LMFDB - Embedded newform 2640.2.f.a.1121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2640,2,Mod(1121,2640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2640, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2640.1121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2640 = 2^{4} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2640.f (of order $2$, degree $1$, not 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:	$21.0805061336$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.2051727616.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 37x^{4} + 36x^{2} + 4 $ x^8 + 11x^6 + 37x^4 + 36*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 330)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1121.2
Root			$1.18994i$ of defining polynomial
Character	$\chi$	$=$	2640.1121
Dual form			2640.2.f.a.1121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38699 + 1.03743i) q^{3} -1.00000i q^{5} +0.394100i q^{7} +(0.847487 - 2.87781i) q^{9} +O(q^{10})$	\(q+(-1.38699 + 1.03743i) q^{3} -1.00000i q^{5} +0.394100i q^{7} +(0.847487 - 2.87781i) q^{9} +(3.26480 - 0.584041i) q^{11} +2.37988i q^{13} +(1.03743 + 1.38699i) q^{15} +0.906774 q^{17} -3.69497i q^{19} +(-0.408850 - 0.546613i) q^{21} -3.54796i q^{23} -1.00000 q^{25} +(1.81006 + 4.87070i) q^{27} +3.37573 q^{29} -3.66654 q^{31} +(-3.92234 + 4.19705i) q^{33} +0.394100 q^{35} -4.58753 q^{37} +(-2.46896 - 3.30087i) q^{39} -8.14971 q^{41} -2.60175i q^{43} +(-2.87781 - 0.847487i) q^{45} +3.39825i q^{47} +6.84469 q^{49} +(-1.25769 + 0.940713i) q^{51} +6.45474i q^{53} +(-0.584041 - 3.26480i) q^{55} +(3.83327 + 5.12489i) q^{57} -7.76983i q^{59} -12.8346i q^{61} +(1.13414 + 0.333995i) q^{63} +2.37988 q^{65} +11.9195 q^{67} +(3.68076 + 4.92099i) q^{69} -2.58753i q^{71} -11.8911i q^{73} +(1.38699 - 1.03743i) q^{75} +(0.230170 + 1.28666i) q^{77} -2.56633i q^{79} +(-7.56353 - 4.87781i) q^{81} -1.69767 q^{83} -0.906774i q^{85} +(-4.68211 + 3.50208i) q^{87} +15.3036i q^{89} -0.937911 q^{91} +(5.08545 - 3.80377i) q^{93} -3.69497 q^{95} -10.1213 q^{97} +(1.08612 - 9.89042i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 2 * q^9	$ 8 q - 2 q^{3} + 2 q^{9} - 6 q^{11} - 4 q^{15} + 4 q^{17} - 8 q^{21} - 8 q^{25} + 22 q^{27} - 4 q^{29} + 4 q^{31} - 2 q^{33} - 12 q^{37} + 8 q^{39} - 16 q^{41} - 4 q^{49} + 28 q^{51} + 6 q^{55} + 14 q^{57} - 14 q^{63} + 4 q^{65} + 12 q^{67} + 8 q^{69} + 2 q^{75} + 36 q^{77} + 2 q^{81} + 72 q^{83} + 22 q^{87} + 48 q^{91} + 8 q^{93} - 20 q^{95} - 8 q^{97} + 6 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 + 2 * q^9 - 6 * q^11 - 4 * q^15 + 4 * q^17 - 8 * q^21 - 8 * q^25 + 22 * q^27 - 4 * q^29 + 4 * q^31 - 2 * q^33 - 12 * q^37 + 8 * q^39 - 16 * q^41 - 4 * q^49 + 28 * q^51 + 6 * q^55 + 14 * q^57 - 14 * q^63 + 4 * q^65 + 12 * q^67 + 8 * q^69 + 2 * q^75 + 36 * q^77 + 2 * q^81 + 72 * q^83 + 22 * q^87 + 48 * q^91 + 8 * q^93 - 20 * q^95 - 8 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2640\mathbb{Z}\right)^\times$.

$n$	$661$	$881$	$991$	$1057$	$1201$
$\chi(n)$	$1$	$-1$	$1$	$1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.38699	+	1.03743i	−0.800780	+	0.598959i
$3$	−1.38699	+	1.03743i	−0.800780	+	0.598959i
$4$		0			0
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$			0.394100i			0.148956i	0.997223	+	0.0744779i	$0.0237290\pi$
$7$			0.394100i			0.148956i	−0.997223	+	0.0744779i	$0.976271\pi$
$8$		0			0
$9$	0.847487	−	2.87781i	0.282496	−	0.959269i
$10$		0			0
$11$	3.26480	−	0.584041i	0.984373	−	0.176095i
$11$	3.26480	−	0.584041i	0.984373	−	0.176095i
$12$		0			0
$13$			2.37988i			0.660060i	0.943970	+	0.330030i	$0.107059\pi$
$13$			2.37988i			0.660060i	−0.943970	+	0.330030i	$0.892941\pi$
$14$		0			0
$15$	1.03743	+	1.38699i	0.267863	+	0.358119i
$16$		0			0
$17$	0.906774			0.219925			0.109963	−	0.993936i	$-0.464927\pi$
$17$	0.906774			0.219925			0.109963	+	0.993936i	$0.464927\pi$
$18$		0			0
$19$		−	3.69497i		−	0.847685i	−0.905736	−	0.423843i	$-0.860681\pi$
$19$		−	3.69497i		−	0.847685i	0.905736	−	0.423843i	$-0.139319\pi$
$20$		0			0
$21$	−0.408850	−	0.546613i	−0.0892184	−	0.119281i
$22$		0			0
$23$		−	3.54796i		−	0.739801i	−0.929071	−	0.369901i	$-0.879392\pi$
$23$		−	3.54796i		−	0.739801i	0.929071	−	0.369901i	$-0.120608\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	1.81006	+	4.87070i	0.348346	+	0.937366i
$28$		0			0
$29$	3.37573			0.626857			0.313429	−	0.949612i	$-0.398522\pi$
$29$	3.37573			0.626857			0.313429	+	0.949612i	$0.398522\pi$
$30$		0			0
$31$	−3.66654			−0.658530			−0.329265	−	0.944238i	$-0.606801\pi$
$31$	−3.66654			−0.658530			−0.329265	+	0.944238i	$0.606801\pi$
$32$		0			0
$33$	−3.92234	+	4.19705i	−0.682792	+	0.730613i
$34$		0			0
$35$	0.394100			0.0666150
$36$		0			0
$37$	−4.58753			−0.754185			−0.377093	−	0.926176i	$-0.623076\pi$
$37$	−4.58753			−0.754185			−0.377093	+	0.926176i	$0.623076\pi$
$38$		0			0
$39$	−2.46896	−	3.30087i	−0.395349	−	0.528563i
$40$		0			0
$41$	−8.14971			−1.27277			−0.636386	−	0.771371i	$-0.719571\pi$
$41$	−8.14971			−1.27277			−0.636386	+	0.771371i	$0.719571\pi$
$42$		0			0
$43$		−	2.60175i		−	0.396763i	−0.980125	−	0.198381i	$-0.936432\pi$
$43$		−	2.60175i		−	0.396763i	0.980125	−	0.198381i	$-0.0635685\pi$
$44$		0			0
$45$	−2.87781	−	0.847487i	−0.428998	−	0.126336i
$46$		0			0
$47$			3.39825i			0.495686i	0.968800	+	0.247843i	$0.0797217\pi$
$47$			3.39825i			0.495686i	−0.968800	+	0.247843i	$0.920278\pi$
$48$		0			0
$49$	6.84469			0.977812
$50$		0			0
$51$	−1.25769	+	0.940713i	−0.176111	+	0.131726i
$52$		0			0
$53$			6.45474i			0.886626i	0.896367	+	0.443313i	$0.146197\pi$
$53$			6.45474i			0.886626i	−0.896367	+	0.443313i	$0.853803\pi$
$54$		0			0
$55$	−0.584041	−	3.26480i	−0.0787520	−	0.440225i
$56$		0			0
$57$	3.83327	+	5.12489i	0.507729	+	0.678809i
$58$		0			0
$59$		−	7.76983i		−	1.01155i	−0.862667	−	0.505773i	$-0.831207\pi$
$59$		−	7.76983i		−	1.01155i	0.862667	−	0.505773i	$-0.168793\pi$
$60$		0			0
$61$		−	12.8346i		−	1.64330i	−0.569989	−	0.821652i	$-0.693053\pi$
$61$		−	12.8346i		−	1.64330i	0.569989	−	0.821652i	$-0.306947\pi$
$62$		0			0
$63$	1.13414	+	0.333995i	0.142889	+	0.0420794i
$64$		0			0
$65$	2.37988			0.295188
$66$		0			0
$67$	11.9195			1.45620			0.728102	−	0.685469i	$-0.240403\pi$
$67$	11.9195			1.45620			0.728102	+	0.685469i	$0.240403\pi$
$68$		0			0
$69$	3.68076	+	4.92099i	0.443111	+	0.592418i
$70$		0			0
$71$		−	2.58753i		−	0.307083i	−0.988142	−	0.153542i	$-0.950932\pi$
$71$		−	2.58753i		−	0.307083i	0.988142	−	0.153542i	$-0.0490679\pi$
$72$		0			0
$73$		−	11.8911i		−	1.39175i	−0.718164	−	0.695874i	$-0.755017\pi$
$73$		−	11.8911i		−	1.39175i	0.718164	−	0.695874i	$-0.244983\pi$
$74$		0			0
$75$	1.38699	−	1.03743i	0.160156	−	0.119792i
$76$		0			0
$77$	0.230170	+	1.28666i	0.0262303	+	0.146628i
$78$		0			0
$79$		−	2.56633i		−	0.288735i	−0.989524	−	0.144368i	$-0.953885\pi$
$79$		−	2.56633i		−	0.288735i	0.989524	−	0.144368i	$-0.0461148\pi$
$80$		0			0
$81$	−7.56353	−	4.87781i	−0.840392	−	0.541978i
$82$		0			0
$83$	−1.69767			−0.186344			−0.0931720	−	0.995650i	$-0.529701\pi$
$83$	−1.69767			−0.186344			−0.0931720	+	0.995650i	$0.529701\pi$
$84$		0			0
$85$		−	0.906774i		−	0.0983535i
$86$		0			0
$87$	−4.68211	+	3.50208i	−0.501974	+	0.375462i
$88$		0			0
$89$			15.3036i			1.62218i	0.584924	+	0.811088i	$0.301124\pi$
$89$			15.3036i			1.62218i	−0.584924	+	0.811088i	$0.698876\pi$
$90$		0			0
$91$	−0.937911			−0.0983198
$92$		0			0
$93$	5.08545	−	3.80377i	0.527337	−	0.394432i
$94$		0			0
$95$	−3.69497			−0.379096
$96$		0			0
$97$	−10.1213			−1.02766			−0.513830	−	0.857892i	$-0.671774\pi$
$97$	−10.1213			−1.02766			−0.513830	+	0.857892i	$0.671774\pi$
$98$		0			0
$99$	1.08612	−	9.89042i	0.109159	−	0.994024i
$100$		0			0
$101$	3.01837			0.300339			0.150170	−	0.988660i	$-0.452018\pi$
$101$	3.01837			0.300339			0.150170	+	0.988660i	$0.452018\pi$
$102$		0			0
$103$	−0.601748			−0.0592920			−0.0296460	−	0.999560i	$-0.509438\pi$
$103$	−0.601748			−0.0592920			−0.0296460	+	0.999560i	$0.509438\pi$
$104$		0			0
$105$	−0.546613	+	0.408850i	−0.0533440	+	0.0398997i
$106$		0			0
$107$	15.2456			1.47385			0.736926	−	0.675974i	$-0.236277\pi$
$107$	15.2456			1.47385			0.736926	+	0.675974i	$0.236277\pi$
$108$		0			0
$109$		−	18.3770i		−	1.76020i	−0.474793	−	0.880098i	$-0.657477\pi$
$109$		−	18.3770i		−	1.76020i	0.474793	−	0.880098i	$-0.342523\pi$
$110$		0			0
$111$	6.36286	−	4.75923i	0.603936	−	0.451726i
$112$		0			0
$113$		−	6.37988i		−	0.600169i	−0.953913	−	0.300084i	$-0.902985\pi$
$113$		−	6.37988i		−	0.600169i	0.953913	−	0.300084i	$-0.0970148\pi$
$114$		0			0
$115$	−3.54796			−0.330849
$116$		0			0
$117$	6.84884	+	2.01692i	0.633175	+	0.186464i
$118$		0			0
$119$			0.357360i			0.0327591i
$120$		0			0
$121$	10.3178	−	3.81355i	0.937981	−	0.346686i
$122$		0			0
$123$	11.3036	−	8.45474i	1.01921	−	0.762338i
$124$		0			0
$125$			1.00000i			0.0894427i
$126$		0			0
$127$			22.0338i			1.95519i	0.210502	+	0.977593i	$0.432490\pi$
$127$			22.0338i			1.95519i	−0.210502	+	0.977593i	$0.567510\pi$
$128$		0			0
$129$	2.69913	+	3.60860i	0.237645	+	0.317720i
$130$		0			0
$131$	−1.97748			−0.172773			−0.0863865	−	0.996262i	$-0.527532\pi$
$131$	−1.97748			−0.172773			−0.0863865	+	0.996262i	$0.527532\pi$
$132$		0			0
$133$	1.45619			0.126268
$134$		0			0
$135$	4.87070	−	1.81006i	0.419203	−	0.155785i
$136$		0			0
$137$		−	19.6172i		−	1.67601i	−0.545661	−	0.838006i	$-0.683721\pi$
$137$		−	19.6172i		−	1.67601i	0.545661	−	0.838006i	$-0.316279\pi$
$138$		0			0
$139$		−	18.7230i		−	1.58807i	−0.607875	−	0.794033i	$-0.707978\pi$
$139$		−	18.7230i		−	1.58807i	0.607875	−	0.794033i	$-0.292022\pi$
$140$		0			0
$141$	−3.52544	−	4.71334i	−0.296896	−	0.396935i
$142$		0			0
$143$	1.38995	+	7.76983i	0.116233	+	0.649746i
$144$		0			0
$145$		−	3.37573i		−	0.280339i
$146$		0			0
$147$	−9.49352	+	7.10087i	−0.783012	+	0.585670i
$148$		0			0
$149$	22.0113			1.80324			0.901619	−	0.432532i	$-0.142380\pi$
$149$	22.0113			1.80324			0.901619	+	0.432532i	$0.142380\pi$
$150$		0			0
$151$		−	13.9278i		−	1.13343i	−0.823913	−	0.566716i	$-0.808214\pi$
$151$		−	13.9278i		−	1.13343i	0.823913	−	0.566716i	$-0.191786\pi$
$152$		0			0
$153$	0.768479	−	2.60952i	0.0621279	−	0.210967i
$154$		0			0
$155$			3.66654i			0.294503i
$156$		0			0
$157$	2.62427			0.209440			0.104720	−	0.994502i	$-0.466605\pi$
$157$	2.62427			0.209440			0.104720	+	0.994502i	$0.466605\pi$
$158$		0			0
$159$	−6.69632	−	8.95266i	−0.531053	−	0.709992i
$160$		0			0
$161$	1.39825			0.110198
$162$		0			0
$163$	−6.77398			−0.530579			−0.265290	−	0.964169i	$-0.585468\pi$
$163$	−6.77398			−0.530579			−0.265290	+	0.964169i	$0.585468\pi$
$164$		0			0
$165$	4.19705	+	3.92234i	0.326740	+	0.305354i
$166$		0			0
$167$	16.7542			1.29648			0.648238	−	0.761438i	$-0.275506\pi$
$167$	16.7542			1.29648			0.648238	+	0.761438i	$0.275506\pi$
$168$		0			0
$169$	7.33616			0.564320
$170$		0			0
$171$	−10.6334	−	3.13144i	−0.813158	−	0.239467i
$172$		0			0
$173$	13.0959			0.995665			0.497832	−	0.867273i	$-0.334129\pi$
$173$	13.0959			0.995665			0.497832	+	0.867273i	$0.334129\pi$
$174$		0			0
$175$		−	0.394100i		−	0.0297912i
$176$		0			0
$177$	8.06064	+	10.7767i	0.605875	+	0.810025i
$178$		0			0
$179$			14.9816i			1.11978i	0.828567	+	0.559890i	$0.189157\pi$
$179$			14.9816i			1.11978i	−0.828567	+	0.559890i	$0.810843\pi$
$180$		0			0
$181$	23.9687			1.78158			0.890788	−	0.454419i	$-0.150153\pi$
$181$	23.9687			1.78158			0.890788	+	0.454419i	$0.150153\pi$
$182$		0			0
$183$	13.3150	+	17.8015i	0.984272	+	1.31592i
$184$		0			0
$185$			4.58753i			0.337282i
$186$		0			0
$187$	2.96043	−	0.529593i	0.216488	−	0.0387277i
$188$		0			0
$189$	−1.91954	+	0.713344i	−0.139626	+	0.0518881i
$190$		0			0
$191$			21.9249i			1.58643i	0.608940	+	0.793217i	$0.291595\pi$
$191$			21.9249i			1.58643i	−0.608940	+	0.793217i	$0.708405\pi$
$192$		0			0
$193$		−	21.8699i		−	1.57423i	−0.616806	−	0.787115i	$-0.711574\pi$
$193$		−	21.8699i		−	1.57423i	0.616806	−	0.787115i	$-0.288426\pi$
$194$		0			0
$195$	−3.30087	+	2.46896i	−0.236381	+	0.176806i
$196$		0			0
$197$	18.0338			1.28486			0.642429	−	0.766345i	$-0.277927\pi$
$197$	18.0338			1.28486			0.642429	+	0.766345i	$0.277927\pi$
$198$		0			0
$199$	3.81625			0.270527			0.135263	−	0.990810i	$-0.456812\pi$
$199$	3.81625			0.270527			0.135263	+	0.990810i	$0.456812\pi$
$200$		0			0
$201$	−16.5323	+	12.3657i	−1.16610	+	0.872207i
$202$		0			0
$203$			1.33037i			0.0933740i
$204$		0			0
$205$			8.14971i			0.569201i
$206$		0			0
$207$	−10.2103	−	3.00685i	−0.709668	−	0.208991i
$208$		0			0
$209$	−2.15802	−	12.0633i	−0.149273	−	0.834439i
$210$		0			0
$211$		−	19.0903i		−	1.31423i	−0.753789	−	0.657116i	$-0.771776\pi$
$211$		−	19.0903i		−	1.31423i	0.753789	−	0.657116i	$-0.228224\pi$
$212$		0			0
$213$	2.68438	+	3.58888i	0.183930	+	0.245906i
$214$		0			0
$215$	−2.60175			−0.177438
$216$		0			0
$217$		−	1.44498i		−	0.0980918i
$218$		0			0
$219$	12.3362	+	16.4929i	0.833601	+	1.11448i
$220$		0			0
$221$			2.15802i			0.145164i
$222$		0			0
$223$	2.17815			0.145860			0.0729298	−	0.997337i	$-0.476765\pi$
$223$	2.17815			0.145860			0.0729298	+	0.997337i	$0.476765\pi$
$224$		0			0
$225$	−0.847487	+	2.87781i	−0.0564991	+	0.191854i
$226$		0			0
$227$	6.83890			0.453914			0.226957	−	0.973905i	$-0.427122\pi$
$227$	6.83890			0.453914			0.226957	+	0.973905i	$0.427122\pi$
$228$		0			0
$229$	−23.8474			−1.57588			−0.787940	−	0.615752i	$-0.788852\pi$
$229$	−23.8474			−1.57588			−0.787940	+	0.615752i	$0.788852\pi$
$230$		0			0
$231$	−1.65406	−	1.54579i	−0.108829	−	0.101706i
$232$		0			0
$233$	−10.5760			−0.692858			−0.346429	−	0.938076i	$-0.612606\pi$
$233$	−10.5760			−0.692858			−0.346429	+	0.938076i	$0.612606\pi$
$234$		0			0
$235$	3.39825			0.221678
$236$		0			0
$237$	2.66239	+	3.55948i	0.172941	+	0.231213i
$238$		0			0
$239$	−22.4290			−1.45081			−0.725406	−	0.688322i	$-0.758348\pi$
$239$	−22.4290			−1.45081			−0.725406	+	0.688322i	$0.758348\pi$
$240$		0			0
$241$		−	4.78820i		−	0.308435i	−0.988037	−	0.154218i	$-0.950714\pi$
$241$		−	4.78820i		−	0.308435i	0.988037	−	0.154218i	$-0.0492857\pi$
$242$		0			0
$243$	15.5509	−	1.08115i	0.997592	−	0.0693556i
$244$		0			0
$245$		−	6.84469i		−	0.437291i
$246$		0			0
$247$	8.79360			0.559523
$248$		0			0
$249$	2.35466	−	1.76121i	0.149220	−	0.111612i
$250$		0			0
$251$		−	11.5042i		−	0.726141i	−0.931762	−	0.363071i	$-0.881728\pi$
$251$		−	11.5042i		−	0.726141i	0.931762	−	0.363071i	$-0.118272\pi$
$252$		0			0
$253$	−2.07216	−	11.5834i	−0.130275	−	0.728241i
$254$		0			0
$255$	0.940713	+	1.25769i	0.0589097	+	0.0787594i
$256$		0			0
$257$			16.3431i			1.01946i	0.860335	+	0.509729i	$0.170254\pi$
$257$			16.3431i			1.01946i	−0.860335	+	0.509729i	$0.829746\pi$
$258$		0			0
$259$		−	1.80795i		−	0.112340i
$260$		0			0
$261$	2.86089	−	9.71469i	0.177084	−	0.601324i
$262$		0			0
$263$	−3.23463			−0.199456			−0.0997280	−	0.995015i	$-0.531797\pi$
$263$	−3.23463			−0.199456			−0.0997280	+	0.995015i	$0.531797\pi$
$264$		0			0
$265$	6.45474			0.396511
$266$		0			0
$267$	−15.8764	−	21.2259i	−0.971617	−	1.29901i
$268$		0			0
$269$		−	8.94622i		−	0.545460i	−0.962091	−	0.272730i	$-0.912073\pi$
$269$		−	8.94622i		−	0.545460i	0.962091	−	0.272730i	$-0.0879266\pi$
$270$		0			0
$271$		−	3.38297i		−	0.205501i	−0.994707	−	0.102750i	$-0.967236\pi$
$271$		−	3.38297i		−	0.205501i	0.994707	−	0.102750i	$-0.0327643\pi$
$272$		0			0
$273$	1.30087	−	0.973015i	0.0787325	−	0.0588896i
$274$		0			0
$275$	−3.26480	+	0.584041i	−0.196875	+	0.0352190i
$276$		0			0
$277$			5.76983i			0.346675i	0.984862	+	0.173338i	$0.0554552\pi$
$277$			5.76983i			0.346675i	−0.984862	+	0.173338i	$0.944545\pi$
$278$		0			0
$279$	−3.10734	+	10.5516i	−0.186032	+	0.631707i
$280$		0			0
$281$	−0.115874			−0.00691245			−0.00345623	−	0.999994i	$-0.501100\pi$
$281$	−0.115874			−0.00691245			−0.00345623	+	0.999994i	$0.501100\pi$
$282$		0			0
$283$		−	21.1805i		−	1.25905i	−0.776981	−	0.629524i	$-0.783250\pi$
$283$		−	21.1805i		−	1.25905i	0.776981	−	0.629524i	$-0.216750\pi$
$284$		0			0
$285$	5.12489	−	3.83327i	0.303573	−	0.227063i
$286$		0			0
$287$		−	3.21180i		−	0.189587i
$288$		0			0
$289$	−16.1778			−0.951633
$290$		0			0
$291$	14.0381	−	10.5001i	0.822929	−	0.615526i
$292$		0			0
$293$	−16.5143			−0.964776			−0.482388	−	0.875958i	$-0.660231\pi$
$293$	−16.5143			−0.964776			−0.482388	+	0.875958i	$0.660231\pi$
$294$		0			0
$295$	−7.76983			−0.452377
$296$		0			0
$297$	8.75416	+	14.8447i	0.507968	+	0.861376i
$298$		0			0
$299$	8.44373			0.488314
$300$		0			0
$301$	1.02535			0.0591001
$302$		0			0
$303$	−4.18645	+	3.13134i	−0.240505	+	0.179891i
$304$		0			0
$305$	−12.8346			−0.734908
$306$		0			0
$307$		−	17.6526i		−	1.00749i	−0.863853	−	0.503744i	$-0.831955\pi$
$307$		−	17.6526i		−	1.00749i	0.863853	−	0.503744i	$-0.168045\pi$
$308$		0			0
$309$	0.834619	−	0.624270i	0.0474798	−	0.0355135i
$310$		0			0
$311$		−	4.13549i		−	0.234502i	−0.993102	−	0.117251i	$-0.962592\pi$
$311$		−	4.13549i		−	0.234502i	0.993102	−	0.117251i	$-0.0374083\pi$
$312$		0			0
$313$	−12.1580			−0.687212			−0.343606	−	0.939114i	$-0.611648\pi$
$313$	−12.1580			−0.687212			−0.343606	+	0.939114i	$0.611648\pi$
$314$		0			0
$315$	0.333995	−	1.13414i	0.0188185	−	0.0639017i
$316$		0			0
$317$			6.97195i			0.391584i	0.980645	+	0.195792i	$0.0627277\pi$
$317$			6.97195i			0.391584i	−0.980645	+	0.195792i	$0.937272\pi$
$318$		0			0
$319$	11.0211	−	1.97156i	0.617061	−	0.110386i
$320$		0			0
$321$	−21.1456	+	15.8162i	−1.18023	+	0.882777i
$322$		0			0
$323$		−	3.35051i		−	0.186427i
$324$		0			0
$325$		−	2.37988i		−	0.132012i
$326$		0			0
$327$	19.0648	+	25.4887i	1.05429	+	1.40953i
$328$		0			0
$329$	−1.33925			−0.0738353
$330$		0			0
$331$	5.39825			0.296715			0.148357	−	0.988934i	$-0.452601\pi$
$331$	5.39825			0.296715			0.148357	+	0.988934i	$0.452601\pi$
$332$		0			0
$333$	−3.88787	+	13.2020i	−0.213054	+	0.723466i
$334$		0			0
$335$		−	11.9195i		−	0.651234i
$336$		0			0
$337$			24.7657i			1.34907i	0.738242	+	0.674536i	$0.235656\pi$
$337$			24.7657i			1.34907i	−0.738242	+	0.674536i	$0.764344\pi$
$338$		0			0
$339$	6.61867	+	8.84884i	0.359477	+	0.480603i
$340$		0			0
$341$	−11.9705	+	2.14141i	−0.648239	+	0.115964i
$342$		0			0
$343$			5.45619i			0.294607i
$344$		0			0
$345$	4.92099	−	3.68076i	0.264937	−	0.198165i
$346$		0			0
$347$	30.3416			1.62882			0.814410	−	0.580290i	$-0.197061\pi$
$347$	30.3416			1.62882			0.814410	+	0.580290i	$0.197061\pi$
$348$		0			0
$349$			21.6172i			1.15714i	0.815632	+	0.578572i	$0.196390\pi$
$349$			21.6172i			1.15714i	−0.815632	+	0.578572i	$0.803610\pi$
$350$		0			0
$351$	−11.5917	+	4.30773i	−0.618718	+	0.229929i
$352$		0			0
$353$		−	7.70465i		−	0.410077i	−0.978754	−	0.205039i	$-0.934268\pi$
$353$		−	7.70465i		−	0.410077i	0.978754	−	0.205039i	$-0.0657320\pi$
$354$		0			0
$355$	−2.58753			−0.137332
$356$		0			0
$357$	−0.370735	−	0.495654i	−0.0196214	−	0.0262328i
$358$		0			0
$359$	0.344467			0.0181803			0.00909014	−	0.999959i	$-0.497106\pi$
$359$	0.344467			0.0181803			0.00909014	+	0.999959i	$0.497106\pi$
$360$		0			0
$361$	5.34717			0.281430
$362$		0			0
$363$	−10.3544	+	15.9933i	−0.543465	+	0.839432i
$364$		0			0
$365$	−11.8911			−0.622409
$366$		0			0
$367$	−27.9687			−1.45995			−0.729976	−	0.683473i	$-0.760469\pi$
$367$	−27.9687			−1.45995			−0.729976	+	0.683473i	$0.760469\pi$
$368$		0			0
$369$	−6.90677	+	23.4533i	−0.359552	+	1.22093i
$370$		0			0
$371$	−2.54381			−0.132068
$372$		0			0
$373$			21.8911i			1.13348i	0.823897	+	0.566739i	$0.191795\pi$
$373$			21.8911i			1.13348i	−0.823897	+	0.566739i	$0.808205\pi$
$374$		0			0
$375$	−1.03743	−	1.38699i	−0.0535725	−	0.0716239i
$376$		0			0
$377$			8.03384i			0.413764i
$378$		0			0
$379$	29.8023			1.53084			0.765422	−	0.643529i	$-0.222530\pi$
$379$	29.8023			1.53084			0.765422	+	0.643529i	$0.222530\pi$
$380$		0			0
$381$	−22.8585	−	30.5607i	−1.17108	−	1.56567i
$382$		0			0
$383$		−	31.3017i		−	1.59944i	−0.600370	−	0.799722i	$-0.704980\pi$
$383$		−	31.3017i		−	1.59944i	0.600370	−	0.799722i	$-0.295020\pi$
$384$		0			0
$385$	1.28666	−	0.230170i	0.0655741	−	0.0117306i
$386$		0			0
$387$	−7.48733	−	2.20495i	−0.380602	−	0.112084i
$388$		0			0
$389$		−	16.5733i		−	0.840300i	−0.907455	−	0.420150i	$-0.861977\pi$
$389$		−	16.5733i		−	0.840300i	0.907455	−	0.420150i	$-0.138023\pi$
$390$		0			0
$391$		−	3.21720i		−	0.162701i
$392$		0			0
$393$	2.74274	−	2.05149i	0.138353	−	0.103484i
$394$		0			0
$395$	−2.56633			−0.129126
$396$		0			0
$397$	3.94798			0.198143			0.0990716	−	0.995080i	$-0.468413\pi$
$397$	3.94798			0.198143			0.0990716	+	0.995080i	$0.468413\pi$
$398$		0			0
$399$	−2.01972	+	1.51069i	−0.101112	+	0.0756291i
$400$		0			0
$401$		−	4.72486i		−	0.235948i	−0.993017	−	0.117974i	$-0.962360\pi$
$401$		−	4.72486i		−	0.235948i	0.993017	−	0.117974i	$-0.0376400\pi$
$402$		0			0
$403$		−	8.72593i		−	0.434669i
$404$		0			0
$405$	−4.87781	+	7.56353i	−0.242380	+	0.375835i
$406$		0			0
$407$	−14.9774	+	2.67930i	−0.742400	+	0.132808i
$408$		0			0
$409$		−	12.1497i		−	0.600765i	−0.953819	−	0.300382i	$-0.902886\pi$
$409$		−	12.1497i		−	0.600765i	0.953819	−	0.300382i	$-0.0971143\pi$
$410$		0			0
$411$	20.3514	+	27.2089i	1.00386	+	1.34212i
$412$		0			0
$413$	3.06209			0.150676
$414$		0			0
$415$			1.69767i			0.0833356i
$416$		0			0
$417$	19.4238	+	25.9687i	0.951187	+	1.27169i
$418$		0			0
$419$		−	7.01547i		−	0.342728i	−0.985208	−	0.171364i	$-0.945183\pi$
$419$		−	7.01547i		−	0.342728i	0.985208	−	0.171364i	$-0.0548174\pi$
$420$		0			0
$421$	−13.0085			−0.633995			−0.316997	−	0.948426i	$-0.602675\pi$
$421$	−13.0085			−0.633995			−0.316997	+	0.948426i	$0.602675\pi$
$422$		0			0
$423$	9.77951	+	2.87997i	0.475496	+	0.140029i
$424$		0			0
$425$	−0.906774			−0.0439850
$426$		0			0
$427$	5.05812			0.244780
$428$		0			0
$429$	−9.98848	−	9.33471i	−0.482248	−	0.450684i
$430$		0			0
$431$	−23.5397			−1.13387			−0.566933	−	0.823764i	$-0.691870\pi$
$431$	−23.5397			−1.13387			−0.566933	+	0.823764i	$0.691870\pi$
$432$		0			0
$433$	3.05919			0.147015			0.0735076	−	0.997295i	$-0.476581\pi$
$433$	3.05919			0.147015			0.0735076	+	0.997295i	$0.476581\pi$
$434$		0			0
$435$	3.50208	+	4.68211i	0.167912	+	0.224490i
$436$		0			0
$437$	−13.1096			−0.627119
$438$		0			0
$439$			27.8461i			1.32902i	0.747279	+	0.664510i	$0.231360\pi$
$439$			27.8461i			1.32902i	−0.747279	+	0.664510i	$0.768640\pi$
$440$		0			0
$441$	5.80078	−	19.6977i	0.276228	−	0.937985i
$442$		0			0
$443$			28.5213i			1.35509i	0.735483	+	0.677544i	$0.236956\pi$
$443$			28.5213i			1.35509i	−0.735483	+	0.677544i	$0.763044\pi$
$444$		0			0
$445$	15.3036			0.725459
$446$		0			0
$447$	−30.5295	+	22.8352i	−1.44400	+	1.08007i
$448$		0			0
$449$			4.00000i			0.188772i	0.995536	+	0.0943858i	$0.0300887\pi$
$449$			4.00000i			0.188772i	−0.995536	+	0.0943858i	$0.969911\pi$
$450$		0			0
$451$	−26.6071	+	4.75976i	−1.25288	+	0.224129i
$452$		0			0
$453$	14.4491	+	19.3178i	0.678880	+	0.907629i
$454$		0			0
$455$			0.937911i			0.0439700i
$456$		0			0
$457$		−	13.0651i		−	0.611160i	−0.952166	−	0.305580i	$-0.901150\pi$
$457$		−	13.0651i		−	0.611160i	0.952166	−	0.305580i	$-0.0988503\pi$
$458$		0			0
$459$	1.64131	+	4.41662i	0.0766100	+	0.206150i
$460$		0			0
$461$	−20.1355			−0.937803			−0.468902	−	0.883250i	$-0.655350\pi$
$461$	−20.1355			−0.937803			−0.468902	+	0.883250i	$0.655350\pi$
$462$		0			0
$463$	12.6071			0.585904			0.292952	−	0.956127i	$-0.405362\pi$
$463$	12.6071			0.585904			0.292952	+	0.956127i	$0.405362\pi$
$464$		0			0
$465$	−3.80377	−	5.08545i	−0.176396	−	0.235832i
$466$		0			0
$467$		−	14.9843i		−	0.693392i	−0.937978	−	0.346696i	$-0.887304\pi$
$467$		−	14.9843i		−	0.693392i	0.937978	−	0.346696i	$-0.112696\pi$
$468$		0			0
$469$			4.69749i			0.216910i
$470$		0			0
$471$	−3.63984	+	2.72249i	−0.167715	+	0.125446i
$472$		0			0
$473$	−1.51953	−	8.49418i	−0.0698679	−	0.390563i
$474$		0			0
$475$			3.69497i			0.169537i
$476$		0			0
$477$	18.5755	+	5.47031i	0.850513	+	0.250468i
$478$		0			0
$479$	−23.7060			−1.08315			−0.541577	−	0.840651i	$-0.682173\pi$
$479$	−23.7060			−1.08315			−0.541577	+	0.840651i	$0.682173\pi$
$480$		0			0
$481$		−	10.9178i		−	0.497808i
$482$		0			0
$483$	−1.93936	+	1.45059i	−0.0882440	+	0.0660039i
$484$		0			0
$485$			10.1213i			0.459583i
$486$		0			0
$487$	−10.3279			−0.468000			−0.234000	−	0.972237i	$-0.575182\pi$
$487$	−10.3279			−0.468000			−0.234000	+	0.972237i	$0.575182\pi$
$488$		0			0
$489$	9.39545	−	7.02752i	0.424877	−	0.317795i
$490$		0			0
$491$	−21.1608			−0.954975			−0.477488	−	0.878638i	$-0.658452\pi$
$491$	−21.1608			−0.954975			−0.477488	+	0.878638i	$0.658452\pi$
$492$		0			0
$493$	3.06102			0.137862
$494$		0			0
$495$	−9.89042	−	1.08612i	−0.444541	−	0.0488173i
$496$		0			0
$497$	1.01975			0.0457418
$498$		0			0
$499$	−23.6325			−1.05794			−0.528968	−	0.848642i	$-0.677421\pi$
$499$	−23.6325			−1.05794			−0.528968	+	0.848642i	$0.677421\pi$
$500$		0			0
$501$	−23.2379	+	17.3812i	−1.03819	+	0.776536i
$502$		0			0
$503$	−13.5195			−0.602806			−0.301403	−	0.953497i	$-0.597455\pi$
$503$	−13.5195			−0.602806			−0.301403	+	0.953497i	$0.597455\pi$
$504$		0			0
$505$		−	3.01837i		−	0.134316i
$506$		0			0
$507$	−10.1752	+	7.61074i	−0.451896	+	0.338005i
$508$		0			0
$509$			31.0930i			1.37817i	0.724679	+	0.689087i	$0.241988\pi$
$509$			31.0930i			1.37817i	−0.724679	+	0.689087i	$0.758012\pi$
$510$		0			0
$511$	4.68628			0.207309
$512$		0			0
$513$	17.9971	−	6.68812i	0.794591	−	0.295288i
$514$		0			0
$515$			0.601748i			0.0265162i
$516$		0			0
$517$	1.98472	+	11.0946i	0.0872878	+	0.487940i
$518$		0			0
$519$	−18.1639	+	13.5861i	−0.797308	+	0.596363i
$520$		0			0
$521$		−	2.40699i		−	0.105452i	−0.998609	−	0.0527261i	$-0.983209\pi$
$521$		−	2.40699i		−	0.105452i	0.998609	−	0.0527261i	$-0.0167910\pi$
$522$		0			0
$523$		−	11.7967i		−	0.515833i	−0.966167	−	0.257917i	$-0.916964\pi$
$523$		−	11.7967i		−	0.515833i	0.966167	−	0.257917i	$-0.0830360\pi$
$524$		0			0
$525$	0.408850	+	0.546613i	0.0178437	+	0.0238561i
$526$		0			0
$527$	−3.32472			−0.144827
$528$		0			0
$529$	10.4120			0.452694
$530$		0			0
$531$	−22.3601	−	6.58483i	−0.970344	−	0.285757i
$532$		0			0
$533$		−	19.3953i		−	0.840106i
$534$		0			0
$535$		−	15.2456i		−	0.659126i
$536$		0			0
$537$	−15.5424	−	20.7794i	−0.670702	−	0.896697i
$538$		0			0
$539$	22.3465	−	3.99758i	0.962532	−	0.172188i
$540$		0			0
$541$		−	28.7472i		−	1.23594i	−0.786203	−	0.617969i	$-0.787956\pi$
$541$		−	28.7472i		−	1.23594i	0.786203	−	0.617969i	$-0.212044\pi$
$542$		0			0
$543$	−33.2443	+	24.8658i	−1.42665	+	1.06709i
$544$		0			0
$545$	−18.3770			−0.787183
$546$		0			0
$547$			19.6663i			0.840872i	0.907322	+	0.420436i	$0.138123\pi$
$547$			19.6663i			0.840872i	−0.907322	+	0.420436i	$0.861877\pi$
$548$		0			0
$549$	−36.9355	−	10.8772i	−1.57637	−	0.464226i
$550$		0			0
$551$		−	12.4732i		−	0.531378i
$552$		0			0
$553$	1.01139			0.0430087
$554$		0			0
$555$	−4.75923	−	6.36286i	−0.202018	−	0.270088i
$556$		0			0
$557$	14.2710			0.604681			0.302341	−	0.953200i	$-0.402232\pi$
$557$	14.2710			0.604681			0.302341	+	0.953200i	$0.402232\pi$
$558$		0			0
$559$	6.19185			0.261887
$560$		0			0
$561$	−3.55668	+	3.80578i	−0.150163	+	0.160680i
$562$		0			0
$563$	−40.9573			−1.72614			−0.863072	−	0.505082i	$-0.831462\pi$
$563$	−40.9573			−1.72614			−0.863072	+	0.505082i	$0.831462\pi$
$564$		0			0
$565$	−6.37988			−0.268404
$566$		0			0
$567$	1.92234	−	2.98079i	0.0807308	−	0.125181i
$568$		0			0
$569$	29.3162			1.22900			0.614500	−	0.788917i	$-0.289358\pi$
$569$	29.3162			1.22900			0.614500	+	0.788917i	$0.289358\pi$
$570$		0			0
$571$		−	19.6381i		−	0.821829i	−0.911674	−	0.410914i	$-0.865209\pi$
$571$		−	19.6381i		−	0.821829i	0.911674	−	0.410914i	$-0.134791\pi$
$572$		0			0
$573$	−22.7455	−	30.4097i	−0.950209	−	1.27038i
$574$		0			0
$575$			3.54796i			0.147960i
$576$		0			0
$577$	4.75146			0.197806			0.0989029	−	0.995097i	$-0.468467\pi$
$577$	4.75146			0.197806			0.0989029	+	0.995097i	$0.468467\pi$
$578$		0			0
$579$	22.6885	+	30.3334i	0.942900	+	1.26061i
$580$		0			0
$581$		−	0.669053i		−	0.0277570i
$582$		0			0
$583$	3.76983	+	21.0734i	0.156130	+	0.872771i
$584$		0			0
$585$	2.01692	−	6.84884i	0.0833893	−	0.283165i
$586$		0			0
$587$			23.3572i			0.964056i	0.876156	+	0.482028i	$0.160100\pi$
$587$			23.3572i			0.964056i	−0.876156	+	0.482028i	$0.839900\pi$
$588$		0			0
$589$			13.5478i			0.558226i
$590$		0			0
$591$	−25.0128	+	18.7088i	−1.02889	+	0.769577i
$592$		0			0
$593$	−27.7315			−1.13880			−0.569398	−	0.822062i	$-0.692824\pi$
$593$	−27.7315			−1.13880			−0.569398	+	0.822062i	$0.692824\pi$
$594$		0			0
$595$	0.357360			0.0146503
$596$		0			0
$597$	−5.29310	+	3.95908i	−0.216632	+	0.162034i
$598$		0			0
$599$		−	9.59602i		−	0.392083i	−0.980596	−	0.196041i	$-0.937191\pi$
$599$		−	9.59602i		−	0.392083i	0.980596	−	0.196041i	$-0.0628087\pi$
$600$		0			0
$601$			11.8503i			0.483383i	0.970353	+	0.241692i	$0.0777023\pi$
$601$			11.8503i			0.483383i	−0.970353	+	0.241692i	$0.922298\pi$
$602$		0			0
$603$	10.1017	−	34.3021i	0.411371	−	1.39689i
$604$		0			0
$605$	−3.81355	−	10.3178i	−0.155043	−	0.419478i
$606$		0			0
$607$			23.9338i			0.971441i	0.874114	+	0.485721i	$0.161443\pi$
$607$			23.9338i			0.971441i	−0.874114	+	0.485721i	$0.838557\pi$
$608$		0			0
$609$	−1.38017	−	1.84522i	−0.0559272	−	0.0747720i
$610$		0			0
$611$	−8.08744			−0.327183
$612$		0			0
$613$			38.0977i			1.53875i	0.638797	+	0.769376i	$0.279432\pi$
$613$			38.0977i			1.53875i	−0.638797	+	0.769376i	$0.720568\pi$
$614$		0			0
$615$	−8.45474	−	11.3036i	−0.340928	−	0.455804i
$616$		0			0
$617$			42.1905i			1.69853i	0.527969	+	0.849263i	$0.322954\pi$
$617$			42.1905i			1.69853i	−0.527969	+	0.849263i	$0.677046\pi$
$618$		0			0
$619$	−23.2596			−0.934882			−0.467441	−	0.884024i	$-0.654824\pi$
$619$	−23.2596			−0.934882			−0.467441	+	0.884024i	$0.654824\pi$
$620$		0			0
$621$	17.2811	−	6.42202i	0.693465	−	0.257707i
$622$		0			0
$623$	−6.03114			−0.241632
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	15.5080	+	14.4930i	0.619329	+	0.578793i
$628$		0			0
$629$	−4.15985			−0.165864
$630$		0			0
$631$	−10.8902			−0.433531			−0.216765	−	0.976224i	$-0.569551\pi$
$631$	−10.8902			−0.433531			−0.216765	+	0.976224i	$0.569551\pi$
$632$		0			0
$633$	19.8048	+	26.4781i	0.787171	+	1.05241i
$634$		0			0
$635$	22.0338			0.874386
$636$		0			0
$637$			16.2895i			0.645415i
$638$		0			0
$639$	−7.44641	−	2.19290i	−0.294575	−	0.0867497i
$640$		0			0
$641$		−	20.2076i		−	0.798154i	−0.916917	−	0.399077i	$-0.869331\pi$
$641$		−	20.2076i		−	0.798154i	0.916917	−	0.399077i	$-0.130669\pi$
$642$		0			0
$643$	37.2937			1.47072			0.735360	−	0.677677i	$-0.237013\pi$
$643$	37.2937			1.47072			0.735360	+	0.677677i	$0.237013\pi$
$644$		0			0
$645$	3.60860	−	2.69913i	0.142089	−	0.106278i
$646$		0			0
$647$			21.5681i			0.847929i	0.905679	+	0.423965i	$0.139362\pi$
$647$			21.5681i			0.847929i	−0.905679	+	0.423965i	$0.860638\pi$
$648$		0			0
$649$	−4.53790	−	25.3669i	−0.178128	−	0.995738i
$650$		0			0
$651$	1.49906	+	2.00418i	0.0587530	+	0.0785499i
$652$		0			0
$653$			32.8837i			1.28684i	0.765513	+	0.643420i	$0.222485\pi$
$653$			32.8837i			1.28684i	−0.765513	+	0.643420i	$0.777515\pi$
$654$		0			0
$655$			1.97748i			0.0772665i
$656$		0			0
$657$	−34.2203	−	10.0776i	−1.33506	−	0.393163i
$658$		0			0
$659$	36.5278			1.42292			0.711460	−	0.702727i	$-0.248034\pi$
$659$	36.5278			1.42292			0.711460	+	0.702727i	$0.248034\pi$
$660$		0			0
$661$	−30.7936			−1.19773			−0.598866	−	0.800849i	$-0.704382\pi$
$661$	−30.7936			−1.19773			−0.598866	+	0.800849i	$0.704382\pi$
$662$		0			0
$663$	−2.23879	−	2.99315i	−0.0869472	−	0.116244i
$664$		0			0
$665$		−	1.45619i		−	0.0564686i
$666$		0			0
$667$		−	11.9770i		−	0.463750i
$668$		0			0
$669$	−3.02107	+	2.25967i	−0.116801	+	0.0873639i
$670$		0			0
$671$	−7.49594	−	41.9024i	−0.289378	−	1.61762i
$672$		0			0
$673$		−	13.8699i		−	0.534646i	−0.963607	−	0.267323i	$-0.913861\pi$
$673$		−	13.8699i		−	0.534646i	0.963607	−	0.267323i	$-0.0861390\pi$
$674$		0			0
$675$	−1.81006	−	4.87070i	−0.0696692	−	0.187473i
$676$		0			0
$677$	−36.4913			−1.40247			−0.701237	−	0.712928i	$-0.747368\pi$
$677$	−36.4913			−1.40247			−0.701237	+	0.712928i	$0.747368\pi$
$678$		0			0
$679$		−	3.98879i		−	0.153076i
$680$		0			0
$681$	−9.48549	+	7.09486i	−0.363485	+	0.271876i
$682$		0			0
$683$		−	11.3518i		−	0.434366i	−0.976131	−	0.217183i	$-0.930313\pi$
$683$		−	11.3518i		−	0.434366i	0.976131	−	0.217183i	$-0.0696868\pi$
$684$		0			0
$685$	−19.6172			−0.749535
$686$		0			0
$687$	33.0761	−	24.7399i	1.26193	−	0.943888i
$688$		0			0
$689$	−15.3615			−0.585227
$690$		0			0
$691$	36.6578			1.39453			0.697265	−	0.716813i	$-0.254400\pi$
$691$	36.6578			1.39453			0.697265	+	0.716813i	$0.254400\pi$
$692$		0			0
$693$	3.89781	+	0.428038i	0.148066	+	0.0162598i
$694$		0			0
$695$	−18.7230			−0.710205
$696$		0			0
$697$	−7.38995			−0.279914
$698$		0			0
$699$	14.6688	−	10.9718i	0.554826	−	0.414993i
$700$		0			0
$701$	−1.64422			−0.0621012			−0.0310506	−	0.999518i	$-0.509885\pi$
$701$	−1.64422			−0.0621012			−0.0310506	+	0.999518i	$0.509885\pi$
$702$		0			0
$703$			16.9508i			0.639312i
$704$		0			0
$705$	−4.71334	+	3.52544i	−0.177515	+	0.132776i
$706$		0			0
$707$			1.18954i			0.0447372i
$708$		0			0
$709$	48.7172			1.82961			0.914807	−	0.403892i	$-0.132343\pi$
$709$	48.7172			1.82961			0.914807	+	0.403892i	$0.132343\pi$
$710$		0			0
$711$	−7.38541	−	2.17493i	−0.276974	−	0.0815664i
$712$		0			0
$713$			13.0087i			0.487181i
$714$		0			0
$715$	7.76983	−	1.38995i	0.290575	−	0.0519811i
$716$		0			0
$717$	31.1088	−	23.2685i	1.16178	−	0.868977i
$718$		0			0
$719$		−	22.9460i		−	0.855740i	−0.903840	−	0.427870i	$-0.859264\pi$
$719$		−	22.9460i		−	0.855740i	0.903840	−	0.427870i	$-0.140736\pi$
$720$		0			0
$721$		−	0.237149i		−	0.00883189i
$722$		0			0
$723$	4.96741	+	6.64119i	0.184740	+	0.246988i
$724$		0			0
$725$	−3.37573			−0.125371
$726$		0			0
$727$	22.0623			0.818244			0.409122	−	0.912480i	$-0.365835\pi$
$727$	22.0623			0.818244			0.409122	+	0.912480i	$0.365835\pi$
$728$		0			0
$729$	−20.4474	+	17.6325i	−0.757310	+	0.653055i
$730$		0			0
$731$		−	2.35920i		−	0.0872581i
$732$		0			0
$733$			27.0522i			0.999196i	0.866257	+	0.499598i	$0.166519\pi$
$733$			27.0522i			0.999196i	−0.866257	+	0.499598i	$0.833481\pi$
$734$		0			0
$735$	7.10087	+	9.49352i	0.261919	+	0.350174i
$736$		0			0
$737$	38.9149	−	6.96150i	1.43345	−	0.256430i
$738$		0			0
$739$			28.2286i			1.03841i	0.854651	+	0.519203i	$0.173771\pi$
$739$			28.2286i			1.03841i	−0.854651	+	0.519203i	$0.826229\pi$
$740$		0			0
$741$	−12.1966	+	9.12273i	−0.448055	+	0.335132i
$742$		0			0
$743$	4.98591			0.182915			0.0914576	−	0.995809i	$-0.470847\pi$
$743$	4.98591			0.182915			0.0914576	+	0.995809i	$0.470847\pi$
$744$		0			0
$745$		−	22.0113i		−	0.806432i
$746$		0			0
$747$	−1.43876	+	4.88558i	−0.0526414	+	0.178754i
$748$		0			0
$749$			6.00830i			0.219539i
$750$		0			0
$751$	−7.87312			−0.287294			−0.143647	−	0.989629i	$-0.545883\pi$
$751$	−7.87312			−0.287294			−0.143647	+	0.989629i	$0.545883\pi$
$752$		0			0
$753$	11.9348	+	15.9563i	0.434929	+	0.581479i
$754$		0			0
$755$	−13.9278			−0.506886
$756$		0			0
$757$	−13.2250			−0.480669			−0.240335	−	0.970690i	$-0.577257\pi$
$757$	−13.2250			−0.480669			−0.240335	+	0.970690i	$0.577257\pi$
$758$		0			0
$759$	14.8910	+	13.9163i	0.540508	+	0.505131i
$760$		0			0
$761$	40.3923			1.46422			0.732109	−	0.681187i	$-0.238536\pi$
$761$	40.3923			1.46422			0.732109	+	0.681187i	$0.238536\pi$
$762$		0			0
$763$	7.24237			0.262191
$764$		0			0
$765$	−2.60952	−	0.768479i	−0.0943474	−	0.0277844i
$766$		0			0
$767$	18.4913			0.667681
$768$		0			0
$769$			14.2433i			0.513627i	0.966461	+	0.256814i	$0.0826727\pi$
$769$			14.2433i			0.513627i	−0.966461	+	0.256814i	$0.917327\pi$
$770$		0			0
$771$	−16.9548	−	22.6678i	−0.610613	−	0.816360i
$772$		0			0
$773$			7.21450i			0.259488i	0.991548	+	0.129744i	$0.0414155\pi$
$773$			7.21450i			0.259488i	−0.991548	+	0.129744i	$0.958585\pi$
$774$		0			0
$775$	3.66654			0.131706
$776$		0			0
$777$	1.87561	+	2.50760i	0.0672872	+	0.0899598i
$778$		0			0
$779$			30.1130i			1.07891i
$780$		0			0
$781$	−1.51122	−	8.44776i	−0.0540758	−	0.302285i
$782$		0			0
$783$	6.11027	+	16.4422i	0.218363	+	0.587595i
$784$		0			0
$785$		−	2.62427i		−	0.0936642i
$786$		0			0
$787$			8.68088i			0.309440i	0.987958	+	0.154720i	$0.0494475\pi$
$787$			8.68088i			0.309440i	−0.987958	+	0.154720i	$0.950552\pi$
$788$		0			0
$789$	4.48641	−	3.35570i	0.159720	−	0.119466i
$790$		0			0
$791$	2.51431			0.0893986
$792$		0			0
$793$	30.5449			1.08468
$794$		0			0
$795$	−8.95266	+	6.69632i	−0.317518	+	0.237494i
$796$		0			0
$797$		−	41.6239i		−	1.47440i	−0.675677	−	0.737198i	$-0.736149\pi$
$797$		−	41.6239i		−	1.47440i	0.675677	−	0.737198i	$-0.263851\pi$
$798$		0			0
$799$			3.08145i			0.109014i
$800$		0			0
$801$	44.0407	+	12.9696i	1.55610	+	0.458258i
$802$		0			0
$803$	−6.94489	−	38.8220i	−0.245080	−	1.37000i
$804$		0			0
$805$		−	1.39825i		−	0.0492819i
$806$		0			0
$807$	9.28105	+	12.4083i	0.326709	+	0.436793i
$808$		0			0
$809$	7.92917			0.278775			0.139387	−	0.990238i	$-0.455487\pi$
$809$	7.92917			0.278775			0.139387	+	0.990238i	$0.455487\pi$
$810$		0			0
$811$		−	29.9743i		−	1.05254i	−0.850318	−	0.526269i	$-0.823590\pi$
$811$		−	29.9743i		−	1.05254i	0.850318	−	0.526269i	$-0.176410\pi$
$812$		0			0
$813$	3.50959	+	4.69215i	0.123087	+	0.164561i
$814$		0			0
$815$			6.77398i			0.237282i
$816$		0			0
$817$	−9.61339			−0.336330
$818$		0			0
$819$	−0.794867	+	2.69913i	−0.0277749	+	0.0943151i
$820$		0			0
$821$	7.46210			0.260429			0.130215	−	0.991486i	$-0.458433\pi$
$821$	7.46210			0.260429			0.130215	+	0.991486i	$0.458433\pi$
$822$		0			0
$823$	−45.0224			−1.56938			−0.784692	−	0.619886i	$-0.787179\pi$
$823$	−45.0224			−1.56938			−0.784692	+	0.619886i	$0.787179\pi$
$824$		0			0
$825$	3.92234	−	4.19705i	0.136558	−	0.146123i
$826$		0			0
$827$	35.9716			1.25085			0.625427	−	0.780283i	$-0.284925\pi$
$827$	35.9716			1.25085			0.625427	+	0.780283i	$0.284925\pi$
$828$		0			0
$829$	−7.50832			−0.260775			−0.130387	−	0.991463i	$-0.541622\pi$
$829$	−7.50832			−0.260775			−0.130387	+	0.991463i	$0.541622\pi$
$830$		0			0
$831$	−5.98578	−	8.00270i	−0.207644	−	0.277611i
$832$		0			0
$833$	6.20658			0.215045
$834$		0			0
$835$		−	16.7542i		−	0.579802i
$836$		0			0
$837$	−6.63665	−	17.8586i	−0.229396	−	0.617283i
$838$		0			0
$839$			41.7806i			1.44243i	0.692713	+	0.721214i	$0.256415\pi$
$839$			41.7806i			1.44243i	−0.692713	+	0.721214i	$0.743585\pi$
$840$		0			0
$841$	−17.6044			−0.607050
$842$		0			0
$843$	0.160716	−	0.120211i	0.00553535	−	0.00414028i
$844$		0			0
$845$		−	7.33616i		−	0.252372i
$846$		0			0
$847$	1.50292	+	4.06624i	0.0516409	+	0.139718i
$848$		0			0
$849$	21.9732	+	29.3771i	0.754118	+	1.00822i
$850$		0			0
$851$			16.2764i			0.557947i
$852$		0			0
$853$			35.6816i			1.22172i	0.791740	+	0.610858i	$0.209175\pi$
$853$			35.6816i			1.22172i	−0.791740	+	0.610858i	$0.790825\pi$
$854$		0			0
$855$	−3.13144	+	10.6334i	−0.107093	+	0.363655i
$856$		0			0
$857$	39.8584			1.36154			0.680768	−	0.732499i	$-0.261646\pi$
$857$	39.8584			1.36154			0.680768	+	0.732499i	$0.261646\pi$
$858$		0			0
$859$	−44.9857			−1.53489			−0.767446	−	0.641113i	$-0.778473\pi$
$859$	−44.9857			−1.53489			−0.767446	+	0.641113i	$0.778473\pi$
$860$		0			0
$861$	3.33201	+	4.45474i	0.113555	+	0.151817i
$862$		0			0
$863$			18.8644i			0.642153i	0.947053	+	0.321076i	$0.104045\pi$
$863$			18.8644i			0.642153i	−0.947053	+	0.321076i	$0.895955\pi$
$864$		0			0
$865$		−	13.0959i		−	0.445275i
$866$		0			0
$867$	22.4384	−	16.7833i	0.762048	−	0.569989i
$868$		0			0
$869$	−1.49884	−	8.37856i	−0.0508448	−	0.284223i
$870$		0			0
$871$			28.3671i			0.961182i
$872$		0			0
$873$	−8.57765	+	29.1271i	−0.290309	+	0.985802i
$874$		0			0
$875$	−0.394100			−0.0133230
$876$		0			0
$877$		−	39.1853i		−	1.32319i	−0.749860	−	0.661597i	$-0.769879\pi$
$877$		−	39.1853i		−	1.32319i	0.749860	−	0.661597i	$-0.230121\pi$
$878$		0			0
$879$	22.9052	−	17.1324i	0.772573	−	0.577862i
$880$		0			0
$881$			32.2286i			1.08581i	0.839794	+	0.542904i	$0.182675\pi$
$881$			32.2286i			1.08581i	−0.839794	+	0.542904i	$0.817325\pi$
$882$		0			0
$883$	−44.2593			−1.48944			−0.744721	−	0.667375i	$-0.767418\pi$
$883$	−44.2593			−1.48944			−0.744721	+	0.667375i	$0.767418\pi$
$884$		0			0
$885$	10.7767	−	8.06064i	0.362254	−	0.270955i
$886$		0			0
$887$	28.6557			0.962165			0.481082	−	0.876675i	$-0.340244\pi$
$887$	28.6557			0.962165			0.481082	+	0.876675i	$0.340244\pi$
$888$		0			0
$889$	−8.68353			−0.291236
$890$		0			0
$891$	−27.5422	−	11.5076i	−0.922699	−	0.385520i
$892$		0			0
$893$	12.5565			0.420186
$894$		0			0
$895$	14.9816			0.500781
$896$		0			0
$897$	−11.7114	+	8.75976i	−0.391032	+	0.292480i
$898$		0			0
$899$	−12.3772			−0.412804
$900$		0			0
$901$			5.85299i			0.194991i
$902$		0			0
$903$	−1.42215	+	1.06373i	−0.0473262	+	0.0353986i
$904$		0			0
$905$		−	23.9687i		−	0.796745i
$906$		0			0
$907$	−7.17532			−0.238253			−0.119126	−	0.992879i	$-0.538009\pi$
$907$	−7.17532			−0.238253			−0.119126	+	0.992879i	$0.538009\pi$
$908$		0			0
$909$	2.55803	−	8.68628i	0.0848445	−	0.288106i
$910$		0			0
$911$			32.0314i			1.06125i	0.847607	+	0.530625i	$0.178043\pi$
$911$			32.0314i			1.06125i	−0.847607	+	0.530625i	$0.821957\pi$
$912$		0			0
$913$	−5.54256	+	0.991511i	−0.183432	+	0.0328142i
$914$		0			0
$915$	17.8015	−	13.3150i	0.588499	−	0.440180i
$916$		0			0
$917$		−	0.779324i		−	0.0257355i
$918$		0			0
$919$		−	8.61703i		−	0.284250i	−0.989849	−	0.142125i	$-0.954607\pi$
$919$		−	8.61703i		−	0.284250i	0.989849	−	0.142125i	$-0.0453934\pi$
$920$		0			0
$921$	18.3133	+	24.4840i	0.603445	+	0.806776i
$922$		0			0
$923$	6.15802			0.202694
$924$		0			0
$925$	4.58753			0.150837
$926$		0			0
$927$	−0.509974	+	1.73171i	−0.0167497	+	0.0568770i
$928$		0			0
$929$			2.05503i			0.0674235i	0.999432	+	0.0337117i	$0.0107328\pi$
$929$			2.05503i			0.0674235i	−0.999432	+	0.0337117i	$0.989267\pi$
$930$		0			0
$931$		−	25.2909i		−	0.828877i
$932$		0			0
$933$	4.29028	+	5.73589i	0.140457	+	0.187785i
$934$		0			0
$935$	−0.529593	−	2.96043i	−0.0173195	−	0.0968165i
$936$		0			0
$937$		−	19.8342i		−	0.647956i	−0.946065	−	0.323978i	$-0.894980\pi$
$937$		−	19.8342i		−	0.647956i	0.946065	−	0.323978i	$-0.105020\pi$
$938$		0			0
$939$	16.8631	−	12.6131i	0.550305	−	0.411612i
$940$		0			0
$941$	6.98887			0.227831			0.113915	−	0.993490i	$-0.463661\pi$
$941$	6.98887			0.227831			0.113915	+	0.993490i	$0.463661\pi$
$942$		0			0
$943$			28.9149i			0.941598i
$944$		0			0
$945$	0.713344	+	1.91954i	0.0232051	+	0.0624427i
$946$		0			0
$947$			29.3913i			0.955090i	0.878607	+	0.477545i	$0.158473\pi$
$947$			29.3913i			0.955090i	−0.878607	+	0.477545i	$0.841527\pi$
$948$		0			0
$949$	28.2994			0.918638
$950$		0			0
$951$	−7.23290	−	9.67003i	−0.234543	−	0.313572i
$952$		0			0
$953$	0.203883			0.00660443			0.00330221	−	0.999995i	$-0.498949\pi$
$953$	0.203883			0.00660443			0.00330221	+	0.999995i	$0.498949\pi$
$954$		0			0
$955$	21.9249			0.709474
$956$		0			0
$957$	−13.2408	+	14.1681i	−0.428013	+	0.457990i
$958$		0			0
$959$	7.73114			0.249652
$960$		0			0
$961$	−17.5565			−0.566339
$962$		0			0
$963$	12.9205	−	43.8740i	0.416357	−	1.41382i
$964$		0			0
$965$	−21.8699			−0.704017
$966$		0			0
$967$		−	55.4842i		−	1.78425i	−0.451786	−	0.892126i	$-0.649213\pi$
$967$		−	55.4842i		−	1.78425i	0.451786	−	0.892126i	$-0.350787\pi$
$968$		0			0
$969$	3.47591	+	4.64712i	0.111662	+	0.149287i
$970$		0			0
$971$			15.0321i			0.482402i	0.970475	+	0.241201i	$0.0775413\pi$
$971$			15.0321i			0.482402i	−0.970475	+	0.241201i	$0.922459\pi$
$972$		0			0
$973$	7.37874			0.236552
$974$		0			0
$975$	2.46896	+	3.30087i	0.0790699	+	0.105713i
$976$		0			0
$977$		−	44.5267i		−	1.42454i	−0.701908	−	0.712268i	$-0.747668\pi$
$977$		−	44.5267i		−	1.42454i	0.701908	−	0.712268i	$-0.252332\pi$
$978$		0			0
$979$	8.93791	+	49.9631i	0.285657	+	1.59683i
$980$		0			0
$981$	−52.8854	−	15.5743i	−1.68850	−	0.497248i
$982$		0			0
$983$			20.2004i			0.644293i	0.946690	+	0.322146i	$0.104404\pi$
$983$			20.2004i			0.644293i	−0.946690	+	0.322146i	$0.895596\pi$
$984$		0			0
$985$		−	18.0338i		−	0.574606i
$986$		0			0
$987$	1.85753	−	1.38938i	0.0591258	−	0.0442243i
$988$		0			0
$989$	−9.23091			−0.293526
$990$		0			0
$991$	39.1668			1.24417			0.622087	−	0.782949i	$-0.286285\pi$
$991$	39.1668			1.24417			0.622087	+	0.782949i	$0.286285\pi$
$992$		0			0
$993$	−7.48733	+	5.60030i	−0.237603	+	0.177720i
$994$		0			0
$995$		−	3.81625i		−	0.120983i
$996$		0			0
$997$			20.6426i			0.653757i	0.945066	+	0.326878i	$0.105997\pi$
$997$			20.6426i			0.653757i	−0.945066	+	0.326878i	$0.894003\pi$
$998$		0			0
$999$	−8.30370	−	22.3445i	−0.262717	−	0.706948i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2640.2.f.a.1121.2		8
3.2	odd	2		2640.2.f.b.1121.1		8
4.3	odd	2		330.2.d.b.131.7	yes	8
11.10	odd	2		2640.2.f.b.1121.2		8
12.11	even	2		330.2.d.a.131.8	yes	8
20.3	even	4		1650.2.f.d.1649.4		8
20.7	even	4		1650.2.f.f.1649.5		8
20.19	odd	2		1650.2.d.c.1451.2		8
33.32	even	2	inner	2640.2.f.a.1121.1		8
44.43	even	2		330.2.d.a.131.7	✓	8
60.23	odd	4		1650.2.f.e.1649.5		8
60.47	odd	4		1650.2.f.c.1649.4		8
60.59	even	2		1650.2.d.f.1451.1		8
132.131	odd	2		330.2.d.b.131.8	yes	8
220.43	odd	4		1650.2.f.c.1649.8		8
220.87	odd	4		1650.2.f.e.1649.1		8
220.219	even	2		1650.2.d.f.1451.2		8
660.263	even	4		1650.2.f.f.1649.1		8
660.527	even	4		1650.2.f.d.1649.8		8
660.659	odd	2		1650.2.d.c.1451.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.d.a.131.7	✓	8	44.43	even	2
330.2.d.a.131.8	yes	8	12.11	even	2
330.2.d.b.131.7	yes	8	4.3	odd	2
330.2.d.b.131.8	yes	8	132.131	odd	2
1650.2.d.c.1451.1		8	660.659	odd	2
1650.2.d.c.1451.2		8	20.19	odd	2
1650.2.d.f.1451.1		8	60.59	even	2
1650.2.d.f.1451.2		8	220.219	even	2
1650.2.f.c.1649.4		8	60.47	odd	4
1650.2.f.c.1649.8		8	220.43	odd	4
1650.2.f.d.1649.4		8	20.3	even	4
1650.2.f.d.1649.8		8	660.527	even	4
1650.2.f.e.1649.1		8	220.87	odd	4
1650.2.f.e.1649.5		8	60.23	odd	4
1650.2.f.f.1649.1		8	660.263	even	4
1650.2.f.f.1649.5		8	20.7	even	4
2640.2.f.a.1121.1		8	33.32	even	2	inner
2640.2.f.a.1121.2		8	1.1	even	1	trivial
2640.2.f.b.1121.1		8	3.2	odd	2
2640.2.f.b.1121.2		8	11.10	odd	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:	\( N \)	\(=\)	\( 2640 = 2^{4} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2640.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.38699 + 1.03743i) q^{3} -1.00000i q^{5} +0.394100i q^{7} +(0.847487 - 2.87781i) q^{9} +O(q^{10})\)	\(q+(-1.38699 + 1.03743i) q^{3} -1.00000i q^{5} +0.394100i q^{7} +(0.847487 - 2.87781i) q^{9} +(3.26480 - 0.584041i) q^{11} +2.37988i q^{13} +(1.03743 + 1.38699i) q^{15} +0.906774 q^{17} -3.69497i q^{19} +(-0.408850 - 0.546613i) q^{21} -3.54796i q^{23} -1.00000 q^{25} +(1.81006 + 4.87070i) q^{27} +3.37573 q^{29} -3.66654 q^{31} +(-3.92234 + 4.19705i) q^{33} +0.394100 q^{35} -4.58753 q^{37} +(-2.46896 - 3.30087i) q^{39} -8.14971 q^{41} -2.60175i q^{43} +(-2.87781 - 0.847487i) q^{45} +3.39825i q^{47} +6.84469 q^{49} +(-1.25769 + 0.940713i) q^{51} +6.45474i q^{53} +(-0.584041 - 3.26480i) q^{55} +(3.83327 + 5.12489i) q^{57} -7.76983i q^{59} -12.8346i q^{61} +(1.13414 + 0.333995i) q^{63} +2.37988 q^{65} +11.9195 q^{67} +(3.68076 + 4.92099i) q^{69} -2.58753i q^{71} -11.8911i q^{73} +(1.38699 - 1.03743i) q^{75} +(0.230170 + 1.28666i) q^{77} -2.56633i q^{79} +(-7.56353 - 4.87781i) q^{81} -1.69767 q^{83} -0.906774i q^{85} +(-4.68211 + 3.50208i) q^{87} +15.3036i q^{89} -0.937911 q^{91} +(5.08545 - 3.80377i) q^{93} -3.69497 q^{95} -10.1213 q^{97} +(1.08612 - 9.89042i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 2 * q^9	\( 8 q - 2 q^{3} + 2 q^{9} - 6 q^{11} - 4 q^{15} + 4 q^{17} - 8 q^{21} - 8 q^{25} + 22 q^{27} - 4 q^{29} + 4 q^{31} - 2 q^{33} - 12 q^{37} + 8 q^{39} - 16 q^{41} - 4 q^{49} + 28 q^{51} + 6 q^{55} + 14 q^{57} - 14 q^{63} + 4 q^{65} + 12 q^{67} + 8 q^{69} + 2 q^{75} + 36 q^{77} + 2 q^{81} + 72 q^{83} + 22 q^{87} + 48 q^{91} + 8 q^{93} - 20 q^{95} - 8 q^{97} + 6 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 + 2 * q^9 - 6 * q^11 - 4 * q^15 + 4 * q^17 - 8 * q^21 - 8 * q^25 + 22 * q^27 - 4 * q^29 + 4 * q^31 - 2 * q^33 - 12 * q^37 + 8 * q^39 - 16 * q^41 - 4 * q^49 + 28 * q^51 + 6 * q^55 + 14 * q^57 - 14 * q^63 + 4 * q^65 + 12 * q^67 + 8 * q^69 + 2 * q^75 + 36 * q^77 + 2 * q^81 + 72 * q^83 + 22 * q^87 + 48 * q^91 + 8 * q^93 - 20 * q^95 - 8 * q^97 + 6 * q^99

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