LMFDB - Embedded newform 192.10.f.d.95.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,10,Mod(95,192)]

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([1, 1, 1]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("192.95");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	192.f (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:	$98.8868805435$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			95.4
Character	$\chi$	$=$	192.95
Dual form			192.10.f.d.95.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-133.007 + 44.6342i) q^{3} +1420.93 q^{5} -268.525i q^{7} +(15698.6 - 11873.3i) q^{9} +O(q^{10})$	\(q+(-133.007 + 44.6342i) q^{3} +1420.93 q^{5} -268.525i q^{7} +(15698.6 - 11873.3i) q^{9} -3573.03i q^{11} +24491.6i q^{13} +(-188994. + 63422.1i) q^{15} +461965. i q^{17} -281202. q^{19} +(11985.4 + 35715.7i) q^{21} -81394.6 q^{23} +65923.7 q^{25} +(-1.55806e6 + 2.27992e6i) q^{27} +6.98225e6 q^{29} -3.97331e6i q^{31} +(159479. + 475237. i) q^{33} -381556. i q^{35} -6.19685e6i q^{37} +(-1.09316e6 - 3.25755e6i) q^{39} +1.56632e7i q^{41} -2.58366e7 q^{43} +(2.23066e7 - 1.68711e7i) q^{45} +1.87746e7 q^{47} +4.02815e7 q^{49} +(-2.06194e7 - 6.14444e7i) q^{51} -3.23042e7 q^{53} -5.07703e6i q^{55} +(3.74017e7 - 1.25512e7i) q^{57} -8.09685e7i q^{59} -9.71844e7i q^{61} +(-3.18828e6 - 4.21546e6i) q^{63} +3.48009e7i q^{65} -6.32121e7 q^{67} +(1.08260e7 - 3.63298e6i) q^{69} +2.04533e8 q^{71} +2.16120e7 q^{73} +(-8.76830e6 + 2.94245e6i) q^{75} -959448. q^{77} +1.79225e8i q^{79} +(1.05470e8 - 3.72788e8i) q^{81} +4.03711e8i q^{83} +6.56421e8i q^{85} +(-9.28686e8 + 3.11647e8i) q^{87} +9.79593e8i q^{89} +6.57661e6 q^{91} +(1.77345e8 + 5.28477e8i) q^{93} -3.99569e8 q^{95} +6.36224e8 q^{97} +(-4.24236e7 - 5.60915e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 36864 q^{9}+O(q^{10}) $ 48 * q - 36864 * q^9	$ 48 q - 36864 q^{9} + 16263984 q^{25} - 17348496 q^{33} - 236733840 q^{49} + 22572912 q^{57} + 210002592 q^{73} - 666528336 q^{81} - 5058961536 q^{97}+O(q^{100}) $ 48 * q - 36864 * q^9 + 16263984 * q^25 - 17348496 * q^33 - 236733840 * q^49 + 22572912 * q^57 + 210002592 * q^73 - 666528336 * q^81 - 5058961536 * 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
$3$	−133.007	+	44.6342i	−0.948043	+	0.318143i
$3$	−133.007	+	44.6342i	−0.948043	+	0.318143i
$4$		0			0
$5$	1420.93			1.01674			0.508368	−	0.861140i	$-0.330249\pi$
$5$	1420.93			1.01674			0.508368	+	0.861140i	$0.330249\pi$
$6$		0			0
$7$		−	268.525i		−	0.0422711i	−0.999777	−	0.0211356i	$-0.993272\pi$
$7$		−	268.525i		−	0.0422711i	0.999777	−	0.0211356i	$-0.00672816\pi$
$8$		0			0
$9$	15698.6	−	11873.3i	0.797571	−	0.603226i
$10$		0			0
$11$		−	3573.03i		−	0.0735817i	−0.999323	−	0.0367908i	$-0.988286\pi$
$11$		−	3573.03i		−	0.0735817i	0.999323	−	0.0367908i	$-0.0117135\pi$
$12$		0			0
$13$			24491.6i			0.237833i	0.992904	+	0.118916i	$0.0379421\pi$
$13$			24491.6i			0.237833i	−0.992904	+	0.118916i	$0.962058\pi$
$14$		0			0
$15$	−188994.	+	63422.1i	−0.963910	+	0.323467i
$16$		0			0
$17$			461965.i			1.34149i	0.741686	+	0.670747i	$0.234026\pi$
$17$			461965.i			1.34149i	−0.741686	+	0.670747i	$0.765974\pi$
$18$		0			0
$19$	−281202.			−0.495025			−0.247512	−	0.968885i	$-0.579613\pi$
$19$	−281202.			−0.495025			−0.247512	+	0.968885i	$0.579613\pi$
$20$		0			0
$21$	11985.4	+	35715.7i	0.0134482	+	0.0400748i
$22$		0			0
$23$	−81394.6			−0.0606485			−0.0303243	−	0.999540i	$-0.509654\pi$
$23$	−81394.6			−0.0606485			−0.0303243	+	0.999540i	$0.509654\pi$
$24$		0			0
$25$	65923.7			0.0337529
$26$		0			0
$27$	−1.55806e6	+	2.27992e6i	−0.564219	+	0.825625i
$28$		0			0
$29$	6.98225e6			1.83318			0.916589	−	0.399831i	$-0.130931\pi$
$29$	6.98225e6			1.83318			0.916589	+	0.399831i	$0.130931\pi$
$30$		0			0
$31$		−	3.97331e6i		−	0.772724i	−0.922347	−	0.386362i	$-0.873732\pi$
$31$		−	3.97331e6i		−	0.772724i	0.922347	−	0.386362i	$-0.126268\pi$
$32$		0			0
$33$	159479.	+	475237.i	0.0234095	+	0.0697586i
$34$		0			0
$35$		−	381556.i		−	0.0429786i
$36$		0			0
$37$		−	6.19685e6i		−	0.543580i	−0.962357	−	0.271790i	$-0.912384\pi$
$37$		−	6.19685e6i		−	0.543580i	0.962357	−	0.271790i	$-0.0876156\pi$
$38$		0			0
$39$	−1.09316e6	−	3.25755e6i	−0.0756648	−	0.225476i
$40$		0			0
$41$			1.56632e7i			0.865670i	0.901473	+	0.432835i	$0.142487\pi$
$41$			1.56632e7i			0.865670i	−0.901473	+	0.432835i	$0.857513\pi$
$42$		0			0
$43$	−2.58366e7			−1.15246			−0.576232	−	0.817286i	$-0.695478\pi$
$43$	−2.58366e7			−1.15246			−0.576232	+	0.817286i	$0.695478\pi$
$44$		0			0
$45$	2.23066e7	−	1.68711e7i	0.810919	−	0.613322i
$46$		0			0
$47$	1.87746e7			0.561217			0.280609	−	0.959822i	$-0.409464\pi$
$47$	1.87746e7			0.561217			0.280609	+	0.959822i	$0.409464\pi$
$48$		0			0
$49$	4.02815e7			0.998213
$50$		0			0
$51$	−2.06194e7	−	6.14444e7i	−0.426786	−	1.27179i
$52$		0			0
$53$	−3.23042e7			−0.562364			−0.281182	−	0.959654i	$-0.590727\pi$
$53$	−3.23042e7			−0.562364			−0.281182	+	0.959654i	$0.590727\pi$
$54$		0			0
$55$		−	5.07703e6i		−	0.0748132i
$56$		0			0
$57$	3.74017e7	−	1.25512e7i	0.469305	−	0.157488i
$58$		0			0
$59$		−	8.09685e7i		−	0.869925i	−0.900449	−	0.434963i	$-0.856762\pi$
$59$		−	8.09685e7i		−	0.869925i	0.900449	−	0.434963i	$-0.143238\pi$
$60$		0			0
$61$		−	9.71844e7i		−	0.898695i	−0.893357	−	0.449347i	$-0.851657\pi$
$61$		−	9.71844e7i		−	0.898695i	0.893357	−	0.449347i	$-0.148343\pi$
$62$		0			0
$63$	−3.18828e6	−	4.21546e6i	−0.0254990	−	0.0337142i
$64$		0			0
$65$			3.48009e7i			0.241813i
$66$		0			0
$67$	−6.32121e7			−0.383234			−0.191617	−	0.981470i	$-0.561373\pi$
$67$	−6.32121e7			−0.383234			−0.191617	+	0.981470i	$0.561373\pi$
$68$		0			0
$69$	1.08260e7	−	3.63298e6i	0.0574974	−	0.0192949i
$70$		0			0
$71$	2.04533e8			0.955214			0.477607	−	0.878574i	$-0.341504\pi$
$71$	2.04533e8			0.955214			0.477607	+	0.878574i	$0.341504\pi$
$72$		0			0
$73$	2.16120e7			0.0890721			0.0445361	−	0.999008i	$-0.485819\pi$
$73$	2.16120e7			0.0890721			0.0445361	+	0.999008i	$0.485819\pi$
$74$		0			0
$75$	−8.76830e6	+	2.94245e6i	−0.0319992	+	0.0107383i
$76$		0			0
$77$	−959448.			−0.00311038
$78$		0			0
$79$			1.79225e8i			0.517697i	0.965918	+	0.258849i	$0.0833431\pi$
$79$			1.79225e8i			0.517697i	−0.965918	+	0.258849i	$0.916657\pi$
$80$		0			0
$81$	1.05470e8	−	3.72788e8i	0.272238	−	0.962230i
$82$		0			0
$83$			4.03711e8i			0.933726i	0.884330	+	0.466863i	$0.154616\pi$
$83$			4.03711e8i			0.933726i	−0.884330	+	0.466863i	$0.845384\pi$
$84$		0			0
$85$			6.56421e8i			1.36395i
$86$		0			0
$87$	−9.28686e8	+	3.11647e8i	−1.73793	+	0.583212i
$88$		0			0
$89$			9.79593e8i			1.65497i	0.561486	+	0.827486i	$0.310230\pi$
$89$			9.79593e8i			1.65497i	−0.561486	+	0.827486i	$0.689770\pi$
$90$		0			0
$91$	6.57661e6			0.0100535
$92$		0			0
$93$	1.77345e8	+	5.28477e8i	0.245837	+	0.732576i
$94$		0			0
$95$	−3.99569e8			−0.503310
$96$		0			0
$97$	6.36224e8			0.729688			0.364844	−	0.931069i	$-0.381122\pi$
$97$	6.36224e8			0.729688			0.364844	+	0.931069i	$0.381122\pi$
$98$		0			0
$99$	−4.24236e7	−	5.60915e7i	−0.0443863	−	0.0586866i
$100$		0			0
$101$	−1.04215e9			−0.996512			−0.498256	−	0.867030i	$-0.666026\pi$
$101$	−1.04215e9			−0.996512			−0.498256	+	0.867030i	$0.666026\pi$
$102$		0			0
$103$			1.89027e9i			1.65484i	0.561585	+	0.827419i	$0.310192\pi$
$103$			1.89027e9i			1.65484i	−0.561585	+	0.827419i	$0.689808\pi$
$104$		0			0
$105$	1.70304e7	+	5.07495e7i	0.0136733	+	0.0407456i
$106$		0			0
$107$			1.21466e9i			0.895836i	0.894075	+	0.447918i	$0.147834\pi$
$107$			1.21466e9i			0.895836i	−0.894075	+	0.447918i	$0.852166\pi$
$108$		0			0
$109$			1.60109e9i			1.08642i	0.839598	+	0.543209i	$0.182791\pi$
$109$			1.60109e9i			1.08642i	−0.839598	+	0.543209i	$0.817209\pi$
$110$		0			0
$111$	2.76591e8	+	8.24223e8i	0.172936	+	0.515337i
$112$		0			0
$113$		−	9.41112e8i		−	0.542985i	−0.962440	−	0.271493i	$-0.912483\pi$
$113$		−	9.41112e8i		−	0.542985i	0.962440	−	0.271493i	$-0.0875173\pi$
$114$		0			0
$115$	−1.15656e8			−0.0616635
$116$		0			0
$117$	2.90796e8	+	3.84483e8i	0.143467	+	0.189689i
$118$		0			0
$119$	1.24049e8			0.0567065
$120$		0			0
$121$	2.34518e9			0.994586
$122$		0			0
$123$	−6.99113e8	−	2.08331e9i	−0.275406	−	0.820692i
$124$		0			0
$125$	−2.68159e9			−0.982419
$126$		0			0
$127$			2.07882e9i			0.709086i	0.935040	+	0.354543i	$0.115364\pi$
$127$			2.07882e9i			0.709086i	−0.935040	+	0.354543i	$0.884636\pi$
$128$		0			0
$129$	3.43644e9	−	1.15320e9i	1.09259	−	0.366648i
$130$		0			0
$131$		−	4.49192e9i		−	1.33264i	−0.745668	−	0.666318i	$-0.767869\pi$
$131$		−	4.49192e9i		−	1.33264i	0.745668	−	0.666318i	$-0.232131\pi$
$132$		0			0
$133$			7.55098e7i			0.0209253i
$134$		0			0
$135$	−2.21390e9	+	3.23961e9i	−0.573662	+	0.839443i
$136$		0			0
$137$			5.40471e9i			1.31078i	0.755290	+	0.655390i	$0.227496\pi$
$137$			5.40471e9i			1.31078i	−0.755290	+	0.655390i	$0.772504\pi$
$138$		0			0
$139$	−5.93414e9			−1.34832			−0.674158	−	0.738588i	$-0.735493\pi$
$139$	−5.93414e9			−1.34832			−0.674158	+	0.738588i	$0.735493\pi$
$140$		0			0
$141$	−2.49715e9	+	8.37990e8i	−0.532058	+	0.178547i
$142$		0			0
$143$	8.75092e7			0.0175001
$144$		0			0
$145$	9.92131e9			1.86386
$146$		0			0
$147$	−5.35771e9	+	1.79793e9i	−0.946349	+	0.317574i
$148$		0			0
$149$	6.41930e9			1.06696			0.533481	−	0.845812i	$-0.320883\pi$
$149$	6.41930e9			1.06696			0.533481	+	0.845812i	$0.320883\pi$
$150$		0			0
$151$			1.10558e10i			1.73060i	0.501257	+	0.865298i	$0.332871\pi$
$151$			1.10558e10i			1.73060i	−0.501257	+	0.865298i	$0.667129\pi$
$152$		0			0
$153$	5.48504e9	+	7.25219e9i	0.809224	+	1.06994i
$154$		0			0
$155$		−	5.64580e9i		−	0.785657i
$156$		0			0
$157$			3.83670e9i			0.503976i	0.967730	+	0.251988i	$0.0810843\pi$
$157$			3.83670e9i			0.503976i	−0.967730	+	0.251988i	$0.918916\pi$
$158$		0			0
$159$	4.29668e9	−	1.44187e9i	0.533145	−	0.178912i
$160$		0			0
$161$			2.18565e7i			0.00256368i
$162$		0			0
$163$	−1.08285e10			−1.20150			−0.600750	−	0.799437i	$-0.705131\pi$
$163$	−1.08285e10			−1.20150			−0.600750	+	0.799437i	$0.705131\pi$
$164$		0			0
$165$	2.26609e8	+	6.75280e8i	0.0238013	+	0.0709261i
$166$		0			0
$167$	−1.74232e10			−1.73342			−0.866709	−	0.498815i	$-0.833769\pi$
$167$	−1.74232e10			−1.73342			−0.866709	+	0.498815i	$0.833769\pi$
$168$		0			0
$169$	1.00047e10			0.943435
$170$		0			0
$171$	−4.41447e9	+	3.33879e9i	−0.394817	+	0.298612i
$172$		0			0
$173$	8.57130e9			0.727510			0.363755	−	0.931495i	$-0.381494\pi$
$173$	8.57130e9			0.727510			0.363755	+	0.931495i	$0.381494\pi$
$174$		0			0
$175$		−	1.77022e7i		−	0.00142678i
$176$		0			0
$177$	3.61396e9	+	1.07694e10i	0.276760	+	0.824726i
$178$		0			0
$179$			5.62090e9i			0.409229i	0.978843	+	0.204615i	$0.0655941\pi$
$179$			5.62090e9i			0.409229i	−0.978843	+	0.204615i	$0.934406\pi$
$180$		0			0
$181$			1.25292e10i			0.867704i	0.900984	+	0.433852i	$0.142846\pi$
$181$			1.25292e10i			0.867704i	−0.900984	+	0.433852i	$0.857154\pi$
$182$		0			0
$183$	4.33775e9	+	1.29262e10i	0.285913	+	0.852001i
$184$		0			0
$185$		−	8.80531e9i		−	0.552677i
$186$		0			0
$187$	1.65061e9			0.0987093
$188$		0			0
$189$	6.12216e8	+	4.18379e8i	0.0349001	+	0.0238502i
$190$		0			0
$191$	3.94073e9			0.214253			0.107127	−	0.994245i	$-0.465835\pi$
$191$	3.94073e9			0.214253			0.107127	+	0.994245i	$0.465835\pi$
$192$		0			0
$193$	3.71020e9			0.192482			0.0962408	−	0.995358i	$-0.469318\pi$
$193$	3.71020e9			0.192482			0.0962408	+	0.995358i	$0.469318\pi$
$194$		0			0
$195$	−1.55331e9	−	4.62875e9i	−0.0769312	−	0.229249i
$196$		0			0
$197$	−3.00603e10			−1.42199			−0.710994	−	0.703198i	$-0.751755\pi$
$197$	−3.00603e10			−1.42199			−0.710994	+	0.703198i	$0.751755\pi$
$198$		0			0
$199$			4.00524e10i			1.81046i	0.424920	+	0.905231i	$0.360302\pi$
$199$			4.00524e10i			1.81046i	−0.424920	+	0.905231i	$0.639698\pi$
$200$		0			0
$201$	8.40764e9	−	2.82142e9i	0.363322	−	0.121923i
$202$		0			0
$203$		−	1.87491e9i		−	0.0774905i
$204$		0			0
$205$			2.22563e10i			0.880158i
$206$		0			0
$207$	−1.27778e9	+	9.66421e8i	−0.0483715	+	0.0365847i
$208$		0			0
$209$			1.00474e9i			0.0364247i
$210$		0			0
$211$	2.87701e10			0.999241			0.499620	−	0.866245i	$-0.333473\pi$
$211$	2.87701e10			0.999241			0.499620	+	0.866245i	$0.333473\pi$
$212$		0			0
$213$	−2.72042e10	+	9.12915e9i	−0.905583	+	0.303894i
$214$		0			0
$215$	−3.67121e10			−1.17175
$216$		0			0
$217$	−1.06693e9			−0.0326639
$218$		0			0
$219$	−2.87454e9	+	9.64633e8i	−0.0844442	+	0.0283376i
$220$		0			0
$221$	−1.13143e10			−0.319051
$222$		0			0
$223$		−	1.67543e10i		−	0.453685i	−0.973931	−	0.226843i	$-0.927160\pi$
$223$		−	1.67543e10i		−	0.453685i	0.973931	−	0.226843i	$-0.0728403\pi$
$224$		0			0
$225$	1.03491e9	−	7.82732e8i	0.0269204	−	0.0203606i
$226$		0			0
$227$		−	3.56558e10i		−	0.891280i	−0.895212	−	0.445640i	$-0.852976\pi$
$227$		−	3.56558e10i		−	0.891280i	0.895212	−	0.445640i	$-0.147024\pi$
$228$		0			0
$229$			4.62846e9i			0.111218i	0.998453	+	0.0556092i	$0.0177101\pi$
$229$			4.62846e9i			0.111218i	−0.998453	+	0.0556092i	$0.982290\pi$
$230$		0			0
$231$	1.27613e8	−	4.28242e7i	0.00294877	−	0.000989544i
$232$		0			0
$233$		−	3.23365e10i		−	0.718773i	−0.933189	−	0.359387i	$-0.882986\pi$
$233$		−	3.23365e10i		−	0.718773i	0.933189	−	0.359387i	$-0.117014\pi$
$234$		0			0
$235$	2.66775e10			0.570610
$236$		0			0
$237$	−7.99955e9	−	2.38381e10i	−0.164702	−	0.490799i
$238$		0			0
$239$	7.55498e10			1.49776			0.748881	−	0.662704i	$-0.230591\pi$
$239$	7.55498e10			1.49776			0.748881	+	0.662704i	$0.230591\pi$
$240$		0			0
$241$	−6.31066e10			−1.20503			−0.602515	−	0.798108i	$-0.705835\pi$
$241$	−6.31066e10			−1.20503			−0.602515	+	0.798108i	$0.705835\pi$
$242$		0			0
$243$	2.61079e9	+	5.42909e10i	0.0480335	+	0.998846i
$244$		0			0
$245$	5.72373e10			1.01492
$246$		0			0
$247$		−	6.88708e9i		−	0.117733i
$248$		0			0
$249$	−1.80193e10	−	5.36963e10i	−0.297058	−	0.885213i
$250$		0			0
$251$			9.89862e10i			1.57414i	0.616864	+	0.787070i	$0.288403\pi$
$251$			9.89862e10i			1.57414i	−0.616864	+	0.787070i	$0.711597\pi$
$252$		0			0
$253$			2.90825e8i			0.00446262i
$254$		0			0
$255$	−2.92988e10	−	8.73084e10i	−0.433929	−	1.29308i
$256$		0			0
$257$			9.50770e10i			1.35949i	0.733448	+	0.679746i	$0.237910\pi$
$257$			9.50770e10i			1.35949i	−0.733448	+	0.679746i	$0.762090\pi$
$258$		0			0
$259$	−1.66401e9			−0.0229777
$260$		0			0
$261$	1.09611e11	−	8.29023e10i	1.46209	−	1.10582i
$262$		0			0
$263$	2.96199e10			0.381753			0.190876	−	0.981614i	$-0.438867\pi$
$263$	2.96199e10			0.381753			0.190876	+	0.981614i	$0.438867\pi$
$264$		0			0
$265$	−4.59021e10			−0.571776
$266$		0			0
$267$	−4.37233e10	−	1.30293e11i	−0.526517	−	1.56899i
$268$		0			0
$269$	−1.46725e10			−0.170852			−0.0854258	−	0.996345i	$-0.527225\pi$
$269$	−1.46725e10			−0.170852			−0.0854258	+	0.996345i	$0.527225\pi$
$270$		0			0
$271$		−	1.06295e11i		−	1.19716i	−0.801064	−	0.598579i	$-0.795732\pi$
$271$		−	1.06295e11i		−	1.19716i	0.801064	−	0.598579i	$-0.204268\pi$
$272$		0			0
$273$	−8.74733e8	+	2.93542e8i	−0.00953112	+	0.00319844i
$274$		0			0
$275$		−	2.35547e8i		−	0.00248360i
$276$		0			0
$277$		−	9.50882e10i		−	0.970438i	−0.874393	−	0.485219i	$-0.838740\pi$
$277$		−	9.50882e10i		−	0.970438i	0.874393	−	0.485219i	$-0.161260\pi$
$278$		0			0
$279$	−4.71762e10	−	6.23753e10i	−0.466127	−	0.616302i
$280$		0			0
$281$			1.24976e10i			0.119577i	0.998211	+	0.0597885i	$0.0190426\pi$
$281$			1.24976e10i			0.119577i	−0.998211	+	0.0597885i	$0.980957\pi$
$282$		0			0
$283$	6.97437e10			0.646347			0.323174	−	0.946340i	$-0.395250\pi$
$283$	6.97437e10			0.646347			0.323174	+	0.946340i	$0.395250\pi$
$284$		0			0
$285$	5.31453e10	−	1.78344e10i	0.477159	−	0.160124i
$286$		0			0
$287$	4.20596e9			0.0365928
$288$		0			0
$289$	−9.48236e10			−0.799606
$290$		0			0
$291$	−8.46220e10	+	2.83973e10i	−0.691775	+	0.232145i
$292$		0			0
$293$	2.74028e10			0.217215			0.108608	−	0.994085i	$-0.465361\pi$
$293$	2.74028e10			0.217215			0.108608	+	0.994085i	$0.465361\pi$
$294$		0			0
$295$		−	1.15051e11i		−	0.884484i
$296$		0			0
$297$	8.14623e9	+	5.56700e9i	0.0607509	+	0.0415162i
$298$		0			0
$299$		−	1.99348e9i		−	0.0144242i
$300$		0			0
$301$			6.93778e9i			0.0487160i
$302$		0			0
$303$	1.38612e11	−	4.65153e10i	0.944736	−	0.317033i
$304$		0			0
$305$		−	1.38092e11i		−	0.913736i
$306$		0			0
$307$	1.88040e11			1.20817			0.604085	−	0.796920i	$-0.293539\pi$
$307$	1.88040e11			1.20817			0.604085	+	0.796920i	$0.293539\pi$
$308$		0			0
$309$	−8.43705e10	−	2.51418e11i	−0.526475	−	1.56886i
$310$		0			0
$311$	2.54482e11			1.54254			0.771269	−	0.636510i	$-0.219623\pi$
$311$	2.54482e11			1.54254			0.771269	+	0.636510i	$0.219623\pi$
$312$		0			0
$313$	−2.37470e11			−1.39849			−0.699246	−	0.714882i	$-0.746481\pi$
$313$	−2.37470e11			−1.39849			−0.699246	+	0.714882i	$0.746481\pi$
$314$		0			0
$315$	−4.53033e9	−	5.98989e9i	−0.0259258	−	0.0342785i
$316$		0			0
$317$	−2.96141e10			−0.164714			−0.0823571	−	0.996603i	$-0.526245\pi$
$317$	−2.96141e10			−0.164714			−0.0823571	+	0.996603i	$0.526245\pi$
$318$		0			0
$319$		−	2.49478e10i		−	0.134888i
$320$		0			0
$321$	−5.42155e10	−	1.61558e11i	−0.285004	−	0.849291i
$322$		0			0
$323$		−	1.29905e11i		−	0.664073i
$324$		0			0
$325$			1.61458e9i			0.00802756i
$326$		0			0
$327$	−7.14634e10	−	2.12956e11i	−0.345636	−	1.02997i
$328$		0			0
$329$		−	5.04146e9i		−	0.0237233i
$330$		0			0
$331$	2.98976e11			1.36902			0.684512	−	0.729002i	$-0.260015\pi$
$331$	2.98976e11			1.36902			0.684512	+	0.729002i	$0.260015\pi$
$332$		0			0
$333$	−7.35770e10	−	9.72818e10i	−0.327901	−	0.433543i
$334$		0			0
$335$	−8.98201e10			−0.389648
$336$		0			0
$337$	−1.91583e11			−0.809138			−0.404569	−	0.914507i	$-0.632578\pi$
$337$	−1.91583e11			−0.809138			−0.404569	+	0.914507i	$0.632578\pi$
$338$		0			0
$339$	4.20057e10	+	1.25174e11i	0.172747	+	0.514774i
$340$		0			0
$341$	−1.41967e10			−0.0568583
$342$		0			0
$343$		−	2.16526e10i		−	0.0844667i
$344$		0			0
$345$	1.53830e10	−	5.16222e9i	0.0584597	−	0.0196178i
$346$		0			0
$347$			2.20148e11i			0.815139i	0.913174	+	0.407570i	$0.133624\pi$
$347$			2.20148e11i			0.815139i	−0.913174	+	0.407570i	$0.866376\pi$
$348$		0			0
$349$			4.37568e11i			1.57882i	0.613869	+	0.789408i	$0.289612\pi$
$349$			4.37568e11i			1.57882i	−0.613869	+	0.789408i	$0.710388\pi$
$350$		0			0
$351$	−5.58389e10	−	3.81594e10i	−0.196361	−	0.134190i
$352$		0			0
$353$		−	2.19352e11i		−	0.751893i	−0.926641	−	0.375946i	$-0.877318\pi$
$353$		−	2.19352e11i		−	0.751893i	0.926641	−	0.375946i	$-0.122682\pi$
$354$		0			0
$355$	2.90627e11			0.971200
$356$		0			0
$357$	−1.64994e10	+	5.53683e9i	−0.0537602	+	0.0180407i
$358$		0			0
$359$	−1.33681e11			−0.424761			−0.212380	−	0.977187i	$-0.568122\pi$
$359$	−1.33681e11			−0.424761			−0.212380	+	0.977187i	$0.568122\pi$
$360$		0			0
$361$	−2.43613e11			−0.754950
$362$		0			0
$363$	−3.11925e11	+	1.04675e11i	−0.942910	+	0.316420i
$364$		0			0
$365$	3.07092e10			0.0905629
$366$		0			0
$367$			5.84135e11i			1.68080i	0.541967	+	0.840400i	$0.317680\pi$
$367$			5.84135e11i			1.68080i	−0.541967	+	0.840400i	$0.682320\pi$
$368$		0			0
$369$	1.85973e11	+	2.45890e11i	0.522194	+	0.690433i
$370$		0			0
$371$			8.67449e9i			0.0237718i
$372$		0			0
$373$			2.49616e11i			0.667702i	0.942626	+	0.333851i	$0.108348\pi$
$373$			2.49616e11i			0.667702i	−0.942626	+	0.333851i	$0.891652\pi$
$374$		0			0
$375$	3.56669e11	−	1.19690e11i	0.931375	−	0.312549i
$376$		0			0
$377$			1.71006e11i			0.435990i
$378$		0			0
$379$	1.59310e11			0.396612			0.198306	−	0.980140i	$-0.436456\pi$
$379$	1.59310e11			0.396612			0.198306	+	0.980140i	$0.436456\pi$
$380$		0			0
$381$	−9.27862e10	−	2.76496e11i	−0.225591	−	0.672244i
$382$		0			0
$383$	−7.61511e11			−1.80835			−0.904174	−	0.427165i	$-0.859512\pi$
$383$	−7.61511e11			−1.80835			−0.904174	+	0.427165i	$0.859512\pi$
$384$		0			0
$385$	−1.36331e9			−0.00316244
$386$		0			0
$387$	−4.05598e11	+	3.06766e11i	−0.919172	+	0.695196i
$388$		0			0
$389$	1.79411e11			0.397261			0.198631	−	0.980074i	$-0.436351\pi$
$389$	1.79411e11			0.397261			0.198631	+	0.980074i	$0.436351\pi$
$390$		0			0
$391$		−	3.76014e10i		−	0.0813596i
$392$		0			0
$393$	2.00493e11	+	5.97456e11i	0.423968	+	1.26340i
$394$		0			0
$395$			2.54666e11i			0.526362i
$396$		0			0
$397$			7.85731e11i			1.58751i	0.608238	+	0.793755i	$0.291877\pi$
$397$			7.85731e11i			1.58751i	−0.608238	+	0.793755i	$0.708123\pi$
$398$		0			0
$399$	−3.37032e9	−	1.00433e10i	−0.00665722	−	0.0198380i
$400$		0			0
$401$		−	4.25969e11i		−	0.822675i	−0.911483	−	0.411337i	$-0.865062\pi$
$401$		−	4.25969e11i		−	0.822675i	0.911483	−	0.411337i	$-0.134938\pi$
$402$		0			0
$403$	9.73126e10			0.183779
$404$		0			0
$405$	1.49866e11	−	5.29706e11i	0.276794	−	0.978334i
$406$		0			0
$407$	−2.21415e10			−0.0399975
$408$		0			0
$409$	1.36893e11			0.241894			0.120947	−	0.992659i	$-0.461407\pi$
$409$	1.36893e11			0.241894			0.120947	+	0.992659i	$0.461407\pi$
$410$		0			0
$411$	−2.41235e11	−	7.18863e11i	−0.417015	−	1.24268i
$412$		0			0
$413$	−2.17421e10			−0.0367727
$414$		0			0
$415$			5.73647e11i			0.949354i
$416$		0			0
$417$	7.89281e11	−	2.64866e11i	1.27826	−	0.428957i
$418$		0			0
$419$		−	7.64510e11i		−	1.21177i	−0.795553	−	0.605885i	$-0.792819\pi$
$419$		−	7.64510e11i		−	1.21177i	0.795553	−	0.605885i	$-0.207181\pi$
$420$		0			0
$421$		−	3.32632e11i		−	0.516054i	−0.966138	−	0.258027i	$-0.916928\pi$
$421$		−	3.32632e11i		−	0.516054i	0.966138	−	0.258027i	$-0.0830724\pi$
$422$		0			0
$423$	2.94735e11	−	2.22917e11i	0.447610	−	0.338541i
$424$		0			0
$425$			3.04544e10i			0.0452794i
$426$		0			0
$427$	−2.60965e10			−0.0379888
$428$		0			0
$429$	−1.16393e10	+	3.90590e9i	−0.0165909	+	0.00556754i
$430$		0			0
$431$	9.62398e11			1.34341			0.671703	−	0.740821i	$-0.265563\pi$
$431$	9.62398e11			1.34341			0.671703	+	0.740821i	$0.265563\pi$
$432$		0			0
$433$	4.79018e11			0.654872			0.327436	−	0.944873i	$-0.393815\pi$
$433$	4.79018e11			0.654872			0.327436	+	0.944873i	$0.393815\pi$
$434$		0			0
$435$	−1.31960e12	+	4.42829e11i	−1.76702	+	0.592973i
$436$		0			0
$437$	2.28883e10			0.0300225
$438$		0			0
$439$			7.00834e11i			0.900585i	0.892881	+	0.450293i	$0.148680\pi$
$439$			7.00834e11i			0.900585i	−0.892881	+	0.450293i	$0.851320\pi$
$440$		0			0
$441$	6.32362e11	−	4.78274e11i	0.796145	−	0.602148i
$442$		0			0
$443$		−	5.57637e11i		−	0.687915i	−0.938985	−	0.343958i	$-0.888232\pi$
$443$		−	5.57637e11i		−	0.687915i	0.938985	−	0.343958i	$-0.111768\pi$
$444$		0			0
$445$			1.39194e12i			1.68267i
$446$		0			0
$447$	−8.53810e11	+	2.86520e11i	−1.01153	+	0.339446i
$448$		0			0
$449$			1.49305e12i			1.73367i	0.498598	+	0.866833i	$0.333848\pi$
$449$			1.49305e12i			1.73367i	−0.498598	+	0.866833i	$0.666152\pi$
$450$		0			0
$451$	5.59650e10			0.0636974
$452$		0			0
$453$	−4.93469e11	−	1.47050e12i	−0.550577	−	1.64068i
$454$		0			0
$455$	9.34492e9			0.0102217
$456$		0			0
$457$	1.19837e12			1.28520			0.642599	−	0.766203i	$-0.277856\pi$
$457$	1.19837e12			1.28520			0.642599	+	0.766203i	$0.277856\pi$
$458$		0			0
$459$	−1.05324e12	−	7.19770e11i	−1.10757	−	0.756897i
$460$		0			0
$461$	−6.87549e11			−0.709006			−0.354503	−	0.935055i	$-0.615350\pi$
$461$	−6.87549e11			−0.709006			−0.354503	+	0.935055i	$0.615350\pi$
$462$		0			0
$463$			1.66888e12i			1.68776i	0.536530	+	0.843881i	$0.319735\pi$
$463$			1.66888e12i			1.68776i	−0.536530	+	0.843881i	$0.680265\pi$
$464$		0			0
$465$	2.51996e11	+	7.50930e11i	0.249951	+	0.744836i
$466$		0			0
$467$		−	1.19176e12i		−	1.15948i	−0.814802	−	0.579739i	$-0.803155\pi$
$467$		−	1.19176e12i		−	1.15948i	0.814802	−	0.579739i	$-0.196845\pi$
$468$		0			0
$469$			1.69740e10i			0.0161997i
$470$		0			0
$471$	−1.71248e11	−	5.10307e11i	−0.160336	−	0.477791i
$472$		0			0
$473$			9.23150e10i			0.0848002i
$474$		0			0
$475$	−1.85379e10			−0.0167085
$476$		0			0
$477$	−5.07130e11	+	3.83557e11i	−0.448525	+	0.339233i
$478$		0			0
$479$	−1.25993e12			−1.09354			−0.546770	−	0.837283i	$-0.684143\pi$
$479$	−1.25993e12			−1.09354			−0.546770	+	0.837283i	$0.684143\pi$
$480$		0			0
$481$	1.51771e11			0.129281
$482$		0			0
$483$	−9.75546e8	−	2.90706e9i	−0.000815616	−	0.00243048i
$484$		0			0
$485$	9.04031e11			0.741900
$486$		0			0
$487$			1.09251e12i			0.880126i	0.897967	+	0.440063i	$0.145044\pi$
$487$			1.09251e12i			0.880126i	−0.897967	+	0.440063i	$0.854956\pi$
$488$		0			0
$489$	1.44026e12	−	4.83321e11i	1.13907	−	0.382248i
$490$		0			0
$491$			1.83966e12i			1.42847i	0.699908	+	0.714233i	$0.253224\pi$
$491$			1.83966e12i			1.42847i	−0.699908	+	0.714233i	$0.746776\pi$
$492$		0			0
$493$			3.22555e12i			2.45920i
$494$		0			0
$495$	−6.02811e10	−	7.97022e10i	−0.0451292	−	0.0596688i
$496$		0			0
$497$		−	5.49222e10i		−	0.0403780i
$498$		0			0
$499$	8.01795e11			0.578910			0.289455	−	0.957192i	$-0.406526\pi$
$499$	8.01795e11			0.578910			0.289455	+	0.957192i	$0.406526\pi$
$500$		0			0
$501$	2.31740e12	−	7.77669e11i	1.64335	−	0.551474i
$502$		0			0
$503$	1.79633e11			0.125121			0.0625604	−	0.998041i	$-0.480073\pi$
$503$	1.79633e11			0.125121			0.0625604	+	0.998041i	$0.480073\pi$
$504$		0			0
$505$	−1.48082e12			−1.01319
$506$		0			0
$507$	−1.33069e12	+	4.46550e11i	−0.894417	+	0.300147i
$508$		0			0
$509$	−1.69644e12			−1.12023			−0.560117	−	0.828414i	$-0.689244\pi$
$509$	−1.69644e12			−1.12023			−0.560117	+	0.828414i	$0.689244\pi$
$510$		0			0
$511$		−	5.80336e9i		−	0.00376518i
$512$		0			0
$513$	4.38130e11	−	6.41118e11i	0.279303	−	0.408705i
$514$		0			0
$515$			2.68594e12i			1.68253i
$516$		0			0
$517$		−	6.70823e10i		−	0.0412953i
$518$		0			0
$519$	−1.14004e12	+	3.82573e11i	−0.689711	+	0.231452i
$520$		0			0
$521$			2.95078e11i			0.175456i	0.996144	+	0.0877279i	$0.0279606\pi$
$521$			2.95078e11i			0.175456i	−0.996144	+	0.0877279i	$0.972039\pi$
$522$		0			0
$523$	1.91020e12			1.11640			0.558201	−	0.829706i	$-0.311492\pi$
$523$	1.91020e12			1.11640			0.558201	+	0.829706i	$0.311492\pi$
$524$		0			0
$525$	7.90122e8	+	2.35451e9i	0.000453918	+	0.00135264i
$526$		0			0
$527$	1.83553e12			1.03660
$528$		0			0
$529$	−1.79453e12			−0.996322
$530$		0			0
$531$	−9.61362e11	−	1.27109e12i	−0.524761	−	0.693827i
$532$		0			0
$533$	−3.83616e11			−0.205885
$534$		0			0
$535$			1.72595e12i			0.910829i
$536$		0			0
$537$	−2.50884e11	−	7.47617e11i	−0.130193	−	0.387967i
$538$		0			0
$539$		−	1.43927e11i		−	0.0734502i
$540$		0			0
$541$			2.93106e12i			1.47108i	0.677479	+	0.735542i	$0.263072\pi$
$541$			2.93106e12i			1.47108i	−0.677479	+	0.735542i	$0.736928\pi$
$542$		0			0
$543$	−5.59233e11	−	1.66647e12i	−0.276054	−	0.822620i
$544$		0			0
$545$			2.27504e12i			1.10460i
$546$		0			0
$547$	1.91268e12			0.913482			0.456741	−	0.889600i	$-0.349017\pi$
$547$	1.91268e12			0.913482			0.456741	+	0.889600i	$0.349017\pi$
$548$		0			0
$549$	−1.15390e12	−	1.52566e12i	−0.542116	−	0.716773i
$550$		0			0
$551$	−1.96342e12			−0.907468
$552$		0			0
$553$	4.81263e10			0.0218837
$554$		0			0
$555$	3.93018e11	+	1.17116e12i	0.175830	+	0.523962i
$556$		0			0
$557$	−5.19206e11			−0.228555			−0.114278	−	0.993449i	$-0.536455\pi$
$557$	−5.19206e11			−0.228555			−0.114278	+	0.993449i	$0.536455\pi$
$558$		0			0
$559$		−	6.32780e11i		−	0.274094i
$560$		0			0
$561$	−2.19543e11	+	7.36738e10i	−0.0935807	+	0.0314036i
$562$		0			0
$563$		−	3.41887e11i		−	0.143415i	−0.997426	−	0.0717076i	$-0.977155\pi$
$563$		−	3.41887e11i		−	0.143415i	0.997426	−	0.0717076i	$-0.0228448\pi$
$564$		0			0
$565$		−	1.33726e12i		−	0.552073i
$566$		0			0
$567$	−1.00103e11	−	2.83215e10i	−0.0406746	−	0.0115078i
$568$		0			0
$569$		−	3.73896e12i		−	1.49536i	−0.664060	−	0.747680i	$-0.731168\pi$
$569$		−	3.73896e12i		−	1.49536i	0.664060	−	0.747680i	$-0.268832\pi$
$570$		0			0
$571$	1.76736e12			0.695765			0.347883	−	0.937538i	$-0.386901\pi$
$571$	1.76736e12			0.695765			0.347883	+	0.937538i	$0.386901\pi$
$572$		0			0
$573$	−5.24144e11	+	1.75891e11i	−0.203121	+	0.0681630i
$574$		0			0
$575$	−5.36583e9			−0.00204707
$576$		0			0
$577$	−2.87748e11			−0.108074			−0.0540370	−	0.998539i	$-0.517209\pi$
$577$	−2.87748e11			−0.108074			−0.0540370	+	0.998539i	$0.517209\pi$
$578$		0			0
$579$	−4.93481e11	+	1.65602e11i	−0.182481	+	0.0612366i
$580$		0			0
$581$	1.08407e11			0.0394697
$582$		0			0
$583$			1.15424e11i			0.0413797i
$584$		0			0
$585$	4.13201e11	+	5.46325e11i	0.145868	+	0.192863i
$586$		0			0
$587$		−	5.27974e12i		−	1.83545i	−0.397222	−	0.917723i	$-0.630026\pi$
$587$		−	5.27974e12i		−	1.83545i	0.397222	−	0.917723i	$-0.369974\pi$
$588$		0			0
$589$			1.11730e12i			0.382518i
$590$		0			0
$591$	3.99823e12	−	1.34172e12i	1.34810	−	0.452395i
$592$		0			0
$593$		−	2.78399e12i		−	0.924532i	−0.886741	−	0.462266i	$-0.847037\pi$
$593$		−	2.78399e12i		−	0.924532i	0.886741	−	0.462266i	$-0.152963\pi$
$594$		0			0
$595$	1.76265e11			0.0576555
$596$		0			0
$597$	−1.78770e12	−	5.32724e12i	−0.575985	−	1.71640i
$598$		0			0
$599$	3.55363e12			1.12785			0.563926	−	0.825825i	$-0.309290\pi$
$599$	3.55363e12			1.12785			0.563926	+	0.825825i	$0.309290\pi$
$600$		0			0
$601$	−3.58476e12			−1.12079			−0.560396	−	0.828225i	$-0.689351\pi$
$601$	−3.58476e12			−1.12079			−0.560396	+	0.828225i	$0.689351\pi$
$602$		0			0
$603$	−9.92340e11	+	7.50536e11i	−0.305656	+	0.231176i
$604$		0			0
$605$	3.33234e12			1.01123
$606$		0			0
$607$		−	5.37651e12i		−	1.60750i	−0.594967	−	0.803750i	$-0.702835\pi$
$607$		−	5.37651e12i		−	1.60750i	0.594967	−	0.803750i	$-0.297165\pi$
$608$		0			0
$609$	8.36851e10	+	2.49376e11i	0.0246530	+	0.0734643i
$610$		0			0
$611$			4.59821e11i			0.133476i
$612$		0			0
$613$		−	5.70775e12i		−	1.63265i	−0.577593	−	0.816325i	$-0.696008\pi$
$613$		−	5.70775e12i		−	1.63265i	0.577593	−	0.816325i	$-0.303992\pi$
$614$		0			0
$615$	−9.93392e11	−	2.96024e12i	−0.280016	−	0.834428i
$616$		0			0
$617$			3.67128e12i			1.01985i	0.860220	+	0.509923i	$0.170326\pi$
$617$			3.67128e12i			1.01985i	−0.860220	+	0.509923i	$0.829674\pi$
$618$		0			0
$619$	1.14073e12			0.312303			0.156152	−	0.987733i	$-0.450091\pi$
$619$	1.14073e12			0.312303			0.156152	+	0.987733i	$0.450091\pi$
$620$		0			0
$621$	1.26818e11	−	1.85573e11i	0.0342191	−	0.0500729i
$622$		0			0
$623$	2.63046e11			0.0699576
$624$		0			0
$625$	−3.93911e12			−1.03261
$626$		0			0
$627$	−4.48458e10	−	1.33638e11i	−0.0115883	−	0.0345322i
$628$		0			0
$629$	2.86273e12			0.729209
$630$		0			0
$631$		−	1.70454e12i		−	0.428031i	−0.976830	−	0.214015i	$-0.931346\pi$
$631$		−	1.70454e12i		−	0.428031i	0.976830	−	0.214015i	$-0.0686543\pi$
$632$		0			0
$633$	−3.82661e12	+	1.28413e12i	−0.947323	+	0.317901i
$634$		0			0
$635$			2.95386e12i			0.720954i
$636$		0			0
$637$			9.86558e11i			0.237408i
$638$		0			0
$639$	3.21088e12	−	2.42848e12i	0.761850	−	0.576209i
$640$		0			0
$641$		−	5.72956e12i		−	1.34048i	−0.742145	−	0.670240i	$-0.766191\pi$
$641$		−	5.72956e12i		−	1.34048i	0.742145	−	0.670240i	$-0.233809\pi$
$642$		0			0
$643$	1.09028e12			0.251530			0.125765	−	0.992060i	$-0.459861\pi$
$643$	1.09028e12			0.251530			0.125765	+	0.992060i	$0.459861\pi$
$644$		0			0
$645$	4.88295e12	−	1.63861e12i	1.11087	−	0.372784i
$646$		0			0
$647$	−1.72204e12			−0.386344			−0.193172	−	0.981165i	$-0.561877\pi$
$647$	−1.72204e12			−0.386344			−0.193172	+	0.981165i	$0.561877\pi$
$648$		0			0
$649$	−2.89303e11			−0.0640105
$650$		0			0
$651$	1.41909e11	−	4.76217e10i	0.0309668	−	0.0103918i
$652$		0			0
$653$	−7.33517e11			−0.157870			−0.0789352	−	0.996880i	$-0.525152\pi$
$653$	−7.33517e11			−0.157870			−0.0789352	+	0.996880i	$0.525152\pi$
$654$		0			0
$655$		−	6.38272e12i		−	1.35494i
$656$		0			0
$657$	3.39277e11	−	2.56605e11i	0.0710413	−	0.0537306i
$658$		0			0
$659$		−	1.01680e11i		−	0.0210015i	−0.999945	−	0.0105007i	$-0.996657\pi$
$659$		−	1.01680e11i		−	0.0210015i	0.999945	−	0.0105007i	$-0.00334255\pi$
$660$		0			0
$661$		−	8.16786e12i		−	1.66418i	−0.554637	−	0.832092i	$-0.687143\pi$
$661$		−	8.16786e12i		−	1.66418i	0.554637	−	0.832092i	$-0.312857\pi$
$662$		0			0
$663$	1.50487e12	−	5.05002e11i	0.302474	−	0.101504i
$664$		0			0
$665$			1.07294e11i			0.0212755i
$666$		0			0
$667$	−5.68317e11			−0.111179
$668$		0			0
$669$	7.47815e11	+	2.22844e12i	0.144337	+	0.430113i
$670$		0			0
$671$	−3.47243e11			−0.0661275
$672$		0			0
$673$	−1.94369e11			−0.0365224			−0.0182612	−	0.999833i	$-0.505813\pi$
$673$	−1.94369e11			−0.0365224			−0.0182612	+	0.999833i	$0.505813\pi$
$674$		0			0
$675$	−1.02713e11	+	1.50301e11i	−0.0190441	+	0.0278673i
$676$		0			0
$677$	8.04081e12			1.47113			0.735564	−	0.677455i	$-0.236917\pi$
$677$	8.04081e12			1.47113			0.735564	+	0.677455i	$0.236917\pi$
$678$		0			0
$679$		−	1.70842e11i		−	0.0308447i
$680$		0			0
$681$	1.59147e12	+	4.74247e12i	0.283554	+	0.844972i
$682$		0			0
$683$			3.50991e12i			0.617168i	0.951197	+	0.308584i	$0.0998551\pi$
$683$			3.50991e12i			0.617168i	−0.951197	+	0.308584i	$0.900145\pi$
$684$		0			0
$685$			7.67973e12i			1.33272i
$686$		0			0
$687$	−2.06587e11	−	6.15616e11i	−0.0353833	−	0.105440i
$688$		0			0
$689$		−	7.91182e11i		−	0.133749i
$690$		0			0
$691$	1.07806e12			0.179884			0.0899418	−	0.995947i	$-0.471332\pi$
$691$	1.07806e12			0.179884			0.0899418	+	0.995947i	$0.471332\pi$
$692$		0			0
$693$	−1.50620e10	+	1.13918e10i	−0.00248075	+	0.00187626i
$694$		0			0
$695$	−8.43202e12			−1.37088
$696$		0			0
$697$	−7.23583e12			−1.16129
$698$		0			0
$699$	1.44331e12	+	4.30098e12i	0.228672	+	0.681428i
$700$		0			0
$701$	−1.04283e13			−1.63111			−0.815553	−	0.578683i	$-0.803567\pi$
$701$	−1.04283e13			−1.63111			−0.815553	+	0.578683i	$0.803567\pi$
$702$		0			0
$703$			1.74257e12i			0.269085i
$704$		0			0
$705$	−3.54829e12	+	1.19073e12i	−0.540963	+	0.181535i
$706$		0			0
$707$			2.79842e11i			0.0421237i
$708$		0			0
$709$		−	6.63751e12i		−	0.986500i	−0.869888	−	0.493250i	$-0.835809\pi$
$709$		−	6.63751e12i		−	0.986500i	0.869888	−	0.493250i	$-0.164191\pi$
$710$		0			0
$711$	2.12799e12	+	2.81357e12i	0.312288	+	0.412900i
$712$		0			0
$713$			3.23406e11i			0.0468646i
$714$		0			0
$715$	1.24345e11			0.0177930
$716$		0			0
$717$	−1.00486e13	+	3.37210e12i	−1.41994	+	0.476502i
$718$		0			0
$719$	5.95422e12			0.830893			0.415446	−	0.909618i	$-0.363625\pi$
$719$	5.95422e12			0.830893			0.415446	+	0.909618i	$0.363625\pi$
$720$		0			0
$721$	5.07584e11			0.0699519
$722$		0			0
$723$	8.39360e12	−	2.81671e12i	1.14242	−	0.383371i
$724$		0			0
$725$	4.60296e11			0.0618751
$726$		0			0
$727$			7.95586e11i			0.105629i	0.998604	+	0.0528144i	$0.0168192\pi$
$727$			7.95586e11i			0.105629i	−0.998604	+	0.0528144i	$0.983181\pi$
$728$		0			0
$729$	−2.77048e12	−	7.10452e12i	−0.363313	−	0.931667i
$730$		0			0
$731$		−	1.19356e13i		−	1.54602i
$732$		0			0
$733$			8.17071e12i			1.04542i	0.852510	+	0.522711i	$0.175079\pi$
$733$			8.17071e12i			1.04542i	−0.852510	+	0.522711i	$0.824921\pi$
$734$		0			0
$735$	−7.61294e12	+	2.55474e12i	−0.962187	+	0.322889i
$736$		0			0
$737$			2.25859e11i			0.0281990i
$738$		0			0
$739$	6.08873e11			0.0750977			0.0375489	−	0.999295i	$-0.488045\pi$
$739$	6.08873e11			0.0750977			0.0375489	+	0.999295i	$0.488045\pi$
$740$		0			0
$741$	3.07399e11	+	9.16028e11i	0.0374559	+	0.111616i
$742$		0			0
$743$	9.22856e12			1.11092			0.555462	−	0.831542i	$-0.312542\pi$
$743$	9.22856e12			1.11092			0.555462	+	0.831542i	$0.312542\pi$
$744$		0			0
$745$	9.12139e12			1.08482
$746$		0			0
$747$	4.79338e12	+	6.33770e12i	0.563248	+	0.744713i
$748$		0			0
$749$	3.26167e11			0.0378680
$750$		0			0
$751$			2.92185e12i			0.335180i	0.985857	+	0.167590i	$0.0535985\pi$
$751$			2.92185e12i			0.335180i	−0.985857	+	0.167590i	$0.946401\pi$
$752$		0			0
$753$	−4.41817e12	−	1.31658e13i	−0.500801	−	1.49235i
$754$		0			0
$755$			1.57096e13i			1.75956i
$756$		0			0
$757$		−	6.08897e12i		−	0.673927i	−0.941518	−	0.336963i	$-0.890600\pi$
$757$		−	6.08897e12i		−	0.673927i	0.941518	−	0.336963i	$-0.109400\pi$
$758$		0			0
$759$	−1.29807e10	−	3.86817e10i	−0.00141975	−	0.00423075i
$760$		0			0
$761$		−	1.39307e12i		−	0.150571i	−0.997162	−	0.0752854i	$-0.976013\pi$
$761$		−	1.39307e12i		−	0.150571i	0.997162	−	0.0752854i	$-0.0239868\pi$
$762$		0			0
$763$	4.29933e11			0.0459241
$764$		0			0
$765$	7.79387e12	+	1.03049e13i	0.822767	+	1.08784i
$766$		0			0
$767$	1.98305e12			0.206897
$768$		0			0
$769$	9.51291e12			0.980946			0.490473	−	0.871456i	$-0.336824\pi$
$769$	9.51291e12			0.980946			0.490473	+	0.871456i	$0.336824\pi$
$770$		0			0
$771$	−4.24368e12	−	1.26459e13i	−0.432512	−	1.28886i
$772$		0			0
$773$	−1.35193e13			−1.36190			−0.680952	−	0.732328i	$-0.738434\pi$
$773$	−1.35193e13			−1.36190			−0.680952	+	0.732328i	$0.738434\pi$
$774$		0			0
$775$		−	2.61935e11i		−	0.0260817i
$776$		0			0
$777$	2.21325e11	−	7.42717e10i	0.0217839	−	0.00731020i
$778$		0			0
$779$		−	4.40451e12i		−	0.428528i
$780$		0			0
$781$		−	7.30802e11i		−	0.0702862i
$782$		0			0
$783$	−1.08788e13	+	1.59190e13i	−1.03431	+	1.51352i
$784$		0			0
$785$			5.45170e12i			0.512411i
$786$		0			0
$787$	−8.83515e12			−0.820971			−0.410485	−	0.911867i	$-0.634641\pi$
$787$	−8.83515e12			−0.820971			−0.410485	+	0.911867i	$0.634641\pi$
$788$		0			0
$789$	−3.93964e12	+	1.32206e12i	−0.361918	+	0.121452i
$790$		0			0
$791$	−2.52712e11			−0.0229526
$792$		0			0
$793$	2.38020e12			0.213739
$794$		0			0
$795$	6.10529e12	−	2.04880e12i	0.542068	−	0.181906i
$796$		0			0
$797$	−4.38301e12			−0.384778			−0.192389	−	0.981319i	$-0.561624\pi$
$797$	−4.38301e12			−0.384778			−0.192389	+	0.981319i	$0.561624\pi$
$798$		0			0
$799$			8.67322e12i			0.752870i
$800$		0			0
$801$	1.16310e13	+	1.53782e13i	0.998322	+	1.31996i
$802$		0			0
$803$		−	7.72203e10i		−	0.00655407i
$804$		0			0
$805$			3.10566e10i			0.00260659i
$806$		0			0
$807$	1.95154e12	−	6.54895e11i	0.161975	−	0.0543552i
$808$		0			0
$809$			1.35039e13i			1.10839i	0.832388	+	0.554193i	$0.186973\pi$
$809$			1.35039e13i			1.10839i	−0.832388	+	0.554193i	$0.813027\pi$
$810$		0			0
$811$	−2.07379e13			−1.68334			−0.841669	−	0.539994i	$-0.818426\pi$
$811$	−2.07379e13			−1.68334			−0.841669	+	0.539994i	$0.818426\pi$
$812$		0			0
$813$	4.74439e12	+	1.41380e13i	0.380867	+	1.13496i
$814$		0			0
$815$	−1.53866e13			−1.22161
$816$		0			0
$817$	7.26530e12			0.570498
$818$		0			0
$819$	1.03243e11	−	7.80860e10i	0.00801835	−	0.00606451i
$820$		0			0
$821$	7.28923e12			0.559935			0.279967	−	0.960010i	$-0.409676\pi$
$821$	7.28923e12			0.559935			0.279967	+	0.960010i	$0.409676\pi$
$822$		0			0
$823$		−	1.03353e12i		−	0.0785282i	−0.999229	−	0.0392641i	$-0.987499\pi$
$823$		−	1.03353e12i		−	0.0785282i	0.999229	−	0.0392641i	$-0.0125014\pi$
$824$		0			0
$825$	1.05135e10	+	3.13294e10i	0.000790138	+	0.00235456i
$826$		0			0
$827$			1.15285e12i			0.0857035i	0.999081	+	0.0428518i	$0.0136443\pi$
$827$			1.15285e12i			0.0857035i	−0.999081	+	0.0428518i	$0.986356\pi$
$828$		0			0
$829$		−	7.35505e12i		−	0.540867i	−0.962739	−	0.270433i	$-0.912833\pi$
$829$		−	7.35505e12i		−	0.540867i	0.962739	−	0.270433i	$-0.0871670\pi$
$830$		0			0
$831$	4.24418e12	+	1.26474e13i	0.308738	+	0.920017i
$832$		0			0
$833$			1.86086e13i			1.33910i
$834$		0			0
$835$	−2.47571e13			−1.76243
$836$		0			0
$837$	9.05883e12	+	6.19066e12i	0.637980	+	0.435986i
$838$		0			0
$839$	−5.16976e12			−0.360198			−0.180099	−	0.983648i	$-0.557642\pi$
$839$	−5.16976e12			−0.360198			−0.180099	+	0.983648i	$0.557642\pi$
$840$		0			0
$841$	3.42447e13			2.36054
$842$		0			0
$843$	−5.57819e11	−	1.66226e12i	−0.0380425	−	0.113364i
$844$		0			0
$845$	1.42159e13			0.959225
$846$		0			0
$847$		−	6.29740e11i		−	0.0420423i
$848$		0			0
$849$	−9.27638e12	+	3.11295e12i	−0.612765	+	0.205631i
$850$		0			0
$851$			5.04390e11i			0.0329673i
$852$		0			0
$853$			1.11156e11i			0.00718892i	0.999994	+	0.00359446i	$0.00114415\pi$
$853$			1.11156e11i			0.00718892i	−0.999994	+	0.00359446i	$0.998856\pi$
$854$		0			0
$855$	−6.27266e12	+	4.74420e12i	−0.401425	+	0.303609i
$856$		0			0
$857$		−	2.46140e13i		−	1.55872i	−0.626575	−	0.779361i	$-0.715544\pi$
$857$		−	2.46140e13i		−	1.55872i	0.626575	−	0.779361i	$-0.284456\pi$
$858$		0			0
$859$	−1.94777e13			−1.22059			−0.610294	−	0.792175i	$-0.708949\pi$
$859$	−1.94777e13			−1.22059			−0.610294	+	0.792175i	$0.708949\pi$
$860$		0			0
$861$	−5.59420e11	+	1.87729e11i	−0.0346916	+	0.0116417i
$862$		0			0
$863$	6.09058e12			0.373775			0.186887	−	0.982381i	$-0.440160\pi$
$863$	6.09058e12			0.373775			0.186887	+	0.982381i	$0.440160\pi$
$864$		0			0
$865$	1.21792e13			0.739686
$866$		0			0
$867$	1.26122e13	−	4.23237e12i	0.758061	−	0.254389i
$868$		0			0
$869$	6.40375e11			0.0380930
$870$		0			0
$871$		−	1.54817e12i		−	0.0911456i
$872$		0			0
$873$	9.98781e12	−	7.55407e12i	0.581977	−	0.440166i
$874$		0			0
$875$			7.20073e11i			0.0415279i
$876$		0			0
$877$		−	1.69267e13i		−	0.966217i	−0.875561	−	0.483108i	$-0.839508\pi$
$877$		−	1.69267e13i		−	0.966217i	0.875561	−	0.483108i	$-0.160492\pi$
$878$		0			0
$879$	−3.64475e12	+	1.22310e12i	−0.205929	+	0.0691054i
$880$		0			0
$881$			1.58275e13i			0.885157i	0.896730	+	0.442578i	$0.145936\pi$
$881$			1.58275e13i			0.885157i	−0.896730	+	0.442578i	$0.854064\pi$
$882$		0			0
$883$	−1.32952e12			−0.0735988			−0.0367994	−	0.999323i	$-0.511716\pi$
$883$	−1.32952e12			−0.0735988			−0.0367994	+	0.999323i	$0.511716\pi$
$884$		0			0
$885$	5.13519e12	+	1.53025e13i	0.281392	+	0.838529i
$886$		0			0
$887$	2.75334e13			1.49349			0.746747	−	0.665108i	$-0.231615\pi$
$887$	2.75334e13			1.49349			0.746747	+	0.665108i	$0.231615\pi$
$888$		0			0
$889$	5.58214e11			0.0299739
$890$		0			0
$891$	−1.33198e12	−	3.76849e11i	−0.0708025	−	0.0200317i
$892$		0			0
$893$	−5.27946e12			−0.277816
$894$		0			0
$895$			7.98691e12i			0.416078i
$896$		0			0
$897$	8.89774e10	+	2.65147e11i	0.00458896	+	0.0136748i
$898$		0			0
$899$		−	2.77426e13i		−	1.41654i
$900$		0			0
$901$		−	1.49234e13i		−	0.754408i
$902$		0			0
$903$	−3.09662e11	−	9.22771e11i	−0.0154986	−	0.0461848i
$904$		0			0
$905$			1.78032e13i			0.882226i
$906$		0			0
$907$	−8.44067e12			−0.414137			−0.207068	−	0.978326i	$-0.566392\pi$
$907$	−8.44067e12			−0.414137			−0.207068	+	0.978326i	$0.566392\pi$
$908$		0			0
$909$	−1.63602e13	+	1.23737e13i	−0.794788	+	0.601121i
$910$		0			0
$911$	−3.61367e13			−1.73826			−0.869132	−	0.494579i	$-0.835322\pi$
$911$	−3.61367e13			−1.73826			−0.869132	+	0.494579i	$0.835322\pi$
$912$		0			0
$913$	1.44247e12			0.0687051
$914$		0			0
$915$	6.16364e12	+	1.83672e13i	0.290698	+	0.866261i
$916$		0			0
$917$	−1.20619e12			−0.0563320
$918$		0			0
$919$		−	2.84724e12i		−	0.131675i	−0.997830	−	0.0658376i	$-0.979028\pi$
$919$		−	2.84724e12i		−	0.131675i	0.997830	−	0.0658376i	$-0.0209719\pi$
$920$		0			0
$921$	−2.50106e13	+	8.39302e12i	−1.14540	+	0.384370i
$922$		0			0
$923$			5.00934e12i			0.227181i
$924$		0			0
$925$		−	4.08520e11i		−	0.0183474i
$926$		0			0
$927$	2.24437e13	+	2.96745e13i	0.998241	+	1.31985i
$928$		0			0
$929$		−	3.29567e13i		−	1.45169i	−0.687860	−	0.725843i	$-0.741450\pi$
$929$		−	3.29567e13i		−	1.45169i	0.687860	−	0.725843i	$-0.258550\pi$
$930$		0			0
$931$	−1.13272e13			−0.494140
$932$		0			0
$933$	−3.38478e13	+	1.13586e13i	−1.46239	+	0.490747i
$934$		0			0
$935$	2.34541e12			0.100361
$936$		0			0
$937$	1.79858e13			0.762259			0.381130	−	0.924522i	$-0.375535\pi$
$937$	1.79858e13			0.762259			0.381130	+	0.924522i	$0.375535\pi$
$938$		0			0
$939$	3.15851e13	−	1.05993e13i	1.32583	−	0.444920i
$940$		0			0
$941$	−1.16150e13			−0.482909			−0.241455	−	0.970412i	$-0.577624\pi$
$941$	−1.16150e13			−0.482909			−0.241455	+	0.970412i	$0.577624\pi$
$942$		0			0
$943$		−	1.27490e12i		−	0.0525016i
$944$		0			0
$945$	8.69918e11	+	5.94488e11i	0.0354842	+	0.0242494i
$946$		0			0
$947$		−	2.31541e13i		−	0.935518i	−0.883856	−	0.467759i	$-0.845061\pi$
$947$		−	2.31541e13i		−	0.935518i	0.883856	−	0.467759i	$-0.154939\pi$
$948$		0			0
$949$			5.29312e11i			0.0211843i
$950$		0			0
$951$	3.93887e12	−	1.32180e12i	0.156156	−	0.0524026i
$952$		0			0
$953$		−	2.60494e13i		−	1.02301i	−0.859281	−	0.511504i	$-0.829088\pi$
$953$		−	2.60494e13i		−	1.02301i	0.859281	−	0.511504i	$-0.170912\pi$
$954$		0			0
$955$	5.59952e12			0.217839
$956$		0			0
$957$	1.11352e12	+	3.31822e12i	0.0429137	+	0.127880i
$958$		0			0
$959$	1.45130e12			0.0554082
$960$		0			0
$961$	1.06524e13			0.402897
$962$		0			0
$963$	1.44220e13	+	1.90685e13i	0.540391	+	0.714493i
$964$		0			0
$965$	5.27194e12			0.195703
$966$		0			0
$967$		−	5.38929e12i		−	0.198204i	−0.995077	−	0.0991020i	$-0.968403\pi$
$967$		−	5.38929e12i		−	0.198204i	0.995077	−	0.0991020i	$-0.0315970\pi$
$968$		0			0
$969$	5.79822e12	+	1.72783e13i	0.211270	+	0.629569i
$970$		0			0
$971$		−	2.31422e11i		−	0.00835445i	−0.999991	−	0.00417722i	$-0.998670\pi$
$971$		−	2.31422e11i		−	0.00835445i	0.999991	−	0.00417722i	$-0.00132966\pi$
$972$		0			0
$973$			1.59347e12i			0.0569948i
$974$		0			0
$975$	−7.20653e10	−	2.14750e11i	−0.00255391	−	0.00761047i
$976$		0			0
$977$		−	1.47909e13i		−	0.519361i	−0.965695	−	0.259680i	$-0.916383\pi$
$977$		−	1.47909e13i		−	0.519361i	0.965695	−	0.259680i	$-0.0836172\pi$
$978$		0			0
$979$	3.50012e12			0.121776
$980$		0			0
$981$	1.90102e13	+	2.51349e13i	0.655355	+	0.866495i
$982$		0			0
$983$	−5.01727e13			−1.71387			−0.856933	−	0.515428i	$-0.827633\pi$
$983$	−5.01727e13			−1.71387			−0.856933	+	0.515428i	$0.827633\pi$
$984$		0			0
$985$	−4.27137e13			−1.44579
$986$		0			0
$987$	2.25021e11	+	6.70548e11i	0.00754739	+	0.0224907i
$988$		0			0
$989$	2.10296e12			0.0698952
$990$		0			0
$991$		−	4.14293e13i		−	1.36451i	−0.731114	−	0.682255i	$-0.760999\pi$
$991$		−	4.14293e13i		−	1.36451i	0.731114	−	0.682255i	$-0.239001\pi$
$992$		0			0
$993$	−3.97659e13	+	1.33446e13i	−1.29789	+	0.435545i
$994$		0			0
$995$			5.69117e13i			1.84076i
$996$		0			0
$997$		−	5.50828e12i		−	0.176558i	−0.996096	−	0.0882790i	$-0.971863\pi$
$997$		−	5.50828e12i		−	0.176558i	0.996096	−	0.0882790i	$-0.0281367\pi$
$998$		0			0
$999$	1.41283e13	+	9.65508e12i	0.448793	+	0.306698i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.10.f.d.95.4	yes	48
3.2	odd	2	inner	192.10.f.d.95.1	✓	48
4.3	odd	2	inner	192.10.f.d.95.46	yes	48
8.3	odd	2	inner	192.10.f.d.95.3	yes	48
8.5	even	2	inner	192.10.f.d.95.45	yes	48
12.11	even	2	inner	192.10.f.d.95.47	yes	48
24.5	odd	2	inner	192.10.f.d.95.48	yes	48
24.11	even	2	inner	192.10.f.d.95.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.10.f.d.95.1	✓	48	3.2	odd	2	inner
192.10.f.d.95.2	yes	48	24.11	even	2	inner
192.10.f.d.95.3	yes	48	8.3	odd	2	inner
192.10.f.d.95.4	yes	48	1.1	even	1	trivial
192.10.f.d.95.45	yes	48	8.5	even	2	inner
192.10.f.d.95.46	yes	48	4.3	odd	2	inner
192.10.f.d.95.47	yes	48	12.11	even	2	inner
192.10.f.d.95.48	yes	48	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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	192.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-133.007 + 44.6342i) q^{3} +1420.93 q^{5} -268.525i q^{7} +(15698.6 - 11873.3i) q^{9} +O(q^{10})\)	\(q+(-133.007 + 44.6342i) q^{3} +1420.93 q^{5} -268.525i q^{7} +(15698.6 - 11873.3i) q^{9} -3573.03i q^{11} +24491.6i q^{13} +(-188994. + 63422.1i) q^{15} +461965. i q^{17} -281202. q^{19} +(11985.4 + 35715.7i) q^{21} -81394.6 q^{23} +65923.7 q^{25} +(-1.55806e6 + 2.27992e6i) q^{27} +6.98225e6 q^{29} -3.97331e6i q^{31} +(159479. + 475237. i) q^{33} -381556. i q^{35} -6.19685e6i q^{37} +(-1.09316e6 - 3.25755e6i) q^{39} +1.56632e7i q^{41} -2.58366e7 q^{43} +(2.23066e7 - 1.68711e7i) q^{45} +1.87746e7 q^{47} +4.02815e7 q^{49} +(-2.06194e7 - 6.14444e7i) q^{51} -3.23042e7 q^{53} -5.07703e6i q^{55} +(3.74017e7 - 1.25512e7i) q^{57} -8.09685e7i q^{59} -9.71844e7i q^{61} +(-3.18828e6 - 4.21546e6i) q^{63} +3.48009e7i q^{65} -6.32121e7 q^{67} +(1.08260e7 - 3.63298e6i) q^{69} +2.04533e8 q^{71} +2.16120e7 q^{73} +(-8.76830e6 + 2.94245e6i) q^{75} -959448. q^{77} +1.79225e8i q^{79} +(1.05470e8 - 3.72788e8i) q^{81} +4.03711e8i q^{83} +6.56421e8i q^{85} +(-9.28686e8 + 3.11647e8i) q^{87} +9.79593e8i q^{89} +6.57661e6 q^{91} +(1.77345e8 + 5.28477e8i) q^{93} -3.99569e8 q^{95} +6.36224e8 q^{97} +(-4.24236e7 - 5.60915e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 36864 q^{9}+O(q^{10}) \) 48 * q - 36864 * q^9	\( 48 q - 36864 q^{9} + 16263984 q^{25} - 17348496 q^{33} - 236733840 q^{49} + 22572912 q^{57} + 210002592 q^{73} - 666528336 q^{81} - 5058961536 q^{97}+O(q^{100}) \) 48 * q - 36864 * q^9 + 16263984 * q^25 - 17348496 * q^33 - 236733840 * q^49 + 22572912 * q^57 + 210002592 * q^73 - 666528336 * q^81 - 5058961536 * q^97

Introduction

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