LMFDB - Embedded newform 1665.2.c.e.334.1

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			334.1
Root			$-1.68489i$ of defining polynomial
Character	$\chi$	$=$	1665.334
Dual form			1665.2.c.e.334.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.68489i q^{2} -5.20864 q^{4} +(-0.587164 + 2.15760i) q^{5} -3.48285i q^{7} +8.61484i q^{8} +(5.79292 + 1.57647i) q^{10} +3.18991 q^{11} +1.81648i q^{13} -9.35107 q^{14} +12.7126 q^{16} -2.82645i q^{17} +5.72714 q^{19} +(3.05832 - 11.2382i) q^{20} -8.56456i q^{22} -1.43274i q^{23} +(-4.31048 - 2.53373i) q^{25} +4.87704 q^{26} +18.1409i q^{28} -2.30634 q^{29} +6.00714 q^{31} -16.9023i q^{32} -7.58870 q^{34} +(7.51460 + 2.04500i) q^{35} -1.00000i q^{37} -15.3767i q^{38} +(-18.5874 - 5.05832i) q^{40} -7.82452 q^{41} -11.6967i q^{43} -16.6151 q^{44} -3.84676 q^{46} -2.42814i q^{47} -5.13024 q^{49} +(-6.80279 + 11.5732i) q^{50} -9.46137i q^{52} -9.32573i q^{53} +(-1.87300 + 6.88255i) q^{55} +30.0042 q^{56} +6.19227i q^{58} +2.86539 q^{59} -4.67275 q^{61} -16.1285i q^{62} -19.9557 q^{64} +(-3.91923 - 1.06657i) q^{65} +6.00752i q^{67} +14.7219i q^{68} +(5.49061 - 20.1759i) q^{70} -3.40566 q^{71} -1.89975i q^{73} -2.68489 q^{74} -29.8306 q^{76} -11.1100i q^{77} +1.60903 q^{79} +(-7.46440 + 27.4288i) q^{80} +21.0080i q^{82} +7.37571i q^{83} +(6.09834 + 1.65959i) q^{85} -31.4043 q^{86} +27.4806i q^{88} -8.48746 q^{89} +6.32652 q^{91} +7.46264i q^{92} -6.51929 q^{94} +(-3.36277 + 12.3569i) q^{95} +9.00003i q^{97} +13.7741i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	2.68489i		−	1.89850i	−0.314516	−	0.949252i	$-0.601842\pi$
$2$		−	2.68489i		−	1.89850i	0.314516	−	0.949252i	$-0.398158\pi$
$3$		0			0
$3$		0			0
$4$	−5.20864			−2.60432
$5$	−0.587164	+	2.15760i	−0.262588	+	0.964908i
$5$	−0.587164	+	2.15760i	−0.262588	+	0.964908i
$6$		0			0
$7$		−	3.48285i		−	1.31639i	−0.752846	−	0.658197i	$-0.771320\pi$
$7$		−	3.48285i		−	1.31639i	0.752846	−	0.658197i	$-0.228680\pi$
$8$			8.61484i			3.04581i
$9$		0			0
$10$	5.79292	+	1.57647i	1.83188	+	0.498524i
$11$	3.18991			0.961794			0.480897	−	0.876777i	$-0.340311\pi$
$11$	3.18991			0.961794			0.480897	+	0.876777i	$0.340311\pi$
$12$		0			0
$13$			1.81648i			0.503800i	0.967753	+	0.251900i	$0.0810554\pi$
$13$			1.81648i			0.503800i	−0.967753	+	0.251900i	$0.918945\pi$
$14$	−9.35107			−2.49918
$15$		0			0
$16$	12.7126			3.17816
$17$		−	2.82645i		−	0.685514i	−0.939424	−	0.342757i	$-0.888639\pi$
$17$		−	2.82645i		−	0.685514i	0.939424	−	0.342757i	$-0.111361\pi$
$18$		0			0
$19$	5.72714			1.31389			0.656947	−	0.753936i	$-0.271847\pi$
$19$	5.72714			1.31389			0.656947	+	0.753936i	$0.271847\pi$
$20$	3.05832	−	11.2382i	0.683862	−	2.51293i
$21$		0			0
$22$		−	8.56456i		−	1.82597i
$23$		−	1.43274i		−	0.298748i	−0.988781	−	0.149374i	$-0.952274\pi$
$23$		−	1.43274i		−	0.298748i	0.988781	−	0.149374i	$-0.0477258\pi$
$24$		0			0
$25$	−4.31048	−	2.53373i	−0.862095	−	0.506746i
$26$	4.87704			0.956467
$27$		0			0
$28$			18.1409i			3.42831i
$29$	−2.30634			−0.428276			−0.214138	−	0.976803i	$-0.568694\pi$
$29$	−2.30634			−0.428276			−0.214138	+	0.976803i	$0.568694\pi$
$30$		0			0
$31$	6.00714			1.07891			0.539457	−	0.842013i	$-0.318629\pi$
$31$	6.00714			1.07891			0.539457	+	0.842013i	$0.318629\pi$
$32$		−	16.9023i		−	2.98794i
$33$		0			0
$34$	−7.58870			−1.30145
$35$	7.51460	+	2.04500i	1.27020	+	0.345669i
$36$		0			0
$37$		−	1.00000i		−	0.164399i
$37$		−	1.00000i		−	0.164399i
$38$		−	15.3767i		−	2.49444i
$39$		0			0
$40$	−18.5874	−	5.05832i	−2.93892	−	0.799791i
$41$	−7.82452			−1.22198			−0.610992	−	0.791636i	$-0.709229\pi$
$41$	−7.82452			−1.22198			−0.610992	+	0.791636i	$0.709229\pi$
$42$		0			0
$43$		−	11.6967i		−	1.78373i	−0.452305	−	0.891863i	$-0.649398\pi$
$43$		−	11.6967i		−	1.78373i	0.452305	−	0.891863i	$-0.350602\pi$
$44$	−16.6151			−2.50482
$45$		0			0
$46$	−3.84676			−0.567174
$47$		−	2.42814i		−	0.354181i	−0.984195	−	0.177090i	$-0.943332\pi$
$47$		−	2.42814i		−	0.354181i	0.984195	−	0.177090i	$-0.0566685\pi$
$48$		0			0
$49$	−5.13024			−0.732892
$50$	−6.80279	+	11.5732i	−0.962059	+	1.63669i
$51$		0			0
$52$		−	9.46137i		−	1.31206i
$53$		−	9.32573i		−	1.28099i	−0.767964	−	0.640493i	$-0.778730\pi$
$53$		−	9.32573i		−	1.28099i	0.767964	−	0.640493i	$-0.221270\pi$
$54$		0			0
$55$	−1.87300	+	6.88255i	−0.252555	+	0.928043i
$56$	30.0042			4.00948
$57$		0			0
$58$			6.19227i			0.813084i
$59$	2.86539			0.373042			0.186521	−	0.982451i	$-0.440279\pi$
$59$	2.86539			0.373042			0.186521	+	0.982451i	$0.440279\pi$
$60$		0			0
$61$	−4.67275			−0.598285			−0.299142	−	0.954208i	$-0.596701\pi$
$61$	−4.67275			−0.598285			−0.299142	+	0.954208i	$0.596701\pi$
$62$		−	16.1285i		−	2.04832i
$63$		0			0
$64$	−19.9557			−2.49446
$65$	−3.91923	−	1.06657i	−0.486121	−	0.132292i
$66$		0			0
$67$			6.00752i			0.733936i	0.930234	+	0.366968i	$0.119604\pi$
$67$			6.00752i			0.733936i	−0.930234	+	0.366968i	$0.880396\pi$
$68$			14.7219i			1.78530i
$69$		0			0
$70$	5.49061	−	20.1759i	0.656253	−	2.41148i
$71$	−3.40566			−0.404177			−0.202089	−	0.979367i	$-0.564773\pi$
$71$	−3.40566			−0.404177			−0.202089	+	0.979367i	$0.564773\pi$
$72$		0			0
$73$		−	1.89975i		−	0.222349i	−0.993801	−	0.111174i	$-0.964539\pi$
$73$		−	1.89975i		−	0.222349i	0.993801	−	0.111174i	$-0.0354612\pi$
$74$	−2.68489			−0.312112
$75$		0			0
$76$	−29.8306			−3.42180
$77$		−	11.1100i		−	1.26610i
$78$		0			0
$79$	1.60903			0.181031			0.0905153	−	0.995895i	$-0.471149\pi$
$79$	1.60903			0.181031			0.0905153	+	0.995895i	$0.471149\pi$
$80$	−7.46440	+	27.4288i	−0.834545	+	3.06663i
$81$		0			0
$82$			21.0080i			2.31994i
$83$			7.37571i			0.809589i	0.914408	+	0.404795i	$0.132657\pi$
$83$			7.37571i			0.809589i	−0.914408	+	0.404795i	$0.867343\pi$
$84$		0			0
$85$	6.09834	+	1.65959i	0.661458	+	0.180008i
$86$	−31.4043			−3.38641
$87$		0			0
$88$			27.4806i			2.92944i
$89$	−8.48746			−0.899669			−0.449834	−	0.893112i	$-0.648517\pi$
$89$	−8.48746			−0.899669			−0.449834	+	0.893112i	$0.648517\pi$
$90$		0			0
$91$	6.32652			0.663199
$92$			7.46264i			0.778034i
$93$		0			0
$94$	−6.51929			−0.672413
$95$	−3.36277	+	12.3569i	−0.345013	+	1.26779i
$96$		0			0
$97$			9.00003i			0.913814i	0.889514	+	0.456907i	$0.151043\pi$
$97$			9.00003i			0.913814i	−0.889514	+	0.456907i	$0.848957\pi$
$98$			13.7741i			1.39140i
$99$		0			0
$100$	22.4517	+	13.1973i	2.24517	+	1.31973i
$101$	12.9479			1.28836			0.644182	−	0.764872i	$-0.277198\pi$
$101$	12.9479			1.28836			0.644182	+	0.764872i	$0.277198\pi$
$102$		0			0
$103$		−	7.46684i		−	0.735729i	−0.929879	−	0.367865i	$-0.880089\pi$
$103$		−	7.46684i		−	0.735729i	0.929879	−	0.367865i	$-0.119911\pi$
$104$	−15.6487			−1.53448
$105$		0			0
$106$	−25.0386			−2.43196
$107$		−	11.2215i		−	1.08482i	−0.840113	−	0.542411i	$-0.817511\pi$
$107$		−	11.2215i		−	1.08482i	0.840113	−	0.542411i	$-0.182489\pi$
$108$		0			0
$109$	−2.67262			−0.255991			−0.127996	−	0.991775i	$-0.540854\pi$
$109$	−2.67262			−0.255991			−0.127996	+	0.991775i	$0.540854\pi$
$110$	18.4789	+	5.02880i	1.76189	+	0.479477i
$111$		0			0
$112$		−	44.2762i		−	4.18371i
$113$		−	18.6735i		−	1.75666i	−0.478057	−	0.878329i	$-0.658659\pi$
$113$		−	18.6735i		−	1.75666i	0.478057	−	0.878329i	$-0.341341\pi$
$114$		0			0
$115$	3.09129	+	0.841255i	0.288264	+	0.0784475i
$116$	12.0129			1.11537
$117$		0			0
$118$		−	7.69326i		−	0.708222i
$119$	−9.84409			−0.902406
$120$		0			0
$121$	−0.824470			−0.0749518
$122$			12.5458i			1.13585i
$123$		0			0
$124$	−31.2890			−2.80984
$125$	7.99773	−	7.81257i	0.715339	−	0.698778i
$126$		0			0
$127$			2.42257i			0.214968i	0.994207	+	0.107484i	$0.0342794\pi$
$127$			2.42257i			0.214968i	−0.994207	+	0.107484i	$0.965721\pi$
$128$			19.7741i			1.74780i
$129$		0			0
$130$	−2.86362	+	10.5227i	−0.251156	+	0.922903i
$131$	−11.2791			−0.985462			−0.492731	−	0.870182i	$-0.664001\pi$
$131$	−11.2791			−0.985462			−0.492731	+	0.870182i	$0.664001\pi$
$132$		0			0
$133$		−	19.9467i		−	1.72960i
$134$	16.1295			1.39338
$135$		0			0
$136$	24.3494			2.08794
$137$			5.25383i			0.448865i	0.974490	+	0.224433i	$0.0720529\pi$
$137$			5.25383i			0.448865i	−0.974490	+	0.224433i	$0.927947\pi$
$138$		0			0
$139$	3.02727			0.256769			0.128385	−	0.991724i	$-0.459021\pi$
$139$	3.02727			0.256769			0.128385	+	0.991724i	$0.459021\pi$
$140$	−39.1408	−	10.6517i	−3.30800	−	0.900231i
$141$		0			0
$142$			9.14382i			0.767332i
$143$			5.79440i			0.484552i
$144$		0			0
$145$	1.35420	−	4.97616i	0.112460	−	0.413247i
$146$	−5.10061			−0.422130
$147$		0			0
$148$			5.20864i			0.428147i
$149$	0.862201			0.0706343			0.0353171	−	0.999376i	$-0.488756\pi$
$149$	0.862201			0.0706343			0.0353171	+	0.999376i	$0.488756\pi$
$150$		0			0
$151$	−1.86529			−0.151795			−0.0758976	−	0.997116i	$-0.524182\pi$
$151$	−1.86529			−0.151795			−0.0758976	+	0.997116i	$0.524182\pi$
$152$			49.3384i			4.00187i
$153$		0			0
$154$	−29.8291			−2.40370
$155$	−3.52718	+	12.9610i	−0.283310	+	1.04105i
$156$		0			0
$157$		−	19.7022i		−	1.57241i	−0.617968	−	0.786204i	$-0.712044\pi$
$157$		−	19.7022i		−	1.57241i	0.617968	−	0.786204i	$-0.287956\pi$
$158$		−	4.32008i		−	0.343687i
$159$		0			0
$160$	36.4685	+	9.92445i	2.88309	+	0.784596i
$161$	−4.99003			−0.393269
$162$		0			0
$163$		−	21.8944i		−	1.71490i	−0.514564	−	0.857452i	$-0.672046\pi$
$163$		−	21.8944i		−	1.71490i	0.514564	−	0.857452i	$-0.327954\pi$
$164$	40.7551			3.18244
$165$		0			0
$166$	19.8030			1.53701
$167$		−	17.7381i		−	1.37262i	−0.727311	−	0.686308i	$-0.759230\pi$
$167$		−	17.7381i		−	1.37262i	0.727311	−	0.686308i	$-0.240770\pi$
$168$		0			0
$169$	9.70041			0.746185
$170$	4.45581	−	16.3734i	0.341745	−	1.25578i
$171$		0			0
$172$			60.9238i			4.64539i
$173$			18.1222i			1.37780i	0.724855	+	0.688901i	$0.241907\pi$
$173$			18.1222i			1.37780i	−0.724855	+	0.688901i	$0.758093\pi$
$174$		0			0
$175$	−8.82460	+	15.0127i	−0.667077	+	1.13486i
$176$	40.5522			3.05673
$177$		0			0
$178$			22.7879i			1.70802i
$179$	−18.6485			−1.39385			−0.696926	−	0.717143i	$-0.745449\pi$
$179$	−18.6485			−1.39385			−0.696926	+	0.717143i	$0.745449\pi$
$180$		0			0
$181$	8.72883			0.648809			0.324404	−	0.945919i	$-0.394836\pi$
$181$	8.72883			0.648809			0.324404	+	0.945919i	$0.394836\pi$
$182$		−	16.9860i		−	1.25909i
$183$		0			0
$184$	12.3429			0.909928
$185$	2.15760	+	0.587164i	0.158630	+	0.0431691i
$186$		0			0
$187$		−	9.01611i		−	0.659324i
$188$			12.6473i			0.922399i
$189$		0			0
$190$	33.1768	+	9.02866i	2.40690	+	0.655008i
$191$	24.5046			1.77309			0.886544	−	0.462644i	$-0.153099\pi$
$191$	24.5046			1.77309			0.886544	+	0.462644i	$0.153099\pi$
$192$		0			0
$193$			5.02850i			0.361959i	0.983487	+	0.180980i	$0.0579268\pi$
$193$			5.02850i			0.361959i	−0.983487	+	0.180980i	$0.942073\pi$
$194$	24.1641			1.73488
$195$		0			0
$196$	26.7216			1.90868
$197$		−	5.67179i		−	0.404098i	−0.979375	−	0.202049i	$-0.935240\pi$
$197$		−	5.67179i		−	0.404098i	0.979375	−	0.202049i	$-0.0647600\pi$
$198$		0			0
$199$	9.87685			0.700151			0.350076	−	0.936721i	$-0.386156\pi$
$199$	9.87685			0.700151			0.350076	+	0.936721i	$0.386156\pi$
$200$	21.8277	−	37.1341i	1.54345	−	2.62578i
$201$		0			0
$202$		−	34.7637i		−	2.44597i
$203$			8.03263i			0.563780i
$204$		0			0
$205$	4.59428	−	16.8822i	0.320878	−	1.17910i
$206$	−20.0476			−1.39679
$207$		0			0
$208$			23.0922i			1.60116i
$209$	18.2690			1.26370
$210$		0			0
$211$	9.45435			0.650864			0.325432	−	0.945565i	$-0.394490\pi$
$211$	9.45435			0.650864			0.325432	+	0.945565i	$0.394490\pi$
$212$			48.5743i			3.33610i
$213$		0			0
$214$	−30.1285			−2.05954
$215$	25.2368	+	6.86787i	1.72113	+	0.468385i
$216$		0			0
$217$		−	20.9220i		−	1.42028i
$218$			7.17570i			0.486000i
$219$		0			0
$220$	9.75578	−	35.8487i	0.657735	−	2.41692i
$221$	5.13418			0.345362
$222$		0			0
$223$			12.4583i			0.834270i	0.908844	+	0.417135i	$0.136966\pi$
$223$			12.4583i			0.834270i	−0.908844	+	0.417135i	$0.863034\pi$
$224$	−58.8683			−3.93331
$225$		0			0
$226$	−50.1364			−3.33502
$227$		−	21.2771i		−	1.41221i	−0.708107	−	0.706105i	$-0.750451\pi$
$227$		−	21.2771i		−	1.41221i	0.708107	−	0.706105i	$-0.249549\pi$
$228$		0			0
$229$	15.8819			1.04950			0.524752	−	0.851255i	$-0.324158\pi$
$229$	15.8819			1.04950			0.524752	+	0.851255i	$0.324158\pi$
$230$	2.25868	−	8.29977i	0.148933	−	0.547271i
$231$		0			0
$232$		−	19.8687i		−	1.30445i
$233$		−	15.5581i		−	1.01924i	−0.860399	−	0.509621i	$-0.829786\pi$
$233$		−	15.5581i		−	1.01924i	0.860399	−	0.509621i	$-0.170214\pi$
$234$		0			0
$235$	5.23895	+	1.42572i	0.341752	+	0.0930034i
$236$	−14.9248			−0.971521
$237$		0			0
$238$			26.4303i			1.71322i
$239$	3.01333			0.194916			0.0974581	−	0.995240i	$-0.468929\pi$
$239$	3.01333			0.194916			0.0974581	+	0.995240i	$0.468929\pi$
$240$		0			0
$241$	−12.5699			−0.809698			−0.404849	−	0.914384i	$-0.632676\pi$
$241$	−12.5699			−0.809698			−0.404849	+	0.914384i	$0.632676\pi$
$242$			2.21361i			0.142296i
$243$		0			0
$244$	24.3387			1.55812
$245$	3.01229	−	11.0690i	0.192448	−	0.707173i
$246$		0			0
$247$			10.4032i			0.661940i
$248$			51.7506i			3.28617i
$249$		0			0
$250$	−20.9759	−	21.4730i	−1.32663	−	1.35807i
$251$	−5.84923			−0.369200			−0.184600	−	0.982814i	$-0.559099\pi$
$251$	−5.84923			−0.369200			−0.184600	+	0.982814i	$0.559099\pi$
$252$		0			0
$253$		−	4.57032i		−	0.287334i
$254$	6.50432			0.408117
$255$		0			0
$256$	13.1800			0.823752
$257$		−	11.7124i		−	0.730597i	−0.930891	−	0.365298i	$-0.880967\pi$
$257$		−	11.7124i		−	0.730597i	0.930891	−	0.365298i	$-0.119033\pi$
$258$		0			0
$259$	−3.48285			−0.216414
$260$	20.4139	+	5.55538i	1.26601	+	0.344530i
$261$		0			0
$262$			30.2832i			1.87090i
$263$		−	0.696631i		−	0.0429561i	−0.999769	−	0.0214780i	$-0.993163\pi$
$263$		−	0.696631i		−	0.0429561i	0.999769	−	0.0214780i	$-0.00683720\pi$
$264$		0			0
$265$	20.1212	+	5.47573i	1.23603	+	0.336371i
$266$	−53.5548			−3.28366
$267$		0			0
$268$		−	31.2910i		−	1.91140i
$269$	19.4644			1.18677			0.593383	−	0.804921i	$-0.297792\pi$
$269$	19.4644			1.18677			0.593383	+	0.804921i	$0.297792\pi$
$270$		0			0
$271$	−20.7858			−1.26265			−0.631325	−	0.775518i	$-0.717489\pi$
$271$	−20.7858			−1.26265			−0.631325	+	0.775518i	$0.717489\pi$
$272$		−	35.9316i		−	2.17867i
$273$		0			0
$274$	14.1060			0.852173
$275$	−13.7500	−	8.08237i	−0.829158	−	0.487385i
$276$		0			0
$277$			6.29904i			0.378472i	0.981932	+	0.189236i	$0.0606012\pi$
$277$			6.29904i			0.378472i	−0.981932	+	0.189236i	$0.939399\pi$
$278$		−	8.12788i		−	0.487478i
$279$		0			0
$280$	−17.6174	+	64.7371i	−1.05284	+	3.86878i
$281$	1.46824			0.0875878			0.0437939	−	0.999041i	$-0.486056\pi$
$281$	1.46824			0.0875878			0.0437939	+	0.999041i	$0.486056\pi$
$282$		0			0
$283$			0.325582i			0.0193538i	0.999953	+	0.00967692i	$0.00308031\pi$
$283$			0.325582i			0.0193538i	−0.999953	+	0.00967692i	$0.996920\pi$
$284$	17.7388			1.05261
$285$		0			0
$286$	15.5573			0.919924
$287$			27.2516i			1.60861i
$288$		0			0
$289$	9.01119			0.530070
$290$	−13.3604	−	3.63587i	−0.784552	−	0.213506i
$291$		0			0
$292$			9.89509i			0.579067i
$293$			1.23431i			0.0721090i	0.999350	+	0.0360545i	$0.0114790\pi$
$293$			1.23431i			0.0721090i	−0.999350	+	0.0360545i	$0.988521\pi$
$294$		0			0
$295$	−1.68245	+	6.18237i	−0.0979563	+	0.359951i
$296$	8.61484			0.500728
$297$		0			0
$298$		−	2.31492i		−	0.134100i
$299$	2.60255			0.150509
$300$		0			0
$301$	−40.7378			−2.34809
$302$			5.00810i			0.288184i
$303$		0			0
$304$	72.8070			4.17577
$305$	2.74367	−	10.0819i	0.157102	−	0.577290i
$306$		0			0
$307$			11.0805i			0.632397i	0.948693	+	0.316198i	$0.102406\pi$
$307$			11.0805i			0.632397i	−0.948693	+	0.316198i	$0.897594\pi$
$308$			57.8679i			3.29733i
$309$		0			0
$310$	34.7989	+	9.47009i	1.97644	+	0.537865i
$311$	33.7268			1.91247			0.956236	−	0.292597i	$-0.0945196\pi$
$311$	33.7268			1.91247			0.956236	+	0.292597i	$0.0945196\pi$
$312$		0			0
$313$			31.0364i			1.75428i	0.480235	+	0.877140i	$0.340552\pi$
$313$			31.0364i			1.75428i	−0.480235	+	0.877140i	$0.659448\pi$
$314$	−52.8983			−2.98522
$315$		0			0
$316$	−8.38088			−0.471461
$317$		−	9.28000i		−	0.521217i	−0.965445	−	0.260608i	$-0.916077\pi$
$317$		−	9.28000i		−	0.521217i	0.965445	−	0.260608i	$-0.0839231\pi$
$318$		0			0
$319$	−7.35701			−0.411914
$320$	11.7173	−	43.0564i	0.655015	−	2.40693i
$321$		0			0
$322$			13.3977i			0.746624i
$323$		−	16.1874i		−	0.900694i
$324$		0			0
$325$	4.60246	−	7.82988i	0.255299	−	0.434324i
$326$	−58.7842			−3.25575
$327$		0			0
$328$		−	67.4070i		−	3.72193i
$329$	−8.45684			−0.466241
$330$		0			0
$331$	−10.7993			−0.593584			−0.296792	−	0.954942i	$-0.595917\pi$
$331$	−10.7993			−0.593584			−0.296792	+	0.954942i	$0.595917\pi$
$332$		−	38.4174i		−	2.10843i
$333$		0			0
$334$	−47.6249			−2.60592
$335$	−12.9618	−	3.52740i	−0.708180	−	0.192722i
$336$		0			0
$337$			3.06665i			0.167051i	0.996506	+	0.0835256i	$0.0266180\pi$
$337$			3.06665i			0.167051i	−0.996506	+	0.0835256i	$0.973382\pi$
$338$		−	26.0445i		−	1.41664i
$339$		0			0
$340$	−31.7641	−	8.64419i	−1.72265	−	0.468797i
$341$	19.1622			1.03769
$342$		0			0
$343$		−	6.51209i		−	0.351620i
$344$	100.765			5.43289
$345$		0			0
$346$	48.6560			2.61576
$347$			26.0726i			1.39965i	0.714315	+	0.699825i	$0.246739\pi$
$347$			26.0726i			1.39965i	−0.714315	+	0.699825i	$0.753261\pi$
$348$		0			0
$349$	−12.2055			−0.653346			−0.326673	−	0.945137i	$-0.605928\pi$
$349$	−12.2055			−0.653346			−0.326673	+	0.945137i	$0.605928\pi$
$350$	40.3076	+	23.6931i	2.15453	+	1.26645i
$351$		0			0
$352$		−	53.9170i		−	2.87378i
$353$			11.8648i			0.631498i	0.948843	+	0.315749i	$0.102256\pi$
$353$			11.8648i			0.631498i	−0.948843	+	0.315749i	$0.897744\pi$
$354$		0			0
$355$	1.99968	−	7.34805i	0.106132	−	0.389994i
$356$	44.2081			2.34302
$357$		0			0
$358$			50.0691i			2.64623i
$359$	7.36628			0.388777			0.194389	−	0.980925i	$-0.437728\pi$
$359$	7.36628			0.388777			0.194389	+	0.980925i	$0.437728\pi$
$360$		0			0
$361$	13.8001			0.726320
$362$		−	23.4359i		−	1.23177i
$363$		0			0
$364$	−32.9525			−1.72718
$365$	4.09889	+	1.11546i	0.214546	+	0.0583860i
$366$		0			0
$367$			20.4826i			1.06918i	0.845111	+	0.534590i	$0.179534\pi$
$367$			20.4826i			1.06918i	−0.845111	+	0.534590i	$0.820466\pi$
$368$		−	18.2139i		−	0.949467i
$369$		0			0
$370$	1.57647	−	5.79292i	0.0819568	−	0.301160i
$371$	−32.4801			−1.68628
$372$		0			0
$373$		−	16.5915i		−	0.859075i	−0.903049	−	0.429538i	$-0.858677\pi$
$373$		−	16.5915i		−	0.859075i	0.903049	−	0.429538i	$-0.141323\pi$
$374$	−24.2073			−1.25173
$375$		0			0
$376$	20.9180			1.07877
$377$		−	4.18941i		−	0.215766i
$378$		0			0
$379$	15.9199			0.817752			0.408876	−	0.912590i	$-0.365921\pi$
$379$	15.9199			0.817752			0.408876	+	0.912590i	$0.365921\pi$
$380$	17.5154	−	64.3625i	0.898523	−	3.30172i
$381$		0			0
$382$		−	65.7921i		−	3.36622i
$383$			30.4997i			1.55846i	0.626738	+	0.779230i	$0.284390\pi$
$383$			30.4997i			1.55846i	−0.626738	+	0.779230i	$0.715610\pi$
$384$		0			0
$385$	23.9709	+	6.52338i	1.22167	+	0.332462i
$386$	13.5010			0.687181
$387$		0			0
$388$		−	46.8779i		−	2.37986i
$389$	−29.8769			−1.51482			−0.757409	−	0.652941i	$-0.773535\pi$
$389$	−29.8769			−1.51482			−0.757409	+	0.652941i	$0.773535\pi$
$390$		0			0
$391$	−4.04957			−0.204796
$392$		−	44.1962i		−	2.23225i
$393$		0			0
$394$	−15.2281			−0.767182
$395$	−0.944767	+	3.47165i	−0.0475364	+	0.174678i
$396$		0			0
$397$			0.946163i			0.0474866i	0.999718	+	0.0237433i	$0.00755843\pi$
$397$			0.946163i			0.0474866i	−0.999718	+	0.0237433i	$0.992442\pi$
$398$		−	26.5183i		−	1.32924i
$399$		0			0
$400$	−54.7975	−	32.2104i	−2.73988	−	1.61052i
$401$	−37.3648			−1.86591			−0.932955	−	0.359994i	$-0.882779\pi$
$401$	−37.3648			−1.86591			−0.932955	+	0.359994i	$0.882779\pi$
$402$		0			0
$403$			10.9118i			0.543557i
$404$	−67.4409			−3.35531
$405$		0			0
$406$	21.5667			1.07034
$407$		−	3.18991i		−	0.158118i
$408$		0			0
$409$	−22.9171			−1.13318			−0.566589	−	0.824000i	$-0.691737\pi$
$409$	−22.9171			−1.13318			−0.566589	+	0.824000i	$0.691737\pi$
$410$	−45.3268	−	12.3351i	−2.23853	−	0.609189i
$411$		0			0
$412$			38.8920i			1.91607i
$413$		−	9.97973i		−	0.491070i
$414$		0			0
$415$	−15.9138	−	4.33075i	−0.781179	−	0.212588i
$416$	30.7027			1.50533
$417$		0			0
$418$		−	49.0504i		−	2.39913i
$419$	18.8458			0.920678			0.460339	−	0.887743i	$-0.347728\pi$
$419$	18.8458			0.920678			0.460339	+	0.887743i	$0.347728\pi$
$420$		0			0
$421$	14.7293			0.717861			0.358931	−	0.933364i	$-0.383141\pi$
$421$	14.7293			0.717861			0.358931	+	0.933364i	$0.383141\pi$
$422$		−	25.3839i		−	1.23567i
$423$		0			0
$424$	80.3397			3.90164
$425$	−7.16145	+	12.1833i	−0.347382	+	0.590979i
$426$		0			0
$427$			16.2745i			0.787578i
$428$			58.4487i			2.82523i
$429$		0			0
$430$	18.4395	−	67.7579i	0.889230	−	3.26758i
$431$	24.7947			1.19432			0.597159	−	0.802123i	$-0.296296\pi$
$431$	24.7947			1.19432			0.597159	+	0.802123i	$0.296296\pi$
$432$		0			0
$433$			26.6307i			1.27979i	0.768463	+	0.639894i	$0.221022\pi$
$433$			26.6307i			1.27979i	−0.768463	+	0.639894i	$0.778978\pi$
$434$	−56.1732			−2.69640
$435$		0			0
$436$	13.9207			0.666682
$437$		−	8.20552i		−	0.392523i
$438$		0			0
$439$	−2.93896			−0.140269			−0.0701344	−	0.997538i	$-0.522343\pi$
$439$	−2.93896			−0.140269			−0.0701344	+	0.997538i	$0.522343\pi$
$440$	−59.2921	−	16.1356i	−2.82664	−	0.769235i
$441$		0			0
$442$		−	13.7847i		−	0.655672i
$443$			12.1586i			0.577671i	0.957379	+	0.288836i	$0.0932681\pi$
$443$			12.1586i			0.577671i	−0.957379	+	0.288836i	$0.906732\pi$
$444$		0			0
$445$	4.98353	−	18.3125i	0.236242	−	0.868098i
$446$	33.4492			1.58387
$447$		0			0
$448$			69.5027i			3.28369i
$449$	−12.0740			−0.569809			−0.284904	−	0.958556i	$-0.591962\pi$
$449$	−12.0740			−0.569809			−0.284904	+	0.958556i	$0.591962\pi$
$450$		0			0
$451$	−24.9595			−1.17530
$452$			97.2637i			4.57490i
$453$		0			0
$454$	−57.1266			−2.68109
$455$	−3.71470	+	13.6501i	−0.174148	+	0.639926i
$456$		0			0
$457$			14.3829i			0.672803i	0.941719	+	0.336401i	$0.109210\pi$
$457$			14.3829i			0.672803i	−0.941719	+	0.336401i	$0.890790\pi$
$458$		−	42.6411i		−	1.99249i
$459$		0			0
$460$	−16.1014	−	4.38179i	−0.750732	−	0.204302i
$461$	16.2105			0.754997			0.377498	−	0.926010i	$-0.376784\pi$
$461$	16.2105			0.754997			0.377498	+	0.926010i	$0.376784\pi$
$462$		0			0
$463$			26.8128i			1.24609i	0.782184	+	0.623047i	$0.214106\pi$
$463$			26.8128i			1.24609i	−0.782184	+	0.623047i	$0.785894\pi$
$464$	−29.3196			−1.36113
$465$		0			0
$466$	−41.7717			−1.93504
$467$		−	8.58230i		−	0.397141i	−0.980087	−	0.198571i	$-0.936370\pi$
$467$		−	8.58230i		−	0.397141i	0.980087	−	0.198571i	$-0.0636299\pi$
$468$		0			0
$469$	20.9233			0.966148
$470$	3.82789	−	14.0660i	0.176567	−	0.648817i
$471$		0			0
$472$			24.6849i			1.13621i
$473$		−	37.3114i		−	1.71558i
$474$		0			0
$475$	−24.6867	−	14.5110i	−1.13270	−	0.665811i
$476$	51.2743			2.35015
$477$		0			0
$478$		−	8.09047i		−	0.370049i
$479$	2.01066			0.0918693			0.0459346	−	0.998944i	$-0.485373\pi$
$479$	2.01066			0.0918693			0.0459346	+	0.998944i	$0.485373\pi$
$480$		0			0
$481$	1.81648			0.0828242
$482$			33.7488i			1.53722i
$483$		0			0
$484$	4.29437			0.195199
$485$	−19.4185	−	5.28449i	−0.881747	−	0.239956i
$486$		0			0
$487$		−	38.1485i		−	1.72867i	−0.502915	−	0.864336i	$-0.667739\pi$
$487$		−	38.1485i		−	1.72867i	0.502915	−	0.864336i	$-0.332261\pi$
$488$		−	40.2550i		−	1.82226i
$489$		0			0
$490$	−29.7191	−	8.08767i	−1.34257	−	0.365364i
$491$	−21.6136			−0.975409			−0.487705	−	0.873009i	$-0.662166\pi$
$491$	−21.6136			−0.975409			−0.487705	+	0.873009i	$0.662166\pi$
$492$		0			0
$493$			6.51874i			0.293589i
$494$	27.9315			1.25670
$495$		0			0
$496$	76.3666			3.42896
$497$			11.8614i			0.532056i
$498$		0			0
$499$	−37.8811			−1.69579			−0.847896	−	0.530162i	$-0.822131\pi$
$499$	−37.8811			−1.69579			−0.847896	+	0.530162i	$0.822131\pi$
$500$	−41.6573	+	40.6929i	−1.86297	+	1.81984i
$501$		0			0
$502$			15.7045i			0.700928i
$503$		−	0.494731i		−	0.0220590i	−0.999939	−	0.0110295i	$-0.996489\pi$
$503$		−	0.494731i		−	0.0220590i	0.999939	−	0.0110295i	$-0.00351087\pi$
$504$		0			0
$505$	−7.60254	+	27.9364i	−0.338309	+	1.24315i
$506$	−12.2708			−0.545504
$507$		0			0
$508$		−	12.6183i		−	0.559845i
$509$	−2.62220			−0.116227			−0.0581136	−	0.998310i	$-0.518509\pi$
$509$	−2.62220			−0.116227			−0.0581136	+	0.998310i	$0.518509\pi$
$510$		0			0
$511$	−6.61653			−0.292698
$512$			4.16132i			0.183906i
$513$		0			0
$514$	−31.4464			−1.38704
$515$	16.1104	+	4.38426i	0.709911	+	0.193193i
$516$		0			0
$517$		−	7.74555i		−	0.340649i
$518$			9.35107i			0.410862i
$519$		0			0
$520$	9.18833	−	33.7636i	0.402935	−	1.48063i
$521$	−5.05777			−0.221585			−0.110792	−	0.993844i	$-0.535339\pi$
$521$	−5.05777			−0.221585			−0.110792	+	0.993844i	$0.535339\pi$
$522$		0			0
$523$		−	18.1730i		−	0.794648i	−0.917678	−	0.397324i	$-0.869939\pi$
$523$		−	18.1730i		−	0.794648i	0.917678	−	0.397324i	$-0.130061\pi$
$524$	58.7489			2.56646
$525$		0			0
$526$	−1.87038			−0.0815523
$527$		−	16.9789i		−	0.739611i
$528$		0			0
$529$	20.9472			0.910750
$530$	14.7017	−	54.0232i	0.638603	−	2.34662i
$531$		0			0
$532$			103.895i			4.50444i
$533$		−	14.2131i		−	0.615636i
$534$		0			0
$535$	24.2115	+	6.58886i	1.04675	+	0.284861i
$536$	−51.7538			−2.23543
$537$		0			0
$538$		−	52.2598i		−	2.25308i
$539$	−16.3650			−0.704891
$540$		0			0
$541$	6.96392			0.299402			0.149701	−	0.988731i	$-0.452169\pi$
$541$	6.96392			0.299402			0.149701	+	0.988731i	$0.452169\pi$
$542$			55.8077i			2.39715i
$543$		0			0
$544$	−47.7736			−2.04828
$545$	1.56927	−	5.76646i	0.0672201	−	0.247008i
$546$		0			0
$547$		−	28.2295i		−	1.20701i	−0.797360	−	0.603504i	$-0.793771\pi$
$547$		−	28.2295i		−	1.20701i	0.797360	−	0.603504i	$-0.206229\pi$
$548$		−	27.3653i		−	1.16899i
$549$		0			0
$550$	−21.7003	+	36.9173i	−0.925303	+	1.57416i
$551$	−13.2087			−0.562710
$552$		0			0
$553$		−	5.60402i		−	0.238307i
$554$	16.9122			0.718531
$555$		0			0
$556$	−15.7679			−0.668710
$557$			20.4748i			0.867545i	0.901022	+	0.433773i	$0.142818\pi$
$557$			20.4748i			0.867545i	−0.901022	+	0.433773i	$0.857182\pi$
$558$		0			0
$559$	21.2467			0.898642
$560$	95.5303	+	25.9974i	4.03689	+	1.09859i
$561$		0			0
$562$		−	3.94206i		−	0.166286i
$563$		−	4.03262i		−	0.169955i	−0.996383	−	0.0849774i	$-0.972918\pi$
$563$		−	4.03262i		−	0.169955i	0.996383	−	0.0849774i	$-0.0270818\pi$
$564$		0			0
$565$	40.2900	+	10.9644i	1.69501	+	0.461277i
$566$	0.874152			0.0367433
$567$		0			0
$568$		−	29.3392i		−	1.23105i
$569$	24.6352			1.03276			0.516381	−	0.856359i	$-0.327279\pi$
$569$	24.6352			1.03276			0.516381	+	0.856359i	$0.327279\pi$
$570$		0			0
$571$	31.7960			1.33062			0.665311	−	0.746566i	$-0.268299\pi$
$571$	31.7960			1.33062			0.665311	+	0.746566i	$0.268299\pi$
$572$		−	30.1809i		−	1.26193i
$573$		0			0
$574$	73.1676			3.05396
$575$	−3.63018	+	6.17581i	−0.151389	+	0.257549i
$576$		0			0
$577$			39.0173i			1.62431i	0.583442	+	0.812155i	$0.301706\pi$
$577$			39.0173i			1.62431i	−0.583442	+	0.812155i	$0.698294\pi$
$578$		−	24.1941i		−	1.00634i
$579$		0			0
$580$	−7.05353	+	25.9190i	−0.292882	+	1.07623i
$581$	25.6885			1.06574
$582$		0			0
$583$		−	29.7482i		−	1.23205i
$584$	16.3660			0.677231
$585$		0			0
$586$	3.31398			0.136899
$587$		−	28.0766i		−	1.15884i	−0.815028	−	0.579422i	$-0.803278\pi$
$587$		−	28.0766i		−	1.15884i	0.815028	−	0.579422i	$-0.196722\pi$
$588$		0			0
$589$	34.4037			1.41758
$590$	16.5990	+	4.51721i	0.683369	+	0.185970i
$591$		0			0
$592$		−	12.7126i		−	0.522486i
$593$			21.1330i			0.867829i	0.900954	+	0.433915i	$0.142868\pi$
$593$			21.1330i			0.867829i	−0.900954	+	0.433915i	$0.857132\pi$
$594$		0			0
$595$	5.78009	−	21.2396i	0.236961	−	0.870739i
$596$	−4.49090			−0.183954
$597$		0			0
$598$		−	6.98755i		−	0.285742i
$599$	14.1739			0.579129			0.289564	−	0.957159i	$-0.406490\pi$
$599$	14.1739			0.579129			0.289564	+	0.957159i	$0.406490\pi$
$600$		0			0
$601$	48.8255			1.99164			0.995818	−	0.0913627i	$-0.0291223\pi$
$601$	48.8255			1.99164			0.995818	+	0.0913627i	$0.0291223\pi$
$602$			109.376i			4.45785i
$603$		0			0
$604$	9.71563			0.395323
$605$	0.484099	−	1.77888i	0.0196814	−	0.0723216i
$606$		0			0
$607$			8.91773i			0.361959i	0.983487	+	0.180980i	$0.0579268\pi$
$607$			8.91773i			0.361959i	−0.983487	+	0.180980i	$0.942073\pi$
$608$		−	96.8020i		−	3.92584i
$609$		0			0
$610$	−27.0689	−	7.36646i	−1.09599	−	0.298259i
$611$	4.41066			0.178436
$612$		0			0
$613$			43.5970i			1.76087i	0.474171	+	0.880433i	$0.342748\pi$
$613$			43.5970i			1.76087i	−0.474171	+	0.880433i	$0.657252\pi$
$614$	29.7499			1.20061
$615$		0			0
$616$	95.7107			3.85629
$617$			25.4049i			1.02276i	0.859353	+	0.511382i	$0.170866\pi$
$617$			25.4049i			1.02276i	−0.859353	+	0.511382i	$0.829134\pi$
$618$		0			0
$619$	4.97246			0.199860			0.0999299	−	0.994994i	$-0.468138\pi$
$619$	4.97246			0.199860			0.0999299	+	0.994994i	$0.468138\pi$
$620$	18.3718	−	67.5092i	0.737829	−	2.71124i
$621$		0			0
$622$		−	90.5528i		−	3.63084i
$623$			29.5605i			1.18432i
$624$		0			0
$625$	12.1604	+	21.8432i	0.486417	+	0.873727i
$626$	83.3293			3.33051
$627$		0			0
$628$			102.622i			4.09505i
$629$	−2.82645			−0.112698
$630$		0			0
$631$	−0.771437			−0.0307104			−0.0153552	−	0.999882i	$-0.504888\pi$
$631$	−0.771437			−0.0307104			−0.0153552	+	0.999882i	$0.504888\pi$
$632$			13.8616i			0.551384i
$633$		0			0
$634$	−24.9158			−0.989532
$635$	−5.22693	−	1.42244i	−0.207424	−	0.0564479i
$636$		0			0
$637$		−	9.31897i		−	0.369231i
$638$			19.7528i			0.782020i
$639$		0			0
$640$	−42.6647	−	11.6107i	−1.68647	−	0.458952i
$641$	−41.6238			−1.64404			−0.822020	−	0.569459i	$-0.807153\pi$
$641$	−41.6238			−1.64404			−0.822020	+	0.569459i	$0.807153\pi$
$642$		0			0
$643$			7.31649i			0.288534i	0.989539	+	0.144267i	$0.0460825\pi$
$643$			7.31649i			0.288534i	−0.989539	+	0.144267i	$0.953918\pi$
$644$	25.9913			1.02420
$645$		0			0
$646$	−43.4615			−1.70997
$647$			43.4618i			1.70866i	0.519733	+	0.854329i	$0.326032\pi$
$647$			43.4618i			1.70866i	−0.519733	+	0.854329i	$0.673968\pi$
$648$		0			0
$649$	9.14034			0.358790
$650$	−21.0224	−	12.3571i	−0.824566	−	0.484686i
$651$		0			0
$652$			114.040i			4.46616i
$653$			22.9698i			0.898878i	0.893311	+	0.449439i	$0.148376\pi$
$653$			22.9698i			0.898878i	−0.893311	+	0.449439i	$0.851624\pi$
$654$		0			0
$655$	6.62270	−	24.3359i	0.258770	−	0.950881i
$656$	−99.4703			−3.88366
$657$		0			0
$658$			22.7057i			0.885160i
$659$	35.7491			1.39259			0.696294	−	0.717757i	$-0.254831\pi$
$659$	35.7491			1.39259			0.696294	+	0.717757i	$0.254831\pi$
$660$		0			0
$661$	27.3305			1.06303			0.531516	−	0.847048i	$-0.321622\pi$
$661$	27.3305			1.06303			0.531516	+	0.847048i	$0.321622\pi$
$662$			28.9950i			1.12692i
$663$		0			0
$664$	−63.5406			−2.46585
$665$	43.0371	+	11.7120i	1.66891	+	0.454172i
$666$		0			0
$667$			3.30439i			0.127947i
$668$			92.3913i			3.57473i
$669$		0			0
$670$	−9.47068	+	34.8011i	−0.365884	+	1.34448i
$671$	−14.9057			−0.575427
$672$		0			0
$673$		−	19.6281i		−	0.756609i	−0.925681	−	0.378305i	$-0.876507\pi$
$673$		−	19.6281i		−	0.756609i	0.925681	−	0.378305i	$-0.123493\pi$
$674$	8.23363			0.317147
$675$		0			0
$676$	−50.5259			−1.94330
$677$		−	3.03052i		−	0.116472i	−0.998303	−	0.0582362i	$-0.981452\pi$
$677$		−	3.03052i		−	0.116472i	0.998303	−	0.0582362i	$-0.0185477\pi$
$678$		0			0
$679$	31.3457			1.20294
$680$	−14.2971	+	52.5363i	−0.548268	+	2.01467i
$681$		0			0
$682$		−	51.4485i		−	1.97007i
$683$			44.7410i			1.71197i	0.517004	+	0.855983i	$0.327047\pi$
$683$			44.7410i			1.71197i	−0.517004	+	0.855983i	$0.672953\pi$
$684$		0			0
$685$	−11.3357	−	3.08486i	−0.433114	−	0.117866i
$686$	−17.4843			−0.667552
$687$		0			0
$688$		−	148.696i		−	5.66897i
$689$	16.9400			0.645361
$690$		0			0
$691$	−13.7681			−0.523764			−0.261882	−	0.965100i	$-0.584343\pi$
$691$	−13.7681			−0.523764			−0.261882	+	0.965100i	$0.584343\pi$
$692$		−	94.3917i		−	3.58824i
$693$		0			0
$694$	70.0020			2.65724
$695$	−1.77750	+	6.53163i	−0.0674245	+	0.247759i
$696$		0			0
$697$			22.1156i			0.837688i
$698$			32.7705i			1.24038i
$699$		0			0
$700$	45.9641	−	78.1959i	1.73728	−	2.95553i
$701$	12.2193			0.461517			0.230758	−	0.973011i	$-0.425879\pi$
$701$	12.2193			0.461517			0.230758	+	0.973011i	$0.425879\pi$
$702$		0			0
$703$		−	5.72714i		−	0.216003i
$704$	−63.6569			−2.39916
$705$		0			0
$706$	31.8556			1.19890
$707$		−	45.0956i		−	1.69599i
$708$		0			0
$709$	4.22619			0.158718			0.0793589	−	0.996846i	$-0.474713\pi$
$709$	4.22619			0.158718			0.0793589	+	0.996846i	$0.474713\pi$
$710$	−19.7287	−	5.36892i	−0.740405	−	0.201492i
$711$		0			0
$712$		−	73.1181i		−	2.74022i
$713$		−	8.60669i		−	0.322323i
$714$		0			0
$715$	−12.5020	−	3.40226i	−0.467548	−	0.127237i
$716$	97.1331			3.63003
$717$		0			0
$718$		−	19.7777i		−	0.738095i
$719$	19.2764			0.718888			0.359444	−	0.933167i	$-0.382966\pi$
$719$	19.2764			0.718888			0.359444	+	0.933167i	$0.382966\pi$
$720$		0			0
$721$	−26.0059			−0.968509
$722$		−	37.0517i		−	1.37892i
$723$		0			0
$724$	−45.4653			−1.68970
$725$	9.94142	+	5.84364i	0.369215	+	0.217027i
$726$		0			0
$727$			16.6423i			0.617227i	0.951187	+	0.308614i	$0.0998650\pi$
$727$			16.6423i			0.617227i	−0.951187	+	0.308614i	$0.900135\pi$
$728$			54.5019i			2.01998i
$729$		0			0
$730$	2.99490	−	11.0051i	0.110846	−	0.407316i
$731$	−33.0600			−1.22277
$732$		0			0
$733$		−	1.77985i		−	0.0657404i	−0.999460	−	0.0328702i	$-0.989535\pi$
$733$		−	1.77985i		−	0.0657404i	0.999460	−	0.0328702i	$-0.0104648\pi$
$734$	54.9934			2.02984
$735$		0			0
$736$	−24.2167			−0.892640
$737$			19.1635i			0.705895i
$738$		0			0
$739$	−32.6285			−1.20026			−0.600130	−	0.799903i	$-0.704884\pi$
$739$	−32.6285			−1.20026			−0.600130	+	0.799903i	$0.704884\pi$
$740$	−11.2382	−	3.05832i	−0.413123	−	0.112426i
$741$		0			0
$742$			87.2055i			3.20142i
$743$		−	21.1995i		−	0.777734i	−0.921294	−	0.388867i	$-0.872866\pi$
$743$		−	21.1995i		−	0.777734i	0.921294	−	0.388867i	$-0.127134\pi$
$744$		0			0
$745$	−0.506254	+	1.86029i	−0.0185477	+	0.0681556i
$746$	−44.5464			−1.63096
$747$		0			0
$748$			46.9617i			1.71709i
$749$	−39.0828			−1.42805
$750$		0			0
$751$	−53.3277			−1.94595			−0.972977	−	0.230901i	$-0.925833\pi$
$751$	−53.3277			−1.94595			−0.972977	+	0.230901i	$0.925833\pi$
$752$		−	30.8680i		−	1.12564i
$753$		0			0
$754$	−11.2481			−0.409632
$755$	1.09523	−	4.02455i	0.0398596	−	0.146469i
$756$		0			0
$757$		−	26.9137i		−	0.978197i	−0.872229	−	0.489098i	$-0.837326\pi$
$757$		−	26.9137i		−	0.978197i	0.872229	−	0.489098i	$-0.162674\pi$
$758$		−	42.7433i		−	1.55251i
$759$		0			0
$760$	−106.452	−	28.9697i	−3.86144	−	1.05084i
$761$	19.7208			0.714879			0.357439	−	0.933936i	$-0.383650\pi$
$761$	19.7208			0.714879			0.357439	+	0.933936i	$0.383650\pi$
$762$		0			0
$763$			9.30835i			0.336985i
$764$	−127.635			−4.61769
$765$		0			0
$766$	81.8883			2.95874
$767$			5.20492i			0.187939i
$768$		0			0
$769$	40.4230			1.45769			0.728846	−	0.684678i	$-0.240057\pi$
$769$	40.4230			1.45769			0.728846	+	0.684678i	$0.240057\pi$
$770$	17.5146	−	64.3592i	0.631181	−	2.31935i
$771$		0			0
$772$		−	26.1916i		−	0.942657i
$773$		−	14.1890i		−	0.510342i	−0.966896	−	0.255171i	$-0.917868\pi$
$773$		−	14.1890i		−	0.510342i	0.966896	−	0.255171i	$-0.0821317\pi$
$774$		0			0
$775$	−25.8937	−	15.2205i	−0.930127	−	0.546736i
$776$	−77.5338			−2.78330
$777$		0			0
$778$			80.2161i			2.87589i
$779$	−44.8121			−1.60556
$780$		0			0
$781$	−10.8637			−0.388735
$782$			10.8727i			0.388806i
$783$		0			0
$784$	−65.2189			−2.32925
$785$	42.5095	+	11.5684i	1.51723	+	0.412895i
$786$		0			0
$787$			48.0720i			1.71358i	0.515665	+	0.856790i	$0.327545\pi$
$787$			48.0720i			1.71358i	−0.515665	+	0.856790i	$0.672455\pi$
$788$			29.5423i			1.05240i
$789$		0			0
$790$	9.32101	+	2.53660i	0.331627	+	0.0902480i
$791$	−65.0371			−2.31245
$792$		0			0
$793$		−	8.48795i		−	0.301416i
$794$	2.54034			0.0901535
$795$		0			0
$796$	−51.4449			−1.82342
$797$		−	35.1334i		−	1.24449i	−0.782822	−	0.622245i	$-0.786221\pi$
$797$		−	35.1334i		−	1.24449i	0.782822	−	0.622245i	$-0.213779\pi$
$798$		0			0
$799$	−6.86301			−0.242796
$800$	−42.8260	+	72.8572i	−1.51413	+	2.57589i
$801$		0			0
$802$			100.320i			3.54244i
$803$		−	6.06002i		−	0.213854i
$804$		0			0
$805$	2.92997	−	10.7665i	0.103268	−	0.379469i
$806$	29.2971			1.03195
$807$		0			0
$808$			111.544i			3.92411i
$809$	−18.5994			−0.653922			−0.326961	−	0.945038i	$-0.606025\pi$
$809$	−18.5994			−0.653922			−0.326961	+	0.945038i	$0.606025\pi$
$810$		0			0
$811$	−41.2856			−1.44973			−0.724867	−	0.688889i	$-0.758099\pi$
$811$	−41.2856			−1.44973			−0.724867	+	0.688889i	$0.758099\pi$
$812$		−	41.8391i		−	1.46826i
$813$		0			0
$814$	−8.56456			−0.300188
$815$	47.2394	+	12.8556i	1.65473	+	0.450313i
$816$		0			0
$817$		−	66.9884i		−	2.34363i
$818$			61.5300i			2.15134i
$819$		0			0
$820$	−23.9299	+	87.9332i	−0.835669	+	3.07076i
$821$	−5.64400			−0.196977			−0.0984885	−	0.995138i	$-0.531401\pi$
$821$	−5.64400			−0.196977			−0.0984885	+	0.995138i	$0.531401\pi$
$822$		0			0
$823$			52.1526i			1.81792i	0.416879	+	0.908962i	$0.363124\pi$
$823$			52.1526i			1.81792i	−0.416879	+	0.908962i	$0.636876\pi$
$824$	64.3256			2.24089
$825$		0			0
$826$	−26.7945			−0.932299
$827$			10.2565i			0.356654i	0.983971	+	0.178327i	$0.0570686\pi$
$827$			10.2565i			0.356654i	−0.983971	+	0.178327i	$0.942931\pi$
$828$		0			0
$829$	10.0803			0.350105			0.175052	−	0.984559i	$-0.443990\pi$
$829$	10.0803			0.350105			0.175052	+	0.984559i	$0.443990\pi$
$830$	−11.6276	+	42.7269i	−0.403599	+	1.48307i
$831$		0			0
$832$		−	36.2491i		−	1.25671i
$833$			14.5004i			0.502408i
$834$		0			0
$835$	38.2717	+	10.4152i	1.32445	+	0.360432i
$836$	−95.1569			−3.29107
$837$		0			0
$838$		−	50.5990i		−	1.74791i
$839$	42.0725			1.45250			0.726252	−	0.687428i	$-0.241260\pi$
$839$	42.0725			1.45250			0.726252	+	0.687428i	$0.241260\pi$
$840$		0			0
$841$	−23.6808			−0.816579
$842$		−	39.5465i		−	1.36286i
$843$		0			0
$844$	−49.2443			−1.69506
$845$	−5.69573	+	20.9296i	−0.195939	+	0.720000i
$846$		0			0
$847$			2.87151i			0.0986661i
$848$		−	118.555i		−	4.07118i
$849$		0			0
$850$	32.7109	+	19.2277i	1.12198	+	0.659505i
$851$	−1.43274			−0.0491138
$852$		0			0
$853$			13.3261i			0.456277i	0.973629	+	0.228138i	$0.0732638\pi$
$853$			13.3261i			0.456277i	−0.973629	+	0.228138i	$0.926736\pi$
$854$	43.6952			1.49522
$855$		0			0
$856$	96.6714			3.30416
$857$			32.2245i			1.10077i	0.834912	+	0.550383i	$0.185518\pi$
$857$			32.2245i			1.10077i	−0.834912	+	0.550383i	$0.814482\pi$
$858$		0			0
$859$	28.0054			0.955530			0.477765	−	0.878488i	$-0.341447\pi$
$859$	28.0054			0.955530			0.477765	+	0.878488i	$0.341447\pi$
$860$	−131.449	−	35.7722i	−4.48238	−	1.21982i
$861$		0			0
$862$		−	66.5711i		−	2.26742i
$863$		−	47.0680i		−	1.60221i	−0.598521	−	0.801107i	$-0.704245\pi$
$863$		−	47.0680i		−	1.60221i	0.598521	−	0.801107i	$-0.295755\pi$
$864$		0			0
$865$	−39.1004	−	10.6407i	−1.32945	−	0.361794i
$866$	71.5005			2.42968
$867$		0			0
$868$			108.975i			3.69885i
$869$	5.13268			0.174114
$870$		0			0
$871$	−10.9125			−0.369757
$872$		−	23.0242i		−	0.779699i
$873$		0			0
$874$	−22.0309			−0.745207
$875$	−27.2100	−	27.8549i	−0.919866	−	0.941667i
$876$		0			0
$877$			16.9389i			0.571986i	0.958232	+	0.285993i	$0.0923235\pi$
$877$			16.9389i			0.571986i	−0.958232	+	0.285993i	$0.907677\pi$
$878$			7.89078i			0.266301i
$879$		0			0
$880$	−23.8108	+	87.4954i	−0.802661	+	2.94947i
$881$	−34.0552			−1.14735			−0.573674	−	0.819084i	$-0.694482\pi$
$881$	−34.0552			−1.14735			−0.573674	+	0.819084i	$0.694482\pi$
$882$		0			0
$883$			7.85431i			0.264319i	0.991228	+	0.132159i	$0.0421910\pi$
$883$			7.85431i			0.264319i	−0.991228	+	0.132159i	$0.957809\pi$
$884$	−26.7421			−0.899433
$885$		0			0
$886$	32.6444			1.09671
$887$		−	50.8348i		−	1.70687i	−0.521203	−	0.853433i	$-0.674517\pi$
$887$		−	50.8348i		−	1.70687i	0.521203	−	0.853433i	$-0.325483\pi$
$888$		0			0
$889$	8.43743			0.282982
$890$	−49.1672	−	13.3802i	−1.64809	−	0.448506i
$891$		0			0
$892$		−	64.8908i		−	2.17271i
$893$		−	13.9063i		−	0.465356i
$894$		0			0
$895$	10.9497	−	40.2359i	0.366008	−	1.34494i
$896$	68.8704			2.30080
$897$		0			0
$898$			32.4174i			1.08178i
$899$	−13.8545			−0.462074
$900$		0			0
$901$	−26.3587			−0.878135
$902$			67.0136i			2.23131i
$903$		0			0
$904$	160.870			5.35044
$905$	−5.12525	+	18.8333i	−0.170369	+	0.626041i
$906$		0			0
$907$		−	55.4966i		−	1.84273i	−0.388695	−	0.921366i	$-0.627074\pi$
$907$		−	55.4966i		−	1.84273i	0.388695	−	0.921366i	$-0.372926\pi$
$908$			110.825i			3.67784i
$909$		0			0
$910$	36.6490	+	9.97357i	1.21490	+	0.330621i
$911$	−35.8745			−1.18858			−0.594288	−	0.804252i	$-0.702566\pi$
$911$	−35.8745			−1.18858			−0.594288	+	0.804252i	$0.702566\pi$
$912$		0			0
$913$			23.5278i			0.778658i
$914$	38.6165			1.27732
$915$		0			0
$916$	−82.7230			−2.73324
$917$			39.2835i			1.29726i
$918$		0			0
$919$	43.0966			1.42162			0.710812	−	0.703382i	$-0.248328\pi$
$919$	43.0966			1.42162			0.710812	+	0.703382i	$0.248328\pi$
$920$	−7.24728	+	26.6310i	−0.238936	+	0.877997i
$921$		0			0
$922$		−	43.5233i		−	1.43336i
$923$		−	6.18630i		−	0.203625i
$924$		0			0
$925$	−2.53373	+	4.31048i	−0.0833085	+	0.141728i
$926$	71.9893			2.36572
$927$		0			0
$928$			38.9825i			1.27966i
$929$	41.5247			1.36238			0.681190	−	0.732107i	$-0.261463\pi$
$929$	41.5247			1.36238			0.681190	+	0.732107i	$0.261463\pi$
$930$		0			0
$931$	−29.3816			−0.962942
$932$			81.0363i			2.65443i
$933$		0			0
$934$	−23.0425			−0.753975
$935$	19.4532	+	5.29394i	0.636187	+	0.173130i
$936$		0			0
$937$		−	18.2330i		−	0.595647i	−0.954621	−	0.297823i	$-0.903739\pi$
$937$		−	18.2330i		−	0.595647i	0.954621	−	0.297823i	$-0.0962606\pi$
$938$		−	56.1768i		−	1.83424i
$939$		0			0
$940$	−27.2878	−	7.42604i	−0.890030	−	0.242211i
$941$	37.9004			1.23552			0.617759	−	0.786367i	$-0.288041\pi$
$941$	37.9004			1.23552			0.617759	+	0.786367i	$0.288041\pi$
$942$		0			0
$943$			11.2105i			0.365065i
$944$	36.4267			1.18559
$945$		0			0
$946$	−100.177			−3.25703
$947$		−	1.57146i		−	0.0510655i	−0.999674	−	0.0255328i	$-0.991872\pi$
$947$		−	1.57146i		−	0.0510655i	0.999674	−	0.0255328i	$-0.00812821\pi$
$948$		0			0
$949$	3.45085			0.112019
$950$	−38.9605	+	66.2811i	−1.26404	+	2.15044i
$951$		0			0
$952$		−	84.8053i		−	2.74856i
$953$		−	15.7102i		−	0.508904i	−0.967085	−	0.254452i	$-0.918105\pi$
$953$		−	15.7102i		−	0.508904i	0.967085	−	0.254452i	$-0.0818951\pi$
$954$		0			0
$955$	−14.3882	+	52.8710i	−0.465591	+	1.71087i
$956$	−15.6954			−0.507624
$957$		0			0
$958$		−	5.39840i		−	0.174414i
$959$	18.2983			0.590883
$960$		0			0
$961$	5.08577			0.164057
$962$		−	4.87704i		−	0.157242i
$963$		0			0
$964$	65.4720			2.10871
$965$	−10.8495	−	2.95255i	−0.349257	−	0.0950460i
$966$		0			0
$967$		−	4.31176i		−	0.138657i	−0.997594	−	0.0693285i	$-0.977914\pi$
$967$		−	4.31176i		−	0.138657i	0.997594	−	0.0693285i	$-0.0220856\pi$
$968$		−	7.10268i		−	0.228289i
$969$		0			0
$970$	−14.1883	+	52.1364i	−0.455558	+	1.67400i
$971$	−4.36056			−0.139937			−0.0699686	−	0.997549i	$-0.522290\pi$
$971$	−4.36056			−0.139937			−0.0699686	+	0.997549i	$0.522290\pi$
$972$		0			0
$973$		−	10.5435i		−	0.338010i
$974$	−102.424			−3.28189
$975$		0			0
$976$	−59.4030			−1.90144
$977$			29.2433i			0.935576i	0.883841	+	0.467788i	$0.154949\pi$
$977$			29.2433i			0.935576i	−0.883841	+	0.467788i	$0.845051\pi$
$978$		0			0
$979$	−27.0742			−0.865296
$980$	−15.6899	+	57.6545i	−0.501197	+	1.84170i
$981$		0			0
$982$			58.0302i			1.85182i
$983$			23.6085i			0.752995i	0.926418	+	0.376498i	$0.122872\pi$
$983$			23.6085i			0.752995i	−0.926418	+	0.376498i	$0.877128\pi$
$984$		0			0
$985$	12.2374	+	3.33027i	0.389918	+	0.106111i
$986$	17.5021			0.557381
$987$		0			0
$988$		−	54.1866i		−	1.72390i
$989$	−16.7583			−0.532884
$990$		0			0
$991$	−37.2039			−1.18182			−0.590910	−	0.806738i	$-0.701231\pi$
$991$	−37.2039			−1.18182			−0.590910	+	0.806738i	$0.701231\pi$
$992$		−	101.535i		−	3.22373i
$993$		0			0
$994$	31.8465			1.01011
$995$	−5.79933	+	21.3103i	−0.183851	+	0.675582i
$996$		0			0
$997$		−	57.1337i		−	1.80944i	−0.426004	−	0.904721i	$-0.640079\pi$
$997$		−	57.1337i		−	1.80944i	0.426004	−	0.904721i	$-0.359921\pi$
$998$			101.707i			3.21947i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1665.2.c.e.334.1		18
3.2	odd	2		185.2.b.a.149.18	yes	18
5.2	odd	4		8325.2.a.cr.1.9		9
5.3	odd	4		8325.2.a.cq.1.1		9
5.4	even	2	inner	1665.2.c.e.334.18		18
15.2	even	4		925.2.a.l.1.1		9
15.8	even	4		925.2.a.m.1.9		9
15.14	odd	2		185.2.b.a.149.1	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.b.a.149.1	✓	18	15.14	odd	2
185.2.b.a.149.18	yes	18	3.2	odd	2
925.2.a.l.1.1		9	15.2	even	4
925.2.a.m.1.9		9	15.8	even	4
1665.2.c.e.334.1		18	1.1	even	1	trivial
1665.2.c.e.334.18		18	5.4	even	2	inner
8325.2.a.cq.1.1		9	5.3	odd	4
8325.2.a.cr.1.9		9	5.2	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)

\(f(q)\)	\(=\)	\(q-2.68489i q^{2} -5.20864 q^{4} +(-0.587164 + 2.15760i) q^{5} -3.48285i q^{7} +8.61484i q^{8} +(5.79292 + 1.57647i) q^{10} +3.18991 q^{11} +1.81648i q^{13} -9.35107 q^{14} +12.7126 q^{16} -2.82645i q^{17} +5.72714 q^{19} +(3.05832 - 11.2382i) q^{20} -8.56456i q^{22} -1.43274i q^{23} +(-4.31048 - 2.53373i) q^{25} +4.87704 q^{26} +18.1409i q^{28} -2.30634 q^{29} +6.00714 q^{31} -16.9023i q^{32} -7.58870 q^{34} +(7.51460 + 2.04500i) q^{35} -1.00000i q^{37} -15.3767i q^{38} +(-18.5874 - 5.05832i) q^{40} -7.82452 q^{41} -11.6967i q^{43} -16.6151 q^{44} -3.84676 q^{46} -2.42814i q^{47} -5.13024 q^{49} +(-6.80279 + 11.5732i) q^{50} -9.46137i q^{52} -9.32573i q^{53} +(-1.87300 + 6.88255i) q^{55} +30.0042 q^{56} +6.19227i q^{58} +2.86539 q^{59} -4.67275 q^{61} -16.1285i q^{62} -19.9557 q^{64} +(-3.91923 - 1.06657i) q^{65} +6.00752i q^{67} +14.7219i q^{68} +(5.49061 - 20.1759i) q^{70} -3.40566 q^{71} -1.89975i q^{73} -2.68489 q^{74} -29.8306 q^{76} -11.1100i q^{77} +1.60903 q^{79} +(-7.46440 + 27.4288i) q^{80} +21.0080i q^{82} +7.37571i q^{83} +(6.09834 + 1.65959i) q^{85} -31.4043 q^{86} +27.4806i q^{88} -8.48746 q^{89} +6.32652 q^{91} +7.46264i q^{92} -6.51929 q^{94} +(-3.36277 + 12.3569i) q^{95} +9.00003i q^{97} +13.7741i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 22 q^{4} - 2 q^{5} + 6 q^{10} - 8 q^{14} + 22 q^{16} + 8 q^{19} + 4 q^{20} - 18 q^{25} + 12 q^{26} - 4 q^{29} - 12 q^{31} - 12 q^{34} + 2 q^{35} - 6 q^{40} - 4 q^{41} + 8 q^{44} + 32 q^{46} + 14 q^{49}+ \cdots + 44 q^{95}+O(q^{100}) \) 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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