LMFDB - Embedded newform 585.2.c.c.469.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(469,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, 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("585.469");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 16x^{8} + 90x^{6} + 208x^{4} + 169x^{2} + 16 $ x^10 + 16x^8 + 90x^6 + 208x^4 + 169x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			469.7
Root			$1.22308i$ of defining polynomial
Character	$\chi$	$=$	585.469
Dual form			585.2.c.c.469.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.22308i q^{2} +0.504085 q^{4} +(0.638796 - 2.14288i) q^{5} -4.18388i q^{7} +3.06269i q^{8} +O(q^{10})$	\(q+1.22308i q^{2} +0.504085 q^{4} +(0.638796 - 2.14288i) q^{5} -4.18388i q^{7} +3.06269i q^{8} +(2.62091 + 0.781296i) q^{10} -1.89812 q^{11} -1.00000i q^{13} +5.11720 q^{14} -2.73773 q^{16} -1.73773i q^{17} +1.11720 q^{19} +(0.322008 - 1.08019i) q^{20} -2.32154i q^{22} -9.30108i q^{23} +(-4.18388 - 2.73773i) q^{25} +1.22308 q^{26} -2.10903i q^{28} +5.00817 q^{29} +10.0095 q^{31} +2.77692i q^{32} +2.12537 q^{34} +(-8.96556 - 2.67265i) q^{35} +11.3011i q^{37} +1.36642i q^{38} +(6.56297 + 1.95643i) q^{40} -8.02349 q^{41} +1.00817i q^{43} -0.956813 q^{44} +11.3759 q^{46} +5.63584i q^{47} -10.5048 q^{49} +(3.34845 - 5.11720i) q^{50} -0.504085i q^{52} -0.174373i q^{53} +(-1.21251 + 4.06744i) q^{55} +12.8139 q^{56} +6.12537i q^{58} +8.64402 q^{59} +3.27044 q^{61} +12.2424i q^{62} -8.87184 q^{64} +(-2.14288 - 0.638796i) q^{65} +11.4543i q^{67} -0.875963i q^{68} +(3.26885 - 10.9656i) q^{70} +5.37357 q^{71} -4.01634i q^{73} -13.8221 q^{74} +0.563165 q^{76} +7.94149i q^{77} +0.613690 q^{79} +(-1.74885 + 5.86662i) q^{80} -9.81334i q^{82} +9.08333i q^{83} +(-3.72374 - 1.11005i) q^{85} -1.23307 q^{86} -5.81334i q^{88} -1.46831 q^{89} -4.18388 q^{91} -4.68854i q^{92} -6.89307 q^{94} +(0.713664 - 2.39403i) q^{95} -3.85359i q^{97} -12.8482i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 12 q^{4} + 2 q^{5}+O(q^{10}) $ 10 * q - 12 * q^4 + 2 * q^5	$ 10 q - 12 q^{4} + 2 q^{5} + 4 q^{10} - 10 q^{11} + 24 q^{14} - 16 q^{19} - 32 q^{20} + 10 q^{25} + 16 q^{29} + 24 q^{31} - 40 q^{34} - 12 q^{35} + 36 q^{40} - 10 q^{41} + 36 q^{44} - 24 q^{46} - 44 q^{49} - 40 q^{50} + 2 q^{55} + 16 q^{59} + 26 q^{61} + 32 q^{64} + 56 q^{70} - 10 q^{71} + 24 q^{74} - 2 q^{79} + 12 q^{80} - 4 q^{85} + 38 q^{89} + 10 q^{91} + 24 q^{94} + 48 q^{95}+O(q^{100}) $ 10 * q - 12 * q^4 + 2 * q^5 + 4 * q^10 - 10 * q^11 + 24 * q^14 - 16 * q^19 - 32 * q^20 + 10 * q^25 + 16 * q^29 + 24 * q^31 - 40 * q^34 - 12 * q^35 + 36 * q^40 - 10 * q^41 + 36 * q^44 - 24 * q^46 - 44 * q^49 - 40 * q^50 + 2 * q^55 + 16 * q^59 + 26 * q^61 + 32 * q^64 + 56 * q^70 - 10 * q^71 + 24 * q^74 - 2 * q^79 + 12 * q^80 - 4 * q^85 + 38 * q^89 + 10 * q^91 + 24 * q^94 + 48 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$			1.22308i			0.864845i	0.901671	+	0.432423i	$0.142341\pi$
$2$			1.22308i			0.864845i	−0.901671	+	0.432423i	$0.857659\pi$
$3$		0			0
$3$		0			0
$4$	0.504085			0.252043
$5$	0.638796	−	2.14288i	0.285678	−	0.958326i
$5$	0.638796	−	2.14288i	0.285678	−	0.958326i
$6$		0			0
$7$		−	4.18388i		−	1.58136i	−0.612231	−	0.790679i	$-0.709728\pi$
$7$		−	4.18388i		−	1.58136i	0.612231	−	0.790679i	$-0.290272\pi$
$8$			3.06269i			1.08282i
$9$		0			0
$10$	2.62091	+	0.781296i	0.828803	+	0.247067i
$11$	−1.89812			−0.572304			−0.286152	−	0.958184i	$-0.592376\pi$
$11$	−1.89812			−0.572304			−0.286152	+	0.958184i	$0.592376\pi$
$12$		0			0
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	5.11720			1.36763
$15$		0			0
$16$	−2.73773			−0.684432
$17$		−	1.73773i		−	0.421461i	−0.977544	−	0.210730i	$-0.932416\pi$
$17$		−	1.73773i		−	0.421461i	0.977544	−	0.210730i	$-0.0675842\pi$
$18$		0			0
$19$	1.11720			0.256304			0.128152	−	0.991755i	$-0.459095\pi$
$19$	1.11720			0.256304			0.128152	+	0.991755i	$0.459095\pi$
$20$	0.322008	−	1.08019i	0.0720031	−	0.241539i
$21$		0			0
$22$		−	2.32154i		−	0.494954i
$23$		−	9.30108i		−	1.93941i	−0.244280	−	0.969705i	$-0.578552\pi$
$23$		−	9.30108i		−	1.93941i	0.244280	−	0.969705i	$-0.421448\pi$
$24$		0			0
$25$	−4.18388	−	2.73773i	−0.836776	−	0.547546i
$26$	1.22308			0.239865
$27$		0			0
$28$		−	2.10903i		−	0.398570i
$29$	5.00817			0.929994			0.464997	−	0.885312i	$-0.346055\pi$
$29$	5.00817			0.929994			0.464997	+	0.885312i	$0.346055\pi$
$30$		0			0
$31$	10.0095			1.79776			0.898880	−	0.438194i	$-0.144382\pi$
$31$	10.0095			1.79776			0.898880	+	0.438194i	$0.144382\pi$
$32$			2.77692i			0.490895i
$33$		0			0
$34$	2.12537			0.364498
$35$	−8.96556	−	2.67265i	−1.51546	−	0.451759i
$36$		0			0
$37$			11.3011i			1.85789i	0.370222	+	0.928943i	$0.379282\pi$
$37$			11.3011i			1.85789i	−0.370222	+	0.928943i	$0.620718\pi$
$38$			1.36642i			0.221663i
$39$		0			0
$40$	6.56297	+	1.95643i	1.03770	+	0.309339i
$41$	−8.02349			−1.25306			−0.626529	−	0.779398i	$-0.715525\pi$
$41$	−8.02349			−1.25306			−0.626529	+	0.779398i	$0.715525\pi$
$42$		0			0
$43$			1.00817i			0.153745i	0.997041	+	0.0768723i	$0.0244934\pi$
$43$			1.00817i			0.153745i	−0.997041	+	0.0768723i	$0.975507\pi$
$44$	−0.956813			−0.144245
$45$		0			0
$46$	11.3759			1.67729
$47$			5.63584i			0.822072i	0.911619	+	0.411036i	$0.134833\pi$
$47$			5.63584i			0.822072i	−0.911619	+	0.411036i	$0.865167\pi$
$48$		0			0
$49$	−10.5048			−1.50069
$50$	3.34845	−	5.11720i	0.473542	−	0.723682i
$51$		0			0
$52$		−	0.504085i		−	0.0699040i
$53$		−	0.174373i		−	0.0239520i	−0.999928	−	0.0119760i	$-0.996188\pi$
$53$		−	0.174373i		−	0.0239520i	0.999928	−	0.0119760i	$-0.00381217\pi$
$54$		0			0
$55$	−1.21251	+	4.06744i	−0.163495	+	0.548453i
$56$	12.8139			1.71233
$57$		0			0
$58$			6.12537i			0.804301i
$59$	8.64402			1.12535			0.562677	−	0.826677i	$-0.309771\pi$
$59$	8.64402			1.12535			0.562677	+	0.826677i	$0.309771\pi$
$60$		0			0
$61$	3.27044			0.418737			0.209369	−	0.977837i	$-0.432859\pi$
$61$	3.27044			0.418737			0.209369	+	0.977837i	$0.432859\pi$
$62$			12.2424i			1.55478i
$63$		0			0
$64$	−8.87184			−1.10898
$65$	−2.14288	−	0.638796i	−0.265792	−	0.0792329i
$66$		0			0
$67$			11.4543i			1.39937i	0.714452	+	0.699684i	$0.246676\pi$
$67$			11.4543i			1.39937i	−0.714452	+	0.699684i	$0.753324\pi$
$68$		−	0.875963i		−	0.106226i
$69$		0			0
$70$	3.26885	−	10.9656i	0.390702	−	1.31063i
$71$	5.37357			0.637726			0.318863	−	0.947801i	$-0.396699\pi$
$71$	5.37357			0.637726			0.318863	+	0.947801i	$0.396699\pi$
$72$		0			0
$73$		−	4.01634i		−	0.470077i	−0.971986	−	0.235039i	$-0.924478\pi$
$73$		−	4.01634i		−	0.470077i	0.971986	−	0.235039i	$-0.0755216\pi$
$74$	−13.8221			−1.60678
$75$		0			0
$76$	0.563165			0.0645995
$77$			7.94149i			0.905017i
$78$		0			0
$79$	0.613690			0.0690456			0.0345228	−	0.999404i	$-0.489009\pi$
$79$	0.613690			0.0690456			0.0345228	+	0.999404i	$0.489009\pi$
$80$	−1.74885	+	5.86662i	−0.195527	+	0.655909i
$81$		0			0
$82$		−	9.81334i		−	1.08370i
$83$			9.08333i			0.997025i	0.866882	+	0.498513i	$0.166120\pi$
$83$			9.08333i			0.997025i	−0.866882	+	0.498513i	$0.833880\pi$
$84$		0			0
$85$	−3.72374	−	1.11005i	−0.403897	−	0.120402i
$86$	−1.23307			−0.132965
$87$		0			0
$88$		−	5.81334i		−	0.619704i
$89$	−1.46831			−0.155640			−0.0778201	−	0.996967i	$-0.524796\pi$
$89$	−1.46831			−0.155640			−0.0778201	+	0.996967i	$0.524796\pi$
$90$		0			0
$91$	−4.18388			−0.438590
$92$		−	4.68854i		−	0.488814i
$93$		0			0
$94$	−6.89307			−0.710965
$95$	0.713664	−	2.39403i	0.0732204	−	0.245622i
$96$		0			0
$97$		−	3.85359i		−	0.391273i	−0.980676	−	0.195637i	$-0.937323\pi$
$97$		−	3.85359i		−	0.391273i	0.980676	−	0.195637i	$-0.0626773\pi$
$98$		−	12.8482i		−	1.29787i
$99$		0			0
$100$	−2.10903	−	1.38005i	−0.210903	−	0.138005i
$101$	2.57152			0.255876			0.127938	−	0.991782i	$-0.459164\pi$
$101$	2.57152			0.255876			0.127938	+	0.991782i	$0.459164\pi$
$102$		0			0
$103$		−	1.53272i		−	0.151023i	−0.997145	−	0.0755115i	$-0.975941\pi$
$103$		−	1.53272i		−	0.151023i	0.997145	−	0.0755115i	$-0.0240589\pi$
$104$	3.06269			0.300321
$105$		0			0
$106$	0.213272			0.0207148
$107$		−	8.63003i		−	0.834297i	−0.908838	−	0.417148i	$-0.863030\pi$
$107$		−	8.63003i		−	0.834297i	0.908838	−	0.417148i	$-0.136970\pi$
$108$		0			0
$109$	−12.0306			−1.15233			−0.576163	−	0.817335i	$-0.695451\pi$
$109$	−12.0306			−1.15233			−0.576163	+	0.817335i	$0.695451\pi$
$110$	−4.97479	−	1.48299i	−0.474327	−	0.141398i
$111$		0			0
$112$			11.4543i			1.08233i
$113$			7.93111i			0.746096i	0.927812	+	0.373048i	$0.121687\pi$
$113$			7.93111i			0.746096i	−0.927812	+	0.373048i	$0.878313\pi$
$114$		0			0
$115$	−19.9311	−	5.94149i	−1.85859	−	0.554047i
$116$	2.52454			0.234398
$117$		0			0
$118$			10.5723i			0.973258i
$119$	−7.27044			−0.666480
$120$		0			0
$121$	−7.39715			−0.672468
$122$			4.00000i			0.362143i
$123$		0			0
$124$	5.04564			0.453112
$125$	−8.53927	+	7.21671i	−0.763776	+	0.645482i
$126$		0			0
$127$			2.35142i			0.208655i	0.994543	+	0.104327i	$0.0332690\pi$
$127$			2.35142i			0.208655i	−0.994543	+	0.104327i	$0.966731\pi$
$128$		−	5.29709i		−	0.468201i
$129$		0			0
$130$	0.781296	−	2.62091i	0.0685242	−	0.229869i
$131$	9.46383			0.826859			0.413429	−	0.910536i	$-0.364331\pi$
$131$	9.46383			0.826859			0.413429	+	0.910536i	$0.364331\pi$
$132$		0			0
$133$		−	4.67424i		−	0.405308i
$134$	−14.0095			−1.21024
$135$		0			0
$136$	5.32211			0.456368
$137$			4.48953i			0.383566i	0.981437	+	0.191783i	$0.0614270\pi$
$137$			4.48953i			0.383566i	−0.981437	+	0.191783i	$0.938573\pi$
$138$		0			0
$139$	13.5048			1.14547			0.572733	−	0.819742i	$-0.305883\pi$
$139$	13.5048			1.14547			0.572733	+	0.819742i	$0.305883\pi$
$140$	−4.51940	−	1.34724i	−0.381959	−	0.113863i
$141$		0			0
$142$			6.57229i			0.551534i
$143$			1.89812i			0.158729i
$144$		0			0
$145$	3.19920	−	10.7319i	0.265679	−	0.891237i
$146$	4.91229			0.406544
$147$		0			0
$148$			5.69671i			0.468267i
$149$	5.44034			0.445690			0.222845	−	0.974854i	$-0.428466\pi$
$149$	5.44034			0.445690			0.222845	+	0.974854i	$0.428466\pi$
$150$		0			0
$151$	−8.55039			−0.695821			−0.347911	−	0.937528i	$-0.613109\pi$
$151$	−8.55039			−0.695821			−0.347911	+	0.937528i	$0.613109\pi$
$152$			3.42164i			0.277532i
$153$		0			0
$154$	−9.71305			−0.782700
$155$	6.39403	−	21.4492i	0.513581	−	1.72284i
$156$		0			0
$157$			17.1430i			1.36816i	0.729405	+	0.684082i	$0.239797\pi$
$157$			17.1430i			1.36816i	−0.729405	+	0.684082i	$0.760203\pi$
$158$			0.750590i			0.0597137i
$159$		0			0
$160$	5.95062	+	1.77389i	0.470438	+	0.140238i
$161$	−38.9146			−3.06690
$162$		0			0
$163$		−	18.2145i		−	1.42667i	−0.700823	−	0.713336i	$-0.747184\pi$
$163$		−	18.2145i		−	1.42667i	0.700823	−	0.713336i	$-0.252816\pi$
$164$	−4.04452			−0.315824
$165$		0			0
$166$	−11.1096			−0.862273
$167$			7.97296i			0.616967i	0.951230	+	0.308483i	$0.0998214\pi$
$167$			7.97296i			0.616967i	−0.951230	+	0.308483i	$0.900179\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	1.35768	−	4.55442i	0.104129	−	0.349308i
$171$		0			0
$172$			0.508204i			0.0387502i
$173$		−	12.9086i		−	0.981426i	−0.871321	−	0.490713i	$-0.836736\pi$
$173$		−	12.9086i		−	0.981426i	0.871321	−	0.490713i	$-0.163264\pi$
$174$		0			0
$175$	−11.4543	+	17.5048i	−0.865865	+	1.32324i
$176$	5.19653			0.391703
$177$		0			0
$178$		−	1.79585i		−	0.134605i
$179$	−7.47546			−0.558742			−0.279371	−	0.960183i	$-0.590126\pi$
$179$	−7.47546			−0.558742			−0.279371	+	0.960183i	$0.590126\pi$
$180$		0			0
$181$	−6.16275			−0.458073			−0.229037	−	0.973418i	$-0.573558\pi$
$181$	−6.16275			−0.458073			−0.229037	+	0.973418i	$0.573558\pi$
$182$		−	5.11720i		−	0.379312i
$183$		0			0
$184$	28.4863			2.10004
$185$	24.2169	+	7.21909i	1.78046	+	0.530758i
$186$		0			0
$187$			3.29841i			0.241204i
$188$			2.84095i			0.207197i
$189$		0			0
$190$	2.92808	+	0.872866i	0.212425	+	0.0633243i
$191$	−3.79776			−0.274796			−0.137398	−	0.990516i	$-0.543874\pi$
$191$	−3.79776			−0.274796			−0.137398	+	0.990516i	$0.543874\pi$
$192$		0			0
$193$		−	17.3174i		−	1.24654i	−0.782009	−	0.623268i	$-0.785805\pi$
$193$		−	17.3174i		−	1.24654i	0.782009	−	0.623268i	$-0.214195\pi$
$194$	4.71324			0.338391
$195$		0			0
$196$	−5.29534			−0.378238
$197$			6.31640i			0.450025i	0.974356	+	0.225012i	$0.0722423\pi$
$197$			6.31640i			0.450025i	−0.974356	+	0.225012i	$0.927758\pi$
$198$		0			0
$199$	2.77377			0.196627			0.0983135	−	0.995155i	$-0.468655\pi$
$199$	2.77377			0.196627			0.0983135	+	0.995155i	$0.468655\pi$
$200$	8.38480	−	12.8139i	0.592895	−	0.906080i
$201$		0			0
$202$			3.14517i			0.221293i
$203$		−	20.9536i		−	1.47065i
$204$		0			0
$205$	−5.12537	+	17.1934i	−0.357972	+	1.20084i
$206$	1.87463			0.130611
$207$		0			0
$208$			2.73773i			0.189827i
$209$	−2.12058			−0.146684
$210$		0			0
$211$	10.7928			0.743005			0.371503	−	0.928432i	$-0.378843\pi$
$211$	10.7928			0.743005			0.371503	+	0.928432i	$0.378843\pi$
$212$		−	0.0878990i		−	0.00603693i
$213$		0			0
$214$	10.5552			0.721538
$215$	2.16039	+	0.644015i	0.147337	+	0.0439215i
$216$		0			0
$217$		−	41.8786i		−	2.84290i
$218$		−	14.7144i		−	0.996584i
$219$		0			0
$220$	−0.611208	+	2.05034i	−0.0412076	+	0.138234i
$221$	−1.73773			−0.116892
$222$		0			0
$223$			23.1526i			1.55041i	0.631710	+	0.775205i	$0.282353\pi$
$223$			23.1526i			1.55041i	−0.631710	+	0.775205i	$0.717647\pi$
$224$	11.6183			0.776281
$225$		0			0
$226$	−9.70035			−0.645258
$227$			25.0690i			1.66389i	0.554858	+	0.831945i	$0.312773\pi$
$227$			25.0690i			1.66389i	−0.554858	+	0.831945i	$0.687227\pi$
$228$		0			0
$229$	−0.786917			−0.0520009			−0.0260005	−	0.999662i	$-0.508277\pi$
$229$	−0.786917			−0.0520009			−0.0260005	+	0.999662i	$0.508277\pi$
$230$	7.26690	−	24.3773i	0.479165	−	1.60739i
$231$		0			0
$232$			15.3385i			1.00702i
$233$			1.85627i			0.121608i	0.998150	+	0.0608040i	$0.0193665\pi$
$233$			1.85627i			0.121608i	−0.998150	+	0.0608040i	$0.980634\pi$
$234$		0			0
$235$	12.0769	+	3.60015i	0.787813	+	0.234848i
$236$	4.35732			0.283637
$237$		0			0
$238$		−	8.89230i		−	0.576402i
$239$	−7.35723			−0.475900			−0.237950	−	0.971277i	$-0.576475\pi$
$239$	−7.35723			−0.475900			−0.237950	+	0.971277i	$0.576475\pi$
$240$		0			0
$241$	−16.0497			−1.03385			−0.516924	−	0.856031i	$-0.672923\pi$
$241$	−16.0497			−1.03385			−0.516924	+	0.856031i	$0.672923\pi$
$242$		−	9.04728i		−	0.581581i
$243$		0			0
$244$	1.64858			0.105540
$245$	−6.71045	+	22.5106i	−0.428715	+	1.43815i
$246$		0			0
$247$		−	1.11720i		−	0.0710859i
$248$			30.6560i			1.94666i
$249$		0			0
$250$	−8.82658	−	10.4442i	−0.558242	−	0.660548i
$251$	−16.1185			−1.01739			−0.508697	−	0.860946i	$-0.669872\pi$
$251$	−16.1185			−1.01739			−0.508697	+	0.860946i	$0.669872\pi$
$252$		0			0
$253$			17.6545i			1.10993i
$254$	−2.87596			−0.180454
$255$		0			0
$256$	−11.2649			−0.704059
$257$			9.78194i			0.610180i	0.952323	+	0.305090i	$0.0986866\pi$
$257$			9.78194i			0.610180i	−0.952323	+	0.305090i	$0.901313\pi$
$258$		0			0
$259$	47.2824			2.93798
$260$	−1.08019	−	0.322008i	−0.0669908	−	0.0199701i
$261$		0			0
$262$			11.5750i			0.715105i
$263$		−	3.12518i		−	0.192707i	−0.995347	−	0.0963535i	$-0.969282\pi$
$263$		−	3.12518i		−	0.192707i	0.995347	−	0.0963535i	$-0.0307179\pi$
$264$		0			0
$265$	−0.373661	−	0.111389i	−0.0229538	−	0.00684257i
$266$	5.71695			0.350529
$267$		0			0
$268$			5.77395i			0.352700i
$269$	15.8444			0.966048			0.483024	−	0.875607i	$-0.339538\pi$
$269$	15.8444			0.966048			0.483024	+	0.875607i	$0.339538\pi$
$270$		0			0
$271$	6.44501			0.391506			0.195753	−	0.980653i	$-0.437285\pi$
$271$	6.44501			0.391506			0.195753	+	0.980653i	$0.437285\pi$
$272$			4.75742i			0.288461i
$273$		0			0
$274$	−5.49103			−0.331725
$275$	7.94149	+	5.19653i	0.478890	+	0.313362i
$276$		0			0
$277$		−	13.6676i		−	0.821206i	−0.911814	−	0.410603i	$-0.865318\pi$
$277$		−	13.6676i		−	0.821206i	0.911814	−	0.410603i	$-0.134682\pi$
$278$			16.5175i			0.990651i
$279$		0			0
$280$	8.18547	−	27.4587i	0.489176	−	1.64097i
$281$	21.2966			1.27045			0.635224	−	0.772328i	$-0.280908\pi$
$281$	21.2966			1.27045			0.635224	+	0.772328i	$0.280908\pi$
$282$		0			0
$283$		−	22.1524i		−	1.31682i	−0.752659	−	0.658411i	$-0.771229\pi$
$283$		−	22.1524i		−	1.31682i	0.752659	−	0.658411i	$-0.228771\pi$
$284$	2.70874			0.160734
$285$		0			0
$286$	−2.32154			−0.137276
$287$			33.5693i			1.98153i
$288$		0			0
$289$	13.9803			0.822371
$290$	13.1259	+	3.91286i	0.770782	+	0.229771i
$291$		0			0
$292$		−	2.02458i		−	0.118479i
$293$		−	21.9677i		−	1.28336i	−0.766971	−	0.641682i	$-0.778237\pi$
$293$		−	21.9677i		−	1.28336i	0.766971	−	0.641682i	$-0.221763\pi$
$294$		0			0
$295$	5.52176	−	18.5231i	0.321489	−	1.07846i
$296$	−34.6117			−2.01176
$297$		0			0
$298$			6.65395i			0.385453i
$299$	−9.30108			−0.537895
$300$		0			0
$301$	4.21806			0.243125
$302$		−	10.4578i		−	0.601778i
$303$		0			0
$304$	−3.05860			−0.175422
$305$	2.08915	−	7.00817i	0.119624	−	0.401287i
$306$		0			0
$307$			24.5516i			1.40124i	0.713537	+	0.700618i	$0.247092\pi$
$307$			24.5516i			1.40124i	−0.713537	+	0.700618i	$0.752908\pi$
$308$			4.00319i			0.228103i
$309$		0			0
$310$	26.2340	+	7.82039i	1.48999	+	0.444168i
$311$	28.3295			1.60642			0.803210	−	0.595697i	$-0.203124\pi$
$311$	28.3295			1.60642			0.803210	+	0.595697i	$0.203124\pi$
$312$		0			0
$313$			18.1497i			1.02588i	0.858424	+	0.512941i	$0.171444\pi$
$313$			18.1497i			1.02588i	−0.858424	+	0.512941i	$0.828556\pi$
$314$	−20.9673			−1.18325
$315$		0			0
$316$	0.309352			0.0174024
$317$		−	10.3021i		−	0.578624i	−0.957235	−	0.289312i	$-0.906574\pi$
$317$		−	10.3021i		−	0.578624i	0.957235	−	0.289312i	$-0.0934265\pi$
$318$		0			0
$319$	−9.50609			−0.532239
$320$	−5.66730	+	19.0113i	−0.316812	+	1.06276i
$321$		0			0
$322$		−	47.5955i		−	2.65239i
$323$		−	1.94139i		−	0.108022i
$324$		0			0
$325$	−2.73773	+	4.18388i	−0.151862	+	0.232080i
$326$	22.2777			1.23385
$327$		0			0
$328$		−	24.5734i		−	1.35684i
$329$	23.5797			1.29999
$330$		0			0
$331$	33.3002			1.83034			0.915172	−	0.403062i	$-0.132054\pi$
$331$	33.3002			1.83034			0.915172	+	0.403062i	$0.132054\pi$
$332$			4.57877i			0.251293i
$333$		0			0
$334$	−9.75154			−0.533581
$335$	24.5453	+	7.31697i	1.34105	+	0.399769i
$336$		0			0
$337$		−	13.2437i		−	0.721431i	−0.932676	−	0.360716i	$-0.882532\pi$
$337$		−	13.2437i		−	0.721431i	0.932676	−	0.360716i	$-0.117468\pi$
$338$		−	1.22308i		−	0.0665266i
$339$		0			0
$340$	−1.87708	−	0.559562i	−0.101799	−	0.0303465i
$341$	−18.9992			−1.02887
$342$		0			0
$343$			14.6639i			0.791774i
$344$	−3.08771			−0.166478
$345$		0			0
$346$	15.7883			0.848782
$347$		−	24.0250i		−	1.28973i	−0.764297	−	0.644864i	$-0.776914\pi$
$347$		−	24.0250i		−	1.28973i	0.764297	−	0.644864i	$-0.223086\pi$
$348$		0			0
$349$	−6.23173			−0.333577			−0.166789	−	0.985993i	$-0.553340\pi$
$349$	−6.23173			−0.333577			−0.166789	+	0.985993i	$0.553340\pi$
$350$	−21.4098	−	14.0095i	−1.14440	−	0.748840i
$351$		0			0
$352$		−	5.27093i		−	0.280941i
$353$			30.2041i			1.60760i	0.594898	+	0.803801i	$0.297192\pi$
$353$			30.2041i			1.60760i	−0.594898	+	0.803801i	$0.702808\pi$
$354$		0			0
$355$	3.43262	−	11.5149i	0.182184	−	0.611149i
$356$	−0.740151			−0.0392279
$357$		0			0
$358$		−	9.14305i		−	0.483225i
$359$	12.8525			0.678329			0.339164	−	0.940727i	$-0.389856\pi$
$359$	12.8525			0.678329			0.339164	+	0.940727i	$0.389856\pi$
$360$		0			0
$361$	−17.7519			−0.934308
$362$		−	7.53751i		−	0.396163i
$363$		0			0
$364$	−2.10903			−0.110543
$365$	−8.60654	−	2.56562i	−0.450487	−	0.134291i
$366$		0			0
$367$			27.3923i			1.42986i	0.699194	+	0.714932i	$0.253543\pi$
$367$			27.3923i			1.42986i	−0.699194	+	0.714932i	$0.746457\pi$
$368$			25.4638i			1.32739i
$369$		0			0
$370$	−8.82949	+	29.6191i	−0.459023	+	1.53982i
$371$	−0.729557			−0.0378767
$372$		0			0
$373$			18.9113i			0.979191i	0.871950	+	0.489595i	$0.162856\pi$
$373$			18.9113i			0.979191i	−0.871950	+	0.489595i	$0.837144\pi$
$374$	−4.03421			−0.208604
$375$		0			0
$376$	−17.2608			−0.890159
$377$		−	5.00817i		−	0.257934i
$378$		0			0
$379$	−20.7424			−1.06546			−0.532732	−	0.846284i	$-0.678834\pi$
$379$	−20.7424			−1.06546			−0.532732	+	0.846284i	$0.678834\pi$
$380$	0.359748	−	1.20680i	0.0184547	−	0.0619073i
$381$		0			0
$382$		−	4.64495i		−	0.237656i
$383$		−	21.0833i		−	1.07731i	−0.842527	−	0.538654i	$-0.818933\pi$
$383$		−	21.0833i		−	1.07731i	0.842527	−	0.538654i	$-0.181067\pi$
$384$		0			0
$385$	17.0177	+	5.07299i	0.867301	+	0.258544i
$386$	21.1805			1.07806
$387$		0			0
$388$		−	1.94254i		−	0.0986175i
$389$	−22.4583			−1.13868			−0.569341	−	0.822101i	$-0.692802\pi$
$389$	−22.4583			−1.13868			−0.569341	+	0.822101i	$0.692802\pi$
$390$		0			0
$391$	−16.1627			−0.817385
$392$		−	32.1731i		−	1.62498i
$393$		0			0
$394$	−7.72544			−0.389202
$395$	0.392023	−	1.31507i	0.0197248	−	0.0661681i
$396$		0			0
$397$			17.3038i			0.868450i	0.900804	+	0.434225i	$0.142978\pi$
$397$			17.3038i			0.868450i	−0.900804	+	0.434225i	$0.857022\pi$
$398$			3.39253i			0.170052i
$399$		0			0
$400$	11.4543	+	7.49515i	0.572716	+	0.374758i
$401$	8.01044			0.400022			0.200011	−	0.979794i	$-0.435902\pi$
$401$	8.01044			0.400022			0.200011	+	0.979794i	$0.435902\pi$
$402$		0			0
$403$		−	10.0095i		−	0.498609i
$404$	1.29627			0.0644917
$405$		0			0
$406$	25.6278			1.27189
$407$		−	21.4508i		−	1.06328i
$408$		0			0
$409$	−26.6885			−1.31966			−0.659832	−	0.751413i	$-0.729372\pi$
$409$	−26.6885			−1.31966			−0.659832	+	0.751413i	$0.729372\pi$
$410$	−21.0288	−	6.26872i	−1.03854	−	0.309590i
$411$		0			0
$412$		−	0.772619i		−	0.0380642i
$413$		−	36.1655i		−	1.77959i
$414$		0			0
$415$	19.4645	+	5.80240i	0.955475	+	0.284828i
$416$	2.77692			0.136150
$417$		0			0
$418$		−	2.59363i		−	0.126859i
$419$	1.83868			0.0898253			0.0449127	−	0.998991i	$-0.485699\pi$
$419$	1.83868			0.0898253			0.0449127	+	0.998991i	$0.485699\pi$
$420$		0			0
$421$	6.16399			0.300415			0.150207	−	0.988655i	$-0.452006\pi$
$421$	6.16399			0.300415			0.150207	+	0.988655i	$0.452006\pi$
$422$			13.2004i			0.642585i
$423$		0			0
$424$	0.534051			0.0259358
$425$	−4.75742	+	7.27044i	−0.230769	+	0.352668i
$426$		0			0
$427$		−	13.6831i		−	0.662173i
$428$		−	4.35027i		−	0.210278i
$429$		0			0
$430$	−0.787680	+	2.64232i	−0.0379853	+	0.127424i
$431$	31.1292			1.49944			0.749720	−	0.661756i	$-0.230188\pi$
$431$	31.1292			1.49944			0.749720	+	0.661756i	$0.230188\pi$
$432$		0			0
$433$		−	4.01634i		−	0.193013i	−0.995332	−	0.0965065i	$-0.969233\pi$
$433$		−	4.01634i		−	0.193013i	0.995332	−	0.0965065i	$-0.0307669\pi$
$434$	51.2207			2.45867
$435$		0			0
$436$	−6.06447			−0.290435
$437$		−	10.3912i		−	0.497078i
$438$		0			0
$439$	20.3808			0.972723			0.486362	−	0.873758i	$-0.338324\pi$
$439$	20.3808			0.972723			0.486362	+	0.873758i	$0.338324\pi$
$440$	−12.4573	−	3.71354i	−0.593878	−	0.177036i
$441$		0			0
$442$		−	2.12537i		−	0.101094i
$443$		−	14.4967i		−	0.688758i	−0.938831	−	0.344379i	$-0.888090\pi$
$443$		−	14.4967i		−	0.688758i	0.938831	−	0.344379i	$-0.111910\pi$
$444$		0			0
$445$	−0.937948	+	3.14641i	−0.0444630	+	0.149154i
$446$	−28.3173			−1.34086
$447$		0			0
$448$			37.1187i			1.75370i
$449$	−3.09141			−0.145893			−0.0729464	−	0.997336i	$-0.523240\pi$
$449$	−3.09141			−0.145893			−0.0729464	+	0.997336i	$0.523240\pi$
$450$		0			0
$451$	15.2295			0.717130
$452$			3.99796i			0.188048i
$453$		0			0
$454$	−30.6613			−1.43901
$455$	−2.67265	+	8.96556i	−0.125296	+	0.420312i
$456$		0			0
$457$			23.7556i			1.11124i	0.831436	+	0.555620i	$0.187519\pi$
$457$			23.7556i			1.11124i	−0.831436	+	0.555620i	$0.812481\pi$
$458$		−	0.962459i		−	0.0449728i
$459$		0			0
$460$	−10.0470	−	2.99502i	−0.468443	−	0.139643i
$461$	−38.1201			−1.77543			−0.887716	−	0.460392i	$-0.847709\pi$
$461$	−38.1201			−1.77543			−0.887716	+	0.460392i	$0.847709\pi$
$462$		0			0
$463$		−	26.7670i		−	1.24397i	−0.783029	−	0.621985i	$-0.786327\pi$
$463$		−	26.7670i		−	1.24397i	0.783029	−	0.621985i	$-0.213673\pi$
$464$	−13.7110			−0.636517
$465$		0			0
$466$	−2.27035			−0.105172
$467$			5.70861i			0.264163i	0.991239	+	0.132082i	$0.0421661\pi$
$467$			5.70861i			0.264163i	−0.991239	+	0.132082i	$0.957834\pi$
$468$		0			0
$469$	47.9235			2.21290
$470$	−4.40326	+	14.7710i	−0.203107	+	0.681336i
$471$		0			0
$472$			26.4739i			1.21856i
$473$		−	1.91363i		−	0.0879886i
$474$		0			0
$475$	−4.67424	−	3.05860i	−0.214469	−	0.140338i
$476$	−3.66492			−0.167981
$477$		0			0
$478$		−	8.99845i		−	0.411580i
$479$	−41.9688			−1.91760			−0.958802	−	0.284074i	$-0.908314\pi$
$479$	−41.9688			−1.91760			−0.958802	+	0.284074i	$0.908314\pi$
$480$		0			0
$481$	11.3011			0.515285
$482$		−	19.6299i		−	0.894119i
$483$		0			0
$484$	−3.72879			−0.169491
$485$	−8.25779	−	2.46166i	−0.374967	−	0.111778i
$486$		0			0
$487$		−	27.1205i		−	1.22895i	−0.788938	−	0.614473i	$-0.789369\pi$
$487$		−	27.1205i		−	1.22895i	0.788938	−	0.614473i	$-0.210631\pi$
$488$			10.0163i			0.453418i
$489$		0			0
$490$	−27.5322	−	8.20739i	−1.24378	−	0.370772i
$491$	2.50973			0.113262			0.0566312	−	0.998395i	$-0.481964\pi$
$491$	2.50973			0.113262			0.0566312	+	0.998395i	$0.481964\pi$
$492$		0			0
$493$		−	8.70284i		−	0.391956i
$494$	1.36642			0.0614783
$495$		0			0
$496$	−27.4033			−1.23044
$497$		−	22.4824i		−	1.00847i
$498$		0			0
$499$	17.3400			0.776244			0.388122	−	0.921608i	$-0.373124\pi$
$499$	17.3400			0.776244			0.388122	+	0.921608i	$0.373124\pi$
$500$	−4.30452	+	3.63784i	−0.192504	+	0.162689i
$501$		0			0
$502$		−	19.7142i		−	0.879888i
$503$			0.235551i			0.0105027i	0.999986	+	0.00525136i	$0.00167157\pi$
$503$			0.235551i			0.0105027i	−0.999986	+	0.00525136i	$0.998328\pi$
$504$		0			0
$505$	1.64268	−	5.51047i	0.0730983	−	0.245213i
$506$	−21.5928			−0.959919
$507$		0			0
$508$			1.18532i			0.0525899i
$509$	30.4076			1.34779			0.673896	−	0.738826i	$-0.264619\pi$
$509$	30.4076			1.34779			0.673896	+	0.738826i	$0.264619\pi$
$510$		0			0
$511$	−16.8039			−0.743360
$512$		−	24.3721i		−	1.07710i
$513$		0			0
$514$	−11.9641			−0.527712
$515$	−3.28443	−	0.979092i	−0.144729	−	0.0431440i
$516$		0			0
$517$		−	10.6975i		−	0.470475i
$518$			57.8299i			2.54090i
$519$		0			0
$520$	1.95643	−	6.56297i	0.0857952	−	0.287805i
$521$	−34.5000			−1.51147			−0.755735	−	0.654877i	$-0.772720\pi$
$521$	−34.5000			−1.51147			−0.755735	+	0.654877i	$0.772720\pi$
$522$		0			0
$523$		−	31.5967i		−	1.38163i	−0.723034	−	0.690813i	$-0.757253\pi$
$523$		−	31.5967i		−	1.38163i	0.723034	−	0.690813i	$-0.242747\pi$
$524$	4.77058			0.208404
$525$		0			0
$526$	3.82234			0.166662
$527$		−	17.3938i		−	0.757686i
$528$		0			0
$529$	−63.5101			−2.76131
$530$	0.136237	−	0.457016i	0.00591777	−	0.0198515i
$531$		0			0
$532$		−	2.35622i		−	0.102155i
$533$			8.02349i			0.347536i
$534$		0			0
$535$	−18.4931	−	5.51283i	−0.799528	−	0.238340i
$536$	−35.0810			−1.51527
$537$		0			0
$538$			19.3789i			0.835482i
$539$	19.9394			0.858852
$540$		0			0
$541$	−36.5481			−1.57133			−0.785663	−	0.618655i	$-0.787678\pi$
$541$	−36.5481			−1.57133			−0.785663	+	0.618655i	$0.787678\pi$
$542$			7.88273i			0.338592i
$543$		0			0
$544$	4.82554			0.206893
$545$	−7.68512	+	25.7802i	−0.329195	+	1.10430i
$546$		0			0
$547$			24.4439i			1.04514i	0.852595	+	0.522572i	$0.175027\pi$
$547$			24.4439i			1.04514i	−0.852595	+	0.522572i	$0.824973\pi$
$548$			2.26310i			0.0966750i
$549$		0			0
$550$	−6.35575	+	9.71305i	−0.271010	+	0.414166i
$551$	5.59514			0.238361
$552$		0			0
$553$		−	2.56761i		−	0.109186i
$554$	16.7165			0.710216
$555$		0			0
$556$	6.80759			0.288706
$557$		−	30.8005i		−	1.30506i	−0.757762	−	0.652530i	$-0.773707\pi$
$557$		−	30.8005i		−	1.30506i	0.757762	−	0.652530i	$-0.226293\pi$
$558$		0			0
$559$	1.00817			0.0426411
$560$	24.5453	+	7.31697i	1.03723	+	0.309199i
$561$		0			0
$562$			26.0474i			1.09874i
$563$			2.32559i			0.0980121i	0.998798	+	0.0490060i	$0.0156054\pi$
$563$			2.32559i			0.0980121i	−0.998798	+	0.0490060i	$0.984395\pi$
$564$		0			0
$565$	16.9954	+	5.06636i	0.715003	+	0.213143i
$566$	27.0940			1.13885
$567$		0			0
$568$			16.4576i			0.690544i
$569$	27.3891			1.14821			0.574105	−	0.818782i	$-0.305350\pi$
$569$	27.3891			1.14821			0.574105	+	0.818782i	$0.305350\pi$
$570$		0			0
$571$	−5.97175			−0.249910			−0.124955	−	0.992162i	$-0.539879\pi$
$571$	−5.97175			−0.249910			−0.124955	+	0.992162i	$0.539879\pi$
$572$			0.956813i			0.0400064i
$573$		0			0
$574$	−41.0578			−1.71372
$575$	−25.4638	+	38.9146i	−1.06192	+	1.62285i
$576$		0			0
$577$		−	7.66635i		−	0.319154i	−0.987185	−	0.159577i	$-0.948987\pi$
$577$		−	7.66635i		−	0.319154i	0.987185	−	0.159577i	$-0.0510131\pi$
$578$			17.0990i			0.711223i
$579$		0			0
$580$	1.61267	−	5.40980i	0.0669624	−	0.224630i
$581$	38.0036			1.57665
$582$		0			0
$583$			0.330981i			0.0137078i
$584$	12.3008			0.509010
$585$		0			0
$586$	26.8681			1.10991
$587$		−	11.6195i		−	0.479588i	−0.970824	−	0.239794i	$-0.922920\pi$
$587$		−	11.6195i		−	0.479588i	0.970824	−	0.239794i	$-0.0770799\pi$
$588$		0			0
$589$	11.1826			0.460773
$590$	22.6552	+	6.75353i	0.932698	+	0.278039i
$591$		0			0
$592$		−	30.9393i		−	1.27160i
$593$			24.3280i			0.999032i	0.866305	+	0.499516i	$0.166489\pi$
$593$			24.3280i			0.999032i	−0.866305	+	0.499516i	$0.833511\pi$
$594$		0			0
$595$	−4.64433	+	15.5797i	−0.190399	+	0.638705i
$596$	2.74239			0.112333
$597$		0			0
$598$		−	11.3759i		−	0.465196i
$599$	−0.702208			−0.0286914			−0.0143457	−	0.999897i	$-0.504567\pi$
$599$	−0.702208			−0.0286914			−0.0143457	+	0.999897i	$0.504567\pi$
$600$		0			0
$601$	−4.61254			−0.188150			−0.0940748	−	0.995565i	$-0.529989\pi$
$601$	−4.61254			−0.188150			−0.0940748	+	0.995565i	$0.529989\pi$
$602$			5.15901i			0.210266i
$603$		0			0
$604$	−4.31013			−0.175377
$605$	−4.72527	+	15.8512i	−0.192110	+	0.644444i
$606$		0			0
$607$		−	18.0763i		−	0.733693i	−0.930281	−	0.366847i	$-0.880437\pi$
$607$		−	18.0763i		−	0.733693i	0.930281	−	0.366847i	$-0.119563\pi$
$608$			3.10239i			0.125818i
$609$		0			0
$610$	8.57152	+	2.55518i	0.347051	+	0.103456i
$611$	5.63584			0.228002
$612$		0			0
$613$			34.4468i			1.39129i	0.718384	+	0.695647i	$0.244882\pi$
$613$			34.4468i			1.39129i	−0.718384	+	0.695647i	$0.755118\pi$
$614$	−30.0285			−1.21185
$615$		0			0
$616$	−24.3223			−0.979974
$617$			39.0566i			1.57236i	0.617997	+	0.786180i	$0.287944\pi$
$617$			39.0566i			1.57236i	−0.617997	+	0.786180i	$0.712056\pi$
$618$		0			0
$619$	4.92711			0.198037			0.0990186	−	0.995086i	$-0.468430\pi$
$619$	4.92711			0.198037			0.0990186	+	0.995086i	$0.468430\pi$
$620$	3.22314	−	10.8122i	0.129444	−	0.434229i
$621$		0			0
$622$			34.6491i			1.38930i
$623$			6.14322i			0.246123i
$624$		0			0
$625$	10.0097	+	22.9086i	0.400388	+	0.916346i
$626$	−22.1985			−0.887229
$627$		0			0
$628$			8.64156i			0.344836i
$629$	19.6382			0.783026
$630$		0			0
$631$	6.90181			0.274757			0.137378	−	0.990519i	$-0.456132\pi$
$631$	6.90181			0.274757			0.137378	+	0.990519i	$0.456132\pi$
$632$			1.87954i			0.0747641i
$633$		0			0
$634$	12.6003			0.500420
$635$	5.03881	+	1.50208i	0.199959	+	0.0596081i
$636$		0			0
$637$			10.5048i			0.416217i
$638$		−	11.6267i		−	0.460304i
$639$		0			0
$640$	−11.3510	−	3.38376i	−0.448689	−	0.133755i
$641$	−12.4366			−0.491218			−0.245609	−	0.969369i	$-0.578988\pi$
$641$	−12.4366			−0.491218			−0.245609	+	0.969369i	$0.578988\pi$
$642$		0			0
$643$		−	23.6920i		−	0.934322i	−0.884172	−	0.467161i	$-0.845277\pi$
$643$		−	23.6920i		−	0.934322i	0.884172	−	0.467161i	$-0.154723\pi$
$644$	−19.6163			−0.772990
$645$		0			0
$646$	2.37447			0.0934223
$647$			20.7168i			0.814461i	0.913325	+	0.407230i	$0.133505\pi$
$647$			20.7168i			0.814461i	−0.913325	+	0.407230i	$0.866495\pi$
$648$		0			0
$649$	−16.4074			−0.644045
$650$	−5.11720	−	3.34845i	−0.200713	−	0.131337i
$651$		0			0
$652$		−	9.18167i		−	0.359582i
$653$			13.7390i			0.537648i	0.963189	+	0.268824i	$0.0866349\pi$
$653$			13.7390i			0.537648i	−0.963189	+	0.268824i	$0.913365\pi$
$654$		0			0
$655$	6.04546	−	20.2799i	0.236215	−	0.792400i
$656$	21.9661			0.857633
$657$		0			0
$658$			28.8398i			1.12429i
$659$	−19.4786			−0.758780			−0.379390	−	0.925237i	$-0.623866\pi$
$659$	−19.4786			−0.758780			−0.379390	+	0.925237i	$0.623866\pi$
$660$		0			0
$661$	40.7519			1.58506			0.792532	−	0.609831i	$-0.208763\pi$
$661$	40.7519			1.58506			0.792532	+	0.609831i	$0.208763\pi$
$662$			40.7287i			1.58297i
$663$		0			0
$664$	−27.8194			−1.07960
$665$	−10.0163	−	2.98589i	−0.388417	−	0.115788i
$666$		0			0
$667$		−	46.5814i		−	1.80364i
$668$			4.01905i			0.155502i
$669$		0			0
$670$	−8.94922	+	30.0207i	−0.345738	+	1.15980i
$671$	−6.20768			−0.239645
$672$		0			0
$673$			23.4755i			0.904912i	0.891787	+	0.452456i	$0.149452\pi$
$673$			23.4755i			0.904912i	−0.891787	+	0.452456i	$0.850548\pi$
$674$	16.1981			0.623927
$675$		0			0
$676$	−0.504085			−0.0193879
$677$			18.6618i			0.717232i	0.933485	+	0.358616i	$0.116751\pi$
$677$			18.6618i			0.717232i	−0.933485	+	0.358616i	$0.883249\pi$
$678$		0			0
$679$	−16.1230			−0.618743
$680$	3.39975	−	11.4047i	0.130374	−	0.437349i
$681$		0			0
$682$		−	23.2375i		−	0.889809i
$683$			18.3291i			0.701343i	0.936498	+	0.350672i	$0.114047\pi$
$683$			18.3291i			0.701343i	−0.936498	+	0.350672i	$0.885953\pi$
$684$		0			0
$685$	9.62053	+	2.86789i	0.367581	+	0.109577i
$686$	−17.9350			−0.684762
$687$		0			0
$688$		−	2.76010i		−	0.105228i
$689$	−0.174373			−0.00664310
$690$		0			0
$691$	26.9911			1.02679			0.513394	−	0.858153i	$-0.328388\pi$
$691$	26.9911			1.02679			0.513394	+	0.858153i	$0.328388\pi$
$692$		−	6.50706i		−	0.247361i
$693$		0			0
$694$	29.3844			1.11542
$695$	8.62684	−	28.9393i	0.327235	−	1.09773i
$696$		0			0
$697$			13.9426i			0.528115i
$698$		−	7.62188i		−	0.288493i
$699$		0			0
$700$	−5.77395	+	8.82394i	−0.218235	+	0.333513i
$701$	−15.2498			−0.575976			−0.287988	−	0.957634i	$-0.592986\pi$
$701$	−15.2498			−0.575976			−0.287988	+	0.957634i	$0.592986\pi$
$702$		0			0
$703$			12.6256i			0.476183i
$704$	16.8398			0.634674
$705$		0			0
$706$	−36.9419			−1.39033
$707$		−	10.7589i		−	0.404632i
$708$		0			0
$709$	−15.1710			−0.569760			−0.284880	−	0.958563i	$-0.591954\pi$
$709$	−15.1710			−0.569760			−0.284880	+	0.958563i	$0.591954\pi$
$710$	14.0836	+	4.19835i	0.528549	+	0.157561i
$711$		0			0
$712$		−	4.49696i		−	0.168531i
$713$		−	93.0992i		−	3.48659i
$714$		0			0
$715$	4.06744	+	1.21251i	0.152114	+	0.0453453i
$716$	−3.76827			−0.140827
$717$		0			0
$718$			15.7196i			0.586649i
$719$	9.25854			0.345285			0.172643	−	0.984985i	$-0.444769\pi$
$719$	9.25854			0.345285			0.172643	+	0.984985i	$0.444769\pi$
$720$		0			0
$721$	−6.41270			−0.238821
$722$		−	21.7119i		−	0.808032i
$723$		0			0
$724$	−3.10655			−0.115454
$725$	−20.9536	−	13.7110i	−0.778196	−	0.509214i
$726$		0			0
$727$		−	28.5175i		−	1.05765i	−0.848730	−	0.528827i	$-0.822632\pi$
$727$		−	28.5175i		−	1.05765i	0.848730	−	0.528827i	$-0.177368\pi$
$728$		−	12.8139i		−	0.474915i
$729$		0			0
$730$	3.13795	−	10.5265i	0.116141	−	0.389602i
$731$	1.75193			0.0647973
$732$		0			0
$733$		−	20.7882i		−	0.767828i	−0.923369	−	0.383914i	$-0.874576\pi$
$733$		−	20.7882i		−	0.767828i	0.923369	−	0.383914i	$-0.125424\pi$
$734$	−33.5028			−1.23661
$735$		0			0
$736$	25.8284			0.952047
$737$		−	21.7416i		−	0.800864i
$738$		0			0
$739$	23.9528			0.881117			0.440558	−	0.897724i	$-0.354780\pi$
$739$	23.9528			0.881117			0.440558	+	0.897724i	$0.354780\pi$
$740$	12.2074	+	3.63903i	0.448752	+	0.133774i
$741$		0			0
$742$		−	0.892304i		−	0.0327575i
$743$		−	13.0976i		−	0.480505i	−0.970710	−	0.240253i	$-0.922770\pi$
$743$		−	13.0976i		−	0.480505i	0.970710	−	0.240253i	$-0.0772303\pi$
$744$		0			0
$745$	3.47527	−	11.6580i	0.127324	−	0.427116i
$746$	−23.1300			−0.846849
$747$		0			0
$748$			1.66268i			0.0607936i
$749$	−36.1070			−1.31932
$750$		0			0
$751$	37.3273			1.36209			0.681046	−	0.732240i	$-0.261525\pi$
$751$	37.3273			1.36209			0.681046	+	0.732240i	$0.261525\pi$
$752$		−	15.4294i		−	0.562653i
$753$		0			0
$754$	6.12537			0.223073
$755$	−5.46196	+	18.3225i	−0.198781	+	0.666823i
$756$		0			0
$757$		−	15.6701i		−	0.569539i	−0.958596	−	0.284770i	$-0.908083\pi$
$757$		−	15.6701i		−	0.569539i	0.958596	−	0.284770i	$-0.0919171\pi$
$758$		−	25.3695i		−	0.921461i
$759$		0			0
$760$	7.33217	+	2.18573i	0.265966	+	0.0792848i
$761$	15.9872			0.579535			0.289768	−	0.957097i	$-0.406422\pi$
$761$	15.9872			0.579535			0.289768	+	0.957097i	$0.406422\pi$
$762$		0			0
$763$			50.3347i			1.82224i
$764$	−1.91439			−0.0692604
$765$		0			0
$766$	25.7865			0.931705
$767$		−	8.64402i		−	0.312117i
$768$		0			0
$769$	30.5787			1.10270			0.551349	−	0.834275i	$-0.314113\pi$
$769$	30.5787			1.10270			0.551349	+	0.834275i	$0.314113\pi$
$770$	−6.20466	+	20.8139i	−0.223600	+	0.750081i
$771$		0			0
$772$		−	8.72946i		−	0.314180i
$773$			13.3491i			0.480136i	0.970756	+	0.240068i	$0.0771697\pi$
$773$			13.3491i			0.480136i	−0.970756	+	0.240068i	$0.922830\pi$
$774$		0			0
$775$	−41.8786	−	27.4033i	−1.50432	−	0.984356i
$776$	11.8024			0.423680
$777$		0			0
$778$		−	27.4682i		−	0.984784i
$779$	−8.96386			−0.321164
$780$		0			0
$781$	−10.1997			−0.364973
$782$		−	19.7683i		−	0.706912i
$783$		0			0
$784$	28.7594			1.02712
$785$	36.7355	+	10.9509i	1.31115	+	0.390855i
$786$		0			0
$787$		−	50.0198i		−	1.78301i	−0.453009	−	0.891506i	$-0.649649\pi$
$787$		−	50.0198i		−	1.78301i	0.453009	−	0.891506i	$-0.350351\pi$
$788$			3.18400i			0.113425i
$789$		0			0
$790$	1.60843	+	0.479474i	0.0572252	+	0.0170589i
$791$	33.1828			1.17985
$792$		0			0
$793$		−	3.27044i		−	0.116137i
$794$	−21.1638			−0.751075
$795$		0			0
$796$	1.39821			0.0495584
$797$		−	17.6557i		−	0.625397i	−0.949852	−	0.312698i	$-0.898767\pi$
$797$		−	17.6557i		−	0.625397i	0.949852	−	0.312698i	$-0.101233\pi$
$798$		0			0
$799$	9.79356			0.346471
$800$	7.60246	−	11.6183i	0.268788	−	0.410769i
$801$		0			0
$802$			9.79737i			0.345957i
$803$			7.62349i			0.269027i
$804$		0			0
$805$	−24.8585	+	83.3894i	−0.876147	+	2.93909i
$806$	12.2424			0.431220
$807$		0			0
$808$			7.87577i			0.277069i
$809$	−9.94274			−0.349568			−0.174784	−	0.984607i	$-0.555923\pi$
$809$	−9.94274			−0.349568			−0.174784	+	0.984607i	$0.555923\pi$
$810$		0			0
$811$	−38.3512			−1.34669			−0.673346	−	0.739328i	$-0.735143\pi$
$811$	−38.3512			−1.34669			−0.673346	+	0.739328i	$0.735143\pi$
$812$		−	10.5624i		−	0.370667i
$813$		0			0
$814$	26.2359			0.919569
$815$	−39.0315	−	11.6354i	−1.36722	−	0.407569i
$816$		0			0
$817$			1.12633i			0.0394053i
$818$		−	32.6421i		−	1.14130i
$819$		0			0
$820$	−2.58362	+	8.66693i	−0.0902241	+	0.302662i
$821$	51.5792			1.80013			0.900064	−	0.435758i	$-0.143520\pi$
$821$	51.5792			1.80013			0.900064	+	0.435758i	$0.143520\pi$
$822$		0			0
$823$		−	39.8188i		−	1.38800i	−0.719977	−	0.693998i	$-0.755848\pi$
$823$		−	39.8188i		−	1.38800i	0.719977	−	0.693998i	$-0.244152\pi$
$824$	4.69423			0.163531
$825$		0			0
$826$	44.2332			1.53907
$827$		−	16.8916i		−	0.587377i	−0.955901	−	0.293689i	$-0.905117\pi$
$827$		−	16.8916i		−	0.587377i	0.955901	−	0.293689i	$-0.0948829\pi$
$828$		0			0
$829$	−19.4332			−0.674943			−0.337471	−	0.941336i	$-0.609572\pi$
$829$	−19.4332			−0.674943			−0.337471	+	0.941336i	$0.609572\pi$
$830$	−7.09677	+	23.8066i	−0.246333	+	0.826338i
$831$		0			0
$832$			8.87184i			0.307576i
$833$			18.2546i			0.632483i
$834$		0			0
$835$	17.0851	+	5.09310i	0.591255	+	0.176254i
$836$	−1.06895			−0.0369705
$837$		0			0
$838$			2.24884i			0.0776850i
$839$	−36.2400			−1.25114			−0.625571	−	0.780167i	$-0.715134\pi$
$839$	−36.2400			−1.25114			−0.625571	+	0.780167i	$0.715134\pi$
$840$		0			0
$841$	−3.91823			−0.135111
$842$			7.53903i			0.259812i
$843$		0			0
$844$	5.44048			0.187269
$845$	−0.638796	+	2.14288i	−0.0219752	+	0.0737174i
$846$		0			0
$847$			30.9488i			1.06341i
$848$			0.477387i			0.0163935i
$849$		0			0
$850$	−8.89230	−	5.81869i	−0.305004	−	0.199579i
$851$	105.112			3.60320
$852$		0			0
$853$			2.44146i			0.0835940i	0.999126	+	0.0417970i	$0.0133083\pi$
$853$			2.44146i			0.0835940i	−0.999126	+	0.0417970i	$0.986692\pi$
$854$	16.7355			0.572678
$855$		0			0
$856$	26.4311			0.903396
$857$		−	20.9217i		−	0.714672i	−0.933976	−	0.357336i	$-0.883685\pi$
$857$		−	20.9217i		−	0.714672i	0.933976	−	0.357336i	$-0.116315\pi$
$858$		0			0
$859$	−14.7240			−0.502376			−0.251188	−	0.967938i	$-0.580821\pi$
$859$	−14.7240			−0.502376			−0.251188	+	0.967938i	$0.580821\pi$
$860$	1.08902	+	0.324639i	0.0371353	+	0.0110701i
$861$		0			0
$862$			38.0733i			1.29678i
$863$			21.1748i			0.720799i	0.932798	+	0.360399i	$0.117360\pi$
$863$			21.1748i			0.720799i	−0.932798	+	0.360399i	$0.882640\pi$
$864$		0			0
$865$	−27.6617	−	8.24599i	−0.940526	−	0.280372i
$866$	4.91229			0.166926
$867$		0			0
$868$		−	21.1104i		−	0.716533i
$869$	−1.16486			−0.0395150
$870$		0			0
$871$	11.4543			0.388115
$872$		−	36.8461i		−	1.24777i
$873$		0			0
$874$	12.7092			0.429896
$875$	30.1938	+	35.7273i	1.02074	+	1.20780i
$876$		0			0
$877$			36.7401i			1.24062i	0.784355	+	0.620312i	$0.212994\pi$
$877$			36.7401i			1.24062i	−0.784355	+	0.620312i	$0.787006\pi$
$878$			24.9273i			0.841255i
$879$		0			0
$880$	3.31952	−	11.1355i	0.111901	−	0.375379i
$881$	16.7074			0.562886			0.281443	−	0.959578i	$-0.409187\pi$
$881$	16.7074			0.562886			0.281443	+	0.959578i	$0.409187\pi$
$882$		0			0
$883$		−	41.2791i		−	1.38915i	−0.719420	−	0.694576i	$-0.755592\pi$
$883$		−	41.2791i		−	1.38915i	0.719420	−	0.694576i	$-0.244408\pi$
$884$	−0.875963			−0.0294618
$885$		0			0
$886$	17.7305			0.595669
$887$			47.5592i			1.59688i	0.602073	+	0.798441i	$0.294342\pi$
$887$			47.5592i			1.59688i	−0.602073	+	0.798441i	$0.705658\pi$
$888$		0			0
$889$	9.83805			0.329958
$890$	−3.84829	−	1.14718i	−0.128995	−	0.0384536i
$891$		0			0
$892$			11.6709i			0.390769i
$893$			6.29638i			0.210700i
$894$		0			0
$895$	−4.77529	+	16.0190i	−0.159620	+	0.535457i
$896$	−22.1624			−0.740394
$897$		0			0
$898$		−	3.78103i		−	0.126175i
$899$	50.1293			1.67191
$900$		0			0
$901$	−0.303013			−0.0100948
$902$			18.6269i			0.620207i
$903$		0			0
$904$	−24.2905			−0.807890
$905$	−3.93674	+	13.2060i	−0.130862	+	0.438983i
$906$		0			0
$907$			16.1360i			0.535788i	0.963448	+	0.267894i	$0.0863277\pi$
$907$			16.1360i			0.535788i	−0.963448	+	0.267894i	$0.913672\pi$
$908$			12.6369i			0.419371i
$909$		0			0
$910$	−10.9656	−	3.26885i	−0.363505	−	0.108361i
$911$	−42.5496			−1.40973			−0.704866	−	0.709341i	$-0.748993\pi$
$911$	−42.5496			−1.40973			−0.704866	+	0.709341i	$0.748993\pi$
$912$		0			0
$913$		−	17.2412i		−	0.570601i
$914$	−29.0549			−0.961050
$915$		0			0
$916$	−0.396673			−0.0131065
$917$		−	39.5955i		−	1.30756i
$918$		0			0
$919$	31.3306			1.03350			0.516750	−	0.856136i	$-0.327142\pi$
$919$	31.3306			1.03350			0.516750	+	0.856136i	$0.327142\pi$
$920$	18.1969	−	61.0427i	0.599935	−	2.01252i
$921$		0			0
$922$		−	46.6238i		−	1.53547i
$923$		−	5.37357i		−	0.176873i
$924$		0			0
$925$	30.9393	−	47.2824i	1.01728	−	1.55463i
$926$	32.7381			1.07584
$927$		0			0
$928$			13.9073i			0.456530i
$929$	−33.9021			−1.11229			−0.556145	−	0.831085i	$-0.687720\pi$
$929$	−33.9021			−1.11229			−0.556145	+	0.831085i	$0.687720\pi$
$930$		0			0
$931$	−11.7360			−0.384633
$932$			0.935716i			0.0306504i
$933$		0			0
$934$	−6.98207			−0.228460
$935$	7.06810	+	2.10701i	0.231152	+	0.0689066i
$936$		0			0
$937$		−	36.0449i		−	1.17754i	−0.808302	−	0.588768i	$-0.799613\pi$
$937$		−	36.0449i		−	1.17754i	0.808302	−	0.588768i	$-0.200387\pi$
$938$			58.6141i			1.91382i
$939$		0			0
$940$	6.08781	+	1.81478i	0.198562	+	0.0591918i
$941$	−46.8764			−1.52813			−0.764063	−	0.645141i	$-0.776799\pi$
$941$	−46.8764			−1.52813			−0.764063	+	0.645141i	$0.776799\pi$
$942$		0			0
$943$			74.6271i			2.43019i
$944$	−23.6650			−0.770229
$945$		0			0
$946$	2.34051			0.0760965
$947$			23.2987i			0.757107i	0.925579	+	0.378553i	$0.123578\pi$
$947$			23.2987i			0.757107i	−0.925579	+	0.378553i	$0.876422\pi$
$948$		0			0
$949$	−4.01634			−0.130376
$950$	3.74089	−	5.71695i	0.121371	−	0.185482i
$951$		0			0
$952$		−	22.2671i		−	0.721680i
$953$		−	17.2170i		−	0.557713i	−0.960333	−	0.278857i	$-0.910045\pi$
$953$		−	17.2170i		−	0.557713i	0.960333	−	0.278857i	$-0.0899554\pi$
$954$		0			0
$955$	−2.42599	+	8.13815i	−0.0785033	+	0.263344i
$956$	−3.70867			−0.119947
$957$		0			0
$958$		−	51.3311i		−	1.65843i
$959$	18.7836			0.606556
$960$		0			0
$961$	69.1902			2.23194
$962$			13.8221i			0.445642i
$963$		0			0
$964$	−8.09039			−0.260574
$965$	−37.1092	−	11.0623i	−1.19459	−	0.356108i
$966$		0			0
$967$		−	2.31848i		−	0.0745573i	−0.999305	−	0.0372787i	$-0.988131\pi$
$967$		−	2.31848i		−	0.0745573i	0.999305	−	0.0372787i	$-0.0118689\pi$
$968$		−	22.6552i		−	0.728164i
$969$		0			0
$970$	3.01080	−	10.0999i	0.0966709	−	0.324289i
$971$	16.4953			0.529358			0.264679	−	0.964337i	$-0.414734\pi$
$971$	16.4953			0.529358			0.264679	+	0.964337i	$0.414734\pi$
$972$		0			0
$973$		−	56.5027i		−	1.81139i
$974$	33.1704			1.06285
$975$		0			0
$976$	−8.95358			−0.286597
$977$		−	30.2337i		−	0.967263i	−0.875272	−	0.483631i	$-0.839318\pi$
$977$		−	30.2337i		−	0.967263i	0.875272	−	0.483631i	$-0.160682\pi$
$978$		0			0
$979$	2.78702			0.0890735
$980$	−3.38264	+	11.3473i	−0.108054	+	0.362476i
$981$		0			0
$982$			3.06959i			0.0979545i
$983$			27.7015i			0.883539i	0.897129	+	0.441770i	$0.145649\pi$
$983$			27.7015i			0.883539i	−0.897129	+	0.441770i	$0.854351\pi$
$984$		0			0
$985$	13.5353	+	4.03489i	0.431270	+	0.128562i
$986$	10.6442			0.338981
$987$		0			0
$988$		−	0.563165i		−	0.0179167i
$989$	9.37708			0.298174
$990$		0			0
$991$	−45.3385			−1.44022			−0.720112	−	0.693858i	$-0.755910\pi$
$991$	−45.3385			−1.44022			−0.720112	+	0.693858i	$0.755910\pi$
$992$			27.7956i			0.882512i
$993$		0			0
$994$	27.4977			0.872173
$995$	1.77187	−	5.94385i	0.0561721	−	0.188433i
$996$		0			0
$997$		−	13.2601i		−	0.419950i	−0.977707	−	0.209975i	$-0.932662\pi$
$997$		−	13.2601i		−	0.419950i	0.977707	−	0.209975i	$-0.0673383\pi$
$998$			21.2081i			0.671331i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.c.c.469.7		10
3.2	odd	2		195.2.c.b.79.4	✓	10
5.2	odd	4		2925.2.a.bl.1.2		5
5.3	odd	4		2925.2.a.bm.1.4		5
5.4	even	2	inner	585.2.c.c.469.4		10
12.11	even	2		3120.2.l.p.1249.8		10
15.2	even	4		975.2.a.r.1.4		5
15.8	even	4		975.2.a.s.1.2		5
15.14	odd	2		195.2.c.b.79.7	yes	10
60.59	even	2		3120.2.l.p.1249.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.c.b.79.4	✓	10	3.2	odd	2
195.2.c.b.79.7	yes	10	15.14	odd	2
585.2.c.c.469.4		10	5.4	even	2	inner
585.2.c.c.469.7		10	1.1	even	1	trivial
975.2.a.r.1.4		5	15.2	even	4
975.2.a.s.1.2		5	15.8	even	4
2925.2.a.bl.1.2		5	5.2	odd	4
2925.2.a.bm.1.4		5	5.3	odd	4
3120.2.l.p.1249.3		10	60.59	even	2
3120.2.l.p.1249.8		10	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.22308i q^{2} +0.504085 q^{4} +(0.638796 - 2.14288i) q^{5} -4.18388i q^{7} +3.06269i q^{8} +O(q^{10})\)	\(q+1.22308i q^{2} +0.504085 q^{4} +(0.638796 - 2.14288i) q^{5} -4.18388i q^{7} +3.06269i q^{8} +(2.62091 + 0.781296i) q^{10} -1.89812 q^{11} -1.00000i q^{13} +5.11720 q^{14} -2.73773 q^{16} -1.73773i q^{17} +1.11720 q^{19} +(0.322008 - 1.08019i) q^{20} -2.32154i q^{22} -9.30108i q^{23} +(-4.18388 - 2.73773i) q^{25} +1.22308 q^{26} -2.10903i q^{28} +5.00817 q^{29} +10.0095 q^{31} +2.77692i q^{32} +2.12537 q^{34} +(-8.96556 - 2.67265i) q^{35} +11.3011i q^{37} +1.36642i q^{38} +(6.56297 + 1.95643i) q^{40} -8.02349 q^{41} +1.00817i q^{43} -0.956813 q^{44} +11.3759 q^{46} +5.63584i q^{47} -10.5048 q^{49} +(3.34845 - 5.11720i) q^{50} -0.504085i q^{52} -0.174373i q^{53} +(-1.21251 + 4.06744i) q^{55} +12.8139 q^{56} +6.12537i q^{58} +8.64402 q^{59} +3.27044 q^{61} +12.2424i q^{62} -8.87184 q^{64} +(-2.14288 - 0.638796i) q^{65} +11.4543i q^{67} -0.875963i q^{68} +(3.26885 - 10.9656i) q^{70} +5.37357 q^{71} -4.01634i q^{73} -13.8221 q^{74} +0.563165 q^{76} +7.94149i q^{77} +0.613690 q^{79} +(-1.74885 + 5.86662i) q^{80} -9.81334i q^{82} +9.08333i q^{83} +(-3.72374 - 1.11005i) q^{85} -1.23307 q^{86} -5.81334i q^{88} -1.46831 q^{89} -4.18388 q^{91} -4.68854i q^{92} -6.89307 q^{94} +(0.713664 - 2.39403i) q^{95} -3.85359i q^{97} -12.8482i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 12 q^{4} + 2 q^{5}+O(q^{10}) \) 10 * q - 12 * q^4 + 2 * q^5	\( 10 q - 12 q^{4} + 2 q^{5} + 4 q^{10} - 10 q^{11} + 24 q^{14} - 16 q^{19} - 32 q^{20} + 10 q^{25} + 16 q^{29} + 24 q^{31} - 40 q^{34} - 12 q^{35} + 36 q^{40} - 10 q^{41} + 36 q^{44} - 24 q^{46} - 44 q^{49} - 40 q^{50} + 2 q^{55} + 16 q^{59} + 26 q^{61} + 32 q^{64} + 56 q^{70} - 10 q^{71} + 24 q^{74} - 2 q^{79} + 12 q^{80} - 4 q^{85} + 38 q^{89} + 10 q^{91} + 24 q^{94} + 48 q^{95}+O(q^{100}) \) 10 * q - 12 * q^4 + 2 * q^5 + 4 * q^10 - 10 * q^11 + 24 * q^14 - 16 * q^19 - 32 * q^20 + 10 * q^25 + 16 * q^29 + 24 * q^31 - 40 * q^34 - 12 * q^35 + 36 * q^40 - 10 * q^41 + 36 * q^44 - 24 * q^46 - 44 * q^49 - 40 * q^50 + 2 * q^55 + 16 * q^59 + 26 * q^61 + 32 * q^64 + 56 * q^70 - 10 * q^71 + 24 * q^74 - 2 * q^79 + 12 * q^80 - 4 * q^85 + 38 * q^89 + 10 * q^91 + 24 * q^94 + 48 * q^95

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