LMFDB - Embedded newform 855.2.k.g.676.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("855.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.3518667.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 7x^{4} - 8x^{3} + 43x^{2} - 42x + 49 $ x^6 - x^5 + 7x^4 - 8x^3 + 43x^2 - 42x + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			676.3
Root			$1.14257 - 1.97899i$ of defining polynomial
Character	$\chi$	$=$	855.676
Dual form			855.2.k.g.406.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14257 - 1.97899i) q^{2} +(-1.61094 - 2.79023i) q^{4} +(-0.500000 + 0.866025i) q^{5} +3.50702 q^{7} -2.79216 q^{8} +O(q^{10})$	\(q+(1.14257 - 1.97899i) q^{2} +(-1.61094 - 2.79023i) q^{4} +(-0.500000 + 0.866025i) q^{5} +3.50702 q^{7} -2.79216 q^{8} +(1.14257 + 1.97899i) q^{10} +4.50702 q^{11} +(2.50000 + 4.33013i) q^{13} +(4.00702 - 6.94036i) q^{14} +(0.0316332 - 0.0547902i) q^{16} +(0.0793049 - 0.137360i) q^{17} +(-4.26053 + 0.920816i) q^{19} +3.22188 q^{20} +(5.14959 - 8.91935i) q^{22} +(0.579305 + 1.00339i) q^{23} +(-0.500000 - 0.866025i) q^{25} +11.4257 q^{26} +(-5.64959 - 9.78538i) q^{28} +(-1.75351 - 3.03717i) q^{29} -2.28514 q^{31} +(-2.86445 - 4.96137i) q^{32} +(-0.181223 - 0.313888i) q^{34} +(-1.75351 + 3.03717i) q^{35} -10.9648 q^{37} +(-3.04567 + 9.48365i) q^{38} +(1.39608 - 2.41808i) q^{40} +(3.03865 - 5.26310i) q^{41} +(1.67420 - 2.89981i) q^{43} +(-7.26053 - 12.5756i) q^{44} +2.64759 q^{46} +(1.53163 + 2.65287i) q^{47} +5.29918 q^{49} -2.28514 q^{50} +(8.05469 - 13.9511i) q^{52} +(-2.87147 - 4.97353i) q^{53} +(-2.25351 + 3.90319i) q^{55} -9.79216 q^{56} -8.01404 q^{58} +(1.53163 - 2.65287i) q^{59} +(0.436734 + 0.756445i) q^{61} +(-2.61094 + 4.52228i) q^{62} -12.9648 q^{64} -5.00000 q^{65} +(4.22188 + 7.31250i) q^{67} -0.511021 q^{68} +(4.00702 + 6.94036i) q^{70} +(-8.11796 + 14.0607i) q^{71} +(3.57930 - 6.19954i) q^{73} +(-12.5281 + 21.6993i) q^{74} +(9.43273 + 10.4045i) q^{76} +15.8062 q^{77} +(5.06327 - 8.76983i) q^{79} +(0.0316332 + 0.0547902i) q^{80} +(-6.94375 - 12.0269i) q^{82} -4.85543 q^{83} +(0.0793049 + 0.137360i) q^{85} +(-3.82580 - 6.62647i) q^{86} -12.5843 q^{88} +(-0.556248 - 0.963449i) q^{89} +(8.76755 + 15.1858i) q^{91} +(1.86645 - 3.23278i) q^{92} +7.00000 q^{94} +(1.33281 - 4.15013i) q^{95} +(-0.809757 + 1.40254i) q^{97} +(6.05469 - 10.4870i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 7 q^{4} - 3 q^{5} + 4 q^{7} + 12 q^{8}+O(q^{10}) $ 6 * q + q^2 - 7 * q^4 - 3 * q^5 + 4 * q^7 + 12 * q^8	$ 6 q + q^{2} - 7 q^{4} - 3 q^{5} + 4 q^{7} + 12 q^{8} + q^{10} + 10 q^{11} + 15 q^{13} + 7 q^{14} - 3 q^{16} + q^{17} + 14 q^{20} + 8 q^{22} + 4 q^{23} - 3 q^{25} + 10 q^{26} - 11 q^{28} - 2 q^{29} - 2 q^{31} - 6 q^{32} + 25 q^{34} - 2 q^{35} - 4 q^{37} + 19 q^{38} - 6 q^{40} - 2 q^{41} + q^{43} - 18 q^{44} - 48 q^{46} + 6 q^{47} - 14 q^{49} - 2 q^{50} + 35 q^{52} + 11 q^{53} - 5 q^{55} - 30 q^{56} - 14 q^{58} + 6 q^{59} + 9 q^{61} - 13 q^{62} - 16 q^{64} - 30 q^{65} + 20 q^{67} - 68 q^{68} + 7 q^{70} - 29 q^{71} + 22 q^{73} - 7 q^{74} - 19 q^{76} + 32 q^{77} + 24 q^{79} - 3 q^{80} - 31 q^{82} + 6 q^{83} + q^{85} - 32 q^{86} - 18 q^{88} - 14 q^{89} + 10 q^{91} + 41 q^{92} + 42 q^{94} - 7 q^{97} + 23 q^{98}+O(q^{100}) $ 6 * q + q^2 - 7 * q^4 - 3 * q^5 + 4 * q^7 + 12 * q^8 + q^10 + 10 * q^11 + 15 * q^13 + 7 * q^14 - 3 * q^16 + q^17 + 14 * q^20 + 8 * q^22 + 4 * q^23 - 3 * q^25 + 10 * q^26 - 11 * q^28 - 2 * q^29 - 2 * q^31 - 6 * q^32 + 25 * q^34 - 2 * q^35 - 4 * q^37 + 19 * q^38 - 6 * q^40 - 2 * q^41 + q^43 - 18 * q^44 - 48 * q^46 + 6 * q^47 - 14 * q^49 - 2 * q^50 + 35 * q^52 + 11 * q^53 - 5 * q^55 - 30 * q^56 - 14 * q^58 + 6 * q^59 + 9 * q^61 - 13 * q^62 - 16 * q^64 - 30 * q^65 + 20 * q^67 - 68 * q^68 + 7 * q^70 - 29 * q^71 + 22 * q^73 - 7 * q^74 - 19 * q^76 + 32 * q^77 + 24 * q^79 - 3 * q^80 - 31 * q^82 + 6 * q^83 + q^85 - 32 * q^86 - 18 * q^88 - 14 * q^89 + 10 * q^91 + 41 * q^92 + 42 * q^94 - 7 * q^97 + 23 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.14257	−	1.97899i	0.807920	−	1.39936i	−0.106382	−	0.994325i	$-0.533927\pi$
$2$	1.14257	−	1.97899i	0.807920	−	1.39936i	0.914302	−	0.405033i	$-0.132740\pi$
$3$		0			0
$3$		0			0
$4$	−1.61094	−	2.79023i	−0.805469	−	1.39511i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	3.50702			1.32553			0.662764	−	0.748828i	$-0.269383\pi$
$7$	3.50702			1.32553			0.662764	+	0.748828i	$0.269383\pi$
$8$	−2.79216			−0.987178
$9$		0			0
$10$	1.14257	+	1.97899i	0.361313	+	0.625812i
$11$	4.50702			1.35892			0.679459	−	0.733714i	$-0.262215\pi$
$11$	4.50702			1.35892			0.679459	+	0.733714i	$0.262215\pi$
$12$		0			0
$13$	2.50000	+	4.33013i	0.693375	+	1.20096i	0.970725	+	0.240192i	$0.0772105\pi$
$13$	2.50000	+	4.33013i	0.693375	+	1.20096i	−0.277350	+	0.960769i	$0.589456\pi$
$14$	4.00702	−	6.94036i	1.07092	−	1.85489i
$15$		0			0
$16$	0.0316332	−	0.0547902i	0.00790829	−	0.0136976i
$17$	0.0793049	−	0.137360i	0.0192343	−	0.0333147i	−0.856248	−	0.516565i	$-0.827210\pi$
$17$	0.0793049	−	0.137360i	0.0192343	−	0.0333147i	0.875482	+	0.483250i	$0.160544\pi$
$18$		0			0
$19$	−4.26053	+	0.920816i	−0.977432	+	0.211250i
$19$	−4.26053	+	0.920816i	−0.977432	+	0.211250i
$20$	3.22188			0.720433
$21$		0			0
$22$	5.14959	−	8.91935i	1.09790	−	1.90161i
$23$	0.579305	+	1.00339i	0.120793	+	0.209220i	0.920081	−	0.391729i	$-0.128123\pi$
$23$	0.579305	+	1.00339i	0.120793	+	0.209220i	−0.799287	+	0.600949i	$0.794789\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	11.4257			2.24077
$27$		0			0
$28$	−5.64959	−	9.78538i	−1.06767	−	1.84926i
$29$	−1.75351	−	3.03717i	−0.325619	−	0.563988i	0.656019	−	0.754745i	$-0.272239\pi$
$29$	−1.75351	−	3.03717i	−0.325619	−	0.563988i	−0.981637	+	0.190757i	$0.938906\pi$
$30$		0			0
$31$	−2.28514			−0.410424			−0.205212	−	0.978718i	$-0.565788\pi$
$31$	−2.28514			−0.410424			−0.205212	+	0.978718i	$0.565788\pi$
$32$	−2.86445	−	4.96137i	−0.506368	−	0.877054i
$33$		0			0
$34$	−0.181223	−	0.313888i	−0.0310795	−	0.0538313i
$35$	−1.75351	+	3.03717i	−0.296397	+	0.513375i
$36$		0			0
$37$	−10.9648			−1.80260			−0.901302	−	0.433192i	$-0.857387\pi$
$37$	−10.9648			−1.80260			−0.901302	+	0.433192i	$0.857387\pi$
$38$	−3.04567	+	9.48365i	−0.494073	+	1.53845i
$39$		0			0
$40$	1.39608	−	2.41808i	0.220740	−	0.382332i
$41$	3.03865	−	5.26310i	0.474558	−	0.821958i	−0.525018	−	0.851091i	$-0.675941\pi$
$41$	3.03865	−	5.26310i	0.474558	−	0.821958i	0.999576	+	0.0291332i	$0.00927470\pi$
$42$		0			0
$43$	1.67420	−	2.89981i	0.255314	−	0.442216i	−0.709667	−	0.704537i	$-0.751155\pi$
$43$	1.67420	−	2.89981i	0.255314	−	0.442216i	0.964981	+	0.262321i	$0.0844879\pi$
$44$	−7.26053	−	12.5756i	−1.09457	−	1.89584i
$45$		0			0
$46$	2.64759			0.390366
$47$	1.53163	+	2.65287i	0.223412	+	0.386960i	0.955842	−	0.293882i	$-0.0949472\pi$
$47$	1.53163	+	2.65287i	0.223412	+	0.386960i	−0.732430	+	0.680842i	$0.761614\pi$
$48$		0			0
$49$	5.29918			0.757026
$50$	−2.28514			−0.323168
$51$		0			0
$52$	8.05469	−	13.9511i	1.11698	−	1.93467i
$53$	−2.87147	−	4.97353i	−0.394426	−	0.683166i	0.598602	−	0.801047i	$-0.295723\pi$
$53$	−2.87147	−	4.97353i	−0.394426	−	0.683166i	−0.993028	+	0.117881i	$0.962390\pi$
$54$		0			0
$55$	−2.25351	+	3.90319i	−0.303863	+	0.526306i
$56$	−9.79216			−1.30853
$57$		0			0
$58$	−8.01404			−1.05229
$59$	1.53163	−	2.65287i	0.199402	−	0.345374i	−0.748933	−	0.662646i	$-0.769433\pi$
$59$	1.53163	−	2.65287i	0.199402	−	0.345374i	0.948335	+	0.317272i	$0.102767\pi$
$60$		0			0
$61$	0.436734	+	0.756445i	0.0559180	+	0.0968528i	0.892629	−	0.450791i	$-0.148858\pi$
$61$	0.436734	+	0.756445i	0.0559180	+	0.0968528i	−0.836711	+	0.547644i	$0.815525\pi$
$62$	−2.61094	+	4.52228i	−0.331589	+	0.574330i
$63$		0			0
$64$	−12.9648			−1.62060
$65$	−5.00000			−0.620174
$66$		0			0
$67$	4.22188	+	7.31250i	0.515784	+	0.893365i	0.999832	+	0.0183230i	$0.00583273\pi$
$67$	4.22188	+	7.31250i	0.515784	+	0.893365i	−0.484048	+	0.875042i	$0.660834\pi$
$68$	−0.511021			−0.0619704
$69$		0			0
$70$	4.00702	+	6.94036i	0.478930	+	0.829532i
$71$	−8.11796	+	14.0607i	−0.963424	+	1.66870i	−0.249634	+	0.968340i	$0.580310\pi$
$71$	−8.11796	+	14.0607i	−0.963424	+	1.66870i	−0.713790	+	0.700359i	$0.753023\pi$
$72$		0			0
$73$	3.57930	−	6.19954i	0.418926	−	0.725601i	−0.576906	−	0.816811i	$-0.695740\pi$
$73$	3.57930	−	6.19954i	0.418926	−	0.725601i	0.995832	+	0.0912097i	$0.0290733\pi$
$74$	−12.5281	+	21.6993i	−1.45636	+	2.52249i
$75$		0			0
$76$	9.43273	+	10.4045i	1.08201	+	1.19347i
$77$	15.8062			1.80128
$78$		0			0
$79$	5.06327	−	8.76983i	0.569662	−	0.986683i	−0.426937	−	0.904281i	$-0.640407\pi$
$79$	5.06327	−	8.76983i	0.569662	−	0.986683i	0.996599	−	0.0824022i	$-0.0262592\pi$
$80$	0.0316332	+	0.0547902i	0.00353669	+	0.00612574i
$81$		0			0
$82$	−6.94375	−	12.0269i	−0.766809	−	1.32815i
$83$	−4.85543			−0.532952			−0.266476	−	0.963841i	$-0.585859\pi$
$83$	−4.85543			−0.532952			−0.266476	+	0.963841i	$0.585859\pi$
$84$		0			0
$85$	0.0793049	+	0.137360i	0.00860183	+	0.0148988i
$86$	−3.82580	−	6.62647i	−0.412546	−	0.714551i
$87$		0			0
$88$	−12.5843			−1.34149
$89$	−0.556248	−	0.963449i	−0.0589621	−	0.102125i	0.835038	−	0.550193i	$-0.185446\pi$
$89$	−0.556248	−	0.963449i	−0.0589621	−	0.102125i	−0.894000	+	0.448067i	$0.852112\pi$
$90$		0			0
$91$	8.76755	+	15.1858i	0.919089	+	1.59191i
$92$	1.86645	−	3.23278i	0.194591	−	0.337041i
$93$		0			0
$94$	7.00000			0.721995
$95$	1.33281	−	4.15013i	0.136744	−	0.425795i
$96$		0			0
$97$	−0.809757	+	1.40254i	−0.0822184	+	0.142406i	−0.904203	−	0.427104i	$-0.859534\pi$
$97$	−0.809757	+	1.40254i	−0.0822184	+	0.142406i	0.821984	+	0.569510i	$0.192867\pi$
$98$	6.05469	−	10.4870i	0.611616	−	1.05935i
$99$		0			0
$100$	−1.61094	+	2.79023i	−0.161094	+	0.279023i
$101$	6.15661	+	10.6636i	0.612605	+	1.06106i	0.990800	+	0.135337i	$0.0432118\pi$
$101$	6.15661	+	10.6636i	0.612605	+	1.06106i	−0.378194	+	0.925726i	$0.623455\pi$
$102$		0			0
$103$	10.6164			1.04606			0.523032	−	0.852313i	$-0.324801\pi$
$103$	10.6164			1.04606			0.523032	+	0.852313i	$0.324801\pi$
$104$	−6.98040	−	12.0904i	−0.684485	−	1.18556i
$105$		0			0
$106$	−13.1234			−1.27466
$107$	2.17265			0.210038			0.105019	−	0.994470i	$-0.466510\pi$
$107$	2.17265			0.210038			0.105019	+	0.994470i	$0.466510\pi$
$108$		0			0
$109$	−7.91012	+	13.7007i	−0.757652	+	1.31229i	0.186393	+	0.982475i	$0.440320\pi$
$109$	−7.91012	+	13.7007i	−0.757652	+	1.31229i	−0.944045	+	0.329816i	$0.893013\pi$
$110$	5.14959	+	8.91935i	0.490994	+	0.850427i
$111$		0			0
$112$	0.110938	−	0.192150i	0.0104827	−	0.0181565i
$113$	−9.83828			−0.925507			−0.462754	−	0.886487i	$-0.653139\pi$
$113$	−9.83828			−0.925507			−0.462754	+	0.886487i	$0.653139\pi$
$114$		0			0
$115$	−1.15861			−0.108041
$116$	−5.64959	+	9.78538i	−0.524551	+	0.908549i
$117$		0			0
$118$	−3.50000	−	6.06218i	−0.322201	−	0.558069i
$119$	0.278124	−	0.481725i	0.0254956	−	0.0441596i
$120$		0			0
$121$	9.31322			0.846656
$122$	1.99600			0.180709
$123$		0			0
$124$	3.68122	+	6.37607i	0.330584	+	0.572588i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−7.85543	−	13.6060i	−0.697056	−	1.20734i	−0.969483	−	0.245160i	$-0.921159\pi$
$127$	−7.85543	−	13.6060i	−0.697056	−	1.20734i	0.272426	−	0.962177i	$-0.412174\pi$
$128$	−9.08432	+	15.7345i	−0.802948	+	1.39075i
$129$		0			0
$130$	−5.71286	+	9.89496i	−0.501051	+	0.867845i
$131$	−5.76755	+	9.98968i	−0.503913	+	0.872803i	0.496077	+	0.868279i	$0.334773\pi$
$131$	−5.76755	+	9.98968i	−0.503913	+	0.872803i	−0.999990	+	0.00452412i	$0.998560\pi$
$132$		0			0
$133$	−14.9418	+	3.22932i	−1.29561	+	0.280017i
$134$	19.2952			1.66685
$135$		0			0
$136$	−0.221432	+	0.383532i	−0.0189876	+	0.0328876i
$137$	0.0546904	+	0.0947266i	0.00467252	+	0.00809304i	0.868352	−	0.495948i	$-0.165179\pi$
$137$	0.0546904	+	0.0947266i	0.00467252	+	0.00809304i	−0.863680	+	0.504041i	$0.831846\pi$
$138$		0			0
$139$	−0.721876	−	1.25033i	−0.0612287	−	0.106051i	0.833786	−	0.552088i	$-0.186169\pi$
$139$	−0.721876	−	1.25033i	−0.0612287	−	0.106051i	−0.895015	+	0.446036i	$0.852835\pi$
$140$	11.2992			0.954955
$141$		0			0
$142$	18.5507	+	32.1307i	1.55674	+	2.69635i
$143$	11.2675	+	19.5160i	0.942240	+	1.63201i
$144$		0			0
$145$	3.50702			0.291242
$146$	−8.17922	−	14.1668i	−0.676917	−	1.17245i
$147$		0			0
$148$	17.6636	+	30.5943i	1.45194	+	2.51484i
$149$	0.864447	−	1.49727i	0.0708183	−	0.122661i	−0.828442	−	0.560075i	$-0.810772\pi$
$149$	0.864447	−	1.49727i	0.0708183	−	0.122661i	0.899260	+	0.437414i	$0.144106\pi$
$150$		0			0
$151$	−20.1406			−1.63902			−0.819508	−	0.573068i	$-0.805753\pi$
$151$	−20.1406			−1.63902			−0.819508	+	0.573068i	$0.805753\pi$
$152$	11.8961	−	2.57107i	0.964900	−	0.208541i
$153$		0			0
$154$	18.0597	−	31.2803i	1.45529	−	2.52064i
$155$	1.14257	−	1.97899i	0.0917735	−	0.158956i
$156$		0			0
$157$	−1.88906	+	3.27195i	−0.150764	+	0.261130i	−0.931508	−	0.363720i	$-0.881507\pi$
$157$	−1.88906	+	3.27195i	−0.150764	+	0.261130i	0.780745	+	0.624850i	$0.214840\pi$
$158$	−11.5703	−	20.0403i	−0.920482	−	1.59432i
$159$		0			0
$160$	5.72889			0.452909
$161$	2.03163	+	3.51889i	0.160115	+	0.277328i
$162$		0			0
$163$	−1.61640			−0.126606			−0.0633031	−	0.997994i	$-0.520163\pi$
$163$	−1.61640			−0.126606			−0.0633031	+	0.997994i	$0.520163\pi$
$164$	−19.5803			−1.52897
$165$		0			0
$166$	−5.54767	+	9.60885i	−0.430583	+	0.745791i
$167$	3.24649	+	5.62309i	0.251221	+	0.435128i	0.963862	−	0.266401i	$-0.0858346\pi$
$167$	3.24649	+	5.62309i	0.251221	+	0.435128i	−0.712641	+	0.701529i	$0.752501\pi$
$168$		0			0
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$	0.362446			0.0277983
$171$		0			0
$172$	−10.7882			−0.822589
$173$	4.26053	−	7.37945i	0.323922	−	0.561049i	−0.657372	−	0.753567i	$-0.728332\pi$
$173$	4.26053	−	7.37945i	0.323922	−	0.561049i	0.981294	+	0.192517i	$0.0616651\pi$
$174$		0			0
$175$	−1.75351	−	3.03717i	−0.132553	−	0.229588i
$176$	0.142571	−	0.246941i	0.0107467	−	0.0186139i
$177$		0			0
$178$	−2.54221			−0.190547
$179$	10.2711			0.767698			0.383849	−	0.923396i	$-0.374598\pi$
$179$	10.2711			0.767698			0.383849	+	0.923396i	$0.374598\pi$
$180$		0			0
$181$	−6.13355	−	10.6236i	−0.455903	−	0.789648i	0.542836	−	0.839838i	$-0.317350\pi$
$181$	−6.13355	−	10.6236i	−0.455903	−	0.789648i	−0.998740	+	0.0501908i	$0.984017\pi$
$182$	40.0702			2.97020
$183$		0			0
$184$	−1.61751	−	2.80161i	−0.119245	−	0.206538i
$185$	5.48240	−	9.49580i	0.403074	−	0.698145i
$186$		0			0
$187$	0.357429	−	0.619085i	0.0261378	−	0.0452720i
$188$	4.93473	−	8.54721i	0.359902	−	0.623369i
$189$		0			0
$190$	−6.69024	−	7.37945i	−0.485361	−	0.535362i
$191$	−5.71085			−0.413223			−0.206611	−	0.978423i	$-0.566244\pi$
$191$	−5.71085			−0.413223			−0.206611	+	0.978423i	$0.566244\pi$
$192$		0			0
$193$	5.07930	−	8.79761i	0.365616	−	0.633266i	−0.623259	−	0.782016i	$-0.714192\pi$
$193$	5.07930	−	8.79761i	0.365616	−	0.633266i	0.988875	+	0.148750i	$0.0475249\pi$
$194$	1.85041	+	3.20500i	0.132852	+	0.230106i
$195$		0			0
$196$	−8.53665	−	14.7859i	−0.609761	−	1.05614i
$197$	−16.2038			−1.15448			−0.577238	−	0.816576i	$-0.695869\pi$
$197$	−16.2038			−1.15448			−0.577238	+	0.816576i	$0.695869\pi$
$198$		0			0
$199$	−0.167186	−	0.289574i	−0.0118515	−	0.0205274i	0.860039	−	0.510229i	$-0.170439\pi$
$199$	−0.167186	−	0.289574i	−0.0118515	−	0.0205274i	−0.871890	+	0.489701i	$0.837106\pi$
$200$	1.39608	+	2.41808i	0.0987178	+	0.170984i
$201$		0			0
$202$	28.1375			1.97974
$203$	−6.14959	−	10.6514i	−0.431617	−	0.747582i
$204$		0			0
$205$	3.03865	+	5.26310i	0.212229	+	0.367591i
$206$	12.1300	−	21.0098i	0.845137	−	1.46382i
$207$		0			0
$208$	0.316332			0.0219336
$209$	−19.2023	+	4.15013i	−1.32825	+	0.287071i
$210$		0			0
$211$	−1.01404	+	1.75636i	−0.0698092	+	0.120913i	−0.898817	−	0.438324i	$-0.855572\pi$
$211$	−1.01404	+	1.75636i	−0.0698092	+	0.120913i	0.829008	+	0.559237i	$0.188906\pi$
$212$	−9.25151	+	16.0241i	−0.635396	+	1.10054i
$213$		0			0
$214$	2.48240	−	4.29965i	0.169694	−	0.293918i
$215$	1.67420	+	2.89981i	0.114180	+	0.197765i
$216$		0			0
$217$	−8.01404			−0.544028
$218$	18.0757	+	31.3081i	1.22424	+	2.12045i
$219$		0			0
$220$	14.5211			0.979009
$221$	0.793049			0.0533463
$222$		0			0
$223$	9.61596	−	16.6553i	0.643932	−	1.11532i	−0.340615	−	0.940203i	$-0.610635\pi$
$223$	9.61596	−	16.6553i	0.643932	−	1.11532i	0.984547	−	0.175120i	$-0.0560314\pi$
$224$	−10.0457	−	17.3996i	−0.671205	−	1.16256i
$225$		0			0
$226$	−11.2409	+	19.4699i	−0.747736	+	1.29512i
$227$	−4.00000			−0.265489			−0.132745	−	0.991150i	$-0.542379\pi$
$227$	−4.00000			−0.265489			−0.132745	+	0.991150i	$0.542379\pi$
$228$		0			0
$229$	−12.9788			−0.857666			−0.428833	−	0.903384i	$-0.641075\pi$
$229$	−12.9788			−0.857666			−0.428833	+	0.903384i	$0.641075\pi$
$230$	−1.32379	+	2.29288i	−0.0872884	+	0.151188i
$231$		0			0
$232$	4.89608	+	8.48026i	0.321443	+	0.556756i
$233$	13.5367	−	23.4462i	0.886815	−	1.53601i	0.0431968	−	0.999067i	$-0.486246\pi$
$233$	13.5367	−	23.4462i	0.886815	−	1.53601i	0.843619	−	0.536943i	$-0.180421\pi$
$234$		0			0
$235$	−3.06327			−0.199825
$236$	−9.86946			−0.642447
$237$		0			0
$238$	−0.635553	−	1.10081i	−0.0411968	−	0.0713549i
$239$	−20.0602			−1.29758			−0.648792	−	0.760966i	$-0.724725\pi$
$239$	−20.0602			−1.29758			−0.648792	+	0.760966i	$0.724725\pi$
$240$		0			0
$241$	10.7922	+	18.6926i	0.695184	+	1.20409i	0.970119	+	0.242631i	$0.0780105\pi$
$241$	10.7922	+	18.6926i	0.695184	+	1.20409i	−0.274934	+	0.961463i	$0.588656\pi$
$242$	10.6410	−	18.4308i	0.684030	−	1.18478i
$243$		0			0
$244$	1.40710	−	2.43717i	0.0900805	−	0.156024i
$245$	−2.64959	+	4.58922i	−0.169276	+	0.293195i
$246$		0			0
$247$	−14.6386	−	16.1466i	−0.931430	−	1.02738i
$248$	6.38049			0.405161
$249$		0			0
$250$	1.14257	−	1.97899i	0.0722626	−	0.125162i
$251$	−3.63400	−	6.29426i	−0.229376	−	0.397290i	0.728248	−	0.685314i	$-0.240335\pi$
$251$	−3.63400	−	6.29426i	−0.229376	−	0.397290i	−0.957623	+	0.288024i	$0.907002\pi$
$252$		0			0
$253$	2.61094	+	4.52228i	0.164148	+	0.284313i
$254$	−35.9015			−2.25266
$255$		0			0
$256$	7.79416	+	13.4999i	0.487135	+	0.843743i
$257$	7.53865	+	13.0573i	0.470248	+	0.814494i	0.999421	−	0.0340202i	$-0.0108311\pi$
$257$	7.53865	+	13.0573i	0.470248	+	0.814494i	−0.529173	+	0.848514i	$0.677498\pi$
$258$		0			0
$259$	−38.4538			−2.38940
$260$	8.05469	+	13.9511i	0.499531	+	0.865213i
$261$		0			0
$262$	13.1797	+	22.8279i	0.814242	+	1.41031i
$263$	10.0773	−	17.4544i	0.621393	−	1.07628i	−0.367833	−	0.929892i	$-0.619900\pi$
$263$	10.0773	−	17.4544i	0.621393	−	1.07628i	0.989227	−	0.146393i	$-0.0467663\pi$
$264$		0			0
$265$	5.74293			0.352786
$266$	−10.6812	+	33.2593i	−0.654908	+	2.03926i
$267$		0			0
$268$	13.6024	−	23.5600i	0.830897	−	1.43915i
$269$	−3.86245	+	6.68995i	−0.235497	+	0.407894i	−0.959417	−	0.281991i	$-0.909005\pi$
$269$	−3.86245	+	6.68995i	−0.235497	+	0.407894i	0.723920	+	0.689884i	$0.242339\pi$
$270$		0			0
$271$	2.64257	−	4.57707i	0.160525	−	0.278037i	−0.774532	−	0.632534i	$-0.782015\pi$
$271$	2.64257	−	4.57707i	0.160525	−	0.278037i	0.935057	+	0.354497i	$0.115348\pi$
$272$	−0.00501733	−	0.00869027i	−0.000304220	−	0.000526925i
$273$		0			0
$274$	0.249951			0.0151001
$275$	−2.25351	−	3.90319i	−0.135892	−	0.235371i
$276$		0			0
$277$	30.6264			1.84016			0.920082	−	0.391726i	$-0.128122\pi$
$277$	30.6264			1.84016			0.920082	+	0.391726i	$0.128122\pi$
$278$	−3.29918			−0.197872
$279$		0			0
$280$	4.89608	−	8.48026i	0.292597	−	0.506792i
$281$	6.68122	+	11.5722i	0.398568	+	0.690341i	0.993550	−	0.113399i	$-0.0361738\pi$
$281$	6.68122	+	11.5722i	0.398568	+	0.690341i	−0.594981	+	0.803740i	$0.702841\pi$
$282$		0			0
$283$	−2.04767	+	3.54667i	−0.121721	+	0.210828i	−0.920447	−	0.390868i	$-0.872175\pi$
$283$	−2.04767	+	3.54667i	−0.121721	+	0.210828i	0.798725	+	0.601696i	$0.205508\pi$
$284$	52.3101			3.10403
$285$		0			0
$286$	51.4959			3.04502
$287$	10.6566	−	18.4578i	0.629040	−	1.08953i
$288$		0			0
$289$	8.48742	+	14.7006i	0.499260	+	0.864744i
$290$	4.00702	−	6.94036i	0.235300	−	0.407552i
$291$		0			0
$292$	−23.0642			−1.34973
$293$	−12.1726			−0.711134			−0.355567	−	0.934651i	$-0.615712\pi$
$293$	−12.1726			−0.711134			−0.355567	+	0.934651i	$0.615712\pi$
$294$		0			0
$295$	1.53163	+	2.65287i	0.0891751	+	0.154456i
$296$	30.6155			1.77949
$297$		0			0
$298$	−1.97539	−	3.42147i	−0.114431	−	0.198200i
$299$	−2.89652	+	5.01693i	−0.167510	+	0.290136i
$300$		0			0
$301$	5.87147	−	10.1697i	0.338426	−	0.586170i
$302$	−23.0120	+	39.8580i	−1.32419	+	2.29357i
$303$		0			0
$304$	−0.0843223	+	0.262564i	−0.00483621	+	0.0150591i
$305$	−0.873467			−0.0500146
$306$		0			0
$307$	−12.2675	+	21.2480i	−0.700146	+	1.21269i	0.268269	+	0.963344i	$0.413548\pi$
$307$	−12.2675	+	21.2480i	−0.700146	+	1.21269i	−0.968415	+	0.249344i	$0.919785\pi$
$308$	−25.4628	−	44.1029i	−1.45088	−	2.51299i
$309$		0			0
$310$	−2.61094	−	4.52228i	−0.148291	−	0.256848i
$311$	10.2038			0.578606			0.289303	−	0.957238i	$-0.406576\pi$
$311$	10.2038			0.578606			0.289303	+	0.957238i	$0.406576\pi$
$312$		0			0
$313$	15.9910	+	27.6972i	0.903864	+	1.56554i	0.822435	+	0.568859i	$0.192615\pi$
$313$	15.9910	+	27.6972i	0.903864	+	1.56554i	0.0814282	+	0.996679i	$0.474052\pi$
$314$	4.31678	+	7.47687i	0.243610	+	0.421944i
$315$		0			0
$316$	−32.6264			−1.83538
$317$	1.11796	+	1.93636i	0.0627907	+	0.108757i	0.895712	−	0.444635i	$-0.146667\pi$
$317$	1.11796	+	1.93636i	0.0627907	+	0.108757i	−0.832921	+	0.553392i	$0.813333\pi$
$318$		0			0
$319$	−7.90310	−	13.6886i	−0.442489	−	0.766413i
$320$	6.48240	−	11.2279i	0.362377	−	0.627656i
$321$		0			0
$322$	9.28514			0.517441
$323$	−0.211397	+	0.658252i	−0.0117625	+	0.0366261i
$324$		0			0
$325$	2.50000	−	4.33013i	0.138675	−	0.240192i
$326$	−1.84685	+	3.19884i	−0.102288	+	0.177167i
$327$		0			0
$328$	−8.48441	+	14.6954i	−0.468473	+	0.811419i
$329$	5.37147	+	9.30365i	0.296139	+	0.512927i
$330$		0			0
$331$	−10.0913			−0.554670			−0.277335	−	0.960773i	$-0.589451\pi$
$331$	−10.0913			−0.554670			−0.277335	+	0.960773i	$0.589451\pi$
$332$	7.82179	+	13.5477i	0.429277	+	0.743529i
$333$		0			0
$334$	14.8374			0.811866
$335$	−8.44375			−0.461331
$336$		0			0
$337$	−2.80620	+	4.86048i	−0.152863	+	0.264767i	−0.932279	−	0.361740i	$-0.882183\pi$
$337$	−2.80620	+	4.86048i	−0.152863	+	0.264767i	0.779416	+	0.626507i	$0.215516\pi$
$338$	13.7109	+	23.7479i	0.745772	+	1.29172i
$339$		0			0
$340$	0.255511	−	0.442557i	0.0138570	−	0.0240010i
$341$	−10.2992			−0.557732
$342$		0			0
$343$	−5.96481			−0.322069
$344$	−4.67465	+	8.09673i	−0.252040	+	0.436546i
$345$		0			0
$346$	−9.73591	−	16.8631i	−0.523406	−	0.906566i
$347$	2.73747	−	4.74144i	0.146955	−	0.254534i	−0.783146	−	0.621838i	$-0.786386\pi$
$347$	2.73747	−	4.74144i	0.146955	−	0.254534i	0.930101	+	0.367305i	$0.119719\pi$
$348$		0			0
$349$	−18.8202			−1.00742			−0.503712	−	0.863872i	$-0.668033\pi$
$349$	−18.8202			−1.00742			−0.503712	+	0.863872i	$0.668033\pi$
$350$	−8.01404			−0.428368
$351$		0			0
$352$	−12.9101	−	22.3610i	−0.688112	−	1.19184i
$353$	12.7008			0.675996			0.337998	−	0.941147i	$-0.390250\pi$
$353$	12.7008			0.675996			0.337998	+	0.941147i	$0.390250\pi$
$354$		0			0
$355$	−8.11796	−	14.0607i	−0.430856	−	0.746265i
$356$	−1.79216	+	3.10411i	−0.0949843	+	0.164518i
$357$		0			0
$358$	11.7355	−	20.3264i	0.620239	−	1.07429i
$359$	−5.54021	+	9.59592i	−0.292401	+	0.506453i	−0.974377	−	0.224921i	$-0.927788\pi$
$359$	−5.54021	+	9.59592i	−0.292401	+	0.506453i	0.681976	+	0.731375i	$0.261121\pi$
$360$		0			0
$361$	17.3042	−	7.84632i	0.910747	−	0.412964i
$362$	−28.0321			−1.47333
$363$		0			0
$364$	28.2479	−	48.9269i	1.48059	−	2.56447i
$365$	3.57930	+	6.19954i	0.187349	+	0.324499i
$366$		0			0
$367$	10.3202	+	17.8752i	0.538712	+	0.933076i	0.998974	+	0.0452932i	$0.0144222\pi$
$367$	10.3202	+	17.8752i	0.538712	+	0.933076i	−0.460262	+	0.887783i	$0.652244\pi$
$368$	0.0733010			0.00382108
$369$		0			0
$370$	−12.5281	−	21.6993i	−0.651304	−	1.12809i
$371$	−10.0703	−	17.4422i	−0.522823	−	0.905556i
$372$		0			0
$373$	4.55313			0.235752			0.117876	−	0.993028i	$-0.462391\pi$
$373$	4.55313			0.235752			0.117876	+	0.993028i	$0.462391\pi$
$374$	−0.816776	−	1.41470i	−0.0422345	−	0.0731522i
$375$		0			0
$376$	−4.27657	−	7.40723i	−0.220547	−	0.381999i
$377$	8.76755	−	15.1858i	0.451552	−	0.782110i
$378$		0			0
$379$	−19.9187			−1.02315			−0.511577	−	0.859237i	$-0.670939\pi$
$379$	−19.9187			−1.02315			−0.511577	+	0.859237i	$0.670939\pi$
$380$	−13.7269	+	2.96675i	−0.704175	+	0.152191i
$381$		0			0
$382$	−6.52506	+	11.3017i	−0.333851	+	0.578247i
$383$	−9.98742	+	17.2987i	−0.510333	+	0.883923i	0.489595	+	0.871950i	$0.337145\pi$
$383$	−9.98742	+	17.2987i	−0.510333	+	0.883923i	−0.999928	+	0.0119734i	$0.996189\pi$
$384$		0			0
$385$	−7.90310	+	13.6886i	−0.402779	+	0.697634i
$386$	−11.6069	−	20.1038i	−0.590777	−	1.02326i
$387$		0			0
$388$	5.21787			0.264897
$389$	6.90110	+	11.9531i	0.349900	+	0.606044i	0.986231	−	0.165372i	$-0.0528824\pi$
$389$	6.90110	+	11.9531i	0.349900	+	0.606044i	−0.636332	+	0.771416i	$0.719549\pi$
$390$		0			0
$391$	0.183767			0.00929349
$392$	−14.7962			−0.747319
$393$		0			0
$394$	−18.5140	+	32.0673i	−0.932724	+	1.61552i
$395$	5.06327	+	8.76983i	0.254761	+	0.441258i
$396$		0			0
$397$	8.27457	−	14.3320i	0.415289	−	0.719301i	−0.580170	−	0.814495i	$-0.697014\pi$
$397$	8.27457	−	14.3320i	0.415289	−	0.719301i	0.995459	+	0.0951945i	$0.0303473\pi$
$398$	−0.764087			−0.0383002
$399$		0			0
$400$	−0.0632663			−0.00316332
$401$	4.26253	−	7.38292i	0.212861	−	0.368685i	−0.739748	−	0.672884i	$-0.765055\pi$
$401$	4.26253	−	7.38292i	0.212861	−	0.368685i	0.952609	+	0.304199i	$0.0983887\pi$
$402$		0			0
$403$	−5.71286	−	9.89496i	−0.284578	−	0.492903i
$404$	19.8358	−	34.3567i	0.986869	−	1.70931i
$405$		0			0
$406$	−28.1054			−1.39485
$407$	−49.4186			−2.44959
$408$		0			0
$409$	5.78314	+	10.0167i	0.285958	+	0.495294i	0.972841	−	0.231474i	$-0.0743549\pi$
$409$	5.78314	+	10.0167i	0.285958	+	0.495294i	−0.686883	+	0.726768i	$0.741022\pi$
$410$	13.8875			0.685855
$411$		0			0
$412$	−17.1024	−	29.6222i	−0.842573	−	1.45938i
$413$	5.37147	−	9.30365i	0.264313	−	0.457803i
$414$		0			0
$415$	2.42771	−	4.20492i	0.119172	−	0.206412i
$416$	14.3222	−	24.8068i	0.702205	−	1.21626i
$417$		0			0
$418$	−13.7269	+	42.7430i	−0.671404	+	2.09063i
$419$	21.7149			1.06084			0.530420	−	0.847735i	$-0.322034\pi$
$419$	21.7149			1.06084			0.530420	+	0.847735i	$0.322034\pi$
$420$		0			0
$421$	3.46135	−	5.99523i	0.168696	−	0.292190i	−0.769266	−	0.638929i	$-0.779378\pi$
$421$	3.46135	−	5.99523i	0.168696	−	0.292190i	0.937962	+	0.346739i	$0.112711\pi$
$422$	2.31722	+	4.01354i	0.112800	+	0.195376i
$423$		0			0
$424$	8.01760	+	13.8869i	0.389369	+	0.674407i
$425$	−0.158610			−0.00769371
$426$		0			0
$427$	1.53163	+	2.65287i	0.0741209	+	0.128381i
$428$	−3.50000	−	6.06218i	−0.169179	−	0.293026i
$429$		0			0
$430$	7.65159			0.368992
$431$	−13.9894	−	24.2304i	−0.673847	−	1.16714i	−0.976805	−	0.214133i	$-0.931307\pi$
$431$	−13.9894	−	24.2304i	−0.673847	−	1.16714i	0.302958	−	0.953004i	$-0.402026\pi$
$432$		0			0
$433$	−3.12698	−	5.41608i	−0.150273	−	0.260280i	0.781055	−	0.624462i	$-0.214682\pi$
$433$	−3.12698	−	5.41608i	−0.150273	−	0.260280i	−0.931328	+	0.364182i	$0.881349\pi$
$434$	−9.15661	+	15.8597i	−0.439531	+	0.761290i
$435$		0			0
$436$	50.9708			2.44106
$437$	−3.39208	−	3.74152i	−0.162265	−	0.178981i
$438$		0			0
$439$	−15.5988	+	27.0179i	−0.744490	+	1.28949i	0.205942	+	0.978564i	$0.433974\pi$
$439$	−15.5988	+	27.0179i	−0.744490	+	1.28949i	−0.950433	+	0.310931i	$0.899359\pi$
$440$	6.29216	−	10.8983i	0.299967	−	0.519558i
$441$		0			0
$442$	0.906115	−	1.56944i	0.0430995	−	0.0746505i
$443$	−16.3519	−	28.3223i	−0.776901	−	1.34563i	−0.933720	−	0.358004i	$-0.883457\pi$
$443$	−16.3519	−	28.3223i	−0.776901	−	1.34563i	0.156819	−	0.987627i	$-0.449876\pi$
$444$		0			0
$445$	1.11250			0.0527373
$446$	−21.9738	−	38.0598i	−1.04049	−	1.80218i
$447$		0			0
$448$	−45.4678			−2.14815
$449$	−25.6304			−1.20958			−0.604788	−	0.796387i	$-0.706742\pi$
$449$	−25.6304			−1.20958			−0.604788	+	0.796387i	$0.706742\pi$
$450$		0			0
$451$	13.6953	−	23.7209i	0.644885	−	1.11697i
$452$	15.8489	+	27.4510i	0.745467	+	1.29119i
$453$		0			0
$454$	−4.57028	+	7.91597i	−0.214494	+	0.371515i
$455$	−17.5351			−0.822058
$456$		0			0
$457$	33.1646			1.55138			0.775688	−	0.631116i	$-0.217403\pi$
$457$	33.1646			1.55138			0.775688	+	0.631116i	$0.217403\pi$
$458$	−14.8293	+	25.6850i	−0.692926	+	1.20018i
$459$		0			0
$460$	1.86645	+	3.23278i	0.0870236	+	0.150729i
$461$	1.08788	−	1.88426i	0.0506677	−	0.0877590i	−0.839579	−	0.543237i	$-0.817198\pi$
$461$	1.08788	−	1.88426i	0.0506677	−	0.0877590i	0.890247	+	0.455478i	$0.150532\pi$
$462$		0			0
$463$	−6.20072			−0.288172			−0.144086	−	0.989565i	$-0.546024\pi$
$463$	−6.20072			−0.288172			−0.144086	+	0.989565i	$0.546024\pi$
$464$	−0.221876			−0.0103003
$465$		0			0
$466$	−30.9332	−	53.5778i	−1.43295	−	2.48195i
$467$	17.1546			0.793821			0.396910	−	0.917857i	$-0.370082\pi$
$467$	17.1546			0.793821			0.396910	+	0.917857i	$0.370082\pi$
$468$		0			0
$469$	14.8062	+	25.6451i	0.683687	+	1.18418i
$470$	−3.50000	+	6.06218i	−0.161443	+	0.279627i
$471$		0			0
$472$	−4.27657	+	7.40723i	−0.196845	+	0.340945i
$473$	7.54567	−	13.0695i	0.346950	−	0.600936i
$474$		0			0
$475$	2.92771	+	3.22932i	0.134333	+	0.148171i
$476$	−1.79216			−0.0821436
$477$		0			0
$478$	−22.9202	+	39.6989i	−1.04834	+	1.81578i
$479$	−17.8891	−	30.9848i	−0.817372	−	1.41573i	−0.907612	−	0.419810i	$-0.862097\pi$
$479$	−17.8891	−	30.9848i	−0.817372	−	1.41573i	0.0902399	−	0.995920i	$-0.471237\pi$
$480$		0			0
$481$	−27.4120	−	47.4790i	−1.24988	−	2.16486i
$482$	49.3233			2.24661
$483$		0			0
$484$	−15.0030	−	25.9860i	−0.681955	−	1.18118i
$485$	−0.809757	−	1.40254i	−0.0367692	−	0.0636861i
$486$		0			0
$487$	−23.7149			−1.07462			−0.537311	−	0.843384i	$-0.680560\pi$
$487$	−23.7149			−1.07462			−0.537311	+	0.843384i	$0.680560\pi$
$488$	−1.21943	−	2.11212i	−0.0552010	−	0.0956110i
$489$		0			0
$490$	6.05469	+	10.4870i	0.273523	+	0.473756i
$491$	−19.5933	+	33.9367i	−0.884235	+	1.53154i	−0.0376474	+	0.999291i	$0.511986\pi$
$491$	−19.5933	+	33.9367i	−0.884235	+	1.53154i	−0.846588	+	0.532249i	$0.821347\pi$
$492$		0			0
$493$	−0.556248			−0.0250521
$494$	−48.6796	+	10.5210i	−2.19020	+	0.473361i
$495$		0			0
$496$	−0.0722863	+	0.125204i	−0.00324575	+	0.00562180i
$497$	−28.4698	+	49.3112i	−1.27705	+	2.21191i
$498$		0			0
$499$	4.68824	−	8.12027i	0.209875	−	0.363513i	−0.741800	−	0.670621i	$-0.766028\pi$
$499$	4.68824	−	8.12027i	0.209875	−	0.363513i	0.951675	+	0.307107i	$0.0993611\pi$
$500$	−1.61094	−	2.79023i	−0.0720433	−	0.124783i
$501$		0			0
$502$	−16.6084			−0.741269
$503$	6.74649	+	11.6853i	0.300811	+	0.521020i	0.976320	−	0.216332i	$-0.0694093\pi$
$503$	6.74649	+	11.6853i	0.300811	+	0.521020i	−0.675509	+	0.737352i	$0.736076\pi$
$504$		0			0
$505$	−12.3132			−0.547931
$506$	11.9327			0.530475
$507$		0			0
$508$	−25.3092	+	43.8368i	−1.12291	+	1.94495i
$509$	12.8534	+	22.2628i	0.569718	+	0.986781i	0.996594	+	0.0824703i	$0.0262809\pi$
$509$	12.8534	+	22.2628i	0.569718	+	0.986781i	−0.426875	+	0.904310i	$0.640386\pi$
$510$		0			0
$511$	12.5527	−	21.7419i	0.555298	−	0.961805i
$512$	−0.715746			−0.0316318
$513$		0			0
$514$	34.4538			1.51969
$515$	−5.30820	+	9.19407i	−0.233907	+	0.405139i
$516$		0			0
$517$	6.90310	+	11.9565i	0.303598	+	0.525847i
$518$	−43.9362	+	76.0997i	−1.93045	+	3.34363i
$519$		0			0
$520$	13.9608			0.612222
$521$	37.7358			1.65324			0.826618	−	0.562763i	$-0.190262\pi$
$521$	37.7358			1.65324			0.826618	+	0.562763i	$0.190262\pi$
$522$		0			0
$523$	−19.2003	−	33.2559i	−0.839570	−	1.45418i	−0.890255	−	0.455462i	$-0.849474\pi$
$523$	−19.2003	−	33.2559i	−0.839570	−	1.45418i	0.0506855	−	0.998715i	$-0.483859\pi$
$524$	37.1646			1.62354
$525$		0			0
$526$	−23.0281	−	39.8858i	−1.00407	−	1.73910i
$527$	−0.181223	+	0.313888i	−0.00789420	+	0.0136732i
$528$		0			0
$529$	10.8288	−	18.7561i	0.470818	−	0.815481i
$530$	6.56171	−	11.3652i	0.285022	−	0.493673i
$531$		0			0
$532$	33.0808	+	36.4886i	1.43423	+	1.58198i
$533$	30.3865			1.31619
$534$		0			0
$535$	−1.08632	+	1.88157i	−0.0469659	+	0.0813473i
$536$	−11.7882	−	20.4177i	−0.509171	−	0.881910i
$537$		0			0
$538$	8.82624	+	15.2875i	0.380526	+	0.659091i
$539$	23.8835			1.02874
$540$		0			0
$541$	6.40310	+	11.0905i	0.275291	+	0.476818i	0.970208	−	0.242272i	$-0.0778926\pi$
$541$	6.40310	+	11.0905i	0.275291	+	0.476818i	−0.694918	+	0.719089i	$0.744559\pi$
$542$	−6.03865	−	10.4593i	−0.259382	−	0.449263i
$543$		0			0
$544$	−0.908659			−0.0389584
$545$	−7.91012	−	13.7007i	−0.338832	−	0.586875i
$546$		0			0
$547$	9.12853	+	15.8111i	0.390308	+	0.676033i	0.992490	−	0.122326i	$-0.0390352\pi$
$547$	9.12853	+	15.8111i	0.390308	+	0.676033i	−0.602182	+	0.798359i	$0.705702\pi$
$548$	0.176206	−	0.305197i	0.00752714	−	0.0130374i
$549$		0			0
$550$	−10.2992			−0.439159
$551$	10.2675	+	11.3253i	0.437412	+	0.482473i
$552$		0			0
$553$	17.7570	−	30.7560i	0.755103	−	1.30788i
$554$	34.9929	−	60.6095i	1.48671	−	2.57505i
$555$		0			0
$556$	−2.32580	+	4.02840i	−0.0986357	+	0.170842i
$557$	7.45233	+	12.9078i	0.315765	+	0.546922i	0.979600	−	0.200958i	$-0.0644054\pi$
$557$	7.45233	+	12.9078i	0.315765	+	0.546922i	−0.663835	+	0.747879i	$0.731072\pi$
$558$		0			0
$559$	16.7420			0.708113
$560$	0.110938	+	0.192150i	0.00468799	+	0.00811984i
$561$		0			0
$562$	30.5351			1.28805
$563$	−45.7810			−1.92944			−0.964720	−	0.263276i	$-0.915197\pi$
$563$	−45.7810			−1.92944			−0.964720	+	0.263276i	$0.915197\pi$
$564$		0			0
$565$	4.91914	−	8.52020i	0.206950	−	0.358447i
$566$	4.67922	+	8.10465i	0.196682	+	0.340664i
$567$		0			0
$568$	22.6666	−	39.2598i	0.951071	−	1.64730i
$569$	−0.379598			−0.0159136			−0.00795679	−	0.999968i	$-0.502533\pi$
$569$	−0.379598			−0.0159136			−0.00795679	+	0.999968i	$0.502533\pi$
$570$		0			0
$571$	−15.8514			−0.663361			−0.331681	−	0.943392i	$-0.607616\pi$
$571$	−15.8514			−0.663361			−0.331681	+	0.943392i	$0.607616\pi$
$572$	36.3026	−	62.8780i	1.51789	−	2.62906i
$573$		0			0
$574$	−24.3519	−	42.1787i	−1.01643	−	1.76050i
$575$	0.579305	−	1.00339i	0.0241587	−	0.0418441i
$576$		0			0
$577$	−19.2350			−0.800765			−0.400382	−	0.916348i	$-0.631123\pi$
$577$	−19.2350			−0.800765			−0.400382	+	0.916348i	$0.631123\pi$
$578$	38.7899			1.61345
$579$		0			0
$580$	−5.64959	−	9.78538i	−0.234586	−	0.406316i
$581$	−17.0281			−0.706444
$582$		0			0
$583$	−12.9418	−	22.4158i	−0.535993	−	0.928366i
$584$	−9.99400	+	17.3101i	−0.413554	+	0.716297i
$585$		0			0
$586$	−13.9081	+	24.0896i	−0.574539	+	0.995131i
$587$	20.4242	−	35.3757i	0.842995	−	1.46011i	−0.0443559	−	0.999016i	$-0.514124\pi$
$587$	20.4242	−	35.3757i	0.842995	−	1.46011i	0.887351	−	0.461095i	$-0.152543\pi$
$588$		0			0
$589$	9.73591	−	2.10419i	0.401161	−	0.0867018i
$590$	7.00000			0.288185
$591$		0			0
$592$	−0.346852	+	0.600764i	−0.0142555	+	0.0246913i
$593$	−7.12342	−	12.3381i	−0.292524	−	0.506666i	0.681882	−	0.731462i	$-0.261162\pi$
$593$	−7.12342	−	12.3381i	−0.292524	−	0.506666i	−0.974406	+	0.224796i	$0.927828\pi$
$594$		0			0
$595$	0.278124	+	0.481725i	0.0114020	+	0.0197488i
$596$	−5.57028			−0.228168
$597$		0			0
$598$	6.61897	+	11.4644i	0.270670	+	0.468814i
$599$	−7.92571	−	13.7277i	−0.323836	−	0.560900i	0.657440	−	0.753507i	$-0.271639\pi$
$599$	−7.92571	−	13.7277i	−0.323836	−	0.560900i	−0.981276	+	0.192607i	$0.938306\pi$
$600$		0			0
$601$	16.4718			0.671900			0.335950	−	0.941880i	$-0.390943\pi$
$601$	16.4718			0.671900			0.335950	+	0.941880i	$0.390943\pi$
$602$	−13.4171	−	23.2392i	−0.546842	−	0.947158i
$603$		0			0
$604$	32.4452	+	56.1968i	1.32018	+	2.28661i
$605$	−4.65661	+	8.06548i	−0.189318	+	0.327908i
$606$		0			0
$607$	−10.3914			−0.421774			−0.210887	−	0.977510i	$-0.567635\pi$
$607$	−10.3914			−0.421774			−0.210887	+	0.977510i	$0.567635\pi$
$608$	16.7726	+	18.5004i	0.680217	+	0.750291i
$609$		0			0
$610$	−0.997999	+	1.72858i	−0.0404078	+	0.0699883i
$611$	−7.65817	+	13.2643i	−0.309816	+	0.536617i
$612$		0			0
$613$	10.8925	−	18.8664i	0.439945	−	0.762007i	−0.557740	−	0.830016i	$-0.688331\pi$
$613$	10.8925	−	18.8664i	0.439945	−	0.762007i	0.997685	+	0.0680090i	$0.0216647\pi$
$614$	28.0331	+	48.5547i	1.13132	+	1.95951i
$615$		0			0
$616$	−44.1335			−1.77819
$617$	−21.3855	−	37.0408i	−0.860948	−	1.49121i	−0.871015	−	0.491256i	$-0.836538\pi$
$617$	−21.3855	−	37.0408i	−0.860948	−	1.49121i	0.0100671	−	0.999949i	$-0.496795\pi$
$618$		0			0
$619$	28.7882			1.15709			0.578547	−	0.815649i	$-0.303620\pi$
$619$	28.7882			1.15709			0.578547	+	0.815649i	$0.303620\pi$
$620$	−7.36245			−0.295683
$621$		0			0
$622$	11.6586	−	20.1933i	0.467468	−	0.809678i
$623$	−1.95077	−	3.37883i	−0.0781560	−	0.135370i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	73.0833			2.92100
$627$		0			0
$628$	12.1726			0.485742
$629$	−0.869563	+	1.50613i	−0.0346718	+	0.0600532i
$630$		0			0
$631$	9.69370	+	16.7900i	0.385900	+	0.668399i	0.991894	−	0.127071i	$-0.0405576\pi$
$631$	9.69370	+	16.7900i	0.385900	+	0.668399i	−0.605993	+	0.795470i	$0.707224\pi$
$632$	−14.1375	+	24.4868i	−0.562358	+	0.974032i
$633$		0			0
$634$	5.10938			0.202919
$635$	15.7109			0.623466
$636$		0			0
$637$	13.2479	+	22.9461i	0.524903	+	0.909158i
$638$	−36.1194			−1.42998
$639$		0			0
$640$	−9.08432	−	15.7345i	−0.359089	−	0.621961i
$641$	20.3433	−	35.2356i	0.803512	−	1.39172i	−0.113779	−	0.993506i	$-0.536296\pi$
$641$	20.3433	−	35.2356i	0.803512	−	1.39172i	0.917291	−	0.398217i	$-0.130371\pi$
$642$		0			0
$643$	17.0527	−	29.5361i	0.672492	−	1.16479i	−0.304703	−	0.952448i	$-0.598557\pi$
$643$	17.0527	−	29.5361i	0.672492	−	1.16479i	0.977195	−	0.212344i	$-0.0681096\pi$
$644$	6.54567	−	11.3374i	0.257936	−	0.446757i
$645$		0			0
$646$	1.06114	+	1.17045i	0.0417499	+	0.0460509i
$647$	48.0029			1.88719			0.943595	−	0.331103i	$-0.107421\pi$
$647$	48.0029			1.88719			0.943595	+	0.331103i	$0.107421\pi$
$648$		0			0
$649$	6.90310	−	11.9565i	0.270970	−	0.469334i
$650$	−5.71286	−	9.89496i	−0.224077	−	0.388112i
$651$		0			0
$652$	2.60392	+	4.51012i	0.101977	+	0.176630i
$653$	−3.90866			−0.152958			−0.0764788	−	0.997071i	$-0.524368\pi$
$653$	−3.90866			−0.152958			−0.0764788	+	0.997071i	$0.524368\pi$
$654$		0			0
$655$	−5.76755	−	9.98968i	−0.225357	−	0.390329i
$656$	−0.192244	−	0.332977i	−0.00750588	−	0.0130006i
$657$		0			0
$658$	24.5491			0.957025
$659$	6.54411	+	11.3347i	0.254922	+	0.441539i	0.964874	−	0.262711i	$-0.0846167\pi$
$659$	6.54411	+	11.3347i	0.254922	+	0.441539i	−0.709952	+	0.704250i	$0.751283\pi$
$660$		0			0
$661$	11.9714	+	20.7350i	0.465633	+	0.806500i	0.999230	−	0.0392391i	$-0.0124934\pi$
$661$	11.9714	+	20.7350i	0.465633	+	0.806500i	−0.533597	+	0.845739i	$0.679160\pi$
$662$	−11.5301	+	19.9707i	−0.448129	+	0.776182i
$663$		0			0
$664$	13.5571			0.526119
$665$	4.67420	−	14.5546i	0.181258	−	0.564403i
$666$		0			0
$667$	2.03163	−	3.51889i	0.0786652	−	0.136252i
$668$	10.4598	−	18.1169i	0.404701	−	0.700963i
$669$		0			0
$670$	−9.64759	+	16.7101i	−0.372719	+	0.645568i
$671$	1.96837	+	3.40931i	0.0759880	+	0.131615i
$672$		0			0
$673$	−11.3304			−0.436754			−0.218377	−	0.975865i	$-0.570076\pi$
$673$	−11.3304			−0.436754			−0.218377	+	0.975865i	$0.570076\pi$
$674$	6.41256	+	11.1069i	0.247003	+	0.427821i
$675$		0			0
$676$	38.6625			1.48702
$677$	−8.90466			−0.342234			−0.171117	−	0.985251i	$-0.554738\pi$
$677$	−8.90466			−0.342234			−0.171117	+	0.985251i	$0.554738\pi$
$678$		0			0
$679$	−2.83983	+	4.91873i	−0.108983	+	0.188764i
$680$	−0.221432	−	0.383532i	−0.00849153	−	0.0147078i
$681$		0			0
$682$	−11.7675	+	20.3820i	−0.450603	+	0.780467i
$683$	26.6977			1.02156			0.510780	−	0.859712i	$-0.329357\pi$
$683$	26.6977			1.02156			0.510780	+	0.859712i	$0.329357\pi$
$684$		0			0
$685$	−0.109381			−0.00417923
$686$	−6.81522	+	11.8043i	−0.260206	+	0.450690i
$687$		0			0
$688$	−0.105921	−	0.183460i	−0.00403819	−	0.00699435i
$689$	14.3573	−	24.8676i	0.546971	−	0.947381i
$690$		0			0
$691$	35.9708			1.36840			0.684198	−	0.729297i	$-0.260153\pi$
$691$	35.9708			1.36840			0.684198	+	0.729297i	$0.260153\pi$
$692$	−27.4538			−1.04364
$693$		0			0
$694$	−6.25551	−	10.8349i	−0.237456	−	0.411286i
$695$	1.44375			0.0547646
$696$		0			0
$697$	−0.481960	−	0.834779i	−0.0182555	−	0.0316195i
$698$	−21.5035	+	37.2451i	−0.813918	+	1.40975i
$699$		0			0
$700$	−5.64959	+	9.78538i	−0.213534	+	0.369852i
$701$	1.22543	−	2.12252i	0.0462840	−	0.0801663i	−0.841955	−	0.539547i	$-0.818595\pi$
$701$	1.22543	−	2.12252i	0.0462840	−	0.0801663i	0.888239	+	0.459381i	$0.151929\pi$
$702$		0			0
$703$	46.7159	−	10.0966i	1.76192	−	0.380799i
$704$	−58.4326			−2.20226
$705$		0			0
$706$	14.5116	−	25.1348i	0.546151	−	0.945961i
$707$	21.5913	+	37.3973i	0.812026	+	1.40647i
$708$		0			0
$709$	25.1440	+	43.5507i	0.944304	+	1.63558i	0.757139	+	0.653254i	$0.226597\pi$
$709$	25.1440	+	43.5507i	0.944304	+	1.63558i	0.187165	+	0.982329i	$0.440070\pi$
$710$	−37.1014			−1.39239
$711$		0			0
$712$	1.55313	+	2.69011i	0.0582061	+	0.100816i
$713$	−1.32379	−	2.29288i	−0.0495765	−	0.0858690i
$714$		0			0
$715$	−22.5351			−0.842765
$716$	−16.5461	−	28.6587i	−0.618357	−	1.07103i
$717$		0			0
$718$	12.6602	+	21.9281i	0.472473	+	0.818348i
$719$	−24.0491	+	41.6543i	−0.896881	+	1.55344i	−0.0654223	+	0.997858i	$0.520839\pi$
$719$	−24.0491	+	41.6543i	−0.896881	+	1.55344i	−0.831459	+	0.555586i	$0.812494\pi$
$720$		0			0
$721$	37.2319			1.38659
$722$	4.24347	−	43.2098i	0.157926	−	1.60810i
$723$		0			0
$724$	−19.7615	+	34.2280i	−0.734432	+	1.27207i
$725$	−1.75351	+	3.03717i	−0.0651237	+	0.112798i
$726$		0			0
$727$	8.33983	−	14.4450i	0.309307	−	0.535736i	−0.668904	−	0.743349i	$-0.733236\pi$
$727$	8.33983	−	14.4450i	0.309307	−	0.535736i	0.978211	+	0.207613i	$0.0665695\pi$
$728$	−24.4804	−	42.4013i	−0.907304	−	1.57150i
$729$		0			0
$730$	16.3584			0.605453
$731$	−0.265545	−	0.459938i	−0.00982155	−	0.0170114i
$732$		0			0
$733$	−4.13365			−0.152680			−0.0763399	−	0.997082i	$-0.524323\pi$
$733$	−4.13365			−0.152680			−0.0763399	+	0.997082i	$0.524323\pi$
$734$	47.1664			1.74094
$735$		0			0
$736$	3.31878	−	5.74829i	0.122332	−	0.211885i
$737$	19.0281	+	32.9576i	0.700908	+	1.21401i
$738$		0			0
$739$	−23.4870	+	40.6806i	−0.863982	+	1.49646i	0.00407159	+	0.999992i	$0.498704\pi$
$739$	−23.4870	+	40.6806i	−0.863982	+	1.49646i	−0.868054	+	0.496470i	$0.834629\pi$
$740$	−35.3273			−1.29866
$741$		0			0
$742$	−46.0241			−1.68960
$743$	20.6069	−	35.6923i	0.755995	−	1.30942i	−0.188883	−	0.982000i	$-0.560487\pi$
$743$	20.6069	−	35.6923i	0.755995	−	1.30942i	0.944878	−	0.327422i	$-0.106180\pi$
$744$		0			0
$745$	0.864447	+	1.49727i	0.0316709	+	0.0548556i
$746$	5.20228	−	9.01061i	0.190469	−	0.329902i
$747$		0			0
$748$	−2.30318			−0.0842127
$749$	7.61951			0.278411
$750$		0			0
$751$	−2.98942	−	5.17783i	−0.109086	−	0.188942i	0.806314	−	0.591487i	$-0.201459\pi$
$751$	−2.98942	−	5.17783i	−0.109086	−	0.188942i	−0.915400	+	0.402545i	$0.868126\pi$
$752$	0.193802			0.00706722
$753$		0			0
$754$	−20.0351	−	34.7018i	−0.729635	−	1.26376i
$755$	10.0703	−	17.4422i	0.366495	−	0.634788i
$756$		0			0
$757$	−18.1968	+	31.5178i	−0.661375	+	1.14553i	0.318880	+	0.947795i	$0.396693\pi$
$757$	−18.1968	+	31.5178i	−0.661375	+	1.14553i	−0.980255	+	0.197739i	$0.936640\pi$
$758$	−22.7585	+	39.4189i	−0.826627	+	1.43176i
$759$		0			0
$760$	−3.72143	+	11.5878i	−0.134991	+	0.420335i
$761$	2.71397			0.0983813			0.0491907	−	0.998789i	$-0.484336\pi$
$761$	2.71397			0.0983813			0.0491907	+	0.998789i	$0.484336\pi$
$762$		0			0
$763$	−27.7409	+	48.0487i	−1.00429	+	1.73948i
$764$	9.19983	+	15.9346i	0.332838	+	0.576493i
$765$		0			0
$766$	22.8227	+	39.5300i	0.824617	+	1.42828i
$767$	15.3163			0.553041
$768$		0			0
$769$	−19.8995	−	34.4670i	−0.717596	−	1.24291i	−0.961950	−	0.273226i	$-0.911909\pi$
$769$	−19.8995	−	34.4670i	−0.717596	−	1.24291i	0.244354	−	0.969686i	$-0.421424\pi$
$770$	18.0597	+	31.2803i	0.650827	+	1.12726i
$771$		0			0
$772$	−32.7298			−1.17797
$773$	22.4874	+	38.9494i	0.808816	+	1.40091i	0.913684	+	0.406425i	$0.133225\pi$
$773$	22.4874	+	38.9494i	0.808816	+	1.40091i	−0.104868	+	0.994486i	$0.533442\pi$
$774$		0			0
$775$	1.14257	+	1.97899i	0.0410424	+	0.0710875i
$776$	2.26097	−	3.91612i	0.0811642	−	0.140580i
$777$		0			0
$778$	31.5400			1.13076
$779$	−8.09992	+	25.2216i	−0.290210	+	0.903658i
$780$		0			0
$781$	−36.5878	+	63.3719i	−1.30921	+	2.26762i
$782$	0.209967	−	0.363673i	0.00750840	−	0.0130049i
$783$		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)

\(f(q)\)	\(=\)	\(q+(1.14257 - 1.97899i) q^{2} +(-1.61094 - 2.79023i) q^{4} +(-0.500000 + 0.866025i) q^{5} +3.50702 q^{7} -2.79216 q^{8} +O(q^{10})\)	\(q+(1.14257 - 1.97899i) q^{2} +(-1.61094 - 2.79023i) q^{4} +(-0.500000 + 0.866025i) q^{5} +3.50702 q^{7} -2.79216 q^{8} +(1.14257 + 1.97899i) q^{10} +4.50702 q^{11} +(2.50000 + 4.33013i) q^{13} +(4.00702 - 6.94036i) q^{14} +(0.0316332 - 0.0547902i) q^{16} +(0.0793049 - 0.137360i) q^{17} +(-4.26053 + 0.920816i) q^{19} +3.22188 q^{20} +(5.14959 - 8.91935i) q^{22} +(0.579305 + 1.00339i) q^{23} +(-0.500000 - 0.866025i) q^{25} +11.4257 q^{26} +(-5.64959 - 9.78538i) q^{28} +(-1.75351 - 3.03717i) q^{29} -2.28514 q^{31} +(-2.86445 - 4.96137i) q^{32} +(-0.181223 - 0.313888i) q^{34} +(-1.75351 + 3.03717i) q^{35} -10.9648 q^{37} +(-3.04567 + 9.48365i) q^{38} +(1.39608 - 2.41808i) q^{40} +(3.03865 - 5.26310i) q^{41} +(1.67420 - 2.89981i) q^{43} +(-7.26053 - 12.5756i) q^{44} +2.64759 q^{46} +(1.53163 + 2.65287i) q^{47} +5.29918 q^{49} -2.28514 q^{50} +(8.05469 - 13.9511i) q^{52} +(-2.87147 - 4.97353i) q^{53} +(-2.25351 + 3.90319i) q^{55} -9.79216 q^{56} -8.01404 q^{58} +(1.53163 - 2.65287i) q^{59} +(0.436734 + 0.756445i) q^{61} +(-2.61094 + 4.52228i) q^{62} -12.9648 q^{64} -5.00000 q^{65} +(4.22188 + 7.31250i) q^{67} -0.511021 q^{68} +(4.00702 + 6.94036i) q^{70} +(-8.11796 + 14.0607i) q^{71} +(3.57930 - 6.19954i) q^{73} +(-12.5281 + 21.6993i) q^{74} +(9.43273 + 10.4045i) q^{76} +15.8062 q^{77} +(5.06327 - 8.76983i) q^{79} +(0.0316332 + 0.0547902i) q^{80} +(-6.94375 - 12.0269i) q^{82} -4.85543 q^{83} +(0.0793049 + 0.137360i) q^{85} +(-3.82580 - 6.62647i) q^{86} -12.5843 q^{88} +(-0.556248 - 0.963449i) q^{89} +(8.76755 + 15.1858i) q^{91} +(1.86645 - 3.23278i) q^{92} +7.00000 q^{94} +(1.33281 - 4.15013i) q^{95} +(-0.809757 + 1.40254i) q^{97} +(6.05469 - 10.4870i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 7 q^{4} - 3 q^{5} + 4 q^{7} + 12 q^{8}+O(q^{10}) \) 6 * q + q^2 - 7 * q^4 - 3 * q^5 + 4 * q^7 + 12 * q^8	\( 6 q + q^{2} - 7 q^{4} - 3 q^{5} + 4 q^{7} + 12 q^{8} + q^{10} + 10 q^{11} + 15 q^{13} + 7 q^{14} - 3 q^{16} + q^{17} + 14 q^{20} + 8 q^{22} + 4 q^{23} - 3 q^{25} + 10 q^{26} - 11 q^{28} - 2 q^{29} - 2 q^{31} - 6 q^{32} + 25 q^{34} - 2 q^{35} - 4 q^{37} + 19 q^{38} - 6 q^{40} - 2 q^{41} + q^{43} - 18 q^{44} - 48 q^{46} + 6 q^{47} - 14 q^{49} - 2 q^{50} + 35 q^{52} + 11 q^{53} - 5 q^{55} - 30 q^{56} - 14 q^{58} + 6 q^{59} + 9 q^{61} - 13 q^{62} - 16 q^{64} - 30 q^{65} + 20 q^{67} - 68 q^{68} + 7 q^{70} - 29 q^{71} + 22 q^{73} - 7 q^{74} - 19 q^{76} + 32 q^{77} + 24 q^{79} - 3 q^{80} - 31 q^{82} + 6 q^{83} + q^{85} - 32 q^{86} - 18 q^{88} - 14 q^{89} + 10 q^{91} + 41 q^{92} + 42 q^{94} - 7 q^{97} + 23 q^{98}+O(q^{100}) \) 6 * q + q^2 - 7 * q^4 - 3 * q^5 + 4 * q^7 + 12 * q^8 + q^10 + 10 * q^11 + 15 * q^13 + 7 * q^14 - 3 * q^16 + q^17 + 14 * q^20 + 8 * q^22 + 4 * q^23 - 3 * q^25 + 10 * q^26 - 11 * q^28 - 2 * q^29 - 2 * q^31 - 6 * q^32 + 25 * q^34 - 2 * q^35 - 4 * q^37 + 19 * q^38 - 6 * q^40 - 2 * q^41 + q^43 - 18 * q^44 - 48 * q^46 + 6 * q^47 - 14 * q^49 - 2 * q^50 + 35 * q^52 + 11 * q^53 - 5 * q^55 - 30 * q^56 - 14 * q^58 + 6 * q^59 + 9 * q^61 - 13 * q^62 - 16 * q^64 - 30 * q^65 + 20 * q^67 - 68 * q^68 + 7 * q^70 - 29 * q^71 + 22 * q^73 - 7 * q^74 - 19 * q^76 + 32 * q^77 + 24 * q^79 - 3 * q^80 - 31 * q^82 + 6 * q^83 + q^85 - 32 * q^86 - 18 * q^88 - 14 * q^89 + 10 * q^91 + 41 * q^92 + 42 * q^94 - 7 * q^97 + 23 * q^98

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