LMFDB - Embedded newform 567.2.w.a.37.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(37,567)]

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([14, 6]))

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

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

chi := DirichletCharacter("567.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.w (of order $9$, 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 $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			37.4
Character	$\chi$	$=$	567.37
Dual form			567.2.w.a.46.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.351787 - 1.99508i) q^{2} +(-1.97722 + 0.719650i) q^{4} +(-0.155052 + 0.879341i) q^{5} +(-1.72949 + 2.00222i) q^{7} +(0.105462 + 0.182666i) q^{8} +1.80890 q^{10} +(0.545772 + 3.09523i) q^{11} +(3.46133 + 2.90440i) q^{13} +(4.60300 + 2.74612i) q^{14} +(-2.89636 + 2.43033i) q^{16} -5.74615 q^{17} +1.22738 q^{19} +(-0.326246 - 1.85024i) q^{20} +(5.98324 - 2.17772i) q^{22} +(4.25634 + 3.57150i) q^{23} +(3.94926 + 1.43741i) q^{25} +(4.57688 - 7.92738i) q^{26} +(1.97869 - 5.20345i) q^{28} +(0.0345809 - 0.0290169i) q^{29} +(0.226384 - 0.0823972i) q^{31} +(6.19078 + 5.19468i) q^{32} +(2.02142 + 11.4640i) q^{34} +(-1.49247 - 1.83126i) q^{35} +(5.13755 + 8.89849i) q^{37} +(-0.431777 - 2.44873i) q^{38} +(-0.176978 + 0.0644148i) q^{40} +(-3.74834 - 3.14523i) q^{41} +(-6.92531 - 2.52060i) q^{43} +(-3.30659 - 5.72718i) q^{44} +(5.62811 - 9.74817i) q^{46} +(-5.21418 - 1.89781i) q^{47} +(-1.01774 - 6.92562i) q^{49} +(1.47846 - 8.38478i) q^{50} +(-8.93398 - 3.25170i) q^{52} +(3.82297 + 6.62158i) q^{53} -2.80638 q^{55} +(-0.548134 - 0.104761i) q^{56} +(-0.0700562 - 0.0587841i) q^{58} +(2.88652 + 2.42208i) q^{59} +(-0.765603 - 0.278657i) q^{61} +(-0.244029 - 0.422670i) q^{62} +(4.40506 - 7.62979i) q^{64} +(-3.09065 + 2.59336i) q^{65} +(0.114256 - 0.647980i) q^{67} +(11.3614 - 4.13522i) q^{68} +(-3.12848 + 3.62182i) q^{70} +(-3.75882 + 6.51047i) q^{71} +(4.87293 - 8.44017i) q^{73} +(15.9459 - 13.3802i) q^{74} +(-2.42681 + 0.883285i) q^{76} +(-7.14122 - 4.26040i) q^{77} +(-2.29784 - 13.0317i) q^{79} +(-1.68801 - 2.92371i) q^{80} +(-4.95638 + 8.58471i) q^{82} +(-4.92372 + 4.13150i) q^{83} +(0.890949 - 5.05282i) q^{85} +(-2.59259 + 14.7033i) q^{86} +(-0.507835 + 0.426124i) q^{88} +12.6111 q^{89} +(-11.8016 + 1.90720i) q^{91} +(-10.9860 - 3.99856i) q^{92} +(-1.95200 + 11.0704i) q^{94} +(-0.190307 + 1.07929i) q^{95} +(-11.8862 - 4.32622i) q^{97} +(-13.4592 + 4.46682i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} - 6 q^{10} - 3 q^{11} - 12 q^{13} - 15 q^{14} - 9 q^{16} + 54 q^{17} - 6 q^{19} + 18 q^{20} - 12 q^{22} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29}+ \cdots - 99 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8 - 6 * q^10 - 3 * q^11 - 12 * q^13 - 15 * q^14 - 9 * q^16 + 54 * q^17 - 6 * q^19 + 18 * q^20 - 12 * q^22 - 3 * q^25 - 30 * q^26 - 12 * q^28 + 30 * q^29 - 3 * q^31 - 51 * q^32 - 18 * q^34 + 12 * q^35 + 3 * q^37 + 57 * q^38 - 66 * q^40 - 12 * q^43 - 3 * q^44 + 3 * q^46 + 21 * q^47 + 12 * q^49 + 39 * q^50 + 9 * q^52 - 9 * q^53 - 24 * q^55 - 57 * q^56 - 3 * q^58 + 18 * q^59 + 33 * q^61 - 75 * q^62 - 30 * q^64 - 81 * q^65 - 3 * q^67 - 6 * q^68 - 42 * q^70 + 18 * q^71 + 21 * q^73 + 93 * q^74 - 24 * q^76 - 87 * q^77 + 15 * q^79 - 102 * q^80 - 6 * q^82 + 42 * q^83 - 63 * q^85 - 159 * q^86 + 57 * q^88 + 150 * q^89 + 6 * q^91 + 66 * q^92 + 33 * q^94 + 147 * q^95 - 12 * q^97 - 99 * q^98

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−0.351787	−	1.99508i	−0.248751	−	1.41074i	−0.811617	−	0.584190i	$-0.801412\pi$
$2$	−0.351787	−	1.99508i	−0.248751	−	1.41074i	0.562866	−	0.826548i	$-0.309699\pi$
$3$		0			0
$3$		0			0
$4$	−1.97722	+	0.719650i	−0.988611	+	0.359825i
$5$	−0.155052	+	0.879341i	−0.0693412	+	0.393253i	0.930308	+	0.366778i	$0.119539\pi$
$5$	−0.155052	+	0.879341i	−0.0693412	+	0.393253i	−0.999649	+	0.0264748i	$0.991572\pi$
$6$		0			0
$7$	−1.72949	+	2.00222i	−0.653685	+	0.756767i
$7$	−1.72949	+	2.00222i	−0.653685	+	0.756767i
$8$	0.105462	+	0.182666i	0.0372866	+	0.0645823i
$9$		0			0
$10$	1.80890			0.572026
$11$	0.545772	+	3.09523i	0.164556	+	0.933245i	0.949521	+	0.313704i	$0.101570\pi$
$11$	0.545772	+	3.09523i	0.164556	+	0.933245i	−0.784964	+	0.619541i	$0.787319\pi$
$12$		0			0
$13$	3.46133	+	2.90440i	0.960001	+	0.805536i	0.980953	−	0.194244i	$-0.0622253\pi$
$13$	3.46133	+	2.90440i	0.960001	+	0.805536i	−0.0209522	+	0.999780i	$0.506670\pi$
$14$	4.60300	+	2.74612i	1.23020	+	0.733932i
$15$		0			0
$16$	−2.89636	+	2.43033i	−0.724090	+	0.607583i
$17$	−5.74615			−1.39365			−0.696823	−	0.717243i	$-0.745404\pi$
$17$	−5.74615			−1.39365			−0.696823	+	0.717243i	$0.745404\pi$
$18$		0			0
$19$	1.22738			0.281581			0.140790	−	0.990039i	$-0.455036\pi$
$19$	1.22738			0.281581			0.140790	+	0.990039i	$0.455036\pi$
$20$	−0.326246	−	1.85024i	−0.0729509	−	0.413725i
$21$		0			0
$22$	5.98324	−	2.17772i	1.27563	−	0.464292i
$23$	4.25634	+	3.57150i	0.887509	+	0.744709i	0.967709	−	0.252070i	$-0.0811114\pi$
$23$	4.25634	+	3.57150i	0.887509	+	0.744709i	−0.0801999	+	0.996779i	$0.525556\pi$
$24$		0			0
$25$	3.94926	+	1.43741i	0.789853	+	0.287483i
$26$	4.57688	−	7.92738i	0.897599	−	1.55469i
$27$		0			0
$28$	1.97869	−	5.20345i	0.373937	−	0.983360i
$29$	0.0345809	−	0.0290169i	0.00642152	−	0.00538829i	−0.639571	−	0.768732i	$-0.720888\pi$
$29$	0.0345809	−	0.0290169i	0.00642152	−	0.00538829i	0.645993	+	0.763344i	$0.276444\pi$
$30$		0			0
$31$	0.226384	−	0.0823972i	0.0406599	−	0.0147990i	−0.321610	−	0.946872i	$-0.604224\pi$
$31$	0.226384	−	0.0823972i	0.0406599	−	0.0147990i	0.362270	+	0.932073i	$0.382002\pi$
$32$	6.19078	+	5.19468i	1.09439	+	0.918298i
$33$		0			0
$34$	2.02142	+	11.4640i	0.346671	+	1.96607i
$35$	−1.49247	−	1.83126i	−0.252274	−	0.309539i
$36$		0			0
$37$	5.13755	+	8.89849i	0.844607	+	1.46290i	0.885962	+	0.463758i	$0.153499\pi$
$37$	5.13755	+	8.89849i	0.844607	+	1.46290i	−0.0413547	+	0.999145i	$0.513167\pi$
$38$	−0.431777	−	2.44873i	−0.0700435	−	0.397236i
$39$		0			0
$40$	−0.176978	+	0.0644148i	−0.0279827	+	0.0101849i
$41$	−3.74834	−	3.14523i	−0.585392	−	0.491203i	0.301321	−	0.953523i	$-0.402573\pi$
$41$	−3.74834	−	3.14523i	−0.585392	−	0.491203i	−0.886713	+	0.462320i	$0.847017\pi$
$42$		0			0
$43$	−6.92531	−	2.52060i	−1.05610	−	0.384389i	−0.245138	−	0.969488i	$-0.578833\pi$
$43$	−6.92531	−	2.52060i	−1.05610	−	0.384389i	−0.810961	+	0.585100i	$0.801055\pi$
$44$	−3.30659	−	5.72718i	−0.498487	−	0.863405i
$45$		0			0
$46$	5.62811	−	9.74817i	0.829820	−	1.43729i
$47$	−5.21418	−	1.89781i	−0.760567	−	0.276824i	−0.0675215	−	0.997718i	$-0.521509\pi$
$47$	−5.21418	−	1.89781i	−0.760567	−	0.276824i	−0.693045	+	0.720894i	$0.743731\pi$
$48$		0			0
$49$	−1.01774	−	6.92562i	−0.145391	−	0.989374i
$50$	1.47846	−	8.38478i	0.209086	−	1.18579i
$51$		0			0
$52$	−8.93398	−	3.25170i	−1.23892	−	0.450930i
$53$	3.82297	+	6.62158i	0.525126	+	0.909545i	0.999572	+	0.0292600i	$0.00931508\pi$
$53$	3.82297	+	6.62158i	0.525126	+	0.909545i	−0.474446	+	0.880285i	$0.657352\pi$
$54$		0			0
$55$	−2.80638			−0.378412
$56$	−0.548134	−	0.104761i	−0.0732475	−	0.0139992i
$57$		0			0
$58$	−0.0700562	−	0.0587841i	−0.00919883	−	0.00771874i
$59$	2.88652	+	2.42208i	0.375793	+	0.315328i	0.811048	−	0.584979i	$-0.198897\pi$
$59$	2.88652	+	2.42208i	0.375793	+	0.315328i	−0.435255	+	0.900307i	$0.643342\pi$
$60$		0			0
$61$	−0.765603	−	0.278657i	−0.0980254	−	0.0356783i	0.292542	−	0.956253i	$-0.405499\pi$
$61$	−0.765603	−	0.278657i	−0.0980254	−	0.0356783i	−0.390567	+	0.920574i	$0.627721\pi$
$62$	−0.244029	−	0.422670i	−0.0309917	−	0.0536791i
$63$		0			0
$64$	4.40506	−	7.62979i	0.550633	−	0.953724i
$65$	−3.09065	+	2.59336i	−0.383347	+	0.321667i
$66$		0			0
$67$	0.114256	−	0.647980i	0.0139586	−	0.0791633i	−0.977033	−	0.213090i	$-0.931647\pi$
$67$	0.114256	−	0.647980i	0.0139586	−	0.0791633i	0.990991	+	0.133926i	$0.0427585\pi$
$68$	11.3614	−	4.13522i	1.37777	−	0.501469i
$69$		0			0
$70$	−3.12848	+	3.62182i	−0.373925	+	0.432890i
$71$	−3.75882	+	6.51047i	−0.446090	+	0.772650i	−0.998127	−	0.0611691i	$-0.980517\pi$
$71$	−3.75882	+	6.51047i	−0.446090	+	0.772650i	0.552038	+	0.833819i	$0.313850\pi$
$72$		0			0
$73$	4.87293	−	8.44017i	0.570334	−	0.987847i	−0.426198	−	0.904630i	$-0.640147\pi$
$73$	4.87293	−	8.44017i	0.570334	−	0.987847i	0.996531	−	0.0832170i	$-0.0265195\pi$
$74$	15.9459	−	13.3802i	1.85367	−	1.55542i
$75$		0			0
$76$	−2.42681	+	0.883285i	−0.278374	+	0.101320i
$77$	−7.14122	−	4.26040i	−0.813817	−	0.485518i
$78$		0			0
$79$	−2.29784	−	13.0317i	−0.258527	−	1.46618i	−0.786854	−	0.617139i	$-0.788292\pi$
$79$	−2.29784	−	13.0317i	−0.258527	−	1.46618i	0.528327	−	0.849041i	$-0.322820\pi$
$80$	−1.68801	−	2.92371i	−0.188725	−	0.326881i
$81$		0			0
$82$	−4.95638	+	8.58471i	−0.547341	+	0.948022i
$83$	−4.92372	+	4.13150i	−0.540449	+	0.453490i	−0.871691	−	0.490055i	$-0.836977\pi$
$83$	−4.92372	+	4.13150i	−0.540449	+	0.453490i	0.331242	+	0.943546i	$0.392532\pi$
$84$		0			0
$85$	0.890949	−	5.05282i	0.0966370	−	0.548055i
$86$	−2.59259	+	14.7033i	−0.279566	+	1.58550i
$87$		0			0
$88$	−0.507835	+	0.426124i	−0.0541354	+	0.0454250i
$89$	12.6111			1.33678			0.668388	−	0.743812i	$-0.266984\pi$
$89$	12.6111			1.33678			0.668388	+	0.743812i	$0.266984\pi$
$90$		0			0
$91$	−11.8016	+	1.90720i	−1.23714	+	0.199929i
$92$	−10.9860	−	3.99856i	−1.14537	−	0.416879i
$93$		0			0
$94$	−1.95200	+	11.0704i	−0.201334	+	1.14182i
$95$	−0.190307	+	1.07929i	−0.0195251	+	0.110732i
$96$		0			0
$97$	−11.8862	−	4.32622i	−1.20686	−	0.439261i	−0.341246	−	0.939974i	$-0.610849\pi$
$97$	−11.8862	−	4.32622i	−1.20686	−	0.439261i	−0.865613	+	0.500713i	$0.833071\pi$
$98$	−13.4592	+	4.46682i	−1.35958	+	0.451217i
$99$		0			0
$100$	−8.84301			−0.884301
$101$	−7.78093	+	6.52898i	−0.774232	+	0.649658i	−0.941789	−	0.336205i	$-0.890857\pi$
$101$	−7.78093	+	6.52898i	−0.774232	+	0.649658i	0.167557	+	0.985862i	$0.446412\pi$
$102$		0			0
$103$	−2.60057	+	14.7486i	−0.256242	+	1.45322i	0.536622	+	0.843823i	$0.319700\pi$
$103$	−2.60057	+	14.7486i	−0.256242	+	1.45322i	−0.792864	+	0.609399i	$0.791411\pi$
$104$	−0.165496	+	0.938575i	−0.0162282	+	0.0920348i
$105$		0			0
$106$	11.8657	−	9.95654i	1.15250	−	0.967065i
$107$	−7.28317	+	12.6148i	−0.704090	+	1.21952i	0.262929	+	0.964815i	$0.415312\pi$
$107$	−7.28317	+	12.6148i	−0.704090	+	1.21952i	−0.967019	+	0.254705i	$0.918022\pi$
$108$		0			0
$109$	−1.69401	−	2.93411i	−0.162257	−	0.281037i	0.773421	−	0.633893i	$-0.218544\pi$
$109$	−1.69401	−	2.93411i	−0.162257	−	0.281037i	−0.935678	+	0.352856i	$0.885211\pi$
$110$	0.987249	+	5.59897i	0.0941305	+	0.533841i
$111$		0			0
$112$	0.143166	−	10.0024i	0.0135279	−	0.945135i
$113$	12.6640	−	4.60933i	1.19133	−	0.433609i	0.331140	−	0.943582i	$-0.392567\pi$
$113$	12.6640	−	4.60933i	1.19133	−	0.433609i	0.860191	+	0.509973i	$0.170344\pi$
$114$		0			0
$115$	−3.80052	+	3.18901i	−0.354400	+	0.297377i
$116$	−0.0474922	+	0.0822590i	−0.00440954	+	0.00763755i
$117$		0			0
$118$	3.81681	−	6.61092i	0.351366	−	0.608584i
$119$	9.93789	−	11.5050i	0.911005	−	1.05466i
$120$		0			0
$121$	1.05407	−	0.383649i	0.0958243	−	0.0348772i
$122$	−0.286614	+	1.62547i	−0.0259488	+	0.147163i
$123$		0			0
$124$	−0.388315	+	0.325835i	−0.0348717	+	0.0292609i
$125$	−4.10858	+	7.11627i	−0.367483	+	0.636499i
$126$		0			0
$127$	5.56469	+	9.63833i	0.493786	+	0.855263i	0.999974	−	0.00716008i	$-0.00227914\pi$
$127$	5.56469	+	9.63833i	0.493786	+	0.855263i	−0.506188	+	0.862423i	$0.668946\pi$
$128$	−1.58349	−	0.576343i	−0.139962	−	0.0509420i
$129$		0			0
$130$	6.26122	+	5.25379i	0.549145	+	0.460788i
$131$	−6.02780	−	5.05793i	−0.526651	−	0.441913i	0.340292	−	0.940320i	$-0.389474\pi$
$131$	−6.02780	−	5.05793i	−0.526651	−	0.441913i	−0.866943	+	0.498407i	$0.833919\pi$
$132$		0			0
$133$	−2.12274	+	2.45748i	−0.184065	+	0.213091i
$134$	−1.33297			−0.115151
$135$		0			0
$136$	−0.606003	−	1.04963i	−0.0519643	−	0.0900048i
$137$	1.64156	+	0.597477i	0.140248	+	0.0510459i	0.411190	−	0.911550i	$-0.365113\pi$
$137$	1.64156	+	0.597477i	0.140248	+	0.0510459i	−0.270943	+	0.962595i	$0.587335\pi$
$138$		0			0
$139$	−2.01511	+	11.4282i	−0.170919	+	0.969330i	0.771830	+	0.635828i	$0.219341\pi$
$139$	−2.01511	+	11.4282i	−0.170919	+	0.969330i	−0.942749	+	0.333502i	$0.891770\pi$
$140$	4.26881	+	2.54674i	0.360780	+	0.215239i
$141$		0			0
$142$	14.3112	+	5.20886i	1.20097	+	0.437118i
$143$	−7.10068	+	12.2987i	−0.593789	+	1.02847i
$144$		0			0
$145$	0.0201539	+	0.0349075i	0.00167369	+	0.00289891i
$146$	−18.5531	−	6.75277i	−1.53546	−	0.558863i
$147$		0			0
$148$	−16.5619	−	13.8971i	−1.36138	−	1.14233i
$149$	8.57674	−	3.12168i	0.702634	−	0.255738i	0.0340988	−	0.999418i	$-0.489144\pi$
$149$	8.57674	−	3.12168i	0.702634	−	0.255738i	0.668535	+	0.743681i	$0.266922\pi$
$150$		0			0
$151$	1.62003	+	9.18763i	0.131836	+	0.747678i	0.977011	+	0.213189i	$0.0683850\pi$
$151$	1.62003	+	9.18763i	0.131836	+	0.747678i	−0.845175	+	0.534490i	$0.820504\pi$
$152$	0.129443	+	0.224201i	0.0104992	+	0.0181851i
$153$		0			0
$154$	−5.98768	+	15.7461i	−0.482501	+	1.26886i
$155$	0.0373540	+	0.211845i	0.00300034	+	0.0170158i
$156$		0			0
$157$	10.0221	+	8.40952i	0.799849	+	0.671153i	0.948162	−	0.317787i	$-0.102940\pi$
$157$	10.0221	+	8.40952i	0.799849	+	0.671153i	−0.148313	+	0.988940i	$0.547384\pi$
$158$	−25.1910	+	9.16877i	−2.00409	+	0.729428i
$159$		0			0
$160$	−5.52778	+	4.63836i	−0.437010	+	0.366695i
$161$	−14.5122	+	2.34526i	−1.14372	+	0.184832i
$162$		0			0
$163$	2.67921	−	4.64053i	0.209852	−	0.363474i	−0.741816	−	0.670604i	$-0.766035\pi$
$163$	2.67921	−	4.64053i	0.209852	−	0.363474i	0.951668	+	0.307129i	$0.0993684\pi$
$164$	9.67477	+	3.52133i	0.755472	+	0.274969i
$165$		0			0
$166$	9.97478	+	8.36984i	0.774193	+	0.649625i
$167$	−6.66051	+	2.42423i	−0.515406	+	0.187592i	−0.586610	−	0.809869i	$-0.699538\pi$
$167$	−6.66051	+	2.42423i	−0.515406	+	0.187592i	0.0712043	+	0.997462i	$0.477316\pi$
$168$		0			0
$169$	1.28784	+	7.30371i	0.0990647	+	0.561824i
$170$	−10.3942			−0.797201
$171$		0			0
$172$	15.5068			1.18238
$173$	13.8890	−	11.6542i	1.05596	−	0.886054i	0.0622501	−	0.998061i	$-0.480172\pi$
$173$	13.8890	−	11.6542i	1.05596	−	0.886054i	0.993707	+	0.112007i	$0.0357279\pi$
$174$		0			0
$175$	−9.70822	+	5.42129i	−0.733872	+	0.409811i
$176$	−9.10318	−	7.63847i	−0.686178	−	0.575772i
$177$		0			0
$178$	−4.43643	−	25.1603i	−0.332525	−	1.88584i
$179$	15.9280			1.19052			0.595259	−	0.803534i	$-0.297049\pi$
$179$	15.9280			1.19052			0.595259	+	0.803534i	$0.297049\pi$
$180$		0			0
$181$	−11.7915	−	20.4235i	−0.876456	−	1.51807i	−0.855203	−	0.518293i	$-0.826568\pi$
$181$	−11.7915	−	20.4235i	−0.876456	−	1.51807i	−0.0212529	−	0.999774i	$-0.506766\pi$
$182$	7.95668	+	22.8742i	0.589788	+	1.69555i
$183$		0			0
$184$	−0.203508	+	1.15415i	−0.0150028	+	0.0850851i
$185$	−8.62139	+	3.13793i	−0.633857	+	0.230705i
$186$		0			0
$187$	−3.13608	−	17.7856i	−0.229333	−	1.30061i
$188$	11.6754			0.851513
$189$		0			0
$190$	2.22022			0.161071
$191$	−3.73858	−	21.2025i	−0.270514	−	1.53416i	−0.752860	−	0.658181i	$-0.771326\pi$
$191$	−3.73858	−	21.2025i	−0.270514	−	1.53416i	0.482345	−	0.875981i	$-0.339785\pi$
$192$		0			0
$193$	−8.25517	+	3.00464i	−0.594220	+	0.216278i	−0.621584	−	0.783347i	$-0.713511\pi$
$193$	−8.25517	+	3.00464i	−0.594220	+	0.216278i	0.0273645	+	0.999626i	$0.491289\pi$
$194$	−4.44976	+	25.2359i	−0.319474	+	1.81183i
$195$		0			0
$196$	6.99632	+	12.9611i	0.499737	+	0.925791i
$197$	−1.67466	−	2.90060i	−0.119315	−	0.206659i	0.800182	−	0.599758i	$-0.204736\pi$
$197$	−1.67466	−	2.90060i	−0.119315	−	0.206659i	−0.919496	+	0.393099i	$0.871403\pi$
$198$		0			0
$199$	−11.4381			−0.810825			−0.405413	−	0.914134i	$-0.632872\pi$
$199$	−11.4381			−0.810825			−0.405413	+	0.914134i	$0.632872\pi$
$200$	0.153932	+	0.872991i	0.0108846	+	0.0617298i
$201$		0			0
$202$	15.7631	+	13.2268i	1.10909	+	0.930635i
$203$	−0.00170932	+	0.119423i	−0.000119971	+	0.00838184i
$204$		0			0
$205$	3.34692	−	2.80840i	0.233759	−	0.196147i
$206$	30.3395			2.11386
$207$		0			0
$208$	−17.0839			−1.18456
$209$	0.669870	+	3.79902i	0.0463359	+	0.262784i
$210$		0			0
$211$	16.9946	−	6.18552i	1.16995	−	0.425829i	0.317311	−	0.948322i	$-0.397220\pi$
$211$	16.9946	−	6.18552i	1.16995	−	0.425829i	0.852644	+	0.522493i	$0.174998\pi$
$212$	−12.3241	−	10.3411i	−0.846422	−	0.710233i
$213$		0			0
$214$	27.7297	+	10.0928i	1.89557	+	0.689930i
$215$	3.29025	−	5.69888i	0.224393	−	0.388660i
$216$		0			0
$217$	−0.226552	+	0.595776i	−0.0153794	+	0.0404439i
$218$	−5.25786	+	4.41187i	−0.356107	+	0.298810i
$219$		0			0
$220$	5.54884	−	2.01961i	0.374103	−	0.136162i
$221$	−19.8893	−	16.6891i	−1.33790	−	1.12263i
$222$		0			0
$223$	−2.13914	−	12.1316i	−0.143247	−	0.812395i	−0.968758	−	0.248008i	$-0.920224\pi$
$223$	−2.13914	−	12.1316i	−0.143247	−	0.812395i	0.825511	−	0.564386i	$-0.190887\pi$
$224$	−21.1078	+	3.41114i	−1.41032	+	0.227916i
$225$		0			0
$226$	−13.6510	−	23.6443i	−0.908053	−	1.57279i
$227$	4.13532	+	23.4526i	0.274471	+	1.55660i	0.740638	+	0.671904i	$0.234523\pi$
$227$	4.13532	+	23.4526i	0.274471	+	1.55660i	−0.466168	+	0.884696i	$0.654366\pi$
$228$		0			0
$229$	21.2430	−	7.73183i	1.40378	−	0.510933i	0.474481	−	0.880266i	$-0.342636\pi$
$229$	21.2430	−	7.73183i	1.40378	−	0.510933i	0.929297	+	0.369333i	$0.120414\pi$
$230$	7.69932	+	6.46050i	0.507678	+	0.425993i
$231$		0			0
$232$	0.00894740	+	0.00325659i	0.000587425	+	0.000213805i
$233$	0.152366	+	0.263905i	0.00998180	+	0.0172890i	0.870973	−	0.491331i	$-0.163489\pi$
$233$	0.152366	+	0.263905i	0.00998180	+	0.0172890i	−0.860991	+	0.508620i	$0.830156\pi$
$234$		0			0
$235$	2.47729	−	4.29079i	0.161600	−	0.279900i
$236$	−7.45035	−	2.71171i	−0.484977	−	0.176517i
$237$		0			0
$238$	−26.4495	−	15.7796i	−1.71447	−	1.02284i
$239$	4.19570	−	23.7950i	0.271397	−	1.53917i	−0.478780	−	0.877935i	$-0.658921\pi$
$239$	4.19570	−	23.7950i	0.271397	−	1.53917i	0.750178	−	0.661236i	$-0.229968\pi$
$240$		0			0
$241$	−13.4282	−	4.88748i	−0.864989	−	0.314830i	−0.128853	−	0.991664i	$-0.541129\pi$
$241$	−13.4282	−	4.88748i	−0.864989	−	0.314830i	−0.736136	+	0.676834i	$0.763352\pi$
$242$	−1.13622	−	1.96799i	−0.0730390	−	0.126507i
$243$		0			0
$244$	1.71430			0.109747
$245$	6.24778	+	0.178888i	0.399156	+	0.0114287i
$246$		0			0
$247$	4.24838	+	3.56481i	0.270318	+	0.226823i
$248$	0.0389263	+	0.0326630i	0.00247182	+	0.00207410i
$249$		0			0
$250$	15.6429	+	5.69355i	0.989345	+	0.360092i
$251$	−1.67494	−	2.90107i	−0.105721	−	0.183114i	0.808312	−	0.588755i	$-0.200382\pi$
$251$	−1.67494	−	2.90107i	−0.105721	−	0.183114i	−0.914033	+	0.405641i	$0.867048\pi$
$252$		0			0
$253$	−8.73159	+	15.1236i	−0.548951	+	0.950810i
$254$	17.2717	−	14.4927i	1.08372	−	0.909351i
$255$		0			0
$256$	2.46692	−	13.9906i	0.154183	−	0.874413i
$257$	16.9888	−	6.18343i	1.05973	−	0.385711i	0.247405	−	0.968912i	$-0.420422\pi$
$257$	16.9888	−	6.18343i	1.05973	−	0.385711i	0.812328	+	0.583201i	$0.198200\pi$
$258$		0			0
$259$	−26.7020	−	5.10336i	−1.65918	−	0.317107i
$260$	4.24458	−	7.35183i	0.263238	−	0.455941i
$261$		0			0
$262$	−7.97049	+	13.8053i	−0.492418	+	0.852893i
$263$	18.5162	−	15.5369i	1.14176	−	0.958049i	0.142263	−	0.989829i	$-0.454562\pi$
$263$	18.5162	−	15.5369i	1.14176	−	0.958049i	0.999495	+	0.0317800i	$0.0101176\pi$
$264$		0			0
$265$	−6.41539	+	2.33501i	−0.394094	+	0.143439i
$266$	5.64964	+	3.37054i	0.346402	+	0.206661i
$267$		0			0
$268$	0.240409	+	1.36342i	0.0146853	+	0.0832844i
$269$	−7.45250	−	12.9081i	−0.454387	−	0.787022i	0.544266	−	0.838913i	$-0.316808\pi$
$269$	−7.45250	−	12.9081i	−0.454387	−	0.787022i	−0.998653	+	0.0518912i	$0.983475\pi$
$270$		0			0
$271$	−2.69114	+	4.66119i	−0.163475	+	0.283147i	−0.936113	−	0.351700i	$-0.885604\pi$
$271$	−2.69114	+	4.66119i	−0.163475	+	0.283147i	0.772638	+	0.634847i	$0.218937\pi$
$272$	16.6429	−	13.9651i	1.00912	−	0.846756i
$273$		0			0
$274$	0.614540	−	3.48523i	0.0371257	−	0.210550i
$275$	−2.29372	+	13.0084i	−0.138317	+	0.784434i
$276$		0			0
$277$	−0.775246	+	0.650509i	−0.0465800	+	0.0390853i	−0.665780	−	0.746148i	$-0.731901\pi$
$277$	−0.775246	+	0.650509i	−0.0465800	+	0.0390853i	0.619200	+	0.785233i	$0.287457\pi$
$278$	23.5092			1.40999
$279$		0			0
$280$	0.177109	−	0.465753i	0.0105843	−	0.0278341i
$281$	12.2222	+	4.44851i	0.729114	+	0.265376i	0.679790	−	0.733407i	$-0.262071\pi$
$281$	12.2222	+	4.44851i	0.729114	+	0.265376i	0.0493245	+	0.998783i	$0.484293\pi$
$282$		0			0
$283$	−3.28461	+	18.6280i	−0.195250	+	1.10732i	0.716812	+	0.697266i	$0.245600\pi$
$283$	−3.28461	+	18.6280i	−0.195250	+	1.10732i	−0.912062	+	0.410052i	$0.865511\pi$
$284$	2.74676	−	15.5777i	0.162990	−	0.924365i
$285$		0			0
$286$	27.0350	+	9.83992i	1.59861	+	0.581847i
$287$	12.7801	−	2.06535i	0.754388	−	0.121914i
$288$		0			0
$289$	16.0182			0.942247
$290$	0.0625536	−	0.0524887i	0.00367328	−	0.00308224i
$291$		0			0
$292$	−3.56091	+	20.1949i	−0.208386	+	1.18182i
$293$	0.436945	−	2.47804i	0.0255266	−	0.144769i	−0.969381	−	0.245563i	$-0.921027\pi$
$293$	0.436945	−	2.47804i	0.0255266	−	0.144769i	0.994907	+	0.100794i	$0.0321384\pi$
$294$		0			0
$295$	−2.57739	+	2.16269i	−0.150062	+	0.125917i
$296$	−1.08364	+	1.87691i	−0.0629851	+	0.109093i
$297$		0			0
$298$	−9.24520	−	16.0132i	−0.535560	−	0.927617i
$299$	4.35956	+	24.7243i	0.252120	+	1.42984i
$300$		0			0
$301$	17.0240	−	9.50660i	0.981249	−	0.547951i
$302$	17.7602	−	6.46418i	1.02198	−	0.371972i
$303$		0			0
$304$	−3.55494	+	2.98295i	−0.203890	+	0.171084i
$305$	0.363742	−	0.630020i	0.0208278	−	0.0360748i
$306$		0			0
$307$	3.33310	−	5.77311i	0.190230	−	0.329489i	−0.755096	−	0.655614i	$-0.772410\pi$
$307$	3.33310	−	5.77311i	0.190230	−	0.329489i	0.945326	+	0.326125i	$0.105743\pi$
$308$	17.1858	+	3.28459i	0.979250	+	0.187157i
$309$		0			0
$310$	0.409508	−	0.149049i	0.0232585	−	0.00846540i
$311$	2.53672	−	14.3865i	0.143844	−	0.815782i	−0.824444	−	0.565944i	$-0.808512\pi$
$311$	2.53672	−	14.3865i	0.143844	−	0.815782i	0.968288	−	0.249837i	$-0.0803772\pi$
$312$		0			0
$313$	16.7927	−	14.0907i	0.949177	−	0.796454i	−0.0299819	−	0.999550i	$-0.509545\pi$
$313$	16.7927	−	14.0907i	0.949177	−	0.796454i	0.979159	+	0.203097i	$0.0651005\pi$
$314$	13.2521	−	22.9533i	0.747858	−	1.29533i
$315$		0			0
$316$	13.9216	+	24.1129i	0.783151	+	1.35646i
$317$	−8.74471	−	3.18282i	−0.491152	−	0.178765i	0.0845581	−	0.996419i	$-0.473052\pi$
$317$	−8.74471	−	3.18282i	−0.491152	−	0.178765i	−0.575710	+	0.817654i	$0.695274\pi$
$318$		0			0
$319$	0.108687	+	0.0911992i	0.00608530	+	0.00510618i
$320$	6.02617	+	5.05656i	0.336873	+	0.282670i
$321$		0			0
$322$	9.78420	+	28.1280i	0.545252	+	1.56751i
$323$	−7.05271			−0.392423
$324$		0			0
$325$	9.49489	+	16.4456i	0.526681	+	0.912239i
$326$	−10.2008	−	3.71277i	−0.564968	−	0.205631i
$327$		0			0
$328$	0.179219	−	1.01640i	0.00989570	−	0.0561213i
$329$	12.8177	−	7.15768i	0.706662	−	0.394616i
$330$		0			0
$331$	−12.7757	−	4.64997i	−0.702215	−	0.255585i	−0.0338587	−	0.999427i	$-0.510780\pi$
$331$	−12.7757	−	4.64997i	−0.702215	−	0.255585i	−0.668356	+	0.743841i	$0.733002\pi$
$332$	6.76207	−	11.7122i	0.371117	−	0.642793i
$333$		0			0
$334$	7.17963	+	12.4355i	0.392852	+	0.680439i
$335$	0.552080	+	0.200941i	0.0301633	+	0.0109786i
$336$		0			0
$337$	−18.7794	−	15.7578i	−1.02298	−	0.858382i	−0.0329809	−	0.999456i	$-0.510500\pi$
$337$	−18.7794	−	15.7578i	−1.02298	−	0.858382i	−0.989999	+	0.141074i	$0.954944\pi$
$338$	14.1185	−	5.13870i	0.767944	−	0.279509i
$339$		0			0
$340$	1.87466	+	10.6317i	0.101668	+	0.576586i
$341$	0.378592	+	0.655741i	0.0205019	+	0.0355104i
$342$		0			0
$343$	15.6268	+	9.94005i	0.843766	+	0.536712i
$344$	−0.269930	−	1.53085i	−0.0145537	−	0.0825379i
$345$		0			0
$346$	−28.1371	−	23.6098i	−1.51266	−	1.26927i
$347$	−11.7888	+	4.29078i	−0.632858	+	0.230341i	−0.638475	−	0.769643i	$-0.720434\pi$
$347$	−11.7888	+	4.29078i	−0.632858	+	0.230341i	0.00561693	+	0.999984i	$0.498212\pi$
$348$		0			0
$349$	19.9884	−	16.7723i	1.06996	−	0.897800i	0.0749083	−	0.997190i	$-0.476134\pi$
$349$	19.9884	−	16.7723i	1.06996	−	0.897800i	0.995049	+	0.0993900i	$0.0316891\pi$
$350$	14.2312	+	17.4616i	0.760687	+	0.933361i
$351$		0			0
$352$	−12.7000	+	21.9970i	−0.676910	+	1.17244i
$353$	−22.3840	−	8.14711i	−1.19138	−	0.433627i	−0.331172	−	0.943570i	$-0.607444\pi$
$353$	−22.3840	−	8.14711i	−1.19138	−	0.433627i	−0.860208	+	0.509944i	$0.829666\pi$
$354$		0			0
$355$	−5.14211	−	4.31474i	−0.272915	−	0.229003i
$356$	−24.9350	+	9.07560i	−1.32155	+	0.481006i
$357$		0			0
$358$	−5.60328	−	31.7778i	−0.296143	−	1.67951i
$359$	18.6890			0.986366			0.493183	−	0.869926i	$-0.335833\pi$
$359$	18.6890			0.986366			0.493183	+	0.869926i	$0.335833\pi$
$360$		0			0
$361$	−17.4935			−0.920712
$362$	−36.5985	+	30.7098i	−1.92357	+	1.61407i
$363$		0			0
$364$	21.9618	−	12.2640i	1.15111	−	0.642807i
$365$	6.66623	+	5.59363i	0.348926	+	0.292784i
$366$		0			0
$367$	4.28546	+	24.3040i	0.223699	+	1.26866i	0.865157	+	0.501501i	$0.167219\pi$
$367$	4.28546	+	24.3040i	0.223699	+	1.26866i	−0.641458	+	0.767158i	$0.721670\pi$
$368$	−21.0078			−1.09511
$369$		0			0
$370$	9.29333	+	16.0965i	0.483137	+	0.836818i
$371$	−19.8696	−	3.79753i	−1.03158	−	0.197158i
$372$		0			0
$373$	5.21360	−	29.5678i	0.269950	−	1.53096i	−0.484610	−	0.874730i	$-0.661038\pi$
$373$	5.21360	−	29.5678i	0.269950	−	1.53096i	0.754560	−	0.656231i	$-0.227850\pi$
$374$	−34.3806	+	12.5135i	−1.77778	+	0.647058i
$375$		0			0
$376$	−0.203235	−	1.15260i	−0.0104810	−	0.0594410i
$377$	0.203973			0.0105051
$378$		0			0
$379$	29.6444			1.52273			0.761365	−	0.648324i	$-0.224530\pi$
$379$	29.6444			1.52273			0.761365	+	0.648324i	$0.224530\pi$
$380$	−0.400429	−	2.27094i	−0.0205416	−	0.116497i
$381$		0			0
$382$	−40.9857	+	14.9176i	−2.09701	+	0.763249i
$383$	−0.542179	+	3.07485i	−0.0277040	+	0.157117i	−0.995521	−	0.0945361i	$-0.969863\pi$
$383$	−0.542179	+	3.07485i	−0.0277040	+	0.157117i	0.967817	+	0.251654i	$0.0809743\pi$
$384$		0			0
$385$	4.85360	−	5.61898i	0.247363	−	0.286370i
$386$	8.89856	+	15.4128i	0.452925	+	0.784489i
$387$		0			0
$388$	26.6150			1.35117
$389$	1.24377	+	7.05376i	0.0630615	+	0.357640i	0.999968	+	0.00805830i	$0.00256506\pi$
$389$	1.24377	+	7.05376i	0.0630615	+	0.357640i	−0.936906	+	0.349581i	$0.886324\pi$
$390$		0			0
$391$	−24.4576	−	20.5223i	−1.23687	−	1.03786i
$392$	1.15774	−	0.916300i	0.0584749	−	0.0462801i
$393$		0			0
$394$	−5.19781	+	4.36148i	−0.261862	+	0.219728i
$395$	11.8156			0.594507
$396$		0			0
$397$	18.4934			0.928157			0.464079	−	0.885794i	$-0.346386\pi$
$397$	18.4934			0.928157			0.464079	+	0.885794i	$0.346386\pi$
$398$	4.02378	+	22.8200i	0.201694	+	1.14386i
$399$		0			0
$400$	−14.9319	+	5.43476i	−0.746594	+	0.271738i
$401$	14.0554	+	11.7939i	0.701896	+	0.588960i	0.922312	−	0.386445i	$-0.126297\pi$
$401$	14.0554	+	11.7939i	0.701896	+	0.588960i	−0.220417	+	0.975406i	$0.570742\pi$
$402$		0			0
$403$	1.02291	+	0.372308i	0.0509546	+	0.0185460i
$404$	10.6861	−	18.5088i	0.531651	−	0.920847i
$405$		0			0
$406$	0.238860	−	0.0386012i	0.0118544	−	0.00191574i
$407$	−24.7389	+	20.7584i	−1.22626	+	1.02896i
$408$		0			0
$409$	0.100901	−	0.0367251i	0.00498925	−	0.00181594i	−0.339524	−	0.940597i	$-0.610266\pi$
$409$	0.100901	−	0.0367251i	0.00498925	−	0.00181594i	0.344514	+	0.938781i	$0.388044\pi$
$410$	−6.78039	−	5.68942i	−0.334860	−	0.280981i
$411$		0			0
$412$	−5.47191	−	31.0328i	−0.269582	−	1.52887i
$413$	−9.84174	+	1.59048i	−0.484280	+	0.0782626i
$414$		0			0
$415$	−2.86956	−	4.97023i	−0.140861	−	0.243979i
$416$	6.34090	+	35.9610i	0.310888	+	1.76313i
$417$		0			0
$418$	7.34372	−	2.67289i	0.359193	−	0.130736i
$419$	−1.12657	−	0.945301i	−0.0550364	−	0.0461810i	0.614855	−	0.788641i	$-0.289215\pi$
$419$	−1.12657	−	0.945301i	−0.0550364	−	0.0461810i	−0.669891	+	0.742460i	$0.733659\pi$
$420$		0			0
$421$	29.7174	+	10.8162i	1.44834	+	0.527152i	0.942126	−	0.335258i	$-0.108823\pi$
$421$	29.7174	+	10.8162i	1.44834	+	0.527152i	0.506211	+	0.862410i	$0.331046\pi$
$422$	−18.3191	−	31.7296i	−0.891760	−	1.54457i
$423$		0			0
$424$	−0.806361	+	1.39666i	−0.0391603	+	0.0678277i
$425$	−22.6930	−	8.25959i	−1.10077	−	0.400649i
$426$		0			0
$427$	1.88203	−	1.05097i	0.0910779	−	0.0508600i
$428$	5.32219	−	30.1836i	0.257258	−	1.45898i
$429$		0			0
$430$	−12.5272	−	4.55953i	−0.604116	−	0.219880i
$431$	13.4216	+	23.2470i	0.646498	+	1.11977i	0.983953	+	0.178425i	$0.0571003\pi$
$431$	13.4216	+	23.2470i	0.646498	+	1.11977i	−0.337456	+	0.941341i	$0.609566\pi$
$432$		0			0
$433$	4.77702			0.229569			0.114785	−	0.993390i	$-0.463382\pi$
$433$	4.77702			0.229569			0.114785	+	0.993390i	$0.463382\pi$
$434$	1.26832	+	0.242405i	0.0608814	+	0.0116358i
$435$		0			0
$436$	5.46096	+	4.58229i	0.261533	+	0.219452i
$437$	5.22416	+	4.38359i	0.249905	+	0.209695i
$438$		0			0
$439$	−18.9217	−	6.88695i	−0.903086	−	0.328696i	−0.151597	−	0.988442i	$-0.548442\pi$
$439$	−18.9217	−	6.88695i	−0.903086	−	0.328696i	−0.751489	+	0.659746i	$0.770664\pi$
$440$	−0.295968	−	0.512631i	−0.0141097	−	0.0244387i
$441$		0			0
$442$	−26.2994	+	45.5519i	−1.25094	+	2.16668i
$443$	−20.6066	+	17.2910i	−0.979048	+	0.821518i	−0.983945	−	0.178470i	$-0.942885\pi$
$443$	−20.6066	+	17.2910i	−0.979048	+	0.821518i	0.00489783	+	0.999988i	$0.498441\pi$
$444$		0			0
$445$	−1.95537	+	11.0895i	−0.0926936	+	0.525692i
$446$	−23.4511	+	8.53551i	−1.11044	+	0.404168i
$447$		0			0
$448$	7.65798	+	22.0155i	0.361806	+	1.04014i
$449$	−7.02501	+	12.1677i	−0.331531	+	0.574228i	−0.982812	−	0.184608i	$-0.940898\pi$
$449$	−7.02501	+	12.1677i	−0.331531	+	0.574228i	0.651281	+	0.758836i	$0.274232\pi$
$450$		0			0
$451$	7.68946	−	13.3185i	0.362083	−	0.627145i
$452$	−21.7225	+	18.2273i	−1.02174	+	0.857341i
$453$		0			0
$454$	45.3351	−	16.5006i	2.12768	−	0.774412i
$455$	0.152769	−	10.6733i	0.00716194	−	0.500373i
$456$		0			0
$457$	6.37787	+	36.1707i	0.298344	+	1.69199i	0.653291	+	0.757107i	$0.273388\pi$
$457$	6.37787	+	36.1707i	0.298344	+	1.69199i	−0.354947	+	0.934886i	$0.615501\pi$
$458$	−22.8987	−	39.6617i	−1.06998	−	1.85327i
$459$		0			0
$460$	5.21949	−	9.04043i	0.243360	−	0.421512i
$461$	32.4211	−	27.2046i	1.51000	−	1.26704i	0.646251	−	0.763125i	$-0.276336\pi$
$461$	32.4211	−	27.2046i	1.51000	−	1.26704i	0.863752	−	0.503917i	$-0.168108\pi$
$462$		0			0
$463$	−3.29439	+	18.6834i	−0.153103	+	0.868293i	0.807396	+	0.590010i	$0.200876\pi$
$463$	−3.29439	+	18.6834i	−0.153103	+	0.868293i	−0.960499	+	0.278283i	$0.910235\pi$
$464$	−0.0296382	+	0.168086i	−0.00137592	+	0.00780322i
$465$		0			0
$466$	0.472912	−	0.396820i	0.0219072	−	0.0183824i
$467$	−14.9158			−0.690219			−0.345110	−	0.938562i	$-0.612158\pi$
$467$	−14.9158			−0.690219			−0.345110	+	0.938562i	$0.612158\pi$
$468$		0			0
$469$	1.09979	+	1.34944i	0.0507836	+	0.0623113i
$470$	−9.43196	−	3.43295i	−0.435064	−	0.158350i
$471$		0			0
$472$	−0.138013	+	0.782710i	−0.00635255	+	0.0360271i
$473$	4.02220	−	22.8111i	0.184941	−	1.04885i
$474$		0			0
$475$	4.84725	+	1.76426i	0.222407	+	0.0809496i
$476$	−11.3698	+	29.8998i	−0.521135	+	1.37046i
$477$		0			0
$478$	−48.9490			−2.23888
$479$	−10.1870	+	8.54789i	−0.465455	+	0.390563i	−0.845133	−	0.534555i	$-0.820479\pi$
$479$	−10.1870	+	8.54789i	−0.465455	+	0.390563i	0.379678	+	0.925119i	$0.376035\pi$
$480$		0			0
$481$	−8.06205	+	45.7221i	−0.367598	+	2.08475i
$482$	−5.02705	+	28.5098i	−0.228976	+	1.29859i
$483$		0			0
$484$	−1.80803	+	1.51712i	−0.0821833	+	0.0689600i
$485$	5.64719	−	9.78122i	0.256426	−	0.444143i
$486$		0			0
$487$	6.60006	+	11.4316i	0.299077	+	0.518017i	0.975925	−	0.218106i	$-0.0699878\pi$
$487$	6.60006	+	11.4316i	0.299077	+	0.518017i	−0.676848	+	0.736123i	$0.736654\pi$
$488$	−0.0298412	−	0.169238i	−0.00135085	−	0.00766103i
$489$		0			0
$490$	−1.84099	−	12.5278i	−0.0831676	−	0.565948i
$491$	−15.3102	+	5.57245i	−0.690939	+	0.251481i	−0.663537	−	0.748143i	$-0.730946\pi$
$491$	−15.3102	+	5.57245i	−0.690939	+	0.251481i	−0.0274020	+	0.999624i	$0.508723\pi$
$492$		0			0
$493$	−0.198707	+	0.166735i	−0.00894932	+	0.00750937i
$494$	5.61757	−	9.72992i	0.252747	−	0.437770i
$495$		0			0
$496$	−0.455438	+	0.788842i	−0.0204498	+	0.0354200i
$497$	−6.53452	−	18.7857i	−0.293113	−	0.842656i
$498$		0			0
$499$	−0.207754	+	0.0756161i	−0.00930033	+	0.00338504i	−0.346666	−	0.937989i	$-0.612686\pi$
$499$	−0.207754	+	0.0756161i	−0.00930033	+	0.00338504i	0.337366	+	0.941374i	$0.390464\pi$
$500$	3.00235	−	17.0272i	0.134269	−	0.761479i
$501$		0			0
$502$	−5.19867	+	4.36220i	−0.232028	+	0.194695i
$503$	−0.112688	+	0.195182i	−0.00502452	+	0.00870272i	−0.868527	−	0.495642i	$-0.834933\pi$
$503$	−0.112688	+	0.195182i	−0.00502452	+	0.00870272i	0.863502	+	0.504345i	$0.168266\pi$
$504$		0			0
$505$	−4.53475	−	7.85442i	−0.201794	−	0.349517i
$506$	33.2445	+	12.1000i	1.47790	+	0.537910i
$507$		0			0
$508$	−17.9389	−	15.0525i	−0.795908	−	0.667846i
$509$	24.8793	+	20.8762i	1.10275	+	0.925320i	0.997607	−	0.0691366i	$-0.0220244\pi$
$509$	24.8793	+	20.8762i	1.10275	+	0.925320i	0.105146	+	0.994457i	$0.466469\pi$
$510$		0			0
$511$	8.47136	+	24.3538i	0.374751	+	1.07735i
$512$	−32.1505			−1.42086
$513$		0			0
$514$	−18.3129	−	31.7189i	−0.807748	−	1.39906i
$515$	−12.5658	−	4.57358i	−0.553716	−	0.201536i
$516$		0			0
$517$	3.02839	−	17.1748i	0.133188	−	0.755348i
$518$	−0.788200	+	55.0681i	−0.0346315	+	2.41955i
$519$		0			0
$520$	−0.799667	−	0.291055i	−0.0350677	−	0.0127636i
$521$	11.7781	−	20.4003i	0.516009	−	0.893754i	−0.483818	−	0.875169i	$-0.660750\pi$
$521$	11.7781	−	20.4003i	0.516009	−	0.893754i	0.999827	−	0.0185855i	$-0.00591630\pi$
$522$		0			0
$523$	6.29514	+	10.9035i	0.275267	+	0.476777i	0.970202	−	0.242296i	$-0.0779004\pi$
$523$	6.29514	+	10.9035i	0.275267	+	0.476777i	−0.694935	+	0.719072i	$0.744567\pi$
$524$	15.5582	+	5.66274i	0.679665	+	0.247378i
$525$		0			0
$526$	−37.5113	−	31.4757i	−1.63557	−	1.37241i
$527$	−1.30084	+	0.473466i	−0.0566654	+	0.0206245i
$528$		0			0
$529$	1.36697	+	7.75246i	0.0594334	+	0.337063i
$530$	6.91539	+	11.9778i	0.300386	+	0.520283i
$531$		0			0
$532$	2.42860	−	6.38662i	0.105293	−	0.276895i
$533$	−3.83923	−	21.7734i	−0.166296	−	0.943110i
$534$		0			0
$535$	−9.96346	−	8.36033i	−0.430758	−	0.361449i
$536$	0.130414	−	0.0474668i	0.00563302	−	0.00205025i
$537$		0			0
$538$	−23.1311	+	19.4093i	−0.997252	+	0.836794i
$539$	20.8809	−	6.92994i	0.899404	−	0.298494i
$540$		0			0
$541$	5.81252	−	10.0676i	0.249900	−	0.432839i	−0.713598	−	0.700555i	$-0.752936\pi$
$541$	5.81252	−	10.0676i	0.249900	−	0.432839i	0.963498	+	0.267716i	$0.0862690\pi$
$542$	10.2462	+	3.72930i	0.440111	+	0.160187i
$543$		0			0
$544$	−35.5731	−	29.8494i	−1.52518	−	1.27978i
$545$	2.84274	−	1.03467i	0.121770	−	0.0443205i
$546$		0			0
$547$	−5.74175	−	32.5631i	−0.245500	−	1.39230i	−0.819330	−	0.573323i	$-0.805654\pi$
$547$	−5.74175	−	32.5631i	−0.245500	−	1.39230i	0.573830	−	0.818974i	$-0.305457\pi$
$548$	−3.67570			−0.157018
$549$		0			0
$550$	26.7597			1.14104
$551$	0.0424440	−	0.0356147i	0.00180818	−	0.00151724i
$552$		0			0
$553$	30.0664	+	17.9374i	1.27855	+	0.762776i
$554$	1.57054	+	1.31784i	0.0667259	+	0.0559897i
$555$		0			0
$556$	−4.24002	−	24.0463i	−0.179817	−	1.01979i
$557$	31.4617			1.33307			0.666537	−	0.745472i	$-0.267776\pi$
$557$	31.4617			1.33307			0.666537	+	0.745472i	$0.267776\pi$
$558$		0			0
$559$	−16.6499	−	28.8385i	−0.704217	−	1.21974i
$560$	8.77329	+	1.67677i	0.370739	+	0.0708566i
$561$		0			0
$562$	4.57555	−	25.9492i	0.193008	−	1.09460i
$563$	11.7079	−	4.26132i	0.493428	−	0.179593i	−0.0833076	−	0.996524i	$-0.526548\pi$
$563$	11.7079	−	4.26132i	0.493428	−	0.179593i	0.576736	+	0.816931i	$0.304326\pi$
$564$		0			0
$565$	2.08959	+	11.8507i	0.0879099	+	0.498562i
$566$	38.3198			1.61070
$567$		0			0
$568$	−1.58566			−0.0665327
$569$	5.48364	+	31.0993i	0.229886	+	1.30375i	0.853121	+	0.521714i	$0.174707\pi$
$569$	5.48364	+	31.0993i	0.229886	+	1.30375i	−0.623234	+	0.782035i	$0.714182\pi$
$570$		0			0
$571$	−11.7658	+	4.28241i	−0.492384	+	0.179213i	−0.576266	−	0.817263i	$-0.695491\pi$
$571$	−11.7658	+	4.28241i	−0.492384	+	0.179213i	0.0838813	+	0.996476i	$0.473268\pi$
$572$	5.18884	−	29.4274i	0.216956	−	1.23042i
$573$		0			0
$574$	−8.61643	−	24.7709i	−0.359643	−	1.03392i
$575$	11.6757	+	20.2229i	0.486911	+	0.843354i
$576$		0			0
$577$	12.4119			0.516713			0.258357	−	0.966050i	$-0.416819\pi$
$577$	12.4119			0.516713			0.258357	+	0.966050i	$0.416819\pi$
$578$	−5.63500	−	31.9577i	−0.234385	−	1.32926i
$579$		0			0
$580$	−0.0649699	−	0.0545162i	−0.00269773	−	0.00226366i
$581$	0.243378	−	17.0037i	0.0100970	−	0.705434i
$582$		0			0
$583$	−18.4088	+	15.4468i	−0.762416	+	0.639743i
$584$	2.05565			0.0850633
$585$		0			0
$586$	−5.09761			−0.210580
$587$	0.730292	+	4.14169i	0.0301424	+	0.170946i	0.996163	−	0.0875200i	$-0.0278942\pi$
$587$	0.730292	+	4.14169i	0.0301424	+	0.170946i	−0.966020	+	0.258466i	$0.916783\pi$
$588$		0			0
$589$	0.277860	−	0.101133i	0.0114490	−	0.00416710i
$590$	5.22145	+	4.38131i	0.214964	+	0.180376i
$591$		0			0
$592$	−36.5065	−	13.2873i	−1.50041	−	0.546103i
$593$	−11.3399	+	19.6412i	−0.465673	+	0.806569i	−0.999232	−	0.0391942i	$-0.987521\pi$
$593$	−11.3399	+	19.6412i	−0.465673	+	0.806569i	0.533559	+	0.845763i	$0.320854\pi$
$594$		0			0
$595$	8.57596	+	10.5227i	0.351580	+	0.431387i
$596$	−14.7116	+	12.3445i	−0.602611	+	0.505651i
$597$		0			0
$598$	47.7934	−	17.3954i	1.95442	−	0.711350i
$599$	4.77957	+	4.01053i	0.195288	+	0.163866i	0.735188	−	0.677863i	$-0.237094\pi$
$599$	4.77957	+	4.01053i	0.195288	+	0.163866i	−0.539901	+	0.841729i	$0.681538\pi$
$600$		0			0
$601$	4.34521	+	24.6429i	0.177245	+	1.00520i	0.935521	+	0.353271i	$0.114931\pi$
$601$	4.34521	+	24.6429i	0.177245	+	1.00520i	−0.758276	+	0.651933i	$0.773958\pi$
$602$	−24.9553	−	30.6201i	−1.01710	−	1.24798i
$603$		0			0
$604$	−9.81503	−	17.0001i	−0.399368	−	0.691725i
$605$	0.173924	+	0.986370i	0.00707100	+	0.0401016i
$606$		0			0
$607$	11.3906	−	4.14582i	0.462328	−	0.168274i	−0.100346	−	0.994953i	$-0.531995\pi$
$607$	11.3906	−	4.14582i	0.462328	−	0.168274i	0.562674	+	0.826679i	$0.309773\pi$
$608$	7.59844	+	6.37585i	0.308158	+	0.258575i
$609$		0			0
$610$	−1.38490	−	0.504063i	−0.0560731	−	0.0204089i
$611$	−12.5360	−	21.7130i	−0.507153	−	0.878415i
$612$		0			0
$613$	2.16690	−	3.75318i	0.0875202	−	0.151589i	−0.818942	−	0.573876i	$-0.805439\pi$
$613$	2.16690	−	3.75318i	0.0875202	−	0.151589i	0.906462	+	0.422287i	$0.138772\pi$
$614$	−12.6904	−	4.61892i	−0.512142	−	0.186404i
$615$		0			0
$616$	0.0251021	−	1.75377i	0.00101139	−	0.0706615i
$617$	−4.00429	+	22.7095i	−0.161207	+	0.914249i	0.791683	+	0.610932i	$0.209205\pi$
$617$	−4.00429	+	22.7095i	−0.161207	+	0.914249i	−0.952890	+	0.303317i	$0.901906\pi$
$618$		0			0
$619$	−5.53714	−	2.01536i	−0.222557	−	0.0810040i	0.228335	−	0.973583i	$-0.426672\pi$
$619$	−5.53714	−	2.01536i	−0.222557	−	0.0810040i	−0.450892	+	0.892579i	$0.648894\pi$
$620$	−0.226311	−	0.391983i	−0.00908888	−	0.0157424i
$621$		0			0
$622$	−29.5946			−1.18664
$623$	−21.8108	+	25.2502i	−0.873831	+	1.01163i
$624$		0			0
$625$	10.4768	+	8.79104i	0.419070	+	0.351642i
$626$	−34.0196	−	28.5458i	−1.35970	−	1.14092i
$627$		0			0
$628$	−25.8678	−	9.41511i	−1.03224	−	0.375704i
$629$	−29.5211	−	51.1320i	−1.17708	−	2.03877i
$630$		0			0
$631$	13.0197	−	22.5509i	0.518308	−	0.897735i	−0.481466	−	0.876465i	$-0.659895\pi$
$631$	13.0197	−	22.5509i	0.518308	−	0.897735i	0.999774	−	0.0212707i	$-0.00677118\pi$
$632$	2.13812	−	1.79409i	0.0850497	−	0.0713652i
$633$		0			0
$634$	−3.27371	+	18.5661i	−0.130016	+	0.737355i
$635$	−9.33819	+	3.39882i	−0.370575	+	0.134878i
$636$		0			0
$637$	16.5921	−	26.9278i	0.657401	−	1.06692i
$638$	0.143715	−	0.248922i	0.00568975	−	0.00985493i
$639$		0			0
$640$	0.752324	−	1.30306i	0.0297382	−	0.0515081i
$641$	16.4390	−	13.7940i	0.649301	−	0.544829i	−0.257557	−	0.966263i	$-0.582918\pi$
$641$	16.4390	−	13.7940i	0.649301	−	0.544829i	0.906859	+	0.421434i	$0.138473\pi$
$642$		0			0
$643$	−36.9983	+	13.4663i	−1.45907	+	0.531058i	−0.945109	−	0.326756i	$-0.894044\pi$
$643$	−36.9983	+	13.4663i	−1.45907	+	0.531058i	−0.513961	+	0.857814i	$0.671822\pi$
$644$	27.0061	−	15.0808i	1.06419	−	0.594267i
$645$		0			0
$646$	2.48105	+	14.0708i	0.0976158	+	0.553607i
$647$	0.110173	+	0.190824i	0.00433133	+	0.00750208i	0.868183	−	0.496244i	$-0.165288\pi$
$647$	0.110173	+	0.190824i	0.00433133	+	0.00750208i	−0.863852	+	0.503746i	$0.831955\pi$
$648$		0			0
$649$	−5.92150	+	10.2563i	−0.232439	+	0.402597i
$650$	29.4702	−	24.7285i	1.15592	−	0.969930i
$651$		0			0
$652$	−1.95784	+	11.1035i	−0.0766749	+	0.434845i
$653$	−4.32225	+	24.5127i	−0.169143	+	0.959256i	0.775547	+	0.631290i	$0.217474\pi$
$653$	−4.32225	+	24.5127i	−0.169143	+	0.959256i	−0.944690	+	0.327966i	$0.893637\pi$
$654$		0			0
$655$	5.38226	−	4.51625i	0.210302	−	0.176465i
$656$	18.5005			0.722323
$657$		0			0
$658$	−18.7893	−	23.0544i	−0.732483	−	0.898754i
$659$	0.718602	+	0.261550i	0.0279928	+	0.0101885i	0.355979	−	0.934494i	$-0.384148\pi$
$659$	0.718602	+	0.261550i	0.0279928	+	0.0101885i	−0.327986	+	0.944683i	$0.606370\pi$
$660$		0			0
$661$	−3.69556	+	20.9586i	−0.143741	+	0.815193i	0.824629	+	0.565674i	$0.191384\pi$
$661$	−3.69556	+	20.9586i	−0.143741	+	0.815193i	−0.968370	+	0.249520i	$0.919727\pi$
$662$	−4.78276	+	27.1244i	−0.185887	+	1.05422i
$663$		0			0
$664$	−1.27395	−	0.463681i	−0.0494390	−	0.0179943i
$665$	−1.83183	−	2.24765i	−0.0710353	−	0.0871601i
$666$		0			0
$667$	0.250822			0.00971187
$668$	11.4247	−	9.58648i	0.442036	−	0.370912i
$669$		0			0
$670$	0.206679	−	1.17213i	0.00798470	−	0.0452835i
$671$	0.444661	−	2.52180i	0.0171659	−	0.0973529i
$672$		0			0
$673$	−18.7235	+	15.7109i	−0.721737	+	0.605609i	−0.927865	−	0.372916i	$-0.878358\pi$
$673$	−18.7235	+	15.7109i	−0.721737	+	0.605609i	0.206128	+	0.978525i	$0.433914\pi$
$674$	−24.8318	+	43.0099i	−0.956485	+	1.65668i
$675$		0			0
$676$	−7.80247	−	13.5143i	−0.300095	−	0.519779i
$677$	−4.91971	−	27.9011i	−0.189080	−	1.07233i	−0.920600	−	0.390506i	$-0.872300\pi$
$677$	−4.91971	−	27.9011i	−0.189080	−	1.07233i	0.731520	−	0.681820i	$-0.238811\pi$
$678$		0			0
$679$	29.2190	−	16.3166i	1.12132	−	0.626173i
$680$	1.01694	−	0.370137i	0.0389980	−	0.0141941i
$681$		0			0
$682$	1.17507	−	0.986005i	0.0449959	−	0.0377561i
$683$	−1.72661	+	2.99057i	−0.0660668	+	0.114431i	−0.897167	−	0.441692i	$-0.854378\pi$
$683$	−1.72661	+	2.99057i	−0.0660668	+	0.114431i	0.831100	+	0.556123i	$0.187712\pi$
$684$		0			0
$685$	−0.779912	+	1.35085i	−0.0297989	+	0.0516132i
$686$	14.3339	−	34.6735i	0.547272	−	1.32384i
$687$		0			0
$688$	26.1841	−	9.53022i	0.998259	−	0.363336i
$689$	−5.99917	+	34.0230i	−0.228550	+	1.29617i
$690$		0			0
$691$	37.7308	−	31.6599i	1.43535	−	1.20440i	0.492884	−	0.870095i	$-0.335943\pi$
$691$	37.7308	−	31.6599i	1.43535	−	1.20440i	0.942465	−	0.334306i	$-0.108502\pi$
$692$	−19.0746	+	33.0382i	−0.725107	+	1.25592i
$693$		0			0
$694$	12.7076	+	22.0103i	0.482375	+	0.835499i
$695$	−9.73687	−	3.54393i	−0.369340	−	0.134429i
$696$		0			0
$697$	21.5385	+	18.0730i	0.815829	+	0.684562i
$698$	−40.4938	−	33.9784i	−1.53271	−	1.28610i
$699$		0			0
$700$	15.2939	−	17.7056i	0.578054	−	0.669209i
$701$	26.2546			0.991624			0.495812	−	0.868430i	$-0.334870\pi$
$701$	26.2546			0.991624			0.495812	+	0.868430i	$0.334870\pi$
$702$		0			0
$703$	6.30573	+	10.9218i	0.237825	+	0.411925i
$704$	26.0201	+	9.47053i	0.980668	+	0.356934i
$705$		0			0
$706$	−8.37976	+	47.5240i	−0.315377	+	1.78859i
$707$	0.384608	−	26.8709i	0.0144647	−	1.01058i
$708$		0			0
$709$	7.39480	+	2.69149i	0.277718	+	0.101081i	0.477124	−	0.878836i	$-0.341679\pi$
$709$	7.39480	+	2.69149i	0.277718	+	0.101081i	−0.199407	+	0.979917i	$0.563901\pi$
$710$	−6.79934	+	11.7768i	−0.255175	+	0.441976i
$711$		0			0
$712$	1.33000	+	2.30363i	0.0498439	+	0.0863321i
$713$	1.25785	+	0.457821i	0.0471069	+	0.0171455i
$714$		0			0
$715$	−9.71382	−	8.15086i	−0.363276	−	0.304825i
$716$	−31.4933	+	11.4626i	−1.17696	+	0.428378i
$717$		0			0
$718$	−6.57454	−	37.2861i	−0.245360	−	1.39150i
$719$	−5.36852	−	9.29854i	−0.200212	−	0.346777i	0.748385	−	0.663265i	$-0.230830\pi$
$719$	−5.36852	−	9.29854i	−0.200212	−	0.346777i	−0.948597	+	0.316488i	$0.897496\pi$
$720$		0			0
$721$	−25.0322	−	30.7144i	−0.932248	−	1.14387i
$722$	6.15400	+	34.9011i	0.229028	+	1.29888i
$723$		0			0
$724$	38.0122	+	31.8960i	1.41271	+	1.18541i
$725$	0.178279	−	0.0648881i	0.00662110	−	0.00240988i
$726$		0			0
$727$	−3.16208	+	2.65330i	−0.117275	+	0.0984056i	−0.699539	−	0.714594i	$-0.746611\pi$
$727$	−3.16208	+	2.65330i	−0.117275	+	0.0984056i	0.582264	+	0.813000i	$0.302167\pi$
$728$	−1.59301	−	1.95461i	−0.0590407	−	0.0724428i
$729$		0			0
$730$	8.81467	−	15.2675i	0.326246	−	0.565074i
$731$	39.7938	+	14.4838i	1.47183	+	0.535701i
$732$		0			0
$733$	−15.0457	−	12.6249i	−0.555726	−	0.466310i	0.321148	−	0.947029i	$-0.395931\pi$
$733$	−15.0457	−	12.6249i	−0.555726	−	0.466310i	−0.876875	+	0.480719i	$0.840376\pi$
$734$	46.9810	−	17.0997i	1.73410	−	0.631161i
$735$		0			0
$736$	7.79730	+	44.2207i	0.287412	+	1.63000i
$737$	2.06800			0.0761758
$738$		0			0
$739$	−25.9618			−0.955019			−0.477509	−	0.878627i	$-0.658460\pi$
$739$	−25.9618			−0.955019			−0.477509	+	0.878627i	$0.658460\pi$
$740$	14.7882	−	12.4088i	0.543625	−	0.456155i
$741$		0			0
$742$	−0.586519	+	40.9775i	−0.0215318	+	1.50433i
$743$	11.7874	+	9.89080i	0.432438	+	0.362858i	0.832871	−	0.553468i	$-0.186696\pi$
$743$	11.7874	+	9.89080i	0.432438	+	0.362858i	−0.400433	+	0.916326i	$0.631140\pi$
$744$		0			0
$745$	1.41518	+	8.02590i	0.0518483	+	0.294046i
$746$	−60.8243			−2.22694
$747$		0			0
$748$	19.0002	+	32.9092i	0.694715	+	1.20328i
$749$	−12.6614	−	36.3996i	−0.462639	−	1.33001i
$750$		0			0
$751$	−2.84804	+	16.1520i	−0.103927	+	0.589396i	0.887717	+	0.460389i	$0.152290\pi$
$751$	−2.84804	+	16.1520i	−0.103927	+	0.589396i	−0.991644	+	0.129007i	$0.958821\pi$
$752$	19.7144	−	7.17547i	0.718912	−	0.261662i
$753$		0			0
$754$	−0.0717550	−	0.406943i	−0.00261316	−	0.0148200i
$755$	−8.33024			−0.303169
$756$		0			0
$757$	−15.8693			−0.576779			−0.288389	−	0.957513i	$-0.593120\pi$
$757$	−15.8693			−0.576779			−0.288389	+	0.957513i	$0.593120\pi$
$758$	−10.4285	−	59.1430i	−0.378781	−	2.14817i
$759$		0			0
$760$	−0.217220	+	0.0790615i	−0.00787939	+	0.00286786i
$761$	4.30253	−	24.4009i	0.155967	−	0.884531i	−0.801930	−	0.597418i	$-0.796193\pi$
$761$	4.30253	−	24.4009i	0.155967	−	0.884531i	0.957897	−	0.287113i	$-0.0926956\pi$
$762$		0			0
$763$	8.80448	+	1.68274i	0.318744	+	0.0609191i
$764$	22.6504	+	39.2317i	0.819463	+	1.41935i
$765$		0			0
$766$	6.32531			0.228543
$767$	2.95652	+	16.7673i	0.106754	+	0.605431i
$768$		0			0
$769$	−18.0600	−	15.1541i	−0.651261	−	0.546473i	0.256193	−	0.966626i	$-0.417532\pi$
$769$	−18.0600	−	15.1541i	−0.651261	−	0.546473i	−0.907453	+	0.420153i	$0.861976\pi$
$770$	−12.9178	−	7.70666i	−0.465524	−	0.277729i
$771$		0			0
$772$	14.1600	−	11.8817i	0.509630	−	0.427630i
$773$	−6.30291			−0.226700			−0.113350	−	0.993555i	$-0.536158\pi$
$773$	−6.30291			−0.226700			−0.113350	+	0.993555i	$0.536158\pi$
$774$		0			0
$775$	1.01249			0.0363697
$776$	−0.463292	−	2.62746i	−0.0166312	−	0.0943203i
$777$		0			0
$778$	13.6353	−	4.96284i	0.488849	−	0.177927i
$779$	−4.60064	−	3.86040i	−0.164835	−	0.138313i
$780$		0			0
$781$	−22.2028	−	8.08116i	−0.794479	−	0.289167i
$782$	−32.3399	+	56.0144i	−1.15647	+	2.00307i
$783$		0			0
$784$	19.7793	+	17.5856i	0.706404	+	0.628058i
$785$	−8.94878	+	7.50892i	−0.319396	+	0.268005i
$786$		0			0
$787$	6.97760	−	2.53964i	0.248725	−	0.0905284i	−0.214649	−	0.976691i	$-0.568861\pi$
$787$	6.97760	−	2.53964i	0.248725	−	0.0905284i	0.463374	+	0.886163i	$0.346639\pi$
$788$	5.39859	+	4.52996i	0.192317	+	0.161373i
$789$		0			0
$790$	−4.15657	−	23.5731i	−0.147884	−	0.838693i
$791$	−12.6734	+	33.3279i	−0.450615	+	1.18500i
$792$		0			0
$793$	−1.84068	−	3.18814i	−0.0653643	−	0.113214i
$794$	−6.50574	−	36.8959i	−0.230880	−	1.30939i
$795$		0			0
$796$	22.6157	−	8.23143i	0.801591	−	0.291755i
$797$	−2.15575	−	1.80889i	−0.0763606	−	0.0640741i	0.603808	−	0.797129i	$-0.293649\pi$
$797$	−2.15575	−	1.80889i	−0.0763606	−	0.0640741i	−0.680169	+	0.733055i	$0.738094\pi$
$798$		0			0
$799$	29.9615	+	10.9051i	1.05996	+	0.385794i
$800$	16.9821	+	29.4139i	0.600408	+	1.03994i
$801$		0			0
$802$	18.5853	−	32.1908i	0.656271	−	1.13670i
$803$	28.7837	+	10.4764i	1.01576	+	0.369705i
$804$		0			0
$805$	0.187858	−	13.1248i	0.00662112	−	0.462589i
$806$	0.382940	−	2.17176i	0.0134885	−	0.0764969i
$807$		0			0
$808$	−2.01322	−	0.732753i	−0.0708249	−	0.0257781i
$809$	13.4130	+	23.2321i	0.471577	+	0.816796i	0.999471	−	0.0325145i	$-0.0103515\pi$
$809$	13.4130	+	23.2321i	0.471577	+	0.816796i	−0.527894	+	0.849310i	$0.677018\pi$
$810$		0			0
$811$	10.4409			0.366628			0.183314	−	0.983054i	$-0.441317\pi$
$811$	10.4409			0.366628			0.183314	+	0.983054i	$0.441317\pi$
$812$	−0.0825629	−	0.237356i	−0.00289739	−	0.00832955i
$813$		0			0
$814$	50.1176	+	42.0537i	1.75662	+	1.47398i
$815$	3.66519	+	3.07546i	0.128386	+	0.107729i
$816$		0			0
$817$	−8.49999	−	3.09374i	−0.297377	−	0.108236i
$818$	−0.108766	−	0.188387i	−0.00380290	−	0.00658681i
$819$		0			0
$820$	−4.59653	+	7.96143i	−0.160518	+	0.278025i
$821$	25.1065	−	21.0669i	0.876223	−	0.735239i	−0.0891758	−	0.996016i	$-0.528423\pi$
$821$	25.1065	−	21.0669i	0.876223	−	0.735239i	0.965399	+	0.260777i	$0.0839788\pi$
$822$		0			0
$823$	−0.718184	+	4.07302i	−0.0250343	+	0.141977i	−0.994763	−	0.102208i	$-0.967409\pi$
$823$	−0.718184	+	4.07302i	−0.0250343	+	0.141977i	0.969729	+	0.244185i	$0.0785203\pi$
$824$	−2.96834	+	1.08039i	−0.103407	+	0.0376370i
$825$		0			0
$826$	6.63535	+	19.0756i	0.230873	+	0.663725i
$827$	1.68730	−	2.92249i	0.0586731	−	0.101625i	−0.835197	−	0.549951i	$-0.814646\pi$
$827$	1.68730	−	2.92249i	0.0586731	−	0.101625i	0.893870	+	0.448326i	$0.147980\pi$
$828$		0			0
$829$	−2.13210	+	3.69291i	−0.0740510	+	0.128260i	−0.900673	−	0.434497i	$-0.856926\pi$
$829$	−2.13210	+	3.69291i	−0.0740510	+	0.128260i	0.826622	+	0.562757i	$0.190259\pi$
$830$	−8.90655	+	7.47348i	−0.309151	+	0.259408i
$831$		0			0
$832$	37.4074	−	13.6152i	1.29687	−	0.472021i
$833$	5.84808	+	39.7956i	0.202624	+	1.37884i
$834$		0			0
$835$	−1.09900	−	6.23274i	−0.0380325	−	0.215693i
$836$	−4.05845	−	7.02944i	−0.140364	−	0.243118i
$837$		0			0
$838$	−1.48964	+	2.58014i	−0.0514589	+	0.0891294i
$839$	−32.5305	+	27.2963i	−1.12308	+	0.942374i	−0.998756	−	0.0498679i	$-0.984120\pi$
$839$	−32.5305	+	27.2963i	−1.12308	+	0.942374i	−0.124322	+	0.992242i	$0.539676\pi$
$840$		0			0
$841$	−5.03544	+	28.5574i	−0.173636	+	0.984739i
$842$	11.1251	−	63.0937i	0.383397	−	2.17435i
$843$		0			0
$844$	−29.1506	+	24.4603i	−1.00341	+	0.841958i
$845$	−6.62213			−0.227808
$846$		0			0
$847$	−1.05485	+	2.77399i	−0.0362450	+	0.0953154i
$848$	−27.1654	−	9.88738i	−0.932862	−	0.339534i
$849$		0			0
$850$	−8.49546	+	48.1802i	−0.291392	+	1.65257i
$851$	−9.91377	+	56.2238i	−0.339839	+	1.92733i
$852$		0			0
$853$	12.8564	+	4.67934i	0.440194	+	0.160218i	0.552603	−	0.833444i	$-0.313635\pi$
$853$	12.8564	+	4.67934i	0.440194	+	0.160218i	−0.112409	+	0.993662i	$0.535857\pi$
$854$	−2.75885	−	3.38510i	−0.0944058	−	0.115836i
$855$		0			0
$856$	−3.07240			−0.105013
$857$	15.9711	−	13.4014i	0.545563	−	0.457782i	−0.327872	−	0.944722i	$-0.606332\pi$
$857$	15.9711	−	13.4014i	0.545563	−	0.457782i	0.873435	+	0.486940i	$0.161887\pi$
$858$		0			0
$859$	−7.24341	+	41.0794i	−0.247142	+	1.40161i	0.568323	+	0.822805i	$0.307592\pi$
$859$	−7.24341	+	41.0794i	−0.247142	+	1.40161i	−0.815465	+	0.578806i	$0.803519\pi$
$860$	−2.40436	+	13.6358i	−0.0819879	+	0.464976i
$861$		0			0
$862$	41.6581	−	34.9553i	1.41888	−	1.19058i
$863$	19.8828	−	34.4380i	0.676818	−	1.17228i	−0.299116	−	0.954217i	$-0.596692\pi$
$863$	19.8828	−	34.4380i	0.676818	−	1.17228i	0.975934	−	0.218066i	$-0.0699749\pi$
$864$		0			0
$865$	8.09452	+	14.0201i	0.275222	+	0.476699i
$866$	−1.68050	−	9.53057i	−0.0571056	−	0.323862i
$867$		0			0
$868$	0.0191943	−	1.34102i	0.000651496	−	0.0455172i
$869$	39.0819	−	14.2247i	1.32576	−	0.482539i
$870$		0			0
$871$	2.27747	−	1.91103i	0.0771693	−	0.0647527i
$872$	0.357309	−	0.618877i	0.0121000	−	0.0209578i
$873$		0			0
$874$	6.90784	−	11.9647i	0.233661	−	0.404713i
$875$	−7.14257	−	20.5338i	−0.241463	−	0.694169i
$876$		0			0
$877$	−10.8684	+	3.95578i	−0.367001	+	0.133577i	−0.518936	−	0.854813i	$-0.673672\pi$
$877$	−10.8684	+	3.95578i	−0.367001	+	0.133577i	0.151935	+	0.988390i	$0.451449\pi$
$878$	−7.08362	+	40.1732i	−0.239061	+	1.35578i
$879$		0			0
$880$	8.12828	−	6.82044i	0.274004	−	0.229917i
$881$	−27.8765	+	48.2835i	−0.939183	+	1.62671i	−0.172183	+	0.985065i	$0.555082\pi$
$881$	−27.8765	+	48.2835i	−0.939183	+	1.62671i	−0.767000	+	0.641648i	$0.778251\pi$
$882$		0			0
$883$	2.15109	+	3.72580i	0.0723900	+	0.125383i	0.899948	−	0.435997i	$-0.143604\pi$
$883$	2.15109	+	3.72580i	0.0723900	+	0.125383i	−0.827558	+	0.561380i	$0.810271\pi$
$884$	51.3360	+	18.6848i	1.72662	+	0.628436i
$885$		0			0
$886$	41.7461	+	35.0291i	1.40249	+	1.17683i
$887$	−25.8665	−	21.7046i	−0.868513	−	0.728769i	0.0952713	−	0.995451i	$-0.469628\pi$
$887$	−25.8665	−	21.7046i	−0.868513	−	0.728769i	−0.963785	+	0.266682i	$0.914073\pi$
$888$		0			0
$889$	−28.9221	−	5.52766i	−0.970015	−	0.185392i
$890$	22.8123			0.764671
$891$		0			0
$892$	12.9601	+	22.4475i	0.433936	+	0.751599i
$893$	−6.39979	−	2.32933i	−0.214161	−	0.0779482i
$894$		0			0
$895$	−2.46967	+	14.0062i	−0.0825519	+	0.468175i
$896$	3.89259	−	2.17371i	0.130042	−	0.0726185i
$897$		0			0
$898$	26.7469	+	9.73506i	0.892554	+	0.324863i
$899$	0.00543768	−	0.00941834i	0.000181357	−	0.000314119i
$900$		0			0
$901$	−21.9674	−	38.0486i	−0.731839	−	1.26758i
$902$	−29.2767	−	10.6558i	−0.974806	−	0.354800i
$903$		0			0
$904$	2.17755	+	1.82718i	0.0724242	+	0.0607711i
$905$	19.7875	−	7.20206i	0.657759	−	0.239405i
$906$		0			0
$907$	−6.05264	−	34.3262i	−0.200975	−	1.13978i	−0.903650	−	0.428272i	$-0.859122\pi$
$907$	−6.05264	−	34.3262i	−0.200975	−	1.13978i	0.702675	−	0.711511i	$-0.251989\pi$
$908$	−25.0541	−	43.3949i	−0.831449	−	1.44011i
$909$		0			0
$910$	−21.3479	+	3.44995i	−0.707677	+	0.114365i
$911$	−4.81005	−	27.2792i	−0.159364	−	0.903799i	−0.954687	−	0.297612i	$-0.903810\pi$
$911$	−4.81005	−	27.2792i	−0.159364	−	0.903799i	0.795323	−	0.606186i	$-0.207301\pi$
$912$		0			0
$913$	−15.4751	−	12.9852i	−0.512152	−	0.429747i
$914$	69.9199	−	25.4488i	2.31274	−	0.841770i
$915$		0			0
$916$	−36.4380	+	30.5751i	−1.20394	+	1.01023i
$917$	20.5521	−	3.32134i	0.678689	−	0.109680i
$918$		0			0
$919$	3.35232	−	5.80639i	0.110583	−	0.191535i	−0.805423	−	0.592701i	$-0.798062\pi$
$919$	3.35232	−	5.80639i	0.110583	−	0.191535i	0.916005	+	0.401166i	$0.131395\pi$
$920$	−0.983337	−	0.357905i	−0.0324197	−	0.0117998i
$921$		0			0
$922$	−65.6807	−	55.1127i	−2.16308	−	1.81504i
$923$	−31.9195	+	11.6178i	−1.05064	+	0.382403i
$924$		0			0
$925$	7.49870	+	42.5273i	0.246556	+	1.39829i
$926$	38.4340			1.26302
$927$		0			0
$928$	0.364816			0.0119757
$929$	21.2390	−	17.8217i	0.696830	−	0.584710i	−0.224040	−	0.974580i	$-0.571925\pi$
$929$	21.2390	−	17.8217i	0.696830	−	0.584710i	0.920870	+	0.389870i	$0.127480\pi$
$930$		0			0
$931$	−1.24915	−	8.50038i	−0.0409394	−	0.278589i
$932$	−0.491180	−	0.412149i	−0.0160891	−	0.0135004i
$933$		0			0
$934$	5.24717	+	29.7582i	0.171693	+	0.973718i
$935$	16.1259			0.527373
$936$		0			0
$937$	5.30815	+	9.19398i	0.173410	+	0.300354i	0.939610	−	0.342248i	$-0.111188\pi$
$937$	5.30815	+	9.19398i	0.173410	+	0.300354i	−0.766200	+	0.642602i	$0.777855\pi$
$938$	2.30535	−	2.66889i	0.0752725	−	0.0871424i
$939$		0			0
$940$	−1.81028	+	10.2666i	−0.0590449	+	0.334860i
$941$	−23.9722	+	8.72516i	−0.781471	+	0.284432i	−0.701786	−	0.712388i	$-0.747614\pi$
$941$	−23.9722	+	8.72516i	−0.781471	+	0.284432i	−0.0796851	+	0.996820i	$0.525391\pi$
$942$		0			0
$943$	−4.72104	−	26.7744i	−0.153738	−	0.871893i
$944$	−14.2469			−0.463696
$945$		0			0
$946$	−46.9249			−1.52566
$947$	6.50665	+	36.9010i	0.211438	+	1.19912i	0.886982	+	0.461803i	$0.152797\pi$
$947$	6.50665	+	36.9010i	0.211438	+	1.19912i	−0.675545	+	0.737319i	$0.736092\pi$
$948$		0			0
$949$	41.3805	−	15.0613i	1.34327	−	0.488909i
$950$	1.81464	−	10.2913i	0.0588746	−	0.333895i
$951$		0			0
$952$	3.14966	+	0.601970i	0.102081	+	0.0195100i
$953$	12.1658	+	21.0717i	0.394088	+	0.682581i	0.992984	−	0.118246i	$-0.0377271\pi$
$953$	12.1658	+	21.0717i	0.394088	+	0.682581i	−0.598896	+	0.800827i	$0.704394\pi$
$954$		0			0
$955$	19.2239			0.622072
$956$	8.82824	+	50.0675i	0.285526	+	1.61930i
$957$		0			0
$958$	20.6374	+	17.3168i	0.666765	+	0.559482i
$959$	−4.03533	+	2.25342i	−0.130308	+	0.0727667i
$960$		0			0
$961$	−23.7029	+	19.8891i	−0.764610	+	0.641584i
$962$	94.0556			3.03248
$963$		0			0
$964$	30.0679			0.968422
$965$	−1.36212	−	7.72498i	−0.0438483	−	0.248676i
$966$		0			0
$967$	25.7639	−	9.37729i	0.828511	−	0.301553i	0.107263	−	0.994231i	$-0.465791\pi$
$967$	25.7639	−	9.37729i	0.828511	−	0.301553i	0.721247	+	0.692678i	$0.243569\pi$
$968$	0.181244	+	0.152082i	0.00582542	+	0.00488810i
$969$		0			0
$970$	−21.5010	−	7.82572i	−0.690355	−	0.251269i
$971$	19.2320	−	33.3107i	0.617183	−	1.06899i	−0.372814	−	0.927906i	$-0.621607\pi$
$971$	19.2320	−	33.3107i	0.617183	−	1.06899i	0.989997	−	0.141086i	$-0.0450595\pi$
$972$		0			0
$973$	−19.3967	−	23.7997i	−0.621829	−	0.762983i
$974$	20.4853	−	17.1892i	0.656391	−	0.550777i
$975$		0			0
$976$	2.89469	−	1.05358i	0.0926567	−	0.0337243i
$977$	−2.29374	−	1.92468i	−0.0733834	−	0.0615759i	0.605358	−	0.795953i	$-0.293030\pi$
$977$	−2.29374	−	1.92468i	−0.0733834	−	0.0615759i	−0.678742	+	0.734377i	$0.737474\pi$
$978$		0			0
$979$	6.88280	+	39.0343i	0.219975	+	1.24754i
$980$	−12.4820	+	4.14252i	−0.398723	+	0.132328i
$981$		0			0
$982$	16.5034	+	28.5848i	0.526646	+	0.912178i
$983$	−1.90484	−	10.8029i	−0.0607551	−	0.344559i	−0.999999	−	0.00130907i	$-0.999583\pi$
$983$	−1.90484	−	10.8029i	−0.0607551	−	0.344559i	0.939244	−	0.343250i	$-0.111528\pi$
$984$		0			0
$985$	2.81027	−	1.02286i	0.0895428	−	0.0325909i
$986$	0.402553	+	0.337782i	0.0128199	+	0.0107572i
$987$		0			0
$988$	−10.9654	−	3.99108i	−0.348856	−	0.126973i
$989$	−20.4741	−	35.4623i	−0.651040	−	1.12763i
$990$		0			0
$991$	−22.3557	+	38.7211i	−0.710151	+	1.23002i	0.254650	+	0.967033i	$0.418040\pi$
$991$	−22.3557	+	38.7211i	−0.710151	+	1.23002i	−0.964800	+	0.262984i	$0.915293\pi$
$992$	1.82952	+	0.665892i	0.0580874	+	0.0211421i
$993$		0			0
$994$	−35.1804	+	19.6455i	−1.11585	+	0.623118i
$995$	1.77349	−	10.0580i	0.0562235	−	0.318860i
$996$		0			0
$997$	1.61995	+	0.589615i	0.0513044	+	0.0186733i	0.367545	−	0.930006i	$-0.380198\pi$
$997$	1.61995	+	0.589615i	0.0513044	+	0.0186733i	−0.316240	+	0.948679i	$0.602421\pi$
$998$	0.223946	+	0.387885i	0.00708888	+	0.0122783i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.w.a.37.4		132
3.2	odd	2		189.2.w.a.184.19	yes	132
7.4	even	3		567.2.u.a.361.19		132
21.11	odd	6		189.2.u.a.130.4	yes	132
27.11	odd	18		189.2.u.a.16.4	✓	132
27.16	even	9		567.2.u.a.289.19		132
189.11	odd	18		189.2.w.a.151.19	yes	132
189.151	even	9	inner	567.2.w.a.46.4		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.16.4	✓	132	27.11	odd	18
189.2.u.a.130.4	yes	132	21.11	odd	6
189.2.w.a.151.19	yes	132	189.11	odd	18
189.2.w.a.184.19	yes	132	3.2	odd	2
567.2.u.a.289.19		132	27.16	even	9
567.2.u.a.361.19		132	7.4	even	3
567.2.w.a.37.4		132	1.1	even	1	trivial
567.2.w.a.46.4		132	189.151	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.w (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.351787 - 1.99508i) q^{2} +(-1.97722 + 0.719650i) q^{4} +(-0.155052 + 0.879341i) q^{5} +(-1.72949 + 2.00222i) q^{7} +(0.105462 + 0.182666i) q^{8} +1.80890 q^{10} +(0.545772 + 3.09523i) q^{11} +(3.46133 + 2.90440i) q^{13} +(4.60300 + 2.74612i) q^{14} +(-2.89636 + 2.43033i) q^{16} -5.74615 q^{17} +1.22738 q^{19} +(-0.326246 - 1.85024i) q^{20} +(5.98324 - 2.17772i) q^{22} +(4.25634 + 3.57150i) q^{23} +(3.94926 + 1.43741i) q^{25} +(4.57688 - 7.92738i) q^{26} +(1.97869 - 5.20345i) q^{28} +(0.0345809 - 0.0290169i) q^{29} +(0.226384 - 0.0823972i) q^{31} +(6.19078 + 5.19468i) q^{32} +(2.02142 + 11.4640i) q^{34} +(-1.49247 - 1.83126i) q^{35} +(5.13755 + 8.89849i) q^{37} +(-0.431777 - 2.44873i) q^{38} +(-0.176978 + 0.0644148i) q^{40} +(-3.74834 - 3.14523i) q^{41} +(-6.92531 - 2.52060i) q^{43} +(-3.30659 - 5.72718i) q^{44} +(5.62811 - 9.74817i) q^{46} +(-5.21418 - 1.89781i) q^{47} +(-1.01774 - 6.92562i) q^{49} +(1.47846 - 8.38478i) q^{50} +(-8.93398 - 3.25170i) q^{52} +(3.82297 + 6.62158i) q^{53} -2.80638 q^{55} +(-0.548134 - 0.104761i) q^{56} +(-0.0700562 - 0.0587841i) q^{58} +(2.88652 + 2.42208i) q^{59} +(-0.765603 - 0.278657i) q^{61} +(-0.244029 - 0.422670i) q^{62} +(4.40506 - 7.62979i) q^{64} +(-3.09065 + 2.59336i) q^{65} +(0.114256 - 0.647980i) q^{67} +(11.3614 - 4.13522i) q^{68} +(-3.12848 + 3.62182i) q^{70} +(-3.75882 + 6.51047i) q^{71} +(4.87293 - 8.44017i) q^{73} +(15.9459 - 13.3802i) q^{74} +(-2.42681 + 0.883285i) q^{76} +(-7.14122 - 4.26040i) q^{77} +(-2.29784 - 13.0317i) q^{79} +(-1.68801 - 2.92371i) q^{80} +(-4.95638 + 8.58471i) q^{82} +(-4.92372 + 4.13150i) q^{83} +(0.890949 - 5.05282i) q^{85} +(-2.59259 + 14.7033i) q^{86} +(-0.507835 + 0.426124i) q^{88} +12.6111 q^{89} +(-11.8016 + 1.90720i) q^{91} +(-10.9860 - 3.99856i) q^{92} +(-1.95200 + 11.0704i) q^{94} +(-0.190307 + 1.07929i) q^{95} +(-11.8862 - 4.32622i) q^{97} +(-13.4592 + 4.46682i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} - 6 q^{10} - 3 q^{11} - 12 q^{13} - 15 q^{14} - 9 q^{16} + 54 q^{17} - 6 q^{19} + 18 q^{20} - 12 q^{22} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29}+ \cdots - 99 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8 - 6 * q^10 - 3 * q^11 - 12 * q^13 - 15 * q^14 - 9 * q^16 + 54 * q^17 - 6 * q^19 + 18 * q^20 - 12 * q^22 - 3 * q^25 - 30 * q^26 - 12 * q^28 + 30 * q^29 - 3 * q^31 - 51 * q^32 - 18 * q^34 + 12 * q^35 + 3 * q^37 + 57 * q^38 - 66 * q^40 - 12 * q^43 - 3 * q^44 + 3 * q^46 + 21 * q^47 + 12 * q^49 + 39 * q^50 + 9 * q^52 - 9 * q^53 - 24 * q^55 - 57 * q^56 - 3 * q^58 + 18 * q^59 + 33 * q^61 - 75 * q^62 - 30 * q^64 - 81 * q^65 - 3 * q^67 - 6 * q^68 - 42 * q^70 + 18 * q^71 + 21 * q^73 + 93 * q^74 - 24 * q^76 - 87 * q^77 + 15 * q^79 - 102 * q^80 - 6 * q^82 + 42 * q^83 - 63 * q^85 - 159 * q^86 + 57 * q^88 + 150 * q^89 + 6 * q^91 + 66 * q^92 + 33 * q^94 + 147 * q^95 - 12 * q^97 - 99 * q^98

Introduction

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