LMFDB - Embedded newform 384.6.c.a.383.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,6,Mod(383,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("384.383");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	384.c (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:	$61.5873868082$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 306 x^{18} + 37827 x^{16} + 2442168 x^{14} + 88368509 x^{12} + 1774000974 x^{10} + \cdots + 2870280625 $ x^20 + 306x^18 + 37827x^16 + 2442168x^14 + 88368509x^12 + 1774000974x^10 + 18093172325x^8 + 74958811500x^6 + 79355888475x^4 + 28497132750*x^2 + 2870280625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{88}\cdot 3^{14}\cdot 41^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			383.8
Root			$9.62962i$ of defining polynomial
Character	$\chi$	$=$	384.383
Dual form			384.6.c.a.383.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.16061 + 14.7095i) q^{3} -48.6693i q^{5} +167.754i q^{7} +(-189.736 - 151.820i) q^{9} +O(q^{10})$	\(q+(-5.16061 + 14.7095i) q^{3} -48.6693i q^{5} +167.754i q^{7} +(-189.736 - 151.820i) q^{9} -319.315 q^{11} -152.547 q^{13} +(715.899 + 251.163i) q^{15} -1323.90i q^{17} +1617.20i q^{19} +(-2467.58 - 865.716i) q^{21} -1222.40 q^{23} +756.298 q^{25} +(3212.34 - 2007.43i) q^{27} -4549.54i q^{29} +5353.25i q^{31} +(1647.86 - 4696.95i) q^{33} +8164.49 q^{35} -3269.34 q^{37} +(787.239 - 2243.89i) q^{39} +13077.7i q^{41} -20435.5i q^{43} +(-7388.96 + 9234.33i) q^{45} -20059.0 q^{47} -11334.6 q^{49} +(19473.8 + 6832.12i) q^{51} -33272.4i q^{53} +15540.9i q^{55} +(-23788.2 - 8345.77i) q^{57} -5883.70 q^{59} +22967.3 q^{61} +(25468.4 - 31829.1i) q^{63} +7424.38i q^{65} -13938.9i q^{67} +(6308.32 - 17980.8i) q^{69} +65642.7 q^{71} +55673.0 q^{73} +(-3902.96 + 11124.7i) q^{75} -53566.6i q^{77} -82204.2i q^{79} +(12950.6 + 57611.3i) q^{81} +19118.5 q^{83} -64433.2 q^{85} +(66921.3 + 23478.4i) q^{87} +97061.0i q^{89} -25590.5i q^{91} +(-78743.3 - 27626.0i) q^{93} +78708.3 q^{95} +159302. q^{97} +(60585.7 + 48478.3i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3}+O(q^{10}) $ 20 * q - 2 * q^3	$ 20 q - 2 q^{3} - 948 q^{11} - 852 q^{15} - 1640 q^{21} - 328 q^{23} - 12500 q^{25} - 2030 q^{27} + 2836 q^{33} + 7184 q^{35} - 15056 q^{37} + 12980 q^{39} - 11800 q^{45} - 36640 q^{47} - 33388 q^{49} - 1936 q^{51} + 15404 q^{57} - 62908 q^{59} - 73264 q^{61} - 23608 q^{63} + 84024 q^{69} - 34888 q^{71} + 52568 q^{73} - 115698 q^{75} + 55444 q^{81} + 225172 q^{83} + 30112 q^{85} + 225700 q^{87} + 148016 q^{93} - 418616 q^{95} + 7600 q^{97} - 378260 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 - 948 * q^11 - 852 * q^15 - 1640 * q^21 - 328 * q^23 - 12500 * q^25 - 2030 * q^27 + 2836 * q^33 + 7184 * q^35 - 15056 * q^37 + 12980 * q^39 - 11800 * q^45 - 36640 * q^47 - 33388 * q^49 - 1936 * q^51 + 15404 * q^57 - 62908 * q^59 - 73264 * q^61 - 23608 * q^63 + 84024 * q^69 - 34888 * q^71 + 52568 * q^73 - 115698 * q^75 + 55444 * q^81 + 225172 * q^83 + 30112 * q^85 + 225700 * q^87 + 148016 * q^93 - 418616 * q^95 + 7600 * q^97 - 378260 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$1$	$-1$

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
$3$	−5.16061	+	14.7095i	−0.331053	+	0.943612i
$3$	−5.16061	+	14.7095i	−0.331053	+	0.943612i
$4$		0			0
$5$		−	48.6693i		−	0.870623i	−0.900280	−	0.435312i	$-0.856638\pi$
$5$		−	48.6693i		−	0.870623i	0.900280	−	0.435312i	$-0.143362\pi$
$6$		0			0
$7$			167.754i			1.29398i	0.762497	+	0.646992i	$0.223973\pi$
$7$			167.754i			1.29398i	−0.762497	+	0.646992i	$0.776027\pi$
$8$		0			0
$9$	−189.736	−	151.820i	−0.780807	−	0.624772i
$10$		0			0
$11$	−319.315			−0.795679			−0.397840	−	0.917455i	$-0.630240\pi$
$11$	−319.315			−0.795679			−0.397840	+	0.917455i	$0.630240\pi$
$12$		0			0
$13$	−152.547			−0.250349			−0.125175	−	0.992135i	$-0.539949\pi$
$13$	−152.547			−0.250349			−0.125175	+	0.992135i	$0.539949\pi$
$14$		0			0
$15$	715.899	+	251.163i	0.821530	+	0.288223i
$16$		0			0
$17$		−	1323.90i		−	1.11105i	−0.831501	−	0.555523i	$-0.812518\pi$
$17$		−	1323.90i		−	1.11105i	0.831501	−	0.555523i	$-0.187482\pi$
$18$		0			0
$19$			1617.20i			1.02773i	0.857870	+	0.513867i	$0.171788\pi$
$19$			1617.20i			1.02773i	−0.857870	+	0.513867i	$0.828212\pi$
$20$		0			0
$21$	−2467.58	−	865.716i	−1.22102	−	0.428378i
$22$		0			0
$23$	−1222.40			−0.481829			−0.240914	−	0.970546i	$-0.577447\pi$
$23$	−1222.40			−0.481829			−0.240914	+	0.970546i	$0.577447\pi$
$24$		0			0
$25$	756.298			0.242015
$26$		0			0
$27$	3212.34	−	2007.43i	0.848031	−	0.529946i
$28$		0			0
$29$		−	4549.54i		−	1.00455i	−0.864707	−	0.502276i	$-0.832496\pi$
$29$		−	4549.54i		−	1.00455i	0.864707	−	0.502276i	$-0.167504\pi$
$30$		0			0
$31$			5353.25i			1.00049i	0.865884	+	0.500245i	$0.166757\pi$
$31$			5353.25i			1.00049i	−0.865884	+	0.500245i	$0.833243\pi$
$32$		0			0
$33$	1647.86	−	4696.95i	0.263412	−	0.750813i
$34$		0			0
$35$	8164.49			1.12657
$36$		0			0
$37$	−3269.34			−0.392605			−0.196303	−	0.980543i	$-0.562894\pi$
$37$	−3269.34			−0.392605			−0.196303	+	0.980543i	$0.562894\pi$
$38$		0			0
$39$	787.239	−	2243.89i	0.0828791	−	0.236233i
$40$		0			0
$41$			13077.7i			1.21499i	0.794323	+	0.607495i	$0.207826\pi$
$41$			13077.7i			1.21499i	−0.794323	+	0.607495i	$0.792174\pi$
$42$		0			0
$43$		−	20435.5i		−	1.68544i	−0.538350	−	0.842721i	$-0.680952\pi$
$43$		−	20435.5i		−	1.68544i	0.538350	−	0.842721i	$-0.319048\pi$
$44$		0			0
$45$	−7388.96	+	9234.33i	−0.543941	+	0.679789i
$46$		0			0
$47$	−20059.0			−1.32454			−0.662269	−	0.749266i	$-0.730406\pi$
$47$	−20059.0			−1.32454			−0.662269	+	0.749266i	$0.730406\pi$
$48$		0			0
$49$	−11334.6			−0.674395
$50$		0			0
$51$	19473.8	+	6832.12i	1.04840	+	0.367816i
$52$		0			0
$53$		−	33272.4i		−	1.62703i	−0.581546	−	0.813513i	$-0.697552\pi$
$53$		−	33272.4i		−	1.62703i	0.581546	−	0.813513i	$-0.302448\pi$
$54$		0			0
$55$			15540.9i			0.692737i
$56$		0			0
$57$	−23788.2	−	8345.77i	−0.969783	−	0.340235i
$58$		0			0
$59$	−5883.70			−0.220050			−0.110025	−	0.993929i	$-0.535093\pi$
$59$	−5883.70			−0.220050			−0.110025	+	0.993929i	$0.535093\pi$
$60$		0			0
$61$	22967.3			0.790289			0.395144	−	0.918619i	$-0.370695\pi$
$61$	22967.3			0.790289			0.395144	+	0.918619i	$0.370695\pi$
$62$		0			0
$63$	25468.4	−	31829.1i	0.808445	−	1.01035i
$64$		0			0
$65$			7424.38i			0.217960i
$66$		0			0
$67$		−	13938.9i		−	0.379352i	−0.981847	−	0.189676i	$-0.939256\pi$
$67$		−	13938.9i		−	0.379352i	0.981847	−	0.189676i	$-0.0607438\pi$
$68$		0			0
$69$	6308.32	−	17980.8i	0.159511	−	0.454659i
$70$		0			0
$71$	65642.7			1.54540			0.772700	−	0.634772i	$-0.218906\pi$
$71$	65642.7			1.54540			0.772700	+	0.634772i	$0.218906\pi$
$72$		0			0
$73$	55673.0			1.22275			0.611375	−	0.791341i	$-0.290617\pi$
$73$	55673.0			1.22275			0.611375	+	0.791341i	$0.290617\pi$
$74$		0			0
$75$	−3902.96	+	11124.7i	−0.0801200	+	0.228369i
$76$		0			0
$77$		−	53566.6i		−	1.02960i
$78$		0			0
$79$		−	82204.2i		−	1.48192i	−0.671546	−	0.740962i	$-0.734370\pi$
$79$		−	82204.2i		−	1.48192i	0.671546	−	0.740962i	$-0.265630\pi$
$80$		0			0
$81$	12950.6	+	57611.3i	0.219320	+	0.975653i
$82$		0			0
$83$	19118.5			0.304620			0.152310	−	0.988333i	$-0.451329\pi$
$83$	19118.5			0.304620			0.152310	+	0.988333i	$0.451329\pi$
$84$		0			0
$85$	−64433.2			−0.967302
$86$		0			0
$87$	66921.3	+	23478.4i	0.947908	+	0.332561i
$88$		0			0
$89$			97061.0i			1.29888i	0.760412	+	0.649441i	$0.224997\pi$
$89$			97061.0i			1.29888i	−0.760412	+	0.649441i	$0.775003\pi$
$90$		0			0
$91$		−	25590.5i		−	0.323948i
$92$		0			0
$93$	−78743.3	−	27626.0i	−0.944075	−	0.331216i
$94$		0			0
$95$	78708.3			0.894770
$96$		0			0
$97$	159302.			1.71906			0.859532	−	0.511082i	$-0.170755\pi$
$97$	159302.			1.71906			0.859532	+	0.511082i	$0.170755\pi$
$98$		0			0
$99$	60585.7	+	48478.3i	0.621272	+	0.497118i
$100$		0			0
$101$			77267.6i			0.753692i	0.926276	+	0.376846i	$0.122991\pi$
$101$			77267.6i			0.753692i	−0.926276	+	0.376846i	$0.877009\pi$
$102$		0			0
$103$			43795.1i			0.406755i	0.979100	+	0.203377i	$0.0651918\pi$
$103$			43795.1i			0.406755i	−0.979100	+	0.203377i	$0.934808\pi$
$104$		0			0
$105$	−42133.8	+	120095.i	−0.372956	+	1.06305i
$106$		0			0
$107$	220827.			1.86463			0.932315	−	0.361647i	$-0.117785\pi$
$107$	220827.			1.86463			0.932315	+	0.361647i	$0.117785\pi$
$108$		0			0
$109$	152973.			1.23325			0.616623	−	0.787259i	$-0.288500\pi$
$109$	152973.			1.23325			0.616623	+	0.787259i	$0.288500\pi$
$110$		0			0
$111$	16871.8	−	48090.3i	0.129973	−	0.370467i
$112$		0			0
$113$			142603.i			1.05059i	0.850922	+	0.525293i	$0.176044\pi$
$113$			142603.i			1.05059i	−0.850922	+	0.525293i	$0.823956\pi$
$114$		0			0
$115$			59493.2i			0.419491i
$116$		0			0
$117$	28943.8	+	23159.7i	0.195475	+	0.156411i
$118$		0			0
$119$	222090.			1.43768
$120$		0			0
$121$	−59088.7			−0.366894
$122$		0			0
$123$	−192366.	−	67489.1i	−1.14648	−	0.402227i
$124$		0			0
$125$		−	188900.i		−	1.08133i
$126$		0			0
$127$			49483.5i			0.272240i	0.990692	+	0.136120i	$0.0434632\pi$
$127$			49483.5i			0.272240i	−0.990692	+	0.136120i	$0.956537\pi$
$128$		0			0
$129$	300595.	+	105460.i	1.59040	+	0.557972i
$130$		0			0
$131$	260380.			1.32565			0.662826	−	0.748773i	$-0.269357\pi$
$131$	260380.			1.32565			0.662826	+	0.748773i	$0.269357\pi$
$132$		0			0
$133$	−271293.			−1.32987
$134$		0			0
$135$	−97700.4	−	156342.i	−0.461383	−	0.738316i
$136$		0			0
$137$		−	107894.i		−	0.491132i	−0.969380	−	0.245566i	$-0.921026\pi$
$137$		−	107894.i		−	0.491132i	0.969380	−	0.245566i	$-0.0789737\pi$
$138$		0			0
$139$		−	91076.8i		−	0.399826i	−0.979814	−	0.199913i	$-0.935934\pi$
$139$		−	91076.8i		−	0.399826i	0.979814	−	0.199913i	$-0.0640659\pi$
$140$		0			0
$141$	103517.	−	295057.i	0.438493	−	1.24985i
$142$		0			0
$143$	48710.8			0.199198
$144$		0			0
$145$	−221423.			−0.874587
$146$		0			0
$147$	58493.2	−	166725.i	0.223261	−	0.636367i
$148$		0			0
$149$		−	396732.i		−	1.46397i	−0.681322	−	0.731984i	$-0.738595\pi$
$149$		−	396732.i		−	1.46397i	0.681322	−	0.731984i	$-0.261405\pi$
$150$		0			0
$151$		−	396191.i		−	1.41404i	−0.707192	−	0.707022i	$-0.750038\pi$
$151$		−	396191.i		−	1.41404i	0.707192	−	0.707022i	$-0.249962\pi$
$152$		0			0
$153$	−200994.	+	251191.i	−0.694150	+	0.867513i
$154$		0			0
$155$	260539.			0.871050
$156$		0			0
$157$	−92070.4			−0.298106			−0.149053	−	0.988829i	$-0.547623\pi$
$157$	−92070.4			−0.298106			−0.149053	+	0.988829i	$0.547623\pi$
$158$		0			0
$159$	489419.	+	171706.i	1.53528	+	0.538633i
$160$		0			0
$161$		−	205062.i		−	0.623478i
$162$		0			0
$163$		−	299401.i		−	0.882640i	−0.897350	−	0.441320i	$-0.854510\pi$
$163$		−	299401.i		−	0.882640i	0.897350	−	0.441320i	$-0.145490\pi$
$164$		0			0
$165$	−228598.	−	80200.4i	−0.653675	−	0.229333i
$166$		0			0
$167$	−61166.1			−0.169715			−0.0848574	−	0.996393i	$-0.527043\pi$
$167$	−61166.1			−0.169715			−0.0848574	+	0.996393i	$0.527043\pi$
$168$		0			0
$169$	−348022.			−0.937325
$170$		0			0
$171$	245523.	−	306842.i	0.642100	−	0.802463i
$172$		0			0
$173$		−	349424.i		−	0.887641i	−0.896116	−	0.443821i	$-0.853623\pi$
$173$		−	349424.i		−	0.887641i	0.896116	−	0.443821i	$-0.146377\pi$
$174$		0			0
$175$			126872.i			0.313164i
$176$		0			0
$177$	30363.5	−	86546.0i	0.0728482	−	0.207641i
$178$		0			0
$179$	−172914.			−0.403365			−0.201682	−	0.979451i	$-0.564641\pi$
$179$	−172914.			−0.403365			−0.201682	+	0.979451i	$0.564641\pi$
$180$		0			0
$181$	−370619.			−0.840874			−0.420437	−	0.907322i	$-0.638123\pi$
$181$	−370619.			−0.840874			−0.420437	+	0.907322i	$0.638123\pi$
$182$		0			0
$183$	−118525.	+	337837.i	−0.261628	+	0.745726i
$184$		0			0
$185$			159117.i			0.341811i
$186$		0			0
$187$			422741.i			0.884036i
$188$		0			0
$189$	336756.	+	538884.i	0.685742	+	1.09734i
$190$		0			0
$191$	−636934.			−1.26331			−0.631656	−	0.775249i	$-0.717625\pi$
$191$	−636934.			−1.26331			−0.631656	+	0.775249i	$0.717625\pi$
$192$		0			0
$193$	791811.			1.53013			0.765064	−	0.643954i	$-0.222707\pi$
$193$	791811.			1.53013			0.765064	+	0.643954i	$0.222707\pi$
$194$		0			0
$195$	−109209.	−	38314.4i	−0.205670	−	0.0721564i
$196$		0			0
$197$		−	229538.i		−	0.421395i	−0.977551	−	0.210698i	$-0.932426\pi$
$197$		−	229538.i		−	0.421395i	0.977551	−	0.210698i	$-0.0675735\pi$
$198$		0			0
$199$			42046.2i			0.0752651i	0.999292	+	0.0376325i	$0.0119816\pi$
$199$			42046.2i			0.0752651i	−0.999292	+	0.0376325i	$0.988018\pi$
$200$		0			0
$201$	205034.	+	71933.4i	0.357961	+	0.125586i
$202$		0			0
$203$	763206.			1.29987
$204$		0			0
$205$	636484.			1.05780
$206$		0			0
$207$	231933.	+	185584.i	0.376215	+	0.301033i
$208$		0			0
$209$		−	516398.i		−	0.817747i
$210$		0			0
$211$		−	80176.3i		−	0.123977i	−0.998077	−	0.0619883i	$-0.980256\pi$
$211$		−	80176.3i		−	0.123977i	0.998077	−	0.0619883i	$-0.0197442\pi$
$212$		0			0
$213$	−338757.	+	965569.i	−0.511610	+	1.45826i
$214$		0			0
$215$	−994581.			−1.46739
$216$		0			0
$217$	−898031.			−1.29462
$218$		0			0
$219$	−287307.	+	818919.i	−0.404795	+	1.15380i
$220$		0			0
$221$			201957.i			0.278150i
$222$		0			0
$223$			73558.4i			0.0990536i	0.998773	+	0.0495268i	$0.0157713\pi$
$223$			73558.4i			0.0990536i	−0.998773	+	0.0495268i	$0.984229\pi$
$224$		0			0
$225$	−143497.	−	114821.i	−0.188967	−	0.151204i
$226$		0			0
$227$	−359120.			−0.462568			−0.231284	−	0.972886i	$-0.574293\pi$
$227$	−359120.			−0.462568			−0.231284	+	0.972886i	$0.574293\pi$
$228$		0			0
$229$	−867580.			−1.09325			−0.546627	−	0.837376i	$-0.684088\pi$
$229$	−867580.			−1.09325			−0.546627	+	0.837376i	$0.684088\pi$
$230$		0			0
$231$	787935.	+	276436.i	0.971539	+	0.340851i
$232$		0			0
$233$			520013.i			0.627515i	0.949503	+	0.313758i	$0.101588\pi$
$233$			520013.i			0.627515i	−0.949503	+	0.313758i	$0.898412\pi$
$234$		0			0
$235$			976257.i			1.15317i
$236$		0			0
$237$	1.20918e6	+	424224.i	1.39836	+	0.490596i
$238$		0			0
$239$	206539.			0.233888			0.116944	−	0.993139i	$-0.462690\pi$
$239$	206539.			0.233888			0.116944	+	0.993139i	$0.462690\pi$
$240$		0			0
$241$	1.65009e6			1.83006			0.915030	−	0.403385i	$-0.132166\pi$
$241$	1.65009e6			1.83006			0.915030	+	0.403385i	$0.132166\pi$
$242$		0			0
$243$	−914264.	−	106813.i	−0.993244	−	0.116041i
$244$		0			0
$245$			551645.i			0.587144i
$246$		0			0
$247$		−	246701.i		−	0.257293i
$248$		0			0
$249$	−98663.3	+	281223.i	−0.100846	+	0.287443i
$250$		0			0
$251$	−1.56162e6			−1.56455			−0.782277	−	0.622931i	$-0.785942\pi$
$251$	−1.56162e6			−1.56455			−0.782277	+	0.622931i	$0.785942\pi$
$252$		0			0
$253$	390330.			0.383381
$254$		0			0
$255$	332515.	−	947777.i	0.320229	−	0.912758i
$256$		0			0
$257$		−	1.51207e6i		−	1.42804i	−0.700127	−	0.714019i	$-0.746873\pi$
$257$		−	1.51207e6i		−	1.42804i	0.700127	−	0.714019i	$-0.253127\pi$
$258$		0			0
$259$		−	548447.i		−	0.508025i
$260$		0			0
$261$	−690710.	+	863213.i	−0.627616	+	0.784362i
$262$		0			0
$263$	−387053.			−0.345049			−0.172524	−	0.985005i	$-0.555192\pi$
$263$	−387053.			−0.345049			−0.172524	+	0.985005i	$0.555192\pi$
$264$		0			0
$265$	−1.61935e6			−1.41653
$266$		0			0
$267$	−1.42771e6	−	500894.i	−1.22564	−	0.429999i
$268$		0			0
$269$		−	1.62869e6i		−	1.37233i	−0.727446	−	0.686165i	$-0.759293\pi$
$269$		−	1.62869e6i		−	1.37233i	0.727446	−	0.686165i	$-0.240707\pi$
$270$		0			0
$271$			549923.i			0.454861i	0.973794	+	0.227431i	$0.0730325\pi$
$271$			549923.i			0.454861i	−0.973794	+	0.227431i	$0.926968\pi$
$272$		0			0
$273$	376423.	+	132063.i	0.305681	+	0.107244i
$274$		0			0
$275$	−241498.			−0.192567
$276$		0			0
$277$	1.37805e6			1.07911			0.539553	−	0.841951i	$-0.318593\pi$
$277$	1.37805e6			1.07911			0.539553	+	0.841951i	$0.318593\pi$
$278$		0			0
$279$	812728.	−	1.01570e6i	0.625078	−	0.781190i
$280$		0			0
$281$		−	2.03707e6i		−	1.53900i	−0.638645	−	0.769502i	$-0.720505\pi$
$281$		−	2.03707e6i		−	1.53900i	0.638645	−	0.769502i	$-0.279495\pi$
$282$		0			0
$283$		−	1.15726e6i		−	0.858947i	−0.903079	−	0.429473i	$-0.858699\pi$
$283$		−	1.15726e6i		−	0.858947i	0.903079	−	0.429473i	$-0.141301\pi$
$284$		0			0
$285$	−406183.	+	1.15776e6i	−0.296217	+	0.844315i
$286$		0			0
$287$	−2.19385e6			−1.57218
$288$		0			0
$289$	−332847.			−0.234423
$290$		0			0
$291$	−822096.	+	2.34325e6i	−0.569102	+	1.62213i
$292$		0			0
$293$			2.48372e6i			1.69018i	0.534621	+	0.845092i	$0.320454\pi$
$293$			2.48372e6i			1.69018i	−0.534621	+	0.845092i	$0.679546\pi$
$294$		0			0
$295$			286356.i			0.191580i
$296$		0			0
$297$	−1.02575e6	+	641004.i	−0.674761	+	0.421667i
$298$		0			0
$299$	186474.			0.120626
$300$		0			0
$301$	3.42814e6			2.18094
$302$		0			0
$303$	−1.13656e6	−	398748.i	−0.711193	−	0.249512i
$304$		0			0
$305$		−	1.11780e6i		−	0.688044i
$306$		0			0
$307$			2.54604e6i			1.54177i	0.636976	+	0.770884i	$0.280185\pi$
$307$			2.54604e6i			1.54177i	−0.636976	+	0.770884i	$0.719815\pi$
$308$		0			0
$309$	−644202.	−	226010.i	−0.383819	−	0.134658i
$310$		0			0
$311$	−2.66268e6			−1.56106			−0.780528	−	0.625121i	$-0.785050\pi$
$311$	−2.66268e6			−1.56106			−0.780528	+	0.625121i	$0.785050\pi$
$312$		0			0
$313$	−400195.			−0.230893			−0.115446	−	0.993314i	$-0.536830\pi$
$313$	−400195.			−0.230893			−0.115446	+	0.993314i	$0.536830\pi$
$314$		0			0
$315$	−1.54910e6	−	1.23953e6i	−0.879636	−	0.703851i
$316$		0			0
$317$			1.54428e6i			0.863136i	0.902080	+	0.431568i	$0.142039\pi$
$317$			1.54428e6i			0.863136i	−0.902080	+	0.431568i	$0.857961\pi$
$318$		0			0
$319$			1.45274e6i			0.799302i
$320$		0			0
$321$	−1.13960e6	+	3.24824e6i	−0.617292	+	1.75949i
$322$		0			0
$323$	2.14101e6			1.14186
$324$		0			0
$325$	−115371.			−0.0605884
$326$		0			0
$327$	−789436.	+	2.25015e6i	−0.408270	+	1.16371i
$328$		0			0
$329$		−	3.36498e6i		−	1.71393i
$330$		0			0
$331$		−	337952.i		−	0.169545i	−0.996400	−	0.0847725i	$-0.972984\pi$
$331$		−	337952.i		−	0.169545i	0.996400	−	0.0847725i	$-0.0270163\pi$
$332$		0			0
$333$	620313.	+	496351.i	0.306549	+	0.245289i
$334$		0			0
$335$	−678398.			−0.330273
$336$		0			0
$337$	1.92048e6			0.921158			0.460579	−	0.887619i	$-0.347642\pi$
$337$	1.92048e6			0.921158			0.460579	+	0.887619i	$0.347642\pi$
$338$		0			0
$339$	−2.09761e6	−	735917.i	−0.991345	−	0.347800i
$340$		0			0
$341$		−	1.70937e6i		−	0.796070i
$342$		0			0
$343$			918027.i			0.421328i
$344$		0			0
$345$	−875113.	−	307021.i	−0.395837	−	0.138874i
$346$		0			0
$347$	1.67762e6			0.747946			0.373973	−	0.927440i	$-0.377995\pi$
$347$	1.67762e6			0.747946			0.373973	+	0.927440i	$0.377995\pi$
$348$		0			0
$349$	−3.93176e6			−1.72792			−0.863960	−	0.503560i	$-0.832023\pi$
$349$	−3.93176e6			−1.72792			−0.863960	+	0.503560i	$0.832023\pi$
$350$		0			0
$351$	−490034.	+	306229.i	−0.212304	+	0.132672i
$352$		0			0
$353$		−	3.20933e6i		−	1.37081i	−0.728161	−	0.685406i	$-0.759625\pi$
$353$		−	3.20933e6i		−	1.37081i	0.728161	−	0.685406i	$-0.240375\pi$
$354$		0			0
$355$		−	3.19479e6i		−	1.34546i
$356$		0			0
$357$	−1.14612e6	+	3.26682e6i	−0.475948	+	1.35661i
$358$		0			0
$359$	−913329.			−0.374017			−0.187008	−	0.982358i	$-0.559879\pi$
$359$	−913329.			−0.374017			−0.187008	+	0.982358i	$0.559879\pi$
$360$		0			0
$361$	−139253.			−0.0562389
$362$		0			0
$363$	304934.	−	869163.i	0.121462	−	0.346206i
$364$		0			0
$365$		−	2.70957e6i		−	1.06455i
$366$		0			0
$367$		−	205159.i		−	0.0795106i	−0.999209	−	0.0397553i	$-0.987342\pi$
$367$		−	205159.i		−	0.0795106i	0.999209	−	0.0397553i	$-0.0126578\pi$
$368$		0			0
$369$	1.98546e6	−	2.48132e6i	0.759092	−	0.948673i
$370$		0			0
$371$	5.58160e6			2.10535
$372$		0			0
$373$	−2.30940e6			−0.859465			−0.429732	−	0.902956i	$-0.641392\pi$
$373$	−2.30940e6			−0.859465			−0.429732	+	0.902956i	$0.641392\pi$
$374$		0			0
$375$	2.77862e6	+	974840.i	1.02035	+	0.357977i
$376$		0			0
$377$			694021.i			0.251489i
$378$		0			0
$379$			1.30015e6i			0.464939i	0.972604	+	0.232470i	$0.0746806\pi$
$379$			1.30015e6i			0.464939i	−0.972604	+	0.232470i	$0.925319\pi$
$380$		0			0
$381$	−727876.	−	255365.i	−0.256889	−	0.0901259i
$382$		0			0
$383$	−421140.			−0.146700			−0.0733499	−	0.997306i	$-0.523369\pi$
$383$	−421140.			−0.146700			−0.0733499	+	0.997306i	$0.523369\pi$
$384$		0			0
$385$	−2.60705e6			−0.896390
$386$		0			0
$387$	−3.10251e6	+	3.87735e6i	−1.05302	+	1.31601i
$388$		0			0
$389$		−	3.99605e6i		−	1.33893i	−0.742844	−	0.669464i	$-0.766524\pi$
$389$		−	3.99605e6i		−	1.33893i	0.742844	−	0.669464i	$-0.233476\pi$
$390$		0			0
$391$			1.61833e6i			0.535334i
$392$		0			0
$393$	−1.34372e6	+	3.83005e6i	−0.438862	+	1.25090i
$394$		0			0
$395$	−4.00082e6			−1.29020
$396$		0			0
$397$	1.38885e6			0.442262			0.221131	−	0.975244i	$-0.429025\pi$
$397$	1.38885e6			0.442262			0.221131	+	0.975244i	$0.429025\pi$
$398$		0			0
$399$	1.40004e6	−	3.99058e6i	0.440259	−	1.25488i
$400$		0			0
$401$		−	1.31621e6i		−	0.408758i	−0.978892	−	0.204379i	$-0.934483\pi$
$401$		−	1.31621e6i		−	0.408758i	0.978892	−	0.204379i	$-0.0655174\pi$
$402$		0			0
$403$		−	816624.i		−	0.250472i
$404$		0			0
$405$	2.80390e6	−	630297.i	0.849426	−	0.190945i
$406$		0			0
$407$	1.04395e6			0.312388
$408$		0			0
$409$	2.83849e6			0.839033			0.419516	−	0.907748i	$-0.362200\pi$
$409$	2.83849e6			0.839033			0.419516	+	0.907748i	$0.362200\pi$
$410$		0			0
$411$	1.58707e6	+	556802.i	0.463438	+	0.162591i
$412$		0			0
$413$		−	987017.i		−	0.284741i
$414$		0			0
$415$		−	930485.i		−	0.265210i
$416$		0			0
$417$	1.33969e6	+	470012.i	0.377280	+	0.132364i
$418$		0			0
$419$	−983535.			−0.273687			−0.136844	−	0.990593i	$-0.543696\pi$
$419$	−983535.			−0.273687			−0.136844	+	0.990593i	$0.543696\pi$
$420$		0			0
$421$	−3.50363e6			−0.963414			−0.481707	−	0.876332i	$-0.659983\pi$
$421$	−3.50363e6			−0.963414			−0.481707	+	0.876332i	$0.659983\pi$
$422$		0			0
$423$	3.80591e6	+	3.04535e6i	1.03421	+	0.827534i
$424$		0			0
$425$		−	1.00126e6i		−	0.268890i
$426$		0			0
$427$			3.85287e6i			1.02262i
$428$		0			0
$429$	−251377.	+	716509.i	−0.0659452	+	0.187966i
$430$		0			0
$431$	−4.96042e6			−1.28625			−0.643125	−	0.765762i	$-0.722362\pi$
$431$	−4.96042e6			−1.28625			−0.643125	+	0.765762i	$0.722362\pi$
$432$		0			0
$433$	−3.86224e6			−0.989964			−0.494982	−	0.868903i	$-0.664825\pi$
$433$	−3.86224e6			−0.989964			−0.494982	+	0.868903i	$0.664825\pi$
$434$		0			0
$435$	1.14268e6	−	3.25701e6i	0.289535	−	0.825270i
$436$		0			0
$437$		−	1.97687e6i		−	0.495192i
$438$		0			0
$439$		−	7.78526e6i		−	1.92802i	−0.265862	−	0.964011i	$-0.585657\pi$
$439$		−	7.78526e6i		−	1.92802i	0.265862	−	0.964011i	$-0.414343\pi$
$440$		0			0
$441$	2.15057e6	+	1.72081e6i	0.526572	+	0.421343i
$442$		0			0
$443$	6.74367e6			1.63263			0.816314	−	0.577609i	$-0.196014\pi$
$443$	6.74367e6			1.63263			0.816314	+	0.577609i	$0.196014\pi$
$444$		0			0
$445$	4.72389e6			1.13084
$446$		0			0
$447$	5.83571e6	+	2.04738e6i	1.38142	+	0.484651i
$448$		0			0
$449$			3.85833e6i			0.903200i	0.892221	+	0.451600i	$0.149147\pi$
$449$			3.85833e6i			0.903200i	−0.892221	+	0.451600i	$0.850853\pi$
$450$		0			0
$451$		−	4.17592e6i		−	0.966743i
$452$		0			0
$453$	5.82776e6	+	2.04459e6i	1.33431	+	0.468124i
$454$		0			0
$455$	−1.24547e6			−0.282037
$456$		0			0
$457$	1.64250e6			0.367888			0.183944	−	0.982937i	$-0.441114\pi$
$457$	1.64250e6			0.367888			0.183944	+	0.982937i	$0.441114\pi$
$458$		0			0
$459$	−2.65764e6	−	4.25281e6i	−0.588794	−	0.942202i
$460$		0			0
$461$			77799.5i			0.0170500i	0.999964	+	0.00852500i	$0.00271363\pi$
$461$			77799.5i			0.0170500i	−0.999964	+	0.00852500i	$0.997286\pi$
$462$		0			0
$463$		−	213758.i		−	0.0463414i	−0.999732	−	0.0231707i	$-0.992624\pi$
$463$		−	213758.i		−	0.0463414i	0.999732	−	0.0231707i	$-0.00737613\pi$
$464$		0			0
$465$	−1.34454e6	+	3.83238e6i	−0.288364	+	0.821933i
$466$		0			0
$467$	−2.85122e6			−0.604977			−0.302489	−	0.953153i	$-0.597817\pi$
$467$	−2.85122e6			−0.604977			−0.302489	+	0.953153i	$0.597817\pi$
$468$		0			0
$469$	2.33832e6			0.490875
$470$		0			0
$471$	475140.	−	1.35431e6i	0.0986891	−	0.281297i
$472$		0			0
$473$			6.52537e6i			1.34107i
$474$		0			0
$475$			1.22309e6i			0.248728i
$476$		0			0
$477$	−5.05141e6	+	6.31298e6i	−1.01652	+	1.27039i
$478$		0			0
$479$	8.52181e6			1.69704			0.848522	−	0.529161i	$-0.177493\pi$
$479$	8.52181e6			1.69704			0.848522	+	0.529161i	$0.177493\pi$
$480$		0			0
$481$	498730.			0.0982886
$482$		0			0
$483$	3.01636e6	+	1.05825e6i	0.588322	+	0.206405i
$484$		0			0
$485$		−	7.75312e6i		−	1.49666i
$486$		0			0
$487$		−	6.25067e6i		−	1.19427i	−0.802139	−	0.597137i	$-0.796305\pi$
$487$		−	6.25067e6i		−	1.19427i	0.802139	−	0.597137i	$-0.203695\pi$
$488$		0			0
$489$	4.40402e6	+	1.54509e6i	0.832870	+	0.292201i
$490$		0			0
$491$	5.91380e6			1.10704			0.553519	−	0.832837i	$-0.313285\pi$
$491$	5.91380e6			1.10704			0.553519	+	0.832837i	$0.313285\pi$
$492$		0			0
$493$	−6.02313e6			−1.11610
$494$		0			0
$495$	2.35941e6	−	2.94866e6i	0.432803	−	0.540894i
$496$		0			0
$497$			1.10119e7i			1.99972i
$498$		0			0
$499$			916915.i			0.164846i	0.996597	+	0.0824228i	$0.0262658\pi$
$499$			916915.i			0.164846i	−0.996597	+	0.0824228i	$0.973734\pi$
$500$		0			0
$501$	315655.	−	899720.i	0.0561847	−	0.160145i
$502$		0			0
$503$	−4.30667e6			−0.758964			−0.379482	−	0.925199i	$-0.623898\pi$
$503$	−4.30667e6			−0.758964			−0.379482	+	0.925199i	$0.623898\pi$
$504$		0			0
$505$	3.76056e6			0.656181
$506$		0			0
$507$	1.79601e6	−	5.11922e6i	0.310305	−	0.884471i
$508$		0			0
$509$		−	3.12915e6i		−	0.535342i	−0.963510	−	0.267671i	$-0.913746\pi$
$509$		−	3.12915e6i		−	0.535342i	0.963510	−	0.267671i	$-0.0862540\pi$
$510$		0			0
$511$			9.33939e6i			1.58222i
$512$		0			0
$513$	3.24643e6	+	5.19501e6i	0.544644	+	0.871551i
$514$		0			0
$515$	2.13148e6			0.354130
$516$		0			0
$517$	6.40514e6			1.05391
$518$		0			0
$519$	5.13984e6	+	1.80324e6i	0.837589	+	0.293857i
$520$		0			0
$521$			181277.i			0.0292583i	0.999893	+	0.0146292i	$0.00465677\pi$
$521$			181277.i			0.0292583i	−0.999893	+	0.0146292i	$0.995343\pi$
$522$		0			0
$523$			7.82852e6i			1.25148i	0.780030	+	0.625742i	$0.215204\pi$
$523$			7.82852e6i			1.25148i	−0.780030	+	0.625742i	$0.784796\pi$
$524$		0			0
$525$	−1.86622e6	−	654739.i	−0.295505	−	0.103674i
$526$		0			0
$527$	7.08715e6			1.11159
$528$		0			0
$529$	−4.94209e6			−0.767841
$530$		0			0
$531$	1.11635e6	+	893261.i	0.171816	+	0.137481i
$532$		0			0
$533$		−	1.99498e6i		−	0.304172i
$534$		0			0
$535$		−	1.07475e7i		−	1.62339i
$536$		0			0
$537$	892343.	−	2.54347e6i	0.133535	−	0.380620i
$538$		0			0
$539$	3.61930e6			0.536602
$540$		0			0
$541$	−1.25741e7			−1.84706			−0.923532	−	0.383520i	$-0.874712\pi$
$541$	−1.25741e7			−1.84706			−0.923532	+	0.383520i	$0.874712\pi$
$542$		0			0
$543$	1.91262e6	−	5.45160e6i	0.278374	−	0.793459i
$544$		0			0
$545$		−	7.44511e6i		−	1.07369i
$546$		0			0
$547$		−	3.40198e6i		−	0.486143i	−0.970008	−	0.243071i	$-0.921845\pi$
$547$		−	3.40198e6i		−	0.486143i	0.970008	−	0.243071i	$-0.0781549\pi$
$548$		0			0
$549$	−4.35773e6	−	3.48689e6i	−0.617063	−	0.493750i
$550$		0			0
$551$	7.35754e6			1.03241
$552$		0			0
$553$	1.37901e7			1.91759
$554$		0			0
$555$	−2.34052e6	−	821140.i	−0.322537	−	0.113158i
$556$		0			0
$557$		−	7.75680e6i		−	1.05936i	−0.848197	−	0.529681i	$-0.822311\pi$
$557$		−	7.75680e6i		−	1.05936i	0.848197	−	0.529681i	$-0.177689\pi$
$558$		0			0
$559$			3.11738e6i			0.421950i
$560$		0			0
$561$	−6.21829e6	−	2.18160e6i	−0.834187	−	0.292663i
$562$		0			0
$563$	3.17845e6			0.422614			0.211307	−	0.977420i	$-0.432228\pi$
$563$	3.17845e6			0.422614			0.211307	+	0.977420i	$0.432228\pi$
$564$		0			0
$565$	6.94037e6			0.914664
$566$		0			0
$567$	−9.66456e6	+	2.17252e6i	−1.26248	+	0.283796i
$568$		0			0
$569$		−	1.26620e7i		−	1.63954i	−0.572691	−	0.819771i	$-0.694100\pi$
$569$		−	1.26620e7i		−	1.63954i	0.572691	−	0.819771i	$-0.305900\pi$
$570$		0			0
$571$		−	3.92129e6i		−	0.503314i	−0.967816	−	0.251657i	$-0.919025\pi$
$571$		−	3.92129e6i		−	0.503314i	0.967816	−	0.251657i	$-0.0809755\pi$
$572$		0			0
$573$	3.28697e6	−	9.36895e6i	0.418224	−	1.19208i
$574$		0			0
$575$	−924496.			−0.116610
$576$		0			0
$577$	−1.12254e6			−0.140366			−0.0701828	−	0.997534i	$-0.522358\pi$
$577$	−1.12254e6			−0.140366			−0.0701828	+	0.997534i	$0.522358\pi$
$578$		0			0
$579$	−4.08623e6	+	1.16471e7i	−0.506554	+	1.44385i
$580$		0			0
$581$			3.20722e6i			0.394174i
$582$		0			0
$583$			1.06244e7i			1.29459i
$584$		0			0
$585$	1.12717e6	−	1.40867e6i	0.136175	−	0.170185i
$586$		0			0
$587$	3.81465e6			0.456940			0.228470	−	0.973551i	$-0.426628\pi$
$587$	3.81465e6			0.456940			0.228470	+	0.973551i	$0.426628\pi$
$588$		0			0
$589$	−8.65730e6			−1.02824
$590$		0			0
$591$	3.37638e6	+	1.18456e6i	0.397633	+	0.139504i
$592$		0			0
$593$			6.15809e6i			0.719133i	0.933119	+	0.359567i	$0.117075\pi$
$593$			6.15809e6i			0.719133i	−0.933119	+	0.359567i	$0.882925\pi$
$594$		0			0
$595$		−	1.08090e7i		−	1.25167i
$596$		0			0
$597$	−618476.	−	216984.i	−0.0710210	−	0.0249168i
$598$		0			0
$599$	8.31895e6			0.947331			0.473665	−	0.880705i	$-0.342931\pi$
$599$	8.31895e6			0.947331			0.473665	+	0.880705i	$0.342931\pi$
$600$		0			0
$601$	−1.13436e7			−1.28104			−0.640521	−	0.767941i	$-0.721282\pi$
$601$	−1.13436e7			−1.28104			−0.640521	+	0.767941i	$0.721282\pi$
$602$		0			0
$603$	−2.11620e6	+	2.64472e6i	−0.237009	+	0.296201i
$604$		0			0
$605$			2.87581e6i			0.319427i
$606$		0			0
$607$			1.37972e7i			1.51991i	0.649974	+	0.759956i	$0.274780\pi$
$607$			1.37972e7i			1.51991i	−0.649974	+	0.759956i	$0.725220\pi$
$608$		0			0
$609$	−3.93861e6	+	1.12263e7i	−0.430328	+	1.22658i
$610$		0			0
$611$	3.05995e6			0.331597
$612$		0			0
$613$	−1.47858e6			−0.158926			−0.0794629	−	0.996838i	$-0.525321\pi$
$613$	−1.47858e6			−0.158926			−0.0794629	+	0.996838i	$0.525321\pi$
$614$		0			0
$615$	−3.28465e6	+	9.36234e6i	−0.350188	+	0.998152i
$616$		0			0
$617$		−	1.64855e6i		−	0.174337i	−0.996194	−	0.0871684i	$-0.972218\pi$
$617$		−	1.64855e6i		−	0.174337i	0.996194	−	0.0871684i	$-0.0277818\pi$
$618$		0			0
$619$			3.87090e6i			0.406056i	0.979173	+	0.203028i	$0.0650782\pi$
$619$			3.87090e6i			0.406056i	−0.979173	+	0.203028i	$0.934922\pi$
$620$		0			0
$621$	−3.92675e6	+	2.45388e6i	−0.408606	+	0.255343i
$622$		0			0
$623$	−1.62824e7			−1.68073
$624$		0			0
$625$	−6.83021e6			−0.699413
$626$		0			0
$627$	7.59594e6	+	2.66493e6i	0.771636	+	0.270718i
$628$		0			0
$629$			4.32828e6i			0.436203i
$630$		0			0
$631$		−	1.47448e7i		−	1.47423i	−0.675765	−	0.737117i	$-0.736187\pi$
$631$		−	1.47448e7i		−	1.47423i	0.675765	−	0.737117i	$-0.263813\pi$
$632$		0			0
$633$	1.17935e6	+	413759.i	0.116986	+	0.0410429i
$634$		0			0
$635$	2.40833e6			0.237018
$636$		0			0
$637$	1.72906e6			0.168834
$638$		0			0
$639$	−1.24548e7	−	9.96585e6i	−1.20666	−	0.965522i
$640$		0			0
$641$		−	1.09176e7i		−	1.04950i	−0.851256	−	0.524750i	$-0.824159\pi$
$641$		−	1.09176e7i		−	1.04950i	0.851256	−	0.524750i	$-0.175841\pi$
$642$		0			0
$643$		−	1.82933e7i		−	1.74487i	−0.488726	−	0.872437i	$-0.662538\pi$
$643$		−	1.82933e7i		−	1.74487i	0.488726	−	0.872437i	$-0.337462\pi$
$644$		0			0
$645$	5.13265e6	−	1.46298e7i	0.485783	−	1.38464i
$646$		0			0
$647$	−381744.			−0.0358518			−0.0179259	−	0.999839i	$-0.505706\pi$
$647$	−381744.			−0.0358518			−0.0179259	+	0.999839i	$0.505706\pi$
$648$		0			0
$649$	1.87876e6			0.175089
$650$		0			0
$651$	4.63439e6	−	1.32095e7i	0.428588	−	1.22162i
$652$		0			0
$653$			1.41687e7i			1.30031i	0.759800	+	0.650157i	$0.225297\pi$
$653$			1.41687e7i			1.30031i	−0.759800	+	0.650157i	$0.774703\pi$
$654$		0			0
$655$		−	1.26725e7i		−	1.15414i
$656$		0			0
$657$	−1.05632e7	−	8.45225e6i	−0.954731	−	0.763939i
$658$		0			0
$659$	−2.91811e6			−0.261751			−0.130876	−	0.991399i	$-0.541779\pi$
$659$	−2.91811e6			−0.261751			−0.130876	+	0.991399i	$0.541779\pi$
$660$		0			0
$661$	1.08812e7			0.968662			0.484331	−	0.874885i	$-0.339063\pi$
$661$	1.08812e7			0.968662			0.484331	+	0.874885i	$0.339063\pi$
$662$		0			0
$663$	−2.97068e6	−	1.04222e6i	−0.262465	−	0.0920824i
$664$		0			0
$665$			1.32037e7i			1.15782i
$666$		0			0
$667$			5.56134e6i			0.484022i
$668$		0			0
$669$	−1.08200e6	−	379607.i	−0.0934682	−	0.0327920i
$670$		0			0
$671$	−7.33382e6			−0.628816
$672$		0			0
$673$	1.31612e7			1.12010			0.560049	−	0.828459i	$-0.310782\pi$
$673$	1.31612e7			1.12010			0.560049	+	0.828459i	$0.310782\pi$
$674$		0			0
$675$	2.42949e6	−	1.51822e6i	0.205237	−	0.128255i
$676$		0			0
$677$			5.27738e6i			0.442534i	0.975213	+	0.221267i	$0.0710193\pi$
$677$			5.27738e6i			0.442534i	−0.975213	+	0.221267i	$0.928981\pi$
$678$		0			0
$679$			2.67236e7i			2.22444i
$680$		0			0
$681$	1.85328e6	−	5.28246e6i	0.153135	−	0.436484i
$682$		0			0
$683$	−7.46685e6			−0.612471			−0.306236	−	0.951956i	$-0.599070\pi$
$683$	−7.46685e6			−0.612471			−0.306236	+	0.951956i	$0.599070\pi$
$684$		0			0
$685$	−5.25115e6			−0.427591
$686$		0			0
$687$	4.47724e6	−	1.27616e7i	0.361925	−	1.03161i
$688$		0			0
$689$			5.07562e6i			0.407325i
$690$		0			0
$691$			4.56640e6i			0.363814i	0.983316	+	0.181907i	$0.0582269\pi$
$691$			4.56640e6i			0.363814i	−0.983316	+	0.181907i	$0.941773\pi$
$692$		0			0
$693$	−8.13246e6	+	1.01635e7i	−0.643263	+	0.803916i
$694$		0			0
$695$	−4.43264e6			−0.348097
$696$		0			0
$697$	1.73136e7			1.34991
$698$		0			0
$699$	−7.64911e6	−	2.68359e6i	−0.592131	−	0.207741i
$700$		0			0
$701$		−	967522.i		−	0.0743645i	−0.999309	−	0.0371822i	$-0.988162\pi$
$701$		−	967522.i		−	0.0743645i	0.999309	−	0.0371822i	$-0.0118382\pi$
$702$		0			0
$703$		−	5.28720e6i		−	0.403494i
$704$		0			0
$705$	−1.43602e7	−	5.03808e6i	−1.08815	−	0.381762i
$706$		0			0
$707$	−1.29620e7			−0.975265
$708$		0			0
$709$	2.59701e7			1.94025			0.970125	−	0.242606i	$-0.0780023\pi$
$709$	2.59701e7			1.94025			0.970125	+	0.242606i	$0.0780023\pi$
$710$		0			0
$711$	−1.24802e7	+	1.55971e7i	−0.925865	+	1.15710i
$712$		0			0
$713$		−	6.54379e6i		−	0.482065i
$714$		0			0
$715$		−	2.37072e6i		−	0.173426i
$716$		0			0
$717$	−1.06587e6	+	3.03808e6i	−0.0774295	+	0.220700i
$718$		0			0
$719$	1.05306e7			0.759677			0.379838	−	0.925053i	$-0.375980\pi$
$719$	1.05306e7			0.759677			0.379838	+	0.925053i	$0.375980\pi$
$720$		0			0
$721$	−7.34683e6			−0.526334
$722$		0			0
$723$	−8.51549e6	+	2.42720e7i	−0.605848	+	1.72687i
$724$		0			0
$725$		−	3.44081e6i		−	0.243117i
$726$		0			0
$727$		−	2.45606e7i		−	1.72347i	−0.507358	−	0.861735i	$-0.669378\pi$
$727$		−	2.45606e7i		−	1.72347i	0.507358	−	0.861735i	$-0.330622\pi$
$728$		0			0
$729$	6.28933e6	−	1.28971e7i	0.438314	−	0.898822i
$730$		0			0
$731$	−2.70545e7			−1.87260
$732$		0			0
$733$	1.82797e7			1.25664			0.628318	−	0.777957i	$-0.283744\pi$
$733$	1.82797e7			1.25664			0.628318	+	0.777957i	$0.283744\pi$
$734$		0			0
$735$	−8.11440e6	−	2.84683e6i	−0.554036	−	0.194376i
$736$		0			0
$737$			4.45091e6i			0.301843i
$738$		0			0
$739$			2.01860e7i			1.35969i	0.733356	+	0.679844i	$0.237953\pi$
$739$			2.01860e7i			1.35969i	−0.733356	+	0.679844i	$0.762047\pi$
$740$		0			0
$741$	3.62883e6	+	1.27313e6i	0.242785	+	0.0851777i
$742$		0			0
$743$	2.29183e7			1.52304			0.761518	−	0.648143i	$-0.224454\pi$
$743$	2.29183e7			1.52304			0.761518	+	0.648143i	$0.224454\pi$
$744$		0			0
$745$	−1.93087e7			−1.27456
$746$		0			0
$747$	−3.62747e6	−	2.90257e6i	−0.237850	−	0.190318i
$748$		0			0
$749$			3.70447e7i			2.41280i
$750$		0			0
$751$			2.29724e7i			1.48630i	0.669126	+	0.743149i	$0.266669\pi$
$751$			2.29724e7i			1.48630i	−0.669126	+	0.743149i	$0.733331\pi$
$752$		0			0
$753$	8.05891e6	−	2.29706e7i	0.517951	−	1.47633i
$754$		0			0
$755$	−1.92824e7			−1.23110
$756$		0			0
$757$	−1.71489e7			−1.08767			−0.543835	−	0.839192i	$-0.683028\pi$
$757$	−1.71489e7			−1.08767			−0.543835	+	0.839192i	$0.683028\pi$
$758$		0			0
$759$	−2.01434e6	+	5.74154e6i	−0.126920	+	0.361763i
$760$		0			0
$761$		−	6.55577e6i		−	0.410357i	−0.978725	−	0.205178i	$-0.934223\pi$
$761$		−	6.55577e6i		−	0.410357i	0.978725	−	0.205178i	$-0.0657775\pi$
$762$		0			0
$763$			2.56620e7i			1.59580i
$764$		0			0
$765$	1.22253e7	+	9.78222e6i	0.755277	+	0.604343i
$766$		0			0
$767$	897544.			0.0550893
$768$		0			0
$769$	−2.14557e7			−1.30836			−0.654180	−	0.756339i	$-0.726986\pi$
$769$	−2.14557e7			−1.30836			−0.654180	+	0.756339i	$0.726986\pi$
$770$		0			0
$771$	2.22417e7	+	7.80322e6i	1.34751	+	0.472757i
$772$		0			0
$773$			1.13075e7i			0.680640i	0.940310	+	0.340320i	$0.110535\pi$
$773$			1.13075e7i			0.680640i	−0.940310	+	0.340320i	$0.889465\pi$
$774$		0			0
$775$			4.04865e6i			0.242134i
$776$		0			0
$777$	8.06736e6	+	2.83032e6i	0.479379	+	0.168184i
$778$		0			0
$779$	−2.11494e7			−1.24869
$780$		0			0
$781$	−2.09607e7			−1.22964
$782$		0			0
$783$	−9.13290e6	−	1.46147e7i	−0.532359	−	0.851892i
$784$		0			0
$785$			4.48100e6i			0.259538i
$786$		0			0
$787$			619355.i			0.0356454i	0.999841	+	0.0178227i	$0.00567344\pi$
$787$			619355.i			0.0356454i	−0.999841	+	0.0178227i	$0.994327\pi$
$788$		0			0
$789$	1.99743e6	−	5.69333e6i	0.114230	−	0.325592i
$790$		0			0
$791$	−2.39222e7			−1.35944
$792$		0			0
$793$	−3.50361e6			−0.197848
$794$		0			0
$795$	8.35682e6	−	2.38197e7i	0.468946	−	1.33665i
$796$		0			0
$797$			2.08343e6i			0.116180i	0.998311	+	0.0580901i	$0.0185011\pi$
$797$			2.08343e6i			0.116180i	−0.998311	+	0.0580901i	$0.981499\pi$
$798$		0			0
$799$			2.65560e7i			1.47162i
$800$		0			0
$801$	1.47358e7	−	1.84160e7i	0.811505	−	1.01418i
$802$		0			0
$803$	−1.77772e7			−0.972916
$804$		0			0
$805$	−9.98025e6			−0.542815
$806$		0			0
$807$	2.39572e7	+	8.40506e6i	1.29495	+	0.454315i
$808$		0			0
$809$		−	343117.i		−	0.0184320i	−0.999958	−	0.00921598i	$-0.997066\pi$
$809$		−	343117.i		−	0.0184320i	0.999958	−	0.00921598i	$-0.00293358\pi$
$810$		0			0
$811$		−	3.02023e6i		−	0.161246i	−0.996745	−	0.0806228i	$-0.974309\pi$
$811$		−	3.02023e6i		−	0.161246i	0.996745	−	0.0806228i	$-0.0256909\pi$
$812$		0			0
$813$	−8.08907e6	−	2.83794e6i	−0.429212	−	0.150583i
$814$		0			0
$815$	−1.45716e7			−0.768447
$816$		0			0
$817$	3.30484e7			1.73219
$818$		0			0
$819$	−3.88514e6	+	4.85545e6i	−0.202394	+	0.252941i
$820$		0			0
$821$			4.37269e6i			0.226407i	0.993572	+	0.113204i	$0.0361113\pi$
$821$			4.37269e6i			0.226407i	−0.993572	+	0.113204i	$0.963889\pi$
$822$		0			0
$823$		−	2.95780e7i		−	1.52219i	−0.648641	−	0.761095i	$-0.724662\pi$
$823$		−	2.95780e7i		−	1.52219i	0.648641	−	0.761095i	$-0.275338\pi$
$824$		0			0
$825$	1.24628e6	−	3.55230e6i	0.0637499	−	0.181708i
$826$		0			0
$827$	−2.90787e7			−1.47846			−0.739232	−	0.673451i	$-0.764811\pi$
$827$	−2.90787e7			−1.47846			−0.739232	+	0.673451i	$0.764811\pi$
$828$		0			0
$829$	2.57279e7			1.30023			0.650113	−	0.759838i	$-0.274722\pi$
$829$	2.57279e7			1.30023			0.650113	+	0.759838i	$0.274722\pi$
$830$		0			0
$831$	−7.11157e6	+	2.02703e7i	−0.357242	+	1.01826i
$832$		0			0
$833$			1.50058e7i			0.749284i
$834$		0			0
$835$			2.97691e6i			0.147758i
$836$		0			0
$837$	1.07463e7	+	1.71964e7i	0.530206	+	0.848447i
$838$		0			0
$839$	−1.13952e7			−0.558877			−0.279439	−	0.960164i	$-0.590148\pi$
$839$	−1.13952e7			−0.558877			−0.279439	+	0.960164i	$0.590148\pi$
$840$		0			0
$841$	−187181.			−0.00912581
$842$		0			0
$843$	2.99642e7	+	1.05125e7i	1.45222	+	0.509492i
$844$		0			0
$845$			1.69380e7i			0.816057i
$846$		0			0
$847$		−	9.91239e6i		−	0.474756i
$848$		0			0
$849$	1.70227e7	+	5.97219e6i	0.810513	+	0.284357i
$850$		0			0
$851$	3.99644e6			0.189169
$852$		0			0
$853$	−3.53215e6			−0.166213			−0.0831067	−	0.996541i	$-0.526484\pi$
$853$	−3.53215e6			−0.166213			−0.0831067	+	0.996541i	$0.526484\pi$
$854$		0			0
$855$	−1.49338e7	−	1.19495e7i	−0.698643	−	0.559027i
$856$		0			0
$857$			2.78472e7i			1.29518i	0.761990	+	0.647589i	$0.224223\pi$
$857$			2.78472e7i			1.29518i	−0.761990	+	0.647589i	$0.775777\pi$
$858$		0			0
$859$			9.12202e6i			0.421801i	0.977508	+	0.210901i	$0.0676397\pi$
$859$			9.12202e6i			0.421801i	−0.977508	+	0.210901i	$0.932360\pi$
$860$		0			0
$861$	1.13216e7	−	3.22703e7i	0.520475	−	1.48353i
$862$		0			0
$863$	3.82202e7			1.74689			0.873445	−	0.486923i	$-0.161881\pi$
$863$	3.82202e7			1.74689			0.873445	+	0.486923i	$0.161881\pi$
$864$		0			0
$865$	−1.70062e7			−0.772801
$866$		0			0
$867$	1.71770e6	−	4.89600e6i	0.0776066	−	0.221204i
$868$		0			0
$869$			2.62491e7i			1.17914i
$870$		0			0
$871$			2.12635e6i			0.0949706i
$872$		0			0
$873$	−3.02254e7	−	2.41852e7i	−1.34226	−	1.07402i
$874$		0			0
$875$	3.16888e7			1.39922
$876$		0			0
$877$	1.52280e7			0.668566			0.334283	−	0.942473i	$-0.391506\pi$
$877$	1.52280e7			0.668566			0.334283	+	0.942473i	$0.391506\pi$
$878$		0			0
$879$	−3.65342e7	−	1.28175e7i	−1.59488	−	0.559541i
$880$		0			0
$881$		−	2.39351e7i		−	1.03895i	−0.854485	−	0.519477i	$-0.826127\pi$
$881$		−	2.39351e7i		−	1.03895i	0.854485	−	0.519477i	$-0.173873\pi$
$882$		0			0
$883$		−	4.20111e7i		−	1.81327i	−0.421919	−	0.906634i	$-0.638643\pi$
$883$		−	4.20111e7i		−	1.81327i	0.421919	−	0.906634i	$-0.361357\pi$
$884$		0			0
$885$	−4.21214e6	−	1.47777e6i	−0.180777	−	0.0634233i
$886$		0			0
$887$	−1.42404e7			−0.607735			−0.303867	−	0.952714i	$-0.598278\pi$
$887$	−1.42404e7			−0.607735			−0.303867	+	0.952714i	$0.598278\pi$
$888$		0			0
$889$	−8.30108e6			−0.352274
$890$		0			0
$891$	−4.13533e6	−	1.83962e7i	−0.174508	−	0.776307i
$892$		0			0
$893$		−	3.24395e7i		−	1.36127i
$894$		0			0
$895$			8.41562e6i			0.351179i
$896$		0			0
$897$	−962318.	+	2.74292e6i	−0.0399335	+	0.113824i
$898$		0			0
$899$	2.43548e7			1.00505
$900$		0			0
$901$	−4.40493e7			−1.80770
$902$		0			0
$903$	−1.76913e7	+	5.04261e7i	−0.722006	+	2.05796i
$904$		0			0
$905$			1.80378e7i			0.732084i
$906$		0			0
$907$			9.67370e6i			0.390458i	0.980758	+	0.195229i	$0.0625450\pi$
$907$			9.67370e6i			0.390458i	−0.980758	+	0.195229i	$0.937455\pi$
$908$		0			0
$909$	1.17307e7	−	1.46604e7i	0.470886	−	0.588488i
$910$		0			0
$911$	−915385.			−0.0365433			−0.0182716	−	0.999833i	$-0.505816\pi$
$911$	−915385.			−0.0365433			−0.0182716	+	0.999833i	$0.505816\pi$
$912$		0			0
$913$	−6.10484e6			−0.242380
$914$		0			0
$915$	1.64423e7	+	5.76855e6i	0.649246	+	0.227779i
$916$		0			0
$917$			4.36799e7i			1.71537i
$918$		0			0
$919$		−	2.37044e7i		−	0.925849i	−0.886398	−	0.462925i	$-0.846800\pi$
$919$		−	2.37044e7i		−	0.925849i	0.886398	−	0.462925i	$-0.153200\pi$
$920$		0			0
$921$	−3.74508e7	−	1.31391e7i	−1.45483	−	0.510408i
$922$		0			0
$923$	−1.00136e7			−0.386890
$924$		0			0
$925$	−2.47260e6			−0.0950166
$926$		0			0
$927$	6.64896e6	−	8.30952e6i	0.254129	−	0.317597i
$928$		0			0
$929$			726976.i			0.0276364i	0.999905	+	0.0138182i	$0.00439860\pi$
$929$			726976.i			0.0276364i	−0.999905	+	0.0138182i	$0.995601\pi$
$930$		0			0
$931$		−	1.83303e7i		−	0.693099i
$932$		0			0
$933$	1.37411e7	−	3.91666e7i	0.516793	−	1.47303i
$934$		0			0
$935$	2.05745e7			0.769662
$936$		0			0
$937$	−1.31585e7			−0.489617			−0.244808	−	0.969571i	$-0.578725\pi$
$937$	−1.31585e7			−0.489617			−0.244808	+	0.969571i	$0.578725\pi$
$938$		0			0
$939$	2.06525e6	−	5.88665e6i	0.0764379	−	0.217873i
$940$		0			0
$941$		−	2.83098e7i		−	1.04223i	−0.853488	−	0.521113i	$-0.825517\pi$
$941$		−	2.83098e7i		−	1.04223i	0.853488	−	0.521113i	$-0.174483\pi$
$942$		0			0
$943$		−	1.59862e7i		−	0.585417i
$944$		0			0
$945$	2.62271e7	−	1.63897e7i	0.955369	−	0.597023i
$946$		0			0
$947$	−3.47806e7			−1.26026			−0.630132	−	0.776488i	$-0.716999\pi$
$947$	−3.47806e7			−1.26026			−0.630132	+	0.776488i	$0.716999\pi$
$948$		0			0
$949$	−8.49277e6			−0.306115
$950$		0			0
$951$	−2.27156e7	−	7.96946e6i	−0.814465	−	0.285744i
$952$		0			0
$953$		−	2.91370e7i		−	1.03923i	−0.854399	−	0.519617i	$-0.826075\pi$
$953$		−	2.91370e7i		−	1.03923i	0.854399	−	0.519617i	$-0.173925\pi$
$954$		0			0
$955$			3.09991e7i			1.09987i
$956$		0			0
$957$	−2.13690e7	−	7.49702e6i	−0.754231	−	0.264612i
$958$		0			0
$959$	1.80998e7			0.635516
$960$		0			0
$961$	−28086.4			−0.000981042
$962$		0			0
$963$	−4.18989e7	−	3.35259e7i	−1.45592	−	1.16497i
$964$		0			0
$965$		−	3.85369e7i		−	1.33217i
$966$		0			0
$967$			1.15601e7i			0.397554i	0.980045	+	0.198777i	$0.0636969\pi$
$967$			1.15601e7i			0.397554i	−0.980045	+	0.198777i	$0.936303\pi$
$968$		0			0
$969$	−1.10489e7	+	3.14931e7i	−0.378017	+	1.07747i
$970$		0			0
$971$	1.20504e7			0.410161			0.205080	−	0.978745i	$-0.434254\pi$
$971$	1.20504e7			0.410161			0.205080	+	0.978745i	$0.434254\pi$
$972$		0			0
$973$	1.52785e7			0.517368
$974$		0			0
$975$	595387.	−	1.69705e6i	0.0200580	−	0.0571720i
$976$		0			0
$977$			2.16156e7i			0.724487i	0.932084	+	0.362243i	$0.117989\pi$
$977$			2.16156e7i			0.724487i	−0.932084	+	0.362243i	$0.882011\pi$
$978$		0			0
$979$		−	3.09931e7i		−	1.03349i
$980$		0			0
$981$	−2.90246e7	−	2.32244e7i	−0.962927	−	0.770497i
$982$		0			0
$983$	3.88290e7			1.28166			0.640829	−	0.767684i	$-0.278591\pi$
$983$	3.88290e7			1.28166			0.640829	+	0.767684i	$0.278591\pi$
$984$		0			0
$985$	−1.11715e7			−0.366876
$986$		0			0
$987$	4.94971e7	+	1.73654e7i	1.61729	+	0.567403i
$988$		0			0
$989$			2.49803e7i			0.812094i
$990$		0			0
$991$			4.70519e7i			1.52192i	0.648797	+	0.760962i	$0.275272\pi$
$991$			4.70519e7i			1.52192i	−0.648797	+	0.760962i	$0.724728\pi$
$992$		0			0
$993$	4.97109e6	+	1.74404e6i	0.159985	+	0.0561285i
$994$		0			0
$995$	2.04636e6			0.0655275
$996$		0			0
$997$	−5.60514e6			−0.178586			−0.0892932	−	0.996005i	$-0.528461\pi$
$997$	−5.60514e6			−0.178586			−0.0892932	+	0.996005i	$0.528461\pi$
$998$		0			0
$999$	−1.05022e7	+	6.56299e6i	−0.332942	+	0.208060i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.6.c.a.383.8	yes	20
3.2	odd	2		384.6.c.d.383.14	yes	20
4.3	odd	2		384.6.c.d.383.13	yes	20
8.3	odd	2		384.6.c.b.383.8	yes	20
8.5	even	2		384.6.c.c.383.13	yes	20
12.11	even	2	inner	384.6.c.a.383.7	✓	20
24.5	odd	2		384.6.c.b.383.7	yes	20
24.11	even	2		384.6.c.c.383.14	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.6.c.a.383.7	✓	20	12.11	even	2	inner
384.6.c.a.383.8	yes	20	1.1	even	1	trivial
384.6.c.b.383.7	yes	20	24.5	odd	2
384.6.c.b.383.8	yes	20	8.3	odd	2
384.6.c.c.383.13	yes	20	8.5	even	2
384.6.c.c.383.14	yes	20	24.11	even	2
384.6.c.d.383.13	yes	20	4.3	odd	2
384.6.c.d.383.14	yes	20	3.2	odd	2

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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	384.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.16061 + 14.7095i) q^{3} -48.6693i q^{5} +167.754i q^{7} +(-189.736 - 151.820i) q^{9} +O(q^{10})\)	\(q+(-5.16061 + 14.7095i) q^{3} -48.6693i q^{5} +167.754i q^{7} +(-189.736 - 151.820i) q^{9} -319.315 q^{11} -152.547 q^{13} +(715.899 + 251.163i) q^{15} -1323.90i q^{17} +1617.20i q^{19} +(-2467.58 - 865.716i) q^{21} -1222.40 q^{23} +756.298 q^{25} +(3212.34 - 2007.43i) q^{27} -4549.54i q^{29} +5353.25i q^{31} +(1647.86 - 4696.95i) q^{33} +8164.49 q^{35} -3269.34 q^{37} +(787.239 - 2243.89i) q^{39} +13077.7i q^{41} -20435.5i q^{43} +(-7388.96 + 9234.33i) q^{45} -20059.0 q^{47} -11334.6 q^{49} +(19473.8 + 6832.12i) q^{51} -33272.4i q^{53} +15540.9i q^{55} +(-23788.2 - 8345.77i) q^{57} -5883.70 q^{59} +22967.3 q^{61} +(25468.4 - 31829.1i) q^{63} +7424.38i q^{65} -13938.9i q^{67} +(6308.32 - 17980.8i) q^{69} +65642.7 q^{71} +55673.0 q^{73} +(-3902.96 + 11124.7i) q^{75} -53566.6i q^{77} -82204.2i q^{79} +(12950.6 + 57611.3i) q^{81} +19118.5 q^{83} -64433.2 q^{85} +(66921.3 + 23478.4i) q^{87} +97061.0i q^{89} -25590.5i q^{91} +(-78743.3 - 27626.0i) q^{93} +78708.3 q^{95} +159302. q^{97} +(60585.7 + 48478.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3}+O(q^{10}) \) 20 * q - 2 * q^3	\( 20 q - 2 q^{3} - 948 q^{11} - 852 q^{15} - 1640 q^{21} - 328 q^{23} - 12500 q^{25} - 2030 q^{27} + 2836 q^{33} + 7184 q^{35} - 15056 q^{37} + 12980 q^{39} - 11800 q^{45} - 36640 q^{47} - 33388 q^{49} - 1936 q^{51} + 15404 q^{57} - 62908 q^{59} - 73264 q^{61} - 23608 q^{63} + 84024 q^{69} - 34888 q^{71} + 52568 q^{73} - 115698 q^{75} + 55444 q^{81} + 225172 q^{83} + 30112 q^{85} + 225700 q^{87} + 148016 q^{93} - 418616 q^{95} + 7600 q^{97} - 378260 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 - 948 * q^11 - 852 * q^15 - 1640 * q^21 - 328 * q^23 - 12500 * q^25 - 2030 * q^27 + 2836 * q^33 + 7184 * q^35 - 15056 * q^37 + 12980 * q^39 - 11800 * q^45 - 36640 * q^47 - 33388 * q^49 - 1936 * q^51 + 15404 * q^57 - 62908 * q^59 - 73264 * q^61 - 23608 * q^63 + 84024 * q^69 - 34888 * q^71 + 52568 * q^73 - 115698 * q^75 + 55444 * q^81 + 225172 * q^83 + 30112 * q^85 + 225700 * q^87 + 148016 * q^93 - 418616 * q^95 + 7600 * q^97 - 378260 * q^99

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