LMFDB - Embedded newform 192.11.h.c.161.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,11,Mod(161,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("192.161");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	192.h (of order $2$, degree $1$, 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:	$121.988592513$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			161.18
Character	$\chi$	$=$	192.161
Dual form			192.11.h.c.161.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(194.524 - 145.635i) q^{3} +4363.03 q^{5} +17194.1 q^{7} +(16630.1 - 56658.8i) q^{9} +O(q^{10})$	\(q+(194.524 - 145.635i) q^{3} +4363.03 q^{5} +17194.1 q^{7} +(16630.1 - 56658.8i) q^{9} -112023. q^{11} +234490. i q^{13} +(848714. - 635408. i) q^{15} +714601. i q^{17} +4.17837e6i q^{19} +(3.34467e6 - 2.50406e6i) q^{21} +2.35471e6i q^{23} +9.27041e6 q^{25} +(-5.01653e6 - 1.34434e7i) q^{27} +3.11938e7 q^{29} +5.50245e7 q^{31} +(-2.17912e7 + 1.63145e7i) q^{33} +7.50186e7 q^{35} -4.78694e7i q^{37} +(3.41498e7 + 4.56139e7i) q^{39} +6.69440e7i q^{41} -9.32927e7i q^{43} +(7.25578e7 - 2.47204e8i) q^{45} +2.42952e8i q^{47} +1.31633e7 q^{49} +(1.04071e8 + 1.39007e8i) q^{51} -3.64746e8 q^{53} -4.88761e8 q^{55} +(6.08516e8 + 8.12794e8i) q^{57} +1.19948e9 q^{59} +1.19879e9i q^{61} +(2.85941e8 - 9.74200e8i) q^{63} +1.02309e9i q^{65} -2.65123e8i q^{67} +(3.42927e8 + 4.58048e8i) q^{69} -1.13781e9i q^{71} +1.17504e9 q^{73} +(1.80332e9 - 1.35009e9i) q^{75} -1.92615e9 q^{77} -4.32571e9 q^{79} +(-2.93366e9 - 1.88449e9i) q^{81} +1.07734e9 q^{83} +3.11783e9i q^{85} +(6.06794e9 - 4.54290e9i) q^{87} -7.97007e8i q^{89} +4.03185e9i q^{91} +(1.07036e10 - 8.01347e9i) q^{93} +1.82304e10i q^{95} +3.54176e9 q^{97} +(-1.86296e9 + 6.34711e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 328392 q^{9}+O(q^{10}) $ 24 * q + 328392 * q^9	$ 24 q + 328392 q^{9} + 47919720 q^{25} - 29516256 q^{33} + 1766081064 q^{49} + 4276148496 q^{57} + 9990750000 q^{73} - 12450970728 q^{81} - 48470791152 q^{97}+O(q^{100}) $ 24 * q + 328392 * q^9 + 47919720 * q^25 - 29516256 * q^33 + 1766081064 * q^49 + 4276148496 * q^57 + 9990750000 * q^73 - 12450970728 * q^81 - 48470791152 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	194.524	−	145.635i	0.800510	−	0.599319i
$3$	194.524	−	145.635i	0.800510	−	0.599319i
$4$		0			0
$5$	4363.03			1.39617			0.698085	−	0.716015i	$-0.254036\pi$
$5$	4363.03			1.39617			0.698085	+	0.716015i	$0.254036\pi$
$6$		0			0
$7$	17194.1			1.02303			0.511517	−	0.859273i	$-0.329084\pi$
$7$	17194.1			1.02303			0.511517	+	0.859273i	$0.329084\pi$
$8$		0			0
$9$	16630.1	−	56658.8i	0.281633	−	0.959522i
$10$		0			0
$11$	−112023.			−0.695577			−0.347788	−	0.937573i	$-0.613067\pi$
$11$	−112023.			−0.695577			−0.347788	+	0.937573i	$0.613067\pi$
$12$		0			0
$13$			234490.i			0.631549i	0.948834	+	0.315775i	$0.102264\pi$
$13$			234490.i			0.631549i	−0.948834	+	0.315775i	$0.897736\pi$
$14$		0			0
$15$	848714.	−	635408.i	1.11765	−	0.836751i
$16$		0			0
$17$			714601.i			0.503291i	0.967819	+	0.251645i	$0.0809717\pi$
$17$			714601.i			0.503291i	−0.967819	+	0.251645i	$0.919028\pi$
$18$		0			0
$19$			4.17837e6i			1.68748i	0.536750	+	0.843741i	$0.319652\pi$
$19$			4.17837e6i			1.68748i	−0.536750	+	0.843741i	$0.680348\pi$
$20$		0			0
$21$	3.34467e6	−	2.50406e6i	0.818950	−	0.613124i
$22$		0			0
$23$			2.35471e6i			0.365846i	0.983127	+	0.182923i	$0.0585559\pi$
$23$			2.35471e6i			0.365846i	−0.983127	+	0.182923i	$0.941444\pi$
$24$		0			0
$25$	9.27041e6			0.949289
$26$		0			0
$27$	−5.01653e6	−	1.34434e7i	−0.349610	−	0.936895i
$28$		0			0
$29$	3.11938e7			1.52082			0.760411	−	0.649442i	$-0.224998\pi$
$29$	3.11938e7			1.52082			0.760411	+	0.649442i	$0.224998\pi$
$30$		0			0
$31$	5.50245e7			1.92198			0.960988	−	0.276591i	$-0.0892049\pi$
$31$	5.50245e7			1.92198			0.960988	+	0.276591i	$0.0892049\pi$
$32$		0			0
$33$	−2.17912e7	+	1.63145e7i	−0.556816	+	0.416873i
$34$		0			0
$35$	7.50186e7			1.42833
$36$		0			0
$37$		−	4.78694e7i		−	0.690318i	−0.938544	−	0.345159i	$-0.887825\pi$
$37$		−	4.78694e7i		−	0.690318i	0.938544	−	0.345159i	$-0.112175\pi$
$38$		0			0
$39$	3.41498e7	+	4.56139e7i	0.378500	+	0.505562i
$40$		0			0
$41$			6.69440e7i			0.577819i	0.957356	+	0.288910i	$0.0932927\pi$
$41$			6.69440e7i			0.577819i	−0.957356	+	0.288910i	$0.906707\pi$
$42$		0			0
$43$		−	9.32927e7i		−	0.634608i	−0.948324	−	0.317304i	$-0.897222\pi$
$43$		−	9.32927e7i		−	0.634608i	0.948324	−	0.317304i	$-0.102778\pi$
$44$		0			0
$45$	7.25578e7	−	2.47204e8i	0.393207	−	1.33966i
$46$		0			0
$47$			2.42952e8i			1.05933i	0.848207	+	0.529665i	$0.177682\pi$
$47$			2.42952e8i			1.05933i	−0.848207	+	0.529665i	$0.822318\pi$
$48$		0			0
$49$	1.31633e7			0.0466000
$50$		0			0
$51$	1.04071e8	+	1.39007e8i	0.301632	+	0.402890i
$52$		0			0
$53$	−3.64746e8			−0.872190			−0.436095	−	0.899901i	$-0.643639\pi$
$53$	−3.64746e8			−0.872190			−0.436095	+	0.899901i	$0.643639\pi$
$54$		0			0
$55$	−4.88761e8			−0.971143
$56$		0			0
$57$	6.08516e8	+	8.12794e8i	1.01134	+	1.35085i
$58$		0			0
$59$	1.19948e9			1.67778			0.838889	−	0.544303i	$-0.183206\pi$
$59$	1.19948e9			1.67778			0.838889	+	0.544303i	$0.183206\pi$
$60$		0			0
$61$			1.19879e9i			1.41937i	0.704520	+	0.709684i	$0.251162\pi$
$61$			1.19879e9i			1.41937i	−0.704520	+	0.709684i	$0.748838\pi$
$62$		0			0
$63$	2.85941e8	−	9.74200e8i	0.288120	−	0.981625i
$64$		0			0
$65$			1.02309e9i			0.881750i
$66$		0			0
$67$		−	2.65123e8i		−	0.196369i	−0.995168	−	0.0981846i	$-0.968696\pi$
$67$		−	2.65123e8i		−	0.196369i	0.995168	−	0.0981846i	$-0.0313036\pi$
$68$		0			0
$69$	3.42927e8	+	4.58048e8i	0.219259	+	0.292863i
$70$		0			0
$71$		−	1.13781e9i		−	0.630634i	−0.948986	−	0.315317i	$-0.897889\pi$
$71$		−	1.13781e9i		−	0.630634i	0.948986	−	0.315317i	$-0.102111\pi$
$72$		0			0
$73$	1.17504e9			0.566814			0.283407	−	0.959000i	$-0.408535\pi$
$73$	1.17504e9			0.566814			0.283407	+	0.959000i	$0.408535\pi$
$74$		0			0
$75$	1.80332e9	−	1.35009e9i	0.759916	−	0.568927i
$76$		0			0
$77$	−1.92615e9			−0.711599
$78$		0			0
$79$	−4.32571e9			−1.40579			−0.702897	−	0.711292i	$-0.748111\pi$
$79$	−4.32571e9			−1.40579			−0.702897	+	0.711292i	$0.748111\pi$
$80$		0			0
$81$	−2.93366e9	−	1.88449e9i	−0.841366	−	0.540466i
$82$		0			0
$83$	1.07734e9			0.273502			0.136751	−	0.990605i	$-0.456334\pi$
$83$	1.07734e9			0.273502			0.136751	+	0.990605i	$0.456334\pi$
$84$		0			0
$85$			3.11783e9i			0.702680i
$86$		0			0
$87$	6.06794e9	−	4.54290e9i	1.21743	−	0.911458i
$88$		0			0
$89$		−	7.97007e8i		−	0.142729i	−0.997450	−	0.0713644i	$-0.977265\pi$
$89$		−	7.97007e8i		−	0.142729i	0.997450	−	0.0713644i	$-0.0227353\pi$
$90$		0			0
$91$			4.03185e9i			0.646097i
$92$		0			0
$93$	1.07036e10	−	8.01347e9i	1.53856	−	1.15188i
$94$		0			0
$95$			1.82304e10i			2.35601i
$96$		0			0
$97$	3.54176e9			0.412439			0.206220	−	0.978506i	$-0.433884\pi$
$97$	3.54176e9			0.412439			0.206220	+	0.978506i	$0.433884\pi$
$98$		0			0
$99$	−1.86296e9	+	6.34711e9i	−0.195897	+	0.667421i
$100$		0			0
$101$	−1.24059e10			−1.18038			−0.590190	−	0.807264i	$-0.700947\pi$
$101$	−1.24059e10			−1.18038			−0.590190	+	0.807264i	$0.700947\pi$
$102$		0			0
$103$	8.55856e9			0.738268			0.369134	−	0.929376i	$-0.379654\pi$
$103$	8.55856e9			0.738268			0.369134	+	0.929376i	$0.379654\pi$
$104$		0			0
$105$	1.45929e10	−	1.09253e10i	1.14339	−	0.856026i
$106$		0			0
$107$	−7.78002e9			−0.554705			−0.277352	−	0.960768i	$-0.589457\pi$
$107$	−7.78002e9			−0.554705			−0.277352	+	0.960768i	$0.589457\pi$
$108$		0			0
$109$		−	2.09445e10i		−	1.36125i	−0.732633	−	0.680623i	$-0.761709\pi$
$109$		−	2.09445e10i		−	1.36125i	0.732633	−	0.680623i	$-0.238291\pi$
$110$		0			0
$111$	−6.97144e9	−	9.31175e9i	−0.413721	−	0.552607i
$112$		0			0
$113$		−	3.24155e10i		−	1.75938i	−0.475543	−	0.879692i	$-0.657748\pi$
$113$		−	3.24155e10i		−	1.75938i	0.475543	−	0.879692i	$-0.342252\pi$
$114$		0			0
$115$			1.02737e10i			0.510783i
$116$		0			0
$117$	1.32859e10	+	3.89960e9i	0.605986	+	0.177865i
$118$		0			0
$119$			1.22870e10i			0.514884i
$120$		0			0
$121$	−1.33882e10			−0.516173
$122$		0			0
$123$	9.74936e9	+	1.30222e10i	0.346298	+	0.462550i
$124$		0			0
$125$	−2.16066e9			−0.0708005
$126$		0			0
$127$	1.29728e10			0.392660			0.196330	−	0.980538i	$-0.437098\pi$
$127$	1.29728e10			0.392660			0.196330	+	0.980538i	$0.437098\pi$
$128$		0			0
$129$	−1.35866e10	−	1.81477e10i	−0.380333	−	0.508010i
$130$		0			0
$131$	2.37581e10			0.615822			0.307911	−	0.951415i	$-0.400370\pi$
$131$	2.37581e10			0.615822			0.307911	+	0.951415i	$0.400370\pi$
$132$		0			0
$133$			7.18436e10i			1.72635i
$134$		0			0
$135$	−2.18873e10	−	5.86541e10i	−0.488115	−	1.30806i
$136$		0			0
$137$		−	8.84156e10i		−	1.83200i	−0.401175	−	0.916001i	$-0.631398\pi$
$137$		−	8.84156e10i		−	1.83200i	0.401175	−	0.916001i	$-0.368602\pi$
$138$		0			0
$139$			4.74577e10i			0.914604i	0.889311	+	0.457302i	$0.151184\pi$
$139$			4.74577e10i			0.914604i	−0.889311	+	0.457302i	$0.848816\pi$
$140$		0			0
$141$	3.53822e10	+	4.72600e10i	0.634877	+	0.848004i
$142$		0			0
$143$		−	2.62683e10i		−	0.439291i
$144$		0			0
$145$	1.36099e11			2.12332
$146$		0			0
$147$	2.56058e9	−	1.91704e9i	0.0373037	−	0.0279283i
$148$		0			0
$149$	−1.14921e11			−1.56483			−0.782415	−	0.622757i	$-0.786012\pi$
$149$	−1.14921e11			−1.56483			−0.782415	+	0.622757i	$0.786012\pi$
$150$		0			0
$151$	−4.54928e10			−0.579506			−0.289753	−	0.957101i	$-0.593573\pi$
$151$	−4.54928e10			−0.579506			−0.289753	+	0.957101i	$0.593573\pi$
$152$		0			0
$153$	4.04885e10	+	1.18839e10i	0.482919	+	0.141743i
$154$		0			0
$155$	2.40074e11			2.68340
$156$		0			0
$157$		−	1.83277e11i		−	1.92137i	−0.277648	−	0.960683i	$-0.589555\pi$
$157$		−	1.83277e11i		−	1.92137i	0.277648	−	0.960683i	$-0.410445\pi$
$158$		0			0
$159$	−7.09518e10	+	5.31196e10i	−0.698197	+	0.522720i
$160$		0			0
$161$			4.04872e10i			0.374273i
$162$		0			0
$163$			1.53087e11i			1.33045i	0.746641	+	0.665227i	$0.231665\pi$
$163$			1.53087e11i			1.33045i	−0.746641	+	0.665227i	$0.768335\pi$
$164$		0			0
$165$	−9.50757e10	+	7.11805e10i	−0.777410	+	0.582025i
$166$		0			0
$167$			6.97503e10i			0.536987i	0.963281	+	0.268494i	$0.0865258\pi$
$167$			6.97503e10i			0.536987i	−0.963281	+	0.268494i	$0.913474\pi$
$168$		0			0
$169$	8.28730e10			0.601145
$170$		0			0
$171$	2.36742e11	+	6.94869e10i	1.61918	+	0.475250i
$172$		0			0
$173$	2.43391e11			1.57063			0.785317	−	0.619094i	$-0.212500\pi$
$173$	2.43391e11			1.57063			0.785317	+	0.619094i	$0.212500\pi$
$174$		0			0
$175$	1.59397e11			0.971156
$176$		0			0
$177$	2.33328e11	−	1.74686e11i	1.34308	−	1.00552i
$178$		0			0
$179$	1.68970e11			0.919483			0.459742	−	0.888053i	$-0.347942\pi$
$179$	1.68970e11			0.919483			0.459742	+	0.888053i	$0.347942\pi$
$180$		0			0
$181$		−	9.60579e9i		−	0.0494470i	−0.999694	−	0.0247235i	$-0.992129\pi$
$181$		−	9.60579e9i		−	0.0494470i	0.999694	−	0.0247235i	$-0.00787054\pi$
$182$		0			0
$183$	1.74586e11	+	2.33194e11i	0.850654	+	1.13622i
$184$		0			0
$185$		−	2.08856e11i		−	0.963802i
$186$		0			0
$187$		−	8.00520e10i		−	0.350077i
$188$		0			0
$189$	−8.62549e10	−	2.31148e11i	−0.357663	−	0.958476i
$190$		0			0
$191$		−	2.17475e11i		−	0.855546i	−0.903886	−	0.427773i	$-0.859298\pi$
$191$		−	2.17475e11i		−	0.855546i	0.903886	−	0.427773i	$-0.140702\pi$
$192$		0			0
$193$	−1.89281e10			−0.0706837			−0.0353419	−	0.999375i	$-0.511252\pi$
$193$	−1.89281e10			−0.0706837			−0.0353419	+	0.999375i	$0.511252\pi$
$194$		0			0
$195$	1.48997e11	+	1.99015e11i	0.528450	+	0.705850i
$196$		0			0
$197$	3.49018e11			1.17630			0.588148	−	0.808754i	$-0.299857\pi$
$197$	3.49018e11			1.17630			0.588148	+	0.808754i	$0.299857\pi$
$198$		0			0
$199$	−5.19373e10			−0.166423			−0.0832116	−	0.996532i	$-0.526518\pi$
$199$	−5.19373e10			−0.166423			−0.0832116	+	0.996532i	$0.526518\pi$
$200$		0			0
$201$	−3.86111e10	−	5.15728e10i	−0.117688	−	0.157195i
$202$		0			0
$203$	5.36351e11			1.55585
$204$		0			0
$205$			2.92079e11i			0.806734i
$206$		0			0
$207$	1.33415e11	+	3.91591e10i	0.351037	+	0.103034i
$208$		0			0
$209$		−	4.68075e11i		−	1.17377i
$210$		0			0
$211$			6.23029e11i			1.48969i	0.667238	+	0.744845i	$0.267476\pi$
$211$			6.23029e11i			1.48969i	−0.667238	+	0.744845i	$0.732524\pi$
$212$		0			0
$213$	−1.65704e11	−	2.21331e11i	−0.377951	−	0.504829i
$214$		0			0
$215$		−	4.07039e11i		−	0.886020i
$216$		0			0
$217$	9.46099e11			1.96625
$218$		0			0
$219$	2.28574e11	−	1.71127e11i	0.453740	−	0.339702i
$220$		0			0
$221$	−1.67567e11			−0.317853
$222$		0			0
$223$	−3.45840e11			−0.627121			−0.313561	−	0.949568i	$-0.601522\pi$
$223$	−3.45840e11			−0.627121			−0.313561	+	0.949568i	$0.601522\pi$
$224$		0			0
$225$	1.54168e11	−	5.25250e11i	0.267351	−	0.910864i
$226$		0			0
$227$	−9.00884e11			−1.49465			−0.747325	−	0.664459i	$-0.768662\pi$
$227$	−9.00884e11			−1.49465			−0.747325	+	0.664459i	$0.768662\pi$
$228$		0			0
$229$			6.45482e11i			1.02496i	0.858700	+	0.512479i	$0.171273\pi$
$229$			6.45482e11i			1.02496i	−0.858700	+	0.512479i	$0.828727\pi$
$230$		0			0
$231$	−3.74681e11	+	2.80513e11i	−0.569642	+	0.426475i
$232$		0			0
$233$		−	8.51009e11i		−	1.23924i	−0.784903	−	0.619619i	$-0.787287\pi$
$233$		−	8.51009e11i		−	1.23924i	0.784903	−	0.619619i	$-0.212713\pi$
$234$		0			0
$235$			1.06001e12i			1.47900i
$236$		0			0
$237$	−8.41454e11	+	6.29973e11i	−1.12535	+	0.842520i
$238$		0			0
$239$		−	5.97209e11i		−	0.765838i	−0.923782	−	0.382919i	$-0.874919\pi$
$239$		−	5.97209e11i		−	0.765838i	0.923782	−	0.382919i	$-0.125081\pi$
$240$		0			0
$241$	−8.01857e11			−0.986306			−0.493153	−	0.869943i	$-0.664156\pi$
$241$	−8.01857e11			−0.986306			−0.493153	+	0.869943i	$0.664156\pi$
$242$		0			0
$243$	−8.45114e11	+	6.06645e10i	−0.997434	+	0.0715984i
$244$		0			0
$245$	5.74320e10			0.0650614
$246$		0			0
$247$	−9.79786e11			−1.06573
$248$		0			0
$249$	2.09568e11	−	1.56897e11i	0.218941	−	0.163915i
$250$		0			0
$251$	1.30528e12			1.31019			0.655095	−	0.755547i	$-0.272629\pi$
$251$	1.30528e12			1.31019			0.655095	+	0.755547i	$0.272629\pi$
$252$		0			0
$253$		−	2.63782e11i		−	0.254474i
$254$		0			0
$255$	4.54063e11	+	6.06492e11i	0.421129	+	0.562502i
$256$		0			0
$257$		−	7.91758e11i		−	0.706199i	−0.935586	−	0.353099i	$-0.885128\pi$
$257$		−	7.91758e11i		−	0.706199i	0.935586	−	0.353099i	$-0.114872\pi$
$258$		0			0
$259$		−	8.23074e11i		−	0.706220i
$260$		0			0
$261$	5.18757e11	−	1.76740e12i	0.428313	−	1.45926i
$262$		0			0
$263$			1.43195e12i			1.13802i	0.822330	+	0.569010i	$0.192674\pi$
$263$			1.43195e12i			1.13802i	−0.822330	+	0.569010i	$0.807326\pi$
$264$		0			0
$265$	−1.59140e12			−1.21773
$266$		0			0
$267$	−1.16072e11	−	1.55037e11i	−0.0855402	−	0.114256i
$268$		0			0
$269$	−7.12488e11			−0.505844			−0.252922	−	0.967487i	$-0.581392\pi$
$269$	−7.12488e11			−0.505844			−0.252922	+	0.967487i	$0.581392\pi$
$270$		0			0
$271$	6.82942e11			0.467237			0.233619	−	0.972328i	$-0.424943\pi$
$271$	6.82942e11			0.467237			0.233619	+	0.972328i	$0.424943\pi$
$272$		0			0
$273$	5.87177e11	+	7.84292e11i	0.387218	+	0.517207i
$274$		0			0
$275$	−1.03850e12			−0.660304
$276$		0			0
$277$		−	1.67022e12i		−	1.02418i	−0.858932	−	0.512089i	$-0.828872\pi$
$277$		−	1.67022e12i		−	1.02418i	0.858932	−	0.512089i	$-0.171128\pi$
$278$		0			0
$279$	9.15065e11	−	3.11762e12i	0.541291	−	1.84418i
$280$		0			0
$281$			2.05930e12i			1.17541i	0.809077	+	0.587703i	$0.199968\pi$
$281$			2.05930e12i			1.17541i	−0.809077	+	0.587703i	$0.800032\pi$
$282$		0			0
$283$		−	1.72749e12i		−	0.951666i	−0.879536	−	0.475833i	$-0.842147\pi$
$283$		−	1.72749e12i		−	0.951666i	0.879536	−	0.475833i	$-0.157853\pi$
$284$		0			0
$285$	2.65497e12	+	3.54624e12i	1.41200	+	1.88601i
$286$		0			0
$287$			1.15104e12i			0.591129i
$288$		0			0
$289$	1.50534e12			0.746698
$290$		0			0
$291$	6.88956e11	−	5.15802e11i	0.330162	−	0.247183i
$292$		0			0
$293$	1.43453e12			0.664312			0.332156	−	0.943224i	$-0.392224\pi$
$293$	1.43453e12			0.664312			0.332156	+	0.943224i	$0.392224\pi$
$294$		0			0
$295$	5.23339e12			2.34246
$296$		0			0
$297$	5.61968e11	+	1.50598e12i	0.243181	+	0.651682i
$298$		0			0
$299$	−5.52156e11			−0.231050
$300$		0			0
$301$		−	1.60409e12i		−	0.649226i
$302$		0			0
$303$	−2.41325e12	+	1.80673e12i	−0.944907	+	0.707425i
$304$		0			0
$305$			5.23037e12i			1.98168i
$306$		0			0
$307$			2.88455e12i			1.05776i	0.848698	+	0.528878i	$0.177387\pi$
$307$			2.88455e12i			1.05776i	−0.848698	+	0.528878i	$0.822613\pi$
$308$		0			0
$309$	1.66484e12	−	1.24642e12i	0.590991	−	0.442459i
$310$		0			0
$311$			1.66278e12i			0.571523i	0.958301	+	0.285761i	$0.0922464\pi$
$311$			1.66278e12i			0.571523i	−0.958301	+	0.285761i	$0.907754\pi$
$312$		0			0
$313$	−4.33282e12			−1.44228			−0.721139	−	0.692791i	$-0.756381\pi$
$313$	−4.33282e12			−1.44228			−0.721139	+	0.692791i	$0.756381\pi$
$314$		0			0
$315$	1.24757e12	−	4.25046e12i	0.402265	−	1.37051i
$316$		0			0
$317$	−4.19805e12			−1.31145			−0.655725	−	0.755000i	$-0.727637\pi$
$317$	−4.19805e12			−1.31145			−0.655725	+	0.755000i	$0.727637\pi$
$318$		0			0
$319$	−3.49443e12			−1.05785
$320$		0			0
$321$	−1.51340e12	+	1.13304e12i	−0.444047	+	0.332445i
$322$		0			0
$323$	−2.98587e12			−0.849295
$324$		0			0
$325$			2.17382e12i			0.599523i
$326$		0			0
$327$	−3.05024e12	−	4.07420e12i	−0.815822	−	1.08969i
$328$		0			0
$329$			4.17735e12i			1.08373i
$330$		0			0
$331$		−	2.00790e12i		−	0.505362i	−0.967550	−	0.252681i	$-0.918688\pi$
$331$		−	2.00790e12i		−	0.505362i	0.967550	−	0.252681i	$-0.0813124\pi$
$332$		0			0
$333$	−2.71222e12	−	7.96075e11i	−0.662376	−	0.194416i
$334$		0			0
$335$		−	1.15674e12i		−	0.274165i
$336$		0			0
$337$	−3.05817e12			−0.703578			−0.351789	−	0.936079i	$-0.614427\pi$
$337$	−3.05817e12			−0.703578			−0.351789	+	0.936079i	$0.614427\pi$
$338$		0			0
$339$	−4.72082e12	−	6.30560e12i	−1.05443	−	1.40841i
$340$		0			0
$341$	−6.16403e12			−1.33688
$342$		0			0
$343$	−4.63059e12			−0.975361
$344$		0			0
$345$	1.49620e12	+	1.99848e12i	0.306122	+	0.408887i
$346$		0			0
$347$	−2.73058e12			−0.542760			−0.271380	−	0.962472i	$-0.587480\pi$
$347$	−2.73058e12			−0.542760			−0.271380	+	0.962472i	$0.587480\pi$
$348$		0			0
$349$			2.19363e12i			0.423679i	0.977304	+	0.211839i	$0.0679454\pi$
$349$			2.19363e12i			0.423679i	−0.977304	+	0.211839i	$0.932055\pi$
$350$		0			0
$351$	3.15235e12	−	1.17632e12i	0.591696	−	0.220796i
$352$		0			0
$353$		−	1.64111e11i		−	0.0299409i	−0.999888	−	0.0149704i	$-0.995235\pi$
$353$		−	1.64111e11i		−	0.0299409i	0.999888	−	0.0149704i	$-0.00476542\pi$
$354$		0			0
$355$		−	4.96429e12i		−	0.880472i
$356$		0			0
$357$	1.78941e12	+	2.39011e12i	0.308580	+	0.412170i
$358$		0			0
$359$			4.97242e12i			0.833865i	0.908937	+	0.416933i	$0.136895\pi$
$359$			4.97242e12i			0.833865i	−0.908937	+	0.416933i	$0.863105\pi$
$360$		0			0
$361$	−1.13277e13			−1.84760
$362$		0			0
$363$	−2.60433e12	+	1.94979e12i	−0.413202	+	0.309352i
$364$		0			0
$365$	5.12676e12			0.791368
$366$		0			0
$367$	3.10568e12			0.466473			0.233236	−	0.972420i	$-0.425068\pi$
$367$	3.10568e12			0.466473			0.233236	+	0.972420i	$0.425068\pi$
$368$		0			0
$369$	3.79297e12	+	1.11329e12i	0.554431	+	0.162733i
$370$		0			0
$371$	−6.27149e12			−0.892281
$372$		0			0
$373$			5.62487e12i			0.779055i	0.921015	+	0.389527i	$0.127362\pi$
$373$			5.62487e12i			0.779055i	−0.921015	+	0.389527i	$0.872638\pi$
$374$		0			0
$375$	−4.20300e11	+	3.14667e11i	−0.0566765	+	0.0424321i
$376$		0			0
$377$			7.31463e12i			0.960474i
$378$		0			0
$379$			3.23442e12i			0.413619i	0.978381	+	0.206810i	$0.0663081\pi$
$379$			3.23442e12i			0.413619i	−0.978381	+	0.206810i	$0.933692\pi$
$380$		0			0
$381$	2.52353e12	−	1.88929e12i	0.314328	−	0.235329i
$382$		0			0
$383$		−	1.27946e13i		−	1.55250i	−0.630424	−	0.776251i	$-0.717119\pi$
$383$		−	1.27946e13i		−	1.55250i	0.630424	−	0.776251i	$-0.282881\pi$
$384$		0			0
$385$	−8.40383e12			−0.993513
$386$		0			0
$387$	−5.28586e12	−	1.55147e12i	−0.608920	−	0.178726i
$388$		0			0
$389$	6.86274e12			0.770459			0.385229	−	0.922821i	$-0.374122\pi$
$389$	6.86274e12			0.770459			0.385229	+	0.922821i	$0.374122\pi$
$390$		0			0
$391$	−1.68268e12			−0.184127
$392$		0			0
$393$	4.62152e12	−	3.46000e12i	0.492972	−	0.369074i
$394$		0			0
$395$	−1.88732e13			−1.96273
$396$		0			0
$397$		−	1.64010e13i		−	1.66310i	−0.555453	−	0.831548i	$-0.687455\pi$
$397$		−	1.64010e13i		−	1.66310i	0.555453	−	0.831548i	$-0.312545\pi$
$398$		0			0
$399$	1.04629e13	+	1.39753e13i	1.03464	+	1.38196i
$400$		0			0
$401$		−	2.02574e13i		−	1.95372i	−0.213876	−	0.976861i	$-0.568609\pi$
$401$		−	2.02574e13i		−	1.95372i	0.213876	−	0.976861i	$-0.431391\pi$
$402$		0			0
$403$			1.29027e13i			1.21382i
$404$		0			0
$405$	−1.27997e13	−	8.22208e12i	−1.17469	−	0.754582i
$406$		0			0
$407$			5.36249e12i			0.480169i
$408$		0			0
$409$	−2.60506e12			−0.227615			−0.113807	−	0.993503i	$-0.536305\pi$
$409$	−2.60506e12			−0.227615			−0.113807	+	0.993503i	$0.536305\pi$
$410$		0			0
$411$	−1.28764e13	−	1.71990e13i	−1.09795	−	1.46654i
$412$		0			0
$413$	2.06241e13			1.71642
$414$		0			0
$415$	4.70045e12			0.381856
$416$		0			0
$417$	6.91149e12	+	9.23167e12i	0.548140	+	0.732150i
$418$		0			0
$419$	1.84246e13			1.42668			0.713340	−	0.700818i	$-0.247181\pi$
$419$	1.84246e13			1.42668			0.713340	+	0.700818i	$0.247181\pi$
$420$		0			0
$421$			1.58911e13i			1.20156i	0.799416	+	0.600778i	$0.205142\pi$
$421$			1.58911e13i			1.20156i	−0.799416	+	0.600778i	$0.794858\pi$
$422$		0			0
$423$	1.37654e13	+	4.04033e12i	1.01645	+	0.298342i
$424$		0			0
$425$			6.62464e12i			0.477769i
$426$		0			0
$427$			2.06122e13i			1.45206i
$428$		0			0
$429$	−3.82558e12	−	5.10982e12i	−0.263276	−	0.351657i
$430$		0			0
$431$		−	1.72758e13i		−	1.16159i	−0.814050	−	0.580795i	$-0.802742\pi$
$431$		−	1.72758e13i		−	1.16159i	0.814050	−	0.580795i	$-0.197258\pi$
$432$		0			0
$433$	−1.59298e13			−1.04657			−0.523287	−	0.852157i	$-0.675294\pi$
$433$	−1.59298e13			−1.04657			−0.523287	+	0.852157i	$0.675294\pi$
$434$		0			0
$435$	2.64746e13	−	1.98208e13i	1.69974	−	1.27255i
$436$		0			0
$437$	−9.83886e12			−0.617359
$438$		0			0
$439$	−1.22417e13			−0.750792			−0.375396	−	0.926865i	$-0.622493\pi$
$439$	−1.22417e13			−0.750792			−0.375396	+	0.926865i	$0.622493\pi$
$440$		0			0
$441$	2.18908e11	−	7.45819e11i	0.0131241	−	0.0447137i
$442$		0			0
$443$	5.89310e11			0.0345402			0.0172701	−	0.999851i	$-0.494502\pi$
$443$	5.89310e11			0.0345402			0.0172701	+	0.999851i	$0.494502\pi$
$444$		0			0
$445$		−	3.47736e12i		−	0.199274i
$446$		0			0
$447$	−2.23548e13	+	1.67364e13i	−1.25266	+	0.937833i
$448$		0			0
$449$			6.22107e12i			0.340905i	0.985366	+	0.170452i	$0.0545229\pi$
$449$			6.22107e12i			0.340905i	−0.985366	+	0.170452i	$0.945477\pi$
$450$		0			0
$451$		−	7.49929e12i		−	0.401918i
$452$		0			0
$453$	−8.84944e12	+	6.62533e12i	−0.463901	+	0.347309i
$454$		0			0
$455$			1.75911e13i			0.902061i
$456$		0			0
$457$	5.40044e12			0.270925			0.135462	−	0.990783i	$-0.456748\pi$
$457$	5.40044e12			0.270925			0.135462	+	0.990783i	$0.456748\pi$
$458$		0			0
$459$	9.60669e12	−	3.58482e12i	0.471531	−	0.175956i
$460$		0			0
$461$	−1.53272e13			−0.736137			−0.368068	−	0.929799i	$-0.619981\pi$
$461$	−1.53272e13			−0.736137			−0.368068	+	0.929799i	$0.619981\pi$
$462$		0			0
$463$	−8.63932e12			−0.406045			−0.203023	−	0.979174i	$-0.565077\pi$
$463$	−8.63932e12			−0.406045			−0.203023	+	0.979174i	$0.565077\pi$
$464$		0			0
$465$	4.67001e13	−	3.49630e13i	2.14809	−	1.60822i
$466$		0			0
$467$	2.72643e13			1.22747			0.613734	−	0.789513i	$-0.289667\pi$
$467$	2.72643e13			1.22747			0.613734	+	0.789513i	$0.289667\pi$
$468$		0			0
$469$		−	4.55856e12i		−	0.200892i
$470$		0			0
$471$	−2.66915e13	−	3.56518e13i	−1.15151	−	1.53807i
$472$		0			0
$473$			1.04510e13i			0.441418i
$474$		0			0
$475$			3.87352e13i			1.60191i
$476$		0			0
$477$	−6.06577e12	+	2.06661e13i	−0.245637	+	0.836886i
$478$		0			0
$479$		−	3.00962e13i		−	1.19353i	−0.802415	−	0.596767i	$-0.796452\pi$
$479$		−	3.00962e13i		−	1.19353i	0.802415	−	0.596767i	$-0.203548\pi$
$480$		0			0
$481$	1.12249e13			0.435970
$482$		0			0
$483$	5.89634e12	+	7.87574e12i	0.224309	+	0.299609i
$484$		0			0
$485$	1.54528e13			0.575835
$486$		0			0
$487$	3.37106e13			1.23061			0.615307	−	0.788287i	$-0.289032\pi$
$487$	3.37106e13			1.23061			0.615307	+	0.788287i	$0.289032\pi$
$488$		0			0
$489$	2.22947e13	+	2.97791e13i	0.797367	+	1.06504i
$490$		0			0
$491$	3.36881e13			1.18051			0.590255	−	0.807217i	$-0.299027\pi$
$491$	3.36881e13			1.18051			0.590255	+	0.807217i	$0.299027\pi$
$492$		0			0
$493$			2.22911e13i			0.765416i
$494$		0			0
$495$	−8.12816e12	+	2.76926e13i	−0.273506	+	0.931833i
$496$		0			0
$497$		−	1.95636e13i		−	0.645160i
$498$		0			0
$499$			5.41020e13i			1.74868i	0.485312	+	0.874341i	$0.338706\pi$
$499$			5.41020e13i			1.74868i	−0.485312	+	0.874341i	$0.661294\pi$
$500$		0			0
$501$	1.01581e13	+	1.35681e13i	0.321827	+	0.429864i
$502$		0			0
$503$		−	1.49560e13i		−	0.464490i	−0.972657	−	0.232245i	$-0.925393\pi$
$503$		−	1.49560e13i		−	0.464490i	0.972657	−	0.232245i	$-0.0746071\pi$
$504$		0			0
$505$	−5.41274e13			−1.64801
$506$		0			0
$507$	1.61208e13	−	1.20692e13i	0.481223	−	0.360278i
$508$		0			0
$509$	1.36587e12			0.0399778			0.0199889	−	0.999800i	$-0.493637\pi$
$509$	1.36587e12			0.0399778			0.0199889	+	0.999800i	$0.493637\pi$
$510$		0			0
$511$	2.02039e13			0.579870
$512$		0			0
$513$	5.61716e13	−	2.09609e13i	1.58099	−	0.589961i
$514$		0			0
$515$	3.73412e13			1.03075
$516$		0			0
$517$		−	2.72163e13i		−	0.736845i
$518$		0			0
$519$	4.73455e13	−	3.54462e13i	1.25731	−	0.941311i
$520$		0			0
$521$		−	4.27057e13i		−	1.11249i	−0.831017	−	0.556247i	$-0.812241\pi$
$521$		−	4.27057e13i		−	1.11249i	0.831017	−	0.556247i	$-0.187759\pi$
$522$		0			0
$523$			1.82867e13i			0.467332i	0.972317	+	0.233666i	$0.0750723\pi$
$523$			1.82867e13i			0.467332i	−0.972317	+	0.233666i	$0.924928\pi$
$524$		0			0
$525$	3.10065e13	−	2.32137e13i	0.777420	−	0.582033i
$526$		0			0
$527$			3.93206e13i			0.967313i
$528$		0			0
$529$	3.58819e13			0.866157
$530$		0			0
$531$	1.99476e13	−	6.79614e13i	0.472517	−	1.60987i
$532$		0			0
$533$	−1.56977e13			−0.364921
$534$		0			0
$535$	−3.39445e13			−0.774462
$536$		0			0
$537$	3.28687e13	−	2.46078e13i	0.736055	−	0.551064i
$538$		0			0
$539$	−1.47460e12			−0.0324138
$540$		0			0
$541$		−	2.16205e13i		−	0.466530i	−0.972413	−	0.233265i	$-0.925059\pi$
$541$		−	2.16205e13i		−	0.466530i	0.972413	−	0.233265i	$-0.0749409\pi$
$542$		0			0
$543$	−1.39894e12	−	1.86856e12i	−0.0296346	−	0.0395829i
$544$		0			0
$545$		−	9.13814e13i		−	1.90053i
$546$		0			0
$547$			8.56628e13i			1.74927i	0.484786	+	0.874633i	$0.338898\pi$
$547$			8.56628e13i			1.74927i	−0.484786	+	0.874633i	$0.661102\pi$
$548$		0			0
$549$	6.79222e13	+	1.99361e13i	1.36191	+	0.399740i
$550$		0			0
$551$			1.30339e14i			2.56636i
$552$		0			0
$553$	−7.43768e13			−1.43818
$554$		0			0
$555$	−3.04166e13	−	4.06274e13i	−0.577625	−	0.771533i
$556$		0			0
$557$	−6.55943e13			−1.22346			−0.611730	−	0.791066i	$-0.709526\pi$
$557$	−6.55943e13			−1.22346			−0.611730	+	0.791066i	$0.709526\pi$
$558$		0			0
$559$	2.18762e13			0.400786
$560$		0			0
$561$	−1.16583e13	−	1.55720e13i	−0.209808	−	0.280241i
$562$		0			0
$563$	−1.08813e13			−0.192370			−0.0961851	−	0.995363i	$-0.530664\pi$
$563$	−1.08813e13			−0.192370			−0.0961851	+	0.995363i	$0.530664\pi$
$564$		0			0
$565$		−	1.41430e14i		−	2.45640i
$566$		0			0
$567$	−5.04418e13	−	3.24022e13i	−0.860747	−	0.552915i
$568$		0			0
$569$			7.97329e12i			0.133683i	0.997764	+	0.0668415i	$0.0212922\pi$
$569$			7.97329e12i			0.133683i	−0.997764	+	0.0668415i	$0.978708\pi$
$570$		0			0
$571$			9.72531e13i			1.60222i	0.598516	+	0.801111i	$0.295757\pi$
$571$			9.72531e13i			1.60222i	−0.598516	+	0.801111i	$0.704243\pi$
$572$		0			0
$573$	−3.16719e13	−	4.23042e13i	−0.512745	−	0.684873i
$574$		0			0
$575$			2.18291e13i			0.347294i
$576$		0			0
$577$	3.95759e13			0.618803			0.309401	−	0.950932i	$-0.399871\pi$
$577$	3.95759e13			0.618803			0.309401	+	0.950932i	$0.399871\pi$
$578$		0			0
$579$	−3.68196e12	+	2.75658e12i	−0.0565830	+	0.0423621i
$580$		0			0
$581$	1.85239e13			0.279802
$582$		0			0
$583$	4.08600e13			0.606675
$584$		0			0
$585$	5.79669e13	+	1.70141e13i	0.846059	+	0.248330i
$586$		0			0
$587$	−1.76105e13			−0.252686			−0.126343	−	0.991987i	$-0.540324\pi$
$587$	−1.76105e13			−0.252686			−0.126343	+	0.991987i	$0.540324\pi$
$588$		0			0
$589$			2.29913e14i			3.24330i
$590$		0			0
$591$	6.78923e13	−	5.08290e13i	0.941636	−	0.704976i
$592$		0			0
$593$		−	1.08821e14i		−	1.48402i	−0.670391	−	0.742008i	$-0.733874\pi$
$593$		−	1.08821e14i		−	1.48402i	0.670391	−	0.742008i	$-0.266126\pi$
$594$		0			0
$595$			5.36084e13i			0.718866i
$596$		0			0
$597$	−1.01031e13	+	7.56387e12i	−0.133224	+	0.0997407i
$598$		0			0
$599$		−	1.51629e14i		−	1.96629i	−0.182830	−	0.983144i	$-0.558526\pi$
$599$		−	1.51629e14i		−	1.96629i	0.182830	−	0.983144i	$-0.441474\pi$
$600$		0			0
$601$	−1.18085e14			−1.50599			−0.752995	−	0.658026i	$-0.771392\pi$
$601$	−1.18085e14			−1.50599			−0.752995	+	0.658026i	$0.771392\pi$
$602$		0			0
$603$	−1.50216e13	−	4.40903e12i	−0.188421	−	0.0553040i
$604$		0			0
$605$	−5.84131e13			−0.720665
$606$		0			0
$607$	−1.64168e14			−1.99226			−0.996128	−	0.0879104i	$-0.971981\pi$
$607$	−1.64168e14			−1.99226			−0.996128	+	0.0879104i	$0.971981\pi$
$608$		0			0
$609$	1.04333e14	−	7.81112e13i	1.24548	−	0.932453i
$610$		0			0
$611$	−5.69698e13			−0.669019
$612$		0			0
$613$			6.60077e13i			0.762592i	0.924453	+	0.381296i	$0.124522\pi$
$613$			6.60077e13i			0.762592i	−0.924453	+	0.381296i	$0.875478\pi$
$614$		0			0
$615$	4.25367e13	+	5.68163e13i	0.483491	+	0.645799i
$616$		0			0
$617$			1.31893e14i			1.47502i	0.675338	+	0.737508i	$0.263998\pi$
$617$			1.31893e14i			1.47502i	−0.675338	+	0.737508i	$0.736002\pi$
$618$		0			0
$619$		−	4.25649e13i		−	0.468380i	−0.972191	−	0.234190i	$-0.924756\pi$
$619$		−	4.25649e13i		−	0.468380i	0.972191	−	0.234190i	$-0.0752438\pi$
$620$		0			0
$621$	3.16554e13	−	1.18125e13i	0.342759	−	0.127904i
$622$		0			0
$623$		−	1.37038e13i		−	0.146017i
$624$		0			0
$625$	−9.99583e13			−1.04814
$626$		0			0
$627$	−6.81680e13	−	9.10519e13i	−0.703465	−	0.939618i
$628$		0			0
$629$	3.42075e13			0.347431
$630$		0			0
$631$	−5.47244e13			−0.547059			−0.273530	−	0.961864i	$-0.588191\pi$
$631$	−5.47244e13			−0.547059			−0.273530	+	0.961864i	$0.588191\pi$
$632$		0			0
$633$	9.07345e13	+	1.21194e14i	0.892800	+	1.19251i
$634$		0			0
$635$	5.66009e13			0.548220
$636$		0			0
$637$			3.08667e12i			0.0294302i
$638$		0			0
$639$	−6.44669e13	−	1.89219e13i	−0.605107	−	0.177607i
$640$		0			0
$641$			1.01704e14i			0.939822i	0.882714	+	0.469911i	$0.155714\pi$
$641$			1.01704e14i			0.939822i	−0.882714	+	0.469911i	$0.844286\pi$
$642$		0			0
$643$		−	5.47952e13i		−	0.498525i	−0.968436	−	0.249263i	$-0.919812\pi$
$643$		−	5.47952e13i		−	0.498525i	0.968436	−	0.249263i	$-0.0801883\pi$
$644$		0			0
$645$	−5.92790e13	−	7.91788e13i	−0.531009	−	0.709268i
$646$		0			0
$647$			9.76034e12i			0.0860882i	0.999073	+	0.0430441i	$0.0137056\pi$
$647$			9.76034e12i			0.0860882i	−0.999073	+	0.0430441i	$0.986294\pi$
$648$		0			0
$649$	−1.34370e14			−1.16702
$650$		0			0
$651$	1.84039e14	−	1.37785e14i	1.57400	−	1.17841i
$652$		0			0
$653$	1.39040e14			1.17105			0.585523	−	0.810656i	$-0.300889\pi$
$653$	1.39040e14			1.17105			0.585523	+	0.810656i	$0.300889\pi$
$654$		0			0
$655$	1.03657e14			0.859792
$656$		0			0
$657$	1.95412e13	−	6.65767e13i	0.159633	−	0.543870i
$658$		0			0
$659$	−7.49044e13			−0.602671			−0.301336	−	0.953518i	$-0.597432\pi$
$659$	−7.49044e13			−0.602671			−0.301336	+	0.953518i	$0.597432\pi$
$660$		0			0
$661$			1.25482e14i			0.994433i	0.867627	+	0.497216i	$0.165644\pi$
$661$			1.25482e14i			0.994433i	−0.867627	+	0.497216i	$0.834356\pi$
$662$		0			0
$663$	−3.25957e13	+	2.44035e13i	−0.254445	+	0.190495i
$664$		0			0
$665$			3.13456e14i			2.41028i
$666$		0			0
$667$			7.34523e13i			0.556386i
$668$		0			0
$669$	−6.72742e13	+	5.03663e13i	−0.502017	+	0.375846i
$670$		0			0
$671$		−	1.34293e14i		−	0.987279i
$672$		0			0
$673$	−7.74860e13			−0.561239			−0.280620	−	0.959819i	$-0.590540\pi$
$673$	−7.74860e13			−0.561239			−0.280620	+	0.959819i	$0.590540\pi$
$674$		0			0
$675$	−4.65052e13	−	1.24626e14i	−0.331881	−	0.889385i
$676$		0			0
$677$	−1.34765e14			−0.947618			−0.473809	−	0.880628i	$-0.657121\pi$
$677$	−1.34765e14			−0.947618			−0.473809	+	0.880628i	$0.657121\pi$
$678$		0			0
$679$	6.08975e13			0.421940
$680$		0			0
$681$	−1.75243e14	+	1.31200e14i	−1.19648	+	0.895772i
$682$		0			0
$683$	−8.51005e12			−0.0572570			−0.0286285	−	0.999590i	$-0.509114\pi$
$683$	−8.51005e12			−0.0572570			−0.0286285	+	0.999590i	$0.509114\pi$
$684$		0			0
$685$		−	3.85760e14i		−	2.55779i
$686$		0			0
$687$	9.40044e13	+	1.25562e14i	0.614278	+	0.820490i
$688$		0			0
$689$		−	8.55292e13i		−	0.550831i
$690$		0			0
$691$		−	4.64235e12i		−	0.0294678i	−0.999891	−	0.0147339i	$-0.995310\pi$
$691$		−	4.64235e12i		−	0.0294678i	0.999891	−	0.0147339i	$-0.00469011\pi$
$692$		0			0
$693$	−3.20321e13	+	1.09133e14i	−0.200410	+	0.682795i
$694$		0			0
$695$			2.07060e14i			1.27694i
$696$		0			0
$697$	−4.78382e13			−0.290811
$698$		0			0
$699$	−1.23936e14	−	1.65542e14i	−0.742699	−	0.992023i
$700$		0			0
$701$	2.21260e14			1.30711			0.653555	−	0.756879i	$-0.273277\pi$
$701$	2.21260e14			1.30711			0.653555	+	0.756879i	$0.273277\pi$
$702$		0			0
$703$	2.00016e14			1.16490
$704$		0			0
$705$	1.54374e14	+	2.06197e14i	0.886396	+	1.18396i
$706$		0			0
$707$	−2.13309e14			−1.20757
$708$		0			0
$709$		−	1.89881e14i		−	1.05987i	−0.848039	−	0.529933i	$-0.822217\pi$
$709$		−	1.89881e14i		−	1.05987i	0.848039	−	0.529933i	$-0.177783\pi$
$710$		0			0
$711$	−7.19371e13	+	2.45090e14i	−0.395918	+	1.34889i
$712$		0			0
$713$			1.29567e14i			0.703147i
$714$		0			0
$715$		−	1.14610e14i		−	0.613325i
$716$		0			0
$717$	−8.69743e13	−	1.16171e14i	−0.458982	−	0.613061i
$718$		0			0
$719$		−	5.12641e13i		−	0.266790i	−0.991063	−	0.133395i	$-0.957412\pi$
$719$		−	5.12641e13i		−	0.266790i	0.991063	−	0.133395i	$-0.0425878\pi$
$720$		0			0
$721$	1.47157e14			0.755274
$722$		0			0
$723$	−1.55980e14	+	1.16778e14i	−0.789548	+	0.591112i
$724$		0			0
$725$	2.89179e14			1.44370
$726$		0			0
$727$	−1.85574e14			−0.913789			−0.456894	−	0.889521i	$-0.651038\pi$
$727$	−1.85574e14			−0.913789			−0.456894	+	0.889521i	$0.651038\pi$
$728$		0			0
$729$	−1.55560e14	+	1.34879e14i	−0.755545	+	0.655096i
$730$		0			0
$731$	6.66671e13			0.319392
$732$		0			0
$733$			3.90937e13i			0.184751i	0.995724	+	0.0923756i	$0.0294461\pi$
$733$			3.90937e13i			0.184751i	−0.995724	+	0.0923756i	$0.970554\pi$
$734$		0			0
$735$	1.11719e13	−	8.36409e12i	0.0520823	−	0.0389926i
$736$		0			0
$737$			2.96999e13i			0.136590i
$738$		0			0
$739$			1.68885e14i			0.766246i	0.923697	+	0.383123i	$0.125152\pi$
$739$			1.68885e14i			0.766246i	−0.923697	+	0.383123i	$0.874848\pi$
$740$		0			0
$741$	−1.90592e14	+	1.42691e14i	−0.853126	+	0.638712i
$742$		0			0
$743$		−	3.96253e14i		−	1.74996i	−0.484158	−	0.874981i	$-0.660874\pi$
$743$		−	3.96253e14i		−	1.74996i	0.484158	−	0.874981i	$-0.339126\pi$
$744$		0			0
$745$	−5.01403e14			−2.18477
$746$		0			0
$747$	1.79163e13	−	6.10406e13i	0.0770272	−	0.262432i
$748$		0			0
$749$	−1.33771e14			−0.567482
$750$		0			0
$751$	−1.45687e14			−0.609849			−0.304924	−	0.952377i	$-0.598631\pi$
$751$	−1.45687e14			−0.609849			−0.304924	+	0.952377i	$0.598631\pi$
$752$		0			0
$753$	2.53908e14	−	1.90093e14i	1.04882	−	0.785222i
$754$		0			0
$755$	−1.98487e14			−0.809089
$756$		0			0
$757$			2.44154e14i			0.982166i	0.871113	+	0.491083i	$0.163399\pi$
$757$			2.44154e14i			0.982166i	−0.871113	+	0.491083i	$0.836601\pi$
$758$		0			0
$759$	−3.84158e13	−	5.13120e13i	−0.152511	−	0.203709i
$760$		0			0
$761$			3.69564e14i			1.44799i	0.689803	+	0.723997i	$0.257697\pi$
$761$			3.69564e14i			1.44799i	−0.689803	+	0.723997i	$0.742303\pi$
$762$		0			0
$763$		−	3.60122e14i		−	1.39260i
$764$		0			0
$765$	1.76652e14	+	5.18499e13i	0.674237	+	0.197898i
$766$		0			0
$767$			2.81267e14i			1.05960i
$768$		0			0
$769$	−1.04914e14			−0.390124			−0.195062	−	0.980791i	$-0.562491\pi$
$769$	−1.04914e14			−0.390124			−0.195062	+	0.980791i	$0.562491\pi$
$770$		0			0
$771$	−1.15307e14	−	1.54016e14i	−0.423239	−	0.565319i
$772$		0			0
$773$	−1.50820e14			−0.546463			−0.273231	−	0.961948i	$-0.588092\pi$
$773$	−1.50820e14			−0.546463			−0.273231	+	0.961948i	$0.588092\pi$
$774$		0			0
$775$	5.10100e14			1.82451
$776$		0			0
$777$	−1.19868e14	−	1.60108e14i	−0.423251	−	0.565336i
$778$		0			0
$779$	−2.79717e14			−0.975060
$780$		0			0
$781$			1.27461e14i			0.438654i
$782$		0			0
$783$	−1.56484e14	−	4.19351e14i	−0.531695	−	1.42485i
$784$		0			0
$785$		−	7.99644e14i		−	2.68255i
$786$		0			0
$787$		−	1.90507e14i		−	0.631012i	−0.948924	−	0.315506i	$-0.897826\pi$
$787$		−	1.90507e14i		−	0.631012i	0.948924	−	0.315506i	$-0.102174\pi$
$788$		0			0
$789$	2.08542e14	+	2.78549e14i	0.682038	+	0.910997i
$790$		0			0
$791$		−	5.57357e14i		−	1.79991i
$792$		0			0
$793$	−2.81105e14			−0.896401
$794$		0			0
$795$	−3.09565e14	+	2.31762e14i	−0.974801	+	0.729806i
$796$		0			0
$797$	−1.35188e14			−0.420384			−0.210192	−	0.977660i	$-0.567409\pi$
$797$	−1.35188e14			−0.420384			−0.210192	+	0.977660i	$0.567409\pi$
$798$		0			0
$799$	−1.73614e14			−0.533151
$800$		0			0
$801$	−4.51575e13	−	1.32543e13i	−0.136952	−	0.0401971i
$802$		0			0
$803$	−1.31632e14			−0.394262
$804$		0			0
$805$			1.76647e14i			0.522549i
$806$		0			0
$807$	−1.38596e14	+	1.03763e14i	−0.404933	+	0.303162i
$808$		0			0
$809$		−	1.46243e12i		−	0.00422020i	−0.999998	−	0.00211010i	$-0.999328\pi$
$809$		−	1.46243e12i		−	0.00422020i	0.999998	−	0.00211010i	$-0.000671666\pi$
$810$		0			0
$811$			3.56493e14i			1.01612i	0.861320	+	0.508062i	$0.169638\pi$
$811$			3.56493e14i			1.01612i	−0.861320	+	0.508062i	$0.830362\pi$
$812$		0			0
$813$	1.32849e14	−	9.94600e13i	0.374028	−	0.280024i
$814$		0			0
$815$			6.67923e14i			1.85754i
$816$		0			0
$817$	3.89812e14			1.07089
$818$		0			0
$819$	2.28440e14	+	6.70502e13i	0.619944	+	0.181962i
$820$		0			0
$821$	−6.87840e14			−1.84405			−0.922023	−	0.387136i	$-0.873465\pi$
$821$	−6.87840e14			−1.84405			−0.922023	+	0.387136i	$0.873465\pi$
$822$		0			0
$823$	−4.22102e14			−1.11794			−0.558970	−	0.829188i	$-0.688803\pi$
$823$	−4.22102e14			−1.11794			−0.558970	+	0.829188i	$0.688803\pi$
$824$		0			0
$825$	−2.02013e14	+	1.51242e14i	−0.528580	+	0.395733i
$826$		0			0
$827$	2.59642e14			0.671192			0.335596	−	0.942006i	$-0.391062\pi$
$827$	2.59642e14			0.671192			0.335596	+	0.942006i	$0.391062\pi$
$828$		0			0
$829$		−	3.04989e14i		−	0.778953i	−0.921036	−	0.389476i	$-0.872656\pi$
$829$		−	3.04989e14i		−	0.778953i	0.921036	−	0.389476i	$-0.127344\pi$
$830$		0			0
$831$	−2.43242e14	−	3.24898e14i	−0.613810	−	0.819865i
$832$		0			0
$833$			9.40654e12i			0.0234533i
$834$		0			0
$835$			3.04323e14i			0.749725i
$836$		0			0
$837$	−2.76032e14	−	7.39718e14i	−0.671942	−	1.80069i
$838$		0			0
$839$			3.97379e14i			0.955863i	0.878397	+	0.477931i	$0.158613\pi$
$839$			3.97379e14i			0.955863i	−0.878397	+	0.477931i	$0.841387\pi$
$840$		0			0
$841$	5.52346e14			1.31290
$842$		0			0
$843$	2.99905e14	+	4.00583e14i	0.704443	+	0.940924i
$844$		0			0
$845$	3.61577e14			0.839301
$846$		0			0
$847$	−2.30199e14			−0.528063
$848$		0			0
$849$	−2.51583e14	−	3.36039e14i	−0.570352	−	0.761818i
$850$		0			0
$851$	1.12719e14			0.252550
$852$		0			0
$853$			7.10903e13i			0.157422i	0.996897	+	0.0787109i	$0.0250804\pi$
$853$			7.10903e13i			0.157422i	−0.996897	+	0.0787109i	$0.974920\pi$
$854$		0			0
$855$	1.03291e15	+	3.03174e14i	2.26065	+	0.663530i
$856$		0			0
$857$			5.53324e14i			1.19695i	0.801142	+	0.598474i	$0.204226\pi$
$857$			5.53324e14i			1.19695i	−0.801142	+	0.598474i	$0.795774\pi$
$858$		0			0
$859$		−	2.16233e13i		−	0.0462334i	−0.999733	−	0.0231167i	$-0.992641\pi$
$859$		−	2.16233e13i		−	0.0462334i	0.999733	−	0.0231167i	$-0.00735894\pi$
$860$		0			0
$861$	1.67632e14	+	2.23906e14i	0.354275	+	0.473205i
$862$		0			0
$863$			4.53175e14i			0.946698i	0.880875	+	0.473349i	$0.156955\pi$
$863$			4.53175e14i			0.946698i	−0.880875	+	0.473349i	$0.843045\pi$
$864$		0			0
$865$	1.06192e15			2.19287
$866$		0			0
$867$	2.92824e14	−	2.19229e14i	0.597739	−	0.447511i
$868$		0			0
$869$	4.84580e14			0.977838
$870$		0			0
$871$	6.21686e13			0.124017
$872$		0			0
$873$	5.88999e13	−	2.00672e14i	0.116156	−	0.395745i
$874$		0			0
$875$	−3.71507e13			−0.0724313
$876$		0			0
$877$			2.77391e14i			0.534680i	0.963602	+	0.267340i	$0.0861446\pi$
$877$			2.77391e14i			0.534680i	−0.963602	+	0.267340i	$0.913855\pi$
$878$		0			0
$879$	2.79051e14	−	2.08917e14i	0.531788	−	0.398135i
$880$		0			0
$881$		−	7.90063e14i		−	1.48861i	−0.667838	−	0.744307i	$-0.732780\pi$
$881$		−	7.90063e14i		−	1.48861i	0.667838	−	0.744307i	$-0.267220\pi$
$882$		0			0
$883$		−	5.57036e14i		−	1.03772i	−0.854859	−	0.518860i	$-0.826357\pi$
$883$		−	5.57036e14i		−	1.03772i	0.854859	−	0.518860i	$-0.173643\pi$
$884$		0			0
$885$	1.01802e15	−	7.62162e14i	1.87516	−	1.40388i
$886$		0			0
$887$		−	2.75260e14i		−	0.501331i	−0.968074	−	0.250666i	$-0.919351\pi$
$887$		−	2.75260e14i		−	0.501331i	0.968074	−	0.250666i	$-0.0806495\pi$
$888$		0			0
$889$	2.23057e14			0.401705
$890$		0			0
$891$	3.28639e14	+	2.11107e14i	0.585235	+	0.375935i
$892$		0			0
$893$	−1.01514e15			−1.78760
$894$		0			0
$895$	7.37220e14			1.28375
$896$		0			0
$897$	−1.07407e14	+	8.04130e13i	−0.184958	+	0.138473i
$898$		0			0
$899$	1.71642e15			2.92298
$900$		0			0
$901$		−	2.60648e14i		−	0.438965i
$902$		0			0
$903$	−2.33611e14	−	3.12034e14i	−0.389094	−	0.519712i
$904$		0			0
$905$		−	4.19104e13i		−	0.0690365i
$906$		0			0
$907$			2.86644e13i			0.0466989i	0.999727	+	0.0233494i	$0.00743303\pi$
$907$			2.86644e13i			0.0466989i	−0.999727	+	0.0233494i	$0.992567\pi$
$908$		0			0
$909$	−2.06312e14	+	7.02905e14i	−0.332434	+	1.13260i
$910$		0			0
$911$			4.61514e14i			0.735518i	0.929921	+	0.367759i	$0.119875\pi$
$911$			4.61514e14i			0.735518i	−0.929921	+	0.367759i	$0.880125\pi$
$912$		0			0
$913$	−1.20687e14			−0.190242
$914$		0			0
$915$	7.61723e14	+	1.01743e15i	1.18766	+	1.58635i
$916$		0			0
$917$	4.08500e14			0.630007
$918$		0			0
$919$	−1.01313e14			−0.154557			−0.0772785	−	0.997010i	$-0.524623\pi$
$919$	−1.01313e14			−0.154557			−0.0772785	+	0.997010i	$0.524623\pi$
$920$		0			0
$921$	4.20090e14	+	5.61114e14i	0.633934	+	0.846745i
$922$		0			0
$923$	2.66804e14			0.398276
$924$		0			0
$925$		−	4.43769e14i		−	0.655312i
$926$		0			0
$927$	1.42330e14	−	4.84918e14i	0.207921	−	0.708385i
$928$		0			0
$929$			5.24681e13i			0.0758257i	0.999281	+	0.0379129i	$0.0120709\pi$
$929$			5.24681e13i			0.0758257i	−0.999281	+	0.0379129i	$0.987929\pi$
$930$		0			0
$931$			5.50013e13i			0.0786366i
$932$		0			0
$933$	2.42159e14	+	3.23451e14i	0.342524	+	0.457510i
$934$		0			0
$935$		−	3.49269e14i		−	0.488768i
$936$		0			0
$937$	−3.62526e14			−0.501927			−0.250964	−	0.967996i	$-0.580747\pi$
$937$	−3.62526e14			−0.501927			−0.250964	+	0.967996i	$0.580747\pi$
$938$		0			0
$939$	−8.42837e14	+	6.31008e14i	−1.15456	+	0.864385i
$940$		0			0
$941$	1.53175e14			0.207606			0.103803	−	0.994598i	$-0.466899\pi$
$941$	1.53175e14			0.207606			0.103803	+	0.994598i	$0.466899\pi$
$942$		0			0
$943$	−1.57634e14			−0.211393
$944$		0			0
$945$	−3.76333e14	−	1.00851e15i	−0.499359	−	1.33820i
$946$		0			0
$947$	1.07288e15			1.40865			0.704323	−	0.709879i	$-0.251250\pi$
$947$	1.07288e15			1.40865			0.704323	+	0.709879i	$0.251250\pi$
$948$		0			0
$949$			2.75536e14i			0.357971i
$950$		0			0
$951$	−8.16622e14	+	6.11382e14i	−1.04983	+	0.785977i
$952$		0			0
$953$		−	8.08413e14i		−	1.02842i	−0.857665	−	0.514208i	$-0.828086\pi$
$953$		−	8.08413e14i		−	1.02842i	0.857665	−	0.514208i	$-0.171914\pi$
$954$		0			0
$955$		−	9.48852e14i		−	1.19449i
$956$		0			0
$957$	−6.79751e14	+	5.08910e14i	−0.846818	+	0.633989i
$958$		0			0
$959$		−	1.52023e15i		−	1.87420i
$960$		0			0
$961$	2.20807e15			2.69399
$962$		0			0
$963$	−1.29383e14	+	4.40807e14i	−0.156223	+	0.532251i
$964$		0			0
$965$	−8.25837e13			−0.0986865
$966$		0			0
$967$	−1.42743e15			−1.68820			−0.844098	−	0.536189i	$-0.819864\pi$
$967$	−1.42743e15			−1.68820			−0.844098	+	0.536189i	$0.819864\pi$
$968$		0			0
$969$	−5.80823e14	+	4.34846e14i	−0.679869	+	0.508999i
$970$		0			0
$971$	−2.06392e14			−0.239109			−0.119554	−	0.992828i	$-0.538147\pi$
$971$	−2.06392e14			−0.239109			−0.119554	+	0.992828i	$0.538147\pi$
$972$		0			0
$973$			8.15995e14i			0.935672i
$974$		0			0
$975$	3.16583e14	+	4.22859e14i	0.359306	+	0.479924i
$976$		0			0
$977$		−	7.05279e14i		−	0.792297i	−0.918186	−	0.396149i	$-0.870346\pi$
$977$		−	7.05279e14i		−	0.792297i	0.918186	−	0.396149i	$-0.129654\pi$
$978$		0			0
$979$			8.92833e13i			0.0992789i
$980$		0			0
$981$	−1.18669e15	−	3.48309e14i	−1.30615	−	0.383372i
$982$		0			0
$983$			1.33249e15i			1.45176i	0.687821	+	0.725880i	$0.258567\pi$
$983$			1.33249e15i			1.45176i	−0.687821	+	0.725880i	$0.741433\pi$
$984$		0			0
$985$	1.52277e15			1.64231
$986$		0			0
$987$	6.08367e14	+	8.12595e14i	0.649501	+	0.867538i
$988$		0			0
$989$	2.19677e14			0.232169
$990$		0			0
$991$	2.64164e14			0.276379			0.138189	−	0.990406i	$-0.455872\pi$
$991$	2.64164e14			0.276379			0.138189	+	0.990406i	$0.455872\pi$
$992$		0			0
$993$	−2.92420e14	−	3.90585e14i	−0.302873	−	0.404548i
$994$		0			0
$995$	−2.26604e14			−0.232355
$996$		0			0
$997$			2.51365e14i			0.255169i	0.991828	+	0.127585i	$0.0407224\pi$
$997$			2.51365e14i			0.255169i	−0.991828	+	0.127585i	$0.959278\pi$
$998$		0			0
$999$	−6.43529e14	+	2.40138e14i	−0.646756	+	0.241342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.11.h.c.161.18	yes	24
3.2	odd	2	inner	192.11.h.c.161.5	✓	24
4.3	odd	2	inner	192.11.h.c.161.8	yes	24
8.3	odd	2	inner	192.11.h.c.161.17	yes	24
8.5	even	2	inner	192.11.h.c.161.7	yes	24
12.11	even	2	inner	192.11.h.c.161.19	yes	24
24.5	odd	2	inner	192.11.h.c.161.20	yes	24
24.11	even	2	inner	192.11.h.c.161.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.11.h.c.161.5	✓	24	3.2	odd	2	inner
192.11.h.c.161.6	yes	24	24.11	even	2	inner
192.11.h.c.161.7	yes	24	8.5	even	2	inner
192.11.h.c.161.8	yes	24	4.3	odd	2	inner
192.11.h.c.161.17	yes	24	8.3	odd	2	inner
192.11.h.c.161.18	yes	24	1.1	even	1	trivial
192.11.h.c.161.19	yes	24	12.11	even	2	inner
192.11.h.c.161.20	yes	24	24.5	odd	2	inner

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	192.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(194.524 - 145.635i) q^{3} +4363.03 q^{5} +17194.1 q^{7} +(16630.1 - 56658.8i) q^{9} +O(q^{10})\)	\(q+(194.524 - 145.635i) q^{3} +4363.03 q^{5} +17194.1 q^{7} +(16630.1 - 56658.8i) q^{9} -112023. q^{11} +234490. i q^{13} +(848714. - 635408. i) q^{15} +714601. i q^{17} +4.17837e6i q^{19} +(3.34467e6 - 2.50406e6i) q^{21} +2.35471e6i q^{23} +9.27041e6 q^{25} +(-5.01653e6 - 1.34434e7i) q^{27} +3.11938e7 q^{29} +5.50245e7 q^{31} +(-2.17912e7 + 1.63145e7i) q^{33} +7.50186e7 q^{35} -4.78694e7i q^{37} +(3.41498e7 + 4.56139e7i) q^{39} +6.69440e7i q^{41} -9.32927e7i q^{43} +(7.25578e7 - 2.47204e8i) q^{45} +2.42952e8i q^{47} +1.31633e7 q^{49} +(1.04071e8 + 1.39007e8i) q^{51} -3.64746e8 q^{53} -4.88761e8 q^{55} +(6.08516e8 + 8.12794e8i) q^{57} +1.19948e9 q^{59} +1.19879e9i q^{61} +(2.85941e8 - 9.74200e8i) q^{63} +1.02309e9i q^{65} -2.65123e8i q^{67} +(3.42927e8 + 4.58048e8i) q^{69} -1.13781e9i q^{71} +1.17504e9 q^{73} +(1.80332e9 - 1.35009e9i) q^{75} -1.92615e9 q^{77} -4.32571e9 q^{79} +(-2.93366e9 - 1.88449e9i) q^{81} +1.07734e9 q^{83} +3.11783e9i q^{85} +(6.06794e9 - 4.54290e9i) q^{87} -7.97007e8i q^{89} +4.03185e9i q^{91} +(1.07036e10 - 8.01347e9i) q^{93} +1.82304e10i q^{95} +3.54176e9 q^{97} +(-1.86296e9 + 6.34711e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 328392 q^{9}+O(q^{10}) \) 24 * q + 328392 * q^9	\( 24 q + 328392 q^{9} + 47919720 q^{25} - 29516256 q^{33} + 1766081064 q^{49} + 4276148496 q^{57} + 9990750000 q^{73} - 12450970728 q^{81} - 48470791152 q^{97}+O(q^{100}) \) 24 * q + 328392 * q^9 + 47919720 * q^25 - 29516256 * q^33 + 1766081064 * q^49 + 4276148496 * q^57 + 9990750000 * q^73 - 12450970728 * q^81 - 48470791152 * q^97

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