LMFDB - Embedded newform 342.2.u.d.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(55,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("342.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.u (of order $9$, degree $6$, 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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			55.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	342.55
Dual form			342.2.u.d.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(-1.55303 + 0.565258i) q^{5} +(-0.0923963 - 0.160035i) q^{7} +(0.500000 - 0.866025i) q^{8} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(-1.55303 + 0.565258i) q^{5} +(-0.0923963 - 0.160035i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.286989 - 1.62760i) q^{10} +(-2.17365 + 3.76487i) q^{11} +(-4.96064 + 4.16247i) q^{13} +(0.173648 - 0.0632028i) q^{14} +(0.766044 + 0.642788i) q^{16} +(0.368241 - 2.08840i) q^{17} +(-4.11721 - 1.43128i) q^{19} +1.65270 q^{20} +(-3.33022 - 2.79439i) q^{22} +(0.0996702 + 0.0362770i) q^{23} +(-1.73783 + 1.45821i) q^{25} +(-3.23783 - 5.60808i) q^{26} +(0.0320889 + 0.181985i) q^{28} +(-0.692066 - 3.92490i) q^{29} +(1.61334 + 2.79439i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(1.99273 + 0.725293i) q^{34} +(0.233956 + 0.196312i) q^{35} +4.06418 q^{37} +(2.12449 - 3.80612i) q^{38} +(-0.286989 + 1.62760i) q^{40} +(6.61721 + 5.55250i) q^{41} +(-0.0393628 + 0.0143269i) q^{43} +(3.33022 - 2.79439i) q^{44} +(-0.0530334 + 0.0918566i) q^{46} +(1.37551 + 7.80093i) q^{47} +(3.48293 - 6.03260i) q^{49} +(-1.13429 - 1.96464i) q^{50} +(6.08512 - 2.21480i) q^{52} +(-8.65657 - 3.15074i) q^{53} +(1.24763 - 7.07564i) q^{55} -0.184793 q^{56} +3.98545 q^{58} +(-1.75237 + 9.93821i) q^{59} +(-3.37939 - 1.23000i) q^{61} +(-3.03209 + 1.10359i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(5.35117 - 9.26849i) q^{65} +(-1.38666 - 7.86414i) q^{67} +(-1.06031 + 1.83651i) q^{68} +(-0.233956 + 0.196312i) q^{70} +(-3.79813 + 1.38241i) q^{71} +(11.6420 + 9.76882i) q^{73} +(-0.705737 + 4.00243i) q^{74} +(3.37939 + 2.75314i) q^{76} +0.803348 q^{77} +(9.49660 + 7.96859i) q^{79} +(-1.55303 - 0.565258i) q^{80} +(-6.61721 + 5.55250i) q^{82} +(4.22803 + 7.32316i) q^{83} +(0.608593 + 3.45150i) q^{85} +(-0.00727396 - 0.0412527i) q^{86} +(2.17365 + 3.76487i) q^{88} +(13.7404 - 11.5295i) q^{89} +(1.12449 + 0.409279i) q^{91} +(-0.0812519 - 0.0681784i) q^{92} -7.92127 q^{94} +(7.20321 - 0.104455i) q^{95} +(1.85591 - 10.5254i) q^{97} +(5.33615 + 4.47756i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} + 3 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q + 3 * q^5 + 3 * q^7 + 3 * q^8	$ 6 q + 3 q^{5} + 3 q^{7} + 3 q^{8} + 6 q^{10} - 12 q^{11} - 21 q^{13} - 3 q^{17} + 6 q^{19} + 12 q^{20} + 3 q^{22} + 15 q^{23} + 9 q^{25} - 9 q^{28} - 15 q^{29} + 3 q^{31} - 6 q^{34} + 6 q^{35} + 6 q^{37} + 6 q^{40} + 9 q^{41} - 9 q^{43} - 3 q^{44} + 12 q^{46} + 21 q^{47} + 3 q^{50} + 15 q^{52} - 30 q^{53} - 9 q^{55} + 6 q^{56} - 12 q^{58} - 27 q^{59} - 9 q^{61} - 9 q^{62} - 3 q^{64} + 6 q^{65} - 15 q^{67} - 12 q^{68} - 6 q^{70} - 9 q^{71} + 12 q^{73} + 6 q^{74} + 9 q^{76} - 42 q^{77} + 15 q^{79} + 3 q^{80} - 9 q^{82} + 3 q^{83} - 36 q^{85} - 18 q^{86} + 12 q^{88} + 48 q^{89} - 6 q^{91} - 3 q^{92} - 30 q^{94} + 48 q^{95} + 18 q^{97} + 36 q^{98}+O(q^{100}) $ 6 * q + 3 * q^5 + 3 * q^7 + 3 * q^8 + 6 * q^10 - 12 * q^11 - 21 * q^13 - 3 * q^17 + 6 * q^19 + 12 * q^20 + 3 * q^22 + 15 * q^23 + 9 * q^25 - 9 * q^28 - 15 * q^29 + 3 * q^31 - 6 * q^34 + 6 * q^35 + 6 * q^37 + 6 * q^40 + 9 * q^41 - 9 * q^43 - 3 * q^44 + 12 * q^46 + 21 * q^47 + 3 * q^50 + 15 * q^52 - 30 * q^53 - 9 * q^55 + 6 * q^56 - 12 * q^58 - 27 * q^59 - 9 * q^61 - 9 * q^62 - 3 * q^64 + 6 * q^65 - 15 * q^67 - 12 * q^68 - 6 * q^70 - 9 * q^71 + 12 * q^73 + 6 * q^74 + 9 * q^76 - 42 * q^77 + 15 * q^79 + 3 * q^80 - 9 * q^82 + 3 * q^83 - 36 * q^85 - 18 * q^86 + 12 * q^88 + 48 * q^89 - 6 * q^91 - 3 * q^92 - 30 * q^94 + 48 * q^95 + 18 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$		0			0
$3$		0			0
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	−1.55303	+	0.565258i	−0.694538	+	0.252791i	−0.665077	−	0.746775i	$-0.731601\pi$
$5$	−1.55303	+	0.565258i	−0.694538	+	0.252791i	−0.0294608	+	0.999566i	$0.509379\pi$
$6$		0			0
$7$	−0.0923963	−	0.160035i	−0.0349225	−	0.0604876i	0.848036	−	0.529939i	$-0.177785\pi$
$7$	−0.0923963	−	0.160035i	−0.0349225	−	0.0604876i	−0.882958	+	0.469451i	$0.844452\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$		0			0
$10$	−0.286989	−	1.62760i	−0.0907539	−	0.514691i
$11$	−2.17365	+	3.76487i	−0.655380	+	1.13515i	0.326419	+	0.945225i	$0.394158\pi$
$11$	−2.17365	+	3.76487i	−0.655380	+	1.13515i	−0.981798	+	0.189926i	$0.939175\pi$
$12$		0			0
$13$	−4.96064	+	4.16247i	−1.37583	+	1.15446i	−0.405108	+	0.914269i	$0.632766\pi$
$13$	−4.96064	+	4.16247i	−1.37583	+	1.15446i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	0.173648	−	0.0632028i	0.0464094	−	0.0168917i
$15$		0			0
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	0.368241	−	2.08840i	0.0893115	−	0.506511i	−0.907031	−	0.421064i	$-0.861657\pi$
$17$	0.368241	−	2.08840i	0.0893115	−	0.506511i	0.996343	−	0.0854474i	$-0.0272319\pi$
$18$		0			0
$19$	−4.11721	−	1.43128i	−0.944553	−	0.328359i
$19$	−4.11721	−	1.43128i	−0.944553	−	0.328359i
$20$	1.65270			0.369556
$21$		0			0
$22$	−3.33022	−	2.79439i	−0.710006	−	0.595766i
$23$	0.0996702	+	0.0362770i	0.0207827	+	0.00756428i	0.352391	−	0.935853i	$-0.385369\pi$
$23$	0.0996702	+	0.0362770i	0.0207827	+	0.00756428i	−0.331608	+	0.943417i	$0.607591\pi$
$24$		0			0
$25$	−1.73783	+	1.45821i	−0.347565	+	0.291642i
$26$	−3.23783	−	5.60808i	−0.634990	−	1.09983i
$27$		0			0
$28$	0.0320889	+	0.181985i	0.00606423	+	0.0343920i
$29$	−0.692066	−	3.92490i	−0.128514	−	0.728836i	−0.979159	−	0.203096i	$-0.934900\pi$
$29$	−0.692066	−	3.92490i	−0.128514	−	0.728836i	0.850645	−	0.525740i	$-0.176212\pi$
$30$		0			0
$31$	1.61334	+	2.79439i	0.289765	+	0.501887i	0.973753	−	0.227606i	$-0.0730897\pi$
$31$	1.61334	+	2.79439i	0.289765	+	0.501887i	−0.683989	+	0.729492i	$0.739756\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$		0			0
$34$	1.99273	+	0.725293i	0.341750	+	0.124387i
$35$	0.233956	+	0.196312i	0.0395457	+	0.0331828i
$36$		0			0
$37$	4.06418			0.668147			0.334073	−	0.942547i	$-0.391577\pi$
$37$	4.06418			0.668147			0.334073	+	0.942547i	$0.391577\pi$
$38$	2.12449	−	3.80612i	0.344637	−	0.617434i
$39$		0			0
$40$	−0.286989	+	1.62760i	−0.0453769	+	0.257345i
$41$	6.61721	+	5.55250i	1.03343	+	0.867155i	0.991256	−	0.131955i	$-0.0421255\pi$
$41$	6.61721	+	5.55250i	1.03343	+	0.867155i	0.0421791	+	0.999110i	$0.486570\pi$
$42$		0			0
$43$	−0.0393628	+	0.0143269i	−0.00600278	+	0.00218483i	−0.345020	−	0.938595i	$-0.612128\pi$
$43$	−0.0393628	+	0.0143269i	−0.00600278	+	0.00218483i	0.339017	+	0.940780i	$0.389906\pi$
$44$	3.33022	−	2.79439i	0.502050	−	0.421270i
$45$		0			0
$46$	−0.0530334	+	0.0918566i	−0.00781935	+	0.0135435i
$47$	1.37551	+	7.80093i	0.200639	+	1.13788i	0.904155	+	0.427204i	$0.140501\pi$
$47$	1.37551	+	7.80093i	0.200639	+	1.13788i	−0.703516	+	0.710679i	$0.748388\pi$
$48$		0			0
$49$	3.48293	−	6.03260i	0.497561	−	0.861801i
$50$	−1.13429	−	1.96464i	−0.160412	−	0.277842i
$51$		0			0
$52$	6.08512	−	2.21480i	0.843855	−	0.307138i
$53$	−8.65657	−	3.15074i	−1.18907	−	0.432787i	−0.329674	−	0.944095i	$-0.606939\pi$
$53$	−8.65657	−	3.15074i	−1.18907	−	0.432787i	−0.859398	+	0.511308i	$0.829161\pi$
$54$		0			0
$55$	1.24763	−	7.07564i	0.168230	−	0.954079i
$56$	−0.184793			−0.0246939
$57$		0			0
$58$	3.98545			0.523315
$59$	−1.75237	+	9.93821i	−0.228140	+	1.29384i	0.628452	+	0.777849i	$0.283689\pi$
$59$	−1.75237	+	9.93821i	−0.228140	+	1.29384i	−0.856591	+	0.515996i	$0.827422\pi$
$60$		0			0
$61$	−3.37939	−	1.23000i	−0.432686	−	0.157485i	0.116489	−	0.993192i	$-0.462836\pi$
$61$	−3.37939	−	1.23000i	−0.432686	−	0.157485i	−0.549175	+	0.835707i	$0.685058\pi$
$62$	−3.03209	+	1.10359i	−0.385076	+	0.140156i
$63$		0			0
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	5.35117	−	9.26849i	0.663731	−	1.14962i
$66$		0			0
$67$	−1.38666	−	7.86414i	−0.169407	−	0.960757i	−0.944403	−	0.328790i	$-0.893359\pi$
$67$	−1.38666	−	7.86414i	−0.169407	−	0.960757i	0.774996	−	0.631967i	$-0.217752\pi$
$68$	−1.06031	+	1.83651i	−0.128581	+	0.222709i
$69$		0			0
$70$	−0.233956	+	0.196312i	−0.0279630	+	0.0234638i
$71$	−3.79813	+	1.38241i	−0.450755	+	0.164062i	−0.557415	−	0.830234i	$-0.688207\pi$
$71$	−3.79813	+	1.38241i	−0.450755	+	0.164062i	0.106659	+	0.994296i	$0.465985\pi$
$72$		0			0
$73$	11.6420	+	9.76882i	1.36260	+	1.14335i	0.975171	+	0.221453i	$0.0710798\pi$
$73$	11.6420	+	9.76882i	1.36260	+	1.14335i	0.387425	+	0.921901i	$0.373365\pi$
$74$	−0.705737	+	4.00243i	−0.0820403	+	0.465273i
$75$		0			0
$76$	3.37939	+	2.75314i	0.387642	+	0.315806i
$77$	0.803348			0.0915500
$78$		0			0
$79$	9.49660	+	7.96859i	1.06845	+	0.896536i	0.994911	−	0.100756i	$-0.0321261\pi$
$79$	9.49660	+	7.96859i	1.06845	+	0.896536i	0.0735394	+	0.997292i	$0.476571\pi$
$80$	−1.55303	−	0.565258i	−0.173634	−	0.0631978i
$81$		0			0
$82$	−6.61721	+	5.55250i	−0.730749	+	0.613171i
$83$	4.22803	+	7.32316i	0.464086	+	0.803821i	0.999160	−	0.0409847i	$-0.0130495\pi$
$83$	4.22803	+	7.32316i	0.464086	+	0.803821i	−0.535074	+	0.844805i	$0.679716\pi$
$84$		0			0
$85$	0.608593	+	3.45150i	0.0660112	+	0.374368i
$86$	−0.00727396	−	0.0412527i	−0.000784371	−	0.00444839i
$87$		0			0
$88$	2.17365	+	3.76487i	0.231712	+	0.401336i
$89$	13.7404	−	11.5295i	1.45647	−	1.22213i	0.528795	−	0.848750i	$-0.322644\pi$
$89$	13.7404	−	11.5295i	1.45647	−	1.22213i	0.927679	−	0.373378i	$-0.121800\pi$
$90$		0			0
$91$	1.12449	+	0.409279i	0.117878	+	0.0429041i
$92$	−0.0812519	−	0.0681784i	−0.00847110	−	0.00710809i
$93$		0			0
$94$	−7.92127			−0.817017
$95$	7.20321	−	0.104455i	0.739034	−	0.0107169i
$96$		0			0
$97$	1.85591	−	10.5254i	0.188440	−	1.06869i	−0.733016	−	0.680211i	$-0.761888\pi$
$97$	1.85591	−	10.5254i	0.188440	−	1.06869i	0.921456	−	0.388483i	$-0.127001\pi$
$98$	5.33615	+	4.47756i	0.539033	+	0.452302i
$99$		0			0
$100$	2.13176	−	0.775897i	0.213176	−	0.0775897i
$101$	−6.17752	+	5.18355i	−0.614686	+	0.515783i	−0.896128	−	0.443795i	$-0.853632\pi$
$101$	−6.17752	+	5.18355i	−0.614686	+	0.515783i	0.281442	+	0.959578i	$0.409187\pi$
$102$		0			0
$103$	−8.96451	+	15.5270i	−0.883299	+	1.52992i	−0.0356484	+	0.999364i	$0.511350\pi$
$103$	−8.96451	+	15.5270i	−0.883299	+	1.52992i	−0.847651	+	0.530555i	$0.821984\pi$
$104$	1.12449	+	6.37727i	0.110265	+	0.625343i
$105$		0			0
$106$	4.60607	−	7.97794i	0.447381	−	0.774886i
$107$	−6.99407	−	12.1141i	−0.676142	−	1.17111i	−0.976134	−	0.217171i	$-0.930317\pi$
$107$	−6.99407	−	12.1141i	−0.676142	−	1.17111i	0.299991	−	0.953942i	$-0.403016\pi$
$108$		0			0
$109$	4.48545	−	1.63257i	0.429628	−	0.156372i	−0.118149	−	0.992996i	$-0.537696\pi$
$109$	4.48545	−	1.63257i	0.429628	−	0.156372i	0.547778	+	0.836624i	$0.315474\pi$
$110$	6.75150	+	2.45734i	0.643730	+	0.234299i
$111$		0			0
$112$	0.0320889	−	0.181985i	0.00303211	−	0.0171960i
$113$	0.753718			0.0709038			0.0354519	−	0.999371i	$-0.488713\pi$
$113$	0.753718			0.0709038			0.0354519	+	0.999371i	$0.488713\pi$
$114$		0			0
$115$	−0.175297			−0.0163465
$116$	−0.692066	+	3.92490i	−0.0642568	+	0.364418i
$117$		0			0
$118$	−9.48293	−	3.45150i	−0.872974	−	0.317737i
$119$	−0.368241	+	0.134029i	−0.0337566	+	0.0122864i
$120$		0			0
$121$	−3.94949	−	6.84072i	−0.359045	−	0.621884i
$122$	1.79813	−	3.11446i	0.162795	−	0.281970i
$123$		0			0
$124$	−0.560307	−	3.17766i	−0.0503171	−	0.285362i
$125$	6.00640	−	10.4034i	0.537228	−	0.930507i
$126$		0			0
$127$	−8.29086	+	6.95686i	−0.735695	+	0.617321i	−0.931678	−	0.363286i	$-0.881655\pi$
$127$	−8.29086	+	6.95686i	−0.735695	+	0.617321i	0.195983	+	0.980607i	$0.437210\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$		0			0
$130$	8.19846	+	6.87933i	0.719053	+	0.603357i
$131$	−1.88326	+	10.6805i	−0.164541	+	0.933157i	0.784996	+	0.619501i	$0.212665\pi$
$131$	−1.88326	+	10.6805i	−0.164541	+	0.933157i	−0.949537	+	0.313656i	$0.898446\pi$
$132$		0			0
$133$	0.151359	+	0.791143i	0.0131245	+	0.0686008i
$134$	7.98545			0.689838
$135$		0			0
$136$	−1.62449	−	1.36310i	−0.139298	−	0.116885i
$137$	−13.1099	−	4.77163i	−1.12006	−	0.407668i	−0.285384	−	0.958413i	$-0.592121\pi$
$137$	−13.1099	−	4.77163i	−1.12006	−	0.407668i	−0.834673	+	0.550746i	$0.814343\pi$
$138$		0			0
$139$	4.57011	−	3.83478i	0.387631	−	0.325261i	−0.428058	−	0.903751i	$-0.640802\pi$
$139$	4.57011	−	3.83478i	0.387631	−	0.325261i	0.815690	+	0.578490i	$0.196358\pi$
$140$	−0.152704	−	0.264490i	−0.0129058	−	0.0223535i
$141$		0			0
$142$	−0.701867	−	3.98048i	−0.0588993	−	0.334035i
$143$	−4.88847	−	27.7239i	−0.408794	−	2.31839i
$144$		0			0
$145$	3.29339	+	5.70431i	0.273501	+	0.473717i
$146$	−11.6420	+	9.76882i	−0.963501	+	0.808473i
$147$		0			0
$148$	−3.81908	−	1.39003i	−0.313926	−	0.114260i
$149$	10.8931	+	9.14036i	0.892394	+	0.748807i	0.968689	−	0.248278i	$-0.0798646\pi$
$149$	10.8931	+	9.14036i	0.892394	+	0.748807i	−0.0762949	+	0.997085i	$0.524309\pi$
$150$		0			0
$151$	−15.2003			−1.23698			−0.618490	−	0.785792i	$-0.712255\pi$
$151$	−15.2003			−1.23698			−0.618490	+	0.785792i	$0.712255\pi$
$152$	−3.29813	+	2.84997i	−0.267514	+	0.231163i
$153$		0			0
$154$	−0.139500	+	0.791143i	−0.0112412	+	0.0637521i
$155$	−4.08512	−	3.42782i	−0.328125	−	0.275329i
$156$		0			0
$157$	−8.83662	+	3.21627i	−0.705239	+	0.256686i	−0.669646	−	0.742680i	$-0.733554\pi$
$157$	−8.83662	+	3.21627i	−0.705239	+	0.256686i	−0.0355929	+	0.999366i	$0.511332\pi$
$158$	−9.49660	+	7.96859i	−0.755509	+	0.633947i
$159$		0			0
$160$	0.826352	−	1.43128i	0.0653288	−	0.113153i
$161$	−0.00340357	−	0.0193026i	−0.000268239	−	0.00152126i
$162$		0			0
$163$	3.81180	−	6.60224i	0.298564	−	0.517127i	−0.677244	−	0.735758i	$-0.736826\pi$
$163$	3.81180	−	6.60224i	0.298564	−	0.517127i	0.975808	+	0.218631i	$0.0701592\pi$
$164$	−4.31908	−	7.48086i	−0.337263	−	0.584157i
$165$		0			0
$166$	−7.94609	+	2.89214i	−0.616736	+	0.224474i
$167$	−16.1630	−	5.88284i	−1.25073	−	0.455228i	−0.370081	−	0.929000i	$-0.620670\pi$
$167$	−16.1630	−	5.88284i	−1.25073	−	0.455228i	−0.880648	+	0.473772i	$0.842892\pi$
$168$		0			0
$169$	5.02435	−	28.4945i	0.386488	−	2.19188i
$170$	−3.50475			−0.268802
$171$		0			0
$172$	0.0418891			0.00319401
$173$	1.15018	−	6.52298i	0.0874464	−	0.495933i	−0.909355	−	0.416020i	$-0.863425\pi$
$173$	1.15018	−	6.52298i	0.0874464	−	0.495933i	0.996802	−	0.0799130i	$-0.0254643\pi$
$174$		0			0
$175$	0.393933	+	0.143380i	0.0297785	+	0.0108385i
$176$	−4.08512	+	1.48686i	−0.307928	+	0.112077i
$177$		0			0
$178$	8.96838	+	15.5337i	0.672208	+	1.16430i
$179$	−10.7121	+	18.5540i	−0.800662	+	1.38679i	0.118518	+	0.992952i	$0.462186\pi$
$179$	−10.7121	+	18.5540i	−0.800662	+	1.38679i	−0.919181	+	0.393836i	$0.871148\pi$
$180$		0			0
$181$	−2.98411	−	16.9237i	−0.221807	−	1.25793i	−0.868696	−	0.495346i	$-0.835041\pi$
$181$	−2.98411	−	16.9237i	−0.221807	−	1.25793i	0.646889	−	0.762584i	$-0.276070\pi$
$182$	−0.598326	+	1.03633i	−0.0443509	+	0.0768180i
$183$		0			0
$184$	0.0812519	−	0.0681784i	0.00598997	−	0.00502618i
$185$	−6.31180	+	2.29731i	−0.464053	+	0.168901i
$186$		0			0
$187$	7.06212	+	5.92582i	0.516433	+	0.433339i
$188$	1.37551	−	7.80093i	0.100320	−	0.568941i
$189$		0			0
$190$	−1.14796	+	7.11192i	−0.0832815	+	0.515953i
$191$	6.57398			0.475676			0.237838	−	0.971305i	$-0.423561\pi$
$191$	6.57398			0.475676			0.237838	+	0.971305i	$0.423561\pi$
$192$		0			0
$193$	−8.69253	−	7.29390i	−0.625702	−	0.525027i	0.273888	−	0.961762i	$-0.411690\pi$
$193$	−8.69253	−	7.29390i	−0.625702	−	0.525027i	−0.899590	+	0.436735i	$0.856135\pi$
$194$	10.0432	+	3.65544i	0.721062	+	0.262445i
$195$		0			0
$196$	−5.33615	+	4.47756i	−0.381154	+	0.319826i
$197$	3.22416	+	5.58440i	0.229712	+	0.397872i	0.957723	−	0.287693i	$-0.0928884\pi$
$197$	3.22416	+	5.58440i	0.229712	+	0.397872i	−0.728011	+	0.685565i	$0.759555\pi$
$198$		0			0
$199$	2.90420	+	16.4705i	0.205873	+	1.16757i	0.896060	+	0.443934i	$0.146417\pi$
$199$	2.90420	+	16.4705i	0.205873	+	1.16757i	−0.690186	+	0.723632i	$0.742471\pi$
$200$	0.393933	+	2.23411i	0.0278553	+	0.157975i
$201$		0			0
$202$	−4.03209	−	6.98378i	−0.283697	−	0.491377i
$203$	−0.564178	+	0.473401i	−0.0395975	+	0.0332263i
$204$		0			0
$205$	−13.4153	−	4.88279i	−0.936968	−	0.341029i
$206$	−13.7344	−	11.5245i	−0.956923	−	0.802953i
$207$		0			0
$208$	−6.47565			−0.449006
$209$	14.3380	−	12.3897i	0.991778	−	0.857010i
$210$		0			0
$211$	−0.847296	+	4.80526i	−0.0583303	+	0.330807i	−0.999983	−	0.00577769i	$-0.998161\pi$
$211$	−0.847296	+	4.80526i	−0.0583303	+	0.330807i	0.941653	+	0.336585i	$0.109272\pi$
$212$	7.05690	+	5.92145i	0.484670	+	0.406687i
$213$		0			0
$214$	13.1446	−	4.78423i	0.898543	−	0.327043i
$215$	0.0530334	−	0.0445003i	0.00361685	−	0.00303490i
$216$		0			0
$217$	0.298133	−	0.516382i	0.0202386	−	0.0350543i
$218$	0.828878	+	4.70080i	0.0561387	+	0.318378i
$219$		0			0
$220$	−3.59240	+	6.22221i	−0.242199	+	0.419502i
$221$	6.86618	+	11.8926i	0.461869	+	0.799981i
$222$		0			0
$223$	−27.0453	+	9.84370i	−1.81109	+	0.659183i	−0.814182	+	0.580609i	$0.802814\pi$
$223$	−27.0453	+	9.84370i	−1.81109	+	0.659183i	−0.996908	+	0.0785736i	$0.974963\pi$
$224$	0.173648	+	0.0632028i	0.0116024	+	0.00422291i
$225$		0			0
$226$	−0.130882	+	0.742267i	−0.00870613	+	0.0493749i
$227$	3.75608			0.249300			0.124650	−	0.992201i	$-0.460219\pi$
$227$	3.75608			0.249300			0.124650	+	0.992201i	$0.460219\pi$
$228$		0			0
$229$	17.5175			1.15759			0.578796	−	0.815472i	$-0.303523\pi$
$229$	17.5175			1.15759			0.578796	+	0.815472i	$0.303523\pi$
$230$	0.0304400	−	0.172634i	0.00200716	−	0.0113831i
$231$		0			0
$232$	−3.74510	−	1.36310i	−0.245878	−	0.0894922i
$233$	−6.58260	+	2.39587i	−0.431240	+	0.156959i	−0.548515	−	0.836141i	$-0.684807\pi$
$233$	−6.58260	+	2.39587i	−0.431240	+	0.156959i	0.117274	+	0.993100i	$0.462584\pi$
$234$		0			0
$235$	−6.54576	−	11.3376i	−0.426998	−	0.739583i
$236$	5.04576	−	8.73951i	0.328451	−	0.568894i
$237$		0			0
$238$	−0.0680482	−	0.385920i	−0.00441091	−	0.0250155i
$239$	0.467911	−	0.810446i	0.0302667	−	0.0524234i	−0.850495	−	0.525983i	$-0.823698\pi$
$239$	0.467911	−	0.810446i	0.0302667	−	0.0524234i	0.880762	+	0.473559i	$0.157031\pi$
$240$		0			0
$241$	−22.0082	+	18.4671i	−1.41767	+	1.18957i	−0.465101	+	0.885258i	$0.653982\pi$
$241$	−22.0082	+	18.4671i	−1.41767	+	1.18957i	−0.952573	+	0.304311i	$0.901574\pi$
$242$	7.42262	−	2.70161i	0.477144	−	0.173666i
$243$		0			0
$244$	2.75490	+	2.31164i	0.176364	+	0.147987i
$245$	−1.99912	+	11.3376i	−0.127719	+	0.724332i
$246$		0			0
$247$	26.3817	−	10.0377i	1.67863	−	0.638683i
$248$	3.22668			0.204894
$249$		0			0
$250$	9.20233	+	7.72167i	0.582007	+	0.488362i
$251$	22.7271	+	8.27201i	1.43452	+	0.522124i	0.938225	−	0.346027i	$-0.112469\pi$
$251$	22.7271	+	8.27201i	1.43452	+	0.522124i	0.496300	+	0.868151i	$0.334692\pi$
$252$		0			0
$253$	−0.353226	+	0.296392i	−0.0222071	+	0.0186340i
$254$	−5.41147	−	9.37295i	−0.339546	−	0.588111i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−1.52822	−	8.66696i	−0.0953277	−	0.540630i	−0.994646	−	0.103336i	$-0.967048\pi$
$257$	−1.52822	−	8.66696i	−0.0953277	−	0.540630i	0.899319	−	0.437294i	$-0.144063\pi$
$258$		0			0
$259$	−0.375515	−	0.650411i	−0.0233334	−	0.0404146i
$260$	−8.19846	+	6.87933i	−0.508447	+	0.426638i
$261$		0			0
$262$	−10.1912	−	3.70929i	−0.629614	−	0.229161i
$263$	−1.00206	−	0.840828i	−0.0617896	−	0.0518477i	0.611370	−	0.791345i	$-0.290619\pi$
$263$	−1.00206	−	0.840828i	−0.0617896	−	0.0518477i	−0.673159	+	0.739497i	$0.735063\pi$
$264$		0			0
$265$	15.2249			0.935260
$266$	−0.805407	+	0.0116794i	−0.0493827	+	0.000716110i
$267$		0			0
$268$	−1.38666	+	7.86414i	−0.0847037	+	0.480379i
$269$	−6.70368	−	5.62505i	−0.408730	−	0.342966i	0.415126	−	0.909764i	$-0.363737\pi$
$269$	−6.70368	−	5.62505i	−0.408730	−	0.342966i	−0.823857	+	0.566798i	$0.808182\pi$
$270$		0			0
$271$	12.9179	−	4.70172i	0.784705	−	0.285609i	0.0815717	−	0.996667i	$-0.474006\pi$
$271$	12.9179	−	4.70172i	0.784705	−	0.285609i	0.703133	+	0.711058i	$0.251784\pi$
$272$	1.62449	−	1.36310i	0.0984989	−	0.0826504i
$273$		0			0
$274$	6.97565	−	12.0822i	0.421415	−	0.729911i
$275$	−1.71254	−	9.71232i	−0.103270	−	0.585675i
$276$		0			0
$277$	−12.5039	+	21.6573i	−0.751285	+	1.30126i	0.195915	+	0.980621i	$0.437232\pi$
$277$	−12.5039	+	21.6573i	−0.751285	+	1.30126i	−0.947200	+	0.320643i	$0.896101\pi$
$278$	2.98293	+	5.16658i	0.178904	+	0.309871i
$279$		0			0
$280$	0.286989	−	0.104455i	0.0171509	−	0.00624241i
$281$	11.4226	+	4.15749i	0.681416	+	0.248015i	0.659456	−	0.751744i	$-0.270787\pi$
$281$	11.4226	+	4.15749i	0.681416	+	0.248015i	0.0219608	+	0.999759i	$0.493009\pi$
$282$		0			0
$283$	−1.85756	+	10.5348i	−0.110421	+	0.626227i	0.878495	+	0.477751i	$0.158548\pi$
$283$	−1.85756	+	10.5348i	−0.110421	+	0.626227i	−0.988916	+	0.148476i	$0.952563\pi$
$284$	4.04189			0.239842
$285$		0			0
$286$	28.1516			1.66464
$287$	0.277189	−	1.57202i	0.0163619	−	0.0927932i
$288$		0			0
$289$	11.7490	+	4.27628i	0.691116	+	0.251546i
$290$	−6.18954	+	2.25281i	−0.363462	+	0.132289i
$291$		0			0
$292$	−7.59879	−	13.1615i	−0.444686	−	0.770218i
$293$	−6.67365	+	11.5591i	−0.389879	+	0.675290i	−0.992433	−	0.122788i	$-0.960816\pi$
$293$	−6.67365	+	11.5591i	−0.389879	+	0.675290i	0.602554	+	0.798078i	$0.294150\pi$
$294$		0			0
$295$	−2.89615	−	16.4249i	−0.168621	−	0.956295i
$296$	2.03209	−	3.51968i	0.118113	−	0.204577i
$297$		0			0
$298$	−10.8931	+	9.14036i	−0.631018	+	0.529487i
$299$	−0.645430	+	0.234917i	−0.0373262	+	0.0135856i
$300$		0			0
$301$	0.00592979	+	0.00497568i	0.000341787	+	0.000286794i
$302$	2.63950	−	14.9693i	0.151886	−	0.861389i
$303$		0			0
$304$	−2.23396	−	3.74292i	−0.128126	−	0.214671i
$305$	5.94356			0.340327
$306$		0			0
$307$	11.9987	+	10.0681i	0.684799	+	0.574615i	0.917404	−	0.397956i	$-0.130280\pi$
$307$	11.9987	+	10.0681i	0.684799	+	0.574615i	−0.232605	+	0.972571i	$0.574725\pi$
$308$	−0.754900	−	0.274761i	−0.0430144	−	0.0156560i
$309$		0			0
$310$	4.08512	−	3.42782i	0.232019	−	0.194687i
$311$	4.55303	+	7.88609i	0.258179	+	0.447179i	0.965754	−	0.259459i	$-0.0835443\pi$
$311$	4.55303	+	7.88609i	0.258179	+	0.447179i	−0.707575	+	0.706638i	$0.750211\pi$
$312$		0			0
$313$	3.08172	+	17.4773i	0.174189	+	0.987875i	0.939076	+	0.343710i	$0.111684\pi$
$313$	3.08172	+	17.4773i	0.174189	+	0.987875i	−0.764887	+	0.644165i	$0.777205\pi$
$314$	−1.63294	−	9.26087i	−0.0921522	−	0.522621i
$315$		0			0
$316$	−6.19846	−	10.7361i	−0.348691	−	0.603950i
$317$	−23.7822	+	19.9557i	−1.33574	+	1.12082i	−0.353046	+	0.935606i	$0.614854\pi$
$317$	−23.7822	+	19.9557i	−1.33574	+	1.12082i	−0.982698	+	0.185216i	$0.940701\pi$
$318$		0			0
$319$	16.2811	+	5.92582i	0.911564	+	0.331782i
$320$	1.26604	+	1.06234i	0.0707740	+	0.0593865i
$321$		0			0
$322$	0.0196004			0.00109229
$323$	−4.50521	+	8.07132i	−0.250677	+	0.449100i
$324$		0			0
$325$	2.55097	−	14.4673i	0.141503	−	0.802501i
$326$	5.84002	+	4.90036i	0.323449	+	0.271406i
$327$		0			0
$328$	8.11721	−	2.95442i	0.448198	−	0.163131i
$329$	1.12133	−	0.940908i	0.0618209	−	0.0518739i
$330$		0			0
$331$	5.03983	−	8.72924i	0.277014	−	0.479802i	−0.693627	−	0.720334i	$-0.743988\pi$
$331$	5.03983	−	8.72924i	0.277014	−	0.479802i	0.970641	+	0.240532i	$0.0773218\pi$
$332$	−1.46838	−	8.32759i	−0.0805877	−	0.457036i
$333$		0			0
$334$	8.60014	−	14.8959i	0.470579	−	0.815066i
$335$	6.59879	+	11.4294i	0.360531	+	0.624457i
$336$		0			0
$337$	7.87211	−	2.86521i	0.428821	−	0.156078i	−0.118587	−	0.992944i	$-0.537837\pi$
$337$	7.87211	−	2.86521i	0.428821	−	0.156078i	0.547409	+	0.836865i	$0.315614\pi$
$338$	27.1891	+	9.89603i	1.47889	+	0.538273i
$339$		0			0
$340$	0.608593	−	3.45150i	0.0330056	−	0.187184i
$341$	−14.0273			−0.759623
$342$		0			0
$343$	−2.58079			−0.139349
$344$	−0.00727396	+	0.0412527i	−0.000392186	+	0.00222420i
$345$		0			0
$346$	6.22416	+	2.26541i	0.334613	+	0.121789i
$347$	12.2306	−	4.45156i	0.656570	−	0.238972i	0.00781546	−	0.999969i	$-0.497512\pi$
$347$	12.2306	−	4.45156i	0.656570	−	0.238972i	0.648755	+	0.760997i	$0.275290\pi$
$348$		0			0
$349$	3.35369	+	5.80877i	0.179519	+	0.310936i	0.941716	−	0.336409i	$-0.109213\pi$
$349$	3.35369	+	5.80877i	0.179519	+	0.310936i	−0.762197	+	0.647345i	$0.775879\pi$
$350$	−0.209607	+	0.363051i	−0.0112040	+	0.0194059i
$351$		0			0
$352$	−0.754900	−	4.28125i	−0.0402363	−	0.228191i
$353$	5.32295	−	9.21962i	0.283312	−	0.490711i	−0.688886	−	0.724869i	$-0.741900\pi$
$353$	5.32295	−	9.21962i	0.283312	−	0.490711i	0.972198	+	0.234159i	$0.0752335\pi$
$354$		0			0
$355$	5.11721	−	4.29385i	0.271593	−	0.227894i
$356$	−16.8550	+	6.13473i	−0.893315	+	0.325140i
$357$		0			0
$358$	−16.4119	−	13.7713i	−0.867398	−	0.727833i
$359$	5.06418	−	28.7204i	0.267277	−	1.51580i	−0.495195	−	0.868782i	$-0.664903\pi$
$359$	5.06418	−	28.7204i	0.267277	−	1.51580i	0.762472	−	0.647022i	$-0.223986\pi$
$360$		0			0
$361$	14.9029	+	11.7858i	0.784361	+	0.620305i
$362$	17.1848			0.903213
$363$		0			0
$364$	−0.916689	−	0.769193i	−0.0480475	−	0.0403167i
$365$	−23.6024	−	8.59056i	−1.23540	−	0.449650i
$366$		0			0
$367$	−2.71095	+	2.27476i	−0.141511	+	0.118741i	−0.710795	−	0.703399i	$-0.751665\pi$
$367$	−2.71095	+	2.27476i	−0.141511	+	0.118741i	0.569285	+	0.822141i	$0.307220\pi$
$368$	0.0530334	+	0.0918566i	0.00276456	+	0.00478836i
$369$		0			0
$370$	−1.16637	−	6.61484i	−0.0606369	−	0.343889i
$371$	0.295607	+	1.67647i	0.0153472	+	0.0870380i
$372$		0			0
$373$	−5.10472	−	8.84164i	−0.264313	−	0.457803i	0.703071	−	0.711120i	$-0.251812\pi$
$373$	−5.10472	−	8.84164i	−0.264313	−	0.457803i	−0.967383	+	0.253317i	$0.918478\pi$
$374$	−7.06212	+	5.92582i	−0.365173	+	0.306417i
$375$		0			0
$376$	7.44356	+	2.70924i	0.383872	+	0.139718i
$377$	19.7704	+	16.5893i	1.01823	+	0.854393i
$378$		0			0
$379$	12.6287			0.648691			0.324345	−	0.945939i	$-0.394856\pi$
$379$	12.6287			0.648691			0.324345	+	0.945939i	$0.394856\pi$
$380$	−6.80453	−	2.36549i	−0.349065	−	0.121347i
$381$		0			0
$382$	−1.14156	+	6.47410i	−0.0584073	+	0.331244i
$383$	6.67546	+	5.60138i	0.341100	+	0.286217i	0.797205	−	0.603709i	$-0.206311\pi$
$383$	6.67546	+	5.60138i	0.341100	+	0.286217i	−0.456105	+	0.889926i	$0.650756\pi$
$384$		0			0
$385$	−1.24763	+	0.454099i	−0.0635849	+	0.0231430i
$386$	8.69253	−	7.29390i	0.442438	−	0.371250i
$387$		0			0
$388$	−5.34389	+	9.25589i	−0.271295	+	0.469897i
$389$	1.50118	+	8.51363i	0.0761130	+	0.431658i	0.998923	+	0.0464023i	$0.0147756\pi$
$389$	1.50118	+	8.51363i	0.0761130	+	0.431658i	−0.922810	+	0.385256i	$0.874113\pi$
$390$		0			0
$391$	0.112463	−	0.194792i	0.00568752	−	0.00985108i
$392$	−3.48293	−	6.03260i	−0.175914	−	0.304693i
$393$		0			0
$394$	−6.05943	+	2.20545i	−0.305270	+	0.111109i
$395$	−19.2528	−	7.00746i	−0.968716	−	0.352584i
$396$		0			0
$397$	−1.19372	+	6.76990i	−0.0599109	+	0.339771i	−0.999999	−	0.00115924i	$-0.999631\pi$
$397$	−1.19372	+	6.76990i	−0.0599109	+	0.339771i	0.940088	+	0.340931i	$0.110742\pi$
$398$	−16.7246			−0.838330
$399$		0			0
$400$	−2.26857			−0.113429
$401$	5.11200	−	28.9916i	0.255281	−	1.44777i	−0.540070	−	0.841620i	$-0.681602\pi$
$401$	5.11200	−	28.9916i	0.255281	−	1.44777i	0.795351	−	0.606150i	$-0.207287\pi$
$402$		0			0
$403$	−19.6348	−	7.14647i	−0.978077	−	0.355991i
$404$	7.57785	−	2.75811i	0.377012	−	0.137221i
$405$		0			0
$406$	−0.368241	−	0.637812i	−0.0182755	−	0.0316541i
$407$	−8.83409	+	15.3011i	−0.437890	+	0.758447i
$408$		0			0
$409$	−3.69459	−	20.9531i	−0.182686	−	1.03606i	−0.928893	−	0.370349i	$-0.879238\pi$
$409$	−3.69459	−	20.9531i	−0.182686	−	1.03606i	0.746207	−	0.665714i	$-0.231873\pi$
$410$	7.13816	−	12.3636i	0.352528	−	0.610597i
$411$		0			0
$412$	13.7344	−	11.5245i	0.676646	−	0.567774i
$413$	1.75237	−	0.637812i	0.0862287	−	0.0313847i
$414$		0			0
$415$	−10.7057	−	8.98318i	−0.525524	−	0.440967i
$416$	1.12449	−	6.37727i	0.0551324	−	0.312671i
$417$		0			0
$418$	9.71167	+	16.2716i	0.475013	+	0.795869i
$419$	−15.8922			−0.776384			−0.388192	−	0.921579i	$-0.626900\pi$
$419$	−15.8922			−0.776384			−0.388192	+	0.921579i	$0.626900\pi$
$420$		0			0
$421$	15.0103	+	12.5951i	0.731556	+	0.613848i	0.930555	−	0.366151i	$-0.119325\pi$
$421$	15.0103	+	12.5951i	0.731556	+	0.613848i	−0.199000	+	0.980000i	$0.563769\pi$
$422$	−4.58512	−	1.66885i	−0.223200	−	0.0812383i
$423$		0			0
$424$	−7.05690	+	5.92145i	−0.342714	+	0.287571i
$425$	2.40538	+	4.16624i	0.116678	+	0.202093i
$426$		0			0
$427$	0.115400	+	0.654467i	0.00558461	+	0.0316719i
$428$	2.42902	+	13.7756i	0.117411	+	0.665870i
$429$		0			0
$430$	0.0346151	+	0.0599551i	0.00166929	+	0.00289129i
$431$	3.18273	−	2.67063i	0.153307	−	0.128640i	−0.562908	−	0.826520i	$-0.690317\pi$
$431$	3.18273	−	2.67063i	0.153307	−	0.128640i	0.716215	+	0.697880i	$0.245873\pi$
$432$		0			0
$433$	3.34730	+	1.21832i	0.160861	+	0.0585485i	0.421195	−	0.906970i	$-0.361611\pi$
$433$	3.34730	+	1.21832i	0.160861	+	0.0585485i	−0.260335	+	0.965518i	$0.583833\pi$
$434$	0.456767	+	0.383273i	0.0219255	+	0.0183977i
$435$		0			0
$436$	−4.77332			−0.228600
$437$	−0.358441	−	0.292016i	−0.0171465	−	0.0139690i
$438$		0			0
$439$	−1.42649	+	8.09002i	−0.0680826	+	0.386116i	0.931658	+	0.363337i	$0.118363\pi$
$439$	−1.42649	+	8.09002i	−0.0680826	+	0.386116i	−0.999741	+	0.0227790i	$0.992749\pi$
$440$	−5.50387	−	4.61830i	−0.262387	−	0.220169i
$441$		0			0
$442$	−12.9042	+	4.69674i	−0.613790	+	0.223401i
$443$	14.5137	−	12.1784i	0.689565	−	0.578614i	−0.229219	−	0.973375i	$-0.573617\pi$
$443$	14.5137	−	12.1784i	0.689565	−	0.578614i	0.918784	+	0.394761i	$0.129173\pi$
$444$		0			0
$445$	−14.8221	+	25.6726i	−0.702634	+	1.21700i
$446$	−4.99778	−	28.3438i	−0.236652	−	1.34212i
$447$		0			0
$448$	−0.0923963	+	0.160035i	−0.00436531	+	0.00756094i
$449$	5.24628	+	9.08683i	0.247587	+	0.428834i	0.962856	−	0.270016i	$-0.0870289\pi$
$449$	5.24628	+	9.08683i	0.247587	+	0.428834i	−0.715269	+	0.698850i	$0.753696\pi$
$450$		0			0
$451$	−35.2879	+	12.8438i	−1.66164	+	0.604789i
$452$	−0.708263	−	0.257787i	−0.0333139	−	0.0121253i
$453$		0			0
$454$	−0.652237	+	3.69902i	−0.0306110	+	0.173604i
$455$	−1.97771			−0.0927165
$456$		0			0
$457$	−0.415593			−0.0194406			−0.00972031	−	0.999953i	$-0.503094\pi$
$457$	−0.415593			−0.0194406			−0.00972031	+	0.999953i	$0.503094\pi$
$458$	−3.04189	+	17.2514i	−0.142138	+	0.806105i
$459$		0			0
$460$	0.164725	+	0.0599551i	0.00768036	+	0.00279542i
$461$	23.7344	−	8.63862i	1.10542	−	0.402341i	0.276110	−	0.961126i	$-0.410955\pi$
$461$	23.7344	−	8.63862i	1.10542	−	0.402341i	0.829312	+	0.558785i	$0.188732\pi$
$462$		0			0
$463$	−9.39558	−	16.2736i	−0.436650	−	0.756300i	0.560779	−	0.827966i	$-0.310502\pi$
$463$	−9.39558	−	16.2736i	−0.436650	−	0.756300i	−0.997429	+	0.0716660i	$0.977168\pi$
$464$	1.99273	−	3.45150i	0.0925100	−	0.160232i
$465$		0			0
$466$	−1.21641	−	6.89863i	−0.0563493	−	0.319573i
$467$	−8.56670	+	14.8380i	−0.396420	+	0.686619i	−0.993281	−	0.115725i	$-0.963081\pi$
$467$	−8.56670	+	14.8380i	−0.396420	+	0.686619i	0.596861	+	0.802344i	$0.296414\pi$
$468$		0			0
$469$	−1.13041	+	0.948531i	−0.0521977	+	0.0437991i
$470$	12.3020	−	4.47756i	0.567449	−	0.206535i
$471$		0			0
$472$	7.73055	+	6.48670i	0.355827	+	0.298575i
$473$	0.0316221	−	0.179338i	0.00145398	−	0.00824595i
$474$		0			0
$475$	9.24211	−	3.51643i	0.424057	−	0.161345i
$476$	0.391874			0.0179615
$477$		0			0
$478$	0.716881	+	0.601535i	0.0327894	+	0.0275136i
$479$	−10.2973	−	3.74789i	−0.470494	−	0.171246i	0.0958823	−	0.995393i	$-0.469433\pi$
$479$	−10.2973	−	3.74789i	−0.470494	−	0.171246i	−0.566376	+	0.824147i	$0.691655\pi$
$480$		0			0
$481$	−20.1609	+	16.9170i	−0.919258	+	0.771349i
$482$	−14.3648	−	24.8806i	−0.654300	−	1.13328i
$483$		0			0
$484$	1.37164	+	7.77898i	0.0623475	+	0.353590i
$485$	3.06728	+	17.3954i	0.139278	+	0.789884i
$486$		0			0
$487$	−8.44016	−	14.6188i	−0.382460	−	0.662440i	0.608953	−	0.793206i	$-0.291590\pi$
$487$	−8.44016	−	14.6188i	−0.382460	−	0.662440i	−0.991413	+	0.130766i	$0.958256\pi$
$488$	−2.75490	+	2.31164i	−0.124708	+	0.104643i
$489$		0			0
$490$	−10.8182	−	3.93750i	−0.488716	−	0.177878i
$491$	8.62314	+	7.23567i	0.389157	+	0.326541i	0.816285	−	0.577650i	$-0.196030\pi$
$491$	8.62314	+	7.23567i	0.389157	+	0.326541i	−0.427128	+	0.904191i	$0.640475\pi$
$492$		0			0
$493$	−8.45161			−0.380641
$494$	5.30406	+	27.7239i	0.238641	+	1.24736i
$495$		0			0
$496$	−0.560307	+	3.17766i	−0.0251585	+	0.142681i
$497$	0.572167	+	0.480105i	0.0256652	+	0.0215357i
$498$		0			0
$499$	9.18139	−	3.34175i	0.411015	−	0.149597i	−0.128233	−	0.991744i	$-0.540931\pi$
$499$	9.18139	−	3.34175i	0.411015	−	0.149597i	0.539249	+	0.842147i	$0.318708\pi$
$500$	−9.20233	+	7.72167i	−0.411541	+	0.345324i
$501$		0			0
$502$	−12.0929	+	20.9455i	−0.539731	+	0.934841i
$503$	6.50093	+	36.8686i	0.289862	+	1.64389i	0.687381	+	0.726297i	$0.258760\pi$
$503$	6.50093	+	36.8686i	0.289862	+	1.64389i	−0.397519	+	0.917594i	$0.630129\pi$
$504$		0			0
$505$	6.66385	−	11.5421i	0.296537	−	0.513618i
$506$	−0.230552	−	0.399328i	−0.0102493	−	0.0177523i
$507$		0			0
$508$	10.1702	−	3.70167i	0.451232	−	0.164235i
$509$	−3.49273	−	1.27125i	−0.154812	−	0.0563471i	0.263452	−	0.964673i	$-0.415139\pi$
$509$	−3.49273	−	1.27125i	−0.154812	−	0.0563471i	−0.418264	+	0.908326i	$0.637361\pi$
$510$		0			0
$511$	0.487674	−	2.76573i	0.0215734	−	0.122349i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	8.80066			0.388180
$515$	5.14543	−	29.1812i	0.226735	−	1.28588i
$516$		0			0
$517$	−32.3594	−	11.7778i	−1.42316	−	0.517989i
$518$	0.705737	−	0.256867i	0.0310083	−	0.0112861i
$519$		0			0
$520$	−5.35117	−	9.26849i	−0.234664	−	0.406450i
$521$	−0.446089	+	0.772649i	−0.0195435	+	0.0338504i	−0.875632	−	0.482979i	$-0.839555\pi$
$521$	−0.446089	+	0.772649i	−0.0195435	+	0.0338504i	0.856088	+	0.516830i	$0.172888\pi$
$522$		0			0
$523$	−2.44238	−	13.8514i	−0.106798	−	0.605681i	−0.990487	−	0.137606i	$-0.956059\pi$
$523$	−2.44238	−	13.8514i	−0.106798	−	0.605681i	0.883689	−	0.468074i	$-0.155052\pi$
$524$	5.42262	−	9.39225i	0.236888	−	0.410302i
$525$		0			0
$526$	1.00206	−	0.840828i	0.0436919	−	0.0366618i
$527$	6.42989	−	2.34029i	0.280091	−	0.101945i
$528$		0			0
$529$	−17.6104	−	14.7769i	−0.765670	−	0.642473i
$530$	−2.64378	+	14.9936i	−0.114839	+	0.651281i
$531$		0			0
$532$	0.128356	−	0.795199i	0.00556492	−	0.0344763i
$533$	−55.9377			−2.42293
$534$		0			0
$535$	17.7096	+	14.8601i	0.765653	+	0.642459i
$536$	−7.50387	−	2.73119i	−0.324118	−	0.117969i
$537$		0			0
$538$	6.70368	−	5.62505i	0.289016	−	0.242513i
$539$	15.1413	+	26.2255i	0.652182	+	1.12961i
$540$		0			0
$541$	4.44862	+	25.2294i	0.191261	+	1.08469i	0.917644	+	0.397404i	$0.130089\pi$
$541$	4.44862	+	25.2294i	0.191261	+	1.08469i	−0.726383	+	0.687290i	$0.758800\pi$
$542$	2.38713	+	13.5381i	0.102536	+	0.581510i
$543$		0			0
$544$	1.06031	+	1.83651i	0.0454603	+	0.0787396i
$545$	−6.04323	+	5.07087i	−0.258864	+	0.217212i
$546$		0			0
$547$	−34.1263	−	12.4210i	−1.45914	−	0.531082i	−0.514008	−	0.857785i	$-0.671840\pi$
$547$	−34.1263	−	12.4210i	−1.45914	−	0.531082i	−0.945127	+	0.326704i	$0.894062\pi$
$548$	10.6873	+	8.96773i	0.456540	+	0.383082i
$549$		0			0
$550$	9.86215			0.420523
$551$	−2.76827	+	17.1502i	−0.117932	+	0.730623i
$552$		0			0
$553$	0.397804	−	2.25606i	0.0169163	−	0.0959373i
$554$	−19.1570	−	16.0747i	−0.813905	−	0.682947i
$555$		0			0
$556$	−5.60607	+	2.04044i	−0.237750	+	0.0865340i
$557$	−17.8635	+	14.9893i	−0.756900	+	0.635115i	−0.937318	−	0.348475i	$-0.886700\pi$
$557$	−17.8635	+	14.9893i	−0.756900	+	0.635115i	0.180418	+	0.983590i	$0.442255\pi$
$558$		0			0
$559$	0.135630	−	0.234917i	0.00573652	−	0.00993594i
$560$	0.0530334	+	0.300767i	0.00224107	+	0.0127097i
$561$		0			0
$562$	−6.07785	+	10.5271i	−0.256379	+	0.444061i
$563$	2.26991	+	3.93161i	0.0956655	+	0.165698i	0.909886	−	0.414858i	$-0.136169\pi$
$563$	2.26991	+	3.93161i	0.0956655	+	0.165698i	−0.814221	+	0.580556i	$0.802835\pi$
$564$		0			0
$565$	−1.17055	+	0.426045i	−0.0492454	+	0.0179239i
$566$	−10.0522	−	3.65869i	−0.422524	−	0.153786i
$567$		0			0
$568$	−0.701867	+	3.98048i	−0.0294497	+	0.167017i
$569$	6.26621			0.262693			0.131347	−	0.991337i	$-0.458070\pi$
$569$	6.26621			0.262693			0.131347	+	0.991337i	$0.458070\pi$
$570$		0			0
$571$	1.03777			0.0434293			0.0217147	−	0.999764i	$-0.493087\pi$
$571$	1.03777			0.0434293			0.0217147	+	0.999764i	$0.493087\pi$
$572$	−4.88847	+	27.7239i	−0.204397	+	1.15919i
$573$		0			0
$574$	1.50000	+	0.545955i	0.0626088	+	0.0227877i
$575$	−0.226109	+	0.0822969i	−0.00942940	+	0.00343202i
$576$		0			0
$577$	20.1211	+	34.8507i	0.837652	+	1.45086i	0.891853	+	0.452325i	$0.149405\pi$
$577$	20.1211	+	34.8507i	0.837652	+	1.45086i	−0.0542015	+	0.998530i	$0.517261\pi$
$578$	−6.25150	+	10.8279i	−0.260028	+	0.450382i
$579$		0			0
$580$	−1.14378	−	6.48670i	−0.0474929	−	0.269346i
$581$	0.781308	−	1.35326i	0.0324141	−	0.0561429i
$582$		0			0
$583$	30.6785	−	25.7423i	1.27057	−	1.06614i
$584$	14.2811	−	5.19788i	0.590954	−	0.215090i
$585$		0			0
$586$	−10.2246	−	8.57948i	−0.422375	−	0.354415i
$587$	8.37598	−	47.5026i	0.345714	−	1.96064i	0.0789482	−	0.996879i	$-0.474844\pi$
$587$	8.37598	−	47.5026i	0.345714	−	1.96064i	0.266766	−	0.963761i	$-0.414045\pi$
$588$		0			0
$589$	−2.64290	−	13.8142i	−0.108899	−	0.569206i
$590$	16.6783			0.686634
$591$		0			0
$592$	3.11334	+	2.61240i	0.127958	+	0.107369i
$593$	−16.4217	−	5.97702i	−0.674360	−	0.245447i	−0.0179361	−	0.999839i	$-0.505710\pi$
$593$	−16.4217	−	5.97702i	−0.674360	−	0.245447i	−0.656424	+	0.754392i	$0.727932\pi$
$594$		0			0
$595$	0.496130	−	0.416302i	0.0203393	−	0.0170667i
$596$	−7.10994	−	12.3148i	−0.291234	−	0.504433i
$597$		0			0
$598$	−0.119271	−	0.676417i	−0.00487734	−	0.0276608i
$599$	−3.80376	−	21.5722i	−0.155417	−	0.881416i	−0.958403	−	0.285418i	$-0.907868\pi$
$599$	−3.80376	−	21.5722i	−0.155417	−	0.881416i	0.802986	−	0.595998i	$-0.203243\pi$
$600$		0			0
$601$	−4.63903	−	8.03504i	−0.189230	−	0.327756i	0.755764	−	0.654844i	$-0.227266\pi$
$601$	−4.63903	−	8.03504i	−0.189230	−	0.327756i	−0.944994	+	0.327088i	$0.893933\pi$
$602$	−0.00592979	+	0.00497568i	−0.000241680	+	0.000202794i
$603$		0			0
$604$	14.2836	+	5.19880i	0.581191	+	0.211536i
$605$	10.0005	+	8.39139i	0.406577	+	0.341158i
$606$		0			0
$607$	29.3354			1.19069			0.595344	−	0.803471i	$-0.297016\pi$
$607$	29.3354			1.19069			0.595344	+	0.803471i	$0.297016\pi$
$608$	4.07398	−	1.55007i	0.165222	−	0.0628635i
$609$		0			0
$610$	−1.03209	+	5.85327i	−0.0417881	+	0.236992i
$611$	−39.2946	−	32.9721i	−1.58969	−	1.33391i
$612$		0			0
$613$	22.7875	−	8.29396i	0.920377	−	0.334990i	0.161988	−	0.986793i	$-0.448209\pi$
$613$	22.7875	−	8.29396i	0.920377	−	0.334990i	0.758388	+	0.651803i	$0.225987\pi$
$614$	−11.9987	+	10.0681i	−0.484226	+	0.406314i
$615$		0			0
$616$	0.401674	−	0.695720i	0.0161839	−	0.0280313i
$617$	−3.47834	−	19.7266i	−0.140033	−	0.794165i	−0.971222	−	0.238176i	$-0.923451\pi$
$617$	−3.47834	−	19.7266i	−0.140033	−	0.794165i	0.831189	−	0.555989i	$-0.187660\pi$
$618$		0			0
$619$	4.00774	−	6.94161i	0.161085	−	0.279007i	−0.774173	−	0.632974i	$-0.781834\pi$
$619$	4.00774	−	6.94161i	0.161085	−	0.279007i	0.935258	+	0.353967i	$0.115167\pi$
$620$	2.66637	+	4.61830i	0.107084	+	0.185475i
$621$		0			0
$622$	−8.55690	+	3.11446i	−0.343101	+	0.124878i
$623$	−3.11468	−	1.13365i	−0.124787	−	0.0454188i
$624$		0			0
$625$	−1.47787	+	8.38144i	−0.0591149	+	0.335257i
$626$	−17.7469			−0.709309
$627$		0			0
$628$	9.40373			0.375250
$629$	1.49660	−	8.48762i	0.0596732	−	0.338424i
$630$		0			0
$631$	−3.74763	−	1.36402i	−0.149191	−	0.0543010i	0.266345	−	0.963878i	$-0.414184\pi$
$631$	−3.74763	−	1.36402i	−0.149191	−	0.0543010i	−0.415536	+	0.909577i	$0.636406\pi$
$632$	11.6493	−	4.24000i	0.463384	−	0.168658i
$633$		0			0
$634$	−15.5228	−	26.8862i	−0.616487	−	1.06779i
$635$	8.94356	−	15.4907i	0.354914	−	0.614730i
$636$		0			0
$637$	7.83300	+	44.4231i	0.310355	+	1.76011i
$638$	−8.66297	+	15.0047i	−0.342970	+	0.594042i
$639$		0			0
$640$	−1.26604	+	1.06234i	−0.0500448	+	0.0419926i
$641$	−26.2221	+	9.54406i	−1.03571	+	0.376968i	−0.803253	−	0.595639i	$-0.796899\pi$
$641$	−26.2221	+	9.54406i	−1.03571	+	0.376968i	−0.232458	+	0.972606i	$0.574677\pi$
$642$		0			0
$643$	−8.27584	−	6.94426i	−0.326367	−	0.273855i	0.464850	−	0.885389i	$-0.346108\pi$
$643$	−8.27584	−	6.94426i	−0.326367	−	0.273855i	−0.791218	+	0.611534i	$0.790553\pi$
$644$	−0.00340357	+	0.0193026i	−0.000134119	+	0.000760628i
$645$		0			0
$646$	−7.16637	−	5.83834i	−0.281957	−	0.229706i
$647$	34.4662			1.35500			0.677502	−	0.735521i	$-0.263062\pi$
$647$	34.4662			1.35500			0.677502	+	0.735521i	$0.263062\pi$
$648$		0			0
$649$	−33.6070	−	28.1996i	−1.31919	−	1.10693i
$650$	13.8045	+	5.02444i	0.541458	+	0.197075i
$651$		0			0
$652$	−5.84002	+	4.90036i	−0.228713	+	0.191913i
$653$	−11.4971	−	19.9135i	−0.449915	−	0.779275i	0.548465	−	0.836173i	$-0.315212\pi$
$653$	−11.4971	−	19.9135i	−0.449915	−	0.779275i	−0.998380	+	0.0568980i	$0.981879\pi$
$654$		0			0
$655$	−3.11246	−	17.6517i	−0.121614	−	0.689707i
$656$	1.50000	+	8.50692i	0.0585652	+	0.332140i
$657$		0			0
$658$	0.731896	+	1.26768i	0.0285323	+	0.0494194i
$659$	26.0742	−	21.8788i	1.01571	−	0.852279i	0.0266245	−	0.999646i	$-0.491524\pi$
$659$	26.0742	−	21.8788i	1.01571	−	0.852279i	0.989082	+	0.147367i	$0.0470797\pi$
$660$		0			0
$661$	−8.04411	−	2.92782i	−0.312880	−	0.113879i	0.180807	−	0.983519i	$-0.442129\pi$
$661$	−8.04411	−	2.92782i	−0.312880	−	0.113879i	−0.493687	+	0.869640i	$0.664351\pi$
$662$	7.72147	+	6.47908i	0.300103	+	0.251817i
$663$		0			0
$664$	8.45605			0.328158
$665$	−0.682266	−	1.14311i	−0.0264572	−	0.0443281i
$666$		0			0
$667$	0.0734053	−	0.416302i	0.00284226	−	0.0161193i
$668$	13.1762	+	11.0561i	0.509801	+	0.427774i
$669$		0			0
$670$	−12.4017	+	4.51384i	−0.479118	+	0.174385i
$671$	11.9764	−	10.0494i	0.462343	−	0.387951i
$672$		0			0
$673$	6.07011	−	10.5137i	0.233985	−	0.405275i	−0.724992	−	0.688757i	$-0.758157\pi$
$673$	6.07011	−	10.5137i	0.233985	−	0.405275i	0.958977	+	0.283483i	$0.0914899\pi$
$674$	1.45471	+	8.25006i	0.0560332	+	0.317780i
$675$		0			0
$676$	−14.4670	+	25.0576i	−0.556424	+	0.963755i
$677$	0.776722	+	1.34532i	0.0298519	+	0.0517049i	0.880565	−	0.473925i	$-0.157163\pi$
$677$	0.776722	+	1.34532i	0.0298519	+	0.0517049i	−0.850714	+	0.525630i	$0.823830\pi$
$678$		0			0
$679$	−1.85591	+	0.675498i	−0.0712235	+	0.0259232i
$680$	3.29339	+	1.19869i	0.126296	+	0.0459678i
$681$		0			0
$682$	2.43582	−	13.8142i	0.0932725	−	0.528974i
$683$	35.3892			1.35413			0.677065	−	0.735923i	$-0.263252\pi$
$683$	35.3892			1.35413			0.677065	+	0.735923i	$0.263252\pi$
$684$		0			0
$685$	23.0574			0.880977
$686$	0.448149	−	2.54158i	0.0171104	−	0.0970379i
$687$		0			0
$688$	−0.0393628	−	0.0143269i	−0.00150069	−	0.000546208i
$689$	56.0570	−	20.4031i	2.13560	−	0.777295i
$690$		0			0
$691$	19.6411	+	34.0195i	0.747185	+	1.29416i	0.949167	+	0.314772i	$0.101928\pi$
$691$	19.6411	+	34.0195i	0.747185	+	1.29416i	−0.201983	+	0.979389i	$0.564738\pi$
$692$	−3.31180	+	5.73621i	−0.125896	+	0.218058i
$693$		0			0
$694$	2.26011	+	12.8177i	0.0857928	+	0.486555i
$695$	−4.92989	+	8.53882i	−0.187001	+	0.323896i
$696$		0			0
$697$	14.0326	−	11.7747i	0.531521	−	0.445999i
$698$	−6.30288	+	2.29406i	−0.238568	+	0.0868315i
$699$		0			0
$700$	−0.321137	−	0.269466i	−0.0121378	−	0.0101849i
$701$	−2.89171	+	16.3997i	−0.109218	+	0.619409i	0.880233	+	0.474542i	$0.157386\pi$
$701$	−2.89171	+	16.3997i	−0.109218	+	0.619409i	−0.989451	+	0.144866i	$0.953725\pi$
$702$		0			0
$703$	−16.7331	−	5.81699i	−0.631100	−	0.219392i
$704$	4.34730			0.163845
$705$		0			0
$706$	8.15523	+	6.84305i	0.306926	+	0.257542i
$707$	1.40033	+	0.509678i	0.0526648	+	0.0191684i
$708$		0			0
$709$	33.3723	−	28.0027i	1.25332	−	1.05166i	0.256964	−	0.966421i	$-0.417278\pi$
$709$	33.3723	−	28.0027i	1.25332	−	1.05166i	0.996360	−	0.0852428i	$-0.0271666\pi$
$710$	3.34002	+	5.78509i	0.125349	+	0.217111i
$711$		0			0
$712$	−3.11468	−	17.6643i	−0.116728	−	0.661996i
$713$	0.0594300	+	0.337044i	0.00222567	+	0.0126224i
$714$		0			0
$715$	23.2631	+	40.2929i	0.869991	+	1.50687i
$716$	16.4119	−	13.7713i	0.613343	−	0.514656i
$717$		0			0
$718$	27.4047	+	9.97448i	1.02273	+	0.372244i
$719$	−4.94949	−	4.15312i	−0.184585	−	0.154885i	0.545813	−	0.837907i	$-0.316221\pi$
$719$	−4.94949	−	4.15312i	−0.184585	−	0.154885i	−0.730398	+	0.683022i	$0.760665\pi$
$720$		0			0
$721$	3.31315			0.123388
$722$	−14.1946	+	12.6299i	−0.528268	+	0.470035i
$723$		0			0
$724$	−2.98411	+	16.9237i	−0.110903	+	0.628965i
$725$	6.92602	+	5.81162i	0.257226	+	0.215838i
$726$		0			0
$727$	−1.73308	+	0.630789i	−0.0642763	+	0.0233947i	−0.373958	−	0.927446i	$-0.622000\pi$
$727$	−1.73308	+	0.630789i	−0.0642763	+	0.0233947i	0.309682	+	0.950840i	$0.399777\pi$
$728$	0.916689	−	0.769193i	0.0339747	−	0.0285082i
$729$		0			0
$730$	12.5586	−	21.7521i	0.464813	−	0.805080i
$731$	0.0154253	+	0.0874810i	0.000570524	+	0.00323560i
$732$		0			0
$733$	−16.1793	+	28.0234i	−0.597597	+	1.03507i	0.395578	+	0.918433i	$0.370544\pi$
$733$	−16.1793	+	28.0234i	−0.597597	+	1.03507i	−0.993175	+	0.116636i	$0.962789\pi$
$734$	−1.76945	−	3.06477i	−0.0653115	−	0.113123i
$735$		0			0
$736$	−0.0996702	+	0.0362770i	−0.00367389	+	0.00133719i
$737$	32.6215	+	11.8733i	1.20163	+	0.437358i
$738$		0			0
$739$	−1.89899	+	10.7697i	−0.0698553	+	0.396169i	0.929753	+	0.368184i	$0.120020\pi$
$739$	−1.89899	+	10.7697i	−0.0698553	+	0.396169i	−0.999608	+	0.0279854i	$0.991091\pi$
$740$	6.71688			0.246917
$741$		0			0
$742$	−1.70233			−0.0624946
$743$	1.81820	−	10.3115i	0.0667033	−	0.378293i	−0.933121	−	0.359562i	$-0.882926\pi$
$743$	1.81820	−	10.3115i	0.0667033	−	0.378293i	0.999825	−	0.0187314i	$-0.00596273\pi$
$744$		0			0
$745$	−22.0839	−	8.03790i	−0.809093	−	0.294486i
$746$	9.59374	−	3.49184i	0.351252	−	0.127845i
$747$		0			0
$748$	−4.60947	−	7.98384i	−0.168539	−	0.291918i
$749$	−1.29245	+	2.23859i	−0.0472252	+	0.0817964i
$750$		0			0
$751$	−4.58079	−	25.9789i	−0.167155	−	0.947984i	−0.946814	−	0.321780i	$-0.895719\pi$
$751$	−4.58079	−	25.9789i	−0.167155	−	0.947984i	0.779659	−	0.626204i	$-0.215392\pi$
$752$	−3.96064	+	6.86002i	−0.144430	+	0.250159i
$753$		0			0
$754$	−19.7704	+	16.5893i	−0.719995	+	0.604147i
$755$	23.6065	−	8.59208i	0.859130	−	0.312698i
$756$		0			0
$757$	17.4715	+	14.6604i	0.635014	+	0.532840i	0.902482	−	0.430727i	$-0.141743\pi$
$757$	17.4715	+	14.6604i	0.635014	+	0.532840i	−0.267469	+	0.963567i	$0.586187\pi$
$758$	−2.19294	+	12.4368i	−0.0796513	+	0.451725i
$759$		0			0
$760$	3.51114	−	6.29039i	0.127363	−	0.228176i
$761$	−41.5012			−1.50442			−0.752209	−	0.658924i	$-0.771012\pi$
$761$	−41.5012			−1.50442			−0.752209	+	0.658924i	$0.771012\pi$
$762$		0			0
$763$	−0.675708	−	0.566986i	−0.0244623	−	0.0205263i
$764$	−6.17752	−	2.24843i	−0.223495	−	0.0813454i
$765$		0			0
$766$	−6.67546	+	5.60138i	−0.241194	+	0.202386i
$767$	−32.6746	−	56.5940i	−1.17981	−	2.04349i
$768$		0			0
$769$	3.29948	+	18.7123i	0.118982	+	0.674782i	0.984701	+	0.174251i	$0.0557505\pi$
$769$	3.29948	+	18.7123i	0.118982	+	0.674782i	−0.865719	+	0.500530i	$0.833138\pi$
$770$	−0.230552	−	1.30753i	−0.00830852	−	0.0471199i
$771$		0			0
$772$	5.67365	+	9.82705i	0.204199	+	0.353683i
$773$	−13.1329	+	11.0198i	−0.472359	+	0.396356i	−0.847654	−	0.530549i	$-0.821986\pi$
$773$	−13.1329	+	11.0198i	−0.472359	+	0.396356i	0.375295	+	0.926905i	$0.377541\pi$
$774$		0			0
$775$	−6.87851	−	2.50357i	−0.247083	−	0.0899310i
$776$	−8.18732	−	6.86998i	−0.293908	−	0.246618i
$777$		0			0
$778$	−8.64496			−0.309937
$779$	−19.2973	−	32.3319i	−0.691396	−	1.15841i
$780$		0			0
$781$	3.05122	−	17.3043i	0.109181	−	0.619198i
$782$	0.172304	+	0.144580i	0.00616158	+	0.00517018i
$783$		0			0
$784$	6.54576	−	2.38246i	0.233777	−	0.0850879i
$785$	11.9055	−	9.98994i	0.424927	−	0.356556i
$786$		0			0
$787$	9.10014	−	15.7619i	0.324385	−	0.561851i	−0.657003	−	0.753888i	$-0.728176\pi$
$787$	9.10014	−	15.7619i	0.324385	−	0.561851i	0.981388	+	0.192037i	$0.0615094\pi$
$788$	−1.11974	−	6.35035i	−0.0398890	−	0.226222i
$789$		0			0
$790$	10.2442	−	17.7435i	0.364473	−	0.631286i
$791$	−0.0696407	−	0.120621i	−0.00247614	−	0.00428880i
$792$		0			0
$793$	21.8837	−	7.96502i	0.777114	−	0.282846i
$794$	−6.45976	−	2.35116i	−0.229248	−	0.0834396i
$795$		0			0
$796$	2.90420	−	16.4705i	0.102937	−	0.583783i
$797$	26.4584			0.937205			0.468603	−	0.883409i	$-0.344758\pi$
$797$	26.4584			0.937205			0.468603	+	0.883409i	$0.344758\pi$
$798$		0			0
$799$	16.7980			0.594270
$800$	0.393933	−	2.23411i	0.0139276	−	0.0789876i
$801$		0			0
$802$	27.6634	+	10.0687i	0.976830	+	0.355537i
$803$	−62.0840	+	22.5967i	−2.19090	+	0.797421i
$804$		0			0
$805$	0.0161968	+	0.0280537i	0.000570862	+	0.000988762i
$806$	10.4474	−	18.0955i	0.367995	−	0.637386i
$807$		0			0
$808$	1.40033	+	7.94166i	0.0492634	+	0.279387i
$809$	−15.2836	+	26.4719i	−0.537342	+	0.930704i	0.461704	+	0.887034i	$0.347238\pi$
$809$	−15.2836	+	26.4719i	−0.537342	+	0.930704i	−0.999046	+	0.0436699i	$0.986095\pi$
$810$		0			0
$811$	−5.25284	+	4.40766i	−0.184452	+	0.154774i	−0.730338	−	0.683086i	$-0.760638\pi$
$811$	−5.25284	+	4.40766i	−0.184452	+	0.154774i	0.545886	+	0.837859i	$0.316193\pi$
$812$	0.692066	−	0.251892i	0.0242868	−	0.00883966i
$813$		0			0
$814$	−13.5346	−	11.3569i	−0.474388	−	0.398059i
$815$	−2.18789	+	12.4081i	−0.0766385	+	0.434638i
$816$		0			0
$817$	0.182571	−	0.00264750i	0.00638735	−	9.26245e-5i
$818$	21.2763			0.743909
$819$		0			0
$820$	10.9363	+	9.17664i	0.381912	+	0.320462i
$821$	37.2870	+	13.5714i	1.30133	+	0.473644i	0.897429	−	0.441160i	$-0.145433\pi$
$821$	37.2870	+	13.5714i	1.30133	+	0.473644i	0.403898	+	0.914804i	$0.367655\pi$
$822$		0			0
$823$	−35.7900	+	30.0314i	−1.24756	+	1.04683i	−0.250666	+	0.968074i	$0.580650\pi$
$823$	−35.7900	+	30.0314i	−1.24756	+	1.04683i	−0.996894	+	0.0787539i	$0.974906\pi$
$824$	8.96451	+	15.5270i	0.312293	+	0.540908i
$825$		0			0
$826$	0.323826	+	1.83651i	0.0112673	+	0.0639002i
$827$	7.27884	+	41.2803i	0.253110	+	1.43546i	0.800878	+	0.598828i	$0.204367\pi$
$827$	7.27884	+	41.2803i	0.253110	+	1.43546i	−0.547768	+	0.836630i	$0.684522\pi$
$828$		0			0
$829$	0.251030	+	0.434796i	0.00871862	+	0.0151011i	0.870352	−	0.492430i	$-0.163891\pi$
$829$	0.251030	+	0.434796i	0.00871862	+	0.0151011i	−0.861633	+	0.507532i	$0.830558\pi$
$830$	10.7057	−	8.98318i	0.371602	−	0.311811i
$831$		0			0
$832$	6.08512	+	2.21480i	0.210964	+	0.0767845i
$833$	−11.3159	−	9.49519i	−0.392073	−	0.328989i
$834$		0			0
$835$	28.4270			0.983755
$836$	−17.7108	+	6.73859i	−0.612540	+	0.233059i
$837$		0			0
$838$	2.75965	−	15.6507i	0.0953305	−	0.540646i
$839$	24.0646	+	20.1926i	0.830804	+	0.697127i	0.955475	−	0.295071i	$-0.0953433\pi$
$839$	24.0646	+	20.1926i	0.830804	+	0.697127i	−0.124672	+	0.992198i	$0.539788\pi$
$840$		0			0
$841$	12.3252	−	4.48599i	0.425006	−	0.154689i
$842$	−15.0103	+	12.5951i	−0.517288	+	0.434056i
$843$		0			0
$844$	2.43969	−	4.22567i	0.0839777	−	0.145454i
$845$	8.30376	+	47.0930i	0.285658	+	1.62005i
$846$		0			0
$847$	−0.729837	+	1.26411i	−0.0250775	+	0.0434355i
$848$	−4.60607	−	7.97794i	−0.158173	−	0.273964i
$849$		0			0
$850$	−4.52064	+	1.64538i	−0.155057	+	0.0564360i
$851$	0.405078	+	0.147436i	0.0138859	+	0.00505405i
$852$		0			0
$853$	3.26682	−	18.5270i	0.111854	−	0.634354i	−0.876406	−	0.481572i	$-0.840066\pi$
$853$	3.26682	−	18.5270i	0.111854	−	0.634354i	0.988260	−	0.152781i	$-0.0488230\pi$
$854$	−0.664563			−0.0227409
$855$		0			0
$856$	−13.9881			−0.478105
$857$	−5.20305	+	29.5080i	−0.177733	+	1.00797i	0.757209	+	0.653172i	$0.226562\pi$
$857$	−5.20305	+	29.5080i	−0.177733	+	1.00797i	−0.934942	+	0.354800i	$0.884549\pi$
$858$		0			0
$859$	31.1698	+	11.3449i	1.06350	+	0.387083i	0.813743	−	0.581225i	$-0.197427\pi$
$859$	31.1698	+	11.3449i	1.06350	+	0.387083i	0.249758	+	0.968308i	$0.419649\pi$
$860$	−0.0650551	+	0.0236781i	−0.00221836	+	0.000807417i
$861$		0			0
$862$	2.07738	+	3.59813i	0.0707559	+	0.122553i
$863$	−19.1238	+	33.1233i	−0.650981	+	1.12753i	0.331905	+	0.943313i	$0.392309\pi$
$863$	−19.1238	+	33.1233i	−0.650981	+	1.12753i	−0.982885	+	0.184219i	$0.941025\pi$
$864$		0			0
$865$	1.90090	+	10.7806i	0.0646326	+	0.366550i
$866$	−1.78106	+	3.08489i	−0.0605229	+	0.104829i
$867$		0			0
$868$	−0.456767	+	0.383273i	−0.0155037	+	0.0130091i
$869$	−50.6430	+	18.4325i	−1.71794	+	0.625281i
$870$		0			0
$871$	39.6129	+	33.2392i	1.34223	+	1.12627i
$872$	0.828878	−	4.70080i	0.0280694	−	0.159189i
$873$		0			0
$874$	0.349823	−	0.302287i	0.0118329	−	0.0102250i
$875$	−2.21987			−0.0750455
$876$		0			0
$877$	−36.8981	−	30.9612i	−1.24596	−	1.04549i	−0.997034	−	0.0769627i	$-0.975478\pi$
$877$	−36.8981	−	30.9612i	−1.24596	−	1.04549i	−0.248927	−	0.968522i	$-0.580078\pi$
$878$	−7.71941	−	2.80963i	−0.260517	−	0.0948206i
$879$		0			0
$880$	5.50387	−	4.61830i	0.185535	−	0.155683i
$881$	18.8542	+	32.6564i	0.635213	+	1.10022i	0.986470	+	0.163942i	$0.0524209\pi$
$881$	18.8542	+	32.6564i	0.635213	+	1.10022i	−0.351257	+	0.936279i	$0.614246\pi$
$882$		0			0
$883$	−5.27022	−	29.8889i	−0.177357	−	1.00584i	−0.935388	−	0.353623i	$-0.884950\pi$
$883$	−5.27022	−	29.8889i	−0.177357	−	1.00584i	0.758031	−	0.652219i	$-0.226162\pi$
$884$	−2.38460	−	13.5237i	−0.0802028	−	0.454853i
$885$		0			0
$886$	9.47313	+	16.4079i	0.318256	+	0.551235i
$887$	0.709856	−	0.595640i	0.0238346	−	0.0199996i	−0.630793	−	0.775952i	$-0.717270\pi$
$887$	0.709856	−	0.595640i	0.0238346	−	0.0199996i	0.654627	+	0.755952i	$0.272826\pi$
$888$		0			0
$889$	1.87939	+	0.684040i	0.0630326	+	0.0229420i
$890$	−22.7087	−	19.0549i	−0.761198	−	0.638721i
$891$		0			0
$892$	28.7811			0.963661
$893$	5.50206	−	34.0868i	0.184119	−	1.14067i
$894$		0			0
$895$	6.14853	−	34.8700i	0.205523	−	1.16558i
$896$	−0.141559	−	0.118782i	−0.00472916	−	0.00396824i
$897$		0			0
$898$	−9.85978	+	3.58867i	−0.329025	+	0.119755i
$899$	9.85117	−	8.26611i	0.328555	−	0.275690i
$900$		0			0
$901$	−9.76769	+	16.9181i	−0.325409	+	0.563625i
$902$	−6.52094	−	36.9821i	−0.217124	−	1.23137i
$903$		0			0
$904$	0.376859	−	0.652739i	0.0125341	−	0.0217098i
$905$	14.2007	+	24.5963i	0.472047	+	0.817609i
$906$		0			0
$907$	3.98932	−	1.45199i	0.132463	−	0.0482127i	−0.274938	−	0.961462i	$-0.588657\pi$
$907$	3.98932	−	1.45199i	0.132463	−	0.0482127i	0.407401	+	0.913249i	$0.366435\pi$
$908$	−3.52956	−	1.28466i	−0.117133	−	0.0426328i
$909$		0			0
$910$	0.343426	−	1.94767i	0.0113845	−	0.0645645i
$911$	56.5509			1.87361			0.936807	−	0.349847i	$-0.113766\pi$
$911$	56.5509			1.87361			0.936807	+	0.349847i	$0.113766\pi$
$912$		0			0
$913$	−36.7610			−1.21661
$914$	0.0721670	−	0.409279i	0.00238707	−	0.0135378i
$915$		0			0
$916$	−16.4611	−	5.99135i	−0.543890	−	0.197960i
$917$	1.88326	−	0.685449i	0.0621906	−	0.0226355i
$918$		0			0
$919$	−29.4778	−	51.0570i	−0.972382	−	1.68421i	−0.688318	−	0.725409i	$-0.741650\pi$
$919$	−29.4778	−	51.0570i	−0.972382	−	1.68421i	−0.284064	−	0.958805i	$-0.591683\pi$
$920$	−0.0876485	+	0.151812i	−0.00288969	+	0.00500508i
$921$		0			0
$922$	4.38594	+	24.8739i	0.144443	+	0.819179i
$923$	13.0869	−	22.6672i	0.430762	−	0.746101i
$924$		0			0
$925$	−7.06283	+	5.92642i	−0.232225	+	0.194860i
$926$	17.6579	−	6.42696i	0.580275	−	0.211203i
$927$		0			0
$928$	3.05303	+	2.56180i	0.100221	+	0.0840952i
$929$	2.15446	−	12.2185i	0.0706855	−	0.400877i	−0.928852	−	0.370452i	$-0.879203\pi$
$929$	2.15446	−	12.2185i	0.0706855	−	0.400877i	0.999537	−	0.0304252i	$-0.00968613\pi$
$930$		0			0
$931$	−22.9743	+	19.8525i	−0.752953	+	0.650638i
$932$	7.00505			0.229458
$933$		0			0
$934$	−13.1250	−	11.0131i	−0.429462	−	0.360361i
$935$	−14.3173	−	5.21108i	−0.468227	−	0.170421i
$936$		0			0
$937$	21.2973	−	17.8705i	0.695751	−	0.583804i	−0.224810	−	0.974403i	$-0.572176\pi$
$937$	21.2973	−	17.8705i	0.695751	−	0.583804i	0.920561	+	0.390598i	$0.127732\pi$
$938$	−0.737826	−	1.27795i	−0.0240909	−	0.0417266i
$939$		0			0
$940$	2.27332	+	12.8926i	0.0741475	+	0.420511i
$941$	3.46632	+	19.6585i	0.112999	+	0.640848i	0.987722	+	0.156224i	$0.0499323\pi$
$941$	3.46632	+	19.6585i	0.112999	+	0.640848i	−0.874723	+	0.484623i	$0.838957\pi$
$942$		0			0
$943$	0.458111	+	0.793471i	0.0149181	+	0.0258390i
$944$	−7.73055	+	6.48670i	−0.251608	+	0.211124i
$945$		0			0
$946$	0.171122	+	0.0622833i	0.00556365	+	0.00202500i
$947$	−22.9807	−	19.2831i	−0.746773	−	0.626617i	0.187875	−	0.982193i	$-0.439840\pi$
$947$	−22.9807	−	19.2831i	−0.746773	−	0.626617i	−0.934647	+	0.355576i	$0.884285\pi$
$948$		0			0
$949$	−98.4143			−3.19466
$950$	1.85814	+	9.71232i	0.0602859	+	0.315109i
$951$		0			0
$952$	−0.0680482	+	0.385920i	−0.00220545	+	0.0125077i
$953$	−17.5713	−	14.7441i	−0.569190	−	0.477607i	0.312187	−	0.950021i	$-0.398938\pi$
$953$	−17.5713	−	14.7441i	−0.569190	−	0.477607i	−0.881377	+	0.472414i	$0.843383\pi$
$954$		0			0
$955$	−10.2096	+	3.71599i	−0.330375	+	0.120247i
$956$	−0.716881	+	0.601535i	−0.0231856	+	0.0194550i
$957$		0			0
$958$	5.47906	−	9.49000i	0.177020	−	0.306608i
$959$	0.447682	+	2.53893i	0.0144564	+	0.0819863i
$960$		0			0
$961$	10.2943	−	17.8302i	0.332073	−	0.575167i
$962$	−13.1591	−	22.7922i	−0.424266	−	0.734851i
$963$		0			0
$964$	26.9971	−	9.82613i	0.869517	−	0.316478i
$965$	17.6227	+	6.41415i	0.567296	+	0.206479i
$966$		0			0
$967$	−6.57233	+	37.2735i	−0.211352	+	1.19864i	0.675774	+	0.737109i	$0.263809\pi$
$967$	−6.57233	+	37.2735i	−0.211352	+	1.19864i	−0.887126	+	0.461527i	$0.847302\pi$
$968$	−7.89899			−0.253883
$969$		0			0
$970$	−17.6637			−0.567149
$971$	5.09421	−	28.8907i	0.163481	−	0.927146i	−0.787136	−	0.616779i	$-0.788437\pi$
$971$	5.09421	−	28.8907i	0.163481	−	0.927146i	0.950617	−	0.310367i	$-0.100452\pi$
$972$		0			0
$973$	−1.03596	−	0.377058i	−0.0332113	−	0.0120879i
$974$	15.8623	−	5.77341i	0.508261	−	0.184992i
$975$		0			0
$976$	−1.79813	−	3.11446i	−0.0575568	−	0.0996914i
$977$	7.08054	−	12.2638i	0.226526	−	0.392355i	−0.730250	−	0.683180i	$-0.760596\pi$
$977$	7.08054	−	12.2638i	0.226526	−	0.392355i	0.956776	+	0.290825i	$0.0939297\pi$
$978$		0			0
$979$	13.5405	+	76.7918i	0.432755	+	2.45428i
$980$	5.75624	−	9.97011i	0.183876	−	0.318483i
$981$		0			0
$982$	−8.62314	+	7.23567i	−0.275175	+	0.230900i
$983$	−32.6724	+	11.8918i	−1.04209	+	0.379288i	−0.805671	−	0.592364i	$-0.798195\pi$
$983$	−32.6724	+	11.8918i	−1.04209	+	0.379288i	−0.236416	+	0.971652i	$0.575973\pi$
$984$		0			0
$985$	−8.16385	−	6.85028i	−0.260122	−	0.218268i
$986$	1.46761	−	8.32321i	0.0467381	−	0.265065i
$987$		0			0
$988$	−28.2237	+	0.409279i	−0.897917	+	0.0130209i
$989$	−0.00444304			−0.000141280
$990$		0			0
$991$	−4.20393	−	3.52751i	−0.133542	−	0.112055i	0.573570	−	0.819156i	$-0.305558\pi$
$991$	−4.20393	−	3.52751i	−0.133542	−	0.112055i	−0.707112	+	0.707101i	$0.750002\pi$
$992$	−3.03209	−	1.10359i	−0.0962689	−	0.0350390i
$993$		0			0
$994$	−0.572167	+	0.480105i	−0.0181480	+	0.0152280i
$995$	−13.8204	−	23.9377i	−0.438137	−	0.758875i
$996$		0			0
$997$	−1.67128	−	9.47832i	−0.0529301	−	0.300182i	0.946838	−	0.321710i	$-0.104258\pi$
$997$	−1.67128	−	9.47832i	−0.0529301	−	0.300182i	−0.999768	+	0.0215289i	$0.993147\pi$
$998$	1.69665	+	9.62219i	0.0537066	+	0.304585i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.u.d.55.1		6
3.2	odd	2		114.2.i.b.55.1	✓	6
12.11	even	2		912.2.bo.c.625.1		6
19.3	odd	18		6498.2.a.bt.1.2		3
19.9	even	9	inner	342.2.u.d.199.1		6
19.16	even	9		6498.2.a.bo.1.2		3
57.35	odd	18		2166.2.a.t.1.2		3
57.41	even	18		2166.2.a.n.1.2		3
57.47	odd	18		114.2.i.b.85.1	yes	6
228.47	even	18		912.2.bo.c.769.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.b.55.1	✓	6	3.2	odd	2
114.2.i.b.85.1	yes	6	57.47	odd	18
342.2.u.d.55.1		6	1.1	even	1	trivial
342.2.u.d.199.1		6	19.9	even	9	inner
912.2.bo.c.625.1		6	12.11	even	2
912.2.bo.c.769.1		6	228.47	even	18
2166.2.a.n.1.2		3	57.41	even	18
2166.2.a.t.1.2		3	57.35	odd	18
6498.2.a.bo.1.2		3	19.16	even	9
6498.2.a.bt.1.2		3	19.3	odd	18

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(-1.55303 + 0.565258i) q^{5} +(-0.0923963 - 0.160035i) q^{7} +(0.500000 - 0.866025i) q^{8} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(-1.55303 + 0.565258i) q^{5} +(-0.0923963 - 0.160035i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.286989 - 1.62760i) q^{10} +(-2.17365 + 3.76487i) q^{11} +(-4.96064 + 4.16247i) q^{13} +(0.173648 - 0.0632028i) q^{14} +(0.766044 + 0.642788i) q^{16} +(0.368241 - 2.08840i) q^{17} +(-4.11721 - 1.43128i) q^{19} +1.65270 q^{20} +(-3.33022 - 2.79439i) q^{22} +(0.0996702 + 0.0362770i) q^{23} +(-1.73783 + 1.45821i) q^{25} +(-3.23783 - 5.60808i) q^{26} +(0.0320889 + 0.181985i) q^{28} +(-0.692066 - 3.92490i) q^{29} +(1.61334 + 2.79439i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(1.99273 + 0.725293i) q^{34} +(0.233956 + 0.196312i) q^{35} +4.06418 q^{37} +(2.12449 - 3.80612i) q^{38} +(-0.286989 + 1.62760i) q^{40} +(6.61721 + 5.55250i) q^{41} +(-0.0393628 + 0.0143269i) q^{43} +(3.33022 - 2.79439i) q^{44} +(-0.0530334 + 0.0918566i) q^{46} +(1.37551 + 7.80093i) q^{47} +(3.48293 - 6.03260i) q^{49} +(-1.13429 - 1.96464i) q^{50} +(6.08512 - 2.21480i) q^{52} +(-8.65657 - 3.15074i) q^{53} +(1.24763 - 7.07564i) q^{55} -0.184793 q^{56} +3.98545 q^{58} +(-1.75237 + 9.93821i) q^{59} +(-3.37939 - 1.23000i) q^{61} +(-3.03209 + 1.10359i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(5.35117 - 9.26849i) q^{65} +(-1.38666 - 7.86414i) q^{67} +(-1.06031 + 1.83651i) q^{68} +(-0.233956 + 0.196312i) q^{70} +(-3.79813 + 1.38241i) q^{71} +(11.6420 + 9.76882i) q^{73} +(-0.705737 + 4.00243i) q^{74} +(3.37939 + 2.75314i) q^{76} +0.803348 q^{77} +(9.49660 + 7.96859i) q^{79} +(-1.55303 - 0.565258i) q^{80} +(-6.61721 + 5.55250i) q^{82} +(4.22803 + 7.32316i) q^{83} +(0.608593 + 3.45150i) q^{85} +(-0.00727396 - 0.0412527i) q^{86} +(2.17365 + 3.76487i) q^{88} +(13.7404 - 11.5295i) q^{89} +(1.12449 + 0.409279i) q^{91} +(-0.0812519 - 0.0681784i) q^{92} -7.92127 q^{94} +(7.20321 - 0.104455i) q^{95} +(1.85591 - 10.5254i) q^{97} +(5.33615 + 4.47756i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} + 3 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q + 3 * q^5 + 3 * q^7 + 3 * q^8	\( 6 q + 3 q^{5} + 3 q^{7} + 3 q^{8} + 6 q^{10} - 12 q^{11} - 21 q^{13} - 3 q^{17} + 6 q^{19} + 12 q^{20} + 3 q^{22} + 15 q^{23} + 9 q^{25} - 9 q^{28} - 15 q^{29} + 3 q^{31} - 6 q^{34} + 6 q^{35} + 6 q^{37} + 6 q^{40} + 9 q^{41} - 9 q^{43} - 3 q^{44} + 12 q^{46} + 21 q^{47} + 3 q^{50} + 15 q^{52} - 30 q^{53} - 9 q^{55} + 6 q^{56} - 12 q^{58} - 27 q^{59} - 9 q^{61} - 9 q^{62} - 3 q^{64} + 6 q^{65} - 15 q^{67} - 12 q^{68} - 6 q^{70} - 9 q^{71} + 12 q^{73} + 6 q^{74} + 9 q^{76} - 42 q^{77} + 15 q^{79} + 3 q^{80} - 9 q^{82} + 3 q^{83} - 36 q^{85} - 18 q^{86} + 12 q^{88} + 48 q^{89} - 6 q^{91} - 3 q^{92} - 30 q^{94} + 48 q^{95} + 18 q^{97} + 36 q^{98}+O(q^{100}) \) 6 * q + 3 * q^5 + 3 * q^7 + 3 * q^8 + 6 * q^10 - 12 * q^11 - 21 * q^13 - 3 * q^17 + 6 * q^19 + 12 * q^20 + 3 * q^22 + 15 * q^23 + 9 * q^25 - 9 * q^28 - 15 * q^29 + 3 * q^31 - 6 * q^34 + 6 * q^35 + 6 * q^37 + 6 * q^40 + 9 * q^41 - 9 * q^43 - 3 * q^44 + 12 * q^46 + 21 * q^47 + 3 * q^50 + 15 * q^52 - 30 * q^53 - 9 * q^55 + 6 * q^56 - 12 * q^58 - 27 * q^59 - 9 * q^61 - 9 * q^62 - 3 * q^64 + 6 * q^65 - 15 * q^67 - 12 * q^68 - 6 * q^70 - 9 * q^71 + 12 * q^73 + 6 * q^74 + 9 * q^76 - 42 * q^77 + 15 * q^79 + 3 * q^80 - 9 * q^82 + 3 * q^83 - 36 * q^85 - 18 * q^86 + 12 * q^88 + 48 * q^89 - 6 * q^91 - 3 * q^92 - 30 * q^94 + 48 * q^95 + 18 * q^97 + 36 * q^98

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