LMFDB - Embedded newform 567.2.ba.a.530.9

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			530.9
Character	$\chi$	$=$	567.530
Dual form			567.2.ba.a.521.9

$q$-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 $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{18}\right)$

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	−0.344790	−	0.938680i	$-0.612050\pi$
$2$	−0.491776	+	0.0867134i	−0.347738	+	0.0613156i	−0.00294872	+	0.999996i	$0.500939\pi$
$3$		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	−0.984830	−	0.173524i	$-0.944484\pi$
$5$	−9.76251e−5	0	0.000553660i	−4.36593e−5	0	0.000247604i	0.984786	+	0.173772i	$0.0555956\pi$
$6$		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	0.581463	−	0.813573i	$-0.302481\pi$
$11$	4.66356	−	0.822312i	1.40612	−	0.247936i	0.824654	+	0.565637i	$0.191370\pi$
$12$		0			0
$13$	−1.77003	+	2.10944i	−0.490918	+	0.585053i	−0.953451	−	0.301549i	$-0.902496\pi$
$13$	−1.77003	+	2.10944i	−0.490918	+	0.585053i	0.462533	+	0.886602i	$0.346941\pi$
$14$	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	$0.203650\pi$
$19$			5.20473i			1.19405i	−0.802224	+	0.597024i	$0.796350\pi$
$20$	−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	−0.861821	−	0.507213i	$-0.830676\pi$
$23$	−1.01988	+	1.21545i	−0.212661	+	0.253439i	0.649160	+	0.760651i	$0.275120\pi$
$24$		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	0.980434	+	0.196847i	$0.0630702\pi$
$29$	5.40692	+	6.44372i	1.00404	+	1.19657i	0.0236057	+	0.999721i	$0.492485\pi$
$30$		0			0
$31$	2.76219	+	7.58906i	0.496104	+	1.36304i	0.895011	+	0.446044i	$0.147167\pi$
$31$	2.76219	+	7.58906i	0.496104	+	1.36304i	−0.398907	+	0.916991i	$0.630610\pi$
$32$	−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	0.769077	−	0.639156i	$-0.220716\pi$
$37$	−1.02790	−	1.78038i	−0.168986	−	0.292693i	−0.938064	+	0.346463i	$0.887383\pi$
$38$	−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	0.138642	−	0.990343i	$-0.455726\pi$
$41$	−5.20305	−	4.36588i	−0.812580	−	0.681836i	−0.951222	+	0.308507i	$0.900171\pi$
$42$		0			0
$43$	−6.39715	−	2.32837i	−0.975556	−	0.355073i	−0.195445	−	0.980715i	$-0.562615\pi$
$43$	−6.39715	−	2.32837i	−0.975556	−	0.355073i	−0.780111	+	0.625641i	$0.784837\pi$
$44$	−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	0.795916	−	0.605407i	$-0.206990\pi$
$47$	6.96860	+	2.53636i	1.01647	+	0.369967i	0.220559	+	0.975374i	$0.429212\pi$
$48$		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	0.280269	−	0.959921i	$-0.409576\pi$
$53$	9.11266	−	5.26120i	1.25172	−	0.722681i	0.971451	+	0.237241i	$0.0762430\pi$
$54$		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	0.986817	+	0.161840i	$0.0517429\pi$
$59$	10.1204	+	8.49198i	1.31756	+	1.10556i	0.330740	+	0.943722i	$0.392702\pi$
$60$		0			0
$61$	1.24316	−	3.41555i	0.159170	−	0.437317i	−0.834314	−	0.551290i	$-0.814136\pi$
$61$	1.24316	−	3.41555i	0.159170	−	0.437317i	0.993484	+	0.113974i	$0.0363579\pi$
$62$	−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	−0.953903	−	0.300114i	$-0.902975\pi$
$67$	0.369304	−	2.09442i	0.0451176	−	0.255875i	0.999021	+	0.0442393i	$0.0140864\pi$
$68$	−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	−0.0216981	−	0.999765i	$-0.506907\pi$
$71$	−7.56979	−	4.37042i	−0.898369	−	0.518673i	−0.876671	+	0.481091i	$0.840241\pi$
$72$		0			0
$73$	6.22020	+	3.59123i	0.728019	+	0.420322i	0.817697	−	0.575649i	$-0.195250\pi$
$73$	6.22020	+	3.59123i	0.728019	+	0.420322i	−0.0896781	+	0.995971i	$0.528584\pi$
$74$	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	0.999577	−	0.0290673i	$-0.00925372\pi$
$79$	0.447434	+	2.53753i	0.0503403	+	0.285494i	−0.949237	+	0.314561i	$0.898143\pi$
$80$	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	−0.558082	−	0.829786i	$-0.688462\pi$
$83$	1.47761	−	1.23986i	0.162188	−	0.136092i	0.720270	+	0.693694i	$0.244018\pi$
$84$		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	−0.966961	−	0.254923i	$-0.917950\pi$
$97$	−0.614218	+	1.68755i	−0.0623644	+	0.171345i	0.904597	+	0.426268i	$0.140172\pi$
$98$	−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	−0.465855	−	0.884861i	$-0.654253\pi$
$101$	3.26288	−	2.73788i	0.324668	−	0.272429i	0.790523	+	0.612432i	$0.209809\pi$
$102$		0			0
$103$	−15.8365	−	2.79240i	−1.56041	−	0.275143i	−0.674245	−	0.738508i	$-0.735531\pi$
$103$	−15.8365	−	2.79240i	−1.56041	−	0.275143i	−0.886168	+	0.463365i	$0.846642\pi$
$104$	−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	0.321853	−	0.946790i	$-0.395694\pi$
$107$	−3.48765	−	2.01360i	−0.337164	−	0.194662i	−0.659017	+	0.752128i	$0.729028\pi$
$108$		0			0
$109$	0.587845	+	1.01818i	0.0563054	+	0.0975238i	0.892804	−	0.450445i	$-0.148735\pi$
$109$	0.587845	+	1.01818i	0.0563054	+	0.0975238i	−0.836499	+	0.547969i	$0.815401\pi$
$110$	−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	0.914166	+	0.405340i	$0.132847\pi$
$113$	5.04317	+	13.8560i	0.474422	+	1.30346i	−0.439745	+	0.898123i	$0.644931\pi$
$114$		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	0.670142	−	0.742233i	$-0.266233\pi$
$127$	−3.46785	−	6.00649i	−0.307722	−	0.532990i	−0.977864	+	0.209243i	$0.932900\pi$
$128$	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	0.193287	−	0.981142i	$-0.438085\pi$
$131$	−8.46265	−	7.10101i	−0.739385	−	0.620418i	−0.932672	+	0.360724i	$0.882530\pi$
$132$		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	−0.701777	−	0.712397i	$-0.747610\pi$
$137$	3.43808	−	9.44606i	0.293735	−	0.807031i	0.995512	−	0.0946343i	$-0.0301682\pi$
$138$		0			0
$139$	0.409252	+	0.0721623i	0.0347123	+	0.00612072i	0.190977	−	0.981594i	$-0.438834\pi$
$139$	0.409252	+	0.0721623i	0.0347123	+	0.00612072i	−0.156265	+	0.987715i	$0.549945\pi$
$140$	−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	0.926119	−	0.377231i	$-0.123124\pi$
$149$	−0.315032	−	0.865543i	−0.0258084	−	0.0709081i	−0.951928	+	0.306323i	$0.900901\pi$
$150$		0			0
$151$	−0.209027	−	1.18545i	−0.0170104	−	0.0964707i	0.975121	−	0.221675i	$-0.0711524\pi$
$151$	−0.209027	−	1.18545i	−0.0170104	−	0.0964707i	−0.992131	+	0.125204i	$0.960041\pi$
$152$	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	−0.975828	−	0.218540i	$-0.929871\pi$
$157$	−7.40718	+	8.82753i	−0.591157	+	0.704514i	0.384671	+	0.923054i	$0.374315\pi$
$158$	−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	−0.968372	−	0.249510i	$-0.919730\pi$
$163$	−3.42292	+	5.92867i	−0.268104	+	0.464369i	0.700268	+	0.713880i	$0.253064\pi$
$164$	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	−0.505073	−	0.863076i	$-0.668535\pi$
$167$	−4.35768	+	1.58606i	−0.337207	+	0.122733i	0.167866	+	0.985810i	$0.446312\pi$
$168$		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	−0.440838	+	0.897587i	$0.645319\pi$
$173$	−18.4317	+	15.4661i	−1.40134	+	1.17586i	−0.960501	+	0.278276i	$0.910237\pi$
$174$		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	$-0.626653\pi$
$179$		−	24.6678i		−	1.84376i	0.387475	−	0.921880i	$-0.373347\pi$
$180$		0			0
$181$	7.78429	−	4.49426i	0.578601	−	0.334056i	−0.181976	−	0.983303i	$-0.558249\pi$
$181$	7.78429	−	4.49426i	0.578601	−	0.334056i	0.760577	+	0.649247i	$0.224916\pi$
$182$	−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	−0.857159	−	0.515051i	$-0.827773\pi$
$191$	−20.5434	+	3.62235i	−1.48647	+	0.262104i	−0.629308	+	0.777156i	$0.716662\pi$
$192$		0			0
$193$	17.1757	−	6.25143i	1.23633	−	0.449988i	0.360571	−	0.932732i	$-0.382582\pi$
$193$	17.1757	−	6.25143i	1.23633	−	0.449988i	0.875762	+	0.482744i	$0.160360\pi$
$194$	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	−0.147118	−	0.989119i	$-0.547000\pi$
$197$	8.92564	−	5.15322i	0.635925	−	0.367152i	0.783043	+	0.621967i	$0.213666\pi$
$198$		0			0
$199$			11.1728i			0.792020i	0.918246	+	0.396010i	$0.129605\pi$
$199$			11.1728i			0.792020i	−0.918246	+	0.396010i	$0.870395\pi$
$200$	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	0.571302	−	0.820740i	$-0.306439\pi$
$211$	22.3190	−	8.12346i	1.53651	−	0.559242i	0.965204	+	0.261498i	$0.0842165\pi$
$212$	−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	−0.898924	−	0.438105i	$-0.855650\pi$
$223$	−23.8004	+	4.19666i	−1.59380	+	0.281029i	−0.694871	+	0.719134i	$0.744539\pi$
$224$	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	0.950174	−	0.311719i	$-0.100905\pi$
$227$	−0.742956	−	4.21351i	−0.0493117	−	0.279661i	−0.999486	+	0.0320585i	$0.989794\pi$
$228$		0			0
$229$	4.43062	+	12.1730i	0.292784	+	0.804417i	0.995657	+	0.0931013i	$0.0296780\pi$
$229$	4.43062	+	12.1730i	0.292784	+	0.804417i	−0.702873	+	0.711315i	$0.748100\pi$
$230$	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	−0.147251	−	0.989099i	$-0.547043\pi$
$233$	9.70366	−	5.60241i	0.635708	−	0.367026i	0.782959	+	0.622073i	$0.213709\pi$
$234$		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	−0.240733	−	0.970591i	$-0.577388\pi$
$239$	−12.3508	−	2.17779i	−0.798909	−	0.140869i	−0.558177	+	0.829722i	$0.688499\pi$
$240$		0			0
$241$	−6.86595	+	18.8641i	−0.442275	+	1.21514i	0.495717	+	0.868484i	$0.334905\pi$
$241$	−6.86595	+	18.8641i	−0.442275	+	1.21514i	−0.937992	+	0.346656i	$0.887317\pi$
$242$	−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	0.964276	+	0.264899i	$0.0853386\pi$
$251$	11.2730	+	19.5255i	0.711547	+	1.23244i	−0.252729	+	0.967537i	$0.581328\pi$
$252$		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	0.724537	−	0.689236i	$-0.242054\pi$
$257$	27.6153	−	10.0512i	1.72260	−	0.626974i	0.998060	+	0.0622616i	$0.0198313\pi$
$258$		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	0.988013	−	0.154371i	$-0.0493352\pi$
$263$	10.7751	+	12.8412i	0.664420	+	0.791825i	−0.323593	+	0.946197i	$0.604891\pi$
$264$		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	0.973238	−	0.229799i	$-0.0738069\pi$
$269$	4.71711	+	8.17027i	0.287607	+	0.498150i	−0.685631	+	0.727949i	$0.740474\pi$
$270$		0			0
$271$	−3.40065	−	1.96337i	−0.206575	−	0.119266i	0.393144	−	0.919477i	$-0.371388\pi$
$271$	−3.40065	−	1.96337i	−0.206575	−	0.119266i	−0.599719	+	0.800211i	$0.704721\pi$
$272$	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	−0.993706	−	0.112018i	$-0.964269\pi$
$277$	−17.5744	+	14.7467i	−1.05595	+	0.886043i	−0.0622389	+	0.998061i	$0.519824\pi$
$278$	−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	−0.956528	−	0.291639i	$-0.905799\pi$
$281$	−0.608889	+	1.67291i	−0.0363233	+	0.0997974i	0.920205	+	0.391436i	$0.128022\pi$
$282$		0			0
$283$	−4.38907	−	0.773911i	−0.260903	−	0.0460042i	0.0416665	−	0.999132i	$-0.486733\pi$
$283$	−4.38907	−	0.773911i	−0.260903	−	0.0460042i	−0.302569	+	0.953127i	$0.597844\pi$
$284$	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	0.927443	+	0.373965i	$0.122002\pi$
$293$	−1.23196	+	6.98681i	−0.0719721	+	0.408174i	−0.999415	+	0.0342085i	$0.989109\pi$
$294$		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	0.312313	−	0.949979i	$-0.398896\pi$
$307$	−6.20672	−	3.58345i	−0.354236	−	0.204518i	−0.666549	+	0.745461i	$0.732229\pi$
$308$	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	−0.626122	−	0.779725i	$-0.715359\pi$
$311$	4.03708	−	22.8954i	0.228922	−	1.29828i	0.855044	−	0.518556i	$-0.173530\pi$
$312$		0			0
$313$	15.3541	+	18.2983i	0.867863	+	1.03428i	0.999078	+	0.0429247i	$0.0136676\pi$
$313$	15.3541	+	18.2983i	0.867863	+	1.03428i	−0.131216	+	0.991354i	$0.541888\pi$
$314$	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	−0.279574	−	0.960124i	$-0.590193\pi$
$317$	9.82360	−	26.9901i	0.551748	−	1.51592i	0.831322	−	0.555791i	$-0.187585\pi$
$318$		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	0.910784	−	0.412884i	$-0.135478\pi$
$331$	24.4353	+	8.89374i	1.34309	+	0.488844i	0.432304	+	0.901728i	$0.357701\pi$
$332$	−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	0.775817	−	0.630958i	$-0.217338\pi$
$337$	5.30836	+	4.45424i	0.289165	+	0.242638i	−0.486653	+	0.873596i	$0.661782\pi$
$338$	−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	0.953364	−	0.301823i	$-0.0975950\pi$
$347$	0.540900	+	1.48611i	0.0290370	+	0.0797786i	−0.924327	+	0.381601i	$0.875373\pi$
$348$		0			0
$349$	−11.3433	−	13.5184i	−0.607194	−	0.723626i	0.371618	−	0.928386i	$-0.378803\pi$
$349$	−11.3433	−	13.5184i	−0.607194	−	0.723626i	−0.978812	+	0.204760i	$0.934359\pi$
$350$	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	0.409182	−	0.912453i	$-0.365814\pi$
$353$	2.55746	+	0.930839i	0.136120	+	0.0495435i	−0.273062	+	0.961996i	$0.588036\pi$
$354$		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	$0.206301\pi$
$359$			22.8763i			1.20737i	−0.797224	+	0.603683i	$0.793699\pi$
$360$		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	0.0195487	−	0.999809i	$-0.493777\pi$
$367$	7.27732	−	1.28319i	0.379873	−	0.0669819i	0.360325	+	0.932827i	$0.382666\pi$
$368$			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	−0.390798	−	0.920477i	$-0.627801\pi$
$373$	5.62504	−	31.9012i	0.291254	−	1.65178i	0.682051	−	0.731304i	$-0.261088\pi$
$374$	−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	−0.986041	−	0.166500i	$-0.946753\pi$
$383$	−0.0493036	+	0.279615i	−0.00251930	+	0.0142876i	0.983522	+	0.180787i	$0.0578646\pi$
$384$		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	−0.155024	−	0.987911i	$-0.549545\pi$
$389$	0.733433	−	0.129324i	0.0371865	−	0.00655699i	0.192211	+	0.981354i	$0.438434\pi$
$390$		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	$0.137899\pi$
$397$			16.7288i			0.839593i	−0.907618	+	0.419797i	$0.862101\pi$
$398$	−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	−0.383023	−	0.923739i	$-0.625117\pi$
$401$	11.8787	−	14.1565i	0.593194	−	0.706941i	0.976216	+	0.216798i	$0.0695613\pi$
$402$		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	−0.994253	−	0.107052i	$-0.965859\pi$
$409$	−6.09589	−	16.7483i	−0.301423	−	0.828152i	0.692831	−	0.721100i	$-0.256363\pi$
$410$	−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	0.622715	−	0.782449i	$-0.286030\pi$
$419$	−0.812929	−	0.682129i	−0.0397142	−	0.0333242i	−0.662429	+	0.749125i	$0.730474\pi$
$420$		0			0
$421$	−14.4175	−	5.24755i	−0.702667	−	0.255750i	−0.0341181	−	0.999418i	$-0.510862\pi$
$421$	−14.4175	−	5.24755i	−0.702667	−	0.255750i	−0.668549	+	0.743668i	$0.733084\pi$
$422$	−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	−0.418479	−	0.908226i	$-0.637437\pi$
$431$	3.29736	−	1.90373i	0.158828	−	0.0916996i	0.577308	+	0.816527i	$0.304103\pi$
$432$		0			0
$433$		−	29.5261i		−	1.41893i	−0.704739	−	0.709467i	$-0.748936\pi$
$433$		−	29.5261i		−	1.41893i	0.704739	−	0.709467i	$-0.251064\pi$
$434$	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	−0.728974	−	0.684541i	$-0.760003\pi$
$439$	5.64596	−	15.5122i	0.269467	−	0.740355i	0.998441	−	0.0558134i	$-0.0177752\pi$
$440$	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	−0.999622	−	0.0275061i	$-0.991243\pi$
$443$	−17.9563	−	21.3994i	−0.853127	−	1.01672i	0.146494	−	0.989212i	$-0.453201\pi$
$444$		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	−0.0567572	−	0.998388i	$-0.518076\pi$
$449$	−20.1252	−	11.6193i	−0.949765	−	0.548347i	−0.893008	+	0.450041i	$0.851409\pi$
$450$		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	0.965551	+	0.260215i	$0.0837936\pi$
$457$	3.14739	+	17.8497i	0.147229	+	0.834976i	−0.818322	+	0.574760i	$0.805095\pi$
$458$	−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	−0.624429	−	0.781081i	$-0.714668\pi$
$461$	0.780576	−	0.654981i	0.0363550	−	0.0305055i	0.660784	+	0.750576i	$0.270224\pi$
$462$		0			0
$463$	5.96496	−	33.8290i	0.277215	−	1.57216i	−0.454621	−	0.890685i	$-0.650225\pi$
$463$	5.96496	−	33.8290i	0.277215	−	1.57216i	0.731837	−	0.681480i	$-0.238663\pi$
$464$	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	−0.256381	+	0.966576i	$0.582530\pi$
$479$	−27.4187	+	23.0070i	−1.25279	+	1.05122i	−0.996411	+	0.0846415i	$0.973026\pi$
$480$		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	−0.925071	−	0.379793i	$-0.875995\pi$
$487$	−17.4657	−	30.2515i	−0.791446	−	1.37082i	0.133625	−	0.991032i	$-0.457338\pi$
$488$	−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	0.994912	−	0.100752i	$-0.0321249\pi$
$491$	3.72269	+	10.2280i	0.168003	+	0.461584i	−0.826909	+	0.562336i	$0.809903\pi$
$492$		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	−0.472033	−	0.881581i	$-0.656480\pi$
$499$	−5.96349	+	2.17053i	−0.266962	+	0.0971663i	0.205071	+	0.978747i	$0.434258\pi$
$500$	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	−0.676275	−	0.736649i	$-0.736407\pi$
$503$	6.72425	−	11.6468i	0.299820	−	0.519303i	0.976095	+	0.217346i	$0.0697401\pi$
$504$		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	0.300350	−	0.953829i	$-0.402896\pi$
$509$	−13.2396	−	11.1093i	−0.586833	−	0.492411i	−0.887183	+	0.461418i	$0.847341\pi$
$510$		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	−0.362881	−	0.931835i	$-0.618207\pi$
$521$	14.2785	−	24.7311i	0.625553	−	1.08349i	0.988434	−	0.151653i	$-0.0484597\pi$
$522$		0			0
$523$	−13.1449	+	7.58924i	−0.574788	+	0.331854i	−0.759059	−	0.651021i	$-0.774341\pi$
$523$	−13.1449	+	7.58924i	−0.574788	+	0.331854i	0.184271	+	0.982875i	$0.441008\pi$
$524$	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	−0.610980	−	0.791646i	$-0.709224\pi$
$541$	8.84080	−	15.3127i	0.380096	−	0.658345i	0.991076	+	0.133301i	$0.0425577\pi$
$542$	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	0.946855	−	0.321660i	$-0.104241\pi$
$547$	−1.23750	−	7.01822i	−0.0529117	−	0.300077i	−0.999767	+	0.0215823i	$0.993130\pi$
$548$			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	$0.0518074\pi$
$557$			7.64857i			0.324080i	−0.986784	+	0.162040i	$0.948193\pi$
$558$		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	−0.937733	−	0.347356i	$-0.887080\pi$
$563$	−33.9970	+	12.3739i	−1.43280	+	0.521498i	−0.495070	+	0.868853i	$0.664857\pi$
$564$		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	−0.0623521	−	0.998054i	$-0.519860\pi$
$569$	5.25761	−	0.927059i	0.220411	−	0.0388643i	0.282763	+	0.959190i	$0.408749\pi$
$570$		0			0
$571$	−34.9232	+	12.7110i	−1.46149	+	0.531939i	−0.945775	−	0.324822i	$-0.894696\pi$
$571$	−34.9232	+	12.7110i	−1.46149	+	0.531939i	−0.515715	+	0.856760i	$0.672473\pi$
$572$	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	$-0.823020\pi$
$577$		−	25.3559i		−	1.05558i	0.849374	−	0.527791i	$-0.176980\pi$
$578$	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	−0.985312	−	0.170762i	$-0.945377\pi$
$587$	−2.85469	−	16.1897i	−0.117826	−	0.668222i	0.867487	−	0.497460i	$-0.165734\pi$
$588$		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	−0.358569	−	0.933503i	$-0.616735\pi$
$593$	15.3209	−	26.5365i	0.629153	−	1.08973i	0.987722	−	0.156222i	$-0.0499315\pi$
$594$		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	−0.958954	−	0.283561i	$-0.908484\pi$
$599$	−12.5598	+	14.9682i	−0.513181	+	0.611585i	0.445773	+	0.895146i	$0.352929\pi$
$600$		0			0
$601$	−20.6262	+	3.63695i	−0.841360	+	0.148354i	−0.577688	−	0.816258i	$-0.696045\pi$
$601$	−20.6262	+	3.63695i	−0.841360	+	0.148354i	−0.263672	+	0.964612i	$0.584934\pi$
$602$	−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	−0.973590	−	0.228302i	$-0.926683\pi$
$607$	−9.22736	−	25.3520i	−0.374527	−	1.02900i	0.599063	−	0.800702i	$-0.295540\pi$
$608$	−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	−0.455366	−	0.890304i	$-0.650492\pi$
$613$	13.4525	−	23.3005i	0.543343	−	0.941097i	0.998709	−	0.0507931i	$-0.0161749\pi$
$614$	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	0.600995	−	0.799253i	$-0.294771\pi$
$617$	22.1664	+	3.90853i	0.892386	+	0.157352i	0.291390	+	0.956604i	$0.405882\pi$
$618$		0			0
$619$	3.67268	−	10.0906i	0.147617	−	0.405575i	−0.843742	−	0.536749i	$-0.819652\pi$
$619$	3.67268	−	10.0906i	0.147617	−	0.405575i	0.991359	+	0.131173i	$0.0418745\pi$
$620$	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	−0.868619	−	0.495481i	$-0.834992\pi$
$631$	−0.130873	+	0.226679i	−0.00520998	+	0.00902394i	0.863409	+	0.504505i	$0.168325\pi$
$632$	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	0.756166	+	0.654380i	$0.227070\pi$
$641$	32.1360	+	38.2982i	1.26930	+	1.51269i	0.513131	+	0.858310i	$0.328485\pi$
$642$		0			0
$643$	5.42130	+	14.8949i	0.213795	+	0.587397i	0.999514	−	0.0311869i	$-0.00992871\pi$
$643$	5.42130	+	14.8949i	0.213795	+	0.587397i	−0.785718	+	0.618584i	$0.787706\pi$
$644$	−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	0.679565	−	0.733615i	$-0.262169\pi$
$647$	−7.51759	−	13.0208i	−0.295547	−	0.511902i	−0.975112	+	0.221713i	$0.928835\pi$
$648$		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	−0.130912	−	0.991394i	$-0.541791\pi$
$653$	−15.1536	−	2.67199i	−0.593007	−	0.104563i	−0.462094	+	0.886831i	$0.652902\pi$
$654$		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	−0.782245	−	0.622971i	$-0.785926\pi$
$659$	5.58157	−	15.3352i	0.217427	−	0.597376i	0.999672	+	0.0255942i	$0.00814779\pi$
$660$		0			0
$661$	29.6565	+	5.22925i	1.15351	+	0.203394i	0.717506	−	0.696553i	$-0.245284\pi$
$661$	29.6565	+	5.22925i	1.15351	+	0.203394i	0.436000	+	0.899947i	$0.356395\pi$
$662$	−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	−0.463801	−	0.885939i	$-0.653515\pi$
$673$	8.51271	−	7.14301i	0.328141	−	0.275343i	0.791942	+	0.610597i	$0.209070\pi$
$674$	−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	−0.893494	−	0.449075i	$-0.851754\pi$
$677$	−5.39839	−	30.6158i	−0.207477	−	1.17666i	0.686017	−	0.727585i	$-0.259357\pi$
$678$		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	0.129490	−	0.991581i	$-0.458666\pi$
$683$	−17.3662	−	10.0264i	−0.664500	−	0.383649i	−0.793989	+	0.607932i	$0.791999\pi$
$684$		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	0.697106	−	0.716968i	$-0.254471\pi$
$691$	−3.41783	−	4.07321i	−0.130020	−	0.154952i	−0.827127	+	0.562016i	$0.810026\pi$
$692$	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	$0.0977973\pi$
$701$			16.0144i			0.604857i	−0.953172	+	0.302428i	$0.902203\pi$
$702$		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	0.337706	−	0.941252i	$-0.390349\pi$
$709$	−0.229579	−	0.0835600i	−0.00862202	−	0.00313816i	−0.346328	+	0.938114i	$0.612571\pi$
$710$	−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	0.981201	+	0.192989i	$0.0618182\pi$
$719$	17.6366	+	30.5475i	0.657734	+	1.13923i	−0.323467	+	0.946239i	$0.604848\pi$
$720$		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	0.959098	+	0.283075i	$0.0913546\pi$
$727$	28.8861	+	34.4251i	1.07133	+	1.27676i	0.112229	+	0.993682i	$0.464201\pi$
$728$	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	−0.0663525	+	0.997796i	$0.521136\pi$
$733$	−28.0884	+	33.4744i	−1.03747	+	1.23641i	−0.971115	+	0.238610i	$0.923308\pi$
$734$	−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	−0.960868	−	0.277007i	$-0.910657\pi$
$743$	−14.2073	+	16.9316i	−0.521216	+	0.621161i	0.439652	+	0.898168i	$0.355102\pi$
$744$		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	−0.500229	−	0.865893i	$-0.666751\pi$
$751$	7.28917	−	41.3389i	0.265985	−	1.50848i	0.766214	−	0.642585i	$-0.222138\pi$
$752$	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	−0.684877	−	0.728659i	$-0.740144\pi$
$761$	5.73553	−	32.5278i	0.207913	−	1.17913i	0.892790	−	0.450474i	$-0.148745\pi$
$762$		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	−0.993852	−	0.110713i	$-0.964687\pi$
$769$	−19.7511	+	23.5384i	−0.712241	+	0.848816i	0.281611	+	0.959529i	$0.409131\pi$
$770$	−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	−0.785171	−	0.619279i	$-0.787425\pi$
$787$	−16.3204	−	44.8400i	−0.581760	−	1.59837i	0.203411	−	0.979093i	$-0.434797\pi$
$788$	−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	0.992602	−	0.121413i	$-0.0387426\pi$
$797$	29.5128	+	24.7642i	1.04540	+	0.877192i	0.0527949	+	0.998605i	$0.483187\pi$
$798$		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	0.313775	−	0.949497i	$-0.398406\pi$
$809$	36.7753	−	21.2322i	1.29295	−	0.746486i	0.979176	+	0.203011i	$0.0650728\pi$
$810$		0			0
$811$			22.9043i			0.804277i	0.915579	+	0.402139i	$0.131733\pi$
$811$			22.9043i			0.804277i	−0.915579	+	0.402139i	$0.868267\pi$
$812$	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	0.742472	−	0.669878i	$-0.233653\pi$
$821$	−1.32257	−	1.57617i	−0.0461579	−	0.0550089i	−0.788629	+	0.614869i	$0.789209\pi$
$822$		0			0
$823$	0.562875	−	3.19222i	0.0196206	−	0.111274i	−0.973425	−	0.229008i	$-0.926452\pi$
$823$	0.562875	−	3.19222i	0.0196206	−	0.111274i	0.993045	+	0.117734i	$0.0375630\pi$
$824$	−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	−0.982251	−	0.187574i	$-0.939938\pi$
$827$	−47.0423	−	27.1599i	−1.63582	−	0.944441i	−0.653569	−	0.756867i	$-0.726729\pi$
$828$		0			0
$829$	−7.34388	−	4.23999i	−0.255063	−	0.147261i	0.367017	−	0.930214i	$-0.380379\pi$
$829$	−7.34388	−	4.23999i	−0.255063	−	0.147261i	−0.622081	+	0.782953i	$0.713712\pi$
$830$	−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	−0.421002	−	0.907060i	$-0.638321\pi$
$839$	11.5622	−	9.70185i	0.399172	−	0.334945i	0.820173	+	0.572115i	$0.193877\pi$
$840$		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	−0.817283	−	0.576236i	$-0.804521\pi$
$853$	5.23344	−	14.3788i	0.179190	−	0.492319i	0.996473	+	0.0839170i	$0.0267430\pi$
$854$	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	−0.383580	−	0.923507i	$-0.625309\pi$
$857$	13.4455	−	11.2821i	0.459289	−	0.385389i	0.842869	+	0.538118i	$0.180865\pi$
$858$		0			0
$859$	−15.6157	−	2.75347i	−0.532801	−	0.0939472i	−0.0992264	−	0.995065i	$-0.531637\pi$
$859$	−15.6157	−	2.75347i	−0.532801	−	0.0939472i	−0.433575	+	0.901118i	$0.642748\pi$
$860$	−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	0.529730	−	0.848166i	$-0.322293\pi$
$863$	1.76440	+	1.01868i	0.0600610	+	0.0346762i	−0.469669	+	0.882843i	$0.655627\pi$
$864$		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	−0.0369427	−	0.999317i	$-0.511762\pi$
$877$	17.0905	−	6.22045i	0.577106	−	0.210050i	0.614049	+	0.789268i	$0.289540\pi$
$878$	−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	−0.547889	−	0.836551i	$-0.684568\pi$
$881$	13.3725	−	23.1618i	0.450530	−	0.780341i	0.998419	+	0.0562101i	$0.0179017\pi$
$882$		0			0
$883$	10.5208	+	18.2226i	0.354054	+	0.613240i	0.986956	−	0.160992i	$-0.0514694\pi$
$883$	10.5208	+	18.2226i	0.354054	+	0.613240i	−0.632901	+	0.774232i	$0.718136\pi$
$884$	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	0.882564	−	0.470192i	$-0.155815\pi$
$887$	17.0586	+	14.3138i	0.572771	+	0.480612i	−0.309793	+	0.950804i	$0.600260\pi$
$888$		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	0.993418	−	0.114543i	$-0.0365404\pi$
$907$	0.624448	+	3.54142i	0.0207345	+	0.117591i	−0.972684	+	0.232134i	$0.925429\pi$
$908$	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	0.774585	−	0.632470i	$-0.217959\pi$
$911$	51.8774	−	9.14738i	1.71877	−	0.303066i	0.944189	+	0.329403i	$0.106848\pi$
$912$		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	−0.0716603	+	0.997429i	$0.522830\pi$
$919$	−27.2723	+	47.2370i	−0.899629	+	1.55820i	−0.827969	+	0.560774i	$0.810504\pi$
$920$	−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	0.0598303	−	0.998209i	$-0.480944\pi$
$929$	32.1029	−	26.9376i	1.05326	−	0.883793i	0.993433	+	0.114416i	$0.0364996\pi$
$930$		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	−0.844083	−	0.536212i	$-0.819855\pi$
$937$	−24.5420	+	14.1693i	−0.801751	+	0.462891i	0.0423320	+	0.999104i	$0.486521\pi$
$938$	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	−0.0811321	−	0.996703i	$-0.525854\pi$
$941$	15.2577	−	5.55334i	0.497386	−	0.181034i	0.578518	+	0.815670i	$0.303631\pi$
$942$		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	−0.328440	−	0.944525i	$-0.606523\pi$
$947$	−9.66361	+	1.70396i	−0.314025	+	0.0553711i	0.0144143	+	0.999896i	$0.495412\pi$
$948$		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	0.184458	−	0.982840i	$-0.440947\pi$
$953$	34.8176	−	20.1019i	1.12785	−	0.651166i	0.943394	+	0.331675i	$0.107614\pi$
$954$		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	−0.442820	−	0.896611i	$-0.646022\pi$
$967$	−6.39685	+	2.32826i	−0.205709	+	0.0748719i	0.237111	+	0.971483i	$0.423800\pi$
$968$	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	−0.529538	−	0.848286i	$-0.677635\pi$
$971$	14.6415	−	25.3599i	0.469869	−	0.813836i	0.999406	+	0.0344500i	$0.0109679\pi$
$972$		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	−0.679518	−	0.733659i	$-0.737811\pi$
$977$	5.03211	−	5.99703i	0.160991	−	0.191862i	0.840510	+	0.541796i	$0.182256\pi$
$978$		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	0.996941	−	0.0781524i	$-0.0249021\pi$
$983$	1.04697	+	5.93768i	0.0333932	+	0.189382i	−0.963548	+	0.267535i	$0.913791\pi$
$984$		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	−0.988034	−	0.154239i	$-0.950707\pi$
$991$	−11.3468	+	19.6532i	−0.360442	+	0.624304i	0.627592	+	0.778543i	$0.284041\pi$
$992$	−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	−0.875606	−	0.483026i	$-0.839538\pi$
$997$	3.33531	−	9.16369i	0.105630	−	0.290217i	0.981236	+	0.192809i	$0.0617598\pi$
$998$	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.530.9		132
3.2	odd	2		189.2.ba.a.5.14	✓	132
7.3	odd	6		567.2.bd.a.206.14		132
21.17	even	6		189.2.bd.a.59.9	yes	132
27.11	odd	18		567.2.bd.a.278.14		132
27.16	even	9		189.2.bd.a.173.9	yes	132
189.38	even	18	inner	567.2.ba.a.521.9		132
189.178	odd	18		189.2.ba.a.38.14	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.5.14	✓	132	3.2	odd	2
189.2.ba.a.38.14	yes	132	189.178	odd	18
189.2.bd.a.59.9	yes	132	21.17	even	6
189.2.bd.a.173.9	yes	132	27.16	even	9
567.2.ba.a.521.9		132	189.38	even	18	inner
567.2.ba.a.530.9		132	1.1	even	1	trivial
567.2.bd.a.206.14		132	7.3	odd	6
567.2.bd.a.278.14		132	27.11	odd	18

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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