LMFDB - Embedded newform 3330.2.d.p.1999.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3330,2,Mod(1999,3330)]

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, 0]))

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

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

chi := DirichletCharacter("3330.1999");

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.d (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} - 2x^{9} + 2x^{8} - 4x^{7} + 51x^{6} - 124x^{5} + 154x^{4} - 46x^{3} + x^{2} + 4x + 8 $ x^10 - 2x^9 + 2x^8 - 4x^7 + 51x^6 - 124x^5 + 154x^4 - 46x^3 + x^2 + 4x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 370)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1999.6
Root			$1.24331 - 1.24331i$ of defining polynomial
Character	$\chi$	$=$	3330.1999
Dual form			3330.2.d.p.1999.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(-2.07757 - 0.826871i) q^{5} -4.67211i q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(-2.07757 - 0.826871i) q^{5} -4.67211i q^{7} -1.00000i q^{8} +(0.826871 - 2.07757i) q^{10} -0.0451320 q^{11} +5.26514i q^{13} +4.67211 q^{14} +1.00000 q^{16} +3.60861i q^{17} +6.22000 q^{19} +(2.07757 + 0.826871i) q^{20} -0.0451320i q^{22} +2.20164i q^{23} +(3.63257 + 3.43576i) q^{25} -5.26514 q^{26} +4.67211i q^{28} -4.20386 q^{29} -3.01051 q^{31} +1.00000i q^{32} -3.60861 q^{34} +(-3.86323 + 9.70662i) q^{35} -1.00000i q^{37} +6.22000i q^{38} +(-0.826871 + 2.07757i) q^{40} +7.38299 q^{41} -5.54789i q^{43} +0.0451320 q^{44} -2.20164 q^{46} -4.28072i q^{47} -14.8286 q^{49} +(-3.43576 + 3.63257i) q^{50} -5.26514i q^{52} -6.10215i q^{53} +(0.0937647 + 0.0373183i) q^{55} -4.67211 q^{56} -4.20386i q^{58} +13.5275 q^{59} -4.27299 q^{61} -3.01051i q^{62} -1.00000 q^{64} +(4.35359 - 10.9387i) q^{65} -12.3751i q^{67} -3.60861i q^{68} +(-9.70662 - 3.86323i) q^{70} +4.49354 q^{71} +7.03811i q^{73} +1.00000 q^{74} -6.22000 q^{76} +0.210861i q^{77} +8.72499 q^{79} +(-2.07757 - 0.826871i) q^{80} +7.38299i q^{82} +0.880231i q^{83} +(2.98386 - 7.49713i) q^{85} +5.54789 q^{86} +0.0451320i q^{88} +9.97602 q^{89} +24.5993 q^{91} -2.20164i q^{92} +4.28072 q^{94} +(-12.9225 - 5.14314i) q^{95} -0.240408i q^{97} -14.8286i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{4} - 6 q^{5}+O(q^{10}) $ 10 * q - 10 * q^4 - 6 * q^5	$ 10 q - 10 q^{4} - 6 q^{5} + 2 q^{10} - 6 q^{11} - 2 q^{14} + 10 q^{16} - 8 q^{19} + 6 q^{20} + 4 q^{25} + 12 q^{26} + 22 q^{29} + 46 q^{31} - 18 q^{34} - 32 q^{35} - 2 q^{40} + 14 q^{41} + 6 q^{44} + 12 q^{46} - 60 q^{49} - 8 q^{50} + 42 q^{55} + 2 q^{56} + 40 q^{59} - 18 q^{61} - 10 q^{64} - 4 q^{65} - 6 q^{70} - 12 q^{71} + 10 q^{74} + 8 q^{76} - 40 q^{79} - 6 q^{80} + 36 q^{85} + 34 q^{86} + 24 q^{89} + 32 q^{91} - 24 q^{94} - 12 q^{95}+O(q^{100}) $ 10 * q - 10 * q^4 - 6 * q^5 + 2 * q^10 - 6 * q^11 - 2 * q^14 + 10 * q^16 - 8 * q^19 + 6 * q^20 + 4 * q^25 + 12 * q^26 + 22 * q^29 + 46 * q^31 - 18 * q^34 - 32 * q^35 - 2 * q^40 + 14 * q^41 + 6 * q^44 + 12 * q^46 - 60 * q^49 - 8 * q^50 + 42 * q^55 + 2 * q^56 + 40 * q^59 - 18 * q^61 - 10 * q^64 - 4 * q^65 - 6 * q^70 - 12 * q^71 + 10 * q^74 + 8 * q^76 - 40 * q^79 - 6 * q^80 + 36 * q^85 + 34 * q^86 + 24 * q^89 + 32 * q^91 - 24 * q^94 - 12 * q^95

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−2.07757	−	0.826871i	−0.929116	−	0.369788i
$5$	−2.07757	−	0.826871i	−0.929116	−	0.369788i
$6$		0			0
$7$		−	4.67211i		−	1.76589i	−0.469475	−	0.882946i	$-0.655557\pi$
$7$		−	4.67211i		−	1.76589i	0.469475	−	0.882946i	$-0.344443\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	0.826871	−	2.07757i	0.261480	−	0.656984i
$11$	−0.0451320			−0.0136078			−0.00680390	−	0.999977i	$-0.502166\pi$
$11$	−0.0451320			−0.0136078			−0.00680390	+	0.999977i	$0.502166\pi$
$12$		0			0
$13$			5.26514i			1.46029i	0.683294	+	0.730143i	$0.260547\pi$
$13$			5.26514i			1.46029i	−0.683294	+	0.730143i	$0.739453\pi$
$14$	4.67211			1.24867
$15$		0			0
$16$	1.00000			0.250000
$17$			3.60861i			0.875217i	0.899166	+	0.437608i	$0.144174\pi$
$17$			3.60861i			0.875217i	−0.899166	+	0.437608i	$0.855826\pi$
$18$		0			0
$19$	6.22000			1.42697			0.713483	−	0.700672i	$-0.247116\pi$
$19$	6.22000			1.42697			0.713483	+	0.700672i	$0.247116\pi$
$20$	2.07757	+	0.826871i	0.464558	+	0.184894i
$21$		0			0
$22$		−	0.0451320i		−	0.00962217i
$23$			2.20164i			0.459073i	0.973300	+	0.229536i	$0.0737210\pi$
$23$			2.20164i			0.459073i	−0.973300	+	0.229536i	$0.926279\pi$
$24$		0			0
$25$	3.63257	+	3.43576i	0.726514	+	0.687152i
$26$	−5.26514			−1.03258
$27$		0			0
$28$			4.67211i			0.882946i
$29$	−4.20386			−0.780637			−0.390319	−	0.920680i	$-0.627635\pi$
$29$	−4.20386			−0.780637			−0.390319	+	0.920680i	$0.627635\pi$
$30$		0			0
$31$	−3.01051			−0.540704			−0.270352	−	0.962762i	$-0.587140\pi$
$31$	−3.01051			−0.540704			−0.270352	+	0.962762i	$0.587140\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−3.60861			−0.618872
$35$	−3.86323	+	9.70662i	−0.653006	+	1.64072i
$36$		0			0
$37$		−	1.00000i		−	0.164399i
$37$		−	1.00000i		−	0.164399i
$38$			6.22000i			1.00902i
$39$		0			0
$40$	−0.826871	+	2.07757i	−0.130740	+	0.328492i
$41$	7.38299			1.15303			0.576515	−	0.817087i	$-0.304412\pi$
$41$	7.38299			1.15303			0.576515	+	0.817087i	$0.304412\pi$
$42$		0			0
$43$		−	5.54789i		−	0.846046i	−0.906119	−	0.423023i	$-0.860969\pi$
$43$		−	5.54789i		−	0.846046i	0.906119	−	0.423023i	$-0.139031\pi$
$44$	0.0451320			0.00680390
$45$		0			0
$46$	−2.20164			−0.324613
$47$		−	4.28072i		−	0.624407i	−0.950015	−	0.312204i	$-0.898933\pi$
$47$		−	4.28072i		−	0.624407i	0.950015	−	0.312204i	$-0.101067\pi$
$48$		0			0
$49$	−14.8286			−2.11837
$50$	−3.43576	+	3.63257i	−0.485890	+	0.513723i
$51$		0			0
$52$		−	5.26514i		−	0.730143i
$53$		−	6.10215i		−	0.838194i	−0.907941	−	0.419097i	$-0.862347\pi$
$53$		−	6.10215i		−	0.838194i	0.907941	−	0.419097i	$-0.137653\pi$
$54$		0			0
$55$	0.0937647	+	0.0373183i	0.0126432	+	0.00503200i
$56$	−4.67211			−0.624337
$57$		0			0
$58$		−	4.20386i		−	0.551994i
$59$	13.5275			1.76113			0.880565	−	0.473926i	$-0.157164\pi$
$59$	13.5275			1.76113			0.880565	+	0.473926i	$0.157164\pi$
$60$		0			0
$61$	−4.27299			−0.547100			−0.273550	−	0.961858i	$-0.588198\pi$
$61$	−4.27299			−0.547100			−0.273550	+	0.961858i	$0.588198\pi$
$62$		−	3.01051i		−	0.382335i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	4.35359	−	10.9387i	0.539996	−	1.35678i
$66$		0			0
$67$		−	12.3751i		−	1.51186i	−0.654650	−	0.755932i	$-0.727184\pi$
$67$		−	12.3751i		−	1.51186i	0.654650	−	0.755932i	$-0.272816\pi$
$68$		−	3.60861i		−	0.437608i
$69$		0			0
$70$	−9.70662	−	3.86323i	−1.16016	−	0.461745i
$71$	4.49354			0.533285			0.266642	−	0.963796i	$-0.414086\pi$
$71$	4.49354			0.533285			0.266642	+	0.963796i	$0.414086\pi$
$72$		0			0
$73$			7.03811i			0.823748i	0.911241	+	0.411874i	$0.135126\pi$
$73$			7.03811i			0.823748i	−0.911241	+	0.411874i	$0.864874\pi$
$74$	1.00000			0.116248
$75$		0			0
$76$	−6.22000			−0.713483
$77$			0.210861i			0.0240299i
$78$		0			0
$79$	8.72499			0.981638			0.490819	−	0.871262i	$-0.336698\pi$
$79$	8.72499			0.981638			0.490819	+	0.871262i	$0.336698\pi$
$80$	−2.07757	−	0.826871i	−0.232279	−	0.0924470i
$81$		0			0
$82$			7.38299i			0.815315i
$83$			0.880231i			0.0966179i	0.998832	+	0.0483090i	$0.0153832\pi$
$83$			0.880231i			0.0966179i	−0.998832	+	0.0483090i	$0.984617\pi$
$84$		0			0
$85$	2.98386	−	7.49713i	0.323645	−	0.813178i
$86$	5.54789			0.598245
$87$		0			0
$88$			0.0451320i			0.00481108i
$89$	9.97602			1.05746			0.528728	−	0.848791i	$-0.322669\pi$
$89$	9.97602			1.05746			0.528728	+	0.848791i	$0.322669\pi$
$90$		0			0
$91$	24.5993			2.57871
$92$		−	2.20164i		−	0.229536i
$93$		0			0
$94$	4.28072			0.441523
$95$	−12.9225	−	5.14314i	−1.32582	−	0.527675i
$96$		0			0
$97$		−	0.240408i		−	0.0244097i	−0.999926	−	0.0122049i	$-0.996115\pi$
$97$		−	0.240408i		−	0.0244097i	0.999926	−	0.0122049i	$-0.00388502\pi$
$98$		−	14.8286i		−	1.49792i
$99$		0			0
$100$	−3.63257	−	3.43576i	−0.363257	−	0.343576i
$101$	5.61775			0.558987			0.279494	−	0.960148i	$-0.409833\pi$
$101$	5.61775			0.558987			0.279494	+	0.960148i	$0.409833\pi$
$102$		0			0
$103$		−	12.5663i		−	1.23819i	−0.785316	−	0.619095i	$-0.787499\pi$
$103$		−	12.5663i		−	1.23819i	0.785316	−	0.619095i	$-0.212501\pi$
$104$	5.26514			0.516289
$105$		0			0
$106$	6.10215			0.592693
$107$		−	17.9395i		−	1.73427i	−0.498070	−	0.867137i	$-0.665958\pi$
$107$		−	17.9395i		−	1.73427i	0.498070	−	0.867137i	$-0.334042\pi$
$108$		0			0
$109$	−3.09936			−0.296865			−0.148433	−	0.988923i	$-0.547423\pi$
$109$	−3.09936			−0.296865			−0.148433	+	0.988923i	$0.547423\pi$
$110$	−0.0373183	+	0.0937647i	−0.00355816	+	0.00894011i
$111$		0			0
$112$		−	4.67211i		−	0.441473i
$113$		−	4.36184i		−	0.410328i	−0.978728	−	0.205164i	$-0.934227\pi$
$113$		−	4.36184i		−	0.410328i	0.978728	−	0.205164i	$-0.0657727\pi$
$114$		0			0
$115$	1.82047	−	4.57405i	0.169760	−	0.426532i
$116$	4.20386			0.390319
$117$		0			0
$118$			13.5275i			1.24531i
$119$	16.8598			1.54554
$120$		0			0
$121$	−10.9980			−0.999815
$122$		−	4.27299i		−	0.386858i
$123$		0			0
$124$	3.01051			0.270352
$125$	−4.70597	−	10.1417i	−0.420915	−	0.907100i
$126$		0			0
$127$		−	17.6572i		−	1.56683i	−0.621502	−	0.783413i	$-0.713477\pi$
$127$		−	17.6572i		−	1.56683i	0.621502	−	0.783413i	$-0.286523\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	10.9387	+	4.35359i	0.959385	+	0.381835i
$131$	10.3103			0.900812			0.450406	−	0.892824i	$-0.351279\pi$
$131$	10.3103			0.900812			0.450406	+	0.892824i	$0.351279\pi$
$132$		0			0
$133$		−	29.0605i		−	2.51987i
$134$	12.3751			1.06905
$135$		0			0
$136$	3.60861			0.309436
$137$			3.21863i			0.274986i	0.990503	+	0.137493i	$0.0439045\pi$
$137$			3.21863i			0.274986i	−0.990503	+	0.137493i	$0.956095\pi$
$138$		0			0
$139$	−20.9400			−1.77611			−0.888055	−	0.459737i	$-0.847944\pi$
$139$	−20.9400			−1.77611			−0.888055	+	0.459737i	$0.847944\pi$
$140$	3.86323	−	9.70662i	0.326503	−	0.820359i
$141$		0			0
$142$			4.49354i			0.377089i
$143$		−	0.237626i		−	0.0198713i
$144$		0			0
$145$	8.73380	+	3.47605i	0.725303	+	0.288670i
$146$	−7.03811			−0.582478
$147$		0			0
$148$			1.00000i			0.0821995i
$149$	−21.9832			−1.80093			−0.900467	−	0.434924i	$-0.856775\pi$
$149$	−21.9832			−1.80093			−0.900467	+	0.434924i	$0.856775\pi$
$150$		0			0
$151$	14.1877			1.15458			0.577290	−	0.816539i	$-0.304110\pi$
$151$	14.1877			1.15458			0.577290	+	0.816539i	$0.304110\pi$
$152$		−	6.22000i		−	0.504509i
$153$		0			0
$154$	−0.210861			−0.0169917
$155$	6.25454	+	2.48931i	0.502377	+	0.199946i
$156$		0			0
$157$			19.9316i			1.59072i	0.606139	+	0.795359i	$0.292717\pi$
$157$			19.9316i			1.59072i	−0.606139	+	0.795359i	$0.707283\pi$
$158$			8.72499i			0.694123i
$159$		0			0
$160$	0.826871	−	2.07757i	0.0653699	−	0.164246i
$161$	10.2863			0.810673
$162$		0			0
$163$			8.65087i			0.677588i	0.940861	+	0.338794i	$0.110019\pi$
$163$			8.65087i			0.677588i	−0.940861	+	0.338794i	$0.889981\pi$
$164$	−7.38299			−0.576515
$165$		0			0
$166$	−0.880231			−0.0683192
$167$		−	11.9640i		−	0.925803i	−0.886410	−	0.462901i	$-0.846808\pi$
$167$		−	11.9640i		−	0.925803i	0.886410	−	0.462901i	$-0.153192\pi$
$168$		0			0
$169$	−14.7216			−1.13243
$170$	7.49713	+	2.98386i	0.575004	+	0.228851i
$171$		0			0
$172$			5.54789i			0.423023i
$173$			5.33508i			0.405619i	0.979218	+	0.202809i	$0.0650071\pi$
$173$			5.33508i			0.405619i	−0.979218	+	0.202809i	$0.934993\pi$
$174$		0			0
$175$	16.0523	−	16.9718i	1.21344	−	1.28294i
$176$	−0.0451320			−0.00340195
$177$		0			0
$178$			9.97602i			0.747734i
$179$	−5.27905			−0.394575			−0.197288	−	0.980346i	$-0.563213\pi$
$179$	−5.27905			−0.394575			−0.197288	+	0.980346i	$0.563213\pi$
$180$		0			0
$181$	17.7448			1.31896			0.659478	−	0.751723i	$-0.270777\pi$
$181$	17.7448			1.31896			0.659478	+	0.751723i	$0.270777\pi$
$182$			24.5993i			1.82342i
$183$		0			0
$184$	2.20164			0.162307
$185$	−0.826871	+	2.07757i	−0.0607928	+	0.152746i
$186$		0			0
$187$		−	0.162864i		−	0.0119098i
$188$			4.28072i			0.312204i
$189$		0			0
$190$	5.14314	−	12.9225i	0.373123	−	0.937495i
$191$	3.11649			0.225501			0.112751	−	0.993623i	$-0.464034\pi$
$191$	3.11649			0.225501			0.112751	+	0.993623i	$0.464034\pi$
$192$		0			0
$193$		−	8.78278i		−	0.632198i	−0.948726	−	0.316099i	$-0.897627\pi$
$193$		−	8.78278i		−	0.632198i	0.948726	−	0.316099i	$-0.102373\pi$
$194$	0.240408			0.0172603
$195$		0			0
$196$	14.8286			1.05919
$197$			7.00278i			0.498928i	0.968384	+	0.249464i	$0.0802544\pi$
$197$			7.00278i			0.498928i	−0.968384	+	0.249464i	$0.919746\pi$
$198$		0			0
$199$	−17.3202			−1.22780			−0.613900	−	0.789384i	$-0.710400\pi$
$199$	−17.3202			−1.22780			−0.613900	+	0.789384i	$0.710400\pi$
$200$	3.43576	−	3.63257i	0.242945	−	0.256861i
$201$		0			0
$202$			5.61775i			0.395264i
$203$			19.6409i			1.37852i
$204$		0			0
$205$	−15.3387	−	6.10478i	−1.07130	−	0.426377i
$206$	12.5663			0.875533
$207$		0			0
$208$			5.26514i			0.365071i
$209$	−0.280721			−0.0194179
$210$		0			0
$211$	6.77438			0.466368			0.233184	−	0.972433i	$-0.425086\pi$
$211$	6.77438			0.466368			0.233184	+	0.972433i	$0.425086\pi$
$212$			6.10215i			0.419097i
$213$		0			0
$214$	17.9395			1.22632
$215$	−4.58739	+	11.5261i	−0.312858	+	0.786075i
$216$		0			0
$217$			14.0654i			0.954825i
$218$		−	3.09936i		−	0.209915i
$219$		0			0
$220$	−0.0937647	−	0.0373183i	−0.00632161	−	0.00251600i
$221$	−18.9998			−1.27807
$222$		0			0
$223$		−	10.2559i		−	0.686784i	−0.939192	−	0.343392i	$-0.888424\pi$
$223$		−	10.2559i		−	0.686784i	0.939192	−	0.343392i	$-0.111576\pi$
$224$	4.67211			0.312168
$225$		0			0
$226$	4.36184			0.290145
$227$		−	11.2744i		−	0.748306i	−0.927367	−	0.374153i	$-0.877934\pi$
$227$		−	11.2744i		−	0.748306i	0.927367	−	0.374153i	$-0.122066\pi$
$228$		0			0
$229$	9.40494			0.621496			0.310748	−	0.950492i	$-0.399421\pi$
$229$	9.40494			0.621496			0.310748	+	0.950492i	$0.399421\pi$
$230$	4.57405	+	1.82047i	0.301604	+	0.120038i
$231$		0			0
$232$			4.20386i			0.275997i
$233$			3.22867i			0.211517i	0.994392	+	0.105759i	$0.0337271\pi$
$233$			3.22867i			0.211517i	−0.994392	+	0.105759i	$0.966273\pi$
$234$		0			0
$235$	−3.53961	+	8.89348i	−0.230898	+	0.580147i
$236$	−13.5275			−0.880565
$237$		0			0
$238$			16.8598i			1.09286i
$239$	−17.8612			−1.15534			−0.577672	−	0.816269i	$-0.696039\pi$
$239$	−17.8612			−1.15534			−0.577672	+	0.816269i	$0.696039\pi$
$240$		0			0
$241$	26.6840			1.71887			0.859434	−	0.511248i	$-0.170816\pi$
$241$	26.6840			1.71887			0.859434	+	0.511248i	$0.170816\pi$
$242$		−	10.9980i		−	0.706976i
$243$		0			0
$244$	4.27299			0.273550
$245$	30.8074	+	12.2614i	1.96821	+	0.783349i
$246$		0			0
$247$			32.7492i			2.08378i
$248$			3.01051i			0.191168i
$249$		0			0
$250$	10.1417	−	4.70597i	0.641417	−	0.297632i
$251$	30.1552			1.90338			0.951690	−	0.307060i	$-0.0993453\pi$
$251$	30.1552			1.90338			0.951690	+	0.307060i	$0.0993453\pi$
$252$		0			0
$253$		−	0.0993641i		−	0.00624697i
$254$	17.6572			1.10791
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	3.15376i		−	0.196726i	−0.995151	−	0.0983632i	$-0.968639\pi$
$257$		−	3.15376i		−	0.196726i	0.995151	−	0.0983632i	$-0.0313607\pi$
$258$		0			0
$259$	−4.67211			−0.290311
$260$	−4.35359	+	10.9387i	−0.269998	+	0.678388i
$261$		0			0
$262$			10.3103i			0.636970i
$263$		−	14.0332i		−	0.865322i	−0.901557	−	0.432661i	$-0.857575\pi$
$263$		−	14.0332i		−	0.865322i	0.901557	−	0.432661i	$-0.142425\pi$
$264$		0			0
$265$	−5.04569	+	12.6776i	−0.309954	+	0.778780i
$266$	29.0605			1.78182
$267$		0			0
$268$			12.3751i			0.755932i
$269$	−30.1257			−1.83679			−0.918397	−	0.395660i	$-0.870516\pi$
$269$	−30.1257			−1.83679			−0.918397	+	0.395660i	$0.870516\pi$
$270$		0			0
$271$	14.8802			0.903910			0.451955	−	0.892041i	$-0.350727\pi$
$271$	14.8802			0.903910			0.451955	+	0.892041i	$0.350727\pi$
$272$			3.60861i			0.218804i
$273$		0			0
$274$	−3.21863			−0.194445
$275$	−0.163945	−	0.155063i	−0.00988625	−	0.00935063i
$276$		0			0
$277$		−	0.147278i		−	0.00884908i	−0.999990	−	0.00442454i	$-0.998592\pi$
$277$		−	0.147278i		−	0.00884908i	0.999990	−	0.00442454i	$-0.00140838\pi$
$278$		−	20.9400i		−	1.25590i
$279$		0			0
$280$	9.70662	+	3.86323i	0.580082	+	0.230872i
$281$	25.5247			1.52268			0.761339	−	0.648354i	$-0.224542\pi$
$281$	25.5247			1.52268			0.761339	+	0.648354i	$0.224542\pi$
$282$		0			0
$283$			0.0562691i			0.00334485i	0.999999	+	0.00167242i	$0.000532349\pi$
$283$			0.0562691i			0.00334485i	−0.999999	+	0.00167242i	$0.999468\pi$
$284$	−4.49354			−0.266642
$285$		0			0
$286$	0.237626			0.0140511
$287$		−	34.4942i		−	2.03613i
$288$		0			0
$289$	3.97793			0.233996
$290$	−3.47605	+	8.73380i	−0.204121	+	0.512866i
$291$		0			0
$292$		−	7.03811i		−	0.411874i
$293$		−	13.7033i		−	0.800557i	−0.916394	−	0.400278i	$-0.868913\pi$
$293$		−	13.7033i		−	0.800557i	0.916394	−	0.400278i	$-0.131087\pi$
$294$		0			0
$295$	−28.1043	−	11.1855i	−1.63629	−	0.651245i
$296$	−1.00000			−0.0581238
$297$		0			0
$298$		−	21.9832i		−	1.27345i
$299$	−11.5919			−0.670377
$300$		0			0
$301$	−25.9204			−1.49403
$302$			14.1877i			0.816411i
$303$		0			0
$304$	6.22000			0.356742
$305$	8.87742	+	3.53321i	0.508320	+	0.202311i
$306$		0			0
$307$			17.5823i			1.00348i	0.865020	+	0.501738i	$0.167306\pi$
$307$			17.5823i			1.00348i	−0.865020	+	0.501738i	$0.832694\pi$
$308$		−	0.210861i		−	0.0120149i
$309$		0			0
$310$	−2.48931	+	6.25454i	−0.141383	+	0.355234i
$311$	−0.353133			−0.0200244			−0.0100122	−	0.999950i	$-0.503187\pi$
$311$	−0.353133			−0.0200244			−0.0100122	+	0.999950i	$0.503187\pi$
$312$		0			0
$313$		−	18.8717i		−	1.06669i	−0.845897	−	0.533346i	$-0.820934\pi$
$313$		−	18.8717i		−	1.06669i	0.845897	−	0.533346i	$-0.179066\pi$
$314$	−19.9316			−1.12481
$315$		0			0
$316$	−8.72499			−0.490819
$317$			15.1979i			0.853601i	0.904346	+	0.426800i	$0.140359\pi$
$317$			15.1979i			0.853601i	−0.904346	+	0.426800i	$0.859641\pi$
$318$		0			0
$319$	0.189728			0.0106228
$320$	2.07757	+	0.826871i	0.116140	+	0.0462235i
$321$		0			0
$322$			10.2863i			0.573232i
$323$			22.4456i			1.24890i
$324$		0			0
$325$	−18.0897	+	19.1260i	−1.00344	+	1.06092i
$326$	−8.65087			−0.479127
$327$		0			0
$328$		−	7.38299i		−	0.407658i
$329$	−20.0000			−1.10264
$330$		0			0
$331$	−23.0210			−1.26535			−0.632674	−	0.774418i	$-0.718043\pi$
$331$	−23.0210			−1.26535			−0.632674	+	0.774418i	$0.718043\pi$
$332$		−	0.880231i		−	0.0483090i
$333$		0			0
$334$	11.9640			0.654641
$335$	−10.2326	+	25.7102i	−0.559069	+	1.40470i
$336$		0			0
$337$		−	34.0776i		−	1.85633i	−0.372173	−	0.928163i	$-0.621387\pi$
$337$		−	34.0776i		−	1.85633i	0.372173	−	0.928163i	$-0.378613\pi$
$338$		−	14.7216i		−	0.800752i
$339$		0			0
$340$	−2.98386	+	7.49713i	−0.161822	+	0.406589i
$341$	0.135870			0.00735779
$342$		0			0
$343$			36.5761i			1.97493i
$344$	−5.54789			−0.299122
$345$		0			0
$346$	−5.33508			−0.286816
$347$			13.8449i			0.743236i	0.928386	+	0.371618i	$0.121197\pi$
$347$			13.8449i			0.743236i	−0.928386	+	0.371618i	$0.878803\pi$
$348$		0			0
$349$	−11.3765			−0.608970			−0.304485	−	0.952517i	$-0.598484\pi$
$349$	−11.3765			−0.608970			−0.304485	+	0.952517i	$0.598484\pi$
$350$	16.9718	+	16.0523i	0.907179	+	0.858029i
$351$		0			0
$352$		−	0.0451320i		−	0.00240554i
$353$		−	19.2631i		−	1.02527i	−0.858606	−	0.512636i	$-0.828669\pi$
$353$		−	19.2631i		−	1.02527i	0.858606	−	0.512636i	$-0.171331\pi$
$354$		0			0
$355$	−9.33562	−	3.71558i	−0.495483	−	0.197202i
$356$	−9.97602			−0.528728
$357$		0			0
$358$		−	5.27905i		−	0.279007i
$359$	14.6645			0.773961			0.386980	−	0.922088i	$-0.373518\pi$
$359$	14.6645			0.773961			0.386980	+	0.922088i	$0.373518\pi$
$360$		0			0
$361$	19.6884			1.03623
$362$			17.7448i			0.932643i
$363$		0			0
$364$	−24.5993			−1.28935
$365$	5.81961	−	14.6221i	0.304612	−	0.765357i
$366$		0			0
$367$		−	0.868349i		−	0.0453275i	−0.999743	−	0.0226637i	$-0.992785\pi$
$367$		−	0.868349i		−	0.0453275i	0.999743	−	0.0226637i	$-0.00721471\pi$
$368$			2.20164i			0.114768i
$369$		0			0
$370$	−2.07757	−	0.826871i	−0.108008	−	0.0429870i
$371$	−28.5099			−1.48016
$372$		0			0
$373$			32.4555i			1.68048i	0.542214	+	0.840240i	$0.317586\pi$
$373$			32.4555i			1.68048i	−0.542214	+	0.840240i	$0.682414\pi$
$374$	0.162864			0.00842148
$375$		0			0
$376$	−4.28072			−0.220761
$377$		−	22.1339i		−	1.13995i
$378$		0			0
$379$	30.2511			1.55389			0.776947	−	0.629566i	$-0.216767\pi$
$379$	30.2511			1.55389			0.776947	+	0.629566i	$0.216767\pi$
$380$	12.9225	+	5.14314i	0.662909	+	0.263838i
$381$		0			0
$382$			3.11649i			0.159453i
$383$		−	14.4935i		−	0.740585i	−0.928915	−	0.370293i	$-0.879257\pi$
$383$		−	14.4935i		−	0.740585i	0.928915	−	0.370293i	$-0.120743\pi$
$384$		0			0
$385$	0.174355	−	0.438079i	0.00888597	−	0.0223266i
$386$	8.78278			0.447032
$387$		0			0
$388$			0.240408i			0.0122049i
$389$	36.9033			1.87107			0.935537	−	0.353229i	$-0.114916\pi$
$389$	36.9033			1.87107			0.935537	+	0.353229i	$0.114916\pi$
$390$		0			0
$391$	−7.94485			−0.401788
$392$			14.8286i			0.748958i
$393$		0			0
$394$	−7.00278			−0.352795
$395$	−18.1267	−	7.21444i	−0.912056	−	0.362998i
$396$		0			0
$397$		−	22.9365i		−	1.15115i	−0.817749	−	0.575575i	$-0.804778\pi$
$397$		−	22.9365i		−	1.15115i	0.817749	−	0.575575i	$-0.195222\pi$
$398$		−	17.3202i		−	0.868185i
$399$		0			0
$400$	3.63257	+	3.43576i	0.181628	+	0.171788i
$401$	−27.4332			−1.36995			−0.684973	−	0.728568i	$-0.740186\pi$
$401$	−27.4332			−1.36995			−0.684973	+	0.728568i	$0.740186\pi$
$402$		0			0
$403$		−	15.8508i		−	0.789582i
$404$	−5.61775			−0.279494
$405$		0			0
$406$	−19.6409			−0.974761
$407$			0.0451320i			0.00223711i
$408$		0			0
$409$	21.3920			1.05777			0.528883	−	0.848695i	$-0.322611\pi$
$409$	21.3920			1.05777			0.528883	+	0.848695i	$0.322611\pi$
$410$	6.10478	−	15.3387i	0.301494	−	0.757522i
$411$		0			0
$412$			12.5663i			0.619095i
$413$		−	63.2019i		−	3.10996i
$414$		0			0
$415$	0.727838	−	1.82874i	0.0357282	−	0.0897693i
$416$	−5.26514			−0.258144
$417$		0			0
$418$		−	0.280721i		−	0.0137305i
$419$	23.0891			1.12797			0.563987	−	0.825784i	$-0.309267\pi$
$419$	23.0891			1.12797			0.563987	+	0.825784i	$0.309267\pi$
$420$		0			0
$421$	−1.83757			−0.0895576			−0.0447788	−	0.998997i	$-0.514258\pi$
$421$	−1.83757			−0.0895576			−0.0447788	+	0.998997i	$0.514258\pi$
$422$			6.77438i			0.329772i
$423$		0			0
$424$	−6.10215			−0.296346
$425$	−12.3983	+	13.1085i	−0.601407	+	0.635857i
$426$		0			0
$427$			19.9639i			0.966120i
$428$			17.9395i			0.867137i
$429$		0			0
$430$	−11.5261	−	4.58739i	−0.555839	−	0.221224i
$431$	15.9796			0.769710			0.384855	−	0.922977i	$-0.374251\pi$
$431$	15.9796			0.769710			0.384855	+	0.922977i	$0.374251\pi$
$432$		0			0
$433$		−	25.2525i		−	1.21356i	−0.794870	−	0.606779i	$-0.792461\pi$
$433$		−	25.2525i		−	1.21356i	0.794870	−	0.606779i	$-0.207539\pi$
$434$	−14.0654			−0.675163
$435$		0			0
$436$	3.09936			0.148433
$437$			13.6942i			0.655082i
$438$		0			0
$439$	9.30792			0.444243			0.222121	−	0.975019i	$-0.428702\pi$
$439$	9.30792			0.444243			0.222121	+	0.975019i	$0.428702\pi$
$440$	0.0373183	−	0.0937647i	0.00177908	−	0.00447005i
$441$		0			0
$442$		−	18.9998i		−	0.903729i
$443$			9.52445i			0.452520i	0.974067	+	0.226260i	$0.0726500\pi$
$443$			9.52445i			0.452520i	−0.974067	+	0.226260i	$0.927350\pi$
$444$		0			0
$445$	−20.7258	−	8.24888i	−0.982499	−	0.391035i
$446$	10.2559			0.485629
$447$		0			0
$448$			4.67211i			0.220736i
$449$	5.43278			0.256389			0.128194	−	0.991749i	$-0.459082\pi$
$449$	5.43278			0.256389			0.128194	+	0.991749i	$0.459082\pi$
$450$		0			0
$451$	−0.333209			−0.0156902
$452$			4.36184i			0.205164i
$453$		0			0
$454$	11.2744			0.529132
$455$	−51.1067	−	20.3404i	−2.39592	−	0.953575i
$456$		0			0
$457$		−	7.54789i		−	0.353076i	−0.984294	−	0.176538i	$-0.943510\pi$
$457$		−	7.54789i		−	0.353076i	0.984294	−	0.176538i	$-0.0564898\pi$
$458$			9.40494i			0.439464i
$459$		0			0
$460$	−1.82047	+	4.57405i	−0.0848798	+	0.213266i
$461$	35.4323			1.65025			0.825124	−	0.564952i	$-0.191105\pi$
$461$	35.4323			1.65025			0.825124	+	0.564952i	$0.191105\pi$
$462$		0			0
$463$			20.9124i			0.971883i	0.873991	+	0.485942i	$0.161523\pi$
$463$			20.9124i			0.971883i	−0.873991	+	0.485942i	$0.838477\pi$
$464$	−4.20386			−0.195159
$465$		0			0
$466$	−3.22867			−0.149565
$467$			6.62523i			0.306579i	0.988181	+	0.153289i	$0.0489867\pi$
$467$			6.62523i			0.306579i	−0.988181	+	0.153289i	$0.951013\pi$
$468$		0			0
$469$	−57.8180			−2.66979
$470$	−8.89348	−	3.53961i	−0.410226	−	0.163270i
$471$		0			0
$472$		−	13.5275i		−	0.622653i
$473$			0.250387i			0.0115128i
$474$		0			0
$475$	22.5946	+	21.3704i	1.03671	+	0.980543i
$476$	−16.8598			−0.772769
$477$		0			0
$478$		−	17.8612i		−	0.816952i
$479$	−29.4581			−1.34597			−0.672987	−	0.739655i	$-0.734989\pi$
$479$	−29.4581			−1.34597			−0.672987	+	0.739655i	$0.734989\pi$
$480$		0			0
$481$	5.26514			0.240070
$482$			26.6840i			1.21542i
$483$		0			0
$484$	10.9980			0.499907
$485$	−0.198786	+	0.499463i	−0.00902642	+	0.0226795i
$486$		0			0
$487$		−	8.80654i		−	0.399063i	−0.979891	−	0.199531i	$-0.936058\pi$
$487$		−	8.80654i		−	0.399063i	0.979891	−	0.199531i	$-0.0639419\pi$
$488$			4.27299i			0.193429i
$489$		0			0
$490$	−12.2614	+	30.8074i	−0.553912	+	1.39174i
$491$	−5.14258			−0.232082			−0.116041	−	0.993244i	$-0.537020\pi$
$491$	−5.14258			−0.232082			−0.116041	+	0.993244i	$0.537020\pi$
$492$		0			0
$493$		−	15.1701i		−	0.683227i
$494$	−32.7492			−1.47345
$495$		0			0
$496$	−3.01051			−0.135176
$497$		−	20.9943i		−	0.941723i
$498$		0			0
$499$	12.9692			0.580579			0.290290	−	0.956939i	$-0.406248\pi$
$499$	12.9692			0.580579			0.290290	+	0.956939i	$0.406248\pi$
$500$	4.70597	+	10.1417i	0.210457	+	0.453550i
$501$		0			0
$502$			30.1552i			1.34589i
$503$		−	17.2091i		−	0.767314i	−0.923476	−	0.383657i	$-0.874664\pi$
$503$		−	17.2091i		−	0.767314i	0.923476	−	0.383657i	$-0.125336\pi$
$504$		0			0
$505$	−11.6713	−	4.64516i	−0.519364	−	0.206707i
$506$	0.0993641			0.00441727
$507$		0			0
$508$			17.6572i			0.783413i
$509$	−12.1085			−0.536698			−0.268349	−	0.963322i	$-0.586478\pi$
$509$	−12.1085			−0.536698			−0.268349	+	0.963322i	$0.586478\pi$
$510$		0			0
$511$	32.8828			1.45465
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	3.15376			0.139107
$515$	−10.3907	+	26.1072i	−0.457868	+	1.15042i
$516$		0			0
$517$			0.193197i			0.00849681i
$518$		−	4.67211i		−	0.205281i
$519$		0			0
$520$	−10.9387	−	4.35359i	−0.479692	−	0.190918i
$521$	18.7936			0.823362			0.411681	−	0.911328i	$-0.364942\pi$
$521$	18.7936			0.823362			0.411681	+	0.911328i	$0.364942\pi$
$522$		0			0
$523$		−	42.9985i		−	1.88019i	−0.340909	−	0.940096i	$-0.610735\pi$
$523$		−	42.9985i		−	1.88019i	0.340909	−	0.940096i	$-0.389265\pi$
$524$	−10.3103			−0.450406
$525$		0			0
$526$	14.0332			0.611875
$527$		−	10.8638i		−	0.473233i
$528$		0			0
$529$	18.1528			0.789252
$530$	−12.6776	−	5.04569i	−0.550680	−	0.219171i
$531$		0			0
$532$			29.0605i			1.25993i
$533$			38.8725i			1.68375i
$534$		0			0
$535$	−14.8336	+	37.2704i	−0.641314	+	1.61134i
$536$	−12.3751			−0.534525
$537$		0			0
$538$		−	30.1257i		−	1.29881i
$539$	0.669244			0.0288264
$540$		0			0
$541$	30.1751			1.29733			0.648664	−	0.761075i	$-0.275328\pi$
$541$	30.1751			1.29733			0.648664	+	0.761075i	$0.275328\pi$
$542$			14.8802i			0.639161i
$543$		0			0
$544$	−3.60861			−0.154718
$545$	6.43914	+	2.56278i	0.275822	+	0.109777i
$546$		0			0
$547$			31.6736i			1.35426i	0.735862	+	0.677132i	$0.236777\pi$
$547$			31.6736i			1.35426i	−0.735862	+	0.677132i	$0.763223\pi$
$548$		−	3.21863i		−	0.137493i
$549$		0			0
$550$	0.155063	−	0.163945i	0.00661189	−	0.00699063i
$551$	−26.1480			−1.11394
$552$		0			0
$553$		−	40.7641i		−	1.73347i
$554$	0.147278			0.00625724
$555$		0			0
$556$	20.9400			0.888055
$557$		−	0.708971i		−	0.0300401i	−0.999887	−	0.0150200i	$-0.995219\pi$
$557$		−	0.708971i		−	0.0300401i	0.999887	−	0.0150200i	$-0.00478120\pi$
$558$		0			0
$559$	29.2104			1.23547
$560$	−3.86323	+	9.70662i	−0.163251	+	0.410180i
$561$		0			0
$562$			25.5247i			1.07670i
$563$			29.9399i			1.26182i	0.775857	+	0.630908i	$0.217318\pi$
$563$			29.9399i			1.26182i	−0.775857	+	0.630908i	$0.782682\pi$
$564$		0			0
$565$	−3.60668	+	9.06202i	−0.151734	+	0.381242i
$566$	−0.0562691			−0.00236517
$567$		0			0
$568$		−	4.49354i		−	0.188545i
$569$	21.1453			0.886456			0.443228	−	0.896409i	$-0.353833\pi$
$569$	21.1453			0.886456			0.443228	+	0.896409i	$0.353833\pi$
$570$		0			0
$571$	−19.5326			−0.817416			−0.408708	−	0.912665i	$-0.634020\pi$
$571$	−19.5326			−0.817416			−0.408708	+	0.912665i	$0.634020\pi$
$572$			0.237626i			0.00993564i
$573$		0			0
$574$	34.4942			1.43976
$575$	−7.56429	+	7.99759i	−0.315453	+	0.333523i
$576$		0			0
$577$		−	1.08303i		−	0.0450873i	−0.999746	−	0.0225436i	$-0.992824\pi$
$577$		−	1.08303i		−	0.0450873i	0.999746	−	0.0225436i	$-0.00717647\pi$
$578$			3.97793i			0.165460i
$579$		0			0
$580$	−8.73380	−	3.47605i	−0.362651	−	0.144335i
$581$	4.11254			0.170617
$582$		0			0
$583$			0.275402i			0.0114060i
$584$	7.03811			0.291239
$585$		0			0
$586$	13.7033			0.566079
$587$			1.16839i			0.0482244i	0.999709	+	0.0241122i	$0.00767590\pi$
$587$			1.16839i			0.0482244i	−0.999709	+	0.0241122i	$0.992324\pi$
$588$		0			0
$589$	−18.7254			−0.771566
$590$	11.1855	−	28.1043i	0.460499	−	1.15703i
$591$		0			0
$592$		−	1.00000i		−	0.0410997i
$593$			6.01305i			0.246926i	0.992349	+	0.123463i	$0.0394001\pi$
$593$			6.01305i			0.246926i	−0.992349	+	0.123463i	$0.960600\pi$
$594$		0			0
$595$	−35.0274	−	13.9409i	−1.43598	−	0.571521i
$596$	21.9832			0.900467
$597$		0			0
$598$		−	11.5919i		−	0.474028i
$599$	−11.9208			−0.487072			−0.243536	−	0.969892i	$-0.578307\pi$
$599$	−11.9208			−0.487072			−0.243536	+	0.969892i	$0.578307\pi$
$600$		0			0
$601$	21.7772			0.888309			0.444155	−	0.895950i	$-0.353504\pi$
$601$	21.7772			0.888309			0.444155	+	0.895950i	$0.353504\pi$
$602$		−	25.9204i		−	1.05644i
$603$		0			0
$604$	−14.1877			−0.577290
$605$	22.8490	+	9.09390i	0.928944	+	0.369720i
$606$		0			0
$607$		−	5.16486i		−	0.209635i	−0.994491	−	0.104818i	$-0.966574\pi$
$607$		−	5.16486i		−	0.209635i	0.994491	−	0.104818i	$-0.0334259\pi$
$608$			6.22000i			0.252254i
$609$		0			0
$610$	−3.53321	+	8.87742i	−0.143056	+	0.359436i
$611$	22.5386			0.911813
$612$		0			0
$613$		−	39.5817i		−	1.59869i	−0.600873	−	0.799344i	$-0.705180\pi$
$613$		−	39.5817i		−	1.59869i	0.600873	−	0.799344i	$-0.294820\pi$
$614$	−17.5823			−0.709565
$615$		0			0
$616$	0.210861			0.00849585
$617$			44.9917i			1.81130i	0.424027	+	0.905650i	$0.360616\pi$
$617$			44.9917i			1.81130i	−0.424027	+	0.905650i	$0.639384\pi$
$618$		0			0
$619$	−30.0465			−1.20767			−0.603836	−	0.797108i	$-0.706362\pi$
$619$	−30.0465			−1.20767			−0.603836	+	0.797108i	$0.706362\pi$
$620$	−6.25454	−	2.48931i	−0.251188	−	0.0999729i
$621$		0			0
$622$		−	0.353133i		−	0.0141594i
$623$		−	46.6091i		−	1.86735i
$624$		0			0
$625$	1.39110	+	24.9613i	0.0556438	+	0.998451i
$626$	18.8717			0.754265
$627$		0			0
$628$		−	19.9316i		−	0.795359i
$629$	3.60861			0.143885
$630$		0			0
$631$	5.01448			0.199623			0.0998116	−	0.995006i	$-0.468176\pi$
$631$	5.01448			0.199623			0.0998116	+	0.995006i	$0.468176\pi$
$632$		−	8.72499i		−	0.347061i
$633$		0			0
$634$	−15.1979			−0.603587
$635$	−14.6003	+	36.6841i	−0.579393	+	1.45576i
$636$		0			0
$637$		−	78.0747i		−	3.09343i
$638$			0.189728i			0.00751142i
$639$		0			0
$640$	−0.826871	+	2.07757i	−0.0326850	+	0.0821230i
$641$	−18.9133			−0.747031			−0.373515	−	0.927624i	$-0.621848\pi$
$641$	−18.9133			−0.747031			−0.373515	+	0.927624i	$0.621848\pi$
$642$		0			0
$643$			22.9344i			0.904444i	0.891906	+	0.452222i	$0.149368\pi$
$643$			22.9344i			0.904444i	−0.891906	+	0.452222i	$0.850632\pi$
$644$	−10.2863			−0.405336
$645$		0			0
$646$	−22.4456			−0.883109
$647$			10.4741i			0.411779i	0.978575	+	0.205889i	$0.0660087\pi$
$647$			10.4741i			0.411779i	−0.978575	+	0.205889i	$0.933991\pi$
$648$		0			0
$649$	−0.610522			−0.0239651
$650$	−19.1260	−	18.0897i	−0.750182	−	0.709538i
$651$		0			0
$652$		−	8.65087i		−	0.338794i
$653$			44.7251i			1.75023i	0.483916	+	0.875115i	$0.339214\pi$
$653$			44.7251i			1.75023i	−0.483916	+	0.875115i	$0.660786\pi$
$654$		0			0
$655$	−21.4203	−	8.52526i	−0.836959	−	0.333110i
$656$	7.38299			0.288257
$657$		0			0
$658$		−	20.0000i		−	0.779681i
$659$	15.1056			0.588431			0.294215	−	0.955739i	$-0.404942\pi$
$659$	15.1056			0.588431			0.294215	+	0.955739i	$0.404942\pi$
$660$		0			0
$661$	34.9654			1.36000			0.679998	−	0.733214i	$-0.261981\pi$
$661$	34.9654			1.36000			0.679998	+	0.733214i	$0.261981\pi$
$662$		−	23.0210i		−	0.894736i
$663$		0			0
$664$	0.880231			0.0341596
$665$	−24.0293	+	60.3752i	−0.931817	+	2.34125i
$666$		0			0
$667$		−	9.25537i		−	0.358369i
$668$			11.9640i			0.462901i
$669$		0			0
$670$	−25.7102	−	10.2326i	−0.993271	−	0.395322i
$671$	0.192848			0.00744483
$672$		0			0
$673$			35.2496i			1.35877i	0.733782	+	0.679385i	$0.237754\pi$
$673$			35.2496i			1.35877i	−0.733782	+	0.679385i	$0.762246\pi$
$674$	34.0776			1.31262
$675$		0			0
$676$	14.7216			0.566217
$677$		−	23.2835i		−	0.894858i	−0.894320	−	0.447429i	$-0.852340\pi$
$677$		−	23.2835i		−	0.894858i	0.894320	−	0.447429i	$-0.147660\pi$
$678$		0			0
$679$	−1.12321			−0.0431049
$680$	−7.49713	−	2.98386i	−0.287502	−	0.114426i
$681$		0			0
$682$			0.135870i			0.00520274i
$683$			11.8131i			0.452017i	0.974125	+	0.226008i	$0.0725676\pi$
$683$			11.8131i			0.452017i	−0.974125	+	0.226008i	$0.927432\pi$
$684$		0			0
$685$	2.66140	−	6.68693i	0.101687	−	0.255494i
$686$	−36.5761			−1.39648
$687$		0			0
$688$		−	5.54789i		−	0.211511i
$689$	32.1286			1.22400
$690$		0			0
$691$	14.1858			0.539652			0.269826	−	0.962909i	$-0.413034\pi$
$691$	14.1858			0.539652			0.269826	+	0.962909i	$0.413034\pi$
$692$		−	5.33508i		−	0.202809i
$693$		0			0
$694$	−13.8449			−0.525547
$695$	43.5043	+	17.3147i	1.65021	+	0.656784i
$696$		0			0
$697$			26.6423i			1.00915i
$698$		−	11.3765i		−	0.430607i
$699$		0			0
$700$	−16.0523	+	16.9718i	−0.606718	+	0.641472i
$701$	−19.2184			−0.725870			−0.362935	−	0.931815i	$-0.618225\pi$
$701$	−19.2184			−0.725870			−0.362935	+	0.931815i	$0.618225\pi$
$702$		0			0
$703$		−	6.22000i		−	0.234592i
$704$	0.0451320			0.00170097
$705$		0			0
$706$	19.2631			0.724976
$707$		−	26.2468i		−	0.987111i
$708$		0			0
$709$	−4.52525			−0.169949			−0.0849746	−	0.996383i	$-0.527081\pi$
$709$	−4.52525			−0.169949			−0.0849746	+	0.996383i	$0.527081\pi$
$710$	3.71558	−	9.33562i	0.139443	−	0.350360i
$711$		0			0
$712$		−	9.97602i		−	0.373867i
$713$		−	6.62805i		−	0.248222i
$714$		0			0
$715$	−0.196486	+	0.493684i	−0.00734816	+	0.0184627i
$716$	5.27905			0.197288
$717$		0			0
$718$			14.6645i			0.547273i
$719$	0.915477			0.0341415			0.0170708	−	0.999854i	$-0.494566\pi$
$719$	0.915477			0.0341415			0.0170708	+	0.999854i	$0.494566\pi$
$720$		0			0
$721$	−58.7110			−2.18651
$722$			19.6884i			0.732728i
$723$		0			0
$724$	−17.7448			−0.659478
$725$	−15.2708	−	14.4435i	−0.567143	−	0.536417i
$726$		0			0
$727$			11.7429i			0.435521i	0.976002	+	0.217760i	$0.0698752\pi$
$727$			11.7429i			0.435521i	−0.976002	+	0.217760i	$0.930125\pi$
$728$		−	24.5993i		−	0.911710i
$729$		0			0
$730$	14.6221	+	5.81961i	0.541189	+	0.215393i
$731$	20.0202			0.740473
$732$		0			0
$733$			27.6776i			1.02230i	0.859493	+	0.511148i	$0.170780\pi$
$733$			27.6776i			1.02230i	−0.859493	+	0.511148i	$0.829220\pi$
$734$	0.868349			0.0320514
$735$		0			0
$736$	−2.20164			−0.0811534
$737$			0.558514i			0.0205731i
$738$		0			0
$739$	6.52187			0.239911			0.119956	−	0.992779i	$-0.461725\pi$
$739$	6.52187			0.239911			0.119956	+	0.992779i	$0.461725\pi$
$740$	0.826871	−	2.07757i	0.0303964	−	0.0763729i
$741$		0			0
$742$		−	28.5099i		−	1.04663i
$743$		−	43.0091i		−	1.57785i	−0.614489	−	0.788925i	$-0.710638\pi$
$743$		−	43.0091i		−	1.57785i	0.614489	−	0.788925i	$-0.289362\pi$
$744$		0			0
$745$	45.6716	+	18.1773i	1.67328	+	0.665964i
$746$	−32.4555			−1.18828
$747$		0			0
$748$			0.162864i			0.00595489i
$749$	−83.8152			−3.06254
$750$		0			0
$751$	−29.7068			−1.08402			−0.542008	−	0.840373i	$-0.682336\pi$
$751$	−29.7068			−1.08402			−0.542008	+	0.840373i	$0.682336\pi$
$752$		−	4.28072i		−	0.156102i
$753$		0			0
$754$	22.1339			0.806069
$755$	−29.4759	−	11.7314i	−1.07274	−	0.426950i
$756$		0			0
$757$		−	32.7918i		−	1.19184i	−0.803044	−	0.595920i	$-0.796788\pi$
$757$		−	32.7918i		−	1.19184i	0.803044	−	0.595920i	$-0.203212\pi$
$758$			30.2511i			1.09877i
$759$		0			0
$760$	−5.14314	+	12.9225i	−0.186561	+	0.468747i
$761$	−22.9411			−0.831616			−0.415808	−	0.909452i	$-0.636501\pi$
$761$	−22.9411			−0.831616			−0.415808	+	0.909452i	$0.636501\pi$
$762$		0			0
$763$			14.4806i			0.524232i
$764$	−3.11649			−0.112751
$765$		0			0
$766$	14.4935			0.523673
$767$			71.2241i			2.57175i
$768$		0			0
$769$	−10.8123			−0.389902			−0.194951	−	0.980813i	$-0.562455\pi$
$769$	−10.8123			−0.389902			−0.194951	+	0.980813i	$0.562455\pi$
$770$	0.438079	+	0.174355i	0.0157873	+	0.00628333i
$771$		0			0
$772$			8.78278i			0.316099i
$773$			37.9989i			1.36673i	0.730079	+	0.683363i	$0.239483\pi$
$773$			37.9989i			1.36673i	−0.730079	+	0.683363i	$0.760517\pi$
$774$		0			0
$775$	−10.9359	−	10.3434i	−0.392829	−	0.371546i
$776$	−0.240408			−0.00863014
$777$		0			0
$778$			36.9033i			1.32305i
$779$	45.9222			1.64533
$780$		0			0
$781$	−0.202802			−0.00725683
$782$		−	7.94485i		−	0.284107i
$783$		0			0
$784$	−14.8286			−0.529593
$785$	16.4809	−	41.4093i	0.588228	−	1.47796i
$786$		0			0
$787$		−	31.7730i		−	1.13258i	−0.824205	−	0.566292i	$-0.808377\pi$
$787$		−	31.7730i		−	1.13258i	0.824205	−	0.566292i	$-0.191623\pi$
$788$		−	7.00278i		−	0.249464i
$789$		0			0
$790$	7.21444	−	18.1267i	0.256678	−	0.644921i
$791$	−20.3790			−0.724594
$792$		0			0
$793$		−	22.4979i		−	0.798923i
$794$	22.9365			0.813986
$795$		0			0
$796$	17.3202			0.613900
$797$			9.02551i			0.319700i	0.987141	+	0.159850i	$0.0511011\pi$
$797$			9.02551i			0.319700i	−0.987141	+	0.159850i	$0.948899\pi$
$798$		0			0
$799$	15.4475			0.546492
$800$	−3.43576	+	3.63257i	−0.121472	+	0.128431i
$801$		0			0
$802$		−	27.4332i		−	0.968698i
$803$		−	0.317643i		−	0.0112094i
$804$		0			0
$805$	−21.3704	−	8.50543i	−0.753209	−	0.299777i
$806$	15.8508			0.558319
$807$		0			0
$808$		−	5.61775i		−	0.197632i
$809$	29.7376			1.04552			0.522759	−	0.852481i	$-0.324903\pi$
$809$	29.7376			1.04552			0.522759	+	0.852481i	$0.324903\pi$
$810$		0			0
$811$	15.7650			0.553585			0.276793	−	0.960930i	$-0.410729\pi$
$811$	15.7650			0.553585			0.276793	+	0.960930i	$0.410729\pi$
$812$		−	19.6409i		−	0.689260i
$813$		0			0
$814$	−0.0451320			−0.00158187
$815$	7.15315	−	17.9728i	0.250564	−	0.629558i
$816$		0			0
$817$		−	34.5079i		−	1.20728i
$818$			21.3920i			0.747954i
$819$		0			0
$820$	15.3387	+	6.10478i	0.535649	+	0.213188i
$821$	4.27798			0.149303			0.0746513	−	0.997210i	$-0.476216\pi$
$821$	4.27798			0.149303			0.0746513	+	0.997210i	$0.476216\pi$
$822$		0			0
$823$		−	13.8985i		−	0.484471i	−0.970217	−	0.242236i	$-0.922119\pi$
$823$		−	13.8985i		−	0.484471i	0.970217	−	0.242236i	$-0.0778807\pi$
$824$	−12.5663			−0.437766
$825$		0			0
$826$	63.2019			2.19908
$827$		−	30.4944i		−	1.06039i	−0.847875	−	0.530197i	$-0.822118\pi$
$827$		−	30.4944i		−	1.06039i	0.847875	−	0.530197i	$-0.177882\pi$
$828$		0			0
$829$	−0.493020			−0.0171233			−0.00856165	−	0.999963i	$-0.502725\pi$
$829$	−0.493020			−0.0171233			−0.00856165	+	0.999963i	$0.502725\pi$
$830$	1.82874	+	0.727838i	0.0634765	+	0.0252636i
$831$		0			0
$832$		−	5.26514i		−	0.182536i
$833$		−	53.5107i		−	1.85404i
$834$		0			0
$835$	−9.89270	+	24.8560i	−0.342351	+	0.860178i
$836$	0.280721			0.00970894
$837$		0			0
$838$			23.0891i			0.797598i
$839$	−27.9308			−0.964278			−0.482139	−	0.876095i	$-0.660140\pi$
$839$	−27.9308			−0.964278			−0.482139	+	0.876095i	$0.660140\pi$
$840$		0			0
$841$	−11.3276			−0.390606
$842$		−	1.83757i		−	0.0633268i
$843$		0			0
$844$	−6.77438			−0.233184
$845$	30.5852	+	12.1729i	1.05216	+	0.418761i
$846$		0			0
$847$			51.3837i			1.76556i
$848$		−	6.10215i		−	0.209549i
$849$		0			0
$850$	−13.1085	−	12.3983i	−0.449619	−	0.425259i
$851$	2.20164			0.0754711
$852$		0			0
$853$			31.4029i			1.07521i	0.843195	+	0.537607i	$0.180672\pi$
$853$			31.4029i			1.07521i	−0.843195	+	0.537607i	$0.819328\pi$
$854$	−19.9639			−0.683150
$855$		0			0
$856$	−17.9395			−0.613158
$857$			39.7806i			1.35888i	0.733731	+	0.679441i	$0.237777\pi$
$857$			39.7806i			1.35888i	−0.733731	+	0.679441i	$0.762223\pi$
$858$		0			0
$859$	−41.8673			−1.42849			−0.714247	−	0.699894i	$-0.753231\pi$
$859$	−41.8673			−1.42849			−0.714247	+	0.699894i	$0.753231\pi$
$860$	4.58739	−	11.5261i	0.156429	−	0.393037i
$861$		0			0
$862$			15.9796i			0.544267i
$863$			8.52387i			0.290156i	0.989420	+	0.145078i	$0.0463433\pi$
$863$			8.52387i			0.290156i	−0.989420	+	0.145078i	$0.953657\pi$
$864$		0			0
$865$	4.41142	−	11.0840i	0.149993	−	0.376867i
$866$	25.2525			0.858116
$867$		0			0
$868$		−	14.0654i		−	0.477412i
$869$	−0.393776			−0.0133579
$870$		0			0
$871$	65.1568			2.20775
$872$			3.09936i			0.104958i
$873$		0			0
$874$	−13.6942			−0.463213
$875$	−47.3831	+	21.9868i	−1.60184	+	0.743290i
$876$		0			0
$877$			37.1163i			1.25333i	0.779289	+	0.626664i	$0.215580\pi$
$877$			37.1163i			1.25333i	−0.779289	+	0.626664i	$0.784420\pi$
$878$			9.30792i			0.314127i
$879$		0			0
$880$	0.0937647	+	0.0373183i	0.00316081	+	0.00125800i
$881$	−29.8633			−1.00612			−0.503060	−	0.864252i	$-0.667792\pi$
$881$	−29.8633			−1.00612			−0.503060	+	0.864252i	$0.667792\pi$
$882$		0			0
$883$		−	9.98952i		−	0.336174i	−0.985772	−	0.168087i	$-0.946241\pi$
$883$		−	9.98952i		−	0.336174i	0.985772	−	0.168087i	$-0.0537590\pi$
$884$	18.9998			0.639033
$885$		0			0
$886$	−9.52445			−0.319980
$887$			23.2703i			0.781340i	0.920531	+	0.390670i	$0.127757\pi$
$887$			23.2703i			0.781340i	−0.920531	+	0.390670i	$0.872243\pi$
$888$		0			0
$889$	−82.4965			−2.76684
$890$	8.24888	−	20.7258i	0.276503	−	0.694732i
$891$		0			0
$892$			10.2559i			0.343392i
$893$		−	26.6261i		−	0.891008i
$894$		0			0
$895$	10.9676	+	4.36510i	0.366606	+	0.145909i
$896$	−4.67211			−0.156084
$897$		0			0
$898$			5.43278i			0.181294i
$899$	12.6558			0.422094
$900$		0			0
$901$	22.0203			0.733602
$902$		−	0.333209i		−	0.0110946i
$903$		0			0
$904$	−4.36184			−0.145073
$905$	−36.8659	−	14.6726i	−1.22546	−	0.487735i
$906$		0			0
$907$			34.0053i			1.12913i	0.825389	+	0.564564i	$0.190956\pi$
$907$			34.0053i			1.12913i	−0.825389	+	0.564564i	$0.809044\pi$
$908$			11.2744i			0.374153i
$909$		0			0
$910$	20.3404	−	51.1067i	0.674279	−	1.69417i
$911$	29.2297			0.968424			0.484212	−	0.874951i	$-0.339106\pi$
$911$	29.2297			0.968424			0.484212	+	0.874951i	$0.339106\pi$
$912$		0			0
$913$		−	0.0397266i		−	0.00131476i
$914$	7.54789			0.249662
$915$		0			0
$916$	−9.40494			−0.310748
$917$		−	48.1707i		−	1.59074i
$918$		0			0
$919$	−43.0238			−1.41923			−0.709613	−	0.704592i	$-0.751130\pi$
$919$	−43.0238			−1.41923			−0.709613	+	0.704592i	$0.751130\pi$
$920$	−4.57405	−	1.82047i	−0.150802	−	0.0600191i
$921$		0			0
$922$			35.4323i			1.16690i
$923$			23.6591i			0.778748i
$924$		0			0
$925$	3.43576	−	3.63257i	0.112967	−	0.119438i
$926$	−20.9124			−0.687225
$927$		0			0
$928$		−	4.20386i		−	0.137998i
$929$	10.7786			0.353635			0.176817	−	0.984244i	$-0.443420\pi$
$929$	10.7786			0.353635			0.176817	+	0.984244i	$0.443420\pi$
$930$		0			0
$931$	−92.2340			−3.02285
$932$		−	3.22867i		−	0.105759i
$933$		0			0
$934$	−6.62523			−0.216784
$935$	−0.134667	+	0.338360i	−0.00440409	+	0.0110656i
$936$		0			0
$937$		−	36.5755i		−	1.19487i	−0.801918	−	0.597435i	$-0.796187\pi$
$937$		−	36.5755i		−	1.19487i	0.801918	−	0.597435i	$-0.203813\pi$
$938$		−	57.8180i		−	1.88782i
$939$		0			0
$940$	3.53961	−	8.89348i	0.115449	−	0.290073i
$941$	−58.9579			−1.92197			−0.960986	−	0.276596i	$-0.910794\pi$
$941$	−58.9579			−1.92197			−0.960986	+	0.276596i	$0.910794\pi$
$942$		0			0
$943$			16.2547i			0.529325i
$944$	13.5275			0.440282
$945$		0			0
$946$	−0.250387			−0.00814079
$947$			9.63990i			0.313255i	0.987658	+	0.156627i	$0.0500621\pi$
$947$			9.63990i			0.313255i	−0.987658	+	0.156627i	$0.949938\pi$
$948$		0			0
$949$	−37.0566			−1.20291
$950$	−21.3704	+	22.5946i	−0.693349	+	0.733065i
$951$		0			0
$952$		−	16.8598i		−	0.546430i
$953$		−	31.4809i		−	1.01977i	−0.860243	−	0.509884i	$-0.829688\pi$
$953$		−	31.4809i		−	1.01977i	0.860243	−	0.509884i	$-0.170312\pi$
$954$		0			0
$955$	−6.47471	−	2.57693i	−0.209517	−	0.0833876i
$956$	17.8612			0.577672
$957$		0			0
$958$		−	29.4581i		−	0.951747i
$959$	15.0378			0.485596
$960$		0			0
$961$	−21.9368			−0.707639
$962$			5.26514i			0.169755i
$963$		0			0
$964$	−26.6840			−0.859434
$965$	−7.26223	+	18.2468i	−0.233779	+	0.587386i
$966$		0			0
$967$		−	25.5439i		−	0.821438i	−0.911762	−	0.410719i	$-0.865278\pi$
$967$		−	25.5439i		−	0.821438i	0.911762	−	0.410719i	$-0.134722\pi$
$968$			10.9980i			0.353488i
$969$		0			0
$970$	−0.499463	−	0.198786i	−0.0160368	−	0.00638264i
$971$	−43.7224			−1.40312			−0.701559	−	0.712611i	$-0.747512\pi$
$971$	−43.7224			−1.40312			−0.701559	+	0.712611i	$0.747512\pi$
$972$		0			0
$973$			97.8341i			3.13642i
$974$	8.80654			0.282180
$975$		0			0
$976$	−4.27299			−0.136775
$977$		−	44.6598i		−	1.42879i	−0.699741	−	0.714396i	$-0.746701\pi$
$977$		−	44.6598i		−	1.42879i	0.699741	−	0.714396i	$-0.253299\pi$
$978$		0			0
$979$	−0.450237			−0.0143896
$980$	−30.8074	−	12.2614i	−0.984107	−	0.391675i
$981$		0			0
$982$		−	5.14258i		−	0.164106i
$983$		−	9.17840i		−	0.292745i	−0.989230	−	0.146373i	$-0.953240\pi$
$983$		−	9.17840i		−	0.292745i	0.989230	−	0.146373i	$-0.0467599\pi$
$984$		0			0
$985$	5.79040	−	14.5487i	0.184497	−	0.463562i
$986$	15.1701			0.483114
$987$		0			0
$988$		−	32.7492i		−	1.04189i
$989$	12.2144			0.388397
$990$		0			0
$991$	16.1246			0.512216			0.256108	−	0.966648i	$-0.417560\pi$
$991$	16.1246			0.512216			0.256108	+	0.966648i	$0.417560\pi$
$992$		−	3.01051i		−	0.0955839i
$993$		0			0
$994$	20.9943			0.665899
$995$	35.9840	+	14.3216i	1.14077	+	0.454026i
$996$		0			0
$997$		−	8.99979i		−	0.285026i	−0.989793	−	0.142513i	$-0.954482\pi$
$997$		−	8.99979i		−	0.285026i	0.989793	−	0.142513i	$-0.0455183\pi$
$998$			12.9692i			0.410532i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3330.2.d.p.1999.6		10
3.2	odd	2		370.2.b.d.149.4	✓	10
5.4	even	2	inner	3330.2.d.p.1999.1		10
15.2	even	4		1850.2.a.be.1.4		5
15.8	even	4		1850.2.a.bd.1.2		5
15.14	odd	2		370.2.b.d.149.7	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.b.d.149.4	✓	10	3.2	odd	2
370.2.b.d.149.7	yes	10	15.14	odd	2
1850.2.a.bd.1.2		5	15.8	even	4
1850.2.a.be.1.4		5	15.2	even	4
3330.2.d.p.1999.1		10	5.4	even	2	inner
3330.2.d.p.1999.6		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.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-2.07757 - 0.826871i) q^{5} -4.67211i q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-2.07757 - 0.826871i) q^{5} -4.67211i q^{7} -1.00000i q^{8} +(0.826871 - 2.07757i) q^{10} -0.0451320 q^{11} +5.26514i q^{13} +4.67211 q^{14} +1.00000 q^{16} +3.60861i q^{17} +6.22000 q^{19} +(2.07757 + 0.826871i) q^{20} -0.0451320i q^{22} +2.20164i q^{23} +(3.63257 + 3.43576i) q^{25} -5.26514 q^{26} +4.67211i q^{28} -4.20386 q^{29} -3.01051 q^{31} +1.00000i q^{32} -3.60861 q^{34} +(-3.86323 + 9.70662i) q^{35} -1.00000i q^{37} +6.22000i q^{38} +(-0.826871 + 2.07757i) q^{40} +7.38299 q^{41} -5.54789i q^{43} +0.0451320 q^{44} -2.20164 q^{46} -4.28072i q^{47} -14.8286 q^{49} +(-3.43576 + 3.63257i) q^{50} -5.26514i q^{52} -6.10215i q^{53} +(0.0937647 + 0.0373183i) q^{55} -4.67211 q^{56} -4.20386i q^{58} +13.5275 q^{59} -4.27299 q^{61} -3.01051i q^{62} -1.00000 q^{64} +(4.35359 - 10.9387i) q^{65} -12.3751i q^{67} -3.60861i q^{68} +(-9.70662 - 3.86323i) q^{70} +4.49354 q^{71} +7.03811i q^{73} +1.00000 q^{74} -6.22000 q^{76} +0.210861i q^{77} +8.72499 q^{79} +(-2.07757 - 0.826871i) q^{80} +7.38299i q^{82} +0.880231i q^{83} +(2.98386 - 7.49713i) q^{85} +5.54789 q^{86} +0.0451320i q^{88} +9.97602 q^{89} +24.5993 q^{91} -2.20164i q^{92} +4.28072 q^{94} +(-12.9225 - 5.14314i) q^{95} -0.240408i q^{97} -14.8286i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{4} - 6 q^{5}+O(q^{10}) \) 10 * q - 10 * q^4 - 6 * q^5	\( 10 q - 10 q^{4} - 6 q^{5} + 2 q^{10} - 6 q^{11} - 2 q^{14} + 10 q^{16} - 8 q^{19} + 6 q^{20} + 4 q^{25} + 12 q^{26} + 22 q^{29} + 46 q^{31} - 18 q^{34} - 32 q^{35} - 2 q^{40} + 14 q^{41} + 6 q^{44} + 12 q^{46} - 60 q^{49} - 8 q^{50} + 42 q^{55} + 2 q^{56} + 40 q^{59} - 18 q^{61} - 10 q^{64} - 4 q^{65} - 6 q^{70} - 12 q^{71} + 10 q^{74} + 8 q^{76} - 40 q^{79} - 6 q^{80} + 36 q^{85} + 34 q^{86} + 24 q^{89} + 32 q^{91} - 24 q^{94} - 12 q^{95}+O(q^{100}) \) 10 * q - 10 * q^4 - 6 * q^5 + 2 * q^10 - 6 * q^11 - 2 * q^14 + 10 * q^16 - 8 * q^19 + 6 * q^20 + 4 * q^25 + 12 * q^26 + 22 * q^29 + 46 * q^31 - 18 * q^34 - 32 * q^35 - 2 * q^40 + 14 * q^41 + 6 * q^44 + 12 * q^46 - 60 * q^49 - 8 * q^50 + 42 * q^55 + 2 * q^56 + 40 * q^59 - 18 * q^61 - 10 * q^64 - 4 * q^65 - 6 * q^70 - 12 * q^71 + 10 * q^74 + 8 * q^76 - 40 * q^79 - 6 * q^80 + 36 * q^85 + 34 * q^86 + 24 * q^89 + 32 * q^91 - 24 * q^94 - 12 * q^95

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