LMFDB - Embedded newform 855.2.k.j.406.5

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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 13 x^{10} - 10 x^{9} + 44 x^{8} - 20 x^{7} + 119 x^{6} + 13 x^{5} + 83 x^{4} + 14 x^{3} + 46 x^{2} + 12 x + 4 $ x^12 - 3x^11 + 13x^10 - 10x^9 + 44x^8 - 20x^7 + 119x^6 + 13x^5 + 83x^4 + 14x^3 + 46x^2 + 12*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			406.5
Root			$0.964458 + 1.67049i$ of defining polynomial
Character	$\chi$	$=$	855.406
Dual form			855.2.k.j.676.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.464458 + 0.804466i) q^{2} +(0.568557 - 0.984769i) q^{4} +(-0.500000 - 0.866025i) q^{5} -3.66299 q^{7} +2.91412 q^{8} +O(q^{10})$	\(q+(0.464458 + 0.804466i) q^{2} +(0.568557 - 0.984769i) q^{4} +(-0.500000 - 0.866025i) q^{5} -3.66299 q^{7} +2.91412 q^{8} +(0.464458 - 0.804466i) q^{10} +1.41795 q^{11} +(1.38214 - 2.39394i) q^{13} +(-1.70131 - 2.94675i) q^{14} +(0.216373 + 0.374768i) q^{16} +(-1.62252 - 2.81029i) q^{17} +(-4.34588 + 0.336682i) q^{19} -1.13711 q^{20} +(0.658577 + 1.14069i) q^{22} +(4.21364 - 7.29823i) q^{23} +(-0.500000 + 0.866025i) q^{25} +2.56778 q^{26} +(-2.08262 + 3.60720i) q^{28} +(0.917170 - 1.58858i) q^{29} +4.85783 q^{31} +(2.71313 - 4.69927i) q^{32} +(1.50719 - 2.61053i) q^{34} +(1.83150 + 3.17225i) q^{35} -9.00891 q^{37} +(-2.28933 - 3.33973i) q^{38} +(-1.45706 - 2.52370i) q^{40} +(-1.82098 - 3.15403i) q^{41} +(-4.41899 - 7.65392i) q^{43} +(0.806183 - 1.39635i) q^{44} +7.82823 q^{46} +(5.37200 - 9.30458i) q^{47} +6.41753 q^{49} -0.928917 q^{50} +(-1.57165 - 2.72218i) q^{52} +(-3.56193 + 6.16945i) q^{53} +(-0.708973 - 1.22798i) q^{55} -10.6744 q^{56} +1.70395 q^{58} +(2.65227 + 4.59387i) q^{59} +(1.64399 - 2.84747i) q^{61} +(2.25626 + 3.90796i) q^{62} +5.90603 q^{64} -2.76428 q^{65} +(-6.32544 + 10.9560i) q^{67} -3.68999 q^{68} +(-1.70131 + 2.94675i) q^{70} +(7.28608 + 12.6199i) q^{71} +(-0.964193 - 1.67003i) q^{73} +(-4.18426 - 7.24736i) q^{74} +(-2.13932 + 4.47111i) q^{76} -5.19393 q^{77} +(6.25028 + 10.8258i) q^{79} +(0.216373 - 0.374768i) q^{80} +(1.69154 - 2.92983i) q^{82} +6.46857 q^{83} +(-1.62252 + 2.81029i) q^{85} +(4.10487 - 7.10985i) q^{86} +4.13206 q^{88} +(5.27117 - 9.12994i) q^{89} +(-5.06277 + 8.76897i) q^{91} +(-4.79138 - 8.29892i) q^{92} +9.98029 q^{94} +(2.46451 + 3.59530i) q^{95} +(0.311714 + 0.539905i) q^{97} +(2.98067 + 5.16268i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 5 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 - 5 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8	$ 12 q - 3 q^{2} - 5 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} - 3 q^{10} - 8 q^{13} - 10 q^{14} - 3 q^{16} - 4 q^{17} - 6 q^{19} + 10 q^{20} + 2 q^{23} - 6 q^{25} + 40 q^{26} - 26 q^{28} - 4 q^{29} + 24 q^{31} - 15 q^{32} + 7 q^{34} - 2 q^{35} + 29 q^{38} - 6 q^{40} - 12 q^{41} - 4 q^{43} - 6 q^{44} + 48 q^{46} - 6 q^{47} + 32 q^{49} + 6 q^{50} - 20 q^{52} - 26 q^{53} + 44 q^{56} - 20 q^{58} - 16 q^{59} + 20 q^{61} + 25 q^{62} + 28 q^{64} + 16 q^{65} - 12 q^{67} - 54 q^{68} - 10 q^{70} + 8 q^{71} - 4 q^{73} + 16 q^{74} - 66 q^{76} - 48 q^{77} - 12 q^{79} - 3 q^{80} + 26 q^{82} + 44 q^{83} - 4 q^{85} + 44 q^{86} - 32 q^{88} + 8 q^{89} + 2 q^{91} - 36 q^{92} - 14 q^{94} + 6 q^{95} + 30 q^{97} - 49 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 - 5 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 - 3 * q^10 - 8 * q^13 - 10 * q^14 - 3 * q^16 - 4 * q^17 - 6 * q^19 + 10 * q^20 + 2 * q^23 - 6 * q^25 + 40 * q^26 - 26 * q^28 - 4 * q^29 + 24 * q^31 - 15 * q^32 + 7 * q^34 - 2 * q^35 + 29 * q^38 - 6 * q^40 - 12 * q^41 - 4 * q^43 - 6 * q^44 + 48 * q^46 - 6 * q^47 + 32 * q^49 + 6 * q^50 - 20 * q^52 - 26 * q^53 + 44 * q^56 - 20 * q^58 - 16 * q^59 + 20 * q^61 + 25 * q^62 + 28 * q^64 + 16 * q^65 - 12 * q^67 - 54 * q^68 - 10 * q^70 + 8 * q^71 - 4 * q^73 + 16 * q^74 - 66 * q^76 - 48 * q^77 - 12 * q^79 - 3 * q^80 + 26 * q^82 + 44 * q^83 - 4 * q^85 + 44 * q^86 - 32 * q^88 + 8 * q^89 + 2 * q^91 - 36 * q^92 - 14 * q^94 + 6 * q^95 + 30 * q^97 - 49 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.464458	+	0.804466i	0.328422	+	0.568843i	0.982199	−	0.187844i	$-0.0601500\pi$
$2$	0.464458	+	0.804466i	0.328422	+	0.568843i	−0.653777	+	0.756687i	$0.726817\pi$
$3$		0			0
$3$		0			0
$4$	0.568557	−	0.984769i	0.284278	−	0.492385i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−3.66299			−1.38448			−0.692241	−	0.721667i	$-0.743376\pi$
$7$	−3.66299			−1.38448			−0.692241	+	0.721667i	$0.743376\pi$
$8$	2.91412			1.03030
$9$		0			0
$10$	0.464458	−	0.804466i	0.146875	−	0.254394i
$11$	1.41795			0.427527			0.213763	−	0.976885i	$-0.431428\pi$
$11$	1.41795			0.427527			0.213763	+	0.976885i	$0.431428\pi$
$12$		0			0
$13$	1.38214	−	2.39394i	0.383336	−	0.663958i	−0.608200	−	0.793784i	$-0.708108\pi$
$13$	1.38214	−	2.39394i	0.383336	−	0.663958i	0.991537	+	0.129825i	$0.0414416\pi$
$14$	−1.70131	−	2.94675i	−0.454694	−	0.787553i
$15$		0			0
$16$	0.216373	+	0.374768i	0.0540931	+	0.0936921i
$17$	−1.62252	−	2.81029i	−0.393520	−	0.681596i	0.599391	−	0.800456i	$-0.295409\pi$
$17$	−1.62252	−	2.81029i	−0.393520	−	0.681596i	−0.992911	+	0.118860i	$0.962076\pi$
$18$		0			0
$19$	−4.34588	+	0.336682i	−0.997013	+	0.0772401i
$19$	−4.34588	+	0.336682i	−0.997013	+	0.0772401i
$20$	−1.13711			−0.254266
$21$		0			0
$22$	0.658577	+	1.14069i	0.140409	+	0.243196i
$23$	4.21364	−	7.29823i	0.878604	−	1.52179i	0.0257305	−	0.999669i	$-0.491809\pi$
$23$	4.21364	−	7.29823i	0.878604	−	1.52179i	0.852873	−	0.522118i	$-0.174858\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.56778			0.503584
$27$		0			0
$28$	−2.08262	+	3.60720i	−0.393578	+	0.681698i
$29$	0.917170	−	1.58858i	0.170314	−	0.294993i	−0.768216	−	0.640191i	$-0.778855\pi$
$29$	0.917170	−	1.58858i	0.170314	−	0.294993i	0.938530	+	0.345199i	$0.112188\pi$
$30$		0			0
$31$	4.85783			0.872493			0.436246	−	0.899827i	$-0.356308\pi$
$31$	4.85783			0.872493			0.436246	+	0.899827i	$0.356308\pi$
$32$	2.71313	−	4.69927i	0.479617	−	0.830722i
$33$		0			0
$34$	1.50719	−	2.61053i	0.258481	−	0.447702i
$35$	1.83150	+	3.17225i	0.309580	+	0.536207i
$36$		0			0
$37$	−9.00891			−1.48106			−0.740528	−	0.672026i	$-0.765424\pi$
$37$	−9.00891			−1.48106			−0.740528	+	0.672026i	$0.765424\pi$
$38$	−2.28933	−	3.33973i	−0.371378	−	0.541776i
$39$		0			0
$40$	−1.45706	−	2.52370i	−0.230381	−	0.399032i
$41$	−1.82098	−	3.15403i	−0.284390	−	0.492577i	0.688071	−	0.725643i	$-0.258458\pi$
$41$	−1.82098	−	3.15403i	−0.284390	−	0.492577i	−0.972461	+	0.233066i	$0.925124\pi$
$42$		0			0
$43$	−4.41899	−	7.65392i	−0.673890	−	1.16721i	−0.976792	−	0.214190i	$-0.931289\pi$
$43$	−4.41899	−	7.65392i	−0.673890	−	1.16721i	0.302902	−	0.953022i	$-0.402044\pi$
$44$	0.806183	−	1.39635i	0.121537	−	0.210508i
$45$		0			0
$46$	7.82823			1.15421
$47$	5.37200	−	9.30458i	0.783587	−	1.35721i	−0.146252	−	0.989247i	$-0.546721\pi$
$47$	5.37200	−	9.30458i	0.783587	−	1.35721i	0.929839	−	0.367966i	$-0.119946\pi$
$48$		0			0
$49$	6.41753			0.916789
$50$	−0.928917			−0.131369
$51$		0			0
$52$	−1.57165	−	2.72218i	−0.217949	−	0.377498i
$53$	−3.56193	+	6.16945i	−0.489269	+	0.847439i	−0.999924	−	0.0123469i	$-0.996070\pi$
$53$	−3.56193	+	6.16945i	−0.489269	+	0.847439i	0.510655	+	0.859786i	$0.329403\pi$
$54$		0			0
$55$	−0.708973	−	1.22798i	−0.0955979	−	0.165580i
$56$	−10.6744			−1.42643
$57$		0			0
$58$	1.70395			0.223739
$59$	2.65227	+	4.59387i	0.345296	+	0.598070i	0.985408	−	0.170212i	$-0.0544452\pi$
$59$	2.65227	+	4.59387i	0.345296	+	0.598070i	−0.640111	+	0.768282i	$0.721112\pi$
$60$		0			0
$61$	1.64399	−	2.84747i	0.210491	−	0.364581i	−0.741377	−	0.671088i	$-0.765827\pi$
$61$	1.64399	−	2.84747i	0.210491	−	0.364581i	0.951868	+	0.306507i	$0.0991604\pi$
$62$	2.25626	+	3.90796i	0.286545	+	0.496311i
$63$		0			0
$64$	5.90603			0.738253
$65$	−2.76428			−0.342867
$66$		0			0
$67$	−6.32544	+	10.9560i	−0.772775	+	1.33849i	0.163262	+	0.986583i	$0.447799\pi$
$67$	−6.32544	+	10.9560i	−0.772775	+	1.33849i	−0.936037	+	0.351903i	$0.885535\pi$
$68$	−3.68999			−0.447477
$69$		0			0
$70$	−1.70131	+	2.94675i	−0.203345	+	0.352204i
$71$	7.28608	+	12.6199i	0.864699	+	1.49770i	0.867346	+	0.497706i	$0.165824\pi$
$71$	7.28608	+	12.6199i	0.864699	+	1.49770i	−0.00264644	+	0.999996i	$0.500842\pi$
$72$		0			0
$73$	−0.964193	−	1.67003i	−0.112850	−	0.195462i	0.804068	−	0.594537i	$-0.202665\pi$
$73$	−0.964193	−	1.67003i	−0.112850	−	0.195462i	−0.916918	+	0.399075i	$0.869331\pi$
$74$	−4.18426	−	7.24736i	−0.486411	−	0.842488i
$75$		0			0
$76$	−2.13932	+	4.47111i	−0.245397	+	0.512871i
$77$	−5.19393			−0.591903
$78$		0			0
$79$	6.25028	+	10.8258i	0.703211	+	1.21800i	0.967333	+	0.253508i	$0.0815845\pi$
$79$	6.25028	+	10.8258i	0.703211	+	1.21800i	−0.264122	+	0.964489i	$0.585082\pi$
$80$	0.216373	−	0.374768i	0.0241912	−	0.0419004i
$81$		0			0
$82$	1.69154	−	2.92983i	0.186799	−	0.323546i
$83$	6.46857			0.710018			0.355009	−	0.934863i	$-0.384478\pi$
$83$	6.46857			0.710018			0.355009	+	0.934863i	$0.384478\pi$
$84$		0			0
$85$	−1.62252	+	2.81029i	−0.175987	+	0.304819i
$86$	4.10487	−	7.10985i	0.442640	−	0.766675i
$87$		0			0
$88$	4.13206			0.440479
$89$	5.27117	−	9.12994i	0.558743	−	0.967772i	−0.438858	−	0.898556i	$-0.644617\pi$
$89$	5.27117	−	9.12994i	0.558743	−	0.967772i	0.997602	−	0.0692157i	$-0.0220497\pi$
$90$		0			0
$91$	−5.06277	+	8.76897i	−0.530722	+	0.919238i
$92$	−4.79138	−	8.29892i	−0.499536	−	0.865222i
$93$		0			0
$94$	9.98029			1.02939
$95$	2.46451	+	3.59530i	0.252854	+	0.368870i
$96$		0			0
$97$	0.311714	+	0.539905i	0.0316498	+	0.0548190i	0.881416	−	0.472340i	$-0.156591\pi$
$97$	0.311714	+	0.539905i	0.0316498	+	0.0548190i	−0.849767	+	0.527159i	$0.823257\pi$
$98$	2.98067	+	5.16268i	0.301094	+	0.521509i
$99$		0			0
$100$	0.568557	+	0.984769i	0.0568557	+	0.0984769i
$101$	−6.10551	+	10.5751i	−0.607521	+	1.05226i	0.384126	+	0.923281i	$0.374503\pi$
$101$	−6.10551	+	10.5751i	−0.607521	+	1.05226i	−0.991648	+	0.128977i	$0.958831\pi$
$102$		0			0
$103$	12.7435			1.25566			0.627828	−	0.778352i	$-0.283944\pi$
$103$	12.7435			1.25566			0.627828	+	0.778352i	$0.283944\pi$
$104$	4.02772	−	6.97621i	0.394950	−	0.684074i
$105$		0			0
$106$	−6.61748			−0.642746
$107$	16.3829			1.58379			0.791896	−	0.610656i	$-0.209094\pi$
$107$	16.3829			1.58379			0.791896	+	0.610656i	$0.209094\pi$
$108$		0			0
$109$	2.72026	+	4.71164i	0.260554	+	0.451293i	0.966389	−	0.257083i	$-0.0827615\pi$
$109$	2.72026	+	4.71164i	0.260554	+	0.451293i	−0.705835	+	0.708376i	$0.749428\pi$
$110$	0.658577	−	1.14069i	0.0627928	−	0.108760i
$111$		0			0
$112$	−0.792572	−	1.37277i	−0.0748910	−	0.129715i
$113$	−9.46975			−0.890839			−0.445420	−	0.895322i	$-0.646946\pi$
$113$	−9.46975			−0.890839			−0.445420	+	0.895322i	$0.646946\pi$
$114$		0			0
$115$	−8.42727			−0.785847
$116$	−1.04293	−	1.80640i	−0.0968333	−	0.167720i
$117$		0			0
$118$	−2.46374	+	4.26732i	−0.226805	+	0.392839i
$119$	5.94330	+	10.2941i	0.544821	+	0.943658i
$120$		0			0
$121$	−8.98943			−0.817221
$122$	3.05425			0.276519
$123$		0			0
$124$	2.76195	−	4.78385i	0.248031	−	0.429602i
$125$	1.00000			0.0894427
$126$		0			0
$127$	0.171100	−	0.296354i	0.0151827	−	0.0262971i	−0.858334	−	0.513091i	$-0.828500\pi$
$127$	0.171100	−	0.296354i	0.0151827	−	0.0262971i	0.873517	+	0.486794i	$0.161834\pi$
$128$	−2.68315	−	4.64735i	−0.237159	−	0.410771i
$129$		0			0
$130$	−1.28389	−	2.22377i	−0.112605	−	0.195037i
$131$	−0.618905	−	1.07198i	−0.0540740	−	0.0936590i	0.837721	−	0.546098i	$-0.183887\pi$
$131$	−0.618905	−	1.07198i	−0.0540740	−	0.0936590i	−0.891795	+	0.452439i	$0.850554\pi$
$132$		0			0
$133$	15.9189	−	1.23326i	1.38035	−	0.106938i
$134$	−11.7516			−1.01518
$135$		0			0
$136$	−4.72823	−	8.18953i	−0.405442	−	0.702246i
$137$	−2.87141	+	4.97344i	−0.245322	+	0.424909i	−0.962222	−	0.272266i	$-0.912227\pi$
$137$	−2.87141	+	4.97344i	−0.245322	+	0.424909i	0.716900	+	0.697176i	$0.245560\pi$
$138$		0			0
$139$	10.3730	−	17.9666i	0.879830	−	1.52391i	0.0283041	−	0.999599i	$-0.490989\pi$
$139$	10.3730	−	17.9666i	0.879830	−	1.52391i	0.851526	−	0.524312i	$-0.175677\pi$
$140$	4.16524			0.352027
$141$		0			0
$142$	−6.76817	+	11.7228i	−0.567972	+	0.983756i
$143$	1.95980	−	3.39447i	0.163887	−	0.283860i
$144$		0			0
$145$	−1.83434			−0.152334
$146$	0.895655	−	1.55132i	0.0741250	−	0.128388i
$147$		0			0
$148$	−5.12208	+	8.87170i	−0.421032	+	0.729249i
$149$	10.6969	+	18.5276i	0.876324	+	1.51784i	0.855346	+	0.518057i	$0.173345\pi$
$149$	10.6969	+	18.5276i	0.876324	+	1.51784i	0.0209780	+	0.999780i	$0.493322\pi$
$150$		0			0
$151$	−1.35031			−0.109886			−0.0549432	−	0.998489i	$-0.517498\pi$
$151$	−1.35031			−0.109886			−0.0549432	+	0.998489i	$0.517498\pi$
$152$	−12.6644	+	0.981131i	−1.02722	+	0.0795802i
$153$		0			0
$154$	−2.41236	−	4.17834i	−0.194394	−	0.336700i
$155$	−2.42892	−	4.20701i	−0.195095	−	0.337915i
$156$		0			0
$157$	−6.14413	−	10.6419i	−0.490355	−	0.849319i	0.509584	−	0.860421i	$-0.329799\pi$
$157$	−6.14413	−	10.6419i	−0.490355	−	0.849319i	−0.999938	+	0.0111018i	$0.996466\pi$
$158$	−5.80599	+	10.0563i	−0.461900	+	0.800034i
$159$		0			0
$160$	−5.42625			−0.428983
$161$	−15.4345	+	26.7334i	−1.21641	+	2.10689i
$162$		0			0
$163$	1.45723			0.114139			0.0570696	−	0.998370i	$-0.481824\pi$
$163$	1.45723			0.114139			0.0570696	+	0.998370i	$0.481824\pi$
$164$	−4.14133			−0.323383
$165$		0			0
$166$	3.00438	+	5.20375i	0.233185	+	0.403889i
$167$	−8.08781	+	14.0085i	−0.625854	+	1.08401i	0.362521	+	0.931975i	$0.381916\pi$
$167$	−8.08781	+	14.0085i	−0.625854	+	1.08401i	−0.988375	+	0.152035i	$0.951417\pi$
$168$		0			0
$169$	2.67938	+	4.64083i	0.206106	+	0.356987i
$170$	−3.01438			−0.231192
$171$		0			0
$172$	−10.0498			−0.766289
$173$	1.82710	+	3.16463i	0.138912	+	0.240603i	0.927085	−	0.374851i	$-0.122306\pi$
$173$	1.82710	+	3.16463i	0.138912	+	0.240603i	−0.788173	+	0.615454i	$0.788973\pi$
$174$		0			0
$175$	1.83150	−	3.17225i	0.138448	−	0.239799i
$176$	0.306805	+	0.531401i	0.0231263	+	0.0400559i
$177$		0			0
$178$	9.79297			0.734014
$179$	9.16937			0.685351			0.342676	−	0.939454i	$-0.388667\pi$
$179$	9.16937			0.685351			0.342676	+	0.939454i	$0.388667\pi$
$180$		0			0
$181$	3.81471	−	6.60727i	0.283545	−	0.491115i	−0.688710	−	0.725037i	$-0.741823\pi$
$181$	3.81471	−	6.60727i	0.283545	−	0.491115i	0.972255	+	0.233922i	$0.0751561\pi$
$182$	−9.40578			−0.697203
$183$		0			0
$184$	12.2790	−	21.2679i	0.905222	−	1.56789i
$185$	4.50445	+	7.80194i	0.331174	+	0.573610i
$186$		0			0
$187$	−2.30065	−	3.98485i	−0.168240	−	0.291401i
$188$	−6.10858	−	10.5804i	−0.445514	−	0.771653i
$189$		0			0
$190$	−1.74763	+	3.65248i	−0.126786	+	0.264979i
$191$	−8.25384			−0.597227			−0.298613	−	0.954374i	$-0.596524\pi$
$191$	−8.25384			−0.597227			−0.298613	+	0.954374i	$0.596524\pi$
$192$		0			0
$193$	−1.64118	−	2.84261i	−0.118135	−	0.204615i	0.800894	−	0.598806i	$-0.204358\pi$
$193$	−1.64118	−	2.84261i	−0.118135	−	0.204615i	−0.919029	+	0.394191i	$0.871025\pi$
$194$	−0.289557	+	0.501527i	−0.0207889	+	0.0360075i
$195$		0			0
$196$	3.64873	−	6.31978i	0.260623	−	0.451413i
$197$	13.8640			0.987770			0.493885	−	0.869527i	$-0.335576\pi$
$197$	13.8640			0.987770			0.493885	+	0.869527i	$0.335576\pi$
$198$		0			0
$199$	−7.02823	+	12.1733i	−0.498218	+	0.862939i	−0.999998	−	0.00205634i	$-0.999345\pi$
$199$	−7.02823	+	12.1733i	−0.498218	+	0.862939i	0.501780	+	0.864995i	$0.332679\pi$
$200$	−1.45706	+	2.52370i	−0.103030	+	0.178453i
$201$		0			0
$202$	−11.3430			−0.798093
$203$	−3.35959	+	5.81898i	−0.235797	+	0.408412i
$204$		0			0
$205$	−1.82098	+	3.15403i	−0.127183	+	0.220287i
$206$	5.91883	+	10.2517i	0.412385	+	0.714271i
$207$		0			0
$208$	1.19623			0.0829435
$209$	−6.16222	+	0.477397i	−0.426250	+	0.0330222i
$210$		0			0
$211$	2.72258	+	4.71564i	0.187430	+	0.324638i	0.944393	−	0.328820i	$-0.106651\pi$
$211$	2.72258	+	4.71564i	0.187430	+	0.324638i	−0.756963	+	0.653458i	$0.773318\pi$
$212$	4.05032	+	7.01537i	0.278177	+	0.481817i
$213$		0			0
$214$	7.60916	+	13.1795i	0.520151	+	0.900929i
$215$	−4.41899	+	7.65392i	−0.301373	+	0.521993i
$216$		0			0
$217$	−17.7942			−1.20795
$218$	−2.52690	+	4.37672i	−0.171143	+	0.296429i
$219$		0			0
$220$	−1.61237			−0.108706
$221$	−8.97022			−0.603402
$222$		0			0
$223$	−5.51057	−	9.54459i	−0.369015	−	0.639153i	0.620397	−	0.784288i	$-0.286972\pi$
$223$	−5.51057	−	9.54459i	−0.369015	−	0.639153i	−0.989412	+	0.145135i	$0.953638\pi$
$224$	−9.93816	+	17.2134i	−0.664021	+	1.15012i
$225$		0			0
$226$	−4.39831	−	7.61809i	−0.292571	−	0.506748i
$227$	−10.1940			−0.676603			−0.338301	−	0.941038i	$-0.609852\pi$
$227$	−10.1940			−0.676603			−0.338301	+	0.941038i	$0.609852\pi$
$228$		0			0
$229$	−5.53708			−0.365901			−0.182950	−	0.983122i	$-0.558565\pi$
$229$	−5.53708			−0.365901			−0.182950	+	0.983122i	$0.558565\pi$
$230$	−3.91412	−	6.77945i	−0.258089	−	0.447024i
$231$		0			0
$232$	2.67274	−	4.62932i	0.175474	−	0.303930i
$233$	4.76246	+	8.24882i	0.311999	+	0.540398i	0.978795	−	0.204842i	$-0.0656681\pi$
$233$	4.76246	+	8.24882i	0.311999	+	0.540398i	−0.666796	+	0.745240i	$0.732335\pi$
$234$		0			0
$235$	−10.7440			−0.700862
$236$	6.03186			0.392641
$237$		0			0
$238$	−5.52083	+	9.56235i	−0.357862	+	0.619835i
$239$	−10.9781			−0.710117			−0.355059	−	0.934844i	$-0.615539\pi$
$239$	−10.9781			−0.710117			−0.355059	+	0.934844i	$0.615539\pi$
$240$		0			0
$241$	−3.38450	+	5.86213i	−0.218015	+	0.377613i	−0.954201	−	0.299166i	$-0.903292\pi$
$241$	−3.38450	+	5.86213i	−0.218015	+	0.377613i	0.736186	+	0.676779i	$0.236625\pi$
$242$	−4.17522	−	7.23169i	−0.268393	−	0.464870i
$243$		0			0
$244$	−1.86940	−	3.23790i	−0.119676	−	0.207285i
$245$	−3.20876	−	5.55774i	−0.205000	−	0.355071i
$246$		0			0
$247$	−5.20061	+	10.8691i	−0.330907	+	0.691584i
$248$	14.1563			0.898926
$249$		0			0
$250$	0.464458	+	0.804466i	0.0293749	+	0.0508789i
$251$	9.63128	−	16.6819i	0.607921	−	1.05295i	−0.383661	−	0.923474i	$-0.625337\pi$
$251$	9.63128	−	16.6819i	0.607921	−	1.05295i	0.991582	−	0.129477i	$-0.0413297\pi$
$252$		0			0
$253$	5.97471	−	10.3485i	0.375627	−	0.650605i
$254$	0.317875			0.0199452
$255$		0			0
$256$	8.39845	−	14.5465i	0.524903	−	0.909158i
$257$	4.99004	−	8.64300i	0.311270	−	0.539135i	−0.667368	−	0.744728i	$-0.732579\pi$
$257$	4.99004	−	8.64300i	0.311270	−	0.539135i	0.978638	+	0.205593i	$0.0659123\pi$
$258$		0			0
$259$	32.9996			2.05049
$260$	−1.57165	+	2.72218i	−0.0974696	+	0.168822i
$261$		0			0
$262$	0.574912	−	0.995776i	0.0355182	−	0.0615193i
$263$	−1.73632	−	3.00739i	−0.107066	−	0.185444i	0.807514	−	0.589848i	$-0.200812\pi$
$263$	−1.73632	−	3.00739i	−0.107066	−	0.185444i	−0.914580	+	0.404404i	$0.867479\pi$
$264$		0			0
$265$	7.12387			0.437616
$266$	8.38579	+	12.2334i	0.514166	+	0.750079i
$267$		0			0
$268$	7.19274	+	12.4582i	0.439366	+	0.761005i
$269$	−11.5745	−	20.0476i	−0.705708	−	1.22232i	−0.966435	−	0.256910i	$-0.917296\pi$
$269$	−11.5745	−	20.0476i	−0.705708	−	1.22232i	0.260727	−	0.965413i	$-0.416038\pi$
$270$		0			0
$271$	−10.8902	−	18.8624i	−0.661532	−	1.14581i	−0.980213	−	0.197946i	$-0.936573\pi$
$271$	−10.8902	−	18.8624i	−0.661532	−	1.14581i	0.318681	−	0.947862i	$-0.396760\pi$
$272$	0.702140	−	1.21614i	0.0425735	−	0.0737394i
$273$		0			0
$274$	−5.33461			−0.322276
$275$	−0.708973	+	1.22798i	−0.0427527	+	0.0740498i
$276$		0			0
$277$	−20.7409			−1.24620			−0.623101	−	0.782141i	$-0.714127\pi$
$277$	−20.7409			−1.24620			−0.623101	+	0.782141i	$0.714127\pi$
$278$	19.2714			1.15582
$279$		0			0
$280$	5.33720	+	9.24430i	0.318959	+	0.552452i
$281$	12.7958	−	22.1629i	0.763332	−	1.32213i	−0.177793	−	0.984068i	$-0.556896\pi$
$281$	12.7958	−	22.1629i	0.763332	−	1.32213i	0.941124	−	0.338061i	$-0.109771\pi$
$282$		0			0
$283$	7.04996	+	12.2109i	0.419077	+	0.725862i	0.995847	−	0.0910442i	$-0.0290205\pi$
$283$	7.04996	+	12.2109i	0.419077	+	0.725862i	−0.576770	+	0.816907i	$0.695687\pi$
$284$	16.5702			0.983261
$285$		0			0
$286$	3.64098			0.215296
$287$	6.67025	+	11.5532i	0.393732	+	0.681964i
$288$		0			0
$289$	3.23483	−	5.60289i	0.190284	−	0.329582i
$290$	−0.851974	−	1.47566i	−0.0500297	−	0.0866539i
$291$		0			0
$292$	−2.19280			−0.128324
$293$	2.14559			0.125347			0.0626733	−	0.998034i	$-0.480037\pi$
$293$	2.14559			0.125347			0.0626733	+	0.998034i	$0.480037\pi$
$294$		0			0
$295$	2.65227	−	4.59387i	0.154421	−	0.267465i
$296$	−26.2530			−1.52593
$297$		0			0
$298$	−9.93653	+	17.2106i	−0.575607	+	0.996981i
$299$	−11.6477	−	20.1743i	−0.673602	−	1.16671i
$300$		0			0
$301$	16.1867	+	28.0363i	0.932988	+	1.61598i
$302$	−0.627161	−	1.08627i	−0.0360891	−	0.0625081i
$303$		0			0
$304$	−1.06651	−	1.55585i	−0.0611683	−	0.0892340i
$305$	−3.28797			−0.188269
$306$		0			0
$307$	−6.17252	−	10.6911i	−0.352285	−	0.610175i	0.634365	−	0.773034i	$-0.281262\pi$
$307$	−6.17252	−	10.6911i	−0.352285	−	0.610175i	−0.986649	+	0.162859i	$0.947928\pi$
$308$	−2.95304	+	5.11482i	−0.168265	+	0.291444i
$309$		0			0
$310$	2.25626	−	3.90796i	0.128147	−	0.221957i
$311$	31.2434			1.77165			0.885825	−	0.464020i	$-0.153593\pi$
$311$	31.2434			1.77165			0.885825	+	0.464020i	$0.153593\pi$
$312$		0			0
$313$	16.7182	−	28.9568i	0.944970	−	1.63674i	0.189158	−	0.981947i	$-0.439424\pi$
$313$	16.7182	−	28.9568i	0.944970	−	1.63674i	0.755812	−	0.654789i	$-0.227243\pi$
$314$	5.70738	−	9.88548i	0.322086	−	0.557870i
$315$		0			0
$316$	14.2146			0.799631
$317$	−3.05432	+	5.29024i	−0.171548	+	0.297129i	−0.938961	−	0.344023i	$-0.888210\pi$
$317$	−3.05432	+	5.29024i	−0.171548	+	0.297129i	0.767413	+	0.641153i	$0.221543\pi$
$318$		0			0
$319$	1.30050	−	2.25253i	0.0728139	−	0.126117i
$320$	−2.95301	−	5.11477i	−0.165078	−	0.285924i
$321$		0			0
$322$	−28.6748			−1.59798
$323$	7.99747	+	11.6669i	0.444991	+	0.649165i
$324$		0			0
$325$	1.38214	+	2.39394i	0.0766673	+	0.132792i
$326$	0.676823	+	1.17229i	0.0374858	+	0.0649272i
$327$		0			0
$328$	−5.30656	−	9.19122i	−0.293006	−	0.507500i
$329$	−19.6776	+	34.0826i	−1.08486	+	1.87904i
$330$		0			0
$331$	−3.39081			−0.186376			−0.0931879	−	0.995649i	$-0.529706\pi$
$331$	−3.39081			−0.186376			−0.0931879	+	0.995649i	$0.529706\pi$
$332$	3.67775	−	6.37005i	0.201843	−	0.349602i
$333$		0			0
$334$	−15.0258			−0.822176
$335$	12.6509			0.691191
$336$		0			0
$337$	1.08496	+	1.87920i	0.0591013	+	0.102366i	0.894062	−	0.447943i	$-0.147843\pi$
$337$	1.08496	+	1.87920i	0.0591013	+	0.102366i	−0.834961	+	0.550309i	$0.814510\pi$
$338$	−2.48892	+	4.31094i	−0.135380	+	0.234484i
$339$		0			0
$340$	1.84499	+	3.19562i	0.100059	+	0.173307i
$341$	6.88815			0.373014
$342$		0			0
$343$	2.13360			0.115203
$344$	−12.8775	−	22.3044i	−0.694306	−	1.20257i
$345$		0			0
$346$	−1.69723	+	2.93968i	−0.0912434	+	0.158038i
$347$	1.37869	+	2.38796i	0.0740118	+	0.128192i	0.900656	−	0.434533i	$-0.143086\pi$
$347$	1.37869	+	2.38796i	0.0740118	+	0.128192i	−0.826644	+	0.562725i	$0.809753\pi$
$348$		0			0
$349$	−20.7472			−1.11057			−0.555285	−	0.831660i	$-0.687391\pi$
$349$	−20.7472			−1.11057			−0.555285	+	0.831660i	$0.687391\pi$
$350$	3.40262			0.181878
$351$		0			0
$352$	3.84706	−	6.66331i	0.205049	−	0.355156i
$353$	−10.5842			−0.563341			−0.281670	−	0.959511i	$-0.590888\pi$
$353$	−10.5842			−0.563341			−0.281670	+	0.959511i	$0.590888\pi$
$354$		0			0
$355$	7.28608	−	12.6199i	0.386705	−	0.669793i
$356$	−5.99393	−	10.3818i	−0.317677	−	0.550233i
$357$		0			0
$358$	4.25879	+	7.37645i	0.225084	+	0.389857i
$359$	17.6905	+	30.6408i	0.933666	+	1.61716i	0.776995	+	0.629507i	$0.216743\pi$
$359$	17.6905	+	30.6408i	0.933666	+	1.61716i	0.156671	+	0.987651i	$0.449924\pi$
$360$		0			0
$361$	18.7733	−	2.92636i	0.988068	−	0.154019i
$362$	7.08710			0.372490
$363$		0			0
$364$	5.75694	+	9.97132i	0.301746	+	0.522639i
$365$	−0.964193	+	1.67003i	−0.0504682	+	0.0874135i
$366$		0			0
$367$	−12.3001	+	21.3045i	−0.642062	+	1.11208i	0.342909	+	0.939368i	$0.388588\pi$
$367$	−12.3001	+	21.3045i	−0.642062	+	1.11208i	−0.984972	+	0.172716i	$0.944746\pi$
$368$	3.64686			0.190106
$369$		0			0
$370$	−4.18426	+	7.24736i	−0.217529	+	0.376772i
$371$	13.0473	−	22.5987i	0.677384	−	1.17326i
$372$		0			0
$373$	6.14967			0.318418			0.159209	−	0.987245i	$-0.449106\pi$
$373$	6.14967			0.318418			0.159209	+	0.987245i	$0.449106\pi$
$374$	2.13711	−	3.70159i	0.110508	−	0.191405i
$375$		0			0
$376$	15.6546	−	27.1146i	0.807327	−	1.39833i
$377$	−2.53531	−	4.39129i	−0.130575	−	0.226163i
$378$		0			0
$379$	26.9469			1.38417			0.692084	−	0.721817i	$-0.256693\pi$
$379$	26.9469			1.38417			0.692084	+	0.721817i	$0.256693\pi$
$380$	4.94176	−	0.382846i	0.253507	−	0.0196396i
$381$		0			0
$382$	−3.83356	−	6.63993i	−0.196142	−	0.339728i
$383$	−10.9735	−	19.0067i	−0.560721	−	0.971197i	−0.997434	−	0.0715958i	$-0.977191\pi$
$383$	−10.9735	−	19.0067i	−0.560721	−	0.971197i	0.436713	−	0.899601i	$-0.356143\pi$
$384$		0			0
$385$	2.59696	+	4.49807i	0.132354	+	0.229243i
$386$	1.52452	−	2.64055i	0.0775960	−	0.134400i
$387$		0			0
$388$	0.708909			0.0359894
$389$	−3.56161	+	6.16889i	−0.180581	+	0.312775i	−0.942079	−	0.335392i	$-0.891131\pi$
$389$	−3.56161	+	6.16889i	−0.180581	+	0.312775i	0.761498	+	0.648168i	$0.224464\pi$
$390$		0			0
$391$	−27.3469			−1.38299
$392$	18.7014			0.944565
$393$		0			0
$394$	6.43926	+	11.1531i	0.324405	+	0.561886i
$395$	6.25028	−	10.8258i	0.314486	−	0.544705i
$396$		0			0
$397$	15.4994	+	26.8457i	0.777891	+	1.34735i	0.933155	+	0.359474i	$0.117044\pi$
$397$	15.4994	+	26.8457i	0.777891	+	1.34735i	−0.155264	+	0.987873i	$0.549623\pi$
$398$	−13.0573			−0.654502
$399$		0			0
$400$	−0.432745			−0.0216373
$401$	−16.4801	−	28.5444i	−0.822978	−	1.42544i	−0.903455	−	0.428684i	$-0.858977\pi$
$401$	−16.4801	−	28.5444i	−0.822978	−	1.42544i	0.0804761	−	0.996757i	$-0.474356\pi$
$402$		0			0
$403$	6.71420	−	11.6293i	0.334458	−	0.579299i
$404$	6.94266	+	12.0250i	0.345410	+	0.598268i
$405$		0			0
$406$	−6.24155			−0.309763
$407$	−12.7741			−0.633191
$408$		0			0
$409$	−0.452483	+	0.783723i	−0.0223738	+	0.0387526i	−0.876996	−	0.480499i	$-0.840456\pi$
$409$	−0.452483	+	0.783723i	−0.0223738	+	0.0387526i	0.854622	+	0.519251i	$0.173789\pi$
$410$	−3.38308			−0.167078
$411$		0			0
$412$	7.24541	−	12.5494i	0.356956	−	0.618266i
$413$	−9.71525	−	16.8273i	−0.478056	−	0.828017i
$414$		0			0
$415$	−3.23429	−	5.60195i	−0.158765	−	0.274989i
$416$	−7.49983	−	12.9901i	−0.367710	−	0.636892i
$417$		0			0
$418$	−3.24614	−	4.73556i	−0.158774	−	0.231624i
$419$	8.99889			0.439625			0.219812	−	0.975542i	$-0.429456\pi$
$419$	8.99889			0.439625			0.219812	+	0.975542i	$0.429456\pi$
$420$		0			0
$421$	18.6169	+	32.2454i	0.907331	+	1.57154i	0.817758	+	0.575563i	$0.195217\pi$
$421$	18.6169	+	32.2454i	0.907331	+	1.57154i	0.0895733	+	0.995980i	$0.471450\pi$
$422$	−2.52905	+	4.38044i	−0.123112	+	0.213236i
$423$		0			0
$424$	−10.3799	+	17.9785i	−0.504092	+	0.873113i
$425$	3.24505			0.157408
$426$		0			0
$427$	−6.02192	+	10.4303i	−0.291421	+	0.504756i
$428$	9.31459	−	16.1333i	0.450238	−	0.779835i
$429$		0			0
$430$	−8.20975			−0.395909
$431$	−7.09976	+	12.2971i	−0.341983	+	0.592332i	−0.984801	−	0.173687i	$-0.944432\pi$
$431$	−7.09976	+	12.2971i	−0.341983	+	0.592332i	0.642818	+	0.766019i	$0.277765\pi$
$432$		0			0
$433$	−15.9712	+	27.6630i	−0.767528	+	1.32940i	0.171371	+	0.985207i	$0.445180\pi$
$433$	−15.9712	+	27.6630i	−0.767528	+	1.32940i	−0.938899	+	0.344192i	$0.888153\pi$
$434$	−8.26467	−	14.3148i	−0.396717	−	0.687134i
$435$		0			0
$436$	6.18650			0.296280
$437$	−15.8548	+	33.1359i	−0.758436	+	1.58510i
$438$		0			0
$439$	−1.17614	−	2.03713i	−0.0561340	−	0.0972270i	0.836593	−	0.547825i	$-0.184544\pi$
$439$	−1.17614	−	2.03713i	−0.0561340	−	0.0972270i	−0.892727	+	0.450598i	$0.851211\pi$
$440$	−2.06603	−	3.57847i	−0.0984941	−	0.170597i
$441$		0			0
$442$	−4.16629	−	7.21623i	−0.198170	−	0.343241i
$443$	19.0498	−	32.9952i	0.905082	−	1.56765i	0.0842740	−	0.996443i	$-0.473143\pi$
$443$	19.0498	−	32.9952i	0.905082	−	1.56765i	0.820808	−	0.571205i	$-0.193524\pi$
$444$		0			0
$445$	−10.5423			−0.499755
$446$	5.11886	−	8.86613i	0.242385	−	0.419824i
$447$		0			0
$448$	−21.6337			−1.02210
$449$	37.3376			1.76207			0.881034	−	0.473053i	$-0.156848\pi$
$449$	37.3376			1.76207			0.881034	+	0.473053i	$0.156848\pi$
$450$		0			0
$451$	−2.58205	−	4.47225i	−0.121584	−	0.210590i
$452$	−5.38409	+	9.32552i	−0.253246	+	0.438636i
$453$		0			0
$454$	−4.73471	−	8.20076i	−0.222211	−	0.384881i
$455$	10.1255			0.474692
$456$		0			0
$457$	1.83835			0.0859946			0.0429973	−	0.999075i	$-0.486309\pi$
$457$	1.83835			0.0859946			0.0429973	+	0.999075i	$0.486309\pi$
$458$	−2.57175	−	4.45439i	−0.120170	−	0.208140i
$459$		0			0
$460$	−4.79138	+	8.29892i	−0.223399	+	0.386939i
$461$	−1.53672	−	2.66167i	−0.0715720	−	0.123966i	0.828018	−	0.560701i	$-0.189468\pi$
$461$	−1.53672	−	2.66167i	−0.0715720	−	0.123966i	−0.899590	+	0.436735i	$0.856135\pi$
$462$		0			0
$463$	19.8824			0.924013			0.462007	−	0.886876i	$-0.347130\pi$
$463$	19.8824			0.924013			0.462007	+	0.886876i	$0.347130\pi$
$464$	0.793802			0.0368513
$465$		0			0
$466$	−4.42393	+	7.66247i	−0.204934	+	0.354957i
$467$	23.0483			1.06655			0.533273	−	0.845943i	$-0.320962\pi$
$467$	23.0483			1.06655			0.533273	+	0.845943i	$0.320962\pi$
$468$		0			0
$469$	23.1700	−	40.1317i	1.06989	−	1.85311i
$470$	−4.99014	−	8.64318i	−0.230178	−	0.398680i
$471$		0			0
$472$	7.72902	+	13.3871i	0.355757	+	0.616190i
$473$	−6.26589	−	10.8528i	−0.288106	−	0.499014i
$474$		0			0
$475$	1.88136	−	3.93198i	0.0863229	−	0.180412i
$476$	13.5164			0.619524
$477$		0			0
$478$	−5.09889	−	8.83154i	−0.233218	−	0.403945i
$479$	15.2877	−	26.4791i	0.698515	−	1.20986i	−0.270467	−	0.962729i	$-0.587178\pi$
$479$	15.2877	−	26.4791i	0.698515	−	1.20986i	0.968981	−	0.247134i	$-0.0794886\pi$
$480$		0			0
$481$	−12.4516	+	21.5667i	−0.567742	+	0.983359i
$482$	−6.28784			−0.286403
$483$		0			0
$484$	−5.11100	+	8.85251i	−0.232318	+	0.402387i
$485$	0.311714	−	0.539905i	0.0141542	−	0.0245158i
$486$		0			0
$487$	35.0987			1.59047			0.795237	−	0.606299i	$-0.207347\pi$
$487$	35.0987			1.59047			0.795237	+	0.606299i	$0.207347\pi$
$488$	4.79077	−	8.29786i	0.216868	−	0.375627i
$489$		0			0
$490$	2.98067	−	5.16268i	0.134653	−	0.233226i
$491$	−12.7839	−	22.1424i	−0.576930	−	0.999272i	−0.995829	−	0.0912390i	$-0.970917\pi$
$491$	−12.7839	−	22.1424i	−0.576930	−	0.999272i	0.418899	−	0.908033i	$-0.362416\pi$
$492$		0			0
$493$	−5.95252			−0.268088
$494$	−11.1593	+	0.864527i	−0.502080	+	0.0388969i
$495$		0			0
$496$	1.05110	+	1.82056i	0.0471959	+	0.0817457i
$497$	−26.6889	−	46.2265i	−1.19716	−	2.07354i
$498$		0			0
$499$	19.2357	+	33.3171i	0.861106	+	1.49148i	0.870862	+	0.491527i	$0.163561\pi$
$499$	19.2357	+	33.3171i	0.861106	+	1.49148i	−0.00975600	+	0.999952i	$0.503105\pi$
$500$	0.568557	−	0.984769i	0.0254266	−	0.0440402i
$501$		0			0
$502$	17.8933			0.798618
$503$	−19.0094	+	32.9252i	−0.847587	+	1.46806i	0.0357690	+	0.999360i	$0.488612\pi$
$503$	−19.0094	+	32.9252i	−0.847587	+	1.46806i	−0.883356	+	0.468703i	$0.844721\pi$
$504$		0			0
$505$	12.2110			0.543384
$506$	11.1000			0.493456
$507$		0			0
$508$	−0.194560	−	0.336988i	−0.00863220	−	0.0149514i
$509$	6.63084	−	11.4850i	0.293907	−	0.509062i	−0.680823	−	0.732448i	$-0.738378\pi$
$509$	6.63084	−	11.4850i	0.293907	−	0.509062i	0.974730	+	0.223386i	$0.0717111\pi$
$510$		0			0
$511$	3.53183	+	6.11732i	0.156239	+	0.270614i
$512$	4.87032			0.215240
$513$		0			0
$514$	9.27066			0.408911
$515$	−6.37176	−	11.0362i	−0.280773	−	0.486313i
$516$		0			0
$517$	7.61721	−	13.1934i	0.335005	−	0.580245i
$518$	15.3269	+	26.5470i	0.673427	+	1.16641i
$519$		0			0
$520$	−8.05543			−0.353254
$521$	37.1676			1.62834			0.814171	−	0.580625i	$-0.197192\pi$
$521$	37.1676			1.62834			0.814171	+	0.580625i	$0.197192\pi$
$522$		0			0
$523$	−12.9538	+	22.4367i	−0.566431	+	0.981087i	0.430484	+	0.902598i	$0.358343\pi$
$523$	−12.9538	+	22.4367i	−0.566431	+	0.981087i	−0.996915	+	0.0784886i	$0.974991\pi$
$524$	−1.40753			−0.0614883
$525$		0			0
$526$	1.61289	−	2.79362i	0.0703256	−	0.121807i
$527$	−7.88195	−	13.6519i	−0.343343	−	0.594688i
$528$		0			0
$529$	−24.0095	−	41.5856i	−1.04389	−	1.80807i
$530$	3.30874	+	5.73090i	0.143722	+	0.248935i
$531$		0			0
$532$	7.83633	−	16.3776i	0.339748	−	0.710061i
$533$	−10.0674			−0.436068
$534$		0			0
$535$	−8.19143	−	14.1880i	−0.354147	−	0.613400i
$536$	−18.4331	+	31.9270i	−0.796187	+	1.37904i
$537$		0			0
$538$	10.7517	−	18.6225i	0.463540	−	0.802875i
$539$	9.09970			0.391952
$540$		0			0
$541$	1.08156	−	1.87332i	0.0465000	−	0.0805403i	−0.841839	−	0.539729i	$-0.818527\pi$
$541$	1.08156	−	1.87332i	0.0465000	−	0.0805403i	0.888339	+	0.459189i	$0.151860\pi$
$542$	10.1161	−	17.5216i	0.434523	−	0.752616i
$543$		0			0
$544$	−17.6084			−0.754956
$545$	2.72026	−	4.71164i	0.116523	−	0.201824i
$546$		0			0
$547$	2.95615	−	5.12020i	0.126396	−	0.218924i	−0.795882	−	0.605452i	$-0.792992\pi$
$547$	2.95615	−	5.12020i	0.126396	−	0.218924i	0.922278	+	0.386528i	$0.126326\pi$
$548$	3.26512	+	5.65536i	0.139479	+	0.241585i
$549$		0			0
$550$	−1.31715			−0.0561636
$551$	−3.45106	+	7.21259i	−0.147020	+	0.307267i
$552$		0			0
$553$	−22.8947	−	39.6548i	−0.973583	−	1.68630i
$554$	−9.63330	−	16.6854i	−0.409280	−	0.708893i
$555$		0			0
$556$	−11.7953	−	20.4301i	−0.500234	−	0.866430i
$557$	−1.03098	+	1.78570i	−0.0436839	+	0.0756627i	−0.887041	−	0.461691i	$-0.847243\pi$
$557$	−1.03098	+	1.78570i	−0.0436839	+	0.0756627i	0.843357	+	0.537354i	$0.180576\pi$
$558$		0			0
$559$	−24.4306			−1.03331
$560$	−0.792572	+	1.37277i	−0.0334923	+	0.0580103i
$561$		0			0
$562$	23.7724			1.00278
$563$	−2.26488			−0.0954533			−0.0477267	−	0.998860i	$-0.515198\pi$
$563$	−2.26488			−0.0954533			−0.0477267	+	0.998860i	$0.515198\pi$
$564$		0			0
$565$	4.73488	+	8.20105i	0.199198	+	0.345021i
$566$	−6.54883	+	11.3429i	−0.275268	+	0.476778i
$567$		0			0
$568$	21.2325	+	36.7758i	0.890896	+	1.54308i
$569$	−23.5361			−0.986687			−0.493343	−	0.869835i	$-0.664225\pi$
$569$	−23.5361			−0.986687			−0.493343	+	0.869835i	$0.664225\pi$
$570$		0			0
$571$	−22.3091			−0.933607			−0.466803	−	0.884361i	$-0.654594\pi$
$571$	−22.3091			−0.933607			−0.466803	+	0.884361i	$0.654594\pi$
$572$	−2.22851	−	3.85990i	−0.0931788	−	0.161390i
$573$		0			0
$574$	−6.19610	+	10.7320i	−0.258620	+	0.447944i
$575$	4.21364	+	7.29823i	0.175721	+	0.304357i
$576$		0			0
$577$	16.4111			0.683203			0.341601	−	0.939845i	$-0.389031\pi$
$577$	16.4111			0.683203			0.341601	+	0.939845i	$0.389031\pi$
$578$	6.00978			0.249974
$579$		0			0
$580$	−1.04293	+	1.80640i	−0.0433052	+	0.0750067i
$581$	−23.6944			−0.983007
$582$		0			0
$583$	−5.05063	+	8.74795i	−0.209176	+	0.362303i
$584$	−2.80977	−	4.86667i	−0.116269	−	0.201384i
$585$		0			0
$586$	0.996536	+	1.72605i	0.0411665	+	0.0713025i
$587$	13.6467	+	23.6368i	0.563261	+	0.975596i	0.997209	+	0.0746585i	$0.0237867\pi$
$587$	13.6467	+	23.6368i	0.563261	+	0.975596i	−0.433948	+	0.900938i	$0.642880\pi$
$588$		0			0
$589$	−21.1115	+	1.63554i	−0.869886	+	0.0673915i
$590$	4.92748			0.202861
$591$		0			0
$592$	−1.94928	−	3.37625i	−0.0801149	−	0.138763i
$593$	15.1560	−	26.2510i	0.622383	−	1.07800i	−0.366657	−	0.930356i	$-0.619498\pi$
$593$	15.1560	−	26.2510i	0.622383	−	1.07800i	0.989041	−	0.147644i	$-0.0471689\pi$
$594$		0			0
$595$	5.94330	−	10.2941i	0.243651	−	0.422017i
$596$	24.3272			0.996480
$597$		0			0
$598$	10.8197	−	18.7403i	0.442451	−	0.766347i
$599$	−0.449215	+	0.778062i	−0.0183544	+	0.0317908i	−0.875057	−	0.484020i	$-0.839176\pi$
$599$	−0.449215	+	0.778062i	−0.0183544	+	0.0317908i	0.856702	+	0.515811i	$0.172509\pi$
$600$		0			0
$601$	−0.853573			−0.0348180			−0.0174090	−	0.999848i	$-0.505542\pi$
$601$	−0.853573			−0.0348180			−0.0174090	+	0.999848i	$0.505542\pi$
$602$	−15.0361	+	26.0433i	−0.612827	+	1.06145i
$603$		0			0
$604$	−0.767726	+	1.32974i	−0.0312383	+	0.0541064i
$605$	4.49471	+	7.78507i	0.182736	+	0.316508i
$606$		0			0
$607$	2.19123			0.0889392			0.0444696	−	0.999011i	$-0.485840\pi$
$607$	2.19123			0.0889392			0.0444696	+	0.999011i	$0.485840\pi$
$608$	−10.2087	+	21.3359i	−0.414019	+	0.865286i
$609$		0			0
$610$	−1.52713	−	2.64506i	−0.0618316	−	0.107095i
$611$	−14.8497	−	25.7205i	−0.600755	−	1.04054i
$612$		0			0
$613$	−13.8771	−	24.0359i	−0.560492	−	0.970800i	−0.997453	−	0.0713203i	$-0.977279\pi$
$613$	−13.8771	−	24.0359i	−0.560492	−	0.970800i	0.436962	−	0.899480i	$-0.356055\pi$
$614$	5.73376	−	9.93116i	0.231396	−	0.400789i
$615$		0			0
$616$	−15.1357			−0.609835
$617$	−6.78871	+	11.7584i	−0.273303	+	0.473375i	−0.969706	−	0.244277i	$-0.921450\pi$
$617$	−6.78871	+	11.7584i	−0.273303	+	0.473375i	0.696403	+	0.717651i	$0.254783\pi$
$618$		0			0
$619$	2.70380			0.108675			0.0543375	−	0.998523i	$-0.482695\pi$
$619$	2.70380			0.108675			0.0543375	+	0.998523i	$0.482695\pi$
$620$	−5.52391			−0.221846
$621$		0			0
$622$	14.5113	+	25.1342i	0.581848	+	1.00779i
$623$	−19.3083	+	33.4429i	−0.773570	+	1.33986i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	31.0597			1.24139
$627$		0			0
$628$	−13.9731			−0.557589
$629$	14.6172	+	25.3177i	0.582825	+	1.00948i
$630$		0			0
$631$	−3.22888	+	5.59259i	−0.128540	+	0.222638i	−0.923111	−	0.384533i	$-0.874362\pi$
$631$	−3.22888	+	5.59259i	−0.128540	+	0.222638i	0.794571	+	0.607171i	$0.207696\pi$
$632$	18.2140	+	31.5476i	0.724516	+	1.25490i
$633$		0			0
$634$	−5.67442			−0.225360
$635$	−0.342200			−0.0135798
$636$		0			0
$637$	8.86992	−	15.3631i	0.351439	−	0.608710i
$638$	2.41611			0.0956546
$639$		0			0
$640$	−2.68315	+	4.64735i	−0.106061	+	0.183703i
$641$	−12.2784	−	21.2668i	−0.484968	−	0.839989i	0.514883	−	0.857261i	$-0.327835\pi$
$641$	−12.2784	−	21.2668i	−0.484968	−	0.839989i	−0.999851	+	0.0172712i	$0.994502\pi$
$642$		0			0
$643$	−10.7699	−	18.6540i	−0.424722	−	0.735641i	0.571672	−	0.820482i	$-0.306295\pi$
$643$	−10.7699	−	18.6540i	−0.424722	−	0.735641i	−0.996394	+	0.0848414i	$0.972962\pi$
$644$	17.5508	+	30.3989i	0.691599	+	1.19788i
$645$		0			0
$646$	−5.67114	+	11.8525i	−0.223128	+	0.466330i
$647$	−17.5491			−0.689926			−0.344963	−	0.938616i	$-0.612109\pi$
$647$	−17.5491			−0.689926			−0.344963	+	0.938616i	$0.612109\pi$
$648$		0			0
$649$	3.76077	+	6.51385i	0.147623	+	0.255691i
$650$	−1.28389	+	2.22377i	−0.0503584	+	0.0872233i
$651$		0			0
$652$	0.828518	−	1.43504i	0.0324473	−	0.0562003i
$653$	−13.6647			−0.534740			−0.267370	−	0.963594i	$-0.586155\pi$
$653$	−13.6647			−0.534740			−0.267370	+	0.963594i	$0.586155\pi$
$654$		0			0
$655$	−0.618905	+	1.07198i	−0.0241826	+	0.0418856i
$656$	0.788021	−	1.36489i	0.0307671	−	0.0532901i
$657$		0			0
$658$	−36.5577			−1.42517
$659$	−2.56623	+	4.44485i	−0.0999662	+	0.173147i	−0.911670	−	0.410922i	$-0.865207\pi$
$659$	−2.56623	+	4.44485i	−0.0999662	+	0.173147i	0.811704	+	0.584069i	$0.198540\pi$
$660$		0			0
$661$	−12.5958	+	21.8166i	−0.489921	+	0.848569i	−0.999933	−	0.0115990i	$-0.996308\pi$
$661$	−12.5958	+	21.8166i	−0.489921	+	0.848569i	0.510011	+	0.860168i	$0.329641\pi$
$662$	−1.57489	−	2.72779i	−0.0612099	−	0.106019i
$663$		0			0
$664$	18.8502			0.731529
$665$	−9.02750	−	13.1696i	−0.350071	−	0.510694i
$666$		0			0
$667$	−7.72924	−	13.3874i	−0.299277	−	0.518364i
$668$	9.19676	+	15.9293i	0.355833	+	0.616322i
$669$		0			0
$670$	5.87580	+	10.1772i	0.227002	+	0.393179i
$671$	2.33109	−	4.03756i	0.0899905	−	0.155868i
$672$		0			0
$673$	17.1038			0.659304			0.329652	−	0.944103i	$-0.393069\pi$
$673$	17.1038			0.659304			0.329652	+	0.944103i	$0.393069\pi$
$674$	−1.00783	+	1.74562i	−0.0388203	+	0.0672387i
$675$		0			0
$676$	6.09352			0.234366
$677$	−0.430567			−0.0165480			−0.00827401	−	0.999966i	$-0.502634\pi$
$677$	−0.430567			−0.0165480			−0.00827401	+	0.999966i	$0.502634\pi$
$678$		0			0
$679$	−1.14181	−	1.97767i	−0.0438185	−	0.0758959i
$680$	−4.72823	+	8.18953i	−0.181319	+	0.314054i
$681$		0			0
$682$	3.19926	+	5.54128i	0.122506	+	0.212186i
$683$	27.9032			1.06769			0.533843	−	0.845584i	$-0.320747\pi$
$683$	27.9032			1.06769			0.533843	+	0.845584i	$0.320747\pi$
$684$		0			0
$685$	5.74283			0.219422
$686$	0.990967	+	1.71641i	0.0378353	+	0.0655327i
$687$		0			0
$688$	1.91230	−	3.31220i	0.0729056	−	0.126276i
$689$	9.84618	+	17.0541i	0.375109	+	0.649709i
$690$		0			0
$691$	10.4084			0.395954			0.197977	−	0.980207i	$-0.436563\pi$
$691$	10.4084			0.395954			0.197977	+	0.980207i	$0.436563\pi$
$692$	4.15525			0.157959
$693$		0			0
$694$	−1.28069	+	2.21821i	−0.0486141	+	0.0842022i
$695$	−20.7461			−0.786944
$696$		0			0
$697$	−5.90917	+	10.2350i	−0.223826	+	0.387678i
$698$	−9.63619	−	16.6904i	−0.364735	−	0.631740i
$699$		0			0
$700$	−2.08262	−	3.60720i	−0.0787157	−	0.136340i
$701$	−10.8642	−	18.8173i	−0.410335	−	0.710721i	0.584591	−	0.811328i	$-0.301255\pi$
$701$	−10.8642	−	18.8173i	−0.410335	−	0.710721i	−0.994926	+	0.100607i	$0.967921\pi$
$702$		0			0
$703$	39.1516	−	3.03314i	1.47663	−	0.114397i
$704$	8.37442			0.315623
$705$		0			0
$706$	−4.91593	−	8.51464i	−0.185013	−	0.320453i
$707$	22.3645	−	38.7364i	0.841102	−	1.45683i
$708$		0			0
$709$	−12.0501	+	20.8713i	−0.452550	+	0.783840i	−0.998544	−	0.0539495i	$-0.982819\pi$
$709$	−12.0501	+	20.8713i	−0.452550	+	0.783840i	0.545993	+	0.837789i	$0.316152\pi$
$710$	13.5363			0.508009
$711$		0			0
$712$	15.3608	−	26.6057i	0.575671	−	0.997092i
$713$	20.4691	−	35.4536i	0.766575	−	1.32775i
$714$		0			0
$715$	−3.91960			−0.146585
$716$	5.21331	−	9.02972i	0.194831	−	0.337456i
$717$		0			0
$718$	−16.4330	+	28.4627i	−0.613273	+	1.06222i
$719$	3.05117	+	5.28479i	0.113790	+	0.197089i	0.917295	−	0.398208i	$-0.130368\pi$
$719$	3.05117	+	5.28479i	0.113790	+	0.197089i	−0.803506	+	0.595297i	$0.797034\pi$
$720$		0			0
$721$	−46.6794			−1.73843
$722$	11.0736	+	13.7433i	0.412115	+	0.511472i
$723$		0			0
$724$	−4.33776	−	7.51322i	−0.161212	−	0.279227i
$725$	0.917170	+	1.58858i	0.0340628	+	0.0589986i
$726$		0			0
$727$	−5.35126	−	9.26866i	−0.198467	−	0.343756i	0.749564	−	0.661932i	$-0.230263\pi$
$727$	−5.35126	−	9.26866i	−0.198467	−	0.343756i	−0.948032	+	0.318176i	$0.896930\pi$
$728$	−14.7535	+	25.5538i	−0.546801	+	0.947087i
$729$		0			0
$730$	−1.79131			−0.0662994
$731$	−14.3398	+	24.8373i	−0.530378	+	0.918642i
$732$		0			0
$733$	−12.7580			−0.471226			−0.235613	−	0.971847i	$-0.575710\pi$
$733$	−12.7580			−0.471226			−0.235613	+	0.971847i	$0.575710\pi$
$734$	−22.8516			−0.843469
$735$		0			0
$736$	−22.8642	−	39.6020i	−0.842787	−	1.45975i
$737$	−8.96913	+	15.5350i	−0.330382	+	0.572238i
$738$		0			0
$739$	−6.64437	−	11.5084i	−0.244417	−	0.423343i	0.717551	−	0.696506i	$-0.245263\pi$
$739$	−6.64437	−	11.5084i	−0.244417	−	0.423343i	−0.961968	+	0.273164i	$0.911930\pi$
$740$	10.2442			0.376583
$741$		0			0
$742$	24.2398			0.889871
$743$	−18.1671	−	31.4663i	−0.666486	−	1.15439i	−0.978880	−	0.204436i	$-0.934464\pi$
$743$	−18.1671	−	31.4663i	−0.666486	−	1.15439i	0.312394	−	0.949953i	$-0.398869\pi$
$744$		0			0
$745$	10.6969	−	18.5276i	0.391904	−	0.678798i
$746$	2.85627	+	4.94720i	0.104575	+	0.181130i
$747$		0			0
$748$	−5.23220			−0.191308
$749$	−60.0103			−2.19273
$750$		0			0
$751$	3.79143	−	6.56696i	0.138351	−	0.239632i	−0.788521	−	0.615007i	$-0.789153\pi$
$751$	3.79143	−	6.56696i	0.138351	−	0.239632i	0.926873	+	0.375376i	$0.122486\pi$
$752$	4.64942			0.169547
$753$		0			0
$754$	2.35509	−	4.07914i	0.0857675	−	0.148554i
$755$	0.675153	+	1.16940i	0.0245713	+	0.0425588i
$756$		0			0
$757$	9.24433	+	16.0116i	0.335991	+	0.581953i	0.983675	−	0.179956i	$-0.0575956\pi$
$757$	9.24433	+	16.0116i	0.335991	+	0.581953i	−0.647684	+	0.761909i	$0.724262\pi$
$758$	12.5157	+	21.6778i	0.454591	+	0.787374i
$759$		0			0
$760$	7.18188	+	10.4771i	0.260514	+	0.380045i
$761$	6.84628			0.248177			0.124089	−	0.992271i	$-0.460399\pi$
$761$	6.84628			0.248177			0.124089	+	0.992271i	$0.460399\pi$
$762$		0			0
$763$	−9.96431	−	17.2587i	−0.360732	−	0.624807i
$764$	−4.69278	+	8.12813i	−0.169779	+	0.294065i
$765$		0			0
$766$	10.1935	−	17.6556i	0.368306	−	0.637924i
$767$	14.6632			0.529458
$768$		0			0
$769$	−10.0541	+	17.4141i	−0.362558	+	0.627970i	−0.988381	−	0.151996i	$-0.951430\pi$
$769$	−10.0541	+	17.4141i	−0.362558	+	0.627970i	0.625823	+	0.779965i	$0.284763\pi$
$770$	−2.41236	+	4.17834i	−0.0869355	+	0.150577i
$771$		0			0
$772$	−3.73242			−0.134333
$773$	−27.0407	+	46.8359i	−0.972587	+	1.68457i	−0.284910	+	0.958554i	$0.591964\pi$
$773$	−27.0407	+	46.8359i	−0.972587	+	1.68457i	−0.687677	+	0.726017i	$0.741369\pi$
$774$		0			0
$775$	−2.42892	+	4.20701i	−0.0872493	+	0.151120i
$776$	0.908372	+	1.57335i	0.0326086	+	0.0564798i
$777$		0			0
$778$	−6.61688			−0.237227
$779$	8.97567	+	13.0939i	0.321587	+	0.469139i
$780$		0			0
$781$	10.3313	+	17.8943i	0.369682	+	0.640308i
$782$	−12.7015	−	21.9996i	−0.454205	−	0.786706i
$783$		0			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)

\(f(q)\)	\(=\)	\(q+(0.464458 + 0.804466i) q^{2} +(0.568557 - 0.984769i) q^{4} +(-0.500000 - 0.866025i) q^{5} -3.66299 q^{7} +2.91412 q^{8} +O(q^{10})\)	\(q+(0.464458 + 0.804466i) q^{2} +(0.568557 - 0.984769i) q^{4} +(-0.500000 - 0.866025i) q^{5} -3.66299 q^{7} +2.91412 q^{8} +(0.464458 - 0.804466i) q^{10} +1.41795 q^{11} +(1.38214 - 2.39394i) q^{13} +(-1.70131 - 2.94675i) q^{14} +(0.216373 + 0.374768i) q^{16} +(-1.62252 - 2.81029i) q^{17} +(-4.34588 + 0.336682i) q^{19} -1.13711 q^{20} +(0.658577 + 1.14069i) q^{22} +(4.21364 - 7.29823i) q^{23} +(-0.500000 + 0.866025i) q^{25} +2.56778 q^{26} +(-2.08262 + 3.60720i) q^{28} +(0.917170 - 1.58858i) q^{29} +4.85783 q^{31} +(2.71313 - 4.69927i) q^{32} +(1.50719 - 2.61053i) q^{34} +(1.83150 + 3.17225i) q^{35} -9.00891 q^{37} +(-2.28933 - 3.33973i) q^{38} +(-1.45706 - 2.52370i) q^{40} +(-1.82098 - 3.15403i) q^{41} +(-4.41899 - 7.65392i) q^{43} +(0.806183 - 1.39635i) q^{44} +7.82823 q^{46} +(5.37200 - 9.30458i) q^{47} +6.41753 q^{49} -0.928917 q^{50} +(-1.57165 - 2.72218i) q^{52} +(-3.56193 + 6.16945i) q^{53} +(-0.708973 - 1.22798i) q^{55} -10.6744 q^{56} +1.70395 q^{58} +(2.65227 + 4.59387i) q^{59} +(1.64399 - 2.84747i) q^{61} +(2.25626 + 3.90796i) q^{62} +5.90603 q^{64} -2.76428 q^{65} +(-6.32544 + 10.9560i) q^{67} -3.68999 q^{68} +(-1.70131 + 2.94675i) q^{70} +(7.28608 + 12.6199i) q^{71} +(-0.964193 - 1.67003i) q^{73} +(-4.18426 - 7.24736i) q^{74} +(-2.13932 + 4.47111i) q^{76} -5.19393 q^{77} +(6.25028 + 10.8258i) q^{79} +(0.216373 - 0.374768i) q^{80} +(1.69154 - 2.92983i) q^{82} +6.46857 q^{83} +(-1.62252 + 2.81029i) q^{85} +(4.10487 - 7.10985i) q^{86} +4.13206 q^{88} +(5.27117 - 9.12994i) q^{89} +(-5.06277 + 8.76897i) q^{91} +(-4.79138 - 8.29892i) q^{92} +9.98029 q^{94} +(2.46451 + 3.59530i) q^{95} +(0.311714 + 0.539905i) q^{97} +(2.98067 + 5.16268i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 5 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 - 5 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8	\( 12 q - 3 q^{2} - 5 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} - 3 q^{10} - 8 q^{13} - 10 q^{14} - 3 q^{16} - 4 q^{17} - 6 q^{19} + 10 q^{20} + 2 q^{23} - 6 q^{25} + 40 q^{26} - 26 q^{28} - 4 q^{29} + 24 q^{31} - 15 q^{32} + 7 q^{34} - 2 q^{35} + 29 q^{38} - 6 q^{40} - 12 q^{41} - 4 q^{43} - 6 q^{44} + 48 q^{46} - 6 q^{47} + 32 q^{49} + 6 q^{50} - 20 q^{52} - 26 q^{53} + 44 q^{56} - 20 q^{58} - 16 q^{59} + 20 q^{61} + 25 q^{62} + 28 q^{64} + 16 q^{65} - 12 q^{67} - 54 q^{68} - 10 q^{70} + 8 q^{71} - 4 q^{73} + 16 q^{74} - 66 q^{76} - 48 q^{77} - 12 q^{79} - 3 q^{80} + 26 q^{82} + 44 q^{83} - 4 q^{85} + 44 q^{86} - 32 q^{88} + 8 q^{89} + 2 q^{91} - 36 q^{92} - 14 q^{94} + 6 q^{95} + 30 q^{97} - 49 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 5 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 - 3 * q^10 - 8 * q^13 - 10 * q^14 - 3 * q^16 - 4 * q^17 - 6 * q^19 + 10 * q^20 + 2 * q^23 - 6 * q^25 + 40 * q^26 - 26 * q^28 - 4 * q^29 + 24 * q^31 - 15 * q^32 + 7 * q^34 - 2 * q^35 + 29 * q^38 - 6 * q^40 - 12 * q^41 - 4 * q^43 - 6 * q^44 + 48 * q^46 - 6 * q^47 + 32 * q^49 + 6 * q^50 - 20 * q^52 - 26 * q^53 + 44 * q^56 - 20 * q^58 - 16 * q^59 + 20 * q^61 + 25 * q^62 + 28 * q^64 + 16 * q^65 - 12 * q^67 - 54 * q^68 - 10 * q^70 + 8 * q^71 - 4 * q^73 + 16 * q^74 - 66 * q^76 - 48 * q^77 - 12 * q^79 - 3 * q^80 + 26 * q^82 + 44 * q^83 - 4 * q^85 + 44 * q^86 - 32 * q^88 + 8 * q^89 + 2 * q^91 - 36 * q^92 - 14 * q^94 + 6 * q^95 + 30 * q^97 - 49 * q^98

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