LMFDB - Embedded newform 855.2.c.g.514.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [855,2,Mod(514,855)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(855, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("855.514"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,0,-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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 25x^{12} + 242x^{10} + 1134x^{8} + 2605x^{6} + 2545x^{4} + 552x^{2} + 16 $ x^14 + 25x^12 + 242x^10 + 1134x^8 + 2605x^6 + 2545x^4 + 552x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 285)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			514.5
Root			$-1.57229i$ of defining polynomial
Character	$\chi$	$=$	855.514
Dual form			855.2.c.g.514.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.57229i q^{2} -0.472094 q^{4} +(1.72335 - 1.42481i) q^{5} +1.87913i q^{7} -2.40231i q^{8} +(-2.24021 - 2.70960i) q^{10} -1.92081 q^{11} -0.248324i q^{13} +2.95453 q^{14} -4.72132 q^{16} -7.06596i q^{17} -1.00000 q^{19} +(-0.813582 + 0.672643i) q^{20} +3.02007i q^{22} -1.20286i q^{23} +(0.939849 - 4.91087i) q^{25} -0.390437 q^{26} -0.887125i q^{28} +2.58170 q^{29} +8.69676 q^{31} +2.61865i q^{32} -11.1097 q^{34} +(2.67739 + 3.23839i) q^{35} -7.86387i q^{37} +1.57229i q^{38} +(-3.42283 - 4.14001i) q^{40} -1.52589 q^{41} -4.15375i q^{43} +0.906802 q^{44} -1.89124 q^{46} +5.96879i q^{47} +3.46888 q^{49} +(-7.72132 - 1.47772i) q^{50} +0.117232i q^{52} +7.11918i q^{53} +(-3.31022 + 2.73678i) q^{55} +4.51425 q^{56} -4.05918i q^{58} -11.8573 q^{59} +5.87781 q^{61} -13.6738i q^{62} -5.32535 q^{64} +(-0.353813 - 0.427948i) q^{65} +9.53623i q^{67} +3.33580i q^{68} +(5.09169 - 4.20964i) q^{70} +9.53623 q^{71} +6.69123i q^{73} -12.3643 q^{74} +0.472094 q^{76} -3.60944i q^{77} +0.348185 q^{79} +(-8.13646 + 6.72696i) q^{80} +2.39913i q^{82} +2.41705i q^{83} +(-10.0676 - 12.1771i) q^{85} -6.53090 q^{86} +4.61438i q^{88} -17.3414 q^{89} +0.466632 q^{91} +0.567862i q^{92} +9.38467 q^{94} +(-1.72335 + 1.42481i) q^{95} -7.70088i q^{97} -5.45408i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 22 q^{4} - 2 q^{5} + 2 q^{10} + 8 q^{11} - 8 q^{14} + 38 q^{16} - 14 q^{19} - 12 q^{20} - 4 q^{25} + 40 q^{26} - 12 q^{29} + 8 q^{31} - 4 q^{34} + 14 q^{35} + 18 q^{40} - 4 q^{41} - 64 q^{44} - 8 q^{46}+ \cdots + 2 q^{95}+O(q^{100}) $ 14 * q - 22 * q^4 - 2 * q^5 + 2 * q^10 + 8 * q^11 - 8 * q^14 + 38 * q^16 - 14 * q^19 - 12 * q^20 - 4 * q^25 + 40 * q^26 - 12 * q^29 + 8 * q^31 - 4 * q^34 + 14 * q^35 + 18 * q^40 - 4 * q^41 - 64 * q^44 - 8 * q^46 - 34 * q^49 - 4 * q^50 - 2 * q^55 + 44 * q^56 - 36 * q^59 + 24 * q^61 - 22 * q^64 + 12 * q^65 - 60 * q^70 + 36 * q^71 + 12 * q^74 + 22 * q^76 + 8 * q^79 - 36 * q^80 - 18 * q^85 + 92 * q^86 - 16 * q^89 + 24 * q^91 + 40 * q^94 + 2 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.57229i		−	1.11178i	−0.831257	−	0.555888i	$-0.812378\pi$
$2$		−	1.57229i		−	1.11178i	0.831257	−	0.555888i	$-0.187622\pi$
$3$		0			0
$3$		0			0
$4$	−0.472094			−0.236047
$5$	1.72335	−	1.42481i	0.770704	−	0.637193i
$5$	1.72335	−	1.42481i	0.770704	−	0.637193i
$6$		0			0
$7$			1.87913i			0.710244i	0.934820	+	0.355122i	$0.115561\pi$
$7$			1.87913i			0.710244i	−0.934820	+	0.355122i	$0.884439\pi$
$8$		−	2.40231i		−	0.849345i
$9$		0			0
$10$	−2.24021	−	2.70960i	−0.708416	−	0.856851i
$11$	−1.92081			−0.579146			−0.289573	−	0.957156i	$-0.593513\pi$
$11$	−1.92081			−0.579146			−0.289573	+	0.957156i	$0.593513\pi$
$12$		0			0
$13$		−	0.248324i		−	0.0688726i	−0.999407	−	0.0344363i	$-0.989036\pi$
$13$		−	0.248324i		−	0.0688726i	0.999407	−	0.0344363i	$-0.0109636\pi$
$14$	2.95453			0.789632
$15$		0			0
$16$	−4.72132			−1.18033
$17$		−	7.06596i		−	1.71375i	−0.515527	−	0.856873i	$-0.672404\pi$
$17$		−	7.06596i		−	1.71375i	0.515527	−	0.856873i	$-0.327596\pi$
$18$		0			0
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	−0.813582	+	0.672643i	−0.181922	+	0.150408i
$21$		0			0
$22$			3.02007i			0.643880i
$23$		−	1.20286i		−	0.250813i	−0.992105	−	0.125406i	$-0.959977\pi$
$23$		−	1.20286i		−	0.250813i	0.992105	−	0.125406i	$-0.0400235\pi$
$24$		0			0
$25$	0.939849	−	4.91087i	0.187970	−	0.982175i
$26$	−0.390437			−0.0765709
$27$		0			0
$28$		−	0.887125i		−	0.167651i
$29$	2.58170			0.479409			0.239705	−	0.970846i	$-0.422949\pi$
$29$	2.58170			0.479409			0.239705	+	0.970846i	$0.422949\pi$
$30$		0			0
$31$	8.69676			1.56198			0.780992	−	0.624541i	$-0.214714\pi$
$31$	8.69676			1.56198			0.780992	+	0.624541i	$0.214714\pi$
$32$			2.61865i			0.462917i
$33$		0			0
$34$	−11.1097			−1.90530
$35$	2.67739	+	3.23839i	0.452562	+	0.547388i
$36$		0			0
$37$		−	7.86387i		−	1.29281i	−0.762993	−	0.646406i	$-0.776271\pi$
$37$		−	7.86387i		−	1.29281i	0.762993	−	0.646406i	$-0.223729\pi$
$38$			1.57229i			0.255059i
$39$		0			0
$40$	−3.42283	−	4.14001i	−0.541197	−	0.654594i
$41$	−1.52589			−0.238303			−0.119152	−	0.992876i	$-0.538017\pi$
$41$	−1.52589			−0.238303			−0.119152	+	0.992876i	$0.538017\pi$
$42$		0			0
$43$		−	4.15375i		−	0.633441i	−0.948519	−	0.316720i	$-0.897418\pi$
$43$		−	4.15375i		−	0.633441i	0.948519	−	0.316720i	$-0.102582\pi$
$44$	0.906802			0.136706
$45$		0			0
$46$	−1.89124			−0.278848
$47$			5.96879i			0.870638i	0.900276	+	0.435319i	$0.143364\pi$
$47$			5.96879i			0.870638i	−0.900276	+	0.435319i	$0.856636\pi$
$48$		0			0
$49$	3.46888			0.495554
$50$	−7.72132	−	1.47772i	−1.09196	−	0.208981i
$51$		0			0
$52$			0.117232i			0.0162572i
$53$			7.11918i			0.977894i	0.872313	+	0.488947i	$0.162619\pi$
$53$			7.11918i			0.977894i	−0.872313	+	0.488947i	$0.837381\pi$
$54$		0			0
$55$	−3.31022	+	2.73678i	−0.446350	+	0.369028i
$56$	4.51425			0.603242
$57$		0			0
$58$		−	4.05918i		−	0.532996i
$59$	−11.8573			−1.54369			−0.771844	−	0.635812i	$-0.780665\pi$
$59$	−11.8573			−1.54369			−0.771844	+	0.635812i	$0.780665\pi$
$60$		0			0
$61$	5.87781			0.752576			0.376288	−	0.926503i	$-0.377200\pi$
$61$	5.87781			0.752576			0.376288	+	0.926503i	$0.377200\pi$
$62$		−	13.6738i		−	1.73658i
$63$		0			0
$64$	−5.32535			−0.665669
$65$	−0.353813	−	0.427948i	−0.0438851	−	0.0530804i
$66$		0			0
$67$			9.53623i			1.16504i	0.812818	+	0.582518i	$0.197932\pi$
$67$			9.53623i			1.16504i	−0.812818	+	0.582518i	$0.802068\pi$
$68$			3.33580i			0.404525i
$69$		0			0
$70$	5.09169	−	4.20964i	0.608573	−	0.503148i
$71$	9.53623			1.13174			0.565871	−	0.824494i	$-0.308540\pi$
$71$	9.53623			1.13174			0.565871	+	0.824494i	$0.308540\pi$
$72$		0			0
$73$			6.69123i			0.783149i	0.920146	+	0.391575i	$0.128070\pi$
$73$			6.69123i			0.783149i	−0.920146	+	0.391575i	$0.871930\pi$
$74$	−12.3643			−1.43732
$75$		0			0
$76$	0.472094			0.0541529
$77$		−	3.60944i		−	0.411334i
$78$		0			0
$79$	0.348185			0.0391739			0.0195869	−	0.999808i	$-0.493765\pi$
$79$	0.348185			0.0391739			0.0195869	+	0.999808i	$0.493765\pi$
$80$	−8.13646	+	6.72696i	−0.909684	+	0.752097i
$81$		0			0
$82$			2.39913i			0.264940i
$83$			2.41705i			0.265306i	0.991163	+	0.132653i	$0.0423496\pi$
$83$			2.41705i			0.265306i	−0.991163	+	0.132653i	$0.957650\pi$
$84$		0			0
$85$	−10.0676	−	12.1771i	−1.09199	−	1.32079i
$86$	−6.53090			−0.704245
$87$		0			0
$88$			4.61438i			0.491894i
$89$	−17.3414			−1.83818			−0.919090	−	0.394048i	$-0.871074\pi$
$89$	−17.3414			−1.83818			−0.919090	+	0.394048i	$0.871074\pi$
$90$		0			0
$91$	0.466632			0.0489163
$92$			0.567862i			0.0592037i
$93$		0			0
$94$	9.38467			0.967955
$95$	−1.72335	+	1.42481i	−0.176812	+	0.146182i
$96$		0			0
$97$		−	7.70088i		−	0.781905i	−0.920411	−	0.390953i	$-0.872146\pi$
$97$		−	7.70088i		−	0.781905i	0.920411	−	0.390953i	$-0.127854\pi$
$98$		−	5.45408i		−	0.550945i
$99$		0			0
$100$	−0.443697	+	2.31840i	−0.0443697	+	0.231840i
$101$	8.41297			0.837122			0.418561	−	0.908189i	$-0.362535\pi$
$101$	8.41297			0.837122			0.418561	+	0.908189i	$0.362535\pi$
$102$		0			0
$103$			9.64843i			0.950688i	0.879800	+	0.475344i	$0.157676\pi$
$103$			9.64843i			0.950688i	−0.879800	+	0.475344i	$0.842324\pi$
$104$	−0.596550			−0.0584966
$105$		0			0
$106$	11.1934			1.08720
$107$		−	0.241744i		−	0.0233703i	−0.999932	−	0.0116852i	$-0.996280\pi$
$107$		−	0.241744i		−	0.0233703i	0.999932	−	0.0116852i	$-0.00371958\pi$
$108$		0			0
$109$	−3.05581			−0.292694			−0.146347	−	0.989233i	$-0.546752\pi$
$109$	−3.05581			−0.292694			−0.146347	+	0.989233i	$0.546752\pi$
$110$	4.30301	+	5.20462i	0.410276	+	0.496241i
$111$		0			0
$112$		−	8.87196i		−	0.838321i
$113$			16.5767i			1.55940i	0.626152	+	0.779701i	$0.284629\pi$
$113$			16.5767i			1.55940i	−0.626152	+	0.779701i	$0.715371\pi$
$114$		0			0
$115$	−1.71384	−	2.07294i	−0.159816	−	0.193303i
$116$	−1.21880			−0.113163
$117$		0			0
$118$			18.6431i			1.71624i
$119$	13.2778			1.21718
$120$		0			0
$121$	−7.31050			−0.664590
$122$		−	9.24161i		−	0.836696i
$123$		0			0
$124$	−4.10569			−0.368702
$125$	−5.37736	−	9.80224i	−0.480966	−	0.876739i
$126$		0			0
$127$			21.5565i			1.91283i	0.292007	+	0.956416i	$0.405677\pi$
$127$			21.5565i			1.91283i	−0.292007	+	0.956416i	$0.594323\pi$
$128$			13.6103i			1.20299i
$129$		0			0
$130$	−0.672858	+	0.556297i	−0.0590135	+	0.0487905i
$131$	18.3504			1.60328			0.801642	−	0.597804i	$-0.203960\pi$
$131$	18.3504			1.60328			0.801642	+	0.597804i	$0.203960\pi$
$132$		0			0
$133$		−	1.87913i		−	0.162941i
$134$	14.9937			1.29526
$135$		0			0
$136$	−16.9746			−1.45556
$137$			9.63542i			0.823209i	0.911362	+	0.411605i	$0.135032\pi$
$137$			9.63542i			0.823209i	−0.911362	+	0.411605i	$0.864968\pi$
$138$		0			0
$139$	14.9629			1.26914			0.634568	−	0.772867i	$-0.281178\pi$
$139$	14.9629			1.26914			0.634568	+	0.772867i	$0.281178\pi$
$140$	−1.26398	−	1.52882i	−0.106826	−	0.129209i
$141$		0			0
$142$		−	14.9937i		−	1.25824i
$143$			0.476982i			0.0398872i
$144$		0			0
$145$	4.44916	−	3.67842i	0.369483	−	0.305476i
$146$	10.5206			0.870687
$147$		0			0
$148$			3.71249i			0.305165i
$149$	14.2063			1.16383			0.581915	−	0.813250i	$-0.302304\pi$
$149$	14.2063			1.16383			0.581915	+	0.813250i	$0.302304\pi$
$150$		0			0
$151$	−2.26811			−0.184577			−0.0922883	−	0.995732i	$-0.529418\pi$
$151$	−2.26811			−0.184577			−0.0922883	+	0.995732i	$0.529418\pi$
$152$			2.40231i			0.194853i
$153$		0			0
$154$	−5.67509			−0.457312
$155$	14.9875	−	12.3912i	1.20383	−	0.995286i
$156$		0			0
$157$		−	1.23885i		−	0.0988706i	−0.998777	−	0.0494353i	$-0.984258\pi$
$157$		−	1.23885i		−	0.0988706i	0.998777	−	0.0494353i	$-0.0157422\pi$
$158$		−	0.547448i		−	0.0435526i
$159$		0			0
$160$	3.73108	+	4.51285i	0.294968	+	0.356772i
$161$	2.26032			0.178138
$162$		0			0
$163$			4.19752i			0.328775i	0.986396	+	0.164388i	$0.0525648\pi$
$163$			4.19752i			0.328775i	−0.986396	+	0.164388i	$0.947435\pi$
$164$	0.720362			0.0562508
$165$		0			0
$166$	3.80030			0.294961
$167$		−	16.5980i		−	1.28439i	−0.766541	−	0.642195i	$-0.778024\pi$
$167$		−	16.5980i		−	1.28439i	0.766541	−	0.642195i	$-0.221976\pi$
$168$		0			0
$169$	12.9383			0.995257
$170$	−19.1459	+	15.8292i	−1.46843	+	1.21405i
$171$		0			0
$172$			1.96096i			0.149522i
$173$		−	0.784955i		−	0.0596790i	−0.999555	−	0.0298395i	$-0.990500\pi$
$173$		−	0.784955i		−	0.0596790i	0.999555	−	0.0298395i	$-0.00949962\pi$
$174$		0			0
$175$	9.22816	+	1.76610i	0.697583	+	0.133504i
$176$	9.06874			0.683582
$177$		0			0
$178$			27.2656i			2.04365i
$179$	−23.1704			−1.73183			−0.865917	−	0.500188i	$-0.833264\pi$
$179$	−23.1704			−1.73183			−0.865917	+	0.500188i	$0.833264\pi$
$180$		0			0
$181$	8.11162			0.602932			0.301466	−	0.953477i	$-0.402524\pi$
$181$	8.11162			0.602932			0.301466	+	0.953477i	$0.402524\pi$
$182$		−	0.733680i		−	0.0543840i
$183$		0			0
$184$	−2.88963			−0.213027
$185$	−11.2045	−	13.5522i	−0.823772	−	0.996376i
$186$		0			0
$187$			13.5724i			0.992509i
$188$		−	2.81783i		−	0.205512i
$189$		0			0
$190$	2.24021	+	2.70960i	0.162522	+	0.196575i
$191$	20.7192			1.49919			0.749595	−	0.661897i	$-0.230248\pi$
$191$	20.7192			1.49919			0.749595	+	0.661897i	$0.230248\pi$
$192$		0			0
$193$		−	3.71249i		−	0.267231i	−0.991033	−	0.133615i	$-0.957341\pi$
$193$		−	3.71249i		−	0.267231i	0.991033	−	0.133615i	$-0.0426587\pi$
$194$	−12.1080			−0.869304
$195$		0			0
$196$	−1.63764			−0.116974
$197$			7.81160i			0.556554i	0.960501	+	0.278277i	$0.0897632\pi$
$197$			7.81160i			0.556554i	−0.960501	+	0.278277i	$0.910237\pi$
$198$		0			0
$199$	−5.87477			−0.416451			−0.208226	−	0.978081i	$-0.566769\pi$
$199$	−5.87477			−0.416451			−0.208226	+	0.978081i	$0.566769\pi$
$200$	−11.7974	−	2.25781i	−0.834205	−	0.159651i
$201$		0			0
$202$		−	13.2276i		−	0.930692i
$203$			4.85134i			0.340497i
$204$		0			0
$205$	−2.62963	+	2.17409i	−0.183661	+	0.151845i
$206$	15.1701			1.05695
$207$		0			0
$208$			1.17241i			0.0812923i
$209$	1.92081			0.132865
$210$		0			0
$211$	−9.79251			−0.674144			−0.337072	−	0.941479i	$-0.609437\pi$
$211$	−9.79251			−0.674144			−0.337072	+	0.941479i	$0.609437\pi$
$212$		−	3.36092i		−	0.230829i
$213$		0			0
$214$	−0.380092			−0.0259826
$215$	−5.91829	−	7.15835i	−0.403624	−	0.488196i
$216$		0			0
$217$			16.3423i			1.10939i
$218$			4.80462i			0.325410i
$219$		0			0
$220$	1.56274	−	1.29202i	0.105360	−	0.0871079i
$221$	−1.75464			−0.118030
$222$		0			0
$223$		−	20.4327i		−	1.36827i	−0.729354	−	0.684137i	$-0.760179\pi$
$223$		−	20.4327i		−	1.36827i	0.729354	−	0.684137i	$-0.239821\pi$
$224$	−4.92079			−0.328784
$225$		0			0
$226$	26.0633			1.73371
$227$			10.0931i			0.669903i	0.942235	+	0.334952i	$0.108720\pi$
$227$			10.0931i			0.669903i	−0.942235	+	0.334952i	$0.891280\pi$
$228$		0			0
$229$	14.5637			0.962397			0.481198	−	0.876612i	$-0.340202\pi$
$229$	14.5637			0.962397			0.481198	+	0.876612i	$0.340202\pi$
$230$	−3.25926	+	2.69465i	−0.214909	+	0.177680i
$231$		0			0
$232$		−	6.20204i		−	0.407184i
$233$		−	25.8921i		−	1.69625i	−0.529797	−	0.848125i	$-0.677732\pi$
$233$		−	25.8921i		−	1.69625i	0.529797	−	0.848125i	$-0.322268\pi$
$234$		0			0
$235$	8.50438	+	10.2863i	0.554764	+	0.671004i
$236$	5.59776			0.364383
$237$		0			0
$238$		−	20.8766i		−	1.35323i
$239$	18.7389			1.21212			0.606061	−	0.795418i	$-0.292749\pi$
$239$	18.7389			1.21212			0.606061	+	0.795418i	$0.292749\pi$
$240$		0			0
$241$	28.4586			1.83318			0.916589	−	0.399831i	$-0.130931\pi$
$241$	28.4586			1.83318			0.916589	+	0.399831i	$0.130931\pi$
$242$			11.4942i			0.738876i
$243$		0			0
$244$	−2.77488			−0.177643
$245$	5.97808	−	4.94248i	0.381926	−	0.315764i
$246$		0			0
$247$			0.248324i			0.0158005i
$248$		−	20.8923i		−	1.32666i
$249$		0			0
$250$	−15.4120	+	8.45477i	−0.974738	+	0.534727i
$251$	−1.22886			−0.0775650			−0.0387825	−	0.999248i	$-0.512348\pi$
$251$	−1.22886			−0.0775650			−0.0387825	+	0.999248i	$0.512348\pi$
$252$		0			0
$253$			2.31046i			0.145257i
$254$	33.8931			2.12664
$255$		0			0
$256$	10.7486			0.671789
$257$			5.56841i			0.347348i	0.984803	+	0.173674i	$0.0555639\pi$
$257$			5.56841i			0.347348i	−0.984803	+	0.173674i	$0.944436\pi$
$258$		0			0
$259$	14.7772			0.918212
$260$	0.167033	+	0.202032i	0.0103590	+	0.0125295i
$261$		0			0
$262$		−	28.8522i		−	1.78249i
$263$		−	10.7855i		−	0.665063i	−0.943092	−	0.332531i	$-0.892097\pi$
$263$		−	10.7855i		−	0.665063i	0.943092	−	0.332531i	$-0.107903\pi$
$264$		0			0
$265$	10.1435	+	12.2688i	0.623108	+	0.753667i
$266$	−2.95453			−0.181154
$267$		0			0
$268$		−	4.50200i		−	0.275003i
$269$	−22.8529			−1.39337			−0.696684	−	0.717378i	$-0.745342\pi$
$269$	−22.8529			−1.39337			−0.696684	+	0.717378i	$0.745342\pi$
$270$		0			0
$271$	−9.95413			−0.604670			−0.302335	−	0.953202i	$-0.597766\pi$
$271$	−9.95413			−0.604670			−0.302335	+	0.953202i	$0.597766\pi$
$272$			33.3606i			2.02278i
$273$		0			0
$274$	15.1497			0.915225
$275$	−1.80527	+	9.43285i	−0.108862	+	0.568822i
$276$		0			0
$277$		−	14.4026i		−	0.865371i	−0.901545	−	0.432686i	$-0.857566\pi$
$277$		−	14.4026i		−	0.865371i	0.901545	−	0.432686i	$-0.142434\pi$
$278$		−	23.5260i		−	1.41100i
$279$		0			0
$280$	7.77962	−	6.43193i	0.464921	−	0.384381i
$281$	−5.34285			−0.318728			−0.159364	−	0.987220i	$-0.550944\pi$
$281$	−5.34285			−0.318728			−0.159364	+	0.987220i	$0.550944\pi$
$282$		0			0
$283$		−	5.73067i		−	0.340653i	−0.985388	−	0.170326i	$-0.945518\pi$
$283$		−	5.73067i		−	0.340653i	0.985388	−	0.170326i	$-0.0544822\pi$
$284$	−4.50200			−0.267144
$285$		0			0
$286$	0.749954			0.0443457
$287$		−	2.86733i		−	0.169253i
$288$		0			0
$289$	−32.9278			−1.93693
$290$	−5.78354	−	6.99537i	−0.339621	−	0.410782i
$291$		0			0
$292$		−	3.15889i		−	0.184860i
$293$			27.4793i			1.60536i	0.596412	+	0.802678i	$0.296592\pi$
$293$			27.4793i			1.60536i	−0.596412	+	0.802678i	$0.703408\pi$
$294$		0			0
$295$	−20.4342	+	16.8944i	−1.18973	+	0.983628i
$296$	−18.8915			−1.09804
$297$		0			0
$298$		−	22.3365i		−	1.29392i
$299$	−0.298698			−0.0172741
$300$		0			0
$301$	7.80543			0.449897
$302$			3.56613i			0.205208i
$303$		0			0
$304$	4.72132			0.270786
$305$	10.1295	−	8.37474i	0.580014	−	0.479536i
$306$		0			0
$307$			10.7031i			0.610858i	0.952215	+	0.305429i	$0.0987999\pi$
$307$			10.7031i			0.610858i	−0.952215	+	0.305429i	$0.901200\pi$
$308$			1.70400i			0.0970943i
$309$		0			0
$310$	−19.4826	−	23.5647i	−1.10654	−	1.33839i
$311$	11.5209			0.653288			0.326644	−	0.945148i	$-0.394082\pi$
$311$	11.5209			0.653288			0.326644	+	0.945148i	$0.394082\pi$
$312$		0			0
$313$		−	18.1596i		−	1.02644i	−0.858257	−	0.513221i	$-0.828452\pi$
$313$		−	18.1596i		−	1.02644i	0.858257	−	0.513221i	$-0.171548\pi$
$314$	−1.94782			−0.109922
$315$		0			0
$316$	−0.164376			−0.00924688
$317$			19.7109i			1.10707i	0.832824	+	0.553537i	$0.186722\pi$
$317$			19.7109i			1.10707i	−0.832824	+	0.553537i	$0.813278\pi$
$318$		0			0
$319$	−4.95895			−0.277648
$320$	−9.17742	+	7.58759i	−0.513034	+	0.424159i
$321$		0			0
$322$		−	3.55388i		−	0.198050i
$323$			7.06596i			0.393160i
$324$		0			0
$325$	−1.21949	−	0.233387i	−0.0676449	−	0.0129460i
$326$	6.59972			0.365525
$327$		0			0
$328$			3.66565i			0.202402i
$329$	−11.2161			−0.618365
$330$		0			0
$331$	−1.88788			−0.103767			−0.0518836	−	0.998653i	$-0.516522\pi$
$331$	−1.88788			−0.103767			−0.0518836	+	0.998653i	$0.516522\pi$
$332$		−	1.14108i		−	0.0626247i
$333$		0			0
$334$	−26.0968			−1.42796
$335$	13.5873	+	16.4342i	0.742353	+	0.897898i
$336$		0			0
$337$			14.0147i			0.763429i	0.924280	+	0.381714i	$0.124666\pi$
$337$			14.0147i			0.763429i	−0.924280	+	0.381714i	$0.875334\pi$
$338$		−	20.3428i		−	1.10650i
$339$		0			0
$340$	4.75287	+	5.74874i	0.257760	+	0.311769i
$341$	−16.7048			−0.904616
$342$		0			0
$343$			19.6724i			1.06221i
$344$	−9.97859			−0.538010
$345$		0			0
$346$	−1.23418			−0.0663498
$347$			1.05107i			0.0564245i	0.999602	+	0.0282122i	$0.00898142\pi$
$347$			1.05107i			0.0564245i	−0.999602	+	0.0282122i	$0.991019\pi$
$348$		0			0
$349$	−35.4633			−1.89831			−0.949153	−	0.314815i	$-0.898057\pi$
$349$	−35.4633			−1.89831			−0.949153	+	0.314815i	$0.898057\pi$
$350$	2.77682	−	14.5093i	0.148427	−	0.775557i
$351$		0			0
$352$		−	5.02993i		−	0.268096i
$353$			5.28721i			0.281410i	0.990052	+	0.140705i	$0.0449368\pi$
$353$			5.28721i			0.281410i	−0.990052	+	0.140705i	$0.955063\pi$
$354$		0			0
$355$	16.4342	−	13.5873i	0.872239	−	0.721138i
$356$	8.18675			0.433897
$357$		0			0
$358$			36.4305i			1.92541i
$359$	16.0220			0.845607			0.422803	−	0.906221i	$-0.361046\pi$
$359$	16.0220			0.845607			0.422803	+	0.906221i	$0.361046\pi$
$360$		0			0
$361$	1.00000			0.0526316
$362$		−	12.7538i		−	0.670326i
$363$		0			0
$364$	−0.220294			−0.0115466
$365$	9.53371	+	11.5313i	0.499017	+	0.603576i
$366$		0			0
$367$			27.7038i			1.44613i	0.690782	+	0.723063i	$0.257267\pi$
$367$			27.7038i			1.44613i	−0.690782	+	0.723063i	$0.742733\pi$
$368$			5.67907i			0.296042i
$369$		0			0
$370$	−21.3080	+	17.6167i	−1.10775	+	0.915850i
$371$	−13.3778			−0.694543
$372$		0			0
$373$		−	11.7532i		−	0.608559i	−0.952583	−	0.304279i	$-0.901584\pi$
$373$		−	11.7532i		−	0.608559i	0.952583	−	0.304279i	$-0.0984156\pi$
$374$	21.3397			1.10345
$375$		0			0
$376$	14.3389			0.739472
$377$		−	0.641096i		−	0.0330181i
$378$		0			0
$379$	7.04988			0.362128			0.181064	−	0.983471i	$-0.442046\pi$
$379$	7.04988			0.362128			0.181064	+	0.983471i	$0.442046\pi$
$380$	0.813582	−	0.672643i	0.0417359	−	0.0345059i
$381$		0			0
$382$		−	32.5766i		−	1.66676i
$383$			7.01682i			0.358543i	0.983800	+	0.179271i	$0.0573740\pi$
$383$			7.01682i			0.358543i	−0.983800	+	0.179271i	$0.942626\pi$
$384$		0			0
$385$	−5.14276	−	6.22033i	−0.262099	−	0.317017i
$386$	−5.83711			−0.297101
$387$		0			0
$388$			3.63554i			0.184567i
$389$	−38.1712			−1.93536			−0.967679	−	0.252185i	$-0.918851\pi$
$389$	−38.1712			−1.93536			−0.967679	+	0.252185i	$0.918851\pi$
$390$		0			0
$391$	−8.49933			−0.429830
$392$		−	8.33332i		−	0.420896i
$393$		0			0
$394$	12.2821			0.618763
$395$	0.600044	−	0.496097i	0.0301915	−	0.0249613i
$396$		0			0
$397$			7.84847i			0.393904i	0.980413	+	0.196952i	$0.0631042\pi$
$397$			7.84847i			0.393904i	−0.980413	+	0.196952i	$0.936896\pi$
$398$			9.23683i			0.463001i
$399$		0			0
$400$	−4.43733	+	23.1858i	−0.221866	+	1.15929i
$401$	−0.879277			−0.0439090			−0.0219545	−	0.999759i	$-0.506989\pi$
$401$	−0.879277			−0.0439090			−0.0219545	+	0.999759i	$0.506989\pi$
$402$		0			0
$403$		−	2.15961i		−	0.107578i
$404$	−3.97171			−0.197600
$405$		0			0
$406$	7.62771			0.378557
$407$			15.1050i			0.748727i
$408$		0			0
$409$	−38.8153			−1.91929			−0.959647	−	0.281207i	$-0.909265\pi$
$409$	−38.8153			−1.91929			−0.959647	+	0.281207i	$0.909265\pi$
$410$	3.41830	+	4.13454i	0.168818	+	0.204190i
$411$		0			0
$412$		−	4.55497i		−	0.224407i
$413$		−	22.2814i		−	1.09639i
$414$		0			0
$415$	3.44383	+	4.16542i	0.169051	+	0.204472i
$416$	0.650274			0.0318823
$417$		0			0
$418$		−	3.02007i		−	0.147716i
$419$	−31.2248			−1.52543			−0.762716	−	0.646734i	$-0.776134\pi$
$419$	−31.2248			−1.52543			−0.762716	+	0.646734i	$0.776134\pi$
$420$		0			0
$421$	−4.46904			−0.217808			−0.108904	−	0.994052i	$-0.534734\pi$
$421$	−4.46904			−0.217808			−0.108904	+	0.994052i	$0.534734\pi$
$422$			15.3967i			0.749498i
$423$		0			0
$424$	17.1025			0.830570
$425$	−34.7000	−	6.64094i	−1.68320	−	0.322133i
$426$		0			0
$427$			11.0452i			0.534512i
$428$			0.114126i			0.00551649i
$429$		0			0
$430$	−11.2550	+	9.30527i	−0.542764	+	0.448740i
$431$	−26.0794			−1.25620			−0.628101	−	0.778132i	$-0.716167\pi$
$431$	−26.0794			−1.25620			−0.628101	+	0.778132i	$0.716167\pi$
$432$		0			0
$433$			15.4199i			0.741035i	0.928825	+	0.370518i	$0.120820\pi$
$433$			15.4199i			0.741035i	−0.928825	+	0.370518i	$0.879180\pi$
$434$	25.6949			1.23339
$435$		0			0
$436$	1.44263			0.0690895
$437$			1.20286i			0.0575404i
$438$		0			0
$439$	26.1326			1.24724			0.623620	−	0.781728i	$-0.285661\pi$
$439$	26.1326			1.24724			0.623620	+	0.781728i	$0.285661\pi$
$440$	6.57460	+	7.95217i	0.313432	+	0.379105i
$441$		0			0
$442$			2.75881i			0.131223i
$443$		−	18.7686i		−	0.891721i	−0.895102	−	0.445861i	$-0.852898\pi$
$443$		−	18.7686i		−	0.891721i	0.895102	−	0.445861i	$-0.147102\pi$
$444$		0			0
$445$	−29.8852	+	24.7081i	−1.41669	+	1.17128i
$446$	−32.1261			−1.52121
$447$		0			0
$448$		−	10.0070i		−	0.472787i
$449$	18.5078			0.873438			0.436719	−	0.899598i	$-0.356140\pi$
$449$	18.5078			0.873438			0.436719	+	0.899598i	$0.356140\pi$
$450$		0			0
$451$	2.93093			0.138012
$452$		−	7.82575i		−	0.368092i
$453$		0			0
$454$	15.8693			0.744783
$455$	0.804168	−	0.664860i	0.0377000	−	0.0311691i
$456$		0			0
$457$		−	35.7154i		−	1.67070i	−0.549722	−	0.835348i	$-0.685266\pi$
$457$		−	35.7154i		−	1.67070i	0.549722	−	0.835348i	$-0.314734\pi$
$458$		−	22.8984i		−	1.06997i
$459$		0			0
$460$	0.809093	+	0.978623i	0.0377242	+	0.0456285i
$461$	30.7787			1.43351			0.716753	−	0.697327i	$-0.245628\pi$
$461$	30.7787			1.43351			0.716753	+	0.697327i	$0.245628\pi$
$462$		0			0
$463$		−	31.1807i		−	1.44909i	−0.689226	−	0.724546i	$-0.742049\pi$
$463$		−	31.1807i		−	1.44909i	0.689226	−	0.724546i	$-0.257951\pi$
$464$	−12.1890			−0.565860
$465$		0			0
$466$	−40.7099			−1.88585
$467$			8.01621i			0.370946i	0.982649	+	0.185473i	$0.0593817\pi$
$467$			8.01621i			0.370946i	−0.982649	+	0.185473i	$0.940618\pi$
$468$		0			0
$469$	−17.9198			−0.827459
$470$	16.1730	−	13.3713i	0.746007	−	0.616774i
$471$		0			0
$472$			28.4849i			1.31112i
$473$			7.97856i			0.366854i
$474$		0			0
$475$	−0.939849	+	4.91087i	−0.0431232	+	0.225326i
$476$	−6.26839			−0.287311
$477$		0			0
$478$		−	29.4630i		−	1.34761i
$479$	−4.00338			−0.182919			−0.0914596	−	0.995809i	$-0.529153\pi$
$479$	−4.00338			−0.182919			−0.0914596	+	0.995809i	$0.529153\pi$
$480$		0			0
$481$	−1.95279			−0.0890394
$482$		−	44.7451i		−	2.03808i
$483$		0			0
$484$	3.45124			0.156875
$485$	−10.9723	−	13.2713i	−0.498225	−	0.602618i
$486$		0			0
$487$		−	17.5299i		−	0.794358i	−0.917741	−	0.397179i	$-0.869989\pi$
$487$		−	17.5299i		−	0.794358i	0.917741	−	0.397179i	$-0.130011\pi$
$488$		−	14.1203i		−	0.639197i
$489$		0			0
$490$	−7.77101	−	9.39927i	−0.351059	−	0.424616i
$491$	−15.7747			−0.711901			−0.355951	−	0.934505i	$-0.615843\pi$
$491$	−15.7747			−0.711901			−0.355951	+	0.934505i	$0.615843\pi$
$492$		0			0
$493$		−	18.2422i		−	0.821586i
$494$	0.390437			0.0175666
$495$		0			0
$496$	−41.0602			−1.84366
$497$			17.9198i			0.803813i
$498$		0			0
$499$	−31.4231			−1.40669			−0.703347	−	0.710847i	$-0.748312\pi$
$499$	−31.4231			−1.40669			−0.703347	+	0.710847i	$0.748312\pi$
$500$	2.53862	+	4.62758i	0.113531	+	0.206952i
$501$		0			0
$502$			1.93212i			0.0862349i
$503$			15.7396i			0.701796i	0.936414	+	0.350898i	$0.114124\pi$
$503$			15.7396i			0.701796i	−0.936414	+	0.350898i	$0.885876\pi$
$504$		0			0
$505$	14.4985	−	11.9869i	0.645173	−	0.533408i
$506$	3.63271			0.161494
$507$		0			0
$508$		−	10.1767i		−	0.451518i
$509$	17.2396			0.764131			0.382066	−	0.924135i	$-0.375213\pi$
$509$	17.2396			0.764131			0.382066	+	0.924135i	$0.375213\pi$
$510$		0			0
$511$	−12.5737			−0.556227
$512$			10.3206i			0.456112i
$513$		0			0
$514$	8.75516			0.386173
$515$	13.7471	+	16.6276i	0.605772	+	0.732699i
$516$		0			0
$517$		−	11.4649i		−	0.504226i
$518$		−	23.2341i		−	1.02085i
$519$		0			0
$520$	−1.02806	+	0.849969i	−0.0450836	+	0.0372736i
$521$	28.3700			1.24291			0.621457	−	0.783448i	$-0.286541\pi$
$521$	28.3700			1.24291			0.621457	+	0.783448i	$0.286541\pi$
$522$		0			0
$523$		−	31.3645i		−	1.37148i	−0.727849	−	0.685738i	$-0.759480\pi$
$523$		−	31.3645i		−	1.37148i	0.727849	−	0.685738i	$-0.240520\pi$
$524$	−8.66313			−0.378451
$525$		0			0
$526$	−16.9579			−0.739401
$527$		−	61.4510i		−	2.67685i
$528$		0			0
$529$	21.5531			0.937093
$530$	19.2901	−	15.9484i	0.837910	−	0.692756i
$531$		0			0
$532$			0.887125i			0.0384618i
$533$			0.378913i			0.0164126i
$534$		0			0
$535$	−0.344439	−	0.416609i	−0.0148914	−	0.0180116i
$536$	22.9090			0.989517
$537$		0			0
$538$			35.9314i			1.54911i
$539$	−6.66305			−0.286998
$540$		0			0
$541$	−12.6888			−0.545536			−0.272768	−	0.962080i	$-0.587939\pi$
$541$	−12.6888			−0.545536			−0.272768	+	0.962080i	$0.587939\pi$
$542$			15.6508i			0.672258i
$543$		0			0
$544$	18.5033			0.793323
$545$	−5.26622	+	4.35394i	−0.225580	+	0.186502i
$546$		0			0
$547$		−	19.2634i		−	0.823644i	−0.911264	−	0.411822i	$-0.864893\pi$
$547$		−	19.2634i		−	0.823644i	0.911264	−	0.411822i	$-0.135107\pi$
$548$		−	4.54883i		−	0.194316i
$549$		0			0
$550$	14.8312	+	2.83841i	0.632403	+	0.121030i
$551$	−2.58170			−0.109984
$552$		0			0
$553$			0.654284i			0.0278230i
$554$	−22.6451			−0.962099
$555$		0			0
$556$	−7.06389			−0.299576
$557$			21.6253i			0.916294i	0.888877	+	0.458147i	$0.151487\pi$
$557$			21.6253i			0.916294i	−0.888877	+	0.458147i	$0.848513\pi$
$558$		0			0
$559$	−1.03147			−0.0436267
$560$	−12.6408	−	15.2895i	−0.534172	−	0.646097i
$561$		0			0
$562$			8.40051i			0.354354i
$563$			39.1301i			1.64914i	0.565761	+	0.824569i	$0.308582\pi$
$563$			39.1301i			1.64914i	−0.565761	+	0.824569i	$0.691418\pi$
$564$		0			0
$565$	23.6185	+	28.5673i	0.993640	+	1.20184i
$566$	−9.01027			−0.378730
$567$		0			0
$568$		−	22.9090i		−	0.961240i
$569$	10.5271			0.441320			0.220660	−	0.975351i	$-0.429179\pi$
$569$	10.5271			0.441320			0.220660	+	0.975351i	$0.429179\pi$
$570$		0			0
$571$	43.1731			1.80674			0.903368	−	0.428866i	$-0.141087\pi$
$571$	43.1731			1.80674			0.903368	+	0.428866i	$0.141087\pi$
$572$		−	0.225180i		−	0.00941527i
$573$		0			0
$574$	−4.50828			−0.188172
$575$	−5.90708	−	1.13050i	−0.246342	−	0.0471453i
$576$		0			0
$577$		−	13.8196i		−	0.575316i	−0.957733	−	0.287658i	$-0.907123\pi$
$577$		−	13.8196i		−	0.575316i	0.957733	−	0.287658i	$-0.0928767\pi$
$578$			51.7720i			2.15343i
$579$		0			0
$580$	−2.10042	+	1.73656i	−0.0872153	+	0.0721068i
$581$	−4.54195			−0.188432
$582$		0			0
$583$		−	13.6746i		−	0.566343i
$584$	16.0744			0.665164
$585$		0			0
$586$	43.2054			1.78480
$587$			16.3981i			0.676822i	0.940998	+	0.338411i	$0.109889\pi$
$587$			16.3981i			0.676822i	−0.940998	+	0.338411i	$0.890111\pi$
$588$		0			0
$589$	−8.69676			−0.358344
$590$	26.5628	+	32.1285i	1.09357	+	1.32271i
$591$		0			0
$592$			37.1278i			1.52594i
$593$		−	26.5182i		−	1.08897i	−0.838770	−	0.544485i	$-0.816725\pi$
$593$		−	26.5182i		−	1.08897i	0.838770	−	0.544485i	$-0.183275\pi$
$594$		0			0
$595$	22.8823	−	18.9184i	0.938084	−	0.775577i
$596$	−6.70674			−0.274719
$597$		0			0
$598$			0.469639i			0.0192050i
$599$	−7.85156			−0.320806			−0.160403	−	0.987052i	$-0.551279\pi$
$599$	−7.85156			−0.320806			−0.160403	+	0.987052i	$0.551279\pi$
$600$		0			0
$601$	−8.31507			−0.339179			−0.169589	−	0.985515i	$-0.554244\pi$
$601$	−8.31507			−0.339179			−0.169589	+	0.985515i	$0.554244\pi$
$602$		−	12.2724i		−	0.500185i
$603$		0			0
$604$	1.07076			0.0435688
$605$	−12.5985	+	10.4160i	−0.512203	+	0.423472i
$606$		0			0
$607$			26.6353i			1.08109i	0.841314	+	0.540546i	$0.181782\pi$
$607$			26.6353i			1.08109i	−0.841314	+	0.540546i	$0.818218\pi$
$608$		−	2.61865i		−	0.106200i
$609$		0			0
$610$	−13.1675	−	15.9265i	−0.533137	−	0.644845i
$611$	1.48219			0.0599631
$612$		0			0
$613$		−	38.7710i		−	1.56595i	−0.622056	−	0.782973i	$-0.713702\pi$
$613$		−	38.7710i		−	1.56595i	0.622056	−	0.782973i	$-0.286298\pi$
$614$	16.8284			0.679138
$615$		0			0
$616$	−8.67101			−0.349365
$617$		−	23.1535i		−	0.932125i	−0.884752	−	0.466063i	$-0.845672\pi$
$617$		−	23.1535i		−	0.932125i	0.884752	−	0.466063i	$-0.154328\pi$
$618$		0			0
$619$	−47.6444			−1.91499			−0.957495	−	0.288449i	$-0.906860\pi$
$619$	−47.6444			−1.91499			−0.957495	+	0.288449i	$0.906860\pi$
$620$	−7.07553	+	5.84982i	−0.284160	+	0.234934i
$621$		0			0
$622$		−	18.1141i		−	0.726310i
$623$		−	32.5866i		−	1.30556i
$624$		0			0
$625$	−23.2334	−	9.23096i	−0.929335	−	0.369239i
$626$	−28.5522			−1.14117
$627$		0			0
$628$			0.584852i			0.0233381i
$629$	−55.5658			−2.21555
$630$		0			0
$631$	29.4039			1.17055			0.585275	−	0.810835i	$-0.300987\pi$
$631$	29.4039			1.17055			0.585275	+	0.810835i	$0.300987\pi$
$632$		−	0.836449i		−	0.0332721i
$633$		0			0
$634$	30.9912			1.23082
$635$	30.7139	+	37.1494i	1.21884	+	1.47423i
$636$		0			0
$637$		−	0.861404i		−	0.0341301i
$638$			7.79690i			0.308682i
$639$		0			0
$640$	19.3920	+	23.4553i	0.766538	+	0.927151i
$641$	11.0401			0.436059			0.218029	−	0.975942i	$-0.430037\pi$
$641$	11.0401			0.436059			0.218029	+	0.975942i	$0.430037\pi$
$642$		0			0
$643$			19.6424i			0.774622i	0.921949	+	0.387311i	$0.126596\pi$
$643$			19.6424i			0.774622i	−0.921949	+	0.387311i	$0.873404\pi$
$644$	−1.06708			−0.0420490
$645$		0			0
$646$	11.1097			0.437107
$647$		−	32.7753i		−	1.28853i	−0.764803	−	0.644265i	$-0.777163\pi$
$647$		−	32.7753i		−	1.28853i	0.764803	−	0.644265i	$-0.222837\pi$
$648$		0			0
$649$	22.7756			0.894020
$650$	−0.366952	+	1.91738i	−0.0143930	+	0.0752060i
$651$		0			0
$652$		−	1.98163i		−	0.0776065i
$653$			10.5395i			0.412442i	0.978505	+	0.206221i	$0.0661167\pi$
$653$			10.5395i			0.412442i	−0.978505	+	0.206221i	$0.933883\pi$
$654$		0			0
$655$	31.6242	−	26.1458i	1.23566	−	1.02160i
$656$	7.20419			0.281276
$657$		0			0
$658$			17.6350i			0.687484i
$659$	29.1597			1.13590			0.567950	−	0.823063i	$-0.307737\pi$
$659$	29.1597			1.13590			0.567950	+	0.823063i	$0.307737\pi$
$660$		0			0
$661$	−48.4368			−1.88397			−0.941987	−	0.335649i	$-0.891044\pi$
$661$	−48.4368			−1.88397			−0.941987	+	0.335649i	$0.891044\pi$
$662$			2.96829i			0.115366i
$663$		0			0
$664$	5.80651			0.225336
$665$	−2.67739	−	3.23839i	−0.103825	−	0.125579i
$666$		0			0
$667$		−	3.10541i		−	0.120242i
$668$			7.83581i			0.303177i
$669$		0			0
$670$	25.8394	−	21.3632i	0.998262	−	0.825331i
$671$	−11.2901			−0.435851
$672$		0			0
$673$		−	0.819338i		−	0.0315831i	−0.999875	−	0.0157916i	$-0.994973\pi$
$673$		−	0.819338i		−	0.0315831i	0.999875	−	0.0157916i	$-0.00502682\pi$
$674$	22.0351			0.848762
$675$		0			0
$676$	−6.10811			−0.234927
$677$			3.76524i			0.144710i	0.997379	+	0.0723549i	$0.0230514\pi$
$677$			3.76524i			0.144710i	−0.997379	+	0.0723549i	$0.976949\pi$
$678$		0			0
$679$	14.4709			0.555343
$680$	−29.2532	+	24.1856i	−1.12181	+	0.927474i
$681$		0			0
$682$			26.2648i			1.00573i
$683$		−	36.9829i		−	1.41511i	−0.706657	−	0.707556i	$-0.749798\pi$
$683$		−	36.9829i		−	1.41511i	0.706657	−	0.707556i	$-0.250202\pi$
$684$		0			0
$685$	13.7286	+	16.6052i	0.524543	+	0.634451i
$686$	30.9306			1.18094
$687$		0			0
$688$			19.6112i			0.747669i
$689$	1.76786			0.0673501
$690$		0			0
$691$	10.0198			0.381171			0.190585	−	0.981671i	$-0.438961\pi$
$691$	10.0198			0.381171			0.190585	+	0.981671i	$0.438961\pi$
$692$			0.370573i			0.0140871i
$693$		0			0
$694$	1.65259			0.0627314
$695$	25.7862	−	21.3192i	0.978128	−	0.808684i
$696$		0			0
$697$			10.7818i			0.408391i
$698$			55.7585i			2.11049i
$699$		0			0
$700$	−4.35656	−	0.833764i	−0.164663	−	0.0315133i
$701$	15.6128			0.589688			0.294844	−	0.955545i	$-0.404732\pi$
$701$	15.6128			0.589688			0.294844	+	0.955545i	$0.404732\pi$
$702$		0			0
$703$			7.86387i			0.296592i
$704$	10.2290			0.385519
$705$		0			0
$706$	8.31302			0.312865
$707$			15.8090i			0.594560i
$708$		0			0
$709$	−11.5966			−0.435519			−0.217759	−	0.976002i	$-0.569875\pi$
$709$	−11.5966			−0.435519			−0.217759	+	0.976002i	$0.569875\pi$
$710$	−21.3632	−	25.8394i	−0.801745	−	0.969734i
$711$		0			0
$712$			41.6593i			1.56125i
$713$		−	10.4610i		−	0.391766i
$714$		0			0
$715$	0.679607	+	0.822006i	0.0254159	+	0.0307413i
$716$	10.9386			0.408794
$717$		0			0
$718$		−	25.1912i		−	0.940126i
$719$	−13.1532			−0.490532			−0.245266	−	0.969456i	$-0.578875\pi$
$719$	−13.1532			−0.490532			−0.245266	+	0.969456i	$0.578875\pi$
$720$		0			0
$721$	−18.1306			−0.675220
$722$		−	1.57229i		−	0.0585146i
$723$		0			0
$724$	−3.82945			−0.142320
$725$	2.42641	−	12.6784i	0.0901145	−	0.470864i
$726$		0			0
$727$			26.7258i			0.991203i	0.868550	+	0.495602i	$0.165052\pi$
$727$			26.7258i			0.991203i	−0.868550	+	0.495602i	$0.834948\pi$
$728$		−	1.12099i		−	0.0415468i
$729$		0			0
$730$	18.1306	−	14.9898i	0.671042	−	0.554796i
$731$	−29.3502			−1.08556
$732$		0			0
$733$			1.01889i			0.0376337i	0.999823	+	0.0188169i	$0.00598994\pi$
$733$			1.01889i			0.0376337i	−0.999823	+	0.0188169i	$0.994010\pi$
$734$	43.5584			1.60777
$735$		0			0
$736$	3.14987			0.116106
$737$		−	18.3173i		−	0.674725i
$738$		0			0
$739$	30.1705			1.10984			0.554920	−	0.831904i	$-0.312749\pi$
$739$	30.1705			1.10984			0.554920	+	0.831904i	$0.312749\pi$
$740$	5.28958	+	6.39791i	0.194449	+	0.235192i
$741$		0			0
$742$			21.0338i			0.772177i
$743$			8.28423i			0.303919i	0.988387	+	0.151959i	$0.0485583\pi$
$743$			8.28423i			0.303919i	−0.988387	+	0.151959i	$0.951442\pi$
$744$		0			0
$745$	24.4825	−	20.2413i	0.896968	−	0.741584i
$746$	−18.4795			−0.676581
$747$		0			0
$748$		−	6.40743i		−	0.234279i
$749$	0.454268			0.0165986
$750$		0			0
$751$	−3.74254			−0.136567			−0.0682836	−	0.997666i	$-0.521752\pi$
$751$	−3.74254			−0.136567			−0.0682836	+	0.997666i	$0.521752\pi$
$752$		−	28.1806i		−	1.02764i
$753$		0			0
$754$	−1.00799			−0.0367088
$755$	−3.90875	+	3.23163i	−0.142254	+	0.117611i
$756$		0			0
$757$		−	29.6308i		−	1.07695i	−0.842642	−	0.538475i	$-0.819001\pi$
$757$		−	29.6308i		−	1.07695i	0.842642	−	0.538475i	$-0.180999\pi$
$758$		−	11.0845i		−	0.402605i
$759$		0			0
$760$	3.42283	+	4.14001i	0.124159	+	0.150174i
$761$	43.2167			1.56660			0.783302	−	0.621642i	$-0.213534\pi$
$761$	43.2167			1.56660			0.783302	+	0.621642i	$0.213534\pi$
$762$		0			0
$763$		−	5.74226i		−	0.207884i
$764$	−9.78142			−0.353880
$765$		0			0
$766$	11.0325			0.398619
$767$			2.94445i			0.106318i
$768$		0			0
$769$	7.30244			0.263333			0.131666	−	0.991294i	$-0.457967\pi$
$769$	7.30244			0.263333			0.131666	+	0.991294i	$0.457967\pi$
$770$	−9.78015	+	8.08591i	−0.352452	+	0.291396i
$771$		0			0
$772$			1.75264i			0.0630791i
$773$			42.4163i			1.52561i	0.646630	+	0.762804i	$0.276178\pi$
$773$			42.4163i			1.52561i	−0.646630	+	0.762804i	$0.723822\pi$
$774$		0			0
$775$	8.17365	−	42.7087i	0.293606	−	1.53414i
$776$	−18.4999			−0.664107
$777$		0			0
$778$			60.0162i			2.15169i
$779$	1.52589			0.0546705
$780$		0			0
$781$	−18.3173			−0.655443
$782$			13.3634i			0.477875i
$783$		0			0
$784$	−16.3777			−0.584917
$785$	−1.76512	−	2.13496i	−0.0629997	−	0.0762000i
$786$		0			0
$787$			34.5998i			1.23335i	0.787218	+	0.616675i	$0.211521\pi$
$787$			34.5998i			1.23335i	−0.787218	+	0.616675i	$0.788479\pi$
$788$		−	3.68781i		−	0.131373i
$789$		0			0
$790$	−0.780008	−	0.943443i	−0.0277514	−	0.0335662i
$791$	−31.1497			−1.10755
$792$		0			0
$793$		−	1.45960i		−	0.0518319i
$794$	12.3401			0.437933
$795$		0			0
$796$	2.77344			0.0983021
$797$		−	31.9016i		−	1.13001i	−0.825087	−	0.565006i	$-0.808874\pi$
$797$		−	31.9016i		−	1.13001i	0.825087	−	0.565006i	$-0.191126\pi$
$798$		0			0
$799$	42.1752			1.49205
$800$	12.8599	+	2.46114i	0.454665	+	0.0870145i
$801$		0			0
$802$			1.38248i			0.0488170i
$803$		−	12.8526i		−	0.453557i
$804$		0			0
$805$	3.89532	−	3.22052i	0.137292	−	0.113508i
$806$	−3.39553			−0.119603
$807$		0			0
$808$		−	20.2106i		−	0.711005i
$809$	7.96516			0.280040			0.140020	−	0.990149i	$-0.455283\pi$
$809$	7.96516			0.280040			0.140020	+	0.990149i	$0.455283\pi$
$810$		0			0
$811$	−8.45805			−0.297002			−0.148501	−	0.988912i	$-0.547445\pi$
$811$	−8.45805			−0.297002			−0.148501	+	0.988912i	$0.547445\pi$
$812$		−	2.29029i		−	0.0803734i
$813$		0			0
$814$	23.7494			0.832417
$815$	5.98066	+	7.23379i	0.209493	+	0.253389i
$816$		0			0
$817$			4.15375i			0.145321i
$818$			61.0289i			2.13383i
$819$		0			0
$820$	1.24143	−	1.02638i	0.0433527	−	0.0358426i
$821$	−29.8649			−1.04229			−0.521147	−	0.853467i	$-0.674496\pi$
$821$	−29.8649			−1.04229			−0.521147	+	0.853467i	$0.674496\pi$
$822$		0			0
$823$			29.4632i			1.02702i	0.858083	+	0.513512i	$0.171656\pi$
$823$			29.4632i			1.02702i	−0.858083	+	0.513512i	$0.828344\pi$
$824$	23.1785			0.807462
$825$		0			0
$826$	−35.0328			−1.21895
$827$		−	35.7491i		−	1.24312i	−0.783368	−	0.621558i	$-0.786500\pi$
$827$		−	35.7491i		−	1.24312i	0.783368	−	0.621558i	$-0.213500\pi$
$828$		0			0
$829$	−30.6073			−1.06303			−0.531517	−	0.847047i	$-0.678378\pi$
$829$	−30.6073			−1.06303			−0.531517	+	0.847047i	$0.678378\pi$
$830$	6.54924	−	5.41470i	0.227328	−	0.187947i
$831$		0			0
$832$			1.32241i			0.0458463i
$833$		−	24.5110i		−	0.849254i
$834$		0			0
$835$	−23.6489	−	28.6041i	−0.818405	−	0.989885i
$836$	−0.906802			−0.0313624
$837$		0			0
$838$			49.0944i			1.69594i
$839$	20.2431			0.698868			0.349434	−	0.936961i	$-0.386374\pi$
$839$	20.2431			0.698868			0.349434	+	0.936961i	$0.386374\pi$
$840$		0			0
$841$	−22.3348			−0.770167
$842$			7.02662i			0.242153i
$843$		0			0
$844$	4.62299			0.159130
$845$	22.2972	−	18.4346i	0.767048	−	0.634171i
$846$		0			0
$847$		−	13.7374i		−	0.472021i
$848$		−	33.6119i		−	1.15424i
$849$		0			0
$850$	−10.4415	+	54.5585i	−0.358140	+	1.87134i
$851$	−9.45911			−0.324254
$852$		0			0
$853$			36.5320i			1.25083i	0.780292	+	0.625415i	$0.215070\pi$
$853$			36.5320i			1.25083i	−0.780292	+	0.625415i	$0.784930\pi$
$854$	17.3662			0.594258
$855$		0			0
$856$	−0.580745			−0.0198495
$857$			22.5292i			0.769584i	0.923003	+	0.384792i	$0.125727\pi$
$857$			22.5292i			0.769584i	−0.923003	+	0.384792i	$0.874273\pi$
$858$		0			0
$859$	−4.59482			−0.156773			−0.0783866	−	0.996923i	$-0.524977\pi$
$859$	−4.59482			−0.156773			−0.0783866	+	0.996923i	$0.524977\pi$
$860$	2.79399	+	3.37942i	0.0952743	+	0.115237i
$861$		0			0
$862$			41.0044i			1.39662i
$863$			11.5034i			0.391579i	0.980646	+	0.195789i	$0.0627269\pi$
$863$			11.5034i			0.391579i	−0.980646	+	0.195789i	$0.937273\pi$
$864$		0			0
$865$	−1.11841	−	1.35275i	−0.0380271	−	0.0459949i
$866$	24.2446			0.823866
$867$		0			0
$868$		−	7.71512i		−	0.261868i
$869$	−0.668797			−0.0226874
$870$		0			0
$871$	2.36807			0.0802390
$872$			7.34101i			0.248598i
$873$		0			0
$874$	1.89124			0.0639721
$875$	18.4197	−	10.1047i	0.622698	−	0.341603i
$876$		0			0
$877$		−	9.18451i		−	0.310139i	−0.987904	−	0.155069i	$-0.950440\pi$
$877$		−	9.18451i		−	0.310139i	0.987904	−	0.155069i	$-0.0495601\pi$
$878$		−	41.0880i		−	1.38665i
$879$		0			0
$880$	15.6286	−	12.9212i	0.526840	−	0.435574i
$881$	−46.8437			−1.57821			−0.789103	−	0.614261i	$-0.789454\pi$
$881$	−46.8437			−1.57821			−0.789103	+	0.614261i	$0.789454\pi$
$882$		0			0
$883$		−	29.8269i		−	1.00375i	−0.864939	−	0.501877i	$-0.832643\pi$
$883$		−	29.8269i		−	1.00375i	0.864939	−	0.501877i	$-0.167357\pi$
$884$	0.828357			0.0278607
$885$		0			0
$886$	−29.5096			−0.991395
$887$		−	20.4681i		−	0.687252i	−0.939107	−	0.343626i	$-0.888345\pi$
$887$		−	20.4681i		−	0.687252i	0.939107	−	0.343626i	$-0.111655\pi$
$888$		0			0
$889$	−40.5075			−1.35858
$890$	38.8483	+	46.9881i	1.30220	+	1.57505i
$891$		0			0
$892$			9.64615i			0.322977i
$893$		−	5.96879i		−	0.199738i
$894$		0			0
$895$	−39.9306	+	33.0133i	−1.33473	+	1.10351i
$896$	−25.5755			−0.854417
$897$		0			0
$898$		−	29.0996i		−	0.971068i
$899$	22.4524			0.748830
$900$		0			0
$901$	50.3038			1.67586
$902$		−	4.60828i		−	0.153439i
$903$		0			0
$904$	39.8223			1.32447
$905$	13.9791	−	11.5575i	0.464682	−	0.384184i
$906$		0			0
$907$		−	16.6266i		−	0.552076i	−0.961147	−	0.276038i	$-0.910978\pi$
$907$		−	16.6266i		−	0.552076i	0.961147	−	0.276038i	$-0.0890215\pi$
$908$		−	4.76490i		−	0.158129i
$909$		0			0
$910$	−1.04535	−	1.26439i	−0.0346531	−	0.0419140i
$911$	40.6554			1.34697			0.673487	−	0.739199i	$-0.264796\pi$
$911$	40.6554			1.34697			0.673487	+	0.739199i	$0.264796\pi$
$912$		0			0
$913$		−	4.64269i		−	0.153651i
$914$	−56.1549			−1.85744
$915$		0			0
$916$	−6.87544			−0.227171
$917$			34.4828i			1.13872i
$918$		0			0
$919$	−23.9633			−0.790477			−0.395238	−	0.918579i	$-0.629338\pi$
$919$	−23.9633			−0.790477			−0.395238	+	0.918579i	$0.629338\pi$
$920$	−4.97984	+	4.11717i	−0.164181	+	0.135739i
$921$		0			0
$922$		−	48.3930i		−	1.59374i
$923$		−	2.36807i		−	0.0779460i
$924$		0			0
$925$	−38.6185	−	7.39086i	−1.26977	−	0.243010i
$926$	−49.0252			−1.61107
$927$		0			0
$928$			6.76057i			0.221927i
$929$	−17.6807			−0.580085			−0.290043	−	0.957014i	$-0.593669\pi$
$929$	−17.6807			−0.580085			−0.290043	+	0.957014i	$0.593669\pi$
$930$		0			0
$931$	−3.46888			−0.113688
$932$			12.2235i			0.400395i
$933$		0			0
$934$	12.6038			0.412409
$935$	19.3380	+	23.3899i	0.632420	+	0.764931i
$936$		0			0
$937$			45.8986i			1.49944i	0.661754	+	0.749721i	$0.269812\pi$
$937$			45.8986i			1.49944i	−0.661754	+	0.749721i	$0.730188\pi$
$938$			28.1751i			0.919950i
$939$		0			0
$940$	−4.01487	−	4.85610i	−0.130951	−	0.158389i
$941$	−7.89440			−0.257350			−0.128675	−	0.991687i	$-0.541072\pi$
$941$	−7.89440			−0.257350			−0.128675	+	0.991687i	$0.541072\pi$
$942$		0			0
$943$			1.83542i			0.0597695i
$944$	55.9820			1.82206
$945$		0			0
$946$	12.5446			0.407860
$947$			51.7953i			1.68312i	0.540162	+	0.841561i	$0.318363\pi$
$947$			51.7953i			1.68312i	−0.540162	+	0.841561i	$0.681637\pi$
$948$		0			0
$949$	1.66159			0.0539375
$950$	7.72132	+	1.47772i	0.250513	+	0.0479434i
$951$		0			0
$952$		−	31.8975i		−	1.03380i
$953$		−	11.5807i		−	0.375137i	−0.982252	−	0.187568i	$-0.939939\pi$
$953$		−	11.5807i		−	0.375137i	0.982252	−	0.187568i	$-0.0600606\pi$
$954$		0			0
$955$	35.7064	−	29.5209i	1.15543	−	0.955274i
$956$	−8.84655			−0.286118
$957$		0			0
$958$			6.29447i			0.203365i
$959$	−18.1062			−0.584679
$960$		0			0
$961$	44.6337			1.43980
$962$			3.07034i			0.0989919i
$963$		0			0
$964$	−13.4351			−0.432716
$965$	−5.28958	−	6.39791i	−0.170278	−	0.205956i
$966$		0			0
$967$			60.5547i			1.94731i	0.228032	+	0.973654i	$0.426771\pi$
$967$			60.5547i			1.94731i	−0.228032	+	0.973654i	$0.573229\pi$
$968$			17.5621i			0.564467i
$969$		0			0
$970$	−20.8663	+	17.2516i	−0.669976	+	0.553915i
$971$	4.19412			0.134596			0.0672978	−	0.997733i	$-0.478562\pi$
$971$	4.19412			0.134596			0.0672978	+	0.997733i	$0.478562\pi$
$972$		0			0
$973$			28.1172i			0.901395i
$974$	−27.5621			−0.883148
$975$		0			0
$976$	−27.7510			−0.888287
$977$			12.7754i			0.408720i	0.978896	+	0.204360i	$0.0655114\pi$
$977$			12.7754i			0.408720i	−0.978896	+	0.204360i	$0.934489\pi$
$978$		0			0
$979$	33.3094			1.06457
$980$	−2.82222	+	2.33332i	−0.0901524	+	0.0745351i
$981$		0			0
$982$			24.8024i			0.791475i
$983$			35.8198i			1.14247i	0.820785	+	0.571237i	$0.193536\pi$
$983$			35.8198i			1.14247i	−0.820785	+	0.571237i	$0.806464\pi$
$984$		0			0
$985$	11.1300	+	13.4621i	0.354632	+	0.428938i
$986$	−28.6820			−0.913420
$987$		0			0
$988$		−	0.117232i		−	0.00372965i
$989$	−4.99636			−0.158875
$990$		0			0
$991$	−19.1653			−0.608807			−0.304404	−	0.952543i	$-0.598457\pi$
$991$	−19.1653			−0.608807			−0.304404	+	0.952543i	$0.598457\pi$
$992$			22.7738i			0.723069i
$993$		0			0
$994$	28.1751			0.893660
$995$	−10.1243	+	8.37041i	−0.320961	+	0.265360i
$996$		0			0
$997$			9.88660i			0.313112i	0.987669	+	0.156556i	$0.0500391\pi$
$997$			9.88660i			0.313112i	−0.987669	+	0.156556i	$0.949961\pi$
$998$			49.4063i			1.56393i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.c.g.514.5		14
3.2	odd	2		285.2.c.b.229.10	yes	14
5.2	odd	4		4275.2.a.bw.1.5		7
5.3	odd	4		4275.2.a.bv.1.3		7
5.4	even	2	inner	855.2.c.g.514.10		14
15.2	even	4		1425.2.a.y.1.3		7
15.8	even	4		1425.2.a.z.1.5		7
15.14	odd	2		285.2.c.b.229.5	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.c.b.229.5	✓	14	15.14	odd	2
285.2.c.b.229.10	yes	14	3.2	odd	2
855.2.c.g.514.5		14	1.1	even	1	trivial
855.2.c.g.514.10		14	5.4	even	2	inner
1425.2.a.y.1.3		7	15.2	even	4
1425.2.a.z.1.5		7	15.8	even	4
4275.2.a.bv.1.3		7	5.3	odd	4
4275.2.a.bw.1.5		7	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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.57229i q^{2} -0.472094 q^{4} +(1.72335 - 1.42481i) q^{5} +1.87913i q^{7} -2.40231i q^{8} +(-2.24021 - 2.70960i) q^{10} -1.92081 q^{11} -0.248324i q^{13} +2.95453 q^{14} -4.72132 q^{16} -7.06596i q^{17} -1.00000 q^{19} +(-0.813582 + 0.672643i) q^{20} +3.02007i q^{22} -1.20286i q^{23} +(0.939849 - 4.91087i) q^{25} -0.390437 q^{26} -0.887125i q^{28} +2.58170 q^{29} +8.69676 q^{31} +2.61865i q^{32} -11.1097 q^{34} +(2.67739 + 3.23839i) q^{35} -7.86387i q^{37} +1.57229i q^{38} +(-3.42283 - 4.14001i) q^{40} -1.52589 q^{41} -4.15375i q^{43} +0.906802 q^{44} -1.89124 q^{46} +5.96879i q^{47} +3.46888 q^{49} +(-7.72132 - 1.47772i) q^{50} +0.117232i q^{52} +7.11918i q^{53} +(-3.31022 + 2.73678i) q^{55} +4.51425 q^{56} -4.05918i q^{58} -11.8573 q^{59} +5.87781 q^{61} -13.6738i q^{62} -5.32535 q^{64} +(-0.353813 - 0.427948i) q^{65} +9.53623i q^{67} +3.33580i q^{68} +(5.09169 - 4.20964i) q^{70} +9.53623 q^{71} +6.69123i q^{73} -12.3643 q^{74} +0.472094 q^{76} -3.60944i q^{77} +0.348185 q^{79} +(-8.13646 + 6.72696i) q^{80} +2.39913i q^{82} +2.41705i q^{83} +(-10.0676 - 12.1771i) q^{85} -6.53090 q^{86} +4.61438i q^{88} -17.3414 q^{89} +0.466632 q^{91} +0.567862i q^{92} +9.38467 q^{94} +(-1.72335 + 1.42481i) q^{95} -7.70088i q^{97} -5.45408i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 22 q^{4} - 2 q^{5} + 2 q^{10} + 8 q^{11} - 8 q^{14} + 38 q^{16} - 14 q^{19} - 12 q^{20} - 4 q^{25} + 40 q^{26} - 12 q^{29} + 8 q^{31} - 4 q^{34} + 14 q^{35} + 18 q^{40} - 4 q^{41} - 64 q^{44} - 8 q^{46}+ \cdots + 2 q^{95}+O(q^{100}) \) 14 * q - 22 * q^4 - 2 * q^5 + 2 * q^10 + 8 * q^11 - 8 * q^14 + 38 * q^16 - 14 * q^19 - 12 * q^20 - 4 * q^25 + 40 * q^26 - 12 * q^29 + 8 * q^31 - 4 * q^34 + 14 * q^35 + 18 * q^40 - 4 * q^41 - 64 * q^44 - 8 * q^46 - 34 * q^49 - 4 * q^50 - 2 * q^55 + 44 * q^56 - 36 * q^59 + 24 * q^61 - 22 * q^64 + 12 * q^65 - 60 * q^70 + 36 * q^71 + 12 * q^74 + 22 * q^76 + 8 * q^79 - 36 * q^80 - 18 * q^85 + 92 * q^86 - 16 * q^89 + 24 * q^91 + 40 * q^94 + 2 * q^95

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