LMFDB - Embedded newform 855.2.c.g.514.9

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			514.9
Root			$0.498112i$ of defining polynomial
Character	$\chi$	$=$	855.514
Dual form			855.2.c.g.514.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.498112i q^{2} +1.75188 q^{4} +(-0.192457 - 2.22777i) q^{5} -4.62756i q^{7} +1.86886i q^{8} +(1.10968 - 0.0958652i) q^{10} -4.13949 q^{11} +2.39138i q^{13} +2.30504 q^{14} +2.57287 q^{16} -7.34369i q^{17} -1.00000 q^{19} +(-0.337163 - 3.90280i) q^{20} -2.06193i q^{22} +2.69642i q^{23} +(-4.92592 + 0.857501i) q^{25} -1.19117 q^{26} -8.10695i q^{28} +0.979369 q^{29} -5.10751 q^{31} +5.01929i q^{32} +3.65798 q^{34} +(-10.3091 + 0.890607i) q^{35} -9.85293i q^{37} -0.498112i q^{38} +(4.16339 - 0.359675i) q^{40} +4.52440 q^{41} +3.43961i q^{43} -7.25190 q^{44} -1.34312 q^{46} +5.09235i q^{47} -14.4143 q^{49} +(-0.427131 - 2.45366i) q^{50} +4.18942i q^{52} -3.36319i q^{53} +(0.796674 + 9.22182i) q^{55} +8.64825 q^{56} +0.487835i q^{58} +13.4994 q^{59} +6.64096 q^{61} -2.54411i q^{62} +2.64557 q^{64} +(5.32744 - 0.460238i) q^{65} -7.28441i q^{67} -12.8653i q^{68} +(-0.443622 - 5.13511i) q^{70} +7.28441 q^{71} -3.82343i q^{73} +4.90786 q^{74} -1.75188 q^{76} +19.1557i q^{77} +16.1586 q^{79} +(-0.495167 - 5.73176i) q^{80} +2.25366i q^{82} -3.92122i q^{83} +(-16.3601 + 1.41335i) q^{85} -1.71331 q^{86} -7.73611i q^{88} +2.34446 q^{89} +11.0662 q^{91} +4.72382i q^{92} -2.53656 q^{94} +(0.192457 + 2.22777i) q^{95} +2.34256i q^{97} -7.17994i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			0.498112i			0.352218i	0.984371	+	0.176109i	$0.0563512\pi$
$2$			0.498112i			0.352218i	−0.984371	+	0.176109i	$0.943649\pi$
$3$		0			0
$3$		0			0
$4$	1.75188			0.875942
$5$	−0.192457	−	2.22777i	−0.0860695	−	0.996289i
$5$	−0.192457	−	2.22777i	−0.0860695	−	0.996289i
$6$		0			0
$7$		−	4.62756i		−	1.74905i	−0.484977	−	0.874527i	$-0.661172\pi$
$7$		−	4.62756i		−	1.74905i	0.484977	−	0.874527i	$-0.338828\pi$
$8$			1.86886i			0.660741i
$9$		0			0
$10$	1.10968	−	0.0958652i	0.350911	−	0.0303152i
$11$	−4.13949			−1.24810			−0.624051	−	0.781384i	$-0.714514\pi$
$11$	−4.13949			−1.24810			−0.624051	+	0.781384i	$0.714514\pi$
$12$		0			0
$13$			2.39138i			0.663249i	0.943411	+	0.331624i	$0.107597\pi$
$13$			2.39138i			0.663249i	−0.943411	+	0.331624i	$0.892403\pi$
$14$	2.30504			0.616049
$15$		0			0
$16$	2.57287			0.643217
$17$		−	7.34369i		−	1.78111i	−0.454879	−	0.890553i	$-0.650317\pi$
$17$		−	7.34369i		−	1.78111i	0.454879	−	0.890553i	$-0.349683\pi$
$18$		0			0
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	−0.337163	−	3.90280i	−0.0753919	−	0.872692i
$21$		0			0
$22$		−	2.06193i		−	0.439604i
$23$			2.69642i			0.562243i	0.959672	+	0.281121i	$0.0907063\pi$
$23$			2.69642i			0.562243i	−0.959672	+	0.281121i	$0.909294\pi$
$24$		0			0
$25$	−4.92592	+	0.857501i	−0.985184	+	0.171500i
$26$	−1.19117			−0.233608
$27$		0			0
$28$		−	8.10695i		−	1.53207i
$29$	0.979369			0.181864			0.0909321	−	0.995857i	$-0.471015\pi$
$29$	0.979369			0.181864			0.0909321	+	0.995857i	$0.471015\pi$
$30$		0			0
$31$	−5.10751			−0.917336			−0.458668	−	0.888608i	$-0.651673\pi$
$31$	−5.10751			−0.917336			−0.458668	+	0.888608i	$0.651673\pi$
$32$			5.01929i			0.887294i
$33$		0			0
$34$	3.65798			0.627338
$35$	−10.3091	+	0.890607i	−1.74256	+	0.150540i
$36$		0			0
$37$		−	9.85293i		−	1.61981i	−0.586560	−	0.809906i	$-0.699518\pi$
$37$		−	9.85293i		−	1.61981i	0.586560	−	0.809906i	$-0.300482\pi$
$38$		−	0.498112i		−	0.0808044i
$39$		0			0
$40$	4.16339	−	0.359675i	0.658289	−	0.0568697i
$41$	4.52440			0.706593			0.353296	−	0.935511i	$-0.385061\pi$
$41$	4.52440			0.706593			0.353296	+	0.935511i	$0.385061\pi$
$42$		0			0
$43$			3.43961i			0.524535i	0.964995	+	0.262268i	$0.0844703\pi$
$43$			3.43961i			0.524535i	−0.964995	+	0.262268i	$0.915530\pi$
$44$	−7.25190			−1.09327
$45$		0			0
$46$	−1.34312			−0.198032
$47$			5.09235i			0.742795i	0.928474	+	0.371398i	$0.121121\pi$
$47$			5.09235i			0.742795i	−0.928474	+	0.371398i	$0.878879\pi$
$48$		0			0
$49$	−14.4143			−2.05919
$50$	−0.427131	−	2.45366i	−0.0604055	−	0.347000i
$51$		0			0
$52$			4.18942i			0.580968i
$53$		−	3.36319i		−	0.461970i	−0.972957	−	0.230985i	$-0.925805\pi$
$53$		−	3.36319i		−	0.461970i	0.972957	−	0.230985i	$-0.0741949\pi$
$54$		0			0
$55$	0.796674	+	9.22182i	0.107423	+	1.24347i
$56$	8.64825			1.15567
$57$		0			0
$58$			0.487835i			0.0640559i
$59$	13.4994			1.75748			0.878738	−	0.477304i	$-0.158386\pi$
$59$	13.4994			1.75748			0.878738	+	0.477304i	$0.158386\pi$
$60$		0			0
$61$	6.64096			0.850287			0.425144	−	0.905126i	$-0.360224\pi$
$61$	6.64096			0.850287			0.425144	+	0.905126i	$0.360224\pi$
$62$		−	2.54411i		−	0.323102i
$63$		0			0
$64$	2.64557			0.330696
$65$	5.32744	−	0.460238i	0.660788	−	0.0570855i
$66$		0			0
$67$		−	7.28441i		−	0.889933i	−0.895547	−	0.444966i	$-0.853216\pi$
$67$		−	7.28441i		−	0.889933i	0.895547	−	0.444966i	$-0.146784\pi$
$68$		−	12.8653i		−	1.56015i
$69$		0			0
$70$	−0.443622	−	5.13511i	−0.0530230	−	0.613763i
$71$	7.28441			0.864501			0.432250	−	0.901754i	$-0.357720\pi$
$71$	7.28441			0.864501			0.432250	+	0.901754i	$0.357720\pi$
$72$		0			0
$73$		−	3.82343i		−	0.447499i	−0.974647	−	0.223749i	$-0.928170\pi$
$73$		−	3.82343i		−	0.447499i	0.974647	−	0.223749i	$-0.0718297\pi$
$74$	4.90786			0.570527
$75$		0			0
$76$	−1.75188			−0.200955
$77$			19.1557i			2.18300i
$78$		0			0
$79$	16.1586			1.81799			0.908995	−	0.416807i	$-0.136851\pi$
$79$	16.1586			1.81799			0.908995	+	0.416807i	$0.136851\pi$
$80$	−0.495167	−	5.73176i	−0.0553614	−	0.640830i
$81$		0			0
$82$			2.25366i			0.248875i
$83$		−	3.92122i		−	0.430410i	−0.976569	−	0.215205i	$-0.930958\pi$
$83$		−	3.92122i		−	0.430410i	0.976569	−	0.215205i	$-0.0690419\pi$
$84$		0			0
$85$	−16.3601	+	1.41335i	−1.77450	+	0.153299i
$86$	−1.71331			−0.184751
$87$		0			0
$88$		−	7.73611i		−	0.824672i
$89$	2.34446			0.248513			0.124256	−	0.992250i	$-0.460345\pi$
$89$	2.34446			0.248513			0.124256	+	0.992250i	$0.460345\pi$
$90$		0			0
$91$	11.0662			1.16006
$92$			4.72382i			0.492492i
$93$		0			0
$94$	−2.53656			−0.261626
$95$	0.192457	+	2.22777i	0.0197457	+	0.228564i
$96$		0			0
$97$			2.34256i			0.237851i	0.992903	+	0.118926i	$0.0379450\pi$
$97$			2.34256i			0.237851i	−0.992903	+	0.118926i	$0.962055\pi$
$98$		−	7.17994i		−	0.725284i
$99$		0			0
$100$	−8.62964	+	1.50224i	−0.862964	+	0.150224i
$101$	7.44953			0.741256			0.370628	−	0.928781i	$-0.379143\pi$
$101$	7.44953			0.741256			0.370628	+	0.928781i	$0.379143\pi$
$102$		0			0
$103$			8.17714i			0.805718i	0.915262	+	0.402859i	$0.131983\pi$
$103$			8.17714i			0.805718i	−0.915262	+	0.402859i	$0.868017\pi$
$104$	−4.46915			−0.438236
$105$		0			0
$106$	1.67525			0.162714
$107$		−	5.25512i		−	0.508032i	−0.967200	−	0.254016i	$-0.918248\pi$
$107$		−	5.25512i		−	0.508032i	0.967200	−	0.254016i	$-0.0817516\pi$
$108$		0			0
$109$	−7.50377			−0.718731			−0.359365	−	0.933197i	$-0.617007\pi$
$109$	−7.50377			−0.718731			−0.359365	+	0.933197i	$0.617007\pi$
$110$	−4.59350	+	0.396833i	−0.437973	+	0.0378365i
$111$		0			0
$112$		−	11.9061i		−	1.12502i
$113$		−	3.70723i		−	0.348747i	−0.984680	−	0.174374i	$-0.944210\pi$
$113$		−	3.70723i		−	0.348747i	0.984680	−	0.174374i	$-0.0557901\pi$
$114$		0			0
$115$	6.00701	−	0.518946i	0.560156	−	0.0483919i
$116$	1.71574			0.159303
$117$		0			0
$118$			6.72423i			0.619015i
$119$	−33.9834			−3.11525
$120$		0			0
$121$	6.13535			0.557759
$122$			3.30794i			0.299487i
$123$		0			0
$124$	−8.94777			−0.803533
$125$	2.85834	+	10.8088i	0.255658	+	0.966767i
$126$		0			0
$127$			18.4105i			1.63367i	0.576872	+	0.816834i	$0.304273\pi$
$127$			18.4105i			1.63367i	−0.576872	+	0.816834i	$0.695727\pi$
$128$			11.3564i			1.00377i
$129$		0			0
$130$	0.229250	+	2.65366i	0.0201066	+	0.232741i
$131$	10.6541			0.930850			0.465425	−	0.885087i	$-0.345901\pi$
$131$	10.6541			0.930850			0.465425	+	0.885087i	$0.345901\pi$
$132$		0			0
$133$			4.62756i			0.401260i
$134$	3.62845			0.313451
$135$		0			0
$136$	13.7243			1.17685
$137$		−	2.31966i		−	0.198182i	−0.995078	−	0.0990911i	$-0.968406\pi$
$137$		−	2.31966i		−	0.198182i	0.995078	−	0.0990911i	$-0.0315935\pi$
$138$		0			0
$139$	15.8160			1.34149			0.670746	−	0.741687i	$-0.265974\pi$
$139$	15.8160			1.34149			0.670746	+	0.741687i	$0.265974\pi$
$140$	−18.0604	+	1.56024i	−1.52638	+	0.131864i
$141$		0			0
$142$			3.62845i			0.304493i
$143$		−	9.89908i		−	0.827802i
$144$		0			0
$145$	−0.188487	−	2.18181i	−0.0156530	−	0.181189i
$146$	1.90450			0.157617
$147$		0			0
$148$		−	17.2612i		−	1.41886i
$149$	−7.70875			−0.631525			−0.315763	−	0.948838i	$-0.602260\pi$
$149$	−7.70875			−0.631525			−0.315763	+	0.948838i	$0.602260\pi$
$150$		0			0
$151$	−19.2214			−1.56421			−0.782106	−	0.623145i	$-0.785855\pi$
$151$	−19.2214			−1.56421			−0.782106	+	0.623145i	$0.785855\pi$
$152$		−	1.86886i		−	0.151584i
$153$		0			0
$154$	−9.54169			−0.768892
$155$	0.982977	+	11.3784i	0.0789546	+	0.913932i
$156$		0			0
$157$		−	13.6082i		−	1.08605i	−0.839716	−	0.543025i	$-0.817279\pi$
$157$		−	13.6082i		−	1.08605i	0.839716	−	0.543025i	$-0.182721\pi$
$158$			8.04882i			0.640329i
$159$		0			0
$160$	11.1818	−	0.965999i	0.884001	−	0.0763689i
$161$	12.4779			0.983392
$162$		0			0
$163$		−	3.12532i		−	0.244794i	−0.992481	−	0.122397i	$-0.960942\pi$
$163$		−	3.12532i		−	0.244794i	0.992481	−	0.122397i	$-0.0390581\pi$
$164$	7.92623			0.618934
$165$		0			0
$166$	1.95321			0.151598
$167$			2.86858i			0.221977i	0.993822	+	0.110989i	$0.0354017\pi$
$167$			2.86858i			0.221977i	−0.993822	+	0.110989i	$0.964598\pi$
$168$		0			0
$169$	7.28131			0.560101
$170$	−0.704005	−	8.14914i	−0.0539947	−	0.625010i
$171$		0			0
$172$			6.02579i			0.459462i
$173$			4.85404i			0.369046i	0.982828	+	0.184523i	$0.0590739\pi$
$173$			4.85404i			0.369046i	−0.982828	+	0.184523i	$0.940926\pi$
$174$		0			0
$175$	3.96814	+	22.7950i	0.299963	+	1.72314i
$176$	−10.6504			−0.802801
$177$		0			0
$178$			1.16781i			0.0875307i
$179$	−16.7731			−1.25368			−0.626839	−	0.779149i	$-0.715652\pi$
$179$	−16.7731			−1.25368			−0.626839	+	0.779149i	$0.715652\pi$
$180$		0			0
$181$	17.0075			1.26416			0.632080	−	0.774903i	$-0.282201\pi$
$181$	17.0075			1.26416			0.632080	+	0.774903i	$0.282201\pi$
$182$			5.51223i			0.408594i
$183$		0			0
$184$	−5.03923			−0.371497
$185$	−21.9501	+	1.89627i	−1.61380	+	0.139416i
$186$		0			0
$187$			30.3991i			2.22300i
$188$			8.92120i			0.650646i
$189$		0			0
$190$	−1.10968	+	0.0958652i	−0.0805046	+	0.00695479i
$191$	−2.57283			−0.186163			−0.0930816	−	0.995658i	$-0.529672\pi$
$191$	−2.57283			−0.186163			−0.0930816	+	0.995658i	$0.529672\pi$
$192$		0			0
$193$			17.2612i			1.24249i	0.783617	+	0.621244i	$0.213372\pi$
$193$			17.2612i			1.24249i	−0.783617	+	0.621244i	$0.786628\pi$
$194$	−1.16686			−0.0837755
$195$		0			0
$196$	−25.2522			−1.80373
$197$		−	18.5625i		−	1.32252i	−0.750156	−	0.661260i	$-0.770022\pi$
$197$		−	18.5625i		−	1.32252i	0.750156	−	0.661260i	$-0.229978\pi$
$198$		0			0
$199$	4.24470			0.300899			0.150449	−	0.988618i	$-0.451928\pi$
$199$	4.24470			0.300899			0.150449	+	0.988618i	$0.451928\pi$
$200$	−1.60255	−	9.20585i	−0.113317	−	0.650952i
$201$		0			0
$202$			3.71070i			0.261084i
$203$		−	4.53209i		−	0.318090i
$204$		0			0
$205$	−0.870754	−	10.0793i	−0.0608161	−	0.703971i
$206$	−4.07313			−0.283788
$207$		0			0
$208$			6.15270i			0.426613i
$209$	4.13949			0.286334
$210$		0			0
$211$	−1.20969			−0.0832786			−0.0416393	−	0.999133i	$-0.513258\pi$
$211$	−1.20969			−0.0832786			−0.0416393	+	0.999133i	$0.513258\pi$
$212$		−	5.89193i		−	0.404659i
$213$		0			0
$214$	2.61764			0.178938
$215$	7.66265	−	0.661977i	0.522589	−	0.0451465i
$216$		0			0
$217$			23.6353i			1.60447i
$218$		−	3.73772i		−	0.253150i
$219$		0			0
$220$	1.39568	+	16.1556i	0.0940968	+	1.08921i
$221$	17.5615			1.18132
$222$		0			0
$223$			6.22370i			0.416770i	0.978047	+	0.208385i	$0.0668206\pi$
$223$			6.22370i			0.416770i	−0.978047	+	0.208385i	$0.933179\pi$
$224$	23.2271			1.55192
$225$		0			0
$226$	1.84662			0.122835
$227$			24.8143i			1.64698i	0.567328	+	0.823492i	$0.307977\pi$
$227$			24.8143i			1.64698i	−0.567328	+	0.823492i	$0.692023\pi$
$228$		0			0
$229$	−0.919180			−0.0607411			−0.0303706	−	0.999539i	$-0.509669\pi$
$229$	−0.919180			−0.0607411			−0.0303706	+	0.999539i	$0.509669\pi$
$230$	0.258493	+	2.99216i	0.0170445	+	0.197297i
$231$		0			0
$232$			1.83030i			0.120165i
$233$			13.9328i			0.912769i	0.889783	+	0.456385i	$0.150856\pi$
$233$			13.9328i			0.912769i	−0.889783	+	0.456385i	$0.849144\pi$
$234$		0			0
$235$	11.3446	−	0.980059i	0.740039	−	0.0639320i
$236$	23.6494			1.53945
$237$		0			0
$238$		−	16.9275i		−	1.09725i
$239$	−17.7987			−1.15130			−0.575650	−	0.817696i	$-0.695251\pi$
$239$	−17.7987			−1.15130			−0.575650	+	0.817696i	$0.695251\pi$
$240$		0			0
$241$	−10.5443			−0.679217			−0.339609	−	0.940567i	$-0.610295\pi$
$241$	−10.5443			−0.679217			−0.339609	+	0.940567i	$0.610295\pi$
$242$			3.05609i			0.196453i
$243$		0			0
$244$	11.6342			0.744803
$245$	2.77414	+	32.1118i	0.177233	+	2.05155i
$246$		0			0
$247$		−	2.39138i		−	0.152160i
$248$		−	9.54521i		−	0.606121i
$249$		0			0
$250$	−5.38399	+	1.42378i	−0.340513	+	0.0900474i
$251$	14.9840			0.945784			0.472892	−	0.881120i	$-0.343210\pi$
$251$	14.9840			0.945784			0.472892	+	0.881120i	$0.343210\pi$
$252$		0			0
$253$		−	11.1618i		−	0.701736i
$254$	−9.17049			−0.575408
$255$		0			0
$256$	−0.365609			−0.0228506
$257$		−	4.89838i		−	0.305553i	−0.988261	−	0.152776i	$-0.951179\pi$
$257$		−	4.89838i		−	0.305553i	0.988261	−	0.152776i	$-0.0488214\pi$
$258$		0			0
$259$	−45.5950			−2.83314
$260$	9.33306	−	0.806284i	0.578812	−	0.0500036i
$261$		0			0
$262$			5.30692i			0.327863i
$263$			13.6398i			0.841063i	0.907278	+	0.420532i	$0.138156\pi$
$263$			13.6398i			0.841063i	−0.907278	+	0.420532i	$0.861844\pi$
$264$		0			0
$265$	−7.49242	+	0.647271i	−0.460256	+	0.0397615i
$266$	−2.30504			−0.141331
$267$		0			0
$268$		−	12.7614i		−	0.779530i
$269$	−15.7729			−0.961692			−0.480846	−	0.876805i	$-0.659670\pi$
$269$	−15.7729			−0.961692			−0.480846	+	0.876805i	$0.659670\pi$
$270$		0			0
$271$	−5.12680			−0.311431			−0.155715	−	0.987802i	$-0.549768\pi$
$271$	−5.12680			−0.311431			−0.155715	+	0.987802i	$0.549768\pi$
$272$		−	18.8944i		−	1.14564i
$273$		0			0
$274$	1.15545			0.0698034
$275$	20.3908	−	3.54961i	1.22961	−	0.214050i
$276$		0			0
$277$		−	8.63811i		−	0.519013i	−0.965741	−	0.259507i	$-0.916440\pi$
$277$		−	8.63811i		−	0.519013i	0.965741	−	0.259507i	$-0.0835600\pi$
$278$			7.87811i			0.472498i
$279$		0			0
$280$	−1.66442	−	19.2663i	−0.0994681	−	1.15138i
$281$	−18.5875			−1.10884			−0.554420	−	0.832237i	$-0.687060\pi$
$281$	−18.5875			−1.10884			−0.554420	+	0.832237i	$0.687060\pi$
$282$		0			0
$283$			20.0035i			1.18908i	0.804065	+	0.594541i	$0.202666\pi$
$283$			20.0035i			1.18908i	−0.804065	+	0.594541i	$0.797334\pi$
$284$	12.7614			0.757253
$285$		0			0
$286$	4.93085			0.291567
$287$		−	20.9369i		−	1.23587i
$288$		0			0
$289$	−36.9298			−2.17234
$290$	1.08678	−	0.0938874i	0.0638182	−	0.00551326i
$291$		0			0
$292$		−	6.69821i		−	0.391983i
$293$		−	11.0837i		−	0.647519i	−0.946139	−	0.323760i	$-0.895053\pi$
$293$		−	11.0837i		−	0.647519i	0.946139	−	0.323760i	$-0.104947\pi$
$294$		0			0
$295$	−2.59806	−	30.0736i	−0.151265	−	1.75095i
$296$	18.4137			1.07028
$297$		0			0
$298$		−	3.83982i		−	0.222435i
$299$	−6.44816			−0.372907
$300$		0			0
$301$	15.9170			0.917440
$302$		−	9.57439i		−	0.550944i
$303$		0			0
$304$	−2.57287			−0.147564
$305$	−1.27810	−	14.7945i	−0.0731838	−	0.847132i
$306$		0			0
$307$		−	26.2854i		−	1.50019i	−0.661331	−	0.750094i	$-0.730008\pi$
$307$		−	26.2854i		−	1.50019i	0.661331	−	0.750094i	$-0.269992\pi$
$308$			33.5586i			1.91218i
$309$		0			0
$310$	−5.66769	+	0.489632i	−0.321903	+	0.0278093i
$311$	−26.1287			−1.48162			−0.740811	−	0.671714i	$-0.765558\pi$
$311$	−26.1287			−1.48162			−0.740811	+	0.671714i	$0.765558\pi$
$312$		0			0
$313$			3.78602i			0.213998i	0.994259	+	0.106999i	$0.0341242\pi$
$313$			3.78602i			0.213998i	−0.994259	+	0.106999i	$0.965876\pi$
$314$	6.77840			0.382527
$315$		0			0
$316$	28.3081			1.59245
$317$		−	11.8420i		−	0.665113i	−0.943083	−	0.332556i	$-0.892089\pi$
$317$		−	11.8420i		−	0.665113i	0.943083	−	0.332556i	$-0.107911\pi$
$318$		0			0
$319$	−4.05408			−0.226985
$320$	−0.509159	−	5.89372i	−0.0284628	−	0.329469i
$321$		0			0
$322$			6.21537i			0.346369i
$323$			7.34369i			0.408614i
$324$		0			0
$325$	−2.05061	−	11.7797i	−0.113747	−	0.653422i
$326$	1.55676			0.0862209
$327$		0			0
$328$			8.45546i			0.466875i
$329$	23.5651			1.29919
$330$		0			0
$331$	34.2726			1.88379			0.941897	−	0.335902i	$-0.109041\pi$
$331$	34.2726			1.88379			0.941897	+	0.335902i	$0.109041\pi$
$332$		−	6.86952i		−	0.377014i
$333$		0			0
$334$	−1.42887			−0.0781844
$335$	−16.2280	+	1.40194i	−0.886630	+	0.0765960i
$336$		0			0
$337$			10.4980i			0.571861i	0.958250	+	0.285930i	$0.0923026\pi$
$337$			10.4980i			0.571861i	−0.958250	+	0.285930i	$0.907697\pi$
$338$			3.62691i			0.197278i
$339$		0			0
$340$	−28.6609	+	2.47602i	−1.55436	+	0.134281i
$341$	21.1425			1.14493
$342$		0			0
$343$			34.3102i			1.85258i
$344$	−6.42814			−0.346582
$345$		0			0
$346$	−2.41785			−0.129985
$347$		−	18.8198i		−	1.01030i	−0.863031	−	0.505151i	$-0.831437\pi$
$347$		−	18.8198i		−	1.01030i	0.863031	−	0.505151i	$-0.168563\pi$
$348$		0			0
$349$	14.4077			0.771227			0.385613	−	0.922660i	$-0.373990\pi$
$349$	14.4077			0.771227			0.385613	+	0.922660i	$0.373990\pi$
$350$	−11.3545	+	1.97658i	−0.606921	+	0.105652i
$351$		0			0
$352$		−	20.7773i		−	1.10743i
$353$		−	5.41582i		−	0.288255i	−0.989559	−	0.144127i	$-0.953962\pi$
$353$		−	5.41582i		−	0.288255i	0.989559	−	0.144127i	$-0.0460375\pi$
$354$		0			0
$355$	−1.40194	−	16.2280i	−0.0744071	−	0.861293i
$356$	4.10723			0.217683
$357$		0			0
$358$		−	8.35487i		−	0.441569i
$359$	−20.7304			−1.09411			−0.547055	−	0.837097i	$-0.684251\pi$
$359$	−20.7304			−1.09411			−0.547055	+	0.837097i	$0.684251\pi$
$360$		0			0
$361$	1.00000			0.0526316
$362$			8.47166i			0.445260i
$363$		0			0
$364$	19.3868			1.01614
$365$	−8.51773	+	0.735847i	−0.445838	+	0.0385160i
$366$		0			0
$367$		−	2.60433i		−	0.135945i	−0.997687	−	0.0679725i	$-0.978347\pi$
$367$		−	2.60433i		−	0.135945i	0.997687	−	0.0679725i	$-0.0216530\pi$
$368$			6.93754i			0.361644i
$369$		0			0
$370$	−0.944553	−	10.9336i	−0.0491050	−	0.568410i
$371$	−15.5634			−0.808011
$372$		0			0
$373$			5.98299i			0.309787i	0.987931	+	0.154894i	$0.0495035\pi$
$373$			5.98299i			0.309787i	−0.987931	+	0.154894i	$0.950497\pi$
$374$	−15.1422			−0.782982
$375$		0			0
$376$	−9.51687			−0.490795
$377$			2.34204i			0.120621i
$378$		0			0
$379$	7.44400			0.382372			0.191186	−	0.981554i	$-0.438767\pi$
$379$	7.44400			0.382372			0.191186	+	0.981554i	$0.438767\pi$
$380$	0.337163	+	3.90280i	0.0172961	+	0.200209i
$381$		0			0
$382$		−	1.28156i		−	0.0655701i
$383$			15.5789i			0.796044i	0.917376	+	0.398022i	$0.130303\pi$
$383$			15.5789i			0.796044i	−0.917376	+	0.398022i	$0.869697\pi$
$384$		0			0
$385$	42.6745	−	3.68666i	2.17490	−	0.187889i
$386$	−8.59801			−0.437627
$387$		0			0
$388$			4.10390i			0.208344i
$389$	16.7532			0.849421			0.424711	−	0.905329i	$-0.360376\pi$
$389$	16.7532			0.849421			0.424711	+	0.905329i	$0.360376\pi$
$390$		0			0
$391$	19.8017			1.00141
$392$		−	26.9383i		−	1.36059i
$393$		0			0
$394$	9.24618			0.465816
$395$	−3.10985	−	35.9978i	−0.156473	−	1.81124i
$396$		0			0
$397$			6.65505i			0.334008i	0.985956	+	0.167004i	$0.0534092\pi$
$397$			6.65505i			0.334008i	−0.985956	+	0.167004i	$0.946591\pi$
$398$			2.11433i			0.105982i
$399$		0			0
$400$	−12.6737	+	2.20624i	−0.633687	+	0.110312i
$401$	30.8633			1.54124			0.770619	−	0.637296i	$-0.219947\pi$
$401$	30.8633			1.54124			0.770619	+	0.637296i	$0.219947\pi$
$402$		0			0
$403$		−	12.2140i		−	0.608422i
$404$	13.0507			0.649297
$405$		0			0
$406$	2.25749			0.112037
$407$			40.7861i			2.02169i
$408$		0			0
$409$	26.4257			1.30667			0.653334	−	0.757070i	$-0.273370\pi$
$409$	26.4257			1.30667			0.653334	+	0.757070i	$0.273370\pi$
$410$	5.02063	−	0.433733i	0.247951	−	0.0214205i
$411$		0			0
$412$			14.3254i			0.705762i
$413$		−	62.4694i		−	3.07392i
$414$		0			0
$415$	−8.73557	+	0.754667i	−0.428812	+	0.0370451i
$416$	−12.0030			−0.588497
$417$		0			0
$418$			2.06193i			0.100852i
$419$	−4.25514			−0.207877			−0.103939	−	0.994584i	$-0.533145\pi$
$419$	−4.25514			−0.207877			−0.103939	+	0.994584i	$0.533145\pi$
$420$		0			0
$421$	−13.3331			−0.649818			−0.324909	−	0.945745i	$-0.605334\pi$
$421$	−13.3331			−0.649818			−0.324909	+	0.945745i	$0.605334\pi$
$422$		−	0.602562i		−	0.0293323i
$423$		0			0
$424$	6.28533			0.305243
$425$	6.29722	+	36.1744i	0.305460	+	1.75472i
$426$		0			0
$427$		−	30.7314i		−	1.48720i
$428$		−	9.20637i		−	0.445006i
$429$		0			0
$430$	0.329739	+	3.81686i	0.0159014	+	0.184065i
$431$	17.7752			0.856199			0.428100	−	0.903732i	$-0.359183\pi$
$431$	17.7752			0.856199			0.428100	+	0.903732i	$0.359183\pi$
$432$		0			0
$433$		−	31.2503i		−	1.50179i	−0.660421	−	0.750896i	$-0.729622\pi$
$433$		−	31.2503i		−	1.50179i	0.660421	−	0.750896i	$-0.270378\pi$
$434$	−11.7730			−0.565123
$435$		0			0
$436$	−13.1457			−0.629567
$437$		−	2.69642i		−	0.128987i
$438$		0			0
$439$	11.8467			0.565412			0.282706	−	0.959207i	$-0.408768\pi$
$439$	11.8467			0.565412			0.282706	+	0.959207i	$0.408768\pi$
$440$	−17.2343	+	1.48887i	−0.821612	+	0.0709791i
$441$		0			0
$442$			8.74761i			0.416081i
$443$			31.3323i			1.48864i	0.667820	+	0.744322i	$0.267227\pi$
$443$			31.3323i			1.48864i	−0.667820	+	0.744322i	$0.732773\pi$
$444$		0			0
$445$	−0.451209	−	5.22293i	−0.0213894	−	0.247590i
$446$	−3.10010			−0.146794
$447$		0			0
$448$		−	12.2425i		−	0.578405i
$449$	−8.67661			−0.409475			−0.204737	−	0.978817i	$-0.565634\pi$
$449$	−8.67661			−0.409475			−0.204737	+	0.978817i	$0.565634\pi$
$450$		0			0
$451$	−18.7287			−0.881900
$452$		−	6.49465i		−	0.305482i
$453$		0			0
$454$	−12.3603			−0.580098
$455$	−2.12978	−	24.6531i	−0.0998456	−	1.15575i
$456$		0			0
$457$			25.3250i			1.18465i	0.805697	+	0.592327i	$0.201791\pi$
$457$			25.3250i			1.18465i	−0.805697	+	0.592327i	$0.798209\pi$
$458$		−	0.457854i		−	0.0213941i
$459$		0			0
$460$	10.5236	−	0.909133i	0.490664	−	0.0423885i
$461$	24.3053			1.13201			0.566005	−	0.824402i	$-0.308488\pi$
$461$	24.3053			1.13201			0.566005	+	0.824402i	$0.308488\pi$
$462$		0			0
$463$		−	15.8208i		−	0.735256i	−0.929973	−	0.367628i	$-0.880170\pi$
$463$		−	15.8208i		−	0.735256i	0.929973	−	0.367628i	$-0.119830\pi$
$464$	2.51979			0.116978
$465$		0			0
$466$	−6.94010			−0.321494
$467$			1.84478i			0.0853661i	0.999089	+	0.0426831i	$0.0135906\pi$
$467$			1.84478i			0.0853661i	−0.999089	+	0.0426831i	$0.986409\pi$
$468$		0			0
$469$	−33.7091			−1.55654
$470$	0.488179	+	5.65087i	0.0225180	+	0.260655i
$471$		0			0
$472$			25.2285i			1.16124i
$473$		−	14.2382i		−	0.654673i
$474$		0			0
$475$	4.92592	−	0.857501i	0.226017	−	0.0393448i
$476$	−59.5350			−2.72878
$477$		0			0
$478$		−	8.86572i		−	0.405509i
$479$	−10.9945			−0.502350			−0.251175	−	0.967942i	$-0.580817\pi$
$479$	−10.9945			−0.502350			−0.251175	+	0.967942i	$0.580817\pi$
$480$		0			0
$481$	23.5621			1.07434
$482$		−	5.25224i		−	0.239233i
$483$		0			0
$484$	10.7484			0.488564
$485$	5.21869	−	0.450843i	0.236969	−	0.0204717i
$486$		0			0
$487$		−	32.2455i		−	1.46118i	−0.682816	−	0.730590i	$-0.739245\pi$
$487$		−	32.2455i		−	1.46118i	0.682816	−	0.730590i	$-0.260755\pi$
$488$			12.4110i			0.561820i
$489$		0			0
$490$	−15.9953	+	1.38183i	−0.722592	+	0.0624248i
$491$	5.50201			0.248302			0.124151	−	0.992263i	$-0.460379\pi$
$491$	5.50201			0.248302			0.124151	+	0.992263i	$0.460379\pi$
$492$		0			0
$493$		−	7.19218i		−	0.323920i
$494$	1.19117			0.0535934
$495$		0			0
$496$	−13.1409			−0.590046
$497$		−	33.7091i		−	1.51206i
$498$		0			0
$499$	16.5316			0.740054			0.370027	−	0.929021i	$-0.379348\pi$
$499$	16.5316			0.740054			0.370027	+	0.929021i	$0.379348\pi$
$500$	5.00749	+	18.9357i	0.223942	+	0.846832i
$501$		0			0
$502$			7.46373i			0.333122i
$503$		−	19.6030i		−	0.874056i	−0.899448	−	0.437028i	$-0.856031\pi$
$503$		−	19.6030i		−	0.874056i	0.899448	−	0.437028i	$-0.143969\pi$
$504$		0			0
$505$	−1.43372	−	16.5958i	−0.0637995	−	0.738505i
$506$	5.55982			0.247164
$507$		0			0
$508$			32.2531i			1.43100i
$509$	−21.3635			−0.946922			−0.473461	−	0.880815i	$-0.656996\pi$
$509$	−21.3635			−0.946922			−0.473461	+	0.880815i	$0.656996\pi$
$510$		0			0
$511$	−17.6932			−0.782699
$512$			22.5306i			0.995723i
$513$		0			0
$514$	2.43994			0.107621
$515$	18.2168	−	1.57375i	0.802728	−	0.0693477i
$516$		0			0
$517$		−	21.0797i		−	0.927084i
$518$		−	22.7114i		−	0.997883i
$519$		0			0
$520$	0.860119	+	9.95623i	0.0377187	+	0.436610i
$521$	−25.7832			−1.12958			−0.564791	−	0.825234i	$-0.691043\pi$
$521$	−25.7832			−1.12958			−0.564791	+	0.825234i	$0.691043\pi$
$522$		0			0
$523$			24.4480i			1.06904i	0.845157	+	0.534518i	$0.179507\pi$
$523$			24.4480i			1.06904i	−0.845157	+	0.534518i	$0.820493\pi$
$524$	18.6647			0.815371
$525$		0			0
$526$	−6.79412			−0.296238
$527$			37.5080i			1.63387i
$528$		0			0
$529$	15.7293			0.683883
$530$	−0.322413	−	3.73207i	−0.0140047	−	0.162111i
$531$		0			0
$532$			8.10695i			0.351481i
$533$			10.8196i			0.468647i
$534$		0			0
$535$	−11.7072	+	1.01139i	−0.506147	+	0.0437260i
$536$	13.6135			0.588015
$537$		0			0
$538$		−	7.85668i		−	0.338726i
$539$	59.6679			2.57008
$540$		0			0
$541$	7.46518			0.320953			0.160477	−	0.987040i	$-0.448697\pi$
$541$	7.46518			0.320953			0.160477	+	0.987040i	$0.448697\pi$
$542$		−	2.55372i		−	0.109692i
$543$		0			0
$544$	36.8601			1.58037
$545$	1.44415	+	16.7167i	0.0618608	+	0.716064i
$546$		0			0
$547$			6.04764i			0.258578i	0.991607	+	0.129289i	$0.0412696\pi$
$547$			6.04764i			0.258578i	−0.991607	+	0.129289i	$0.958730\pi$
$548$		−	4.06378i		−	0.173596i
$549$		0			0
$550$	1.76810	+	10.1569i	0.0753922	+	0.433091i
$551$	−0.979369			−0.0417225
$552$		0			0
$553$		−	74.7751i		−	3.17976i
$554$	4.30274			0.182806
$555$		0			0
$556$	27.7077			1.17507
$557$		−	28.3330i		−	1.20051i	−0.799809	−	0.600255i	$-0.795066\pi$
$557$		−	28.3330i		−	1.20051i	0.799809	−	0.600255i	$-0.204934\pi$
$558$		0			0
$559$	−8.22540			−0.347897
$560$	−26.5241	+	2.29142i	−1.12085	+	0.0968300i
$561$		0			0
$562$		−	9.25868i		−	0.390554i
$563$			39.5993i			1.66891i	0.551074	+	0.834457i	$0.314218\pi$
$563$			39.5993i			1.66891i	−0.551074	+	0.834457i	$0.685782\pi$
$564$		0			0
$565$	−8.25887	+	0.713484i	−0.347453	+	0.0300165i
$566$	−9.96396			−0.418816
$567$		0			0
$568$			13.6135i			0.571211i
$569$	30.6989			1.28697			0.643483	−	0.765461i	$-0.277489\pi$
$569$	30.6989			1.28697			0.643483	+	0.765461i	$0.277489\pi$
$570$		0			0
$571$	−39.4360			−1.65035			−0.825173	−	0.564880i	$-0.808923\pi$
$571$	−39.4360			−1.65035			−0.825173	+	0.564880i	$0.808923\pi$
$572$		−	17.3420i		−	0.725107i
$573$		0			0
$574$	10.4289			0.435295
$575$	−2.31218	−	13.2824i	−0.0964247	−	0.553912i
$576$		0			0
$577$		−	8.15383i		−	0.339448i	−0.985492	−	0.169724i	$-0.945712\pi$
$577$		−	8.15383i		−	0.339448i	0.985492	−	0.169724i	$-0.0542877\pi$
$578$		−	18.3952i		−	0.765138i
$579$		0			0
$580$	−0.330207	−	3.82228i	−0.0137111	−	0.158711i
$581$	−18.1457			−0.752809
$582$		0			0
$583$			13.9219i			0.576586i
$584$	7.14545			0.295681
$585$		0			0
$586$	5.52094			0.228068
$587$			10.8871i			0.449360i	0.974433	+	0.224680i	$0.0721337\pi$
$587$			10.8871i			0.449360i	−0.974433	+	0.224680i	$0.927866\pi$
$588$		0			0
$589$	5.10751			0.210451
$590$	14.9800	−	1.29413i	0.616718	−	0.0532783i
$591$		0			0
$592$		−	25.3503i		−	1.04189i
$593$			3.13220i			0.128624i	0.997930	+	0.0643120i	$0.0204853\pi$
$593$			3.13220i			0.128624i	−0.997930	+	0.0643120i	$0.979515\pi$
$594$		0			0
$595$	6.54035	+	75.7072i	0.268128	+	3.10369i
$596$	−13.5048			−0.553180
$597$		0			0
$598$		−	3.21191i		−	0.131345i
$599$	24.2488			0.990778			0.495389	−	0.868671i	$-0.335025\pi$
$599$	24.2488			0.990778			0.495389	+	0.868671i	$0.335025\pi$
$600$		0			0
$601$	−9.24528			−0.377123			−0.188561	−	0.982061i	$-0.560382\pi$
$601$	−9.24528			−0.377123			−0.188561	+	0.982061i	$0.560382\pi$
$602$			7.92844i			0.323139i
$603$		0			0
$604$	−33.6736			−1.37016
$605$	−1.18079	−	13.6681i	−0.0480060	−	0.555689i
$606$		0			0
$607$			42.6285i			1.73024i	0.501569	+	0.865118i	$0.332756\pi$
$607$			42.6285i			1.73024i	−0.501569	+	0.865118i	$0.667244\pi$
$608$		−	5.01929i		−	0.203559i
$609$		0			0
$610$	7.36933	−	0.636637i	0.298375	−	0.0257767i
$611$	−12.1777			−0.492658
$612$		0			0
$613$		−	45.2670i		−	1.82832i	−0.405356	−	0.914159i	$-0.632852\pi$
$613$		−	45.2670i		−	1.82832i	0.405356	−	0.914159i	$-0.367148\pi$
$614$	13.0931			0.528394
$615$		0			0
$616$	−35.7993			−1.44240
$617$			8.02773i			0.323184i	0.986858	+	0.161592i	$0.0516629\pi$
$617$			8.02773i			0.323184i	−0.986858	+	0.161592i	$0.948337\pi$
$618$		0			0
$619$	−15.1856			−0.610361			−0.305181	−	0.952294i	$-0.598717\pi$
$619$	−15.1856			−0.610361			−0.305181	+	0.952294i	$0.598717\pi$
$620$	1.72206	+	19.9336i	0.0691597	+	0.800551i
$621$		0			0
$622$		−	13.0150i		−	0.521854i
$623$		−	10.8491i		−	0.434662i
$624$		0			0
$625$	23.5294	−	8.44796i	0.941175	−	0.337918i
$626$	−1.88586			−0.0753741
$627$		0			0
$628$		−	23.8400i		−	0.951318i
$629$	−72.3569			−2.88506
$630$		0			0
$631$	4.77803			0.190210			0.0951052	−	0.995467i	$-0.469681\pi$
$631$	4.77803			0.190210			0.0951052	+	0.995467i	$0.469681\pi$
$632$			30.1982i			1.20122i
$633$		0			0
$634$	5.89864			0.234265
$635$	41.0144	−	3.54324i	1.62761	−	0.140609i
$636$		0			0
$637$		−	34.4701i		−	1.36575i
$638$		−	2.01939i		−	0.0799483i
$639$		0			0
$640$	25.2994	−	2.18562i	1.00005	−	0.0863941i
$641$	28.6332			1.13094			0.565472	−	0.824767i	$-0.308694\pi$
$641$	28.6332			1.13094			0.565472	+	0.824767i	$0.308694\pi$
$642$		0			0
$643$			33.5682i			1.32380i	0.749593	+	0.661899i	$0.230249\pi$
$643$			33.5682i			1.32380i	−0.749593	+	0.661899i	$0.769751\pi$
$644$	21.8598			0.861395
$645$		0			0
$646$	−3.65798			−0.143921
$647$			29.3005i			1.15192i	0.817478	+	0.575960i	$0.195372\pi$
$647$			29.3005i			1.15192i	−0.817478	+	0.575960i	$0.804628\pi$
$648$		0			0
$649$	−55.8807			−2.19351
$650$	5.86763	−	1.02143i	0.230147	−	0.0400639i
$651$		0			0
$652$		−	5.47520i		−	0.214425i
$653$		−	47.8047i		−	1.87074i	−0.353666	−	0.935372i	$-0.615065\pi$
$653$		−	47.8047i		−	1.87074i	0.353666	−	0.935372i	$-0.384935\pi$
$654$		0			0
$655$	−2.05045	−	23.7348i	−0.0801178	−	0.927396i
$656$	11.6407			0.454493
$657$		0			0
$658$			11.7381i			0.457598i
$659$	17.6309			0.686801			0.343401	−	0.939189i	$-0.388421\pi$
$659$	17.6309			0.686801			0.343401	+	0.939189i	$0.388421\pi$
$660$		0			0
$661$	−14.5024			−0.564079			−0.282039	−	0.959403i	$-0.591011\pi$
$661$	−14.5024			−0.564079			−0.282039	+	0.959403i	$0.591011\pi$
$662$			17.0716i			0.663507i
$663$		0			0
$664$	7.32820			0.284389
$665$	10.3091	−	0.890607i	0.399771	−	0.0345363i
$666$		0			0
$667$			2.64079i			0.102252i
$668$			5.02541i			0.194439i
$669$		0			0
$670$	−0.698322	−	8.08336i	−0.0269785	−	0.312287i
$671$	−27.4901			−1.06125
$672$		0			0
$673$			34.8772i			1.34442i	0.740361	+	0.672209i	$0.234654\pi$
$673$			34.8772i			1.34442i	−0.740361	+	0.672209i	$0.765346\pi$
$674$	−5.22916			−0.201420
$675$		0			0
$676$	12.7560			0.490616
$677$			15.0784i			0.579512i	0.957101	+	0.289756i	$0.0935741\pi$
$677$			15.0784i			0.579512i	−0.957101	+	0.289756i	$0.906426\pi$
$678$		0			0
$679$	10.8403			0.416014
$680$	−2.64134	−	30.5746i	−0.101291	−	1.17248i
$681$		0			0
$682$			10.5313i			0.403265i
$683$		−	28.5584i		−	1.09276i	−0.837539	−	0.546378i	$-0.816006\pi$
$683$		−	28.5584i		−	1.09276i	0.837539	−	0.546378i	$-0.183994\pi$
$684$		0			0
$685$	−5.16768	+	0.446436i	−0.197447	+	0.0170574i
$686$	−17.0903			−0.652511
$687$		0			0
$688$			8.84966i			0.337390i
$689$	8.04267			0.306401
$690$		0			0
$691$	−45.5752			−1.73376			−0.866882	−	0.498514i	$-0.833879\pi$
$691$	−45.5752			−1.73376			−0.866882	+	0.498514i	$0.833879\pi$
$692$			8.50371i			0.323263i
$693$		0			0
$694$	9.37438			0.355847
$695$	−3.04389	−	35.2343i	−0.115461	−	1.33651i
$696$		0			0
$697$		−	33.2258i		−	1.25852i
$698$			7.17665i			0.271640i
$699$		0			0
$700$	6.95172	+	39.9342i	0.262750	+	1.50937i
$701$	−47.2207			−1.78350			−0.891750	−	0.452528i	$-0.850522\pi$
$701$	−47.2207			−1.78350			−0.891750	+	0.452528i	$0.850522\pi$
$702$		0			0
$703$			9.85293i			0.371610i
$704$	−10.9513			−0.412742
$705$		0			0
$706$	2.69768			0.101529
$707$		−	34.4731i		−	1.29650i
$708$		0			0
$709$	−21.4475			−0.805479			−0.402739	−	0.915315i	$-0.631942\pi$
$709$	−21.4475			−0.805479			−0.402739	+	0.915315i	$0.631942\pi$
$710$	8.08336	−	0.698322i	0.303363	−	0.0262075i
$711$		0			0
$712$			4.38147i			0.164203i
$713$		−	13.7720i		−	0.515765i
$714$		0			0
$715$	−22.0529	+	1.90515i	−0.824730	+	0.0712485i
$716$	−29.3845			−1.09815
$717$		0			0
$718$		−	10.3261i		−	0.385365i
$719$	30.7936			1.14841			0.574203	−	0.818713i	$-0.305312\pi$
$719$	30.7936			1.14841			0.574203	+	0.818713i	$0.305312\pi$
$720$		0			0
$721$	37.8402			1.40924
$722$			0.498112i			0.0185378i
$723$		0			0
$724$	29.7952			1.10733
$725$	−4.82429	+	0.839809i	−0.179170	+	0.0311897i
$726$		0			0
$727$		−	35.1442i		−	1.30343i	−0.758465	−	0.651714i	$-0.774050\pi$
$727$		−	35.1442i		−	1.30343i	0.758465	−	0.651714i	$-0.225950\pi$
$728$			20.6812i			0.766498i
$729$		0			0
$730$	−0.366534	−	4.24278i	−0.0135660	−	0.157032i
$731$	25.2594			0.934253
$732$		0			0
$733$			13.1160i			0.484449i	0.970220	+	0.242225i	$0.0778771\pi$
$733$			13.1160i			0.484449i	−0.970220	+	0.242225i	$0.922123\pi$
$734$	1.29725			0.0478823
$735$		0			0
$736$	−13.5341			−0.498874
$737$			30.1537i			1.11073i
$738$		0			0
$739$	−15.7315			−0.578691			−0.289346	−	0.957225i	$-0.593438\pi$
$739$	−15.7315			−0.578691			−0.289346	+	0.957225i	$0.593438\pi$
$740$	−38.4540	+	3.32204i	−1.41360	+	0.122121i
$741$		0			0
$742$		−	7.75231i		−	0.284596i
$743$		−	5.59959i		−	0.205429i	−0.994711	−	0.102715i	$-0.967247\pi$
$743$		−	5.59959i		−	0.205429i	0.994711	−	0.102715i	$-0.0327528\pi$
$744$		0			0
$745$	1.48360	+	17.1733i	0.0543550	+	0.629182i
$746$	−2.98020			−0.109113
$747$		0			0
$748$			53.2557i			1.94722i
$749$	−24.3184			−0.888575
$750$		0			0
$751$	−1.87281			−0.0683397			−0.0341698	−	0.999416i	$-0.510879\pi$
$751$	−1.87281			−0.0683397			−0.0341698	+	0.999416i	$0.510879\pi$
$752$			13.1019i			0.477779i
$753$		0			0
$754$	−1.16660			−0.0424850
$755$	3.69929	+	42.8208i	0.134631	+	1.55841i
$756$		0			0
$757$			30.2362i			1.09895i	0.835509	+	0.549476i	$0.185173\pi$
$757$			30.2362i			1.09895i	−0.835509	+	0.549476i	$0.814827\pi$
$758$			3.70794i			0.134679i
$759$		0			0
$760$	−4.16339	+	0.359675i	−0.151022	+	0.0130468i
$761$	17.5630			0.636659			0.318330	−	0.947980i	$-0.396878\pi$
$761$	17.5630			0.636659			0.318330	+	0.947980i	$0.396878\pi$
$762$		0			0
$763$			34.7241i			1.25710i
$764$	−4.50730			−0.163068
$765$		0			0
$766$	−7.76003			−0.280381
$767$			32.2822i			1.16564i
$768$		0			0
$769$	−18.2587			−0.658426			−0.329213	−	0.944256i	$-0.606783\pi$
$769$	−18.2587			−0.658426			−0.329213	+	0.944256i	$0.606783\pi$
$770$	1.83637	+	21.2567i	0.0661781	+	0.766038i
$771$		0			0
$772$			30.2396i			1.08835i
$773$			7.79018i			0.280193i	0.990138	+	0.140097i	$0.0447413\pi$
$773$			7.79018i			0.280193i	−0.990138	+	0.140097i	$0.955259\pi$
$774$		0			0
$775$	25.1592	−	4.37969i	0.903745	−	0.157323i
$776$	−4.37792			−0.157158
$777$		0			0
$778$			8.34497i			0.299182i
$779$	−4.52440			−0.162103
$780$		0			0
$781$	−30.1537			−1.07898
$782$			9.86345i			0.352716i
$783$		0			0
$784$	−37.0861			−1.32451
$785$	−30.3159	+	2.61899i	−1.08202	+	0.0934758i
$786$		0			0
$787$			1.66566i			0.0593744i	0.999559	+	0.0296872i	$0.00945111\pi$
$787$			1.66566i			0.0593744i	−0.999559	+	0.0296872i	$0.990549\pi$
$788$		−	32.5193i		−	1.15845i
$789$		0			0
$790$	17.9309	−	1.54905i	0.637953	−	0.0551128i
$791$	−17.1555			−0.609978
$792$		0			0
$793$			15.8810i			0.563952i
$794$	−3.31496			−0.117644
$795$		0			0
$796$	7.43622			0.263570
$797$			26.1199i			0.925215i	0.886563	+	0.462607i	$0.153086\pi$
$797$			26.1199i			0.925215i	−0.886563	+	0.462607i	$0.846914\pi$
$798$		0			0
$799$	37.3966			1.32300
$800$	−4.30405	−	24.7246i	−0.152171	−	0.874148i
$801$		0			0
$802$			15.3734i			0.542852i
$803$			15.8270i			0.558524i
$804$		0			0
$805$	−2.40145	−	27.7978i	−0.0846401	−	0.979743i
$806$	6.08393			0.214297
$807$		0			0
$808$			13.9221i			0.489778i
$809$	10.7020			0.376261			0.188130	−	0.982144i	$-0.439757\pi$
$809$	10.7020			0.376261			0.188130	+	0.982144i	$0.439757\pi$
$810$		0			0
$811$	41.3040			1.45038			0.725190	−	0.688549i	$-0.241752\pi$
$811$	41.3040			1.45038			0.725190	+	0.688549i	$0.241752\pi$
$812$		−	7.93969i		−	0.278629i
$813$		0			0
$814$	−20.3160			−0.712076
$815$	−6.96249	+	0.601490i	−0.243885	+	0.0210693i
$816$		0			0
$817$		−	3.43961i		−	0.120337i
$818$			13.1630i			0.460232i
$819$		0			0
$820$	−1.52546	−	17.6578i	−0.0532714	−	0.616638i
$821$	−31.6822			−1.10572			−0.552858	−	0.833276i	$-0.686463\pi$
$821$	−31.6822			−1.10572			−0.552858	+	0.833276i	$0.686463\pi$
$822$		0			0
$823$			20.7292i			0.722575i	0.932454	+	0.361288i	$0.117663\pi$
$823$			20.7292i			0.722575i	−0.932454	+	0.361288i	$0.882337\pi$
$824$	−15.2819			−0.532371
$825$		0			0
$826$	31.1168			1.08269
$827$		−	24.6668i		−	0.857750i	−0.903364	−	0.428875i	$-0.858910\pi$
$827$		−	24.6668i		−	0.857750i	0.903364	−	0.428875i	$-0.141090\pi$
$828$		0			0
$829$	52.3442			1.81799			0.908995	−	0.416808i	$-0.136851\pi$
$829$	52.3442			1.81799			0.908995	+	0.416808i	$0.136851\pi$
$830$	−0.375908	−	4.35129i	−0.0130480	−	0.151036i
$831$		0			0
$832$			6.32655i			0.219334i
$833$			105.854i			3.66763i
$834$		0			0
$835$	6.39053	−	0.552078i	0.221153	−	0.0191054i
$836$	7.25190			0.250812
$837$		0			0
$838$		−	2.11954i		−	0.0732182i
$839$	−1.72696			−0.0596214			−0.0298107	−	0.999556i	$-0.509490\pi$
$839$	−1.72696			−0.0596214			−0.0298107	+	0.999556i	$0.509490\pi$
$840$		0			0
$841$	−28.0408			−0.966925
$842$		−	6.64140i		−	0.228878i
$843$		0			0
$844$	−2.11924			−0.0729473
$845$	−1.40134	−	16.2211i	−0.0482076	−	0.558022i
$846$		0			0
$847$		−	28.3917i		−	0.975550i
$848$		−	8.65306i		−	0.297147i
$849$		0			0
$850$	−18.0189	+	3.13672i	−0.618044	+	0.107589i
$851$	26.5676			0.910727
$852$		0			0
$853$			5.71206i			0.195577i	0.995207	+	0.0977886i	$0.0311769\pi$
$853$			5.71206i			0.195577i	−0.995207	+	0.0977886i	$0.968823\pi$
$854$	15.3077			0.523818
$855$		0			0
$856$	9.82108			0.335677
$857$		−	8.45967i		−	0.288977i	−0.989507	−	0.144488i	$-0.953846\pi$
$857$		−	8.45967i		−	0.288977i	0.989507	−	0.144488i	$-0.0461536\pi$
$858$		0			0
$859$	9.60383			0.327678			0.163839	−	0.986487i	$-0.447612\pi$
$859$	9.60383			0.327678			0.163839	+	0.986487i	$0.447612\pi$
$860$	13.4241	−	1.15971i	0.457757	−	0.0395457i
$861$		0			0
$862$			8.85402i			0.301569i
$863$		−	7.21724i		−	0.245678i	−0.992427	−	0.122839i	$-0.960800\pi$
$863$		−	7.21724i		−	0.245678i	0.992427	−	0.122839i	$-0.0391999\pi$
$864$		0			0
$865$	10.8137	−	0.934194i	0.367676	−	0.0317636i
$866$	15.5661			0.528958
$867$		0			0
$868$			41.4063i			1.40542i
$869$	−66.8885			−2.26904
$870$		0			0
$871$	17.4198			0.590247
$872$		−	14.0235i		−	0.474895i
$873$		0			0
$874$	1.34312			0.0454317
$875$	50.0183	−	13.2272i	1.69093	−	0.447160i
$876$		0			0
$877$			12.7856i			0.431740i	0.976422	+	0.215870i	$0.0692588\pi$
$877$			12.7856i			0.431740i	−0.976422	+	0.215870i	$0.930741\pi$
$878$			5.90098i			0.199148i
$879$		0			0
$880$	2.04974	+	23.7265i	0.0690966	+	0.799822i
$881$	52.4525			1.76717			0.883586	−	0.468270i	$-0.155122\pi$
$881$	52.4525			1.76717			0.883586	+	0.468270i	$0.155122\pi$
$882$		0			0
$883$		−	13.2387i		−	0.445517i	−0.974874	−	0.222758i	$-0.928494\pi$
$883$		−	13.2387i		−	0.445517i	0.974874	−	0.222758i	$-0.0715061\pi$
$884$	30.7658			1.03477
$885$		0			0
$886$	−15.6070			−0.524328
$887$			33.9046i			1.13840i	0.822198	+	0.569202i	$0.192748\pi$
$887$			33.9046i			1.13840i	−0.822198	+	0.569202i	$0.807252\pi$
$888$		0			0
$889$	85.1958			2.85737
$890$	2.60160	−	0.224753i	0.0872059	−	0.00753372i
$891$		0			0
$892$			10.9032i			0.365066i
$893$		−	5.09235i		−	0.170409i
$894$		0			0
$895$	3.22810	+	37.3666i	0.107903	+	1.24903i
$896$	52.5523			1.75565
$897$		0			0
$898$		−	4.32192i		−	0.144224i
$899$	−5.00213			−0.166830
$900$		0			0
$901$	−24.6983			−0.822818
$902$		−	9.32898i		−	0.310621i
$903$		0			0
$904$	6.92830			0.230432
$905$	−3.27322	−	37.8889i	−0.108806	−	1.25947i
$906$		0			0
$907$		−	26.0357i		−	0.864502i	−0.901753	−	0.432251i	$-0.857719\pi$
$907$		−	26.0357i		−	0.864502i	0.901753	−	0.432251i	$-0.142281\pi$
$908$			43.4718i			1.44266i
$909$		0			0
$910$	12.2800	−	1.06087i	0.407077	−	0.0351674i
$911$	−53.0788			−1.75858			−0.879289	−	0.476289i	$-0.841982\pi$
$911$	−53.0788			−1.75858			−0.879289	+	0.476289i	$0.841982\pi$
$912$		0			0
$913$			16.2318i			0.537195i
$914$	−12.6147			−0.417257
$915$		0			0
$916$	−1.61030			−0.0532057
$917$		−	49.3023i		−	1.62811i
$918$		0			0
$919$	−28.1784			−0.929521			−0.464760	−	0.885436i	$-0.653860\pi$
$919$	−28.1784			−0.929521			−0.464760	+	0.885436i	$0.653860\pi$
$920$	0.969836	+	11.2262i	0.0319745	+	0.370118i
$921$		0			0
$922$			12.1067i			0.398714i
$923$			17.4198i			0.573379i
$924$		0			0
$925$	8.44890	+	48.5347i	0.277798	+	1.59581i
$926$	7.88054			0.258971
$927$		0			0
$928$			4.91574i			0.161367i
$929$	2.33284			0.0765381			0.0382690	−	0.999267i	$-0.487816\pi$
$929$	2.33284			0.0765381			0.0382690	+	0.999267i	$0.487816\pi$
$930$		0			0
$931$	14.4143			0.472410
$932$			24.4087i			0.799533i
$933$		0			0
$934$	−0.918906			−0.0300675
$935$	67.7222	−	5.85053i	2.21475	−	0.191333i
$936$		0			0
$937$		−	1.92340i		−	0.0628349i	−0.999506	−	0.0314174i	$-0.989998\pi$
$937$		−	1.92340i		−	0.0628349i	0.999506	−	0.0314174i	$-0.0100021\pi$
$938$		−	16.7909i		−	0.548242i
$939$		0			0
$940$	19.8744	−	1.71695i	0.648231	−	0.0560007i
$941$	−55.5001			−1.80925			−0.904626	−	0.426205i	$-0.859850\pi$
$941$	−55.5001			−1.80925			−0.904626	+	0.426205i	$0.859850\pi$
$942$		0			0
$943$			12.1997i			0.397276i
$944$	34.7323			1.13044
$945$		0			0
$946$	7.09222			0.230588
$947$		−	37.1931i		−	1.20861i	−0.796752	−	0.604307i	$-0.793450\pi$
$947$		−	37.1931i		−	1.20861i	0.796752	−	0.604307i	$-0.206550\pi$
$948$		0			0
$949$	9.14327			0.296803
$950$	0.427131	+	2.45366i	0.0138580	+	0.0796072i
$951$		0			0
$952$		−	63.5101i		−	2.05837i
$953$		−	54.4958i		−	1.76529i	−0.470039	−	0.882646i	$-0.655760\pi$
$953$		−	54.4958i		−	1.76529i	0.470039	−	0.882646i	$-0.344240\pi$
$954$		0			0
$955$	0.495159	+	5.73167i	0.0160230	+	0.185472i
$956$	−31.1812			−1.00847
$957$		0			0
$958$		−	5.47648i		−	0.176937i
$959$	−10.7344			−0.346631
$960$		0			0
$961$	−4.91335			−0.158495
$962$			11.7366i			0.378402i
$963$		0			0
$964$	−18.4724			−0.594955
$965$	38.4540	−	3.32204i	1.23788	−	0.106940i
$966$		0			0
$967$			28.6863i			0.922490i	0.887273	+	0.461245i	$0.152597\pi$
$967$			28.6863i			0.922490i	−0.887273	+	0.461245i	$0.847403\pi$
$968$			11.4661i			0.368534i
$969$		0			0
$970$	0.224570	+	2.59949i	0.00721052	+	0.0834647i
$971$	−35.0585			−1.12508			−0.562540	−	0.826770i	$-0.690176\pi$
$971$	−35.0585			−1.12508			−0.562540	+	0.826770i	$0.690176\pi$
$972$		0			0
$973$		−	73.1893i		−	2.34634i
$974$	16.0618			0.514655
$975$		0			0
$976$	17.0863			0.546919
$977$			49.1831i			1.57351i	0.617267	+	0.786754i	$0.288240\pi$
$977$			49.1831i			1.57351i	−0.617267	+	0.786754i	$0.711760\pi$
$978$		0			0
$979$	−9.70487			−0.310169
$980$	4.85997	+	56.2561i	0.155246	+	1.79704i
$981$		0			0
$982$			2.74062i			0.0874567i
$983$		−	7.88117i		−	0.251370i	−0.992070	−	0.125685i	$-0.959887\pi$
$983$		−	7.88117i		−	0.251370i	0.992070	−	0.125685i	$-0.0401129\pi$
$984$		0			0
$985$	−41.3529	+	3.57248i	−1.31761	+	0.113829i
$986$	3.58251			0.114090
$987$		0			0
$988$		−	4.18942i		−	0.133283i
$989$	−9.27463			−0.294916
$990$		0			0
$991$	24.6229			0.782174			0.391087	−	0.920354i	$-0.372099\pi$
$991$	24.6229			0.782174			0.391087	+	0.920354i	$0.372099\pi$
$992$		−	25.6361i		−	0.813946i
$993$		0			0
$994$	16.7909			0.532574
$995$	−0.816922	−	9.45621i	−0.0258982	−	0.299782i
$996$		0			0
$997$		−	47.6543i		−	1.50923i	−0.656169	−	0.754614i	$-0.727824\pi$
$997$		−	47.6543i		−	1.50923i	0.656169	−	0.754614i	$-0.272176\pi$
$998$			8.23456i			0.260661i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.c.g.514.9		14
3.2	odd	2		285.2.c.b.229.6	✓	14
5.2	odd	4		4275.2.a.bv.1.4		7
5.3	odd	4		4275.2.a.bw.1.4		7
5.4	even	2	inner	855.2.c.g.514.6		14
15.2	even	4		1425.2.a.z.1.4		7
15.8	even	4		1425.2.a.y.1.4		7
15.14	odd	2		285.2.c.b.229.9	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.c.b.229.6	✓	14	3.2	odd	2
285.2.c.b.229.9	yes	14	15.14	odd	2
855.2.c.g.514.6		14	5.4	even	2	inner
855.2.c.g.514.9		14	1.1	even	1	trivial
1425.2.a.y.1.4		7	15.8	even	4
1425.2.a.z.1.4		7	15.2	even	4
4275.2.a.bv.1.4		7	5.2	odd	4
4275.2.a.bw.1.4		7	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.498112i q^{2} +1.75188 q^{4} +(-0.192457 - 2.22777i) q^{5} -4.62756i q^{7} +1.86886i q^{8} +(1.10968 - 0.0958652i) q^{10} -4.13949 q^{11} +2.39138i q^{13} +2.30504 q^{14} +2.57287 q^{16} -7.34369i q^{17} -1.00000 q^{19} +(-0.337163 - 3.90280i) q^{20} -2.06193i q^{22} +2.69642i q^{23} +(-4.92592 + 0.857501i) q^{25} -1.19117 q^{26} -8.10695i q^{28} +0.979369 q^{29} -5.10751 q^{31} +5.01929i q^{32} +3.65798 q^{34} +(-10.3091 + 0.890607i) q^{35} -9.85293i q^{37} -0.498112i q^{38} +(4.16339 - 0.359675i) q^{40} +4.52440 q^{41} +3.43961i q^{43} -7.25190 q^{44} -1.34312 q^{46} +5.09235i q^{47} -14.4143 q^{49} +(-0.427131 - 2.45366i) q^{50} +4.18942i q^{52} -3.36319i q^{53} +(0.796674 + 9.22182i) q^{55} +8.64825 q^{56} +0.487835i q^{58} +13.4994 q^{59} +6.64096 q^{61} -2.54411i q^{62} +2.64557 q^{64} +(5.32744 - 0.460238i) q^{65} -7.28441i q^{67} -12.8653i q^{68} +(-0.443622 - 5.13511i) q^{70} +7.28441 q^{71} -3.82343i q^{73} +4.90786 q^{74} -1.75188 q^{76} +19.1557i q^{77} +16.1586 q^{79} +(-0.495167 - 5.73176i) q^{80} +2.25366i q^{82} -3.92122i q^{83} +(-16.3601 + 1.41335i) q^{85} -1.71331 q^{86} -7.73611i q^{88} +2.34446 q^{89} +11.0662 q^{91} +4.72382i q^{92} -2.53656 q^{94} +(0.192457 + 2.22777i) q^{95} +2.34256i q^{97} -7.17994i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 22 q^{4} - 2 q^{5} + 2 q^{10} + 8 q^{11} - 8 q^{14} + 38 q^{16} - 14 q^{19} - 12 q^{20} - 4 q^{25} + 40 q^{26} - 12 q^{29} + 8 q^{31} - 4 q^{34} + 14 q^{35} + 18 q^{40} - 4 q^{41} - 64 q^{44} - 8 q^{46}+ \cdots + 2 q^{95}+O(q^{100}) \) 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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