LMFDB - Embedded newform 1665.2.c.e.334.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1665,2,Mod(334,1665)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1665.334"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1665, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1665 = 3^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1665.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [18,0,0,-22,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$13.2950919365$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 28x^{16} + 306x^{14} + 1684x^{12} + 5049x^{10} + 8280x^{8} + 7004x^{6} + 2672x^{4} + 368x^{2} + 16 $ x^18 + 28x^16 + 306x^14 + 1684x^12 + 5049x^10 + 8280x^8 + 7004x^6 + 2672x^4 + 368x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			334.13
Root			$0.356037i$ of defining polynomial
Character	$\chi$	$=$	1665.334
Dual form			1665.2.c.e.334.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.35604i q^{2} +0.161165 q^{4} +(0.722164 - 2.11624i) q^{5} -0.748140i q^{7} +2.93062i q^{8} +(2.86970 + 0.979281i) q^{10} -5.40521 q^{11} +5.16556i q^{13} +1.01451 q^{14} -3.65170 q^{16} +3.44151i q^{17} -5.38802 q^{19} +(0.116388 - 0.341064i) q^{20} -7.32966i q^{22} +3.48474i q^{23} +(-3.95696 - 3.05655i) q^{25} -7.00469 q^{26} -0.120574i q^{28} +6.47076 q^{29} -2.23046 q^{31} +0.909404i q^{32} -4.66682 q^{34} +(-1.58325 - 0.540280i) q^{35} +1.00000i q^{37} -7.30635i q^{38} +(6.20190 + 2.11639i) q^{40} +6.44821 q^{41} +2.71018i q^{43} -0.871130 q^{44} -4.72543 q^{46} +10.3708i q^{47} +6.44029 q^{49} +(4.14479 - 5.36578i) q^{50} +0.832507i q^{52} +4.64473i q^{53} +(-3.90345 + 11.4387i) q^{55} +2.19251 q^{56} +8.77459i q^{58} -12.7207 q^{59} -10.3592 q^{61} -3.02459i q^{62} -8.53658 q^{64} +(10.9316 + 3.73038i) q^{65} +6.09691i q^{67} +0.554651i q^{68} +(0.732640 - 2.14694i) q^{70} +2.80433 q^{71} -1.51542i q^{73} -1.35604 q^{74} -0.868359 q^{76} +4.04385i q^{77} +13.9090 q^{79} +(-2.63712 + 7.72787i) q^{80} +8.74401i q^{82} -1.14982i q^{83} +(7.28307 + 2.48534i) q^{85} -3.67511 q^{86} -15.8406i q^{88} -0.373310 q^{89} +3.86456 q^{91} +0.561617i q^{92} -14.0632 q^{94} +(-3.89103 + 11.4023i) q^{95} -8.96381i q^{97} +8.73326i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 22 q^{4} - 2 q^{5} + 6 q^{10} - 8 q^{14} + 22 q^{16} + 8 q^{19} + 4 q^{20} - 18 q^{25} + 12 q^{26} - 4 q^{29} - 12 q^{31} - 12 q^{34} + 2 q^{35} - 6 q^{40} - 4 q^{41} + 8 q^{44} + 32 q^{46} + 14 q^{49}+ \cdots + 44 q^{95}+O(q^{100}) $ 18 * q - 22 * q^4 - 2 * q^5 + 6 * q^10 - 8 * q^14 + 22 * q^16 + 8 * q^19 + 4 * q^20 - 18 * q^25 + 12 * q^26 - 4 * q^29 - 12 * q^31 - 12 * q^34 + 2 * q^35 - 6 * q^40 - 4 * q^41 + 8 * q^44 + 32 * q^46 + 14 * q^49 - 8 * q^50 - 34 * q^55 + 48 * q^56 + 20 * q^59 + 16 * q^61 - 30 * q^64 - 20 * q^65 + 40 * q^70 - 16 * q^71 - 10 * q^74 - 96 * q^76 + 52 * q^79 - 36 * q^80 - 8 * q^85 + 32 * q^86 - 16 * q^89 - 36 * q^91 + 52 * q^94 + 44 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1665\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$			1.35604i			0.958863i	0.877579	+	0.479431i	$0.159157\pi$
$2$			1.35604i			0.958863i	−0.877579	+	0.479431i	$0.840843\pi$
$3$		0			0
$3$		0			0
$4$	0.161165			0.0805825
$5$	0.722164	−	2.11624i	0.322962	−	0.946412i
$5$	0.722164	−	2.11624i	0.322962	−	0.946412i
$6$		0			0
$7$		−	0.748140i		−	0.282770i	−0.989955	−	0.141385i	$-0.954844\pi$
$7$		−	0.748140i		−	0.282770i	0.989955	−	0.141385i	$-0.0451556\pi$
$8$			2.93062i			1.03613i
$9$		0			0
$10$	2.86970	+	0.979281i	0.907479	+	0.309676i
$11$	−5.40521			−1.62973			−0.814866	−	0.579650i	$-0.803189\pi$
$11$	−5.40521			−1.62973			−0.814866	+	0.579650i	$0.803189\pi$
$12$		0			0
$13$			5.16556i			1.43267i	0.697757	+	0.716334i	$0.254181\pi$
$13$			5.16556i			1.43267i	−0.697757	+	0.716334i	$0.745819\pi$
$14$	1.01451			0.271138
$15$		0			0
$16$	−3.65170			−0.912924
$17$			3.44151i			0.834690i	0.908748	+	0.417345i	$0.137039\pi$
$17$			3.44151i			0.834690i	−0.908748	+	0.417345i	$0.862961\pi$
$18$		0			0
$19$	−5.38802			−1.23610			−0.618048	−	0.786140i	$-0.712076\pi$
$19$	−5.38802			−1.23610			−0.618048	+	0.786140i	$0.712076\pi$
$20$	0.116388	−	0.341064i	0.0260250	−	0.0762642i
$21$		0			0
$22$		−	7.32966i		−	1.56269i
$23$			3.48474i			0.726618i	0.931669	+	0.363309i	$0.118353\pi$
$23$			3.48474i			0.726618i	−0.931669	+	0.363309i	$0.881647\pi$
$24$		0			0
$25$	−3.95696	−	3.05655i	−0.791392	−	0.611310i
$26$	−7.00469			−1.37373
$27$		0			0
$28$		−	0.120574i		−	0.0227863i
$29$	6.47076			1.20159			0.600795	−	0.799403i	$-0.294851\pi$
$29$	6.47076			1.20159			0.600795	+	0.799403i	$0.294851\pi$
$30$		0			0
$31$	−2.23046			−0.400603			−0.200301	−	0.979734i	$-0.564192\pi$
$31$	−2.23046			−0.400603			−0.200301	+	0.979734i	$0.564192\pi$
$32$			0.909404i			0.160761i
$33$		0			0
$34$	−4.66682			−0.800353
$35$	−1.58325	−	0.540280i	−0.267617	−	0.0913240i
$36$		0			0
$37$			1.00000i			0.164399i
$37$			1.00000i			0.164399i
$38$		−	7.30635i		−	1.18525i
$39$		0			0
$40$	6.20190	+	2.11639i	0.980606	+	0.334630i
$41$	6.44821			1.00704			0.503521	−	0.863983i	$-0.332038\pi$
$41$	6.44821			1.00704			0.503521	+	0.863983i	$0.332038\pi$
$42$		0			0
$43$			2.71018i			0.413299i	0.978415	+	0.206649i	$0.0662560\pi$
$43$			2.71018i			0.413299i	−0.978415	+	0.206649i	$0.933744\pi$
$44$	−0.871130			−0.131328
$45$		0			0
$46$	−4.72543			−0.696726
$47$			10.3708i			1.51274i	0.654144	+	0.756370i	$0.273029\pi$
$47$			10.3708i			1.51274i	−0.654144	+	0.756370i	$0.726971\pi$
$48$		0			0
$49$	6.44029			0.920041
$50$	4.14479	−	5.36578i	0.586162	−	0.758836i
$51$		0			0
$52$			0.832507i			0.115448i
$53$			4.64473i			0.638002i	0.947754	+	0.319001i	$0.103347\pi$
$53$			4.64473i			0.638002i	−0.947754	+	0.319001i	$0.896653\pi$
$54$		0			0
$55$	−3.90345	+	11.4387i	−0.526341	+	1.54240i
$56$	2.19251			0.292987
$57$		0			0
$58$			8.77459i			1.15216i
$59$	−12.7207			−1.65609			−0.828046	−	0.560660i	$-0.810548\pi$
$59$	−12.7207			−1.65609			−0.828046	+	0.560660i	$0.810548\pi$
$60$		0			0
$61$	−10.3592			−1.32635			−0.663177	−	0.748462i	$-0.730792\pi$
$61$	−10.3592			−1.32635			−0.663177	+	0.748462i	$0.730792\pi$
$62$		−	3.02459i		−	0.384123i
$63$		0			0
$64$	−8.53658			−1.06707
$65$	10.9316	+	3.73038i	1.35589	+	0.462697i
$66$		0			0
$67$			6.09691i			0.744857i	0.928061	+	0.372428i	$0.121475\pi$
$67$			6.09691i			0.744857i	−0.928061	+	0.372428i	$0.878525\pi$
$68$			0.554651i			0.0672613i
$69$		0			0
$70$	0.732640	−	2.14694i	0.0875672	−	0.256608i
$71$	2.80433			0.332813			0.166407	−	0.986057i	$-0.446784\pi$
$71$	2.80433			0.332813			0.166407	+	0.986057i	$0.446784\pi$
$72$		0			0
$73$		−	1.51542i		−	0.177367i	−0.996060	−	0.0886833i	$-0.971734\pi$
$73$		−	1.51542i		−	0.177367i	0.996060	−	0.0886833i	$-0.0282659\pi$
$74$	−1.35604			−0.157636
$75$		0			0
$76$	−0.868359			−0.0996076
$77$			4.04385i			0.460840i
$78$		0			0
$79$	13.9090			1.56489			0.782444	−	0.622721i	$-0.213973\pi$
$79$	13.9090			1.56489			0.782444	+	0.622721i	$0.213973\pi$
$80$	−2.63712	+	7.72787i	−0.294839	+	0.864002i
$81$		0			0
$82$			8.74401i			0.965614i
$83$		−	1.14982i		−	0.126209i	−0.998007	−	0.0631047i	$-0.979900\pi$
$83$		−	1.14982i		−	0.126209i	0.998007	−	0.0631047i	$-0.0201002\pi$
$84$		0			0
$85$	7.28307	+	2.48534i	0.789960	+	0.269573i
$86$	−3.67511			−0.396297
$87$		0			0
$88$		−	15.8406i		−	1.68861i
$89$	−0.373310			−0.0395707			−0.0197854	−	0.999804i	$-0.506298\pi$
$89$	−0.373310			−0.0395707			−0.0197854	+	0.999804i	$0.506298\pi$
$90$		0			0
$91$	3.86456			0.405116
$92$			0.561617i			0.0585526i
$93$		0			0
$94$	−14.0632			−1.45051
$95$	−3.89103	+	11.4023i	−0.399211	+	1.16986i
$96$		0			0
$97$		−	8.96381i		−	0.910137i	−0.890456	−	0.455069i	$-0.849615\pi$
$97$		−	8.96381i		−	0.910137i	0.890456	−	0.455069i	$-0.150385\pi$
$98$			8.73326i			0.882193i
$99$		0			0
$100$	−0.637723	−	0.492608i	−0.0637723	−	0.0492608i
$101$	13.9235			1.38544			0.692722	−	0.721205i	$-0.256411\pi$
$101$	13.9235			1.38544			0.692722	+	0.721205i	$0.256411\pi$
$102$		0			0
$103$			2.98700i			0.294318i	0.989113	+	0.147159i	$0.0470128\pi$
$103$			2.98700i			0.294318i	−0.989113	+	0.147159i	$0.952987\pi$
$104$	−15.1383			−1.48443
$105$		0			0
$106$	−6.29842			−0.611756
$107$			6.58927i			0.637009i	0.947921	+	0.318504i	$0.103181\pi$
$107$			6.58927i			0.637009i	−0.947921	+	0.318504i	$0.896819\pi$
$108$		0			0
$109$	−17.9577			−1.72004			−0.860019	−	0.510263i	$-0.829548\pi$
$109$	−17.9577			−1.72004			−0.860019	+	0.510263i	$0.829548\pi$
$110$	−15.5113	−	5.29322i	−1.47895	−	0.504688i
$111$		0			0
$112$			2.73198i			0.258148i
$113$		−	19.7970i		−	1.86235i	−0.364576	−	0.931173i	$-0.618786\pi$
$113$		−	19.7970i		−	1.86235i	0.364576	−	0.931173i	$-0.381214\pi$
$114$		0			0
$115$	7.37454	+	2.51655i	0.687680	+	0.234670i
$116$	1.04286			0.0968271
$117$		0			0
$118$		−	17.2497i		−	1.58797i
$119$	2.57473			0.236026
$120$		0			0
$121$	18.2163			1.65602
$122$		−	14.0474i		−	1.27179i
$123$		0			0
$124$	−0.359472			−0.0322815
$125$	−9.32597	+	6.16655i	−0.834140	+	0.551553i
$126$		0			0
$127$			0.141983i			0.0125989i	0.999980	+	0.00629947i	$0.00200520\pi$
$127$			0.141983i			0.0125989i	−0.999980	+	0.00629947i	$0.997995\pi$
$128$		−	9.75710i		−	0.862414i
$129$		0			0
$130$	−5.05853	+	14.8236i	−0.443663	+	1.30012i
$131$	0.435890			0.0380839			0.0190420	−	0.999819i	$-0.493938\pi$
$131$	0.435890			0.0380839			0.0190420	+	0.999819i	$0.493938\pi$
$132$		0			0
$133$			4.03099i			0.349531i
$134$	−8.26764			−0.714215
$135$		0			0
$136$	−10.0858			−0.864847
$137$			3.78307i			0.323209i	0.986856	+	0.161605i	$0.0516669\pi$
$137$			3.78307i			0.323209i	−0.986856	+	0.161605i	$0.948333\pi$
$138$		0			0
$139$	12.7579			1.08211			0.541055	−	0.840987i	$-0.318025\pi$
$139$	12.7579			1.08211			0.541055	+	0.840987i	$0.318025\pi$
$140$	−0.255164	−	0.0870742i	−0.0215653	−	0.00735911i
$141$		0			0
$142$			3.80278i			0.319122i
$143$		−	27.9209i		−	2.33486i
$144$		0			0
$145$	4.67295	−	13.6937i	0.388068	−	1.13720i
$146$	2.05497			0.170070
$147$		0			0
$148$			0.161165i			0.0132477i
$149$	−3.72013			−0.304765			−0.152382	−	0.988322i	$-0.548695\pi$
$149$	−3.72013			−0.304765			−0.152382	+	0.988322i	$0.548695\pi$
$150$		0			0
$151$	−7.59391			−0.617984			−0.308992	−	0.951065i	$-0.599992\pi$
$151$	−7.59391			−0.617984			−0.308992	+	0.951065i	$0.599992\pi$
$152$		−	15.7902i		−	1.28076i
$153$		0			0
$154$	−5.48361			−0.441882
$155$	−1.61076	+	4.72019i	−0.129379	+	0.379135i
$156$		0			0
$157$			16.0657i			1.28218i	0.767464	+	0.641092i	$0.221519\pi$
$157$			16.0657i			1.28218i	−0.767464	+	0.641092i	$0.778481\pi$
$158$			18.8611i			1.50051i
$159$		0			0
$160$	1.92452	+	0.656739i	0.152147	+	0.0519198i
$161$	2.60707			0.205466
$162$		0			0
$163$		−	6.99182i		−	0.547641i	−0.961781	−	0.273821i	$-0.911713\pi$
$163$		−	6.99182i		−	0.547641i	0.961781	−	0.273821i	$-0.0882875\pi$
$164$	1.03923			0.0811499
$165$		0			0
$166$	1.55920			0.121017
$167$		−	16.3483i		−	1.26507i	−0.774532	−	0.632534i	$-0.782015\pi$
$167$		−	16.3483i		−	1.26507i	0.774532	−	0.632534i	$-0.217985\pi$
$168$		0			0
$169$	−13.6830			−1.05254
$170$	−3.37021	+	9.87611i	−0.258483	+	0.757463i
$171$		0			0
$172$			0.436786i			0.0333046i
$173$		−	6.21965i		−	0.472871i	−0.971647	−	0.236436i	$-0.924021\pi$
$173$		−	6.21965i		−	0.472871i	0.971647	−	0.236436i	$-0.0759793\pi$
$174$		0			0
$175$	−2.28673	+	2.96036i	−0.172860	+	0.223782i
$176$	19.7382			1.48782
$177$		0			0
$178$		−	0.506222i		−	0.0379429i
$179$	−10.9497			−0.818418			−0.409209	−	0.912441i	$-0.634195\pi$
$179$	−10.9497			−0.818418			−0.409209	+	0.912441i	$0.634195\pi$
$180$		0			0
$181$	8.75050			0.650419			0.325210	−	0.945642i	$-0.394565\pi$
$181$	8.75050			0.650419			0.325210	+	0.945642i	$0.394565\pi$
$182$			5.24049i			0.388451i
$183$		0			0
$184$	−10.2124			−0.752870
$185$	2.11624	+	0.722164i	0.155589	+	0.0530946i
$186$		0			0
$187$		−	18.6021i		−	1.36032i
$188$			1.67141i			0.121900i
$189$		0			0
$190$	−15.4620	−	5.27638i	−1.12173	−	0.382789i
$191$	−15.7914			−1.14263			−0.571314	−	0.820732i	$-0.693566\pi$
$191$	−15.7914			−1.14263			−0.571314	+	0.820732i	$0.693566\pi$
$192$		0			0
$193$		−	10.9845i		−	0.790681i	−0.918535	−	0.395341i	$-0.870627\pi$
$193$		−	10.9845i		−	0.790681i	0.918535	−	0.395341i	$-0.129373\pi$
$194$	12.1553			0.872697
$195$		0			0
$196$	1.03795			0.0741391
$197$		−	9.86682i		−	0.702982i	−0.936191	−	0.351491i	$-0.885675\pi$
$197$		−	9.86682i		−	0.702982i	0.936191	−	0.351491i	$-0.114325\pi$
$198$		0			0
$199$	−5.58756			−0.396091			−0.198046	−	0.980193i	$-0.563459\pi$
$199$	−5.58756			−0.396091			−0.198046	+	0.980193i	$0.563459\pi$
$200$	8.95758	−	11.5963i	0.633396	−	0.819985i
$201$		0			0
$202$			18.8808i			1.32845i
$203$		−	4.84104i		−	0.339774i
$204$		0			0
$205$	4.65667	−	13.6460i	0.325236	−	0.953076i
$206$	−4.05048			−0.282210
$207$		0			0
$208$		−	18.8630i		−	1.30792i
$209$	29.1233			2.01450
$210$		0			0
$211$	−1.95780			−0.134781			−0.0673904	−	0.997727i	$-0.521467\pi$
$211$	−1.95780			−0.134781			−0.0673904	+	0.997727i	$0.521467\pi$
$212$			0.748567i			0.0514118i
$213$		0			0
$214$	−8.93529			−0.610804
$215$	5.73540	+	1.95720i	0.391151	+	0.133480i
$216$		0			0
$217$			1.66870i			0.113279i
$218$		−	24.3513i		−	1.64928i
$219$		0			0
$220$	−0.629099	+	1.84352i	−0.0424138	+	0.124290i
$221$	−17.7773			−1.19583
$222$		0			0
$223$			8.97271i			0.600857i	0.953804	+	0.300429i	$0.0971297\pi$
$223$			8.97271i			0.600857i	−0.953804	+	0.300429i	$0.902870\pi$
$224$	0.680362			0.0454586
$225$		0			0
$226$	26.8455			1.78573
$227$			7.78659i			0.516814i	0.966036	+	0.258407i	$0.0831976\pi$
$227$			7.78659i			0.516814i	−0.966036	+	0.258407i	$0.916802\pi$
$228$		0			0
$229$	9.69814			0.640871			0.320435	−	0.947270i	$-0.396171\pi$
$229$	9.69814			0.640871			0.320435	+	0.947270i	$0.396171\pi$
$230$	−3.41254	+	10.0001i	−0.225016	+	0.659390i
$231$		0			0
$232$			18.9633i			1.24500i
$233$		−	22.4897i		−	1.47335i	−0.676246	−	0.736676i	$-0.736394\pi$
$233$		−	22.4897i		−	1.47335i	0.676246	−	0.736676i	$-0.263606\pi$
$234$		0			0
$235$	21.9472	+	7.48944i	1.43168	+	0.488557i
$236$	−2.05013			−0.133452
$237$		0			0
$238$			3.49143i			0.226316i
$239$	−22.3620			−1.44648			−0.723238	−	0.690598i	$-0.757347\pi$
$239$	−22.3620			−1.44648			−0.723238	+	0.690598i	$0.757347\pi$
$240$		0			0
$241$	−4.78481			−0.308217			−0.154108	−	0.988054i	$-0.549250\pi$
$241$	−4.78481			−0.308217			−0.154108	+	0.988054i	$0.549250\pi$
$242$			24.7019i			1.58790i
$243$		0			0
$244$	−1.66953			−0.106881
$245$	4.65094	−	13.6292i	0.297138	−	0.870738i
$246$		0			0
$247$		−	27.8321i		−	1.77092i
$248$		−	6.53663i		−	0.415076i
$249$		0			0
$250$	−8.36207	−	12.6464i	−0.528864	−	0.799825i
$251$	0.357304			0.0225529			0.0112764	−	0.999936i	$-0.496411\pi$
$251$	0.357304			0.0225529			0.0112764	+	0.999936i	$0.496411\pi$
$252$		0			0
$253$		−	18.8357i		−	1.18419i
$254$	−0.192534			−0.0120807
$255$		0			0
$256$	−3.84217			−0.240135
$257$			7.93068i			0.494702i	0.968926	+	0.247351i	$0.0795601\pi$
$257$			7.93068i			0.494702i	−0.968926	+	0.247351i	$0.920440\pi$
$258$		0			0
$259$	0.748140			0.0464872
$260$	1.76179	+	0.601206i	0.109261	+	0.0372852i
$261$		0			0
$262$			0.591083i			0.0365172i
$263$			2.56626i			0.158242i	0.996865	+	0.0791211i	$0.0252114\pi$
$263$			2.56626i			0.158242i	−0.996865	+	0.0791211i	$0.974789\pi$
$264$		0			0
$265$	9.82936	+	3.35425i	0.603813	+	0.206050i
$266$	−5.46617			−0.335153
$267$		0			0
$268$			0.982609i			0.0600224i
$269$	0.834873			0.0509031			0.0254516	−	0.999676i	$-0.491898\pi$
$269$	0.834873			0.0509031			0.0254516	+	0.999676i	$0.491898\pi$
$270$		0			0
$271$	14.5172			0.881855			0.440928	−	0.897543i	$-0.354650\pi$
$271$	14.5172			0.881855			0.440928	+	0.897543i	$0.354650\pi$
$272$		−	12.5674i		−	0.762008i
$273$		0			0
$274$	−5.12998			−0.309913
$275$	21.3882	+	16.5213i	1.28976	+	0.996270i
$276$		0			0
$277$			31.2010i			1.87469i	0.348406	+	0.937344i	$0.386723\pi$
$277$			31.2010i			1.87469i	−0.348406	+	0.937344i	$0.613277\pi$
$278$			17.3002i			1.03759i
$279$		0			0
$280$	1.58335	−	4.63989i	0.0946236	−	0.277286i
$281$	13.0674			0.779533			0.389767	−	0.920914i	$-0.372556\pi$
$281$	13.0674			0.779533			0.389767	+	0.920914i	$0.372556\pi$
$282$		0			0
$283$		−	3.47900i		−	0.206805i	−0.994640	−	0.103402i	$-0.967027\pi$
$283$		−	3.47900i		−	0.206805i	0.994640	−	0.103402i	$-0.0329730\pi$
$284$	0.451960			0.0268189
$285$		0			0
$286$	37.8618			2.23881
$287$		−	4.82417i		−	0.284762i
$288$		0			0
$289$	5.15599			0.303293
$290$	18.5692	+	6.33669i	1.09042	+	0.372103i
$291$		0			0
$292$		−	0.244233i		−	0.0142926i
$293$			30.0461i			1.75531i	0.479293	+	0.877655i	$0.340893\pi$
$293$			30.0461i			1.75531i	−0.479293	+	0.877655i	$0.659107\pi$
$294$		0			0
$295$	−9.18643	+	26.9201i	−0.534854	+	1.56735i
$296$	−2.93062			−0.170339
$297$		0			0
$298$		−	5.04463i		−	0.292228i
$299$	−18.0006			−1.04100
$300$		0			0
$301$	2.02760			0.116869
$302$		−	10.2976i		−	0.592562i
$303$		0			0
$304$	19.6754			1.12846
$305$	−7.48101	+	21.9225i	−0.428362	+	1.25528i
$306$		0			0
$307$		−	26.3957i		−	1.50648i	−0.657745	−	0.753241i	$-0.728490\pi$
$307$		−	26.3957i		−	1.50648i	0.657745	−	0.753241i	$-0.271510\pi$
$308$			0.651727i			0.0371356i
$309$		0			0
$310$	−6.40076	−	2.18425i	−0.363538	−	0.124057i
$311$	14.8744			0.843447			0.421724	−	0.906724i	$-0.361425\pi$
$311$	14.8744			0.843447			0.421724	+	0.906724i	$0.361425\pi$
$312$		0			0
$313$			0.373591i			0.0211166i	0.999944	+	0.0105583i	$0.00336088\pi$
$313$			0.373591i			0.0211166i	−0.999944	+	0.0105583i	$0.996639\pi$
$314$	−21.7857			−1.22944
$315$		0			0
$316$	2.24165			0.126103
$317$		−	5.02971i		−	0.282497i	−0.989974	−	0.141248i	$-0.954888\pi$
$317$		−	5.02971i		−	0.282497i	0.989974	−	0.141248i	$-0.0451116\pi$
$318$		0			0
$319$	−34.9758			−1.95827
$320$	−6.16481	+	18.0655i	−0.344623	+	1.00989i
$321$		0			0
$322$			3.53528i			0.197014i
$323$		−	18.5429i		−	1.03176i
$324$		0			0
$325$	15.7888	−	20.4399i	0.875804	−	1.13380i
$326$	9.48116			0.525113
$327$		0			0
$328$			18.8972i			1.04343i
$329$	7.75883			0.427758
$330$		0			0
$331$	2.14829			0.118081			0.0590404	−	0.998256i	$-0.481196\pi$
$331$	2.14829			0.118081			0.0590404	+	0.998256i	$0.481196\pi$
$332$		−	0.185311i		−	0.0101703i
$333$		0			0
$334$	22.1689			1.21303
$335$	12.9025	+	4.40297i	0.704941	+	0.240560i
$336$		0			0
$337$			14.2432i			0.775878i	0.921685	+	0.387939i	$0.126813\pi$
$337$			14.2432i			0.775878i	−0.921685	+	0.387939i	$0.873187\pi$
$338$		−	18.5546i		−	1.00924i
$339$		0			0
$340$	1.17378	+	0.400549i	0.0636569	+	0.0217228i
$341$	12.0561			0.652875
$342$		0			0
$343$		−	10.0552i		−	0.542931i
$344$	−7.94251			−0.428231
$345$		0			0
$346$	8.43408			0.453419
$347$			21.3584i			1.14658i	0.819353	+	0.573289i	$0.194333\pi$
$347$			21.3584i			1.14658i	−0.819353	+	0.573289i	$0.805667\pi$
$348$		0			0
$349$	8.65232			0.463148			0.231574	−	0.972817i	$-0.425612\pi$
$349$	8.65232			0.463148			0.231574	+	0.972817i	$0.425612\pi$
$350$	−4.01436	−	3.10088i	−0.214576	−	0.165749i
$351$		0			0
$352$		−	4.91552i		−	0.261998i
$353$			24.5145i			1.30477i	0.757886	+	0.652387i	$0.226232\pi$
$353$			24.5145i			1.30477i	−0.757886	+	0.652387i	$0.773768\pi$
$354$		0			0
$355$	2.02519	−	5.93465i	0.107486	−	0.314979i
$356$	−0.0601644			−0.00318871
$357$		0			0
$358$		−	14.8482i		−	0.784750i
$359$	20.8964			1.10287			0.551434	−	0.834218i	$-0.314081\pi$
$359$	20.8964			1.10287			0.551434	+	0.834218i	$0.314081\pi$
$360$		0			0
$361$	10.0307			0.527933
$362$			11.8660i			0.623663i
$363$		0			0
$364$	0.622832			0.0326453
$365$	−3.20700	−	1.09438i	−0.167862	−	0.0572826i
$366$		0			0
$367$			0.961719i			0.0502013i	0.999685	+	0.0251007i	$0.00799063\pi$
$367$			0.961719i			0.0502013i	−0.999685	+	0.0251007i	$0.992009\pi$
$368$		−	12.7252i		−	0.663347i
$369$		0			0
$370$	−0.979281	+	2.86970i	−0.0509104	+	0.149189i
$371$	3.47491			0.180408
$372$		0			0
$373$			16.9978i			0.880114i	0.897970	+	0.440057i	$0.145042\pi$
$373$			16.9978i			0.880114i	−0.897970	+	0.440057i	$0.854958\pi$
$374$	25.2251			1.30436
$375$		0			0
$376$	−30.3929			−1.56740
$377$			33.4251i			1.72148i
$378$		0			0
$379$	−12.9112			−0.663203			−0.331601	−	0.943420i	$-0.607589\pi$
$379$	−12.9112			−0.663203			−0.331601	+	0.943420i	$0.607589\pi$
$380$	−0.627098	+	1.83766i	−0.0321694	+	0.0942699i
$381$		0			0
$382$		−	21.4138i		−	1.09562i
$383$		−	13.8233i		−	0.706337i	−0.935560	−	0.353168i	$-0.885104\pi$
$383$		−	13.8233i		−	0.706337i	0.935560	−	0.353168i	$-0.114896\pi$
$384$		0			0
$385$	8.55777	+	2.92033i	0.436144	+	0.148834i
$386$	14.8954			0.758155
$387$		0			0
$388$		−	1.44465i		−	0.0733411i
$389$	−10.0408			−0.509089			−0.254544	−	0.967061i	$-0.581926\pi$
$389$	−10.0408			−0.509089			−0.254544	+	0.967061i	$0.581926\pi$
$390$		0			0
$391$	−11.9928			−0.606500
$392$			18.8740i			0.953282i
$393$		0			0
$394$	13.3798			0.674063
$395$	10.0446	−	29.4349i	0.505399	−	1.48103i
$396$		0			0
$397$		−	4.87476i		−	0.244657i	−0.992490	−	0.122329i	$-0.960964\pi$
$397$		−	4.87476i		−	0.244657i	0.992490	−	0.122329i	$-0.0390362\pi$
$398$		−	7.57693i		−	0.379797i
$399$		0			0
$400$	14.4496	+	11.1616i	0.722480	+	0.558079i
$401$	5.97844			0.298549			0.149275	−	0.988796i	$-0.452306\pi$
$401$	5.97844			0.298549			0.149275	+	0.988796i	$0.452306\pi$
$402$		0			0
$403$		−	11.5216i		−	0.573930i
$404$	2.24398			0.111642
$405$		0			0
$406$	6.56462			0.325797
$407$		−	5.40521i		−	0.267926i
$408$		0			0
$409$	28.3419			1.40142			0.700709	−	0.713447i	$-0.252867\pi$
$409$	28.3419			1.40142			0.700709	+	0.713447i	$0.252867\pi$
$410$	18.5044	+	6.31461i	0.913869	+	0.311856i
$411$		0			0
$412$			0.481399i			0.0237168i
$413$			9.51686i			0.468294i
$414$		0			0
$415$	−2.43330	−	0.830360i	−0.119446	−	0.0407608i
$416$	−4.69758			−0.230318
$417$		0			0
$418$			39.4923i			1.93163i
$419$	9.61738			0.469840			0.234920	−	0.972015i	$-0.424517\pi$
$419$	9.61738			0.469840			0.234920	+	0.972015i	$0.424517\pi$
$420$		0			0
$421$	−8.65638			−0.421886			−0.210943	−	0.977498i	$-0.567653\pi$
$421$	−8.65638			−0.421886			−0.210943	+	0.977498i	$0.567653\pi$
$422$		−	2.65485i		−	0.129236i
$423$		0			0
$424$	−13.6119			−0.661053
$425$	10.5191	−	13.6179i	0.510254	−	0.660566i
$426$		0			0
$427$			7.75011i			0.375054i
$428$			1.06196i			0.0513317i
$429$		0			0
$430$	−2.65403	+	7.77741i	−0.127989	+	0.375060i
$431$	−34.7519			−1.67394			−0.836969	−	0.547250i	$-0.815675\pi$
$431$	−34.7519			−1.67394			−0.836969	+	0.547250i	$0.815675\pi$
$432$		0			0
$433$			27.9319i			1.34232i	0.741312	+	0.671161i	$0.234204\pi$
$433$			27.9319i			1.34232i	−0.741312	+	0.671161i	$0.765796\pi$
$434$	−2.26281			−0.108619
$435$		0			0
$436$	−2.89415			−0.138605
$437$		−	18.7758i		−	0.898169i
$438$		0			0
$439$	23.0305			1.09919			0.549593	−	0.835433i	$-0.314783\pi$
$439$	23.0305			1.09919			0.549593	+	0.835433i	$0.314783\pi$
$440$	−33.5225	−	11.4395i	−1.59812	−	0.545357i
$441$		0			0
$442$		−	24.1067i		−	1.14664i
$443$		−	27.7267i		−	1.31733i	−0.752435	−	0.658667i	$-0.771121\pi$
$443$		−	27.7267i		−	1.31733i	0.752435	−	0.658667i	$-0.228879\pi$
$444$		0			0
$445$	−0.269591	+	0.790014i	−0.0127798	+	0.0374502i
$446$	−12.1673			−0.576139
$447$		0			0
$448$			6.38656i			0.301736i
$449$	26.4363			1.24761			0.623804	−	0.781581i	$-0.285586\pi$
$449$	26.4363			1.24761			0.623804	+	0.781581i	$0.285586\pi$
$450$		0			0
$451$	−34.8539			−1.64121
$452$		−	3.19058i		−	0.150072i
$453$		0			0
$454$	−10.5589			−0.495554
$455$	2.79085	−	8.17835i	0.130837	−	0.383407i
$456$		0			0
$457$		−	26.3869i		−	1.23433i	−0.786835	−	0.617164i	$-0.788282\pi$
$457$		−	26.3869i		−	1.23433i	0.786835	−	0.617164i	$-0.211718\pi$
$458$			13.1510i			0.614507i
$459$		0			0
$460$	1.18852	+	0.405580i	0.0554149	+	0.0189103i
$461$	12.8328			0.597684			0.298842	−	0.954303i	$-0.403400\pi$
$461$	12.8328			0.597684			0.298842	+	0.954303i	$0.403400\pi$
$462$		0			0
$463$			8.59902i			0.399630i	0.979834	+	0.199815i	$0.0640341\pi$
$463$			8.59902i			0.399630i	−0.979834	+	0.199815i	$0.935966\pi$
$464$	−23.6293			−1.09696
$465$		0			0
$466$	30.4969			1.41274
$467$			29.1169i			1.34737i	0.739018	+	0.673686i	$0.235290\pi$
$467$			29.1169i			1.34737i	−0.739018	+	0.673686i	$0.764710\pi$
$468$		0			0
$469$	4.56135			0.210623
$470$	−10.1560	+	29.7612i	−0.468459	+	1.37278i
$471$		0			0
$472$		−	37.2795i		−	1.71593i
$473$		−	14.6491i		−	0.673566i
$474$		0			0
$475$	21.3202	+	16.4687i	0.978236	+	0.755637i
$476$	0.414957			0.0190195
$477$		0			0
$478$		−	30.3237i		−	1.38697i
$479$	35.3714			1.61616			0.808081	−	0.589072i	$-0.200507\pi$
$479$	35.3714			1.61616			0.808081	+	0.589072i	$0.200507\pi$
$480$		0			0
$481$	−5.16556			−0.235529
$482$		−	6.48837i		−	0.295537i
$483$		0			0
$484$	2.93582			0.133446
$485$	−18.9696	−	6.47334i	−0.861365	−	0.293939i
$486$		0			0
$487$			37.1133i			1.68176i	0.541219	+	0.840882i	$0.317963\pi$
$487$			37.1133i			1.68176i	−0.541219	+	0.840882i	$0.682037\pi$
$488$		−	30.3587i		−	1.37428i
$489$		0			0
$490$	18.4817	+	6.30685i	0.834918	+	0.284914i
$491$	30.6327			1.38243			0.691217	−	0.722647i	$-0.257075\pi$
$491$	30.6327			1.38243			0.691217	+	0.722647i	$0.257075\pi$
$492$		0			0
$493$			22.2692i			1.00295i
$494$	37.7414			1.69806
$495$		0			0
$496$	8.14496			0.365720
$497$		−	2.09804i		−	0.0941098i
$498$		0			0
$499$	26.3356			1.17894			0.589472	−	0.807789i	$-0.299336\pi$
$499$	26.3356			1.17894			0.589472	+	0.807789i	$0.299336\pi$
$500$	−1.50302	+	0.993832i	−0.0672170	+	0.0444455i
$501$		0			0
$502$			0.484518i			0.0216251i
$503$		−	20.8358i		−	0.929023i	−0.885567	−	0.464511i	$-0.846230\pi$
$503$		−	20.8358i		−	0.929023i	0.885567	−	0.464511i	$-0.153770\pi$
$504$		0			0
$505$	10.0551	−	29.4656i	0.447445	−	1.31120i
$506$	25.5419			1.13548
$507$		0			0
$508$			0.0228827i			0.00101525i
$509$	3.57224			0.158337			0.0791685	−	0.996861i	$-0.474773\pi$
$509$	3.57224			0.158337			0.0791685	+	0.996861i	$0.474773\pi$
$510$		0			0
$511$	−1.13375			−0.0501540
$512$		−	24.7243i		−	1.09267i
$513$		0			0
$514$	−10.7543			−0.474352
$515$	6.32121	+	2.15710i	0.278546	+	0.0950533i
$516$		0			0
$517$		−	56.0565i		−	2.46536i
$518$			1.01451i			0.0445748i
$519$		0			0
$520$	−10.9323	+	32.0363i	−0.479414	+	1.40488i
$521$	−36.9568			−1.61911			−0.809554	−	0.587045i	$-0.800291\pi$
$521$	−36.9568			−1.61911			−0.809554	+	0.587045i	$0.800291\pi$
$522$		0			0
$523$		−	16.0177i		−	0.700405i	−0.936674	−	0.350203i	$-0.886113\pi$
$523$		−	16.0177i		−	0.700405i	0.936674	−	0.350203i	$-0.113887\pi$
$524$	0.0702502			0.00306890
$525$		0			0
$526$	−3.47994			−0.151733
$527$		−	7.67616i		−	0.334379i
$528$		0			0
$529$	10.8566			0.472027
$530$	−4.54849	+	13.3290i	−0.197574	+	0.578974i
$531$		0			0
$532$			0.649655i			0.0281661i
$533$			33.3086i			1.44276i
$534$		0			0
$535$	13.9445	+	4.75853i	0.602873	+	0.205729i
$536$	−17.8677			−0.771768
$537$		0			0
$538$			1.13212i			0.0488091i
$539$	−34.8111			−1.49942
$540$		0			0
$541$	−9.82948			−0.422602			−0.211301	−	0.977421i	$-0.567770\pi$
$541$	−9.82948			−0.422602			−0.211301	+	0.977421i	$0.567770\pi$
$542$			19.6858i			0.845578i
$543$		0			0
$544$	−3.12973			−0.134186
$545$	−12.9684	+	38.0029i	−0.555506	+	1.62786i
$546$		0			0
$547$			16.7689i			0.716987i	0.933532	+	0.358493i	$0.116709\pi$
$547$			16.7689i			0.716987i	−0.933532	+	0.358493i	$0.883291\pi$
$548$			0.609698i			0.0260450i
$549$		0			0
$550$	−22.4035	+	29.0032i	−0.955286	+	1.23670i
$551$	−34.8646			−1.48528
$552$		0			0
$553$		−	10.4059i		−	0.442504i
$554$	−42.3097			−1.79757
$555$		0			0
$556$	2.05612			0.0871990
$557$			35.3749i			1.49888i	0.662072	+	0.749440i	$0.269677\pi$
$557$			35.3749i			1.49888i	−0.662072	+	0.749440i	$0.730323\pi$
$558$		0			0
$559$	−13.9996			−0.592120
$560$	5.78153	+	1.97294i	0.244314	+	0.0833719i
$561$		0			0
$562$			17.7198i			0.747465i
$563$		−	16.7458i		−	0.705751i	−0.935670	−	0.352876i	$-0.885204\pi$
$563$		−	16.7458i		−	0.705751i	0.935670	−	0.352876i	$-0.114796\pi$
$564$		0			0
$565$	−41.8953	−	14.2967i	−1.76255	−	0.601467i
$566$	4.71765			0.198298
$567$		0			0
$568$			8.21844i			0.344838i
$569$	−26.0953			−1.09397			−0.546987	−	0.837141i	$-0.684225\pi$
$569$	−26.0953			−1.09397			−0.546987	+	0.837141i	$0.684225\pi$
$570$		0			0
$571$	24.5326			1.02666			0.513328	−	0.858193i	$-0.328413\pi$
$571$	24.5326			1.02666			0.513328	+	0.858193i	$0.328413\pi$
$572$		−	4.49987i		−	0.188149i
$573$		0			0
$574$	6.54175			0.273047
$575$	10.6513	−	13.7890i	0.444188	−	0.575039i
$576$		0			0
$577$			21.9665i			0.914479i	0.889344	+	0.457239i	$0.151162\pi$
$577$			21.9665i			0.914479i	−0.889344	+	0.457239i	$0.848838\pi$
$578$			6.99171i			0.290817i
$579$		0			0
$580$	0.753116	−	2.20694i	0.0312714	−	0.0916383i
$581$	−0.860228			−0.0356883
$582$		0			0
$583$		−	25.1057i		−	1.03977i
$584$	4.44112			0.183775
$585$		0			0
$586$	−40.7436			−1.68310
$587$			14.6771i			0.605788i	0.953024	+	0.302894i	$0.0979529\pi$
$587$			14.6771i			0.605788i	−0.953024	+	0.302894i	$0.902047\pi$
$588$		0			0
$589$	12.0178			0.495183
$590$	−36.5046	−	12.4571i	−1.50287	−	0.512852i
$591$		0			0
$592$		−	3.65170i		−	0.150084i
$593$			6.40723i			0.263113i	0.991309	+	0.131557i	$0.0419976\pi$
$593$			6.40723i			0.263113i	−0.991309	+	0.131557i	$0.958002\pi$
$594$		0			0
$595$	1.85938	−	5.44876i	0.0762272	−	0.223377i
$596$	−0.599554			−0.0245587
$597$		0			0
$598$		−	24.4095i		−	0.998178i
$599$	19.0689			0.779133			0.389566	−	0.920998i	$-0.372625\pi$
$599$	19.0689			0.779133			0.389566	+	0.920998i	$0.372625\pi$
$600$		0			0
$601$	22.2923			0.909320			0.454660	−	0.890665i	$-0.349761\pi$
$601$	22.2923			0.909320			0.454660	+	0.890665i	$0.349761\pi$
$602$			2.74949i			0.112061i
$603$		0			0
$604$	−1.22387			−0.0497987
$605$	13.1551	−	38.5500i	0.534832	−	1.56728i
$606$		0			0
$607$			16.2888i			0.661143i	0.943781	+	0.330571i	$0.107241\pi$
$607$			16.2888i			0.661143i	−0.943781	+	0.330571i	$0.892759\pi$
$608$		−	4.89988i		−	0.198717i
$609$		0			0
$610$	−29.7277	−	10.1445i	−1.20364	−	0.410740i
$611$	−53.5711			−2.16726
$612$		0			0
$613$		−	1.73076i		−	0.0699046i	−0.999389	−	0.0349523i	$-0.988872\pi$
$613$		−	1.73076i		−	0.0699046i	0.999389	−	0.0349523i	$-0.0111279\pi$
$614$	35.7935			1.44451
$615$		0			0
$616$	−11.8510			−0.477490
$617$		−	18.1783i		−	0.731830i	−0.930648	−	0.365915i	$-0.880756\pi$
$617$		−	18.1783i		−	0.731830i	0.930648	−	0.365915i	$-0.119244\pi$
$618$		0			0
$619$	−32.8475			−1.32025			−0.660127	−	0.751154i	$-0.729497\pi$
$619$	−32.8475			−1.32025			−0.660127	+	0.751154i	$0.729497\pi$
$620$	−0.259598	+	0.760730i	−0.0104257	+	0.0305516i
$621$		0			0
$622$			20.1702i			0.808750i
$623$			0.279288i			0.0111894i
$624$		0			0
$625$	6.31503	+	24.1893i	0.252601	+	0.967570i
$626$	−0.506603			−0.0202479
$627$		0			0
$628$			2.58923i			0.103322i
$629$	−3.44151			−0.137222
$630$		0			0
$631$	−24.9007			−0.991280			−0.495640	−	0.868528i	$-0.665066\pi$
$631$	−24.9007			−0.991280			−0.495640	+	0.868528i	$0.665066\pi$
$632$			40.7621i			1.62143i
$633$		0			0
$634$	6.82048			0.270876
$635$	0.300470	+	0.102535i	0.0119238	+	0.00406898i
$636$		0			0
$637$			33.2677i			1.31811i
$638$		−	47.4285i		−	1.87771i
$639$		0			0
$640$	−20.6484	−	7.04623i	−0.816199	−	0.278527i
$641$	31.7199			1.25286			0.626430	−	0.779477i	$-0.284515\pi$
$641$	31.7199			1.25286			0.626430	+	0.779477i	$0.284515\pi$
$642$		0			0
$643$		−	32.4283i		−	1.27885i	−0.768854	−	0.639424i	$-0.779173\pi$
$643$		−	32.4283i		−	1.27885i	0.768854	−	0.639424i	$-0.220827\pi$
$644$	0.420168			0.0165570
$645$		0			0
$646$	25.1449			0.989312
$647$			45.5239i			1.78973i	0.446339	+	0.894864i	$0.352728\pi$
$647$			45.5239i			1.78973i	−0.446339	+	0.894864i	$0.647272\pi$
$648$		0			0
$649$	68.7580			2.69899
$650$	27.7172	+	21.4102i	1.08716	+	0.839775i
$651$		0			0
$652$		−	1.12684i		−	0.0441303i
$653$		−	18.4351i		−	0.721421i	−0.932678	−	0.360710i	$-0.882534\pi$
$653$		−	18.4351i		−	0.721421i	0.932678	−	0.360710i	$-0.117466\pi$
$654$		0			0
$655$	0.314784	−	0.922449i	0.0122996	−	0.0360431i
$656$	−23.5469			−0.919352
$657$		0			0
$658$			10.5213i			0.410161i
$659$	44.1954			1.72161			0.860805	−	0.508935i	$-0.169961\pi$
$659$	44.1954			1.72161			0.860805	+	0.508935i	$0.169961\pi$
$660$		0			0
$661$	11.9408			0.464443			0.232222	−	0.972663i	$-0.425401\pi$
$661$	11.9408			0.464443			0.232222	+	0.972663i	$0.425401\pi$
$662$			2.91316i			0.113223i
$663$		0			0
$664$	3.36969			0.130769
$665$	8.53055	+	2.91104i	0.330801	+	0.112885i
$666$		0			0
$667$			22.5489i			0.873097i
$668$		−	2.63477i		−	0.101942i
$669$		0			0
$670$	−5.97059	+	17.4963i	−0.230664	+	0.675942i
$671$	55.9934			2.16160
$672$		0			0
$673$		−	36.3828i		−	1.40245i	−0.712938	−	0.701227i	$-0.752636\pi$
$673$		−	36.3828i		−	1.40245i	0.712938	−	0.701227i	$-0.247364\pi$
$674$	−19.3143			−0.743960
$675$		0			0
$676$	−2.20522			−0.0848161
$677$		−	6.30279i		−	0.242236i	−0.992638	−	0.121118i	$-0.961352\pi$
$677$		−	6.30279i		−	0.242236i	0.992638	−	0.121118i	$-0.0386479\pi$
$678$		0			0
$679$	−6.70619			−0.257360
$680$	−7.28358	+	21.3439i	−0.279312	+	0.818502i
$681$		0			0
$682$			16.3485i			0.626017i
$683$			5.75633i			0.220260i	0.993917	+	0.110130i	$0.0351267\pi$
$683$			5.75633i			0.220260i	−0.993917	+	0.110130i	$0.964873\pi$
$684$		0			0
$685$	8.00589	+	2.73200i	0.305889	+	0.104384i
$686$	13.6352			0.520596
$687$		0			0
$688$		−	9.89676i		−	0.377310i
$689$	−23.9926			−0.914045
$690$		0			0
$691$	46.6320			1.77397			0.886983	−	0.461802i	$-0.152797\pi$
$691$	46.6320			1.77397			0.886983	+	0.461802i	$0.152797\pi$
$692$		−	1.00239i		−	0.0381051i
$693$		0			0
$694$	−28.9627			−1.09941
$695$	9.21329	−	26.9988i	0.349480	−	1.02412i
$696$		0			0
$697$			22.1916i			0.840567i
$698$			11.7329i			0.444095i
$699$		0			0
$700$	−0.368540	+	0.477106i	−0.0139295	+	0.0180329i
$701$	−4.14142			−0.156419			−0.0782096	−	0.996937i	$-0.524920\pi$
$701$	−4.14142			−0.156419			−0.0782096	+	0.996937i	$0.524920\pi$
$702$		0			0
$703$		−	5.38802i		−	0.203213i
$704$	46.1420			1.73904
$705$		0			0
$706$	−33.2425			−1.25110
$707$		−	10.4168i		−	0.391762i
$708$		0			0
$709$	42.7621			1.60596			0.802981	−	0.596004i	$-0.203246\pi$
$709$	42.7621			1.60596			0.802981	+	0.596004i	$0.203246\pi$
$710$	8.04760	+	2.74623i	0.302021	+	0.103064i
$711$		0			0
$712$		−	1.09403i		−	0.0410004i
$713$		−	7.77257i		−	0.291085i
$714$		0			0
$715$	−59.0874	−	20.1635i	−2.20974	−	0.754071i
$716$	−1.76470			−0.0659501
$717$		0			0
$718$			28.3363i			1.05750i
$719$	−6.85976			−0.255826			−0.127913	−	0.991785i	$-0.540828\pi$
$719$	−6.85976			−0.255826			−0.127913	+	0.991785i	$0.540828\pi$
$720$		0			0
$721$	2.23469			0.0832243
$722$			13.6020i			0.506215i
$723$		0			0
$724$	1.41027			0.0524124
$725$	−25.6045	−	19.7782i	−0.950929	−	0.734544i
$726$		0			0
$727$		−	7.85944i		−	0.291490i	−0.989322	−	0.145745i	$-0.953442\pi$
$727$		−	7.85944i		−	0.291490i	0.989322	−	0.145745i	$-0.0465580\pi$
$728$			11.3256i			0.419753i
$729$		0			0
$730$	1.48402	−	4.34881i	0.0549261	−	0.160957i
$731$	−9.32713			−0.344976
$732$		0			0
$733$		−	12.8442i		−	0.474411i	−0.971459	−	0.237206i	$-0.923769\pi$
$733$		−	12.8442i		−	0.474411i	0.971459	−	0.237206i	$-0.0762315\pi$
$734$	−1.30413			−0.0481362
$735$		0			0
$736$	−3.16903			−0.116812
$737$		−	32.9551i		−	1.21392i
$738$		0			0
$739$	−13.2976			−0.489160			−0.244580	−	0.969629i	$-0.578650\pi$
$739$	−13.2976			−0.489160			−0.244580	+	0.969629i	$0.578650\pi$
$740$	0.341064	+	0.116388i	0.0125378	+	0.00427849i
$741$		0			0
$742$			4.71210i			0.172987i
$743$		−	36.2989i		−	1.33168i	−0.746096	−	0.665839i	$-0.768074\pi$
$743$		−	36.2989i		−	1.33168i	0.746096	−	0.665839i	$-0.231926\pi$
$744$		0			0
$745$	−2.68654	+	7.87269i	−0.0984274	+	0.288433i
$746$	−23.0497			−0.843908
$747$		0			0
$748$		−	2.99800i		−	0.109618i
$749$	4.92970			0.180127
$750$		0			0
$751$	−24.5638			−0.896346			−0.448173	−	0.893947i	$-0.647925\pi$
$751$	−24.5638			−0.896346			−0.448173	+	0.893947i	$0.647925\pi$
$752$		−	37.8711i		−	1.38102i
$753$		0			0
$754$	−45.3257			−1.65066
$755$	−5.48405	+	16.0706i	−0.199585	+	0.584867i
$756$		0			0
$757$		−	26.5324i		−	0.964336i	−0.876079	−	0.482168i	$-0.839850\pi$
$757$		−	26.5324i		−	0.964336i	0.876079	−	0.482168i	$-0.160150\pi$
$758$		−	17.5080i		−	0.635920i
$759$		0			0
$760$	−33.4159	−	11.4031i	−1.21212	−	0.413635i
$761$	2.08409			0.0755481			0.0377740	−	0.999286i	$-0.487973\pi$
$761$	2.08409			0.0755481			0.0377740	+	0.999286i	$0.487973\pi$
$762$		0			0
$763$			13.4349i			0.486376i
$764$	−2.54502			−0.0920757
$765$		0			0
$766$	18.7449			0.677280
$767$		−	65.7095i		−	2.37263i
$768$		0			0
$769$	−37.4780			−1.35149			−0.675746	−	0.737135i	$-0.736178\pi$
$769$	−37.4780			−1.35149			−0.675746	+	0.737135i	$0.736178\pi$
$770$	−3.96007	+	11.6047i	−0.142711	+	0.418203i
$771$		0			0
$772$		−	1.77032i		−	0.0637150i
$773$			51.5098i			1.85268i	0.376692	+	0.926339i	$0.377062\pi$
$773$			51.5098i			1.85268i	−0.376692	+	0.926339i	$0.622938\pi$
$774$		0			0
$775$	8.82584	+	6.81751i	0.317033	+	0.244892i
$776$	26.2695			0.943021
$777$		0			0
$778$		−	13.6157i		−	0.488146i
$779$	−34.7431			−1.24480
$780$		0			0
$781$	−15.1580			−0.542396
$782$		−	16.2626i		−	0.581550i
$783$		0			0
$784$	−23.5180			−0.839927
$785$	33.9990	+	11.6021i	1.21348	+	0.414097i
$786$		0			0
$787$			30.5759i			1.08991i	0.838464	+	0.544957i	$0.183454\pi$
$787$			30.5759i			1.08991i	−0.838464	+	0.544957i	$0.816546\pi$
$788$		−	1.59019i		−	0.0566480i
$789$		0			0
$790$	39.9148	+	13.6208i	1.42010	+	0.484608i
$791$	−14.8109			−0.526617
$792$		0			0
$793$		−	53.5109i		−	1.90023i
$794$	6.61035			0.234593
$795$		0			0
$796$	−0.900518			−0.0319180
$797$			14.8601i			0.526373i	0.964745	+	0.263186i	$0.0847735\pi$
$797$			14.8601i			0.526373i	−0.964745	+	0.263186i	$0.915227\pi$
$798$		0			0
$799$	−35.6913			−1.26267
$800$	2.77964	−	3.59847i	0.0982750	−	0.127225i
$801$		0			0
$802$			8.10699i			0.286268i
$803$			8.19116i			0.289060i
$804$		0			0
$805$	1.88273	−	5.51719i	0.0663576	−	0.194456i
$806$	15.6237			0.550321
$807$		0			0
$808$			40.8046i			1.43550i
$809$	−17.9217			−0.630094			−0.315047	−	0.949076i	$-0.602020\pi$
$809$	−17.9217			−0.630094			−0.315047	+	0.949076i	$0.602020\pi$
$810$		0			0
$811$	−25.4430			−0.893425			−0.446712	−	0.894678i	$-0.647405\pi$
$811$	−25.4430			−0.893425			−0.446712	+	0.894678i	$0.647405\pi$
$812$		−	0.780205i		−	0.0273798i
$813$		0			0
$814$	7.32966			0.256904
$815$	−14.7964	−	5.04924i	−0.518294	−	0.176867i
$816$		0			0
$817$		−	14.6025i		−	0.510877i
$818$			38.4327i			1.34377i
$819$		0			0
$820$	0.750491	−	2.19925i	0.0262083	−	0.0768012i
$821$	−33.2113			−1.15908			−0.579541	−	0.814943i	$-0.696768\pi$
$821$	−33.2113			−1.15908			−0.579541	+	0.814943i	$0.696768\pi$
$822$		0			0
$823$		−	50.9984i		−	1.77769i	−0.458205	−	0.888847i	$-0.651507\pi$
$823$		−	50.9984i		−	1.77769i	0.458205	−	0.888847i	$-0.348493\pi$
$824$	−8.75375			−0.304951
$825$		0			0
$826$	−12.9052			−0.449030
$827$			41.5779i			1.44580i	0.690951	+	0.722902i	$0.257192\pi$
$827$			41.5779i			1.44580i	−0.690951	+	0.722902i	$0.742808\pi$
$828$		0			0
$829$	17.8704			0.620665			0.310332	−	0.950628i	$-0.399560\pi$
$829$	17.8704			0.620665			0.310332	+	0.950628i	$0.399560\pi$
$830$	1.12600	−	3.29965i	0.0390840	−	0.114532i
$831$		0			0
$832$		−	44.0962i		−	1.52876i
$833$			22.1643i			0.767948i
$834$		0			0
$835$	−34.5969	−	11.8061i	−1.19728	−	0.408569i
$836$	4.69366			0.162334
$837$		0			0
$838$			13.0415i			0.450512i
$839$	26.2881			0.907565			0.453783	−	0.891112i	$-0.350074\pi$
$839$	26.2881			0.907565			0.453783	+	0.891112i	$0.350074\pi$
$840$		0			0
$841$	12.8708			0.443820
$842$		−	11.7384i		−	0.404531i
$843$		0			0
$844$	−0.315529			−0.0108610
$845$	−9.88137	+	28.9565i	−0.339929	+	0.996135i
$846$		0			0
$847$		−	13.6283i		−	0.468275i
$848$		−	16.9611i		−	0.582448i
$849$		0			0
$850$	18.4664	+	14.2643i	0.633392	+	0.489263i
$851$	−3.48474			−0.119455
$852$		0			0
$853$		−	32.1407i		−	1.10047i	−0.835008	−	0.550237i	$-0.814537\pi$
$853$		−	32.1407i		−	1.10047i	0.835008	−	0.550237i	$-0.185463\pi$
$854$	−10.5094			−0.359625
$855$		0			0
$856$	−19.3106			−0.660024
$857$		−	47.5492i		−	1.62425i	−0.583483	−	0.812125i	$-0.698310\pi$
$857$		−	47.5492i		−	1.62425i	0.583483	−	0.812125i	$-0.301690\pi$
$858$		0			0
$859$	−13.3037			−0.453917			−0.226959	−	0.973904i	$-0.572878\pi$
$859$	−13.3037			−0.453917			−0.226959	+	0.973904i	$0.572878\pi$
$860$	0.924345	+	0.315431i	0.0315199	+	0.0107561i
$861$		0			0
$862$		−	47.1248i		−	1.60508i
$863$			4.07561i			0.138735i	0.997591	+	0.0693676i	$0.0220981\pi$
$863$			4.07561i			0.138735i	−0.997591	+	0.0693676i	$0.977902\pi$
$864$		0			0
$865$	−13.1623	−	4.49161i	−0.447531	−	0.152719i
$866$	−37.8767			−1.28710
$867$		0			0
$868$			0.268935i			0.00912826i
$869$	−75.1812			−2.55035
$870$		0			0
$871$	−31.4940			−1.06713
$872$		−	52.6272i		−	1.78218i
$873$		0			0
$874$	25.4607			0.861221
$875$	4.61345	+	6.97713i	0.155963	+	0.235870i
$876$		0			0
$877$			26.7909i			0.904665i	0.891849	+	0.452333i	$0.149408\pi$
$877$			26.7909i			0.904665i	−0.891849	+	0.452333i	$0.850592\pi$
$878$			31.2302i			1.05397i
$879$		0			0
$880$	14.2542	−	41.7707i	0.480509	−	1.40809i
$881$	−10.8047			−0.364018			−0.182009	−	0.983297i	$-0.558260\pi$
$881$	−10.8047			−0.364018			−0.182009	+	0.983297i	$0.558260\pi$
$882$		0			0
$883$			47.6789i			1.60452i	0.596974	+	0.802261i	$0.296370\pi$
$883$			47.6789i			1.60452i	−0.596974	+	0.802261i	$0.703630\pi$
$884$	−2.86508			−0.0963632
$885$		0			0
$886$	37.5984			1.26314
$887$			44.6016i			1.49757i	0.662811	+	0.748787i	$0.269363\pi$
$887$			44.6016i			1.49757i	−0.662811	+	0.748787i	$0.730637\pi$
$888$		0			0
$889$	0.106223			0.00356261
$890$	−1.07129	−	0.365575i	−0.0359096	−	0.0122541i
$891$		0			0
$892$			1.44609i			0.0484185i
$893$		−	55.8782i		−	1.86989i
$894$		0			0
$895$	−7.90747	+	23.1722i	−0.264318	+	0.774560i
$896$	−7.29968			−0.243865
$897$		0			0
$898$			35.8487i			1.19629i
$899$	−14.4328			−0.481360
$900$		0			0
$901$	−15.9849			−0.532534
$902$		−	47.2632i		−	1.57369i
$903$		0			0
$904$	58.0175			1.92963
$905$	6.31930	−	18.5182i	0.210060	−	0.615565i
$906$		0			0
$907$		−	0.577224i		−	0.0191664i	−0.999954	−	0.00958321i	$-0.996950\pi$
$907$		−	0.577224i		−	0.0191664i	0.999954	−	0.00958321i	$-0.00305048\pi$
$908$			1.25493i			0.0416461i
$909$		0			0
$910$	11.0901	+	3.78449i	0.367635	+	0.125455i
$911$	−14.8648			−0.492492			−0.246246	−	0.969207i	$-0.579197\pi$
$911$	−14.8648			−0.492492			−0.246246	+	0.969207i	$0.579197\pi$
$912$		0			0
$913$			6.21503i			0.205687i
$914$	35.7816			1.18355
$915$		0			0
$916$	1.56300			0.0516430
$917$		−	0.326107i		−	0.0107690i
$918$		0			0
$919$	5.47645			0.180651			0.0903257	−	0.995912i	$-0.471209\pi$
$919$	5.47645			0.180651			0.0903257	+	0.995912i	$0.471209\pi$
$920$	−7.37505	+	21.6120i	−0.243148	+	0.712526i
$921$		0			0
$922$			17.4018i			0.573097i
$923$			14.4860i			0.476811i
$924$		0			0
$925$	3.05655	−	3.95696i	0.100499	−	0.130104i
$926$	−11.6606			−0.383190
$927$		0			0
$928$			5.88454i			0.193169i
$929$	8.07412			0.264903			0.132452	−	0.991189i	$-0.457715\pi$
$929$	8.07412			0.264903			0.132452	+	0.991189i	$0.457715\pi$
$930$		0			0
$931$	−34.7004			−1.13726
$932$		−	3.62456i		−	0.118726i
$933$		0			0
$934$	−39.4836			−1.29194
$935$	−39.3665	−	13.4338i	−1.28742	−	0.439331i
$936$		0			0
$937$			4.83794i			0.158048i	0.996873	+	0.0790242i	$0.0251805\pi$
$937$			4.83794i			0.158048i	−0.996873	+	0.0790242i	$0.974820\pi$
$938$			6.18535i			0.201959i
$939$		0			0
$940$	3.53711	+	1.20703i	0.115368	+	0.0393691i
$941$	9.67126			0.315274			0.157637	−	0.987497i	$-0.449612\pi$
$941$	9.67126			0.315274			0.157637	+	0.987497i	$0.449612\pi$
$942$		0			0
$943$			22.4703i			0.731734i
$944$	46.4521			1.51189
$945$		0			0
$946$	19.8647			0.645857
$947$			22.6385i			0.735653i	0.929894	+	0.367827i	$0.119898\pi$
$947$			22.6385i			0.735653i	−0.929894	+	0.367827i	$0.880102\pi$
$948$		0			0
$949$	7.82800			0.254107
$950$	−22.3322	+	28.9109i	−0.724552	+	0.937994i
$951$		0			0
$952$			7.54557i			0.244553i
$953$		−	31.8539i		−	1.03185i	−0.856634	−	0.515924i	$-0.827449\pi$
$953$		−	31.8539i		−	1.03185i	0.856634	−	0.515924i	$-0.172551\pi$
$954$		0			0
$955$	−11.4040	+	33.4185i	−0.369025	+	1.08140i
$956$	−3.60397			−0.116561
$957$		0			0
$958$			47.9649i			1.54968i
$959$	2.83027			0.0913941
$960$		0			0
$961$	−26.0250			−0.839518
$962$		−	7.00469i		−	0.225840i
$963$		0			0
$964$	−0.771143			−0.0248368
$965$	−23.2459	−	7.93261i	−0.748310	−	0.255360i
$966$		0			0
$967$		−	21.4942i		−	0.691206i	−0.938381	−	0.345603i	$-0.887674\pi$
$967$		−	21.4942i		−	0.691206i	0.938381	−	0.345603i	$-0.112326\pi$
$968$			53.3849i			1.71586i
$969$		0			0
$970$	8.77809	−	25.7235i	0.281847	−	0.825931i
$971$	−26.3424			−0.845368			−0.422684	−	0.906277i	$-0.638912\pi$
$971$	−26.3424			−0.845368			−0.422684	+	0.906277i	$0.638912\pi$
$972$		0			0
$973$		−	9.54469i		−	0.305989i
$974$	−50.3270			−1.61258
$975$		0			0
$976$	37.8285			1.21086
$977$		−	8.62429i		−	0.275916i	−0.990438	−	0.137958i	$-0.955946\pi$
$977$		−	8.62429i		−	0.275916i	0.990438	−	0.137958i	$-0.0440538\pi$
$978$		0			0
$979$	2.01782			0.0644897
$980$	0.749569	−	2.19655i	0.0239441	−	0.0701662i
$981$		0			0
$982$			41.5391i			1.32557i
$983$			48.7498i			1.55488i	0.628959	+	0.777438i	$0.283481\pi$
$983$			48.7498i			1.55488i	−0.628959	+	0.777438i	$0.716519\pi$
$984$		0			0
$985$	−20.8806	−	7.12547i	−0.665311	−	0.227036i
$986$	−30.1979			−0.961696
$987$		0			0
$988$		−	4.48556i		−	0.142705i
$989$	−9.44427			−0.300310
$990$		0			0
$991$	9.04494			0.287322			0.143661	−	0.989627i	$-0.454112\pi$
$991$	9.04494			0.287322			0.143661	+	0.989627i	$0.454112\pi$
$992$		−	2.02839i		−	0.0644014i
$993$		0			0
$994$	2.84501			0.0902383
$995$	−4.03513	+	11.8246i	−0.127922	+	0.374866i
$996$		0			0
$997$			38.5413i			1.22062i	0.792164	+	0.610308i	$0.208954\pi$
$997$			38.5413i			1.22062i	−0.792164	+	0.610308i	$0.791046\pi$
$998$			35.7121i			1.13045i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1665.2.c.e.334.13		18
3.2	odd	2		185.2.b.a.149.6	✓	18
5.2	odd	4		8325.2.a.cq.1.4		9
5.3	odd	4		8325.2.a.cr.1.6		9
5.4	even	2	inner	1665.2.c.e.334.6		18
15.2	even	4		925.2.a.m.1.6		9
15.8	even	4		925.2.a.l.1.4		9
15.14	odd	2		185.2.b.a.149.13	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.b.a.149.6	✓	18	3.2	odd	2
185.2.b.a.149.13	yes	18	15.14	odd	2
925.2.a.l.1.4		9	15.8	even	4
925.2.a.m.1.6		9	15.2	even	4
1665.2.c.e.334.6		18	5.4	even	2	inner
1665.2.c.e.334.13		18	1.1	even	1	trivial
8325.2.a.cq.1.4		9	5.2	odd	4
8325.2.a.cr.1.6		9	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1665 = 3^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1665.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.35604i q^{2} +0.161165 q^{4} +(0.722164 - 2.11624i) q^{5} -0.748140i q^{7} +2.93062i q^{8} +(2.86970 + 0.979281i) q^{10} -5.40521 q^{11} +5.16556i q^{13} +1.01451 q^{14} -3.65170 q^{16} +3.44151i q^{17} -5.38802 q^{19} +(0.116388 - 0.341064i) q^{20} -7.32966i q^{22} +3.48474i q^{23} +(-3.95696 - 3.05655i) q^{25} -7.00469 q^{26} -0.120574i q^{28} +6.47076 q^{29} -2.23046 q^{31} +0.909404i q^{32} -4.66682 q^{34} +(-1.58325 - 0.540280i) q^{35} +1.00000i q^{37} -7.30635i q^{38} +(6.20190 + 2.11639i) q^{40} +6.44821 q^{41} +2.71018i q^{43} -0.871130 q^{44} -4.72543 q^{46} +10.3708i q^{47} +6.44029 q^{49} +(4.14479 - 5.36578i) q^{50} +0.832507i q^{52} +4.64473i q^{53} +(-3.90345 + 11.4387i) q^{55} +2.19251 q^{56} +8.77459i q^{58} -12.7207 q^{59} -10.3592 q^{61} -3.02459i q^{62} -8.53658 q^{64} +(10.9316 + 3.73038i) q^{65} +6.09691i q^{67} +0.554651i q^{68} +(0.732640 - 2.14694i) q^{70} +2.80433 q^{71} -1.51542i q^{73} -1.35604 q^{74} -0.868359 q^{76} +4.04385i q^{77} +13.9090 q^{79} +(-2.63712 + 7.72787i) q^{80} +8.74401i q^{82} -1.14982i q^{83} +(7.28307 + 2.48534i) q^{85} -3.67511 q^{86} -15.8406i q^{88} -0.373310 q^{89} +3.86456 q^{91} +0.561617i q^{92} -14.0632 q^{94} +(-3.89103 + 11.4023i) q^{95} -8.96381i q^{97} +8.73326i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 22 q^{4} - 2 q^{5} + 6 q^{10} - 8 q^{14} + 22 q^{16} + 8 q^{19} + 4 q^{20} - 18 q^{25} + 12 q^{26} - 4 q^{29} - 12 q^{31} - 12 q^{34} + 2 q^{35} - 6 q^{40} - 4 q^{41} + 8 q^{44} + 32 q^{46} + 14 q^{49}+ \cdots + 44 q^{95}+O(q^{100}) \) 18 * q - 22 * q^4 - 2 * q^5 + 6 * q^10 - 8 * q^14 + 22 * q^16 + 8 * q^19 + 4 * q^20 - 18 * q^25 + 12 * q^26 - 4 * q^29 - 12 * q^31 - 12 * q^34 + 2 * q^35 - 6 * q^40 - 4 * q^41 + 8 * q^44 + 32 * q^46 + 14 * q^49 - 8 * q^50 - 34 * q^55 + 48 * q^56 + 20 * q^59 + 16 * q^61 - 30 * q^64 - 20 * q^65 + 40 * q^70 - 16 * q^71 - 10 * q^74 - 96 * q^76 + 52 * q^79 - 36 * q^80 - 8 * q^85 + 32 * q^86 - 16 * q^89 - 36 * q^91 + 52 * q^94 + 44 * q^95

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