LMFDB - Embedded newform 1134.2.d.a.1133.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(1133,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1134.1133");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 $ x^16 - 6x^14 + 9x^12 + 54x^10 - 288x^8 + 486x^6 + 729x^4 - 4374*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1133.8
Root			$-1.62181 + 0.608059i$ of defining polynomial
Character	$\chi$	$=$	1134.1133
Dual form			1134.2.d.a.1133.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +3.89111 q^{5} +(-2.44383 + 1.01375i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +3.89111 q^{5} +(-2.44383 + 1.01375i) q^{7} +1.00000i q^{8} -3.89111i q^{10} +3.94462i q^{11} +2.84849i q^{13} +(1.01375 + 2.44383i) q^{14} +1.00000 q^{16} -0.742117 q^{17} +1.78474i q^{19} -3.89111 q^{20} +3.94462 q^{22} +6.25311i q^{23} +10.1408 q^{25} +2.84849 q^{26} +(2.44383 - 1.01375i) q^{28} -2.88766i q^{29} +3.51174i q^{31} -1.00000i q^{32} +0.742117i q^{34} +(-9.50923 + 3.94462i) q^{35} +3.00158 q^{37} +1.78474 q^{38} +3.89111i q^{40} -10.4941 q^{41} -0.943042 q^{43} -3.94462i q^{44} +6.25311 q^{46} +2.18525 q^{47} +(4.94462 - 4.95487i) q^{49} -10.1408i q^{50} -2.84849i q^{52} +15.3490i q^{55} +(-1.01375 - 2.44383i) q^{56} -2.88766 q^{58} +0.0211346 q^{59} +2.46911i q^{61} +3.51174 q^{62} -1.00000 q^{64} +11.0838i q^{65} +13.4493 q^{67} +0.742117 q^{68} +(3.94462 + 9.50923i) q^{70} -1.94304i q^{71} -4.85486i q^{73} -3.00158i q^{74} -1.78474i q^{76} +(-3.99886 - 9.63998i) q^{77} +3.63613 q^{79} +3.89111 q^{80} +10.4941i q^{82} -8.05995 q^{83} -2.88766 q^{85} +0.943042i q^{86} -3.94462 q^{88} +9.26646 q^{89} +(-2.88766 - 6.96124i) q^{91} -6.25311i q^{92} -2.18525i q^{94} +6.94462i q^{95} -18.8196i q^{97} +(-4.95487 - 4.94462i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 4 q^{7}+O(q^{10}) $ 16 * q - 16 * q^4 - 4 * q^7	$ 16 q - 16 q^{4} - 4 q^{7} + 16 q^{16} + 16 q^{25} + 4 q^{28} - 8 q^{37} - 8 q^{43} + 24 q^{46} + 16 q^{49} + 24 q^{58} - 16 q^{64} + 56 q^{67} + 8 q^{79} + 24 q^{85} + 24 q^{91}+O(q^{100}) $ 16 * q - 16 * q^4 - 4 * q^7 + 16 * q^16 + 16 * q^25 + 4 * q^28 - 8 * q^37 - 8 * q^43 + 24 * q^46 + 16 * q^49 + 24 * q^58 - 16 * q^64 + 56 * q^67 + 8 * q^79 + 24 * q^85 + 24 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	3.89111			1.74016			0.870080	−	0.492911i	$-0.164067\pi$
$5$	3.89111			1.74016			0.870080	+	0.492911i	$0.164067\pi$
$6$		0			0
$7$	−2.44383	+	1.01375i	−0.923681	+	0.383162i
$7$	−2.44383	+	1.01375i	−0.923681	+	0.383162i
$8$			1.00000i			0.353553i
$9$		0			0
$10$		−	3.89111i		−	1.23048i
$11$			3.94462i			1.18935i	0.803967	+	0.594674i	$0.202719\pi$
$11$			3.94462i			1.18935i	−0.803967	+	0.594674i	$0.797281\pi$
$12$		0			0
$13$			2.84849i			0.790030i	0.918675	+	0.395015i	$0.129261\pi$
$13$			2.84849i			0.790030i	−0.918675	+	0.395015i	$0.870739\pi$
$14$	1.01375	+	2.44383i	0.270936	+	0.653141i
$15$		0			0
$16$	1.00000			0.250000
$17$	−0.742117			−0.179990			−0.0899949	−	0.995942i	$-0.528685\pi$
$17$	−0.742117			−0.179990			−0.0899949	+	0.995942i	$0.528685\pi$
$18$		0			0
$19$			1.78474i			0.409447i	0.978820	+	0.204723i	$0.0656295\pi$
$19$			1.78474i			0.409447i	−0.978820	+	0.204723i	$0.934370\pi$
$20$	−3.89111			−0.870080
$21$		0			0
$22$	3.94462			0.840996
$23$			6.25311i			1.30386i	0.758278	+	0.651932i	$0.226041\pi$
$23$			6.25311i			1.30386i	−0.758278	+	0.651932i	$0.773959\pi$
$24$		0			0
$25$	10.1408			2.02815
$26$	2.84849			0.558636
$27$		0			0
$28$	2.44383	−	1.01375i	0.461841	−	0.191581i
$29$		−	2.88766i		−	0.536225i	−0.963388	−	0.268113i	$-0.913600\pi$
$29$		−	2.88766i		−	0.536225i	0.963388	−	0.268113i	$-0.0864000\pi$
$30$		0			0
$31$			3.51174i			0.630726i	0.948971	+	0.315363i	$0.102126\pi$
$31$			3.51174i			0.630726i	−0.948971	+	0.315363i	$0.897874\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$			0.742117i			0.127272i
$35$	−9.50923	+	3.94462i	−1.60735	+	0.666762i
$36$		0			0
$37$	3.00158			0.493456			0.246728	−	0.969085i	$-0.420645\pi$
$37$	3.00158			0.493456			0.246728	+	0.969085i	$0.420645\pi$
$38$	1.78474			0.289523
$39$		0			0
$40$			3.89111i			0.615239i
$41$	−10.4941			−1.63890			−0.819452	−	0.573148i	$-0.805722\pi$
$41$	−10.4941			−1.63890			−0.819452	+	0.573148i	$0.805722\pi$
$42$		0			0
$43$	−0.943042			−0.143813			−0.0719063	−	0.997411i	$-0.522908\pi$
$43$	−0.943042			−0.143813			−0.0719063	+	0.997411i	$0.522908\pi$
$44$		−	3.94462i		−	0.594674i
$45$		0			0
$46$	6.25311			0.921971
$47$	2.18525			0.318752			0.159376	−	0.987218i	$-0.449052\pi$
$47$	2.18525			0.318752			0.159376	+	0.987218i	$0.449052\pi$
$48$		0			0
$49$	4.94462	−	4.95487i	0.706374	−	0.707839i
$50$		−	10.1408i		−	1.43412i
$51$		0			0
$52$		−	2.84849i		−	0.395015i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$		0			0
$55$			15.3490i			2.06965i
$56$	−1.01375	−	2.44383i	−0.135468	−	0.326571i
$57$		0			0
$58$	−2.88766			−0.379169
$59$	0.0211346			0.00275149			0.00137575	−	0.999999i	$-0.499562\pi$
$59$	0.0211346			0.00275149			0.00137575	+	0.999999i	$0.499562\pi$
$60$		0			0
$61$			2.46911i			0.316138i	0.987428	+	0.158069i	$0.0505268\pi$
$61$			2.46911i			0.316138i	−0.987428	+	0.158069i	$0.949473\pi$
$62$	3.51174			0.445991
$63$		0			0
$64$	−1.00000			−0.125000
$65$			11.0838i			1.37478i
$66$		0			0
$67$	13.4493			1.64309			0.821544	−	0.570144i	$-0.193113\pi$
$67$	13.4493			1.64309			0.821544	+	0.570144i	$0.193113\pi$
$68$	0.742117			0.0899949
$69$		0			0
$70$	3.94462	+	9.50923i	0.471472	+	1.13657i
$71$		−	1.94304i		−	0.230597i	−0.993331	−	0.115298i	$-0.963218\pi$
$71$		−	1.94304i		−	0.230597i	0.993331	−	0.115298i	$-0.0367824\pi$
$72$		0			0
$73$		−	4.85486i		−	0.568218i	−0.958792	−	0.284109i	$-0.908302\pi$
$73$		−	4.85486i		−	0.568218i	0.958792	−	0.284109i	$-0.0916978\pi$
$74$		−	3.00158i		−	0.348926i
$75$		0			0
$76$		−	1.78474i		−	0.204723i
$77$	−3.99886	−	9.63998i	−0.455712	−	1.09858i
$78$		0			0
$79$	3.63613			0.409096			0.204548	−	0.978856i	$-0.434427\pi$
$79$	3.63613			0.409096			0.204548	+	0.978856i	$0.434427\pi$
$80$	3.89111			0.435040
$81$		0			0
$82$			10.4941i			1.15888i
$83$	−8.05995			−0.884695			−0.442347	−	0.896844i	$-0.645854\pi$
$83$	−8.05995			−0.884695			−0.442347	+	0.896844i	$0.645854\pi$
$84$		0			0
$85$	−2.88766			−0.313211
$86$			0.943042i			0.101691i
$87$		0			0
$88$	−3.94462			−0.420498
$89$	9.26646			0.982243			0.491122	−	0.871091i	$-0.336587\pi$
$89$	9.26646			0.982243			0.491122	+	0.871091i	$0.336587\pi$
$90$		0			0
$91$	−2.88766	−	6.96124i	−0.302709	−	0.729736i
$92$		−	6.25311i		−	0.651932i
$93$		0			0
$94$		−	2.18525i		−	0.225392i
$95$			6.94462i			0.712503i
$96$		0			0
$97$		−	18.8196i		−	1.91084i	−0.295248	−	0.955421i	$-0.595402\pi$
$97$		−	18.8196i		−	1.91084i	0.295248	−	0.955421i	$-0.404598\pi$
$98$	−4.95487	−	4.94462i	−0.500517	−	0.499482i
$99$		0			0
$100$	−10.1408			−1.01408
$101$	8.28158			0.824048			0.412024	−	0.911173i	$-0.364822\pi$
$101$	8.28158			0.824048			0.412024	+	0.911173i	$0.364822\pi$
$102$		0			0
$103$		−	17.0487i		−	1.67986i	−0.542697	−	0.839929i	$-0.682597\pi$
$103$		−	17.0487i		−	1.67986i	0.542697	−	0.839929i	$-0.317403\pi$
$104$	−2.84849			−0.279318
$105$		0			0
$106$		0			0
$107$			14.3369i			1.38600i	0.720936	+	0.693001i	$0.243712\pi$
$107$			14.3369i			1.38600i	−0.720936	+	0.693001i	$0.756288\pi$
$108$		0			0
$109$	11.2800			1.08042			0.540212	−	0.841529i	$-0.318344\pi$
$109$	11.2800			1.08042			0.540212	+	0.841529i	$0.318344\pi$
$110$	15.3490			1.46347
$111$		0			0
$112$	−2.44383	+	1.01375i	−0.230920	+	0.0957904i
$113$			9.83228i			0.924943i	0.886634	+	0.462472i	$0.153037\pi$
$113$			9.83228i			0.924943i	−0.886634	+	0.462472i	$0.846963\pi$
$114$		0			0
$115$			24.3316i			2.26893i
$116$			2.88766i			0.268113i
$117$		0			0
$118$		−	0.0211346i		−	0.00194560i
$119$	1.81361	−	0.752321i	0.166253	−	0.0689652i
$120$		0			0
$121$	−4.56002			−0.414548
$122$	2.46911			0.223543
$123$		0			0
$124$		−	3.51174i		−	0.315363i
$125$	20.0033			1.78915
$126$		0			0
$127$	2.94462			0.261293			0.130646	−	0.991429i	$-0.458295\pi$
$127$	2.94462			0.261293			0.130646	+	0.991429i	$0.458295\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	11.0838			0.972115
$131$	15.0651			1.31624			0.658122	−	0.752911i	$-0.271351\pi$
$131$	15.0651			1.31624			0.658122	+	0.752911i	$0.271351\pi$
$132$		0			0
$133$	−1.80928	−	4.36160i	−0.156884	−	0.378198i
$134$		−	13.4493i		−	1.16184i
$135$		0			0
$136$		−	0.742117i		−	0.0636360i
$137$		−	15.7199i		−	1.34305i	−0.740984	−	0.671523i	$-0.765641\pi$
$137$		−	15.7199i		−	1.34305i	0.740984	−	0.671523i	$-0.234359\pi$
$138$		0			0
$139$			3.30675i			0.280475i	0.990118	+	0.140237i	$0.0447866\pi$
$139$			3.30675i			0.280475i	−0.990118	+	0.140237i	$0.955213\pi$
$140$	9.50923	−	3.94462i	0.803676	−	0.333381i
$141$		0			0
$142$	−1.94304			−0.163056
$143$	−11.2362			−0.939620
$144$		0			0
$145$		−	11.2362i		−	0.933118i
$146$	−4.85486			−0.401791
$147$		0			0
$148$	−3.00158			−0.246728
$149$		−	11.0016i		−	0.901284i	−0.892705	−	0.450642i	$-0.851195\pi$
$149$		−	11.0016i		−	0.901284i	0.892705	−	0.450642i	$-0.148805\pi$
$150$		0			0
$151$	−1.43998			−0.117184			−0.0585918	−	0.998282i	$-0.518661\pi$
$151$	−1.43998			−0.117184			−0.0585918	+	0.998282i	$0.518661\pi$
$152$	−1.78474			−0.144761
$153$		0			0
$154$	−9.63998	+	3.99886i	−0.776812	+	0.322237i
$155$			13.6646i			1.09756i
$156$		0			0
$157$			16.6071i			1.32539i	0.748890	+	0.662695i	$0.230587\pi$
$157$			16.6071i			1.32539i	−0.748890	+	0.662695i	$0.769413\pi$
$158$		−	3.63613i		−	0.289275i
$159$		0			0
$160$		−	3.89111i		−	0.307620i
$161$	−6.33909	−	15.2815i	−0.499591	−	1.20435i
$162$		0			0
$163$	−12.3955			−0.970887			−0.485444	−	0.874268i	$-0.661342\pi$
$163$	−12.3955			−0.970887			−0.485444	+	0.874268i	$0.661342\pi$
$164$	10.4941			0.819452
$165$		0			0
$166$			8.05995i			0.625574i
$167$	−11.7217			−0.907056			−0.453528	−	0.891242i	$-0.649835\pi$
$167$	−11.7217			−0.907056			−0.453528	+	0.891242i	$0.649835\pi$
$168$		0			0
$169$	4.88608			0.375853
$170$			2.88766i			0.221474i
$171$		0			0
$172$	0.943042			0.0719063
$173$	−16.7710			−1.27507			−0.637536	−	0.770420i	$-0.720046\pi$
$173$	−16.7710			−1.27507			−0.637536	+	0.770420i	$0.720046\pi$
$174$		0			0
$175$	−24.7823	+	10.2802i	−1.87337	+	0.777111i
$176$			3.94462i			0.297337i
$177$		0			0
$178$		−	9.26646i		−	0.694551i
$179$		−	5.77532i		−	0.431668i	−0.976430	−	0.215834i	$-0.930753\pi$
$179$		−	5.77532i		−	0.431668i	0.976430	−	0.215834i	$-0.0692470\pi$
$180$		0			0
$181$		−	5.53310i		−	0.411272i	−0.978629	−	0.205636i	$-0.934074\pi$
$181$		−	5.53310i		−	0.411272i	0.978629	−	0.205636i	$-0.0659263\pi$
$182$	−6.96124	+	2.88766i	−0.516001	+	0.214048i
$183$		0			0
$184$	−6.25311			−0.460985
$185$	11.6795			0.858692
$186$		0			0
$187$		−	2.92737i		−	0.214070i
$188$	−2.18525			−0.159376
$189$		0			0
$190$	6.94462			0.503816
$191$		−	6.21372i		−	0.449609i	−0.974404	−	0.224805i	$-0.927826\pi$
$191$		−	6.21372i		−	0.449609i	0.974404	−	0.224805i	$-0.0721744\pi$
$192$		0			0
$193$	−7.80542			−0.561847			−0.280923	−	0.959730i	$-0.590641\pi$
$193$	−7.80542			−0.561847			−0.280923	+	0.959730i	$0.590641\pi$
$194$	−18.8196			−1.35117
$195$		0			0
$196$	−4.94462	+	4.95487i	−0.353187	+	0.353919i
$197$			12.7737i			0.910092i	0.890468	+	0.455046i	$0.150377\pi$
$197$			12.7737i			0.910092i	−0.890468	+	0.455046i	$0.849623\pi$
$198$		0			0
$199$		−	1.81201i		−	0.128450i	−0.997935	−	0.0642250i	$-0.979542\pi$
$199$		−	1.81201i		−	0.128450i	0.997935	−	0.0642250i	$-0.0204575\pi$
$200$			10.1408i			0.717061i
$201$		0			0
$202$		−	8.28158i		−	0.582690i
$203$	2.92737	+	7.05696i	0.205461	+	0.495301i
$204$		0			0
$205$	−40.8338			−2.85195
$206$	−17.0487			−1.18784
$207$		0			0
$208$			2.84849i			0.197507i
$209$	−7.04011			−0.486975
$210$		0			0
$211$	3.77532			0.259904			0.129952	−	0.991520i	$-0.458518\pi$
$211$	3.77532			0.259904			0.129952	+	0.991520i	$0.458518\pi$
$212$		0			0
$213$		0			0
$214$	14.3369			0.980052
$215$	−3.66949			−0.250257
$216$		0			0
$217$	−3.56002	−	8.58209i	−0.241670	−	0.582590i
$218$		−	11.2800i		−	0.763976i
$219$		0			0
$220$		−	15.3490i		−	1.03483i
$221$		−	2.11392i		−	0.142197i
$222$		0			0
$223$		−	12.7782i		−	0.855691i	−0.903852	−	0.427846i	$-0.859273\pi$
$223$		−	12.7782i		−	0.855691i	0.903852	−	0.427846i	$-0.140727\pi$
$224$	1.01375	+	2.44383i	0.0677341	+	0.163285i
$225$		0			0
$226$	9.83228			0.654034
$227$	−19.9822			−1.32627			−0.663133	−	0.748502i	$-0.730773\pi$
$227$	−19.9822			−1.32627			−0.663133	+	0.748502i	$0.730773\pi$
$228$		0			0
$229$			10.1314i			0.669500i	0.942307	+	0.334750i	$0.108652\pi$
$229$			10.1314i			0.669500i	−0.942307	+	0.334750i	$0.891348\pi$
$230$	24.3316			1.60438
$231$		0			0
$232$	2.88766			0.189584
$233$			7.31007i			0.478898i	0.970909	+	0.239449i	$0.0769669\pi$
$233$			7.31007i			0.478898i	−0.970909	+	0.239449i	$0.923033\pi$
$234$		0			0
$235$	8.50307			0.554679
$236$	−0.0211346			−0.00137575
$237$		0			0
$238$	−0.752321	−	1.81361i	−0.0487658	−	0.117559i
$239$		−	8.40988i		−	0.543990i	−0.962299	−	0.271995i	$-0.912317\pi$
$239$		−	8.40988i		−	0.543990i	0.962299	−	0.271995i	$-0.0876834\pi$
$240$		0			0
$241$			8.95213i			0.576657i	0.957531	+	0.288329i	$0.0930996\pi$
$241$			8.95213i			0.576657i	−0.957531	+	0.288329i	$0.906900\pi$
$242$			4.56002i			0.293129i
$243$		0			0
$244$		−	2.46911i		−	0.158069i
$245$	19.2401	−	19.2800i	1.22920	−	1.23175i
$246$		0			0
$247$	−5.08381			−0.323475
$248$	−3.51174			−0.222995
$249$		0			0
$250$		−	20.0033i		−	1.26512i
$251$	−12.6432			−0.798033			−0.399017	−	0.916944i	$-0.630648\pi$
$251$	−12.6432			−0.798033			−0.399017	+	0.916944i	$0.630648\pi$
$252$		0			0
$253$	−24.6661			−1.55075
$254$		−	2.94462i		−	0.184762i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−16.3066			−1.01718			−0.508588	−	0.861010i	$-0.669832\pi$
$257$	−16.3066			−1.01718			−0.508588	+	0.861010i	$0.669832\pi$
$258$		0			0
$259$	−7.33535	+	3.04285i	−0.455796	+	0.189074i
$260$		−	11.0838i		−	0.687389i
$261$		0			0
$262$		−	15.0651i		−	0.930725i
$263$			23.7215i			1.46273i	0.681985	+	0.731366i	$0.261117\pi$
$263$			23.7215i			1.46273i	−0.681985	+	0.731366i	$0.738883\pi$
$264$		0			0
$265$		0			0
$266$	−4.36160	+	1.80928i	−0.267427	+	0.110934i
$267$		0			0
$268$	−13.4493			−0.821544
$269$	−7.28288			−0.444045			−0.222022	−	0.975042i	$-0.571266\pi$
$269$	−7.28288			−0.444045			−0.222022	+	0.975042i	$0.571266\pi$
$270$		0			0
$271$		−	22.6879i		−	1.37819i	−0.724669	−	0.689097i	$-0.758007\pi$
$271$		−	22.6879i		−	1.37819i	0.724669	−	0.689097i	$-0.241993\pi$
$272$	−0.742117			−0.0449974
$273$		0			0
$274$	−15.7199			−0.949677
$275$			40.0015i			2.41218i
$276$		0			0
$277$	24.1676			1.45209			0.726046	−	0.687646i	$-0.241356\pi$
$277$	24.1676			1.45209			0.726046	+	0.687646i	$0.241356\pi$
$278$	3.30675			0.198326
$279$		0			0
$280$	−3.94462	−	9.50923i	−0.235736	−	0.568285i
$281$		−	4.74847i		−	0.283270i	−0.989919	−	0.141635i	$-0.954764\pi$
$281$		−	4.74847i		−	0.283270i	0.989919	−	0.141635i	$-0.0452359\pi$
$282$		0			0
$283$		−	29.3853i		−	1.74677i	−0.487027	−	0.873387i	$-0.661919\pi$
$283$		−	29.3853i		−	1.74677i	0.487027	−	0.873387i	$-0.338081\pi$
$284$			1.94304i			0.115298i
$285$		0			0
$286$			11.2362i			0.664412i
$287$	25.6458	−	10.6384i	1.51382	−	0.627965i
$288$		0			0
$289$	−16.4493			−0.967604
$290$	−11.2362			−0.659814
$291$		0			0
$292$			4.85486i			0.284109i
$293$	6.62413			0.386986			0.193493	−	0.981102i	$-0.438018\pi$
$293$	6.62413			0.386986			0.193493	+	0.981102i	$0.438018\pi$
$294$		0			0
$295$	0.0822372			0.00478803
$296$			3.00158i			0.174463i
$297$		0			0
$298$	−11.0016			−0.637304
$299$	−17.8119			−1.03009
$300$		0			0
$301$	2.30464	−	0.956010i	0.132837	−	0.0551035i
$302$			1.43998i			0.0828613i
$303$		0			0
$304$			1.78474i			0.102362i
$305$			9.60761i			0.550130i
$306$		0			0
$307$			21.7242i			1.23987i	0.784655	+	0.619933i	$0.212840\pi$
$307$			21.7242i			1.23987i	−0.784655	+	0.619933i	$0.787160\pi$
$308$	3.99886	+	9.63998i	0.227856	+	0.549289i
$309$		0			0
$310$	13.6646			0.776095
$311$	6.29800			0.357127			0.178563	−	0.983928i	$-0.442855\pi$
$311$	6.29800			0.357127			0.178563	+	0.983928i	$0.442855\pi$
$312$		0			0
$313$			22.2191i			1.25590i	0.778256	+	0.627948i	$0.216105\pi$
$313$			22.2191i			1.25590i	−0.778256	+	0.627948i	$0.783895\pi$
$314$	16.6071			0.937192
$315$		0			0
$316$	−3.63613			−0.204548
$317$			15.6614i			0.879632i	0.898088	+	0.439816i	$0.144956\pi$
$317$			15.6614i			0.879632i	−0.898088	+	0.439816i	$0.855044\pi$
$318$		0			0
$319$	11.3907			0.637758
$320$	−3.89111			−0.217520
$321$		0			0
$322$	−15.2815	+	6.33909i	−0.851607	+	0.353264i
$323$		−	1.32448i		−	0.0736963i
$324$		0			0
$325$			28.8859i			1.60230i
$326$			12.3955i			0.686521i
$327$		0			0
$328$		−	10.4941i		−	0.579440i
$329$	−5.34039	+	2.21530i	−0.294425	+	0.122133i
$330$		0			0
$331$	1.27226			0.0699296			0.0349648	−	0.999389i	$-0.488868\pi$
$331$	1.27226			0.0699296			0.0349648	+	0.999389i	$0.488868\pi$
$332$	8.05995			0.442347
$333$		0			0
$334$			11.7217i			0.641386i
$335$	52.3326			2.85924
$336$		0			0
$337$	7.56002			0.411821			0.205910	−	0.978571i	$-0.433984\pi$
$337$	7.56002			0.411821			0.205910	+	0.978571i	$0.433984\pi$
$338$		−	4.88608i		−	0.265768i
$339$		0			0
$340$	2.88766			0.156605
$341$	−13.8525			−0.750153
$342$		0			0
$343$	−7.06081	+	17.1215i	−0.381248	+	0.924473i
$344$		−	0.943042i		−	0.0508454i
$345$		0			0
$346$			16.7710i			0.901613i
$347$		−	22.1091i		−	1.18688i	−0.804879	−	0.593439i	$-0.797770\pi$
$347$		−	22.1091i		−	1.18688i	0.804879	−	0.593439i	$-0.202230\pi$
$348$		0			0
$349$			14.7435i			0.789200i	0.918853	+	0.394600i	$0.129117\pi$
$349$			14.7435i			0.789200i	−0.918853	+	0.394600i	$0.870883\pi$
$350$	10.2802	+	24.7823i	0.549501	+	1.32467i
$351$		0			0
$352$	3.94462			0.210249
$353$	17.2776			0.919595			0.459798	−	0.888024i	$-0.347922\pi$
$353$	17.2776			0.919595			0.459798	+	0.888024i	$0.347922\pi$
$354$		0			0
$355$		−	7.56060i		−	0.401275i
$356$	−9.26646			−0.491122
$357$		0			0
$358$	−5.77532			−0.305235
$359$			10.9129i			0.575963i	0.957636	+	0.287982i	$0.0929842\pi$
$359$			10.9129i			0.575963i	−0.957636	+	0.287982i	$0.907016\pi$
$360$		0			0
$361$	15.8147			0.832353
$362$	−5.53310			−0.290813
$363$		0			0
$364$	2.88766	+	6.96124i	0.151355	+	0.364868i
$365$		−	18.8908i		−	0.988791i
$366$		0			0
$367$		−	35.7272i		−	1.86494i	−0.361242	−	0.932472i	$-0.617647\pi$
$367$		−	35.7272i		−	1.86494i	0.361242	−	0.932472i	$-0.382353\pi$
$368$			6.25311i			0.325966i
$369$		0			0
$370$		−	11.6795i		−	0.607187i
$371$		0			0
$372$		0			0
$373$	−32.0600			−1.66001			−0.830003	−	0.557760i	$-0.811661\pi$
$373$	−32.0600			−1.66001			−0.830003	+	0.557760i	$0.811661\pi$
$374$	−2.92737			−0.151371
$375$		0			0
$376$			2.18525i			0.112696i
$377$	8.22549			0.423634
$378$		0			0
$379$	34.8891			1.79214			0.896068	−	0.443918i	$-0.146412\pi$
$379$	34.8891			1.79214			0.896068	+	0.443918i	$0.146412\pi$
$380$		−	6.94462i		−	0.356251i
$381$		0			0
$382$	−6.21372			−0.317922
$383$	−17.5342			−0.895957			−0.447978	−	0.894044i	$-0.647856\pi$
$383$	−17.5342			−0.895957			−0.447978	+	0.894044i	$0.647856\pi$
$384$		0			0
$385$	−15.5600	−	37.5103i	−0.793012	−	1.91170i
$386$			7.80542i			0.397286i
$387$		0			0
$388$			18.8196i			0.955421i
$389$		−	7.62171i		−	0.386436i	−0.981156	−	0.193218i	$-0.938108\pi$
$389$		−	7.62171i		−	0.386436i	0.981156	−	0.193218i	$-0.0618925\pi$
$390$		0			0
$391$		−	4.64054i		−	0.234682i
$392$	4.95487	+	4.94462i	0.250259	+	0.249741i
$393$		0			0
$394$	12.7737			0.643532
$395$	14.1486			0.711893
$396$		0			0
$397$			37.6469i			1.88944i	0.327873	+	0.944722i	$0.393668\pi$
$397$			37.6469i			1.88944i	−0.327873	+	0.944722i	$0.606332\pi$
$398$	−1.81201			−0.0908278
$399$		0			0
$400$	10.1408			0.507039
$401$		−	21.4415i		−	1.07074i	−0.844619	−	0.535368i	$-0.820173\pi$
$401$		−	21.4415i		−	1.07074i	0.844619	−	0.535368i	$-0.179827\pi$
$402$		0			0
$403$	−10.0032			−0.498293
$404$	−8.28158			−0.412024
$405$		0			0
$406$	7.05696	−	2.92737i	0.350231	−	0.145283i
$407$			11.8401i			0.586891i
$408$		0			0
$409$		−	29.5703i		−	1.46216i	−0.682293	−	0.731079i	$-0.739017\pi$
$409$		−	29.5703i		−	1.46216i	0.682293	−	0.731079i	$-0.260983\pi$
$410$			40.8338i			2.01664i
$411$		0			0
$412$			17.0487i			0.839929i
$413$	−0.0516494	+	0.0214252i	−0.00254150	+	0.00105427i
$414$		0			0
$415$	−31.3622			−1.53951
$416$	2.84849			0.139659
$417$		0			0
$418$			7.04011i			0.344343i
$419$	7.12962			0.348305			0.174152	−	0.984719i	$-0.444281\pi$
$419$	7.12962			0.348305			0.174152	+	0.984719i	$0.444281\pi$
$420$		0			0
$421$	4.62014			0.225172			0.112586	−	0.993642i	$-0.464087\pi$
$421$	4.62014			0.225172			0.112586	+	0.993642i	$0.464087\pi$
$422$		−	3.77532i		−	0.183780i
$423$		0			0
$424$		0			0
$425$	−7.52564			−0.365047
$426$		0			0
$427$	−2.50307	−	6.03410i	−0.121132	−	0.292010i
$428$		−	14.3369i		−	0.693001i
$429$		0			0
$430$			3.66949i			0.176958i
$431$		−	4.00771i		−	0.193045i	−0.995331	−	0.0965223i	$-0.969228\pi$
$431$		−	4.00771i		−	0.193045i	0.995331	−	0.0965223i	$-0.0307719\pi$
$432$		0			0
$433$		−	29.4125i		−	1.41348i	−0.707475	−	0.706738i	$-0.750166\pi$
$433$		−	29.4125i		−	1.41348i	0.707475	−	0.706738i	$-0.249834\pi$
$434$	−8.58209	+	3.56002i	−0.411953	+	0.170887i
$435$		0			0
$436$	−11.2800			−0.540212
$437$	−11.1602			−0.533863
$438$		0			0
$439$		−	21.3769i		−	1.02027i	−0.860096	−	0.510133i	$-0.829596\pi$
$439$		−	21.3769i		−	1.02027i	0.860096	−	0.510133i	$-0.170404\pi$
$440$	−15.3490			−0.731733
$441$		0			0
$442$	−2.11392			−0.100549
$443$			5.83386i			0.277175i	0.990350	+	0.138587i	$0.0442562\pi$
$443$			5.83386i			0.277175i	−0.990350	+	0.138587i	$0.955744\pi$
$444$		0			0
$445$	36.0569			1.70926
$446$	−12.7782			−0.605065
$447$		0			0
$448$	2.44383	−	1.01375i	0.115460	−	0.0478952i
$449$		−	22.5823i		−	1.06573i	−0.846202	−	0.532863i	$-0.821116\pi$
$449$		−	22.5823i		−	1.06573i	0.846202	−	0.532863i	$-0.178884\pi$
$450$		0			0
$451$		−	41.3953i		−	1.94923i
$452$		−	9.83228i		−	0.462472i
$453$		0			0
$454$			19.9822i			0.937811i
$455$	−11.2362	−	27.0870i	−0.526762	−	1.26986i
$456$		0			0
$457$	39.8623			1.86468			0.932340	−	0.361584i	$-0.117764\pi$
$457$	39.8623			1.86468			0.932340	+	0.361584i	$0.117764\pi$
$458$	10.1314			0.473408
$459$		0			0
$460$		−	24.3316i		−	1.13447i
$461$	7.36507			0.343026			0.171513	−	0.985182i	$-0.445135\pi$
$461$	7.36507			0.343026			0.171513	+	0.985182i	$0.445135\pi$
$462$		0			0
$463$	28.6914			1.33340			0.666702	−	0.745325i	$-0.267706\pi$
$463$	28.6914			1.33340			0.666702	+	0.745325i	$0.267706\pi$
$464$		−	2.88766i		−	0.134056i
$465$		0			0
$466$	7.31007			0.338632
$467$	−13.6704			−0.632590			−0.316295	−	0.948661i	$-0.602439\pi$
$467$	−13.6704			−0.632590			−0.316295	+	0.948661i	$0.602439\pi$
$468$		0			0
$469$	−32.8677	+	13.6342i	−1.51769	+	0.629569i
$470$		−	8.50307i		−	0.392217i
$471$		0			0
$472$			0.0211346i			0.000972799i
$473$		−	3.71994i		−	0.171043i
$474$		0			0
$475$			18.0986i			0.830422i
$476$	−1.81361	+	0.752321i	−0.0831266	+	0.0344826i
$477$		0			0
$478$	−8.40988			−0.384659
$479$	−10.4107			−0.475679			−0.237839	−	0.971304i	$-0.576439\pi$
$479$	−10.4107			−0.475679			−0.237839	+	0.971304i	$0.576439\pi$
$480$		0			0
$481$			8.54997i			0.389845i
$482$	8.95213			0.407758
$483$		0			0
$484$	4.56002			0.207274
$485$		−	73.2292i		−	3.32517i
$486$		0			0
$487$	2.33850			0.105968			0.0529838	−	0.998595i	$-0.483127\pi$
$487$	2.33850			0.105968			0.0529838	+	0.998595i	$0.483127\pi$
$488$	−2.46911			−0.111772
$489$		0			0
$490$	−19.2800	−	19.2401i	−0.870980	−	0.869178i
$491$			33.8844i			1.52918i	0.644516	+	0.764591i	$0.277059\pi$
$491$			33.8844i			1.52918i	−0.644516	+	0.764591i	$0.722941\pi$
$492$		0			0
$493$			2.14298i			0.0965151i
$494$			5.08381i			0.228732i
$495$		0			0
$496$			3.51174i			0.157682i
$497$	1.96976	+	4.74847i	0.0883558	+	0.212998i
$498$		0			0
$499$	−16.6045			−0.743317			−0.371659	−	0.928369i	$-0.621211\pi$
$499$	−16.6045			−0.743317			−0.371659	+	0.928369i	$0.621211\pi$
$500$	−20.0033			−0.894576
$501$		0			0
$502$			12.6432i			0.564295i
$503$	−35.3661			−1.57690			−0.788449	−	0.615100i	$-0.789115\pi$
$503$	−35.3661			−1.57690			−0.788449	+	0.615100i	$0.789115\pi$
$504$		0			0
$505$	32.2246			1.43398
$506$			24.6661i			1.09654i
$507$		0			0
$508$	−2.94462			−0.130646
$509$	37.0582			1.64257			0.821287	−	0.570515i	$-0.193256\pi$
$509$	37.0582			1.64257			0.821287	+	0.570515i	$0.193256\pi$
$510$		0			0
$511$	4.92162	+	11.8645i	0.217720	+	0.524853i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$			16.3066i			0.719252i
$515$		−	66.3384i		−	2.92322i
$516$		0			0
$517$			8.61999i			0.379107i
$518$	3.04285	+	7.33535i	0.133695	+	0.322297i
$519$		0			0
$520$	−11.0838			−0.486057
$521$	1.78309			0.0781187			0.0390594	−	0.999237i	$-0.487564\pi$
$521$	1.78309			0.0781187			0.0390594	+	0.999237i	$0.487564\pi$
$522$		0			0
$523$		−	24.0538i		−	1.05180i	−0.850546	−	0.525901i	$-0.823728\pi$
$523$		−	24.0538i		−	1.05180i	0.850546	−	0.525901i	$-0.176272\pi$
$524$	−15.0651			−0.658122
$525$		0			0
$526$	23.7215			1.03431
$527$		−	2.60612i		−	0.113524i
$528$		0			0
$529$	−16.1014			−0.700060
$530$		0			0
$531$		0			0
$532$	1.80928	+	4.36160i	0.0784422	+	0.189099i
$533$		−	29.8924i		−	1.29478i
$534$		0			0
$535$			55.7866i			2.41187i
$536$			13.4493i			0.580920i
$537$		0			0
$538$			7.28288i			0.313987i
$539$	19.5451	+	19.5046i	0.841866	+	0.840124i
$540$		0			0
$541$	30.0032			1.28994			0.644968	−	0.764209i	$-0.276871\pi$
$541$	30.0032			1.28994			0.644968	+	0.764209i	$0.276871\pi$
$542$	−22.6879			−0.974530
$543$		0			0
$544$			0.742117i			0.0318180i
$545$	43.8916			1.88011
$546$		0			0
$547$	21.5632			0.921975			0.460987	−	0.887407i	$-0.347495\pi$
$547$	21.5632			0.921975			0.460987	+	0.887407i	$0.347495\pi$
$548$			15.7199i			0.671523i
$549$		0			0
$550$	40.0015			1.70567
$551$	5.15372			0.219556
$552$		0			0
$553$	−8.88608	+	3.68613i	−0.377875	+	0.156750i
$554$		−	24.1676i		−	1.02678i
$555$		0			0
$556$		−	3.30675i		−	0.140237i
$557$		−	36.9477i		−	1.56552i	−0.622321	−	0.782762i	$-0.713810\pi$
$557$		−	36.9477i		−	1.56552i	0.622321	−	0.782762i	$-0.286190\pi$
$558$		0			0
$559$		−	2.68625i		−	0.113616i
$560$	−9.50923	+	3.94462i	−0.401838	+	0.166691i
$561$		0			0
$562$	−4.74847			−0.200302
$563$	−15.1684			−0.639273			−0.319637	−	0.947540i	$-0.603561\pi$
$563$	−15.1684			−0.639273			−0.319637	+	0.947540i	$0.603561\pi$
$564$		0			0
$565$			38.2585i			1.60955i
$566$	−29.3853			−1.23516
$567$		0			0
$568$	1.94304			0.0815282
$569$		−	36.7292i		−	1.53977i	−0.638183	−	0.769885i	$-0.720314\pi$
$569$		−	36.7292i		−	1.53977i	0.638183	−	0.769885i	$-0.279686\pi$
$570$		0			0
$571$	11.2277			0.469866			0.234933	−	0.972012i	$-0.424513\pi$
$571$	11.2277			0.469866			0.234933	+	0.972012i	$0.424513\pi$
$572$	11.2362			0.469810
$573$		0			0
$574$	−10.6384	−	25.6458i	−0.444038	−	1.07044i
$575$			63.4114i			2.64444i
$576$		0			0
$577$			36.5515i			1.52166i	0.648952	+	0.760829i	$0.275208\pi$
$577$			36.5515i			1.52166i	−0.648952	+	0.760829i	$0.724792\pi$
$578$			16.4493i			0.684199i
$579$		0			0
$580$			11.2362i			0.466559i
$581$	19.6972	−	8.17078i	0.817176	−	0.338981i
$582$		0			0
$583$		0			0
$584$	4.85486			0.200896
$585$		0			0
$586$		−	6.62413i		−	0.273640i
$587$	−9.99475			−0.412528			−0.206264	−	0.978496i	$-0.566131\pi$
$587$	−9.99475			−0.412528			−0.206264	+	0.978496i	$0.566131\pi$
$588$		0			0
$589$	−6.26753			−0.258249
$590$		−	0.0822372i		−	0.00338565i
$591$		0			0
$592$	3.00158			0.123364
$593$	7.78223			0.319578			0.159789	−	0.987151i	$-0.448919\pi$
$593$	7.78223			0.319578			0.159789	+	0.987151i	$0.448919\pi$
$594$		0			0
$595$	7.05696	−	2.92737i	0.289307	−	0.120010i
$596$			11.0016i			0.450642i
$597$		0			0
$598$			17.8119i			0.728385i
$599$		−	25.0124i		−	1.02198i	−0.859586	−	0.510990i	$-0.829279\pi$
$599$		−	25.0124i		−	1.02198i	0.859586	−	0.510990i	$-0.170721\pi$
$600$		0			0
$601$			30.0136i			1.22428i	0.790750	+	0.612139i	$0.209691\pi$
$601$			30.0136i			1.22428i	−0.790750	+	0.612139i	$0.790309\pi$
$602$	−0.956010	−	2.30464i	−0.0389640	−	0.0939300i
$603$		0			0
$604$	1.43998			0.0585918
$605$	−17.7436			−0.721379
$606$		0			0
$607$		−	4.58280i		−	0.186010i	−0.995666	−	0.0930050i	$-0.970353\pi$
$607$		−	4.58280i		−	0.186010i	0.995666	−	0.0930050i	$-0.0296473\pi$
$608$	1.78474			0.0723807
$609$		0			0
$610$	9.60761			0.389001
$611$			6.22468i			0.251823i
$612$		0			0
$613$	30.5522			1.23399			0.616996	−	0.786966i	$-0.288349\pi$
$613$	30.5522			1.23399			0.616996	+	0.786966i	$0.288349\pi$
$614$	21.7242			0.876717
$615$		0			0
$616$	9.63998	−	3.99886i	0.388406	−	0.161119i
$617$			32.6185i			1.31317i	0.754252	+	0.656585i	$0.228000\pi$
$617$			32.6185i			1.31317i	−0.754252	+	0.656585i	$0.772000\pi$
$618$		0			0
$619$		−	20.0045i		−	0.804049i	−0.915629	−	0.402024i	$-0.868307\pi$
$619$		−	20.0045i		−	0.804049i	0.915629	−	0.402024i	$-0.131693\pi$
$620$		−	13.6646i		−	0.548782i
$621$		0			0
$622$		−	6.29800i		−	0.252527i
$623$	−22.6457	+	9.39388i	−0.907280	+	0.376358i
$624$		0			0
$625$	27.1314			1.08526
$626$	22.2191			0.888052
$627$		0			0
$628$		−	16.6071i		−	0.662695i
$629$	−2.22752			−0.0888171
$630$		0			0
$631$	6.09634			0.242692			0.121346	−	0.992610i	$-0.461279\pi$
$631$	6.09634			0.242692			0.121346	+	0.992610i	$0.461279\pi$
$632$			3.63613i			0.144637i
$633$		0			0
$634$	15.6614			0.621994
$635$	11.4579			0.454691
$636$		0			0
$637$	14.1139	+	14.0847i	0.559214	+	0.558057i
$638$		−	11.3907i		−	0.450963i
$639$		0			0
$640$			3.89111i			0.153810i
$641$			33.4415i			1.32086i	0.750888	+	0.660429i	$0.229626\pi$
$641$			33.4415i			1.32086i	−0.750888	+	0.660429i	$0.770374\pi$
$642$		0			0
$643$			19.1705i			0.756012i	0.925803	+	0.378006i	$0.123390\pi$
$643$			19.1705i			0.756012i	−0.925803	+	0.378006i	$0.876610\pi$
$644$	6.33909	+	15.2815i	0.249795	+	0.602177i
$645$		0			0
$646$	−1.32448			−0.0521111
$647$	44.6049			1.75360			0.876800	−	0.480854i	$-0.159673\pi$
$647$	44.6049			1.75360			0.876800	+	0.480854i	$0.159673\pi$
$648$		0			0
$649$			0.0833680i			0.00327248i
$650$	28.8859			1.13300
$651$		0			0
$652$	12.3955			0.485444
$653$			0.652123i			0.0255195i	0.999919	+	0.0127598i	$0.00406167\pi$
$653$			0.652123i			0.0255195i	−0.999919	+	0.0127598i	$0.995938\pi$
$654$		0			0
$655$	58.6200			2.29047
$656$	−10.4941			−0.409726
$657$		0			0
$658$	2.21530	+	5.34039i	0.0863614	+	0.208190i
$659$			30.3384i			1.18182i	0.806739	+	0.590908i	$0.201231\pi$
$659$			30.3384i			1.18182i	−0.806739	+	0.590908i	$0.798769\pi$
$660$		0			0
$661$		−	12.8176i		−	0.498548i	−0.968433	−	0.249274i	$-0.919808\pi$
$661$		−	12.8176i		−	0.498548i	0.968433	−	0.249274i	$-0.0801919\pi$
$662$		−	1.27226i		−	0.0494477i
$663$		0			0
$664$		−	8.05995i		−	0.312787i
$665$	−7.04011	−	16.9715i	−0.273004	−	0.658126i
$666$		0			0
$667$	18.0569			0.699165
$668$	11.7217			0.453528
$669$		0			0
$670$		−	52.3326i		−	2.02179i
$671$	−9.73972			−0.375998
$672$		0			0
$673$	−22.4493			−0.865355			−0.432678	−	0.901549i	$-0.642431\pi$
$673$	−22.4493			−0.865355			−0.432678	+	0.901549i	$0.642431\pi$
$674$		−	7.56002i		−	0.291201i
$675$		0			0
$676$	−4.88608			−0.187926
$677$	51.1807			1.96703			0.983516	−	0.180820i	$-0.0578752\pi$
$677$	51.1807			1.96703			0.983516	+	0.180820i	$0.0578752\pi$
$678$		0			0
$679$	19.0784	+	45.9919i	0.732161	+	1.76501i
$680$		−	2.88766i		−	0.110737i
$681$		0			0
$682$			13.8525i			0.530438i
$683$		−	14.5616i		−	0.557184i	−0.960410	−	0.278592i	$-0.910132\pi$
$683$		−	14.5616i		−	0.557184i	0.960410	−	0.278592i	$-0.0898677\pi$
$684$		0			0
$685$		−	61.1681i		−	2.33711i
$686$	17.1215	+	7.06081i	0.653701	+	0.269583i
$687$		0			0
$688$	−0.943042			−0.0359532
$689$		0			0
$690$		0			0
$691$			24.4515i			0.930180i	0.885263	+	0.465090i	$0.153978\pi$
$691$			24.4515i			0.930180i	−0.885263	+	0.465090i	$0.846022\pi$
$692$	16.7710			0.637536
$693$		0			0
$694$	−22.1091			−0.839250
$695$			12.8669i			0.488071i
$696$		0			0
$697$	7.78785			0.294986
$698$	14.7435			0.558048
$699$		0			0
$700$	24.7823	−	10.2802i	0.936684	−	0.388556i
$701$		−	2.21697i		−	0.0837337i	−0.999123	−	0.0418669i	$-0.986669\pi$
$701$		−	2.21697i		−	0.0837337i	0.999123	−	0.0418669i	$-0.0133305\pi$
$702$		0			0
$703$			5.35703i			0.202044i
$704$		−	3.94462i		−	0.148668i
$705$		0			0
$706$		−	17.2776i		−	0.650252i
$707$	−20.2388	+	8.39546i	−0.761158	+	0.315744i
$708$		0			0
$709$	−24.3923			−0.916072			−0.458036	−	0.888934i	$-0.651447\pi$
$709$	−24.3923			−0.916072			−0.458036	+	0.888934i	$0.651447\pi$
$710$	−7.56060			−0.283744
$711$		0			0
$712$			9.26646i			0.347275i
$713$	−21.9593			−0.822381
$714$		0			0
$715$	−43.7214			−1.63509
$716$			5.77532i			0.215834i
$717$		0			0
$718$	10.9129			0.407267
$719$	2.22752			0.0830725			0.0415363	−	0.999137i	$-0.486775\pi$
$719$	2.22752			0.0830725			0.0415363	+	0.999137i	$0.486775\pi$
$720$		0			0
$721$	17.2831	+	41.6641i	0.643657	+	1.55165i
$722$		−	15.8147i		−	0.588563i
$723$		0			0
$724$			5.53310i			0.205636i
$725$		−	29.2831i		−	1.08755i
$726$		0			0
$727$		−	12.1105i		−	0.449152i	−0.974457	−	0.224576i	$-0.927900\pi$
$727$		−	12.1105i		−	0.449152i	0.974457	−	0.224576i	$-0.0720997\pi$
$728$	6.96124	−	2.88766i	0.258001	−	0.107024i
$729$		0			0
$730$	−18.8908			−0.699180
$731$	0.699848			0.0258848
$732$		0			0
$733$			15.6661i			0.578641i	0.957232	+	0.289321i	$0.0934293\pi$
$733$			15.6661i			0.578641i	−0.957232	+	0.289321i	$0.906571\pi$
$734$	−35.7272			−1.31871
$735$		0			0
$736$	6.25311			0.230493
$737$			53.0522i			1.95420i
$738$		0			0
$739$	−8.10454			−0.298130			−0.149065	−	0.988827i	$-0.547626\pi$
$739$	−8.10454			−0.298130			−0.149065	+	0.988827i	$0.547626\pi$
$740$	−11.6795			−0.429346
$741$		0			0
$742$		0			0
$743$			12.1739i			0.446618i	0.974748	+	0.223309i	$0.0716860\pi$
$743$			12.1739i			0.446618i	−0.974748	+	0.223309i	$0.928314\pi$
$744$		0			0
$745$		−	42.8084i		−	1.56838i
$746$			32.0600i			1.17380i
$747$		0			0
$748$			2.92737i			0.107035i
$749$	−14.5341	−	35.0370i	−0.531063	−	1.28022i
$750$		0			0
$751$	34.6123			1.26302			0.631511	−	0.775367i	$-0.282435\pi$
$751$	34.6123			1.26302			0.631511	+	0.775367i	$0.282435\pi$
$752$	2.18525			0.0796879
$753$		0			0
$754$		−	8.22549i		−	0.299555i
$755$	−5.60311			−0.203918
$756$		0			0
$757$	−39.0553			−1.41949			−0.709744	−	0.704459i	$-0.751190\pi$
$757$	−39.0553			−1.41949			−0.709744	+	0.704459i	$0.751190\pi$
$758$		−	34.8891i		−	1.26723i
$759$		0			0
$760$	−6.94462			−0.251908
$761$	10.2252			0.370665			0.185332	−	0.982676i	$-0.440664\pi$
$761$	10.2252			0.370665			0.185332	+	0.982676i	$0.440664\pi$
$762$		0			0
$763$	−27.5663	+	11.4351i	−0.997968	+	0.413977i
$764$			6.21372i			0.224805i
$765$		0			0
$766$			17.5342i			0.633537i
$767$			0.0602018i			0.00217376i
$768$		0			0
$769$		−	30.8011i		−	1.11072i	−0.831611	−	0.555359i	$-0.812581\pi$
$769$		−	30.8011i		−	1.11072i	0.831611	−	0.555359i	$-0.187419\pi$
$770$	−37.5103	+	15.5600i	−1.35178	+	0.560744i
$771$		0			0
$772$	7.80542			0.280923
$773$	35.7833			1.28704			0.643518	−	0.765431i	$-0.277474\pi$
$773$	35.7833			1.28704			0.643518	+	0.765431i	$0.277474\pi$
$774$		0			0
$775$			35.6117i			1.27921i
$776$	18.8196			0.675584
$777$		0			0
$778$	−7.62171			−0.273252
$779$		−	18.7292i		−	0.671044i
$780$		0			0
$781$	7.66456			0.274260
$782$	−4.64054			−0.165945
$783$		0			0
$784$	4.94462	−	4.95487i	0.176594	−	0.176960i
$785$			64.6200i			2.30639i
$786$		0			0
$787$			15.3413i			0.546857i	0.961892	+	0.273429i	$0.0881578\pi$
$787$			15.3413i			0.546857i	−0.961892	+	0.273429i	$0.911842\pi$
$788$		−	12.7737i		−	0.455046i
$789$		0			0
$790$		−	14.1486i		−	0.503384i
$791$	−9.96748	−	24.0284i	−0.354403	−	0.854353i
$792$		0			0
$793$	−7.03326			−0.249758
$794$	37.6469			1.33604
$795$		0			0
$796$			1.81201i			0.0642250i
$797$	−35.0400			−1.24118			−0.620590	−	0.784135i	$-0.713107\pi$
$797$	−35.0400			−1.24118			−0.620590	+	0.784135i	$0.713107\pi$
$798$		0			0
$799$	−1.62171			−0.0573721
$800$		−	10.1408i		−	0.358530i
$801$		0			0
$802$	−21.4415			−0.757124
$803$	19.1506			0.675809
$804$		0			0
$805$	−24.6661	−	59.4622i	−0.869367	−	2.09577i
$806$			10.0032i			0.352346i
$807$		0			0
$808$			8.28158i			0.291345i
$809$			27.2925i			0.959553i	0.877391	+	0.479777i	$0.159282\pi$
$809$			27.2925i			0.959553i	−0.877391	+	0.479777i	$0.840718\pi$
$810$		0			0
$811$			27.7628i			0.974883i	0.873156	+	0.487442i	$0.162070\pi$
$811$			27.7628i			0.974883i	−0.873156	+	0.487442i	$0.837930\pi$
$812$	−2.92737	−	7.05696i	−0.102731	−	0.247651i
$813$		0			0
$814$	11.8401			0.414995
$815$	−48.2322			−1.68950
$816$		0			0
$817$		−	1.68308i		−	0.0588836i
$818$	−29.5703			−1.03390
$819$		0			0
$820$	40.8338			1.42598
$821$		−	44.4523i		−	1.55140i	−0.631104	−	0.775698i	$-0.717398\pi$
$821$		−	44.4523i		−	1.55140i	0.631104	−	0.775698i	$-0.282602\pi$
$822$		0			0
$823$	−51.1153			−1.78177			−0.890884	−	0.454231i	$-0.849914\pi$
$823$	−51.1153			−1.78177			−0.890884	+	0.454231i	$0.849914\pi$
$824$	17.0487			0.593919
$825$		0			0
$826$	0.0214252	+	0.0516494i	0.000745479	+	0.00179711i
$827$		−	14.5414i		−	0.505653i	−0.967512	−	0.252826i	$-0.918640\pi$
$827$		−	14.5414i		−	0.505653i	0.967512	−	0.252826i	$-0.0813601\pi$
$828$		0			0
$829$		−	27.9681i		−	0.971373i	−0.874133	−	0.485686i	$-0.838570\pi$
$829$		−	27.9681i		−	0.971373i	0.874133	−	0.485686i	$-0.161430\pi$
$830$			31.3622i			1.08860i
$831$		0			0
$832$		−	2.84849i		−	0.0987537i
$833$	−3.66949	+	3.67709i	−0.127140	+	0.127404i
$834$		0			0
$835$	−45.6107			−1.57842
$836$	7.04011			0.243487
$837$		0			0
$838$		−	7.12962i		−	0.246289i
$839$	−0.998707			−0.0344792			−0.0172396	−	0.999851i	$-0.505488\pi$
$839$	−0.998707			−0.0344792			−0.0172396	+	0.999851i	$0.505488\pi$
$840$		0			0
$841$	20.6614			0.712462
$842$		−	4.62014i		−	0.159220i
$843$		0			0
$844$	−3.77532			−0.129952
$845$	19.0123			0.654044
$846$		0			0
$847$	11.1439	−	4.62273i	0.382910	−	0.158839i
$848$		0			0
$849$		0			0
$850$			7.52564i			0.258127i
$851$			18.7692i			0.643400i
$852$		0			0
$853$		−	9.80040i		−	0.335559i	−0.985825	−	0.167780i	$-0.946340\pi$
$853$		−	9.80040i		−	0.335559i	0.985825	−	0.167780i	$-0.0536597\pi$
$854$	−6.03410	+	2.50307i	−0.206483	+	0.0856531i
$855$		0			0
$856$	−14.3369			−0.490026
$857$	7.70003			0.263028			0.131514	−	0.991314i	$-0.458016\pi$
$857$	7.70003			0.263028			0.131514	+	0.991314i	$0.458016\pi$
$858$		0			0
$859$		−	18.9396i		−	0.646210i	−0.946363	−	0.323105i	$-0.895273\pi$
$859$		−	18.9396i		−	0.646210i	0.946363	−	0.323105i	$-0.104727\pi$
$860$	3.66949			0.125128
$861$		0			0
$862$	−4.00771			−0.136503
$863$			17.4540i			0.594141i	0.954856	+	0.297070i	$0.0960096\pi$
$863$			17.4540i			0.594141i	−0.954856	+	0.297070i	$0.903990\pi$
$864$		0			0
$865$	−65.2578			−2.21883
$866$	−29.4125			−0.999479
$867$		0			0
$868$	3.56002	+	8.58209i	0.120835	+	0.291295i
$869$			14.3431i			0.486558i
$870$		0			0
$871$			38.3101i			1.29809i
$872$			11.2800i			0.381988i
$873$		0			0
$874$			11.1602i			0.377498i
$875$	−48.8848	+	20.2784i	−1.65261	+	0.685535i
$876$		0			0
$877$	0.392305			0.0132472			0.00662360	−	0.999978i	$-0.497892\pi$
$877$	0.392305			0.0132472			0.00662360	+	0.999978i	$0.497892\pi$
$878$	−21.3769			−0.721436
$879$		0			0
$880$			15.3490i			0.517414i
$881$	−37.0259			−1.24744			−0.623718	−	0.781650i	$-0.714378\pi$
$881$	−37.0259			−1.24744			−0.623718	+	0.781650i	$0.714378\pi$
$882$		0			0
$883$	−29.9586			−1.00819			−0.504094	−	0.863649i	$-0.668174\pi$
$883$	−29.9586			−1.00819			−0.504094	+	0.863649i	$0.668174\pi$
$884$			2.11392i			0.0710987i
$885$		0			0
$886$	5.83386			0.195992
$887$	−28.9859			−0.973252			−0.486626	−	0.873610i	$-0.661773\pi$
$887$	−28.9859			−0.973252			−0.486626	+	0.873610i	$0.661773\pi$
$888$		0			0
$889$	−7.19615	+	2.98511i	−0.241351	+	0.100117i
$890$		−	36.0569i		−	1.20863i
$891$		0			0
$892$			12.7782i			0.427846i
$893$			3.90010i			0.130512i
$894$		0			0
$895$		−	22.4724i		−	0.751171i
$896$	−1.01375	−	2.44383i	−0.0338670	−	0.0816427i
$897$		0			0
$898$	−22.5823			−0.753582
$899$	10.1407			0.338211
$900$		0			0
$901$		0			0
$902$	−41.3953			−1.37831
$903$		0			0
$904$	−9.83228			−0.327017
$905$		−	21.5299i		−	0.715679i
$906$		0			0
$907$	−3.89546			−0.129347			−0.0646733	−	0.997906i	$-0.520601\pi$
$907$	−3.89546			−0.129347			−0.0646733	+	0.997906i	$0.520601\pi$
$908$	19.9822			0.663133
$909$		0			0
$910$	−27.0870	+	11.2362i	−0.897924	+	0.372477i
$911$			1.53308i			0.0507931i	0.999677	+	0.0253966i	$0.00808484\pi$
$911$			1.53308i			0.0507931i	−0.999677	+	0.0253966i	$0.991915\pi$
$912$		0			0
$913$		−	31.7935i		−	1.05221i
$914$		−	39.8623i		−	1.31853i
$915$		0			0
$916$		−	10.1314i		−	0.334750i
$917$	−36.8166	+	15.2723i	−1.21579	+	0.504334i
$918$		0			0
$919$	28.2531			0.931984			0.465992	−	0.884789i	$-0.345698\pi$
$919$	28.2531			0.931984			0.465992	+	0.884789i	$0.345698\pi$
$920$	−24.3316			−0.802188
$921$		0			0
$922$		−	7.36507i		−	0.242556i
$923$	5.53474			0.182178
$924$		0			0
$925$	30.4383			1.00081
$926$		−	28.6914i		−	0.942859i
$927$		0			0
$928$	−2.88766			−0.0947921
$929$	3.28726			0.107851			0.0539257	−	0.998545i	$-0.482827\pi$
$929$	3.28726			0.107851			0.0539257	+	0.998545i	$0.482827\pi$
$930$		0			0
$931$	8.84314	+	8.82485i	0.289822	+	0.289223i
$932$		−	7.31007i		−	0.239449i
$933$		0			0
$934$			13.6704i			0.447308i
$935$		−	11.3907i		−	0.372517i
$936$		0			0
$937$		−	35.5084i		−	1.16001i	−0.814613	−	0.580005i	$-0.803051\pi$
$937$		−	35.5084i		−	1.16001i	0.814613	−	0.580005i	$-0.196949\pi$
$938$	13.6342	+	32.8677i	0.445172	+	1.07317i
$939$		0			0
$940$	−8.50307			−0.277339
$941$	12.4988			0.407450			0.203725	−	0.979028i	$-0.434695\pi$
$941$	12.4988			0.407450			0.203725	+	0.979028i	$0.434695\pi$
$942$		0			0
$943$		−	65.6208i		−	2.13691i
$944$	0.0211346			0.000687873
$945$		0			0
$946$	−3.71994			−0.120946
$947$			36.1154i			1.17359i	0.809734	+	0.586796i	$0.199611\pi$
$947$			36.1154i			1.17359i	−0.809734	+	0.586796i	$0.800389\pi$
$948$		0			0
$949$	13.8290			0.448910
$950$	18.0986			0.587197
$951$		0			0
$952$	0.752321	+	1.81361i	0.0243829	+	0.0587794i
$953$			45.2925i			1.46717i	0.679599	+	0.733584i	$0.262154\pi$
$953$			45.2925i			1.46717i	−0.679599	+	0.733584i	$0.737846\pi$
$954$		0			0
$955$		−	24.1783i		−	0.782392i
$956$			8.40988i			0.271995i
$957$		0			0
$958$			10.4107i			0.336356i
$959$	15.9361	+	38.4169i	0.514604	+	1.24055i
$960$		0			0
$961$	18.6677			0.602184
$962$	8.54997			0.275662
$963$		0			0
$964$		−	8.95213i		−	0.288329i
$965$	−30.3718			−0.977703
$966$		0			0
$967$	−23.9999			−0.771785			−0.385893	−	0.922544i	$-0.626106\pi$
$967$	−23.9999			−0.771785			−0.385893	+	0.922544i	$0.626106\pi$
$968$		−	4.56002i		−	0.146565i
$969$		0			0
$970$	−73.2292			−2.35125
$971$	33.3626			1.07066			0.535328	−	0.844644i	$-0.320188\pi$
$971$	33.3626			1.07066			0.535328	+	0.844644i	$0.320188\pi$
$972$		0			0
$973$	−3.35222	−	8.08113i	−0.107467	−	0.259069i
$974$		−	2.33850i		−	0.0749304i
$975$		0			0
$976$			2.46911i			0.0790344i
$977$			34.5077i			1.10400i	0.833844	+	0.552000i	$0.186135\pi$
$977$			34.5077i			1.10400i	−0.833844	+	0.552000i	$0.813865\pi$
$978$		0			0
$979$			36.5527i			1.16823i
$980$	−19.2401	+	19.2800i	−0.614602	+	0.615876i
$981$		0			0
$982$	33.8844			1.08130
$983$	−2.41302			−0.0769633			−0.0384817	−	0.999259i	$-0.512252\pi$
$983$	−2.41302			−0.0769633			−0.0384817	+	0.999259i	$0.512252\pi$
$984$		0			0
$985$			49.7041i			1.58370i
$986$	2.14298			0.0682465
$987$		0			0
$988$	5.08381			0.161738
$989$		−	5.89695i		−	0.187512i
$990$		0			0
$991$	48.5982			1.54377			0.771887	−	0.635760i	$-0.219313\pi$
$991$	48.5982			1.54377			0.771887	+	0.635760i	$0.219313\pi$
$992$	3.51174			0.111498
$993$		0			0
$994$	4.74847	−	1.96976i	0.150612	−	0.0624770i
$995$		−	7.05074i		−	0.223523i
$996$		0			0
$997$		−	44.8542i		−	1.42055i	−0.703926	−	0.710274i	$-0.748571\pi$
$997$		−	44.8542i		−	1.42055i	0.703926	−	0.710274i	$-0.251429\pi$
$998$			16.6045i			0.525605i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.d.a.1133.8		16
3.2	odd	2	inner	1134.2.d.a.1133.9		16
7.6	odd	2	inner	1134.2.d.a.1133.1		16
9.2	odd	6		378.2.m.a.125.8		16
9.4	even	3		378.2.m.a.251.5		16
9.5	odd	6		126.2.m.a.83.1	yes	16
9.7	even	3		126.2.m.a.41.4	yes	16
21.20	even	2	inner	1134.2.d.a.1133.16		16
36.7	odd	6		1008.2.cc.b.545.2		16
36.11	even	6		3024.2.cc.b.881.8		16
36.23	even	6		1008.2.cc.b.209.7		16
36.31	odd	6		3024.2.cc.b.2897.1		16
63.2	odd	6		2646.2.t.a.2285.1		16
63.4	even	3		2646.2.t.a.1979.4		16
63.5	even	6		882.2.l.a.227.5		16
63.11	odd	6		2646.2.l.b.1097.8		16
63.13	odd	6		378.2.m.a.251.8		16
63.16	even	3		882.2.t.b.815.6		16
63.20	even	6		378.2.m.a.125.5		16
63.23	odd	6		882.2.l.a.227.8		16
63.25	even	3		882.2.l.a.509.1		16
63.31	odd	6		2646.2.t.a.1979.1		16
63.32	odd	6		882.2.t.b.803.7		16
63.34	odd	6		126.2.m.a.41.1	✓	16
63.38	even	6		2646.2.l.b.1097.5		16
63.40	odd	6		2646.2.l.b.521.4		16
63.41	even	6		126.2.m.a.83.4	yes	16
63.47	even	6		2646.2.t.a.2285.4		16
63.52	odd	6		882.2.l.a.509.4		16
63.58	even	3		2646.2.l.b.521.1		16
63.59	even	6		882.2.t.b.803.6		16
63.61	odd	6		882.2.t.b.815.7		16
252.83	odd	6		3024.2.cc.b.881.1		16
252.139	even	6		3024.2.cc.b.2897.8		16
252.167	odd	6		1008.2.cc.b.209.2		16
252.223	even	6		1008.2.cc.b.545.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.1	✓	16	63.34	odd	6
126.2.m.a.41.4	yes	16	9.7	even	3
126.2.m.a.83.1	yes	16	9.5	odd	6
126.2.m.a.83.4	yes	16	63.41	even	6
378.2.m.a.125.5		16	63.20	even	6
378.2.m.a.125.8		16	9.2	odd	6
378.2.m.a.251.5		16	9.4	even	3
378.2.m.a.251.8		16	63.13	odd	6
882.2.l.a.227.5		16	63.5	even	6
882.2.l.a.227.8		16	63.23	odd	6
882.2.l.a.509.1		16	63.25	even	3
882.2.l.a.509.4		16	63.52	odd	6
882.2.t.b.803.6		16	63.59	even	6
882.2.t.b.803.7		16	63.32	odd	6
882.2.t.b.815.6		16	63.16	even	3
882.2.t.b.815.7		16	63.61	odd	6
1008.2.cc.b.209.2		16	252.167	odd	6
1008.2.cc.b.209.7		16	36.23	even	6
1008.2.cc.b.545.2		16	36.7	odd	6
1008.2.cc.b.545.7		16	252.223	even	6
1134.2.d.a.1133.1		16	7.6	odd	2	inner
1134.2.d.a.1133.8		16	1.1	even	1	trivial
1134.2.d.a.1133.9		16	3.2	odd	2	inner
1134.2.d.a.1133.16		16	21.20	even	2	inner
2646.2.l.b.521.1		16	63.58	even	3
2646.2.l.b.521.4		16	63.40	odd	6
2646.2.l.b.1097.5		16	63.38	even	6
2646.2.l.b.1097.8		16	63.11	odd	6
2646.2.t.a.1979.1		16	63.31	odd	6
2646.2.t.a.1979.4		16	63.4	even	3
2646.2.t.a.2285.1		16	63.2	odd	6
2646.2.t.a.2285.4		16	63.47	even	6
3024.2.cc.b.881.1		16	252.83	odd	6
3024.2.cc.b.881.8		16	36.11	even	6
3024.2.cc.b.2897.1		16	36.31	odd	6
3024.2.cc.b.2897.8		16	252.139	even	6

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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +3.89111 q^{5} +(-2.44383 + 1.01375i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +3.89111 q^{5} +(-2.44383 + 1.01375i) q^{7} +1.00000i q^{8} -3.89111i q^{10} +3.94462i q^{11} +2.84849i q^{13} +(1.01375 + 2.44383i) q^{14} +1.00000 q^{16} -0.742117 q^{17} +1.78474i q^{19} -3.89111 q^{20} +3.94462 q^{22} +6.25311i q^{23} +10.1408 q^{25} +2.84849 q^{26} +(2.44383 - 1.01375i) q^{28} -2.88766i q^{29} +3.51174i q^{31} -1.00000i q^{32} +0.742117i q^{34} +(-9.50923 + 3.94462i) q^{35} +3.00158 q^{37} +1.78474 q^{38} +3.89111i q^{40} -10.4941 q^{41} -0.943042 q^{43} -3.94462i q^{44} +6.25311 q^{46} +2.18525 q^{47} +(4.94462 - 4.95487i) q^{49} -10.1408i q^{50} -2.84849i q^{52} +15.3490i q^{55} +(-1.01375 - 2.44383i) q^{56} -2.88766 q^{58} +0.0211346 q^{59} +2.46911i q^{61} +3.51174 q^{62} -1.00000 q^{64} +11.0838i q^{65} +13.4493 q^{67} +0.742117 q^{68} +(3.94462 + 9.50923i) q^{70} -1.94304i q^{71} -4.85486i q^{73} -3.00158i q^{74} -1.78474i q^{76} +(-3.99886 - 9.63998i) q^{77} +3.63613 q^{79} +3.89111 q^{80} +10.4941i q^{82} -8.05995 q^{83} -2.88766 q^{85} +0.943042i q^{86} -3.94462 q^{88} +9.26646 q^{89} +(-2.88766 - 6.96124i) q^{91} -6.25311i q^{92} -2.18525i q^{94} +6.94462i q^{95} -18.8196i q^{97} +(-4.95487 - 4.94462i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 4 q^{7}+O(q^{10}) \) 16 * q - 16 * q^4 - 4 * q^7	\( 16 q - 16 q^{4} - 4 q^{7} + 16 q^{16} + 16 q^{25} + 4 q^{28} - 8 q^{37} - 8 q^{43} + 24 q^{46} + 16 q^{49} + 24 q^{58} - 16 q^{64} + 56 q^{67} + 8 q^{79} + 24 q^{85} + 24 q^{91}+O(q^{100}) \) 16 * q - 16 * q^4 - 4 * q^7 + 16 * q^16 + 16 * q^25 + 4 * q^28 - 8 * q^37 - 8 * q^43 + 24 * q^46 + 16 * q^49 + 24 * q^58 - 16 * q^64 + 56 * q^67 + 8 * q^79 + 24 * q^85 + 24 * q^91

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