LMFDB - Embedded newform 441.2.bb.c.109.4

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:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			109.4
Character	$\chi$	$=$	441.109
Dual form			441.2.bb.c.352.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29251 - 1.19927i) q^{2} +(0.0828637 - 1.10574i) q^{4} +(-1.35494 + 3.45233i) q^{5} +(1.47509 - 2.19638i) q^{7} +(0.979680 + 1.22848i) q^{8} +O(q^{10})$	\(q+(1.29251 - 1.19927i) q^{2} +(0.0828637 - 1.10574i) q^{4} +(-1.35494 + 3.45233i) q^{5} +(1.47509 - 2.19638i) q^{7} +(0.979680 + 1.22848i) q^{8} +(2.38902 + 6.08712i) q^{10} +(1.46421 + 0.451650i) q^{11} +(0.545602 + 2.39044i) q^{13} +(-0.727497 - 4.60789i) q^{14} +(4.93244 + 0.743446i) q^{16} +(3.98718 - 2.71841i) q^{17} +(1.90634 + 3.30188i) q^{19} +(3.70511 + 1.78429i) q^{20} +(2.43416 - 1.17223i) q^{22} +(-3.98222 - 2.71503i) q^{23} +(-6.41749 - 5.95456i) q^{25} +(3.57198 + 2.43534i) q^{26} +(-2.30640 - 1.81307i) q^{28} +(-0.292476 - 0.140849i) q^{29} +(-3.32500 + 5.75907i) q^{31} +(4.67031 - 3.18416i) q^{32} +(1.89335 - 8.29529i) q^{34} +(5.58399 + 8.06848i) q^{35} +(-0.669188 - 8.92969i) q^{37} +(6.42382 + 1.98149i) q^{38} +(-5.56853 + 1.71766i) q^{40} +(-1.52030 - 1.90640i) q^{41} +(-3.39704 + 4.25975i) q^{43} +(0.620737 - 1.58161i) q^{44} +(-8.40312 + 1.26657i) q^{46} +(-6.44765 + 5.98255i) q^{47} +(-2.64821 - 6.47974i) q^{49} -15.4358 q^{50} +(2.68841 - 0.405213i) q^{52} +(0.754653 - 10.0701i) q^{53} +(-3.54317 + 4.44299i) q^{55} +(4.14333 - 0.339634i) q^{56} +(-0.546945 + 0.168710i) q^{58} +(-4.97979 - 12.6883i) q^{59} +(0.0620258 + 0.827677i) q^{61} +(2.60911 + 11.4312i) q^{62} +(-0.00219938 + 0.00963609i) q^{64} +(-8.99184 - 1.35530i) q^{65} +(6.41336 - 11.1083i) q^{67} +(-2.67546 - 4.63404i) q^{68} +(16.8937 + 3.73185i) q^{70} +(-0.993012 + 0.478209i) q^{71} +(-4.14492 - 3.84592i) q^{73} +(-11.5741 - 10.7392i) q^{74} +(3.80898 - 1.83431i) q^{76} +(3.15184 - 2.54975i) q^{77} +(5.85694 + 10.1445i) q^{79} +(-9.24979 + 16.0211i) q^{80} +(-4.25130 - 0.640780i) q^{82} +(-1.63242 + 7.15209i) q^{83} +(3.98247 + 17.4484i) q^{85} +(0.717904 + 9.57976i) q^{86} +(0.879617 + 2.24123i) q^{88} +(15.7596 - 4.86121i) q^{89} +(6.05513 + 2.32776i) q^{91} +(-3.33210 + 4.17832i) q^{92} +(-1.15894 + 15.4650i) q^{94} +(-13.9822 + 2.10747i) q^{95} -10.1265 q^{97} +(-11.1938 - 5.19919i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} + 3 q^{4} - 6 q^{8}+O(q^{10}) $ 48 * q + q^2 + 3 * q^4 - 6 * q^8	$ 48 q + q^{2} + 3 q^{4} - 6 q^{8} + 30 q^{10} + 9 q^{11} + 42 q^{14} + 29 q^{16} + 5 q^{17} - 26 q^{19} + 5 q^{20} + q^{22} + 4 q^{23} - 56 q^{25} + 62 q^{26} + 7 q^{28} - 12 q^{29} - 36 q^{31} + 14 q^{32} - 76 q^{34} - 7 q^{35} - 20 q^{37} + 60 q^{38} + 28 q^{40} - 41 q^{41} + 12 q^{43} - 44 q^{44} + 16 q^{46} - 13 q^{47} - 84 q^{49} + 12 q^{50} + 92 q^{52} - 14 q^{53} - 38 q^{55} - 105 q^{56} + 3 q^{58} - 57 q^{59} + 11 q^{61} + 16 q^{62} - 110 q^{64} - 21 q^{65} + 34 q^{67} - 22 q^{68} - 6 q^{71} - 69 q^{73} + 90 q^{74} - 49 q^{76} + 34 q^{79} - 55 q^{80} + 91 q^{82} - 28 q^{83} - 44 q^{85} + 26 q^{86} + 45 q^{88} - 11 q^{89} - 84 q^{92} + 90 q^{94} - 150 q^{95} + 124 q^{97} - 119 q^{98}+O(q^{100}) $ 48 * q + q^2 + 3 * q^4 - 6 * q^8 + 30 * q^10 + 9 * q^11 + 42 * q^14 + 29 * q^16 + 5 * q^17 - 26 * q^19 + 5 * q^20 + q^22 + 4 * q^23 - 56 * q^25 + 62 * q^26 + 7 * q^28 - 12 * q^29 - 36 * q^31 + 14 * q^32 - 76 * q^34 - 7 * q^35 - 20 * q^37 + 60 * q^38 + 28 * q^40 - 41 * q^41 + 12 * q^43 - 44 * q^44 + 16 * q^46 - 13 * q^47 - 84 * q^49 + 12 * q^50 + 92 * q^52 - 14 * q^53 - 38 * q^55 - 105 * q^56 + 3 * q^58 - 57 * q^59 + 11 * q^61 + 16 * q^62 - 110 * q^64 - 21 * q^65 + 34 * q^67 - 22 * q^68 - 6 * q^71 - 69 * q^73 + 90 * q^74 - 49 * q^76 + 34 * q^79 - 55 * q^80 + 91 * q^82 - 28 * q^83 - 44 * q^85 + 26 * q^86 + 45 * q^88 - 11 * q^89 - 84 * q^92 + 90 * q^94 - 150 * q^95 + 124 * q^97 - 119 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{20}{21}\right)$	$1$

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 $

$2$	1.29251	−	1.19927i	0.913943	−	0.848015i	−0.0748677	−	0.997193i	$-0.523853\pi$
$2$	1.29251	−	1.19927i	0.913943	−	0.848015i	0.988810	+	0.149179i	$0.0476630\pi$
$3$		0			0
$3$		0			0
$4$	0.0828637	−	1.10574i	0.0414319	−	0.552870i
$5$	−1.35494	+	3.45233i	−0.605948	+	1.54393i	0.217214	+	0.976124i	$0.430303\pi$
$5$	−1.35494	+	3.45233i	−0.605948	+	1.54393i	−0.823162	+	0.567807i	$0.807792\pi$
$6$		0			0
$7$	1.47509	−	2.19638i	0.557532	−	0.830155i
$7$	1.47509	−	2.19638i	0.557532	−	0.830155i
$8$	0.979680	+	1.22848i	0.346369	+	0.434333i
$9$		0			0
$10$	2.38902	+	6.08712i	0.755474	+	1.92492i
$11$	1.46421	+	0.451650i	0.441477	+	0.136177i	0.507521	−	0.861639i	$-0.330562\pi$
$11$	1.46421	+	0.451650i	0.441477	+	0.136177i	−0.0660448	+	0.997817i	$0.521038\pi$
$12$		0			0
$13$	0.545602	+	2.39044i	0.151323	+	0.662988i	0.992502	+	0.122231i	$0.0390049\pi$
$13$	0.545602	+	2.39044i	0.151323	+	0.662988i	−0.841179	+	0.540757i	$0.818138\pi$
$14$	−0.727497	−	4.60789i	−0.194432	−	1.23151i
$15$		0			0
$16$	4.93244	+	0.743446i	1.23311	+	0.185861i
$17$	3.98718	−	2.71841i	0.967032	−	0.659311i	0.0267267	−	0.999643i	$-0.491492\pi$
$17$	3.98718	−	2.71841i	0.967032	−	0.659311i	0.940306	+	0.340331i	$0.110539\pi$
$18$		0			0
$19$	1.90634	+	3.30188i	0.437344	+	0.757503i	0.997484	−	0.0708956i	$-0.0225857\pi$
$19$	1.90634	+	3.30188i	0.437344	+	0.757503i	−0.560139	+	0.828398i	$0.689252\pi$
$20$	3.70511	+	1.78429i	0.828487	+	0.398978i
$21$		0			0
$22$	2.43416	−	1.17223i	0.518965	−	0.249920i
$23$	−3.98222	−	2.71503i	−0.830350	−	0.566123i	0.0718629	−	0.997415i	$-0.477106\pi$
$23$	−3.98222	−	2.71503i	−0.830350	−	0.566123i	−0.902213	+	0.431292i	$0.858058\pi$
$24$		0			0
$25$	−6.41749	−	5.95456i	−1.28350	−	1.19091i
$26$	3.57198	+	2.43534i	0.700524	+	0.477609i
$27$		0			0
$28$	−2.30640	−	1.81307i	−0.435868	−	0.342637i
$29$	−0.292476	−	0.140849i	−0.0543114	−	0.0261550i	0.406531	−	0.913637i	$-0.366738\pi$
$29$	−0.292476	−	0.140849i	−0.0543114	−	0.0261550i	−0.460842	+	0.887482i	$0.652453\pi$
$30$		0			0
$31$	−3.32500	+	5.75907i	−0.597188	+	1.03436i	0.396047	+	0.918230i	$0.370382\pi$
$31$	−3.32500	+	5.75907i	−0.597188	+	1.03436i	−0.993234	+	0.116129i	$0.962951\pi$
$32$	4.67031	−	3.18416i	0.825602	−	0.562886i
$33$		0			0
$34$	1.89335	−	8.29529i	0.324706	−	1.42263i
$35$	5.58399	+	8.06848i	0.943867	+	1.36382i
$36$		0			0
$37$	−0.669188	−	8.92969i	−0.110014	−	1.46803i	−0.730015	−	0.683431i	$-0.760487\pi$
$37$	−0.669188	−	8.92969i	−0.110014	−	1.46803i	0.620001	−	0.784601i	$-0.287132\pi$
$38$	6.42382	+	1.98149i	1.04208	+	0.321440i
$39$		0			0
$40$	−5.56853	+	1.71766i	−0.880462	+	0.271587i
$41$	−1.52030	−	1.90640i	−0.237431	−	0.297729i	0.648813	−	0.760948i	$-0.275266\pi$
$41$	−1.52030	−	1.90640i	−0.237431	−	0.297729i	−0.886244	+	0.463219i	$0.846694\pi$
$42$		0			0
$43$	−3.39704	+	4.25975i	−0.518044	+	0.649607i	−0.970192	−	0.242336i	$-0.922086\pi$
$43$	−3.39704	+	4.25975i	−0.518044	+	0.649607i	0.452148	+	0.891943i	$0.350658\pi$
$44$	0.620737	−	1.58161i	0.0935796	−	0.238437i
$45$		0			0
$46$	−8.40312	+	1.26657i	−1.23897	+	0.186745i
$47$	−6.44765	+	5.98255i	−0.940487	+	0.872644i	−0.992027	−	0.126027i	$-0.959777\pi$
$47$	−6.44765	+	5.98255i	−0.940487	+	0.872644i	0.0515402	+	0.998671i	$0.483587\pi$
$48$		0			0
$49$	−2.64821	−	6.47974i	−0.378316	−	0.925677i
$50$	−15.4358			−2.18295
$51$		0			0
$52$	2.68841	−	0.405213i	0.372815	−	0.0561929i
$53$	0.754653	−	10.0701i	0.103660	−	1.38324i	−0.666555	−	0.745456i	$-0.732232\pi$
$53$	0.754653	−	10.0701i	0.103660	−	1.38324i	0.770215	−	0.637785i	$-0.220149\pi$
$54$		0			0
$55$	−3.54317	+	4.44299i	−0.477761	+	0.599093i
$56$	4.14333	−	0.339634i	0.553676	−	0.0453856i
$57$		0			0
$58$	−0.546945	+	0.168710i	−0.0718173	+	0.0221527i
$59$	−4.97979	−	12.6883i	−0.648313	−	1.65187i	−0.753520	−	0.657424i	$-0.771646\pi$
$59$	−4.97979	−	12.6883i	−0.648313	−	1.65187i	0.105207	−	0.994450i	$-0.466449\pi$
$60$		0			0
$61$	0.0620258	+	0.827677i	0.00794159	+	0.105973i	0.999766	−	0.0216379i	$-0.00688811\pi$
$61$	0.0620258	+	0.827677i	0.00794159	+	0.105973i	−0.991824	+	0.127611i	$0.959269\pi$
$62$	2.60911	+	11.4312i	0.331357	+	1.45177i
$63$		0			0
$64$	−0.00219938	+	0.00963609i	−0.000274922	+	0.00120451i
$65$	−8.99184	−	1.35530i	−1.11530	−	0.168105i
$66$		0			0
$67$	6.41336	−	11.1083i	0.783517	−	1.35709i	−0.146364	−	0.989231i	$-0.546757\pi$
$67$	6.41336	−	11.1083i	0.783517	−	1.35709i	0.929881	−	0.367860i	$-0.119910\pi$
$68$	−2.67546	−	4.63404i	−0.324447	−	0.561959i
$69$		0			0
$70$	16.8937	+	3.73185i	2.01918	+	0.446042i
$71$	−0.993012	+	0.478209i	−0.117849	+	0.0567530i	−0.491879	−	0.870663i	$-0.663690\pi$
$71$	−0.993012	+	0.478209i	−0.117849	+	0.0567530i	0.374030	+	0.927416i	$0.377976\pi$
$72$		0			0
$73$	−4.14492	−	3.84592i	−0.485126	−	0.450131i	0.399294	−	0.916823i	$-0.369255\pi$
$73$	−4.14492	−	3.84592i	−0.485126	−	0.450131i	−0.884420	+	0.466692i	$0.845446\pi$
$74$	−11.5741	−	10.7392i	−1.34546	−	1.24840i
$75$		0			0
$76$	3.80898	−	1.83431i	0.436920	−	0.210410i
$77$	3.15184	−	2.54975i	0.359186	−	0.290571i
$78$		0			0
$79$	5.85694	+	10.1445i	0.658958	+	1.14135i	0.980886	+	0.194584i	$0.0623357\pi$
$79$	5.85694	+	10.1445i	0.658958	+	1.14135i	−0.321928	+	0.946764i	$0.604331\pi$
$80$	−9.24979	+	16.0211i	−1.03416	+	1.79121i
$81$		0			0
$82$	−4.25130	−	0.640780i	−0.469477	−	0.0707623i
$83$	−1.63242	+	7.15209i	−0.179181	+	0.785044i	0.802828	+	0.596211i	$0.203328\pi$
$83$	−1.63242	+	7.15209i	−0.179181	+	0.785044i	−0.982009	+	0.188833i	$0.939529\pi$
$84$		0			0
$85$	3.98247	+	17.4484i	0.431960	+	1.89254i
$86$	0.717904	+	9.57976i	0.0774135	+	1.03301i
$87$		0			0
$88$	0.879617	+	2.24123i	0.0937675	+	0.238916i
$89$	15.7596	−	4.86121i	1.67052	−	0.515287i	0.692080	−	0.721821i	$-0.256695\pi$
$89$	15.7596	−	4.86121i	1.67052	−	0.515287i	0.978439	+	0.206534i	$0.0662184\pi$
$90$		0			0
$91$	6.05513	+	2.32776i	0.634750	+	0.244016i
$92$	−3.33210	+	4.17832i	−0.347395	+	0.435620i
$93$		0			0
$94$	−1.15894	+	15.4650i	−0.119536	+	1.59509i
$95$	−13.9822	+	2.10747i	−1.43454	+	0.216222i
$96$		0			0
$97$	−10.1265			−1.02819			−0.514096	−	0.857733i	$-0.671872\pi$
$97$	−10.1265			−1.02819			−0.514096	+	0.857733i	$0.671872\pi$
$98$	−11.1938	−	5.19919i	−1.13075	−	0.525198i
$99$		0			0
$100$	−7.11597	+	6.60265i	−0.711597	+	0.660265i
$101$	14.6241	−	2.20423i	1.45515	−	0.219329i	0.626645	−	0.779304i	$-0.284427\pi$
$101$	14.6241	−	2.20423i	1.45515	−	0.219329i	0.828509	+	0.559975i	$0.189189\pi$
$102$		0			0
$103$	1.59332	−	4.05970i	0.156994	−	0.400014i	−0.830636	−	0.556816i	$-0.812023\pi$
$103$	1.59332	−	4.05970i	0.156994	−	0.400014i	0.987630	+	0.156801i	$0.0501182\pi$
$104$	−2.40209	+	3.01212i	−0.235544	+	0.295363i
$105$		0			0
$106$	−11.1015	−	13.9208i	−1.07827	−	1.35211i
$107$	9.53503	−	2.94117i	0.921786	−	0.284333i	0.202689	−	0.979243i	$-0.435032\pi$
$107$	9.53503	−	2.94117i	0.921786	−	0.284333i	0.719097	+	0.694910i	$0.244556\pi$
$108$		0			0
$109$	4.90154	+	1.51193i	0.469483	+	0.144816i	0.520464	−	0.853883i	$-0.325759\pi$
$109$	4.90154	+	1.51193i	0.469483	+	0.144816i	−0.0509818	+	0.998700i	$0.516235\pi$
$110$	0.748785	+	9.99184i	0.0713938	+	0.952684i
$111$		0			0
$112$	8.90869	−	9.73689i	0.841792	−	0.920049i
$113$	−2.55860	+	11.2100i	−0.240693	+	1.05455i	0.699695	+	0.714442i	$0.253319\pi$
$113$	−2.55860	+	11.2100i	−0.240693	+	1.05455i	−0.940388	+	0.340104i	$0.889538\pi$
$114$		0			0
$115$	14.7689	−	10.0692i	1.37720	−	0.938961i
$116$	−0.179978	+	0.311731i	−0.0167105	+	0.0289435i
$117$		0			0
$118$	−21.6532	−	10.4276i	−1.99333	−	0.959940i
$119$	−0.0892275	−	12.7673i	−0.00817947	−	1.17037i
$120$		0			0
$121$	−7.14870	−	4.87390i	−0.649882	−	0.443082i
$122$	1.07278	+	0.995395i	0.0971250	+	0.0901188i
$123$		0			0
$124$	6.09251	+	4.15380i	0.547123	+	0.373022i
$125$	12.5453	−	6.04151i	1.12209	−	0.540369i
$126$		0			0
$127$	−14.2735	−	6.87378i	−1.26657	−	0.609949i	−0.324667	−	0.945828i	$-0.605252\pi$
$127$	−14.2735	−	6.87378i	−1.26657	−	0.609949i	−0.941905	+	0.335879i	$0.890967\pi$
$128$	5.66121	+	9.80550i	0.500385	+	0.866692i
$129$		0			0
$130$	−13.2474	+	9.03194i	−1.16188	+	0.792154i
$131$	−2.15484	−	0.324791i	−0.188270	−	0.0283771i	0.0542306	−	0.998528i	$-0.482729\pi$
$131$	−2.15484	−	0.324791i	−0.188270	−	0.0283771i	−0.242500	+	0.970151i	$0.577967\pi$
$132$		0			0
$133$	10.0642	+	0.683515i	0.872679	+	0.0592682i
$134$	−5.03252	−	22.0489i	−0.434744	−	1.90474i
$135$		0			0
$136$	7.24567	+	2.23499i	0.621311	+	0.191649i
$137$	−0.947454	−	2.41407i	−0.0809465	−	0.206248i	0.884671	−	0.466216i	$-0.154383\pi$
$137$	−0.947454	−	2.41407i	−0.0809465	−	0.206248i	−0.965617	+	0.259968i	$0.916288\pi$
$138$		0			0
$139$	7.41880	+	9.30288i	0.629254	+	0.789060i	0.989613	−	0.143754i	$-0.0459174\pi$
$139$	7.41880	+	9.30288i	0.629254	+	0.789060i	−0.360359	+	0.932814i	$0.617346\pi$
$140$	9.38435	−	5.50586i	0.793122	−	0.465330i
$141$		0			0
$142$	−0.709974	+	1.80898i	−0.0595797	+	0.151806i
$143$	−0.280763	+	3.74653i	−0.0234786	+	0.313300i
$144$		0			0
$145$	0.882545	−	0.818883i	0.0732914	−	0.0680045i
$146$	−9.96966			−0.825095
$147$		0			0
$148$	−9.92936			−0.816189
$149$	−3.63965	+	3.37710i	−0.298172	+	0.276663i	−0.815043	−	0.579400i	$-0.803287\pi$
$149$	−3.63965	+	3.37710i	−0.298172	+	0.276663i	0.516872	+	0.856063i	$0.327096\pi$
$150$		0			0
$151$	−0.471771	+	6.29535i	−0.0383922	+	0.512308i	0.944547	+	0.328377i	$0.106501\pi$
$151$	−0.471771	+	6.29535i	−0.0383922	+	0.512308i	−0.982939	+	0.183931i	$0.941118\pi$
$152$	−2.18869	+	5.57669i	−0.177526	+	0.452329i
$153$		0			0
$154$	1.01594	−	7.07550i	0.0818668	−	0.570160i
$155$	−15.3771	−	19.2822i	−1.23511	−	1.54878i
$156$		0			0
$157$	−5.47350	−	13.9462i	−0.436832	−	1.11303i	−0.964618	−	0.263653i	$-0.915073\pi$
$157$	−5.47350	−	13.9462i	−0.436832	−	1.11303i	0.527785	−	0.849378i	$-0.323023\pi$
$158$	19.7362	+	6.08782i	1.57013	+	0.484321i
$159$		0			0
$160$	4.66480	+	20.4378i	0.368785	+	1.61575i
$161$	−11.8374	+	4.74156i	−0.932916	+	0.373688i
$162$		0			0
$163$	6.77720	+	1.02150i	0.530832	+	0.0800100i	0.408989	−	0.912539i	$-0.365882\pi$
$163$	6.77720	+	1.02150i	0.530832	+	0.0800100i	0.121843	+	0.992549i	$0.461120\pi$
$164$	−2.23396	+	1.52308i	−0.174443	+	0.118933i
$165$		0			0
$166$	6.46740	+	11.2019i	0.501968	+	0.869433i
$167$	−6.01094	−	2.89472i	−0.465141	−	0.224000i	0.186609	−	0.982434i	$-0.440250\pi$
$167$	−6.01094	−	2.89472i	−0.465141	−	0.224000i	−0.651750	+	0.758434i	$0.725965\pi$
$168$		0			0
$169$	6.29609	−	3.03204i	0.484315	−	0.233234i
$170$	26.0727	+	17.7761i	1.99969	+	1.36336i
$171$		0			0
$172$	4.42869	+	4.10922i	0.337684	+	0.313325i
$173$	−17.8020	−	12.1372i	−1.35346	−	0.922776i	−0.353544	−	0.935418i	$-0.615023\pi$
$173$	−17.8020	−	12.1372i	−1.35346	−	0.922776i	−0.999920	+	0.0126419i	$0.995976\pi$
$174$		0			0
$175$	−22.5449	+	5.31176i	−1.70423	+	0.401531i
$176$	6.88636	+	3.31630i	0.519079	+	0.249975i
$177$		0			0
$178$	14.5396	−	25.1833i	1.08979	−	1.88757i
$179$	−9.67175	+	6.59408i	−0.722900	+	0.492865i	−0.868008	−	0.496551i	$-0.834600\pi$
$179$	−9.67175	+	6.59408i	−0.722900	+	0.492865i	0.145107	+	0.989416i	$0.453647\pi$
$180$		0			0
$181$	−1.94849	+	8.53690i	−0.144830	+	0.634543i	0.849443	+	0.527680i	$0.176938\pi$
$181$	−1.94849	+	8.53690i	−0.144830	+	0.634543i	−0.994274	+	0.106863i	$0.965919\pi$
$182$	10.6179	−	4.25311i	0.787054	−	0.315261i
$183$		0			0
$184$	−0.565939	−	7.55193i	−0.0417216	−	0.556736i
$185$	31.7350	+	9.78895i	2.33320	+	0.719698i
$186$		0			0
$187$	7.06584	−	2.17952i	0.516705	−	0.159383i
$188$	6.08086	+	7.62516i	0.443492	+	0.556122i
$189$		0			0
$190$	−15.5447	+	19.4924i	−1.12773	+	1.41413i
$191$	−3.52558	+	8.98303i	−0.255102	+	0.649989i	−0.999849	−	0.0173574i	$-0.994475\pi$
$191$	−3.52558	+	8.98303i	−0.255102	+	0.649989i	0.744747	+	0.667346i	$0.232570\pi$
$192$		0			0
$193$	7.61479	−	1.14774i	0.548124	−	0.0826165i	0.130859	−	0.991401i	$-0.458227\pi$
$193$	7.61479	−	1.14774i	0.548124	−	0.0826165i	0.417266	+	0.908785i	$0.362988\pi$
$194$	−13.0886	+	12.1445i	−0.939708	+	0.871921i
$195$		0			0
$196$	−7.38434	+	2.39130i	−0.527453	+	0.170807i
$197$	12.6320			0.899991			0.449995	−	0.893031i	$-0.351426\pi$
$197$	12.6320			0.899991			0.449995	+	0.893031i	$0.351426\pi$
$198$		0			0
$199$	−17.1268	+	2.58145i	−1.21408	+	0.182994i	−0.724694	−	0.689071i	$-0.758019\pi$
$199$	−17.1268	+	2.58145i	−1.21408	+	0.182994i	−0.489391	+	0.872065i	$0.662781\pi$
$200$	1.02797	−	13.7173i	0.0726885	−	0.969961i
$201$		0			0
$202$	16.2583	−	20.3873i	1.14393	−	1.43445i
$203$	−0.740787	+	0.434625i	−0.0519931	+	0.0305047i
$204$		0			0
$205$	8.64144	−	2.66553i	0.603544	−	0.186169i
$206$	−2.80932	−	7.15803i	−0.195735	−	0.498724i
$207$		0			0
$208$	0.913987	+	12.1963i	0.0633736	+	0.845662i
$209$	1.29999	+	5.69565i	0.0899225	+	0.393976i
$210$		0			0
$211$	3.92739	−	17.2070i	0.270373	−	1.18458i	−0.639202	−	0.769039i	$-0.720735\pi$
$211$	3.92739	−	17.2070i	0.270373	−	1.18458i	0.909574	−	0.415541i	$-0.136408\pi$
$212$	−11.0724	−	1.66890i	−0.760457	−	0.114620i
$213$		0			0
$214$	8.79685	−	15.2366i	0.601340	−	1.04155i
$215$	−10.1033	−	17.4994i	−0.689040	−	1.19345i
$216$		0			0
$217$	7.74445	+	15.7981i	0.525728	+	1.07245i
$218$	8.14851	−	3.92411i	0.551886	−	0.265774i
$219$		0			0
$220$	4.61919	+	4.28598i	0.311426	+	0.288961i
$221$	8.67360	+	8.04792i	0.583449	+	0.541362i
$222$		0			0
$223$	3.95716	−	1.90567i	0.264991	−	0.127613i	−0.296671	−	0.954980i	$-0.595876\pi$
$223$	3.95716	−	1.90567i	0.264991	−	0.127613i	0.561662	+	0.827367i	$0.310162\pi$
$224$	−0.104515	−	14.9547i	−0.00698321	−	0.999205i
$225$		0			0
$226$	10.1368	+	17.5575i	0.674291	+	1.16791i
$227$	5.53734	−	9.59096i	0.367526	−	0.636574i	−0.621652	−	0.783294i	$-0.713538\pi$
$227$	5.53734	−	9.59096i	0.367526	−	0.636574i	0.989178	+	0.146719i	$0.0468714\pi$
$228$		0			0
$229$	−15.2949	−	2.30533i	−1.01071	−	0.152341i	−0.377249	−	0.926112i	$-0.623130\pi$
$229$	−15.2949	−	2.30533i	−1.01071	−	0.152341i	−0.633465	+	0.773771i	$0.718368\pi$
$230$	7.01312	−	30.7265i	0.462432	−	2.02605i
$231$		0			0
$232$	−0.113503	−	0.497288i	−0.00745182	−	0.0326485i
$233$	0.533326	+	7.11675i	0.0349394	+	0.466234i	0.987043	+	0.160457i	$0.0512969\pi$
$233$	0.533326	+	7.11675i	0.0349394	+	0.466234i	−0.952103	+	0.305776i	$0.901084\pi$
$234$		0			0
$235$	−11.9176	−	30.3654i	−0.777416	−	1.98082i
$236$	−14.4426	+	4.45495i	−0.940132	+	0.289992i
$237$		0			0
$238$	−15.4268	−	16.3948i	−0.999970	−	1.06272i
$239$	−5.42588	+	6.80384i	−0.350971	+	0.440104i	−0.925711	−	0.378233i	$-0.876532\pi$
$239$	−5.42588	+	6.80384i	−0.350971	+	0.440104i	0.574740	+	0.818336i	$0.305103\pi$
$240$		0			0
$241$	−0.105909	+	1.41326i	−0.00682222	+	0.0910362i	−0.999576	−	0.0291341i	$-0.990725\pi$
$241$	−0.105909	+	1.41326i	−0.00682222	+	0.0910362i	0.992753	+	0.120170i	$0.0383441\pi$
$242$	−15.0849	+	2.27368i	−0.969694	+	0.146158i
$243$		0			0
$244$	0.920335			0.0589184
$245$	25.9584	−	0.362852i	1.65842	−	0.0231818i
$246$		0			0
$247$	−6.85283	+	6.35850i	−0.436035	+	0.404581i
$248$	−10.3323	+	1.55735i	−0.656104	+	0.0988918i
$249$		0			0
$250$	8.96953	−	22.8540i	0.567283	−	1.44541i
$251$	0.322941	−	0.404955i	0.0203838	−	0.0255605i	−0.771535	−	0.636187i	$-0.780511\pi$
$251$	0.322941	−	0.404955i	0.0203838	−	0.0255605i	0.791919	+	0.610626i	$0.209082\pi$
$252$		0			0
$253$	−4.60457	−	5.77395i	−0.289487	−	0.363005i
$254$	−26.6922	+	8.23347i	−1.67482	+	0.516614i
$255$		0			0
$256$	19.0578	+	5.87854i	1.19111	+	0.367409i
$257$	0.444646	+	5.93339i	0.0277363	+	0.370115i	0.993750	+	0.111625i	$0.0356057\pi$
$257$	0.444646	+	5.93339i	0.0277363	+	0.370115i	−0.966014	+	0.258489i	$0.916775\pi$
$258$		0			0
$259$	−20.6002	−	11.7023i	−1.28003	−	0.727147i
$260$	−2.24371	+	9.83033i	−0.139149	+	0.609651i
$261$		0			0
$262$	−3.17467	+	2.16445i	−0.196132	+	0.133720i
$263$	0.399740	−	0.692371i	0.0246490	−	0.0426934i	−0.853438	−	0.521195i	$-0.825487\pi$
$263$	0.399740	−	0.692371i	0.0246490	−	0.0426934i	0.878087	+	0.478501i	$0.158820\pi$
$264$		0			0
$265$	33.7430	+	16.2498i	2.07281	+	0.998215i
$266$	13.8278	−	11.1863i	0.847838	−	0.685877i
$267$		0			0
$268$	−11.7514	−	8.01198i	−0.717832	−	0.489410i
$269$	−7.15066	−	6.63485i	−0.435984	−	0.404534i	0.431410	−	0.902156i	$-0.358016\pi$
$269$	−7.15066	−	6.63485i	−0.435984	−	0.404534i	−0.867394	+	0.497622i	$0.834207\pi$
$270$		0			0
$271$	−1.84271	−	1.25634i	−0.111937	−	0.0763172i	0.506058	−	0.862500i	$-0.331102\pi$
$271$	−1.84271	−	1.25634i	−0.111937	−	0.0763172i	−0.617995	+	0.786182i	$0.712055\pi$
$272$	21.6875	−	10.4441i	1.31500	−	0.633270i
$273$		0			0
$274$	−4.11973	−	1.98396i	−0.248882	−	0.119855i
$275$	−6.70719	−	11.6172i	−0.404459	−	0.700543i
$276$		0			0
$277$	−6.45172	+	4.39871i	−0.387646	+	0.264293i	−0.741424	−	0.671037i	$-0.765849\pi$
$277$	−6.45172	+	4.39871i	−0.387646	+	0.264293i	0.353778	+	0.935329i	$0.384897\pi$
$278$	20.7456	+	3.12689i	1.24424	+	0.187538i
$279$		0			0
$280$	−4.44144	+	14.7644i	−0.265427	+	0.882339i
$281$	5.12842	+	22.4691i	0.305936	+	1.34039i	0.861008	+	0.508591i	$0.169833\pi$
$281$	5.12842	+	22.4691i	0.305936	+	1.34039i	−0.555072	+	0.831802i	$0.687309\pi$
$282$		0			0
$283$	6.97028	+	2.15005i	0.414340	+	0.127807i	0.494915	−	0.868942i	$-0.335199\pi$
$283$	6.97028	+	2.15005i	0.414340	+	0.127807i	−0.0805744	+	0.996749i	$0.525675\pi$
$284$	0.446490	+	1.13764i	0.0264943	+	0.0675064i
$285$		0			0
$286$	4.13022	+	5.17914i	0.244225	+	0.306249i
$287$	−6.42976	+	0.527056i	−0.379537	+	0.0311111i
$288$		0			0
$289$	2.29702	−	5.85271i	0.135119	−	0.344277i
$290$	0.158634	−	2.11683i	0.00931533	−	0.124304i
$291$		0			0
$292$	−4.59605	+	4.26451i	−0.268963	+	0.249562i
$293$	10.7872			0.630196			0.315098	−	0.949059i	$-0.397963\pi$
$293$	10.7872			0.630196			0.315098	+	0.949059i	$0.397963\pi$
$294$		0			0
$295$	50.5515			2.94322
$296$	10.3144	−	9.57033i	0.599510	−	0.556264i
$297$		0			0
$298$	−0.654213	+	8.72987i	−0.0378976	+	0.505708i
$299$	4.31740	−	11.0006i	0.249682	−	0.636179i
$300$		0			0
$301$	4.34512	+	13.7447i	0.250448	+	0.792233i
$302$	6.94008	+	8.70258i	0.399356	+	0.500777i
$303$		0			0
$304$	6.94814	+	17.7036i	0.398503	+	1.01537i
$305$	−2.94146	−	0.907320i	−0.168427	−	0.0519530i
$306$		0			0
$307$	5.86375	+	25.6908i	0.334662	+	1.46625i	0.809991	+	0.586442i	$0.199472\pi$
$307$	5.86375	+	25.6908i	0.334662	+	1.46625i	−0.475329	+	0.879808i	$0.657671\pi$
$308$	−2.55818	−	3.69640i	−0.145766	−	0.210622i
$309$		0			0
$310$	−42.9996	−	6.48115i	−2.44222	−	0.368105i
$311$	−3.26235	+	2.22424i	−0.184991	+	0.126125i	−0.652275	−	0.757983i	$-0.726185\pi$
$311$	−3.26235	+	2.22424i	−0.184991	+	0.126125i	0.467284	+	0.884108i	$0.345233\pi$
$312$		0			0
$313$	−7.25731	−	12.5700i	−0.410207	−	0.710500i	0.584705	−	0.811246i	$-0.301210\pi$
$313$	−7.25731	−	12.5700i	−0.410207	−	0.710500i	−0.994912	+	0.100746i	$0.967877\pi$
$314$	−23.7999	−	11.4614i	−1.34311	−	0.646806i
$315$		0			0
$316$	11.7025	−	5.63564i	0.658319	−	0.317030i
$317$	10.0067	+	6.82245i	0.562032	+	0.383187i	0.810753	−	0.585388i	$-0.199058\pi$
$317$	10.0067	+	6.82245i	0.562032	+	0.383187i	−0.248721	+	0.968575i	$0.580010\pi$
$318$		0			0
$319$	−0.364632	−	0.338329i	−0.0204155	−	0.0189428i
$320$	−0.0302870	−	0.0206493i	−0.00169309	−	0.00115433i
$321$		0			0
$322$	−9.61350	+	20.3248i	−0.535739	+	1.13266i
$323$	16.5768	+	7.98295i	0.922356	+	0.444183i
$324$		0			0
$325$	10.7326	−	18.5894i	0.595338	−	1.03116i
$326$	9.98466	−	6.80743i	0.552999	−	0.377028i
$327$		0			0
$328$	0.852562	−	3.73532i	0.0470748	−	0.206248i
$329$	3.62910	+	22.9863i	0.200079	+	1.26728i
$330$		0			0
$331$	1.32769	+	17.7167i	0.0729762	+	0.973800i	0.906743	+	0.421684i	$0.138561\pi$
$331$	1.32769	+	17.7167i	0.0729762	+	0.973800i	−0.833767	+	0.552117i	$0.813820\pi$
$332$	7.77308	+	2.39768i	0.426603	+	0.131590i
$333$		0			0
$334$	−11.2408	+	3.46732i	−0.615067	+	0.189723i
$335$	29.6597	+	37.1921i	1.62048	+	2.03202i
$336$		0			0
$337$	3.59469	−	4.50760i	0.195815	−	0.245545i	−0.674224	−	0.738527i	$-0.735522\pi$
$337$	3.59469	−	4.50760i	0.195815	−	0.245545i	0.870039	+	0.492982i	$0.164093\pi$
$338$	4.50152	−	11.4697i	0.244850	−	0.623868i
$339$		0			0
$340$	19.6233	−	2.95774i	1.06422	−	0.160406i
$341$	−7.46959	+	6.93076i	−0.404501	+	0.375322i
$342$		0			0
$343$	−18.1383	−	3.74171i	−0.979379	−	0.202033i
$344$	−8.56104			−0.461580
$345$		0			0
$346$	−37.5652	+	5.66204i	−2.01952	+	0.304393i
$347$	−1.48889	+	19.8679i	−0.0799279	+	1.06656i	0.802667	+	0.596428i	$0.203414\pi$
$347$	−1.48889	+	19.8679i	−0.0799279	+	1.06656i	−0.882594	+	0.470135i	$0.844205\pi$
$348$		0			0
$349$	−10.7668	+	13.5012i	−0.576334	+	0.722700i	−0.981483	−	0.191550i	$-0.938648\pi$
$349$	−10.7668	+	13.5012i	−0.576334	+	0.722700i	0.405148	+	0.914251i	$0.367220\pi$
$350$	−22.7692	+	33.9030i	−1.21707	+	1.81219i
$351$		0			0
$352$	8.27645	−	2.55295i	0.441136	−	0.136073i
$353$	0.974430	+	2.48281i	0.0518637	+	0.132147i	0.954458	−	0.298346i	$-0.0964350\pi$
$353$	0.974430	+	2.48281i	0.0518637	+	0.132147i	−0.902594	+	0.430493i	$0.858340\pi$
$354$		0			0
$355$	−0.305465	−	4.07615i	−0.0162124	−	0.216340i
$356$	−4.06933	−	17.8289i	−0.215674	−	0.944929i
$357$		0			0
$358$	−4.59271	+	20.1220i	−0.242732	+	1.06348i
$359$	2.55918	+	0.385734i	0.135068	+	0.0203583i	0.216228	−	0.976343i	$-0.430624\pi$
$359$	2.55918	+	0.385734i	0.135068	+	0.0203583i	−0.0811602	+	0.996701i	$0.525863\pi$
$360$		0			0
$361$	2.23173	−	3.86548i	0.117460	−	0.203446i
$362$	7.71964	+	13.3708i	0.405735	+	0.702754i
$363$		0			0
$364$	3.07565	−	6.50251i	0.161208	−	0.340824i
$365$	18.8935	−	9.09864i	0.988932	−	0.476245i
$366$		0			0
$367$	−6.74234	−	6.25597i	−0.351947	−	0.326559i	0.484310	−	0.874896i	$-0.339071\pi$
$367$	−6.74234	−	6.25597i	−0.351947	−	0.326559i	−0.836257	+	0.548337i	$0.815261\pi$
$368$	−17.6236	−	16.3523i	−0.918692	−	0.852422i
$369$		0			0
$370$	52.7574	−	25.4066i	2.74273	−	1.32083i
$371$	−21.0047	−	16.5119i	−1.09051	−	0.857254i
$372$		0			0
$373$	14.6509	+	25.3760i	0.758593	+	1.31392i	0.943568	+	0.331178i	$0.107446\pi$
$373$	14.6509	+	25.3760i	0.758593	+	1.31392i	−0.184976	+	0.982743i	$0.559221\pi$
$374$	6.51882	−	11.2909i	0.337080	−	0.583840i
$375$		0			0
$376$	−13.6661	−	2.05983i	−0.704774	−	0.106228i
$377$	0.177115	−	0.775992i	0.00912190	−	0.0399656i
$378$		0			0
$379$	−3.13439	−	13.7327i	−0.161003	−	0.705400i	−0.989395	−	0.145251i	$-0.953601\pi$
$379$	−3.13439	−	13.7327i	−0.161003	−	0.705400i	0.828392	−	0.560149i	$-0.189256\pi$
$380$	1.17170	+	15.6353i	0.0601070	+	0.802072i
$381$		0			0
$382$	6.21627	+	15.8388i	0.318052	+	0.810383i
$383$	−7.35630	+	2.26912i	−0.375889	+	0.115946i	−0.476942	−	0.878935i	$-0.658255\pi$
$383$	−7.35630	+	2.26912i	−0.375889	+	0.115946i	0.101053	+	0.994881i	$0.467779\pi$
$384$		0			0
$385$	4.53202	+	14.3360i	0.230973	+	0.730629i
$386$	8.46573	−	10.6157i	0.430894	−	0.540324i
$387$		0			0
$388$	−0.839120	+	11.1973i	−0.0425999	+	0.568456i
$389$	6.88617	−	1.03792i	0.349143	−	0.0526248i	0.0278701	−	0.999612i	$-0.491128\pi$
$389$	6.88617	−	1.03792i	0.349143	−	0.0526248i	0.321273	+	0.946987i	$0.395889\pi$
$390$		0			0
$391$	−23.2584			−1.17623
$392$	5.36582	−	9.60134i	0.271015	−	0.484941i
$393$		0			0
$394$	16.3269	−	15.1492i	0.822540	−	0.763205i
$395$	−42.9581	+	6.47489i	−2.16146	+	0.325787i
$396$		0			0
$397$	−6.54571	+	16.6782i	−0.328520	+	0.837055i	0.667221	+	0.744860i	$0.267484\pi$
$397$	−6.54571	+	16.6782i	−0.328520	+	0.837055i	−0.995741	+	0.0921953i	$0.970612\pi$
$398$	−19.0407	+	23.8762i	−0.954422	+	1.19681i
$399$		0			0
$400$	−27.2270	−	34.1416i	−1.36135	−	1.70708i
$401$	−29.8365	+	9.20333i	−1.48996	+	0.459593i	−0.929574	−	0.368637i	$-0.879825\pi$
$401$	−29.8365	+	9.20333i	−1.48996	+	0.459593i	−0.560389	+	0.828229i	$0.689348\pi$
$402$		0			0
$403$	−15.5808	−	4.80604i	−0.776136	−	0.239406i
$404$	−1.22550	−	16.3531i	−0.0609708	−	0.813598i
$405$		0			0
$406$	−0.436241	+	1.45016i	−0.0216503	+	0.0719704i
$407$	3.05326	−	13.3772i	0.151344	−	0.663083i
$408$		0			0
$409$	26.8912	−	18.3341i	1.32968	−	0.906562i	0.330378	−	0.943849i	$-0.392824\pi$
$409$	26.8912	−	18.3341i	1.32968	−	0.906562i	0.999305	+	0.0372863i	$0.0118713\pi$
$410$	7.97244	−	13.8087i	0.393731	−	0.681962i
$411$		0			0
$412$	−4.35695	−	2.09819i	−0.214651	−	0.103371i
$413$	−35.2140	−	7.77886i	−1.73277	−	0.382773i
$414$		0			0
$415$	−22.4796	−	15.3263i	−1.10348	−	0.752339i
$416$	10.1597	+	9.42680i	0.498119	+	0.462187i
$417$		0			0
$418$	8.51090	+	5.80263i	0.416282	+	0.283816i
$419$	−10.8281	+	5.21453i	−0.528986	+	0.254746i	−0.679260	−	0.733898i	$-0.737699\pi$
$419$	−10.8281	+	5.21453i	−0.528986	+	0.254746i	0.150273	+	0.988644i	$0.451985\pi$
$420$		0			0
$421$	20.5266	+	9.88509i	1.00041	+	0.481770i	0.861076	−	0.508476i	$-0.169791\pi$
$421$	20.5266	+	9.88509i	1.00041	+	0.481770i	0.139329	+	0.990246i	$0.455505\pi$
$422$	−15.5597	−	26.9503i	−0.757436	−	1.31192i
$423$		0			0
$424$	13.1103	−	8.93844i	0.636692	−	0.434089i
$425$	−41.7746	−	6.29651i	−2.02637	−	0.305425i
$426$		0			0
$427$	1.90939	+	1.08467i	0.0924019	+	0.0524907i
$428$	−2.46206	−	10.7870i	−0.119008	−	0.521408i
$429$		0			0
$430$	−34.0452	−	10.5016i	−1.64181	−	0.506431i
$431$	8.63029	+	21.9896i	0.415707	+	1.05920i	0.973391	+	0.229150i	$0.0735947\pi$
$431$	8.63029	+	21.9896i	0.415707	+	1.05920i	−0.557684	+	0.830053i	$0.688310\pi$
$432$		0			0
$433$	−24.3742	−	30.5643i	−1.17135	−	1.46883i	−0.853812	−	0.520582i	$-0.825715\pi$
$433$	−24.3742	−	30.5643i	−1.17135	−	1.46883i	−0.317539	−	0.948245i	$-0.602856\pi$
$434$	28.9561	+	11.1315i	1.38994	+	0.534330i
$435$		0			0
$436$	2.07796	−	5.29454i	0.0995160	−	0.253563i
$437$	1.37324	−	18.3246i	0.0656908	−	0.876583i
$438$		0			0
$439$	−23.2822	+	21.6027i	−1.11120	+	1.03104i	−0.111895	+	0.993720i	$0.535692\pi$
$439$	−23.2822	+	21.6027i	−1.11120	+	1.03104i	−0.999303	+	0.0373216i	$0.988117\pi$
$440$	−8.92930			−0.425687
$441$		0			0
$442$	20.8624			0.992322
$443$	20.0415	−	18.5958i	0.952203	−	0.883515i	−0.0410884	−	0.999156i	$-0.513083\pi$
$443$	20.0415	−	18.5958i	0.952203	−	0.883515i	0.993291	+	0.115641i	$0.0368921\pi$
$444$		0			0
$445$	−4.57089	+	60.9942i	−0.216681	+	2.89140i
$446$	2.82925	−	7.20881i	0.133969	−	0.341347i
$447$		0			0
$448$	0.0179203	+	0.0190448i	0.000846654	+	0.000899782i
$449$	−18.4433	−	23.1271i	−0.870392	−	1.09144i	−0.995064	−	0.0992386i	$-0.968359\pi$
$449$	−18.4433	−	23.1271i	−0.870392	−	1.09144i	0.124672	−	0.992198i	$-0.460212\pi$
$450$		0			0
$451$	−1.36502	−	3.47801i	−0.0642762	−	0.163773i
$452$	12.1833	+	3.75805i	0.573054	+	0.176764i
$453$		0			0
$454$	−4.34512	−	19.0372i	−0.203926	−	0.893460i
$455$	−16.2406	+	17.7504i	−0.761369	+	0.832150i
$456$		0			0
$457$	11.1968	+	1.68765i	0.523766	+	0.0789450i	0.405603	−	0.914049i	$-0.367061\pi$
$457$	11.1968	+	1.68765i	0.523766	+	0.0789450i	0.118163	+	0.992994i	$0.462300\pi$
$458$	−22.5335	+	15.3631i	−1.05292	+	0.717870i
$459$		0			0
$460$	−9.91015	−	17.1649i	−0.462063	−	0.800317i
$461$	−2.81159	−	1.35399i	−0.130949	−	0.0630617i	0.367262	−	0.930117i	$-0.380295\pi$
$461$	−2.81159	−	1.35399i	−0.130949	−	0.0630617i	−0.498211	+	0.867056i	$0.666009\pi$
$462$		0			0
$463$	23.4297	−	11.2832i	1.08887	−	0.524373i	0.198729	−	0.980054i	$-0.436319\pi$
$463$	23.4297	−	11.2832i	1.08887	−	0.524373i	0.890143	+	0.455681i	$0.150604\pi$
$464$	−1.33791	−	0.912169i	−0.0621107	−	0.0423464i
$465$		0			0
$466$	9.22426	+	8.55886i	0.427305	+	0.396482i
$467$	15.5444	+	10.5980i	0.719307	+	0.490415i	0.866805	−	0.498647i	$-0.166170\pi$
$467$	15.5444	+	10.5980i	0.719307	+	0.490415i	−0.147498	+	0.989062i	$0.547122\pi$
$468$		0			0
$469$	−14.9377	−	30.4719i	−0.689761	−	1.40706i
$470$	−51.8201	−	24.9552i	−2.39028	−	1.15110i
$471$		0			0
$472$	10.7087	−	18.5480i	0.492908	−	0.853742i
$473$	−6.89791	+	4.70291i	−0.317166	+	0.216240i
$474$		0			0
$475$	7.42731	−	32.5412i	0.340788	−	1.49309i
$476$	−14.1247	−	0.959281i	−0.647403	−	0.0439686i
$477$		0			0
$478$	1.14666	+	15.3011i	0.0524471	+	0.699858i
$479$	3.56428	+	1.09944i	0.162856	+	0.0502345i	0.375111	−	0.926980i	$-0.377605\pi$
$479$	3.56428	+	1.09944i	0.162856	+	0.0502345i	−0.212255	+	0.977214i	$0.568081\pi$
$480$		0			0
$481$	20.9808	−	6.47171i	0.956640	−	0.295084i
$482$	1.55800	+	1.95367i	0.0709649	+	0.0889872i
$483$		0			0
$484$	−5.98163	+	7.50073i	−0.271892	+	0.340942i
$485$	13.7208	−	34.9601i	0.623031	−	1.58746i
$486$		0			0
$487$	−21.5102	+	3.24214i	−0.974719	+	0.146915i	−0.617042	−	0.786930i	$-0.711669\pi$
$487$	−21.5102	+	3.24214i	−0.974719	+	0.146915i	−0.357677	+	0.933845i	$0.616431\pi$
$488$	−0.956019	+	0.887056i	−0.0432770	+	0.0401551i
$489$		0			0
$490$	33.1163	−	31.6002i	1.49604	−	1.42755i
$491$	28.2597			1.27534			0.637671	−	0.770309i	$-0.279898\pi$
$491$	28.2597			1.27534			0.637671	+	0.770309i	$0.279898\pi$
$492$		0			0
$493$	−1.54904	+	0.233480i	−0.0697652	+	0.0105154i
$494$	−1.23177	+	16.4368i	−0.0554200	+	0.739528i
$495$		0			0
$496$	−20.6819	+	25.9343i	−0.928646	+	1.16448i
$497$	−0.414451	+	2.88644i	−0.0185907	+	0.129474i
$498$		0			0
$499$	−24.5279	+	7.56585i	−1.09802	+	0.338694i	−0.790261	−	0.612771i	$-0.790055\pi$
$499$	−24.5279	+	7.56585i	−1.09802	+	0.338694i	−0.307758	+	0.951465i	$0.599579\pi$
$500$	−5.64078	−	14.3725i	−0.252263	−	0.642757i
$501$		0			0
$502$	−0.0682478	−	0.910703i	−0.00304605	−	0.0406467i
$503$	1.98012	+	8.67545i	0.0882890	+	0.386819i	0.999695	−	0.0246886i	$-0.00785942\pi$
$503$	1.98012	+	8.67545i	0.0882890	+	0.386819i	−0.911406	+	0.411508i	$0.865002\pi$
$504$		0			0
$505$	−12.2051	+	53.4740i	−0.543119	+	2.37956i
$506$	−12.8760	−	1.94074i	−0.572408	−	0.0862766i
$507$		0			0
$508$	−8.78336	+	15.2132i	−0.389699	+	0.674978i
$509$	9.34843	+	16.1920i	0.414362	+	0.717696i	0.995361	−	0.0962082i	$-0.0306715\pi$
$509$	9.34843	+	16.1920i	0.414362	+	0.717696i	−0.580999	+	0.813904i	$0.697338\pi$
$510$		0			0
$511$	−14.5613	+	3.43075i	−0.644152	+	0.151767i
$512$	11.2800	−	5.43218i	0.498512	−	0.240071i
$513$		0			0
$514$	7.69047	+	7.13572i	0.339212	+	0.314743i
$515$	11.8566	+	11.0013i	0.522464	+	0.484776i
$516$		0			0
$517$	−12.1427	+	5.84764i	−0.534037	+	0.257179i
$518$	−40.6602	+	9.57987i	−1.78651	+	0.420915i
$519$		0			0
$520$	−7.14417	−	12.3741i	−0.313293	−	0.542639i
$521$	−0.924888	+	1.60195i	−0.0405201	+	0.0701829i	−0.885574	−	0.464498i	$-0.846235\pi$
$521$	−0.924888	+	1.60195i	−0.0405201	+	0.0701829i	0.845054	+	0.534681i	$0.179568\pi$
$522$		0			0
$523$	0.816930	+	0.123132i	0.0357219	+	0.00538420i	0.166879	−	0.985977i	$-0.446631\pi$
$523$	0.816930	+	0.123132i	0.0357219	+	0.00538420i	−0.131157	+	0.991362i	$0.541869\pi$
$524$	−0.537692	+	2.35578i	−0.0234892	+	0.102913i
$525$		0			0
$526$	−0.313674	−	1.37429i	−0.0136768	−	0.0599221i
$527$	2.39815	+	32.0011i	0.104465	+	1.39399i
$528$		0			0
$529$	0.0838221	+	0.213575i	0.00364444	+	0.00928588i
$530$	63.1011	−	19.4641i	2.74093	−	0.845466i
$531$		0			0
$532$	1.58975	−	11.0718i	0.0689243	−	0.480022i
$533$	3.72764	−	4.67431i	0.161462	−	0.202467i
$534$		0			0
$535$	−2.76551	+	36.9032i	−0.119564	+	1.59546i
$536$	19.9293	−	3.00386i	0.860816	−	0.129747i
$537$		0			0
$538$	−17.1993			−0.741515
$539$	−0.950974	−	10.6838i	−0.0409614	−	0.460183i
$540$		0			0
$541$	3.86840	−	3.58935i	0.166316	−	0.154318i	−0.592624	−	0.805479i	$-0.701908\pi$
$541$	3.86840	−	3.58935i	0.166316	−	0.154318i	0.758940	+	0.651161i	$0.225718\pi$
$542$	−3.88842	+	0.586085i	−0.167022	+	0.0251745i
$543$		0			0
$544$	9.96549	−	25.3916i	0.427267	−	1.08866i
$545$	−11.8610	+	14.8732i	−0.508068	+	0.637098i
$546$		0			0
$547$	7.51384	+	9.42206i	0.321269	+	0.402858i	0.916072	−	0.401013i	$-0.131342\pi$
$547$	7.51384	+	9.42206i	0.321269	+	0.402858i	−0.594804	+	0.803871i	$0.702770\pi$
$548$	−2.74785	+	0.847598i	−0.117382	+	0.0362076i
$549$		0			0
$550$	−22.6013	−	6.97158i	−0.963723	−	0.297269i
$551$	−0.0924924	−	1.23423i	−0.00394031	−	0.0525798i
$552$		0			0
$553$	30.9208	+	2.10000i	1.31489	+	0.0893009i
$554$	−3.06366	+	13.4227i	−0.130162	+	0.570278i
$555$		0			0
$556$	10.9013	−	7.43238i	0.462318	−	0.315203i
$557$	−10.9839	+	19.0247i	−0.465404	+	0.806103i	−0.999220	−	0.0394978i	$-0.987424\pi$
$557$	−10.9839	+	19.0247i	−0.465404	+	0.806103i	0.533816	+	0.845601i	$0.320758\pi$
$558$		0			0
$559$	−12.0361	−	5.79628i	−0.509073	−	0.245157i
$560$	21.5442	+	43.9487i	0.910410	+	1.85717i
$561$		0			0
$562$	33.5751	+	22.8911i	1.41628	+	0.965604i
$563$	−3.71871	−	3.45046i	−0.156725	−	0.145419i	0.597913	−	0.801561i	$-0.295997\pi$
$563$	−3.71871	−	3.45046i	−0.156725	−	0.145419i	−0.754638	+	0.656142i	$0.772187\pi$
$564$		0			0
$565$	−35.2338	−	24.0220i	−1.48230	−	1.01061i
$566$	11.5877	−	5.58032i	0.487066	−	0.234558i
$567$		0			0
$568$	−1.56030	−	0.751403i	−0.0654689	−	0.0315282i
$569$	11.8056	+	20.4479i	0.494916	+	0.857219i	0.999983	−	0.00586077i	$-0.00186555\pi$
$569$	11.8056	+	20.4479i	0.494916	+	0.857219i	−0.505067	+	0.863080i	$0.668532\pi$
$570$		0			0
$571$	−33.7234	+	22.9922i	−1.41128	+	0.962194i	−0.412595	+	0.910915i	$0.635378\pi$
$571$	−33.7234	+	22.9922i	−1.41128	+	0.962194i	−0.998684	+	0.0512795i	$0.983670\pi$
$572$	4.11942	+	0.620902i	0.172241	+	0.0259612i
$573$		0			0
$574$	−7.67845	+	8.39227i	−0.320492	+	0.350287i
$575$	9.38903	+	41.1360i	0.391549	+	1.71549i
$576$		0			0
$577$	14.2656	+	4.40034i	0.593883	+	0.183189i	0.577104	−	0.816671i	$-0.304183\pi$
$577$	14.2656	+	4.40034i	0.593883	+	0.183189i	0.0167788	+	0.999859i	$0.494659\pi$
$578$	−4.05008	−	10.3194i	−0.168461	−	0.429232i
$579$		0			0
$580$	−0.832340	−	1.04372i	−0.0345610	−	0.0433382i
$581$	13.3008	+	14.1354i	0.551809	+	0.586435i
$582$		0			0
$583$	5.65315	−	14.4040i	0.234129	−	0.596552i
$584$	0.663944	−	8.85972i	0.0274742	−	0.366618i
$585$		0			0
$586$	13.9426	−	12.9368i	0.575963	−	0.534415i
$587$	−7.84343			−0.323733			−0.161867	−	0.986813i	$-0.551751\pi$
$587$	−7.84343			−0.323733			−0.161867	+	0.986813i	$0.551751\pi$
$588$		0			0
$589$	−25.3543			−1.04471
$590$	65.3384	−	60.6251i	2.68994	−	2.49590i
$591$		0			0
$592$	3.33801	−	44.5427i	0.137191	−	1.83069i
$593$	13.6329	−	34.7360i	0.559835	−	1.42644i	−0.318285	−	0.947995i	$-0.603107\pi$
$593$	13.6329	−	34.7360i	0.559835	−	1.42644i	0.878120	−	0.478440i	$-0.158798\pi$
$594$		0			0
$595$	44.1978	+	16.9909i	1.81193	+	0.696558i
$596$	3.43260	+	4.30434i	0.140605	+	0.176313i
$597$		0			0
$598$	−7.61240	−	19.3961i	−0.311294	−	0.793165i
$599$	−29.2778	−	9.03099i	−1.19626	−	0.368996i	−0.368257	−	0.929724i	$-0.620045\pi$
$599$	−29.2778	−	9.03099i	−1.19626	−	0.368996i	−0.828000	+	0.560728i	$0.810521\pi$
$600$		0			0
$601$	−5.56614	−	24.3868i	−0.227048	−	0.994760i	−0.952033	−	0.305996i	$-0.901011\pi$
$601$	−5.56614	−	24.3868i	−0.227048	−	0.994760i	0.724985	−	0.688764i	$-0.241847\pi$
$602$	22.0998	+	12.5542i	0.900721	+	0.511672i
$603$		0			0
$604$	6.92192	+	1.04331i	0.281649	+	0.0424517i
$605$	26.5124	−	18.0758i	1.07788	−	0.734888i
$606$		0			0
$607$	8.15727	+	14.1288i	0.331093	+	0.573470i	0.982726	−	0.185064i	$-0.0592492\pi$
$607$	8.15727	+	14.1288i	0.331093	+	0.573470i	−0.651633	+	0.758534i	$0.725916\pi$
$608$	19.4169	+	9.35070i	0.787460	+	0.379221i
$609$		0			0
$610$	−4.88999	+	2.35490i	−0.197990	+	0.0953469i
$611$	−17.8187	−	12.1486i	−0.720869	−	0.491480i
$612$		0			0
$613$	30.0431	+	27.8760i	1.21343	+	1.12590i	0.988452	+	0.151536i	$0.0484220\pi$
$613$	30.0431	+	27.8760i	1.21343	+	1.12590i	0.224979	+	0.974364i	$0.427769\pi$
$614$	38.3892	+	26.1733i	1.54926	+	1.05627i
$615$		0			0
$616$	6.22011	+	1.37404i	0.250615	+	0.0553615i
$617$	23.5649	+	11.3482i	0.948685	+	0.456863i	0.843225	−	0.537561i	$-0.180654\pi$
$617$	23.5649	+	11.3482i	0.948685	+	0.456863i	0.105460	+	0.994424i	$0.466368\pi$
$618$		0			0
$619$	−16.1668	+	28.0017i	−0.649798	+	1.12548i	0.333373	+	0.942795i	$0.391813\pi$
$619$	−16.1668	+	28.0017i	−0.649798	+	1.12548i	−0.983171	+	0.182688i	$0.941520\pi$
$620$	−22.5953	+	15.4052i	−0.907449	+	0.618688i
$621$		0			0
$622$	−1.54916	+	6.78730i	−0.0621156	+	0.272146i
$623$	12.5698	−	41.7850i	0.503600	−	1.67408i
$624$		0			0
$625$	0.588015	+	7.84652i	0.0235206	+	0.313861i
$626$	−24.4550	−	7.54338i	−0.977420	−	0.301494i
$627$		0			0
$628$	−15.8745	+	4.89662i	−0.633460	+	0.195396i
$629$	−26.9427	−	33.7851i	−1.07428	−	1.34710i
$630$		0			0
$631$	20.6736	−	25.9239i	0.823004	−	1.03201i	−0.175863	−	0.984415i	$-0.556272\pi$
$631$	20.6736	−	25.9239i	0.823004	−	1.03201i	0.998867	−	0.0475993i	$-0.0151571\pi$
$632$	−6.72441	+	17.1335i	−0.267483	+	0.681535i
$633$		0			0
$634$	21.1157	−	3.18268i	0.838613	−	0.126401i
$635$	43.0704	−	39.9635i	1.70920	−	1.58590i
$636$		0			0
$637$	14.0445	−	9.86574i	0.556464	−	0.390895i
$638$	−0.877041			−0.0347224
$639$		0			0
$640$	−41.5225	+	6.25851i	−1.64132	+	0.247389i
$641$	2.07077	−	27.6326i	0.0817906	−	1.09142i	−0.793740	−	0.608257i	$-0.791869\pi$
$641$	2.07077	−	27.6326i	0.0817906	−	1.09142i	0.875530	−	0.483163i	$-0.160512\pi$
$642$		0			0
$643$	−8.52919	+	10.6953i	−0.336358	+	0.421780i	−0.921031	−	0.389489i	$-0.872651\pi$
$643$	−8.52919	+	10.6953i	−0.336358	+	0.421780i	0.584673	+	0.811269i	$0.301223\pi$
$644$	4.26205	+	13.4820i	0.167948	+	0.531264i
$645$		0			0
$646$	30.9994	−	9.56205i	1.21965	−	0.376214i
$647$	−5.97551	−	15.2254i	−0.234922	−	0.598570i	0.763989	−	0.645229i	$-0.223238\pi$
$647$	−5.97551	−	15.2254i	−0.234922	−	0.598570i	−0.998911	+	0.0466584i	$0.985143\pi$
$648$		0			0
$649$	−1.56080	−	20.8275i	−0.0612669	−	0.817550i
$650$	−8.42180	−	36.8983i	−0.330330	−	1.44727i
$651$		0			0
$652$	1.69110	−	7.40918i	0.0662284	−	0.290166i
$653$	−11.9605	−	1.80276i	−0.468051	−	0.0705474i	−0.0892176	−	0.996012i	$-0.528437\pi$
$653$	−11.9605	−	1.80276i	−0.468051	−	0.0705474i	−0.378834	+	0.925465i	$0.623675\pi$
$654$		0			0
$655$	4.04097	−	6.99917i	0.157894	−	0.273480i
$656$	−6.08149	−	10.5334i	−0.237442	−	0.411262i
$657$		0			0
$658$	32.2575	+	25.3578i	1.25753	+	0.988549i
$659$	−14.7861	+	7.12063i	−0.575986	+	0.277380i	−0.699114	−	0.715010i	$-0.746422\pi$
$659$	−14.7861	+	7.12063i	−0.575986	+	0.277380i	0.123127	+	0.992391i	$0.460708\pi$
$660$		0			0
$661$	2.83118	+	2.62696i	0.110120	+	0.102177i	0.733312	−	0.679893i	$-0.237974\pi$
$661$	2.83118	+	2.62696i	0.110120	+	0.102177i	−0.623191	+	0.782070i	$0.714164\pi$
$662$	22.9633	+	21.3068i	0.892493	+	0.828113i
$663$		0			0
$664$	−10.3854	+	5.00137i	−0.403034	+	0.194091i
$665$	−15.9962	+	33.8189i	−0.620304	+	1.31144i
$666$		0			0
$667$	0.782293	+	1.35497i	0.0302905	+	0.0524647i
$668$	−3.69889	+	6.40667i	−0.143114	+	0.247882i
$669$		0			0
$670$	82.9391	+	12.5011i	3.20422	+	0.482958i
$671$	−0.283001	+	1.23991i	−0.0109251	+	0.0478661i
$672$		0			0
$673$	−3.31065	−	14.5049i	−0.127616	−	0.559122i	−0.997794	−	0.0663849i	$-0.978853\pi$
$673$	−3.31065	−	14.5049i	−0.127616	−	0.559122i	0.870178	−	0.492737i	$-0.164004\pi$
$674$	−0.759674	−	10.1371i	−0.0292615	−	0.390468i
$675$		0			0
$676$	−2.83093	−	7.21308i	−0.108882	−	0.277426i
$677$	−21.9247	+	6.76288i	−0.842635	+	0.259918i	−0.685876	−	0.727718i	$-0.740581\pi$
$677$	−21.9247	+	6.76288i	−0.842635	+	0.259918i	−0.156759	+	0.987637i	$0.550105\pi$
$678$		0			0
$679$	−14.9375	+	22.2417i	−0.573250	+	0.853559i
$680$	−17.5334	+	21.9862i	−0.672375	+	0.843132i
$681$		0			0
$682$	−1.34263	+	17.9162i	−0.0514120	+	0.686045i
$683$	47.2922	−	7.12816i	1.80959	−	0.272751i	0.844667	−	0.535292i	$-0.179799\pi$
$683$	47.2922	−	7.12816i	1.80959	−	0.272751i	0.964921	+	0.262541i	$0.0845605\pi$
$684$		0			0
$685$	9.61793			0.367482
$686$	−27.9313	+	16.9167i	−1.06642	+	0.645881i
$687$		0			0
$688$	−19.9226	+	18.4855i	−0.759542	+	0.704752i
$689$	24.4838	−	3.69033i	0.932757	−	0.140591i
$690$		0			0
$691$	−8.01919	+	20.4326i	−0.305064	+	0.777291i	0.693329	+	0.720621i	$0.256143\pi$
$691$	−8.01919	+	20.4326i	−0.305064	+	0.777291i	−0.998393	+	0.0566696i	$0.981952\pi$
$692$	−14.8957	+	18.6787i	−0.566251	+	0.710057i
$693$		0			0
$694$	21.9026	+	27.4650i	0.831412	+	1.04256i
$695$	−42.1687	+	13.0073i	−1.59955	+	0.493396i
$696$		0			0
$697$	−11.2441	−	3.46834i	−0.425900	−	0.131373i
$698$	2.27537	+	30.3627i	0.0861241	+	1.14925i
$699$		0			0
$700$	4.00527	+	25.3689i	0.151385	+	0.958855i
$701$	−7.92279	+	34.7120i	−0.299240	+	1.31106i	0.572023	+	0.820238i	$0.306159\pi$
$701$	−7.92279	+	34.7120i	−0.299240	+	1.31106i	−0.871263	+	0.490817i	$0.836698\pi$
$702$		0			0
$703$	28.2091	−	19.2326i	1.06392	−	0.725372i
$704$	−0.00757249	+	0.0131159i	−0.000285399	+	0.000494326i
$705$		0			0
$706$	4.23703	+	2.04044i	0.159463	+	0.0767932i
$707$	16.7306	−	35.3716i	0.629218	−	1.33029i
$708$		0			0
$709$	5.69323	+	3.88158i	0.213814	+	0.145776i	0.665492	−	0.746405i	$-0.268222\pi$
$709$	5.69323	+	3.88158i	0.213814	+	0.145776i	−0.451678	+	0.892181i	$0.649174\pi$
$710$	−5.28324	−	4.90213i	−0.198277	−	0.183974i
$711$		0			0
$712$	21.4113	+	14.5980i	0.802423	+	0.547083i
$713$	28.8769	−	13.9064i	1.08145	−	0.520798i
$714$		0			0
$715$	−12.5538	−	6.04561i	−0.469487	−	0.226093i
$716$	6.48990	+	11.2408i	0.242539	+	0.420090i
$717$		0			0
$718$	3.77036	−	2.57059i	0.140709	−	0.0959335i
$719$	12.9449	+	1.95112i	0.482762	+	0.0727647i	0.385914	−	0.922535i	$-0.373886\pi$
$719$	12.9449	+	1.95112i	0.482762	+	0.0727647i	0.0968475	+	0.995299i	$0.469124\pi$
$720$		0			0
$721$	−6.56638	−	9.48797i	−0.244545	−	0.353350i
$722$	−1.75123	−	7.67262i	−0.0651739	−	0.285546i
$723$		0			0
$724$	9.27813	+	2.86192i	0.344819	+	0.106363i
$725$	1.03827	+	2.64546i	0.0385603	+	0.0982500i
$726$		0			0
$727$	20.7873	+	26.0664i	0.770958	+	0.966750i	0.999978	−	0.00667133i	$-0.00212357\pi$
$727$	20.7873	+	26.0664i	0.770958	+	0.966750i	−0.229020	+	0.973422i	$0.573552\pi$
$728$	3.07248	+	9.71907i	0.113874	+	0.360213i
$729$		0			0
$730$	13.5083	−	34.4186i	0.499965	−	1.27389i
$731$	−1.96484	+	26.2189i	−0.0726722	+	0.969743i
$732$		0			0
$733$	26.1585	−	24.2716i	0.966188	−	0.896491i	−0.0284828	−	0.999594i	$-0.509068\pi$
$733$	26.1585	−	24.2716i	0.966188	−	0.896491i	0.994671	+	0.103103i	$0.0328771\pi$
$734$	−16.2172			−0.598586
$735$		0			0
$736$	−27.2433			−1.00420
$737$	14.4076	−	13.3683i	0.530710	−	0.492427i
$738$		0			0
$739$	2.92618	−	39.0472i	0.107641	−	1.43637i	−0.638006	−	0.770032i	$-0.720240\pi$
$739$	2.92618	−	39.0472i	0.107641	−	1.43637i	0.745647	−	0.666341i	$-0.232141\pi$
$740$	13.4537	−	34.2795i	0.494568	−	1.26014i
$741$		0			0
$742$	−46.9511	+	3.84864i	−1.72363	+	0.141288i
$743$	−10.4863	−	13.1494i	−0.384704	−	0.482404i	0.551343	−	0.834279i	$-0.314116\pi$
$743$	−10.4863	−	13.1494i	−0.384704	−	0.482404i	−0.936047	+	0.351875i	$0.885544\pi$
$744$		0			0
$745$	−6.72737	−	17.1411i	−0.246472	−	0.628000i
$746$	49.3692	+	15.2284i	1.80753	+	0.557550i
$747$		0			0
$748$	−1.82448	−	7.99358i	−0.0667097	−	0.292274i
$749$	7.60510	−	25.2811i	0.277884	−	0.923750i
$750$		0			0
$751$	2.48062	+	0.373893i	0.0905190	+	0.0136435i	0.194146	−	0.980973i	$-0.437807\pi$
$751$	2.48062	+	0.373893i	0.0905190	+	0.0136435i	−0.103627	+	0.994616i	$0.533045\pi$
$752$	−36.2504	+	24.7151i	−1.32191	+	0.901266i
$753$		0			0
$754$	−0.701704	−	1.21539i	−0.0255546	−	0.0442618i
$755$	−21.0944	−	10.1585i	−0.767704	−	0.369707i
$756$		0			0
$757$	8.89451	−	4.28337i	0.323276	−	0.155682i	−0.265206	−	0.964192i	$-0.585440\pi$
$757$	8.89451	−	4.28337i	0.323276	−	0.155682i	0.588482	+	0.808510i	$0.299726\pi$
$758$	−20.5205	−	13.9906i	−0.745337	−	0.508162i
$759$		0			0
$760$	−16.2870	−	15.1122i	−0.590793	−	0.548176i
$761$	8.92521	+	6.08511i	0.323539	+	0.220585i	0.714187	−	0.699955i	$-0.246797\pi$
$761$	8.92521	+	6.08511i	0.323539	+	0.220585i	−0.390648	+	0.920540i	$0.627749\pi$
$762$		0			0
$763$	10.5510	−	8.53545i	0.381972	−	0.309004i
$764$	9.64074	+	4.64274i	0.348790	+	0.167968i
$765$		0			0
$766$	−6.78679	+	11.7551i	−0.245217	+	0.424728i
$767$	27.6136	−	18.8266i	0.997068	−	0.679790i
$768$		0			0
$769$	10.6919	−	46.8444i	0.385561	−	1.68925i	−0.294139	−	0.955763i	$-0.595033\pi$
$769$	10.6919	−	46.8444i	0.385561	−	1.68925i	0.679700	−	0.733490i	$-0.262110\pi$
$770$	23.0504	+	13.0943i	0.830680	+	0.471884i
$771$		0			0
$772$	−0.638117	−	8.51508i	−0.0229663	−	0.306464i
$773$	−21.4724	−	6.62337i	−0.772310	−	0.238226i	−0.116539	−	0.993186i	$-0.537180\pi$
$773$	−21.4724	−	6.62337i	−0.772310	−	0.238226i	−0.655771	+	0.754960i	$0.727656\pi$
$774$		0			0
$775$	55.6309	−	17.1598i	1.99832	−	0.616400i
$776$	−9.92074	−	12.4402i	−0.356134	−	0.446578i
$777$		0			0
$778$	7.65569	−	9.59993i	0.274470	−	0.344174i
$779$	3.39648	−	8.65409i	0.121691	−	0.310065i
$780$		0			0
$781$	−1.66996	+	0.251706i	−0.0597560	+	0.00900676i
$782$	−30.0617	+	27.8932i	−1.07500	+	0.997457i
$783$		0			0
$784$	−8.24482	−	33.9297i	−0.294458	−	1.21178i
$785$	55.5633			1.98314
$786$		0			0
$787$	−22.4600	+	3.38531i	−0.800614	+	0.120673i	−0.536590	−	0.843843i	$-0.680288\pi$
$787$	−22.4600	+	3.38531i	−0.800614	+	0.120673i	−0.264024	+	0.964516i	$0.585050\pi$
$788$	1.04673	−	13.9677i	0.0372883	−	0.497578i
$789$		0			0
$790$	−47.7586	+	59.8874i	−1.69918	+	2.13070i
$791$	20.8472	+	22.1554i	0.741243	+	0.787756i
$792$		0			0
$793$	−1.94467	+	0.599851i	−0.0690572	+	0.0213013i
$794$	11.5413	+	29.4068i	0.409587	+	1.04361i
$795$		0			0
$796$	1.43522	+	19.1517i	0.0508700	+	0.678812i
$797$	0.220958	+	0.968080i	0.00782673	+	0.0342912i	0.978691	−	0.205341i	$-0.0658303\pi$
$797$	0.220958	+	0.968080i	0.00782673	+	0.0342912i	−0.970864	+	0.239632i	$0.922973\pi$
$798$		0			0
$799$	−9.44490	+	41.3808i	−0.334137	+	1.46395i
$800$	−48.9320	−	7.37530i	−1.73001	−	0.260756i
$801$		0			0
$802$	−27.5266	+	47.6775i	−0.971999	+	1.68355i
$803$	−4.33203	−	7.50330i	−0.152874	−	0.264786i
$804$		0			0
$805$	−0.330507	−	47.2911i	−0.0116488	−	1.66679i
$806$	−25.9021	+	12.4738i	−0.912363	+	0.439371i
$807$		0			0
$808$	17.0348	+	15.8060i	0.599283	+	0.556053i
$809$	−1.76852	−	1.64095i	−0.0621780	−	0.0576928i	0.648472	−	0.761239i	$-0.275408\pi$
$809$	−1.76852	−	1.64095i	−0.0621780	−	0.0576928i	−0.710650	+	0.703546i	$0.751599\pi$
$810$		0			0
$811$	21.8023	−	10.4994i	0.765581	−	0.368684i	−0.00998586	−	0.999950i	$-0.503179\pi$
$811$	21.8023	−	10.4994i	0.765581	−	0.368684i	0.775566	+	0.631266i	$0.217464\pi$
$812$	0.419197	+	0.855132i	0.0147109	+	0.0300093i
$813$		0			0
$814$	−12.0966	−	20.9519i	−0.423984	−	0.734362i
$815$	−12.7093	+	22.0131i	−0.445186	+	0.771085i
$816$		0			0
$817$	−20.5411	−	3.09607i	−0.718642	−	0.108318i
$818$	12.7695	−	55.9469i	0.446475	−	1.95614i
$819$		0			0
$820$	−2.23132	−	9.77605i	−0.0779211	−	0.341395i
$821$	−2.33086	−	31.1032i	−0.0813477	−	1.08551i	−0.877234	−	0.480063i	$-0.840614\pi$
$821$	−2.33086	−	31.1032i	−0.0813477	−	1.08551i	0.795886	−	0.605446i	$-0.207005\pi$
$822$		0			0
$823$	17.0660	+	43.4836i	0.594885	+	1.51574i	0.837958	+	0.545734i	$0.183749\pi$
$823$	17.0660	+	43.4836i	0.594885	+	1.51574i	−0.243074	+	0.970008i	$0.578156\pi$
$824$	6.54820	−	2.01985i	0.228117	−	0.0703649i
$825$		0			0
$826$	−54.8434	+	32.1770i	−1.90825	+	1.11958i
$827$	7.74360	−	9.71016i	0.269271	−	0.337655i	−0.628750	−	0.777607i	$-0.716433\pi$
$827$	7.74360	−	9.71016i	0.269271	−	0.337655i	0.898021	+	0.439952i	$0.145005\pi$
$828$		0			0
$829$	−2.15466	+	28.7519i	−0.0748344	+	0.998595i	0.825785	+	0.563986i	$0.190733\pi$
$829$	−2.15466	+	28.7519i	−0.0748344	+	0.998595i	−0.900619	+	0.434610i	$0.856886\pi$
$830$	−47.4355	+	7.14976i	−1.64651	+	0.248172i
$831$		0			0
$832$	−0.0242345			−0.000840178
$833$	−28.1735	−	18.6369i	−0.976153	−	0.645731i
$834$		0			0
$835$	18.1380	−	16.8296i	0.627692	−	0.582413i
$836$	6.40562	−	0.965493i	0.221543	−	0.0333923i
$837$		0			0
$838$	−7.74175	+	19.7257i	−0.267434	+	0.681412i
$839$	−18.4580	+	23.1456i	−0.637242	+	0.799076i	−0.990655	−	0.136391i	$-0.956450\pi$
$839$	−18.4580	+	23.1456i	−0.637242	+	0.799076i	0.353413	+	0.935467i	$0.385021\pi$
$840$		0			0
$841$	−18.0155	−	22.5907i	−0.621224	−	0.778990i
$842$	38.3858	−	11.8404i	1.32286	−	0.408049i
$843$		0			0
$844$	−18.7010	−	5.76851i	−0.643716	−	0.198560i
$845$	1.93677	+	25.8444i	0.0666270	+	0.889076i
$846$		0			0
$847$	−21.2499	+	8.51184i	−0.730156	+	0.292470i
$848$	11.2089	−	49.1093i	0.384915	−	1.68642i
$849$		0			0
$850$	−61.5453	+	41.9609i	−2.11099	+	1.43925i
$851$	−21.5795	+	37.3768i	−0.739737	+	1.28126i
$852$		0			0
$853$	−20.9733	−	10.1002i	−0.718112	−	0.345825i	0.0388842	−	0.999244i	$-0.487620\pi$
$853$	−20.9733	−	10.1002i	−0.718112	−	0.345825i	−0.756996	+	0.653419i	$0.773334\pi$
$854$	3.76872	−	0.887941i	0.128963	−	0.0303847i
$855$		0			0
$856$	12.9544	+	8.83219i	0.442774	+	0.301878i
$857$	11.9213	+	11.0614i	0.407224	+	0.377849i	0.857020	−	0.515283i	$-0.172313\pi$
$857$	11.9213	+	11.0614i	0.407224	+	0.377849i	−0.449796	+	0.893131i	$0.648503\pi$
$858$		0			0
$859$	16.0034	+	10.9109i	0.546030	+	0.372277i	0.804693	−	0.593691i	$-0.202330\pi$
$859$	16.0034	+	10.9109i	0.546030	+	0.372277i	−0.258664	+	0.965967i	$0.583282\pi$
$860$	−20.1870	+	9.72156i	−0.688372	+	0.331502i
$861$		0			0
$862$	37.5263	+	18.0717i	1.27815	+	0.615526i
$863$	19.0272	+	32.9562i	0.647695	+	1.12184i	0.983672	+	0.179971i	$0.0576002\pi$
$863$	19.0272	+	32.9562i	0.647695	+	1.12184i	−0.335977	+	0.941870i	$0.609066\pi$
$864$		0			0
$865$	66.0225	−	45.0134i	2.24483	−	1.53050i
$866$	−68.1589	−	10.2733i	−2.31613	−	0.349101i
$867$		0			0
$868$	18.1103	−	7.25425i	0.614705	−	0.246225i
$869$	3.99404	+	17.4990i	0.135488	+	0.593614i
$870$		0			0
$871$	30.0528	+	9.27005i	1.01830	+	0.314104i
$872$	2.94457	+	7.50265i	0.0997158	+	0.254072i
$873$		0			0
$874$	−20.2013	−	25.3316i	−0.683318	−	0.856853i
$875$	5.23601	−	36.4661i	0.177010	−	1.23278i
$876$		0			0
$877$	19.3539	−	49.3129i	0.653534	−	1.66518i	−0.0895528	−	0.995982i	$-0.528544\pi$
$877$	19.3539	−	49.3129i	0.653534	−	1.66518i	0.743087	−	0.669195i	$-0.233361\pi$
$878$	−4.18489	+	55.8435i	−0.141233	+	1.88463i
$879$		0			0
$880$	−20.7796	+	19.2806i	−0.700480	+	0.649950i
$881$	−26.7189			−0.900181			−0.450091	−	0.892983i	$-0.648608\pi$
$881$	−26.7189			−0.900181			−0.450091	+	0.892983i	$0.648608\pi$
$882$		0			0
$883$	8.27752			0.278561			0.139280	−	0.990253i	$-0.455521\pi$
$883$	8.27752			0.278561			0.139280	+	0.990253i	$0.455521\pi$
$884$	9.61763	−	8.92386i	0.323476	−	0.300142i
$885$		0			0
$886$	3.60239	−	48.0706i	0.121025	−	1.61496i
$887$	1.29682	−	3.30423i	0.0435428	−	0.110945i	−0.907448	−	0.420164i	$-0.861972\pi$
$887$	1.29682	−	3.30423i	0.0435428	−	0.110945i	0.950991	+	0.309219i	$0.100068\pi$
$888$		0			0
$889$	−36.1522	+	21.2107i	−1.21251	+	0.711386i
$890$	67.2409	+	84.3174i	2.25392	+	2.82633i
$891$		0			0
$892$	−1.77927	−	4.53349i	−0.0595742	−	0.151793i
$893$	−32.0451	−	9.88459i	−1.07235	−	0.330775i
$894$		0			0
$895$	−9.66034	−	42.3247i	−0.322909	−	1.41476i
$896$	29.8875	+	2.02982i	0.998470	+	0.0678114i
$897$		0			0
$898$	−51.5739	−	7.77351i	−1.72104	−	0.259405i
$899$	1.78364	−	1.21607i	0.0594878	−	0.0405581i
$900$		0			0
$901$	−24.3658	−	42.2029i	−0.811744	−	1.40598i
$902$	−5.93539	−	2.85833i	−0.197627	−	0.0951721i
$903$		0			0
$904$	−16.2778	+	7.83899i	−0.541393	+	0.260721i
$905$	−26.8321	−	18.2938i	−0.891931	−	0.608108i
$906$		0			0
$907$	−23.9142	−	22.1891i	−0.794058	−	0.736778i	0.174744	−	0.984614i	$-0.444090\pi$
$907$	−23.9142	−	22.1891i	−0.794058	−	0.736778i	−0.968802	+	0.247835i	$0.920281\pi$
$908$	−10.1463	−	6.91760i	−0.336715	−	0.229569i
$909$		0			0
$910$	0.296459	+	42.4194i	0.00982753	+	1.40619i
$911$	−49.1801	−	23.6839i	−1.62941	−	0.784682i	−0.999971	−	0.00763196i	$-0.997571\pi$
$911$	−49.1801	−	23.6839i	−1.62941	−	0.784682i	−0.629439	−	0.777050i	$-0.716715\pi$
$912$		0			0
$913$	−5.62045	+	9.73490i	−0.186010	+	0.322178i
$914$	16.4960	−	11.2468i	0.545639	−	0.372010i
$915$		0			0
$916$	−3.81649	+	16.7211i	−0.126100	+	0.552481i
$917$	−3.89196	+	4.25377i	−0.128524	+	0.140472i
$918$		0			0
$919$	−2.64558	−	35.3028i	−0.0872696	−	1.16453i	−0.853191	−	0.521598i	$-0.825336\pi$
$919$	−2.64558	−	35.3028i	−0.0872696	−	1.16453i	0.765922	−	0.642934i	$-0.222283\pi$
$920$	26.8386	+	8.27862i	0.884843	+	0.272938i
$921$		0			0
$922$	−5.25782	+	1.62182i	−0.173157	+	0.0534119i
$923$	−1.68492	−	2.11282i	−0.0554597	−	0.0695443i
$924$		0			0
$925$	−48.8779	+	61.2909i	−1.60709	+	2.01523i
$926$	16.7516	−	42.6823i	0.550490	−	1.40263i
$927$		0			0
$928$	−1.81444	+	0.273483i	−0.0595619	+	0.00897751i
$929$	2.03945	−	1.89233i	0.0669122	−	0.0620854i	−0.646008	−	0.763331i	$-0.723563\pi$
$929$	2.03945	−	1.89233i	0.0669122	−	0.0620854i	0.712920	+	0.701245i	$0.247372\pi$
$930$		0			0
$931$	16.3469	−	21.0967i	0.535748	−	0.691415i
$932$	7.91346			0.259214
$933$		0			0
$934$	32.8011	−	4.94397i	1.07328	−	0.161772i
$935$	−2.04936	+	27.3468i	−0.0670211	+	0.894335i
$936$		0			0
$937$	−22.0499	+	27.6497i	−0.720340	+	0.903278i	−0.998357	−	0.0572984i	$-0.981751\pi$
$937$	−22.0499	+	27.6497i	−0.720340	+	0.903278i	0.278017	+	0.960576i	$0.410323\pi$
$938$	−55.8514	−	21.4708i	−1.82361	−	0.701047i
$939$		0			0
$940$	−34.5638	+	10.6615i	−1.12735	+	0.347741i
$941$	−8.60529	−	21.9259i	−0.280524	−	0.714764i	−0.999799	−	0.0200387i	$-0.993621\pi$
$941$	−8.60529	−	21.9259i	−0.280524	−	0.714764i	0.719275	−	0.694726i	$-0.244474\pi$
$942$		0			0
$943$	0.878243	+	11.7193i	0.0285995	+	0.381634i
$944$	−15.1294	−	66.2864i	−0.492422	−	2.15744i
$945$		0			0
$946$	−3.27553	+	14.3510i	−0.106497	+	0.466593i
$947$	−3.76677	−	0.567749i	−0.122404	−	0.0184494i	0.0875547	−	0.996160i	$-0.472095\pi$
$947$	−3.76677	−	0.567749i	−0.122404	−	0.0184494i	−0.209958	+	0.977710i	$0.567333\pi$
$948$		0			0
$949$	6.93196	−	12.0065i	0.225021	−	0.389748i
$950$	−29.4259	−	50.9672i	−0.954703	−	1.65359i
$951$		0			0
$952$	15.5969	−	12.6175i	0.505499	−	0.408934i
$953$	28.4404	−	13.6962i	0.921276	−	0.443663i	0.0877497	−	0.996143i	$-0.472032\pi$
$953$	28.4404	−	13.6962i	0.921276	−	0.443663i	0.833527	+	0.552479i	$0.186318\pi$
$954$		0			0
$955$	−26.2355	−	24.3430i	−0.848960	−	0.787719i
$956$	7.07366	+	6.56340i	0.228779	+	0.212275i
$957$		0			0
$958$	5.92540	−	2.85352i	0.191441	−	0.0921931i
$959$	−6.69981	−	1.48000i	−0.216348	−	0.0477918i
$960$		0			0
$961$	−6.61125	−	11.4510i	−0.213266	−	0.369388i
$962$	19.3565	−	33.5264i	0.624078	−	1.08094i
$963$		0			0
$964$	1.55392	+	0.234216i	0.0500485	+	0.00754359i
$965$	−6.35519	+	27.8439i	−0.204581	+	0.896327i
$966$		0			0
$967$	−9.65016	−	42.2801i	−0.310328	−	1.35964i	−0.853971	−	0.520320i	$-0.825813\pi$
$967$	−9.65016	−	42.2801i	−0.310328	−	1.35964i	0.543643	−	0.839317i	$-0.317045\pi$
$968$	−1.01595	−	13.5569i	−0.0326538	−	0.435735i
$969$		0			0
$970$	−24.1924	−	61.6413i	−0.776772	−	1.97918i
$971$	2.12634	−	0.655889i	0.0682375	−	0.0210485i	−0.260448	−	0.965488i	$-0.583870\pi$
$971$	2.12634	−	0.655889i	0.0682375	−	0.0210485i	0.328686	+	0.944439i	$0.393394\pi$
$972$		0			0
$973$	31.3761	−	2.57194i	1.00587	−	0.0824526i
$974$	−23.9139	+	29.9871i	−0.766250	+	0.960848i
$975$		0			0
$976$	−0.309394	+	4.12858i	−0.00990347	+	0.132153i
$977$	−47.5441	+	7.16612i	−1.52107	+	0.229264i	−0.855787	−	0.517328i	$-0.826927\pi$
$977$	−47.5441	+	7.16612i	−1.52107	+	0.229264i	−0.665282	+	0.746592i	$0.731689\pi$
$978$		0			0
$979$	25.2710			0.807666
$980$	1.74979	−	28.7333i	0.0558949	−	0.917851i
$981$		0			0
$982$	36.5259	−	33.8911i	1.16559	−	1.08151i
$983$	−5.62082	+	0.847202i	−0.179276	+	0.0270215i	−0.238067	−	0.971249i	$-0.576514\pi$
$983$	−5.62082	+	0.847202i	−0.179276	+	0.0270215i	0.0587905	+	0.998270i	$0.481276\pi$
$984$		0			0
$985$	−17.1156	+	43.6098i	−0.545348	+	1.38952i
$986$	−1.72214	+	2.15950i	−0.0548441	+	0.0687724i
$987$		0			0
$988$	6.46299	+	8.10433i	0.205615	+	0.257833i
$989$	25.0931	−	7.74020i	0.797915	−	0.246124i
$990$		0			0
$991$	−3.69609	−	1.14009i	−0.117410	−	0.0362163i	0.235493	−	0.971876i	$-0.424329\pi$
$991$	−3.69609	−	1.14009i	−0.117410	−	0.0362163i	−0.352904	+	0.935660i	$0.614806\pi$
$992$	2.80904	+	37.4840i	0.0891870	+	1.19012i
$993$		0			0
$994$	2.92595	+	4.22779i	0.0928054	+	0.134097i
$995$	14.2938	−	62.6251i	0.453143	−	1.98535i
$996$		0			0
$997$	−0.533910	+	0.364013i	−0.0169091	+	0.0115284i	−0.571745	−	0.820431i	$-0.693733\pi$
$997$	−0.533910	+	0.364013i	−0.0169091	+	0.0115284i	0.554836	+	0.831960i	$0.312781\pi$
$998$	−22.6290	+	39.1946i	−0.716308	+	1.24068i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.c.109.4		48
3.2	odd	2		147.2.m.a.109.1	yes	48
49.9	even	21	inner	441.2.bb.c.352.4		48
147.95	odd	42		7203.2.a.i.1.20		24
147.101	even	42		7203.2.a.k.1.20		24
147.107	odd	42		147.2.m.a.58.1	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.a.58.1	✓	48	147.107	odd	42
147.2.m.a.109.1	yes	48	3.2	odd	2
441.2.bb.c.109.4		48	1.1	even	1	trivial
441.2.bb.c.352.4		48	49.9	even	21	inner
7203.2.a.i.1.20		24	147.95	odd	42
7203.2.a.k.1.20		24	147.101	even	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)

\(f(q)\)	\(=\)	\(q+(1.29251 - 1.19927i) q^{2} +(0.0828637 - 1.10574i) q^{4} +(-1.35494 + 3.45233i) q^{5} +(1.47509 - 2.19638i) q^{7} +(0.979680 + 1.22848i) q^{8} +O(q^{10})\)	\(q+(1.29251 - 1.19927i) q^{2} +(0.0828637 - 1.10574i) q^{4} +(-1.35494 + 3.45233i) q^{5} +(1.47509 - 2.19638i) q^{7} +(0.979680 + 1.22848i) q^{8} +(2.38902 + 6.08712i) q^{10} +(1.46421 + 0.451650i) q^{11} +(0.545602 + 2.39044i) q^{13} +(-0.727497 - 4.60789i) q^{14} +(4.93244 + 0.743446i) q^{16} +(3.98718 - 2.71841i) q^{17} +(1.90634 + 3.30188i) q^{19} +(3.70511 + 1.78429i) q^{20} +(2.43416 - 1.17223i) q^{22} +(-3.98222 - 2.71503i) q^{23} +(-6.41749 - 5.95456i) q^{25} +(3.57198 + 2.43534i) q^{26} +(-2.30640 - 1.81307i) q^{28} +(-0.292476 - 0.140849i) q^{29} +(-3.32500 + 5.75907i) q^{31} +(4.67031 - 3.18416i) q^{32} +(1.89335 - 8.29529i) q^{34} +(5.58399 + 8.06848i) q^{35} +(-0.669188 - 8.92969i) q^{37} +(6.42382 + 1.98149i) q^{38} +(-5.56853 + 1.71766i) q^{40} +(-1.52030 - 1.90640i) q^{41} +(-3.39704 + 4.25975i) q^{43} +(0.620737 - 1.58161i) q^{44} +(-8.40312 + 1.26657i) q^{46} +(-6.44765 + 5.98255i) q^{47} +(-2.64821 - 6.47974i) q^{49} -15.4358 q^{50} +(2.68841 - 0.405213i) q^{52} +(0.754653 - 10.0701i) q^{53} +(-3.54317 + 4.44299i) q^{55} +(4.14333 - 0.339634i) q^{56} +(-0.546945 + 0.168710i) q^{58} +(-4.97979 - 12.6883i) q^{59} +(0.0620258 + 0.827677i) q^{61} +(2.60911 + 11.4312i) q^{62} +(-0.00219938 + 0.00963609i) q^{64} +(-8.99184 - 1.35530i) q^{65} +(6.41336 - 11.1083i) q^{67} +(-2.67546 - 4.63404i) q^{68} +(16.8937 + 3.73185i) q^{70} +(-0.993012 + 0.478209i) q^{71} +(-4.14492 - 3.84592i) q^{73} +(-11.5741 - 10.7392i) q^{74} +(3.80898 - 1.83431i) q^{76} +(3.15184 - 2.54975i) q^{77} +(5.85694 + 10.1445i) q^{79} +(-9.24979 + 16.0211i) q^{80} +(-4.25130 - 0.640780i) q^{82} +(-1.63242 + 7.15209i) q^{83} +(3.98247 + 17.4484i) q^{85} +(0.717904 + 9.57976i) q^{86} +(0.879617 + 2.24123i) q^{88} +(15.7596 - 4.86121i) q^{89} +(6.05513 + 2.32776i) q^{91} +(-3.33210 + 4.17832i) q^{92} +(-1.15894 + 15.4650i) q^{94} +(-13.9822 + 2.10747i) q^{95} -10.1265 q^{97} +(-11.1938 - 5.19919i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} + 3 q^{4} - 6 q^{8}+O(q^{10}) \) 48 * q + q^2 + 3 * q^4 - 6 * q^8	\( 48 q + q^{2} + 3 q^{4} - 6 q^{8} + 30 q^{10} + 9 q^{11} + 42 q^{14} + 29 q^{16} + 5 q^{17} - 26 q^{19} + 5 q^{20} + q^{22} + 4 q^{23} - 56 q^{25} + 62 q^{26} + 7 q^{28} - 12 q^{29} - 36 q^{31} + 14 q^{32} - 76 q^{34} - 7 q^{35} - 20 q^{37} + 60 q^{38} + 28 q^{40} - 41 q^{41} + 12 q^{43} - 44 q^{44} + 16 q^{46} - 13 q^{47} - 84 q^{49} + 12 q^{50} + 92 q^{52} - 14 q^{53} - 38 q^{55} - 105 q^{56} + 3 q^{58} - 57 q^{59} + 11 q^{61} + 16 q^{62} - 110 q^{64} - 21 q^{65} + 34 q^{67} - 22 q^{68} - 6 q^{71} - 69 q^{73} + 90 q^{74} - 49 q^{76} + 34 q^{79} - 55 q^{80} + 91 q^{82} - 28 q^{83} - 44 q^{85} + 26 q^{86} + 45 q^{88} - 11 q^{89} - 84 q^{92} + 90 q^{94} - 150 q^{95} + 124 q^{97} - 119 q^{98}+O(q^{100}) \) 48 * q + q^2 + 3 * q^4 - 6 * q^8 + 30 * q^10 + 9 * q^11 + 42 * q^14 + 29 * q^16 + 5 * q^17 - 26 * q^19 + 5 * q^20 + q^22 + 4 * q^23 - 56 * q^25 + 62 * q^26 + 7 * q^28 - 12 * q^29 - 36 * q^31 + 14 * q^32 - 76 * q^34 - 7 * q^35 - 20 * q^37 + 60 * q^38 + 28 * q^40 - 41 * q^41 + 12 * q^43 - 44 * q^44 + 16 * q^46 - 13 * q^47 - 84 * q^49 + 12 * q^50 + 92 * q^52 - 14 * q^53 - 38 * q^55 - 105 * q^56 + 3 * q^58 - 57 * q^59 + 11 * q^61 + 16 * q^62 - 110 * q^64 - 21 * q^65 + 34 * q^67 - 22 * q^68 - 6 * q^71 - 69 * q^73 + 90 * q^74 - 49 * q^76 + 34 * q^79 - 55 * q^80 + 91 * q^82 - 28 * q^83 - 44 * q^85 + 26 * q^86 + 45 * q^88 - 11 * q^89 - 84 * q^92 + 90 * q^94 - 150 * q^95 + 124 * q^97 - 119 * q^98

Introduction

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