LMFDB - Embedded newform 1152.2.w.b.719.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(143,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1, 4]))

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

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

chi := DirichletCharacter("1152.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.w (of order $8$, degree $4$, 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:	$9.19876631285$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			719.6
Character	$\chi$	$=$	1152.719
Dual form			1152.2.w.b.431.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.65625 + 0.686041i) q^{5} +(0.456585 - 0.456585i) q^{7} +O(q^{10})$	$q+(1.65625 + 0.686041i) q^{5} +(0.456585 - 0.456585i) q^{7} +(-2.79166 - 1.15634i) q^{11} +(-1.29543 - 3.12746i) q^{13} +3.55642 q^{17} +(5.61657 - 2.32646i) q^{19} +(4.10130 - 4.10130i) q^{23} +(-1.26302 - 1.26302i) q^{25} +(1.87699 + 4.53146i) q^{29} -0.580857i q^{31} +(1.06946 - 0.442983i) q^{35} +(2.58037 - 6.22957i) q^{37} +(2.98306 + 2.98306i) q^{41} +(2.78658 - 6.72741i) q^{43} +8.67935i q^{47} +6.58306i q^{49} +(-3.70833 + 8.95270i) q^{53} +(-3.83039 - 3.83039i) q^{55} +(1.77297 - 4.28032i) q^{59} +(-9.49421 + 3.93263i) q^{61} -6.06857i q^{65} +(-3.50440 - 8.46037i) q^{67} +(7.84134 + 7.84134i) q^{71} +(10.7396 - 10.7396i) q^{73} +(-1.80260 + 0.746662i) q^{77} +5.27177 q^{79} +(1.80609 + 4.36028i) q^{83} +(5.89033 + 2.43985i) q^{85} +(12.4990 - 12.4990i) q^{89} +(-2.01943 - 0.836474i) q^{91} +10.8985 q^{95} +9.99452 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 8 q^{11} - 16 q^{29} - 24 q^{35} - 16 q^{53} + 32 q^{55} - 32 q^{59} + 32 q^{61} + 16 q^{67} - 16 q^{71} - 16 q^{77} + 32 q^{79} + 40 q^{83} + 48 q^{91} + 80 q^{95}+O(q^{100}) $ 32 * q + 8 * q^11 - 16 * q^29 - 24 * q^35 - 16 * q^53 + 32 * q^55 - 32 * q^59 + 32 * q^61 + 16 * q^67 - 16 * q^71 - 16 * q^77 + 32 * q^79 + 40 * q^83 + 48 * q^91 + 80 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{8}\right)$

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
$5$	1.65625	+	0.686041i	0.740698	+	0.306807i	0.720940	−	0.692998i	$-0.243710\pi$
$5$	1.65625	+	0.686041i	0.740698	+	0.306807i	0.0197579	+	0.999805i	$0.493710\pi$
$6$		0			0
$7$	0.456585	−	0.456585i	0.172573	−	0.172573i	−0.615536	−	0.788109i	$-0.711060\pi$
$7$	0.456585	−	0.456585i	0.172573	−	0.172573i	0.788109	+	0.615536i	$0.211060\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.79166	−	1.15634i	−0.841718	−	0.348651i	−0.0801871	−	0.996780i	$-0.525552\pi$
$11$	−2.79166	−	1.15634i	−0.841718	−	0.348651i	−0.761531	+	0.648129i	$0.775552\pi$
$12$		0			0
$13$	−1.29543	−	3.12746i	−0.359289	−	0.867400i	−0.995400	−	0.0958031i	$-0.969458\pi$
$13$	−1.29543	−	3.12746i	−0.359289	−	0.867400i	0.636111	−	0.771597i	$-0.280542\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.55642			0.862560			0.431280	−	0.902218i	$-0.358062\pi$
$17$	3.55642			0.862560			0.431280	+	0.902218i	$0.358062\pi$
$18$		0			0
$19$	5.61657	−	2.32646i	1.28853	−	0.533726i	0.369982	−	0.929039i	$-0.379364\pi$
$19$	5.61657	−	2.32646i	1.28853	−	0.533726i	0.918547	+	0.395313i	$0.129364\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.10130	−	4.10130i	0.855180	−	0.855180i	−0.135586	−	0.990766i	$-0.543292\pi$
$23$	4.10130	−	4.10130i	0.855180	−	0.855180i	0.990766	+	0.135586i	$0.0432917\pi$
$24$		0			0
$25$	−1.26302	−	1.26302i	−0.252604	−	0.252604i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.87699	+	4.53146i	0.348548	+	0.841470i	0.996792	+	0.0800372i	$0.0255039\pi$
$29$	1.87699	+	4.53146i	0.348548	+	0.841470i	−0.648243	+	0.761433i	$0.724496\pi$
$30$		0			0
$31$		−	0.580857i		−	0.104325i	−0.998639	−	0.0521625i	$-0.983389\pi$
$31$		−	0.580857i		−	0.104325i	0.998639	−	0.0521625i	$-0.0166114\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.06946	−	0.442983i	0.180771	−	0.0748778i
$36$		0			0
$37$	2.58037	−	6.22957i	0.424210	−	1.02413i	−0.556881	−	0.830592i	$-0.688002\pi$
$37$	2.58037	−	6.22957i	0.424210	−	1.02413i	0.981092	−	0.193543i	$-0.0619978\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.98306	+	2.98306i	0.465876	+	0.465876i	0.900576	−	0.434699i	$-0.143145\pi$
$41$	2.98306	+	2.98306i	0.465876	+	0.465876i	−0.434699	+	0.900576i	$0.643145\pi$
$42$		0			0
$43$	2.78658	−	6.72741i	0.424950	−	1.02592i	−0.555917	−	0.831238i	$-0.687633\pi$
$43$	2.78658	−	6.72741i	0.424950	−	1.02592i	0.980866	−	0.194682i	$-0.0623674\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			8.67935i			1.26601i	0.774147	+	0.633006i	$0.218179\pi$
$47$			8.67935i			1.26601i	−0.774147	+	0.633006i	$0.781821\pi$
$48$		0			0
$49$			6.58306i			0.940437i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.70833	+	8.95270i	−0.509378	+	1.22975i	0.434864	+	0.900496i	$0.356797\pi$
$53$	−3.70833	+	8.95270i	−0.509378	+	1.22975i	−0.944242	+	0.329252i	$0.893203\pi$
$54$		0			0
$55$	−3.83039	−	3.83039i	−0.516490	−	0.516490i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.77297	−	4.28032i	0.230820	−	0.557250i	−0.765454	−	0.643491i	$-0.777485\pi$
$59$	1.77297	−	4.28032i	0.230820	−	0.557250i	0.996274	+	0.0862410i	$0.0274855\pi$
$60$		0			0
$61$	−9.49421	+	3.93263i	−1.21561	+	0.503522i	−0.896011	−	0.444031i	$-0.853548\pi$
$61$	−9.49421	+	3.93263i	−1.21561	+	0.503522i	−0.319598	+	0.947553i	$0.603548\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	6.06857i		−	0.752714i
$66$		0			0
$67$	−3.50440	−	8.46037i	−0.428131	−	1.03360i	−0.979880	−	0.199589i	$-0.936039\pi$
$67$	−3.50440	−	8.46037i	−0.428131	−	1.03360i	0.551749	−	0.834010i	$-0.313961\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	7.84134	+	7.84134i	0.930596	+	0.930596i	0.997743	−	0.0671471i	$-0.0213897\pi$
$71$	7.84134	+	7.84134i	0.930596	+	0.930596i	−0.0671471	+	0.997743i	$0.521390\pi$
$72$		0			0
$73$	10.7396	−	10.7396i	1.25698	−	1.25698i	0.304453	−	0.952527i	$-0.401526\pi$
$73$	10.7396	−	10.7396i	1.25698	−	1.25698i	0.952527	−	0.304453i	$-0.0984738\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.80260	+	0.746662i	−0.205425	+	0.0850900i
$78$		0			0
$79$	5.27177			0.593121			0.296560	−	0.955014i	$-0.404160\pi$
$79$	5.27177			0.593121			0.296560	+	0.955014i	$0.404160\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.80609	+	4.36028i	0.198244	+	0.478603i	0.991472	−	0.130322i	$-0.0416011\pi$
$83$	1.80609	+	4.36028i	0.198244	+	0.478603i	−0.793228	+	0.608925i	$0.791601\pi$
$84$		0			0
$85$	5.89033	+	2.43985i	0.638896	+	0.264639i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	12.4990	−	12.4990i	1.32489	−	1.32489i	0.415125	−	0.909764i	$-0.363738\pi$
$89$	12.4990	−	12.4990i	1.32489	−	1.32489i	0.909764	−	0.415125i	$-0.136262\pi$
$90$		0			0
$91$	−2.01943	−	0.836474i	−0.211693	−	0.0876863i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	10.8985			1.11816
$96$		0			0
$97$	9.99452			1.01479			0.507395	−	0.861714i	$-0.330608\pi$
$97$	9.99452			1.01479			0.507395	+	0.861714i	$0.330608\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.85763	−	1.59788i	−0.383849	−	0.158995i	0.182411	−	0.983222i	$-0.441610\pi$
$101$	−3.85763	−	1.59788i	−0.383849	−	0.158995i	−0.566259	+	0.824227i	$0.691610\pi$
$102$		0			0
$103$	−1.59155	+	1.59155i	−0.156820	+	0.156820i	−0.781156	−	0.624336i	$-0.785370\pi$
$103$	−1.59155	+	1.59155i	−0.156820	+	0.156820i	0.624336	+	0.781156i	$0.285370\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−16.1209	−	6.67752i	−1.55847	−	0.645540i	−0.573648	−	0.819102i	$-0.694472\pi$
$107$	−16.1209	−	6.67752i	−1.55847	−	0.645540i	−0.984823	+	0.173562i	$0.944472\pi$
$108$		0			0
$109$	−4.94159	−	11.9301i	−0.473318	−	1.14269i	−0.962688	−	0.270615i	$-0.912773\pi$
$109$	−4.94159	−	11.9301i	−0.473318	−	1.14269i	0.489369	−	0.872077i	$-0.337227\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−5.30221			−0.498790			−0.249395	−	0.968402i	$-0.580232\pi$
$113$	−5.30221			−0.498790			−0.249395	+	0.968402i	$0.580232\pi$
$114$		0			0
$115$	9.60644	−	3.97912i	0.895805	−	0.371054i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.62381	−	1.62381i	0.148855	−	0.148855i
$120$		0			0
$121$	−1.32193	−	1.32193i	−0.120176	−	0.120176i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−4.65560	−	11.2396i	−0.416410	−	1.00530i
$126$		0			0
$127$			22.3469i			1.98297i	0.130223	+	0.991485i	$0.458431\pi$
$127$			22.3469i			1.98297i	−0.130223	+	0.991485i	$0.541569\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1.42416	−	0.589906i	0.124429	−	0.0515403i	−0.319600	−	0.947553i	$-0.603549\pi$
$131$	1.42416	−	0.589906i	0.124429	−	0.0515403i	0.444029	+	0.896012i	$0.353549\pi$
$132$		0			0
$133$	1.50221	−	3.62667i	0.130259	−	0.314472i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.460816	−	0.460816i	−0.0393702	−	0.0393702i	0.687148	−	0.726518i	$-0.258863\pi$
$137$	−0.460816	−	0.460816i	−0.0393702	−	0.0393702i	−0.726518	+	0.687148i	$0.758863\pi$
$138$		0			0
$139$	−8.10753	+	19.5733i	−0.687672	+	1.66019i	0.0617480	+	0.998092i	$0.480333\pi$
$139$	−8.10753	+	19.5733i	−0.687672	+	1.66019i	−0.749420	+	0.662095i	$0.769667\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			10.2288i			0.855373i
$144$		0			0
$145$			8.79292i			0.730212i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−4.69000	+	11.3227i	−0.384220	+	0.927589i	0.606919	+	0.794764i	$0.292405\pi$
$149$	−4.69000	+	11.3227i	−0.384220	+	0.927589i	−0.991139	+	0.132826i	$0.957595\pi$
$150$		0			0
$151$	−7.98867	−	7.98867i	−0.650109	−	0.650109i	0.302910	−	0.953019i	$-0.402042\pi$
$151$	−7.98867	−	7.98867i	−0.650109	−	0.650109i	−0.953019	+	0.302910i	$0.902042\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.398492	−	0.962044i	0.0320076	−	0.0772732i
$156$		0			0
$157$	−3.47084	+	1.43767i	−0.277003	+	0.114739i	−0.516860	−	0.856070i	$-0.672899\pi$
$157$	−3.47084	+	1.43767i	−0.277003	+	0.114739i	0.239857	+	0.970808i	$0.422899\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	3.74518i		−	0.295162i
$162$		0			0
$163$	−0.897968	−	2.16789i	−0.0703343	−	0.169802i	0.884803	−	0.465965i	$-0.154293\pi$
$163$	−0.897968	−	2.16789i	−0.0703343	−	0.169802i	−0.955137	+	0.296163i	$0.904293\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.17718	+	4.17718i	0.323240	+	0.323240i	0.850009	−	0.526769i	$-0.176597\pi$
$167$	4.17718	+	4.17718i	0.323240	+	0.323240i	−0.526769	+	0.850009i	$0.676597\pi$
$168$		0			0
$169$	1.08956	−	1.08956i	0.0838119	−	0.0838119i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−5.46721	+	2.26459i	−0.415664	+	0.172174i	−0.580707	−	0.814113i	$-0.697224\pi$
$173$	−5.46721	+	2.26459i	−0.415664	+	0.172174i	0.165043	+	0.986286i	$0.447224\pi$
$174$		0			0
$175$	−1.15335			−0.0871854
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−2.19833	−	5.30724i	−0.164311	−	0.396681i	0.820183	−	0.572101i	$-0.193872\pi$
$179$	−2.19833	−	5.30724i	−0.164311	−	0.396681i	−0.984494	+	0.175420i	$0.943872\pi$
$180$		0			0
$181$	0.557980	+	0.231123i	0.0414743	+	0.0171792i	0.403324	−	0.915057i	$-0.367855\pi$
$181$	0.557980	+	0.231123i	0.0414743	+	0.0171792i	−0.361850	+	0.932236i	$0.617855\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	8.54748	−	8.54748i	0.628423	−	0.628423i
$186$		0			0
$187$	−9.92834	−	4.11245i	−0.726032	−	0.300732i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−23.5071			−1.70091			−0.850457	−	0.526044i	$-0.823675\pi$
$191$	−23.5071			−1.70091			−0.850457	+	0.526044i	$0.823675\pi$
$192$		0			0
$193$	−9.17175			−0.660197			−0.330098	−	0.943946i	$-0.607082\pi$
$193$	−9.17175			−0.660197			−0.330098	+	0.943946i	$0.607082\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	8.13281	+	3.36872i	0.579439	+	0.240011i	0.653100	−	0.757272i	$-0.273468\pi$
$197$	8.13281	+	3.36872i	0.579439	+	0.240011i	−0.0736610	+	0.997283i	$0.523468\pi$
$198$		0			0
$199$	−13.2257	+	13.2257i	−0.937548	+	0.937548i	−0.998161	−	0.0606129i	$-0.980694\pi$
$199$	−13.2257	+	13.2257i	−0.937548	+	0.937548i	0.0606129	+	0.998161i	$0.480694\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2.92600	+	1.21199i	0.205365	+	0.0850650i
$204$		0			0
$205$	2.89419	+	6.98720i	0.202139	+	0.488008i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−18.3697			−1.27066
$210$		0			0
$211$	19.9447	−	8.26135i	1.37305	−	0.568735i	0.430434	−	0.902622i	$-0.358360\pi$
$211$	19.9447	−	8.26135i	1.37305	−	0.568735i	0.942613	+	0.333887i	$0.108360\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	9.23056	−	9.23056i	0.629519	−	0.629519i
$216$		0			0
$217$	−0.265211	−	0.265211i	−0.0180037	−	0.0180037i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−4.60712	−	11.1226i	−0.309908	−	0.748185i
$222$		0			0
$223$			13.8784i			0.929363i	0.885478	+	0.464682i	$0.153831\pi$
$223$			13.8784i			0.929363i	−0.885478	+	0.464682i	$0.846169\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−17.3888	+	7.20270i	−1.15414	+	0.478060i	−0.875919	−	0.482458i	$-0.839744\pi$
$227$	−17.3888	+	7.20270i	−1.15414	+	0.478060i	−0.278219	+	0.960518i	$0.589744\pi$
$228$		0			0
$229$	−3.50393	+	8.45924i	−0.231546	+	0.559002i	−0.996360	−	0.0852496i	$-0.972831\pi$
$229$	−3.50393	+	8.45924i	−0.231546	+	0.559002i	0.764813	+	0.644252i	$0.222831\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	5.85253	+	5.85253i	0.383412	+	0.383412i	0.872330	−	0.488918i	$-0.162608\pi$
$233$	5.85253	+	5.85253i	0.383412	+	0.383412i	−0.488918	+	0.872330i	$0.662608\pi$
$234$		0			0
$235$	−5.95439	+	14.3752i	−0.388422	+	0.937733i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	7.83888i		−	0.507055i	−0.967328	−	0.253527i	$-0.918409\pi$
$239$		−	7.83888i		−	0.507055i	0.967328	−	0.253527i	$-0.0815908\pi$
$240$		0			0
$241$			29.7873i			1.91877i	0.282104	+	0.959384i	$0.408968\pi$
$241$			29.7873i			1.91877i	−0.282104	+	0.959384i	$0.591032\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−4.51625	+	10.9032i	−0.288533	+	0.696580i
$246$		0			0
$247$	−14.5518	−	14.5518i	−0.925908	−	0.925908i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−0.558412	+	1.34813i	−0.0352466	+	0.0850929i	−0.940523	−	0.339731i	$-0.889664\pi$
$251$	−0.558412	+	1.34813i	−0.0352466	+	0.0850929i	0.905276	+	0.424824i	$0.139664\pi$
$252$		0			0
$253$	−16.1919	+	6.70692i	−1.01798	+	0.421661i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	4.05507i		−	0.252948i	−0.991970	−	0.126474i	$-0.959634\pi$
$257$		−	4.05507i		−	0.252948i	0.991970	−	0.126474i	$-0.0403661\pi$
$258$		0			0
$259$	−1.66617	−	4.02249i	−0.103531	−	0.249945i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−8.79592	−	8.79592i	−0.542380	−	0.542380i	0.381846	−	0.924226i	$-0.375288\pi$
$263$	−8.79592	−	8.79592i	−0.542380	−	0.542380i	−0.924226	+	0.381846i	$0.875288\pi$
$264$		0			0
$265$	−12.2838	+	12.2838i	−0.754591	+	0.754591i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.15796	−	0.479643i	0.0706021	−	0.0292443i	−0.347103	−	0.937827i	$-0.612835\pi$
$269$	1.15796	−	0.479643i	0.0706021	−	0.0292443i	0.417705	+	0.908583i	$0.362835\pi$
$270$		0			0
$271$	25.5808			1.55392			0.776961	−	0.629549i	$-0.216760\pi$
$271$	25.5808			1.55392			0.776961	+	0.629549i	$0.216760\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.06544	+	4.98642i	0.124551	+	0.300692i
$276$		0			0
$277$	7.32573	+	3.03442i	0.440161	+	0.182320i	0.591747	−	0.806123i	$-0.298438\pi$
$277$	7.32573	+	3.03442i	0.440161	+	0.182320i	−0.151587	+	0.988444i	$0.548438\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−15.2794	+	15.2794i	−0.911490	+	0.911490i	−0.996390	−	0.0848997i	$-0.972943\pi$
$281$	−15.2794	+	15.2794i	−0.911490	+	0.911490i	0.0848997	+	0.996390i	$0.472943\pi$
$282$		0			0
$283$	10.6335	+	4.40456i	0.632098	+	0.261824i	0.675644	−	0.737228i	$-0.263866\pi$
$283$	10.6335	+	4.40456i	0.632098	+	0.261824i	−0.0435461	+	0.999051i	$0.513866\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.72405			0.160795
$288$		0			0
$289$	−4.35184			−0.255991
$290$		0			0
$291$		0			0
$292$		0			0
$293$	8.77403	+	3.63432i	0.512584	+	0.212319i	0.623956	−	0.781460i	$-0.285524\pi$
$293$	8.77403	+	3.63432i	0.512584	+	0.212319i	−0.111372	+	0.993779i	$0.535524\pi$
$294$		0			0
$295$	5.87295	−	5.87295i	0.341936	−	0.341936i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−18.1396	−	7.51367i	−1.04904	−	0.434527i
$300$		0			0
$301$	−1.79932	−	4.34395i	−0.103711	−	0.250381i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−18.4227			−1.05488
$306$		0			0
$307$	−10.2808	+	4.25844i	−0.586755	+	0.243042i	−0.656254	−	0.754540i	$-0.727860\pi$
$307$	−10.2808	+	4.25844i	−0.586755	+	0.243042i	0.0694988	+	0.997582i	$0.477860\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1.40680	−	1.40680i	0.0797723	−	0.0797723i	−0.666095	−	0.745867i	$-0.732035\pi$
$311$	1.40680	−	1.40680i	0.0797723	−	0.0797723i	0.745867	+	0.666095i	$0.232035\pi$
$312$		0			0
$313$	−6.25438	−	6.25438i	−0.353518	−	0.353518i	0.507899	−	0.861417i	$-0.330422\pi$
$313$	−6.25438	−	6.25438i	−0.353518	−	0.353518i	−0.861417	+	0.507899i	$0.830422\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.54838	−	6.15234i	−0.143131	−	0.345550i	0.836015	−	0.548707i	$-0.184880\pi$
$317$	−2.54838	−	6.15234i	−0.143131	−	0.345550i	−0.979146	+	0.203157i	$0.934880\pi$
$318$		0			0
$319$		−	14.8207i		−	0.829802i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	19.9749	−	8.27387i	1.11143	−	0.460371i
$324$		0			0
$325$	−2.31388	+	5.58621i	−0.128351	+	0.309867i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	3.96286	+	3.96286i	0.218480	+	0.218480i
$330$		0			0
$331$	−2.67191	+	6.45057i	−0.146862	+	0.354555i	−0.980142	−	0.198295i	$-0.936460\pi$
$331$	−2.67191	+	6.45057i	−0.146862	+	0.354555i	0.833281	+	0.552850i	$0.186460\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		−	16.4167i		−	0.896938i
$336$		0			0
$337$			5.72840i			0.312046i	0.987753	+	0.156023i	$0.0498674\pi$
$337$			5.72840i			0.312046i	−0.987753	+	0.156023i	$0.950133\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.671670	+	1.62156i	−0.0363730	+	0.0878122i
$342$		0			0
$343$	6.20182	+	6.20182i	0.334867	+	0.334867i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	8.72462	−	21.0631i	0.468362	−	1.13073i	−0.496515	−	0.868028i	$-0.665387\pi$
$347$	8.72462	−	21.0631i	0.468362	−	1.13073i	0.964878	−	0.262699i	$-0.0846126\pi$
$348$		0			0
$349$	−23.6969	+	9.81557i	−1.26847	+	0.525415i	−0.912497	−	0.409083i	$-0.865849\pi$
$349$	−23.6969	+	9.81557i	−1.26847	+	0.525415i	−0.355968	+	0.934498i	$0.615849\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			19.1720i			1.02042i	0.860049	+	0.510211i	$0.170433\pi$
$353$			19.1720i			1.02042i	−0.860049	+	0.510211i	$0.829567\pi$
$354$		0			0
$355$	7.60774	+	18.3667i	0.403777	+	0.974804i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−19.4520	−	19.4520i	−1.02664	−	1.02664i	−0.999635	−	0.0270016i	$-0.991404\pi$
$359$	−19.4520	−	19.4520i	−1.02664	−	1.02664i	−0.0270016	−	0.999635i	$-0.508596\pi$
$360$		0			0
$361$	12.6984	−	12.6984i	0.668336	−	0.668336i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	25.1554	−	10.4197i	1.31669	−	0.545392i
$366$		0			0
$367$	−19.4899			−1.01737			−0.508683	−	0.860954i	$-0.669867\pi$
$367$	−19.4899			−1.01737			−0.508683	+	0.860954i	$0.669867\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	2.39450	+	5.78084i	0.124316	+	0.300126i
$372$		0			0
$373$	32.4958	+	13.4602i	1.68257	+	0.696943i	0.999443	−	0.0333572i	$-0.0106199\pi$
$373$	32.4958	+	13.4602i	1.68257	+	0.696943i	0.683126	+	0.730300i	$0.260620\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	11.7404	−	11.7404i	0.604662	−	0.604662i
$378$		0			0
$379$	−11.4703	−	4.75115i	−0.589189	−	0.244050i	0.0681125	−	0.997678i	$-0.478302\pi$
$379$	−11.4703	−	4.75115i	−0.589189	−	0.244050i	−0.657302	+	0.753627i	$0.728302\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−21.4414			−1.09560			−0.547801	−	0.836609i	$-0.684535\pi$
$383$	−21.4414			−1.09560			−0.547801	+	0.836609i	$0.684535\pi$
$384$		0			0
$385$	−3.49780			−0.178264
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−22.8503	−	9.46489i	−1.15855	−	0.479889i	−0.281161	−	0.959661i	$-0.590719\pi$
$389$	−22.8503	−	9.46489i	−1.15855	−	0.479889i	−0.877393	+	0.479772i	$0.840719\pi$
$390$		0			0
$391$	14.5860	−	14.5860i	0.737644	−	0.737644i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	8.73137	+	3.61665i	0.439323	+	0.181974i
$396$		0			0
$397$	2.00126	+	4.83148i	0.100441	+	0.242485i	0.966110	−	0.258131i	$-0.0831067\pi$
$397$	2.00126	+	4.83148i	0.100441	+	0.242485i	−0.865669	+	0.500616i	$0.833107\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	16.4805			0.822996			0.411498	−	0.911411i	$-0.365006\pi$
$401$	16.4805			0.822996			0.411498	+	0.911411i	$0.365006\pi$
$402$		0			0
$403$	−1.81660	+	0.752462i	−0.0904915	+	0.0374828i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−14.4070	+	14.4070i	−0.714131	+	0.714131i
$408$		0			0
$409$	−14.4679	−	14.4679i	−0.715393	−	0.715393i	0.252265	−	0.967658i	$-0.418824\pi$
$409$	−14.4679	−	14.4679i	−0.715393	−	0.715393i	−0.967658	+	0.252265i	$0.918824\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−1.14482	−	2.76384i	−0.0563329	−	0.136000i
$414$		0			0
$415$			8.46076i			0.415323i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	13.2299	−	5.48000i	0.646322	−	0.267715i	−0.0353481	−	0.999375i	$-0.511254\pi$
$419$	13.2299	−	5.48000i	0.646322	−	0.267715i	0.681670	+	0.731660i	$0.261254\pi$
$420$		0			0
$421$	3.58725	−	8.66038i	0.174832	−	0.422081i	−0.812037	−	0.583606i	$-0.801641\pi$
$421$	3.58725	−	8.66038i	0.174832	−	0.422081i	0.986869	+	0.161525i	$0.0516412\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−4.49184	−	4.49184i	−0.217886	−	0.217886i
$426$		0			0
$427$	−2.53933	+	6.13050i	−0.122887	+	0.296676i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			29.9638i			1.44330i	0.692256	+	0.721652i	$0.256617\pi$
$431$			29.9638i			1.44330i	−0.692256	+	0.721652i	$0.743383\pi$
$432$		0			0
$433$		−	30.4045i		−	1.46115i	−0.682834	−	0.730574i	$-0.739253\pi$
$433$		−	30.4045i		−	1.46115i	0.682834	−	0.730574i	$-0.260747\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	13.4937	−	32.5767i	0.645492	−	1.55836i
$438$		0			0
$439$	10.1550	+	10.1550i	0.484670	+	0.484670i	0.906619	−	0.421949i	$-0.138654\pi$
$439$	10.1550	+	10.1550i	0.484670	+	0.484670i	−0.421949	+	0.906619i	$0.638654\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−12.0051	+	28.9828i	−0.570379	+	1.37702i	0.330854	+	0.943682i	$0.392663\pi$
$443$	−12.0051	+	28.9828i	−0.570379	+	1.37702i	−0.901233	+	0.433335i	$0.857337\pi$
$444$		0			0
$445$	29.2763	−	12.1266i	1.38783	−	0.574857i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			22.5653i			1.06492i	0.846454	+	0.532462i	$0.178733\pi$
$449$			22.5653i			1.06492i	−0.846454	+	0.532462i	$0.821267\pi$
$450$		0			0
$451$	−4.87826	−	11.7772i	−0.229708	−	0.554564i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.77082	−	2.77082i	−0.129898	−	0.129898i
$456$		0			0
$457$	9.14050	−	9.14050i	0.427575	−	0.427575i	−0.460227	−	0.887801i	$-0.652232\pi$
$457$	9.14050	−	9.14050i	0.427575	−	0.427575i	0.887801	+	0.460227i	$0.152232\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2.78980	−	1.15557i	0.129934	−	0.0538203i	−0.316769	−	0.948503i	$-0.602598\pi$
$461$	2.78980	−	1.15557i	0.129934	−	0.0538203i	0.446703	+	0.894682i	$0.352598\pi$
$462$		0			0
$463$	33.4593			1.55499			0.777494	−	0.628891i	$-0.216491\pi$
$463$	33.4593			1.55499			0.777494	+	0.628891i	$0.216491\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	14.0784	+	33.9882i	0.651470	+	1.57279i	0.810645	+	0.585538i	$0.199117\pi$
$467$	14.0784	+	33.9882i	0.651470	+	1.57279i	−0.159175	+	0.987250i	$0.550883\pi$
$468$		0			0
$469$	−5.46294	−	2.26282i	−0.252255	−	0.104487i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−15.5584	+	15.5584i	−0.715376	+	0.715376i
$474$		0			0
$475$	−10.0322	−	4.15548i	−0.460309	−	0.190666i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	2.68362			0.122618			0.0613088	−	0.998119i	$-0.480473\pi$
$479$	2.68362			0.122618			0.0613088	+	0.998119i	$0.480473\pi$
$480$		0			0
$481$	−22.8254			−1.04075
$482$		0			0
$483$		0			0
$484$		0			0
$485$	16.5534	+	6.85666i	0.751653	+	0.311345i
$486$		0			0
$487$	−2.23834	+	2.23834i	−0.101429	+	0.101429i	−0.756000	−	0.654571i	$-0.772849\pi$
$487$	−2.23834	+	2.23834i	−0.101429	+	0.101429i	0.654571	+	0.756000i	$0.272849\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	12.4388	+	5.15233i	0.561356	+	0.232521i	0.645274	−	0.763951i	$-0.276743\pi$
$491$	12.4388	+	5.15233i	0.561356	+	0.232521i	−0.0839179	+	0.996473i	$0.526743\pi$
$492$		0			0
$493$	6.67538	+	16.1158i	0.300644	+	0.725818i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	7.16048			0.321191
$498$		0			0
$499$	−24.8865	+	10.3083i	−1.11407	+	0.461464i	−0.862338	−	0.506333i	$-0.831001\pi$
$499$	−24.8865	+	10.3083i	−1.11407	+	0.461464i	−0.251734	+	0.967796i	$0.581001\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	22.4779	−	22.4779i	1.00224	−	1.00224i	0.00224387	−	0.999997i	$-0.499286\pi$
$503$	22.4779	−	22.4779i	1.00224	−	1.00224i	0.999997	−	0.00224387i	$-0.000714246\pi$
$504$		0			0
$505$	−5.29299	−	5.29299i	−0.235535	−	0.235535i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	5.50936	+	13.3008i	0.244198	+	0.589546i	0.997692	−	0.0679092i	$-0.0216328\pi$
$509$	5.50936	+	13.3008i	0.244198	+	0.589546i	−0.753493	+	0.657455i	$0.771633\pi$
$510$		0			0
$511$		−	9.80713i		−	0.433842i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−3.72787	+	1.54413i	−0.164269	+	0.0680426i
$516$		0			0
$517$	10.0363	−	24.2298i	0.441396	−	1.06563i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	5.57998	+	5.57998i	0.244463	+	0.244463i	0.818694	−	0.574230i	$-0.194699\pi$
$521$	5.57998	+	5.57998i	0.244463	+	0.244463i	−0.574230	+	0.818694i	$0.694699\pi$
$522$		0			0
$523$	3.24273	−	7.82865i	0.141795	−	0.342323i	−0.836989	−	0.547220i	$-0.815686\pi$
$523$	3.24273	−	7.82865i	0.141795	−	0.342323i	0.978783	+	0.204897i	$0.0656860\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	2.06577i		−	0.0899865i
$528$		0			0
$529$		−	10.6413i		−	0.462665i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	5.46504	−	13.1938i	0.236717	−	0.571485i
$534$		0			0
$535$	−22.1193	−	22.1193i	−0.956300	−	0.956300i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	7.61228	−	18.3777i	0.327884	−	0.791583i
$540$		0			0
$541$	10.7796	−	4.46504i	0.463450	−	0.191967i	−0.138726	−	0.990331i	$-0.544301\pi$
$541$	10.7796	−	4.46504i	0.463450	−	0.191967i	0.602176	+	0.798364i	$0.294301\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		−	23.1493i		−	0.991607i
$546$		0			0
$547$	2.24172	+	5.41200i	0.0958492	+	0.231400i	0.964531	−	0.263970i	$-0.0850321\pi$
$547$	2.24172	+	5.41200i	0.0958492	+	0.231400i	−0.868682	+	0.495371i	$0.835032\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	21.0845	+	21.0845i	0.898229	+	0.898229i
$552$		0			0
$553$	2.40701	−	2.40701i	0.102357	−	0.102357i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−9.25052	+	3.83169i	−0.391957	+	0.162354i	−0.569953	−	0.821677i	$-0.693039\pi$
$557$	−9.25052	+	3.83169i	−0.391957	+	0.162354i	0.177996	+	0.984031i	$0.443039\pi$
$558$		0			0
$559$	−24.6495			−1.04256
$560$		0			0
$561$		0			0
$562$		0			0
$563$	7.82586	+	18.8933i	0.329820	+	0.796257i	0.998605	+	0.0528009i	$0.0168149\pi$
$563$	7.82586	+	18.8933i	0.329820	+	0.796257i	−0.668785	+	0.743456i	$0.733185\pi$
$564$		0			0
$565$	−8.78179	−	3.63754i	−0.369453	−	0.153032i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−31.2631	+	31.2631i	−1.31062	+	1.31062i	−0.389659	+	0.920959i	$0.627407\pi$
$569$	−31.2631	+	31.2631i	−1.31062	+	1.31062i	−0.920959	+	0.389659i	$0.872593\pi$
$570$		0			0
$571$	−0.191448	−	0.0793005i	−0.00801186	−	0.00331862i	0.378674	−	0.925530i	$-0.376380\pi$
$571$	−0.191448	−	0.0793005i	−0.00801186	−	0.00331862i	−0.386686	+	0.922212i	$0.626380\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−10.3601			−0.432044
$576$		0			0
$577$	38.6731			1.60998			0.804991	−	0.593287i	$-0.202170\pi$
$577$	38.6731			1.60998			0.804991	+	0.593287i	$0.202170\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	2.81547	+	1.16621i	0.116805	+	0.0483824i
$582$		0			0
$583$	20.7048	−	20.7048i	0.857506	−	0.857506i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	43.3422	+	17.9529i	1.78892	+	0.740997i	0.990262	+	0.139217i	$0.0444587\pi$
$587$	43.3422	+	17.9529i	1.78892	+	0.740997i	0.798662	+	0.601779i	$0.205541\pi$
$588$		0			0
$589$	−1.35134	−	3.26242i	−0.0556809	−	0.134426i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−17.0532			−0.700290			−0.350145	−	0.936695i	$-0.613868\pi$
$593$	−17.0532			−0.700290			−0.350145	+	0.936695i	$0.613868\pi$
$594$		0			0
$595$	3.80344	−	1.57544i	0.155926	−	0.0645866i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	1.20304	−	1.20304i	0.0491549	−	0.0491549i	−0.682102	−	0.731257i	$-0.738934\pi$
$599$	1.20304	−	1.20304i	0.0491549	−	0.0491549i	0.731257	+	0.682102i	$0.238934\pi$
$600$		0			0
$601$	−7.21057	−	7.21057i	−0.294125	−	0.294125i	0.544582	−	0.838707i	$-0.316688\pi$
$601$	−7.21057	−	7.21057i	−0.294125	−	0.294125i	−0.838707	+	0.544582i	$0.816688\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.28255	−	3.09635i	−0.0521431	−	0.125884i
$606$		0			0
$607$		−	39.4020i		−	1.59928i	−0.600480	−	0.799640i	$-0.705024\pi$
$607$		−	39.4020i		−	1.59928i	0.600480	−	0.799640i	$-0.294976\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	27.1443	−	11.2435i	1.09814	−	0.454864i
$612$		0			0
$613$	−4.28364	+	10.3416i	−0.173015	+	0.417694i	−0.986472	−	0.163930i	$-0.947583\pi$
$613$	−4.28364	+	10.3416i	−0.173015	+	0.417694i	0.813457	+	0.581625i	$0.197583\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−3.31416	−	3.31416i	−0.133423	−	0.133423i	0.637241	−	0.770664i	$-0.280075\pi$
$617$	−3.31416	−	3.31416i	−0.133423	−	0.133423i	−0.770664	+	0.637241i	$0.780075\pi$
$618$		0			0
$619$	9.98010	−	24.0941i	0.401134	−	0.968423i	−0.586257	−	0.810125i	$-0.699399\pi$
$619$	9.98010	−	24.0941i	0.401134	−	0.968423i	0.987391	−	0.158298i	$-0.0506008\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		−	11.4137i		−	0.457280i
$624$		0			0
$625$		−	12.8786i		−	0.515146i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	9.17690	−	22.1550i	0.365907	−	0.883377i
$630$		0			0
$631$	13.8296	+	13.8296i	0.550550	+	0.550550i	0.926599	−	0.376050i	$-0.122718\pi$
$631$	13.8296	+	13.8296i	0.550550	+	0.550550i	−0.376050	+	0.926599i	$0.622718\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−15.3309	+	37.0121i	−0.608389	+	1.46878i
$636$		0			0
$637$	20.5882	−	8.52793i	0.815736	−	0.337889i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	4.78350i		−	0.188937i	−0.995528	−	0.0944684i	$-0.969885\pi$
$641$		−	4.78350i		−	0.188937i	0.995528	−	0.0944684i	$-0.0301151\pi$
$642$		0			0
$643$	4.20578	+	10.1536i	0.165860	+	0.400421i	0.984855	−	0.173379i	$-0.0554687\pi$
$643$	4.20578	+	10.1536i	0.165860	+	0.400421i	−0.818995	+	0.573800i	$0.805469\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−11.3311	−	11.3311i	−0.445473	−	0.445473i	0.448373	−	0.893846i	$-0.352003\pi$
$647$	−11.3311	−	11.3311i	−0.445473	−	0.445473i	−0.893846	+	0.448373i	$0.852003\pi$
$648$		0			0
$649$	−9.89904	+	9.89904i	−0.388571	+	0.388571i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	27.7945	−	11.5129i	1.08768	−	0.450533i	0.234485	−	0.972120i	$-0.424660\pi$
$653$	27.7945	−	11.5129i	1.08768	−	0.450533i	0.853198	+	0.521587i	$0.174660\pi$
$654$		0			0
$655$	2.76346			0.107977
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−7.68871	−	18.5622i	−0.299510	−	0.723080i	−0.999956	−	0.00937514i	$-0.997016\pi$
$659$	−7.68871	−	18.5622i	−0.299510	−	0.723080i	0.700446	−	0.713705i	$-0.252984\pi$
$660$		0			0
$661$	7.39058	+	3.06128i	0.287460	+	0.119070i	0.521754	−	0.853096i	$-0.325278\pi$
$661$	7.39058	+	3.06128i	0.287460	+	0.119070i	−0.234294	+	0.972166i	$0.575278\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	4.97609	−	4.97609i	0.192964	−	0.192964i
$666$		0			0
$667$	26.2830	+	10.8868i	1.01768	+	0.421537i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	31.0521			1.19875
$672$		0			0
$673$	13.4300			0.517690			0.258845	−	0.965919i	$-0.416658\pi$
$673$	13.4300			0.517690			0.258845	+	0.965919i	$0.416658\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−12.8609	−	5.32714i	−0.494283	−	0.204739i	0.121596	−	0.992580i	$-0.461199\pi$
$677$	−12.8609	−	5.32714i	−0.494283	−	0.204739i	−0.615879	+	0.787841i	$0.711199\pi$
$678$		0			0
$679$	4.56335	−	4.56335i	0.175125	−	0.175125i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.117538	−	0.0486859i	−0.00449748	−	0.00186292i	0.380434	−	0.924808i	$-0.375775\pi$
$683$	−0.117538	−	0.0486859i	−0.00449748	−	0.00186292i	−0.384931	+	0.922945i	$0.625775\pi$
$684$		0			0
$685$	−0.447088	−	1.07937i	−0.0170824	−	0.0412405i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	32.8031			1.24970
$690$		0			0
$691$	9.94322	−	4.11862i	0.378258	−	0.156680i	−0.185450	−	0.982654i	$-0.559374\pi$
$691$	9.94322	−	4.11862i	0.378258	−	0.156680i	0.563708	+	0.825974i	$0.309374\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−26.8562	+	26.8562i	−1.01871	+	1.01871i
$696$		0			0
$697$	10.6090	+	10.6090i	0.401846	+	0.401846i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−4.26297	−	10.2917i	−0.161010	−	0.388713i	0.822700	−	0.568476i	$-0.192467\pi$
$701$	−4.26297	−	10.2917i	−0.161010	−	0.388713i	−0.983710	+	0.179763i	$0.942467\pi$
$702$		0			0
$703$		−	40.9919i		−	1.54604i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.49091	+	1.03177i	−0.0936803	+	0.0388036i
$708$		0			0
$709$	−4.70620	+	11.3618i	−0.176745	+	0.426700i	−0.987280	−	0.158990i	$-0.949176\pi$
$709$	−4.70620	+	11.3618i	−0.176745	+	0.426700i	0.810535	+	0.585690i	$0.199176\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−2.38227	−	2.38227i	−0.0892166	−	0.0892166i
$714$		0			0
$715$	−7.01736	+	16.9414i	−0.262434	+	0.633573i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	31.7208i		−	1.18299i	−0.806310	−	0.591493i	$-0.798539\pi$
$719$		−	31.7208i		−	1.18299i	0.806310	−	0.591493i	$-0.201461\pi$
$720$		0			0
$721$			1.45335i			0.0541257i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	3.35265	−	8.09401i	0.124514	−	0.300604i
$726$		0			0
$727$	19.1550	+	19.1550i	0.710421	+	0.710421i	0.966623	−	0.256202i	$-0.0824714\pi$
$727$	19.1550	+	19.1550i	0.710421	+	0.710421i	−0.256202	+	0.966623i	$0.582471\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	9.91027	−	23.9255i	0.366545	−	0.884917i
$732$		0			0
$733$	40.7560	−	16.8817i	1.50536	−	0.623539i	0.530763	−	0.847520i	$-0.321905\pi$
$733$	40.7560	−	16.8817i	1.50536	−	0.623539i	0.974593	+	0.223981i	$0.0719054\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			27.6708i			1.01927i
$738$		0			0
$739$	−8.11044	−	19.5803i	−0.298348	−	0.720275i	−0.999970	−	0.00772594i	$-0.997541\pi$
$739$	−8.11044	−	19.5803i	−0.298348	−	0.720275i	0.701623	−	0.712549i	$-0.252459\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.927600	+	0.927600i	0.0340303	+	0.0340303i	0.723917	−	0.689887i	$-0.242340\pi$
$743$	0.927600	+	0.927600i	0.0340303	+	0.0340303i	−0.689887	+	0.723917i	$0.742340\pi$
$744$		0			0
$745$	−15.5356	+	15.5356i	−0.569182	+	0.569182i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−10.4094	+	4.31173i	−0.380353	+	0.157547i
$750$		0			0
$751$	−31.0488			−1.13299			−0.566493	−	0.824066i	$-0.691700\pi$
$751$	−31.0488			−1.13299			−0.566493	+	0.824066i	$0.691700\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−7.75068	−	18.7118i	−0.282076	−	0.680992i
$756$		0			0
$757$	−23.3806	−	9.68456i	−0.849782	−	0.351991i	−0.0850792	−	0.996374i	$-0.527114\pi$
$757$	−23.3806	−	9.68456i	−0.849782	−	0.351991i	−0.764703	+	0.644383i	$0.777114\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	7.78273	−	7.78273i	0.282124	−	0.282124i	−0.551832	−	0.833956i	$-0.686071\pi$
$761$	7.78273	−	7.78273i	0.282124	−	0.282124i	0.833956	+	0.551832i	$0.186071\pi$
$762$		0			0
$763$	−7.70334	−	3.19083i	−0.278880	−	0.115516i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−15.6833			−0.566290
$768$		0			0
$769$	−50.8529			−1.83380			−0.916902	−	0.399113i	$-0.869318\pi$
$769$	−50.8529			−1.83380			−0.916902	+	0.399113i	$0.869318\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	37.9455	+	15.7175i	1.36480	+	0.565320i	0.940374	−	0.340141i	$-0.110475\pi$
$773$	37.9455	+	15.7175i	1.36480	+	0.565320i	0.424429	+	0.905461i	$0.360475\pi$
$774$		0			0
$775$	−0.733635	+	0.733635i	−0.0263529	+	0.0263529i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	23.6945	+	9.81460i	0.848945	+	0.351645i
$780$		0			0
$781$	−12.8231	−	30.9577i	−0.458846	−	1.10775i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−6.73488			−0.240378
$786$		0			0
$787$	−21.7835	+	9.02304i	−0.776499	+	0.321637i	−0.735502	−	0.677523i	$-0.763054\pi$
$787$	−21.7835	+	9.02304i	−0.776499	+	0.321637i	−0.0409975	+	0.999159i	$0.513054\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−2.42091	+	2.42091i	−0.0860777	+	0.0860777i
$792$		0			0
$793$	24.5983	+	24.5983i	0.873510	+	0.873510i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	11.4401	+	27.6189i	0.405231	+	0.978313i	0.986375	+	0.164513i	$0.0526052\pi$
$797$	11.4401	+	27.6189i	0.405231	+	0.978313i	−0.581144	+	0.813800i	$0.697395\pi$
$798$		0			0
$799$			30.8674i			1.09201i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−42.4002	+	17.5627i	−1.49627	+	0.619775i
$804$		0			0
$805$	2.56935	−	6.20296i	0.0905577	−	0.218626i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−5.79612	−	5.79612i	−0.203781	−	0.203781i	0.597837	−	0.801618i	$-0.296027\pi$
$809$	−5.79612	−	5.79612i	−0.203781	−	0.203781i	−0.801618	+	0.597837i	$0.796027\pi$
$810$		0			0
$811$	19.2750	−	46.5341i	0.676838	−	1.63403i	−0.0929028	−	0.995675i	$-0.529615\pi$
$811$	19.2750	−	46.5341i	0.676838	−	1.63403i	0.769741	−	0.638356i	$-0.220385\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		−	4.20661i		−	0.147351i
$816$		0			0
$817$		−	44.2678i		−	1.54873i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−16.7271	+	40.3828i	−0.583779	+	1.40937i	0.305583	+	0.952165i	$0.401149\pi$
$821$	−16.7271	+	40.3828i	−0.583779	+	1.40937i	−0.889363	+	0.457202i	$0.848851\pi$
$822$		0			0
$823$	8.13069	+	8.13069i	0.283418	+	0.283418i	0.834471	−	0.551053i	$-0.185774\pi$
$823$	8.13069	+	8.13069i	0.283418	+	0.283418i	−0.551053	+	0.834471i	$0.685774\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−15.6826	+	37.8612i	−0.545339	+	1.31656i	0.375573	+	0.926793i	$0.377446\pi$
$827$	−15.6826	+	37.8612i	−0.545339	+	1.31656i	−0.920912	+	0.389771i	$0.872554\pi$
$828$		0			0
$829$	−15.7729	+	6.53333i	−0.547814	+	0.226912i	−0.639385	−	0.768886i	$-0.720811\pi$
$829$	−15.7729	+	6.53333i	−0.547814	+	0.226912i	0.0915711	+	0.995799i	$0.470811\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$			23.4122i			0.811183i
$834$		0			0
$835$	4.05274	+	9.78417i	0.140251	+	0.338595i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−8.63280	−	8.63280i	−0.298037	−	0.298037i	0.542207	−	0.840245i	$-0.317589\pi$
$839$	−8.63280	−	8.63280i	−0.298037	−	0.298037i	−0.840245	+	0.542207i	$0.817589\pi$
$840$		0			0
$841$	3.49509	−	3.49509i	0.120520	−	0.120520i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	2.55206	−	1.05710i	0.0877934	−	0.0363652i
$846$		0			0
$847$	−1.20715			−0.0414781
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−14.9664	−	36.1322i	−0.513043	−	1.23860i
$852$		0			0
$853$	−20.9586	−	8.68133i	−0.717608	−	0.297243i	−0.00615957	−	0.999981i	$-0.501961\pi$
$853$	−20.9586	−	8.68133i	−0.717608	−	0.297243i	−0.711449	+	0.702738i	$0.751961\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	19.1816	−	19.1816i	0.655232	−	0.655232i	−0.299016	−	0.954248i	$-0.596658\pi$
$857$	19.1816	−	19.1816i	0.655232	−	0.655232i	0.954248	+	0.299016i	$0.0966584\pi$
$858$		0			0
$859$	43.8743	+	18.1733i	1.49697	+	0.620066i	0.972821	−	0.231559i	$-0.0743827\pi$
$859$	43.8743	+	18.1733i	1.49697	+	0.620066i	0.524151	+	0.851625i	$0.324383\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	41.7776			1.42212			0.711062	−	0.703129i	$-0.248214\pi$
$863$	41.7776			1.42212			0.711062	+	0.703129i	$0.248214\pi$
$864$		0			0
$865$	−10.6087			−0.360706
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−14.7170	−	6.09598i	−0.499240	−	0.206792i
$870$		0			0
$871$	−21.9197	+	21.9197i	−0.742722	+	0.742722i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−7.25752	−	3.00616i	−0.245349	−	0.101627i
$876$		0			0
$877$	20.1913	+	48.7461i	0.681811	+	1.64604i	0.760660	+	0.649151i	$0.224876\pi$
$877$	20.1913	+	48.7461i	0.681811	+	1.64604i	−0.0788487	+	0.996887i	$0.525124\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.703923			0.0237158			0.0118579	−	0.999930i	$-0.496225\pi$
$881$	0.703923			0.0237158			0.0118579	+	0.999930i	$0.496225\pi$
$882$		0			0
$883$	−0.756687	+	0.313430i	−0.0254645	+	0.0105478i	−0.395379	−	0.918518i	$-0.629387\pi$
$883$	−0.756687	+	0.313430i	−0.0254645	+	0.0105478i	0.369915	+	0.929066i	$0.379387\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−20.2480	+	20.2480i	−0.679862	+	0.679862i	−0.959969	−	0.280106i	$-0.909630\pi$
$887$	−20.2480	+	20.2480i	−0.679862	+	0.679862i	0.280106	+	0.959969i	$0.409630\pi$
$888$		0			0
$889$	10.2033	+	10.2033i	0.342207	+	0.342207i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	20.1921	+	48.7481i	0.675704	+	1.63129i
$894$		0			0
$895$		−	10.2983i		−	0.344233i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	2.63213	−	1.09026i	0.0877864	−	0.0363623i
$900$		0			0
$901$	−13.1884	+	31.8396i	−0.439369	+	1.06073i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.765595	+	0.765595i	0.0254492	+	0.0254492i
$906$		0			0
$907$	2.52443	−	6.09451i	0.0838223	−	0.202365i	−0.876411	−	0.481564i	$-0.840069\pi$
$907$	2.52443	−	6.09451i	0.0838223	−	0.202365i	0.960233	+	0.279199i	$0.0900689\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	44.3943i		−	1.47085i	−0.677608	−	0.735424i	$-0.736983\pi$
$911$		−	44.3943i		−	1.47085i	0.677608	−	0.735424i	$-0.263017\pi$
$912$		0			0
$913$		−	14.2609i		−	0.471966i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.380907	−	0.919592i	0.0125787	−	0.0303676i
$918$		0			0
$919$	13.6702	+	13.6702i	0.450938	+	0.450938i	0.895666	−	0.444728i	$-0.146700\pi$
$919$	13.6702	+	13.6702i	0.450938	+	0.450938i	−0.444728	+	0.895666i	$0.646700\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	14.3655	−	34.6814i	0.472846	−	1.14155i
$924$		0			0
$925$	−11.1271	+	4.60901i	−0.365858	+	0.151543i
$926$		0			0
$927$		0			0
$928$		0			0
$929$		−	29.8610i		−	0.979709i	−0.871804	−	0.489855i	$-0.837050\pi$
$929$		−	29.8610i		−	0.979709i	0.871804	−	0.489855i	$-0.162950\pi$
$930$		0			0
$931$	15.3152	+	36.9742i	0.501936	+	1.21178i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−13.6225	−	13.6225i	−0.445503	−	0.445503i
$936$		0			0
$937$	−25.0276	+	25.0276i	−0.817617	+	0.817617i	−0.985762	−	0.168145i	$-0.946222\pi$
$937$	−25.0276	+	25.0276i	−0.817617	+	0.817617i	0.168145	+	0.985762i	$0.446222\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−39.6214	+	16.4117i	−1.29162	+	0.535007i	−0.919468	−	0.393165i	$-0.871380\pi$
$941$	−39.6214	+	16.4117i	−1.29162	+	0.535007i	−0.372152	+	0.928172i	$0.621380\pi$
$942$		0			0
$943$	24.4689			0.796816
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−17.0273	−	41.1075i	−0.553312	−	1.33581i	−0.914977	−	0.403505i	$-0.867792\pi$
$947$	−17.0273	−	41.1075i	−0.553312	−	1.33581i	0.361665	−	0.932308i	$-0.382208\pi$
$948$		0			0
$949$	−47.5003	−	19.6753i	−1.54192	−	0.638686i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−12.7204	+	12.7204i	−0.412054	+	0.412054i	−0.882454	−	0.470400i	$-0.844110\pi$
$953$	−12.7204	+	12.7204i	−0.412054	+	0.412054i	0.470400	+	0.882454i	$0.344110\pi$
$954$		0			0
$955$	−38.9337	−	16.1268i	−1.25986	−	0.521853i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−0.420804			−0.0135885
$960$		0			0
$961$	30.6626			0.989116
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−15.1907	−	6.29220i	−0.489006	−	0.202553i
$966$		0			0
$967$	−13.4994	+	13.4994i	−0.434112	+	0.434112i	−0.890025	−	0.455913i	$-0.849313\pi$
$967$	−13.4994	+	13.4994i	−0.434112	+	0.434112i	0.455913	+	0.890025i	$0.349313\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−28.1525	−	11.6611i	−0.903457	−	0.374224i	−0.117909	−	0.993024i	$-0.537619\pi$
$971$	−28.1525	−	11.6611i	−0.903457	−	0.374224i	−0.785548	+	0.618800i	$0.787619\pi$
$972$		0			0
$973$	5.23511	+	12.6387i	0.167830	+	0.405177i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	30.5548			0.977534			0.488767	−	0.872414i	$-0.337447\pi$
$977$	30.5548			0.977534			0.488767	+	0.872414i	$0.337447\pi$
$978$		0			0
$979$	−49.3461	+	20.4398i	−1.57711	+	0.653259i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−30.3548	+	30.3548i	−0.968168	+	0.968168i	−0.999509	−	0.0313409i	$-0.990022\pi$
$983$	−30.3548	+	30.3548i	−0.968168	+	0.968168i	0.0313409	+	0.999509i	$0.490022\pi$
$984$		0			0
$985$	11.1589	+	11.1589i	0.355552	+	0.355552i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−16.1625	−	39.0197i	−0.513937	−	1.24075i
$990$		0			0
$991$			45.5684i			1.44753i	0.690048	+	0.723764i	$0.257589\pi$
$991$			45.5684i			1.44753i	−0.690048	+	0.723764i	$0.742411\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−30.9786	+	12.8317i	−0.982086	+	0.406793i
$996$		0			0
$997$	−4.87805	+	11.7767i	−0.154490	+	0.372971i	−0.982108	−	0.188321i	$-0.939695\pi$
$997$	−4.87805	+	11.7767i	−0.154490	+	0.372971i	0.827618	+	0.561292i	$0.189695\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.w.b.719.6		32
3.2	odd	2		1152.2.w.a.719.3		32
4.3	odd	2		288.2.w.a.107.7	yes	32
12.11	even	2		288.2.w.b.107.2	yes	32
32.3	odd	8		1152.2.w.a.431.3		32
32.29	even	8		288.2.w.b.35.2	yes	32
96.29	odd	8		288.2.w.a.35.7	✓	32
96.35	even	8	inner	1152.2.w.b.431.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.35.7	✓	32	96.29	odd	8
288.2.w.a.107.7	yes	32	4.3	odd	2
288.2.w.b.35.2	yes	32	32.29	even	8
288.2.w.b.107.2	yes	32	12.11	even	2
1152.2.w.a.431.3		32	32.3	odd	8
1152.2.w.a.719.3		32	3.2	odd	2
1152.2.w.b.431.6		32	96.35	even	8	inner
1152.2.w.b.719.6		32	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.w (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.65625 + 0.686041i) q^{5} +(0.456585 - 0.456585i) q^{7} +O(q^{10})\)	\(q+(1.65625 + 0.686041i) q^{5} +(0.456585 - 0.456585i) q^{7} +(-2.79166 - 1.15634i) q^{11} +(-1.29543 - 3.12746i) q^{13} +3.55642 q^{17} +(5.61657 - 2.32646i) q^{19} +(4.10130 - 4.10130i) q^{23} +(-1.26302 - 1.26302i) q^{25} +(1.87699 + 4.53146i) q^{29} -0.580857i q^{31} +(1.06946 - 0.442983i) q^{35} +(2.58037 - 6.22957i) q^{37} +(2.98306 + 2.98306i) q^{41} +(2.78658 - 6.72741i) q^{43} +8.67935i q^{47} +6.58306i q^{49} +(-3.70833 + 8.95270i) q^{53} +(-3.83039 - 3.83039i) q^{55} +(1.77297 - 4.28032i) q^{59} +(-9.49421 + 3.93263i) q^{61} -6.06857i q^{65} +(-3.50440 - 8.46037i) q^{67} +(7.84134 + 7.84134i) q^{71} +(10.7396 - 10.7396i) q^{73} +(-1.80260 + 0.746662i) q^{77} +5.27177 q^{79} +(1.80609 + 4.36028i) q^{83} +(5.89033 + 2.43985i) q^{85} +(12.4990 - 12.4990i) q^{89} +(-2.01943 - 0.836474i) q^{91} +10.8985 q^{95} +9.99452 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 8 q^{11} - 16 q^{29} - 24 q^{35} - 16 q^{53} + 32 q^{55} - 32 q^{59} + 32 q^{61} + 16 q^{67} - 16 q^{71} - 16 q^{77} + 32 q^{79} + 40 q^{83} + 48 q^{91} + 80 q^{95}+O(q^{100}) \) 32 * q + 8 * q^11 - 16 * q^29 - 24 * q^35 - 16 * q^53 + 32 * q^55 - 32 * q^59 + 32 * q^61 + 16 * q^67 - 16 * q^71 - 16 * q^77 + 32 * q^79 + 40 * q^83 + 48 * q^91 + 80 * q^95

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