LMFDB - Embedded newform 3330.2.e.c.739.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("3330.739");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$26.5901838731$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 19x^{8} + 103x^{6} + 210x^{4} + 140x^{2} + 16 $ x^10 + 19x^8 + 103x^6 + 210x^4 + 140x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 370)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			739.3
Root			$-1.76216i$ of defining polynomial
Character	$\chi$	$=$	3330.739
Dual form			3330.2.e.c.739.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(-1.62868 - 1.53213i) q^{5} -1.22131i q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.62868 - 1.53213i) q^{5} -1.22131i q^{7} -1.00000 q^{8} +(1.62868 + 1.53213i) q^{10} -1.87120 q^{11} -6.50491 q^{13} +1.22131i q^{14} +1.00000 q^{16} -0.765994 q^{17} -3.34507i q^{19} +(-1.62868 - 1.53213i) q^{20} +1.87120 q^{22} +1.38964 q^{23} +(0.305180 + 4.99068i) q^{25} +6.50491 q^{26} -1.22131i q^{28} -1.72909i q^{29} -4.11288i q^{31} -1.00000 q^{32} +0.765994 q^{34} +(-1.87120 + 1.98912i) q^{35} +(-1.76599 - 5.82076i) q^{37} +3.34507i q^{38} +(1.62868 + 1.53213i) q^{40} -3.73892 q^{41} -4.91814 q^{43} -1.87120 q^{44} -1.38964 q^{46} +6.30775i q^{47} +5.50840 q^{49} +(-0.305180 - 4.99068i) q^{50} -6.50491 q^{52} +2.57768i q^{53} +(3.04759 + 2.86692i) q^{55} +1.22131i q^{56} +1.72909i q^{58} +10.5664i q^{59} +11.1550i q^{61} +4.11288i q^{62} +1.00000 q^{64} +(10.5944 + 9.96634i) q^{65} -11.1219i q^{67} -0.765994 q^{68} +(1.87120 - 1.98912i) q^{70} -0.963126 q^{71} +9.03119i q^{73} +(1.76599 + 5.82076i) q^{74} -3.34507i q^{76} +2.28532i q^{77} -10.3333i q^{79} +(-1.62868 - 1.53213i) q^{80} +3.73892 q^{82} +0.00656819i q^{83} +(1.24756 + 1.17360i) q^{85} +4.91814 q^{86} +1.87120 q^{88} -4.70144i q^{89} +7.94452i q^{91} +1.38964 q^{92} -6.30775i q^{94} +(-5.12507 + 5.44804i) q^{95} +0.403430 q^{97} -5.50840 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 10 q^{4} - 3 q^{5} - 10 q^{8}+O(q^{10}) $ 10 * q - 10 * q^2 + 10 * q^4 - 3 * q^5 - 10 * q^8	$ 10 q - 10 q^{2} + 10 q^{4} - 3 q^{5} - 10 q^{8} + 3 q^{10} + 2 q^{13} + 10 q^{16} + 18 q^{17} - 3 q^{20} + 10 q^{23} + 5 q^{25} - 2 q^{26} - 10 q^{32} - 18 q^{34} + 8 q^{37} + 3 q^{40} + 4 q^{41} + 10 q^{43} - 10 q^{46} - 8 q^{49} - 5 q^{50} + 2 q^{52} - 5 q^{55} + 10 q^{64} - 2 q^{65} + 18 q^{68} + 20 q^{71} - 8 q^{74} - 3 q^{80} - 4 q^{82} - 28 q^{85} - 10 q^{86} + 10 q^{92} - 2 q^{95} - 2 q^{97} + 8 q^{98}+O(q^{100}) $ 10 * q - 10 * q^2 + 10 * q^4 - 3 * q^5 - 10 * q^8 + 3 * q^10 + 2 * q^13 + 10 * q^16 + 18 * q^17 - 3 * q^20 + 10 * q^23 + 5 * q^25 - 2 * q^26 - 10 * q^32 - 18 * q^34 + 8 * q^37 + 3 * q^40 + 4 * q^41 + 10 * q^43 - 10 * q^46 - 8 * q^49 - 5 * q^50 + 2 * q^52 - 5 * q^55 + 10 * q^64 - 2 * q^65 + 18 * q^68 + 20 * q^71 - 8 * q^74 - 3 * q^80 - 4 * q^82 - 28 * q^85 - 10 * q^86 + 10 * q^92 - 2 * q^95 - 2 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−1.62868	−	1.53213i	−0.728367	−	0.685188i
$5$	−1.62868	−	1.53213i	−0.728367	−	0.685188i
$6$		0			0
$7$		−	1.22131i		−	0.461612i	−0.973000	−	0.230806i	$-0.925864\pi$
$7$		−	1.22131i		−	0.461612i	0.973000	−	0.230806i	$-0.0741363\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.62868	+	1.53213i	0.515033	+	0.484501i
$11$	−1.87120			−0.564189			−0.282094	−	0.959387i	$-0.591029\pi$
$11$	−1.87120			−0.564189			−0.282094	+	0.959387i	$0.591029\pi$
$12$		0			0
$13$	−6.50491			−1.80414			−0.902069	−	0.431592i	$-0.857952\pi$
$13$	−6.50491			−1.80414			−0.902069	+	0.431592i	$0.857952\pi$
$14$			1.22131i			0.326409i
$15$		0			0
$16$	1.00000			0.250000
$17$	−0.765994			−0.185781			−0.0928904	−	0.995676i	$-0.529611\pi$
$17$	−0.765994			−0.185781			−0.0928904	+	0.995676i	$0.529611\pi$
$18$		0			0
$19$		−	3.34507i		−	0.767412i	−0.923455	−	0.383706i	$-0.874648\pi$
$19$		−	3.34507i		−	0.767412i	0.923455	−	0.383706i	$-0.125352\pi$
$20$	−1.62868	−	1.53213i	−0.364183	−	0.342594i
$21$		0			0
$22$	1.87120			0.398942
$23$	1.38964			0.289760			0.144880	−	0.989449i	$-0.453720\pi$
$23$	1.38964			0.289760			0.144880	+	0.989449i	$0.453720\pi$
$24$		0			0
$25$	0.305180	+	4.99068i	0.0610360	+	0.998136i
$26$	6.50491			1.27572
$27$		0			0
$28$		−	1.22131i		−	0.230806i
$29$		−	1.72909i		−	0.321084i	−0.987029	−	0.160542i	$-0.948676\pi$
$29$		−	1.72909i		−	0.321084i	0.987029	−	0.160542i	$-0.0513243\pi$
$30$		0			0
$31$		−	4.11288i		−	0.738695i	−0.929291	−	0.369348i	$-0.879581\pi$
$31$		−	4.11288i		−	0.738695i	0.929291	−	0.369348i	$-0.120419\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	0.765994			0.131367
$35$	−1.87120	+	1.98912i	−0.316291	+	0.336223i
$36$		0			0
$37$	−1.76599	−	5.82076i	−0.290328	−	0.956927i
$37$	−1.76599	−	5.82076i	−0.290328	−	0.956927i
$38$			3.34507i			0.542642i
$39$		0			0
$40$	1.62868	+	1.53213i	0.257517	+	0.242250i
$41$	−3.73892			−0.583921			−0.291960	−	0.956430i	$-0.594308\pi$
$41$	−3.73892			−0.583921			−0.291960	+	0.956430i	$0.594308\pi$
$42$		0			0
$43$	−4.91814			−0.750009			−0.375005	−	0.927023i	$-0.622359\pi$
$43$	−4.91814			−0.750009			−0.375005	+	0.927023i	$0.622359\pi$
$44$	−1.87120			−0.282094
$45$		0			0
$46$	−1.38964			−0.204891
$47$			6.30775i			0.920080i	0.887898	+	0.460040i	$0.152165\pi$
$47$			6.30775i			0.920080i	−0.887898	+	0.460040i	$0.847835\pi$
$48$		0			0
$49$	5.50840			0.786914
$50$	−0.305180	−	4.99068i	−0.0431590	−	0.705788i
$51$		0			0
$52$	−6.50491			−0.902069
$53$			2.57768i			0.354072i	0.984204	+	0.177036i	$0.0566509\pi$
$53$			2.57768i			0.354072i	−0.984204	+	0.177036i	$0.943349\pi$
$54$		0			0
$55$	3.04759	+	2.86692i	0.410936	+	0.386575i
$56$			1.22131i			0.163205i
$57$		0			0
$58$			1.72909i			0.227041i
$59$			10.5664i			1.37563i	0.725887	+	0.687814i	$0.241429\pi$
$59$			10.5664i			1.37563i	−0.725887	+	0.687814i	$0.758571\pi$
$60$		0			0
$61$			11.1550i			1.42825i	0.700020	+	0.714123i	$0.253174\pi$
$61$			11.1550i			1.42825i	−0.700020	+	0.714123i	$0.746826\pi$
$62$			4.11288i			0.522337i
$63$		0			0
$64$	1.00000			0.125000
$65$	10.5944	+	9.96634i	1.31407	+	1.23617i
$66$		0			0
$67$		−	11.1219i		−	1.35875i	−0.733789	−	0.679377i	$-0.762250\pi$
$67$		−	11.1219i		−	1.35875i	0.733789	−	0.679377i	$-0.237750\pi$
$68$	−0.765994			−0.0928904
$69$		0			0
$70$	1.87120	−	1.98912i	0.223651	−	0.237746i
$71$	−0.963126			−0.114302			−0.0571510	−	0.998366i	$-0.518202\pi$
$71$	−0.963126			−0.114302			−0.0571510	+	0.998366i	$0.518202\pi$
$72$		0			0
$73$			9.03119i			1.05702i	0.848927	+	0.528511i	$0.177249\pi$
$73$			9.03119i			1.05702i	−0.848927	+	0.528511i	$0.822751\pi$
$74$	1.76599	+	5.82076i	0.205293	+	0.676650i
$75$		0			0
$76$		−	3.34507i		−	0.383706i
$77$			2.28532i			0.260436i
$78$		0			0
$79$		−	10.3333i		−	1.16259i	−0.813694	−	0.581293i	$-0.802547\pi$
$79$		−	10.3333i		−	1.16259i	0.813694	−	0.581293i	$-0.197453\pi$
$80$	−1.62868	−	1.53213i	−0.182092	−	0.171297i
$81$		0			0
$82$	3.73892			0.412894
$83$			0.00656819i			0.000720953i	1.00000		0.000360477i	$0.000114743\pi$
$83$			0.00656819i			0.000720953i	−1.00000		0.000360477i	$0.999885\pi$
$84$		0			0
$85$	1.24756	+	1.17360i	0.135317	+	0.127295i
$86$	4.91814			0.530337
$87$		0			0
$88$	1.87120			0.199471
$89$		−	4.70144i		−	0.498352i	−0.968458	−	0.249176i	$-0.919840\pi$
$89$		−	4.70144i		−	0.498352i	0.968458	−	0.249176i	$-0.0801598\pi$
$90$		0			0
$91$			7.94452i			0.832812i
$92$	1.38964			0.144880
$93$		0			0
$94$		−	6.30775i		−	0.650595i
$95$	−5.12507	+	5.44804i	−0.525821	+	0.558957i
$96$		0			0
$97$	0.403430			0.0409621			0.0204811	−	0.999790i	$-0.493480\pi$
$97$	0.403430			0.0409621			0.0204811	+	0.999790i	$0.493480\pi$
$98$	−5.50840			−0.556432
$99$		0			0
$100$	0.305180	+	4.99068i	0.0305180	+	0.499068i
$101$	19.3724			1.92762			0.963812	−	0.266582i	$-0.0858943\pi$
$101$	19.3724			1.92762			0.963812	+	0.266582i	$0.0858943\pi$
$102$		0			0
$103$	5.56165			0.548005			0.274003	−	0.961729i	$-0.411652\pi$
$103$	5.56165			0.548005			0.274003	+	0.961729i	$0.411652\pi$
$104$	6.50491			0.637859
$105$		0			0
$106$		−	2.57768i		−	0.250367i
$107$		−	1.93484i		−	0.187048i	−0.995617	−	0.0935241i	$-0.970187\pi$
$107$		−	1.93484i		−	0.187048i	0.995617	−	0.0935241i	$-0.0298132\pi$
$108$		0			0
$109$			8.70619i			0.833901i	0.908929	+	0.416951i	$0.136901\pi$
$109$			8.70619i			0.833901i	−0.908929	+	0.416951i	$0.863099\pi$
$110$	−3.04759	−	2.86692i	−0.290576	−	0.273350i
$111$		0			0
$112$		−	1.22131i		−	0.115403i
$113$	−14.7585			−1.38837			−0.694183	−	0.719798i	$-0.744234\pi$
$113$	−14.7585			−1.38837			−0.694183	+	0.719798i	$0.744234\pi$
$114$		0			0
$115$	−2.26327	−	2.12910i	−0.211051	−	0.198540i
$116$		−	1.72909i		−	0.160542i
$117$		0			0
$118$		−	10.5664i		−	0.972715i
$119$			0.935517i			0.0857587i
$120$		0			0
$121$	−7.49860			−0.681691
$122$		−	11.1550i		−	1.00992i
$123$		0			0
$124$		−	4.11288i		−	0.369348i
$125$	7.14931	−	8.59578i	0.639453	−	0.768830i
$126$		0			0
$127$			11.1280i			0.987453i	0.869617	+	0.493727i	$0.164366\pi$
$127$			11.1280i			0.987453i	−0.869617	+	0.493727i	$0.835634\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	−10.5944	−	9.96634i	−0.929191	−	0.874106i
$131$		−	12.8363i		−	1.12152i	−0.827980	−	0.560758i	$-0.810510\pi$
$131$		−	12.8363i		−	1.12152i	0.827980	−	0.560758i	$-0.189490\pi$
$132$		0			0
$133$	−4.08537			−0.354247
$134$			11.1219i			0.960785i
$135$		0			0
$136$	0.765994			0.0656834
$137$			12.0355i			1.02826i	0.857713	+	0.514129i	$0.171885\pi$
$137$			12.0355i			1.02826i	−0.857713	+	0.514129i	$0.828115\pi$
$138$		0			0
$139$	−9.78562			−0.830005			−0.415003	−	0.909820i	$-0.636219\pi$
$139$	−9.78562			−0.830005			−0.415003	+	0.909820i	$0.636219\pi$
$140$	−1.87120	+	1.98912i	−0.158145	+	0.168111i
$141$		0			0
$142$	0.963126			0.0808237
$143$	12.1720			1.01787
$144$		0			0
$145$	−2.64919	+	2.81613i	−0.220003	+	0.233867i
$146$		−	9.03119i		−	0.747427i
$147$		0			0
$148$	−1.76599	−	5.82076i	−0.145164	−	0.478464i
$149$	11.8876			0.973868			0.486934	−	0.873439i	$-0.338115\pi$
$149$	11.8876			0.973868			0.486934	+	0.873439i	$0.338115\pi$
$150$		0			0
$151$	21.3141			1.73452			0.867259	−	0.497857i	$-0.165880\pi$
$151$	21.3141			1.73452			0.867259	+	0.497857i	$0.165880\pi$
$152$			3.34507i			0.271321i
$153$		0			0
$154$		−	2.28532i		−	0.184156i
$155$	−6.30145	+	6.69856i	−0.506145	+	0.538041i
$156$		0			0
$157$			15.3009i			1.22115i	0.791960	+	0.610573i	$0.209061\pi$
$157$			15.3009i			1.22115i	−0.791960	+	0.610573i	$0.790939\pi$
$158$			10.3333i			0.822072i
$159$		0			0
$160$	1.62868	+	1.53213i	0.128758	+	0.121125i
$161$		−	1.69718i		−	0.133757i
$162$		0			0
$163$	14.9177			1.16844			0.584221	−	0.811595i	$-0.301400\pi$
$163$	14.9177			1.16844			0.584221	+	0.811595i	$0.301400\pi$
$164$	−3.73892			−0.291960
$165$		0			0
$166$		−	0.00656819i		−	0.000509791i
$167$	17.3041			1.33903			0.669514	−	0.742800i	$-0.266502\pi$
$167$	17.3041			1.33903			0.669514	+	0.742800i	$0.266502\pi$
$168$		0			0
$169$	29.3139			2.25491
$170$	−1.24756	−	1.17360i	−0.0956832	−	0.0900109i
$171$		0			0
$172$	−4.91814			−0.375005
$173$		−	19.7322i		−	1.50021i	−0.661317	−	0.750107i	$-0.730002\pi$
$173$		−	19.7322i		−	1.50021i	0.661317	−	0.750107i	$-0.269998\pi$
$174$		0			0
$175$	6.09517	−	0.372720i	0.460752	−	0.0281750i
$176$	−1.87120			−0.141047
$177$		0			0
$178$			4.70144i			0.352388i
$179$		−	3.70357i		−	0.276818i	−0.990375	−	0.138409i	$-0.955801\pi$
$179$		−	3.70357i		−	0.276818i	0.990375	−	0.138409i	$-0.0441988\pi$
$180$		0			0
$181$	−10.4093			−0.773714			−0.386857	−	0.922140i	$-0.626439\pi$
$181$	−10.4093			−0.773714			−0.386857	+	0.922140i	$0.626439\pi$
$182$		−	7.94452i		−	0.588887i
$183$		0			0
$184$	−1.38964			−0.102446
$185$	−6.04191	+	12.1859i	−0.444210	+	0.895923i
$186$		0			0
$187$	1.43333			0.104815
$188$			6.30775i			0.460040i
$189$		0			0
$190$	5.12507	−	5.44804i	0.371812	−	0.395242i
$191$			23.0954i			1.67113i	0.549395	+	0.835563i	$0.314858\pi$
$191$			23.0954i			1.67113i	−0.549395	+	0.835563i	$0.685142\pi$
$192$		0			0
$193$	12.4951			0.899418			0.449709	−	0.893175i	$-0.351528\pi$
$193$	12.4951			0.899418			0.449709	+	0.893175i	$0.351528\pi$
$194$	−0.403430			−0.0289646
$195$		0			0
$196$	5.50840			0.393457
$197$			5.51302i			0.392786i	0.980525	+	0.196393i	$0.0629229\pi$
$197$			5.51302i			0.392786i	−0.980525	+	0.196393i	$0.937077\pi$
$198$		0			0
$199$			18.8033i			1.33293i	0.745537	+	0.666464i	$0.232193\pi$
$199$			18.8033i			1.33293i	−0.745537	+	0.666464i	$0.767807\pi$
$200$	−0.305180	−	4.99068i	−0.0215795	−	0.352894i
$201$		0			0
$202$	−19.3724			−1.36304
$203$	−2.11176			−0.148216
$204$		0			0
$205$	6.08949	+	5.72849i	0.425309	+	0.400095i
$206$	−5.56165			−0.387498
$207$		0			0
$208$	−6.50491			−0.451034
$209$			6.25931i			0.432965i
$210$		0			0
$211$	−26.6632			−1.83557			−0.917784	−	0.397081i	$-0.870023\pi$
$211$	−26.6632			−1.83557			−0.917784	+	0.397081i	$0.870023\pi$
$212$			2.57768i			0.177036i
$213$		0			0
$214$			1.93484i			0.132263i
$215$	8.01006	+	7.53521i	0.546282	+	0.513897i
$216$		0			0
$217$	−5.02311			−0.340991
$218$		−	8.70619i		−	0.589657i
$219$		0			0
$220$	3.04759	+	2.86692i	0.205468	+	0.193288i
$221$	4.98272			0.335174
$222$		0			0
$223$			10.8630i			0.727441i	0.931508	+	0.363721i	$0.118494\pi$
$223$			10.8630i			0.727441i	−0.931508	+	0.363721i	$0.881506\pi$
$224$			1.22131i			0.0816023i
$225$		0			0
$226$	14.7585			0.981723
$227$	6.82427			0.452942			0.226471	−	0.974018i	$-0.427281\pi$
$227$	6.82427			0.452942			0.226471	+	0.974018i	$0.427281\pi$
$228$		0			0
$229$	2.56189			0.169294			0.0846471	−	0.996411i	$-0.473024\pi$
$229$	2.56189			0.169294			0.0846471	+	0.996411i	$0.473024\pi$
$230$	2.26327	+	2.12910i	0.149236	+	0.140389i
$231$		0			0
$232$			1.72909i			0.113520i
$233$		−	23.3423i		−	1.52921i	−0.644502	−	0.764603i	$-0.722935\pi$
$233$		−	23.3423i		−	1.52921i	0.644502	−	0.764603i	$-0.277065\pi$
$234$		0			0
$235$	9.66427	−	10.2733i	0.630428	−	0.670156i
$236$			10.5664i			0.687814i
$237$		0			0
$238$		−	0.935517i		−	0.0606405i
$239$		−	5.19256i		−	0.335879i	−0.985797	−	0.167940i	$-0.946289\pi$
$239$		−	5.19256i		−	0.335879i	0.985797	−	0.167940i	$-0.0537113\pi$
$240$		0			0
$241$			15.5243i			1.00001i	0.866022	+	0.500005i	$0.166669\pi$
$241$			15.5243i			1.00001i	−0.866022	+	0.500005i	$0.833331\pi$
$242$	7.49860			0.482028
$243$		0			0
$244$			11.1550i			0.714123i
$245$	−8.97140	−	8.43956i	−0.573162	−	0.539184i
$246$		0			0
$247$			21.7594i			1.38452i
$248$			4.11288i			0.261168i
$249$		0			0
$250$	−7.14931	+	8.59578i	−0.452162	+	0.543645i
$251$			3.85199i			0.243136i	0.992583	+	0.121568i	$0.0387922\pi$
$251$			3.85199i			0.243136i	−0.992583	+	0.121568i	$0.961208\pi$
$252$		0			0
$253$	−2.60030			−0.163479
$254$		−	11.1280i		−	0.698235i
$255$		0			0
$256$	1.00000			0.0625000
$257$	3.34529			0.208673			0.104337	−	0.994542i	$-0.466728\pi$
$257$	3.34529			0.208673			0.104337	+	0.994542i	$0.466728\pi$
$258$		0			0
$259$	−7.10896	+	2.15683i	−0.441729	+	0.134019i
$260$	10.5944	+	9.96634i	0.657037	+	0.618086i
$261$		0			0
$262$			12.8363i			0.793031i
$263$		−	1.14405i		−	0.0705454i	−0.999378	−	0.0352727i	$-0.988770\pi$
$263$		−	1.14405i		−	0.0705454i	0.999378	−	0.0352727i	$-0.0112300\pi$
$264$		0			0
$265$	3.94934	−	4.19821i	0.242606	−	0.257894i
$266$	4.08537			0.250490
$267$		0			0
$268$		−	11.1219i		−	0.679377i
$269$	−15.1344			−0.922760			−0.461380	−	0.887203i	$-0.652645\pi$
$269$	−15.1344			−0.922760			−0.461380	+	0.887203i	$0.652645\pi$
$270$		0			0
$271$	−18.2842			−1.11069			−0.555344	−	0.831621i	$-0.687413\pi$
$271$	−18.2842			−1.11069			−0.555344	+	0.831621i	$0.687413\pi$
$272$	−0.765994			−0.0464452
$273$		0			0
$274$		−	12.0355i		−	0.727088i
$275$	−0.571054	−	9.33857i	−0.0344359	−	0.563137i
$276$		0			0
$277$	−2.58352			−0.155229			−0.0776145	−	0.996983i	$-0.524730\pi$
$277$	−2.58352			−0.155229			−0.0776145	+	0.996983i	$0.524730\pi$
$278$	9.78562			0.586902
$279$		0			0
$280$	1.87120	−	1.98912i	0.111826	−	0.118873i
$281$			19.3056i			1.15168i	0.817563	+	0.575839i	$0.195325\pi$
$281$			19.3056i			1.15168i	−0.817563	+	0.575839i	$0.804675\pi$
$282$		0			0
$283$	−9.02942			−0.536743			−0.268372	−	0.963315i	$-0.586486\pi$
$283$	−9.02942			−0.536743			−0.268372	+	0.963315i	$0.586486\pi$
$284$	−0.963126			−0.0571510
$285$		0			0
$286$	−12.1720			−0.719746
$287$			4.56638i			0.269545i
$288$		0			0
$289$	−16.4133			−0.965485
$290$	2.64919	−	2.81613i	0.155566	−	0.165369i
$291$		0			0
$292$			9.03119i			0.528511i
$293$			13.0845i			0.764405i	0.924079	+	0.382203i	$0.124834\pi$
$293$			13.0845i			0.764405i	−0.924079	+	0.382203i	$0.875166\pi$
$294$		0			0
$295$	16.1890	−	17.2092i	0.942563	−	1.00196i
$296$	1.76599	+	5.82076i	0.102646	+	0.338325i
$297$		0			0
$298$	−11.8876			−0.688629
$299$	−9.03948			−0.522767
$300$		0			0
$301$			6.00658i			0.346213i
$302$	−21.3141			−1.22649
$303$		0			0
$304$		−	3.34507i		−	0.191853i
$305$	17.0908	−	18.1678i	0.978616	−	1.04029i
$306$		0			0
$307$			7.60942i			0.434293i	0.976139	+	0.217146i	$0.0696749\pi$
$307$			7.60942i			0.434293i	−0.976139	+	0.217146i	$0.930325\pi$
$308$			2.28532i			0.130218i
$309$		0			0
$310$	6.30145	−	6.69856i	0.357898	−	0.380453i
$311$			15.2359i			0.863950i	0.901886	+	0.431975i	$0.142183\pi$
$311$			15.2359i			0.863950i	−0.901886	+	0.431975i	$0.857817\pi$
$312$		0			0
$313$	10.0000			0.565233			0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000			0.565233			0.282617	+	0.959233i	$0.408798\pi$
$314$		−	15.3009i		−	0.863480i
$315$		0			0
$316$		−	10.3333i		−	0.581293i
$317$			34.1403i			1.91751i	0.284230	+	0.958756i	$0.408262\pi$
$317$			34.1403i			1.91751i	−0.284230	+	0.958756i	$0.591738\pi$
$318$		0			0
$319$			3.23548i			0.181152i
$320$	−1.62868	−	1.53213i	−0.0910458	−	0.0856484i
$321$		0			0
$322$			1.69718i			0.0945803i
$323$			2.56230i			0.142570i
$324$		0			0
$325$	−1.98517	−	32.4639i	−0.110117	−	1.80077i
$326$	−14.9177			−0.826213
$327$		0			0
$328$	3.73892			0.206447
$329$	7.70373			0.424720
$330$		0			0
$331$			27.2567i			1.49817i	0.662476	+	0.749083i	$0.269506\pi$
$331$			27.2567i			1.49817i	−0.662476	+	0.749083i	$0.730494\pi$
$332$			0.00656819i			0.000360477i
$333$		0			0
$334$	−17.3041			−0.946836
$335$	−17.0401	+	18.1140i	−0.931002	+	0.989672i
$336$		0			0
$337$		−	22.5315i		−	1.22737i	−0.789552	−	0.613683i	$-0.789687\pi$
$337$		−	22.5315i		−	1.22737i	0.789552	−	0.613683i	$-0.210313\pi$
$338$	−29.3139			−1.59446
$339$		0			0
$340$	1.24756	+	1.17360i	0.0676583	+	0.0636473i
$341$			7.69603i			0.416764i
$342$		0			0
$343$		−	15.2766i		−	0.824861i
$344$	4.91814			0.265168
$345$		0			0
$346$			19.7322i			1.06081i
$347$	−34.7252			−1.86415			−0.932073	−	0.362272i	$-0.882001\pi$
$347$	−34.7252			−1.86415			−0.932073	+	0.362272i	$0.882001\pi$
$348$		0			0
$349$	15.9343			0.852942			0.426471	−	0.904501i	$-0.359757\pi$
$349$	15.9343			0.852942			0.426471	+	0.904501i	$0.359757\pi$
$350$	−6.09517	+	0.372720i	−0.325801	+	0.0199227i
$351$		0			0
$352$	1.87120			0.0997354
$353$	20.1925			1.07474			0.537370	−	0.843347i	$-0.319418\pi$
$353$	20.1925			1.07474			0.537370	+	0.843347i	$0.319418\pi$
$354$		0			0
$355$	1.56862	+	1.47563i	0.0832538	+	0.0783183i
$356$		−	4.70144i		−	0.249176i
$357$		0			0
$358$			3.70357i			0.195740i
$359$	30.8657			1.62903			0.814515	−	0.580143i	$-0.197003\pi$
$359$	30.8657			1.62903			0.814515	+	0.580143i	$0.197003\pi$
$360$		0			0
$361$	7.81050			0.411079
$362$	10.4093			0.547099
$363$		0			0
$364$			7.94452i			0.416406i
$365$	13.8369	−	14.7089i	0.724258	−	0.769899i
$366$		0			0
$367$			28.9254i			1.50989i	0.655786	+	0.754947i	$0.272337\pi$
$367$			28.9254i			1.50989i	−0.655786	+	0.754947i	$0.727663\pi$
$368$	1.38964			0.0724400
$369$		0			0
$370$	6.04191	−	12.1859i	0.314104	−	0.633513i
$371$	3.14815			0.163444
$372$		0			0
$373$		−	27.8899i		−	1.44408i	−0.691849	−	0.722042i	$-0.743204\pi$
$373$		−	27.8899i		−	1.44408i	0.691849	−	0.722042i	$-0.256796\pi$
$374$	−1.43333			−0.0741157
$375$		0			0
$376$		−	6.30775i		−	0.325298i
$377$			11.2476i			0.579280i
$378$		0			0
$379$	−5.73365			−0.294518			−0.147259	−	0.989098i	$-0.547045\pi$
$379$	−5.73365			−0.294518			−0.147259	+	0.989098i	$0.547045\pi$
$380$	−5.12507	+	5.44804i	−0.262911	+	0.279479i
$381$		0			0
$382$		−	23.0954i		−	1.18166i
$383$	17.8363			0.911391			0.455696	−	0.890136i	$-0.349391\pi$
$383$	17.8363			0.911391			0.455696	+	0.890136i	$0.349391\pi$
$384$		0			0
$385$	3.50140	−	3.72205i	0.178448	−	0.189693i
$386$	−12.4951			−0.635985
$387$		0			0
$388$	0.403430			0.0204811
$389$		−	29.8974i		−	1.51586i	−0.652337	−	0.757929i	$-0.726211\pi$
$389$		−	29.8974i		−	1.51586i	0.652337	−	0.757929i	$-0.273789\pi$
$390$		0			0
$391$	−1.06446			−0.0538318
$392$	−5.50840			−0.278216
$393$		0			0
$394$		−	5.51302i		−	0.277742i
$395$	−15.8319	+	16.8296i	−0.796589	+	0.846789i
$396$		0			0
$397$		−	13.2064i		−	0.662812i	−0.943488	−	0.331406i	$-0.892477\pi$
$397$		−	13.2064i		−	0.662812i	0.943488	−	0.331406i	$-0.107523\pi$
$398$		−	18.8033i		−	0.942523i
$399$		0			0
$400$	0.305180	+	4.99068i	0.0152590	+	0.249534i
$401$			23.0269i			1.14991i	0.818185	+	0.574954i	$0.194980\pi$
$401$			23.0269i			1.14991i	−0.818185	+	0.574954i	$0.805020\pi$
$402$		0			0
$403$			26.7539i			1.33271i
$404$	19.3724			0.963812
$405$		0			0
$406$	2.11176			0.104805
$407$	3.30453	+	10.8918i	0.163800	+	0.539888i
$408$		0			0
$409$			9.77049i			0.483120i	0.970386	+	0.241560i	$0.0776590\pi$
$409$			9.77049i			0.483120i	−0.970386	+	0.241560i	$0.922341\pi$
$410$	−6.08949	−	5.72849i	−0.300739	−	0.282910i
$411$		0			0
$412$	5.56165			0.274003
$413$	12.9049			0.635006
$414$		0			0
$415$	0.0100633	−	0.0106975i	0.000493988	−	0.000525118i
$416$	6.50491			0.318930
$417$		0			0
$418$		−	6.25931i		−	0.306153i
$419$	−2.06109			−0.100691			−0.0503455	−	0.998732i	$-0.516032\pi$
$419$	−2.06109			−0.100691			−0.0503455	+	0.998732i	$0.516032\pi$
$420$		0			0
$421$		−	12.8910i		−	0.628271i	−0.949378	−	0.314135i	$-0.898285\pi$
$421$		−	12.8910i		−	0.628271i	0.949378	−	0.314135i	$-0.101715\pi$
$422$	26.6632			1.29794
$423$		0			0
$424$		−	2.57768i		−	0.125183i
$425$	−0.233766	−	3.82283i	−0.0113393	−	0.185434i
$426$		0			0
$427$	13.6237			0.659296
$428$		−	1.93484i		−	0.0935241i
$429$		0			0
$430$	−8.01006	−	7.53521i	−0.386280	−	0.363380i
$431$		−	9.41662i		−	0.453582i	−0.973943	−	0.226791i	$-0.927176\pi$
$431$		−	9.41662i		−	0.453582i	0.973943	−	0.226791i	$-0.0728235\pi$
$432$		0			0
$433$		−	3.07581i		−	0.147814i	−0.997265	−	0.0739069i	$-0.976453\pi$
$433$		−	3.07581i		−	0.147814i	0.997265	−	0.0739069i	$-0.0235468\pi$
$434$	5.02311			0.241117
$435$		0			0
$436$			8.70619i			0.416951i
$437$		−	4.64844i		−	0.222365i
$438$		0			0
$439$		−	1.93763i		−	0.0924780i	−0.998930	−	0.0462390i	$-0.985276\pi$
$439$		−	1.93763i		−	0.0924780i	0.998930	−	0.0462390i	$-0.0147236\pi$
$440$	−3.04759	−	2.86692i	−0.145288	−	0.136675i
$441$		0			0
$442$	−4.98272			−0.237004
$443$		−	26.5690i		−	1.26233i	−0.775649	−	0.631165i	$-0.782577\pi$
$443$		−	26.5690i		−	1.26233i	0.775649	−	0.631165i	$-0.217423\pi$
$444$		0			0
$445$	−7.20320	+	7.65713i	−0.341465	+	0.362983i
$446$		−	10.8630i		−	0.514379i
$447$		0			0
$448$		−	1.22131i		−	0.0577015i
$449$		−	0.777045i		−	0.0366710i	−0.999832	−	0.0183355i	$-0.994163\pi$
$449$		−	0.777045i		−	0.0366710i	0.999832	−	0.0183355i	$-0.00583670\pi$
$450$		0			0
$451$	6.99627			0.329442
$452$	−14.7585			−0.694183
$453$		0			0
$454$	−6.82427			−0.320279
$455$	12.1720	−	12.9391i	0.570633	−	0.606593i
$456$		0			0
$457$	−21.1753			−0.990537			−0.495268	−	0.868740i	$-0.664930\pi$
$457$	−21.1753			−0.990537			−0.495268	+	0.868740i	$0.664930\pi$
$458$	−2.56189			−0.119709
$459$		0			0
$460$	−2.26327	−	2.12910i	−0.105526	−	0.0992699i
$461$			23.9797i			1.11685i	0.829556	+	0.558424i	$0.188594\pi$
$461$			23.9797i			1.11685i	−0.829556	+	0.558424i	$0.811406\pi$
$462$		0			0
$463$	25.1591			1.16924			0.584622	−	0.811306i	$-0.301243\pi$
$463$	25.1591			1.16924			0.584622	+	0.811306i	$0.301243\pi$
$464$		−	1.72909i		−	0.0802711i
$465$		0			0
$466$			23.3423i			1.08131i
$467$	15.6162			0.722632			0.361316	−	0.932443i	$-0.382328\pi$
$467$	15.6162			0.722632			0.361316	+	0.932443i	$0.382328\pi$
$468$		0			0
$469$	−13.5833			−0.627218
$470$	−9.66427	+	10.2733i	−0.445780	+	0.473872i
$471$		0			0
$472$		−	10.5664i		−	0.486358i
$473$	9.20284			0.423147
$474$		0			0
$475$	16.6942	−	1.02085i	0.765981	−	0.0468398i
$476$			0.935517i			0.0428793i
$477$		0			0
$478$			5.19256i			0.237502i
$479$			31.4974i			1.43915i	0.694414	+	0.719576i	$0.255664\pi$
$479$			31.4974i			1.43915i	−0.694414	+	0.719576i	$0.744336\pi$
$480$		0			0
$481$	11.4876	+	37.8635i	0.523791	+	1.72643i
$482$		−	15.5243i		−	0.707114i
$483$		0			0
$484$	−7.49860			−0.340845
$485$	−0.657058	−	0.618106i	−0.0298355	−	0.0280667i
$486$		0			0
$487$	−24.2768			−1.10009			−0.550043	−	0.835137i	$-0.685389\pi$
$487$	−24.2768			−1.10009			−0.550043	+	0.835137i	$0.685389\pi$
$488$		−	11.1550i		−	0.504961i
$489$		0			0
$490$	8.97140	+	8.43956i	0.405287	+	0.381260i
$491$	−16.5129			−0.745218			−0.372609	−	0.927988i	$-0.621537\pi$
$491$	−16.5129			−0.745218			−0.372609	+	0.927988i	$0.621537\pi$
$492$		0			0
$493$			1.32447i			0.0596513i
$494$		−	21.7594i		−	0.979001i
$495$		0			0
$496$		−	4.11288i		−	0.184674i
$497$			1.17628i			0.0527632i
$498$		0			0
$499$			22.8436i			1.02262i	0.859397	+	0.511310i	$0.170839\pi$
$499$			22.8436i			1.02262i	−0.859397	+	0.511310i	$0.829161\pi$
$500$	7.14931	−	8.59578i	0.319727	−	0.384415i
$501$		0			0
$502$		−	3.85199i		−	0.171923i
$503$	−37.0666			−1.65272			−0.826359	−	0.563144i	$-0.809592\pi$
$503$	−37.0666			−1.65272			−0.826359	+	0.563144i	$0.809592\pi$
$504$		0			0
$505$	−31.5514	−	29.6809i	−1.40402	−	1.32078i
$506$	2.60030			0.115597
$507$		0			0
$508$			11.1280i			0.493727i
$509$	−20.0939			−0.890645			−0.445323	−	0.895370i	$-0.646911\pi$
$509$	−20.0939			−0.890645			−0.445323	+	0.895370i	$0.646911\pi$
$510$		0			0
$511$	11.0299			0.487934
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−3.34529			−0.147554
$515$	−9.05813	−	8.52114i	−0.399149	−	0.375486i
$516$		0			0
$517$		−	11.8031i		−	0.519099i
$518$	7.10896	−	2.15683i	0.312350	−	0.0947656i
$519$		0			0
$520$	−10.5944	−	9.96634i	−0.464595	−	0.437053i
$521$	−32.3101			−1.41553			−0.707766	−	0.706447i	$-0.750297\pi$
$521$	−32.3101			−1.41553			−0.707766	+	0.706447i	$0.750297\pi$
$522$		0			0
$523$	38.5348			1.68501			0.842505	−	0.538688i	$-0.181080\pi$
$523$	38.5348			1.68501			0.842505	+	0.538688i	$0.181080\pi$
$524$		−	12.8363i		−	0.560758i
$525$		0			0
$526$			1.14405i			0.0498831i
$527$			3.15044i			0.137235i
$528$		0			0
$529$	−21.0689			−0.916039
$530$	−3.94934	+	4.19821i	−0.171548	+	0.182359i
$531$		0			0
$532$	−4.08537			−0.177123
$533$	24.3213			1.05347
$534$		0			0
$535$	−2.96442	+	3.15123i	−0.128163	+	0.136240i
$536$			11.1219i			0.480392i
$537$		0			0
$538$	15.1344			0.652490
$539$	−10.3073			−0.443968
$540$		0			0
$541$			40.6354i			1.74705i	0.486776	+	0.873527i	$0.338173\pi$
$541$			40.6354i			1.74705i	−0.486776	+	0.873527i	$0.661827\pi$
$542$	18.2842			0.785374
$543$		0			0
$544$	0.765994			0.0328417
$545$	13.3390	−	14.1796i	0.571379	−	0.607386i
$546$		0			0
$547$	26.6260			1.13845			0.569223	−	0.822183i	$-0.307244\pi$
$547$	26.6260			1.13845			0.569223	+	0.822183i	$0.307244\pi$
$548$			12.0355i			0.514129i
$549$		0			0
$550$	0.571054	+	9.33857i	0.0243498	+	0.398198i
$551$	−5.78394			−0.246404
$552$		0			0
$553$	−12.6202			−0.536664
$554$	2.58352			0.109763
$555$		0			0
$556$	−9.78562			−0.415003
$557$	−31.8613			−1.35001			−0.675004	−	0.737814i	$-0.735858\pi$
$557$	−31.8613			−1.35001			−0.675004	+	0.737814i	$0.735858\pi$
$558$		0			0
$559$	31.9921			1.35312
$560$	−1.87120	+	1.98912i	−0.0790727	+	0.0840557i
$561$		0			0
$562$		−	19.3056i		−	0.814360i
$563$	−0.477178			−0.0201107			−0.0100553	−	0.999949i	$-0.503201\pi$
$563$	−0.477178			−0.0201107			−0.0100553	+	0.999949i	$0.503201\pi$
$564$		0			0
$565$	24.0369	+	22.6119i	1.01124	+	0.951291i
$566$	9.02942			0.379535
$567$		0			0
$568$	0.963126			0.0404119
$569$		−	10.3567i		−	0.434175i	−0.976152	−	0.217087i	$-0.930344\pi$
$569$		−	10.3567i		−	0.434175i	0.976152	−	0.217087i	$-0.0696557\pi$
$570$		0			0
$571$	−1.56306			−0.0654119			−0.0327059	−	0.999465i	$-0.510412\pi$
$571$	−1.56306			−0.0654119			−0.0327059	+	0.999465i	$0.510412\pi$
$572$	12.1720			0.508937
$573$		0			0
$574$		−	4.56638i		−	0.190597i
$575$	0.424091	+	6.93524i	0.0176858	+	0.289220i
$576$		0			0
$577$	19.1344			0.796575			0.398287	−	0.917261i	$-0.369605\pi$
$577$	19.1344			0.796575			0.398287	+	0.917261i	$0.369605\pi$
$578$	16.4133			0.682701
$579$		0			0
$580$	−2.64919	+	2.81613i	−0.110001	+	0.116934i
$581$	0.00802181			0.000332801
$582$		0			0
$583$		−	4.82337i		−	0.199763i
$584$		−	9.03119i		−	0.373713i
$585$		0			0
$586$		−	13.0845i		−	0.540516i
$587$	7.16828			0.295867			0.147933	−	0.988997i	$-0.452738\pi$
$587$	7.16828			0.295867			0.147933	+	0.988997i	$0.452738\pi$
$588$		0			0
$589$	−13.7579			−0.566884
$590$	−16.1890	+	17.2092i	−0.666492	+	0.708493i
$591$		0			0
$592$	−1.76599	−	5.82076i	−0.0725819	−	0.239232i
$593$		−	36.6287i		−	1.50416i	−0.659071	−	0.752081i	$-0.729050\pi$
$593$		−	36.6287i		−	1.50416i	0.659071	−	0.752081i	$-0.270950\pi$
$594$		0			0
$595$	1.43333	−	1.52366i	0.0587608	−	0.0624638i
$596$	11.8876			0.486934
$597$		0			0
$598$	9.03948			0.369652
$599$	−38.3505			−1.56696			−0.783480	−	0.621417i	$-0.786557\pi$
$599$	−38.3505			−1.56696			−0.783480	+	0.621417i	$0.786557\pi$
$600$		0			0
$601$	−20.5311			−0.837480			−0.418740	−	0.908106i	$-0.637528\pi$
$601$	−20.5311			−0.837480			−0.418740	+	0.908106i	$0.637528\pi$
$602$		−	6.00658i		−	0.244810i
$603$		0			0
$604$	21.3141			0.867259
$605$	12.2128	+	11.4888i	0.496521	+	0.467086i
$606$		0			0
$607$	35.3953			1.43665			0.718326	−	0.695706i	$-0.244909\pi$
$607$	35.3953			1.43665			0.718326	+	0.695706i	$0.244909\pi$
$608$			3.34507i			0.135661i
$609$		0			0
$610$	−17.0908	+	18.1678i	−0.691986	+	0.735594i
$611$		−	41.0314i		−	1.65995i
$612$		0			0
$613$		−	10.3293i		−	0.417198i	−0.978001	−	0.208599i	$-0.933110\pi$
$613$		−	10.3293i		−	0.417198i	0.978001	−	0.208599i	$-0.0668904\pi$
$614$		−	7.60942i		−	0.307091i
$615$		0			0
$616$		−	2.28532i		−	0.0920782i
$617$			2.91338i			0.117288i	0.998279	+	0.0586441i	$0.0186777\pi$
$617$			2.91338i			0.117288i	−0.998279	+	0.0586441i	$0.981322\pi$
$618$		0			0
$619$	30.7715			1.23681			0.618405	−	0.785860i	$-0.287779\pi$
$619$	30.7715			1.23681			0.618405	+	0.785860i	$0.287779\pi$
$620$	−6.30145	+	6.69856i	−0.253072	+	0.269021i
$621$		0			0
$622$		−	15.2359i		−	0.610905i
$623$	−5.74193			−0.230045
$624$		0			0
$625$	−24.8137	+	3.04611i	−0.992549	+	0.121844i
$626$	−10.0000			−0.399680
$627$		0			0
$628$			15.3009i			0.610573i
$629$	1.35274	+	4.45867i	0.0539373	+	0.177779i
$630$		0			0
$631$			12.8167i			0.510225i	0.966911	+	0.255113i	$0.0821126\pi$
$631$			12.8167i			0.510225i	−0.966911	+	0.255113i	$0.917887\pi$
$632$			10.3333i			0.411036i
$633$		0			0
$634$		−	34.1403i		−	1.35589i
$635$	17.0495	−	18.1240i	0.676591	−	0.719228i
$636$		0			0
$637$	−35.8316			−1.41970
$638$		−	3.23548i		−	0.128094i
$639$		0			0
$640$	1.62868	+	1.53213i	0.0643791	+	0.0605626i
$641$	−39.8277			−1.57310			−0.786550	−	0.617527i	$-0.788135\pi$
$641$	−39.8277			−1.57310			−0.786550	+	0.617527i	$0.788135\pi$
$642$		0			0
$643$	15.9821			0.630273			0.315137	−	0.949046i	$-0.397950\pi$
$643$	15.9821			0.630273			0.315137	+	0.949046i	$0.397950\pi$
$644$		−	1.69718i		−	0.0668784i
$645$		0			0
$646$		−	2.56230i		−	0.100812i
$647$	37.8647			1.48861			0.744307	−	0.667838i	$-0.232780\pi$
$647$	37.8647			1.48861			0.744307	+	0.667838i	$0.232780\pi$
$648$		0			0
$649$		−	19.7719i		−	0.776113i
$650$	1.98517	+	32.4639i	0.0778648	+	1.27334i
$651$		0			0
$652$	14.9177			0.584221
$653$	−9.60006			−0.375679			−0.187840	−	0.982200i	$-0.560149\pi$
$653$	−9.60006			−0.375679			−0.187840	+	0.982200i	$0.560149\pi$
$654$		0			0
$655$	−19.6669	+	20.9062i	−0.768449	+	0.816875i
$656$	−3.73892			−0.145980
$657$		0			0
$658$	−7.70373			−0.300323
$659$	−30.3448			−1.18207			−0.591033	−	0.806647i	$-0.701280\pi$
$659$	−30.3448			−1.18207			−0.591033	+	0.806647i	$0.701280\pi$
$660$		0			0
$661$		−	28.0304i		−	1.09026i	−0.838353	−	0.545128i	$-0.816481\pi$
$661$		−	28.0304i		−	1.09026i	0.838353	−	0.545128i	$-0.183519\pi$
$662$		−	27.2567i		−	1.05936i
$663$		0			0
$664$		−	0.00656819i		−	0.000254895i
$665$	6.65375	+	6.25931i	0.258022	+	0.242725i
$666$		0			0
$667$		−	2.40281i		−	0.0930374i
$668$	17.3041			0.669514
$669$		0			0
$670$	17.0401	−	18.1140i	0.658318	−	0.699804i
$671$		−	20.8732i		−	0.805800i
$672$		0			0
$673$			1.70175i			0.0655975i	0.999462	+	0.0327987i	$0.0104420\pi$
$673$			1.70175i			0.0655975i	−0.999462	+	0.0327987i	$0.989558\pi$
$674$			22.5315i			0.867879i
$675$		0			0
$676$	29.3139			1.12746
$677$			3.49272i			0.134236i	0.997745	+	0.0671180i	$0.0213804\pi$
$677$			3.49272i			0.134236i	−0.997745	+	0.0671180i	$0.978620\pi$
$678$		0			0
$679$		−	0.492714i		−	0.0189086i
$680$	−1.24756	−	1.17360i	−0.0478416	−	0.0450055i
$681$		0			0
$682$		−	7.69603i		−	0.294696i
$683$	−18.9186			−0.723901			−0.361950	−	0.932197i	$-0.617889\pi$
$683$	−18.9186			−0.723901			−0.361950	+	0.932197i	$0.617889\pi$
$684$		0			0
$685$	18.4398	−	19.6019i	0.704550	−	0.748949i
$686$			15.2766i			0.583265i
$687$		0			0
$688$	−4.91814			−0.187502
$689$		−	16.7676i		−	0.638795i
$690$		0			0
$691$	4.56018			0.173477			0.0867386	−	0.996231i	$-0.472355\pi$
$691$	4.56018			0.173477			0.0867386	+	0.996231i	$0.472355\pi$
$692$		−	19.7322i		−	0.750107i
$693$		0			0
$694$	34.7252			1.31815
$695$	15.9376	+	14.9928i	0.604548	+	0.568709i
$696$		0			0
$697$	2.86399			0.108481
$698$	−15.9343			−0.603121
$699$		0			0
$700$	6.09517	−	0.372720i	0.230376	−	0.0140875i
$701$		−	18.9895i		−	0.717224i	−0.933487	−	0.358612i	$-0.883250\pi$
$701$		−	18.9895i		−	0.717224i	0.933487	−	0.358612i	$-0.116750\pi$
$702$		0			0
$703$	−19.4709	+	5.90737i	−0.734357	+	0.222801i
$704$	−1.87120			−0.0705236
$705$		0			0
$706$	−20.1925			−0.759956
$707$		−	23.6597i		−	0.889815i
$708$		0			0
$709$			10.8195i			0.406336i	0.979144	+	0.203168i	$0.0651238\pi$
$709$			10.8195i			0.406336i	−0.979144	+	0.203168i	$0.934876\pi$
$710$	−1.56862	−	1.47563i	−0.0588693	−	0.0553794i
$711$		0			0
$712$			4.70144i			0.176194i
$713$		−	5.71542i		−	0.214044i
$714$		0			0
$715$	−19.8243	−	18.6490i	−0.741386	−	0.697435i
$716$		−	3.70357i		−	0.138409i
$717$		0			0
$718$	−30.8657			−1.15190
$719$	8.43399			0.314535			0.157267	−	0.987556i	$-0.449732\pi$
$719$	8.43399			0.314535			0.157267	+	0.987556i	$0.449732\pi$
$720$		0			0
$721$		−	6.79250i		−	0.252966i
$722$	−7.81050			−0.290677
$723$		0			0
$724$	−10.4093			−0.386857
$725$	8.62934	−	0.527685i	0.320486	−	0.0195977i
$726$		0			0
$727$	16.7156			0.619947			0.309974	−	0.950745i	$-0.399680\pi$
$727$	16.7156			0.619947			0.309974	+	0.950745i	$0.399680\pi$
$728$		−	7.94452i		−	0.294444i
$729$		0			0
$730$	−13.8369	+	14.7089i	−0.512128	+	0.544401i
$731$	3.76726			0.139337
$732$		0			0
$733$		−	10.4157i		−	0.384711i	−0.981325	−	0.192356i	$-0.938387\pi$
$733$		−	10.4157i		−	0.384711i	0.981325	−	0.192356i	$-0.0616127\pi$
$734$		−	28.9254i		−	1.06766i
$735$		0			0
$736$	−1.38964			−0.0512228
$737$			20.8113i			0.766594i
$738$		0			0
$739$	−19.7975			−0.728261			−0.364131	−	0.931348i	$-0.618634\pi$
$739$	−19.7975			−0.728261			−0.364131	+	0.931348i	$0.618634\pi$
$740$	−6.04191	+	12.1859i	−0.222105	+	0.447961i
$741$		0			0
$742$	−3.14815			−0.115572
$743$			34.4142i			1.26253i	0.775566	+	0.631267i	$0.217465\pi$
$743$			34.4142i			1.26253i	−0.775566	+	0.631267i	$0.782535\pi$
$744$		0			0
$745$	−19.3610	−	18.2133i	−0.709333	−	0.667282i
$746$			27.8899i			1.02112i
$747$		0			0
$748$	1.43333			0.0524077
$749$	−2.36304			−0.0863437
$750$		0			0
$751$	−40.7020			−1.48524			−0.742618	−	0.669715i	$-0.766416\pi$
$751$	−40.7020			−1.48524			−0.742618	+	0.669715i	$0.766416\pi$
$752$			6.30775i			0.230020i
$753$		0			0
$754$		−	11.2476i		−	0.409613i
$755$	−34.7138	−	32.6559i	−1.26337	−	1.18847i
$756$		0			0
$757$	−2.06470			−0.0750426			−0.0375213	−	0.999296i	$-0.511946\pi$
$757$	−2.06470			−0.0750426			−0.0375213	+	0.999296i	$0.511946\pi$
$758$	5.73365			0.208256
$759$		0			0
$760$	5.12507	−	5.44804i	0.185906	−	0.197621i
$761$	−9.07263			−0.328883			−0.164441	−	0.986387i	$-0.552582\pi$
$761$	−9.07263			−0.328883			−0.164441	+	0.986387i	$0.552582\pi$
$762$		0			0
$763$	10.6330			0.384939
$764$			23.0954i			0.835563i
$765$		0			0
$766$	−17.8363			−0.644451
$767$		−	68.7335i		−	2.48182i
$768$		0			0
$769$		−	50.9991i		−	1.83907i	−0.393002	−	0.919537i	$-0.628564\pi$
$769$		−	50.9991i		−	1.83907i	0.393002	−	0.919537i	$-0.371436\pi$
$770$	−3.50140	+	3.72205i	−0.126182	+	0.134133i
$771$		0			0
$772$	12.4951			0.449709
$773$		−	40.9981i		−	1.47460i	−0.675565	−	0.737300i	$-0.736100\pi$
$773$		−	40.9981i		−	1.47460i	0.675565	−	0.737300i	$-0.263900\pi$
$774$		0			0
$775$	20.5261	−	1.25517i	0.737318	−	0.0450870i
$776$	−0.403430			−0.0144823
$777$		0			0
$778$			29.8974i			1.07187i
$779$			12.5069i			0.448108i
$780$		0			0
$781$	1.80220			0.0644879
$782$	1.06446			0.0380648
$783$		0			0
$784$	5.50840			0.196729
$785$	23.4429	−	24.9202i	0.836713	−	0.889441i
$786$		0			0
$787$		−	30.4357i		−	1.08492i	−0.840083	−	0.542458i	$-0.817494\pi$
$787$		−	30.4357i		−	1.08492i	0.840083	−	0.542458i	$-0.182506\pi$
$788$			5.51302i			0.196393i
$789$		0			0
$790$	15.8319	−	16.8296i	0.563274	−	0.598770i
$791$			18.0248i			0.640887i
$792$		0			0
$793$		−	72.5620i		−	2.57675i
$794$			13.2064i			0.468679i
$795$		0			0
$796$			18.8033i			0.666464i
$797$	0.999495			0.0354039			0.0177020	−	0.999843i	$-0.494365\pi$
$797$	0.999495			0.0354039			0.0177020	+	0.999843i	$0.494365\pi$
$798$		0			0
$799$		−	4.83170i		−	0.170933i
$800$	−0.305180	−	4.99068i	−0.0107898	−	0.176447i
$801$		0			0
$802$		−	23.0269i		−	0.813108i
$803$		−	16.8992i		−	0.596360i
$804$		0			0
$805$	−2.60030	+	2.76416i	−0.0916484	+	0.0974239i
$806$		−	26.7539i		−	0.942367i
$807$		0			0
$808$	−19.3724			−0.681518
$809$		−	21.8030i		−	0.766552i	−0.923634	−	0.383276i	$-0.874796\pi$
$809$		−	21.8030i		−	0.766552i	0.923634	−	0.383276i	$-0.125204\pi$
$810$		0			0
$811$	−40.9653			−1.43848			−0.719242	−	0.694759i	$-0.755511\pi$
$811$	−40.9653			−1.43848			−0.719242	+	0.694759i	$0.755511\pi$
$812$	−2.11176			−0.0741082
$813$		0			0
$814$	−3.30453	−	10.8918i	−0.115824	−	0.381758i
$815$	−24.2961	−	22.8557i	−0.851054	−	0.800601i
$816$		0			0
$817$			16.4515i			0.575566i
$818$		−	9.77049i		−	0.341617i
$819$		0			0
$820$	6.08949	+	5.72849i	0.212654	+	0.200048i
$821$	−36.2693			−1.26581			−0.632904	−	0.774230i	$-0.718137\pi$
$821$	−36.2693			−1.26581			−0.632904	+	0.774230i	$0.718137\pi$
$822$		0			0
$823$		−	48.5397i		−	1.69199i	−0.533194	−	0.845993i	$-0.679008\pi$
$823$		−	48.5397i		−	1.69199i	0.533194	−	0.845993i	$-0.320992\pi$
$824$	−5.56165			−0.193749
$825$		0			0
$826$	−12.9049			−0.449017
$827$	−39.6895			−1.38014			−0.690069	−	0.723743i	$-0.742420\pi$
$827$	−39.6895			−1.38014			−0.690069	+	0.723743i	$0.742420\pi$
$828$		0			0
$829$		−	53.4506i		−	1.85641i	−0.372064	−	0.928207i	$-0.621350\pi$
$829$		−	53.4506i		−	1.85641i	0.372064	−	0.928207i	$-0.378650\pi$
$830$	−0.0100633	+	0.0106975i	−0.000349302	+	0.000371315i
$831$		0			0
$832$	−6.50491			−0.225517
$833$	−4.21940			−0.146194
$834$		0			0
$835$	−28.1827	−	26.5120i	−0.975303	−	0.917485i
$836$			6.25931i			0.216483i
$837$		0			0
$838$	2.06109			0.0711993
$839$	33.5857			1.15951			0.579753	−	0.814792i	$-0.303149\pi$
$839$	33.5857			1.15951			0.579753	+	0.814792i	$0.303149\pi$
$840$		0			0
$841$	26.0102			0.896905
$842$			12.8910i			0.444255i
$843$		0			0
$844$	−26.6632			−0.917784
$845$	−47.7428	−	44.9125i	−1.64240	−	1.54504i
$846$		0			0
$847$			9.15813i			0.314677i
$848$			2.57768i			0.0885180i
$849$		0			0
$850$	0.233766	+	3.82283i	0.00801811	+	0.131122i
$851$	−2.45409	−	8.08876i	−0.0841253	−	0.277279i
$852$		0			0
$853$	0.641846			0.0219764			0.0109882	−	0.999940i	$-0.496502\pi$
$853$	0.641846			0.0219764			0.0109882	+	0.999940i	$0.496502\pi$
$854$	−13.6237			−0.466192
$855$		0			0
$856$			1.93484i			0.0661315i
$857$	−20.5938			−0.703470			−0.351735	−	0.936100i	$-0.614408\pi$
$857$	−20.5938			−0.703470			−0.351735	+	0.936100i	$0.614408\pi$
$858$		0			0
$859$			6.18892i			0.211163i	0.994411	+	0.105582i	$0.0336704\pi$
$859$			6.18892i			0.211163i	−0.994411	+	0.105582i	$0.966330\pi$
$860$	8.01006	+	7.53521i	0.273141	+	0.256949i
$861$		0			0
$862$			9.41662i			0.320731i
$863$			48.8873i			1.66414i	0.554669	+	0.832071i	$0.312845\pi$
$863$			48.8873i			1.66414i	−0.554669	+	0.832071i	$0.687155\pi$
$864$		0			0
$865$	−30.2323	+	32.1374i	−1.02793	+	1.09271i
$866$			3.07581i			0.104520i
$867$		0			0
$868$	−5.02311			−0.170495
$869$			19.3357i			0.655918i
$870$		0			0
$871$			72.3469i			2.45138i
$872$		−	8.70619i		−	0.294829i
$873$		0			0
$874$			4.64844i			0.157236i
$875$	−10.4981	−	8.73153i	−0.354901	−	0.295180i
$876$		0			0
$877$		−	2.65696i		−	0.0897190i	−0.998993	−	0.0448595i	$-0.985716\pi$
$877$		−	2.65696i		−	0.0897190i	0.998993	−	0.0448595i	$-0.0142840\pi$
$878$			1.93763i			0.0653918i
$879$		0			0
$880$	3.04759	+	2.86692i	0.102734	+	0.0966438i
$881$	1.97718			0.0666130			0.0333065	−	0.999445i	$-0.489396\pi$
$881$	1.97718			0.0666130			0.0333065	+	0.999445i	$0.489396\pi$
$882$		0			0
$883$	−35.6965			−1.20128			−0.600641	−	0.799519i	$-0.705088\pi$
$883$	−35.6965			−1.20128			−0.600641	+	0.799519i	$0.705088\pi$
$884$	4.98272			0.167587
$885$		0			0
$886$			26.5690i			0.892602i
$887$			0.181192i			0.00608382i	0.999995	+	0.00304191i	$0.000968271\pi$
$887$			0.181192i			0.00608382i	−0.999995	+	0.00304191i	$0.999032\pi$
$888$		0			0
$889$	13.5908			0.455820
$890$	7.20320	−	7.65713i	0.241452	−	0.256668i
$891$		0			0
$892$			10.8630i			0.363721i
$893$	21.0999			0.706081
$894$		0			0
$895$	−5.67434	+	6.03192i	−0.189672	+	0.201625i
$896$			1.22131i			0.0408011i
$897$		0			0
$898$			0.777045i			0.0259303i
$899$	−7.11155			−0.237184
$900$		0			0
$901$		−	1.97449i		−	0.0657798i
$902$	−6.99627			−0.232950
$903$		0			0
$904$	14.7585			0.490862
$905$	16.9533	+	15.9483i	0.563548	+	0.530139i
$906$		0			0
$907$	−28.0542			−0.931525			−0.465762	−	0.884910i	$-0.654220\pi$
$907$	−28.0542			−0.931525			−0.465762	+	0.884910i	$0.654220\pi$
$908$	6.82427			0.226471
$909$		0			0
$910$	−12.1720	+	12.9391i	−0.403498	+	0.428926i
$911$			33.0379i			1.09459i	0.836939	+	0.547297i	$0.184343\pi$
$911$			33.0379i			1.09459i	−0.836939	+	0.547297i	$0.815657\pi$
$912$		0			0
$913$		−	0.0122904i		−	0.000406754i
$914$	21.1753			0.700415
$915$		0			0
$916$	2.56189			0.0846471
$917$	−15.6772			−0.517705
$918$		0			0
$919$		−	24.1489i		−	0.796600i	−0.917255	−	0.398300i	$-0.869600\pi$
$919$		−	24.1489i		−	0.796600i	0.917255	−	0.398300i	$-0.130400\pi$
$920$	2.26327	+	2.12910i	0.0746180	+	0.0701944i
$921$		0			0
$922$		−	23.9797i		−	0.789731i
$923$	6.26505			0.206217
$924$		0			0
$925$	28.5106	−	10.5899i	0.937423	−	0.348193i
$926$	−25.1591			−0.826781
$927$		0			0
$928$			1.72909i			0.0567602i
$929$	−30.9086			−1.01408			−0.507039	−	0.861923i	$-0.669260\pi$
$929$	−30.9086			−1.01408			−0.507039	+	0.861923i	$0.669260\pi$
$930$		0			0
$931$		−	18.4260i		−	0.603887i
$932$		−	23.3423i		−	0.764603i
$933$		0			0
$934$	−15.6162			−0.510978
$935$	−2.33443	−	2.19604i	−0.0763441	−	0.0718182i
$936$		0			0
$937$			33.6530i			1.09940i	0.835363	+	0.549698i	$0.185257\pi$
$937$			33.6530i			1.09940i	−0.835363	+	0.549698i	$0.814743\pi$
$938$	13.5833			0.443510
$939$		0			0
$940$	9.66427	−	10.2733i	0.315214	−	0.335078i
$941$	33.8242			1.10264			0.551319	−	0.834294i	$-0.314125\pi$
$941$	33.8242			1.10264			0.551319	+	0.834294i	$0.314125\pi$
$942$		0			0
$943$	−5.19575			−0.169197
$944$			10.5664i			0.343907i
$945$		0			0
$946$	−9.20284			−0.299210
$947$	17.3591			0.564095			0.282048	−	0.959400i	$-0.408986\pi$
$947$	17.3591			0.564095			0.282048	+	0.959400i	$0.408986\pi$
$948$		0			0
$949$		−	58.7471i		−	1.90701i
$950$	−16.6942	+	1.02085i	−0.541630	+	0.0331207i
$951$		0			0
$952$		−	0.935517i		−	0.0303203i
$953$		−	15.0520i		−	0.487582i	−0.969828	−	0.243791i	$-0.921609\pi$
$953$		−	15.0520i		−	0.487582i	0.969828	−	0.243791i	$-0.0783911\pi$
$954$		0			0
$955$	35.3851	−	37.6150i	1.14503	−	1.21719i
$956$		−	5.19256i		−	0.167940i
$957$		0			0
$958$		−	31.4974i		−	1.01763i
$959$	14.6990			0.474657
$960$		0			0
$961$	14.0842			0.454329
$962$	−11.4876	−	37.8635i	−0.370376	−	1.22077i
$963$		0			0
$964$			15.5243i			0.500005i
$965$	−20.3505	−	19.1441i	−0.655106	−	0.616270i
$966$		0			0
$967$	−23.3045			−0.749423			−0.374712	−	0.927141i	$-0.622258\pi$
$967$	−23.3045			−0.749423			−0.374712	+	0.927141i	$0.622258\pi$
$968$	7.49860			0.241014
$969$		0			0
$970$	0.657058	+	0.618106i	0.0210969	+	0.0198462i
$971$	40.7911			1.30905			0.654524	−	0.756041i	$-0.272869\pi$
$971$	40.7911			1.30905			0.654524	+	0.756041i	$0.272869\pi$
$972$		0			0
$973$			11.9513i			0.383140i
$974$	24.2768			0.777878
$975$		0			0
$976$			11.1550i			0.357061i
$977$	−2.64739			−0.0846976			−0.0423488	−	0.999103i	$-0.513484\pi$
$977$	−2.64739			−0.0846976			−0.0423488	+	0.999103i	$0.513484\pi$
$978$		0			0
$979$			8.79735i			0.281165i
$980$	−8.97140	−	8.43956i	−0.286581	−	0.269592i
$981$		0			0
$982$	16.5129			0.526949
$983$			27.8528i			0.888367i	0.895936	+	0.444183i	$0.146506\pi$
$983$			27.8528i			0.888367i	−0.895936	+	0.444183i	$0.853494\pi$
$984$		0			0
$985$	8.44664	−	8.97893i	0.269132	−	0.286093i
$986$		−	1.32447i		−	0.0421798i
$987$		0			0
$988$			21.7594i			0.692258i
$989$	−6.83444			−0.217323
$990$		0			0
$991$			47.8484i			1.51995i	0.649950	+	0.759977i	$0.274790\pi$
$991$			47.8484i			1.51995i	−0.649950	+	0.759977i	$0.725210\pi$
$992$			4.11288i			0.130584i
$993$		0			0
$994$		−	1.17628i		−	0.0373092i
$995$	28.8090	−	30.6245i	0.913306	−	0.970861i
$996$		0			0
$997$	3.95282			0.125187			0.0625936	−	0.998039i	$-0.480063\pi$
$997$	3.95282			0.125187			0.0625936	+	0.998039i	$0.480063\pi$
$998$		−	22.8436i		−	0.723101i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3330.2.e.c.739.3		10
3.2	odd	2		370.2.c.b.369.8	yes	10
5.4	even	2		3330.2.e.d.739.7		10
15.2	even	4		1850.2.d.i.1701.18		20
15.8	even	4		1850.2.d.i.1701.3		20
15.14	odd	2		370.2.c.a.369.3	✓	10
37.36	even	2		3330.2.e.d.739.8		10
111.110	odd	2		370.2.c.a.369.8	yes	10
185.184	even	2	inner	3330.2.e.c.739.4		10
555.332	even	4		1850.2.d.i.1701.8		20
555.443	even	4		1850.2.d.i.1701.13		20
555.554	odd	2		370.2.c.b.369.3	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.c.a.369.3	✓	10	15.14	odd	2
370.2.c.a.369.8	yes	10	111.110	odd	2
370.2.c.b.369.3	yes	10	555.554	odd	2
370.2.c.b.369.8	yes	10	3.2	odd	2
1850.2.d.i.1701.3		20	15.8	even	4
1850.2.d.i.1701.8		20	555.332	even	4
1850.2.d.i.1701.13		20	555.443	even	4
1850.2.d.i.1701.18		20	15.2	even	4
3330.2.e.c.739.3		10	1.1	even	1	trivial
3330.2.e.c.739.4		10	185.184	even	2	inner
3330.2.e.d.739.7		10	5.4	even	2
3330.2.e.d.739.8		10	37.36	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.62868 - 1.53213i) q^{5} -1.22131i q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.62868 - 1.53213i) q^{5} -1.22131i q^{7} -1.00000 q^{8} +(1.62868 + 1.53213i) q^{10} -1.87120 q^{11} -6.50491 q^{13} +1.22131i q^{14} +1.00000 q^{16} -0.765994 q^{17} -3.34507i q^{19} +(-1.62868 - 1.53213i) q^{20} +1.87120 q^{22} +1.38964 q^{23} +(0.305180 + 4.99068i) q^{25} +6.50491 q^{26} -1.22131i q^{28} -1.72909i q^{29} -4.11288i q^{31} -1.00000 q^{32} +0.765994 q^{34} +(-1.87120 + 1.98912i) q^{35} +(-1.76599 - 5.82076i) q^{37} +3.34507i q^{38} +(1.62868 + 1.53213i) q^{40} -3.73892 q^{41} -4.91814 q^{43} -1.87120 q^{44} -1.38964 q^{46} +6.30775i q^{47} +5.50840 q^{49} +(-0.305180 - 4.99068i) q^{50} -6.50491 q^{52} +2.57768i q^{53} +(3.04759 + 2.86692i) q^{55} +1.22131i q^{56} +1.72909i q^{58} +10.5664i q^{59} +11.1550i q^{61} +4.11288i q^{62} +1.00000 q^{64} +(10.5944 + 9.96634i) q^{65} -11.1219i q^{67} -0.765994 q^{68} +(1.87120 - 1.98912i) q^{70} -0.963126 q^{71} +9.03119i q^{73} +(1.76599 + 5.82076i) q^{74} -3.34507i q^{76} +2.28532i q^{77} -10.3333i q^{79} +(-1.62868 - 1.53213i) q^{80} +3.73892 q^{82} +0.00656819i q^{83} +(1.24756 + 1.17360i) q^{85} +4.91814 q^{86} +1.87120 q^{88} -4.70144i q^{89} +7.94452i q^{91} +1.38964 q^{92} -6.30775i q^{94} +(-5.12507 + 5.44804i) q^{95} +0.403430 q^{97} -5.50840 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 10 q^{4} - 3 q^{5} - 10 q^{8}+O(q^{10}) \) 10 * q - 10 * q^2 + 10 * q^4 - 3 * q^5 - 10 * q^8	\( 10 q - 10 q^{2} + 10 q^{4} - 3 q^{5} - 10 q^{8} + 3 q^{10} + 2 q^{13} + 10 q^{16} + 18 q^{17} - 3 q^{20} + 10 q^{23} + 5 q^{25} - 2 q^{26} - 10 q^{32} - 18 q^{34} + 8 q^{37} + 3 q^{40} + 4 q^{41} + 10 q^{43} - 10 q^{46} - 8 q^{49} - 5 q^{50} + 2 q^{52} - 5 q^{55} + 10 q^{64} - 2 q^{65} + 18 q^{68} + 20 q^{71} - 8 q^{74} - 3 q^{80} - 4 q^{82} - 28 q^{85} - 10 q^{86} + 10 q^{92} - 2 q^{95} - 2 q^{97} + 8 q^{98}+O(q^{100}) \) 10 * q - 10 * q^2 + 10 * q^4 - 3 * q^5 - 10 * q^8 + 3 * q^10 + 2 * q^13 + 10 * q^16 + 18 * q^17 - 3 * q^20 + 10 * q^23 + 5 * q^25 - 2 * q^26 - 10 * q^32 - 18 * q^34 + 8 * q^37 + 3 * q^40 + 4 * q^41 + 10 * q^43 - 10 * q^46 - 8 * q^49 - 5 * q^50 + 2 * q^52 - 5 * q^55 + 10 * q^64 - 2 * q^65 + 18 * q^68 + 20 * q^71 - 8 * q^74 - 3 * q^80 - 4 * q^82 - 28 * q^85 - 10 * q^86 + 10 * q^92 - 2 * q^95 - 2 * q^97 + 8 * q^98

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