LMFDB - Embedded newform 3330.2.e.d.739.10

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			739.10
Root			$0.987983i$ of defining polynomial
Character	$\chi$	$=$	3330.739
Dual form			3330.2.e.d.739.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

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	$-0.661015\pi$
$13$	−3.49410			−0.969088			−0.484544	+	0.874767i	$0.661015\pi$
$14$			4.78937i			1.28001i
$15$		0			0
$16$	1.00000			0.250000
$17$	−4.96343			−1.20381			−0.601905	−	0.798568i	$-0.705591\pi$
$17$	−4.96343			−1.20381			−0.601905	+	0.798568i	$0.705591\pi$
$18$		0			0
$19$			7.33092i			1.68183i	0.541168	+	0.840915i	$0.317982\pi$
$19$			7.33092i			1.68183i	−0.541168	+	0.840915i	$0.682018\pi$
$20$	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	$-0.441640\pi$
$23$	1.74873			0.364635			0.182318	+	0.983240i	$0.441640\pi$
$24$		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	$-0.740051\pi$
$29$		−	7.85004i		−	1.45772i	0.684665	−	0.728858i	$-0.259949\pi$
$30$		0			0
$31$			3.24097i			0.582096i	0.956708	+	0.291048i	$0.0940039\pi$
$31$			3.24097i			0.582096i	−0.956708	+	0.291048i	$0.905996\pi$
$32$	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	$-0.456949\pi$
$43$	1.76838			0.269676			0.134838	+	0.990868i	$0.456949\pi$
$44$	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	$0.0447182\pi$
$59$			2.15110i			0.280049i	−0.990148	+	0.140025i	$0.955282\pi$
$60$		0			0
$61$		−	3.06584i		−	0.392541i	−0.980550	−	0.196270i	$-0.937117\pi$
$61$		−	3.06584i		−	0.392541i	0.980550	−	0.196270i	$-0.0628830\pi$
$62$			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	$-0.898624\pi$
$79$		−	5.56622i		−	0.626248i	0.949712	−	0.313124i	$-0.101376\pi$
$80$	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	$0.147959\pi$
$89$			8.45791i			0.896537i	−0.893899	+	0.448268i	$0.852041\pi$
$90$		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	$-0.440716\pi$
$97$	3.64747			0.370345			0.185172	+	0.982706i	$0.440716\pi$
$98$	−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	$-0.685518\pi$
$103$	−11.1716			−1.10077			−0.550383	+	0.834912i	$0.685518\pi$
$104$	−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	$-0.979587\pi$
$109$		−	1.33812i		−	0.128169i	0.997944	−	0.0640846i	$-0.0204127\pi$
$110$	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	$-0.479158\pi$
$113$	1.39109			0.130863			0.0654315	+	0.997857i	$0.479158\pi$
$114$		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	$-0.912699\pi$
$131$		−	6.19975i		−	0.541675i	0.962625	−	0.270837i	$-0.0873006\pi$
$132$		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	$-0.237231\pi$
$163$	18.7651			1.46979			0.734896	+	0.678180i	$0.237231\pi$
$164$	0.530665			0.0414380
$165$		0			0
$166$		−	3.77680i		−	0.293136i
$167$	−7.19692			−0.556914			−0.278457	−	0.960449i	$-0.589823\pi$
$167$	−7.19692			−0.556914			−0.278457	+	0.960449i	$0.589823\pi$
$168$		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	$-0.861448\pi$
$179$		−	11.2829i		−	0.843320i	0.906754	−	0.421660i	$-0.138552\pi$
$180$		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
$185$	−1.57968	−	13.5094i	−0.116140	−	0.993233i
$186$		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	$0.330657\pi$
$191$			23.8204i			1.72358i	−0.507264	+	0.861791i	$0.669343\pi$
$192$		0			0
$193$	8.40405			0.604937			0.302468	−	0.953159i	$-0.402189\pi$
$193$	8.40405			0.604937			0.302468	+	0.953159i	$0.402189\pi$
$194$	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	$0.216654\pi$
$199$			17.7545i			1.25858i	−0.777170	+	0.629290i	$0.783346\pi$
$200$	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	$-0.438960\pi$
$227$	5.74303			0.381178			0.190589	+	0.981670i	$0.438960\pi$
$228$		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	$-0.961942\pi$
$239$		−	3.68796i		−	0.238554i	0.992861	−	0.119277i	$-0.0380577\pi$
$240$		0			0
$241$			11.3613i			0.731844i	0.930646	+	0.365922i	$0.119246\pi$
$241$			11.3613i			0.731844i	−0.930646	+	0.365922i	$0.880754\pi$
$242$	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	$-0.867347\pi$
$251$		−	12.8260i		−	0.809567i	0.914412	−	0.404784i	$-0.132653\pi$
$252$		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	$-0.644130\pi$
$257$	−14.0268			−0.874965			−0.437483	+	0.899227i	$0.644130\pi$
$258$		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	$-0.264406\pi$
$277$	22.4482			1.34878			0.674391	+	0.738374i	$0.264406\pi$
$278$	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	$-0.942251\pi$
$281$		−	6.04908i		−	0.360858i	0.983588	−	0.180429i	$-0.0577486\pi$
$282$		0			0
$283$	10.8317			0.643878			0.321939	−	0.946760i	$-0.395665\pi$
$283$	10.8317			0.643878			0.321939	+	0.946760i	$0.395665\pi$
$284$	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	$-0.779414\pi$
$311$		−	22.5322i		−	1.27768i	0.769339	−	0.638841i	$-0.220586\pi$
$312$		0			0
$313$	−10.0000			−0.565233			−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000			−0.565233			−0.282617	+	0.959233i	$0.591202\pi$
$314$			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	$-0.825054\pi$
$331$		−	19.0068i		−	1.04471i	0.852728	−	0.522355i	$-0.174946\pi$
$332$		−	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	$-0.804219\pi$
$347$	−30.4282			−1.63347			−0.816736	+	0.577011i	$0.804219\pi$
$348$		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	$-0.413087\pi$
$353$	10.1331			0.539332			0.269666	+	0.962954i	$0.413087\pi$
$354$		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
$370$	−1.57968	−	13.5094i	−0.0821235	−	0.702322i
$371$	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	$-0.595237\pi$
$383$	−11.5368			−0.589501			−0.294751	+	0.955574i	$0.595237\pi$
$384$		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	$-0.930449\pi$
$389$		−	8.55057i		−	0.433531i	0.976224	−	0.216766i	$-0.0695507\pi$
$390$		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	$0.282970\pi$
$401$			31.0959i			1.55285i	−0.630207	+	0.776427i	$0.717030\pi$
$402$		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	$0.396177\pi$
$409$			38.3150i			1.89455i	−0.320417	+	0.947277i	$0.603823\pi$
$410$	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	$-0.804545\pi$
$421$		−	23.6443i		−	1.15235i	0.817326	−	0.576175i	$-0.195455\pi$
$422$	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	$-0.718552\pi$
$431$		−	32.1126i		−	1.54681i	0.633912	−	0.773406i	$-0.281448\pi$
$432$		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	$-0.766562\pi$
$439$		−	28.0499i		−	1.33875i	0.742924	−	0.669375i	$-0.233438\pi$
$440$	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	$0.134078\pi$
$449$			17.3278i			0.817747i	−0.912591	+	0.408874i	$0.865922\pi$
$450$		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	$-0.476082\pi$
$457$	3.20960			0.150139			0.0750693	+	0.997178i	$0.476082\pi$
$458$	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	$-0.708739\pi$
$461$		−	34.0347i		−	1.58515i	0.609773	−	0.792576i	$-0.291261\pi$
$462$		0			0
$463$	26.0543			1.21085			0.605423	−	0.795904i	$-0.293004\pi$
$463$	26.0543			1.21085			0.605423	+	0.795904i	$0.293004\pi$
$464$		−	7.85004i		−	0.364429i
$465$		0			0
$466$			17.2961i			0.801224i
$467$	20.3289			0.940710			0.470355	−	0.882477i	$-0.344126\pi$
$467$	20.3289			0.940710			0.470355	+	0.882477i	$0.344126\pi$
$468$		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	$0.0454567\pi$
$479$			6.22972i			0.284643i	−0.989820	+	0.142322i	$0.954543\pi$
$480$		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	$-0.743200\pi$
$487$	−30.5352			−1.38368			−0.691841	+	0.722050i	$0.743200\pi$
$488$		−	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	$-0.729337\pi$
$499$		−	33.5739i		−	1.50297i	0.659747	−	0.751487i	$-0.270663\pi$
$500$	−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	$-0.487370\pi$
$503$	1.77931			0.0793357			0.0396679	+	0.999213i	$0.487370\pi$
$504$		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	$-0.727463\pi$
$523$	−29.9729			−1.31062			−0.655312	+	0.755359i	$0.727463\pi$
$524$		−	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	$-0.868203\pi$
$541$		−	18.7155i		−	0.804644i	0.915498	−	0.402322i	$-0.131797\pi$
$542$	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	$-0.744310\pi$
$547$	−32.4792			−1.38871			−0.694355	+	0.719633i	$0.744310\pi$
$548$		−	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	$-0.389808\pi$
$557$	16.0158			0.678612			0.339306	+	0.940676i	$0.389808\pi$
$558$		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	$-0.395458\pi$
$563$	15.3069			0.645109			0.322554	+	0.946551i	$0.395458\pi$
$564$		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	$-0.811338\pi$
$569$		−	26.6494i		−	1.11720i	0.829437	−	0.558601i	$-0.188662\pi$
$570$		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	$-0.523484\pi$
$577$	−3.54110			−0.147418			−0.0737091	+	0.997280i	$0.523484\pi$
$578$	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	$-0.580319\pi$
$587$	−12.0976			−0.499320			−0.249660	+	0.968334i	$0.580319\pi$
$588$		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	$-0.780852\pi$
$607$	−38.0508			−1.54443			−0.772217	+	0.635359i	$0.780852\pi$
$608$			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	$-0.774911\pi$
$631$		−	32.6385i		−	1.29932i	0.760225	−	0.649660i	$-0.225089\pi$
$632$		−	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	$-0.436275\pi$
$643$	10.0853			0.397727			0.198864	+	0.980027i	$0.436275\pi$
$644$			8.37532i			0.330034i
$645$		0			0
$646$		−	36.3865i		−	1.43161i
$647$	38.5061			1.51383			0.756916	−	0.653512i	$-0.226705\pi$
$647$	38.5061			1.51383			0.756916	+	0.653512i	$0.226705\pi$
$648$		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	$-0.486272\pi$
$653$	2.20349			0.0862293			0.0431146	+	0.999070i	$0.486272\pi$
$654$		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	$-0.823809\pi$
$661$		−	27.0306i		−	1.05137i	0.850680	−	0.525684i	$-0.176191\pi$
$662$		−	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	$-0.153580\pi$
$683$	46.3018			1.77169			0.885845	+	0.463981i	$0.153580\pi$
$684$		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	$-0.665909\pi$
$701$		−	45.9214i		−	1.73443i	0.497936	−	0.867214i	$-0.334091\pi$
$702$		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	$0.452309\pi$
$709$			52.6575i			1.97759i	−0.149266	+	0.988797i	$0.547691\pi$
$710$	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	$-0.421447\pi$
$727$	13.1733			0.488571			0.244286	+	0.969703i	$0.421447\pi$
$728$		−	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	$0.459248\pi$
$740$	−1.57968	−	13.5094i	−0.0580701	−	0.496616i
$741$		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	$-0.350230\pi$
$757$	24.9464			0.906693			0.453347	+	0.891334i	$0.350230\pi$
$758$	−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	$-0.839508\pi$
$769$		−	26.7939i		−	0.966214i	0.875561	−	0.483107i	$-0.160492\pi$
$770$	−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	$-0.507694\pi$
$797$	−1.36472			−0.0483407			−0.0241704	+	0.999708i	$0.507694\pi$
$798$		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	$0.00356247\pi$
$809$			0.636644i			0.0223832i	−0.999937	+	0.0111916i	$0.996438\pi$
$810$		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	$-0.543905\pi$
$827$	−7.90798			−0.274988			−0.137494	+	0.990503i	$0.543905\pi$
$828$		0			0
$829$			21.7391i			0.755030i	0.926003	+	0.377515i	$0.123221\pi$
$829$			21.7391i			0.755030i	−0.926003	+	0.377515i	$0.876779\pi$
$830$	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	$-0.191777\pi$
$853$	48.1277			1.64786			0.823930	+	0.566691i	$0.191777\pi$
$854$	14.6834			0.502457
$855$		0			0
$856$			6.51807i			0.222783i
$857$	−40.0486			−1.36803			−0.684017	−	0.729466i	$-0.739769\pi$
$857$	−40.0486			−1.36803			−0.684017	+	0.729466i	$0.739769\pi$
$858$		0			0
$859$			7.66509i			0.261530i	0.991413	+	0.130765i	$0.0417433\pi$
$859$			7.66509i			0.261530i	−0.991413	+	0.130765i	$0.958257\pi$
$860$	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	$-0.699097\pi$
$883$	−34.7959			−1.17098			−0.585488	+	0.810681i	$0.699097\pi$
$884$	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	$-0.708296\pi$
$907$	−36.6618			−1.21734			−0.608668	+	0.793425i	$0.708296\pi$
$908$	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	$-0.889508\pi$
$911$		−	20.5358i		−	0.680381i	0.940356	−	0.340191i	$-0.110492\pi$
$912$		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	$0.246461\pi$
$919$			42.3926i			1.39840i	−0.714925	+	0.699202i	$0.753539\pi$
$920$	3.24208	+	2.18613i	0.106888	+	0.0720747i
$921$		0			0
$922$		−	34.0347i		−	1.12087i
$923$	−29.6201			−0.974958
$924$		0			0
$925$	13.9598	−	27.0208i	0.458997	−	0.888438i
$926$	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	$-0.480489\pi$
$947$	3.77013			0.122513			0.0612564	+	0.998122i	$0.480489\pi$
$948$		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	$-0.251782\pi$
$967$	43.7304			1.40627			0.703137	+	0.711055i	$0.251782\pi$
$968$	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	$-0.657304\pi$
$977$	−29.6513			−0.948628			−0.474314	+	0.880356i	$0.657304\pi$
$978$		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	$0.106851\pi$
$991$			20.7399i			0.658824i	−0.944186	+	0.329412i	$0.893149\pi$
$992$			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	$-0.418347\pi$
$997$	16.0224			0.507435			0.253718	+	0.967278i	$0.418347\pi$
$998$		−	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.d.739.10		10
3.2	odd	2		370.2.c.a.369.4	✓	10
5.4	even	2		3330.2.e.c.739.2		10
15.2	even	4		1850.2.d.i.1701.4		20
15.8	even	4		1850.2.d.i.1701.17		20
15.14	odd	2		370.2.c.b.369.7	yes	10
37.36	even	2		3330.2.e.c.739.1		10
111.110	odd	2		370.2.c.b.369.4	yes	10
185.184	even	2	inner	3330.2.e.d.739.9		10
555.332	even	4		1850.2.d.i.1701.14		20
555.443	even	4		1850.2.d.i.1701.7		20
555.554	odd	2		370.2.c.a.369.7	yes	10

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

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)

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