LMFDB - Embedded newform 3456.2.i.e.1153.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3456,2,Mod(1153,3456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("3456.1153");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3456 = 2^{7} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3456.i (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:	$27.5962989386$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.8528759163648.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + x^{8} + 9x^{6} - 36x^{5} + 27x^{4} + 27x^{2} - 162x + 243 $ x^10 - 2x^9 + x^8 + 9x^6 - 36x^5 + 27x^4 + 27x^2 - 162x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 1152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1153.1
Root			$-1.13593 - 1.30754i$ of defining polynomial
Character	$\chi$	$=$	3456.1153
Dual form			3456.2.i.e.2305.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59327 - 2.75962i) q^{5} +(-0.607060 + 1.05146i) q^{7} +O(q^{10})$	$q+(-1.59327 - 2.75962i) q^{5} +(-0.607060 + 1.05146i) q^{7} +(0.312284 - 0.540892i) q^{11} +(1.06440 + 1.84360i) q^{13} +1.83869 q^{17} -7.15403 q^{19} +(0.780986 + 1.35271i) q^{23} +(-2.57702 + 4.46352i) q^{25} +(4.87551 - 8.44463i) q^{29} +(-3.32024 - 5.75083i) q^{31} +3.86884 q^{35} -6.73511 q^{37} +(5.64365 + 9.77508i) q^{41} +(-4.51144 + 7.81404i) q^{43} +(-1.36043 + 2.35634i) q^{47} +(2.76296 + 4.78558i) q^{49} -7.60144 q^{53} -1.99021 q^{55} +(-4.02547 - 6.97231i) q^{59} +(2.79700 - 4.84455i) q^{61} +(3.39176 - 5.87471i) q^{65} +(3.95957 + 6.85817i) q^{67} -8.11222 q^{71} -5.66806 q^{73} +(0.379150 + 0.656707i) q^{77} +(-3.21415 + 5.56707i) q^{79} +(-3.27735 + 5.67653i) q^{83} +(-2.92953 - 5.07409i) q^{85} -5.02926 q^{89} -2.58463 q^{91} +(11.3983 + 19.7424i) q^{95} +(-4.70138 + 8.14302i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{7}+O(q^{10}) $ 10 * q - 4 * q^7	$ 10 q - 4 q^{7} - q^{11} + 6 q^{13} + 6 q^{17} - 18 q^{19} - 4 q^{23} + q^{25} + 4 q^{29} - 8 q^{31} - 24 q^{35} - 20 q^{37} + 5 q^{41} + 13 q^{43} + 6 q^{47} + 3 q^{49} + 12 q^{55} - 13 q^{59} + 10 q^{61} + 17 q^{67} - 8 q^{71} - 34 q^{73} - 8 q^{77} - 6 q^{79} + 12 q^{83} + 18 q^{85} - 44 q^{89} - 36 q^{91} + 6 q^{95} + 27 q^{97}+O(q^{100}) $ 10 * q - 4 * q^7 - q^11 + 6 * q^13 + 6 * q^17 - 18 * q^19 - 4 * q^23 + q^25 + 4 * q^29 - 8 * q^31 - 24 * q^35 - 20 * q^37 + 5 * q^41 + 13 * q^43 + 6 * q^47 + 3 * q^49 + 12 * q^55 - 13 * q^59 + 10 * q^61 + 17 * q^67 - 8 * q^71 - 34 * q^73 - 8 * q^77 - 6 * q^79 + 12 * q^83 + 18 * q^85 - 44 * q^89 - 36 * q^91 + 6 * q^95 + 27 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3456\mathbb{Z}\right)^\times$.

$n$	$2053$	$2431$	$2945$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	−1.59327	−	2.75962i	−0.712532	−	1.23414i	−0.963904	−	0.266251i	$-0.914215\pi$
$5$	−1.59327	−	2.75962i	−0.712532	−	1.23414i	0.251372	−	0.967891i	$-0.419118\pi$
$6$		0			0
$7$	−0.607060	+	1.05146i	−0.229447	+	0.397414i	−0.957644	−	0.287954i	$-0.907025\pi$
$7$	−0.607060	+	1.05146i	−0.229447	+	0.397414i	0.728197	+	0.685368i	$0.240358\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.312284	−	0.540892i	0.0941572	−	0.163085i	−0.815099	−	0.579321i	$-0.803318\pi$
$11$	0.312284	−	0.540892i	0.0941572	−	0.163085i	0.909257	+	0.416236i	$0.136651\pi$
$12$		0			0
$13$	1.06440	+	1.84360i	0.295212	+	0.511323i	0.975034	−	0.222054i	$-0.0712763\pi$
$13$	1.06440	+	1.84360i	0.295212	+	0.511323i	−0.679822	+	0.733377i	$0.737943\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.83869			0.445947			0.222974	−	0.974824i	$-0.428424\pi$
$17$	1.83869			0.445947			0.222974	+	0.974824i	$0.428424\pi$
$18$		0			0
$19$	−7.15403			−1.64125			−0.820624	−	0.571469i	$-0.806374\pi$
$19$	−7.15403			−1.64125			−0.820624	+	0.571469i	$0.806374\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.780986	+	1.35271i	0.162847	+	0.282059i	0.935889	−	0.352296i	$-0.114599\pi$
$23$	0.780986	+	1.35271i	0.162847	+	0.282059i	−0.773042	+	0.634355i	$0.781266\pi$
$24$		0			0
$25$	−2.57702	+	4.46352i	−0.515403	+	0.892705i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.87551	−	8.44463i	0.905360	−	1.56813i	0.0849260	−	0.996387i	$-0.472935\pi$
$29$	4.87551	−	8.44463i	0.905360	−	1.56813i	0.820434	−	0.571742i	$-0.193732\pi$
$30$		0			0
$31$	−3.32024	−	5.75083i	−0.596333	−	1.03288i	−0.993357	−	0.115071i	$-0.963290\pi$
$31$	−3.32024	−	5.75083i	−0.596333	−	1.03288i	0.397024	−	0.917808i	$-0.370043\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.86884			0.653953
$36$		0			0
$37$	−6.73511			−1.10724			−0.553622	−	0.832768i	$-0.686755\pi$
$37$	−6.73511			−1.10724			−0.553622	+	0.832768i	$0.686755\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.64365	+	9.77508i	0.881389	+	1.52661i	0.849797	+	0.527110i	$0.176724\pi$
$41$	5.64365	+	9.77508i	0.881389	+	1.52661i	0.0315923	+	0.999501i	$0.489942\pi$
$42$		0			0
$43$	−4.51144	+	7.81404i	−0.687988	+	1.19163i	0.284500	+	0.958676i	$0.408172\pi$
$43$	−4.51144	+	7.81404i	−0.687988	+	1.19163i	−0.972488	+	0.232954i	$0.925161\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.36043	+	2.35634i	−0.198440	+	0.343708i	−0.948023	−	0.318203i	$-0.896921\pi$
$47$	−1.36043	+	2.35634i	−0.198440	+	0.343708i	0.749583	+	0.661910i	$0.230254\pi$
$48$		0			0
$49$	2.76296	+	4.78558i	0.394708	+	0.683655i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−7.60144			−1.04414			−0.522069	−	0.852903i	$-0.674840\pi$
$53$	−7.60144			−1.04414			−0.522069	+	0.852903i	$0.674840\pi$
$54$		0			0
$55$	−1.99021			−0.268360
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.02547	−	6.97231i	−0.524071	−	0.907718i	−0.999607	−	0.0280214i	$-0.991079\pi$
$59$	−4.02547	−	6.97231i	−0.524071	−	0.907718i	0.475536	−	0.879696i	$-0.342254\pi$
$60$		0			0
$61$	2.79700	−	4.84455i	0.358119	−	0.620281i	−0.629527	−	0.776978i	$-0.716751\pi$
$61$	2.79700	−	4.84455i	0.358119	−	0.620281i	0.987647	+	0.156698i	$0.0500848\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.39176	−	5.87471i	0.420697	−	0.728668i
$66$		0			0
$67$	3.95957	+	6.85817i	0.483738	+	0.837859i	0.999826	−	0.0186768i	$-0.00594534\pi$
$67$	3.95957	+	6.85817i	0.483738	+	0.837859i	−0.516087	+	0.856536i	$0.672612\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−8.11222			−0.962743			−0.481371	−	0.876517i	$-0.659861\pi$
$71$	−8.11222			−0.962743			−0.481371	+	0.876517i	$0.659861\pi$
$72$		0			0
$73$	−5.66806			−0.663397			−0.331698	−	0.943386i	$-0.607622\pi$
$73$	−5.66806			−0.663397			−0.331698	+	0.943386i	$0.607622\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.379150	+	0.656707i	0.0432082	+	0.0748387i
$78$		0			0
$79$	−3.21415	+	5.56707i	−0.361620	+	0.626344i	−0.988228	−	0.152991i	$-0.951110\pi$
$79$	−3.21415	+	5.56707i	−0.361620	+	0.626344i	0.626607	+	0.779335i	$0.284443\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.27735	+	5.67653i	−0.359736	+	0.623080i	−0.987917	−	0.154987i	$-0.950466\pi$
$83$	−3.27735	+	5.67653i	−0.359736	+	0.623080i	0.628181	+	0.778067i	$0.283800\pi$
$84$		0			0
$85$	−2.92953	−	5.07409i	−0.317752	−	0.550362i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.02926			−0.533100			−0.266550	−	0.963821i	$-0.585884\pi$
$89$	−5.02926			−0.533100			−0.266550	+	0.963821i	$0.585884\pi$
$90$		0			0
$91$	−2.58463			−0.270942
$92$		0			0
$93$		0			0
$94$		0			0
$95$	11.3983	+	19.7424i	1.16944	+	2.02553i
$96$		0			0
$97$	−4.70138	+	8.14302i	−0.477353	+	0.826799i	−0.999663	−	0.0259565i	$-0.991737\pi$
$97$	−4.70138	+	8.14302i	−0.477353	+	0.826799i	0.522311	+	0.852755i	$0.325070\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.25154	−	10.8280i	0.622052	−	1.07743i	−0.367051	−	0.930201i	$-0.619633\pi$
$101$	6.25154	−	10.8280i	0.622052	−	1.07743i	0.989103	−	0.147225i	$-0.0470340\pi$
$102$		0			0
$103$	7.87656	+	13.6426i	0.776100	+	1.34425i	0.934174	+	0.356818i	$0.116138\pi$
$103$	7.87656	+	13.6426i	0.776100	+	1.34425i	−0.158073	+	0.987427i	$0.550528\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	13.8684			1.34071			0.670353	−	0.742043i	$-0.266143\pi$
$107$	13.8684			1.34071			0.670353	+	0.742043i	$0.266143\pi$
$108$		0			0
$109$	16.1671			1.54853			0.774265	−	0.632862i	$-0.218120\pi$
$109$	16.1671			1.54853			0.774265	+	0.632862i	$0.218120\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.10460	−	3.64527i	−0.197984	−	0.342918i	0.749891	−	0.661562i	$-0.230106\pi$
$113$	−2.10460	−	3.64527i	−0.197984	−	0.342918i	−0.947875	+	0.318644i	$0.896773\pi$
$114$		0			0
$115$	2.48864	−	4.31045i	0.232067	−	0.401952i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.11619	+	1.93330i	−0.102321	+	0.177226i
$120$		0			0
$121$	5.30496	+	9.18846i	0.482269	+	0.835314i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.490836			0.0439017
$126$		0			0
$127$	−0.515228			−0.0457191			−0.0228595	−	0.999739i	$-0.507277\pi$
$127$	−0.515228			−0.0457191			−0.0228595	+	0.999739i	$0.507277\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	11.3026	+	19.5766i	0.987510	+	1.71042i	0.630201	+	0.776432i	$0.282973\pi$
$131$	11.3026	+	19.5766i	0.987510	+	1.71042i	0.357310	+	0.933986i	$0.383694\pi$
$132$		0			0
$133$	4.34293	−	7.52217i	0.376579	−	0.652255i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.62941	+	8.01837i	−0.395517	+	0.685055i	−0.993167	−	0.116702i	$-0.962768\pi$
$137$	−4.62941	+	8.01837i	−0.395517	+	0.685055i	0.597650	+	0.801757i	$0.296101\pi$
$138$		0			0
$139$	9.22132	+	15.9718i	0.782142	+	1.35471i	0.930692	+	0.365805i	$0.119206\pi$
$139$	9.22132	+	15.9718i	0.782142	+	1.35471i	−0.148550	+	0.988905i	$0.547460\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.32958			0.111185
$144$		0			0
$145$	−31.0720			−2.58039
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2.82223	−	4.88824i	−0.231206	−	0.400460i	0.726957	−	0.686683i	$-0.240934\pi$
$149$	−2.82223	−	4.88824i	−0.231206	−	0.400460i	−0.958163	+	0.286222i	$0.907600\pi$
$150$		0			0
$151$	−3.11543	+	5.39609i	−0.253530	+	0.439128i	−0.964495	−	0.264100i	$-0.914925\pi$
$151$	−3.11543	+	5.39609i	−0.253530	+	0.439128i	0.710965	+	0.703228i	$0.248258\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−10.5801	+	18.3252i	−0.849812	+	1.47192i
$156$		0			0
$157$	7.76557	+	13.4504i	0.619760	+	1.07346i	0.989529	+	0.144332i	$0.0461034\pi$
$157$	7.76557	+	13.4504i	0.619760	+	1.07346i	−0.369769	+	0.929124i	$0.620563\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.89642			−0.149459
$162$		0			0
$163$	−15.3264			−1.20046			−0.600228	−	0.799829i	$-0.704923\pi$
$163$	−15.3264			−1.20046			−0.600228	+	0.799829i	$0.704923\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.36488	+	7.56020i	0.337765	+	0.585026i	0.984012	−	0.178102i	$-0.0569958\pi$
$167$	4.36488	+	7.56020i	0.337765	+	0.585026i	−0.646247	+	0.763128i	$0.723662\pi$
$168$		0			0
$169$	4.23409	−	7.33366i	0.325699	−	0.564128i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−11.1252	+	19.2695i	−0.845837	+	1.46503i	0.0390556	+	0.999237i	$0.487565\pi$
$173$	−11.1252	+	19.2695i	−0.845837	+	1.46503i	−0.884892	+	0.465795i	$0.845768\pi$
$174$		0			0
$175$	−3.12881	−	5.41925i	−0.236516	−	0.409657i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1.29457			0.0967606			0.0483803	−	0.998829i	$-0.484594\pi$
$179$	1.29457			0.0967606			0.0483803	+	0.998829i	$0.484594\pi$
$180$		0			0
$181$	−6.67493			−0.496143			−0.248072	−	0.968742i	$-0.579797\pi$
$181$	−6.67493			−0.496143			−0.248072	+	0.968742i	$0.579797\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	10.7308	+	18.5864i	0.788947	+	1.36650i
$186$		0			0
$187$	0.574193	−	0.994531i	0.0419891	−	0.0727273i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.169031	+	0.292771i	−0.0122307	+	0.0211842i	−0.872076	−	0.489371i	$-0.837227\pi$
$191$	−0.169031	+	0.292771i	−0.0122307	+	0.0211842i	0.859845	+	0.510555i	$0.170560\pi$
$192$		0			0
$193$	−6.36013	−	11.0161i	−0.457812	−	0.792954i	0.541033	−	0.841001i	$-0.318033\pi$
$193$	−6.36013	−	11.0161i	−0.457812	−	0.792954i	−0.998845	+	0.0480477i	$0.984700\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−7.25803			−0.517114			−0.258557	−	0.965996i	$-0.583247\pi$
$197$	−7.25803			−0.517114			−0.258557	+	0.965996i	$0.583247\pi$
$198$		0			0
$199$	−0.112216			−0.00795476			−0.00397738	−	0.999992i	$-0.501266\pi$
$199$	−0.112216			−0.00795476			−0.00397738	+	0.999992i	$0.501266\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	5.91945	+	10.2528i	0.415464	+	0.719605i
$204$		0			0
$205$	17.9837	−	31.1487i	1.25604	−	2.17552i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−2.23409	+	3.86956i	−0.154535	+	0.267663i
$210$		0			0
$211$	−0.746256	−	1.29255i	−0.0513744	−	0.0889830i	0.839195	−	0.543831i	$-0.183027\pi$
$211$	−0.746256	−	1.29255i	−0.0513744	−	0.0889830i	−0.890569	+	0.454848i	$0.849694\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	28.7517			1.96085
$216$		0			0
$217$	8.06234			0.547307
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.95711	+	3.38981i	0.131649	+	0.228023i
$222$		0			0
$223$	−13.7863	+	23.8786i	−0.923200	+	1.59903i	−0.128770	+	0.991674i	$0.541103\pi$
$223$	−13.7863	+	23.8786i	−0.923200	+	1.59903i	−0.794430	+	0.607355i	$0.792230\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.586489	−	1.01583i	0.0389267	−	0.0674229i	−0.845906	−	0.533333i	$-0.820939\pi$
$227$	0.586489	−	1.01583i	0.0389267	−	0.0674229i	0.884832	+	0.465910i	$0.154273\pi$
$228$		0			0
$229$	2.81718	+	4.87950i	0.186164	+	0.322446i	0.943968	−	0.330036i	$-0.107061\pi$
$229$	2.81718	+	4.87950i	0.186164	+	0.322446i	−0.757804	+	0.652482i	$0.773728\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	14.3065			0.937247			0.468623	−	0.883398i	$-0.344750\pi$
$233$	14.3065			0.937247			0.468623	+	0.883398i	$0.344750\pi$
$234$		0			0
$235$	8.67016			0.565579
$236$		0			0
$237$		0			0
$238$		0			0
$239$	2.43313	+	4.21431i	0.157386	+	0.272601i	0.933925	−	0.357468i	$-0.116360\pi$
$239$	2.43313	+	4.21431i	0.157386	+	0.272601i	−0.776539	+	0.630069i	$0.783027\pi$
$240$		0			0
$241$	2.68209	−	4.64552i	0.172769	−	0.299244i	−0.766618	−	0.642103i	$-0.778062\pi$
$241$	2.68209	−	4.64552i	0.172769	−	0.299244i	0.939387	+	0.342859i	$0.111395\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	8.80427	−	15.2494i	0.562484	−	0.974251i
$246$		0			0
$247$	−7.61478	−	13.1892i	−0.484517	−	0.839208i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−14.7664			−0.932047			−0.466023	−	0.884772i	$-0.654314\pi$
$251$	−14.7664			−0.932047			−0.466023	+	0.884772i	$0.654314\pi$
$252$		0			0
$253$	0.975557			0.0613328
$254$		0			0
$255$		0			0
$256$		0			0
$257$	4.19564	+	7.26707i	0.261717	+	0.453307i	0.966698	−	0.255919i	$-0.0823780\pi$
$257$	4.19564	+	7.26707i	0.261717	+	0.453307i	−0.704981	+	0.709226i	$0.749045\pi$
$258$		0			0
$259$	4.08861	−	7.08169i	0.254054	−	0.440035i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−4.85651	+	8.41172i	−0.299465	+	0.518689i	−0.976014	−	0.217709i	$-0.930142\pi$
$263$	−4.85651	+	8.41172i	−0.299465	+	0.518689i	0.676549	+	0.736398i	$0.263475\pi$
$264$		0			0
$265$	12.1111	+	20.9771i	0.743981	+	1.28861i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.519050			−0.0316471			−0.0158235	−	0.999875i	$-0.505037\pi$
$269$	−0.519050			−0.0316471			−0.0158235	+	0.999875i	$0.505037\pi$
$270$		0			0
$271$	16.9533			1.02984			0.514920	−	0.857238i	$-0.327821\pi$
$271$	16.9533			1.02984			0.514920	+	0.857238i	$0.327821\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.60952	+	2.78777i	0.0970579	+	0.168109i
$276$		0			0
$277$	11.3626	−	19.6805i	0.682710	−	1.18249i	−0.291441	−	0.956589i	$-0.594135\pi$
$277$	11.3626	−	19.6805i	0.682710	−	1.18249i	0.974151	−	0.225899i	$-0.0725321\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−5.83592	+	10.1081i	−0.348142	+	0.602999i	−0.985919	−	0.167221i	$-0.946521\pi$
$281$	−5.83592	+	10.1081i	−0.348142	+	0.602999i	0.637778	+	0.770220i	$0.279854\pi$
$282$		0			0
$283$	−13.0284	−	22.5658i	−0.774456	−	1.34140i	−0.935100	−	0.354385i	$-0.884690\pi$
$283$	−13.0284	−	22.5658i	−0.774456	−	1.34140i	0.160644	−	0.987012i	$-0.448643\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−13.7041			−0.808929
$288$		0			0
$289$	−13.6192			−0.801131
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−14.6664	−	25.4030i	−0.856823	−	1.48406i	−0.874944	−	0.484224i	$-0.839102\pi$
$293$	−14.6664	−	25.4030i	−0.856823	−	1.48406i	0.0181212	−	0.999836i	$-0.494232\pi$
$294$		0			0
$295$	−12.8273	+	22.2175i	−0.746835	+	1.29356i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.66257	+	2.87965i	−0.0961488	+	0.166535i
$300$		0			0
$301$	−5.47742	−	9.48718i	−0.315713	−	0.546832i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−17.8255			−1.02069
$306$		0			0
$307$	−11.2190			−0.640305			−0.320152	−	0.947366i	$-0.603734\pi$
$307$	−11.2190			−0.640305			−0.320152	+	0.947366i	$0.603734\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−17.1358	−	29.6801i	−0.971682	−	1.68300i	−0.690476	−	0.723355i	$-0.742599\pi$
$311$	−17.1358	−	29.6801i	−0.971682	−	1.68300i	−0.281206	−	0.959648i	$-0.590734\pi$
$312$		0			0
$313$	10.8824	−	18.8489i	0.615109	−	1.06540i	−0.375256	−	0.926921i	$-0.622445\pi$
$313$	10.8824	−	18.8489i	0.615109	−	1.06540i	0.990365	−	0.138479i	$-0.0442214\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.30124	+	5.71791i	−0.185416	+	0.321150i	−0.943717	−	0.330755i	$-0.892697\pi$
$317$	−3.30124	+	5.71791i	−0.185416	+	0.321150i	0.758301	+	0.651905i	$0.226030\pi$
$318$		0			0
$319$	−3.04509	−	5.27425i	−0.170492	−	0.295301i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−13.1540			−0.731910
$324$		0			0
$325$	−10.9719			−0.608614
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.65173	−	2.86088i	−0.0910629	−	0.157725i
$330$		0			0
$331$	−5.88444	+	10.1921i	−0.323438	+	0.560211i	−0.981195	−	0.193019i	$-0.938172\pi$
$331$	−5.88444	+	10.1921i	−0.323438	+	0.560211i	0.657757	+	0.753230i	$0.271505\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	12.6173	−	21.8538i	0.689358	−	1.19400i
$336$		0			0
$337$	6.15221	+	10.6559i	0.335132	+	0.580466i	0.983510	−	0.180853i	$-0.0578857\pi$
$337$	6.15221	+	10.6559i	0.335132	+	0.580466i	−0.648378	+	0.761319i	$0.724552\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−4.14743			−0.224596
$342$		0			0
$343$	−15.2080			−0.821153
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.05467	−	5.29084i	−0.163983	−	0.284027i	0.772310	−	0.635245i	$-0.219101\pi$
$347$	−3.05467	−	5.29084i	−0.163983	−	0.284027i	−0.936294	+	0.351218i	$0.885768\pi$
$348$		0			0
$349$	−11.5970	+	20.0866i	−0.620772	+	1.07521i	0.368570	+	0.929600i	$0.379847\pi$
$349$	−11.5970	+	20.0866i	−0.620772	+	1.07521i	−0.989342	+	0.145609i	$0.953486\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−5.54985	+	9.61263i	−0.295389	+	0.511629i	−0.975075	−	0.221874i	$-0.928783\pi$
$353$	−5.54985	+	9.61263i	−0.295389	+	0.511629i	0.679686	+	0.733503i	$0.262116\pi$
$354$		0			0
$355$	12.9249	+	22.3867i	0.685985	+	1.18816i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2.34365			−0.123693			−0.0618466	−	0.998086i	$-0.519699\pi$
$359$	−2.34365			−0.123693			−0.0618466	+	0.998086i	$0.519699\pi$
$360$		0			0
$361$	32.1802			1.69369
$362$		0			0
$363$		0			0
$364$		0			0
$365$	9.03075	+	15.6417i	0.472691	+	0.818725i
$366$		0			0
$367$	−10.2442	+	17.7435i	−0.534745	+	0.926206i	0.464431	+	0.885610i	$0.346259\pi$
$367$	−10.2442	+	17.7435i	−0.534745	+	0.926206i	−0.999176	+	0.0405961i	$0.987074\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	4.61453	−	7.99259i	0.239574	−	0.414955i
$372$		0			0
$373$	−3.91408	−	6.77939i	−0.202663	−	0.351023i	0.746722	−	0.665136i	$-0.231626\pi$
$373$	−3.91408	−	6.77939i	−0.202663	−	0.351023i	−0.949386	+	0.314113i	$0.898293\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	20.7580			1.06909
$378$		0			0
$379$	−23.6174			−1.21314			−0.606571	−	0.795029i	$-0.707455\pi$
$379$	−23.6174			−1.21314			−0.606571	+	0.795029i	$0.707455\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−8.08388	−	14.0017i	−0.413067	−	0.715453i	0.582157	−	0.813077i	$-0.302209\pi$
$383$	−8.08388	−	14.0017i	−0.413067	−	0.715453i	−0.995223	+	0.0976240i	$0.968876\pi$
$384$		0			0
$385$	1.20818	−	2.09262i	0.0615744	−	0.106650i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	0.466974	−	0.808822i	0.0236765	−	0.0410089i	−0.853944	−	0.520364i	$-0.825796\pi$
$389$	0.466974	−	0.808822i	0.0236765	−	0.0410089i	0.877621	+	0.479355i	$0.159129\pi$
$390$		0			0
$391$	1.43599	+	2.48721i	0.0726211	+	0.125783i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	20.4840			1.03066
$396$		0			0
$397$	−19.5828			−0.982833			−0.491417	−	0.870925i	$-0.663521\pi$
$397$	−19.5828			−0.982833			−0.491417	+	0.870925i	$0.663521\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−8.55347	−	14.8150i	−0.427140	−	0.739828i	0.569478	−	0.822007i	$-0.307145\pi$
$401$	−8.55347	−	14.8150i	−0.427140	−	0.739828i	−0.996618	+	0.0821788i	$0.973812\pi$
$402$		0			0
$403$	7.06815	−	12.2424i	0.352090	−	0.609837i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.10327	+	3.64296i	−0.104255	+	0.180575i
$408$		0			0
$409$	7.41720	+	12.8470i	0.366757	+	0.635242i	0.989056	−	0.147538i	$-0.0471348\pi$
$409$	7.41720	+	12.8470i	0.366757	+	0.635242i	−0.622300	+	0.782779i	$0.713801\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	9.77479			0.480986
$414$		0			0
$415$	20.8868			1.02529
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−6.76913	−	11.7245i	−0.330694	−	0.572778i	0.651954	−	0.758258i	$-0.273949\pi$
$419$	−6.76913	−	11.7245i	−0.330694	−	0.572778i	−0.982648	+	0.185480i	$0.940616\pi$
$420$		0			0
$421$	−10.7346	+	18.5928i	−0.523171	+	0.906158i	0.476466	+	0.879193i	$0.341918\pi$
$421$	−10.7346	+	18.5928i	−0.523171	+	0.906158i	−0.999636	+	0.0269650i	$0.991416\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−4.73833	+	8.20703i	−0.229843	+	0.398099i
$426$		0			0
$427$	3.39589	+	5.88186i	0.164339	+	0.284643i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−0.628294			−0.0302638			−0.0151319	−	0.999886i	$-0.504817\pi$
$431$	−0.628294			−0.0302638			−0.0151319	+	0.999886i	$0.504817\pi$
$432$		0			0
$433$	−13.9996			−0.672777			−0.336389	−	0.941723i	$-0.609206\pi$
$433$	−13.9996			−0.672777			−0.336389	+	0.941723i	$0.609206\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−5.58720	−	9.67731i	−0.267272	−	0.462929i
$438$		0			0
$439$	17.6162	−	30.5121i	0.840774	−	1.45626i	−0.0484677	−	0.998825i	$-0.515434\pi$
$439$	17.6162	−	30.5121i	0.840774	−	1.45626i	0.889241	−	0.457438i	$-0.151233\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	11.5936	−	20.0806i	0.550827	−	0.954060i	−0.447388	−	0.894340i	$-0.647646\pi$
$443$	11.5936	−	20.0806i	0.550827	−	0.954060i	0.998215	−	0.0597201i	$-0.0190208\pi$
$444$		0			0
$445$	8.01296	+	13.8789i	0.379851	+	0.657921i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	2.37349			0.112012			0.0560061	−	0.998430i	$-0.482163\pi$
$449$	2.37349			0.112012			0.0560061	+	0.998430i	$0.482163\pi$
$450$		0			0
$451$	7.04968			0.331956
$452$		0			0
$453$		0			0
$454$		0			0
$455$	4.11801	+	7.13260i	0.193055	+	0.334381i
$456$		0			0
$457$	−2.87416	+	4.97818i	−0.134447	+	0.232870i	−0.925386	−	0.379026i	$-0.876259\pi$
$457$	−2.87416	+	4.97818i	−0.134447	+	0.232870i	0.790939	+	0.611895i	$0.209593\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−10.0780	+	17.4555i	−0.469378	+	0.812986i	−0.999387	−	0.0350058i	$-0.988855\pi$
$461$	−10.0780	+	17.4555i	−0.469378	+	0.812986i	0.530009	+	0.847992i	$0.322188\pi$
$462$		0			0
$463$	−13.8516	−	23.9918i	−0.643741	−	1.11499i	−0.984591	−	0.174874i	$-0.944048\pi$
$463$	−13.8516	−	23.9918i	−0.643741	−	1.11499i	0.340850	−	0.940118i	$-0.389285\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−36.7764			−1.70181			−0.850904	−	0.525322i	$-0.823945\pi$
$467$	−36.7764			−1.70181			−0.850904	+	0.525322i	$0.823945\pi$
$468$		0			0
$469$	−9.61478			−0.443969
$470$		0			0
$471$		0			0
$472$		0			0
$473$	2.81770	+	4.88040i	0.129558	+	0.224401i
$474$		0			0
$475$	18.4361	−	31.9322i	0.845905	−	1.46515i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−2.76037	+	4.78109i	−0.126124	+	0.218454i	−0.922172	−	0.386780i	$-0.873587\pi$
$479$	−2.76037	+	4.78109i	−0.126124	+	0.218454i	0.796048	+	0.605234i	$0.206920\pi$
$480$		0			0
$481$	−7.16887	−	12.4169i	−0.326872	−	0.566160i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	29.9623			1.36052
$486$		0			0
$487$	22.2903			1.01007			0.505035	−	0.863099i	$-0.331480\pi$
$487$	22.2903			1.01007			0.505035	+	0.863099i	$0.331480\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.207080	+	0.358672i	0.00934537	+	0.0161867i	0.870660	−	0.491885i	$-0.163692\pi$
$491$	0.207080	+	0.358672i	0.00934537	+	0.0161867i	−0.861315	+	0.508071i	$0.830359\pi$
$492$		0			0
$493$	8.96454	−	15.5270i	0.403743	−	0.699303i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.92460	−	8.52966i	0.220899	−	0.382607i
$498$		0			0
$499$	10.7069	+	18.5448i	0.479305	+	0.830181i	0.999718	−	0.0237336i	$-0.00755533\pi$
$499$	10.7069	+	18.5448i	0.479305	+	0.830181i	−0.520413	+	0.853915i	$0.674222\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	20.8397			0.929198			0.464599	−	0.885521i	$-0.346198\pi$
$503$	20.8397			0.929198			0.464599	+	0.885521i	$0.346198\pi$
$504$		0			0
$505$	−39.8416			−1.77293
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1.79067	−	3.10154i	−0.0793703	−	0.137473i	0.823608	−	0.567159i	$-0.191958\pi$
$509$	−1.79067	−	3.10154i	−0.0793703	−	0.137473i	−0.902978	+	0.429686i	$0.858624\pi$
$510$		0			0
$511$	3.44085	−	5.95973i	0.152214	−	0.263643i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	25.0990	−	43.4727i	1.10599	−	1.91564i
$516$		0			0
$517$	0.849684	+	1.47170i	0.0373691	+	0.0647251i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	6.33816			0.277680			0.138840	−	0.990315i	$-0.455663\pi$
$521$	6.33816			0.277680			0.138840	+	0.990315i	$0.455663\pi$
$522$		0			0
$523$	−20.9934			−0.917978			−0.458989	−	0.888442i	$-0.651788\pi$
$523$	−20.9934			−0.917978			−0.458989	+	0.888442i	$0.651788\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−6.10489	−	10.5740i	−0.265933	−	0.460610i
$528$		0			0
$529$	10.2801	−	17.8057i	0.446962	−	0.774161i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−12.0142	+	20.8093i	−0.520394	+	0.901349i
$534$		0			0
$535$	−22.0960	−	38.2715i	−0.955295	−	1.65462i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	3.45131			0.148658
$540$		0			0
$541$	−1.88956			−0.0812384			−0.0406192	−	0.999175i	$-0.512933\pi$
$541$	−1.88956			−0.0812384			−0.0406192	+	0.999175i	$0.512933\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−25.7586	−	44.6152i	−1.10338	−	1.91110i
$546$		0			0
$547$	−5.95041	+	10.3064i	−0.254421	+	0.440671i	−0.964738	−	0.263211i	$-0.915218\pi$
$547$	−5.95041	+	10.3064i	−0.254421	+	0.440671i	0.710317	+	0.703882i	$0.248552\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−34.8796	+	60.4132i	−1.48592	+	2.57369i
$552$		0			0
$553$	−3.90236	−	6.75909i	−0.165945	−	0.287426i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	6.55236			0.277632			0.138816	−	0.990318i	$-0.455670\pi$
$557$	6.55236			0.277632			0.138816	+	0.990318i	$0.455670\pi$
$558$		0			0
$559$	−19.2080			−0.812410
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.42079	+	2.46088i	0.0598791	+	0.103714i	0.894411	−	0.447246i	$-0.147595\pi$
$563$	1.42079	+	2.46088i	0.0598791	+	0.103714i	−0.834532	+	0.550960i	$0.814262\pi$
$564$		0			0
$565$	−6.70638	+	11.6158i	−0.282140	+	0.488680i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	6.59442	−	11.4219i	0.276453	−	0.478830i	−0.694048	−	0.719929i	$-0.744174\pi$
$569$	6.59442	−	11.4219i	0.276453	−	0.478830i	0.970501	+	0.241099i	$0.0775078\pi$
$570$		0			0
$571$	9.97548	+	17.2780i	0.417461	+	0.723064i	0.995683	−	0.0928157i	$-0.0295867\pi$
$571$	9.97548	+	17.2780i	0.417461	+	0.723064i	−0.578222	+	0.815879i	$0.696253\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−8.05045			−0.335727
$576$		0			0
$577$	1.34556			0.0560164			0.0280082	−	0.999608i	$-0.491084\pi$
$577$	1.34556			0.0560164			0.0280082	+	0.999608i	$0.491084\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−3.97909	−	6.89199i	−0.165081	−	0.285928i
$582$		0			0
$583$	−2.37381	+	4.11155i	−0.0983131	+	0.170283i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−10.2237	+	17.7079i	−0.421976	+	0.730884i	−0.996133	−	0.0878615i	$-0.971997\pi$
$587$	−10.2237	+	17.7079i	−0.421976	+	0.730884i	0.574157	+	0.818745i	$0.305330\pi$
$588$		0			0
$589$	23.7531	+	41.1416i	0.978730	+	1.69521i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	25.0810			1.02995			0.514976	−	0.857204i	$-0.327801\pi$
$593$	25.0810			1.02995			0.514976	+	0.857204i	$0.327801\pi$
$594$		0			0
$595$	7.11359			0.291629
$596$		0			0
$597$		0			0
$598$		0			0
$599$	2.37676	+	4.11668i	0.0971119	+	0.168203i	0.910488	−	0.413535i	$-0.135706\pi$
$599$	2.37676	+	4.11668i	0.0971119	+	0.168203i	−0.813376	+	0.581738i	$0.802373\pi$
$600$		0			0
$601$	19.9340	−	34.5267i	0.813124	−	1.40837i	−0.0975429	−	0.995231i	$-0.531098\pi$
$601$	19.9340	−	34.5267i	0.813124	−	1.40837i	0.910667	−	0.413141i	$-0.135568\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	16.9045	−	29.2794i	0.687264	−	1.19038i
$606$		0			0
$607$	21.0643	+	36.4844i	0.854973	+	1.48086i	0.876670	+	0.481093i	$0.159760\pi$
$607$	21.0643	+	36.4844i	0.854973	+	1.48086i	−0.0216961	+	0.999765i	$0.506907\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−5.79221			−0.234328
$612$		0			0
$613$	−37.0554			−1.49665			−0.748327	−	0.663330i	$-0.769143\pi$
$613$	−37.0554			−1.49665			−0.748327	+	0.663330i	$0.769143\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−12.0793	−	20.9220i	−0.486295	−	0.842288i	0.513581	−	0.858041i	$-0.328319\pi$
$617$	−12.0793	−	20.9220i	−0.486295	−	0.842288i	−0.999876	+	0.0157534i	$0.994985\pi$
$618$		0			0
$619$	24.2530	−	42.0074i	0.974810	−	1.68842i	0.294248	−	0.955729i	$-0.404931\pi$
$619$	24.2530	−	42.0074i	0.974810	−	1.68842i	0.680562	−	0.732691i	$-0.261736\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	3.05306	−	5.28805i	0.122318	−	0.211861i
$624$		0			0
$625$	12.1031	+	20.9631i	0.484122	+	0.838524i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−12.3838			−0.493773
$630$		0			0
$631$	38.3164			1.52535			0.762677	−	0.646780i	$-0.223885\pi$
$631$	38.3164			1.52535			0.762677	+	0.646780i	$0.223885\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.820897	+	1.42184i	0.0325763	+	0.0564238i
$636$		0			0
$637$	−5.88180	+	10.1876i	−0.233045	+	0.403647i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	13.3651	−	23.1491i	0.527890	−	0.914333i	−0.471581	−	0.881823i	$-0.656317\pi$
$641$	13.3651	−	23.1491i	0.527890	−	0.914333i	0.999471	−	0.0325101i	$-0.0103501\pi$
$642$		0			0
$643$	−7.35536	−	12.7399i	−0.290067	−	0.502411i	0.683758	−	0.729709i	$-0.260344\pi$
$643$	−7.35536	−	12.7399i	−0.290067	−	0.502411i	−0.973825	+	0.227298i	$0.927011\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	7.36931			0.289717			0.144859	−	0.989452i	$-0.453727\pi$
$647$	7.36931			0.289717			0.144859	+	0.989452i	$0.453727\pi$
$648$		0			0
$649$	−5.02835			−0.197380
$650$		0			0
$651$		0			0
$652$		0			0
$653$	12.2260	+	21.1760i	0.478440	+	0.828683i	0.999694	−	0.0247186i	$-0.00786899\pi$
$653$	12.2260	+	21.1760i	0.478440	+	0.828683i	−0.521254	+	0.853401i	$0.674536\pi$
$654$		0			0
$655$	36.0161	−	62.3817i	1.40727	−	2.43746i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	3.95593	−	6.85187i	0.154101	−	0.266911i	−0.778630	−	0.627483i	$-0.784085\pi$
$659$	3.95593	−	6.85187i	0.154101	−	0.266911i	0.932731	+	0.360572i	$0.117419\pi$
$660$		0			0
$661$	14.7468	+	25.5423i	0.573585	+	0.993479i	0.996194	+	0.0871663i	$0.0277811\pi$
$661$	14.7468	+	25.5423i	0.573585	+	0.993479i	−0.422609	+	0.906312i	$0.638886\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−27.6778			−1.07330
$666$		0			0
$667$	15.2308			0.589740
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1.74692	−	3.02575i	−0.0674390	−	0.116808i
$672$		0			0
$673$	−9.26908	+	16.0545i	−0.357297	+	0.618856i	−0.987508	−	0.157567i	$-0.949635\pi$
$673$	−9.26908	+	16.0545i	−0.357297	+	0.618856i	0.630211	+	0.776424i	$0.282968\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−12.4799	+	21.6158i	−0.479642	+	0.830764i	−0.999727	−	0.0233505i	$-0.992567\pi$
$677$	−12.4799	+	21.6158i	−0.479642	+	0.830764i	0.520086	+	0.854114i	$0.325900\pi$
$678$		0			0
$679$	−5.70803	−	9.88661i	−0.219054	−	0.379413i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	23.8166			0.911315			0.455658	−	0.890155i	$-0.349404\pi$
$683$	23.8166			0.911315			0.455658	+	0.890155i	$0.349404\pi$
$684$		0			0
$685$	29.5036			1.12727
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−8.09100	−	14.0140i	−0.308242	−	0.533891i
$690$		0			0
$691$	0.926507	−	1.60476i	0.0352460	−	0.0610479i	−0.847864	−	0.530213i	$-0.822112\pi$
$691$	0.926507	−	1.60476i	0.0352460	−	0.0610479i	0.883110	+	0.469165i	$0.155445\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	29.3841	−	50.8947i	1.11460	−	1.93055i
$696$		0			0
$697$	10.3769	+	17.9733i	0.393053	+	0.680788i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	25.9501			0.980122			0.490061	−	0.871688i	$-0.336974\pi$
$701$	25.9501			0.980122			0.490061	+	0.871688i	$0.336974\pi$
$702$		0			0
$703$	48.1832			1.81726
$704$		0			0
$705$		0			0
$706$		0			0
$707$	7.59012	+	13.1465i	0.285456	+	0.494424i
$708$		0			0
$709$	−2.18041	+	3.77658i	−0.0818869	+	0.141832i	−0.904060	−	0.427405i	$-0.859428\pi$
$709$	−2.18041	+	3.77658i	−0.0818869	+	0.141832i	0.822174	+	0.569237i	$0.192761\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	5.18612	−	8.98263i	0.194222	−	0.336402i
$714$		0			0
$715$	−2.11839	−	3.66915i	−0.0792232	−	0.137219i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−30.3650			−1.13242			−0.566212	−	0.824260i	$-0.691592\pi$
$719$	−30.3650			−1.13242			−0.566212	+	0.824260i	$0.691592\pi$
$720$		0			0
$721$	−19.1262			−0.712296
$722$		0			0
$723$		0			0
$724$		0			0
$725$	25.1286	+	43.5239i	0.933251	+	1.61644i
$726$		0			0
$727$	−6.47800	+	11.2202i	−0.240256	+	0.416135i	−0.960787	−	0.277287i	$-0.910565\pi$
$727$	−6.47800	+	11.2202i	−0.240256	+	0.416135i	0.720531	+	0.693422i	$0.243898\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−8.29512	+	14.3676i	−0.306806	+	0.531404i
$732$		0			0
$733$	10.6357	+	18.4216i	0.392838	+	0.680416i	0.992823	−	0.119596i	$-0.0381599\pi$
$733$	10.6357	+	18.4216i	0.392838	+	0.680416i	−0.599985	+	0.800012i	$0.704827\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.94604			0.182190
$738$		0			0
$739$	11.4687			0.421883			0.210942	−	0.977499i	$-0.432347\pi$
$739$	11.4687			0.421883			0.210942	+	0.977499i	$0.432347\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−18.0094	−	31.1932i	−0.660701	−	1.14437i	−0.980432	−	0.196859i	$-0.936926\pi$
$743$	−18.0094	−	31.1932i	−0.660701	−	1.14437i	0.319731	−	0.947508i	$-0.396407\pi$
$744$		0			0
$745$	−8.99314	+	15.5766i	−0.329483	+	0.570682i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−8.41893	+	14.5820i	−0.307621	+	0.532815i
$750$		0			0
$751$	4.34620	+	7.52783i	0.158595	+	0.274695i	0.934362	−	0.356325i	$-0.115970\pi$
$751$	4.34620	+	7.52783i	0.158595	+	0.274695i	−0.775767	+	0.631019i	$0.782637\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	19.8549			0.722594
$756$		0			0
$757$	−26.7265			−0.971390			−0.485695	−	0.874128i	$-0.661433\pi$
$757$	−26.7265			−0.971390			−0.485695	+	0.874128i	$0.661433\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−12.0267	−	20.8309i	−0.435969	−	0.755121i	0.561405	−	0.827541i	$-0.310261\pi$
$761$	−12.0267	−	20.8309i	−0.435969	−	0.755121i	−0.997374	+	0.0724203i	$0.976928\pi$
$762$		0			0
$763$	−9.81441	+	16.9991i	−0.355305	+	0.615407i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	8.56944	−	14.8427i	0.309424	−	0.535939i
$768$		0			0
$769$	−1.00296	−	1.73717i	−0.0361675	−	0.0626439i	0.847375	−	0.530995i	$-0.178182\pi$
$769$	−1.00296	−	1.73717i	−0.0361675	−	0.0626439i	−0.883543	+	0.468351i	$0.844848\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	30.0297			1.08009			0.540046	−	0.841635i	$-0.318407\pi$
$773$	30.0297			1.08009			0.540046	+	0.841635i	$0.318407\pi$
$774$		0			0
$775$	34.2253			1.22941
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−40.3748	−	69.9313i	−1.44658	−	2.50555i
$780$		0			0
$781$	−2.53332	+	4.38783i	−0.0906491	+	0.157009i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	24.7453	−	42.8601i	0.883198	−	1.52974i
$786$		0			0
$787$	2.04245	+	3.53763i	0.0728054	+	0.126103i	0.900130	−	0.435622i	$-0.143471\pi$
$787$	2.04245	+	3.53763i	0.0728054	+	0.126103i	−0.827324	+	0.561724i	$0.810138\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	5.11047			0.181707
$792$		0			0
$793$	11.9085			0.422885
$794$		0			0
$795$		0			0
$796$		0			0
$797$	8.31103	+	14.3951i	0.294392	+	0.509901i	0.974843	−	0.222892i	$-0.0715496\pi$
$797$	8.31103	+	14.3951i	0.294392	+	0.509901i	−0.680451	+	0.732793i	$0.738216\pi$
$798$		0			0
$799$	−2.50141	+	4.33258i	−0.0884937	+	0.153276i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.77005	+	3.06581i	−0.0624635	+	0.108190i
$804$		0			0
$805$	3.02151	+	5.23341i	0.106494	+	0.184453i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−48.2163			−1.69519			−0.847597	−	0.530641i	$-0.821951\pi$
$809$	−48.2163			−1.69519			−0.847597	+	0.530641i	$0.821951\pi$
$810$		0			0
$811$	−6.91987			−0.242990			−0.121495	−	0.992592i	$-0.538769\pi$
$811$	−6.91987			−0.242990			−0.121495	+	0.992592i	$0.538769\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	24.4191	+	42.2951i	0.855363	+	1.48153i
$816$		0			0
$817$	32.2750	−	55.9019i	1.12916	−	1.95576i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	7.53494	−	13.0509i	0.262971	−	0.455479i	−0.704059	−	0.710142i	$-0.748631\pi$
$821$	7.53494	−	13.0509i	0.262971	−	0.455479i	0.967030	+	0.254662i	$0.0819643\pi$
$822$		0			0
$823$	−22.6790	−	39.2812i	−0.790541	−	1.36926i	−0.925632	−	0.378424i	$-0.876466\pi$
$823$	−22.6790	−	39.2812i	−0.790541	−	1.36926i	0.135091	−	0.990833i	$-0.456867\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	11.3507			0.394702			0.197351	−	0.980333i	$-0.436766\pi$
$827$	11.3507			0.394702			0.197351	+	0.980333i	$0.436766\pi$
$828$		0			0
$829$	−29.8614			−1.03713			−0.518566	−	0.855038i	$-0.673534\pi$
$829$	−29.8614			−1.03713			−0.518566	+	0.855038i	$0.673534\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	5.08021	+	8.79919i	0.176019	+	0.304874i
$834$		0			0
$835$	13.9089	−	24.0909i	0.481336	−	0.833699i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−13.0215	+	22.5539i	−0.449551	+	0.778646i	−0.998357	−	0.0573042i	$-0.981749\pi$
$839$	−13.0215	+	22.5539i	−0.449551	+	0.778646i	0.548805	+	0.835950i	$0.315083\pi$
$840$		0			0
$841$	−33.0412	−	57.2291i	−1.13935	−	1.97342i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−26.9842			−0.928284
$846$		0			0
$847$	−12.8817			−0.442621
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−5.26002	−	9.11063i	−0.180311	−	0.312308i
$852$		0			0
$853$	−1.04718	+	1.81377i	−0.0358547	+	0.0621021i	−0.883396	−	0.468627i	$-0.844749\pi$
$853$	−1.04718	+	1.81377i	−0.0358547	+	0.0621021i	0.847541	+	0.530730i	$0.178082\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−5.47263	+	9.47887i	−0.186941	+	0.323792i	−0.944229	−	0.329290i	$-0.893191\pi$
$857$	−5.47263	+	9.47887i	−0.186941	+	0.323792i	0.757288	+	0.653082i	$0.226524\pi$
$858$		0			0
$859$	13.4294	+	23.2603i	0.458204	+	0.793633i	0.998866	−	0.0476073i	$-0.0151596\pi$
$859$	13.4294	+	23.2603i	0.458204	+	0.793633i	−0.540662	+	0.841240i	$0.681826\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−49.4778			−1.68424			−0.842121	−	0.539288i	$-0.818693\pi$
$863$	−49.4778			−1.68424			−0.842121	+	0.539288i	$0.818693\pi$
$864$		0			0
$865$	70.9021			2.41074
$866$		0			0
$867$		0			0
$868$		0			0
$869$	2.00746	+	3.47701i	0.0680983	+	0.117950i
$870$		0			0
$871$	−8.42916	+	14.5997i	−0.285611	+	0.494693i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.297967	+	0.516093i	−0.0100731	+	0.0174471i
$876$		0			0
$877$	−11.3449	−	19.6499i	−0.383090	−	0.663531i	0.608412	−	0.793621i	$-0.291807\pi$
$877$	−11.3449	−	19.6499i	−0.383090	−	0.663531i	−0.991502	+	0.130090i	$0.958473\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−10.8224			−0.364616			−0.182308	−	0.983241i	$-0.558357\pi$
$881$	−10.8224			−0.364616			−0.182308	+	0.983241i	$0.558357\pi$
$882$		0			0
$883$	32.7591			1.10243			0.551215	−	0.834363i	$-0.314164\pi$
$883$	32.7591			1.10243			0.551215	+	0.834363i	$0.314164\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−16.6048	−	28.7604i	−0.557535	−	0.965679i	−0.997701	−	0.0677629i	$-0.978414\pi$
$887$	−16.6048	−	28.7604i	−0.557535	−	0.965679i	0.440166	−	0.897916i	$-0.354919\pi$
$888$		0			0
$889$	0.312774	−	0.541741i	0.0104901	−	0.0181694i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	9.73260	−	16.8574i	0.325689	−	0.564110i
$894$		0			0
$895$	−2.06260	−	3.57252i	−0.0689450	−	0.119416i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−64.7515			−2.15958
$900$		0			0
$901$	−13.9767			−0.465630
$902$		0			0
$903$		0			0
$904$		0			0
$905$	10.6350	+	18.4203i	0.353518	+	0.612311i
$906$		0			0
$907$	10.2085	−	17.6816i	0.338966	−	0.587107i	−0.645272	−	0.763953i	$-0.723256\pi$
$907$	10.2085	−	17.6816i	0.338966	−	0.587107i	0.984239	+	0.176846i	$0.0565895\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	29.7162	−	51.4700i	0.984541	−	1.70528i	0.340585	−	0.940214i	$-0.389375\pi$
$911$	29.7162	−	51.4700i	0.984541	−	1.70528i	0.643957	−	0.765062i	$-0.277292\pi$
$912$		0			0
$913$	2.04693	+	3.54538i	0.0677434	+	0.117335i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−27.4454			−0.906325
$918$		0			0
$919$	−23.2045			−0.765447			−0.382724	−	0.923863i	$-0.625014\pi$
$919$	−23.2045			−0.765447			−0.382724	+	0.923863i	$0.625014\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−8.63467	−	14.9557i	−0.284214	−	0.492272i
$924$		0			0
$925$	17.3565	−	30.0623i	0.570678	−	0.988443i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.370924	−	0.642460i	0.0121696	−	0.0210784i	−0.859876	−	0.510502i	$-0.829460\pi$
$929$	0.370924	−	0.642460i	0.0121696	−	0.0210784i	0.872046	+	0.489424i	$0.162793\pi$
$930$		0			0
$931$	−19.7663	−	34.2362i	−0.647814	−	1.12205i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−3.65938			−0.119674
$936$		0			0
$937$	2.43708			0.0796161			0.0398080	−	0.999207i	$-0.487325\pi$
$937$	2.43708			0.0796161			0.0398080	+	0.999207i	$0.487325\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−5.25473	−	9.10146i	−0.171299	−	0.296699i	0.767575	−	0.640959i	$-0.221463\pi$
$941$	−5.25473	−	9.10146i	−0.171299	−	0.296699i	−0.938874	+	0.344260i	$0.888130\pi$
$942$		0			0
$943$	−8.81521	+	15.2684i	−0.287063	+	0.497207i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	26.4659	−	45.8403i	0.860026	−	1.48961i	−0.0118761	−	0.999929i	$-0.503780\pi$
$947$	26.4659	−	45.8403i	0.860026	−	1.48961i	0.871902	−	0.489680i	$-0.162886\pi$
$948$		0			0
$949$	−6.03311	−	10.4496i	−0.195843	−	0.339210i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	14.5979			0.472873			0.236437	−	0.971647i	$-0.424020\pi$
$953$	14.5979			0.472873			0.236437	+	0.971647i	$0.424020\pi$
$954$		0			0
$955$	1.07725			0.0348590
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−5.62065	−	9.73526i	−0.181500	−	0.314368i
$960$		0			0
$961$	−6.54800	+	11.3415i	−0.211226	+	0.365854i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−20.2668	+	35.1031i	−0.652411	+	1.13001i
$966$		0			0
$967$	27.3029	+	47.2900i	0.878003	+	1.52075i	0.853529	+	0.521045i	$0.174458\pi$
$967$	27.3029	+	47.2900i	0.878003	+	1.52075i	0.0244732	+	0.999700i	$0.492209\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−41.5365			−1.33297			−0.666485	−	0.745519i	$-0.732202\pi$
$971$	−41.5365			−1.33297			−0.666485	+	0.745519i	$0.732202\pi$
$972$		0			0
$973$	−22.3916			−0.717841
$974$		0			0
$975$		0			0
$976$		0			0
$977$	30.4039	+	52.6611i	0.972707	+	1.68478i	0.687303	+	0.726371i	$0.258794\pi$
$977$	30.4039	+	52.6611i	0.972707	+	1.68478i	0.285404	+	0.958407i	$0.407872\pi$
$978$		0			0
$979$	−1.57056	+	2.72028i	−0.0501952	+	0.0869406i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	14.9506	−	25.8952i	0.476851	−	0.825929i	−0.522797	−	0.852457i	$-0.675112\pi$
$983$	14.9506	−	25.8952i	0.476851	−	0.825929i	0.999648	+	0.0265275i	$0.00844494\pi$
$984$		0			0
$985$	11.5640	+	20.0294i	0.368460	+	0.638191i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−14.0935			−0.448146
$990$		0			0
$991$	−56.3402			−1.78971			−0.894853	−	0.446361i	$-0.852720\pi$
$991$	−56.3402			−1.78971			−0.894853	+	0.446361i	$0.852720\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.178790	+	0.309673i	0.00566802	+	0.00981730i
$996$		0			0
$997$	5.26572	−	9.12049i	0.166767	−	0.288849i	−0.770514	−	0.637423i	$-0.780001\pi$
$997$	5.26572	−	9.12049i	0.166767	−	0.288849i	0.937281	+	0.348574i	$0.113334\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3456.2.i.e.1153.1		10
3.2	odd	2		1152.2.i.e.385.3	✓	10
4.3	odd	2		3456.2.i.h.1153.1		10
8.3	odd	2		3456.2.i.g.1153.5		10
8.5	even	2		3456.2.i.f.1153.5		10
9.4	even	3	inner	3456.2.i.e.2305.1		10
9.5	odd	6		1152.2.i.e.769.3	yes	10
12.11	even	2		1152.2.i.h.385.3	yes	10
24.5	odd	2		1152.2.i.g.385.3	yes	10
24.11	even	2		1152.2.i.f.385.3	yes	10
36.23	even	6		1152.2.i.h.769.3	yes	10
36.31	odd	6		3456.2.i.h.2305.1		10
72.5	odd	6		1152.2.i.g.769.3	yes	10
72.13	even	6		3456.2.i.f.2305.5		10
72.59	even	6		1152.2.i.f.769.3	yes	10
72.67	odd	6		3456.2.i.g.2305.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.i.e.385.3	✓	10	3.2	odd	2
1152.2.i.e.769.3	yes	10	9.5	odd	6
1152.2.i.f.385.3	yes	10	24.11	even	2
1152.2.i.f.769.3	yes	10	72.59	even	6
1152.2.i.g.385.3	yes	10	24.5	odd	2
1152.2.i.g.769.3	yes	10	72.5	odd	6
1152.2.i.h.385.3	yes	10	12.11	even	2
1152.2.i.h.769.3	yes	10	36.23	even	6
3456.2.i.e.1153.1		10	1.1	even	1	trivial
3456.2.i.e.2305.1		10	9.4	even	3	inner
3456.2.i.f.1153.5		10	8.5	even	2
3456.2.i.f.2305.5		10	72.13	even	6
3456.2.i.g.1153.5		10	8.3	odd	2
3456.2.i.g.2305.5		10	72.67	odd	6
3456.2.i.h.1153.1		10	4.3	odd	2
3456.2.i.h.2305.1		10	36.31	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:	\( N \)	\(=\)	\( 3456 = 2^{7} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3456.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.59327 - 2.75962i) q^{5} +(-0.607060 + 1.05146i) q^{7} +O(q^{10})\)	\(q+(-1.59327 - 2.75962i) q^{5} +(-0.607060 + 1.05146i) q^{7} +(0.312284 - 0.540892i) q^{11} +(1.06440 + 1.84360i) q^{13} +1.83869 q^{17} -7.15403 q^{19} +(0.780986 + 1.35271i) q^{23} +(-2.57702 + 4.46352i) q^{25} +(4.87551 - 8.44463i) q^{29} +(-3.32024 - 5.75083i) q^{31} +3.86884 q^{35} -6.73511 q^{37} +(5.64365 + 9.77508i) q^{41} +(-4.51144 + 7.81404i) q^{43} +(-1.36043 + 2.35634i) q^{47} +(2.76296 + 4.78558i) q^{49} -7.60144 q^{53} -1.99021 q^{55} +(-4.02547 - 6.97231i) q^{59} +(2.79700 - 4.84455i) q^{61} +(3.39176 - 5.87471i) q^{65} +(3.95957 + 6.85817i) q^{67} -8.11222 q^{71} -5.66806 q^{73} +(0.379150 + 0.656707i) q^{77} +(-3.21415 + 5.56707i) q^{79} +(-3.27735 + 5.67653i) q^{83} +(-2.92953 - 5.07409i) q^{85} -5.02926 q^{89} -2.58463 q^{91} +(11.3983 + 19.7424i) q^{95} +(-4.70138 + 8.14302i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{7}+O(q^{10}) \) 10 * q - 4 * q^7	\( 10 q - 4 q^{7} - q^{11} + 6 q^{13} + 6 q^{17} - 18 q^{19} - 4 q^{23} + q^{25} + 4 q^{29} - 8 q^{31} - 24 q^{35} - 20 q^{37} + 5 q^{41} + 13 q^{43} + 6 q^{47} + 3 q^{49} + 12 q^{55} - 13 q^{59} + 10 q^{61} + 17 q^{67} - 8 q^{71} - 34 q^{73} - 8 q^{77} - 6 q^{79} + 12 q^{83} + 18 q^{85} - 44 q^{89} - 36 q^{91} + 6 q^{95} + 27 q^{97}+O(q^{100}) \) 10 * q - 4 * q^7 - q^11 + 6 * q^13 + 6 * q^17 - 18 * q^19 - 4 * q^23 + q^25 + 4 * q^29 - 8 * q^31 - 24 * q^35 - 20 * q^37 + 5 * q^41 + 13 * q^43 + 6 * q^47 + 3 * q^49 + 12 * q^55 - 13 * q^59 + 10 * q^61 + 17 * q^67 - 8 * q^71 - 34 * q^73 - 8 * q^77 - 6 * q^79 + 12 * q^83 + 18 * q^85 - 44 * q^89 - 36 * q^91 + 6 * q^95 + 27 * q^97

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