LMFDB - Embedded newform 1404.2.cj.a.1061.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1404,2,Mod(125,1404)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1404, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 10, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1404.125"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1404 = 2^{2} \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1404.cj (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$11.2109964438$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 468)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			1061.3
Character	$\chi$	$=$	1404.1061
Dual form			1404.2.cj.a.1097.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.73979 - 0.734125i) q^{5} +(-0.507313 - 1.89332i) q^{7} +(0.591661 - 0.158535i) q^{11} +(3.30116 + 1.44996i) q^{13} -0.329188 q^{17} +(-2.29971 - 2.29971i) q^{19} +(-0.458575 - 0.794276i) q^{23} +(2.63740 + 1.52270i) q^{25} +(-3.53714 - 2.04217i) q^{29} +(-0.970663 + 3.62256i) q^{31} +5.55973i q^{35} +(-5.24778 + 5.24778i) q^{37} +(-5.06836 - 1.35806i) q^{41} +(-6.65352 - 3.84141i) q^{43} +(-4.75386 + 1.27379i) q^{47} +(2.73489 - 1.57899i) q^{49} +10.3025i q^{53} -1.73741 q^{55} +(-2.05912 + 7.68473i) q^{59} +(-3.51473 + 6.08768i) q^{61} +(-7.98004 - 6.39604i) q^{65} +(-3.19344 + 11.9181i) q^{67} +(-0.769386 + 0.769386i) q^{71} +(-5.02343 + 5.02343i) q^{73} +(-0.600315 - 1.03978i) q^{77} +(-4.63505 + 8.02814i) q^{79} +(-4.47998 - 16.7195i) q^{83} +(0.901908 + 0.241666i) q^{85} +(-8.13868 - 8.13868i) q^{89} +(1.07051 - 6.98572i) q^{91} +(4.61246 + 7.98901i) q^{95} +(-7.50874 + 2.01196i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{7} + 12 q^{11} + 4 q^{19} - 4 q^{31} - 4 q^{37} - 24 q^{41} - 66 q^{47} + 78 q^{65} - 14 q^{67} + 28 q^{73} - 24 q^{79} + 78 q^{83} + 36 q^{85} - 8 q^{91} + 26 q^{97}+O(q^{100}) $ 56 * q - 2 * q^7 + 12 * q^11 + 4 * q^19 - 4 * q^31 - 4 * q^37 - 24 * q^41 - 66 * q^47 + 78 * q^65 - 14 * q^67 + 28 * q^73 - 24 * q^79 + 78 * q^83 + 36 * q^85 - 8 * q^91 + 26 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1404\mathbb{Z}\right)^\times$.

$n$	$677$	$703$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$5$	−2.73979	−	0.734125i	−1.22527	−	0.328311i	−0.412536	−	0.910941i	$-0.635357\pi$
$5$	−2.73979	−	0.734125i	−1.22527	−	0.328311i	−0.812737	+	0.582631i	$0.802023\pi$
$6$		0			0
$7$	−0.507313	−	1.89332i	−0.191746	−	0.715607i	−0.993085	−	0.117396i	$-0.962545\pi$
$7$	−0.507313	−	1.89332i	−0.191746	−	0.715607i	0.801339	−	0.598211i	$-0.204121\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.591661	−	0.158535i	0.178393	−	0.0478001i	−0.168517	−	0.985699i	$-0.553898\pi$
$11$	0.591661	−	0.158535i	0.178393	−	0.0478001i	0.346909	+	0.937899i	$0.387231\pi$
$12$		0			0
$13$	3.30116	+	1.44996i	0.915576	+	0.402145i
$13$	3.30116	+	1.44996i	0.915576	+	0.402145i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.329188			−0.0798399			−0.0399200	−	0.999203i	$-0.512710\pi$
$17$	−0.329188			−0.0798399			−0.0399200	+	0.999203i	$0.512710\pi$
$18$		0			0
$19$	−2.29971	−	2.29971i	−0.527590	−	0.527590i	0.392263	−	0.919853i	$-0.371692\pi$
$19$	−2.29971	−	2.29971i	−0.527590	−	0.527590i	−0.919853	+	0.392263i	$0.871692\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.458575	−	0.794276i	−0.0956196	−	0.165618i	0.814247	−	0.580518i	$-0.197150\pi$
$23$	−0.458575	−	0.794276i	−0.0956196	−	0.165618i	−0.909867	+	0.414900i	$0.863817\pi$
$24$		0			0
$25$	2.63740	+	1.52270i	0.527480	+	0.304541i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.53714	−	2.04217i	−0.656830	−	0.379221i	0.134238	−	0.990949i	$-0.457141\pi$
$29$	−3.53714	−	2.04217i	−0.656830	−	0.379221i	−0.791068	+	0.611728i	$0.790475\pi$
$30$		0			0
$31$	−0.970663	+	3.62256i	−0.174336	+	0.650632i	0.822327	+	0.569015i	$0.192675\pi$
$31$	−0.970663	+	3.62256i	−0.174336	+	0.650632i	−0.996664	+	0.0816173i	$0.973991\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			5.55973i			0.939767i
$36$		0			0
$37$	−5.24778	+	5.24778i	−0.862730	+	0.862730i	−0.991654	−	0.128925i	$-0.958847\pi$
$37$	−5.24778	+	5.24778i	−0.862730	+	0.862730i	0.128925	+	0.991654i	$0.458847\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5.06836	−	1.35806i	−0.791545	−	0.212094i	−0.159677	−	0.987169i	$-0.551045\pi$
$41$	−5.06836	−	1.35806i	−0.791545	−	0.212094i	−0.631869	+	0.775075i	$0.717712\pi$
$42$		0			0
$43$	−6.65352	−	3.84141i	−1.01465	−	0.585810i	−0.102102	−	0.994774i	$-0.532557\pi$
$43$	−6.65352	−	3.84141i	−1.01465	−	0.585810i	−0.912550	+	0.408964i	$0.865890\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.75386	+	1.27379i	−0.693421	+	0.185802i	−0.588282	−	0.808656i	$-0.700196\pi$
$47$	−4.75386	+	1.27379i	−0.693421	+	0.185802i	−0.105139	+	0.994457i	$0.533529\pi$
$48$		0			0
$49$	2.73489	−	1.57899i	0.390698	−	0.225570i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			10.3025i			1.41516i	0.706633	+	0.707581i	$0.250213\pi$
$53$			10.3025i			1.41516i	−0.706633	+	0.707581i	$0.749787\pi$
$54$		0			0
$55$	−1.73741			−0.234273
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.05912	+	7.68473i	−0.268074	+	1.00047i	0.692268	+	0.721641i	$0.256612\pi$
$59$	−2.05912	+	7.68473i	−0.268074	+	1.00047i	−0.960342	+	0.278826i	$0.910055\pi$
$60$		0			0
$61$	−3.51473	+	6.08768i	−0.450015	+	0.779448i	−0.998386	−	0.0567865i	$-0.981915\pi$
$61$	−3.51473	+	6.08768i	−0.450015	+	0.779448i	0.548372	+	0.836235i	$0.315248\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−7.98004	−	6.39604i	−0.989802	−	0.793331i
$66$		0			0
$67$	−3.19344	+	11.9181i	−0.390140	+	1.45602i	0.439762	+	0.898115i	$0.355063\pi$
$67$	−3.19344	+	11.9181i	−0.390140	+	1.45602i	−0.829902	+	0.557909i	$0.811604\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.769386	+	0.769386i	−0.0913093	+	0.0913093i	−0.751286	−	0.659977i	$-0.770566\pi$
$71$	−0.769386	+	0.769386i	−0.0913093	+	0.0913093i	0.659977	+	0.751286i	$0.270566\pi$
$72$		0			0
$73$	−5.02343	+	5.02343i	−0.587949	+	0.587949i	−0.937075	−	0.349127i	$-0.886478\pi$
$73$	−5.02343	+	5.02343i	−0.587949	+	0.587949i	0.349127	+	0.937075i	$0.386478\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.600315	−	1.03978i	−0.0684122	−	0.118493i
$78$		0			0
$79$	−4.63505	+	8.02814i	−0.521484	+	0.903236i	0.478204	+	0.878249i	$0.341288\pi$
$79$	−4.63505	+	8.02814i	−0.521484	+	0.903236i	−0.999688	+	0.0249875i	$0.992045\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.47998	−	16.7195i	−0.491742	−	1.83521i	−0.547562	−	0.836765i	$-0.684444\pi$
$83$	−4.47998	−	16.7195i	−0.491742	−	1.83521i	0.0558197	−	0.998441i	$-0.482223\pi$
$84$		0			0
$85$	0.901908	+	0.241666i	0.0978257	+	0.0262123i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−8.13868	−	8.13868i	−0.862699	−	0.862699i	0.128952	−	0.991651i	$-0.458839\pi$
$89$	−8.13868	−	8.13868i	−0.862699	−	0.862699i	−0.991651	+	0.128952i	$0.958839\pi$
$90$		0			0
$91$	1.07051	−	6.98572i	0.112220	−	0.732303i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	4.61246	+	7.98901i	0.473228	+	0.819655i
$96$		0			0
$97$	−7.50874	+	2.01196i	−0.762397	+	0.204284i	−0.619010	−	0.785383i	$-0.712466\pi$
$97$	−7.50874	+	2.01196i	−0.762397	+	0.204284i	−0.143387	+	0.989667i	$0.545799\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.13315	−	10.6229i	0.610271	−	1.05702i	−0.380923	−	0.924607i	$-0.624394\pi$
$101$	6.13315	−	10.6229i	0.610271	−	1.05702i	0.991194	−	0.132414i	$-0.0422729\pi$
$102$		0			0
$103$	8.32770	−	4.80800i	0.820553	−	0.473746i	−0.0300543	−	0.999548i	$-0.509568\pi$
$103$	8.32770	−	4.80800i	0.820553	−	0.473746i	0.850607	+	0.525802i	$0.176235\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			1.85058i			0.178902i	0.995991	+	0.0894511i	$0.0285113\pi$
$107$			1.85058i			0.178902i	−0.995991	+	0.0894511i	$0.971489\pi$
$108$		0			0
$109$	0.523808	+	0.523808i	0.0501717	+	0.0501717i	0.731748	−	0.681576i	$-0.238705\pi$
$109$	0.523808	+	0.523808i	0.0501717	+	0.0501717i	−0.681576	+	0.731748i	$0.738705\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	15.5927	−	9.00243i	1.46683	−	0.846877i	0.467523	−	0.883981i	$-0.345146\pi$
$113$	15.5927	−	9.00243i	1.46683	−	0.846877i	0.999311	+	0.0371036i	$0.0118131\pi$
$114$		0			0
$115$	0.673304	+	2.51280i	0.0627859	+	0.234320i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.167002	+	0.623259i	0.0153090	+	0.0571340i
$120$		0			0
$121$	−9.20135	+	5.31240i	−0.836486	+	0.482946i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	3.92026	+	3.92026i	0.350639	+	0.350639i
$126$		0			0
$127$		−	15.2754i		−	1.35547i	−0.735305	−	0.677737i	$-0.762961\pi$
$127$		−	15.2754i		−	1.35547i	0.735305	−	0.677737i	$-0.237039\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	9.56197	−	5.52061i	0.835434	−	0.482338i	−0.0202759	−	0.999794i	$-0.506454\pi$
$131$	9.56197	−	5.52061i	0.835434	−	0.482338i	0.855709	+	0.517457i	$0.173121\pi$
$132$		0			0
$133$	−3.18741	+	5.52076i	−0.276384	+	0.478711i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−14.2810	+	3.82658i	−1.22011	+	0.326927i	−0.810720	−	0.585434i	$-0.800924\pi$
$137$	−14.2810	+	3.82658i	−1.22011	+	0.326927i	−0.409387	+	0.912361i	$0.634258\pi$
$138$		0			0
$139$	6.38084	+	11.0519i	0.541216	+	0.937414i	0.998835	+	0.0482650i	$0.0153692\pi$
$139$	6.38084	+	11.0519i	0.541216	+	0.937414i	−0.457619	+	0.889149i	$0.651297\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2.18303	+	0.334533i	0.182554	+	0.0279751i
$144$		0			0
$145$	8.19182	+	8.19182i	0.680293	+	0.680293i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−4.63919	−	1.24307i	−0.380057	−	0.101836i	0.0637324	−	0.997967i	$-0.479700\pi$
$149$	−4.63919	−	1.24307i	−0.380057	−	0.101836i	−0.443790	+	0.896131i	$0.646366\pi$
$150$		0			0
$151$	−2.79405	−	10.4275i	−0.227377	−	0.848581i	−0.981438	−	0.191778i	$-0.938575\pi$
$151$	−2.79405	−	10.4275i	−0.227377	−	0.848581i	0.754062	−	0.656803i	$-0.228092\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	5.31883	−	9.21249i	0.427219	−	0.739965i
$156$		0			0
$157$	−3.88990	−	6.73750i	−0.310448	−	0.537711i	0.668012	−	0.744151i	$-0.267146\pi$
$157$	−3.88990	−	6.73750i	−0.310448	−	0.537711i	−0.978459	+	0.206440i	$0.933812\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.27118	+	1.27118i	−0.100183	+	0.100183i
$162$		0			0
$163$	11.6439	−	11.6439i	0.912020	−	0.912020i	−0.0844107	−	0.996431i	$-0.526901\pi$
$163$	11.6439	−	11.6439i	0.912020	−	0.912020i	0.996431	+	0.0844107i	$0.0269008\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.23932	−	4.62520i	0.0959014	−	0.357909i	−0.901253	−	0.433293i	$-0.857352\pi$
$167$	1.23932	−	4.62520i	0.0959014	−	0.357909i	0.997155	+	0.0753839i	$0.0240182\pi$
$168$		0			0
$169$	8.79526	+	9.57306i	0.676558	+	0.736389i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.66477	+	16.7399i	−0.734799	+	1.27271i	0.220013	+	0.975497i	$0.429390\pi$
$173$	−9.66477	+	16.7399i	−0.734799	+	1.27271i	−0.954812	+	0.297212i	$0.903943\pi$
$174$		0			0
$175$	1.54498	−	5.76593i	0.116789	−	0.435863i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−12.5587			−0.938684			−0.469342	−	0.883017i	$-0.655509\pi$
$179$	−12.5587			−0.938684			−0.469342	+	0.883017i	$0.655509\pi$
$180$		0			0
$181$			21.1579i			1.57265i	0.617811	+	0.786327i	$0.288020\pi$
$181$			21.1579i			1.57265i	−0.617811	+	0.786327i	$0.711980\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	18.2304	−	10.5253i	1.34032	−	0.773836i
$186$		0			0
$187$	−0.194768	+	0.0521879i	−0.0142428	+	0.00381636i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	18.1736	+	10.4925i	1.31500	+	0.759213i	0.982919	−	0.184039i	$-0.0589172\pi$
$191$	18.1736	+	10.4925i	1.31500	+	0.759213i	0.332077	+	0.943252i	$0.392251\pi$
$192$		0			0
$193$	−8.76182	−	2.34772i	−0.630690	−	0.168993i	−0.0707070	−	0.997497i	$-0.522526\pi$
$193$	−8.76182	−	2.34772i	−0.630690	−	0.168993i	−0.559983	+	0.828504i	$0.689192\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−11.0033	+	11.0033i	−0.783953	+	0.783953i	−0.980495	−	0.196542i	$-0.937029\pi$
$197$	−11.0033	+	11.0033i	−0.783953	+	0.783953i	0.196542	+	0.980495i	$0.437029\pi$
$198$		0			0
$199$		−	9.40693i		−	0.666839i	−0.942778	−	0.333420i	$-0.891797\pi$
$199$		−	9.40693i		−	0.666839i	0.942778	−	0.333420i	$-0.108203\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−2.07204	+	7.73295i	−0.145428	+	0.542746i
$204$		0			0
$205$	12.8893	+	7.44163i	0.900226	+	0.519746i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.72524	−	0.996065i	−0.119337	−	0.0688993i
$210$		0			0
$211$	−11.9952	−	20.7763i	−0.825784	−	1.43030i	−0.901318	−	0.433157i	$-0.857399\pi$
$211$	−11.9952	−	20.7763i	−0.825784	−	1.43030i	0.0755338	−	0.997143i	$-0.475934\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	15.4092	+	15.4092i	1.05090	+	1.05090i
$216$		0			0
$217$	7.35110			0.499025
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.08670	−	0.477309i	−0.0730995	−	0.0321073i
$222$		0			0
$223$	23.0018	−	6.16331i	1.54031	−	0.412726i	0.613947	−	0.789347i	$-0.289581\pi$
$223$	23.0018	−	6.16331i	1.54031	−	0.412726i	0.926367	+	0.376621i	$0.122914\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−7.21963	−	26.9440i	−0.479183	−	1.78834i	−0.604935	−	0.796275i	$-0.706801\pi$
$227$	−7.21963	−	26.9440i	−0.479183	−	1.78834i	0.125751	−	0.992062i	$-0.459866\pi$
$228$		0			0
$229$	−2.73139	−	0.731872i	−0.180495	−	0.0483635i	0.167439	−	0.985882i	$-0.446450\pi$
$229$	−2.73139	−	0.731872i	−0.180495	−	0.0483635i	−0.347934	+	0.937519i	$0.613117\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.37193			−0.351927			−0.175963	−	0.984397i	$-0.556304\pi$
$233$	−5.37193			−0.351927			−0.175963	+	0.984397i	$0.556304\pi$
$234$		0			0
$235$	13.9597			0.910631
$236$		0			0
$237$		0			0
$238$		0			0
$239$	3.30632	+	0.885927i	0.213868	+	0.0573058i	0.364162	−	0.931336i	$-0.381355\pi$
$239$	3.30632	+	0.885927i	0.213868	+	0.0573058i	−0.150294	+	0.988641i	$0.548022\pi$
$240$		0			0
$241$	−7.46235	−	27.8499i	−0.480692	−	1.79397i	−0.598722	−	0.800957i	$-0.704325\pi$
$241$	−7.46235	−	27.8499i	−0.480692	−	1.79397i	0.118030	−	0.993010i	$-0.462342\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−8.65220	+	2.31835i	−0.552769	+	0.148114i
$246$		0			0
$247$	−4.25723	−	10.9262i	−0.270881	−	0.695217i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	0.889720			0.0561587			0.0280793	−	0.999606i	$-0.491061\pi$
$251$	0.889720			0.0561587			0.0280793	+	0.999606i	$0.491061\pi$
$252$		0			0
$253$	−0.397242	−	0.397242i	−0.0249744	−	0.0249744i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	12.1369	+	21.0217i	0.757079	+	1.31130i	0.944334	+	0.328987i	$0.106707\pi$
$257$	12.1369	+	21.0217i	0.757079	+	1.31130i	−0.187256	+	0.982311i	$0.559959\pi$
$258$		0			0
$259$	12.5980	+	7.27345i	0.782801	+	0.451950i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	16.3337	+	9.43028i	1.00718	+	0.581496i	0.910365	−	0.413806i	$-0.135801\pi$
$263$	16.3337	+	9.43028i	1.00718	+	0.581496i	0.0968159	+	0.995302i	$0.469134\pi$
$264$		0			0
$265$	7.56335	−	28.2268i	0.464613	−	1.73396i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			24.2986i			1.48151i	0.671774	+	0.740757i	$0.265533\pi$
$269$			24.2986i			1.48151i	−0.671774	+	0.740757i	$0.734467\pi$
$270$		0			0
$271$	−10.8607	+	10.8607i	−0.659741	+	0.659741i	−0.955319	−	0.295578i	$-0.904488\pi$
$271$	−10.8607	+	10.8607i	−0.659741	+	0.659741i	0.295578	+	0.955319i	$0.404488\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.80185	+	0.482804i	0.108656	+	0.0291142i
$276$		0			0
$277$	−3.90814	−	2.25637i	−0.234818	−	0.135572i	0.377975	−	0.925816i	$-0.376621\pi$
$277$	−3.90814	−	2.25637i	−0.234818	−	0.135572i	−0.612793	+	0.790244i	$0.709954\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−17.8164	+	4.77388i	−1.06284	+	0.284786i	−0.747546	−	0.664210i	$-0.768768\pi$
$281$	−17.8164	+	4.77388i	−1.06284	+	0.284786i	−0.315289	+	0.948996i	$0.602102\pi$
$282$		0			0
$283$	−2.60463	+	1.50378i	−0.154829	+	0.0893906i	−0.575413	−	0.817863i	$-0.695159\pi$
$283$	−2.60463	+	1.50378i	−0.154829	+	0.0893906i	0.420584	+	0.907254i	$0.361825\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			10.2850i			0.607104i
$288$		0			0
$289$	−16.8916			−0.993626
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.64326	−	6.13275i	0.0960005	−	0.358279i	−0.901169	−	0.433469i	$-0.857290\pi$
$293$	1.64326	−	6.13275i	0.0960005	−	0.358279i	0.997169	+	0.0751896i	$0.0239562\pi$
$294$		0			0
$295$	11.2831	−	19.5429i	0.656928	−	1.13783i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.362164	−	3.28694i	−0.0209445	−	0.190089i
$300$		0			0
$301$	−3.89760	+	14.5460i	−0.224654	+	0.838420i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	14.0987	−	14.0987i	0.807292	−	0.807292i
$306$		0			0
$307$	1.50595	−	1.50595i	0.0859492	−	0.0859492i	−0.662825	−	0.748774i	$-0.730643\pi$
$307$	1.50595	−	1.50595i	0.0859492	−	0.0859492i	0.748774	+	0.662825i	$0.230643\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−6.93805	−	12.0170i	−0.393420	−	0.681424i	0.599478	−	0.800391i	$-0.295375\pi$
$311$	−6.93805	−	12.0170i	−0.393420	−	0.681424i	−0.992898	+	0.118967i	$0.962042\pi$
$312$		0			0
$313$	3.70337	−	6.41442i	0.209327	−	0.362565i	−0.742176	−	0.670205i	$-0.766206\pi$
$313$	3.70337	−	6.41442i	0.209327	−	0.362565i	0.951503	+	0.307641i	$0.0995394\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	8.34561	+	31.1462i	0.468736	+	1.74935i	0.644197	+	0.764860i	$0.277192\pi$
$317$	8.34561	+	31.1462i	0.468736	+	1.74935i	−0.175461	+	0.984486i	$0.556141\pi$
$318$		0			0
$319$	−2.41654	−	0.647510i	−0.135300	−	0.0362536i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	0.757039	+	0.757039i	0.0421228	+	0.0421228i
$324$		0			0
$325$	6.49862	+	8.85080i	0.360478	+	0.490954i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	4.82339	+	8.35436i	0.265922	+	0.460591i
$330$		0			0
$331$	−8.03717	+	2.15355i	−0.441763	+	0.118370i	−0.472843	−	0.881147i	$-0.656772\pi$
$331$	−8.03717	+	2.15355i	−0.441763	+	0.118370i	0.0310796	+	0.999517i	$0.490105\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	17.4987	−	30.3087i	0.956057	−	1.65594i
$336$		0			0
$337$	6.73189	−	3.88666i	0.366709	−	0.211720i	−0.305310	−	0.952253i	$-0.598760\pi$
$337$	6.73189	−	3.88666i	0.366709	−	0.211720i	0.672020	+	0.740533i	$0.265427\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			2.29721i			0.124401i
$342$		0			0
$343$	−14.0790	−	14.0790i	−0.760195	−	0.760195i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	27.0008	−	15.5889i	1.44948	−	0.836856i	0.451027	−	0.892510i	$-0.351058\pi$
$347$	27.0008	−	15.5889i	1.44948	−	0.836856i	0.998450	+	0.0556541i	$0.0177244\pi$
$348$		0			0
$349$	1.29126	+	4.81905i	0.0691195	+	0.257958i	0.991836	−	0.127522i	$-0.0407025\pi$
$349$	1.29126	+	4.81905i	0.0691195	+	0.257958i	−0.922716	+	0.385480i	$0.874036\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.749885	+	2.79861i	0.0399124	+	0.148955i	0.983006	−	0.183571i	$-0.0587657\pi$
$353$	0.749885	+	2.79861i	0.0399124	+	0.148955i	−0.943094	+	0.332526i	$0.892099\pi$
$354$		0			0
$355$	2.67278	−	1.54313i	0.141857	−	0.0819009i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−20.8996	−	20.8996i	−1.10304	−	1.10304i	−0.994042	−	0.108997i	$-0.965236\pi$
$359$	−20.8996	−	20.8996i	−1.10304	−	1.10304i	−0.108997	−	0.994042i	$-0.534764\pi$
$360$		0			0
$361$		−	8.42265i		−	0.443297i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	17.4510	−	10.0753i	0.913427	−	0.527368i
$366$		0			0
$367$	5.85980	−	10.1495i	0.305879	−	0.529798i	−0.671577	−	0.740934i	$-0.734383\pi$
$367$	5.85980	−	10.1495i	0.305879	−	0.529798i	0.977457	+	0.211136i	$0.0677163\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	19.5060	−	5.22661i	1.01270	−	0.271352i
$372$		0			0
$373$	6.42101	+	11.1215i	0.332467	+	0.575850i	0.982995	−	0.183632i	$-0.0587856\pi$
$373$	6.42101	+	11.1215i	0.332467	+	0.575850i	−0.650528	+	0.759482i	$0.725452\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−8.71559	−	11.8702i	−0.448876	−	0.611346i
$378$		0			0
$379$	9.13990	+	9.13990i	0.469485	+	0.469485i	0.901748	−	0.432263i	$-0.142285\pi$
$379$	9.13990	+	9.13990i	0.469485	+	0.469485i	−0.432263	+	0.901748i	$0.642285\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	14.8266	+	3.97277i	0.757603	+	0.202999i	0.616888	−	0.787051i	$-0.288393\pi$
$383$	14.8266	+	3.97277i	0.757603	+	0.202999i	0.140715	+	0.990050i	$0.455060\pi$
$384$		0			0
$385$	0.881413	+	3.28948i	0.0449210	+	0.167647i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−19.1965	+	33.2493i	−0.973302	+	1.68581i	−0.287875	+	0.957668i	$0.592949\pi$
$389$	−19.1965	+	33.2493i	−0.973302	+	1.68581i	−0.685428	+	0.728141i	$0.740385\pi$
$390$		0			0
$391$	0.150958	+	0.261466i	0.00763426	+	0.0132229i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	18.5927	−	18.5927i	0.935502	−	0.935502i
$396$		0			0
$397$	10.6225	−	10.6225i	0.533130	−	0.533130i	−0.388372	−	0.921503i	$-0.626962\pi$
$397$	10.6225	−	10.6225i	0.533130	−	0.533130i	0.921503	+	0.388372i	$0.126962\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	4.33401	−	16.1747i	0.216430	−	0.807727i	−0.769228	−	0.638974i	$-0.779359\pi$
$401$	4.33401	−	16.1747i	0.216430	−	0.807727i	0.985658	−	0.168753i	$-0.0539742\pi$
$402$		0			0
$403$	−8.45687	+	10.5512i	−0.421267	+	0.525594i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.27295	+	3.93686i	−0.112666	+	0.195143i
$408$		0			0
$409$	3.69860	−	13.8034i	0.182884	−	0.682532i	−0.812190	−	0.583394i	$-0.801725\pi$
$409$	3.69860	−	13.8034i	0.182884	−	0.682532i	0.995074	−	0.0991389i	$-0.0316088\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	15.5943			0.767344
$414$		0			0
$415$			49.0969i			2.41007i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	4.26586	−	2.46289i	0.208401	−	0.120320i	−0.392167	−	0.919894i	$-0.628275\pi$
$419$	4.26586	−	2.46289i	0.208401	−	0.120320i	0.600568	+	0.799574i	$0.294941\pi$
$420$		0			0
$421$	9.31053	−	2.49475i	0.453768	−	0.121587i	−0.0246942	−	0.999695i	$-0.507861\pi$
$421$	9.31053	−	2.49475i	0.453768	−	0.121587i	0.478462	+	0.878108i	$0.341195\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.868202	−	0.501257i	−0.0421140	−	0.0243145i
$426$		0			0
$427$	13.3090	+	3.56614i	0.644068	+	0.172577i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	0.315102	−	0.315102i	0.0151779	−	0.0151779i	−0.699477	−	0.714655i	$-0.746584\pi$
$431$	0.315102	−	0.315102i	0.0151779	−	0.0151779i	0.714655	+	0.699477i	$0.246584\pi$
$432$		0			0
$433$		−	30.2736i		−	1.45485i	−0.686185	−	0.727427i	$-0.740716\pi$
$433$		−	30.2736i		−	1.45485i	0.686185	−	0.727427i	$-0.259284\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.772015	+	2.88120i	−0.0369305	+	0.137826i
$438$		0			0
$439$	−31.2977	−	18.0697i	−1.49376	−	0.862421i	−0.493783	−	0.869585i	$-0.664386\pi$
$439$	−31.2977	−	18.0697i	−1.49376	−	0.862421i	−0.999974	+	0.00716374i	$0.997720\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.98825	−	1.14792i	−0.0944646	−	0.0545391i	0.452024	−	0.892006i	$-0.350702\pi$
$443$	−1.98825	−	1.14792i	−0.0944646	−	0.0545391i	−0.546488	+	0.837467i	$0.684036\pi$
$444$		0			0
$445$	16.3235	+	28.2731i	0.773808	+	1.34027i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−6.47243	−	6.47243i	−0.305453	−	0.305453i	0.537690	−	0.843143i	$-0.319297\pi$
$449$	−6.47243	−	6.47243i	−0.305453	−	0.305453i	−0.843143	+	0.537690i	$0.819297\pi$
$450$		0			0
$451$	−3.21405			−0.151344
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−8.06137	+	18.3535i	−0.377923	+	0.860428i
$456$		0			0
$457$	23.4658	−	6.28764i	1.09768	−	0.294123i	0.335862	−	0.941911i	$-0.390972\pi$
$457$	23.4658	−	6.28764i	1.09768	−	0.294123i	0.761821	+	0.647788i	$0.224306\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−4.36996	−	16.3089i	−0.203530	−	0.759583i	−0.989893	−	0.141818i	$-0.954705\pi$
$461$	−4.36996	−	16.3089i	−0.203530	−	0.759583i	0.786363	−	0.617764i	$-0.211961\pi$
$462$		0			0
$463$	24.6867	+	6.61478i	1.14729	+	0.307415i	0.781878	−	0.623432i	$-0.214262\pi$
$463$	24.6867	+	6.61478i	1.14729	+	0.307415i	0.365410	+	0.930847i	$0.380929\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−23.4460			−1.08495			−0.542477	−	0.840071i	$-0.682513\pi$
$467$	−23.4460			−1.08495			−0.542477	+	0.840071i	$0.682513\pi$
$468$		0			0
$469$	24.1848			1.11675
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4.54563	−	1.21800i	−0.209008	−	0.0560036i
$474$		0			0
$475$	−2.56348	−	9.56704i	−0.117621	−	0.438966i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	18.5359	−	4.96669i	0.846928	−	0.226934i	0.190843	−	0.981621i	$-0.438878\pi$
$479$	18.5359	−	4.96669i	0.846928	−	0.226934i	0.656085	+	0.754687i	$0.272211\pi$
$480$		0			0
$481$	−24.9328	+	9.71469i	−1.13684	+	0.442952i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	22.0494			1.00121
$486$		0			0
$487$	−15.8625	−	15.8625i	−0.718800	−	0.718800i	0.249560	−	0.968359i	$-0.419714\pi$
$487$	−15.8625	−	15.8625i	−0.718800	−	0.718800i	−0.968359	+	0.249560i	$0.919714\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−3.74118	−	6.47991i	−0.168837	−	0.292434i	0.769174	−	0.639039i	$-0.220668\pi$
$491$	−3.74118	−	6.47991i	−0.168837	−	0.292434i	−0.938011	+	0.346605i	$0.887334\pi$
$492$		0			0
$493$	1.16438	+	0.672258i	0.0524412	+	0.0302770i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.84701	+	1.06637i	0.0828498	+	0.0478334i
$498$		0			0
$499$	−3.00769	+	11.2248i	−0.134643	+	0.502493i	0.865357	+	0.501157i	$0.167092\pi$
$499$	−3.00769	+	11.2248i	−0.134643	+	0.502493i	−0.999999	+	0.00133618i	$0.999575\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			9.78116i			0.436120i	0.975935	+	0.218060i	$0.0699729\pi$
$503$			9.78116i			0.436120i	−0.975935	+	0.218060i	$0.930027\pi$
$504$		0			0
$505$	−24.6021	+	24.6021i	−1.09478	+	1.09478i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−16.6846	−	4.47063i	−0.739533	−	0.198157i	−0.130662	−	0.991427i	$-0.541710\pi$
$509$	−16.6846	−	4.47063i	−0.739533	−	0.198157i	−0.608870	+	0.793270i	$0.708377\pi$
$510$		0			0
$511$	12.0594	+	6.96251i	0.533477	+	0.308003i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−26.3459	+	7.05935i	−1.16094	+	0.311072i
$516$		0			0
$517$	−2.61073	+	1.50731i	−0.114820	+	0.0662913i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	7.17847i		−	0.314495i	−0.987559	−	0.157247i	$-0.949738\pi$
$521$		−	7.17847i		−	0.314495i	0.987559	−	0.157247i	$-0.0502620\pi$
$522$		0			0
$523$	24.9245			1.08987			0.544936	−	0.838478i	$-0.316554\pi$
$523$	24.9245			1.08987			0.544936	+	0.838478i	$0.316554\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.319531	−	1.19251i	0.0139190	−	0.0519464i
$528$		0			0
$529$	11.0794	−	19.1901i	0.481714	−	0.834353i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−14.7623	−	11.8321i	−0.639427	−	0.512504i
$534$		0			0
$535$	1.35856	−	5.07020i	0.0587355	−	0.219204i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.36780	−	1.36780i	0.0589154	−	0.0589154i
$540$		0			0
$541$	−27.7003	+	27.7003i	−1.19093	+	1.19093i	−0.214120	+	0.976807i	$0.568688\pi$
$541$	−27.7003	+	27.7003i	−1.19093	+	1.19093i	−0.976807	+	0.214120i	$0.931312\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−1.05059	−	1.81967i	−0.0450021	−	0.0779460i
$546$		0			0
$547$	−15.7394	+	27.2614i	−0.672966	+	1.16561i	0.304093	+	0.952642i	$0.401647\pi$
$547$	−15.7394	+	27.2614i	−0.672966	+	1.16561i	−0.977059	+	0.212969i	$0.931687\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	3.43800	+	12.8308i	0.146464	+	0.546610i
$552$		0			0
$553$	17.5513	+	4.70284i	0.746355	+	0.199985i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.834344	−	0.834344i	−0.0353523	−	0.0353523i	0.689210	−	0.724562i	$-0.257958\pi$
$557$	−0.834344	−	0.834344i	−0.0353523	−	0.0353523i	−0.724562	+	0.689210i	$0.757958\pi$
$558$		0			0
$559$	−16.3944	−	22.3284i	−0.693410	−	0.944391i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.64883	+	2.85585i	0.0694898	+	0.120360i	0.898677	−	0.438611i	$-0.144530\pi$
$563$	1.64883	+	2.85585i	0.0694898	+	0.120360i	−0.829187	+	0.558971i	$0.811196\pi$
$564$		0			0
$565$	−49.3296	+	13.2178i	−2.07531	+	0.556078i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	10.9777	−	19.0140i	0.460210	−	0.797107i	−0.538761	−	0.842459i	$-0.681107\pi$
$569$	10.9777	−	19.0140i	0.460210	−	0.797107i	0.998971	+	0.0453513i	$0.0144407\pi$
$570$		0			0
$571$	−36.3726	+	20.9997i	−1.52215	+	0.878811i	−0.522488	+	0.852647i	$0.674996\pi$
$571$	−36.3726	+	20.9997i	−1.52215	+	0.878811i	−0.999658	+	0.0261646i	$0.991671\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	2.79310i		−	0.116480i
$576$		0			0
$577$	−8.86716	−	8.86716i	−0.369145	−	0.369145i	0.498021	−	0.867165i	$-0.334060\pi$
$577$	−8.86716	−	8.86716i	−0.369145	−	0.369145i	−0.867165	+	0.498021i	$0.834060\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−29.3826	+	16.9641i	−1.21900	+	0.703788i
$582$		0			0
$583$	1.63331	+	6.09560i	0.0676449	+	0.252454i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.536579	+	2.00254i	0.0221470	+	0.0826537i	0.976115	−	0.217255i	$-0.0697104\pi$
$587$	0.536579	+	2.00254i	0.0221470	+	0.0826537i	−0.953968	+	0.299909i	$0.903044\pi$
$588$		0			0
$589$	10.5631	−	6.09861i	0.435245	−	0.251289i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	17.1296	+	17.1296i	0.703427	+	0.703427i	0.965145	−	0.261717i	$-0.0842888\pi$
$593$	17.1296	+	17.1296i	0.703427	+	0.703427i	−0.261717	+	0.965145i	$0.584289\pi$
$594$		0			0
$595$		−	1.83020i		−	0.0750309i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	1.29688	−	0.748751i	0.0529889	−	0.0305931i	−0.473272	−	0.880917i	$-0.656927\pi$
$599$	1.29688	−	0.748751i	0.0529889	−	0.0305931i	0.526260	+	0.850323i	$0.323594\pi$
$600$		0			0
$601$	−9.10896	+	15.7772i	−0.371562	+	0.643565i	−0.989806	−	0.142422i	$-0.954511\pi$
$601$	−9.10896	+	15.7772i	−0.371562	+	0.643565i	0.618244	+	0.785986i	$0.287844\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	29.1098	−	7.79994i	1.18348	−	0.317113i
$606$		0			0
$607$	−0.761886	−	1.31963i	−0.0309240	−	0.0535619i	0.850149	−	0.526542i	$-0.176512\pi$
$607$	−0.761886	−	1.31963i	−0.0309240	−	0.0535619i	−0.881073	+	0.472980i	$0.843178\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−17.5402	−	2.68790i	−0.709599	−	0.108741i
$612$		0			0
$613$	−25.9101	−	25.9101i	−1.04650	−	1.04650i	−0.998865	−	0.0476336i	$-0.984832\pi$
$613$	−25.9101	−	25.9101i	−1.04650	−	1.04650i	−0.0476336	−	0.998865i	$-0.515168\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−27.2538	−	7.30263i	−1.09720	−	0.293993i	−0.335574	−	0.942014i	$-0.608930\pi$
$617$	−27.2538	−	7.30263i	−1.09720	−	0.293993i	−0.761623	+	0.648021i	$0.775597\pi$
$618$		0			0
$619$	2.02380	+	7.55294i	0.0813435	+	0.303578i	0.994597	−	0.103814i	$-0.0331048\pi$
$619$	2.02380	+	7.55294i	0.0813435	+	0.303578i	−0.913253	+	0.407392i	$0.866438\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−11.2803	+	19.5380i	−0.451934	+	0.782773i
$624$		0			0
$625$	−15.4763	−	26.8057i	−0.619051	−	1.07223i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1.72751	−	1.72751i	0.0688803	−	0.0688803i
$630$		0			0
$631$	−10.5595	+	10.5595i	−0.420368	+	0.420368i	−0.885330	−	0.464963i	$-0.846068\pi$
$631$	−10.5595	+	10.5595i	−0.420368	+	0.420368i	0.464963	+	0.885330i	$0.346068\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−11.2141	+	41.8515i	−0.445017	+	1.66082i
$636$		0			0
$637$	11.3178	−	1.24702i	0.448426	−	0.0494087i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	3.66091	−	6.34089i	0.144597	−	0.250450i	−0.784625	−	0.619970i	$-0.787145\pi$
$641$	3.66091	−	6.34089i	0.144597	−	0.250450i	0.929223	+	0.369520i	$0.120478\pi$
$642$		0			0
$643$	9.98668	−	37.2708i	0.393836	−	1.46982i	−0.429917	−	0.902869i	$-0.641457\pi$
$643$	9.98668	−	37.2708i	0.393836	−	1.46982i	0.823753	−	0.566949i	$-0.191876\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−16.7465			−0.658373			−0.329186	−	0.944265i	$-0.606774\pi$
$647$	−16.7465			−0.658373			−0.329186	+	0.944265i	$0.606774\pi$
$648$		0			0
$649$			4.87320i			0.191290i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−30.1333	+	17.3975i	−1.17921	+	0.680816i	−0.955831	−	0.293917i	$-0.905041\pi$
$653$	−30.1333	+	17.3975i	−1.17921	+	0.680816i	−0.223376	+	0.974732i	$0.571708\pi$
$654$		0			0
$655$	−30.2507	+	8.10564i	−1.18199	+	0.316713i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	0.801546	+	0.462773i	0.0312238	+	0.0180271i	0.515531	−	0.856871i	$-0.327595\pi$
$659$	0.801546	+	0.462773i	0.0312238	+	0.0180271i	−0.484307	+	0.874898i	$0.660928\pi$
$660$		0			0
$661$	−11.7073	−	3.13696i	−0.455361	−	0.122013i	0.0238460	−	0.999716i	$-0.492409\pi$
$661$	−11.7073	−	3.13696i	−0.455361	−	0.122013i	−0.479207	+	0.877702i	$0.659076\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	12.7858	−	12.7858i	0.495812	−	0.495812i
$666$		0			0
$667$			3.74595i			0.145044i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1.11442	+	4.15905i	−0.0430215	+	0.160558i
$672$		0			0
$673$	14.4389	+	8.33628i	0.556577	+	0.321340i	0.751771	−	0.659425i	$-0.229200\pi$
$673$	14.4389	+	8.33628i	0.556577	+	0.321340i	−0.195193	+	0.980765i	$0.562533\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−9.98589	−	5.76536i	−0.383789	−	0.221581i	0.295677	−	0.955288i	$-0.404455\pi$
$677$	−9.98589	−	5.76536i	−0.383789	−	0.221581i	−0.679466	+	0.733707i	$0.737788\pi$
$678$		0			0
$679$	7.61857	+	13.1957i	0.292374	+	0.506406i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	30.5505	+	30.5505i	1.16898	+	1.16898i	0.982449	+	0.186534i	$0.0597254\pi$
$683$	30.5505	+	30.5505i	1.16898	+	1.16898i	0.186534	+	0.982449i	$0.440275\pi$
$684$		0			0
$685$	41.9362			1.60230
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−14.9382	+	34.0103i	−0.569100	+	1.29569i
$690$		0			0
$691$	14.2621	−	3.82152i	0.542556	−	0.145377i	0.0228759	−	0.999738i	$-0.492718\pi$
$691$	14.2621	−	3.82152i	0.542556	−	0.145377i	0.519680	+	0.854361i	$0.326051\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−9.36868	−	34.9644i	−0.355374	−	1.32627i
$696$		0			0
$697$	1.66845	+	0.447059i	0.0631969	+	0.0169336i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−29.4233			−1.11130			−0.555652	−	0.831415i	$-0.687531\pi$
$701$	−29.4233			−1.11130			−0.555652	+	0.831415i	$0.687531\pi$
$702$		0			0
$703$	24.1368			0.910335
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−23.2240	−	6.22286i	−0.873429	−	0.234035i
$708$		0			0
$709$	1.20861	+	4.51061i	0.0453904	+	0.169399i	0.984900	−	0.173122i	$-0.0553856\pi$
$709$	1.20861	+	4.51061i	0.0453904	+	0.169399i	−0.939510	+	0.342522i	$0.888719\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	3.32244	−	0.890245i	0.124426	−	0.0333399i
$714$		0			0
$715$	−5.73547	−	2.51917i	−0.214495	−	0.0942117i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−19.8659			−0.740872			−0.370436	−	0.928858i	$-0.620792\pi$
$719$	−19.8659			−0.740872			−0.370436	+	0.928858i	$0.620792\pi$
$720$		0			0
$721$	−13.3278	−	13.3278i	−0.496354	−	0.496354i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−6.21923	−	10.7720i	−0.230976	−	0.400063i
$726$		0			0
$727$	−13.8730	−	8.00959i	−0.514521	−	0.297059i	0.220169	−	0.975462i	$-0.429339\pi$
$727$	−13.8730	−	8.00959i	−0.514521	−	0.297059i	−0.734690	+	0.678403i	$0.762673\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.19026	+	1.26455i	0.0810098	+	0.0467710i
$732$		0			0
$733$	−6.38561	+	23.8314i	−0.235858	+	0.880234i	0.741902	+	0.670508i	$0.233924\pi$
$733$	−6.38561	+	23.8314i	−0.235858	+	0.880234i	−0.977760	+	0.209726i	$0.932743\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			7.55773i			0.278393i
$738$		0			0
$739$	8.61409	−	8.61409i	0.316874	−	0.316874i	−0.530691	−	0.847565i	$-0.678068\pi$
$739$	8.61409	−	8.61409i	0.316874	−	0.316874i	0.847565	+	0.530691i	$0.178068\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−33.7923	−	9.05462i	−1.23972	−	0.332182i	−0.421363	−	0.906892i	$-0.638448\pi$
$743$	−33.7923	−	9.05462i	−1.23972	−	0.332182i	−0.818357	+	0.574710i	$0.805115\pi$
$744$		0			0
$745$	11.7979	+	6.81150i	0.432240	+	0.249554i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	3.50374	−	0.938823i	0.128024	−	0.0343039i
$750$		0			0
$751$	−38.9810	+	22.5057i	−1.42244	+	0.821243i	−0.996507	−	0.0835132i	$-0.973386\pi$
$751$	−38.9810	+	22.5057i	−1.42244	+	0.821243i	−0.425929	+	0.904757i	$0.640053\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			30.6205i			1.11439i
$756$		0			0
$757$	29.8931			1.08648			0.543241	−	0.839577i	$-0.317197\pi$
$757$	29.8931			1.08648			0.543241	+	0.839577i	$0.317197\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	7.44060	−	27.7687i	0.269721	−	1.00661i	−0.689575	−	0.724214i	$-0.742203\pi$
$761$	7.44060	−	27.7687i	0.269721	−	1.00661i	0.959297	−	0.282400i	$-0.0911306\pi$
$762$		0			0
$763$	0.726001	−	1.25747i	0.0262830	−	0.0455235i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−17.9400	+	22.3829i	−0.647775	+	0.808198i
$768$		0			0
$769$	−3.14317	+	11.7305i	−0.113346	+	0.423011i	−0.999158	−	0.0410325i	$-0.986935\pi$
$769$	−3.14317	+	11.7305i	−0.113346	+	0.423011i	0.885812	+	0.464044i	$0.153602\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	20.2102	−	20.2102i	0.726909	−	0.726909i	−0.243093	−	0.970003i	$-0.578162\pi$
$773$	20.2102	−	20.2102i	0.726909	−	0.726909i	0.970003	+	0.243093i	$0.0781622\pi$
$774$		0			0
$775$	−8.07612	+	8.07612i	−0.290103	+	0.290103i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	8.53262	+	14.7789i	0.305713	+	0.529510i
$780$		0			0
$781$	−0.333241	+	0.577190i	−0.0119243	+	0.0206535i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	5.71135	+	21.3150i	0.203847	+	0.760767i
$786$		0			0
$787$	37.3018	+	9.99498i	1.32967	+	0.356283i	0.852590	−	0.522580i	$-0.175030\pi$
$787$	37.3018	+	9.99498i	1.32967	+	0.356283i	0.477075	+	0.878863i	$0.341697\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−24.9548	−	24.9548i	−0.887292	−	0.887292i
$792$		0			0
$793$	−20.4295	+	15.0002i	−0.725474	+	0.532673i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−26.6753	−	46.2030i	−0.944887	−	1.63659i	−0.755976	−	0.654599i	$-0.772838\pi$
$797$	−26.6753	−	46.2030i	−0.944887	−	1.63659i	−0.188911	−	0.981994i	$-0.560496\pi$
$798$		0			0
$799$	1.56492	−	0.419318i	0.0553627	−	0.0148344i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−2.17578	+	3.76856i	−0.0767816	+	0.132990i
$804$		0			0
$805$	4.41596	−	2.54956i	0.155642	−	0.0898601i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			11.7326i			0.412496i	0.978500	+	0.206248i	$0.0661253\pi$
$809$			11.7326i			0.412496i	−0.978500	+	0.206248i	$0.933875\pi$
$810$		0			0
$811$	22.6077	+	22.6077i	0.793864	+	0.793864i	0.982120	−	0.188256i	$-0.0602834\pi$
$811$	22.6077	+	22.6077i	0.793864	+	0.793864i	−0.188256	+	0.982120i	$0.560283\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−40.4499	+	23.3538i	−1.41690	+	0.818048i
$816$		0			0
$817$	6.46704	+	24.1353i	0.226253	+	0.844388i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	2.37398	+	8.85980i	0.0828524	+	0.309209i	0.994899	−	0.100878i	$-0.0321651\pi$
$821$	2.37398	+	8.85980i	0.0828524	+	0.309209i	−0.912046	+	0.410087i	$0.865498\pi$
$822$		0			0
$823$	15.7820	−	9.11177i	0.550128	−	0.317616i	−0.199046	−	0.979990i	$-0.563784\pi$
$823$	15.7820	−	9.11177i	0.550128	−	0.317616i	0.749173	+	0.662374i	$0.230451\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−15.8768	−	15.8768i	−0.552091	−	0.552091i	0.374953	−	0.927044i	$-0.377659\pi$
$827$	−15.8768	−	15.8768i	−0.552091	−	0.552091i	−0.927044	+	0.374953i	$0.877659\pi$
$828$		0			0
$829$		−	38.3708i		−	1.33267i	−0.745652	−	0.666336i	$-0.767862\pi$
$829$		−	38.3708i		−	1.33267i	0.745652	−	0.666336i	$-0.232138\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.900293	+	0.519785i	−0.0311933	+	0.0180095i
$834$		0			0
$835$	−6.79096	+	11.7623i	−0.235011	+	0.407051i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	48.0316	−	12.8700i	1.65823	−	0.444323i	0.696333	−	0.717719i	$-0.254814\pi$
$839$	48.0316	−	12.8700i	1.65823	−	0.444323i	0.961901	+	0.273397i	$0.0881471\pi$
$840$		0			0
$841$	−6.15911	−	10.6679i	−0.212383	−	0.367858i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−17.0694	−	32.6850i	−0.587204	−	1.12440i
$846$		0			0
$847$	14.7260	+	14.7260i	0.505993	+	0.505993i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	6.57469	+	1.76168i	0.225377	+	0.0603897i
$852$		0			0
$853$	−0.0169231	−	0.0631577i	−0.000579435	−	0.00216248i	0.965636	−	0.259900i	$-0.0836896\pi$
$853$	−0.0169231	−	0.0631577i	−0.000579435	−	0.00216248i	−0.966215	+	0.257738i	$0.917023\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−25.2762	+	43.7796i	−0.863418	+	1.49548i	0.00519107	+	0.999987i	$0.498348\pi$
$857$	−25.2762	+	43.7796i	−0.863418	+	1.49548i	−0.868609	+	0.495498i	$0.834986\pi$
$858$		0			0
$859$	−10.9462	−	18.9593i	−0.373478	−	0.646883i	0.616620	−	0.787261i	$-0.288502\pi$
$859$	−10.9462	−	18.9593i	−0.373478	−	0.646883i	−0.990098	+	0.140378i	$0.955168\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	35.0101	−	35.0101i	1.19176	−	1.19176i	0.215183	−	0.976574i	$-0.430965\pi$
$863$	35.0101	−	35.0101i	1.19176	−	1.19176i	0.976574	−	0.215183i	$-0.0690348\pi$
$864$		0			0
$865$	38.7686	−	38.7686i	1.31817	−	1.31817i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.46964	+	5.48476i	−0.0498540	+	0.186058i
$870$		0			0
$871$	−27.8227	+	34.7131i	−0.942736	+	1.17621i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	5.43351	−	9.41111i	0.183686	−	0.318154i
$876$		0			0
$877$	−9.45057	+	35.2700i	−0.319123	+	1.19098i	0.600966	+	0.799275i	$0.294783\pi$
$877$	−9.45057	+	35.2700i	−0.319123	+	1.19098i	−0.920089	+	0.391709i	$0.871884\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	39.1376			1.31858			0.659289	−	0.751889i	$-0.270857\pi$
$881$	39.1376			1.31858			0.659289	+	0.751889i	$0.270857\pi$
$882$		0			0
$883$			26.4173i			0.889013i	0.895776	+	0.444506i	$0.146621\pi$
$883$			26.4173i			0.889013i	−0.895776	+	0.444506i	$0.853379\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−7.90171	+	4.56206i	−0.265314	+	0.153179i	−0.626756	−	0.779216i	$-0.715618\pi$
$887$	−7.90171	+	4.56206i	−0.265314	+	0.153179i	0.361442	+	0.932394i	$0.382284\pi$
$888$		0			0
$889$	−28.9212	+	7.74942i	−0.969987	+	0.259907i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	13.8619	+	8.00315i	0.463869	+	0.267815i
$894$		0			0
$895$	34.4083	+	9.21968i	1.15014	+	0.308180i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	10.8313	−	10.8313i	0.361242	−	0.361242i
$900$		0			0
$901$		−	3.39147i		−	0.112986i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	15.5325	−	57.9683i	0.516319	−	1.92693i
$906$		0			0
$907$	−6.32175	−	3.64986i	−0.209910	−	0.121192i	0.391359	−	0.920238i	$-0.372005\pi$
$907$	−6.32175	−	3.64986i	−0.209910	−	0.121192i	−0.601270	+	0.799046i	$0.705338\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1.74335	−	1.00652i	−0.0577596	−	0.0333475i	0.470842	−	0.882218i	$-0.343950\pi$
$911$	−1.74335	−	1.00652i	−0.0577596	−	0.0333475i	−0.528602	+	0.848870i	$0.677283\pi$
$912$		0			0
$913$	−5.30126	−	9.18206i	−0.175446	−	0.303882i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−15.3032	−	15.3032i	−0.505356	−	0.505356i
$918$		0			0
$919$	11.0173			0.363427			0.181713	−	0.983352i	$-0.441836\pi$
$919$	11.0173			0.363427			0.181713	+	0.983352i	$0.441836\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−3.65544	+	1.42429i	−0.120320	+	0.0468810i
$924$		0			0
$925$	−21.8313	+	5.84968i	−0.717809	+	0.192336i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−4.98816	−	18.6161i	−0.163656	−	0.610773i	−0.998208	−	0.0598435i	$-0.980940\pi$
$929$	−4.98816	−	18.6161i	−0.163656	−	0.610773i	0.834552	−	0.550930i	$-0.185727\pi$
$930$		0			0
$931$	−9.92067	−	2.65824i	−0.325137	−	0.0871202i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.571937			0.0187043
$936$		0			0
$937$	−34.3465			−1.12205			−0.561026	−	0.827798i	$-0.689593\pi$
$937$	−34.3465			−1.12205			−0.561026	+	0.827798i	$0.689593\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−37.6670	−	10.0928i	−1.22791	−	0.329017i	−0.414143	−	0.910212i	$-0.635919\pi$
$941$	−37.6670	−	10.0928i	−1.22791	−	0.329017i	−0.813765	+	0.581195i	$0.802585\pi$
$942$		0			0
$943$	1.24555	+	4.64845i	0.0405607	+	0.151374i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−12.3309	+	3.30407i	−0.400702	+	0.107368i	−0.453541	−	0.891235i	$-0.649840\pi$
$947$	−12.3309	+	3.30407i	−0.400702	+	0.107368i	0.0528395	+	0.998603i	$0.483173\pi$
$948$		0			0
$949$	−23.8669	+	9.29938i	−0.774752	+	0.301871i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	50.6036			1.63921			0.819605	−	0.572929i	$-0.194193\pi$
$953$	50.6036			1.63921			0.819605	+	0.572929i	$0.194193\pi$
$954$		0			0
$955$	−42.0891	−	42.0891i	−1.36197	−	1.36197i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	14.4899	+	25.0972i	0.467902	+	0.810431i
$960$		0			0
$961$	14.6660	+	8.46742i	0.473097	+	0.273143i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	22.2821	+	12.8646i	0.717285	+	0.414125i
$966$		0			0
$967$	−2.22003	+	8.28527i	−0.0713914	+	0.266436i	−0.992391	−	0.123128i	$-0.960708\pi$
$967$	−2.22003	+	8.28527i	−0.0713914	+	0.266436i	0.920999	+	0.389564i	$0.127374\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	30.6193i		−	0.982619i	−0.870985	−	0.491309i	$-0.836518\pi$
$971$		−	30.6193i		−	0.982619i	0.870985	−	0.491309i	$-0.163482\pi$
$972$		0			0
$973$	17.6878	−	17.6878i	0.567044	−	0.567044i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	21.0021	+	5.62750i	0.671917	+	0.180040i	0.578618	−	0.815599i	$-0.303592\pi$
$977$	21.0021	+	5.62750i	0.671917	+	0.180040i	0.0932987	+	0.995638i	$0.470259\pi$
$978$		0			0
$979$	−6.10561	−	3.52508i	−0.195136	−	0.112662i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−21.1423	+	5.66506i	−0.674335	+	0.180687i	−0.579707	−	0.814825i	$-0.696833\pi$
$983$	−21.1423	+	5.66506i	−0.674335	+	0.180687i	−0.0946281	+	0.995513i	$0.530166\pi$
$984$		0			0
$985$	38.2246	−	22.0690i	1.21794	−	0.703176i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			7.04631i			0.224060i
$990$		0			0
$991$	−8.94034			−0.283999			−0.142000	−	0.989867i	$-0.545353\pi$
$991$	−8.94034			−0.283999			−0.142000	+	0.989867i	$0.545353\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−6.90586	+	25.7730i	−0.218931	+	0.817060i
$996$		0			0
$997$	16.9719	−	29.3961i	0.537504	−	0.930985i	−0.461533	−	0.887123i	$-0.652701\pi$
$997$	16.9719	−	29.3961i	0.537504	−	0.930985i	0.999038	−	0.0438619i	$-0.0139662\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1404.2.cj.a.1061.3		56
3.2	odd	2		468.2.cg.a.281.10	yes	56
9.4	even	3		468.2.cg.a.437.10	yes	56
9.5	odd	6	inner	1404.2.cj.a.125.3		56
13.5	odd	4	inner	1404.2.cj.a.629.3		56
39.5	even	4		468.2.cg.a.317.10	yes	56
117.5	even	12	inner	1404.2.cj.a.1097.3		56
117.31	odd	12		468.2.cg.a.5.10	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
468.2.cg.a.5.10	✓	56	117.31	odd	12
468.2.cg.a.281.10	yes	56	3.2	odd	2
468.2.cg.a.317.10	yes	56	39.5	even	4
468.2.cg.a.437.10	yes	56	9.4	even	3
1404.2.cj.a.125.3		56	9.5	odd	6	inner
1404.2.cj.a.629.3		56	13.5	odd	4	inner
1404.2.cj.a.1061.3		56	1.1	even	1	trivial
1404.2.cj.a.1097.3		56	117.5	even	12	inner

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:	\( N \)	\(=\)	\( 1404 = 2^{2} \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1404.cj (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.73979 - 0.734125i) q^{5} +(-0.507313 - 1.89332i) q^{7} +(0.591661 - 0.158535i) q^{11} +(3.30116 + 1.44996i) q^{13} -0.329188 q^{17} +(-2.29971 - 2.29971i) q^{19} +(-0.458575 - 0.794276i) q^{23} +(2.63740 + 1.52270i) q^{25} +(-3.53714 - 2.04217i) q^{29} +(-0.970663 + 3.62256i) q^{31} +5.55973i q^{35} +(-5.24778 + 5.24778i) q^{37} +(-5.06836 - 1.35806i) q^{41} +(-6.65352 - 3.84141i) q^{43} +(-4.75386 + 1.27379i) q^{47} +(2.73489 - 1.57899i) q^{49} +10.3025i q^{53} -1.73741 q^{55} +(-2.05912 + 7.68473i) q^{59} +(-3.51473 + 6.08768i) q^{61} +(-7.98004 - 6.39604i) q^{65} +(-3.19344 + 11.9181i) q^{67} +(-0.769386 + 0.769386i) q^{71} +(-5.02343 + 5.02343i) q^{73} +(-0.600315 - 1.03978i) q^{77} +(-4.63505 + 8.02814i) q^{79} +(-4.47998 - 16.7195i) q^{83} +(0.901908 + 0.241666i) q^{85} +(-8.13868 - 8.13868i) q^{89} +(1.07051 - 6.98572i) q^{91} +(4.61246 + 7.98901i) q^{95} +(-7.50874 + 2.01196i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{7} + 12 q^{11} + 4 q^{19} - 4 q^{31} - 4 q^{37} - 24 q^{41} - 66 q^{47} + 78 q^{65} - 14 q^{67} + 28 q^{73} - 24 q^{79} + 78 q^{83} + 36 q^{85} - 8 q^{91} + 26 q^{97}+O(q^{100}) \) 56 * q - 2 * q^7 + 12 * q^11 + 4 * q^19 - 4 * q^31 - 4 * q^37 - 24 * q^41 - 66 * q^47 + 78 * q^65 - 14 * q^67 + 28 * q^73 - 24 * q^79 + 78 * q^83 + 36 * q^85 - 8 * q^91 + 26 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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