LMFDB - Embedded newform 1305.2.c.k.784.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1305,2,Mod(784,1305)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1305, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1305.784");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1305 = 3^{2} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1305.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.4204774638$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 20x^{10} + 148x^{8} + 502x^{6} + 792x^{4} + 496x^{2} + 45 $ x^12 + 20x^10 + 148x^8 + 502x^6 + 792x^4 + 496*x^2 + 45
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			784.9
Root			$1.35513i$ of defining polynomial
Character	$\chi$	$=$	1305.784
Dual form			1305.2.c.k.784.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.35513i q^{2} +0.163621 q^{4} +(-1.94590 + 1.10158i) q^{5} -1.26969i q^{7} +2.93199i q^{8} +(-1.49278 - 2.63695i) q^{10} +0.474782 q^{11} +0.407685i q^{13} +1.72060 q^{14} -3.64599 q^{16} +2.97132i q^{17} -5.80491 q^{19} +(-0.318389 + 0.180241i) q^{20} +0.643392i q^{22} +3.06516i q^{23} +(2.57305 - 4.28712i) q^{25} -0.552466 q^{26} -0.207747i q^{28} -1.00000 q^{29} -4.49210 q^{31} +0.923188i q^{32} -4.02653 q^{34} +(1.39866 + 2.47069i) q^{35} +7.20325i q^{37} -7.86641i q^{38} +(-3.22981 - 5.70536i) q^{40} -12.0668 q^{41} +1.03847i q^{43} +0.0776841 q^{44} -4.15369 q^{46} +2.97132i q^{47} +5.38789 q^{49} +(5.80961 + 3.48682i) q^{50} +0.0667056i q^{52} -7.87199i q^{53} +(-0.923879 + 0.523010i) q^{55} +3.72271 q^{56} -1.35513i q^{58} -4.45891 q^{59} -1.71609 q^{61} -6.08739i q^{62} -8.54301 q^{64} +(-0.449097 - 0.793314i) q^{65} -15.7754i q^{67} +0.486169i q^{68} +(-3.34811 + 1.89537i) q^{70} -9.00806 q^{71} +0.677990i q^{73} -9.76134 q^{74} -0.949802 q^{76} -0.602826i q^{77} -1.63957 q^{79} +(7.09473 - 4.01634i) q^{80} -16.3521i q^{82} +15.5423i q^{83} +(-3.27314 - 5.78189i) q^{85} -1.40726 q^{86} +1.39206i q^{88} +13.4175 q^{89} +0.517633 q^{91} +0.501523i q^{92} -4.02653 q^{94} +(11.2958 - 6.39456i) q^{95} +7.10733i q^{97} +7.30129i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 16 q^{4} - 10 q^{10} - 12 q^{11} + 16 q^{14} + 16 q^{16} + 20 q^{19} + 14 q^{20} + 8 q^{25} - 56 q^{26} - 12 q^{29} - 16 q^{31} - 4 q^{34} - 16 q^{35} + 16 q^{40} - 32 q^{41} + 68 q^{44} + 20 q^{46}+ \cdots - 8 q^{95}+O(q^{100}) $ 12 * q - 16 * q^4 - 10 * q^10 - 12 * q^11 + 16 * q^14 + 16 * q^16 + 20 * q^19 + 14 * q^20 + 8 * q^25 - 56 * q^26 - 12 * q^29 - 16 * q^31 - 4 * q^34 - 16 * q^35 + 16 * q^40 - 32 * q^41 + 68 * q^44 + 20 * q^46 + 4 * q^49 - 8 * q^50 + 4 * q^55 - 76 * q^56 + 44 * q^59 - 52 * q^61 - 36 * q^64 - 8 * q^65 - 30 * q^70 - 20 * q^71 + 20 * q^74 - 28 * q^76 + 4 * q^79 + 34 * q^80 + 20 * q^85 - 36 * q^86 + 68 * q^89 + 48 * q^91 - 4 * q^94 - 8 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1305\mathbb{Z}\right)^\times$.

$n$	$146$	$262$	$901$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$			1.35513i			0.958222i	0.877754	+	0.479111i	$0.159041\pi$
$2$			1.35513i			0.958222i	−0.877754	+	0.479111i	$0.840959\pi$
$3$		0			0
$3$		0			0
$4$	0.163621			0.0818103
$5$	−1.94590	+	1.10158i	−0.870233	+	0.492640i
$5$	−1.94590	+	1.10158i	−0.870233	+	0.492640i
$6$		0			0
$7$		−	1.26969i		−	0.479897i	−0.970786	−	0.239949i	$-0.922869\pi$
$7$		−	1.26969i		−	0.479897i	0.970786	−	0.239949i	$-0.0771306\pi$
$8$			2.93199i			1.03661i
$9$		0			0
$10$	−1.49278	−	2.63695i	−0.472059	−	0.833877i
$11$	0.474782			0.143152			0.0715761	−	0.997435i	$-0.477197\pi$
$11$	0.474782			0.143152			0.0715761	+	0.997435i	$0.477197\pi$
$12$		0			0
$13$			0.407685i			0.113071i	0.998401	+	0.0565357i	$0.0180055\pi$
$13$			0.407685i			0.113071i	−0.998401	+	0.0565357i	$0.981995\pi$
$14$	1.72060			0.459848
$15$		0			0
$16$	−3.64599			−0.911497
$17$			2.97132i			0.720651i	0.932827	+	0.360326i	$0.117334\pi$
$17$			2.97132i			0.720651i	−0.932827	+	0.360326i	$0.882666\pi$
$18$		0			0
$19$	−5.80491			−1.33174			−0.665868	−	0.746069i	$-0.731939\pi$
$19$	−5.80491			−1.33174			−0.665868	+	0.746069i	$0.731939\pi$
$20$	−0.318389	+	0.180241i	−0.0711940	+	0.0403030i
$21$		0			0
$22$			0.643392i			0.137172i
$23$			3.06516i			0.639130i	0.947564	+	0.319565i	$0.103537\pi$
$23$			3.06516i			0.639130i	−0.947564	+	0.319565i	$0.896463\pi$
$24$		0			0
$25$	2.57305	−	4.28712i	0.514611	−	0.857424i
$26$	−0.552466			−0.108348
$27$		0			0
$28$		−	0.207747i		−	0.0392605i
$29$	−1.00000			−0.185695
$29$	−1.00000			−0.185695
$30$		0			0
$31$	−4.49210			−0.806805			−0.403403	−	0.915023i	$-0.632173\pi$
$31$	−4.49210			−0.806805			−0.403403	+	0.915023i	$0.632173\pi$
$32$			0.923188i			0.163198i
$33$		0			0
$34$	−4.02653			−0.690544
$35$	1.39866	+	2.47069i	0.236417	+	0.417623i
$36$		0			0
$37$			7.20325i			1.18421i	0.805862	+	0.592103i	$0.201702\pi$
$37$			7.20325i			1.18421i	−0.805862	+	0.592103i	$0.798298\pi$
$38$		−	7.86641i		−	1.27610i
$39$		0			0
$40$	−3.22981	−	5.70536i	−0.510678	−	0.902096i
$41$	−12.0668			−1.88452			−0.942259	−	0.334886i	$-0.891302\pi$
$41$	−12.0668			−1.88452			−0.942259	+	0.334886i	$0.891302\pi$
$42$		0			0
$43$			1.03847i			0.158365i	0.996860	+	0.0791827i	$0.0252310\pi$
$43$			1.03847i			0.158365i	−0.996860	+	0.0791827i	$0.974769\pi$
$44$	0.0776841			0.0117113
$45$		0			0
$46$	−4.15369			−0.612428
$47$			2.97132i			0.433412i	0.976237	+	0.216706i	$0.0695313\pi$
$47$			2.97132i			0.433412i	−0.976237	+	0.216706i	$0.930469\pi$
$48$		0			0
$49$	5.38789			0.769698
$50$	5.80961	+	3.48682i	0.821603	+	0.493111i
$51$		0			0
$52$			0.0667056i			0.00925040i
$53$		−	7.87199i		−	1.08130i	−0.841247	−	0.540651i	$-0.818178\pi$
$53$		−	7.87199i		−	1.08130i	0.841247	−	0.540651i	$-0.181822\pi$
$54$		0			0
$55$	−0.923879	+	0.523010i	−0.124576	+	0.0705226i
$56$	3.72271			0.497469
$57$		0			0
$58$		−	1.35513i		−	0.177937i
$59$	−4.45891			−0.580501			−0.290250	−	0.956951i	$-0.593739\pi$
$59$	−4.45891			−0.580501			−0.290250	+	0.956951i	$0.593739\pi$
$60$		0			0
$61$	−1.71609			−0.219722			−0.109861	−	0.993947i	$-0.535041\pi$
$61$	−1.71609			−0.219722			−0.109861	+	0.993947i	$0.535041\pi$
$62$		−	6.08739i		−	0.773099i
$63$		0			0
$64$	−8.54301			−1.06788
$65$	−0.449097	−	0.793314i	−0.0557036	−	0.0983985i
$66$		0			0
$67$		−	15.7754i		−	1.92727i	−0.267218	−	0.963636i	$-0.586104\pi$
$67$		−	15.7754i		−	1.92727i	0.267218	−	0.963636i	$-0.413896\pi$
$68$			0.486169i			0.0589567i
$69$		0			0
$70$	−3.34811	+	1.89537i	−0.400175	+	0.226540i
$71$	−9.00806			−1.06906			−0.534530	−	0.845149i	$-0.679511\pi$
$71$	−9.00806			−1.06906			−0.534530	+	0.845149i	$0.679511\pi$
$72$		0			0
$73$			0.677990i			0.0793527i	0.999213	+	0.0396763i	$0.0126327\pi$
$73$			0.677990i			0.0793527i	−0.999213	+	0.0396763i	$0.987367\pi$
$74$	−9.76134			−1.13473
$75$		0			0
$76$	−0.949802			−0.108950
$77$		−	0.602826i		−	0.0686984i
$78$		0			0
$79$	−1.63957			−0.184466			−0.0922329	−	0.995737i	$-0.529400\pi$
$79$	−1.63957			−0.184466			−0.0922329	+	0.995737i	$0.529400\pi$
$80$	7.09473	−	4.01634i	0.793215	−	0.449040i
$81$		0			0
$82$		−	16.3521i		−	1.80579i
$83$			15.5423i			1.70599i	0.521919	+	0.852995i	$0.325216\pi$
$83$			15.5423i			1.70599i	−0.521919	+	0.852995i	$0.674784\pi$
$84$		0			0
$85$	−3.27314	−	5.78189i	−0.355022	−	0.627135i
$86$	−1.40726			−0.151749
$87$		0			0
$88$			1.39206i			0.148394i
$89$	13.4175			1.42225			0.711126	−	0.703065i	$-0.248186\pi$
$89$	13.4175			1.42225			0.711126	+	0.703065i	$0.248186\pi$
$90$		0			0
$91$	0.517633			0.0542627
$92$			0.501523i			0.0522874i
$93$		0			0
$94$	−4.02653			−0.415305
$95$	11.2958	−	6.39456i	1.15892	−	0.656068i
$96$		0			0
$97$			7.10733i			0.721640i	0.932636	+	0.360820i	$0.117503\pi$
$97$			7.10733i			0.721640i	−0.932636	+	0.360820i	$0.882497\pi$
$98$			7.30129i			0.737542i
$99$		0			0
$100$	0.421004	−	0.701461i	0.0421004	−	0.0701461i
$101$	−4.68433			−0.466108			−0.233054	−	0.972464i	$-0.574872\pi$
$101$	−4.68433			−0.466108			−0.233054	+	0.972464i	$0.574872\pi$
$102$		0			0
$103$			15.5180i			1.52904i	0.644601	+	0.764519i	$0.277024\pi$
$103$			15.5180i			1.52904i	−0.644601	+	0.764519i	$0.722976\pi$
$104$	−1.19533			−0.117212
$105$		0			0
$106$	10.6676			1.03613
$107$			0.676108i			0.0653618i	0.999466	+	0.0326809i	$0.0104045\pi$
$107$			0.676108i			0.0653618i	−0.999466	+	0.0326809i	$0.989595\pi$
$108$		0			0
$109$	7.44734			0.713326			0.356663	−	0.934233i	$-0.383914\pi$
$109$	7.44734			0.713326			0.356663	+	0.934233i	$0.383914\pi$
$110$	−0.708746	−	1.25198i	−0.0675763	−	0.119371i
$111$		0			0
$112$			4.62927i			0.437425i
$113$		−	14.1017i		−	1.32658i	−0.748363	−	0.663290i	$-0.769160\pi$
$113$		−	14.1017i		−	1.32658i	0.748363	−	0.663290i	$-0.230840\pi$
$114$		0			0
$115$	−3.37651	−	5.96449i	−0.314861	−	0.556192i
$116$	−0.163621			−0.0151918
$117$		0			0
$118$		−	6.04241i		−	0.556249i
$119$	3.77265			0.345839
$120$		0			0
$121$	−10.7746			−0.979507
$122$		−	2.32552i		−	0.210543i
$123$		0			0
$124$	−0.735000			−0.0660050
$125$	−0.284311	+	11.1767i	−0.0254295	+	0.999677i
$126$		0			0
$127$			11.5508i			1.02497i	0.858696	+	0.512486i	$0.171275\pi$
$127$			11.5508i			1.02497i	−0.858696	+	0.512486i	$0.828725\pi$
$128$		−	9.73053i		−	0.860065i
$129$		0			0
$130$	1.07504	−	0.608585i	0.0942876	−	0.0533764i
$131$	−10.2432			−0.894954			−0.447477	−	0.894296i	$-0.647677\pi$
$131$	−10.2432			−0.894954			−0.447477	+	0.894296i	$0.647677\pi$
$132$		0			0
$133$			7.37043i			0.639097i
$134$	21.3777			1.84676
$135$		0			0
$136$	−8.71188			−0.747038
$137$			2.06577i			0.176491i	0.996099	+	0.0882455i	$0.0281260\pi$
$137$			2.06577i			0.176491i	−0.996099	+	0.0882455i	$0.971874\pi$
$138$		0			0
$139$	−3.48237			−0.295370			−0.147685	−	0.989034i	$-0.547182\pi$
$139$	−3.48237			−0.295370			−0.147685	+	0.989034i	$0.547182\pi$
$140$	0.228850	+	0.404255i	0.0193413	+	0.0341658i
$141$		0			0
$142$		−	12.2071i		−	1.02440i
$143$			0.193562i			0.0161864i
$144$		0			0
$145$	1.94590	−	1.10158i	0.161598	−	0.0914810i
$146$	−0.918765			−0.0760375
$147$		0			0
$148$			1.17860i			0.0968802i
$149$	10.8558			0.889343			0.444672	−	0.895694i	$-0.353320\pi$
$149$	10.8558			0.889343			0.444672	+	0.895694i	$0.353320\pi$
$150$		0			0
$151$	11.3555			0.924097			0.462048	−	0.886855i	$-0.347115\pi$
$151$	11.3555			0.924097			0.462048	+	0.886855i	$0.347115\pi$
$152$		−	17.0199i		−	1.38050i
$153$		0			0
$154$	0.816908			0.0658283
$155$	8.74118	−	4.94840i	0.702109	−	0.397465i
$156$		0			0
$157$		−	16.9813i		−	1.35526i	−0.735405	−	0.677628i	$-0.763008\pi$
$157$		−	16.9813i		−	1.35526i	0.735405	−	0.677628i	$-0.236992\pi$
$158$		−	2.22183i		−	0.176759i
$159$		0			0
$160$	−1.01696	−	1.79643i	−0.0803980	−	0.142020i
$161$	3.89180			0.306717
$162$		0			0
$163$			7.78532i			0.609793i	0.952385	+	0.304897i	$0.0986219\pi$
$163$			7.78532i			0.609793i	−0.952385	+	0.304897i	$0.901378\pi$
$164$	−1.97438			−0.154173
$165$		0			0
$166$	−21.0619			−1.63472
$167$		−	2.06389i		−	0.159709i	−0.996807	−	0.0798544i	$-0.974554\pi$
$167$		−	2.06389i		−	0.159709i	0.996807	−	0.0798544i	$-0.0254455\pi$
$168$		0			0
$169$	12.8338			0.987215
$170$	7.83522	−	4.43553i	0.600934	−	0.340190i
$171$		0			0
$172$			0.169915i			0.0129559i
$173$			0.522120i			0.0396960i	0.999803	+	0.0198480i	$0.00631823\pi$
$173$			0.522120i			0.0396960i	−0.999803	+	0.0198480i	$0.993682\pi$
$174$		0			0
$175$	−5.44331	−	3.26698i	−0.411476	−	0.246960i
$176$	−1.73105			−0.130483
$177$		0			0
$178$			18.1825i			1.36283i
$179$	10.4805			0.783346			0.391673	−	0.920104i	$-0.371896\pi$
$179$	10.4805			0.783346			0.391673	+	0.920104i	$0.371896\pi$
$180$		0			0
$181$	12.2724			0.912197			0.456099	−	0.889929i	$-0.349246\pi$
$181$	12.2724			0.912197			0.456099	+	0.889929i	$0.349246\pi$
$182$			0.701461i			0.0519957i
$183$		0			0
$184$	−8.98701			−0.662531
$185$	−7.93494	−	14.0168i	−0.583388	−	1.03054i
$186$		0			0
$187$			1.41073i			0.103163i
$188$			0.486169i			0.0354575i
$189$		0			0
$190$	8.66546	+	15.3072i	0.628658	+	1.11050i
$191$	−9.69478			−0.701490			−0.350745	−	0.936471i	$-0.614072\pi$
$191$	−9.69478			−0.701490			−0.350745	+	0.936471i	$0.614072\pi$
$192$		0			0
$193$			11.0857i			0.797963i	0.916959	+	0.398982i	$0.130636\pi$
$193$			11.0857i			0.797963i	−0.916959	+	0.398982i	$0.869364\pi$
$194$	−9.63136			−0.691491
$195$		0			0
$196$	0.881569			0.0629692
$197$		−	2.00431i		−	0.142801i	−0.997448	−	0.0714007i	$-0.977253\pi$
$197$		−	2.00431i		−	0.142801i	0.997448	−	0.0714007i	$-0.0227469\pi$
$198$		0			0
$199$	18.1170			1.28428			0.642140	−	0.766588i	$-0.278047\pi$
$199$	18.1170			1.28428			0.642140	+	0.766588i	$0.278047\pi$
$200$	12.5698	+	7.54416i	0.888818	+	0.533453i
$201$		0			0
$202$		−	6.34788i		−	0.446635i
$203$			1.26969i			0.0891147i
$204$		0			0
$205$	23.4808	−	13.2925i	1.63997	−	0.928390i
$206$	−21.0290			−1.46516
$207$		0			0
$208$		−	1.48641i		−	0.103064i
$209$	−2.75607			−0.190641
$210$		0			0
$211$	18.4829			1.27241			0.636206	−	0.771519i	$-0.280503\pi$
$211$	18.4829			1.27241			0.636206	+	0.771519i	$0.280503\pi$
$212$		−	1.28802i		−	0.0884615i
$213$		0			0
$214$	−0.916215			−0.0626312
$215$	−1.14396	−	2.02076i	−0.0780172	−	0.137815i
$216$		0			0
$217$			5.70357i			0.387184i
$218$			10.0921i			0.683525i
$219$		0			0
$220$	−0.151166	+	0.0855751i	−0.0101916	+	0.00576947i
$221$	−1.21136			−0.0814851
$222$		0			0
$223$			21.6226i			1.44796i	0.689823	+	0.723978i	$0.257688\pi$
$223$			21.6226i			1.44796i	−0.689823	+	0.723978i	$0.742312\pi$
$224$	1.17216			0.0783184
$225$		0			0
$226$	19.1097			1.27116
$227$			19.5621i			1.29838i	0.760625	+	0.649191i	$0.224892\pi$
$227$			19.5621i			1.29838i	−0.760625	+	0.649191i	$0.775108\pi$
$228$		0			0
$229$	−10.7779			−0.712220			−0.356110	−	0.934444i	$-0.615897\pi$
$229$	−10.7779			−0.712220			−0.356110	+	0.934444i	$0.615897\pi$
$230$	8.08267	−	4.57561i	0.532955	−	0.301707i
$231$		0			0
$232$		−	2.93199i		−	0.192494i
$233$			4.25222i			0.278572i	0.990252	+	0.139286i	$0.0444808\pi$
$233$			4.25222i			0.278572i	−0.990252	+	0.139286i	$0.955519\pi$
$234$		0			0
$235$	−3.27314	−	5.78189i	−0.213516	−	0.377169i
$236$	−0.729569			−0.0474909
$237$		0			0
$238$			5.11244i			0.331390i
$239$	16.8385			1.08919			0.544596	−	0.838699i	$-0.316683\pi$
$239$	16.8385			1.08919			0.544596	+	0.838699i	$0.316683\pi$
$240$		0			0
$241$	21.8396			1.40681			0.703405	−	0.710789i	$-0.251662\pi$
$241$	21.8396			1.40681			0.703405	+	0.710789i	$0.251662\pi$
$242$		−	14.6010i		−	0.938586i
$243$		0			0
$244$	−0.280787			−0.0179755
$245$	−10.4843	+	5.93518i	−0.669817	+	0.379185i
$246$		0			0
$247$		−	2.36657i		−	0.150581i
$248$		−	13.1708i		−	0.836346i
$249$		0			0
$250$	−15.1459	−	0.385278i	−0.957912	−	0.0243671i
$251$	−2.24264			−0.141554			−0.0707772	−	0.997492i	$-0.522548\pi$
$251$	−2.24264			−0.141554			−0.0707772	+	0.997492i	$0.522548\pi$
$252$		0			0
$253$			1.45528i			0.0914929i
$254$	−15.6529			−0.982150
$255$		0			0
$256$	−3.89989			−0.243743
$257$			1.27685i			0.0796479i	0.999207	+	0.0398239i	$0.0126797\pi$
$257$			1.27685i			0.0796479i	−0.999207	+	0.0398239i	$0.987320\pi$
$258$		0			0
$259$	9.14589			0.568298
$260$	−0.0734814	−	0.129802i	−0.00455712	−	0.00805001i
$261$		0			0
$262$		−	13.8809i		−	0.857564i
$263$			19.6767i			1.21332i	0.794963	+	0.606658i	$0.207490\pi$
$263$			19.6767i			1.21332i	−0.794963	+	0.606658i	$0.792510\pi$
$264$		0			0
$265$	8.67161	+	15.3181i	0.532693	+	0.940984i
$266$	−9.98789			−0.612397
$267$		0			0
$268$		−	2.58118i		−	0.157671i
$269$	−11.7353			−0.715516			−0.357758	−	0.933814i	$-0.616459\pi$
$269$	−11.7353			−0.715516			−0.357758	+	0.933814i	$0.616459\pi$
$270$		0			0
$271$	−9.92348			−0.602809			−0.301404	−	0.953496i	$-0.597455\pi$
$271$	−9.92348			−0.602809			−0.301404	+	0.953496i	$0.597455\pi$
$272$		−	10.8334i		−	0.656871i
$273$		0			0
$274$	−2.79940			−0.169118
$275$	1.22164	−	2.03545i	0.0736677	−	0.122742i
$276$		0			0
$277$			1.50995i			0.0907242i	0.998971	+	0.0453621i	$0.0144442\pi$
$277$			1.50995i			0.0907242i	−0.998971	+	0.0453621i	$0.985556\pi$
$278$		−	4.71906i		−	0.283031i
$279$		0			0
$280$	−7.24403	+	4.10086i	−0.432914	+	0.245073i
$281$	−25.3285			−1.51097			−0.755487	−	0.655164i	$-0.772600\pi$
$281$	−25.3285			−1.51097			−0.755487	+	0.655164i	$0.772600\pi$
$282$		0			0
$283$		−	2.09287i		−	0.124408i	−0.998063	−	0.0622041i	$-0.980187\pi$
$283$		−	2.09287i		−	0.124408i	0.998063	−	0.0622041i	$-0.0198130\pi$
$284$	−1.47390			−0.0874601
$285$		0			0
$286$	−0.262301			−0.0155102
$287$			15.3211i			0.904375i
$288$		0			0
$289$	8.17125			0.480662
$290$	1.49278	+	2.63695i	0.0876592	+	0.154847i
$291$		0			0
$292$			0.110933i			0.00649186i
$293$			10.8526i			0.634013i	0.948423	+	0.317007i	$0.102678\pi$
$293$			10.8526i			0.634013i	−0.948423	+	0.317007i	$0.897322\pi$
$294$		0			0
$295$	8.67660	−	4.91184i	0.505171	−	0.285978i
$296$	−21.1198			−1.22757
$297$		0			0
$298$			14.7111i			0.852189i
$299$	−1.24962			−0.0722674
$300$		0			0
$301$	1.31854			0.0759991
$302$			15.3882i			0.885490i
$303$		0			0
$304$	21.1646			1.21387
$305$	3.33933	−	1.89040i	0.191210	−	0.108244i
$306$		0			0
$307$			16.8956i			0.964281i	0.876094	+	0.482141i	$0.160141\pi$
$307$			16.8956i			0.964281i	−0.876094	+	0.482141i	$0.839859\pi$
$308$		−	0.0986347i		−	0.00562023i
$309$		0			0
$310$	6.70573	+	11.8454i	0.380860	+	0.672776i
$311$	10.6643			0.604717			0.302359	−	0.953194i	$-0.402226\pi$
$311$	10.6643			0.604717			0.302359	+	0.953194i	$0.402226\pi$
$312$		0			0
$313$			13.8702i			0.783991i	0.919967	+	0.391995i	$0.128215\pi$
$313$			13.8702i			0.783991i	−0.919967	+	0.391995i	$0.871785\pi$
$314$	23.0119			1.29864
$315$		0			0
$316$	−0.268267			−0.0150912
$317$		−	1.33953i		−	0.0752355i	−0.999292	−	0.0376178i	$-0.988023\pi$
$317$		−	1.33953i		−	0.0752355i	0.999292	−	0.0376178i	$-0.0119769\pi$
$318$		0			0
$319$	−0.474782			−0.0265827
$320$	16.6239	−	9.41079i	0.929302	−	0.526079i
$321$		0			0
$322$			5.27390i			0.293903i
$323$		−	17.2482i		−	0.959718i
$324$		0			0
$325$	1.74779	+	1.04900i	0.0969502	+	0.0581878i
$326$	−10.5501			−0.584317
$327$		0			0
$328$		−	35.3797i		−	1.95352i
$329$	3.77265			0.207993
$330$		0			0
$331$	−3.00072			−0.164934			−0.0824672	−	0.996594i	$-0.526280\pi$
$331$	−3.00072			−0.164934			−0.0824672	+	0.996594i	$0.526280\pi$
$332$			2.54304i			0.139567i
$333$		0			0
$334$	2.79685			0.153037
$335$	17.3778	+	30.6974i	0.949452	+	1.67718i
$336$		0			0
$337$			24.2763i			1.32241i	0.750203	+	0.661207i	$0.229956\pi$
$337$			24.2763i			1.32241i	−0.750203	+	0.661207i	$0.770044\pi$
$338$			17.3915i			0.945971i
$339$		0			0
$340$	−0.535553	−	0.946037i	−0.0290444	−	0.0513060i
$341$	−2.13277			−0.115496
$342$		0			0
$343$		−	15.7288i		−	0.849274i
$344$	−3.04479			−0.164164
$345$		0			0
$346$	−0.707540			−0.0380376
$347$		−	14.0792i		−	0.755809i	−0.925845	−	0.377904i	$-0.876645\pi$
$347$		−	14.0792i		−	0.755809i	0.925845	−	0.377904i	$-0.123355\pi$
$348$		0			0
$349$	17.9641			0.961597			0.480798	−	0.876831i	$-0.340347\pi$
$349$	17.9641			0.961597			0.480798	+	0.876831i	$0.340347\pi$
$350$	4.42718	−	7.37640i	0.236643	−	0.394285i
$351$		0			0
$352$			0.438313i			0.0233622i
$353$			9.49061i			0.505134i	0.967579	+	0.252567i	$0.0812748\pi$
$353$			9.49061i			0.505134i	−0.967579	+	0.252567i	$0.918725\pi$
$354$		0			0
$355$	17.5288	−	9.92308i	0.930331	−	0.526662i
$356$	2.19538			0.116355
$357$		0			0
$358$			14.2024i			0.750620i
$359$	−4.09130			−0.215931			−0.107965	−	0.994155i	$-0.534434\pi$
$359$	−4.09130			−0.215931			−0.107965	+	0.994155i	$0.534434\pi$
$360$		0			0
$361$	14.6969			0.773523
$362$			16.6307i			0.874088i
$363$		0			0
$364$	0.0846954			0.00443925
$365$	−0.746858	−	1.31930i	−0.0390923	−	0.0690553i
$366$		0			0
$367$			18.8383i			0.983351i	0.870778	+	0.491676i	$0.163615\pi$
$367$			18.8383i			0.983351i	−0.870778	+	0.491676i	$0.836385\pi$
$368$		−	11.1755i		−	0.582565i
$369$		0			0
$370$	18.9946	−	10.7529i	0.987482	−	0.559015i
$371$	−9.99498			−0.518914
$372$		0			0
$373$		−	7.23999i		−	0.374872i	−0.982277	−	0.187436i	$-0.939982\pi$
$373$		−	7.23999i		−	0.374872i	0.982277	−	0.187436i	$-0.0600178\pi$
$374$	−1.91172			−0.0988529
$375$		0			0
$376$	−8.71188			−0.449281
$377$		−	0.407685i		−	0.0209968i
$378$		0			0
$379$	−20.2420			−1.03976			−0.519881	−	0.854239i	$-0.674024\pi$
$379$	−20.2420			−1.03976			−0.519881	+	0.854239i	$0.674024\pi$
$380$	1.84822	−	1.04628i	0.0948117	−	0.0536731i
$381$		0			0
$382$		−	13.1377i		−	0.672183i
$383$		−	4.34201i		−	0.221866i	−0.993828	−	0.110933i	$-0.964616\pi$
$383$		−	4.34201i		−	0.221866i	0.993828	−	0.110933i	$-0.0353840\pi$
$384$		0			0
$385$	0.664060	+	1.17304i	0.0338436	+	0.0597836i
$386$	−15.0225			−0.764626
$387$		0			0
$388$			1.16290i			0.0590375i
$389$	−0.508687			−0.0257915			−0.0128957	−	0.999917i	$-0.504105\pi$
$389$	−0.508687			−0.0257915			−0.0128957	+	0.999917i	$0.504105\pi$
$390$		0			0
$391$	−9.10757			−0.460590
$392$			15.7972i			0.797881i
$393$		0			0
$394$	2.71611			0.136835
$395$	3.19044	−	1.80611i	0.160528	−	0.0908753i
$396$		0			0
$397$			31.2135i			1.56656i	0.621669	+	0.783280i	$0.286455\pi$
$397$			31.2135i			1.56656i	−0.621669	+	0.783280i	$0.713545\pi$
$398$			24.5509i			1.23063i
$399$		0			0
$400$	−9.38132	+	15.6308i	−0.469066	+	0.781539i
$401$	5.60957			0.280129			0.140064	−	0.990142i	$-0.455269\pi$
$401$	5.60957			0.280129			0.140064	+	0.990142i	$0.455269\pi$
$402$		0			0
$403$		−	1.83136i		−	0.0912267i
$404$	−0.766452			−0.0381324
$405$		0			0
$406$	−1.72060			−0.0853917
$407$			3.41997i			0.169522i
$408$		0			0
$409$	9.68080			0.478685			0.239342	−	0.970935i	$-0.423068\pi$
$409$	9.68080			0.478685			0.239342	+	0.970935i	$0.423068\pi$
$410$	18.0131	+	31.8195i	0.889603	+	1.57145i
$411$		0			0
$412$			2.53907i			0.125091i
$413$			5.66143i			0.278581i
$414$		0			0
$415$	−17.1211	−	30.2438i	−0.840439	−	1.48461i
$416$	−0.376370			−0.0184530
$417$		0			0
$418$		−	3.73483i		−	0.182677i
$419$	−18.2788			−0.892979			−0.446489	−	0.894789i	$-0.647326\pi$
$419$	−18.2788			−0.892979			−0.446489	+	0.894789i	$0.647326\pi$
$420$		0			0
$421$	26.0517			1.26968			0.634842	−	0.772642i	$-0.281065\pi$
$421$	26.0517			1.26968			0.634842	+	0.772642i	$0.281065\pi$
$422$			25.0467i			1.21925i
$423$		0			0
$424$	23.0806			1.12089
$425$	12.7384	+	7.64537i	0.617904	+	0.370855i
$426$		0			0
$427$			2.17890i			0.105444i
$428$			0.110625i			0.00534727i
$429$		0			0
$430$	2.73839	−	1.55021i	0.132057	−	0.0747578i
$431$	−6.19278			−0.298296			−0.149148	−	0.988815i	$-0.547653\pi$
$431$	−6.19278			−0.298296			−0.149148	+	0.988815i	$0.547653\pi$
$432$		0			0
$433$		−	35.1538i		−	1.68938i	−0.535253	−	0.844692i	$-0.679784\pi$
$433$		−	35.1538i		−	1.68938i	0.535253	−	0.844692i	$-0.320216\pi$
$434$	−7.72909			−0.371008
$435$		0			0
$436$	1.21854			0.0583574
$437$		−	17.7930i		−	0.851153i
$438$		0			0
$439$	20.1018			0.959408			0.479704	−	0.877430i	$-0.340744\pi$
$439$	20.1018			0.959408			0.479704	+	0.877430i	$0.340744\pi$
$440$	−1.53346	−	2.70880i	−0.0731047	−	0.129137i
$441$		0			0
$442$		−	1.64156i		−	0.0780808i
$443$		−	20.8513i		−	0.990676i	−0.868700	−	0.495338i	$-0.835044\pi$
$443$		−	20.8513i		−	0.990676i	0.868700	−	0.495338i	$-0.164956\pi$
$444$		0			0
$445$	−26.1091	+	14.7804i	−1.23769	+	0.700659i
$446$	−29.3014			−1.38746
$447$		0			0
$448$			10.8470i			0.512471i
$449$	39.5199			1.86506			0.932529	−	0.361094i	$-0.117597\pi$
$449$	39.5199			1.86506			0.932529	+	0.361094i	$0.117597\pi$
$450$		0			0
$451$	−5.72910			−0.269773
$452$		−	2.30733i		−	0.108528i
$453$		0			0
$454$	−26.5092			−1.24414
$455$	−1.00726	+	0.570213i	−0.0472212	+	0.0267320i
$456$		0			0
$457$			25.6115i			1.19806i	0.800728	+	0.599028i	$0.204446\pi$
$457$			25.6115i			1.19806i	−0.800728	+	0.599028i	$0.795554\pi$
$458$		−	14.6054i		−	0.682465i
$459$		0			0
$460$	−0.552466	−	0.975914i	−0.0257589	−	0.0455022i
$461$	0.911675			0.0424609			0.0212305	−	0.999775i	$-0.493242\pi$
$461$	0.911675			0.0424609			0.0212305	+	0.999775i	$0.493242\pi$
$462$		0			0
$463$		−	25.9744i		−	1.20713i	−0.797312	−	0.603567i	$-0.793746\pi$
$463$		−	25.9744i		−	1.20713i	0.797312	−	0.603567i	$-0.206254\pi$
$464$	3.64599			0.169261
$465$		0			0
$466$	−5.76231			−0.266934
$467$		−	15.8506i		−	0.733479i	−0.930324	−	0.366739i	$-0.880474\pi$
$467$		−	15.8506i		−	0.733479i	0.930324	−	0.366739i	$-0.119526\pi$
$468$		0			0
$469$	−20.0299			−0.924893
$470$	7.83522	−	4.43553i	0.361412	−	0.204596i
$471$		0			0
$472$		−	13.0735i		−	0.601756i
$473$			0.493048i			0.0226704i
$474$		0			0
$475$	−14.9363	+	24.8863i	−0.685326	+	1.14186i
$476$	0.617284			0.0282932
$477$		0			0
$478$			22.8184i			1.04369i
$479$	16.3087			0.745162			0.372581	−	0.928000i	$-0.378473\pi$
$479$	16.3087			0.745162			0.372581	+	0.928000i	$0.378473\pi$
$480$		0			0
$481$	−2.93666			−0.133900
$482$			29.5955i			1.34804i
$483$		0			0
$484$	−1.76294			−0.0801338
$485$	−7.82927	−	13.8301i	−0.355509	−	0.627995i
$486$		0			0
$487$			9.93950i			0.450402i	0.974312	+	0.225201i	$0.0723039\pi$
$487$			9.93950i			0.450402i	−0.974312	+	0.225201i	$0.927696\pi$
$488$		−	5.03155i		−	0.227767i
$489$		0			0
$490$	−8.04294	−	14.2076i	−0.363343	−	0.641833i
$491$	−38.0638			−1.71779			−0.858897	−	0.512149i	$-0.828850\pi$
$491$	−38.0638			−1.71779			−0.858897	+	0.512149i	$0.828850\pi$
$492$		0			0
$493$		−	2.97132i		−	0.133822i
$494$	3.20702			0.144290
$495$		0			0
$496$	16.3781			0.735401
$497$			11.4374i			0.513039i
$498$		0			0
$499$	−44.3795			−1.98670			−0.993349	−	0.115143i	$-0.963267\pi$
$499$	−44.3795			−1.98670			−0.993349	+	0.115143i	$0.963267\pi$
$500$	−0.0465190	+	1.82874i	−0.00208039	+	0.0817838i
$501$		0			0
$502$		−	3.03908i		−	0.135641i
$503$			3.18073i			0.141822i	0.997483	+	0.0709108i	$0.0225906\pi$
$503$			3.18073i			0.141822i	−0.997483	+	0.0709108i	$0.977409\pi$
$504$		0			0
$505$	9.11524	−	5.16015i	0.405623	−	0.229624i
$506$	−1.97210			−0.0876705
$507$		0			0
$508$			1.88995i			0.0838532i
$509$	30.5882			1.35580			0.677899	−	0.735155i	$-0.262891\pi$
$509$	30.5882			1.35580			0.677899	+	0.735155i	$0.262891\pi$
$510$		0			0
$511$	0.860836			0.0380811
$512$		−	24.7459i		−	1.09363i
$513$		0			0
$514$	−1.73030			−0.0763203
$515$	−17.0943	−	30.1966i	−0.753266	−	1.33062i
$516$		0			0
$517$			1.41073i			0.0620439i
$518$			12.3939i			0.544555i
$519$		0			0
$520$	2.32599	−	1.31675i	0.102001	−	0.0577431i
$521$	−28.7858			−1.26113			−0.630564	−	0.776138i	$-0.717176\pi$
$521$	−28.7858			−1.26113			−0.630564	+	0.776138i	$0.717176\pi$
$522$		0			0
$523$		−	27.2018i		−	1.18945i	−0.803928	−	0.594726i	$-0.797261\pi$
$523$		−	27.2018i		−	1.18945i	0.803928	−	0.594726i	$-0.202739\pi$
$524$	−1.67600			−0.0732164
$525$		0			0
$526$	−26.6645			−1.16263
$527$		−	13.3475i		−	0.581425i
$528$		0			0
$529$	13.6048			0.591513
$530$	−20.7580	+	11.7512i	−0.901672	+	0.510438i
$531$		0			0
$532$			1.20595i			0.0522847i
$533$		−	4.91945i		−	0.213085i
$534$		0			0
$535$	−0.744785	−	1.31564i	−0.0321999	−	0.0568800i
$536$	46.2533			1.99784
$537$		0			0
$538$		−	15.9029i		−	0.685623i
$539$	2.55807			0.110184
$540$		0			0
$541$	5.84584			0.251332			0.125666	−	0.992073i	$-0.459893\pi$
$541$	5.84584			0.251332			0.125666	+	0.992073i	$0.459893\pi$
$542$		−	13.4476i		−	0.577625i
$543$		0			0
$544$	−2.74309			−0.117609
$545$	−14.4918	+	8.20382i	−0.620760	+	0.351413i
$546$		0			0
$547$		−	18.9324i		−	0.809489i	−0.914430	−	0.404745i	$-0.867360\pi$
$547$		−	18.9324i		−	0.809489i	0.914430	−	0.404745i	$-0.132640\pi$
$548$			0.338003i			0.0144388i
$549$		0			0
$550$	2.75830	+	1.65548i	0.117614	+	0.0705900i
$551$	5.80491			0.247297
$552$		0			0
$553$			2.08174i			0.0885247i
$554$	−2.04618			−0.0869340
$555$		0			0
$556$	−0.569787			−0.0241643
$557$		−	29.6529i		−	1.25643i	−0.778038	−	0.628217i	$-0.783785\pi$
$557$		−	29.6529i		−	1.25643i	0.778038	−	0.628217i	$-0.216215\pi$
$558$		0			0
$559$	−0.423369			−0.0179066
$560$	−5.09950	−	9.00810i	−0.215493	−	0.380662i
$561$		0			0
$562$		−	34.3235i		−	1.44785i
$563$		−	19.3966i		−	0.817471i	−0.912653	−	0.408736i	$-0.865970\pi$
$563$		−	19.3966i		−	0.817471i	0.912653	−	0.408736i	$-0.134030\pi$
$564$		0			0
$565$	15.5342	+	27.4406i	0.653527	+	1.15443i
$566$	2.83611			0.119211
$567$		0			0
$568$		−	26.4115i		−	1.10820i
$569$	−6.00700			−0.251826			−0.125913	−	0.992041i	$-0.540186\pi$
$569$	−6.00700			−0.251826			−0.125913	+	0.992041i	$0.540186\pi$
$570$		0			0
$571$	−28.1469			−1.17791			−0.588957	−	0.808165i	$-0.700461\pi$
$571$	−28.1469			−1.17791			−0.588957	+	0.808165i	$0.700461\pi$
$572$			0.0316706i			0.00132422i
$573$		0			0
$574$	−20.7621			−0.866592
$575$	13.1407	+	7.88682i	0.548005	+	0.328903i
$576$		0			0
$577$			32.9966i			1.37367i	0.726815	+	0.686834i	$0.241000\pi$
$577$			32.9966i			1.37367i	−0.726815	+	0.686834i	$0.759000\pi$
$578$			11.0731i			0.460581i
$579$		0			0
$580$	0.318389	−	0.180241i	0.0132204	−	0.00748409i
$581$	19.7339			0.818700
$582$		0			0
$583$		−	3.73748i		−	0.154791i
$584$	−1.98786			−0.0822581
$585$		0			0
$586$	−14.7066			−0.607526
$587$		−	7.81241i		−	0.322453i	−0.986917	−	0.161226i	$-0.948455\pi$
$587$		−	7.81241i		−	0.322453i	0.986917	−	0.161226i	$-0.0515449\pi$
$588$		0			0
$589$	26.0762			1.07445
$590$	6.65618	+	11.7579i	0.274031	+	0.484066i
$591$		0			0
$592$		−	26.2629i		−	1.07940i
$593$		−	33.5131i		−	1.37622i	−0.725608	−	0.688108i	$-0.758441\pi$
$593$		−	33.5131i		−	1.37622i	0.725608	−	0.688108i	$-0.241559\pi$
$594$		0			0
$595$	−7.34121	+	4.15587i	−0.300960	+	0.170374i
$596$	1.77623			0.0727574
$597$		0			0
$598$		−	1.69340i		−	0.0692482i
$599$	27.1213			1.10815			0.554074	−	0.832468i	$-0.313073\pi$
$599$	27.1213			1.10815			0.554074	+	0.832468i	$0.313073\pi$
$600$		0			0
$601$	−17.4641			−0.712376			−0.356188	−	0.934414i	$-0.615924\pi$
$601$	−17.4641			−0.712376			−0.356188	+	0.934414i	$0.615924\pi$
$602$			1.78679i			0.0728240i
$603$		0			0
$604$	1.85799			0.0756006
$605$	20.9663	−	11.8690i	0.852400	−	0.482545i
$606$		0			0
$607$		−	32.9273i		−	1.33648i	−0.743947	−	0.668239i	$-0.767049\pi$
$607$		−	32.9273i		−	1.33648i	0.743947	−	0.668239i	$-0.232951\pi$
$608$		−	5.35902i		−	0.217337i
$609$		0			0
$610$	2.56174	+	4.52523i	0.103722	+	0.183221i
$611$	−1.21136			−0.0490065
$612$		0			0
$613$			2.97228i			0.120049i	0.998197	+	0.0600245i	$0.0191179\pi$
$613$			2.97228i			0.120049i	−0.998197	+	0.0600245i	$0.980882\pi$
$614$	−22.8957			−0.923996
$615$		0			0
$616$	1.76748			0.0712138
$617$			0.0642578i			0.00258692i	0.999999	+	0.00129346i	$0.000411722\pi$
$617$			0.0642578i			0.00258692i	−0.999999	+	0.00129346i	$0.999588\pi$
$618$		0			0
$619$	−7.45588			−0.299677			−0.149839	−	0.988710i	$-0.547875\pi$
$619$	−7.45588			−0.299677			−0.149839	+	0.988710i	$0.547875\pi$
$620$	1.43024	−	0.809660i	0.0574397	−	0.0325167i
$621$		0			0
$622$			14.4515i			0.579454i
$623$		−	17.0360i		−	0.682535i
$624$		0			0
$625$	−11.7588	−	22.0620i	−0.470352	−	0.882479i
$626$	−18.7960			−0.751237
$627$		0			0
$628$		−	2.77849i		−	0.110874i
$629$	−21.4032			−0.853400
$630$		0			0
$631$	−38.0735			−1.51568			−0.757841	−	0.652439i	$-0.773746\pi$
$631$	−38.0735			−1.51568			−0.757841	+	0.652439i	$0.773746\pi$
$632$		−	4.80720i		−	0.191220i
$633$		0			0
$634$	1.81524			0.0720924
$635$	−12.7241	−	22.4768i	−0.504942	−	0.891964i
$636$		0			0
$637$			2.19656i			0.0870309i
$638$		−	0.643392i		−	0.0254721i
$639$		0			0
$640$	10.7189	+	18.9346i	0.423703	+	0.748457i
$641$	4.49665			0.177607			0.0888035	−	0.996049i	$-0.471696\pi$
$641$	4.49665			0.177607			0.0888035	+	0.996049i	$0.471696\pi$
$642$		0			0
$643$		−	20.9607i		−	0.826610i	−0.910593	−	0.413305i	$-0.864374\pi$
$643$		−	20.9607i		−	0.826610i	0.910593	−	0.413305i	$-0.135626\pi$
$644$	0.636778			0.0250926
$645$		0			0
$646$	23.3736			0.919623
$647$		−	37.8398i		−	1.48764i	−0.668381	−	0.743819i	$-0.733013\pi$
$647$		−	37.8398i		−	1.48764i	0.668381	−	0.743819i	$-0.266987\pi$
$648$		0			0
$649$	−2.11701			−0.0831000
$650$	−1.42153	+	2.36849i	−0.0557568	+	0.0928998i
$651$		0			0
$652$			1.27384i			0.0498873i
$653$		−	48.0703i		−	1.88114i	−0.339606	−	0.940568i	$-0.610294\pi$
$653$		−	48.0703i		−	1.88114i	0.339606	−	0.940568i	$-0.389706\pi$
$654$		0			0
$655$	19.9323	−	11.2837i	0.778818	−	0.440890i
$656$	43.9954			1.71773
$657$		0			0
$658$			5.11244i			0.199304i
$659$	26.0861			1.01617			0.508084	−	0.861307i	$-0.330354\pi$
$659$	26.0861			1.01617			0.508084	+	0.861307i	$0.330354\pi$
$660$		0			0
$661$	5.00120			0.194524			0.0972620	−	0.995259i	$-0.468992\pi$
$661$	5.00120			0.194524			0.0972620	+	0.995259i	$0.468992\pi$
$662$		−	4.06636i		−	0.158044i
$663$		0			0
$664$	−45.5699			−1.76845
$665$	−8.11910	−	14.3421i	−0.314845	−	0.556163i
$666$		0			0
$667$		−	3.06516i		−	0.118683i
$668$		−	0.337695i		−	0.0130658i
$669$		0			0
$670$	−41.5989	+	23.5492i	−1.60711	+	0.909786i
$671$	−0.814768			−0.0314538
$672$		0			0
$673$			26.1113i			1.00652i	0.864136	+	0.503258i	$0.167866\pi$
$673$			26.1113i			1.00652i	−0.864136	+	0.503258i	$0.832134\pi$
$674$	−32.8976			−1.26717
$675$		0			0
$676$	2.09987			0.0807643
$677$			32.0992i			1.23367i	0.787092	+	0.616836i	$0.211586\pi$
$677$			32.0992i			1.23367i	−0.787092	+	0.616836i	$0.788414\pi$
$678$		0			0
$679$	9.02410			0.346313
$680$	16.9524	−	9.59681i	0.650097	−	0.368021i
$681$		0			0
$682$		−	2.89018i		−	0.110671i
$683$			4.70468i			0.180020i	0.995941	+	0.0900098i	$0.0286898\pi$
$683$			4.70468i			0.180020i	−0.995941	+	0.0900098i	$0.971310\pi$
$684$		0			0
$685$	−2.27561	−	4.01979i	−0.0869466	−	0.153588i
$686$	21.3145			0.813793
$687$		0			0
$688$		−	3.78625i		−	0.144349i
$689$	3.20929			0.122264
$690$		0			0
$691$	0.881335			0.0335276			0.0167638	−	0.999859i	$-0.494664\pi$
$691$	0.881335			0.0335276			0.0167638	+	0.999859i	$0.494664\pi$
$692$			0.0854295i			0.00324754i
$693$		0			0
$694$	19.0791			0.724233
$695$	6.77634	−	3.83610i	0.257041	−	0.145511i
$696$		0			0
$697$		−	35.8543i		−	1.35808i
$698$			24.3437i			0.921423i
$699$		0			0
$700$	−0.890637	−	0.534545i	−0.0336629	−	0.0202039i
$701$	45.1606			1.70569			0.852847	−	0.522161i	$-0.174874\pi$
$701$	45.1606			1.70569			0.852847	+	0.522161i	$0.174874\pi$
$702$		0			0
$703$		−	41.8142i		−	1.57705i
$704$	−4.05607			−0.152869
$705$		0			0
$706$	−12.8610			−0.484031
$707$			5.94764i			0.223684i
$708$		0			0
$709$	−18.8061			−0.706277			−0.353139	−	0.935571i	$-0.614886\pi$
$709$	−18.8061			−0.706277			−0.353139	+	0.935571i	$0.614886\pi$
$710$	13.4471	+	23.7538i	0.504660	+	0.891464i
$711$		0			0
$712$			39.3399i			1.47433i
$713$		−	13.7690i		−	0.515653i
$714$		0			0
$715$	−0.213223	−	0.376652i	−0.00797409	−	0.0140860i
$716$	1.71482			0.0640857
$717$		0			0
$718$		−	5.54425i		−	0.206910i
$719$	−18.7384			−0.698824			−0.349412	−	0.936969i	$-0.613619\pi$
$719$	−18.7384			−0.698824			−0.349412	+	0.936969i	$0.613619\pi$
$720$		0			0
$721$	19.7031			0.733782
$722$			19.9163i			0.741207i
$723$		0			0
$724$	2.00801			0.0746271
$725$	−2.57305	+	4.28712i	−0.0955608	+	0.159220i
$726$		0			0
$727$		−	20.2155i		−	0.749752i	−0.927075	−	0.374876i	$-0.877685\pi$
$727$		−	20.2155i		−	0.749752i	0.927075	−	0.374876i	$-0.122315\pi$
$728$			1.51769i			0.0562495i
$729$		0			0
$730$	1.78782	−	1.01209i	0.0661703	−	0.0374591i
$731$	−3.08563			−0.114126
$732$		0			0
$733$		−	45.1963i		−	1.66936i	−0.550732	−	0.834682i	$-0.685651\pi$
$733$		−	45.1963i		−	1.66936i	0.550732	−	0.834682i	$-0.314349\pi$
$734$	−25.5284			−0.942269
$735$		0			0
$736$	−2.82972			−0.104305
$737$		−	7.48988i		−	0.275893i
$738$		0			0
$739$	−42.2473			−1.55409			−0.777046	−	0.629443i	$-0.783283\pi$
$739$	−42.2473			−1.55409			−0.777046	+	0.629443i	$0.783283\pi$
$740$	−1.29832	−	2.29344i	−0.0477271	−	0.0843084i
$741$		0			0
$742$		−	13.5445i		−	0.497235i
$743$			38.5919i			1.41580i	0.706313	+	0.707900i	$0.250357\pi$
$743$			38.5919i			1.41580i	−0.706313	+	0.707900i	$0.749643\pi$
$744$		0			0
$745$	−21.1243	+	11.9585i	−0.773936	+	0.438127i
$746$	9.81113			0.359211
$747$		0			0
$748$			0.230825i			0.00843978i
$749$	0.858447			0.0313670
$750$		0			0
$751$	−1.50634			−0.0549670			−0.0274835	−	0.999622i	$-0.508749\pi$
$751$	−1.50634			−0.0549670			−0.0274835	+	0.999622i	$0.508749\pi$
$752$		−	10.8334i		−	0.395053i
$753$		0			0
$754$	0.552466			0.0201196
$755$	−22.0966	+	12.5090i	−0.804179	+	0.455247i
$756$		0			0
$757$			17.3890i			0.632016i	0.948757	+	0.316008i	$0.102343\pi$
$757$			17.3890i			0.632016i	−0.948757	+	0.316008i	$0.897657\pi$
$758$		−	27.4306i		−	0.996324i
$759$		0			0
$760$	18.7488	+	33.1191i	0.680089	+	1.20135i
$761$	−9.21457			−0.334028			−0.167014	−	0.985955i	$-0.553413\pi$
$761$	−9.21457			−0.334028			−0.167014	+	0.985955i	$0.553413\pi$
$762$		0			0
$763$		−	9.45581i		−	0.342323i
$764$	−1.58626			−0.0573890
$765$		0			0
$766$	5.88399			0.212597
$767$		−	1.81783i		−	0.0656381i
$768$		0			0
$769$	−25.6939			−0.926547			−0.463273	−	0.886215i	$-0.653325\pi$
$769$	−25.6939			−0.926547			−0.463273	+	0.886215i	$0.653325\pi$
$770$	−1.58962	+	0.899888i	−0.0572860	+	0.0324297i
$771$		0			0
$772$			1.81384i			0.0652816i
$773$			42.9070i			1.54326i	0.636074	+	0.771628i	$0.280557\pi$
$773$			42.9070i			1.54326i	−0.636074	+	0.771628i	$0.719443\pi$
$774$		0			0
$775$	−11.5584	+	19.2582i	−0.415191	+	0.691774i
$776$	−20.8386			−0.748062
$777$		0			0
$778$		−	0.689338i		−	0.0247140i
$779$	70.0466			2.50968
$780$		0			0
$781$	−4.27687			−0.153038
$782$		−	12.3420i		−	0.441347i
$783$		0			0
$784$	−19.6442			−0.701578
$785$	18.7062	+	33.0439i	0.667653	+	1.17939i
$786$		0			0
$787$			22.2120i			0.791772i	0.918300	+	0.395886i	$0.129562\pi$
$787$			22.2120i			0.791772i	−0.918300	+	0.395886i	$0.870438\pi$
$788$		−	0.327947i		−	0.0116826i
$789$		0			0
$790$	2.44752	+	4.32346i	0.0870788	+	0.153822i
$791$	−17.9048			−0.636622
$792$		0			0
$793$		−	0.699623i		−	0.0248443i
$794$	−42.2984			−1.50111
$795$		0			0
$796$	2.96431			0.105067
$797$			46.2386i			1.63785i	0.573897	+	0.818927i	$0.305431\pi$
$797$			46.2386i			1.63785i	−0.573897	+	0.818927i	$0.694569\pi$
$798$		0			0
$799$	−8.82875			−0.312339
$800$	3.95782	+	2.37541i	0.139930	+	0.0839835i
$801$		0			0
$802$			7.60171i			0.268426i
$803$			0.321897i			0.0113595i
$804$		0			0
$805$	−7.57305	+	4.28712i	−0.266915	+	0.151101i
$806$	2.48174			0.0874154
$807$		0			0
$808$		−	13.7344i		−	0.483175i
$809$	23.9257			0.841184			0.420592	−	0.907250i	$-0.361822\pi$
$809$	23.9257			0.841184			0.420592	+	0.907250i	$0.361822\pi$
$810$		0			0
$811$	−52.0210			−1.82670			−0.913352	−	0.407170i	$-0.866516\pi$
$811$	−52.0210			−1.82670			−0.913352	+	0.407170i	$0.866516\pi$
$812$			0.207747i			0.00729050i
$813$		0			0
$814$	−4.63451			−0.162440
$815$	−8.57613	−	15.1494i	−0.300409	−	0.530662i
$816$		0			0
$817$		−	6.02823i		−	0.210901i
$818$			13.1188i			0.458686i
$819$		0			0
$820$	3.84194	−	2.17493i	0.134166	−	0.0759518i
$821$	−15.0444			−0.525052			−0.262526	−	0.964925i	$-0.584556\pi$
$821$	−15.0444			−0.525052			−0.262526	+	0.964925i	$0.584556\pi$
$822$		0			0
$823$			44.8652i			1.56390i	0.623339	+	0.781952i	$0.285776\pi$
$823$			44.8652i			1.56390i	−0.623339	+	0.781952i	$0.714224\pi$
$824$	−45.4987			−1.58502
$825$		0			0
$826$	−7.67198			−0.266942
$827$			41.5569i			1.44508i	0.691331	+	0.722538i	$0.257025\pi$
$827$			41.5569i			1.44508i	−0.691331	+	0.722538i	$0.742975\pi$
$828$		0			0
$829$	25.3645			0.880946			0.440473	−	0.897766i	$-0.354811\pi$
$829$	25.3645			0.880946			0.440473	+	0.897766i	$0.354811\pi$
$830$	40.9843	−	23.2013i	1.42258	−	0.805328i
$831$		0			0
$832$		−	3.48286i		−	0.120746i
$833$			16.0092i			0.554684i
$834$		0			0
$835$	2.27354	+	4.01613i	0.0786790	+	0.138984i
$836$	−0.450949			−0.0155964
$837$		0			0
$838$		−	24.7702i		−	0.855672i
$839$	−3.34480			−0.115475			−0.0577376	−	0.998332i	$-0.518389\pi$
$839$	−3.34480			−0.115475			−0.0577376	+	0.998332i	$0.518389\pi$
$840$		0			0
$841$	1.00000			0.0344828
$842$			35.3035i			1.21664i
$843$		0			0
$844$	3.02417			0.104096
$845$	−24.9733	+	14.1374i	−0.859107	+	0.486342i
$846$		0			0
$847$			13.6804i			0.470063i
$848$			28.7012i			0.985603i
$849$		0			0
$850$	−10.3605	+	17.2622i	−0.355361	+	0.592089i
$851$	−22.0791			−0.756862
$852$		0			0
$853$		−	45.8873i		−	1.57115i	−0.618766	−	0.785575i	$-0.712367\pi$
$853$		−	45.8873i		−	1.57115i	0.618766	−	0.785575i	$-0.287633\pi$
$854$	−2.95269			−0.101039
$855$		0			0
$856$	−1.98234			−0.0677550
$857$		−	51.8755i		−	1.77203i	−0.463652	−	0.886017i	$-0.653461\pi$
$857$		−	51.8755i		−	1.77203i	0.463652	−	0.886017i	$-0.346539\pi$
$858$		0			0
$859$	−31.7698			−1.08397			−0.541987	−	0.840387i	$-0.682328\pi$
$859$	−31.7698			−1.08397			−0.541987	+	0.840387i	$0.682328\pi$
$860$	−0.187175	−	0.330638i	−0.00638260	−	0.0112747i
$861$		0			0
$862$		−	8.39203i		−	0.285834i
$863$			39.9472i			1.35982i	0.733296	+	0.679909i	$0.237981\pi$
$863$			39.9472i			1.35982i	−0.733296	+	0.679909i	$0.762019\pi$
$864$		0			0
$865$	−0.575155	−	1.01599i	−0.0195559	−	0.0345448i
$866$	47.6380			1.61880
$867$		0			0
$868$			0.933222i			0.0316756i
$869$	−0.778438			−0.0264067
$870$		0			0
$871$	6.43139			0.217920
$872$			21.8355i			0.739444i
$873$		0			0
$874$	24.1118			0.815594
$875$	14.1910	+	0.360986i	0.479742	+	0.0122036i
$876$		0			0
$877$		−	44.8875i		−	1.51574i	−0.652403	−	0.757872i	$-0.726239\pi$
$877$		−	44.8875i		−	1.51574i	0.652403	−	0.757872i	$-0.273761\pi$
$878$			27.2406i			0.919326i
$879$		0			0
$880$	3.36845	−	1.90689i	0.113550	−	0.0642811i
$881$	3.90189			0.131458			0.0657290	−	0.997838i	$-0.479063\pi$
$881$	3.90189			0.131458			0.0657290	+	0.997838i	$0.479063\pi$
$882$		0			0
$883$		−	52.7256i		−	1.77436i	−0.461427	−	0.887178i	$-0.652662\pi$
$883$		−	52.7256i		−	1.77436i	0.461427	−	0.887178i	$-0.347338\pi$
$884$	−0.198204			−0.00666632
$885$		0			0
$886$	28.2563			0.949288
$887$		−	20.7833i		−	0.697834i	−0.937154	−	0.348917i	$-0.886550\pi$
$887$		−	20.7833i		−	0.697834i	0.937154	−	0.348917i	$-0.113450\pi$
$888$		0			0
$889$	14.6660			0.491881
$890$	−20.0294	−	35.3813i	−0.671387	−	1.18598i
$891$		0			0
$892$			3.53790i			0.118458i
$893$		−	17.2482i		−	0.577190i
$894$		0			0
$895$	−20.3939	+	11.5450i	−0.681694	+	0.385908i
$896$	−12.3547			−0.412743
$897$		0			0
$898$			53.5546i			1.78714i
$899$	4.49210			0.149820
$900$		0			0
$901$	23.3902			0.779241
$902$		−	7.76368i		−	0.258502i
$903$		0			0
$904$	41.3461			1.37515
$905$	−23.8808	+	13.5190i	−0.793824	+	0.449385i
$906$		0			0
$907$		−	26.2116i		−	0.870342i	−0.900348	−	0.435171i	$-0.856688\pi$
$907$		−	26.2116i		−	0.870342i	0.900348	−	0.435171i	$-0.143312\pi$
$908$			3.20076i			0.106221i
$909$		0			0
$910$	−0.772713	−	1.36497i	−0.0256152	−	0.0452484i
$911$	−31.4264			−1.04120			−0.520601	−	0.853800i	$-0.674292\pi$
$911$	−31.4264			−1.04120			−0.520601	+	0.853800i	$0.674292\pi$
$912$		0			0
$913$			7.37921i			0.244216i
$914$	−34.7070			−1.14800
$915$		0			0
$916$	−1.76348			−0.0582669
$917$			13.0057i			0.429486i
$918$		0			0
$919$	21.0083			0.693000			0.346500	−	0.938050i	$-0.387370\pi$
$919$	21.0083			0.693000			0.346500	+	0.938050i	$0.387370\pi$
$920$	17.4878	−	9.89989i	0.576557	−	0.326390i
$921$		0			0
$922$			1.23544i			0.0406870i
$923$		−	3.67245i		−	0.120880i
$924$		0			0
$925$	30.8812	+	18.5343i	1.01537	+	0.609405i
$926$	35.1988			1.15670
$927$		0			0
$928$		−	0.923188i		−	0.0303051i
$929$	37.3920			1.22679			0.613395	−	0.789776i	$-0.289803\pi$
$929$	37.3920			1.22679			0.613395	+	0.789776i	$0.289803\pi$
$930$		0			0
$931$	−31.2762			−1.02504
$932$			0.695750i			0.0227901i
$933$		0			0
$934$	21.4796			0.702836
$935$	−1.55403	−	2.74514i	−0.0508222	−	0.0897757i
$936$		0			0
$937$		−	13.8377i		−	0.452057i	−0.974121	−	0.226029i	$-0.927426\pi$
$937$		−	13.8377i		−	0.452057i	0.974121	−	0.226029i	$-0.0725743\pi$
$938$		−	27.1431i		−	0.886253i
$939$		0			0
$940$	−0.535553	−	0.946037i	−0.0174678	−	0.0308563i
$941$	−14.5708			−0.474995			−0.237497	−	0.971388i	$-0.576327\pi$
$941$	−14.5708			−0.474995			−0.237497	+	0.971388i	$0.576327\pi$
$942$		0			0
$943$		−	36.9867i		−	1.20445i
$944$	16.2571			0.529125
$945$		0			0
$946$	−0.668144			−0.0217232
$947$		−	43.4267i		−	1.41118i	−0.708622	−	0.705589i	$-0.750683\pi$
$947$		−	43.4267i		−	1.41118i	0.708622	−	0.705589i	$-0.249317\pi$
$948$		0			0
$949$	−0.276406			−0.00897252
$950$	−33.7242	−	20.2407i	−1.09416	−	0.656695i
$951$		0			0
$952$			11.0614i			0.358501i
$953$			51.0500i			1.65367i	0.562442	+	0.826836i	$0.309862\pi$
$953$			51.0500i			1.65367i	−0.562442	+	0.826836i	$0.690138\pi$
$954$		0			0
$955$	18.8651	−	10.6796i	0.610459	−	0.345582i
$956$	2.75512			0.0891071
$957$		0			0
$958$			22.1004i			0.714030i
$959$	2.62289			0.0846976
$960$		0			0
$961$	−10.8210			−0.349065
$962$		−	3.97955i		−	0.128306i
$963$		0			0
$964$	3.57340			0.115091
$965$	−12.2117	−	21.5716i	−0.393109	−	0.694414i
$966$		0			0
$967$			56.0658i			1.80295i	0.432828	+	0.901477i	$0.357516\pi$
$967$			56.0658i			1.80295i	−0.432828	+	0.901477i	$0.642484\pi$
$968$		−	31.5910i		−	1.01537i
$969$		0			0
$970$	18.7417	−	10.6097i	0.601758	−	0.340657i
$971$	6.58898			0.211450			0.105725	−	0.994395i	$-0.466284\pi$
$971$	6.58898			0.211450			0.105725	+	0.994395i	$0.466284\pi$
$972$		0			0
$973$			4.42152i			0.141748i
$974$	−13.4693			−0.431585
$975$		0			0
$976$	6.25683			0.200276
$977$		−	29.3327i		−	0.938437i	−0.883082	−	0.469218i	$-0.844536\pi$
$977$		−	29.3327i		−	0.938437i	0.883082	−	0.469218i	$-0.155464\pi$
$978$		0			0
$979$	6.37039			0.203599
$980$	−1.71545	+	0.971117i	−0.0547979	+	0.0310212i
$981$		0			0
$982$		−	51.5814i		−	1.64603i
$983$			13.6719i			0.436064i	0.975942	+	0.218032i	$0.0699638\pi$
$983$			13.6719i			0.436064i	−0.975942	+	0.218032i	$0.930036\pi$
$984$		0			0
$985$	2.20791	+	3.90019i	0.0703497	+	0.124270i
$986$	4.02653			0.128231
$987$		0			0
$988$		−	0.387220i		−	0.0123191i
$989$	−3.18308			−0.101216
$990$		0			0
$991$	19.7210			0.626459			0.313230	−	0.949677i	$-0.398589\pi$
$991$	19.7210			0.626459			0.313230	+	0.949677i	$0.398589\pi$
$992$		−	4.14705i		−	0.131669i
$993$		0			0
$994$	−15.4992			−0.491606
$995$	−35.2539	+	19.9573i	−1.11762	+	0.632688i
$996$		0			0
$997$			53.4618i			1.69315i	0.532268	+	0.846576i	$0.321340\pi$
$997$			53.4618i			1.69315i	−0.532268	+	0.846576i	$0.678660\pi$
$998$		−	60.1400i		−	1.90370i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1305.2.c.k.784.9	yes	12
3.2	odd	2		1305.2.c.l.784.4	yes	12
5.2	odd	4		6525.2.a.ce.1.4		12
5.3	odd	4		6525.2.a.ce.1.9		12
5.4	even	2	inner	1305.2.c.k.784.4	✓	12
15.2	even	4		6525.2.a.cf.1.9		12
15.8	even	4		6525.2.a.cf.1.4		12
15.14	odd	2		1305.2.c.l.784.9	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1305.2.c.k.784.4	✓	12	5.4	even	2	inner
1305.2.c.k.784.9	yes	12	1.1	even	1	trivial
1305.2.c.l.784.4	yes	12	3.2	odd	2
1305.2.c.l.784.9	yes	12	15.14	odd	2
6525.2.a.ce.1.4		12	5.2	odd	4
6525.2.a.ce.1.9		12	5.3	odd	4
6525.2.a.cf.1.4		12	15.8	even	4
6525.2.a.cf.1.9		12	15.2	even	4

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:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1305.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.35513i q^{2} +0.163621 q^{4} +(-1.94590 + 1.10158i) q^{5} -1.26969i q^{7} +2.93199i q^{8} +(-1.49278 - 2.63695i) q^{10} +0.474782 q^{11} +0.407685i q^{13} +1.72060 q^{14} -3.64599 q^{16} +2.97132i q^{17} -5.80491 q^{19} +(-0.318389 + 0.180241i) q^{20} +0.643392i q^{22} +3.06516i q^{23} +(2.57305 - 4.28712i) q^{25} -0.552466 q^{26} -0.207747i q^{28} -1.00000 q^{29} -4.49210 q^{31} +0.923188i q^{32} -4.02653 q^{34} +(1.39866 + 2.47069i) q^{35} +7.20325i q^{37} -7.86641i q^{38} +(-3.22981 - 5.70536i) q^{40} -12.0668 q^{41} +1.03847i q^{43} +0.0776841 q^{44} -4.15369 q^{46} +2.97132i q^{47} +5.38789 q^{49} +(5.80961 + 3.48682i) q^{50} +0.0667056i q^{52} -7.87199i q^{53} +(-0.923879 + 0.523010i) q^{55} +3.72271 q^{56} -1.35513i q^{58} -4.45891 q^{59} -1.71609 q^{61} -6.08739i q^{62} -8.54301 q^{64} +(-0.449097 - 0.793314i) q^{65} -15.7754i q^{67} +0.486169i q^{68} +(-3.34811 + 1.89537i) q^{70} -9.00806 q^{71} +0.677990i q^{73} -9.76134 q^{74} -0.949802 q^{76} -0.602826i q^{77} -1.63957 q^{79} +(7.09473 - 4.01634i) q^{80} -16.3521i q^{82} +15.5423i q^{83} +(-3.27314 - 5.78189i) q^{85} -1.40726 q^{86} +1.39206i q^{88} +13.4175 q^{89} +0.517633 q^{91} +0.501523i q^{92} -4.02653 q^{94} +(11.2958 - 6.39456i) q^{95} +7.10733i q^{97} +7.30129i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 16 q^{4} - 10 q^{10} - 12 q^{11} + 16 q^{14} + 16 q^{16} + 20 q^{19} + 14 q^{20} + 8 q^{25} - 56 q^{26} - 12 q^{29} - 16 q^{31} - 4 q^{34} - 16 q^{35} + 16 q^{40} - 32 q^{41} + 68 q^{44} + 20 q^{46}+ \cdots - 8 q^{95}+O(q^{100}) \) 12 * q - 16 * q^4 - 10 * q^10 - 12 * q^11 + 16 * q^14 + 16 * q^16 + 20 * q^19 + 14 * q^20 + 8 * q^25 - 56 * q^26 - 12 * q^29 - 16 * q^31 - 4 * q^34 - 16 * q^35 + 16 * q^40 - 32 * q^41 + 68 * q^44 + 20 * q^46 + 4 * q^49 - 8 * q^50 + 4 * q^55 - 76 * q^56 + 44 * q^59 - 52 * q^61 - 36 * q^64 - 8 * q^65 - 30 * q^70 - 20 * q^71 + 20 * q^74 - 28 * q^76 + 4 * q^79 + 34 * q^80 + 20 * q^85 - 36 * q^86 + 68 * q^89 + 48 * q^91 - 4 * q^94 - 8 * q^95

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