LMFDB - Embedded newform 441.2.bb.e.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$5$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			37.2
Character	$\chi$	$=$	441.37
Dual form			441.2.bb.e.298.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04710 + 0.713898i) q^{2} +(-0.143921 + 0.366706i) q^{4} +(-1.23854 - 0.382039i) q^{5} +(2.59083 + 0.536271i) q^{7} +(-0.675095 - 2.95778i) q^{8} +O(q^{10})$	\(q+(-1.04710 + 0.713898i) q^{2} +(-0.143921 + 0.366706i) q^{4} +(-1.23854 - 0.382039i) q^{5} +(2.59083 + 0.536271i) q^{7} +(-0.675095 - 2.95778i) q^{8} +(1.56961 - 0.484160i) q^{10} +(0.384291 + 5.12800i) q^{11} +(-1.76984 - 0.852310i) q^{13} +(-3.09570 + 1.28806i) q^{14} +(2.24089 + 2.07925i) q^{16} +(4.91447 + 0.740736i) q^{17} +(-3.33107 + 5.76957i) q^{19} +(0.318349 - 0.399197i) q^{20} +(-4.06326 - 5.09517i) q^{22} +(-4.69902 + 0.708264i) q^{23} +(-2.74316 - 1.87026i) q^{25} +(2.46166 - 0.371035i) q^{26} +(-0.569530 + 0.872893i) q^{28} +(-4.28689 + 5.37560i) q^{29} +(-0.371361 - 0.643217i) q^{31} +(2.16912 + 0.326943i) q^{32} +(-5.67473 + 2.73281i) q^{34} +(-3.00397 - 1.65399i) q^{35} +(-3.11350 - 7.93306i) q^{37} +(-0.630943 - 8.41934i) q^{38} +(-0.293857 + 3.92125i) q^{40} +(1.45940 + 6.39404i) q^{41} +(-2.60820 + 11.4273i) q^{43} +(-1.93578 - 0.597108i) q^{44} +(4.41470 - 4.09625i) q^{46} +(-2.15329 + 1.46809i) q^{47} +(6.42483 + 2.77878i) q^{49} +4.20753 q^{50} +(0.567265 - 0.526345i) q^{52} +(0.584212 - 1.48855i) q^{53} +(1.48314 - 6.49805i) q^{55} +(-0.162885 - 8.02516i) q^{56} +(0.651164 - 8.68918i) q^{58} +(3.40655 - 1.05078i) q^{59} +(0.0708345 + 0.180483i) q^{61} +(0.848043 + 0.408396i) q^{62} +(-8.01310 + 3.85891i) q^{64} +(1.86640 + 1.73177i) q^{65} +(3.84338 + 6.65692i) q^{67} +(-0.978930 + 1.69556i) q^{68} +(4.32624 - 0.412643i) q^{70} +(-3.49267 - 4.37967i) q^{71} +(2.28205 + 1.55588i) q^{73} +(8.92353 + 6.08396i) q^{74} +(-1.63633 - 2.05189i) q^{76} +(-1.75437 + 13.4919i) q^{77} +(-0.398609 + 0.690411i) q^{79} +(-1.98109 - 3.43134i) q^{80} +(-6.09283 - 5.65332i) q^{82} +(-2.92509 + 1.40865i) q^{83} +(-5.80377 - 2.79495i) q^{85} +(-5.42686 - 13.8274i) q^{86} +(14.9081 - 4.59854i) q^{88} +(0.432462 - 5.77081i) q^{89} +(-4.12829 - 3.15731i) q^{91} +(0.416566 - 1.82509i) q^{92} +(1.20664 - 3.07446i) q^{94} +(6.32986 - 5.87325i) q^{95} +15.6804 q^{97} +(-8.71118 + 1.67703i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) $ 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8	$ 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8} - 34 q^{10} + 11 q^{11} - 2 q^{13} - 40 q^{14} - 31 q^{16} + 9 q^{17} - 29 q^{19} + 43 q^{20} + 9 q^{22} + 4 q^{23} + 55 q^{25} - 36 q^{26} - 57 q^{28} - 4 q^{29} - 39 q^{31} + 92 q^{32} - 36 q^{34} + 33 q^{35} - 24 q^{37} - 118 q^{38} - 35 q^{41} + 2 q^{43} - 40 q^{44} - 40 q^{46} + 5 q^{47} + 129 q^{49} + 176 q^{50} - 6 q^{52} - 26 q^{53} + 2 q^{55} - 63 q^{56} + 11 q^{58} + 41 q^{59} + 6 q^{61} - 36 q^{62} + 74 q^{64} + 51 q^{65} - 55 q^{67} + 22 q^{68} - 68 q^{70} + 66 q^{71} + 24 q^{73} - 28 q^{74} + 3 q^{76} + 34 q^{77} - 51 q^{79} + 5 q^{80} - 41 q^{82} - 30 q^{83} + 68 q^{85} - 110 q^{86} + 129 q^{88} - 75 q^{89} + 5 q^{91} + 38 q^{94} - 36 q^{95} - 168 q^{97} - 227 q^{98}+O(q^{100}) $ 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8 - 34 * q^10 + 11 * q^11 - 2 * q^13 - 40 * q^14 - 31 * q^16 + 9 * q^17 - 29 * q^19 + 43 * q^20 + 9 * q^22 + 4 * q^23 + 55 * q^25 - 36 * q^26 - 57 * q^28 - 4 * q^29 - 39 * q^31 + 92 * q^32 - 36 * q^34 + 33 * q^35 - 24 * q^37 - 118 * q^38 - 35 * q^41 + 2 * q^43 - 40 * q^44 - 40 * q^46 + 5 * q^47 + 129 * q^49 + 176 * q^50 - 6 * q^52 - 26 * q^53 + 2 * q^55 - 63 * q^56 + 11 * q^58 + 41 * q^59 + 6 * q^61 - 36 * q^62 + 74 * q^64 + 51 * q^65 - 55 * q^67 + 22 * q^68 - 68 * q^70 + 66 * q^71 + 24 * q^73 - 28 * q^74 + 3 * q^76 + 34 * q^77 - 51 * q^79 + 5 * q^80 - 41 * q^82 - 30 * q^83 + 68 * q^85 - 110 * q^86 + 129 * q^88 - 75 * q^89 + 5 * q^91 + 38 * q^94 - 36 * q^95 - 168 * q^97 - 227 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{16}{21}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.04710	+	0.713898i	−0.740409	+	0.504802i	−0.873815	−	0.486259i	$-0.838361\pi$
$2$	−1.04710	+	0.713898i	−0.740409	+	0.504802i	0.133405	+	0.991062i	$0.457409\pi$
$3$		0			0
$3$		0			0
$4$	−0.143921	+	0.366706i	−0.0719607	+	0.183353i
$5$	−1.23854	−	0.382039i	−0.553892	−	0.170853i	0.00515834	−	0.999987i	$-0.498358\pi$
$5$	−1.23854	−	0.382039i	−0.553892	−	0.170853i	−0.559051	+	0.829134i	$0.688834\pi$
$6$		0			0
$7$	2.59083	+	0.536271i	0.979243	+	0.202691i
$7$	2.59083	+	0.536271i	0.979243	+	0.202691i
$8$	−0.675095	−	2.95778i	−0.238682	−	1.04573i
$9$		0			0
$10$	1.56961	−	0.484160i	0.496354	−	0.153105i
$11$	0.384291	+	5.12800i	0.115868	+	1.54615i	0.687831	+	0.725871i	$0.258563\pi$
$11$	0.384291	+	5.12800i	0.115868	+	1.54615i	−0.571963	+	0.820280i	$0.693818\pi$
$12$		0			0
$13$	−1.76984	−	0.852310i	−0.490865	−	0.236388i	0.172042	−	0.985090i	$-0.444963\pi$
$13$	−1.76984	−	0.852310i	−0.490865	−	0.236388i	−0.662907	+	0.748701i	$0.730678\pi$
$14$	−3.09570	+	1.28806i	−0.827359	+	0.344250i
$15$		0			0
$16$	2.24089	+	2.07925i	0.560224	+	0.519812i
$17$	4.91447	+	0.740736i	1.19193	+	0.179655i	0.714898	−	0.699229i	$-0.246473\pi$
$17$	4.91447	+	0.740736i	1.19193	+	0.179655i	0.477035	+	0.878884i	$0.341711\pi$
$18$		0			0
$19$	−3.33107	+	5.76957i	−0.764199	+	1.32363i	0.176470	+	0.984306i	$0.443532\pi$
$19$	−3.33107	+	5.76957i	−0.764199	+	1.32363i	−0.940669	+	0.339325i	$0.889801\pi$
$20$	0.318349	−	0.399197i	0.0711849	−	0.0892631i
$21$		0			0
$22$	−4.06326	−	5.09517i	−0.866290	−	1.08629i
$23$	−4.69902	+	0.708264i	−0.979814	+	0.147683i	−0.619371	−	0.785098i	$-0.712612\pi$
$23$	−4.69902	+	0.708264i	−0.979814	+	0.147683i	−0.360443	+	0.932781i	$0.617374\pi$
$24$		0			0
$25$	−2.74316	−	1.87026i	−0.548633	−	0.374052i
$26$	2.46166	−	0.371035i	0.482770	−	0.0727659i
$27$		0			0
$28$	−0.569530	+	0.872893i	−0.107631	+	0.164961i
$29$	−4.28689	+	5.37560i	−0.796056	+	0.998223i	0.203759	+	0.979021i	$0.434684\pi$
$29$	−4.28689	+	5.37560i	−0.796056	+	0.998223i	−0.999816	+	0.0192020i	$0.993887\pi$
$30$		0			0
$31$	−0.371361	−	0.643217i	−0.0666985	−	0.115525i	0.830748	−	0.556649i	$-0.187913\pi$
$31$	−0.371361	−	0.643217i	−0.0666985	−	0.115525i	−0.897446	+	0.441124i	$0.854580\pi$
$32$	2.16912	+	0.326943i	0.383450	+	0.0577959i
$33$		0			0
$34$	−5.67473	+	2.73281i	−0.973208	+	0.468672i
$35$	−3.00397	−	1.65399i	−0.507764	−	0.279576i
$36$		0			0
$37$	−3.11350	−	7.93306i	−0.511856	−	1.30419i	−0.920232	−	0.391374i	$-0.872000\pi$
$37$	−3.11350	−	7.93306i	−0.511856	−	1.30419i	0.408376	−	0.912814i	$-0.366095\pi$
$38$	−0.630943	−	8.41934i	−0.102352	−	1.36580i
$39$		0			0
$40$	−0.293857	+	3.92125i	−0.0464629	+	0.620004i
$41$	1.45940	+	6.39404i	0.227920	+	0.998582i	0.951333	+	0.308166i	$0.0997153\pi$
$41$	1.45940	+	6.39404i	0.227920	+	0.998582i	−0.723413	+	0.690416i	$0.757428\pi$
$42$		0			0
$43$	−2.60820	+	11.4273i	−0.397746	+	1.74264i	0.238490	+	0.971145i	$0.423348\pi$
$43$	−2.60820	+	11.4273i	−0.397746	+	1.74264i	−0.636236	+	0.771495i	$0.719509\pi$
$44$	−1.93578	−	0.597108i	−0.291829	−	0.0900174i
$45$		0			0
$46$	4.41470	−	4.09625i	0.650913	−	0.603959i
$47$	−2.15329	+	1.46809i	−0.314090	+	0.214143i	−0.710096	−	0.704105i	$-0.751348\pi$
$47$	−2.15329	+	1.46809i	−0.314090	+	0.214143i	0.396006	+	0.918248i	$0.370396\pi$
$48$		0			0
$49$	6.42483	+	2.77878i	0.917832	+	0.396968i
$50$	4.20753			0.595035
$51$		0			0
$52$	0.567265	−	0.526345i	0.0786655	−	0.0729909i
$53$	0.584212	−	1.48855i	0.0802477	−	0.204468i	−0.885119	−	0.465365i	$-0.845923\pi$
$53$	0.584212	−	1.48855i	0.0802477	−	0.204468i	0.965367	+	0.260897i	$0.0840183\pi$
$54$		0			0
$55$	1.48314	−	6.49805i	0.199986	−	0.876197i
$56$	−0.162885	−	8.02516i	−0.0217664	−	1.07241i
$57$		0			0
$58$	0.651164	−	8.68918i	0.0855020	−	1.14094i
$59$	3.40655	−	1.05078i	0.443495	−	0.136800i	−0.0649614	−	0.997888i	$-0.520692\pi$
$59$	3.40655	−	1.05078i	0.443495	−	0.136800i	0.508457	+	0.861088i	$0.330216\pi$
$60$		0			0
$61$	0.0708345	+	0.180483i	0.00906943	+	0.0231085i	0.935337	−	0.353759i	$-0.115097\pi$
$61$	0.0708345	+	0.180483i	0.00906943	+	0.0231085i	−0.926267	+	0.376867i	$0.877001\pi$
$62$	0.848043	+	0.408396i	0.107702	+	0.0518663i
$63$		0			0
$64$	−8.01310	+	3.85891i	−1.00164	+	0.482363i
$65$	1.86640	+	1.73177i	0.231499	+	0.214799i
$66$		0			0
$67$	3.84338	+	6.65692i	0.469543	+	0.813273i	0.999394	−	0.0348185i	$-0.0110853\pi$
$67$	3.84338	+	6.65692i	0.469543	+	0.813273i	−0.529850	+	0.848091i	$0.677752\pi$
$68$	−0.978930	+	1.69556i	−0.118713	+	0.205616i
$69$		0			0
$70$	4.32624	−	0.412643i	0.517084	−	0.0493202i
$71$	−3.49267	−	4.37967i	−0.414503	−	0.519771i	0.530122	−	0.847921i	$-0.322146\pi$
$71$	−3.49267	−	4.37967i	−0.414503	−	0.519771i	−0.944625	+	0.328151i	$0.893575\pi$
$72$		0			0
$73$	2.28205	+	1.55588i	0.267094	+	0.182102i	0.689460	−	0.724324i	$-0.257848\pi$
$73$	2.28205	+	1.55588i	0.267094	+	0.182102i	−0.422366	+	0.906425i	$0.638800\pi$
$74$	8.92353	+	6.08396i	1.03734	+	0.707246i
$75$		0			0
$76$	−1.63633	−	2.05189i	−0.187699	−	0.235368i
$77$	−1.75437	+	13.4919i	−0.199928	+	1.53754i
$78$		0			0
$79$	−0.398609	+	0.690411i	−0.0448470	+	0.0776773i	−0.887578	−	0.460658i	$-0.847613\pi$
$79$	−0.398609	+	0.690411i	−0.0448470	+	0.0776773i	0.842731	+	0.538336i	$0.180947\pi$
$80$	−1.98109	−	3.43134i	−0.221492	−	0.383636i
$81$		0			0
$82$	−6.09283	−	5.65332i	−0.672841	−	0.624305i
$83$	−2.92509	+	1.40865i	−0.321070	+	0.154619i	−0.587476	−	0.809242i	$-0.699878\pi$
$83$	−2.92509	+	1.40865i	−0.321070	+	0.154619i	0.266406	+	0.963861i	$0.414164\pi$
$84$		0			0
$85$	−5.80377	−	2.79495i	−0.629508	−	0.303155i
$86$	−5.42686	−	13.8274i	−0.585194	−	1.49105i
$87$		0			0
$88$	14.9081	−	4.59854i	1.58921	−	0.490206i
$89$	0.432462	−	5.77081i	0.0458409	−	0.611705i	−0.926221	−	0.376981i	$-0.876962\pi$
$89$	0.432462	−	5.77081i	0.0458409	−	0.611705i	0.972062	−	0.234724i	$-0.0754186\pi$
$90$		0			0
$91$	−4.12829	−	3.15731i	−0.432762	−	0.330976i
$92$	0.416566	−	1.82509i	0.0434300	−	0.190279i
$93$		0			0
$94$	1.20664	−	3.07446i	0.124455	−	0.317107i
$95$	6.32986	−	5.87325i	0.649430	−	0.602583i
$96$		0			0
$97$	15.6804			1.59210			0.796051	−	0.605229i	$-0.206919\pi$
$97$	15.6804			1.59210			0.796051	+	0.605229i	$0.206919\pi$
$98$	−8.71118	+	1.67703i	−0.879962	+	0.169405i
$99$		0			0
$100$	1.08064	−	0.736765i	0.108064	−	0.0736765i
$101$	11.6133	−	10.7756i	1.15557	−	1.07221i	0.159186	−	0.987249i	$-0.449113\pi$
$101$	11.6133	−	10.7756i	1.15557	−	1.07221i	0.996384	−	0.0849632i	$-0.0270773\pi$
$102$		0			0
$103$	15.2635	+	4.70815i	1.50395	+	0.463908i	0.933850	−	0.357665i	$-0.116427\pi$
$103$	15.2635	+	4.70815i	1.50395	+	0.463908i	0.570103	+	0.821573i	$0.306903\pi$
$104$	−1.32614	+	5.81019i	−0.130039	+	0.569736i
$105$		0			0
$106$	0.450946	+	1.97572i	0.0437997	+	0.191899i
$107$	0.611614	−	8.16143i	0.0591270	−	0.788995i	−0.886290	−	0.463131i	$-0.846726\pi$
$107$	0.611614	−	8.16143i	0.0591270	−	0.788995i	0.945417	−	0.325864i	$-0.105655\pi$
$108$		0			0
$109$	0.515336	+	6.87668i	0.0493603	+	0.658667i	0.965932	+	0.258796i	$0.0833259\pi$
$109$	0.515336	+	6.87668i	0.0493603	+	0.658667i	−0.916572	+	0.399871i	$0.869055\pi$
$110$	3.08596	+	7.86290i	0.294235	+	0.749698i
$111$		0			0
$112$	4.69074	+	6.58871i	0.443234	+	0.622574i
$113$	5.96397	−	2.87210i	0.561044	−	0.270184i	−0.131795	−	0.991277i	$-0.542074\pi$
$113$	5.96397	−	2.87210i	0.561044	−	0.270184i	0.692839	+	0.721093i	$0.256360\pi$
$114$		0			0
$115$	6.09052	+	0.917998i	0.567944	+	0.0856037i
$116$	−1.35429	−	2.34569i	−0.125742	−	0.217792i
$117$		0			0
$118$	−2.81684	+	3.53220i	−0.259311	+	0.325166i
$119$	12.3353	+	4.55461i	1.13078	+	0.417520i
$120$		0			0
$121$	−15.2716	+	2.30182i	−1.38833	+	0.209257i
$122$	−0.203017	−	0.138415i	−0.0183803	−	0.0125315i
$123$		0			0
$124$	0.289318	−	0.0436077i	0.0259816	−	0.00391609i
$125$	6.72361	+	8.43114i	0.601378	+	0.754104i
$126$		0			0
$127$	6.06281	−	7.60252i	0.537987	−	0.674614i	−0.436332	−	0.899786i	$-0.643723\pi$
$127$	6.06281	−	7.60252i	0.537987	−	0.674614i	0.974319	+	0.225171i	$0.0722941\pi$
$128$	3.44200	−	5.96172i	0.304233	−	0.526946i
$129$		0			0
$130$	−3.19061	−	0.480907i	−0.279835	−	0.0421784i
$131$	9.73116	+	9.02919i	0.850215	+	0.788884i	0.979229	−	0.202759i	$-0.0649907\pi$
$131$	9.73116	+	9.02919i	0.850215	+	0.788884i	−0.129014	+	0.991643i	$0.541181\pi$
$132$		0			0
$133$	−11.7243	+	13.1616i	−1.01662	+	1.14126i
$134$	−8.77675	−	4.22666i	−0.758196	−	0.365128i
$135$		0			0
$136$	−1.12679	−	15.0360i	−0.0966216	−	1.28933i
$137$	−2.46893	+	0.761565i	−0.210935	+	0.0650649i	−0.398422	−	0.917202i	$-0.630442\pi$
$137$	−2.46893	+	0.761565i	−0.210935	+	0.0650649i	0.187487	+	0.982267i	$0.439966\pi$
$138$		0			0
$139$	−3.09166	−	13.5454i	−0.262231	−	1.14891i	−0.918825	−	0.394665i	$-0.870861\pi$
$139$	−3.09166	−	13.5454i	−0.262231	−	1.14891i	0.656594	−	0.754244i	$-0.271997\pi$
$140$	1.03887	−	0.863530i	0.0878002	−	0.0729816i
$141$		0			0
$142$	6.78380	+	2.09252i	0.569284	+	0.175601i
$143$	3.69051	−	9.40328i	0.308616	−	0.786341i
$144$		0			0
$145$	7.36318	−	5.02013i	0.611479	−	0.416899i
$146$	−3.50027			−0.289684
$147$		0			0
$148$	3.35720			0.275960
$149$	4.05791	−	2.76664i	0.332437	−	0.226652i	−0.385585	−	0.922672i	$-0.626000\pi$
$149$	4.05791	−	2.76664i	0.332437	−	0.226652i	0.718022	+	0.696021i	$0.245048\pi$
$150$		0			0
$151$	−4.03953	+	10.2925i	−0.328732	+	0.837596i	0.666979	+	0.745077i	$0.267587\pi$
$151$	−4.03953	+	10.2925i	−0.328732	+	0.837596i	−0.995711	+	0.0925191i	$0.970508\pi$
$152$	19.3139	+	5.95756i	1.56657	+	0.483222i
$153$		0			0
$154$	−7.79484	−	15.3797i	−0.628126	−	1.23933i
$155$	0.214212	+	0.938525i	0.0172059	+	0.0753841i
$156$		0			0
$157$	−2.14918	+	0.662934i	−0.171523	+	0.0529079i	−0.379327	−	0.925263i	$-0.623845\pi$
$157$	−2.14918	+	0.662934i	−0.171523	+	0.0529079i	0.207804	+	0.978170i	$0.433368\pi$
$158$	−0.0755012	−	1.00749i	−0.00600655	−	0.0801519i
$159$		0			0
$160$	−2.56164	−	1.23362i	−0.202516	−	0.0975264i
$161$	−12.5542	−	0.684956i	−0.989410	−	0.0539821i
$162$		0			0
$163$	−8.04955	−	7.46889i	−0.630490	−	0.585009i	0.298820	−	0.954309i	$-0.403407\pi$
$163$	−8.04955	−	7.46889i	−0.630490	−	0.585009i	−0.929310	+	0.369300i	$0.879597\pi$
$164$	−2.55477	−	0.385070i	−0.199494	−	0.0300689i
$165$		0			0
$166$	2.05722	−	3.56321i	0.159671	−	0.276559i
$167$	3.74177	−	4.69203i	0.289547	−	0.363080i	−0.615689	−	0.787989i	$-0.711122\pi$
$167$	3.74177	−	4.69203i	0.289547	−	0.363080i	0.905236	+	0.424909i	$0.139694\pi$
$168$		0			0
$169$	−5.69947	−	7.14691i	−0.438421	−	0.549762i
$170$	8.07242	−	1.21672i	0.619127	−	0.0933183i
$171$		0			0
$172$	−3.81507	−	2.60107i	−0.290896	−	0.198330i
$173$	−19.7631	+	2.97881i	−1.50256	+	0.226475i	−0.848188	−	0.529696i	$-0.822306\pi$
$173$	−19.7631	+	2.97881i	−1.50256	+	0.226475i	−0.654375	+	0.756171i	$0.727068\pi$
$174$		0			0
$175$	−6.10412	−	6.31661i	−0.461428	−	0.477490i
$176$	−9.80123	+	12.2903i	−0.738795	+	0.926420i
$177$		0			0
$178$	3.66694	+	6.35133i	0.274849	+	0.476052i
$179$	15.2602	+	2.30011i	1.14060	+	0.171918i	0.692058	−	0.721842i	$-0.256704\pi$
$179$	15.2602	+	2.30011i	1.14060	+	0.171918i	0.448545	+	0.893760i	$0.351942\pi$
$180$		0			0
$181$	−15.9822	+	7.69663i	−1.18795	+	0.572086i	−0.920217	−	0.391408i	$-0.871988\pi$
$181$	−15.9822	+	7.69663i	−1.18795	+	0.572086i	−0.267731	+	0.963494i	$0.586274\pi$
$182$	6.57671	+	0.358825i	0.487498	+	0.0265979i
$183$		0			0
$184$	5.26718	+	13.4206i	0.388302	+	0.989376i
$185$	0.825452	+	11.0149i	0.0606885	+	0.809831i
$186$		0			0
$187$	−1.90992	+	25.4860i	−0.139667	+	1.86372i
$188$	−0.228452	−	1.00091i	−0.0166616	−	0.0729992i
$189$		0			0
$190$	−2.43507	+	10.6687i	−0.176659	+	0.773992i
$191$	−7.25297	−	2.23724i	−0.524806	−	0.161881i	0.0210210	−	0.999779i	$-0.493308\pi$
$191$	−7.25297	−	2.23724i	−0.524806	−	0.161881i	−0.545827	+	0.837898i	$0.683785\pi$
$192$		0			0
$193$	−2.81424	+	2.61124i	−0.202574	+	0.187961i	−0.774936	−	0.632040i	$-0.782218\pi$
$193$	−2.81424	+	2.61124i	−0.202574	+	0.187961i	0.572362	+	0.820001i	$0.306027\pi$
$194$	−16.4189	+	11.1942i	−1.17881	+	0.803697i
$195$		0			0
$196$	−1.94366	+	1.95610i	−0.138833	+	0.139721i
$197$	−15.1253			−1.07763			−0.538817	−	0.842423i	$-0.681129\pi$
$197$	−15.1253			−1.07763			−0.538817	+	0.842423i	$0.681129\pi$
$198$		0			0
$199$	7.44157	−	6.90477i	0.527519	−	0.489466i	−0.370859	−	0.928689i	$-0.620937\pi$
$199$	7.44157	−	6.90477i	0.527519	−	0.489466i	0.898378	+	0.439223i	$0.144746\pi$
$200$	−3.67992	+	9.37629i	−0.260210	+	0.663004i
$201$		0			0
$202$	−4.46760	+	19.5738i	−0.314339	+	1.37721i
$203$	−13.9894	+	11.6283i	−0.981863	+	0.816149i
$204$		0			0
$205$	0.635251	−	8.47683i	0.0443678	−	0.592048i
$206$	−19.3435	+	5.96667i	−1.34772	+	0.415717i
$207$		0			0
$208$	−2.19386	−	5.58987i	−0.152117	−	0.387588i
$209$	−30.8665	−	14.8645i	−2.13508	−	1.02820i
$210$		0			0
$211$	15.6902	−	7.55598i	1.08016	−	0.520175i	0.192789	−	0.981240i	$-0.438247\pi$
$211$	15.6902	−	7.55598i	1.08016	−	0.520175i	0.887366	+	0.461065i	$0.152532\pi$
$212$	0.461779	+	0.428468i	0.0317151	+	0.0294273i
$213$		0			0
$214$	5.18601	+	8.98243i	0.354508	+	0.614027i
$215$	7.59601	−	13.1567i	0.518044	−	0.897278i
$216$		0			0
$217$	−0.617197	−	1.86562i	−0.0418981	−	0.126646i
$218$	−5.44886	−	6.83266i	−0.369043	−	0.462766i
$219$		0			0
$220$	2.16942	+	1.47908i	0.146262	+	0.0997199i
$221$	−8.06648	−	5.49963i	−0.542610	−	0.369945i
$222$		0			0
$223$	15.1743	+	19.0279i	1.01614	+	1.27420i	0.961240	+	0.275712i	$0.0889136\pi$
$223$	15.1743	+	19.0279i	1.01614	+	1.27420i	0.0549032	+	0.998492i	$0.482515\pi$
$224$	5.44451	+	2.01029i	0.363776	+	0.134318i
$225$		0			0
$226$	−4.19447	+	7.26504i	−0.279012	+	0.483263i
$227$	8.13785	+	14.0952i	0.540128	+	0.935529i	0.998896	+	0.0469733i	$0.0149576\pi$
$227$	8.13785	+	14.0952i	0.540128	+	0.935529i	−0.458768	+	0.888556i	$0.651709\pi$
$228$		0			0
$229$	−17.3233	−	16.0737i	−1.14476	−	1.06218i	−0.997324	−	0.0731087i	$-0.976708\pi$
$229$	−17.3233	−	16.0737i	−1.14476	−	1.06218i	−0.147434	−	0.989072i	$-0.547102\pi$
$230$	−7.03272	+	3.38678i	−0.463724	+	0.223318i
$231$		0			0
$232$	18.7939	+	9.05067i	1.23388	+	0.594206i
$233$	−1.47586	−	3.76042i	−0.0966866	−	0.246354i	0.874345	−	0.485305i	$-0.161291\pi$
$233$	−1.47586	−	3.76042i	−0.0966866	−	0.246354i	−0.971031	+	0.238952i	$0.923196\pi$
$234$		0			0
$235$	3.22781	−	0.995647i	0.210559	−	0.0649488i
$236$	−0.104948	+	1.40043i	−0.00683153	+	0.0911604i
$237$		0			0
$238$	−16.1678	+	4.03705i	−1.04800	+	0.261683i
$239$	0.722936	−	3.16739i	0.0467628	−	0.204881i	−0.946150	−	0.323730i	$-0.895063\pi$
$239$	0.722936	−	3.16739i	0.0467628	−	0.204881i	0.992912	+	0.118848i	$0.0379203\pi$
$240$		0			0
$241$	0.329737	−	0.840155i	0.0212402	−	0.0541192i	−0.919860	−	0.392246i	$-0.871698\pi$
$241$	0.329737	−	0.840155i	0.0212402	−	0.0541192i	0.941100	+	0.338127i	$0.109793\pi$
$242$	14.3476	−	13.3126i	0.922296	−	0.855766i
$243$		0			0
$244$	−0.0763790			−0.00488966
$245$	−6.89581	−	5.89616i	−0.440557	−	0.376692i
$246$		0			0
$247$	10.8129	−	7.37212i	0.688009	−	0.469077i
$248$	−1.65179	+	1.53264i	−0.104889	+	0.0973227i
$249$		0			0
$250$	−13.0592	−	4.02824i	−0.825939	−	0.254769i
$251$	−3.25109	+	14.2440i	−0.205207	+	0.899072i	0.762499	+	0.646990i	$0.223972\pi$
$251$	−3.25109	+	14.2440i	−0.205207	+	0.899072i	−0.967706	+	0.252082i	$0.918885\pi$
$252$		0			0
$253$	−5.43777	−	23.8244i	−0.341870	−	1.49783i
$254$	−0.920918	+	12.2888i	−0.0577836	+	0.771068i
$255$		0			0
$256$	−0.677324	−	9.03827i	−0.0423328	−	0.564892i
$257$	3.39676	+	8.65480i	0.211884	+	0.539872i	0.996818	−	0.0797073i	$-0.0253986\pi$
$257$	3.39676	+	8.65480i	0.211884	+	0.539872i	−0.784934	+	0.619579i	$0.787303\pi$
$258$		0			0
$259$	−3.81228	−	22.2229i	−0.236884	−	1.38086i
$260$	−0.903665	+	0.435182i	−0.0560429	+	0.0269889i
$261$		0			0
$262$	−16.6354	−	2.50738i	−1.02774	−	0.154907i
$263$	−7.03797	−	12.1901i	−0.433980	−	0.751675i	0.563232	−	0.826299i	$-0.309558\pi$
$263$	−7.03797	−	12.1901i	−0.433980	−	0.751675i	−0.997212	+	0.0746239i	$0.976224\pi$
$264$		0			0
$265$	−1.29225	+	1.62044i	−0.0793826	+	0.0995426i
$266$	2.88038	−	22.1515i	0.176608	−	1.35819i
$267$		0			0
$268$	−2.99428	+	0.451315i	−0.182905	+	0.0275684i
$269$	4.06619	+	2.77228i	0.247920	+	0.169029i	0.680904	−	0.732372i	$-0.261587\pi$
$269$	4.06619	+	2.77228i	0.247920	+	0.169029i	−0.432984	+	0.901402i	$0.642539\pi$
$270$		0			0
$271$	2.21691	−	0.334146i	0.134668	−	0.0202979i	−0.0813624	−	0.996685i	$-0.525927\pi$
$271$	2.21691	−	0.334146i	0.134668	−	0.0202979i	0.216030	+	0.976387i	$0.430689\pi$
$272$	9.47263	+	11.8783i	0.574362	+	0.720228i
$273$		0			0
$274$	2.04153	−	2.56000i	0.123333	−	0.154655i
$275$	8.53652	−	14.7857i	0.514771	−	0.891610i
$276$		0			0
$277$	9.40006	+	1.41683i	0.564795	+	0.0851291i	0.425232	−	0.905084i	$-0.360192\pi$
$277$	9.40006	+	1.41683i	0.564795	+	0.0851291i	0.139562	+	0.990213i	$0.455430\pi$
$278$	12.9073	+	11.9763i	0.774131	+	0.718288i
$279$		0			0
$280$	−2.86419	+	10.0017i	−0.171168	+	0.597717i
$281$	−16.4140	−	7.90459i	−0.979180	−	0.471548i	−0.125357	−	0.992112i	$-0.540008\pi$
$281$	−16.4140	−	7.90459i	−0.979180	−	0.471548i	−0.853823	+	0.520564i	$0.825722\pi$
$282$		0			0
$283$	−0.00381786	−	0.0509458i	−0.000226948	−	0.00302841i	0.997089	−	0.0762442i	$-0.0242929\pi$
$283$	−0.00381786	−	0.0509458i	−0.000226948	−	0.00302841i	−0.997316	+	0.0732158i	$0.976674\pi$
$284$	2.10872	−	0.650454i	0.125129	−	0.0385973i
$285$		0			0
$286$	2.84866	+	12.4808i	0.168445	+	0.738005i
$287$	0.352119	+	17.3485i	0.0207849	+	1.02405i
$288$		0			0
$289$	7.35854	+	2.26981i	0.432855	+	0.133518i
$290$	−4.12610	+	10.5131i	−0.242293	+	0.617352i
$291$		0			0
$292$	−0.898986	+	0.612918i	−0.0526092	+	0.0358683i
$293$	17.2829			1.00968			0.504839	−	0.863213i	$-0.331552\pi$
$293$	17.2829			1.00968			0.504839	+	0.863213i	$0.331552\pi$
$294$		0			0
$295$	−4.62059			−0.269021
$296$	−21.3624	+	14.5646i	−1.24166	+	0.846552i
$297$		0			0
$298$	−2.27393	+	5.79387i	−0.131725	+	0.335630i
$299$	8.92018	+	2.75151i	0.515867	+	0.159124i
$300$		0			0
$301$	−12.8855	+	28.2074i	−0.742708	+	1.62585i
$302$	−3.11806	−	13.6611i	−0.179424	−	0.786108i
$303$		0			0
$304$	−19.4609	+	6.00290i	−1.11616	+	0.344290i
$305$	−0.0187797	−	0.250598i	−0.00107532	−	0.0143492i
$306$		0			0
$307$	26.3755	+	12.7018i	1.50533	+	0.724928i	0.991149	−	0.132754i	$-0.0423821\pi$
$307$	26.3755	+	12.7018i	1.50533	+	0.724928i	0.514180	+	0.857682i	$0.328096\pi$
$308$	−4.69506	−	2.58511i	−0.267526	−	0.147300i
$309$		0			0
$310$	−0.894312	−	0.829801i	−0.0507935	−	0.0471295i
$311$	13.9247	+	2.09881i	0.789595	+	0.119012i	0.531445	−	0.847093i	$-0.321649\pi$
$311$	13.9247	+	2.09881i	0.789595	+	0.119012i	0.258150	+	0.966105i	$0.416887\pi$
$312$		0			0
$313$	13.1768	−	22.8229i	0.744796	−	1.29002i	−0.205494	−	0.978658i	$-0.565880\pi$
$313$	13.1768	−	22.8229i	0.744796	−	1.29002i	0.950290	−	0.311366i	$-0.100787\pi$
$314$	1.77713	−	2.22845i	0.100289	−	0.125759i
$315$		0			0
$316$	−0.195809	−	0.245537i	−0.0110151	−	0.0138125i
$317$	27.5759	−	4.15639i	1.54882	−	0.233446i	0.681729	−	0.731605i	$-0.261228\pi$
$317$	27.5759	−	4.15639i	1.54882	−	0.233446i	0.867086	+	0.498158i	$0.165990\pi$
$318$		0			0
$319$	−29.2135	−	19.9174i	−1.63564	−	1.11516i
$320$	11.3988	−	1.71809i	0.637212	−	0.0960443i
$321$		0			0
$322$	13.6345	−	8.24521i	0.759819	−	0.459488i
$323$	−20.6441	+	25.8869i	−1.14867	+	1.44039i
$324$		0			0
$325$	3.26092	+	5.64808i	0.180883	+	0.313299i
$326$	13.7607	+	2.07409i	0.762134	+	0.114873i
$327$		0			0
$328$	17.9270	−	8.63318i	0.989852	−	0.476687i
$329$	−6.36611	+	2.64883i	−0.350975	+	0.146035i
$330$		0			0
$331$	0.122323	+	0.311674i	0.00672349	+	0.0171312i	0.934196	−	0.356760i	$-0.116119\pi$
$331$	0.122323	+	0.311674i	0.00672349	+	0.0171312i	−0.927473	+	0.373891i	$0.878023\pi$
$332$	−0.0955767	−	1.27538i	−0.00524545	−	0.0699957i
$333$		0			0
$334$	−0.568361	+	7.58425i	−0.0310993	+	0.414992i
$335$	−2.21697	−	9.71319i	−0.121126	−	0.530688i
$336$		0			0
$337$	−1.38884	+	6.08492i	−0.0756552	+	0.331467i	−0.998565	−	0.0535486i	$-0.982947\pi$
$337$	−1.38884	+	6.08492i	−0.0756552	+	0.331467i	0.922910	+	0.385016i	$0.125804\pi$
$338$	11.0701	+	3.41466i	0.602132	+	0.185733i
$339$		0			0
$340$	1.86021	−	1.72603i	0.100884	−	0.0936069i
$341$	3.15571	−	2.15152i	0.170891	−	0.116512i
$342$		0			0
$343$	15.1555	+	10.6448i	0.818319	+	0.574765i
$344$	35.5601			1.91727
$345$		0			0
$346$	18.5673	−	17.2280i	0.998186	−	0.926181i
$347$	5.40006	−	13.7591i	0.289890	−	0.738628i	−0.709533	−	0.704672i	$-0.751094\pi$
$347$	5.40006	−	13.7591i	0.289890	−	0.738628i	0.999423	−	0.0339561i	$-0.0108106\pi$
$348$		0			0
$349$	−1.45835	+	6.38945i	−0.0780637	+	0.342019i	−0.998844	−	0.0480613i	$-0.984696\pi$
$349$	−1.45835	+	6.38945i	−0.0780637	+	0.342019i	0.920781	+	0.390081i	$0.127553\pi$
$350$	10.9010	+	2.25638i	0.582684	+	0.120608i
$351$		0			0
$352$	−0.842989	+	11.2489i	−0.0449315	+	0.599569i
$353$	−19.0208	+	5.86715i	−1.01238	+	0.312277i	−0.756191	−	0.654351i	$-0.772942\pi$
$353$	−19.0208	+	5.86715i	−1.01238	+	0.312277i	−0.256186	+	0.966628i	$0.582466\pi$
$354$		0			0
$355$	2.65261	+	6.75873i	0.140786	+	0.358716i
$356$	2.05395	+	0.989130i	0.108859	+	0.0524238i
$357$		0			0
$358$	−17.6210	+	8.48581i	−0.931297	+	0.448489i
$359$	−7.08012	−	6.56939i	−0.373674	−	0.346719i	0.470872	−	0.882202i	$-0.343939\pi$
$359$	−7.08012	−	6.56939i	−0.373674	−	0.346719i	−0.844546	+	0.535482i	$0.820130\pi$
$360$		0			0
$361$	−12.6920	−	21.9832i	−0.668000	−	1.15701i
$362$	11.2403	−	19.4688i	0.590778	−	1.02326i
$363$		0			0
$364$	1.75195	−	1.05946i	0.0918272	−	0.0555310i
$365$	−2.23201	−	2.79885i	−0.116829	−	0.146499i
$366$		0			0
$367$	−5.56061	−	3.79116i	−0.290261	−	0.197897i	0.409431	−	0.912341i	$-0.365727\pi$
$367$	−5.56061	−	3.79116i	−0.290261	−	0.197897i	−0.699692	+	0.714444i	$0.746680\pi$
$368$	−12.0027	−	8.18328i	−0.625683	−	0.426583i
$369$		0			0
$370$	−8.72785	−	10.9444i	−0.453739	−	0.568971i
$371$	2.31186	−	3.54328i	0.120026	−	0.183958i
$372$		0			0
$373$	−9.73996	+	16.8701i	−0.504316	+	0.873501i	0.495671	+	0.868510i	$0.334922\pi$
$373$	−9.73996	+	16.8701i	−0.504316	+	0.873501i	−0.999988	+	0.00499116i	$0.998411\pi$
$374$	−16.1946	−	28.0498i	−0.837402	−	1.45042i
$375$		0			0
$376$	5.79597	+	5.37787i	0.298904	+	0.277343i
$377$	12.1688	−	5.86018i	0.626724	−	0.301815i
$378$		0			0
$379$	8.59499	+	4.13913i	0.441495	+	0.212613i	0.641407	−	0.767201i	$-0.278351\pi$
$379$	8.59499	+	4.13913i	0.441495	+	0.212613i	−0.199912	+	0.979814i	$0.564065\pi$
$380$	1.24275	+	3.16649i	0.0637519	+	0.162437i
$381$		0			0
$382$	9.19172	−	2.83527i	0.470289	−	0.145065i
$383$	0.311903	−	4.16206i	0.0159375	−	0.212671i	−0.983549	−	0.180640i	$-0.942183\pi$
$383$	0.311903	−	4.16206i	0.0159375	−	0.212671i	0.999487	−	0.0320316i	$-0.0101977\pi$
$384$		0			0
$385$	7.32728	−	16.0400i	0.373433	−	0.817474i
$386$	1.08263	−	4.74330i	0.0551043	−	0.241428i
$387$		0			0
$388$	−2.25674	+	5.75009i	−0.114569	+	0.291917i
$389$	−22.9633	+	21.3068i	−1.16429	+	1.08030i	−0.168775	+	0.985655i	$0.553981\pi$
$389$	−22.9633	+	21.3068i	−1.16429	+	1.08030i	−0.995511	+	0.0946454i	$0.969828\pi$
$390$		0			0
$391$	−23.6178			−1.19440
$392$	3.88165	−	20.8792i	0.196053	−	1.05456i
$393$		0			0
$394$	15.8377	−	10.7979i	0.797890	−	0.543992i
$395$	0.757457	−	0.702818i	0.0381118	−	0.0353626i
$396$		0			0
$397$	19.0764	+	5.88430i	0.957419	+	0.295325i	0.733810	−	0.679354i	$-0.237740\pi$
$397$	19.0764	+	5.88430i	0.957419	+	0.295325i	0.223609	+	0.974679i	$0.428216\pi$
$398$	−2.86274	+	12.5425i	−0.143496	+	0.628698i
$399$		0			0
$400$	−2.25842	−	9.89477i	−0.112921	−	0.494738i
$401$	−1.39757	+	18.6493i	−0.0697916	+	0.931304i	0.846911	+	0.531734i	$0.178459\pi$
$401$	−1.39757	+	18.6493i	−0.0697916	+	0.931304i	−0.916703	+	0.399569i	$0.869160\pi$
$402$		0			0
$403$	0.109030	+	1.45491i	0.00543118	+	0.0724740i
$404$	2.28007	+	5.80952i	0.113438	+	0.289034i
$405$		0			0
$406$	6.34681	−	22.1630i	0.314987	−	1.09993i
$407$	39.4843	−	19.0146i	1.95716	−	0.942520i
$408$		0			0
$409$	37.8348	+	5.70268i	1.87081	+	0.281979i	0.983733	−	0.179639i	$-0.0574929\pi$
$409$	37.8348	+	5.70268i	1.87081	+	0.281979i	0.887079	+	0.461618i	$0.152731\pi$
$410$	5.38643	+	9.32957i	0.266017	+	0.460755i
$411$		0			0
$412$	−3.92325	+	4.91960i	−0.193285	+	0.242371i
$413$	9.38931	−	0.895566i	0.462018	−	0.0440679i
$414$		0			0
$415$	4.16100	−	0.627170i	0.204255	−	0.0307866i
$416$	−3.56034	−	2.42740i	−0.174560	−	0.119013i
$417$		0			0
$418$	42.9320	−	6.47095i	2.09987	−	0.316505i
$419$	−5.60936	−	7.03391i	−0.274035	−	0.343629i	0.625701	−	0.780063i	$-0.284813\pi$
$419$	−5.60936	−	7.03391i	−0.274035	−	0.343629i	−0.899736	+	0.436434i	$0.856241\pi$
$420$		0			0
$421$	8.77356	−	11.0017i	0.427597	−	0.536190i	−0.520630	−	0.853782i	$-0.674303\pi$
$421$	8.77356	−	11.0017i	0.427597	−	0.536190i	0.948227	+	0.317592i	$0.102874\pi$
$422$	−11.0349	+	19.1130i	−0.537171	+	0.930408i
$423$		0			0
$424$	−4.79721	−	0.723062i	−0.232973	−	0.0351150i
$425$	−12.0958	−	11.2233i	−0.586734	−	0.544409i
$426$		0			0
$427$	0.0867324	+	0.505589i	0.00419728	+	0.0244672i
$428$	2.90482	+	1.39889i	0.140410	+	0.0676178i
$429$		0			0
$430$	1.43877	+	19.1991i	0.0693838	+	0.925863i
$431$	15.4143	−	4.75467i	0.742479	−	0.229024i	0.0996375	−	0.995024i	$-0.468232\pi$
$431$	15.4143	−	4.75467i	0.742479	−	0.229024i	0.642841	+	0.765999i	$0.277756\pi$
$432$		0			0
$433$	−4.27778	−	18.7422i	−0.205577	−	0.900692i	−0.967469	−	0.252988i	$-0.918587\pi$
$433$	−4.27778	−	18.7422i	−0.205577	−	0.900692i	0.761892	−	0.647704i	$-0.224270\pi$
$434$	1.97813	+	1.51287i	0.0949531	+	0.0726199i
$435$		0			0
$436$	−2.59589	−	0.800726i	−0.124321	−	0.0383478i
$437$	11.5664	−	29.4706i	0.553295	−	1.40977i
$438$		0			0
$439$	−9.19564	+	6.26948i	−0.438884	+	0.299226i	−0.762531	−	0.646952i	$-0.776043\pi$
$439$	−9.19564	+	6.26948i	−0.438884	+	0.299226i	0.323647	+	0.946178i	$0.395091\pi$
$440$	−20.2211			−0.964003
$441$		0			0
$442$	12.3726			0.588503
$443$	15.1248	−	10.3119i	0.718603	−	0.489935i	−0.147966	−	0.988992i	$-0.547273\pi$
$443$	15.1248	−	10.3119i	0.718603	−	0.489935i	0.866569	+	0.499057i	$0.166320\pi$
$444$		0			0
$445$	−2.74030	+	6.98216i	−0.129903	+	0.330986i
$446$	−29.4729	−	9.09119i	−1.39558	−	0.430480i
$447$		0			0
$448$	−22.8300	+	5.70059i	−1.07862	+	0.269327i
$449$	−1.23583	−	5.41453i	−0.0583225	−	0.255527i	0.937359	−	0.348366i	$-0.113263\pi$
$449$	−1.23583	−	5.41453i	−0.0583225	−	0.255527i	−0.995681	+	0.0928382i	$0.970406\pi$
$450$		0			0
$451$	−32.2278	+	9.94097i	−1.51755	+	0.468102i
$452$	0.194872	+	2.60038i	0.00916599	+	0.122312i
$453$		0			0
$454$	−18.5836	−	8.94941i	−0.872173	−	0.420017i
$455$	3.90684	+	5.48762i	0.183155	+	0.257264i
$456$		0			0
$457$	−2.78891	−	2.58773i	−0.130460	−	0.121049i	0.612245	−	0.790668i	$-0.290267\pi$
$457$	−2.78891	−	2.58773i	−0.130460	−	0.121049i	−0.742704	+	0.669620i	$0.766457\pi$
$458$	29.6142	+	4.46362i	1.38378	+	0.208571i
$459$		0			0
$460$	−1.21319	+	2.10131i	−0.0565653	+	0.0979740i
$461$	10.4950	−	13.1603i	0.488802	−	0.612938i	−0.474861	−	0.880061i	$-0.657501\pi$
$461$	10.4950	−	13.1603i	0.488802	−	0.612938i	0.963663	+	0.267123i	$0.0860729\pi$
$462$		0			0
$463$	−25.4236	−	31.8802i	−1.18154	−	1.48160i	−0.840721	−	0.541468i	$-0.817869\pi$
$463$	−25.4236	−	31.8802i	−1.18154	−	1.48160i	−0.340814	−	0.940131i	$-0.610703\pi$
$464$	−20.7837	+	3.13263i	−0.964857	+	0.145429i
$465$		0			0
$466$	4.22993	+	2.88391i	0.195948	+	0.133595i
$467$	−26.9834	+	4.06709i	−1.24864	+	0.188202i	−0.739900	−	0.672717i	$-0.765127\pi$
$467$	−26.9834	+	4.06709i	−1.24864	+	0.188202i	−0.508741	+	0.860920i	$0.669889\pi$
$468$		0			0
$469$	6.38763	+	19.3081i	0.294953	+	0.891564i
$470$	−2.66904	+	3.34687i	−0.123113	+	0.154379i
$471$		0			0
$472$	−5.40773	−	9.36647i	−0.248911	−	0.431127i
$473$	−59.6013	−	8.98345i	−2.74047	−	0.413059i
$474$		0			0
$475$	19.9283	−	9.59694i	0.914371	−	0.440338i
$476$	−3.44552	+	3.86793i	−0.157925	+	0.177286i
$477$		0			0
$478$	1.50421	+	3.83266i	0.0688009	+	0.175302i
$479$	3.18428	+	42.4912i	0.145493	+	1.94147i	0.300968	+	0.953634i	$0.402690\pi$
$479$	3.18428	+	42.4912i	0.145493	+	1.94147i	−0.155475	+	0.987840i	$0.549691\pi$
$480$		0			0
$481$	−1.25104	+	16.6939i	−0.0570423	+	0.761177i
$482$	0.254519	+	1.11512i	0.0115930	+	0.0507924i
$483$		0			0
$484$	1.35382	−	5.93146i	0.0615372	−	0.269612i
$485$	−19.4208	−	5.99052i	−0.881853	−	0.272016i
$486$		0			0
$487$	23.3725	−	21.6865i	1.05911	−	0.982708i	0.0592285	−	0.998244i	$-0.481136\pi$
$487$	23.3725	−	21.6865i	1.05911	−	0.982708i	0.999879	+	0.0155360i	$0.00494548\pi$
$488$	0.486011	−	0.331357i	0.0220007	−	0.0149998i
$489$		0			0
$490$	11.4298	+	1.25095i	0.516348	+	0.0565120i
$491$	36.8731			1.66406			0.832030	−	0.554731i	$-0.187179\pi$
$491$	36.8731			1.66406			0.832030	+	0.554731i	$0.187179\pi$
$492$		0			0
$493$	−25.0497	+	23.2427i	−1.12818	+	1.04680i
$494$	−6.05922	+	15.4386i	−0.272617	+	0.694618i
$495$		0			0
$496$	0.505225	−	2.21353i	0.0226853	−	0.0993906i
$497$	−6.70023	−	13.2200i	−0.300546	−	0.592998i
$498$		0			0
$499$	−2.65655	+	35.4492i	−0.118923	+	1.58692i	0.544554	+	0.838726i	$0.316699\pi$
$499$	−2.65655	+	35.4492i	−0.118923	+	1.58692i	−0.663477	+	0.748197i	$0.730920\pi$
$500$	−4.05942	+	1.25217i	−0.181543	+	0.0559985i
$501$		0			0
$502$	−6.76454	−	17.2358i	−0.301916	−	0.769270i
$503$	33.9264	+	16.3381i	1.51270	+	0.728480i	0.992115	−	0.125327i	$-0.0399980\pi$
$503$	33.9264	+	16.3381i	1.51270	+	0.728480i	0.520589	+	0.853807i	$0.325712\pi$
$504$		0			0
$505$	−18.5003	+	8.90927i	−0.823252	+	0.396457i
$506$	22.7021	+	21.0645i	1.00923	+	0.936430i
$507$		0			0
$508$	1.91532	+	3.31743i	0.0849786	+	0.147187i
$509$	17.0829	−	29.5885i	0.757187	−	1.31149i	−0.187093	−	0.982342i	$-0.559907\pi$
$509$	17.0829	−	29.5885i	0.757187	−	1.31149i	0.944280	−	0.329143i	$-0.106760\pi$
$510$		0			0
$511$	5.07804	+	5.25481i	0.224639	+	0.232459i
$512$	15.7458	+	19.7447i	0.695874	+	0.872599i
$513$		0			0
$514$	−9.73539	−	6.63747i	−0.429409	−	0.292766i
$515$	−17.1057	−	11.6625i	−0.753768	−	0.513910i
$516$		0			0
$517$	−8.35586	−	10.4779i	−0.367490	−	0.460818i
$518$	19.8567	+	20.5480i	0.872455	+	0.902825i
$519$		0			0
$520$	3.86220	−	6.68952i	0.169369	−	0.293355i
$521$	−11.8828	−	20.5817i	−0.520597	−	0.901700i	−0.999713	−	0.0239489i	$-0.992376\pi$
$521$	−11.8828	−	20.5817i	−0.520597	−	0.901700i	0.479116	−	0.877751i	$-0.340957\pi$
$522$		0			0
$523$	−25.9861	−	24.1116i	−1.13629	−	1.05433i	−0.997954	−	0.0639403i	$-0.979633\pi$
$523$	−25.9861	−	24.1116i	−1.13629	−	1.05433i	−0.138339	−	0.990385i	$-0.544176\pi$
$524$	−4.71158	+	2.26898i	−0.205826	+	0.0991207i
$525$		0			0
$526$	16.0719	+	7.73984i	0.700770	+	0.337473i
$527$	−1.34859	−	3.43615i	−0.0587455	−	0.149681i
$528$		0			0
$529$	−0.398987	+	0.123071i	−0.0173473	+	0.00535092i
$530$	0.196289	−	2.61929i	0.00852624	−	0.113775i
$531$		0			0
$532$	−3.13908	−	6.19361i	−0.136096	−	0.268527i
$533$	2.86681	−	12.5603i	0.124175	−	0.544047i
$534$		0			0
$535$	−3.87549	+	9.87460i	−0.167552	+	0.426916i
$536$	17.0951	−	15.8619i	0.738396	−	0.685131i
$537$		0			0
$538$	−6.23683			−0.268889
$539$	−11.7806	+	34.0144i	−0.507425	+	1.46510i
$540$		0			0
$541$	9.80988	−	6.68827i	0.421760	−	0.287551i	−0.333783	−	0.942650i	$-0.608325\pi$
$541$	9.80988	−	6.68827i	0.421760	−	0.287551i	0.755543	+	0.655099i	$0.227373\pi$
$542$	−2.08278	+	1.93253i	−0.0894629	+	0.0830094i
$543$		0			0
$544$	10.4179	+	3.21350i	0.446664	+	0.137778i
$545$	1.98890	−	8.71393i	0.0851950	−	0.373264i
$546$		0			0
$547$	6.70837	+	29.3913i	0.286829	+	1.25668i	0.888849	+	0.458200i	$0.151506\pi$
$547$	6.70837	+	29.3913i	0.286829	+	1.25668i	−0.602020	+	0.798481i	$0.705637\pi$
$548$	0.0760621	−	1.01498i	0.00324921	−	0.0433577i
$549$		0			0
$550$	1.61692	+	21.5762i	0.0689455	+	0.920014i
$551$	−16.7350	−	42.6400i	−0.712934	−	1.81653i
$552$		0			0
$553$	−1.40298	+	1.57498i	−0.0596606	+	0.0669748i
$554$	−10.8542	+	5.22713i	−0.461153	+	0.222079i
$555$		0			0
$556$	5.41215	+	0.815751i	0.229526	+	0.0345955i
$557$	15.2097	+	26.3439i	0.644454	+	1.11623i	0.984427	+	0.175793i	$0.0562488\pi$
$557$	15.2097	+	26.3439i	0.644454	+	1.11623i	−0.339973	+	0.940435i	$0.610418\pi$
$558$		0			0
$559$	14.3556	−	18.0014i	0.607179	−	0.761379i
$560$	−3.29253	−	9.95243i	−0.139135	−	0.420567i
$561$		0			0
$562$	22.8302	−	3.44109i	0.963032	−	0.145154i
$563$	−24.1875	−	16.4907i	−1.01938	−	0.695001i	−0.0663244	−	0.997798i	$-0.521127\pi$
$563$	−24.1875	−	16.4907i	−1.01938	−	0.695001i	−0.953055	+	0.302797i	$0.902080\pi$
$564$		0			0
$565$	−8.48388	+	1.27874i	−0.356919	+	0.0537970i
$566$	0.0403678	+	0.0506196i	0.00169678	+	0.00212770i
$567$		0			0
$568$	−10.5962	+	13.2873i	−0.444608	+	0.557521i
$569$	−3.68242	+	6.37814i	−0.154375	+	0.267385i	−0.932831	−	0.360313i	$-0.882670\pi$
$569$	−3.68242	+	6.37814i	−0.154375	+	0.267385i	0.778456	+	0.627699i	$0.216003\pi$
$570$		0			0
$571$	−30.9968	−	4.67201i	−1.29717	−	0.195518i	−0.536085	−	0.844164i	$-0.680097\pi$
$571$	−30.9968	−	4.67201i	−1.29717	−	0.195518i	−0.761090	+	0.648646i	$0.775335\pi$
$572$	2.91709	+	2.70667i	0.121970	+	0.113171i
$573$		0			0
$574$	−12.7538	−	17.9142i	−0.532333	−	0.747725i
$575$	14.2148	+	6.84550i	0.592800	+	0.285477i
$576$		0			0
$577$	2.10433	+	28.0804i	0.0876046	+	1.16900i	0.851747	+	0.523954i	$0.175544\pi$
$577$	2.10433	+	28.0804i	0.0876046	+	1.16900i	−0.764142	+	0.645048i	$0.776837\pi$
$578$	−9.32552	+	2.87654i	−0.387891	+	0.119648i
$579$		0			0
$580$	0.781192	+	3.42263i	0.0324372	+	0.142117i
$581$	−8.33383	+	2.08093i	−0.345746	+	0.0863316i
$582$		0			0
$583$	7.85779	+	2.42381i	0.325436	+	0.100384i
$584$	3.06135	−	7.80018i	0.126679	−	0.322774i
$585$		0			0
$586$	−18.0969	+	12.3382i	−0.747575	+	0.509688i
$587$	26.7457			1.10391			0.551957	−	0.833872i	$-0.313881\pi$
$587$	26.7457			1.10391			0.551957	+	0.833872i	$0.313881\pi$
$588$		0			0
$589$	4.94812			0.203884
$590$	4.83821	−	3.29863i	0.199186	−	0.135803i
$591$		0			0
$592$	9.51777	−	24.2509i	0.391178	−	0.996705i
$593$	11.9241	+	3.67810i	0.489664	+	0.151041i	0.529748	−	0.848155i	$-0.322286\pi$
$593$	11.9241	+	3.67810i	0.489664	+	0.151041i	−0.0400841	+	0.999196i	$0.512763\pi$
$594$		0			0
$595$	−13.5378	−	10.3536i	−0.554994	−	0.424458i
$596$	0.430521	+	1.88624i	0.0176348	+	0.0772633i
$597$		0			0
$598$	−11.3046	+	3.48700i	−0.462279	+	0.142594i
$599$	3.22721	+	43.0641i	0.131860	+	1.75955i	0.535407	+	0.844594i	$0.320158\pi$
$599$	3.22721	+	43.0641i	0.131860	+	1.75955i	−0.403547	+	0.914959i	$0.632223\pi$
$600$		0			0
$601$	−24.0754	−	11.5941i	−0.982055	−	0.472933i	−0.127243	−	0.991872i	$-0.540613\pi$
$601$	−24.0754	−	11.5941i	−0.982055	−	0.472933i	−0.854811	+	0.518939i	$0.826327\pi$
$602$	−6.64485	−	38.7348i	−0.270824	−	1.57871i
$603$		0			0
$604$	−3.19296	−	2.96264i	−0.129920	−	0.120548i
$605$	19.7939	+	2.98345i	0.804735	+	0.121294i
$606$		0			0
$607$	−0.668278	+	1.15749i	−0.0271246	+	0.0469812i	−0.879269	−	0.476325i	$-0.841968\pi$
$607$	−0.668278	+	1.15749i	−0.0271246	+	0.0469812i	0.852144	+	0.523307i	$0.175302\pi$
$608$	−9.11181	+	11.4259i	−0.369533	+	0.463379i
$609$		0			0
$610$	0.198565	+	0.248993i	0.00803968	+	0.0100814i
$611$	5.06225	−	0.763011i	0.204797	−	0.0308681i
$612$		0			0
$613$	18.8665	+	12.8629i	0.762009	+	0.519529i	0.880856	−	0.473384i	$-0.156968\pi$
$613$	18.8665	+	12.8629i	0.762009	+	0.519529i	−0.118847	+	0.992913i	$0.537920\pi$
$614$	−36.6855	+	5.52944i	−1.48050	+	0.223150i
$615$		0			0
$616$	41.0904	−	3.91927i	1.65558	−	0.157912i
$617$	−20.8942	+	26.2005i	−0.841170	+	1.05479i	0.156574	+	0.987666i	$0.449955\pi$
$617$	−20.8942	+	26.2005i	−0.841170	+	1.05479i	−0.997744	+	0.0671278i	$0.978616\pi$
$618$		0			0
$619$	−2.98276	−	5.16628i	−0.119887	−	0.207650i	0.799836	−	0.600219i	$-0.204920\pi$
$619$	−2.98276	−	5.16628i	−0.119887	−	0.207650i	−0.919723	+	0.392569i	$0.871587\pi$
$620$	−0.374992	−	0.0565210i	−0.0150601	−	0.00226994i
$621$		0			0
$622$	−16.0788	+	7.74315i	−0.644701	+	0.310472i
$623$	4.21515	−	14.7193i	0.168877	−	0.589716i
$624$		0			0
$625$	0.958339	+	2.44181i	0.0383336	+	0.0976723i
$626$	2.49584	+	33.3046i	0.0997537	+	1.33112i
$627$		0			0
$628$	0.0662112	−	0.883527i	0.00264212	−	0.0352566i
$629$	−9.42487	−	41.2930i	−0.375794	−	1.64646i
$630$		0			0
$631$	−2.79688	+	12.2539i	−0.111342	+	0.487821i	0.888253	+	0.459355i	$0.151919\pi$
$631$	−2.79688	+	12.2539i	−0.111342	+	0.487821i	−0.999595	+	0.0284658i	$0.990938\pi$
$632$	2.31119	+	0.712906i	0.0919340	+	0.0283579i
$633$		0			0
$634$	−25.9074	+	24.0385i	−1.02891	+	0.954692i
$635$	−10.4135	+	7.09980i	−0.413247	+	0.281747i
$636$		0			0
$637$	−9.00254	−	10.3939i	−0.356693	−	0.411823i
$638$	44.8084			1.77398
$639$		0			0
$640$	−6.54067	+	6.06885i	−0.258543	+	0.239892i
$641$	−10.6970	+	27.2555i	−0.422507	+	1.07653i	0.548218	+	0.836335i	$0.315306\pi$
$641$	−10.6970	+	27.2555i	−0.422507	+	1.07653i	−0.970725	+	0.240194i	$0.922789\pi$
$642$		0			0
$643$	4.35457	−	19.0786i	0.171727	−	0.752387i	−0.813560	−	0.581481i	$-0.802473\pi$
$643$	4.35457	−	19.0786i	0.171727	−	0.752387i	0.985287	−	0.170906i	$-0.0546694\pi$
$644$	2.05800	−	4.50512i	0.0810965	−	0.177527i
$645$		0			0
$646$	3.13577	−	41.8439i	0.123375	−	1.64633i
$647$	−22.7715	+	7.02407i	−0.895239	+	0.276145i	−0.708036	−	0.706176i	$-0.750419\pi$
$647$	−22.7715	+	7.02407i	−0.895239	+	0.276145i	−0.187203	+	0.982321i	$0.559942\pi$
$648$		0			0
$649$	6.69752	+	17.0650i	0.262901	+	0.669860i
$650$	−7.44666	−	3.58612i	−0.292082	−	0.140659i
$651$		0			0
$652$	3.89739	−	1.87688i	0.152634	−	0.0735045i
$653$	20.6986	+	19.2055i	0.809998	+	0.751568i	0.971939	−	0.235232i	$-0.0755851\pi$
$653$	20.6986	+	19.2055i	0.809998	+	0.751568i	−0.161941	+	0.986800i	$0.551776\pi$
$654$		0			0
$655$	−8.60293	−	14.9007i	−0.336144	−	0.582219i
$656$	−10.0244	+	17.3628i	−0.391388	+	0.677905i
$657$		0			0
$658$	4.77494	−	7.31834i	0.186147	−	0.285299i
$659$	−5.69201	−	7.13756i	−0.221729	−	0.278040i	0.658508	−	0.752574i	$-0.271188\pi$
$659$	−5.69201	−	7.13756i	−0.221729	−	0.278040i	−0.880237	+	0.474534i	$0.842617\pi$
$660$		0			0
$661$	−15.7727	−	10.7536i	−0.613485	−	0.418267i	0.216318	−	0.976323i	$-0.430595\pi$
$661$	−15.7727	−	10.7536i	−0.613485	−	0.418267i	−0.829803	+	0.558056i	$0.811548\pi$
$662$	−0.350588	−	0.239027i	−0.0136260	−	0.00929004i
$663$		0			0
$664$	6.14119	+	7.70081i	0.238324	+	0.298849i
$665$	19.5493	−	11.8221i	0.758088	−	0.458441i
$666$		0			0
$667$	16.3369	−	28.2963i	0.632566	−	1.09564i
$668$	1.18207	+	2.04741i	0.0457358	+	0.0792167i
$669$		0			0
$670$	9.25562	+	8.58796i	0.357576	+	0.331782i
$671$	−0.898299	+	0.432598i	−0.0346784	+	0.0167003i
$672$		0			0
$673$	17.5683	+	8.46045i	0.677208	+	0.326126i	0.740681	−	0.671857i	$-0.234503\pi$
$673$	17.5683	+	8.46045i	0.677208	+	0.326126i	−0.0634723	+	0.997984i	$0.520217\pi$
$674$	−2.88976	−	7.36300i	−0.111310	−	0.283612i
$675$		0			0
$676$	3.44109	−	1.06144i	0.132350	−	0.0408244i
$677$	−1.95992	+	26.1533i	−0.0753257	+	1.00515i	0.823635	+	0.567121i	$0.191943\pi$
$677$	−1.95992	+	26.1533i	−0.0753257	+	1.00515i	−0.898960	+	0.438030i	$0.855676\pi$
$678$		0			0
$679$	40.6253	+	8.40893i	1.55905	+	0.322705i
$680$	−4.34876	+	19.0532i	−0.166767	+	0.730656i
$681$		0			0
$682$	−1.76836	+	4.50571i	−0.0677140	+	0.172533i
$683$	−14.4035	+	13.3645i	−0.551135	+	0.511378i	−0.905851	−	0.423596i	$-0.860768\pi$
$683$	−14.4035	+	13.3645i	−0.551135	+	0.511378i	0.354717	+	0.934974i	$0.384577\pi$
$684$		0			0
$685$	3.34882			0.127952
$686$	−23.4685	−	0.326655i	−0.896033	−	0.0124718i
$687$		0			0
$688$	−29.6048	+	20.1842i	−1.12867	+	0.769515i
$689$	−2.30267	+	2.13656i	−0.0877246	+	0.0813966i
$690$		0			0
$691$	−26.4356	−	8.15430i	−1.00566	−	0.310204i	−0.252181	−	0.967680i	$-0.581148\pi$
$691$	−26.4356	−	8.15430i	−1.00566	−	0.310204i	−0.753476	+	0.657476i	$0.771624\pi$
$692$	1.75199	−	7.67597i	0.0666007	−	0.291797i
$693$		0			0
$694$	4.16823	+	18.2622i	0.158224	+	0.693224i
$695$	−1.34575	+	17.9577i	−0.0510470	+	0.681175i
$696$		0			0
$697$	2.43586	+	32.5043i	0.0922649	+	1.23119i
$698$	−3.03438	−	7.73148i	−0.114853	−	0.292641i
$699$		0			0
$700$	3.19485	−	1.32932i	0.120754	−	0.0502436i
$701$	−39.2378	+	18.8959i	−1.48199	+	0.713689i	−0.987809	−	0.155669i	$-0.950247\pi$
$701$	−39.2378	+	18.8959i	−1.48199	+	0.713689i	−0.494182	+	0.869359i	$0.664532\pi$
$702$		0			0
$703$	56.1417	+	8.46199i	2.11742	+	0.319150i
$704$	−22.8678	−	39.6082i	−0.861864	−	1.49279i
$705$		0			0
$706$	15.7281	−	19.7224i	0.591935	−	0.742263i
$707$	35.8668	−	21.6899i	1.34891	−	0.815732i
$708$		0			0
$709$	−4.89507	+	0.737812i	−0.183838	+	0.0277091i	−0.240316	−	0.970695i	$-0.577251\pi$
$709$	−4.89507	+	0.737812i	−0.183838	+	0.0277091i	0.0564779	+	0.998404i	$0.482013\pi$
$710$	−7.60258	−	5.18335i	−0.285320	−	0.194528i
$711$		0			0
$712$	−17.3608	+	2.61671i	−0.650622	+	0.0980655i
$713$	2.20060	+	2.75947i	0.0824133	+	0.103343i
$714$		0			0
$715$	−8.16327	+	10.2364i	−0.305289	+	0.382820i
$716$	−3.03974	+	5.26498i	−0.113600	+	0.196761i
$717$		0			0
$718$	12.1034	+	1.82430i	0.451697	+	0.0680823i
$719$	−23.5822	−	21.8811i	−0.879467	−	0.816026i	0.104472	−	0.994528i	$-0.466685\pi$
$719$	−23.5822	−	21.8811i	−0.879467	−	0.816026i	−0.983940	+	0.178501i	$0.942875\pi$
$720$		0			0
$721$	37.0202	+	20.3834i	1.37871	+	0.759117i
$722$	28.9835	+	13.9577i	1.07865	+	0.519452i
$723$		0			0
$724$	−0.522216	−	6.96848i	−0.0194080	−	0.258982i
$725$	21.8134	−	6.72855i	0.810130	−	0.249892i
$726$		0			0
$727$	−5.12061	−	22.4348i	−0.189913	−	0.832062i	−0.976661	−	0.214788i	$-0.931094\pi$
$727$	−5.12061	−	22.4348i	−0.189913	−	0.832062i	0.786748	−	0.617274i	$-0.211763\pi$
$728$	−6.55164	+	14.3421i	−0.242820	+	0.531552i
$729$		0			0
$730$	4.33522	+	1.33724i	0.160454	+	0.0494934i
$731$	−21.2825	+	54.2269i	−0.787161	+	2.00565i
$732$		0			0
$733$	10.2494	−	6.98796i	0.378572	−	0.258106i	−0.359052	−	0.933317i	$-0.616900\pi$
$733$	10.2494	−	6.98796i	0.378572	−	0.258106i	0.737624	+	0.675211i	$0.235948\pi$
$734$	8.52900			0.314811
$735$		0			0
$736$	−10.4243			−0.384246
$737$	−32.6597	+	22.2670i	−1.20304	+	0.820217i
$738$		0			0
$739$	−7.17040	+	18.2699i	−0.263767	+	0.672069i	−0.999989	−	0.00467196i	$-0.998513\pi$
$739$	−7.17040	+	18.2699i	−0.263767	+	0.672069i	0.736222	+	0.676741i	$0.236608\pi$
$740$	−4.15803	−	1.28258i	−0.152852	−	0.0471486i
$741$		0			0
$742$	0.108803	+	5.36060i	0.00399427	+	0.196794i
$743$	−6.83118	−	29.9294i	−0.250612	−	1.09800i	−0.930962	−	0.365115i	$-0.881030\pi$
$743$	−6.83118	−	29.9294i	−0.250612	−	1.09800i	0.680351	−	0.732887i	$-0.261827\pi$
$744$		0			0
$745$	−6.08285	+	1.87631i	−0.222858	+	0.0687427i
$746$	−1.84486	−	24.6180i	−0.0675452	−	0.901329i
$747$		0			0
$748$	−9.07101	−	4.36837i	−0.331669	−	0.159723i
$749$	5.96133	−	20.8169i	0.217822	−	0.760633i
$750$		0			0
$751$	−6.80010	−	6.30957i	−0.248139	−	0.230240i	0.546290	−	0.837596i	$-0.316040\pi$
$751$	−6.80010	−	6.30957i	−0.248139	−	0.230240i	−0.794430	+	0.607356i	$0.792230\pi$
$752$	−7.87782	−	1.18739i	−0.287275	−	0.0432997i
$753$		0			0
$754$	−8.55833	+	14.8235i	−0.311676	+	0.539838i
$755$	8.93528	−	11.2045i	0.325188	−	0.407773i
$756$		0			0
$757$	22.2301	+	27.8756i	0.807965	+	1.01316i	0.999498	+	0.0316701i	$0.0100826\pi$
$757$	22.2301	+	27.8756i	0.807965	+	1.01316i	−0.191533	+	0.981486i	$0.561346\pi$
$758$	−11.9547	+	1.80188i	−0.434215	+	0.0654473i
$759$		0			0
$760$	−21.6451	−	14.7574i	−0.785150	−	0.535306i
$761$	39.9221	−	6.01729i	1.44717	−	0.218126i	0.622006	−	0.783013i	$-0.286318\pi$
$761$	39.9221	−	6.01729i	1.44717	−	0.218126i	0.825169	+	0.564886i	$0.191080\pi$
$762$		0			0
$763$	−2.35262	+	18.0927i	−0.0851704	+	0.655000i
$764$	1.86427	−	2.33772i	0.0674469	−	0.0845757i
$765$		0			0
$766$	2.64469	+	4.58074i	0.0955566	+	0.165509i
$767$	−6.92464	−	1.04372i	−0.250034	−	0.0376866i
$768$		0			0
$769$	0.250639	−	0.120701i	0.00903826	−	0.00435260i	−0.429359	−	0.903134i	$-0.641261\pi$
$769$	0.250639	−	0.120701i	0.00903826	−	0.00435260i	0.438397	+	0.898781i	$0.355546\pi$
$770$	3.77856	+	22.0264i	0.136170	+	0.793775i
$771$		0			0
$772$	−0.552526	−	1.40781i	−0.0198858	−	0.0506683i
$773$	−0.556338	−	7.42382i	−0.0200101	−	0.267016i	−0.998231	−	0.0594508i	$-0.981065\pi$
$773$	−0.556338	−	7.42382i	−0.0200101	−	0.267016i	0.978221	−	0.207565i	$-0.0665540\pi$
$774$		0			0
$775$	−0.184276	+	2.45899i	−0.00661939	+	0.0883296i
$776$	−10.5858	−	46.3792i	−0.380006	−	1.66492i
$777$		0			0
$778$	8.83389	−	38.7038i	0.316710	−	1.38760i
$779$	−41.7523	−	12.8789i	−1.49593	−	0.461433i
$780$		0			0
$781$	21.1167	−	19.5935i	0.755616	−	0.701110i
$782$	24.7302	−	16.8607i	0.884348	−	0.602939i
$783$		0			0
$784$	8.61960	+	19.5857i	0.307843	+	0.699491i
$785$	2.91511			0.104045
$786$		0			0
$787$	32.5011	−	30.1566i	1.15854	−	1.07497i	0.162442	−	0.986718i	$-0.448063\pi$
$787$	32.5011	−	30.1566i	1.15854	−	1.07497i	0.996098	−	0.0882504i	$-0.0281276\pi$
$788$	2.17686	−	5.54654i	0.0775473	−	0.197587i
$789$		0			0
$790$	−0.291391	+	1.27667i	−0.0103672	+	0.0454217i
$791$	16.9919	−	4.24282i	0.604162	−	0.150857i
$792$		0			0
$793$	0.0284621	−	0.379800i	0.00101072	−	0.0134871i
$794$	−24.1757	+	7.45721i	−0.857963	+	0.264646i
$795$		0			0
$796$	1.46102	+	3.72261i	0.0517844	+	0.131944i
$797$	−28.7027	−	13.8225i	−1.01670	−	0.489617i	−0.150127	−	0.988667i	$-0.547968\pi$
$797$	−28.7027	−	13.8225i	−1.01670	−	0.489617i	−0.866573	+	0.499050i	$0.833683\pi$
$798$		0			0
$799$	−11.6697	+	5.61985i	−0.412846	+	0.198816i
$800$	−5.33880	−	4.95368i	−0.188755	−	0.175139i
$801$		0			0
$802$	−11.8503	−	20.5254i	−0.418450	−	0.724777i
$803$	−7.10157	+	12.3003i	−0.250609	+	0.434067i
$804$		0			0
$805$	15.2872	+	5.64454i	0.538803	+	0.198944i
$806$	−1.15282	−	1.44559i	−0.0406064	−	0.0509188i
$807$		0			0
$808$	−39.7120	−	27.0752i	−1.39706	−	0.952501i
$809$	−10.0026	−	6.81969i	−0.351674	−	0.239767i	0.374579	−	0.927195i	$-0.377787\pi$
$809$	−10.0026	−	6.81969i	−0.351674	−	0.239767i	−0.726253	+	0.687428i	$0.758740\pi$
$810$		0			0
$811$	27.4858	+	34.4662i	0.965159	+	1.21027i	0.977627	+	0.210348i	$0.0674598\pi$
$811$	27.4858	+	34.4662i	0.965159	+	1.21027i	−0.0124679	+	0.999922i	$0.503969\pi$
$812$	−2.25080	−	6.80356i	−0.0789877	−	0.238758i
$813$		0			0
$814$	−27.7693	+	48.0979i	−0.973315	+	1.68583i
$815$	7.11629	+	12.3258i	0.249273	+	0.431753i
$816$		0			0
$817$	−57.2423	−	53.1131i	−2.00265	−	1.85819i
$818$	−43.6878	+	21.0390i	−1.52751	+	0.735610i
$819$		0			0
$820$	3.01708	+	1.45295i	0.105361	+	0.0507392i
$821$	10.6041	+	27.0189i	0.370086	+	0.942965i	0.987683	+	0.156469i	$0.0500113\pi$
$821$	10.6041	+	27.0189i	0.370086	+	0.942965i	−0.617596	+	0.786495i	$0.711893\pi$
$822$		0			0
$823$	−35.1638	+	10.8466i	−1.22573	+	0.378089i	−0.839014	−	0.544109i	$-0.816868\pi$
$823$	−35.1638	+	10.8466i	−1.22573	+	0.378089i	−0.386719	+	0.922198i	$0.626392\pi$
$824$	3.62142	−	48.3245i	0.126158	−	1.68346i
$825$		0			0
$826$	−9.19217	+	7.64076i	−0.319837	+	0.265856i
$827$	−8.74499	+	38.3143i	−0.304093	+	1.33232i	0.559793	+	0.828632i	$0.310881\pi$
$827$	−8.74499	+	38.3143i	−0.304093	+	1.33232i	−0.863886	+	0.503687i	$0.831977\pi$
$828$		0			0
$829$	12.3823	−	31.5496i	0.430055	−	1.09576i	−0.537536	−	0.843241i	$-0.680645\pi$
$829$	12.3823	−	31.5496i	0.430055	−	1.09576i	0.967591	−	0.252522i	$-0.0812599\pi$
$830$	−3.90923	+	3.62724i	−0.135691	+	0.125903i
$831$		0			0
$832$	17.4709			0.605694
$833$	29.5163	+	18.4153i	1.02268	+	0.638052i
$834$		0			0
$835$	−6.42687	+	4.38177i	−0.222411	+	0.151637i
$836$	9.89326	−	9.17960i	0.342165	−	0.317483i
$837$		0			0
$838$	10.8950	+	3.36067i	0.376363	+	0.116093i
$839$	2.89379	−	12.6785i	0.0999046	−	0.437711i	−0.900093	−	0.435697i	$-0.856502\pi$
$839$	2.89379	−	12.6785i	0.0999046	−	0.437711i	0.999998	−	0.00201363i	$-0.000640959\pi$
$840$		0			0
$841$	−4.06646	−	17.8163i	−0.140223	−	0.614356i
$842$	−1.33267	+	17.7833i	−0.0459269	+	0.612852i
$843$		0			0
$844$	0.512673	+	6.84114i	0.0176469	+	0.235482i
$845$	4.32862	+	11.0292i	0.148909	+	0.379414i
$846$		0			0
$847$	−40.8005	−	2.22607i	−1.40192	−	0.0764888i
$848$	4.40422	−	2.12096i	0.151241	−	0.0728341i
$849$		0			0
$850$	20.6778	+	3.11667i	0.709242	+	0.106901i
$851$	20.2491	+	35.0725i	0.694130	+	1.20227i
$852$		0			0
$853$	−0.703148	+	0.881720i	−0.0240753	+	0.0301895i	−0.793723	−	0.608279i	$-0.791860\pi$
$853$	−0.703148	+	0.881720i	−0.0240753	+	0.0301895i	0.769648	+	0.638468i	$0.220432\pi$
$854$	−0.451756	−	0.467482i	−0.0154588	−	0.0159969i
$855$		0			0
$856$	−24.5526	+	3.70072i	−0.839192	+	0.126488i
$857$	31.1594	+	21.2441i	1.06439	+	0.725686i	0.963092	−	0.269171i	$-0.0867496\pi$
$857$	31.1594	+	21.2441i	1.06439	+	0.725686i	0.101293	+	0.994857i	$0.467702\pi$
$858$		0			0
$859$	−13.9388	+	2.10094i	−0.475586	+	0.0716831i	−0.382462	−	0.923971i	$-0.624924\pi$
$859$	−13.9388	+	2.10094i	−0.475586	+	0.0716831i	−0.0931245	+	0.995654i	$0.529685\pi$
$860$	3.73140	+	4.67903i	0.127240	+	0.159554i
$861$		0			0
$862$	−12.7459	+	15.9828i	−0.434126	+	0.544377i
$863$	12.1919	−	21.1169i	0.415015	−	0.718828i	−0.580415	−	0.814321i	$-0.697110\pi$
$863$	12.1919	−	21.1169i	0.415015	−	0.718828i	0.995430	+	0.0954933i	$0.0304428\pi$
$864$		0			0
$865$	25.6155	+	3.86091i	0.870951	+	0.131275i
$866$	17.8593	+	16.5710i	0.606882	+	0.563105i
$867$		0			0
$868$	0.772961	+	0.0421727i	0.0262360	+	0.00143143i
$869$	−3.69361	−	1.77875i	−0.125297	−	0.0603399i
$870$		0			0
$871$	−1.12840	−	15.0574i	−0.0382343	−	0.510202i
$872$	19.9918	−	6.16667i	0.677009	−	0.208830i
$873$		0			0
$874$	8.92793	+	39.1158i	0.301992	+	1.32311i
$875$	12.8984	+	25.4493i	0.436045	+	0.860345i
$876$		0			0
$877$	−32.7933	−	10.1154i	−1.10735	−	0.341573i	−0.313441	−	0.949608i	$-0.601482\pi$
$877$	−32.7933	−	10.1154i	−1.10735	−	0.341573i	−0.793910	+	0.608035i	$0.791958\pi$
$878$	5.15295	−	13.1295i	0.173904	−	0.443099i
$879$		0			0
$880$	16.8346	−	11.4776i	0.567495	−	0.386911i
$881$	43.1907			1.45513			0.727567	−	0.686037i	$-0.240651\pi$
$881$	43.1907			1.45513			0.727567	+	0.686037i	$0.240651\pi$
$882$		0			0
$883$	−0.746853			−0.0251336			−0.0125668	−	0.999921i	$-0.504000\pi$
$883$	−0.746853			−0.0251336			−0.0125668	+	0.999921i	$0.504000\pi$
$884$	3.17769	−	2.16651i	0.106877	−	0.0728676i
$885$		0			0
$886$	−8.47549	+	21.5952i	−0.284740	+	0.725505i
$887$	−2.79177	−	0.861148i	−0.0937386	−	0.0289145i	0.247531	−	0.968880i	$-0.420381\pi$
$887$	−2.79177	−	0.861148i	−0.0937386	−	0.0289145i	−0.341270	+	0.939965i	$0.610857\pi$
$888$		0			0
$889$	19.7847	−	16.4455i	0.663558	−	0.551566i
$890$	−2.11520	−	9.26730i	−0.0709017	−	0.310640i
$891$		0			0
$892$	−9.16155	+	2.82596i	−0.306751	+	0.0946203i
$893$	−1.29750	−	17.3139i	−0.0434191	−	0.579387i
$894$		0			0
$895$	−18.0217	−	8.67878i	−0.602398	−	0.290100i
$896$	12.1147	−	13.6000i	0.404725	−	0.454343i
$897$		0			0
$898$	5.15946	+	4.78728i	0.172173	+	0.159754i
$899$	5.04966	+	0.761114i	0.168416	+	0.0253846i
$900$		0			0
$901$	3.97371	−	6.88267i	0.132384	−	0.229295i
$902$	26.6488	−	33.4166i	0.887309	−	1.11265i
$903$		0			0
$904$	−12.5213	−	15.7012i	−0.416452	−	0.522215i
$905$	22.7350	−	3.42675i	0.755738	−	0.113909i
$906$		0			0
$907$	1.40630	+	0.958801i	0.0466955	+	0.0318365i	0.586443	−	0.809991i	$-0.300528\pi$
$907$	1.40630	+	0.958801i	0.0466955	+	0.0318365i	−0.539747	+	0.841827i	$0.681480\pi$
$908$	−6.33999	+	0.955600i	−0.210400	+	0.0317127i
$909$		0			0
$910$	−8.00844	−	2.95698i	−0.265477	−	0.0980230i
$911$	14.6000	−	18.3078i	0.483720	−	0.606565i	−0.478751	−	0.877951i	$-0.658910\pi$
$911$	14.6000	−	18.3078i	0.483720	−	0.606565i	0.962471	+	0.271386i	$0.0874818\pi$
$912$		0			0
$913$	−8.34764	−	14.4585i	−0.276266	−	0.478508i
$914$	4.76763	+	0.718604i	0.157699	+	0.0237693i
$915$		0			0
$916$	8.38752	−	4.03922i	0.277132	−	0.133460i
$917$	20.3697	+	28.6117i	0.672667	+	0.944840i
$918$		0			0
$919$	2.16924	+	5.52712i	0.0715565	+	0.182323i	0.962177	−	0.272423i	$-0.0878251\pi$
$919$	2.16924	+	5.52712i	0.0715565	+	0.182323i	−0.890621	+	0.454746i	$0.849730\pi$
$920$	−1.39644	−	18.6342i	−0.0460392	−	0.614350i
$921$		0			0
$922$	−1.59416	+	21.2725i	−0.0525007	+	0.700574i
$923$	2.44863	+	10.7281i	0.0805976	+	0.353121i
$924$		0			0
$925$	−6.29604	+	27.5847i	−0.207012	+	0.906981i
$926$	49.3802	+	15.2318i	1.62273	+	0.500547i
$927$		0			0
$928$	−11.0563	+	10.2588i	−0.362941	+	0.336760i
$929$	−24.8458	+	16.9396i	−0.815165	+	0.555770i	−0.897592	−	0.440827i	$-0.854685\pi$
$929$	−24.8458	+	16.9396i	−0.815165	+	0.555770i	0.0824273	+	0.996597i	$0.473733\pi$
$930$		0			0
$931$	−37.4339	+	27.8122i	−1.22685	+	0.911509i
$932$	1.59138			0.0521273
$933$		0			0
$934$	25.3507	−	23.5220i	0.829500	−	0.769664i
$935$	12.1022	−	30.8358i	0.395784	−	1.00844i
$936$		0			0
$937$	−0.899131	+	3.93935i	−0.0293733	+	0.128693i	−0.987489	−	0.157689i	$-0.949596\pi$
$937$	−0.899131	+	3.93935i	−0.0293733	+	0.128693i	0.958115	+	0.286382i	$0.0924527\pi$
$938$	−20.4725	−	15.6573i	−0.668450	−	0.511229i
$939$		0			0
$940$	−0.0994413	+	1.32695i	−0.00324342	+	0.0432804i
$941$	−17.6905	+	5.45678i	−0.576692	+	0.177886i	−0.569362	−	0.822087i	$-0.692810\pi$
$941$	−17.6905	+	5.45678i	−0.576692	+	0.177886i	−0.00733054	+	0.999973i	$0.502333\pi$
$942$		0			0
$943$	−11.3864	−	29.0121i	−0.370793	−	0.944765i
$944$	9.81856	+	4.72837i	0.319567	+	0.153895i
$945$		0			0
$946$	68.8216	−	33.1427i	2.23758	−	1.07756i
$947$	−27.6104	−	25.6187i	−0.897218	−	0.832497i	0.0893244	−	0.996003i	$-0.471529\pi$
$947$	−27.6104	−	25.6187i	−0.897218	−	0.832497i	−0.986542	+	0.163506i	$0.947720\pi$
$948$		0			0
$949$	−2.71278	−	4.69867i	−0.0880605	−	0.152525i
$950$	−14.0156	+	24.2757i	−0.454725	+	0.787607i
$951$		0			0
$952$	5.14404	−	39.5600i	0.166719	−	1.28215i
$953$	−23.6501	−	29.6563i	−0.766103	−	0.960663i	0.233829	−	0.972278i	$-0.424874\pi$
$953$	−23.6501	−	29.6563i	−0.766103	−	0.960663i	−0.999933	+	0.0116146i	$0.996303\pi$
$954$		0			0
$955$	8.12838	+	5.54183i	0.263028	+	0.179330i
$956$	1.05745	+	0.720960i	0.0342005	+	0.0233175i
$957$		0			0
$958$	−33.6687	−	42.2192i	−1.08779	−	1.36404i
$959$	−6.80500	+	0.649070i	−0.219745	+	0.0209596i
$960$		0			0
$961$	15.2242	−	26.3691i	0.491103	−	0.850615i
$962$	−10.6078	−	18.3733i	−0.342009	−	0.592377i
$963$		0			0
$964$	0.260634	+	0.241833i	0.00839445	+	0.00778891i
$965$	4.48315	−	2.15897i	0.144318	−	0.0694997i
$966$		0			0
$967$	−7.10037	−	3.41936i	−0.228333	−	0.109959i	0.316220	−	0.948686i	$-0.397586\pi$
$967$	−7.10037	−	3.41936i	−0.228333	−	0.109959i	−0.544553	+	0.838727i	$0.683301\pi$
$968$	17.1181	+	43.6161i	0.550195	+	1.40188i
$969$		0			0
$970$	24.6121	−	7.59182i	0.790246	−	0.243759i
$971$	−0.161725	+	2.15808i	−0.00519002	+	0.0692559i	−0.999197	−	0.0400571i	$-0.987246\pi$
$971$	−0.161725	+	2.15808i	−0.00519002	+	0.0692559i	0.994007	+	0.109313i	$0.0348651\pi$
$972$		0			0
$973$	−0.745945	−	36.7520i	−0.0239139	−	1.17821i
$974$	−8.99129	+	39.3934i	−0.288100	+	1.26225i
$975$		0			0
$976$	−0.216537	+	0.551727i	−0.00693118	+	0.0176603i
$977$	−11.3942	+	10.5723i	−0.364533	+	0.338237i	−0.841079	−	0.540913i	$-0.818079\pi$
$977$	−11.3942	+	10.5723i	−0.364533	+	0.338237i	0.476546	+	0.879149i	$0.341888\pi$
$978$		0			0
$979$	29.7589			0.951099
$980$	3.15461	−	1.68015i	0.100770	−	0.0536704i
$981$		0			0
$982$	−38.6097	+	26.3237i	−1.23209	+	0.840022i
$983$	23.0963	−	21.4303i	0.736659	−	0.683520i	−0.219748	−	0.975557i	$-0.570524\pi$
$983$	23.0963	−	21.4303i	0.736659	−	0.683520i	0.956407	+	0.292037i	$0.0943331\pi$
$984$		0			0
$985$	18.7333	+	5.77846i	0.596893	+	0.184117i
$986$	9.63651	−	42.2203i	0.306889	−	1.34457i
$987$		0			0
$988$	1.14719	+	5.02617i	0.0364970	+	0.159904i
$989$	4.16246	−	55.5442i	0.132359	−	1.76620i
$990$		0			0
$991$	2.41521	+	32.2288i	0.0767218	+	1.02378i	0.894155	+	0.447757i	$0.147777\pi$
$991$	2.41521	+	32.2288i	0.0767218	+	1.02378i	−0.817433	+	0.576023i	$0.804604\pi$
$992$	−0.595234	−	1.51663i	−0.0188987	−	0.0481531i
$993$		0			0
$994$	16.4535	+	9.05934i	0.521874	+	0.287345i
$995$	−11.8546	+	5.70886i	−0.375815	+	0.180983i
$996$		0			0
$997$	−32.2096	−	4.85482i	−1.02009	−	0.153754i	−0.382359	−	0.924014i	$-0.624888\pi$
$997$	−32.2096	−	4.85482i	−1.02009	−	0.153754i	−0.637729	+	0.770260i	$0.720126\pi$
$998$	−22.5254	−	39.0152i	−0.713031	−	1.23501i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.e.37.2		60
3.2	odd	2		147.2.m.b.37.4	yes	60
49.4	even	21	inner	441.2.bb.e.298.2		60
147.2	odd	42		7203.2.a.n.1.19		30
147.47	even	42		7203.2.a.m.1.19		30
147.53	odd	42		147.2.m.b.4.4	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.b.4.4	✓	60	147.53	odd	42
147.2.m.b.37.4	yes	60	3.2	odd	2
441.2.bb.e.37.2		60	1.1	even	1	trivial
441.2.bb.e.298.2		60	49.4	even	21	inner
7203.2.a.m.1.19		30	147.47	even	42
7203.2.a.n.1.19		30	147.2	odd	42

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04710 + 0.713898i) q^{2} +(-0.143921 + 0.366706i) q^{4} +(-1.23854 - 0.382039i) q^{5} +(2.59083 + 0.536271i) q^{7} +(-0.675095 - 2.95778i) q^{8} +O(q^{10})\)	\(q+(-1.04710 + 0.713898i) q^{2} +(-0.143921 + 0.366706i) q^{4} +(-1.23854 - 0.382039i) q^{5} +(2.59083 + 0.536271i) q^{7} +(-0.675095 - 2.95778i) q^{8} +(1.56961 - 0.484160i) q^{10} +(0.384291 + 5.12800i) q^{11} +(-1.76984 - 0.852310i) q^{13} +(-3.09570 + 1.28806i) q^{14} +(2.24089 + 2.07925i) q^{16} +(4.91447 + 0.740736i) q^{17} +(-3.33107 + 5.76957i) q^{19} +(0.318349 - 0.399197i) q^{20} +(-4.06326 - 5.09517i) q^{22} +(-4.69902 + 0.708264i) q^{23} +(-2.74316 - 1.87026i) q^{25} +(2.46166 - 0.371035i) q^{26} +(-0.569530 + 0.872893i) q^{28} +(-4.28689 + 5.37560i) q^{29} +(-0.371361 - 0.643217i) q^{31} +(2.16912 + 0.326943i) q^{32} +(-5.67473 + 2.73281i) q^{34} +(-3.00397 - 1.65399i) q^{35} +(-3.11350 - 7.93306i) q^{37} +(-0.630943 - 8.41934i) q^{38} +(-0.293857 + 3.92125i) q^{40} +(1.45940 + 6.39404i) q^{41} +(-2.60820 + 11.4273i) q^{43} +(-1.93578 - 0.597108i) q^{44} +(4.41470 - 4.09625i) q^{46} +(-2.15329 + 1.46809i) q^{47} +(6.42483 + 2.77878i) q^{49} +4.20753 q^{50} +(0.567265 - 0.526345i) q^{52} +(0.584212 - 1.48855i) q^{53} +(1.48314 - 6.49805i) q^{55} +(-0.162885 - 8.02516i) q^{56} +(0.651164 - 8.68918i) q^{58} +(3.40655 - 1.05078i) q^{59} +(0.0708345 + 0.180483i) q^{61} +(0.848043 + 0.408396i) q^{62} +(-8.01310 + 3.85891i) q^{64} +(1.86640 + 1.73177i) q^{65} +(3.84338 + 6.65692i) q^{67} +(-0.978930 + 1.69556i) q^{68} +(4.32624 - 0.412643i) q^{70} +(-3.49267 - 4.37967i) q^{71} +(2.28205 + 1.55588i) q^{73} +(8.92353 + 6.08396i) q^{74} +(-1.63633 - 2.05189i) q^{76} +(-1.75437 + 13.4919i) q^{77} +(-0.398609 + 0.690411i) q^{79} +(-1.98109 - 3.43134i) q^{80} +(-6.09283 - 5.65332i) q^{82} +(-2.92509 + 1.40865i) q^{83} +(-5.80377 - 2.79495i) q^{85} +(-5.42686 - 13.8274i) q^{86} +(14.9081 - 4.59854i) q^{88} +(0.432462 - 5.77081i) q^{89} +(-4.12829 - 3.15731i) q^{91} +(0.416566 - 1.82509i) q^{92} +(1.20664 - 3.07446i) q^{94} +(6.32986 - 5.87325i) q^{95} +15.6804 q^{97} +(-8.71118 + 1.67703i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) \) 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8	\( 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8} - 34 q^{10} + 11 q^{11} - 2 q^{13} - 40 q^{14} - 31 q^{16} + 9 q^{17} - 29 q^{19} + 43 q^{20} + 9 q^{22} + 4 q^{23} + 55 q^{25} - 36 q^{26} - 57 q^{28} - 4 q^{29} - 39 q^{31} + 92 q^{32} - 36 q^{34} + 33 q^{35} - 24 q^{37} - 118 q^{38} - 35 q^{41} + 2 q^{43} - 40 q^{44} - 40 q^{46} + 5 q^{47} + 129 q^{49} + 176 q^{50} - 6 q^{52} - 26 q^{53} + 2 q^{55} - 63 q^{56} + 11 q^{58} + 41 q^{59} + 6 q^{61} - 36 q^{62} + 74 q^{64} + 51 q^{65} - 55 q^{67} + 22 q^{68} - 68 q^{70} + 66 q^{71} + 24 q^{73} - 28 q^{74} + 3 q^{76} + 34 q^{77} - 51 q^{79} + 5 q^{80} - 41 q^{82} - 30 q^{83} + 68 q^{85} - 110 q^{86} + 129 q^{88} - 75 q^{89} + 5 q^{91} + 38 q^{94} - 36 q^{95} - 168 q^{97} - 227 q^{98}+O(q^{100}) \) 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8 - 34 * q^10 + 11 * q^11 - 2 * q^13 - 40 * q^14 - 31 * q^16 + 9 * q^17 - 29 * q^19 + 43 * q^20 + 9 * q^22 + 4 * q^23 + 55 * q^25 - 36 * q^26 - 57 * q^28 - 4 * q^29 - 39 * q^31 + 92 * q^32 - 36 * q^34 + 33 * q^35 - 24 * q^37 - 118 * q^38 - 35 * q^41 + 2 * q^43 - 40 * q^44 - 40 * q^46 + 5 * q^47 + 129 * q^49 + 176 * q^50 - 6 * q^52 - 26 * q^53 + 2 * q^55 - 63 * q^56 + 11 * q^58 + 41 * q^59 + 6 * q^61 - 36 * q^62 + 74 * q^64 + 51 * q^65 - 55 * q^67 + 22 * q^68 - 68 * q^70 + 66 * q^71 + 24 * q^73 - 28 * q^74 + 3 * q^76 + 34 * q^77 - 51 * q^79 + 5 * q^80 - 41 * q^82 - 30 * q^83 + 68 * q^85 - 110 * q^86 + 129 * q^88 - 75 * q^89 + 5 * q^91 + 38 * q^94 - 36 * q^95 - 168 * q^97 - 227 * q^98

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