LMFDB - Embedded newform 2736.2.bm.r.559.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2736,2,Mod(559,2736)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2736, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 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("2736.559");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2736 = 2^{4} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2736.bm (of order $6$, degree $2$, 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:	$21.8470699930$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 30x^{5} - 5x^{4} + 114x^{3} + 300x^{2} + 116x + 19 $ x^8 - 2x^7 - 30x^5 - 5x^4 + 114x^3 + 300x^2 + 116x + 19
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 912)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			559.3
Root			$-1.27736 - 1.04884i$ of defining polynomial
Character	$\chi$	$=$	2736.559
Dual form			2736.2.bm.r.1855.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.912850 - 1.58110i) q^{5} +4.99333i q^{7} +O(q^{10})$	$q+(0.912850 - 1.58110i) q^{5} +4.99333i q^{7} +3.82973i q^{11} +(1.00771 - 0.581803i) q^{13} +(3.73720 - 6.47303i) q^{17} +(-3.22949 - 2.92752i) q^{19} +(2.24626 - 1.29688i) q^{23} +(0.833411 + 1.44351i) q^{25} +(6.63328 - 3.82973i) q^{29} -0.158876 q^{31} +(7.89497 + 4.55816i) q^{35} +8.25462i q^{37} +(1.07038 + 0.617985i) q^{41} +(1.90245 + 1.09838i) q^{43} +(0.0858062 - 0.0495402i) q^{47} -17.9334 q^{49} +(-2.82435 + 1.63064i) q^{53} +(6.05519 + 3.49597i) q^{55} +(-5.14234 + 8.90680i) q^{59} +(5.64100 + 9.77049i) q^{61} -2.12439i q^{65} +(6.97575 + 12.0824i) q^{67} +(-1.91151 + 3.31082i) q^{71} +(-2.32570 + 4.02823i) q^{73} -19.1231 q^{77} +(4.74626 - 8.22077i) q^{79} -2.83193i q^{83} +(-6.82301 - 11.8178i) q^{85} +(-11.9102 + 6.87633i) q^{89} +(2.90514 + 5.03185i) q^{91} +(-7.57675 + 2.43377i) q^{95} +(8.50771 + 4.91193i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{5}+O(q^{10}) $ 8 * q + 2 * q^5	$ 8 q + 2 q^{5} - 4 q^{17} - 6 q^{23} - 12 q^{25} + 12 q^{29} - 28 q^{31} - 18 q^{35} + 12 q^{41} - 18 q^{43} - 12 q^{47} - 24 q^{49} + 6 q^{53} + 12 q^{55} - 10 q^{59} - 4 q^{61} + 6 q^{67} + 8 q^{71} - 8 q^{73} - 28 q^{77} + 14 q^{79} - 8 q^{85} - 54 q^{89} + 26 q^{91} - 38 q^{95} + 60 q^{97}+O(q^{100}) $ 8 * q + 2 * q^5 - 4 * q^17 - 6 * q^23 - 12 * q^25 + 12 * q^29 - 28 * q^31 - 18 * q^35 + 12 * q^41 - 18 * q^43 - 12 * q^47 - 24 * q^49 + 6 * q^53 + 12 * q^55 - 10 * q^59 - 4 * q^61 + 6 * q^67 + 8 * q^71 - 8 * q^73 - 28 * q^77 + 14 * q^79 - 8 * q^85 - 54 * q^89 + 26 * q^91 - 38 * q^95 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times$.

$n$	$1009$	$1217$	$1711$	$2053$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$1$

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
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.912850	−	1.58110i	0.408239	−	0.707090i	−0.586454	−	0.809983i	$-0.699476\pi$
$5$	0.912850	−	1.58110i	0.408239	−	0.707090i	0.994692	+	0.102892i	$0.0328098\pi$
$6$		0			0
$7$			4.99333i			1.88730i	0.330941	+	0.943652i	$0.392634\pi$
$7$			4.99333i			1.88730i	−0.330941	+	0.943652i	$0.607366\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$			3.82973i			1.15471i	0.816494	+	0.577353i	$0.195914\pi$
$11$			3.82973i			1.15471i	−0.816494	+	0.577353i	$0.804086\pi$
$12$		0			0
$13$	1.00771	−	0.581803i	0.279489	−	0.161363i	−0.353703	−	0.935358i	$-0.615078\pi$
$13$	1.00771	−	0.581803i	0.279489	−	0.161363i	0.633192	+	0.773995i	$0.281744\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.73720	−	6.47303i	0.906405	−	1.56994i	0.0873854	−	0.996175i	$-0.472149\pi$
$17$	3.73720	−	6.47303i	0.906405	−	1.56994i	0.819020	−	0.573765i	$-0.194518\pi$
$18$		0			0
$19$	−3.22949	−	2.92752i	−0.740896	−	0.671619i
$19$	−3.22949	−	2.92752i	−0.740896	−	0.671619i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.24626	−	1.29688i	0.468378	−	0.270418i	−0.247183	−	0.968969i	$-0.579505\pi$
$23$	2.24626	−	1.29688i	0.468378	−	0.270418i	0.715560	+	0.698551i	$0.246171\pi$
$24$		0			0
$25$	0.833411	+	1.44351i	0.166682	+	0.288702i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	6.63328	−	3.82973i	1.23177	−	0.711163i	0.264371	−	0.964421i	$-0.414836\pi$
$29$	6.63328	−	3.82973i	1.23177	−	0.711163i	0.967399	+	0.253258i	$0.0815022\pi$
$30$		0			0
$31$	−0.158876			−0.0285350			−0.0142675	−	0.999898i	$-0.504542\pi$
$31$	−0.158876			−0.0285350			−0.0142675	+	0.999898i	$0.504542\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	7.89497	+	4.55816i	1.33449	+	0.770470i
$36$		0			0
$37$			8.25462i			1.35705i	0.734577	+	0.678525i	$0.237381\pi$
$37$			8.25462i			1.35705i	−0.734577	+	0.678525i	$0.762619\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.07038	+	0.617985i	0.167166	+	0.0965130i	0.581249	−	0.813726i	$-0.302564\pi$
$41$	1.07038	+	0.617985i	0.167166	+	0.0965130i	−0.414083	+	0.910239i	$0.635898\pi$
$42$		0			0
$43$	1.90245	+	1.09838i	0.290121	+	0.167501i	0.637996	−	0.770039i	$-0.279764\pi$
$43$	1.90245	+	1.09838i	0.290121	+	0.167501i	−0.347876	+	0.937541i	$0.613097\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.0858062	−	0.0495402i	0.0125161	−	0.00722618i	−0.493729	−	0.869616i	$-0.664366\pi$
$47$	0.0858062	−	0.0495402i	0.0125161	−	0.00722618i	0.506245	+	0.862390i	$0.331033\pi$
$48$		0			0
$49$	−17.9334			−2.56191
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2.82435	+	1.63064i	−0.387955	+	0.223986i	−0.681274	−	0.732029i	$-0.738574\pi$
$53$	−2.82435	+	1.63064i	−0.387955	+	0.223986i	0.293319	+	0.956015i	$0.405240\pi$
$54$		0			0
$55$	6.05519	+	3.49597i	0.816482	+	0.471396i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−5.14234	+	8.90680i	−0.669476	+	1.15957i	0.308575	+	0.951200i	$0.400148\pi$
$59$	−5.14234	+	8.90680i	−0.669476	+	1.15957i	−0.978051	+	0.208366i	$0.933185\pi$
$60$		0			0
$61$	5.64100	+	9.77049i	0.722256	+	1.25098i	0.960094	+	0.279679i	$0.0902279\pi$
$61$	5.64100	+	9.77049i	0.722256	+	1.25098i	−0.237838	+	0.971305i	$0.576439\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	2.12439i		−	0.263499i
$66$		0			0
$67$	6.97575	+	12.0824i	0.852224	+	1.47610i	0.879197	+	0.476459i	$0.158080\pi$
$67$	6.97575	+	12.0824i	0.852224	+	1.47610i	−0.0269729	+	0.999636i	$0.508587\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.91151	+	3.31082i	−0.226854	+	0.392923i	−0.956874	−	0.290503i	$-0.906177\pi$
$71$	−1.91151	+	3.31082i	−0.226854	+	0.392923i	0.730020	+	0.683426i	$0.239511\pi$
$72$		0			0
$73$	−2.32570	+	4.02823i	−0.272202	+	0.471469i	−0.969426	−	0.245386i	$-0.921085\pi$
$73$	−2.32570	+	4.02823i	−0.272202	+	0.471469i	0.697223	+	0.716854i	$0.254419\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−19.1231			−2.17928
$78$		0			0
$79$	4.74626	−	8.22077i	0.533996	−	0.924908i	−0.465215	−	0.885198i	$-0.654023\pi$
$79$	4.74626	−	8.22077i	0.533996	−	0.924908i	0.999211	−	0.0397107i	$-0.0126436\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	2.83193i		−	0.310844i	−0.987848	−	0.155422i	$-0.950326\pi$
$83$		−	2.83193i		−	0.310844i	0.987848	−	0.155422i	$-0.0496738\pi$
$84$		0			0
$85$	−6.82301	−	11.8178i	−0.740059	−	1.28182i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−11.9102	+	6.87633i	−1.26247	+	0.728890i	−0.973553	−	0.228463i	$-0.926630\pi$
$89$	−11.9102	+	6.87633i	−1.26247	+	0.728890i	−0.288922	+	0.957353i	$0.593297\pi$
$90$		0			0
$91$	2.90514	+	5.03185i	0.304541	+	0.527481i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−7.57675	+	2.43377i	−0.777358	+	0.249699i
$96$		0			0
$97$	8.50771	+	4.91193i	0.863827	+	0.498731i	0.865292	−	0.501268i	$-0.167133\pi$
$97$	8.50771	+	4.91193i	0.863827	+	0.498731i	−0.00146478	+	0.999999i	$0.500466\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.57833	+	13.1260i	0.754072	+	1.30609i	0.945834	+	0.324649i	$0.105246\pi$
$101$	7.57833	+	13.1260i	0.754072	+	1.30609i	−0.191763	+	0.981441i	$0.561420\pi$
$102$		0			0
$103$	−10.6487			−1.04925			−0.524624	−	0.851334i	$-0.675794\pi$
$103$	−10.6487			−1.04925			−0.524624	+	0.851334i	$0.675794\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	11.3336			1.09566			0.547832	−	0.836588i	$-0.315453\pi$
$107$	11.3336			1.09566			0.547832	+	0.836588i	$0.315453\pi$
$108$		0			0
$109$	6.14100	+	3.54551i	0.588201	+	0.339598i	0.764386	−	0.644759i	$-0.223042\pi$
$109$	6.14100	+	3.54551i	0.588201	+	0.339598i	−0.176185	+	0.984357i	$0.556376\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	13.6536i		−	1.28442i	−0.766528	−	0.642211i	$-0.778017\pi$
$113$		−	13.6536i		−	1.28442i	0.766528	−	0.642211i	$-0.221983\pi$
$114$		0			0
$115$		−	4.73542i		−	0.441580i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	32.3220	+	18.6611i	2.96295	+	1.71066i
$120$		0			0
$121$	−3.66682			−0.333348
$122$		0			0
$123$		0			0
$124$		0			0
$125$	12.1716			1.08866
$126$		0			0
$127$	−1.00000	−	1.73205i	−0.0887357	−	0.153695i	0.818241	−	0.574875i	$-0.194949\pi$
$127$	−1.00000	−	1.73205i	−0.0887357	−	0.153695i	−0.906977	+	0.421180i	$0.861616\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	11.2116	+	6.47303i	0.979563	+	0.565551i	0.902138	−	0.431447i	$-0.141997\pi$
$131$	11.2116	+	6.47303i	0.979563	+	0.565551i	0.0774250	+	0.996998i	$0.475330\pi$
$132$		0			0
$133$	14.6181	−	16.1259i	1.26755	−	1.39830i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	0.965250	−	0.261329i	$-0.0841608\pi$
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	−0.708942	+	0.705266i	$0.750827\pi$
$138$		0			0
$139$	7.26916	−	4.19685i	0.616562	−	0.355972i	−0.158967	−	0.987284i	$-0.550816\pi$
$139$	7.26916	−	4.19685i	0.616562	−	0.355972i	0.775529	+	0.631311i	$0.217483\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2.22815	+	3.85927i	0.186327	+	0.322728i
$144$		0			0
$145$		−	13.9839i		−	1.16130i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2.63463	+	4.56331i	−0.215837	+	0.373841i	−0.953531	−	0.301294i	$-0.902581\pi$
$149$	−2.63463	+	4.56331i	−0.215837	+	0.373841i	0.737694	+	0.675135i	$0.235915\pi$
$150$		0			0
$151$	−4.34860			−0.353884			−0.176942	−	0.984221i	$-0.556621\pi$
$151$	−4.34860			−0.353884			−0.176942	+	0.984221i	$0.556621\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.145030	+	0.251199i	−0.0116491	+	0.0201768i
$156$		0			0
$157$	3.97441	−	6.88388i	0.317192	−	0.549393i	−0.662709	−	0.748877i	$-0.730593\pi$
$157$	3.97441	−	6.88388i	0.317192	−	0.549393i	0.979901	+	0.199484i	$0.0639266\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	6.47575	+	11.2163i	0.510361	+	0.883971i
$162$		0			0
$163$		−	6.13022i		−	0.480156i	−0.970754	−	0.240078i	$-0.922827\pi$
$163$		−	6.13022i		−	0.480156i	0.970754	−	0.240078i	$-0.0771731\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−11.2463	−	19.4791i	−0.870262	−	1.50734i	−0.861726	−	0.507374i	$-0.830616\pi$
$167$	−11.2463	−	19.4791i	−0.870262	−	1.50734i	−0.00853590	−	0.999964i	$-0.502717\pi$
$168$		0			0
$169$	−5.82301	+	10.0858i	−0.447924	+	0.775827i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−13.2666	−	7.65946i	−1.00864	−	0.582338i	−0.0978458	−	0.995202i	$-0.531195\pi$
$173$	−13.2666	−	7.65946i	−1.00864	−	0.582338i	−0.910793	+	0.412864i	$0.864529\pi$
$174$		0			0
$175$	−7.20793	+	4.16150i	−0.544869	+	0.314580i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−20.2793			−1.51575			−0.757873	−	0.652402i	$-0.773761\pi$
$179$	−20.2793			−1.51575			−0.757873	+	0.652402i	$0.773761\pi$
$180$		0			0
$181$	11.6181	−	6.70771i	0.863566	−	0.498580i	−0.00163872	−	0.999999i	$-0.500522\pi$
$181$	11.6181	−	6.70771i	0.863566	−	0.498580i	0.865205	+	0.501419i	$0.167188\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	13.0514	+	7.53523i	0.959557	+	0.554001i
$186$		0			0
$187$	24.7899	+	14.3125i	1.81282	+	1.04663i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	15.6389i		−	1.13159i	−0.824546	−	0.565795i	$-0.808569\pi$
$191$		−	15.6389i		−	1.13159i	0.824546	−	0.565795i	$-0.191431\pi$
$192$		0			0
$193$	−16.9773	−	9.80187i	−1.22206	−	0.705554i	−0.256699	−	0.966491i	$-0.582635\pi$
$193$	−16.9773	−	9.80187i	−1.22206	−	0.705554i	−0.965356	+	0.260937i	$0.915968\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	4.17430			0.297407			0.148703	−	0.988882i	$-0.452490\pi$
$197$	4.17430			0.297407			0.148703	+	0.988882i	$0.452490\pi$
$198$		0			0
$199$	19.4899	−	11.2525i	1.38160	−	0.797670i	0.389255	−	0.921130i	$-0.372733\pi$
$199$	19.4899	−	11.2525i	1.38160	−	0.797670i	0.992349	+	0.123460i	$0.0393992\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	19.1231	+	33.1222i	1.34218	+	2.32472i
$204$		0			0
$205$	1.95419	−	1.12825i	0.136487	−	0.0788007i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	11.2116	−	12.3681i	0.775523	−	0.855518i
$210$		0			0
$211$	−9.53573	+	16.5164i	−0.656467	+	1.13703i	0.325057	+	0.945694i	$0.394617\pi$
$211$	−9.53573	+	16.5164i	−0.656467	+	1.13703i	−0.981524	+	0.191340i	$0.938717\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	3.47330	−	2.00531i	0.236877	−	0.136761i
$216$		0			0
$217$		−	0.793322i		−	0.0538542i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		−	8.69727i		−	0.585041i
$222$		0			0
$223$	−6.92056	+	11.9868i	−0.463435	+	0.802693i	−0.999129	−	0.0417189i	$-0.986717\pi$
$223$	−6.92056	+	11.9868i	−0.463435	+	0.802693i	0.535694	+	0.844412i	$0.320050\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.53833			0.367592			0.183796	−	0.982964i	$-0.441161\pi$
$227$	5.53833			0.367592			0.183796	+	0.982964i	$0.441161\pi$
$228$		0			0
$229$	−1.31822			−0.0871105			−0.0435552	−	0.999051i	$-0.513868\pi$
$229$	−1.31822			−0.0871105			−0.0435552	+	0.999051i	$0.513868\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−2.56290	+	4.43908i	−0.167901	+	0.290814i	−0.937682	−	0.347495i	$-0.887032\pi$
$233$	−2.56290	+	4.43908i	−0.167901	+	0.290814i	0.769780	+	0.638309i	$0.220366\pi$
$234$		0			0
$235$		−	0.180891i		−	0.0118000i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			5.42569i			0.350958i	0.984483	+	0.175479i	$0.0561475\pi$
$239$			5.42569i			0.350958i	−0.984483	+	0.175479i	$0.943853\pi$
$240$		0			0
$241$	26.4153	−	15.2509i	1.70156	−	0.982395i	0.757371	−	0.652985i	$-0.226484\pi$
$241$	26.4153	−	15.2509i	1.70156	−	0.982395i	0.944187	−	0.329410i	$-0.106850\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−16.3705	+	28.3545i	−1.04587	+	1.81150i
$246$		0			0
$247$	−4.95764	−	1.07117i	−0.315447	−	0.0681570i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−20.2974	+	11.7187i	−1.28116	+	0.739679i	−0.977061	−	0.212961i	$-0.931689\pi$
$251$	−20.2974	+	11.7187i	−1.28116	+	0.739679i	−0.304101	+	0.952640i	$0.598356\pi$
$252$		0			0
$253$	4.96670	+	8.60257i	0.312254	+	0.540839i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−9.45764	+	5.46037i	−0.589951	+	0.340609i	−0.765078	−	0.643937i	$-0.777300\pi$
$257$	−9.45764	+	5.46037i	−0.589951	+	0.340609i	0.175127	+	0.984546i	$0.443966\pi$
$258$		0			0
$259$	−41.2181			−2.56117
$260$		0			0
$261$		0			0
$262$		0			0
$263$	12.1962	+	7.04147i	0.752049	+	0.434196i	0.826434	−	0.563034i	$-0.190366\pi$
$263$	12.1962	+	7.04147i	0.752049	+	0.434196i	−0.0743847	+	0.997230i	$0.523699\pi$
$264$		0			0
$265$			5.95412i			0.365759i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−18.4576	−	10.6565i	−1.12538	−	0.649740i	−0.182613	−	0.983185i	$-0.558455\pi$
$269$	−18.4576	−	10.6565i	−1.12538	−	0.649740i	−0.942769	+	0.333445i	$0.891789\pi$
$270$		0			0
$271$	−1.21053	−	0.698898i	−0.0735343	−	0.0424551i	0.462782	−	0.886472i	$-0.346851\pi$
$271$	−1.21053	−	0.698898i	−0.0735343	−	0.0424551i	−0.536316	+	0.844017i	$0.680185\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−5.52826	+	3.19174i	−0.333366	+	0.192469i
$276$		0			0
$277$	−0.703049			−0.0422421			−0.0211211	−	0.999777i	$-0.506724\pi$
$277$	−0.703049			−0.0422421			−0.0211211	+	0.999777i	$0.506724\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	2.56694	−	1.48202i	0.153131	−	0.0884100i	−0.421477	−	0.906839i	$-0.638488\pi$
$281$	2.56694	−	1.48202i	0.153131	−	0.0884100i	0.574607	+	0.818429i	$0.305155\pi$
$282$		0			0
$283$	11.2974	+	6.52257i	0.671562	+	0.387726i	0.796668	−	0.604417i	$-0.206594\pi$
$283$	11.2974	+	6.52257i	0.671562	+	0.387726i	−0.125106	+	0.992143i	$0.539927\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.08581	+	5.34477i	−0.182149	+	0.315492i
$288$		0			0
$289$	−19.4334	−	33.6596i	−1.14314	−	1.97998i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			7.92036i			0.462713i	0.972869	+	0.231356i	$0.0743163\pi$
$293$			7.92036i			0.462713i	−0.972869	+	0.231356i	$0.925684\pi$
$294$		0			0
$295$	9.38837	+	16.2611i	0.546612	+	0.946760i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.50906	−	2.61376i	0.0872710	−	0.151158i
$300$		0			0
$301$	−5.48458	+	9.49956i	−0.316126	+	0.547546i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	20.5975			1.17941
$306$		0			0
$307$	5.22949	−	9.05775i	0.298463	−	0.516953i	−0.677322	−	0.735687i	$-0.736859\pi$
$307$	5.22949	−	9.05775i	0.298463	−	0.516953i	0.975784	+	0.218734i	$0.0701928\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		−	21.9806i		−	1.24640i	−0.782061	−	0.623202i	$-0.785831\pi$
$311$		−	21.9806i		−	1.24640i	0.782061	−	0.623202i	$-0.214169\pi$
$312$		0			0
$313$	14.4438	+	25.0174i	0.816411	+	1.41407i	0.908310	+	0.418298i	$0.137373\pi$
$313$	14.4438	+	25.0174i	0.816411	+	1.41407i	−0.0918985	+	0.995768i	$0.529294\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.511979	+	0.295591i	−0.0287556	+	0.0166021i	−0.514309	−	0.857605i	$-0.671952\pi$
$317$	−0.511979	+	0.295591i	−0.0287556	+	0.0166021i	0.485553	+	0.874207i	$0.338618\pi$
$318$		0			0
$319$	14.6668	+	25.4037i	0.821184	+	1.42233i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−31.0192	+	9.96385i	−1.72595	+	0.554403i
$324$		0			0
$325$	1.67968	+	0.969763i	0.0931718	+	0.0537927i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.247371	+	0.428459i	0.0136380	+	0.0236217i
$330$		0			0
$331$	−11.4254			−0.627999			−0.314000	−	0.949423i	$-0.601669\pi$
$331$	−11.4254			−0.627999			−0.314000	+	0.949423i	$0.601669\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	25.4713			1.39164
$336$		0			0
$337$	−6.78176	−	3.91545i	−0.369426	−	0.213288i	0.303782	−	0.952742i	$-0.401751\pi$
$337$	−6.78176	−	3.91545i	−0.369426	−	0.213288i	−0.673208	+	0.739453i	$0.735084\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	0.608453i		−	0.0329496i
$342$		0			0
$343$		−	54.5941i		−	2.94780i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	10.3475	+	5.97413i	0.555482	+	0.320708i	0.751330	−	0.659926i	$-0.229413\pi$
$347$	10.3475	+	5.97413i	0.555482	+	0.320708i	−0.195848	+	0.980634i	$0.562746\pi$
$348$		0			0
$349$	−14.2053			−0.760394			−0.380197	−	0.924905i	$-0.624144\pi$
$349$	−14.2053			−0.760394			−0.380197	+	0.924905i	$0.624144\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−18.9153			−1.00676			−0.503379	−	0.864066i	$-0.667910\pi$
$353$	−18.9153			−1.00676			−0.503379	+	0.864066i	$0.667910\pi$
$354$		0			0
$355$	3.48983	+	6.04457i	0.185221	+	0.320812i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−14.6338	−	8.44880i	−0.772340	−	0.445911i	0.0613687	−	0.998115i	$-0.480453\pi$
$359$	−14.6338	−	8.44880i	−0.772340	−	0.445911i	−0.833709	+	0.552204i	$0.813787\pi$
$360$		0			0
$361$	1.85924	+	18.9088i	0.0978546	+	0.995201i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	4.24603	+	7.35433i	0.222247	+	0.384943i
$366$		0			0
$367$	20.7617	−	11.9868i	1.08375	−	0.625704i	0.151845	−	0.988404i	$-0.451478\pi$
$367$	20.7617	−	11.9868i	1.08375	−	0.625704i	0.931906	+	0.362700i	$0.118145\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−8.14234	−	14.1029i	−0.422729	−	0.732189i
$372$		0			0
$373$			2.10166i			0.108820i	0.998519	+	0.0544098i	$0.0173277\pi$
$373$			2.10166i			0.108820i	−0.998519	+	0.0544098i	$0.982672\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	4.45630	−	7.71853i	0.229511	−	0.397525i
$378$		0			0
$379$	−0.923156			−0.0474193			−0.0237097	−	0.999719i	$-0.507548\pi$
$379$	−0.923156			−0.0474193			−0.0237097	+	0.999719i	$0.507548\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	14.1951	−	24.5866i	0.725335	−	1.25632i	−0.233502	−	0.972356i	$-0.575018\pi$
$383$	14.1951	−	24.5866i	0.725335	−	1.25632i	0.958836	−	0.283960i	$-0.0916483\pi$
$384$		0			0
$385$	−17.4565	+	30.2356i	−0.889667	+	1.54095i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−4.94370	−	8.56274i	−0.250655	−	0.434148i	0.713051	−	0.701112i	$-0.247313\pi$
$389$	−4.94370	−	8.56274i	−0.250655	−	0.434148i	−0.963706	+	0.266964i	$0.913979\pi$
$390$		0			0
$391$		−	19.3868i		−	0.980433i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−8.66524	−	15.0086i	−0.435996	−	0.755167i
$396$		0			0
$397$	6.83072	−	11.8312i	0.342824	−	0.593789i	−0.642132	−	0.766594i	$-0.721950\pi$
$397$	6.83072	−	11.8312i	0.342824	−	0.593789i	0.984956	+	0.172805i	$0.0552832\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	30.6538	+	17.6980i	1.53078	+	0.883796i	0.999326	+	0.0367080i	$0.0116871\pi$
$401$	30.6538	+	17.6980i	1.53078	+	0.883796i	0.531453	+	0.847088i	$0.321646\pi$
$402$		0			0
$403$	−0.160102	+	0.0924347i	−0.00797522	+	0.00460450i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−31.6130			−1.56700
$408$		0			0
$409$	15.1410	−	8.74166i	0.748674	−	0.432247i	−0.0765405	−	0.997066i	$-0.524387\pi$
$409$	15.1410	−	8.74166i	0.748674	−	0.432247i	0.825215	+	0.564819i	$0.191054\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−44.4746	−	25.6774i	−2.18845	−	1.26350i
$414$		0			0
$415$	−4.47757	−	2.58512i	−0.219795	−	0.126899i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	20.5655i		−	1.00469i	−0.864667	−	0.502345i	$-0.832471\pi$
$419$		−	20.5655i		−	1.00469i	0.864667	−	0.502345i	$-0.167529\pi$
$420$		0			0
$421$	2.03108	+	1.17265i	0.0989890	+	0.0571513i	0.548677	−	0.836034i	$-0.315132\pi$
$421$	2.03108	+	1.17265i	0.0989890	+	0.0571513i	−0.449688	+	0.893186i	$0.648465\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	12.4585			0.604327
$426$		0			0
$427$	−48.7873	+	28.1674i	−2.36099	+	1.36312i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−5.21161	−	9.02678i	−0.251035	−	0.434805i	0.712776	−	0.701391i	$-0.247437\pi$
$431$	−5.21161	−	9.02678i	−0.251035	−	0.434805i	−0.963811	+	0.266587i	$0.914104\pi$
$432$		0			0
$433$	−2.68680	+	1.55123i	−0.129120	+	0.0745472i	−0.563168	−	0.826342i	$-0.690418\pi$
$433$	−2.68680	+	1.55123i	−0.129120	+	0.0745472i	0.434049	+	0.900889i	$0.357084\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−11.0509	−	2.38772i	−0.528637	−	0.114220i
$438$		0			0
$439$	5.30624	−	9.19068i	0.253253	−	0.438647i	−0.711166	−	0.703024i	$-0.751833\pi$
$439$	5.30624	−	9.19068i	0.253253	−	0.438647i	0.964420	+	0.264376i	$0.0851661\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−16.8438	+	9.72478i	−0.800274	+	0.462038i	−0.843567	−	0.537024i	$-0.819548\pi$
$443$	−16.8438	+	9.72478i	−0.800274	+	0.462038i	0.0432932	+	0.999062i	$0.486215\pi$
$444$		0			0
$445$			25.1082i			1.19024i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	10.3750i		−	0.489628i	−0.969570	−	0.244814i	$-0.921273\pi$
$449$		−	10.3750i		−	0.489628i	0.969570	−	0.244814i	$-0.0787269\pi$
$450$		0			0
$451$	−2.36672	+	4.09927i	−0.111444	+	0.193027i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	10.6078			0.497302
$456$		0			0
$457$	−23.9483			−1.12026			−0.560128	−	0.828406i	$-0.689248\pi$
$457$	−23.9483			−1.12026			−0.560128	+	0.828406i	$0.689248\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	16.1090	−	27.9017i	0.750273	−	1.29951i	−0.197418	−	0.980319i	$-0.563256\pi$
$461$	16.1090	−	27.9017i	0.750273	−	1.29951i	0.947690	−	0.319191i	$-0.103411\pi$
$462$		0			0
$463$			14.0506i			0.652986i	0.945200	+	0.326493i	$0.105867\pi$
$463$			14.0506i			0.652986i	−0.945200	+	0.326493i	$0.894133\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			27.3890i			1.26741i	0.773574	+	0.633706i	$0.218467\pi$
$467$			27.3890i			1.26741i	−0.773574	+	0.633706i	$0.781533\pi$
$468$		0			0
$469$	−60.3313	+	34.8323i	−2.78584	+	1.60840i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4.20649	+	7.28586i	−0.193415	+	0.335004i
$474$		0			0
$475$	1.53441	−	7.10164i	0.0704037	−	0.325845i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	19.8140	−	11.4396i	0.905327	−	0.522691i	0.0264023	−	0.999651i	$-0.491595\pi$
$479$	19.8140	−	11.4396i	0.905327	−	0.522691i	0.878925	+	0.476961i	$0.158262\pi$
$480$		0			0
$481$	4.80256	+	8.31828i	0.218978	+	0.379281i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	15.5325	−	8.96771i	0.705296	−	0.407203i
$486$		0			0
$487$	−3.11288			−0.141058			−0.0705291	−	0.997510i	$-0.522469\pi$
$487$	−3.11288			−0.141058			−0.0705291	+	0.997510i	$0.522469\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1.41361	+	0.816146i	0.0637952	+	0.0368322i	0.531558	−	0.847022i	$-0.321607\pi$
$491$	1.41361	+	0.816146i	0.0637952	+	0.0368322i	−0.467763	+	0.883854i	$0.654940\pi$
$492$		0			0
$493$		−	57.2499i		−	2.57841i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−16.5321	−	9.54479i	−0.741564	−	0.428142i
$498$		0			0
$499$	−1.97260	−	1.13888i	−0.0883055	−	0.0509832i	0.455197	−	0.890391i	$-0.349569\pi$
$499$	−1.97260	−	1.13888i	−0.0883055	−	0.0509832i	−0.543503	+	0.839408i	$0.682902\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	30.0411	−	17.3442i	1.33947	−	0.773341i	0.352738	−	0.935722i	$-0.385251\pi$
$503$	30.0411	−	17.3442i	1.33947	−	0.773341i	0.986728	+	0.162381i	$0.0519174\pi$
$504$		0			0
$505$	27.6715			1.23137
$506$		0			0
$507$		0			0
$508$		0			0
$509$	36.8310	−	21.2644i	1.63251	−	0.942528i	0.649190	−	0.760626i	$-0.275108\pi$
$509$	36.8310	−	21.2644i	1.63251	−	0.942528i	0.983317	−	0.181902i	$-0.0582253\pi$
$510$		0			0
$511$	−20.1143	−	11.6130i	−0.889804	−	0.513729i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−9.72067	+	16.8367i	−0.428344	+	0.741913i
$516$		0			0
$517$	0.189726	+	0.328614i	0.00834412	+	0.0144524i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			33.0231i			1.44677i	0.690445	+	0.723385i	$0.257415\pi$
$521$			33.0231i			1.44677i	−0.690445	+	0.723385i	$0.742585\pi$
$522$		0			0
$523$	−13.2604	−	22.9677i	−0.579838	−	1.00431i	−0.995497	−	0.0947890i	$-0.969782\pi$
$523$	−13.2604	−	22.9677i	−0.579838	−	1.00431i	0.415659	−	0.909521i	$-0.363551\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.593753	+	1.02841i	−0.0258643	+	0.0447982i
$528$		0			0
$529$	−8.13621	+	14.0923i	−0.353748	+	0.612710i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1.43818			0.0622946
$534$		0			0
$535$	10.3459	−	17.9196i	0.447293	−	0.774734i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	68.6800i		−	2.95826i
$540$		0			0
$541$	17.4488	+	30.2222i	0.750183	+	1.29936i	0.947734	+	0.319063i	$0.103368\pi$
$541$	17.4488	+	30.2222i	0.750183	+	1.29936i	−0.197550	+	0.980293i	$0.563299\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	11.2116	−	6.47303i	0.480253	−	0.277274i
$546$		0			0
$547$	−5.20524	−	9.01575i	−0.222560	−	0.385486i	0.733024	−	0.680202i	$-0.238108\pi$
$547$	−5.20524	−	9.01575i	−0.222560	−	0.385486i	−0.955585	+	0.294717i	$0.904775\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−32.6338	−	7.05100i	−1.39024	−	0.300383i
$552$		0			0
$553$	41.0490	+	23.6997i	1.74558	+	1.00781i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−7.49252	−	12.9774i	−0.317468	−	0.549871i	0.662491	−	0.749070i	$-0.269499\pi$
$557$	−7.49252	−	12.9774i	−0.317468	−	0.549871i	−0.979959	+	0.199199i	$0.936166\pi$
$558$		0			0
$559$	2.55616			0.108114
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−17.8614			−0.752769			−0.376384	−	0.926464i	$-0.622833\pi$
$563$	−17.8614			−0.752769			−0.376384	+	0.926464i	$0.622833\pi$
$564$		0			0
$565$	−21.5877	−	12.4637i	−0.908202	−	0.524351i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	33.5325i		−	1.40576i	−0.711311	−	0.702878i	$-0.751898\pi$
$569$		−	33.5325i		−	1.40576i	0.711311	−	0.702878i	$-0.248102\pi$
$570$		0			0
$571$		−	15.6638i		−	0.655510i	−0.944763	−	0.327755i	$-0.893708\pi$
$571$		−	15.6638i		−	0.655510i	0.944763	−	0.327755i	$-0.106292\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	3.74412	+	2.16167i	0.156141	+	0.0901478i
$576$		0			0
$577$	31.8972			1.32790			0.663948	−	0.747779i	$-0.268880\pi$
$577$	31.8972			1.32790			0.663948	+	0.747779i	$0.268880\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	14.1408			0.586658
$582$		0			0
$583$	−6.24492	−	10.8165i	−0.258638	−	0.447974i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	14.5826	+	8.41927i	0.601888	+	0.347500i	0.769784	−	0.638304i	$-0.220364\pi$
$587$	14.5826	+	8.41927i	0.601888	+	0.347500i	−0.167896	+	0.985805i	$0.553697\pi$
$588$		0			0
$589$	0.513089	+	0.465113i	0.0211415	+	0.0191647i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	10.9256	+	18.9237i	0.448660	+	0.777102i	0.998299	−	0.0583003i	$-0.0185681\pi$
$593$	10.9256	+	18.9237i	0.448660	+	0.777102i	−0.549639	+	0.835402i	$0.685235\pi$
$594$		0			0
$595$	59.0102	−	34.0696i	2.41918	−	1.39672i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−20.7180	−	35.8846i	−0.846514	−	1.46620i	−0.884300	−	0.466919i	$-0.845364\pi$
$599$	−20.7180	−	35.8846i	−0.846514	−	1.46620i	0.0377863	−	0.999286i	$-0.487969\pi$
$600$		0			0
$601$		−	0.432352i		−	0.0176360i	−0.999961	−	0.00881799i	$-0.997193\pi$
$601$		−	0.432352i		−	0.0176360i	0.999961	−	0.00881799i	$-0.00280689\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−3.34726	+	5.79762i	−0.136085	+	0.235707i
$606$		0			0
$607$	−39.9948			−1.62334			−0.811670	−	0.584117i	$-0.801441\pi$
$607$	−39.9948			−1.62334			−0.811670	+	0.584117i	$0.801441\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.0576453	−	0.0998446i	0.00233208	−	0.00403928i
$612$		0			0
$613$	−2.49229	+	4.31677i	−0.100663	+	0.174353i	−0.911958	−	0.410284i	$-0.865430\pi$
$613$	−2.49229	+	4.31677i	−0.100663	+	0.174353i	0.811295	+	0.584637i	$0.198763\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−22.9139	−	39.6881i	−0.922480	−	1.59778i	−0.795564	−	0.605869i	$-0.792825\pi$
$617$	−22.9139	−	39.6881i	−0.922480	−	1.59778i	−0.126916	−	0.991913i	$-0.540508\pi$
$618$		0			0
$619$			21.8455i			0.878043i	0.898476	+	0.439022i	$0.144675\pi$
$619$			21.8455i			0.878043i	−0.898476	+	0.439022i	$0.855325\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−34.3358	−	59.4714i	−1.37564	−	2.38267i
$624$		0			0
$625$	6.94379	−	12.0270i	0.277752	−	0.481080i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	53.4324	+	30.8492i	2.13049	+	1.23004i
$630$		0			0
$631$	23.0531	−	13.3097i	0.917728	−	0.529851i	0.0348185	−	0.999394i	$-0.488915\pi$
$631$	23.0531	−	13.3097i	0.917728	−	0.529851i	0.882910	+	0.469543i	$0.155581\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−3.65140			−0.144901
$636$		0			0
$637$	−18.0717	+	10.4337i	−0.716027	+	0.413398i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−4.42167	−	2.55285i	−0.174646	−	0.100832i	0.410129	−	0.912028i	$-0.365484\pi$
$641$	−4.42167	−	2.55285i	−0.174646	−	0.100832i	−0.584775	+	0.811196i	$0.698817\pi$
$642$		0			0
$643$	0.870748	+	0.502727i	0.0343389	+	0.0198256i	0.517071	−	0.855942i	$-0.327022\pi$
$643$	0.870748	+	0.502727i	0.0343389	+	0.0198256i	−0.482732	+	0.875768i	$0.660356\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			25.7740i			1.01328i	0.862158	+	0.506640i	$0.169113\pi$
$647$			25.7740i			1.01328i	−0.862158	+	0.506640i	$0.830887\pi$
$648$		0			0
$649$	−34.1106	−	19.6938i	−1.33896	−	0.773048i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	14.9359			0.584487			0.292243	−	0.956344i	$-0.405598\pi$
$653$	14.9359			0.584487			0.292243	+	0.956344i	$0.405598\pi$
$654$		0			0
$655$	20.4690	−	11.8178i	0.799791	−	0.461760i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	4.04738	+	7.01027i	0.157664	+	0.273082i	0.934026	−	0.357206i	$-0.116270\pi$
$659$	4.04738	+	7.01027i	0.157664	+	0.273082i	−0.776362	+	0.630287i	$0.782937\pi$
$660$		0			0
$661$	15.2208	−	8.78771i	0.592019	−	0.341802i	−0.173876	−	0.984767i	$-0.555629\pi$
$661$	15.2208	−	8.78771i	0.592019	−	0.341802i	0.765895	+	0.642965i	$0.222296\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−12.1526	−	37.8332i	−0.471259	−	1.46711i
$666$		0			0
$667$	9.93339	−	17.2051i	0.384623	−	0.666186i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−37.4183	+	21.6035i	−1.44452	+	0.833993i
$672$		0			0
$673$		−	5.53985i		−	0.213546i	−0.994283	−	0.106773i	$-0.965948\pi$
$673$		−	5.53985i		−	0.213546i	0.994283	−	0.106773i	$-0.0340518\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			13.7230i			0.527416i	0.964603	+	0.263708i	$0.0849456\pi$
$677$			13.7230i			0.527416i	−0.964603	+	0.263708i	$0.915054\pi$
$678$		0			0
$679$	−24.5269	+	42.4819i	−0.941256	+	1.63030i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	23.1589			0.886150			0.443075	−	0.896485i	$-0.353888\pi$
$683$	23.1589			0.886150			0.443075	+	0.896485i	$0.353888\pi$
$684$		0			0
$685$	10.9542			0.418538
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.89742	+	3.28644i	−0.0722861	+	0.125203i
$690$		0			0
$691$			45.8007i			1.74234i	0.490980	+	0.871171i	$0.336639\pi$
$691$			45.8007i			1.74234i	−0.490980	+	0.871171i	$0.663361\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	15.3244i		−	0.581287i
$696$		0			0
$697$	8.00047	−	4.61907i	0.303039	−	0.174960i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−3.61274	+	6.25745i	−0.136451	+	0.236341i	−0.926151	−	0.377153i	$-0.876903\pi$
$701$	−3.61274	+	6.25745i	−0.136451	+	0.236341i	0.789700	+	0.613494i	$0.210236\pi$
$702$		0			0
$703$	24.1656	−	26.6582i	0.911422	−	1.00543i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−65.5428	+	37.8411i	−2.46499	+	1.42316i
$708$		0			0
$709$	−16.9076	−	29.2848i	−0.634977	−	1.09981i	−0.986520	−	0.163641i	$-0.947676\pi$
$709$	−16.9076	−	29.2848i	−0.634977	−	1.09981i	0.351543	−	0.936172i	$-0.385657\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−0.356877	+	0.206043i	−0.0133652	+	0.00771638i
$714$		0			0
$715$	8.13585			0.304264
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−23.4424	−	13.5345i	−0.874256	−	0.504752i	−0.00549567	−	0.999985i	$-0.501749\pi$
$719$	−23.4424	−	13.5345i	−0.874256	−	0.504752i	−0.868760	+	0.495233i	$0.835083\pi$
$720$		0			0
$721$		−	53.1726i		−	1.98025i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	11.0565	+	6.38348i	0.410629	+	0.237076i
$726$		0			0
$727$	−12.1279	−	7.00206i	−0.449800	−	0.259692i	0.257946	−	0.966159i	$-0.416954\pi$
$727$	−12.1279	−	7.00206i	−0.449800	−	0.259692i	−0.707746	+	0.706467i	$0.750288\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	14.2197	−	8.20974i	0.525934	−	0.303648i
$732$		0			0
$733$	8.34907			0.308380			0.154190	−	0.988041i	$-0.450723\pi$
$733$	8.34907			0.308380			0.154190	+	0.988041i	$0.450723\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−46.2722	+	26.7152i	−1.70446	+	0.984069i
$738$		0			0
$739$	−25.9427	−	14.9780i	−0.954317	−	0.550975i	−0.0598977	−	0.998205i	$-0.519077\pi$
$739$	−25.9427	−	14.9780i	−0.954317	−	0.550975i	−0.894419	+	0.447229i	$0.852411\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	23.6386	−	40.9433i	0.867218	−	1.50206i	0.00238915	−	0.999997i	$-0.499240\pi$
$743$	23.6386	−	40.9433i	0.867218	−	1.50206i	0.864828	−	0.502068i	$-0.167427\pi$
$744$		0			0
$745$	4.81004	+	8.33123i	0.176226	+	0.305233i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			56.5927i			2.06785i
$750$		0			0
$751$	16.5114	+	28.5986i	0.602509	+	1.04358i	0.992440	+	0.122732i	$0.0391657\pi$
$751$	16.5114	+	28.5986i	0.602509	+	1.04358i	−0.389931	+	0.920844i	$0.627501\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−3.96962	+	6.87558i	−0.144469	+	0.250228i
$756$		0			0
$757$	−10.8643	+	18.8175i	−0.394868	+	0.683932i	−0.993084	−	0.117403i	$-0.962543\pi$
$757$	−10.8643	+	18.8175i	−0.394868	+	0.683932i	0.598216	+	0.801335i	$0.295876\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−28.1510			−1.02047			−0.510236	−	0.860034i	$-0.670442\pi$
$761$	−28.1510			−1.02047			−0.510236	+	0.860034i	$0.670442\pi$
$762$		0			0
$763$	−17.7039	+	30.6641i	−0.640924	+	1.11011i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			11.9673i			0.432115i
$768$		0			0
$769$	8.81822	+	15.2736i	0.317993	+	0.550780i	0.980069	−	0.198656i	$-0.0636578\pi$
$769$	8.81822	+	15.2736i	0.317993	+	0.550780i	−0.662076	+	0.749437i	$0.730324\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	22.9759	−	13.2651i	0.826385	−	0.477114i	−0.0262280	−	0.999656i	$-0.508350\pi$
$773$	22.9759	−	13.2651i	0.826385	−	0.477114i	0.852613	+	0.522542i	$0.175016\pi$
$774$		0			0
$775$	−0.132409	−	0.229340i	−0.00475628	−	0.00823812i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.64762	−	5.12934i	−0.0590323	−	0.183778i
$780$		0			0
$781$	−12.6796	−	7.32055i	−0.453710	−	0.261950i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−7.25607	−	12.5679i	−0.258980	−	0.448567i
$786$		0			0
$787$	−51.8183			−1.84712			−0.923561	−	0.383451i	$-0.874736\pi$
$787$	−51.8183			−1.84712			−0.923561	+	0.383451i	$0.874736\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	68.1769			2.42409
$792$		0			0
$793$	11.3690	+	6.56390i	0.403725	+	0.233091i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	22.0033i		−	0.779397i	−0.920942	−	0.389699i	$-0.872579\pi$
$797$		−	22.0033i		−	0.779397i	0.920942	−	0.389699i	$-0.127421\pi$
$798$		0			0
$799$		−	0.740568i		−	0.0261994i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−15.4270	−	8.90680i	−0.544408	−	0.314314i
$804$		0			0
$805$	23.6456			0.833396
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−19.1593			−0.673607			−0.336803	−	0.941575i	$-0.609346\pi$
$809$	−19.1593			−0.673607			−0.336803	+	0.941575i	$0.609346\pi$
$810$		0			0
$811$	−15.1412	−	26.2254i	−0.531681	−	0.920898i	−0.999316	−	0.0369764i	$-0.988227\pi$
$811$	−15.1412	−	26.2254i	−0.531681	−	0.920898i	0.467636	−	0.883921i	$-0.345106\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−9.69251	−	5.59597i	−0.339514	−	0.196018i
$816$		0			0
$817$	−2.92841	−	9.11667i	−0.102452	−	0.318952i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.78947	−	3.09946i	−0.0624530	−	0.108172i	0.833108	−	0.553110i	$-0.186559\pi$
$821$	−1.78947	−	3.09946i	−0.0624530	−	0.108172i	−0.895561	+	0.444938i	$0.853226\pi$
$822$		0			0
$823$	−25.7052	+	14.8409i	−0.896028	+	0.517322i	−0.875909	−	0.482476i	$-0.839738\pi$
$823$	−25.7052	+	14.8409i	−0.896028	+	0.517322i	−0.0201184	+	0.999798i	$0.506404\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	6.31822	+	10.9435i	0.219706	+	0.380542i	0.954718	−	0.297512i	$-0.0961568\pi$
$827$	6.31822	+	10.9435i	0.219706	+	0.380542i	−0.735012	+	0.678054i	$0.762824\pi$
$828$		0			0
$829$		−	33.3267i		−	1.15748i	−0.815511	−	0.578742i	$-0.803544\pi$
$829$		−	33.3267i		−	1.15748i	0.815511	−	0.578742i	$-0.196456\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−67.0208	+	116.083i	−2.32213	+	4.02205i
$834$		0			0
$835$	−41.0646			−1.42110
$836$		0			0
$837$		0			0
$838$		0			0
$839$	9.97450	−	17.2763i	0.344358	−	0.596446i	−0.640879	−	0.767642i	$-0.721430\pi$
$839$	9.97450	−	17.2763i	0.344358	−	0.596446i	0.985237	+	0.171196i	$0.0547632\pi$
$840$		0			0
$841$	14.8336	−	25.6926i	0.511505	−	0.885953i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	10.6311	+	18.4135i	0.365720	+	0.633445i
$846$		0			0
$847$		−	18.3097i		−	0.629128i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	10.7052	+	18.5420i	0.366971	+	0.635613i
$852$		0			0
$853$	1.95630	−	3.38840i	0.0669823	−	0.116017i	−0.830589	−	0.556885i	$-0.811996\pi$
$853$	1.95630	−	3.38840i	0.0669823	−	0.116017i	0.897572	+	0.440869i	$0.145330\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−4.83862	−	2.79358i	−0.165284	−	0.0954269i	0.415076	−	0.909787i	$-0.363755\pi$
$857$	−4.83862	−	2.79358i	−0.165284	−	0.0954269i	−0.580360	+	0.814360i	$0.697088\pi$
$858$		0			0
$859$	28.4810	−	16.4435i	0.971760	−	0.561046i	0.0719873	−	0.997406i	$-0.477066\pi$
$859$	28.4810	−	16.4435i	0.971760	−	0.561046i	0.899772	+	0.436360i	$0.143733\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	8.80712			0.299798			0.149899	−	0.988701i	$-0.452105\pi$
$863$	8.80712			0.299798			0.149899	+	0.988701i	$0.452105\pi$
$864$		0			0
$865$	−24.2208	+	13.9839i	−0.823531	+	0.475466i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	31.4833	+	18.1769i	1.06800	+	0.616609i
$870$		0			0
$871$	14.0591	+	8.11703i	0.476375	+	0.275035i
$872$		0			0
$873$		0			0
$874$		0			0
$875$			60.7769i			2.05464i
$876$		0			0
$877$	20.2586	+	11.6963i	0.684085	+	0.394957i	0.801392	−	0.598139i	$-0.204093\pi$
$877$	20.2586	+	11.6963i	0.684085	+	0.394957i	−0.117307	+	0.993096i	$0.537426\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	2.94396			0.0991845			0.0495922	−	0.998770i	$-0.484208\pi$
$881$	2.94396			0.0991845			0.0495922	+	0.998770i	$0.484208\pi$
$882$		0			0
$883$	−4.80013	+	2.77136i	−0.161537	+	0.0932636i	−0.578589	−	0.815619i	$-0.696397\pi$
$883$	−4.80013	+	2.77136i	−0.161537	+	0.0932636i	0.417052	+	0.908883i	$0.363063\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	6.76020	+	11.7090i	0.226985	+	0.393150i	0.956913	−	0.290374i	$-0.0937797\pi$
$887$	6.76020	+	11.7090i	0.226985	+	0.393150i	−0.729928	+	0.683524i	$0.760446\pi$
$888$		0			0
$889$	8.64871	−	4.99333i	0.290068	−	0.167471i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.422140	−	0.0912097i	−0.0141264	−	0.00305222i
$894$		0			0
$895$	−18.5120	+	32.0636i	−0.618786	+	1.07177i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−1.05387	+	0.608453i	−0.0351486	+	0.0202930i
$900$		0			0
$901$			24.3762i			0.812088i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	24.4925i		−	0.814159i
$906$		0			0
$907$	−1.63328	+	2.82893i	−0.0542323	+	0.0939332i	−0.891867	−	0.452298i	$-0.850604\pi$
$907$	−1.63328	+	2.82893i	−0.0542323	+	0.0939332i	0.837635	+	0.546231i	$0.183938\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−42.3199			−1.40212			−0.701061	−	0.713101i	$-0.747290\pi$
$911$	−42.3199			−1.40212			−0.701061	+	0.713101i	$0.747290\pi$
$912$		0			0
$913$	10.8455			0.358934
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−32.3220	+	55.9833i	−1.06737	+	1.84873i
$918$		0			0
$919$		−	0.647260i		−	0.0213511i	−0.999943	−	0.0106756i	$-0.996602\pi$
$919$		−	0.647260i		−	0.0213511i	0.999943	−	0.0106756i	$-0.00339820\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			4.44848i			0.146423i
$924$		0			0
$925$	−11.9156	+	6.87949i	−0.391784	+	0.226196i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−6.07173	+	10.5165i	−0.199207	+	0.345036i	−0.948271	−	0.317461i	$-0.897170\pi$
$929$	−6.07173	+	10.5165i	−0.199207	+	0.345036i	0.749065	+	0.662497i	$0.230503\pi$
$930$		0			0
$931$	57.9157	+	52.5004i	1.89811	+	1.72063i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	45.2590	−	26.1303i	1.48013	−	0.854552i
$936$		0			0
$937$	−15.6537	−	27.1131i	−0.511385	−	0.885745i	−0.999913	−	0.0131968i	$-0.995799\pi$
$937$	−15.6537	−	27.1131i	−0.511385	−	0.885745i	0.488528	−	0.872548i	$-0.337534\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−27.8310	+	16.0683i	−0.907266	+	0.523810i	−0.879550	−	0.475806i	$-0.842156\pi$
$941$	−27.8310	+	16.0683i	−0.907266	+	0.523810i	−0.0277152	+	0.999616i	$0.508823\pi$
$942$		0			0
$943$	3.20581			0.104395
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−51.2522	−	29.5905i	−1.66547	−	0.961562i	−0.970031	−	0.242980i	$-0.921875\pi$
$947$	−51.2522	−	29.5905i	−1.66547	−	0.961562i	−0.695442	−	0.718582i	$-0.744792\pi$
$948$		0			0
$949$			5.41239i			0.175694i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−27.1853	−	15.6954i	−0.880617	−	0.508425i	−0.00975528	−	0.999952i	$-0.503105\pi$
$953$	−27.1853	−	15.6954i	−0.880617	−	0.508425i	−0.870862	+	0.491528i	$0.836439\pi$
$954$		0			0
$955$	−24.7267	−	14.2760i	−0.800137	−	0.461959i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−25.9461	+	14.9800i	−0.837844	+	0.483730i
$960$		0			0
$961$	−30.9748			−0.999186
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−30.9955	+	17.8953i	−0.997780	+	0.576069i
$966$		0			0
$967$	7.65177	+	4.41775i	0.246064	+	0.142065i	0.617961	−	0.786209i	$-0.287959\pi$
$967$	7.65177	+	4.41775i	0.246064	+	0.142065i	−0.371896	+	0.928274i	$0.621292\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	12.4040	−	21.4844i	0.398064	−	0.689467i	−0.595423	−	0.803412i	$-0.703015\pi$
$971$	12.4040	−	21.4844i	0.398064	−	0.689467i	0.993487	+	0.113945i	$0.0363488\pi$
$972$		0			0
$973$	20.9563	+	36.2974i	0.671828	+	1.16364i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	40.2360i		−	1.28726i	−0.765336	−	0.643631i	$-0.777427\pi$
$977$		−	40.2360i		−	1.28726i	0.765336	−	0.643631i	$-0.222573\pi$
$978$		0			0
$979$	−26.3345	−	45.6127i	−0.841654	−	1.45779i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	3.20942	−	5.55887i	0.102365	−	0.177301i	−0.810294	−	0.586024i	$-0.800693\pi$
$983$	3.20942	−	5.55887i	0.102365	−	0.177301i	0.912658	+	0.408723i	$0.134026\pi$
$984$		0			0
$985$	3.81051	−	6.59999i	0.121413	−	0.210293i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	5.69786			0.181181
$990$		0			0
$991$	24.9947	−	43.2921i	0.793983	−	1.37522i	−0.129499	−	0.991580i	$-0.541337\pi$
$991$	24.9947	−	43.2921i	0.793983	−	1.37522i	0.923483	−	0.383640i	$-0.125330\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	41.0874i		−	1.30256i
$996$		0			0
$997$	−20.6258	−	35.7249i	−0.653226	−	1.13142i	−0.982335	−	0.187129i	$-0.940082\pi$
$997$	−20.6258	−	35.7249i	−0.653226	−	1.13142i	0.329110	−	0.944292i	$-0.393251\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2736.2.bm.r.559.3		8
3.2	odd	2		912.2.bb.h.559.2	yes	8
4.3	odd	2		2736.2.bm.s.559.3		8
12.11	even	2		912.2.bb.g.559.2	yes	8
19.12	odd	6		2736.2.bm.s.1855.3		8
57.50	even	6		912.2.bb.g.31.2	✓	8
76.31	even	6	inner	2736.2.bm.r.1855.3		8
228.107	odd	6		912.2.bb.h.31.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.bb.g.31.2	✓	8	57.50	even	6
912.2.bb.g.559.2	yes	8	12.11	even	2
912.2.bb.h.31.2	yes	8	228.107	odd	6
912.2.bb.h.559.2	yes	8	3.2	odd	2
2736.2.bm.r.559.3		8	1.1	even	1	trivial
2736.2.bm.r.1855.3		8	76.31	even	6	inner
2736.2.bm.s.559.3		8	4.3	odd	2
2736.2.bm.s.1855.3		8	19.12	odd	6

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:	\( N \)	\(=\)	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2736.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.912850 - 1.58110i) q^{5} +4.99333i q^{7} +O(q^{10})\)	\(q+(0.912850 - 1.58110i) q^{5} +4.99333i q^{7} +3.82973i q^{11} +(1.00771 - 0.581803i) q^{13} +(3.73720 - 6.47303i) q^{17} +(-3.22949 - 2.92752i) q^{19} +(2.24626 - 1.29688i) q^{23} +(0.833411 + 1.44351i) q^{25} +(6.63328 - 3.82973i) q^{29} -0.158876 q^{31} +(7.89497 + 4.55816i) q^{35} +8.25462i q^{37} +(1.07038 + 0.617985i) q^{41} +(1.90245 + 1.09838i) q^{43} +(0.0858062 - 0.0495402i) q^{47} -17.9334 q^{49} +(-2.82435 + 1.63064i) q^{53} +(6.05519 + 3.49597i) q^{55} +(-5.14234 + 8.90680i) q^{59} +(5.64100 + 9.77049i) q^{61} -2.12439i q^{65} +(6.97575 + 12.0824i) q^{67} +(-1.91151 + 3.31082i) q^{71} +(-2.32570 + 4.02823i) q^{73} -19.1231 q^{77} +(4.74626 - 8.22077i) q^{79} -2.83193i q^{83} +(-6.82301 - 11.8178i) q^{85} +(-11.9102 + 6.87633i) q^{89} +(2.90514 + 5.03185i) q^{91} +(-7.57675 + 2.43377i) q^{95} +(8.50771 + 4.91193i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{5}+O(q^{10}) \) 8 * q + 2 * q^5	\( 8 q + 2 q^{5} - 4 q^{17} - 6 q^{23} - 12 q^{25} + 12 q^{29} - 28 q^{31} - 18 q^{35} + 12 q^{41} - 18 q^{43} - 12 q^{47} - 24 q^{49} + 6 q^{53} + 12 q^{55} - 10 q^{59} - 4 q^{61} + 6 q^{67} + 8 q^{71} - 8 q^{73} - 28 q^{77} + 14 q^{79} - 8 q^{85} - 54 q^{89} + 26 q^{91} - 38 q^{95} + 60 q^{97}+O(q^{100}) \) 8 * q + 2 * q^5 - 4 * q^17 - 6 * q^23 - 12 * q^25 + 12 * q^29 - 28 * q^31 - 18 * q^35 + 12 * q^41 - 18 * q^43 - 12 * q^47 - 24 * q^49 + 6 * q^53 + 12 * q^55 - 10 * q^59 - 4 * q^61 + 6 * q^67 + 8 * q^71 - 8 * q^73 - 28 * q^77 + 14 * q^79 - 8 * q^85 - 54 * q^89 + 26 * q^91 - 38 * q^95 + 60 * q^97

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