LMFDB - Embedded newform 441.2.bb.e.100.1

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			100.1
Character	$\chi$	$=$	441.100
Dual form			441.2.bb.e.172.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.27757 - 0.702538i) q^{2} +(3.04130 + 2.07352i) q^{4} +(3.42100 - 0.515632i) q^{5} +(2.20464 - 1.46273i) q^{7} +(-2.49792 - 3.13230i) q^{8} +O(q^{10})$	\(q+(-2.27757 - 0.702538i) q^{2} +(3.04130 + 2.07352i) q^{4} +(3.42100 - 0.515632i) q^{5} +(2.20464 - 1.46273i) q^{7} +(-2.49792 - 3.13230i) q^{8} +(-8.15382 - 1.22899i) q^{10} +(3.68575 - 3.41988i) q^{11} +(0.138027 + 0.604735i) q^{13} +(-6.04884 + 1.78264i) q^{14} +(0.799079 + 2.03602i) q^{16} +(0.352700 + 4.70646i) q^{17} +(-1.52702 + 2.64487i) q^{19} +(11.4735 + 5.52532i) q^{20} +(-10.7972 + 5.19964i) q^{22} +(-0.217678 + 2.90471i) q^{23} +(6.65947 - 2.05417i) q^{25} +(0.110483 - 1.47430i) q^{26} +(9.73797 + 0.122759i) q^{28} +(-7.28014 - 3.50593i) q^{29} +(1.74798 + 3.02759i) q^{31} +(0.209212 + 2.79174i) q^{32} +(2.50316 - 10.9671i) q^{34} +(6.78782 - 6.14078i) q^{35} +(-3.54005 + 2.41357i) q^{37} +(5.33602 - 4.95110i) q^{38} +(-10.1605 - 9.42757i) q^{40} +(-5.76293 - 7.22648i) q^{41} +(4.76320 - 5.97286i) q^{43} +(18.3007 - 2.75838i) q^{44} +(2.53645 - 6.46277i) q^{46} +(3.44501 + 1.06264i) q^{47} +(2.72084 - 6.44958i) q^{49} -16.6106 q^{50} +(-0.834151 + 2.12538i) q^{52} +(4.76028 + 3.24551i) q^{53} +(10.8455 - 13.5999i) q^{55} +(-10.0887 - 3.25178i) q^{56} +(14.1180 + 13.0996i) q^{58} +(-10.0458 - 1.51416i) q^{59} +(-6.30699 + 4.30003i) q^{61} +(-1.85415 - 8.12358i) q^{62} +(2.45821 - 10.7701i) q^{64} +(0.784010 + 1.99762i) q^{65} +(-0.311368 - 0.539305i) q^{67} +(-8.68628 + 15.0451i) q^{68} +(-19.7739 + 9.21737i) q^{70} +(9.03366 - 4.35038i) q^{71} +(-1.60225 + 0.494230i) q^{73} +(9.75835 - 3.01005i) q^{74} +(-10.1283 + 4.87755i) q^{76} +(3.12338 - 12.9308i) q^{77} +(-1.91890 + 3.32364i) q^{79} +(3.78348 + 6.55319i) q^{80} +(8.04861 + 20.5075i) q^{82} +(-2.19538 + 9.61859i) q^{83} +(3.63338 + 15.9189i) q^{85} +(-15.0447 + 10.2573i) q^{86} +(-19.9188 - 3.00228i) q^{88} +(2.05518 + 1.90693i) q^{89} +(1.18886 + 1.13132i) q^{91} +(-6.68502 + 8.38275i) q^{92} +(-7.09970 - 4.84050i) q^{94} +(-3.86014 + 9.83548i) q^{95} -0.516475 q^{97} +(-10.7280 + 12.7779i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{13}{21}\right)$	$1$

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 $

$2$	−2.27757	−	0.702538i	−1.61049	−	0.496770i	−0.646544	−	0.762877i	$-0.723786\pi$
$2$	−2.27757	−	0.702538i	−1.61049	−	0.496770i	−0.963943	+	0.266107i	$0.914262\pi$
$3$		0			0
$3$		0			0
$4$	3.04130	+	2.07352i	1.52065	+	1.03676i
$5$	3.42100	−	0.515632i	1.52992	−	0.230598i	0.670513	−	0.741898i	$-0.266074\pi$
$5$	3.42100	−	0.515632i	1.52992	−	0.230598i	0.859402	+	0.511300i	$0.170836\pi$
$6$		0			0
$7$	2.20464	−	1.46273i	0.833274	−	0.552860i
$7$	2.20464	−	1.46273i	0.833274	−	0.552860i
$8$	−2.49792	−	3.13230i	−0.883150	−	1.10743i
$9$		0			0
$10$	−8.15382	−	1.22899i	−2.57846	−	0.388641i
$11$	3.68575	−	3.41988i	1.11130	−	1.03113i	0.111996	−	0.993709i	$-0.464275\pi$
$11$	3.68575	−	3.41988i	1.11130	−	1.03113i	0.999300	−	0.0374234i	$-0.0119150\pi$
$12$		0			0
$13$	0.138027	+	0.604735i	0.0382817	+	0.167723i	0.990455	−	0.137835i	$-0.0440142\pi$
$13$	0.138027	+	0.604735i	0.0382817	+	0.167723i	−0.952174	+	0.305558i	$0.901157\pi$
$14$	−6.04884	+	1.78264i	−1.61662	+	0.476430i
$15$		0			0
$16$	0.799079	+	2.03602i	0.199770	+	0.509005i
$17$	0.352700	+	4.70646i	0.0855423	+	1.14148i	0.860493	+	0.509462i	$0.170155\pi$
$17$	0.352700	+	4.70646i	0.0855423	+	1.14148i	−0.774951	+	0.632021i	$0.782225\pi$
$18$		0			0
$19$	−1.52702	+	2.64487i	−0.350322	+	0.606775i	−0.986306	−	0.164927i	$-0.947261\pi$
$19$	−1.52702	+	2.64487i	−0.350322	+	0.606775i	0.635984	+	0.771702i	$0.280594\pi$
$20$	11.4735	+	5.52532i	2.56554	+	1.23550i
$21$		0			0
$22$	−10.7972	+	5.19964i	−2.30196	+	1.10857i
$23$	−0.217678	+	2.90471i	−0.0453891	+	0.605675i	0.927413	+	0.374038i	$0.122027\pi$
$23$	−0.217678	+	2.90471i	−0.0453891	+	0.605675i	−0.972802	+	0.231637i	$0.925592\pi$
$24$		0			0
$25$	6.65947	−	2.05417i	1.33189	−	0.410835i
$26$	0.110483	−	1.47430i	0.0216676	−	0.289133i
$27$		0			0
$28$	9.73797	+	0.122759i	1.84030	+	0.0231992i
$29$	−7.28014	−	3.50593i	−1.35189	−	0.651035i	−0.389076	−	0.921206i	$-0.627206\pi$
$29$	−7.28014	−	3.50593i	−1.35189	−	0.651035i	−0.962813	+	0.270170i	$0.912920\pi$
$30$		0			0
$31$	1.74798	+	3.02759i	0.313946	+	0.543771i	0.979213	−	0.202835i	$-0.0650155\pi$
$31$	1.74798	+	3.02759i	0.313946	+	0.543771i	−0.665267	+	0.746606i	$0.731682\pi$
$32$	0.209212	+	2.79174i	0.0369839	+	0.493515i
$33$		0			0
$34$	2.50316	−	10.9671i	0.429289	−	1.88084i
$35$	6.78782	−	6.14078i	1.14735	−	1.03798i
$36$		0			0
$37$	−3.54005	+	2.41357i	−0.581981	+	0.396788i	−0.818218	−	0.574907i	$-0.805038\pi$
$37$	−3.54005	+	2.41357i	−0.581981	+	0.396788i	0.236237	+	0.971695i	$0.424086\pi$
$38$	5.33602	−	4.95110i	0.865617	−	0.803175i
$39$		0			0
$40$	−10.1605	−	9.42757i	−1.60652	−	1.49063i
$41$	−5.76293	−	7.22648i	−0.900018	−	1.12859i	−0.991150	−	0.132748i	$-0.957620\pi$
$41$	−5.76293	−	7.22648i	−0.900018	−	1.12859i	0.0911316	−	0.995839i	$-0.470952\pi$
$42$		0			0
$43$	4.76320	−	5.97286i	0.726381	−	0.910853i	−0.272299	−	0.962213i	$-0.587784\pi$
$43$	4.76320	−	5.97286i	0.726381	−	0.910853i	0.998680	+	0.0513594i	$0.0163554\pi$
$44$	18.3007	−	2.75838i	2.75893	−	0.415842i
$45$		0			0
$46$	2.53645	−	6.46277i	0.373979	−	0.952884i
$47$	3.44501	+	1.06264i	0.502506	+	0.155002i	0.535637	−	0.844449i	$-0.320072\pi$
$47$	3.44501	+	1.06264i	0.502506	+	0.155002i	−0.0331310	+	0.999451i	$0.510548\pi$
$48$		0			0
$49$	2.72084	−	6.44958i	0.388691	−	0.921368i
$50$	−16.6106			−2.34909
$51$		0			0
$52$	−0.834151	+	2.12538i	−0.115676	+	0.294738i
$53$	4.76028	+	3.24551i	0.653875	+	0.445804i	0.844281	−	0.535901i	$-0.180028\pi$
$53$	4.76028	+	3.24551i	0.653875	+	0.445804i	−0.190406	+	0.981705i	$0.560980\pi$
$54$		0			0
$55$	10.8455	−	13.5999i	1.46241	−	1.83381i
$56$	−10.0887	−	3.25178i	−1.34816	−	0.434538i
$57$		0			0
$58$	14.1180	+	13.0996i	1.85378	+	1.72006i
$59$	−10.0458	−	1.51416i	−1.30785	−	0.197126i	−0.542126	−	0.840297i	$-0.682380\pi$
$59$	−10.0458	−	1.51416i	−1.30785	−	0.197126i	−0.765723	+	0.643171i	$0.777619\pi$
$60$		0			0
$61$	−6.30699	+	4.30003i	−0.807527	+	0.550562i	−0.895240	−	0.445583i	$-0.852996\pi$
$61$	−6.30699	+	4.30003i	−0.807527	+	0.550562i	0.0877137	+	0.996146i	$0.472044\pi$
$62$	−1.85415	−	8.12358i	−0.235478	−	1.03170i
$63$		0			0
$64$	2.45821	−	10.7701i	0.307277	−	1.34627i
$65$	0.784010	+	1.99762i	0.0972444	+	0.247775i
$66$		0			0
$67$	−0.311368	−	0.539305i	−0.0380397	−	0.0658866i	0.846379	−	0.532581i	$-0.178778\pi$
$67$	−0.311368	−	0.539305i	−0.0380397	−	0.0658866i	−0.884418	+	0.466695i	$0.845445\pi$
$68$	−8.68628	+	15.0451i	−1.05337	+	1.82448i
$69$		0			0
$70$	−19.7739	+	9.21737i	−2.36343	+	1.10169i
$71$	9.03366	−	4.35038i	1.07210	−	0.516295i	0.187316	−	0.982300i	$-0.440021\pi$
$71$	9.03366	−	4.35038i	1.07210	−	0.516295i	0.884782	+	0.466005i	$0.154307\pi$
$72$		0			0
$73$	−1.60225	+	0.494230i	−0.187530	+	0.0578452i	−0.387098	−	0.922039i	$-0.626522\pi$
$73$	−1.60225	+	0.494230i	−0.187530	+	0.0578452i	0.199568	+	0.979884i	$0.436046\pi$
$74$	9.75835	−	3.01005i	1.13438	−	0.349911i
$75$		0			0
$76$	−10.1283	+	4.87755i	−1.16180	+	0.559493i
$77$	3.12338	−	12.9308i	0.355942	−	1.47361i
$78$		0			0
$79$	−1.91890	+	3.32364i	−0.215894	+	0.373939i	−0.953549	−	0.301239i	$-0.902600\pi$
$79$	−1.91890	+	3.32364i	−0.215894	+	0.373939i	0.737655	+	0.675178i	$0.235933\pi$
$80$	3.78348	+	6.55319i	0.423006	+	0.732668i
$81$		0			0
$82$	8.04861	+	20.5075i	0.888820	+	2.26468i
$83$	−2.19538	+	9.61859i	−0.240974	+	1.05578i	0.699158	+	0.714967i	$0.253559\pi$
$83$	−2.19538	+	9.61859i	−0.240974	+	1.05578i	−0.940132	+	0.340810i	$0.889299\pi$
$84$		0			0
$85$	3.63338	+	15.9189i	0.394096	+	1.72665i
$86$	−15.0447	+	10.2573i	−1.62231	+	1.10607i
$87$		0			0
$88$	−19.9188	−	3.00228i	−2.12335	−	0.320044i
$89$	2.05518	+	1.90693i	0.217849	+	0.202134i	0.781546	−	0.623847i	$-0.214431\pi$
$89$	2.05518	+	1.90693i	0.217849	+	0.202134i	−0.563698	+	0.825981i	$0.690622\pi$
$90$		0			0
$91$	1.18886	+	1.13132i	0.124627	+	0.118595i
$92$	−6.68502	+	8.38275i	−0.696961	+	0.873962i
$93$		0			0
$94$	−7.09970	−	4.84050i	−0.732278	−	0.499259i
$95$	−3.86014	+	9.83548i	−0.396042	+	1.00910i
$96$		0			0
$97$	−0.516475			−0.0524401			−0.0262200	−	0.999656i	$-0.508347\pi$
$97$	−0.516475			−0.0524401			−0.0262200	+	0.999656i	$0.508347\pi$
$98$	−10.7280	+	12.7779i	−1.08369	+	1.29076i
$99$		0			0
$100$	24.5128	+	7.56120i	2.45128	+	0.756120i
$101$	4.98165	−	12.6930i	0.495692	−	1.26300i	−0.436063	−	0.899916i	$-0.643627\pi$
$101$	4.98165	−	12.6930i	0.495692	−	1.26300i	0.931755	−	0.363087i	$-0.118277\pi$
$102$		0			0
$103$	8.08469	−	1.21857i	0.796609	−	0.120069i	0.261888	−	0.965098i	$-0.415655\pi$
$103$	8.08469	−	1.21857i	0.796609	−	0.120069i	0.534721	+	0.845029i	$0.320417\pi$
$104$	1.54943	−	1.94292i	0.151934	−	0.190519i
$105$		0			0
$106$	−8.56180	−	10.7362i	−0.831595	−	1.04279i
$107$	10.0253	+	9.30214i	0.969185	+	0.899272i	0.994948	−	0.100396i	$-0.0320109\pi$
$107$	10.0253	+	9.30214i	0.969185	+	0.899272i	−0.0257626	+	0.999668i	$0.508201\pi$
$108$		0			0
$109$	−5.94490	+	5.51606i	−0.569419	+	0.528343i	−0.911485	−	0.411332i	$-0.865064\pi$
$109$	−5.94490	+	5.51606i	−0.569419	+	0.528343i	0.342067	+	0.939676i	$0.388873\pi$
$110$	−34.2559	+	23.3553i	−3.26618	+	2.22684i
$111$		0			0
$112$	4.73983	+	3.31984i	0.447872	+	0.313696i
$113$	0.476358	−	2.08706i	0.0448120	−	0.196334i	−0.947567	−	0.319557i	$-0.896466\pi$
$113$	0.476358	−	2.08706i	0.0448120	−	0.196334i	0.992379	+	0.123223i	$0.0393230\pi$
$114$		0			0
$115$	0.753088	+	10.0493i	0.0702258	+	0.937098i
$116$	−14.8715	−	25.7581i	−1.38078	−	2.39158i
$117$		0			0
$118$	21.8162	+	10.5061i	2.00835	+	0.967169i
$119$	7.66185	+	9.86011i	0.702361	+	0.903875i
$120$		0			0
$121$	1.06717	−	14.2404i	0.0970155	−	1.29458i
$122$	17.3856	−	5.36273i	1.57401	−	0.485519i
$123$		0			0
$124$	−0.961647	+	12.8323i	−0.0863584	+	1.15237i
$125$	6.13769	−	2.95575i	0.548971	−	0.264371i
$126$		0			0
$127$	−17.3725	−	8.36616i	−1.54156	−	0.742377i	−0.546116	−	0.837710i	$-0.683894\pi$
$127$	−17.3725	−	8.36616i	−1.54156	−	0.742377i	−0.995445	+	0.0953331i	$0.969608\pi$
$128$	−10.3656	+	17.9538i	−0.916200	+	1.58690i
$129$		0			0
$130$	−0.382232	−	5.10053i	−0.0335240	−	0.447346i
$131$	4.46332	+	11.3724i	0.389962	+	0.993608i	0.982199	+	0.187844i	$0.0601499\pi$
$131$	4.46332	+	11.3724i	0.389962	+	0.993608i	−0.592236	+	0.805764i	$0.701755\pi$
$132$		0			0
$133$	0.502220	+	8.06460i	0.0435480	+	0.699289i
$134$	0.330281	+	1.44706i	0.0285319	+	0.125007i
$135$		0			0
$136$	13.8610	−	12.8611i	1.18857	−	1.10283i
$137$	−16.6731	−	2.51307i	−1.42448	−	0.214706i	−0.608852	−	0.793284i	$-0.708370\pi$
$137$	−16.6731	−	2.51307i	−1.42448	−	0.214706i	−0.815627	+	0.578578i	$0.803608\pi$
$138$		0			0
$139$	−0.718293	−	0.900711i	−0.0609248	−	0.0763973i	0.750435	−	0.660944i	$-0.229844\pi$
$139$	−0.718293	−	0.900711i	−0.0609248	−	0.0763973i	−0.811360	+	0.584547i	$0.801272\pi$
$140$	33.3768	−	4.60125i	2.82086	−	0.388877i
$141$		0			0
$142$	−23.6311	+	3.56182i	−1.98308	+	0.298901i
$143$	2.57685	+	1.75687i	0.215487	+	0.146917i
$144$		0			0
$145$	−26.7131	−	8.23990i	−2.21840	−	0.684287i
$146$	3.99646			0.330750
$147$		0			0
$148$	−15.7709			−1.29636
$149$	−11.8023	−	3.64053i	−0.966883	−	0.298244i	−0.229191	−	0.973382i	$-0.573608\pi$
$149$	−11.8023	−	3.64053i	−0.966883	−	0.298244i	−0.737692	+	0.675138i	$0.764084\pi$
$150$		0			0
$151$	−5.93016	−	4.04312i	−0.482590	−	0.329024i	0.297468	−	0.954732i	$-0.403858\pi$
$151$	−5.93016	−	4.04312i	−0.482590	−	0.329024i	−0.780058	+	0.625708i	$0.784810\pi$
$152$	12.0989	−	1.82362i	0.981351	−	0.147915i
$153$		0			0
$154$	−16.1981	+	27.2567i	−1.30528	+	2.19640i
$155$	7.54095	+	9.45605i	0.605704	+	0.759528i
$156$		0			0
$157$	−11.5101	−	1.73487i	−0.918609	−	0.138458i	−0.327316	−	0.944915i	$-0.606144\pi$
$157$	−11.5101	−	1.73487i	−0.918609	−	0.138458i	−0.591293	+	0.806457i	$0.701382\pi$
$158$	6.70543	−	6.22173i	0.533455	−	0.494974i
$159$		0			0
$160$	2.15523	+	9.44267i	0.170386	+	0.746508i
$161$	3.76892	+	6.72224i	0.297032	+	0.529787i
$162$		0			0
$163$	1.83607	+	4.67824i	0.143812	+	0.366428i	0.984572	−	0.174981i	$-0.0559863\pi$
$163$	1.83607	+	4.67824i	0.143812	+	0.366428i	−0.840759	+	0.541409i	$0.817891\pi$
$164$	−2.54251	−	33.9275i	−0.198537	−	2.64929i
$165$		0			0
$166$	11.7576	−	20.3647i	0.912564	−	1.58061i
$167$	6.66921	+	3.21172i	0.516079	+	0.248530i	0.673747	−	0.738962i	$-0.264684\pi$
$167$	6.66921	+	3.21172i	0.516079	+	0.248530i	−0.157669	+	0.987492i	$0.550398\pi$
$168$		0			0
$169$	11.3659	−	5.47355i	0.874303	−	0.421042i
$170$	2.90834	−	38.8090i	0.223059	−	2.97652i
$171$		0			0
$172$	26.8712	−	8.28867i	2.04891	−	0.632005i
$173$	0.975149	−	13.0125i	0.0741392	−	0.989319i	−0.828799	−	0.559547i	$-0.810975\pi$
$173$	0.975149	−	13.0125i	0.0741392	−	0.989319i	0.902938	−	0.429771i	$-0.141406\pi$
$174$		0			0
$175$	11.6770	−	14.2697i	0.882698	−	1.07869i
$176$	9.90815	+	4.77151i	0.746855	+	0.359666i
$177$		0			0
$178$	−3.34113	−	5.78701i	−0.250429	−	0.433755i
$179$	−0.497769	−	6.64227i	−0.0372050	−	0.496466i	−0.984416	−	0.175855i	$-0.943731\pi$
$179$	−0.497769	−	6.64227i	−0.0372050	−	0.496466i	0.947211	−	0.320611i	$-0.103888\pi$
$180$		0			0
$181$	4.07522	−	17.8547i	0.302909	−	1.32713i	−0.562804	−	0.826590i	$-0.690277\pi$
$181$	4.07522	−	17.8547i	0.302909	−	1.32713i	0.865713	−	0.500541i	$-0.166865\pi$
$182$	−1.91292	−	3.41189i	−0.141795	−	0.252906i
$183$		0			0
$184$	9.64217	−	6.57392i	0.710831	−	0.484636i
$185$	−10.8660	+	10.0822i	−0.798883	+	0.741255i
$186$		0			0
$187$	17.3955	+	16.1406i	1.27208	+	1.18032i
$188$	8.27388	+	10.3751i	0.603435	+	0.756683i
$189$		0			0
$190$	15.7015	−	19.6891i	1.13911	−	1.42840i
$191$	10.7758	−	1.62419i	0.779707	−	0.117522i	0.252884	−	0.967497i	$-0.418621\pi$
$191$	10.7758	−	1.62419i	0.779707	−	0.117522i	0.526824	+	0.849975i	$0.323383\pi$
$192$		0			0
$193$	−5.28915	+	13.4765i	−0.380722	+	0.970063i	0.604165	+	0.796860i	$0.293507\pi$
$193$	−5.28915	+	13.4765i	−0.380722	+	0.970063i	−0.984886	+	0.173203i	$0.944588\pi$
$194$	1.17631	+	0.362843i	0.0844541	+	0.0260506i
$195$		0			0
$196$	21.6482	−	13.9734i	1.54630	−	0.998099i
$197$	−5.99363			−0.427029			−0.213514	−	0.976940i	$-0.568491\pi$
$197$	−5.99363			−0.427029			−0.213514	+	0.976940i	$0.568491\pi$
$198$		0			0
$199$	−5.93001	+	15.1094i	−0.420367	+	1.07108i	0.551212	+	0.834365i	$0.314165\pi$
$199$	−5.93001	+	15.1094i	−0.420367	+	1.07108i	−0.971580	+	0.236713i	$0.923930\pi$
$200$	−23.0691	−	15.7283i	−1.63123	−	1.11216i
$201$		0			0
$202$	−20.2634	+	25.4095i	−1.42573	+	1.78781i
$203$	−21.1783	+	2.91959i	−1.48643	+	0.204915i
$204$		0			0
$205$	−23.4412	−	21.7502i	−1.63720	−	1.51910i
$206$	−19.2696	−	2.90442i	−1.34257	−	0.202361i
$207$		0			0
$208$	−1.12096	+	0.764256i	−0.0777245	+	0.0529917i
$209$	3.41693	+	14.9706i	0.236354	+	1.03554i
$210$		0			0
$211$	1.74529	−	7.64662i	0.120151	−	0.526415i	−0.878650	−	0.477466i	$-0.841555\pi$
$211$	1.74529	−	7.64662i	0.120151	−	0.526415i	0.998801	−	0.0489496i	$-0.0155874\pi$
$212$	7.74782	+	19.7411i	0.532122	+	1.35583i
$213$		0			0
$214$	−16.2983	−	28.2295i	−1.11413	−	1.92973i
$215$	13.2151	−	22.8892i	0.901261	−	1.56103i
$216$		0			0
$217$	8.28220	+	4.11791i	0.562233	+	0.279542i
$218$	17.4152	−	8.38672i	1.17951	−	0.568020i
$219$		0			0
$220$	61.1842	−	18.8728i	4.12504	−	1.27241i
$221$	−2.79748	+	0.862907i	−0.188179	+	0.0580454i
$222$		0			0
$223$	−6.23886	+	3.00447i	−0.417785	+	0.201195i	−0.630953	−	0.775821i	$-0.717336\pi$
$223$	−6.23886	+	3.00447i	−0.417785	+	0.201195i	0.213168	+	0.977015i	$0.431622\pi$
$224$	4.54481	+	5.84876i	0.303663	+	0.390787i
$225$		0			0
$226$	−2.55118	+	4.41878i	−0.169702	+	0.293933i
$227$	6.80293	+	11.7830i	0.451526	+	0.782066i	0.998481	−	0.0550959i	$-0.0175465\pi$
$227$	6.80293	+	11.7830i	0.451526	+	0.782066i	−0.546955	+	0.837162i	$0.684213\pi$
$228$		0			0
$229$	6.68252	+	17.0268i	0.441593	+	1.12516i	0.962436	+	0.271509i	$0.0875227\pi$
$229$	6.68252	+	17.0268i	0.441593	+	1.12516i	−0.520842	+	0.853653i	$0.674382\pi$
$230$	5.34477	−	23.4170i	0.352424	−	1.54407i
$231$		0			0
$232$	7.20362	+	31.5611i	0.472941	+	2.07209i
$233$	−9.95890	+	6.78986i	−0.652429	+	0.444819i	−0.843770	−	0.536705i	$-0.819669\pi$
$233$	−9.95890	+	6.78986i	−0.652429	+	0.444819i	0.191341	+	0.981524i	$0.438716\pi$
$234$		0			0
$235$	12.3333	+	1.85894i	0.804534	+	0.121264i
$236$	−27.4126	−	25.4352i	−1.78441	−	1.65569i
$237$		0			0
$238$	−10.5233	−	27.8399i	−0.682126	−	1.80459i
$239$	−3.07736	+	3.85888i	−0.199058	+	0.249610i	−0.871335	−	0.490689i	$-0.836745\pi$
$239$	−3.07736	+	3.85888i	−0.199058	+	0.249610i	0.672277	+	0.740300i	$0.265316\pi$
$240$		0			0
$241$	5.49385	+	3.74565i	0.353890	+	0.241278i	0.727196	−	0.686430i	$-0.240823\pi$
$241$	5.49385	+	3.74565i	0.353890	+	0.241278i	−0.373305	+	0.927709i	$0.621776\pi$
$242$	−12.4350	+	31.6838i	−0.799351	+	2.03671i
$243$		0			0
$244$	−28.0977			−1.79877
$245$	5.98236	−	23.4669i	0.382199	−	1.49925i
$246$		0			0
$247$	−1.81022	−	0.558378i	−0.115181	−	0.0355287i
$248$	5.11699	−	13.0379i	0.324929	−	0.827906i
$249$		0			0
$250$	−16.0556	+	2.41999i	−1.01544	+	0.153053i
$251$	−7.40198	+	9.28179i	−0.467209	+	0.585862i	−0.958485	−	0.285142i	$-0.907959\pi$
$251$	−7.40198	+	9.28179i	−0.467209	+	0.585862i	0.491276	+	0.871004i	$0.336531\pi$
$252$		0			0
$253$	9.13146	+	11.4505i	0.574090	+	0.719886i
$254$	33.6896	+	31.2594i	2.11387	+	1.96139i
$255$		0			0
$256$	20.0255	−	18.5809i	1.25159	−	1.16131i
$257$	−6.20302	+	4.22915i	−0.386934	+	0.263807i	−0.741126	−	0.671366i	$-0.765708\pi$
$257$	−6.20302	+	4.22915i	−0.386934	+	0.263807i	0.354193	+	0.935172i	$0.384756\pi$
$258$		0			0
$259$	−4.27413	+	10.4992i	−0.265581	+	0.652387i
$260$	−1.75771	+	7.70104i	−0.109009	+	0.477598i
$261$		0			0
$262$	−2.17603	−	29.0370i	−0.134435	−	1.79391i
$263$	−9.80317	−	16.9796i	−0.604489	−	1.04701i	−0.992132	−	0.125197i	$-0.960044\pi$
$263$	−9.80317	−	16.9796i	−0.604489	−	1.04701i	0.387642	−	0.921810i	$-0.373290\pi$
$264$		0			0
$265$	17.9584	+	8.64830i	1.10318	+	0.531261i
$266$	4.52185	−	18.7205i	0.277252	−	1.14783i
$267$		0			0
$268$	0.171298	−	2.28582i	0.0104637	−	0.139629i
$269$	−4.69460	+	1.44809i	−0.286235	+	0.0882917i	−0.434548	−	0.900649i	$-0.643092\pi$
$269$	−4.69460	+	1.44809i	−0.286235	+	0.0882917i	0.148313	+	0.988940i	$0.452616\pi$
$270$		0			0
$271$	0.278373	−	3.71463i	0.0169099	−	0.225648i	−0.982346	−	0.187074i	$-0.940100\pi$
$271$	0.278373	−	3.71463i	0.0169099	−	0.225648i	0.999256	−	0.0385735i	$-0.0122814\pi$
$272$	−9.30060	+	4.47893i	−0.563932	+	0.271575i
$273$		0			0
$274$	36.2087	+	17.4372i	2.18745	+	1.05342i
$275$	17.5201	−	30.3457i	1.05650	−	1.82992i
$276$		0			0
$277$	1.92013	+	25.6224i	0.115370	+	1.53950i	0.691641	+	0.722241i	$0.256888\pi$
$277$	1.92013	+	25.6224i	0.115370	+	1.53950i	−0.576272	+	0.817258i	$0.695493\pi$
$278$	1.00318	+	2.55606i	0.0601668	+	0.153302i
$279$		0			0
$280$	−36.1902	−	5.92227i	−2.16278	−	0.353923i
$281$	−4.72320	−	20.6937i	−0.281762	−	1.23448i	−0.895532	−	0.444996i	$-0.853205\pi$
$281$	−4.72320	−	20.6937i	−0.281762	−	1.23448i	0.613770	−	0.789485i	$-0.289652\pi$
$282$		0			0
$283$	6.41989	−	5.95679i	0.381623	−	0.354094i	−0.465915	−	0.884830i	$-0.654275\pi$
$283$	6.41989	−	5.95679i	0.381623	−	0.354094i	0.847538	+	0.530735i	$0.178084\pi$
$284$	36.4947	+	5.50069i	2.16556	+	0.326406i
$285$		0			0
$286$	−4.63470	−	5.81173i	−0.274056	−	0.343655i
$287$	−23.2756	−	7.50215i	−1.37391	−	0.442838i
$288$		0			0
$289$	−5.21620	+	0.786216i	−0.306835	+	0.0462480i
$290$	55.0522	+	37.5340i	3.23278	+	2.20407i
$291$		0			0
$292$	−5.89773	−	1.81921i	−0.345139	−	0.106461i
$293$	−15.1133			−0.882929			−0.441464	−	0.897279i	$-0.645541\pi$
$293$	−15.1133			−0.882929			−0.441464	+	0.897279i	$0.645541\pi$
$294$		0			0
$295$	−35.1473			−2.04635
$296$	16.4028	+	5.05959i	0.953393	+	0.294083i
$297$		0			0
$298$	24.3230	+	16.5831i	1.40899	+	0.960636i
$299$	−1.78663	+	0.269291i	−0.103323	+	0.0155735i
$300$		0			0
$301$	1.76443	−	20.1353i	0.101700	−	1.16058i
$302$	10.6659	+	13.3747i	0.613756	+	0.769625i
$303$		0			0
$304$	−6.60522	−	0.995577i	−0.378836	−	0.0571003i
$305$	−19.3589	+	17.9625i	−1.10849	+	1.02853i
$306$		0			0
$307$	−0.0921804	−	0.403869i	−0.00526101	−	0.0230500i	0.972229	−	0.234030i	$-0.0751915\pi$
$307$	−0.0921804	−	0.403869i	−0.00526101	−	0.0230500i	−0.977490	+	0.210980i	$0.932334\pi$
$308$	36.3115	−	32.8502i	2.06904	−	1.87181i
$309$		0			0
$310$	−10.5318	−	26.8347i	−0.598167	−	1.52411i
$311$	2.38155	+	31.7795i	0.135045	+	1.80205i	0.494803	+	0.869005i	$0.335240\pi$
$311$	2.38155	+	31.7795i	0.135045	+	1.80205i	−0.359758	+	0.933046i	$0.617141\pi$
$312$		0			0
$313$	3.10650	−	5.38062i	0.175590	−	0.304130i	−0.764775	−	0.644297i	$-0.777150\pi$
$313$	3.10650	−	5.38062i	0.175590	−	0.304130i	0.940365	+	0.340167i	$0.110483\pi$
$314$	24.9964	+	12.0376i	1.41063	+	0.679322i
$315$		0			0
$316$	−12.7276	+	6.12929i	−0.715984	+	0.344800i
$317$	−0.796854	+	10.6333i	−0.0447558	+	0.597224i	0.929066	+	0.369913i	$0.120613\pi$
$317$	−0.796854	+	10.6333i	−0.0447558	+	0.597224i	−0.973822	+	0.227311i	$0.927007\pi$
$318$		0			0
$319$	−38.8227	+	11.9752i	−2.17365	+	0.670483i
$320$	2.85611	−	38.1121i	0.159661	−	2.13053i
$321$		0			0
$322$	−3.86135	−	17.9582i	−0.215184	−	1.00077i
$323$	−12.9866	−	6.25400i	−0.722591	−	0.347982i
$324$		0			0
$325$	2.16142	+	3.74368i	0.119894	+	0.207662i
$326$	−0.895150	−	11.9449i	−0.0495778	−	0.661569i
$327$		0			0
$328$	−8.24014	+	36.1024i	−0.454986	+	1.99342i
$329$	9.14934	−	2.69637i	0.504420	−	0.148656i
$330$		0			0
$331$	1.06844	−	0.728449i	0.0587267	−	0.0400392i	−0.533601	−	0.845736i	$-0.679162\pi$
$331$	1.06844	−	0.728449i	0.0587267	−	0.0400392i	0.592328	+	0.805697i	$0.298209\pi$
$332$	−26.6212	+	24.7009i	−1.46103	+	1.35564i
$333$		0			0
$334$	−12.9332	−	12.0003i	−0.707676	−	0.656627i
$335$	−1.34327	−	1.68441i	−0.0733908	−	0.0920291i
$336$		0			0
$337$	−19.3177	+	24.2236i	−1.05230	+	1.31954i	−0.106674	+	0.994294i	$0.534020\pi$
$337$	−19.3177	+	24.2236i	−1.05230	+	1.31954i	−0.945628	+	0.325251i	$0.894551\pi$
$338$	−29.7321	+	4.48140i	−1.61722	+	0.243756i
$339$		0			0
$340$	−21.9580	+	55.9481i	−1.19084	+	3.03421i
$341$	16.7966	+	5.18107i	0.909587	+	0.280570i
$342$		0			0
$343$	−3.43555	−	18.1988i	−0.185502	−	0.982644i
$344$	−30.6069			−1.65021
$345$		0			0
$346$	−11.3627	+	28.9517i	−0.610863	+	1.55645i
$347$	−20.6021	−	14.0463i	−1.10598	−	0.754045i	−0.134441	−	0.990922i	$-0.542924\pi$
$347$	−20.6021	−	14.0463i	−1.10598	−	0.754045i	−0.971540	+	0.236877i	$0.923876\pi$
$348$		0			0
$349$	−6.63965	+	8.32586i	−0.355413	+	0.445673i	−0.927109	−	0.374792i	$-0.877714\pi$
$349$	−6.63965	+	8.32586i	−0.355413	+	0.445673i	0.571696	+	0.820465i	$0.306286\pi$
$350$	−36.6202	+	24.2968i	−1.95743	+	1.29872i
$351$		0			0
$352$	10.3185	+	9.57420i	0.549980	+	0.510306i
$353$	14.1683	+	2.13553i	0.754104	+	0.113663i	0.514834	−	0.857290i	$-0.327854\pi$
$353$	14.1683	+	2.13553i	0.754104	+	0.113663i	0.239271	+	0.970953i	$0.423092\pi$
$354$		0			0
$355$	28.6609	−	19.5407i	1.52116	−	1.03711i
$356$	2.29636	+	10.0610i	0.121707	+	0.533232i
$357$		0			0
$358$	−3.53274	+	15.4779i	−0.186711	+	0.818035i
$359$	−8.07825	−	20.5831i	−0.426354	−	1.08633i	−0.969151	−	0.246468i	$-0.920730\pi$
$359$	−8.07825	−	20.5831i	−0.426354	−	1.08633i	0.542797	−	0.839864i	$-0.317365\pi$
$360$		0			0
$361$	4.83643	+	8.37695i	0.254549	+	0.440892i
$362$	−21.8252	+	37.8024i	−1.14711	+	1.98685i
$363$		0			0
$364$	1.26986	+	5.90583i	0.0665590	+	0.309550i
$365$	−5.22646	+	2.51693i	−0.273565	+	0.131742i
$366$		0			0
$367$	22.8827	−	7.05839i	1.19447	−	0.368445i	0.367142	−	0.930165i	$-0.380336\pi$
$367$	22.8827	−	7.05839i	1.19447	−	0.368445i	0.827327	+	0.561720i	$0.189860\pi$
$368$	−6.08800	+	1.87790i	−0.317359	+	0.0978923i
$369$		0			0
$370$	31.8312	−	15.3291i	1.65482	−	0.796921i
$371$	15.2420	+	0.192144i	0.791325	+	0.00997560i
$372$		0			0
$373$	−2.47333	+	4.28394i	−0.128064	+	0.221814i	−0.922927	−	0.384976i	$-0.874210\pi$
$373$	−2.47333	+	4.28394i	−0.128064	+	0.221814i	0.794862	+	0.606790i	$0.207543\pi$
$374$	−28.2800	−	48.9825i	−1.46233	−	2.53282i
$375$		0			0
$376$	−5.27685	−	13.4452i	−0.272133	−	0.693382i
$377$	1.11530	−	4.88647i	0.0574411	−	0.251666i
$378$		0			0
$379$	1.64659	+	7.21416i	0.0845794	+	0.370567i	0.999449	−	0.0331821i	$-0.0105641\pi$
$379$	1.64659	+	7.21416i	0.0845794	+	0.370567i	−0.914870	+	0.403749i	$0.867707\pi$
$380$	−32.1339	+	21.9085i	−1.64844	+	1.12388i
$381$		0			0
$382$	−25.6837	−	3.87119i	−1.31409	−	0.198067i
$383$	16.3999	+	15.2169i	0.837995	+	0.777545i	0.977111	−	0.212731i	$-0.0682357\pi$
$383$	16.3999	+	15.2169i	0.837995	+	0.777545i	−0.139116	+	0.990276i	$0.544426\pi$
$384$		0			0
$385$	4.01750	−	45.8469i	0.204751	−	2.33657i
$386$	21.5142	−	26.9780i	1.09504	−	1.37314i
$387$		0			0
$388$	−1.57076	−	1.07092i	−0.0797430	−	0.0543679i
$389$	−5.64656	+	14.3872i	−0.286292	+	0.729460i	0.713299	+	0.700860i	$0.247200\pi$
$389$	−5.64656	+	14.3872i	−0.286292	+	0.729460i	−0.999591	+	0.0286002i	$0.990895\pi$
$390$		0			0
$391$	−13.7477			−0.695250
$392$	−26.9984	+	7.58809i	−1.36363	+	0.383256i
$393$		0			0
$394$	13.6509	+	4.21076i	0.687724	+	0.212135i
$395$	−4.85079	+	12.3596i	−0.244069	+	0.621879i
$396$		0			0
$397$	28.1620	−	4.24474i	1.41341	−	0.213037i	0.602459	−	0.798150i	$-0.294188\pi$
$397$	28.1620	−	4.24474i	1.41341	−	0.213037i	0.810952	+	0.585112i	$0.198950\pi$
$398$	24.1210	−	30.2467i	1.20907	−	1.51613i
$399$		0			0
$400$	9.50378	+	11.9174i	0.475189	+	0.595868i
$401$	−28.5943	−	26.5316i	−1.42793	−	1.32493i	−0.868165	−	0.496275i	$-0.834701\pi$
$401$	−28.5943	−	26.5316i	−1.42793	−	1.32493i	−0.559766	−	0.828651i	$-0.689109\pi$
$402$		0			0
$403$	−1.58962	+	1.47495i	−0.0791846	+	0.0734726i
$404$	41.4700	−	28.2738i	2.06321	−	1.40667i
$405$		0			0
$406$	50.2862	+	8.22899i	2.49566	+	0.408398i
$407$	−4.79365	+	21.0024i	−0.237612	+	1.04105i
$408$		0			0
$409$	−0.0148165	−	0.197712i	−0.000732627	−	0.00977623i	0.996826	−	0.0796173i	$-0.0253698\pi$
$409$	−0.0148165	−	0.197712i	−0.000732627	−	0.00977623i	−0.997558	+	0.0698411i	$0.977751\pi$
$410$	38.1086	+	66.0060i	1.88205	+	3.25980i
$411$		0			0
$412$	27.1147	+	13.0578i	1.33585	+	0.643310i
$413$	−24.3621	+	11.3561i	−1.19878	+	0.558797i
$414$		0			0
$415$	−2.55073	+	34.0372i	−0.125211	+	1.67082i
$416$	−1.65939	+	0.511854i	−0.0813582	+	0.0250957i
$417$		0			0
$418$	2.73508	−	36.4971i	0.133777	−	1.78513i
$419$	17.5801	−	8.46611i	0.858842	−	0.413597i	0.0479902	−	0.998848i	$-0.484718\pi$
$419$	17.5801	−	8.46611i	0.858842	−	0.413597i	0.810852	+	0.585251i	$0.199004\pi$
$420$		0			0
$421$	−25.6710	−	12.3625i	−1.25113	−	0.602512i	−0.313315	−	0.949649i	$-0.601439\pi$
$421$	−25.6710	−	12.3625i	−1.25113	−	0.602512i	−0.937814	+	0.347138i	$0.887154\pi$
$422$	−9.34708	+	16.1896i	−0.455009	+	0.788098i
$423$		0			0
$424$	−1.72493	−	23.0176i	−0.0837702	−	1.11784i
$425$	12.0167	+	30.6180i	0.582894	+	1.48519i
$426$		0			0
$427$	−7.61482	+	18.7054i	−0.368507	+	0.905219i
$428$	11.2018	+	49.0784i	0.541460	+	2.37229i
$429$		0			0
$430$	−46.1789	+	42.8477i	−2.22694	+	2.06630i
$431$	37.9493	+	5.71994i	1.82795	+	0.275520i	0.970861	−	0.239643i	$-0.0770304\pi$
$431$	37.9493	+	5.71994i	1.82795	+	0.275520i	0.857092	+	0.515163i	$0.172268\pi$
$432$		0			0
$433$	9.69904	+	12.1622i	0.466106	+	0.584479i	0.958213	−	0.286056i	$-0.0923444\pi$
$433$	9.69904	+	12.1622i	0.466106	+	0.584479i	−0.492107	+	0.870535i	$0.663773\pi$
$434$	−15.9703	−	15.1974i	−0.766601	−	0.729498i
$435$		0			0
$436$	−29.5179	+	4.44911i	−1.41365	+	0.213074i
$437$	−7.35020	−	5.01128i	−0.351608	−	0.239722i
$438$		0			0
$439$	32.5101	+	10.0280i	1.55162	+	0.478612i	0.947896	−	0.318580i	$-0.103206\pi$
$439$	32.5101	+	10.0280i	1.55162	+	0.478612i	0.603726	+	0.797192i	$0.293682\pi$
$440$	−69.6902			−3.32235
$441$		0			0
$442$	6.97768			0.331894
$443$	−10.6159	−	3.27457i	−0.504376	−	0.155580i	0.0321169	−	0.999484i	$-0.489775\pi$
$443$	−10.6159	−	3.27457i	−0.504376	−	0.155580i	−0.536493	+	0.843905i	$0.680251\pi$
$444$		0			0
$445$	8.01404	+	5.46388i	0.379902	+	0.259013i
$446$	16.3202	−	2.45988i	0.772784	−	0.116478i
$447$		0			0
$448$	−10.3343	−	27.3399i	−0.488252	−	1.29169i
$449$	15.7766	+	19.7833i	0.744546	+	0.933631i	0.999444	−	0.0333369i	$-0.0106134\pi$
$449$	15.7766	+	19.7833i	0.744546	+	0.933631i	−0.254898	+	0.966968i	$0.582042\pi$
$450$		0			0
$451$	−45.9544	−	6.92651i	−2.16391	−	0.326157i
$452$	5.77632	−	5.35964i	0.271695	−	0.252096i
$453$		0			0
$454$	−7.21614	−	31.6160i	−0.338670	−	1.48381i
$455$	4.65044	+	3.25724i	0.218016	+	0.152702i
$456$		0			0
$457$	−10.5185	−	26.8008i	−0.492036	−	1.25369i	−0.934199	−	0.356752i	$-0.883884\pi$
$457$	−10.5185	−	26.8008i	−0.492036	−	1.25369i	0.442163	−	0.896935i	$-0.354211\pi$
$458$	−3.25796	−	43.4745i	−0.152235	−	2.03143i
$459$		0			0
$460$	−18.5470	+	32.1244i	−0.864759	+	1.49781i
$461$	6.76334	+	3.25705i	0.315000	+	0.151696i	0.584703	−	0.811248i	$-0.301211\pi$
$461$	6.76334	+	3.25705i	0.315000	+	0.151696i	−0.269703	+	0.962944i	$0.586925\pi$
$462$		0			0
$463$	25.5039	−	12.2820i	1.18527	−	0.570794i	0.265824	−	0.964021i	$-0.414356\pi$
$463$	25.5039	−	12.2820i	1.18527	−	0.570794i	0.919441	+	0.393228i	$0.128642\pi$
$464$	1.32074	−	17.6240i	0.0613138	−	0.818175i
$465$		0			0
$466$	27.4523	−	8.46790i	1.27170	−	0.392268i
$467$	0.336549	−	4.49094i	0.0155736	−	0.207816i	−0.983989	−	0.178231i	$-0.942962\pi$
$467$	0.336549	−	4.49094i	0.0155736	−	0.207816i	0.999562	−	0.0295847i	$-0.00941846\pi$
$468$		0			0
$469$	−1.47531	−	0.733524i	−0.0681236	−	0.0338710i
$470$	−26.7840	−	12.8985i	−1.23545	−	0.594962i
$471$		0			0
$472$	20.3508	+	35.2486i	0.936721	+	1.62245i
$473$	−2.87049	−	38.3041i	−0.131985	−	1.76122i
$474$		0			0
$475$	−4.73610	+	20.7502i	−0.217307	+	0.952085i
$476$	2.85682	+	45.8746i	0.130942	+	2.10266i
$477$		0			0
$478$	9.71992	−	6.62693i	0.444579	−	0.303109i
$479$	−12.1612	+	11.2840i	−0.555661	+	0.515578i	−0.907259	−	0.420573i	$-0.861829\pi$
$479$	−12.1612	+	11.2840i	−0.555661	+	0.515578i	0.351598	+	0.936151i	$0.385639\pi$
$480$		0			0
$481$	−1.94819	−	1.80766i	−0.0888298	−	0.0824220i
$482$	−9.88119	−	12.3906i	−0.450076	−	0.564378i
$483$		0			0
$484$	32.7734	−	41.0965i	1.48970	−	1.86802i
$485$	−1.76686	+	0.266311i	−0.0802289	+	0.0120926i
$486$		0			0
$487$	11.4322	−	29.1289i	0.518044	−	1.31995i	−0.397450	−	0.917624i	$-0.630105\pi$
$487$	11.4322	−	29.1289i	0.518044	−	1.31995i	0.915494	−	0.402331i	$-0.131800\pi$
$488$	29.2233	+	9.01421i	1.32288	+	0.408054i
$489$		0			0
$490$	−30.1117	+	49.2448i	−1.36031	+	2.22465i
$491$	5.08998			0.229708			0.114854	−	0.993382i	$-0.463360\pi$
$491$	5.08998			0.229708			0.114854	+	0.993382i	$0.463360\pi$
$492$		0			0
$493$	13.9328	−	35.5002i	0.627502	−	1.59885i
$494$	3.73062	+	2.54349i	0.167848	+	0.114437i
$495$		0			0
$496$	−4.76746	+	5.97820i	−0.214065	+	0.268429i
$497$	13.5525	−	22.8048i	0.607912	−	1.02294i
$498$		0			0
$499$	−11.2650	−	10.4524i	−0.504289	−	0.467912i	0.386525	−	0.922279i	$-0.373675\pi$
$499$	−11.2650	−	10.4524i	−0.504289	−	0.467912i	−0.890815	+	0.454367i	$0.849866\pi$
$500$	24.7954	+	3.73730i	1.10888	+	0.167137i
$501$		0			0
$502$	23.3794	−	15.9398i	1.04347	−	0.711427i
$503$	−5.35978	−	23.4827i	−0.238981	−	1.04704i	−0.941932	−	0.335804i	$-0.890992\pi$
$503$	−5.35978	−	23.4827i	−0.238981	−	1.04704i	0.702951	−	0.711238i	$-0.251865\pi$
$504$		0			0
$505$	10.4973	−	45.9915i	0.467122	−	2.04659i
$506$	−12.7532	−	32.4945i	−0.566947	−	1.44456i
$507$		0			0
$508$	−35.4876	−	61.4663i	−1.57451	−	2.72713i
$509$	−2.34253	+	4.05739i	−0.103831	+	0.179840i	−0.913260	−	0.407377i	$-0.866443\pi$
$509$	−2.34253	+	4.05739i	−0.103831	+	0.179840i	0.809429	+	0.587218i	$0.199777\pi$
$510$		0			0
$511$	−2.80946	+	3.43326i	−0.124283	+	0.151879i
$512$	−21.3068	+	10.2608i	−0.941638	+	0.453469i
$513$		0			0
$514$	17.0990	−	5.27433i	0.754203	−	0.232641i
$515$	27.0294	−	8.33745i	1.19106	−	0.367392i
$516$		0			0
$517$	16.3315	−	7.86486i	0.718261	−	0.345896i
$518$	17.1107	−	20.9099i	0.751801	−	0.918729i
$519$		0			0
$520$	4.29876	−	7.44567i	0.188513	−	0.326514i
$521$	7.74762	+	13.4193i	0.339429	+	0.587909i	0.984326	−	0.176361i	$-0.0564327\pi$
$521$	7.74762	+	13.4193i	0.339429	+	0.587909i	−0.644896	+	0.764270i	$0.723099\pi$
$522$		0			0
$523$	−13.6757	−	34.8452i	−0.597998	−	1.52367i	−0.833910	−	0.551900i	$-0.813903\pi$
$523$	−13.6757	−	34.8452i	−0.597998	−	1.52367i	0.235912	−	0.971774i	$-0.424192\pi$
$524$	−10.0066	+	43.8416i	−0.437138	+	1.91523i
$525$		0			0
$526$	10.3986	+	45.5594i	0.453402	+	1.98648i
$527$	−13.6327	+	9.29462i	−0.593850	+	0.404880i
$528$		0			0
$529$	14.3531	+	2.16339i	0.624049	+	0.0940602i
$530$	−34.8258	−	32.3136i	−1.51274	−	1.40361i
$531$		0			0
$532$	−15.1947	+	25.5682i	−0.658775	+	1.10852i
$533$	3.57467	−	4.48249i	0.154836	−	0.194158i
$534$		0			0
$535$	39.0931	+	26.6532i	1.69014	+	1.15232i
$536$	−0.911491	+	2.32244i	−0.0393704	+	0.100314i
$537$		0			0
$538$	11.7096			0.504838
$539$	−12.0284	−	33.0765i	−0.518102	−	1.42470i
$540$		0			0
$541$	−16.7939	−	5.18023i	−0.722026	−	0.222715i	−0.0881026	−	0.996111i	$-0.528080\pi$
$541$	−16.7939	−	5.18023i	−0.722026	−	0.222715i	−0.633923	+	0.773396i	$0.718557\pi$
$542$	−3.24368	+	8.26477i	−0.139328	+	0.355002i
$543$		0			0
$544$	−13.0654	+	1.96930i	−0.560176	+	0.0844329i
$545$	−17.4932	+	21.9358i	−0.749328	+	0.939627i
$546$		0			0
$547$	−2.81646	−	3.53173i	−0.120423	−	0.151006i	0.717966	−	0.696078i	$-0.245073\pi$
$547$	−2.81646	−	3.53173i	−0.120423	−	0.151006i	−0.838389	+	0.545073i	$0.816502\pi$
$548$	−45.4970	−	42.2151i	−1.94354	−	1.80334i
$549$		0			0
$550$	−61.2224	+	56.8061i	−2.61053	+	2.42222i
$551$	20.3897	−	13.9014i	0.868628	−	0.592221i
$552$		0			0
$553$	0.631107	+	10.1343i	0.0268374	+	0.430952i
$554$	13.6275	−	59.7058i	0.578975	−	2.53666i
$555$		0			0
$556$	−0.316900	−	4.22873i	−0.0134395	−	0.179338i
$557$	13.6181	+	23.5872i	0.577017	+	0.999422i	0.995819	+	0.0913448i	$0.0291165\pi$
$557$	13.6181	+	23.5872i	0.577017	+	0.999422i	−0.418803	+	0.908077i	$0.637550\pi$
$558$		0			0
$559$	4.26945	+	2.05606i	0.180578	+	0.0869620i
$560$	17.9267	+	8.91317i	0.757543	+	0.376650i
$561$		0			0
$562$	−3.78067	+	50.4496i	−0.159478	+	2.12809i
$563$	31.3421	−	9.66776i	1.32091	−	0.407448i	0.447437	−	0.894315i	$-0.352337\pi$
$563$	31.3421	−	9.66776i	1.32091	−	0.407448i	0.873476	+	0.486868i	$0.161861\pi$
$564$		0			0
$565$	0.553463	−	7.38545i	0.0232844	−	0.310708i
$566$	−18.8066	+	9.05680i	−0.790502	+	0.380686i
$567$		0			0
$568$	−36.1921	−	17.4292i	−1.51859	−	0.731312i
$569$	−8.07118	+	13.9797i	−0.338362	+	0.586059i	−0.984125	−	0.177478i	$-0.943206\pi$
$569$	−8.07118	+	13.9797i	−0.338362	+	0.586059i	0.645763	+	0.763538i	$0.276539\pi$
$570$		0			0
$571$	−0.673269	−	8.98415i	−0.0281754	−	0.375975i	−0.993412	−	0.114597i	$-0.963442\pi$
$571$	−0.673269	−	8.98415i	−0.0281754	−	0.375975i	0.965237	−	0.261378i	$-0.0841768\pi$
$572$	4.19407	+	10.6863i	0.175363	+	0.446818i
$573$		0			0
$574$	47.7412	+	33.4387i	1.99268	+	1.39570i
$575$	4.51717	+	19.7910i	0.188379	+	0.825342i
$576$		0			0
$577$	−17.8959	+	16.6049i	−0.745015	+	0.691273i	−0.958315	−	0.285714i	$-0.907769\pi$
$577$	−17.8959	+	16.6049i	−0.745015	+	0.691273i	0.213300	+	0.976987i	$0.431579\pi$
$578$	12.4326	+	1.87392i	0.517129	+	0.0779447i
$579$		0			0
$580$	−64.1570	−	80.4503i	−2.66397	−	3.34052i
$581$	9.22940	+	24.4167i	0.382900	+	1.01298i
$582$		0			0
$583$	28.6445	−	4.31746i	1.18633	−	0.178811i
$584$	5.55038	+	3.78419i	0.229676	+	0.156591i
$585$		0			0
$586$	34.4217	+	10.6177i	1.42195	+	0.438612i
$587$	19.1087			0.788702			0.394351	−	0.918960i	$-0.370969\pi$
$587$	19.1087			0.788702			0.394351	+	0.918960i	$0.370969\pi$
$588$		0			0
$589$	−10.6768			−0.439929
$590$	80.0505	+	24.6923i	3.29563	+	1.01657i
$591$		0			0
$592$	−7.74285	−	5.27899i	−0.318229	−	0.216965i
$593$	−32.8040	+	4.94440i	−1.34710	+	0.203042i	−0.782668	−	0.622439i	$-0.786142\pi$
$593$	−32.8040	+	4.94440i	−1.34710	+	0.203042i	−0.564430	+	0.825481i	$0.690904\pi$
$594$		0			0
$595$	31.2954	+	29.7807i	1.28298	+	1.22089i
$596$	−28.3456	−	35.5443i	−1.16108	−	1.45595i
$597$		0			0
$598$	4.25836	+	0.641845i	0.174137	+	0.0262470i
$599$	20.7679	−	19.2698i	0.848552	−	0.787342i	−0.130393	−	0.991462i	$-0.541624\pi$
$599$	20.7679	−	19.2698i	0.848552	−	0.787342i	0.978946	+	0.204121i	$0.0654335\pi$
$600$		0			0
$601$	0.0527713	+	0.231206i	0.00215259	+	0.00943110i	0.975993	−	0.217803i	$-0.0698890\pi$
$601$	0.0527713	+	0.231206i	0.00215259	+	0.00943110i	−0.973840	+	0.227234i	$0.927032\pi$
$602$	−18.1644	+	44.6200i	−0.740326	+	1.81857i
$603$		0			0
$604$	−9.65191	−	24.5927i	−0.392731	−	1.00066i
$605$	−3.69202	−	49.2666i	−0.150102	−	2.00297i
$606$		0			0
$607$	−16.3417	+	28.3047i	−0.663290	+	1.14885i	0.316456	+	0.948607i	$0.397507\pi$
$607$	−16.3417	+	28.3047i	−0.663290	+	1.14885i	−0.979746	+	0.200244i	$0.935826\pi$
$608$	−7.70328	−	3.70970i	−0.312409	−	0.150448i
$609$		0			0
$610$	56.7107	−	27.3104i	2.29615	−	1.10577i
$611$	−0.167115	+	2.22999i	−0.00676073	+	0.0902157i
$612$		0			0
$613$	−18.6374	+	5.74887i	−0.752756	+	0.232195i	−0.647306	−	0.762230i	$-0.724104\pi$
$613$	−18.6374	+	5.74887i	−0.752756	+	0.232195i	−0.105450	+	0.994425i	$0.533628\pi$
$614$	−0.0737856	+	0.984601i	−0.00297775	+	0.0397352i
$615$		0			0
$616$	−48.3052	+	22.5169i	−1.94627	+	0.907233i
$617$	15.3858	+	7.40939i	0.619407	+	0.298291i	0.717148	−	0.696921i	$-0.245447\pi$
$617$	15.3858	+	7.40939i	0.619407	+	0.298291i	−0.0977407	+	0.995212i	$0.531162\pi$
$618$		0			0
$619$	−3.94511	−	6.83314i	−0.158568	−	0.274647i	0.775785	−	0.630998i	$-0.217354\pi$
$619$	−3.94511	−	6.83314i	−0.158568	−	0.274647i	−0.934352	+	0.356351i	$0.884021\pi$
$620$	3.32695	+	44.3950i	0.133613	+	1.78295i
$621$		0			0
$622$	16.9022	−	74.0533i	0.677716	−	2.96927i
$623$	7.32025	+	1.19791i	0.293280	+	0.0479931i
$624$		0			0
$625$	−9.31773	+	6.35272i	−0.372709	+	0.254109i
$626$	−10.8554	+	10.0723i	−0.433868	+	0.402570i
$627$		0			0
$628$	−31.4085	−	29.1428i	−1.25333	−	1.16292i
$629$	−12.6079	−	15.8098i	−0.502711	−	0.630379i
$630$		0			0
$631$	14.8564	−	18.6293i	0.591424	−	0.741622i	−0.392590	−	0.919714i	$-0.628421\pi$
$631$	14.8564	−	18.6293i	0.591424	−	0.741622i	0.984014	+	0.178091i	$0.0569922\pi$
$632$	15.2039	−	2.29162i	0.604779	−	0.0911557i
$633$		0			0
$634$	9.28518	−	23.6582i	0.368761	−	0.939589i
$635$	−63.7451	−	19.6628i	−2.52965	−	0.780293i
$636$		0			0
$637$	4.27583	+	0.755170i	0.169415	+	0.0299209i
$638$	96.8345			3.83371
$639$		0			0
$640$	−26.2032	+	66.7646i	−1.03577	+	2.63910i
$641$	9.14754	+	6.23669i	0.361306	+	0.246334i	0.730343	−	0.683080i	$-0.239360\pi$
$641$	9.14754	+	6.23669i	0.361306	+	0.246334i	−0.369037	+	0.929415i	$0.620312\pi$
$642$		0			0
$643$	−23.4886	+	29.4538i	−0.926302	+	1.16155i	0.0602642	+	0.998182i	$0.480806\pi$
$643$	−23.4886	+	29.4538i	−0.926302	+	1.16155i	−0.986566	+	0.163363i	$0.947766\pi$
$644$	−2.47632	+	28.2593i	−0.0975808	+	1.11357i
$645$		0			0
$646$	25.1842	+	23.3675i	0.990857	+	0.919381i
$647$	−23.0777	−	3.47841i	−0.907279	−	0.136750i	−0.321207	−	0.947009i	$-0.604089\pi$
$647$	−23.0777	−	3.47841i	−0.907279	−	0.136750i	−0.586072	+	0.810259i	$0.699327\pi$
$648$		0			0
$649$	−42.2045	+	28.7745i	−1.65667	+	1.12950i
$650$	−2.29270	−	10.0450i	−0.0899272	−	0.393997i
$651$		0			0
$652$	−4.11639	+	18.0351i	−0.161210	+	0.706308i
$653$	−6.50914	−	16.5850i	−0.254722	−	0.649022i	0.745117	−	0.666934i	$-0.232394\pi$
$653$	−6.50914	−	16.5850i	−0.254722	−	0.649022i	−0.999840	+	0.0179114i	$0.994298\pi$
$654$		0			0
$655$	21.1330	+	36.6034i	0.825733	+	1.43021i
$656$	10.1082	−	17.5080i	0.394660	−	0.683571i
$657$		0			0
$658$	−22.7326	−	0.286572i	−0.886209	−	0.0111717i
$659$	−35.0055	+	16.8578i	−1.36362	+	0.656686i	−0.965441	−	0.260622i	$-0.916073\pi$
$659$	−35.0055	+	16.8578i	−1.36362	+	0.656686i	−0.398180	+	0.917307i	$0.630358\pi$
$660$		0			0
$661$	1.14562	−	0.353376i	0.0445593	−	0.0137447i	−0.272395	−	0.962185i	$-0.587816\pi$
$661$	1.14562	−	0.353376i	0.0445593	−	0.0137447i	0.316955	+	0.948441i	$0.397340\pi$
$662$	−2.94521	+	0.908477i	−0.114469	+	0.0353090i
$663$		0			0
$664$	35.6122	−	17.1499i	1.38202	−	0.665546i
$665$	5.87646	+	27.3300i	0.227879	+	1.05981i
$666$		0			0
$667$	11.7685	−	20.3836i	0.455677	−	0.789255i
$668$	13.6235	+	23.5966i	0.527108	+	0.912978i
$669$		0			0
$670$	1.87604	+	4.78007i	0.0724777	+	0.184670i
$671$	−8.54041	+	37.4180i	−0.329699	+	1.44450i
$672$		0			0
$673$	4.52405	+	19.8212i	0.174389	+	0.764050i	0.984157	+	0.177299i	$0.0567360\pi$
$673$	4.52405	+	19.8212i	0.174389	+	0.764050i	−0.809768	+	0.586751i	$0.800407\pi$
$674$	61.0155	−	41.5996i	2.35023	−	1.60236i
$675$		0			0
$676$	45.9168	+	6.92084i	1.76603	+	0.266186i
$677$	33.4375	+	31.0255i	1.28511	+	1.19241i	0.969933	+	0.243373i	$0.0782539\pi$
$677$	33.4375	+	31.0255i	1.28511	+	1.19241i	0.315176	+	0.949033i	$0.397937\pi$
$678$		0			0
$679$	−1.13864	+	0.755464i	−0.0436969	+	0.0289920i
$680$	40.7868	−	51.1450i	1.56410	−	1.96132i
$681$		0			0
$682$	−34.6156	−	23.6005i	−1.32550	−	0.903710i
$683$	−6.25054	+	15.9261i	−0.239170	+	0.609396i	−0.999179	−	0.0405171i	$-0.987099\pi$
$683$	−6.25054	+	15.9261i	−0.239170	+	0.609396i	0.760009	+	0.649913i	$0.225195\pi$
$684$		0			0
$685$	−58.3344			−2.22884
$686$	−4.96065	+	43.8627i	−0.189399	+	1.67469i
$687$		0			0
$688$	15.9670	+	4.92518i	0.608738	+	0.187771i
$689$	−1.30562	+	3.32668i	−0.0497403	+	0.126736i
$690$		0			0
$691$	−9.14144	+	1.37785i	−0.347757	+	0.0524159i	−0.320598	−	0.947215i	$-0.603884\pi$
$691$	−9.14144	+	1.37785i	−0.347757	+	0.0524159i	−0.0271585	+	0.999631i	$0.508646\pi$
$692$	29.9474	−	37.5528i	1.13843	−	1.42754i
$693$		0			0
$694$	37.0548	+	46.4653i	1.40658	+	1.76380i
$695$	−2.92171	−	2.71095i	−0.110827	−	0.102832i
$696$		0			0
$697$	31.9785	−	29.6717i	1.21127	−	1.12390i
$698$	20.9715	−	14.2981i	0.793784	−	0.541193i
$699$		0			0
$700$	65.1018	−	19.1860i	2.46062	−	0.725161i
$701$	6.54105	−	28.6582i	0.247052	−	1.08241i	−0.687389	−	0.726289i	$-0.741243\pi$
$701$	6.54105	−	28.6582i	0.247052	−	1.08241i	0.934441	−	0.356117i	$-0.115900\pi$
$702$		0			0
$703$	−0.977853	−	13.0485i	−0.0368804	−	0.492135i
$704$	−27.7722	−	48.1028i	−1.04670	−	1.81294i
$705$		0			0
$706$	−30.7691	−	14.8176i	−1.15801	−	0.557669i
$707$	−7.58377	−	35.2703i	−0.285217	−	1.32648i
$708$		0			0
$709$	0.0957375	−	1.27753i	0.00359550	−	0.0479786i	−0.995117	−	0.0986978i	$-0.968532\pi$
$709$	0.0957375	−	1.27753i	0.00359550	−	0.0479786i	0.998713	+	0.0507192i	$0.0161513\pi$
$710$	−79.0054	+	24.3699i	−2.96502	+	0.914587i
$711$		0			0
$712$	0.839384	−	11.2008i	0.0314572	−	0.419768i
$713$	−9.17478	+	4.41834i	−0.343598	+	0.165468i
$714$		0			0
$715$	9.72130	+	4.68153i	0.363556	+	0.175079i
$716$	12.2590	−	21.2333i	0.458141	−	0.793524i
$717$		0			0
$718$	3.93843	+	52.5547i	0.146981	+	1.96132i
$719$	1.82054	+	4.63865i	0.0678946	+	0.172992i	0.960794	−	0.277264i	$-0.0894277\pi$
$719$	1.82054	+	4.63865i	0.0678946	+	0.172992i	−0.892899	+	0.450257i	$0.851332\pi$
$720$		0			0
$721$	16.0414	−	14.5122i	0.597411	−	0.540464i
$722$	−5.13020	−	22.4769i	−0.190926	−	0.836503i
$723$		0			0
$724$	49.4162	−	45.8515i	1.83654	−	1.70406i
$725$	−55.6837	−	8.39296i	−2.06804	−	0.311707i
$726$		0			0
$727$	14.0808	+	17.6568i	0.522229	+	0.654854i	0.971081	−	0.238752i	$-0.0767383\pi$
$727$	14.0808	+	17.6568i	0.522229	+	0.654854i	−0.448852	+	0.893606i	$0.648167\pi$
$728$	0.573953	−	6.54984i	0.0212721	−	0.242753i
$729$		0			0
$730$	13.6719	−	2.06070i	0.506019	−	0.0762701i
$731$	29.7910	+	20.3112i	1.10186	+	0.751235i
$732$		0			0
$733$	20.1874	+	6.22699i	0.745639	+	0.229999i	0.644215	−	0.764844i	$-0.277184\pi$
$733$	20.1874	+	6.22699i	0.745639	+	0.229999i	0.101424	+	0.994843i	$0.467660\pi$
$734$	−57.0759			−2.10671
$735$		0			0
$736$	−8.15476			−0.300589
$737$	−2.99198	−	0.922905i	−0.110211	−	0.0339956i
$738$		0			0
$739$	−35.5703	−	24.2514i	−1.30848	−	0.892104i	−0.310193	−	0.950674i	$-0.600394\pi$
$739$	−35.5703	−	24.2514i	−1.30848	−	0.892104i	−0.998283	+	0.0585699i	$0.981346\pi$
$740$	−53.9523	+	8.13201i	−1.98333	+	0.298939i
$741$		0			0
$742$	−34.5798	−	11.1457i	−1.26946	−	0.409172i
$743$	18.9705	+	23.7882i	0.695960	+	0.872706i	0.996714	−	0.0809958i	$-0.0258100\pi$
$743$	18.9705	+	23.7882i	0.695960	+	0.872706i	−0.300755	+	0.953701i	$0.597239\pi$
$744$		0			0
$745$	−42.2528	−	6.36859i	−1.54802	−	0.233327i
$746$	8.64282	−	8.01937i	0.316436	−	0.293610i
$747$		0			0
$748$	19.4369	+	85.1584i	0.710682	+	3.11370i
$749$	35.7087	+	5.84348i	1.30477	+	0.213516i
$750$		0			0
$751$	14.0982	+	35.9217i	0.514452	+	1.31080i	0.918267	+	0.395961i	$0.129589\pi$
$751$	14.0982	+	35.9217i	0.514452	+	1.31080i	−0.403815	+	0.914841i	$0.632316\pi$
$752$	0.589268	+	7.86324i	0.0214884	+	0.286743i
$753$		0			0
$754$	−5.97312	+	10.3457i	−0.217528	+	0.376770i
$755$	−22.3718	−	10.7737i	−0.814194	−	0.392095i
$756$		0			0
$757$	−37.4323	+	18.0264i	−1.36050	+	0.655182i	−0.964748	−	0.263176i	$-0.915230\pi$
$757$	−37.4323	+	18.0264i	−1.36050	+	0.655182i	−0.395751	+	0.918358i	$0.629516\pi$
$758$	1.31801	−	17.5876i	0.0478721	−	0.638809i
$759$		0			0
$760$	40.4500	−	12.4772i	1.46727	−	0.452594i
$761$	−1.76849	+	23.5988i	−0.0641076	+	0.855456i	0.868759	+	0.495235i	$0.164918\pi$
$761$	−1.76849	+	23.5988i	−0.0641076	+	0.855456i	−0.932867	+	0.360221i	$0.882701\pi$
$762$		0			0
$763$	−5.03783	+	20.8567i	−0.182382	+	0.755064i
$764$	36.1401	+	17.4042i	1.30750	+	0.629661i
$765$		0			0
$766$	−26.6615	−	46.1791i	−0.963319	−	1.66852i
$767$	−0.470923	−	6.28403i	−0.0170040	−	0.226903i
$768$		0			0
$769$	6.92352	−	30.3339i	0.249669	−	1.09387i	−0.682226	−	0.731141i	$-0.738988\pi$
$769$	6.92352	−	30.3339i	0.249669	−	1.09387i	0.931895	−	0.362728i	$-0.118155\pi$
$770$	−41.3593	+	101.597i	−1.49049	+	3.66131i
$771$		0			0
$772$	−44.0298	+	30.0190i	−1.58467	+	1.08041i
$773$	18.3338	−	17.0113i	0.659421	−	0.611853i	−0.277779	−	0.960645i	$-0.589598\pi$
$773$	18.3338	−	17.0113i	0.659421	−	0.611853i	0.937200	+	0.348792i	$0.113408\pi$
$774$		0			0
$775$	17.8598	+	16.5715i	0.641543	+	0.595265i
$776$	1.29012	+	1.61775i	0.0463124	+	0.0580740i
$777$		0			0
$778$	22.9680	−	28.8010i	0.823443	−	1.03257i
$779$	27.9132	−	4.20724i	1.00010	−	0.150740i
$780$		0			0
$781$	18.4181	−	46.9284i	0.659050	−	1.67923i
$782$	31.3114	+	9.65827i	1.11969	+	0.345379i
$783$		0			0
$784$	15.3056	+	0.385953i	0.546630	+	0.0137840i
$785$	−40.2707			−1.43732
$786$		0			0
$787$	0.682339	−	1.73857i	0.0243228	−	0.0619734i	−0.918196	−	0.396125i	$-0.870355\pi$
$787$	0.682339	−	1.73857i	0.0243228	−	0.0619734i	0.942519	+	0.334152i	$0.108450\pi$
$788$	−18.2284	−	12.4279i	−0.649361	−	0.442727i
$789$		0			0
$790$	19.7311	−	24.7420i	0.702001	−	0.880282i
$791$	−2.00261	−	5.29799i	−0.0712047	−	0.188375i
$792$		0			0
$793$	−3.47091	−	3.22054i	−0.123256	−	0.114365i
$794$	−67.1231	−	10.1172i	−2.38211	−	0.359045i
$795$		0			0
$796$	−49.3647	+	33.6563i	−1.74968	+	1.19291i
$797$	−8.77478	−	38.4448i	−0.310819	−	1.36179i	−0.853170	−	0.521634i	$-0.825323\pi$
$797$	−8.77478	−	38.4448i	−0.310819	−	1.36179i	0.542351	−	0.840152i	$-0.317534\pi$
$798$		0			0
$799$	−3.78623	+	16.5886i	−0.133947	+	0.586861i
$800$	7.12797	+	18.1618i	0.252012	+	0.642116i
$801$		0			0
$802$	46.4861	+	80.5163i	1.64148	+	2.84313i
$803$	−4.21530	+	7.30112i	−0.148755	+	0.257651i
$804$		0			0
$805$	16.3596	+	21.0534i	0.576602	+	0.742034i
$806$	4.65669	−	2.24254i	0.164025	−	0.0789902i
$807$		0			0
$808$	−52.2021	+	16.1022i	−1.83646	+	0.566474i
$809$	−36.7782	+	11.3446i	−1.29305	+	0.398854i	−0.863573	−	0.504224i	$-0.831779\pi$
$809$	−36.7782	+	11.3446i	−1.29305	+	0.398854i	−0.429478	+	0.903077i	$0.641303\pi$
$810$		0			0
$811$	−14.0239	+	6.75356i	−0.492446	+	0.237149i	−0.663590	−	0.748097i	$-0.730968\pi$
$811$	−14.0239	+	6.75356i	−0.492446	+	0.237149i	0.171144	+	0.985246i	$0.445254\pi$
$812$	−70.4634	−	35.0344i	−2.47278	−	1.22946i
$813$		0			0
$814$	25.6728	−	44.4667i	0.899833	−	1.55856i
$815$	8.69345	+	15.0575i	0.304518	+	0.527441i
$816$		0			0
$817$	8.52397	+	21.7187i	0.298216	+	0.759842i
$818$	−0.105155	+	0.460713i	−0.00367665	+	0.0161084i
$819$		0			0
$820$	−26.1920	−	114.755i	−0.914665	−	4.00741i
$821$	0.0825612	−	0.0562892i	0.00288140	−	0.00196451i	−0.561878	−	0.827220i	$-0.689921\pi$
$821$	0.0825612	−	0.0562892i	0.00288140	−	0.00196451i	0.564760	+	0.825255i	$0.308969\pi$
$822$		0			0
$823$	7.02771	+	1.05926i	0.244970	+	0.0369234i	0.270380	−	0.962754i	$-0.412851\pi$
$823$	7.02771	+	1.05926i	0.244970	+	0.0369234i	−0.0254092	+	0.999677i	$0.508089\pi$
$824$	−24.0119	−	22.2798i	−0.836493	−	0.776152i
$825$		0			0
$826$	63.4645	−	8.74907i	2.20821	−	0.304419i
$827$	20.3825	−	25.5588i	0.708768	−	0.888766i	−0.288877	−	0.957366i	$-0.593282\pi$
$827$	20.3825	−	25.5588i	0.708768	−	0.888766i	0.997644	+	0.0685999i	$0.0218532\pi$
$828$		0			0
$829$	−17.2835	−	11.7837i	−0.600282	−	0.409265i	0.224697	−	0.974429i	$-0.427861\pi$
$829$	−17.2835	−	11.7837i	−0.600282	−	0.409265i	−0.824979	+	0.565163i	$0.808813\pi$
$830$	29.7219	−	75.7301i	1.03166	−	2.62863i
$831$		0			0
$832$	6.85238			0.237563
$833$	31.3143	+	10.5307i	1.08498	+	0.364868i
$834$		0			0
$835$	24.4714	+	7.54842i	0.846867	+	0.261224i
$836$	−20.6499	+	52.6151i	−0.714191	+	1.81973i
$837$		0			0
$838$	−45.9876	+	6.93152i	−1.58862	+	0.239445i
$839$	−0.594839	+	0.745904i	−0.0205361	+	0.0257515i	−0.791994	−	0.610530i	$-0.790957\pi$
$839$	−0.594839	+	0.745904i	−0.0205361	+	0.0257515i	0.771457	+	0.636281i	$0.219528\pi$
$840$		0			0
$841$	22.6277	+	28.3743i	0.780266	+	0.978423i
$842$	49.7825	+	46.1914i	1.71562	+	1.59186i
$843$		0			0
$844$	21.1634	−	19.6368i	0.728475	−	0.675926i
$845$	36.0605	−	24.5856i	1.24052	−	0.845771i
$846$		0			0
$847$	−18.4772	−	32.9559i	−0.634883	−	1.13238i
$848$	−2.80407	+	12.2854i	−0.0962923	+	0.421884i
$849$		0			0
$850$	−5.85855	−	78.1769i	−0.200946	−	2.68144i
$851$	−6.24013	−	10.8082i	−0.213909	−	0.370501i
$852$		0			0
$853$	−16.9164	−	8.14649i	−0.579205	−	0.278931i	0.121256	−	0.992621i	$-0.461308\pi$
$853$	−16.9164	−	8.14649i	−0.579205	−	0.278931i	−0.700461	+	0.713691i	$0.747022\pi$
$854$	30.4846	−	37.2533i	1.04316	−	1.27478i
$855$		0			0
$856$	4.09458	−	54.6384i	0.139950	−	1.86750i
$857$	16.1654	−	4.98637i	0.552200	−	0.170331i	−0.00608360	−	0.999981i	$-0.501936\pi$
$857$	16.1654	−	4.98637i	0.552200	−	0.170331i	0.558283	+	0.829650i	$0.311460\pi$
$858$		0			0
$859$	2.00626	−	26.7717i	0.0684527	−	0.913438i	−0.852240	−	0.523150i	$-0.824757\pi$
$859$	2.00626	−	26.7717i	0.0684527	−	0.913438i	0.920693	−	0.390287i	$-0.127624\pi$
$860$	87.6523	−	42.2111i	2.98892	−	1.43939i
$861$		0			0
$862$	−82.4138	−	39.6884i	−2.80703	−	1.35179i
$863$	2.64069	−	4.57381i	0.0898902	−	0.155694i	−0.817574	−	0.575823i	$-0.804682\pi$
$863$	2.64069	−	4.57381i	0.0898902	−	0.155694i	0.907465	+	0.420129i	$0.138015\pi$
$864$		0			0
$865$	−3.37366	−	45.0184i	−0.114708	−	1.53067i
$866$	−13.5459	−	34.5143i	−0.460307	−	1.17284i
$867$		0			0
$868$	16.6501	+	29.6971i	0.565141	+	1.00799i
$869$	4.29384	+	18.8125i	0.145658	+	0.638171i
$870$		0			0
$871$	0.283160	−	0.262734i	0.00959450	−	0.00890240i
$872$	32.1279	+	4.84250i	1.08799	+	0.163988i
$873$		0			0
$874$	13.2200	+	16.5774i	0.447173	+	0.560738i
$875$	9.20789	−	15.4941i	0.311283	−	0.523798i
$876$		0			0
$877$	22.8977	−	3.45127i	0.773201	−	0.116541i	0.249421	−	0.968395i	$-0.419760\pi$
$877$	22.8977	−	3.45127i	0.773201	−	0.116541i	0.523780	+	0.851854i	$0.324522\pi$
$878$	−66.9990	−	45.6792i	−2.26111	−	1.54160i
$879$		0			0
$880$	36.3561	+	11.2144i	1.22556	+	0.378036i
$881$	28.5949			0.963385			0.481693	−	0.876340i	$-0.340022\pi$
$881$	28.5949			0.963385			0.481693	+	0.876340i	$0.340022\pi$
$882$		0			0
$883$	−19.4299			−0.653868			−0.326934	−	0.945047i	$-0.606016\pi$
$883$	−19.4299			−0.653868			−0.326934	+	0.945047i	$0.606016\pi$
$884$	−10.2972	−	3.17627i	−0.346333	−	0.106830i
$885$		0			0
$886$	21.8780	+	14.9161i	0.735005	+	0.501118i
$887$	32.7693	−	4.93917i	1.10028	−	0.165841i	0.426296	−	0.904584i	$-0.359818\pi$
$887$	32.7693	−	4.93917i	1.10028	−	0.165841i	0.673988	+	0.738742i	$0.264580\pi$
$888$		0			0
$889$	−50.5375	+	6.96698i	−1.69497	+	0.233665i
$890$	−14.4140	−	18.0745i	−0.483157	−	0.605860i
$891$		0			0
$892$	−25.2041	−	3.79891i	−0.843895	−	0.127197i
$893$	−8.07114	+	7.48892i	−0.270090	+	0.250607i
$894$		0			0
$895$	−5.12783	−	22.4665i	−0.171404	−	0.750972i
$896$	3.40914	+	54.7436i	0.113891	+	1.82886i
$897$		0			0
$898$	−22.0339	−	56.1416i	−0.735282	−	1.87347i
$899$	−2.11102	−	28.1696i	−0.0704064	−	0.939508i
$900$		0			0
$901$	−13.5959	+	23.5487i	−0.452944	+	0.784522i
$902$	99.7984	+	48.0604i	3.32292	+	1.60024i
$903$		0			0
$904$	−7.72720	+	3.72123i	−0.257003	+	0.123766i
$905$	4.73485	−	63.1822i	0.157392	−	2.10025i
$906$		0			0
$907$	−29.2541	+	9.02371i	−0.971368	+	0.299627i	−0.739527	−	0.673126i	$-0.764951\pi$
$907$	−29.2541	+	9.02371i	−0.971368	+	0.299627i	−0.231841	+	0.972754i	$0.574475\pi$
$908$	−3.74261	+	49.9417i	−0.124203	+	1.65737i
$909$		0			0
$910$	−8.30339	−	10.6857i	−0.275255	−	0.354228i
$911$	−3.62468	−	1.74555i	−0.120091	−	0.0578328i	0.372874	−	0.927882i	$-0.378373\pi$
$911$	−3.62468	−	1.74555i	−0.120091	−	0.0578328i	−0.492965	+	0.870049i	$0.664087\pi$
$912$		0			0
$913$	24.8028	+	42.9597i	0.820852	+	1.42176i
$914$	5.12815	+	68.4304i	0.169624	+	2.26348i
$915$		0			0
$916$	−14.9819	+	65.6400i	−0.495016	+	2.16881i
$917$	26.4747	+	18.5433i	0.874272	+	0.612353i
$918$		0			0
$919$	−11.2596	+	7.67663i	−0.371418	+	0.253229i	−0.734616	−	0.678483i	$-0.762637\pi$
$919$	−11.2596	+	7.67663i	−0.371418	+	0.253229i	0.363197	+	0.931712i	$0.381685\pi$
$920$	29.5961	−	27.4612i	0.975755	−	0.905368i
$921$		0			0
$922$	−13.1158	−	12.1697i	−0.431946	−	0.400787i
$923$	3.87771	+	4.86250i	0.127637	+	0.160051i
$924$		0			0
$925$	−18.6170	+	23.3449i	−0.612122	+	0.767577i
$926$	−66.7155	+	10.0557i	−2.19241	+	0.330452i
$927$		0			0
$928$	8.26457	−	21.0578i	0.271298	−	0.691256i
$929$	−25.1860	−	7.76885i	−0.826325	−	0.254888i	−0.147383	−	0.989079i	$-0.547085\pi$
$929$	−25.1860	−	7.76885i	−0.826325	−	0.254888i	−0.678942	+	0.734192i	$0.737561\pi$
$930$		0			0
$931$	12.9035	+	17.0449i	0.422897	+	0.558624i
$932$	−44.3669			−1.45329
$933$		0			0
$934$	−3.92157	+	9.99200i	−0.128318	+	0.326948i
$935$	67.8324	+	46.2474i	2.21836	+	1.51245i
$936$		0			0
$937$	31.2145	−	39.1417i	1.01973	−	1.27870i	0.0598775	−	0.998206i	$-0.480929\pi$
$937$	31.2145	−	39.1417i	1.01973	−	1.27870i	0.959855	−	0.280498i	$-0.0904996\pi$
$938$	2.84480	+	2.70712i	0.0928861	+	0.0883905i
$939$		0			0
$940$	33.6546	+	31.2270i	1.09769	+	1.01851i
$941$	−4.19777	−	0.632712i	−0.136843	−	0.0206258i	0.0802633	−	0.996774i	$-0.474424\pi$
$941$	−4.19777	−	0.632712i	−0.136843	−	0.0206258i	−0.217107	+	0.976148i	$0.569662\pi$
$942$		0			0
$943$	22.2453	−	15.1666i	0.724408	−	0.493893i
$944$	−4.94452	−	21.6633i	−0.160930	−	0.705082i
$945$		0			0
$946$	−20.3723	+	89.2569i	−0.662361	+	2.90199i
$947$	8.26913	+	21.0694i	0.268711	+	0.684664i	0.999997	+	0.00259268i	$0.000825278\pi$
$947$	8.26913	+	21.0694i	0.268711	+	0.684664i	−0.731286	+	0.682071i	$0.761079\pi$
$948$		0			0
$949$	−0.520032	−	0.900722i	−0.0168809	−	0.0292387i
$950$	25.3646	−	43.9328i	0.822937	−	1.42537i
$951$		0			0
$952$	11.7461	−	48.6290i	0.380693	−	1.57608i
$953$	−3.24191	+	1.56122i	−0.105016	+	0.0505729i	−0.485654	−	0.874151i	$-0.661419\pi$
$953$	−3.24191	+	1.56122i	−0.105016	+	0.0505729i	0.380638	+	0.924724i	$0.375704\pi$
$954$		0			0
$955$	36.0264	−	11.1127i	1.16579	−	0.359597i
$956$	−17.3607	+	5.35505i	−0.561484	+	0.173195i
$957$		0			0
$958$	35.6255	−	17.1564i	1.15101	−	0.554297i
$959$	−40.4341	+	18.8479i	−1.30568	+	0.608630i
$960$		0			0
$961$	9.38914	−	16.2625i	0.302875	−	0.524596i
$962$	3.16720	+	5.48575i	0.102115	+	0.176868i
$963$		0			0
$964$	8.94178	+	22.7833i	0.287995	+	0.733800i
$965$	−11.1452	+	48.8304i	−0.358778	+	1.57191i
$966$		0			0
$967$	−7.16780	−	31.4042i	−0.230501	−	1.00989i	−0.949226	−	0.314596i	$-0.898131\pi$
$967$	−7.16780	−	31.4042i	−0.230501	−	1.00989i	0.718725	−	0.695295i	$-0.244726\pi$
$968$	−47.2709	+	32.2287i	−1.51934	+	1.03587i
$969$		0			0
$970$	4.21124	+	0.634743i	0.135215	+	0.0203804i
$971$	−18.0266	−	16.7262i	−0.578501	−	0.536770i	0.335733	−	0.941957i	$-0.391016\pi$
$971$	−18.0266	−	16.7262i	−0.578501	−	0.536770i	−0.914234	+	0.405187i	$0.867206\pi$
$972$		0			0
$973$	−2.90107	−	0.935070i	−0.0930041	−	0.0299770i
$974$	−46.5019	+	58.3115i	−1.49002	+	1.86842i
$975$		0			0
$976$	−13.7947	−	9.40509i	−0.441559	−	0.301050i
$977$	7.25133	−	18.4761i	0.231991	−	0.591102i	−0.766714	−	0.641989i	$-0.778109\pi$
$977$	7.25133	−	18.4761i	0.231991	−	0.591102i	0.998704	+	0.0508866i	$0.0162047\pi$
$978$		0			0
$979$	14.0963			0.450521
$980$	66.8534	−	58.9654i	2.13555	−	1.88358i
$981$		0			0
$982$	−11.5928	−	3.57591i	−0.369941	−	0.114112i
$983$	−1.73909	+	4.43114i	−0.0554685	+	0.141331i	−0.955922	−	0.293621i	$-0.905140\pi$
$983$	−1.73909	+	4.43114i	−0.0554685	+	0.141331i	0.900453	+	0.434953i	$0.143235\pi$
$984$		0			0
$985$	−20.5042	+	3.09051i	−0.653318	+	0.0984718i
$986$	−56.6732	+	71.0660i	−1.80484	+	2.26320i
$987$		0			0
$988$	−4.34760	−	5.45172i	−0.138316	−	0.173442i
$989$	16.3126	+	15.1359i	0.518711	+	0.481294i
$990$		0			0
$991$	−29.0981	+	26.9991i	−0.924332	+	0.857654i	−0.990126	−	0.140179i	$-0.955232\pi$
$991$	−29.0981	+	26.9991i	−0.924332	+	0.857654i	0.0657946	+	0.997833i	$0.479042\pi$
$992$	−8.08656	+	5.51332i	−0.256748	+	0.175048i
$993$		0			0
$994$	−46.8880	+	42.4185i	−1.48720	+	1.34543i
$995$	−12.4956	+	54.7469i	−0.396138	+	1.73559i
$996$		0			0
$997$	3.69668	+	49.3287i	0.117075	+	1.56226i	0.678420	+	0.734674i	$0.262665\pi$
$997$	3.69668	+	49.3287i	0.117075	+	1.56226i	−0.561345	+	0.827582i	$0.689716\pi$
$998$	18.3136	+	31.7201i	0.579707	+	1.00408i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.e.100.1		60
3.2	odd	2		147.2.m.b.100.5	yes	60
49.25	even	21	inner	441.2.bb.e.172.1		60
147.5	even	42		7203.2.a.m.1.26		30
147.44	odd	42		7203.2.a.n.1.26		30
147.74	odd	42		147.2.m.b.25.5	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.b.25.5	✓	60	147.74	odd	42
147.2.m.b.100.5	yes	60	3.2	odd	2
441.2.bb.e.100.1		60	1.1	even	1	trivial
441.2.bb.e.172.1		60	49.25	even	21	inner
7203.2.a.m.1.26		30	147.5	even	42
7203.2.a.n.1.26		30	147.44	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)

\(f(q)\)	\(=\)	\(q+(-2.27757 - 0.702538i) q^{2} +(3.04130 + 2.07352i) q^{4} +(3.42100 - 0.515632i) q^{5} +(2.20464 - 1.46273i) q^{7} +(-2.49792 - 3.13230i) q^{8} +O(q^{10})\)	\(q+(-2.27757 - 0.702538i) q^{2} +(3.04130 + 2.07352i) q^{4} +(3.42100 - 0.515632i) q^{5} +(2.20464 - 1.46273i) q^{7} +(-2.49792 - 3.13230i) q^{8} +(-8.15382 - 1.22899i) q^{10} +(3.68575 - 3.41988i) q^{11} +(0.138027 + 0.604735i) q^{13} +(-6.04884 + 1.78264i) q^{14} +(0.799079 + 2.03602i) q^{16} +(0.352700 + 4.70646i) q^{17} +(-1.52702 + 2.64487i) q^{19} +(11.4735 + 5.52532i) q^{20} +(-10.7972 + 5.19964i) q^{22} +(-0.217678 + 2.90471i) q^{23} +(6.65947 - 2.05417i) q^{25} +(0.110483 - 1.47430i) q^{26} +(9.73797 + 0.122759i) q^{28} +(-7.28014 - 3.50593i) q^{29} +(1.74798 + 3.02759i) q^{31} +(0.209212 + 2.79174i) q^{32} +(2.50316 - 10.9671i) q^{34} +(6.78782 - 6.14078i) q^{35} +(-3.54005 + 2.41357i) q^{37} +(5.33602 - 4.95110i) q^{38} +(-10.1605 - 9.42757i) q^{40} +(-5.76293 - 7.22648i) q^{41} +(4.76320 - 5.97286i) q^{43} +(18.3007 - 2.75838i) q^{44} +(2.53645 - 6.46277i) q^{46} +(3.44501 + 1.06264i) q^{47} +(2.72084 - 6.44958i) q^{49} -16.6106 q^{50} +(-0.834151 + 2.12538i) q^{52} +(4.76028 + 3.24551i) q^{53} +(10.8455 - 13.5999i) q^{55} +(-10.0887 - 3.25178i) q^{56} +(14.1180 + 13.0996i) q^{58} +(-10.0458 - 1.51416i) q^{59} +(-6.30699 + 4.30003i) q^{61} +(-1.85415 - 8.12358i) q^{62} +(2.45821 - 10.7701i) q^{64} +(0.784010 + 1.99762i) q^{65} +(-0.311368 - 0.539305i) q^{67} +(-8.68628 + 15.0451i) q^{68} +(-19.7739 + 9.21737i) q^{70} +(9.03366 - 4.35038i) q^{71} +(-1.60225 + 0.494230i) q^{73} +(9.75835 - 3.01005i) q^{74} +(-10.1283 + 4.87755i) q^{76} +(3.12338 - 12.9308i) q^{77} +(-1.91890 + 3.32364i) q^{79} +(3.78348 + 6.55319i) q^{80} +(8.04861 + 20.5075i) q^{82} +(-2.19538 + 9.61859i) q^{83} +(3.63338 + 15.9189i) q^{85} +(-15.0447 + 10.2573i) q^{86} +(-19.9188 - 3.00228i) q^{88} +(2.05518 + 1.90693i) q^{89} +(1.18886 + 1.13132i) q^{91} +(-6.68502 + 8.38275i) q^{92} +(-7.09970 - 4.84050i) q^{94} +(-3.86014 + 9.83548i) q^{95} -0.516475 q^{97} +(-10.7280 + 12.7779i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) \) 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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