LMFDB - Embedded newform 5292.2.w.b.521.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5292,2,Mod(521,5292)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5292, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5292.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5292.w (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$42.2568327497$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.6
Root			$-1.61108 + 0.635951i$ of defining polynomial
Character	$\chi$	$=$	5292.521
Dual form			5292.2.w.b.1097.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09150 - 1.89054i) q^{5} +O(q^{10})$	$q+(1.09150 - 1.89054i) q^{5} +(1.26889 - 0.732592i) q^{11} +(-2.92752 + 1.69021i) q^{13} +(1.32136 - 2.28866i) q^{17} +(-6.87816 + 3.97111i) q^{19} +(3.47245 + 2.00482i) q^{23} +(0.117249 + 0.203081i) q^{25} +(6.71261 + 3.87553i) q^{29} -0.706968i q^{31} +(1.41738 + 2.45498i) q^{37} +(3.74173 + 6.48086i) q^{41} +(-1.27112 + 2.20164i) q^{43} -12.5508 q^{47} +(2.41675 + 1.39531i) q^{53} -3.19850i q^{55} +13.4330 q^{59} +7.79493i q^{61} +7.37945i q^{65} +5.84058 q^{67} -11.6854i q^{71} +(3.95924 + 2.28587i) q^{73} +9.38377 q^{79} +(1.70847 - 2.95917i) q^{83} +(-2.88452 - 4.99614i) q^{85} +(4.61937 + 8.00099i) q^{89} +17.3379i q^{95} +(-6.38394 - 3.68577i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 6 q^{11} + 3 q^{13} + 9 q^{17} - 21 q^{23} - 8 q^{25} - 6 q^{29} + q^{37} - 6 q^{41} - 2 q^{43} - 36 q^{47} - 30 q^{59} + 14 q^{67} + 2 q^{79} + 6 q^{85} + 21 q^{89} + 3 q^{97}+O(q^{100}) $ 16 * q + 6 * q^11 + 3 * q^13 + 9 * q^17 - 21 * q^23 - 8 * q^25 - 6 * q^29 + q^37 - 6 * q^41 - 2 * q^43 - 36 * q^47 - 30 * q^59 + 14 * q^67 + 2 * q^79 + 6 * q^85 + 21 * q^89 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5292\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$	$2647$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.09150	−	1.89054i	0.488134	−	0.845473i	−0.511773	−	0.859121i	$-0.671011\pi$
$5$	1.09150	−	1.89054i	0.488134	−	0.845473i	0.999907	+	0.0136476i	$0.00434429\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.26889	−	0.732592i	0.382584	−	0.220885i	−0.296358	−	0.955077i	$-0.595772\pi$
$11$	1.26889	−	0.732592i	0.382584	−	0.220885i	0.678942	+	0.734192i	$0.262439\pi$
$12$		0			0
$13$	−2.92752	+	1.69021i	−0.811948	+	0.468779i	−0.847632	−	0.530585i	$-0.821972\pi$
$13$	−2.92752	+	1.69021i	−0.811948	+	0.468779i	0.0356837	+	0.999363i	$0.488639\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.32136	−	2.28866i	0.320476	−	0.555081i	−0.660110	−	0.751169i	$-0.729491\pi$
$17$	1.32136	−	2.28866i	0.320476	−	0.555081i	0.980586	+	0.196088i	$0.0628238\pi$
$18$		0			0
$19$	−6.87816	+	3.97111i	−1.57796	+	0.911034i	−0.582813	+	0.812606i	$0.698048\pi$
$19$	−6.87816	+	3.97111i	−1.57796	+	0.911034i	−0.995144	+	0.0984279i	$0.968619\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.47245	+	2.00482i	0.724056	+	0.418034i	0.816244	−	0.577708i	$-0.196053\pi$
$23$	3.47245	+	2.00482i	0.724056	+	0.418034i	−0.0921879	+	0.995742i	$0.529386\pi$
$24$		0			0
$25$	0.117249	+	0.203081i	0.0234498	+	0.0406163i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	6.71261	+	3.87553i	1.24650	+	0.719667i	0.970410	−	0.241464i	$-0.0776276\pi$
$29$	6.71261	+	3.87553i	1.24650	+	0.719667i	0.276091	+	0.961132i	$0.410961\pi$
$30$		0			0
$31$		−	0.706968i		−	0.126975i	−0.997983	−	0.0634876i	$-0.979778\pi$
$31$		−	0.706968i		−	0.126975i	0.997983	−	0.0634876i	$-0.0202223\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.41738	+	2.45498i	0.233016	+	0.403596i	0.958694	−	0.284438i	$-0.0918071\pi$
$37$	1.41738	+	2.45498i	0.233016	+	0.403596i	−0.725678	+	0.688034i	$0.758474\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.74173	+	6.48086i	0.584360	+	1.01214i	0.994955	+	0.100323i	$0.0319876\pi$
$41$	3.74173	+	6.48086i	0.584360	+	1.01214i	−0.410595	+	0.911818i	$0.634679\pi$
$42$		0			0
$43$	−1.27112	+	2.20164i	−0.193844	+	0.335748i	−0.946521	−	0.322642i	$-0.895429\pi$
$43$	−1.27112	+	2.20164i	−0.193844	+	0.335748i	0.752677	+	0.658390i	$0.228762\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−12.5508			−1.83072			−0.915358	−	0.402640i	$-0.868093\pi$
$47$	−12.5508			−1.83072			−0.915358	+	0.402640i	$0.868093\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.41675	+	1.39531i	0.331966	+	0.191661i	0.656714	−	0.754140i	$-0.271946\pi$
$53$	2.41675	+	1.39531i	0.331966	+	0.191661i	−0.324748	+	0.945801i	$0.605279\pi$
$54$		0			0
$55$		−	3.19850i		−	0.431286i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	13.4330			1.74883			0.874414	−	0.485180i	$-0.161246\pi$
$59$	13.4330			1.74883			0.874414	+	0.485180i	$0.161246\pi$
$60$		0			0
$61$			7.79493i			0.998039i	0.866591	+	0.499020i	$0.166306\pi$
$61$			7.79493i			0.998039i	−0.866591	+	0.499020i	$0.833694\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			7.37945i			0.915308i
$66$		0			0
$67$	5.84058			0.713541			0.356770	−	0.934192i	$-0.383878\pi$
$67$	5.84058			0.713541			0.356770	+	0.934192i	$0.383878\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	11.6854i		−	1.38680i	−0.720554	−	0.693398i	$-0.756113\pi$
$71$		−	11.6854i		−	1.38680i	0.720554	−	0.693398i	$-0.243887\pi$
$72$		0			0
$73$	3.95924	+	2.28587i	0.463394	+	0.267541i	0.713470	−	0.700685i	$-0.247122\pi$
$73$	3.95924	+	2.28587i	0.463394	+	0.267541i	−0.250076	+	0.968226i	$0.580456\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	9.38377			1.05576			0.527879	−	0.849320i	$-0.322988\pi$
$79$	9.38377			1.05576			0.527879	+	0.849320i	$0.322988\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.70847	−	2.95917i	0.187529	−	0.324811i	−0.756896	−	0.653535i	$-0.773285\pi$
$83$	1.70847	−	2.95917i	0.187529	−	0.324811i	0.944426	+	0.328724i	$0.106619\pi$
$84$		0			0
$85$	−2.88452	−	4.99614i	−0.312871	−	0.541908i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.61937	+	8.00099i	0.489653	+	0.848103i	0.999929	−	0.0119070i	$-0.00379021\pi$
$89$	4.61937	+	8.00099i	0.489653	+	0.848103i	−0.510276	+	0.860010i	$0.670457\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$			17.3379i			1.77883i
$96$		0			0
$97$	−6.38394	−	3.68577i	−0.648191	−	0.374233i	0.139572	−	0.990212i	$-0.455427\pi$
$97$	−6.38394	−	3.68577i	−0.648191	−	0.374233i	−0.787763	+	0.615979i	$0.788761\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.96357	+	6.86510i	0.394390	+	0.683103i	0.993023	−	0.117920i	$-0.0376226\pi$
$101$	3.96357	+	6.86510i	0.394390	+	0.683103i	−0.598633	+	0.801023i	$0.704289\pi$
$102$		0			0
$103$	3.26825	+	1.88693i	0.322031	+	0.185924i	0.652297	−	0.757963i	$-0.273805\pi$
$103$	3.26825	+	1.88693i	0.322031	+	0.185924i	−0.330267	+	0.943888i	$0.607139\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.88241	−	3.97356i	0.665347	−	0.384138i	−0.128964	−	0.991649i	$-0.541165\pi$
$107$	6.88241	−	3.97356i	0.665347	−	0.384138i	0.794311	+	0.607511i	$0.207832\pi$
$108$		0			0
$109$	0.505142	−	0.874932i	0.0483838	−	0.0838033i	−0.840819	−	0.541316i	$-0.817926\pi$
$109$	0.505142	−	0.874932i	0.0483838	−	0.0838033i	0.889203	+	0.457513i	$0.151260\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	10.5557	−	6.09431i	0.992992	−	0.573304i	0.0868250	−	0.996224i	$-0.472328\pi$
$113$	10.5557	−	6.09431i	0.992992	−	0.573304i	0.906167	+	0.422919i	$0.138995\pi$
$114$		0			0
$115$	7.58037	−	4.37653i	0.706873	−	0.408113i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−4.42662	+	7.66713i	−0.402420	+	0.697012i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.4269			1.02206
$126$		0			0
$127$	6.79350			0.602826			0.301413	−	0.953494i	$-0.402542\pi$
$127$	6.79350			0.602826			0.301413	+	0.953494i	$0.402542\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.86790	−	11.8956i	0.600051	−	1.03932i	−0.392761	−	0.919640i	$-0.628480\pi$
$131$	6.86790	−	11.8956i	0.600051	−	1.03932i	0.992813	−	0.119679i	$-0.0381865\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−17.4028	+	10.0475i	−1.48682	+	0.858416i	−0.999887	−	0.0150235i	$-0.995218\pi$
$137$	−17.4028	+	10.0475i	−1.48682	+	0.858416i	−0.486933	+	0.873439i	$0.661884\pi$
$138$		0			0
$139$	−8.51403	+	4.91558i	−0.722151	+	0.416934i	−0.815544	−	0.578695i	$-0.803562\pi$
$139$	−8.51403	+	4.91558i	−0.722151	+	0.416934i	0.0933930	+	0.995629i	$0.470229\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.47646	+	4.28936i	−0.207092	+	0.358694i
$144$		0			0
$145$	14.6536	−	8.46029i	1.21692	−	0.702589i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−17.3512	−	10.0177i	−1.42146	−	0.820682i	−0.425038	−	0.905175i	$-0.639739\pi$
$149$	−17.3512	−	10.0177i	−1.42146	−	0.820682i	−0.996424	+	0.0844939i	$0.973073\pi$
$150$		0			0
$151$	11.1168	+	19.2549i	0.904675	+	1.56694i	0.821353	+	0.570420i	$0.193220\pi$
$151$	11.1168	+	19.2549i	0.904675	+	1.56694i	0.0833218	+	0.996523i	$0.473447\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.33655	−	0.771657i	−0.107354	−	0.0619810i
$156$		0			0
$157$		−	8.02869i		−	0.640759i	−0.947289	−	0.320380i	$-0.896189\pi$
$157$		−	8.02869i		−	0.640759i	0.947289	−	0.320380i	$-0.103811\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−6.22604	−	10.7838i	−0.487661	−	0.844654i	0.512238	−	0.858844i	$-0.328817\pi$
$163$	−6.22604	−	10.7838i	−0.487661	−	0.844654i	−0.999899	+	0.0141893i	$0.995483\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9.85984	−	17.0777i	−0.762978	−	1.32152i	−0.941309	−	0.337546i	$-0.890403\pi$
$167$	−9.85984	−	17.0777i	−0.762978	−	1.32152i	0.178332	−	0.983970i	$-0.442930\pi$
$168$		0			0
$169$	−0.786412	+	1.36211i	−0.0604933	+	0.104777i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.82747			0.138940			0.0694699	−	0.997584i	$-0.477869\pi$
$173$	1.82747			0.138940			0.0694699	+	0.997584i	$0.477869\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−12.1182	−	6.99645i	−0.905757	−	0.522939i	−0.0266934	−	0.999644i	$-0.508498\pi$
$179$	−12.1182	−	6.99645i	−0.905757	−	0.522939i	−0.879064	+	0.476705i	$0.841831\pi$
$180$		0			0
$181$		−	16.3594i		−	1.21599i	−0.793942	−	0.607994i	$-0.791975\pi$
$181$		−	16.3594i		−	1.21599i	0.793942	−	0.607994i	$-0.208025\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	6.18830			0.454973
$186$		0			0
$187$		−	3.87206i		−	0.283153i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			13.6631i			0.988624i	0.869285	+	0.494312i	$0.164580\pi$
$191$			13.6631i			0.988624i	−0.869285	+	0.494312i	$0.835420\pi$
$192$		0			0
$193$	−4.37769			−0.315113			−0.157557	−	0.987510i	$-0.550362\pi$
$193$	−4.37769			−0.315113			−0.157557	+	0.987510i	$0.550362\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			1.00603i			0.0716767i	0.999358	+	0.0358384i	$0.0114101\pi$
$197$			1.00603i			0.0716767i	−0.999358	+	0.0358384i	$0.988590\pi$
$198$		0			0
$199$	5.67639	+	3.27726i	0.402388	+	0.232319i	0.687514	−	0.726171i	$-0.258702\pi$
$199$	5.67639	+	3.27726i	0.402388	+	0.232319i	−0.285126	+	0.958490i	$0.592035\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	16.3364			1.14098
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−5.81840	+	10.0778i	−0.402467	+	0.697094i
$210$		0			0
$211$	−9.11202	−	15.7825i	−0.627297	−	1.08651i	−0.988092	−	0.153866i	$-0.950828\pi$
$211$	−9.11202	−	15.7825i	−0.627297	−	1.08651i	0.360794	−	0.932645i	$-0.382506\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.77486	+	4.80620i	0.189244	+	0.327780i
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$			8.93345i			0.600929i
$222$		0			0
$223$	8.71705	+	5.03279i	0.583737	+	0.337021i	0.762617	−	0.646850i	$-0.223914\pi$
$223$	8.71705	+	5.03279i	0.583737	+	0.337021i	−0.178880	+	0.983871i	$0.557247\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.94372	+	17.2230i	0.659988	+	1.14313i	0.980618	+	0.195928i	$0.0627720\pi$
$227$	9.94372	+	17.2230i	0.659988	+	1.14313i	−0.320630	+	0.947204i	$0.603895\pi$
$228$		0			0
$229$	15.3854	+	8.88275i	1.01669	+	0.586988i	0.913145	−	0.407636i	$-0.133647\pi$
$229$	15.3854	+	8.88275i	1.01669	+	0.586988i	0.103549	+	0.994624i	$0.466980\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	13.9077	−	8.02962i	0.911124	−	0.526038i	0.0303317	−	0.999540i	$-0.490344\pi$
$233$	13.9077	−	8.02962i	0.911124	−	0.526038i	0.880793	+	0.473502i	$0.157010\pi$
$234$		0			0
$235$	−13.6992	+	23.7277i	−0.893636	+	1.54782i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	7.11117	−	4.10564i	0.459983	−	0.265572i	−0.252054	−	0.967713i	$-0.581106\pi$
$239$	7.11117	−	4.10564i	0.459983	−	0.265572i	0.712037	+	0.702142i	$0.247773\pi$
$240$		0			0
$241$	24.6614	−	14.2382i	1.58858	−	0.917166i	0.595037	−	0.803698i	$-0.297137\pi$
$241$	24.6614	−	14.2382i	1.58858	−	0.917166i	0.993542	−	0.113468i	$-0.0361959\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	13.4240	−	23.2510i	0.854147	−	1.47943i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	0.656343			0.0414280			0.0207140	−	0.999785i	$-0.493406\pi$
$251$	0.656343			0.0414280			0.0207140	+	0.999785i	$0.493406\pi$
$252$		0			0
$253$	5.87486			0.369349
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3.82042	+	6.61716i	−0.238311	+	0.412767i	−0.960230	−	0.279211i	$-0.909927\pi$
$257$	−3.82042	+	6.61716i	−0.238311	+	0.412767i	0.721918	+	0.691978i	$0.243261\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	5.73888	−	3.31334i	0.353874	−	0.204310i	−0.312516	−	0.949913i	$-0.601172\pi$
$263$	5.73888	−	3.31334i	0.353874	−	0.204310i	0.666390	+	0.745603i	$0.267838\pi$
$264$		0			0
$265$	5.27577	−	3.04597i	0.324088	−	0.187112i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	4.38347	−	7.59239i	0.267265	−	0.462916i	−0.700890	−	0.713270i	$-0.747214\pi$
$269$	4.38347	−	7.59239i	0.267265	−	0.462916i	0.968154	+	0.250354i	$0.0805469\pi$
$270$		0			0
$271$	−14.2608	+	8.23346i	−0.866280	+	0.500147i	−0.866110	−	0.499853i	$-0.833387\pi$
$271$	−14.2608	+	8.23346i	−0.866280	+	0.500147i	−0.000169619		1.00000i	$0.500054\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.297551	+	0.171791i	0.0179430	+	0.0103594i
$276$		0			0
$277$	8.88732	+	15.3933i	0.533987	+	0.924893i	0.999212	+	0.0397001i	$0.0126402\pi$
$277$	8.88732	+	15.3933i	0.533987	+	0.924893i	−0.465225	+	0.885193i	$0.654026\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	14.0252	+	8.09748i	0.836676	+	0.483055i	0.856133	−	0.516755i	$-0.172860\pi$
$281$	14.0252	+	8.09748i	0.836676	+	0.483055i	−0.0194568	+	0.999811i	$0.506194\pi$
$282$		0			0
$283$		−	28.3729i		−	1.68660i	−0.537447	−	0.843298i	$-0.680611\pi$
$283$		−	28.3729i		−	1.68660i	0.537447	−	0.843298i	$-0.319389\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	5.00804	+	8.67417i	0.294590	+	0.510246i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.38260	−	7.59088i	−0.256034	−	0.443464i	0.709142	−	0.705066i	$-0.249083\pi$
$293$	−4.38260	−	7.59088i	−0.256034	−	0.443464i	−0.965176	+	0.261602i	$0.915749\pi$
$294$		0			0
$295$	14.6621	−	25.3956i	0.853663	−	1.47859i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−13.5542			−0.783861
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	14.7366	+	8.50818i	0.843816	+	0.487177i
$306$		0			0
$307$			12.8497i			0.733372i	0.930345	+	0.366686i	$0.119508\pi$
$307$			12.8497i			0.733372i	−0.930345	+	0.366686i	$0.880492\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−6.59343			−0.373879			−0.186939	−	0.982371i	$-0.559857\pi$
$311$	−6.59343			−0.373879			−0.186939	+	0.982371i	$0.559857\pi$
$312$		0			0
$313$		−	3.41458i		−	0.193004i	−0.995333	−	0.0965018i	$-0.969235\pi$
$313$		−	3.41458i		−	0.193004i	0.995333	−	0.0965018i	$-0.0307654\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			32.1010i			1.80297i	0.432810	+	0.901485i	$0.357522\pi$
$317$			32.1010i			1.80297i	−0.432810	+	0.901485i	$0.642478\pi$
$318$		0			0
$319$	11.3567			0.635854
$320$		0			0
$321$		0			0
$322$		0			0
$323$			20.9890i			1.16786i
$324$		0			0
$325$	−0.686498	−	0.396350i	−0.0380801	−	0.0219855i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−28.8833			−1.58757			−0.793784	−	0.608199i	$-0.791892\pi$
$331$	−28.8833			−1.58757			−0.793784	+	0.608199i	$0.791892\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	6.37501	−	11.0418i	0.348304	−	0.603280i
$336$		0			0
$337$	4.82568	+	8.35833i	0.262872	+	0.455307i	0.967004	−	0.254762i	$-0.0819971\pi$
$337$	4.82568	+	8.35833i	0.262872	+	0.455307i	−0.704132	+	0.710069i	$0.748664\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.517919	−	0.897063i	−0.0280469	−	0.0485787i
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$			12.3273i			0.661766i	0.943672	+	0.330883i	$0.107347\pi$
$347$			12.3273i			0.661766i	−0.943672	+	0.330883i	$0.892653\pi$
$348$		0			0
$349$	10.2211	+	5.90115i	0.547123	+	0.315881i	0.747961	−	0.663743i	$-0.231033\pi$
$349$	10.2211	+	5.90115i	0.547123	+	0.315881i	−0.200838	+	0.979624i	$0.564366\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	6.59855	+	11.4290i	0.351205	+	0.608305i	0.986461	−	0.163997i	$-0.0524386\pi$
$353$	6.59855	+	11.4290i	0.351205	+	0.608305i	−0.635256	+	0.772302i	$0.719105\pi$
$354$		0			0
$355$	−22.0916	−	12.7546i	−1.17250	−	0.676943i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	5.22483	−	3.01656i	0.275756	−	0.159208i	−0.355745	−	0.934583i	$-0.615773\pi$
$359$	5.22483	−	3.01656i	0.275756	−	0.159208i	0.631501	+	0.775375i	$0.282439\pi$
$360$		0			0
$361$	22.0394	−	38.1733i	1.15997	−	2.00912i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	8.64304	−	4.99006i	0.452397	−	0.261192i
$366$		0			0
$367$	−14.8755	+	8.58836i	−0.776494	+	0.448309i	−0.835186	−	0.549967i	$-0.814640\pi$
$367$	−14.8755	+	8.58836i	−0.776494	+	0.448309i	0.0586924	+	0.998276i	$0.481307\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−2.35902	+	4.08595i	−0.122146	+	0.211562i	−0.920614	−	0.390475i	$-0.872311\pi$
$373$	−2.35902	+	4.08595i	−0.122146	+	0.211562i	0.798468	+	0.602037i	$0.205644\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−26.2017			−1.34946
$378$		0			0
$379$	9.34015			0.479771			0.239886	−	0.970801i	$-0.422890\pi$
$379$	9.34015			0.479771			0.239886	+	0.970801i	$0.422890\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.85036	−	4.93696i	0.145646	−	0.252267i	−0.783968	−	0.620802i	$-0.786807\pi$
$383$	2.85036	−	4.93696i	0.145646	−	0.252267i	0.929614	+	0.368535i	$0.120140\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−6.63671	+	3.83171i	−0.336495	+	0.194275i	−0.658721	−	0.752387i	$-0.728902\pi$
$389$	−6.63671	+	3.83171i	−0.336495	+	0.194275i	0.322226	+	0.946663i	$0.395569\pi$
$390$		0			0
$391$	9.17668	−	5.29816i	0.464085	−	0.267939i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	10.2424	−	17.7404i	0.515351	−	0.892615i
$396$		0			0
$397$	1.12810	−	0.651310i	0.0566178	−	0.0326883i	−0.471424	−	0.881907i	$-0.656260\pi$
$397$	1.12810	−	0.651310i	0.0566178	−	0.0326883i	0.528042	+	0.849218i	$0.322926\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	8.18778	+	4.72722i	0.408878	+	0.236066i	0.690308	−	0.723516i	$-0.257475\pi$
$401$	8.18778	+	4.72722i	0.408878	+	0.236066i	−0.281429	+	0.959582i	$0.590809\pi$
$402$		0			0
$403$	1.19492	+	2.06966i	0.0595233	+	0.103097i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.59700	+	2.07673i	0.178296	+	0.102940i
$408$		0			0
$409$			19.0736i			0.943126i	0.881832	+	0.471563i	$0.156310\pi$
$409$			19.0736i			0.943126i	−0.881832	+	0.471563i	$0.843690\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−3.72961	−	6.45987i	−0.183079	−	0.317102i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−4.20003	−	7.27466i	−0.205185	−	0.355390i	0.745007	−	0.667057i	$-0.232446\pi$
$419$	−4.20003	−	7.27466i	−0.205185	−	0.355390i	−0.950192	+	0.311666i	$0.899113\pi$
$420$		0			0
$421$	19.7178	−	34.1522i	0.960985	−	1.66448i	0.240951	−	0.970537i	$-0.422541\pi$
$421$	19.7178	−	34.1522i	0.960985	−	1.66448i	0.720035	−	0.693938i	$-0.244126\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.619711			0.0300604
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−10.3340	−	5.96634i	−0.497772	−	0.287389i	0.230021	−	0.973186i	$-0.426120\pi$
$431$	−10.3340	−	5.96634i	−0.497772	−	0.287389i	−0.727793	+	0.685797i	$0.759454\pi$
$432$		0			0
$433$			12.2121i			0.586875i	0.955978	+	0.293437i	$0.0947992\pi$
$433$			12.2121i			0.586875i	−0.955978	+	0.293437i	$0.905201\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−31.8454			−1.52337
$438$		0			0
$439$			16.7015i			0.797120i	0.917142	+	0.398560i	$0.130490\pi$
$439$			16.7015i			0.797120i	−0.917142	+	0.398560i	$0.869510\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	30.2997i		−	1.43958i	−0.694190	−	0.719791i	$-0.744237\pi$
$443$		−	30.2997i		−	1.43958i	0.694190	−	0.719791i	$-0.255763\pi$
$444$		0			0
$445$	20.1682			0.956065
$446$		0			0
$447$		0			0
$448$		0			0
$449$			30.1253i			1.42170i	0.703343	+	0.710851i	$0.251690\pi$
$449$			30.1253i			1.42170i	−0.703343	+	0.710851i	$0.748310\pi$
$450$		0			0
$451$	9.49566	+	5.48232i	0.447133	+	0.258152i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	25.2318			1.18029			0.590146	−	0.807297i	$-0.299070\pi$
$457$	25.2318			1.18029			0.590146	+	0.807297i	$0.299070\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−12.3174	+	21.3344i	−0.573680	+	0.993643i	0.422503	+	0.906361i	$0.361151\pi$
$461$	−12.3174	+	21.3344i	−0.573680	+	0.993643i	−0.996184	+	0.0872820i	$0.972182\pi$
$462$		0			0
$463$	−6.33215	−	10.9676i	−0.294280	−	0.509708i	0.680537	−	0.732713i	$-0.261746\pi$
$463$	−6.33215	−	10.9676i	−0.294280	−	0.509708i	−0.974817	+	0.223006i	$0.928413\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	10.4723	+	18.1385i	0.484599	+	0.839350i	0.999843	−	0.0176932i	$-0.00563223\pi$
$467$	10.4723	+	18.1385i	0.484599	+	0.839350i	−0.515245	+	0.857043i	$0.672299\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$			3.72485i			0.171269i
$474$		0			0
$475$	−1.61291	−	0.931217i	−0.0740056	−	0.0427271i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	15.8852	+	27.5141i	0.725816	+	1.25715i	0.958637	+	0.284630i	$0.0918707\pi$
$479$	15.8852	+	27.5141i	0.725816	+	1.25715i	−0.232822	+	0.972519i	$0.574796\pi$
$480$		0			0
$481$	−8.29884	−	4.79134i	−0.378394	−	0.218466i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−13.9362	+	8.04605i	−0.632809	+	0.365352i
$486$		0			0
$487$	−17.7821	+	30.7995i	−0.805784	+	1.39566i	0.109977	+	0.993934i	$0.464922\pi$
$487$	−17.7821	+	30.7995i	−0.805784	+	1.39566i	−0.915761	+	0.401724i	$0.868411\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−2.75734	+	1.59195i	−0.124437	+	0.0718437i	−0.560926	−	0.827866i	$-0.689555\pi$
$491$	−2.75734	+	1.59195i	−0.124437	+	0.0718437i	0.436490	+	0.899709i	$0.356222\pi$
$492$		0			0
$493$	17.7395	−	10.2419i	0.798947	−	0.461272i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−16.0214	+	27.7498i	−0.717215	+	1.24225i	0.244884	+	0.969552i	$0.421250\pi$
$499$	−16.0214	+	27.7498i	−0.717215	+	1.24225i	−0.962099	+	0.272700i	$0.912083\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	11.6608			0.519930			0.259965	−	0.965618i	$-0.416289\pi$
$503$	11.6608			0.519930			0.259965	+	0.965618i	$0.416289\pi$
$504$		0			0
$505$	17.3050			0.770061
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−13.4427	+	23.2834i	−0.595836	+	1.03202i	0.397592	+	0.917562i	$0.369846\pi$
$509$	−13.4427	+	23.2834i	−0.595836	+	1.03202i	−0.993428	+	0.114457i	$0.963487\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	7.13461	−	4.11917i	0.314388	−	0.181512i
$516$		0			0
$517$	−15.9255	+	9.19459i	−0.700402	+	0.404378i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	17.0385	−	29.5116i	0.746471	−	1.29293i	−0.203033	−	0.979172i	$-0.565080\pi$
$521$	17.0385	−	29.5116i	0.746471	−	1.29293i	0.949504	−	0.313754i	$-0.101587\pi$
$522$		0			0
$523$	−4.71003	+	2.71933i	−0.205955	+	0.118908i	−0.599430	−	0.800427i	$-0.704606\pi$
$523$	−4.71003	+	2.71933i	−0.205955	+	0.118908i	0.393475	+	0.919335i	$0.371273\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.61801	−	0.934157i	−0.0704815	−	0.0406925i
$528$		0			0
$529$	−3.46140	−	5.99532i	−0.150496	−	0.260666i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−21.9080	−	12.6486i	−0.948940	−	0.547871i
$534$		0			0
$535$		−	17.3486i		−	0.750045i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	11.8329	+	20.4952i	0.508737	+	0.881158i	0.999949	+	0.0101183i	$0.00322080\pi$
$541$	11.8329	+	20.4952i	0.508737	+	0.881158i	−0.491212	+	0.871040i	$0.663446\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−1.10273	−	1.90998i	−0.0472356	−	0.0818145i
$546$		0			0
$547$	−12.0824	+	20.9273i	−0.516606	+	0.894788i	0.483208	+	0.875505i	$0.339471\pi$
$547$	−12.0824	+	20.9273i	−0.516606	+	0.894788i	−0.999814	+	0.0192822i	$0.993862\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−61.5605			−2.62257
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	7.36315	+	4.25111i	0.311987	+	0.180126i	0.647815	−	0.761798i	$-0.275683\pi$
$557$	7.36315	+	4.25111i	0.311987	+	0.180126i	−0.335829	+	0.941923i	$0.609016\pi$
$558$		0			0
$559$		−	8.59381i		−	0.363480i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.947553			0.0399346			0.0199673	−	0.999801i	$-0.493644\pi$
$563$	0.947553			0.0399346			0.0199673	+	0.999801i	$0.493644\pi$
$564$		0			0
$565$		−	26.6078i		−	1.11940i
$566$		0			0
$567$		0			0
$568$		0			0
$569$			18.2280i			0.764158i	0.924130	+	0.382079i	$0.124792\pi$
$569$			18.2280i			0.764158i	−0.924130	+	0.382079i	$0.875208\pi$
$570$		0			0
$571$	−12.2424			−0.512330			−0.256165	−	0.966633i	$-0.582459\pi$
$571$	−12.2424			−0.512330			−0.256165	+	0.966633i	$0.582459\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			0.940253i			0.0392112i
$576$		0			0
$577$	10.2500	+	5.91784i	0.426713	+	0.246363i	0.697945	−	0.716151i	$-0.254098\pi$
$577$	10.2500	+	5.91784i	0.426713	+	0.246363i	−0.271232	+	0.962514i	$0.587431\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	4.08878			0.169340
$584$		0			0
$585$		0			0
$586$		0			0
$587$	3.57681	−	6.19521i	0.147631	−	0.255704i	−0.782721	−	0.622373i	$-0.786169\pi$
$587$	3.57681	−	6.19521i	0.147631	−	0.255704i	0.930351	+	0.366669i	$0.119502\pi$
$588$		0			0
$589$	2.80745	+	4.86264i	0.115679	+	0.200362i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	13.4811	+	23.3500i	0.553603	+	0.958869i	0.998011	+	0.0630442i	$0.0200809\pi$
$593$	13.4811	+	23.3500i	0.553603	+	0.958869i	−0.444408	+	0.895825i	$0.646586\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	35.2441i		−	1.44004i	−0.693955	−	0.720018i	$-0.744133\pi$
$599$		−	35.2441i		−	1.44004i	0.693955	−	0.720018i	$-0.255867\pi$
$600$		0			0
$601$	−3.39266	−	1.95875i	−0.138389	−	0.0798991i	0.429207	−	0.903206i	$-0.358793\pi$
$601$	−3.39266	−	1.95875i	−0.138389	−	0.0798991i	−0.567596	+	0.823307i	$0.692126\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	9.66332	+	16.7374i	0.392870	+	0.680470i
$606$		0			0
$607$	12.5377	+	7.23862i	0.508888	+	0.293807i	0.732376	−	0.680900i	$-0.238411\pi$
$607$	12.5377	+	7.23862i	0.508888	+	0.293807i	−0.223488	+	0.974707i	$0.571744\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	36.7426	−	21.2134i	1.48645	−	0.858201i
$612$		0			0
$613$	−6.51761	+	11.2888i	−0.263244	+	0.455952i	−0.967102	−	0.254389i	$-0.918126\pi$
$613$	−6.51761	+	11.2888i	−0.263244	+	0.455952i	0.703858	+	0.710341i	$0.251459\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.14491	−	1.81571i	0.126609	−	0.0730979i	−0.435358	−	0.900258i	$-0.643378\pi$
$617$	3.14491	−	1.81571i	0.126609	−	0.0730979i	0.561967	+	0.827160i	$0.310045\pi$
$618$		0			0
$619$	14.2737	−	8.24091i	0.573708	−	0.331230i	−0.184921	−	0.982753i	$-0.559203\pi$
$619$	14.2737	−	8.24091i	0.573708	−	0.331230i	0.758629	+	0.651523i	$0.225870\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	11.8863	−	20.5876i	0.475450	−	0.823504i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	7.49147			0.298704
$630$		0			0
$631$	−34.8383			−1.38689			−0.693446	−	0.720508i	$-0.743909\pi$
$631$	−34.8383			−1.38689			−0.693446	+	0.720508i	$0.743909\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	7.41512	−	12.8434i	0.294260	−	0.509673i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−7.25538	+	4.18889i	−0.286570	+	0.165451i	−0.636394	−	0.771364i	$-0.719575\pi$
$641$	−7.25538	+	4.18889i	−0.286570	+	0.165451i	0.349824	+	0.936815i	$0.386241\pi$
$642$		0			0
$643$	18.0021	−	10.3935i	0.709934	−	0.409881i	−0.101103	−	0.994876i	$-0.532237\pi$
$643$	18.0021	−	10.3935i	0.709934	−	0.409881i	0.811037	+	0.584995i	$0.198904\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.74770	−	8.22325i	0.186651	−	0.323289i	−0.757480	−	0.652858i	$-0.773570\pi$
$647$	4.74770	−	8.22325i	0.186651	−	0.323289i	0.944132	+	0.329568i	$0.106903\pi$
$648$		0			0
$649$	17.0450	−	9.84091i	0.669073	−	0.386290i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	6.64747	+	3.83792i	0.260136	+	0.150189i	0.624396	−	0.781108i	$-0.285345\pi$
$653$	6.64747	+	3.83792i	0.260136	+	0.150189i	−0.364261	+	0.931297i	$0.618678\pi$
$654$		0			0
$655$	−14.9927	−	25.9680i	−0.585811	−	1.01465i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−38.0493	−	21.9678i	−1.48219	−	0.855743i	−0.482395	−	0.875954i	$-0.660233\pi$
$659$	−38.0493	−	21.9678i	−1.48219	−	0.855743i	−0.999796	+	0.0202102i	$0.993566\pi$
$660$		0			0
$661$			25.5938i			0.995484i	0.867325	+	0.497742i	$0.165837\pi$
$661$			25.5938i			0.995484i	−0.867325	+	0.497742i	$0.834163\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	15.5395	+	26.9151i	0.601691	+	1.04216i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	5.71051	+	9.89089i	0.220452	+	0.381834i
$672$		0			0
$673$	−7.64671	+	13.2445i	−0.294759	+	0.510538i	−0.974929	−	0.222517i	$-0.928573\pi$
$673$	−7.64671	+	13.2445i	−0.294759	+	0.510538i	0.680170	+	0.733055i	$0.261906\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	45.2918			1.74070			0.870352	−	0.492430i	$-0.163891\pi$
$677$	45.2918			1.74070			0.870352	+	0.492430i	$0.163891\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−24.0891	−	13.9079i	−0.921744	−	0.532169i	−0.0375529	−	0.999295i	$-0.511956\pi$
$683$	−24.0891	−	13.9079i	−0.921744	−	0.532169i	−0.884191	+	0.467126i	$0.845290\pi$
$684$		0			0
$685$			43.8674i			1.67609i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−9.43345			−0.359386
$690$		0			0
$691$			16.2946i			0.619875i	0.950757	+	0.309938i	$0.100308\pi$
$691$			16.2946i			0.619875i	−0.950757	+	0.309938i	$0.899692\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			21.4614i			0.814079i
$696$		0			0
$697$	19.7766			0.749093
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	0.393403i		−	0.0148586i	−0.999972	−	0.00742932i	$-0.997635\pi$
$701$		−	0.393403i		−	0.0148586i	0.999972	−	0.00742932i	$-0.00236485\pi$
$702$		0			0
$703$	−19.4980	−	11.2572i	−0.735379	−	0.424572i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−32.6366			−1.22569			−0.612846	−	0.790202i	$-0.709975\pi$
$709$	−32.6366			−1.22569			−0.612846	+	0.790202i	$0.709975\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1.41734	−	2.45491i	0.0530799	−	0.0919372i
$714$		0			0
$715$	5.40612	+	9.36368i	0.202178	+	0.350182i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	0.106604	+	0.184643i	0.00397565	+	0.00688602i	0.868006	−	0.496553i	$-0.165401\pi$
$719$	0.106604	+	0.184643i	0.00397565	+	0.00688602i	−0.864031	+	0.503439i	$0.832068\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$			1.81761i			0.0675042i
$726$		0			0
$727$	−31.8208	−	18.3717i	−1.18017	−	0.681370i	−0.224114	−	0.974563i	$-0.571949\pi$
$727$	−31.8208	−	18.3717i	−1.18017	−	0.681370i	−0.956053	+	0.293193i	$0.905282\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	3.35920	+	5.81831i	0.124245	+	0.215198i
$732$		0			0
$733$	−9.41829	−	5.43765i	−0.347873	−	0.200844i	0.315875	−	0.948801i	$-0.397702\pi$
$733$	−9.41829	−	5.43765i	−0.347873	−	0.200844i	−0.663748	+	0.747956i	$0.731035\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	7.41104	−	4.27877i	0.272989	−	0.157610i
$738$		0			0
$739$	6.91282	−	11.9734i	0.254292	−	0.440447i	−0.710411	−	0.703787i	$-0.751491\pi$
$739$	6.91282	−	11.9734i	0.254292	−	0.440447i	0.964703	+	0.263340i	$0.0848242\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	15.8751	−	9.16552i	0.582403	−	0.336250i	−0.179685	−	0.983724i	$-0.557508\pi$
$743$	15.8751	−	9.16552i	0.582403	−	0.336250i	0.762088	+	0.647474i	$0.224175\pi$
$744$		0			0
$745$	−37.8776	+	21.8687i	−1.38773	+	0.801206i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	9.97084	−	17.2700i	0.363841	−	0.630191i	−0.624748	−	0.780826i	$-0.714798\pi$
$751$	9.97084	−	17.2700i	0.363841	−	0.630191i	0.988589	+	0.150635i	$0.0481318\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	48.5362			1.76641
$756$		0			0
$757$	−46.9292			−1.70567			−0.852836	−	0.522178i	$-0.825119\pi$
$757$	−46.9292			−1.70567			−0.852836	+	0.522178i	$0.825119\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	26.7769	−	46.3789i	0.970661	−	1.68123i	0.277093	−	0.960843i	$-0.410629\pi$
$761$	26.7769	−	46.3789i	0.970661	−	1.68123i	0.693568	−	0.720391i	$-0.256038\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−39.3254	+	22.7045i	−1.41996	+	0.819813i
$768$		0			0
$769$	34.7306	−	20.0517i	1.25242	−	0.723085i	0.280830	−	0.959758i	$-0.409390\pi$
$769$	34.7306	−	20.0517i	1.25242	−	0.723085i	0.971589	+	0.236673i	$0.0760570\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−7.82375	+	13.5511i	−0.281401	+	0.487400i	−0.971730	−	0.236095i	$-0.924132\pi$
$773$	−7.82375	+	13.5511i	−0.281401	+	0.487400i	0.690329	+	0.723495i	$0.257466\pi$
$774$		0			0
$775$	0.143572	−	0.0828913i	0.00515726	−	0.00297755i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−51.4724	−	29.7176i	−1.84419	−	1.06474i
$780$		0			0
$781$	−8.56060	−	14.8274i	−0.306322	−	0.530566i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−15.1785	−	8.76333i	−0.541745	−	0.312777i
$786$		0			0
$787$			46.1788i			1.64610i	0.567972	+	0.823048i	$0.307728\pi$
$787$			46.1788i			1.64610i	−0.567972	+	0.823048i	$0.692272\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−13.1750	−	22.8198i	−0.467859	−	0.810356i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−16.9388	−	29.3388i	−0.600002	−	1.03923i	−0.992820	−	0.119618i	$-0.961833\pi$
$797$	−16.9388	−	29.3388i	−0.600002	−	1.03923i	0.392818	−	0.919616i	$-0.371500\pi$
$798$		0			0
$799$	−16.5840	+	28.7244i	−0.586701	+	1.01620i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	6.69844			0.236383
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	33.7873	+	19.5071i	1.18790	+	0.685834i	0.957829	−	0.287340i	$-0.0927711\pi$
$809$	33.7873	+	19.5071i	1.18790	+	0.685834i	0.230070	+	0.973174i	$0.426104\pi$
$810$		0			0
$811$		−	7.73397i		−	0.271577i	−0.990738	−	0.135788i	$-0.956643\pi$
$811$		−	7.73397i		−	0.271577i	0.990738	−	0.135788i	$-0.0433567\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−27.1829			−0.952177
$816$		0			0
$817$		−	20.1910i		−	0.706394i
$818$		0			0
$819$		0			0
$820$		0			0
$821$			0.512269i			0.0178783i	0.999960	+	0.00893915i	$0.00284546\pi$
$821$			0.512269i			0.0178783i	−0.999960	+	0.00893915i	$0.997155\pi$
$822$		0			0
$823$	−48.3506			−1.68540			−0.842698	−	0.538387i	$-0.819034\pi$
$823$	−48.3506			−1.68540			−0.842698	+	0.538387i	$0.819034\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	17.3086i		−	0.601879i	−0.953643	−	0.300940i	$-0.902700\pi$
$827$		−	17.3086i		−	0.601879i	0.953643	−	0.300940i	$-0.0973003\pi$
$828$		0			0
$829$	−33.0205	−	19.0644i	−1.14685	−	0.662134i	−0.198733	−	0.980054i	$-0.563683\pi$
$829$	−33.0205	−	19.0644i	−1.14685	−	0.662134i	−0.948118	+	0.317919i	$0.897016\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−43.0481			−1.48974
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−15.2026	+	26.3317i	−0.524852	+	0.909071i	0.474729	+	0.880132i	$0.342546\pi$
$839$	−15.2026	+	26.3317i	−0.524852	+	0.909071i	−0.999581	+	0.0289389i	$0.990787\pi$
$840$		0			0
$841$	15.5394	+	26.9151i	0.535842	+	0.928106i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.71674	+	2.97348i	0.0590577	+	0.102291i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$			11.3664i			0.389635i
$852$		0			0
$853$	−27.7143	−	16.0008i	−0.948919	−	0.547858i	−0.0561738	−	0.998421i	$-0.517890\pi$
$853$	−27.7143	−	16.0008i	−0.948919	−	0.547858i	−0.892745	+	0.450563i	$0.851223\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−22.5774	−	39.1053i	−0.771230	−	1.33581i	−0.936889	−	0.349627i	$-0.886308\pi$
$857$	−22.5774	−	39.1053i	−0.771230	−	1.33581i	0.165659	−	0.986183i	$-0.447025\pi$
$858$		0			0
$859$	15.7911	+	9.11701i	0.538786	+	0.311068i	0.744587	−	0.667526i	$-0.232647\pi$
$859$	15.7911	+	9.11701i	0.538786	+	0.311068i	−0.205801	+	0.978594i	$0.565980\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	6.61966	−	3.82186i	0.225336	−	0.130098i	−0.383083	−	0.923714i	$-0.625138\pi$
$863$	6.61966	−	3.82186i	0.225336	−	0.130098i	0.608419	+	0.793616i	$0.291804\pi$
$864$		0			0
$865$	1.99468	−	3.45489i	0.0678213	−	0.117470i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	11.9069	−	6.87448i	0.403915	−	0.233201i
$870$		0			0
$871$	−17.0984	+	9.87179i	−0.579358	+	0.334493i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−8.01581	+	13.8838i	−0.270675	+	0.468822i	−0.969035	−	0.246924i	$-0.920580\pi$
$877$	−8.01581	+	13.8838i	−0.270675	+	0.468822i	0.698360	+	0.715747i	$0.253913\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	24.7532			0.833958			0.416979	−	0.908916i	$-0.363089\pi$
$881$	24.7532			0.833958			0.416979	+	0.908916i	$0.363089\pi$
$882$		0			0
$883$	−11.6958			−0.393595			−0.196798	−	0.980444i	$-0.563054\pi$
$883$	−11.6958			−0.393595			−0.196798	+	0.980444i	$0.563054\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	27.5429	−	47.7058i	0.924801	−	1.60180i	0.132921	−	0.991127i	$-0.457564\pi$
$887$	27.5429	−	47.7058i	0.924801	−	1.60180i	0.791880	−	0.610676i	$-0.209102\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	86.3261	−	49.8404i	2.88879	−	1.66785i
$894$		0			0
$895$	−26.4541	+	15.2733i	−0.884262	+	0.510529i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	2.73987	−	4.74560i	0.0913799	−	0.158275i
$900$		0			0
$901$	6.38677	−	3.68741i	0.212774	−	0.122845i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−30.9281	−	17.8563i	−1.02808	−	0.593565i
$906$		0			0
$907$	12.9383	+	22.4098i	0.429610	+	0.744107i	0.996839	−	0.0794540i	$-0.0253177\pi$
$907$	12.9383	+	22.4098i	0.429610	+	0.744107i	−0.567228	+	0.823560i	$0.691984\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	3.86306	+	2.23034i	0.127989	+	0.0738944i	0.562627	−	0.826711i	$-0.309791\pi$
$911$	3.86306	+	2.23034i	0.127989	+	0.0738944i	−0.434639	+	0.900605i	$0.643124\pi$
$912$		0			0
$913$		−	5.00646i		−	0.165690i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−21.2352	−	36.7805i	−0.700485	−	1.21328i	−0.968296	−	0.249804i	$-0.919634\pi$
$919$	−21.2352	−	36.7805i	−0.700485	−	1.21328i	0.267811	−	0.963471i	$-0.413700\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	19.7507	+	34.2091i	0.650101	+	1.12601i
$924$		0			0
$925$	−0.332373	+	0.575688i	−0.0109284	+	0.0189285i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−15.4502			−0.506903			−0.253452	−	0.967348i	$-0.581566\pi$
$929$	−15.4502			−0.506903			−0.253452	+	0.967348i	$0.581566\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−7.32027	−	4.22636i	−0.239398	−	0.138217i
$936$		0			0
$937$		−	46.1410i		−	1.50736i	−0.657241	−	0.753680i	$-0.728277\pi$
$937$		−	46.1410i		−	1.50736i	0.657241	−	0.753680i	$-0.271723\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−41.0104			−1.33690			−0.668451	−	0.743756i	$-0.733042\pi$
$941$	−41.0104			−1.33690			−0.668451	+	0.743756i	$0.733042\pi$
$942$		0			0
$943$			30.0060i			0.977128i
$944$		0			0
$945$		0			0
$946$		0			0
$947$			9.82254i			0.319190i	0.987183	+	0.159595i	$0.0510188\pi$
$947$			9.82254i			0.319190i	−0.987183	+	0.159595i	$0.948981\pi$
$948$		0			0
$949$	−15.4544			−0.501670
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	17.0826i		−	0.553359i	−0.960962	−	0.276679i	$-0.910766\pi$
$953$		−	17.0826i		−	0.553359i	0.960962	−	0.276679i	$-0.0892340\pi$
$954$		0			0
$955$	25.8305	+	14.9132i	0.835855	+	0.482581i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	30.5002			0.983877
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−4.77826	+	8.27619i	−0.153818	+	0.266420i
$966$		0			0
$967$	21.3240	+	36.9343i	0.685735	+	1.18773i	0.973205	+	0.229938i	$0.0738523\pi$
$967$	21.3240	+	36.9343i	0.685735	+	1.18773i	−0.287471	+	0.957789i	$0.592814\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	11.7562	+	20.3623i	0.377275	+	0.653459i	0.990665	−	0.136321i	$-0.0435280\pi$
$971$	11.7562	+	20.3623i	0.377275	+	0.653459i	−0.613390	+	0.789780i	$0.710195\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	34.8654i		−	1.11544i	−0.830028	−	0.557722i	$-0.811675\pi$
$977$		−	34.8654i		−	1.11544i	0.830028	−	0.557722i	$-0.188325\pi$
$978$		0			0
$979$	11.7229	+	6.76824i	0.374666	+	0.216314i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−13.1804	−	22.8292i	−0.420390	−	0.728137i	0.575587	−	0.817740i	$-0.304773\pi$
$983$	−13.1804	−	22.8292i	−0.420390	−	0.728137i	−0.995978	+	0.0896033i	$0.971440\pi$
$984$		0			0
$985$	1.90194	+	1.09808i	0.0606008	+	0.0349879i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−8.82780	+	5.09673i	−0.280708	+	0.162067i
$990$		0			0
$991$	0.0805213	−	0.139467i	0.00255784	−	0.00443031i	−0.864744	−	0.502214i	$-0.832519\pi$
$991$	0.0805213	−	0.139467i	0.00255784	−	0.00443031i	0.867301	+	0.497783i	$0.165852\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	12.3916	−	7.15427i	0.392839	−	0.226806i
$996$		0			0
$997$	−14.5820	+	8.41890i	−0.461816	+	0.266629i	−0.712807	−	0.701360i	$-0.752577\pi$
$997$	−14.5820	+	8.41890i	−0.461816	+	0.266629i	0.250992	+	0.967989i	$0.419243\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5292.2.w.b.521.6		16
3.2	odd	2		1764.2.w.b.1109.7		16
7.2	even	3		756.2.bm.a.89.3		16
7.3	odd	6		5292.2.x.a.4409.3		16
7.4	even	3		5292.2.x.b.4409.6		16
7.5	odd	6		5292.2.bm.a.4625.6		16
7.6	odd	2		756.2.w.a.521.3		16
9.4	even	3		1764.2.bm.a.1697.5		16
9.5	odd	6		5292.2.bm.a.2285.6		16
21.2	odd	6		252.2.bm.a.173.4	yes	16
21.5	even	6		1764.2.bm.a.1685.5		16
21.11	odd	6		1764.2.x.b.1469.2		16
21.17	even	6		1764.2.x.a.1469.7		16
21.20	even	2		252.2.w.a.101.2	yes	16
28.23	odd	6		3024.2.df.d.1601.3		16
28.27	even	2		3024.2.ca.d.2033.3		16
63.2	odd	6		2268.2.t.a.2105.3		16
63.4	even	3		1764.2.x.a.293.7		16
63.5	even	6	inner	5292.2.w.b.1097.6		16
63.13	odd	6		252.2.bm.a.185.4	yes	16
63.16	even	3		2268.2.t.b.2105.6		16
63.20	even	6		2268.2.t.b.1781.6		16
63.23	odd	6		756.2.w.a.341.3		16
63.31	odd	6		1764.2.x.b.293.2		16
63.32	odd	6		5292.2.x.a.881.3		16
63.34	odd	6		2268.2.t.a.1781.3		16
63.40	odd	6		1764.2.w.b.509.7		16
63.41	even	6		756.2.bm.a.17.3		16
63.58	even	3		252.2.w.a.5.2	✓	16
63.59	even	6		5292.2.x.b.881.6		16
84.23	even	6		1008.2.df.d.929.5		16
84.83	odd	2		1008.2.ca.d.353.7		16
252.23	even	6		3024.2.ca.d.2609.3		16
252.139	even	6		1008.2.df.d.689.5		16
252.167	odd	6		3024.2.df.d.17.3		16
252.247	odd	6		1008.2.ca.d.257.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.2	✓	16	63.58	even	3
252.2.w.a.101.2	yes	16	21.20	even	2
252.2.bm.a.173.4	yes	16	21.2	odd	6
252.2.bm.a.185.4	yes	16	63.13	odd	6
756.2.w.a.341.3		16	63.23	odd	6
756.2.w.a.521.3		16	7.6	odd	2
756.2.bm.a.17.3		16	63.41	even	6
756.2.bm.a.89.3		16	7.2	even	3
1008.2.ca.d.257.7		16	252.247	odd	6
1008.2.ca.d.353.7		16	84.83	odd	2
1008.2.df.d.689.5		16	252.139	even	6
1008.2.df.d.929.5		16	84.23	even	6
1764.2.w.b.509.7		16	63.40	odd	6
1764.2.w.b.1109.7		16	3.2	odd	2
1764.2.x.a.293.7		16	63.4	even	3
1764.2.x.a.1469.7		16	21.17	even	6
1764.2.x.b.293.2		16	63.31	odd	6
1764.2.x.b.1469.2		16	21.11	odd	6
1764.2.bm.a.1685.5		16	21.5	even	6
1764.2.bm.a.1697.5		16	9.4	even	3
2268.2.t.a.1781.3		16	63.34	odd	6
2268.2.t.a.2105.3		16	63.2	odd	6
2268.2.t.b.1781.6		16	63.20	even	6
2268.2.t.b.2105.6		16	63.16	even	3
3024.2.ca.d.2033.3		16	28.27	even	2
3024.2.ca.d.2609.3		16	252.23	even	6
3024.2.df.d.17.3		16	252.167	odd	6
3024.2.df.d.1601.3		16	28.23	odd	6
5292.2.w.b.521.6		16	1.1	even	1	trivial
5292.2.w.b.1097.6		16	63.5	even	6	inner
5292.2.x.a.881.3		16	63.32	odd	6
5292.2.x.a.4409.3		16	7.3	odd	6
5292.2.x.b.881.6		16	63.59	even	6
5292.2.x.b.4409.6		16	7.4	even	3
5292.2.bm.a.2285.6		16	9.5	odd	6
5292.2.bm.a.4625.6		16	7.5	odd	6

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5292.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.09150 - 1.89054i) q^{5} +O(q^{10})\)	\(q+(1.09150 - 1.89054i) q^{5} +(1.26889 - 0.732592i) q^{11} +(-2.92752 + 1.69021i) q^{13} +(1.32136 - 2.28866i) q^{17} +(-6.87816 + 3.97111i) q^{19} +(3.47245 + 2.00482i) q^{23} +(0.117249 + 0.203081i) q^{25} +(6.71261 + 3.87553i) q^{29} -0.706968i q^{31} +(1.41738 + 2.45498i) q^{37} +(3.74173 + 6.48086i) q^{41} +(-1.27112 + 2.20164i) q^{43} -12.5508 q^{47} +(2.41675 + 1.39531i) q^{53} -3.19850i q^{55} +13.4330 q^{59} +7.79493i q^{61} +7.37945i q^{65} +5.84058 q^{67} -11.6854i q^{71} +(3.95924 + 2.28587i) q^{73} +9.38377 q^{79} +(1.70847 - 2.95917i) q^{83} +(-2.88452 - 4.99614i) q^{85} +(4.61937 + 8.00099i) q^{89} +17.3379i q^{95} +(-6.38394 - 3.68577i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 6 q^{11} + 3 q^{13} + 9 q^{17} - 21 q^{23} - 8 q^{25} - 6 q^{29} + q^{37} - 6 q^{41} - 2 q^{43} - 36 q^{47} - 30 q^{59} + 14 q^{67} + 2 q^{79} + 6 q^{85} + 21 q^{89} + 3 q^{97}+O(q^{100}) \) 16 * q + 6 * q^11 + 3 * q^13 + 9 * q^17 - 21 * q^23 - 8 * q^25 - 6 * q^29 + q^37 - 6 * q^41 - 2 * q^43 - 36 * q^47 - 30 * q^59 + 14 * q^67 + 2 * q^79 + 6 * q^85 + 21 * q^89 + 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more