LMFDB - Embedded newform 855.2.k.h.676.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(406,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("855.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.k (of order $3$, degree $2$, 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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.4601315889.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9 $ x^8 - x^7 + 6x^6 - 3x^5 + 26x^4 - 14x^3 + 31x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			676.3
Root			$0.689667 - 1.19454i$ of defining polynomial
Character	$\chi$	$=$	855.676
Dual form			855.2.k.h.406.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.548719 - 0.950409i) q^{2} +(0.397815 + 0.689035i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.89307 q^{7} +3.06803 q^{8} +O(q^{10})$	\(q+(0.548719 - 0.950409i) q^{2} +(0.397815 + 0.689035i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.89307 q^{7} +3.06803 q^{8} +(-0.548719 - 0.950409i) q^{10} -0.134400 q^{11} +(-1.75687 - 3.04298i) q^{13} +(1.03876 - 1.79919i) q^{14} +(0.887858 - 1.53781i) q^{16} +(-0.830615 + 1.43867i) q^{17} +(2.10596 - 3.81640i) q^{19} +0.795629 q^{20} +(-0.0737478 + 0.127735i) q^{22} +(2.68492 + 4.65042i) q^{23} +(-0.500000 - 0.866025i) q^{25} -3.85611 q^{26} +(0.753090 + 1.30439i) q^{28} +(2.48530 + 4.30466i) q^{29} +6.56472 q^{31} +(2.09366 + 3.62633i) q^{32} +(0.911548 + 1.57885i) q^{34} +(0.946534 - 1.63944i) q^{35} -1.69819 q^{37} +(-2.47156 - 4.09566i) q^{38} +(1.53402 - 2.65699i) q^{40} +(5.31637 - 9.20823i) q^{41} +(-4.25392 + 7.36801i) q^{43} +(-0.0534662 - 0.0926063i) q^{44} +5.89307 q^{46} +(-5.55771 - 9.62623i) q^{47} -3.41630 q^{49} -1.09744 q^{50} +(1.39781 - 2.42109i) q^{52} +(-0.132424 - 0.229365i) q^{53} +(-0.0672000 + 0.116394i) q^{55} +5.80799 q^{56} +5.45492 q^{58} +(-3.44833 + 5.97269i) q^{59} +(-4.58794 - 7.94655i) q^{61} +(3.60219 - 6.23917i) q^{62} +8.14676 q^{64} -3.51373 q^{65} +(1.47677 + 2.55784i) q^{67} -1.32172 q^{68} +(-1.03876 - 1.79919i) q^{70} +(0.664176 - 1.15039i) q^{71} +(3.17119 - 5.49266i) q^{73} +(-0.931830 + 1.61398i) q^{74} +(3.46742 - 0.0671384i) q^{76} -0.254428 q^{77} +(0.733639 - 1.27070i) q^{79} +(-0.887858 - 1.53781i) q^{80} +(-5.83439 - 10.1055i) q^{82} -7.44736 q^{83} +(0.830615 + 1.43867i) q^{85} +(4.66842 + 8.08593i) q^{86} -0.412343 q^{88} +(4.86804 + 8.43169i) q^{89} +(-3.32587 - 5.76057i) q^{91} +(-2.13620 + 3.70001i) q^{92} -12.1985 q^{94} +(-2.25212 - 3.73202i) q^{95} +(-8.73447 + 15.1285i) q^{97} +(-1.87459 + 3.24688i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 5 q^{4} + 4 q^{5} - 8 q^{7} - 24 q^{8}+O(q^{10}) $ 8 * q + q^2 - 5 * q^4 + 4 * q^5 - 8 * q^7 - 24 * q^8	$ 8 q + q^{2} - 5 q^{4} + 4 q^{5} - 8 q^{7} - 24 q^{8} - q^{10} + 4 q^{11} - 7 q^{13} - q^{14} - 7 q^{16} - q^{17} + 5 q^{19} - 10 q^{20} - 2 q^{22} + 2 q^{23} - 4 q^{25} - 6 q^{26} + 19 q^{28} - q^{29} + 30 q^{32} - 15 q^{34} - 4 q^{35} - 4 q^{37} - 13 q^{38} - 12 q^{40} - 8 q^{41} - q^{43} - 12 q^{44} + 24 q^{46} - 12 q^{47} - 20 q^{49} - 2 q^{50} + 3 q^{52} - 5 q^{53} + 2 q^{55} + 82 q^{56} - 54 q^{58} - 5 q^{59} + 37 q^{62} + 112 q^{64} - 14 q^{65} - 4 q^{67} - 32 q^{68} + q^{70} + 20 q^{71} + 20 q^{73} + 25 q^{74} + 63 q^{76} - 28 q^{77} - 17 q^{79} + 7 q^{80} - 21 q^{82} - 2 q^{83} + q^{85} + 8 q^{86} - 14 q^{88} + 11 q^{89} - 6 q^{91} - q^{92} - 62 q^{94} + 4 q^{95} - q^{97} + 9 q^{98}+O(q^{100}) $ 8 * q + q^2 - 5 * q^4 + 4 * q^5 - 8 * q^7 - 24 * q^8 - q^10 + 4 * q^11 - 7 * q^13 - q^14 - 7 * q^16 - q^17 + 5 * q^19 - 10 * q^20 - 2 * q^22 + 2 * q^23 - 4 * q^25 - 6 * q^26 + 19 * q^28 - q^29 + 30 * q^32 - 15 * q^34 - 4 * q^35 - 4 * q^37 - 13 * q^38 - 12 * q^40 - 8 * q^41 - q^43 - 12 * q^44 + 24 * q^46 - 12 * q^47 - 20 * q^49 - 2 * q^50 + 3 * q^52 - 5 * q^53 + 2 * q^55 + 82 * q^56 - 54 * q^58 - 5 * q^59 + 37 * q^62 + 112 * q^64 - 14 * q^65 - 4 * q^67 - 32 * q^68 + q^70 + 20 * q^71 + 20 * q^73 + 25 * q^74 + 63 * q^76 - 28 * q^77 - 17 * q^79 + 7 * q^80 - 21 * q^82 - 2 * q^83 + q^85 + 8 * q^86 - 14 * q^88 + 11 * q^89 - 6 * q^91 - q^92 - 62 * q^94 + 4 * q^95 - q^97 + 9 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.548719	−	0.950409i	0.388003	−	0.672041i	−0.604178	−	0.796850i	$-0.706498\pi$
$2$	0.548719	−	0.950409i	0.388003	−	0.672041i	0.992181	+	0.124809i	$0.0398317\pi$
$3$		0			0
$3$		0			0
$4$	0.397815	+	0.689035i	0.198907	+	0.344518i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	1.89307			0.715512			0.357756	−	0.933815i	$-0.383542\pi$
$7$	1.89307			0.715512			0.357756	+	0.933815i	$0.383542\pi$
$8$	3.06803			1.08471
$9$		0			0
$10$	−0.548719	−	0.950409i	−0.173520	−	0.300546i
$11$	−0.134400			−0.0405231			−0.0202615	−	0.999795i	$-0.506450\pi$
$11$	−0.134400			−0.0405231			−0.0202615	+	0.999795i	$0.506450\pi$
$12$		0			0
$13$	−1.75687	−	3.04298i	−0.487267	−	0.843972i	0.512626	−	0.858612i	$-0.328673\pi$
$13$	−1.75687	−	3.04298i	−0.487267	−	0.843972i	−0.999893	+	0.0146407i	$0.995340\pi$
$14$	1.03876	−	1.79919i	0.277621	−	0.480854i
$15$		0			0
$16$	0.887858	−	1.53781i	0.221964	−	0.384454i
$17$	−0.830615	+	1.43867i	−0.201454	+	0.348928i	−0.948997	−	0.315285i	$-0.897900\pi$
$17$	−0.830615	+	1.43867i	−0.201454	+	0.348928i	0.747543	+	0.664213i	$0.231233\pi$
$18$		0			0
$19$	2.10596	−	3.81640i	0.483141	−	0.875543i
$19$	2.10596	−	3.81640i	0.483141	−	0.875543i
$20$	0.795629			0.177908
$21$		0			0
$22$	−0.0737478	+	0.127735i	−0.0157231	+	0.0272332i
$23$	2.68492	+	4.65042i	0.559844	+	0.969679i	0.997509	+	0.0705407i	$0.0224725\pi$
$23$	2.68492	+	4.65042i	0.559844	+	0.969679i	−0.437664	+	0.899138i	$0.644194\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−3.85611			−0.756245
$27$		0			0
$28$	0.753090	+	1.30439i	0.142321	+	0.246507i
$29$	2.48530	+	4.30466i	0.461508	+	0.799355i	0.999036	−	0.0438905i	$-0.0139753\pi$
$29$	2.48530	+	4.30466i	0.461508	+	0.799355i	−0.537528	+	0.843246i	$0.680642\pi$
$30$		0			0
$31$	6.56472			1.17906			0.589529	−	0.807747i	$-0.299313\pi$
$31$	6.56472			1.17906			0.589529	+	0.807747i	$0.299313\pi$
$32$	2.09366	+	3.62633i	0.370111	+	0.641050i
$33$		0			0
$34$	0.911548	+	1.57885i	0.156329	+	0.270770i
$35$	0.946534	−	1.63944i	0.159993	−	0.277117i
$36$		0			0
$37$	−1.69819			−0.279181			−0.139590	−	0.990209i	$-0.544579\pi$
$37$	−1.69819			−0.279181			−0.139590	+	0.990209i	$0.544579\pi$
$38$	−2.47156	−	4.09566i	−0.400940	−	0.664404i
$39$		0			0
$40$	1.53402	−	2.65699i	0.242549	−	0.420107i
$41$	5.31637	−	9.20823i	0.830278	−	1.43808i	−0.0675398	−	0.997717i	$-0.521515\pi$
$41$	5.31637	−	9.20823i	0.830278	−	1.43808i	0.897818	−	0.440367i	$-0.145152\pi$
$42$		0			0
$43$	−4.25392	+	7.36801i	−0.648717	+	1.12361i	0.334713	+	0.942320i	$0.391361\pi$
$43$	−4.25392	+	7.36801i	−0.648717	+	1.12361i	−0.983430	+	0.181290i	$0.941973\pi$
$44$	−0.0534662	−	0.0926063i	−0.00806034	−	0.0139609i
$45$		0			0
$46$	5.89307			0.868885
$47$	−5.55771	−	9.62623i	−0.810675	−	1.40413i	−0.912392	−	0.409316i	$-0.865767\pi$
$47$	−5.55771	−	9.62623i	−0.810675	−	1.40413i	0.101718	−	0.994813i	$-0.467566\pi$
$48$		0			0
$49$	−3.41630			−0.488042
$50$	−1.09744			−0.155201
$51$		0			0
$52$	1.39781	−	2.42109i	0.193842	−	0.335744i
$53$	−0.132424	−	0.229365i	−0.0181898	−	0.0315057i	0.856787	−	0.515670i	$-0.172457\pi$
$53$	−0.132424	−	0.229365i	−0.0181898	−	0.0315057i	−0.874977	+	0.484164i	$0.839124\pi$
$54$		0			0
$55$	−0.0672000	+	0.116394i	−0.00906124	+	0.0156945i
$56$	5.80799			0.776125
$57$		0			0
$58$	5.45492			0.716266
$59$	−3.44833	+	5.97269i	−0.448935	+	0.777578i	−0.998317	−	0.0579932i	$-0.981530\pi$
$59$	−3.44833	+	5.97269i	−0.448935	+	0.777578i	0.549382	+	0.835571i	$0.314863\pi$
$60$		0			0
$61$	−4.58794	−	7.94655i	−0.587426	−	1.01745i	−0.994568	−	0.104087i	$-0.966808\pi$
$61$	−4.58794	−	7.94655i	−0.587426	−	1.01745i	0.407142	−	0.913365i	$-0.366525\pi$
$62$	3.60219	−	6.23917i	0.457478	−	0.792375i
$63$		0			0
$64$	8.14676			1.01834
$65$	−3.51373			−0.435825
$66$		0			0
$67$	1.47677	+	2.55784i	0.180416	+	0.312490i	0.942022	−	0.335550i	$-0.108922\pi$
$67$	1.47677	+	2.55784i	0.180416	+	0.312490i	−0.761606	+	0.648040i	$0.775589\pi$
$68$	−1.32172			−0.160282
$69$		0			0
$70$	−1.03876	−	1.79919i	−0.124156	−	0.215044i
$71$	0.664176	−	1.15039i	0.0788232	−	0.136526i	−0.823919	−	0.566707i	$-0.808217\pi$
$71$	0.664176	−	1.15039i	0.0788232	−	0.136526i	0.902742	+	0.430181i	$0.141550\pi$
$72$		0			0
$73$	3.17119	−	5.49266i	0.371159	−	0.642867i	−0.618585	−	0.785718i	$-0.712294\pi$
$73$	3.17119	−	5.49266i	0.371159	−	0.642867i	0.989744	+	0.142851i	$0.0456271\pi$
$74$	−0.931830	+	1.61398i	−0.108323	+	0.187621i
$75$		0			0
$76$	3.46742	−	0.0671384i	0.397740	−	0.00770130i
$77$	−0.254428			−0.0289948
$78$		0			0
$79$	0.733639	−	1.27070i	0.0825408	−	0.142965i	−0.821800	−	0.569776i	$-0.807030\pi$
$79$	0.733639	−	1.27070i	0.0825408	−	0.142965i	0.904341	+	0.426811i	$0.140363\pi$
$80$	−0.887858	−	1.53781i	−0.0992655	−	0.171933i
$81$		0			0
$82$	−5.83439	−	10.1055i	−0.644301	−	1.11596i
$83$	−7.44736			−0.817454			−0.408727	−	0.912657i	$-0.634027\pi$
$83$	−7.44736			−0.817454			−0.408727	+	0.912657i	$0.634027\pi$
$84$		0			0
$85$	0.830615	+	1.43867i	0.0900928	+	0.156045i
$86$	4.66842	+	8.08593i	0.503408	+	0.871929i
$87$		0			0
$88$	−0.412343			−0.0439559
$89$	4.86804	+	8.43169i	0.516011	+	0.893757i	0.999827	+	0.0185878i	$0.00591701\pi$
$89$	4.86804	+	8.43169i	0.516011	+	0.893757i	−0.483816	+	0.875170i	$0.660750\pi$
$90$		0			0
$91$	−3.32587	−	5.76057i	−0.348646	−	0.603872i
$92$	−2.13620	+	3.70001i	−0.222714	+	0.385753i
$93$		0			0
$94$	−12.1985			−1.25818
$95$	−2.25212	−	3.73202i	−0.231063	−	0.382897i
$96$		0			0
$97$	−8.73447	+	15.1285i	−0.886851	+	1.53607i	−0.0432737	+	0.999063i	$0.513779\pi$
$97$	−8.73447	+	15.1285i	−0.886851	+	1.53607i	−0.843577	+	0.537008i	$0.819555\pi$
$98$	−1.87459	+	3.24688i	−0.189362	+	0.327984i
$99$		0			0
$100$	0.397815	−	0.689035i	0.0397815	−	0.0689035i
$101$	2.69865	+	4.67420i	0.268526	+	0.465101i	0.968481	−	0.249086i	$-0.0801301\pi$
$101$	2.69865	+	4.67420i	0.268526	+	0.465101i	−0.699955	+	0.714187i	$0.746797\pi$
$102$		0			0
$103$	2.14750			0.211599			0.105800	−	0.994387i	$-0.466260\pi$
$103$	2.14750			0.211599			0.105800	+	0.994387i	$0.466260\pi$
$104$	−5.39012	−	9.33596i	−0.528545	−	0.915467i
$105$		0			0
$106$	−0.290654			−0.0282308
$107$	1.00093			0.0967631			0.0483815	−	0.998829i	$-0.484594\pi$
$107$	1.00093			0.0967631			0.0483815	+	0.998829i	$0.484594\pi$
$108$		0			0
$109$	−8.13145	+	14.0841i	−0.778852	+	1.34901i	0.153752	+	0.988109i	$0.450864\pi$
$109$	−8.13145	+	14.0841i	−0.778852	+	1.34901i	−0.932604	+	0.360902i	$0.882469\pi$
$110$	0.0737478	+	0.127735i	0.00703158	+	0.0121790i
$111$		0			0
$112$	1.68077	−	2.91119i	0.158818	−	0.275081i
$113$	−0.843010			−0.0793037			−0.0396519	−	0.999214i	$-0.512625\pi$
$113$	−0.843010			−0.0793037			−0.0396519	+	0.999214i	$0.512625\pi$
$114$		0			0
$115$	5.36984			0.500740
$116$	−1.97737	+	3.42491i	−0.183595	+	0.317995i
$117$		0			0
$118$	3.78433	+	6.55466i	0.348376	+	0.603405i
$119$	−1.57241	+	2.72349i	−0.144143	+	0.249662i
$120$		0			0
$121$	−10.9819			−0.998358
$122$	−10.0700			−0.911692
$123$		0			0
$124$	2.61154	+	4.52332i	0.234523	+	0.406206i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−9.36984	−	16.2290i	−0.831439	−	1.44009i	−0.896897	−	0.442239i	$-0.854184\pi$
$127$	−9.36984	−	16.2290i	−0.831439	−	1.44009i	0.0654584	−	0.997855i	$-0.479149\pi$
$128$	0.282960	−	0.490101i	0.0250104	−	0.0433193i
$129$		0			0
$130$	−1.92805	+	3.33949i	−0.169101	+	0.292892i
$131$	1.44322	−	2.49973i	0.126095	−	0.218402i	−0.796066	−	0.605210i	$-0.793089\pi$
$131$	1.44322	−	2.49973i	0.126095	−	0.218402i	0.922160	+	0.386808i	$0.126422\pi$
$132$		0			0
$133$	3.98673	−	7.22471i	0.345693	−	0.626461i
$134$	3.24133			0.280008
$135$		0			0
$136$	−2.54835	+	4.41387i	−0.218519	+	0.378487i
$137$	−9.41579	−	16.3086i	−0.804445	−	1.39334i	−0.916665	−	0.399656i	$-0.869129\pi$
$137$	−9.41579	−	16.3086i	−0.804445	−	1.39334i	0.112220	−	0.993683i	$-0.464204\pi$
$138$		0			0
$139$	9.08974	+	15.7439i	0.770982	+	1.33538i	0.937025	+	0.349262i	$0.113568\pi$
$139$	9.08974	+	15.7439i	0.770982	+	1.33538i	−0.166043	+	0.986118i	$0.553099\pi$
$140$	1.50618			0.127295
$141$		0			0
$142$	−0.728892	−	1.26248i	−0.0611672	−	0.105945i
$143$	0.236123	+	0.408977i	0.0197456	+	0.0342003i
$144$		0			0
$145$	4.97059			0.412785
$146$	−3.48018	−	6.02785i	−0.288022	−	0.498868i
$147$		0			0
$148$	−0.675565	−	1.17011i	−0.0555311	−	0.0961827i
$149$	−11.1272	+	19.2728i	−0.911573	+	1.57889i	−0.0997308	+	0.995014i	$0.531798\pi$
$149$	−11.1272	+	19.2728i	−0.911573	+	1.57889i	−0.811842	+	0.583877i	$0.801535\pi$
$150$		0			0
$151$	3.33482			0.271384			0.135692	−	0.990751i	$-0.456674\pi$
$151$	3.33482			0.271384			0.135692	+	0.990751i	$0.456674\pi$
$152$	6.46116	−	11.7088i	0.524069	−	0.949712i
$153$		0			0
$154$	−0.139610	+	0.241811i	−0.0112501	+	0.0194857i
$155$	3.28236	−	5.68521i	0.263645	−	0.456647i
$156$		0			0
$157$	−3.63145	+	6.28986i	−0.289822	+	0.501986i	−0.973767	−	0.227548i	$-0.926929\pi$
$157$	−3.63145	+	6.28986i	−0.289822	+	0.501986i	0.683945	+	0.729533i	$0.260263\pi$
$158$	−0.805123	−	1.39451i	−0.0640522	−	0.110942i
$159$		0			0
$160$	4.18732			0.331037
$161$	5.08273	+	8.80355i	0.400576	+	0.693817i
$162$		0			0
$163$	−19.7783			−1.54916			−0.774578	−	0.632478i	$-0.782038\pi$
$163$	−19.7783			−1.54916			−0.774578	+	0.632478i	$0.782038\pi$
$164$	8.45972			0.660593
$165$		0			0
$166$	−4.08651	+	7.07805i	−0.317175	+	0.549363i
$167$	−1.70160	−	2.94726i	−0.131674	−	0.228066i	0.792648	−	0.609679i	$-0.208702\pi$
$167$	−1.70160	−	2.94726i	−0.131674	−	0.228066i	−0.924322	+	0.381614i	$0.875368\pi$
$168$		0			0
$169$	0.326838	−	0.566100i	0.0251414	−	0.0435461i
$170$	1.82310			0.139825
$171$		0			0
$172$	−6.76909			−0.516138
$173$	−5.29286	+	9.16750i	−0.402409	+	0.696992i	−0.994016	−	0.109234i	$-0.965160\pi$
$173$	−5.29286	+	9.16750i	−0.402409	+	0.696992i	0.591607	+	0.806226i	$0.298494\pi$
$174$		0			0
$175$	−0.946534	−	1.63944i	−0.0715512	−	0.123930i
$176$	−0.119328	+	0.206682i	−0.00899469	+	0.0155793i
$177$		0			0
$178$	10.6847			0.800855
$179$	14.6024			1.09144			0.545718	−	0.837969i	$-0.316257\pi$
$179$	14.6024			1.09144			0.545718	+	0.837969i	$0.316257\pi$
$180$		0			0
$181$	2.71630	+	4.70478i	0.201901	+	0.349703i	0.949141	−	0.314851i	$-0.101955\pi$
$181$	2.71630	+	4.70478i	0.201901	+	0.349703i	−0.747240	+	0.664555i	$0.768621\pi$
$182$	−7.29987			−0.541102
$183$		0			0
$184$	8.23742	+	14.2676i	0.607270	+	1.05182i
$185$	−0.849095	+	1.47068i	−0.0624267	+	0.108126i
$186$		0			0
$187$	0.111635	−	0.193357i	0.00816353	−	0.0141396i
$188$	4.42187	−	7.65891i	0.322498	−	0.558583i
$189$		0			0
$190$	−4.78273	+	0.0926063i	−0.346975	+	0.00671836i
$191$	−20.4758			−1.48157			−0.740787	−	0.671740i	$-0.765547\pi$
$191$	−20.4758			−1.48157			−0.740787	+	0.671740i	$0.765547\pi$
$192$		0			0
$193$	−5.51176	+	9.54664i	−0.396745	+	0.687182i	−0.993322	−	0.115373i	$-0.963194\pi$
$193$	−5.51176	+	9.54664i	−0.396745	+	0.687182i	0.596577	+	0.802556i	$0.296527\pi$
$194$	9.58554	+	16.6026i	0.688202	+	1.19200i
$195$		0			0
$196$	−1.35905	−	2.35395i	−0.0970752	−	0.168139i
$197$	19.8532			1.41448			0.707242	−	0.706971i	$-0.249939\pi$
$197$	19.8532			1.41448			0.707242	+	0.706971i	$0.249939\pi$
$198$		0			0
$199$	−10.5013	−	18.1888i	−0.744417	−	1.28937i	−0.950467	−	0.310826i	$-0.899394\pi$
$199$	−10.5013	−	18.1888i	−0.744417	−	1.28937i	0.206050	−	0.978542i	$-0.433939\pi$
$200$	−1.53402	−	2.65699i	−0.108471	−	0.187878i
$201$		0			0
$202$	5.92321			0.416756
$203$	4.70483	+	8.14901i	0.330215	+	0.571948i
$204$		0			0
$205$	−5.31637	−	9.20823i	−0.371312	−	0.643131i
$206$	1.17837	−	2.04100i	0.0821011	−	0.142203i
$207$		0			0
$208$	−6.23939			−0.432624
$209$	−0.283041	+	0.512924i	−0.0195784	+	0.0354797i
$210$		0			0
$211$	6.41284	−	11.1074i	0.441478	−	0.764663i	−0.556321	−	0.830967i	$-0.687788\pi$
$211$	6.41284	−	11.1074i	0.441478	−	0.764663i	0.997799	+	0.0663046i	$0.0211209\pi$
$212$	0.105360	−	0.182489i	0.00723617	−	0.0125334i
$213$		0			0
$214$	0.549227	−	0.951289i	0.0375444	−	0.0650288i
$215$	4.25392	+	7.36801i	0.290115	+	0.502494i
$216$		0			0
$217$	12.4275			0.843630
$218$	8.92377	+	15.4564i	0.604394	+	1.04684i
$219$		0			0
$220$	−0.106932			−0.00720939
$221$	5.83712			0.392647
$222$		0			0
$223$	−10.1972	+	17.6621i	−0.682856	+	1.18274i	0.291249	+	0.956647i	$0.405929\pi$
$223$	−10.1972	+	17.6621i	−0.682856	+	1.18274i	−0.974105	+	0.226095i	$0.927404\pi$
$224$	3.96344	+	6.86488i	0.264819	+	0.458679i
$225$		0			0
$226$	−0.462576	+	0.801205i	−0.0307701	+	0.0532954i
$227$	−25.4172			−1.68700			−0.843500	−	0.537129i	$-0.819509\pi$
$227$	−25.4172			−1.68700			−0.843500	+	0.537129i	$0.819509\pi$
$228$		0			0
$229$	2.21553			0.146406			0.0732030	−	0.997317i	$-0.476678\pi$
$229$	2.21553			0.146406			0.0732030	+	0.997317i	$0.476678\pi$
$230$	2.94653	−	5.10355i	0.194289	−	0.336518i
$231$		0			0
$232$	7.62496	+	13.2068i	0.500603	+	0.867071i
$233$	−7.07882	+	12.2609i	−0.463749	+	0.803236i	−0.999144	−	0.0413652i	$-0.986829\pi$
$233$	−7.07882	+	12.2609i	−0.463749	+	0.803236i	0.535395	+	0.844602i	$0.320163\pi$
$234$		0			0
$235$	−11.1154			−0.725089
$236$	−5.48719			−0.357186
$237$		0			0
$238$	1.72562	+	2.98887i	0.111855	+	0.193739i
$239$	−3.01476			−0.195008			−0.0975042	−	0.995235i	$-0.531086\pi$
$239$	−3.01476			−0.195008			−0.0975042	+	0.995235i	$0.531086\pi$
$240$		0			0
$241$	11.8896	+	20.5934i	0.765877	+	1.32654i	0.939781	+	0.341776i	$0.111028\pi$
$241$	11.8896	+	20.5934i	0.765877	+	1.32654i	−0.173904	+	0.984763i	$0.555638\pi$
$242$	−6.02600	+	10.4373i	−0.387366	+	0.670937i
$243$		0			0
$244$	3.65030	−	6.32251i	0.233687	−	0.404757i
$245$	−1.70815	+	2.95860i	−0.109130	+	0.189018i
$246$		0			0
$247$	−15.3131	+	0.296503i	−0.974352	+	0.0188660i
$248$	20.1407			1.27894
$249$		0			0
$250$	−0.548719	+	0.950409i	−0.0347040	+	0.0601092i
$251$	8.59495	+	14.8869i	0.542509	+	0.939653i	0.998759	+	0.0498012i	$0.0158588\pi$
$251$	8.59495	+	14.8869i	0.542509	+	0.939653i	−0.456250	+	0.889851i	$0.650808\pi$
$252$		0			0
$253$	−0.360853	−	0.625016i	−0.0226866	−	0.0392944i
$254$	−20.5656			−1.29040
$255$		0			0
$256$	7.83623	+	13.5727i	0.489764	+	0.848297i
$257$	−9.77143	−	16.9246i	−0.609525	−	1.05573i	−0.991319	−	0.131481i	$-0.958027\pi$
$257$	−9.77143	−	16.9246i	−0.609525	−	1.05573i	0.381794	−	0.924248i	$-0.375307\pi$
$258$		0			0
$259$	−3.21479			−0.199757
$260$	−1.39781	−	2.42109i	−0.0866888	−	0.150149i
$261$		0			0
$262$	−1.58384	−	2.74330i	−0.0978502	−	0.169482i
$263$	4.40680	−	7.63280i	0.271735	−	0.470659i	−0.697571	−	0.716515i	$-0.745736\pi$
$263$	4.40680	−	7.63280i	0.271735	−	0.470659i	0.969306	+	0.245857i	$0.0790692\pi$
$264$		0			0
$265$	−0.264847			−0.0162694
$266$	−4.67883	−	7.75336i	−0.286878	−	0.475389i
$267$		0			0
$268$	−1.17496	+	2.03510i	−0.0717723	+	0.124313i
$269$	0.144181	−	0.249729i	0.00879088	−	0.0152263i	−0.861596	−	0.507594i	$-0.830535\pi$
$269$	0.144181	−	0.249729i	0.00879088	−	0.0152263i	0.870387	+	0.492368i	$0.163868\pi$
$270$		0			0
$271$	12.4356	−	21.5391i	0.755409	−	1.30841i	−0.189761	−	0.981830i	$-0.560771\pi$
$271$	12.4356	−	21.5391i	0.755409	−	1.30841i	0.945171	−	0.326577i	$-0.105895\pi$
$272$	1.47494	+	2.55466i	0.0894311	+	0.154899i
$273$		0			0
$274$	−20.6665			−1.24851
$275$	0.0672000	+	0.116394i	0.00405231	+	0.00701881i
$276$		0			0
$277$	−4.40486			−0.264662			−0.132331	−	0.991206i	$-0.542246\pi$
$277$	−4.40486			−0.264662			−0.132331	+	0.991206i	$0.542246\pi$
$278$	19.9509			1.19657
$279$		0			0
$280$	2.90399	−	5.02987i	0.173547	−	0.300592i
$281$	−16.3607	−	28.3376i	−0.975998	−	1.69048i	−0.676600	−	0.736350i	$-0.736548\pi$
$281$	−16.3607	−	28.3376i	−0.975998	−	1.69048i	−0.299398	−	0.954128i	$-0.596786\pi$
$282$		0			0
$283$	0.664463	−	1.15088i	0.0394982	−	0.0684129i	−0.845600	−	0.533816i	$-0.820757\pi$
$283$	0.664463	−	1.15088i	0.0394982	−	0.0684129i	0.885099	+	0.465403i	$0.154091\pi$
$284$	1.05688			0.0627140
$285$		0			0
$286$	0.518260			0.0306454
$287$	10.0643	−	17.4318i	0.594074	−	1.02897i
$288$		0			0
$289$	7.12016	+	12.3325i	0.418833	+	0.725440i
$290$	2.72746	−	4.72410i	0.160162	−	0.277409i
$291$		0			0
$292$	5.04618			0.295305
$293$	7.72365			0.451220			0.225610	−	0.974218i	$-0.427562\pi$
$293$	7.72365			0.451220			0.225610	+	0.974218i	$0.427562\pi$
$294$		0			0
$295$	3.44833	+	5.97269i	0.200770	+	0.347743i
$296$	−5.21010			−0.302831
$297$		0			0
$298$	12.2114	+	21.1507i	0.707386	+	1.22523i
$299$	9.43409	−	16.3403i	0.545588	−	0.944986i
$300$		0			0
$301$	−8.05296	+	13.9481i	−0.464165	+	0.803957i
$302$	1.82988	−	3.16944i	0.105298	−	0.182381i
$303$		0			0
$304$	−3.99912	−	6.62700i	−0.229366	−	0.380085i
$305$	−9.17589			−0.525410
$306$		0			0
$307$	4.55001	−	7.88085i	0.259683	−	0.449784i	−0.706474	−	0.707739i	$-0.749715\pi$
$307$	4.55001	−	7.88085i	0.259683	−	0.449784i	0.966157	+	0.257955i	$0.0830486\pi$
$308$	−0.101215	−	0.175310i	−0.00576727	−	0.00998921i
$309$		0			0
$310$	−3.60219	−	6.23917i	−0.204590	−	0.354361i
$311$	12.4569			0.706364			0.353182	−	0.935555i	$-0.385100\pi$
$311$	12.4569			0.706364			0.353182	+	0.935555i	$0.385100\pi$
$312$		0			0
$313$	−1.02277	−	1.77148i	−0.0578101	−	0.100130i	0.835672	−	0.549229i	$-0.185078\pi$
$313$	−1.02277	−	1.77148i	−0.0578101	−	0.100130i	−0.893482	+	0.449099i	$0.851745\pi$
$314$	3.98530	+	6.90274i	0.224903	+	0.389544i
$315$		0			0
$316$	1.16741			0.0656719
$317$	11.7856	+	20.4133i	0.661947	+	1.14653i	0.980103	+	0.198487i	$0.0636029\pi$
$317$	11.7856	+	20.4133i	0.661947	+	1.14653i	−0.318157	+	0.948038i	$0.603064\pi$
$318$		0			0
$319$	−0.334024	−	0.578546i	−0.0187017	−	0.0323923i
$320$	4.07338	−	7.05530i	0.227709	−	0.394403i
$321$		0			0
$322$	11.1560			0.621698
$323$	3.74129	+	6.19974i	0.208171	+	0.344963i
$324$		0			0
$325$	−1.75687	+	3.04298i	−0.0974534	+	0.168794i
$326$	−10.8527	+	18.7975i	−0.601077	+	1.04110i
$327$		0			0
$328$	16.3108	−	28.2511i	0.900613	−	1.55991i
$329$	−10.5211	−	18.2231i	−0.580048	−	1.00467i
$330$		0			0
$331$	−18.7175			−1.02881			−0.514403	−	0.857549i	$-0.671986\pi$
$331$	−18.7175			−1.02881			−0.514403	+	0.857549i	$0.671986\pi$
$332$	−2.96267	−	5.13150i	−0.162598	−	0.281627i
$333$		0			0
$334$	−3.73480			−0.204359
$335$	2.95354			0.161369
$336$		0			0
$337$	16.3440	−	28.3087i	0.890316	−	1.54207i	0.0508197	−	0.998708i	$-0.483817\pi$
$337$	16.3440	−	28.3087i	0.890316	−	1.54207i	0.839497	−	0.543365i	$-0.182850\pi$
$338$	−0.358684	−	0.621259i	−0.0195098	−	0.0337921i
$339$		0			0
$340$	−0.660861	+	1.14465i	−0.0358402	+	0.0620771i
$341$	−0.882297			−0.0477791
$342$		0			0
$343$	−19.7188			−1.06471
$344$	−13.0512	+	22.6053i	−0.703671	+	1.21879i
$345$		0			0
$346$	5.80859	+	10.0608i	0.312271	+	0.540870i
$347$	−1.28333	+	2.22279i	−0.0688927	+	0.119326i	−0.898414	−	0.439149i	$-0.855280\pi$
$347$	−1.28333	+	2.22279i	−0.0688927	+	0.119326i	0.829521	+	0.558475i	$0.188613\pi$
$348$		0			0
$349$	16.6195			0.889619			0.444810	−	0.895625i	$-0.353271\pi$
$349$	16.6195			0.889619			0.444810	+	0.895625i	$0.353271\pi$
$350$	−2.07752			−0.111048
$351$		0			0
$352$	−0.281388	−	0.487378i	−0.0149980	−	0.0259773i
$353$	−28.3629			−1.50961			−0.754803	−	0.655951i	$-0.772268\pi$
$353$	−28.3629			−1.50961			−0.754803	+	0.655951i	$0.772268\pi$
$354$		0			0
$355$	−0.664176	−	1.15039i	−0.0352508	−	0.0610562i
$356$	−3.87315	+	6.70850i	−0.205277	+	0.355550i
$357$		0			0
$358$	8.01262	−	13.8783i	0.423480	−	0.733489i
$359$	8.69427	−	15.0589i	0.458866	−	0.794780i	−0.540035	−	0.841643i	$-0.681589\pi$
$359$	8.69427	−	15.0589i	0.458866	−	0.794780i	0.998901	+	0.0468628i	$0.0149224\pi$
$360$		0			0
$361$	−10.1298	−	16.0744i	−0.533150	−	0.846021i
$362$	5.96195			0.313353
$363$		0			0
$364$	2.64616	−	4.58328i	0.138696	−	0.240229i
$365$	−3.17119	−	5.49266i	−0.165987	−	0.287499i
$366$		0			0
$367$	−12.9024	−	22.3477i	−0.673501	−	1.16654i	−0.976905	−	0.213676i	$-0.931456\pi$
$367$	−12.9024	−	22.3477i	−0.673501	−	1.16654i	0.303404	−	0.952862i	$-0.401877\pi$
$368$	9.53531			0.497062
$369$		0			0
$370$	0.931830	+	1.61398i	0.0484435	+	0.0839067i
$371$	−0.250687	−	0.434203i	−0.0130150	−	0.0225427i
$372$		0			0
$373$	27.0663			1.40144			0.700719	−	0.713437i	$-0.252862\pi$
$373$	27.0663			1.40144			0.700719	+	0.713437i	$0.252862\pi$
$374$	−0.122512	−	0.212197i	−0.00633495	−	0.0109724i
$375$		0			0
$376$	−17.0512	−	29.5336i	−0.879349	−	1.52308i
$377$	8.73267	−	15.1254i	0.449755	−	0.778999i
$378$		0			0
$379$	12.4028			0.637092			0.318546	−	0.947907i	$-0.396806\pi$
$379$	12.4028			0.637092			0.318546	+	0.947907i	$0.396806\pi$
$380$	1.67557	−	3.03644i	0.0859547	−	0.155766i
$381$		0			0
$382$	−11.2354	+	19.4604i	−0.574855	+	0.995678i
$383$	−2.67971	+	4.64139i	−0.136927	+	0.237164i	−0.926332	−	0.376709i	$-0.877056\pi$
$383$	−2.67971	+	4.64139i	−0.136927	+	0.237164i	0.789405	+	0.613873i	$0.210389\pi$
$384$		0			0
$385$	−0.127214	+	0.220341i	−0.00648343	+	0.0112296i
$386$	6.04881	+	10.4769i	0.307877	+	0.533258i
$387$		0			0
$388$	−13.8988			−0.705605
$389$	4.28467	+	7.42126i	0.217241	+	0.376273i	0.953964	−	0.299923i	$-0.0969608\pi$
$389$	4.28467	+	7.42126i	0.217241	+	0.376273i	−0.736722	+	0.676195i	$0.763628\pi$
$390$		0			0
$391$	−8.92053			−0.451131
$392$	−10.4813			−0.529386
$393$		0			0
$394$	10.8939	−	18.8687i	0.548824	−	0.950592i
$395$	−0.733639	−	1.27070i	−0.0369134	−	0.0639359i
$396$		0			0
$397$	5.32227	−	9.21844i	0.267117	−	0.462660i	−0.700999	−	0.713162i	$-0.747262\pi$
$397$	5.32227	−	9.21844i	0.267117	−	0.462660i	0.968116	+	0.250502i	$0.0805957\pi$
$398$	−23.0490			−1.15534
$399$		0			0
$400$	−1.77572			−0.0887858
$401$	3.82604	−	6.62690i	0.191063	−	0.330932i	−0.754539	−	0.656255i	$-0.772140\pi$
$401$	3.82604	−	6.62690i	0.191063	−	0.330932i	0.945603	+	0.325323i	$0.105473\pi$
$402$		0			0
$403$	−11.5333	−	19.9763i	−0.574516	−	0.995091i
$404$	−2.14713	+	3.71893i	−0.106824	+	0.185024i
$405$		0			0
$406$	10.3265			0.512497
$407$	0.228237			0.0113133
$408$		0			0
$409$	8.84435	+	15.3189i	0.437325	+	0.757469i	0.997482	−	0.0709173i	$-0.0225927\pi$
$409$	8.84435	+	15.3189i	0.437325	+	0.757469i	−0.560157	+	0.828386i	$0.689259\pi$
$410$	−11.6688			−0.576280
$411$		0			0
$412$	0.854305	+	1.47970i	0.0420886	+	0.0728996i
$413$	−6.52793	+	11.3067i	−0.321218	+	0.556367i
$414$		0			0
$415$	−3.72368	+	6.44961i	−0.182788	+	0.316599i
$416$	7.35657	−	12.7420i	0.360685	−	0.624726i
$417$		0			0
$418$	0.332178	+	0.550456i	0.0162473	+	0.0269237i
$419$	−1.18732			−0.0580045			−0.0290023	−	0.999579i	$-0.509233\pi$
$419$	−1.18732			−0.0580045			−0.0290023	+	0.999579i	$0.509233\pi$
$420$		0			0
$421$	−16.6836	+	28.8969i	−0.813111	+	1.40835i	0.0975661	+	0.995229i	$0.468894\pi$
$421$	−16.6836	+	28.8969i	−0.813111	+	1.40835i	−0.910677	+	0.413120i	$0.864439\pi$
$422$	−7.03770	−	12.1896i	−0.342590	−	0.593383i
$423$		0			0
$424$	−0.406280	−	0.703698i	−0.0197307	−	0.0341746i
$425$	1.66123			0.0805815
$426$		0			0
$427$	−8.68529	−	15.0434i	−0.420311	−	0.727999i
$428$	0.398183	+	0.689673i	0.0192469	+	0.0333366i
$429$		0			0
$430$	9.33683			0.450262
$431$	−3.08799	−	5.34855i	−0.148743	−	0.257631i	0.782020	−	0.623253i	$-0.214189\pi$
$431$	−3.08799	−	5.34855i	−0.148743	−	0.257631i	−0.930763	+	0.365623i	$0.880856\pi$
$432$		0			0
$433$	9.27761	+	16.0693i	0.445854	+	0.772241i	0.998111	−	0.0614325i	$-0.0195669\pi$
$433$	9.27761	+	16.0693i	0.445854	+	0.772241i	−0.552258	+	0.833673i	$0.686234\pi$
$434$	6.81918	−	11.8112i	0.327331	−	0.566954i
$435$		0			0
$436$	−12.9392			−0.619677
$437$	23.4022	−	0.453129i	1.11948	−	0.0216761i
$438$		0			0
$439$	0.113656	−	0.196858i	0.00542450	−	0.00939550i	−0.863300	−	0.504690i	$-0.831607\pi$
$439$	0.113656	−	0.196858i	0.00542450	−	0.00939550i	0.868725	+	0.495295i	$0.164940\pi$
$440$	−0.206172	+	0.357100i	−0.00982884	+	0.0170241i
$441$		0			0
$442$	3.20294	−	5.54765i	0.152348	−	0.263875i
$443$	−17.4913	−	30.2959i	−0.831038	−	1.43940i	−0.897216	−	0.441593i	$-0.854414\pi$
$443$	−17.4913	−	30.2959i	−0.831038	−	1.43940i	0.0661770	−	0.997808i	$-0.478920\pi$
$444$		0			0
$445$	9.73608			0.461534
$446$	11.1908	+	19.3831i	0.529901	+	0.917815i
$447$		0			0
$448$	15.4224			0.728638
$449$	16.9509			0.799961			0.399980	−	0.916524i	$-0.369017\pi$
$449$	16.9509			0.799961			0.399980	+	0.916524i	$0.369017\pi$
$450$		0			0
$451$	−0.714520	+	1.23759i	−0.0336454	+	0.0582756i
$452$	−0.335362	−	0.580864i	−0.0157741	−	0.0273215i
$453$		0			0
$454$	−13.9469	+	24.1568i	−0.654561	+	1.13373i
$455$	−6.65174			−0.311838
$456$		0			0
$457$	1.60241			0.0749578			0.0374789	−	0.999297i	$-0.488067\pi$
$457$	1.60241			0.0749578			0.0374789	+	0.999297i	$0.488067\pi$
$458$	1.21570	−	2.10566i	0.0568060	−	0.0983909i
$459$		0			0
$460$	2.13620	+	3.70001i	0.0996009	+	0.172514i
$461$	−4.37081	+	7.57046i	−0.203569	+	0.352592i	−0.949676	−	0.313234i	$-0.898587\pi$
$461$	−4.37081	+	7.57046i	−0.203569	+	0.352592i	0.746107	+	0.665826i	$0.231921\pi$
$462$		0			0
$463$	21.1886			0.984718			0.492359	−	0.870392i	$-0.336135\pi$
$463$	21.1886			0.984718			0.492359	+	0.870392i	$0.336135\pi$
$464$	8.82636			0.409753
$465$		0			0
$466$	7.76857	+	13.4556i	0.359872	+	0.623316i
$467$	−20.4516			−0.946388			−0.473194	−	0.880958i	$-0.656899\pi$
$467$	−20.4516			−0.946388			−0.473194	+	0.880958i	$0.656899\pi$
$468$		0			0
$469$	2.79563	+	4.84217i	0.129090	+	0.223591i
$470$	−6.09924	+	10.5642i	−0.281337	+	0.487290i
$471$		0			0
$472$	−10.5796	+	18.3244i	−0.486965	+	0.843449i
$473$	0.571727	−	0.990259i	0.0262880	−	0.0455322i
$474$		0			0
$475$	−4.35808	+	0.0843840i	−0.199963	+	0.00387180i
$476$	−2.50211			−0.114684
$477$		0			0
$478$	−1.65425	+	2.86525i	−0.0756639	+	0.131054i
$479$	11.7746	+	20.3942i	0.537994	+	0.931833i	0.999012	+	0.0444419i	$0.0141510\pi$
$479$	11.7746	+	20.3942i	0.537994	+	0.931833i	−0.461018	+	0.887391i	$0.652516\pi$
$480$		0			0
$481$	2.98350	+	5.16757i	0.136036	+	0.235621i
$482$	26.0962			1.18865
$483$		0			0
$484$	−4.36877	−	7.56694i	−0.198581	−	0.343952i
$485$	8.73447	+	15.1285i	0.396612	+	0.686952i
$486$		0			0
$487$	36.0392			1.63309			0.816546	−	0.577280i	$-0.195886\pi$
$487$	36.0392			1.63309			0.816546	+	0.577280i	$0.195886\pi$
$488$	−14.0760	−	24.3803i	−0.637188	−	1.10364i
$489$		0			0
$490$	1.87459	+	3.24688i	0.0846852	+	0.146679i
$491$	10.0297	−	17.3720i	0.452635	−	0.783988i	−0.545913	−	0.837842i	$-0.683817\pi$
$491$	10.0297	−	17.3720i	0.452635	−	0.783988i	0.998549	+	0.0538541i	$0.0171506\pi$
$492$		0			0
$493$	−8.25729			−0.371890
$494$	−8.12081	+	14.7164i	−0.365373	+	0.662124i
$495$		0			0
$496$	5.82853	−	10.0953i	0.261709	−	0.453293i
$497$	1.25733	−	2.17776i	0.0563989	−	0.0976858i
$498$		0			0
$499$	18.4364	−	31.9328i	0.825328	−	1.42951i	−0.0763399	−	0.997082i	$-0.524323\pi$
$499$	18.4364	−	31.9328i	0.825328	−	1.42951i	0.901668	−	0.432429i	$-0.142343\pi$
$500$	−0.397815	−	0.689035i	−0.0177908	−	0.0308146i
$501$		0			0
$502$	18.8649			0.841980
$503$	−10.8244	−	18.7483i	−0.482634	−	0.835947i	0.517167	−	0.855884i	$-0.326987\pi$
$503$	−10.8244	−	18.7483i	−0.482634	−	0.835947i	−0.999801	+	0.0199377i	$0.993653\pi$
$504$		0			0
$505$	5.39731			0.240177
$506$	−0.792028			−0.0352099
$507$		0			0
$508$	7.45492	−	12.9123i	0.330759	−	0.572891i
$509$	−18.2279	−	31.5717i	−0.807938	−	1.39939i	−0.914289	−	0.405062i	$-0.867250\pi$
$509$	−18.2279	−	31.5717i	−0.807938	−	1.39939i	0.106351	−	0.994329i	$-0.466083\pi$
$510$		0			0
$511$	6.00327	−	10.3980i	0.265569	−	0.459979i
$512$	18.3314			0.810141
$513$		0			0
$514$	−21.4471			−0.945990
$515$	1.07375	−	1.85979i	0.0473150	−	0.0819520i
$516$		0			0
$517$	0.746955	+	1.29376i	0.0328511	+	0.0568997i
$518$	−1.76402	+	3.05537i	−0.0775065	+	0.134245i
$519$		0			0
$520$	−10.7802			−0.472745
$521$	22.6092			0.990528			0.495264	−	0.868742i	$-0.335071\pi$
$521$	22.6092			0.990528			0.495264	+	0.868742i	$0.335071\pi$
$522$		0			0
$523$	−0.266456	−	0.461515i	−0.0116513	−	0.0201806i	0.860141	−	0.510056i	$-0.170375\pi$
$523$	−0.266456	−	0.461515i	−0.0116513	−	0.0201806i	−0.871792	+	0.489876i	$0.837042\pi$
$524$	2.29654			0.100325
$525$		0			0
$526$	−4.83619	−	8.37653i	−0.210868	−	0.365234i
$527$	−5.45275	+	9.44444i	−0.237525	+	0.411406i
$528$		0			0
$529$	−2.91759	+	5.05341i	−0.126852	+	0.219714i
$530$	−0.145327	+	0.251713i	−0.00631259	+	0.0109337i
$531$		0			0
$532$	6.56406	−	0.127098i	0.284588	−	0.00551038i
$533$	−37.3606			−1.61827
$534$		0			0
$535$	0.500463	−	0.866827i	0.0216369	−	0.0374762i
$536$	4.53078	+	7.84754i	0.195700	+	0.338962i
$537$		0			0
$538$	−0.158230	−	0.274062i	−0.00682178	−	0.0118157i
$539$	0.459150			0.0197770
$540$		0			0
$541$	−2.50820	−	4.34433i	−0.107836	−	0.186777i	0.807057	−	0.590473i	$-0.201059\pi$
$541$	−2.50820	−	4.34433i	−0.107836	−	0.186777i	−0.914893	+	0.403696i	$0.867725\pi$
$542$	−13.6473	−	23.6378i	−0.586202	−	1.01533i
$543$		0			0
$544$	−6.95610			−0.298240
$545$	8.13145	+	14.0841i	0.348313	+	0.603296i
$546$		0			0
$547$	−11.3149	−	19.5981i	−0.483792	−	0.837952i	0.516035	−	0.856568i	$-0.327408\pi$
$547$	−11.3149	−	19.5981i	−0.483792	−	0.837952i	−0.999827	+	0.0186154i	$0.994074\pi$
$548$	7.49148	−	12.9756i	0.320020	−	0.554291i
$549$		0			0
$550$	0.147496			0.00628923
$551$	21.6622	−	0.419439i	0.922843	−	0.0178687i
$552$		0			0
$553$	1.38883	−	2.40552i	0.0590590	−	0.102293i
$554$	−2.41703	+	4.18642i	−0.102690	+	0.177864i
$555$		0			0
$556$	−7.23207	+	12.5263i	−0.306708	+	0.531234i
$557$	17.6277	+	30.5321i	0.746910	+	1.29369i	0.949297	+	0.314381i	$0.101797\pi$
$557$	17.6277	+	30.5321i	0.746910	+	1.29369i	−0.202387	+	0.979306i	$0.564870\pi$
$558$		0			0
$559$	29.8943			1.26439
$560$	−1.68077	−	2.91119i	−0.0710257	−	0.123020i
$561$		0			0
$562$	−35.9097			−1.51476
$563$	24.6295			1.03801			0.519005	−	0.854771i	$-0.326302\pi$
$563$	24.6295			1.03801			0.519005	+	0.854771i	$0.326302\pi$
$564$		0			0
$565$	−0.421505	+	0.730068i	−0.0177329	+	0.0307142i
$566$	−0.729207	−	1.26302i	−0.0306509	−	0.0530888i
$567$		0			0
$568$	2.03771	−	3.52942i	0.0855005	−	0.148091i
$569$	20.0193			0.839252			0.419626	−	0.907697i	$-0.362161\pi$
$569$	20.0193			0.839252			0.419626	+	0.907697i	$0.362161\pi$
$570$		0			0
$571$	−16.6121			−0.695195			−0.347597	−	0.937644i	$-0.613002\pi$
$571$	−16.6121			−0.695195			−0.347597	+	0.937644i	$0.613002\pi$
$572$	−0.187866	+	0.325394i	−0.00785508	+	0.0136054i
$573$		0			0
$574$	−11.0449	−	19.1303i	−0.461005	−	0.798484i
$575$	2.68492	−	4.65042i	0.111969	−	0.193936i
$576$		0			0
$577$	12.4486			0.518244			0.259122	−	0.965845i	$-0.416567\pi$
$577$	12.4486			0.518244			0.259122	+	0.965845i	$0.416567\pi$
$578$	15.6279			0.650034
$579$		0			0
$580$	1.97737	+	3.42491i	0.0821060	+	0.142212i
$581$	−14.0984			−0.584899
$582$		0			0
$583$	0.0177977	+	0.0308266i	0.000737107	+	0.00127671i
$584$	9.72930	−	16.8516i	0.402601	−	0.697326i
$585$		0			0
$586$	4.23811	−	7.34063i	0.175075	−	0.303238i
$587$	2.25572	−	3.90702i	0.0931036	−	0.161260i	−0.815712	−	0.578458i	$-0.803655\pi$
$587$	2.25572	−	3.90702i	0.0931036	−	0.161260i	0.908816	+	0.417198i	$0.136988\pi$
$588$		0			0
$589$	13.8250	−	25.0536i	0.569651	−	1.03232i
$590$	7.56867			0.311597
$591$		0			0
$592$	−1.50775	+	2.61150i	−0.0619682	+	0.107332i
$593$	9.80411	+	16.9812i	0.402606	+	0.697335i	0.994040	−	0.109019i	$-0.0347710\pi$
$593$	9.80411	+	16.9812i	0.402606	+	0.697335i	−0.591433	+	0.806354i	$0.701438\pi$
$594$		0			0
$595$	1.57241	+	2.72349i	0.0644625	+	0.111652i
$596$	−17.7062			−0.725274
$597$		0			0
$598$	−10.3533	−	17.9325i	−0.423379	−	0.733315i
$599$	5.38795	+	9.33221i	0.220146	+	0.381304i	0.954852	−	0.297082i	$-0.0960134\pi$
$599$	5.38795	+	9.33221i	0.220146	+	0.381304i	−0.734706	+	0.678385i	$0.762680\pi$
$600$		0			0
$601$	15.0244			0.612860			0.306430	−	0.951893i	$-0.400866\pi$
$601$	15.0244			0.612860			0.306430	+	0.951893i	$0.400866\pi$
$602$	8.83763	+	15.3072i	0.360195	+	0.623876i
$603$		0			0
$604$	1.32664	+	2.29781i	0.0539802	+	0.0934964i
$605$	−5.49097	+	9.51064i	−0.223240	+	0.386662i
$606$		0			0
$607$	25.1901			1.02243			0.511217	−	0.859452i	$-0.329195\pi$
$607$	25.1901			1.02243			0.511217	+	0.859452i	$0.329195\pi$
$608$	18.2487	−	0.353343i	0.740082	−	0.0143300i
$609$		0			0
$610$	−5.03499	+	8.72085i	−0.203861	+	0.353097i
$611$	−19.5283	+	33.8240i	−0.790030	+	1.36837i
$612$		0			0
$613$	−8.11753	+	14.0600i	−0.327864	+	0.567877i	−0.982088	−	0.188424i	$-0.939662\pi$
$613$	−8.11753	+	14.0600i	−0.327864	+	0.567877i	0.654224	+	0.756301i	$0.272995\pi$
$614$	−4.99336	−	8.64875i	−0.201516	−	0.349035i
$615$		0			0
$616$	−0.780593			−0.0314510
$617$	3.25913	+	5.64498i	0.131208	+	0.227258i	0.924142	−	0.382048i	$-0.124781\pi$
$617$	3.25913	+	5.64498i	0.131208	+	0.227258i	−0.792935	+	0.609307i	$0.791448\pi$
$618$		0			0
$619$	−4.39112			−0.176494			−0.0882470	−	0.996099i	$-0.528126\pi$
$619$	−4.39112			−0.176494			−0.0882470	+	0.996099i	$0.528126\pi$
$620$	5.22308			0.209764
$621$		0			0
$622$	6.83532	−	11.8391i	0.274071	−	0.474705i
$623$	9.21553	+	15.9618i	0.369212	+	0.639494i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−2.24484			−0.0897220
$627$		0			0
$628$	−5.77858			−0.230590
$629$	1.41054	−	2.44313i	0.0562420	−	0.0974140i
$630$		0			0
$631$	17.3104	+	29.9826i	0.689118	+	1.19359i	0.972124	+	0.234469i	$0.0753350\pi$
$631$	17.3104	+	29.9826i	0.689118	+	1.19359i	−0.283006	+	0.959118i	$0.591332\pi$
$632$	2.25083	−	3.89855i	0.0895331	−	0.155076i
$633$		0			0
$634$	25.8680			1.02735
$635$	−18.7397			−0.743661
$636$		0			0
$637$	6.00198	+	10.3957i	0.237807	+	0.411894i
$638$	−0.733141			−0.0290253
$639$		0			0
$640$	−0.282960	−	0.490101i	−0.0111850	−	0.0193730i
$641$	3.70621	−	6.41934i	0.146386	−	0.253549i	−0.783503	−	0.621388i	$-0.786569\pi$
$641$	3.70621	−	6.41934i	0.146386	−	0.253549i	0.929889	+	0.367839i	$0.119902\pi$
$642$		0			0
$643$	8.27294	−	14.3292i	0.326253	−	0.565087i	−0.655512	−	0.755185i	$-0.727547\pi$
$643$	8.27294	−	14.3292i	0.326253	−	0.565087i	0.981765	+	0.190098i	$0.0608805\pi$
$644$	−4.04397	+	7.00437i	−0.159355	+	0.276011i
$645$		0			0
$646$	7.94520	−	0.153840i	0.312600	−	0.00605276i
$647$	−29.4822			−1.15907			−0.579533	−	0.814949i	$-0.696765\pi$
$647$	−29.4822			−1.15907			−0.579533	+	0.814949i	$0.696765\pi$
$648$		0			0
$649$	0.463456	−	0.802729i	0.0181922	−	0.0315099i
$650$	1.92805	+	3.33949i	0.0756245	+	0.130985i
$651$		0			0
$652$	−7.86810	−	13.6279i	−0.308138	−	0.533712i
$653$	−6.57421			−0.257269			−0.128634	−	0.991692i	$-0.541059\pi$
$653$	−6.57421			−0.257269			−0.128634	+	0.991692i	$0.541059\pi$
$654$		0			0
$655$	−1.44322	−	2.49973i	−0.0563912	−	0.0976725i
$656$	−9.44037	−	16.3512i	−0.368584	−	0.638407i
$657$		0			0
$658$	−23.0925			−0.900241
$659$	−13.1685	−	22.8085i	−0.512972	−	0.888494i	−0.999887	−	0.0150445i	$-0.995211\pi$
$659$	−13.1685	−	22.8085i	−0.512972	−	0.888494i	0.486915	−	0.873450i	$-0.338122\pi$
$660$		0			0
$661$	−1.89210	−	3.27721i	−0.0735941	−	0.127469i	0.826880	−	0.562378i	$-0.190114\pi$
$661$	−1.89210	−	3.27721i	−0.0735941	−	0.127469i	−0.900474	+	0.434910i	$0.856780\pi$
$662$	−10.2706	+	17.7893i	−0.399180	+	0.691399i
$663$		0			0
$664$	−22.8487			−0.886703
$665$	−4.26341	−	7.06496i	−0.165328	−	0.273967i
$666$		0			0
$667$	−13.3456	+	23.1153i	−0.516745	+	0.895029i
$668$	1.35384	−	2.34492i	0.0523817	−	0.0907278i
$669$		0			0
$670$	1.62067	−	2.80708i	0.0626118	−	0.108447i
$671$	0.616619	+	1.06802i	0.0238043	+	0.0412303i
$672$		0			0
$673$	−21.0431			−0.811150			−0.405575	−	0.914062i	$-0.632929\pi$
$673$	−21.0431			−0.811150			−0.405575	+	0.914062i	$0.632929\pi$
$674$	−17.9366	−	31.0670i	−0.690891	−	1.19666i
$675$		0			0
$676$	0.520083			0.0200032
$677$	15.2744			0.587043			0.293522	−	0.955952i	$-0.405173\pi$
$677$	15.2744			0.587043			0.293522	+	0.955952i	$0.405173\pi$
$678$		0			0
$679$	−16.5349	+	28.6394i	−0.634553	+	1.09908i
$680$	2.54835	+	4.41387i	0.0977248	+	0.169264i
$681$		0			0
$682$	−0.484133	+	0.838544i	−0.0185384	+	0.0321095i
$683$	8.60225			0.329156			0.164578	−	0.986364i	$-0.447374\pi$
$683$	8.60225			0.329156			0.164578	+	0.986364i	$0.447374\pi$
$684$		0			0
$685$	−18.8316			−0.719518
$686$	−10.8201	+	18.7409i	−0.413112	+	0.715530i
$687$		0			0
$688$	7.55375	+	13.0835i	0.287984	+	0.498803i
$689$	−0.465302	+	0.805926i	−0.0177266	+	0.0307033i
$690$		0			0
$691$	34.1079			1.29753			0.648763	−	0.760990i	$-0.275286\pi$
$691$	34.1079			1.29753			0.648763	+	0.760990i	$0.275286\pi$
$692$	−8.42231			−0.320168
$693$		0			0
$694$	1.40837	+	2.43937i	0.0534611	+	0.0925974i
$695$	18.1795			0.689587
$696$		0			0
$697$	8.83172	+	15.2970i	0.334525	+	0.579414i
$698$	9.11942	−	15.7953i	0.345175	−	0.597861i
$699$		0			0
$700$	0.753090	−	1.30439i	0.0284641	−	0.0493013i
$701$	5.36463	−	9.29181i	0.202619	−	0.350947i	−0.746752	−	0.665102i	$-0.768388\pi$
$701$	5.36463	−	9.29181i	0.202619	−	0.350947i	0.949372	+	0.314155i	$0.101721\pi$
$702$		0			0
$703$	−3.57633	+	6.48098i	−0.134884	+	0.244435i
$704$	−1.09492			−0.0412665
$705$		0			0
$706$	−15.5633	+	26.9564i	−0.585732	+	1.01452i
$707$	5.10873	+	8.84859i	0.192134	+	0.332785i
$708$		0			0
$709$	14.4238	+	24.9828i	0.541697	+	0.938247i	0.998807	+	0.0488369i	$0.0155514\pi$
$709$	14.4238	+	24.9828i	0.541697	+	0.938247i	−0.457109	+	0.889410i	$0.651115\pi$
$710$	−1.45778			−0.0547096
$711$		0			0
$712$	14.9353	+	25.8687i	0.559724	+	0.969470i
$713$	17.6257	+	30.5287i	0.660089	+	1.14331i
$714$		0			0
$715$	0.472245			0.0176610
$716$	5.80905	+	10.0616i	0.217095	+	0.376019i
$717$		0			0
$718$	−9.54143	−	16.5262i	−0.356083	−	0.616754i
$719$	−10.0278	+	17.3686i	−0.373972	+	0.647739i	−0.990173	−	0.139851i	$-0.955338\pi$
$719$	−10.0278	+	17.3686i	−0.373972	+	0.647739i	0.616200	+	0.787589i	$0.288671\pi$
$720$		0			0
$721$	4.06535			0.151402
$722$	−20.8357	+	0.807171i	−0.775424	+	0.0300398i
$723$		0			0
$724$	−2.16117	+	3.74326i	−0.0803193	+	0.139117i
$725$	2.48530	−	4.30466i	0.0923016	−	0.159871i
$726$		0			0
$727$	0.390261	−	0.675951i	0.0144740	−	0.0250697i	−0.858698	−	0.512482i	$-0.828726\pi$
$727$	0.390261	−	0.675951i	0.0144740	−	0.0250697i	0.873172	+	0.487413i	$0.162059\pi$
$728$	−10.2039	−	17.6736i	−0.378180	−	0.655028i
$729$		0			0
$730$	−6.96036			−0.257615
$731$	−7.06674	−	12.2399i	−0.261373	−	0.452711i
$732$		0			0
$733$	−26.8391			−0.991326			−0.495663	−	0.868515i	$-0.665075\pi$
$733$	−26.8391			−0.991326			−0.495663	+	0.868515i	$0.665075\pi$
$734$	−28.3192			−1.04528
$735$		0			0
$736$	−11.2426	+	19.4728i	−0.414409	+	0.717777i
$737$	−0.198478	−	0.343774i	−0.00731103	−	0.0126631i
$738$		0			0
$739$	−10.3265	+	17.8861i	−0.379867	+	0.657949i	−0.991043	−	0.133546i	$-0.957364\pi$
$739$	−10.3265	+	17.8861i	−0.379867	+	0.657949i	0.611175	+	0.791495i	$0.290697\pi$
$740$	−1.35113			−0.0496685
$741$		0			0
$742$	−0.550227			−0.0201995
$743$	0.736585	−	1.27580i	0.0270227	−	0.0468047i	−0.852198	−	0.523220i	$-0.824731\pi$
$743$	0.736585	−	1.27580i	0.0270227	−	0.0468047i	0.879220	+	0.476415i	$0.158064\pi$
$744$		0			0
$745$	11.1272	+	19.2728i	0.407668	+	0.706102i
$746$	14.8518	−	25.7240i	0.543762	−	0.941824i
$747$		0			0
$748$	0.177639			0.00649514
$749$	1.89482			0.0692352
$750$		0			0
$751$	−7.78121	−	13.4775i	−0.283940	−	0.491799i	0.688411	−	0.725321i	$-0.258308\pi$
$751$	−7.78121	−	13.4775i	−0.283940	−	0.491799i	−0.972352	+	0.233521i	$0.924975\pi$
$752$	−19.7378			−0.719764
$753$		0			0
$754$	−9.58356	−	16.5992i	−0.349013	−	0.604508i
$755$	1.66741	−	2.88804i	0.0606832	−	0.105106i
$756$		0			0
$757$	−10.0878	+	17.4726i	−0.366647	+	0.635052i	−0.989039	−	0.147654i	$-0.952828\pi$
$757$	−10.0878	+	17.4726i	−0.366647	+	0.635052i	0.622392	+	0.782706i	$0.286161\pi$
$758$	6.80568	−	11.7878i	0.247193	−	0.428152i
$759$		0			0
$760$	−6.90957	−	11.4499i	−0.250637	−	0.415333i
$761$	15.1076			0.547649			0.273825	−	0.961780i	$-0.411711\pi$
$761$	15.1076			0.547649			0.273825	+	0.961780i	$0.411711\pi$
$762$		0			0
$763$	−15.3934	+	26.6621i	−0.557278	+	0.965234i
$764$	−8.14556	−	14.1085i	−0.294696	−	0.510428i
$765$		0			0
$766$	2.94082	+	5.09364i	0.106256	+	0.184041i
$767$	24.2331			0.875005
$768$		0			0
$769$	−25.8290	−	44.7372i	−0.931418	−	1.61326i	−0.780900	−	0.624656i	$-0.785239\pi$
$769$	−25.8290	−	44.7372i	−0.931418	−	1.61326i	−0.150518	−	0.988607i	$-0.548094\pi$
$770$	0.139610	+	0.241811i	0.00503118	+	0.00871426i
$771$		0			0
$772$	−8.77063			−0.315662
$773$	15.0779	+	26.1157i	0.542314	+	0.939316i	0.998771	+	0.0495699i	$0.0157851\pi$
$773$	15.0779	+	26.1157i	0.542314	+	0.939316i	−0.456457	+	0.889746i	$0.650882\pi$
$774$		0			0
$775$	−3.28236	−	5.68521i	−0.117906	−	0.204219i
$776$	−26.7976	+	46.4148i	−0.961978	+	1.66620i
$777$		0			0
$778$	9.40431			0.337161
$779$	−23.9462	−	39.6816i	−0.857962	−	1.42174i
$780$		0			0
$781$	−0.0892652	+	0.154612i	−0.00319416	+	0.00553244i
$782$	−4.89487	+	8.47816i	−0.175040	+	0.303178i
$783$		0

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.548719 - 0.950409i) q^{2} +(0.397815 + 0.689035i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.89307 q^{7} +3.06803 q^{8} +O(q^{10})\)	\(q+(0.548719 - 0.950409i) q^{2} +(0.397815 + 0.689035i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.89307 q^{7} +3.06803 q^{8} +(-0.548719 - 0.950409i) q^{10} -0.134400 q^{11} +(-1.75687 - 3.04298i) q^{13} +(1.03876 - 1.79919i) q^{14} +(0.887858 - 1.53781i) q^{16} +(-0.830615 + 1.43867i) q^{17} +(2.10596 - 3.81640i) q^{19} +0.795629 q^{20} +(-0.0737478 + 0.127735i) q^{22} +(2.68492 + 4.65042i) q^{23} +(-0.500000 - 0.866025i) q^{25} -3.85611 q^{26} +(0.753090 + 1.30439i) q^{28} +(2.48530 + 4.30466i) q^{29} +6.56472 q^{31} +(2.09366 + 3.62633i) q^{32} +(0.911548 + 1.57885i) q^{34} +(0.946534 - 1.63944i) q^{35} -1.69819 q^{37} +(-2.47156 - 4.09566i) q^{38} +(1.53402 - 2.65699i) q^{40} +(5.31637 - 9.20823i) q^{41} +(-4.25392 + 7.36801i) q^{43} +(-0.0534662 - 0.0926063i) q^{44} +5.89307 q^{46} +(-5.55771 - 9.62623i) q^{47} -3.41630 q^{49} -1.09744 q^{50} +(1.39781 - 2.42109i) q^{52} +(-0.132424 - 0.229365i) q^{53} +(-0.0672000 + 0.116394i) q^{55} +5.80799 q^{56} +5.45492 q^{58} +(-3.44833 + 5.97269i) q^{59} +(-4.58794 - 7.94655i) q^{61} +(3.60219 - 6.23917i) q^{62} +8.14676 q^{64} -3.51373 q^{65} +(1.47677 + 2.55784i) q^{67} -1.32172 q^{68} +(-1.03876 - 1.79919i) q^{70} +(0.664176 - 1.15039i) q^{71} +(3.17119 - 5.49266i) q^{73} +(-0.931830 + 1.61398i) q^{74} +(3.46742 - 0.0671384i) q^{76} -0.254428 q^{77} +(0.733639 - 1.27070i) q^{79} +(-0.887858 - 1.53781i) q^{80} +(-5.83439 - 10.1055i) q^{82} -7.44736 q^{83} +(0.830615 + 1.43867i) q^{85} +(4.66842 + 8.08593i) q^{86} -0.412343 q^{88} +(4.86804 + 8.43169i) q^{89} +(-3.32587 - 5.76057i) q^{91} +(-2.13620 + 3.70001i) q^{92} -12.1985 q^{94} +(-2.25212 - 3.73202i) q^{95} +(-8.73447 + 15.1285i) q^{97} +(-1.87459 + 3.24688i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 5 q^{4} + 4 q^{5} - 8 q^{7} - 24 q^{8}+O(q^{10}) \) 8 * q + q^2 - 5 * q^4 + 4 * q^5 - 8 * q^7 - 24 * q^8	\( 8 q + q^{2} - 5 q^{4} + 4 q^{5} - 8 q^{7} - 24 q^{8} - q^{10} + 4 q^{11} - 7 q^{13} - q^{14} - 7 q^{16} - q^{17} + 5 q^{19} - 10 q^{20} - 2 q^{22} + 2 q^{23} - 4 q^{25} - 6 q^{26} + 19 q^{28} - q^{29} + 30 q^{32} - 15 q^{34} - 4 q^{35} - 4 q^{37} - 13 q^{38} - 12 q^{40} - 8 q^{41} - q^{43} - 12 q^{44} + 24 q^{46} - 12 q^{47} - 20 q^{49} - 2 q^{50} + 3 q^{52} - 5 q^{53} + 2 q^{55} + 82 q^{56} - 54 q^{58} - 5 q^{59} + 37 q^{62} + 112 q^{64} - 14 q^{65} - 4 q^{67} - 32 q^{68} + q^{70} + 20 q^{71} + 20 q^{73} + 25 q^{74} + 63 q^{76} - 28 q^{77} - 17 q^{79} + 7 q^{80} - 21 q^{82} - 2 q^{83} + q^{85} + 8 q^{86} - 14 q^{88} + 11 q^{89} - 6 q^{91} - q^{92} - 62 q^{94} + 4 q^{95} - q^{97} + 9 q^{98}+O(q^{100}) \) 8 * q + q^2 - 5 * q^4 + 4 * q^5 - 8 * q^7 - 24 * q^8 - q^10 + 4 * q^11 - 7 * q^13 - q^14 - 7 * q^16 - q^17 + 5 * q^19 - 10 * q^20 - 2 * q^22 + 2 * q^23 - 4 * q^25 - 6 * q^26 + 19 * q^28 - q^29 + 30 * q^32 - 15 * q^34 - 4 * q^35 - 4 * q^37 - 13 * q^38 - 12 * q^40 - 8 * q^41 - q^43 - 12 * q^44 + 24 * q^46 - 12 * q^47 - 20 * q^49 - 2 * q^50 + 3 * q^52 - 5 * q^53 + 2 * q^55 + 82 * q^56 - 54 * q^58 - 5 * q^59 + 37 * q^62 + 112 * q^64 - 14 * q^65 - 4 * q^67 - 32 * q^68 + q^70 + 20 * q^71 + 20 * q^73 + 25 * q^74 + 63 * q^76 - 28 * q^77 - 17 * q^79 + 7 * q^80 - 21 * q^82 - 2 * q^83 + q^85 + 8 * q^86 - 14 * q^88 + 11 * q^89 - 6 * q^91 - q^92 - 62 * q^94 + 4 * q^95 - q^97 + 9 * q^98

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