LMFDB - Embedded newform 441.2.bb.d.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 49)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73170 - 1.60678i) q^{2} +(0.267571 - 3.57049i) q^{4} +(0.567937 - 1.44708i) q^{5} +(-2.62161 - 0.356599i) q^{7} +(-2.32789 - 2.91908i) q^{8} +O(q^{10})$	\(q+(1.73170 - 1.60678i) q^{2} +(0.267571 - 3.57049i) q^{4} +(0.567937 - 1.44708i) q^{5} +(-2.62161 - 0.356599i) q^{7} +(-2.32789 - 2.91908i) q^{8} +(-1.34164 - 3.41845i) q^{10} +(0.663342 + 0.204614i) q^{11} +(-0.928088 - 4.06622i) q^{13} +(-5.11281 + 3.59482i) q^{14} +(-1.64048 - 0.247262i) q^{16} +(0.659346 - 0.449534i) q^{17} +(1.05437 + 1.82622i) q^{19} +(-5.01482 - 2.41501i) q^{20} +(1.47747 - 0.711514i) q^{22} +(4.52784 + 3.08703i) q^{23} +(1.89377 + 1.75716i) q^{25} +(-8.14068 - 5.55022i) q^{26} +(-1.97470 + 9.26502i) q^{28} +(-0.0358031 - 0.0172419i) q^{29} +(1.21615 - 2.10644i) q^{31} +(2.93166 - 1.99877i) q^{32} +(0.419484 - 1.83788i) q^{34} +(-2.00494 + 3.59115i) q^{35} +(0.720079 + 9.60878i) q^{37} +(4.76018 + 1.46832i) q^{38} +(-5.54623 + 1.71079i) q^{40} +(-2.97571 - 3.73142i) q^{41} +(-4.04621 + 5.07379i) q^{43} +(0.908064 - 2.31371i) q^{44} +(12.8010 - 1.92944i) q^{46} +(-4.10689 + 3.81064i) q^{47} +(6.74567 + 1.86973i) q^{49} +6.10281 q^{50} +(-14.7667 + 2.22573i) q^{52} +(0.686072 - 9.15499i) q^{53} +(0.672829 - 0.843700i) q^{55} +(5.06187 + 8.48281i) q^{56} +(-0.0897040 + 0.0276700i) q^{58} +(3.92848 + 10.0096i) q^{59} +(-0.356368 - 4.75540i) q^{61} +(-1.27857 - 5.60180i) q^{62} +(2.60348 - 11.4066i) q^{64} +(-6.41124 - 0.966339i) q^{65} +(3.95660 - 6.85303i) q^{67} +(-1.42864 - 2.47447i) q^{68} +(2.29825 + 9.44027i) q^{70} +(3.10167 - 1.49368i) q^{71} +(-1.84688 - 1.71365i) q^{73} +(16.6861 + 15.4825i) q^{74} +(6.80263 - 3.27598i) q^{76} +(-1.66606 - 0.772965i) q^{77} +(5.31518 + 9.20616i) q^{79} +(-1.28949 + 2.23347i) q^{80} +(-11.1486 - 1.68038i) q^{82} +(-2.05809 + 9.01706i) q^{83} +(-0.276045 - 1.20943i) q^{85} +(1.14565 + 15.2876i) q^{86} +(-0.946901 - 2.41266i) q^{88} +(0.0252783 - 0.00779732i) q^{89} +(0.983073 + 10.9910i) q^{91} +(12.2337 - 15.3406i) q^{92} +(-0.989033 + 13.1977i) q^{94} +(3.24150 - 0.488578i) q^{95} -11.7290 q^{97} +(14.6857 - 7.60100i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8}+O(q^{10}) $ 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8	$ 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8} - 14 q^{10} + 3 q^{11} - 14 q^{13} - 21 q^{14} - 3 q^{16} + 7 q^{17} + 21 q^{19} - 14 q^{20} - 20 q^{22} - 15 q^{23} - 4 q^{25} + 28 q^{28} - 12 q^{29} + 35 q^{31} - 45 q^{32} + 70 q^{34} + 15 q^{37} + 28 q^{38} - 42 q^{40} + 42 q^{41} - 30 q^{43} + 50 q^{44} - 78 q^{46} - 21 q^{47} - 70 q^{49} - 40 q^{50} - 70 q^{52} - 11 q^{53} - 7 q^{55} + 28 q^{56} + 16 q^{58} + 28 q^{59} + 7 q^{61} + 28 q^{62} - 32 q^{64} - 14 q^{65} + 11 q^{67} - 77 q^{68} + 70 q^{70} - 19 q^{71} + 7 q^{73} - 34 q^{74} + 119 q^{76} - 7 q^{77} + 15 q^{79} - 70 q^{80} - 14 q^{82} - 26 q^{85} + 33 q^{86} - 77 q^{88} + 14 q^{89} + 84 q^{91} + 38 q^{92} + 14 q^{94} + 61 q^{95} + 161 q^{98}+O(q^{100}) $ 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8 - 14 * q^10 + 3 * q^11 - 14 * q^13 - 21 * q^14 - 3 * q^16 + 7 * q^17 + 21 * q^19 - 14 * q^20 - 20 * q^22 - 15 * q^23 - 4 * q^25 + 28 * q^28 - 12 * q^29 + 35 * q^31 - 45 * q^32 + 70 * q^34 + 15 * q^37 + 28 * q^38 - 42 * q^40 + 42 * q^41 - 30 * q^43 + 50 * q^44 - 78 * q^46 - 21 * q^47 - 70 * q^49 - 40 * q^50 - 70 * q^52 - 11 * q^53 - 7 * q^55 + 28 * q^56 + 16 * q^58 + 28 * q^59 + 7 * q^61 + 28 * q^62 - 32 * q^64 - 14 * q^65 + 11 * q^67 - 77 * q^68 + 70 * q^70 - 19 * q^71 + 7 * q^73 - 34 * q^74 + 119 * q^76 - 7 * q^77 + 15 * q^79 - 70 * q^80 - 14 * q^82 - 26 * q^85 + 33 * q^86 - 77 * q^88 + 14 * q^89 + 84 * q^91 + 38 * q^92 + 14 * q^94 + 61 * q^95 + 161 * 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 $

$2$	1.73170	−	1.60678i	1.22449	−	1.13616i	0.238191	−	0.971218i	$-0.423446\pi$
$2$	1.73170	−	1.60678i	1.22449	−	1.13616i	0.986303	−	0.164945i	$-0.0527448\pi$
$3$		0			0
$3$		0			0
$4$	0.267571	−	3.57049i	0.133786	−	1.78525i
$5$	0.567937	−	1.44708i	0.253989	−	0.647154i	−0.745831	−	0.666135i	$-0.767947\pi$
$5$	0.567937	−	1.44708i	0.253989	−	0.647154i	0.999820	+	0.0189819i	$0.00604250\pi$
$6$		0			0
$7$	−2.62161	−	0.356599i	−0.990875	−	0.134782i
$7$	−2.62161	−	0.356599i	−0.990875	−	0.134782i
$8$	−2.32789	−	2.91908i	−0.823032	−	1.03205i
$9$		0			0
$10$	−1.34164	−	3.41845i	−0.424265	−	1.08101i
$11$	0.663342	+	0.204614i	0.200005	+	0.0616934i	0.393139	−	0.919479i	$-0.371389\pi$
$11$	0.663342	+	0.204614i	0.200005	+	0.0616934i	−0.193134	+	0.981172i	$0.561865\pi$
$12$		0			0
$13$	−0.928088	−	4.06622i	−0.257405	−	1.12777i	−0.924014	−	0.382359i	$-0.875112\pi$
$13$	−0.928088	−	4.06622i	−0.257405	−	1.12777i	0.666608	−	0.745408i	$-0.267745\pi$
$14$	−5.11281	+	3.59482i	−1.36645	+	0.960757i
$15$		0			0
$16$	−1.64048	−	0.247262i	−0.410119	−	0.0618155i
$17$	0.659346	−	0.449534i	0.159915	−	0.109028i	−0.480719	−	0.876875i	$-0.659624\pi$
$17$	0.659346	−	0.449534i	0.159915	−	0.109028i	0.640634	+	0.767847i	$0.278672\pi$
$18$		0			0
$19$	1.05437	+	1.82622i	0.241889	+	0.418964i	0.961252	−	0.275670i	$-0.0888997\pi$
$19$	1.05437	+	1.82622i	0.241889	+	0.418964i	−0.719363	+	0.694634i	$0.755566\pi$
$20$	−5.01482	−	2.41501i	−1.12135	−	0.540013i
$21$		0			0
$22$	1.47747	−	0.711514i	0.314999	−	0.151695i
$23$	4.52784	+	3.08703i	0.944119	+	0.643690i	0.934386	−	0.356263i	$-0.115949\pi$
$23$	4.52784	+	3.08703i	0.944119	+	0.643690i	0.00973344	+	0.999953i	$0.496902\pi$
$24$		0			0
$25$	1.89377	+	1.75716i	0.378755	+	0.351433i
$26$	−8.14068	−	5.55022i	−1.59652	−	1.08849i
$27$		0			0
$28$	−1.97470	+	9.26502i	−0.373184	+	1.75092i
$29$	−0.0358031	−	0.0172419i	−0.00664847	−	0.00320174i	0.430557	−	0.902564i	$-0.358317\pi$
$29$	−0.0358031	−	0.0172419i	−0.00664847	−	0.00320174i	−0.437205	+	0.899362i	$0.644032\pi$
$30$		0			0
$31$	1.21615	−	2.10644i	0.218428	−	0.378328i	−0.735900	−	0.677090i	$-0.763241\pi$
$31$	1.21615	−	2.10644i	0.218428	−	0.378328i	0.954327	+	0.298763i	$0.0965739\pi$
$32$	2.93166	−	1.99877i	0.518249	−	0.353336i
$33$		0			0
$34$	0.419484	−	1.83788i	0.0719409	−	0.315194i
$35$	−2.00494	+	3.59115i	−0.338896	+	0.607015i
$36$		0			0
$37$	0.720079	+	9.60878i	0.118380	+	1.57967i	0.667937	+	0.744218i	$0.267178\pi$
$37$	0.720079	+	9.60878i	0.118380	+	1.57967i	−0.549557	+	0.835456i	$0.685203\pi$
$38$	4.76018	+	1.46832i	0.772203	+	0.238193i
$39$		0			0
$40$	−5.54623	+	1.71079i	−0.876936	+	0.270499i
$41$	−2.97571	−	3.73142i	−0.464728	−	0.582750i	0.493144	−	0.869948i	$-0.335848\pi$
$41$	−2.97571	−	3.73142i	−0.464728	−	0.582750i	−0.957871	+	0.287198i	$0.907276\pi$
$42$		0			0
$43$	−4.04621	+	5.07379i	−0.617042	+	0.773746i	−0.987925	−	0.154933i	$-0.950484\pi$
$43$	−4.04621	+	5.07379i	−0.617042	+	0.773746i	0.370883	+	0.928680i	$0.379055\pi$
$44$	0.908064	−	2.31371i	0.136896	−	0.348805i
$45$		0			0
$46$	12.8010	−	1.92944i	1.88740	−	0.284480i
$47$	−4.10689	+	3.81064i	−0.599052	+	0.555839i	−0.920328	−	0.391147i	$-0.872079\pi$
$47$	−4.10689	+	3.81064i	−0.599052	+	0.555839i	0.321277	+	0.946985i	$0.395888\pi$
$48$		0			0
$49$	6.74567	+	1.86973i	0.963668	+	0.267104i
$50$	6.10281			0.863068
$51$		0			0
$52$	−14.7667	+	2.22573i	−2.04778	+	0.308653i
$53$	0.686072	−	9.15499i	0.0942392	−	1.25753i	−0.726875	−	0.686770i	$-0.759028\pi$
$53$	0.686072	−	9.15499i	0.0942392	−	1.25753i	0.821114	−	0.570764i	$-0.193353\pi$
$54$		0			0
$55$	0.672829	−	0.843700i	0.0907242	−	0.113765i
$56$	5.06187	+	8.48281i	0.676421	+	1.13356i
$57$		0			0
$58$	−0.0897040	+	0.0276700i	−0.0117787	+	0.00363325i
$59$	3.92848	+	10.0096i	0.511445	+	1.30314i	0.920540	+	0.390648i	$0.127749\pi$
$59$	3.92848	+	10.0096i	0.511445	+	1.30314i	−0.409095	+	0.912492i	$0.634156\pi$
$60$		0			0
$61$	−0.356368	−	4.75540i	−0.0456283	−	0.608867i	−0.972412	−	0.233271i	$-0.925057\pi$
$61$	−0.356368	−	4.75540i	−0.0456283	−	0.608867i	0.926784	−	0.375596i	$-0.122562\pi$
$62$	−1.27857	−	5.60180i	−0.162379	−	0.711429i
$63$		0			0
$64$	2.60348	−	11.4066i	0.325436	−	1.42583i
$65$	−6.41124	−	0.966339i	−0.795216	−	0.119860i
$66$		0			0
$67$	3.95660	−	6.85303i	0.483375	−	0.837231i	−0.516442	−	0.856322i	$-0.672744\pi$
$67$	3.95660	−	6.85303i	0.483375	−	0.837231i	0.999818	+	0.0190912i	$0.00607728\pi$
$68$	−1.42864	−	2.47447i	−0.173248	−	0.300074i
$69$		0			0
$70$	2.29825	+	9.44027i	0.274693	+	1.12833i
$71$	3.10167	−	1.49368i	0.368100	−	0.177268i	−0.240684	−	0.970603i	$-0.577372\pi$
$71$	3.10167	−	1.49368i	0.368100	−	0.177268i	0.608784	+	0.793336i	$0.291658\pi$
$72$		0			0
$73$	−1.84688	−	1.71365i	−0.216161	−	0.200568i	0.564659	−	0.825324i	$-0.309008\pi$
$73$	−1.84688	−	1.71365i	−0.216161	−	0.200568i	−0.780820	+	0.624757i	$0.785198\pi$
$74$	16.6861	+	15.4825i	1.93972	+	1.79980i
$75$		0			0
$76$	6.80263	−	3.27598i	0.780316	−	0.375780i
$77$	−1.66606	−	0.772965i	−0.189865	−	0.0880875i
$78$		0			0
$79$	5.31518	+	9.20616i	0.598004	+	1.03577i	0.993115	+	0.117140i	$0.0373727\pi$
$79$	5.31518	+	9.20616i	0.598004	+	1.03577i	−0.395111	+	0.918633i	$0.629294\pi$
$80$	−1.28949	+	2.23347i	−0.144170	+	0.249709i
$81$		0			0
$82$	−11.1486	−	1.68038i	−1.23116	−	0.185567i
$83$	−2.05809	+	9.01706i	−0.225904	+	0.989751i	0.727037	+	0.686598i	$0.240897\pi$
$83$	−2.05809	+	9.01706i	−0.225904	+	0.989751i	−0.952942	+	0.303154i	$0.901960\pi$
$84$		0			0
$85$	−0.276045	−	1.20943i	−0.0299413	−	0.131181i
$86$	1.14565	+	15.2876i	0.123539	+	1.64851i
$87$		0			0
$88$	−0.946901	−	2.41266i	−0.100940	−	0.257191i
$89$	0.0252783	−	0.00779732i	0.00267949	−	0.000826514i	−0.293415	−	0.955985i	$-0.594792\pi$
$89$	0.0252783	−	0.00779732i	0.00267949	−	0.000826514i	0.296095	+	0.955159i	$0.404316\pi$
$90$		0			0
$91$	0.983073	+	10.9910i	0.103054	+	1.15217i
$92$	12.2337	−	15.3406i	1.27545	−	1.59937i
$93$		0			0
$94$	−0.989033	+	13.1977i	−0.102011	+	1.36124i
$95$	3.24150	−	0.488578i	0.332571	−	0.0501271i
$96$		0			0
$97$	−11.7290			−1.19089			−0.595447	−	0.803394i	$-0.703025\pi$
$97$	−11.7290			−1.19089			−0.595447	+	0.803394i	$0.703025\pi$
$98$	14.6857	−	7.60100i	1.48348	−	0.767817i
$99$		0			0
$100$	6.78066	−	6.29154i	0.678066	−	0.629154i
$101$	−18.4994	+	2.78833i	−1.84076	+	0.277449i	−0.974867	−	0.222787i	$-0.928484\pi$
$101$	−18.4994	+	2.78833i	−1.84076	+	0.277449i	−0.865889	+	0.500237i	$0.833246\pi$
$102$		0			0
$103$	2.74860	−	7.00332i	0.270828	−	0.690058i	−0.729156	−	0.684348i	$-0.760087\pi$
$103$	2.74860	−	7.00332i	0.270828	−	0.690058i	0.999984	−	0.00571039i	$-0.00181768\pi$
$104$	−9.70913	+	12.1749i	−0.952059	+	1.19384i
$105$		0			0
$106$	−13.5220	−	16.9560i	−1.31337	−	1.64691i
$107$	−4.60124	+	1.41929i	−0.444818	+	0.137208i	−0.509069	−	0.860725i	$-0.670010\pi$
$107$	−4.60124	+	1.41929i	−0.444818	+	0.137208i	0.0642510	+	0.997934i	$0.479534\pi$
$108$		0			0
$109$	11.2668	+	3.47535i	1.07916	+	0.332878i	0.782849	−	0.622212i	$-0.213766\pi$
$109$	11.2668	+	3.47535i	1.07916	+	0.332878i	0.296315	+	0.955090i	$0.404242\pi$
$110$	−0.190505	−	2.54212i	−0.0181640	−	0.242381i
$111$		0			0
$112$	4.21251	+	1.23322i	0.398045	+	0.116528i
$113$	−2.44118	+	10.6955i	−0.229647	+	1.00615i	0.720281	+	0.693682i	$0.244013\pi$
$113$	−2.44118	+	10.6955i	−0.229647	+	1.00615i	−0.949928	+	0.312468i	$0.898844\pi$
$114$		0			0
$115$	7.03870	−	4.79890i	0.656362	−	0.447500i
$116$	−0.0711419	+	0.123221i	−0.00660536	+	0.0114408i
$117$		0			0
$118$	22.8862	+	11.0214i	2.10684	+	1.01460i
$119$	−1.88885	+	0.943381i	−0.173151	+	0.0864796i
$120$		0			0
$121$	−8.69047	−	5.92506i	−0.790043	−	0.538642i
$122$	−8.25800	−	7.66230i	−0.747644	−	0.693712i
$123$		0			0
$124$	−7.19562	−	4.90589i	−0.646186	−	0.440562i
$125$	10.6213	−	5.11493i	0.949994	−	0.457493i
$126$		0			0
$127$	−12.6746	−	6.10376i	−1.12469	−	0.541621i	−0.223350	−	0.974738i	$-0.571699\pi$
$127$	−12.6746	−	6.10376i	−1.12469	−	0.541621i	−0.901337	+	0.433118i	$0.857414\pi$
$128$	−10.2713	−	17.7903i	−0.907859	−	1.57246i
$129$		0			0
$130$	−12.6550	+	8.62804i	−1.10992	+	0.756729i
$131$	13.9784	+	2.10690i	1.22130	+	0.184081i	0.727875	−	0.685710i	$-0.240508\pi$
$131$	13.9784	+	2.10690i	1.22130	+	0.184081i	0.493421	+	0.869790i	$0.335746\pi$
$132$		0			0
$133$	−2.11292	−	5.16363i	−0.183213	−	0.447744i
$134$	−4.15968	−	18.2247i	−0.359341	−	1.57438i
$135$		0			0
$136$	−2.84711	−	0.878216i	−0.244137	−	0.0753064i
$137$	−0.903392	−	2.30181i	−0.0771820	−	0.196657i	0.887075	−	0.461625i	$-0.152734\pi$
$137$	−0.903392	−	2.30181i	−0.0771820	−	0.196657i	−0.964257	+	0.264969i	$0.914638\pi$
$138$		0			0
$139$	−1.67222	−	2.09690i	−0.141836	−	0.177856i	0.705840	−	0.708372i	$-0.250570\pi$
$139$	−1.67222	−	2.09690i	−0.141836	−	0.177856i	−0.847675	+	0.530515i	$0.821998\pi$
$140$	12.2857	+	8.11950i	1.03833	+	0.686223i
$141$		0			0
$142$	2.97112	−	7.57029i	0.249331	−	0.635285i
$143$	0.216365	−	2.88719i	0.0180934	−	0.241439i
$144$		0			0
$145$	−0.0452843	+	0.0420177i	−0.00376065	+	0.00348938i
$146$	−5.95169			−0.492565
$147$		0			0
$148$	34.5008			2.83595
$149$	1.99199	−	1.84829i	0.163190	−	0.151418i	−0.594351	−	0.804206i	$-0.702591\pi$
$149$	1.99199	−	1.84829i	0.163190	−	0.151418i	0.757541	+	0.652788i	$0.226401\pi$
$150$		0			0
$151$	0.0875117	−	1.16776i	0.00712160	−	0.0950312i	−0.992510	−	0.122161i	$-0.961018\pi$
$151$	0.0875117	−	1.16776i	0.00712160	−	0.0950312i	0.999632	+	0.0271296i	$0.00863669\pi$
$152$	2.87643	−	7.32903i	0.233309	−	0.594463i
$153$		0			0
$154$	−4.12709	+	1.33845i	−0.332570	+	0.107855i
$155$	−2.35749	−	2.95620i	−0.189358	−	0.237447i
$156$		0			0
$157$	3.73500	+	9.51664i	0.298086	+	0.759510i	0.998932	+	0.0461981i	$0.0147106\pi$
$157$	3.73500	+	9.51664i	0.298086	+	0.759510i	−0.700846	+	0.713312i	$0.747194\pi$
$158$	23.9965	+	7.40195i	1.90906	+	0.588867i
$159$		0			0
$160$	−1.22738	−	5.37752i	−0.0970332	−	0.425130i
$161$	−10.7694	−	9.70760i	−0.848747	−	0.765066i
$162$		0			0
$163$	−5.26945	−	0.794243i	−0.412736	−	0.0622099i	−0.0606074	−	0.998162i	$-0.519304\pi$
$163$	−5.26945	−	0.794243i	−0.412736	−	0.0622099i	−0.352128	+	0.935952i	$0.614542\pi$
$164$	−14.1192	+	9.62632i	−1.10253	+	0.751690i
$165$		0			0
$166$	10.9244	+	18.9217i	0.847901	+	1.46861i
$167$	−1.38071	−	0.664915i	−0.106843	−	0.0514526i	0.379699	−	0.925110i	$-0.376028\pi$
$167$	−1.38071	−	0.664915i	−0.106843	−	0.0514526i	−0.486542	+	0.873657i	$0.661742\pi$
$168$		0			0
$169$	−3.96021	+	1.90714i	−0.304632	+	0.146703i
$170$	−2.42132	−	1.65083i	−0.185706	−	0.126613i
$171$		0			0
$172$	17.0333	+	15.8046i	1.29878	+	1.20509i
$173$	−4.57736	−	3.12079i	−0.348010	−	0.237269i	0.376681	−	0.926343i	$-0.377065\pi$
$173$	−4.57736	−	3.12079i	−0.348010	−	0.237269i	−0.724691	+	0.689074i	$0.758018\pi$
$174$		0			0
$175$	−4.33813	−	5.28192i	−0.327932	−	0.399275i
$176$	−1.03760	−	0.499683i	−0.0782123	−	0.0376650i
$177$		0			0
$178$	0.0312457	−	0.0541192i	0.00234197	−	0.00405641i
$179$	−10.5296	+	7.17896i	−0.787019	+	0.536581i	−0.888838	−	0.458222i	$-0.848486\pi$
$179$	−10.5296	+	7.17896i	−0.787019	+	0.536581i	0.101818	+	0.994803i	$0.467534\pi$
$180$		0			0
$181$	4.08394	−	17.8929i	0.303557	−	1.32997i	−0.561158	−	0.827708i	$-0.689644\pi$
$181$	4.08394	−	17.8929i	0.303557	−	1.32997i	0.864716	−	0.502262i	$-0.167499\pi$
$182$	19.3625	+	17.4535i	1.43524	+	1.29374i
$183$		0			0
$184$	−1.52902	−	20.4034i	−0.112721	−	1.50416i
$185$	14.3136	+	4.41517i	1.05236	+	0.324610i
$186$		0			0
$187$	0.529352	−	0.163284i	0.0387101	−	0.0119405i
$188$	12.5070	+	15.6832i	0.912165	+	1.14382i
$189$		0			0
$190$	4.82826	−	6.05445i	0.350279	−	0.439236i
$191$	7.19141	−	18.3234i	0.520352	−	1.32584i	−0.393327	−	0.919399i	$-0.628676\pi$
$191$	7.19141	−	18.3234i	0.520352	−	1.32584i	0.913679	−	0.406437i	$-0.133229\pi$
$192$		0			0
$193$	−15.4072	+	2.32226i	−1.10903	+	0.167160i	−0.677918	−	0.735137i	$-0.737118\pi$
$193$	−15.4072	+	2.32226i	−1.10903	+	0.167160i	−0.431115	+	0.902297i	$0.641880\pi$
$194$	−20.3110	+	18.8458i	−1.45824	+	1.35305i
$195$		0			0
$196$	8.48080	−	23.5851i	0.605772	−	1.68465i
$197$	−16.2192			−1.15557			−0.577786	−	0.816188i	$-0.696083\pi$
$197$	−16.2192			−1.15557			−0.577786	+	0.816188i	$0.696083\pi$
$198$		0			0
$199$	−21.7207	+	3.27387i	−1.53974	+	0.232079i	−0.863404	−	0.504514i	$-0.831672\pi$
$199$	−21.7207	+	3.27387i	−1.53974	+	0.232079i	−0.676337	+	0.736592i	$0.736434\pi$
$200$	0.720811	−	9.61855i	0.0509690	−	0.680134i
$201$		0			0
$202$	−27.5550	+	34.5529i	−1.93877	+	2.43113i
$203$	0.0877134	+	0.0579689i	0.00615627	+	0.00406862i
$204$		0			0
$205$	−7.08967	+	2.18687i	−0.495164	+	0.152738i
$206$	−6.49305	−	16.5440i	−0.452392	−	1.15268i
$207$		0			0
$208$	0.517085	+	6.90002i	0.0358534	+	0.478430i
$209$	0.325737	+	1.42715i	0.0225317	+	0.0987179i
$210$		0			0
$211$	−6.15510	+	26.9673i	−0.423735	+	1.85650i	0.0861819	+	0.996279i	$0.472533\pi$
$211$	−6.15510	+	26.9673i	−0.423735	+	1.85650i	−0.509917	+	0.860224i	$0.670324\pi$
$212$	−32.5042	−	4.89923i	−2.23240	−	0.336480i
$213$		0			0
$214$	−5.68745	+	9.85095i	−0.388786	+	0.673397i
$215$	5.04419	+	8.73679i	0.344011	+	0.595844i
$216$		0			0
$217$	−3.93944	+	5.08858i	−0.267426	+	0.345436i
$218$	25.0948	−	12.0850i	1.69963	−	0.818500i
$219$		0			0
$220$	−2.83240	−	2.62808i	−0.190960	−	0.177185i
$221$	−2.43984	−	2.26384i	−0.164121	−	0.152282i
$222$		0			0
$223$	−2.05848	+	0.991311i	−0.137846	+	0.0663831i	−0.501535	−	0.865137i	$-0.667231\pi$
$223$	−2.05848	+	0.991311i	−0.137846	+	0.0663831i	0.363689	+	0.931520i	$0.381517\pi$
$224$	−8.39843	+	4.19457i	−0.561144	+	0.280262i
$225$		0			0
$226$	12.9579	+	22.4438i	0.861949	+	1.49294i
$227$	−12.9143	+	22.3682i	−0.857149	+	1.48463i	0.0174870	+	0.999847i	$0.494433\pi$
$227$	−12.9143	+	22.3682i	−0.857149	+	1.48463i	−0.874637	+	0.484779i	$0.838900\pi$
$228$		0			0
$229$	7.46898	+	1.12577i	0.493564	+	0.0743928i	0.391108	−	0.920345i	$-0.372092\pi$
$229$	7.46898	+	1.12577i	0.493564	+	0.0743928i	0.102456	+	0.994738i	$0.467330\pi$
$230$	4.47811	−	19.6199i	0.295278	−	1.29370i
$231$		0			0
$232$	0.0330153	+	0.144649i	0.00216756	+	0.00949669i
$233$	0.442674	+	5.90707i	0.0290005	+	0.386985i	0.992752	+	0.120183i	$0.0383481\pi$
$233$	0.442674	+	5.90707i	0.0290005	+	0.386985i	−0.963751	+	0.266802i	$0.914033\pi$
$234$		0			0
$235$	3.18184	+	8.10720i	0.207560	+	0.528855i
$236$	36.7904	−	11.3483i	2.39485	−	0.738713i
$237$		0			0
$238$	−1.75511	+	4.66861i	−0.113767	+	0.302621i
$239$	−3.75792	+	4.71229i	−0.243080	+	0.304813i	−0.888373	−	0.459123i	$-0.848164\pi$
$239$	−3.75792	+	4.71229i	−0.243080	+	0.304813i	0.645293	+	0.763935i	$0.276735\pi$
$240$		0			0
$241$	−0.545639	+	7.28105i	−0.0351477	+	0.469013i	0.951664	+	0.307141i	$0.0993723\pi$
$241$	−0.545639	+	7.28105i	−0.0351477	+	0.469013i	−0.986812	+	0.161872i	$0.948247\pi$
$242$	−24.5695	+	3.70326i	−1.57939	+	0.238054i
$243$		0			0
$244$	−17.0745			−1.09308
$245$	6.53676	−	8.69964i	0.417618	−	0.555799i
$246$		0			0
$247$	6.44728	−	5.98220i	0.410230	−	0.380638i
$248$	−8.97993	+	1.35351i	−0.570226	+	0.0859478i
$249$		0			0
$250$	10.1742	−	25.9235i	0.643474	−	1.63955i
$251$	−1.84792	+	2.31721i	−0.116639	+	0.146261i	−0.836723	−	0.547626i	$-0.815532\pi$
$251$	−1.84792	+	2.31721i	−0.116639	+	0.146261i	0.720084	+	0.693887i	$0.244103\pi$
$252$		0			0
$253$	2.37185	+	2.97421i	0.149117	+	0.186987i
$254$	−31.7559	+	9.79540i	−1.99254	+	0.614618i
$255$		0			0
$256$	−24.0115	−	7.40657i	−1.50072	−	0.462910i
$257$	−1.94985	−	26.0190i	−0.121629	−	1.62302i	−0.640354	−	0.768080i	$-0.721212\pi$
$257$	−1.94985	−	26.0190i	−0.121629	−	1.62302i	0.518726	−	0.854941i	$-0.326407\pi$
$258$		0			0
$259$	1.53872	−	25.4473i	0.0956115	−	1.58122i
$260$	−5.16577	+	22.6327i	−0.320368	+	1.40362i
$261$		0			0
$262$	27.5916	−	18.8116i	1.70462	−	1.16219i
$263$	−2.47707	+	4.29042i	−0.152743	+	0.264559i	−0.932235	−	0.361854i	$-0.882144\pi$
$263$	−2.47707	+	4.29042i	−0.152743	+	0.264559i	0.779492	+	0.626412i	$0.215477\pi$
$264$		0			0
$265$	−12.8583	−	6.19225i	−0.789882	−	0.380387i
$266$	−11.9557	−	5.54684i	−0.733053	−	0.340099i
$267$		0			0
$268$	−23.4100	−	15.9607i	−1.42999	−	0.974954i
$269$	11.8287	+	10.9755i	0.721211	+	0.669186i	0.952790	−	0.303630i	$-0.0981988\pi$
$269$	11.8287	+	10.9755i	0.721211	+	0.669186i	−0.231579	+	0.972816i	$0.574389\pi$
$270$		0			0
$271$	−1.44638	−	0.986124i	−0.0878613	−	0.0599028i	0.518593	−	0.855021i	$-0.326456\pi$
$271$	−1.44638	−	0.986124i	−0.0878613	−	0.0599028i	−0.606454	+	0.795119i	$0.707409\pi$
$272$	−1.19279	+	0.574419i	−0.0723237	+	0.0348293i
$273$		0			0
$274$	−5.26289	−	2.53448i	−0.317943	−	0.153113i
$275$	0.896679	+	1.55309i	0.0540718	+	0.0936550i
$276$		0			0
$277$	13.3638	−	9.11129i	0.802953	−	0.547444i	−0.0908704	−	0.995863i	$-0.528965\pi$
$277$	13.3638	−	9.11129i	0.802953	−	0.547444i	0.893824	+	0.448418i	$0.148013\pi$
$278$	−6.26502	−	0.944300i	−0.375751	−	0.0566353i
$279$		0			0
$280$	15.1501	−	2.50723i	0.905393	−	0.149836i
$281$	0.859518	+	3.76580i	0.0512746	+	0.224649i	0.994073	−	0.108715i	$-0.0346736\pi$
$281$	0.859518	+	3.76580i	0.0512746	+	0.224649i	−0.942798	+	0.333363i	$0.891816\pi$
$282$		0			0
$283$	28.6147	+	8.82648i	1.70097	+	0.524680i	0.984866	−	0.173315i	$-0.0554478\pi$
$283$	28.6147	+	8.82648i	1.70097	+	0.524680i	0.716103	+	0.697995i	$0.245924\pi$
$284$	−4.50327	−	11.4741i	−0.267220	−	0.680865i
$285$		0			0
$286$	−4.26440	−	5.34739i	−0.252159	−	0.316198i
$287$	6.47052	+	10.8435i	0.381943	+	0.640069i
$288$		0			0
$289$	−5.97814	+	15.2321i	−0.351655	+	0.896003i
$290$	−0.0109055	+	0.145524i	−0.000640392	+	0.00854544i
$291$		0			0
$292$	−6.61275	+	6.13574i	−0.386982	+	0.359067i
$293$	−12.3352			−0.720633			−0.360316	−	0.932830i	$-0.617331\pi$
$293$	−12.3352			−0.720633			−0.360316	+	0.932830i	$0.617331\pi$
$294$		0			0
$295$	16.7158			0.973233
$296$	26.3725	−	24.4701i	1.53287	−	1.42230i
$297$		0			0
$298$	0.479715	−	6.40136i	0.0277892	−	0.370821i
$299$	8.35030	−	21.2762i	0.482910	−	1.23044i
$300$		0			0
$301$	12.4169	−	11.8586i	0.715699	−	0.683520i
$302$	−1.72479	−	2.16282i	−0.0992506	−	0.124456i
$303$		0			0
$304$	−1.27811	−	3.25658i	−0.0733048	−	0.186778i
$305$	−7.08384	−	2.18507i	−0.405619	−	0.125117i
$306$		0			0
$307$	1.11320	+	4.87723i	0.0635334	+	0.278358i	0.996709	−	0.0810628i	$-0.0258314\pi$
$307$	1.11320	+	4.87723i	0.0635334	+	0.278358i	−0.933176	+	0.359421i	$0.882974\pi$
$308$	−3.20566	+	5.74183i	−0.182659	+	0.327171i
$309$		0			0
$310$	−8.83240	−	1.33127i	−0.501647	−	0.0756111i
$311$	24.7865	−	16.8992i	1.40551	−	0.958264i	0.406510	−	0.913646i	$-0.366746\pi$
$311$	24.7865	−	16.8992i	1.40551	−	0.958264i	0.999004	−	0.0446173i	$-0.0142069\pi$
$312$		0			0
$313$	0.512483	+	0.887647i	0.0289672	+	0.0501727i	0.880146	−	0.474704i	$-0.157445\pi$
$313$	0.512483	+	0.887647i	0.0289672	+	0.0501727i	−0.851178	+	0.524877i	$0.824111\pi$
$314$	21.7590	+	10.4786i	1.22793	+	0.591341i
$315$		0			0
$316$	34.2927	−	16.5145i	1.92912	−	0.929013i
$317$	0.386466	+	0.263488i	0.0217061	+	0.0147989i	0.574124	−	0.818768i	$-0.305343\pi$
$317$	0.386466	+	0.263488i	0.0217061	+	0.0147989i	−0.552418	+	0.833567i	$0.686295\pi$
$318$		0			0
$319$	−0.0202218	−	0.0187631i	−0.00113220	−	0.00105053i
$320$	−15.0277	−	10.2457i	−0.840072	−	0.572751i
$321$		0			0
$322$	−34.2473	+	0.493409i	−1.90853	+	0.0274966i
$323$	1.51614	+	0.730136i	0.0843605	+	0.0406259i
$324$		0			0
$325$	5.38743	−	9.33130i	0.298841	−	0.517608i
$326$	−10.4013	+	7.09146i	−0.576073	+	0.392760i
$327$		0			0
$328$	−3.96519	+	17.3726i	−0.218941	+	0.959244i
$329$	12.1255	−	8.52549i	0.668503	−	0.470026i
$330$		0			0
$331$	−0.957891	−	12.7822i	−0.0526504	−	0.702571i	−0.959606	−	0.281346i	$-0.909219\pi$
$331$	−0.957891	−	12.7822i	−0.0526504	−	0.702571i	0.906956	−	0.421225i	$-0.138400\pi$
$332$	31.6447	+	9.76109i	1.73673	+	0.535709i
$333$		0			0
$334$	−3.45934	+	1.06706i	−0.189287	+	0.0583872i
$335$	−7.66978	−	9.61760i	−0.419045	−	0.525466i
$336$		0			0
$337$	−9.17474	+	11.5048i	−0.499780	+	0.626704i	−0.966180	−	0.257870i	$-0.916979\pi$
$337$	−9.17474	+	11.5048i	−0.499780	+	0.626704i	0.466400	+	0.884574i	$0.345551\pi$
$338$	−3.79353	+	9.66576i	−0.206341	+	0.525748i
$339$		0			0
$340$	−4.39213	+	0.662007i	−0.238197	+	0.0359024i
$341$	1.23773	−	1.14845i	0.0670270	−	0.0621919i
$342$		0			0
$343$	−17.0178	−	7.30720i	−0.918874	−	0.394552i
$344$	24.2299			1.30639
$345$		0			0
$346$	−12.9410	+	1.95054i	−0.695713	+	0.104862i
$347$	2.46104	−	32.8403i	0.132115	−	1.76296i	−0.400215	−	0.916421i	$-0.631064\pi$
$347$	2.46104	−	32.8403i	0.132115	−	1.76296i	0.532330	−	0.846537i	$-0.321316\pi$
$348$		0			0
$349$	−5.15105	+	6.45921i	−0.275729	+	0.345754i	−0.900344	−	0.435180i	$-0.856685\pi$
$349$	−5.15105	+	6.45921i	−0.275729	+	0.345754i	0.624614	+	0.780934i	$0.285256\pi$
$350$	−15.9992	−	2.17626i	−0.855193	−	0.116326i
$351$		0			0
$352$	2.35367	−	0.726011i	0.125451	−	0.0386965i
$353$	1.16444	+	2.96694i	0.0619768	+	0.157914i	0.958508	−	0.285067i	$-0.0920159\pi$
$353$	1.16444	+	2.96694i	0.0619768	+	0.157914i	−0.896531	+	0.442982i	$0.853921\pi$
$354$		0			0
$355$	−0.399928	−	5.33667i	−0.0212260	−	0.283241i
$356$	−0.0210765	−	0.0923423i	−0.00111705	−	0.00489413i
$357$		0			0
$358$	−6.69906	+	29.3505i	−0.354056	+	1.55122i
$359$	4.23152	+	0.637799i	0.223331	+	0.0336618i	0.259754	−	0.965675i	$-0.416358\pi$
$359$	4.23152	+	0.637799i	0.223331	+	0.0336618i	−0.0364233	+	0.999336i	$0.511596\pi$
$360$		0			0
$361$	7.27661	−	12.6035i	0.382979	−	0.663340i
$362$	−21.6778	−	37.5471i	−1.13936	−	1.97343i
$363$		0			0
$364$	39.5063	−	0.569178i	2.07069	−	0.0298330i
$365$	−3.52870	+	1.69933i	−0.184701	+	0.0889471i
$366$		0			0
$367$	25.3701	+	23.5400i	1.32431	+	1.22878i	0.953978	+	0.299876i	$0.0969454\pi$
$367$	25.3701	+	23.5400i	1.32431	+	1.22878i	0.370329	+	0.928901i	$0.379245\pi$
$368$	−6.66450	−	6.18375i	−0.347411	−	0.322350i
$369$		0			0
$370$	31.8810	−	15.3531i	1.65742	−	0.798170i
$371$	−5.06328	+	23.7562i	−0.262872	+	1.23336i
$372$		0			0
$373$	−10.9041	−	18.8864i	−0.564590	−	0.977899i	−0.997088	−	0.0762639i	$-0.975701\pi$
$373$	−10.9041	−	18.8864i	−0.564590	−	0.977899i	0.432497	−	0.901635i	$-0.357632\pi$
$374$	0.654317	−	1.13331i	0.0338339	−	0.0586020i
$375$		0			0
$376$	20.6839	+	3.11760i	1.06669	+	0.160778i
$377$	−0.0368808	+	0.161585i	−0.00189946	+	0.00832207i
$378$		0			0
$379$	1.33904	+	5.86672i	0.0687819	+	0.301353i	0.997605	−	0.0691708i	$-0.0220353\pi$
$379$	1.33904	+	5.86672i	0.0687819	+	0.301353i	−0.928823	+	0.370524i	$0.879178\pi$
$380$	−0.877131	−	11.7045i	−0.0449959	−	0.600428i
$381$		0			0
$382$	−16.9883	−	43.2856i	−0.869199	−	2.21468i
$383$	23.1787	−	7.14968i	1.18438	−	0.365331i	0.360857	−	0.932621i	$-0.382484\pi$
$383$	23.1787	−	7.14968i	1.18438	−	0.365331i	0.823518	+	0.567290i	$0.192008\pi$
$384$		0			0
$385$	−2.06476	+	1.97192i	−0.105230	+	0.100498i
$386$	−22.9492	+	28.7774i	−1.16808	+	1.46473i
$387$		0			0
$388$	−3.13833	+	41.8781i	−0.159325	+	2.12604i
$389$	20.2800	−	3.05672i	1.02824	−	0.154982i	0.386805	−	0.922162i	$-0.373579\pi$
$389$	20.2800	−	3.05672i	1.02824	−	0.154982i	0.641432	+	0.767180i	$0.278341\pi$
$390$		0			0
$391$	4.37313			0.221159
$392$	−10.2453	−	24.0437i	−0.517465	−	1.21439i
$393$		0			0
$394$	−28.0868	+	26.0607i	−1.41499	+	1.31292i
$395$	16.3407	−	2.46297i	0.822191	−	0.123925i
$396$		0			0
$397$	1.62820	−	4.14859i	0.0817171	−	0.208212i	−0.884175	−	0.467155i	$-0.845279\pi$
$397$	1.62820	−	4.14859i	0.0817171	−	0.208212i	0.965893	+	0.258943i	$0.0833742\pi$
$398$	−32.3533	+	40.5697i	−1.62172	+	2.03358i
$399$		0			0
$400$	−2.67221	−	3.35084i	−0.133610	−	0.167542i
$401$	29.9897	−	9.25061i	1.49762	−	0.461954i	0.565695	−	0.824614i	$-0.308608\pi$
$401$	29.9897	−	9.25061i	1.49762	−	0.461954i	0.931921	+	0.362661i	$0.118132\pi$
$402$		0			0
$403$	−9.69395	−	2.99019i	−0.482890	−	0.148952i
$404$	5.00581	+	66.7979i	0.249049	+	3.32332i
$405$		0			0
$406$	0.245036	−	0.0405516i	0.0121609	−	0.00201254i
$407$	−1.48843	+	6.52125i	−0.0737788	+	0.323246i
$408$		0			0
$409$	11.4790	−	7.82622i	0.567598	−	0.386982i	−0.245248	−	0.969460i	$-0.578869\pi$
$409$	11.4790	−	7.82622i	0.567598	−	0.386982i	0.812846	+	0.582479i	$0.197917\pi$
$410$	−8.76333	+	15.1785i	−0.432790	+	0.749614i
$411$		0			0
$412$	−24.2699	−	11.6878i	−1.19569	−	0.575814i
$413$	−6.72952	−	27.6422i	−0.331138	−	1.36018i
$414$		0			0
$415$	11.8795	+	8.09934i	0.583144	+	0.397581i
$416$	−10.8483	−	10.0657i	−0.531881	−	0.493513i
$417$		0			0
$418$	2.85719	+	1.94800i	0.139750	+	0.0952797i
$419$	−12.4309	+	5.98640i	−0.607289	+	0.292455i	−0.712145	−	0.702033i	$-0.752276\pi$
$419$	−12.4309	+	5.98640i	−0.607289	+	0.292455i	0.104856	+	0.994487i	$0.466562\pi$
$420$		0			0
$421$	−7.73392	−	3.72446i	−0.376928	−	0.181519i	0.235821	−	0.971797i	$-0.424222\pi$
$421$	−7.73392	−	3.72446i	−0.376928	−	0.181519i	−0.612749	+	0.790277i	$0.709936\pi$
$422$	32.6717	+	56.5890i	1.59043	+	2.75471i
$423$		0			0
$424$	−28.3212	+	19.3091i	−1.37540	+	0.937732i
$425$	2.03856	+	0.307263i	0.0988845	+	0.0149044i
$426$		0			0
$427$	−0.761516	+	12.5939i	−0.0368523	+	0.609461i
$428$	3.83642	+	16.8085i	0.185440	+	0.812467i
$429$		0			0
$430$	22.7731	+	7.02456i	1.09822	+	0.338755i
$431$	5.47589	+	13.9523i	0.263764	+	0.672061i	0.999989	−	0.00467656i	$-0.00148860\pi$
$431$	5.47589	+	13.9523i	0.263764	+	0.672061i	−0.736225	+	0.676737i	$0.763393\pi$
$432$		0			0
$433$	−7.66601	−	9.61287i	−0.368405	−	0.461965i	0.562730	−	0.826641i	$-0.309751\pi$
$433$	−7.66601	−	9.61287i	−0.368405	−	0.461965i	−0.931135	+	0.364676i	$0.881180\pi$
$434$	1.35432	+	15.1417i	0.0650096	+	0.726824i
$435$		0			0
$436$	15.4234	−	39.2981i	0.738646	−	1.88204i
$437$	−0.863582	+	11.5237i	−0.0413107	+	0.551254i
$438$		0			0
$439$	2.96251	−	2.74881i	0.141393	−	0.131193i	−0.606306	−	0.795232i	$-0.707349\pi$
$439$	2.96251	−	2.74881i	0.141393	−	0.131193i	0.747699	+	0.664038i	$0.231159\pi$
$440$	−4.02910			−0.192080
$441$		0			0
$442$	−7.86254			−0.373983
$443$	−9.09794	+	8.44165i	−0.432256	+	0.401075i	−0.866066	−	0.499929i	$-0.833359\pi$
$443$	−9.09794	+	8.44165i	−0.432256	+	0.401075i	0.433810	+	0.901004i	$0.357169\pi$
$444$		0			0
$445$	0.00307313	−	0.0410081i	0.000145680	−	0.00194397i
$446$	−1.97184	+	5.02417i	−0.0933693	+	0.237901i
$447$		0			0
$448$	−10.8929	+	28.9753i	−0.514642	+	1.36895i
$449$	−4.20919	−	5.27815i	−0.198644	−	0.249092i	0.672526	−	0.740074i	$-0.265209\pi$
$449$	−4.20919	−	5.27815i	−0.198644	−	0.249092i	−0.871170	+	0.490982i	$0.836638\pi$
$450$		0			0
$451$	−1.21041	−	3.08408i	−0.0569960	−	0.145224i
$452$	37.5351	+	11.5780i	1.76550	+	0.544585i
$453$		0			0
$454$	13.5771	+	59.4852i	0.637205	+	2.79178i
$455$	16.4632	+	4.81961i	0.771805	+	0.225947i
$456$		0			0
$457$	4.90668	+	0.739563i	0.229525	+	0.0345953i	0.262797	−	0.964851i	$-0.415355\pi$
$457$	4.90668	+	0.739563i	0.229525	+	0.0345953i	−0.0332728	+	0.999446i	$0.510593\pi$
$458$	14.7429	−	10.0515i	0.688889	−	0.469676i
$459$		0			0
$460$	−15.2511	−	26.4157i	−0.711086	−	1.23164i
$461$	−35.4998	−	17.0958i	−1.65339	−	0.796231i	−0.999204	−	0.0398990i	$-0.987296\pi$
$461$	−35.4998	−	17.0958i	−1.65339	−	0.796231i	−0.654188	−	0.756332i	$-0.726989\pi$
$462$		0			0
$463$	6.40555	−	3.08475i	0.297691	−	0.143360i	−0.279076	−	0.960269i	$-0.590028\pi$
$463$	6.40555	−	3.08475i	0.297691	−	0.143360i	0.576767	+	0.816909i	$0.304314\pi$
$464$	0.0544709	+	0.0371376i	0.00252875	+	0.00172407i
$465$		0			0
$466$	10.2579	+	9.51797i	0.475190	+	0.440912i
$467$	9.27934	+	6.32655i	0.429397	+	0.292758i	0.758668	−	0.651478i	$-0.225851\pi$
$467$	9.27934	+	6.32655i	0.429397	+	0.292758i	−0.329271	+	0.944235i	$0.606803\pi$
$468$		0			0
$469$	−12.8164	+	16.5550i	−0.591808	+	0.764441i
$470$	18.5365	+	8.92669i	0.855023	+	0.411757i
$471$		0			0
$472$	20.0738	−	34.7688i	0.923970	−	1.60036i
$473$	−3.72219	+	2.53775i	−0.171147	+	0.116686i
$474$		0			0
$475$	−1.21224	+	5.31115i	−0.0556212	+	0.243692i
$476$	2.86293	+	6.99655i	0.131222	+	0.320686i
$477$		0			0
$478$	1.06402	+	14.1984i	0.0486673	+	0.649419i
$479$	23.9595	+	7.39053i	1.09474	+	0.337682i	0.788975	−	0.614426i	$-0.210612\pi$
$479$	23.9595	+	7.39053i	1.09474	+	0.337682i	0.305763	+	0.952108i	$0.401088\pi$
$480$		0			0
$481$	38.4031	−	11.8458i	1.75103	−	0.540122i
$482$	10.7541	+	13.4853i	0.489838	+	0.614237i
$483$		0			0
$484$	−23.4807	+	29.4439i	−1.06731	+	1.33836i
$485$	−6.66130	+	16.9727i	−0.302474	+	0.770692i
$486$		0			0
$487$	10.1960	−	1.53679i	0.462023	−	0.0696388i	0.0860937	−	0.996287i	$-0.472562\pi$
$487$	10.1960	−	1.53679i	0.462023	−	0.0696388i	0.375930	+	0.926648i	$0.377323\pi$
$488$	−13.0518	+	12.1103i	−0.590827	+	0.548208i
$489$		0			0
$490$	−2.65871	−	25.5682i	−0.120108	−	1.15506i
$491$	10.2368			0.461979			0.230989	−	0.972956i	$-0.425804\pi$
$491$	10.2368			0.461979			0.230989	+	0.972956i	$0.425804\pi$
$492$		0			0
$493$	−0.0313575	+	0.00472638i	−0.00141227	+	0.000212865i
$494$	1.55265	−	20.7187i	0.0698571	−	0.932178i
$495$		0			0
$496$	−2.51591	+	3.15485i	−0.112968	+	0.141657i
$497$	−8.66400	+	2.80980i	−0.388634	+	0.126037i
$498$		0			0
$499$	23.2549	−	7.17318i	1.04103	−	0.321116i	0.273328	−	0.961921i	$-0.411876\pi$
$499$	23.2549	−	7.17318i	1.04103	−	0.321116i	0.767704	+	0.640805i	$0.221399\pi$
$500$	−15.4209	−	39.2917i	−0.689642	−	1.75718i
$501$		0			0
$502$	0.523221	+	6.98190i	0.0233525	+	0.311617i
$503$	3.01324	+	13.2019i	0.134354	+	0.588642i	0.996617	+	0.0821824i	$0.0261890\pi$
$503$	3.01324	+	13.2019i	0.134354	+	0.588642i	−0.862264	+	0.506460i	$0.830954\pi$
$504$		0			0
$505$	−6.47153	+	28.3536i	−0.287980	+	1.26172i
$506$	8.88623	+	1.33938i	0.395041	+	0.0595429i
$507$		0			0
$508$	−25.1848	+	43.6213i	−1.11739	+	1.93538i
$509$	21.5379	+	37.3047i	0.954650	+	1.65350i	0.735166	+	0.677887i	$0.237104\pi$
$509$	21.5379	+	37.3047i	0.954650	+	1.65350i	0.219484	+	0.975616i	$0.429563\pi$
$510$		0			0
$511$	4.23070	+	5.15112i	0.187155	+	0.227872i
$512$	−16.4650	+	7.92911i	−0.727656	+	0.350421i
$513$		0			0
$514$	−45.1833	−	41.9240i	−1.99295	−	1.84919i
$515$	−8.57333	−	7.95489i	−0.377786	−	0.350534i
$516$		0			0
$517$	−3.50398	+	1.68743i	−0.154105	+	0.0742131i
$518$	−38.2235	−	46.5393i	−1.67944	−	2.04482i
$519$		0			0
$520$	12.1038	+	20.9644i	0.530788	+	0.919352i
$521$	7.71291	−	13.3592i	0.337909	−	0.585275i	−0.646130	−	0.763227i	$-0.723614\pi$
$521$	7.71291	−	13.3592i	0.337909	−	0.585275i	0.984039	+	0.177952i	$0.0569471\pi$
$522$		0			0
$523$	−14.3006	−	2.15547i	−0.625322	−	0.0942521i	−0.171265	−	0.985225i	$-0.554786\pi$
$523$	−14.3006	−	2.15547i	−0.625322	−	0.0942521i	−0.454057	+	0.890973i	$0.650024\pi$
$524$	11.2629	−	49.3459i	0.492022	−	2.15569i
$525$		0			0
$526$	2.60421	+	11.4098i	0.113549	+	0.497491i
$527$	−0.145051	−	1.93557i	−0.00631853	−	0.0843150i
$528$		0			0
$529$	2.56872	+	6.54500i	0.111684	+	0.284565i
$530$	−32.2163	+	9.93742i	−1.39939	+	0.431654i
$531$		0			0
$532$	−19.0021	+	6.16251i	−0.823844	+	0.267179i
$533$	−12.4111	+	15.5630i	−0.537583	+	0.674107i
$534$		0			0
$535$	−0.559381	+	7.46443i	−0.0241842	+	0.322715i
$536$	−29.2150	+	4.40346i	−1.26190	+	0.190200i
$537$		0			0
$538$	38.1189			1.64342
$539$	4.09211	+	2.62053i	0.176260	+	0.112874i
$540$		0			0
$541$	−6.81561	+	6.32396i	−0.293026	+	0.271888i	−0.812962	−	0.582317i	$-0.802146\pi$
$541$	−6.81561	+	6.32396i	−0.293026	+	0.271888i	0.519936	+	0.854205i	$0.325956\pi$
$542$	−4.08917	+	0.616343i	−0.175645	+	0.0264742i
$543$		0			0
$544$	1.03446	−	2.63576i	0.0443521	−	0.113007i
$545$	11.4279	−	14.3302i	0.489519	−	0.613837i
$546$		0			0
$547$	−0.922752	−	1.15709i	−0.0394540	−	0.0494738i	0.761713	−	0.647915i	$-0.224359\pi$
$547$	−0.922752	−	1.15709i	−0.0394540	−	0.0494738i	−0.801167	+	0.598441i	$0.795787\pi$
$548$	−8.46031	+	2.60966i	−0.361406	+	0.111479i
$549$		0			0
$550$	4.04825	+	1.24872i	0.172618	+	0.0532456i
$551$	−0.00626224	−	0.0835638i	−0.000266780	−	0.00355994i
$552$		0			0
$553$	−10.6514	−	26.0303i	−0.452944	−	1.10692i
$554$	8.50222	−	37.2507i	0.361225	−	1.58263i
$555$		0			0
$556$	−7.93439	+	5.40957i	−0.336493	+	0.229417i
$557$	7.54680	−	13.0714i	0.319768	−	0.553855i	−0.660671	−	0.750675i	$-0.729728\pi$
$557$	7.54680	−	13.0714i	0.319768	−	0.553855i	0.980440	+	0.196820i	$0.0630616\pi$
$558$		0			0
$559$	24.3864	+	11.7439i	1.03144	+	0.496713i
$560$	4.17700	−	5.39545i	0.176511	−	0.227999i
$561$		0			0
$562$	7.53922	+	5.14015i	0.318023	+	0.216824i
$563$	−12.2577	−	11.3734i	−0.516598	−	0.479333i	0.378250	−	0.925704i	$-0.376526\pi$
$563$	−12.2577	−	11.3734i	−0.516598	−	0.479333i	−0.894848	+	0.446370i	$0.852716\pi$
$564$		0			0
$565$	14.0908	+	9.60696i	0.592805	+	0.404168i
$566$	63.7342	−	30.6928i	2.67895	−	1.29011i
$567$		0			0
$568$	−11.5805	−	5.57688i	−0.485907	−	0.234001i
$569$	−14.4235	−	24.9822i	−0.604664	−	1.04731i	−0.992104	−	0.125415i	$-0.959974\pi$
$569$	−14.4235	−	24.9822i	−0.604664	−	1.04731i	0.387440	−	0.921895i	$-0.373359\pi$
$570$		0			0
$571$	11.3766	−	7.75642i	0.476095	−	0.324596i	−0.301386	−	0.953502i	$-0.597449\pi$
$571$	11.3766	−	7.75642i	0.476095	−	0.324596i	0.777481	+	0.628906i	$0.216497\pi$
$572$	−10.2508	−	1.54506i	−0.428608	−	0.0646023i
$573$		0			0
$574$	28.6280	+	8.38088i	1.19491	+	0.349811i
$575$	3.15028	+	13.8023i	0.131376	+	0.575595i
$576$		0			0
$577$	20.8094	+	6.41885i	0.866307	+	0.267220i	0.695887	−	0.718151i	$-0.255011\pi$
$577$	20.8094	+	6.41885i	0.866307	+	0.267220i	0.170420	+	0.985372i	$0.445488\pi$
$578$	14.1222	+	35.9828i	0.587407	+	1.49669i
$579$		0			0
$580$	0.137907	+	0.172930i	0.00572628	+	0.00718052i
$581$	8.61098	−	22.9053i	0.357244	−	0.950272i
$582$		0			0
$583$	2.32834	−	5.93251i	0.0964299	−	0.245699i
$584$	−0.702961	+	9.38037i	−0.0290887	+	0.388162i
$585$		0			0
$586$	−21.3609	+	19.8200i	−0.882410	+	0.818757i
$587$	−25.3416			−1.04596			−0.522979	−	0.852345i	$-0.675180\pi$
$587$	−25.3416			−1.04596			−0.522979	+	0.852345i	$0.675180\pi$
$588$		0			0
$589$	5.12910			0.211341
$590$	28.9467	−	26.8586i	1.19172	−	1.10575i
$591$		0			0
$592$	1.19461	−	15.9410i	0.0490984	−	0.655172i
$593$	0.851564	−	2.16975i	0.0349696	−	0.0891010i	−0.912322	−	0.409473i	$-0.865713\pi$
$593$	0.851564	−	2.16975i	0.0349696	−	0.0891010i	0.947292	+	0.320372i	$0.103808\pi$
$594$		0			0
$595$	0.292399	+	3.26910i	0.0119872	+	0.134020i
$596$	−6.06632	−	7.60692i	−0.248486	−	0.311592i
$597$		0			0
$598$	−19.7260	−	50.2610i	−0.806656	−	2.05533i
$599$	−19.4122	−	5.98787i	−0.793160	−	0.244658i	−0.128408	−	0.991721i	$-0.540987\pi$
$599$	−19.4122	−	5.98787i	−0.793160	−	0.244658i	−0.664752	+	0.747064i	$0.731463\pi$
$600$		0			0
$601$	−5.83473	−	25.5636i	−0.238004	−	1.04276i	−0.942802	−	0.333354i	$-0.891820\pi$
$601$	−5.83473	−	25.5636i	−0.238004	−	1.04276i	0.704798	−	0.709408i	$-0.251038\pi$
$602$	2.44812	−	40.4867i	0.0997777	−	1.65012i
$603$		0			0
$604$	−4.14607	−	0.624920i	−0.168701	−	0.0254276i
$605$	−13.5097	+	9.21074i	−0.549246	+	0.374470i
$606$		0			0
$607$	−9.93633	−	17.2102i	−0.403303	−	0.698541i	0.590819	−	0.806804i	$-0.298805\pi$
$607$	−9.93633	−	17.2102i	−0.403303	−	0.698541i	−0.994122	+	0.108263i	$0.965471\pi$
$608$	6.74126	+	3.24642i	0.273394	+	0.131660i
$609$		0			0
$610$	−15.7780	+	7.59827i	−0.638832	+	0.307645i
$611$	19.3065	+	13.1629i	0.781056	+	0.532515i
$612$		0			0
$613$	−14.5834	−	13.5314i	−0.589018	−	0.546529i	0.328357	−	0.944554i	$-0.393505\pi$
$613$	−14.5834	−	13.5314i	−0.589018	−	0.546529i	−0.917375	+	0.398025i	$0.869696\pi$
$614$	9.76434	+	6.65721i	0.394057	+	0.268663i
$615$		0			0
$616$	1.62205	+	6.66273i	0.0653543	+	0.268449i
$617$	−19.5919	−	9.43496i	−0.788740	−	0.379837i	−0.00425965	−	0.999991i	$-0.501356\pi$
$617$	−19.5919	−	9.43496i	−0.788740	−	0.379837i	−0.784480	+	0.620154i	$0.787070\pi$
$618$		0			0
$619$	−13.2441	+	22.9395i	−0.532327	+	0.922017i	0.466961	+	0.884278i	$0.345349\pi$
$619$	−13.2441	+	22.9395i	−0.532327	+	0.922017i	−0.999288	+	0.0377391i	$0.987984\pi$
$620$	−11.1859	+	7.62640i	−0.449235	+	0.306284i
$621$		0			0
$622$	15.7695	−	69.0906i	0.632299	−	2.77028i
$623$	−0.0690503	+	0.0114273i	−0.00276644	+	0.000457825i
$624$		0			0
$625$	−0.404211	−	5.39382i	−0.0161685	−	0.215753i
$626$	2.31372	+	0.713687i	0.0924747	+	0.0285247i
$627$		0			0
$628$	34.9785	−	10.7894i	1.39579	−	0.430545i
$629$	4.79426	+	6.01181i	0.191160	+	0.239707i
$630$		0			0
$631$	0.0524457	−	0.0657648i	0.00208783	−	0.00261806i	−0.780786	−	0.624798i	$-0.785181\pi$
$631$	0.0524457	−	0.0657648i	0.00208783	−	0.00261806i	0.782874	+	0.622180i	$0.213753\pi$
$632$	14.5004	−	36.9463i	0.576793	−	1.46965i
$633$		0			0
$634$	1.09261	−	0.164684i	0.0433930	−	0.00654044i
$635$	−16.0310	+	14.8746i	−0.636170	+	0.590280i
$636$		0			0
$637$	1.34215	−	29.1647i	0.0531780	−	1.15555i
$638$	−0.0651661			−0.00257995
$639$		0			0
$640$	−31.5774	+	4.75953i	−1.24821	+	0.188137i
$641$	−2.47475	+	33.0232i	−0.0977466	+	1.30434i	0.705508	+	0.708702i	$0.250719\pi$
$641$	−2.47475	+	33.0232i	−0.0977466	+	1.30434i	−0.803255	+	0.595635i	$0.796900\pi$
$642$		0			0
$643$	−5.03595	+	6.31488i	−0.198598	+	0.249034i	−0.871151	−	0.491014i	$-0.836626\pi$
$643$	−5.03595	+	6.31488i	−0.198598	+	0.249034i	0.672553	+	0.740049i	$0.265198\pi$
$644$	−37.5425	+	35.8545i	−1.47938	+	1.41287i
$645$		0			0
$646$	3.79867	−	1.17173i	0.149457	−	0.0461012i
$647$	−10.3838	−	26.4574i	−0.408228	−	1.04015i	−0.976156	−	0.217070i	$-0.930350\pi$
$647$	−10.3838	−	26.4574i	−0.408228	−	1.04015i	0.567928	−	0.823079i	$-0.307745\pi$
$648$		0			0
$649$	0.557822	+	7.44361i	0.0218964	+	0.292187i
$650$	−5.66395	−	24.8154i	−0.222158	−	0.973339i
$651$		0			0
$652$	−4.24579	+	18.6020i	−0.166278	+	0.728512i
$653$	−16.0697	−	2.42212i	−0.628858	−	0.0947851i	−0.173122	−	0.984900i	$-0.555386\pi$
$653$	−16.0697	−	2.42212i	−0.628858	−	0.0947851i	−0.455735	+	0.890115i	$0.650624\pi$
$654$		0			0
$655$	10.9877	−	19.0312i	0.429324	−	0.743612i
$656$	3.95894	+	6.85708i	0.154571	+	0.267724i
$657$		0			0
$658$	7.29916	−	34.2466i	0.284551	−	1.33507i
$659$	16.7515	−	8.06711i	0.652547	−	0.314250i	−0.0781604	−	0.996941i	$-0.524905\pi$
$659$	16.7515	−	8.06711i	0.652547	−	0.314250i	0.730707	+	0.682691i	$0.239190\pi$
$660$		0			0
$661$	−18.5238	−	17.1876i	−0.720494	−	0.668520i	0.232126	−	0.972686i	$-0.425432\pi$
$661$	−18.5238	−	17.1876i	−0.720494	−	0.668520i	−0.952619	+	0.304165i	$0.901622\pi$
$662$	−22.1969	−	20.5957i	−0.862706	−	0.800474i
$663$		0			0
$664$	31.1125	−	14.9830i	1.20740	−	0.581453i
$665$	−8.67218	+	0.124942i	−0.336293	+	0.00484506i
$666$		0			0
$667$	−0.108885	−	0.188594i	−0.00421603	−	0.00730237i
$668$	−2.74351	+	4.75190i	−0.106150	+	0.183857i
$669$		0			0
$670$	−28.7351	−	4.33111i	−1.11013	−	0.167326i
$671$	0.736627	−	3.22737i	0.0284372	−	0.124591i
$672$		0			0
$673$	−10.4442	−	45.7591i	−0.402595	−	1.76389i	−0.616823	−	0.787102i	$-0.711581\pi$
$673$	−10.4442	−	45.7591i	−0.402595	−	1.76389i	0.214228	−	0.976784i	$-0.431276\pi$
$674$	2.59775	+	34.6645i	0.100061	+	1.33523i
$675$		0			0
$676$	5.74978	+	14.6502i	0.221145	+	0.563469i
$677$	6.70509	−	2.06825i	0.257698	−	0.0794892i	−0.163214	−	0.986591i	$-0.552186\pi$
$677$	6.70509	−	2.06825i	0.257698	−	0.0794892i	0.420912	+	0.907101i	$0.361710\pi$
$678$		0			0
$679$	30.7487	+	4.18254i	1.18003	+	0.160511i
$680$	−2.88783	+	3.62122i	−0.110743	+	0.138867i
$681$		0			0
$682$	0.298074	−	3.97752i	0.0114138	−	0.152307i
$683$	−44.3844	+	6.68988i	−1.69832	+	0.255981i	−0.925529	−	0.378676i	$-0.876379\pi$
$683$	−44.3844	+	6.68988i	−1.69832	+	0.255981i	−0.772794	+	0.634657i	$0.781141\pi$
$684$		0			0
$685$	−3.84397			−0.146870
$686$	−41.2107	+	14.6899i	−1.57343	+	0.560865i
$687$		0			0
$688$	7.89227	−	7.32296i	0.300890	−	0.279185i
$689$	−37.8629	+	5.70692i	−1.44246	+	0.217416i
$690$		0			0
$691$	−18.5412	+	47.2421i	−0.705339	+	1.79717i	−0.109631	+	0.993972i	$0.534967\pi$
$691$	−18.5412	+	47.2421i	−0.705339	+	1.79717i	−0.595708	+	0.803201i	$0.703128\pi$
$692$	−12.3675	+	15.5084i	−0.470143	+	0.589541i
$693$		0			0
$694$	−48.5053	−	60.8237i	−1.84123	−	2.30884i
$695$	−3.98409	+	1.22893i	−0.151125	+	0.0466159i
$696$		0			0
$697$	−3.63942	−	1.12261i	−0.137853	−	0.0425220i
$698$	1.45847	+	19.4620i	0.0552041	+	0.736647i
$699$		0			0
$700$	−20.0198	+	14.0760i	−0.756678	+	0.532022i
$701$	−2.81197	+	12.3201i	−0.106207	+	0.465322i	0.893656	+	0.448753i	$0.148132\pi$
$701$	−2.81197	+	12.3201i	−0.106207	+	0.465322i	−0.999863	+	0.0165696i	$0.994726\pi$
$702$		0			0
$703$	−16.7885	+	11.4462i	−0.633192	+	0.431703i
$704$	4.06095	−	7.03377i	0.153053	−	0.265095i
$705$		0			0
$706$	6.78367	+	3.26684i	0.255307	+	0.122949i
$707$	49.4924	−	0.713050i	1.86135	−	0.0268170i
$708$		0			0
$709$	18.1535	+	12.3769i	0.681769	+	0.464823i	0.854026	−	0.520230i	$-0.174154\pi$
$709$	18.1535	+	12.3769i	0.681769	+	0.464823i	−0.172257	+	0.985052i	$0.555106\pi$
$710$	−9.26741	−	8.59890i	−0.347800	−	0.322711i
$711$		0			0
$712$	−0.0816060	−	0.0556380i	−0.00305831	−	0.00208512i
$713$	12.0092	−	5.78332i	0.449747	−	0.216587i
$714$		0			0
$715$	−4.05512	−	1.95284i	−0.151653	−	0.0730321i
$716$	22.8150	+	39.5167i	0.852637	+	1.47681i
$717$		0			0
$718$	8.35251	−	5.69464i	0.311713	−	0.212522i
$719$	−37.4117	−	5.63891i	−1.39522	−	0.210296i	−0.591981	−	0.805952i	$-0.701654\pi$
$719$	−37.4117	−	5.63891i	−1.39522	−	0.210296i	−0.803240	+	0.595656i	$0.796892\pi$
$720$		0			0
$721$	−9.70314	+	17.3798i	−0.361364	+	0.647259i
$722$	−7.65009	−	33.5172i	−0.284707	−	1.24738i
$723$		0			0
$724$	−62.7938	−	19.3693i	−2.33371	−	0.719855i
$725$	−0.0375062	−	0.0955642i	−0.00139294	−	0.00354917i
$726$		0			0
$727$	2.38311	+	2.98832i	0.0883846	+	0.110831i	0.824057	−	0.566506i	$-0.191705\pi$
$727$	2.38311	+	2.98832i	0.0883846	+	0.110831i	−0.735673	+	0.677337i	$0.763134\pi$
$728$	29.7951	−	28.4555i	1.10428	−	1.05463i
$729$		0			0
$730$	−3.38018	+	8.61256i	−0.125106	+	0.318765i
$731$	−0.387010	+	5.16430i	−0.0143141	+	0.191008i
$732$		0			0
$733$	−19.9769	+	18.5358i	−0.737862	+	0.684636i	−0.956684	−	0.291129i	$-0.905969\pi$
$733$	−19.9769	+	18.5358i	−0.737862	+	0.684636i	0.218821	+	0.975765i	$0.429779\pi$
$734$	81.7568			3.01770
$735$		0			0
$736$	19.4443			0.716728
$737$	4.02680	−	3.73633i	0.148329	−	0.137629i
$738$		0			0
$739$	−2.36871	+	31.6082i	−0.0871343	+	1.16273i	0.766638	+	0.642079i	$0.221928\pi$
$739$	−2.36871	+	31.6082i	−0.0871343	+	1.16273i	−0.853772	+	0.520647i	$0.825691\pi$
$740$	19.5943	−	49.9253i	0.720299	−	1.83529i
$741$		0			0
$742$	29.4028	+	49.2740i	1.07941	+	1.80890i
$743$	−21.2921	−	26.6995i	−0.781132	−	0.979509i	−0.999993	−	0.00375264i	$-0.998805\pi$
$743$	−21.2921	−	26.6995i	−0.781132	−	0.979509i	0.218861	−	0.975756i	$-0.429766\pi$
$744$		0			0
$745$	−1.54330	−	3.93227i	−0.0565423	−	0.144067i
$746$	−49.2287	−	15.1850i	−1.80239	−	0.555964i
$747$		0			0
$748$	−0.441363	−	1.93374i	−0.0161378	−	0.0707045i
$749$	12.5688	−	2.08004i	0.459253	−	0.0760028i
$750$		0			0
$751$	−2.14418	−	0.323184i	−0.0782424	−	0.0117931i	0.109804	−	0.993953i	$-0.464978\pi$
$751$	−2.14418	−	0.323184i	−0.0782424	−	0.0117931i	−0.188047	+	0.982160i	$0.560216\pi$
$752$	7.67948	−	5.23578i	0.280042	−	0.190929i
$753$		0			0
$754$	0.195766	+	0.339076i	0.00712936	+	0.0123484i
$755$	−1.64014	−	0.789852i	−0.0596909	−	0.0287456i
$756$		0			0
$757$	40.7751	−	19.6363i	1.48200	−	0.713693i	0.494188	−	0.869355i	$-0.335466\pi$
$757$	40.7751	−	19.6363i	1.48200	−	0.713693i	0.987810	+	0.155663i	$0.0497513\pi$
$758$	11.7453	+	8.00783i	0.426609	+	0.290857i
$759$		0			0
$760$	−8.97205	−	8.32485i	−0.325451	−	0.301974i
$761$	39.1162	+	26.6689i	1.41796	+	0.966749i	0.998253	+	0.0590890i	$0.0188196\pi$
$761$	39.1162	+	26.6689i	1.41796	+	0.966749i	0.419707	+	0.907660i	$0.362133\pi$
$762$		0			0
$763$	−28.2978	−	13.1287i	−1.02445	−	0.475292i
$764$	−63.4994	−	30.5797i	−2.29733	−	1.10633i
$765$		0			0
$766$	28.6505	−	49.6241i	1.03518	−	1.79299i
$767$	37.0553	−	25.2639i	1.33799	−	0.912226i
$768$		0			0
$769$	5.71133	−	25.0230i	0.205956	−	0.902351i	−0.761271	−	0.648434i	$-0.775424\pi$
$769$	5.71133	−	25.0230i	0.205956	−	0.902351i	0.967226	−	0.253916i	$-0.0817188\pi$
$770$	−0.407087	+	6.73238i	−0.0146704	+	0.242618i
$771$		0			0
$772$	4.16909	+	55.6326i	0.150049	+	2.00226i
$773$	−21.9342	−	6.76579i	−0.788917	−	0.243349i	−0.125989	−	0.992032i	$-0.540210\pi$
$773$	−21.9342	−	6.76579i	−0.788917	−	0.243349i	−0.662928	+	0.748683i	$0.730687\pi$
$774$		0			0
$775$	6.00448	−	1.85214i	0.215687	−	0.0665307i
$776$	27.3037	+	34.2377i	0.980145	+	1.22906i
$777$		0			0
$778$	30.2073	−	37.8788i	1.08298	−	1.35802i
$779$	3.67691	−	9.36860i	0.131739	−	0.335665i
$780$		0			0
$781$	2.36309	−	0.356179i	0.0845581	−	0.0127451i
$782$	7.57293	−	7.02666i	0.270808	−	0.251273i
$783$		0			0
$784$	−10.6038	−	4.73519i	−0.378707	−	0.169114i
$785$	15.8926			0.567230
$786$		0			0
$787$	−17.0174	+	2.56495i	−0.606603	+	0.0914307i	−0.445160	−	0.895451i	$-0.646853\pi$
$787$	−17.0174	+	2.56495i	−0.606603	+	0.0914307i	−0.161444	+	0.986882i	$0.551615\pi$
$788$	−4.33980	+	57.9106i	−0.154599	+	2.06298i
$789$		0			0
$790$	24.3397	−	30.5210i	0.865968	−	1.08589i
$791$	10.2138	−	27.1689i	0.363162	−	0.966016i
$792$		0			0
$793$	−19.0058	+	5.86250i	−0.674915	+	0.208184i
$794$	−3.84632	−	9.80025i	−0.136501	−	0.347798i
$795$		0			0
$796$	5.87749	+	78.4296i	0.208322	+	2.77986i
$797$	5.96330	+	26.1269i	0.211231	+	0.925464i	0.963732	+	0.266872i	$0.0859902\pi$
$797$	5.96330	+	26.1269i	0.211231	+	0.925464i	−0.752501	+	0.658591i	$0.771153\pi$
$798$		0			0
$799$	−0.994849	+	4.35872i	−0.0351952	+	0.154200i
$800$	9.06407	+	1.36619i	0.320463	+	0.0483021i
$801$		0			0
$802$	37.0694	−	64.2061i	1.30897	−	2.26720i
$803$	−0.874474	−	1.51463i	−0.0308595	−	0.0534502i
$804$		0			0
$805$	−20.1640	+	10.0709i	−0.710688	+	0.354951i
$806$	−21.5915	+	10.3979i	−0.760529	+	0.366252i
$807$		0			0
$808$	51.2038	+	47.5102i	1.80134	+	1.67140i
$809$	15.7266	+	14.5922i	0.552918	+	0.513033i	0.906407	−	0.422406i	$-0.138814\pi$
$809$	15.7266	+	14.5922i	0.552918	+	0.513033i	−0.353489	+	0.935439i	$0.615005\pi$
$810$		0			0
$811$	−28.1304	+	13.5469i	−0.987791	+	0.475695i	−0.856778	−	0.515686i	$-0.827537\pi$
$811$	−28.1304	+	13.5469i	−0.987791	+	0.475695i	−0.131013	+	0.991381i	$0.541823\pi$
$812$	0.230447	−	0.297669i	0.00808710	−	0.0104461i
$813$		0			0
$814$	7.90069	+	13.6844i	0.276919	+	0.479638i
$815$	−4.14205	+	7.17424i	−0.145090	+	0.251303i
$816$		0			0
$817$	−13.5321	−	2.03963i	−0.473428	−	0.0713577i
$818$	7.30306	−	31.9968i	0.255345	−	1.11874i
$819$		0			0
$820$	5.91123	+	25.8988i	0.206429	+	0.904425i
$821$	−1.65734	−	22.1157i	−0.0578416	−	0.771843i	−0.948421	−	0.317014i	$-0.897320\pi$
$821$	−1.65734	−	22.1157i	−0.0578416	−	0.771843i	0.890579	−	0.454828i	$-0.150299\pi$
$822$		0			0
$823$	0.290456	+	0.740069i	0.0101247	+	0.0257972i	0.935847	−	0.352407i	$-0.114637\pi$
$823$	0.290456	+	0.740069i	0.0101247	+	0.0257972i	−0.925722	+	0.378205i	$0.876542\pi$
$824$	−26.8417	+	8.27956i	−0.935075	+	0.288432i
$825$		0			0
$826$	−56.0683	−	37.0550i	−1.95087	−	1.28931i
$827$	2.16118	−	2.71004i	0.0751516	−	0.0942372i	−0.742835	−	0.669475i	$-0.766519\pi$
$827$	2.16118	−	2.71004i	0.0751516	−	0.0942372i	0.817986	+	0.575238i	$0.195091\pi$
$828$		0			0
$829$	−1.86469	+	24.8826i	−0.0647635	+	0.864208i	0.866340	+	0.499454i	$0.166466\pi$
$829$	−1.86469	+	24.8826i	−0.0647635	+	0.864208i	−0.931104	+	0.364754i	$0.881153\pi$
$830$	33.5856	−	5.06221i	1.16577	−	0.175712i
$831$		0			0
$832$	−48.7981			−1.69177
$833$	5.28824	−	1.79961i	0.183227	−	0.0623529i
$834$		0			0
$835$	−1.74634	+	1.62037i	−0.0604346	+	0.0560751i
$836$	5.18278	−	0.781179i	0.179250	−	0.0270176i
$837$		0			0
$838$	−11.9077	+	30.3403i	−0.411345	+	1.04809i
$839$	−7.60123	+	9.53164i	−0.262424	+	0.329069i	−0.895534	−	0.444992i	$-0.853206\pi$
$839$	−7.60123	+	9.53164i	−0.262424	+	0.329069i	0.633111	+	0.774061i	$0.281778\pi$
$840$		0			0
$841$	−18.0802	−	22.6719i	−0.623456	−	0.781789i
$842$	−19.3772	+	5.97707i	−0.667782	+	0.205983i
$843$		0			0
$844$	94.6395	+	29.1924i	3.25763	+	1.00484i
$845$	0.510629	+	6.81387i	0.0175662	+	0.234404i
$846$		0			0
$847$	20.6701	+	18.6322i	0.710235	+	0.640211i
$848$	−3.38916	+	14.8489i	−0.116384	+	0.509913i
$849$		0			0
$850$	4.02386	−	2.74342i	0.138017	−	0.0940986i
$851$	−26.4022	+	45.7299i	−0.905055	+	1.56760i
$852$		0			0
$853$	16.8204	+	8.10030i	0.575921	+	0.277349i	0.699086	−	0.715037i	$-0.253590\pi$
$853$	16.8204	+	8.10030i	0.575921	+	0.277349i	−0.123165	+	0.992386i	$0.539305\pi$
$854$	18.9169	+	23.0324i	0.647322	+	0.788151i
$855$		0			0
$856$	14.8542	+	10.1274i	0.507706	+	0.346148i
$857$	29.5085	+	27.3799i	1.00799	+	0.935280i	0.997907	−	0.0646690i	$-0.0205992\pi$
$857$	29.5085	+	27.3799i	1.00799	+	0.935280i	0.0100855	+	0.999949i	$0.496790\pi$
$858$		0			0
$859$	3.88072	+	2.64583i	0.132409	+	0.0902746i	0.627713	−	0.778445i	$-0.283991\pi$
$859$	3.88072	+	2.64583i	0.132409	+	0.0902746i	−0.495304	+	0.868719i	$0.664944\pi$
$860$	32.5443	−	15.6725i	1.10975	−	0.534428i
$861$		0			0
$862$	31.9009	+	15.3627i	1.08655	+	0.523254i
$863$	−0.875413	−	1.51626i	−0.0297994	−	0.0516141i	0.850741	−	0.525585i	$-0.176154\pi$
$863$	−0.875413	−	1.51626i	−0.0297994	−	0.0516141i	−0.880541	+	0.473971i	$0.842820\pi$
$864$		0			0
$865$	−7.11568	+	4.85139i	−0.241941	+	0.164952i
$866$	−28.7209	−	4.32899i	−0.975978	−	0.147105i
$867$		0			0
$868$	17.1147	+	15.4273i	0.580910	+	0.523636i
$869$	1.64207	+	7.19439i	0.0557035	+	0.244053i
$870$		0			0
$871$	−31.5380	−	9.72819i	−1.06862	−	0.329627i
$872$	−16.0830	−	40.9789i	−0.544640	−	1.38772i
$873$		0			0
$874$	17.0206	+	21.3431i	0.575730	+	0.721942i
$875$	−29.6688	+	9.62181i	−1.00299	+	0.325276i
$876$		0			0
$877$	−6.21546	+	15.8367i	−0.209881	+	0.534769i	−0.996586	−	0.0825607i	$-0.973690\pi$
$877$	−6.21546	+	15.8367i	−0.209881	+	0.534769i	0.786705	+	0.617329i	$0.211785\pi$
$878$	0.713440	−	9.52019i	0.0240774	−	0.321291i
$879$		0			0
$880$	−1.31237	+	1.21771i	−0.0442401	+	0.0410488i
$881$	39.7542			1.33935			0.669676	−	0.742653i	$-0.266433\pi$
$881$	39.7542			1.33935			0.669676	+	0.742653i	$0.266433\pi$
$882$		0			0
$883$	−36.2060			−1.21843			−0.609215	−	0.793005i	$-0.708515\pi$
$883$	−36.2060			−1.21843			−0.609215	+	0.793005i	$0.708515\pi$
$884$	−8.73585	+	8.10568i	−0.293818	+	0.272624i
$885$		0			0
$886$	−2.19099	+	29.2367i	−0.0736078	+	0.982227i
$887$	−10.8406	+	27.6214i	−0.363992	+	0.927436i	0.625155	+	0.780501i	$0.285036\pi$
$887$	−10.8406	+	27.6214i	−0.363992	+	0.927436i	−0.989146	+	0.146935i	$0.953059\pi$
$888$		0			0
$889$	31.0512	+	20.5214i	1.04142	+	0.688266i
$890$	−0.0605692	−	0.0759513i	−0.00203028	−	0.00254589i
$891$		0			0
$892$	2.98868	+	7.61503i	0.100068	+	0.254970i
$893$	−11.2893	−	3.48228i	−0.377781	−	0.116530i
$894$		0			0
$895$	4.40838	+	19.3144i	0.147356	+	0.645608i
$896$	20.5832	+	50.3020i	0.687636	+	1.68047i
$897$		0			0
$898$	−15.7699	−	2.37692i	−0.526247	−	0.0793190i
$899$	−0.0798611	+	0.0544484i	−0.00266352	+	0.00181595i
$900$		0			0
$901$	−3.66312	−	6.34471i	−0.122036	−	0.211373i
$902$	−7.05149	−	3.39582i	−0.234789	−	0.113068i
$903$		0			0
$904$	36.9038	−	17.7720i	1.22740	−	0.591086i
$905$	−23.5731	−	16.0718i	−0.783595	−	0.534246i
$906$		0			0
$907$	−32.6538	−	30.2983i	−1.08425	−	1.00604i	−0.999954	−	0.00959830i	$-0.996945\pi$
$907$	−32.6538	−	30.2983i	−1.08425	−	1.00604i	−0.0842981	−	0.996441i	$-0.526865\pi$
$908$	76.4098	+	52.0954i	2.53575	+	1.72884i
$909$		0			0
$910$	36.2532	−	18.1066i	1.20178	−	0.600227i
$911$	9.62759	+	4.63640i	0.318976	+	0.153611i	0.586520	−	0.809935i	$-0.300498\pi$
$911$	9.62759	+	4.63640i	0.318976	+	0.153611i	−0.267544	+	0.963546i	$0.586212\pi$
$912$		0			0
$913$	−3.21023	+	5.56028i	−0.106243	+	0.184018i
$914$	9.68518	−	6.60325i	0.320357	−	0.218416i
$915$		0			0
$916$	6.01803	−	26.3667i	0.198841	−	0.871181i
$917$	−35.8945	−	10.5082i	−1.18534	−	0.347010i
$918$		0			0
$919$	−2.39913	−	32.0142i	−0.0791400	−	1.05605i	−0.885504	−	0.464631i	$-0.846187\pi$
$919$	−2.39913	−	32.0142i	−0.0791400	−	1.05605i	0.806364	−	0.591419i	$-0.201432\pi$
$920$	−30.3937	−	9.37520i	−1.00205	−	0.309091i
$921$		0			0
$922$	−88.9440	+	27.4356i	−2.92922	+	0.903543i
$923$	−8.95227	−	11.2258i	−0.294668	−	0.369501i
$924$		0			0
$925$	−15.5205	+	19.4622i	−0.510312	+	0.639912i
$926$	6.13595	−	15.6341i	0.201640	−	0.513770i
$927$		0			0
$928$	−0.139425	+	0.0210150i	−0.00457686	+	0.000689850i
$929$	3.80040	−	3.52626i	0.124687	−	0.115693i	−0.615365	−	0.788242i	$-0.710991\pi$
$929$	3.80040	−	3.52626i	0.124687	−	0.115693i	0.740052	+	0.672550i	$0.234801\pi$
$930$		0			0
$931$	3.69789	+	14.2905i	0.121194	+	0.468352i
$932$	21.2096			0.694744
$933$		0			0
$934$	26.2343	−	3.95419i	0.858414	−	0.129385i
$935$	0.0643544	−	0.858750i	0.00210461	−	0.0280841i
$936$		0			0
$937$	−21.3291	+	26.7458i	−0.696791	+	0.873748i	−0.996779	−	0.0801945i	$-0.974446\pi$
$937$	−21.3291	+	26.7458i	−0.696791	+	0.873748i	0.299988	+	0.953943i	$0.403017\pi$
$938$	4.40612	+	49.2615i	0.143865	+	1.60844i
$939$		0			0
$940$	29.7981	−	9.19149i	0.971906	−	0.299793i
$941$	8.82717	+	22.4913i	0.287758	+	0.733194i	0.999526	+	0.0307802i	$0.00979920\pi$
$941$	8.82717	+	22.4913i	0.287758	+	0.733194i	−0.711769	+	0.702414i	$0.752106\pi$
$942$		0			0
$943$	−1.95453	−	26.0813i	−0.0636481	−	0.849326i
$944$	−3.96958	−	17.3919i	−0.129199	−	0.566057i
$945$		0			0
$946$	−2.36810	+	10.3753i	−0.0769937	+	0.337331i
$947$	−17.6545	−	2.66099i	−0.573694	−	0.0864705i	−0.144214	−	0.989547i	$-0.546065\pi$
$947$	−17.6545	−	2.66099i	−0.573694	−	0.0864705i	−0.429481	+	0.903076i	$0.641303\pi$
$948$		0			0
$949$	−5.25402	+	9.10023i	−0.170553	+	0.295406i
$950$	6.43462	+	11.1451i	0.208767	+	0.361595i
$951$		0			0
$952$	7.15083	+	3.31762i	0.231760	+	0.107525i
$953$	−17.5916	+	8.47169i	−0.569849	+	0.274425i	−0.696541	−	0.717517i	$-0.745278\pi$
$953$	−17.5916	+	8.47169i	−0.569849	+	0.274425i	0.126692	+	0.991942i	$0.459564\pi$
$954$		0			0
$955$	−22.4312	−	20.8131i	−0.725855	−	0.673495i
$956$	15.8197	+	14.6785i	0.511645	+	0.474737i
$957$		0			0
$958$	53.3655	−	25.6995i	1.72416	−	0.830313i
$959$	1.54752	+	6.35659i	0.0499720	+	0.205265i
$960$		0			0
$961$	12.5419	+	21.7233i	0.404579	+	0.700751i
$962$	47.4690	−	82.2186i	1.53046	−	2.65084i
$963$		0			0
$964$	25.8509	+	3.89640i	0.832602	+	0.125495i
$965$	−5.38981	+	23.6143i	−0.173504	+	0.760171i
$966$		0			0
$967$	−1.14669	−	5.02398i	−0.0368751	−	0.161560i	0.953138	−	0.302536i	$-0.0978332\pi$
$967$	−1.14669	−	5.02398i	−0.0368751	−	0.161560i	−0.990013	+	0.140976i	$0.954976\pi$
$968$	2.93471	+	39.1610i	0.0943253	+	1.25868i
$969$		0			0
$970$	15.7361	+	40.0948i	0.505254	+	1.28737i
$971$	−54.6110	+	16.8453i	−1.75255	+	0.540591i	−0.993839	−	0.110834i	$-0.964648\pi$
$971$	−54.6110	+	16.8453i	−1.75255	+	0.540591i	−0.758713	+	0.651425i	$0.774171\pi$
$972$		0			0
$973$	3.63615	+	6.09355i	0.116570	+	0.195350i
$974$	15.1870	−	19.0439i	0.486623	−	0.610206i
$975$		0			0
$976$	−0.591217	+	7.88924i	−0.0189244	+	0.252528i
$977$	55.8267	−	8.41452i	1.78605	−	0.269204i	0.829029	−	0.559206i	$-0.188894\pi$
$977$	55.8267	−	8.41452i	1.78605	−	0.269204i	0.957026	+	0.290002i	$0.0936559\pi$
$978$		0			0
$979$	0.0183636			0.000586903
$980$	−29.3129	−	25.6672i	−0.936368	−	0.819910i
$981$		0			0
$982$	17.7270	−	16.4482i	0.565690	−	0.524883i
$983$	−3.31541	+	0.499718i	−0.105745	+	0.0159385i	−0.201702	−	0.979447i	$-0.564647\pi$
$983$	−3.31541	+	0.499718i	−0.105745	+	0.0159385i	0.0959565	+	0.995386i	$0.469409\pi$
$984$		0			0
$985$	−9.21149	+	23.4705i	−0.293503	+	0.747832i
$986$	−0.0467073	+	0.0585691i	−0.00148746	+	0.00186522i
$987$		0			0
$988$	−19.6343	−	24.6206i	−0.624650	−	0.783286i
$989$	−33.9835	+	10.4825i	−1.08061	+	0.333325i
$990$		0			0
$991$	−31.8228	−	9.81604i	−1.01089	−	0.311817i	−0.255296	−	0.966863i	$-0.582173\pi$
$991$	−31.8228	−	9.81604i	−1.01089	−	0.311817i	−0.755589	+	0.655046i	$0.772649\pi$
$992$	−0.644944	−	8.60618i	−0.0204770	−	0.273246i
$993$		0			0
$994$	−10.4887	+	18.7869i	−0.332681	+	0.595883i
$995$	−7.59844	+	33.2909i	−0.240887	+	1.05539i
$996$		0			0
$997$	32.4613	−	22.1317i	1.02806	−	0.700919i	0.0729996	−	0.997332i	$-0.476743\pi$
$997$	32.4613	−	22.1317i	1.02806	−	0.700919i	0.955060	+	0.296413i	$0.0957905\pi$
$998$	28.7447	−	49.7872i	0.909896	−	1.57599i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.d.109.4		48
3.2	odd	2		49.2.g.a.11.1	yes	48
12.11	even	2		784.2.bg.c.305.1		48
21.2	odd	6		343.2.g.i.128.4		48
21.5	even	6		343.2.g.h.128.4		48
21.11	odd	6		343.2.e.d.246.1		48
21.17	even	6		343.2.e.c.246.1		48
21.20	even	2		343.2.g.g.312.1		48
49.9	even	21	inner	441.2.bb.d.352.4		48
147.74	odd	42		343.2.e.d.99.1		48
147.83	even	14		343.2.g.h.67.4		48
147.89	even	42		343.2.g.g.177.1		48
147.95	odd	42		2401.2.a.h.1.22		24
147.101	even	42		2401.2.a.i.1.22		24
147.107	odd	42		49.2.g.a.9.1	✓	48
147.113	odd	14		343.2.g.i.67.4		48
147.122	even	42		343.2.e.c.99.1		48
588.107	even	42		784.2.bg.c.401.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.9.1	✓	48	147.107	odd	42
49.2.g.a.11.1	yes	48	3.2	odd	2
343.2.e.c.99.1		48	147.122	even	42
343.2.e.c.246.1		48	21.17	even	6
343.2.e.d.99.1		48	147.74	odd	42
343.2.e.d.246.1		48	21.11	odd	6
343.2.g.g.177.1		48	147.89	even	42
343.2.g.g.312.1		48	21.20	even	2
343.2.g.h.67.4		48	147.83	even	14
343.2.g.h.128.4		48	21.5	even	6
343.2.g.i.67.4		48	147.113	odd	14
343.2.g.i.128.4		48	21.2	odd	6
441.2.bb.d.109.4		48	1.1	even	1	trivial
441.2.bb.d.352.4		48	49.9	even	21	inner
784.2.bg.c.305.1		48	12.11	even	2
784.2.bg.c.401.1		48	588.107	even	42
2401.2.a.h.1.22		24	147.95	odd	42
2401.2.a.i.1.22		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)

\(f(q)\)	\(=\)	\(q+(1.73170 - 1.60678i) q^{2} +(0.267571 - 3.57049i) q^{4} +(0.567937 - 1.44708i) q^{5} +(-2.62161 - 0.356599i) q^{7} +(-2.32789 - 2.91908i) q^{8} +O(q^{10})\)	\(q+(1.73170 - 1.60678i) q^{2} +(0.267571 - 3.57049i) q^{4} +(0.567937 - 1.44708i) q^{5} +(-2.62161 - 0.356599i) q^{7} +(-2.32789 - 2.91908i) q^{8} +(-1.34164 - 3.41845i) q^{10} +(0.663342 + 0.204614i) q^{11} +(-0.928088 - 4.06622i) q^{13} +(-5.11281 + 3.59482i) q^{14} +(-1.64048 - 0.247262i) q^{16} +(0.659346 - 0.449534i) q^{17} +(1.05437 + 1.82622i) q^{19} +(-5.01482 - 2.41501i) q^{20} +(1.47747 - 0.711514i) q^{22} +(4.52784 + 3.08703i) q^{23} +(1.89377 + 1.75716i) q^{25} +(-8.14068 - 5.55022i) q^{26} +(-1.97470 + 9.26502i) q^{28} +(-0.0358031 - 0.0172419i) q^{29} +(1.21615 - 2.10644i) q^{31} +(2.93166 - 1.99877i) q^{32} +(0.419484 - 1.83788i) q^{34} +(-2.00494 + 3.59115i) q^{35} +(0.720079 + 9.60878i) q^{37} +(4.76018 + 1.46832i) q^{38} +(-5.54623 + 1.71079i) q^{40} +(-2.97571 - 3.73142i) q^{41} +(-4.04621 + 5.07379i) q^{43} +(0.908064 - 2.31371i) q^{44} +(12.8010 - 1.92944i) q^{46} +(-4.10689 + 3.81064i) q^{47} +(6.74567 + 1.86973i) q^{49} +6.10281 q^{50} +(-14.7667 + 2.22573i) q^{52} +(0.686072 - 9.15499i) q^{53} +(0.672829 - 0.843700i) q^{55} +(5.06187 + 8.48281i) q^{56} +(-0.0897040 + 0.0276700i) q^{58} +(3.92848 + 10.0096i) q^{59} +(-0.356368 - 4.75540i) q^{61} +(-1.27857 - 5.60180i) q^{62} +(2.60348 - 11.4066i) q^{64} +(-6.41124 - 0.966339i) q^{65} +(3.95660 - 6.85303i) q^{67} +(-1.42864 - 2.47447i) q^{68} +(2.29825 + 9.44027i) q^{70} +(3.10167 - 1.49368i) q^{71} +(-1.84688 - 1.71365i) q^{73} +(16.6861 + 15.4825i) q^{74} +(6.80263 - 3.27598i) q^{76} +(-1.66606 - 0.772965i) q^{77} +(5.31518 + 9.20616i) q^{79} +(-1.28949 + 2.23347i) q^{80} +(-11.1486 - 1.68038i) q^{82} +(-2.05809 + 9.01706i) q^{83} +(-0.276045 - 1.20943i) q^{85} +(1.14565 + 15.2876i) q^{86} +(-0.946901 - 2.41266i) q^{88} +(0.0252783 - 0.00779732i) q^{89} +(0.983073 + 10.9910i) q^{91} +(12.2337 - 15.3406i) q^{92} +(-0.989033 + 13.1977i) q^{94} +(3.24150 - 0.488578i) q^{95} -11.7290 q^{97} +(14.6857 - 7.60100i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8}+O(q^{10}) \) 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8	\( 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8} - 14 q^{10} + 3 q^{11} - 14 q^{13} - 21 q^{14} - 3 q^{16} + 7 q^{17} + 21 q^{19} - 14 q^{20} - 20 q^{22} - 15 q^{23} - 4 q^{25} + 28 q^{28} - 12 q^{29} + 35 q^{31} - 45 q^{32} + 70 q^{34} + 15 q^{37} + 28 q^{38} - 42 q^{40} + 42 q^{41} - 30 q^{43} + 50 q^{44} - 78 q^{46} - 21 q^{47} - 70 q^{49} - 40 q^{50} - 70 q^{52} - 11 q^{53} - 7 q^{55} + 28 q^{56} + 16 q^{58} + 28 q^{59} + 7 q^{61} + 28 q^{62} - 32 q^{64} - 14 q^{65} + 11 q^{67} - 77 q^{68} + 70 q^{70} - 19 q^{71} + 7 q^{73} - 34 q^{74} + 119 q^{76} - 7 q^{77} + 15 q^{79} - 70 q^{80} - 14 q^{82} - 26 q^{85} + 33 q^{86} - 77 q^{88} + 14 q^{89} + 84 q^{91} + 38 q^{92} + 14 q^{94} + 61 q^{95} + 161 q^{98}+O(q^{100}) \) 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8 - 14 * q^10 + 3 * q^11 - 14 * q^13 - 21 * q^14 - 3 * q^16 + 7 * q^17 + 21 * q^19 - 14 * q^20 - 20 * q^22 - 15 * q^23 - 4 * q^25 + 28 * q^28 - 12 * q^29 + 35 * q^31 - 45 * q^32 + 70 * q^34 + 15 * q^37 + 28 * q^38 - 42 * q^40 + 42 * q^41 - 30 * q^43 + 50 * q^44 - 78 * q^46 - 21 * q^47 - 70 * q^49 - 40 * q^50 - 70 * q^52 - 11 * q^53 - 7 * q^55 + 28 * q^56 + 16 * q^58 + 28 * q^59 + 7 * q^61 + 28 * q^62 - 32 * q^64 - 14 * q^65 + 11 * q^67 - 77 * q^68 + 70 * q^70 - 19 * q^71 + 7 * q^73 - 34 * q^74 + 119 * q^76 - 7 * q^77 + 15 * q^79 - 70 * q^80 - 14 * q^82 - 26 * q^85 + 33 * q^86 - 77 * q^88 + 14 * q^89 + 84 * q^91 + 38 * q^92 + 14 * q^94 + 61 * q^95 + 161 * q^98

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