LMFDB - Embedded newform 48.7.e.d.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,7,Mod(17,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("48.17");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	48.e (of order $2$, degree $1$, not 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:	$11.0425960138$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.1173604352.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 14x^{4} - 12x^{3} + 112x^{2} + 192x + 324 $ x^6 - 14x^4 - 12x^3 + 112x^2 + 192x + 324
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{22}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 24)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			17.1
Root			$-0.624336 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	48.17
Dual form			48.7.e.d.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-23.4408 - 13.3988i) q^{3} +100.147i q^{5} -56.7723 q^{7} +(369.944 + 628.158i) q^{9} +O(q^{10})$	\(q+(-23.4408 - 13.3988i) q^{3} +100.147i q^{5} -56.7723 q^{7} +(369.944 + 628.158i) q^{9} -1563.26i q^{11} +2799.15 q^{13} +(1341.85 - 2347.52i) q^{15} -7754.84i q^{17} +10548.4 q^{19} +(1330.79 + 760.681i) q^{21} +18460.5i q^{23} +5595.62 q^{25} +(-255.212 - 19681.3i) q^{27} -20877.9i q^{29} +3285.23 q^{31} +(-20945.8 + 36644.1i) q^{33} -5685.57i q^{35} +39303.2 q^{37} +(-65614.4 - 37505.3i) q^{39} +44619.0i q^{41} -23655.3 q^{43} +(-62908.0 + 37048.7i) q^{45} +65090.8i q^{47} -114426. q^{49} +(-103906. + 181780. i) q^{51} -65760.4i q^{53} +156555. q^{55} +(-247262. - 141335. i) q^{57} -36299.9i q^{59} +412439. q^{61} +(-21002.6 - 35662.0i) q^{63} +280326. i q^{65} +265379. q^{67} +(247348. - 432728. i) q^{69} -552756. i q^{71} +124949. q^{73} +(-131166. - 74974.6i) q^{75} +88749.8i q^{77} +281411. q^{79} +(-257724. + 464766. i) q^{81} -249255. i q^{83} +776622. q^{85} +(-279739. + 489394. i) q^{87} -30731.5i q^{89} -158914. q^{91} +(-77008.6 - 44018.2i) q^{93} +1.05638e6i q^{95} -1.49482e6 q^{97} +(981974. - 578318. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 10 q^{3} - 156 q^{7} - 74 q^{9}+O(q^{10}) $ 6 * q + 10 * q^3 - 156 * q^7 - 74 * q^9	$ 6 q + 10 q^{3} - 156 q^{7} - 74 q^{9} + 156 q^{13} - 2912 q^{15} + 4500 q^{19} - 15108 q^{21} + 21366 q^{25} - 37574 q^{27} + 74244 q^{31} - 83104 q^{33} + 171132 q^{37} - 200444 q^{39} + 291060 q^{43} - 355136 q^{45} + 517746 q^{49} - 452224 q^{51} + 748224 q^{55} - 650420 q^{57} + 592092 q^{61} - 1009788 q^{63} + 570900 q^{67} - 981184 q^{69} + 1119660 q^{73} - 521446 q^{75} + 1053636 q^{79} - 742874 q^{81} + 197376 q^{85} - 1251360 q^{87} - 839640 q^{91} + 354652 q^{93} - 798516 q^{97} + 2849600 q^{99}+O(q^{100}) $ 6 * q + 10 * q^3 - 156 * q^7 - 74 * q^9 + 156 * q^13 - 2912 * q^15 + 4500 * q^19 - 15108 * q^21 + 21366 * q^25 - 37574 * q^27 + 74244 * q^31 - 83104 * q^33 + 171132 * q^37 - 200444 * q^39 + 291060 * q^43 - 355136 * q^45 + 517746 * q^49 - 452224 * q^51 + 748224 * q^55 - 650420 * q^57 + 592092 * q^61 - 1009788 * q^63 + 570900 * q^67 - 981184 * q^69 + 1119660 * q^73 - 521446 * q^75 + 1053636 * q^79 - 742874 * q^81 + 197376 * q^85 - 1251360 * q^87 - 839640 * q^91 + 354652 * q^93 - 798516 * q^97 + 2849600 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$1$	$1$

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
$3$	−23.4408	−	13.3988i	−0.868178	−	0.496252i
$3$	−23.4408	−	13.3988i	−0.868178	−	0.496252i
$4$		0			0
$5$			100.147i			0.801174i	0.916259	+	0.400587i	$0.131194\pi$
$5$			100.147i			0.801174i	−0.916259	+	0.400587i	$0.868806\pi$
$6$		0			0
$7$	−56.7723			−0.165517			−0.0827585	−	0.996570i	$-0.526373\pi$
$7$	−56.7723			−0.165517			−0.0827585	+	0.996570i	$0.526373\pi$
$8$		0			0
$9$	369.944	+	628.158i	0.507467	+	0.861671i
$10$		0			0
$11$		−	1563.26i		−	1.17450i	−0.809406	−	0.587250i	$-0.800211\pi$
$11$		−	1563.26i		−	1.17450i	0.809406	−	0.587250i	$-0.199789\pi$
$12$		0			0
$13$	2799.15			1.27408			0.637040	−	0.770831i	$-0.280159\pi$
$13$	2799.15			1.27408			0.637040	+	0.770831i	$0.280159\pi$
$14$		0			0
$15$	1341.85	−	2347.52i	0.397585	−	0.695562i
$16$		0			0
$17$		−	7754.84i		−	1.57843i	−0.614115	−	0.789216i	$-0.710487\pi$
$17$		−	7754.84i		−	1.57843i	0.614115	−	0.789216i	$-0.289513\pi$
$18$		0			0
$19$	10548.4			1.53788			0.768942	−	0.639318i	$-0.220783\pi$
$19$	10548.4			1.53788			0.768942	+	0.639318i	$0.220783\pi$
$20$		0			0
$21$	1330.79	+	760.681i	0.143698	+	0.0821382i
$22$		0			0
$23$			18460.5i			1.51726i	0.651523	+	0.758628i	$0.274130\pi$
$23$			18460.5i			1.51726i	−0.651523	+	0.758628i	$0.725870\pi$
$24$		0			0
$25$	5595.62			0.358120
$26$		0			0
$27$	−255.212	−	19681.3i	−0.0129661	−	0.999916i
$28$		0			0
$29$		−	20877.9i		−	0.856036i	−0.903770	−	0.428018i	$-0.859212\pi$
$29$		−	20877.9i		−	0.856036i	0.903770	−	0.428018i	$-0.140788\pi$
$30$		0			0
$31$	3285.23			0.110276			0.0551380	−	0.998479i	$-0.482440\pi$
$31$	3285.23			0.110276			0.0551380	+	0.998479i	$0.482440\pi$
$32$		0			0
$33$	−20945.8	+	36644.1i	−0.582848	+	1.01968i
$34$		0			0
$35$		−	5685.57i		−	0.132608i
$36$		0			0
$37$	39303.2			0.775931			0.387966	−	0.921674i	$-0.373178\pi$
$37$	39303.2			0.775931			0.387966	+	0.921674i	$0.373178\pi$
$38$		0			0
$39$	−65614.4	−	37505.3i	−1.10613	−	0.632265i
$40$		0			0
$41$			44619.0i			0.647393i	0.946161	+	0.323697i	$0.104926\pi$
$41$			44619.0i			0.647393i	−0.946161	+	0.323697i	$0.895074\pi$
$42$		0			0
$43$	−23655.3			−0.297525			−0.148763	−	0.988873i	$-0.547529\pi$
$43$	−23655.3			−0.297525			−0.148763	+	0.988873i	$0.547529\pi$
$44$		0			0
$45$	−62908.0	+	37048.7i	−0.690349	+	0.406570i
$46$		0			0
$47$			65090.8i			0.626940i	0.949598	+	0.313470i	$0.101491\pi$
$47$			65090.8i			0.626940i	−0.949598	+	0.313470i	$0.898509\pi$
$48$		0			0
$49$	−114426.			−0.972604
$50$		0			0
$51$	−103906.	+	181780.i	−0.783301	+	1.37036i
$52$		0			0
$53$		−	65760.4i		−	0.441709i	−0.975307	−	0.220855i	$-0.929115\pi$
$53$		−	65760.4i		−	0.441709i	0.975307	−	0.220855i	$-0.0708846\pi$
$54$		0			0
$55$	156555.			0.940979
$56$		0			0
$57$	−247262.	−	141335.i	−1.33516	−	0.763179i
$58$		0			0
$59$		−	36299.9i		−	0.176746i	−0.996087	−	0.0883731i	$-0.971833\pi$
$59$		−	36299.9i		−	0.176746i	0.996087	−	0.0883731i	$-0.0281668\pi$
$60$		0			0
$61$	412439.			1.81707			0.908533	−	0.417813i	$-0.137203\pi$
$61$	412439.			1.81707			0.908533	+	0.417813i	$0.137203\pi$
$62$		0			0
$63$	−21002.6	−	35662.0i	−0.0839945	−	0.142621i
$64$		0			0
$65$			280326.i			1.02076i
$66$		0			0
$67$	265379.			0.882351			0.441176	−	0.897421i	$-0.354562\pi$
$67$	265379.			0.882351			0.441176	+	0.897421i	$0.354562\pi$
$68$		0			0
$69$	247348.	−	432728.i	0.752942	−	1.31725i
$70$		0			0
$71$		−	552756.i		−	1.54440i	−0.635383	−	0.772198i	$-0.719158\pi$
$71$		−	552756.i		−	1.54440i	0.635383	−	0.772198i	$-0.280842\pi$
$72$		0			0
$73$	124949.			0.321191			0.160595	−	0.987020i	$-0.448659\pi$
$73$	124949.			0.321191			0.160595	+	0.987020i	$0.448659\pi$
$74$		0			0
$75$	−131166.	−	74974.6i	−0.310912	−	0.177718i
$76$		0			0
$77$			88749.8i			0.194400i
$78$		0			0
$79$	281411.			0.570769			0.285384	−	0.958413i	$-0.407879\pi$
$79$	281411.			0.570769			0.285384	+	0.958413i	$0.407879\pi$
$80$		0			0
$81$	−257724.	+	464766.i	−0.484954	+	0.874540i
$82$		0			0
$83$		−	249255.i		−	0.435923i	−0.975957	−	0.217962i	$-0.930059\pi$
$83$		−	249255.i		−	0.435923i	0.975957	−	0.217962i	$-0.0699408\pi$
$84$		0			0
$85$	776622.			1.26460
$86$		0			0
$87$	−279739.	+	489394.i	−0.424810	+	0.743192i
$88$		0			0
$89$		−	30731.5i		−	0.0435927i	−0.999762	−	0.0217963i	$-0.993061\pi$
$89$		−	30731.5i		−	0.0435927i	0.999762	−	0.0217963i	$-0.00693854\pi$
$90$		0			0
$91$	−158914.			−0.210882
$92$		0			0
$93$	−77008.6	−	44018.2i	−0.0957393	−	0.0547247i
$94$		0			0
$95$			1.05638e6i			1.23211i
$96$		0			0
$97$	−1.49482e6			−1.63785			−0.818924	−	0.573902i	$-0.805429\pi$
$97$	−1.49482e6			−1.63785			−0.818924	+	0.573902i	$0.805429\pi$
$98$		0			0
$99$	981974.	−	578318.i	1.01203	−	0.596020i
$100$		0			0
$101$		−	1.67793e6i		−	1.62858i	−0.580458	−	0.814290i	$-0.697126\pi$
$101$		−	1.67793e6i		−	1.62858i	0.580458	−	0.814290i	$-0.302874\pi$
$102$		0			0
$103$	−269950.			−0.247042			−0.123521	−	0.992342i	$-0.539419\pi$
$103$	−269950.			−0.247042			−0.123521	+	0.992342i	$0.539419\pi$
$104$		0			0
$105$	−76179.8	+	133274.i	−0.0658070	+	0.115127i
$106$		0			0
$107$			1.00439e6i			0.819884i	0.912112	+	0.409942i	$0.134451\pi$
$107$			1.00439e6i			0.819884i	−0.912112	+	0.409942i	$0.865549\pi$
$108$		0			0
$109$	−790338.			−0.610286			−0.305143	−	0.952307i	$-0.598704\pi$
$109$	−790338.			−0.610286			−0.305143	+	0.952307i	$0.598704\pi$
$110$		0			0
$111$	−921300.	−	526617.i	−0.673647	−	0.385058i
$112$		0			0
$113$			738845.i			0.512057i	0.966669	+	0.256028i	$0.0824141\pi$
$113$			738845.i			0.512057i	−0.966669	+	0.256028i	$0.917586\pi$
$114$		0			0
$115$	−1.84876e6			−1.21559
$116$		0			0
$117$	1.03553e6	+	1.75831e6i	0.646554	+	1.09784i
$118$		0			0
$119$			440260.i			0.261257i
$120$		0			0
$121$	−672217.			−0.379449
$122$		0			0
$123$	597841.	−	1.04591e6i	0.321270	−	0.562053i
$124$		0			0
$125$			2.12518e6i			1.08809i
$126$		0			0
$127$	−1.01875e6			−0.497343			−0.248672	−	0.968588i	$-0.579994\pi$
$127$	−1.01875e6			−0.497343			−0.248672	+	0.968588i	$0.579994\pi$
$128$		0			0
$129$	554500.	+	316953.i	0.258305	+	0.147648i
$130$		0			0
$131$			461949.i			0.205485i	0.994708	+	0.102743i	$0.0327618\pi$
$131$			461949.i			0.205485i	−0.994708	+	0.102743i	$0.967238\pi$
$132$		0			0
$133$	−598854.			−0.254546
$134$		0			0
$135$	1.97102e6	−	25558.6i	0.801107	−	0.0103881i
$136$		0			0
$137$		−	1.86796e6i		−	0.726450i	−0.931701	−	0.363225i	$-0.881676\pi$
$137$		−	1.86796e6i		−	0.726450i	0.931701	−	0.363225i	$-0.118324\pi$
$138$		0			0
$139$	−1.67091e6			−0.622169			−0.311084	−	0.950382i	$-0.600692\pi$
$139$	−1.67091e6			−0.622169			−0.311084	+	0.950382i	$0.600692\pi$
$140$		0			0
$141$	872139.	−	1.52578e6i	0.311120	−	0.544295i
$142$		0			0
$143$		−	4.37580e6i		−	1.49641i
$144$		0			0
$145$	2.09085e6			0.685834
$146$		0			0
$147$	2.68224e6	+	1.53317e6i	0.844394	+	0.482657i
$148$		0			0
$149$		−	1.93135e6i		−	0.583853i	−0.956441	−	0.291926i	$-0.905704\pi$
$149$		−	1.93135e6i		−	0.583853i	0.956441	−	0.291926i	$-0.0942962\pi$
$150$		0			0
$151$	5.45133e6			1.58333			0.791666	−	0.610955i	$-0.209214\pi$
$151$	5.45133e6			1.58333			0.791666	+	0.610955i	$0.209214\pi$
$152$		0			0
$153$	4.87127e6	−	2.86885e6i	1.36009	−	0.801003i
$154$		0			0
$155$			329006.i			0.0883504i
$156$		0			0
$157$	−3.34693e6			−0.864863			−0.432432	−	0.901667i	$-0.642344\pi$
$157$	−3.34693e6			−0.864863			−0.432432	+	0.901667i	$0.642344\pi$
$158$		0			0
$159$	−881111.	+	1.54148e6i	−0.219199	+	0.383482i
$160$		0			0
$161$		−	1.04804e6i		−	0.251132i
$162$		0			0
$163$	−273858.			−0.0632357			−0.0316178	−	0.999500i	$-0.510066\pi$
$163$	−273858.			−0.0632357			−0.0316178	+	0.999500i	$0.510066\pi$
$164$		0			0
$165$	−3.66979e6	−	2.09766e6i	−0.816938	−	0.466963i
$166$		0			0
$167$			879959.i			0.188935i	0.995528	+	0.0944676i	$0.0301149\pi$
$167$			879959.i			0.188935i	−0.995528	+	0.0944676i	$0.969885\pi$
$168$		0			0
$169$	3.00845e6			0.623279
$170$		0			0
$171$	3.90230e6	+	6.62603e6i	0.780426	+	1.32515i
$172$		0			0
$173$			6.14739e6i			1.18728i	0.804732	+	0.593639i	$0.202309\pi$
$173$			6.14739e6i			1.18728i	−0.804732	+	0.593639i	$0.797691\pi$
$174$		0			0
$175$	−317676.			−0.0592748
$176$		0			0
$177$	−486376.	+	850900.i	−0.0877107	+	0.153447i
$178$		0			0
$179$		−	8.87757e6i		−	1.54787i	−0.633264	−	0.773936i	$-0.718285\pi$
$179$		−	8.87757e6i		−	1.54787i	0.633264	−	0.773936i	$-0.281715\pi$
$180$		0			0
$181$	−3.84437e6			−0.648320			−0.324160	−	0.946002i	$-0.605082\pi$
$181$	−3.84437e6			−0.648320			−0.324160	+	0.946002i	$0.605082\pi$
$182$		0			0
$183$	−9.66792e6	−	5.52620e6i	−1.57754	−	0.901723i
$184$		0			0
$185$			3.93609e6i			0.621656i
$186$		0			0
$187$	−1.21228e7			−1.85387
$188$		0			0
$189$	14489.0	+	1.11736e6i	0.00214611	+	0.165503i
$190$		0			0
$191$			9.62289e6i			1.38104i	0.723314	+	0.690519i	$0.242618\pi$
$191$			9.62289e6i			1.38104i	−0.723314	+	0.690519i	$0.757382\pi$
$192$		0			0
$193$	7.10835e6			0.988774			0.494387	−	0.869242i	$-0.335393\pi$
$193$	7.10835e6			0.988774			0.494387	+	0.869242i	$0.335393\pi$
$194$		0			0
$195$	3.75604e6	−	6.57108e6i	0.506554	−	0.886202i
$196$		0			0
$197$			1.13629e7i			1.48624i	0.669156	+	0.743122i	$0.266656\pi$
$197$			1.13629e7i			1.48624i	−0.669156	+	0.743122i	$0.733344\pi$
$198$		0			0
$199$	8.11010e6			1.02912			0.514561	−	0.857454i	$-0.327955\pi$
$199$	8.11010e6			1.02912			0.514561	+	0.857454i	$0.327955\pi$
$200$		0			0
$201$	−6.22069e6	−	3.55576e6i	−0.766038	−	0.437869i
$202$		0			0
$203$			1.18528e6i			0.141689i
$204$		0			0
$205$	−4.46845e6			−0.518675
$206$		0			0
$207$	−1.15961e7	+	6.82933e6i	−1.30738	+	0.769958i
$208$		0			0
$209$		−	1.64898e7i		−	1.80624i
$210$		0			0
$211$	9.05527e6			0.963949			0.481974	−	0.876185i	$-0.339920\pi$
$211$	9.05527e6			0.963949			0.481974	+	0.876185i	$0.339920\pi$
$212$		0			0
$213$	−7.40627e6	+	1.29571e7i	−0.766410	+	1.34081i
$214$		0			0
$215$		−	2.36901e6i		−	0.238370i
$216$		0			0
$217$	−186510.			−0.0182526
$218$		0			0
$219$	−2.92890e6	−	1.67416e6i	−0.278851	−	0.159392i
$220$		0			0
$221$		−	2.17070e7i		−	2.01105i
$222$		0			0
$223$	1.05611e6			0.0952343			0.0476172	−	0.998866i	$-0.484837\pi$
$223$	1.05611e6			0.0952343			0.0476172	+	0.998866i	$0.484837\pi$
$224$		0			0
$225$	2.07006e6	+	3.51493e6i	0.181734	+	0.308581i
$226$		0			0
$227$			1.73074e7i			1.47963i	0.672810	+	0.739815i	$0.265087\pi$
$227$			1.73074e7i			1.47963i	−0.672810	+	0.739815i	$0.734913\pi$
$228$		0			0
$229$	5.72078e6			0.476375			0.238188	−	0.971219i	$-0.423447\pi$
$229$	5.72078e6			0.476375			0.238188	+	0.971219i	$0.423447\pi$
$230$		0			0
$231$	1.18914e6	−	2.08037e6i	0.0964712	−	0.168774i
$232$		0			0
$233$			1.54337e7i			1.22012i	0.792356	+	0.610059i	$0.208854\pi$
$233$			1.54337e7i			1.22012i	−0.792356	+	0.610059i	$0.791146\pi$
$234$		0			0
$235$	−6.51863e6			−0.502288
$236$		0			0
$237$	−6.59651e6	−	3.77058e6i	−0.495529	−	0.283245i
$238$		0			0
$239$			5.15623e6i			0.377692i	0.982007	+	0.188846i	$0.0604748\pi$
$239$			5.15623e6i			0.377692i	−0.982007	+	0.188846i	$0.939525\pi$
$240$		0			0
$241$	2.01708e6			0.144103			0.0720513	−	0.997401i	$-0.477045\pi$
$241$	2.01708e6			0.144103			0.0720513	+	0.997401i	$0.477045\pi$
$242$		0			0
$243$	1.22686e7	−	7.44130e6i	0.855019	−	0.518597i
$244$		0			0
$245$		−	1.14594e7i		−	0.779226i
$246$		0			0
$247$	2.95264e7			1.95939
$248$		0			0
$249$	−3.33972e6	+	5.84275e6i	−0.216328	+	0.378459i
$250$		0			0
$251$		−	7.82106e6i		−	0.494589i	−0.968940	−	0.247294i	$-0.920459\pi$
$251$		−	7.82106e6i		−	0.494589i	0.968940	−	0.247294i	$-0.0795415\pi$
$252$		0			0
$253$	2.88585e7			1.78202
$254$		0			0
$255$	−1.82047e7	−	1.04058e7i	−1.09790	−	0.627561i
$256$		0			0
$257$		−	5.86764e6i		−	0.345672i	−0.984951	−	0.172836i	$-0.944707\pi$
$257$		−	5.86764e6i		−	0.345672i	0.984951	−	0.172836i	$-0.0552930\pi$
$258$		0			0
$259$	−2.23134e6			−0.128430
$260$		0			0
$261$	1.31146e7	−	7.72364e6i	0.737622	−	0.434410i
$262$		0			0
$263$		−	2.84551e7i		−	1.56420i	−0.623150	−	0.782102i	$-0.714147\pi$
$263$		−	2.84551e7i		−	1.56420i	0.623150	−	0.782102i	$-0.285853\pi$
$264$		0			0
$265$	6.58569e6			0.353886
$266$		0			0
$267$	−411765.	+	720371.i	−0.0216330	+	0.0378462i
$268$		0			0
$269$			2.59338e7i			1.33232i	0.745808	+	0.666161i	$0.232064\pi$
$269$			2.59338e7i			1.33232i	−0.745808	+	0.666161i	$0.767936\pi$
$270$		0			0
$271$	9.94363e6			0.499617			0.249808	−	0.968295i	$-0.419632\pi$
$271$	9.94363e6			0.499617			0.249808	+	0.968295i	$0.419632\pi$
$272$		0			0
$273$	3.72508e6	+	2.12926e6i	0.183083	+	0.104651i
$274$		0			0
$275$		−	8.74740e6i		−	0.420611i
$276$		0			0
$277$	−8.05111e6			−0.378806			−0.189403	−	0.981899i	$-0.560655\pi$
$277$	−8.05111e6			−0.378806			−0.189403	+	0.981899i	$0.560655\pi$
$278$		0			0
$279$	1.21535e6	+	2.06365e6i	0.0559615	+	0.0950217i
$280$		0			0
$281$		−	28050.0i		−	0.00126419i	−1.00000		0.000632096i	$-0.999799\pi$
$281$		−	28050.0i		−	0.00126419i	1.00000		0.000632096i	$-0.000201202\pi$
$282$		0			0
$283$	−3.93236e7			−1.73498			−0.867489	−	0.497457i	$-0.834267\pi$
$283$	−3.93236e7			−1.73498			−0.867489	+	0.497457i	$0.834267\pi$
$284$		0			0
$285$	1.41543e7	−	2.47625e7i	0.611439	−	1.06969i
$286$		0			0
$287$		−	2.53312e6i		−	0.107155i
$288$		0			0
$289$	−3.60000e7			−1.49145
$290$		0			0
$291$	3.50398e7	+	2.00288e7i	1.42194	+	0.812786i
$292$		0			0
$293$		−	287438.i		−	0.0114272i	−0.999984	−	0.00571362i	$-0.998181\pi$
$293$		−	287438.i		−	0.0114272i	0.999984	−	0.00571362i	$-0.00181871\pi$
$294$		0			0
$295$	3.63532e6			0.141604
$296$		0			0
$297$	−3.07670e7	+	398962.i	−1.17440	+	0.0152287i
$298$		0			0
$299$			5.16737e7i			1.93311i
$300$		0			0
$301$	1.34297e6			0.0492455
$302$		0			0
$303$	−2.24822e7	+	3.93320e7i	−0.808187	+	1.41390i
$304$		0			0
$305$			4.13045e7i			1.45579i
$306$		0			0
$307$	−3.53898e6			−0.122310			−0.0611552	−	0.998128i	$-0.519478\pi$
$307$	−3.53898e6			−0.122310			−0.0611552	+	0.998128i	$0.519478\pi$
$308$		0			0
$309$	6.32785e6	+	3.61701e6i	0.214477	+	0.122595i
$310$		0			0
$311$			6.30383e6i			0.209567i	0.994495	+	0.104784i	$0.0334150\pi$
$311$			6.30383e6i			0.209567i	−0.994495	+	0.104784i	$0.966585\pi$
$312$		0			0
$313$	−5.52306e7			−1.80114			−0.900569	−	0.434713i	$-0.856850\pi$
$313$	−5.52306e7			−1.80114			−0.900569	+	0.434713i	$0.856850\pi$
$314$		0			0
$315$	3.57143e6	−	2.10334e6i	0.114264	−	0.0672942i
$316$		0			0
$317$		−	2.84353e7i		−	0.892648i	−0.894871	−	0.446324i	$-0.852733\pi$
$317$		−	2.84353e7i		−	0.892648i	0.894871	−	0.446324i	$-0.147267\pi$
$318$		0			0
$319$	−3.26375e7			−1.00541
$320$		0			0
$321$	1.34577e7	−	2.35438e7i	0.406869	−	0.711806i
$322$		0			0
$323$		−	8.18008e7i		−	2.42745i
$324$		0			0
$325$	1.56630e7			0.456273
$326$		0			0
$327$	1.85262e7	+	1.05896e7i	0.529837	+	0.302856i
$328$		0			0
$329$		−	3.69535e6i		−	0.103769i
$330$		0			0
$331$	−3.80117e7			−1.04817			−0.524087	−	0.851665i	$-0.675593\pi$
$331$	−3.80117e7			−1.04817			−0.524087	+	0.851665i	$0.675593\pi$
$332$		0			0
$333$	1.45400e7	+	2.46887e7i	0.393760	+	0.668597i
$334$		0			0
$335$			2.65768e7i			0.706917i
$336$		0			0
$337$	−1.08408e7			−0.283250			−0.141625	−	0.989920i	$-0.545233\pi$
$337$	−1.08408e7			−0.283250			−0.141625	+	0.989920i	$0.545233\pi$
$338$		0			0
$339$	9.89965e6	−	1.73191e7i	0.254109	−	0.444557i
$340$		0			0
$341$		−	5.13567e6i		−	0.129519i
$342$		0			0
$343$	1.31754e7			0.326499
$344$		0			0
$345$	4.33364e7	+	2.47711e7i	1.05535	+	0.603238i
$346$		0			0
$347$			5.28512e6i			0.126493i	0.997998	+	0.0632465i	$0.0201454\pi$
$347$			5.28512e6i			0.126493i	−0.997998	+	0.0632465i	$0.979855\pi$
$348$		0			0
$349$	−3.21105e7			−0.755389			−0.377694	−	0.925930i	$-0.623283\pi$
$349$	−3.21105e7			−0.755389			−0.377694	+	0.925930i	$0.623283\pi$
$350$		0			0
$351$	−714376.	−	5.50911e7i	−0.0165198	−	1.27397i
$352$		0			0
$353$			2.65336e7i			0.603215i	0.953432	+	0.301607i	$0.0975232\pi$
$353$			2.65336e7i			0.603215i	−0.953432	+	0.301607i	$0.902477\pi$
$354$		0			0
$355$	5.53567e7			1.23733
$356$		0			0
$357$	5.89896e6	−	1.03201e7i	0.129650	−	0.226818i
$358$		0			0
$359$			2.46209e6i			0.0532133i	0.999646	+	0.0266066i	$0.00847015\pi$
$359$			2.46209e6i			0.0532133i	−0.999646	+	0.0266066i	$0.991530\pi$
$360$		0			0
$361$	6.42218e7			1.36509
$362$		0			0
$363$	1.57573e7	+	9.00691e6i	0.329429	+	0.188302i
$364$		0			0
$365$			1.25132e7i			0.257330i
$366$		0			0
$367$	−8.45375e7			−1.71022			−0.855109	−	0.518449i	$-0.826510\pi$
$367$	−8.45375e7			−1.71022			−0.855109	+	0.518449i	$0.826510\pi$
$368$		0			0
$369$	−2.80278e7	+	1.65065e7i	−0.557840	+	0.328531i
$370$		0			0
$371$			3.73337e6i			0.0731104i
$372$		0			0
$373$	3.74800e7			0.722226			0.361113	−	0.932522i	$-0.382397\pi$
$373$	3.74800e7			0.722226			0.361113	+	0.932522i	$0.382397\pi$
$374$		0			0
$375$	2.84748e7	−	4.98159e7i	0.539967	−	0.944657i
$376$		0			0
$377$		−	5.84403e7i		−	1.09066i
$378$		0			0
$379$	−7.17708e6			−0.131835			−0.0659175	−	0.997825i	$-0.520997\pi$
$379$	−7.17708e6			−0.131835			−0.0659175	+	0.997825i	$0.520997\pi$
$380$		0			0
$381$	2.38803e7	+	1.36500e7i	0.431783	+	0.246808i
$382$		0			0
$383$			7.49783e7i			1.33456i	0.744805	+	0.667282i	$0.232543\pi$
$383$			7.49783e7i			1.33456i	−0.744805	+	0.667282i	$0.767457\pi$
$384$		0			0
$385$	−8.88801e6			−0.155748
$386$		0			0
$387$	−8.75114e6	−	1.48593e7i	−0.150984	−	0.256369i
$388$		0			0
$389$		−	5.40696e7i		−	0.918553i	−0.888293	−	0.459277i	$-0.848109\pi$
$389$		−	5.40696e7i		−	0.918553i	0.888293	−	0.459277i	$-0.151891\pi$
$390$		0			0
$391$	1.43158e8			2.39489
$392$		0			0
$393$	6.18957e6	−	1.08285e7i	0.101972	−	0.178398i
$394$		0			0
$395$			2.81824e7i			0.457286i
$396$		0			0
$397$	−7.70698e7			−1.23172			−0.615861	−	0.787855i	$-0.711192\pi$
$397$	−7.70698e7			−1.23172			−0.615861	+	0.787855i	$0.711192\pi$
$398$		0			0
$399$	1.40376e7	+	8.02394e6i	0.220991	+	0.126319i
$400$		0			0
$401$		−	7.02798e7i		−	1.08993i	−0.838460	−	0.544964i	$-0.816543\pi$
$401$		−	7.02798e7i		−	1.08993i	0.838460	−	0.544964i	$-0.183457\pi$
$402$		0			0
$403$	9.19587e6			0.140500
$404$		0			0
$405$	−4.65449e7	−	2.58103e7i	−0.700659	−	0.388532i
$406$		0			0
$407$		−	6.14411e7i		−	0.911331i
$408$		0			0
$409$	6.76732e7			0.989115			0.494557	−	0.869145i	$-0.335330\pi$
$409$	6.76732e7			0.989115			0.494557	+	0.869145i	$0.335330\pi$
$410$		0			0
$411$	−2.50284e7	+	4.37865e7i	−0.360502	+	0.630688i
$412$		0			0
$413$			2.06083e6i			0.0292545i
$414$		0			0
$415$	2.49621e7			0.349251
$416$		0			0
$417$	3.91675e7	+	2.23882e7i	0.540154	+	0.308753i
$418$		0			0
$419$			3.73652e7i			0.507956i	0.967210	+	0.253978i	$0.0817390\pi$
$419$			3.73652e7i			0.507956i	−0.967210	+	0.253978i	$0.918261\pi$
$420$		0			0
$421$	4.66720e6			0.0625476			0.0312738	−	0.999511i	$-0.490044\pi$
$421$	4.66720e6			0.0625476			0.0312738	+	0.999511i	$0.490044\pi$
$422$		0			0
$423$	−4.08873e7	+	2.40799e7i	−0.540216	+	0.318151i
$424$		0			0
$425$		−	4.33931e7i		−	0.565268i
$426$		0			0
$427$	−2.34151e7			−0.300755
$428$		0			0
$429$	−5.86305e7	+	1.02572e8i	−0.742595	+	1.29915i
$430$		0			0
$431$		−	9.07386e7i		−	1.13334i	−0.823945	−	0.566670i	$-0.808231\pi$
$431$		−	9.07386e7i		−	1.13334i	0.823945	−	0.566670i	$-0.191769\pi$
$432$		0			0
$433$	4.32787e7			0.533102			0.266551	−	0.963821i	$-0.414116\pi$
$433$	4.32787e7			0.533102			0.266551	+	0.963821i	$0.414116\pi$
$434$		0			0
$435$	−4.90113e7	−	2.80149e7i	−0.595427	−	0.340347i
$436$		0			0
$437$			1.94727e8i			2.33337i
$438$		0			0
$439$	−1.34753e8			−1.59274			−0.796369	−	0.604811i	$-0.793249\pi$
$439$	−1.34753e8			−1.59274			−0.796369	+	0.604811i	$0.793249\pi$
$440$		0			0
$441$	−4.23311e7	−	7.18776e7i	−0.493565	−	0.838065i
$442$		0			0
$443$		−	4.77810e6i		−	0.0549597i	−0.999622	−	0.0274798i	$-0.991252\pi$
$443$		−	4.77810e6i		−	0.0549597i	0.999622	−	0.0274798i	$-0.00874821\pi$
$444$		0			0
$445$	3.07766e6			0.0349253
$446$		0			0
$447$	−2.58779e7	+	4.52725e7i	−0.289738	+	0.506888i
$448$		0			0
$449$			9.07831e7i			1.00292i	0.865181	+	0.501460i	$0.167203\pi$
$449$			9.07831e7i			1.00292i	−0.865181	+	0.501460i	$0.832797\pi$
$450$		0			0
$451$	6.97510e7			0.760363
$452$		0			0
$453$	−1.27784e8	−	7.30414e7i	−1.37461	−	0.785732i
$454$		0			0
$455$		−	1.59148e7i		−	0.168953i
$456$		0			0
$457$	−2.48525e7			−0.260388			−0.130194	−	0.991489i	$-0.541560\pi$
$457$	−2.48525e7			−0.260388			−0.130194	+	0.991489i	$0.541560\pi$
$458$		0			0
$459$	−1.52626e8	+	1.97912e6i	−1.57830	+	0.0204661i
$460$		0			0
$461$			1.05119e8i			1.07294i	0.843918	+	0.536472i	$0.180243\pi$
$461$			1.05119e8i			1.07294i	−0.843918	+	0.536472i	$0.819757\pi$
$462$		0			0
$463$	−2.67674e7			−0.269689			−0.134845	−	0.990867i	$-0.543054\pi$
$463$	−2.67674e7			−0.269689			−0.134845	+	0.990867i	$0.543054\pi$
$464$		0			0
$465$	4.40828e6	−	7.71216e6i	0.0438441	−	0.0767039i
$466$		0			0
$467$			6.62252e7i			0.650239i	0.945673	+	0.325119i	$0.105404\pi$
$467$			6.62252e7i			0.650239i	−0.945673	+	0.325119i	$0.894596\pi$
$468$		0			0
$469$	−1.50662e7			−0.146044
$470$		0			0
$471$	7.84547e7	+	4.48449e7i	0.750856	+	0.429190i
$472$		0			0
$473$			3.69794e7i			0.349443i
$474$		0			0
$475$	5.90245e7			0.550747
$476$		0			0
$477$	4.13079e7	−	2.43276e7i	0.380608	−	0.224153i
$478$		0			0
$479$		−	5.73689e6i		−	0.0522000i	−0.999659	−	0.0261000i	$-0.991691\pi$
$479$		−	5.73689e6i		−	0.0522000i	0.999659	−	0.0261000i	$-0.00830882\pi$
$480$		0			0
$481$	1.10016e8			0.988598
$482$		0			0
$483$	−1.40425e7	+	2.45670e7i	−0.124625	+	0.218027i
$484$		0			0
$485$		−	1.49701e8i		−	1.31220i
$486$		0			0
$487$	−4.23093e7			−0.366310			−0.183155	−	0.983084i	$-0.558631\pi$
$487$	−4.23093e7			−0.366310			−0.183155	+	0.983084i	$0.558631\pi$
$488$		0			0
$489$	6.41945e6	+	3.66937e6i	0.0548998	+	0.0313808i
$490$		0			0
$491$		−	2.08106e8i		−	1.75809i	−0.476743	−	0.879043i	$-0.658183\pi$
$491$		−	2.08106e8i		−	1.75809i	0.476743	−	0.879043i	$-0.341817\pi$
$492$		0			0
$493$	−1.61905e8			−1.35120
$494$		0			0
$495$	5.79167e7	+	9.83415e7i	0.477516	+	0.810814i
$496$		0			0
$497$			3.13812e7i			0.255624i
$498$		0			0
$499$	2.07046e8			1.66635			0.833175	−	0.553010i	$-0.186521\pi$
$499$	2.07046e8			1.66635			0.833175	+	0.553010i	$0.186521\pi$
$500$		0			0
$501$	1.17904e7	−	2.06270e7i	0.0937595	−	0.164029i
$502$		0			0
$503$			1.69353e8i			1.33073i	0.746518	+	0.665365i	$0.231724\pi$
$503$			1.69353e8i			1.33073i	−0.746518	+	0.665365i	$0.768276\pi$
$504$		0			0
$505$	1.68039e8			1.30478
$506$		0			0
$507$	−7.05205e7	−	4.03096e7i	−0.541117	−	0.309303i
$508$		0			0
$509$		−	1.85904e8i		−	1.40973i	−0.709341	−	0.704865i	$-0.751008\pi$
$509$		−	1.85904e8i		−	1.40973i	0.709341	−	0.704865i	$-0.248992\pi$
$510$		0			0
$511$	−7.09363e6			−0.0531625
$512$		0			0
$513$	−2.69206e6	−	2.07606e8i	−0.0199404	−	1.53776i
$514$		0			0
$515$		−	2.70346e7i		−	0.197924i
$516$		0			0
$517$	1.01754e8			0.736340
$518$		0			0
$519$	8.23677e7	−	1.44100e8i	0.589189	−	1.03077i
$520$		0			0
$521$		−	6.72394e7i		−	0.475456i	−0.971332	−	0.237728i	$-0.923597\pi$
$521$		−	6.72394e7i		−	0.475456i	0.971332	−	0.237728i	$-0.0764027\pi$
$522$		0			0
$523$	2.17123e8			1.51775			0.758877	−	0.651234i	$-0.225748\pi$
$523$	2.17123e8			1.51775			0.758877	+	0.651234i	$0.225748\pi$
$524$		0			0
$525$	7.44659e6	+	4.25648e6i	0.0514611	+	0.0294153i
$526$		0			0
$527$		−	2.54765e7i		−	0.174063i
$528$		0			0
$529$	−1.92753e8			−1.30207
$530$		0			0
$531$	2.28021e7	−	1.34289e7i	0.152297	−	0.0896929i
$532$		0			0
$533$			1.24895e8i			0.824830i
$534$		0			0
$535$	−1.00587e8			−0.656870
$536$		0			0
$537$	−1.18949e8	+	2.08098e8i	−0.768135	+	1.34383i
$538$		0			0
$539$			1.78877e8i			1.14232i
$540$		0			0
$541$	2.48308e8			1.56819			0.784097	−	0.620639i	$-0.213127\pi$
$541$	2.48308e8			1.56819			0.784097	+	0.620639i	$0.213127\pi$
$542$		0			0
$543$	9.01152e7	+	5.15100e7i	0.562858	+	0.321730i
$544$		0			0
$545$		−	7.91498e7i		−	0.488945i
$546$		0			0
$547$	−3.01224e8			−1.84046			−0.920232	−	0.391372i	$-0.872001\pi$
$547$	−3.01224e8			−1.84046			−0.920232	+	0.391372i	$0.872001\pi$
$548$		0			0
$549$	1.52579e8	+	2.59077e8i	0.922102	+	1.56571i
$550$		0			0
$551$		−	2.20227e8i		−	1.31649i
$552$		0			0
$553$	−1.59764e7			−0.0944719
$554$		0			0
$555$	5.27390e7	−	9.22653e7i	0.308498	−	0.539709i
$556$		0			0
$557$		−	1.62479e7i		−	0.0940224i	−0.998894	−	0.0470112i	$-0.985030\pi$
$557$		−	1.62479e7i		−	0.0940224i	0.998894	−	0.0470112i	$-0.0149696\pi$
$558$		0			0
$559$	−6.62149e7			−0.379071
$560$		0			0
$561$	2.84169e8	+	1.62431e8i	1.60949	+	0.919986i
$562$		0			0
$563$		−	5.11459e7i		−	0.286606i	−0.989679	−	0.143303i	$-0.954228\pi$
$563$		−	5.11459e7i		−	0.286606i	0.989679	−	0.143303i	$-0.0457724\pi$
$564$		0			0
$565$	−7.39930e7			−0.410247
$566$		0			0
$567$	1.46316e7	−	2.63859e7i	0.0802680	−	0.144751i
$568$		0			0
$569$			2.76329e7i			0.150000i	0.997184	+	0.0749998i	$0.0238956\pi$
$569$			2.76329e7i			0.150000i	−0.997184	+	0.0749998i	$0.976104\pi$
$570$		0			0
$571$	9.21998e7			0.495247			0.247623	−	0.968856i	$-0.420350\pi$
$571$	9.21998e7			0.495247			0.247623	+	0.968856i	$0.420350\pi$
$572$		0			0
$573$	1.28935e8	−	2.25568e8i	0.685343	−	1.19899i
$574$		0			0
$575$			1.03298e8i			0.543359i
$576$		0			0
$577$	−3.18032e8			−1.65555			−0.827776	−	0.561058i	$-0.810394\pi$
$577$	−3.18032e8			−1.65555			−0.827776	+	0.561058i	$0.810394\pi$
$578$		0			0
$579$	−1.66626e8	−	9.52435e7i	−0.858432	−	0.490681i
$580$		0			0
$581$			1.41508e7i			0.0721527i
$582$		0			0
$583$	−1.02800e8			−0.518787
$584$		0			0
$585$	−1.76089e8	+	1.03705e8i	−0.879559	+	0.518002i
$586$		0			0
$587$			8.94211e7i			0.442105i	0.975262	+	0.221053i	$0.0709493\pi$
$587$			8.94211e7i			0.442105i	−0.975262	+	0.221053i	$0.929051\pi$
$588$		0			0
$589$	3.46538e7			0.169592
$590$		0			0
$591$	1.52249e8	−	2.66355e8i	0.737552	−	1.29032i
$592$		0			0
$593$		−	2.11746e8i		−	1.01543i	−0.861525	−	0.507716i	$-0.830490\pi$
$593$		−	2.11746e8i		−	1.01543i	0.861525	−	0.507716i	$-0.169510\pi$
$594$		0			0
$595$	−4.40907e7			−0.209313
$596$		0			0
$597$	−1.90107e8	−	1.08666e8i	−0.893462	−	0.510704i
$598$		0			0
$599$			2.26542e8i			1.05407i	0.849844	+	0.527034i	$0.176696\pi$
$599$			2.26542e8i			1.05407i	−0.849844	+	0.527034i	$0.823304\pi$
$600$		0			0
$601$	−2.01797e8			−0.929589			−0.464795	−	0.885419i	$-0.653872\pi$
$601$	−2.01797e8			−0.929589			−0.464795	+	0.885419i	$0.653872\pi$
$602$		0			0
$603$	9.81752e7	+	1.66700e8i	0.447765	+	0.760296i
$604$		0			0
$605$		−	6.73204e7i		−	0.304005i
$606$		0			0
$607$	−4.43041e7			−0.198097			−0.0990485	−	0.995083i	$-0.531580\pi$
$607$	−4.43041e7			−0.198097			−0.0990485	+	0.995083i	$0.531580\pi$
$608$		0			0
$609$	1.58814e7	−	2.77840e7i	0.0703132	−	0.123011i
$610$		0			0
$611$			1.82199e8i			0.798771i
$612$		0			0
$613$	1.77466e6			0.00770429			0.00385215	−	0.999993i	$-0.498774\pi$
$613$	1.77466e6			0.00770429			0.00385215	+	0.999993i	$0.498774\pi$
$614$		0			0
$615$	1.04744e8	+	5.98719e7i	0.450302	+	0.257394i
$616$		0			0
$617$			4.21693e8i			1.79532i	0.440692	+	0.897658i	$0.354733\pi$
$617$			4.21693e8i			1.79532i	−0.440692	+	0.897658i	$0.645267\pi$
$618$		0			0
$619$	−1.93302e8			−0.815014			−0.407507	−	0.913202i	$-0.633602\pi$
$619$	−1.93302e8			−0.815014			−0.407507	+	0.913202i	$0.633602\pi$
$620$		0			0
$621$	3.63327e8	−	4.71132e6i	1.51713	−	0.0196729i
$622$		0			0
$623$			1.74470e6i			0.00721533i
$624$		0			0
$625$	−1.25398e8			−0.513631
$626$		0			0
$627$	−2.20944e8	+	3.86534e8i	−0.896353	+	1.56814i
$628$		0			0
$629$		−	3.04790e8i		−	1.22476i
$630$		0			0
$631$	−3.10787e8			−1.23701			−0.618507	−	0.785779i	$-0.712262\pi$
$631$	−3.10787e8			−1.23701			−0.618507	+	0.785779i	$0.712262\pi$
$632$		0			0
$633$	−2.12263e8	−	1.21330e8i	−0.836879	−	0.478362i
$634$		0			0
$635$		−	1.02025e8i		−	0.398459i
$636$		0			0
$637$	−3.20296e8			−1.23918
$638$		0			0
$639$	3.47218e8	−	2.04489e8i	1.33076	−	0.783730i
$640$		0			0
$641$			3.67796e8i			1.39648i	0.715866	+	0.698238i	$0.246032\pi$
$641$			3.67796e8i			1.39648i	−0.715866	+	0.698238i	$0.753968\pi$
$642$		0			0
$643$	1.38536e8			0.521110			0.260555	−	0.965459i	$-0.416095\pi$
$643$	1.38536e8			0.521110			0.260555	+	0.965459i	$0.416095\pi$
$644$		0			0
$645$	−3.17419e7	+	5.55315e7i	−0.118291	+	0.206947i
$646$		0			0
$647$			2.01496e8i			0.743966i	0.928240	+	0.371983i	$0.121322\pi$
$647$			2.01496e8i			0.743966i	−0.928240	+	0.371983i	$0.878678\pi$
$648$		0			0
$649$	−5.67462e7			−0.207588
$650$		0			0
$651$	4.37195e6	+	2.49902e6i	0.0158465	+	0.00905787i
$652$		0			0
$653$		−	1.84529e7i		−	0.0662712i	−0.999451	−	0.0331356i	$-0.989451\pi$
$653$		−	1.84529e7i		−	0.0662712i	0.999451	−	0.0331356i	$-0.0105493\pi$
$654$		0			0
$655$	−4.62628e7			−0.164629
$656$		0			0
$657$	4.62240e7	+	7.84876e7i	0.162994	+	0.276761i
$658$		0			0
$659$		−	2.35653e8i		−	0.823410i	−0.911317	−	0.411705i	$-0.864933\pi$
$659$		−	2.35653e8i		−	0.823410i	0.911317	−	0.411705i	$-0.135067\pi$
$660$		0			0
$661$	3.84131e8			1.33007			0.665036	−	0.746811i	$-0.268416\pi$
$661$	3.84131e8			1.33007			0.665036	+	0.746811i	$0.268416\pi$
$662$		0			0
$663$	−2.90848e8	+	5.08829e8i	−0.997988	+	1.74595i
$664$		0			0
$665$		−	5.99733e7i		−	0.203936i
$666$		0			0
$667$	3.85415e8			1.29883
$668$		0			0
$669$	−2.47560e7	−	1.41506e7i	−0.0826804	−	0.0472602i
$670$		0			0
$671$		−	6.44750e8i		−	2.13414i
$672$		0			0
$673$	8.95297e7			0.293712			0.146856	−	0.989158i	$-0.453085\pi$
$673$	8.95297e7			0.293712			0.146856	+	0.989158i	$0.453085\pi$
$674$		0			0
$675$	−1.42807e6	−	1.10129e8i	−0.00464341	−	0.358089i
$676$		0			0
$677$			2.34104e8i			0.754473i	0.926117	+	0.377236i	$0.123126\pi$
$677$			2.34104e8i			0.754473i	−0.926117	+	0.377236i	$0.876874\pi$
$678$		0			0
$679$	8.48644e7			0.271092
$680$		0			0
$681$	2.31898e8	−	4.05698e8i	0.734270	−	1.28458i
$682$		0			0
$683$		−	5.04689e8i		−	1.58402i	−0.610506	−	0.792011i	$-0.709034\pi$
$683$		−	5.04689e8i		−	1.58402i	0.610506	−	0.792011i	$-0.290966\pi$
$684$		0			0
$685$	1.87070e8			0.582013
$686$		0			0
$687$	−1.34100e8	−	7.66517e7i	−0.413578	−	0.236402i
$688$		0			0
$689$		−	1.84073e8i		−	0.562773i
$690$		0			0
$691$	−2.67422e8			−0.810517			−0.405259	−	0.914202i	$-0.632819\pi$
$691$	−2.67422e8			−0.810517			−0.405259	+	0.914202i	$0.632819\pi$
$692$		0			0
$693$	−5.57489e7	+	3.28324e7i	−0.167508	+	0.0986514i
$694$		0			0
$695$		−	1.67336e8i		−	0.498466i
$696$		0			0
$697$	3.46013e8			1.02187
$698$		0			0
$699$	2.06793e8	−	3.61778e8i	0.605486	−	1.05928i
$700$		0			0
$701$			2.42624e8i			0.704336i	0.935937	+	0.352168i	$0.114556\pi$
$701$			2.42624e8i			0.704336i	−0.935937	+	0.352168i	$0.885444\pi$
$702$		0			0
$703$	4.14584e8			1.19329
$704$		0			0
$705$	1.52802e8	+	8.73419e7i	0.436076	+	0.249262i
$706$		0			0
$707$			9.52599e7i			0.269558i
$708$		0			0
$709$	3.69360e8			1.03636			0.518181	−	0.855271i	$-0.326609\pi$
$709$	3.69360e8			1.03636			0.518181	+	0.855271i	$0.326609\pi$
$710$		0			0
$711$	1.04106e8	+	1.76771e8i	0.289647	+	0.491815i
$712$		0			0
$713$			6.06469e7i			0.167317i
$714$		0			0
$715$	4.38222e8			1.19888
$716$		0			0
$717$	6.90873e7	−	1.20866e8i	0.187431	−	0.327904i
$718$		0			0
$719$			4.83852e8i			1.30175i	0.759187	+	0.650873i	$0.225597\pi$
$719$			4.83852e8i			1.30175i	−0.759187	+	0.650873i	$0.774403\pi$
$720$		0			0
$721$	1.53257e7			0.0408897
$722$		0			0
$723$	−4.72820e7	−	2.70265e7i	−0.125107	−	0.0715113i
$724$		0			0
$725$		−	1.16825e8i		−	0.306563i
$726$		0			0
$727$	−1.96871e8			−0.512364			−0.256182	−	0.966629i	$-0.582465\pi$
$727$	−1.96871e8			−0.512364			−0.256182	+	0.966629i	$0.582465\pi$
$728$		0			0
$729$	−3.87290e8	+	1.00458e7i	−0.999664	+	0.0259300i
$730$		0			0
$731$			1.83443e8i			0.469624i
$732$		0			0
$733$	−4.00576e8			−1.01712			−0.508561	−	0.861026i	$-0.669822\pi$
$733$	−4.00576e8			−1.01712			−0.508561	+	0.861026i	$0.669822\pi$
$734$		0			0
$735$	−1.53542e8	+	2.68617e8i	−0.386692	+	0.676507i
$736$		0			0
$737$		−	4.14855e8i		−	1.03632i
$738$		0			0
$739$	−1.55508e8			−0.385319			−0.192659	−	0.981266i	$-0.561711\pi$
$739$	−1.55508e8			−0.385319			−0.192659	+	0.981266i	$0.561711\pi$
$740$		0			0
$741$	−6.92124e8	−	3.95619e8i	−1.70110	−	0.972350i
$742$		0			0
$743$			9.36167e7i			0.228238i	0.993467	+	0.114119i	$0.0364044\pi$
$743$			9.36167e7i			0.228238i	−0.993467	+	0.114119i	$0.963596\pi$
$744$		0			0
$745$	1.93419e8			0.467768
$746$		0			0
$747$	1.56572e8	−	9.22104e7i	0.375622	−	0.221217i
$748$		0			0
$749$		−	5.70217e7i		−	0.135705i
$750$		0			0
$751$	6.15515e8			1.45318			0.726588	−	0.687073i	$-0.241105\pi$
$751$	6.15515e8			1.45318			0.726588	+	0.687073i	$0.241105\pi$
$752$		0			0
$753$	−1.04793e8	+	1.83332e8i	−0.245441	+	0.429391i
$754$		0			0
$755$			5.45933e8i			1.26852i
$756$		0			0
$757$	−5.27277e7			−0.121549			−0.0607745	−	0.998152i	$-0.519357\pi$
$757$	−5.27277e7			−0.121549			−0.0607745	+	0.998152i	$0.519357\pi$
$758$		0			0
$759$	−6.76466e8	−	3.86669e8i	−1.54711	−	0.884330i
$760$		0			0
$761$		−	1.49175e8i		−	0.338487i	−0.985574	−	0.169244i	$-0.945867\pi$
$761$		−	1.49175e8i		−	0.338487i	0.985574	−	0.169244i	$-0.0541325\pi$
$762$		0			0
$763$	4.48693e7			0.101013
$764$		0			0
$765$	2.87307e8	+	4.87842e8i	0.641743	+	1.08967i
$766$		0			0
$767$		−	1.01609e8i		−	0.225189i
$768$		0			0
$769$	4.43701e7			0.0975690			0.0487845	−	0.998809i	$-0.484465\pi$
$769$	4.43701e7			0.0975690			0.0487845	+	0.998809i	$0.484465\pi$
$770$		0			0
$771$	−7.86193e7	+	1.37542e8i	−0.171540	+	0.300105i
$772$		0			0
$773$			2.20439e8i			0.477255i	0.971111	+	0.238627i	$0.0766975\pi$
$773$			2.20439e8i			0.477255i	−0.971111	+	0.238627i	$0.923303\pi$
$774$		0			0
$775$	1.83829e7			0.0394920
$776$		0			0
$777$	5.23043e7	+	2.98972e7i	0.111500	+	0.0637336i
$778$		0			0
$779$			4.70657e8i			0.995616i
$780$		0			0
$781$	−8.64101e8			−1.81389
$782$		0			0
$783$	−4.10905e8	+	5.32827e6i	−0.855964	+	0.0110994i
$784$		0			0
$785$		−	3.35184e8i		−	0.692907i
$786$		0			0
$787$	−7.04884e8			−1.44608			−0.723042	−	0.690804i	$-0.757257\pi$
$787$	−7.04884e8			−1.44608			−0.723042	+	0.690804i	$0.757257\pi$
$788$		0			0
$789$	−3.81265e8	+	6.67012e8i	−0.776240	+	1.35801i
$790$		0			0
$791$		−	4.19460e7i		−	0.0847541i
$792$		0			0
$793$	1.15448e9			2.31509
$794$		0			0
$795$	−1.54374e8	−	8.82404e7i	−0.307236	−	0.175617i
$796$		0			0
$797$			4.00970e8i			0.792021i	0.918246	+	0.396010i	$0.129606\pi$
$797$			4.00970e8i			0.792021i	−0.918246	+	0.396010i	$0.870394\pi$
$798$		0			0
$799$	5.04768e8			0.989582
$800$		0			0
$801$	1.93042e7	−	1.13689e7i	0.0375625	−	0.0221219i
$802$		0			0
$803$		−	1.95327e8i		−	0.377239i
$804$		0			0
$805$	1.04958e8			0.201200
$806$		0			0
$807$	3.47482e8	−	6.07909e8i	0.661168	−	1.15669i
$808$		0			0
$809$		−	1.67848e8i		−	0.317009i	−0.987358	−	0.158505i	$-0.949333\pi$
$809$		−	1.67848e8i		−	0.317009i	0.987358	−	0.158505i	$-0.0506672\pi$
$810$		0			0
$811$	−1.91559e8			−0.359121			−0.179560	−	0.983747i	$-0.557467\pi$
$811$	−1.91559e8			−0.359121			−0.179560	+	0.983747i	$0.557467\pi$
$812$		0			0
$813$	−2.33087e8	−	1.33233e8i	−0.433757	−	0.247936i
$814$		0			0
$815$		−	2.74260e7i		−	0.0506628i
$816$		0			0
$817$	−2.49525e8			−0.457560
$818$		0			0
$819$	−5.87894e7	−	9.98234e7i	−0.107016	−	0.181711i
$820$		0			0
$821$		−	5.22113e8i		−	0.943485i	−0.881736	−	0.471743i	$-0.843625\pi$
$821$		−	5.22113e8i		−	0.943485i	0.881736	−	0.471743i	$-0.156375\pi$
$822$		0			0
$823$	−5.29791e8			−0.950396			−0.475198	−	0.879879i	$-0.657624\pi$
$823$	−5.29791e8			−0.950396			−0.475198	+	0.879879i	$0.657624\pi$
$824$		0			0
$825$	−1.17205e8	+	2.05046e8i	−0.208729	+	0.365166i
$826$		0			0
$827$		−	5.42348e8i		−	0.958875i	−0.877576	−	0.479437i	$-0.840841\pi$
$827$		−	5.42348e8i		−	0.958875i	0.877576	−	0.479437i	$-0.159159\pi$
$828$		0			0
$829$	−6.20518e8			−1.08916			−0.544579	−	0.838709i	$-0.683311\pi$
$829$	−6.20518e8			−1.08916			−0.544579	+	0.838709i	$0.683311\pi$
$830$		0			0
$831$	1.88725e8	+	1.07875e8i	0.328871	+	0.187983i
$832$		0			0
$833$			8.87355e8i			1.53519i
$834$		0			0
$835$	−8.81251e7			−0.151370
$836$		0			0
$837$	−838430.	−	6.46578e7i	−0.00142985	−	0.110267i
$838$		0			0
$839$			2.61174e8i			0.442226i	0.975248	+	0.221113i	$0.0709689\pi$
$839$			2.61174e8i			0.442226i	−0.975248	+	0.221113i	$0.929031\pi$
$840$		0			0
$841$	1.58938e8			0.267202
$842$		0			0
$843$	−375836.	+	657514.i	−0.000627358	+	0.00109754i
$844$		0			0
$845$			3.01286e8i			0.499355i
$846$		0			0
$847$	3.81633e7			0.0628052
$848$		0			0
$849$	9.21777e8	+	5.26889e8i	1.50627	+	0.860987i
$850$		0			0
$851$			7.25556e8i			1.17729i
$852$		0			0
$853$	7.52049e8			1.21171			0.605856	−	0.795574i	$-0.292831\pi$
$853$	7.52049e8			1.21171			0.605856	+	0.795574i	$0.292831\pi$
$854$		0			0
$855$	−6.63576e8	+	3.90803e8i	−1.06168	+	0.625258i
$856$		0			0
$857$		−	7.93429e8i		−	1.26057i	−0.776366	−	0.630283i	$-0.782939\pi$
$857$		−	7.93429e8i		−	1.26057i	0.776366	−	0.630283i	$-0.217061\pi$
$858$		0			0
$859$	−4.32839e8			−0.682884			−0.341442	−	0.939903i	$-0.610915\pi$
$859$	−4.32839e8			−0.682884			−0.341442	+	0.939903i	$0.610915\pi$
$860$		0			0
$861$	−3.39408e7	+	5.93785e7i	−0.0531757	+	0.0930292i
$862$		0			0
$863$		−	1.13018e9i		−	1.75839i	−0.476459	−	0.879197i	$-0.658080\pi$
$863$		−	1.13018e9i		−	1.75839i	0.476459	−	0.879197i	$-0.341920\pi$
$864$		0			0
$865$	−6.15641e8			−0.951216
$866$		0			0
$867$	8.43869e8	+	4.82357e8i	1.29484	+	0.740135i
$868$		0			0
$869$		−	4.39919e8i		−	0.670368i
$870$		0			0
$871$	7.42835e8			1.12419
$872$		0			0
$873$	−5.52999e8	−	9.38983e8i	−0.831155	−	1.41129i
$874$		0			0
$875$		−	1.20651e8i		−	0.180097i
$876$		0			0
$877$	1.28995e8			0.191238			0.0956188	−	0.995418i	$-0.469517\pi$
$877$	1.28995e8			0.191238			0.0956188	+	0.995418i	$0.469517\pi$
$878$		0			0
$879$	−3.85133e6	+	6.73778e6i	−0.00567079	+	0.00992088i
$880$		0			0
$881$			3.32233e8i			0.485865i	0.970043	+	0.242932i	$0.0781093\pi$
$881$			3.32233e8i			0.485865i	−0.970043	+	0.242932i	$0.921891\pi$
$882$		0			0
$883$	3.57193e8			0.518825			0.259412	−	0.965767i	$-0.416471\pi$
$883$	3.57193e8			0.518825			0.259412	+	0.965767i	$0.416471\pi$
$884$		0			0
$885$	−8.52149e7	−	4.87090e7i	−0.122938	−	0.0702715i
$886$		0			0
$887$			6.89244e8i			0.987648i	0.869562	+	0.493824i	$0.164401\pi$
$887$			6.89244e8i			0.987648i	−0.869562	+	0.493824i	$0.835599\pi$
$888$		0			0
$889$	5.78368e7			0.0823187
$890$		0			0
$891$	7.26550e8	+	4.02890e8i	1.02715	+	0.569578i
$892$		0			0
$893$			6.86600e8i			0.964161i
$894$		0			0
$895$	8.89060e8			1.24012
$896$		0			0
$897$	6.92366e8	−	1.21127e9i	0.959308	−	1.67828i
$898$		0			0
$899$		−	6.85887e7i		−	0.0944003i
$900$		0			0
$901$	−5.09961e8			−0.697208
$902$		0			0
$903$	−3.14803e7	−	1.79942e7i	−0.0427539	−	0.0244382i
$904$		0			0
$905$		−	3.85002e8i		−	0.519418i
$906$		0			0
$907$	6.43559e7			0.0862515			0.0431257	−	0.999070i	$-0.486268\pi$
$907$	6.43559e7			0.0862515			0.0431257	+	0.999070i	$0.486268\pi$
$908$		0			0
$909$	1.05400e9	−	6.20739e8i	1.40330	−	0.826452i
$910$		0			0
$911$			1.09003e9i			1.44173i	0.693074	+	0.720867i	$0.256256\pi$
$911$			1.09003e9i			1.44173i	−0.693074	+	0.720867i	$0.743744\pi$
$912$		0			0
$913$	−3.89650e8			−0.511992
$914$		0			0
$915$	5.53431e8	−	9.68211e8i	0.722437	−	1.26388i
$916$		0			0
$917$		−	2.62259e7i		−	0.0340113i
$918$		0			0
$919$	−2.69622e8			−0.347384			−0.173692	−	0.984800i	$-0.555570\pi$
$919$	−2.69622e8			−0.347384			−0.173692	+	0.984800i	$0.555570\pi$
$920$		0			0
$921$	8.29567e7	+	4.74182e7i	0.106187	+	0.0606968i
$922$		0			0
$923$		−	1.54725e9i		−	1.96768i
$924$		0			0
$925$	2.19926e8			0.277876
$926$		0			0
$927$	−9.98663e7	−	1.69571e8i	−0.125366	−	0.212869i
$928$		0			0
$929$			1.39201e8i			0.173618i	0.996225	+	0.0868091i	$0.0276670\pi$
$929$			1.39201e8i			0.173618i	−0.996225	+	0.0868091i	$0.972333\pi$
$930$		0			0
$931$	−1.20700e9			−1.49575
$932$		0			0
$933$	8.44638e7	−	1.47767e8i	0.103998	−	0.181942i
$934$		0			0
$935$		−	1.21406e9i		−	1.48527i
$936$		0			0
$937$	5.69417e8			0.692169			0.346084	−	0.938203i	$-0.387511\pi$
$937$	5.69417e8			0.692169			0.346084	+	0.938203i	$0.387511\pi$
$938$		0			0
$939$	1.29465e9	+	7.40025e8i	1.56371	+	0.893819i
$940$		0			0
$941$		−	5.58214e8i		−	0.669934i	−0.942230	−	0.334967i	$-0.891275\pi$
$941$		−	5.58214e8i		−	0.669934i	0.942230	−	0.334967i	$-0.108725\pi$
$942$		0			0
$943$	−8.23687e8			−0.982262
$944$		0			0
$945$	−1.11900e8	+	1.45102e6i	−0.132597	+	0.00171941i
$946$		0			0
$947$		−	1.25639e9i		−	1.47936i	−0.672957	−	0.739682i	$-0.734976\pi$
$947$		−	1.25639e9i		−	1.47936i	0.672957	−	0.739682i	$-0.265024\pi$
$948$		0			0
$949$	3.49751e8			0.409223
$950$		0			0
$951$	−3.81000e8	+	6.66547e8i	−0.442979	+	0.774978i
$952$		0			0
$953$			1.55995e9i			1.80232i	0.433483	+	0.901162i	$0.357284\pi$
$953$			1.55995e9i			1.80232i	−0.433483	+	0.901162i	$0.642716\pi$
$954$		0			0
$955$	−9.63702e8			−1.10645
$956$		0			0
$957$	7.65050e8	+	4.37304e8i	0.872879	+	0.498939i
$958$		0			0
$959$			1.06048e8i			0.120240i
$960$		0			0
$961$	−8.76711e8			−0.987839
$962$		0			0
$963$	−6.30918e8	+	3.71569e8i	−0.706470	+	0.416064i
$964$		0			0
$965$			7.11879e8i			0.792181i
$966$		0			0
$967$	1.21243e9			1.34084			0.670419	−	0.741983i	$-0.266114\pi$
$967$	1.21243e9			1.34084			0.670419	+	0.741983i	$0.266114\pi$
$968$		0			0
$969$	−1.09603e9	+	1.91748e9i	−1.20463	+	2.10746i
$970$		0			0
$971$			2.86909e8i			0.313390i	0.987647	+	0.156695i	$0.0500840\pi$
$971$			2.86909e8i			0.313390i	−0.987647	+	0.156695i	$0.949916\pi$
$972$		0			0
$973$	9.48613e7			0.102979
$974$		0			0
$975$	−3.67153e8	−	2.09865e8i	−0.396126	−	0.226426i
$976$		0			0
$977$		−	3.70298e8i		−	0.397071i	−0.980094	−	0.198535i	$-0.936382\pi$
$977$		−	3.70298e8i		−	0.397071i	0.980094	−	0.198535i	$-0.0636184\pi$
$978$		0			0
$979$	−4.80413e7			−0.0511996
$980$		0			0
$981$	−2.92381e8	−	4.96457e8i	−0.309700	−	0.525866i
$982$		0			0
$983$			1.61003e9i			1.69501i	0.530788	+	0.847505i	$0.321896\pi$
$983$			1.61003e9i			1.69501i	−0.530788	+	0.847505i	$0.678104\pi$
$984$		0			0
$985$	−1.13796e9			−1.19074
$986$		0			0
$987$	−4.95133e7	+	8.66221e7i	−0.0514957	+	0.0900901i
$988$		0			0
$989$		−	4.36689e8i		−	0.451422i
$990$		0			0
$991$	−1.41865e9			−1.45766			−0.728828	−	0.684696i	$-0.759935\pi$
$991$	−1.41865e9			−1.45766			−0.728828	+	0.684696i	$0.759935\pi$
$992$		0			0
$993$	8.91025e8	+	5.09311e8i	0.910001	+	0.520158i
$994$		0			0
$995$			8.12201e8i			0.824507i
$996$		0			0
$997$	3.15007e8			0.317859			0.158930	−	0.987290i	$-0.449196\pi$
$997$	3.15007e8			0.317859			0.158930	+	0.987290i	$0.449196\pi$
$998$		0			0
$999$	−1.00306e7	−	7.73541e8i	−0.0100608	−	0.775866i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.7.e.d.17.1		6
3.2	odd	2	inner	48.7.e.d.17.2		6
4.3	odd	2		24.7.e.a.17.6	yes	6
8.3	odd	2		192.7.e.h.65.1		6
8.5	even	2		192.7.e.g.65.6		6
12.11	even	2		24.7.e.a.17.5	✓	6
24.5	odd	2		192.7.e.g.65.5		6
24.11	even	2		192.7.e.h.65.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.7.e.a.17.5	✓	6	12.11	even	2
24.7.e.a.17.6	yes	6	4.3	odd	2
48.7.e.d.17.1		6	1.1	even	1	trivial
48.7.e.d.17.2		6	3.2	odd	2	inner
192.7.e.g.65.5		6	24.5	odd	2
192.7.e.g.65.6		6	8.5	even	2
192.7.e.h.65.1		6	8.3	odd	2
192.7.e.h.65.2		6	24.11	even	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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	48.e (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-23.4408 - 13.3988i) q^{3} +100.147i q^{5} -56.7723 q^{7} +(369.944 + 628.158i) q^{9} +O(q^{10})\)	\(q+(-23.4408 - 13.3988i) q^{3} +100.147i q^{5} -56.7723 q^{7} +(369.944 + 628.158i) q^{9} -1563.26i q^{11} +2799.15 q^{13} +(1341.85 - 2347.52i) q^{15} -7754.84i q^{17} +10548.4 q^{19} +(1330.79 + 760.681i) q^{21} +18460.5i q^{23} +5595.62 q^{25} +(-255.212 - 19681.3i) q^{27} -20877.9i q^{29} +3285.23 q^{31} +(-20945.8 + 36644.1i) q^{33} -5685.57i q^{35} +39303.2 q^{37} +(-65614.4 - 37505.3i) q^{39} +44619.0i q^{41} -23655.3 q^{43} +(-62908.0 + 37048.7i) q^{45} +65090.8i q^{47} -114426. q^{49} +(-103906. + 181780. i) q^{51} -65760.4i q^{53} +156555. q^{55} +(-247262. - 141335. i) q^{57} -36299.9i q^{59} +412439. q^{61} +(-21002.6 - 35662.0i) q^{63} +280326. i q^{65} +265379. q^{67} +(247348. - 432728. i) q^{69} -552756. i q^{71} +124949. q^{73} +(-131166. - 74974.6i) q^{75} +88749.8i q^{77} +281411. q^{79} +(-257724. + 464766. i) q^{81} -249255. i q^{83} +776622. q^{85} +(-279739. + 489394. i) q^{87} -30731.5i q^{89} -158914. q^{91} +(-77008.6 - 44018.2i) q^{93} +1.05638e6i q^{95} -1.49482e6 q^{97} +(981974. - 578318. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 10 q^{3} - 156 q^{7} - 74 q^{9}+O(q^{10}) \) 6 * q + 10 * q^3 - 156 * q^7 - 74 * q^9	\( 6 q + 10 q^{3} - 156 q^{7} - 74 q^{9} + 156 q^{13} - 2912 q^{15} + 4500 q^{19} - 15108 q^{21} + 21366 q^{25} - 37574 q^{27} + 74244 q^{31} - 83104 q^{33} + 171132 q^{37} - 200444 q^{39} + 291060 q^{43} - 355136 q^{45} + 517746 q^{49} - 452224 q^{51} + 748224 q^{55} - 650420 q^{57} + 592092 q^{61} - 1009788 q^{63} + 570900 q^{67} - 981184 q^{69} + 1119660 q^{73} - 521446 q^{75} + 1053636 q^{79} - 742874 q^{81} + 197376 q^{85} - 1251360 q^{87} - 839640 q^{91} + 354652 q^{93} - 798516 q^{97} + 2849600 q^{99}+O(q^{100}) \) 6 * q + 10 * q^3 - 156 * q^7 - 74 * q^9 + 156 * q^13 - 2912 * q^15 + 4500 * q^19 - 15108 * q^21 + 21366 * q^25 - 37574 * q^27 + 74244 * q^31 - 83104 * q^33 + 171132 * q^37 - 200444 * q^39 + 291060 * q^43 - 355136 * q^45 + 517746 * q^49 - 452224 * q^51 + 748224 * q^55 - 650420 * q^57 + 592092 * q^61 - 1009788 * q^63 + 570900 * q^67 - 981184 * q^69 + 1119660 * q^73 - 521446 * q^75 + 1053636 * q^79 - 742874 * q^81 + 197376 * q^85 - 1251360 * q^87 - 839640 * q^91 + 354652 * q^93 - 798516 * q^97 + 2849600 * q^99

Introduction

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