LMFDB - Embedded newform 2736.2.s.y.577.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2736,2,Mod(577,2736)]

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([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("2736.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2736 = 2^{4} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2736.s (of order $3$, degree $2$, 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:	$21.8470699930$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.2696112.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} + 18x^{2} - 8x + 4 $ x^6 - x^5 + 5x^4 + 18x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			577.1
Root			$-0.906803 - 1.57063i$ of defining polynomial
Character	$\chi$	$=$	2736.577
Dual form			2736.2.s.y.1873.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.906803 - 1.57063i) q^{5} +2.52444 q^{7} +O(q^{10})$	$q+(-0.906803 - 1.57063i) q^{5} +2.52444 q^{7} -0.813607 q^{11} +(2.16902 - 3.75686i) q^{13} +(-0.458191 - 0.793610i) q^{17} +(-3.22041 - 2.93751i) q^{19} +(0.906803 - 1.57063i) q^{23} +(0.855416 - 1.48162i) q^{25} +(-4.00958 + 6.94479i) q^{29} +9.30833 q^{31} +(-2.28917 - 3.96496i) q^{35} -11.3083 q^{37} +(-5.60278 - 9.70429i) q^{41} +(4.98263 + 8.63017i) q^{43} +(2.82318 - 4.88990i) q^{47} -0.627213 q^{49} +(1.45819 - 2.52566i) q^{53} +(0.737781 + 1.27787i) q^{55} +(-0.948612 - 1.64305i) q^{59} +(-3.29875 + 5.71360i) q^{61} -7.86751 q^{65} +(1.57583 - 2.72941i) q^{67} +(0.355416 + 0.615598i) q^{71} +(-0.313607 - 0.543182i) q^{73} -2.05390 q^{77} +(-5.16902 - 8.95301i) q^{79} +9.86248 q^{83} +(-0.830978 + 1.43930i) q^{85} +(6.79624 - 11.7714i) q^{89} +(5.47556 - 9.48395i) q^{91} +(-1.69346 + 7.72181i) q^{95} +(-2.31361 - 4.00728i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{5} + 4 q^{7}+O(q^{10}) $ 6 * q + q^5 + 4 * q^7	$ 6 q + q^{5} + 4 q^{7} + 8 q^{11} + q^{13} + 11 q^{17} - q^{23} + 6 q^{25} - 3 q^{29} + 12 q^{31} - 12 q^{35} - 24 q^{37} - 19 q^{41} + 5 q^{43} - 17 q^{47} + 22 q^{49} - 5 q^{53} + 10 q^{55} - 13 q^{59} + 3 q^{61} - 42 q^{65} - 9 q^{67} + 3 q^{71} + 11 q^{73} - 20 q^{77} - 19 q^{79} + 24 q^{83} - 17 q^{85} + 3 q^{89} + 44 q^{91} + 13 q^{95} - q^{97}+O(q^{100}) $ 6 * q + q^5 + 4 * q^7 + 8 * q^11 + q^13 + 11 * q^17 - q^23 + 6 * q^25 - 3 * q^29 + 12 * q^31 - 12 * q^35 - 24 * q^37 - 19 * q^41 + 5 * q^43 - 17 * q^47 + 22 * q^49 - 5 * q^53 + 10 * q^55 - 13 * q^59 + 3 * q^61 - 42 * q^65 - 9 * q^67 + 3 * q^71 + 11 * q^73 - 20 * q^77 - 19 * q^79 + 24 * q^83 - 17 * q^85 + 3 * q^89 + 44 * q^91 + 13 * q^95 - q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$1009$	$1217$	$1711$	$2053$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

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
$5$	−0.906803	−	1.57063i	−0.405535	−	0.702407i	0.588849	−	0.808243i	$-0.299581\pi$
$5$	−0.906803	−	1.57063i	−0.405535	−	0.702407i	−0.994384	+	0.105836i	$0.966248\pi$
$6$		0			0
$7$	2.52444			0.954148			0.477074	−	0.878863i	$-0.341697\pi$
$7$	2.52444			0.954148			0.477074	+	0.878863i	$0.341697\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.813607			−0.245312			−0.122656	−	0.992449i	$-0.539141\pi$
$11$	−0.813607			−0.245312			−0.122656	+	0.992449i	$0.539141\pi$
$12$		0			0
$13$	2.16902	−	3.75686i	0.601579	−	1.04196i	−0.391004	−	0.920389i	$-0.627872\pi$
$13$	2.16902	−	3.75686i	0.601579	−	1.04196i	0.992582	−	0.121575i	$-0.0387946\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.458191	−	0.793610i	−0.111128	−	0.192479i	0.805098	−	0.593142i	$-0.202113\pi$
$17$	−0.458191	−	0.793610i	−0.111128	−	0.192479i	−0.916225	+	0.400664i	$0.868780\pi$
$18$		0			0
$19$	−3.22041	−	2.93751i	−0.738813	−	0.673911i
$19$	−3.22041	−	2.93751i	−0.738813	−	0.673911i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.906803	−	1.57063i	0.189082	−	0.327499i	−0.755863	−	0.654730i	$-0.772782\pi$
$23$	0.906803	−	1.57063i	0.189082	−	0.327499i	0.944944	+	0.327231i	$0.106116\pi$
$24$		0			0
$25$	0.855416	−	1.48162i	0.171083	−	0.296325i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.00958	+	6.94479i	−0.744560	+	1.28962i	0.205840	+	0.978586i	$0.434007\pi$
$29$	−4.00958	+	6.94479i	−0.744560	+	1.28962i	−0.950400	+	0.311030i	$0.899326\pi$
$30$		0			0
$31$	9.30833			1.67182			0.835912	−	0.548863i	$-0.184939\pi$
$31$	9.30833			1.67182			0.835912	+	0.548863i	$0.184939\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.28917	−	3.96496i	−0.386940	−	0.670200i
$36$		0			0
$37$	−11.3083			−1.85908			−0.929539	−	0.368725i	$-0.879794\pi$
$37$	−11.3083			−1.85908			−0.929539	+	0.368725i	$0.879794\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5.60278	−	9.70429i	−0.875006	−	1.51556i	−0.856756	−	0.515722i	$-0.827524\pi$
$41$	−5.60278	−	9.70429i	−0.875006	−	1.51556i	−0.0182506	−	0.999833i	$-0.505810\pi$
$42$		0			0
$43$	4.98263	+	8.63017i	0.759844	+	1.31609i	0.942930	+	0.332991i	$0.108058\pi$
$43$	4.98263	+	8.63017i	0.759844	+	1.31609i	−0.183086	+	0.983097i	$0.558609\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.82318	−	4.88990i	0.411804	−	0.713265i	−0.583283	−	0.812269i	$-0.698232\pi$
$47$	2.82318	−	4.88990i	0.411804	−	0.713265i	0.995087	+	0.0990037i	$0.0315656\pi$
$48$		0			0
$49$	−0.627213			−0.0896019
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.45819	−	2.52566i	0.200298	−	0.346926i	−0.748326	−	0.663331i	$-0.769142\pi$
$53$	1.45819	−	2.52566i	0.200298	−	0.346926i	0.948624	+	0.316404i	$0.102476\pi$
$54$		0			0
$55$	0.737781	+	1.27787i	0.0994824	+	0.172309i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.948612	−	1.64305i	−0.123499	−	0.213906i	0.797646	−	0.603125i	$-0.206078\pi$
$59$	−0.948612	−	1.64305i	−0.123499	−	0.213906i	−0.921145	+	0.389219i	$0.872745\pi$
$60$		0			0
$61$	−3.29875	+	5.71360i	−0.422361	+	0.731551i	−0.996170	−	0.0874382i	$-0.972132\pi$
$61$	−3.29875	+	5.71360i	−0.422361	+	0.731551i	0.573809	+	0.818989i	$0.305465\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−7.86751			−0.975844
$66$		0			0
$67$	1.57583	−	2.72941i	0.192518	−	0.333450i	−0.753566	−	0.657372i	$-0.771668\pi$
$67$	1.57583	−	2.72941i	0.192518	−	0.333450i	0.946084	+	0.323922i	$0.105001\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.355416	+	0.615598i	0.0421801	+	0.0730581i	0.886345	−	0.463026i	$-0.153236\pi$
$71$	0.355416	+	0.615598i	0.0421801	+	0.0730581i	−0.844165	+	0.536084i	$0.819903\pi$
$72$		0			0
$73$	−0.313607	−	0.543182i	−0.0367049	−	0.0635747i	0.847089	−	0.531450i	$-0.178353\pi$
$73$	−0.313607	−	0.543182i	−0.0367049	−	0.0635747i	−0.883794	+	0.467876i	$0.845019\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.05390			−0.234064
$78$		0			0
$79$	−5.16902	−	8.95301i	−0.581560	−	1.00729i	−0.995295	−	0.0968945i	$-0.969109\pi$
$79$	−5.16902	−	8.95301i	−0.581560	−	1.00729i	0.413734	−	0.910398i	$-0.364224\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	9.86248			1.08255			0.541274	−	0.840846i	$-0.317942\pi$
$83$	9.86248			1.08255			0.541274	+	0.840846i	$0.317942\pi$
$84$		0			0
$85$	−0.830978	+	1.43930i	−0.0901322	+	0.156114i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.79624	−	11.7714i	0.720399	−	1.24777i	−0.240440	−	0.970664i	$-0.577292\pi$
$89$	6.79624	−	11.7714i	0.720399	−	1.24777i	0.960840	−	0.277105i	$-0.0893749\pi$
$90$		0			0
$91$	5.47556	−	9.48395i	0.573995	−	0.994188i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.69346	+	7.72181i	−0.173745	+	0.792241i
$96$		0			0
$97$	−2.31361	−	4.00728i	−0.234911	−	0.406878i	0.724336	−	0.689447i	$-0.242147\pi$
$97$	−2.31361	−	4.00728i	−0.234911	−	0.406878i	−0.959247	+	0.282569i	$0.908813\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.48514	+	2.57234i	−0.147777	+	0.255957i	−0.930406	−	0.366532i	$-0.880545\pi$
$101$	−1.48514	+	2.57234i	−0.147777	+	0.255957i	0.782629	+	0.622489i	$0.213878\pi$
$102$		0			0
$103$	0.470539			0.0463636			0.0231818	−	0.999731i	$-0.492620\pi$
$103$	0.470539			0.0463636			0.0231818	+	0.999731i	$0.492620\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−10.2056			−0.986608			−0.493304	−	0.869857i	$-0.664211\pi$
$107$	−10.2056			−0.986608			−0.493304	+	0.869857i	$0.664211\pi$
$108$		0			0
$109$	1.87985	+	3.25600i	0.180057	+	0.311868i	0.941900	−	0.335894i	$-0.109038\pi$
$109$	1.87985	+	3.25600i	0.180057	+	0.311868i	−0.761843	+	0.647762i	$0.775705\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	15.0731			1.41795			0.708977	−	0.705232i	$-0.249157\pi$
$113$	15.0731			1.41795			0.708977	+	0.705232i	$0.249157\pi$
$114$		0			0
$115$	−3.28917			−0.306717
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.15667	−	2.00342i	−0.106032	−	0.183653i
$120$		0			0
$121$	−10.3380			−0.939822
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−12.1708			−1.08859
$126$		0			0
$127$	1.51209	−	2.61902i	0.134176	−	0.232400i	−0.791106	−	0.611679i	$-0.790494\pi$
$127$	1.51209	−	2.61902i	0.134176	−	0.232400i	0.925282	+	0.379279i	$0.123828\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.67860	−	13.2997i	−0.670882	−	1.16200i	−0.977654	−	0.210219i	$-0.932582\pi$
$131$	−7.67860	−	13.2997i	−0.670882	−	1.16200i	0.306772	−	0.951783i	$-0.400751\pi$
$132$		0			0
$133$	−8.12972	−	7.41556i	−0.704937	−	0.643011i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.789169	+	1.36688i	−0.0674232	+	0.116780i	−0.897766	−	0.440472i	$-0.854811\pi$
$137$	−0.789169	+	1.36688i	−0.0674232	+	0.116780i	0.830343	+	0.557252i	$0.188144\pi$
$138$		0			0
$139$	−7.76222	+	13.4446i	−0.658383	+	1.14035i	0.322651	+	0.946518i	$0.395426\pi$
$139$	−7.76222	+	13.4446i	−0.658383	+	1.14035i	−0.981034	+	0.193835i	$0.937907\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.76473	+	3.05660i	−0.147574	+	0.255606i
$144$		0			0
$145$	14.5436			1.20778
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.02873	−	15.6382i	−0.739663	−	1.28113i	−0.952647	−	0.304078i	$-0.901652\pi$
$149$	−9.02873	−	15.6382i	−0.739663	−	1.28113i	0.212984	−	0.977056i	$-0.431682\pi$
$150$		0			0
$151$	−7.10278			−0.578016			−0.289008	−	0.957327i	$-0.593325\pi$
$151$	−7.10278			−0.578016			−0.289008	+	0.957327i	$0.593325\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−8.44082	−	14.6199i	−0.677983	−	1.17430i
$156$		0			0
$157$	−11.3746	−	19.7013i	−0.907790	−	1.57234i	−0.817128	−	0.576456i	$-0.804435\pi$
$157$	−11.3746	−	19.7013i	−0.907790	−	1.57234i	−0.0906616	−	0.995882i	$-0.528898\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.28917	−	3.96496i	0.180412	−	0.312482i
$162$		0			0
$163$	−3.76473			−0.294876			−0.147438	−	0.989071i	$-0.547103\pi$
$163$	−3.76473			−0.294876			−0.147438	+	0.989071i	$0.547103\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.74736	+	6.49062i	−0.289979	+	0.502259i	−0.973804	−	0.227387i	$-0.926982\pi$
$167$	−3.74736	+	6.49062i	−0.289979	+	0.502259i	0.683825	+	0.729646i	$0.260315\pi$
$168$		0			0
$169$	−2.90931	−	5.03908i	−0.223793	−	0.387622i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−6.16902	−	10.6851i	−0.469022	−	0.812370i	0.530351	−	0.847778i	$-0.322060\pi$
$173$	−6.16902	−	10.6851i	−0.469022	−	0.812370i	−0.999373	+	0.0354082i	$0.988727\pi$
$174$		0			0
$175$	2.15944	−	3.74027i	0.163239	−	0.282738i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	24.6464			1.84216			0.921078	−	0.389378i	$-0.127310\pi$
$179$	24.6464			1.84216			0.921078	+	0.389378i	$0.127310\pi$
$180$		0			0
$181$	0.465984	−	0.807108i	0.0346363	−	0.0599918i	−0.848188	−	0.529696i	$-0.822306\pi$
$181$	0.465984	−	0.807108i	0.0346363	−	0.0599918i	0.882824	+	0.469704i	$0.155639\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	10.2544	+	17.7612i	0.753920	+	1.30583i
$186$		0			0
$187$	0.372787	+	0.645686i	0.0272609	+	0.0472172i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−12.4111			−0.898036			−0.449018	−	0.893523i	$-0.648226\pi$
$191$	−12.4111			−0.898036			−0.449018	+	0.893523i	$0.648226\pi$
$192$		0			0
$193$	0.830978	+	1.43930i	0.0598151	+	0.103603i	0.894382	−	0.447303i	$-0.147616\pi$
$193$	0.830978	+	1.43930i	0.0598151	+	0.103603i	−0.834567	+	0.550906i	$0.814282\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−5.51388			−0.392847			−0.196424	−	0.980519i	$-0.562933\pi$
$197$	−5.51388			−0.392847			−0.196424	+	0.980519i	$0.562933\pi$
$198$		0			0
$199$	7.98263	−	13.8263i	0.565874	−	0.980122i	−0.431094	−	0.902307i	$-0.641872\pi$
$199$	7.98263	−	13.8263i	0.565874	−	0.980122i	0.996968	−	0.0778148i	$-0.0247943\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−10.1219	+	17.5317i	−0.710420	+	1.23048i
$204$		0			0
$205$	−10.1612	+	17.5998i	−0.709691	+	1.22922i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.62015	+	2.38998i	0.181239	+	0.165318i
$210$		0			0
$211$	−4.18818	−	7.25414i	−0.288326	−	0.499395i	0.685084	−	0.728464i	$-0.259765\pi$
$211$	−4.18818	−	7.25414i	−0.288326	−	0.499395i	−0.973410	+	0.229068i	$0.926432\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	9.03653	−	15.6517i	0.616286	−	1.06744i
$216$		0			0
$217$	23.4983			1.59517
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−3.97530			−0.267408
$222$		0			0
$223$	−1.99042	−	3.44751i	−0.133288	−	0.230862i	0.791654	−	0.610970i	$-0.209220\pi$
$223$	−1.99042	−	3.44751i	−0.133288	−	0.230862i	−0.924942	+	0.380107i	$0.875887\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	12.0680			0.800983			0.400492	−	0.916300i	$-0.368839\pi$
$227$	12.0680			0.800983			0.400492	+	0.916300i	$0.368839\pi$
$228$		0			0
$229$	18.9894			1.25486			0.627429	−	0.778674i	$-0.284107\pi$
$229$	18.9894			1.25486			0.627429	+	0.778674i	$0.284107\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	9.56803	+	16.5723i	0.626823	+	1.08569i	0.988185	+	0.153263i	$0.0489783\pi$
$233$	9.56803	+	16.5723i	0.626823	+	1.08569i	−0.361363	+	0.932425i	$0.617688\pi$
$234$		0			0
$235$	−10.2403			−0.668003
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−2.50885			−0.162284			−0.0811421	−	0.996703i	$-0.525857\pi$
$239$	−2.50885			−0.162284			−0.0811421	+	0.996703i	$0.525857\pi$
$240$		0			0
$241$	1.92166	−	3.32842i	0.123785	−	0.214402i	−0.797472	−	0.603356i	$-0.793830\pi$
$241$	1.92166	−	3.32842i	0.123785	−	0.214402i	0.921257	+	0.388953i	$0.127163\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.568759	+	0.985119i	0.0363367	+	0.0629370i
$246$		0			0
$247$	−18.0209	+	5.72709i	−1.14665	+	0.364406i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	10.4383	−	18.0797i	0.658860	−	1.14118i	−0.322051	−	0.946722i	$-0.604372\pi$
$251$	10.4383	−	18.0797i	0.658860	−	1.14118i	0.980911	−	0.194457i	$-0.0622944\pi$
$252$		0			0
$253$	−0.737781	+	1.27787i	−0.0463839	+	0.0803393i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	14.3519	−	24.8583i	0.895248	−	1.55062i	0.0617510	−	0.998092i	$-0.480332\pi$
$257$	14.3519	−	24.8583i	0.895248	−	1.55062i	0.833497	−	0.552524i	$-0.186335\pi$
$258$		0			0
$259$	−28.5472			−1.77383
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2.63679	+	4.56706i	0.162592	+	0.281617i	0.935797	−	0.352538i	$-0.114681\pi$
$263$	2.63679	+	4.56706i	0.162592	+	0.281617i	−0.773206	+	0.634155i	$0.781348\pi$
$264$		0			0
$265$	−5.28917			−0.324911
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−10.9287	−	18.9291i	−0.666336	−	1.15413i	−0.978921	−	0.204239i	$-0.934528\pi$
$269$	−10.9287	−	18.9291i	−0.666336	−	1.15413i	0.312585	−	0.949890i	$-0.398805\pi$
$270$		0			0
$271$	6.09320	+	10.5537i	0.370135	+	0.641093i	0.989586	−	0.143942i	$-0.0459780\pi$
$271$	6.09320	+	10.5537i	0.370135	+	0.641093i	−0.619451	+	0.785036i	$0.712645\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.695972	+	1.20546i	−0.0419687	+	0.0726919i
$276$		0			0
$277$	0.632236			0.0379874			0.0189937	−	0.999820i	$-0.493954\pi$
$277$	0.632236			0.0379874			0.0189937	+	0.999820i	$0.493954\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−16.5680	+	28.6967i	−0.988366	+	1.71190i	−0.362465	+	0.931997i	$0.618065\pi$
$281$	−16.5680	+	28.6967i	−0.988366	+	1.71190i	−0.625901	+	0.779903i	$0.715268\pi$
$282$		0			0
$283$	−4.47305	−	7.74755i	−0.265895	−	0.460544i	0.701903	−	0.712273i	$-0.252334\pi$
$283$	−4.47305	−	7.74755i	−0.265895	−	0.460544i	−0.967798	+	0.251729i	$0.919001\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−14.1439	−	24.4979i	−0.834886	−	1.44606i
$288$		0			0
$289$	8.08012	−	13.9952i	0.475301	−	0.823246i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	28.0822			1.64058			0.820289	−	0.571950i	$-0.193813\pi$
$293$	28.0822			1.64058			0.820289	+	0.571950i	$0.193813\pi$
$294$		0			0
$295$	−1.72041	+	2.97984i	−0.100166	+	0.173493i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.93375	−	6.81346i	−0.227495	−	0.394033i
$300$		0			0
$301$	12.5783	+	21.7863i	0.725003	+	1.25574i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	11.9653			0.685129
$306$		0			0
$307$	15.6489	+	27.1047i	0.893129	+	1.54694i	0.836103	+	0.548572i	$0.184828\pi$
$307$	15.6489	+	27.1047i	0.893129	+	1.54694i	0.0570254	+	0.998373i	$0.481838\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−9.00502			−0.510628			−0.255314	−	0.966858i	$-0.582179\pi$
$311$	−9.00502			−0.510628			−0.255314	+	0.966858i	$0.582179\pi$
$312$		0			0
$313$	2.18111	−	3.77780i	0.123284	−	0.213534i	−0.797777	−	0.602953i	$-0.793991\pi$
$313$	2.18111	−	3.77780i	0.123284	−	0.213534i	0.921061	+	0.389419i	$0.127324\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.16902	+	3.75686i	−0.121824	+	0.211006i	−0.920487	−	0.390773i	$-0.872208\pi$
$317$	−2.16902	+	3.75686i	−0.121824	+	0.211006i	0.798663	+	0.601779i	$0.205541\pi$
$318$		0			0
$319$	3.26222	−	5.65033i	0.182649	−	0.316358i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−0.855674	+	3.90169i	−0.0476110	+	0.217096i
$324$		0			0
$325$	−3.71083	−	6.42735i	−0.205840	−	0.356525i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	7.12695	−	12.3442i	0.392922	−	0.680560i
$330$		0			0
$331$	10.6081			0.583072			0.291536	−	0.956560i	$-0.405834\pi$
$331$	10.6081			0.583072			0.291536	+	0.956560i	$0.405834\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−5.71585			−0.312291
$336$		0			0
$337$	0.446101	+	0.772669i	0.0243007	+	0.0420900i	0.877920	−	0.478807i	$-0.158931\pi$
$337$	0.446101	+	0.772669i	0.0243007	+	0.0420900i	−0.853619	+	0.520897i	$0.825597\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−7.57331			−0.410118
$342$		0			0
$343$	−19.2544			−1.03964
$344$		0			0
$345$		0			0
$346$		0			0
$347$	8.52695	+	14.7691i	0.457751	+	0.792847i	0.998842	−	0.0481166i	$-0.0153219\pi$
$347$	8.52695	+	14.7691i	0.457751	+	0.792847i	−0.541091	+	0.840964i	$0.681989\pi$
$348$		0			0
$349$	17.8328			0.954566			0.477283	−	0.878750i	$-0.341622\pi$
$349$	17.8328			0.954566			0.477283	+	0.878750i	$0.341622\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	22.4353			1.19411			0.597055	−	0.802201i	$-0.296338\pi$
$353$	22.4353			1.19411			0.597055	+	0.802201i	$0.296338\pi$
$354$		0			0
$355$	0.644584	−	1.11645i	0.0342110	−	0.0592552i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	10.7204	+	18.5683i	0.565802	+	0.979997i	0.996975	+	0.0777278i	$0.0247665\pi$
$359$	10.7204	+	18.5683i	0.565802	+	0.979997i	−0.431173	+	0.902269i	$0.641900\pi$
$360$		0			0
$361$	1.74208	+	18.9200i	0.0916883	+	0.995788i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.568759	+	0.985119i	−0.0297702	+	0.0515635i
$366$		0			0
$367$	−8.79347	+	15.2307i	−0.459015	+	0.795038i	−0.998909	−	0.0466954i	$-0.985131\pi$
$367$	−8.79347	+	15.2307i	−0.459015	+	0.795038i	0.539894	+	0.841733i	$0.318464\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.68111	−	6.37587i	0.191114	−	0.331019i
$372$		0			0
$373$	11.5194			0.596453			0.298226	−	0.954495i	$-0.403605\pi$
$373$	11.5194			0.596453			0.298226	+	0.954495i	$0.403605\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	17.3937	+	30.1268i	0.895823	+	1.55161i
$378$		0			0
$379$	24.5472			1.26090			0.630452	−	0.776229i	$-0.282870\pi$
$379$	24.5472			1.26090			0.630452	+	0.776229i	$0.282870\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	8.31790	+	14.4070i	0.425025	+	0.736165i	0.996423	−	0.0845083i	$-0.0269320\pi$
$383$	8.31790	+	14.4070i	0.425025	+	0.736165i	−0.571398	+	0.820673i	$0.693599\pi$
$384$		0			0
$385$	1.86248	+	3.22591i	0.0949209	+	0.164408i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−12.6637	+	21.9342i	−0.642077	+	1.11211i	0.342891	+	0.939375i	$0.388594\pi$
$389$	−12.6637	+	21.9342i	−0.642077	+	1.11211i	−0.984968	+	0.172735i	$0.944740\pi$
$390$		0			0
$391$	−1.66196			−0.0840487
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−9.37457	+	16.2372i	−0.471686	+	0.816984i
$396$		0			0
$397$	6.87708	+	11.9115i	0.345151	+	0.597819i	0.985381	−	0.170364i	$-0.0544944\pi$
$397$	6.87708	+	11.9115i	0.345151	+	0.597819i	−0.640230	+	0.768183i	$0.721161\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−12.2108	−	21.1498i	−0.609780	−	1.05617i	−0.991276	−	0.131799i	$-0.957925\pi$
$401$	−12.2108	−	21.1498i	−0.609780	−	1.05617i	0.381497	−	0.924370i	$-0.375409\pi$
$402$		0			0
$403$	20.1900	−	34.9700i	1.00573	−	1.74198i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	9.20053			0.456053
$408$		0			0
$409$	3.34333	−	5.79081i	0.165317	−	0.286337i	−0.771451	−	0.636289i	$-0.780469\pi$
$409$	3.34333	−	5.79081i	0.165317	−	0.286337i	0.936768	+	0.349952i	$0.113802\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.39471	−	4.14777i	−0.117836	−	0.204098i
$414$		0			0
$415$	−8.94333	−	15.4903i	−0.439011	−	0.760389i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−7.58890			−0.370742			−0.185371	−	0.982669i	$-0.559349\pi$
$419$	−7.58890			−0.370742			−0.185371	+	0.982669i	$0.559349\pi$
$420$		0			0
$421$	−9.85290	−	17.0657i	−0.480201	−	0.831733i	0.519541	−	0.854446i	$-0.326103\pi$
$421$	−9.85290	−	17.0657i	−0.480201	−	0.831733i	−0.999742	+	0.0227128i	$0.992770\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.56777			−0.0760482
$426$		0			0
$427$	−8.32748	+	14.4236i	−0.402995	+	0.698008i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−15.4426	+	26.7474i	−0.743844	+	1.28838i	0.206889	+	0.978364i	$0.433666\pi$
$431$	−15.4426	+	26.7474i	−0.743844	+	1.28838i	−0.950733	+	0.310011i	$0.899667\pi$
$432$		0			0
$433$	−2.90957	+	5.03953i	−0.139825	+	0.242184i	−0.927430	−	0.373996i	$-0.877987\pi$
$433$	−2.90957	+	5.03953i	−0.139825	+	0.242184i	0.787605	+	0.616180i	$0.211321\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−7.53402	+	2.39433i	−0.360401	+	0.114536i
$438$		0			0
$439$	1.48514	+	2.57234i	0.0708819	+	0.122771i	0.899288	−	0.437357i	$-0.144085\pi$
$439$	1.48514	+	2.57234i	0.0708819	+	0.122771i	−0.828406	+	0.560128i	$0.810752\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−13.2867	+	23.0132i	−0.631268	+	1.09339i	0.356025	+	0.934477i	$0.384132\pi$
$443$	−13.2867	+	23.0132i	−0.631268	+	1.09339i	−0.987293	+	0.158912i	$0.949201\pi$
$444$		0			0
$445$	−24.6514			−1.16859
$446$		0			0
$447$		0			0
$448$		0			0
$449$	8.53303			0.402699			0.201349	−	0.979519i	$-0.435467\pi$
$449$	8.53303			0.402699			0.201349	+	0.979519i	$0.435467\pi$
$450$		0			0
$451$	4.55845	+	7.89547i	0.214649	+	0.371783i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−19.8610			−0.931099
$456$		0			0
$457$	20.2892			0.949087			0.474544	−	0.880232i	$-0.342613\pi$
$457$	20.2892			0.949087			0.474544	+	0.880232i	$0.342613\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	4.24208	+	7.34749i	0.197573	+	0.342207i	0.947741	−	0.319041i	$-0.103361\pi$
$461$	4.24208	+	7.34749i	0.197573	+	0.342207i	−0.750168	+	0.661248i	$0.770027\pi$
$462$		0			0
$463$	−7.72496			−0.359010			−0.179505	−	0.983757i	$-0.557450\pi$
$463$	−7.72496			−0.359010			−0.179505	+	0.983757i	$0.557450\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−7.18639			−0.332547			−0.166273	−	0.986080i	$-0.553173\pi$
$467$	−7.18639			−0.332547			−0.166273	+	0.986080i	$0.553173\pi$
$468$		0			0
$469$	3.97807	−	6.89023i	0.183690	−	0.318161i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4.05390	−	7.02156i	−0.186398	−	0.322852i
$474$		0			0
$475$	−7.10707	+	2.25864i	−0.326095	+	0.103634i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−12.2179	+	21.1620i	−0.558250	+	0.966917i	0.439393	+	0.898295i	$0.355194\pi$
$479$	−12.2179	+	21.1620i	−0.558250	+	0.966917i	−0.997643	+	0.0686223i	$0.978140\pi$
$480$		0			0
$481$	−24.5280	+	42.4838i	−1.11838	+	1.93709i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.19597	+	7.26764i	−0.190529	+	0.330006i
$486$		0			0
$487$	37.2772			1.68919			0.844595	−	0.535406i	$-0.179842\pi$
$487$	37.2772			1.68919			0.844595	+	0.535406i	$0.179842\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	9.42847	+	16.3306i	0.425501	+	0.736989i	0.996467	−	0.0839843i	$-0.0267646\pi$
$491$	9.42847	+	16.3306i	0.425501	+	0.736989i	−0.570966	+	0.820974i	$0.693431\pi$
$492$		0			0
$493$	7.34861			0.330965
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.897225	+	1.55404i	0.0402460	+	0.0697082i
$498$		0			0
$499$	−8.18388	−	14.1749i	−0.366361	−	0.634556i	0.622633	−	0.782514i	$-0.286063\pi$
$499$	−8.18388	−	14.1749i	−0.366361	−	0.634556i	−0.988994	+	0.147959i	$0.952730\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	18.7935	−	32.5512i	0.837959	−	1.45139i	−0.0536389	−	0.998560i	$-0.517082\pi$
$503$	18.7935	−	32.5512i	0.837959	−	1.45139i	0.891598	−	0.452828i	$-0.149585\pi$
$504$		0			0
$505$	5.38692			0.239715
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−7.87985	+	13.6483i	−0.349268	+	0.604951i	−0.986120	−	0.166036i	$-0.946903\pi$
$509$	−7.87985	+	13.6483i	−0.349268	+	0.604951i	0.636851	+	0.770987i	$0.280237\pi$
$510$		0			0
$511$	−0.791680	−	1.37123i	−0.0350219	−	0.0606597i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.426686	−	0.739042i	−0.0188020	−	0.0325661i
$516$		0			0
$517$	−2.29696	+	3.97845i	−0.101020	+	0.174972i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−9.47411			−0.415068			−0.207534	−	0.978228i	$-0.566544\pi$
$521$	−9.47411			−0.415068			−0.207534	+	0.978228i	$0.566544\pi$
$522$		0			0
$523$	−19.1882	+	33.2349i	−0.839040	+	1.45326i	0.0516573	+	0.998665i	$0.483550\pi$
$523$	−19.1882	+	33.2349i	−0.839040	+	1.45326i	−0.890698	+	0.454596i	$0.849784\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4.26499	−	7.38718i	−0.185786	−	0.321790i
$528$		0			0
$529$	9.85542	+	17.0701i	0.428496	+	0.742177i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−48.6102			−2.10554
$534$		0			0
$535$	9.25443	+	16.0291i	0.400104	+	0.693000i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.510305			0.0219804
$540$		0			0
$541$	−0.590685	+	1.02310i	−0.0253955	+	0.0439864i	−0.878444	−	0.477846i	$-0.841418\pi$
$541$	−0.590685	+	1.02310i	−0.0253955	+	0.0439864i	0.853048	+	0.521832i	$0.174751\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	3.40931	−	5.90511i	0.146039	−	0.252947i
$546$		0			0
$547$	11.8013	−	20.4404i	0.504585	−	0.873968i	−0.495401	−	0.868665i	$-0.664979\pi$
$547$	11.8013	−	20.4404i	0.504585	−	0.873968i	0.999986	−	0.00530285i	$-0.00168796\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	33.3129	−	10.5869i	1.41918	−	0.451017i
$552$		0			0
$553$	−13.0489	−	22.6013i	−0.554895	−	0.961106i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.54181	−	2.67049i	0.0653286	−	0.113152i	−0.831511	−	0.555508i	$-0.812524\pi$
$557$	1.54181	−	2.67049i	0.0653286	−	0.113152i	0.896840	+	0.442356i	$0.145857\pi$
$558$		0			0
$559$	43.2297			1.82842
$560$		0			0
$561$		0			0
$562$		0			0
$563$	3.46143			0.145882			0.0729409	−	0.997336i	$-0.476762\pi$
$563$	3.46143			0.145882			0.0729409	+	0.997336i	$0.476762\pi$
$564$		0			0
$565$	−13.6683	−	23.6742i	−0.575030	−	0.995980i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	26.6550			1.11743			0.558717	−	0.829358i	$-0.311294\pi$
$569$	26.6550			1.11743			0.558717	+	0.829358i	$0.311294\pi$
$570$		0			0
$571$	−4.23527			−0.177241			−0.0886203	−	0.996065i	$-0.528246\pi$
$571$	−4.23527			−0.177241			−0.0886203	+	0.996065i	$0.528246\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.55139	−	2.68708i	−0.0646973	−	0.112059i
$576$		0			0
$577$	37.0036			1.54048			0.770239	−	0.637755i	$-0.220137\pi$
$577$	37.0036			1.54048			0.770239	+	0.637755i	$0.220137\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	24.8972			1.03291
$582$		0			0
$583$	−1.18639	+	2.05489i	−0.0491354	+	0.0851050i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	11.0557	+	19.1490i	0.456317	+	0.790364i	0.998763	−	0.0497266i	$-0.0158350\pi$
$587$	11.0557	+	19.1490i	0.456317	+	0.790364i	−0.542446	+	0.840091i	$0.682502\pi$
$588$		0			0
$589$	−29.9766	−	27.3433i	−1.23517	−	1.12666i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−15.7841	+	27.3389i	−0.648177	+	1.12268i	0.335381	+	0.942083i	$0.391135\pi$
$593$	−15.7841	+	27.3389i	−0.648177	+	1.12268i	−0.983558	+	0.180593i	$0.942198\pi$
$594$		0			0
$595$	−2.09775	+	3.63341i	−0.0859994	+	0.148955i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−10.3632	+	17.9496i	−0.423429	+	0.733401i	−0.996272	−	0.0862641i	$-0.972507\pi$
$599$	−10.3632	+	17.9496i	−0.423429	+	0.733401i	0.572843	+	0.819665i	$0.305840\pi$
$600$		0			0
$601$	−22.6902			−0.925553			−0.462777	−	0.886475i	$-0.653147\pi$
$601$	−22.6902			−0.925553			−0.462777	+	0.886475i	$0.653147\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	9.37457	+	16.2372i	0.381131	+	0.660138i
$606$		0			0
$607$	−37.1099			−1.50625			−0.753123	−	0.657880i	$-0.771453\pi$
$607$	−37.1099			−1.50625			−0.753123	+	0.657880i	$0.771453\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−12.2471	−	21.2126i	−0.495465	−	0.858170i
$612$		0			0
$613$	−6.03653	−	10.4556i	−0.243813	−	0.422297i	0.717984	−	0.696059i	$-0.245065\pi$
$613$	−6.03653	−	10.4556i	−0.243813	−	0.422297i	−0.961797	+	0.273763i	$0.911732\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.65165	−	2.86074i	0.0664930	−	0.115169i	−0.830862	−	0.556478i	$-0.812152\pi$
$617$	1.65165	−	2.86074i	0.0664930	−	0.115169i	0.897355	+	0.441309i	$0.145486\pi$
$618$		0			0
$619$	26.0867			1.04851			0.524256	−	0.851561i	$-0.324344\pi$
$619$	26.0867			1.04851			0.524256	+	0.851561i	$0.324344\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	17.1567	−	29.7162i	0.687368	−	1.19056i
$624$		0			0
$625$	6.75945	+	11.7077i	0.270378	+	0.468308i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	5.18137	+	8.97440i	0.206595	+	0.357833i
$630$		0			0
$631$	6.74459	−	11.6820i	0.268498	−	0.465052i	−0.699976	−	0.714166i	$-0.746806\pi$
$631$	6.74459	−	11.6820i	0.268498	−	0.465052i	0.968474	+	0.249114i	$0.0801394\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−5.48467			−0.217653
$636$		0			0
$637$	−1.36044	+	2.35635i	−0.0539026	+	0.0933620i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−2.61334	−	4.52643i	−0.103221	−	0.178783i	0.809789	−	0.586721i	$-0.199581\pi$
$641$	−2.61334	−	4.52643i	−0.103221	−	0.178783i	−0.913010	+	0.407938i	$0.866248\pi$
$642$		0			0
$643$	−14.3058	−	24.7784i	−0.564166	−	0.977165i	−0.997127	−	0.0757517i	$-0.975864\pi$
$643$	−14.3058	−	24.7784i	−0.564166	−	0.977165i	0.432961	−	0.901413i	$-0.357469\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−23.3139			−0.916563			−0.458281	−	0.888807i	$-0.651535\pi$
$647$	−23.3139			−0.916563			−0.458281	+	0.888807i	$0.651535\pi$
$648$		0			0
$649$	0.771797	+	1.33679i	0.0302957	+	0.0524737i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−9.83276			−0.384786			−0.192393	−	0.981318i	$-0.561625\pi$
$653$	−9.83276			−0.384786			−0.192393	+	0.981318i	$0.561625\pi$
$654$		0			0
$655$	−13.9260	+	24.1205i	−0.544132	+	0.942465i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	24.9670	−	43.2442i	0.972578	−	1.68455i	0.284871	−	0.958566i	$-0.408049\pi$
$659$	24.9670	−	43.2442i	0.972578	−	1.68455i	0.687707	−	0.725988i	$-0.258617\pi$
$660$		0			0
$661$	−11.3526	+	19.6634i	−0.441567	+	0.764816i	−0.997806	−	0.0662062i	$-0.978910\pi$
$661$	−11.3526	+	19.6634i	−0.441567	+	0.764816i	0.556239	+	0.831022i	$0.312244\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−4.27504	+	19.4932i	−0.165779	+	0.755915i
$666$		0			0
$667$	7.27180	+	12.5951i	0.281565	+	0.487685i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	2.68388	−	4.64862i	0.103610	−	0.179458i
$672$		0			0
$673$	−3.96169			−0.152712			−0.0763559	−	0.997081i	$-0.524329\pi$
$673$	−3.96169			−0.152712			−0.0763559	+	0.997081i	$0.524329\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	2.74557			0.105521			0.0527605	−	0.998607i	$-0.483198\pi$
$677$	2.74557			0.105521			0.0527605	+	0.998607i	$0.483198\pi$
$678$		0			0
$679$	−5.84056	−	10.1161i	−0.224140	−	0.388222i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	33.7633			1.29192			0.645958	−	0.763373i	$-0.276458\pi$
$683$	33.7633			1.29192			0.645958	+	0.763373i	$0.276458\pi$
$684$		0			0
$685$	2.86248			0.109370
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−6.32570	−	10.9564i	−0.240990	−	0.417407i
$690$		0			0
$691$	−7.58890			−0.288695			−0.144348	−	0.989527i	$-0.546108\pi$
$691$	−7.58890			−0.288695			−0.144348	+	0.989527i	$0.546108\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	28.1552			1.06799
$696$		0			0
$697$	−5.13428	+	8.89283i	−0.194475	+	0.336840i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−17.4157	−	30.1648i	−0.657780	−	1.13931i	−0.981189	−	0.193049i	$-0.938162\pi$
$701$	−17.4157	−	30.1648i	−0.657780	−	1.13931i	0.323409	−	0.946259i	$-0.395171\pi$
$702$		0			0
$703$	36.4174	+	33.2183i	1.37351	+	1.25285i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.74914	+	6.49371i	−0.141001	+	0.244221i
$708$		0			0
$709$	−14.3179	+	24.7993i	−0.537720	+	0.931359i	0.461306	+	0.887241i	$0.347381\pi$
$709$	−14.3179	+	24.7993i	−0.537720	+	0.931359i	−0.999026	+	0.0441176i	$0.985952\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	8.44082	−	14.6199i	0.316111	−	0.547521i
$714$		0			0
$715$	6.40105			0.239386
$716$		0			0
$717$		0			0
$718$		0			0
$719$	20.9721	+	36.3247i	0.782126	+	1.35468i	0.930701	+	0.365781i	$0.119198\pi$
$719$	20.9721	+	36.3247i	0.782126	+	1.35468i	−0.148575	+	0.988901i	$0.547469\pi$
$720$		0			0
$721$	1.18785			0.0442377
$722$		0			0
$723$		0			0
$724$		0			0
$725$	6.85971	+	11.8814i	0.254763	+	0.441263i
$726$		0			0
$727$	19.0365	+	32.9722i	0.706026	+	1.22287i	0.966320	+	0.257343i	$0.0828471\pi$
$727$	19.0365	+	32.9722i	0.706026	+	1.22287i	−0.260294	+	0.965529i	$0.583820\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	4.56599	−	7.90853i	0.168879	−	0.292507i
$732$		0			0
$733$	2.07502			0.0766428			0.0383214	−	0.999265i	$-0.487799\pi$
$733$	2.07502			0.0766428			0.0383214	+	0.999265i	$0.487799\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.28210	+	2.22067i	−0.0472268	+	0.0817993i
$738$		0			0
$739$	16.7658	+	29.0392i	0.616740	+	1.06822i	0.990077	+	0.140528i	$0.0448802\pi$
$739$	16.7658	+	29.0392i	0.616740	+	1.06822i	−0.373337	+	0.927696i	$0.621787\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	21.9154	+	37.9586i	0.803998	+	1.39257i	0.916965	+	0.398967i	$0.130631\pi$
$743$	21.9154	+	37.9586i	0.803998	+	1.39257i	−0.112968	+	0.993599i	$0.536036\pi$
$744$		0			0
$745$	−16.3746	+	28.3616i	−0.599918	+	1.03909i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−25.7633			−0.941370
$750$		0			0
$751$	−6.01737	+	10.4224i	−0.219577	+	0.380319i	−0.954679	−	0.297638i	$-0.903801\pi$
$751$	−6.01737	+	10.4224i	−0.219577	+	0.380319i	0.735102	+	0.677957i	$0.237134\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	6.44082	+	11.1558i	0.234405	+	0.406002i
$756$		0			0
$757$	−7.29095	−	12.6283i	−0.264994	−	0.458983i	0.702568	−	0.711617i	$-0.252037\pi$
$757$	−7.29095	−	12.6283i	−0.264994	−	0.458983i	−0.967562	+	0.252633i	$0.918703\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	41.3069			1.49737			0.748686	−	0.662924i	$-0.230685\pi$
$761$	41.3069			1.49737			0.748686	+	0.662924i	$0.230685\pi$
$762$		0			0
$763$	4.74557	+	8.21958i	0.171801	+	0.297569i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−8.23025			−0.297177
$768$		0			0
$769$	−4.58515	+	7.94171i	−0.165345	+	0.286385i	−0.936778	−	0.349925i	$-0.886207\pi$
$769$	−4.58515	+	7.94171i	−0.165345	+	0.286385i	0.771433	+	0.636311i	$0.219540\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−0.793465	+	1.37432i	−0.0285390	+	0.0494309i	−0.879942	−	0.475081i	$-0.842419\pi$
$773$	−0.793465	+	1.37432i	−0.0285390	+	0.0494309i	0.851403	+	0.524512i	$0.175752\pi$
$774$		0			0
$775$	7.96249	−	13.7914i	0.286021	−	0.495403i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−10.4632	+	47.7100i	−0.374884	+	1.70939i
$780$		0			0
$781$	−0.289169	−	0.500855i	−0.0103473	−	0.0179220i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−20.6290	+	35.7305i	−0.736281	+	1.27528i
$786$		0			0
$787$	17.4514			0.622075			0.311037	−	0.950398i	$-0.399324\pi$
$787$	17.4514			0.622075			0.311037	+	0.950398i	$0.399324\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	38.0510			1.35294
$792$		0			0
$793$	14.3101	+	24.7858i	0.508167	+	0.880171i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	23.5038			0.832548			0.416274	−	0.909239i	$-0.363336\pi$
$797$	23.5038			0.832548			0.416274	+	0.909239i	$0.363336\pi$
$798$		0			0
$799$	−5.17423			−0.183051
$800$		0			0
$801$		0			0
$802$		0			0
$803$	0.255152	+	0.441937i	0.00900413	+	0.0155956i
$804$		0			0
$805$	−8.30330			−0.292653
$806$		0			0
$807$		0			0
$808$		0			0
$809$	35.2686			1.23998			0.619988	−	0.784611i	$-0.287137\pi$
$809$	35.2686			1.23998			0.619988	+	0.784611i	$0.287137\pi$
$810$		0			0
$811$	18.1046	−	31.3580i	0.635737	−	1.10113i	−0.350621	−	0.936517i	$-0.614030\pi$
$811$	18.1046	−	31.3580i	0.635737	−	1.10113i	0.986358	−	0.164612i	$-0.0526371\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	3.41387	+	5.91300i	0.119583	+	0.207123i
$816$		0			0
$817$	9.30509	−	42.4292i	0.325544	−	1.48441i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−4.48237	+	7.76369i	−0.156436	+	0.270955i	−0.933581	−	0.358367i	$-0.883334\pi$
$821$	−4.48237	+	7.76369i	−0.156436	+	0.270955i	0.777145	+	0.629321i	$0.216667\pi$
$822$		0			0
$823$	−2.69346	+	4.66521i	−0.0938881	+	0.162619i	−0.909144	−	0.416482i	$-0.863263\pi$
$823$	−2.69346	+	4.66521i	−0.0938881	+	0.162619i	0.815256	+	0.579101i	$0.196596\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−8.96777	+	15.5326i	−0.311840	+	0.540123i	−0.978761	−	0.205006i	$-0.934279\pi$
$827$	−8.96777	+	15.5326i	−0.311840	+	0.540123i	0.666921	+	0.745129i	$0.267612\pi$
$828$		0			0
$829$	30.6550			1.06469			0.532345	−	0.846527i	$-0.321311\pi$
$829$	30.6550			1.06469			0.532345	+	0.846527i	$0.321311\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.287383	+	0.497762i	0.00995724	+	0.0172464i
$834$		0			0
$835$	13.5925			0.470387
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−13.3320	−	23.0918i	−0.460273	−	0.797216i	0.538701	−	0.842497i	$-0.318915\pi$
$839$	−13.3320	−	23.0918i	−0.460273	−	0.797216i	−0.998974	+	0.0452806i	$0.985582\pi$
$840$		0			0
$841$	−17.6534	−	30.5766i	−0.608739	−	1.05437i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−5.27635	+	9.13891i	−0.181512	+	0.314388i
$846$		0			0
$847$	−26.0978			−0.896729
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−10.2544	+	17.7612i	−0.351517	+	0.608846i
$852$		0			0
$853$	5.53125	+	9.58040i	0.189386	+	0.328027i	0.945046	−	0.326938i	$-0.106017\pi$
$853$	5.53125	+	9.58040i	0.189386	+	0.328027i	−0.755660	+	0.654965i	$0.772684\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.52470	−	2.64085i	−0.0520826	−	0.0902098i	0.838809	−	0.544426i	$-0.183253\pi$
$857$	−1.52470	−	2.64085i	−0.0520826	−	0.0902098i	−0.890891	+	0.454217i	$0.849919\pi$
$858$		0			0
$859$	−7.32999	+	12.6959i	−0.250096	+	0.433179i	−0.963552	−	0.267521i	$-0.913796\pi$
$859$	−7.32999	+	12.6959i	−0.250096	+	0.433179i	0.713456	+	0.700700i	$0.247129\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	8.78943			0.299196			0.149598	−	0.988747i	$-0.452202\pi$
$863$	8.78943			0.299196			0.149598	+	0.988747i	$0.452202\pi$
$864$		0			0
$865$	−11.1882	+	19.3785i	−0.380409	+	0.658889i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	4.20555	+	7.28423i	0.142664	+	0.247100i
$870$		0			0
$871$	−6.83600	−	11.8403i	−0.231629	−	0.401193i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−30.7244			−1.03868
$876$		0			0
$877$	−29.3371	−	50.8133i	−0.990642	−	1.71584i	−0.613521	−	0.789679i	$-0.710247\pi$
$877$	−29.3371	−	50.8133i	−0.990642	−	1.71584i	−0.377122	−	0.926164i	$-0.623086\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−2.55416			−0.0860517			−0.0430259	−	0.999074i	$-0.513700\pi$
$881$	−2.55416			−0.0860517			−0.0430259	+	0.999074i	$0.513700\pi$
$882$		0			0
$883$	12.4972	−	21.6458i	0.420565	−	0.728440i	−0.575430	−	0.817851i	$-0.695165\pi$
$883$	12.4972	−	21.6458i	0.420565	−	0.728440i	0.995995	+	0.0894109i	$0.0284984\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	17.8799	−	30.9688i	0.600347	−	1.03983i	−0.392422	−	0.919785i	$-0.628363\pi$
$887$	17.8799	−	30.9688i	0.600347	−	1.03983i	0.992768	−	0.120046i	$-0.0383041\pi$
$888$		0			0
$889$	3.81718	−	6.61154i	0.128024	−	0.221744i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−23.4559	+	7.45435i	−0.784923	+	0.249450i
$894$		0			0
$895$	−22.3494	−	38.7103i	−0.747058	−	1.29394i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−37.3225	+	64.6444i	−1.24477	+	2.15601i
$900$		0			0
$901$	−2.67252			−0.0890345
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.69022			−0.0561849
$906$		0			0
$907$	−6.12998	−	10.6174i	−0.203543	−	0.352546i	0.746125	−	0.665806i	$-0.231912\pi$
$907$	−6.12998	−	10.6174i	−0.203543	−	0.352546i	−0.949667	+	0.313260i	$0.898579\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	33.0816			1.09604			0.548022	−	0.836464i	$-0.315381\pi$
$911$	33.0816			1.09604			0.548022	+	0.836464i	$0.315381\pi$
$912$		0			0
$913$	−8.02418			−0.265562
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−19.3842	−	33.5743i	−0.640121	−	1.10872i
$918$		0			0
$919$	39.1950			1.29292			0.646462	−	0.762946i	$-0.276248\pi$
$919$	39.1950			1.29292			0.646462	+	0.762946i	$0.276248\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	3.08362			0.101499
$924$		0			0
$925$	−9.67332	+	16.7547i	−0.318057	+	0.550890i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	26.9741	+	46.7205i	0.884992	+	1.53285i	0.845723	+	0.533622i	$0.179170\pi$
$929$	26.9741	+	46.7205i	0.884992	+	1.53285i	0.0392688	+	0.999229i	$0.487497\pi$
$930$		0			0
$931$	2.01988	+	1.84244i	0.0661990	+	0.0603837i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.676089	−	1.17102i	0.0221105	−	0.0382965i
$936$		0			0
$937$	22.1358	−	38.3403i	0.723145	−	1.25252i	−0.236588	−	0.971610i	$-0.576029\pi$
$937$	22.1358	−	38.3403i	0.723145	−	1.25252i	0.959733	−	0.280914i	$-0.0906376\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	7.49650	−	12.9843i	0.244379	−	0.423277i	−0.717578	−	0.696478i	$-0.754749\pi$
$941$	7.49650	−	12.9843i	0.244379	−	0.423277i	0.961957	+	0.273201i	$0.0880826\pi$
$942$		0			0
$943$	−20.3225			−0.661790
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−24.2215	−	41.9528i	−0.787092	−	1.36328i	−0.927741	−	0.373224i	$-0.878252\pi$
$947$	−24.2215	−	41.9528i	−0.787092	−	1.36328i	0.140649	−	0.990059i	$-0.455081\pi$
$948$		0			0
$949$	−2.72088			−0.0883234
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.926686	−	1.60507i	−0.0300183	−	0.0519932i	0.850626	−	0.525771i	$-0.176223\pi$
$953$	−0.926686	−	1.60507i	−0.0300183	−	0.0519932i	−0.880644	+	0.473778i	$0.842890\pi$
$954$		0			0
$955$	11.2544	+	19.4932i	0.364185	+	0.630786i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.99221	+	3.45060i	−0.0643317	+	0.111426i
$960$		0			0
$961$	55.6449			1.79500
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.50707	−	2.61032i	0.0485142	−	0.0840290i
$966$		0			0
$967$	5.27180	+	9.13102i	0.169530	+	0.293634i	0.938255	−	0.345946i	$-0.112442\pi$
$967$	5.27180	+	9.13102i	0.169530	+	0.293634i	−0.768725	+	0.639579i	$0.779109\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−2.97833	−	5.15862i	−0.0955792	−	0.165548i	0.814271	−	0.580485i	$-0.197137\pi$
$971$	−2.97833	−	5.15862i	−0.0955792	−	0.165548i	−0.909850	+	0.414937i	$0.863804\pi$
$972$		0			0
$973$	−19.5952	+	33.9400i	−0.628195	+	1.08806i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	10.7980			0.345459			0.172730	−	0.984969i	$-0.444741\pi$
$977$	10.7980			0.345459			0.172730	+	0.984969i	$0.444741\pi$
$978$		0			0
$979$	−5.52946	+	9.57731i	−0.176722	+	0.306092i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−5.03653	−	8.72352i	−0.160640	−	0.278237i	0.774458	−	0.632625i	$-0.218023\pi$
$983$	−5.03653	−	8.72352i	−0.160640	−	0.278237i	−0.935098	+	0.354388i	$0.884689\pi$
$984$		0			0
$985$	5.00000	+	8.66025i	0.159313	+	0.275939i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	18.0731			0.574690
$990$		0			0
$991$	−18.1585	−	31.4514i	−0.576822	−	0.999086i	−0.995841	−	0.0911082i	$-0.970959\pi$
$991$	−18.1585	−	31.4514i	−0.576822	−	0.999086i	0.419019	−	0.907978i	$-0.362374\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−28.9547			−0.917926
$996$		0			0
$997$	−14.8721	+	25.7592i	−0.471003	+	0.815801i	−0.999450	−	0.0331654i	$-0.989441\pi$
$997$	−14.8721	+	25.7592i	−0.471003	+	0.815801i	0.528447	+	0.848966i	$0.322775\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2736.2.s.y.577.1		6
3.2	odd	2		304.2.i.f.273.1		6
4.3	odd	2		1368.2.s.k.577.1		6
12.11	even	2		152.2.i.c.121.3	yes	6
19.11	even	3	inner	2736.2.s.y.1873.1		6
24.5	odd	2		1216.2.i.m.577.3		6
24.11	even	2		1216.2.i.n.577.1		6
57.11	odd	6		304.2.i.f.49.1		6
57.26	odd	6		5776.2.a.bk.1.3		3
57.50	even	6		5776.2.a.bq.1.1		3
76.11	odd	6		1368.2.s.k.505.1		6
228.11	even	6		152.2.i.c.49.3	✓	6
228.83	even	6		2888.2.a.r.1.1		3
228.107	odd	6		2888.2.a.n.1.3		3
456.11	even	6		1216.2.i.n.961.1		6
456.125	odd	6		1216.2.i.m.961.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.i.c.49.3	✓	6	228.11	even	6
152.2.i.c.121.3	yes	6	12.11	even	2
304.2.i.f.49.1		6	57.11	odd	6
304.2.i.f.273.1		6	3.2	odd	2
1216.2.i.m.577.3		6	24.5	odd	2
1216.2.i.m.961.3		6	456.125	odd	6
1216.2.i.n.577.1		6	24.11	even	2
1216.2.i.n.961.1		6	456.11	even	6
1368.2.s.k.505.1		6	76.11	odd	6
1368.2.s.k.577.1		6	4.3	odd	2
2736.2.s.y.577.1		6	1.1	even	1	trivial
2736.2.s.y.1873.1		6	19.11	even	3	inner
2888.2.a.n.1.3		3	228.107	odd	6
2888.2.a.r.1.1		3	228.83	even	6
5776.2.a.bk.1.3		3	57.26	odd	6
5776.2.a.bq.1.1		3	57.50	even	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.s (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.906803 - 1.57063i) q^{5} +2.52444 q^{7} +O(q^{10})\)	\(q+(-0.906803 - 1.57063i) q^{5} +2.52444 q^{7} -0.813607 q^{11} +(2.16902 - 3.75686i) q^{13} +(-0.458191 - 0.793610i) q^{17} +(-3.22041 - 2.93751i) q^{19} +(0.906803 - 1.57063i) q^{23} +(0.855416 - 1.48162i) q^{25} +(-4.00958 + 6.94479i) q^{29} +9.30833 q^{31} +(-2.28917 - 3.96496i) q^{35} -11.3083 q^{37} +(-5.60278 - 9.70429i) q^{41} +(4.98263 + 8.63017i) q^{43} +(2.82318 - 4.88990i) q^{47} -0.627213 q^{49} +(1.45819 - 2.52566i) q^{53} +(0.737781 + 1.27787i) q^{55} +(-0.948612 - 1.64305i) q^{59} +(-3.29875 + 5.71360i) q^{61} -7.86751 q^{65} +(1.57583 - 2.72941i) q^{67} +(0.355416 + 0.615598i) q^{71} +(-0.313607 - 0.543182i) q^{73} -2.05390 q^{77} +(-5.16902 - 8.95301i) q^{79} +9.86248 q^{83} +(-0.830978 + 1.43930i) q^{85} +(6.79624 - 11.7714i) q^{89} +(5.47556 - 9.48395i) q^{91} +(-1.69346 + 7.72181i) q^{95} +(-2.31361 - 4.00728i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{5} + 4 q^{7}+O(q^{10}) \) 6 * q + q^5 + 4 * q^7	\( 6 q + q^{5} + 4 q^{7} + 8 q^{11} + q^{13} + 11 q^{17} - q^{23} + 6 q^{25} - 3 q^{29} + 12 q^{31} - 12 q^{35} - 24 q^{37} - 19 q^{41} + 5 q^{43} - 17 q^{47} + 22 q^{49} - 5 q^{53} + 10 q^{55} - 13 q^{59} + 3 q^{61} - 42 q^{65} - 9 q^{67} + 3 q^{71} + 11 q^{73} - 20 q^{77} - 19 q^{79} + 24 q^{83} - 17 q^{85} + 3 q^{89} + 44 q^{91} + 13 q^{95} - q^{97}+O(q^{100}) \) 6 * q + q^5 + 4 * q^7 + 8 * q^11 + q^13 + 11 * q^17 - q^23 + 6 * q^25 - 3 * q^29 + 12 * q^31 - 12 * q^35 - 24 * q^37 - 19 * q^41 + 5 * q^43 - 17 * q^47 + 22 * q^49 - 5 * q^53 + 10 * q^55 - 13 * q^59 + 3 * q^61 - 42 * q^65 - 9 * q^67 + 3 * q^71 + 11 * q^73 - 20 * q^77 - 19 * q^79 + 24 * q^83 - 17 * q^85 + 3 * q^89 + 44 * q^91 + 13 * q^95 - q^97

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