LMFDB - Embedded newform 384.6.c.a.383.5

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			383.5
Root			$0.406991i$ of defining polynomial
Character	$\chi$	$=$	384.383
Dual form			384.6.c.a.383.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.1204 - 11.8566i) q^{3} -19.3214i q^{5} -82.7816i q^{7} +(-38.1561 + 239.986i) q^{9} +O(q^{10})$	\(q+(-10.1204 - 11.8566i) q^{3} -19.3214i q^{5} -82.7816i q^{7} +(-38.1561 + 239.986i) q^{9} -332.396 q^{11} +1171.14 q^{13} +(-229.086 + 195.540i) q^{15} -1984.58i q^{17} +1346.21i q^{19} +(-981.506 + 837.781i) q^{21} +1833.50 q^{23} +2751.68 q^{25} +(3231.56 - 1976.34i) q^{27} -1923.64i q^{29} -5801.19i q^{31} +(3363.97 + 3941.07i) q^{33} -1599.46 q^{35} +6805.63 q^{37} +(-11852.4 - 13885.7i) q^{39} -4150.50i q^{41} +8370.22i q^{43} +(4636.87 + 737.231i) q^{45} -1805.52 q^{47} +9954.20 q^{49} +(-23530.3 + 20084.7i) q^{51} +22703.3i q^{53} +6422.36i q^{55} +(15961.5 - 13624.2i) q^{57} +18653.9 q^{59} -19502.5 q^{61} +(19866.4 + 3158.63i) q^{63} -22628.1i q^{65} -50953.6i q^{67} +(-18555.7 - 21739.0i) q^{69} -69899.0 q^{71} +37035.5 q^{73} +(-27848.0 - 32625.5i) q^{75} +27516.3i q^{77} -50543.7i q^{79} +(-56137.2 - 18313.8i) q^{81} -96377.3 q^{83} -38345.0 q^{85} +(-22807.8 + 19468.0i) q^{87} -17995.1i q^{89} -96949.0i q^{91} +(-68782.2 + 58710.2i) q^{93} +26010.8 q^{95} +48381.9 q^{97} +(12682.9 - 79770.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−10.1204	−	11.8566i	−0.649222	−	0.760599i
$3$	−10.1204	−	11.8566i	−0.649222	−	0.760599i
$4$		0			0
$5$		−	19.3214i		−	0.345632i	−0.984954	−	0.172816i	$-0.944713\pi$
$5$		−	19.3214i		−	0.345632i	0.984954	−	0.172816i	$-0.0552867\pi$
$6$		0			0
$7$		−	82.7816i		−	0.638541i	−0.947664	−	0.319271i	$-0.896562\pi$
$7$		−	82.7816i		−	0.638541i	0.947664	−	0.319271i	$-0.103438\pi$
$8$		0			0
$9$	−38.1561	+	239.986i	−0.157021	+	0.987595i
$10$		0			0
$11$	−332.396			−0.828273			−0.414137	−	0.910215i	$-0.635916\pi$
$11$	−332.396			−0.828273			−0.414137	+	0.910215i	$0.635916\pi$
$12$		0			0
$13$	1171.14			1.92199			0.960994	−	0.276568i	$-0.0891971\pi$
$13$	1171.14			1.92199			0.960994	+	0.276568i	$0.0891971\pi$
$14$		0			0
$15$	−229.086	+	195.540i	−0.262888	+	0.224392i
$16$		0			0
$17$		−	1984.58i		−	1.66551i	−0.553644	−	0.832754i	$-0.686763\pi$
$17$		−	1984.58i		−	1.66551i	0.553644	−	0.832754i	$-0.313237\pi$
$18$		0			0
$19$			1346.21i			0.855520i	0.903892	+	0.427760i	$0.140697\pi$
$19$			1346.21i			0.855520i	−0.903892	+	0.427760i	$0.859303\pi$
$20$		0			0
$21$	−981.506	+	837.781i	−0.485674	+	0.414555i
$22$		0			0
$23$	1833.50			0.722704			0.361352	−	0.932429i	$-0.382315\pi$
$23$	1833.50			0.722704			0.361352	+	0.932429i	$0.382315\pi$
$24$		0			0
$25$	2751.68			0.880538
$26$		0			0
$27$	3231.56	−	1976.34i	0.853105	−	0.521739i
$28$		0			0
$29$		−	1923.64i		−	0.424747i	−0.977189	−	0.212373i	$-0.931881\pi$
$29$		−	1923.64i		−	0.424747i	0.977189	−	0.212373i	$-0.0681193\pi$
$30$		0			0
$31$		−	5801.19i		−	1.08421i	−0.840311	−	0.542104i	$-0.817628\pi$
$31$		−	5801.19i		−	1.08421i	0.840311	−	0.542104i	$-0.182372\pi$
$32$		0			0
$33$	3363.97	+	3941.07i	0.537733	+	0.629984i
$34$		0			0
$35$	−1599.46			−0.220701
$36$		0			0
$37$	6805.63			0.817267			0.408634	−	0.912698i	$-0.366005\pi$
$37$	6805.63			0.817267			0.408634	+	0.912698i	$0.366005\pi$
$38$		0			0
$39$	−11852.4	−	13885.7i	−1.24780	−	1.46186i
$40$		0			0
$41$		−	4150.50i		−	0.385603i	−0.981238	−	0.192801i	$-0.938243\pi$
$41$		−	4150.50i		−	0.385603i	0.981238	−	0.192801i	$-0.0617573\pi$
$42$		0			0
$43$			8370.22i			0.690344i	0.938539	+	0.345172i	$0.112179\pi$
$43$			8370.22i			0.690344i	−0.938539	+	0.345172i	$0.887821\pi$
$44$		0			0
$45$	4636.87	+	737.231i	0.341345	+	0.0542716i
$46$		0			0
$47$	−1805.52			−0.119222			−0.0596111	−	0.998222i	$-0.518986\pi$
$47$	−1805.52			−0.119222			−0.0596111	+	0.998222i	$0.518986\pi$
$48$		0			0
$49$	9954.20			0.592265
$50$		0			0
$51$	−23530.3	+	20084.7i	−1.26678	+	1.08128i
$52$		0			0
$53$			22703.3i			1.11019i	0.831786	+	0.555097i	$0.187319\pi$
$53$			22703.3i			1.11019i	−0.831786	+	0.555097i	$0.812681\pi$
$54$		0			0
$55$			6422.36i			0.286278i
$56$		0			0
$57$	15961.5	−	13624.2i	0.650708	−	0.555423i
$58$		0			0
$59$	18653.9			0.697654			0.348827	−	0.937187i	$-0.386580\pi$
$59$	18653.9			0.697654			0.348827	+	0.937187i	$0.386580\pi$
$60$		0			0
$61$	−19502.5			−0.671066			−0.335533	−	0.942028i	$-0.608916\pi$
$61$	−19502.5			−0.671066			−0.335533	+	0.942028i	$0.608916\pi$
$62$		0			0
$63$	19866.4	+	3158.63i	0.630620	+	0.100264i
$64$		0			0
$65$		−	22628.1i		−	0.664302i
$66$		0			0
$67$		−	50953.6i		−	1.38672i	−0.720592	−	0.693359i	$-0.756130\pi$
$67$		−	50953.6i		−	1.38672i	0.720592	−	0.693359i	$-0.243870\pi$
$68$		0			0
$69$	−18555.7	−	21739.0i	−0.469196	−	0.549688i
$70$		0			0
$71$	−69899.0			−1.64560			−0.822801	−	0.568329i	$-0.807590\pi$
$71$	−69899.0			−1.64560			−0.822801	+	0.568329i	$0.807590\pi$
$72$		0			0
$73$	37035.5			0.813414			0.406707	−	0.913559i	$-0.366677\pi$
$73$	37035.5			0.813414			0.406707	+	0.913559i	$0.366677\pi$
$74$		0			0
$75$	−27848.0	−	32625.5i	−0.571665	−	0.669736i
$76$		0			0
$77$			27516.3i			0.528887i
$78$		0			0
$79$		−	50543.7i		−	0.911170i	−0.890192	−	0.455585i	$-0.849430\pi$
$79$		−	50543.7i		−	0.911170i	0.890192	−	0.455585i	$-0.150570\pi$
$80$		0			0
$81$	−56137.2	−	18313.8i	−0.950689	−	0.310147i
$82$		0			0
$83$	−96377.3			−1.53560			−0.767802	−	0.640687i	$-0.778650\pi$
$83$	−96377.3			−1.53560			−0.767802	+	0.640687i	$0.778650\pi$
$84$		0			0
$85$	−38345.0			−0.575653
$86$		0			0
$87$	−22807.8	+	19468.0i	−0.323062	+	0.275755i
$88$		0			0
$89$		−	17995.1i		−	0.240812i	−0.992725	−	0.120406i	$-0.961580\pi$
$89$		−	17995.1i		−	0.240812i	0.992725	−	0.120406i	$-0.0384196\pi$
$90$		0			0
$91$		−	96949.0i		−	1.22727i
$92$		0			0
$93$	−68782.2	+	58710.2i	−0.824648	+	0.703892i
$94$		0			0
$95$	26010.8			0.295695
$96$		0			0
$97$	48381.9			0.522100			0.261050	−	0.965325i	$-0.415931\pi$
$97$	48381.9			0.522100			0.261050	+	0.965325i	$0.415931\pi$
$98$		0			0
$99$	12682.9	−	79770.2i	0.130056	−	0.817999i
$100$		0			0
$101$			101239.i			0.987512i	0.869600	+	0.493756i	$0.164376\pi$
$101$			101239.i			0.987512i	−0.869600	+	0.493756i	$0.835624\pi$
$102$		0			0
$103$		−	26652.9i		−	0.247544i	−0.992311	−	0.123772i	$-0.960501\pi$
$103$		−	26652.9i		−	0.247544i	0.992311	−	0.123772i	$-0.0394991\pi$
$104$		0			0
$105$	16187.1	+	18964.1i	0.143284	+	0.167865i
$106$		0			0
$107$	−12661.8			−0.106914			−0.0534571	−	0.998570i	$-0.517024\pi$
$107$	−12661.8			−0.106914			−0.0534571	+	0.998570i	$0.517024\pi$
$108$		0			0
$109$	−198283.			−1.59852			−0.799262	−	0.600983i	$-0.794776\pi$
$109$	−198283.			−1.59852			−0.799262	+	0.600983i	$0.794776\pi$
$110$		0			0
$111$	−68875.5	−	80691.4i	−0.530588	−	0.621613i
$112$		0			0
$113$		−	225671.i		−	1.66257i	−0.555849	−	0.831284i	$-0.687607\pi$
$113$		−	225671.i		−	1.66257i	0.555849	−	0.831284i	$-0.312393\pi$
$114$		0			0
$115$		−	35425.8i		−	0.249790i
$116$		0			0
$117$	−44686.2	+	281057.i	−0.301793	+	1.89815i
$118$		0			0
$119$	−164287.			−1.06350
$120$		0			0
$121$	−50564.1			−0.313963
$122$		0			0
$123$	−49210.6	+	42004.6i	−0.293289	+	0.250342i
$124$		0			0
$125$		−	113546.i		−	0.649975i
$126$		0			0
$127$			99291.9i			0.546266i	0.961976	+	0.273133i	$0.0880600\pi$
$127$			99291.9i			0.546266i	−0.961976	+	0.273133i	$0.911940\pi$
$128$		0			0
$129$	99242.0	−	84709.7i	0.525075	−	0.448187i
$130$		0			0
$131$	−253584.			−1.29105			−0.645527	−	0.763737i	$-0.723362\pi$
$131$	−253584.			−1.29105			−0.645527	+	0.763737i	$0.723362\pi$
$132$		0			0
$133$	111442.			0.546285
$134$		0			0
$135$	−38185.8	−	62438.4i	−0.180330	−	0.294861i
$136$		0			0
$137$		−	47885.6i		−	0.217973i	−0.994043	−	0.108987i	$-0.965239\pi$
$137$		−	47885.6i		−	0.217973i	0.994043	−	0.108987i	$-0.0347606\pi$
$138$		0			0
$139$		−	199921.i		−	0.877652i	−0.898572	−	0.438826i	$-0.855394\pi$
$139$		−	199921.i		−	0.877652i	0.898572	−	0.438826i	$-0.144606\pi$
$140$		0			0
$141$	18272.5	+	21407.2i	0.0774017	+	0.0906802i
$142$		0			0
$143$	−389282.			−1.59193
$144$		0			0
$145$	−37167.6			−0.146806
$146$		0			0
$147$	−100740.	−	118023.i	−0.384512	−	0.450476i
$148$		0			0
$149$		−	63727.7i		−	0.235159i	−0.993063	−	0.117580i	$-0.962486\pi$
$149$		−	63727.7i		−	0.235159i	0.993063	−	0.117580i	$-0.0375136\pi$
$150$		0			0
$151$		−	446578.i		−	1.59388i	−0.604060	−	0.796939i	$-0.706451\pi$
$151$		−	446578.i		−	1.59388i	0.604060	−	0.796939i	$-0.293549\pi$
$152$		0			0
$153$	476271.	+	75723.9i	1.64485	+	0.261520i
$154$		0			0
$155$	−112087.			−0.374738
$156$		0			0
$157$	−266348.			−0.862384			−0.431192	−	0.902260i	$-0.641907\pi$
$157$	−266348.			−0.862384			−0.431192	+	0.902260i	$0.641907\pi$
$158$		0			0
$159$	269183.	−	229766.i	0.844412	−	0.720762i
$160$		0			0
$161$		−	151780.i		−	0.461476i
$162$		0			0
$163$			244693.i			0.721361i	0.932689	+	0.360680i	$0.117455\pi$
$163$			244693.i			0.721361i	−0.932689	+	0.360680i	$0.882545\pi$
$164$		0			0
$165$	76147.1	−	64996.7i	0.217743	−	0.185858i
$166$		0			0
$167$	199361.			0.553157			0.276579	−	0.960991i	$-0.410799\pi$
$167$	199361.			0.553157			0.276579	+	0.960991i	$0.410799\pi$
$168$		0			0
$169$	1.00028e6			2.69404
$170$		0			0
$171$	−323072.	−	51366.3i	−0.844908	−	0.134335i
$172$		0			0
$173$			322299.i			0.818736i	0.912369	+	0.409368i	$0.134251\pi$
$173$			322299.i			0.818736i	−0.912369	+	0.409368i	$0.865749\pi$
$174$		0			0
$175$		−	227789.i		−	0.562260i
$176$		0			0
$177$	−188785.	−	221171.i	−0.452933	−	0.530635i
$178$		0			0
$179$	853012.			1.98986			0.994930	−	0.100570i	$-0.0320665\pi$
$179$	853012.			1.98986			0.994930	+	0.100570i	$0.0320665\pi$
$180$		0			0
$181$	434775.			0.986434			0.493217	−	0.869906i	$-0.335821\pi$
$181$	434775.			0.986434			0.493217	+	0.869906i	$0.335821\pi$
$182$		0			0
$183$	197372.	+	231232.i	0.435671	+	0.510412i
$184$		0			0
$185$		−	131495.i		−	0.282474i
$186$		0			0
$187$			659666.i			1.37950i
$188$		0			0
$189$	−163605.	−	267514.i	−0.333152	−	0.544743i
$190$		0			0
$191$	−946078.			−1.87648			−0.938239	−	0.345987i	$-0.887544\pi$
$191$	−946078.			−1.87648			−0.938239	+	0.345987i	$0.887544\pi$
$192$		0			0
$193$	−512156.			−0.989712			−0.494856	−	0.868975i	$-0.664779\pi$
$193$	−512156.			−0.989712			−0.494856	+	0.868975i	$0.664779\pi$
$194$		0			0
$195$	−268292.	+	229005.i	−0.505267	+	0.431279i
$196$		0			0
$197$			589256.i			1.08178i	0.841094	+	0.540890i	$0.181912\pi$
$197$			589256.i			1.08178i	−0.841094	+	0.540890i	$0.818088\pi$
$198$		0			0
$199$			2967.84i			0.00531260i	0.999996	+	0.00265630i	$0.000845528\pi$
$199$			2967.84i			0.00531260i	−0.999996	+	0.00265630i	$0.999154\pi$
$200$		0			0
$201$	−604135.	+	515670.i	−1.05474	+	0.900288i
$202$		0			0
$203$	−159242.			−0.271218
$204$		0			0
$205$	−80193.6			−0.133277
$206$		0			0
$207$	−69959.1	+	440013.i	−0.113480	+	0.713739i
$208$		0			0
$209$		−	447476.i		−	0.708604i
$210$		0			0
$211$		−	768116.i		−	1.18774i	−0.804562	−	0.593869i	$-0.797600\pi$
$211$		−	768116.i		−	1.18774i	0.804562	−	0.593869i	$-0.202400\pi$
$212$		0			0
$213$	707404.	+	828762.i	1.06836	+	1.25164i
$214$		0			0
$215$	161725.			0.238605
$216$		0			0
$217$	−480232.			−0.692312
$218$		0			0
$219$	−374813.	−	439114.i	−0.528086	−	0.618682i
$220$		0			0
$221$		−	2.32422e6i		−	3.20109i
$222$		0			0
$223$		−	288136.i		−	0.388003i	−0.981001	−	0.194001i	$-0.937853\pi$
$223$		−	288136.i		−	0.388003i	0.981001	−	0.194001i	$-0.0621466\pi$
$224$		0			0
$225$	−104994.	+	660364.i	−0.138263	+	0.869615i
$226$		0			0
$227$	805116.			1.03704			0.518518	−	0.855067i	$-0.326484\pi$
$227$	805116.			1.03704			0.518518	+	0.855067i	$0.326484\pi$
$228$		0			0
$229$	−164519.			−0.207313			−0.103657	−	0.994613i	$-0.533054\pi$
$229$	−164519.			−0.207313			−0.103657	+	0.994613i	$0.533054\pi$
$230$		0			0
$231$	326248.	−	278475.i	0.402270	−	0.343365i
$232$		0			0
$233$			470691.i			0.567997i	0.958825	+	0.283998i	$0.0916610\pi$
$233$			470691.i			0.567997i	−0.958825	+	0.283998i	$0.908339\pi$
$234$		0			0
$235$			34885.2i			0.0412070i
$236$		0			0
$237$	−599274.	+	511521.i	−0.693035	+	0.591552i
$238$		0			0
$239$	1.53286e6			1.73584			0.867919	−	0.496706i	$-0.165457\pi$
$239$	1.53286e6			1.73584			0.867919	+	0.496706i	$0.165457\pi$
$240$		0			0
$241$	−924322.			−1.02513			−0.512567	−	0.858647i	$-0.671305\pi$
$241$	−924322.			−1.02513			−0.512567	+	0.858647i	$0.671305\pi$
$242$		0			0
$243$	350990.	+	850937.i	0.381311	+	0.924447i
$244$		0			0
$245$		−	192329.i		−	0.204706i
$246$		0			0
$247$			1.57661e6i			1.64430i
$248$		0			0
$249$	975374.	+	1.14270e6i	0.996949	+	1.16798i
$250$		0			0
$251$	1.28007e6			1.28248			0.641238	−	0.767342i	$-0.278421\pi$
$251$	1.28007e6			1.28248			0.641238	+	0.767342i	$0.278421\pi$
$252$		0			0
$253$	−609446.			−0.598596
$254$		0			0
$255$	388065.	+	454639.i	0.373727	+	0.437841i
$256$		0			0
$257$		−	1.72426e6i		−	1.62843i	−0.580561	−	0.814217i	$-0.697167\pi$
$257$		−	1.72426e6i		−	1.62843i	0.580561	−	0.814217i	$-0.302833\pi$
$258$		0			0
$259$		−	563381.i		−	0.521859i
$260$		0			0
$261$	461647.	+	73398.8i	0.419478	+	0.0666942i
$262$		0			0
$263$	39731.5			0.0354197			0.0177099	−	0.999843i	$-0.494362\pi$
$263$	39731.5			0.0354197			0.0177099	+	0.999843i	$0.494362\pi$
$264$		0			0
$265$	438660.			0.383719
$266$		0			0
$267$	−213359.	+	182117.i	−0.183161	+	0.156341i
$268$		0			0
$269$		−	280025.i		−	0.235948i	−0.993017	−	0.117974i	$-0.962360\pi$
$269$		−	280025.i		−	0.235948i	0.993017	−	0.117974i	$-0.0376399\pi$
$270$		0			0
$271$			2.25288e6i			1.86344i	0.363178	+	0.931720i	$0.381692\pi$
$271$			2.25288e6i			1.86344i	−0.363178	+	0.931720i	$0.618308\pi$
$272$		0			0
$273$	−1.14948e6	+	981160.i	−0.933459	+	0.796770i
$274$		0			0
$275$	−914647.			−0.729326
$276$		0			0
$277$	1.14847e6			0.899334			0.449667	−	0.893196i	$-0.351543\pi$
$277$	1.14847e6			0.899334			0.449667	+	0.893196i	$0.351543\pi$
$278$		0			0
$279$	1.39220e6	+	221351.i	1.07076	+	0.170244i
$280$		0			0
$281$			1.52077e6i			1.14894i	0.818524	+	0.574472i	$0.194793\pi$
$281$			1.52077e6i			1.14894i	−0.818524	+	0.574472i	$0.805207\pi$
$282$		0			0
$283$			610831.i			0.453372i	0.973968	+	0.226686i	$0.0727891\pi$
$283$			610831.i			0.453372i	−0.973968	+	0.226686i	$0.927211\pi$
$284$		0			0
$285$	−263239.	−	308399.i	−0.191972	−	0.224906i
$286$		0			0
$287$	−343585.			−0.246223
$288$		0			0
$289$	−2.51871e6			−1.77392
$290$		0			0
$291$	−489643.	−	573643.i	−0.338959	−	0.397108i
$292$		0			0
$293$		−	2.29419e6i		−	1.56121i	−0.625025	−	0.780605i	$-0.714911\pi$
$293$		−	2.29419e6i		−	1.56121i	0.625025	−	0.780605i	$-0.285089\pi$
$294$		0			0
$295$		−	360421.i		−	0.241132i
$296$		0			0
$297$	−1.07416e6	+	656928.i	−0.706604	+	0.432142i
$298$		0			0
$299$	2.14728e6			1.38903
$300$		0			0
$301$	692901.			0.440813
$302$		0			0
$303$	1.20034e6	−	1.02457e6i	0.751101	−	0.641115i
$304$		0			0
$305$			376816.i			0.231942i
$306$		0			0
$307$			2.25996e6i			1.36853i	0.729233	+	0.684265i	$0.239877\pi$
$307$			2.25996e6i			1.36853i	−0.729233	+	0.684265i	$0.760123\pi$
$308$		0			0
$309$	−316012.	+	269737.i	−0.188281	+	0.160711i
$310$		0			0
$311$	−2.99587e6			−1.75639			−0.878196	−	0.478301i	$-0.841253\pi$
$311$	−2.99587e6			−1.75639			−0.878196	+	0.478301i	$0.841253\pi$
$312$		0			0
$313$	686360.			0.395996			0.197998	−	0.980202i	$-0.436556\pi$
$313$	686360.			0.395996			0.197998	+	0.980202i	$0.436556\pi$
$314$		0			0
$315$	61029.2	−	383848.i	0.0346546	−	0.217963i
$316$		0			0
$317$		−	2.99429e6i		−	1.67358i	−0.547525	−	0.836789i	$-0.684430\pi$
$317$		−	2.99429e6i		−	1.67358i	0.547525	−	0.836789i	$-0.315570\pi$
$318$		0			0
$319$			639411.i			0.351806i
$320$		0			0
$321$	128142.	+	150125.i	0.0694111	+	0.0813188i
$322$		0			0
$323$	2.67167e6			1.42488
$324$		0			0
$325$	3.22261e6			1.69238
$326$		0			0
$327$	2.00670e6	+	2.35095e6i	1.03780	+	1.21584i
$328$		0			0
$329$			149464.i			0.0761282i
$330$		0			0
$331$			1.25988e6i			0.632064i	0.948749	+	0.316032i	$0.102351\pi$
$331$			1.25988e6i			0.632064i	−0.948749	+	0.316032i	$0.897649\pi$
$332$		0			0
$333$	−259677.	+	1.63325e6i	−0.128328	+	0.807129i
$334$		0			0
$335$	−984497.			−0.479295
$336$		0			0
$337$	1.52288e6			0.730452			0.365226	−	0.930919i	$-0.380992\pi$
$337$	1.52288e6			0.730452			0.365226	+	0.930919i	$0.380992\pi$
$338$		0			0
$339$	−2.67568e6	+	2.28387e6i	−1.26455	+	1.07938i
$340$		0			0
$341$			1.92829e6i			0.898021i
$342$		0			0
$343$		−	2.21534e6i		−	1.01673i
$344$		0			0
$345$	−420028.	+	358522.i	−0.189990	+	0.162169i
$346$		0			0
$347$	2.32360e6			1.03595			0.517974	−	0.855396i	$-0.326686\pi$
$347$	2.32360e6			1.03595			0.517974	+	0.855396i	$0.326686\pi$
$348$		0			0
$349$	−481189.			−0.211472			−0.105736	−	0.994394i	$-0.533720\pi$
$349$	−481189.			−0.211472			−0.105736	+	0.994394i	$0.533720\pi$
$350$		0			0
$351$	3.78461e6	−	2.31458e6i	1.63966	−	1.00278i
$352$		0			0
$353$			168846.i			0.0721197i	0.999350	+	0.0360598i	$0.0114807\pi$
$353$			168846.i			0.0721197i	−0.999350	+	0.0360598i	$0.988519\pi$
$354$		0			0
$355$			1.35055e6i			0.568774i
$356$		0			0
$357$	1.66264e6	+	1.94788e6i	0.690445	+	0.808893i
$358$		0			0
$359$	272248.			0.111488			0.0557441	−	0.998445i	$-0.482247\pi$
$359$	272248.			0.111488			0.0557441	+	0.998445i	$0.482247\pi$
$360$		0			0
$361$	663806.			0.268085
$362$		0			0
$363$	511728.	+	599517.i	0.203832	+	0.238800i
$364$		0			0
$365$		−	715580.i		−	0.281142i
$366$		0			0
$367$		−	118260.i		−	0.0458325i	−0.999737	−	0.0229163i	$-0.992705\pi$
$367$		−	118260.i		−	0.0458325i	0.999737	−	0.0229163i	$-0.00729511\pi$
$368$		0			0
$369$	996059.	+	158367.i	0.380820	+	0.0605478i
$370$		0			0
$371$	1.87941e6			0.708904
$372$		0			0
$373$	525577.			0.195598			0.0977989	−	0.995206i	$-0.468820\pi$
$373$	525577.			0.195598			0.0977989	+	0.995206i	$0.468820\pi$
$374$		0			0
$375$	−1.34626e6	+	1.14913e6i	−0.494370	+	0.421978i
$376$		0			0
$377$		−	2.25286e6i		−	0.816358i
$378$		0			0
$379$		−	806611.i		−	0.288447i	−0.989545	−	0.144224i	$-0.953932\pi$
$379$		−	806611.i		−	0.288447i	0.989545	−	0.144224i	$-0.0460684\pi$
$380$		0			0
$381$	1.17726e6	−	1.00487e6i	0.415490	−	0.354648i
$382$		0			0
$383$	1.37292e6			0.478241			0.239121	−	0.970990i	$-0.423141\pi$
$383$	1.37292e6			0.478241			0.239121	+	0.970990i	$0.423141\pi$
$384$		0			0
$385$	531654.			0.182800
$386$		0			0
$387$	−2.00873e6	−	319375.i	−0.681781	−	0.108399i
$388$		0			0
$389$		−	5.48298e6i		−	1.83714i	−0.395258	−	0.918570i	$-0.629345\pi$
$389$		−	5.48298e6i		−	1.83714i	0.395258	−	0.918570i	$-0.370655\pi$
$390$		0			0
$391$		−	3.63872e6i		−	1.20367i
$392$		0			0
$393$	2.56637e6	+	3.00664e6i	0.838181	+	0.981974i
$394$		0			0
$395$	−976577.			−0.314930
$396$		0			0
$397$	65596.8			0.0208885			0.0104442	−	0.999945i	$-0.496675\pi$
$397$	65596.8			0.0208885			0.0104442	+	0.999945i	$0.496675\pi$
$398$		0			0
$399$	−1.12783e6	−	1.32132e6i	−0.354660	−	0.415504i
$400$		0			0
$401$		−	2.35838e6i		−	0.732409i	−0.930534	−	0.366205i	$-0.880657\pi$
$401$		−	2.35838e6i		−	0.732409i	0.930534	−	0.366205i	$-0.119343\pi$
$402$		0			0
$403$		−	6.79401e6i		−	2.08384i
$404$		0			0
$405$	−353850.	+	1.08465e6i	−0.107197	+	0.328589i
$406$		0			0
$407$	−2.26216e6			−0.676921
$408$		0			0
$409$	−40774.2			−0.0120525			−0.00602625	−	0.999982i	$-0.501918\pi$
$409$	−40774.2			−0.0120525			−0.00602625	+	0.999982i	$0.501918\pi$
$410$		0			0
$411$	−567758.	+	484620.i	−0.165790	+	0.141513i
$412$		0			0
$413$		−	1.54420e6i		−	0.445481i
$414$		0			0
$415$			1.86215e6i			0.530755i
$416$		0			0
$417$	−2.37038e6	+	2.02328e6i	−0.667541	+	0.569791i
$418$		0			0
$419$	−2.09087e6			−0.581824			−0.290912	−	0.956750i	$-0.593959\pi$
$419$	−2.09087e6			−0.581824			−0.290912	+	0.956750i	$0.593959\pi$
$420$		0			0
$421$	−5.59228e6			−1.53774			−0.768871	−	0.639403i	$-0.779181\pi$
$421$	−5.59228e6			−1.53774			−0.768871	+	0.639403i	$0.779181\pi$
$422$		0			0
$423$	68891.5	−	433298.i	0.0187204	−	0.117743i
$424$		0			0
$425$		−	5.46094e6i		−	1.46654i
$426$		0			0
$427$			1.61445e6i			0.428503i
$428$		0			0
$429$	3.93968e6	+	4.61555e6i	1.03352	+	1.21082i
$430$		0			0
$431$	−3.47562e6			−0.901236			−0.450618	−	0.892717i	$-0.648796\pi$
$431$	−3.47562e6			−0.901236			−0.450618	+	0.892717i	$0.648796\pi$
$432$		0			0
$433$	262773.			0.0673537			0.0336768	−	0.999433i	$-0.489278\pi$
$433$	262773.			0.0673537			0.0336768	+	0.999433i	$0.489278\pi$
$434$		0			0
$435$	376150.	+	440680.i	0.0953098	+	0.111661i
$436$		0			0
$437$			2.46828e6i			0.618288i
$438$		0			0
$439$			5.40059e6i			1.33746i	0.743506	+	0.668729i	$0.233161\pi$
$439$			5.40059e6i			1.33746i	−0.743506	+	0.668729i	$0.766839\pi$
$440$		0			0
$441$	−379814.	+	2.38887e6i	−0.0929981	+	0.584918i
$442$		0			0
$443$	−4.14902e6			−1.00447			−0.502234	−	0.864732i	$-0.667488\pi$
$443$	−4.14902e6			−1.00447			−0.502234	+	0.864732i	$0.667488\pi$
$444$		0			0
$445$	−347690.			−0.0832324
$446$		0			0
$447$	−755591.	+	644948.i	−0.178862	+	0.152671i
$448$		0			0
$449$		−	5.27971e6i		−	1.23593i	−0.786205	−	0.617966i	$-0.787957\pi$
$449$		−	5.27971e6i		−	1.23593i	0.786205	−	0.617966i	$-0.212043\pi$
$450$		0			0
$451$			1.37961e6i			0.319385i
$452$		0			0
$453$	−5.29488e6	+	4.51954e6i	−1.21230	+	1.03478i
$454$		0			0
$455$	−1.87319e6			−0.424184
$456$		0			0
$457$	−6.04997e6			−1.35507			−0.677537	−	0.735489i	$-0.736953\pi$
$457$	−6.04997e6			−1.35507			−0.677537	+	0.735489i	$0.736953\pi$
$458$		0			0
$459$	−3.92221e6	−	6.41329e6i	−0.868960	−	1.42085i
$460$		0			0
$461$			5.14860e6i			1.12833i	0.825661	+	0.564166i	$0.190802\pi$
$461$			5.14860e6i			1.12833i	−0.825661	+	0.564166i	$0.809198\pi$
$462$		0			0
$463$		−	311898.i		−	0.0676176i	−0.999428	−	0.0338088i	$-0.989236\pi$
$463$		−	311898.i		−	0.0676176i	0.999428	−	0.0338088i	$-0.0107637\pi$
$464$		0			0
$465$	1.13437e6	+	1.32897e6i	0.243288	+	0.285025i
$466$		0			0
$467$	3.10534e6			0.658895			0.329448	−	0.944174i	$-0.393137\pi$
$467$	3.10534e6			0.658895			0.329448	+	0.944174i	$0.393137\pi$
$468$		0			0
$469$	−4.21803e6			−0.885477
$470$		0			0
$471$	2.69554e6	+	3.15797e6i	0.559879	+	0.655928i
$472$		0			0
$473$		−	2.78222e6i		−	0.571794i
$474$		0			0
$475$			3.70435e6i			0.753318i
$476$		0			0
$477$	−5.44846e6	−	866269.i	−1.09642	−	0.174324i
$478$		0			0
$479$	−3.51933e6			−0.700845			−0.350422	−	0.936592i	$-0.613962\pi$
$479$	−3.51933e6			−0.700845			−0.350422	+	0.936592i	$0.613962\pi$
$480$		0			0
$481$	7.97036e6			1.57078
$482$		0			0
$483$	−1.79959e6	+	1.53607e6i	−0.350998	+	0.299601i
$484$		0			0
$485$		−	934807.i		−	0.180455i
$486$		0			0
$487$		−	1.00090e7i		−	1.91235i	−0.292791	−	0.956177i	$-0.594584\pi$
$487$		−	1.00090e7i		−	1.91235i	0.292791	−	0.956177i	$-0.405416\pi$
$488$		0			0
$489$	2.90122e6	−	2.47638e6i	0.548666	−	0.468323i
$490$		0			0
$491$	4.74286e6			0.887844			0.443922	−	0.896066i	$-0.353587\pi$
$491$	4.74286e6			0.887844			0.443922	+	0.896066i	$0.353587\pi$
$492$		0			0
$493$	−3.81763e6			−0.707419
$494$		0			0
$495$	−1.54127e6	−	245052.i	−0.282727	−	0.0449517i
$496$		0			0
$497$			5.78635e6i			1.05079i
$498$		0			0
$499$		−	1.00050e7i		−	1.79872i	−0.437209	−	0.899360i	$-0.644033\pi$
$499$		−	1.00050e7i		−	1.79872i	0.437209	−	0.899360i	$-0.355967\pi$
$500$		0			0
$501$	−2.01761e6	−	2.36373e6i	−0.359122	−	0.420731i
$502$		0			0
$503$	118388.			0.0208635			0.0104317	−	0.999946i	$-0.496679\pi$
$503$	118388.			0.0208635			0.0104317	+	0.999946i	$0.496679\pi$
$504$		0			0
$505$	1.95607e6			0.341316
$506$		0			0
$507$	−1.01232e7	−	1.18599e7i	−1.74903	−	2.04908i
$508$		0			0
$509$			6.60168e6i			1.12943i	0.825285	+	0.564716i	$0.191014\pi$
$509$			6.60168e6i			1.12943i	−0.825285	+	0.564716i	$0.808986\pi$
$510$		0			0
$511$		−	3.06586e6i		−	0.519398i
$512$		0			0
$513$	2.66058e6	+	4.35037e6i	0.446358	+	0.729849i
$514$		0			0
$515$	−514973.			−0.0855591
$516$		0			0
$517$	600146.			0.0987485
$518$		0			0
$519$	3.82136e6	−	3.26179e6i	0.622729	−	0.531541i
$520$		0			0
$521$		−	6.04770e6i		−	0.976103i	−0.872815	−	0.488052i	$-0.837708\pi$
$521$		−	6.04770e6i		−	0.976103i	0.872815	−	0.488052i	$-0.162292\pi$
$522$		0			0
$523$		−	1.86066e6i		−	0.297449i	−0.988879	−	0.148724i	$-0.952483\pi$
$523$		−	1.86066e6i		−	0.297449i	0.988879	−	0.148724i	$-0.0475167\pi$
$524$		0			0
$525$	−2.70079e6	+	2.30531e6i	−0.427654	+	0.365032i
$526$		0			0
$527$	−1.15129e7			−1.80576
$528$		0			0
$529$	−3.07463e6			−0.477699
$530$		0			0
$531$	−711762.	+	4.47668e6i	−0.109546	+	0.689000i
$532$		0			0
$533$		−	4.86082e6i		−	0.741125i
$534$		0			0
$535$			244644.i			0.0369530i
$536$		0			0
$537$	−8.63280e6	−	1.01138e7i	−1.29186	−	1.51349i
$538$		0			0
$539$	−3.30873e6			−0.490557
$540$		0			0
$541$	3.48260e6			0.511577			0.255788	−	0.966733i	$-0.417665\pi$
$541$	3.48260e6			0.511577			0.255788	+	0.966733i	$0.417665\pi$
$542$		0			0
$543$	−4.40009e6	−	5.15494e6i	−0.640415	−	0.750281i
$544$		0			0
$545$			3.83111e6i			0.552502i
$546$		0			0
$547$		−	7.39011e6i		−	1.05605i	−0.849230	−	0.528023i	$-0.822934\pi$
$547$		−	7.39011e6i		−	1.05605i	0.849230	−	0.528023i	$-0.177066\pi$
$548$		0			0
$549$	744139.	−	4.68032e6i	0.105372	−	0.662742i
$550$		0			0
$551$	2.58964e6			0.363379
$552$		0			0
$553$	−4.18409e6			−0.581819
$554$		0			0
$555$	−1.55907e6	+	1.33077e6i	−0.214849	+	0.183388i
$556$		0			0
$557$			1.55684e6i			0.212620i	0.994333	+	0.106310i	$0.0339037\pi$
$557$			1.55684e6i			0.212620i	−0.994333	+	0.106310i	$0.966096\pi$
$558$		0			0
$559$			9.80271e6i			1.32683i
$560$		0			0
$561$	7.82137e6	−	6.67607e6i	1.04924	−	0.895599i
$562$		0			0
$563$	−1.43554e6			−0.190873			−0.0954364	−	0.995436i	$-0.530425\pi$
$563$	−1.43554e6			−0.190873			−0.0954364	+	0.995436i	$0.530425\pi$
$564$		0			0
$565$	−4.36028e6			−0.574637
$566$		0			0
$567$	−1.51605e6	+	4.64713e6i	−0.198041	+	0.607054i
$568$		0			0
$569$		−	4.69381e6i		−	0.607778i	−0.952707	−	0.303889i	$-0.901715\pi$
$569$		−	4.69381e6i		−	0.607778i	0.952707	−	0.303889i	$-0.0982852\pi$
$570$		0			0
$571$			6.38793e6i			0.819917i	0.912104	+	0.409959i	$0.134457\pi$
$571$			6.38793e6i			0.819917i	−0.912104	+	0.409959i	$0.865543\pi$
$572$		0			0
$573$	9.57466e6	+	1.12172e7i	1.21825	+	1.42725i
$574$		0			0
$575$	5.04520e6			0.636369
$576$		0			0
$577$	9.73246e6			1.21698			0.608490	−	0.793562i	$-0.291776\pi$
$577$	9.73246e6			1.21698			0.608490	+	0.793562i	$0.291776\pi$
$578$		0			0
$579$	5.18321e6	+	6.07241e6i	0.642543	+	0.752774i
$580$		0			0
$581$			7.97827e6i			0.980547i
$582$		0			0
$583$		−	7.54647e6i		−	0.919544i
$584$		0			0
$585$	5.43043e6	+	863402.i	0.656061	+	0.104309i
$586$		0			0
$587$	−5.95499e6			−0.713323			−0.356661	−	0.934234i	$-0.616085\pi$
$587$	−5.95499e6			−0.713323			−0.356661	+	0.934234i	$0.616085\pi$
$588$		0			0
$589$	7.80964e6			0.927562
$590$		0			0
$591$	6.98655e6	−	5.96349e6i	0.822800	−	0.702315i
$592$		0			0
$593$		−	1.08446e7i		−	1.26642i	−0.773979	−	0.633211i	$-0.781736\pi$
$593$		−	1.08446e7i		−	1.26642i	0.773979	−	0.633211i	$-0.218264\pi$
$594$		0			0
$595$			3.17426e6i			0.367578i
$596$		0			0
$597$	35188.4	−	30035.6i	0.00404076	−	0.00344906i
$598$		0			0
$599$	−1.05961e7			−1.20664			−0.603321	−	0.797499i	$-0.706156\pi$
$599$	−1.05961e7			−1.20664			−0.603321	+	0.797499i	$0.706156\pi$
$600$		0			0
$601$	7.04222e6			0.795286			0.397643	−	0.917540i	$-0.369828\pi$
$601$	7.04222e6			0.795286			0.397643	+	0.917540i	$0.369828\pi$
$602$		0			0
$603$	1.22281e7	+	1.94419e6i	1.36952	+	0.217744i
$604$		0			0
$605$			976972.i			0.108516i
$606$		0			0
$607$			638984.i			0.0703911i	0.999380	+	0.0351956i	$0.0112054\pi$
$607$			638984.i			0.0703911i	−0.999380	+	0.0351956i	$0.988795\pi$
$608$		0			0
$609$	1.61159e6	+	1.88807e6i	0.176081	+	0.206288i
$610$		0			0
$611$	−2.11451e6			−0.229144
$612$		0			0
$613$	−1.19943e7			−1.28921			−0.644603	−	0.764518i	$-0.722977\pi$
$613$	−1.19943e7			−1.28921			−0.644603	+	0.764518i	$0.722977\pi$
$614$		0			0
$615$	811589.	+	950820.i	0.0865263	+	0.101370i
$616$		0			0
$617$			1.01397e7i			1.07229i	0.844126	+	0.536144i	$0.180120\pi$
$617$			1.01397e7i			1.07229i	−0.844126	+	0.536144i	$0.819880\pi$
$618$		0			0
$619$			6.43700e6i			0.675239i	0.941283	+	0.337619i	$0.109622\pi$
$619$			6.43700e6i			0.675239i	−0.941283	+	0.337619i	$0.890378\pi$
$620$		0			0
$621$	5.92505e6	−	3.62362e6i	0.616543	−	0.377063i
$622$		0			0
$623$	−1.48966e6			−0.153768
$624$		0			0
$625$	6.40513e6			0.655886
$626$		0			0
$627$	−5.30552e6	+	4.52862e6i	−0.538964	+	0.460042i
$628$		0			0
$629$		−	1.35063e7i		−	1.36116i
$630$		0			0
$631$		−	1.35312e7i		−	1.35289i	−0.736493	−	0.676445i	$-0.763520\pi$
$631$		−	1.35312e7i		−	1.35289i	0.736493	−	0.676445i	$-0.236480\pi$
$632$		0			0
$633$	−9.10721e6	+	7.77362e6i	−0.903392	+	0.771106i
$634$		0			0
$635$	1.91846e6			0.188807
$636$		0			0
$637$	1.16578e7			1.13833
$638$		0			0
$639$	2.66707e6	−	1.67748e7i	0.258394	−	1.62519i
$640$		0			0
$641$			3.36979e6i			0.323935i	0.986796	+	0.161967i	$0.0517839\pi$
$641$			3.36979e6i			0.323935i	−0.986796	+	0.161967i	$0.948216\pi$
$642$		0			0
$643$		−	5.93188e6i		−	0.565802i	−0.959149	−	0.282901i	$-0.908703\pi$
$643$		−	5.93188e6i		−	0.565802i	0.959149	−	0.282901i	$-0.0912968\pi$
$644$		0			0
$645$	−1.63671e6	−	1.91750e6i	−0.154908	−	0.181483i
$646$		0			0
$647$	1.62942e7			1.53029			0.765143	−	0.643860i	$-0.222668\pi$
$647$	1.62942e7			1.53029			0.765143	+	0.643860i	$0.222668\pi$
$648$		0			0
$649$	−6.20048e6			−0.577848
$650$		0			0
$651$	4.86013e6	+	5.69390e6i	0.449464	+	0.526572i
$652$		0			0
$653$		−	8.96912e6i		−	0.823127i	−0.911381	−	0.411564i	$-0.864983\pi$
$653$		−	8.96912e6i		−	0.823127i	0.911381	−	0.411564i	$-0.135017\pi$
$654$		0			0
$655$			4.89962e6i			0.446230i
$656$		0			0
$657$	−1.41313e6	+	8.88800e6i	−0.127723	+	0.803324i
$658$		0			0
$659$	−8.28105e6			−0.742800			−0.371400	−	0.928473i	$-0.621122\pi$
$659$	−8.28105e6			−0.742800			−0.371400	+	0.928473i	$0.621122\pi$
$660$		0			0
$661$	7.16993e6			0.638280			0.319140	−	0.947708i	$-0.396606\pi$
$661$	7.16993e6			0.638280			0.319140	+	0.947708i	$0.396606\pi$
$662$		0			0
$663$	−2.75573e7	+	2.35220e7i	−2.43474	+	2.07822i
$664$		0			0
$665$		−	2.15322e6i		−	0.188814i
$666$		0			0
$667$		−	3.52700e6i		−	0.306966i
$668$		0			0
$669$	−3.41630e6	+	2.91604e6i	−0.295114	+	0.251900i
$670$		0			0
$671$	6.48254e6			0.555826
$672$		0			0
$673$	781505.			0.0665111			0.0332555	−	0.999447i	$-0.489412\pi$
$673$	781505.			0.0665111			0.0332555	+	0.999447i	$0.489412\pi$
$674$		0			0
$675$	8.89222e6	−	5.43827e6i	0.751192	−	0.459411i
$676$		0			0
$677$		−	976634.i		−	0.0818956i	−0.999161	−	0.0409478i	$-0.986962\pi$
$677$		−	976634.i		−	0.0818956i	0.999161	−	0.0409478i	$-0.0130377\pi$
$678$		0			0
$679$		−	4.00513e6i		−	0.333382i
$680$		0			0
$681$	−8.14808e6	−	9.54591e6i	−0.673267	−	0.788769i
$682$		0			0
$683$	−1.17475e6			−0.0963590			−0.0481795	−	0.998839i	$-0.515342\pi$
$683$	−1.17475e6			−0.0963590			−0.0481795	+	0.998839i	$0.515342\pi$
$684$		0			0
$685$	−925218.			−0.0753386
$686$		0			0
$687$	1.66499e6	+	1.95063e6i	0.134592	+	0.157682i
$688$		0			0
$689$			2.65887e7i			2.13378i
$690$		0			0
$691$			1.25020e7i			0.996058i	0.867161	+	0.498029i	$0.165943\pi$
$691$			1.25020e7i			0.996058i	−0.867161	+	0.498029i	$0.834057\pi$
$692$		0			0
$693$	−6.60351e6	−	1.04991e6i	−0.522326	−	0.0830464i
$694$		0			0
$695$	−3.86277e6			−0.303345
$696$		0			0
$697$	−8.23700e6			−0.642225
$698$		0			0
$699$	5.58077e6	−	4.76356e6i	0.432017	−	0.368756i
$700$		0			0
$701$			1.36812e7i			1.05155i	0.850624	+	0.525774i	$0.176224\pi$
$701$			1.36812e7i			1.05155i	−0.850624	+	0.525774i	$0.823776\pi$
$702$		0			0
$703$			9.16184e6i			0.699189i
$704$		0			0
$705$	413618.	−	353051.i	0.0313420	−	0.0267525i
$706$		0			0
$707$	8.38069e6			0.630567
$708$		0			0
$709$	4.64829e6			0.347278			0.173639	−	0.984809i	$-0.444447\pi$
$709$	4.64829e6			0.347278			0.173639	+	0.984809i	$0.444447\pi$
$710$		0			0
$711$	1.21298e7	+	1.92855e6i	0.899867	+	0.143073i
$712$		0			0
$713$		−	1.06365e7i		−	0.783562i
$714$		0			0
$715$			7.52149e6i			0.550223i
$716$		0			0
$717$	−1.55132e7	−	1.81745e7i	−1.12694	−	1.32028i
$718$		0			0
$719$	1.82672e7			1.31780			0.658899	−	0.752231i	$-0.271022\pi$
$719$	1.82672e7			1.31780			0.658899	+	0.752231i	$0.271022\pi$
$720$		0			0
$721$	−2.20637e6			−0.158067
$722$		0			0
$723$	9.35449e6	+	1.09593e7i	0.665540	+	0.779716i
$724$		0			0
$725$		−	5.29326e6i		−	0.374006i
$726$		0			0
$727$			2.11523e7i			1.48430i	0.670235	+	0.742149i	$0.266193\pi$
$727$			2.11523e7i			1.48430i	−0.670235	+	0.742149i	$0.733807\pi$
$728$		0			0
$729$	6.53704e6	−	1.27733e7i	0.455577	−	0.890196i
$730$		0			0
$731$	1.66114e7			1.14977
$732$		0			0
$733$	2.38899e6			0.164231			0.0821153	−	0.996623i	$-0.473832\pi$
$733$	2.38899e6			0.164231			0.0821153	+	0.996623i	$0.473832\pi$
$734$		0			0
$735$	−2.28037e6	+	1.94645e6i	−0.155699	+	0.132900i
$736$		0			0
$737$			1.69368e7i			1.14858i
$738$		0			0
$739$		−	6.98369e6i		−	0.470407i	−0.971946	−	0.235203i	$-0.924424\pi$
$739$		−	6.98369e6i		−	0.470407i	0.971946	−	0.235203i	$-0.0755756\pi$
$740$		0			0
$741$	1.86931e7	−	1.59558e7i	1.25065	−	1.06752i
$742$		0			0
$743$	1.91909e7			1.27533			0.637665	−	0.770314i	$-0.279901\pi$
$743$	1.91909e7			1.27533			0.637665	+	0.770314i	$0.279901\pi$
$744$		0			0
$745$	−1.23131e6			−0.0812787
$746$		0			0
$747$	3.67738e6	−	2.31292e7i	0.241122	−	1.51656i
$748$		0			0
$749$			1.04816e6i			0.0682691i
$750$		0			0
$751$			3.04159e7i			1.96789i	0.178465	+	0.983946i	$0.442887\pi$
$751$			3.04159e7i			1.96789i	−0.178465	+	0.983946i	$0.557113\pi$
$752$		0			0
$753$	−1.29548e7	−	1.51772e7i	−0.832612	−	0.975450i
$754$		0			0
$755$	−8.62853e6			−0.550896
$756$		0			0
$757$	−6.16178e6			−0.390811			−0.195405	−	0.980723i	$-0.562602\pi$
$757$	−6.16178e6			−0.390811			−0.195405	+	0.980723i	$0.562602\pi$
$758$		0			0
$759$	6.16782e6	+	7.22594e6i	0.388622	+	0.455292i
$760$		0			0
$761$			2.27781e7i			1.42579i	0.701269	+	0.712897i	$0.252617\pi$
$761$			2.27781e7i			1.42579i	−0.701269	+	0.712897i	$0.747383\pi$
$762$		0			0
$763$			1.64142e7i			1.02072i
$764$		0			0
$765$	1.46310e6	−	9.20224e6i	0.0903897	−	0.568513i
$766$		0			0
$767$	2.18464e7			1.34088
$768$		0			0
$769$	−3.17621e7			−1.93684			−0.968419	−	0.249326i	$-0.919791\pi$
$769$	−3.17621e7			−1.93684			−0.968419	+	0.249326i	$0.919791\pi$
$770$		0			0
$771$	−2.04438e7	+	1.74502e7i	−1.23858	+	1.05721i
$772$		0			0
$773$			1.28739e7i			0.774930i	0.921884	+	0.387465i	$0.126649\pi$
$773$			1.28739e7i			0.774930i	−0.921884	+	0.387465i	$0.873351\pi$
$774$		0			0
$775$		−	1.59630e7i		−	0.954687i
$776$		0			0
$777$	−6.67977e6	+	5.70163e6i	−0.396925	+	0.338802i
$778$		0			0
$779$	5.58746e6			0.329891
$780$		0			0
$781$	2.32341e7			1.36301
$782$		0			0
$783$	−3.80178e6	−	6.21637e6i	−0.221607	−	0.362354i
$784$		0			0
$785$			5.14623e6i			0.298068i
$786$		0			0
$787$		−	2.15917e7i		−	1.24265i	−0.783552	−	0.621327i	$-0.786594\pi$
$787$		−	2.15917e7i		−	1.24265i	0.783552	−	0.621327i	$-0.213406\pi$
$788$		0			0
$789$	−402097.	−	471079.i	−0.0229953	−	0.0269402i
$790$		0			0
$791$	−1.86814e7			−1.06162
$792$		0			0
$793$	−2.28402e7			−1.28978
$794$		0			0
$795$	−4.43940e6	−	5.20100e6i	−0.249119	−	0.291856i
$796$		0			0
$797$			1.94436e7i			1.08425i	0.840297	+	0.542126i	$0.182380\pi$
$797$			1.94436e7i			1.08425i	−0.840297	+	0.542126i	$0.817620\pi$
$798$		0			0
$799$			3.58319e6i			0.198565i
$800$		0			0
$801$	4.31855e6	+	686622.i	0.237825	+	0.0378126i
$802$		0			0
$803$	−1.23105e7			−0.673729
$804$		0			0
$805$	−2.93261e6			−0.159501
$806$		0			0
$807$	−3.32013e6	+	2.83396e6i	−0.179462	+	0.153183i
$808$		0			0
$809$			2.43124e7i			1.30604i	0.757341	+	0.653020i	$0.226498\pi$
$809$			2.43124e7i			1.30604i	−0.757341	+	0.653020i	$0.773502\pi$
$810$		0			0
$811$			1.09629e7i			0.585293i	0.956221	+	0.292647i	$0.0945360\pi$
$811$			1.09629e7i			0.585293i	−0.956221	+	0.292647i	$0.905464\pi$
$812$		0			0
$813$	2.67114e7	−	2.28000e7i	1.41733	−	1.20979i
$814$		0			0
$815$	4.72782e6			0.249326
$816$		0			0
$817$	−1.12681e7			−0.590603
$818$		0			0
$819$	2.32664e7	+	3.69920e6i	1.21204	+	0.192707i
$820$		0			0
$821$		−	2.05702e6i		−	0.106507i	−0.998581	−	0.0532537i	$-0.983041\pi$
$821$		−	2.05702e6i		−	0.106507i	0.998581	−	0.0532537i	$-0.0169592\pi$
$822$		0			0
$823$			2.72914e7i			1.40451i	0.711924	+	0.702256i	$0.247824\pi$
$823$			2.72914e7i			1.40451i	−0.711924	+	0.702256i	$0.752176\pi$
$824$		0			0
$825$	9.25657e6	+	1.08446e7i	0.473495	+	0.554725i
$826$		0			0
$827$	1.02167e7			0.519456			0.259728	−	0.965682i	$-0.416367\pi$
$827$	1.02167e7			0.519456			0.259728	+	0.965682i	$0.416367\pi$
$828$		0			0
$829$	−2.19066e7			−1.10710			−0.553551	−	0.832815i	$-0.686728\pi$
$829$	−2.19066e7			−1.10710			−0.553551	+	0.832815i	$0.686728\pi$
$830$		0			0
$831$	−1.16230e7	−	1.36169e7i	−0.583868	−	0.684032i
$832$		0			0
$833$		−	1.97549e7i		−	0.986422i
$834$		0			0
$835$		−	3.85194e6i		−	0.191189i
$836$		0			0
$837$	−1.14651e7	−	1.87469e7i	−0.565674	−	0.924944i
$838$		0			0
$839$	1.65586e7			0.812116			0.406058	−	0.913847i	$-0.366903\pi$
$839$	1.65586e7			0.812116			0.406058	+	0.913847i	$0.366903\pi$
$840$		0			0
$841$	1.68107e7			0.819590
$842$		0			0
$843$	1.80312e7	−	1.53908e7i	0.873886	−	0.745920i
$844$		0			0
$845$		−	1.93268e7i		−	0.931148i
$846$		0			0
$847$			4.18578e6i			0.200479i
$848$		0			0
$849$	7.24235e6	−	6.18183e6i	0.344834	−	0.294339i
$850$		0			0
$851$	1.24781e7			0.590643
$852$		0			0
$853$	7.67539e6			0.361183			0.180592	−	0.983558i	$-0.442199\pi$
$853$	7.67539e6			0.361183			0.180592	+	0.983558i	$0.442199\pi$
$854$		0			0
$855$	−992471.	+	6.24222e6i	−0.0464304	+	0.292027i
$856$		0			0
$857$			3.53759e6i			0.164534i	0.996610	+	0.0822670i	$0.0262160\pi$
$857$			3.53759e6i			0.164534i	−0.996610	+	0.0822670i	$0.973784\pi$
$858$		0			0
$859$			1.36445e7i			0.630921i	0.948939	+	0.315461i	$0.102159\pi$
$859$			1.36445e7i			0.630921i	−0.948939	+	0.315461i	$0.897841\pi$
$860$		0			0
$861$	3.47721e6	+	4.07374e6i	0.159854	+	0.187277i
$862$		0			0
$863$	2.32847e7			1.06425			0.532126	−	0.846665i	$-0.321393\pi$
$863$	2.32847e7			1.06425			0.532126	+	0.846665i	$0.321393\pi$
$864$		0			0
$865$	6.22728e6			0.282982
$866$		0			0
$867$	2.54902e7	+	2.98632e7i	1.15167	+	1.34924i
$868$		0			0
$869$			1.68005e7i			0.754697i
$870$		0			0
$871$		−	5.96739e7i		−	2.66526i
$872$		0			0
$873$	−1.84606e6	+	1.16110e7i	−0.0819806	+	0.515623i
$874$		0			0
$875$	−9.39952e6			−0.415036
$876$		0			0
$877$	−4.33930e7			−1.90511			−0.952556	−	0.304364i	$-0.901556\pi$
$877$	−4.33930e7			−1.90511			−0.952556	+	0.304364i	$0.901556\pi$
$878$		0			0
$879$	−2.72013e7	+	2.32181e7i	−1.18745	+	1.01357i
$880$		0			0
$881$			2.09569e7i			0.909678i	0.890574	+	0.454839i	$0.150303\pi$
$881$			2.09569e7i			0.909678i	−0.890574	+	0.454839i	$0.849697\pi$
$882$		0			0
$883$		−	1.32913e7i		−	0.573674i	−0.957979	−	0.286837i	$-0.907396\pi$
$883$		−	1.32913e7i		−	0.573674i	0.957979	−	0.286837i	$-0.0926037\pi$
$884$		0			0
$885$	−4.27335e6	+	3.64759e6i	−0.183405	+	0.156548i
$886$		0			0
$887$	2.96276e7			1.26441			0.632205	−	0.774801i	$-0.282150\pi$
$887$	2.96276e7			1.26441			0.632205	+	0.774801i	$0.282150\pi$
$888$		0			0
$889$	8.21955e6			0.348814
$890$		0			0
$891$	1.86598e7	+	6.08744e6i	0.787430	+	0.256886i
$892$		0			0
$893$		−	2.43061e6i		−	0.101997i
$894$		0			0
$895$		−	1.64814e7i		−	0.687760i
$896$		0			0
$897$	−2.17313e7	−	2.54594e7i	−0.901789	−	1.05649i
$898$		0			0
$899$	−1.11594e7			−0.460514
$900$		0			0
$901$	4.50565e7			1.84904
$902$		0			0
$903$	−7.01241e6	−	8.21542e6i	−0.286186	−	0.335282i
$904$		0			0
$905$		−	8.40048e6i		−	0.340944i
$906$		0			0
$907$			2.59307e7i			1.04664i	0.852137	+	0.523318i	$0.175306\pi$
$907$			2.59307e7i			1.04664i	−0.852137	+	0.523318i	$0.824694\pi$
$908$		0			0
$909$	−2.42958e7	−	3.86287e6i	−0.975262	−	0.155060i
$910$		0			0
$911$	−2.62650e7			−1.04853			−0.524265	−	0.851555i	$-0.675660\pi$
$911$	−2.62650e7			−1.04853			−0.524265	+	0.851555i	$0.675660\pi$
$912$		0			0
$913$	3.20354e7			1.27190
$914$		0			0
$915$	4.46774e6	−	3.81352e6i	0.176415	−	0.150582i
$916$		0			0
$917$			2.09921e7i			0.824391i
$918$		0			0
$919$			2.40150e7i			0.937982i	0.883203	+	0.468991i	$0.155382\pi$
$919$			2.40150e7i			0.937982i	−0.883203	+	0.468991i	$0.844618\pi$
$920$		0			0
$921$	2.67953e7	−	2.28716e7i	1.04090	−	0.888480i
$922$		0			0
$923$	−8.18616e7			−3.16283
$924$		0			0
$925$	1.87269e7			0.719635
$926$		0			0
$927$	6.39632e6	+	1.01697e6i	0.244473	+	0.0388696i
$928$		0			0
$929$			199297.i			0.00757638i	0.999993	+	0.00378819i	$0.00120582\pi$
$929$			199297.i			0.00757638i	−0.999993	+	0.00378819i	$0.998794\pi$
$930$		0			0
$931$			1.34005e7i			0.506695i
$932$		0			0
$933$	3.03193e7	+	3.55207e7i	1.14029	+	1.33591i
$934$		0			0
$935$	1.27457e7			0.476798
$936$		0			0
$937$	2.11339e7			0.786375			0.393188	−	0.919458i	$-0.371372\pi$
$937$	2.11339e7			0.786375			0.393188	+	0.919458i	$0.371372\pi$
$938$		0			0
$939$	−6.94622e6	−	8.13787e6i	−0.257089	−	0.301194i
$940$		0			0
$941$		−	2.91277e7i		−	1.07234i	−0.844110	−	0.536169i	$-0.819871\pi$
$941$		−	2.91277e7i		−	1.07234i	0.844110	−	0.536169i	$-0.180129\pi$
$942$		0			0
$943$		−	7.60992e6i		−	0.278677i
$944$		0			0
$945$	−5.16875e6	+	3.16108e6i	−0.188281	+	0.115148i
$946$		0			0
$947$	1.30882e7			0.474248			0.237124	−	0.971479i	$-0.423795\pi$
$947$	1.30882e7			0.474248			0.237124	+	0.971479i	$0.423795\pi$
$948$		0			0
$949$	4.33738e7			1.56337
$950$		0			0
$951$	−3.55020e7	+	3.03034e7i	−1.27292	+	1.08652i
$952$		0			0
$953$			3.88256e7i			1.38480i	0.721515	+	0.692398i	$0.243446\pi$
$953$			3.88256e7i			1.38480i	−0.721515	+	0.692398i	$0.756554\pi$
$954$		0			0
$955$			1.82796e7i			0.648572i
$956$		0			0
$957$	7.58122e6	−	6.47108e6i	0.267583	−	0.228400i
$958$		0			0
$959$	−3.96405e6			−0.139185
$960$		0			0
$961$	−5.02465e6			−0.175508
$962$		0			0
$963$	483125.	−	3.03865e6i	0.0167878	−	0.105588i
$964$		0			0
$965$			9.89559e6i			0.342076i
$966$		0			0
$967$		−	3.38341e7i		−	1.16356i	−0.813346	−	0.581780i	$-0.802356\pi$
$967$		−	3.38341e7i		−	1.16356i	0.813346	−	0.581780i	$-0.197644\pi$
$968$		0			0
$969$	−2.70383e7	−	3.16768e7i	−0.925061	−	1.08376i
$970$		0			0
$971$	−3.86651e7			−1.31604			−0.658022	−	0.752998i	$-0.728607\pi$
$971$	−3.86651e7			−1.31604			−0.658022	+	0.752998i	$0.728607\pi$
$972$		0			0
$973$	−1.65498e7			−0.560417
$974$		0			0
$975$	−3.26140e7	−	3.82090e7i	−1.09873	−	1.28723i
$976$		0			0
$977$		−	4.73321e7i		−	1.58643i	−0.608944	−	0.793213i	$-0.708407\pi$
$977$		−	4.73321e7i		−	1.58643i	0.608944	−	0.793213i	$-0.291593\pi$
$978$		0			0
$979$			5.98148e6i			0.199458i
$980$		0			0
$981$	7.56571e6	−	4.75851e7i	0.251002	−	1.57869i
$982$		0			0
$983$	−2.15996e7			−0.712954			−0.356477	−	0.934304i	$-0.616022\pi$
$983$	−2.15996e7			−0.712954			−0.356477	+	0.934304i	$0.616022\pi$
$984$		0			0
$985$	1.13853e7			0.373898
$986$		0			0
$987$	1.77212e6	−	1.51263e6i	0.0579031	−	0.0494241i
$988$		0			0
$989$			1.53468e7i			0.498915i
$990$		0			0
$991$		−	2.42907e7i		−	0.785699i	−0.919603	−	0.392849i	$-0.871489\pi$
$991$		−	2.42907e7i		−	0.785699i	0.919603	−	0.392849i	$-0.128511\pi$
$992$		0			0
$993$	1.49379e7	−	1.27505e7i	0.480747	−	0.410350i
$994$		0			0
$995$	57342.9			0.00183621
$996$		0			0
$997$	−5.08871e7			−1.62132			−0.810662	−	0.585514i	$-0.800893\pi$
$997$	−5.08871e7			−1.62132			−0.810662	+	0.585514i	$0.800893\pi$
$998$		0			0
$999$	2.19928e7	−	1.34503e7i	0.697215	−	0.426400i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.6.c.a.383.5	✓	20
3.2	odd	2		384.6.c.d.383.15	yes	20
4.3	odd	2		384.6.c.d.383.16	yes	20
8.3	odd	2		384.6.c.b.383.5	yes	20
8.5	even	2		384.6.c.c.383.16	yes	20
12.11	even	2	inner	384.6.c.a.383.6	yes	20
24.5	odd	2		384.6.c.b.383.6	yes	20
24.11	even	2		384.6.c.c.383.15	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.6.c.a.383.5	✓	20	1.1	even	1	trivial
384.6.c.a.383.6	yes	20	12.11	even	2	inner
384.6.c.b.383.5	yes	20	8.3	odd	2
384.6.c.b.383.6	yes	20	24.5	odd	2
384.6.c.c.383.15	yes	20	24.11	even	2
384.6.c.c.383.16	yes	20	8.5	even	2
384.6.c.d.383.15	yes	20	3.2	odd	2
384.6.c.d.383.16	yes	20	4.3	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)

\(f(q)\)	\(=\)	\(q+(-10.1204 - 11.8566i) q^{3} -19.3214i q^{5} -82.7816i q^{7} +(-38.1561 + 239.986i) q^{9} +O(q^{10})\)	\(q+(-10.1204 - 11.8566i) q^{3} -19.3214i q^{5} -82.7816i q^{7} +(-38.1561 + 239.986i) q^{9} -332.396 q^{11} +1171.14 q^{13} +(-229.086 + 195.540i) q^{15} -1984.58i q^{17} +1346.21i q^{19} +(-981.506 + 837.781i) q^{21} +1833.50 q^{23} +2751.68 q^{25} +(3231.56 - 1976.34i) q^{27} -1923.64i q^{29} -5801.19i q^{31} +(3363.97 + 3941.07i) q^{33} -1599.46 q^{35} +6805.63 q^{37} +(-11852.4 - 13885.7i) q^{39} -4150.50i q^{41} +8370.22i q^{43} +(4636.87 + 737.231i) q^{45} -1805.52 q^{47} +9954.20 q^{49} +(-23530.3 + 20084.7i) q^{51} +22703.3i q^{53} +6422.36i q^{55} +(15961.5 - 13624.2i) q^{57} +18653.9 q^{59} -19502.5 q^{61} +(19866.4 + 3158.63i) q^{63} -22628.1i q^{65} -50953.6i q^{67} +(-18555.7 - 21739.0i) q^{69} -69899.0 q^{71} +37035.5 q^{73} +(-27848.0 - 32625.5i) q^{75} +27516.3i q^{77} -50543.7i q^{79} +(-56137.2 - 18313.8i) q^{81} -96377.3 q^{83} -38345.0 q^{85} +(-22807.8 + 19468.0i) q^{87} -17995.1i q^{89} -96949.0i q^{91} +(-68782.2 + 58710.2i) q^{93} +26010.8 q^{95} +48381.9 q^{97} +(12682.9 - 79770.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3}+O(q^{10}) \) 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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