LMFDB - Embedded newform 1728.3.o.g.1279.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1728,3,Mod(127,1728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1728, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1728.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1728 = 2^{6} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1728.o (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:	$47.0845896815$
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} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + \cdots + 65536 $ x^16 - 3x^15 + 7x^14 - 30x^13 + 76x^12 - 144x^11 + 424x^10 - 912x^9 + 1552x^8 - 3648x^7 + 6784x^6 - 9216x^5 + 19456x^4 - 30720x^3 + 28672x^2 - 49152*x + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1279.5
Root			$-1.26364 + 1.55023i$ of defining polynomial
Character	$\chi$	$=$	1728.1279
Dual form			1728.3.o.g.127.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35609 - 2.34881i) q^{5} +(-10.0431 + 5.79837i) q^{7} +O(q^{10})$	$q+(1.35609 - 2.34881i) q^{5} +(-10.0431 + 5.79837i) q^{7} +(8.54822 - 4.93532i) q^{11} +(-0.296185 + 0.513008i) q^{13} +8.87968 q^{17} -14.0989i q^{19} +(-18.2754 - 10.5513i) q^{23} +(8.82205 + 15.2802i) q^{25} +(10.1764 + 17.6260i) q^{29} +(-14.3357 - 8.27670i) q^{31} +31.4524i q^{35} +40.6557 q^{37} +(-21.2177 + 36.7502i) q^{41} +(-32.2385 + 18.6129i) q^{43} +(1.57134 - 0.907211i) q^{47} +(42.7423 - 74.0318i) q^{49} -21.1005 q^{53} -26.7709i q^{55} +(-76.6879 - 44.2758i) q^{59} +(-36.4925 - 63.2069i) q^{61} +(0.803307 + 1.39137i) q^{65} +(-38.3110 - 22.1189i) q^{67} +111.798i q^{71} -76.2003 q^{73} +(-57.2337 + 99.1316i) q^{77} +(8.30434 - 4.79451i) q^{79} +(-73.6244 + 42.5070i) q^{83} +(12.0416 - 20.8567i) q^{85} -64.7845 q^{89} -6.86958i q^{91} +(-33.1157 - 19.1193i) q^{95} +(-3.59139 - 6.22047i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{5}+O(q^{10}) $ 16 * q + 6 * q^5	$ 16 q + 6 q^{5} + 46 q^{13} - 12 q^{17} - 30 q^{25} + 42 q^{29} - 56 q^{37} - 84 q^{41} + 58 q^{49} - 72 q^{53} + 34 q^{61} + 30 q^{65} + 116 q^{73} - 330 q^{77} + 140 q^{85} + 384 q^{89} - 148 q^{97}+O(q^{100}) $ 16 * q + 6 * q^5 + 46 * q^13 - 12 * q^17 - 30 * q^25 + 42 * q^29 - 56 * q^37 - 84 * q^41 + 58 * q^49 - 72 * q^53 + 34 * q^61 + 30 * q^65 + 116 * q^73 - 330 * q^77 + 140 * q^85 + 384 * q^89 - 148 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

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
$5$	1.35609	−	2.34881i	0.271218	−	0.469763i	−0.697956	−	0.716140i	$-0.745907\pi$
$5$	1.35609	−	2.34881i	0.271218	−	0.469763i	0.969174	+	0.246378i	$0.0792403\pi$
$6$		0			0
$7$	−10.0431	+	5.79837i	−1.43473	+	0.828339i	−0.997476	−	0.0710013i	$-0.977381\pi$
$7$	−10.0431	+	5.79837i	−1.43473	+	0.828339i	−0.437249	+	0.899340i	$0.644047\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	8.54822	−	4.93532i	0.777111	−	0.448665i	−0.0582943	−	0.998299i	$-0.518566\pi$
$11$	8.54822	−	4.93532i	0.777111	−	0.448665i	0.835406	+	0.549634i	$0.185233\pi$
$12$		0			0
$13$	−0.296185	+	0.513008i	−0.0227835	+	0.0394622i	−0.877192	−	0.480139i	$-0.840586\pi$
$13$	−0.296185	+	0.513008i	−0.0227835	+	0.0394622i	0.854409	+	0.519601i	$0.173920\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	8.87968			0.522334			0.261167	−	0.965294i	$-0.415893\pi$
$17$	8.87968			0.522334			0.261167	+	0.965294i	$0.415893\pi$
$18$		0			0
$19$		−	14.0989i		−	0.742046i	−0.928624	−	0.371023i	$-0.879007\pi$
$19$		−	14.0989i		−	0.742046i	0.928624	−	0.371023i	$-0.120993\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−18.2754	−	10.5513i	−0.794583	−	0.458753i	0.0469902	−	0.998895i	$-0.485037\pi$
$23$	−18.2754	−	10.5513i	−0.794583	−	0.458753i	−0.841574	+	0.540142i	$0.818370\pi$
$24$		0			0
$25$	8.82205	+	15.2802i	0.352882	+	0.611209i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	10.1764	+	17.6260i	0.350910	+	0.607793i	0.986409	−	0.164308i	$-0.0525391\pi$
$29$	10.1764	+	17.6260i	0.350910	+	0.607793i	−0.635499	+	0.772101i	$0.719206\pi$
$30$		0			0
$31$	−14.3357	−	8.27670i	−0.462441	−	0.266990i	0.250629	−	0.968083i	$-0.419362\pi$
$31$	−14.3357	−	8.27670i	−0.462441	−	0.266990i	−0.713070	+	0.701093i	$0.752696\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			31.4524i			0.898641i
$36$		0			0
$37$	40.6557			1.09880			0.549401	−	0.835559i	$-0.314856\pi$
$37$	40.6557			1.09880			0.549401	+	0.835559i	$0.314856\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−21.2177	+	36.7502i	−0.517506	+	0.896346i	0.482288	+	0.876013i	$0.339806\pi$
$41$	−21.2177	+	36.7502i	−0.517506	+	0.896346i	−0.999793	+	0.0203330i	$0.993527\pi$
$42$		0			0
$43$	−32.2385	+	18.6129i	−0.749732	+	0.432858i	−0.825597	−	0.564260i	$-0.809162\pi$
$43$	−32.2385	+	18.6129i	−0.749732	+	0.432858i	0.0758649	+	0.997118i	$0.475828\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.57134	−	0.907211i	0.0334327	−	0.0193024i	−0.483191	−	0.875515i	$-0.660522\pi$
$47$	1.57134	−	0.907211i	0.0334327	−	0.0193024i	0.516623	+	0.856213i	$0.327189\pi$
$48$		0			0
$49$	42.7423	−	74.0318i	0.872291	−	1.51085i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−21.1005			−0.398122			−0.199061	−	0.979987i	$-0.563789\pi$
$53$	−21.1005			−0.398122			−0.199061	+	0.979987i	$0.563789\pi$
$54$		0			0
$55$		−	26.7709i		−	0.486744i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−76.6879	−	44.2758i	−1.29980	−	0.750437i	−0.319427	−	0.947611i	$-0.603490\pi$
$59$	−76.6879	−	44.2758i	−1.29980	−	0.750437i	−0.980369	+	0.197174i	$0.936824\pi$
$60$		0			0
$61$	−36.4925	−	63.2069i	−0.598238	−	1.03618i	−0.993081	−	0.117431i	$-0.962534\pi$
$61$	−36.4925	−	63.2069i	−0.598238	−	1.03618i	0.394843	−	0.918749i	$-0.370799\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.803307	+	1.39137i	0.0123586	+	0.0214057i
$66$		0			0
$67$	−38.3110	−	22.1189i	−0.571807	−	0.330133i	0.186064	−	0.982538i	$-0.440427\pi$
$67$	−38.3110	−	22.1189i	−0.571807	−	0.330133i	−0.757871	+	0.652405i	$0.773760\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			111.798i			1.57462i	0.616557	+	0.787310i	$0.288527\pi$
$71$			111.798i			1.57462i	−0.616557	+	0.787310i	$0.711473\pi$
$72$		0			0
$73$	−76.2003			−1.04384			−0.521920	−	0.852995i	$-0.674784\pi$
$73$	−76.2003			−1.04384			−0.521920	+	0.852995i	$0.674784\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−57.2337	+	99.1316i	−0.743294	+	1.28742i
$78$		0			0
$79$	8.30434	−	4.79451i	0.105118	−	0.0606901i	−0.446519	−	0.894774i	$-0.647337\pi$
$79$	8.30434	−	4.79451i	0.105118	−	0.0606901i	0.551637	+	0.834084i	$0.314003\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−73.6244	+	42.5070i	−0.887041	+	0.512133i	−0.872973	−	0.487768i	$-0.837811\pi$
$83$	−73.6244	+	42.5070i	−0.887041	+	0.512133i	−0.0140672	+	0.999901i	$0.504478\pi$
$84$		0			0
$85$	12.0416	−	20.8567i	0.141666	−	0.245373i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−64.7845			−0.727916			−0.363958	−	0.931415i	$-0.618575\pi$
$89$	−64.7845			−0.727916			−0.363958	+	0.931415i	$0.618575\pi$
$90$		0			0
$91$		−	6.86958i		−	0.0754898i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−33.1157	−	19.1193i	−0.348586	−	0.201256i
$96$		0			0
$97$	−3.59139	−	6.22047i	−0.0370246	−	0.0641285i	0.846919	−	0.531721i	$-0.178455\pi$
$97$	−3.59139	−	6.22047i	−0.0370246	−	0.0641285i	−0.883944	+	0.467593i	$0.845121\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−55.5037	−	96.1353i	−0.549542	−	0.951834i	−0.998306	−	0.0581840i	$-0.981469\pi$
$101$	−55.5037	−	96.1353i	−0.549542	−	0.951834i	0.448764	−	0.893650i	$-0.351864\pi$
$102$		0			0
$103$	−79.6133	−	45.9648i	−0.772945	−	0.446260i	0.0609793	−	0.998139i	$-0.480578\pi$
$103$	−79.6133	−	45.9648i	−0.772945	−	0.446260i	−0.833924	+	0.551879i	$0.813911\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			107.741i			1.00693i	0.864016	+	0.503465i	$0.167942\pi$
$107$			107.741i			1.00693i	−0.864016	+	0.503465i	$0.832058\pi$
$108$		0			0
$109$	−86.5562			−0.794093			−0.397047	−	0.917798i	$-0.629965\pi$
$109$	−86.5562			−0.794093			−0.397047	+	0.917798i	$0.629965\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.35198	−	4.07376i	0.0208140	−	0.0360509i	−0.855431	−	0.517917i	$-0.826708\pi$
$113$	2.35198	−	4.07376i	0.0208140	−	0.0360509i	0.876245	+	0.481866i	$0.160041\pi$
$114$		0			0
$115$	−49.5662	+	28.6170i	−0.431010	+	0.248844i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−89.1793	+	51.4877i	−0.749406	+	0.432670i
$120$		0			0
$121$	−11.7852	+	20.4126i	−0.0973987	+	0.168700i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	115.658			0.925267
$126$		0			0
$127$			8.37118i			0.0659148i	0.999457	+	0.0329574i	$0.0104926\pi$
$127$			8.37118i			0.0659148i	−0.999457	+	0.0329574i	$0.989507\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	115.067	+	66.4338i	0.878372	+	0.507129i	0.870121	−	0.492837i	$-0.164040\pi$
$131$	115.067	+	66.4338i	0.878372	+	0.507129i	0.00825098	+	0.999966i	$0.497374\pi$
$132$		0			0
$133$	81.7506	+	141.596i	0.614666	+	1.06463i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−22.5579	−	39.0715i	−0.164656	−	0.285193i	0.771877	−	0.635772i	$-0.219318\pi$
$137$	−22.5579	−	39.0715i	−0.164656	−	0.285193i	−0.936533	+	0.350579i	$0.885985\pi$
$138$		0			0
$139$	−130.744	−	75.4848i	−0.940601	−	0.543056i	−0.0504522	−	0.998726i	$-0.516066\pi$
$139$	−130.744	−	75.4848i	−0.940601	−	0.543056i	−0.890149	+	0.455670i	$0.849400\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			5.84708i			0.0408887i
$144$		0			0
$145$	55.2003			0.380692
$146$		0			0
$147$		0			0
$148$		0			0
$149$	71.3914	−	123.653i	0.479137	−	0.829889i	−0.520577	−	0.853815i	$-0.674283\pi$
$149$	71.3914	−	123.653i	0.479137	−	0.829889i	0.999714	+	0.0239255i	$0.00761646\pi$
$150$		0			0
$151$	−220.027	+	127.033i	−1.45713	+	0.841276i	−0.998869	−	0.0475407i	$-0.984862\pi$
$151$	−220.027	+	127.033i	−1.45713	+	0.841276i	−0.458263	+	0.888817i	$0.651528\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−38.8808	+	22.4479i	−0.250844	+	0.144825i
$156$		0			0
$157$	−2.65361	+	4.59618i	−0.0169020	+	0.0292751i	−0.874353	−	0.485291i	$-0.838714\pi$
$157$	−2.65361	+	4.59618i	−0.0169020	+	0.0292751i	0.857451	+	0.514566i	$0.172047\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	244.722			1.52001
$162$		0			0
$163$		−	59.5534i		−	0.365359i	−0.983173	−	0.182679i	$-0.941523\pi$
$163$		−	59.5534i		−	0.365359i	0.983173	−	0.182679i	$-0.0584770\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−85.7434	−	49.5040i	−0.513434	−	0.296431i	0.220810	−	0.975317i	$-0.429130\pi$
$167$	−85.7434	−	49.5040i	−0.513434	−	0.296431i	−0.734244	+	0.678886i	$0.762463\pi$
$168$		0			0
$169$	84.3245	+	146.054i	0.498962	+	0.864227i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	19.2965	+	33.4225i	0.111540	+	0.193193i	0.916391	−	0.400283i	$-0.131088\pi$
$173$	19.2965	+	33.4225i	0.111540	+	0.193193i	−0.804851	+	0.593477i	$0.797755\pi$
$174$		0			0
$175$	−177.201	−	102.307i	−1.01258	−	0.584612i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			36.4264i			0.203499i	0.994810	+	0.101750i	$0.0324441\pi$
$179$			36.4264i			0.203499i	−0.994810	+	0.101750i	$0.967556\pi$
$180$		0			0
$181$	18.5921			0.102719			0.0513594	−	0.998680i	$-0.483645\pi$
$181$	18.5921			0.102719			0.0513594	+	0.998680i	$0.483645\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	55.1327	−	95.4927i	0.298015	−	0.516177i
$186$		0			0
$187$	75.9055	−	43.8240i	0.405912	−	0.234353i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−244.973	+	141.435i	−1.28258	+	0.740497i	−0.977319	−	0.211772i	$-0.932077\pi$
$191$	−244.973	+	141.435i	−1.28258	+	0.740497i	−0.305260	+	0.952269i	$0.598743\pi$
$192$		0			0
$193$	−151.542	+	262.479i	−0.785193	+	1.35999i	0.143691	+	0.989623i	$0.454103\pi$
$193$	−151.542	+	262.479i	−0.785193	+	1.35999i	−0.928884	+	0.370372i	$0.879230\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	139.184			0.706520			0.353260	−	0.935525i	$-0.385073\pi$
$197$	139.184			0.706520			0.353260	+	0.935525i	$0.385073\pi$
$198$		0			0
$199$			11.2337i			0.0564505i	0.999602	+	0.0282253i	$0.00898558\pi$
$199$			11.2337i			0.0564505i	−0.999602	+	0.0282253i	$0.991014\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−204.404	−	118.013i	−1.00692	−	0.581344i
$204$		0			0
$205$	57.5462	+	99.6730i	0.280713	+	0.486210i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−69.5825	−	120.520i	−0.332931	−	0.576653i
$210$		0			0
$211$	−112.017	−	64.6728i	−0.530884	−	0.306506i	0.210492	−	0.977595i	$-0.432493\pi$
$211$	−112.017	−	64.6728i	−0.530884	−	0.306506i	−0.741376	+	0.671090i	$0.765827\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			100.963i			0.469595i
$216$		0			0
$217$	191.966			0.884634
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.63003	+	4.55535i	−0.0119006	+	0.0206124i
$222$		0			0
$223$	209.210	−	120.787i	0.938159	−	0.541647i	0.0487765	−	0.998810i	$-0.484468\pi$
$223$	209.210	−	120.787i	0.938159	−	0.541647i	0.889383	+	0.457163i	$0.151134\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−330.710	+	190.936i	−1.45687	+	0.841126i	−0.998856	−	0.0478181i	$-0.984773\pi$
$227$	−330.710	+	190.936i	−1.45687	+	0.841126i	−0.458016	+	0.888944i	$0.651440\pi$
$228$		0			0
$229$	−74.6642	+	129.322i	−0.326044	+	0.564725i	−0.981723	−	0.190315i	$-0.939049\pi$
$229$	−74.6642	+	129.322i	−0.326044	+	0.564725i	0.655679	+	0.755040i	$0.272383\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	218.934			0.939631			0.469816	−	0.882765i	$-0.344320\pi$
$233$	218.934			0.939631			0.469816	+	0.882765i	$0.344320\pi$
$234$		0			0
$235$		−	4.92103i		−	0.0209406i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	218.254	+	126.009i	0.913197	+	0.527235i	0.881458	−	0.472262i	$-0.156562\pi$
$239$	218.254	+	126.009i	0.913197	+	0.527235i	0.0317388	+	0.999496i	$0.489896\pi$
$240$		0			0
$241$	−226.014	−	391.467i	−0.937816	−	1.62435i	−0.769534	−	0.638606i	$-0.779511\pi$
$241$	−226.014	−	391.467i	−0.937816	−	1.62435i	−0.168282	−	0.985739i	$-0.553822\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−115.925	−	200.787i	−0.473162	−	0.819540i
$246$		0			0
$247$	7.23284	+	4.17588i	0.0292828	+	0.0169064i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	139.429i		−	0.555492i	−0.960655	−	0.277746i	$-0.910413\pi$
$251$		−	139.429i		−	0.555492i	0.960655	−	0.277746i	$-0.0895874\pi$
$252$		0			0
$253$	−208.297			−0.823306
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−235.308	+	407.565i	−0.915594	+	1.58586i	−0.109564	+	0.993980i	$0.534946\pi$
$257$	−235.308	+	407.565i	−0.915594	+	1.58586i	−0.806029	+	0.591875i	$0.798388\pi$
$258$		0			0
$259$	−408.308	+	235.737i	−1.57648	+	0.910181i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	22.2028	−	12.8188i	0.0844214	−	0.0487407i	−0.457195	−	0.889366i	$-0.651146\pi$
$263$	22.2028	−	12.8188i	0.0844214	−	0.0487407i	0.541616	+	0.840626i	$0.317813\pi$
$264$		0			0
$265$	−28.6141	+	49.5610i	−0.107978	+	0.187023i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	8.15075			0.0303002			0.0151501	−	0.999885i	$-0.495177\pi$
$269$	8.15075			0.0303002			0.0151501	+	0.999885i	$0.495177\pi$
$270$		0			0
$271$		−	401.979i		−	1.48332i	−0.670777	−	0.741659i	$-0.734039\pi$
$271$		−	401.979i		−	1.48332i	0.670777	−	0.741659i	$-0.265961\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	150.826	+	87.0792i	0.548457	+	0.316652i
$276$		0			0
$277$	−56.2021	−	97.3449i	−0.202896	−	0.351426i	0.746565	−	0.665313i	$-0.231702\pi$
$277$	−56.2021	−	97.3449i	−0.202896	−	0.351426i	−0.949460	+	0.313887i	$0.898369\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−268.867	−	465.692i	−0.956823	−	1.65727i	−0.730141	−	0.683296i	$-0.760546\pi$
$281$	−268.867	−	465.692i	−0.956823	−	1.65727i	−0.226681	−	0.973969i	$-0.572788\pi$
$282$		0			0
$283$	−122.303	−	70.6114i	−0.432164	−	0.249510i	0.268104	−	0.963390i	$-0.413603\pi$
$283$	−122.303	−	70.6114i	−0.432164	−	0.249510i	−0.700268	+	0.713880i	$0.746936\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	492.113i		−	1.71468i
$288$		0			0
$289$	−210.151			−0.727167
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−230.291	+	398.875i	−0.785975	+	1.36135i	0.142440	+	0.989803i	$0.454505\pi$
$293$	−230.291	+	398.875i	−0.785975	+	1.36135i	−0.928415	+	0.371545i	$0.878828\pi$
$294$		0			0
$295$	−207.991	+	120.084i	−0.705055	+	0.407064i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	10.8258	−	6.25029i	0.0362068	−	0.0209040i
$300$		0			0
$301$	215.849	−	373.862i	0.717107	−	1.24206i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−197.948			−0.649011
$306$		0			0
$307$			210.322i			0.685089i	0.939502	+	0.342545i	$0.111289\pi$
$307$			210.322i			0.685089i	−0.939502	+	0.342545i	$0.888711\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	110.993	+	64.0821i	0.356892	+	0.206052i	0.667717	−	0.744416i	$-0.267272\pi$
$311$	110.993	+	64.0821i	0.356892	+	0.206052i	−0.310824	+	0.950467i	$0.600605\pi$
$312$		0			0
$313$	−3.62140	−	6.27245i	−0.0115700	−	0.0200398i	0.860182	−	0.509986i	$-0.170350\pi$
$313$	−3.62140	−	6.27245i	−0.0115700	−	0.0200398i	−0.871752	+	0.489947i	$0.837016\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−120.145	−	208.098i	−0.379007	−	0.656460i	0.611911	−	0.790927i	$-0.290401\pi$
$317$	−120.145	−	208.098i	−0.379007	−	0.656460i	−0.990918	+	0.134467i	$0.957068\pi$
$318$		0			0
$319$	173.980	+	100.447i	0.545392	+	0.314882i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	125.194i		−	0.387596i
$324$		0			0
$325$	−10.4518			−0.0321595
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−10.5207	+	18.2224i	−0.0319778	+	0.0553872i
$330$		0			0
$331$	370.385	−	213.842i	1.11899	−	0.646048i	0.177845	−	0.984058i	$-0.443087\pi$
$331$	370.385	−	213.842i	1.11899	−	0.646048i	0.941142	+	0.338011i	$0.109754\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−103.906	+	59.9904i	−0.310168	+	0.179076i
$336$		0			0
$337$	152.442	−	264.037i	0.452349	−	0.783492i	−0.546182	−	0.837666i	$-0.683919\pi$
$337$	152.442	−	264.037i	0.452349	−	0.783492i	0.998531	+	0.0541746i	$0.0172528\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−163.393			−0.479157
$342$		0			0
$343$			423.102i			1.23353i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	146.406	+	84.5276i	0.421919	+	0.243595i	0.695898	−	0.718140i	$-0.255006\pi$
$347$	146.406	+	84.5276i	0.421919	+	0.243595i	−0.273979	+	0.961736i	$0.588340\pi$
$348$		0			0
$349$	−107.298	−	185.846i	−0.307444	−	0.532509i	0.670358	−	0.742037i	$-0.266140\pi$
$349$	−107.298	−	185.846i	−0.307444	−	0.532509i	−0.977802	+	0.209529i	$0.932807\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	275.895	+	477.865i	0.781574	+	1.35373i	0.931025	+	0.364956i	$0.118916\pi$
$353$	275.895	+	477.865i	0.781574	+	1.35373i	−0.149451	+	0.988769i	$0.547751\pi$
$354$		0			0
$355$	262.593	+	151.608i	0.739698	+	0.427065i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			554.828i			1.54548i	0.634721	+	0.772741i	$0.281115\pi$
$359$			554.828i			1.54548i	−0.634721	+	0.772741i	$0.718885\pi$
$360$		0			0
$361$	162.222			0.449367
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−103.334	+	178.980i	−0.283108	+	0.490357i
$366$		0			0
$367$	−145.642	+	84.0864i	−0.396845	+	0.229118i	−0.685122	−	0.728429i	$-0.740251\pi$
$367$	−145.642	+	84.0864i	−0.396845	+	0.229118i	0.288277	+	0.957547i	$0.406918\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	211.913	−	122.348i	0.571195	−	0.329780i
$372$		0			0
$373$	−171.699	+	297.391i	−0.460318	+	0.797295i	−0.998977	−	0.0452296i	$-0.985598\pi$
$373$	−171.699	+	297.391i	−0.460318	+	0.797295i	0.538658	+	0.842524i	$0.318931\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−12.0564			−0.0319798
$378$		0			0
$379$		−	602.392i		−	1.58943i	−0.606986	−	0.794713i	$-0.707621\pi$
$379$		−	602.392i		−	1.58943i	0.606986	−	0.794713i	$-0.292379\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−315.762	−	182.305i	−0.824443	−	0.475992i	0.0275035	−	0.999622i	$-0.491244\pi$
$383$	−315.762	−	182.305i	−0.824443	−	0.475992i	−0.851946	+	0.523630i	$0.824578\pi$
$384$		0			0
$385$	155.228	+	268.862i	0.403189	+	0.698344i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	107.326	+	185.893i	0.275901	+	0.477875i	0.970362	−	0.241656i	$-0.0776904\pi$
$389$	107.326	+	185.893i	0.275901	+	0.477875i	−0.694461	+	0.719530i	$0.744357\pi$
$390$		0			0
$391$	−162.280	−	93.6923i	−0.415038	−	0.239622i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	26.0071i		−	0.0658409i
$396$		0			0
$397$	684.628			1.72450			0.862251	−	0.506480i	$-0.169054\pi$
$397$	684.628			1.72450			0.862251	+	0.506480i	$0.169054\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−95.1918	+	164.877i	−0.237386	+	0.411164i	−0.959963	−	0.280125i	$-0.909624\pi$
$401$	−95.1918	+	164.877i	−0.237386	+	0.411164i	0.722577	+	0.691290i	$0.242957\pi$
$402$		0			0
$403$	8.49203	−	4.90287i	0.0210720	−	0.0121659i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	347.534	−	200.649i	0.853892	−	0.492995i
$408$		0			0
$409$	188.978	−	327.320i	0.462049	−	0.800293i	−0.537014	−	0.843574i	$-0.680448\pi$
$409$	188.978	−	327.320i	0.462049	−	0.800293i	0.999063	+	0.0432806i	$0.0137809\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1026.91			2.48647
$414$		0			0
$415$			230.573i			0.555598i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	267.326	+	154.341i	0.638009	+	0.368355i	0.783847	−	0.620954i	$-0.213255\pi$
$419$	267.326	+	154.341i	0.638009	+	0.368355i	−0.145838	+	0.989308i	$0.546588\pi$
$420$		0			0
$421$	−176.834	−	306.286i	−0.420034	−	0.727521i	0.575908	−	0.817514i	$-0.304649\pi$
$421$	−176.834	−	306.286i	−0.420034	−	0.727521i	−0.995942	+	0.0899938i	$0.971315\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	78.3369	+	135.684i	0.184322	+	0.319255i
$426$		0			0
$427$	732.995	+	423.195i	1.71662	+	0.991088i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	472.777i		−	1.09693i	−0.836174	−	0.548465i	$-0.815213\pi$
$431$		−	472.777i		−	1.09693i	0.836174	−	0.548465i	$-0.184787\pi$
$432$		0			0
$433$	61.4188			0.141845			0.0709224	−	0.997482i	$-0.477406\pi$
$433$	61.4188			0.141845			0.0709224	+	0.997482i	$0.477406\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−148.762	+	257.663i	−0.340416	+	0.589618i
$438$		0			0
$439$	354.347	−	204.582i	0.807169	−	0.466019i	−0.0388030	−	0.999247i	$-0.512354\pi$
$439$	354.347	−	204.582i	0.807169	−	0.466019i	0.845972	+	0.533228i	$0.179021\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	668.806	−	386.136i	1.50972	−	0.871638i	0.509785	−	0.860302i	$-0.329725\pi$
$443$	668.806	−	386.136i	1.50972	−	0.871638i	0.999936	−	0.0113360i	$-0.00360844\pi$
$444$		0			0
$445$	−87.8536	+	152.167i	−0.197424	+	0.341948i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	789.037			1.75732			0.878660	−	0.477448i	$-0.158438\pi$
$449$	789.037			1.75732			0.878660	+	0.477448i	$0.158438\pi$
$450$		0			0
$451$			418.865i			0.928747i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−16.1354	−	9.31575i	−0.0354623	−	0.0204742i
$456$		0			0
$457$	138.165	+	239.309i	0.302331	+	0.523653i	0.976664	−	0.214775i	$-0.0689018\pi$
$457$	138.165	+	239.309i	0.302331	+	0.523653i	−0.674332	+	0.738428i	$0.735568\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−294.041	−	509.295i	−0.637834	−	1.10476i	−0.985907	−	0.167293i	$-0.946497\pi$
$461$	−294.041	−	509.295i	−0.637834	−	1.10476i	0.348073	−	0.937467i	$-0.386836\pi$
$462$		0			0
$463$	677.285	+	391.031i	1.46282	+	0.844558i	0.999141	−	0.0414459i	$-0.0131964\pi$
$463$	677.285	+	391.031i	1.46282	+	0.844558i	0.463677	+	0.886004i	$0.346530\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			663.203i			1.42014i	0.704133	+	0.710068i	$0.251336\pi$
$467$			663.203i			1.42014i	−0.704133	+	0.710068i	$0.748664\pi$
$468$		0			0
$469$	513.014			1.09385
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−183.721	+	318.214i	−0.388417	+	0.672758i
$474$		0			0
$475$	215.434	−	124.381i	0.453546	−	0.261855i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	562.018	−	324.481i	1.17331	−	0.677414i	0.218856	−	0.975757i	$-0.429767\pi$
$479$	562.018	−	324.481i	1.17331	−	0.677414i	0.954459	+	0.298344i	$0.0964341\pi$
$480$		0			0
$481$	−12.0416	+	20.8567i	−0.0250346	+	0.0433611i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−19.4810			−0.0401669
$486$		0			0
$487$		−	282.104i		−	0.579269i	−0.957137	−	0.289635i	$-0.906466\pi$
$487$		−	282.104i		−	0.579269i	0.957137	−	0.289635i	$-0.0935338\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−652.933	−	376.971i	−1.32980	−	0.767762i	−0.344534	−	0.938774i	$-0.611963\pi$
$491$	−652.933	−	376.971i	−1.32980	−	0.767762i	−0.985269	+	0.171012i	$0.945296\pi$
$492$		0			0
$493$	90.3630	+	156.513i	0.183292	+	0.317471i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−648.247	−	1122.80i	−1.30432	−	2.25915i
$498$		0			0
$499$	−446.169	−	257.596i	−0.894126	−	0.516224i	−0.0188362	−	0.999823i	$-0.505996\pi$
$499$	−446.169	−	257.596i	−0.894126	−	0.516224i	−0.875290	+	0.483599i	$0.839329\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			523.660i			1.04107i	0.853839	+	0.520537i	$0.174268\pi$
$503$			523.660i			1.04107i	−0.853839	+	0.520537i	$0.825732\pi$
$504$		0			0
$505$	−301.072			−0.596182
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−267.685	+	463.645i	−0.525905	+	0.910893i	0.473640	+	0.880719i	$0.342940\pi$
$509$	−267.685	+	463.645i	−0.525905	+	0.910893i	−0.999545	+	0.0301749i	$0.990394\pi$
$510$		0			0
$511$	765.285	−	441.838i	1.49762	−	0.864653i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−215.925	+	124.665i	−0.419273	+	0.242067i
$516$		0			0
$517$	8.95475	−	15.5101i	0.0173206	−	0.0300002i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−177.268			−0.340246			−0.170123	−	0.985423i	$-0.554416\pi$
$521$	−177.268			−0.340246			−0.170123	+	0.985423i	$0.554416\pi$
$522$		0			0
$523$			444.206i			0.849343i	0.905347	+	0.424672i	$0.139610\pi$
$523$			444.206i			0.849343i	−0.905347	+	0.424672i	$0.860390\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−127.296	−	73.4944i	−0.241548	−	0.139458i
$528$		0			0
$529$	−41.8394	−	72.4679i	−0.0790914	−	0.136990i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−12.5688	−	21.7697i	−0.0235812	−	0.0408438i
$534$		0			0
$535$	253.065	+	146.107i	0.473018	+	0.273097i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	843.787i		−	1.56547i
$540$		0			0
$541$	−571.163			−1.05575			−0.527877	−	0.849321i	$-0.677012\pi$
$541$	−571.163			−1.05575			−0.527877	+	0.849321i	$0.677012\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−117.378	+	203.304i	−0.215372	+	0.373036i
$546$		0			0
$547$	139.875	−	80.7569i	0.255713	−	0.147636i	−0.366664	−	0.930353i	$-0.619500\pi$
$547$	139.875	−	80.7569i	0.255713	−	0.147636i	0.622377	+	0.782717i	$0.286167\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	248.507	−	143.476i	0.451011	−	0.260391i
$552$		0			0
$553$	−55.6008	+	96.3034i	−0.100544	+	0.174147i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−568.917			−1.02139			−0.510697	−	0.859761i	$-0.670613\pi$
$557$	−568.917			−1.02139			−0.510697	+	0.859761i	$0.670613\pi$
$558$		0			0
$559$		−	22.0515i		−	0.0394481i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−250.527	−	144.642i	−0.444985	−	0.256912i	0.260725	−	0.965413i	$-0.416038\pi$
$563$	−250.527	−	144.642i	−0.444985	−	0.256912i	−0.705710	+	0.708501i	$0.749372\pi$
$564$		0			0
$565$	−6.37900	−	11.0487i	−0.0112903	−	0.0195553i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	223.117	+	386.450i	0.392121	+	0.679174i	0.992729	−	0.120370i	$-0.0384079\pi$
$569$	223.117	+	386.450i	0.392121	+	0.679174i	−0.600608	+	0.799544i	$0.705075\pi$
$570$		0			0
$571$	372.386	+	214.997i	0.652164	+	0.376527i	0.789285	−	0.614027i	$-0.210451\pi$
$571$	372.386	+	214.997i	0.652164	+	0.376527i	−0.137121	+	0.990554i	$0.543785\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	372.337i		−	0.647542i
$576$		0			0
$577$	50.9694			0.0883353			0.0441676	−	0.999024i	$-0.485936\pi$
$577$	50.9694			0.0883353			0.0441676	+	0.999024i	$0.485936\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	492.943	−	853.803i	0.848440	−	1.46954i
$582$		0			0
$583$	−180.371	+	104.137i	−0.309385	+	0.178623i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	643.771	−	371.681i	1.09671	−	0.633188i	0.161358	−	0.986896i	$-0.448413\pi$
$587$	643.771	−	371.681i	1.09671	−	0.633188i	0.935356	+	0.353708i	$0.115079\pi$
$588$		0			0
$589$	−116.692	+	202.117i	−0.198119	+	0.343152i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	382.547			0.645104			0.322552	−	0.946552i	$-0.395459\pi$
$593$	382.547			0.645104			0.322552	+	0.946552i	$0.395459\pi$
$594$		0			0
$595$			279.287i			0.469391i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	856.248	+	494.355i	1.42946	+	0.825301i	0.997078	−	0.0763888i	$-0.0243390\pi$
$599$	856.248	+	494.355i	1.42946	+	0.825301i	0.432384	+	0.901689i	$0.357672\pi$
$600$		0			0
$601$	−263.280	−	456.015i	−0.438070	−	0.758760i	0.559470	−	0.828850i	$-0.311005\pi$
$601$	−263.280	−	456.015i	−0.438070	−	0.758760i	−0.997541	+	0.0700905i	$0.977671\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	31.9637	+	55.3627i	0.0528325	+	0.0915086i
$606$		0			0
$607$	−447.631	−	258.440i	−0.737448	−	0.425766i	0.0836928	−	0.996492i	$-0.473329\pi$
$607$	−447.631	−	258.440i	−0.737448	−	0.425766i	−0.821141	+	0.570726i	$0.806662\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			1.07481i			0.00175910i
$612$		0			0
$613$	−762.957			−1.24463			−0.622314	−	0.782768i	$-0.713807\pi$
$613$	−762.957			−1.24463			−0.622314	+	0.782768i	$0.713807\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−60.9168	+	105.511i	−0.0987307	+	0.171007i	−0.911160	−	0.412054i	$-0.864812\pi$
$617$	−60.9168	+	105.511i	−0.0987307	+	0.171007i	0.812429	+	0.583060i	$0.198145\pi$
$618$		0			0
$619$	265.675	−	153.388i	0.429200	−	0.247799i	−0.269806	−	0.962915i	$-0.586959\pi$
$619$	265.675	−	153.388i	0.429200	−	0.247799i	0.699006	+	0.715116i	$0.253626\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	650.636	−	375.645i	1.04436	−	0.602961i
$624$		0			0
$625$	−63.7082	+	110.346i	−0.101933	+	0.176553i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	361.010			0.573942
$630$		0			0
$631$			1071.11i			1.69749i	0.528805	+	0.848744i	$0.322640\pi$
$631$			1071.11i			1.69749i	−0.528805	+	0.848744i	$0.677360\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	19.6623	+	11.3521i	0.0309643	+	0.0178773i
$636$		0			0
$637$	25.3193	+	43.8543i	0.0397477	+	0.0688450i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−527.259	−	913.240i	−0.822557	−	1.42471i	−0.903772	−	0.428015i	$-0.859213\pi$
$641$	−527.259	−	913.240i	−0.822557	−	1.42471i	0.0812143	−	0.996697i	$-0.474120\pi$
$642$		0			0
$643$	−42.0680	−	24.2880i	−0.0654246	−	0.0377729i	0.466931	−	0.884294i	$-0.345360\pi$
$643$	−42.0680	−	24.2880i	−0.0654246	−	0.0377729i	−0.532355	+	0.846521i	$0.678693\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	539.373i		−	0.833653i	−0.908986	−	0.416826i	$-0.863142\pi$
$647$		−	539.373i		−	0.833653i	0.908986	−	0.416826i	$-0.136858\pi$
$648$		0			0
$649$	−874.061			−1.34678
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−276.457	+	478.838i	−0.423365	+	0.733290i	−0.996266	−	0.0863348i	$-0.972485\pi$
$653$	−276.457	+	478.838i	−0.423365	+	0.733290i	0.572901	+	0.819624i	$0.305818\pi$
$654$		0			0
$655$	312.081	−	180.180i	0.476460	−	0.275084i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	734.162	−	423.869i	1.11406	−	0.643200i	0.174178	−	0.984714i	$-0.444273\pi$
$659$	734.162	−	423.869i	1.11406	−	0.643200i	0.939877	+	0.341514i	$0.110940\pi$
$660$		0			0
$661$	359.447	−	622.580i	0.543792	−	0.941876i	−0.454890	−	0.890548i	$-0.650321\pi$
$661$	359.447	−	622.580i	0.543792	−	0.941876i	0.998682	−	0.0513280i	$-0.0163454\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	443.444			0.666833
$666$		0			0
$667$		−	429.497i		−	0.643923i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−623.893	−	360.205i	−0.929796	−	0.536818i
$672$		0			0
$673$	288.488	+	499.675i	0.428659	+	0.742460i	0.996754	−	0.0805033i	$-0.0256528\pi$
$673$	288.488	+	499.675i	0.428659	+	0.742460i	−0.568095	+	0.822963i	$0.692319\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−101.021	−	174.974i	−0.149219	−	0.258454i	0.781720	−	0.623629i	$-0.214343\pi$
$677$	−101.021	−	174.974i	−0.149219	−	0.258454i	−0.930939	+	0.365175i	$0.881009\pi$
$678$		0			0
$679$	72.1372	+	41.6484i	0.106240	+	0.0613379i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	568.249i		−	0.831990i	−0.909367	−	0.415995i	$-0.863433\pi$
$683$		−	568.249i		−	0.831990i	0.909367	−	0.415995i	$-0.136567\pi$
$684$		0			0
$685$	−122.362			−0.178631
$686$		0			0
$687$		0			0
$688$		0			0
$689$	6.24965	−	10.8247i	0.00907060	−	0.0157107i
$690$		0			0
$691$	−351.376	+	202.867i	−0.508504	+	0.293585i	−0.732218	−	0.681070i	$-0.761515\pi$
$691$	−351.376	+	202.867i	−0.508504	+	0.293585i	0.223714	+	0.974655i	$0.428182\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−354.600	+	204.728i	−0.510215	+	0.294573i
$696$		0			0
$697$	−188.407	+	326.330i	−0.270311	+	0.468192i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	83.5164			0.119139			0.0595695	−	0.998224i	$-0.481027\pi$
$701$	83.5164			0.119139			0.0595695	+	0.998224i	$0.481027\pi$
$702$		0			0
$703$		−	573.200i		−	0.815363i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1114.86	+	643.663i	1.57688	+	0.910414i
$708$		0			0
$709$	173.908	+	301.217i	0.245286	+	0.424848i	0.962212	−	0.272302i	$-0.0877849\pi$
$709$	173.908	+	301.217i	0.245286	+	0.424848i	−0.716926	+	0.697149i	$0.754452\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	174.660	+	302.520i	0.244965	+	0.424292i
$714$		0			0
$715$	13.7337	+	7.92916i	0.0192080	+	0.0110897i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	536.277i		−	0.745865i	−0.927858	−	0.372933i	$-0.878352\pi$
$719$		−	536.277i		−	0.745865i	0.927858	−	0.372933i	$-0.121648\pi$
$720$		0			0
$721$	1066.08			1.47862
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−179.553	+	310.995i	−0.247659	+	0.428959i
$726$		0			0
$727$	−815.055	+	470.573i	−1.12112	+	0.647280i	−0.941687	−	0.336490i	$-0.890760\pi$
$727$	−815.055	+	470.573i	−1.12112	+	0.647280i	−0.179435	+	0.983770i	$0.557427\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−286.267	+	165.277i	−0.391611	+	0.226096i
$732$		0			0
$733$	−311.063	+	538.777i	−0.424370	+	0.735030i	−0.996361	−	0.0852294i	$-0.972838\pi$
$733$	−311.063	+	538.777i	−0.424370	+	0.735030i	0.571991	+	0.820260i	$0.306171\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−436.655			−0.592477
$738$		0			0
$739$			444.439i			0.601406i	0.953718	+	0.300703i	$0.0972213\pi$
$739$			444.439i			0.601406i	−0.953718	+	0.300703i	$0.902779\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−66.2270	−	38.2362i	−0.0891346	−	0.0514619i	0.454770	−	0.890609i	$-0.349721\pi$
$743$	−66.2270	−	38.2362i	−0.0891346	−	0.0514619i	−0.543905	+	0.839147i	$0.683055\pi$
$744$		0			0
$745$	−193.626	−	335.370i	−0.259901	−	0.450161i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−624.725	−	1082.06i	−0.834079	−	1.44467i
$750$		0			0
$751$	949.025	+	547.920i	1.26368	+	0.729587i	0.973785	−	0.227471i	$-0.0730457\pi$
$751$	949.025	+	547.920i	1.26368	+	0.729587i	0.289897	+	0.957058i	$0.406379\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			689.070i			0.912676i
$756$		0			0
$757$	346.346			0.457525			0.228762	−	0.973482i	$-0.426532\pi$
$757$	346.346			0.457525			0.228762	+	0.973482i	$0.426532\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	106.565	−	184.576i	0.140033	−	0.242544i	−0.787476	−	0.616345i	$-0.788613\pi$
$761$	106.565	−	184.576i	0.140033	−	0.242544i	0.927509	+	0.373802i	$0.121946\pi$
$762$		0			0
$763$	869.291	−	501.885i	1.13931	−	0.657779i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	45.4277	−	26.2277i	0.0592277	−	0.0341952i
$768$		0			0
$769$	−270.786	+	469.015i	−0.352127	+	0.609902i	−0.986622	−	0.163025i	$-0.947875\pi$
$769$	−270.786	+	469.015i	−0.352127	+	0.609902i	0.634495	+	0.772927i	$0.281208\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1255.73			1.62449			0.812245	−	0.583317i	$-0.198245\pi$
$773$	1255.73			1.62449			0.812245	+	0.583317i	$0.198245\pi$
$774$		0			0
$775$		−	292.070i		−	0.376864i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	518.136	+	299.146i	0.665130	+	0.384013i
$780$		0			0
$781$	551.759	+	955.675i	0.706478	+	1.22366i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	7.19706	+	12.4657i	0.00916822	+	0.0158798i
$786$		0			0
$787$	859.448	+	496.202i	1.09206	+	0.630499i	0.934123	−	0.356951i	$-0.116184\pi$
$787$	859.448	+	496.202i	1.09206	+	0.630499i	0.157933	+	0.987450i	$0.449517\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			54.5507i			0.0689643i
$792$		0			0
$793$	43.2342			0.0545198
$794$		0			0
$795$		0			0
$796$		0			0
$797$	319.262	−	552.978i	0.400580	−	0.693824i	−0.593216	−	0.805043i	$-0.702142\pi$
$797$	319.262	−	552.978i	0.400580	−	0.693824i	0.993796	+	0.111219i	$0.0354754\pi$
$798$		0			0
$799$	13.9530	−	8.05574i	0.0174630	−	0.0100823i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−651.377	+	376.073i	−0.811179	+	0.468335i
$804$		0			0
$805$	331.865	−	574.806i	0.412254	−	0.714045i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	174.260			0.215401			0.107701	−	0.994183i	$-0.465651\pi$
$809$	174.260			0.215401			0.107701	+	0.994183i	$0.465651\pi$
$810$		0			0
$811$		−	1182.19i		−	1.45770i	−0.684675	−	0.728849i	$-0.740056\pi$
$811$		−	1182.19i		−	1.45770i	0.684675	−	0.728849i	$-0.259944\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−139.880	−	80.7597i	−0.171632	−	0.0990917i
$816$		0			0
$817$	262.421	+	454.527i	0.321201	+	0.556336i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	293.955	+	509.144i	0.358045	+	0.620151i	0.987634	−	0.156777i	$-0.0501103\pi$
$821$	293.955	+	509.144i	0.358045	+	0.620151i	−0.629590	+	0.776928i	$0.716777\pi$
$822$		0			0
$823$	−98.0750	−	56.6236i	−0.119168	−	0.0688015i	0.439231	−	0.898374i	$-0.355251\pi$
$823$	−98.0750	−	56.6236i	−0.119168	−	0.0688015i	−0.558399	+	0.829573i	$0.688584\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	800.560i		−	0.968030i	−0.875060	−	0.484015i	$-0.839178\pi$
$827$		−	800.560i		−	0.968030i	0.875060	−	0.484015i	$-0.160822\pi$
$828$		0			0
$829$	−1162.87			−1.40274			−0.701369	−	0.712798i	$-0.747427\pi$
$829$	−1162.87			−1.40274			−0.701369	+	0.712798i	$0.747427\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	379.538	−	657.378i	0.455627	−	0.789170i
$834$		0			0
$835$	−232.551	+	134.264i	−0.278505	+	0.160795i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−1355.92	+	782.842i	−1.61612	+	0.933065i	−0.628205	+	0.778048i	$0.716210\pi$
$839$	−1355.92	+	782.842i	−1.61612	+	0.933065i	−0.987912	+	0.155017i	$0.950457\pi$
$840$		0			0
$841$	213.383	−	369.590i	0.253725	−	0.439464i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	457.406			0.541309
$846$		0			0
$847$		−	273.341i		−	0.322717i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−743.000	−	428.971i	−0.873091	−	0.504079i
$852$		0			0
$853$	68.8088	+	119.180i	0.0806668	+	0.139719i	0.903537	−	0.428511i	$-0.140962\pi$
$853$	68.8088	+	119.180i	0.0806668	+	0.139719i	−0.822870	+	0.568230i	$0.807628\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	384.489	+	665.955i	0.448646	+	0.777077i	0.998298	−	0.0583164i	$-0.0185732\pi$
$857$	384.489	+	665.955i	0.448646	+	0.777077i	−0.549653	+	0.835393i	$0.685240\pi$
$858$		0			0
$859$	178.353	+	102.972i	0.207629	+	0.119875i	0.600209	−	0.799843i	$-0.295084\pi$
$859$	178.353	+	102.972i	0.207629	+	0.119875i	−0.392580	+	0.919718i	$0.628417\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			772.757i			0.895431i	0.894176	+	0.447716i	$0.147762\pi$
$863$			772.757i			0.895431i	−0.894176	+	0.447716i	$0.852238\pi$
$864$		0			0
$865$	104.671			0.121007
$866$		0			0
$867$		0			0
$868$		0			0
$869$	47.3249	−	81.9692i	0.0544591	−	0.0943258i
$870$		0			0
$871$	22.6943	−	13.1026i	0.0260555	−	0.0150432i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1161.57	+	670.630i	−1.32750	+	0.766435i
$876$		0			0
$877$	200.096	−	346.577i	0.228160	−	0.395185i	−0.729103	−	0.684404i	$-0.760062\pi$
$877$	200.096	−	346.577i	0.228160	−	0.395185i	0.957263	+	0.289219i	$0.0933957\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	728.323			0.826700			0.413350	−	0.910572i	$-0.364359\pi$
$881$	728.323			0.826700			0.413350	+	0.910572i	$0.364359\pi$
$882$		0			0
$883$			383.413i			0.434216i	0.976148	+	0.217108i	$0.0696625\pi$
$883$			383.413i			0.434216i	−0.976148	+	0.217108i	$0.930338\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1255.91	+	725.098i	1.41590	+	0.817473i	0.995936	−	0.0900662i	$-0.0287079\pi$
$887$	1255.91	+	725.098i	1.41590	+	0.817473i	0.419968	+	0.907539i	$0.362041\pi$
$888$		0			0
$889$	−48.5392	−	84.0724i	−0.0545998	−	0.0945696i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−12.7907	−	22.1541i	−0.0143232	−	0.0248086i
$894$		0			0
$895$	85.5589	+	49.3974i	0.0955965	+	0.0551927i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	336.907i		−	0.374758i
$900$		0			0
$901$	−187.365			−0.207952
$902$		0			0
$903$		0			0
$904$		0			0
$905$	25.2125	−	43.6694i	0.0278592	−	0.0482535i
$906$		0			0
$907$	−533.290	+	307.895i	−0.587971	+	0.339465i	−0.764295	−	0.644867i	$-0.776913\pi$
$907$	−533.290	+	307.895i	−0.587971	+	0.339465i	0.176324	+	0.984332i	$0.443580\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	227.031	−	131.076i	0.249211	−	0.143882i	−0.370192	−	0.928955i	$-0.620708\pi$
$911$	227.031	−	131.076i	0.249211	−	0.143882i	0.619403	+	0.785073i	$0.287375\pi$
$912$		0			0
$913$	−419.572	+	726.720i	−0.459553	+	0.795969i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1540.83			−1.68030
$918$		0			0
$919$			566.458i			0.616385i	0.951324	+	0.308193i	$0.0997241\pi$
$919$			566.458i			0.616385i	−0.951324	+	0.308193i	$0.900276\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−57.3533	−	33.1130i	−0.0621379	−	0.0358754i
$924$		0			0
$925$	358.667	+	621.229i	0.387748	+	0.671599i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−298.745	−	517.442i	−0.321577	−	0.556988i	0.659236	−	0.751936i	$-0.270880\pi$
$929$	−298.745	−	517.442i	−0.321577	−	0.556988i	−0.980814	+	0.194948i	$0.937546\pi$
$930$		0			0
$931$	−1043.77	−	602.618i	−1.12112	−	0.647281i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	237.717i		−	0.254243i
$936$		0			0
$937$	457.785			0.488564			0.244282	−	0.969704i	$-0.421448\pi$
$937$	457.785			0.488564			0.244282	+	0.969704i	$0.421448\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−677.858	+	1174.09i	−0.720360	+	1.24770i	0.240496	+	0.970650i	$0.422690\pi$
$941$	−677.858	+	1174.09i	−0.720360	+	1.24770i	−0.960856	+	0.277049i	$0.910643\pi$
$942$		0			0
$943$	775.526	−	447.750i	0.822403	−	0.474814i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	567.925	−	327.891i	0.599709	−	0.346242i	−0.169218	−	0.985579i	$-0.554124\pi$
$947$	567.925	−	327.891i	0.599709	−	0.346242i	0.768927	+	0.639336i	$0.220791\pi$
$948$		0			0
$949$	22.5694	−	39.0914i	0.0237823	−	0.0411922i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−554.778			−0.582139			−0.291069	−	0.956702i	$-0.594011\pi$
$953$	−554.778			−0.582139			−0.291069	+	0.956702i	$0.594011\pi$
$954$		0			0
$955$			767.193i			0.803344i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	453.102	+	261.599i	0.472474	+	0.272783i
$960$		0			0
$961$	−343.493	−	594.947i	−0.357432	−	0.619091i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	411.009	+	711.889i	0.425917	+	0.737709i
$966$		0			0
$967$	−502.000	−	289.830i	−0.519131	−	0.299720i	0.217448	−	0.976072i	$-0.430227\pi$
$967$	−502.000	−	289.830i	−0.519131	−	0.299720i	−0.736579	+	0.676351i	$0.763560\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			260.660i			0.268445i	0.990951	+	0.134223i	$0.0428537\pi$
$971$			260.660i			0.268445i	−0.990951	+	0.134223i	$0.957146\pi$
$972$		0			0
$973$	1750.76			1.79934
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−638.953	+	1106.70i	−0.653995	+	1.13275i	0.328149	+	0.944626i	$0.393575\pi$
$977$	−638.953	+	1106.70i	−0.653995	+	1.13275i	−0.982145	+	0.188127i	$0.939758\pi$
$978$		0			0
$979$	−553.793	+	319.732i	−0.565672	+	0.326591i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	378.325	−	218.426i	0.384868	−	0.222204i	−0.295066	−	0.955477i	$-0.595342\pi$
$983$	378.325	−	218.426i	0.384868	−	0.222204i	0.679934	+	0.733273i	$0.262008\pi$
$984$		0			0
$985$	188.746	−	326.918i	0.191621	−	0.331897i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	785.562			0.794300
$990$		0			0
$991$		−	1344.50i		−	1.35671i	−0.734734	−	0.678356i	$-0.762693\pi$
$991$		−	1344.50i		−	1.35671i	0.734734	−	0.678356i	$-0.237307\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	26.3858	+	15.2338i	0.0265184	+	0.0153104i
$996$		0			0
$997$	−942.397	−	1632.28i	−0.945233	−	1.63719i	−0.755284	−	0.655398i	$-0.772501\pi$
$997$	−942.397	−	1632.28i	−0.945233	−	1.63719i	−0.189949	−	0.981794i	$-0.560832\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.3.o.g.1279.5		16
3.2	odd	2		576.3.o.g.319.3		16
4.3	odd	2	inner	1728.3.o.g.1279.6		16
8.3	odd	2		108.3.f.c.91.2		16
8.5	even	2		108.3.f.c.91.3		16
9.2	odd	6		576.3.o.g.511.6		16
9.7	even	3	inner	1728.3.o.g.127.6		16
12.11	even	2		576.3.o.g.319.6		16
24.5	odd	2		36.3.f.c.31.6	yes	16
24.11	even	2		36.3.f.c.31.7	yes	16
36.7	odd	6	inner	1728.3.o.g.127.5		16
36.11	even	6		576.3.o.g.511.3		16
72.5	odd	6		324.3.d.i.163.1		8
72.11	even	6		36.3.f.c.7.6	✓	16
72.13	even	6		324.3.d.g.163.8		8
72.29	odd	6		36.3.f.c.7.7	yes	16
72.43	odd	6		108.3.f.c.19.3		16
72.59	even	6		324.3.d.i.163.2		8
72.61	even	6		108.3.f.c.19.2		16
72.67	odd	6		324.3.d.g.163.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.c.7.6	✓	16	72.11	even	6
36.3.f.c.7.7	yes	16	72.29	odd	6
36.3.f.c.31.6	yes	16	24.5	odd	2
36.3.f.c.31.7	yes	16	24.11	even	2
108.3.f.c.19.2		16	72.61	even	6
108.3.f.c.19.3		16	72.43	odd	6
108.3.f.c.91.2		16	8.3	odd	2
108.3.f.c.91.3		16	8.5	even	2
324.3.d.g.163.7		8	72.67	odd	6
324.3.d.g.163.8		8	72.13	even	6
324.3.d.i.163.1		8	72.5	odd	6
324.3.d.i.163.2		8	72.59	even	6
576.3.o.g.319.3		16	3.2	odd	2
576.3.o.g.319.6		16	12.11	even	2
576.3.o.g.511.3		16	36.11	even	6
576.3.o.g.511.6		16	9.2	odd	6
1728.3.o.g.127.5		16	36.7	odd	6	inner
1728.3.o.g.127.6		16	9.7	even	3	inner
1728.3.o.g.1279.5		16	1.1	even	1	trivial
1728.3.o.g.1279.6		16	4.3	odd	2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1728.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.35609 - 2.34881i) q^{5} +(-10.0431 + 5.79837i) q^{7} +O(q^{10})\)	\(q+(1.35609 - 2.34881i) q^{5} +(-10.0431 + 5.79837i) q^{7} +(8.54822 - 4.93532i) q^{11} +(-0.296185 + 0.513008i) q^{13} +8.87968 q^{17} -14.0989i q^{19} +(-18.2754 - 10.5513i) q^{23} +(8.82205 + 15.2802i) q^{25} +(10.1764 + 17.6260i) q^{29} +(-14.3357 - 8.27670i) q^{31} +31.4524i q^{35} +40.6557 q^{37} +(-21.2177 + 36.7502i) q^{41} +(-32.2385 + 18.6129i) q^{43} +(1.57134 - 0.907211i) q^{47} +(42.7423 - 74.0318i) q^{49} -21.1005 q^{53} -26.7709i q^{55} +(-76.6879 - 44.2758i) q^{59} +(-36.4925 - 63.2069i) q^{61} +(0.803307 + 1.39137i) q^{65} +(-38.3110 - 22.1189i) q^{67} +111.798i q^{71} -76.2003 q^{73} +(-57.2337 + 99.1316i) q^{77} +(8.30434 - 4.79451i) q^{79} +(-73.6244 + 42.5070i) q^{83} +(12.0416 - 20.8567i) q^{85} -64.7845 q^{89} -6.86958i q^{91} +(-33.1157 - 19.1193i) q^{95} +(-3.59139 - 6.22047i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{5}+O(q^{10}) \) 16 * q + 6 * q^5	\( 16 q + 6 q^{5} + 46 q^{13} - 12 q^{17} - 30 q^{25} + 42 q^{29} - 56 q^{37} - 84 q^{41} + 58 q^{49} - 72 q^{53} + 34 q^{61} + 30 q^{65} + 116 q^{73} - 330 q^{77} + 140 q^{85} + 384 q^{89} - 148 q^{97}+O(q^{100}) \) 16 * q + 6 * q^5 + 46 * q^13 - 12 * q^17 - 30 * q^25 + 42 * q^29 - 56 * q^37 - 84 * q^41 + 58 * q^49 - 72 * q^53 + 34 * q^61 + 30 * q^65 + 116 * q^73 - 330 * q^77 + 140 * q^85 + 384 * q^89 - 148 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more