LMFDB - Embedded newform 3330.2.e.c.739.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3330,2,Mod(739,3330)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3330, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("3330.739");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3330.e (of order $2$, degree $1$, 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:	$26.5901838731$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 19x^{8} + 103x^{6} + 210x^{4} + 140x^{2} + 16 $ x^10 + 19x^8 + 103x^6 + 210x^4 + 140x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 370)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			739.1
Root			$0.987983i$ of defining polynomial
Character	$\chi$	$=$	3330.739
Dual form			3330.2.e.c.739.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.85396 - 1.25013i) q^{5} +4.78937i q^{7} -1.00000 q^{8} +(1.85396 + 1.25013i) q^{10} +5.98732 q^{11} +3.49410 q^{13} -4.78937i q^{14} +1.00000 q^{16} +4.96343 q^{17} -7.33092i q^{19} +(-1.85396 - 1.25013i) q^{20} -5.98732 q^{22} -1.74873 q^{23} +(1.87436 + 4.63538i) q^{25} -3.49410 q^{26} +4.78937i q^{28} +7.85004i q^{29} -3.24097i q^{31} -1.00000 q^{32} -4.96343 q^{34} +(5.98732 - 8.87932i) q^{35} +(3.96343 - 4.61424i) q^{37} +7.33092i q^{38} +(1.85396 + 1.25013i) q^{40} +0.530665 q^{41} -1.76838 q^{43} +5.98732 q^{44} +1.74873 q^{46} -4.30638i q^{47} -15.9381 q^{49} +(-1.87436 - 4.63538i) q^{50} +3.49410 q^{52} -3.66238i q^{53} +(-11.1003 - 7.48491i) q^{55} -4.78937i q^{56} -7.85004i q^{58} -2.15110i q^{59} +3.06584i q^{61} +3.24097i q^{62} +1.00000 q^{64} +(-6.47793 - 4.36807i) q^{65} +3.79622i q^{67} +4.96343 q^{68} +(-5.98732 + 8.87932i) q^{70} +8.47719 q^{71} -9.05445i q^{73} +(-3.96343 + 4.61424i) q^{74} -7.33092i q^{76} +28.6755i q^{77} +5.56622i q^{79} +(-1.85396 - 1.25013i) q^{80} -0.530665 q^{82} -3.77680i q^{83} +(-9.20203 - 6.20492i) q^{85} +1.76838 q^{86} -5.98732 q^{88} -8.45791i q^{89} +16.7345i q^{91} -1.74873 q^{92} +4.30638i q^{94} +(-9.16459 + 13.5913i) q^{95} -3.64747 q^{97} +15.9381 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 10 q^{4} - 3 q^{5} - 10 q^{8} + 3 q^{10} + 2 q^{13} + 10 q^{16} + 18 q^{17} - 3 q^{20} + 10 q^{23} + 5 q^{25} - 2 q^{26} - 10 q^{32} - 18 q^{34} + 8 q^{37} + 3 q^{40} + 4 q^{41} + 10 q^{43}+ \cdots + 8 q^{98}+O(q^{100}) $ 10 * q - 10 * q^2 + 10 * q^4 - 3 * q^5 - 10 * q^8 + 3 * q^10 + 2 * q^13 + 10 * q^16 + 18 * q^17 - 3 * q^20 + 10 * q^23 + 5 * q^25 - 2 * q^26 - 10 * q^32 - 18 * q^34 + 8 * q^37 + 3 * q^40 + 4 * q^41 + 10 * q^43 - 10 * q^46 - 8 * q^49 - 5 * q^50 + 2 * q^52 - 5 * q^55 + 10 * q^64 - 2 * q^65 + 18 * q^68 + 20 * q^71 - 8 * q^74 - 3 * q^80 - 4 * q^82 - 28 * q^85 - 10 * q^86 + 10 * q^92 - 2 * q^95 - 2 * q^97 + 8 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−1.85396	−	1.25013i	−0.829118	−	0.559074i
$5$	−1.85396	−	1.25013i	−0.829118	−	0.559074i
$6$		0			0
$7$			4.78937i			1.81021i	0.425186	+	0.905106i	$0.360209\pi$
$7$			4.78937i			1.81021i	−0.425186	+	0.905106i	$0.639791\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.85396	+	1.25013i	0.586275	+	0.395325i
$11$	5.98732			1.80525			0.902623	−	0.430432i	$-0.141639\pi$
$11$	5.98732			1.80525			0.902623	+	0.430432i	$0.141639\pi$
$12$		0			0
$13$	3.49410			0.969088			0.484544	−	0.874767i	$-0.338985\pi$
$13$	3.49410			0.969088			0.484544	+	0.874767i	$0.338985\pi$
$14$		−	4.78937i		−	1.28001i
$15$		0			0
$16$	1.00000			0.250000
$17$	4.96343			1.20381			0.601905	−	0.798568i	$-0.294409\pi$
$17$	4.96343			1.20381			0.601905	+	0.798568i	$0.294409\pi$
$18$		0			0
$19$		−	7.33092i		−	1.68183i	−0.541168	−	0.840915i	$-0.682018\pi$
$19$		−	7.33092i		−	1.68183i	0.541168	−	0.840915i	$-0.317982\pi$
$20$	−1.85396	−	1.25013i	−0.414559	−	0.279537i
$21$		0			0
$22$	−5.98732			−1.27650
$23$	−1.74873			−0.364635			−0.182318	−	0.983240i	$-0.558360\pi$
$23$	−1.74873			−0.364635			−0.182318	+	0.983240i	$0.558360\pi$
$24$		0			0
$25$	1.87436	+	4.63538i	0.374873	+	0.927076i
$26$	−3.49410			−0.685249
$27$		0			0
$28$			4.78937i			0.905106i
$29$			7.85004i			1.45772i	0.684665	+	0.728858i	$0.259949\pi$
$29$			7.85004i			1.45772i	−0.684665	+	0.728858i	$0.740051\pi$
$30$		0			0
$31$		−	3.24097i		−	0.582096i	−0.956708	−	0.291048i	$-0.905996\pi$
$31$		−	3.24097i		−	0.582096i	0.956708	−	0.291048i	$-0.0940039\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−4.96343			−0.851222
$35$	5.98732	−	8.87932i	1.01204	−	1.50088i
$36$		0			0
$37$	3.96343	−	4.61424i	0.651584	−	0.758576i
$37$	3.96343	−	4.61424i	0.651584	−	0.758576i
$38$			7.33092i			1.18923i
$39$		0			0
$40$	1.85396	+	1.25013i	0.293137	+	0.197662i
$41$	0.530665			0.0828760			0.0414380	−	0.999141i	$-0.486806\pi$
$41$	0.530665			0.0828760			0.0414380	+	0.999141i	$0.486806\pi$
$42$		0			0
$43$	−1.76838			−0.269676			−0.134838	−	0.990868i	$-0.543051\pi$
$43$	−1.76838			−0.269676			−0.134838	+	0.990868i	$0.543051\pi$
$44$	5.98732			0.902623
$45$		0			0
$46$	1.74873			0.257836
$47$		−	4.30638i		−	0.628150i	−0.949398	−	0.314075i	$-0.898306\pi$
$47$		−	4.30638i		−	0.628150i	0.949398	−	0.314075i	$-0.101694\pi$
$48$		0			0
$49$	−15.9381			−2.27687
$50$	−1.87436	−	4.63538i	−0.265075	−	0.655542i
$51$		0			0
$52$	3.49410			0.484544
$53$		−	3.66238i		−	0.503067i	−0.967849	−	0.251534i	$-0.919065\pi$
$53$		−	3.66238i		−	0.503067i	0.967849	−	0.251534i	$-0.0809349\pi$
$54$		0			0
$55$	−11.1003	−	7.48491i	−1.49676	−	1.00927i
$56$		−	4.78937i		−	0.640007i
$57$		0			0
$58$		−	7.85004i		−	1.03076i
$59$		−	2.15110i		−	0.280049i	−0.990148	−	0.140025i	$-0.955282\pi$
$59$		−	2.15110i		−	0.280049i	0.990148	−	0.140025i	$-0.0447182\pi$
$60$		0			0
$61$			3.06584i			0.392541i	0.980550	+	0.196270i	$0.0628830\pi$
$61$			3.06584i			0.392541i	−0.980550	+	0.196270i	$0.937117\pi$
$62$			3.24097i			0.411604i
$63$		0			0
$64$	1.00000			0.125000
$65$	−6.47793	−	4.36807i	−0.803489	−	0.541792i
$66$		0			0
$67$			3.79622i			0.463782i	0.972742	+	0.231891i	$0.0744912\pi$
$67$			3.79622i			0.463782i	−0.972742	+	0.231891i	$0.925509\pi$
$68$	4.96343			0.601905
$69$		0			0
$70$	−5.98732	+	8.87932i	−0.715622	+	1.06128i
$71$	8.47719			1.00606			0.503028	−	0.864270i	$-0.332219\pi$
$71$	8.47719			1.00606			0.503028	+	0.864270i	$0.332219\pi$
$72$		0			0
$73$		−	9.05445i		−	1.05974i	−0.848078	−	0.529872i	$-0.822240\pi$
$73$		−	9.05445i		−	1.05974i	0.848078	−	0.529872i	$-0.177760\pi$
$74$	−3.96343	+	4.61424i	−0.460740	+	0.536394i
$75$		0			0
$76$		−	7.33092i		−	0.840915i
$77$			28.6755i			3.26788i
$78$		0			0
$79$			5.56622i			0.626248i	0.949712	+	0.313124i	$0.101376\pi$
$79$			5.56622i			0.626248i	−0.949712	+	0.313124i	$0.898624\pi$
$80$	−1.85396	−	1.25013i	−0.207279	−	0.139768i
$81$		0			0
$82$	−0.530665			−0.0586022
$83$		−	3.77680i		−	0.414558i	−0.978282	−	0.207279i	$-0.933539\pi$
$83$		−	3.77680i		−	0.414558i	0.978282	−	0.207279i	$-0.0664607\pi$
$84$		0			0
$85$	−9.20203	−	6.20492i	−0.998100	−	0.673018i
$86$	1.76838			0.190690
$87$		0			0
$88$	−5.98732			−0.638251
$89$		−	8.45791i		−	0.896537i	−0.893899	−	0.448268i	$-0.852041\pi$
$89$		−	8.45791i		−	0.896537i	0.893899	−	0.448268i	$-0.147959\pi$
$90$		0			0
$91$			16.7345i			1.75426i
$92$	−1.74873			−0.182318
$93$		0			0
$94$			4.30638i			0.444169i
$95$	−9.16459	+	13.5913i	−0.940267	+	1.39443i
$96$		0			0
$97$	−3.64747			−0.370345			−0.185172	−	0.982706i	$-0.559284\pi$
$97$	−3.64747			−0.370345			−0.185172	+	0.982706i	$0.559284\pi$
$98$	15.9381			1.60999
$99$		0			0
$100$	1.87436	+	4.63538i	0.187436	+	0.463538i
$101$	−2.30416			−0.229272			−0.114636	−	0.993408i	$-0.536570\pi$
$101$	−2.30416			−0.229272			−0.114636	+	0.993408i	$0.536570\pi$
$102$		0			0
$103$	11.1716			1.10077			0.550383	−	0.834912i	$-0.314482\pi$
$103$	11.1716			1.10077			0.550383	+	0.834912i	$0.314482\pi$
$104$	−3.49410			−0.342625
$105$		0			0
$106$			3.66238i			0.355722i
$107$			6.51807i			0.630126i	0.949071	+	0.315063i	$0.102026\pi$
$107$			6.51807i			0.630126i	−0.949071	+	0.315063i	$0.897974\pi$
$108$		0			0
$109$			1.33812i			0.128169i	0.997944	+	0.0640846i	$0.0204127\pi$
$109$			1.33812i			0.128169i	−0.997944	+	0.0640846i	$0.979587\pi$
$110$	11.1003	+	7.48491i	1.05837	+	0.713659i
$111$		0			0
$112$			4.78937i			0.452553i
$113$	−1.39109			−0.130863			−0.0654315	−	0.997857i	$-0.520842\pi$
$113$	−1.39109			−0.130863			−0.0654315	+	0.997857i	$0.520842\pi$
$114$		0			0
$115$	3.24208	+	2.18613i	0.302326	+	0.203858i
$116$			7.85004i			0.728858i
$117$		0			0
$118$			2.15110i			0.198025i
$119$			23.7717i			2.17915i
$120$		0			0
$121$	24.8480			2.25891
$122$		−	3.06584i		−	0.277568i
$123$		0			0
$124$		−	3.24097i		−	0.291048i
$125$	2.31981	−	10.9370i	0.207490	−	0.978237i
$126$		0			0
$127$			7.51024i			0.666426i	0.942852	+	0.333213i	$0.108133\pi$
$127$			7.51024i			0.666426i	−0.942852	+	0.333213i	$0.891867\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	6.47793	+	4.36807i	0.568152	+	0.383105i
$131$			6.19975i			0.541675i	0.962625	+	0.270837i	$0.0873006\pi$
$131$			6.19975i			0.541675i	−0.962625	+	0.270837i	$0.912699\pi$
$132$		0			0
$133$	35.1105			3.04447
$134$		−	3.79622i		−	0.327943i
$135$		0			0
$136$	−4.96343			−0.425611
$137$		−	8.97186i		−	0.766518i	−0.923641	−	0.383259i	$-0.874802\pi$
$137$		−	8.97186i		−	0.766518i	0.923641	−	0.383259i	$-0.125198\pi$
$138$		0			0
$139$	5.04168			0.427629			0.213815	−	0.976874i	$-0.431411\pi$
$139$	5.04168			0.427629			0.213815	+	0.976874i	$0.431411\pi$
$140$	5.98732	−	8.87932i	0.506021	−	0.750440i
$141$		0			0
$142$	−8.47719			−0.711390
$143$	20.9203			1.74944
$144$		0			0
$145$	9.81355	−	14.5537i	0.814971	−	1.20862i
$146$			9.05445i			0.749352i
$147$		0			0
$148$	3.96343	−	4.61424i	0.325792	−	0.379288i
$149$	21.6451			1.77324			0.886619	−	0.462500i	$-0.153048\pi$
$149$	21.6451			1.77324			0.886619	+	0.462500i	$0.153048\pi$
$150$		0			0
$151$	6.47544			0.526964			0.263482	−	0.964664i	$-0.415129\pi$
$151$	6.47544			0.526964			0.263482	+	0.964664i	$0.415129\pi$
$152$			7.33092i			0.594616i
$153$		0			0
$154$		−	28.6755i		−	2.31074i
$155$	−4.05163	+	6.00865i	−0.325435	+	0.482626i
$156$		0			0
$157$			13.1689i			1.05099i	0.850797	+	0.525495i	$0.176120\pi$
$157$			13.1689i			1.05099i	−0.850797	+	0.525495i	$0.823880\pi$
$158$		−	5.56622i		−	0.442825i
$159$		0			0
$160$	1.85396	+	1.25013i	0.146569	+	0.0988312i
$161$		−	8.37532i		−	0.660067i
$162$		0			0
$163$	−18.7651			−1.46979			−0.734896	−	0.678180i	$-0.762769\pi$
$163$	−18.7651			−1.46979			−0.734896	+	0.678180i	$0.762769\pi$
$164$	0.530665			0.0414380
$165$		0			0
$166$			3.77680i			0.293136i
$167$	7.19692			0.556914			0.278457	−	0.960449i	$-0.410177\pi$
$167$	7.19692			0.556914			0.278457	+	0.960449i	$0.410177\pi$
$168$		0			0
$169$	−0.791278			−0.0608676
$170$	9.20203	+	6.20492i	0.705763	+	0.475896i
$171$		0			0
$172$	−1.76838			−0.134838
$173$		−	9.79406i		−	0.744629i	−0.928107	−	0.372314i	$-0.878564\pi$
$173$		−	9.79406i		−	0.744629i	0.928107	−	0.372314i	$-0.121436\pi$
$174$		0			0
$175$	−22.2006	+	8.97703i	−1.67820	+	0.678600i
$176$	5.98732			0.451311
$177$		0			0
$178$			8.45791i			0.633947i
$179$			11.2829i			0.843320i	0.906754	+	0.421660i	$0.138552\pi$
$179$			11.2829i			0.843320i	−0.906754	+	0.421660i	$0.861448\pi$
$180$		0			0
$181$	1.82697			0.135798			0.0678989	−	0.997692i	$-0.478370\pi$
$181$	1.82697			0.135798			0.0678989	+	0.997692i	$0.478370\pi$
$182$		−	16.7345i		−	1.24045i
$183$		0			0
$184$	1.74873			0.128918
$185$	−13.1164	+	3.59984i	−0.964340	+	0.264665i
$186$		0			0
$187$	29.7177			2.17317
$188$		−	4.30638i		−	0.314075i
$189$		0			0
$190$	9.16459	−	13.5913i	0.664869	−	0.986014i
$191$		−	23.8204i		−	1.72358i	−0.507264	−	0.861791i	$-0.669343\pi$
$191$		−	23.8204i		−	1.72358i	0.507264	−	0.861791i	$-0.330657\pi$
$192$		0			0
$193$	−8.40405			−0.604937			−0.302468	−	0.953159i	$-0.597811\pi$
$193$	−8.40405			−0.604937			−0.302468	+	0.953159i	$0.597811\pi$
$194$	3.64747			0.261873
$195$		0			0
$196$	−15.9381			−1.13843
$197$			4.22797i			0.301230i	0.988592	+	0.150615i	$0.0481254\pi$
$197$			4.22797i			0.301230i	−0.988592	+	0.150615i	$0.951875\pi$
$198$		0			0
$199$		−	17.7545i		−	1.25858i	−0.777170	−	0.629290i	$-0.783346\pi$
$199$		−	17.7545i		−	1.25858i	0.777170	−	0.629290i	$-0.216654\pi$
$200$	−1.87436	−	4.63538i	−0.132538	−	0.327771i
$201$		0			0
$202$	2.30416			0.162120
$203$	−37.5968			−2.63878
$204$		0			0
$205$	−0.983834	−	0.663399i	−0.0687139	−	0.0463338i
$206$	−11.1716			−0.778360
$207$		0			0
$208$	3.49410			0.242272
$209$		−	43.8926i		−	3.03611i
$210$		0			0
$211$	4.57321			0.314833			0.157417	−	0.987532i	$-0.449683\pi$
$211$	4.57321			0.314833			0.157417	+	0.987532i	$0.449683\pi$
$212$		−	3.66238i		−	0.251534i
$213$		0			0
$214$		−	6.51807i		−	0.445566i
$215$	3.27852	+	2.21071i	0.223593	+	0.150769i
$216$		0			0
$217$	15.5222			1.05372
$218$		−	1.33812i		−	0.0906293i
$219$		0			0
$220$	−11.1003	−	7.48491i	−0.748381	−	0.504633i
$221$	17.3427			1.16660
$222$		0			0
$223$			20.3205i			1.36076i	0.732860	+	0.680380i	$0.238185\pi$
$223$			20.3205i			1.36076i	−0.732860	+	0.680380i	$0.761815\pi$
$224$		−	4.78937i		−	0.320003i
$225$		0			0
$226$	1.39109			0.0925341
$227$	−5.74303			−0.381178			−0.190589	−	0.981670i	$-0.561040\pi$
$227$	−5.74303			−0.381178			−0.190589	+	0.981670i	$0.561040\pi$
$228$		0			0
$229$	23.4383			1.54885			0.774423	−	0.632669i	$-0.218040\pi$
$229$	23.4383			1.54885			0.774423	+	0.632669i	$0.218040\pi$
$230$	−3.24208	−	2.18613i	−0.213777	−	0.144149i
$231$		0			0
$232$		−	7.85004i		−	0.515380i
$233$			17.2961i			1.13310i	0.824027	+	0.566551i	$0.191723\pi$
$233$			17.2961i			1.13310i	−0.824027	+	0.566551i	$0.808277\pi$
$234$		0			0
$235$	−5.38352	+	7.98388i	−0.351182	+	0.520811i
$236$		−	2.15110i		−	0.140025i
$237$		0			0
$238$		−	23.7717i		−	1.54089i
$239$			3.68796i			0.238554i	0.992861	+	0.119277i	$0.0380577\pi$
$239$			3.68796i			0.238554i	−0.992861	+	0.119277i	$0.961942\pi$
$240$		0			0
$241$		−	11.3613i		−	0.731844i	−0.930646	−	0.365922i	$-0.880754\pi$
$241$		−	11.3613i		−	0.731844i	0.930646	−	0.365922i	$-0.119246\pi$
$242$	−24.8480			−1.59729
$243$		0			0
$244$			3.06584i			0.196270i
$245$	29.5486	+	19.9246i	1.88779	+	1.27294i
$246$		0			0
$247$		−	25.6150i		−	1.62984i
$248$			3.24097i			0.205802i
$249$		0			0
$250$	−2.31981	+	10.9370i	−0.146718	+	0.691718i
$251$			12.8260i			0.809567i	0.914412	+	0.404784i	$0.132653\pi$
$251$			12.8260i			0.809567i	−0.914412	+	0.404784i	$0.867347\pi$
$252$		0			0
$253$	−10.4702			−0.658256
$254$		−	7.51024i		−	0.471234i
$255$		0			0
$256$	1.00000			0.0625000
$257$	14.0268			0.874965			0.437483	−	0.899227i	$-0.355870\pi$
$257$	14.0268			0.874965			0.437483	+	0.899227i	$0.355870\pi$
$258$		0			0
$259$	22.0993	+	18.9824i	1.37318	+	1.17951i
$260$	−6.47793	−	4.36807i	−0.401744	−	0.270896i
$261$		0			0
$262$		−	6.19975i		−	0.383022i
$263$		−	3.57182i		−	0.220248i	−0.993918	−	0.110124i	$-0.964875\pi$
$263$		−	3.57182i		−	0.220248i	0.993918	−	0.110124i	$-0.0351248\pi$
$264$		0			0
$265$	−4.57844	+	6.78993i	−0.281252	+	0.417102i
$266$	−35.1105			−2.15276
$267$		0			0
$268$			3.79622i			0.231891i
$269$	0.458895			0.0279793			0.0139897	−	0.999902i	$-0.495547\pi$
$269$	0.458895			0.0279793			0.0139897	+	0.999902i	$0.495547\pi$
$270$		0			0
$271$	28.8897			1.75492			0.877462	−	0.479645i	$-0.159235\pi$
$271$	28.8897			1.75492			0.877462	+	0.479645i	$0.159235\pi$
$272$	4.96343			0.300952
$273$		0			0
$274$			8.97186i			0.542010i
$275$	11.2224	+	27.7535i	0.676738	+	1.67360i
$276$		0			0
$277$	−22.4482			−1.34878			−0.674391	−	0.738374i	$-0.735594\pi$
$277$	−22.4482			−1.34878			−0.674391	+	0.738374i	$0.735594\pi$
$278$	−5.04168			−0.302380
$279$		0			0
$280$	−5.98732	+	8.87932i	−0.357811	+	0.530641i
$281$			6.04908i			0.360858i	0.983588	+	0.180429i	$0.0577486\pi$
$281$			6.04908i			0.360858i	−0.983588	+	0.180429i	$0.942251\pi$
$282$		0			0
$283$	−10.8317			−0.643878			−0.321939	−	0.946760i	$-0.604335\pi$
$283$	−10.8317			−0.643878			−0.321939	+	0.946760i	$0.604335\pi$
$284$	8.47719			0.503028
$285$		0			0
$286$	−20.9203			−1.23704
$287$			2.54155i			0.150023i
$288$		0			0
$289$	7.63567			0.449157
$290$	−9.81355	+	14.5537i	−0.576271	+	0.854622i
$291$		0			0
$292$		−	9.05445i		−	0.529872i
$293$		−	23.3144i		−	1.36204i	−0.732264	−	0.681021i	$-0.761536\pi$
$293$		−	23.3144i		−	1.36204i	0.732264	−	0.681021i	$-0.238464\pi$
$294$		0			0
$295$	−2.68915	+	3.98806i	−0.156568	+	0.232194i
$296$	−3.96343	+	4.61424i	−0.230370	+	0.268197i
$297$		0			0
$298$	−21.6451			−1.25387
$299$	−6.11023			−0.353364
$300$		0			0
$301$		−	8.46945i		−	0.488171i
$302$	−6.47544			−0.372620
$303$		0			0
$304$		−	7.33092i		−	0.420457i
$305$	3.83269	−	5.68396i	0.219459	−	0.325462i
$306$		0			0
$307$			14.2651i			0.814153i	0.913394	+	0.407077i	$0.133452\pi$
$307$			14.2651i			0.814153i	−0.913394	+	0.407077i	$0.866548\pi$
$308$			28.6755i			1.63394i
$309$		0			0
$310$	4.05163	−	6.00865i	0.230117	−	0.341268i
$311$			22.5322i			1.27768i	0.769339	+	0.638841i	$0.220586\pi$
$311$			22.5322i			1.27768i	−0.769339	+	0.638841i	$0.779414\pi$
$312$		0			0
$313$	10.0000			0.565233			0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000			0.565233			0.282617	+	0.959233i	$0.408798\pi$
$314$		−	13.1689i		−	0.743162i
$315$		0			0
$316$			5.56622i			0.313124i
$317$			12.3877i			0.695764i	0.937538	+	0.347882i	$0.113099\pi$
$317$			12.3877i			0.695764i	−0.937538	+	0.347882i	$0.886901\pi$
$318$		0			0
$319$			47.0007i			2.63154i
$320$	−1.85396	−	1.25013i	−0.103640	−	0.0698842i
$321$		0			0
$322$			8.37532i			0.466738i
$323$		−	36.3865i		−	2.02460i
$324$		0			0
$325$	6.54921	+	16.1965i	0.363285	+	0.898419i
$326$	18.7651			1.03930
$327$		0			0
$328$	−0.530665			−0.0293011
$329$	20.6249			1.13709
$330$		0			0
$331$			19.0068i			1.04471i	0.852728	+	0.522355i	$0.174946\pi$
$331$			19.0068i			1.04471i	−0.852728	+	0.522355i	$0.825054\pi$
$332$		−	3.77680i		−	0.207279i
$333$		0			0
$334$	−7.19692			−0.393798
$335$	4.74575	−	7.03805i	0.259288	−	0.384530i
$336$		0			0
$337$		−	25.1046i		−	1.36753i	−0.729701	−	0.683766i	$-0.760341\pi$
$337$		−	25.1046i		−	1.36753i	0.729701	−	0.683766i	$-0.239659\pi$
$338$	0.791278			0.0430399
$339$		0			0
$340$	−9.20203	−	6.20492i	−0.499050	−	0.336509i
$341$		−	19.4047i		−	1.05083i
$342$		0			0
$343$		−	42.8078i		−	2.31140i
$344$	1.76838			0.0953449
$345$		0			0
$346$			9.79406i			0.526532i
$347$	30.4282			1.63347			0.816736	−	0.577011i	$-0.195781\pi$
$347$	30.4282			1.63347			0.816736	+	0.577011i	$0.195781\pi$
$348$		0			0
$349$	15.1341			0.810111			0.405056	−	0.914292i	$-0.367252\pi$
$349$	15.1341			0.810111			0.405056	+	0.914292i	$0.367252\pi$
$350$	22.2006	−	8.97703i	1.18667	−	0.479842i
$351$		0			0
$352$	−5.98732			−0.319125
$353$	−10.1331			−0.539332			−0.269666	−	0.962954i	$-0.586913\pi$
$353$	−10.1331			−0.539332			−0.269666	+	0.962954i	$0.586913\pi$
$354$		0			0
$355$	−15.7164	−	10.5976i	−0.834140	−	0.562460i
$356$		−	8.45791i		−	0.448268i
$357$		0			0
$358$		−	11.2829i		−	0.596317i
$359$	26.3685			1.39168			0.695838	−	0.718199i	$-0.255033\pi$
$359$	26.3685			1.39168			0.695838	+	0.718199i	$0.255033\pi$
$360$		0			0
$361$	−34.7424			−1.82855
$362$	−1.82697			−0.0960235
$363$		0			0
$364$			16.7345i			0.877128i
$365$	−11.3192	+	16.7866i	−0.592475	+	0.878653i
$366$		0			0
$367$			2.21157i			0.115443i	0.998333	+	0.0577215i	$0.0183835\pi$
$367$			2.21157i			0.115443i	−0.998333	+	0.0577215i	$0.981616\pi$
$368$	−1.74873			−0.0911588
$369$		0			0
$370$	13.1164	−	3.59984i	0.681892	−	0.187147i
$371$	17.5405			0.910658
$372$		0			0
$373$			6.08275i			0.314953i	0.987523	+	0.157476i	$0.0503358\pi$
$373$			6.08275i			0.314953i	−0.987523	+	0.157476i	$0.949664\pi$
$374$	−29.7177			−1.53666
$375$		0			0
$376$			4.30638i			0.222085i
$377$			27.4288i			1.41266i
$378$		0			0
$379$	−20.0919			−1.03205			−0.516025	−	0.856574i	$-0.672589\pi$
$379$	−20.0919			−1.03205			−0.516025	+	0.856574i	$0.672589\pi$
$380$	−9.16459	+	13.5913i	−0.470133	+	0.697217i
$381$		0			0
$382$			23.8204i			1.21876i
$383$	11.5368			0.589501			0.294751	−	0.955574i	$-0.404763\pi$
$383$	11.5368			0.589501			0.294751	+	0.955574i	$0.404763\pi$
$384$		0			0
$385$	35.8480	−	53.1634i	1.82698	−	2.70946i
$386$	8.40405			0.427755
$387$		0			0
$388$	−3.64747			−0.185172
$389$			8.55057i			0.433531i	0.976224	+	0.216766i	$0.0695507\pi$
$389$			8.55057i			0.433531i	−0.976224	+	0.216766i	$0.930449\pi$
$390$		0			0
$391$	−8.67970			−0.438951
$392$	15.9381			0.804995
$393$		0			0
$394$		−	4.22797i		−	0.213002i
$395$	6.95848	−	10.3196i	0.350119	−	0.519234i
$396$		0			0
$397$			9.84444i			0.494078i	0.969006	+	0.247039i	$0.0794576\pi$
$397$			9.84444i			0.494078i	−0.969006	+	0.247039i	$0.920542\pi$
$398$			17.7545i			0.889951i
$399$		0			0
$400$	1.87436	+	4.63538i	0.0937182	+	0.231769i
$401$		−	31.0959i		−	1.55285i	−0.630207	−	0.776427i	$-0.717030\pi$
$401$		−	31.0959i		−	1.55285i	0.630207	−	0.776427i	$-0.282970\pi$
$402$		0			0
$403$		−	11.3243i		−	0.564102i
$404$	−2.30416			−0.114636
$405$		0			0
$406$	37.5968			1.86590
$407$	23.7304	−	27.6269i	1.17627	−	1.36942i
$408$		0			0
$409$		−	38.3150i		−	1.89455i	−0.320417	−	0.947277i	$-0.603823\pi$
$409$		−	38.3150i		−	1.89455i	0.320417	−	0.947277i	$-0.396177\pi$
$410$	0.983834	+	0.663399i	0.0485881	+	0.0327629i
$411$		0			0
$412$	11.1716			0.550383
$413$	10.3024			0.506948
$414$		0			0
$415$	−4.72148	+	7.00205i	−0.231768	+	0.343717i
$416$	−3.49410			−0.171312
$417$		0			0
$418$			43.8926i			2.14686i
$419$	−29.0183			−1.41764			−0.708819	−	0.705391i	$-0.750772\pi$
$419$	−29.0183			−1.41764			−0.708819	+	0.705391i	$0.750772\pi$
$420$		0			0
$421$			23.6443i			1.15235i	0.817326	+	0.576175i	$0.195455\pi$
$421$			23.6443i			1.15235i	−0.817326	+	0.576175i	$0.804545\pi$
$422$	−4.57321			−0.222621
$423$		0			0
$424$			3.66238i			0.177861i
$425$	9.30328	+	23.0074i	0.451276	+	1.11602i
$426$		0			0
$427$	−14.6834			−0.710582
$428$			6.51807i			0.315063i
$429$		0			0
$430$	−3.27852	−	2.21071i	−0.158104	−	0.106610i
$431$			32.1126i			1.54681i	0.633912	+	0.773406i	$0.281448\pi$
$431$			32.1126i			1.54681i	−0.633912	+	0.773406i	$0.718552\pi$
$432$		0			0
$433$			13.0575i			0.627504i	0.949505	+	0.313752i	$0.101586\pi$
$433$			13.0575i			0.627504i	−0.949505	+	0.313752i	$0.898414\pi$
$434$	−15.5222			−0.745091
$435$		0			0
$436$			1.33812i			0.0640846i
$437$			12.8198i			0.613254i
$438$		0			0
$439$			28.0499i			1.33875i	0.742924	+	0.669375i	$0.233438\pi$
$439$			28.0499i			1.33875i	−0.742924	+	0.669375i	$0.766562\pi$
$440$	11.1003	+	7.48491i	0.529185	+	0.356829i
$441$		0			0
$442$	−17.3427			−0.824909
$443$			6.79629i			0.322902i	0.986881	+	0.161451i	$0.0516173\pi$
$443$			6.79629i			0.322902i	−0.986881	+	0.161451i	$0.948383\pi$
$444$		0			0
$445$	−10.5735	+	15.6807i	−0.501230	+	0.743335i
$446$		−	20.3205i		−	0.962203i
$447$		0			0
$448$			4.78937i			0.226277i
$449$		−	17.3278i		−	0.817747i	−0.912591	−	0.408874i	$-0.865922\pi$
$449$		−	17.3278i		−	0.817747i	0.912591	−	0.408874i	$-0.134078\pi$
$450$		0			0
$451$	3.17726			0.149611
$452$	−1.39109			−0.0654315
$453$		0			0
$454$	5.74303			0.269534
$455$	20.9203	−	31.0252i	0.980758	−	1.45448i
$456$		0			0
$457$	−3.20960			−0.150139			−0.0750693	−	0.997178i	$-0.523918\pi$
$457$	−3.20960			−0.150139			−0.0750693	+	0.997178i	$0.523918\pi$
$458$	−23.4383			−1.09520
$459$		0			0
$460$	3.24208	+	2.18613i	0.151163	+	0.101929i
$461$			34.0347i			1.58515i	0.609773	+	0.792576i	$0.291261\pi$
$461$			34.0347i			1.58515i	−0.609773	+	0.792576i	$0.708739\pi$
$462$		0			0
$463$	−26.0543			−1.21085			−0.605423	−	0.795904i	$-0.706996\pi$
$463$	−26.0543			−1.21085			−0.605423	+	0.795904i	$0.706996\pi$
$464$			7.85004i			0.364429i
$465$		0			0
$466$		−	17.2961i		−	0.801224i
$467$	−20.3289			−0.940710			−0.470355	−	0.882477i	$-0.655874\pi$
$467$	−20.3289			−0.940710			−0.470355	+	0.882477i	$0.655874\pi$
$468$		0			0
$469$	−18.1815			−0.839544
$470$	5.38352	−	7.98388i	0.248323	−	0.368269i
$471$		0			0
$472$			2.15110i			0.0990123i
$473$	−10.5879			−0.486832
$474$		0			0
$475$	33.9816	−	13.7408i	1.55918	−	0.630472i
$476$			23.7717i			1.08958i
$477$		0			0
$478$		−	3.68796i		−	0.168683i
$479$		−	6.22972i		−	0.284643i	−0.989820	−	0.142322i	$-0.954543\pi$
$479$		−	6.22972i		−	0.284643i	0.989820	−	0.142322i	$-0.0454567\pi$
$480$		0			0
$481$	13.8486	−	16.1226i	0.631443	−	0.735127i
$482$			11.3613i			0.517492i
$483$		0			0
$484$	24.8480			1.12946
$485$	6.76228	+	4.55980i	0.307059	+	0.207050i
$486$		0			0
$487$	30.5352			1.38368			0.691841	−	0.722050i	$-0.256800\pi$
$487$	30.5352			1.38368			0.691841	+	0.722050i	$0.256800\pi$
$488$		−	3.06584i		−	0.138784i
$489$		0			0
$490$	−29.5486	−	19.9246i	−1.33487	−	0.900103i
$491$	−24.5944			−1.10993			−0.554965	−	0.831874i	$-0.687268\pi$
$491$	−24.5944			−1.10993			−0.554965	+	0.831874i	$0.687268\pi$
$492$		0			0
$493$			38.9632i			1.75481i
$494$			25.6150i			1.15247i
$495$		0			0
$496$		−	3.24097i		−	0.145524i
$497$			40.6004i			1.82118i
$498$		0			0
$499$			33.5739i			1.50297i	0.659747	+	0.751487i	$0.270663\pi$
$499$			33.5739i			1.50297i	−0.659747	+	0.751487i	$0.729337\pi$
$500$	2.31981	−	10.9370i	0.103745	−	0.489119i
$501$		0			0
$502$		−	12.8260i		−	0.572451i
$503$	−1.77931			−0.0793357			−0.0396679	−	0.999213i	$-0.512630\pi$
$503$	−1.77931			−0.0793357			−0.0396679	+	0.999213i	$0.512630\pi$
$504$		0			0
$505$	4.27183	+	2.88049i	0.190094	+	0.128180i
$506$	10.4702			0.465458
$507$		0			0
$508$			7.51024i			0.333213i
$509$	−29.5114			−1.30807			−0.654035	−	0.756464i	$-0.726925\pi$
$509$	−29.5114			−1.30807			−0.654035	+	0.756464i	$0.726925\pi$
$510$		0			0
$511$	43.3651			1.91836
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−14.0268			−0.618694
$515$	−20.7117	−	13.9659i	−0.912665	−	0.615410i
$516$		0			0
$517$		−	25.7837i		−	1.13397i
$518$	−22.0993	−	18.9824i	−0.970988	−	0.834037i
$519$		0			0
$520$	6.47793	+	4.36807i	0.284076	+	0.191552i
$521$	−29.2841			−1.28296			−0.641481	−	0.767139i	$-0.721680\pi$
$521$	−29.2841			−1.28296			−0.641481	+	0.767139i	$0.721680\pi$
$522$		0			0
$523$	29.9729			1.31062			0.655312	−	0.755359i	$-0.272537\pi$
$523$	29.9729			1.31062			0.655312	+	0.755359i	$0.272537\pi$
$524$			6.19975i			0.270837i
$525$		0			0
$526$			3.57182i			0.155739i
$527$		−	16.0864i		−	0.700732i
$528$		0			0
$529$	−19.9419			−0.867041
$530$	4.57844	−	6.78993i	0.198875	−	0.294936i
$531$		0			0
$532$	35.1105			1.52223
$533$	1.85420			0.0803141
$534$		0			0
$535$	8.14842	−	12.0843i	0.352287	−	0.522449i
$536$		−	3.79622i		−	0.163972i
$537$		0			0
$538$	−0.458895			−0.0197844
$539$	−95.4264			−4.11031
$540$		0			0
$541$			18.7155i			0.804644i	0.915498	+	0.402322i	$0.131797\pi$
$541$			18.7155i			0.804644i	−0.915498	+	0.402322i	$0.868203\pi$
$542$	−28.8897			−1.24092
$543$		0			0
$544$	−4.96343			−0.212805
$545$	1.67283	−	2.48084i	0.0716560	−	0.106267i
$546$		0			0
$547$	32.4792			1.38871			0.694355	−	0.719633i	$-0.255690\pi$
$547$	32.4792			1.38871			0.694355	+	0.719633i	$0.255690\pi$
$548$		−	8.97186i		−	0.383259i
$549$		0			0
$550$	−11.2224	−	27.7535i	−0.478526	−	1.18341i
$551$	57.5480			2.45163
$552$		0			0
$553$	−26.6587			−1.13364
$554$	22.4482			0.953733
$555$		0			0
$556$	5.04168			0.213815
$557$	−16.0158			−0.678612			−0.339306	−	0.940676i	$-0.610192\pi$
$557$	−16.0158			−0.678612			−0.339306	+	0.940676i	$0.610192\pi$
$558$		0			0
$559$	−6.17891			−0.261340
$560$	5.98732	−	8.87932i	0.253011	−	0.375220i
$561$		0			0
$562$		−	6.04908i		−	0.255165i
$563$	−15.3069			−0.645109			−0.322554	−	0.946551i	$-0.604542\pi$
$563$	−15.3069			−0.645109			−0.322554	+	0.946551i	$0.604542\pi$
$564$		0			0
$565$	2.57904	+	1.73904i	0.108501	+	0.0731621i
$566$	10.8317			0.455291
$567$		0			0
$568$	−8.47719			−0.355695
$569$			26.6494i			1.11720i	0.829437	+	0.558601i	$0.188662\pi$
$569$			26.6494i			1.11720i	−0.829437	+	0.558601i	$0.811338\pi$
$570$		0			0
$571$	23.1683			0.969564			0.484782	−	0.874635i	$-0.338899\pi$
$571$	23.1683			0.969564			0.484782	+	0.874635i	$0.338899\pi$
$572$	20.9203			0.874721
$573$		0			0
$574$		−	2.54155i		−	0.106082i
$575$	−3.27776	−	8.10603i	−0.136692	−	0.338045i
$576$		0			0
$577$	3.54110			0.147418			0.0737091	−	0.997280i	$-0.476516\pi$
$577$	3.54110			0.147418			0.0737091	+	0.997280i	$0.476516\pi$
$578$	−7.63567			−0.317602
$579$		0			0
$580$	9.81355	−	14.5537i	0.407485	−	0.604309i
$581$	18.0885			0.750437
$582$		0			0
$583$		−	21.9279i		−	0.908160i
$584$			9.05445i			0.374676i
$585$		0			0
$586$			23.3144i			0.963109i
$587$	12.0976			0.499320			0.249660	−	0.968334i	$-0.419681\pi$
$587$	12.0976			0.499320			0.249660	+	0.968334i	$0.419681\pi$
$588$		0			0
$589$	−23.7593			−0.978986
$590$	2.68915	−	3.98806i	0.110710	−	0.164186i
$591$		0			0
$592$	3.96343	−	4.61424i	0.162896	−	0.189644i
$593$		−	17.2007i		−	0.706348i	−0.935558	−	0.353174i	$-0.885102\pi$
$593$		−	17.2007i		−	0.706348i	0.935558	−	0.353174i	$-0.114898\pi$
$594$		0			0
$595$	29.7177	−	44.0719i	1.21831	−	1.80677i
$596$	21.6451			0.886619
$597$		0			0
$598$	6.11023			0.249866
$599$	−2.41919			−0.0988454			−0.0494227	−	0.998778i	$-0.515738\pi$
$599$	−2.41919			−0.0988454			−0.0494227	+	0.998778i	$0.515738\pi$
$600$		0			0
$601$	−39.0483			−1.59281			−0.796407	−	0.604761i	$-0.793269\pi$
$601$	−39.0483			−1.59281			−0.796407	+	0.604761i	$0.793269\pi$
$602$			8.46945i			0.345189i
$603$		0			0
$604$	6.47544			0.263482
$605$	−46.0674	−	31.0632i	−1.87290	−	1.26290i
$606$		0			0
$607$	38.0508			1.54443			0.772217	−	0.635359i	$-0.219148\pi$
$607$	38.0508			1.54443			0.772217	+	0.635359i	$0.219148\pi$
$608$			7.33092i			0.297308i
$609$		0			0
$610$	−3.83269	+	5.68396i	−0.155181	+	0.230137i
$611$		−	15.0469i		−	0.608733i
$612$		0			0
$613$			7.12176i			0.287645i	0.989603	+	0.143823i	$0.0459395\pi$
$613$			7.12176i			0.287645i	−0.989603	+	0.143823i	$0.954061\pi$
$614$		−	14.2651i		−	0.575693i
$615$		0			0
$616$		−	28.6755i		−	1.15537i
$617$		−	42.6678i		−	1.71774i	−0.512192	−	0.858871i	$-0.671166\pi$
$617$		−	42.6678i		−	1.71774i	0.512192	−	0.858871i	$-0.328834\pi$
$618$		0			0
$619$	−6.30429			−0.253391			−0.126695	−	0.991942i	$-0.540437\pi$
$619$	−6.30429			−0.253391			−0.126695	+	0.991942i	$0.540437\pi$
$620$	−4.05163	+	6.00865i	−0.162717	+	0.241313i
$621$		0			0
$622$		−	22.5322i		−	0.903458i
$623$	40.5081			1.62292
$624$		0			0
$625$	−17.9735	+	17.3768i	−0.718941	+	0.695072i
$626$	−10.0000			−0.399680
$627$		0			0
$628$			13.1689i			0.525495i
$629$	19.6722	−	22.9025i	0.784383	−	0.913181i
$630$		0			0
$631$			32.6385i			1.29932i	0.760225	+	0.649660i	$0.225089\pi$
$631$			32.6385i			1.29932i	−0.760225	+	0.649660i	$0.774911\pi$
$632$		−	5.56622i		−	0.221412i
$633$		0			0
$634$		−	12.3877i		−	0.491979i
$635$	9.38875	−	13.9237i	0.372581	−	0.552546i
$636$		0			0
$637$	−55.6892			−2.20649
$638$		−	47.0007i		−	1.86078i
$639$		0			0
$640$	1.85396	+	1.25013i	0.0732844	+	0.0494156i
$641$	12.1721			0.480767			0.240384	−	0.970678i	$-0.422727\pi$
$641$	12.1721			0.480767			0.240384	+	0.970678i	$0.422727\pi$
$642$		0			0
$643$	−10.0853			−0.397727			−0.198864	−	0.980027i	$-0.563725\pi$
$643$	−10.0853			−0.397727			−0.198864	+	0.980027i	$0.563725\pi$
$644$		−	8.37532i		−	0.330034i
$645$		0			0
$646$			36.3865i			1.43161i
$647$	−38.5061			−1.51383			−0.756916	−	0.653512i	$-0.773295\pi$
$647$	−38.5061			−1.51383			−0.756916	+	0.653512i	$0.773295\pi$
$648$		0			0
$649$		−	12.8793i		−	0.505558i
$650$	−6.54921	−	16.1965i	−0.256881	−	0.635278i
$651$		0			0
$652$	−18.7651			−0.734896
$653$	−2.20349			−0.0862293			−0.0431146	−	0.999070i	$-0.513728\pi$
$653$	−2.20349			−0.0862293			−0.0431146	+	0.999070i	$0.513728\pi$
$654$		0			0
$655$	7.75048	−	11.4941i	0.302836	−	0.449112i
$656$	0.530665			0.0207190
$657$		0			0
$658$	−20.6249			−0.804041
$659$	20.4048			0.794859			0.397430	−	0.917633i	$-0.369902\pi$
$659$	20.4048			0.794859			0.397430	+	0.917633i	$0.369902\pi$
$660$		0			0
$661$			27.0306i			1.05137i	0.850680	+	0.525684i	$0.176191\pi$
$661$			27.0306i			1.05137i	−0.850680	+	0.525684i	$0.823809\pi$
$662$		−	19.0068i		−	0.738721i
$663$		0			0
$664$			3.77680i			0.146568i
$665$	−65.0936	−	43.8926i	−2.52422	−	1.70208i
$666$		0			0
$667$		−	13.7276i		−	0.531535i
$668$	7.19692			0.278457
$669$		0			0
$670$	−4.74575	+	7.03805i	−0.183344	+	0.271904i
$671$			18.3562i			0.708632i
$672$		0			0
$673$			11.6776i			0.450139i	0.974343	+	0.225070i	$0.0722609\pi$
$673$			11.6776i			0.450139i	−0.974343	+	0.225070i	$0.927739\pi$
$674$			25.1046i			0.966991i
$675$		0			0
$676$	−0.791278			−0.0304338
$677$		−	37.2578i		−	1.43193i	−0.698135	−	0.715966i	$-0.745986\pi$
$677$		−	37.2578i		−	1.43193i	0.698135	−	0.715966i	$-0.254014\pi$
$678$		0			0
$679$		−	17.4691i		−	0.670402i
$680$	9.20203	+	6.20492i	0.352882	+	0.237948i
$681$		0			0
$682$			19.4047i			0.743046i
$683$	−46.3018			−1.77169			−0.885845	−	0.463981i	$-0.846420\pi$
$683$	−46.3018			−1.77169			−0.885845	+	0.463981i	$0.846420\pi$
$684$		0			0
$685$	−11.2160	+	16.6335i	−0.428540	+	0.635533i
$686$			42.8078i			1.63441i
$687$		0			0
$688$	−1.76838			−0.0674190
$689$		−	12.7967i		−	0.487516i
$690$		0			0
$691$	29.7037			1.12998			0.564991	−	0.825097i	$-0.308879\pi$
$691$	29.7037			1.12998			0.564991	+	0.825097i	$0.308879\pi$
$692$		−	9.79406i		−	0.372314i
$693$		0			0
$694$	−30.4282			−1.15504
$695$	−9.34708	−	6.30273i	−0.354555	−	0.239076i
$696$		0			0
$697$	2.63392			0.0997669
$698$	−15.1341			−0.572835
$699$		0			0
$700$	−22.2006	+	8.97703i	−0.839102	+	0.339300i
$701$			45.9214i			1.73443i	0.497936	+	0.867214i	$0.334091\pi$
$701$			45.9214i			1.73443i	−0.497936	+	0.867214i	$0.665909\pi$
$702$		0			0
$703$	−33.8266	−	29.0556i	−1.27580	−	1.09585i
$704$	5.98732			0.225656
$705$		0			0
$706$	10.1331			0.381365
$707$		−	11.0355i		−	0.415031i
$708$		0			0
$709$		−	52.6575i		−	1.97759i	−0.149266	−	0.988797i	$-0.547691\pi$
$709$		−	52.6575i		−	1.97759i	0.149266	−	0.988797i	$-0.452309\pi$
$710$	15.7164	+	10.5976i	0.589826	+	0.397719i
$711$		0			0
$712$			8.45791i			0.316974i
$713$			5.66759i			0.212253i
$714$		0			0
$715$	−38.7855	−	26.1530i	−1.45049	−	0.978068i
$716$			11.2829i			0.421660i
$717$		0			0
$718$	−26.3685			−0.984063
$719$	13.3494			0.497850			0.248925	−	0.968523i	$-0.419923\pi$
$719$	13.3494			0.497850			0.248925	+	0.968523i	$0.419923\pi$
$720$		0			0
$721$			53.5048i			1.99262i
$722$	34.7424			1.29298
$723$		0			0
$724$	1.82697			0.0678989
$725$	−36.3879	+	14.7138i	−1.35141	+	0.546458i
$726$		0			0
$727$	−13.1733			−0.488571			−0.244286	−	0.969703i	$-0.578553\pi$
$727$	−13.1733			−0.488571			−0.244286	+	0.969703i	$0.578553\pi$
$728$		−	16.7345i		−	0.620223i
$729$		0			0
$730$	11.3192	−	16.7866i	0.418943	−	0.621301i
$731$	−8.77726			−0.324639
$732$		0			0
$733$		−	32.3264i		−	1.19400i	−0.802241	−	0.597001i	$-0.796359\pi$
$733$		−	32.3264i		−	1.19400i	0.802241	−	0.597001i	$-0.203641\pi$
$734$		−	2.21157i		−	0.0816305i
$735$		0			0
$736$	1.74873			0.0644590
$737$			22.7292i			0.837240i
$738$		0			0
$739$	6.94169			0.255354			0.127677	−	0.991816i	$-0.459248\pi$
$739$	6.94169			0.255354			0.127677	+	0.991816i	$0.459248\pi$
$740$	−13.1164	+	3.59984i	−0.482170	+	0.132333i
$741$		0			0
$742$	−17.5405			−0.643933
$743$			36.0784i			1.32359i	0.749685	+	0.661795i	$0.230205\pi$
$743$			36.0784i			1.32359i	−0.749685	+	0.661795i	$0.769795\pi$
$744$		0			0
$745$	−40.1293	−	27.0592i	−1.47022	−	0.991371i
$746$		−	6.08275i		−	0.222705i
$747$		0			0
$748$	29.7177			1.08659
$749$	−31.2175			−1.14066
$750$		0			0
$751$	−29.9052			−1.09126			−0.545629	−	0.838027i	$-0.683709\pi$
$751$	−29.9052			−1.09126			−0.545629	+	0.838027i	$0.683709\pi$
$752$		−	4.30638i		−	0.157038i
$753$		0			0
$754$		−	27.4288i		−	0.998898i
$755$	−12.0052	−	8.09512i	−0.436915	−	0.294612i
$756$		0			0
$757$	−24.9464			−0.906693			−0.453347	−	0.891334i	$-0.649770\pi$
$757$	−24.9464			−0.906693			−0.453347	+	0.891334i	$0.649770\pi$
$758$	20.0919			0.729769
$759$		0			0
$760$	9.16459	−	13.5913i	0.332434	−	0.493007i
$761$	−11.7647			−0.426469			−0.213235	−	0.977001i	$-0.568400\pi$
$761$	−11.7647			−0.426469			−0.213235	+	0.977001i	$0.568400\pi$
$762$		0			0
$763$	−6.40878			−0.232013
$764$		−	23.8204i		−	0.861791i
$765$		0			0
$766$	−11.5368			−0.416840
$767$		−	7.51615i		−	0.271392i
$768$		0			0
$769$			26.7939i			0.966214i	0.875561	+	0.483107i	$0.160492\pi$
$769$			26.7939i			0.966214i	−0.875561	+	0.483107i	$0.839508\pi$
$770$	−35.8480	+	53.1634i	−1.29187	+	1.91587i
$771$		0			0
$772$	−8.40405			−0.302468
$773$		−	2.77358i		−	0.0997589i	−0.998755	−	0.0498794i	$-0.984116\pi$
$773$		−	2.77358i		−	0.0997589i	0.998755	−	0.0498794i	$-0.0158837\pi$
$774$		0			0
$775$	15.0231	−	6.07477i	0.539647	−	0.218212i
$776$	3.64747			0.130937
$777$		0			0
$778$		−	8.55057i		−	0.306553i
$779$		−	3.89026i		−	0.139383i
$780$		0			0
$781$	50.7556			1.81618
$782$	8.67970			0.310386
$783$		0			0
$784$	−15.9381			−0.569217
$785$	16.4628	−	24.4146i	0.587581	−	0.871395i
$786$		0			0
$787$		−	28.0910i		−	1.00134i	−0.865639	−	0.500669i	$-0.833088\pi$
$787$		−	28.0910i		−	1.00134i	0.865639	−	0.500669i	$-0.166912\pi$
$788$			4.22797i			0.150615i
$789$		0			0
$790$	−6.95848	+	10.3196i	−0.247572	+	0.367154i
$791$		−	6.66246i		−	0.236890i
$792$		0			0
$793$			10.7123i			0.380407i
$794$		−	9.84444i		−	0.349366i
$795$		0			0
$796$		−	17.7545i		−	0.629290i
$797$	1.36472			0.0483407			0.0241704	−	0.999708i	$-0.492306\pi$
$797$	1.36472			0.0483407			0.0241704	+	0.999708i	$0.492306\pi$
$798$		0			0
$799$		−	21.3744i		−	0.756173i
$800$	−1.87436	−	4.63538i	−0.0662688	−	0.163885i
$801$		0			0
$802$			31.0959i			1.09803i
$803$		−	54.2119i		−	1.91310i
$804$		0			0
$805$	−10.4702	+	15.5275i	−0.369026	+	0.547274i
$806$			11.3243i			0.398881i
$807$		0			0
$808$	2.30416			0.0810600
$809$		−	0.636644i		−	0.0223832i	−0.999937	−	0.0111916i	$-0.996438\pi$
$809$		−	0.636644i		−	0.0223832i	0.999937	−	0.0111916i	$-0.00356247\pi$
$810$		0			0
$811$	11.3776			0.399521			0.199760	−	0.979845i	$-0.435984\pi$
$811$	11.3776			0.399521			0.199760	+	0.979845i	$0.435984\pi$
$812$	−37.5968			−1.31939
$813$		0			0
$814$	−23.7304	+	27.6269i	−0.831748	+	0.968324i
$815$	34.7897	+	23.4587i	1.21863	+	0.821722i
$816$		0			0
$817$			12.9639i			0.453549i
$818$			38.3150i			1.33965i
$819$		0			0
$820$	−0.983834	−	0.663399i	−0.0343570	−	0.0231669i
$821$	26.1807			0.913711			0.456856	−	0.889541i	$-0.348976\pi$
$821$	26.1807			0.913711			0.456856	+	0.889541i	$0.348976\pi$
$822$		0			0
$823$		−	21.7020i		−	0.756485i	−0.925707	−	0.378242i	$-0.876529\pi$
$823$		−	21.7020i		−	0.756485i	0.925707	−	0.378242i	$-0.123471\pi$
$824$	−11.1716			−0.389180
$825$		0			0
$826$	−10.3024			−0.358467
$827$	7.90798			0.274988			0.137494	−	0.990503i	$-0.456095\pi$
$827$	7.90798			0.274988			0.137494	+	0.990503i	$0.456095\pi$
$828$		0			0
$829$		−	21.7391i		−	0.755030i	−0.926003	−	0.377515i	$-0.876779\pi$
$829$		−	21.7391i		−	0.755030i	0.926003	−	0.377515i	$-0.123221\pi$
$830$	4.72148	−	7.00205i	0.163885	−	0.243045i
$831$		0			0
$832$	3.49410			0.121136
$833$	−79.1076			−2.74092
$834$		0			0
$835$	−13.3428	−	8.99706i	−0.461748	−	0.311356i
$836$		−	43.8926i		−	1.51806i
$837$		0			0
$838$	29.0183			1.00242
$839$	−11.3258			−0.391011			−0.195506	−	0.980703i	$-0.562635\pi$
$839$	−11.3258			−0.391011			−0.195506	+	0.980703i	$0.562635\pi$
$840$		0			0
$841$	−32.6231			−1.12494
$842$		−	23.6443i		−	0.814835i
$843$		0			0
$844$	4.57321			0.157417
$845$	1.46700	+	0.989199i	0.0504664	+	0.0340295i
$846$		0			0
$847$			119.006i			4.08911i
$848$		−	3.66238i		−	0.125767i
$849$		0			0
$850$	−9.30328	−	23.0074i	−0.319100	−	0.789147i
$851$	−6.93097	+	8.06906i	−0.237591	+	0.276604i
$852$		0			0
$853$	−48.1277			−1.64786			−0.823930	−	0.566691i	$-0.808223\pi$
$853$	−48.1277			−1.64786			−0.823930	+	0.566691i	$0.808223\pi$
$854$	14.6834			0.502457
$855$		0			0
$856$		−	6.51807i		−	0.222783i
$857$	40.0486			1.36803			0.684017	−	0.729466i	$-0.260231\pi$
$857$	40.0486			1.36803			0.684017	+	0.729466i	$0.260231\pi$
$858$		0			0
$859$		−	7.66509i		−	0.261530i	−0.991413	−	0.130765i	$-0.958257\pi$
$859$		−	7.66509i		−	0.261530i	0.991413	−	0.130765i	$-0.0417433\pi$
$860$	3.27852	+	2.21071i	0.111797	+	0.0753844i
$861$		0			0
$862$		−	32.1126i		−	1.09376i
$863$			50.9196i			1.73332i	0.498896	+	0.866662i	$0.333739\pi$
$863$			50.9196i			1.73332i	−0.498896	+	0.866662i	$0.666261\pi$
$864$		0			0
$865$	−12.2438	+	18.1578i	−0.416302	+	0.617385i
$866$		−	13.0575i		−	0.443712i
$867$		0			0
$868$	15.5222			0.526859
$869$			33.3267i			1.13053i
$870$		0			0
$871$			13.2644i			0.449446i
$872$		−	1.33812i		−	0.0453146i
$873$		0			0
$874$		−	12.8198i		−	0.433636i
$875$	52.3815	+	11.1104i	1.77082	+	0.375601i
$876$		0			0
$877$		−	2.50813i		−	0.0846937i	−0.999103	−	0.0423468i	$-0.986517\pi$
$877$		−	2.50813i		−	0.0846937i	0.999103	−	0.0423468i	$-0.0134834\pi$
$878$		−	28.0499i		−	0.946640i
$879$		0			0
$880$	−11.1003	−	7.48491i	−0.374190	−	0.252316i
$881$	−24.0074			−0.808829			−0.404414	−	0.914576i	$-0.632525\pi$
$881$	−24.0074			−0.808829			−0.404414	+	0.914576i	$0.632525\pi$
$882$		0			0
$883$	34.7959			1.17098			0.585488	−	0.810681i	$-0.300903\pi$
$883$	34.7959			1.17098			0.585488	+	0.810681i	$0.300903\pi$
$884$	17.3427			0.583299
$885$		0			0
$886$		−	6.79629i		−	0.228326i
$887$		−	0.672248i		−	0.0225719i	−0.999936	−	0.0112859i	$-0.996408\pi$
$887$		−	0.672248i		−	0.0225719i	0.999936	−	0.0112859i	$-0.00359250\pi$
$888$		0			0
$889$	−35.9693			−1.20637
$890$	10.5735	−	15.6807i	0.354423	−	0.525617i
$891$		0			0
$892$			20.3205i			0.680380i
$893$	−31.5698			−1.05644
$894$		0			0
$895$	14.1050	−	20.9180i	0.471478	−	0.699212i
$896$		−	4.78937i		−	0.160002i
$897$		0			0
$898$			17.3278i			0.578235i
$899$	25.4418			0.848531
$900$		0			0
$901$		−	18.1780i		−	0.605597i
$902$	−3.17726			−0.105791
$903$		0			0
$904$	1.39109			0.0462671
$905$	−3.38714	−	2.28395i	−0.112592	−	0.0759210i
$906$		0			0
$907$	36.6618			1.21734			0.608668	−	0.793425i	$-0.291704\pi$
$907$	36.6618			1.21734			0.608668	+	0.793425i	$0.291704\pi$
$908$	−5.74303			−0.190589
$909$		0			0
$910$	−20.9203	+	31.0252i	−0.693501	+	1.02848i
$911$			20.5358i			0.680381i	0.940356	+	0.340191i	$0.110492\pi$
$911$			20.5358i			0.680381i	−0.940356	+	0.340191i	$0.889508\pi$
$912$		0			0
$913$		−	22.6129i		−	0.748378i
$914$	3.20960			0.106164
$915$		0			0
$916$	23.4383			0.774423
$917$	−29.6929			−0.980546
$918$		0			0
$919$		−	42.3926i		−	1.39840i	−0.714925	−	0.699202i	$-0.753539\pi$
$919$		−	42.3926i		−	1.39840i	0.714925	−	0.699202i	$-0.246461\pi$
$920$	−3.24208	−	2.18613i	−0.106888	−	0.0720747i
$921$		0			0
$922$		−	34.0347i		−	1.12087i
$923$	29.6201			0.974958
$924$		0			0
$925$	28.8177	+	9.72326i	0.947519	+	0.319699i
$926$	26.0543			0.856197
$927$		0			0
$928$		−	7.85004i		−	0.257690i
$929$	−1.22700			−0.0402565			−0.0201282	−	0.999797i	$-0.506407\pi$
$929$	−1.22700			−0.0402565			−0.0201282	+	0.999797i	$0.506407\pi$
$930$		0			0
$931$			116.841i			3.82930i
$932$			17.2961i			0.566551i
$933$		0			0
$934$	20.3289			0.665183
$935$	−55.0955	−	37.1509i	−1.80182	−	1.21496i
$936$		0			0
$937$		−	31.9456i		−	1.04362i	−0.853063	−	0.521808i	$-0.825258\pi$
$937$		−	31.9456i		−	1.04362i	0.853063	−	0.521808i	$-0.174742\pi$
$938$	18.1815			0.593647
$939$		0			0
$940$	−5.38352	+	7.98388i	−0.175591	+	0.260405i
$941$	−6.72808			−0.219329			−0.109665	−	0.993969i	$-0.534978\pi$
$941$	−6.72808			−0.219329			−0.109665	+	0.993969i	$0.534978\pi$
$942$		0			0
$943$	−0.927990			−0.0302195
$944$		−	2.15110i		−	0.0700123i
$945$		0			0
$946$	10.5879			0.344242
$947$	−3.77013			−0.122513			−0.0612564	−	0.998122i	$-0.519511\pi$
$947$	−3.77013			−0.122513			−0.0612564	+	0.998122i	$0.519511\pi$
$948$		0			0
$949$		−	31.6372i		−	1.02699i
$950$	−33.9816	+	13.7408i	−1.10251	+	0.445811i
$951$		0			0
$952$		−	23.7717i		−	0.770446i
$953$		−	13.7237i		−	0.444553i	−0.974984	−	0.222276i	$-0.928651\pi$
$953$		−	13.7237i		−	0.444553i	0.974984	−	0.222276i	$-0.0713487\pi$
$954$		0			0
$955$	−29.7785	+	44.1621i	−0.963610	+	1.42905i
$956$			3.68796i			0.119277i
$957$		0			0
$958$			6.22972i			0.201273i
$959$	42.9696			1.38756
$960$		0			0
$961$	20.4961			0.661164
$962$	−13.8486	+	16.1226i	−0.446498	+	0.519814i
$963$		0			0
$964$		−	11.3613i		−	0.365922i
$965$	15.5808	+	10.5061i	0.501564	+	0.338204i
$966$		0			0
$967$	−43.7304			−1.40627			−0.703137	−	0.711055i	$-0.748218\pi$
$967$	−43.7304			−1.40627			−0.703137	+	0.711055i	$0.748218\pi$
$968$	−24.8480			−0.798646
$969$		0			0
$970$	−6.76228	−	4.55980i	−0.217124	−	0.146406i
$971$	−36.2807			−1.16430			−0.582151	−	0.813081i	$-0.697789\pi$
$971$	−36.2807			−1.16430			−0.582151	+	0.813081i	$0.697789\pi$
$972$		0			0
$973$			24.1465i			0.774100i
$974$	−30.5352			−0.978410
$975$		0			0
$976$			3.06584i			0.0981351i
$977$	29.6513			0.948628			0.474314	−	0.880356i	$-0.342696\pi$
$977$	29.6513			0.948628			0.474314	+	0.880356i	$0.342696\pi$
$978$		0			0
$979$		−	50.6402i		−	1.61847i
$980$	29.5486	+	19.9246i	0.943896	+	0.636469i
$981$		0			0
$982$	24.5944			0.784839
$983$		−	42.0082i		−	1.33985i	−0.742427	−	0.669927i	$-0.766325\pi$
$983$		−	42.0082i		−	1.33985i	0.742427	−	0.669927i	$-0.233675\pi$
$984$		0			0
$985$	5.28550	−	7.83850i	0.168410	−	0.249755i
$986$		−	38.9632i		−	1.24084i
$987$		0			0
$988$		−	25.6150i		−	0.814921i
$989$	3.09243			0.0983334
$990$		0			0
$991$		−	20.7399i		−	0.658824i	−0.944186	−	0.329412i	$-0.893149\pi$
$991$		−	20.7399i		−	0.658824i	0.944186	−	0.329412i	$-0.106851\pi$
$992$			3.24097i			0.102901i
$993$		0			0
$994$		−	40.6004i		−	1.28777i
$995$	−22.1953	+	32.9161i	−0.703639	+	1.04351i
$996$		0			0
$997$	−16.0224			−0.507435			−0.253718	−	0.967278i	$-0.581653\pi$
$997$	−16.0224			−0.507435			−0.253718	+	0.967278i	$0.581653\pi$
$998$		−	33.5739i		−	1.06276i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3330.2.e.c.739.1		10
3.2	odd	2		370.2.c.b.369.4	yes	10
5.4	even	2		3330.2.e.d.739.9		10
15.2	even	4		1850.2.d.i.1701.14		20
15.8	even	4		1850.2.d.i.1701.7		20
15.14	odd	2		370.2.c.a.369.7	yes	10
37.36	even	2		3330.2.e.d.739.10		10
111.110	odd	2		370.2.c.a.369.4	✓	10
185.184	even	2	inner	3330.2.e.c.739.2		10
555.332	even	4		1850.2.d.i.1701.4		20
555.443	even	4		1850.2.d.i.1701.17		20
555.554	odd	2		370.2.c.b.369.7	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.c.a.369.4	✓	10	111.110	odd	2
370.2.c.a.369.7	yes	10	15.14	odd	2
370.2.c.b.369.4	yes	10	3.2	odd	2
370.2.c.b.369.7	yes	10	555.554	odd	2
1850.2.d.i.1701.4		20	555.332	even	4
1850.2.d.i.1701.7		20	15.8	even	4
1850.2.d.i.1701.14		20	15.2	even	4
1850.2.d.i.1701.17		20	555.443	even	4
3330.2.e.c.739.1		10	1.1	even	1	trivial
3330.2.e.c.739.2		10	185.184	even	2	inner
3330.2.e.d.739.9		10	5.4	even	2
3330.2.e.d.739.10		10	37.36	even	2

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:	\( N \)	\(=\)	\( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3330.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.85396 - 1.25013i) q^{5} +4.78937i q^{7} -1.00000 q^{8} +(1.85396 + 1.25013i) q^{10} +5.98732 q^{11} +3.49410 q^{13} -4.78937i q^{14} +1.00000 q^{16} +4.96343 q^{17} -7.33092i q^{19} +(-1.85396 - 1.25013i) q^{20} -5.98732 q^{22} -1.74873 q^{23} +(1.87436 + 4.63538i) q^{25} -3.49410 q^{26} +4.78937i q^{28} +7.85004i q^{29} -3.24097i q^{31} -1.00000 q^{32} -4.96343 q^{34} +(5.98732 - 8.87932i) q^{35} +(3.96343 - 4.61424i) q^{37} +7.33092i q^{38} +(1.85396 + 1.25013i) q^{40} +0.530665 q^{41} -1.76838 q^{43} +5.98732 q^{44} +1.74873 q^{46} -4.30638i q^{47} -15.9381 q^{49} +(-1.87436 - 4.63538i) q^{50} +3.49410 q^{52} -3.66238i q^{53} +(-11.1003 - 7.48491i) q^{55} -4.78937i q^{56} -7.85004i q^{58} -2.15110i q^{59} +3.06584i q^{61} +3.24097i q^{62} +1.00000 q^{64} +(-6.47793 - 4.36807i) q^{65} +3.79622i q^{67} +4.96343 q^{68} +(-5.98732 + 8.87932i) q^{70} +8.47719 q^{71} -9.05445i q^{73} +(-3.96343 + 4.61424i) q^{74} -7.33092i q^{76} +28.6755i q^{77} +5.56622i q^{79} +(-1.85396 - 1.25013i) q^{80} -0.530665 q^{82} -3.77680i q^{83} +(-9.20203 - 6.20492i) q^{85} +1.76838 q^{86} -5.98732 q^{88} -8.45791i q^{89} +16.7345i q^{91} -1.74873 q^{92} +4.30638i q^{94} +(-9.16459 + 13.5913i) q^{95} -3.64747 q^{97} +15.9381 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 10 q^{4} - 3 q^{5} - 10 q^{8} + 3 q^{10} + 2 q^{13} + 10 q^{16} + 18 q^{17} - 3 q^{20} + 10 q^{23} + 5 q^{25} - 2 q^{26} - 10 q^{32} - 18 q^{34} + 8 q^{37} + 3 q^{40} + 4 q^{41} + 10 q^{43}+ \cdots + 8 q^{98}+O(q^{100}) \) 10 * q - 10 * q^2 + 10 * q^4 - 3 * q^5 - 10 * q^8 + 3 * q^10 + 2 * q^13 + 10 * q^16 + 18 * q^17 - 3 * q^20 + 10 * q^23 + 5 * q^25 - 2 * q^26 - 10 * q^32 - 18 * q^34 + 8 * q^37 + 3 * q^40 + 4 * q^41 + 10 * q^43 - 10 * q^46 - 8 * q^49 - 5 * q^50 + 2 * q^52 - 5 * q^55 + 10 * q^64 - 2 * q^65 + 18 * q^68 + 20 * q^71 - 8 * q^74 - 3 * q^80 - 4 * q^82 - 28 * q^85 - 10 * q^86 + 10 * q^92 - 2 * q^95 - 2 * q^97 + 8 * q^98

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