LMFDB - Embedded newform 1305.2.c.k.784.10

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			784.10
Root			$1.78841i$ of defining polynomial
Character	$\chi$	$=$	1305.784
Dual form			1305.2.c.k.784.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.78841i q^{2} -1.19839 q^{4} +(-0.766993 + 2.10041i) q^{5} +4.04635i q^{7} +1.43360i q^{8} +(-3.75638 - 1.37170i) q^{10} -4.80986 q^{11} +0.533576i q^{13} -7.23651 q^{14} -4.96064 q^{16} -0.299844i q^{17} +6.02908 q^{19} +(0.919161 - 2.51712i) q^{20} -8.60198i q^{22} -0.379104i q^{23} +(-3.82344 - 3.22200i) q^{25} -0.954250 q^{26} -4.84912i q^{28} -1.00000 q^{29} +9.14506 q^{31} -6.00444i q^{32} +0.536243 q^{34} +(-8.49899 - 3.10352i) q^{35} -8.51769i q^{37} +10.7824i q^{38} +(-3.01114 - 1.09956i) q^{40} +2.24106 q^{41} +6.01126i q^{43} +5.76411 q^{44} +0.677992 q^{46} -0.299844i q^{47} -9.37293 q^{49} +(5.76224 - 6.83787i) q^{50} -0.639435i q^{52} +11.8608i q^{53} +(3.68913 - 10.1027i) q^{55} -5.80083 q^{56} -1.78841i q^{58} +6.53090 q^{59} -0.755856 q^{61} +16.3551i q^{62} +0.817104 q^{64} +(-1.12073 - 0.409249i) q^{65} -3.95461i q^{67} +0.359332i q^{68} +(5.55036 - 15.1996i) q^{70} -10.6771 q^{71} +11.0455i q^{73} +15.2331 q^{74} -7.22522 q^{76} -19.4624i q^{77} -7.01095 q^{79} +(3.80478 - 10.4194i) q^{80} +4.00793i q^{82} -6.15340i q^{83} +(0.629796 + 0.229979i) q^{85} -10.7506 q^{86} -6.89539i q^{88} +10.0521 q^{89} -2.15903 q^{91} +0.454316i q^{92} +0.536243 q^{94} +(-4.62427 + 12.6635i) q^{95} -2.41013i q^{97} -16.7626i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			1.78841i			1.26459i	0.774726	+	0.632297i	$0.217888\pi$
$2$			1.78841i			1.26459i	−0.774726	+	0.632297i	$0.782112\pi$
$3$		0			0
$3$		0			0
$4$	−1.19839			−0.599197
$5$	−0.766993	+	2.10041i	−0.343010	+	0.939332i
$5$	−0.766993	+	2.10041i	−0.343010	+	0.939332i
$6$		0			0
$7$			4.04635i			1.52938i	0.644401	+	0.764688i	$0.277107\pi$
$7$			4.04635i			1.52938i	−0.644401	+	0.764688i	$0.722893\pi$
$8$			1.43360i			0.506853i
$9$		0			0
$10$	−3.75638	−	1.37170i	−1.18787	−	0.433768i
$11$	−4.80986			−1.45023			−0.725113	−	0.688630i	$-0.758213\pi$
$11$	−4.80986			−1.45023			−0.725113	+	0.688630i	$0.758213\pi$
$12$		0			0
$13$			0.533576i			0.147987i	0.997259	+	0.0739937i	$0.0235745\pi$
$13$			0.533576i			0.147987i	−0.997259	+	0.0739937i	$0.976426\pi$
$14$	−7.23651			−1.93404
$15$		0			0
$16$	−4.96064			−1.24016
$17$		−	0.299844i		−	0.0727229i	−0.999339	−	0.0363615i	$-0.988423\pi$
$17$		−	0.299844i		−	0.0727229i	0.999339	−	0.0363615i	$-0.0115768\pi$
$18$		0			0
$19$	6.02908			1.38317			0.691583	−	0.722297i	$-0.256914\pi$
$19$	6.02908			1.38317			0.691583	+	0.722297i	$0.256914\pi$
$20$	0.919161	−	2.51712i	0.205531	−	0.562845i
$21$		0			0
$22$		−	8.60198i		−	1.83395i
$23$		−	0.379104i		−	0.0790487i	−0.999219	−	0.0395243i	$-0.987416\pi$
$23$		−	0.379104i		−	0.0790487i	0.999219	−	0.0395243i	$-0.0125843\pi$
$24$		0			0
$25$	−3.82344	−	3.22200i	−0.764688	−	0.644400i
$26$	−0.954250			−0.187144
$27$		0			0
$28$		−	4.84912i		−	0.916398i
$29$	−1.00000			−0.185695
$29$	−1.00000			−0.185695
$30$		0			0
$31$	9.14506			1.64250			0.821251	−	0.570567i	$-0.193277\pi$
$31$	9.14506			1.64250			0.821251	+	0.570567i	$0.193277\pi$
$32$		−	6.00444i		−	1.06145i
$33$		0			0
$34$	0.536243			0.0919650
$35$	−8.49899	−	3.10352i	−1.43659	−	0.524591i
$36$		0			0
$37$		−	8.51769i		−	1.40030i	−0.713996	−	0.700150i	$-0.753116\pi$
$37$		−	8.51769i		−	1.40030i	0.713996	−	0.700150i	$-0.246884\pi$
$38$			10.7824i			1.74914i
$39$		0			0
$40$	−3.01114	−	1.09956i	−0.476103	−	0.173855i
$41$	2.24106			0.349995			0.174998	−	0.984569i	$-0.444008\pi$
$41$	2.24106			0.349995			0.174998	+	0.984569i	$0.444008\pi$
$42$		0			0
$43$			6.01126i			0.916708i	0.888770	+	0.458354i	$0.151561\pi$
$43$			6.01126i			0.916708i	−0.888770	+	0.458354i	$0.848439\pi$
$44$	5.76411			0.868972
$45$		0			0
$46$	0.677992			0.0999645
$47$		−	0.299844i		−	0.0437368i	−0.999761	−	0.0218684i	$-0.993039\pi$
$47$		−	0.299844i		−	0.0437368i	0.999761	−	0.0218684i	$-0.00696148\pi$
$48$		0			0
$49$	−9.37293			−1.33899
$50$	5.76224	−	6.83787i	0.814904	−	0.967020i
$51$		0			0
$52$		−	0.639435i		−	0.0886736i
$53$			11.8608i			1.62920i	0.580022	+	0.814601i	$0.303044\pi$
$53$			11.8608i			1.62920i	−0.580022	+	0.814601i	$0.696956\pi$
$54$		0			0
$55$	3.68913	−	10.1027i	0.497442	−	1.36224i
$56$	−5.80083			−0.775168
$57$		0			0
$58$		−	1.78841i		−	0.234829i
$59$	6.53090			0.850251			0.425126	−	0.905134i	$-0.360230\pi$
$59$	6.53090			0.850251			0.425126	+	0.905134i	$0.360230\pi$
$60$		0			0
$61$	−0.755856			−0.0967774			−0.0483887	−	0.998829i	$-0.515409\pi$
$61$	−0.755856			−0.0967774			−0.0483887	+	0.998829i	$0.515409\pi$
$62$			16.3551i			2.07710i
$63$		0			0
$64$	0.817104			0.102138
$65$	−1.12073	−	0.409249i	−0.139009	−	0.0507611i
$66$		0			0
$67$		−	3.95461i		−	0.483133i	−0.970384	−	0.241567i	$-0.922339\pi$
$67$		−	3.95461i		−	0.483133i	0.970384	−	0.241567i	$-0.0776612\pi$
$68$			0.359332i			0.0435754i
$69$		0			0
$70$	5.55036	−	15.1996i	0.663394	−	1.81670i
$71$	−10.6771			−1.26714			−0.633571	−	0.773684i	$-0.718412\pi$
$71$	−10.6771			−1.26714			−0.633571	+	0.773684i	$0.718412\pi$
$72$		0			0
$73$			11.0455i			1.29278i	0.763008	+	0.646389i	$0.223722\pi$
$73$			11.0455i			1.29278i	−0.763008	+	0.646389i	$0.776278\pi$
$74$	15.2331			1.77081
$75$		0			0
$76$	−7.22522			−0.828790
$77$		−	19.4624i		−	2.21794i
$78$		0			0
$79$	−7.01095			−0.788793			−0.394397	−	0.918940i	$-0.629046\pi$
$79$	−7.01095			−0.788793			−0.394397	+	0.918940i	$0.629046\pi$
$80$	3.80478	−	10.4194i	0.425387	−	1.16492i
$81$		0			0
$82$			4.00793i			0.442602i
$83$		−	6.15340i		−	0.675424i	−0.941250	−	0.337712i	$-0.890347\pi$
$83$		−	6.15340i		−	0.675424i	0.941250	−	0.337712i	$-0.109653\pi$
$84$		0			0
$85$	0.629796	+	0.229979i	0.0683110	+	0.0249447i
$86$	−10.7506			−1.15926
$87$		0			0
$88$		−	6.89539i		−	0.735051i
$89$	10.0521			1.06552			0.532760	−	0.846267i	$-0.321155\pi$
$89$	10.0521			1.06552			0.532760	+	0.846267i	$0.321155\pi$
$90$		0			0
$91$	−2.15903			−0.226328
$92$			0.454316i			0.0473658i
$93$		0			0
$94$	0.536243			0.0553093
$95$	−4.62427	+	12.6635i	−0.474440	+	1.29925i
$96$		0			0
$97$		−	2.41013i		−	0.244711i	−0.992486	−	0.122356i	$-0.960955\pi$
$97$		−	2.41013i		−	0.244711i	0.992486	−	0.122356i	$-0.0390449\pi$
$98$		−	16.7626i		−	1.69328i
$99$		0			0
$100$	4.58199	+	3.86123i	0.458199	+	0.386123i
$101$	−16.6038			−1.65214			−0.826071	−	0.563565i	$-0.809429\pi$
$101$	−16.6038			−1.65214			−0.826071	+	0.563565i	$0.809429\pi$
$102$		0			0
$103$		−	13.4127i		−	1.32159i	−0.750566	−	0.660795i	$-0.770219\pi$
$103$		−	13.4127i		−	1.32159i	0.750566	−	0.660795i	$-0.229781\pi$
$104$	−0.764932			−0.0750078
$105$		0			0
$106$	−21.2119			−2.06028
$107$		−	9.12013i		−	0.881676i	−0.897587	−	0.440838i	$-0.854681\pi$
$107$		−	9.12013i		−	0.881676i	0.897587	−	0.440838i	$-0.145319\pi$
$108$		0			0
$109$	−12.7379			−1.22007			−0.610037	−	0.792373i	$-0.708845\pi$
$109$	−12.7379			−1.22007			−0.610037	+	0.792373i	$0.708845\pi$
$110$	18.0677	+	6.59766i	1.72269	+	0.629062i
$111$		0			0
$112$		−	20.0725i		−	1.89667i
$113$			13.7766i			1.29599i	0.761645	+	0.647995i	$0.224392\pi$
$113$			13.7766i			1.29599i	−0.761645	+	0.647995i	$0.775608\pi$
$114$		0			0
$115$	0.796274	+	0.290770i	0.0742529	+	0.0271145i
$116$	1.19839			0.111268
$117$		0			0
$118$			11.6799i			1.07522i
$119$	1.21327			0.111221
$120$		0			0
$121$	12.1347			1.10316
$122$		−	1.35178i		−	0.122384i
$123$		0			0
$124$	−10.9594			−0.984183
$125$	9.70008	−	5.55954i	0.867601	−	0.497260i
$126$		0			0
$127$			6.39541i			0.567501i	0.958898	+	0.283751i	$0.0915788\pi$
$127$			6.39541i			0.567501i	−0.958898	+	0.283751i	$0.908421\pi$
$128$		−	10.5476i		−	0.932283i
$129$		0			0
$130$	0.731904	−	2.00432i	0.0641922	−	0.175790i
$131$	15.6797			1.36994			0.684970	−	0.728572i	$-0.259816\pi$
$131$	15.6797			1.36994			0.684970	+	0.728572i	$0.259816\pi$
$132$		0			0
$133$			24.3958i			2.11538i
$134$	7.07246			0.610967
$135$		0			0
$136$	0.429855			0.0368598
$137$			14.1792i			1.21141i	0.795690	+	0.605704i	$0.207108\pi$
$137$			14.1792i			1.21141i	−0.795690	+	0.605704i	$0.792892\pi$
$138$		0			0
$139$	−6.15903			−0.522402			−0.261201	−	0.965284i	$-0.584119\pi$
$139$	−6.15903			−0.522402			−0.261201	+	0.965284i	$0.584119\pi$
$140$	10.1851	+	3.71924i	0.860802	+	0.314334i
$141$		0			0
$142$		−	19.0950i		−	1.60242i
$143$		−	2.56643i		−	0.214615i
$144$		0			0
$145$	0.766993	−	2.10041i	0.0636953	−	0.174430i
$146$	−19.7538			−1.63484
$147$		0			0
$148$			10.2076i			0.839056i
$149$	3.29888			0.270254			0.135127	−	0.990828i	$-0.456856\pi$
$149$	3.29888			0.270254			0.135127	+	0.990828i	$0.456856\pi$
$150$		0			0
$151$	−11.7747			−0.958209			−0.479104	−	0.877758i	$-0.659039\pi$
$151$	−11.7747			−0.958209			−0.479104	+	0.877758i	$0.659039\pi$
$152$			8.64327i			0.701061i
$153$		0			0
$154$	34.8066			2.80479
$155$	−7.01420	+	19.2084i	−0.563394	+	1.54285i
$156$		0			0
$157$			20.0255i			1.59821i	0.601195	+	0.799103i	$0.294692\pi$
$157$			20.0255i			1.59821i	−0.601195	+	0.799103i	$0.705308\pi$
$158$		−	12.5384i		−	0.997503i
$159$		0			0
$160$	12.6118	+	4.60537i	0.997050	+	0.364086i
$161$	1.53399			0.120895
$162$		0			0
$163$			8.63537i			0.676374i	0.941079	+	0.338187i	$0.109814\pi$
$163$			8.63537i			0.676374i	−0.941079	+	0.338187i	$0.890186\pi$
$164$	−2.68568			−0.209716
$165$		0			0
$166$	11.0048			0.854137
$167$			5.98646i			0.463246i	0.972806	+	0.231623i	$0.0744036\pi$
$167$			5.98646i			0.463246i	−0.972806	+	0.231623i	$0.925596\pi$
$168$		0			0
$169$	12.7153			0.978100
$170$	−0.411295	+	1.12633i	−0.0315449	+	0.0863856i
$171$		0			0
$172$		−	7.20386i		−	0.549289i
$173$		−	7.75331i		−	0.589473i	−0.955579	−	0.294737i	$-0.904768\pi$
$173$		−	7.75331i		−	0.589473i	0.955579	−	0.294737i	$-0.0952319\pi$
$174$		0			0
$175$	13.0373	−	15.4710i	0.985530	−	1.16950i
$176$	23.8600			1.79851
$177$		0			0
$178$			17.9772i			1.34745i
$179$	9.21698			0.688909			0.344455	−	0.938803i	$-0.388064\pi$
$179$	9.21698			0.688909			0.344455	+	0.938803i	$0.388064\pi$
$180$		0			0
$181$	13.9345			1.03574			0.517871	−	0.855459i	$-0.326725\pi$
$181$	13.9345			1.03574			0.517871	+	0.855459i	$0.326725\pi$
$182$		−	3.86123i		−	0.286213i
$183$		0			0
$184$	0.543482			0.0400660
$185$	17.8906	+	6.53301i	1.31535	+	0.480317i
$186$		0			0
$187$			1.44221i			0.105465i
$188$			0.359332i			0.0262070i
$189$		0			0
$190$	−22.6476	−	8.27007i	−1.64303	−	0.599974i
$191$	−15.8529			−1.14708			−0.573538	−	0.819179i	$-0.694430\pi$
$191$	−15.8529			−1.14708			−0.573538	+	0.819179i	$0.694430\pi$
$192$		0			0
$193$			12.3360i			0.887963i	0.896036	+	0.443982i	$0.146434\pi$
$193$			12.3360i			0.887963i	−0.896036	+	0.443982i	$0.853566\pi$
$194$	4.31029			0.309460
$195$		0			0
$196$	11.2325			0.802319
$197$		−	6.51599i		−	0.464245i	−0.972687	−	0.232122i	$-0.925433\pi$
$197$		−	6.51599i		−	0.464245i	0.972687	−	0.232122i	$-0.0745670\pi$
$198$		0			0
$199$	8.40626			0.595904			0.297952	−	0.954581i	$-0.403696\pi$
$199$	8.40626			0.595904			0.297952	+	0.954581i	$0.403696\pi$
$200$	4.61905	−	5.48127i	0.326616	−	0.387584i
$201$		0			0
$202$		−	29.6944i		−	2.08929i
$203$		−	4.04635i		−	0.283998i
$204$		0			0
$205$	−1.71888	+	4.70715i	−0.120052	+	0.328761i
$206$	23.9873			1.67128
$207$		0			0
$208$		−	2.64688i		−	0.183528i
$209$	−28.9990			−2.00591
$210$		0			0
$211$	−9.42279			−0.648692			−0.324346	−	0.945939i	$-0.605144\pi$
$211$	−9.42279			−0.648692			−0.324346	+	0.945939i	$0.605144\pi$
$212$		−	14.2139i		−	0.976214i
$213$		0			0
$214$	16.3105			1.11496
$215$	−12.6261	−	4.61060i	−0.861093	−	0.314440i
$216$		0			0
$217$			37.0041i			2.51200i
$218$		−	22.7806i		−	1.54290i
$219$		0			0
$220$	−4.42103	+	12.1070i	−0.298066	+	0.816253i
$221$	0.159990			0.0107621
$222$		0			0
$223$			18.6498i			1.24889i	0.781071	+	0.624443i	$0.214674\pi$
$223$			18.6498i			1.24889i	−0.781071	+	0.624443i	$0.785326\pi$
$224$	24.2961			1.62335
$225$		0			0
$226$	−24.6381			−1.63890
$227$			4.72192i			0.313405i	0.987646	+	0.156703i	$0.0500864\pi$
$227$			4.72192i			0.313405i	−0.987646	+	0.156703i	$0.949914\pi$
$228$		0			0
$229$	−23.6102			−1.56021			−0.780104	−	0.625650i	$-0.784834\pi$
$229$	−23.6102			−1.56021			−0.780104	+	0.625650i	$0.784834\pi$
$230$	−0.520015	+	1.42406i	−0.0342888	+	0.0938998i
$231$		0			0
$232$		−	1.43360i		−	0.0941201i
$233$		−	15.0959i		−	0.988965i	−0.869188	−	0.494482i	$-0.835358\pi$
$233$		−	15.0959i		−	0.988965i	0.869188	−	0.494482i	$-0.164642\pi$
$234$		0			0
$235$	0.629796	+	0.229979i	0.0410834	+	0.0150022i
$236$	−7.82660			−0.509468
$237$		0			0
$238$			2.16983i			0.140649i
$239$	−16.5534			−1.07075			−0.535374	−	0.844615i	$-0.679829\pi$
$239$	−16.5534			−1.07075			−0.535374	+	0.844615i	$0.679829\pi$
$240$		0			0
$241$	14.0704			0.906356			0.453178	−	0.891420i	$-0.350290\pi$
$241$	14.0704			0.906356			0.453178	+	0.891420i	$0.350290\pi$
$242$			21.7018i			1.39505i
$243$		0			0
$244$	0.905814			0.0579888
$245$	7.18897	−	19.6870i	0.459287	−	1.25776i
$246$		0			0
$247$			3.21697i			0.204691i
$248$			13.1103i			0.832506i
$249$		0			0
$250$	9.94271	+	17.3477i	0.628833	+	1.09716i
$251$	−28.4712			−1.79709			−0.898544	−	0.438883i	$-0.855374\pi$
$251$	−28.4712			−1.79709			−0.898544	+	0.438883i	$0.855374\pi$
$252$		0			0
$253$			1.82344i			0.114638i
$254$	−11.4376			−0.717659
$255$		0			0
$256$	20.4976			1.28110
$257$			16.3705i			1.02117i	0.859829	+	0.510583i	$0.170570\pi$
$257$			16.3705i			1.02117i	−0.859829	+	0.510583i	$0.829430\pi$
$258$		0			0
$259$	34.4655			2.14158
$260$	1.34308	+	0.490442i	0.0832940	+	0.0304159i
$261$		0			0
$262$			28.0416i			1.73242i
$263$			6.95196i			0.428676i	0.976760	+	0.214338i	$0.0687594\pi$
$263$			6.95196i			0.428676i	−0.976760	+	0.214338i	$0.931241\pi$
$264$		0			0
$265$	−24.9125	−	9.09713i	−1.53036	−	0.558832i
$266$	−43.6295			−2.67510
$267$		0			0
$268$			4.73919i			0.289492i
$269$	17.9274			1.09305			0.546525	−	0.837443i	$-0.315950\pi$
$269$	17.9274			1.09305			0.546525	+	0.837443i	$0.315950\pi$
$270$		0			0
$271$	−16.2551			−0.987427			−0.493713	−	0.869625i	$-0.664361\pi$
$271$	−16.2551			−0.987427			−0.493713	+	0.869625i	$0.664361\pi$
$272$			1.48742i			0.0901881i
$273$		0			0
$274$	−25.3581			−1.53194
$275$	18.3902	+	15.4974i	1.10897	+	0.934526i
$276$		0			0
$277$			26.4786i			1.59094i	0.605992	+	0.795471i	$0.292776\pi$
$277$			26.4786i			1.59094i	−0.605992	+	0.795471i	$0.707224\pi$
$278$		−	11.0149i		−	0.660627i
$279$		0			0
$280$	4.44919	−	12.1841i	0.265890	−	0.728140i
$281$	9.09714			0.542690			0.271345	−	0.962482i	$-0.412532\pi$
$281$	9.09714			0.542690			0.271345	+	0.962482i	$0.412532\pi$
$282$		0			0
$283$		−	6.18547i		−	0.367688i	−0.982955	−	0.183844i	$-0.941146\pi$
$283$		−	6.18547i		−	0.367688i	0.982955	−	0.183844i	$-0.0588541\pi$
$284$	12.7954			0.759269
$285$		0			0
$286$	4.58981			0.271401
$287$			9.06811i			0.535274i
$288$		0			0
$289$	16.9101			0.994711
$290$	3.75638	+	1.37170i	0.220582	+	0.0805487i
$291$		0			0
$292$		−	13.2369i		−	0.774629i
$293$			2.22796i			0.130159i	0.997880	+	0.0650795i	$0.0207301\pi$
$293$			2.22796i			0.130159i	−0.997880	+	0.0650795i	$0.979270\pi$
$294$		0			0
$295$	−5.00916	+	13.7176i	−0.291645	+	0.798668i
$296$	12.2109			0.709745
$297$		0			0
$298$			5.89973i			0.341762i
$299$	0.202281			0.0116982
$300$		0			0
$301$	−24.3236			−1.40199
$302$		−	21.0579i		−	1.21175i
$303$		0			0
$304$	−29.9081			−1.71535
$305$	0.579736	−	1.58761i	0.0331956	−	0.0909061i
$306$		0			0
$307$		−	34.9479i		−	1.99458i	−0.0735559	−	0.997291i	$-0.523435\pi$
$307$		−	34.9479i		−	1.99458i	0.0735559	−	0.997291i	$-0.476565\pi$
$308$			23.3236i			1.32898i
$309$		0			0
$310$	−34.3524	−	12.5442i	−1.95108	−	0.712465i
$311$	−11.8968			−0.674608			−0.337304	−	0.941396i	$-0.609515\pi$
$311$	−11.8968			−0.674608			−0.337304	+	0.941396i	$0.609515\pi$
$312$		0			0
$313$		−	2.38938i		−	0.135056i	−0.997717	−	0.0675278i	$-0.978489\pi$
$313$		−	2.38938i		−	0.135056i	0.997717	−	0.0675278i	$-0.0215111\pi$
$314$	−35.8136			−2.02108
$315$		0			0
$316$	8.40188			0.472643
$317$		−	23.9964i		−	1.34777i	−0.738836	−	0.673886i	$-0.764624\pi$
$317$		−	23.9964i		−	1.34777i	0.738836	−	0.673886i	$-0.235376\pi$
$318$		0			0
$319$	4.80986			0.269300
$320$	−0.626714	+	1.71625i	−0.0350344	+	0.0959415i
$321$		0			0
$322$			2.74339i			0.152883i
$323$		−	1.80779i		−	0.100588i
$324$		0			0
$325$	1.71918	−	2.04010i	0.0953631	−	0.113164i
$326$	−15.4435			−0.855339
$327$		0			0
$328$			3.21278i			0.177396i
$329$	1.21327			0.0668900
$330$		0			0
$331$	31.5068			1.73177			0.865885	−	0.500243i	$-0.166756\pi$
$331$	31.5068			1.73177			0.865885	+	0.500243i	$0.166756\pi$
$332$			7.37421i			0.404712i
$333$		0			0
$334$	−10.7062			−0.585818
$335$	8.30631	+	3.03316i	0.453822	+	0.165719i
$336$		0			0
$337$		−	22.5941i		−	1.23078i	−0.788223	−	0.615389i	$-0.788999\pi$
$337$		−	22.5941i		−	1.23078i	0.788223	−	0.615389i	$-0.211001\pi$
$338$			22.7401i			1.23690i
$339$		0			0
$340$	−0.754744	−	0.275605i	−0.0409318	−	0.0149468i
$341$	−43.9865			−2.38200
$342$		0			0
$343$		−	9.60169i		−	0.518443i
$344$	−8.61771			−0.464636
$345$		0			0
$346$	13.8661			0.745444
$347$		−	25.3237i		−	1.35945i	−0.733468	−	0.679724i	$-0.762099\pi$
$347$		−	25.3237i		−	1.35945i	0.733468	−	0.679724i	$-0.237901\pi$
$348$		0			0
$349$	11.9657			0.640511			0.320255	−	0.947331i	$-0.396231\pi$
$349$	11.9657			0.640511			0.320255	+	0.947331i	$0.396231\pi$
$350$	27.6684	+	23.3160i	1.47894	+	1.24630i
$351$		0			0
$352$			28.8805i			1.53934i
$353$			27.8488i			1.48224i	0.671372	+	0.741120i	$0.265705\pi$
$353$			27.8488i			1.48224i	−0.671372	+	0.741120i	$0.734295\pi$
$354$		0			0
$355$	8.18929	−	22.4264i	0.434643	−	1.19027i
$356$	−12.0464			−0.638456
$357$		0			0
$358$			16.4837i			0.871190i
$359$	25.8847			1.36614			0.683071	−	0.730352i	$-0.260644\pi$
$359$	25.8847			1.36614			0.683071	+	0.730352i	$0.260644\pi$
$360$		0			0
$361$	17.3498			0.913150
$362$			24.9205i			1.30979i
$363$		0			0
$364$	2.58738			0.135615
$365$	−23.2001	−	8.47182i	−1.21435	−	0.443436i
$366$		0			0
$367$			30.0434i			1.56825i	0.620602	+	0.784126i	$0.286888\pi$
$367$			30.0434i			1.56825i	−0.620602	+	0.784126i	$0.713112\pi$
$368$			1.88060i			0.0980330i
$369$		0			0
$370$	−11.6837	+	31.9957i	−0.607405	+	1.66338i
$371$	−47.9928			−2.49166
$372$		0			0
$373$			17.3011i			0.895819i	0.894079	+	0.447909i	$0.147831\pi$
$373$			17.3011i			0.895819i	−0.894079	+	0.447909i	$0.852169\pi$
$374$	−2.57925			−0.133370
$375$		0			0
$376$	0.429855			0.0221681
$377$		−	0.533576i		−	0.0274806i
$378$		0			0
$379$	−6.00981			−0.308703			−0.154351	−	0.988016i	$-0.549329\pi$
$379$	−6.00981			−0.308703			−0.154351	+	0.988016i	$0.549329\pi$
$380$	5.54170	−	15.1759i	0.284283	−	0.778509i
$381$		0			0
$382$		−	28.3514i		−	1.45059i
$383$		−	15.9914i		−	0.817124i	−0.912731	−	0.408562i	$-0.866030\pi$
$383$		−	15.9914i		−	0.817124i	0.912731	−	0.408562i	$-0.133970\pi$
$384$		0			0
$385$	40.8789	+	14.9275i	2.08338	+	0.760776i
$386$	−22.0617			−1.12291
$387$		0			0
$388$			2.88828i			0.146630i
$389$	−3.12916			−0.158655			−0.0793274	−	0.996849i	$-0.525277\pi$
$389$	−3.12916			−0.158655			−0.0793274	+	0.996849i	$0.525277\pi$
$390$		0			0
$391$	−0.113672			−0.00574865
$392$		−	13.4370i		−	0.678670i
$393$		0			0
$394$	11.6532			0.587081
$395$	5.37735	−	14.7259i	0.270564	−	0.740939i
$396$		0			0
$397$			39.3500i			1.97492i	0.157863	+	0.987461i	$0.449540\pi$
$397$			39.3500i			1.97492i	−0.157863	+	0.987461i	$0.550460\pi$
$398$			15.0338i			0.753577i
$399$		0			0
$400$	18.9667	+	15.9832i	0.948336	+	0.799159i
$401$	5.07853			0.253610			0.126805	−	0.991928i	$-0.459528\pi$
$401$	5.07853			0.253610			0.126805	+	0.991928i	$0.459528\pi$
$402$		0			0
$403$			4.87959i			0.243070i
$404$	19.8979			0.989960
$405$		0			0
$406$	7.23651			0.359142
$407$			40.9689i			2.03075i
$408$		0			0
$409$	4.17655			0.206517			0.103259	−	0.994655i	$-0.467073\pi$
$409$	4.17655			0.206517			0.103259	+	0.994655i	$0.467073\pi$
$410$	−8.41829	−	3.07405i	−0.415750	−	0.151817i
$411$		0			0
$412$			16.0737i			0.791894i
$413$			26.4263i			1.30035i
$414$		0			0
$415$	12.9247	+	4.71962i	0.634447	+	0.231677i
$416$	3.20383			0.157081
$417$		0			0
$418$		−	51.8620i		−	2.53666i
$419$	16.1637			0.789647			0.394824	−	0.918757i	$-0.370806\pi$
$419$	16.1637			0.789647			0.394824	+	0.918757i	$0.370806\pi$
$420$		0			0
$421$	4.91937			0.239755			0.119878	−	0.992789i	$-0.461750\pi$
$421$	4.91937			0.239755			0.119878	+	0.992789i	$0.461750\pi$
$422$		−	16.8518i		−	0.820331i
$423$		0			0
$424$	−17.0035			−0.825765
$425$	−0.966099	+	1.14644i	−0.0468627	+	0.0556104i
$426$		0			0
$427$		−	3.05846i		−	0.148009i
$428$			10.9295i			0.528298i
$429$		0			0
$430$	8.24562	−	22.5806i	0.397639	−	1.08893i
$431$	41.1719			1.98318			0.991591	−	0.129411i	$-0.0413087\pi$
$431$	41.1719			1.98318			0.991591	+	0.129411i	$0.0413087\pi$
$432$		0			0
$433$		−	22.9724i		−	1.10398i	−0.833850	−	0.551991i	$-0.813868\pi$
$433$		−	22.9724i		−	1.10398i	0.833850	−	0.551991i	$-0.186132\pi$
$434$	−66.1783			−3.17666
$435$		0			0
$436$	15.2651			0.731065
$437$		−	2.28565i		−	0.109337i
$438$		0			0
$439$	−5.53152			−0.264005			−0.132003	−	0.991249i	$-0.542141\pi$
$439$	−5.53152			−0.264005			−0.132003	+	0.991249i	$0.542141\pi$
$440$	14.4831	+	5.28872i	0.690457	+	0.252130i
$441$		0			0
$442$			0.286127i			0.0136097i
$443$		−	3.02219i		−	0.143589i	−0.997419	−	0.0717944i	$-0.977127\pi$
$443$		−	3.02219i		−	0.143589i	0.997419	−	0.0717944i	$-0.0228725\pi$
$444$		0			0
$445$	−7.70989	+	21.1135i	−0.365484	+	1.00088i
$446$	−33.3535			−1.57933
$447$		0			0
$448$			3.30629i			0.156207i
$449$	−7.44290			−0.351252			−0.175626	−	0.984457i	$-0.556195\pi$
$449$	−7.44290			−0.351252			−0.175626	+	0.984457i	$0.556195\pi$
$450$		0			0
$451$	−10.7792			−0.507572
$452$		−	16.5098i		−	0.776554i
$453$		0			0
$454$	−8.44471			−0.396330
$455$	1.65597	−	4.53486i	0.0776328	−	0.212597i
$456$		0			0
$457$		−	2.81240i		−	0.131558i	−0.997834	−	0.0657792i	$-0.979047\pi$
$457$		−	2.81240i		−	0.131558i	0.997834	−	0.0657792i	$-0.0209533\pi$
$458$		−	42.2246i		−	1.97303i
$459$		0			0
$460$	−0.954250	−	0.348458i	−0.0444922	−	0.0162469i
$461$	15.3906			0.716810			0.358405	−	0.933566i	$-0.383321\pi$
$461$	15.3906			0.716810			0.358405	+	0.933566i	$0.383321\pi$
$462$		0			0
$463$			23.7976i			1.10597i	0.833192	+	0.552984i	$0.186511\pi$
$463$			23.7976i			1.10597i	−0.833192	+	0.552984i	$0.813489\pi$
$464$	4.96064			0.230292
$465$		0			0
$466$	26.9976			1.25064
$467$			41.1731i			1.90526i	0.304126	+	0.952632i	$0.401636\pi$
$467$			41.1731i			1.90526i	−0.304126	+	0.952632i	$0.598364\pi$
$468$		0			0
$469$	16.0017			0.738892
$470$	−0.411295	+	1.12633i	−0.0189716	+	0.0519538i
$471$		0			0
$472$			9.36267i			0.430952i
$473$		−	28.9133i		−	1.32943i
$474$		0			0
$475$	−23.0518	−	19.4257i	−1.05769	−	0.891313i
$476$	−1.45398			−0.0666431
$477$		0			0
$478$		−	29.6041i		−	1.35406i
$479$	−21.5362			−0.984013			−0.492007	−	0.870591i	$-0.663736\pi$
$479$	−21.5362			−0.984013			−0.492007	+	0.870591i	$0.663736\pi$
$480$		0			0
$481$	4.54484			0.207227
$482$			25.1636i			1.14617i
$483$		0			0
$484$	−14.5422			−0.661009
$485$	5.06225	+	1.84855i	0.229865	+	0.0839384i
$486$		0			0
$487$			6.21272i			0.281525i	0.990043	+	0.140763i	$0.0449555\pi$
$487$			6.21272i			0.281525i	−0.990043	+	0.140763i	$0.955045\pi$
$488$		−	1.08359i		−	0.0490519i
$489$		0			0
$490$	35.2083	+	12.8568i	1.59055	+	0.580811i
$491$	24.2502			1.09439			0.547197	−	0.837004i	$-0.315695\pi$
$491$	24.2502			1.09439			0.547197	+	0.837004i	$0.315695\pi$
$492$		0			0
$493$			0.299844i			0.0135043i
$494$	−5.75326			−0.258851
$495$		0			0
$496$	−45.3654			−2.03696
$497$		−	43.2034i		−	1.93794i
$498$		0			0
$499$	−35.0007			−1.56685			−0.783424	−	0.621487i	$-0.786529\pi$
$499$	−35.0007			−1.56685			−0.783424	+	0.621487i	$0.786529\pi$
$500$	−11.6245	+	6.66252i	−0.519864	+	0.297957i
$501$		0			0
$502$		−	50.9181i		−	2.27259i
$503$		−	2.11250i		−	0.0941917i	−0.998890	−	0.0470958i	$-0.985003\pi$
$503$		−	2.11250i		−	0.0941917i	0.998890	−	0.0470958i	$-0.0149966\pi$
$504$		0			0
$505$	12.7350	−	34.8748i	0.566701	−	1.55191i
$506$	−3.26104			−0.144971
$507$		0			0
$508$		−	7.66423i		−	0.340045i
$509$	39.5330			1.75227			0.876134	−	0.482068i	$-0.160114\pi$
$509$	39.5330			1.75227			0.876134	+	0.482068i	$0.160114\pi$
$510$		0			0
$511$	−44.6939			−1.97714
$512$			15.5628i			0.687785i
$513$		0			0
$514$	−29.2772			−1.29136
$515$	28.1721	+	10.2874i	1.24141	+	0.453319i
$516$		0			0
$517$			1.44221i			0.0634283i
$518$			61.6384i			2.70823i
$519$		0			0
$520$	0.586698	−	1.60667i	0.0257284	−	0.0704572i
$521$	24.4951			1.07315			0.536575	−	0.843853i	$-0.319718\pi$
$521$	24.4951			1.07315			0.536575	+	0.843853i	$0.319718\pi$
$522$		0			0
$523$		−	13.4730i		−	0.589133i	−0.955631	−	0.294567i	$-0.904825\pi$
$523$		−	13.4730i		−	0.589133i	0.955631	−	0.294567i	$-0.0951753\pi$
$524$	−18.7904			−0.820864
$525$		0			0
$526$	−12.4329			−0.542101
$527$		−	2.74210i		−	0.119448i
$528$		0			0
$529$	22.8563			0.993751
$530$	16.2694	−	44.5536i	0.706696	−	1.93529i
$531$		0			0
$532$		−	29.2358i		−	1.26753i
$533$			1.19578i			0.0517949i
$534$		0			0
$535$	19.1560	+	6.99508i	0.828186	+	0.302424i
$536$	5.66932			0.244877
$537$		0			0
$538$			32.0614i			1.38226i
$539$	45.0825			1.94184
$540$		0			0
$541$	−36.4294			−1.56622			−0.783111	−	0.621882i	$-0.786368\pi$
$541$	−36.4294			−1.56622			−0.783111	+	0.621882i	$0.786368\pi$
$542$		−	29.0707i		−	1.24869i
$543$		0			0
$544$	−1.80040			−0.0771915
$545$	9.76992	−	26.7549i	0.418497	−	1.14605i
$546$		0			0
$547$			27.1863i			1.16240i	0.813760	+	0.581201i	$0.197417\pi$
$547$			27.1863i			1.16240i	−0.813760	+	0.581201i	$0.802583\pi$
$548$		−	16.9922i		−	0.725872i
$549$		0			0
$550$	−27.7156	+	32.8892i	−1.18180	+	1.40240i
$551$	−6.02908			−0.256848
$552$		0			0
$553$		−	28.3687i		−	1.20636i
$554$	−47.3544			−2.01190
$555$		0			0
$556$	7.38095			0.313022
$557$		−	41.0921i		−	1.74113i	−0.492055	−	0.870564i	$-0.663754\pi$
$557$		−	41.0921i		−	1.74113i	0.492055	−	0.870564i	$-0.336246\pi$
$558$		0			0
$559$	−3.20746			−0.135661
$560$	42.1604	+	15.3955i	1.78160	+	0.650577i
$561$		0			0
$562$			16.2694i			0.686282i
$563$		−	26.6574i		−	1.12348i	−0.827315	−	0.561738i	$-0.810133\pi$
$563$		−	26.6574i		−	1.12348i	0.827315	−	0.561738i	$-0.189867\pi$
$564$		0			0
$565$	−28.9364	−	10.5665i	−1.21736	−	0.444537i
$566$	11.0621			0.464976
$567$		0			0
$568$		−	15.3067i		−	0.642254i
$569$	17.9467			0.752363			0.376181	−	0.926546i	$-0.377237\pi$
$569$	17.9467			0.752363			0.376181	+	0.926546i	$0.377237\pi$
$570$		0			0
$571$	−44.9019			−1.87909			−0.939543	−	0.342432i	$-0.888749\pi$
$571$	−44.9019			−1.87909			−0.939543	+	0.342432i	$0.888749\pi$
$572$			3.07559i			0.128597i
$573$		0			0
$574$	−16.2175			−0.676904
$575$	−1.22147	+	1.44948i	−0.0509390	+	0.0604476i
$576$		0			0
$577$			24.3767i			1.01482i	0.861706	+	0.507408i	$0.169396\pi$
$577$			24.3767i			1.01482i	−0.861706	+	0.507408i	$0.830604\pi$
$578$			30.2421i			1.25791i
$579$		0			0
$580$	−0.919161	+	2.51712i	−0.0381661	+	0.104518i
$581$	24.8988			1.03298
$582$		0			0
$583$		−	57.0486i		−	2.36271i
$584$	−15.8348			−0.655248
$585$		0			0
$586$	−3.98450			−0.164598
$587$		−	0.641677i		−	0.0264848i	−0.999912	−	0.0132424i	$-0.995785\pi$
$587$		−	0.641677i		−	0.0264848i	0.999912	−	0.0132424i	$-0.00421532\pi$
$588$		0			0
$589$	55.1363			2.27185
$590$	−24.5326	−	8.95841i	−1.00999	−	0.368812i
$591$		0			0
$592$			42.2532i			1.73660i
$593$			7.16264i			0.294134i	0.989127	+	0.147067i	$0.0469833\pi$
$593$			7.16264i			0.294134i	−0.989127	+	0.147067i	$0.953017\pi$
$594$		0			0
$595$	−0.930574	+	2.54837i	−0.0381498	+	0.104473i
$596$	−3.95336			−0.161936
$597$		0			0
$598$			0.361760i			0.0147935i
$599$	33.7150			1.37756			0.688779	−	0.724971i	$-0.258147\pi$
$599$	33.7150			1.37756			0.688779	+	0.724971i	$0.258147\pi$
$600$		0			0
$601$	12.3214			0.502600			0.251300	−	0.967909i	$-0.419142\pi$
$601$	12.3214			0.502600			0.251300	+	0.967909i	$0.419142\pi$
$602$		−	43.5005i		−	1.77295i
$603$		0			0
$604$	14.1107			0.574156
$605$	−9.30726	+	25.4879i	−0.378394	+	1.03623i
$606$		0			0
$607$			3.07175i			0.124678i	0.998055	+	0.0623392i	$0.0198561\pi$
$607$			3.07175i			0.124678i	−0.998055	+	0.0623392i	$0.980144\pi$
$608$		−	36.2013i		−	1.46816i
$609$		0			0
$610$	2.83928	+	1.03680i	0.114959	+	0.0419790i
$611$	0.159990			0.00647249
$612$		0			0
$613$		−	35.7184i		−	1.44265i	−0.692595	−	0.721327i	$-0.743532\pi$
$613$		−	35.7184i		−	1.44265i	0.692595	−	0.721327i	$-0.256468\pi$
$614$	62.5010			2.52234
$615$		0			0
$616$	27.9011			1.12417
$617$			29.1211i			1.17237i	0.810177	+	0.586185i	$0.199371\pi$
$617$			29.1211i			1.17237i	−0.810177	+	0.586185i	$0.800629\pi$
$618$		0			0
$619$	−11.7565			−0.472534			−0.236267	−	0.971688i	$-0.575924\pi$
$619$	−11.7565			−0.472534			−0.236267	+	0.971688i	$0.575924\pi$
$620$	8.40578	−	23.0192i	0.337584	−	0.924474i
$621$		0			0
$622$		−	21.2764i		−	0.853105i
$623$			40.6742i			1.62958i
$624$		0			0
$625$	4.23742	+	24.6383i	0.169497	+	0.985531i
$626$	4.27317			0.170790
$627$		0			0
$628$		−	23.9984i		−	0.957640i
$629$	−2.55398			−0.101834
$630$		0			0
$631$	30.6569			1.22043			0.610216	−	0.792235i	$-0.291083\pi$
$631$	30.6569			1.22043			0.610216	+	0.792235i	$0.291083\pi$
$632$		−	10.0509i		−	0.399802i
$633$		0			0
$634$	42.9153			1.70438
$635$	−13.4330	−	4.90524i	−0.533072	−	0.194659i
$636$		0			0
$637$		−	5.00117i		−	0.198154i
$638$			8.60198i			0.340556i
$639$		0			0
$640$	22.1542	+	8.08992i	0.875723	+	0.319782i
$641$	45.7844			1.80838			0.904188	−	0.427135i	$-0.140477\pi$
$641$	45.7844			1.80838			0.904188	+	0.427135i	$0.140477\pi$
$642$		0			0
$643$		−	43.7394i		−	1.72491i	−0.506132	−	0.862456i	$-0.668925\pi$
$643$		−	43.7394i		−	1.72491i	0.506132	−	0.862456i	$-0.331075\pi$
$644$	−1.83832			−0.0724400
$645$		0			0
$646$	3.23306			0.127203
$647$		−	10.6969i		−	0.420537i	−0.977644	−	0.210269i	$-0.932566\pi$
$647$		−	10.6969i		−	0.420537i	0.977644	−	0.210269i	$-0.0674338\pi$
$648$		0			0
$649$	−31.4127			−1.23306
$650$	3.64852	+	3.07460i	0.143107	+	0.120596i
$651$		0			0
$652$		−	10.3486i		−	0.405282i
$653$			17.4970i			0.684709i	0.939571	+	0.342355i	$0.111224\pi$
$653$			17.4970i			0.684709i	−0.939571	+	0.342355i	$0.888776\pi$
$654$		0			0
$655$	−12.0262	+	32.9337i	−0.469903	+	1.28683i
$656$	−11.1171			−0.434050
$657$		0			0
$658$			2.16983i			0.0845887i
$659$	38.0331			1.48156			0.740779	−	0.671748i	$-0.234456\pi$
$659$	38.0331			1.48156			0.740779	+	0.671748i	$0.234456\pi$
$660$		0			0
$661$	−1.61112			−0.0626654			−0.0313327	−	0.999509i	$-0.509975\pi$
$661$	−1.61112			−0.0626654			−0.0313327	+	0.999509i	$0.509975\pi$
$662$			56.3469i			2.18999i
$663$		0			0
$664$	8.82149			0.342340
$665$	−51.2411	−	18.7114i	−1.98704	−	0.725597i
$666$		0			0
$667$			0.379104i			0.0146790i
$668$		−	7.17414i		−	0.277576i
$669$		0			0
$670$	−5.42453	+	14.8551i	−0.209568	+	0.573901i
$671$	3.63556			0.140349
$672$		0			0
$673$		−	6.25241i		−	0.241013i	−0.992713	−	0.120506i	$-0.961548\pi$
$673$		−	6.25241i		−	0.241013i	0.992713	−	0.120506i	$-0.0384518\pi$
$674$	40.4074			1.55644
$675$		0			0
$676$	−15.2379			−0.586075
$677$		−	23.4775i		−	0.902312i	−0.892445	−	0.451156i	$-0.851012\pi$
$677$		−	23.4775i		−	0.902312i	0.892445	−	0.451156i	$-0.148988\pi$
$678$		0			0
$679$	9.75221			0.374256
$680$	−0.329696	+	0.902873i	−0.0126433	+	0.0346236i
$681$		0			0
$682$		−	78.6656i		−	3.01226i
$683$			6.95644i			0.266181i	0.991104	+	0.133090i	$0.0424900\pi$
$683$			6.95644i			0.266181i	−0.991104	+	0.133090i	$0.957510\pi$
$684$		0			0
$685$	−29.7821	−	10.8753i	−1.13791	−	0.415525i
$686$	17.1717			0.655619
$687$		0			0
$688$		−	29.8197i		−	1.13686i
$689$	−6.32862			−0.241101
$690$		0			0
$691$	−50.6725			−1.92767			−0.963836	−	0.266498i	$-0.914133\pi$
$691$	−50.6725			−1.92767			−0.963836	+	0.266498i	$0.914133\pi$
$692$			9.29153i			0.353211i
$693$		0			0
$694$	45.2891			1.71915
$695$	4.72394	−	12.9365i	0.179189	−	0.490709i
$696$		0			0
$697$		−	0.671970i		−	0.0254527i
$698$			21.3996i			0.809986i
$699$		0			0
$700$	−15.6239	+	18.5403i	−0.590527	+	0.700759i
$701$	−26.3580			−0.995527			−0.497763	−	0.867313i	$-0.665845\pi$
$701$	−26.3580			−0.995527			−0.497763	+	0.867313i	$0.665845\pi$
$702$		0			0
$703$		−	51.3539i		−	1.93685i
$704$	−3.93015			−0.148123
$705$		0			0
$706$	−49.8049			−1.87443
$707$		−	67.1849i		−	2.52675i
$708$		0			0
$709$	−1.33497			−0.0501357			−0.0250678	−	0.999686i	$-0.507980\pi$
$709$	−1.33497			−0.0501357			−0.0250678	+	0.999686i	$0.507980\pi$
$710$	40.1074	+	14.6458i	1.50520	+	0.549646i
$711$		0			0
$712$			14.4106i			0.540061i
$713$		−	3.46693i		−	0.129838i
$714$		0			0
$715$	5.39054	+	1.96843i	0.201595	+	0.0736152i
$716$	−11.0456			−0.412793
$717$		0			0
$718$			46.2923i			1.72761i
$719$	5.44486			0.203059			0.101530	−	0.994833i	$-0.467626\pi$
$719$	5.44486			0.203059			0.101530	+	0.994833i	$0.467626\pi$
$720$		0			0
$721$	54.2724			2.02121
$722$			31.0286i			1.15476i
$723$		0			0
$724$	−16.6990			−0.620614
$725$	3.82344	+	3.22200i	0.141999	+	0.119662i
$726$		0			0
$727$		−	32.6745i		−	1.21183i	−0.795529	−	0.605916i	$-0.792807\pi$
$727$		−	32.6745i		−	1.21183i	0.795529	−	0.605916i	$-0.207193\pi$
$728$		−	3.09518i		−	0.114715i
$729$		0			0
$730$	15.1511	−	41.4911i	0.560766	−	1.53566i
$731$	1.80244			0.0666657
$732$		0			0
$733$			20.9195i			0.772678i	0.922357	+	0.386339i	$0.126260\pi$
$733$			20.9195i			0.772678i	−0.922357	+	0.386339i	$0.873740\pi$
$734$	−53.7297			−1.98320
$735$		0			0
$736$	−2.27631			−0.0839059
$737$			19.0211i			0.700653i
$738$		0			0
$739$	−13.2392			−0.487011			−0.243505	−	0.969900i	$-0.578297\pi$
$739$	−13.2392			−0.487011			−0.243505	+	0.969900i	$0.578297\pi$
$740$	−21.4400	−	7.82913i	−0.788152	−	0.287804i
$741$		0			0
$742$		−	85.8306i		−	3.15094i
$743$		−	45.8151i		−	1.68079i	−0.541971	−	0.840397i	$-0.682322\pi$
$743$		−	45.8151i		−	1.68079i	0.541971	−	0.840397i	$-0.317678\pi$
$744$		0			0
$745$	−2.53022	+	6.92899i	−0.0926999	+	0.253859i
$746$	−30.9414			−1.13285
$747$		0			0
$748$		−	1.72834i		−	0.0631942i
$749$	36.9032			1.34841
$750$		0			0
$751$	−26.2736			−0.958738			−0.479369	−	0.877614i	$-0.659134\pi$
$751$	−26.2736			−0.958738			−0.479369	+	0.877614i	$0.659134\pi$
$752$			1.48742i			0.0542406i
$753$		0			0
$754$	0.954250			0.0347518
$755$	9.03109	−	24.7316i	0.328675	−	0.900076i
$756$		0			0
$757$			19.2465i			0.699527i	0.936838	+	0.349763i	$0.113738\pi$
$757$			19.2465i			0.699527i	−0.936838	+	0.349763i	$0.886262\pi$
$758$		−	10.7480i		−	0.390384i
$759$		0			0
$760$	−18.1544	−	6.62933i	−0.658529	−	0.240471i
$761$	19.9183			0.722037			0.361019	−	0.932559i	$-0.382429\pi$
$761$	19.9183			0.722037			0.361019	+	0.932559i	$0.382429\pi$
$762$		0			0
$763$		−	51.5422i		−	1.86595i
$764$	18.9980			0.687325
$765$		0			0
$766$	28.5992			1.03333
$767$			3.48473i			0.125826i
$768$		0			0
$769$	−13.5530			−0.488734			−0.244367	−	0.969683i	$-0.578580\pi$
$769$	−13.5530			−0.488734			−0.244367	+	0.969683i	$0.578580\pi$
$770$	−26.6964	+	73.1081i	−0.962072	+	2.63463i
$771$		0			0
$772$		−	14.7834i		−	0.532065i
$773$			4.56321i			0.164127i	0.996627	+	0.0820635i	$0.0261510\pi$
$773$			4.56321i			0.164127i	−0.996627	+	0.0820635i	$0.973849\pi$
$774$		0			0
$775$	−34.9656	−	29.4654i	−1.25600	−	1.05843i
$776$	3.45515			0.124033
$777$		0			0
$778$		−	5.59621i		−	0.200634i
$779$	13.5115			0.484101
$780$		0			0
$781$	51.3555			1.83764
$782$		−	0.203292i		−	0.00726971i
$783$		0			0
$784$	46.4957			1.66056
$785$	−42.0617	−	15.3594i	−1.50124	−	0.548200i
$786$		0			0
$787$		−	17.3056i		−	0.616878i	−0.951244	−	0.308439i	$-0.900193\pi$
$787$		−	17.3056i		−	0.616878i	0.951244	−	0.308439i	$-0.0998066\pi$
$788$			7.80873i			0.278174i
$789$		0			0
$790$	26.3358	+	9.61688i	0.936986	+	0.342153i
$791$	−55.7448			−1.98206
$792$		0			0
$793$		−	0.403307i		−	0.0143218i
$794$	−70.3738			−2.49747
$795$		0			0
$796$	−10.0740			−0.357064
$797$			25.4230i			0.900531i	0.892895	+	0.450265i	$0.148671\pi$
$797$			25.4230i			0.900531i	−0.892895	+	0.450265i	$0.851329\pi$
$798$		0			0
$799$	−0.0899066			−0.00318067
$800$	−19.3463	+	22.9576i	−0.683996	+	0.811675i
$801$		0			0
$802$			9.08247i			0.320713i
$803$		−	53.1273i		−	1.87482i
$804$		0			0
$805$	−1.17656	+	3.22200i	−0.0414682	+	0.113561i
$806$	−8.72668			−0.307384
$807$		0			0
$808$		−	23.8032i		−	0.837393i
$809$	−39.8770			−1.40200			−0.701001	−	0.713160i	$-0.747263\pi$
$809$	−39.8770			−1.40200			−0.701001	+	0.713160i	$0.747263\pi$
$810$		0			0
$811$	37.9902			1.33402			0.667008	−	0.745050i	$-0.267574\pi$
$811$	37.9902			1.33402			0.667008	+	0.745050i	$0.267574\pi$
$812$			4.84912i			0.170171i
$813$		0			0
$814$	−73.2690			−2.56808
$815$	−18.1378	−	6.62327i	−0.635340	−	0.232003i
$816$		0			0
$817$			36.2424i			1.26796i
$818$			7.46937i			0.261160i
$819$		0			0
$820$	2.05990	−	5.64102i	0.0719347	−	0.196993i
$821$	2.02361			0.0706245			0.0353122	−	0.999376i	$-0.488757\pi$
$821$	2.02361			0.0706245			0.0353122	+	0.999376i	$0.488757\pi$
$822$		0			0
$823$		−	1.80919i		−	0.0630642i	−0.999503	−	0.0315321i	$-0.989961\pi$
$823$		−	1.80919i		−	0.0630642i	0.999503	−	0.0315321i	$-0.0100386\pi$
$824$	19.2284			0.669851
$825$		0			0
$826$	−47.2610			−1.64442
$827$			18.8027i			0.653834i	0.945053	+	0.326917i	$0.106010\pi$
$827$			18.8027i			0.653834i	−0.945053	+	0.326917i	$0.893990\pi$
$828$		0			0
$829$	−13.7594			−0.477884			−0.238942	−	0.971034i	$-0.576801\pi$
$829$	−13.7594			−0.477884			−0.238942	+	0.971034i	$0.576801\pi$
$830$	−8.44060	+	23.1146i	−0.292977	+	0.802318i
$831$		0			0
$832$			0.435987i			0.0151151i
$833$			2.81042i			0.0973753i
$834$		0			0
$835$	−12.5740	−	4.59158i	−0.435142	−	0.158898i
$836$	34.7523			1.20193
$837$		0			0
$838$			28.9072i			0.998583i
$839$	−14.1913			−0.489938			−0.244969	−	0.969531i	$-0.578778\pi$
$839$	−14.1913			−0.489938			−0.244969	+	0.969531i	$0.578778\pi$
$840$		0			0
$841$	1.00000			0.0344828
$842$			8.79782i			0.303193i
$843$		0			0
$844$	11.2922			0.388694
$845$	−9.75255	+	26.7073i	−0.335498	+	0.918760i
$846$		0			0
$847$			49.1014i			1.68714i
$848$		−	58.8370i		−	2.02047i
$849$		0			0
$850$	−2.05030	−	1.72778i	−0.0703246	−	0.0592622i
$851$	−3.22909			−0.110692
$852$		0			0
$853$			16.7293i			0.572801i	0.958110	+	0.286401i	$0.0924589\pi$
$853$			16.7293i			0.572801i	−0.958110	+	0.286401i	$0.907541\pi$
$854$	5.46976			0.187171
$855$		0			0
$856$	13.0746			0.446880
$857$			33.2564i			1.13602i	0.823023	+	0.568009i	$0.192286\pi$
$857$			33.2564i			1.13602i	−0.823023	+	0.568009i	$0.807714\pi$
$858$		0			0
$859$	56.5319			1.92884			0.964422	−	0.264366i	$-0.0851628\pi$
$859$	56.5319			1.92884			0.964422	+	0.264366i	$0.0851628\pi$
$860$	15.1311	+	5.52531i	0.515965	+	0.188412i
$861$		0			0
$862$			73.6321i			2.50792i
$863$		−	43.9271i		−	1.49530i	−0.664096	−	0.747648i	$-0.731183\pi$
$863$		−	43.9271i		−	1.49530i	0.664096	−	0.747648i	$-0.268817\pi$
$864$		0			0
$865$	16.2851	+	5.94674i	0.553711	+	0.202195i
$866$	41.0839			1.39609
$867$		0			0
$868$		−	44.3455i		−	1.50519i
$869$	33.7217			1.14393
$870$		0			0
$871$	2.11009			0.0714976
$872$		−	18.2611i		−	0.618397i
$873$		0			0
$874$	4.08767			0.138267
$875$	22.4958	+	39.2499i	0.760498	+	1.32689i
$876$		0			0
$877$		−	13.5059i		−	0.456063i	−0.973654	−	0.228032i	$-0.926771\pi$
$877$		−	13.5059i		−	0.456063i	0.973654	−	0.228032i	$-0.0732290\pi$
$878$		−	9.89261i		−	0.333859i
$879$		0			0
$880$	−18.3004	+	50.1157i	−0.616908	+	1.68940i
$881$	−40.0575			−1.34957			−0.674785	−	0.738014i	$-0.735764\pi$
$881$	−40.0575			−1.34957			−0.674785	+	0.738014i	$0.735764\pi$
$882$		0			0
$883$		−	16.0102i		−	0.538786i	−0.963030	−	0.269393i	$-0.913177\pi$
$883$		−	16.0102i		−	0.538786i	0.963030	−	0.269393i	$-0.0868231\pi$
$884$	−0.191731			−0.00644861
$885$		0			0
$886$	5.40491			0.181581
$887$			13.8430i			0.464802i	0.972620	+	0.232401i	$0.0746581\pi$
$887$			13.8430i			0.464802i	−0.972620	+	0.232401i	$0.925342\pi$
$888$		0			0
$889$	−25.8781			−0.867923
$890$	−37.7595	−	13.7884i	−1.26570	−	0.462188i
$891$		0			0
$892$		−	22.3499i		−	0.748329i
$893$		−	1.80779i		−	0.0604953i
$894$		0			0
$895$	−7.06936	+	19.3594i	−0.236303	+	0.647114i
$896$	42.6792			1.42581
$897$		0			0
$898$		−	13.3109i		−	0.444191i
$899$	−9.14506			−0.305005
$900$		0			0
$901$	3.55639			0.118480
$902$		−	19.2776i		−	0.641873i
$903$		0			0
$904$	−19.7500			−0.656876
$905$	−10.6877	+	29.2681i	−0.355270	+	0.972905i
$906$		0			0
$907$		−	2.47532i		−	0.0821915i	−0.999155	−	0.0410958i	$-0.986915\pi$
$907$		−	2.47532i		−	0.0821915i	0.999155	−	0.0410958i	$-0.0130849\pi$
$908$		−	5.65873i		−	0.187791i
$909$		0			0
$910$	8.11016	+	2.96154i	0.268849	+	0.0981740i
$911$	−4.32063			−0.143149			−0.0715744	−	0.997435i	$-0.522802\pi$
$911$	−4.32063			−0.143149			−0.0715744	+	0.997435i	$0.522802\pi$
$912$		0			0
$913$			29.5970i			0.979518i
$914$	5.02971			0.166368
$915$		0			0
$916$	28.2944			0.934872
$917$			63.4454i			2.09515i
$918$		0			0
$919$	−34.6470			−1.14290			−0.571450	−	0.820637i	$-0.693619\pi$
$919$	−34.6470			−1.14290			−0.571450	+	0.820637i	$0.693619\pi$
$920$	−0.416847	+	1.14153i	−0.0137430	+	0.0376353i
$921$		0			0
$922$			27.5246i			0.906473i
$923$		−	5.69706i		−	0.187521i
$924$		0			0
$925$	−27.4440	+	32.5669i	−0.902353	+	1.07079i
$926$	−42.5597			−1.39860
$927$		0			0
$928$			6.00444i			0.197106i
$929$	9.64854			0.316558			0.158279	−	0.987394i	$-0.449405\pi$
$929$	9.64854			0.316558			0.158279	+	0.987394i	$0.449405\pi$
$930$		0			0
$931$	−56.5102			−1.85205
$932$			18.0908i			0.592585i
$933$		0			0
$934$	−73.6342			−2.40938
$935$	−3.02923	−	1.10616i	−0.0990664	−	0.0361755i
$936$		0			0
$937$			5.16386i			0.168696i	0.996436	+	0.0843480i	$0.0268807\pi$
$937$			5.16386i			0.168696i	−0.996436	+	0.0843480i	$0.973119\pi$
$938$			28.6176i			0.934398i
$939$		0			0
$940$	−0.754744	−	0.275605i	−0.0246170	−	0.00898925i
$941$	−46.0541			−1.50132			−0.750661	−	0.660688i	$-0.770265\pi$
$941$	−46.0541			−1.50132			−0.750661	+	0.660688i	$0.770265\pi$
$942$		0			0
$943$		−	0.849596i		−	0.0276666i
$944$	−32.3975			−1.05445
$945$		0			0
$946$	51.7087			1.68120
$947$		−	7.00646i		−	0.227679i	−0.993499	−	0.113840i	$-0.963685\pi$
$947$		−	7.00646i		−	0.227679i	0.993499	−	0.113840i	$-0.0363150\pi$
$948$		0			0
$949$	−5.89361			−0.191315
$950$	34.7411	−	41.2261i	1.12715	−	1.33755i
$951$		0			0
$952$			1.73934i			0.0563725i
$953$			48.2817i			1.56400i	0.623281	+	0.781998i	$0.285799\pi$
$953$			48.2817i			1.56400i	−0.623281	+	0.781998i	$0.714201\pi$
$954$		0			0
$955$	12.1591	−	33.2976i	0.393459	−	1.07749i
$956$	19.8375			0.641589
$957$		0			0
$958$		−	38.5154i		−	1.24438i
$959$	−57.3738			−1.85270
$960$		0			0
$961$	52.6322			1.69781
$962$			8.12801i			0.262058i
$963$		0			0
$964$	−16.8619			−0.543086
$965$	−25.9106	−	9.46162i	−0.834092	−	0.304580i
$966$		0			0
$967$		−	19.8989i		−	0.639906i	−0.947433	−	0.319953i	$-0.896333\pi$
$967$		−	19.8989i		−	0.639906i	0.947433	−	0.319953i	$-0.103667\pi$
$968$			17.3963i			0.559138i
$969$		0			0
$970$	−3.30596	+	9.05337i	−0.106148	+	0.290686i
$971$	28.8071			0.924464			0.462232	−	0.886759i	$-0.347049\pi$
$971$	28.8071			0.924464			0.462232	+	0.886759i	$0.347049\pi$
$972$		0			0
$973$		−	24.9216i		−	0.798950i
$974$	−11.1109			−0.356015
$975$		0			0
$976$	3.74953			0.120019
$977$			34.4662i			1.10267i	0.834284	+	0.551336i	$0.185882\pi$
$977$			34.4662i			1.10267i	−0.834284	+	0.551336i	$0.814118\pi$
$978$		0			0
$979$	−48.3491			−1.54524
$980$	−8.61523	+	23.5928i	−0.275203	+	0.753644i
$981$		0			0
$982$			43.3691i			1.38396i
$983$		−	21.8433i		−	0.696695i	−0.937366	−	0.348347i	$-0.886743\pi$
$983$		−	21.8433i		−	0.696695i	0.937366	−	0.348347i	$-0.113257\pi$
$984$		0			0
$985$	13.6862	+	4.99772i	0.436080	+	0.159241i
$986$	−0.536243			−0.0170775
$987$		0			0
$988$		−	3.85521i		−	0.122650i
$989$	2.27889			0.0724646
$990$		0			0
$991$	−6.00703			−0.190820			−0.0954099	−	0.995438i	$-0.530416\pi$
$991$	−6.00703			−0.190820			−0.0954099	+	0.995438i	$0.530416\pi$
$992$		−	54.9110i		−	1.74343i
$993$		0			0
$994$	77.2652			2.45070
$995$	−6.44755	+	17.6566i	−0.204401	+	0.559752i
$996$		0			0
$997$			19.9499i			0.631821i	0.948789	+	0.315911i	$0.102310\pi$
$997$			19.9499i			0.631821i	−0.948789	+	0.315911i	$0.897690\pi$
$998$		−	62.5955i		−	1.98143i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1305.2.c.k.784.10	yes	12
3.2	odd	2		1305.2.c.l.784.3	yes	12
5.2	odd	4		6525.2.a.ce.1.3		12
5.3	odd	4		6525.2.a.ce.1.10		12
5.4	even	2	inner	1305.2.c.k.784.3	✓	12
15.2	even	4		6525.2.a.cf.1.10		12
15.8	even	4		6525.2.a.cf.1.3		12
15.14	odd	2		1305.2.c.l.784.10	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1305.2.c.k.784.3	✓	12	5.4	even	2	inner
1305.2.c.k.784.10	yes	12	1.1	even	1	trivial
1305.2.c.l.784.3	yes	12	3.2	odd	2
1305.2.c.l.784.10	yes	12	15.14	odd	2
6525.2.a.ce.1.3		12	5.2	odd	4
6525.2.a.ce.1.10		12	5.3	odd	4
6525.2.a.cf.1.3		12	15.8	even	4
6525.2.a.cf.1.10		12	15.2	even	4

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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)

\(f(q)\)	\(=\)	\(q+1.78841i q^{2} -1.19839 q^{4} +(-0.766993 + 2.10041i) q^{5} +4.04635i q^{7} +1.43360i q^{8} +(-3.75638 - 1.37170i) q^{10} -4.80986 q^{11} +0.533576i q^{13} -7.23651 q^{14} -4.96064 q^{16} -0.299844i q^{17} +6.02908 q^{19} +(0.919161 - 2.51712i) q^{20} -8.60198i q^{22} -0.379104i q^{23} +(-3.82344 - 3.22200i) q^{25} -0.954250 q^{26} -4.84912i q^{28} -1.00000 q^{29} +9.14506 q^{31} -6.00444i q^{32} +0.536243 q^{34} +(-8.49899 - 3.10352i) q^{35} -8.51769i q^{37} +10.7824i q^{38} +(-3.01114 - 1.09956i) q^{40} +2.24106 q^{41} +6.01126i q^{43} +5.76411 q^{44} +0.677992 q^{46} -0.299844i q^{47} -9.37293 q^{49} +(5.76224 - 6.83787i) q^{50} -0.639435i q^{52} +11.8608i q^{53} +(3.68913 - 10.1027i) q^{55} -5.80083 q^{56} -1.78841i q^{58} +6.53090 q^{59} -0.755856 q^{61} +16.3551i q^{62} +0.817104 q^{64} +(-1.12073 - 0.409249i) q^{65} -3.95461i q^{67} +0.359332i q^{68} +(5.55036 - 15.1996i) q^{70} -10.6771 q^{71} +11.0455i q^{73} +15.2331 q^{74} -7.22522 q^{76} -19.4624i q^{77} -7.01095 q^{79} +(3.80478 - 10.4194i) q^{80} +4.00793i q^{82} -6.15340i q^{83} +(0.629796 + 0.229979i) q^{85} -10.7506 q^{86} -6.89539i q^{88} +10.0521 q^{89} -2.15903 q^{91} +0.454316i q^{92} +0.536243 q^{94} +(-4.62427 + 12.6635i) q^{95} -2.41013i q^{97} -16.7626i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 16 q^{4} - 10 q^{10} - 12 q^{11} + 16 q^{14} + 16 q^{16} + 20 q^{19} + 14 q^{20} + 8 q^{25} - 56 q^{26} - 12 q^{29} - 16 q^{31} - 4 q^{34} - 16 q^{35} + 16 q^{40} - 32 q^{41} + 68 q^{44} + 20 q^{46}+ \cdots - 8 q^{95}+O(q^{100}) \) 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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