LMFDB - Embedded newform 855.2.k.j.406.4

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			406.4
Root			$0.414953 + 0.718719i$ of defining polynomial
Character	$\chi$	$=$	855.406
Dual form			855.2.k.j.676.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0850473 - 0.147306i) q^{2} +(0.985534 - 1.70699i) q^{4} +(-0.500000 - 0.866025i) q^{5} -0.218469 q^{7} -0.675457 q^{8} +O(q^{10})$	\(q+(-0.0850473 - 0.147306i) q^{2} +(0.985534 - 1.70699i) q^{4} +(-0.500000 - 0.866025i) q^{5} -0.218469 q^{7} -0.675457 q^{8} +(-0.0850473 + 0.147306i) q^{10} -5.33261 q^{11} +(-3.01725 + 5.22603i) q^{13} +(0.0185802 + 0.0321818i) q^{14} +(-1.91362 - 3.31449i) q^{16} +(-3.27554 - 5.67340i) q^{17} +(1.50507 - 4.09082i) q^{19} -1.97107 q^{20} +(0.453524 + 0.785526i) q^{22} +(-1.90802 + 3.30478i) q^{23} +(-0.500000 + 0.866025i) q^{25} +1.02644 q^{26} +(-0.215309 + 0.372925i) q^{28} +(-0.525141 + 0.909571i) q^{29} +2.65981 q^{31} +(-1.00095 + 1.73370i) q^{32} +(-0.557151 + 0.965014i) q^{34} +(0.109234 + 0.189200i) q^{35} +3.10309 q^{37} +(-0.730604 + 0.126207i) q^{38} +(0.337729 + 0.584963i) q^{40} +(1.75010 + 3.03127i) q^{41} +(-1.39266 - 2.41216i) q^{43} +(-5.25546 + 9.10273i) q^{44} +0.649086 q^{46} +(-4.26432 + 7.38603i) q^{47} -6.95227 q^{49} +0.170095 q^{50} +(5.94720 + 10.3009i) q^{52} +(2.57461 - 4.45936i) q^{53} +(2.66630 + 4.61817i) q^{55} +0.147566 q^{56} +0.178647 q^{58} +(-5.95070 - 10.3069i) q^{59} +(2.25799 - 3.91096i) q^{61} +(-0.226210 - 0.391807i) q^{62} -7.31397 q^{64} +6.03450 q^{65} +(3.30165 - 5.71862i) q^{67} -12.9126 q^{68} +(0.0185802 - 0.0321818i) q^{70} +(-3.12329 - 5.40970i) q^{71} +(-3.31536 - 5.74237i) q^{73} +(-0.263909 - 0.457104i) q^{74} +(-5.49971 - 6.60078i) q^{76} +1.16501 q^{77} +(-1.80793 - 3.13143i) q^{79} +(-1.91362 + 3.31449i) q^{80} +(0.297683 - 0.515602i) q^{82} +8.39679 q^{83} +(-3.27554 + 5.67340i) q^{85} +(-0.236884 + 0.410296i) q^{86} +3.60195 q^{88} +(4.79182 - 8.29967i) q^{89} +(0.659175 - 1.14172i) q^{91} +(3.76083 + 6.51394i) q^{92} +1.45068 q^{94} +(-4.29528 + 0.741981i) q^{95} +(7.95622 + 13.7806i) q^{97} +(0.591272 + 1.02411i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.0850473	−	0.147306i	−0.0601375	−	0.104161i	0.834389	−	0.551176i	$-0.185821\pi$
$2$	−0.0850473	−	0.147306i	−0.0601375	−	0.104161i	−0.894527	+	0.447014i	$0.852487\pi$
$3$		0			0
$3$		0			0
$4$	0.985534	−	1.70699i	0.492767	−	0.853497i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−0.218469			−0.0825735			−0.0412867	−	0.999147i	$-0.513146\pi$
$7$	−0.218469			−0.0825735			−0.0412867	+	0.999147i	$0.513146\pi$
$8$	−0.675457			−0.238810
$9$		0			0
$10$	−0.0850473	+	0.147306i	−0.0268943	+	0.0465823i
$11$	−5.33261			−1.60784			−0.803921	−	0.594737i	$-0.797256\pi$
$11$	−5.33261			−1.60784			−0.803921	+	0.594737i	$0.797256\pi$
$12$		0			0
$13$	−3.01725	+	5.22603i	−0.836834	+	1.44944i	0.0556936	+	0.998448i	$0.482263\pi$
$13$	−3.01725	+	5.22603i	−0.836834	+	1.44944i	−0.892528	+	0.450992i	$0.851070\pi$
$14$	0.0185802	+	0.0321818i	0.00496576	+	0.00860095i
$15$		0			0
$16$	−1.91362	−	3.31449i	−0.478406	−	0.828623i
$17$	−3.27554	−	5.67340i	−0.794435	−	1.37600i	−0.923198	−	0.384326i	$-0.874434\pi$
$17$	−3.27554	−	5.67340i	−0.794435	−	1.37600i	0.128763	−	0.991675i	$-0.458899\pi$
$18$		0			0
$19$	1.50507	−	4.09082i	0.345286	−	0.938497i
$19$	1.50507	−	4.09082i	0.345286	−	0.938497i
$20$	−1.97107			−0.440744
$21$		0			0
$22$	0.453524	+	0.785526i	0.0966916	+	0.167475i
$23$	−1.90802	+	3.30478i	−0.397849	+	0.689094i	−0.993460	−	0.114178i	$-0.963576\pi$
$23$	−1.90802	+	3.30478i	−0.397849	+	0.689094i	0.595612	+	0.803273i	$0.296910\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.02644			0.201301
$27$		0			0
$28$	−0.215309	+	0.372925i	−0.0406895	+	0.0704763i
$29$	−0.525141	+	0.909571i	−0.0975162	+	0.168903i	−0.910656	−	0.413165i	$-0.864423\pi$
$29$	−0.525141	+	0.909571i	−0.0975162	+	0.168903i	0.813140	+	0.582068i	$0.197756\pi$
$30$		0			0
$31$	2.65981			0.477716			0.238858	−	0.971054i	$-0.423227\pi$
$31$	2.65981			0.477716			0.238858	+	0.971054i	$0.423227\pi$
$32$	−1.00095	+	1.73370i	−0.176945	+	0.306478i
$33$		0			0
$34$	−0.557151	+	0.965014i	−0.0955506	+	0.165499i
$35$	0.109234	+	0.189200i	0.0184640	+	0.0319806i
$36$		0			0
$37$	3.10309			0.510145			0.255072	−	0.966922i	$-0.417901\pi$
$37$	3.10309			0.510145			0.255072	+	0.966922i	$0.417901\pi$
$38$	−0.730604	+	0.126207i	−0.118520	+	0.0204735i
$39$		0			0
$40$	0.337729	+	0.584963i	0.0533996	+	0.0924908i
$41$	1.75010	+	3.03127i	0.273320	+	0.473404i	0.969710	−	0.244259i	$-0.0785449\pi$
$41$	1.75010	+	3.03127i	0.273320	+	0.473404i	−0.696390	+	0.717664i	$0.745212\pi$
$42$		0			0
$43$	−1.39266	−	2.41216i	−0.212379	−	0.367852i	0.740079	−	0.672519i	$-0.234788\pi$
$43$	−1.39266	−	2.41216i	−0.212379	−	0.367852i	−0.952459	+	0.304668i	$0.901455\pi$
$44$	−5.25546	+	9.10273i	−0.792291	+	1.37229i
$45$		0			0
$46$	0.649086			0.0957025
$47$	−4.26432	+	7.38603i	−0.622016	+	1.07736i	0.367094	+	0.930184i	$0.380353\pi$
$47$	−4.26432	+	7.38603i	−0.622016	+	1.07736i	−0.989110	+	0.147179i	$0.952981\pi$
$48$		0			0
$49$	−6.95227			−0.993182
$50$	0.170095			0.0240550
$51$		0			0
$52$	5.94720	+	10.3009i	0.824729	+	1.42847i
$53$	2.57461	−	4.45936i	0.353650	−	0.612540i	−0.633236	−	0.773959i	$-0.718274\pi$
$53$	2.57461	−	4.45936i	0.353650	−	0.612540i	0.986886	+	0.161419i	$0.0516070\pi$
$54$		0			0
$55$	2.66630	+	4.61817i	0.359524	+	0.622714i
$56$	0.147566			0.0197194
$57$		0			0
$58$	0.178647			0.0234575
$59$	−5.95070	−	10.3069i	−0.774715	−	1.34185i	−0.934954	−	0.354768i	$-0.884560\pi$
$59$	−5.95070	−	10.3069i	−0.774715	−	1.34185i	0.160239	−	0.987078i	$-0.448773\pi$
$60$		0			0
$61$	2.25799	−	3.91096i	0.289106	−	0.500747i	−0.684490	−	0.729022i	$-0.739975\pi$
$61$	2.25799	−	3.91096i	0.289106	−	0.500747i	0.973597	+	0.228275i	$0.0733085\pi$
$62$	−0.226210	−	0.391807i	−0.0287287	−	0.0497595i
$63$		0			0
$64$	−7.31397			−0.914247
$65$	6.03450			0.748487
$66$		0			0
$67$	3.30165	−	5.71862i	0.403360	−	0.698641i	−0.590769	−	0.806841i	$-0.701175\pi$
$67$	3.30165	−	5.71862i	0.403360	−	0.698641i	0.994129	+	0.108200i	$0.0345088\pi$
$68$	−12.9126			−1.56588
$69$		0			0
$70$	0.0185802	−	0.0321818i	0.00222076	−	0.00384646i
$71$	−3.12329	−	5.40970i	−0.370666	−	0.642013i	0.619002	−	0.785390i	$-0.287537\pi$
$71$	−3.12329	−	5.40970i	−0.370666	−	0.642013i	−0.989668	+	0.143376i	$0.954204\pi$
$72$		0			0
$73$	−3.31536	−	5.74237i	−0.388033	−	0.672093i	0.604152	−	0.796869i	$-0.293512\pi$
$73$	−3.31536	−	5.74237i	−0.388033	−	0.672093i	−0.992185	+	0.124776i	$0.960179\pi$
$74$	−0.263909	−	0.457104i	−0.0306788	−	0.0531373i
$75$		0			0
$76$	−5.49971	−	6.60078i	−0.630859	−	0.757161i
$77$	1.16501			0.132765
$78$		0			0
$79$	−1.80793	−	3.13143i	−0.203409	−	0.352314i	0.746216	−	0.665704i	$-0.231869\pi$
$79$	−1.80793	−	3.13143i	−0.203409	−	0.352314i	−0.949624	+	0.313390i	$0.898535\pi$
$80$	−1.91362	+	3.31449i	−0.213949	+	0.370571i
$81$		0			0
$82$	0.297683	−	0.515602i	0.0328736	−	0.0569387i
$83$	8.39679			0.921668			0.460834	−	0.887486i	$-0.347550\pi$
$83$	8.39679			0.921668			0.460834	+	0.887486i	$0.347550\pi$
$84$		0			0
$85$	−3.27554	+	5.67340i	−0.355282	+	0.615366i
$86$	−0.236884	+	0.410296i	−0.0255439	+	0.0442434i
$87$		0			0
$88$	3.60195			0.383969
$89$	4.79182	−	8.29967i	0.507932	−	0.879764i	−0.492026	−	0.870581i	$-0.663744\pi$
$89$	4.79182	−	8.29967i	0.507932	−	0.879764i	0.999958	−	0.00918326i	$-0.00292317\pi$
$90$		0			0
$91$	0.659175	−	1.14172i	0.0691003	−	0.119685i
$92$	3.76083	+	6.51394i	0.392093	+	0.679126i
$93$		0			0
$94$	1.45068			0.149626
$95$	−4.29528	+	0.741981i	−0.440687	+	0.0761256i
$96$		0			0
$97$	7.95622	+	13.7806i	0.807832	+	1.39921i	0.914362	+	0.404897i	$0.132693\pi$
$97$	7.95622	+	13.7806i	0.807832	+	1.39921i	−0.106530	+	0.994309i	$0.533974\pi$
$98$	0.591272	+	1.02411i	0.0597275	+	0.103451i
$99$		0			0
$100$	0.985534	+	1.70699i	0.0985534	+	0.170699i
$101$	−2.74154	+	4.74848i	−0.272793	+	0.472492i	−0.969576	−	0.244791i	$-0.921281\pi$
$101$	−2.74154	+	4.74848i	−0.272793	+	0.472492i	0.696783	+	0.717282i	$0.254614\pi$
$102$		0			0
$103$	−7.51533			−0.740508			−0.370254	−	0.928931i	$-0.620729\pi$
$103$	−7.51533			−0.740508			−0.370254	+	0.928931i	$0.620729\pi$
$104$	2.03802	−	3.52996i	0.199845	−	0.346141i
$105$		0			0
$106$	−0.875855			−0.0850706
$107$	11.2010			1.08284			0.541421	−	0.840751i	$-0.317886\pi$
$107$	11.2010			1.08284			0.541421	+	0.840751i	$0.317886\pi$
$108$		0			0
$109$	−4.11443	−	7.12641i	−0.394091	−	0.682586i	0.598894	−	0.800829i	$-0.295607\pi$
$109$	−4.11443	−	7.12641i	−0.394091	−	0.682586i	−0.992985	+	0.118243i	$0.962274\pi$
$110$	0.453524	−	0.785526i	0.0432418	−	0.0748970i
$111$		0			0
$112$	0.418067	+	0.724113i	0.0395036	+	0.0684223i
$113$	−11.2410			−1.05746			−0.528731	−	0.848789i	$-0.677332\pi$
$113$	−11.2410			−1.05746			−0.528731	+	0.848789i	$0.677332\pi$
$114$		0			0
$115$	3.81603			0.355847
$116$	1.03509	+	1.79283i	0.0961055	+	0.166460i
$117$		0			0
$118$	−1.01218	+	1.75315i	−0.0931789	+	0.161391i
$119$	0.715603	+	1.23946i	0.0655992	+	0.113621i
$120$		0			0
$121$	17.4367			1.58515
$122$	−0.768145			−0.0695446
$123$		0			0
$124$	2.62133	−	4.54028i	0.235403	−	0.407729i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−4.99890	+	8.65834i	−0.443580	+	0.768304i	−0.997952	−	0.0639656i	$-0.979625\pi$
$127$	−4.99890	+	8.65834i	−0.443580	+	0.768304i	0.554372	+	0.832269i	$0.312959\pi$
$128$	2.62394	+	4.54480i	0.231926	+	0.401707i
$129$		0			0
$130$	−0.513218	−	0.888919i	−0.0450122	−	0.0779634i
$131$	−8.74252	−	15.1425i	−0.763837	−	1.32301i	−0.940859	−	0.338798i	$-0.889980\pi$
$131$	−8.74252	−	15.1425i	−0.763837	−	1.32301i	0.177022	−	0.984207i	$-0.443354\pi$
$132$		0			0
$133$	−0.328811	+	0.893716i	−0.0285115	+	0.0774950i
$134$	−1.12318			−0.0970283
$135$		0			0
$136$	2.21248	+	3.83214i	0.189719	+	0.328603i
$137$	6.68642	−	11.5812i	0.571259	−	0.989450i	−0.425178	−	0.905110i	$-0.639788\pi$
$137$	6.68642	−	11.5812i	0.571259	−	0.989450i	0.996437	−	0.0843402i	$-0.0268783\pi$
$138$		0			0
$139$	4.46095	−	7.72659i	0.378373	−	0.655360i	−0.612453	−	0.790507i	$-0.709817\pi$
$139$	4.46095	−	7.72659i	0.378373	−	0.655360i	0.990826	+	0.135146i	$0.0431505\pi$
$140$	0.430617			0.0363938
$141$		0			0
$142$	−0.531255	+	0.920160i	−0.0445819	+	0.0772181i
$143$	16.0898	−	27.8684i	1.34550	−	2.33047i
$144$		0			0
$145$	1.05028			0.0872212
$146$	−0.563924	+	0.976745i	−0.0466707	+	0.0808360i
$147$		0			0
$148$	3.05820	−	5.29696i	0.251382	−	0.435407i
$149$	8.59072	+	14.8796i	0.703779	+	1.21898i	0.967130	+	0.254281i	$0.0818389\pi$
$149$	8.59072	+	14.8796i	0.703779	+	1.21898i	−0.263351	+	0.964700i	$0.584828\pi$
$150$		0			0
$151$	−20.4475			−1.66399			−0.831996	−	0.554781i	$-0.812802\pi$
$151$	−20.4475			−1.66399			−0.831996	+	0.554781i	$0.812802\pi$
$152$	−1.01661	+	2.76317i	−0.0824578	+	0.224123i
$153$		0			0
$154$	−0.0990808	−	0.171613i	−0.00798416	−	0.0138290i
$155$	−1.32991	−	2.30346i	−0.106821	−	0.185019i
$156$		0			0
$157$	3.15365	+	5.46228i	0.251689	+	0.435937i	0.963991	−	0.265935i	$-0.0856808\pi$
$157$	3.15365	+	5.46228i	0.251689	+	0.435937i	−0.712302	+	0.701873i	$0.752347\pi$
$158$	−0.307520	+	0.532640i	−0.0244650	+	0.0423746i
$159$		0			0
$160$	2.00191			0.158265
$161$	0.416842	−	0.721991i	0.0328517	−	0.0569009i
$162$		0			0
$163$	−4.20330			−0.329228			−0.164614	−	0.986358i	$-0.552638\pi$
$163$	−4.20330			−0.329228			−0.164614	+	0.986358i	$0.552638\pi$
$164$	6.89914			0.538732
$165$		0			0
$166$	−0.714124	−	1.23690i	−0.0554268	−	0.0960020i
$167$	2.32721	−	4.03085i	0.180085	−	0.311916i	−0.761824	−	0.647784i	$-0.775696\pi$
$167$	2.32721	−	4.03085i	0.180085	−	0.311916i	0.941909	+	0.335867i	$0.109029\pi$
$168$		0			0
$169$	−11.7076	−	20.2781i	−0.900584	−	1.55986i
$170$	1.11430			0.0854631
$171$		0			0
$172$	−5.49007			−0.418614
$173$	11.8837	+	20.5831i	0.903500	+	1.56491i	0.822919	+	0.568159i	$0.192344\pi$
$173$	11.8837	+	20.5831i	0.903500	+	1.56491i	0.0805809	+	0.996748i	$0.474322\pi$
$174$		0			0
$175$	0.109234	−	0.189200i	0.00825735	−	0.0143021i
$176$	10.2046	+	17.6749i	0.769200	+	1.33229i
$177$		0			0
$178$	−1.63012			−0.122183
$179$	13.7265			1.02597			0.512984	−	0.858398i	$-0.328540\pi$
$179$	13.7265			1.02597			0.512984	+	0.858398i	$0.328540\pi$
$180$		0			0
$181$	−10.9708	+	19.0020i	−0.815454	+	1.41241i	0.0935470	+	0.995615i	$0.470179\pi$
$181$	−10.9708	+	19.0020i	−0.815454	+	1.41241i	−0.909001	+	0.416793i	$0.863154\pi$
$182$	−0.224244			−0.0166221
$183$		0			0
$184$	1.28878	−	2.23224i	0.0950103	−	0.164563i
$185$	−1.55154	−	2.68735i	−0.114072	−	0.197578i
$186$		0			0
$187$	17.4672	+	30.2540i	1.27732	+	2.21239i
$188$	8.40527	+	14.5584i	0.613017	+	1.06178i
$189$		0			0
$190$	0.474601	+	0.569619i	0.0344311	+	0.0413245i
$191$	11.9978			0.868132			0.434066	−	0.900881i	$-0.357079\pi$
$191$	11.9978			0.868132			0.434066	+	0.900881i	$0.357079\pi$
$192$		0			0
$193$	−5.83782	−	10.1114i	−0.420216	−	0.727835i	0.575745	−	0.817630i	$-0.304712\pi$
$193$	−5.83782	−	10.1114i	−0.420216	−	0.727835i	−0.995960	+	0.0897947i	$0.971379\pi$
$194$	1.35331	−	2.34400i	0.0971620	−	0.168290i
$195$		0			0
$196$	−6.85170	+	11.8675i	−0.489407	+	0.847678i
$197$	10.3275			0.735801			0.367901	−	0.929865i	$-0.380077\pi$
$197$	10.3275			0.735801			0.367901	+	0.929865i	$0.380077\pi$
$198$		0			0
$199$	4.63560	−	8.02910i	0.328609	−	0.569168i	−0.653627	−	0.756817i	$-0.726753\pi$
$199$	4.63560	−	8.02910i	0.328609	−	0.569168i	0.982236	+	0.187649i	$0.0600868\pi$
$200$	0.337729	−	0.584963i	0.0238810	−	0.0413631i
$201$		0			0
$202$	0.932641			0.0656204
$203$	0.114727	−	0.198713i	0.00805225	−	0.0139469i
$204$		0			0
$205$	1.75010	−	3.03127i	0.122232	−	0.211713i
$206$	0.639159	+	1.10706i	0.0445323	+	0.0771322i
$207$		0			0
$208$	23.0955			1.60138
$209$	−8.02593	+	21.8147i	−0.555166	+	1.50895i
$210$		0			0
$211$	0.526860	+	0.912548i	0.0362705	+	0.0628224i	0.883591	−	0.468260i	$-0.155119\pi$
$211$	0.526860	+	0.912548i	0.0362705	+	0.0628224i	−0.847320	+	0.531082i	$0.821786\pi$
$212$	−5.07474	−	8.78970i	−0.348534	−	0.603679i
$213$		0			0
$214$	−0.952615	−	1.64998i	−0.0651195	−	0.112790i
$215$	−1.39266	+	2.41216i	−0.0949789	+	0.164508i
$216$		0			0
$217$	−0.581086			−0.0394467
$218$	−0.699843	+	1.21216i	−0.0473993	+	0.0820980i
$219$		0			0
$220$	10.5109			0.708647
$221$	39.5325			2.65924
$222$		0			0
$223$	−13.0822	−	22.6591i	−0.876052	−	1.51737i	−0.855638	−	0.517574i	$-0.826835\pi$
$223$	−13.0822	−	22.6591i	−0.876052	−	1.51737i	−0.0204133	−	0.999792i	$-0.506498\pi$
$224$	0.218677	−	0.378760i	0.0146110	−	0.0253070i
$225$		0			0
$226$	0.956015	+	1.65587i	0.0635932	+	0.110147i
$227$	−15.2808			−1.01422			−0.507111	−	0.861881i	$-0.669287\pi$
$227$	−15.2808			−1.01422			−0.507111	+	0.861881i	$0.669287\pi$
$228$		0			0
$229$	−13.5223			−0.893581			−0.446791	−	0.894639i	$-0.647433\pi$
$229$	−13.5223			−0.893581			−0.446791	+	0.894639i	$0.647433\pi$
$230$	−0.324543	−	0.562125i	−0.0213997	−	0.0370654i
$231$		0			0
$232$	0.354710	−	0.614376i	0.0232879	−	0.0403358i
$233$	−2.45230	−	4.24751i	−0.160656	−	0.278264i	0.774448	−	0.632637i	$-0.218028\pi$
$233$	−2.45230	−	4.24751i	−0.160656	−	0.278264i	−0.935104	+	0.354373i	$0.884694\pi$
$234$		0			0
$235$	8.52865			0.556348
$236$	−23.4585			−1.52702
$237$		0			0
$238$	0.121720	−	0.210826i	0.00788995	−	0.0136658i
$239$	18.0191			1.16556			0.582780	−	0.812630i	$-0.301965\pi$
$239$	18.0191			1.16556			0.582780	+	0.812630i	$0.301965\pi$
$240$		0			0
$241$	14.5193	−	25.1482i	0.935273	−	1.61994i	0.161125	−	0.986934i	$-0.448488\pi$
$241$	14.5193	−	25.1482i	0.935273	−	1.61994i	0.774147	−	0.633006i	$-0.218179\pi$
$242$	−1.48294	−	2.56853i	−0.0953272	−	0.165112i
$243$		0			0
$244$	−4.45066	−	7.70877i	−0.284924	−	0.493503i
$245$	3.47614	+	6.02084i	0.222082	+	0.384658i
$246$		0			0
$247$	16.8376	+	20.2085i	1.07135	+	1.28584i
$248$	−1.79659			−0.114083
$249$		0			0
$250$	−0.0850473	−	0.147306i	−0.00537886	−	0.00931646i
$251$	14.4094	−	24.9578i	0.909514	−	1.57532i	0.0947735	−	0.995499i	$-0.469787\pi$
$251$	14.4094	−	24.9578i	0.909514	−	1.57532i	0.814741	−	0.579826i	$-0.196879\pi$
$252$		0			0
$253$	10.1747	−	17.6231i	0.639678	−	1.10795i
$254$	1.70057			0.106703
$255$		0			0
$256$	−6.86766	+	11.8951i	−0.429229	+	0.743446i
$257$	5.87925	−	10.1832i	0.366737	−	0.635208i	−0.622316	−	0.782766i	$-0.713808\pi$
$257$	5.87925	−	10.1832i	0.366737	−	0.635208i	0.989053	+	0.147558i	$0.0471414\pi$
$258$		0			0
$259$	−0.677928			−0.0421244
$260$	5.94720	−	10.3009i	0.368830	−	0.638832i
$261$		0			0
$262$	−1.48706	+	2.57565i	−0.0918706	+	0.159124i
$263$	−4.42603	−	7.66611i	−0.272921	−	0.472713i	0.696688	−	0.717375i	$-0.254656\pi$
$263$	−4.42603	−	7.66611i	−0.272921	−	0.472713i	−0.969608	+	0.244662i	$0.921323\pi$
$264$		0			0
$265$	−5.14923			−0.316314
$266$	0.159614	−	0.0275723i	0.00978658	−	0.00169056i
$267$		0			0
$268$	−6.50777	−	11.2718i	−0.397525	−	0.688534i
$269$	−9.01236	−	15.6099i	−0.549493	−	0.951750i	−0.998309	−	0.0581261i	$-0.981487\pi$
$269$	−9.01236	−	15.6099i	−0.549493	−	0.951750i	0.448816	−	0.893624i	$-0.351846\pi$
$270$		0			0
$271$	−0.0833046	−	0.144288i	−0.00506040	−	0.00876486i	0.863484	−	0.504376i	$-0.168277\pi$
$271$	−0.0833046	−	0.144288i	−0.00506040	−	0.00876486i	−0.868545	+	0.495611i	$0.834944\pi$
$272$	−12.5363	+	21.7135i	−0.760124	+	1.31657i
$273$		0			0
$274$	−2.27465			−0.137416
$275$	2.66630	−	4.61817i	0.160784	−	0.278486i
$276$		0			0
$277$	18.4262			1.10712			0.553560	−	0.832809i	$-0.313269\pi$
$277$	18.4262			1.10712			0.553560	+	0.832809i	$0.313269\pi$
$278$	−1.51757			−0.0910175
$279$		0			0
$280$	−0.0737832	−	0.127796i	−0.00440939	−	0.00763728i
$281$	−15.0338	+	26.0394i	−0.896844	+	1.55338i	−0.0653383	+	0.997863i	$0.520813\pi$
$281$	−15.0338	+	26.0394i	−0.896844	+	1.55338i	−0.831506	+	0.555516i	$0.812521\pi$
$282$		0			0
$283$	3.37959	+	5.85362i	0.200896	+	0.347962i	0.948817	−	0.315826i	$-0.102281\pi$
$283$	3.37959	+	5.85362i	0.200896	+	0.347962i	−0.747922	+	0.663787i	$0.768948\pi$
$284$	−12.3124			−0.730609
$285$		0			0
$286$	−5.47358			−0.323659
$287$	−0.382343	−	0.662237i	−0.0225690	−	0.0390906i
$288$		0			0
$289$	−12.9583	+	22.4444i	−0.762253	+	1.32026i
$290$	−0.0893236	−	0.154713i	−0.00524526	−	0.00908506i
$291$		0			0
$292$	−13.0696			−0.764840
$293$	26.0167			1.51991			0.759957	−	0.649973i	$-0.225220\pi$
$293$	26.0167			1.51991			0.759957	+	0.649973i	$0.225220\pi$
$294$		0			0
$295$	−5.95070	+	10.3069i	−0.346463	+	0.600092i
$296$	−2.09600			−0.121828
$297$		0			0
$298$	1.46123	−	2.53093i	0.0846471	−	0.146613i
$299$	−11.5139	−	19.9427i	−0.665867	−	1.15332i
$300$		0			0
$301$	0.304254	+	0.526983i	0.0175369	+	0.0303748i
$302$	1.73900	+	3.01204i	0.100068	+	0.173323i
$303$		0			0
$304$	−16.4391	+	2.83974i	−0.942847	+	0.162870i
$305$	−4.51599			−0.258585
$306$		0			0
$307$	−6.57544	−	11.3890i	−0.375280	−	0.650004i	0.615089	−	0.788458i	$-0.289120\pi$
$307$	−6.57544	−	11.3890i	−0.375280	−	0.650004i	−0.990369	+	0.138454i	$0.955787\pi$
$308$	1.14816	−	1.98866i	0.0654222	−	0.113315i
$309$		0			0
$310$	−0.226210	+	0.391807i	−0.0128478	+	0.0222531i
$311$	−3.98871			−0.226179			−0.113089	−	0.993585i	$-0.536075\pi$
$311$	−3.98871			−0.226179			−0.113089	+	0.993585i	$0.536075\pi$
$312$		0			0
$313$	0.659360	−	1.14205i	0.0372692	−	0.0645522i	−0.846789	−	0.531929i	$-0.821467\pi$
$313$	0.659360	−	1.14205i	0.0372692	−	0.0645522i	0.884058	+	0.467377i	$0.154801\pi$
$314$	0.536418	−	0.929104i	0.0302718	−	0.0524324i
$315$		0			0
$316$	−7.12712			−0.400932
$317$	0.370562	−	0.641833i	0.0208129	−	0.0360489i	−0.855431	−	0.517916i	$-0.826708\pi$
$317$	0.370562	−	0.641833i	0.0208129	−	0.0360489i	0.876244	+	0.481867i	$0.160041\pi$
$318$		0			0
$319$	2.80037	−	4.85038i	0.156791	−	0.271569i
$320$	3.65699	+	6.33409i	0.204432	+	0.354086i
$321$		0			0
$322$	−0.141805			−0.00790249
$323$	−28.1387	+	4.86077i	−1.56568	+	0.270461i
$324$		0			0
$325$	−3.01725	−	5.22603i	−0.167367	−	0.289888i
$326$	0.357480	+	0.619173i	0.0197990	+	0.0342928i
$327$		0			0
$328$	−1.18212	−	2.04749i	−0.0652716	−	0.113054i
$329$	0.931622	−	1.61362i	0.0513620	−	0.0889616i
$330$		0			0
$331$	11.3519			0.623958			0.311979	−	0.950089i	$-0.399008\pi$
$331$	11.3519			0.623958			0.311979	+	0.950089i	$0.399008\pi$
$332$	8.27532	−	14.3333i	0.454167	−	0.786641i
$333$		0			0
$334$	−0.791692			−0.0433195
$335$	−6.60329			−0.360776
$336$		0			0
$337$	12.3960	+	21.4705i	0.675253	+	1.16957i	0.976395	+	0.215993i	$0.0692988\pi$
$337$	12.3960	+	21.4705i	0.675253	+	1.16957i	−0.301142	+	0.953579i	$0.597368\pi$
$338$	−1.99140	+	3.44920i	−0.108318	+	0.187612i
$339$		0			0
$340$	6.45631	+	11.1827i	0.350142	+	0.606464i
$341$	−14.1837			−0.768092
$342$		0			0
$343$	3.04814			0.164584
$344$	0.940684	+	1.62931i	0.0507183	+	0.0878467i
$345$		0			0
$346$	2.02135	−	3.50108i	0.108668	−	0.188219i
$347$	15.6066	+	27.0315i	0.837807	+	1.45112i	0.891724	+	0.452579i	$0.149496\pi$
$347$	15.6066	+	27.0315i	0.837807	+	1.45112i	−0.0539174	+	0.998545i	$0.517171\pi$
$348$		0			0
$349$	2.67972			0.143442			0.0717212	−	0.997425i	$-0.477151\pi$
$349$	2.67972			0.143442			0.0717212	+	0.997425i	$0.477151\pi$
$350$	−0.0371604			−0.00198631
$351$		0			0
$352$	5.33769	−	9.24515i	0.284500	−	0.492768i
$353$	−29.6238			−1.57671			−0.788357	−	0.615218i	$-0.789068\pi$
$353$	−29.6238			−1.57671			−0.788357	+	0.615218i	$0.789068\pi$
$354$		0			0
$355$	−3.12329	+	5.40970i	−0.165767	+	0.287117i
$356$	−9.44500	−	16.3592i	−0.500584	−	0.867037i
$357$		0			0
$358$	−1.16740	−	2.02200i	−0.0616992	−	0.106866i
$359$	−10.9641	−	18.9904i	−0.578664	−	1.00228i	−0.995633	−	0.0933549i	$-0.970241\pi$
$359$	−10.9641	−	18.9904i	−0.578664	−	1.00228i	0.416969	−	0.908921i	$-0.363092\pi$
$360$		0			0
$361$	−14.4695	−	12.3139i	−0.761555	−	0.648100i
$362$	3.73215			0.196158
$363$		0			0
$364$	−1.29928	−	2.25042i	−0.0681007	−	0.117954i
$365$	−3.31536	+	5.74237i	−0.173534	+	0.300569i
$366$		0			0
$367$	−6.87305	+	11.9045i	−0.358770	+	0.621408i	−0.987756	−	0.156009i	$-0.950137\pi$
$367$	−6.87305	+	11.9045i	−0.358770	+	0.621408i	0.628985	+	0.777417i	$0.283470\pi$
$368$	14.6049			0.761332
$369$		0			0
$370$	−0.263909	+	0.457104i	−0.0137200	+	0.0237637i
$371$	−0.562473	+	0.974232i	−0.0292021	+	0.0505796i
$372$		0			0
$373$	−22.8295			−1.18207			−0.591034	−	0.806646i	$-0.701280\pi$
$373$	−22.8295			−1.18207			−0.591034	+	0.806646i	$0.701280\pi$
$374$	2.97107	−	5.14604i	0.153630	−	0.266095i
$375$		0			0
$376$	2.88037	−	4.98894i	0.148544	−	0.257285i
$377$	−3.16896	−	5.48880i	−0.163210	−	0.282688i
$378$		0			0
$379$	28.9938			1.48931			0.744656	−	0.667449i	$-0.232614\pi$
$379$	28.9938			1.48931			0.744656	+	0.667449i	$0.232614\pi$
$380$	−2.96659	+	8.06327i	−0.152183	+	0.413637i
$381$		0			0
$382$	−1.02038	−	1.76735i	−0.0522073	−	0.0904257i
$383$	−13.0687	−	22.6357i	−0.667781	−	1.15663i	−0.978523	−	0.206137i	$-0.933911\pi$
$383$	−13.0687	−	22.6357i	−0.667781	−	1.15663i	0.310742	−	0.950494i	$-0.399422\pi$
$384$		0			0
$385$	−0.582504	−	1.00893i	−0.0296872	−	0.0514197i
$386$	−0.992982	+	1.71989i	−0.0505414	+	0.0875403i
$387$		0			0
$388$	31.3645			1.59229
$389$	−11.7728	+	20.3911i	−0.596906	+	1.03387i	0.396369	+	0.918091i	$0.370270\pi$
$389$	−11.7728	+	20.3911i	−0.596906	+	1.03387i	−0.993275	+	0.115780i	$0.963063\pi$
$390$		0			0
$391$	24.9991			1.26426
$392$	4.69596			0.237182
$393$		0			0
$394$	−0.878323	−	1.52130i	−0.0442493	−	0.0766420i
$395$	−1.80793	+	3.13143i	−0.0909670	+	0.157560i
$396$		0			0
$397$	−7.95863	−	13.7847i	−0.399432	−	0.691837i	0.594224	−	0.804300i	$-0.297459\pi$
$397$	−7.95863	−	13.7847i	−0.399432	−	0.691837i	−0.993656	+	0.112463i	$0.964126\pi$
$398$	−1.57698			−0.0790470
$399$		0			0
$400$	3.82724			0.191362
$401$	−11.1575	−	19.3254i	−0.557179	−	0.965063i	−0.997730	−	0.0673353i	$-0.978550\pi$
$401$	−11.1575	−	19.3254i	−0.557179	−	0.965063i	0.440551	−	0.897728i	$-0.354783\pi$
$402$		0			0
$403$	−8.02531	+	13.9003i	−0.399769	+	0.692421i
$404$	5.40376	+	9.35958i	0.268847	+	0.465657i
$405$		0			0
$406$	−0.0390289			−0.00193697
$407$	−16.5475			−0.820232
$408$		0			0
$409$	0.356179	−	0.616920i	0.0176119	−	0.0305047i	−0.857085	−	0.515175i	$-0.827727\pi$
$409$	0.356179	−	0.616920i	0.0176119	−	0.0305047i	0.874697	+	0.484670i	$0.161060\pi$
$410$	−0.595366			−0.0294030
$411$		0			0
$412$	−7.40662	+	12.8286i	−0.364898	+	0.632022i
$413$	1.30004	+	2.25174i	0.0639709	+	0.110801i
$414$		0			0
$415$	−4.19840	−	7.27183i	−0.206091	−	0.356960i
$416$	−6.04025	−	10.4620i	−0.296148	−	0.512943i
$417$		0			0
$418$	3.89603	−	0.673012i	0.190561	−	0.0329181i
$419$	−30.0670			−1.46887			−0.734434	−	0.678681i	$-0.762552\pi$
$419$	−30.0670			−1.46887			−0.734434	+	0.678681i	$0.762552\pi$
$420$		0			0
$421$	11.4858	+	19.8939i	0.559781	+	0.969570i	0.997514	+	0.0704646i	$0.0224482\pi$
$421$	11.4858	+	19.8939i	0.559781	+	0.969570i	−0.437733	+	0.899105i	$0.644218\pi$
$422$	0.0896160	−	0.155220i	0.00436244	−	0.00755597i
$423$		0			0
$424$	−1.73904	+	3.01211i	−0.0844553	+	0.146281i
$425$	6.55108			0.317774
$426$		0			0
$427$	−0.493301	+	0.854423i	−0.0238725	+	0.0413484i
$428$	11.0390	−	19.1201i	0.533589	−	0.924203i
$429$		0			0
$430$	0.473769			0.0228472
$431$	−11.6935	+	20.2538i	−0.563258	+	0.975592i	0.433951	+	0.900937i	$0.357119\pi$
$431$	−11.6935	+	20.2538i	−0.563258	+	0.975592i	−0.997209	+	0.0746557i	$0.976214\pi$
$432$		0			0
$433$	−16.7300	+	28.9773i	−0.803994	+	1.39256i	0.112974	+	0.993598i	$0.463962\pi$
$433$	−16.7300	+	28.9773i	−0.803994	+	1.39256i	−0.916968	+	0.398961i	$0.869371\pi$
$434$	0.0494198	+	0.0855976i	0.00237223	+	0.00410881i
$435$		0			0
$436$	−16.2197			−0.776780
$437$	10.6475	+	12.7793i	0.509341	+	0.611315i
$438$		0			0
$439$	−8.72611	−	15.1141i	−0.416474	−	0.721355i	0.579108	−	0.815251i	$-0.303401\pi$
$439$	−8.72611	−	15.1141i	−0.416474	−	0.721355i	−0.995582	+	0.0938963i	$0.970068\pi$
$440$	−1.80097	−	3.11938i	−0.0858580	−	0.148710i
$441$		0			0
$442$	−3.36213	−	5.82338i	−0.159920	−	0.276990i
$443$	−7.57846	+	13.1263i	−0.360063	+	0.623648i	−0.987971	−	0.154640i	$-0.950578\pi$
$443$	−7.57846	+	13.1263i	−0.360063	+	0.623648i	0.627908	+	0.778288i	$0.283912\pi$
$444$		0			0
$445$	−9.58364			−0.454308
$446$	−2.22522	+	3.85419i	−0.105367	+	0.182501i
$447$		0			0
$448$	1.59788			0.0754925
$449$	13.1961			0.622762			0.311381	−	0.950285i	$-0.399208\pi$
$449$	13.1961			0.622762			0.311381	+	0.950285i	$0.399208\pi$
$450$		0			0
$451$	−9.33261	−	16.1645i	−0.439455	−	0.761159i
$452$	−11.0784	+	19.1883i	−0.521083	+	0.902542i
$453$		0			0
$454$	1.29959	+	2.25096i	0.0609928	+	0.105643i
$455$	−1.31835			−0.0618052
$456$		0			0
$457$	−4.20019			−0.196477			−0.0982383	−	0.995163i	$-0.531321\pi$
$457$	−4.20019			−0.196477			−0.0982383	+	0.995163i	$0.531321\pi$
$458$	1.15004	+	1.99192i	0.0537377	+	0.0930765i
$459$		0			0
$460$	3.76083	−	6.51394i	0.175349	−	0.303714i
$461$	10.0039	+	17.3273i	0.465928	+	0.807011i	0.999243	−	0.0389056i	$-0.0123872\pi$
$461$	10.0039	+	17.3273i	0.465928	+	0.807011i	−0.533315	+	0.845917i	$0.679054\pi$
$462$		0			0
$463$	−20.4670			−0.951183			−0.475591	−	0.879666i	$-0.657766\pi$
$463$	−20.4670			−0.951183			−0.475591	+	0.879666i	$0.657766\pi$
$464$	4.01968			0.186609
$465$		0			0
$466$	−0.417123	+	0.722479i	−0.0193229	+	0.0334682i
$467$	−39.2577			−1.81663			−0.908314	−	0.418288i	$-0.862630\pi$
$467$	−39.2577			−1.81663			−0.908314	+	0.418288i	$0.862630\pi$
$468$		0			0
$469$	−0.721307	+	1.24934i	−0.0333069	+	0.0576892i
$470$	−0.725338	−	1.25632i	−0.0334574	−	0.0579498i
$471$		0			0
$472$	4.01944	+	6.96188i	0.185010	+	0.320446i
$473$	7.42653	+	12.8631i	0.341472	+	0.591447i
$474$		0			0
$475$	2.79022	+	3.34883i	0.128024	+	0.153655i
$476$	2.82100			0.129301
$477$		0			0
$478$	−1.53248	−	2.65433i	−0.0700939	−	0.121406i
$479$	−3.62557	+	6.27967i	−0.165656	+	0.286925i	−0.936888	−	0.349629i	$-0.886308\pi$
$479$	−3.62557	+	6.27967i	−0.165656	+	0.286925i	0.771232	+	0.636554i	$0.219641\pi$
$480$		0			0
$481$	−9.36279	+	16.2168i	−0.426907	+	0.739424i
$482$	−4.93932			−0.224980
$483$		0			0
$484$	17.1845	−	29.7643i	0.781111	−	1.35292i
$485$	7.95622	−	13.7806i	0.361274	−	0.625744i
$486$		0			0
$487$	−4.16094			−0.188550			−0.0942751	−	0.995546i	$-0.530053\pi$
$487$	−4.16094			−0.188550			−0.0942751	+	0.995546i	$0.530053\pi$
$488$	−1.52518	+	2.64169i	−0.0690415	+	0.119583i
$489$		0			0
$490$	0.591272	−	1.02411i	0.0267109	−	0.0462647i
$491$	2.96842	+	5.14145i	0.133963	+	0.232030i	0.925201	−	0.379478i	$-0.123896\pi$
$491$	2.96842	+	5.14145i	0.133963	+	0.232030i	−0.791238	+	0.611508i	$0.790563\pi$
$492$		0			0
$493$	6.88048			0.309881
$494$	1.54485	−	4.19896i	0.0695063	−	0.188920i
$495$		0			0
$496$	−5.08987	−	8.81592i	−0.228542	−	0.395846i
$497$	0.682342	+	1.18185i	0.0306072	+	0.0530133i
$498$		0			0
$499$	1.19537	+	2.07045i	0.0535123	+	0.0926860i	0.891541	−	0.452941i	$-0.149625\pi$
$499$	1.19537	+	2.07045i	0.0535123	+	0.0926860i	−0.838028	+	0.545627i	$0.816292\pi$
$500$	0.985534	−	1.70699i	0.0440744	−	0.0763391i
$501$		0			0
$502$	−4.90193			−0.218784
$503$	−10.0317	+	17.3754i	−0.447290	+	0.774729i	−0.998209	−	0.0598298i	$-0.980944\pi$
$503$	−10.0317	+	17.3754i	−0.447290	+	0.774729i	0.550918	+	0.834559i	$0.314278\pi$
$504$		0			0
$505$	5.48308			0.243994
$506$	−3.46132			−0.153874
$507$		0			0
$508$	9.85316	+	17.0662i	0.437163	+	0.757189i
$509$	−12.9575	+	22.4430i	−0.574329	+	0.994767i	0.421785	+	0.906696i	$0.361404\pi$
$509$	−12.9575	+	22.4430i	−0.574329	+	0.994767i	−0.996114	+	0.0880712i	$0.971930\pi$
$510$		0			0
$511$	0.724302	+	1.25453i	0.0320413	+	0.0554971i
$512$	12.8321			0.567103
$513$		0			0
$514$	−2.00006			−0.0882187
$515$	3.75767	+	6.50847i	0.165583	+	0.286797i
$516$		0			0
$517$	22.7400	−	39.3868i	1.00010	−	1.73223i
$518$	0.0576560	+	0.0998630i	0.00253326	+	0.00438773i
$519$		0			0
$520$	−4.07604			−0.178746
$521$	21.0579			0.922562			0.461281	−	0.887254i	$-0.347390\pi$
$521$	21.0579			0.922562			0.461281	+	0.887254i	$0.347390\pi$
$522$		0			0
$523$	−9.57494	+	16.5843i	−0.418683	+	0.725180i	−0.995807	−	0.0914762i	$-0.970841\pi$
$523$	−9.57494	+	16.5843i	−0.418683	+	0.725180i	0.577124	+	0.816656i	$0.304175\pi$
$524$	−34.4642			−1.50558
$525$		0			0
$526$	−0.752844	+	1.30396i	−0.0328256	+	0.0568555i
$527$	−8.71231	−	15.0902i	−0.379514	−	0.657338i
$528$		0			0
$529$	4.21896	+	7.30745i	0.183433	+	0.317715i
$530$	0.437928	+	0.758513i	0.0190224	+	0.0329477i
$531$		0			0
$532$	1.20151	+	1.44207i	0.0520923	+	0.0625215i
$533$	−21.1220			−0.914895
$534$		0			0
$535$	−5.60051	−	9.70036i	−0.242131	−	0.419383i
$536$	−2.23012	+	3.86268i	−0.0963265	+	0.166842i
$537$		0			0
$538$	−1.53295	+	2.65515i	−0.0660903	+	0.114472i
$539$	37.0737			1.59688
$540$		0			0
$541$	6.84592	−	11.8575i	0.294329	−	0.509793i	−0.680499	−	0.732749i	$-0.738237\pi$
$541$	6.84592	−	11.8575i	0.294329	−	0.509793i	0.974829	+	0.222956i	$0.0715705\pi$
$542$	−0.0141697	+	0.0245426i	−0.000608639	+	0.00105419i
$543$		0			0
$544$	13.1146			0.562286
$545$	−4.11443	+	7.12641i	−0.176243	+	0.305262i
$546$		0			0
$547$	12.7556	−	22.0934i	0.545391	−	0.944645i	−0.453191	−	0.891413i	$-0.649714\pi$
$547$	12.7556	−	22.0934i	0.545391	−	0.944645i	0.998582	−	0.0532318i	$-0.0169522\pi$
$548$	−13.1794	−	22.8274i	−0.562995	−	0.975137i
$549$		0			0
$550$	−0.907047			−0.0386766
$551$	2.93051	+	3.51722i	0.124844	+	0.149839i
$552$		0			0
$553$	0.394977	+	0.684121i	0.0167961	+	0.0290918i
$554$	−1.56710	−	2.71429i	−0.0665795	−	0.115319i
$555$		0			0
$556$	−8.79283	−	15.2296i	−0.372899	−	0.645880i
$557$	5.49373	−	9.51541i	0.232777	−	0.403181i	−0.725848	−	0.687856i	$-0.758552\pi$
$557$	5.49373	−	9.51541i	0.232777	−	0.403181i	0.958624	+	0.284675i	$0.0918856\pi$
$558$		0			0
$559$	16.8081			0.710905
$560$	0.418067	−	0.724113i	0.0176666	−	0.0305994i
$561$		0			0
$562$	5.11435			0.215736
$563$	5.57158			0.234814			0.117407	−	0.993084i	$-0.462542\pi$
$563$	5.57158			0.234814			0.117407	+	0.993084i	$0.462542\pi$
$564$		0			0
$565$	5.62049	+	9.73498i	0.236456	+	0.409553i
$566$	0.574850	−	0.995669i	0.0241627	−	0.0418511i
$567$		0			0
$568$	2.10965	+	3.65402i	0.0885189	+	0.153319i
$569$	21.9856			0.921685			0.460843	−	0.887482i	$-0.347547\pi$
$569$	21.9856			0.921685			0.460843	+	0.887482i	$0.347547\pi$
$570$		0			0
$571$	36.1104			1.51117			0.755586	−	0.655050i	$-0.227352\pi$
$571$	36.1104			1.51117			0.755586	+	0.655050i	$0.227352\pi$
$572$	−31.7141	−	54.9304i	−1.32603	−	2.29676i
$573$		0			0
$574$	−0.0650344	+	0.112643i	−0.00271449	+	0.00470163i
$575$	−1.90802	−	3.30478i	−0.0795697	−	0.137819i
$576$		0			0
$577$	−15.0931			−0.628333			−0.314166	−	0.949368i	$-0.601725\pi$
$577$	−15.0931			−0.628333			−0.314166	+	0.949368i	$0.601725\pi$
$578$	4.40827			0.183360
$579$		0			0
$580$	1.03509	−	1.79283i	0.0429797	−	0.0744430i
$581$	−1.83444			−0.0761053
$582$		0			0
$583$	−13.7294	+	23.7800i	−0.568614	+	0.984868i
$584$	2.23938	+	3.87872i	0.0926663	+	0.160503i
$585$		0			0
$586$	−2.21265	−	3.83243i	−0.0914039	−	0.158316i
$587$	−16.1610	−	27.9916i	−0.667034	−	1.15534i	−0.978729	−	0.205155i	$-0.934230\pi$
$587$	−16.1610	−	27.9916i	−0.667034	−	1.15534i	0.311695	−	0.950182i	$-0.399103\pi$
$588$		0			0
$589$	4.00320	−	10.8808i	0.164949	−	0.448335i
$590$	2.02436			0.0833417
$591$		0			0
$592$	−5.93814	−	10.2852i	−0.244056	−	0.422717i
$593$	−9.82932	+	17.0249i	−0.403642	+	0.699128i	−0.994162	−	0.107894i	$-0.965589\pi$
$593$	−9.82932	+	17.0249i	−0.403642	+	0.699128i	0.590520	+	0.807023i	$0.298923\pi$
$594$		0			0
$595$	0.715603	−	1.23946i	0.0293369	−	0.0508129i
$596$	33.8658			1.38720
$597$		0			0
$598$	−1.95845	+	3.39214i	−0.0800872	+	0.138715i
$599$	0.491006	−	0.850447i	0.0200620	−	0.0347483i	−0.855820	−	0.517274i	$-0.826947\pi$
$599$	0.491006	−	0.850447i	0.0200620	−	0.0347483i	0.875882	+	0.482525i	$0.160280\pi$
$600$		0			0
$601$	36.2561			1.47892			0.739458	−	0.673203i	$-0.235082\pi$
$601$	36.2561			1.47892			0.739458	+	0.673203i	$0.235082\pi$
$602$	0.0517519	−	0.0896369i	0.00210925	−	0.00365333i
$603$		0			0
$604$	−20.1517	+	34.9037i	−0.819961	+	1.42021i
$605$	−8.71835	−	15.1006i	−0.354451	−	0.613927i
$606$		0			0
$607$	−34.5216			−1.40119			−0.700595	−	0.713559i	$-0.747082\pi$
$607$	−34.5216			−1.40119			−0.700595	+	0.713559i	$0.747082\pi$
$608$	5.58575	+	6.70406i	0.226532	+	0.271885i
$609$		0			0
$610$	0.384072	+	0.665233i	0.0155506	+	0.0269345i
$611$	−25.7331	−	44.5710i	−1.04105	−	1.80315i
$612$		0			0
$613$	17.5283	+	30.3599i	0.707962	+	1.22623i	0.965612	+	0.259988i	$0.0837186\pi$
$613$	17.5283	+	30.3599i	0.707962	+	1.22623i	−0.257650	+	0.966238i	$0.582948\pi$
$614$	−1.11845	+	1.93721i	−0.0451368	+	0.0781793i
$615$		0			0
$616$	−0.786913			−0.0317056
$617$	−20.0581	+	34.7417i	−0.807510	+	1.39865i	0.107073	+	0.994251i	$0.465852\pi$
$617$	−20.0581	+	34.7417i	−0.807510	+	1.39865i	−0.914583	+	0.404398i	$0.867481\pi$
$618$		0			0
$619$	−39.4071			−1.58390			−0.791952	−	0.610583i	$-0.790935\pi$
$619$	−39.4071			−1.58390			−0.791952	+	0.610583i	$0.790935\pi$
$620$	−5.24267			−0.210551
$621$		0			0
$622$	0.339229	+	0.587561i	0.0136018	+	0.0235591i
$623$	−1.04686	+	1.81322i	−0.0419417	+	0.0726452i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−0.224307			−0.00896512
$627$		0			0
$628$	12.4321			0.496095
$629$	−10.1643	−	17.6051i	−0.405276	−	0.701959i
$630$		0			0
$631$	−4.19428	+	7.26471i	−0.166972	+	0.289204i	−0.937354	−	0.348379i	$-0.886732\pi$
$631$	−4.19428	+	7.26471i	−0.166972	+	0.289204i	0.770382	+	0.637583i	$0.220066\pi$
$632$	1.22118	+	2.11515i	0.0485760	+	0.0841361i
$633$		0			0
$634$	−0.126061			−0.00500653
$635$	9.99779			0.396750
$636$		0			0
$637$	20.9767	−	36.3328i	0.831129	−	1.43956i
$638$	−0.952655			−0.0377160
$639$		0			0
$640$	2.62394	−	4.54480i	0.103720	−	0.179649i
$641$	1.14214	+	1.97825i	0.0451120	+	0.0781363i	0.887700	−	0.460423i	$-0.152302\pi$
$641$	1.14214	+	1.97825i	0.0451120	+	0.0781363i	−0.842588	+	0.538559i	$0.818969\pi$
$642$		0			0
$643$	−20.6063	−	35.6912i	−0.812635	−	1.40752i	−0.911014	−	0.412375i	$-0.864699\pi$
$643$	−20.6063	−	35.6912i	−0.812635	−	1.40752i	0.0983795	−	0.995149i	$-0.468634\pi$
$644$	−0.821624	−	1.42309i	−0.0323765	−	0.0560778i
$645$		0			0
$646$	3.10914	+	3.73161i	0.122328	+	0.146818i
$647$	−2.66299			−0.104693			−0.0523465	−	0.998629i	$-0.516670\pi$
$647$	−2.66299			−0.104693			−0.0523465	+	0.998629i	$0.516670\pi$
$648$		0			0
$649$	31.7327	+	54.9627i	1.24562	+	2.15748i
$650$	−0.513218	+	0.888919i	−0.0201301	+	0.0348663i
$651$		0			0
$652$	−4.14250	+	7.17502i	−0.162233	+	0.280995i
$653$	45.2522			1.77086			0.885428	−	0.464777i	$-0.153865\pi$
$653$	45.2522			1.77086			0.885428	+	0.464777i	$0.153865\pi$
$654$		0			0
$655$	−8.74252	+	15.1425i	−0.341599	+	0.591666i
$656$	6.69807	−	11.6014i	0.261516	−	0.452958i
$657$		0			0
$658$	−0.316928			−0.0123551
$659$	−11.6414	+	20.1634i	−0.453483	+	0.785456i	−0.998600	−	0.0529044i	$-0.983152\pi$
$659$	−11.6414	+	20.1634i	−0.453483	+	0.785456i	0.545116	+	0.838360i	$0.316485\pi$
$660$		0			0
$661$	15.0278	−	26.0289i	0.584514	−	1.01241i	−0.410421	−	0.911896i	$-0.634618\pi$
$661$	15.0278	−	26.0289i	0.584514	−	1.01241i	0.994936	−	0.100513i	$-0.0320483\pi$
$662$	−0.965449	−	1.67221i	−0.0375233	−	0.0649922i
$663$		0			0
$664$	−5.67167			−0.220104
$665$	0.938386	−	0.162100i	0.0363890	−	0.00628596i
$666$		0			0
$667$	−2.00395	−	3.47095i	−0.0775934	−	0.134396i
$668$	−4.58709	−	7.94508i	−0.177480	−	0.307404i
$669$		0			0
$670$	0.561592	+	0.972706i	0.0216962	+	0.0375789i
$671$	−12.0410	+	20.8556i	−0.464837	+	0.805122i
$672$		0			0
$673$	−30.4843			−1.17508			−0.587542	−	0.809194i	$-0.699904\pi$
$673$	−30.4843			−1.17508			−0.587542	+	0.809194i	$0.699904\pi$
$674$	2.10849	−	3.65201i	0.0812160	−	0.140670i
$675$		0			0
$676$	−46.1529			−1.77511
$677$	16.7595			0.644118			0.322059	−	0.946720i	$-0.395625\pi$
$677$	16.7595			0.644118			0.322059	+	0.946720i	$0.395625\pi$
$678$		0			0
$679$	−1.73819	−	3.01063i	−0.0667055	−	0.115537i
$680$	2.21248	−	3.83214i	0.0848449	−	0.146956i
$681$		0			0
$682$	1.20629	+	2.08935i	0.0461911	+	0.0800054i
$683$	28.1537			1.07727			0.538636	−	0.842538i	$-0.318940\pi$
$683$	28.1537			1.07727			0.538636	+	0.842538i	$0.318940\pi$
$684$		0			0
$685$	−13.3728			−0.510950
$686$	−0.259236	−	0.449010i	−0.00989767	−	0.0171433i
$687$		0			0
$688$	−5.33006	+	9.23194i	−0.203207	+	0.351964i
$689$	15.5365	+	26.9100i	0.591894	+	1.02519i
$690$		0			0
$691$	−3.71714			−0.141407			−0.0707034	−	0.997497i	$-0.522524\pi$
$691$	−3.71714			−0.141407			−0.0707034	+	0.997497i	$0.522524\pi$
$692$	46.8471			1.78086
$693$		0			0
$694$	2.65460	−	4.59790i	0.100767	−	0.174534i
$695$	−8.92189			−0.338427
$696$		0			0
$697$	11.4651	−	19.8581i	0.434270	−	0.752177i
$698$	−0.227903	−	0.394740i	−0.00862627	−	0.0149411i
$699$		0			0
$700$	−0.215309	−	0.372925i	−0.00813790	−	0.0140953i
$701$	14.6085	+	25.3026i	0.551754	+	0.955667i	0.998148	+	0.0608301i	$0.0193748\pi$
$701$	14.6085	+	25.3026i	0.551754	+	0.955667i	−0.446394	+	0.894837i	$0.647292\pi$
$702$		0			0
$703$	4.67036	−	12.6942i	0.176146	−	0.478769i
$704$	39.0025			1.46996
$705$		0			0
$706$	2.51942	+	4.36377i	0.0948197	+	0.164232i
$707$	0.598941	−	1.03740i	0.0225255	−	0.0390153i
$708$		0			0
$709$	0.863639	−	1.49587i	0.0324346	−	0.0561784i	−0.849352	−	0.527826i	$-0.823007\pi$
$709$	0.863639	−	1.49587i	0.0324346	−	0.0561784i	0.881787	+	0.471648i	$0.156341\pi$
$710$	1.06251			0.0398753
$711$		0			0
$712$	−3.23667	+	5.60607i	−0.121299	+	0.210096i
$713$	−5.07496	+	8.79009i	−0.190059	+	0.329191i
$714$		0			0
$715$	−32.1796			−1.20345
$716$	13.5279	−	23.4311i	0.505563	−	0.875661i
$717$		0			0
$718$	−1.86494	+	3.23017i	−0.0695988	+	0.120549i
$719$	−10.6641	−	18.4708i	−0.397704	−	0.688843i	0.595739	−	0.803178i	$-0.296859\pi$
$719$	−10.6641	−	18.4708i	−0.397704	−	0.688843i	−0.993442	+	0.114336i	$0.963526\pi$
$720$		0			0
$721$	1.64187			0.0611463
$722$	−0.583320	+	3.17872i	−0.0217089	+	0.118300i
$723$		0			0
$724$	21.6242	+	37.4543i	0.803658	+	1.39198i
$725$	−0.525141	−	0.909571i	−0.0195032	−	0.0337806i
$726$		0			0
$727$	−9.58913	−	16.6089i	−0.355641	−	0.615989i	0.631586	−	0.775306i	$-0.282404\pi$
$727$	−9.58913	−	16.6089i	−0.355641	−	0.615989i	−0.987227	+	0.159317i	$0.949071\pi$
$728$	−0.445245	+	0.771186i	−0.0165019	+	0.0285821i
$729$		0			0
$730$	1.12785			0.0417435
$731$	−9.12344	+	15.8023i	−0.337443	+	0.584468i
$732$		0			0
$733$	2.72949			0.100816			0.0504079	−	0.998729i	$-0.483948\pi$
$733$	2.72949			0.100816			0.0504079	+	0.998729i	$0.483948\pi$
$734$	2.33814			0.0863022
$735$		0			0
$736$	−3.81967	−	6.61586i	−0.140795	−	0.243864i
$737$	−17.6064	+	30.4951i	−0.648539	+	1.12330i
$738$		0			0
$739$	−3.87026	−	6.70348i	−0.142370	−	0.246591i	0.786019	−	0.618203i	$-0.212139\pi$
$739$	−3.87026	−	6.70348i	−0.142370	−	0.246591i	−0.928389	+	0.371611i	$0.878806\pi$
$740$	−6.11640			−0.224843
$741$		0			0
$742$	0.191347			0.00702458
$743$	−21.6349	−	37.4727i	−0.793707	−	1.37474i	−0.923657	−	0.383220i	$-0.874815\pi$
$743$	−21.6349	−	37.4727i	−0.793707	−	1.37474i	0.129951	−	0.991520i	$-0.458518\pi$
$744$		0			0
$745$	8.59072	−	14.8796i	0.314740	−	0.545145i
$746$	1.94159	+	3.36293i	0.0710867	+	0.123126i
$747$		0			0
$748$	68.8579			2.51769
$749$	−2.44707			−0.0894141
$750$		0			0
$751$	19.9050	−	34.4766i	0.726346	−	1.25807i	−0.232072	−	0.972699i	$-0.574551\pi$
$751$	19.9050	−	34.4766i	0.726346	−	1.25807i	0.958418	−	0.285369i	$-0.0921161\pi$
$752$	32.6412			1.19030
$753$		0			0
$754$	−0.539023	+	0.933616i	−0.0196301	+	0.0340003i
$755$	10.2237	+	17.7080i	0.372080	+	0.644462i
$756$		0			0
$757$	−13.9025	−	24.0798i	−0.505294	−	0.875196i	−0.999981	−	0.00612436i	$-0.998051\pi$
$757$	−13.9025	−	24.0798i	−0.505294	−	0.875196i	0.494687	−	0.869071i	$-0.335283\pi$
$758$	−2.46584	−	4.27097i	−0.0895635	−	0.155129i
$759$		0			0
$760$	2.90128	−	0.501176i	0.105240	−	0.0181796i
$761$	−34.2239			−1.24061			−0.620307	−	0.784359i	$-0.712992\pi$
$761$	−34.2239			−1.24061			−0.620307	+	0.784359i	$0.712992\pi$
$762$		0			0
$763$	0.898876	+	1.55690i	0.0325415	+	0.0563635i
$764$	11.8243	−	20.4802i	0.427787	−	0.740948i
$765$		0			0
$766$	−2.22292	+	3.85021i	−0.0803174	+	0.139114i
$767$	71.8190			2.59323
$768$		0			0
$769$	−18.2857	+	31.6718i	−0.659401	+	1.14212i	0.321371	+	0.946954i	$0.395856\pi$
$769$	−18.2857	+	31.6718i	−0.659401	+	1.14212i	−0.980771	+	0.195162i	$0.937477\pi$
$770$	−0.0990808	+	0.171613i	−0.00357063	+	0.00618450i
$771$		0			0
$772$	−23.0135			−0.828274
$773$	16.0664	−	27.8278i	0.577868	−	1.00090i	−0.417856	−	0.908513i	$-0.637218\pi$
$773$	16.0664	−	27.8278i	0.577868	−	1.00090i	0.995724	−	0.0923831i	$-0.0294485\pi$
$774$		0			0
$775$	−1.32991	+	2.30346i	−0.0477716	+	0.0827429i
$776$	−5.37409	−	9.30819i	−0.192919	−	0.334145i
$777$		0			0
$778$	4.00499			0.143586
$779$	15.0344	−	2.59708i	0.538662	−	0.0930502i
$780$		0			0
$781$	16.6553	+	28.8478i	0.595973	+	1.03226i
$782$	−2.12611	−	3.68252i	−0.0760294	−	0.131687i
$783$		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)

\(f(q)\)	\(=\)	\(q+(-0.0850473 - 0.147306i) q^{2} +(0.985534 - 1.70699i) q^{4} +(-0.500000 - 0.866025i) q^{5} -0.218469 q^{7} -0.675457 q^{8} +O(q^{10})\)	\(q+(-0.0850473 - 0.147306i) q^{2} +(0.985534 - 1.70699i) q^{4} +(-0.500000 - 0.866025i) q^{5} -0.218469 q^{7} -0.675457 q^{8} +(-0.0850473 + 0.147306i) q^{10} -5.33261 q^{11} +(-3.01725 + 5.22603i) q^{13} +(0.0185802 + 0.0321818i) q^{14} +(-1.91362 - 3.31449i) q^{16} +(-3.27554 - 5.67340i) q^{17} +(1.50507 - 4.09082i) q^{19} -1.97107 q^{20} +(0.453524 + 0.785526i) q^{22} +(-1.90802 + 3.30478i) q^{23} +(-0.500000 + 0.866025i) q^{25} +1.02644 q^{26} +(-0.215309 + 0.372925i) q^{28} +(-0.525141 + 0.909571i) q^{29} +2.65981 q^{31} +(-1.00095 + 1.73370i) q^{32} +(-0.557151 + 0.965014i) q^{34} +(0.109234 + 0.189200i) q^{35} +3.10309 q^{37} +(-0.730604 + 0.126207i) q^{38} +(0.337729 + 0.584963i) q^{40} +(1.75010 + 3.03127i) q^{41} +(-1.39266 - 2.41216i) q^{43} +(-5.25546 + 9.10273i) q^{44} +0.649086 q^{46} +(-4.26432 + 7.38603i) q^{47} -6.95227 q^{49} +0.170095 q^{50} +(5.94720 + 10.3009i) q^{52} +(2.57461 - 4.45936i) q^{53} +(2.66630 + 4.61817i) q^{55} +0.147566 q^{56} +0.178647 q^{58} +(-5.95070 - 10.3069i) q^{59} +(2.25799 - 3.91096i) q^{61} +(-0.226210 - 0.391807i) q^{62} -7.31397 q^{64} +6.03450 q^{65} +(3.30165 - 5.71862i) q^{67} -12.9126 q^{68} +(0.0185802 - 0.0321818i) q^{70} +(-3.12329 - 5.40970i) q^{71} +(-3.31536 - 5.74237i) q^{73} +(-0.263909 - 0.457104i) q^{74} +(-5.49971 - 6.60078i) q^{76} +1.16501 q^{77} +(-1.80793 - 3.13143i) q^{79} +(-1.91362 + 3.31449i) q^{80} +(0.297683 - 0.515602i) q^{82} +8.39679 q^{83} +(-3.27554 + 5.67340i) q^{85} +(-0.236884 + 0.410296i) q^{86} +3.60195 q^{88} +(4.79182 - 8.29967i) q^{89} +(0.659175 - 1.14172i) q^{91} +(3.76083 + 6.51394i) q^{92} +1.45068 q^{94} +(-4.29528 + 0.741981i) q^{95} +(7.95622 + 13.7806i) q^{97} +(0.591272 + 1.02411i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 5 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8}+O(q^{10}) \) 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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