0.857353\pi$
$373$		−	16.7364i		−	0.866577i	0.901255	−	0.433289i	$-0.142647\pi$
$374$	−4.09257	−	0.219334i	−0.211622	−	0.0113415i
$375$			4.27724i			0.220876i
$376$	−31.5836	+	7.84485i	−1.62880	+	0.404567i
$377$	−1.58668			−0.0817179
$378$	1.65916	+	2.40064i	0.0853381	+	0.123475i
$379$			16.7364i			0.859692i	0.902902	+	0.429846i	$0.141432\pi$
$379$			16.7364i			0.859692i	−0.902902	+	0.429846i	$0.858568\pi$
$380$	6.92112	−	18.3156i	0.355046	−	0.939570i
$381$			0.431106i			0.0220862i
$382$	−5.51481	−	7.97936i	−0.282162	−	0.408260i
$383$		−	30.7732i		−	1.57244i	−0.617950	−	0.786218i	$-0.712036\pi$
$383$		−	30.7732i		−	1.57244i	0.617950	−	0.786218i	$-0.287964\pi$
$384$	−3.62347	−	1.88242i	−0.184909	−	0.0960619i
$385$	−4.07630	+	5.27080i	−0.207747	+	0.268625i
$386$	−6.43808	−	9.31524i	−0.327690	−	0.474133i
$387$	18.0809			0.919104
$388$	−3.38317	+	8.95300i	−0.171754	+	0.454520i
$389$	−32.9613			−1.67121			−0.835603	−	0.549334i	$-0.814882\pi$
$389$	−32.9613			−1.67121			−0.835603	+	0.549334i	$0.814882\pi$
$390$	−0.866031	+	0.598544i	−0.0438532	+	0.0303084i
$391$	0.465647			0.0235488
$392$	−4.12584	−	16.6108i	−0.208386	−	0.838970i
$393$		−	3.99676i		−	0.201610i
$394$	−19.6842	−	28.4809i	−0.991673	−	1.43485i
$395$	−7.33187			−0.368906
$396$	9.96934	+	16.2164i	0.500978	+	0.814903i
$397$	12.5684			0.630790			0.315395	−	0.948961i	$-0.397863\pi$
$397$	12.5684			0.630790			0.315395	+	0.948961i	$0.397863\pi$
$398$	−5.70792	−	8.25877i	−0.286112	−	0.413975i
$399$		−	1.66860i		−	0.0835343i
$400$	2.23795	+	1.97311i	0.111898	+	0.0986554i
$401$	−13.4464			−0.671480			−0.335740	−	0.941955i	$-0.608986\pi$
$401$	−13.4464			−0.671480			−0.335740	+	0.941955i	$0.608986\pi$
$402$	0.964732	−	0.666759i	0.0481165	−	0.0332549i
$403$	4.02061			0.200281
$404$	−6.69092	−	2.52838i	−0.332886	−	0.125791i
$405$	16.1800			0.803989
$406$	−1.24267	−	1.79802i	−0.0616727	−	0.0892340i
$407$	−13.8039	+	17.8490i	−0.684236	+	0.884741i
$408$	−0.215019	−	0.865675i	−0.0106450	−	0.0428573i
$409$		−	25.9276i		−	1.28204i	−0.767525	−	0.641020i	$-0.778512\pi$
$409$		−	25.9276i		−	1.28204i	0.767525	−	0.641020i	$-0.221488\pi$
$410$	3.92611	+	5.68067i	0.193897	+	0.280548i
$411$			0.340010i			0.0167715i
$412$	4.30458	+	1.62662i	0.212072	+	0.0801379i
$413$			2.61579i			0.128715i
$414$	−1.22965	−	1.77918i	−0.0604341	−	0.0874419i
$415$	11.0865			0.544213
$416$	−0.665049	+	5.61762i	−0.0326067	+	0.275427i
$417$			5.12318i			0.250883i
$418$	1.19143	−	22.2310i	0.0582749	−	1.08735i
$419$		−	38.0608i		−	1.85939i	−0.368328	−	0.929696i	$-0.620070\pi$
$419$		−	38.0608i		−	1.85939i	0.368328	−	0.929696i	$-0.379930\pi$
$420$	−1.35654	−	0.512609i	−0.0661922	−	0.0250128i
$421$	36.5661			1.78212			0.891062	−	0.453883i	$-0.149961\pi$
$421$	36.5661			1.78212			0.891062	+	0.453883i	$0.149961\pi$
$422$	23.3310	−	16.1249i	1.13574	−	0.784947i
$423$			33.0187i			1.60542i
$424$	1.14207	+	4.59802i	0.0554639	+	0.223300i
$425$			0.651750i			0.0316145i
$426$	0.404470	−	0.279543i	0.0195966	−	0.0135439i
$427$		−	7.61205i		−	0.368373i
$428$	−6.47443	+	17.1335i	−0.312953	+	0.828179i
$429$	−0.732293	+	0.946881i	−0.0353554	+	0.0457159i
$430$	−15.1185	+	10.4489i	−0.729078	+	0.503891i
$431$	−21.6311			−1.04193			−0.520966	−	0.853577i	$-0.674428\pi$
$431$	−21.6311			−1.04193			−0.520966	+	0.853577i	$0.674428\pi$
$432$	−5.60400	+	6.35621i	−0.269623	+	0.305813i
$433$	−21.9800			−1.05629			−0.528145	−	0.849154i	$-0.677112\pi$
$433$	−21.9800			−1.05629			−0.528145	+	0.849154i	$0.677112\pi$
$434$	3.14890	+	4.55614i	0.151152	+	0.218702i
$435$	1.18112			0.0566305
$436$	−31.6689	−	11.9671i	−1.51666	−	0.573119i
$437$			2.52942i			0.120998i
$438$	−1.64058	+	1.13386i	−0.0783901	+	0.0541781i
$439$	6.79746			0.324425			0.162213	−	0.986756i	$-0.448137\pi$
$439$	6.79746			0.324425			0.162213	+	0.986756i	$0.448137\pi$
$440$	−17.7073	−	7.79820i	−0.844164	−	0.371764i
$441$	−17.3655			−0.826928
$442$	−1.01656	+	0.702581i	−0.0483529	+	0.0334184i
$443$		−	31.0242i		−	1.47400i	−0.675890	−	0.737002i	$-0.736241\pi$
$443$		−	31.0242i		−	1.47400i	0.675890	−	0.737002i	$-0.263759\pi$
$444$	−4.59376	−	1.73590i	−0.218010	−	0.0823820i
$445$	25.5816			1.21268
$446$	4.44232	+	6.42758i	0.210350	+	0.304355i
$447$	−6.09028			−0.288060
$448$	−6.88674	+	3.64604i	−0.325368	+	0.172259i
$449$	−5.53697			−0.261306			−0.130653	−	0.991428i	$-0.541707\pi$
$449$	−5.53697			−0.261306			−0.130653	+	0.991428i	$0.541707\pi$
$450$	2.49025	−	1.72110i	0.117392	−	0.0811334i
$451$	6.21101	+	4.80343i	0.292465	+	0.226185i
$452$	−8.84484	+	23.4064i	−0.416026	+	1.10094i
$453$			3.03596i			0.142642i
$454$	−21.2642	+	14.6964i	−0.997977	+	0.689736i
$455$			2.00901i			0.0941841i
$456$	4.70238	−	1.16799i	0.220209	−	0.0546963i
$457$			0.886658i			0.0414761i	0.999785	+	0.0207381i	$0.00660160\pi$
$457$			0.886658i			0.0414761i	−0.999785	+	0.0207381i	$0.993398\pi$
$458$	10.6744	−	7.37745i	0.498783	−	0.344726i
$459$	−1.85109			−0.0864017
$460$	2.05637	+	0.777062i	0.0958785	+	0.0362307i
$461$		−	32.2662i		−	1.50279i	−0.659854	−	0.751394i	$-0.729382\pi$
$461$		−	32.2662i		−	1.50279i	0.659854	−	0.751394i	$-0.270618\pi$
$462$	−1.64653	−	0.0882429i	−0.0766035	−	0.00410543i
$463$		−	11.4838i		−	0.533698i	−0.963738	−	0.266849i	$-0.914018\pi$
$463$		−	11.4838i		−	0.533698i	0.963738	−	0.266849i	$-0.0859825\pi$
$464$	4.19726	−	4.76064i	0.194853	−	0.221007i
$465$	−2.99294			−0.138794
$466$	−14.9786	−	21.6725i	−0.693870	−	1.00396i
$467$		−	11.2170i		−	0.519060i	−0.965735	−	0.259530i	$-0.916432\pi$
$467$		−	11.2170i		−	0.519060i	0.965735	−	0.259530i	$-0.0835676\pi$
$468$	5.36894	+	2.02882i	0.248179	+	0.0937824i
$469$		−	2.23798i		−	0.103340i
$470$	−19.0814	−	27.6088i	−0.880159	−	1.27350i
$471$			6.64357i			0.306120i
$472$	−7.37174	+	1.83102i	−0.339312	+	0.0842795i
$473$	−12.7838	+	16.5299i	−0.587800	+	0.760046i
$474$	−1.03158	−	1.49259i	−0.0473819	−	0.0685567i
$475$	−3.54034			−0.162442
$476$	−1.59233	−	0.601710i	−0.0729841	−	0.0275793i
$477$	4.80694			0.220095
$478$	19.8058	−	13.6885i	0.905898	−	0.626097i
$479$	−14.2899			−0.652921			−0.326461	−	0.945211i	$-0.605856\pi$
$479$	−14.2899			−0.652921			−0.326461	+	0.945211i	$0.605856\pi$
$480$	0.495063	−	4.18176i	0.0225964	−	0.190870i
$481$			6.80331i			0.310204i
$482$	1.74712	+	2.52790i	0.0795792	+	0.115143i
$483$	0.187340			0.00852427
$484$	−21.8740	−	2.35135i	−0.994272	−	0.106880i
$485$	−9.87022			−0.448184
$486$	7.38661	+	10.6877i	0.335063	+	0.484802i
$487$			13.6773i			0.619775i	0.950773	+	0.309888i	$0.100291\pi$
$487$			13.6773i			0.619775i	−0.950773	+	0.309888i	$0.899709\pi$
$488$	21.4520	−	5.32833i	0.971088	−	0.241202i
$489$	−6.60277			−0.298588
$490$	14.5203	−	10.0355i	0.655960	−	0.453356i
$491$	23.9129			1.07917			0.539587	−	0.841930i	$-0.318581\pi$
$491$	23.9129			1.07917			0.539587	+	0.841930i	$0.318581\pi$
$492$	−0.604049	+	1.59851i	−0.0272326	+	0.0720666i
$493$	1.38642			0.0624413
$494$	−3.81645	−	5.52201i	−0.171710	−	0.248447i
$495$	−12.0096	+	15.5289i	−0.539793	+	0.697972i
$496$	−10.6358	+	12.0634i	−0.477560	+	0.541661i
$497$		−	0.938287i		−	0.0420879i
$498$	1.55984	+	2.25693i	0.0698981	+	0.101135i
$499$			7.69190i			0.344337i	0.985068	+	0.172168i	$0.0550773\pi$
$499$			7.69190i			0.344337i	−0.985068	+	0.172168i	$0.944923\pi$
$500$	−8.37844	+	22.1721i	−0.374695	+	0.991568i
$501$			6.46612i			0.288885i
$502$	20.6924	+	29.9398i	0.923547	+	1.33628i
$503$	−35.8340			−1.59776			−0.798880	−	0.601490i	$-0.794574\pi$
$503$	−35.8340			−1.59776			−0.798880	+	0.601490i	$0.794574\pi$
$504$	1.90585	+	7.67303i	0.0848934	+	0.341784i
$505$		−	7.37640i		−	0.328246i
$506$	2.49596	+	0.133767i	0.110959	+	0.00594667i
$507$			0.360913i			0.0160287i
$508$	−0.844468	+	2.23474i	−0.0374672	+	0.0991507i
$509$	10.2670			0.455077			0.227539	−	0.973769i	$-0.426932\pi$
$509$	10.2670			0.455077			0.227539	+	0.973769i	$0.426932\pi$
$510$	0.756730	−	0.523002i	0.0335085	−	0.0231589i
$511$			3.80582i			0.168359i
$512$	−15.0958	−	16.8558i	−0.667145	−	0.744928i
$513$		−	10.0552i		−	0.443949i
$514$	9.26662	−	6.40448i	0.408733	−	0.282490i
$515$			4.74558i			0.209115i
$516$	−4.25427	−	1.60761i	−0.187284	−	0.0707711i
$517$	−30.1863	−	23.3453i	−1.32759	−	1.02672i
$518$	−7.70949	+	5.32829i	−0.338735	+	0.234112i
$519$	7.65345			0.335949
$520$	−5.66174	+	1.40628i	−0.248284	+	0.0616695i
$521$	1.72237			0.0754584			0.0377292	−	0.999288i	$-0.487988\pi$
$521$	1.72237			0.0754584			0.0377292	+	0.999288i	$0.487988\pi$
$522$	−3.66117	−	5.29734i	−0.160245	−	0.231858i
$523$	5.44198			0.237961			0.118981	−	0.992897i	$-0.462037\pi$
$523$	5.44198			0.237961			0.118981	+	0.992897i	$0.462037\pi$
$524$	7.82902	−	20.7182i	0.342012	−	0.905078i
$525$			0.262213i			0.0114439i
$526$	10.9906	−	7.59601i	0.479215	−	0.331202i
$527$	−3.51317			−0.153036
$528$	−0.903864	−	4.70196i	−0.0393356	−	0.204627i
$529$	22.7160			0.987653
$530$	−4.01936	+	2.77792i	−0.174590	+	0.120665i
$531$			7.70669i			0.334442i
$532$	3.26852	−	8.64959i	0.141708	−	0.375007i
$533$	2.36738			0.102543
$534$	3.59927	+	5.20777i	0.155756	+	0.225362i
$535$	−18.8888			−0.816634
$536$	6.30700	−	1.56656i	0.272421	−	0.0676649i
$537$	−4.29331			−0.185270
$538$	35.0463	−	24.2217i	1.51095	−	1.04427i
$539$	12.2780	−	15.8759i	0.528850	−	0.683822i
$540$	−8.17470	−	3.08906i	−0.351783	−	0.132932i
$541$			1.32600i			0.0570092i	0.999594	+	0.0285046i	$0.00907453\pi$
$541$			1.32600i			0.0570092i	−0.999594	+	0.0285046i	$0.990925\pi$
$542$	−9.02110	+	6.23479i	−0.387489	+	0.267807i
$543$			2.29328i			0.0984140i
$544$	0.581114	−	4.90863i	0.0249150	−	0.210456i
$545$		−	34.9133i		−	1.49552i
$546$	−0.408985	+	0.282664i	−0.0175029	+	0.0120969i
$547$	19.9064			0.851136			0.425568	−	0.904927i	$-0.360074\pi$
$547$	19.9064			0.851136			0.425568	+	0.904927i	$0.360074\pi$
$548$	−0.666026	+	1.76253i	−0.0284512	+	0.0752914i
$549$		−	22.4267i		−	0.957150i
$550$	−0.187229	+	3.49351i	−0.00798347	+	0.148964i
$551$			7.53111i			0.320836i
$552$	0.131135	+	0.527955i	0.00558149	+	0.0224713i
$553$	−3.46249			−0.147240
$554$	−14.9986	−	21.7015i	−0.637231	−	0.922007i
$555$		−	5.06439i		−	0.214971i
$556$	−10.0355	+	26.5573i	−0.425600	+	1.12628i
$557$		−	0.0824283i		−	0.00349260i	−0.999998	−	0.00174630i	$-0.999444\pi$
$557$		−	0.0824283i		−	0.00349260i	0.999998	−	0.00174630i	$-0.000555865\pi$
$558$	9.27734	+	13.4234i	0.392741	+	0.568256i
$559$			6.30053i			0.266484i
$560$	−6.02782	−	5.31448i	−0.254722	−	0.224578i
$561$	0.639871	−	0.827376i	0.0270154	−	0.0349318i
$562$	−21.3540	−	30.8970i	−0.900764	−	1.30331i
$563$	−2.00408			−0.0844620			−0.0422310	−	0.999108i	$-0.513447\pi$
$563$	−2.00408			−0.0844620			−0.0422310	+	0.999108i	$0.513447\pi$
$564$	2.93576	−	7.76899i	0.123618	−	0.327134i
$565$	−25.8044			−1.08560
$566$	−1.89669	+	1.31087i	−0.0797239	+	0.0550999i
$567$	7.64103			0.320893
$568$	2.64425	−	0.656788i	0.110950	−	0.0275582i
$569$		−	32.1976i		−	1.34979i	−0.737912	−	0.674897i	$-0.764188\pi$
$569$		−	32.1976i		−	1.34979i	0.737912	−	0.674897i	$-0.235812\pi$
$570$	2.84097	+	4.11059i	0.118995	+	0.172174i
$571$	38.1476			1.59643			0.798215	−	0.602373i	$-0.205778\pi$
$571$	38.1476			1.59643			0.798215	+	0.602373i	$0.205778\pi$
$572$	−5.65081	+	3.47395i	−0.236272	+	0.145253i
$573$	2.47539			0.103411
$574$	1.85411	+	2.68271i	0.0773892	+	0.111974i
$575$		−	0.397488i		−	0.0165764i
$576$	−20.2898	+	10.7420i	−0.845408	+	0.447584i
$577$	41.6990			1.73595			0.867976	−	0.496607i	$-0.165421\pi$
$577$	41.6990			1.73595			0.867976	+	0.496607i	$0.165421\pi$
$578$	−18.8894	+	13.0551i	−0.785697	+	0.543022i
$579$	2.88981			0.120096
$580$	6.12264	+	2.31363i	0.254229	+	0.0960683i
$581$	5.23561			0.217210
$582$	−1.38872	−	2.00933i	−0.0575642	−	0.0832894i
$583$	−3.39867	+	4.39460i	−0.140758	+	0.182006i
$584$	−10.7254	+	2.66402i	−0.443821	+	0.110238i
$585$			5.91899i			0.244720i
$586$	−4.22543	−	6.11376i	−0.174551	−	0.252557i
$587$			35.6406i			1.47104i	0.677501	+	0.735522i	$0.263063\pi$
$587$			35.6406i			1.47104i	−0.677501	+	0.735522i	$0.736937\pi$
$588$	4.08594	+	1.54400i	0.168501	+	0.0636736i
$589$		−	19.0837i		−	0.786329i
$590$	−4.45368	−	6.44401i	−0.183355	−	0.265296i
$591$	8.83547			0.363443
$592$	−20.4125	−	17.9969i	−0.838950	−	0.739668i
$593$			38.6604i			1.58759i	0.608183	+	0.793797i	$0.291899\pi$
$593$			38.6604i			1.58759i	−0.608183	+	0.793797i	$0.708101\pi$
$594$	−9.92224	−	0.531766i	−0.407114	−	0.0218186i
$595$		−	1.75546i		−	0.0719668i
$596$	−31.5705	−	11.9299i	−1.29318	−	0.488667i
$597$	2.56207			0.104859
$598$	0.619979	−	0.428488i	0.0253528	−	0.0175222i
$599$			15.0251i			0.613907i	0.951724	+	0.306954i	$0.0993096\pi$
$599$			15.0251i			0.613907i	−0.951724	+	0.306954i	$0.900690\pi$
$600$	−0.738960	+	0.183546i	−0.0301679	+	0.00749321i
$601$			2.25805i			0.0921077i	0.998939	+	0.0460538i	$0.0146646\pi$
$601$			2.25805i			0.0921077i	−0.998939	+	0.0460538i	$0.985335\pi$
$602$	−7.13974	+	4.93452i	−0.290994	+	0.201116i
$603$		−	6.59357i		−	0.268511i
$604$	−5.94696	+	15.7377i	−0.241979	+	0.640356i
$605$	−5.70561	−	21.9589i	−0.231966	−	0.892756i
$606$	1.50165	−	1.03784i	0.0610004	−	0.0421595i
$607$	33.2059			1.34779			0.673894	−	0.738828i	$-0.264621\pi$
$607$	33.2059			1.34779			0.673894	+	0.738828i	$0.264621\pi$
$608$	26.6639	+	3.15664i	1.08136	+	0.128018i
$609$	0.557788			0.0226027
$610$	12.9604	+	18.7523i	0.524749	+	0.759258i
$611$	−11.5058			−0.465474
$612$	−4.69133	−	1.77277i	−0.189636	−	0.0716598i
$613$			29.5046i			1.19168i	0.803104	+	0.595839i	$0.203180\pi$
$613$			29.5046i			1.19168i	−0.803104	+	0.595839i	$0.796820\pi$
$614$	−14.4122	+	9.96080i	−0.581631	+	0.401985i
$615$	−1.76228			−0.0710620
$616$	−8.36234	−	3.68272i	−0.336928	−	0.148381i
$617$	1.49391			0.0601424			0.0300712	−	0.999548i	$-0.490427\pi$
$617$	1.49391			0.0601424			0.0300712	+	0.999548i	$0.490427\pi$
$618$	−0.966082	+	0.667692i	−0.0388615	+	0.0268585i
$619$			13.3214i			0.535434i	0.963498	+	0.267717i	$0.0862692\pi$
$619$			13.3214i			0.535434i	−0.963498	+	0.267717i	$0.913731\pi$
$620$	−15.5146	−	5.86269i	−0.623083	−	0.235451i
$621$	1.12894			0.0453028
$622$	−9.71128	−	14.0512i	−0.389387	−	0.563403i
$623$	12.0810			0.484013
$624$	−1.08288	−	0.954728i	−0.0433498	−	0.0382197i
$625$	−20.7142			−0.828568
$626$	9.16250	−	6.33252i	0.366207	−	0.253098i
$627$	4.49434	+	3.47581i	0.179487	+	0.138810i
$628$	−13.0137	+	34.4386i	−0.519303	+	1.37425i
$629$		−	5.94467i		−	0.237029i
$630$	−6.70738	+	4.63570i	−0.267228	+	0.184691i
$631$			37.7850i			1.50420i	0.659052	+	0.752098i	$0.270958\pi$
$631$			37.7850i			1.50420i	−0.659052	+	0.752098i	$0.729042\pi$
$632$	−2.42370	−	9.75788i	−0.0964095	−	0.388148i
$633$			7.23785i			0.287679i
$634$	−14.7839	+	10.2177i	−0.587144	+	0.405795i
$635$	−2.46369			−0.0977686
$636$	−1.13103	−	0.427395i	−0.0448482	−	0.0169473i
$637$		−	6.05124i		−	0.239759i
$638$	7.43150	+	0.398279i	0.294216	+	0.0157680i
$639$		−	2.76439i		−	0.109358i
$640$	10.7577	−	20.7074i	0.425235	−	0.818534i
$641$	31.0791			1.22755			0.613775	−	0.789481i	$-0.289650\pi$
$641$	31.0791			1.22755			0.613775	+	0.789481i	$0.289650\pi$
$642$	−2.65761	−	3.84529i	−0.104888	−	0.151761i
$643$			25.3494i			0.999683i	0.866117	+	0.499841i	$0.166608\pi$
$643$			25.3494i			0.999683i	−0.866117	+	0.499841i	$0.833392\pi$
$644$	0.971124	+	0.366969i	0.0382676	+	0.0144606i
$645$		−	4.69012i		−	0.184673i
$646$	3.33478	+	4.82508i	0.131205	+	0.189840i
$647$			23.8227i			0.936566i	0.883579	+	0.468283i	$0.155127\pi$
$647$			23.8227i			0.936566i	−0.883579	+	0.468283i	$0.844873\pi$
$648$	5.34861	+	21.5337i	0.210113	+	0.845923i
$649$	−7.04561	−	5.44889i	−0.276564	−	0.213887i
$650$	0.599740	+	0.867762i	0.0235237	+	0.0340364i
$651$	−1.41342			−0.0553964
$652$	−34.2271	−	12.9338i	−1.34044	−	0.506526i
$653$	4.16043			0.162810			0.0814051	−	0.996681i	$-0.474059\pi$
$653$	4.16043			0.162810			0.0814051	+	0.996681i	$0.474059\pi$
$654$	7.10748	−	4.91222i	0.277925	−	0.192083i
$655$	22.8407			0.892462
$656$	−6.26247	+	7.10306i	−0.244508	+	0.277328i
$657$			11.2128i			0.437451i
$658$	−9.01124	−	13.0383i	−0.351295	−	0.508287i
$659$	−0.655842			−0.0255480			−0.0127740	−	0.999918i	$-0.504066\pi$
$659$	−0.655842			−0.0255480			−0.0127740	+	0.999918i	$0.504066\pi$
$660$	4.20647	−	2.58601i	0.163737	−	0.100660i
$661$	41.0755			1.59765			0.798827	−	0.601561i	$-0.205454\pi$
$661$	41.0755			1.59765			0.798827	+	0.601561i	$0.205454\pi$
$662$	18.8288	+	27.2434i	0.731804	+	1.05884i
$663$		−	0.315362i		−	0.0122476i
$664$	3.66485	+	14.7548i	0.142224	+	0.572598i
$665$	9.53573			0.369780
$666$	−22.7138	+	15.6983i	−0.880142	+	0.608296i
$667$	−0.845548			−0.0327397
$668$	−12.6661	+	33.5187i	−0.490066	+	1.29688i
$669$	−1.99399			−0.0770921
$670$	3.81041	+	5.51327i	0.147209	+	0.212996i
$671$	20.5030	+	15.8564i	0.791508	+	0.612131i
$672$	0.233795	−	1.97485i	0.00901882	−	0.0761814i
$673$		−	44.5164i		−	1.71598i	−0.513664	−	0.857991i	$-0.671712\pi$
$673$		−	44.5164i		−	1.71598i	0.513664	−	0.857991i	$-0.328288\pi$
$674$	22.1625	+	32.0668i	0.853666	+	1.23517i
$675$			1.58014i			0.0608195i
$676$	−0.706971	+	1.87088i	−0.0271912	+	0.0719569i
$677$		−	29.9713i		−	1.15189i	−0.817489	−	0.575945i	$-0.804634\pi$
$677$		−	29.9713i		−	1.15189i	0.817489	−	0.575945i	$-0.195366\pi$
$678$	−3.63061	−	5.25312i	−0.139433	−	0.201745i
$679$	−4.66124			−0.178882
$680$	4.94717	−	1.22880i	0.189715	−	0.0471222i
$681$		−	6.59666i		−	0.252784i
$682$	−18.8313	−	1.00923i	−0.721087	−	0.0386455i
$683$		−	40.0896i		−	1.53398i	−0.641656	−	0.766992i	$-0.721752\pi$
$683$		−	40.0896i		−	1.53398i	0.641656	−	0.766992i	$-0.278248\pi$
$684$	9.62975	−	25.4835i	0.368203	−	0.974387i
$685$	−1.94310			−0.0742419
$686$	14.7896	−	10.2216i	0.564670	−	0.390263i
$687$			3.31146i			0.126340i
$688$	−18.9040	−	16.6669i	−0.720709	−	0.635419i
$689$			1.67504i			0.0638140i
$690$	−0.461512	+	0.318967i	−0.0175695	+	0.0121429i
$691$			44.2297i			1.68258i	0.540587	+	0.841288i	$0.318202\pi$
$691$			44.2297i			1.68258i	−0.540587	+	0.841288i	$0.681798\pi$
$692$	39.6735	+	14.9919i	1.50816	+	0.569906i
$693$	−5.67158	+	7.33356i	−0.215446	+	0.278579i
$694$	−39.7059	+	27.4421i	−1.50722	+	1.04169i
$695$	−29.2780			−1.11058
$696$	0.390444	+	1.57194i	0.0147997	+	0.0595842i
$697$	−2.06860			−0.0783537
$698$	−6.90513	−	9.99101i	−0.261363	−	0.378165i
$699$	6.72332			0.254299
$700$	−0.513634	+	1.35925i	−0.0194135	+	0.0513747i
$701$			17.7126i			0.668997i	0.942396	+	0.334499i	$0.108567\pi$
$701$			17.7126i			0.668997i	−0.942396	+	0.334499i	$0.891433\pi$
$702$	−2.46461	+	1.70338i	−0.0930207	+	0.0642898i
$703$	32.2917			1.21790
$704$	4.52499	−	26.1443i	0.170542	−	0.985350i
$705$	8.56492			0.322573
$706$	−17.4976	+	12.0932i	−0.658533	+	0.455135i
$707$		−	3.48352i		−	0.131011i
$708$	0.685218	−	1.81331i	0.0257521	−	0.0681485i
$709$	12.0556			0.452757			0.226379	−	0.974039i	$-0.427311\pi$
$709$	12.0556			0.452757			0.226379	+	0.974039i	$0.427311\pi$
$710$	1.59754	+	2.31147i	0.0599545	+	0.0867480i
$711$	−10.2012			−0.382577
$712$	8.45650	+	34.0461i	0.316921	+	1.27593i
$713$	2.14260			0.0802410
$714$	0.357367	−	0.246989i	0.0133741	−	0.00924332i
$715$	−5.41125	−	4.18492i	−0.202369	−	0.156507i
$716$	−22.2555	−	8.40992i	−0.831725	−	0.314293i
$717$			6.14424i			0.229461i
$718$	37.7576	−	26.0956i	1.40910	−	0.973878i
$719$			20.0245i			0.746789i	0.927673	+	0.373395i	$0.121806\pi$
$719$			20.0245i			0.746789i	−0.927673	+	0.373395i	$0.878194\pi$
$720$	−17.7592	−	15.6576i	−0.661848	−	0.583524i
$721$			2.24111i			0.0834634i
$722$	−4.10558	+	2.83751i	−0.152794	+	0.105601i
$723$	−0.784216			−0.0291653
$724$	−4.49217	+	11.8878i	−0.166950	+	0.441806i
$725$		−	1.18348i		−	0.0439534i
$726$	3.66752	−	4.25109i	0.136114	−	0.157773i
$727$		−	37.4482i		−	1.38888i	−0.719552	−	0.694439i	$-0.755653\pi$
$727$		−	37.4482i		−	1.38888i	0.719552	−	0.694439i	$-0.244347\pi$
$728$	−2.67377	+	0.664120i	−0.0990965	+	0.0246139i
$729$	20.2184			0.748828
$730$	−6.47982	−	9.37563i	−0.239829	−	0.347008i
$731$		−	5.50534i		−	0.203623i
$732$	−1.99401	+	5.27681i	−0.0737006	+	0.195036i
$733$			28.1807i			1.04088i	0.853898	+	0.520440i	$0.174232\pi$
$733$			28.1807i			1.04088i	−0.853898	+	0.520440i	$0.825768\pi$
$734$	−26.1209	−	37.7943i	−0.964141	−	1.39501i
$735$			4.50454i			0.166153i
$736$	−0.354408	+	2.99366i	−0.0130637	+	0.110348i
$737$	6.02797	+	4.66187i	0.222043	+	0.171722i
$738$	5.46261	+	7.90384i	0.201082	+	0.290944i
$739$	4.98357			0.183324			0.0916619	−	0.995790i	$-0.470782\pi$
$739$	4.98357			0.183324			0.0916619	+	0.995790i	$0.470782\pi$
$740$	9.92033	−	26.2525i	0.364678	−	0.965061i
$741$	1.71306			0.0629309
$742$	−1.89815	+	1.31188i	−0.0696834	+	0.0481606i
$743$	−50.0961			−1.83785			−0.918924	−	0.394434i	$-0.870941\pi$
$743$	−50.0961			−1.83785			−0.918924	+	0.394434i	$0.870941\pi$
$744$	−0.989376	−	3.98326i	−0.0362723	−	0.146033i
$745$		−	34.8048i		−	1.27515i
$746$	13.4571	+	19.4710i	0.492699	+	0.712884i
$747$	15.4252			0.564380
$748$	4.93763	−	3.03550i	0.180537	−	0.110989i
$749$	−8.92028			−0.325940
$750$	−3.43916	−	4.97612i	−0.125581	−	0.181702i
$751$		−	46.6548i		−	1.70246i	−0.524795	−	0.851229i	$-0.675858\pi$
$751$		−	46.6548i		−	1.70246i	0.524795	−	0.851229i	$-0.324142\pi$
$752$	30.4364	−	34.5218i	1.10990	−	1.25888i
$753$	−9.28803			−0.338475
$754$	1.84593	−	1.27578i	0.0672248	−	0.0464613i
$755$	−17.3500			−0.631430
$756$	−3.86052	−	1.45882i	−0.140406	−	0.0530567i
$757$	12.6945			0.461391			0.230695	−	0.973026i	$-0.425900\pi$
$757$	12.6945			0.461391			0.230695	+	0.973026i	$0.425900\pi$
$758$	−13.4571	−	19.4710i	−0.488784	−	0.707220i
$759$	−0.390243	+	0.504598i	−0.0141649	+	0.0183157i
$760$	6.67487	+	26.8733i	0.242123	+	0.974796i
$761$		−	17.0541i		−	0.618211i	−0.951028	−	0.309106i	$-0.899970\pi$
$761$		−	17.0541i		−	0.618211i	0.951028	−	0.309106i	$-0.100030\pi$
$762$	−0.346636	−	0.501546i	−0.0125573	−	0.0181691i
$763$		−	16.4879i		−	0.596902i
$764$	12.8318	+	4.84889i	0.464238	+	0.175427i
$765$		−	5.17195i		−	0.186992i
$766$	24.7435	+	35.8013i	0.894020	+	1.29355i
$767$	−2.68550			−0.0969677
$768$	5.72910	−	0.723493i	0.206731	−	0.0261068i
$769$			30.9405i			1.11574i	0.829928	+	0.557871i	$0.188382\pi$
$769$			30.9405i			1.11574i	−0.829928	+	0.557871i	$0.811618\pi$
$770$	0.504292	−	9.40961i	0.0181734	−	0.339099i
$771$			2.87473i			0.103531i
$772$	14.9800	+	5.66068i	0.539144	+	0.203732i
$773$	−16.6569			−0.599108			−0.299554	−	0.954079i	$-0.596838\pi$
$773$	−16.6569			−0.599108			−0.299554	+	0.954079i	$0.596838\pi$
$774$	−21.0352	+	14.5382i	−0.756095	+	0.522563i
$775$			2.99892i			0.107724i
$776$	−3.26280	−	13.1361i	−0.117128	−	0.471560i
$777$		−	2.39167i		−	0.0858006i
$778$	38.3470	−	26.5029i	1.37481	−	0.950176i
$779$		−	11.2367i		−	0.402597i
$780$	0.526269	−	1.39268i	0.0188435	−	0.0498661i
$781$	2.52726	+	1.95452i	0.0904326	+	0.0699382i
$782$	−0.541731	+	0.374409i	−0.0193723	+	0.0133888i
$783$	3.36132			0.120124
$784$	18.1560	+	16.0074i	0.648430	+	0.571694i
$785$	−37.9668			−1.35509
$786$	3.21364	+	4.64981i	0.114627	+	0.165853i
$787$	−46.5240			−1.65840			−0.829200	−	0.558951i	$-0.811204\pi$
$787$	−46.5240			−1.65840			−0.829200	+	0.558951i	$0.811204\pi$
$788$	45.8009	+	17.3073i	1.63159	+	0.616547i
$789$			3.40956i			0.121384i
$790$	8.52985	−	5.89527i	0.303479	−	0.209744i
$791$	−12.1862			−0.433291
$792$	−24.6372	−	10.8501i	−0.875446	−	0.385541i
$793$	7.81490			0.277515
$794$	−14.6220	+	10.1058i	−0.518915	+	0.358640i
$795$		−	1.24690i		−	0.0442231i
$796$	13.2811	+	5.01869i	0.470737	+	0.177883i
$797$	10.3015			0.364898			0.182449	−	0.983215i	$-0.441598\pi$
$797$	10.3015			0.364898			0.182449	+	0.983215i	$0.441598\pi$
$798$	1.34165	+	1.94124i	0.0474941	+	0.0687190i
$799$	10.0537			0.355673
$800$	−4.19012	−	0.496052i	−0.148143	−	0.0175381i
$801$	35.5931			1.25762
$802$	15.6434	−	10.8117i	0.552389	−	0.381775i
$803$	−10.2509	−	7.92779i	−0.361747	−	0.279766i
$804$	−0.586248	+	1.55141i	−0.0206754	+	0.0547139i
$805$			1.07061i			0.0377342i
$806$	−4.67755	+	3.23281i	−0.164760	+	0.113871i
$807$			10.8722i			0.382720i
$808$	9.81715	−	2.43842i	0.345366	−	0.0857832i
$809$			31.6064i			1.11122i	0.831443	+	0.555611i	$0.187515\pi$
$809$			31.6064i			1.11122i	−0.831443	+	0.555611i	$0.812485\pi$
$810$	−18.8237	+	13.0097i	−0.661397	+	0.457114i
$811$	25.1870			0.884437			0.442218	−	0.896907i	$-0.354192\pi$
$811$	25.1870			0.884437			0.442218	+	0.896907i	$0.354192\pi$
$812$	2.89143	+	1.09262i	0.101469	+	0.0383434i
$813$		−	2.79856i		−	0.0981498i
$814$	1.70773	−	31.8646i	0.0598559	−	1.11685i
$815$		−	37.7336i		−	1.32175i
$816$	0.946208	+	0.834232i	0.0331239	+	0.0292040i
$817$	29.9053			1.04625
$818$	20.8474	+	30.1641i	0.728913	+	1.05466i
$819$			2.79526i			0.0976741i
$820$	−9.13522	−	3.45203i	−0.319016	−	0.120550i
$821$			31.8674i			1.11218i	0.831122	+	0.556090i	$0.187699\pi$
$821$			31.8674i			1.11218i	−0.831122	+	0.556090i	$0.812301\pi$
$822$	−0.273389	−	0.395566i	−0.00953554	−	0.0137969i
$823$		−	11.5193i		−	0.401539i	−0.979639	−	0.200769i	$-0.935656\pi$
$823$		−	11.5193i		−	0.401539i	0.979639	−	0.200769i	$-0.0643442\pi$
$824$	−6.31583	+	1.56875i	−0.220022	+	0.0546499i
$825$	−0.706268	−	0.546209i	−0.0245891	−	0.0190165i
$826$	−2.10326	−	3.04320i	−0.0731817	−	0.105886i
$827$	37.3998			1.30052			0.650259	−	0.759712i	$-0.274660\pi$
$827$	37.3998			1.30052			0.650259	+	0.759712i	$0.274660\pi$
$828$	2.86114	+	1.08117i	0.0994314	+	0.0375733i
$829$	−19.8576			−0.689683			−0.344841	−	0.938661i	$-0.612067\pi$
$829$	−19.8576			−0.689683			−0.344841	+	0.938661i	$0.612067\pi$
$830$	−12.8979	+	8.91420i	−0.447694	+	0.309416i
$831$	6.73231			0.233541
$832$	−3.74320	−	7.07025i	−0.129772	−	0.245117i
$833$			5.28751i			0.183202i
$834$	−4.11935	−	5.96028i	−0.142641	−	0.206388i
$835$	−36.9527			−1.27880
$836$	16.4890	+	26.8214i	0.570284	+	0.927638i
$837$	−8.51751			−0.294408
$838$	30.6032	+	44.2797i	1.05717	+	1.52962i
$839$			10.5516i			0.364282i	0.983272	+	0.182141i	$0.0583027\pi$
$839$			10.5516i			0.364282i	−0.983272	+	0.182141i	$0.941697\pi$
$840$	1.99035	−	0.494371i	0.0686738	−	0.0170574i
$841$	26.4825			0.913188
$842$	−42.5408	+	29.4014i	−1.46605	+	1.01324i
$843$	9.58500			0.330125
$844$	−14.1778	+	37.5192i	−0.488020	+	1.29146i
$845$	−2.06255			−0.0709539
$846$	−26.5490	−	38.4137i	−0.912774	−	1.32069i
$847$	−2.69449	−	10.3701i	−0.0925838	−	0.356322i
$848$	−5.02577	−	4.43101i	−0.172586	−	0.152162i
$849$		−	0.588399i		−	0.0201938i
$850$	−0.524047	−	0.758242i	−0.0179747	−	0.0260075i
$851$			3.62552i			0.124281i
$852$	−0.245788	+	0.650437i	−0.00842056	+	0.0222836i
$853$			32.6534i			1.11803i	0.829157	+	0.559015i	$0.188821\pi$
$853$			32.6534i			1.11803i	−0.829157	+	0.559015i	$0.811179\pi$
$854$	6.12056	+	8.85582i	0.209441	+	0.303040i
$855$	28.0943			0.960804
$856$	−6.24407	−	25.1388i	−0.213418	−	0.859228i
$857$		−	4.69991i		−	0.160546i	−0.996773	−	0.0802730i	$-0.974421\pi$
$857$		−	4.69991i		−	0.160546i	0.996773	−	0.0802730i	$-0.0255792\pi$
$858$	0.0905944	−	1.69040i	0.00309284	−	0.0577095i
$859$		−	28.6385i		−	0.977132i	−0.872527	−	0.488566i	$-0.837520\pi$
$859$		−	28.6385i		−	0.977132i	0.872527	−	0.488566i	$-0.162480\pi$
$860$	9.18720	−	24.3124i	0.313281	−	0.829046i
$861$	−0.832241			−0.0283627
$862$	25.1655	−	17.3927i	0.857139	−	0.592398i
$863$		−	25.1147i		−	0.854914i	−0.904036	−	0.427457i	$-0.859410\pi$
$863$		−	25.1147i		−	0.854914i	0.904036	−	0.427457i	$-0.140590\pi$
$864$	1.40888	−	11.9007i	0.0479312	−	0.404871i
$865$			43.7380i			1.48714i
$866$	25.5714	−	17.6732i	0.868950	−	0.600561i
$867$		−	5.85996i		−	0.199015i
$868$	−7.32683	−	2.76867i	−0.248689	−	0.0939748i
$869$	7.21262	−	9.32618i	0.244671	−	0.316369i
$870$	−1.37411	+	0.949694i	−0.0465867	+	0.0321977i
$871$	2.29762			0.0778518
$872$	46.4657	−	11.5413i	1.57353	−	0.390838i
$873$	−13.7330			−0.464792
$874$	−2.03381	−	2.94271i	−0.0687946	−	0.0995386i
$875$	−11.5436			−0.390244
$876$	0.996949	−	2.63826i	0.0336838	−	0.0891385i
$877$			7.98817i			0.269741i	0.990863	+	0.134871i	$0.0430619\pi$
$877$			7.98817i			0.269741i	−0.990863	+	0.134871i	$0.956938\pi$
$878$	−7.90813	+	5.46558i	−0.266886	+	0.184454i
$879$	1.89663			0.0639719
$880$	26.8708	−	5.16542i	0.905816	−	0.174126i
$881$	−32.9468			−1.11001			−0.555003	−	0.831848i	$-0.687283\pi$
$881$	−32.9468			−1.11001			−0.555003	+	0.831848i	$0.687283\pi$
$882$	20.2029	−	13.9629i	0.680267	−	0.470156i
$883$		−	23.7974i		−	0.800846i	−0.916331	−	0.400423i	$-0.868863\pi$
$883$		−	23.7974i		−	0.800846i	0.916331	−	0.400423i	$-0.131137\pi$
$884$	0.617744	−	1.63476i	0.0207770	−	0.0549828i
$885$	1.99909			0.0671986
$886$	24.9454	+	36.0934i	0.838056	+	1.21258i
$887$	29.4966			0.990398			0.495199	−	0.868780i	$-0.335095\pi$
$887$	29.4966			0.990398			0.495199	+	0.868780i	$0.335095\pi$
$888$	6.74012	−	1.67413i	0.226184	−	0.0561803i
$889$	−1.16348			−0.0390220
$890$	−29.7614	+	20.5692i	−0.997606	+	0.689479i
$891$	−15.9168	+	20.5810i	−0.533233	+	0.689490i
$892$	−10.3363	−	3.90591i	−0.346086	−	0.130780i
$893$			54.6119i			1.82752i
$894$	7.08540	−	4.89696i	0.236971	−	0.163779i
$895$		−	24.5355i		−	0.820131i
$896$	5.08034	−	9.77914i	0.169722	−	0.326698i
$897$			0.192332i			0.00642179i
$898$	6.44167	−	4.45206i	0.214961	−	0.148567i
$899$	6.37940			0.212765
$900$	−1.51328	+	4.00463i	−0.0504425	+	0.133488i
$901$		−	1.46364i		−	0.0487608i
$902$	−11.0881	−	0.594248i	−0.369193	−	0.0197863i
$903$		−	2.21492i		−	0.0737079i
$904$	−8.53015	−	34.3427i	−0.283709	−	1.14222i
$905$	−13.1057			−0.435647
$906$	−2.44110	−	3.53202i	−0.0811001	−	0.117343i
$907$		−	28.8647i		−	0.958435i	−0.877696	−	0.479218i	$-0.840920\pi$
$907$		−	28.8647i		−	0.958435i	0.877696	−	0.479218i	$-0.159080\pi$
$908$	12.9218	−	34.1954i	0.428825	−	1.13481i
$909$		−	10.2632i		−	0.340409i
$910$	−1.61537	−	2.33728i	−0.0535490	−	0.0774799i
$911$		−	44.8287i		−	1.48524i	−0.669713	−	0.742620i	$-0.733583\pi$
$911$		−	44.8287i		−	1.48524i	0.669713	−	0.742620i	$-0.266417\pi$
$912$	−4.53159	+	5.13984i	−0.150056	+	0.170197i
$913$	−10.9062	+	14.1020i	−0.360941	+	0.466710i
$914$	−0.712928	−	1.03153i	−0.0235816	−	0.0341201i
$915$	−5.81741			−0.192318
$916$	−6.48662	+	17.1658i	−0.214324	+	0.567173i
$917$	10.7866			0.356205
$918$	2.15355	−	1.48839i	0.0710778	−	0.0491243i
$919$	27.3277			0.901458			0.450729	−	0.892661i	$-0.351164\pi$
$919$	27.3277			0.901458			0.450729	+	0.892661i	$0.351164\pi$
$920$	−3.01717	+	0.749415i	−0.0994731	+	0.0247075i
$921$		−	4.47102i		−	0.147325i
$922$	25.9440	+	37.5383i	0.854421	+	1.23626i
$923$	0.963290			0.0317071
$924$	1.98651	−	1.22125i	0.0653515	−	0.0401761i
$925$	−5.07451			−0.166849
$926$	9.23369	+	13.3602i	0.303438	+	0.439043i
$927$			6.60280i			0.216864i
$928$	−1.05522	+	8.91335i	−0.0346392	+	0.292595i
$929$	−34.1873			−1.12165			−0.560824	−	0.827935i	$-0.689516\pi$
$929$	−34.1873			−1.12165			−0.560824	+	0.827935i	$0.689516\pi$
$930$	3.48197	−	2.40651i	0.114178	−	0.0789125i
$931$	−28.7220			−0.941326
$932$	34.8520	+	13.1699i	1.14162	+	0.431395i
$933$	4.35903			0.142708
$934$	9.01914	+	13.0498i	0.295115	+	0.427001i
$935$	4.72830	+	3.65674i	0.154632	+	0.119588i
$936$	−7.87749	+	1.95664i	−0.257484	+	0.0639548i
$937$		−	3.42088i		−	0.111755i	−0.998438	−	0.0558776i	$-0.982204\pi$
$937$		−	3.42088i		−	0.111755i	0.998438	−	0.0558776i	$-0.0177957\pi$
$938$	1.79947	+	2.60365i	0.0587549	+	0.0850123i
$939$			2.84243i			0.0927591i
$940$	44.3984	+	16.7773i	1.44811	+	0.547215i
$941$		−	31.5038i		−	1.02699i	−0.858091	−	0.513497i	$-0.828350\pi$
$941$		−	31.5038i		−	1.02699i	0.858091	−	0.513497i	$-0.171650\pi$
$942$	−5.34184	−	7.72909i	−0.174047	−	0.251827i
$943$	1.26159			0.0410830
$944$	7.10399	−	8.05753i	0.231215	−	0.262250i
$945$		−	4.25603i		−	0.138449i
$946$	1.58153	−	29.5098i	0.0514198	−	0.959445i
$947$			30.8709i			1.00317i	0.865108	+	0.501585i	$0.167250\pi$
$947$			30.8709i			1.00317i	−0.865108	+	0.501585i	$0.832750\pi$
$948$	2.40026	+	0.907014i	0.0779568	+	0.0294584i
$949$	−3.90723			−0.126834
$950$	4.11880	−	2.84665i	0.133632	−	0.0923574i
$951$		−	4.58632i		−	0.148722i
$952$	2.33631	−	0.580302i	0.0757204	−	0.0188077i
$953$			13.4496i			0.435674i	0.975985	+	0.217837i	$0.0699002\pi$
$953$			13.4496i			0.435674i	−0.975985	+	0.217837i	$0.930100\pi$
$954$	−5.59236	+	3.86507i	−0.181059	+	0.125136i
$955$			14.1464i			0.457767i
$956$	−12.0356	+	31.8502i	−0.389259	+	1.03011i
$957$	−1.16191	+	1.50239i	−0.0375593	+	0.0485655i
$958$	16.6248	−	11.4899i	0.537122	−	0.371223i
$959$	−0.917632			−0.0296319
$960$	2.78644	+	5.26310i	0.0899320	+	0.169866i
$961$	14.8347			0.478540
$962$	−5.47028	−	7.91493i	−0.176369	−	0.255187i
$963$	−26.2811			−0.846895
$964$	−4.06518	−	1.53615i	−0.130931	−	0.0494762i
$965$			16.5147i			0.531628i
$966$	−0.217950	+	0.150633i	−0.00701244	+	0.00484653i
$967$	−44.0336			−1.41603			−0.708013	−	0.706200i	$-0.750408\pi$
$967$	−44.0336			−1.41603			−0.708013	+	0.706200i	$0.750408\pi$
$968$	27.3387	−	14.8525i	0.878699	−	0.477377i
$969$	−1.49686			−0.0480860
$970$	11.4830	−	7.93627i	0.368696	−	0.254818i
$971$			38.0190i			1.22009i	0.792368	+	0.610044i	$0.208848\pi$
$971$			38.0190i			1.22009i	−0.792368	+	0.610044i	$0.791152\pi$
$972$	−17.1871	−	6.49467i	−0.551276	−	0.208317i
$973$	−13.8266			−0.443261
$974$	−10.9973	−	15.9120i	−0.352378	−	0.509854i
$975$	−0.269201			−0.00862132
$976$	−20.6729	+	23.4477i	−0.661722	+	0.750542i
$977$	47.5898			1.52253			0.761266	−	0.648439i	$-0.224578\pi$
$977$	47.5898			1.52253			0.761266	+	0.648439i	$0.224578\pi$
$978$	7.68163	−	5.30904i	0.245631	−	0.169764i
$979$	−25.1655	+	32.5399i	−0.804293	+	1.03998i
$980$	−8.82369	+	23.3504i	−0.281862	+	0.745902i
$981$		−	48.5769i		−	1.55094i
$982$	−27.8201	+	19.2274i	−0.887775	+	0.613572i
$983$		−	13.0824i		−	0.417263i	−0.977994	−	0.208632i	$-0.933099\pi$
$983$		−	13.0824i		−	0.417263i	0.977994	−	0.208632i	$-0.0669010\pi$
$984$	−0.582557	−	2.34539i	−0.0185712	−	0.0747684i
$985$			50.4931i			1.60884i
$986$	−1.61295	+	1.11477i	−0.0513669	+	0.0355015i
$987$	4.04480			0.128747
$988$	8.88008	+	3.35561i	0.282513	+	0.106756i
$989$			3.35759i			0.106765i
$990$	1.48575	−	27.7227i	0.0472203	−	0.881086i
$991$		−	7.68993i		−	0.244279i	−0.992513	−	0.122139i	$-0.961025\pi$
$991$		−	7.68993i		−	0.244279i	0.992513	−	0.122139i	$-0.0389755\pi$
$992$	2.67390	−	22.5863i	0.0848964	−	0.717114i
$993$	−8.45156			−0.268202
$994$	0.754441	+	1.09160i	0.0239294	+	0.0346234i
$995$			14.6418i			0.464175i
$996$	−3.62942	−	1.37149i	−0.115002	−	0.0434573i
$997$		−	43.7547i		−	1.38573i	−0.721069	−	0.692863i	$-0.756349\pi$
$997$		−	43.7547i		−	1.38573i	0.721069	−	0.692863i	$-0.243651\pi$
$998$	−6.18476	−	8.94871i	−0.195775	−	0.283267i
$999$		−	14.4126i		−	0.455993i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.e.b.131.16	yes	64
4.3	odd	2	inner	572.2.e.b.131.50	yes	64
11.10	odd	2	inner	572.2.e.b.131.49	yes	64
44.43	even	2	inner	572.2.e.b.131.15	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.e.b.131.15	✓	64	44.43	even	2	inner
572.2.e.b.131.16	yes	64	1.1	even	1	trivial
572.2.e.b.131.49	yes	64	11.10	odd	2	inner
572.2.e.b.131.50	yes	64	4.3	odd	2	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16339 + 0.804061i) q^{2} -0.360913i q^{3} +(0.706971 - 1.87088i) q^{4} +2.06255 q^{5} +(0.290196 + 0.419884i) q^{6} +0.974044 q^{7} +(0.681817 + 2.74502i) q^{8} +2.86974 q^{9} +O(q^{10})\)	\(q+(-1.16339 + 0.804061i) q^{2} -0.360913i q^{3} +(0.706971 - 1.87088i) q^{4} +2.06255 q^{5} +(0.290196 + 0.419884i) q^{6} +0.974044 q^{7} +(0.681817 + 2.74502i) q^{8} +2.86974 q^{9} +(-2.39956 + 1.65842i) q^{10} +(-2.02900 + 2.62357i) q^{11} +(-0.675224 - 0.255155i) q^{12} +1.00000i q^{13} +(-1.13320 + 0.783191i) q^{14} -0.744400i q^{15} +(-3.00039 - 2.64531i) q^{16} -0.873790i q^{17} +(-3.33864 + 2.30745i) q^{18} +4.74647 q^{19} +(1.45816 - 3.85878i) q^{20} -0.351545i q^{21} +(0.251015 - 4.68369i) q^{22} +0.532905i q^{23} +(0.990712 - 0.246076i) q^{24} -0.745888 q^{25} +(-0.804061 - 1.16339i) q^{26} -2.11846i q^{27} +(0.688621 - 1.82232i) q^{28} +1.58668i q^{29} +(0.598544 + 0.866031i) q^{30} -4.02061i q^{31} +(5.61762 + 0.665049i) q^{32} +(0.946881 + 0.732293i) q^{33} +(0.702581 + 1.01656i) q^{34} +2.00901 q^{35} +(2.02882 - 5.36894i) q^{36} +6.80331 q^{37} +(-5.52201 + 3.81645i) q^{38} +0.360913 q^{39} +(1.40628 + 5.66174i) q^{40} -2.36738i q^{41} +(0.282664 + 0.408985i) q^{42} +6.30053 q^{43} +(3.47395 + 5.65081i) q^{44} +5.91899 q^{45} +(-0.428488 - 0.619979i) q^{46} +11.5058i q^{47} +(-0.954728 + 1.08288i) q^{48} -6.05124 q^{49} +(0.867762 - 0.599740i) q^{50} -0.315362 q^{51} +(1.87088 + 0.706971i) q^{52} +1.67504 q^{53} +(1.70338 + 2.46461i) q^{54} +(-4.18492 + 5.41125i) q^{55} +(0.664120 + 2.67377i) q^{56} -1.71306i q^{57} +(-1.27578 - 1.84593i) q^{58} +2.68550i q^{59} +(-1.39268 - 0.526269i) q^{60} -7.81490i q^{61} +(3.23281 + 4.67755i) q^{62} +2.79526 q^{63} +(-7.07025 + 3.74320i) q^{64} +2.06255i q^{65} +(-1.69040 - 0.0905944i) q^{66} -2.29762i q^{67} +(-1.63476 - 0.617744i) q^{68} +0.192332 q^{69} +(-2.33728 + 1.61537i) q^{70} -0.963290i q^{71} +(1.95664 + 7.87749i) q^{72} +3.90723i q^{73} +(-7.91493 + 5.47028i) q^{74} +0.269201i q^{75} +(3.35561 - 8.88008i) q^{76} +(-1.97634 + 2.55548i) q^{77} +(-0.419884 + 0.290196i) q^{78} -3.55476 q^{79} +(-6.18844 - 5.45609i) q^{80} +7.84465 q^{81} +(1.90352 + 2.75420i) q^{82} +5.37513 q^{83} +(-0.657698 - 0.248532i) q^{84} -1.80224i q^{85} +(-7.33000 + 5.06601i) q^{86} +0.572651 q^{87} +(-8.58517 - 3.78085i) q^{88} +12.4029 q^{89} +(-6.88611 + 4.75923i) q^{90} +0.974044i q^{91} +(0.997002 + 0.376748i) q^{92} -1.45109 q^{93} +(-9.25136 - 13.3858i) q^{94} +9.78983 q^{95} +(0.240025 - 2.02747i) q^{96} -4.78545 q^{97} +(7.03997 - 4.86557i) q^{98} +(-5.82272 + 7.52898i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9}+O(q^{10}) \) 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9	\( 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9} - 8 q^{12} - 34 q^{14} + 26 q^{16} + 14 q^{20} - 8 q^{22} + 76 q^{25} + 2 q^{26} - 16 q^{33} + 32 q^{34} - 24 q^{36} - 32 q^{37} - 30 q^{38} + 54 q^{42} + 10 q^{44} + 12 q^{45} + 34 q^{48} - 36 q^{49} - 32 q^{53} - 36 q^{56} + 62 q^{58} + 4 q^{60} - 18 q^{64} - 30 q^{66} - 24 q^{69} - 30 q^{70} + 88 q^{77} - 10 q^{78} - 46 q^{80} + 64 q^{81} - 46 q^{82} + 98 q^{86} + 16 q^{88} + 24 q^{89} + 84 q^{92} + 8 q^{93} - 88 q^{97}+O(q^{100}) \) 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9 - 8 * q^12 - 34 * q^14 + 26 * q^16 + 14 * q^20 - 8 * q^22 + 76 * q^25 + 2 * q^26 - 16 * q^33 + 32 * q^34 - 24 * q^36 - 32 * q^37 - 30 * q^38 + 54 * q^42 + 10 * q^44 + 12 * q^45 + 34 * q^48 - 36 * q^49 - 32 * q^53 - 36 * q^56 + 62 * q^58 + 4 * q^60 - 18 * q^64 - 30 * q^66 - 24 * q^69 - 30 * q^70 + 88 * q^77 - 10 * q^78 - 46 * q^80 + 64 * q^81 - 46 * q^82 + 98 * q^86 + 16 * q^88 + 24 * q^89 + 84 * q^92 + 8 * q^93 - 88 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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