LMFDB - Embedded newform 2016.2.bs.a.1711.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2016,2,Mod(271,2016)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2016.271"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2016, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2016 = 2^{5} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2016.bs (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,0,0,0,0,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$16.0978410475$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.144054149089536.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{11} + x^{9} + 48x^{8} - 189x^{7} + 431x^{6} - 654x^{5} + 624x^{4} - 340x^{3} + 96x^{2} - 12x + 4 $ x^12 - 3x^11 + x^9 + 48x^8 - 189x^7 + 431x^6 - 654x^5 + 624x^4 - 340x^3 + 96x^2 - 12*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1711.5
Root			$2.00233 - 0.854000i$ of defining polynomial
Character	$\chi$	$=$	2016.1711
Dual form			2016.2.bs.a.271.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.03926 + 1.80005i) q^{5} +(1.25203 + 2.33076i) q^{7} +(-0.669938 + 1.16037i) q^{11} +2.50406 q^{13} +(2.78212 + 1.60626i) q^{17} +(-3.55442 + 2.05215i) q^{19} +(5.54952 - 3.20402i) q^{23} +(0.339877 - 0.588684i) q^{25} +4.66151i q^{29} +(2.21897 - 3.84337i) q^{31} +(-2.89430 + 4.67598i) q^{35} +(-5.50178 + 3.17646i) q^{37} +5.55076i q^{41} +(0.565988 + 0.980320i) q^{47} +(-3.86485 + 5.83634i) q^{49} +(-7.43567 - 4.29299i) q^{53} -2.78496 q^{55} +(6.29193 + 3.63265i) q^{59} +(-2.57219 - 4.45517i) q^{61} +(2.60236 + 4.50743i) q^{65} +(-3.93243 + 6.81116i) q^{67} -5.29150i q^{71} +(0.480369 + 0.277341i) q^{73} +(-3.54332 - 0.108651i) q^{77} +(5.26862 - 3.04184i) q^{79} +0.503175i q^{83} +6.67728i q^{85} +(-1.50000 + 0.866025i) q^{89} +(3.13515 + 5.83634i) q^{91} +(-7.38794 - 4.26543i) q^{95} +17.2234i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{11} + 6 q^{17} + 6 q^{19} + 18 q^{35} - 12 q^{49} + 42 q^{59} + 12 q^{65} - 30 q^{67} + 18 q^{73} - 18 q^{89} + 72 q^{91}+O(q^{100}) $ 12 * q - 6 * q^11 + 6 * q^17 + 6 * q^19 + 18 * q^35 - 12 * q^49 + 42 * q^59 + 12 * q^65 - 30 * q^67 + 18 * q^73 - 18 * q^89 + 72 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$1765$	$1793$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.03926	+	1.80005i	0.464771	+	0.805007i	0.999191	−	0.0402117i	$-0.0128032\pi$
$5$	1.03926	+	1.80005i	0.464771	+	0.805007i	−0.534420	+	0.845219i	$0.679470\pi$
$6$		0			0
$7$	1.25203	+	2.33076i	0.473222	+	0.880943i
$7$	1.25203	+	2.33076i	0.473222	+	0.880943i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.669938	+	1.16037i	−0.201994	+	0.349864i	−0.949171	−	0.314761i	$-0.898075\pi$
$11$	−0.669938	+	1.16037i	−0.201994	+	0.349864i	0.747177	+	0.664625i	$0.231409\pi$
$12$		0			0
$13$	2.50406			0.694500			0.347250	−	0.937773i	$-0.387116\pi$
$13$	2.50406			0.694500			0.347250	+	0.937773i	$0.387116\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.78212	+	1.60626i	0.674763	+	0.389575i	0.797879	−	0.602818i	$-0.205955\pi$
$17$	2.78212	+	1.60626i	0.674763	+	0.389575i	−0.123116	+	0.992392i	$0.539289\pi$
$18$		0			0
$19$	−3.55442	+	2.05215i	−0.815440	+	0.470795i	−0.848842	−	0.528647i	$-0.822699\pi$
$19$	−3.55442	+	2.05215i	−0.815440	+	0.470795i	0.0334012	+	0.999442i	$0.489366\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	5.54952	−	3.20402i	1.15716	−	0.668084i	0.206535	−	0.978439i	$-0.433781\pi$
$23$	5.54952	−	3.20402i	1.15716	−	0.668084i	0.950621	+	0.310355i	$0.100448\pi$
$24$		0			0
$25$	0.339877	−	0.588684i	0.0679754	−	0.117737i
$26$		0			0
$27$		0			0
$28$		0			0
$29$			4.66151i			0.865621i	0.901485	+	0.432811i	$0.142478\pi$
$29$			4.66151i			0.865621i	−0.901485	+	0.432811i	$0.857522\pi$
$30$		0			0
$31$	2.21897	−	3.84337i	0.398539	−	0.690290i	−0.595007	−	0.803721i	$-0.702851\pi$
$31$	2.21897	−	3.84337i	0.398539	−	0.690290i	0.993546	+	0.113430i	$0.0361839\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.89430	+	4.67598i	−0.489226	+	0.790384i
$36$		0			0
$37$	−5.50178	+	3.17646i	−0.904488	+	0.522206i	−0.878653	−	0.477460i	$-0.841558\pi$
$37$	−5.50178	+	3.17646i	−0.904488	+	0.522206i	−0.0258343	+	0.999666i	$0.508224\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$			5.55076i			0.866882i	0.901182	+	0.433441i	$0.142701\pi$
$41$			5.55076i			0.866882i	−0.901182	+	0.433441i	$0.857299\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.565988	+	0.980320i	0.0825579	+	0.142994i	0.904348	−	0.426796i	$-0.140358\pi$
$47$	0.565988	+	0.980320i	0.0825579	+	0.142994i	−0.821790	+	0.569790i	$0.807024\pi$
$48$		0			0
$49$	−3.86485	+	5.83634i	−0.552122	+	0.833763i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−7.43567	−	4.29299i	−1.02137	−	0.589687i	−0.106868	−	0.994273i	$-0.534082\pi$
$53$	−7.43567	−	4.29299i	−1.02137	−	0.589687i	−0.914500	+	0.404586i	$0.867416\pi$
$54$		0			0
$55$	−2.78496			−0.375524
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.29193	+	3.63265i	0.819140	+	0.472931i	0.850120	−	0.526589i	$-0.176529\pi$
$59$	6.29193	+	3.63265i	0.819140	+	0.472931i	−0.0309798	+	0.999520i	$0.509863\pi$
$60$		0			0
$61$	−2.57219	−	4.45517i	−0.329336	−	0.570426i	0.653045	−	0.757319i	$-0.273491\pi$
$61$	−2.57219	−	4.45517i	−0.329336	−	0.570426i	−0.982380	+	0.186893i	$0.940158\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.60236	+	4.50743i	0.322784	+	0.559078i
$66$		0			0
$67$	−3.93243	+	6.81116i	−0.480422	+	0.832116i	−0.999748	−	0.0224607i	$-0.992850\pi$
$67$	−3.93243	+	6.81116i	−0.480422	+	0.832116i	0.519325	+	0.854577i	$0.326183\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	5.29150i		−	0.627986i	−0.949425	−	0.313993i	$-0.898333\pi$
$71$		−	5.29150i		−	0.627986i	0.949425	−	0.313993i	$-0.101667\pi$
$72$		0			0
$73$	0.480369	+	0.277341i	0.0562230	+	0.0324604i	0.527848	−	0.849339i	$-0.322999\pi$
$73$	0.480369	+	0.277341i	0.0562230	+	0.0324604i	−0.471625	+	0.881799i	$0.656332\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.54332	−	0.108651i	−0.403798	−	0.0123820i
$78$		0			0
$79$	5.26862	−	3.04184i	0.592766	−	0.342233i	−0.173425	−	0.984847i	$-0.555483\pi$
$79$	5.26862	−	3.04184i	0.592766	−	0.342233i	0.766190	+	0.642614i	$0.222150\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			0.503175i			0.0552307i	0.999619	+	0.0276153i	$0.00879135\pi$
$83$			0.503175i			0.0552307i	−0.999619	+	0.0276153i	$0.991209\pi$
$84$		0			0
$85$			6.67728i			0.724252i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.50000	+	0.866025i	−0.159000	+	0.0917985i	−0.577389	−	0.816469i	$-0.695928\pi$
$89$	−1.50000	+	0.866025i	−0.159000	+	0.0917985i	0.418389	+	0.908268i	$0.362595\pi$
$90$		0			0
$91$	3.13515	+	5.83634i	0.328653	+	0.611815i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−7.38794	−	4.26543i	−0.757986	−	0.437624i
$96$		0			0
$97$			17.2234i			1.74878i	0.485228	+	0.874388i	$0.338737\pi$
$97$			17.2234i			1.74878i	−0.485228	+	0.874388i	$0.661263\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.613725	+	1.06300i	−0.0610679	+	0.105773i	−0.894943	−	0.446180i	$-0.852784\pi$
$101$	−0.613725	+	1.06300i	−0.0610679	+	0.105773i	0.833875	+	0.551953i	$0.186117\pi$
$102$		0			0
$103$	−7.62804	−	13.2122i	−0.751613	−	1.30183i	−0.947041	−	0.321114i	$-0.895943\pi$
$103$	−7.62804	−	13.2122i	−0.751613	−	1.30183i	0.195427	−	0.980718i	$-0.437391\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.55442	−	9.62054i	−0.536966	−	0.930053i	−0.999065	−	0.0432246i	$-0.986237\pi$
$107$	−5.55442	−	9.62054i	−0.536966	−	0.930053i	0.462099	−	0.886828i	$-0.347096\pi$
$108$		0			0
$109$	10.9109	+	6.29938i	1.04507	+	0.603372i	0.921265	−	0.388935i	$-0.127157\pi$
$109$	10.9109	+	6.29938i	1.04507	+	0.603372i	0.123805	+	0.992307i	$0.460490\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−20.0629			−1.88736			−0.943680	−	0.330860i	$-0.892661\pi$
$113$	−20.0629			−1.88736			−0.943680	+	0.330860i	$0.892661\pi$
$114$		0			0
$115$	11.5348	+	6.65961i	1.07562	+	0.621012i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.260504	+	8.49552i	−0.0238804	+	0.778783i
$120$		0			0
$121$	4.60236	+	7.97153i	0.418397	+	0.724685i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.8055			1.05591
$126$		0			0
$127$			14.6145i			1.29683i	0.761287	+	0.648415i	$0.224568\pi$
$127$			14.6145i			1.29683i	−0.761287	+	0.648415i	$0.775432\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.27230	+	3.04397i	−0.460643	+	0.265953i	−0.712315	−	0.701860i	$-0.752353\pi$
$131$	−5.27230	+	3.04397i	−0.460643	+	0.265953i	0.251671	+	0.967813i	$0.419020\pi$
$132$		0			0
$133$	−9.23329	−	5.71515i	−0.800628	−	0.495566i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.98685	−	12.1016i	0.596927	−	1.03391i	−0.396345	−	0.918102i	$-0.629722\pi$
$137$	6.98685	−	12.1016i	0.596927	−	1.03391i	0.993272	−	0.115806i	$-0.0369451\pi$
$138$		0			0
$139$			0.503175i			0.0426788i	0.999772	+	0.0213394i	$0.00679305\pi$
$139$			0.503175i			0.0426788i	−0.999772	+	0.0213394i	$0.993207\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.67756	+	2.90562i	−0.140285	+	0.242981i
$144$		0			0
$145$	−8.39096	+	4.84452i	−0.696832	+	0.402316i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.77077	−	2.75440i	0.390836	−	0.225649i	−0.291686	−	0.956514i	$-0.594216\pi$
$149$	4.77077	−	2.75440i	0.390836	−	0.225649i	0.682522	+	0.730865i	$0.260883\pi$
$150$		0			0
$151$	6.09511	+	3.51901i	0.496013	+	0.286373i	0.727066	−	0.686568i	$-0.240884\pi$
$151$	6.09511	+	3.51901i	0.496013	+	0.286373i	−0.231053	+	0.972941i	$0.574217\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	9.22436			0.740918
$156$		0			0
$157$	7.15477	−	12.3924i	0.571013	−	0.989023i	−0.425450	−	0.904982i	$-0.639884\pi$
$157$	7.15477	−	12.3924i	0.571013	−	0.989023i	0.996462	−	0.0840409i	$-0.0267827\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	14.4159	+	8.92306i	1.13614	+	0.703236i
$162$		0			0
$163$	4.15679	+	7.19977i	0.325585	+	0.563929i	0.981631	−	0.190792i	$-0.0611055\pi$
$163$	4.15679	+	7.19977i	0.325585	+	0.563929i	−0.656046	+	0.754721i	$0.727772\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.50406			0.193770			0.0968848	−	0.995296i	$-0.469112\pi$
$167$	2.50406			0.193770			0.0968848	+	0.995296i	$0.469112\pi$
$168$		0			0
$169$	−6.72971			−0.517670
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.71682	+	4.70568i	0.206556	+	0.357766i	0.950627	−	0.310334i	$-0.100441\pi$
$173$	2.71682	+	4.70568i	0.206556	+	0.357766i	−0.744071	+	0.668100i	$0.767108\pi$
$174$		0			0
$175$	1.79761	+	0.0551216i	0.135887	+	0.00416680i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.75915	+	3.04694i	−0.131485	+	0.227739i	−0.924249	−	0.381790i	$-0.875308\pi$
$179$	−1.75915	+	3.04694i	−0.131485	+	0.227739i	0.792764	+	0.609529i	$0.208641\pi$
$180$		0			0
$181$	22.1981			1.64997			0.824985	−	0.565154i	$-0.191183\pi$
$181$	22.1981			1.64997			0.824985	+	0.565154i	$0.191183\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−11.4356	−	6.60233i	−0.840760	−	0.485413i
$186$		0			0
$187$	−3.72770	+	2.15219i	−0.272596	+	0.157383i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.13615	−	0.655958i	0.0822091	−	0.0474635i	−0.458332	−	0.888781i	$-0.651553\pi$
$191$	1.13615	−	0.655958i	0.0822091	−	0.0474635i	0.540541	+	0.841318i	$0.318220\pi$
$192$		0			0
$193$	5.64697	−	9.78084i	0.406478	−	0.704040i	−0.588014	−	0.808851i	$-0.700090\pi$
$193$	5.64697	−	9.78084i	0.406478	−	0.704040i	0.994492	+	0.104810i	$0.0334235\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	5.92149i		−	0.421889i	−0.977498	−	0.210944i	$-0.932346\pi$
$197$		−	5.92149i		−	0.421889i	0.977498	−	0.210944i	$-0.0676539\pi$
$198$		0			0
$199$	−9.30560	+	16.1178i	−0.659657	+	1.14256i	0.321048	+	0.947063i	$0.395965\pi$
$199$	−9.30560	+	16.1178i	−0.659657	+	1.14256i	−0.980704	+	0.195496i	$0.937368\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−10.8649	+	5.83634i	−0.762563	+	0.409631i
$204$		0			0
$205$	−9.99164	+	5.76868i	−0.697847	+	0.402902i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		−	5.49925i		−	0.380391i
$210$		0			0
$211$	−5.72971			−0.394449			−0.197225	−	0.980358i	$-0.563193\pi$
$211$	−5.72971			−0.394449			−0.197225	+	0.980358i	$0.563193\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$	11.7362	+	0.359875i	0.796704	+	0.0244299i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	6.96658	+	4.02216i	0.468623	+	0.270560i
$222$		0			0
$223$	20.8668			1.39734			0.698672	−	0.715442i	$-0.253775\pi$
$223$	20.8668			1.39734			0.698672	+	0.715442i	$0.253775\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	14.2775	+	8.24309i	0.947628	+	0.547113i	0.892343	−	0.451357i	$-0.149060\pi$
$227$	14.2775	+	8.24309i	0.947628	+	0.547113i	0.0552847	+	0.998471i	$0.482393\pi$
$228$		0			0
$229$	−4.24976	−	7.36079i	−0.280832	−	0.486415i	0.690758	−	0.723086i	$-0.257277\pi$
$229$	−4.24976	−	7.36079i	−0.280832	−	0.486415i	−0.971590	+	0.236671i	$0.923944\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.23751	+	3.87548i	0.146584	+	0.253891i	0.929963	−	0.367653i	$-0.119839\pi$
$233$	2.23751	+	3.87548i	0.146584	+	0.253891i	−0.783379	+	0.621545i	$0.786505\pi$
$234$		0			0
$235$	−1.17642	+	2.03762i	−0.0767410	+	0.132919i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			24.5675i			1.58914i	0.607171	+	0.794571i	$0.292304\pi$
$239$			24.5675i			1.58914i	−0.607171	+	0.794571i	$0.707696\pi$
$240$		0			0
$241$	−5.02498	−	2.90117i	−0.323687	−	0.186881i	0.329348	−	0.944209i	$-0.393171\pi$
$241$	−5.02498	−	2.90117i	−0.323687	−	0.186881i	−0.653035	+	0.757328i	$0.726505\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−14.5223	−	0.891454i	−0.927796	−	0.0569529i
$246$		0			0
$247$	−8.90047	+	5.13869i	−0.566323	+	0.326967i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	18.8010i		−	1.18671i	−0.804942	−	0.593353i	$-0.797804\pi$
$251$		−	18.8010i		−	1.18671i	0.804942	−	0.593353i	$-0.202196\pi$
$252$		0			0
$253$			8.58598i			0.539796i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−10.9106	+	6.29923i	−0.680584	+	0.392935i	−0.800075	−	0.599900i	$-0.795207\pi$
$257$	−10.9106	+	6.29923i	−0.680584	+	0.392935i	0.119491	+	0.992835i	$0.461874\pi$
$258$		0			0
$259$	−14.2919	−	8.84631i	−0.888058	−	0.549683i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	4.27292	+	2.46697i	0.263479	+	0.152120i	0.625921	−	0.779887i	$-0.284723\pi$
$263$	4.27292	+	2.46697i	0.263479	+	0.152120i	−0.362441	+	0.932007i	$0.618057\pi$
$264$		0			0
$265$		−	17.8461i		−	1.09628i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	13.1502	−	22.7769i	0.801783	−	1.38873i	−0.116658	−	0.993172i	$-0.537218\pi$
$269$	13.1502	−	22.7769i	0.801783	−	1.38873i	0.918441	−	0.395558i	$-0.129449\pi$
$270$		0			0
$271$	−14.0490	−	24.3336i	−0.853418	−	1.47816i	−0.878105	−	0.478468i	$-0.841192\pi$
$271$	−14.0490	−	24.3336i	−0.853418	−	1.47816i	0.0246868	−	0.999695i	$-0.492141\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.455393	+	0.788764i	0.0274612	+	0.0475643i
$276$		0			0
$277$	−23.3982	−	13.5090i	−1.40586	−	0.811675i	−0.410876	−	0.911691i	$-0.634777\pi$
$277$	−23.3982	−	13.5090i	−1.40586	−	0.811675i	−0.994986	+	0.100017i	$0.968110\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	20.0629			1.19685			0.598426	−	0.801178i	$-0.295793\pi$
$281$	20.0629			1.19685			0.598426	+	0.801178i	$0.295793\pi$
$282$		0			0
$283$	4.75248	+	2.74385i	0.282506	+	0.163105i	0.634557	−	0.772876i	$-0.281183\pi$
$283$	4.75248	+	2.74385i	0.282506	+	0.163105i	−0.352052	+	0.935981i	$0.614516\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−12.9375	+	6.94970i	−0.763674	+	0.410228i
$288$		0			0
$289$	−3.33988	−	5.78484i	−0.196463	−	0.340284i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−13.6931			−0.799957			−0.399978	−	0.916525i	$-0.630982\pi$
$293$	−13.6931			−0.799957			−0.399978	+	0.916525i	$0.630982\pi$
$294$		0			0
$295$			15.1011i			0.879218i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	13.8963	−	8.02304i	0.803644	−	0.463984i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	5.34636	−	9.26016i	0.306131	−	0.530235i
$306$		0			0
$307$		−	24.4197i		−	1.39371i	−0.717213	−	0.696854i	$-0.754583\pi$
$307$		−	24.4197i		−	1.39371i	0.717213	−	0.696854i	$-0.245417\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	8.61539	−	14.9223i	0.488534	−	0.846165i	−0.511379	−	0.859355i	$-0.670865\pi$
$311$	8.61539	−	14.9223i	0.488534	−	0.846165i	0.999913	+	0.0131898i	$0.00419856\pi$
$312$		0			0
$313$	15.0446	−	8.68601i	0.850371	−	0.490962i	−0.0104047	−	0.999946i	$-0.503312\pi$
$313$	15.0446	−	8.68601i	0.850371	−	0.490962i	0.860776	+	0.508984i	$0.169979\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	16.7863	−	9.69155i	0.942810	−	0.544332i	0.0519701	−	0.998649i	$-0.483450\pi$
$317$	16.7863	−	9.69155i	0.942810	−	0.544332i	0.890840	+	0.454317i	$0.150117\pi$
$318$		0			0
$319$	−5.40907	−	3.12293i	−0.302850	−	0.174850i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−13.1851			−0.733639
$324$		0			0
$325$	0.851071	−	1.47410i	0.0472089	−	0.0817682i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.57625	+	2.54657i	−0.0869018	+	0.140397i
$330$		0			0
$331$	−10.4008	−	18.0147i	−0.571678	−	0.990176i	−0.996394	−	0.0848492i	$-0.972959\pi$
$331$	−10.4008	−	18.0147i	−0.571678	−	0.990176i	0.424715	−	0.905327i	$-0.360374\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−16.3473			−0.893146
$336$		0			0
$337$	10.3332			0.562886			0.281443	−	0.959578i	$-0.409187\pi$
$337$	10.3332			0.562886			0.281443	+	0.959578i	$0.409187\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	2.97315	+	5.14965i	0.161005	+	0.278869i
$342$		0			0
$343$	−18.4420	−	1.70077i	−0.995774	−	0.0918328i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−16.8169	+	29.1277i	−0.902779	+	1.56366i	−0.0789080	+	0.996882i	$0.525143\pi$
$347$	−16.8169	+	29.1277i	−0.902779	+	1.56366i	−0.823871	+	0.566777i	$0.808190\pi$
$348$		0			0
$349$	13.3546			0.714858			0.357429	−	0.933940i	$-0.383653\pi$
$349$	13.3546			0.714858			0.357429	+	0.933940i	$0.383653\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.80175	−	3.92699i	−0.362021	−	0.209013i	0.307946	−	0.951404i	$-0.400358\pi$
$353$	−6.80175	−	3.92699i	−0.362021	−	0.209013i	−0.669967	+	0.742391i	$0.733692\pi$
$354$		0			0
$355$	9.52498	−	5.49925i	0.505533	−	0.291870i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	0.140453	−	0.0810905i	0.00741282	−	0.00427979i	−0.496289	−	0.868157i	$-0.665304\pi$
$359$	0.140453	−	0.0810905i	0.00741282	−	0.00427979i	0.503702	+	0.863878i	$0.331971\pi$
$360$		0			0
$361$	−1.07739	+	1.86609i	−0.0567047	+	0.0982154i
$362$		0			0
$363$		0			0
$364$		0			0
$365$			1.15292i			0.0603466i
$366$		0			0
$367$	10.1321	−	17.5493i	0.528891	−	0.916066i	−0.470541	−	0.882378i	$-0.655941\pi$
$367$	10.1321	−	17.5493i	0.528891	−	0.916066i	0.999432	−	0.0336883i	$-0.0107254\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.696241	−	22.7057i	0.0361470	−	1.17882i
$372$		0			0
$373$	5.78269	−	3.33864i	0.299416	−	0.172868i	−0.342764	−	0.939421i	$-0.611363\pi$
$373$	5.78269	−	3.33864i	0.299416	−	0.172868i	0.642181	+	0.766553i	$0.278030\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			11.6727i			0.601174i
$378$		0			0
$379$	4.60350			0.236466			0.118233	−	0.992986i	$-0.462277\pi$
$379$	4.60350			0.236466			0.118233	+	0.992986i	$0.462277\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−5.71038	−	9.89066i	−0.291787	−	0.505389i	0.682446	−	0.730936i	$-0.260916\pi$
$383$	−5.71038	−	9.89066i	−0.291787	−	0.505389i	−0.974232	+	0.225547i	$0.927583\pi$
$384$		0			0
$385$	−3.48685	−	6.49107i	−0.177706	−	0.330815i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−26.0307	−	15.0288i	−1.31981	−	0.761991i	−0.336109	−	0.941823i	$-0.609111\pi$
$389$	−26.0307	−	15.0288i	−1.31981	−	0.761991i	−0.983697	+	0.179832i	$0.942445\pi$
$390$		0			0
$391$	20.5859			1.04107
$392$		0			0
$393$		0			0
$394$		0			0
$395$	10.9509	+	6.32252i	0.551001	+	0.318120i
$396$		0			0
$397$	2.17124	+	3.76069i	0.108971	+	0.188744i	0.915354	−	0.402651i	$-0.131911\pi$
$397$	2.17124	+	3.76069i	0.108971	+	0.188744i	−0.806383	+	0.591394i	$0.798578\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−9.98685	−	17.2977i	−0.498719	−	0.863807i	0.501279	−	0.865285i	$-0.332863\pi$
$401$	−9.98685	−	17.2977i	−0.498719	−	0.863807i	−0.999999	+	0.00147805i	$0.999530\pi$
$402$		0			0
$403$	5.55643	−	9.62402i	0.276786	−	0.479407i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	8.51212i		−	0.421930i
$408$		0			0
$409$	−26.4356	−	15.2626i	−1.30715	−	0.754686i	−0.325534	−	0.945530i	$-0.605544\pi$
$409$	−26.4356	−	15.2626i	−1.30715	−	0.754686i	−0.981620	+	0.190844i	$0.938878\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−0.589147	+	19.2131i	−0.0289900	+	0.945417i
$414$		0			0
$415$	−0.905741	+	0.522930i	−0.0444611	+	0.0256696i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			2.08070i			0.101649i	0.998708	+	0.0508245i	$0.0161849\pi$
$419$			2.08070i			0.101649i	−0.998708	+	0.0508245i	$0.983815\pi$
$420$		0			0
$421$			30.4039i			1.48180i	0.671618	+	0.740898i	$0.265600\pi$
$421$			30.4039i			1.48180i	−0.671618	+	0.740898i	$0.734400\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.89116	−	1.09186i	0.0917345	−	0.0529630i
$426$		0			0
$427$	7.16346	−	11.5732i	0.346664	−	0.560064i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−2.32280	−	1.34107i	−0.111885	−	0.0645970i	0.443013	−	0.896515i	$-0.353910\pi$
$431$	−2.32280	−	1.34107i	−0.111885	−	0.0645970i	−0.554898	+	0.831918i	$0.687243\pi$
$432$		0			0
$433$		−	29.4673i		−	1.41611i	−0.706158	−	0.708054i	$-0.749573\pi$
$433$		−	29.4673i		−	1.41611i	0.706158	−	0.708054i	$-0.250427\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−13.1502	+	22.7769i	−0.629061	+	1.08957i
$438$		0			0
$439$	−3.77648	−	6.54106i	−0.180242	−	0.312188i	0.761721	−	0.647905i	$-0.224355\pi$
$439$	−3.77648	−	6.54106i	−0.180242	−	0.312188i	−0.941963	+	0.335717i	$0.891021\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	3.75915	+	6.51104i	0.178603	+	0.309349i	0.941402	−	0.337286i	$-0.109509\pi$
$443$	3.75915	+	6.51104i	0.178603	+	0.309349i	−0.762799	+	0.646635i	$0.776176\pi$
$444$		0			0
$445$	−3.11778	−	1.80005i	−0.147797	−	0.0853306i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	14.3332			0.676426			0.338213	−	0.941070i	$-0.390178\pi$
$449$	14.3332			0.676426			0.338213	+	0.941070i	$0.390178\pi$
$450$		0			0
$451$	−6.44092	−	3.71866i	−0.303291	−	0.175105i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−7.24749	+	11.7089i	−0.339767	+	0.548922i
$456$		0			0
$457$	−6.48037	−	11.2243i	−0.303139	−	0.525052i	0.673706	−	0.738999i	$-0.264701\pi$
$457$	−6.48037	−	11.2243i	−0.303139	−	0.525052i	−0.976845	+	0.213947i	$0.931368\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	33.3871			1.55499			0.777496	−	0.628888i	$-0.216490\pi$
$461$	33.3871			1.55499			0.777496	+	0.628888i	$0.216490\pi$
$462$		0			0
$463$			29.7739i			1.38371i	0.722036	+	0.691855i	$0.243206\pi$
$463$			29.7739i			1.38371i	−0.722036	+	0.691855i	$0.756794\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	23.5399	−	13.5908i	1.08930	−	0.628907i	0.155909	−	0.987771i	$-0.450169\pi$
$467$	23.5399	−	13.5908i	1.08930	−	0.628907i	0.933390	+	0.358865i	$0.116836\pi$
$468$		0			0
$469$	−20.7987	−	0.637765i	−0.960393	−	0.0294492i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$			2.78991i			0.128010i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	17.2187	−	29.8237i	0.786744	−	1.36268i	−0.141208	−	0.989980i	$-0.545099\pi$
$479$	17.2187	−	29.8237i	0.786744	−	1.36268i	0.927952	−	0.372700i	$-0.121568\pi$
$480$		0			0
$481$	−13.7768	+	7.95402i	−0.628167	+	0.362672i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−31.0031	+	17.8996i	−1.40778	+	0.812781i
$486$		0			0
$487$	−6.82613	−	3.94107i	−0.309321	−	0.178587i	0.337301	−	0.941397i	$-0.390486\pi$
$487$	−6.82613	−	3.94107i	−0.309321	−	0.178587i	−0.646623	+	0.762810i	$0.723819\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−8.06291			−0.363874			−0.181937	−	0.983310i	$-0.558237\pi$
$491$	−8.06291			−0.363874			−0.181937	+	0.983310i	$0.558237\pi$
$492$		0			0
$493$	−7.48759	+	12.9689i	−0.337224	+	0.584089i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	12.3332	−	6.62511i	0.553220	−	0.297177i
$498$		0			0
$499$	−12.0216	−	20.8221i	−0.538163	−	0.932125i	−0.999003	−	0.0446419i	$-0.985785\pi$
$499$	−12.0216	−	20.8221i	−0.538163	−	0.932125i	0.460841	−	0.887483i	$-0.347548\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	40.8993			1.82361			0.911804	−	0.410626i	$-0.134690\pi$
$503$	40.8993			1.82361			0.911804	+	0.410626i	$0.134690\pi$
$504$		0			0
$505$	−2.55128			−0.113530
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−2.02661	−	3.51019i	−0.0898278	−	0.155586i	0.817610	−	0.575772i	$-0.195298\pi$
$509$	−2.02661	−	3.51019i	−0.0898278	−	0.155586i	−0.907438	+	0.420186i	$0.861965\pi$
$510$		0			0
$511$	−0.0449795	+	1.46686i	−0.00198978	+	0.0648902i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	15.8550	−	27.4617i	0.698656	−	1.21011i
$516$		0			0
$517$	−1.51671			−0.0667048
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−27.1927	−	15.6997i	−1.19133	−	0.687817i	−0.232725	−	0.972543i	$-0.574764\pi$
$521$	−27.1927	−	15.6997i	−1.19133	−	0.687817i	−0.958609	+	0.284725i	$0.908098\pi$
$522$		0			0
$523$	11.7132	−	6.76263i	0.512183	−	0.295709i	−0.221547	−	0.975150i	$-0.571111\pi$
$523$	11.7132	−	6.76263i	0.512183	−	0.295709i	0.733731	+	0.679440i	$0.237777\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	12.3469	−	7.12848i	0.537839	−	0.310522i
$528$		0			0
$529$	9.03146	−	15.6429i	0.392672	−	0.680128i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			13.8994i			0.602050i
$534$		0			0
$535$	11.5450	−	19.9965i	0.499133	−	0.864524i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−4.18309	−	8.39464i	−0.180178	−	0.361583i
$540$		0			0
$541$	27.1543	−	15.6775i	1.16745	−	0.674030i	0.214375	−	0.976751i	$-0.431229\pi$
$541$	27.1543	−	15.6775i	1.16745	−	0.674030i	0.953079	+	0.302722i	$0.0978953\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$			26.1868i			1.12172i
$546$		0			0
$547$	44.7293			1.91249			0.956244	−	0.292571i	$-0.0945108\pi$
$547$	44.7293			1.91249			0.956244	+	0.292571i	$0.0945108\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−9.56611	−	16.5690i	−0.407530	−	0.705863i
$552$		0			0
$553$	13.6862	+	8.47140i	0.581998	+	0.360240i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	10.5345	+	6.08208i	0.446360	+	0.257706i	0.706292	−	0.707921i	$-0.250367\pi$
$557$	10.5345	+	6.08208i	0.446360	+	0.257706i	−0.259932	+	0.965627i	$0.583700\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−31.4311	−	18.1468i	−1.32466	−	0.764794i	−0.340194	−	0.940355i	$-0.610493\pi$
$563$	−31.4311	−	18.1468i	−1.32466	−	0.764794i	−0.984469	+	0.175561i	$0.943826\pi$
$564$		0			0
$565$	−20.8506	−	36.1143i	−0.877191	−	1.51934i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	6.01830	+	10.4240i	0.252300	+	0.436997i	0.964159	−	0.265326i	$-0.0854795\pi$
$569$	6.01830	+	10.4240i	0.252300	+	0.436997i	−0.711858	+	0.702323i	$0.752146\pi$
$570$		0			0
$571$	4.10570	−	7.11128i	0.171818	−	0.297598i	−0.767237	−	0.641363i	$-0.778369\pi$
$571$	4.10570	−	7.11128i	0.171818	−	0.297598i	0.939056	+	0.343765i	$0.111702\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	4.35589i		−	0.181653i
$576$		0			0
$577$	14.5500	+	8.40042i	0.605722	+	0.349714i	0.771289	−	0.636485i	$-0.219612\pi$
$577$	14.5500	+	8.40042i	0.605722	+	0.349714i	−0.165567	+	0.986199i	$0.552945\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.17278	+	0.629989i	−0.0486551	+	0.0261364i
$582$		0			0
$583$	9.96289	−	5.75208i	0.412621	−	0.238227i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	25.4261i		−	1.04945i	−0.851273	−	0.524723i	$-0.824169\pi$
$587$		−	25.4261i		−	1.04945i	0.851273	−	0.524723i	$-0.175831\pi$
$588$		0			0
$589$			18.2146i			0.750521i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	19.0694	−	11.0097i	0.783086	−	0.452115i	−0.0544368	−	0.998517i	$-0.517336\pi$
$593$	19.0694	−	11.0097i	0.783086	−	0.452115i	0.837523	+	0.546402i	$0.184003\pi$
$594$		0			0
$595$	−15.5631	+	8.36013i	−0.638025	+	0.342732i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	0.500607	+	0.289026i	0.0204543	+	0.0118093i	0.510192	−	0.860060i	$-0.329574\pi$
$599$	0.500607	+	0.289026i	0.0204543	+	0.0118093i	−0.489738	+	0.871870i	$0.662908\pi$
$600$		0			0
$601$			27.3186i			1.11435i	0.830395	+	0.557175i	$0.188115\pi$
$601$			27.3186i			1.11435i	−0.830395	+	0.557175i	$0.811885\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−9.56611	+	16.5690i	−0.388918	+	0.673625i
$606$		0			0
$607$	5.99963	+	10.3917i	0.243518	+	0.421785i	0.961714	−	0.274056i	$-0.0883653\pi$
$607$	5.99963	+	10.3917i	0.243518	+	0.421785i	−0.718196	+	0.695841i	$0.755032\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.41727	+	2.45478i	0.0573364	+	0.0993096i
$612$		0			0
$613$	3.96050	+	2.28659i	0.159963	+	0.0923547i	0.577845	−	0.816147i	$-0.303894\pi$
$613$	3.96050	+	2.28659i	0.159963	+	0.0923547i	−0.417882	+	0.908501i	$0.637227\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−5.12621			−0.206373			−0.103187	−	0.994662i	$-0.532904\pi$
$617$	−5.12621			−0.206373			−0.103187	+	0.994662i	$0.532904\pi$
$618$		0			0
$619$	−39.5293	−	22.8222i	−1.58881	−	0.917303i	−0.993503	−	0.113808i	$-0.963695\pi$
$619$	−39.5293	−	22.8222i	−1.58881	−	0.917303i	−0.595312	−	0.803495i	$-0.702972\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.89654	−	2.41185i	−0.156111	−	0.0966286i
$624$		0			0
$625$	10.5696	+	18.3071i	0.422783	+	0.732282i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−20.4088			−0.813753
$630$		0			0
$631$		−	17.1345i		−	0.682113i	−0.940043	−	0.341057i	$-0.889215\pi$
$631$		−	17.1345i		−	0.682113i	0.940043	−	0.341057i	$-0.110785\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−26.3069	+	15.1883i	−1.04396	+	0.602729i
$636$		0			0
$637$	−9.67781	+	14.6145i	−0.383449	+	0.579049i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	4.02498	−	6.97146i	0.158977	−	0.275356i	−0.775523	−	0.631319i	$-0.782514\pi$
$641$	4.02498	−	6.97146i	0.158977	−	0.275356i	0.934500	+	0.355963i	$0.115847\pi$
$642$		0			0
$643$			22.2710i			0.878283i	0.898418	+	0.439142i	$0.144717\pi$
$643$			22.2710i			0.878283i	−0.898418	+	0.439142i	$0.855283\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−18.9125	+	32.7574i	−0.743528	+	1.28783i	0.207352	+	0.978266i	$0.433516\pi$
$647$	−18.9125	+	32.7574i	−0.743528	+	1.28783i	−0.950879	+	0.309561i	$0.899818\pi$
$648$		0			0
$649$	−8.43042	+	4.86730i	−0.330923	+	0.191058i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	25.6130	−	14.7877i	1.00231	−	0.578686i	0.0933818	−	0.995630i	$-0.470232\pi$
$653$	25.6130	−	14.7877i	1.00231	−	0.578686i	0.908932	+	0.416944i	$0.136899\pi$
$654$		0			0
$655$	−10.9586	−	6.32694i	−0.428188	−	0.247214i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	18.3961			0.716611			0.358305	−	0.933604i	$-0.383355\pi$
$659$	18.3961			0.716611			0.358305	+	0.933604i	$0.383355\pi$
$660$		0			0
$661$	−5.92732	+	10.2664i	−0.230546	+	0.399317i	−0.957969	−	0.286872i	$-0.907385\pi$
$661$	−5.92732	+	10.2664i	−0.230546	+	0.399317i	0.727423	+	0.686189i	$0.240718\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.691771	−	22.5599i	0.0268257	−	0.874836i
$666$		0			0
$667$	14.9356	+	25.8692i	0.578308	+	1.00166i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	6.89285			0.266095
$672$		0			0
$673$	10.8738			0.419154			0.209577	−	0.977792i	$-0.432791\pi$
$673$	10.8738			0.419154			0.209577	+	0.977792i	$0.432791\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−22.7163	−	39.3458i	−0.873060	−	1.51218i	−0.858815	−	0.512285i	$-0.828799\pi$
$677$	−22.7163	−	39.3458i	−0.873060	−	1.51218i	−0.0142443	−	0.999899i	$-0.504534\pi$
$678$		0			0
$679$	−40.1437	+	21.5642i	−1.54057	+	0.827559i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−12.3693	+	21.4243i	−0.473299	+	0.819778i	−0.999533	−	0.0305620i	$-0.990270\pi$
$683$	−12.3693	+	21.4243i	−0.473299	+	0.819778i	0.526234	+	0.850340i	$0.323604\pi$
$684$		0			0
$685$	29.0446			1.10974
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−18.6193	−	10.7499i	−0.709340	−	0.409538i
$690$		0			0
$691$	4.10457	−	2.36977i	0.156145	−	0.0901504i	−0.419892	−	0.907574i	$-0.637932\pi$
$691$	4.10457	−	2.36977i	0.156145	−	0.0901504i	0.576037	+	0.817424i	$0.304599\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.905741	+	0.522930i	−0.0343567	+	0.0198359i
$696$		0			0
$697$	−8.91594	+	15.4429i	−0.337715	+	0.584940i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			39.8121i			1.50368i	0.659345	+	0.751840i	$0.270834\pi$
$701$			39.8121i			1.50368i	−0.659345	+	0.751840i	$0.729166\pi$
$702$		0			0
$703$	13.0371	−	22.5809i	0.491704	−	0.851656i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.24600	−	0.0995345i	−0.122078	−	0.00374338i
$708$		0			0
$709$	−4.97242	+	2.87083i	−0.186743	+	0.107816i	−0.590457	−	0.807069i	$-0.701052\pi$
$709$	−4.97242	+	2.87083i	−0.186743	+	0.107816i	0.403714	+	0.914885i	$0.367719\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	28.4385i		−	1.06503i
$714$		0			0
$715$	−6.97370			−0.260801
$716$		0			0
$717$		0			0
$718$		0			0
$719$	7.62804	+	13.2122i	0.284478	+	0.492730i	0.972482	−	0.232976i	$-0.0748464\pi$
$719$	7.62804	+	13.2122i	0.284478	+	0.492730i	−0.688005	+	0.725706i	$0.741513\pi$
$720$		0			0
$721$	21.2438	−	34.3211i	0.791160	−	1.27818i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.74416	+	1.58434i	0.101915	+	0.0588409i
$726$		0			0
$727$	40.8993			1.51687			0.758435	−	0.651749i	$-0.225964\pi$
$727$	40.8993			1.51687			0.758435	+	0.651749i	$0.225964\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−12.2037	−	21.1374i	−0.450753	−	0.780728i	0.547680	−	0.836688i	$-0.315511\pi$
$733$	−12.2037	−	21.1374i	−0.450753	−	0.780728i	−0.998433	+	0.0559605i	$0.982178\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.26897	−	9.12612i	−0.194085	−	0.336165i
$738$		0			0
$739$	−15.3996	+	26.6730i	−0.566485	+	0.981181i	0.430425	+	0.902626i	$0.358364\pi$
$739$	−15.3996	+	26.6730i	−0.566485	+	0.981181i	−0.996910	+	0.0785545i	$0.974970\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			23.9376i			0.878184i	0.898442	+	0.439092i	$0.144700\pi$
$743$			23.9376i			0.878184i	−0.898442	+	0.439092i	$0.855300\pi$
$744$		0			0
$745$	9.91613	+	5.72508i	0.363299	+	0.209751i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	15.4689	−	24.9912i	0.565219	−	0.913158i
$750$		0			0
$751$	−11.9543	+	6.90181i	−0.436218	+	0.251851i	−0.701992	−	0.712185i	$-0.747706\pi$
$751$	−11.9543	+	6.90181i	−0.436218	+	0.251851i	0.265774	+	0.964035i	$0.414373\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			14.6287i			0.532392i
$756$		0			0
$757$			2.14156i			0.0778362i	0.999242	+	0.0389181i	$0.0123911\pi$
$757$			2.14156i			0.0778362i	−0.999242	+	0.0389181i	$0.987609\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−36.8321	+	21.2650i	−1.33516	+	0.770856i	−0.986086	−	0.166239i	$-0.946838\pi$
$761$	−36.8321	+	21.2650i	−1.33516	+	0.770856i	−0.349076	+	0.937094i	$0.613504\pi$
$762$		0			0
$763$	−1.02164	+	33.3175i	−0.0369859	+	1.20618i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	15.7554	+	9.09636i	0.568893	+	0.328450i
$768$		0			0
$769$		−	15.6459i		−	0.564206i	−0.959384	−	0.282103i	$-0.908968\pi$
$769$		−	15.6459i		−	0.564206i	0.959384	−	0.282103i	$-0.0910320\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	15.2125	−	26.3489i	0.547156	−	0.947703i	−0.451311	−	0.892367i	$-0.649044\pi$
$773$	15.2125	−	26.3489i	0.547156	−	0.947703i	0.998468	−	0.0553362i	$-0.0176230\pi$
$774$		0			0
$775$	−1.50836	−	2.61255i	−0.0541817	−	0.0938455i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−11.3910	−	19.7297i	−0.408124	−	0.706891i
$780$		0			0
$781$	6.14009	+	3.54498i	0.219710	+	0.126849i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	29.7427			1.06156
$786$		0			0
$787$	28.3722	+	16.3807i	1.01136	+	0.583909i	0.911590	−	0.411102i	$-0.134856\pi$
$787$	28.3722	+	16.3807i	1.01136	+	0.583909i	0.0997704	+	0.995010i	$0.468189\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−25.1193	−	46.7618i	−0.893140	−	1.66266i
$792$		0			0
$793$	−6.44092	−	11.1560i	−0.228724	−	0.396161i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	28.3790			1.00523			0.502617	−	0.864509i	$-0.332370\pi$
$797$	28.3790			1.00523			0.502617	+	0.864509i	$0.332370\pi$
$798$		0			0
$799$			3.63649i			0.128650i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.643636	+	0.371603i	−0.0227134	+	0.0131136i
$804$		0			0
$805$	−1.08006	+	35.2228i	−0.0380672	+	1.24144i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−4.08387	+	7.07347i	−0.143581	+	0.248690i	−0.928843	−	0.370474i	$-0.879195\pi$
$809$	−4.08387	+	7.07347i	−0.143581	+	0.248690i	0.785262	+	0.619164i	$0.212528\pi$
$810$		0			0
$811$		−	22.2710i		−	0.782041i	−0.920382	−	0.391021i	$-0.872122\pi$
$811$		−	22.2710i		−	0.782041i	0.920382	−	0.391021i	$-0.127878\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−8.63997	+	14.9649i	−0.302645	+	0.524196i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−4.52231	+	2.61096i	−0.157830	+	0.0911230i	−0.576835	−	0.816861i	$-0.695712\pi$
$821$	−4.52231	+	2.61096i	−0.157830	+	0.0911230i	0.419005	+	0.907984i	$0.362379\pi$
$822$		0			0
$823$	8.29368	+	4.78836i	0.289099	+	0.166912i	0.637536	−	0.770421i	$-0.279954\pi$
$823$	8.29368	+	4.78836i	0.289099	+	0.166912i	−0.348436	+	0.937333i	$0.613287\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	40.6664			1.41411			0.707055	−	0.707159i	$-0.250023\pi$
$827$	40.6664			1.41411			0.707055	+	0.707159i	$0.250023\pi$
$828$		0			0
$829$	16.6171	−	28.7816i	0.577134	−	0.999625i	−0.418672	−	0.908137i	$-0.637504\pi$
$829$	16.6171	−	28.7816i	0.577134	−	0.999625i	0.995806	−	0.0914880i	$-0.0291623\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−20.1271	+	10.0295i	−0.697364	+	0.347500i
$834$		0			0
$835$	2.60236	+	4.50743i	0.0900586	+	0.155986i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−15.0243			−0.518698			−0.259349	−	0.965784i	$-0.583508\pi$
$839$	−15.0243			−0.518698			−0.259349	+	0.965784i	$0.583508\pi$
$840$		0			0
$841$	7.27029			0.250700
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−6.99392	−	12.1138i	−0.240598	−	0.416728i
$846$		0			0
$847$	−12.8174	+	20.7076i	−0.440411	+	0.711521i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−20.3548	+	35.2556i	−0.697755	+	1.20855i
$852$		0			0
$853$	−12.5203			−0.428686			−0.214343	−	0.976758i	$-0.568761\pi$
$853$	−12.5203			−0.428686			−0.214343	+	0.976758i	$0.568761\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	46.8265	+	27.0353i	1.59956	+	0.923509i	0.991571	+	0.129566i	$0.0413585\pi$
$857$	46.8265	+	27.0353i	1.59956	+	0.923509i	0.607993	+	0.793942i	$0.291975\pi$
$858$		0			0
$859$	−17.0990	+	9.87213i	−0.583411	+	0.336833i	−0.762488	−	0.647002i	$-0.776022\pi$
$859$	−17.0990	+	9.87213i	−0.583411	+	0.336833i	0.179077	+	0.983835i	$0.442689\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−26.3755	+	15.2279i	−0.897833	+	0.518364i	−0.876497	−	0.481408i	$-0.840126\pi$
$863$	−26.3755	+	15.2279i	−0.897833	+	0.518364i	−0.0213367	+	0.999772i	$0.506792\pi$
$864$		0			0
$865$	−5.64697	+	9.78084i	−0.192003	+	0.332559i
$866$		0			0
$867$		0			0
$868$		0			0
$869$			8.15137i			0.276516i
$870$		0			0
$871$	−9.84701	+	17.0555i	−0.333653	+	0.577905i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	14.7808	+	27.5157i	0.499682	+	0.930201i
$876$		0			0
$877$	18.3275	−	10.5814i	0.618877	−	0.357309i	−0.157555	−	0.987510i	$-0.550361\pi$
$877$	18.3275	−	10.5814i	0.618877	−	0.357309i	0.776432	+	0.630201i	$0.217028\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			11.5367i			0.388681i	0.980934	+	0.194340i	$0.0622566\pi$
$881$			11.5367i			0.388681i	−0.980934	+	0.194340i	$0.937743\pi$
$882$		0			0
$883$	−49.8555			−1.67777			−0.838886	−	0.544307i	$-0.816793\pi$
$883$	−49.8555			−1.67777			−0.838886	+	0.544307i	$0.816793\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−5.56575	−	9.64015i	−0.186879	−	0.323685i	0.757329	−	0.653034i	$-0.226504\pi$
$887$	−5.56575	−	9.64015i	−0.186879	−	0.323685i	−0.944208	+	0.329349i	$0.893171\pi$
$888$		0			0
$889$	−34.0629	+	18.2978i	−1.14243	+	0.613688i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−4.02352	−	2.32298i	−0.134642	−	0.0777356i
$894$		0			0
$895$	−7.31287			−0.244442
$896$		0			0
$897$		0			0
$898$		0			0
$899$	17.9159	+	10.3438i	0.597530	+	0.344984i
$900$		0			0
$901$	−13.7913	−	23.8872i	−0.459454	−	0.795798i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	23.0696	+	39.9577i	0.766859	+	1.32824i
$906$		0			0
$907$	−7.20674	+	12.4824i	−0.239296	+	0.414473i	−0.960512	−	0.278237i	$-0.910250\pi$
$907$	−7.20674	+	12.4824i	−0.239296	+	0.414473i	0.721217	+	0.692710i	$0.243583\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			19.1909i			0.635823i	0.948120	+	0.317911i	$0.102981\pi$
$911$			19.1909i			0.635823i	−0.948120	+	0.317911i	$0.897019\pi$
$912$		0			0
$913$	−0.583868	−	0.337096i	−0.0193232	−	0.0111563i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−13.6958	−	8.47733i	−0.452276	−	0.279946i
$918$		0			0
$919$	22.4285	−	12.9491i	0.739848	−	0.427151i	−0.0821662	−	0.996619i	$-0.526184\pi$
$919$	22.4285	−	12.9491i	0.739848	−	0.427151i	0.822014	+	0.569467i	$0.192850\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	13.2502i		−	0.436136i
$924$		0			0
$925$			4.31842i			0.141989i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	36.7480	−	21.2165i	1.20566	−	0.696090i	0.243854	−	0.969812i	$-0.421588\pi$
$929$	36.7480	−	21.2165i	1.20566	−	0.696090i	0.961809	+	0.273722i	$0.0882548\pi$
$930$		0			0
$931$	1.76029	−	28.6761i	0.0576910	−	0.939820i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−7.74809	−	4.47336i	−0.253390	−	0.146295i
$936$		0			0
$937$			46.5547i			1.52088i	0.649410	+	0.760439i	$0.275016\pi$
$937$			46.5547i			1.52088i	−0.649410	+	0.760439i	$0.724984\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.48937	+	2.57967i	−0.0485522	+	0.0840949i	−0.889280	−	0.457363i	$-0.848794\pi$
$941$	−1.48937	+	2.57967i	−0.0485522	+	0.0840949i	0.840728	+	0.541458i	$0.182127\pi$
$942$		0			0
$943$	17.7847	+	30.8040i	0.579150	+	1.00312i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	13.5270	+	23.4294i	0.439568	+	0.761354i	0.997656	−	0.0684276i	$-0.0217982\pi$
$947$	13.5270	+	23.4294i	0.439568	+	0.761354i	−0.558088	+	0.829782i	$0.688465\pi$
$948$		0			0
$949$	1.20287	+	0.694478i	0.0390469	+	0.0225437i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−28.7293			−0.930634			−0.465317	−	0.885144i	$-0.654060\pi$
$953$	−28.7293			−0.930634			−0.465317	+	0.885144i	$0.654060\pi$
$954$		0			0
$955$	2.36152	+	1.36342i	0.0764169	+	0.0441193i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	36.9536	+	1.13313i	1.19329	+	0.0365908i
$960$		0			0
$961$	5.65232	+	9.79010i	0.182333	+	0.315810i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	23.4747			0.755677
$966$		0			0
$967$			13.3546i			0.429453i	0.976674	+	0.214727i	$0.0688861\pi$
$967$			13.3546i			0.429453i	−0.976674	+	0.214727i	$0.931114\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1.71876	+	0.992325i	−0.0551575	+	0.0318452i	−0.527325	−	0.849664i	$-0.676805\pi$
$971$	−1.71876	+	0.992325i	−0.0551575	+	0.0318452i	0.472168	+	0.881509i	$0.343472\pi$
$972$		0			0
$973$	−1.17278	+	0.629989i	−0.0375976	+	0.0201965i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−31.2242	+	54.0818i	−0.998950	+	1.73023i	−0.459792	+	0.888027i	$0.652076\pi$
$977$	−31.2242	+	54.0818i	−0.998950	+	1.73023i	−0.539158	+	0.842205i	$0.681257\pi$
$978$		0			0
$979$		−	2.32073i		−	0.0741710i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	3.64021	−	6.30503i	0.116105	−	0.201099i	−0.802116	−	0.597168i	$-0.796293\pi$
$983$	3.64021	−	6.30503i	0.116105	−	0.201099i	0.918221	+	0.396069i	$0.129626\pi$
$984$		0			0
$985$	10.6590	−	6.15397i	0.339624	−	0.196082i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−31.3345	−	18.0910i	−0.995373	−	0.574679i	−0.0884967	−	0.996076i	$-0.528206\pi$
$991$	−31.3345	−	18.0910i	−0.995373	−	0.574679i	−0.906876	+	0.421398i	$0.861540\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−38.6838			−1.22636
$996$		0			0
$997$	17.1218	−	29.6559i	0.542254	−	0.939211i	−0.456520	−	0.889713i	$-0.650904\pi$
$997$	17.1218	−	29.6559i	0.542254	−	0.939211i	0.998774	−	0.0494984i	$-0.0157623\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2016.2.bs.a.1711.5		12
3.2	odd	2		224.2.q.a.143.5		12
4.3	odd	2		504.2.bk.a.451.5		12
7.5	odd	6	inner	2016.2.bs.a.271.2		12
8.3	odd	2	inner	2016.2.bs.a.1711.2		12
8.5	even	2		504.2.bk.a.451.2		12
12.11	even	2		56.2.m.a.3.2	✓	12
21.2	odd	6		1568.2.q.g.1391.1		12
21.5	even	6		224.2.q.a.47.6		12
21.11	odd	6		1568.2.e.e.783.2		12
21.17	even	6		1568.2.e.e.783.11		12
21.20	even	2		1568.2.q.g.815.2		12
24.5	odd	2		56.2.m.a.3.5	yes	12
24.11	even	2		224.2.q.a.143.6		12
28.19	even	6		504.2.bk.a.19.1		12
56.5	odd	6		504.2.bk.a.19.6		12
56.19	even	6	inner	2016.2.bs.a.271.5		12
84.11	even	6		392.2.e.e.195.6		12
84.23	even	6		392.2.m.g.19.6		12
84.47	odd	6		56.2.m.a.19.6	yes	12
84.59	odd	6		392.2.e.e.195.5		12
84.83	odd	2		392.2.m.g.227.2		12
168.5	even	6		56.2.m.a.19.1	yes	12
168.11	even	6		1568.2.e.e.783.1		12
168.53	odd	6		392.2.e.e.195.8		12
168.59	odd	6		1568.2.e.e.783.12		12
168.83	odd	2		1568.2.q.g.815.1		12
168.101	even	6		392.2.e.e.195.7		12
168.107	even	6		1568.2.q.g.1391.2		12
168.125	even	2		392.2.m.g.227.5		12
168.131	odd	6		224.2.q.a.47.5		12
168.149	odd	6		392.2.m.g.19.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.m.a.3.2	✓	12	12.11	even	2
56.2.m.a.3.5	yes	12	24.5	odd	2
56.2.m.a.19.1	yes	12	168.5	even	6
56.2.m.a.19.6	yes	12	84.47	odd	6
224.2.q.a.47.5		12	168.131	odd	6
224.2.q.a.47.6		12	21.5	even	6
224.2.q.a.143.5		12	3.2	odd	2
224.2.q.a.143.6		12	24.11	even	2
392.2.e.e.195.5		12	84.59	odd	6
392.2.e.e.195.6		12	84.11	even	6
392.2.e.e.195.7		12	168.101	even	6
392.2.e.e.195.8		12	168.53	odd	6
392.2.m.g.19.1		12	168.149	odd	6
392.2.m.g.19.6		12	84.23	even	6
392.2.m.g.227.2		12	84.83	odd	2
392.2.m.g.227.5		12	168.125	even	2
504.2.bk.a.19.1		12	28.19	even	6
504.2.bk.a.19.6		12	56.5	odd	6
504.2.bk.a.451.2		12	8.5	even	2
504.2.bk.a.451.5		12	4.3	odd	2
1568.2.e.e.783.1		12	168.11	even	6
1568.2.e.e.783.2		12	21.11	odd	6
1568.2.e.e.783.11		12	21.17	even	6
1568.2.e.e.783.12		12	168.59	odd	6
1568.2.q.g.815.1		12	168.83	odd	2
1568.2.q.g.815.2		12	21.20	even	2
1568.2.q.g.1391.1		12	21.2	odd	6
1568.2.q.g.1391.2		12	168.107	even	6
2016.2.bs.a.271.2		12	7.5	odd	6	inner
2016.2.bs.a.271.5		12	56.19	even	6	inner
2016.2.bs.a.1711.2		12	8.3	odd	2	inner
2016.2.bs.a.1711.5		12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2016.bs (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.03926 + 1.80005i) q^{5} +(1.25203 + 2.33076i) q^{7} +(-0.669938 + 1.16037i) q^{11} +2.50406 q^{13} +(2.78212 + 1.60626i) q^{17} +(-3.55442 + 2.05215i) q^{19} +(5.54952 - 3.20402i) q^{23} +(0.339877 - 0.588684i) q^{25} +4.66151i q^{29} +(2.21897 - 3.84337i) q^{31} +(-2.89430 + 4.67598i) q^{35} +(-5.50178 + 3.17646i) q^{37} +5.55076i q^{41} +(0.565988 + 0.980320i) q^{47} +(-3.86485 + 5.83634i) q^{49} +(-7.43567 - 4.29299i) q^{53} -2.78496 q^{55} +(6.29193 + 3.63265i) q^{59} +(-2.57219 - 4.45517i) q^{61} +(2.60236 + 4.50743i) q^{65} +(-3.93243 + 6.81116i) q^{67} -5.29150i q^{71} +(0.480369 + 0.277341i) q^{73} +(-3.54332 - 0.108651i) q^{77} +(5.26862 - 3.04184i) q^{79} +0.503175i q^{83} +6.67728i q^{85} +(-1.50000 + 0.866025i) q^{89} +(3.13515 + 5.83634i) q^{91} +(-7.38794 - 4.26543i) q^{95} +17.2234i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{11} + 6 q^{17} + 6 q^{19} + 18 q^{35} - 12 q^{49} + 42 q^{59} + 12 q^{65} - 30 q^{67} + 18 q^{73} - 18 q^{89} + 72 q^{91}+O(q^{100}) \) 12 * q - 6 * q^11 + 6 * q^17 + 6 * q^19 + 18 * q^35 - 12 * q^49 + 42 * q^59 + 12 * q^65 - 30 * q^67 + 18 * q^73 - 18 * q^89 + 72 * q^91

Introduction

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