LMFDB - Embedded newform 567.2.ba.a.521.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(143,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 3]))

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

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

chi := DirichletCharacter("567.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.ba (of order $18$, degree $6$, not 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			521.9
Character	$\chi$	$=$	567.521
Dual form			567.2.ba.a.530.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.491776 - 0.0867134i) q^{2} +(-1.64506 - 0.598753i) q^{4} +(-9.76251e-5 - 0.000553660i) q^{5} +(-2.32328 + 1.26584i) q^{7} +(1.62200 + 0.936464i) q^{8} +0.000280742i q^{10} +(4.66356 + 0.822312i) q^{11} +(-1.77003 - 2.10944i) q^{13} +(1.25230 - 0.421052i) q^{14} +(1.96567 + 1.64940i) q^{16} +0.800172 q^{17} -5.20473i q^{19} +(-0.000170906 + 0.000969257i) q^{20} +(-2.22212 - 0.808787i) q^{22} +(-1.01988 - 1.21545i) q^{23} +(4.69846 - 1.71010i) q^{25} +(0.687542 + 1.19086i) q^{26} +(4.57987 - 0.691318i) q^{28} +(5.40692 - 6.44372i) q^{29} +(2.76219 - 7.58906i) q^{31} +(-3.23144 - 3.85108i) q^{32} +(-0.393506 - 0.0693856i) q^{34} +(0.000927658 + 0.00116273i) q^{35} +(-1.02790 + 1.78038i) q^{37} +(-0.451320 + 2.55956i) q^{38} +(0.000360134 - 0.000989460i) q^{40} +(-5.20305 + 4.36588i) q^{41} +(-6.39715 + 2.32837i) q^{43} +(-7.17948 - 4.14508i) q^{44} +(0.396159 + 0.686167i) q^{46} +(6.96860 - 2.53636i) q^{47} +(3.79528 - 5.88182i) q^{49} +(-2.45888 + 0.433567i) q^{50} +(1.64877 + 4.52997i) q^{52} +(9.11266 + 5.26120i) q^{53} -0.00266231i q^{55} +(-4.95379 - 0.122467i) q^{56} +(-3.21775 + 2.70001i) q^{58} +(10.1204 - 8.49198i) q^{59} +(1.24316 + 3.41555i) q^{61} +(-2.01645 + 3.49260i) q^{62} +(-1.31080 - 2.27037i) q^{64} +(-0.000995113 + 0.00118593i) q^{65} +(0.369304 + 2.09442i) q^{67} +(-1.31633 - 0.479105i) q^{68} +(-0.000355376 - 0.000652243i) q^{70} +(-7.56979 + 4.37042i) q^{71} +(6.22020 - 3.59123i) q^{73} +(0.659882 - 0.786416i) q^{74} +(-3.11635 + 8.56210i) q^{76} +(-11.8757 + 3.99288i) q^{77} +(0.447434 - 2.53753i) q^{79} +(0.000721305 - 0.00124934i) q^{80} +(2.93732 - 1.69586i) q^{82} +(1.47761 + 1.23986i) q^{83} +(-7.81169e-5 - 0.000443023i) q^{85} +(3.34787 - 0.590319i) q^{86} +(6.79425 + 5.70105i) q^{88} +3.23581 q^{89} +(6.78250 + 2.66024i) q^{91} +(0.950016 + 2.61015i) q^{92} +(-3.64693 + 0.643052i) q^{94} +(-0.00288165 + 0.000508113i) q^{95} +(-0.614218 - 1.68755i) q^{97} +(-2.37646 + 2.56344i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34}+ \cdots - 27 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−0.491776	−	0.0867134i	−0.347738	−	0.0613156i	−0.00294872	−	0.999996i	$-0.500939\pi$
$2$	−0.491776	−	0.0867134i	−0.347738	−	0.0613156i	−0.344790	+	0.938680i	$0.612050\pi$
$3$		0			0
$3$		0			0
$4$	−1.64506	−	0.598753i	−0.822530	−	0.299377i
$5$	−9.76251e−5	0	0.000553660i	−4.36593e−5	0	0.000247604i	0.984786	−	0.173772i	$-0.0555956\pi$
$5$	−9.76251e−5	0	0.000553660i	−4.36593e−5	0	0.000247604i	−0.984830	+	0.173524i	$0.944484\pi$
$6$		0			0
$7$	−2.32328	+	1.26584i	−0.878118	+	0.478444i
$7$	−2.32328	+	1.26584i	−0.878118	+	0.478444i
$8$	1.62200	+	0.936464i	0.573465	+	0.331090i
$9$		0			0
$10$		0	0.000280742i		0	8.87784e-5i
$11$	4.66356	+	0.822312i	1.40612	+	0.247936i	0.824654	−	0.565637i	$-0.191370\pi$
$11$	4.66356	+	0.822312i	1.40612	+	0.247936i	0.581463	+	0.813573i	$0.302481\pi$
$12$		0			0
$13$	−1.77003	−	2.10944i	−0.490918	−	0.585053i	0.462533	−	0.886602i	$-0.346941\pi$
$13$	−1.77003	−	2.10944i	−0.490918	−	0.585053i	−0.953451	+	0.301549i	$0.902496\pi$
$14$	1.25230	−	0.421052i	0.334691	−	0.112531i
$15$		0			0
$16$	1.96567	+	1.64940i	0.491418	+	0.412349i
$17$	0.800172			0.194070			0.0970351	−	0.995281i	$-0.469064\pi$
$17$	0.800172			0.194070			0.0970351	+	0.995281i	$0.469064\pi$
$18$		0			0
$19$		−	5.20473i		−	1.19405i	−0.802224	−	0.597024i	$-0.796350\pi$
$19$		−	5.20473i		−	1.19405i	0.802224	−	0.597024i	$-0.203650\pi$
$20$	−0.000170906	0	0.000969257i	−3.82158e−5	0	0.000216732i
$21$		0			0
$22$	−2.22212	−	0.808787i	−0.473758	−	0.172434i
$23$	−1.01988	−	1.21545i	−0.212661	−	0.253439i	0.649160	−	0.760651i	$-0.275120\pi$
$23$	−1.01988	−	1.21545i	−0.212661	−	0.253439i	−0.861821	+	0.507213i	$0.830676\pi$
$24$		0			0
$25$	4.69846	−	1.71010i	0.939693	−	0.342020i
$26$	0.687542	+	1.19086i	0.134838	+	0.233546i
$27$		0			0
$28$	4.57987	−	0.691318i	0.865514	−	0.130647i
$29$	5.40692	−	6.44372i	1.00404	−	1.19657i	0.0236057	−	0.999721i	$-0.492485\pi$
$29$	5.40692	−	6.44372i	1.00404	−	1.19657i	0.980434	−	0.196847i	$-0.0630702\pi$
$30$		0			0
$31$	2.76219	−	7.58906i	0.496104	−	1.36304i	−0.398907	−	0.916991i	$-0.630610\pi$
$31$	2.76219	−	7.58906i	0.496104	−	1.36304i	0.895011	−	0.446044i	$-0.147167\pi$
$32$	−3.23144	−	3.85108i	−0.571243	−	0.680780i
$33$		0			0
$34$	−0.393506	−	0.0693856i	−0.0674856	−	0.0118995i
$35$	0.000927658		0.00116273i	0.000156803		0.000196537i
$36$		0			0
$37$	−1.02790	+	1.78038i	−0.168986	+	0.292693i	−0.938064	−	0.346463i	$-0.887383\pi$
$37$	−1.02790	+	1.78038i	−0.168986	+	0.292693i	0.769077	+	0.639156i	$0.220716\pi$
$38$	−0.451320	+	2.55956i	−0.0732138	+	0.415216i
$39$		0			0
$40$	0.000360134	0	0.000989460i	5.69422e−5	0	0.000156447i
$41$	−5.20305	+	4.36588i	−0.812580	+	0.681836i	−0.951222	−	0.308507i	$-0.900171\pi$
$41$	−5.20305	+	4.36588i	−0.812580	+	0.681836i	0.138642	+	0.990343i	$0.455726\pi$
$42$		0			0
$43$	−6.39715	+	2.32837i	−0.975556	+	0.355073i	−0.780111	−	0.625641i	$-0.784837\pi$
$43$	−6.39715	+	2.32837i	−0.975556	+	0.355073i	−0.195445	+	0.980715i	$0.562615\pi$
$44$	−7.17948	−	4.14508i	−1.08235	−	0.624894i
$45$		0			0
$46$	0.396159	+	0.686167i	0.0584104	+	0.101170i
$47$	6.96860	−	2.53636i	1.01647	−	0.369967i	0.220559	−	0.975374i	$-0.429212\pi$
$47$	6.96860	−	2.53636i	1.01647	−	0.369967i	0.795916	+	0.605407i	$0.206990\pi$
$48$		0			0
$49$	3.79528	−	5.88182i	0.542183	−	0.840261i
$50$	−2.45888	+	0.433567i	−0.347738	+	0.0613156i
$51$		0			0
$52$	1.64877	+	4.52997i	0.228644	+	0.628194i
$53$	9.11266	+	5.26120i	1.25172	+	0.722681i	0.971451	−	0.237241i	$-0.0762430\pi$
$53$	9.11266	+	5.26120i	1.25172	+	0.722681i	0.280269	+	0.959921i	$0.409576\pi$
$54$		0			0
$55$		−	0.00266231i		−	0.000358985i
$56$	−4.95379	−	0.122467i	−0.661978	−	0.0163653i
$57$		0			0
$58$	−3.21775	+	2.70001i	−0.422511	+	0.354529i
$59$	10.1204	−	8.49198i	1.31756	−	1.10556i	0.330740	−	0.943722i	$-0.392702\pi$
$59$	10.1204	−	8.49198i	1.31756	−	1.10556i	0.986817	−	0.161840i	$-0.0517429\pi$
$60$		0			0
$61$	1.24316	+	3.41555i	0.159170	+	0.437317i	0.993484	−	0.113974i	$-0.0363579\pi$
$61$	1.24316	+	3.41555i	0.159170	+	0.437317i	−0.834314	+	0.551290i	$0.814136\pi$
$62$	−2.01645	+	3.49260i	−0.256090	+	0.443560i
$63$		0			0
$64$	−1.31080	−	2.27037i	−0.163850	−	0.283797i
$65$	−0.000995113		0.00118593i	−0.000123429		0.000147096i
$66$		0			0
$67$	0.369304	+	2.09442i	0.0451176	+	0.255875i	0.999021	−	0.0442393i	$-0.0140864\pi$
$67$	0.369304	+	2.09442i	0.0451176	+	0.255875i	−0.953903	+	0.300114i	$0.902975\pi$
$68$	−1.31633	−	0.479105i	−0.159629	−	0.0581001i
$69$		0			0
$70$	−0.000355376	0	0.000652243i	−4.24755e−5	0	7.79579e-5i
$71$	−7.56979	+	4.37042i	−0.898369	+	0.518673i	−0.876671	−	0.481091i	$-0.840241\pi$
$71$	−7.56979	+	4.37042i	−0.898369	+	0.518673i	−0.0216981	+	0.999765i	$0.506907\pi$
$72$		0			0
$73$	6.22020	−	3.59123i	0.728019	−	0.420322i	−0.0896781	−	0.995971i	$-0.528584\pi$
$73$	6.22020	−	3.59123i	0.728019	−	0.420322i	0.817697	+	0.575649i	$0.195250\pi$
$74$	0.659882	−	0.786416i	0.0767097	−	0.0914191i
$75$		0			0
$76$	−3.11635	+	8.56210i	−0.357470	+	0.982140i
$77$	−11.8757	+	3.99288i	−1.35336	+	0.455031i
$78$		0			0
$79$	0.447434	−	2.53753i	0.0503403	−	0.285494i	−0.949237	−	0.314561i	$-0.898143\pi$
$79$	0.447434	−	2.53753i	0.0503403	−	0.285494i	0.999577	+	0.0290673i	$0.00925372\pi$
$80$	0.000721305	−	0.00124934i	8.06443e−5	−	0.000139680i
$81$		0			0
$82$	2.93732	−	1.69586i	0.324373	−	0.187277i
$83$	1.47761	+	1.23986i	0.162188	+	0.136092i	0.720270	−	0.693694i	$-0.244018\pi$
$83$	1.47761	+	1.23986i	0.162188	+	0.136092i	−0.558082	+	0.829786i	$0.688462\pi$
$84$		0			0
$85$	−7.81169e−5	0	0.000443023i	−8.47297e−6	0	4.80526e-5i
$86$	3.34787	−	0.590319i	0.361010	−	0.0636558i
$87$		0			0
$88$	6.79425	+	5.70105i	0.724269	+	0.607734i
$89$	3.23581			0.342995			0.171498	−	0.985185i	$-0.445139\pi$
$89$	3.23581			0.342995			0.171498	+	0.985185i	$0.445139\pi$
$90$		0			0
$91$	6.78250	+	2.66024i	0.710999	+	0.278869i
$92$	0.950016	+	2.61015i	0.0990461	+	0.272127i
$93$		0			0
$94$	−3.64693	+	0.643052i	−0.376152	+	0.0663257i
$95$	−0.00288165		0.000508113i	−0.000295651		5.21313e-5i
$96$		0			0
$97$	−0.614218	−	1.68755i	−0.0623644	−	0.171345i	0.904597	−	0.426268i	$-0.140172\pi$
$97$	−0.614218	−	1.68755i	−0.0623644	−	0.171345i	−0.966961	+	0.254923i	$0.917950\pi$
$98$	−2.37646	+	2.56344i	−0.240059	+	0.258947i
$99$		0			0
$100$	−8.75318			−0.875318
$101$	3.26288	+	2.73788i	0.324668	+	0.272429i	0.790523	−	0.612432i	$-0.209809\pi$
$101$	3.26288	+	2.73788i	0.324668	+	0.272429i	−0.465855	+	0.884861i	$0.654253\pi$
$102$		0			0
$103$	−15.8365	+	2.79240i	−1.56041	+	0.275143i	−0.886168	−	0.463365i	$-0.846642\pi$
$103$	−15.8365	+	2.79240i	−1.56041	+	0.275143i	−0.674245	+	0.738508i	$0.735531\pi$
$104$	−0.895580	−	5.07909i	−0.0878189	−	0.498046i
$105$		0			0
$106$	−4.02517	−	3.37752i	−0.390959	−	0.328054i
$107$	−3.48765	+	2.01360i	−0.337164	+	0.194662i	−0.659017	−	0.752128i	$-0.729028\pi$
$107$	−3.48765	+	2.01360i	−0.337164	+	0.194662i	0.321853	+	0.946790i	$0.395694\pi$
$108$		0			0
$109$	0.587845	−	1.01818i	0.0563054	−	0.0975238i	−0.836499	−	0.547969i	$-0.815401\pi$
$109$	0.587845	−	1.01818i	0.0563054	−	0.0975238i	0.892804	+	0.450445i	$0.148735\pi$
$110$	−0.000230858		0.00130926i	−2.20114e−5		0.000124833i
$111$		0			0
$112$	−6.65469	−	1.34378i	−0.628809	−	0.126975i
$113$	5.04317	−	13.8560i	0.474422	−	1.30346i	−0.439745	−	0.898123i	$-0.644931\pi$
$113$	5.04317	−	13.8560i	0.474422	−	1.30346i	0.914166	−	0.405340i	$-0.132847\pi$
$114$		0			0
$115$	−0.000573380	0	0.000683327i	−5.34679e−5	0	6.37206e-5i
$116$	−12.7529	+	7.36290i	−1.18408	+	0.683628i
$117$		0			0
$118$	−5.71332	+	3.29858i	−0.525953	+	0.303659i
$119$	−1.85903	+	1.01289i	−0.170417	+	0.0928517i
$120$		0			0
$121$	10.7360	+	3.90758i	0.976000	+	0.355235i
$122$	−0.315182	−	1.78749i	−0.0285352	−	0.161831i
$123$		0			0
$124$	−9.08794	+	10.8306i	−0.816121	+	0.972616i
$125$	−0.00281100	−	0.00486880i	−0.000251424	−	0.000435479i
$126$		0			0
$127$	−3.46785	+	6.00649i	−0.307722	+	0.532990i	−0.977864	−	0.209243i	$-0.932900\pi$
$127$	−3.46785	+	6.00649i	−0.307722	+	0.532990i	0.670142	+	0.742233i	$0.266233\pi$
$128$	3.88657	+	10.6783i	0.343528	+	0.943834i
$129$		0			0
$130$	0.000592209	0	0.000496922i	5.19401e−5	0	4.35829e-5i
$131$	−8.46265	+	7.10101i	−0.739385	+	0.620418i	−0.932672	−	0.360724i	$-0.882530\pi$
$131$	−8.46265	+	7.10101i	−0.739385	+	0.620418i	0.193287	+	0.981142i	$0.438085\pi$
$132$		0			0
$133$	6.58838	+	12.0921i	0.571285	+	1.04851i
$134$		−	1.06201i		−	0.0917438i
$135$		0			0
$136$	1.29788	+	0.749332i	0.111292	+	0.0642547i
$137$	3.43808	+	9.44606i	0.293735	+	0.807031i	0.995512	+	0.0946343i	$0.0301682\pi$
$137$	3.43808	+	9.44606i	0.293735	+	0.807031i	−0.701777	+	0.712397i	$0.747610\pi$
$138$		0			0
$139$	0.409252	−	0.0721623i	0.0347123	−	0.00612072i	−0.156265	−	0.987715i	$-0.549945\pi$
$139$	0.409252	−	0.0721623i	0.0347123	−	0.00612072i	0.190977	+	0.981594i	$0.438834\pi$
$140$	−0.000829865	−	0.00246820i	−7.01364e−5	−	0.000208601i
$141$		0			0
$142$	4.10162	−	1.49287i	0.344200	−	0.125279i
$143$	−6.52003	−	11.2930i	−0.545232	−	0.944370i
$144$		0			0
$145$	−0.00409548	−	0.00236453i	−0.000340111	−	0.000196363i
$146$	−3.37035	+	1.22671i	−0.278932	+	0.101523i
$147$		0			0
$148$	2.75697	−	2.31338i	0.226622	−	0.190158i
$149$	−0.315032	+	0.865543i	−0.0258084	+	0.0709081i	−0.951928	−	0.306323i	$-0.900901\pi$
$149$	−0.315032	+	0.865543i	−0.0258084	+	0.0709081i	0.926119	+	0.377231i	$0.123124\pi$
$150$		0			0
$151$	−0.209027	+	1.18545i	−0.0170104	+	0.0964707i	−0.992131	−	0.125204i	$-0.960041\pi$
$151$	−0.209027	+	1.18545i	−0.0170104	+	0.0964707i	0.975121	+	0.221675i	$0.0711524\pi$
$152$	4.87404	−	8.44209i	0.395337	−	0.684744i
$153$		0			0
$154$	6.18642	−	0.933822i	0.498516	−	0.0752495i
$155$	−0.00447142		0.000788431i	−0.000359153		6.33283e-5i
$156$		0			0
$157$	−7.40718	−	8.82753i	−0.591157	−	0.704514i	0.384671	−	0.923054i	$-0.374315\pi$
$157$	−7.40718	−	8.82753i	−0.591157	−	0.704514i	−0.975828	+	0.218540i	$0.929871\pi$
$158$	−0.440075	+	1.20910i	−0.0350105	+	0.0961905i
$159$		0			0
$160$	−0.00181672	+	0.00216508i	−0.000143624	+	0.000171164i
$161$	3.90805	+	1.53282i	0.307997	+	0.120803i
$162$		0			0
$163$	−3.42292	−	5.92867i	−0.268104	−	0.464369i	0.700268	−	0.713880i	$-0.253064\pi$
$163$	−3.42292	−	5.92867i	−0.268104	−	0.464369i	−0.968372	+	0.249510i	$0.919730\pi$
$164$	11.1734	−	4.06679i	0.872498	−	0.317563i
$165$		0			0
$166$	−0.619139	−	0.737861i	−0.0480545	−	0.0572691i
$167$	−4.35768	−	1.58606i	−0.337207	−	0.122733i	0.167866	−	0.985810i	$-0.446312\pi$
$167$	−4.35768	−	1.58606i	−0.337207	−	0.122733i	−0.505073	+	0.863076i	$0.668535\pi$
$168$		0			0
$169$	0.940696	−	5.33495i	0.0723613	−	0.410381i
$170$		0	0.000224642i		0	1.72292e-5i
$171$		0			0
$172$	11.9178			0.908725
$173$	−18.4317	−	15.4661i	−1.40134	−	1.17586i	−0.960501	−	0.278276i	$-0.910237\pi$
$173$	−18.4317	−	15.4661i	−1.40134	−	1.17586i	−0.440838	−	0.897587i	$-0.645319\pi$
$174$		0			0
$175$	−8.75113	+	9.92057i	−0.661524	+	0.749924i
$176$	7.81072	+	9.30846i	0.588755	+	0.701651i
$177$		0			0
$178$	−1.59129	−	0.280588i	−0.119273	−	0.0210310i
$179$			24.6678i			1.84376i	0.387475	+	0.921880i	$0.373347\pi$
$179$			24.6678i			1.84376i	−0.387475	+	0.921880i	$0.626653\pi$
$180$		0			0
$181$	7.78429	+	4.49426i	0.578601	+	0.334056i	0.760577	−	0.649247i	$-0.224916\pi$
$181$	7.78429	+	4.49426i	0.578601	+	0.334056i	−0.181976	+	0.983303i	$0.558249\pi$
$182$	−3.10479	−	1.89638i	−0.230143	−	0.140569i
$183$		0			0
$184$	−0.516030	−	2.92655i	−0.0380422	−	0.215748i
$185$	0.00108608		0.000395299i	7.98498e−5		2.90630e-5i
$186$		0			0
$187$	3.73165	+	0.657991i	0.272885	+	0.0481171i
$188$	−12.9824			−0.946841
$189$		0			0
$190$	0.00146119			0.000106006
$191$	−20.5434	−	3.62235i	−1.48647	−	0.262104i	−0.629308	−	0.777156i	$-0.716662\pi$
$191$	−20.5434	−	3.62235i	−1.48647	−	0.262104i	−0.857159	+	0.515051i	$0.827773\pi$
$192$		0			0
$193$	17.1757	+	6.25143i	1.23633	+	0.449988i	0.875762	−	0.482744i	$-0.160360\pi$
$193$	17.1757	+	6.25143i	1.23633	+	0.449988i	0.360571	+	0.932732i	$0.382582\pi$
$194$	0.155725	+	0.883158i	0.0111804	+	0.0634070i
$195$		0			0
$196$	−9.76522	+	7.40352i	−0.697516	+	0.528823i
$197$	8.92564	+	5.15322i	0.635925	+	0.367152i	0.783043	−	0.621967i	$-0.213666\pi$
$197$	8.92564	+	5.15322i	0.635925	+	0.367152i	−0.147118	+	0.989119i	$0.547000\pi$
$198$		0			0
$199$		−	11.1728i		−	0.792020i	−0.918246	−	0.396010i	$-0.870395\pi$
$199$		−	11.1728i		−	0.792020i	0.918246	−	0.396010i	$-0.129605\pi$
$200$	9.22237	+	1.62615i	0.652120	+	0.114986i
$201$		0			0
$202$	−1.36719	−	1.62936i	−0.0961955	−	0.114641i
$203$	−4.40506	+	21.8149i	−0.309175	+	1.53111i
$204$		0			0
$205$	0.00292516	+	0.00245450i	0.000204302	+	0.000171430i
$206$	8.03013			0.559486
$207$		0			0
$208$		−	7.06595i		−	0.489935i
$209$	4.27991	−	24.2726i	0.296048	−	1.67897i
$210$		0			0
$211$	22.3190	+	8.12346i	1.53651	+	0.559242i	0.965204	−	0.261498i	$-0.0842165\pi$
$211$	22.3190	+	8.12346i	1.53651	+	0.559242i	0.571302	+	0.820740i	$0.306439\pi$
$212$	−11.8407	−	14.1112i	−0.813224	−	0.969163i
$213$		0			0
$214$	1.88975	−	0.687813i	0.129181	−	0.0470179i
$215$	0.00191365	+	0.00331454i	0.000130510	+	0.000226050i
$216$		0			0
$217$	3.18921	+	21.1280i	0.216498	+	1.43426i
$218$	−0.377378	+	0.449742i	−0.0255593	+	0.0304603i
$219$		0			0
$220$	−0.00159406	+	0.00437965i	−0.000107472	+	0.000295276i
$221$	−1.41633	−	1.68791i	−0.0952726	−	0.113541i
$222$		0			0
$223$	−23.8004	−	4.19666i	−1.59380	−	0.281029i	−0.694871	−	0.719134i	$-0.744539\pi$
$223$	−23.8004	−	4.19666i	−1.59380	−	0.281029i	−0.898924	+	0.438105i	$0.855650\pi$
$224$	12.3824	+	4.85664i	0.827334	+	0.324498i
$225$		0			0
$226$	−3.68161	+	6.37674i	−0.244897	+	0.424174i
$227$	−0.742956	+	4.21351i	−0.0493117	+	0.279661i	−0.999486	−	0.0320585i	$-0.989794\pi$
$227$	−0.742956	+	4.21351i	−0.0493117	+	0.279661i	0.950174	+	0.311719i	$0.100905\pi$
$228$		0			0
$229$	4.43062	−	12.1730i	0.292784	−	0.804417i	−0.702873	−	0.711315i	$-0.748100\pi$
$229$	4.43062	−	12.1730i	0.292784	−	0.804417i	0.995657	−	0.0931013i	$-0.0296780\pi$
$230$	0.000341228	0	0.000286324i	2.24999e−5	0	1.88797e-5i
$231$		0			0
$232$	14.8044	−	5.38834i	0.971953	−	0.353762i
$233$	9.70366	+	5.60241i	0.635708	+	0.367026i	0.782959	−	0.622073i	$-0.213709\pi$
$233$	9.70366	+	5.60241i	0.635708	+	0.367026i	−0.147251	+	0.989099i	$0.547043\pi$
$234$		0			0
$235$	−0.00208459	−	0.00361062i	−0.000135984	−	0.000235531i
$236$	−21.7332	+	7.91023i	−1.41471	+	0.514912i
$237$		0			0
$238$	1.00206	−	0.336914i	0.0649536	−	0.0218389i
$239$	−12.3508	+	2.17779i	−0.798909	+	0.140869i	−0.558177	−	0.829722i	$-0.688499\pi$
$239$	−12.3508	+	2.17779i	−0.798909	+	0.140869i	−0.240733	+	0.970591i	$0.577388\pi$
$240$		0			0
$241$	−6.86595	−	18.8641i	−0.442275	−	1.21514i	−0.937992	−	0.346656i	$-0.887317\pi$
$241$	−6.86595	−	18.8641i	−0.442275	−	1.21514i	0.495717	−	0.868484i	$-0.334905\pi$
$242$	−4.94087	−	2.85261i	−0.317611	−	0.183373i
$243$		0			0
$244$		−	6.36314i		−	0.407358i
$245$	−0.00362704	−	0.00152708i	−0.000231723	−	9.75615e-5i
$246$		0			0
$247$	−10.9791	+	9.21254i	−0.698582	+	0.586180i
$248$	11.5872	−	9.72278i	0.735786	−	0.617397i
$249$		0			0
$250$	0.000960194		0.00263811i	6.07280e−5		0.000166849i
$251$	11.2730	−	19.5255i	0.711547	−	1.23244i	−0.252729	−	0.967537i	$-0.581328\pi$
$251$	11.2730	−	19.5255i	0.711547	−	1.23244i	0.964276	−	0.264899i	$-0.0853386\pi$
$252$		0			0
$253$	−3.75681	−	6.50699i	−0.236189	−	0.409091i
$254$	2.22625	−	2.65314i	0.139687	−	0.166473i
$255$		0			0
$256$	−0.0749017	−	0.424789i	−0.00468135	−	0.0265493i
$257$	27.6153	+	10.0512i	1.72260	+	0.626974i	0.998060	−	0.0622616i	$-0.0198313\pi$
$257$	27.6153	+	10.0512i	1.72260	+	0.626974i	0.724537	+	0.689236i	$0.242054\pi$
$258$		0			0
$259$	0.134425	−	5.43750i	0.00835277	−	0.337870i
$260$	0.00234710	−	0.00135510i	0.000145561	−	8.40396e-5i
$261$		0			0
$262$	4.77748	−	2.75828i	0.295154	−	0.170407i
$263$	10.7751	−	12.8412i	0.664420	−	0.791825i	−0.323593	−	0.946197i	$-0.604891\pi$
$263$	10.7751	−	12.8412i	0.664420	−	0.791825i	0.988013	+	0.154371i	$0.0493352\pi$
$264$		0			0
$265$	0.00202329	−	0.00555894i	0.000124290	−	0.000341483i
$266$	−2.19146	−	6.51789i	−0.134367	−	0.399637i
$267$		0			0
$268$	0.646517	−	3.66658i	0.0394923	−	0.223972i
$269$	4.71711	−	8.17027i	0.287607	−	0.498150i	−0.685631	−	0.727949i	$-0.740474\pi$
$269$	4.71711	−	8.17027i	0.287607	−	0.498150i	0.973238	+	0.229799i	$0.0738069\pi$
$270$		0			0
$271$	−3.40065	+	1.96337i	−0.206575	+	0.119266i	−0.599719	−	0.800211i	$-0.704721\pi$
$271$	−3.40065	+	1.96337i	−0.206575	+	0.119266i	0.393144	+	0.919477i	$0.371388\pi$
$272$	1.57288	+	1.31980i	0.0953696	+	0.0800246i
$273$		0			0
$274$	−0.871668	−	4.94347i	−0.0526594	−	0.298646i
$275$	23.3178	−	4.11156i	1.40612	−	0.247936i
$276$		0			0
$277$	−17.5744	−	14.7467i	−1.05595	−	0.886043i	−0.0622389	−	0.998061i	$-0.519824\pi$
$277$	−17.5744	−	14.7467i	−1.05595	−	0.886043i	−0.993706	+	0.112018i	$0.964269\pi$
$278$	−0.207518			−0.0124461
$279$		0			0
$280$	0.000415809		0.00275467i	2.48494e−5		0.000164623i
$281$	−0.608889	−	1.67291i	−0.0363233	−	0.0997974i	0.920205	−	0.391436i	$-0.128022\pi$
$281$	−0.608889	−	1.67291i	−0.0363233	−	0.0997974i	−0.956528	+	0.291639i	$0.905799\pi$
$282$		0			0
$283$	−4.38907	+	0.773911i	−0.260903	+	0.0460042i	−0.302569	−	0.953127i	$-0.597844\pi$
$283$	−4.38907	+	0.773911i	−0.260903	+	0.0460042i	0.0416665	+	0.999132i	$0.486733\pi$
$284$	15.0696	−	2.65717i	0.894214	−	0.157674i
$285$		0			0
$286$	2.22714	+	6.11901i	0.131693	+	0.361825i
$287$	6.56164	−	16.7294i	0.387321	−	0.987507i
$288$		0			0
$289$	−16.3597			−0.962337
$290$	0.00180902	+	0.00151795i	0.000106229	+	8.91371e-5i
$291$		0			0
$292$	−12.3829	+	2.18343i	−0.724652	+	0.127776i
$293$	−1.23196	−	6.98681i	−0.0719721	−	0.408174i	−0.999415	−	0.0342085i	$-0.989109\pi$
$293$	−1.23196	−	6.98681i	−0.0719721	−	0.408174i	0.927443	−	0.373965i	$-0.122002\pi$
$294$		0			0
$295$	−0.00568967	−	0.00477420i	−0.000331265	−	0.000277965i
$296$	−3.33453	+	1.92519i	−0.193815	+	0.111899i
$297$		0			0
$298$	0.229979	−	0.398336i	0.0133223	−	0.0230750i
$299$	−0.758694	+	4.30277i	−0.0438764	+	0.248836i
$300$		0			0
$301$	11.9150	−	13.5073i	0.686771	−	0.778546i
$302$	0.205589	−	0.564852i	0.0118303	−	0.0325036i
$303$		0			0
$304$	8.58466	−	10.2308i	0.492364	−	0.586777i
$305$	0.00176969	−	0.00102173i	0.000101332	−	5.85042e-5i
$306$		0			0
$307$	−6.20672	+	3.58345i	−0.354236	+	0.204518i	−0.666549	−	0.745461i	$-0.732229\pi$
$307$	−6.20672	+	3.58345i	−0.354236	+	0.204518i	0.312313	+	0.949979i	$0.398896\pi$
$308$	21.9270	+	0.542076i	1.24941	+	0.0308877i
$309$		0			0
$310$	0.00213057		0.000775463i	0.000121008		4.40434e-5i
$311$	4.03708	+	22.8954i	0.228922	+	1.29828i	0.855044	+	0.518556i	$0.173530\pi$
$311$	4.03708	+	22.8954i	0.228922	+	1.29828i	−0.626122	+	0.779725i	$0.715359\pi$
$312$		0			0
$313$	15.3541	−	18.2983i	0.867863	−	1.03428i	−0.131216	−	0.991354i	$-0.541888\pi$
$313$	15.3541	−	18.2983i	0.867863	−	1.03428i	0.999078	−	0.0429247i	$-0.0136676\pi$
$314$	2.87721	+	4.98347i	0.162370	+	0.281234i
$315$		0			0
$316$	−2.25541	+	3.90648i	−0.126877	+	0.219757i
$317$	9.82360	+	26.9901i	0.551748	+	1.51592i	0.831322	+	0.555791i	$0.187585\pi$
$317$	9.82360	+	26.9901i	0.551748	+	1.51592i	−0.279574	+	0.960124i	$0.590193\pi$
$318$		0			0
$319$	30.5143	−	25.6045i	1.70847	−	1.43358i
$320$	−0.00112905		0.000947383i	−6.31156e−5		5.29603e-5i
$321$		0			0
$322$	−1.78897	−	1.09268i	−0.0996954	−	0.0608929i
$323$		−	4.16468i		−	0.231729i
$324$		0			0
$325$	−11.9238	−	6.88420i	−0.661412	−	0.381866i
$326$	1.16922	+	3.21239i	0.0647569	+	0.177918i
$327$		0			0
$328$	−12.5279	+	2.20900i	−0.691735	+	0.121972i
$329$	−12.9794	+	14.7138i	−0.715577	+	0.811201i
$330$		0			0
$331$	24.4353	−	8.89374i	1.34309	−	0.488844i	0.432304	−	0.901728i	$-0.357701\pi$
$331$	24.4353	−	8.89374i	1.34309	−	0.488844i	0.910784	+	0.412884i	$0.135478\pi$
$332$	−1.68838	−	2.92436i	−0.0926620	−	0.160495i
$333$		0			0
$334$	2.00547	+	1.15786i	0.109734	+	0.0633551i
$335$	0.00112355		0.000408937i	6.13858e−5		2.23426e-5i
$336$		0			0
$337$	5.30836	−	4.45424i	0.289165	−	0.242638i	−0.486653	−	0.873596i	$-0.661782\pi$
$337$	5.30836	−	4.45424i	0.289165	−	0.242638i	0.775817	+	0.630958i	$0.217338\pi$
$338$	−0.925224	+	2.54203i	−0.0503256	+	0.138268i
$339$		0			0
$340$	−0.000136754	0	0.000775572i	−7.41655e−6	0	4.20613e-5i
$341$	19.1222	−	33.1207i	1.03553	−	1.79358i
$342$		0			0
$343$	−1.37203	+	18.4694i	−0.0740826	+	0.997252i
$344$	−12.5566	−	2.21407i	−0.677008	−	0.119375i
$345$		0			0
$346$	7.72317	+	9.20412i	0.415200	+	0.494817i
$347$	0.540900	−	1.48611i	0.0290370	−	0.0797786i	−0.924327	−	0.381601i	$-0.875373\pi$
$347$	0.540900	−	1.48611i	0.0290370	−	0.0797786i	0.953364	+	0.301823i	$0.0975950\pi$
$348$		0			0
$349$	−11.3433	+	13.5184i	−0.607194	+	0.723626i	−0.978812	−	0.204760i	$-0.934359\pi$
$349$	−11.3433	+	13.5184i	−0.607194	+	0.723626i	0.371618	+	0.928386i	$0.378803\pi$
$350$	5.16384	−	4.11986i	0.276019	−	0.220216i
$351$		0			0
$352$	−11.9032	−	20.6170i	−0.634444	−	1.09889i
$353$	2.55746	−	0.930839i	0.136120	−	0.0495435i	−0.273062	−	0.961996i	$-0.588036\pi$
$353$	2.55746	−	0.930839i	0.136120	−	0.0495435i	0.409182	+	0.912453i	$0.365814\pi$
$354$		0			0
$355$	0.00315873	+	0.00376442i	0.000167648	+	0.000199795i
$356$	−5.32310	−	1.93745i	−0.282124	−	0.102685i
$357$		0			0
$358$	2.13903	−	12.1311i	0.113051	−	0.641146i
$359$		−	22.8763i		−	1.20737i	−0.797224	−	0.603683i	$-0.793699\pi$
$359$		−	22.8763i		−	1.20737i	0.797224	−	0.603683i	$-0.206301\pi$
$360$		0			0
$361$	−8.08924			−0.425750
$362$	−3.43841	−	2.88517i	−0.180719	−	0.151641i
$363$		0			0
$364$	−9.56480	−	8.43730i	−0.501332	−	0.442235i
$365$	−0.00259557	−	0.00309328i	−0.000135858	−	0.000161910i
$366$		0			0
$367$	7.27732	+	1.28319i	0.379873	+	0.0669819i	0.360325	−	0.932827i	$-0.382666\pi$
$367$	7.27732	+	1.28319i	0.379873	+	0.0669819i	0.0195487	+	0.999809i	$0.493777\pi$
$368$		−	4.07137i		−	0.212235i
$369$		0			0
$370$	−0.000499828	0	0.000288576i	−2.59848e−5	0	1.50023e-5i
$371$	−27.8311	−	0.688038i	−1.44492	−	0.0357211i
$372$		0			0
$373$	5.62504	+	31.9012i	0.291254	+	1.65178i	0.682051	+	0.731304i	$0.261088\pi$
$373$	5.62504	+	31.9012i	0.291254	+	1.65178i	−0.390798	+	0.920477i	$0.627801\pi$
$374$	−1.77808	−	0.647169i	−0.0919424	−	0.0334643i
$375$		0			0
$376$	13.6783	+	2.41185i	0.705405	+	0.124382i
$377$	−23.1631			−1.19296
$378$		0			0
$379$	−6.72815			−0.345602			−0.172801	−	0.984957i	$-0.555282\pi$
$379$	−6.72815			−0.345602			−0.172801	+	0.984957i	$0.555282\pi$
$380$	0.00504472		0.000889521i	0.000258789		4.56315e-5i
$381$		0			0
$382$	9.78864	+	3.56278i	0.500831	+	0.182287i
$383$	−0.0493036	−	0.279615i	−0.00251930	−	0.0142876i	0.983522	−	0.180787i	$-0.0578646\pi$
$383$	−0.0493036	−	0.279615i	−0.00251930	−	0.0142876i	−0.986041	+	0.166500i	$0.946753\pi$
$384$		0			0
$385$	0.00337006	+	0.00618529i	0.000171754	+	0.000315231i
$386$	−7.90450	−	4.56367i	−0.402329	−	0.232285i
$387$		0			0
$388$			3.14389i			0.159607i
$389$	0.733433	+	0.129324i	0.0371865	+	0.00655699i	0.192211	−	0.981354i	$-0.438434\pi$
$389$	0.733433	+	0.129324i	0.0371865	+	0.00655699i	−0.155024	+	0.987911i	$0.549545\pi$
$390$		0			0
$391$	−0.816083	−	0.972570i	−0.0412711	−	0.0491850i
$392$	11.6641	−	5.98620i	0.589124	−	0.302349i
$393$		0			0
$394$	−3.94256	−	3.30820i	−0.198623	−	0.166665i
$395$	−0.00144861			−7.28873e−5
$396$		0			0
$397$		−	16.7288i		−	0.839593i	−0.907618	−	0.419797i	$-0.862101\pi$
$397$		−	16.7288i		−	0.839593i	0.907618	−	0.419797i	$-0.137899\pi$
$398$	−0.968833	+	5.49452i	−0.0485632	+	0.275416i
$399$		0			0
$400$	12.0563	+	4.38812i	0.602814	+	0.219406i
$401$	11.8787	+	14.1565i	0.593194	+	0.706941i	0.976216	−	0.216798i	$-0.0695613\pi$
$401$	11.8787	+	14.1565i	0.593194	+	0.706941i	−0.383023	+	0.923739i	$0.625117\pi$
$402$		0			0
$403$	−20.8978	+	7.60619i	−1.04099	+	0.378891i
$404$	−3.72832	−	6.45763i	−0.185491	−	0.321279i
$405$		0			0
$406$	4.05795	−	10.3461i	0.201393	−	0.513467i
$407$	−6.25772	+	7.45767i	−0.310184	+	0.369663i
$408$		0			0
$409$	−6.09589	+	16.7483i	−0.301423	+	0.828152i	0.692831	+	0.721100i	$0.256363\pi$
$409$	−6.09589	+	16.7483i	−0.301423	+	0.828152i	−0.994253	+	0.107052i	$0.965859\pi$
$410$	−0.00122569	−	0.00146072i	−6.05323e−5	−	7.21396e-5i
$411$		0			0
$412$	27.7239	+	4.88847i	1.36586	+	0.240838i
$413$	−12.7629	+	32.5401i	−0.628021	+	1.60119i
$414$		0			0
$415$	0.000542208	0	0.000939132i	2.66159e−5	0	4.61002e-5i
$416$	−2.40387	+	13.6330i	−0.117860	+	0.668415i
$417$		0			0
$418$	−4.20952	+	11.5656i	−0.205894	+	0.565690i
$419$	−0.812929	+	0.682129i	−0.0397142	+	0.0333242i	−0.662429	−	0.749125i	$-0.730474\pi$
$419$	−0.812929	+	0.682129i	−0.0397142	+	0.0333242i	0.622715	+	0.782449i	$0.286030\pi$
$420$		0			0
$421$	−14.4175	+	5.24755i	−0.702667	+	0.255750i	−0.668549	−	0.743668i	$-0.733084\pi$
$421$	−14.4175	+	5.24755i	−0.702667	+	0.255750i	−0.0341181	+	0.999418i	$0.510862\pi$
$422$	−10.2716	−	5.93029i	−0.500011	−	0.288682i
$423$		0			0
$424$	9.85384	+	17.0674i	0.478545	+	0.828864i
$425$	3.75958	−	1.36837i	0.182366	−	0.0663759i
$426$		0			0
$427$	−7.21177	−	6.36165i	−0.349002	−	0.307862i
$428$	6.94305	−	1.22425i	0.335605	−	0.0591762i
$429$		0			0
$430$	−0.000653672	−	0.00179595i	−3.15229e−5	−	8.66084e-5i
$431$	3.29736	+	1.90373i	0.158828	+	0.0916996i	0.577308	−	0.816527i	$-0.304103\pi$
$431$	3.29736	+	1.90373i	0.158828	+	0.0916996i	−0.418479	+	0.908226i	$0.637437\pi$
$432$		0			0
$433$			29.5261i			1.41893i	0.704739	+	0.709467i	$0.251064\pi$
$433$			29.5261i			1.41893i	−0.704739	+	0.709467i	$0.748936\pi$
$434$	0.263703	−	10.6668i	0.0126582	−	0.512023i
$435$		0			0
$436$	−1.57668	+	1.32299i	−0.0755092	+	0.0633598i
$437$	−6.32610	+	5.30822i	−0.302618	+	0.253927i
$438$		0			0
$439$	5.64596	+	15.5122i	0.269467	+	0.740355i	0.998441	+	0.0558134i	$0.0177752\pi$
$439$	5.64596	+	15.5122i	0.269467	+	0.740355i	−0.728974	+	0.684541i	$0.760003\pi$
$440$	0.00249315	−	0.00431827i	0.000118856	−	0.000205865i
$441$		0			0
$442$	0.550152	+	0.952891i	0.0261681	+	0.0453244i
$443$	−17.9563	+	21.3994i	−0.853127	+	1.01672i	0.146494	+	0.989212i	$0.453201\pi$
$443$	−17.9563	+	21.3994i	−0.853127	+	1.01672i	−0.999622	+	0.0275061i	$0.991243\pi$
$444$		0			0
$445$	−0.000315896	−	0.00179154i	−1.49749e−5	−	8.49270e-5i
$446$	11.3406	+	4.12763i	0.536992	+	0.195449i
$447$		0			0
$448$	5.91930	+	3.61545i	0.279661	+	0.170814i
$449$	−20.1252	+	11.6193i	−0.949765	+	0.548347i	−0.893008	−	0.450041i	$-0.851409\pi$
$449$	−20.1252	+	11.6193i	−0.949765	+	0.548347i	−0.0567572	+	0.998388i	$0.518076\pi$
$450$		0			0
$451$	−27.8549	+	16.0820i	−1.31164	+	0.757273i
$452$	−16.5926	+	19.7743i	−0.780452	+	0.930107i
$453$		0			0
$454$	0.730736	−	2.00768i	0.0342952	−	0.0942252i
$455$	0.000810726	−	0.00401490i	3.80074e−5	−	0.000188222i
$456$		0			0
$457$	3.14739	−	17.8497i	0.147229	−	0.834976i	−0.818322	−	0.574760i	$-0.805095\pi$
$457$	3.14739	−	17.8497i	0.147229	−	0.834976i	0.965551	−	0.260215i	$-0.0837936\pi$
$458$	−3.23444	+	5.60221i	−0.151135	+	0.261774i
$459$		0			0
$460$	0.00135239		0.000780802i	6.30555e−5		3.64051e-5i
$461$	0.780576	+	0.654981i	0.0363550	+	0.0305055i	0.660784	−	0.750576i	$-0.270224\pi$
$461$	0.780576	+	0.654981i	0.0363550	+	0.0305055i	−0.624429	+	0.781081i	$0.714668\pi$
$462$		0			0
$463$	5.96496	+	33.8290i	0.277215	+	1.57216i	0.731837	+	0.681480i	$0.238663\pi$
$463$	5.96496	+	33.8290i	0.277215	+	1.57216i	−0.454621	+	0.890685i	$0.650225\pi$
$464$	21.2565	−	3.74809i	0.986807	−	0.174001i
$465$		0			0
$466$	−4.28622	−	3.59657i	−0.198556	−	0.166608i
$467$	1.42508			0.0659449			0.0329724	−	0.999456i	$-0.489503\pi$
$467$	1.42508			0.0659449			0.0329724	+	0.999456i	$0.489503\pi$
$468$		0			0
$469$	−3.50921	−	4.39846i	−0.162040	−	0.203102i
$470$	0.000712064		0.00195638i	3.28451e−5		9.02410e-5i
$471$		0			0
$472$	24.3677	−	4.29668i	1.12161	−	0.197771i
$473$	−31.7482	+	5.59806i	−1.45978	+	0.257399i
$474$		0			0
$475$	−8.90062	−	24.4542i	−0.408388	−	1.12204i
$476$	3.66468	−	0.553173i	0.167970	−	0.0253546i
$477$		0			0
$478$	6.26269			0.286449
$479$	−27.4187	−	23.0070i	−1.25279	−	1.05122i	−0.996411	−	0.0846415i	$-0.973026\pi$
$479$	−27.4187	−	23.0070i	−1.25279	−	1.05122i	−0.256381	−	0.966576i	$-0.582530\pi$
$480$		0			0
$481$	5.57503	−	0.983028i	0.254200	−	0.0448222i
$482$	1.74075	+	9.87226i	0.0792888	+	0.449669i
$483$		0			0
$484$	−15.3217	−	12.8564i	−0.696441	−	0.584383i
$485$	−0.000874365	0	0.000504815i	−3.97029e−5	0	2.29225e-5i
$486$		0			0
$487$	−17.4657	+	30.2515i	−0.791446	+	1.37082i	0.133625	+	0.991032i	$0.457338\pi$
$487$	−17.4657	+	30.2515i	−0.791446	+	1.37082i	−0.925071	+	0.379793i	$0.875995\pi$
$488$	−1.18213	+	6.70421i	−0.0535127	+	0.303485i
$489$		0			0
$490$	0.00165128	+	0.00106549i	7.45970e−5	+	4.81341e-5i
$491$	3.72269	−	10.2280i	0.168003	−	0.461584i	−0.826909	−	0.562336i	$-0.809903\pi$
$491$	3.72269	−	10.2280i	0.168003	−	0.461584i	0.994912	+	0.100752i	$0.0321249\pi$
$492$		0			0
$493$	4.32647	−	5.15608i	0.194854	−	0.232218i
$494$	6.19810	−	3.57847i	0.278866	−	0.161003i
$495$		0			0
$496$	17.9469	−	10.3617i	0.805841	−	0.465252i
$497$	12.0545	−	19.7359i	0.540718	−	0.885276i
$498$		0			0
$499$	−5.96349	−	2.17053i	−0.266962	−	0.0971663i	0.205071	−	0.978747i	$-0.434258\pi$
$499$	−5.96349	−	2.17053i	−0.266962	−	0.0971663i	−0.472033	+	0.881581i	$0.656480\pi$
$500$	0.00170906	+	0.00969257i	7.64316e−5	+	0.000433465i
$501$		0			0
$502$	−7.23693	+	8.62463i	−0.323000	+	0.384936i
$503$	6.72425	+	11.6468i	0.299820	+	0.519303i	0.976095	−	0.217346i	$-0.0697401\pi$
$503$	6.72425	+	11.6468i	0.299820	+	0.519303i	−0.676275	+	0.736649i	$0.736407\pi$
$504$		0			0
$505$	0.00119731	−	0.00207381i	5.32798e−5	−	9.22833e-5i
$506$	1.28327	+	3.52575i	0.0570482	+	0.156739i
$507$		0			0
$508$	9.30123	−	7.80466i	0.412675	−	0.346276i
$509$	−13.2396	+	11.1093i	−0.586833	+	0.492411i	−0.887183	−	0.461418i	$-0.847341\pi$
$509$	−13.2396	+	11.1093i	−0.586833	+	0.492411i	0.300350	+	0.953829i	$0.402896\pi$
$510$		0			0
$511$	−9.90533	+	16.2172i	−0.438186	+	0.717409i
$512$		−	22.5118i		−	0.994888i
$513$		0			0
$514$	−12.7090	−	7.33754i	−0.560570	−	0.323645i
$515$	0.00309207	+	0.00849540i	0.000136253	+	0.000374352i
$516$		0			0
$517$	34.5842	−	6.09812i	1.52101	−	0.268195i
$518$	−0.537611	+	2.66237i	−0.0236213	+	0.116978i
$519$		0			0
$520$	−0.00272466		0.000991693i	−0.000119484		4.34886e-5i
$521$	14.2785	+	24.7311i	0.625553	+	1.08349i	0.988434	+	0.151653i	$0.0484597\pi$
$521$	14.2785	+	24.7311i	0.625553	+	1.08349i	−0.362881	+	0.931835i	$0.618207\pi$
$522$		0			0
$523$	−13.1449	−	7.58924i	−0.574788	−	0.331854i	0.184271	−	0.982875i	$-0.441008\pi$
$523$	−13.1449	−	7.58924i	−0.574788	−	0.331854i	−0.759059	+	0.651021i	$0.774341\pi$
$524$	18.1733	−	6.61455i	0.793905	−	0.288958i
$525$		0			0
$526$	−6.41244	+	5.38068i	−0.279596	+	0.234609i
$527$	2.21023	−	6.07255i	0.0962790	−	0.264525i
$528$		0			0
$529$	3.55675	−	20.1713i	0.154641	−	0.877015i
$530$	−0.00147704	+	0.00255831i	−6.41585e−5	+	0.000111126i
$531$		0			0
$532$	−3.59812	−	23.8370i	−0.155998	−	1.03346i
$533$	18.4191	+	3.24779i	0.797821	+	0.140677i
$534$		0			0
$535$	0.00145533	+	0.00173439i	6.29194e−5	+	7.49844e-5i
$536$	−1.36234	+	3.74300i	−0.0588442	+	0.161673i
$537$		0			0
$538$	−3.02823	+	3.60891i	−0.130556	+	0.155591i
$539$	22.5362	−	24.3094i	0.970703	−	1.04708i
$540$		0			0
$541$	8.84080	+	15.3127i	0.380096	+	0.658345i	0.991076	−	0.133301i	$-0.0425577\pi$
$541$	8.84080	+	15.3127i	0.380096	+	0.658345i	−0.610980	+	0.791646i	$0.709224\pi$
$542$	1.84261	−	0.670655i	0.0791469	−	0.0288071i
$543$		0			0
$544$	−2.58570	−	3.08152i	−0.110861	−	0.132119i
$545$	−0.000621113	0	0.000226067i	−2.66055e−5	0	9.68363e-6i
$546$		0			0
$547$	−1.23750	+	7.01822i	−0.0529117	+	0.300077i	−0.999767	−	0.0215823i	$-0.993130\pi$
$547$	−1.23750	+	7.01822i	−0.0529117	+	0.300077i	0.946855	+	0.321660i	$0.104241\pi$
$548$		−	17.5979i		−	0.751745i
$549$		0			0
$550$	−11.8237			−0.504163
$551$	−33.5378	−	28.1416i	−1.42876	−	1.19887i
$552$		0			0
$553$	2.17260	+	6.46177i	0.0923882	+	0.274782i
$554$	7.36395	+	8.77601i	0.312864	+	0.372857i
$555$		0			0
$556$	−0.716453	−	0.126330i	−0.0303844	−	0.00535758i
$557$		−	7.64857i		−	0.324080i	−0.986784	−	0.162040i	$-0.948193\pi$
$557$		−	7.64857i		−	0.324080i	0.986784	−	0.162040i	$-0.0518074\pi$
$558$		0			0
$559$	16.2347	+	9.37312i	0.686655	+	0.396441i
$560$	−9.43293e−5		0.00381562i	−3.98614e−6		0.000161239i
$561$		0			0
$562$	0.154374	+	0.875496i	0.00651185	+	0.0369306i
$563$	−33.9970	−	12.3739i	−1.43280	−	0.521498i	−0.495070	−	0.868853i	$-0.664857\pi$
$563$	−33.9970	−	12.3739i	−1.43280	−	0.521498i	−0.937733	+	0.347356i	$0.887080\pi$
$564$		0			0
$565$	−0.00816385	−	0.00143951i	−0.000343456	−	6.05605e-5i
$566$	2.22555			0.0935467
$567$		0			0
$568$	−16.3710			−0.686910
$569$	5.25761	+	0.927059i	0.220411	+	0.0388643i	0.282763	−	0.959190i	$-0.408749\pi$
$569$	5.25761	+	0.927059i	0.220411	+	0.0388643i	−0.0623521	+	0.998054i	$0.519860\pi$
$570$		0			0
$571$	−34.9232	−	12.7110i	−1.46149	−	0.531939i	−0.515715	−	0.856760i	$-0.672473\pi$
$571$	−34.9232	−	12.7110i	−1.46149	−	0.531939i	−0.945775	+	0.324822i	$0.894696\pi$
$572$	3.96411	+	22.4816i	0.165748	+	0.940003i
$573$		0			0
$574$	−4.67752	+	7.65815i	−0.195236	+	0.319645i
$575$	−6.87043	−	3.96664i	−0.286517	−	0.165421i
$576$		0			0
$577$			25.3559i			1.05558i	0.849374	+	0.527791i	$0.176980\pi$
$577$			25.3559i			1.05558i	−0.849374	+	0.527791i	$0.823020\pi$
$578$	8.04532	+	1.41861i	0.334641	+	0.0590063i
$579$		0			0
$580$	0.00532154	+	0.00634197i	0.000220965	+	0.000263336i
$581$	−5.00236	−	1.01012i	−0.207533	−	0.0419069i
$582$		0			0
$583$	38.1711	+	32.0294i	1.58089	+	1.32652i
$584$	13.4522			0.556658
$585$		0			0
$586$			3.54278i			0.146351i
$587$	−2.85469	+	16.1897i	−0.117826	+	0.668222i	0.867487	+	0.497460i	$0.165734\pi$
$587$	−2.85469	+	16.1897i	−0.117826	+	0.668222i	−0.985312	+	0.170762i	$0.945377\pi$
$588$		0			0
$589$	−39.4990	−	14.3765i	−1.62753	−	0.592372i
$590$	0.00238406	+	0.00284121i	9.81501e−5	+	0.000116971i
$591$		0			0
$592$	−4.95708	+	1.80423i	−0.203735	+	0.0741533i
$593$	15.3209	+	26.5365i	0.629153	+	1.08973i	0.987722	+	0.156222i	$0.0499315\pi$
$593$	15.3209	+	26.5365i	0.629153	+	1.08973i	−0.358569	+	0.933503i	$0.616735\pi$
$594$		0			0
$595$	0.000742286	0	0.000930384i	3.04307e−5	0	3.81420e-5i
$596$	1.03649	−	1.23524i	0.0424564	−	0.0505976i
$597$		0			0
$598$	0.746216	−	2.05021i	0.0305150	−	0.0838393i
$599$	−12.5598	−	14.9682i	−0.513181	−	0.611585i	0.445773	−	0.895146i	$-0.352929\pi$
$599$	−12.5598	−	14.9682i	−0.513181	−	0.611585i	−0.958954	+	0.283561i	$0.908484\pi$
$600$		0			0
$601$	−20.6262	−	3.63695i	−0.841360	−	0.148354i	−0.263672	−	0.964612i	$-0.584934\pi$
$601$	−20.6262	−	3.63695i	−0.841360	−	0.148354i	−0.577688	+	0.816258i	$0.696045\pi$
$602$	−7.03079	+	5.60936i	−0.286554	+	0.228620i
$603$		0			0
$604$	1.05366	−	1.82498i	0.0428726	−	0.0742576i
$605$	0.00111537	−	0.00632557i	4.53462e−5	−	0.000257171i
$606$		0			0
$607$	−9.22736	+	25.3520i	−0.374527	+	1.02900i	0.599063	+	0.800702i	$0.295540\pi$
$607$	−9.22736	+	25.3520i	−0.374527	+	1.02900i	−0.973590	+	0.228302i	$0.926683\pi$
$608$	−20.0438	+	16.8188i	−0.812884	+	0.682091i
$609$		0			0
$610$	−0.000958889	0	0.000349007i	−3.88243e−5	0	1.41309e-5i
$611$	−17.6849	−	10.2104i	−0.715456	−	0.413069i
$612$		0			0
$613$	13.4525	+	23.3005i	0.543343	+	0.941097i	0.998709	+	0.0507931i	$0.0161749\pi$
$613$	13.4525	+	23.3005i	0.543343	+	0.941097i	−0.455366	+	0.890304i	$0.650492\pi$
$614$	3.36305	−	1.22405i	0.135722	−	0.0493986i
$615$		0			0
$616$	−23.0016	−	4.64469i	−0.926761	−	0.187140i
$617$	22.1664	−	3.90853i	0.892386	−	0.157352i	0.291390	−	0.956604i	$-0.405882\pi$
$617$	22.1664	−	3.90853i	0.892386	−	0.157352i	0.600995	+	0.799253i	$0.294771\pi$
$618$		0			0
$619$	3.67268	+	10.0906i	0.147617	+	0.405575i	0.991359	−	0.131173i	$-0.0418745\pi$
$619$	3.67268	+	10.0906i	0.147617	+	0.405575i	−0.843742	+	0.536749i	$0.819652\pi$
$620$	0.00688367	+	0.00397429i	0.000276455	+	0.000159611i
$621$		0			0
$622$		−	11.6095i		−	0.465499i
$623$	−7.51770	+	4.09603i	−0.301190	+	0.164104i
$624$		0			0
$625$	19.1511	−	16.0697i	0.766044	−	0.642787i
$626$	−9.13746	+	7.66724i	−0.365207	+	0.306445i
$627$		0			0
$628$	6.89975	+	18.9569i	0.275330	+	0.756463i
$629$	−0.822500	+	1.42461i	−0.0327952	+	0.0568030i
$630$		0			0
$631$	−0.130873	−	0.226679i	−0.00520998	−	0.00902394i	0.863409	−	0.504505i	$-0.168325\pi$
$631$	−0.130873	−	0.226679i	−0.00520998	−	0.00902394i	−0.868619	+	0.495481i	$0.834992\pi$
$632$	3.10204	−	3.69687i	0.123393	−	0.147054i
$633$		0			0
$634$	−2.49061	−	14.1249i	−0.0989146	−	0.560973i
$635$	0.00366410	+	0.00133362i	0.000145405	+	5.29233e-5i
$636$		0			0
$637$	−19.1251	+	2.40510i	−0.757765	+	0.0952934i
$638$	−17.2264	+	9.94569i	−0.682001	+	0.393754i
$639$		0			0
$640$	0.00553270	−	0.00319431i	0.000218699	−	0.000126266i
$641$	32.1360	−	38.2982i	1.26930	−	1.51269i	0.513131	−	0.858310i	$-0.328485\pi$
$641$	32.1360	−	38.2982i	1.26930	−	1.51269i	0.756166	−	0.654380i	$-0.227070\pi$
$642$		0			0
$643$	5.42130	−	14.8949i	0.213795	−	0.587397i	−0.785718	−	0.618584i	$-0.787706\pi$
$643$	5.42130	−	14.8949i	0.213795	−	0.587397i	0.999514	+	0.0311869i	$0.00992871\pi$
$644$	−5.51120	−	4.86154i	−0.217172	−	0.191571i
$645$		0			0
$646$	−0.361134	+	2.04809i	−0.0142086	+	0.0805811i
$647$	−7.51759	+	13.0208i	−0.295547	+	0.511902i	−0.975112	−	0.221713i	$-0.928835\pi$
$647$	−7.51759	+	13.0208i	−0.295547	+	0.511902i	0.679565	+	0.733615i	$0.262169\pi$
$648$		0			0
$649$	54.1799	−	31.2808i	2.12675	−	1.22788i
$650$	5.26688	+	4.41943i	0.206584	+	0.173344i
$651$		0			0
$652$	2.08110	+	11.8025i	0.0815022	+	0.462222i
$653$	−15.1536	+	2.67199i	−0.593007	+	0.104563i	−0.462094	−	0.886831i	$-0.652902\pi$
$653$	−15.1536	+	2.67199i	−0.593007	+	0.104563i	−0.130912	+	0.991394i	$0.541791\pi$
$654$		0			0
$655$	0.00475771	+	0.00399219i	0.000185899	+	0.000155988i
$656$	−17.4286			−0.680471
$657$		0			0
$658$	7.65884	−	6.11043i	0.298573	−	0.238209i
$659$	5.58157	+	15.3352i	0.217427	+	0.597376i	0.999672	−	0.0255942i	$-0.00814779\pi$
$659$	5.58157	+	15.3352i	0.217427	+	0.597376i	−0.782245	+	0.622971i	$0.785926\pi$
$660$		0			0
$661$	29.6565	−	5.22925i	1.15351	−	0.203394i	0.436000	−	0.899947i	$-0.356395\pi$
$661$	29.6565	−	5.22925i	1.15351	−	0.203394i	0.717506	+	0.696553i	$0.245284\pi$
$662$	−12.7879	+	2.25486i	−0.497017	+	0.0876375i
$663$		0			0
$664$	1.23560	+	3.39478i	0.0479505	+	0.131743i
$665$	0.00605170	−	0.00482821i	0.000234675	−	0.000187230i
$666$		0			0
$667$	−13.3465			−0.516777
$668$	6.21898	+	5.21834i	0.240620	+	0.201904i
$669$		0			0
$670$	−0.000587993	0	0.000103679i	−2.27162e−5	0	4.00547e-6i
$671$	2.98890	+	16.9509i	0.115385	+	0.654383i
$672$		0			0
$673$	8.51271	+	7.14301i	0.328141	+	0.275343i	0.791942	−	0.610597i	$-0.209070\pi$
$673$	8.51271	+	7.14301i	0.328141	+	0.275343i	−0.463801	+	0.885939i	$0.653515\pi$
$674$	−2.99677	+	1.73018i	−0.115431	+	0.0666442i
$675$		0			0
$676$	−4.74182	+	8.21308i	−0.182378	+	0.315888i
$677$	−5.39839	+	30.6158i	−0.207477	+	1.17666i	0.686017	+	0.727585i	$0.259357\pi$
$677$	−5.39839	+	30.6158i	−0.207477	+	1.17666i	−0.893494	+	0.449075i	$0.851754\pi$
$678$		0			0
$679$	3.56318	+	3.14315i	0.136742	+	0.120623i
$680$	0.000288169	0	0.000791738i	1.10508e−5	0	3.03618e-5i
$681$		0			0
$682$	−12.2759	+	14.6298i	−0.470067	+	0.560204i
$683$	−17.3662	+	10.0264i	−0.664500	+	0.383649i	−0.793989	−	0.607932i	$-0.791999\pi$
$683$	−17.3662	+	10.0264i	−0.664500	+	0.383649i	0.129490	+	0.991581i	$0.458666\pi$
$684$		0			0
$685$	0.00489426	−	0.00282570i	0.000187000	−	0.000107965i
$686$	2.27627	−	8.96382i	0.0869085	−	0.342240i
$687$		0			0
$688$	−16.4151	−	5.97461i	−0.625820	−	0.227780i
$689$	−5.03151	−	28.5351i	−0.191685	−	1.08710i
$690$		0			0
$691$	−3.41783	+	4.07321i	−0.130020	+	0.154952i	−0.827127	−	0.562016i	$-0.810026\pi$
$691$	−3.41783	+	4.07321i	−0.130020	+	0.154952i	0.697106	+	0.716968i	$0.254471\pi$
$692$	21.0610	+	36.4787i	0.800618	+	1.38671i
$693$		0			0
$694$	−0.394867	+	0.683930i	−0.0149890	+	0.0259616i
$695$	−7.99067e−5	0	0.000219542i	−3.03103e−6	0	8.32769e-6i
$696$		0			0
$697$	−4.16334	+	3.49346i	−0.157698	+	0.132324i
$698$	6.75060	−	5.66443i	0.255514	−	0.214402i
$699$		0			0
$700$	20.3361	−	11.0802i	0.768633	−	0.418791i
$701$		−	16.0144i		−	0.604857i	−0.953172	−	0.302428i	$-0.902203\pi$
$701$		−	16.0144i		−	0.604857i	0.953172	−	0.302428i	$-0.0977973\pi$
$702$		0			0
$703$	9.26641	+	5.34997i	0.349489	+	0.201778i
$704$	−4.24605	−	11.6659i	−0.160029	−	0.439676i
$705$		0			0
$706$	−1.33841	+	0.235998i	−0.0503718	+	0.00888192i
$707$	−11.0463	−	2.23057i	−0.415439	−	0.0838893i
$708$		0			0
$709$	−0.229579	+	0.0835600i	−0.00862202	+	0.00313816i	−0.346328	−	0.938114i	$-0.612571\pi$
$709$	−0.229579	+	0.0835600i	−0.00862202	+	0.00313816i	0.337706	+	0.941252i	$0.390349\pi$
$710$	−0.00122696	−	0.00212516i	−4.60470e−5	−	7.97558e-5i
$711$		0			0
$712$	5.24849	+	3.03022i	0.196696	+	0.113562i
$713$	−12.0412	+	4.38265i	−0.450948	+	0.164132i
$714$		0			0
$715$	−0.00561597	+	0.00471236i	−0.000210025	+	0.000176232i
$716$	14.7699	−	40.5801i	0.551979	−	1.51655i
$717$		0			0
$718$	−1.98368	+	11.2500i	−0.0740305	+	0.419848i
$719$	17.6366	−	30.5475i	0.657734	−	1.13923i	−0.323467	−	0.946239i	$-0.604848\pi$
$719$	17.6366	−	30.5475i	0.657734	−	1.13923i	0.981201	−	0.192989i	$-0.0618182\pi$
$720$		0			0
$721$	33.2578	−	26.5340i	1.23859	−	0.988178i
$722$	3.97810	+	0.701446i	0.148049	+	0.0261051i
$723$		0			0
$724$	−10.1147	−	12.0542i	−0.375909	−	0.447991i
$725$	14.3848	−	39.5219i	0.534238	−	1.46781i
$726$		0			0
$727$	28.8861	−	34.4251i	1.07133	−	1.27676i	0.112229	−	0.993682i	$-0.464201\pi$
$727$	28.8861	−	34.4251i	1.07133	−	1.27676i	0.959098	−	0.283075i	$-0.0913546\pi$
$728$	8.51002	+	10.6665i	0.315402	+	0.395326i
$729$		0			0
$730$	0.00100821	+	0.00174627i	3.73155e−5	+	6.46324e-5i
$731$	−5.11882	+	1.86310i	−0.189326	+	0.0689092i
$732$		0			0
$733$	−28.0884	−	33.4744i	−1.03747	−	1.23641i	−0.971115	−	0.238610i	$-0.923308\pi$
$733$	−28.0884	−	33.4744i	−1.03747	−	1.23641i	−0.0663525	−	0.997796i	$-0.521136\pi$
$734$	−3.46755	−	1.26208i	−0.127989	−	0.0465843i
$735$		0			0
$736$	−1.38510	+	7.85530i	−0.0510555	+	0.289550i
$737$			10.0712i			0.370976i
$738$		0			0
$739$	35.4098			1.30257			0.651286	−	0.758833i	$-0.274230\pi$
$739$	35.4098			1.30257			0.651286	+	0.758833i	$0.274230\pi$
$740$	−0.00154997	−	0.00130058i	−5.69781e−5	−	4.78103e-5i
$741$		0			0
$742$	13.6270	+	2.75169i	0.500264	+	0.101018i
$743$	−14.2073	−	16.9316i	−0.521216	−	0.621161i	0.439652	−	0.898168i	$-0.355102\pi$
$743$	−14.2073	−	16.9316i	−0.521216	−	0.621161i	−0.960868	+	0.277007i	$0.910657\pi$
$744$		0			0
$745$	0.000509971	0	8.99217e-5i	1.86839e−5	0	3.29448e-6i
$746$		−	16.1760i		−	0.592246i
$747$		0			0
$748$	−5.74482	−	3.31677i	−0.210051	−	0.121273i
$749$	5.55390	−	9.09297i	0.202935	−	0.332250i
$750$		0			0
$751$	7.28917	+	41.3389i	0.265985	+	1.50848i	0.766214	+	0.642585i	$0.222138\pi$
$751$	7.28917	+	41.3389i	0.265985	+	1.50848i	−0.500229	+	0.865893i	$0.666751\pi$
$752$	17.8815	+	6.50832i	0.652070	+	0.237334i
$753$		0			0
$754$	11.3910	+	2.00855i	0.414837	+	0.0731470i
$755$	0.000676743	0		2.46292e−5	0
$756$		0			0
$757$	7.91633			0.287724			0.143862	−	0.989598i	$-0.454048\pi$
$757$	7.91633			0.287724			0.143862	+	0.989598i	$0.454048\pi$
$758$	3.30875	+	0.583421i	0.120179	+	0.0211908i
$759$		0			0
$760$	−0.00514988	−	0.00187440i	−0.000186806	−	6.79917e-5i
$761$	5.73553	+	32.5278i	0.207913	+	1.17913i	0.892790	+	0.450474i	$0.148745\pi$
$761$	5.73553	+	32.5278i	0.207913	+	1.17913i	−0.684877	+	0.728659i	$0.740144\pi$
$762$		0			0
$763$	−0.0768760	+	3.10964i	−0.00278310	+	0.112576i
$764$	31.6262	+	18.2594i	1.14420	+	0.660602i
$765$		0			0
$766$			0.141783i			0.00512283i
$767$	−35.8267	−	6.31721i	−1.29363	−	0.228101i
$768$		0			0
$769$	−19.7511	−	23.5384i	−0.712241	−	0.848816i	0.281611	−	0.959529i	$-0.409131\pi$
$769$	−19.7511	−	23.5384i	−0.712241	−	0.848816i	−0.993852	+	0.110713i	$0.964687\pi$
$770$	−0.00112097	−	0.00333401i	−4.03969e−5	−	0.000120149i
$771$		0			0
$772$	−24.5120	−	20.5680i	−0.882205	−	0.740258i
$773$	−31.5260			−1.13391			−0.566956	−	0.823748i	$-0.691879\pi$
$773$	−31.5260			−1.13391			−0.566956	+	0.823748i	$0.691879\pi$
$774$		0			0
$775$		−	40.3805i		−	1.45051i
$776$	0.584066	−	3.31240i	0.0209668	−	0.118908i
$777$		0			0
$778$	−0.349471	−	0.127197i	−0.0125291	−	0.00456023i
$779$	22.7232	+	27.0805i	0.814145	+	0.970260i
$780$		0			0
$781$	−38.8960	+	14.1570i	−1.39181	+	0.506577i
$782$	0.316995	+	0.549052i	0.0113357	+	0.0196341i
$783$		0			0
$784$	17.1617	−	5.30183i	0.612919	−	0.189351i
$785$	−0.00416432	+	0.00496285i	−0.000148631	+	0.000177132i
$786$		0			0
$787$	−16.3204	+	44.8400i	−0.581760	+	1.59837i	0.203411	+	0.979093i	$0.434797\pi$
$787$	−16.3204	+	44.8400i	−0.581760	+	1.59837i	−0.785171	+	0.619279i	$0.787425\pi$
$788$	−11.5977	−	13.8216i	−0.413151	−	0.492374i
$789$		0			0
$790$	0.000712390	0	0.000125614i	2.53457e−5	0	4.46913e-6i
$791$	5.82282	+	38.5753i	0.207036	+	1.37158i
$792$		0			0
$793$	5.00447	−	8.66800i	0.177714	−	0.307810i
$794$	−1.45061	+	8.22681i	−0.0514802	+	0.291959i
$795$		0			0
$796$	−6.68976	+	18.3800i	−0.237112	+	0.651460i
$797$	29.5128	−	24.7642i	1.04540	−	0.877192i	0.0527949	−	0.998605i	$-0.483187\pi$
$797$	29.5128	−	24.7642i	1.04540	−	0.877192i	0.992602	+	0.121413i	$0.0387426\pi$
$798$		0			0
$799$	5.57608	−	2.02953i	0.197267	−	0.0717995i
$800$	−21.7685	−	12.5681i	−0.769633	−	0.444348i
$801$		0			0
$802$	−4.61410	−	7.99186i	−0.162930	−	0.282202i
$803$	31.9614	−	11.6330i	1.12789	−	0.410519i
$804$		0			0
$805$	0.000467137	−	0.00231337i	1.64644e−5	−	8.15356e-5i
$806$	10.9366	−	1.92842i	0.385226	−	0.0679257i
$807$		0			0
$808$	2.72847	+	7.49641i	0.0959873	+	0.263723i
$809$	36.7753	+	21.2322i	1.29295	+	0.746486i	0.979176	−	0.203011i	$-0.0650728\pi$
$809$	36.7753	+	21.2322i	1.29295	+	0.746486i	0.313775	+	0.949497i	$0.398406\pi$
$810$		0			0
$811$		−	22.9043i		−	0.804277i	−0.915579	−	0.402139i	$-0.868267\pi$
$811$		−	22.9043i		−	0.804277i	0.915579	−	0.402139i	$-0.131733\pi$
$812$	20.3083	−	33.2493i	0.712683	−	1.16682i
$813$		0			0
$814$	3.72408	−	3.12487i	0.130529	−	0.109527i
$815$	−0.00294830	+	0.00247392i	−0.000103275	+	8.66577e-5i
$816$		0			0
$817$	12.1186	+	33.2955i	0.423975	+	1.16486i
$818$	4.45012	−	7.70784i	0.155595	−	0.269498i
$819$		0			0
$820$	−0.00334243	−	0.00578925i	−0.000116723	−	0.000202169i
$821$	−1.32257	+	1.57617i	−0.0461579	+	0.0550089i	−0.788629	−	0.614869i	$-0.789209\pi$
$821$	−1.32257	+	1.57617i	−0.0461579	+	0.0550089i	0.742472	+	0.669878i	$0.233653\pi$
$822$		0			0
$823$	0.562875	+	3.19222i	0.0196206	+	0.111274i	0.993045	−	0.117734i	$-0.0375630\pi$
$823$	0.562875	+	3.19222i	0.0196206	+	0.111274i	−0.973425	+	0.229008i	$0.926452\pi$
$824$	−28.3018	−	10.3010i	−0.985939	−	0.358852i
$825$		0			0
$826$	9.09815	−	14.8957i	0.316565	−	0.518288i
$827$	−47.0423	+	27.1599i	−1.63582	+	0.944441i	−0.653569	+	0.756867i	$0.726729\pi$
$827$	−47.0423	+	27.1599i	−1.63582	+	0.944441i	−0.982251	+	0.187574i	$0.939938\pi$
$828$		0			0
$829$	−7.34388	+	4.23999i	−0.255063	+	0.147261i	−0.622081	−	0.782953i	$-0.713712\pi$
$829$	−7.34388	+	4.23999i	−0.255063	+	0.147261i	0.367017	+	0.930214i	$0.380379\pi$
$830$	−0.000348080	0	0.000414826i	−1.20820e−5	0	1.43988e-5i
$831$		0			0
$832$	−2.46906	+	6.78368i	−0.0855992	+	0.235182i
$833$	3.03688	−	4.70647i	0.105221	−	0.163070i
$834$		0			0
$835$	−0.000452721		0.00256751i	−1.56671e−5		8.88523e-5i
$836$	−21.5740	+	37.3673i	−0.746153	+	1.29237i
$837$		0			0
$838$	0.458929	−	0.264963i	0.0158534	−	0.00915299i
$839$	11.5622	+	9.70185i	0.399172	+	0.334945i	0.820173	−	0.572115i	$-0.193877\pi$
$839$	11.5622	+	9.70185i	0.399172	+	0.334945i	−0.421002	+	0.907060i	$0.638321\pi$
$840$		0			0
$841$	−7.25090	−	41.1219i	−0.250031	−	1.41800i
$842$	7.54523	−	1.33043i	0.260026	−	0.0458496i
$843$		0			0
$844$	−31.8522	−	26.7272i	−1.09640	−	0.919987i
$845$	−0.00304558			−0.000104771
$846$		0			0
$847$	−29.8891	+	4.51168i	−1.02700	+	0.155023i
$848$	9.23471	+	25.3722i	0.317121	+	0.871284i
$849$		0			0
$850$	−1.96753	+	0.346928i	−0.0674856	+	0.0118995i
$851$	3.21231	−	0.566417i	0.110117	−	0.0194165i
$852$		0			0
$853$	5.23344	+	14.3788i	0.179190	+	0.492319i	0.996473	−	0.0839170i	$-0.0267430\pi$
$853$	5.23344	+	14.3788i	0.179190	+	0.492319i	−0.817283	+	0.576236i	$0.804521\pi$
$854$	2.99494	+	3.75386i	0.102485	+	0.128455i
$855$		0			0
$856$	−7.54264			−0.257802
$857$	13.4455	+	11.2821i	0.459289	+	0.385389i	0.842869	−	0.538118i	$-0.180865\pi$
$857$	13.4455	+	11.2821i	0.459289	+	0.385389i	−0.383580	+	0.923507i	$0.625309\pi$
$858$		0			0
$859$	−15.6157	+	2.75347i	−0.532801	+	0.0939472i	−0.433575	−	0.901118i	$-0.642748\pi$
$859$	−15.6157	+	2.75347i	−0.532801	+	0.0939472i	−0.0992264	+	0.995065i	$0.531637\pi$
$860$	−0.00116348	−	0.00659842i	−3.96743e−5	−	0.000225004i
$861$		0			0
$862$	−1.45649	−	1.22214i	−0.0496081	−	0.0416261i
$863$	1.76440	−	1.01868i	0.0600610	−	0.0346762i	−0.469669	−	0.882843i	$-0.655627\pi$
$863$	1.76440	−	1.01868i	0.0600610	−	0.0346762i	0.529730	+	0.848166i	$0.322293\pi$
$864$		0			0
$865$	−0.00676353	+	0.0117148i	−0.000229967	+	0.000398315i
$866$	2.56031	−	14.5202i	0.0870028	−	0.493417i
$867$		0			0
$868$	7.40402	−	36.6664i	0.251309	−	1.24454i
$869$	4.17328	−	11.4660i	0.141569	−	0.388957i
$870$		0			0
$871$	3.76439	−	4.48622i	0.127551	−	0.152010i
$872$	1.90697	−	1.10099i	0.0645783	−	0.0372843i
$873$		0			0
$874$	3.57132	−	2.06190i	0.120802	−	0.0697448i
$875$	0.0126939	+	0.00775331i	0.000429132	+	0.000262110i
$876$		0			0
$877$	17.0905	+	6.22045i	0.577106	+	0.210050i	0.614049	−	0.789268i	$-0.289540\pi$
$877$	17.0905	+	6.22045i	0.577106	+	0.210050i	−0.0369427	+	0.999317i	$0.511762\pi$
$878$	−1.43144	−	8.11809i	−0.0483087	−	0.273972i
$879$		0			0
$880$	0.00439119	−	0.00523322i	0.000148027	−	0.000176412i
$881$	13.3725	+	23.1618i	0.450530	+	0.780341i	0.998419	−	0.0562101i	$-0.0179017\pi$
$881$	13.3725	+	23.1618i	0.450530	+	0.780341i	−0.547889	+	0.836551i	$0.684568\pi$
$882$		0			0
$883$	10.5208	−	18.2226i	0.354054	−	0.613240i	−0.632901	−	0.774232i	$-0.718136\pi$
$883$	10.5208	−	18.2226i	0.354054	−	0.613240i	0.986956	+	0.160992i	$0.0514694\pi$
$884$	1.31930	+	3.62475i	0.0443729	+	0.121914i
$885$		0			0
$886$	10.6861	−	8.96668i	0.359006	−	0.301242i
$887$	17.0586	−	14.3138i	0.572771	−	0.480612i	−0.309793	−	0.950804i	$-0.600260\pi$
$887$	17.0586	−	14.3138i	0.572771	−	0.480612i	0.882564	+	0.470192i	$0.155815\pi$
$888$		0			0
$889$	0.453511	−	18.3445i	0.0152103	−	0.615256i
$890$		0	0.000908428i		0	3.04506e-5i
$891$		0			0
$892$	36.6404	+	21.1543i	1.22681	+	0.708300i
$893$	−13.2011	−	36.2697i	−0.441758	−	1.21372i
$894$		0			0
$895$	0.0136576	−	0.00240820i	0.000456523	−	8.04973e-5i
$896$	−22.5466	−	19.8888i	−0.753230	−	0.664439i
$897$		0			0
$898$	10.9046	−	3.96896i	0.363892	−	0.132446i
$899$	−33.9668	−	58.8322i	−1.13286	−	1.96216i
$900$		0			0
$901$	7.29169	+	4.20986i	0.242922	+	0.140251i
$902$	15.0929	−	5.49336i	0.502538	−	0.182909i
$903$		0			0
$904$	21.1557	−	17.7517i	0.703627	−	0.590414i
$905$	0.00172835	−	0.00474860i	5.74522e−5	−	0.000157849i
$906$		0			0
$907$	0.624448	−	3.54142i	0.0207345	−	0.117591i	−0.972684	−	0.232134i	$-0.925429\pi$
$907$	0.624448	−	3.54142i	0.0207345	−	0.117591i	0.993418	+	0.114543i	$0.0365404\pi$
$908$	3.74506	−	6.48664i	0.124284	−	0.215267i
$909$		0			0
$910$	−0.000746842		0.00190413i	−2.47576e−5		6.31214e-5i
$911$	51.8774	+	9.14738i	1.71877	+	0.303066i	0.944189	−	0.329403i	$-0.106848\pi$
$911$	51.8774	+	9.14738i	1.71877	+	0.303066i	0.774585	+	0.632470i	$0.217959\pi$
$912$		0			0
$913$	5.87135	+	6.99721i	0.194313	+	0.231574i
$914$	−3.09562	+	8.50515i	−0.102394	+	0.281326i
$915$		0			0
$916$	−14.5773	+	17.3725i	−0.481647	+	0.574005i
$917$	10.6724	−	27.2100i	0.352432	−	0.898555i
$918$		0			0
$919$	−27.2723	−	47.2370i	−0.899629	−	1.55820i	−0.827969	−	0.560774i	$-0.810504\pi$
$919$	−27.2723	−	47.2370i	−0.899629	−	1.55820i	−0.0716603	−	0.997429i	$-0.522830\pi$
$920$	−0.00156994		0.000571410i	−5.17592e−5		1.88388e-5i
$921$		0			0
$922$	−0.327073	−	0.389790i	−0.0107716	−	0.0128371i
$923$	22.6179	+	8.23224i	0.744477	+	0.270968i
$924$		0			0
$925$	−1.78494	+	10.1229i	−0.0586884	+	0.332838i
$926$		−	17.1535i		−	0.563700i
$927$		0			0
$928$	−42.2874			−1.38815
$929$	32.1029	+	26.9376i	1.05326	+	0.883793i	0.993433	−	0.114416i	$-0.0364996\pi$
$929$	32.1029	+	26.9376i	1.05326	+	0.883793i	0.0598303	+	0.998209i	$0.480944\pi$
$930$		0			0
$931$	−30.6133	−	19.7534i	−1.00331	−	0.647392i
$932$	−12.6086	−	15.0264i	−0.413010	−	0.492206i
$933$		0			0
$934$	−0.700821	−	0.123574i	−0.0229316	−	0.00404345i
$935$		−	0.00213030i		−	6.96683e-5i
$936$		0			0
$937$	−24.5420	−	14.1693i	−0.801751	−	0.462891i	0.0423320	−	0.999104i	$-0.486521\pi$
$937$	−24.5420	−	14.1693i	−0.801751	−	0.462891i	−0.844083	+	0.536212i	$0.819855\pi$
$938$	1.34434	+	2.46735i	0.0438943	+	0.0805619i
$939$		0			0
$940$	0.00126741	+	0.00718785i	4.13384e−5	+	0.000234442i
$941$	15.2577	+	5.55334i	0.497386	+	0.181034i	0.578518	−	0.815670i	$-0.303631\pi$
$941$	15.2577	+	5.55334i	0.497386	+	0.181034i	−0.0811321	+	0.996703i	$0.525854\pi$
$942$		0			0
$943$	10.6130	+	1.87136i	0.345608	+	0.0609399i
$944$	33.8999			1.10335
$945$		0			0
$946$	16.0984			0.523405
$947$	−9.66361	−	1.70396i	−0.314025	−	0.0553711i	0.0144143	−	0.999896i	$-0.495412\pi$
$947$	−9.66361	−	1.70396i	−0.314025	−	0.0553711i	−0.328440	+	0.944525i	$0.606523\pi$
$948$		0			0
$949$	−18.5854	−	6.76454i	−0.603308	−	0.219586i
$950$	2.25660	+	12.7978i	0.0732138	+	0.415216i
$951$		0			0
$952$	−3.96388	−	0.0979946i	−0.128470	−	0.00317602i
$953$	34.8176	+	20.1019i	1.12785	+	0.651166i	0.943394	−	0.331675i	$-0.107614\pi$
$953$	34.8176	+	20.1019i	1.12785	+	0.651166i	0.184458	+	0.982840i	$0.440947\pi$
$954$		0			0
$955$			0.0117277i			0.000379499i
$956$	21.6218	+	3.81251i	0.699300	+	0.123305i
$957$		0			0
$958$	11.4888	+	13.6919i	0.371188	+	0.442364i
$959$	−19.9449	−	17.5938i	−0.644054	−	0.568133i
$960$		0			0
$961$	−26.2167	−	21.9984i	−0.845701	−	0.709627i
$962$	−2.82691			−0.0911432
$963$		0			0
$964$			35.1435i			1.13190i
$965$	0.00178439	−	0.0101198i	5.74415e−5	−	0.000325767i
$966$		0			0
$967$	−6.39685	−	2.32826i	−0.205709	−	0.0748719i	0.237111	−	0.971483i	$-0.423800\pi$
$967$	−6.39685	−	2.32826i	−0.205709	−	0.0748719i	−0.442820	+	0.896611i	$0.646022\pi$
$968$	13.7545	+	16.3920i	0.442087	+	0.526859i
$969$		0			0
$970$	0.000473766	0	0.000172437i	1.52117e−5	0	5.53661e-6i
$971$	14.6415	+	25.3599i	0.469869	+	0.813836i	0.999406	−	0.0344500i	$-0.0109679\pi$
$971$	14.6415	+	25.3599i	0.469869	+	0.813836i	−0.529538	+	0.848286i	$0.677635\pi$
$972$		0			0
$973$	−0.859463	+	0.685703i	−0.0275531	+	0.0219826i
$974$	11.2124	−	13.3624i	0.359269	−	0.428160i
$975$		0			0
$976$	−3.18995	+	8.76432i	−0.102108	+	0.280539i
$977$	5.03211	+	5.99703i	0.160991	+	0.191862i	0.840510	−	0.541796i	$-0.182256\pi$
$977$	5.03211	+	5.99703i	0.160991	+	0.191862i	−0.679518	+	0.733659i	$0.737811\pi$
$978$		0			0
$979$	15.0904	+	2.66085i	0.482291	+	0.0850410i
$980$	0.00505236	+	0.00468384i	0.000161392	+	0.000149620i
$981$		0			0
$982$	−2.71764	+	4.70709i	−0.0867233	+	0.150209i
$983$	1.04697	−	5.93768i	0.0333932	−	0.189382i	−0.963548	−	0.267535i	$-0.913791\pi$
$983$	1.04697	−	5.93768i	0.0333932	−	0.189382i	0.996941	+	0.0781524i	$0.0249021\pi$
$984$		0			0
$985$	0.00198176	−	0.00544485i	6.31442e−5	−	0.000173487i
$986$	−2.57475	+	2.16048i	−0.0819969	+	0.0688036i
$987$		0			0
$988$	23.5773	−	8.58143i	0.750093	−	0.273012i
$989$	9.35438	+	5.40075i	0.297452	+	0.171734i
$990$		0			0
$991$	−11.3468	−	19.6532i	−0.360442	−	0.624304i	0.627592	−	0.778543i	$-0.284041\pi$
$991$	−11.3468	−	19.6532i	−0.360442	−	0.624304i	−0.988034	+	0.154239i	$0.950707\pi$
$992$	−38.1519	+	13.8861i	−1.21132	+	0.440886i
$993$		0			0
$994$	−7.63947	+	8.66035i	−0.242309	+	0.274690i
$995$	−0.00618594	+	0.00109075i	−0.000196107	+	3.45790e-5i
$996$		0			0
$997$	3.33531	+	9.16369i	0.105630	+	0.290217i	0.981236	−	0.192809i	$-0.0617598\pi$
$997$	3.33531	+	9.16369i	0.105630	+	0.290217i	−0.875606	+	0.483026i	$0.839538\pi$
$998$	2.74449	+	1.58453i	0.0868752	+	0.0501574i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.ba.a.521.9		132
3.2	odd	2		189.2.ba.a.38.14	yes	132
7.5	odd	6		567.2.bd.a.278.14		132
21.5	even	6		189.2.bd.a.173.9	yes	132
27.5	odd	18		567.2.bd.a.206.14		132
27.22	even	9		189.2.bd.a.59.9	yes	132
189.5	even	18	inner	567.2.ba.a.530.9		132
189.103	odd	18		189.2.ba.a.5.14	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.5.14	✓	132	189.103	odd	18
189.2.ba.a.38.14	yes	132	3.2	odd	2
189.2.bd.a.59.9	yes	132	27.22	even	9
189.2.bd.a.173.9	yes	132	21.5	even	6
567.2.ba.a.521.9		132	1.1	even	1	trivial
567.2.ba.a.530.9		132	189.5	even	18	inner
567.2.bd.a.206.14		132	27.5	odd	18
567.2.bd.a.278.14		132	7.5	odd	6

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.ba (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.491776 - 0.0867134i) q^{2} +(-1.64506 - 0.598753i) q^{4} +(-9.76251e-5 - 0.000553660i) q^{5} +(-2.32328 + 1.26584i) q^{7} +(1.62200 + 0.936464i) q^{8} +0.000280742i q^{10} +(4.66356 + 0.822312i) q^{11} +(-1.77003 - 2.10944i) q^{13} +(1.25230 - 0.421052i) q^{14} +(1.96567 + 1.64940i) q^{16} +0.800172 q^{17} -5.20473i q^{19} +(-0.000170906 + 0.000969257i) q^{20} +(-2.22212 - 0.808787i) q^{22} +(-1.01988 - 1.21545i) q^{23} +(4.69846 - 1.71010i) q^{25} +(0.687542 + 1.19086i) q^{26} +(4.57987 - 0.691318i) q^{28} +(5.40692 - 6.44372i) q^{29} +(2.76219 - 7.58906i) q^{31} +(-3.23144 - 3.85108i) q^{32} +(-0.393506 - 0.0693856i) q^{34} +(0.000927658 + 0.00116273i) q^{35} +(-1.02790 + 1.78038i) q^{37} +(-0.451320 + 2.55956i) q^{38} +(0.000360134 - 0.000989460i) q^{40} +(-5.20305 + 4.36588i) q^{41} +(-6.39715 + 2.32837i) q^{43} +(-7.17948 - 4.14508i) q^{44} +(0.396159 + 0.686167i) q^{46} +(6.96860 - 2.53636i) q^{47} +(3.79528 - 5.88182i) q^{49} +(-2.45888 + 0.433567i) q^{50} +(1.64877 + 4.52997i) q^{52} +(9.11266 + 5.26120i) q^{53} -0.00266231i q^{55} +(-4.95379 - 0.122467i) q^{56} +(-3.21775 + 2.70001i) q^{58} +(10.1204 - 8.49198i) q^{59} +(1.24316 + 3.41555i) q^{61} +(-2.01645 + 3.49260i) q^{62} +(-1.31080 - 2.27037i) q^{64} +(-0.000995113 + 0.00118593i) q^{65} +(0.369304 + 2.09442i) q^{67} +(-1.31633 - 0.479105i) q^{68} +(-0.000355376 - 0.000652243i) q^{70} +(-7.56979 + 4.37042i) q^{71} +(6.22020 - 3.59123i) q^{73} +(0.659882 - 0.786416i) q^{74} +(-3.11635 + 8.56210i) q^{76} +(-11.8757 + 3.99288i) q^{77} +(0.447434 - 2.53753i) q^{79} +(0.000721305 - 0.00124934i) q^{80} +(2.93732 - 1.69586i) q^{82} +(1.47761 + 1.23986i) q^{83} +(-7.81169e-5 - 0.000443023i) q^{85} +(3.34787 - 0.590319i) q^{86} +(6.79425 + 5.70105i) q^{88} +3.23581 q^{89} +(6.78250 + 2.66024i) q^{91} +(0.950016 + 2.61015i) q^{92} +(-3.64693 + 0.643052i) q^{94} +(-0.00288165 + 0.000508113i) q^{95} +(-0.614218 - 1.68755i) q^{97} +(-2.37646 + 2.56344i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34}+ \cdots - 27 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

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