LMFDB - Embedded newform 3456.2.i.e.1153.3

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			1153.3
Root			$-1.41743 + 0.995434i$ of defining polynomial
Character	$\chi$	$=$	3456.1153
Dual form			3456.2.i.e.2305.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.115851 - 0.200661i) q^{5} +(-0.230793 + 0.399745i) q^{7} +O(q^{10})$	$q+(-0.115851 - 0.200661i) q^{5} +(-0.230793 + 0.399745i) q^{7} +(-0.749014 + 1.29733i) q^{11} +(-1.07079 - 1.85466i) q^{13} -1.03644 q^{17} +2.94631 q^{19} +(0.364866 + 0.631966i) q^{23} +(2.47316 - 4.28363i) q^{25} +(-2.33711 + 4.04800i) q^{29} +(2.73632 + 4.73945i) q^{31} +0.106951 q^{35} -2.30039 q^{37} +(1.84151 + 3.18959i) q^{41} +(2.41968 - 4.19101i) q^{43} +(5.40881 - 9.36833i) q^{47} +(3.39347 + 5.87766i) q^{49} -10.0430 q^{53} +0.347097 q^{55} +(2.71613 + 4.70447i) q^{59} +(6.86526 - 11.8910i) q^{61} +(-0.248104 + 0.429729i) q^{65} +(5.58388 + 9.67156i) q^{67} +13.2942 q^{71} +4.24276 q^{73} +(-0.345734 - 0.598829i) q^{77} +(-6.23617 + 10.8014i) q^{79} +(3.62651 - 6.28130i) q^{83} +(0.120073 + 0.207973i) q^{85} +11.8627 q^{89} +0.988520 q^{91} +(-0.341335 - 0.591209i) q^{95} +(-2.21479 + 3.83613i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−0.115851	−	0.200661i	−0.0518103	−	0.0897381i	0.838957	−	0.544198i	$-0.183166\pi$
$5$	−0.115851	−	0.200661i	−0.0518103	−	0.0897381i	−0.890767	+	0.454459i	$0.849832\pi$
$6$		0			0
$7$	−0.230793	+	0.399745i	−0.0872315	+	0.151089i	−0.906340	−	0.422549i	$-0.861135\pi$
$7$	−0.230793	+	0.399745i	−0.0872315	+	0.151089i	0.819108	+	0.573639i	$0.194469\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.749014	+	1.29733i	−0.225836	+	0.391160i	−0.956570	−	0.291503i	$-0.905845\pi$
$11$	−0.749014	+	1.29733i	−0.225836	+	0.391160i	0.730734	+	0.682663i	$0.239178\pi$
$12$		0			0
$13$	−1.07079	−	1.85466i	−0.296983	−	0.514389i	0.678461	−	0.734636i	$-0.262647\pi$
$13$	−1.07079	−	1.85466i	−0.296983	−	0.514389i	−0.975444	+	0.220247i	$0.929314\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.03644			−0.251374			−0.125687	−	0.992070i	$-0.540114\pi$
$17$	−1.03644			−0.251374			−0.125687	+	0.992070i	$0.540114\pi$
$18$		0			0
$19$	2.94631			0.675931			0.337965	−	0.941159i	$-0.390261\pi$
$19$	2.94631			0.675931			0.337965	+	0.941159i	$0.390261\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.364866	+	0.631966i	0.0760798	+	0.131774i	0.901555	−	0.432664i	$-0.142426\pi$
$23$	0.364866	+	0.631966i	0.0760798	+	0.131774i	−0.825476	+	0.564438i	$0.809093\pi$
$24$		0			0
$25$	2.47316	−	4.28363i	0.494631	−	0.856727i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.33711	+	4.04800i	−0.433991	+	0.751694i	−0.997213	−	0.0746115i	$-0.976228\pi$
$29$	−2.33711	+	4.04800i	−0.433991	+	0.751694i	0.563222	+	0.826306i	$0.309562\pi$
$30$		0			0
$31$	2.73632	+	4.73945i	0.491458	+	0.851230i	0.999952	−	0.00983556i	$-0.00313081\pi$
$31$	2.73632	+	4.73945i	0.491458	+	0.851230i	−0.508494	+	0.861066i	$0.669797\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.106951			0.0180780
$36$		0			0
$37$	−2.30039			−0.378182			−0.189091	−	0.981960i	$-0.560554\pi$
$37$	−2.30039			−0.378182			−0.189091	+	0.981960i	$0.560554\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.84151	+	3.18959i	0.287596	+	0.498131i	0.973235	−	0.229811i	$-0.0738107\pi$
$41$	1.84151	+	3.18959i	0.287596	+	0.498131i	−0.685639	+	0.727941i	$0.740477\pi$
$42$		0			0
$43$	2.41968	−	4.19101i	0.368998	−	0.639123i	−0.620411	−	0.784277i	$-0.713034\pi$
$43$	2.41968	−	4.19101i	0.368998	−	0.639123i	0.989409	+	0.145153i	$0.0463676\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.40881	−	9.36833i	0.788956	−	1.36651i	−0.137651	−	0.990481i	$-0.543955\pi$
$47$	5.40881	−	9.36833i	0.788956	−	1.36651i	0.926607	−	0.376031i	$-0.122711\pi$
$48$		0			0
$49$	3.39347	+	5.87766i	0.484781	+	0.839666i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−10.0430			−1.37951			−0.689756	−	0.724042i	$-0.742282\pi$
$53$	−10.0430			−1.37951			−0.689756	+	0.724042i	$0.742282\pi$
$54$		0			0
$55$	0.347097			0.0468026
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.71613	+	4.70447i	0.353610	+	0.612470i	0.986879	−	0.161461i	$-0.0516207\pi$
$59$	2.71613	+	4.70447i	0.353610	+	0.612470i	−0.633269	+	0.773932i	$0.718287\pi$
$60$		0			0
$61$	6.86526	−	11.8910i	0.879007	−	1.52248i	0.0265746	−	0.999647i	$-0.491540\pi$
$61$	6.86526	−	11.8910i	0.879007	−	1.52248i	0.852432	−	0.522838i	$-0.175127\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.248104	+	0.429729i	−0.0307736	+	0.0533014i
$66$		0			0
$67$	5.58388	+	9.67156i	0.682179	+	1.18157i	0.974314	+	0.225192i	$0.0723009\pi$
$67$	5.58388	+	9.67156i	0.682179	+	1.18157i	−0.292135	+	0.956377i	$0.594366\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	13.2942			1.57773			0.788866	−	0.614565i	$-0.210669\pi$
$71$	13.2942			1.57773			0.788866	+	0.614565i	$0.210669\pi$
$72$		0			0
$73$	4.24276			0.496578			0.248289	−	0.968686i	$-0.420132\pi$
$73$	4.24276			0.496578			0.248289	+	0.968686i	$0.420132\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.345734	−	0.598829i	−0.0394001	−	0.0682429i
$78$		0			0
$79$	−6.23617	+	10.8014i	−0.701624	+	1.21525i	0.266272	+	0.963898i	$0.414208\pi$
$79$	−6.23617	+	10.8014i	−0.701624	+	1.21525i	−0.967896	+	0.251351i	$0.919125\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.62651	−	6.28130i	0.398061	−	0.689463i	−0.595425	−	0.803411i	$-0.703016\pi$
$83$	3.62651	−	6.28130i	0.398061	−	0.689463i	0.993487	+	0.113948i	$0.0363497\pi$
$84$		0			0
$85$	0.120073	+	0.207973i	0.0130238	+	0.0225579i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	11.8627			1.25745			0.628724	−	0.777628i	$-0.283577\pi$
$89$	11.8627			1.25745			0.628724	+	0.777628i	$0.283577\pi$
$90$		0			0
$91$	0.988520			0.103625
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.341335	−	0.591209i	−0.0350202	−	0.0606567i
$96$		0			0
$97$	−2.21479	+	3.83613i	−0.224878	+	0.389500i	−0.956283	−	0.292444i	$-0.905532\pi$
$97$	−2.21479	+	3.83613i	−0.224878	+	0.389500i	0.731405	+	0.681943i	$0.238865\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−7.47401	+	12.9454i	−0.743692	+	1.28811i	0.207112	+	0.978317i	$0.433594\pi$
$101$	−7.47401	+	12.9454i	−0.743692	+	1.28811i	−0.950804	+	0.309794i	$0.899740\pi$
$102$		0			0
$103$	0.0310319	+	0.0537488i	0.00305766	+	0.00529603i	0.867550	−	0.497350i	$-0.165693\pi$
$103$	0.0310319	+	0.0537488i	0.00305766	+	0.00529603i	−0.864493	+	0.502646i	$0.832360\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	11.9297			1.15329			0.576645	−	0.816995i	$-0.304362\pi$
$107$	11.9297			1.15329			0.576645	+	0.816995i	$0.304362\pi$
$108$		0			0
$109$	−10.1328			−0.970544			−0.485272	−	0.874363i	$-0.661279\pi$
$109$	−10.1328			−0.970544			−0.485272	+	0.874363i	$0.661279\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.743274	+	1.28739i	0.0699213	+	0.121107i	0.898866	−	0.438223i	$-0.144392\pi$
$113$	0.743274	+	1.28739i	0.0699213	+	0.121107i	−0.828945	+	0.559330i	$0.811059\pi$
$114$		0			0
$115$	0.0845404	−	0.146428i	0.00788343	−	0.0136545i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.239204	−	0.414313i	0.0219278	−	0.0379800i
$120$		0			0
$121$	4.37796	+	7.58284i	0.397996	+	0.689349i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−2.30459			−0.206129
$126$		0			0
$127$	16.5663			1.47002			0.735010	−	0.678056i	$-0.237177\pi$
$127$	16.5663			1.47002			0.735010	+	0.678056i	$0.237177\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1.43125	−	2.47900i	−0.125049	−	0.216591i	0.796703	−	0.604371i	$-0.206576\pi$
$131$	−1.43125	−	2.47900i	−0.125049	−	0.216591i	−0.921752	+	0.387780i	$0.873242\pi$
$132$		0			0
$133$	−0.679988	+	1.17777i	−0.0589624	+	0.102126i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	8.27650	−	14.3353i	0.707109	−	1.22475i	−0.258816	−	0.965927i	$-0.583332\pi$
$137$	8.27650	−	14.3353i	0.707109	−	1.22475i	0.965925	−	0.258822i	$-0.0833343\pi$
$138$		0			0
$139$	3.68545	+	6.38339i	0.312596	+	0.541432i	0.978923	−	0.204227i	$-0.0654682\pi$
$139$	3.68545	+	6.38339i	0.312596	+	0.541432i	−0.666328	+	0.745659i	$0.732135\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.20814			0.268278
$144$		0			0
$145$	1.08303			0.0899408
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.06052	−	1.83688i	−0.0868814	−	0.150483i	0.819310	−	0.573351i	$-0.194357\pi$
$149$	−1.06052	−	1.83688i	−0.0868814	−	0.150483i	−0.906191	+	0.422868i	$0.861023\pi$
$150$		0			0
$151$	−1.97197	+	3.41555i	−0.160476	+	0.277953i	−0.935040	−	0.354543i	$-0.884636\pi$
$151$	−1.97197	+	3.41555i	−0.160476	+	0.277953i	0.774563	+	0.632497i	$0.217970\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.634013	−	1.09814i	0.0509252	−	0.0882050i
$156$		0			0
$157$	−5.77046	−	9.99472i	−0.460532	−	0.797666i	0.538455	−	0.842654i	$-0.319008\pi$
$157$	−5.77046	−	9.99472i	−0.460532	−	0.797666i	−0.998987	+	0.0449886i	$0.985675\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.336834			−0.0265462
$162$		0			0
$163$	−0.716550			−0.0561245			−0.0280623	−	0.999606i	$-0.508934\pi$
$163$	−0.716550			−0.0561245			−0.0280623	+	0.999606i	$0.508934\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.36210	+	7.55538i	0.337550	+	0.584653i	0.983971	−	0.178327i	$-0.0570686\pi$
$167$	4.36210	+	7.55538i	0.337550	+	0.584653i	−0.646422	+	0.762980i	$0.723735\pi$
$168$		0			0
$169$	4.20683	−	7.28645i	0.323602	−	0.560496i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	8.96809	−	15.5332i	0.681832	−	1.18097i	−0.292590	−	0.956238i	$-0.594517\pi$
$173$	8.96809	−	15.5332i	0.681832	−	1.18097i	0.974421	−	0.224729i	$-0.0721496\pi$
$174$		0			0
$175$	1.14157	+	1.97726i	0.0862949	+	0.149467i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	6.66578			0.498224			0.249112	−	0.968475i	$-0.419861\pi$
$179$	6.66578			0.498224			0.249112	+	0.968475i	$0.419861\pi$
$180$		0			0
$181$	−19.1119			−1.42058			−0.710290	−	0.703909i	$-0.751436\pi$
$181$	−19.1119			−1.42058			−0.710290	+	0.703909i	$0.751436\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.266503	+	0.461598i	0.0195937	+	0.0339373i
$186$		0			0
$187$	0.776311	−	1.34461i	0.0567695	−	0.0983276i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.03948	−	1.80042i	0.0752138	−	0.130274i	−0.825965	−	0.563721i	$-0.809369\pi$
$191$	1.03948	−	1.80042i	0.0752138	−	0.130274i	0.901179	+	0.433447i	$0.142703\pi$
$192$		0			0
$193$	10.1978	+	17.6632i	0.734057	+	1.27142i	0.955136	+	0.296168i	$0.0957089\pi$
$193$	10.1978	+	17.6632i	0.734057	+	1.27142i	−0.221079	+	0.975256i	$0.570958\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−16.5458			−1.17884			−0.589419	−	0.807828i	$-0.700643\pi$
$197$	−16.5458			−1.17884			−0.589419	+	0.807828i	$0.700643\pi$
$198$		0			0
$199$	21.2942			1.50951			0.754753	−	0.656009i	$-0.227757\pi$
$199$	21.2942			1.50951			0.754753	+	0.656009i	$0.227757\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.07878	−	1.86850i	−0.0757153	−	0.131143i
$204$		0			0
$205$	0.426684	−	0.739038i	0.0298009	−	0.0516166i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−2.20683	+	3.82234i	−0.152650	+	0.264397i
$210$		0			0
$211$	10.1986	+	17.6645i	0.702101	+	1.21607i	0.967728	+	0.251999i	$0.0810879\pi$
$211$	10.1986	+	17.6645i	0.702101	+	1.21607i	−0.265627	+	0.964076i	$0.585579\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.12129			−0.0764716
$216$		0			0
$217$	−2.52609			−0.171482
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.10981	+	1.92225i	0.0746539	+	0.129304i
$222$		0			0
$223$	2.52026	−	4.36522i	0.168769	−	0.292317i	−0.769218	−	0.638986i	$-0.779354\pi$
$223$	2.52026	−	4.36522i	0.168769	−	0.292317i	0.937987	+	0.346669i	$0.112687\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	8.12047	−	14.0651i	0.538975	−	0.933531i	−0.459985	−	0.887927i	$-0.652145\pi$
$227$	8.12047	−	14.0651i	0.538975	−	0.933531i	0.998960	−	0.0456047i	$-0.0145214\pi$
$228$		0			0
$229$	2.92453	+	5.06544i	0.193259	+	0.334734i	0.946328	−	0.323207i	$-0.104761\pi$
$229$	2.92453	+	5.06544i	0.193259	+	0.334734i	−0.753070	+	0.657941i	$0.771428\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	20.7492			1.35932			0.679662	−	0.733526i	$-0.262127\pi$
$233$	20.7492			1.35932			0.679662	+	0.733526i	$0.262127\pi$
$234$		0			0
$235$	−2.50647			−0.163504
$236$		0			0
$237$		0			0
$238$		0			0
$239$	2.09672	+	3.63163i	0.135626	+	0.234910i	0.925836	−	0.377925i	$-0.123362\pi$
$239$	2.09672	+	3.63163i	0.135626	+	0.234910i	−0.790211	+	0.612835i	$0.790029\pi$
$240$		0			0
$241$	−7.03921	+	12.1923i	−0.453435	+	0.785373i	−0.998597	−	0.0529581i	$-0.983135\pi$
$241$	−7.03921	+	12.1923i	−0.453435	+	0.785373i	0.545161	+	0.838331i	$0.316468\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.786276	−	1.36187i	0.0502334	−	0.0870067i
$246$		0			0
$247$	−3.15487	−	5.46440i	−0.200740	−	0.347692i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	15.3752			0.970476			0.485238	−	0.874382i	$-0.338733\pi$
$251$	15.3752			0.970476			0.485238	+	0.874382i	$0.338733\pi$
$252$		0			0
$253$	−1.09316			−0.0687263
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3.51288	−	6.08448i	−0.219127	−	0.379540i	0.735414	−	0.677618i	$-0.236988\pi$
$257$	−3.51288	−	6.08448i	−0.219127	−	0.379540i	−0.954541	+	0.298078i	$0.903654\pi$
$258$		0			0
$259$	0.530914	−	0.919569i	0.0329894	−	0.0571393i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−5.62093	+	9.73573i	−0.346601	+	0.600331i	−0.985643	−	0.168841i	$-0.945998\pi$
$263$	−5.62093	+	9.73573i	−0.346601	+	0.600331i	0.639042	+	0.769172i	$0.279331\pi$
$264$		0			0
$265$	1.16350	+	2.01523i	0.0714730	+	0.123795i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	20.5678			1.25404			0.627019	−	0.779004i	$-0.284275\pi$
$269$	20.5678			1.25404			0.627019	+	0.779004i	$0.284275\pi$
$270$		0			0
$271$	8.25314			0.501343			0.250671	−	0.968072i	$-0.419349\pi$
$271$	8.25314			0.501343			0.250671	+	0.968072i	$0.419349\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.70486	+	6.41701i	0.223411	+	0.386960i
$276$		0			0
$277$	−6.49837	+	11.2555i	−0.390449	+	0.676278i	−0.992509	−	0.122174i	$-0.961014\pi$
$277$	−6.49837	+	11.2555i	−0.390449	+	0.676278i	0.602060	+	0.798451i	$0.294347\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	9.29955	−	16.1073i	0.554765	−	0.960880i	−0.443157	−	0.896444i	$-0.646142\pi$
$281$	9.29955	−	16.1073i	0.554765	−	0.960880i	0.997922	−	0.0644365i	$-0.0205250\pi$
$282$		0			0
$283$	8.30074	+	14.3773i	0.493428	+	0.854642i	0.999971	−	0.00757254i	$-0.00241044\pi$
$283$	8.30074	+	14.3773i	0.493428	+	0.854642i	−0.506544	+	0.862214i	$0.669077\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.70003			−0.100350
$288$		0			0
$289$	−15.9258			−0.936811
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−6.33729	−	10.9765i	−0.370228	−	0.641254i	0.619372	−	0.785098i	$-0.287387\pi$
$293$	−6.33729	−	10.9765i	−0.370228	−	0.641254i	−0.989601	+	0.143843i	$0.954054\pi$
$294$		0			0
$295$	0.629335	−	1.09004i	0.0366413	−	0.0634646i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.781387	−	1.35340i	0.0451888	−	0.0782692i
$300$		0			0
$301$	1.11689	+	1.93451i	0.0643765	+	0.111503i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−3.18140			−0.182167
$306$		0			0
$307$	−15.4097			−0.879479			−0.439740	−	0.898125i	$-0.644929\pi$
$307$	−15.4097			−0.879479			−0.439740	+	0.898125i	$0.644929\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−12.7683	−	22.1153i	−0.724022	−	1.25404i	−0.959375	−	0.282133i	$-0.908958\pi$
$311$	−12.7683	−	22.1153i	−0.724022	−	1.25404i	0.235354	−	0.971910i	$-0.424375\pi$
$312$		0			0
$313$	9.13328	−	15.8193i	0.516244	−	0.894160i	−0.483579	−	0.875301i	$-0.660663\pi$
$313$	9.13328	−	15.8193i	0.516244	−	0.894160i	0.999822	−	0.0188591i	$-0.00600341\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.22172	+	9.04428i	−0.293281	+	0.507977i	−0.974584	−	0.224024i	$-0.928080\pi$
$317$	−5.22172	+	9.04428i	−0.293281	+	0.507977i	0.681303	+	0.732002i	$0.261414\pi$
$318$		0			0
$319$	−3.50106	−	6.06402i	−0.196022	−	0.339520i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−3.05369			−0.169912
$324$		0			0
$325$	−10.5929			−0.587588
$326$		0			0
$327$		0			0
$328$		0			0
$329$	2.49663	+	4.32429i	0.137644	+	0.238406i
$330$		0			0
$331$	−2.37887	+	4.12032i	−0.130754	+	0.226473i	−0.923968	−	0.382471i	$-0.875073\pi$
$331$	−2.37887	+	4.12032i	−0.130754	+	0.226473i	0.793213	+	0.608944i	$0.208407\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.29380	−	2.24093i	0.0706878	−	0.122435i
$336$		0			0
$337$	13.7810	+	23.8694i	0.750700	+	1.30025i	0.947484	+	0.319804i	$0.103617\pi$
$337$	13.7810	+	23.8694i	0.750700	+	1.30025i	−0.196783	+	0.980447i	$0.563050\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−8.19818			−0.443956
$342$		0			0
$343$	−6.36385			−0.343616
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−10.5341	−	18.2457i	−0.565502	−	0.979478i	−0.997003	−	0.0773655i	$-0.975349\pi$
$347$	−10.5341	−	18.2457i	−0.565502	−	0.979478i	0.431501	−	0.902113i	$-0.357984\pi$
$348$		0			0
$349$	17.7897	−	30.8126i	0.952258	−	1.64936i	0.211738	−	0.977327i	$-0.432088\pi$
$349$	17.7897	−	30.8126i	0.952258	−	1.64936i	0.740521	−	0.672033i	$-0.234579\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−2.52544	+	4.37420i	−0.134416	+	0.232815i	−0.925374	−	0.379055i	$-0.876249\pi$
$353$	−2.52544	+	4.37420i	−0.134416	+	0.232815i	0.790958	+	0.611870i	$0.209582\pi$
$354$		0			0
$355$	−1.54015	−	2.66762i	−0.0817428	−	0.141583i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	18.1271			0.956709			0.478355	−	0.878167i	$-0.341233\pi$
$359$	18.1271			0.956709			0.478355	+	0.878167i	$0.341233\pi$
$360$		0			0
$361$	−10.3192			−0.543118
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.491530	−	0.851355i	−0.0257278	−	0.0445619i
$366$		0			0
$367$	−4.83039	+	8.36649i	−0.252145	+	0.436727i	−0.964116	−	0.265481i	$-0.914469\pi$
$367$	−4.83039	+	8.36649i	−0.252145	+	0.436727i	0.711972	+	0.702208i	$0.247803\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	2.31785	−	4.01464i	0.120337	−	0.208430i
$372$		0			0
$373$	16.0300	+	27.7647i	0.830001	+	1.43760i	0.898037	+	0.439921i	$0.144993\pi$
$373$	16.0300	+	27.7647i	0.830001	+	1.43760i	−0.0680357	+	0.997683i	$0.521673\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	10.0102			0.515551
$378$		0			0
$379$	−16.0684			−0.825377			−0.412689	−	0.910872i	$-0.635410\pi$
$379$	−16.0684			−0.825377			−0.412689	+	0.910872i	$0.635410\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	15.3129	+	26.5228i	0.782454	+	1.35525i	0.930509	+	0.366270i	$0.119365\pi$
$383$	15.3129	+	26.5228i	0.782454	+	1.35525i	−0.148055	+	0.988979i	$0.547301\pi$
$384$		0			0
$385$	−0.0801076	+	0.138750i	−0.00408266	+	0.00707138i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−7.37823	+	12.7795i	−0.374091	+	0.647945i	−0.990191	−	0.139723i	$-0.955379\pi$
$389$	−7.37823	+	12.7795i	−0.374091	+	0.647945i	0.616099	+	0.787669i	$0.288712\pi$
$390$		0			0
$391$	−0.378162	−	0.654997i	−0.0191245	−	0.0331246i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.88988			0.145405
$396$		0			0
$397$	−13.7032			−0.687746			−0.343873	−	0.939016i	$-0.611739\pi$
$397$	−13.7032			−0.687746			−0.343873	+	0.939016i	$0.611739\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.83939	−	6.65002i	−0.191730	−	0.332086i	0.754094	−	0.656767i	$-0.228076\pi$
$401$	−3.83939	−	6.65002i	−0.191730	−	0.332086i	−0.945824	+	0.324681i	$0.894743\pi$
$402$		0			0
$403$	5.86004	−	10.1499i	0.291909	−	0.505601i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.72303	−	2.98437i	0.0854072	−	0.147930i
$408$		0			0
$409$	−6.73882	−	11.6720i	−0.333213	−	0.577142i	0.649927	−	0.759997i	$-0.274800\pi$
$409$	−6.73882	−	11.6720i	−0.333213	−	0.577142i	−0.983140	+	0.182855i	$0.941466\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.50745			−0.123384
$414$		0			0
$415$	−1.68055			−0.0824948
$416$		0			0
$417$		0			0
$418$		0			0
$419$	18.0380	+	31.2427i	0.881213	+	1.52630i	0.849994	+	0.526792i	$0.176605\pi$
$419$	18.0380	+	31.2427i	0.881213	+	1.52630i	0.0312184	+	0.999513i	$0.490061\pi$
$420$		0			0
$421$	2.57726	−	4.46394i	0.125608	−	0.217559i	−0.796362	−	0.604820i	$-0.793245\pi$
$421$	2.57726	−	4.46394i	0.125608	−	0.217559i	0.921970	+	0.387260i	$0.126579\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.56329	+	4.43974i	−0.124338	+	0.215359i
$426$		0			0
$427$	3.16891	+	5.48871i	0.153354	+	0.265617i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−20.7200			−0.998045			−0.499022	−	0.866589i	$-0.666307\pi$
$431$	−20.7200			−0.998045			−0.499022	+	0.866589i	$0.666307\pi$
$432$		0			0
$433$	−23.3719			−1.12318			−0.561592	−	0.827414i	$-0.689811\pi$
$433$	−23.3719			−1.12318			−0.561592	+	0.827414i	$0.689811\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.07501	+	1.86197i	0.0514246	+	0.0890701i
$438$		0			0
$439$	−19.0107	+	32.9274i	−0.907330	+	1.57154i	−0.0895708	+	0.995980i	$0.528550\pi$
$439$	−19.0107	+	32.9274i	−0.907330	+	1.57154i	−0.817759	+	0.575561i	$0.804784\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−8.30811	+	14.3901i	−0.394730	+	0.683693i	−0.993067	−	0.117552i	$-0.962495\pi$
$443$	−8.30811	+	14.3901i	−0.394730	+	0.683693i	0.598336	+	0.801245i	$0.295829\pi$
$444$		0			0
$445$	−1.37432	−	2.38038i	−0.0651488	−	0.112841i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−12.9085			−0.609192			−0.304596	−	0.952482i	$-0.598521\pi$
$449$	−12.9085			−0.609192			−0.304596	+	0.952482i	$0.598521\pi$
$450$		0			0
$451$	−5.51728			−0.259798
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.114521	−	0.198357i	−0.00536884	−	0.00929911i
$456$		0			0
$457$	13.4943	−	23.3728i	0.631237	−	1.09333i	−0.356063	−	0.934462i	$-0.615881\pi$
$457$	13.4943	−	23.3728i	0.631237	−	1.09333i	0.987299	−	0.158872i	$-0.0507856\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	10.0800	−	17.4591i	0.469474	−	0.813152i	−0.529917	−	0.848049i	$-0.677777\pi$
$461$	10.0800	−	17.4591i	0.469474	−	0.813152i	0.999391	+	0.0348972i	$0.0111104\pi$
$462$		0			0
$463$	−17.2220	−	29.8293i	−0.800373	−	1.38629i	−0.919371	−	0.393391i	$-0.871302\pi$
$463$	−17.2220	−	29.8293i	−0.800373	−	1.38629i	0.118999	−	0.992894i	$-0.462032\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−31.6194			−1.46317			−0.731585	−	0.681750i	$-0.761219\pi$
$467$	−31.6194			−1.46317			−0.731585	+	0.681750i	$0.761219\pi$
$468$		0			0
$469$	−5.15487			−0.238030
$470$		0			0
$471$		0			0
$472$		0			0
$473$	3.62475	+	6.27825i	0.166666	+	0.288674i
$474$		0			0
$475$	7.28670	−	12.6209i	0.334337	−	0.579088i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	3.72976	−	6.46014i	0.170417	−	0.295171i	−0.768149	−	0.640272i	$-0.778822\pi$
$479$	3.72976	−	6.46014i	0.170417	−	0.295171i	0.938566	+	0.345100i	$0.112155\pi$
$480$		0			0
$481$	2.46323	+	4.26644i	0.112314	+	0.194533i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.02635			0.0466039
$486$		0			0
$487$	29.4254			1.33339			0.666697	−	0.745329i	$-0.267707\pi$
$487$	29.4254			1.33339			0.666697	+	0.745329i	$0.267707\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−14.4326	−	24.9979i	−0.651332	−	1.12814i	−0.982800	−	0.184674i	$-0.940877\pi$
$491$	−14.4326	−	24.9979i	−0.651332	−	1.12814i	0.331467	−	0.943467i	$-0.392456\pi$
$492$		0			0
$493$	2.42228	−	4.19552i	0.109094	−	0.188957i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−3.06821	+	5.31429i	−0.137628	+	0.238379i
$498$		0			0
$499$	−12.8470	−	22.2517i	−0.575111	−	0.996122i	−0.996030	−	0.0890236i	$-0.971625\pi$
$499$	−12.8470	−	22.2517i	−0.575111	−	0.996122i	0.420918	−	0.907099i	$-0.361708\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−20.7071			−0.923286			−0.461643	−	0.887066i	$-0.652740\pi$
$503$	−20.7071			−0.923286			−0.461643	+	0.887066i	$0.652740\pi$
$504$		0			0
$505$	3.46350			0.154124
$506$		0			0
$507$		0			0
$508$		0			0
$509$	10.7631	+	18.6421i	0.477064	+	0.826299i	0.999654	−	0.0262850i	$-0.00836772\pi$
$509$	10.7631	+	18.6421i	0.477064	+	0.826299i	−0.522591	+	0.852584i	$0.675034\pi$
$510$		0			0
$511$	−0.979199	+	1.69602i	−0.0433172	+	0.0750276i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.00719018	−	0.0124538i	0.000316837	−	0.000548778i
$516$		0			0
$517$	8.10255	+	14.0340i	0.356350	+	0.617216i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−22.2984			−0.976911			−0.488455	−	0.872589i	$-0.662440\pi$
$521$	−22.2984			−0.976911			−0.488455	+	0.872589i	$0.662440\pi$
$522$		0			0
$523$	4.92665			0.215427			0.107714	−	0.994182i	$-0.465647\pi$
$523$	4.92665			0.215427			0.107714	+	0.994182i	$0.465647\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.83604	−	4.91217i	−0.123540	−	0.213977i
$528$		0			0
$529$	11.2337	−	19.4574i	0.488424	−	0.845975i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	3.94373	−	6.83075i	0.170822	−	0.295873i
$534$		0			0
$535$	−1.38208	−	2.39383i	−0.0597523	−	0.103494i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−10.1670			−0.437925
$540$		0			0
$541$	22.0179			0.946622			0.473311	−	0.880895i	$-0.343059\pi$
$541$	22.0179			0.946622			0.473311	+	0.880895i	$0.343059\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.17390	+	2.03325i	0.0502842	+	0.0870948i
$546$		0			0
$547$	15.2563	−	26.4247i	0.652311	−	1.12984i	−0.330249	−	0.943894i	$-0.607133\pi$
$547$	15.2563	−	26.4247i	0.652311	−	1.12984i	0.982561	−	0.185943i	$-0.0595339\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−6.88587	+	11.9267i	−0.293348	+	0.508093i
$552$		0			0
$553$	−2.87853	−	4.98575i	−0.122407	−	0.212016i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	34.8358			1.47604			0.738021	−	0.674778i	$-0.235761\pi$
$557$	34.8358			1.47604			0.738021	+	0.674778i	$0.235761\pi$
$558$		0			0
$559$	−10.3639			−0.438344
$560$		0			0
$561$		0			0
$562$		0			0
$563$	6.86229	+	11.8858i	0.289211	+	0.500928i	0.973622	−	0.228169i	$-0.0732738\pi$
$563$	6.86229	+	11.8858i	0.289211	+	0.500928i	−0.684411	+	0.729097i	$0.739940\pi$
$564$		0			0
$565$	0.172219	−	0.298292i	0.00724529	−	0.0125492i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−14.6770	+	25.4213i	−0.615291	+	1.06572i	0.375042	+	0.927008i	$0.377628\pi$
$569$	−14.6770	+	25.4213i	−0.615291	+	1.06572i	−0.990333	+	0.138708i	$0.955705\pi$
$570$		0			0
$571$	1.60926	+	2.78732i	0.0673455	+	0.116646i	0.897732	−	0.440542i	$-0.145214\pi$
$571$	1.60926	+	2.78732i	0.0673455	+	0.116646i	−0.830387	+	0.557188i	$0.811880\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	3.60948			0.150526
$576$		0			0
$577$	0.782693			0.0325839			0.0162920	−	0.999867i	$-0.494814\pi$
$577$	0.782693			0.0325839			0.0162920	+	0.999867i	$0.494814\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.67395	+	2.89936i	0.0694470	+	0.120286i
$582$		0			0
$583$	7.52235	−	13.0291i	0.311544	−	0.539610i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−12.7201	+	22.0318i	−0.525014	+	0.909350i	0.474562	+	0.880222i	$0.342606\pi$
$587$	−12.7201	+	22.0318i	−0.525014	+	0.909350i	−0.999576	+	0.0291282i	$0.990727\pi$
$588$		0			0
$589$	8.06206	+	13.9639i	0.332192	+	0.575373i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−44.4583			−1.82569			−0.912843	−	0.408311i	$-0.866118\pi$
$593$	−44.4583			−1.82569			−0.912843	+	0.408311i	$0.866118\pi$
$594$		0			0
$595$	−0.110848			−0.00454434
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−23.7554	−	41.1455i	−0.970618	−	1.68116i	−0.693696	−	0.720268i	$-0.744019\pi$
$599$	−23.7554	−	41.1455i	−0.970618	−	1.68116i	−0.276922	−	0.960892i	$-0.589314\pi$
$600$		0			0
$601$	3.61527	−	6.26183i	0.147470	−	0.255425i	−0.782822	−	0.622246i	$-0.786220\pi$
$601$	3.61527	−	6.26183i	0.147470	−	0.255425i	0.930292	+	0.366821i	$0.119554\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.01438	−	1.75697i	0.0412406	−	0.0714308i
$606$		0			0
$607$	−7.00711	−	12.1367i	−0.284410	−	0.492612i	0.688056	−	0.725658i	$-0.258464\pi$
$607$	−7.00711	−	12.1367i	−0.284410	−	0.492612i	−0.972466	+	0.233045i	$0.925131\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−23.1667			−0.937225
$612$		0			0
$613$	12.2357			0.494194			0.247097	−	0.968991i	$-0.420523\pi$
$613$	12.2357			0.494194			0.247097	+	0.968991i	$0.420523\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.07716	−	1.86569i	−0.0433647	−	0.0751099i	0.843528	−	0.537085i	$-0.180474\pi$
$617$	−1.07716	−	1.86569i	−0.0433647	−	0.0751099i	−0.886893	+	0.461975i	$0.847141\pi$
$618$		0			0
$619$	5.94519	−	10.2974i	0.238957	−	0.413886i	−0.721458	−	0.692458i	$-0.756528\pi$
$619$	5.94519	−	10.2974i	0.238957	−	0.413886i	0.960415	+	0.278572i	$0.0898611\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−2.73784	+	4.74207i	−0.109689	+	0.189987i
$624$		0			0
$625$	−12.0988	−	20.9557i	−0.483952	−	0.838229i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	2.38422			0.0950652
$630$		0			0
$631$	−41.3492			−1.64609			−0.823043	−	0.567979i	$-0.807725\pi$
$631$	−41.3492			−1.64609			−0.823043	+	0.567979i	$0.807725\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.91923	−	3.32420i	−0.0761623	−	0.131917i
$636$		0			0
$637$	7.26736	−	12.5874i	0.287943	−	0.498733i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−12.6110	+	21.8429i	−0.498106	+	0.862744i	−0.999998	−	0.00218592i	$-0.999304\pi$
$641$	−12.6110	+	21.8429i	−0.498106	+	0.862744i	0.501892	+	0.864930i	$0.332638\pi$
$642$		0			0
$643$	−7.87820	−	13.6454i	−0.310686	−	0.538124i	0.667825	−	0.744318i	$-0.267225\pi$
$643$	−7.87820	−	13.6454i	−0.310686	−	0.538124i	−0.978511	+	0.206194i	$0.933892\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	21.8197			0.857823			0.428911	−	0.903347i	$-0.358897\pi$
$647$	21.8197			0.857823			0.428911	+	0.903347i	$0.358897\pi$
$648$		0			0
$649$	−8.13768			−0.319432
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−12.5168	−	21.6797i	−0.489819	−	0.848392i	0.510112	−	0.860108i	$-0.329604\pi$
$653$	−12.5168	−	21.6797i	−0.489819	−	0.848392i	−0.999931	+	0.0117162i	$0.996271\pi$
$654$		0			0
$655$	−0.331625	+	0.574392i	−0.0129577	+	0.0224433i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−14.5079	+	25.1285i	−0.565149	+	0.978867i	0.431887	+	0.901928i	$0.357848\pi$
$659$	−14.5079	+	25.1285i	−0.565149	+	0.978867i	−0.997036	+	0.0769388i	$0.975485\pi$
$660$		0			0
$661$	4.99232	+	8.64694i	0.194179	+	0.336327i	0.946631	−	0.322320i	$-0.104463\pi$
$661$	4.99232	+	8.64694i	0.194179	+	0.336327i	−0.752452	+	0.658647i	$0.771129\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.315110			0.0122195
$666$		0			0
$667$	−3.41093			−0.132072
$668$		0			0
$669$		0			0
$670$		0			0
$671$	10.2844	+	17.8130i	0.397023	+	0.687665i
$672$		0			0
$673$	2.42824	−	4.20584i	0.0936019	−	0.162123i	−0.815422	−	0.578866i	$-0.803495\pi$
$673$	2.42824	−	4.20584i	0.0936019	−	0.162123i	0.909024	+	0.416743i	$0.136829\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7.10559	+	12.3072i	−0.273090	+	0.473006i	−0.969651	−	0.244491i	$-0.921379\pi$
$677$	−7.10559	+	12.3072i	−0.273090	+	0.473006i	0.696562	+	0.717497i	$0.254712\pi$
$678$		0			0
$679$	−1.02231	−	1.77070i	−0.0392328	−	0.0679533i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−20.7153			−0.792648			−0.396324	−	0.918111i	$-0.629714\pi$
$683$	−20.7153			−0.792648			−0.396324	+	0.918111i	$0.629714\pi$
$684$		0			0
$685$	−3.83538			−0.146542
$686$		0			0
$687$		0			0
$688$		0			0
$689$	10.7539	+	18.6263i	0.409691	+	0.709606i
$690$		0			0
$691$	6.56378	−	11.3688i	0.249698	−	0.432489i	−0.713744	−	0.700407i	$-0.753002\pi$
$691$	6.56378	−	11.3688i	0.249698	−	0.432489i	0.963442	+	0.267917i	$0.0863353\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.853929	−	1.47905i	0.0323914	−	0.0561035i
$696$		0			0
$697$	−1.90862	−	3.30583i	−0.0722942	−	0.125217i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−13.3554			−0.504426			−0.252213	−	0.967672i	$-0.581158\pi$
$701$	−13.3554			−0.504426			−0.252213	+	0.967672i	$0.581158\pi$
$702$		0			0
$703$	−6.77767			−0.255625
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.44989	−	5.97539i	−0.129747	−	0.224728i
$708$		0			0
$709$	13.5083	−	23.3971i	0.507316	−	0.878697i	−0.492648	−	0.870229i	$-0.663971\pi$
$709$	13.5083	−	23.3971i	0.507316	−	0.878697i	0.999964	−	0.00846836i	$-0.00269560\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.99678	+	3.45852i	−0.0747800	+	0.129523i
$714$		0			0
$715$	−0.371667	−	0.643747i	−0.0138996	−	0.0240748i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−46.5794			−1.73712			−0.868559	−	0.495585i	$-0.834954\pi$
$719$	−46.5794			−1.73712			−0.868559	+	0.495585i	$0.834954\pi$
$720$		0			0
$721$	−0.0286478			−0.00106690
$722$		0			0
$723$		0			0
$724$		0			0
$725$	11.5601	+	20.0227i	0.429331	+	0.743623i
$726$		0			0
$727$	−12.5353	+	21.7119i	−0.464910	+	0.805248i	−0.999197	−	0.0400549i	$-0.987247\pi$
$727$	−12.5353	+	21.7119i	−0.464910	+	0.805248i	0.534287	+	0.845303i	$0.320580\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−2.50786	+	4.34374i	−0.0927566	+	0.160659i
$732$		0			0
$733$	11.8288	+	20.4881i	0.436907	+	0.756746i	0.997449	−	0.0713803i	$-0.0227404\pi$
$733$	11.8288	+	20.4881i	0.436907	+	0.756746i	−0.560542	+	0.828126i	$0.689407\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−16.7296			−0.616243
$738$		0			0
$739$	−32.9834			−1.21332			−0.606658	−	0.794963i	$-0.707490\pi$
$739$	−32.9834			−1.21332			−0.606658	+	0.794963i	$0.707490\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	5.16854	+	8.95218i	0.189615	+	0.328424i	0.945122	−	0.326717i	$-0.105943\pi$
$743$	5.16854	+	8.95218i	0.189615	+	0.328424i	−0.755507	+	0.655141i	$0.772609\pi$
$744$		0			0
$745$	−0.245726	+	0.425610i	−0.00900271	+	0.0155931i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−2.75330	+	4.76885i	−0.100603	+	0.174250i
$750$		0			0
$751$	−11.5268	−	19.9650i	−0.420620	−	0.728535i	0.575381	−	0.817886i	$-0.304854\pi$
$751$	−11.5268	−	19.9650i	−0.420620	−	0.728535i	−0.996000	+	0.0893513i	$0.971521\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	0.913821			0.0332573
$756$		0			0
$757$	4.86572			0.176848			0.0884239	−	0.996083i	$-0.471817\pi$
$757$	4.86572			0.176848			0.0884239	+	0.996083i	$0.471817\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−19.3733	−	33.5556i	−0.702283	−	1.21639i	−0.967663	−	0.252246i	$-0.918831\pi$
$761$	−19.3733	−	33.5556i	−0.702283	−	1.21639i	0.265380	−	0.964144i	$-0.414503\pi$
$762$		0			0
$763$	2.33857	−	4.05052i	0.0846620	−	0.146639i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	5.81679	−	10.0750i	0.210032	−	0.363786i
$768$		0			0
$769$	−14.0001	−	24.2489i	−0.504858	−	0.874439i	−0.999984	−	0.00561822i	$-0.998212\pi$
$769$	−14.0001	−	24.2489i	−0.504858	−	0.874439i	0.495127	−	0.868821i	$-0.335122\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	30.9662			1.11378			0.556888	−	0.830588i	$-0.311995\pi$
$773$	30.9662			1.11378			0.556888	+	0.830588i	$0.311995\pi$
$774$		0			0
$775$	27.0694			0.972362
$776$		0			0
$777$		0			0
$778$		0			0
$779$	5.42567	+	9.39754i	0.194395	+	0.336702i
$780$		0			0
$781$	−9.95755	+	17.2470i	−0.356309	+	0.617146i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.33703	+	2.31580i	−0.0477207	+	0.0826546i
$786$		0			0
$787$	8.48755	+	14.7009i	0.302549	+	0.524030i	0.976713	−	0.214552i	$-0.0688292\pi$
$787$	8.48755	+	14.7009i	0.302549	+	0.524030i	−0.674164	+	0.738582i	$0.735496\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−0.686169			−0.0243974
$792$		0			0
$793$	−29.4049			−1.04420
$794$		0			0
$795$		0			0
$796$		0			0
$797$	12.5688	+	21.7698i	0.445210	+	0.771127i	0.998067	−	0.0621496i	$-0.0197956\pi$
$797$	12.5688	+	21.7698i	0.445210	+	0.771127i	−0.552857	+	0.833276i	$0.686462\pi$
$798$		0			0
$799$	−5.60592	+	9.70974i	−0.198323	+	0.343506i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.17789	+	5.50427i	−0.112145	+	0.194241i
$804$		0			0
$805$	0.0390226	+	0.0675892i	0.00137537	+	0.00238221i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.441024			0.0155056			0.00775279	−	0.999970i	$-0.497532\pi$
$809$	0.441024			0.0155056			0.00775279	+	0.999970i	$0.497532\pi$
$810$		0			0
$811$	−44.8442			−1.57469			−0.787346	−	0.616511i	$-0.788545\pi$
$811$	−44.8442			−1.57469			−0.787346	+	0.616511i	$0.788545\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.0830133	+	0.143783i	0.00290783	+	0.00503651i
$816$		0			0
$817$	7.12914	−	12.3480i	0.249417	−	0.432003i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	13.3775	−	23.1705i	0.466878	−	0.808656i	−0.532406	−	0.846489i	$-0.678712\pi$
$821$	13.3775	−	23.1705i	0.466878	−	0.808656i	0.999284	+	0.0378328i	$0.0120454\pi$
$822$		0			0
$823$	−21.2608	−	36.8247i	−0.741104	−	1.28363i	−0.951993	−	0.306119i	$-0.900969\pi$
$823$	−21.2608	−	36.8247i	−0.741104	−	1.28363i	0.210889	−	0.977510i	$-0.432364\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	17.4800			0.607839			0.303919	−	0.952698i	$-0.401705\pi$
$827$	17.4800			0.607839			0.303919	+	0.952698i	$0.401705\pi$
$828$		0			0
$829$	10.7798			0.374399			0.187200	−	0.982322i	$-0.440059\pi$
$829$	10.7798			0.374399			0.187200	+	0.982322i	$0.440059\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−3.51714	−	6.09186i	−0.121862	−	0.211070i
$834$		0			0
$835$	1.01071	−	1.75060i	0.0349771	−	0.0605821i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−19.8649	+	34.4070i	−0.685811	+	1.18786i	0.287370	+	0.957820i	$0.407219\pi$
$839$	−19.8649	+	34.4070i	−0.685811	+	1.18786i	−0.973181	+	0.230040i	$0.926114\pi$
$840$		0			0
$841$	3.57581	+	6.19348i	0.123304	+	0.213568i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.94947			−0.0670638
$846$		0			0
$847$	−4.04160			−0.138871
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−0.839334	−	1.45377i	−0.0287720	−	0.0498345i
$852$		0			0
$853$	−2.26964	+	3.93113i	−0.0777110	+	0.134599i	−0.902262	−	0.431188i	$-0.858094\pi$
$853$	−2.26964	+	3.93113i	−0.0777110	+	0.134599i	0.824551	+	0.565788i	$0.191428\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.41586	−	2.45234i	0.0483648	−	0.0837702i	−0.840830	−	0.541300i	$-0.817932\pi$
$857$	1.41586	−	2.45234i	0.0483648	−	0.0837702i	0.889194	+	0.457530i	$0.151266\pi$
$858$		0			0
$859$	−11.6443	−	20.1684i	−0.397297	−	0.688138i	0.596095	−	0.802914i	$-0.296718\pi$
$859$	−11.6443	−	20.1684i	−0.397297	−	0.688138i	−0.993391	+	0.114776i	$0.963385\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.111891			0.00380882			0.00190441	−	0.999998i	$-0.499394\pi$
$863$	0.111891			0.00380882			0.00190441	+	0.999998i	$0.499394\pi$
$864$		0			0
$865$	−4.15586			−0.141304
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−9.34196	−	16.1808i	−0.316904	−	0.548894i
$870$		0			0
$871$	11.9583	−	20.7124i	0.405191	−	0.701811i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.531882	−	0.921248i	0.0179809	−	0.0311439i
$876$		0			0
$877$	13.1933	+	22.8515i	0.445506	+	0.771639i	0.998087	−	0.0618200i	$-0.0196905\pi$
$877$	13.1933	+	22.8515i	0.445506	+	0.771639i	−0.552581	+	0.833459i	$0.686357\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	46.5296			1.56762			0.783812	−	0.620999i	$-0.213273\pi$
$881$	46.5296			1.56762			0.783812	+	0.620999i	$0.213273\pi$
$882$		0			0
$883$	−26.7129			−0.898959			−0.449480	−	0.893291i	$-0.648391\pi$
$883$	−26.7129			−0.898959			−0.449480	+	0.893291i	$0.648391\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−20.6389	−	35.7476i	−0.692986	−	1.20029i	−0.970855	−	0.239668i	$-0.922961\pi$
$887$	−20.6389	−	35.7476i	−0.692986	−	1.20029i	0.277869	−	0.960619i	$-0.410372\pi$
$888$		0			0
$889$	−3.82338	+	6.62229i	−0.128232	+	0.222105i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	15.9360	−	27.6020i	0.533280	−	0.923667i
$894$		0			0
$895$	−0.772240	−	1.33756i	−0.0258131	−	0.0447097i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−25.5804			−0.853153
$900$		0			0
$901$	10.4090			0.346774
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.21415	+	3.83501i	0.0736007	+	0.127480i
$906$		0			0
$907$	9.75080	−	16.8889i	0.323770	−	0.560786i	−0.657493	−	0.753461i	$-0.728383\pi$
$907$	9.75080	−	16.8889i	0.323770	−	0.560786i	0.981263	+	0.192675i	$0.0617163\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	3.88772	−	6.73373i	0.128806	−	0.223098i	−0.794408	−	0.607384i	$-0.792219\pi$
$911$	3.88772	−	6.73373i	0.128806	−	0.223098i	0.923214	+	0.384286i	$0.125552\pi$
$912$		0			0
$913$	5.43262	+	9.40957i	0.179793	+	0.311411i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.32129			0.0436329
$918$		0			0
$919$	−44.9999			−1.48441			−0.742205	−	0.670172i	$-0.766220\pi$
$919$	−44.9999			−1.48441			−0.742205	+	0.670172i	$0.766220\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−14.2353	−	24.6562i	−0.468559	−	0.811569i
$924$		0			0
$925$	−5.68923	+	9.85403i	−0.187061	+	0.323999i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.77838	−	3.08024i	0.0583467	−	0.101059i	−0.835377	−	0.549678i	$-0.814750\pi$
$929$	1.77838	−	3.08024i	0.0583467	−	0.101059i	0.893723	+	0.448618i	$0.148084\pi$
$930$		0			0
$931$	9.99823	+	17.3174i	0.327679	+	0.567556i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.359747			−0.0117650
$936$		0			0
$937$	−24.3496			−0.795467			−0.397734	−	0.917501i	$-0.630203\pi$
$937$	−24.3496			−0.795467			−0.397734	+	0.917501i	$0.630203\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−8.01758	−	13.8869i	−0.261366	−	0.452699i	0.705239	−	0.708969i	$-0.250840\pi$
$941$	−8.01758	−	13.8869i	−0.261366	−	0.452699i	−0.966605	+	0.256271i	$0.917506\pi$
$942$		0			0
$943$	−1.34381	+	2.32755i	−0.0437604	+	0.0757953i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	24.6766	−	42.7412i	0.801882	−	1.38890i	−0.116493	−	0.993191i	$-0.537165\pi$
$947$	24.6766	−	42.7412i	0.801882	−	1.38890i	0.918376	−	0.395710i	$-0.129501\pi$
$948$		0			0
$949$	−4.54309	−	7.86887i	−0.147475	−	0.255434i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−43.4970			−1.40900			−0.704502	−	0.709702i	$-0.748830\pi$
$953$	−43.4970			−1.40900			−0.704502	+	0.709702i	$0.748830\pi$
$954$		0			0
$955$	−0.481699			−0.0155874
$956$		0			0
$957$		0			0
$958$		0			0
$959$	3.82031	+	6.61697i	0.123364	+	0.213673i
$960$		0			0
$961$	0.525082	−	0.909469i	0.0169381	−	0.0293377i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	2.36287	−	4.09261i	0.0760635	−	0.131746i
$966$		0			0
$967$	−3.36451	−	5.82750i	−0.108195	−	0.187400i	0.806844	−	0.590765i	$-0.201174\pi$
$967$	−3.36451	−	5.82750i	−0.108195	−	0.187400i	−0.915039	+	0.403365i	$0.867841\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	16.9519			0.544013			0.272007	−	0.962295i	$-0.412313\pi$
$971$	16.9519			0.544013			0.272007	+	0.962295i	$0.412313\pi$
$972$		0			0
$973$	−3.40230			−0.109073
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−19.4250	−	33.6451i	−0.621461	−	1.07640i	−0.989214	−	0.146479i	$-0.953206\pi$
$977$	−19.4250	−	33.6451i	−0.621461	−	1.07640i	0.367753	−	0.929924i	$-0.380127\pi$
$978$		0			0
$979$	−8.88536	+	15.3899i	−0.283977	+	0.491863i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−22.4036	+	38.8041i	−0.714563	+	1.23766i	0.248565	+	0.968615i	$0.420041\pi$
$983$	−22.4036	+	38.8041i	−0.714563	+	1.23766i	−0.963128	+	0.269044i	$0.913292\pi$
$984$		0			0
$985$	1.91685	+	3.32008i	0.0610759	+	0.105787i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	3.53144			0.112293
$990$		0			0
$991$	21.1824			0.672882			0.336441	−	0.941705i	$-0.390777\pi$
$991$	21.1824			0.672882			0.336441	+	0.941705i	$0.390777\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.46696	−	4.27291i	−0.0782080	−	0.135460i
$996$		0			0
$997$	−6.90517	+	11.9601i	−0.218689	+	0.378780i	−0.954407	−	0.298507i	$-0.903511\pi$
$997$	−6.90517	+	11.9601i	−0.218689	+	0.378780i	0.735719	+	0.677287i	$0.236845\pi$
$998$		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.1153.3		10
3.2	odd	2		1152.2.i.e.385.5	✓	10
4.3	odd	2		3456.2.i.h.1153.3		10
8.3	odd	2		3456.2.i.g.1153.3		10
8.5	even	2		3456.2.i.f.1153.3		10
9.4	even	3	inner	3456.2.i.e.2305.3		10
9.5	odd	6		1152.2.i.e.769.5	yes	10
12.11	even	2		1152.2.i.h.385.1	yes	10
24.5	odd	2		1152.2.i.g.385.1	yes	10
24.11	even	2		1152.2.i.f.385.5	yes	10
36.23	even	6		1152.2.i.h.769.1	yes	10
36.31	odd	6		3456.2.i.h.2305.3		10
72.5	odd	6		1152.2.i.g.769.1	yes	10
72.13	even	6		3456.2.i.f.2305.3		10
72.59	even	6		1152.2.i.f.769.5	yes	10
72.67	odd	6		3456.2.i.g.2305.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.i.e.385.5	✓	10	3.2	odd	2
1152.2.i.e.769.5	yes	10	9.5	odd	6
1152.2.i.f.385.5	yes	10	24.11	even	2
1152.2.i.f.769.5	yes	10	72.59	even	6
1152.2.i.g.385.1	yes	10	24.5	odd	2
1152.2.i.g.769.1	yes	10	72.5	odd	6
1152.2.i.h.385.1	yes	10	12.11	even	2
1152.2.i.h.769.1	yes	10	36.23	even	6
3456.2.i.e.1153.3		10	1.1	even	1	trivial
3456.2.i.e.2305.3		10	9.4	even	3	inner
3456.2.i.f.1153.3		10	8.5	even	2
3456.2.i.f.2305.3		10	72.13	even	6
3456.2.i.g.1153.3		10	8.3	odd	2
3456.2.i.g.2305.3		10	72.67	odd	6
3456.2.i.h.1153.3		10	4.3	odd	2
3456.2.i.h.2305.3		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)

\(f(q)\)	\(=\)	\(q+(-0.115851 - 0.200661i) q^{5} +(-0.230793 + 0.399745i) q^{7} +O(q^{10})\)	\(q+(-0.115851 - 0.200661i) q^{5} +(-0.230793 + 0.399745i) q^{7} +(-0.749014 + 1.29733i) q^{11} +(-1.07079 - 1.85466i) q^{13} -1.03644 q^{17} +2.94631 q^{19} +(0.364866 + 0.631966i) q^{23} +(2.47316 - 4.28363i) q^{25} +(-2.33711 + 4.04800i) q^{29} +(2.73632 + 4.73945i) q^{31} +0.106951 q^{35} -2.30039 q^{37} +(1.84151 + 3.18959i) q^{41} +(2.41968 - 4.19101i) q^{43} +(5.40881 - 9.36833i) q^{47} +(3.39347 + 5.87766i) q^{49} -10.0430 q^{53} +0.347097 q^{55} +(2.71613 + 4.70447i) q^{59} +(6.86526 - 11.8910i) q^{61} +(-0.248104 + 0.429729i) q^{65} +(5.58388 + 9.67156i) q^{67} +13.2942 q^{71} +4.24276 q^{73} +(-0.345734 - 0.598829i) q^{77} +(-6.23617 + 10.8014i) q^{79} +(3.62651 - 6.28130i) q^{83} +(0.120073 + 0.207973i) q^{85} +11.8627 q^{89} +0.988520 q^{91} +(-0.341335 - 0.591209i) q^{95} +(-2.21479 + 3.83613i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{7}+O(q^{10}) \) 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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