LMFDB - Embedded newform 1404.2.cj.a.125.3

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			125.3
Character	$\chi$	$=$	1404.125
Dual form			1404.2.cj.a.629.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.734125 - 2.73979i) q^{5} +(1.89332 + 0.507313i) q^{7} +(0.158535 - 0.591661i) q^{11} +(-0.394879 - 3.58386i) q^{13} +0.329188 q^{17} +(-2.29971 - 2.29971i) q^{19} +(0.458575 - 0.794276i) q^{23} +(-2.63740 + 1.52270i) q^{25} +(-3.53714 + 2.04217i) q^{29} +(3.62256 - 0.970663i) q^{31} -5.55973i q^{35} +(-5.24778 + 5.24778i) q^{37} +(-1.35806 - 5.06836i) q^{41} +(6.65352 - 3.84141i) q^{43} +(-1.27379 + 4.75386i) q^{47} +(-2.73489 - 1.57899i) q^{49} -10.3025i q^{53} -1.73741 q^{55} +(-7.68473 + 2.05912i) q^{59} +(-3.51473 - 6.08768i) q^{61} +(-9.52915 + 3.71289i) q^{65} +(11.9181 - 3.19344i) q^{67} +(0.769386 - 0.769386i) q^{71} +(-5.02343 + 5.02343i) q^{73} +(0.600315 - 1.03978i) q^{77} +(-4.63505 - 8.02814i) q^{79} +(-16.7195 - 4.47998i) q^{83} +(-0.241666 - 0.901908i) q^{85} +(8.13868 + 8.13868i) q^{89} +(1.07051 - 6.98572i) q^{91} +(-4.61246 + 7.98901i) q^{95} +(2.01196 - 7.50874i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1404\mathbb{Z}\right)^\times$.

$n$	$677$	$703$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$5$	−0.734125	−	2.73979i	−0.328311	−	1.22527i	−0.910941	−	0.412536i	$-0.864643\pi$
$5$	−0.734125	−	2.73979i	−0.328311	−	1.22527i	0.582631	−	0.812737i	$-0.302023\pi$
$6$		0			0
$7$	1.89332	+	0.507313i	0.715607	+	0.191746i	0.598211	−	0.801339i	$-0.295879\pi$
$7$	1.89332	+	0.507313i	0.715607	+	0.191746i	0.117396	+	0.993085i	$0.462545\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.158535	−	0.591661i	0.0478001	−	0.178393i	−0.937899	−	0.346909i	$-0.887231\pi$
$11$	0.158535	−	0.591661i	0.0478001	−	0.178393i	0.985699	+	0.168517i	$0.0538978\pi$
$12$		0			0
$13$	−0.394879	−	3.58386i	−0.109520	−	0.993985i
$13$	−0.394879	−	3.58386i	−0.109520	−	0.993985i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.329188			0.0798399			0.0399200	−	0.999203i	$-0.487290\pi$
$17$	0.329188			0.0798399			0.0399200	+	0.999203i	$0.487290\pi$
$18$		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	$-0.802850\pi$
$23$	0.458575	−	0.794276i	0.0956196	−	0.165618i	0.909867	+	0.414900i	$0.136183\pi$
$24$		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	−0.791068	−	0.611728i	$-0.790475\pi$
$29$	−3.53714	+	2.04217i	−0.656830	+	0.379221i	0.134238	+	0.990949i	$0.457141\pi$
$30$		0			0
$31$	3.62256	−	0.970663i	0.650632	−	0.174336i	0.0816173	−	0.996664i	$-0.473991\pi$
$31$	3.62256	−	0.970663i	0.650632	−	0.174336i	0.569015	+	0.822327i	$0.307325\pi$
$32$		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
$41$	−1.35806	−	5.06836i	−0.212094	−	0.791545i	−0.987169	−	0.159677i	$-0.948955\pi$
$41$	−1.35806	−	5.06836i	−0.212094	−	0.791545i	0.775075	−	0.631869i	$-0.217712\pi$
$42$		0			0
$43$	6.65352	−	3.84141i	1.01465	−	0.585810i	0.102102	−	0.994774i	$-0.467443\pi$
$43$	6.65352	−	3.84141i	1.01465	−	0.585810i	0.912550	+	0.408964i	$0.134110\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.27379	+	4.75386i	−0.185802	+	0.693421i	0.808656	+	0.588282i	$0.200196\pi$
$47$	−1.27379	+	4.75386i	−0.185802	+	0.693421i	−0.994457	+	0.105139i	$0.966471\pi$
$48$		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	$-0.749787\pi$
$53$		−	10.3025i		−	1.41516i	0.706633	−	0.707581i	$-0.250213\pi$
$54$		0			0
$55$	−1.73741			−0.234273
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−7.68473	+	2.05912i	−1.00047	+	0.268074i	−0.721641	−	0.692268i	$-0.756612\pi$
$59$	−7.68473	+	2.05912i	−1.00047	+	0.268074i	−0.278826	+	0.960342i	$0.589945\pi$
$60$		0			0
$61$	−3.51473	−	6.08768i	−0.450015	−	0.779448i	0.548372	−	0.836235i	$-0.315248\pi$
$61$	−3.51473	−	6.08768i	−0.450015	−	0.779448i	−0.998386	+	0.0567865i	$0.981915\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−9.52915	+	3.71289i	−1.18195	+	0.460528i
$66$		0			0
$67$	11.9181	−	3.19344i	1.45602	−	0.390140i	0.557909	−	0.829902i	$-0.311604\pi$
$67$	11.9181	−	3.19344i	1.45602	−	0.390140i	0.898115	+	0.439762i	$0.144937\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.769386	−	0.769386i	0.0913093	−	0.0913093i	−0.659977	−	0.751286i	$-0.729434\pi$
$71$	0.769386	−	0.769386i	0.0913093	−	0.0913093i	0.751286	+	0.659977i	$0.229434\pi$
$72$		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	−0.999688	−	0.0249875i	$-0.992045\pi$
$79$	−4.63505	−	8.02814i	−0.521484	−	0.903236i	0.478204	−	0.878249i	$-0.341288\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−16.7195	−	4.47998i	−1.83521	−	0.491742i	−0.836765	−	0.547562i	$-0.815556\pi$
$83$	−16.7195	−	4.47998i	−1.83521	−	0.491742i	−0.998441	+	0.0558197i	$0.982223\pi$
$84$		0			0
$85$	−0.241666	−	0.901908i	−0.0262123	−	0.0978257i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	8.13868	+	8.13868i	0.862699	+	0.862699i	0.991651	−	0.128952i	$-0.0411613\pi$
$89$	8.13868	+	8.13868i	0.862699	+	0.862699i	−0.128952	+	0.991651i	$0.541161\pi$
$90$		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
$97$	2.01196	−	7.50874i	0.204284	−	0.762397i	−0.785383	−	0.619010i	$-0.787534\pi$
$97$	2.01196	−	7.50874i	0.204284	−	0.762397i	0.989667	−	0.143387i	$-0.0457994\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.13315	−	10.6229i	−0.610271	−	1.05702i	−0.991194	−	0.132414i	$-0.957727\pi$
$101$	−6.13315	−	10.6229i	−0.610271	−	1.05702i	0.380923	−	0.924607i	$-0.375606\pi$
$102$		0			0
$103$	−8.32770	−	4.80800i	−0.820553	−	0.473746i	0.0300543	−	0.999548i	$-0.490432\pi$
$103$	−8.32770	−	4.80800i	−0.820553	−	0.473746i	−0.850607	+	0.525802i	$0.823765\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	1.85058i		−	0.178902i	−0.995991	−	0.0894511i	$-0.971489\pi$
$107$		−	1.85058i		−	0.178902i	0.995991	−	0.0894511i	$-0.0285113\pi$
$108$		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	0.999311	−	0.0371036i	$-0.0118131\pi$
$113$	15.5927	+	9.00243i	1.46683	+	0.846877i	0.467523	+	0.883981i	$0.345146\pi$
$114$		0			0
$115$	−2.51280	−	0.673304i	−0.234320	−	0.0627859i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.623259	+	0.167002i	0.0571340	+	0.0153090i
$120$		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	0.855709	−	0.517457i	$-0.173121\pi$
$131$	9.56197	+	5.52061i	0.835434	+	0.482338i	−0.0202759	+	0.999794i	$0.506454\pi$
$132$		0			0
$133$	−3.18741	−	5.52076i	−0.276384	−	0.478711i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.82658	+	14.2810i	−0.326927	+	1.22011i	0.585434	+	0.810720i	$0.300924\pi$
$137$	−3.82658	+	14.2810i	−0.326927	+	1.22011i	−0.912361	+	0.409387i	$0.865742\pi$
$138$		0			0
$139$	6.38084	−	11.0519i	0.541216	−	0.937414i	−0.457619	−	0.889149i	$-0.651297\pi$
$139$	6.38084	−	11.0519i	0.541216	−	0.937414i	0.998835	−	0.0482650i	$-0.0153692\pi$
$140$		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
$149$	−1.24307	−	4.63919i	−0.101836	−	0.380057i	0.896131	−	0.443790i	$-0.146366\pi$
$149$	−1.24307	−	4.63919i	−0.101836	−	0.380057i	−0.997967	+	0.0637324i	$0.979700\pi$
$150$		0			0
$151$	10.4275	+	2.79405i	0.848581	+	0.227377i	0.656803	−	0.754062i	$-0.271908\pi$
$151$	10.4275	+	2.79405i	0.848581	+	0.227377i	0.191778	+	0.981438i	$0.438575\pi$
$152$		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	−0.978459	−	0.206440i	$-0.933812\pi$
$157$	−3.88990	+	6.73750i	−0.310448	+	0.537711i	0.668012	+	0.744151i	$0.267146\pi$
$158$		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
$167$	4.62520	−	1.23932i	0.357909	−	0.0959014i	−0.0753839	−	0.997155i	$-0.524018\pi$
$167$	4.62520	−	1.23932i	0.357909	−	0.0959014i	0.433293	+	0.901253i	$0.357352\pi$
$168$		0			0
$169$	−12.6881	+	2.83039i	−0.976011	+	0.217722i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	9.66477	+	16.7399i	0.734799	+	1.27271i	0.954812	+	0.297212i	$0.0960568\pi$
$173$	9.66477	+	16.7399i	0.734799	+	1.27271i	−0.220013	+	0.975497i	$0.570610\pi$
$174$		0			0
$175$	−5.76593	+	1.54498i	−0.435863	+	0.116789i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	12.5587			0.938684			0.469342	−	0.883017i	$-0.344491\pi$
$179$	12.5587			0.938684			0.469342	+	0.883017i	$0.344491\pi$
$180$		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
$187$	0.0521879	−	0.194768i	0.00381636	−	0.0142428i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	18.1736	−	10.4925i	1.31500	−	0.759213i	0.332077	−	0.943252i	$-0.392251\pi$
$191$	18.1736	−	10.4925i	1.31500	−	0.759213i	0.982919	+	0.184039i	$0.0589172\pi$
$192$		0			0
$193$	2.34772	+	8.76182i	0.168993	+	0.630690i	0.997497	+	0.0707070i	$0.0225255\pi$
$193$	2.34772	+	8.76182i	0.168993	+	0.630690i	−0.828504	+	0.559983i	$0.810808\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	11.0033	−	11.0033i	0.783953	−	0.783953i	−0.196542	−	0.980495i	$-0.562971\pi$
$197$	11.0033	−	11.0033i	0.783953	−	0.783953i	0.980495	+	0.196542i	$0.0629713\pi$
$198$		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
$203$	−7.73295	+	2.07204i	−0.542746	+	0.145428i
$204$		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	0.0755338	+	0.997143i	$0.475934\pi$
$211$	−11.9952	+	20.7763i	−0.825784	+	1.43030i	−0.901318	+	0.433157i	$0.857399\pi$
$212$		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
$221$	−0.129990	−	1.17977i	−0.00874406	−	0.0793597i
$222$		0			0
$223$	−6.16331	+	23.0018i	−0.412726	+	1.54031i	0.376621	+	0.926367i	$0.377086\pi$
$223$	−6.16331	+	23.0018i	−0.412726	+	1.54031i	−0.789347	+	0.613947i	$0.789581\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−26.9440	−	7.21963i	−1.78834	−	0.479183i	−0.796275	−	0.604935i	$-0.793199\pi$
$227$	−26.9440	−	7.21963i	−1.78834	−	0.479183i	−0.992062	+	0.125751i	$0.959866\pi$
$228$		0			0
$229$	0.731872	+	2.73139i	0.0483635	+	0.180495i	0.985882	−	0.167439i	$-0.0535499\pi$
$229$	0.731872	+	2.73139i	0.0483635	+	0.180495i	−0.937519	+	0.347934i	$0.886883\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	5.37193			0.351927			0.175963	−	0.984397i	$-0.443696\pi$
$233$	5.37193			0.351927			0.175963	+	0.984397i	$0.443696\pi$
$234$		0			0
$235$	13.9597			0.910631
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.885927	+	3.30632i	0.0573058	+	0.213868i	0.988641	−	0.150294i	$-0.0480220\pi$
$239$	0.885927	+	3.30632i	0.0573058	+	0.213868i	−0.931336	+	0.364162i	$0.881355\pi$
$240$		0			0
$241$	27.8499	+	7.46235i	1.79397	+	0.480692i	0.993010	−	0.118030i	$-0.0376580\pi$
$241$	27.8499	+	7.46235i	1.79397	+	0.480692i	0.800957	+	0.598722i	$0.204325\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2.31835	+	8.65220i	−0.148114	+	0.552769i
$246$		0			0
$247$	−7.33374	+	9.14996i	−0.466635	+	0.582198i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−0.889720			−0.0561587			−0.0280793	−	0.999606i	$-0.508939\pi$
$251$	−0.889720			−0.0561587			−0.0280793	+	0.999606i	$0.508939\pi$
$252$		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	0.187256	+	0.982311i	$0.440041\pi$
$257$	−12.1369	+	21.0217i	−0.757079	+	1.31130i	−0.944334	+	0.328987i	$0.893293\pi$
$258$		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	0.0968159	−	0.995302i	$-0.469134\pi$
$263$	16.3337	−	9.43028i	1.00718	−	0.581496i	0.910365	+	0.413806i	$0.135801\pi$
$264$		0			0
$265$	−28.2268	+	7.56335i	−1.73396	+	0.464613i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	24.2986i		−	1.48151i	−0.671774	−	0.740757i	$-0.734467\pi$
$269$		−	24.2986i		−	1.48151i	0.671774	−	0.740757i	$-0.265533\pi$
$270$		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
$275$	0.482804	+	1.80185i	0.0291142	+	0.108656i
$276$		0			0
$277$	3.90814	−	2.25637i	0.234818	−	0.135572i	−0.377975	−	0.925816i	$-0.623379\pi$
$277$	3.90814	−	2.25637i	0.234818	−	0.135572i	0.612793	+	0.790244i	$0.290046\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−4.77388	+	17.8164i	−0.284786	+	1.06284i	0.664210	+	0.747546i	$0.268768\pi$
$281$	−4.77388	+	17.8164i	−0.284786	+	1.06284i	−0.948996	+	0.315289i	$0.897898\pi$
$282$		0			0
$283$	2.60463	+	1.50378i	0.154829	+	0.0893906i	0.575413	−	0.817863i	$-0.304841\pi$
$283$	2.60463	+	1.50378i	0.154829	+	0.0893906i	−0.420584	+	0.907254i	$0.638175\pi$
$284$		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
$293$	6.13275	−	1.64326i	0.358279	−	0.0960005i	−0.0751896	−	0.997169i	$-0.523956\pi$
$293$	6.13275	−	1.64326i	0.358279	−	0.0960005i	0.433469	+	0.901169i	$0.357290\pi$
$294$		0			0
$295$	11.2831	+	19.5429i	0.656928	+	1.13783i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.02766	−	1.32983i	−0.175094	−	0.0769059i
$300$		0			0
$301$	14.5460	−	3.89760i	0.838420	−	0.224654i
$302$		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	$-0.704625\pi$
$311$	6.93805	−	12.0170i	0.393420	−	0.681424i	0.992898	+	0.118967i	$0.0379583\pi$
$312$		0			0
$313$	3.70337	+	6.41442i	0.209327	+	0.362565i	0.951503	−	0.307641i	$-0.0995394\pi$
$313$	3.70337	+	6.41442i	0.209327	+	0.362565i	−0.742176	+	0.670205i	$0.766206\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	31.1462	+	8.34561i	1.74935	+	0.468736i	0.984486	−	0.175461i	$-0.0561415\pi$
$317$	31.1462	+	8.34561i	1.74935	+	0.468736i	0.764860	+	0.644197i	$0.222808\pi$
$318$		0			0
$319$	0.647510	+	2.41654i	0.0362536	+	0.135300i
$320$		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
$331$	2.15355	−	8.03717i	0.118370	−	0.441763i	−0.881147	−	0.472843i	$-0.843228\pi$
$331$	2.15355	−	8.03717i	0.118370	−	0.441763i	0.999517	+	0.0310796i	$0.00989455\pi$
$332$		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	$-0.401240\pi$
$337$	−6.73189	−	3.88666i	−0.366709	−	0.211720i	−0.672020	+	0.740533i	$0.734573\pi$
$338$		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	0.998450	−	0.0556541i	$-0.0177244\pi$
$347$	27.0008	+	15.5889i	1.44948	+	0.836856i	0.451027	+	0.892510i	$0.351058\pi$
$348$		0			0
$349$	−4.81905	−	1.29126i	−0.257958	−	0.0691195i	0.127522	−	0.991836i	$-0.459297\pi$
$349$	−4.81905	−	1.29126i	−0.257958	−	0.0691195i	−0.385480	+	0.922716i	$0.625964\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	2.79861	+	0.749885i	0.148955	+	0.0399124i	0.332526	−	0.943094i	$-0.392099\pi$
$353$	2.79861	+	0.749885i	0.148955	+	0.0399124i	−0.183571	+	0.983006i	$0.558766\pi$
$354$		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	$0.0347639\pi$
$359$	20.8996	+	20.8996i	1.10304	+	1.10304i	0.108997	+	0.994042i	$0.465236\pi$
$360$		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	0.977457	−	0.211136i	$-0.0677163\pi$
$367$	5.85980	+	10.1495i	0.305879	+	0.529798i	−0.671577	+	0.740934i	$0.734383\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	5.22661	−	19.5060i	0.271352	−	1.01270i
$372$		0			0
$373$	6.42101	−	11.1215i	0.332467	−	0.575850i	−0.650528	−	0.759482i	$-0.725452\pi$
$373$	6.42101	−	11.1215i	0.332467	−	0.575850i	0.982995	+	0.183632i	$0.0587856\pi$
$374$		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
$383$	3.97277	+	14.8266i	0.202999	+	0.757603i	0.990050	+	0.140715i	$0.0449402\pi$
$383$	3.97277	+	14.8266i	0.202999	+	0.757603i	−0.787051	+	0.616888i	$0.788393\pi$
$384$		0			0
$385$	−3.28948	−	0.881413i	−0.167647	−	0.0449210i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	19.1965	+	33.2493i	0.973302	+	1.68581i	0.685428	+	0.728141i	$0.259615\pi$
$389$	19.1965	+	33.2493i	0.973302	+	1.68581i	0.287875	+	0.957668i	$0.407051\pi$
$390$		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
$401$	16.1747	−	4.33401i	0.807727	−	0.216430i	0.168753	−	0.985658i	$-0.446026\pi$
$401$	16.1747	−	4.33401i	0.807727	−	0.216430i	0.638974	+	0.769228i	$0.279359\pi$
$402$		0			0
$403$	−4.90920	−	12.5995i	−0.244545	−	0.627625i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.27295	+	3.93686i	0.112666	+	0.195143i
$408$		0			0
$409$	−13.8034	+	3.69860i	−0.682532	+	0.182884i	−0.583394	−	0.812190i	$-0.698275\pi$
$409$	−13.8034	+	3.69860i	−0.682532	+	0.182884i	−0.0991389	+	0.995074i	$0.531609\pi$
$410$		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	0.600568	−	0.799574i	$-0.294941\pi$
$419$	4.26586	+	2.46289i	0.208401	+	0.120320i	−0.392167	+	0.919894i	$0.628275\pi$
$420$		0			0
$421$	−2.49475	+	9.31053i	−0.121587	+	0.453768i	−0.999695	−	0.0246942i	$-0.992139\pi$
$421$	−2.49475	+	9.31053i	−0.121587	+	0.453768i	0.878108	+	0.478462i	$0.158805\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.868202	+	0.501257i	−0.0421140	+	0.0243145i
$426$		0			0
$427$	−3.56614	−	13.3090i	−0.172577	−	0.644068i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−0.315102	+	0.315102i	−0.0151779	+	0.0151779i	−0.714655	−	0.699477i	$-0.753416\pi$
$431$	−0.315102	+	0.315102i	−0.0151779	+	0.0151779i	0.699477	+	0.714655i	$0.253416\pi$
$432$		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
$437$	−2.88120	+	0.772015i	−0.137826	+	0.0369305i
$438$		0			0
$439$	31.2977	−	18.0697i	1.49376	−	0.862421i	0.493783	−	0.869585i	$-0.335614\pi$
$439$	31.2977	−	18.0697i	1.49376	−	0.862421i	0.999974	+	0.00716374i	$0.00228031\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.98825	+	1.14792i	−0.0944646	+	0.0545391i	−0.546488	−	0.837467i	$-0.684036\pi$
$443$	−1.98825	+	1.14792i	−0.0944646	+	0.0545391i	0.452024	+	0.892006i	$0.350702\pi$
$444$		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	0.843143	−	0.537690i	$-0.180703\pi$
$449$	6.47243	+	6.47243i	0.305453	+	0.305453i	−0.537690	+	0.843143i	$0.680703\pi$
$450$		0			0
$451$	−3.21405			−0.151344
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−19.9253	+	2.19543i	−0.934114	+	0.102923i
$456$		0			0
$457$	−6.28764	+	23.4658i	−0.294123	+	1.09768i	0.647788	+	0.761821i	$0.275694\pi$
$457$	−6.28764	+	23.4658i	−0.294123	+	1.09768i	−0.941911	+	0.335862i	$0.890972\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−16.3089	−	4.36996i	−0.759583	−	0.203530i	−0.141818	−	0.989893i	$-0.545295\pi$
$461$	−16.3089	−	4.36996i	−0.759583	−	0.203530i	−0.617764	+	0.786363i	$0.711961\pi$
$462$		0			0
$463$	−6.61478	−	24.6867i	−0.307415	−	1.14729i	−0.930847	−	0.365410i	$-0.880929\pi$
$463$	−6.61478	−	24.6867i	−0.307415	−	1.14729i	0.623432	−	0.781878i	$-0.285738\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	23.4460			1.08495			0.542477	−	0.840071i	$-0.317487\pi$
$467$	23.4460			1.08495			0.542477	+	0.840071i	$0.317487\pi$
$468$		0			0
$469$	24.1848			1.11675
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.21800	−	4.54563i	−0.0560036	−	0.209008i
$474$		0			0
$475$	9.56704	+	2.56348i	0.438966	+	0.117621i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	4.96669	−	18.5359i	0.226934	−	0.846928i	−0.754687	−	0.656085i	$-0.772211\pi$
$479$	4.96669	−	18.5359i	0.226934	−	0.846928i	0.981621	−	0.190843i	$-0.0611221\pi$
$480$		0			0
$481$	20.8796	+	16.7351i	0.952026	+	0.763054i
$482$		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	$-0.779332\pi$
$491$	3.74118	−	6.47991i	0.168837	−	0.292434i	0.938011	+	0.346605i	$0.112666\pi$
$492$		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
$499$	11.2248	−	3.00769i	0.502493	−	0.134643i	0.00133618	−	0.999999i	$-0.499575\pi$
$499$	11.2248	−	3.00769i	0.502493	−	0.134643i	0.501157	+	0.865357i	$0.332908\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	9.78116i		−	0.436120i	−0.975935	−	0.218060i	$-0.930027\pi$
$503$		−	9.78116i		−	0.436120i	0.975935	−	0.218060i	$-0.0699729\pi$
$504$		0			0
$505$	−24.6021	+	24.6021i	−1.09478	+	1.09478i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−4.47063	−	16.6846i	−0.198157	−	0.739533i	−0.991427	−	0.130662i	$-0.958290\pi$
$509$	−4.47063	−	16.6846i	−0.198157	−	0.739533i	0.793270	−	0.608870i	$-0.208377\pi$
$510$		0			0
$511$	−12.0594	+	6.96251i	−0.533477	+	0.308003i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−7.05935	+	26.3459i	−0.311072	+	1.16094i
$516$		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	$0.0502620\pi$
$521$			7.17847i			0.314495i	−0.987559	+	0.157247i	$0.949738\pi$
$522$		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
$527$	1.19251	−	0.319531i	0.0519464	−	0.0139190i
$528$		0			0
$529$	11.0794	+	19.1901i	0.481714	+	0.834353i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−17.6280	+	6.86851i	−0.763555	+	0.297508i
$534$		0			0
$535$	−5.07020	+	1.35856i	−0.219204	+	0.0587355i
$536$		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	−0.977059	−	0.212969i	$-0.931687\pi$
$547$	−15.7394	−	27.2614i	−0.672966	−	1.16561i	0.304093	−	0.952642i	$-0.401647\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	12.8308	+	3.43800i	0.546610	+	0.146464i
$552$		0			0
$553$	−4.70284	−	17.5513i	−0.199985	−	0.746355i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.834344	+	0.834344i	0.0353523	+	0.0353523i	0.724562	−	0.689210i	$-0.242042\pi$
$557$	0.834344	+	0.834344i	0.0353523	+	0.0353523i	−0.689210	+	0.724562i	$0.742042\pi$
$558$		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	$-0.855470\pi$
$563$	−1.64883	+	2.85585i	−0.0694898	+	0.120360i	0.829187	+	0.558971i	$0.188804\pi$
$564$		0			0
$565$	13.2178	−	49.3296i	0.556078	−	2.07531i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−10.9777	−	19.0140i	−0.460210	−	0.797107i	0.538761	−	0.842459i	$-0.318893\pi$
$569$	−10.9777	−	19.0140i	−0.460210	−	0.797107i	−0.998971	+	0.0453513i	$0.985559\pi$
$570$		0			0
$571$	36.3726	+	20.9997i	1.52215	+	0.878811i	0.999658	+	0.0261646i	$0.00832939\pi$
$571$	36.3726	+	20.9997i	1.52215	+	0.878811i	0.522488	+	0.852647i	$0.325004\pi$
$572$		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
$583$	−6.09560	−	1.63331i	−0.252454	−	0.0676449i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	2.00254	+	0.536579i	0.0826537	+	0.0221470i	0.299909	−	0.953968i	$-0.403044\pi$
$587$	2.00254	+	0.536579i	0.0826537	+	0.0221470i	−0.217255	+	0.976115i	$0.569710\pi$
$588$		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	0.261717	−	0.965145i	$-0.415711\pi$
$593$	−17.1296	−	17.1296i	−0.703427	−	0.703427i	−0.965145	+	0.261717i	$0.915711\pi$
$594$		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	0.526260	−	0.850323i	$-0.323594\pi$
$599$	1.29688	+	0.748751i	0.0529889	+	0.0305931i	−0.473272	+	0.880917i	$0.656927\pi$
$600$		0			0
$601$	−9.10896	−	15.7772i	−0.371562	−	0.643565i	0.618244	−	0.785986i	$-0.287844\pi$
$601$	−9.10896	−	15.7772i	−0.371562	−	0.643565i	−0.989806	+	0.142422i	$0.954511\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	7.79994	−	29.1098i	0.317113	−	1.18348i
$606$		0			0
$607$	−0.761886	+	1.31963i	−0.0309240	+	0.0535619i	−0.881073	−	0.472980i	$-0.843178\pi$
$607$	−0.761886	+	1.31963i	−0.0309240	+	0.0535619i	0.850149	+	0.526542i	$0.176512\pi$
$608$		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
$617$	−7.30263	−	27.2538i	−0.293993	−	1.09720i	−0.942014	−	0.335574i	$-0.891070\pi$
$617$	−7.30263	−	27.2538i	−0.293993	−	1.09720i	0.648021	−	0.761623i	$-0.275597\pi$
$618$		0			0
$619$	−7.55294	−	2.02380i	−0.303578	−	0.0813435i	0.103814	−	0.994597i	$-0.466895\pi$
$619$	−7.55294	−	2.02380i	−0.303578	−	0.0813435i	−0.407392	+	0.913253i	$0.633562\pi$
$620$		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
$635$	−41.8515	+	11.2141i	−1.66082	+	0.445017i
$636$		0			0
$637$	−4.57892	+	10.4250i	−0.181424	+	0.413052i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−3.66091	−	6.34089i	−0.144597	−	0.250450i	0.784625	−	0.619970i	$-0.212855\pi$
$641$	−3.66091	−	6.34089i	−0.144597	−	0.250450i	−0.929223	+	0.369520i	$0.879522\pi$
$642$		0			0
$643$	−37.2708	+	9.98668i	−1.46982	+	0.393836i	−0.902869	−	0.429917i	$-0.858543\pi$
$643$	−37.2708	+	9.98668i	−1.46982	+	0.393836i	−0.566949	+	0.823753i	$0.691876\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	16.7465			0.658373			0.329186	−	0.944265i	$-0.393226\pi$
$647$	16.7465			0.658373			0.329186	+	0.944265i	$0.393226\pi$
$648$		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	−0.223376	−	0.974732i	$-0.571708\pi$
$653$	−30.1333	−	17.3975i	−1.17921	−	0.680816i	−0.955831	+	0.293917i	$0.905041\pi$
$654$		0			0
$655$	8.10564	−	30.2507i	0.316713	−	1.18199i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	0.801546	−	0.462773i	0.0312238	−	0.0180271i	−0.484307	−	0.874898i	$-0.660928\pi$
$659$	0.801546	−	0.462773i	0.0312238	−	0.0180271i	0.515531	+	0.856871i	$0.327595\pi$
$660$		0			0
$661$	3.13696	+	11.7073i	0.122013	+	0.455361i	0.999716	−	0.0238460i	$-0.00759115\pi$
$661$	3.13696	+	11.7073i	0.122013	+	0.455361i	−0.877702	+	0.479207i	$0.840924\pi$
$662$		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
$671$	−4.15905	+	1.11442i	−0.160558	+	0.0430215i
$672$		0			0
$673$	−14.4389	+	8.33628i	−0.556577	+	0.321340i	−0.751771	−	0.659425i	$-0.770800\pi$
$673$	−14.4389	+	8.33628i	−0.556577	+	0.321340i	0.195193	+	0.980765i	$0.437467\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−9.98589	+	5.76536i	−0.383789	+	0.221581i	−0.679466	−	0.733707i	$-0.737788\pi$
$677$	−9.98589	+	5.76536i	−0.383789	+	0.221581i	0.295677	+	0.955288i	$0.404455\pi$
$678$		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	$-0.940275\pi$
$683$	−30.5505	−	30.5505i	−1.16898	−	1.16898i	−0.186534	−	0.982449i	$-0.559725\pi$
$684$		0			0
$685$	41.9362			1.60230
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−36.9228	+	4.06826i	−1.40665	+	0.154988i
$690$		0			0
$691$	−3.82152	+	14.2621i	−0.145377	+	0.542556i	0.854361	+	0.519680i	$0.173949\pi$
$691$	−3.82152	+	14.2621i	−0.145377	+	0.542556i	−0.999738	+	0.0228759i	$0.992718\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−34.9644	−	9.36868i	−1.32627	−	0.355374i
$696$		0			0
$697$	−0.447059	−	1.66845i	−0.0169336	−	0.0631969i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	29.4233			1.11130			0.555652	−	0.831415i	$-0.312469\pi$
$701$	29.4233			1.11130			0.555652	+	0.831415i	$0.312469\pi$
$702$		0			0
$703$	24.1368			0.910335
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−6.22286	−	23.2240i	−0.234035	−	0.873429i
$708$		0			0
$709$	−4.51061	−	1.20861i	−0.169399	−	0.0453904i	0.173122	−	0.984900i	$-0.444614\pi$
$709$	−4.51061	−	1.20861i	−0.169399	−	0.0453904i	−0.342522	+	0.939510i	$0.611281\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.890245	−	3.32244i	0.0333399	−	0.124426i
$714$		0			0
$715$	0.686069	+	6.22665i	0.0256575	+	0.232864i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	19.8659			0.740872			0.370436	−	0.928858i	$-0.379208\pi$
$719$	19.8659			0.740872			0.370436	+	0.928858i	$0.379208\pi$
$720$		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	$-0.570661\pi$
$727$	13.8730	−	8.00959i	0.514521	−	0.297059i	0.734690	+	0.678403i	$0.237327\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.19026	−	1.26455i	0.0810098	−	0.0467710i
$732$		0			0
$733$	23.8314	−	6.38561i	0.880234	−	0.235858i	0.209726	−	0.977760i	$-0.432743\pi$
$733$	23.8314	−	6.38561i	0.880234	−	0.235858i	0.670508	+	0.741902i	$0.266076\pi$
$734$		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
$743$	−9.05462	−	33.7923i	−0.332182	−	1.23972i	−0.906892	−	0.421363i	$-0.861552\pi$
$743$	−9.05462	−	33.7923i	−0.332182	−	1.23972i	0.574710	−	0.818357i	$-0.305115\pi$
$744$		0			0
$745$	−11.7979	+	6.81150i	−0.432240	+	0.249554i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	0.938823	−	3.50374i	0.0343039	−	0.128024i
$750$		0			0
$751$	38.9810	+	22.5057i	1.42244	+	0.821243i	0.996507	−	0.0835132i	$-0.0266141\pi$
$751$	38.9810	+	22.5057i	1.42244	+	0.821243i	0.425929	+	0.904757i	$0.359947\pi$
$752$		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
$761$	27.7687	−	7.44060i	1.00661	−	0.269721i	0.282400	−	0.959297i	$-0.408869\pi$
$761$	27.7687	−	7.44060i	1.00661	−	0.269721i	0.724214	+	0.689575i	$0.242203\pi$
$762$		0			0
$763$	0.726001	+	1.25747i	0.0262830	+	0.0455235i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	10.4141	+	26.7279i	0.376033	+	0.965089i
$768$		0			0
$769$	11.7305	−	3.14317i	0.423011	−	0.113346i	−0.0410325	−	0.999158i	$-0.513065\pi$
$769$	11.7305	−	3.14317i	0.423011	−	0.113346i	0.464044	+	0.885812i	$0.346398\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−20.2102	+	20.2102i	−0.726909	+	0.726909i	−0.970003	−	0.243093i	$-0.921838\pi$
$773$	−20.2102	+	20.2102i	−0.726909	+	0.726909i	0.243093	+	0.970003i	$0.421838\pi$
$774$		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
$785$	21.3150	+	5.71135i	0.760767	+	0.203847i
$786$		0			0
$787$	−9.99498	−	37.3018i	−0.356283	−	1.32967i	−0.878863	−	0.477075i	$-0.841697\pi$
$787$	−9.99498	−	37.3018i	−0.356283	−	1.32967i	0.522580	−	0.852590i	$-0.324970\pi$
$788$		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	0.188911	−	0.981994i	$-0.439504\pi$
$797$	26.6753	−	46.2030i	0.944887	−	1.63659i	0.755976	−	0.654599i	$-0.227162\pi$
$798$		0			0
$799$	−0.419318	+	1.56492i	−0.0148344	+	0.0553627i
$800$		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	$-0.933875\pi$
$809$		−	11.7326i		−	0.412496i	0.978500	−	0.206248i	$-0.0661253\pi$
$810$		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
$817$	−24.1353	−	6.46704i	−0.844388	−	0.226253i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	8.85980	+	2.37398i	0.309209	+	0.0828524i	0.410087	−	0.912046i	$-0.365498\pi$
$821$	8.85980	+	2.37398i	0.309209	+	0.0828524i	−0.100878	+	0.994899i	$0.532165\pi$
$822$		0			0
$823$	−15.7820	−	9.11177i	−0.550128	−	0.317616i	0.199046	−	0.979990i	$-0.436216\pi$
$823$	−15.7820	−	9.11177i	−0.550128	−	0.317616i	−0.749173	+	0.662374i	$0.769549\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	15.8768	+	15.8768i	0.552091	+	0.552091i	0.927044	−	0.374953i	$-0.122341\pi$
$827$	15.8768	+	15.8768i	0.552091	+	0.552091i	−0.374953	+	0.927044i	$0.622341\pi$
$828$		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
$839$	12.8700	−	48.0316i	0.444323	−	1.65823i	−0.273397	−	0.961901i	$-0.588147\pi$
$839$	12.8700	−	48.0316i	0.444323	−	1.65823i	0.717719	−	0.696333i	$-0.245186\pi$
$840$		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
$851$	1.76168	+	6.57469i	0.0603897	+	0.225377i
$852$		0			0
$853$	0.0631577	+	0.0169231i	0.00216248	+	0.000579435i	0.259900	−	0.965636i	$-0.416310\pi$
$853$	0.0631577	+	0.0169231i	0.00216248	+	0.000579435i	−0.257738	+	0.966215i	$0.582977\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	25.2762	+	43.7796i	0.863418	+	1.49548i	0.868609	+	0.495498i	$0.165014\pi$
$857$	25.2762	+	43.7796i	0.863418	+	1.49548i	−0.00519107	+	0.999987i	$0.501652\pi$
$858$		0			0
$859$	−10.9462	+	18.9593i	−0.373478	+	0.646883i	−0.990098	−	0.140378i	$-0.955168\pi$
$859$	−10.9462	+	18.9593i	−0.373478	+	0.646883i	0.616620	+	0.787261i	$0.288502\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−35.0101	+	35.0101i	−1.19176	+	1.19176i	−0.215183	+	0.976574i	$0.569035\pi$
$863$	−35.0101	+	35.0101i	−1.19176	+	1.19176i	−0.976574	+	0.215183i	$0.930965\pi$
$864$		0			0
$865$	38.7686	−	38.7686i	1.31817	−	1.31817i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−5.48476	+	1.46964i	−0.186058	+	0.0498540i
$870$		0			0
$871$	−16.1510	−	41.4517i	−0.547257	−	1.40454i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−5.43351	−	9.41111i	−0.183686	−	0.318154i
$876$		0			0
$877$	35.2700	−	9.45057i	1.19098	−	0.319123i	0.391709	−	0.920089i	$-0.371884\pi$
$877$	35.2700	−	9.45057i	1.19098	−	0.319123i	0.799275	+	0.600966i	$0.205217\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−39.1376			−1.31858			−0.659289	−	0.751889i	$-0.729143\pi$
$881$	−39.1376			−1.31858			−0.659289	+	0.751889i	$0.729143\pi$
$882$		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	0.361442	−	0.932394i	$-0.382284\pi$
$887$	−7.90171	−	4.56206i	−0.265314	−	0.153179i	−0.626756	+	0.779216i	$0.715618\pi$
$888$		0			0
$889$	7.74942	−	28.9212i	0.259907	−	0.969987i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	13.8619	−	8.00315i	0.463869	−	0.267815i
$894$		0			0
$895$	−9.21968	−	34.4083i	−0.308180	−	1.15014i
$896$		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
$905$	57.9683	−	15.5325i	1.92693	−	0.516319i
$906$		0			0
$907$	6.32175	−	3.64986i	0.209910	−	0.121192i	−0.391359	−	0.920238i	$-0.627995\pi$
$907$	6.32175	−	3.64986i	0.209910	−	0.121192i	0.601270	+	0.799046i	$0.294662\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1.74335	+	1.00652i	−0.0577596	+	0.0333475i	−0.528602	−	0.848870i	$-0.677283\pi$
$911$	−1.74335	+	1.00652i	−0.0577596	+	0.0333475i	0.470842	+	0.882218i	$0.343950\pi$
$912$		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
$923$	−3.06119	−	2.45356i	−0.100760	−	0.0807598i
$924$		0			0
$925$	5.84968	−	21.8313i	0.192336	−	0.717809i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−18.6161	−	4.98816i	−0.610773	−	0.163656i	−0.0598435	−	0.998208i	$-0.519060\pi$
$929$	−18.6161	−	4.98816i	−0.610773	−	0.163656i	−0.550930	+	0.834552i	$0.685727\pi$
$930$		0			0
$931$	2.65824	+	9.92067i	0.0871202	+	0.325137i
$932$		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
$941$	−10.0928	−	37.6670i	−0.329017	−	1.22791i	−0.910212	−	0.414143i	$-0.864081\pi$
$941$	−10.0928	−	37.6670i	−0.329017	−	1.22791i	0.581195	−	0.813765i	$-0.302585\pi$
$942$		0			0
$943$	−4.64845	−	1.24555i	−0.151374	−	0.0405607i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−3.30407	+	12.3309i	−0.107368	+	0.400702i	−0.998603	−	0.0528395i	$-0.983173\pi$
$947$	−3.30407	+	12.3309i	−0.107368	+	0.400702i	0.891235	+	0.453541i	$0.149840\pi$
$948$		0			0
$949$	19.9870	+	16.0196i	0.648804	+	0.520020i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−50.6036			−1.63921			−0.819605	−	0.572929i	$-0.805807\pi$
$953$	−50.6036			−1.63921			−0.819605	+	0.572929i	$0.805807\pi$
$954$		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
$967$	8.28527	−	2.22003i	0.266436	−	0.0713914i	−0.123128	−	0.992391i	$-0.539292\pi$
$967$	8.28527	−	2.22003i	0.266436	−	0.0713914i	0.389564	+	0.920999i	$0.372626\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			30.6193i			0.982619i	0.870985	+	0.491309i	$0.163482\pi$
$971$			30.6193i			0.982619i	−0.870985	+	0.491309i	$0.836518\pi$
$972$		0			0
$973$	17.6878	−	17.6878i	0.567044	−	0.567044i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.62750	+	21.0021i	0.180040	+	0.671917i	0.995638	+	0.0932987i	$0.0297412\pi$
$977$	5.62750	+	21.0021i	0.180040	+	0.671917i	−0.815599	+	0.578618i	$0.803592\pi$
$978$		0			0
$979$	6.10561	−	3.52508i	0.195136	−	0.112662i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−5.66506	+	21.1423i	−0.180687	+	0.674335i	0.814825	+	0.579707i	$0.196833\pi$
$983$	−5.66506	+	21.1423i	−0.180687	+	0.674335i	−0.995513	+	0.0946281i	$0.969834\pi$
$984$		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
$995$	−25.7730	+	6.90586i	−0.817060	+	0.218931i
$996$		0			0
$997$	16.9719	+	29.3961i	0.537504	+	0.930985i	0.999038	+	0.0438619i	$0.0139662\pi$
$997$	16.9719	+	29.3961i	0.537504	+	0.930985i	−0.461533	+	0.887123i	$0.652701\pi$
$998$		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.125.3		56
3.2	odd	2		468.2.cg.a.437.10	yes	56
9.2	odd	6	inner	1404.2.cj.a.1061.3		56
9.7	even	3		468.2.cg.a.281.10	yes	56
13.5	odd	4	inner	1404.2.cj.a.1097.3		56
39.5	even	4		468.2.cg.a.5.10	✓	56
117.70	odd	12		468.2.cg.a.317.10	yes	56
117.83	even	12	inner	1404.2.cj.a.629.3		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
468.2.cg.a.5.10	✓	56	39.5	even	4
468.2.cg.a.281.10	yes	56	9.7	even	3
468.2.cg.a.317.10	yes	56	117.70	odd	12
468.2.cg.a.437.10	yes	56	3.2	odd	2
1404.2.cj.a.125.3		56	1.1	even	1	trivial
1404.2.cj.a.629.3		56	117.83	even	12	inner
1404.2.cj.a.1061.3		56	9.2	odd	6	inner
1404.2.cj.a.1097.3		56	13.5	odd	4	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)

\(f(q)\)	\(=\)	\(q+(-0.734125 - 2.73979i) q^{5} +(1.89332 + 0.507313i) q^{7} +(0.158535 - 0.591661i) q^{11} +(-0.394879 - 3.58386i) q^{13} +0.329188 q^{17} +(-2.29971 - 2.29971i) q^{19} +(0.458575 - 0.794276i) q^{23} +(-2.63740 + 1.52270i) q^{25} +(-3.53714 + 2.04217i) q^{29} +(3.62256 - 0.970663i) q^{31} -5.55973i q^{35} +(-5.24778 + 5.24778i) q^{37} +(-1.35806 - 5.06836i) q^{41} +(6.65352 - 3.84141i) q^{43} +(-1.27379 + 4.75386i) q^{47} +(-2.73489 - 1.57899i) q^{49} -10.3025i q^{53} -1.73741 q^{55} +(-7.68473 + 2.05912i) q^{59} +(-3.51473 - 6.08768i) q^{61} +(-9.52915 + 3.71289i) q^{65} +(11.9181 - 3.19344i) q^{67} +(0.769386 - 0.769386i) q^{71} +(-5.02343 + 5.02343i) q^{73} +(0.600315 - 1.03978i) q^{77} +(-4.63505 - 8.02814i) q^{79} +(-16.7195 - 4.47998i) q^{83} +(-0.241666 - 0.901908i) q^{85} +(8.13868 + 8.13868i) q^{89} +(1.07051 - 6.98572i) q^{91} +(-4.61246 + 7.98901i) q^{95} +(2.01196 - 7.50874i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{7} + 12 q^{11} + 4 q^{19} - 4 q^{31} - 4 q^{37} - 24 q^{41} - 66 q^{47} + 78 q^{65} - 14 q^{67} + 28 q^{73} - 24 q^{79} + 78 q^{83} + 36 q^{85} - 8 q^{91} + 26 q^{97}+O(q^{100}) \) 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

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Database

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