LMFDB - Embedded newform 1764.2.b.n.1567.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(1567,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1764.1567");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.b (of order $2$, degree $1$, 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:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$16$
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} + 4 x^{14} + 54 x^{12} - 112 x^{11} - 104 x^{10} + 1312 x^{9} - 3159 x^{8} + 2544 x^{7} + \cdots + 782 $ x^16 + 4x^14 + 54x^12 - 112x^11 - 104x^10 + 1312x^9 - 3159x^8 + 2544x^7 + 4132x^6 - 16824x^5 + 27780x^4 - 26200x^3 + 14608x^2 - 4784*x + 782
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{5}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1567.3
Root			$0.271975 - 1.48800i$ of defining polynomial
Character	$\chi$	$=$	1764.1567
Dual form			1764.2.b.n.1567.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05050 + 0.946809i) q^{2} +(0.207107 - 1.98925i) q^{4} -1.60804i q^{5} +(1.66587 + 2.28580i) q^{8} +O(q^{10})$	\(q+(-1.05050 + 0.946809i) q^{2} +(0.207107 - 1.98925i) q^{4} -1.60804i q^{5} +(1.66587 + 2.28580i) q^{8} +(1.52250 + 1.68925i) q^{10} -2.67798i q^{11} +3.37849i q^{13} +(-3.91421 - 0.823973i) q^{16} -1.60804i q^{17} +4.30629 q^{19} +(-3.19879 - 0.333036i) q^{20} +(2.53553 + 2.81322i) q^{22} +6.46521i q^{23} +2.41421 q^{25} +(-3.19879 - 3.54911i) q^{26} -4.71179 q^{29} +10.3963 q^{31} +(4.89203 - 2.84043i) q^{32} +(1.52250 + 1.68925i) q^{34} +0.242641 q^{37} +(-4.52377 + 4.07724i) q^{38} +(3.67565 - 2.67878i) q^{40} -11.6464i q^{41} +7.95699i q^{43} +(-5.32716 - 0.554628i) q^{44} +(-6.12132 - 6.79172i) q^{46} -9.04753 q^{47} +(-2.53613 + 2.28580i) q^{50} +(6.72066 + 0.699709i) q^{52} +2.46148 q^{53} -4.30629 q^{55} +(4.94975 - 4.46117i) q^{58} +9.04753 q^{59} -3.37849i q^{61} +(-10.9213 + 9.84332i) q^{62} +(-2.44975 + 7.61569i) q^{64} +5.43275 q^{65} -11.2529i q^{67} +(-3.19879 - 0.333036i) q^{68} -8.03394i q^{71} -6.17733i q^{73} +(-0.254894 + 0.229734i) q^{74} +(0.891862 - 8.56628i) q^{76} -3.29589i q^{79} +(-1.32498 + 6.29420i) q^{80} +(11.0270 + 12.2346i) q^{82} +12.7951 q^{83} -2.58579 q^{85} +(-7.53375 - 8.35883i) q^{86} +(6.12132 - 4.46117i) q^{88} -0.275896i q^{89} +(12.8609 + 1.33899i) q^{92} +(9.50445 - 8.56628i) q^{94} -6.92468i q^{95} -12.9343i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{4}+O(q^{10}) $ 16 * q - 8 * q^4	$ 16 q - 8 q^{4} - 40 q^{16} - 16 q^{22} + 16 q^{25} - 64 q^{37} - 64 q^{46} + 40 q^{64} - 64 q^{85} + 64 q^{88}+O(q^{100}) $ 16 * q - 8 * q^4 - 40 * q^16 - 16 * q^22 + 16 * q^25 - 64 * q^37 - 64 * q^46 + 40 * q^64 - 64 * q^85 + 64 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.05050	+	0.946809i	−0.742817	+	0.669495i
$2$	−1.05050	+	0.946809i	−0.742817	+	0.669495i
$3$		0			0
$3$		0			0
$4$	0.207107	−	1.98925i	0.103553	−	0.994624i
$5$		−	1.60804i		−	0.719136i	−0.933119	−	0.359568i	$-0.882924\pi$
$5$		−	1.60804i		−	0.719136i	0.933119	−	0.359568i	$-0.117076\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.66587	+	2.28580i	0.588974	+	0.808152i
$9$		0			0
$10$	1.52250	+	1.68925i	0.481458	+	0.534187i
$11$		−	2.67798i		−	0.807441i	−0.914882	−	0.403721i	$-0.867717\pi$
$11$		−	2.67798i		−	0.807441i	0.914882	−	0.403721i	$-0.132283\pi$
$12$		0			0
$13$			3.37849i			0.937025i	0.883457	+	0.468513i	$0.155210\pi$
$13$			3.37849i			0.937025i	−0.883457	+	0.468513i	$0.844790\pi$
$14$		0			0
$15$		0			0
$16$	−3.91421	−	0.823973i	−0.978553	−	0.205993i
$17$		−	1.60804i		−	0.390007i	−0.980803	−	0.195003i	$-0.937528\pi$
$17$		−	1.60804i		−	0.390007i	0.980803	−	0.195003i	$-0.0624717\pi$
$18$		0			0
$19$	4.30629			0.987931			0.493966	−	0.869481i	$-0.335547\pi$
$19$	4.30629			0.987931			0.493966	+	0.869481i	$0.335547\pi$
$20$	−3.19879	−	0.333036i	−0.715270	−	0.0744690i
$21$		0			0
$22$	2.53553	+	2.81322i	0.540578	+	0.599781i
$23$			6.46521i			1.34809i	0.738690	+	0.674045i	$0.235445\pi$
$23$			6.46521i			1.34809i	−0.738690	+	0.674045i	$0.764555\pi$
$24$		0			0
$25$	2.41421			0.482843
$26$	−3.19879	−	3.54911i	−0.627334	−	0.696038i
$27$		0			0
$28$		0			0
$29$	−4.71179			−0.874958			−0.437479	−	0.899229i	$-0.644129\pi$
$29$	−4.71179			−0.874958			−0.437479	+	0.899229i	$0.644129\pi$
$30$		0			0
$31$	10.3963			1.86723			0.933616	−	0.358275i	$-0.116635\pi$
$31$	10.3963			1.86723			0.933616	+	0.358275i	$0.116635\pi$
$32$	4.89203	−	2.84043i	0.864797	−	0.502121i
$33$		0			0
$34$	1.52250	+	1.68925i	0.261107	+	0.289703i
$35$		0			0
$36$		0			0
$37$	0.242641			0.0398899			0.0199449	−	0.999801i	$-0.493651\pi$
$37$	0.242641			0.0398899			0.0199449	+	0.999801i	$0.493651\pi$
$38$	−4.52377	+	4.07724i	−0.733852	+	0.661415i
$39$		0			0
$40$	3.67565	−	2.67878i	0.581171	−	0.423553i
$41$		−	11.6464i		−	1.81887i	−0.415848	−	0.909434i	$-0.636515\pi$
$41$		−	11.6464i		−	1.81887i	0.415848	−	0.909434i	$-0.363485\pi$
$42$		0			0
$43$			7.95699i			1.21343i	0.794920	+	0.606715i	$0.207513\pi$
$43$			7.95699i			1.21343i	−0.794920	+	0.606715i	$0.792487\pi$
$44$	−5.32716	−	0.554628i	−0.803100	−	0.0836133i
$45$		0			0
$46$	−6.12132	−	6.79172i	−0.902539	−	1.00138i
$47$	−9.04753			−1.31972			−0.659859	−	0.751389i	$-0.729384\pi$
$47$	−9.04753			−1.31972			−0.659859	+	0.751389i	$0.729384\pi$
$48$		0			0
$49$		0			0
$50$	−2.53613	+	2.28580i	−0.358664	+	0.323261i
$51$		0			0
$52$	6.72066	+	0.699709i	0.931988	+	0.0970321i
$53$	2.46148			0.338110			0.169055	−	0.985607i	$-0.445928\pi$
$53$	2.46148			0.338110			0.169055	+	0.985607i	$0.445928\pi$
$54$		0			0
$55$	−4.30629			−0.580660
$56$		0			0
$57$		0			0
$58$	4.94975	−	4.46117i	0.649934	−	0.585780i
$59$	9.04753			1.17789			0.588944	−	0.808174i	$-0.299544\pi$
$59$	9.04753			1.17789			0.588944	+	0.808174i	$0.299544\pi$
$60$		0			0
$61$		−	3.37849i		−	0.432572i	−0.976330	−	0.216286i	$-0.930606\pi$
$61$		−	3.37849i		−	0.432572i	0.976330	−	0.216286i	$-0.0693943\pi$
$62$	−10.9213	+	9.84332i	−1.38701	+	1.25010i
$63$		0			0
$64$	−2.44975	+	7.61569i	−0.306218	+	0.951961i
$65$	5.43275			0.673849
$66$		0			0
$67$		−	11.2529i		−	1.37476i	−0.726299	−	0.687379i	$-0.758761\pi$
$67$		−	11.2529i		−	1.37476i	0.726299	−	0.687379i	$-0.241239\pi$
$68$	−3.19879	−	0.333036i	−0.387910	−	0.0403865i
$69$		0			0
$70$		0			0
$71$		−	8.03394i		−	0.953453i	−0.879052	−	0.476726i	$-0.841823\pi$
$71$		−	8.03394i		−	0.953453i	0.879052	−	0.476726i	$-0.158177\pi$
$72$		0			0
$73$		−	6.17733i		−	0.723002i	−0.932372	−	0.361501i	$-0.882264\pi$
$73$		−	6.17733i		−	0.723002i	0.932372	−	0.361501i	$-0.117736\pi$
$74$	−0.254894	+	0.229734i	−0.0296309	+	0.0267061i
$75$		0			0
$76$	0.891862	−	8.56628i	0.102304	−	0.982620i
$77$		0			0
$78$		0			0
$79$		−	3.29589i		−	0.370817i	−0.982662	−	0.185409i	$-0.940639\pi$
$79$		−	3.29589i		−	0.370817i	0.982662	−	0.185409i	$-0.0593608\pi$
$80$	−1.32498	+	6.29420i	−0.148137	+	0.703713i
$81$		0			0
$82$	11.0270	+	12.2346i	1.21772	+	1.35109i
$83$	12.7951			1.40445			0.702225	−	0.711955i	$-0.252190\pi$
$83$	12.7951			1.40445			0.702225	+	0.711955i	$0.252190\pi$
$84$		0			0
$85$	−2.58579			−0.280468
$86$	−7.53375	−	8.35883i	−0.812385	−	0.901356i
$87$		0			0
$88$	6.12132	−	4.46117i	0.652535	−	0.475562i
$89$		−	0.275896i		−	0.0292449i	−0.999893	−	0.0146224i	$-0.995345\pi$
$89$		−	0.275896i		−	0.0292449i	0.999893	−	0.0146224i	$-0.00465463\pi$
$90$		0			0
$91$		0			0
$92$	12.8609	+	1.33899i	1.34084	+	0.139599i
$93$		0			0
$94$	9.50445	−	8.56628i	0.980309	−	0.883545i
$95$		−	6.92468i		−	0.710457i
$96$		0			0
$97$		−	12.9343i		−	1.31328i	−0.754204	−	0.656640i	$-0.771977\pi$
$97$		−	12.9343i		−	1.31328i	0.754204	−	0.656640i	$-0.228023\pi$
$98$		0			0
$99$		0			0
$100$	0.500000	−	4.80247i	0.0500000	−	0.480247i
$101$		−	16.1947i		−	1.61143i	−0.592304	−	0.805714i	$-0.701782\pi$
$101$		−	16.1947i		−	1.61143i	0.592304	−	0.805714i	$-0.298218\pi$
$102$		0			0
$103$	10.3963			1.02438			0.512189	−	0.858873i	$-0.328835\pi$
$103$	10.3963			1.02438			0.512189	+	0.858873i	$0.328835\pi$
$104$	−7.72255	+	5.62813i	−0.757259	+	0.551884i
$105$		0			0
$106$	−2.58579	+	2.33055i	−0.251154	+	0.226363i
$107$			6.46521i			0.625016i	0.949915	+	0.312508i	$0.101169\pi$
$107$			6.46521i			0.625016i	−0.949915	+	0.312508i	$0.898831\pi$
$108$		0			0
$109$	−7.41421			−0.710153			−0.355076	−	0.934837i	$-0.615545\pi$
$109$	−7.41421			−0.710153			−0.355076	+	0.934837i	$0.615545\pi$
$110$	4.52377	−	4.07724i	0.431324	−	0.388749i
$111$		0			0
$112$		0			0
$113$	−12.6060			−1.18587			−0.592937	−	0.805249i	$-0.702032\pi$
$113$	−12.6060			−1.18587			−0.592937	+	0.805249i	$0.702032\pi$
$114$		0			0
$115$	10.3963			0.969461
$116$	−0.975845	+	9.37293i	−0.0906049	+	0.870254i
$117$		0			0
$118$	−9.50445	+	8.56628i	−0.874955	+	0.788590i
$119$		0			0
$120$		0			0
$121$	3.82843			0.348039
$122$	3.19879	+	3.54911i	0.289604	+	0.321321i
$123$		0			0
$124$	2.15315	−	20.6808i	0.193358	−	1.85719i
$125$		−	11.9223i		−	1.06637i
$126$		0			0
$127$			11.2529i			0.998532i	0.866449	+	0.499266i	$0.166397\pi$
$127$			11.2529i			0.998532i	−0.866449	+	0.499266i	$0.833603\pi$
$128$	−4.63714	−	10.3197i	−0.409869	−	0.912144i
$129$		0			0
$130$	−5.70711	+	5.14377i	−0.500546	+	0.451138i
$131$	12.7951			1.11792			0.558958	−	0.829196i	$-0.311201\pi$
$131$	12.7951			1.11792			0.558958	+	0.829196i	$0.311201\pi$
$132$		0			0
$133$		0			0
$134$	10.6543	+	11.8212i	0.920394	+	1.02119i
$135$		0			0
$136$	3.67565	−	2.67878i	0.315184	−	0.229704i
$137$	−19.0583			−1.62826			−0.814132	−	0.580680i	$-0.802787\pi$
$137$	−19.0583			−1.62826			−0.814132	+	0.580680i	$0.802787\pi$
$138$		0			0
$139$	6.09002			0.516549			0.258274	−	0.966072i	$-0.416846\pi$
$139$	6.09002			0.516549			0.258274	+	0.966072i	$0.416846\pi$
$140$		0			0
$141$		0			0
$142$	7.60660	+	8.43966i	0.638332	+	0.708241i
$143$	9.04753			0.756593
$144$		0			0
$145$			7.57675i			0.629214i
$146$	5.84875	+	6.48929i	0.484046	+	0.537058i
$147$		0			0
$148$	0.0502525	−	0.482672i	0.00413073	−	0.0396754i
$149$	23.7701			1.94733			0.973663	−	0.227993i	$-0.0732165\pi$
$149$	23.7701			1.94733			0.973663	+	0.227993i	$0.0732165\pi$
$150$		0			0
$151$		−	7.95699i		−	0.647531i	−0.946137	−	0.323765i	$-0.895051\pi$
$151$		−	7.95699i		−	0.647531i	0.946137	−	0.323765i	$-0.104949\pi$
$152$	7.17373	+	9.84332i	0.581866	+	0.798398i
$153$		0			0
$154$		0			0
$155$		−	16.7177i		−	1.34279i
$156$		0			0
$157$			10.9552i			0.874323i	0.899383	+	0.437162i	$0.144016\pi$
$157$			10.9552i			0.874323i	−0.899383	+	0.437162i	$0.855984\pi$
$158$	3.12058	+	3.46234i	0.248260	+	0.275449i
$159$		0			0
$160$	−4.56751	−	7.86657i	−0.361094	−	0.621907i
$161$		0			0
$162$		0			0
$163$		−	11.2529i		−	0.881394i	−0.897656	−	0.440697i	$-0.854731\pi$
$163$		−	11.2529i		−	0.881394i	0.897656	−	0.440697i	$-0.145269\pi$
$164$	−23.1677	−	2.41206i	−1.80909	−	0.188350i
$165$		0			0
$166$	−13.4413	+	12.1146i	−1.04325	+	0.940272i
$167$	21.8427			1.69024			0.845119	−	0.534579i	$-0.179530\pi$
$167$	21.8427			1.69024			0.845119	+	0.534579i	$0.179530\pi$
$168$		0			0
$169$	1.58579			0.121984
$170$	2.71637	−	2.44824i	0.208336	−	0.187772i
$171$		0			0
$172$	15.8284	+	1.64795i	1.20691	+	0.125655i
$173$			11.2563i			0.855798i	0.903827	+	0.427899i	$0.140746\pi$
$173$			11.2563i			0.855798i	−0.903827	+	0.427899i	$0.859254\pi$
$174$		0			0
$175$		0			0
$176$	−2.20658	+	10.4822i	−0.166328	+	0.790124i
$177$		0			0
$178$	0.261220	+	0.289829i	0.0195793	+	0.0217236i
$179$			12.4710i			0.932123i	0.884752	+	0.466062i	$0.154328\pi$
$179$			12.4710i			0.932123i	−0.884752	+	0.466062i	$0.845672\pi$
$180$		0			0
$181$			14.9134i			1.10850i	0.832349	+	0.554252i	$0.186996\pi$
$181$			14.9134i			1.10850i	−0.832349	+	0.554252i	$0.813004\pi$
$182$		0			0
$183$		0			0
$184$	−14.7782	+	10.7702i	−1.08946	+	0.793991i
$185$		−	0.390175i		−	0.0286863i
$186$		0			0
$187$	−4.30629			−0.314907
$188$	−1.87381	+	17.9978i	−0.136661	+	1.31262i
$189$		0			0
$190$	6.55635	+	7.27439i	0.475648	+	0.527740i
$191$			10.2524i			0.741841i	0.928665	+	0.370921i	$0.120958\pi$
$191$			10.2524i			0.741841i	−0.928665	+	0.370921i	$0.879042\pi$
$192$		0			0
$193$	−7.65685			−0.551152			−0.275576	−	0.961279i	$-0.588869\pi$
$193$	−7.65685			−0.551152			−0.275576	+	0.961279i	$0.588869\pi$
$194$	12.2463	+	13.5875i	0.879235	+	0.975527i
$195$		0			0
$196$		0			0
$197$	−10.1445			−0.722769			−0.361384	−	0.932417i	$-0.617696\pi$
$197$	−10.1445			−0.722769			−0.361384	+	0.932417i	$0.617696\pi$
$198$		0			0
$199$	−14.7026			−1.04224			−0.521120	−	0.853483i	$-0.674486\pi$
$199$	−14.7026			−1.04224			−0.521120	+	0.853483i	$0.674486\pi$
$200$	4.02177	+	5.51841i	0.284382	+	0.390210i
$201$		0			0
$202$	15.3332	+	17.0125i	1.07884	+	1.19700i
$203$		0			0
$204$		0			0
$205$	−18.7279			−1.30801
$206$	−10.9213	+	9.84332i	−0.760926	+	0.685816i
$207$		0			0
$208$	2.78379	−	13.2241i	0.193021	−	0.916929i
$209$		−	11.5322i		−	0.797696i
$210$		0			0
$211$		−	15.9140i		−	1.09556i	−0.836621	−	0.547782i	$-0.815472\pi$
$211$		−	15.9140i		−	1.09556i	0.836621	−	0.547782i	$-0.184528\pi$
$212$	0.509789	−	4.89649i	0.0350124	−	0.336292i
$213$		0			0
$214$	−6.12132	−	6.79172i	−0.418445	−	0.464272i
$215$	12.7951			0.872622
$216$		0			0
$217$		0			0
$218$	7.78864	−	7.01984i	0.527513	−	0.475444i
$219$		0			0
$220$	−0.891862	+	8.56628i	−0.0601294	+	0.577539i
$221$	5.43275			0.365446
$222$		0			0
$223$	8.61259			0.576741			0.288371	−	0.957519i	$-0.406886\pi$
$223$	8.61259			0.576741			0.288371	+	0.957519i	$0.406886\pi$
$224$		0			0
$225$		0			0
$226$	13.2426	−	11.9355i	0.880887	−	0.793937i
$227$	−3.74761			−0.248738			−0.124369	−	0.992236i	$-0.539691\pi$
$227$	−3.74761			−0.248738			−0.124369	+	0.992236i	$0.539691\pi$
$228$		0			0
$229$		−	4.19825i		−	0.277428i	−0.990332	−	0.138714i	$-0.955703\pi$
$229$		−	4.19825i		−	0.277428i	0.990332	−	0.138714i	$-0.0442969\pi$
$230$	−10.9213	+	9.84332i	−0.720132	+	0.649049i
$231$		0			0
$232$	−7.84924	−	10.7702i	−0.515328	−	0.707099i
$233$	3.69222			0.241885			0.120943	−	0.992660i	$-0.461408\pi$
$233$	3.69222			0.241885			0.120943	+	0.992660i	$0.461408\pi$
$234$		0			0
$235$			14.5488i			0.949058i
$236$	1.87381	−	17.9978i	0.121974	−	1.17156i
$237$		0			0
$238$		0			0
$239$			1.10926i			0.0717518i	0.999356	+	0.0358759i	$0.0114221\pi$
$239$			1.10926i			0.0717518i	−0.999356	+	0.0358759i	$0.988578\pi$
$240$		0			0
$241$		−	1.39942i		−	0.0901444i	−0.998984	−	0.0450722i	$-0.985648\pi$
$241$		−	1.39942i		−	0.0901444i	0.998984	−	0.0450722i	$-0.0143518\pi$
$242$	−4.02177	+	3.62479i	−0.258529	+	0.233010i
$243$		0			0
$244$	−6.72066	−	0.699709i	−0.430246	−	0.0447943i
$245$		0			0
$246$		0			0
$247$			14.5488i			0.925717i
$248$	17.3189	+	23.7639i	1.09975	+	1.50901i
$249$		0			0
$250$	11.2882	+	12.5244i	0.713927	+	0.792115i
$251$	21.8427			1.37870			0.689349	−	0.724430i	$-0.257897\pi$
$251$	21.8427			1.37870			0.689349	+	0.724430i	$0.257897\pi$
$252$		0			0
$253$	17.3137			1.08850
$254$	−10.6543	−	11.8212i	−0.668512	−	0.741726i
$255$		0			0
$256$	14.6421	+	6.45042i	0.915133	+	0.403151i
$257$			14.3107i			0.892679i	0.894864	+	0.446339i	$0.147273\pi$
$257$			14.3107i			0.892679i	−0.894864	+	0.446339i	$0.852727\pi$
$258$		0			0
$259$		0			0
$260$	1.12516	−	10.8071i	0.0697794	−	0.670226i
$261$		0			0
$262$	−13.4413	+	12.1146i	−0.830407	+	0.748440i
$263$		−	2.67798i		−	0.165131i	−0.996586	−	0.0825656i	$-0.973689\pi$
$263$		−	2.67798i		−	0.165131i	0.996586	−	0.0825656i	$-0.0263114\pi$
$264$		0			0
$265$		−	3.95815i		−	0.243147i
$266$		0			0
$267$		0			0
$268$	−22.3848	−	2.33055i	−1.36737	−	0.142361i
$269$		−	16.1947i		−	0.987406i	−0.869631	−	0.493703i	$-0.835643\pi$
$269$		−	16.1947i		−	0.987406i	0.869631	−	0.493703i	$-0.164357\pi$
$270$		0			0
$271$	−16.4863			−1.00147			−0.500737	−	0.865600i	$-0.666937\pi$
$271$	−16.4863			−1.00147			−0.500737	+	0.865600i	$0.666937\pi$
$272$	−1.32498	+	6.29420i	−0.0803388	+	0.381642i
$273$		0			0
$274$	20.0208	−	18.0446i	1.20950	−	1.09011i
$275$		−	6.46521i		−	0.389867i
$276$		0			0
$277$	23.7990			1.42994			0.714971	−	0.699154i	$-0.246440\pi$
$277$	23.7990			1.42994			0.714971	+	0.699154i	$0.246440\pi$
$278$	−6.39757	+	5.76608i	−0.383701	+	0.345827i
$279$		0			0
$280$		0			0
$281$	8.19285			0.488744			0.244372	−	0.969681i	$-0.421418\pi$
$281$	8.19285			0.488744			0.244372	+	0.969681i	$0.421418\pi$
$282$		0			0
$283$	−10.3963			−0.617996			−0.308998	−	0.951063i	$-0.599994\pi$
$283$	−10.3963			−0.617996			−0.308998	+	0.951063i	$0.599994\pi$
$284$	−15.9815	−	1.66388i	−0.948327	−	0.0987333i
$285$		0			0
$286$	−9.50445	+	8.56628i	−0.562010	+	0.506535i
$287$		0			0
$288$		0			0
$289$	14.4142			0.847895
$290$	−7.17373	−	7.95938i	−0.421256	−	0.467391i
$291$		0			0
$292$	−12.2882	−	1.27937i	−0.719115	−	0.0748693i
$293$			1.21786i			0.0711483i	0.999367	+	0.0355741i	$0.0113260\pi$
$293$			1.21786i			0.0711483i	−0.999367	+	0.0355741i	$0.988674\pi$
$294$		0			0
$295$		−	14.5488i		−	0.847063i
$296$	0.404208	+	0.554628i	0.0234941	+	0.0322371i
$297$		0			0
$298$	−24.9706	+	22.5058i	−1.44651	+	1.30372i
$299$	−21.8427			−1.26319
$300$		0			0
$301$		0			0
$302$	7.53375	+	8.35883i	0.433518	+	0.480997i
$303$		0			0
$304$	−16.8557	−	3.54827i	−0.966743	−	0.203507i
$305$	−5.43275			−0.311078
$306$		0			0
$307$	−22.5763			−1.28850			−0.644250	−	0.764815i	$-0.722830\pi$
$307$	−22.5763			−1.28850			−0.644250	+	0.764815i	$0.722830\pi$
$308$		0			0
$309$		0			0
$310$	15.8284	+	17.5619i	0.898994	+	0.997451i
$311$	21.8427			1.23858			0.619292	−	0.785161i	$-0.287420\pi$
$311$	21.8427			1.23858			0.619292	+	0.785161i	$0.287420\pi$
$312$		0			0
$313$		−	6.17733i		−	0.349163i	−0.984643	−	0.174582i	$-0.944143\pi$
$313$		−	6.17733i		−	0.349163i	0.984643	−	0.174582i	$-0.0558573\pi$
$314$	−10.3725	−	11.5085i	−0.585355	−	0.649462i
$315$		0			0
$316$	−6.55635	−	0.682602i	−0.368823	−	0.0383994i
$317$	10.1445			0.569774			0.284887	−	0.958561i	$-0.408044\pi$
$317$	10.1445			0.569774			0.284887	+	0.958561i	$0.408044\pi$
$318$		0			0
$319$			12.6181i			0.706477i
$320$	12.2463	+	3.93929i	0.684590	+	0.220213i
$321$		0			0
$322$		0			0
$323$		−	6.92468i		−	0.385300i
$324$		0			0
$325$			8.15640i			0.452436i
$326$	10.6543	+	11.8212i	0.590089	+	0.654714i
$327$		0			0
$328$	26.6214	−	19.4015i	1.46992	−	1.07127i
$329$		0			0
$330$		0			0
$331$			22.5058i			1.23703i	0.785773	+	0.618514i	$0.212265\pi$
$331$			22.5058i			1.23703i	−0.785773	+	0.618514i	$0.787735\pi$
$332$	2.64996	−	25.4527i	0.145436	−	1.39690i
$333$		0			0
$334$	−22.9458	+	20.6808i	−1.25554	+	1.13161i
$335$	−18.0951			−0.988639
$336$		0			0
$337$	−34.3848			−1.87306			−0.936529	−	0.350590i	$-0.885981\pi$
$337$	−34.3848			−1.87306			−0.936529	+	0.350590i	$0.885981\pi$
$338$	−1.66587	+	1.50144i	−0.0906114	+	0.0816674i
$339$		0			0
$340$	−0.535534	+	5.14377i	−0.0290434	+	0.278960i
$341$		−	27.8411i		−	1.50768i
$342$		0			0
$343$		0			0
$344$	−18.1881	+	13.2553i	−0.980635	+	0.714679i
$345$		0			0
$346$	−10.6575	−	11.8247i	−0.572952	−	0.635701i
$347$		−	14.0397i		−	0.753690i	−0.926276	−	0.376845i	$-0.877009\pi$
$347$		−	14.0397i		−	0.753690i	0.926276	−	0.376845i	$-0.122991\pi$
$348$		0			0
$349$			8.15640i			0.436602i	0.975881	+	0.218301i	$0.0700515\pi$
$349$			8.15640i			0.436602i	−0.975881	+	0.218301i	$0.929949\pi$
$350$		0			0
$351$		0			0
$352$	−7.60660	−	13.1008i	−0.405433	−	0.698273i
$353$		−	1.21786i		−	0.0648203i	−0.999475	−	0.0324101i	$-0.989682\pi$
$353$		−	1.21786i		−	0.0648203i	0.999475	−	0.0324101i	$-0.0103183\pi$
$354$		0			0
$355$	−12.9189			−0.685663
$356$	−0.548825	−	0.0571399i	−0.0290877	−	0.00302841i
$357$		0			0
$358$	−11.8076	−	13.1008i	−0.624052	−	0.692397i
$359$		−	6.46521i		−	0.341221i	−0.985339	−	0.170610i	$-0.945426\pi$
$359$		−	6.46521i		−	0.341221i	0.985339	−	0.170610i	$-0.0545740\pi$
$360$		0			0
$361$	−0.455844			−0.0239918
$362$	−14.1201	−	15.6665i	−0.742137	−	0.823415i
$363$		0			0
$364$		0			0
$365$	−9.93338			−0.519937
$366$		0			0
$367$	−18.2701			−0.953689			−0.476844	−	0.878988i	$-0.658220\pi$
$367$	−18.2701			−0.953689			−0.476844	+	0.878988i	$0.658220\pi$
$368$	5.32716	−	25.3062i	0.277698	−	1.31918i
$369$		0			0
$370$	0.369422	+	0.409880i	0.0192053	+	0.0213086i
$371$		0			0
$372$		0			0
$373$	2.82843			0.146450			0.0732252	−	0.997315i	$-0.476671\pi$
$373$	2.82843			0.146450			0.0732252	+	0.997315i	$0.476671\pi$
$374$	4.52377	−	4.07724i	0.233918	−	0.210829i
$375$		0			0
$376$	−15.0720	−	20.6808i	−0.777280	−	1.06653i
$377$		−	15.9188i		−	0.819858i
$378$		0			0
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$	−13.7749	−	1.43415i	−0.706638	−	0.0735703i
$381$		0			0
$382$	−9.70711	−	10.7702i	−0.496659	−	0.551052i
$383$		0			0			−	1.00000i	$-0.5\pi$
$383$		0			0				1.00000i	$0.5\pi$
$384$		0			0
$385$		0			0
$386$	8.04354	−	7.24958i	0.409405	−	0.368994i
$387$		0			0
$388$	−25.7296	−	2.67878i	−1.30622	−	0.135995i
$389$	0.211161			0.0107063			0.00535315	−	0.999986i	$-0.498296\pi$
$389$	0.211161			0.0107063			0.00535315	+	0.999986i	$0.498296\pi$
$390$		0			0
$391$	10.3963			0.525764
$392$		0			0
$393$		0			0
$394$	10.6569	−	9.60494i	0.536885	−	0.483890i
$395$	−5.29992			−0.266668
$396$		0			0
$397$			7.33664i			0.368216i	0.982906	+	0.184108i	$0.0589395\pi$
$397$			7.33664i			0.368216i	−0.982906	+	0.184108i	$0.941060\pi$
$398$	15.4451	−	13.9206i	0.774193	−	0.697774i
$399$		0			0
$400$	−9.44975	−	1.98925i	−0.472487	−	0.0994624i
$401$	−29.9238			−1.49432			−0.747162	−	0.664642i	$-0.768584\pi$
$401$	−29.9238			−1.49432			−0.747162	+	0.664642i	$0.768584\pi$
$402$		0			0
$403$			35.1239i			1.74964i
$404$	−32.2152	−	3.35402i	−1.60277	−	0.166869i
$405$		0			0
$406$		0			0
$407$		−	0.649787i		−	0.0322087i
$408$		0			0
$409$		−	33.2053i		−	1.64189i	−0.571004	−	0.820947i	$-0.693446\pi$
$409$		−	33.2053i		−	1.64189i	0.571004	−	0.820947i	$-0.306554\pi$
$410$	19.6737	−	17.7318i	0.971615	−	0.875709i
$411$		0			0
$412$	2.15315	−	20.6808i	0.106078	−	1.01887i
$413$		0			0
$414$		0			0
$415$		−	20.5751i		−	1.00999i
$416$	9.59636	+	16.5277i	0.470500	+	0.810337i
$417$		0			0
$418$	10.9188	+	12.1146i	0.534054	+	0.592542i
$419$	−34.6378			−1.69217			−0.846084	−	0.533049i	$-0.821046\pi$
$419$	−34.6378			−1.69217			−0.846084	+	0.533049i	$0.821046\pi$
$420$		0			0
$421$	16.0000			0.779792			0.389896	−	0.920859i	$-0.372511\pi$
$421$	16.0000			0.779792			0.389896	+	0.920859i	$0.372511\pi$
$422$	15.0675	+	16.7177i	0.733474	+	0.813803i
$423$		0			0
$424$	4.10051	+	5.62644i	0.199138	+	0.273244i
$425$		−	3.88215i		−	0.188312i
$426$		0			0
$427$		0			0
$428$	12.8609	+	1.33899i	0.621656	+	0.0647225i
$429$		0			0
$430$	−13.4413	+	12.1146i	−0.648198	+	0.584216i
$431$			2.67798i			0.128994i	0.997918	+	0.0644969i	$0.0205442\pi$
$431$			2.67798i			0.128994i	−0.997918	+	0.0644969i	$0.979456\pi$
$432$		0			0
$433$		−	25.6285i		−	1.23163i	−0.787891	−	0.615814i	$-0.788827\pi$
$433$		−	25.6285i		−	1.23163i	0.787891	−	0.615814i	$-0.211173\pi$
$434$		0			0
$435$		0			0
$436$	−1.53553	+	14.7487i	−0.0735387	+	0.706335i
$437$			27.8411i			1.33182i
$438$		0			0
$439$	−14.7026			−0.701717			−0.350858	−	0.936429i	$-0.614110\pi$
$439$	−14.7026			−0.701717			−0.350858	+	0.936429i	$0.614110\pi$
$440$	−7.17373	−	9.84332i	−0.341994	−	0.469262i
$441$		0			0
$442$	−5.70711	+	5.14377i	−0.271459	+	0.244664i
$443$			33.8948i			1.61039i	0.593010	+	0.805195i	$0.297939\pi$
$443$			33.8948i			1.61039i	−0.593010	+	0.805195i	$0.702061\pi$
$444$		0			0
$445$	−0.443651			−0.0210311
$446$	−9.04753	+	8.15447i	−0.428413	+	0.386125i
$447$		0			0
$448$		0			0
$449$	−8.70264			−0.410703			−0.205351	−	0.978688i	$-0.565834\pi$
$449$	−8.70264			−0.410703			−0.205351	+	0.978688i	$0.565834\pi$
$450$		0			0
$451$	−31.1889			−1.46863
$452$	−2.61079	+	25.0765i	−0.122801	+	1.17950i
$453$		0			0
$454$	3.93687	−	3.54827i	0.184767	−	0.166529i
$455$		0			0
$456$		0			0
$457$	32.4853			1.51960			0.759799	−	0.650158i	$-0.225297\pi$
$457$	32.4853			1.51960			0.759799	+	0.650158i	$0.225297\pi$
$458$	3.97494	+	4.41027i	0.185737	+	0.206078i
$459$		0			0
$460$	2.15315	−	20.6808i	0.100391	−	0.964249i
$461$			29.4491i			1.37158i	0.727798	+	0.685792i	$0.240544\pi$
$461$			29.4491i			1.37158i	−0.727798	+	0.685792i	$0.759456\pi$
$462$		0			0
$463$		−	38.4198i		−	1.78552i	−0.450535	−	0.892759i	$-0.648767\pi$
$463$		−	38.4198i		−	1.78552i	0.450535	−	0.892759i	$-0.351233\pi$
$464$	18.4430	+	3.88239i	0.856193	+	0.180236i
$465$		0			0
$466$	−3.87868	+	3.49582i	−0.179676	+	0.161941i
$467$	−9.04753			−0.418670			−0.209335	−	0.977844i	$-0.567130\pi$
$467$	−9.04753			−0.418670			−0.209335	+	0.977844i	$0.567130\pi$
$468$		0			0
$469$		0			0
$470$	−13.7749	−	15.2835i	−0.635389	−	0.704976i
$471$		0			0
$472$	15.0720	+	20.6808i	0.693746	+	0.951913i
$473$	21.3087			0.979773
$474$		0			0
$475$	10.3963			0.477015
$476$		0			0
$477$		0			0
$478$	−1.05025	−	1.16527i	−0.0480374	−	0.0532984i
$479$	−34.6378			−1.58264			−0.791321	−	0.611401i	$-0.790606\pi$
$479$	−34.6378			−1.58264			−0.791321	+	0.611401i	$0.790606\pi$
$480$		0			0
$481$			0.819760i			0.0373778i
$482$	1.32498	+	1.47009i	0.0603512	+	0.0669608i
$483$		0			0
$484$	0.792893	−	7.61569i	0.0360406	−	0.346168i
$485$	−20.7989			−0.944428
$486$		0			0
$487$			14.5488i			0.659268i	0.944109	+	0.329634i	$0.106925\pi$
$487$			14.5488i			0.659268i	−0.944109	+	0.329634i	$0.893075\pi$
$488$	7.72255	−	5.62813i	0.349584	−	0.254774i
$489$		0			0
$490$		0			0
$491$			32.3261i			1.45886i	0.684058	+	0.729428i	$0.260213\pi$
$491$			32.3261i			1.45886i	−0.684058	+	0.729428i	$0.739787\pi$
$492$		0			0
$493$			7.57675i			0.341239i
$494$	−13.7749	−	15.2835i	−0.619762	−	0.687638i
$495$		0			0
$496$	−40.6934	−	8.56628i	−1.82719	−	0.384637i
$497$		0			0
$498$		0			0
$499$			19.2099i			0.859952i	0.902840	+	0.429976i	$0.141478\pi$
$499$			19.2099i			0.859952i	−0.902840	+	0.429976i	$0.858522\pi$
$500$	−23.7165	−	2.46920i	−1.06063	−	0.110426i
$501$		0			0
$502$	−22.9458	+	20.6808i	−1.02412	+	0.923031i
$503$	5.29992			0.236312			0.118156	−	0.992995i	$-0.462302\pi$
$503$	5.29992			0.236312			0.118156	+	0.992995i	$0.462302\pi$
$504$		0			0
$505$	−26.0416			−1.15884
$506$	−18.1881	+	16.3928i	−0.808559	+	0.728747i
$507$		0			0
$508$	22.3848	+	2.33055i	0.993164	+	0.103401i
$509$		−	1.21786i		−	0.0539808i	−0.999636	−	0.0269904i	$-0.991408\pi$
$509$		−	1.21786i		−	0.0539808i	0.999636	−	0.0269904i	$-0.00859236\pi$
$510$		0			0
$511$		0			0
$512$	−21.4889	+	7.08713i	−0.949684	+	0.313210i
$513$		0			0
$514$	−13.5495	−	15.0334i	−0.597644	−	0.663097i
$515$		−	16.7177i		−	0.736668i
$516$		0			0
$517$			24.2291i			1.06559i
$518$		0			0
$519$		0			0
$520$	9.05025	+	12.4182i	0.396880	+	0.544572i
$521$			15.6429i			0.685327i	0.939458	+	0.342663i	$0.111329\pi$
$521$			15.6429i			0.685327i	−0.939458	+	0.342663i	$0.888671\pi$
$522$		0			0
$523$	14.7026			0.642900			0.321450	−	0.946927i	$-0.395830\pi$
$523$	14.7026			0.642900			0.321450	+	0.946927i	$0.395830\pi$
$524$	2.64996	−	25.4527i	0.115764	−	1.11191i
$525$		0			0
$526$	2.53553	+	2.81322i	0.110555	+	0.122662i
$527$		−	16.7177i		−	0.728233i
$528$		0			0
$529$	−18.7990			−0.817347
$530$	3.74761	+	4.15804i	0.162786	+	0.180614i
$531$		0			0
$532$		0			0
$533$	39.3474			1.70433
$534$		0			0
$535$	10.3963			0.449472
$536$	25.7218	−	18.7459i	1.11101	−	0.809698i
$537$		0			0
$538$	15.3332	+	17.0125i	0.661063	+	0.733462i
$539$		0			0
$540$		0			0
$541$	−33.1127			−1.42363			−0.711813	−	0.702369i	$-0.752126\pi$
$541$	−33.1127			−1.42363			−0.711813	+	0.702369i	$0.752126\pi$
$542$	17.3189	−	15.6094i	0.743911	−	0.670481i
$543$		0			0
$544$	−4.56751	−	7.86657i	−0.195831	−	0.337277i
$545$			11.9223i			0.510697i
$546$		0			0
$547$			3.29589i			0.140922i	0.997515	+	0.0704611i	$0.0224471\pi$
$547$			3.29589i			0.140922i	−0.997515	+	0.0704611i	$0.977553\pi$
$548$	−3.94711	+	37.9118i	−0.168612	+	1.61951i
$549$		0			0
$550$	6.12132	+	6.79172i	0.261014	+	0.289600i
$551$	−20.2904			−0.864399
$552$		0			0
$553$		0			0
$554$	−25.0009	+	22.5331i	−1.06219	+	0.957339i
$555$		0			0
$556$	1.26128	−	12.1146i	0.0534904	−	0.513772i
$557$	31.4532			1.33271			0.666357	−	0.745633i	$-0.267853\pi$
$557$	31.4532			1.33271			0.666357	+	0.745633i	$0.267853\pi$
$558$		0			0
$559$	−26.8826			−1.13701
$560$		0			0
$561$		0			0
$562$	−8.60660	+	7.75706i	−0.363048	+	0.327212i
$563$	3.74761			0.157943			0.0789715	−	0.996877i	$-0.474836\pi$
$563$	3.74761			0.157943			0.0789715	+	0.996877i	$0.474836\pi$
$564$		0			0
$565$			20.2710i			0.852806i
$566$	10.9213	−	9.84332i	0.459058	−	0.413745i
$567$		0			0
$568$	18.3640	−	13.3835i	0.770535	−	0.561559i
$569$	12.0962			0.507100			0.253550	−	0.967322i	$-0.418402\pi$
$569$	12.0962			0.507100			0.253550	+	0.967322i	$0.418402\pi$
$570$		0			0
$571$		−	30.4628i		−	1.27483i	−0.770522	−	0.637413i	$-0.780004\pi$
$571$		−	30.4628i		−	1.27483i	0.770522	−	0.637413i	$-0.219996\pi$
$572$	1.87381	−	17.9978i	0.0783477	−	0.752525i
$573$		0			0
$574$		0			0
$575$			15.6084i			0.650916i
$576$		0			0
$577$			18.8715i			0.785632i	0.919617	+	0.392816i	$0.128499\pi$
$577$			18.8715i			0.785632i	−0.919617	+	0.392816i	$0.871501\pi$
$578$	−15.1422	+	13.6475i	−0.629831	+	0.567661i
$579$		0			0
$580$	15.0720	+	1.56920i	0.625832	+	0.0651573i
$581$		0			0
$582$		0			0
$583$		−	6.59179i		−	0.273004i
$584$	14.1201	−	10.2906i	0.584295	−	0.425829i
$585$		0			0
$586$	−1.15308	−	1.27937i	−0.0476334	−	0.0528501i
$587$	−34.6378			−1.42966			−0.714828	−	0.699300i	$-0.753495\pi$
$587$	−34.6378			−1.42966			−0.714828	+	0.699300i	$0.753495\pi$
$588$		0			0
$589$	44.7696			1.84470
$590$	13.7749	+	15.2835i	0.567104	+	0.629212i
$591$		0			0
$592$	−0.949747	−	0.199929i	−0.0390344	−	0.00821705i
$593$		−	18.4688i		−	0.758421i	−0.925310	−	0.379211i	$-0.876196\pi$
$593$		−	18.4688i		−	0.758421i	0.925310	−	0.379211i	$-0.123804\pi$
$594$		0			0
$595$		0			0
$596$	4.92296	−	47.2847i	0.201652	−	1.93686i
$597$		0			0
$598$	22.9458	−	20.6808i	0.938322	−	0.845702i
$599$			16.5273i			0.675289i	0.941274	+	0.337644i	$0.109630\pi$
$599$			16.5273i			0.675289i	−0.941274	+	0.337644i	$0.890370\pi$
$600$		0			0
$601$		−	16.8925i		−	0.689058i	−0.938776	−	0.344529i	$-0.888039\pi$
$601$		−	16.8925i		−	0.689058i	0.938776	−	0.344529i	$-0.111961\pi$
$602$		0			0
$603$		0			0
$604$	−15.8284	−	1.64795i	−0.644050	−	0.0670540i
$605$		−	6.15626i		−	0.250287i
$606$		0			0
$607$	−2.52257			−0.102388			−0.0511939	−	0.998689i	$-0.516303\pi$
$607$	−2.52257			−0.102388			−0.0511939	+	0.998689i	$0.516303\pi$
$608$	21.0665	−	12.2317i	0.854360	−	0.496061i
$609$		0			0
$610$	5.70711	−	5.14377i	0.231074	−	0.208265i
$611$		−	30.5670i		−	1.23661i
$612$		0			0
$613$	22.0416			0.890253			0.445127	−	0.895468i	$-0.353159\pi$
$613$	22.0416			0.890253			0.445127	+	0.895468i	$0.353159\pi$
$614$	23.7165	−	21.3755i	0.957119	−	0.862644i
$615$		0			0
$616$		0			0
$617$	16.5969			0.668165			0.334082	−	0.942544i	$-0.391574\pi$
$617$	16.5969			0.668165			0.334082	+	0.942544i	$0.391574\pi$
$618$		0			0
$619$	6.09002			0.244778			0.122389	−	0.992482i	$-0.460944\pi$
$619$	6.09002			0.244778			0.122389	+	0.992482i	$0.460944\pi$
$620$	−33.2556	−	3.46234i	−1.33558	−	0.139051i
$621$		0			0
$622$	−22.9458	+	20.6808i	−0.920041	+	0.829226i
$623$		0			0
$624$		0			0
$625$	−7.10051			−0.284020
$626$	5.84875	+	6.48929i	0.233763	+	0.259364i
$627$		0			0
$628$	21.7927	+	2.26890i	0.869623	+	0.0905391i
$629$		−	0.390175i		−	0.0155573i
$630$		0			0
$631$			45.0115i			1.79188i	0.444174	+	0.895941i	$0.353497\pi$
$631$			45.0115i			1.79188i	−0.444174	+	0.895941i	$0.646503\pi$
$632$	7.53375	−	5.49053i	0.299676	−	0.218402i
$633$		0			0
$634$	−10.6569	+	9.60494i	−0.423238	+	0.381461i
$635$	18.0951			0.718081
$636$		0			0
$637$		0			0
$638$	−11.9469	−	13.2553i	−0.472983	−	0.524783i
$639$		0			0
$640$	−16.5945	+	7.45669i	−0.655956	+	0.294752i
$641$	−28.9043			−1.14165			−0.570825	−	0.821072i	$-0.693376\pi$
$641$	−28.9043			−1.14165			−0.570825	+	0.821072i	$0.693376\pi$
$642$		0			0
$643$	45.8915			1.80979			0.904893	−	0.425640i	$-0.139951\pi$
$643$	45.8915			1.80979			0.904893	+	0.425640i	$0.139951\pi$
$644$		0			0
$645$		0			0
$646$	6.55635	+	7.27439i	0.257956	+	0.286207i
$647$	−27.1426			−1.06709			−0.533543	−	0.845773i	$-0.679140\pi$
$647$	−27.1426			−1.06709			−0.533543	+	0.845773i	$0.679140\pi$
$648$		0			0
$649$		−	24.2291i		−	0.951076i
$650$	−7.72255	−	8.56831i	−0.302903	−	0.336077i
$651$		0			0
$652$	−22.3848	−	2.33055i	−0.876655	−	0.0912713i
$653$	−37.3083			−1.45999			−0.729993	−	0.683455i	$-0.760477\pi$
$653$	−37.3083			−1.45999			−0.729993	+	0.683455i	$0.760477\pi$
$654$		0			0
$655$		−	20.5751i		−	0.803935i
$656$	−9.59636	+	45.5867i	−0.374675	+	1.77986i
$657$		0			0
$658$		0			0
$659$			31.6763i			1.23393i	0.786990	+	0.616966i	$0.211639\pi$
$659$			31.6763i			1.23393i	−0.786990	+	0.616966i	$0.788361\pi$
$660$		0			0
$661$			43.5809i			1.69510i	0.530717	+	0.847549i	$0.321923\pi$
$661$			43.5809i			1.69510i	−0.530717	+	0.847549i	$0.678077\pi$
$662$	−21.3087	−	23.6423i	−0.828184	−	0.918886i
$663$		0			0
$664$	21.3151	+	29.2471i	0.827185	+	1.13501i
$665$		0			0
$666$		0			0
$667$		−	30.4628i		−	1.17952i
$668$	4.52377	−	43.4505i	0.175030	−	1.68115i
$669$		0			0
$670$	19.0089	−	17.1326i	0.734378	−	0.661889i
$671$	−9.04753			−0.349276
$672$		0			0
$673$	−16.1005			−0.620629			−0.310314	−	0.950634i	$-0.600434\pi$
$673$	−16.1005			−0.620629			−0.310314	+	0.950634i	$0.600434\pi$
$674$	36.1213	−	32.5558i	1.39134	−	1.25400i
$675$		0			0
$676$	0.328427	−	3.15452i	0.0126318	−	0.121328i
$677$			31.8849i			1.22543i	0.790302	+	0.612717i	$0.209924\pi$
$677$			31.8849i			1.22543i	−0.790302	+	0.612717i	$0.790076\pi$
$678$		0			0
$679$		0			0
$680$	−4.30759	−	5.91059i	−0.165188	−	0.226661i
$681$		0			0
$682$	26.3602	+	29.2471i	1.00938	+	1.11993i
$683$			16.5273i			0.632401i	0.948692	+	0.316201i	$0.102407\pi$
$683$			16.5273i			0.632401i	−0.948692	+	0.316201i	$0.897593\pi$
$684$		0			0
$685$			30.6465i			1.17094i
$686$		0			0
$687$		0			0
$688$	6.55635	−	31.1454i	0.249958	−	1.18741i
$689$			8.31609i			0.316818i
$690$		0			0
$691$	−12.1800			−0.463350			−0.231675	−	0.972793i	$-0.574421\pi$
$691$	−12.1800			−0.463350			−0.231675	+	0.972793i	$0.574421\pi$
$692$	22.3915	+	2.33125i	0.851197	+	0.0886208i
$693$		0			0
$694$	13.2929	+	14.7487i	0.504591	+	0.559853i
$695$		−	9.79298i		−	0.371469i
$696$		0			0
$697$	−18.7279			−0.709371
$698$	−7.72255	−	8.56831i	−0.292303	−	0.324315i
$699$		0			0
$700$		0			0
$701$	19.0583			0.719824			0.359912	−	0.932986i	$-0.382807\pi$
$701$	19.0583			0.719824			0.359912	+	0.932986i	$0.382807\pi$
$702$		0			0
$703$	1.04488			0.0394085
$704$	20.3947	+	6.56037i	0.768653	+	0.247253i
$705$		0			0
$706$	1.15308	+	1.27937i	0.0433968	+	0.0481496i
$707$		0			0
$708$		0			0
$709$	−31.4142			−1.17979			−0.589893	−	0.807482i	$-0.700830\pi$
$709$	−31.4142			−1.17979			−0.589893	+	0.807482i	$0.700830\pi$
$710$	13.5713	−	12.2317i	0.509322	−	0.459048i
$711$		0			0
$712$	0.630642	−	0.459607i	0.0236343	−	0.0172245i
$713$			67.2144i			2.51720i
$714$		0			0
$715$		−	14.5488i		−	0.544093i
$716$	24.8078	+	2.58282i	0.927112	+	0.0965245i
$717$		0			0
$718$	6.12132	+	6.79172i	0.228446	+	0.253465i
$719$	43.6854			1.62919			0.814594	−	0.580031i	$-0.196960\pi$
$719$	43.6854			1.62919			0.814594	+	0.580031i	$0.196960\pi$
$720$		0			0
$721$		0			0
$722$	0.478865	−	0.431597i	0.0178215	−	0.0160624i
$723$		0			0
$724$	29.6664	+	3.08866i	1.10254	+	0.114789i
$725$	−11.3753			−0.422467
$726$		0			0
$727$	1.78372			0.0661547			0.0330773	−	0.999453i	$-0.489469\pi$
$727$	1.78372			0.0661547			0.0330773	+	0.999453i	$0.489469\pi$
$728$		0			0
$729$		0			0
$730$	10.4350	−	9.40501i	0.386218	−	0.348095i
$731$	12.7951			0.473246
$732$		0			0
$733$		−	23.3099i		−	0.860971i	−0.902598	−	0.430485i	$-0.858342\pi$
$733$		−	23.3099i		−	0.860971i	0.902598	−	0.430485i	$-0.141658\pi$
$734$	19.1927	−	17.2982i	0.708416	−	0.638490i
$735$		0			0
$736$	18.3640	+	31.6280i	0.676905	+	1.16582i
$737$	−30.1350			−1.11004
$738$		0			0
$739$		−	31.8280i		−	1.17081i	−0.810741	−	0.585405i	$-0.800935\pi$
$739$		−	31.8280i		−	1.17081i	0.810741	−	0.585405i	$-0.199065\pi$
$740$	−0.776156	−	0.0808080i	−0.0285321	−	0.00297056i
$741$		0			0
$742$		0			0
$743$		−	17.8269i		−	0.654006i	−0.945023	−	0.327003i	$-0.893961\pi$
$743$		−	17.8269i		−	0.654006i	0.945023	−	0.327003i	$-0.106039\pi$
$744$		0			0
$745$		−	38.2233i		−	1.40039i
$746$	−2.97127	+	2.67798i	−0.108786	+	0.0980478i
$747$		0			0
$748$	−0.891862	+	8.56628i	−0.0326097	+	0.313214i
$749$		0			0
$750$		0			0
$751$			36.4891i			1.33150i	0.746173	+	0.665752i	$0.231889\pi$
$751$			36.4891i			1.33150i	−0.746173	+	0.665752i	$0.768111\pi$
$752$	35.4140	+	7.45493i	1.29141	+	0.271853i
$753$		0			0
$754$	15.0720	+	16.7227i	0.548891	+	0.609004i
$755$	−12.7951			−0.465663
$756$		0			0
$757$	11.8995			0.432494			0.216247	−	0.976339i	$-0.430618\pi$
$757$	11.8995			0.432494			0.216247	+	0.976339i	$0.430618\pi$
$758$		0			0
$759$		0			0
$760$	15.8284	−	11.5356i	0.574157	−	0.418441i
$761$		−	8.26875i		−	0.299742i	−0.988706	−	0.149871i	$-0.952114\pi$
$761$		−	8.26875i		−	0.299742i	0.988706	−	0.149871i	$-0.0478858\pi$
$762$		0			0
$763$		0			0
$764$	20.3947	+	2.12335i	0.737853	+	0.0768202i
$765$		0			0
$766$		0			0
$767$			30.5670i			1.10371i
$768$		0			0
$769$		−	43.5809i		−	1.57157i	−0.618502	−	0.785783i	$-0.712260\pi$
$769$		−	43.5809i		−	1.57157i	0.618502	−	0.785783i	$-0.287740\pi$
$770$		0			0
$771$		0			0
$772$	−1.58579	+	15.2314i	−0.0570737	+	0.548189i
$773$			41.7617i			1.50206i	0.660267	+	0.751031i	$0.270443\pi$
$773$			41.7617i			1.50206i	−0.660267	+	0.751031i	$0.729557\pi$
$774$		0			0
$775$	25.0989			0.901580
$776$	29.5652	−	21.5469i	1.06133	−	0.773489i
$777$		0			0
$778$	−0.221825	+	0.199929i	−0.00795283	+	0.00716782i
$779$		−	50.1530i		−	1.79692i
$780$		0			0
$781$	−21.5147			−0.769857
$782$	−10.9213	+	9.84332i	−0.390546	+	0.351996i
$783$		0			0
$784$		0			0
$785$	17.6164			0.628758
$786$		0			0
$787$	44.1078			1.57227			0.786137	−	0.618053i	$-0.212078\pi$
$787$	44.1078			1.57227			0.786137	+	0.618053i	$0.212078\pi$
$788$	−2.10100	+	20.1800i	−0.0748451	+	0.718883i
$789$		0			0
$790$	5.56758	−	5.01801i	0.198085	−	0.178533i
$791$		0			0
$792$		0			0
$793$	11.4142			0.405331
$794$	−6.94640	−	7.70715i	−0.246518	−	0.273517i
$795$		0			0
$796$	−3.04501	+	29.2471i	−0.107927	+	1.03664i
$797$			28.5072i			1.00978i	0.863185	+	0.504888i	$0.168466\pi$
$797$			28.5072i			1.00978i	−0.863185	+	0.504888i	$0.831534\pi$
$798$		0			0
$799$			14.5488i			0.514699i
$800$	11.8104	−	6.85739i	0.417561	−	0.242446i
$801$		0			0
$802$	31.4350	−	28.3321i	1.11001	−	1.00044i
$803$	−16.5428			−0.583781
$804$		0			0
$805$		0			0
$806$	−33.2556	−	36.8977i	−1.17138	−	1.29966i
$807$		0			0
$808$	37.0177	−	26.9782i	1.30228	−	0.949090i
$809$	29.1154			1.02364			0.511822	−	0.859092i	$-0.328971\pi$
$809$	29.1154			1.02364			0.511822	+	0.859092i	$0.328971\pi$
$810$		0			0
$811$	−50.1978			−1.76268			−0.881342	−	0.472479i	$-0.843359\pi$
$811$	−50.1978			−1.76268			−0.881342	+	0.472479i	$0.843359\pi$
$812$		0			0
$813$		0			0
$814$	0.615224	+	0.682602i	0.0215636	+	0.0239252i
$815$	−18.0951			−0.633843
$816$		0			0
$817$			34.2651i			1.19879i
$818$	31.4390	+	34.8822i	1.09924	+	1.21963i
$819$		0			0
$820$	−3.87868	+	37.2545i	−0.135449	+	1.30098i
$821$	19.9905			0.697672			0.348836	−	0.937184i	$-0.386577\pi$
$821$	19.9905			0.697672			0.348836	+	0.937184i	$0.386577\pi$
$822$		0			0
$823$			1.36520i			0.0475880i	0.999717	+	0.0237940i	$0.00757458\pi$
$823$			1.36520i			0.0475880i	−0.999717	+	0.0237940i	$0.992425\pi$
$824$	17.3189	+	23.7639i	0.603333	+	0.827854i
$825$		0			0
$826$		0			0
$827$		−	22.5331i		−	0.783552i	−0.920061	−	0.391776i	$-0.871861\pi$
$827$		−	22.5331i		−	0.783552i	0.920061	−	0.391776i	$-0.128139\pi$
$828$		0			0
$829$		−	0.579658i		−	0.0201323i	−0.999949	−	0.0100662i	$-0.996796\pi$
$829$		−	0.579658i		−	0.0201323i	0.999949	−	0.0100662i	$-0.00320422\pi$
$830$	19.4807	+	21.6142i	0.676184	+	0.750238i
$831$		0			0
$832$	−25.7296	−	8.27645i	−0.892012	−	0.286934i
$833$		0			0
$834$		0			0
$835$		−	35.1239i		−	1.21551i
$836$	−22.9403	−	2.38839i	−0.793408	−	0.0826042i
$837$		0			0
$838$	36.3871	−	32.7954i	1.25697	−	1.13290i
$839$	−39.9377			−1.37880			−0.689402	−	0.724379i	$-0.742127\pi$
$839$	−39.9377			−1.37880			−0.689402	+	0.724379i	$0.742127\pi$
$840$		0			0
$841$	−6.79899			−0.234448
$842$	−16.8080	+	15.1489i	−0.579243	+	0.522067i
$843$		0			0
$844$	−31.6569	−	3.29589i	−1.08967	−	0.113449i
$845$		−	2.55000i		−	0.0877228i
$846$		0			0
$847$		0			0
$848$	−9.63475	−	2.02819i	−0.330859	−	0.0696484i
$849$		0			0
$850$	3.67565	+	4.07820i	0.126074	+	0.139881i
$851$			1.56872i			0.0537752i
$852$		0			0
$853$			39.1425i			1.34021i	0.742265	+	0.670107i	$0.233752\pi$
$853$			39.1425i			1.34021i	−0.742265	+	0.670107i	$0.766248\pi$
$854$		0			0
$855$		0			0
$856$	−14.7782	+	10.7702i	−0.505108	+	0.368118i
$857$			31.8849i			1.08917i	0.838707	+	0.544583i	$0.183312\pi$
$857$			31.8849i			1.08917i	−0.838707	+	0.544583i	$0.816688\pi$
$858$		0			0
$859$	12.9189			0.440786			0.220393	−	0.975411i	$-0.429266\pi$
$859$	12.9189			0.440786			0.220393	+	0.975411i	$0.429266\pi$
$860$	2.64996	−	25.4527i	0.0903629	−	0.867930i
$861$		0			0
$862$	−2.53553	−	2.81322i	−0.0863606	−	0.0958187i
$863$		−	50.6125i		−	1.72287i	−0.507870	−	0.861434i	$-0.669567\pi$
$863$		−	50.6125i		−	1.72287i	0.507870	−	0.861434i	$-0.330433\pi$
$864$		0			0
$865$	18.1005			0.615436
$866$	24.2653	+	26.9228i	0.824569	+	0.914874i
$867$		0			0
$868$		0			0
$869$	−8.82633			−0.299413
$870$		0			0
$871$	38.0178			1.28818
$872$	−12.3511	−	16.9474i	−0.418262	−	0.573911i
$873$		0			0
$874$	−26.3602	−	29.2471i	−0.891647	−	0.989299i
$875$		0			0
$876$		0			0
$877$	−1.75736			−0.0593418			−0.0296709	−	0.999560i	$-0.509446\pi$
$877$	−1.75736			−0.0593418			−0.0296709	+	0.999560i	$0.509446\pi$
$878$	15.4451	−	13.9206i	0.521247	−	0.469796i
$879$		0			0
$880$	16.8557	+	3.54827i	0.568207	+	0.119612i
$881$			33.9974i			1.14540i	0.819765	+	0.572700i	$0.194104\pi$
$881$			33.9974i			1.14540i	−0.819765	+	0.572700i	$0.805896\pi$
$882$		0			0
$883$			44.4461i			1.49573i	0.663852	+	0.747864i	$0.268921\pi$
$883$			44.4461i			1.49573i	−0.663852	+	0.747864i	$0.731079\pi$
$884$	1.12516	−	10.8071i	0.0378432	−	0.363481i
$885$		0			0
$886$	−32.0919	−	35.6065i	−1.07815	−	1.19622i
$887$	9.04753			0.303786			0.151893	−	0.988397i	$-0.451463\pi$
$887$	9.04753			0.303786			0.151893	+	0.988397i	$0.451463\pi$
$888$		0			0
$889$		0			0
$890$	0.466056	−	0.420052i	0.0156222	−	0.0140802i
$891$		0			0
$892$	1.78372	−	17.1326i	0.0597235	−	0.573641i
$893$	−38.9613			−1.30379
$894$		0			0
$895$	20.0538			0.670324
$896$		0			0
$897$		0			0
$898$	9.14214	−	8.23973i	0.305077	−	0.274963i
$899$	−48.9853			−1.63375
$900$		0			0
$901$		−	3.95815i		−	0.131865i
$902$	32.7640	−	29.5299i	1.09092	−	0.983240i
$903$		0			0
$904$	−21.0000	−	28.8148i	−0.698450	−	0.958366i
$905$	23.9813			0.797165
$906$		0			0
$907$		−	21.1406i		−	0.701961i	−0.936383	−	0.350980i	$-0.885848\pi$
$907$		−	21.1406i		−	0.701961i	0.936383	−	0.350980i	$-0.114152\pi$
$908$	−0.776156	+	7.45493i	−0.0257576	+	0.247400i
$909$		0			0
$910$		0			0
$911$			29.4578i			0.975980i	0.872849	+	0.487990i	$0.162270\pi$
$911$			29.4578i			0.975980i	−0.872849	+	0.487990i	$0.837730\pi$
$912$		0			0
$913$		−	34.2651i		−	1.13401i
$914$	−34.1258	+	30.7573i	−1.12878	+	1.01736i
$915$		0			0
$916$	−8.35136	−	0.869487i	−0.275937	−	0.0287286i
$917$		0			0
$918$		0			0
$919$		−	14.5488i		−	0.479920i	−0.970783	−	0.239960i	$-0.922866\pi$
$919$		−	14.5488i		−	0.479920i	0.970783	−	0.239960i	$-0.0771343\pi$
$920$	17.3189	+	23.7639i	0.570988	+	0.783472i
$921$		0			0
$922$	−27.8827	−	30.9364i	−0.918268	−	1.01883i
$923$	27.1426			0.893410
$924$		0			0
$925$	0.585786			0.0192605
$926$	36.3762	+	40.3600i	1.19539	+	1.32631i
$927$		0			0
$928$	−23.0503	+	13.3835i	−0.756662	+	0.439335i
$929$			50.0777i			1.64300i	0.570210	+	0.821499i	$0.306862\pi$
$929$			50.0777i			1.64300i	−0.570210	+	0.821499i	$0.693138\pi$
$930$		0			0
$931$		0			0
$932$	0.764683	−	7.34473i	0.0250480	−	0.240585i
$933$		0			0
$934$	9.50445	−	8.56628i	0.310995	−	0.280297i
$935$			6.92468i			0.226461i
$936$		0			0
$937$		−	49.5181i		−	1.61769i	−0.588025	−	0.808843i	$-0.700094\pi$
$937$		−	49.5181i		−	1.61769i	0.588025	−	0.808843i	$-0.299906\pi$
$938$		0			0
$939$		0			0
$940$	28.9411	+	3.01315i	0.943955	+	0.0982781i
$941$		−	14.0822i		−	0.459066i	−0.973301	−	0.229533i	$-0.926280\pi$
$941$		−	14.0822i		−	0.459066i	0.973301	−	0.229533i	$-0.0737198\pi$
$942$		0			0
$943$	75.2967			2.45200
$944$	−35.4140	−	7.45493i	−1.15263	−	0.242637i
$945$		0			0
$946$	−22.3848	+	20.1752i	−0.727792	+	0.655953i
$947$			20.3146i			0.660135i	0.943957	+	0.330068i	$0.107072\pi$
$947$			20.3146i			0.660135i	−0.943957	+	0.330068i	$0.892928\pi$
$948$		0			0
$949$	20.8701			0.677471
$950$	−10.9213	+	9.84332i	−0.354335	+	0.319359i
$951$		0			0
$952$		0			0
$953$	31.1546			1.00920			0.504598	−	0.863355i	$-0.331641\pi$
$953$	31.1546			1.00920			0.504598	+	0.863355i	$0.331641\pi$
$954$		0			0
$955$	16.4863			0.533485
$956$	2.20658	+	0.229734i	0.0713660	+	0.00743014i
$957$		0			0
$958$	36.3871	−	32.7954i	1.17561	−	1.05957i
$959$		0			0
$960$		0			0
$961$	77.0833			2.48656
$962$	−0.776156	−	0.861159i	−0.0250243	−	0.0277649i
$963$		0			0
$964$	−2.78379	−	0.289829i	−0.0896598	−	0.00933476i
$965$			12.3125i			0.396354i
$966$		0			0
$967$			15.9140i			0.511759i	0.966709	+	0.255880i	$0.0823651\pi$
$967$			15.9140i			0.511759i	−0.966709	+	0.255880i	$0.917635\pi$
$968$	6.37767	+	8.75101i	0.204986	+	0.281268i
$969$		0			0
$970$	21.8492	−	19.6925i	0.701537	−	0.632290i
$971$	48.9853			1.57201			0.786006	−	0.618219i	$-0.212145\pi$
$971$	48.9853			1.57201			0.786006	+	0.618219i	$0.212145\pi$
$972$		0			0
$973$		0			0
$974$	−13.7749	−	15.2835i	−0.441377	−	0.489715i
$975$		0			0
$976$	−2.78379	+	13.2241i	−0.0891069	+	0.423294i
$977$	42.8285			1.37020			0.685102	−	0.728447i	$-0.259758\pi$
$977$	42.8285			1.37020			0.685102	+	0.728447i	$0.259758\pi$
$978$		0			0
$979$	−0.738843			−0.0236135
$980$		0			0
$981$		0			0
$982$	−30.6066	−	33.9586i	−0.976696	−	1.08366i
$983$	18.0951			0.577143			0.288572	−	0.957458i	$-0.406820\pi$
$983$	18.0951			0.577143			0.288572	+	0.957458i	$0.406820\pi$
$984$		0			0
$985$			16.3128i			0.519769i
$986$	−7.17373	−	7.95938i	−0.228458	−	0.253478i
$987$		0			0
$988$	28.9411	+	3.01315i	0.920740	+	0.0958611i
$989$	−51.4436			−1.63581
$990$		0			0
$991$		−	3.29589i		−	0.104698i	−0.998629	−	0.0523488i	$-0.983329\pi$
$991$		−	3.29589i		−	0.104698i	0.998629	−	0.0523488i	$-0.0166707\pi$
$992$	50.8591	−	29.5299i	1.61478	−	0.937577i
$993$		0			0
$994$		0			0
$995$			23.6423i			0.749513i
$996$		0			0
$997$			30.0669i			0.952228i	0.879384	+	0.476114i	$0.157955\pi$
$997$			30.0669i			0.952228i	−0.879384	+	0.476114i	$0.842045\pi$
$998$	−18.1881	−	20.1800i	−0.575734	−	0.638787i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.b.n.1567.3	yes	16
3.2	odd	2	inner	1764.2.b.n.1567.14	yes	16
4.3	odd	2	inner	1764.2.b.n.1567.1	✓	16
7.6	odd	2	inner	1764.2.b.n.1567.4	yes	16
12.11	even	2	inner	1764.2.b.n.1567.16	yes	16
21.20	even	2	inner	1764.2.b.n.1567.13	yes	16
28.27	even	2	inner	1764.2.b.n.1567.2	yes	16
84.83	odd	2	inner	1764.2.b.n.1567.15	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1764.2.b.n.1567.1	✓	16	4.3	odd	2	inner
1764.2.b.n.1567.2	yes	16	28.27	even	2	inner
1764.2.b.n.1567.3	yes	16	1.1	even	1	trivial
1764.2.b.n.1567.4	yes	16	7.6	odd	2	inner
1764.2.b.n.1567.13	yes	16	21.20	even	2	inner
1764.2.b.n.1567.14	yes	16	3.2	odd	2	inner
1764.2.b.n.1567.15	yes	16	84.83	odd	2	inner
1764.2.b.n.1567.16	yes	16	12.11	even	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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05050 + 0.946809i) q^{2} +(0.207107 - 1.98925i) q^{4} -1.60804i q^{5} +(1.66587 + 2.28580i) q^{8} +O(q^{10})\)	\(q+(-1.05050 + 0.946809i) q^{2} +(0.207107 - 1.98925i) q^{4} -1.60804i q^{5} +(1.66587 + 2.28580i) q^{8} +(1.52250 + 1.68925i) q^{10} -2.67798i q^{11} +3.37849i q^{13} +(-3.91421 - 0.823973i) q^{16} -1.60804i q^{17} +4.30629 q^{19} +(-3.19879 - 0.333036i) q^{20} +(2.53553 + 2.81322i) q^{22} +6.46521i q^{23} +2.41421 q^{25} +(-3.19879 - 3.54911i) q^{26} -4.71179 q^{29} +10.3963 q^{31} +(4.89203 - 2.84043i) q^{32} +(1.52250 + 1.68925i) q^{34} +0.242641 q^{37} +(-4.52377 + 4.07724i) q^{38} +(3.67565 - 2.67878i) q^{40} -11.6464i q^{41} +7.95699i q^{43} +(-5.32716 - 0.554628i) q^{44} +(-6.12132 - 6.79172i) q^{46} -9.04753 q^{47} +(-2.53613 + 2.28580i) q^{50} +(6.72066 + 0.699709i) q^{52} +2.46148 q^{53} -4.30629 q^{55} +(4.94975 - 4.46117i) q^{58} +9.04753 q^{59} -3.37849i q^{61} +(-10.9213 + 9.84332i) q^{62} +(-2.44975 + 7.61569i) q^{64} +5.43275 q^{65} -11.2529i q^{67} +(-3.19879 - 0.333036i) q^{68} -8.03394i q^{71} -6.17733i q^{73} +(-0.254894 + 0.229734i) q^{74} +(0.891862 - 8.56628i) q^{76} -3.29589i q^{79} +(-1.32498 + 6.29420i) q^{80} +(11.0270 + 12.2346i) q^{82} +12.7951 q^{83} -2.58579 q^{85} +(-7.53375 - 8.35883i) q^{86} +(6.12132 - 4.46117i) q^{88} -0.275896i q^{89} +(12.8609 + 1.33899i) q^{92} +(9.50445 - 8.56628i) q^{94} -6.92468i q^{95} -12.9343i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{4}+O(q^{10}) \) 16 * q - 8 * q^4	\( 16 q - 8 q^{4} - 40 q^{16} - 16 q^{22} + 16 q^{25} - 64 q^{37} - 64 q^{46} + 40 q^{64} - 64 q^{85} + 64 q^{88}+O(q^{100}) \) 16 * q - 8 * q^4 - 40 * q^16 - 16 * q^22 + 16 * q^25 - 64 * q^37 - 64 * q^46 + 40 * q^64 - 64 * q^85 + 64 * q^88

Introduction

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