LMFDB - Embedded newform 48.7.e.d.17.3

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			17.3
Root			$-2.80354 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	48.17
Dual form			48.7.e.d.17.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.43940 - 26.2209i) q^{3} -10.3581i q^{5} +540.917 q^{7} +(-646.068 - 337.693i) q^{9} +O(q^{10})$	\(q+(6.43940 - 26.2209i) q^{3} -10.3581i q^{5} +540.917 q^{7} +(-646.068 - 337.693i) q^{9} -1653.67i q^{11} -1623.29 q^{13} +(-271.599 - 66.7002i) q^{15} -2239.63i q^{17} -6723.26 q^{19} +(3483.18 - 14183.3i) q^{21} -21240.9i q^{23} +15517.7 q^{25} +(-13014.9 + 14765.9i) q^{27} +9059.70i q^{29} +31494.8 q^{31} +(-43360.6 - 10648.6i) q^{33} -5602.88i q^{35} -21779.2 q^{37} +(-10453.0 + 42564.0i) q^{39} +132823. i q^{41} +67838.7 q^{43} +(-3497.87 + 6692.06i) q^{45} +89854.5i q^{47} +174942. q^{49} +(-58725.1 - 14421.9i) q^{51} -203827. i q^{53} -17128.9 q^{55} +(-43293.8 + 176290. i) q^{57} +90312.3i q^{59} +201749. q^{61} +(-349469. - 182664. i) q^{63} +16814.2i q^{65} +246821. q^{67} +(-556955. - 136779. i) q^{69} -66399.4i q^{71} -259499. q^{73} +(99924.8 - 406888. i) q^{75} -894497. i q^{77} +451176. q^{79} +(303367. + 436346. i) q^{81} -322612. i q^{83} -23198.4 q^{85} +(237553. + 58339.0i) q^{87} +668480. i q^{89} -878064. q^{91} +(202808. - 825821. i) q^{93} +69640.4i q^{95} +777729. q^{97} +(-558433. + 1.06838e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	6.43940	−	26.2209i	0.238496	−	0.971143i
$3$	6.43940	−	26.2209i	0.238496	−	0.971143i
$4$		0			0
$5$		−	10.3581i		−	0.0828650i	−0.999141	−	0.0414325i	$-0.986808\pi$
$5$		−	10.3581i		−	0.0828650i	0.999141	−	0.0414325i	$-0.0131922\pi$
$6$		0			0
$7$	540.917			1.57702			0.788508	−	0.615024i	$-0.210854\pi$
$7$	540.917			1.57702			0.788508	+	0.615024i	$0.210854\pi$
$8$		0			0
$9$	−646.068	−	337.693i	−0.886239	−	0.463228i
$10$		0			0
$11$		−	1653.67i		−	1.24243i	−0.783642	−	0.621213i	$-0.786640\pi$
$11$		−	1653.67i		−	1.24243i	0.783642	−	0.621213i	$-0.213360\pi$
$12$		0			0
$13$	−1623.29			−0.738866			−0.369433	−	0.929257i	$-0.620448\pi$
$13$	−1623.29			−0.738866			−0.369433	+	0.929257i	$0.620448\pi$
$14$		0			0
$15$	−271.599	−	66.7002i	−0.0804738	−	0.0197630i
$16$		0			0
$17$		−	2239.63i		−	0.455858i	−0.973678	−	0.227929i	$-0.926805\pi$
$17$		−	2239.63i		−	0.455858i	0.973678	−	0.227929i	$-0.0731954\pi$
$18$		0			0
$19$	−6723.26			−0.980210			−0.490105	−	0.871663i	$-0.663042\pi$
$19$	−6723.26			−0.980210			−0.490105	+	0.871663i	$0.663042\pi$
$20$		0			0
$21$	3483.18	−	14183.3i	0.376113	−	1.53151i
$22$		0			0
$23$		−	21240.9i		−	1.74578i	−0.487917	−	0.872890i	$-0.662243\pi$
$23$		−	21240.9i		−	1.74578i	0.487917	−	0.872890i	$-0.337757\pi$
$24$		0			0
$25$	15517.7			0.993133
$26$		0			0
$27$	−13014.9	+	14765.9i	−0.661226	+	0.750187i
$28$		0			0
$29$			9059.70i			0.371467i	0.982600	+	0.185733i	$0.0594660\pi$
$29$			9059.70i			0.371467i	−0.982600	+	0.185733i	$0.940534\pi$
$30$		0			0
$31$	31494.8			1.05719			0.528596	−	0.848874i	$-0.322719\pi$
$31$	31494.8			1.05719			0.528596	+	0.848874i	$0.322719\pi$
$32$		0			0
$33$	−43360.6	−	10648.6i	−1.20657	−	0.296314i
$34$		0			0
$35$		−	5602.88i		−	0.130680i
$36$		0			0
$37$	−21779.2			−0.429968			−0.214984	−	0.976618i	$-0.568970\pi$
$37$	−21779.2			−0.429968			−0.214984	+	0.976618i	$0.568970\pi$
$38$		0			0
$39$	−10453.0	+	42564.0i	−0.176217	+	0.717545i
$40$		0			0
$41$			132823.i			1.92718i	0.267382	+	0.963591i	$0.413841\pi$
$41$			132823.i			1.92718i	−0.267382	+	0.963591i	$0.586159\pi$
$42$		0			0
$43$	67838.7			0.853242			0.426621	−	0.904430i	$-0.359704\pi$
$43$	67838.7			0.853242			0.426621	+	0.904430i	$0.359704\pi$
$44$		0			0
$45$	−3497.87	+	6692.06i	−0.0383854	+	0.0734382i
$46$		0			0
$47$			89854.5i			0.865458i	0.901524	+	0.432729i	$0.142449\pi$
$47$			89854.5i			0.865458i	−0.901524	+	0.432729i	$0.857551\pi$
$48$		0			0
$49$	174942.			1.48698
$50$		0			0
$51$	−58725.1	−	14421.9i	−0.442703	−	0.108720i
$52$		0			0
$53$		−	203827.i		−	1.36910i	−0.728968	−	0.684548i	$-0.760000\pi$
$53$		−	203827.i		−	1.36910i	0.728968	−	0.684548i	$-0.240000\pi$
$54$		0			0
$55$	−17128.9			−0.102954
$56$		0			0
$57$	−43293.8	+	176290.i	−0.233777	+	0.951924i
$58$		0			0
$59$			90312.3i			0.439735i	0.975530	+	0.219867i	$0.0705625\pi$
$59$			90312.3i			0.439735i	−0.975530	+	0.219867i	$0.929437\pi$
$60$		0			0
$61$	201749.			0.888835			0.444417	−	0.895820i	$-0.353411\pi$
$61$	201749.			0.888835			0.444417	+	0.895820i	$0.353411\pi$
$62$		0			0
$63$	−349469.	−	182664.i	−1.39761	−	0.730519i
$64$		0			0
$65$			16814.2i			0.0612262i
$66$		0			0
$67$	246821.			0.820649			0.410324	−	0.911940i	$-0.365415\pi$
$67$	246821.			0.820649			0.410324	+	0.911940i	$0.365415\pi$
$68$		0			0
$69$	−556955.	−	136779.i	−1.69540	−	0.416362i
$70$		0			0
$71$		−	66399.4i		−	0.185519i	−0.995689	−	0.0927596i	$-0.970431\pi$
$71$		−	66399.4i		−	0.185519i	0.995689	−	0.0927596i	$-0.0295688\pi$
$72$		0			0
$73$	−259499.			−0.667064			−0.333532	−	0.942739i	$-0.608241\pi$
$73$	−259499.			−0.667064			−0.333532	+	0.942739i	$0.608241\pi$
$74$		0			0
$75$	99924.8	−	406888.i	0.236859	−	0.964475i
$76$		0			0
$77$		−	894497.i		−	1.95933i
$78$		0			0
$79$	451176.			0.915091			0.457545	−	0.889186i	$-0.348729\pi$
$79$	451176.			0.915091			0.457545	+	0.889186i	$0.348729\pi$
$80$		0			0
$81$	303367.	+	436346.i	0.570839	+	0.821062i
$82$		0			0
$83$		−	322612.i		−	0.564217i	−0.959382	−	0.282109i	$-0.908966\pi$
$83$		−	322612.i		−	0.564217i	0.959382	−	0.282109i	$-0.0910338\pi$
$84$		0			0
$85$	−23198.4			−0.0377747
$86$		0			0
$87$	237553.	+	58339.0i	0.360747	+	0.0885934i
$88$		0			0
$89$			668480.i			0.948240i	0.880460	+	0.474120i	$0.157234\pi$
$89$			668480.i			0.948240i	−0.880460	+	0.474120i	$0.842766\pi$
$90$		0			0
$91$	−878064.			−1.16520
$92$		0			0
$93$	202808.	−	825821.i	0.252136	−	1.02668i
$94$		0			0
$95$			69640.4i			0.0812251i
$96$		0			0
$97$	777729.			0.852144			0.426072	−	0.904689i	$-0.359897\pi$
$97$	777729.			0.852144			0.426072	+	0.904689i	$0.359897\pi$
$98$		0			0
$99$	−558433.	+	1.06838e6i	−0.575527	+	1.10109i
$100$		0			0
$101$			653434.i			0.634217i	0.948389	+	0.317108i	$0.102712\pi$
$101$			653434.i			0.634217i	−0.948389	+	0.317108i	$0.897288\pi$
$102$		0			0
$103$	−26759.1			−0.0244883			−0.0122442	−	0.999925i	$-0.503898\pi$
$103$	−26759.1			−0.0244883			−0.0122442	+	0.999925i	$0.503898\pi$
$104$		0			0
$105$	−146912.	−	36079.2i	−0.126909	−	0.0311666i
$106$		0			0
$107$			1.02388e6i			0.835792i	0.908495	+	0.417896i	$0.137232\pi$
$107$			1.02388e6i			0.835792i	−0.908495	+	0.417896i	$0.862768\pi$
$108$		0			0
$109$	−348471.			−0.269084			−0.134542	−	0.990908i	$-0.542956\pi$
$109$	−348471.			−0.269084			−0.134542	+	0.990908i	$0.542956\pi$
$110$		0			0
$111$	−140245.	+	571069.i	−0.102546	+	0.417561i
$112$		0			0
$113$			2.12506e6i			1.47277i	0.676562	+	0.736385i	$0.263469\pi$
$113$			2.12506e6i			1.47277i	−0.676562	+	0.736385i	$0.736531\pi$
$114$		0			0
$115$	−220016.			−0.144664
$116$		0			0
$117$	1.04876e6	+	548174.i	0.654812	+	0.342264i
$118$		0			0
$119$		−	1.21145e6i		−	0.718895i
$120$		0			0
$121$	−963057.			−0.543621
$122$		0			0
$123$	3.48274e6	+	855302.i	1.87157	+	0.459626i
$124$		0			0
$125$		−	322580.i		−	0.165161i
$126$		0			0
$127$	1.18560e6			0.578799			0.289399	−	0.957208i	$-0.406544\pi$
$127$	1.18560e6			0.578799			0.289399	+	0.957208i	$0.406544\pi$
$128$		0			0
$129$	436841.	−	1.77879e6i	0.203495	−	0.828621i
$130$		0			0
$131$		−	2.13635e6i		−	0.950294i	−0.879906	−	0.475147i	$-0.842395\pi$
$131$		−	2.13635e6i		−	0.950294i	0.879906	−	0.475147i	$-0.157605\pi$
$132$		0			0
$133$	−3.63672e6			−1.54581
$134$		0			0
$135$	152947.	+	134810.i	0.0621643	+	0.0547925i
$136$		0			0
$137$		−	1.49279e6i		−	0.580547i	−0.956944	−	0.290274i	$-0.906254\pi$
$137$		−	1.49279e6i		−	0.580547i	0.956944	−	0.290274i	$-0.0937463\pi$
$138$		0			0
$139$	−3.18604e6			−1.18633			−0.593167	−	0.805079i	$-0.702123\pi$
$139$	−3.18604e6			−1.18633			−0.593167	+	0.805079i	$0.702123\pi$
$140$		0			0
$141$	2.35606e6	+	578609.i	0.840484	+	0.206409i
$142$		0			0
$143$			2.68438e6i			0.917986i
$144$		0			0
$145$	93841.5			0.0307816
$146$		0			0
$147$	1.12652e6	−	4.58712e6i	0.354639	−	1.44407i
$148$		0			0
$149$			37127.0i			0.0112236i	0.999984	+	0.00561178i	$0.00178629\pi$
$149$			37127.0i			0.0112236i	−0.999984	+	0.00561178i	$0.998214\pi$
$150$		0			0
$151$	−4.25132e6			−1.23479			−0.617394	−	0.786654i	$-0.711812\pi$
$151$	−4.25132e6			−1.23479			−0.617394	+	0.786654i	$0.711812\pi$
$152$		0			0
$153$	−756308.	+	1.44695e6i	−0.211166	+	0.403999i
$154$		0			0
$155$		−	326227.i		−	0.0876042i
$156$		0			0
$157$	3.00184e6			0.775690			0.387845	−	0.921725i	$-0.373220\pi$
$157$	3.00184e6			0.775690			0.387845	+	0.921725i	$0.373220\pi$
$158$		0			0
$159$	−5.34452e6	−	1.31252e6i	−1.32959	−	0.326525i
$160$		0			0
$161$		−	1.14896e7i		−	2.75312i
$162$		0			0
$163$	−518504.			−0.119726			−0.0598631	−	0.998207i	$-0.519066\pi$
$163$	−518504.			−0.119726			−0.0598631	+	0.998207i	$0.519066\pi$
$164$		0			0
$165$	−110300.	+	449135.i	−0.0245541	+	0.0999827i
$166$		0			0
$167$		−	1.51942e6i		−	0.326233i	−0.986607	−	0.163116i	$-0.947845\pi$
$167$		−	1.51942e6i		−	0.326233i	0.986607	−	0.163116i	$-0.0521546\pi$
$168$		0			0
$169$	−2.19174e6			−0.454077
$170$		0			0
$171$	4.34368e6	+	2.27040e6i	0.868700	+	0.454061i
$172$		0			0
$173$			6.72574e6i			1.29898i	0.760371	+	0.649489i	$0.225017\pi$
$173$			6.72574e6i			1.29898i	−0.760371	+	0.649489i	$0.774983\pi$
$174$		0			0
$175$	8.39379e6			1.56619
$176$		0			0
$177$	2.36807e6	+	581557.i	0.427046	+	0.104875i
$178$		0			0
$179$			5.16193e6i			0.900021i	0.893023	+	0.450011i	$0.148580\pi$
$179$			5.16193e6i			0.900021i	−0.893023	+	0.450011i	$0.851420\pi$
$180$		0			0
$181$	4.43947e6			0.748678			0.374339	−	0.927292i	$-0.377870\pi$
$181$	4.43947e6			0.748678			0.374339	+	0.927292i	$0.377870\pi$
$182$		0			0
$183$	1.29914e6	−	5.29002e6i	0.211984	−	0.863186i
$184$		0			0
$185$			225592.i			0.0356294i
$186$		0			0
$187$	−3.70361e6			−0.566369
$188$		0			0
$189$	−7.03998e6	+	7.98713e6i	−1.04276	+	1.18306i
$190$		0			0
$191$			1.37236e6i			0.196955i	0.995139	+	0.0984777i	$0.0313973\pi$
$191$			1.37236e6i			0.196955i	−0.995139	+	0.0984777i	$0.968603\pi$
$192$		0			0
$193$	−8.78968e6			−1.22265			−0.611323	−	0.791381i	$-0.709363\pi$
$193$	−8.78968e6			−1.22265			−0.611323	+	0.791381i	$0.709363\pi$
$194$		0			0
$195$	440884.	+	108274.i	0.0594594	+	0.0146022i
$196$		0			0
$197$			4.05729e6i			0.530685i	0.964154	+	0.265343i	$0.0854850\pi$
$197$			4.05729e6i			0.530685i	−0.964154	+	0.265343i	$0.914515\pi$
$198$		0			0
$199$	1.08252e7			1.37365			0.686824	−	0.726824i	$-0.259005\pi$
$199$	1.08252e7			1.37365			0.686824	+	0.726824i	$0.259005\pi$
$200$		0			0
$201$	1.58938e6	−	6.47186e6i	0.195722	−	0.796968i
$202$		0			0
$203$			4.90054e6i			0.585809i
$204$		0			0
$205$	1.37580e6			0.159696
$206$		0			0
$207$	−7.17292e6	+	1.37231e7i	−0.808695	+	1.54718i
$208$		0			0
$209$			1.11180e7i			1.21784i
$210$		0			0
$211$	−9.13260e6			−0.972181			−0.486090	−	0.873909i	$-0.661577\pi$
$211$	−9.13260e6			−0.972181			−0.486090	+	0.873909i	$0.661577\pi$
$212$		0			0
$213$	−1.74105e6	−	427572.i	−0.180166	−	0.0442457i
$214$		0			0
$215$		−	702682.i		−	0.0707040i
$216$		0			0
$217$	1.70360e7			1.66721
$218$		0			0
$219$	−1.67102e6	+	6.80430e6i	−0.159092	+	0.647815i
$220$		0			0
$221$			3.63557e6i			0.336818i
$222$		0			0
$223$	1.00422e7			0.905556			0.452778	−	0.891623i	$-0.350433\pi$
$223$	1.00422e7			0.905556			0.452778	+	0.891623i	$0.350433\pi$
$224$		0			0
$225$	−1.00255e7	−	5.24023e6i	−0.880153	−	0.460048i
$226$		0			0
$227$		−	2.05338e7i		−	1.75546i	−0.479153	−	0.877732i	$-0.659056\pi$
$227$		−	2.05338e7i		−	1.75546i	0.479153	−	0.877732i	$-0.340944\pi$
$228$		0			0
$229$	1.86273e7			1.55112			0.775559	−	0.631276i	$-0.217468\pi$
$229$	1.86273e7			1.55112			0.775559	+	0.631276i	$0.217468\pi$
$230$		0			0
$231$	−2.34545e7	−	5.76002e6i	−1.90279	−	0.467292i
$232$		0			0
$233$		−	1.33718e7i		−	1.05711i	−0.848899	−	0.528555i	$-0.822734\pi$
$233$		−	1.33718e7i		−	1.05711i	0.848899	−	0.528555i	$-0.177266\pi$
$234$		0			0
$235$	930724.			0.0717162
$236$		0			0
$237$	2.90530e6	−	1.18302e7i	0.218246	−	0.888685i
$238$		0			0
$239$		−	3.86337e6i		−	0.282991i	−0.989939	−	0.141496i	$-0.954809\pi$
$239$		−	3.86337e6i		−	0.282991i	0.989939	−	0.141496i	$-0.0451911\pi$
$240$		0			0
$241$	2.61725e6			0.186979			0.0934896	−	0.995620i	$-0.470198\pi$
$241$	2.61725e6			0.186979			0.0934896	+	0.995620i	$0.470198\pi$
$242$		0			0
$243$	1.33949e7	−	5.14475e6i	0.933512	−	0.358546i
$244$		0			0
$245$		−	1.81207e6i		−	0.123219i
$246$		0			0
$247$	1.09138e7			0.724244
$248$		0			0
$249$	−8.45917e6	−	2.07743e6i	−0.547936	−	0.134564i
$250$		0			0
$251$			1.46140e7i			0.924163i	0.886838	+	0.462081i	$0.152897\pi$
$251$			1.46140e7i			0.924163i	−0.886838	+	0.462081i	$0.847103\pi$
$252$		0			0
$253$	−3.51254e7			−2.16900
$254$		0			0
$255$	−149384.	+	608282.i	−0.00900913	+	0.0366846i
$256$		0			0
$257$			1.51472e7i			0.892343i	0.894948	+	0.446171i	$0.147213\pi$
$257$			1.51472e7i			0.892343i	−0.894948	+	0.446171i	$0.852787\pi$
$258$		0			0
$259$	−1.17807e7			−0.678067
$260$		0			0
$261$	3.05940e6	−	5.85318e6i	0.172074	−	0.329208i
$262$		0			0
$263$		−	2.80420e7i		−	1.54149i	−0.637142	−	0.770746i	$-0.719884\pi$
$263$		−	2.80420e7i		−	1.54149i	0.637142	−	0.770746i	$-0.280116\pi$
$264$		0			0
$265$	−2.11127e6			−0.113450
$266$		0			0
$267$	1.75281e7	+	4.30461e6i	0.920877	+	0.226152i
$268$		0			0
$269$		−	3.03020e7i		−	1.55674i	−0.627808	−	0.778368i	$-0.716048\pi$
$269$		−	3.03020e7i		−	1.55674i	0.627808	−	0.778368i	$-0.283952\pi$
$270$		0			0
$271$	−7.31140e6			−0.367361			−0.183680	−	0.982986i	$-0.558801\pi$
$271$	−7.31140e6			−0.367361			−0.183680	+	0.982986i	$0.558801\pi$
$272$		0			0
$273$	−5.65421e6	+	2.30236e7i	−0.277897	+	1.13158i
$274$		0			0
$275$		−	2.56611e7i		−	1.23389i
$276$		0			0
$277$	−1.14176e7			−0.537200			−0.268600	−	0.963252i	$-0.586561\pi$
$277$	−1.14176e7			−0.537200			−0.268600	+	0.963252i	$0.586561\pi$
$278$		0			0
$279$	−2.03478e7	−	1.06356e7i	−0.936924	−	0.489721i
$280$		0			0
$281$			9.13488e6i			0.411703i	0.978583	+	0.205851i	$0.0659964\pi$
$281$			9.13488e6i			0.411703i	−0.978583	+	0.205851i	$0.934004\pi$
$282$		0			0
$283$	1.91768e7			0.846089			0.423045	−	0.906109i	$-0.360961\pi$
$283$	1.91768e7			0.846089			0.423045	+	0.906109i	$0.360961\pi$
$284$		0			0
$285$	1.82603e6	+	448443.i	0.0788812	+	0.0193719i
$286$		0			0
$287$			7.18463e7i			3.03920i
$288$		0			0
$289$	1.91216e7			0.792194
$290$		0			0
$291$	5.00811e6	−	2.03927e7i	0.203233	−	0.827554i
$292$		0			0
$293$		−	1.52576e7i		−	0.606575i	−0.952899	−	0.303287i	$-0.901916\pi$
$293$		−	1.52576e7i		−	0.606575i	0.952899	−	0.303287i	$-0.0980842\pi$
$294$		0			0
$295$	935467.			0.0364387
$296$		0			0
$297$	2.44179e7	+	2.15223e7i	0.932051	+	0.821524i
$298$		0			0
$299$			3.44801e7i			1.28990i
$300$		0			0
$301$	3.66951e7			1.34558
$302$		0			0
$303$	1.71336e7	+	4.20772e6i	0.615915	+	0.151258i
$304$		0			0
$305$		−	2.08974e6i		−	0.0736533i
$306$		0			0
$307$	−4.67688e7			−1.61637			−0.808185	−	0.588928i	$-0.799550\pi$
$307$	−4.67688e7			−1.61637			−0.808185	+	0.588928i	$0.799550\pi$
$308$		0			0
$309$	−172312.	+	701646.i	−0.00584038	+	0.0237817i
$310$		0			0
$311$		−	2.04798e7i		−	0.680840i	−0.940274	−	0.340420i	$-0.889431\pi$
$311$		−	2.04798e7i		−	0.680840i	0.940274	−	0.340420i	$-0.110569\pi$
$312$		0			0
$313$	−1.25052e7			−0.407811			−0.203905	−	0.978991i	$-0.565363\pi$
$313$	−1.25052e7			−0.407811			−0.203905	+	0.978991i	$0.565363\pi$
$314$		0			0
$315$	−1.89206e6	+	3.61985e6i	−0.0605345	+	0.115813i
$316$		0			0
$317$			1.49434e7i			0.469107i	0.972103	+	0.234554i	$0.0753629\pi$
$317$			1.49434e7i			0.469107i	−0.972103	+	0.234554i	$0.924637\pi$
$318$		0			0
$319$	1.49817e7			0.461519
$320$		0			0
$321$	2.68471e7	+	6.59318e6i	0.811674	+	0.199333i
$322$		0			0
$323$			1.50576e7i			0.446836i
$324$		0			0
$325$	−2.51897e7			−0.733792
$326$		0			0
$327$	−2.24394e6	+	9.13721e6i	−0.0641754	+	0.261319i
$328$		0			0
$329$			4.86038e7i			1.36484i
$330$		0			0
$331$	−4.80954e7			−1.32623			−0.663116	−	0.748517i	$-0.730766\pi$
$331$	−4.80954e7			−1.32623			−0.663116	+	0.748517i	$0.730766\pi$
$332$		0			0
$333$	1.40708e7	+	7.35469e6i	0.381055	+	0.199174i
$334$		0			0
$335$		−	2.55660e6i		−	0.0680031i
$336$		0			0
$337$	−4.92822e7			−1.28766			−0.643829	−	0.765169i	$-0.722655\pi$
$337$	−4.92822e7			−1.28766			−0.643829	+	0.765169i	$0.722655\pi$
$338$		0			0
$339$	5.57208e7	+	1.36841e7i	1.43027	+	0.351251i
$340$		0			0
$341$		−	5.20819e7i		−	1.31348i
$342$		0			0
$343$	3.09906e7			0.767976
$344$		0			0
$345$	−1.41677e6	+	5.76901e6i	−0.0345019	+	0.140490i
$346$		0			0
$347$			3.12881e7i			0.748843i	0.927259	+	0.374421i	$0.122159\pi$
$347$			3.12881e7i			0.748843i	−0.927259	+	0.374421i	$0.877841\pi$
$348$		0			0
$349$	−5.17935e7			−1.21842			−0.609212	−	0.793007i	$-0.708514\pi$
$349$	−5.17935e7			−1.21842			−0.609212	+	0.793007i	$0.708514\pi$
$350$		0			0
$351$	2.11270e7	−	2.39694e7i	0.488557	−	0.554288i
$352$		0			0
$353$			1.34595e7i			0.305989i	0.988227	+	0.152995i	$0.0488917\pi$
$353$			1.34595e7i			0.305989i	−0.988227	+	0.152995i	$0.951108\pi$
$354$		0			0
$355$	−687773.			−0.0153731
$356$		0			0
$357$	−3.17654e7	−	7.80103e6i	−0.698151	−	0.171454i
$358$		0			0
$359$		−	7.49963e7i		−	1.62090i	−0.585807	−	0.810450i	$-0.699222\pi$
$359$		−	7.49963e7i		−	1.62090i	0.585807	−	0.810450i	$-0.300778\pi$
$360$		0			0
$361$	−1.84366e6			−0.0391885
$362$		0			0
$363$	−6.20151e6	+	2.52522e7i	−0.129652	+	0.527934i
$364$		0			0
$365$			2.68793e6i			0.0552763i
$366$		0			0
$367$	−2.58448e7			−0.522847			−0.261424	−	0.965224i	$-0.584192\pi$
$367$	−2.58448e7			−0.522847			−0.261424	+	0.965224i	$0.584192\pi$
$368$		0			0
$369$	4.48535e7	−	8.58129e7i	0.892725	−	1.70794i
$370$		0			0
$371$		−	1.10253e8i		−	2.15909i
$372$		0			0
$373$	6.24040e7			1.20250			0.601251	−	0.799060i	$-0.294669\pi$
$373$	6.24040e7			1.20250			0.601251	+	0.799060i	$0.294669\pi$
$374$		0			0
$375$	−8.45833e6	−	2.07722e6i	−0.160395	−	0.0393903i
$376$		0			0
$377$		−	1.47065e7i		−	0.274464i
$378$		0			0
$379$	5.81012e7			1.06725			0.533627	−	0.845720i	$-0.320829\pi$
$379$	5.81012e7			1.06725			0.533627	+	0.845720i	$0.320829\pi$
$380$		0			0
$381$	7.63456e6	−	3.10875e7i	0.138041	−	0.562096i
$382$		0			0
$383$			1.70640e7i			0.303728i	0.988401	+	0.151864i	$0.0485276\pi$
$383$			1.70640e7i			0.303728i	−0.988401	+	0.151864i	$0.951472\pi$
$384$		0			0
$385$	−9.26531e6			−0.162360
$386$		0			0
$387$	−4.38284e7	−	2.29087e7i	−0.756177	−	0.395246i
$388$		0			0
$389$			7.35844e7i			1.25008i	0.780594	+	0.625039i	$0.214917\pi$
$389$			7.35844e7i			1.25008i	−0.780594	+	0.625039i	$0.785083\pi$
$390$		0			0
$391$	−4.75718e7			−0.795828
$392$		0			0
$393$	−5.60169e7	−	1.37568e7i	−0.922872	−	0.226642i
$394$		0			0
$395$		−	4.67333e6i		−	0.0758290i
$396$		0			0
$397$	7.24221e7			1.15744			0.578722	−	0.815525i	$-0.303552\pi$
$397$	7.24221e7			1.15744			0.578722	+	0.815525i	$0.303552\pi$
$398$		0			0
$399$	−2.34183e7	+	9.53580e7i	−0.368669	+	1.50120i
$400$		0			0
$401$		−	1.16510e8i		−	1.80688i	−0.428713	−	0.903441i	$-0.641033\pi$
$401$		−	1.16510e8i		−	1.80688i	0.428713	−	0.903441i	$-0.358967\pi$
$402$		0			0
$403$	−5.11251e7			−0.781123
$404$		0			0
$405$	4.51973e6	−	3.14232e6i	0.0680373	−	0.0473026i
$406$		0			0
$407$			3.60156e7i			0.534204i
$408$		0			0
$409$	3.18291e7			0.465216			0.232608	−	0.972571i	$-0.425274\pi$
$409$	3.18291e7			0.465216			0.232608	+	0.972571i	$0.425274\pi$
$410$		0			0
$411$	−3.91423e7	−	9.61269e6i	−0.563795	−	0.138458i
$412$		0			0
$413$			4.88514e7i			0.693469i
$414$		0			0
$415$	−3.34166e6			−0.0467539
$416$		0			0
$417$	−2.05162e7	+	8.35408e7i	−0.282936	+	1.15210i
$418$		0			0
$419$		−	1.37665e7i		−	0.187146i	−0.995612	−	0.0935731i	$-0.970171\pi$
$419$		−	1.37665e7i		−	0.187146i	0.995612	−	0.0935731i	$-0.0298289\pi$
$420$		0			0
$421$	−1.30339e8			−1.74674			−0.873370	−	0.487057i	$-0.838070\pi$
$421$	−1.30339e8			−1.74674			−0.873370	+	0.487057i	$0.838070\pi$
$422$		0			0
$423$	3.03433e7	−	5.80521e7i	0.400905	−	0.767003i
$424$		0			0
$425$		−	3.47539e7i		−	0.452728i
$426$		0			0
$427$	1.09129e8			1.40171
$428$		0			0
$429$	7.03868e7	+	1.72858e7i	0.891496	+	0.218936i
$430$		0			0
$431$			2.76588e7i			0.345463i	0.984969	+	0.172731i	$0.0552592\pi$
$431$			2.76588e7i			0.345463i	−0.984969	+	0.172731i	$0.944741\pi$
$432$		0			0
$433$	9.01833e7			1.11087			0.555434	−	0.831561i	$-0.312552\pi$
$433$	9.01833e7			1.11087			0.555434	+	0.831561i	$0.312552\pi$
$434$		0			0
$435$	604283.	−	2.46061e6i	0.00734130	−	0.0298933i
$436$		0			0
$437$			1.42808e8i			1.71123i
$438$		0			0
$439$	−7.48440e7			−0.884633			−0.442317	−	0.896859i	$-0.645843\pi$
$439$	−7.48440e7			−0.884633			−0.442317	+	0.896859i	$0.645843\pi$
$440$		0			0
$441$	−1.13024e8	−	5.90767e7i	−1.31782	−	0.688811i
$442$		0			0
$443$			1.06780e8i			1.22822i	0.789219	+	0.614112i	$0.210486\pi$
$443$			1.06780e8i			1.22822i	−0.789219	+	0.614112i	$0.789514\pi$
$444$		0			0
$445$	6.92420e6			0.0785759
$446$		0			0
$447$	973501.	+	239075.i	0.0108997	+	0.00267678i
$448$		0			0
$449$			5.40038e7i			0.596603i	0.954472	+	0.298301i	$0.0964200\pi$
$449$			5.40038e7i			0.596603i	−0.954472	+	0.298301i	$0.903580\pi$
$450$		0			0
$451$	2.19646e8			2.39438
$452$		0			0
$453$	−2.73759e7	+	1.11473e8i	−0.294493	+	1.19916i
$454$		0			0
$455$			9.09510e6i			0.0965546i
$456$		0			0
$457$	−2.71219e7			−0.284166			−0.142083	−	0.989855i	$-0.545380\pi$
$457$	−2.71219e7			−0.284166			−0.142083	+	0.989855i	$0.545380\pi$
$458$		0			0
$459$	3.30702e7	+	2.91486e7i	0.341979	+	0.301425i
$460$		0			0
$461$		−	1.08881e8i		−	1.11134i	−0.831403	−	0.555671i	$-0.812462\pi$
$461$		−	1.08881e8i		−	1.11134i	0.831403	−	0.555671i	$-0.187538\pi$
$462$		0			0
$463$	1.36880e8			1.37911			0.689555	−	0.724234i	$-0.257806\pi$
$463$	1.36880e8			1.37911			0.689555	+	0.724234i	$0.257806\pi$
$464$		0			0
$465$	−8.55396e6	−	2.10071e6i	−0.0850762	−	0.0208933i
$466$		0			0
$467$			8.83835e7i			0.867802i	0.900961	+	0.433901i	$0.142863\pi$
$467$			8.83835e7i			0.867802i	−0.900961	+	0.433901i	$0.857137\pi$
$468$		0			0
$469$	1.33509e8			1.29418
$470$		0			0
$471$	1.93300e7	−	7.87108e7i	0.184999	−	0.753307i
$472$		0			0
$473$		−	1.12183e8i		−	1.06009i
$474$		0			0
$475$	−1.04330e8			−0.973479
$476$		0			0
$477$	−6.88310e7	+	1.31686e8i	−0.634204	+	1.21335i
$478$		0			0
$479$			3.25468e7i			0.296144i	0.988977	+	0.148072i	$0.0473067\pi$
$479$			3.25468e7i			0.296144i	−0.988977	+	0.148072i	$0.952693\pi$
$480$		0			0
$481$	3.53539e7			0.317689
$482$		0			0
$483$	−3.01266e8	−	7.39859e7i	−2.67368	−	0.656610i
$484$		0			0
$485$		−	8.05582e6i		−	0.0706129i
$486$		0			0
$487$	−2.91719e7			−0.252568			−0.126284	−	0.991994i	$-0.540305\pi$
$487$	−2.91719e7			−0.252568			−0.126284	+	0.991994i	$0.540305\pi$
$488$		0			0
$489$	−3.33885e6	+	1.35956e7i	−0.0285543	+	0.116271i
$490$		0			0
$491$		−	6.03005e7i		−	0.509421i	−0.967017	−	0.254710i	$-0.918020\pi$
$491$		−	6.03005e7i		−	0.509421i	0.967017	−	0.254710i	$-0.0819802\pi$
$492$		0			0
$493$	2.02904e7			0.169336
$494$		0			0
$495$	1.10664e7	+	5.78432e6i	0.0912415	+	0.0476910i
$496$		0			0
$497$		−	3.59165e7i		−	0.292567i
$498$		0			0
$499$	−2.02435e7			−0.162923			−0.0814617	−	0.996676i	$-0.525959\pi$
$499$	−2.02435e7			−0.162923			−0.0814617	+	0.996676i	$0.525959\pi$
$500$		0			0
$501$	−3.98404e7	−	9.78413e6i	−0.316819	−	0.0778053i
$502$		0			0
$503$			2.40543e6i			0.0189011i	0.999955	+	0.00945057i	$0.00300825\pi$
$503$			2.40543e6i			0.0189011i	−0.999955	+	0.00945057i	$0.996992\pi$
$504$		0			0
$505$	6.76835e6			0.0525544
$506$		0			0
$507$	−1.41135e7	+	5.74694e7i	−0.108296	+	0.440974i
$508$		0			0
$509$			4.35376e7i			0.330150i	0.986281	+	0.165075i	$0.0527866\pi$
$509$			4.35376e7i			0.330150i	−0.986281	+	0.165075i	$0.947213\pi$
$510$		0			0
$511$	−1.40367e8			−1.05197
$512$		0			0
$513$	8.75026e7	−	9.92752e7i	0.648140	−	0.735341i
$514$		0			0
$515$			277174.i			0.00202923i
$516$		0			0
$517$	1.48589e8			1.07527
$518$		0			0
$519$	1.76355e8	+	4.33097e7i	1.26149	+	0.309801i
$520$		0			0
$521$			2.76657e7i			0.195627i	0.995205	+	0.0978133i	$0.0311848\pi$
$521$			2.76657e7i			0.195627i	−0.995205	+	0.0978133i	$0.968815\pi$
$522$		0			0
$523$	−1.00635e8			−0.703465			−0.351732	−	0.936101i	$-0.614407\pi$
$523$	−1.00635e8			−0.703465			−0.351732	+	0.936101i	$0.614407\pi$
$524$		0			0
$525$	5.40510e7	−	2.20092e8i	0.373530	−	1.52099i
$526$		0			0
$527$		−	7.05367e7i		−	0.481929i
$528$		0			0
$529$	−3.03140e8			−2.04775
$530$		0			0
$531$	3.04979e7	−	5.83479e7i	0.203698	−	0.389710i
$532$		0			0
$533$		−	2.15610e8i		−	1.42393i
$534$		0			0
$535$	1.06055e7			0.0692579
$536$		0			0
$537$	1.35350e8	+	3.32397e7i	0.874050	+	0.214652i
$538$		0			0
$539$		−	2.89296e8i		−	1.84746i
$540$		0			0
$541$	−2.47601e8			−1.56373			−0.781863	−	0.623450i	$-0.785731\pi$
$541$	−2.47601e8			−1.56373			−0.781863	+	0.623450i	$0.785731\pi$
$542$		0			0
$543$	2.85875e7	−	1.16407e8i	0.178557	−	0.727074i
$544$		0			0
$545$			3.60951e6i			0.0222976i
$546$		0			0
$547$	2.28109e8			1.39374			0.696868	−	0.717200i	$-0.254576\pi$
$547$	2.28109e8			1.39374			0.696868	+	0.717200i	$0.254576\pi$
$548$		0			0
$549$	−1.30343e8	−	6.81292e7i	−0.787720	−	0.411733i
$550$		0			0
$551$		−	6.09107e7i		−	0.364115i
$552$		0			0
$553$	2.44048e8			1.44311
$554$		0			0
$555$	5.91521e6	+	1.45268e6i	0.0346012	+	0.00849747i
$556$		0			0
$557$			2.08235e8i			1.20500i	0.798119	+	0.602500i	$0.205829\pi$
$557$			2.08235e8i			1.20500i	−0.798119	+	0.602500i	$0.794171\pi$
$558$		0			0
$559$	−1.10122e8			−0.630432
$560$		0			0
$561$	−2.38490e7	+	9.71118e7i	−0.135077	+	0.550026i
$562$		0			0
$563$			1.91148e8i			1.07113i	0.844493	+	0.535567i	$0.179902\pi$
$563$			1.91148e8i			1.07113i	−0.844493	+	0.535567i	$0.820098\pi$
$564$		0			0
$565$	2.20116e7			0.122041
$566$		0			0
$567$	1.64096e8	+	2.36027e8i	0.900222	+	1.29483i
$568$		0			0
$569$			1.97943e8i			1.07449i	0.843426	+	0.537245i	$0.180535\pi$
$569$			1.97943e8i			1.07449i	−0.843426	+	0.537245i	$0.819465\pi$
$570$		0			0
$571$	2.47123e8			1.32741			0.663704	−	0.747996i	$-0.268984\pi$
$571$	2.47123e8			1.32741			0.663704	+	0.747996i	$0.268984\pi$
$572$		0			0
$573$	3.59845e7	+	8.83718e6i	0.191272	+	0.0469732i
$574$		0			0
$575$		−	3.29610e8i		−	1.73379i
$576$		0			0
$577$	−2.20121e8			−1.14587			−0.572933	−	0.819602i	$-0.694195\pi$
$577$	−2.20121e8			−1.14587			−0.572933	+	0.819602i	$0.694195\pi$
$578$		0			0
$579$	−5.66003e7	+	2.30473e8i	−0.291597	+	1.18737i
$580$		0			0
$581$		−	1.74506e8i		−	0.889779i
$582$		0			0
$583$	−3.37062e8			−1.70100
$584$		0			0
$585$	5.67806e6	−	1.08631e7i	0.0283617	−	0.0542610i
$586$		0			0
$587$			1.04252e8i			0.515433i	0.966221	+	0.257716i	$0.0829700\pi$
$587$			1.04252e8i			0.515433i	−0.966221	+	0.257716i	$0.917030\pi$
$588$		0			0
$589$	−2.11748e8			−1.03627
$590$		0			0
$591$	1.06386e8	+	2.61265e7i	0.515371	+	0.126566i
$592$		0			0
$593$			3.36973e8i			1.61596i	0.589208	+	0.807981i	$0.299440\pi$
$593$			3.36973e8i			1.61596i	−0.589208	+	0.807981i	$0.700560\pi$
$594$		0			0
$595$	−1.25484e7			−0.0595713
$596$		0			0
$597$	6.97076e7	−	2.83845e8i	0.327610	−	1.33401i
$598$		0			0
$599$			3.59366e8i			1.67208i	0.548668	+	0.836040i	$0.315135\pi$
$599$			3.59366e8i			1.67208i	−0.548668	+	0.836040i	$0.684865\pi$
$600$		0			0
$601$	4.55242e7			0.209710			0.104855	−	0.994488i	$-0.466562\pi$
$601$	4.55242e7			0.209710			0.104855	+	0.994488i	$0.466562\pi$
$602$		0			0
$603$	−1.59463e8	−	8.33498e7i	−0.727291	−	0.380148i
$604$		0			0
$605$			9.97547e6i			0.0450472i
$606$		0			0
$607$	−1.24532e8			−0.556821			−0.278410	−	0.960462i	$-0.589808\pi$
$607$	−1.24532e8			−0.556821			−0.278410	+	0.960462i	$0.589808\pi$
$608$		0			0
$609$	1.28496e8	+	3.15565e7i	0.568904	+	0.139713i
$610$		0			0
$611$		−	1.45860e8i		−	0.639458i
$612$		0			0
$613$	2.57681e8			1.11867			0.559334	−	0.828942i	$-0.311057\pi$
$613$	2.57681e8			1.11867			0.559334	+	0.828942i	$0.311057\pi$
$614$		0			0
$615$	8.85933e6	−	3.60747e7i	0.0380869	−	0.155088i
$616$		0			0
$617$			1.08074e8i			0.460115i	0.973177	+	0.230058i	$0.0738914\pi$
$617$			1.08074e8i			0.460115i	−0.973177	+	0.230058i	$0.926109\pi$
$618$		0			0
$619$	−1.97356e8			−0.832107			−0.416054	−	0.909340i	$-0.636587\pi$
$619$	−1.97356e8			−0.832107			−0.416054	+	0.909340i	$0.636587\pi$
$620$		0			0
$621$	3.13642e8	+	2.76449e8i	1.30966	+	1.15436i
$622$		0			0
$623$			3.61592e8i			1.49539i
$624$		0			0
$625$	2.39123e8			0.979447
$626$		0			0
$627$	2.91525e8	+	7.15935e7i	1.18269	+	0.290450i
$628$		0			0
$629$			4.87773e7i			0.196005i
$630$		0			0
$631$	−6.19029e7			−0.246390			−0.123195	−	0.992382i	$-0.539314\pi$
$631$	−6.19029e7			−0.246390			−0.123195	+	0.992382i	$0.539314\pi$
$632$		0			0
$633$	−5.88085e7	+	2.39465e8i	−0.231862	+	0.944127i
$634$		0			0
$635$		−	1.22806e7i		−	0.0479622i
$636$		0			0
$637$	−2.83981e8			−1.09868
$638$		0			0
$639$	−2.24226e7	+	4.28985e7i	−0.0859378	+	0.164414i
$640$		0			0
$641$		−	2.03881e8i		−	0.774110i	−0.922057	−	0.387055i	$-0.873492\pi$
$641$		−	2.03881e8i		−	0.774110i	0.922057	−	0.387055i	$-0.126508\pi$
$642$		0			0
$643$	2.27171e7			0.0854516			0.0427258	−	0.999087i	$-0.486396\pi$
$643$	2.27171e7			0.0854516			0.0427258	+	0.999087i	$0.486396\pi$
$644$		0			0
$645$	−1.84249e7	−	4.52485e6i	−0.0686637	−	0.0168626i
$646$		0			0
$647$		−	6.37007e6i		−	0.0235197i	−0.999931	−	0.0117598i	$-0.996257\pi$
$647$		−	6.37007e6i		−	0.0235197i	0.999931	−	0.0117598i	$-0.00374336\pi$
$648$		0			0
$649$	1.49347e8			0.546338
$650$		0			0
$651$	1.09702e8	−	4.46700e8i	0.397623	−	1.61910i
$652$		0			0
$653$		−	5.28765e8i		−	1.89899i	−0.313779	−	0.949496i	$-0.601595\pi$
$653$		−	5.28765e8i		−	1.89899i	0.313779	−	0.949496i	$-0.398405\pi$
$654$		0			0
$655$	−2.21286e7			−0.0787462
$656$		0			0
$657$	1.67654e8	+	8.76312e7i	0.591178	+	0.309003i
$658$		0			0
$659$			1.18602e8i			0.414417i	0.978297	+	0.207208i	$0.0664378\pi$
$659$			1.18602e8i			0.414417i	−0.978297	+	0.207208i	$0.933562\pi$
$660$		0			0
$661$	−3.07386e8			−1.06434			−0.532169	−	0.846638i	$-0.678623\pi$
$661$	−3.07386e8			−1.06434			−0.532169	+	0.846638i	$0.678623\pi$
$662$		0			0
$663$	9.53277e7	+	2.34109e7i	0.327099	+	0.0803299i
$664$		0			0
$665$			3.76696e7i			0.128093i
$666$		0			0
$667$	1.92436e8			0.648499
$668$		0			0
$669$	6.46659e7	−	2.63316e8i	0.215972	−	0.879425i
$670$		0			0
$671$		−	3.33625e8i		−	1.10431i
$672$		0			0
$673$	−3.62228e8			−1.18833			−0.594165	−	0.804343i	$-0.702518\pi$
$673$	−3.62228e8			−1.18833			−0.594165	+	0.804343i	$0.702518\pi$
$674$		0			0
$675$	−2.01962e8	+	2.29133e8i	−0.656686	+	0.745036i
$676$		0			0
$677$		−	1.04147e8i		−	0.335646i	−0.985817	−	0.167823i	$-0.946326\pi$
$677$		−	1.04147e8i		−	0.335646i	0.985817	−	0.167823i	$-0.0536737\pi$
$678$		0			0
$679$	4.20686e8			1.34384
$680$		0			0
$681$	−5.38414e8	−	1.32225e8i	−1.70481	−	0.418672i
$682$		0			0
$683$		−	2.47756e7i		−	0.0777609i	−0.999244	−	0.0388805i	$-0.987621\pi$
$683$		−	2.47756e7i		−	0.0777609i	0.999244	−	0.0388805i	$-0.0123792\pi$
$684$		0			0
$685$	−1.54625e7			−0.0481071
$686$		0			0
$687$	1.19949e8	−	4.88425e8i	0.369936	−	1.50636i
$688$		0			0
$689$			3.30870e8i			1.01158i
$690$		0			0
$691$	−3.15270e8			−0.955539			−0.477770	−	0.878485i	$-0.658555\pi$
$691$	−3.15270e8			−0.955539			−0.477770	+	0.878485i	$0.658555\pi$
$692$		0			0
$693$	−3.02066e8	+	5.77906e8i	−0.907615	+	1.73643i
$694$		0			0
$695$			3.30014e7i			0.0983057i
$696$		0			0
$697$	2.97475e8			0.878521
$698$		0			0
$699$	−3.50619e8	−	8.61061e7i	−1.02661	−	0.252117i
$700$		0			0
$701$		−	1.45804e8i		−	0.423267i	−0.977349	−	0.211634i	$-0.932122\pi$
$701$		−	1.45804e8i		−	0.423267i	0.977349	−	0.211634i	$-0.0678784\pi$
$702$		0			0
$703$	1.46427e8			0.421459
$704$		0			0
$705$	5.99331e6	−	2.44044e7i	0.0171041	−	0.0696467i
$706$		0			0
$707$			3.53453e8i			1.00017i
$708$		0			0
$709$	1.87862e8			0.527109			0.263555	−	0.964644i	$-0.415105\pi$
$709$	1.87862e8			0.527109			0.263555	+	0.964644i	$0.415105\pi$
$710$		0			0
$711$	−2.91490e8	−	1.52359e8i	−0.810989	−	0.423896i
$712$		0			0
$713$		−	6.68978e8i		−	1.84562i
$714$		0			0
$715$	2.78052e7			0.0760689
$716$		0			0
$717$	−1.01301e8	−	2.48778e7i	−0.274825	−	0.0674924i
$718$		0			0
$719$		−	3.29110e8i		−	0.885430i	−0.896662	−	0.442715i	$-0.854015\pi$
$719$		−	3.29110e8i		−	0.885430i	0.896662	−	0.442715i	$-0.145985\pi$
$720$		0			0
$721$	−1.44744e7			−0.0386185
$722$		0			0
$723$	1.68535e7	−	6.86265e7i	0.0445939	−	0.181584i
$724$		0			0
$725$			1.40586e8i			0.368916i
$726$		0			0
$727$	1.29370e8			0.336691			0.168345	−	0.985728i	$-0.446158\pi$
$727$	1.29370e8			0.336691			0.168345	+	0.985728i	$0.446158\pi$
$728$		0			0
$729$	−4.86447e7	−	3.84354e8i	−0.125561	−	0.992086i
$730$		0			0
$731$		−	1.51934e8i		−	0.388957i
$732$		0			0
$733$	3.31083e8			0.840669			0.420335	−	0.907369i	$-0.361913\pi$
$733$	3.31083e8			0.840669			0.420335	+	0.907369i	$0.361913\pi$
$734$		0			0
$735$	−4.75140e7	−	1.16686e7i	−0.119663	−	0.0293872i
$736$		0			0
$737$		−	4.08160e8i		−	1.01960i
$738$		0			0
$739$	2.00902e8			0.497796			0.248898	−	0.968530i	$-0.419932\pi$
$739$	2.00902e8			0.497796			0.248898	+	0.968530i	$0.419932\pi$
$740$		0			0
$741$	7.02783e7	−	2.86169e8i	0.172730	−	0.703345i
$742$		0			0
$743$			3.43251e7i			0.0836847i	0.999124	+	0.0418423i	$0.0133227\pi$
$743$			3.43251e7i			0.0836847i	−0.999124	+	0.0418423i	$0.986677\pi$
$744$		0			0
$745$	384566.			0.000930041
$746$		0			0
$747$	−1.08944e8	+	2.08429e8i	−0.261361	+	0.500031i
$748$		0			0
$749$			5.53834e8i			1.31806i
$750$		0			0
$751$	−3.82231e8			−0.902414			−0.451207	−	0.892419i	$-0.649006\pi$
$751$	−3.82231e8			−0.902414			−0.451207	+	0.892419i	$0.649006\pi$
$752$		0			0
$753$	3.83192e8	+	9.41055e7i	0.897495	+	0.220409i
$754$		0			0
$755$			4.40357e7i			0.102321i
$756$		0			0
$757$	7.85563e8			1.81090			0.905448	−	0.424457i	$-0.139535\pi$
$757$	7.85563e8			1.81090			0.905448	+	0.424457i	$0.139535\pi$
$758$		0			0
$759$	−2.26187e8	+	9.21019e8i	−0.517299	+	2.10641i
$760$		0			0
$761$			5.77337e7i			0.131001i	0.997853	+	0.0655006i	$0.0208644\pi$
$761$			5.77337e7i			0.131001i	−0.997853	+	0.0655006i	$0.979136\pi$
$762$		0			0
$763$	−1.88494e8			−0.424349
$764$		0			0
$765$	1.49877e7	+	7.83394e6i	0.0334774	+	0.0174983i
$766$		0			0
$767$		−	1.46603e8i		−	0.324905i
$768$		0			0
$769$	1.23333e6			0.00271207			0.00135604	−	0.999999i	$-0.499568\pi$
$769$	1.23333e6			0.00271207			0.00135604	+	0.999999i	$0.499568\pi$
$770$		0			0
$771$	3.97172e8	+	9.75386e7i	0.866593	+	0.212821i
$772$		0			0
$773$			8.98385e8i			1.94502i	0.232863	+	0.972510i	$0.425191\pi$
$773$			8.98385e8i			1.94502i	−0.232863	+	0.972510i	$0.574809\pi$
$774$		0			0
$775$	4.88727e8			1.04993
$776$		0			0
$777$	−7.58608e7	+	3.08901e8i	−0.161717	+	0.658500i
$778$		0			0
$779$		−	8.93005e8i		−	1.88904i
$780$		0			0
$781$	−1.09803e8			−0.230494
$782$		0			0
$783$	−1.33775e8	−	1.17911e8i	−0.278669	−	0.245623i
$784$		0			0
$785$		−	3.10934e7i		−	0.0642776i
$786$		0			0
$787$	−1.13010e8			−0.231841			−0.115921	−	0.993258i	$-0.536982\pi$
$787$	−1.13010e8			−0.231841			−0.115921	+	0.993258i	$0.536982\pi$
$788$		0			0
$789$	−7.35285e8	−	1.80574e8i	−1.49701	−	0.367640i
$790$		0			0
$791$			1.14948e9i			2.32258i
$792$		0			0
$793$	−3.27496e8			−0.656730
$794$		0			0
$795$	−1.35953e7	+	5.53592e7i	−0.0270575	+	0.110176i
$796$		0			0
$797$			3.12491e8i			0.617252i	0.951183	+	0.308626i	$0.0998692\pi$
$797$			3.12491e8i			0.617252i	−0.951183	+	0.308626i	$0.900131\pi$
$798$		0			0
$799$	2.01241e8			0.394526
$800$		0			0
$801$	2.25741e8	−	4.31883e8i	0.439252	−	0.840367i
$802$		0			0
$803$			4.29126e8i			0.828778i
$804$		0			0
$805$	−1.19010e8			−0.228138
$806$		0			0
$807$	−7.94546e8	−	1.95127e8i	−1.51181	−	0.371276i
$808$		0			0
$809$			3.83358e8i			0.724034i	0.932172	+	0.362017i	$0.117912\pi$
$809$			3.83358e8i			0.724034i	−0.932172	+	0.362017i	$0.882088\pi$
$810$		0			0
$811$	3.82087e8			0.716307			0.358153	−	0.933663i	$-0.383406\pi$
$811$	3.82087e8			0.716307			0.358153	+	0.933663i	$0.383406\pi$
$812$		0			0
$813$	−4.70810e7	+	1.91711e8i	−0.0876142	+	0.356760i
$814$		0			0
$815$			5.37073e6i			0.00992111i
$816$		0			0
$817$	−4.56097e8			−0.836357
$818$		0			0
$819$	5.67289e8	+	2.96516e8i	1.03265	+	0.539755i
$820$		0			0
$821$			3.52605e8i			0.637175i	0.947894	+	0.318587i	$0.103208\pi$
$821$			3.52605e8i			0.637175i	−0.947894	+	0.318587i	$0.896792\pi$
$822$		0			0
$823$	9.88065e8			1.77250			0.886249	−	0.463208i	$-0.153302\pi$
$823$	9.88065e8			1.77250			0.886249	+	0.463208i	$0.153302\pi$
$824$		0			0
$825$	−6.72858e8	−	1.65242e8i	−1.19829	−	0.294279i
$826$		0			0
$827$		−	1.39767e8i		−	0.247109i	−0.992338	−	0.123555i	$-0.960571\pi$
$827$		−	1.39767e8i		−	0.247109i	0.992338	−	0.123555i	$-0.0394294\pi$
$828$		0			0
$829$	3.82290e8			0.671010			0.335505	−	0.942038i	$-0.391093\pi$
$829$	3.82290e8			0.671010			0.335505	+	0.942038i	$0.391093\pi$
$830$		0			0
$831$	−7.35226e7	+	2.99380e8i	−0.128120	+	0.521698i
$832$		0			0
$833$		−	3.91805e8i		−	0.677852i
$834$		0			0
$835$	−1.57383e7			−0.0270333
$836$		0			0
$837$	−4.09902e8	+	4.65050e8i	−0.699042	+	0.793091i
$838$		0			0
$839$		−	9.06354e8i		−	1.53466i	−0.641253	−	0.767329i	$-0.721585\pi$
$839$		−	9.06354e8i		−	1.53466i	0.641253	−	0.767329i	$-0.278415\pi$
$840$		0			0
$841$	5.12745e8			0.862013
$842$		0			0
$843$	2.39524e8	+	5.88232e7i	0.399822	+	0.0981896i
$844$		0			0
$845$			2.27024e7i			0.0376271i
$846$		0			0
$847$	−5.20934e8			−0.857299
$848$		0			0
$849$	1.23487e8	−	5.02832e8i	0.201789	−	0.821674i
$850$		0			0
$851$			4.62610e8i			0.750630i
$852$		0			0
$853$	5.38288e7			0.0867296			0.0433648	−	0.999059i	$-0.486192\pi$
$853$	5.38288e7			0.0867296			0.0433648	+	0.999059i	$0.486192\pi$
$854$		0			0
$855$	2.35171e7	−	4.49924e7i	0.0376258	−	0.0719849i
$856$		0			0
$857$			1.95308e8i			0.310297i	0.987891	+	0.155148i	$0.0495855\pi$
$857$			1.95308e8i			0.310297i	−0.987891	+	0.155148i	$0.950414\pi$
$858$		0			0
$859$	−3.96279e8			−0.625204			−0.312602	−	0.949884i	$-0.601201\pi$
$859$	−3.96279e8			−0.625204			−0.312602	+	0.949884i	$0.601201\pi$
$860$		0			0
$861$	1.88387e9	+	4.62647e8i	2.95150	+	0.724837i
$862$		0			0
$863$		−	7.93753e8i		−	1.23496i	−0.786587	−	0.617480i	$-0.788154\pi$
$863$		−	7.93753e8i		−	1.23496i	0.786587	−	0.617480i	$-0.211846\pi$
$864$		0			0
$865$	6.96661e7			0.107640
$866$		0			0
$867$	1.23132e8	−	5.01386e8i	0.188935	−	0.769334i
$868$		0			0
$869$		−	7.46095e8i		−	1.13693i
$870$		0			0
$871$	−4.00661e8			−0.606350
$872$		0			0
$873$	−5.02466e8	−	2.62634e8i	−0.755203	−	0.394737i
$874$		0			0
$875$		−	1.74489e8i		−	0.260462i
$876$		0			0
$877$	−1.01599e9			−1.50623			−0.753116	−	0.657888i	$-0.771450\pi$
$877$	−1.01599e9			−1.50623			−0.753116	+	0.657888i	$0.771450\pi$
$878$		0			0
$879$	−4.00069e8	−	9.82501e7i	−0.589071	−	0.144666i
$880$		0			0
$881$		−	1.16725e9i		−	1.70701i	−0.521081	−	0.853507i	$-0.674471\pi$
$881$		−	1.16725e9i		−	1.70701i	0.521081	−	0.853507i	$-0.325529\pi$
$882$		0			0
$883$	−5.82062e8			−0.845448			−0.422724	−	0.906258i	$-0.638926\pi$
$883$	−5.82062e8			−0.845448			−0.422724	+	0.906258i	$0.638926\pi$
$884$		0			0
$885$	6.02385e6	−	2.45288e7i	0.00869049	−	0.0353872i
$886$		0			0
$887$			7.25116e8i			1.03905i	0.854455	+	0.519525i	$0.173891\pi$
$887$			7.25116e8i			1.03905i	−0.854455	+	0.519525i	$0.826109\pi$
$888$		0			0
$889$	6.41311e8			0.912775
$890$		0			0
$891$	7.21572e8	−	5.01669e8i	1.02011	−	0.709225i
$892$		0			0
$893$		−	6.04115e8i		−	0.848331i
$894$		0			0
$895$	5.34679e7			0.0745803
$896$		0			0
$897$	9.04099e8	+	2.22031e8i	1.25268	+	0.307636i
$898$		0			0
$899$			2.85333e8i			0.392711i
$900$		0			0
$901$	−4.56497e8			−0.624114
$902$		0			0
$903$	2.36294e8	−	9.62177e8i	0.320915	−	1.30675i
$904$		0			0
$905$		−	4.59846e7i		−	0.0620393i
$906$		0			0
$907$	−1.28188e9			−1.71801			−0.859006	−	0.511966i	$-0.828918\pi$
$907$	−1.28188e9			−1.71801			−0.859006	+	0.511966i	$0.828918\pi$
$908$		0			0
$909$	2.20660e8	−	4.22163e8i	0.293787	−	0.562067i
$910$		0			0
$911$			6.50694e8i			0.860640i	0.902676	+	0.430320i	$0.141599\pi$
$911$			6.50694e8i			0.860640i	−0.902676	+	0.430320i	$0.858401\pi$
$912$		0			0
$913$	−5.33493e8			−0.700998
$914$		0			0
$915$	−5.47948e7	−	1.34567e7i	−0.0715279	−	0.0175661i
$916$		0			0
$917$		−	1.15559e9i		−	1.49863i
$918$		0			0
$919$	−3.83612e8			−0.494248			−0.247124	−	0.968984i	$-0.579486\pi$
$919$	−3.83612e8			−0.494248			−0.247124	+	0.968984i	$0.579486\pi$
$920$		0			0
$921$	−3.01163e8	+	1.22632e9i	−0.385499	+	1.56973i
$922$		0			0
$923$			1.07785e8i			0.137074i
$924$		0			0
$925$	−3.37963e8			−0.427016
$926$		0			0
$927$	1.72882e7	+	9.03636e6i	0.0217025	+	0.0113437i
$928$		0			0
$929$			1.22578e9i			1.52885i	0.644715	+	0.764423i	$0.276976\pi$
$929$			1.22578e9i			1.52885i	−0.644715	+	0.764423i	$0.723024\pi$
$930$		0			0
$931$	−1.17618e9			−1.45755
$932$		0			0
$933$	−5.36999e8	−	1.31878e8i	−0.661193	−	0.162378i
$934$		0			0
$935$			3.83624e7i			0.0469322i
$936$		0			0
$937$	−4.41812e8			−0.537055			−0.268527	−	0.963272i	$-0.586537\pi$
$937$	−4.41812e8			−0.537055			−0.268527	+	0.963272i	$0.586537\pi$
$938$		0			0
$939$	−8.05262e7	+	3.27898e8i	−0.0972614	+	0.396043i
$940$		0			0
$941$			1.01558e9i			1.21884i	0.792849	+	0.609418i	$0.208597\pi$
$941$			1.01558e9i			1.21884i	−0.792849	+	0.609418i	$0.791403\pi$
$942$		0			0
$943$	2.82129e9			3.36444
$944$		0			0
$945$	8.27318e7	+	7.29210e7i	0.0980340	+	0.0864087i
$946$		0			0
$947$		−	1.20078e9i		−	1.41388i	−0.707273	−	0.706941i	$-0.750075\pi$
$947$		−	1.20078e9i		−	1.41388i	0.707273	−	0.706941i	$-0.249925\pi$
$948$		0			0
$949$	4.21242e8			0.492871
$950$		0			0
$951$	3.91829e8	+	9.62267e7i	0.455570	+	0.111880i
$952$		0			0
$953$		−	9.51725e8i		−	1.09960i	−0.835298	−	0.549798i	$-0.814705\pi$
$953$		−	9.51725e8i		−	1.09960i	0.835298	−	0.549798i	$-0.185295\pi$
$954$		0			0
$955$	1.42151e7			0.0163207
$956$		0			0
$957$	9.64734e7	−	3.92834e8i	0.110071	−	0.448202i
$958$		0			0
$959$		−	8.07476e8i		−	0.915532i
$960$		0			0
$961$	1.04417e8			0.117653
$962$		0			0
$963$	3.45758e8	−	6.61497e8i	0.387163	−	0.740711i
$964$		0			0
$965$			9.10446e7i			0.101315i
$966$		0			0
$967$	−4.92530e8			−0.544694			−0.272347	−	0.962199i	$-0.587800\pi$
$967$	−4.92530e8			−0.544694			−0.272347	+	0.962199i	$0.587800\pi$
$968$		0			0
$969$	3.94824e8	+	9.69620e7i	0.433942	+	0.106569i
$970$		0			0
$971$			1.66285e9i			1.81634i	0.418606	+	0.908168i	$0.362519\pi$
$971$			1.66285e9i			1.81634i	−0.418606	+	0.908168i	$0.637481\pi$
$972$		0			0
$973$	−1.72338e9			−1.87087
$974$		0			0
$975$	−1.62207e8	+	6.60496e8i	−0.175007	+	0.712618i
$976$		0			0
$977$			4.36182e8i			0.467718i	0.972271	+	0.233859i	$0.0751354\pi$
$977$			4.36182e8i			0.467718i	−0.972271	+	0.233859i	$0.924865\pi$
$978$		0			0
$979$	1.10544e9			1.17812
$980$		0			0
$981$	2.25136e8	+	1.17676e8i	0.238472	+	0.124647i
$982$		0			0
$983$			2.38288e8i			0.250866i	0.992102	+	0.125433i	$0.0400320\pi$
$983$			2.38288e8i			0.250866i	−0.992102	+	0.125433i	$0.959968\pi$
$984$		0			0
$985$	4.20259e7			0.0439752
$986$		0			0
$987$	1.27443e9	+	3.12979e8i	1.32546	+	0.325510i
$988$		0			0
$989$		−	1.44096e9i		−	1.48957i
$990$		0			0
$991$	−7.58618e8			−0.779475			−0.389738	−	0.920926i	$-0.627434\pi$
$991$	−7.58618e8			−0.779475			−0.389738	+	0.920926i	$0.627434\pi$
$992$		0			0
$993$	−3.09705e8	+	1.26110e9i	−0.316301	+	1.28796i
$994$		0			0
$995$		−	1.12128e8i		−	0.113827i
$996$		0			0
$997$	1.75735e9			1.77326			0.886631	−	0.462478i	$-0.153040\pi$
$997$	1.75735e9			1.77326			0.886631	+	0.462478i	$0.153040\pi$
$998$		0			0
$999$	2.83454e8	−	3.21590e8i	0.284306	−	0.322557i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.7.e.d.17.3		6
3.2	odd	2	inner	48.7.e.d.17.4		6
4.3	odd	2		24.7.e.a.17.4	yes	6
8.3	odd	2		192.7.e.h.65.3		6
8.5	even	2		192.7.e.g.65.4		6
12.11	even	2		24.7.e.a.17.3	✓	6
24.5	odd	2		192.7.e.g.65.3		6
24.11	even	2		192.7.e.h.65.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.7.e.a.17.3	✓	6	12.11	even	2
24.7.e.a.17.4	yes	6	4.3	odd	2
48.7.e.d.17.3		6	1.1	even	1	trivial
48.7.e.d.17.4		6	3.2	odd	2	inner
192.7.e.g.65.3		6	24.5	odd	2
192.7.e.g.65.4		6	8.5	even	2
192.7.e.h.65.3		6	8.3	odd	2
192.7.e.h.65.4		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)

\(f(q)\)	\(=\)	\(q+(6.43940 - 26.2209i) q^{3} -10.3581i q^{5} +540.917 q^{7} +(-646.068 - 337.693i) q^{9} +O(q^{10})\)	\(q+(6.43940 - 26.2209i) q^{3} -10.3581i q^{5} +540.917 q^{7} +(-646.068 - 337.693i) q^{9} -1653.67i q^{11} -1623.29 q^{13} +(-271.599 - 66.7002i) q^{15} -2239.63i q^{17} -6723.26 q^{19} +(3483.18 - 14183.3i) q^{21} -21240.9i q^{23} +15517.7 q^{25} +(-13014.9 + 14765.9i) q^{27} +9059.70i q^{29} +31494.8 q^{31} +(-43360.6 - 10648.6i) q^{33} -5602.88i q^{35} -21779.2 q^{37} +(-10453.0 + 42564.0i) q^{39} +132823. i q^{41} +67838.7 q^{43} +(-3497.87 + 6692.06i) q^{45} +89854.5i q^{47} +174942. q^{49} +(-58725.1 - 14421.9i) q^{51} -203827. i q^{53} -17128.9 q^{55} +(-43293.8 + 176290. i) q^{57} +90312.3i q^{59} +201749. q^{61} +(-349469. - 182664. i) q^{63} +16814.2i q^{65} +246821. q^{67} +(-556955. - 136779. i) q^{69} -66399.4i q^{71} -259499. q^{73} +(99924.8 - 406888. i) q^{75} -894497. i q^{77} +451176. q^{79} +(303367. + 436346. i) q^{81} -322612. i q^{83} -23198.4 q^{85} +(237553. + 58339.0i) q^{87} +668480. i q^{89} -878064. q^{91} +(202808. - 825821. i) q^{93} +69640.4i q^{95} +777729. q^{97} +(-558433. + 1.06838e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 10 q^{3} - 156 q^{7} - 74 q^{9}+O(q^{10}) \) 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

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