LMFDB - Embedded newform 192.8.f.d.95.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,8,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, 8, names="a")

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

chi := DirichletCharacter("192.95");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 8 $
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:	$59.9779248930$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			95.13
Character	$\chi$	$=$	192.95
Dual form			192.8.f.d.95.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.9724 - 45.2069i) q^{3} -304.295 q^{5} +76.4703i q^{7} +(-1900.32 + 1082.47i) q^{9} +O(q^{10})$	\(q+(-11.9724 - 45.2069i) q^{3} -304.295 q^{5} +76.4703i q^{7} +(-1900.32 + 1082.47i) q^{9} +2835.12i q^{11} +3468.99i q^{13} +(3643.14 + 13756.2i) q^{15} -2157.71i q^{17} +53093.8 q^{19} +(3456.99 - 915.532i) q^{21} -63787.8 q^{23} +14470.6 q^{25} +(71686.4 + 72948.0i) q^{27} +91744.5 q^{29} +108746. i q^{31} +(128167. - 33943.1i) q^{33} -23269.6i q^{35} -459404. i q^{37} +(156822. - 41532.1i) q^{39} +201365. i q^{41} +31114.8 q^{43} +(578260. - 329390. i) q^{45} -1.00453e6 q^{47} +817695. q^{49} +(-97543.3 + 25832.9i) q^{51} -156272. q^{53} -862712. i q^{55} +(-635659. - 2.40021e6i) q^{57} -1.91380e6i q^{59} +2.39030e6i q^{61} +(-82776.7 - 145318. i) q^{63} -1.05560e6i q^{65} -44591.1 q^{67} +(763691. + 2.88365e6i) q^{69} -4.04910e6 q^{71} -3.55097e6 q^{73} +(-173247. - 654169. i) q^{75} -216802. q^{77} -23634.2i q^{79} +(2.43950e6 - 4.11408e6i) q^{81} -5.95079e6i q^{83} +656581. i q^{85} +(-1.09840e6 - 4.14748e6i) q^{87} -1.21029e7i q^{89} -265275. q^{91} +(4.91606e6 - 1.30195e6i) q^{93} -1.61562e7 q^{95} +1.39632e7 q^{97} +(-3.06892e6 - 5.38764e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 15360 q^{9}+O(q^{10}) $ 32 * q - 15360 * q^9	$ 32 q - 15360 q^{9} + 923168 q^{25} - 424800 q^{33} - 6986592 q^{49} - 1707360 q^{57} - 12976960 q^{73} - 57198816 q^{81} - 93958400 q^{97}+O(q^{100}) $ 32 * q - 15360 * q^9 + 923168 * q^25 - 424800 * q^33 - 6986592 * q^49 - 1707360 * q^57 - 12976960 * q^73 - 57198816 * q^81 - 93958400 * 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
$3$	−11.9724	−	45.2069i	−0.256009	−	0.966674i
$3$	−11.9724	−	45.2069i	−0.256009	−	0.966674i
$4$		0			0
$5$	−304.295			−1.08868			−0.544340	−	0.838865i	$-0.683220\pi$
$5$	−304.295			−1.08868			−0.544340	+	0.838865i	$0.683220\pi$
$6$		0			0
$7$			76.4703i			0.0842655i	0.999112	+	0.0421328i	$0.0134152\pi$
$7$			76.4703i			0.0842655i	−0.999112	+	0.0421328i	$0.986585\pi$
$8$		0			0
$9$	−1900.32	+	1082.47i	−0.868918	+	0.494955i
$10$		0			0
$11$			2835.12i			0.642238i	0.947039	+	0.321119i	$0.104059\pi$
$11$			2835.12i			0.642238i	−0.947039	+	0.321119i	$0.895941\pi$
$12$		0			0
$13$			3468.99i			0.437927i	0.975733	+	0.218964i	$0.0702676\pi$
$13$			3468.99i			0.437927i	−0.975733	+	0.218964i	$0.929732\pi$
$14$		0			0
$15$	3643.14	+	13756.2i	0.278712	+	1.05240i
$16$		0			0
$17$		−	2157.71i		−	0.106518i	−0.998581	−	0.0532589i	$-0.983039\pi$
$17$		−	2157.71i		−	0.106518i	0.998581	−	0.0532589i	$-0.0169608\pi$
$18$		0			0
$19$	53093.8			1.77585			0.887925	−	0.459988i	$-0.152146\pi$
$19$	53093.8			1.77585			0.887925	+	0.459988i	$0.152146\pi$
$20$		0			0
$21$	3456.99	−	915.532i	0.0814573	−	0.0215728i
$22$		0			0
$23$	−63787.8			−1.09318			−0.546588	−	0.837402i	$-0.684074\pi$
$23$	−63787.8			−1.09318			−0.546588	+	0.837402i	$0.684074\pi$
$24$		0			0
$25$	14470.6			0.185223
$26$		0			0
$27$	71686.4	+	72948.0i	0.700912	+	0.713248i
$28$		0			0
$29$	91744.5			0.698533			0.349267	−	0.937023i	$-0.386431\pi$
$29$	91744.5			0.698533			0.349267	+	0.937023i	$0.386431\pi$
$30$		0			0
$31$			108746.i			0.655612i	0.944745	+	0.327806i	$0.106309\pi$
$31$			108746.i			0.655612i	−0.944745	+	0.327806i	$0.893691\pi$
$32$		0			0
$33$	128167.	−	33943.1i	0.620835	−	0.164419i
$34$		0			0
$35$		−	23269.6i		−	0.0917381i
$36$		0			0
$37$		−	459404.i		−	1.49104i	−0.666485	−	0.745518i	$-0.732202\pi$
$37$		−	459404.i		−	1.49104i	0.666485	−	0.745518i	$-0.267798\pi$
$38$		0			0
$39$	156822.	−	41532.1i	0.423333	−	0.112113i
$40$		0			0
$41$			201365.i			0.456291i	0.973627	+	0.228145i	$0.0732661\pi$
$41$			201365.i			0.456291i	−0.973627	+	0.228145i	$0.926734\pi$
$42$		0			0
$43$	31114.8			0.0596798			0.0298399	−	0.999555i	$-0.490500\pi$
$43$	31114.8			0.0596798			0.0298399	+	0.999555i	$0.490500\pi$
$44$		0			0
$45$	578260.	−	329390.i	0.945974	−	0.538848i
$46$		0			0
$47$	−1.00453e6			−1.41130			−0.705652	−	0.708559i	$-0.749346\pi$
$47$	−1.00453e6			−1.41130			−0.705652	+	0.708559i	$0.749346\pi$
$48$		0			0
$49$	817695.			0.992899
$50$		0			0
$51$	−97543.3	+	25832.9i	−0.102968	+	0.0272695i
$52$		0			0
$53$	−156272.			−0.144184			−0.0720919	−	0.997398i	$-0.522967\pi$
$53$	−156272.			−0.144184			−0.0720919	+	0.997398i	$0.522967\pi$
$54$		0			0
$55$		−	862712.i		−	0.699192i
$56$		0			0
$57$	−635659.	−	2.40021e6i	−0.454634	−	1.71667i
$58$		0			0
$59$		−	1.91380e6i		−	1.21315i	−0.795025	−	0.606576i	$-0.792543\pi$
$59$		−	1.91380e6i		−	1.21315i	0.795025	−	0.606576i	$-0.207457\pi$
$60$		0			0
$61$			2.39030e6i			1.34833i	0.738579	+	0.674167i	$0.235497\pi$
$61$			2.39030e6i			1.34833i	−0.738579	+	0.674167i	$0.764503\pi$
$62$		0			0
$63$	−82776.7	−	145318.i	−0.0417077	−	0.0732199i
$64$		0			0
$65$		−	1.05560e6i		−	0.476762i
$66$		0			0
$67$	−44591.1			−0.0181128			−0.00905641	−	0.999959i	$-0.502883\pi$
$67$	−44591.1			−0.0181128			−0.00905641	+	0.999959i	$0.502883\pi$
$68$		0			0
$69$	763691.	+	2.88365e6i	0.279863	+	1.05675i
$70$		0			0
$71$	−4.04910e6			−1.34262			−0.671311	−	0.741175i	$-0.734269\pi$
$71$	−4.04910e6			−1.34262			−0.671311	+	0.741175i	$0.734269\pi$
$72$		0			0
$73$	−3.55097e6			−1.06836			−0.534180	−	0.845371i	$-0.679379\pi$
$73$	−3.55097e6			−1.06836			−0.534180	+	0.845371i	$0.679379\pi$
$74$		0			0
$75$	−173247.	−	654169.i	−0.0474189	−	0.179050i
$76$		0			0
$77$	−216802.			−0.0541186
$78$		0			0
$79$		−	23634.2i		−	0.00539319i	−0.999996	−	0.00269660i	$-0.999142\pi$
$79$		−	23634.2i		−	0.00539319i	0.999996	−	0.00269660i	$-0.000858354\pi$
$80$		0			0
$81$	2.43950e6	−	4.11408e6i	0.510038	−	0.860152i
$82$		0			0
$83$		−	5.95079e6i		−	1.14236i	−0.820826	−	0.571178i	$-0.806487\pi$
$83$		−	5.95079e6i		−	1.14236i	0.820826	−	0.571178i	$-0.193513\pi$
$84$		0			0
$85$			656581.i			0.115964i
$86$		0			0
$87$	−1.09840e6	−	4.14748e6i	−0.178831	−	0.675254i
$88$		0			0
$89$		−	1.21029e7i		−	1.81980i	−0.414827	−	0.909900i	$-0.636158\pi$
$89$		−	1.21029e7i		−	1.81980i	0.414827	−	0.909900i	$-0.363842\pi$
$90$		0			0
$91$	−265275.			−0.0369022
$92$		0			0
$93$	4.91606e6	−	1.30195e6i	0.633763	−	0.167843i
$94$		0			0
$95$	−1.61562e7			−1.93333
$96$		0			0
$97$	1.39632e7			1.55340			0.776699	−	0.629872i	$-0.216893\pi$
$97$	1.39632e7			1.55340			0.776699	+	0.629872i	$0.216893\pi$
$98$		0			0
$99$	−3.06892e6	−	5.38764e6i	−0.317879	−	0.558053i
$100$		0			0
$101$	1.79215e7			1.73081			0.865403	−	0.501076i	$-0.167062\pi$
$101$	1.79215e7			1.73081			0.865403	+	0.501076i	$0.167062\pi$
$102$		0			0
$103$		−	1.18445e7i		−	1.06804i	−0.845472	−	0.534020i	$-0.820681\pi$
$103$		−	1.18445e7i		−	1.06804i	0.845472	−	0.534020i	$-0.179319\pi$
$104$		0			0
$105$	−1.05194e6	+	278592.i	−0.0886809	+	0.0234858i
$106$		0			0
$107$		−	6.47225e6i		−	0.510754i	−0.966842	−	0.255377i	$-0.917800\pi$
$107$		−	6.47225e6i		−	0.510754i	0.966842	−	0.255377i	$-0.0821996\pi$
$108$		0			0
$109$		−	1.23036e7i		−	0.909993i	−0.890493	−	0.454997i	$-0.849640\pi$
$109$		−	1.23036e7i		−	0.909993i	0.890493	−	0.454997i	$-0.150360\pi$
$110$		0			0
$111$	−2.07682e7	+	5.50015e6i	−1.44135	+	0.381719i
$112$		0			0
$113$		−	1.85240e7i		−	1.20770i	−0.797096	−	0.603852i	$-0.793632\pi$
$113$		−	1.85240e7i		−	1.20770i	0.797096	−	0.603852i	$-0.206368\pi$
$114$		0			0
$115$	1.94103e7			1.19012
$116$		0			0
$117$	−3.75507e6	−	6.59222e6i	−0.216754	−	0.380523i
$118$		0			0
$119$	165001.			0.00897577
$120$		0			0
$121$	1.14493e7			0.587530
$122$		0			0
$123$	9.10310e6	−	2.41082e6i	0.441084	−	0.116815i
$124$		0			0
$125$	1.93697e7			0.887031
$126$		0			0
$127$			3.70849e7i			1.60651i	0.595634	+	0.803256i	$0.296901\pi$
$127$			3.70849e7i			1.60651i	−0.595634	+	0.803256i	$0.703099\pi$
$128$		0			0
$129$	−372518.	−	1.40660e6i	−0.0152786	−	0.0576909i
$130$		0			0
$131$			2.09242e7i			0.813203i	0.913606	+	0.406601i	$0.133286\pi$
$131$			2.09242e7i			0.813203i	−0.913606	+	0.406601i	$0.866714\pi$
$132$		0			0
$133$			4.06010e6i			0.149643i
$134$		0			0
$135$	−2.18138e7	−	2.21977e7i	−0.763069	−	0.776498i
$136$		0			0
$137$		−	2.47740e7i		−	0.823140i	−0.911378	−	0.411570i	$-0.864981\pi$
$137$		−	2.47740e7i		−	0.823140i	0.911378	−	0.411570i	$-0.135019\pi$
$138$		0			0
$139$	2.04204e7			0.644931			0.322466	−	0.946581i	$-0.395488\pi$
$139$	2.04204e7			0.644931			0.322466	+	0.946581i	$0.395488\pi$
$140$		0			0
$141$	1.20266e7	+	4.54117e7i	0.361307	+	1.36427i
$142$		0			0
$143$	−9.83500e6			−0.281254
$144$		0			0
$145$	−2.79174e7			−0.760479
$146$		0			0
$147$	−9.78976e6	−	3.69655e7i	−0.254192	−	0.959810i
$148$		0			0
$149$	−2.48109e7			−0.614456			−0.307228	−	0.951636i	$-0.599401\pi$
$149$	−2.48109e7			−0.614456			−0.307228	+	0.951636i	$0.599401\pi$
$150$		0			0
$151$		−	3.99781e7i		−	0.944936i	−0.881348	−	0.472468i	$-0.843363\pi$
$151$		−	3.99781e7i		−	0.944936i	0.881348	−	0.472468i	$-0.156637\pi$
$152$		0			0
$153$	2.33565e6	+	4.10035e6i	0.0527215	+	0.0925552i
$154$		0			0
$155$		−	3.30909e7i		−	0.713752i
$156$		0			0
$157$			398897.i			0.00822645i	0.999992	+	0.00411323i	$0.00130928\pi$
$157$			398897.i			0.00822645i	−0.999992	+	0.00411323i	$0.998691\pi$
$158$		0			0
$159$	1.87095e6	+	7.06458e6i	0.0369124	+	0.139379i
$160$		0			0
$161$		−	4.87787e6i		−	0.0921170i
$162$		0			0
$163$	−3.78204e7			−0.684022			−0.342011	−	0.939696i	$-0.611108\pi$
$163$	−3.78204e7			−0.684022			−0.342011	+	0.939696i	$0.611108\pi$
$164$		0			0
$165$	−3.90005e7	+	1.03287e7i	−0.675891	+	0.179000i
$166$		0			0
$167$	6.39693e7			1.06283			0.531415	−	0.847111i	$-0.321660\pi$
$167$	6.39693e7			1.06283			0.531415	+	0.847111i	$0.321660\pi$
$168$		0			0
$169$	5.07146e7			0.808220
$170$		0			0
$171$	−1.00895e8	+	5.74723e7i	−1.54307	+	0.878967i
$172$		0			0
$173$	2.13155e6			0.0312993			0.0156496	−	0.999878i	$-0.495018\pi$
$173$	2.13155e6			0.0312993			0.0156496	+	0.999878i	$0.495018\pi$
$174$		0			0
$175$			1.10657e6i			0.0156079i
$176$		0			0
$177$	−8.65171e7	+	2.29128e7i	−1.17272	+	0.310578i
$178$		0			0
$179$			1.75057e7i			0.228136i	0.993473	+	0.114068i	$0.0363882\pi$
$179$			1.75057e7i			0.228136i	−0.993473	+	0.114068i	$0.963612\pi$
$180$		0			0
$181$		−	7.39249e7i		−	0.926649i	−0.886189	−	0.463325i	$-0.846656\pi$
$181$		−	7.39249e7i		−	0.926649i	0.886189	−	0.463325i	$-0.153344\pi$
$182$		0			0
$183$	1.08058e8	−	2.86175e7i	1.30340	−	0.345186i
$184$		0			0
$185$			1.39794e8i			1.62326i
$186$		0			0
$187$	6.11736e6			0.0684098
$188$		0			0
$189$	−5.57836e6	+	5.48188e6i	−0.0601022	+	0.0590627i
$190$		0			0
$191$	2.42780e7			0.252114			0.126057	−	0.992023i	$-0.459768\pi$
$191$	2.42780e7			0.252114			0.126057	+	0.992023i	$0.459768\pi$
$192$		0			0
$193$	−1.21899e7			−0.122054			−0.0610269	−	0.998136i	$-0.519438\pi$
$193$	−1.21899e7			−0.122054			−0.0610269	+	0.998136i	$0.519438\pi$
$194$		0			0
$195$	−4.77203e7	+	1.26380e7i	−0.460874	+	0.122056i
$196$		0			0
$197$	−1.46040e8			−1.36094			−0.680470	−	0.732776i	$-0.738224\pi$
$197$	−1.46040e8			−1.36094			−0.680470	+	0.732776i	$0.738224\pi$
$198$		0			0
$199$			1.22846e8i			1.10503i	0.833502	+	0.552517i	$0.186333\pi$
$199$			1.22846e8i			1.10503i	−0.833502	+	0.552517i	$0.813667\pi$
$200$		0			0
$201$	533861.	+	2.01582e6i	0.00463706	+	0.0175092i
$202$		0			0
$203$			7.01573e6i			0.0588623i
$204$		0			0
$205$		−	6.12745e7i		−	0.496754i
$206$		0			0
$207$	1.21217e8	−	6.90482e7i	0.949881	−	0.541073i
$208$		0			0
$209$			1.50527e8i			1.14052i
$210$		0			0
$211$	1.86544e8			1.36707			0.683537	−	0.729916i	$-0.260441\pi$
$211$	1.86544e8			1.36707			0.683537	+	0.729916i	$0.260441\pi$
$212$		0			0
$213$	4.84773e7	+	1.83047e8i	0.343724	+	1.29788i
$214$		0			0
$215$	−9.46808e6			−0.0649722
$216$		0			0
$217$	−8.31584e6			−0.0552455
$218$		0			0
$219$	4.25136e7	+	1.60528e8i	0.273510	+	1.03276i
$220$		0			0
$221$	7.48508e6			0.0466470
$222$		0			0
$223$			2.28140e8i			1.37764i	0.724934	+	0.688819i	$0.241870\pi$
$223$			2.28140e8i			1.37764i	−0.724934	+	0.688819i	$0.758130\pi$
$224$		0			0
$225$	−2.74988e7	+	1.56639e7i	−0.160944	+	0.0916772i
$226$		0			0
$227$			3.05420e8i			1.73303i	0.499150	+	0.866516i	$0.333646\pi$
$227$			3.05420e8i			1.73303i	−0.499150	+	0.866516i	$0.666354\pi$
$228$		0			0
$229$		−	2.65227e8i		−	1.45946i	−0.683734	−	0.729731i	$-0.739645\pi$
$229$		−	2.65227e8i		−	1.45946i	0.683734	−	0.729731i	$-0.260355\pi$
$230$		0			0
$231$	2.59564e6	+	9.80095e6i	0.0138549	+	0.0523150i
$232$		0			0
$233$			2.25220e8i			1.16644i	0.812316	+	0.583218i	$0.198207\pi$
$233$			2.25220e8i			1.16644i	−0.812316	+	0.583218i	$0.801793\pi$
$234$		0			0
$235$	3.05674e8			1.53646
$236$		0			0
$237$	−1.06843e6	+	282957.i	−0.00521346	+	0.00138071i
$238$		0			0
$239$	2.48820e8			1.17894			0.589471	−	0.807789i	$-0.299336\pi$
$239$	2.48820e8			1.17894			0.589471	+	0.807789i	$0.299336\pi$
$240$		0			0
$241$	1.68520e8			0.775516			0.387758	−	0.921761i	$-0.373250\pi$
$241$	1.68520e8			0.775516			0.387758	+	0.921761i	$0.373250\pi$
$242$		0			0
$243$	−2.15191e8	−	6.10267e7i	−0.962061	−	0.272834i
$244$		0			0
$245$	−2.48821e8			−1.08095
$246$		0			0
$247$			1.84182e8i			0.777693i
$248$		0			0
$249$	−2.69017e8	+	7.12451e7i	−1.10429	+	0.292454i
$250$		0			0
$251$		−	1.50914e8i		−	0.602380i	−0.953564	−	0.301190i	$-0.902616\pi$
$251$		−	1.50914e8i		−	0.602380i	0.953564	−	0.301190i	$-0.0973838\pi$
$252$		0			0
$253$		−	1.80846e8i		−	0.702080i
$254$		0			0
$255$	2.96820e7	−	7.86083e6i	0.112099	−	0.0296878i
$256$		0			0
$257$			2.75822e8i			1.01359i	0.862066	+	0.506796i	$0.169170\pi$
$257$			2.75822e8i			1.01359i	−0.862066	+	0.506796i	$0.830830\pi$
$258$		0			0
$259$	3.51308e7			0.125643
$260$		0			0
$261$	−1.74344e8	+	9.93105e7i	−0.606968	+	0.345743i
$262$		0			0
$263$	1.21881e8			0.413133			0.206567	−	0.978433i	$-0.433771\pi$
$263$	1.21881e8			0.413133			0.206567	+	0.978433i	$0.433771\pi$
$264$		0			0
$265$	4.75529e7			0.156970
$266$		0			0
$267$	−5.47134e8	+	1.44900e8i	−1.75915	+	0.465886i
$268$		0			0
$269$	4.43702e8			1.38982			0.694910	−	0.719097i	$-0.255444\pi$
$269$	4.43702e8			1.38982			0.694910	+	0.719097i	$0.255444\pi$
$270$		0			0
$271$		−	5.01209e8i		−	1.52977i	−0.644167	−	0.764885i	$-0.722796\pi$
$271$		−	5.01209e8i		−	1.52977i	0.644167	−	0.764885i	$-0.277204\pi$
$272$		0			0
$273$	3.17597e6	+	1.19923e7i	0.00944730	+	0.0356724i
$274$		0			0
$275$			4.10257e7i			0.118957i
$276$		0			0
$277$		−	3.14443e8i		−	0.888921i	−0.895798	−	0.444460i	$-0.853395\pi$
$277$		−	3.14443e8i		−	0.888921i	0.895798	−	0.444460i	$-0.146605\pi$
$278$		0			0
$279$	−1.17714e8	−	2.06653e8i	−0.324499	−	0.569673i
$280$		0			0
$281$		−	7.37476e8i		−	1.98279i	−0.130919	−	0.991393i	$-0.541793\pi$
$281$		−	7.37476e8i		−	1.98279i	0.130919	−	0.991393i	$-0.458207\pi$
$282$		0			0
$283$	−1.27047e8			−0.333206			−0.166603	−	0.986024i	$-0.553280\pi$
$283$	−1.27047e8			−0.333206			−0.166603	+	0.986024i	$0.553280\pi$
$284$		0			0
$285$	1.93428e8	+	7.30371e8i	0.494951	+	1.86890i
$286$		0			0
$287$	−1.53985e7			−0.0384496
$288$		0			0
$289$	4.05683e8			0.988654
$290$		0			0
$291$	−1.67172e8	−	6.31231e8i	−0.397685	−	1.50163i
$292$		0			0
$293$	−4.87722e8			−1.13275			−0.566377	−	0.824146i	$-0.691655\pi$
$293$	−4.87722e8			−1.13275			−0.566377	+	0.824146i	$0.691655\pi$
$294$		0			0
$295$			5.82361e8i			1.32073i
$296$		0			0
$297$	−2.06816e8	+	2.03239e8i	−0.458075	+	0.450153i
$298$		0			0
$299$		−	2.21279e8i		−	0.478731i
$300$		0			0
$301$			2.37936e6i			0.00502895i
$302$		0			0
$303$	−2.14562e8	−	8.10173e8i	−0.443103	−	1.67313i
$304$		0			0
$305$		−	7.27356e8i		−	1.46790i
$306$		0			0
$307$	4.13110e8			0.814857			0.407429	−	0.913237i	$-0.366426\pi$
$307$	4.13110e8			0.814857			0.407429	+	0.913237i	$0.366426\pi$
$308$		0			0
$309$	−5.35454e8	+	1.41807e8i	−1.03245	+	0.273428i
$310$		0			0
$311$	−4.91151e8			−0.925878			−0.462939	−	0.886390i	$-0.653205\pi$
$311$	−4.91151e8			−0.925878			−0.462939	+	0.886390i	$0.653205\pi$
$312$		0			0
$313$	−2.96743e8			−0.546984			−0.273492	−	0.961874i	$-0.588179\pi$
$313$	−2.96743e8			−0.546984			−0.273492	+	0.961874i	$0.588179\pi$
$314$		0			0
$315$	2.51885e7	+	4.42197e7i	0.0454063	+	0.0797130i
$316$		0			0
$317$	1.06348e9			1.87508			0.937541	−	0.347874i	$-0.113096\pi$
$317$	1.06348e9			1.87508			0.937541	+	0.347874i	$0.113096\pi$
$318$		0			0
$319$			2.60106e8i			0.448625i
$320$		0			0
$321$	−2.92590e8	+	7.74882e7i	−0.493733	+	0.130758i
$322$		0			0
$323$		−	1.14561e8i		−	0.189160i
$324$		0			0
$325$			5.01983e7i			0.0811143i
$326$		0			0
$327$	−5.56206e8	+	1.47303e8i	−0.879667	+	0.232967i
$328$		0			0
$329$		−	7.68167e7i		−	0.118924i
$330$		0			0
$331$	8.41622e8			1.27561			0.637807	−	0.770196i	$-0.279842\pi$
$331$	8.41622e8			1.27561			0.637807	+	0.770196i	$0.279842\pi$
$332$		0			0
$333$	4.97290e8	+	8.73016e8i	0.737997	+	1.29559i
$334$		0			0
$335$	1.35689e7			0.0197191
$336$		0			0
$337$	2.99554e8			0.426354			0.213177	−	0.977014i	$-0.431619\pi$
$337$	2.99554e8			0.426354			0.213177	+	0.977014i	$0.431619\pi$
$338$		0			0
$339$	−8.37413e8	+	2.21776e8i	−1.16746	+	0.309184i
$340$		0			0
$341$	−3.08307e8			−0.421059
$342$		0			0
$343$			1.25506e8i			0.167933i
$344$		0			0
$345$	−2.32388e8	−	8.77480e8i	−0.304681	−	1.15046i
$346$		0			0
$347$		−	4.16379e8i		−	0.534978i	−0.963561	−	0.267489i	$-0.913806\pi$
$347$		−	4.16379e8i		−	0.534978i	0.963561	−	0.267489i	$-0.0861939\pi$
$348$		0			0
$349$		−	5.75605e8i		−	0.724829i	−0.932017	−	0.362415i	$-0.881952\pi$
$349$		−	5.75605e8i		−	0.724829i	0.932017	−	0.362415i	$-0.118048\pi$
$350$		0			0
$351$	−2.53056e8	+	2.48680e8i	−0.312351	+	0.306948i
$352$		0			0
$353$		−	9.01332e8i		−	1.09062i	−0.838234	−	0.545310i	$-0.816412\pi$
$353$		−	9.01332e8i		−	1.09062i	0.838234	−	0.545310i	$-0.183588\pi$
$354$		0			0
$355$	1.23212e9			1.46169
$356$		0			0
$357$	−1.97545e6	−	7.45917e6i	−0.00229788	−	0.00867665i
$358$		0			0
$359$	−1.16418e9			−1.32797			−0.663986	−	0.747745i	$-0.731137\pi$
$359$	−1.16418e9			−1.32797			−0.663986	+	0.747745i	$0.731137\pi$
$360$		0			0
$361$	1.92508e9			2.15364
$362$		0			0
$363$	−1.37075e8	−	5.17587e8i	−0.150413	−	0.567950i
$364$		0			0
$365$	1.08054e9			1.16310
$366$		0			0
$367$		−	4.07058e8i		−	0.429859i	−0.976630	−	0.214929i	$-0.931048\pi$
$367$		−	4.07058e8i		−	0.429859i	0.976630	−	0.214929i	$-0.0689521\pi$
$368$		0			0
$369$	−2.17972e8	−	3.82660e8i	−0.225843	−	0.396479i
$370$		0			0
$371$		−	1.19502e7i		−	0.0121497i
$372$		0			0
$373$		−	1.58334e9i		−	1.57977i	−0.613255	−	0.789885i	$-0.710140\pi$
$373$		−	1.58334e9i		−	1.57977i	0.613255	−	0.789885i	$-0.289860\pi$
$374$		0			0
$375$	−2.31902e8	−	8.75646e8i	−0.227088	−	0.857470i
$376$		0			0
$377$			3.18261e8i			0.305907i
$378$		0			0
$379$	4.74568e8			0.447777			0.223888	−	0.974615i	$-0.428125\pi$
$379$	4.74568e8			0.447777			0.223888	+	0.974615i	$0.428125\pi$
$380$		0			0
$381$	1.67649e9	−	4.43994e8i	1.55297	−	0.411282i
$382$		0			0
$383$	−1.67769e9			−1.52587			−0.762933	−	0.646477i	$-0.776242\pi$
$383$	−1.67769e9			−1.52587			−0.762933	+	0.646477i	$0.776242\pi$
$384$		0			0
$385$	6.59719e7			0.0589178
$386$		0			0
$387$	−5.91282e7	+	3.36807e7i	−0.0518569	+	0.0295388i
$388$		0			0
$389$	−1.85128e8			−0.159459			−0.0797296	−	0.996817i	$-0.525406\pi$
$389$	−1.85128e8			−0.159459			−0.0797296	+	0.996817i	$0.525406\pi$
$390$		0			0
$391$			1.37636e8i			0.116443i
$392$		0			0
$393$	9.45917e8	−	2.50512e8i	0.786102	−	0.208188i
$394$		0			0
$395$			7.19177e6i			0.00587146i
$396$		0			0
$397$		−	6.09106e8i		−	0.488569i	−0.969704	−	0.244285i	$-0.921447\pi$
$397$		−	6.09106e8i		−	0.488569i	0.969704	−	0.244285i	$-0.0785531\pi$
$398$		0			0
$399$	1.83545e8	−	4.86091e7i	0.144656	−	0.0383100i
$400$		0			0
$401$			6.95927e8i			0.538962i	0.963006	+	0.269481i	$0.0868522\pi$
$401$			6.95927e8i			0.538962i	−0.963006	+	0.269481i	$0.913148\pi$
$402$		0			0
$403$	−3.77239e8			−0.287110
$404$		0			0
$405$	−7.42327e8	+	1.25189e9i	−0.555268	+	0.936430i
$406$		0			0
$407$	1.30246e9			0.957601
$408$		0			0
$409$	−2.13941e8			−0.154619			−0.0773096	−	0.997007i	$-0.524633\pi$
$409$	−2.13941e8			−0.154619			−0.0773096	+	0.997007i	$0.524633\pi$
$410$		0			0
$411$	−1.11995e9	+	2.96603e8i	−0.795708	+	0.210732i
$412$		0			0
$413$	1.46349e8			0.102227
$414$		0			0
$415$			1.81080e9i			1.24366i
$416$		0			0
$417$	−2.44481e8	−	9.23144e8i	−0.165108	−	0.623438i
$418$		0			0
$419$		−	1.32583e9i		−	0.880518i	−0.897871	−	0.440259i	$-0.854887\pi$
$419$		−	1.32583e9i		−	0.880518i	0.897871	−	0.440259i	$-0.145113\pi$
$420$		0			0
$421$		−	4.54072e8i		−	0.296577i	−0.988944	−	0.148288i	$-0.952624\pi$
$421$		−	4.54072e8i		−	0.296577i	0.988944	−	0.148288i	$-0.0473764\pi$
$422$		0			0
$423$	1.90893e9	−	1.08737e9i	1.22631	−	0.698532i
$424$		0			0
$425$		−	3.12233e7i		−	0.0197295i
$426$		0			0
$427$	−1.82787e8			−0.113618
$428$		0			0
$429$	1.17748e8	+	4.44610e8i	0.0720036	+	0.271881i
$430$		0			0
$431$	−6.80936e8			−0.409672			−0.204836	−	0.978796i	$-0.565666\pi$
$431$	−6.80936e8			−0.409672			−0.204836	+	0.978796i	$0.565666\pi$
$432$		0			0
$433$	−2.26660e9			−1.34173			−0.670867	−	0.741578i	$-0.734078\pi$
$433$	−2.26660e9			−1.34173			−0.670867	+	0.741578i	$0.734078\pi$
$434$		0			0
$435$	3.34238e8	+	1.26206e9i	0.194690	+	0.735135i
$436$		0			0
$437$	−3.38674e9			−1.94132
$438$		0			0
$439$		−	1.23047e9i		−	0.694136i	−0.937840	−	0.347068i	$-0.887177\pi$
$439$		−	1.23047e9i		−	0.694136i	0.937840	−	0.347068i	$-0.112823\pi$
$440$		0			0
$441$	−1.55389e9	+	8.85129e8i	−0.862748	+	0.491441i
$442$		0			0
$443$			7.85208e8i			0.429113i	0.976712	+	0.214556i	$0.0688306\pi$
$443$			7.85208e8i			0.429113i	−0.976712	+	0.214556i	$0.931169\pi$
$444$		0			0
$445$			3.68285e9i			1.98118i
$446$		0			0
$447$	2.97046e8	+	1.12162e9i	0.157307	+	0.593979i
$448$		0			0
$449$			1.64374e9i			0.856980i	0.903547	+	0.428490i	$0.140954\pi$
$449$			1.64374e9i			0.856980i	−0.903547	+	0.428490i	$0.859046\pi$
$450$		0			0
$451$	−5.70894e8			−0.293047
$452$		0			0
$453$	−1.80728e9	+	4.78633e8i	−0.913446	+	0.241913i
$454$		0			0
$455$	8.07220e7			0.0401746
$456$		0			0
$457$	1.19500e9			0.585683			0.292841	−	0.956161i	$-0.405399\pi$
$457$	1.19500e9			0.585683			0.292841	+	0.956161i	$0.405399\pi$
$458$		0			0
$459$	1.57401e8	−	1.54678e8i	0.0759735	−	0.0746595i
$460$		0			0
$461$	2.58763e9			1.23013			0.615063	−	0.788478i	$-0.289131\pi$
$461$	2.58763e9			1.23013			0.615063	+	0.788478i	$0.289131\pi$
$462$		0			0
$463$			5.23534e7i			0.0245139i	0.999925	+	0.0122569i	$0.00390160\pi$
$463$			5.23534e7i			0.0245139i	−0.999925	+	0.0122569i	$0.996098\pi$
$464$		0			0
$465$	−1.49593e9	+	3.96176e8i	−0.689965	+	0.182727i
$466$		0			0
$467$		−	5.58151e8i		−	0.253596i	−0.991929	−	0.126798i	$-0.959530\pi$
$467$		−	5.58151e8i		−	0.253596i	0.991929	−	0.126798i	$-0.0404701\pi$
$468$		0			0
$469$		−	3.40990e6i		−	0.00152629i
$470$		0			0
$471$	1.80329e7	−	4.77575e6i	0.00795230	−	0.00210605i
$472$		0			0
$473$			8.82140e7i			0.0383287i
$474$		0			0
$475$	7.68297e8			0.328929
$476$		0			0
$477$	2.96968e8	−	1.69160e8i	0.125284	−	0.0713646i
$478$		0			0
$479$	4.21879e9			1.75394			0.876968	−	0.480549i	$-0.159563\pi$
$479$	4.21879e9			1.75394			0.876968	+	0.480549i	$0.159563\pi$
$480$		0			0
$481$	1.59367e9			0.652966
$482$		0			0
$483$	−2.20513e8	+	5.83997e7i	−0.0890472	+	0.0235828i
$484$		0			0
$485$	−4.24892e9			−1.69115
$486$		0			0
$487$		−	4.20380e8i		−	0.164927i	−0.996594	−	0.0824634i	$-0.973721\pi$
$487$		−	4.20380e8i		−	0.164927i	0.996594	−	0.0824634i	$-0.0262787\pi$
$488$		0			0
$489$	4.52801e8	+	1.70974e9i	0.175116	+	0.661226i
$490$		0			0
$491$			2.85403e9i			1.08811i	0.839049	+	0.544056i	$0.183112\pi$
$491$			2.85403e9i			1.08811i	−0.839049	+	0.544056i	$0.816888\pi$
$492$		0			0
$493$		−	1.97958e8i		−	0.0744062i
$494$		0			0
$495$	9.33858e8	+	1.63943e9i	0.346069	+	0.607541i
$496$		0			0
$497$		−	3.09636e8i		−	0.113137i
$498$		0			0
$499$	−1.98512e9			−0.715213			−0.357606	−	0.933872i	$-0.616407\pi$
$499$	−1.98512e9			−0.715213			−0.357606	+	0.933872i	$0.616407\pi$
$500$		0			0
$501$	−7.65865e8	−	2.89185e9i	−0.272095	−	1.02741i
$502$		0			0
$503$	4.06401e9			1.42386			0.711930	−	0.702251i	$-0.247822\pi$
$503$	4.06401e9			1.42386			0.711930	+	0.702251i	$0.247822\pi$
$504$		0			0
$505$	−5.45341e9			−1.88429
$506$		0			0
$507$	−6.07174e8	−	2.29265e9i	−0.206912	−	0.781285i
$508$		0			0
$509$	1.43692e9			0.482970			0.241485	−	0.970405i	$-0.422366\pi$
$509$	1.43692e9			0.482970			0.241485	+	0.970405i	$0.422366\pi$
$510$		0			0
$511$		−	2.71544e8i		−	0.0900259i
$512$		0			0
$513$	3.80610e9	+	3.87309e9i	1.24471	+	1.26662i
$514$		0			0
$515$			3.60423e9i			1.16275i
$516$		0			0
$517$		−	2.84796e9i		−	0.906393i
$518$		0			0
$519$	−2.55197e7	−	9.63607e7i	−0.00801291	−	0.0302562i
$520$		0			0
$521$			5.30235e9i			1.64262i	0.570484	+	0.821309i	$0.306756\pi$
$521$			5.30235e9i			1.64262i	−0.570484	+	0.821309i	$0.693244\pi$
$522$		0			0
$523$	−4.36409e9			−1.33395			−0.666973	−	0.745082i	$-0.732410\pi$
$523$	−4.36409e9			−1.33395			−0.666973	+	0.745082i	$0.732410\pi$
$524$		0			0
$525$	5.00245e7	−	1.32483e7i	0.0150878	−	0.00399578i
$526$		0			0
$527$	2.34642e8			0.0698343
$528$		0			0
$529$	6.64055e8			0.195034
$530$		0			0
$531$	2.07163e9	+	3.63685e9i	0.600456	+	1.05413i
$532$		0			0
$533$	−6.98536e8			−0.199822
$534$		0			0
$535$			1.96947e9i			0.556048i
$536$		0			0
$537$	7.91379e8	−	2.09585e8i	0.220534	−	0.0584051i
$538$		0			0
$539$			2.31826e9i			0.637678i
$540$		0			0
$541$		−	3.56612e9i		−	0.968291i	−0.874988	−	0.484145i	$-0.839131\pi$
$541$		−	3.56612e9i		−	0.968291i	0.874988	−	0.484145i	$-0.160869\pi$
$542$		0			0
$543$	−3.34191e9	+	8.85056e8i	−0.895768	+	0.237231i
$544$		0			0
$545$			3.74392e9i			0.990691i
$546$		0			0
$547$	8.15972e8			0.213167			0.106583	−	0.994304i	$-0.466009\pi$
$547$	8.15972e8			0.213167			0.106583	+	0.994304i	$0.466009\pi$
$548$		0			0
$549$	−2.58742e9	−	4.54234e9i	−0.667366	−	1.17159i
$550$		0			0
$551$	4.87107e9			1.24049
$552$		0			0
$553$	1.80731e6			0.000454460
$554$		0			0
$555$	6.31966e9	−	1.67367e9i	1.56916	−	0.415570i
$556$		0			0
$557$	3.50056e9			0.858310			0.429155	−	0.903231i	$-0.358811\pi$
$557$	3.50056e9			0.858310			0.429155	+	0.903231i	$0.358811\pi$
$558$		0			0
$559$			1.07937e8i			0.0261354i
$560$		0			0
$561$	−7.32393e7	−	2.76547e8i	−0.0175135	−	0.0661300i
$562$		0			0
$563$		−	4.19239e9i		−	0.990108i	−0.868862	−	0.495054i	$-0.835148\pi$
$563$		−	4.19239e9i		−	0.990108i	0.868862	−	0.495054i	$-0.164852\pi$
$564$		0			0
$565$			5.63677e9i			1.31480i
$566$		0			0
$567$	3.14605e8	+	1.86549e8i	0.0724811	+	0.0429786i
$568$		0			0
$569$		−	6.73091e9i		−	1.53172i	−0.643005	−	0.765862i	$-0.722312\pi$
$569$		−	6.73091e9i		−	1.53172i	0.643005	−	0.765862i	$-0.277688\pi$
$570$		0			0
$571$	2.93447e9			0.659634			0.329817	−	0.944045i	$-0.393013\pi$
$571$	2.93447e9			0.659634			0.329817	+	0.944045i	$0.393013\pi$
$572$		0			0
$573$	−2.90666e8	−	1.09753e9i	−0.0645435	−	0.243712i
$574$		0			0
$575$	−9.23045e8			−0.202481
$576$		0			0
$577$	2.53372e9			0.549089			0.274544	−	0.961574i	$-0.411473\pi$
$577$	2.53372e9			0.549089			0.274544	+	0.961574i	$0.411473\pi$
$578$		0			0
$579$	1.45943e8	+	5.51070e8i	0.0312469	+	0.117986i
$580$		0			0
$581$	4.55059e8			0.0962612
$582$		0			0
$583$		−	4.43050e8i		−	0.0926004i
$584$		0			0
$585$	1.14265e9	+	2.00598e9i	0.235976	+	0.414268i
$586$		0			0
$587$			6.06882e9i			1.23843i	0.785222	+	0.619215i	$0.212549\pi$
$587$			6.06882e9i			1.23843i	−0.785222	+	0.619215i	$0.787451\pi$
$588$		0			0
$589$			5.77374e9i			1.16427i
$590$		0			0
$591$	1.74844e9	+	6.60200e9i	0.348414	+	1.31559i
$592$		0			0
$593$		−	3.01043e9i		−	0.592840i	−0.955058	−	0.296420i	$-0.904207\pi$
$593$		−	3.01043e9i		−	0.592840i	0.955058	−	0.296420i	$-0.0957927\pi$
$594$		0			0
$595$	−5.02090e7			−0.00977174
$596$		0			0
$597$	5.55349e9	−	1.47076e9i	1.06821	−	0.282899i
$598$		0			0
$599$	−8.96463e9			−1.70427			−0.852135	−	0.523321i	$-0.824693\pi$
$599$	−8.96463e9			−1.70427			−0.852135	+	0.523321i	$0.824693\pi$
$600$		0			0
$601$	−4.88395e9			−0.917721			−0.458861	−	0.888508i	$-0.651742\pi$
$601$	−4.88395e9			−0.917721			−0.458861	+	0.888508i	$0.651742\pi$
$602$		0			0
$603$	8.47375e7	−	4.82684e7i	0.0157386	−	0.00896504i
$604$		0			0
$605$	−3.48396e9			−0.639632
$606$		0			0
$607$		−	9.06856e9i		−	1.64580i	−0.568184	−	0.822902i	$-0.692354\pi$
$607$		−	9.06856e9i		−	1.64580i	0.568184	−	0.822902i	$-0.307646\pi$
$608$		0			0
$609$	3.17159e8	−	8.39950e7i	0.0569006	−	0.0150693i
$610$		0			0
$611$		−	3.48471e9i		−	0.618048i
$612$		0			0
$613$			1.08850e10i			1.90860i	0.298847	+	0.954301i	$0.403398\pi$
$613$			1.08850e10i			1.90860i	−0.298847	+	0.954301i	$0.596602\pi$
$614$		0			0
$615$	−2.77003e9	+	7.33602e8i	−0.480199	+	0.127174i
$616$		0			0
$617$			2.13218e9i			0.365449i	0.983164	+	0.182724i	$0.0584916\pi$
$617$			2.13218e9i			0.365449i	−0.983164	+	0.182724i	$0.941508\pi$
$618$		0			0
$619$	−7.78089e9			−1.31860			−0.659298	−	0.751882i	$-0.729147\pi$
$619$	−7.78089e9			−1.31860			−0.659298	+	0.751882i	$0.729147\pi$
$620$		0			0
$621$	−4.57272e9	−	4.65319e9i	−0.766220	−	0.779705i
$622$		0			0
$623$	9.25511e8			0.153346
$624$		0			0
$625$	−7.02463e9			−1.15092
$626$		0			0
$627$	6.80486e9	−	1.80217e9i	1.10251	−	0.291984i
$628$		0			0
$629$	−9.91260e8			−0.158822
$630$		0			0
$631$			2.07117e9i			0.328180i	0.986445	+	0.164090i	$0.0524688\pi$
$631$			2.07117e9i			0.328180i	−0.986445	+	0.164090i	$0.947531\pi$
$632$		0			0
$633$	−2.23337e9	−	8.43306e9i	−0.349984	−	1.32152i
$634$		0			0
$635$		−	1.12848e10i		−	1.74898i
$636$		0			0
$637$			2.83658e9i			0.434818i
$638$		0			0
$639$	7.69460e9	−	4.38302e9i	1.16663	−	0.664539i
$640$		0			0
$641$		−	6.16049e9i		−	0.923873i	−0.886913	−	0.461937i	$-0.847155\pi$
$641$		−	6.16049e9i		−	0.923873i	0.886913	−	0.461937i	$-0.152845\pi$
$642$		0			0
$643$	−1.10125e10			−1.63361			−0.816806	−	0.576913i	$-0.804257\pi$
$643$	−1.10125e10			−1.63361			−0.816806	+	0.576913i	$0.804257\pi$
$644$		0			0
$645$	1.13355e8	+	4.28022e8i	0.0166335	+	0.0628069i
$646$		0			0
$647$	−7.71145e9			−1.11936			−0.559682	−	0.828708i	$-0.689077\pi$
$647$	−7.71145e9			−1.11936			−0.559682	+	0.828708i	$0.689077\pi$
$648$		0			0
$649$	5.42585e9			0.779133
$650$		0			0
$651$	9.95603e7	+	3.75933e8i	0.0141434	+	0.0534044i
$652$		0			0
$653$	−1.21368e8			−0.0170572			−0.00852861	−	0.999964i	$-0.502715\pi$
$653$	−1.21368e8			−0.0170572			−0.00852861	+	0.999964i	$0.502715\pi$
$654$		0			0
$655$		−	6.36713e9i		−	0.885317i
$656$		0			0
$657$	6.74800e9	−	3.84381e9i	0.928317	−	0.528790i
$658$		0			0
$659$		−	2.70059e9i		−	0.367586i	−0.982965	−	0.183793i	$-0.941162\pi$
$659$		−	2.70059e9i		−	0.367586i	0.982965	−	0.183793i	$-0.0588376\pi$
$660$		0			0
$661$		−	4.44602e9i		−	0.598778i	−0.954131	−	0.299389i	$-0.903217\pi$
$661$		−	4.44602e9i		−	0.598778i	0.954131	−	0.299389i	$-0.0967829\pi$
$662$		0			0
$663$	−8.96142e7	−	3.38377e8i	−0.0119421	−	0.0450925i
$664$		0			0
$665$		−	1.23547e9i		−	0.162913i
$666$		0			0
$667$	−5.85218e9			−0.763620
$668$		0			0
$669$	1.03135e10	−	2.73138e9i	1.33173	−	0.352688i
$670$		0			0
$671$	−6.77677e9			−0.865952
$672$		0			0
$673$	−5.27001e9			−0.666436			−0.333218	−	0.942850i	$-0.608135\pi$
$673$	−5.27001e9			−0.666436			−0.333218	+	0.942850i	$0.608135\pi$
$674$		0			0
$675$	1.03734e9	+	1.05560e9i	0.129825	+	0.132110i
$676$		0			0
$677$	1.29659e10			1.60599			0.802993	−	0.595988i	$-0.203240\pi$
$677$	1.29659e10			1.60599			0.802993	+	0.595988i	$0.203240\pi$
$678$		0			0
$679$			1.06777e9i			0.130898i
$680$		0			0
$681$	1.38071e10	−	3.65660e9i	1.67528	−	0.443672i
$682$		0			0
$683$		−	7.80300e9i		−	0.937107i	−0.883435	−	0.468553i	$-0.844775\pi$
$683$		−	7.80300e9i		−	0.937107i	0.883435	−	0.468553i	$-0.155225\pi$
$684$		0			0
$685$			7.53860e9i			0.896135i
$686$		0			0
$687$	−1.19901e10	+	3.17539e9i	−1.41082	+	0.373636i
$688$		0			0
$689$		−	5.42108e8i		−	0.0631420i
$690$		0			0
$691$	−2.04910e9			−0.236260			−0.118130	−	0.992998i	$-0.537690\pi$
$691$	−2.04910e9			−0.236260			−0.118130	+	0.992998i	$0.537690\pi$
$692$		0			0
$693$	4.11995e8	−	2.34681e8i	0.0470246	−	0.0267863i
$694$		0			0
$695$	−6.21384e9			−0.702123
$696$		0			0
$697$	4.34488e8			0.0486030
$698$		0			0
$699$	1.01815e10	−	2.69642e9i	1.12756	−	0.298619i
$700$		0			0
$701$	−5.56296e9			−0.609948			−0.304974	−	0.952361i	$-0.598648\pi$
$701$	−5.56296e9			−0.609948			−0.304974	+	0.952361i	$0.598648\pi$
$702$		0			0
$703$		−	2.43915e10i		−	2.64786i
$704$		0			0
$705$	−3.65964e9	−	1.38186e10i	−0.393348	−	1.48525i
$706$		0			0
$707$			1.37046e9i			0.145847i
$708$		0			0
$709$		−	1.99480e9i		−	0.210202i	−0.994462	−	0.105101i	$-0.966483\pi$
$709$		−	1.99480e9i		−	0.210202i	0.994462	−	0.105101i	$-0.0335166\pi$
$710$		0			0
$711$	2.55833e7	+	4.49126e7i	0.00266939	+	0.00468624i
$712$		0			0
$713$		−	6.93666e9i		−	0.716699i
$714$		0			0
$715$	2.99274e9			0.306195
$716$		0			0
$717$	−2.97897e9	−	1.12484e10i	−0.301821	−	1.13965i
$718$		0			0
$719$	−5.83315e9			−0.585264			−0.292632	−	0.956225i	$-0.594531\pi$
$719$	−5.83315e9			−0.585264			−0.292632	+	0.956225i	$0.594531\pi$
$720$		0			0
$721$	9.05755e8			0.0899989
$722$		0			0
$723$	−2.01758e9	−	7.61825e9i	−0.198539	−	0.749671i
$724$		0			0
$725$	1.32759e9			0.129385
$726$		0			0
$727$			1.55291e10i			1.49891i	0.662057	+	0.749453i	$0.269684\pi$
$727$			1.55291e10i			1.49891i	−0.662057	+	0.749453i	$0.730316\pi$
$728$		0			0
$729$	−1.82477e8	+	1.04588e10i	−0.0174447	+	0.999848i
$730$		0			0
$731$		−	6.71367e7i		−	0.00635695i
$732$		0			0
$733$			9.38052e9i			0.879758i	0.898057	+	0.439879i	$0.144979\pi$
$733$			9.38052e9i			0.879758i	−0.898057	+	0.439879i	$0.855021\pi$
$734$		0			0
$735$	2.97898e9	+	1.12484e10i	0.276733	+	1.04493i
$736$		0			0
$737$		−	1.26421e8i		−	0.0116328i
$738$		0			0
$739$	1.06129e10			0.967340			0.483670	−	0.875250i	$-0.339303\pi$
$739$	1.06129e10			0.967340			0.483670	+	0.875250i	$0.339303\pi$
$740$		0			0
$741$	8.32630e9	−	2.20510e9i	0.751776	−	0.199097i
$742$		0			0
$743$	−5.75220e8			−0.0514485			−0.0257243	−	0.999669i	$-0.508189\pi$
$743$	−5.75220e8			−0.0514485			−0.0257243	+	0.999669i	$0.508189\pi$
$744$		0			0
$745$	7.54984e9			0.668946
$746$		0			0
$747$	6.44154e9	+	1.13084e10i	0.565415	+	0.992614i
$748$		0			0
$749$	4.94935e8			0.0430390
$750$		0			0
$751$			6.31510e9i			0.544052i	0.962290	+	0.272026i	$0.0876937\pi$
$751$			6.31510e9i			0.544052i	−0.962290	+	0.272026i	$0.912306\pi$
$752$		0			0
$753$	−6.82233e9	+	1.80679e9i	−0.582305	+	0.154215i
$754$		0			0
$755$			1.21651e10i			1.02873i
$756$		0			0
$757$			7.30865e9i			0.612353i	0.951975	+	0.306176i	$0.0990498\pi$
$757$			7.30865e9i			0.612353i	−0.951975	+	0.306176i	$0.900950\pi$
$758$		0			0
$759$	−8.17547e9	+	2.16515e9i	−0.678682	+	0.179739i
$760$		0			0
$761$			2.14732e8i			0.0176624i	0.999961	+	0.00883121i	$0.00281110\pi$
$761$			2.14732e8i			0.0176624i	−0.999961	+	0.00883121i	$0.997189\pi$
$762$		0			0
$763$	9.40858e8			0.0766811
$764$		0			0
$765$	−7.10727e8	−	1.24772e9i	−0.0573968	−	0.100763i
$766$		0			0
$767$	6.63897e9			0.531272
$768$		0			0
$769$	−2.71075e9			−0.214955			−0.107477	−	0.994208i	$-0.534277\pi$
$769$	−2.71075e9			−0.214955			−0.107477	+	0.994208i	$0.534277\pi$
$770$		0			0
$771$	1.24690e10	−	3.30224e9i	0.979812	−	0.259489i
$772$		0			0
$773$	1.57027e10			1.22277			0.611386	−	0.791333i	$-0.290612\pi$
$773$	1.57027e10			1.22277			0.611386	+	0.791333i	$0.290612\pi$
$774$		0			0
$775$			1.57361e9i			0.121435i
$776$		0			0
$777$	−4.20599e8	−	1.58815e9i	−0.0321658	−	0.121456i
$778$		0			0
$779$			1.06913e10i			0.810304i
$780$		0			0
$781$		−	1.14797e10i		−	0.862284i
$782$		0			0
$783$	6.57683e9	+	6.69258e9i	0.489610	+	0.498227i
$784$		0			0
$785$		−	1.21383e8i		−	0.00895597i
$786$		0			0
$787$	−1.33127e9			−0.0973540			−0.0486770	−	0.998815i	$-0.515500\pi$
$787$	−1.33127e9			−0.0973540			−0.0486770	+	0.998815i	$0.515500\pi$
$788$		0			0
$789$	−1.45920e9	−	5.50985e9i	−0.105766	−	0.399365i
$790$		0			0
$791$	1.41654e9			0.101768
$792$		0			0
$793$	−8.29193e9			−0.590472
$794$		0			0
$795$	−5.69321e8	−	2.14972e9i	−0.0401858	−	0.151739i
$796$		0			0
$797$	−2.10097e10			−1.46999			−0.734996	−	0.678071i	$-0.762816\pi$
$797$	−2.10097e10			−1.46999			−0.734996	+	0.678071i	$0.762816\pi$
$798$		0			0
$799$			2.16748e9i			0.150329i
$800$		0			0
$801$	1.31010e10	+	2.29994e10i	0.900720	+	1.58126i
$802$		0			0
$803$		−	1.00674e10i		−	0.686142i
$804$		0			0
$805$			1.48431e9i			0.100286i
$806$		0			0
$807$	−5.31217e9	−	2.00584e10i	−0.355807	−	1.34350i
$808$		0			0
$809$		−	2.69839e9i		−	0.179178i	−0.995979	−	0.0895892i	$-0.971445\pi$
$809$		−	2.69839e9i		−	0.179178i	0.995979	−	0.0895892i	$-0.0285554\pi$
$810$		0			0
$811$	−1.20210e9			−0.0791349			−0.0395675	−	0.999217i	$-0.512598\pi$
$811$	−1.20210e9			−0.0791349			−0.0395675	+	0.999217i	$0.512598\pi$
$812$		0			0
$813$	−2.26581e10	+	6.00066e9i	−1.47879	+	0.391636i
$814$		0			0
$815$	1.15086e10			0.744681
$816$		0			0
$817$	1.65200e9			0.105982
$818$		0			0
$819$	5.04109e8	−	2.87152e8i	0.0320650	−	0.0182649i
$820$		0			0
$821$	2.22684e10			1.40439			0.702196	−	0.711984i	$-0.252203\pi$
$821$	2.22684e10			1.40439			0.702196	+	0.711984i	$0.252203\pi$
$822$		0			0
$823$		−	6.35480e9i		−	0.397377i	−0.980063	−	0.198688i	$-0.936332\pi$
$823$		−	6.35480e9i		−	0.397377i	0.980063	−	0.198688i	$-0.0636682\pi$
$824$		0			0
$825$	1.85464e9	−	4.91175e8i	0.114993	−	0.0304542i
$826$		0			0
$827$		−	1.18453e10i		−	0.728245i	−0.931351	−	0.364123i	$-0.881369\pi$
$827$		−	1.18453e10i		−	0.728245i	0.931351	−	0.364123i	$-0.118631\pi$
$828$		0			0
$829$		−	1.59259e10i		−	0.970873i	−0.874272	−	0.485436i	$-0.838661\pi$
$829$		−	1.59259e10i		−	0.970873i	0.874272	−	0.485436i	$-0.161339\pi$
$830$		0			0
$831$	−1.42150e10	+	3.76463e9i	−0.859297	+	0.227572i
$832$		0			0
$833$		−	1.76435e9i		−	0.105761i
$834$		0			0
$835$	−1.94656e10			−1.15708
$836$		0			0
$837$	−7.93280e9	+	7.79560e9i	−0.467614	+	0.459526i
$838$		0			0
$839$	2.26573e10			1.32447			0.662234	−	0.749297i	$-0.269609\pi$
$839$	2.26573e10			1.32447			0.662234	+	0.749297i	$0.269609\pi$
$840$		0			0
$841$	−8.83282e9			−0.512051
$842$		0			0
$843$	−3.33390e10	+	8.82934e9i	−1.91671	+	0.507612i
$844$		0			0
$845$	−1.54322e10			−0.879892
$846$		0			0
$847$			8.75531e8i			0.0495085i
$848$		0			0
$849$	1.52106e9	+	5.74341e9i	0.0853038	+	0.322101i
$850$		0			0
$851$			2.93043e10i			1.62997i
$852$		0			0
$853$			2.25662e10i			1.24491i	0.782658	+	0.622453i	$0.213864\pi$
$853$			2.25662e10i			1.24491i	−0.782658	+	0.622453i	$0.786136\pi$
$854$		0			0
$855$	3.07020e10	−	1.74886e10i	1.67991	−	0.956913i
$856$		0			0
$857$			1.60123e10i			0.869002i	0.900671	+	0.434501i	$0.143075\pi$
$857$			1.60123e10i			0.869002i	−0.900671	+	0.434501i	$0.856925\pi$
$858$		0			0
$859$	−1.04261e10			−0.561234			−0.280617	−	0.959820i	$-0.590539\pi$
$859$	−1.04261e10			−0.561234			−0.280617	+	0.959820i	$0.590539\pi$
$860$		0			0
$861$	1.84356e8	+	6.96117e8i	0.00984345	+	0.0371682i
$862$		0			0
$863$	1.17098e10			0.620169			0.310085	−	0.950709i	$-0.399643\pi$
$863$	1.17098e10			0.620169			0.310085	+	0.950709i	$0.399643\pi$
$864$		0			0
$865$	−6.48621e8			−0.0340749
$866$		0			0
$867$	−4.85699e9	−	1.83397e10i	−0.253105	−	0.955706i
$868$		0			0
$869$	6.70057e7			0.00346372
$870$		0			0
$871$		−	1.54686e8i		−	0.00793210i
$872$		0			0
$873$	−2.65345e10	+	1.51147e10i	−1.34978	+	0.768863i
$874$		0			0
$875$			1.48121e9i			0.0747461i
$876$		0			0
$877$		−	1.81153e10i		−	0.906875i	−0.891288	−	0.453438i	$-0.850197\pi$
$877$		−	1.81153e10i		−	0.906875i	0.891288	−	0.453438i	$-0.149803\pi$
$878$		0			0
$879$	5.83919e9	+	2.20484e10i	0.289996	+	1.09500i
$880$		0			0
$881$			1.03436e10i			0.509630i	0.966990	+	0.254815i	$0.0820146\pi$
$881$			1.03436e10i			0.509630i	−0.966990	+	0.254815i	$0.917985\pi$
$882$		0			0
$883$	−1.27014e10			−0.620854			−0.310427	−	0.950597i	$-0.600472\pi$
$883$	−1.27014e10			−0.620854			−0.310427	+	0.950597i	$0.600472\pi$
$884$		0			0
$885$	2.63267e10	−	6.97225e9i	1.27672	−	0.338120i
$886$		0			0
$887$	3.53098e10			1.69888			0.849439	−	0.527687i	$-0.176941\pi$
$887$	3.53098e10			1.69888			0.849439	+	0.527687i	$0.176941\pi$
$888$		0			0
$889$	−2.83589e9			−0.135374
$890$		0			0
$891$	1.16639e10	+	6.91625e9i	0.552423	+	0.327566i
$892$		0			0
$893$	−5.33343e10			−2.50626
$894$		0			0
$895$		−	5.32691e9i		−	0.248367i
$896$		0			0
$897$	−1.00034e10	+	2.64924e9i	−0.462777	+	0.122560i
$898$		0			0
$899$			9.97684e9i			0.457967i
$900$		0			0
$901$			3.37190e8i			0.0153581i
$902$		0			0
$903$	1.07563e8	−	2.84866e7i	0.00486135	−	0.00128746i
$904$		0			0
$905$			2.24950e10i			1.00882i
$906$		0			0
$907$	3.30822e10			1.47221			0.736103	−	0.676870i	$-0.236664\pi$
$907$	3.30822e10			1.47221			0.736103	+	0.676870i	$0.236664\pi$
$908$		0			0
$909$	−3.40566e10	+	1.93994e10i	−1.50393	+	0.856672i
$910$		0			0
$911$	−1.29490e10			−0.567441			−0.283721	−	0.958907i	$-0.591569\pi$
$911$	−1.29490e10			−0.567441			−0.283721	+	0.958907i	$0.591569\pi$
$912$		0			0
$913$	1.68712e10			0.733665
$914$		0			0
$915$	−3.28815e10	+	8.70818e9i	−1.41899	+	0.375797i
$916$		0			0
$917$	−1.60008e9			−0.0685250
$918$		0			0
$919$			2.72295e10i			1.15727i	0.815587	+	0.578635i	$0.196414\pi$
$919$			2.72295e10i			1.15727i	−0.815587	+	0.578635i	$0.803586\pi$
$920$		0			0
$921$	−4.94591e9	−	1.86754e10i	−0.208611	−	0.787701i
$922$		0			0
$923$		−	1.40463e10i		−	0.587971i
$924$		0			0
$925$		−	6.64783e9i		−	0.276175i
$926$		0			0
$927$	1.28213e10	+	2.25084e10i	0.528632	+	0.928039i
$928$		0			0
$929$			2.58564e10i			1.05807i	0.848600	+	0.529034i	$0.177446\pi$
$929$			2.58564e10i			1.05807i	−0.848600	+	0.529034i	$0.822554\pi$
$930$		0			0
$931$	4.34146e10			1.76324
$932$		0			0
$933$	5.88024e9	+	2.22034e10i	0.237033	+	0.895022i
$934$		0			0
$935$	−1.86148e9			−0.0744763
$936$		0			0
$937$	−2.42793e10			−0.964156			−0.482078	−	0.876128i	$-0.660118\pi$
$937$	−2.42793e10			−0.964156			−0.482078	+	0.876128i	$0.660118\pi$
$938$		0			0
$939$	3.55271e9	+	1.34148e10i	0.140033	+	0.528755i
$940$		0			0
$941$	2.00311e10			0.783683			0.391841	−	0.920033i	$-0.371838\pi$
$941$	2.00311e10			0.783683			0.391841	+	0.920033i	$0.371838\pi$
$942$		0			0
$943$		−	1.28447e10i		−	0.498806i
$944$		0			0
$945$	1.69747e9	−	1.66811e9i	0.0654320	−	0.0643004i
$946$		0			0
$947$			1.94545e10i			0.744382i	0.928156	+	0.372191i	$0.121393\pi$
$947$			1.94545e10i			0.744382i	−0.928156	+	0.372191i	$0.878607\pi$
$948$		0			0
$949$		−	1.23183e10i		−	0.467864i
$950$		0			0
$951$	−1.27323e10	−	4.80764e10i	−0.480039	−	1.81259i
$952$		0			0
$953$		−	6.37142e9i		−	0.238458i	−0.992867	−	0.119229i	$-0.961958\pi$
$953$		−	6.37142e9i		−	0.238458i	0.992867	−	0.119229i	$-0.0380422\pi$
$954$		0			0
$955$	−7.38769e9			−0.274471
$956$		0			0
$957$	1.17586e10	−	3.11409e9i	0.433674	−	0.114852i
$958$		0			0
$959$	1.89447e9			0.0693623
$960$		0			0
$961$	1.56869e10			0.570173
$962$		0			0
$963$	7.00600e9	+	1.22994e10i	0.252801	+	0.443804i
$964$		0			0
$965$	3.70934e9			0.132877
$966$		0			0
$967$			4.36195e10i			1.55127i	0.631179	+	0.775637i	$0.282571\pi$
$967$			4.36195e10i			1.55127i	−0.631179	+	0.775637i	$0.717429\pi$
$968$		0			0
$969$	−5.17895e9	+	1.37157e9i	−0.182856	+	0.0484266i
$970$		0			0
$971$			1.57572e10i			0.552347i	0.961108	+	0.276174i	$0.0890665\pi$
$971$			1.57572e10i			0.552347i	−0.961108	+	0.276174i	$0.910934\pi$
$972$		0			0
$973$			1.56156e9i			0.0543455i
$974$		0			0
$975$	2.26931e9	−	6.00993e8i	0.0784111	−	0.0207660i
$976$		0			0
$977$			1.06795e10i			0.366369i	0.983079	+	0.183185i	$0.0586407\pi$
$977$			1.06795e10i			0.366369i	−0.983079	+	0.183185i	$0.941359\pi$
$978$		0			0
$979$	3.43131e10			1.16875
$980$		0			0
$981$	1.33182e10	+	2.33808e10i	0.450406	+	0.790710i
$982$		0			0
$983$	−3.22063e10			−1.08144			−0.540721	−	0.841202i	$-0.681849\pi$
$983$	−3.22063e10			−1.08144			−0.540721	+	0.841202i	$0.681849\pi$
$984$		0			0
$985$	4.44392e10			1.48163
$986$		0			0
$987$	−3.47265e9	+	9.19679e8i	−0.114961	+	0.0304457i
$988$		0			0
$989$	−1.98474e9			−0.0652405
$990$		0			0
$991$			4.06068e10i			1.32538i	0.748893	+	0.662691i	$0.230586\pi$
$991$			4.06068e10i			1.32538i	−0.748893	+	0.662691i	$0.769414\pi$
$992$		0			0
$993$	−1.00762e10	−	3.80471e10i	−0.326569	−	1.23310i
$994$		0			0
$995$		−	3.73815e10i		−	1.20303i
$996$		0			0
$997$		−	6.00141e10i		−	1.91787i	−0.283619	−	0.958937i	$-0.591535\pi$
$997$		−	6.00141e10i		−	1.91787i	0.283619	−	0.958937i	$-0.408465\pi$
$998$		0			0
$999$	3.35126e10	−	3.29330e10i	1.06348	−	1.04509i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.8.f.d.95.13	✓	32
3.2	odd	2	inner	192.8.f.d.95.16	yes	32
4.3	odd	2	inner	192.8.f.d.95.19	yes	32
8.3	odd	2	inner	192.8.f.d.95.14	yes	32
8.5	even	2	inner	192.8.f.d.95.20	yes	32
12.11	even	2	inner	192.8.f.d.95.18	yes	32
24.5	odd	2	inner	192.8.f.d.95.17	yes	32
24.11	even	2	inner	192.8.f.d.95.15	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.8.f.d.95.13	✓	32	1.1	even	1	trivial
192.8.f.d.95.14	yes	32	8.3	odd	2	inner
192.8.f.d.95.15	yes	32	24.11	even	2	inner
192.8.f.d.95.16	yes	32	3.2	odd	2	inner
192.8.f.d.95.17	yes	32	24.5	odd	2	inner
192.8.f.d.95.18	yes	32	12.11	even	2	inner
192.8.f.d.95.19	yes	32	4.3	odd	2	inner
192.8.f.d.95.20	yes	32	8.5	even	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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	192.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-11.9724 - 45.2069i) q^{3} -304.295 q^{5} +76.4703i q^{7} +(-1900.32 + 1082.47i) q^{9} +O(q^{10})\)	\(q+(-11.9724 - 45.2069i) q^{3} -304.295 q^{5} +76.4703i q^{7} +(-1900.32 + 1082.47i) q^{9} +2835.12i q^{11} +3468.99i q^{13} +(3643.14 + 13756.2i) q^{15} -2157.71i q^{17} +53093.8 q^{19} +(3456.99 - 915.532i) q^{21} -63787.8 q^{23} +14470.6 q^{25} +(71686.4 + 72948.0i) q^{27} +91744.5 q^{29} +108746. i q^{31} +(128167. - 33943.1i) q^{33} -23269.6i q^{35} -459404. i q^{37} +(156822. - 41532.1i) q^{39} +201365. i q^{41} +31114.8 q^{43} +(578260. - 329390. i) q^{45} -1.00453e6 q^{47} +817695. q^{49} +(-97543.3 + 25832.9i) q^{51} -156272. q^{53} -862712. i q^{55} +(-635659. - 2.40021e6i) q^{57} -1.91380e6i q^{59} +2.39030e6i q^{61} +(-82776.7 - 145318. i) q^{63} -1.05560e6i q^{65} -44591.1 q^{67} +(763691. + 2.88365e6i) q^{69} -4.04910e6 q^{71} -3.55097e6 q^{73} +(-173247. - 654169. i) q^{75} -216802. q^{77} -23634.2i q^{79} +(2.43950e6 - 4.11408e6i) q^{81} -5.95079e6i q^{83} +656581. i q^{85} +(-1.09840e6 - 4.14748e6i) q^{87} -1.21029e7i q^{89} -265275. q^{91} +(4.91606e6 - 1.30195e6i) q^{93} -1.61562e7 q^{95} +1.39632e7 q^{97} +(-3.06892e6 - 5.38764e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 15360 q^{9}+O(q^{10}) \) 32 * q - 15360 * q^9	\( 32 q - 15360 q^{9} + 923168 q^{25} - 424800 q^{33} - 6986592 q^{49} - 1707360 q^{57} - 12976960 q^{73} - 57198816 q^{81} - 93958400 q^{97}+O(q^{100}) \) 32 * q - 15360 * q^9 + 923168 * q^25 - 424800 * q^33 - 6986592 * q^49 - 1707360 * q^57 - 12976960 * q^73 - 57198816 * q^81 - 93958400 * q^97

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