LMFDB - Embedded newform 3330.2.d.p.1999.7

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			1999.7
Root			$-1.95884 + 1.95884i$ of defining polynomial
Character	$\chi$	$=$	3330.1999
Dual form			3330.2.d.p.1999.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(-1.74265 - 1.40113i) q^{5} +3.20984i q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(-1.74265 - 1.40113i) q^{5} +3.20984i q^{7} -1.00000i q^{8} +(1.40113 - 1.74265i) q^{10} -3.82327 q^{11} +0.147332i q^{13} -3.20984 q^{14} +1.00000 q^{16} +0.978989i q^{17} -2.67594 q^{19} +(1.74265 + 1.40113i) q^{20} -3.82327i q^{22} +2.33616i q^{23} +(1.07367 + 4.88336i) q^{25} -0.147332 q^{26} -3.20984i q^{28} +6.30425 q^{29} -3.62372 q^{31} +1.00000i q^{32} -0.978989 q^{34} +(4.49740 - 5.59362i) q^{35} -1.00000i q^{37} -2.67594i q^{38} +(-1.40113 + 1.74265i) q^{40} -11.8265 q^{41} -4.53390i q^{43} +3.82327 q^{44} -2.33616 q^{46} +6.23085i q^{47} -3.30305 q^{49} +(-4.88336 + 1.07367i) q^{50} -0.147332i q^{52} -11.2978i q^{53} +(6.66263 + 5.35690i) q^{55} +3.20984 q^{56} +6.30425i q^{58} +6.92858 q^{59} +10.4885 q^{61} -3.62372i q^{62} -1.00000 q^{64} +(0.206432 - 0.256749i) q^{65} -2.80936i q^{67} -0.978989i q^{68} +(5.59362 + 4.49740i) q^{70} +12.3189 q^{71} -13.9966i q^{73} +1.00000 q^{74} +2.67594 q^{76} -12.2721i q^{77} -15.6057 q^{79} +(-1.74265 - 1.40113i) q^{80} -11.8265i q^{82} -13.5371i q^{83} +(1.37169 - 1.70604i) q^{85} +4.53390 q^{86} +3.82327i q^{88} -6.46929 q^{89} -0.472913 q^{91} -2.33616i q^{92} -6.23085 q^{94} +(4.66323 + 3.74934i) q^{95} +3.07063i q^{97} -3.30305i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.74265	−	1.40113i	−0.779337	−	0.626605i
$5$	−1.74265	−	1.40113i	−0.779337	−	0.626605i
$6$		0			0
$7$			3.20984i			1.21320i	0.795006	+	0.606602i	$0.207468\pi$
$7$			3.20984i			1.21320i	−0.795006	+	0.606602i	$0.792532\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	1.40113	−	1.74265i	0.443076	−	0.551075i
$11$	−3.82327			−1.15276			−0.576380	−	0.817182i	$-0.695535\pi$
$11$	−3.82327			−1.15276			−0.576380	+	0.817182i	$0.695535\pi$
$12$		0			0
$13$			0.147332i			0.0408626i	0.999791	+	0.0204313i	$0.00650394\pi$
$13$			0.147332i			0.0408626i	−0.999791	+	0.0204313i	$0.993496\pi$
$14$	−3.20984			−0.857865
$15$		0			0
$16$	1.00000			0.250000
$17$			0.978989i			0.237440i	0.992928	+	0.118720i	$0.0378790\pi$
$17$			0.978989i			0.237440i	−0.992928	+	0.118720i	$0.962121\pi$
$18$		0			0
$19$	−2.67594			−0.613903			−0.306951	−	0.951725i	$-0.599309\pi$
$19$	−2.67594			−0.613903			−0.306951	+	0.951725i	$0.599309\pi$
$20$	1.74265	+	1.40113i	0.389669	+	0.313302i
$21$		0			0
$22$		−	3.82327i		−	0.815124i
$23$			2.33616i			0.487122i	0.969886	+	0.243561i	$0.0783157\pi$
$23$			2.33616i			0.487122i	−0.969886	+	0.243561i	$0.921684\pi$
$24$		0			0
$25$	1.07367	+	4.88336i	0.214733	+	0.976673i
$26$	−0.147332			−0.0288942
$27$		0			0
$28$		−	3.20984i		−	0.606602i
$29$	6.30425			1.17067			0.585335	−	0.810792i	$-0.300963\pi$
$29$	6.30425			1.17067			0.585335	+	0.810792i	$0.300963\pi$
$30$		0			0
$31$	−3.62372			−0.650839			−0.325420	−	0.945570i	$-0.605506\pi$
$31$	−3.62372			−0.650839			−0.325420	+	0.945570i	$0.605506\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−0.978989			−0.167895
$35$	4.49740	−	5.59362i	0.760199	−	0.945495i
$36$		0			0
$37$		−	1.00000i		−	0.164399i
$37$		−	1.00000i		−	0.164399i
$38$		−	2.67594i		−	0.434095i
$39$		0			0
$40$	−1.40113	+	1.74265i	−0.221538	+	0.275537i
$41$	−11.8265			−1.84698			−0.923491	−	0.383620i	$-0.874677\pi$
$41$	−11.8265			−1.84698			−0.923491	+	0.383620i	$0.874677\pi$
$42$		0			0
$43$		−	4.53390i		−	0.691413i	−0.938343	−	0.345706i	$-0.887639\pi$
$43$		−	4.53390i		−	0.691413i	0.938343	−	0.345706i	$-0.112361\pi$
$44$	3.82327			0.576380
$45$		0			0
$46$	−2.33616			−0.344448
$47$			6.23085i			0.908863i	0.890782	+	0.454431i	$0.150157\pi$
$47$			6.23085i			0.908863i	−0.890782	+	0.454431i	$0.849843\pi$
$48$		0			0
$49$	−3.30305			−0.471864
$50$	−4.88336	+	1.07367i	−0.690612	+	0.151839i
$51$		0			0
$52$		−	0.147332i		−	0.0204313i
$53$		−	11.2978i		−	1.55188i	−0.630807	−	0.775939i	$-0.717276\pi$
$53$		−	11.2978i		−	1.55188i	0.630807	−	0.775939i	$-0.282724\pi$
$54$		0			0
$55$	6.66263	+	5.35690i	0.898389	+	0.722325i
$56$	3.20984			0.428932
$57$		0			0
$58$			6.30425i			0.827788i
$59$	6.92858			0.902025			0.451012	−	0.892518i	$-0.351063\pi$
$59$	6.92858			0.902025			0.451012	+	0.892518i	$0.351063\pi$
$60$		0			0
$61$	10.4885			1.34291			0.671457	−	0.741044i	$-0.265669\pi$
$61$	10.4885			1.34291			0.671457	+	0.741044i	$0.265669\pi$
$62$		−	3.62372i		−	0.460213i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.206432	−	0.256749i	0.0256047	−	0.0318458i
$66$		0			0
$67$		−	2.80936i		−	0.343218i	−0.985165	−	0.171609i	$-0.945103\pi$
$67$		−	2.80936i		−	0.343218i	0.985165	−	0.171609i	$-0.0548966\pi$
$68$		−	0.978989i		−	0.118720i
$69$		0			0
$70$	5.59362	+	4.49740i	0.668566	+	0.537542i
$71$	12.3189			1.46198			0.730990	−	0.682388i	$-0.239059\pi$
$71$	12.3189			1.46198			0.730990	+	0.682388i	$0.239059\pi$
$72$		0			0
$73$		−	13.9966i		−	1.63818i	−0.573665	−	0.819090i	$-0.694479\pi$
$73$		−	13.9966i		−	1.63818i	0.573665	−	0.819090i	$-0.305521\pi$
$74$	1.00000			0.116248
$75$		0			0
$76$	2.67594			0.306951
$77$		−	12.2721i		−	1.39853i
$78$		0			0
$79$	−15.6057			−1.75578			−0.877890	−	0.478861i	$-0.841050\pi$
$79$	−15.6057			−1.75578			−0.877890	+	0.478861i	$0.841050\pi$
$80$	−1.74265	−	1.40113i	−0.194834	−	0.156651i
$81$		0			0
$82$		−	11.8265i		−	1.30601i
$83$		−	13.5371i		−	1.48589i	−0.669354	−	0.742944i	$-0.733429\pi$
$83$		−	13.5371i		−	1.48589i	0.669354	−	0.742944i	$-0.266571\pi$
$84$		0			0
$85$	1.37169	−	1.70604i	0.148781	−	0.185046i
$86$	4.53390			0.488903
$87$		0			0
$88$			3.82327i			0.407562i
$89$	−6.46929			−0.685743			−0.342872	−	0.939382i	$-0.611400\pi$
$89$	−6.46929			−0.685743			−0.342872	+	0.939382i	$0.611400\pi$
$90$		0			0
$91$	−0.472913			−0.0495747
$92$		−	2.33616i		−	0.243561i
$93$		0			0
$94$	−6.23085			−0.642663
$95$	4.66323	+	3.74934i	0.478437	+	0.384674i
$96$		0			0
$97$			3.07063i			0.311775i	0.987775	+	0.155887i	$0.0498237\pi$
$97$			3.07063i			0.311775i	−0.987775	+	0.155887i	$0.950176\pi$
$98$		−	3.30305i		−	0.333658i
$99$		0			0
$100$	−1.07367	−	4.88336i	−0.107367	−	0.488336i
$101$	6.57513			0.654250			0.327125	−	0.944981i	$-0.393920\pi$
$101$	6.57513			0.654250			0.327125	+	0.944981i	$0.393920\pi$
$102$		0			0
$103$		−	2.52180i		−	0.248480i	−0.992252	−	0.124240i	$-0.960351\pi$
$103$		−	2.52180i		−	0.248480i	0.992252	−	0.124240i	$-0.0396493\pi$
$104$	0.147332			0.0144471
$105$		0			0
$106$	11.2978			1.09734
$107$			5.70291i			0.551321i	0.961255	+	0.275661i	$0.0888966\pi$
$107$			5.70291i			0.551321i	−0.961255	+	0.275661i	$0.911103\pi$
$108$		0			0
$109$	−11.9318			−1.14286			−0.571428	−	0.820652i	$-0.693610\pi$
$109$	−11.9318			−1.14286			−0.571428	+	0.820652i	$0.693610\pi$
$110$	−5.35690	+	6.66263i	−0.510761	+	0.635257i
$111$		0			0
$112$			3.20984i			0.303301i
$113$			2.18044i			0.205119i	0.994727	+	0.102559i	$0.0327031\pi$
$113$			2.18044i			0.205119i	−0.994727	+	0.102559i	$0.967297\pi$
$114$		0			0
$115$	3.27326	−	4.07111i	0.305233	−	0.379633i
$116$	−6.30425			−0.585335
$117$		0			0
$118$			6.92858i			0.637828i
$119$	−3.14239			−0.288063
$120$		0			0
$121$	3.61741			0.328856
$122$			10.4885i			0.949583i
$123$		0			0
$124$	3.62372			0.325420
$125$	4.97120	−	10.0143i	0.444638	−	0.895710i
$126$		0			0
$127$			5.39390i			0.478631i	0.970942	+	0.239316i	$0.0769231\pi$
$127$			5.39390i			0.478631i	−0.970942	+	0.239316i	$0.923077\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	0.256749	+	0.206432i	0.0225184	+	0.0181053i
$131$	8.97060			0.783765			0.391883	−	0.920015i	$-0.371824\pi$
$131$	8.97060			0.783765			0.391883	+	0.920015i	$0.371824\pi$
$132$		0			0
$133$		−	8.58933i		−	0.744789i
$134$	2.80936			0.242692
$135$		0			0
$136$	0.978989			0.0839476
$137$		−	2.70352i		−	0.230978i	−0.993309	−	0.115489i	$-0.963157\pi$
$137$		−	2.70352i		−	0.230978i	0.993309	−	0.115489i	$-0.0368434\pi$
$138$		0			0
$139$	−4.30358			−0.365025			−0.182512	−	0.983204i	$-0.558423\pi$
$139$	−4.30358			−0.365025			−0.182512	+	0.983204i	$0.558423\pi$
$140$	−4.49740	+	5.59362i	−0.380100	+	0.472748i
$141$		0			0
$142$			12.3189i			1.03378i
$143$		−	0.563292i		−	0.0471048i
$144$		0			0
$145$	−10.9861	−	8.83308i	−0.912346	−	0.733547i
$146$	13.9966			1.15837
$147$		0			0
$148$			1.00000i			0.0821995i
$149$	21.6949			1.77732			0.888659	−	0.458568i	$-0.151638\pi$
$149$	21.6949			1.77732			0.888659	+	0.458568i	$0.151638\pi$
$150$		0			0
$151$	2.06744			0.168246			0.0841230	−	0.996455i	$-0.473191\pi$
$151$	2.06744			0.168246			0.0841230	+	0.996455i	$0.473191\pi$
$152$			2.67594i			0.217047i
$153$		0			0
$154$	12.2721			0.988912
$155$	6.31488	+	5.07731i	0.507223	+	0.407819i
$156$		0			0
$157$		−	18.5439i		−	1.47996i	−0.672627	−	0.739982i	$-0.734834\pi$
$157$		−	18.5439i		−	1.47996i	0.672627	−	0.739982i	$-0.265166\pi$
$158$		−	15.6057i		−	1.24152i
$159$		0			0
$160$	1.40113	−	1.74265i	0.110769	−	0.137769i
$161$	−7.49868			−0.590979
$162$		0			0
$163$		−	21.6240i		−	1.69372i	−0.531817	−	0.846860i	$-0.678490\pi$
$163$		−	21.6240i		−	1.69372i	0.531817	−	0.846860i	$-0.321510\pi$
$164$	11.8265			0.923491
$165$		0			0
$166$	13.5371			1.05068
$167$		−	11.7729i		−	0.911012i	−0.890233	−	0.455506i	$-0.849458\pi$
$167$		−	11.7729i		−	0.911012i	0.890233	−	0.455506i	$-0.150542\pi$
$168$		0			0
$169$	12.9783			0.998330
$170$	1.70604	+	1.37169i	0.130847	+	0.105204i
$171$		0			0
$172$			4.53390i			0.345706i
$173$		−	14.0158i		−	1.06560i	−0.846240	−	0.532801i	$-0.821139\pi$
$173$		−	14.0158i		−	1.06560i	0.846240	−	0.532801i	$-0.178861\pi$
$174$		0			0
$175$	−15.6748	+	3.44629i	−1.18490	+	0.260515i
$176$	−3.82327			−0.288190
$177$		0			0
$178$		−	6.46929i		−	0.484894i
$179$	−12.4160			−0.928019			−0.464009	−	0.885830i	$-0.653590\pi$
$179$	−12.4160			−0.928019			−0.464009	+	0.885830i	$0.653590\pi$
$180$		0			0
$181$	8.19748			0.609314			0.304657	−	0.952462i	$-0.401458\pi$
$181$	8.19748			0.609314			0.304657	+	0.952462i	$0.401458\pi$
$182$		−	0.472913i		−	0.0350546i
$183$		0			0
$184$	2.33616			0.172224
$185$	−1.40113	+	1.74265i	−0.103013	+	0.128122i
$186$		0			0
$187$		−	3.74294i		−	0.273711i
$188$		−	6.23085i		−	0.454431i
$189$		0			0
$190$	−3.74934	+	4.66323i	−0.272006	+	0.338306i
$191$	−8.00137			−0.578959			−0.289479	−	0.957184i	$-0.593482\pi$
$191$	−8.00137			−0.578959			−0.289479	+	0.957184i	$0.593482\pi$
$192$		0			0
$193$		−	14.0420i		−	1.01077i	−0.862895	−	0.505383i	$-0.831351\pi$
$193$		−	14.0420i		−	1.01077i	0.862895	−	0.505383i	$-0.168649\pi$
$194$	−3.07063			−0.220458
$195$		0			0
$196$	3.30305			0.235932
$197$			3.36608i			0.239823i	0.992785	+	0.119912i	$0.0382612\pi$
$197$			3.36608i			0.239823i	−0.992785	+	0.119912i	$0.961739\pi$
$198$		0			0
$199$	14.8890			1.05545			0.527725	−	0.849415i	$-0.323045\pi$
$199$	14.8890			1.05545			0.527725	+	0.849415i	$0.323045\pi$
$200$	4.88336	−	1.07367i	0.345306	−	0.0759197i
$201$		0			0
$202$			6.57513i			0.462624i
$203$			20.2356i			1.42026i
$204$		0			0
$205$	20.6094	+	16.5704i	1.43942	+	1.15733i
$206$	2.52180			0.175702
$207$		0			0
$208$			0.147332i			0.0102157i
$209$	10.2308			0.707683
$210$		0			0
$211$	−9.80544			−0.675035			−0.337517	−	0.941319i	$-0.609587\pi$
$211$	−9.80544			−0.675035			−0.337517	+	0.941319i	$0.609587\pi$
$212$			11.2978i			0.775939i
$213$		0			0
$214$	−5.70291			−0.389843
$215$	−6.35258	+	7.90100i	−0.433242	+	0.538844i
$216$		0			0
$217$		−	11.6316i		−	0.789601i
$218$		−	11.9318i		−	0.808121i
$219$		0			0
$220$	−6.66263	−	5.35690i	−0.449194	−	0.361162i
$221$	−0.144237			−0.00970241
$222$		0			0
$223$		−	15.4447i		−	1.03425i	−0.855910	−	0.517125i	$-0.827002\pi$
$223$		−	15.4447i		−	1.03425i	0.855910	−	0.517125i	$-0.172998\pi$
$224$	−3.20984			−0.214466
$225$		0			0
$226$	−2.18044			−0.145041
$227$			6.46090i			0.428825i	0.976743	+	0.214413i	$0.0687837\pi$
$227$			6.46090i			0.428825i	−0.976743	+	0.214413i	$0.931216\pi$
$228$		0			0
$229$	−7.97458			−0.526975			−0.263488	−	0.964663i	$-0.584873\pi$
$229$	−7.97458			−0.526975			−0.263488	+	0.964663i	$0.584873\pi$
$230$	4.07111	+	3.27326i	0.268441	+	0.215832i
$231$		0			0
$232$		−	6.30425i		−	0.413894i
$233$		−	25.2907i		−	1.65685i	−0.560103	−	0.828423i	$-0.689238\pi$
$233$		−	25.2907i		−	1.65685i	0.560103	−	0.828423i	$-0.310762\pi$
$234$		0			0
$235$	8.73023	−	10.8582i	0.569497	−	0.708310i
$236$	−6.92858			−0.451012
$237$		0			0
$238$		−	3.14239i		−	0.203691i
$239$	5.11481			0.330850			0.165425	−	0.986222i	$-0.447100\pi$
$239$	5.11481			0.330850			0.165425	+	0.986222i	$0.447100\pi$
$240$		0			0
$241$	16.4415			1.05909			0.529544	−	0.848282i	$-0.322363\pi$
$241$	16.4415			1.05909			0.529544	+	0.848282i	$0.322363\pi$
$242$			3.61741i			0.232536i
$243$		0			0
$244$	−10.4885			−0.671457
$245$	5.75606	+	4.62800i	0.367741	+	0.295672i
$246$		0			0
$247$		−	0.394252i		−	0.0250857i
$248$			3.62372i			0.230107i
$249$		0			0
$250$	10.0143	+	4.97120i	0.633363	+	0.314407i
$251$	−6.35586			−0.401178			−0.200589	−	0.979675i	$-0.564286\pi$
$251$	−6.35586			−0.401178			−0.200589	+	0.979675i	$0.564286\pi$
$252$		0			0
$253$		−	8.93177i		−	0.561535i
$254$	−5.39390			−0.338444
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	5.45772i		−	0.340443i	−0.985406	−	0.170222i	$-0.945552\pi$
$257$		−	5.45772i		−	0.340443i	0.985406	−	0.170222i	$-0.0544484\pi$
$258$		0			0
$259$	3.20984			0.199450
$260$	−0.206432	+	0.256749i	−0.0128024	+	0.0159229i
$261$		0			0
$262$			8.97060i			0.554206i
$263$			14.8882i			0.918044i	0.888425	+	0.459022i	$0.151800\pi$
$263$			14.8882i			0.918044i	−0.888425	+	0.459022i	$0.848200\pi$
$264$		0			0
$265$	−15.8298	+	19.6882i	−0.972414	+	1.20944i
$266$	8.58933			0.526646
$267$		0			0
$268$			2.80936i			0.171609i
$269$	15.5573			0.948546			0.474273	−	0.880378i	$-0.342711\pi$
$269$	15.5573			0.948546			0.474273	+	0.880378i	$0.342711\pi$
$270$		0			0
$271$	0.462920			0.0281204			0.0140602	−	0.999901i	$-0.495524\pi$
$271$	0.462920			0.0281204			0.0140602	+	0.999901i	$0.495524\pi$
$272$			0.978989i			0.0593599i
$273$		0			0
$274$	2.70352			0.163326
$275$	−4.10492	−	18.6704i	−0.247536	−	1.12587i
$276$		0			0
$277$		−	9.12112i		−	0.548035i	−0.961725	−	0.274018i	$-0.911647\pi$
$277$		−	9.12112i		−	0.548035i	0.961725	−	0.274018i	$-0.0883526\pi$
$278$		−	4.30358i		−	0.258111i
$279$		0			0
$280$	−5.59362	−	4.49740i	−0.334283	−	0.268771i
$281$	24.8734			1.48382			0.741912	−	0.670497i	$-0.233919\pi$
$281$	24.8734			1.48382			0.741912	+	0.670497i	$0.233919\pi$
$282$		0			0
$283$			19.7259i			1.17258i	0.810100	+	0.586292i	$0.199413\pi$
$283$			19.7259i			1.17258i	−0.810100	+	0.586292i	$0.800587\pi$
$284$	−12.3189			−0.730990
$285$		0			0
$286$	0.563292			0.0333081
$287$		−	37.9610i		−	2.24077i
$288$		0			0
$289$	16.0416			0.943622
$290$	8.83308	−	10.9861i	0.518696	−	0.645126i
$291$		0			0
$292$			13.9966i			0.819090i
$293$			2.65528i			0.155123i	0.996988	+	0.0775615i	$0.0247134\pi$
$293$			2.65528i			0.155123i	−0.996988	+	0.0775615i	$0.975287\pi$
$294$		0			0
$295$	−12.0741	−	9.70785i	−0.702981	−	0.565213i
$296$	−1.00000			−0.0581238
$297$		0			0
$298$			21.6949i			1.25675i
$299$	−0.344191			−0.0199051
$300$		0			0
$301$	14.5531			0.838825
$302$			2.06744i			0.118968i
$303$		0			0
$304$	−2.67594			−0.153476
$305$	−18.2778	−	14.6957i	−1.04658	−	0.841476i
$306$		0			0
$307$			25.3545i			1.44706i	0.690295	+	0.723528i	$0.257481\pi$
$307$			25.3545i			1.44706i	−0.690295	+	0.723528i	$0.742519\pi$
$308$			12.2721i			0.699267i
$309$		0			0
$310$	−5.07731	+	6.31488i	−0.288372	+	0.358661i
$311$	−11.1234			−0.630748			−0.315374	−	0.948967i	$-0.602130\pi$
$311$	−11.1234			−0.630748			−0.315374	+	0.948967i	$0.602130\pi$
$312$		0			0
$313$			3.49109i			0.197328i	0.995121	+	0.0986640i	$0.0314569\pi$
$313$			3.49109i			0.197328i	−0.995121	+	0.0986640i	$0.968543\pi$
$314$	18.5439			1.04649
$315$		0			0
$316$	15.6057			0.877890
$317$			18.3656i			1.03152i	0.856734	+	0.515759i	$0.172490\pi$
$317$			18.3656i			1.03152i	−0.856734	+	0.515759i	$0.827510\pi$
$318$		0			0
$319$	−24.1029			−1.34950
$320$	1.74265	+	1.40113i	0.0974172	+	0.0783256i
$321$		0			0
$322$		−	7.49868i		−	0.417885i
$323$		−	2.61972i		−	0.145765i
$324$		0			0
$325$	−0.719477	+	0.158186i	−0.0399094	+	0.00877457i
$326$	21.6240			1.19764
$327$		0			0
$328$			11.8265i			0.653007i
$329$	−20.0000			−1.10264
$330$		0			0
$331$	−21.9365			−1.20574			−0.602870	−	0.797839i	$-0.705976\pi$
$331$	−21.9365			−1.20574			−0.602870	+	0.797839i	$0.705976\pi$
$332$			13.5371i			0.742944i
$333$		0			0
$334$	11.7729			0.644183
$335$	−3.93628	+	4.89574i	−0.215062	+	0.267483i
$336$		0			0
$337$			8.65472i			0.471453i	0.971819	+	0.235726i	$0.0757469\pi$
$337$			8.65472i			0.471453i	−0.971819	+	0.235726i	$0.924253\pi$
$338$			12.9783i			0.705926i
$339$		0			0
$340$	−1.37169	+	1.70604i	−0.0743904	+	0.0925228i
$341$	13.8545			0.750262
$342$		0			0
$343$			11.8666i			0.640737i
$344$	−4.53390			−0.244451
$345$		0			0
$346$	14.0158			0.753495
$347$		−	21.3265i		−	1.14486i	−0.819952	−	0.572432i	$-0.806000\pi$
$347$		−	21.3265i		−	1.14486i	0.819952	−	0.572432i	$-0.194000\pi$
$348$		0			0
$349$	1.16305			0.0622569			0.0311285	−	0.999515i	$-0.490090\pi$
$349$	1.16305			0.0622569			0.0311285	+	0.999515i	$0.490090\pi$
$350$	−3.44629	−	15.6748i	−0.184212	−	0.837853i
$351$		0			0
$352$		−	3.82327i		−	0.203781i
$353$			0.470079i			0.0250198i	0.999922	+	0.0125099i	$0.00398213\pi$
$353$			0.470079i			0.0250198i	−0.999922	+	0.0125099i	$0.996018\pi$
$354$		0			0
$355$	−21.4675	−	17.2603i	−1.13938	−	0.916083i
$356$	6.46929			0.342872
$357$		0			0
$358$		−	12.4160i		−	0.656208i
$359$	−33.3086			−1.75796			−0.878981	−	0.476856i	$-0.841776\pi$
$359$	−33.3086			−1.75796			−0.878981	+	0.476856i	$0.841776\pi$
$360$		0			0
$361$	−11.8393			−0.623123
$362$			8.19748i			0.430850i
$363$		0			0
$364$	0.472913			0.0247874
$365$	−19.6111	+	24.3912i	−1.02649	+	1.27669i
$366$		0			0
$367$			11.1884i			0.584029i	0.956414	+	0.292014i	$0.0943255\pi$
$367$			11.1884i			0.584029i	−0.956414	+	0.292014i	$0.905674\pi$
$368$			2.33616i			0.121781i
$369$		0			0
$370$	−1.74265	−	1.40113i	−0.0905961	−	0.0728413i
$371$	36.2642			1.88275
$372$		0			0
$373$			23.1634i			1.19936i	0.800242	+	0.599678i	$0.204705\pi$
$373$			23.1634i			1.19936i	−0.800242	+	0.599678i	$0.795295\pi$
$374$	3.74294			0.193543
$375$		0			0
$376$	6.23085			0.321331
$377$			0.928820i			0.0478366i
$378$		0			0
$379$	26.7721			1.37519			0.687595	−	0.726095i	$-0.258667\pi$
$379$	26.7721			1.37519			0.687595	+	0.726095i	$0.258667\pi$
$380$	−4.66323	−	3.74934i	−0.239219	−	0.192337i
$381$		0			0
$382$		−	8.00137i		−	0.409386i
$383$		−	22.3189i		−	1.14044i	−0.821492	−	0.570220i	$-0.806858\pi$
$383$		−	22.3189i		−	1.14044i	0.821492	−	0.570220i	$-0.193142\pi$
$384$		0			0
$385$	−17.1948	+	21.3860i	−0.876327	+	1.08993i
$386$	14.0420			0.714720
$387$		0			0
$388$		−	3.07063i		−	0.155887i
$389$	−24.3011			−1.23211			−0.616057	−	0.787701i	$-0.711271\pi$
$389$	−24.3011			−1.23211			−0.616057	+	0.787701i	$0.711271\pi$
$390$		0			0
$391$	−2.28707			−0.115662
$392$			3.30305i			0.166829i
$393$		0			0
$394$	−3.36608			−0.169581
$395$	27.1953	+	21.8657i	1.36835	+	1.10018i
$396$		0			0
$397$		−	28.1888i		−	1.41476i	−0.706835	−	0.707378i	$-0.749878\pi$
$397$		−	28.1888i		−	1.41476i	0.706835	−	0.707378i	$-0.250122\pi$
$398$			14.8890i			0.746316i
$399$		0			0
$400$	1.07367	+	4.88336i	0.0536833	+	0.244168i
$401$	15.9528			0.796644			0.398322	−	0.917246i	$-0.369593\pi$
$401$	15.9528			0.796644			0.398322	+	0.917246i	$0.369593\pi$
$402$		0			0
$403$		−	0.533891i		−	0.0265950i
$404$	−6.57513			−0.327125
$405$		0			0
$406$	−20.2356			−1.00428
$407$			3.82327i			0.189513i
$408$		0			0
$409$	−31.6014			−1.56259			−0.781294	−	0.624164i	$-0.785440\pi$
$409$	−31.6014			−1.56259			−0.781294	+	0.624164i	$0.785440\pi$
$410$	−16.5704	+	20.6094i	−0.818354	+	1.01783i
$411$		0			0
$412$			2.52180i			0.124240i
$413$			22.2396i			1.09434i
$414$		0			0
$415$	−18.9672	+	23.5904i	−0.931064	+	1.15801i
$416$	−0.147332			−0.00722356
$417$		0			0
$418$			10.2308i			0.500407i
$419$	−18.4266			−0.900197			−0.450098	−	0.892979i	$-0.648611\pi$
$419$	−18.4266			−0.900197			−0.450098	+	0.892979i	$0.648611\pi$
$420$		0			0
$421$	−19.1570			−0.933655			−0.466828	−	0.884348i	$-0.654603\pi$
$421$	−19.1570			−0.933655			−0.466828	+	0.884348i	$0.654603\pi$
$422$		−	9.80544i		−	0.477322i
$423$		0			0
$424$	−11.2978			−0.548672
$425$	−4.78076	+	1.05111i	−0.231901	+	0.0509862i
$426$		0			0
$427$			33.6663i			1.62923i
$428$		−	5.70291i		−	0.275661i
$429$		0			0
$430$	−7.90100	−	6.35258i	−0.381020	−	0.306349i
$431$	10.3947			0.500694			0.250347	−	0.968156i	$-0.419455\pi$
$431$	10.3947			0.500694			0.250347	+	0.968156i	$0.419455\pi$
$432$		0			0
$433$			3.36622i			0.161770i	0.996723	+	0.0808852i	$0.0257747\pi$
$433$			3.36622i			0.161770i	−0.996723	+	0.0808852i	$0.974225\pi$
$434$	11.6316			0.558332
$435$		0			0
$436$	11.9318			0.571428
$437$		−	6.25142i		−	0.299046i
$438$		0			0
$439$	32.5045			1.55135			0.775677	−	0.631130i	$-0.217409\pi$
$439$	32.5045			1.55135			0.775677	+	0.631130i	$0.217409\pi$
$440$	5.35690	−	6.66263i	0.255380	−	0.317628i
$441$		0			0
$442$		−	0.144237i		−	0.00686064i
$443$			23.5479i			1.11879i	0.828900	+	0.559397i	$0.188967\pi$
$443$			23.5479i			1.11879i	−0.828900	+	0.559397i	$0.811033\pi$
$444$		0			0
$445$	11.2737	+	9.06432i	0.534425	+	0.429690i
$446$	15.4447			0.731325
$447$		0			0
$448$		−	3.20984i		−	0.151651i
$449$	12.5629			0.592878			0.296439	−	0.955052i	$-0.404201\pi$
$449$	12.5629			0.592878			0.296439	+	0.955052i	$0.404201\pi$
$450$		0			0
$451$	45.2158			2.12913
$452$		−	2.18044i		−	0.102559i
$453$		0			0
$454$	−6.46090			−0.303225
$455$	0.824122	+	0.662612i	0.0386354	+	0.0310637i
$456$		0			0
$457$		−	6.53390i		−	0.305643i	−0.988254	−	0.152821i	$-0.951164\pi$
$457$		−	6.53390i		−	0.305643i	0.988254	−	0.152821i	$-0.0488359\pi$
$458$		−	7.97458i		−	0.372628i
$459$		0			0
$460$	−3.27326	+	4.07111i	−0.152617	+	0.189816i
$461$	−24.7616			−1.15326			−0.576631	−	0.817005i	$-0.695633\pi$
$461$	−24.7616			−1.15326			−0.576631	+	0.817005i	$0.695633\pi$
$462$		0			0
$463$			25.9239i			1.20479i	0.798200	+	0.602393i	$0.205786\pi$
$463$			25.9239i			1.20479i	−0.798200	+	0.602393i	$0.794214\pi$
$464$	6.30425			0.292667
$465$		0			0
$466$	25.2907			1.17157
$467$			28.8182i			1.33355i	0.745261	+	0.666773i	$0.232325\pi$
$467$			28.8182i			1.33355i	−0.745261	+	0.666773i	$0.767675\pi$
$468$		0			0
$469$	9.01759			0.416394
$470$	10.8582	+	8.73023i	0.500851	+	0.402696i
$471$		0			0
$472$		−	6.92858i		−	0.318914i
$473$			17.3343i			0.797033i
$474$		0			0
$475$	−2.87307	−	13.0676i	−0.131825	−	0.599582i
$476$	3.14239			0.144031
$477$		0			0
$478$			5.11481i			0.233946i
$479$	−41.7873			−1.90931			−0.954655	−	0.297714i	$-0.903776\pi$
$479$	−41.7873			−1.90931			−0.954655	+	0.297714i	$0.903776\pi$
$480$		0			0
$481$	0.147332			0.00671778
$482$			16.4415i			0.748888i
$483$		0			0
$484$	−3.61741			−0.164428
$485$	4.30235	−	5.35103i	0.195360	−	0.242978i
$486$		0			0
$487$		−	9.34463i		−	0.423446i	−0.977330	−	0.211723i	$-0.932093\pi$
$487$		−	9.34463i		−	0.423446i	0.977330	−	0.211723i	$-0.0679074\pi$
$488$		−	10.4885i		−	0.474791i
$489$		0			0
$490$	−4.62800	+	5.75606i	−0.209072	+	0.260032i
$491$	10.7558			0.485404			0.242702	−	0.970101i	$-0.421966\pi$
$491$	10.7558			0.485404			0.242702	+	0.970101i	$0.421966\pi$
$492$		0			0
$493$			6.17179i			0.277963i
$494$	0.394252			0.0177383
$495$		0			0
$496$	−3.62372			−0.162710
$497$			39.5415i			1.77368i
$498$		0			0
$499$	−29.0702			−1.30136			−0.650680	−	0.759352i	$-0.725516\pi$
$499$	−29.0702			−1.30136			−0.650680	+	0.759352i	$0.725516\pi$
$500$	−4.97120	+	10.0143i	−0.222319	+	0.447855i
$501$		0			0
$502$		−	6.35586i		−	0.283676i
$503$		−	36.2683i		−	1.61712i	−0.588412	−	0.808561i	$-0.700247\pi$
$503$		−	36.2683i		−	1.61712i	0.588412	−	0.808561i	$-0.299753\pi$
$504$		0			0
$505$	−11.4582	−	9.21261i	−0.509881	−	0.409956i
$506$	8.93177			0.397065
$507$		0			0
$508$		−	5.39390i		−	0.239316i
$509$	−22.2170			−0.984751			−0.492375	−	0.870383i	$-0.663871\pi$
$509$	−22.2170			−0.984751			−0.492375	+	0.870383i	$0.663871\pi$
$510$		0			0
$511$	44.9268			1.98745
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	5.45772			0.240730
$515$	−3.53337	+	4.39462i	−0.155699	+	0.193650i
$516$		0			0
$517$		−	23.8222i		−	1.04770i
$518$			3.20984i			0.141032i
$519$		0			0
$520$	−0.256749	−	0.206432i	−0.0112592	−	0.00905263i
$521$	−41.2732			−1.80821			−0.904107	−	0.427306i	$-0.859463\pi$
$521$	−41.2732			−1.80821			−0.904107	+	0.427306i	$0.859463\pi$
$522$		0			0
$523$			11.0354i			0.482545i	0.970457	+	0.241273i	$0.0775648\pi$
$523$			11.0354i			0.482545i	−0.970457	+	0.241273i	$0.922435\pi$
$524$	−8.97060			−0.391883
$525$		0			0
$526$	−14.8882			−0.649155
$527$		−	3.54758i		−	0.154535i
$528$		0			0
$529$	17.5424			0.762712
$530$	−19.6882	−	15.8298i	−0.855201	−	0.687601i
$531$		0			0
$532$			8.58933i			0.372395i
$533$		−	1.74242i		−	0.0754726i
$534$		0			0
$535$	7.99052	−	9.93818i	0.345460	−	0.429665i
$536$	−2.80936			−0.121346
$537$		0			0
$538$			15.5573i			0.670723i
$539$	12.6285			0.543946
$540$		0			0
$541$	−32.2338			−1.38584			−0.692920	−	0.721014i	$-0.743676\pi$
$541$	−32.2338			−1.38584			−0.692920	+	0.721014i	$0.743676\pi$
$542$			0.462920i			0.0198841i
$543$		0			0
$544$	−0.978989			−0.0419738
$545$	20.7929	+	16.7180i	0.890670	+	0.716119i
$546$		0			0
$547$		−	15.0234i		−	0.642355i	−0.947019	−	0.321177i	$-0.895921\pi$
$547$		−	15.0234i		−	0.642355i	0.947019	−	0.321177i	$-0.104079\pi$
$548$			2.70352i			0.115489i
$549$		0			0
$550$	18.6704	−	4.10492i	0.796110	−	0.175034i
$551$	−16.8698			−0.718677
$552$		0			0
$553$		−	50.0918i		−	2.13012i
$554$	9.12112			0.387519
$555$		0			0
$556$	4.30358			0.182512
$557$			39.1275i			1.65788i	0.559334	+	0.828942i	$0.311057\pi$
$557$			39.1275i			1.65788i	−0.559334	+	0.828942i	$0.688943\pi$
$558$		0			0
$559$	0.667989			0.0282529
$560$	4.49740	−	5.59362i	0.190050	−	0.236374i
$561$		0			0
$562$			24.8734i			1.04922i
$563$			27.1970i			1.14622i	0.819479	+	0.573109i	$0.194263\pi$
$563$			27.1970i			1.14622i	−0.819479	+	0.573109i	$0.805737\pi$
$564$		0			0
$565$	3.05508	−	3.79975i	0.128528	−	0.159857i
$566$	−19.7259			−0.829142
$567$		0			0
$568$		−	12.3189i		−	0.516888i
$569$	−33.4499			−1.40229			−0.701146	−	0.713018i	$-0.747328\pi$
$569$	−33.4499			−1.40229			−0.701146	+	0.713018i	$0.747328\pi$
$570$		0			0
$571$	28.9145			1.21003			0.605017	−	0.796213i	$-0.293166\pi$
$571$	28.9145			1.21003			0.605017	+	0.796213i	$0.293166\pi$
$572$			0.563292i			0.0235524i
$573$		0			0
$574$	37.9610			1.58446
$575$	−11.4083	+	2.50825i	−0.475759	+	0.104601i
$576$		0			0
$577$		−	33.5613i		−	1.39717i	−0.715525	−	0.698587i	$-0.753812\pi$
$577$		−	33.5613i		−	1.39717i	0.715525	−	0.698587i	$-0.246188\pi$
$578$			16.0416i			0.667242i
$579$		0			0
$580$	10.9861	+	8.83308i	0.456173	+	0.366774i
$581$	43.4518			1.80268
$582$		0			0
$583$			43.1948i			1.78894i
$584$	−13.9966			−0.579184
$585$		0			0
$586$	−2.65528			−0.109689
$587$		−	4.83581i		−	0.199595i	−0.995008	−	0.0997976i	$-0.968180\pi$
$587$		−	4.83581i		−	0.199595i	0.995008	−	0.0997976i	$-0.0318195\pi$
$588$		0			0
$589$	9.69686			0.399552
$590$	9.70785	−	12.0741i	0.399666	−	0.497083i
$591$		0			0
$592$		−	1.00000i		−	0.0410997i
$593$		−	43.1680i		−	1.77270i	−0.463020	−	0.886348i	$-0.653234\pi$
$593$		−	43.1680i		−	1.77270i	0.463020	−	0.886348i	$-0.346766\pi$
$594$		0			0
$595$	5.47610	+	4.40290i	0.224498	+	0.180501i
$596$	−21.6949			−0.888659
$597$		0			0
$598$		−	0.344191i		−	0.0140750i
$599$	−38.7714			−1.58416			−0.792078	−	0.610420i	$-0.791001\pi$
$599$	−38.7714			−1.58416			−0.792078	+	0.610420i	$0.791001\pi$
$600$		0			0
$601$	1.56064			0.0636597			0.0318299	−	0.999493i	$-0.489867\pi$
$601$	1.56064			0.0636597			0.0318299	+	0.999493i	$0.489867\pi$
$602$			14.5531i			0.593139i
$603$		0			0
$604$	−2.06744			−0.0841230
$605$	−6.30389	−	5.06847i	−0.256289	−	0.206062i
$606$		0			0
$607$		−	21.0494i		−	0.854370i	−0.904164	−	0.427185i	$-0.859505\pi$
$607$		−	21.0494i		−	0.854370i	0.904164	−	0.427185i	$-0.140495\pi$
$608$		−	2.67594i		−	0.108524i
$609$		0			0
$610$	14.6957	−	18.2778i	0.595013	−	0.740045i
$611$	−0.918005			−0.0371385
$612$		0			0
$613$		−	5.28786i		−	0.213574i	−0.994282	−	0.106787i	$-0.965944\pi$
$613$		−	5.28786i		−	0.213574i	0.994282	−	0.106787i	$-0.0340564\pi$
$614$	−25.3545			−1.02322
$615$		0			0
$616$	−12.2721			−0.494456
$617$		−	34.8545i		−	1.40319i	−0.712576	−	0.701595i	$-0.752472\pi$
$617$		−	34.8545i		−	1.40319i	0.712576	−	0.701595i	$-0.247528\pi$
$618$		0			0
$619$	7.30122			0.293461			0.146730	−	0.989177i	$-0.453125\pi$
$619$	7.30122			0.293461			0.146730	+	0.989177i	$0.453125\pi$
$620$	−6.31488	−	5.07731i	−0.253612	−	0.203910i
$621$		0			0
$622$		−	11.1234i		−	0.446006i
$623$		−	20.7654i		−	0.831946i
$624$		0			0
$625$	−22.6945	+	10.4862i	−0.907779	+	0.419448i
$626$	−3.49109			−0.139532
$627$		0			0
$628$			18.5439i			0.739982i
$629$	0.978989			0.0390348
$630$		0			0
$631$	24.2752			0.966381			0.483190	−	0.875515i	$-0.339478\pi$
$631$	24.2752			0.966381			0.483190	+	0.875515i	$0.339478\pi$
$632$			15.6057i			0.620762i
$633$		0			0
$634$	−18.3656			−0.729393
$635$	7.55756	−	9.39969i	0.299913	−	0.373015i
$636$		0			0
$637$		−	0.486646i		−	0.0192816i
$638$		−	24.1029i		−	0.954241i
$639$		0			0
$640$	−1.40113	+	1.74265i	−0.0553845	+	0.0688843i
$641$	8.22087			0.324705			0.162353	−	0.986733i	$-0.448092\pi$
$641$	8.22087			0.324705			0.162353	+	0.986733i	$0.448092\pi$
$642$		0			0
$643$			29.7758i			1.17424i	0.809499	+	0.587121i	$0.199739\pi$
$643$			29.7758i			1.17424i	−0.809499	+	0.587121i	$0.800261\pi$
$644$	7.49868			0.295489
$645$		0			0
$646$	2.61972			0.103071
$647$		−	35.6356i		−	1.40098i	−0.713662	−	0.700490i	$-0.752965\pi$
$647$		−	35.6356i		−	1.40098i	0.713662	−	0.700490i	$-0.247035\pi$
$648$		0			0
$649$	−26.4899			−1.03982
$650$	−0.158186	−	0.719477i	−0.00620455	−	0.0282202i
$651$		0			0
$652$			21.6240i			0.846860i
$653$		−	37.6128i		−	1.47190i	−0.677035	−	0.735951i	$-0.736736\pi$
$653$		−	37.6128i		−	1.47190i	0.677035	−	0.735951i	$-0.263264\pi$
$654$		0			0
$655$	−15.6326	−	12.5690i	−0.610818	−	0.491111i
$656$	−11.8265			−0.461746
$657$		0			0
$658$		−	20.0000i		−	0.779681i
$659$	45.0553			1.75510			0.877552	−	0.479481i	$-0.159175\pi$
$659$	45.0553			1.75510			0.877552	+	0.479481i	$0.159175\pi$
$660$		0			0
$661$	7.32365			0.284857			0.142429	−	0.989805i	$-0.454509\pi$
$661$	7.32365			0.284857			0.142429	+	0.989805i	$0.454509\pi$
$662$		−	21.9365i		−	0.852587i
$663$		0			0
$664$	−13.5371			−0.525341
$665$	−12.0348	+	14.9682i	−0.466688	+	0.580442i
$666$		0			0
$667$			14.7277i			0.570260i
$668$			11.7729i			0.455506i
$669$		0			0
$670$	−4.89574	−	3.93628i	−0.189139	−	0.152072i
$671$	−40.1003			−1.54806
$672$		0			0
$673$		−	8.58807i		−	0.331046i	−0.986206	−	0.165523i	$-0.947069\pi$
$673$		−	8.58807i		−	0.331046i	0.986206	−	0.165523i	$-0.0529312\pi$
$674$	−8.65472			−0.333368
$675$		0			0
$676$	−12.9783			−0.499165
$677$		−	9.13523i		−	0.351096i	−0.984471	−	0.175548i	$-0.943830\pi$
$677$		−	9.13523i		−	0.351096i	0.984471	−	0.175548i	$-0.0561697\pi$
$678$		0			0
$679$	−9.85621			−0.378247
$680$	−1.70604	−	1.37169i	−0.0654235	−	0.0526020i
$681$		0			0
$682$			13.8545i			0.530515i
$683$			40.7414i			1.55893i	0.626449	+	0.779463i	$0.284508\pi$
$683$			40.7414i			1.55893i	−0.626449	+	0.779463i	$0.715492\pi$
$684$		0			0
$685$	−3.78799	+	4.71130i	−0.144732	+	0.180009i
$686$	−11.8666			−0.453069
$687$		0			0
$688$		−	4.53390i		−	0.172853i
$689$	1.66454			0.0634139
$690$		0			0
$691$	−28.7543			−1.09387			−0.546933	−	0.837176i	$-0.684205\pi$
$691$	−28.7543			−1.09387			−0.546933	+	0.837176i	$0.684205\pi$
$692$			14.0158i			0.532801i
$693$		0			0
$694$	21.3265			0.809541
$695$	7.49964	+	6.02988i	0.284477	+	0.228726i
$696$		0			0
$697$		−	11.5780i		−	0.438547i
$698$			1.16305i			0.0440223i
$699$		0			0
$700$	15.6748	−	3.44629i	0.592452	−	0.130258i
$701$	7.87020			0.297253			0.148627	−	0.988893i	$-0.452515\pi$
$701$	7.87020			0.297253			0.148627	+	0.988893i	$0.452515\pi$
$702$		0			0
$703$			2.67594i			0.100925i
$704$	3.82327			0.144095
$705$		0			0
$706$	−0.470079			−0.0176917
$707$			21.1051i			0.793738i
$708$		0			0
$709$	−33.0458			−1.24106			−0.620530	−	0.784182i	$-0.713083\pi$
$709$	−33.0458			−1.24106			−0.620530	+	0.784182i	$0.713083\pi$
$710$	17.2603	−	21.4675i	0.647769	−	0.805660i
$711$		0			0
$712$			6.46929i			0.242447i
$713$		−	8.46558i		−	0.317039i
$714$		0			0
$715$	−0.789245	+	0.981621i	−0.0295161	+	0.0367105i
$716$	12.4160			0.464009
$717$		0			0
$718$		−	33.3086i		−	1.24307i
$719$	4.94138			0.184282			0.0921412	−	0.995746i	$-0.470629\pi$
$719$	4.94138			0.184282			0.0921412	+	0.995746i	$0.470629\pi$
$720$		0			0
$721$	8.09456			0.301457
$722$		−	11.8393i		−	0.440615i
$723$		0			0
$724$	−8.19748			−0.304657
$725$	6.76866	+	30.7859i	0.251382	+	1.14336i
$726$		0			0
$727$		−	42.5178i		−	1.57690i	−0.615101	−	0.788448i	$-0.710885\pi$
$727$		−	42.5178i		−	1.57690i	0.615101	−	0.788448i	$-0.289115\pi$
$728$			0.472913i			0.0175273i
$729$		0			0
$730$	−24.3912	−	19.6111i	−0.902759	−	0.725839i
$731$	4.43863			0.164169
$732$		0			0
$733$			10.2114i			0.377167i	0.982057	+	0.188584i	$0.0603896\pi$
$733$			10.2114i			0.377167i	−0.982057	+	0.188584i	$0.939610\pi$
$734$	−11.1884			−0.412971
$735$		0			0
$736$	−2.33616			−0.0861119
$737$			10.7410i			0.395648i
$738$		0			0
$739$	−25.5528			−0.939975			−0.469988	−	0.882673i	$-0.655742\pi$
$739$	−25.5528			−0.939975			−0.469988	+	0.882673i	$0.655742\pi$
$740$	1.40113	−	1.74265i	0.0515066	−	0.0640611i
$741$		0			0
$742$			36.2642i			1.33130i
$743$		−	44.2852i		−	1.62467i	−0.583193	−	0.812334i	$-0.698197\pi$
$743$		−	44.2852i		−	1.62467i	0.583193	−	0.812334i	$-0.301803\pi$
$744$		0			0
$745$	−37.8067	−	30.3974i	−1.38513	−	1.11368i
$746$	−23.1634			−0.848072
$747$		0			0
$748$			3.74294i			0.136855i
$749$	−18.3054			−0.668865
$750$		0			0
$751$	41.2897			1.50668			0.753342	−	0.657629i	$-0.228440\pi$
$751$	41.2897			1.50668			0.753342	+	0.657629i	$0.228440\pi$
$752$			6.23085i			0.227216i
$753$		0			0
$754$	−0.928820			−0.0338256
$755$	−3.60283	−	2.89676i	−0.131120	−	0.105424i
$756$		0			0
$757$		−	6.57802i		−	0.239082i	−0.992829	−	0.119541i	$-0.961858\pi$
$757$		−	6.57802i		−	0.239082i	0.992829	−	0.119541i	$-0.0381423\pi$
$758$			26.7721i			0.972406i
$759$		0			0
$760$	3.74934	−	4.66323i	0.136003	−	0.169153i
$761$	−20.3166			−0.736475			−0.368237	−	0.929732i	$-0.620039\pi$
$761$	−20.3166			−0.736475			−0.368237	+	0.929732i	$0.620039\pi$
$762$		0			0
$763$		−	38.2990i		−	1.38652i
$764$	8.00137			0.289479
$765$		0			0
$766$	22.3189			0.806413
$767$			1.02080i			0.0368591i
$768$		0			0
$769$	−25.2435			−0.910303			−0.455151	−	0.890414i	$-0.650415\pi$
$769$	−25.2435			−0.910303			−0.455151	+	0.890414i	$0.650415\pi$
$770$	−21.3860	−	17.1948i	−0.770696	−	0.619657i
$771$		0			0
$772$			14.0420i			0.505383i
$773$			48.9781i			1.76162i	0.473470	+	0.880810i	$0.343001\pi$
$773$			48.9781i			1.76162i	−0.473470	+	0.880810i	$0.656999\pi$
$774$		0			0
$775$	−3.89067	−	17.6959i	−0.139757	−	0.635657i
$776$	3.07063			0.110229
$777$		0			0
$778$		−	24.3011i		−	0.871237i
$779$	31.6469			1.13387
$780$		0			0
$781$	−47.0984			−1.68531
$782$		−	2.28707i		−	0.0817855i
$783$		0			0
$784$	−3.30305			−0.117966
$785$	−25.9824	+	32.3155i	−0.927352	+	1.15339i
$786$		0			0
$787$			3.78073i			0.134768i	0.997727	+	0.0673842i	$0.0214653\pi$
$787$			3.78073i			0.134768i	−0.997727	+	0.0673842i	$0.978535\pi$
$788$		−	3.36608i		−	0.119912i
$789$		0			0
$790$	−21.8657	+	27.1953i	−0.777945	+	0.967566i
$791$	−6.99886			−0.248851
$792$		0			0
$793$			1.54529i			0.0548750i
$794$	28.1888			1.00038
$795$		0			0
$796$	−14.8890			−0.527725
$797$		−	29.5487i		−	1.04667i	−0.852128	−	0.523334i	$-0.824688\pi$
$797$		−	29.5487i		−	1.04667i	0.852128	−	0.523334i	$-0.175312\pi$
$798$		0			0
$799$	−6.09993			−0.215800
$800$	−4.88336	+	1.07367i	−0.172653	+	0.0379598i
$801$		0			0
$802$			15.9528i			0.563312i
$803$			53.5129i			1.88843i
$804$		0			0
$805$	13.0676	+	10.5066i	0.460572	+	0.370310i
$806$	0.533891			0.0188055
$807$		0			0
$808$		−	6.57513i		−	0.231312i
$809$	47.4231			1.66731			0.833654	−	0.552287i	$-0.186245\pi$
$809$	47.4231			1.66731			0.833654	+	0.552287i	$0.186245\pi$
$810$		0			0
$811$	25.6962			0.902317			0.451159	−	0.892444i	$-0.351011\pi$
$811$	25.6962			0.902317			0.451159	+	0.892444i	$0.351011\pi$
$812$		−	20.2356i		−	0.710131i
$813$		0			0
$814$	−3.82327			−0.134006
$815$	−30.2980	+	37.6830i	−1.06129	+	1.31998i
$816$		0			0
$817$			12.1324i			0.424460i
$818$		−	31.6014i		−	1.10492i
$819$		0			0
$820$	−20.6094	−	16.5704i	−0.719711	−	0.578664i
$821$	−0.286013			−0.00998192			−0.00499096	−	0.999988i	$-0.501589\pi$
$821$	−0.286013			−0.00998192			−0.00499096	+	0.999988i	$0.501589\pi$
$822$		0			0
$823$			44.6093i			1.55498i	0.628893	+	0.777491i	$0.283508\pi$
$823$			44.6093i			1.55498i	−0.628893	+	0.777491i	$0.716492\pi$
$824$	−2.52180			−0.0878510
$825$		0			0
$826$	−22.2396			−0.773815
$827$		−	55.1277i		−	1.91698i	−0.285131	−	0.958488i	$-0.592037\pi$
$827$		−	55.1277i		−	1.91698i	0.285131	−	0.958488i	$-0.407963\pi$
$828$		0			0
$829$	17.2029			0.597482			0.298741	−	0.954334i	$-0.403433\pi$
$829$	17.2029			0.597482			0.298741	+	0.954334i	$0.403433\pi$
$830$	−23.5904	−	18.9672i	−0.818835	−	0.658362i
$831$		0			0
$832$		−	0.147332i		−	0.00510783i
$833$		−	3.23365i		−	0.112039i
$834$		0			0
$835$	−16.4953	+	20.5160i	−0.570844	+	0.709985i
$836$	−10.2308			−0.353841
$837$		0			0
$838$		−	18.4266i		−	0.636535i
$839$	27.3527			0.944320			0.472160	−	0.881513i	$-0.343474\pi$
$839$	27.3527			0.944320			0.472160	+	0.881513i	$0.343474\pi$
$840$		0			0
$841$	10.7436			0.370467
$842$		−	19.1570i		−	0.660194i
$843$		0			0
$844$	9.80544			0.337517
$845$	−22.6166	−	18.1843i	−0.778036	−	0.625558i
$846$		0			0
$847$			11.6113i			0.398969i
$848$		−	11.2978i		−	0.387970i
$849$		0			0
$850$	−1.05111	−	4.78076i	−0.0360527	−	0.163979i
$851$	2.33616			0.0800824
$852$		0			0
$853$		−	51.8565i		−	1.77553i	−0.460294	−	0.887766i	$-0.652256\pi$
$853$		−	51.8565i		−	1.77553i	0.460294	−	0.887766i	$-0.347744\pi$
$854$	−33.6663			−1.15204
$855$		0			0
$856$	5.70291			0.194921
$857$		−	4.63553i		−	0.158347i	−0.996861	−	0.0791733i	$-0.974772\pi$
$857$		−	4.63553i		−	0.158347i	0.996861	−	0.0791733i	$-0.0252280\pi$
$858$		0			0
$859$	−43.1006			−1.47057			−0.735287	−	0.677755i	$-0.762953\pi$
$859$	−43.1006			−1.47057			−0.735287	+	0.677755i	$0.762953\pi$
$860$	6.35258	−	7.90100i	0.216621	−	0.269422i
$861$		0			0
$862$			10.3947i			0.354044i
$863$		−	11.2463i		−	0.382829i	−0.981509	−	0.191414i	$-0.938693\pi$
$863$		−	11.2463i		−	0.382829i	0.981509	−	0.191414i	$-0.0613074\pi$
$864$		0			0
$865$	−19.6380	+	24.4247i	−0.667711	+	0.830464i
$866$	−3.36622			−0.114389
$867$		0			0
$868$			11.6316i			0.394801i
$869$	59.6649			2.02399
$870$		0			0
$871$	0.413910			0.0140248
$872$			11.9318i			0.404061i
$873$		0			0
$874$	6.25142			0.211457
$875$	32.1444	+	15.9568i	1.08668	+	0.539437i
$876$		0			0
$877$			17.9444i			0.605939i	0.953000	+	0.302969i	$0.0979780\pi$
$877$			17.9444i			0.605939i	−0.953000	+	0.302969i	$0.902022\pi$
$878$			32.5045i			1.09697i
$879$		0			0
$880$	6.66263	+	5.35690i	0.224597	+	0.180581i
$881$	16.6495			0.560935			0.280468	−	0.959864i	$-0.409511\pi$
$881$	16.6495			0.560935			0.280468	+	0.959864i	$0.409511\pi$
$882$		0			0
$883$			28.7758i			0.968383i	0.874962	+	0.484191i	$0.160886\pi$
$883$			28.7758i			0.968383i	−0.874962	+	0.484191i	$0.839114\pi$
$884$	0.144237			0.00485121
$885$		0			0
$886$	−23.5479			−0.791107
$887$		−	23.6957i		−	0.795625i	−0.917467	−	0.397812i	$-0.869770\pi$
$887$		−	23.6957i		−	0.795625i	0.917467	−	0.397812i	$-0.130230\pi$
$888$		0			0
$889$	−17.3135			−0.580678
$890$	−9.06432	+	11.2737i	−0.303837	+	0.377896i
$891$		0			0
$892$			15.4447i			0.517125i
$893$		−	16.6734i		−	0.557953i
$894$		0			0
$895$	21.6368	+	17.3965i	0.723240	+	0.581501i
$896$	3.20984			0.107233
$897$		0			0
$898$			12.5629i			0.419228i
$899$	−22.8448			−0.761918
$900$		0			0
$901$	11.0605			0.368478
$902$			45.2158i			1.50552i
$903$		0			0
$904$	2.18044			0.0725204
$905$	−14.2853	−	11.4857i	−0.474861	−	0.381799i
$906$		0			0
$907$			5.56548i			0.184799i	0.995722	+	0.0923994i	$0.0294537\pi$
$907$			5.56548i			0.184799i	−0.995722	+	0.0923994i	$0.970546\pi$
$908$		−	6.46090i		−	0.214413i
$909$		0			0
$910$	−0.662612	+	0.824122i	−0.0219654	+	0.0273194i
$911$	17.2514			0.571565			0.285782	−	0.958295i	$-0.407747\pi$
$911$	17.2514			0.571565			0.285782	+	0.958295i	$0.407747\pi$
$912$		0			0
$913$			51.7559i			1.71287i
$914$	6.53390			0.216122
$915$		0			0
$916$	7.97458			0.263488
$917$			28.7942i			0.950867i
$918$		0			0
$919$	8.34007			0.275114			0.137557	−	0.990494i	$-0.456075\pi$
$919$	8.34007			0.275114			0.137557	+	0.990494i	$0.456075\pi$
$920$	−4.07111	−	3.27326i	−0.134220	−	0.107916i
$921$		0			0
$922$		−	24.7616i		−	0.815480i
$923$			1.81497i			0.0597403i
$924$		0			0
$925$	4.88336	−	1.07367i	0.160564	−	0.0353019i
$926$	−25.9239			−0.851913
$927$		0			0
$928$			6.30425i			0.206947i
$929$	−48.2529			−1.58313			−0.791564	−	0.611087i	$-0.790733\pi$
$929$	−48.2529			−1.58313			−0.791564	+	0.611087i	$0.790733\pi$
$930$		0			0
$931$	8.83876			0.289679
$932$			25.2907i			0.828423i
$933$		0			0
$934$	−28.8182			−0.942959
$935$	−5.24435	+	6.52264i	−0.171509	+	0.213313i
$936$		0			0
$937$			30.2000i			0.986592i	0.869862	+	0.493296i	$0.164208\pi$
$937$			30.2000i			0.986592i	−0.869862	+	0.493296i	$0.835792\pi$
$938$			9.01759i			0.294435i
$939$		0			0
$940$	−8.73023	+	10.8582i	−0.284749	+	0.354155i
$941$	−14.9206			−0.486399			−0.243199	−	0.969976i	$-0.578197\pi$
$941$	−14.9206			−0.486399			−0.243199	+	0.969976i	$0.578197\pi$
$942$		0			0
$943$		−	27.6285i		−	0.899707i
$944$	6.92858			0.225506
$945$		0			0
$946$	−17.3343			−0.563587
$947$		−	48.1091i		−	1.56334i	−0.623694	−	0.781668i	$-0.714369\pi$
$947$		−	48.1091i		−	1.56334i	0.623694	−	0.781668i	$-0.285631\pi$
$948$		0			0
$949$	2.06215			0.0669403
$950$	13.0676	−	2.87307i	0.423969	−	0.0932146i
$951$		0			0
$952$			3.14239i			0.101846i
$953$			8.67149i			0.280897i	0.990088	+	0.140449i	$0.0448545\pi$
$953$			8.67149i			0.280897i	−0.990088	+	0.140449i	$0.955146\pi$
$954$		0			0
$955$	13.9436	+	11.2110i	0.451204	+	0.362778i
$956$	−5.11481			−0.165425
$957$		0			0
$958$		−	41.7873i		−	1.35009i
$959$	8.67787			0.280223
$960$		0			0
$961$	−17.8686			−0.576408
$962$			0.147332i			0.00475018i
$963$		0			0
$964$	−16.4415			−0.529544
$965$	−19.6747	+	24.4703i	−0.633351	+	0.787728i
$966$		0			0
$967$			18.5944i			0.597955i	0.954260	+	0.298978i	$0.0966456\pi$
$967$			18.5944i			0.597955i	−0.954260	+	0.298978i	$0.903354\pi$
$968$		−	3.61741i		−	0.116268i
$969$		0			0
$970$	5.35103	+	4.30235i	0.171811	+	0.138140i
$971$	32.6679			1.04836			0.524182	−	0.851606i	$-0.324371\pi$
$971$	32.6679			1.04836			0.524182	+	0.851606i	$0.324371\pi$
$972$		0			0
$973$		−	13.8138i		−	0.442850i
$974$	9.34463			0.299421
$975$		0			0
$976$	10.4885			0.335728
$977$			28.1856i			0.901737i	0.892590	+	0.450868i	$0.148886\pi$
$977$			28.1856i			0.901737i	−0.892590	+	0.450868i	$0.851114\pi$
$978$		0			0
$979$	24.7338			0.790497
$980$	−5.75606	−	4.62800i	−0.183871	−	0.147836i
$981$		0			0
$982$			10.7558i			0.343232i
$983$			25.3845i			0.809639i	0.914397	+	0.404819i	$0.132666\pi$
$983$			25.3845i			0.809639i	−0.914397	+	0.404819i	$0.867334\pi$
$984$		0			0
$985$	4.71632	−	5.86591i	0.150274	−	0.186903i
$986$	−6.17179			−0.196550
$987$		0			0
$988$			0.394252i			0.0125428i
$989$	10.5919			0.336803
$990$		0			0
$991$	−21.1083			−0.670527			−0.335264	−	0.942124i	$-0.608825\pi$
$991$	−21.1083			−0.670527			−0.335264	+	0.942124i	$0.608825\pi$
$992$		−	3.62372i		−	0.115053i
$993$		0			0
$994$	−39.5415			−1.25418
$995$	−25.9463	−	20.8614i	−0.822552	−	0.661350i
$996$		0			0
$997$		−	39.0978i		−	1.23824i	−0.785296	−	0.619120i	$-0.787489\pi$
$997$		−	39.0978i		−	1.23824i	0.785296	−	0.619120i	$-0.212511\pi$
$998$		−	29.0702i		−	0.920201i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3330.2.d.p.1999.7		10
3.2	odd	2		370.2.b.d.149.2	✓	10
5.4	even	2	inner	3330.2.d.p.1999.2		10
15.2	even	4		1850.2.a.be.1.2		5
15.8	even	4		1850.2.a.bd.1.4		5
15.14	odd	2		370.2.b.d.149.9	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.b.d.149.2	✓	10	3.2	odd	2
370.2.b.d.149.9	yes	10	15.14	odd	2
1850.2.a.bd.1.4		5	15.8	even	4
1850.2.a.be.1.2		5	15.2	even	4
3330.2.d.p.1999.2		10	5.4	even	2	inner
3330.2.d.p.1999.7		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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-1.74265 - 1.40113i) q^{5} +3.20984i q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-1.74265 - 1.40113i) q^{5} +3.20984i q^{7} -1.00000i q^{8} +(1.40113 - 1.74265i) q^{10} -3.82327 q^{11} +0.147332i q^{13} -3.20984 q^{14} +1.00000 q^{16} +0.978989i q^{17} -2.67594 q^{19} +(1.74265 + 1.40113i) q^{20} -3.82327i q^{22} +2.33616i q^{23} +(1.07367 + 4.88336i) q^{25} -0.147332 q^{26} -3.20984i q^{28} +6.30425 q^{29} -3.62372 q^{31} +1.00000i q^{32} -0.978989 q^{34} +(4.49740 - 5.59362i) q^{35} -1.00000i q^{37} -2.67594i q^{38} +(-1.40113 + 1.74265i) q^{40} -11.8265 q^{41} -4.53390i q^{43} +3.82327 q^{44} -2.33616 q^{46} +6.23085i q^{47} -3.30305 q^{49} +(-4.88336 + 1.07367i) q^{50} -0.147332i q^{52} -11.2978i q^{53} +(6.66263 + 5.35690i) q^{55} +3.20984 q^{56} +6.30425i q^{58} +6.92858 q^{59} +10.4885 q^{61} -3.62372i q^{62} -1.00000 q^{64} +(0.206432 - 0.256749i) q^{65} -2.80936i q^{67} -0.978989i q^{68} +(5.59362 + 4.49740i) q^{70} +12.3189 q^{71} -13.9966i q^{73} +1.00000 q^{74} +2.67594 q^{76} -12.2721i q^{77} -15.6057 q^{79} +(-1.74265 - 1.40113i) q^{80} -11.8265i q^{82} -13.5371i q^{83} +(1.37169 - 1.70604i) q^{85} +4.53390 q^{86} +3.82327i q^{88} -6.46929 q^{89} -0.472913 q^{91} -2.33616i q^{92} -6.23085 q^{94} +(4.66323 + 3.74934i) q^{95} +3.07063i q^{97} -3.30305i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{4} - 6 q^{5}+O(q^{10}) \) 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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