LMFDB - Embedded newform 504.3.e.a.251.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,3,Mod(251,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.251"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	504.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-128] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(16)] == traces)

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

Self dual:	no
Analytic conductor:	$13.7330053238$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.2
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	504.251
Dual form			504.3.e.a.251.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41421 - 1.41421i) q^{2} +4.00000i q^{4} +6.92820i q^{5} +(-4.89898 - 5.00000i) q^{7} +(5.65685 - 5.65685i) q^{8} +(9.79796 - 9.79796i) q^{10} -9.89949i q^{11} -19.5959 q^{13} +(-0.142865 + 13.9993i) q^{14} -16.0000 q^{16} +6.92820 q^{17} -9.79796i q^{19} -27.7128 q^{20} +(-14.0000 + 14.0000i) q^{22} +41.0122 q^{23} -23.0000 q^{25} +(27.7128 + 27.7128i) q^{26} +(20.0000 - 19.5959i) q^{28} +18.3848 q^{29} +39.1918 q^{31} +(22.6274 + 22.6274i) q^{32} +(-9.79796 - 9.79796i) q^{34} +(34.6410 - 33.9411i) q^{35} -26.0000i q^{37} +(-13.8564 + 13.8564i) q^{38} +(39.1918 + 39.1918i) q^{40} +62.3538 q^{41} +48.0000 q^{43} +39.5980 q^{44} +(-58.0000 - 58.0000i) q^{46} +27.7128i q^{47} +(-1.00000 + 48.9898i) q^{49} +(32.5269 + 32.5269i) q^{50} -78.3837i q^{52} -52.3259 q^{53} +68.5857 q^{55} +(-55.9971 - 0.571458i) q^{56} +(-26.0000 - 26.0000i) q^{58} -69.2820 q^{59} +29.3939 q^{61} +(-55.4256 - 55.4256i) q^{62} -64.0000i q^{64} -135.765i q^{65} -14.0000 q^{67} +27.7128i q^{68} +(-96.9898 - 0.989795i) q^{70} -41.0122 q^{71} -29.3939i q^{73} +(-36.7696 + 36.7696i) q^{74} +39.1918 q^{76} +(-49.4975 + 48.4974i) q^{77} -48.0000i q^{79} -110.851i q^{80} +(-88.1816 - 88.1816i) q^{82} +110.851 q^{83} +48.0000i q^{85} +(-67.8823 - 67.8823i) q^{86} +(-56.0000 - 56.0000i) q^{88} +145.492 q^{89} +(96.0000 + 97.9796i) q^{91} +164.049i q^{92} +(39.1918 - 39.1918i) q^{94} +67.8823 q^{95} -166.565i q^{97} +(70.6962 - 67.8678i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 128 q^{16} - 112 q^{22} - 184 q^{25} + 160 q^{28} + 384 q^{43} - 464 q^{46} - 8 q^{49} - 208 q^{58} - 112 q^{67} - 384 q^{70} - 448 q^{88} + 768 q^{91}+O(q^{100}) $ 8 * q - 128 * q^16 - 112 * q^22 - 184 * q^25 + 160 * q^28 + 384 * q^43 - 464 * q^46 - 8 * q^49 - 208 * q^58 - 112 * q^67 - 384 * q^70 - 448 * q^88 + 768 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	−1.41421	−	1.41421i	−0.707107	−	0.707107i
$2$	−1.41421	−	1.41421i	−0.707107	−	0.707107i
$3$		0			0
$3$		0			0
$4$			4.00000i			1.00000i
$5$			6.92820i			1.38564i	0.721110	+	0.692820i	$0.243632\pi$
$5$			6.92820i			1.38564i	−0.721110	+	0.692820i	$0.756368\pi$
$6$		0			0
$7$	−4.89898	−	5.00000i	−0.699854	−	0.714286i
$7$	−4.89898	−	5.00000i	−0.699854	−	0.714286i
$8$	5.65685	−	5.65685i	0.707107	−	0.707107i
$9$		0			0
$10$	9.79796	−	9.79796i	0.979796	−	0.979796i
$11$		−	9.89949i		−	0.899954i	−0.893040	−	0.449977i	$-0.851432\pi$
$11$		−	9.89949i		−	0.899954i	0.893040	−	0.449977i	$-0.148568\pi$
$12$		0			0
$13$	−19.5959			−1.50738			−0.753689	−	0.657231i	$-0.771728\pi$
$13$	−19.5959			−1.50738			−0.753689	+	0.657231i	$0.771728\pi$
$14$	−0.142865	+	13.9993i	−0.0102046	+	0.999948i
$15$		0			0
$16$	−16.0000			−1.00000
$17$	6.92820			0.407541			0.203771	−	0.979019i	$-0.434680\pi$
$17$	6.92820			0.407541			0.203771	+	0.979019i	$0.434680\pi$
$18$		0			0
$19$		−	9.79796i		−	0.515682i	−0.966187	−	0.257841i	$-0.916989\pi$
$19$		−	9.79796i		−	0.515682i	0.966187	−	0.257841i	$-0.0830111\pi$
$20$	−27.7128			−1.38564
$21$		0			0
$22$	−14.0000	+	14.0000i	−0.636364	+	0.636364i
$23$	41.0122			1.78314			0.891569	−	0.452884i	$-0.149605\pi$
$23$	41.0122			1.78314			0.891569	+	0.452884i	$0.149605\pi$
$24$		0			0
$25$	−23.0000			−0.920000
$26$	27.7128	+	27.7128i	1.06588	+	1.06588i
$27$		0			0
$28$	20.0000	−	19.5959i	0.714286	−	0.699854i
$29$	18.3848			0.633958			0.316979	−	0.948433i	$-0.397332\pi$
$29$	18.3848			0.633958			0.316979	+	0.948433i	$0.397332\pi$
$30$		0			0
$31$	39.1918			1.26425			0.632126	−	0.774865i	$-0.282182\pi$
$31$	39.1918			1.26425			0.632126	+	0.774865i	$0.282182\pi$
$32$	22.6274	+	22.6274i	0.707107	+	0.707107i
$33$		0			0
$34$	−9.79796	−	9.79796i	−0.288175	−	0.288175i
$35$	34.6410	−	33.9411i	0.989743	−	0.969746i
$36$		0			0
$37$		−	26.0000i		−	0.702703i	−0.936244	−	0.351351i	$-0.885722\pi$
$37$		−	26.0000i		−	0.702703i	0.936244	−	0.351351i	$-0.114278\pi$
$38$	−13.8564	+	13.8564i	−0.364642	+	0.364642i
$39$		0			0
$40$	39.1918	+	39.1918i	0.979796	+	0.979796i
$41$	62.3538			1.52083			0.760413	−	0.649440i	$-0.224997\pi$
$41$	62.3538			1.52083			0.760413	+	0.649440i	$0.224997\pi$
$42$		0			0
$43$	48.0000			1.11628			0.558140	−	0.829747i	$-0.311515\pi$
$43$	48.0000			1.11628			0.558140	+	0.829747i	$0.311515\pi$
$44$	39.5980			0.899954
$45$		0			0
$46$	−58.0000	−	58.0000i	−1.26087	−	1.26087i
$47$			27.7128i			0.589634i	0.955554	+	0.294817i	$0.0952587\pi$
$47$			27.7128i			0.589634i	−0.955554	+	0.294817i	$0.904741\pi$
$48$		0			0
$49$	−1.00000	+	48.9898i	−0.0204082	+	0.999792i
$50$	32.5269	+	32.5269i	0.650538	+	0.650538i
$51$		0			0
$52$		−	78.3837i		−	1.50738i
$53$	−52.3259			−0.987281			−0.493641	−	0.869666i	$-0.664334\pi$
$53$	−52.3259			−0.987281			−0.493641	+	0.869666i	$0.664334\pi$
$54$		0			0
$55$	68.5857			1.24701
$56$	−55.9971	−	0.571458i	−0.999948	−	0.0102046i
$57$		0			0
$58$	−26.0000	−	26.0000i	−0.448276	−	0.448276i
$59$	−69.2820			−1.17427			−0.587136	−	0.809488i	$-0.699745\pi$
$59$	−69.2820			−1.17427			−0.587136	+	0.809488i	$0.699745\pi$
$60$		0			0
$61$	29.3939			0.481867			0.240933	−	0.970542i	$-0.422546\pi$
$61$	29.3939			0.481867			0.240933	+	0.970542i	$0.422546\pi$
$62$	−55.4256	−	55.4256i	−0.893962	−	0.893962i
$63$		0			0
$64$		−	64.0000i		−	1.00000i
$65$		−	135.765i		−	2.08868i
$66$		0			0
$67$	−14.0000			−0.208955			−0.104478	−	0.994527i	$-0.533317\pi$
$67$	−14.0000			−0.208955			−0.104478	+	0.994527i	$0.533317\pi$
$68$			27.7128i			0.407541i
$69$		0			0
$70$	−96.9898	−	0.989795i	−1.38557	−	0.0141399i
$71$	−41.0122			−0.577637			−0.288818	−	0.957384i	$-0.593262\pi$
$71$	−41.0122			−0.577637			−0.288818	+	0.957384i	$0.593262\pi$
$72$		0			0
$73$		−	29.3939i		−	0.402656i	−0.979524	−	0.201328i	$-0.935474\pi$
$73$		−	29.3939i		−	0.402656i	0.979524	−	0.201328i	$-0.0645257\pi$
$74$	−36.7696	+	36.7696i	−0.496886	+	0.496886i
$75$		0			0
$76$	39.1918			0.515682
$77$	−49.4975	+	48.4974i	−0.642824	+	0.629837i
$78$		0			0
$79$		−	48.0000i		−	0.607595i	−0.952737	−	0.303797i	$-0.901745\pi$
$79$		−	48.0000i		−	0.607595i	0.952737	−	0.303797i	$-0.0982546\pi$
$80$		−	110.851i		−	1.38564i
$81$		0			0
$82$	−88.1816	−	88.1816i	−1.07539	−	1.07539i
$83$	110.851			1.33556			0.667779	−	0.744360i	$-0.267245\pi$
$83$	110.851			1.33556			0.667779	+	0.744360i	$0.267245\pi$
$84$		0			0
$85$			48.0000i			0.564706i
$86$	−67.8823	−	67.8823i	−0.789328	−	0.789328i
$87$		0			0
$88$	−56.0000	−	56.0000i	−0.636364	−	0.636364i
$89$	145.492			1.63474			0.817372	−	0.576110i	$-0.195430\pi$
$89$	145.492			1.63474			0.817372	+	0.576110i	$0.195430\pi$
$90$		0			0
$91$	96.0000	+	97.9796i	1.05495	+	1.07670i
$92$			164.049i			1.78314i
$93$		0			0
$94$	39.1918	−	39.1918i	0.416934	−	0.416934i
$95$	67.8823			0.714550
$96$		0			0
$97$		−	166.565i		−	1.71717i	−0.512673	−	0.858584i	$-0.671345\pi$
$97$		−	166.565i		−	1.71717i	0.512673	−	0.858584i	$-0.328655\pi$
$98$	70.6962	−	67.8678i	0.721390	−	0.692529i
$99$		0			0
$100$		−	92.0000i		−	0.920000i
$101$		−	159.349i		−	1.57771i	−0.614580	−	0.788855i	$-0.710674\pi$
$101$		−	159.349i		−	1.57771i	0.614580	−	0.788855i	$-0.289326\pi$
$102$		0			0
$103$	−97.9796			−0.951258			−0.475629	−	0.879646i	$-0.657780\pi$
$103$	−97.9796			−0.951258			−0.475629	+	0.879646i	$0.657780\pi$
$104$	−110.851	+	110.851i	−1.06588	+	1.06588i
$105$		0			0
$106$	74.0000	+	74.0000i	0.698113	+	0.698113i
$107$		−	57.9828i		−	0.541895i	−0.962594	−	0.270947i	$-0.912663\pi$
$107$		−	57.9828i		−	0.541895i	0.962594	−	0.270947i	$-0.0873370\pi$
$108$		0			0
$109$			122.000i			1.11927i	0.828741	+	0.559633i	$0.189058\pi$
$109$			122.000i			1.11927i	−0.828741	+	0.559633i	$0.810942\pi$
$110$	−96.9948	−	96.9948i	−0.881771	−	0.881771i
$111$		0			0
$112$	78.3837	+	80.0000i	0.699854	+	0.714286i
$113$		−	66.4680i		−	0.588213i	−0.955773	−	0.294106i	$-0.904978\pi$
$113$		−	66.4680i		−	0.588213i	0.955773	−	0.294106i	$-0.0950220\pi$
$114$		0			0
$115$			284.141i			2.47079i
$116$			73.5391i			0.633958i
$117$		0			0
$118$	97.9796	+	97.9796i	0.830336	+	0.830336i
$119$	−33.9411	−	34.6410i	−0.285220	−	0.291101i
$120$		0			0
$121$	23.0000			0.190083
$122$	−41.5692	−	41.5692i	−0.340731	−	0.340731i
$123$		0			0
$124$			156.767i			1.26425i
$125$			13.8564i			0.110851i
$126$		0			0
$127$		−	240.000i		−	1.88976i	−0.327411	−	0.944882i	$-0.606176\pi$
$127$		−	240.000i		−	1.88976i	0.327411	−	0.944882i	$-0.393824\pi$
$128$	−90.5097	+	90.5097i	−0.707107	+	0.707107i
$129$		0			0
$130$	−192.000	+	192.000i	−1.47692	+	1.47692i
$131$	−27.7128			−0.211548			−0.105774	−	0.994390i	$-0.533732\pi$
$131$	−27.7128			−0.211548			−0.105774	+	0.994390i	$0.533732\pi$
$132$		0			0
$133$	−48.9898	+	48.0000i	−0.368344	+	0.360902i
$134$	19.7990	+	19.7990i	0.147754	+	0.147754i
$135$		0			0
$136$	39.1918	−	39.1918i	0.288175	−	0.288175i
$137$			35.3553i			0.258068i	0.991640	+	0.129034i	$0.0411877\pi$
$137$			35.3553i			0.258068i	−0.991640	+	0.129034i	$0.958812\pi$
$138$		0			0
$139$			19.5959i			0.140978i	0.997513	+	0.0704889i	$0.0224559\pi$
$139$			19.5959i			0.140978i	−0.997513	+	0.0704889i	$0.977544\pi$
$140$	135.765	+	138.564i	0.969746	+	0.989743i
$141$		0			0
$142$	58.0000	+	58.0000i	0.408451	+	0.408451i
$143$			193.990i			1.35657i
$144$		0			0
$145$			127.373i			0.878438i
$146$	−41.5692	+	41.5692i	−0.284721	+	0.284721i
$147$		0			0
$148$	104.000			0.702703
$149$	151.321			1.01558			0.507788	−	0.861482i	$-0.330463\pi$
$149$	151.321			1.01558			0.507788	+	0.861482i	$0.330463\pi$
$150$		0			0
$151$			10.0000i			0.0662252i	0.999452	+	0.0331126i	$0.0105420\pi$
$151$			10.0000i			0.0662252i	−0.999452	+	0.0331126i	$0.989458\pi$
$152$	−55.4256	−	55.4256i	−0.364642	−	0.364642i
$153$		0			0
$154$	138.586	+	1.41429i	0.899907	+	0.00918368i
$155$			271.529i			1.75180i
$156$		0			0
$157$	−205.757			−1.31056			−0.655278	−	0.755388i	$-0.727448\pi$
$157$	−205.757			−1.31056			−0.655278	+	0.755388i	$0.727448\pi$
$158$	−67.8823	+	67.8823i	−0.429634	+	0.429634i
$159$		0			0
$160$	−156.767	+	156.767i	−0.979796	+	0.979796i
$161$	−200.918	−	205.061i	−1.24794	−	1.27367i
$162$		0			0
$163$	302.000			1.85276			0.926380	−	0.376589i	$-0.122903\pi$
$163$	302.000			1.85276			0.926380	+	0.376589i	$0.122903\pi$
$164$			249.415i			1.52083i
$165$		0			0
$166$	−156.767	−	156.767i	−0.944382	−	0.944382i
$167$		−	69.2820i		−	0.414862i	−0.978250	−	0.207431i	$-0.933490\pi$
$167$		−	69.2820i		−	0.414862i	0.978250	−	0.207431i	$-0.0665103\pi$
$168$		0			0
$169$	215.000			1.27219
$170$	67.8823	−	67.8823i	0.399307	−	0.399307i
$171$		0			0
$172$			192.000i			1.11628i
$173$		−	297.913i		−	1.72204i	−0.508572	−	0.861019i	$-0.669826\pi$
$173$		−	297.913i		−	1.72204i	0.508572	−	0.861019i	$-0.330174\pi$
$174$		0			0
$175$	112.677	+	115.000i	0.643866	+	0.657143i
$176$			158.392i			0.899954i
$177$		0			0
$178$	−205.757	−	205.757i	−1.15594	−	1.15594i
$179$			111.723i			0.624150i	0.950057	+	0.312075i	$0.101024\pi$
$179$			111.723i			0.624150i	−0.950057	+	0.312075i	$0.898976\pi$
$180$		0			0
$181$	−235.151			−1.29918			−0.649588	−	0.760286i	$-0.725059\pi$
$181$	−235.151			−1.29918			−0.649588	+	0.760286i	$0.725059\pi$
$182$	2.79956	−	274.329i	0.0153822	−	1.50730i
$183$		0			0
$184$	232.000	−	232.000i	1.26087	−	1.26087i
$185$	180.133			0.973693
$186$		0			0
$187$		−	68.5857i		−	0.366769i
$188$	−110.851			−0.589634
$189$		0			0
$190$	−96.0000	−	96.0000i	−0.505263	−	0.505263i
$191$	74.9533			0.392426			0.196213	−	0.980561i	$-0.437136\pi$
$191$	74.9533			0.392426			0.196213	+	0.980561i	$0.437136\pi$
$192$		0			0
$193$	−336.000			−1.74093			−0.870466	−	0.492228i	$-0.836183\pi$
$193$	−336.000			−1.74093			−0.870466	+	0.492228i	$0.836183\pi$
$194$	−235.559	+	235.559i	−1.21422	+	1.21422i
$195$		0			0
$196$	−195.959	−	4.00000i	−0.999792	−	0.0204082i
$197$	−188.090			−0.954774			−0.477387	−	0.878693i	$-0.658416\pi$
$197$	−188.090			−0.954774			−0.477387	+	0.878693i	$0.658416\pi$
$198$		0			0
$199$	88.1816			0.443124			0.221562	−	0.975146i	$-0.428885\pi$
$199$	88.1816			0.443124			0.221562	+	0.975146i	$0.428885\pi$
$200$	−130.108	+	130.108i	−0.650538	+	0.650538i
$201$		0			0
$202$	−225.353	+	225.353i	−1.11561	+	1.11561i
$203$	−90.0666	−	91.9239i	−0.443678	−	0.452827i
$204$		0			0
$205$			432.000i			2.10732i
$206$	138.564	+	138.564i	0.672641	+	0.672641i
$207$		0			0
$208$	313.535			1.50738
$209$	−96.9948			−0.464090
$210$		0			0
$211$	144.000			0.682464			0.341232	−	0.939979i	$-0.389156\pi$
$211$	144.000			0.682464			0.341232	+	0.939979i	$0.389156\pi$
$212$		−	209.304i		−	0.987281i
$213$		0			0
$214$	−82.0000	+	82.0000i	−0.383178	+	0.383178i
$215$			332.554i			1.54676i
$216$		0			0
$217$	−192.000	−	195.959i	−0.884793	−	0.903038i
$218$	172.534	−	172.534i	0.791441	−	0.791441i
$219$		0			0
$220$			274.343i			1.24701i
$221$	−135.765			−0.614319
$222$		0			0
$223$	107.778			0.483307			0.241654	−	0.970363i	$-0.422310\pi$
$223$	107.778			0.483307			0.241654	+	0.970363i	$0.422310\pi$
$224$	2.28583	−	223.988i	0.0102046	−	0.999948i
$225$		0			0
$226$	−94.0000	+	94.0000i	−0.415929	+	0.415929i
$227$	−166.277			−0.732497			−0.366249	−	0.930517i	$-0.619358\pi$
$227$	−166.277			−0.732497			−0.366249	+	0.930517i	$0.619358\pi$
$228$		0			0
$229$	78.3837			0.342287			0.171143	−	0.985246i	$-0.445254\pi$
$229$	78.3837			0.342287			0.171143	+	0.985246i	$0.445254\pi$
$230$	401.836	−	401.836i	1.74711	−	1.74711i
$231$		0			0
$232$	104.000	−	104.000i	0.448276	−	0.448276i
$233$			100.409i			0.430941i	0.976510	+	0.215470i	$0.0691284\pi$
$233$			100.409i			0.430941i	−0.976510	+	0.215470i	$0.930872\pi$
$234$		0			0
$235$	−192.000			−0.817021
$236$		−	277.128i		−	1.17427i
$237$		0			0
$238$	−0.989795	+	96.9898i	−0.00415880	+	0.407520i
$239$	264.458			1.10652			0.553259	−	0.833009i	$-0.313384\pi$
$239$	264.458			1.10652			0.553259	+	0.833009i	$0.313384\pi$
$240$		0			0
$241$			225.353i			0.935075i	0.883973	+	0.467537i	$0.154859\pi$
$241$			225.353i			0.935075i	−0.883973	+	0.467537i	$0.845141\pi$
$242$	−32.5269	−	32.5269i	−0.134409	−	0.134409i
$243$		0			0
$244$			117.576i			0.481867i
$245$	−339.411	−	6.92820i	−1.38535	−	0.0282784i
$246$		0			0
$247$			192.000i			0.777328i
$248$	221.703	−	221.703i	0.893962	−	0.893962i
$249$		0			0
$250$	19.5959	−	19.5959i	0.0783837	−	0.0783837i
$251$	13.8564			0.0552048			0.0276024	−	0.999619i	$-0.491213\pi$
$251$	13.8564			0.0552048			0.0276024	+	0.999619i	$0.491213\pi$
$252$		0			0
$253$		−	406.000i		−	1.60474i
$254$	−339.411	+	339.411i	−1.33626	+	1.33626i
$255$		0			0
$256$	256.000			1.00000
$257$	242.487			0.943530			0.471765	−	0.881724i	$-0.343617\pi$
$257$	242.487			0.943530			0.471765	+	0.881724i	$0.343617\pi$
$258$		0			0
$259$	−130.000	+	127.373i	−0.501931	+	0.491789i
$260$	543.058			2.08868
$261$		0			0
$262$	39.1918	+	39.1918i	0.149587	+	0.149587i
$263$	94.7523			0.360275			0.180137	−	0.983641i	$-0.442346\pi$
$263$	94.7523			0.360275			0.180137	+	0.983641i	$0.442346\pi$
$264$		0			0
$265$		−	362.524i		−	1.36802i
$266$	137.164	+	1.39978i	0.515655	+	0.00526234i
$267$		0			0
$268$		−	56.0000i		−	0.208955i
$269$			297.913i			1.10748i	0.832689	+	0.553741i	$0.186800\pi$
$269$			297.913i			1.10748i	−0.832689	+	0.553741i	$0.813200\pi$
$270$		0			0
$271$	254.747			0.940026			0.470013	−	0.882660i	$-0.344249\pi$
$271$	254.747			0.940026			0.470013	+	0.882660i	$0.344249\pi$
$272$	−110.851			−0.407541
$273$		0			0
$274$	50.0000	−	50.0000i	0.182482	−	0.182482i
$275$			227.688i			0.827958i
$276$		0			0
$277$			336.000i			1.21300i	0.795085	+	0.606498i	$0.207426\pi$
$277$			336.000i			1.21300i	−0.795085	+	0.606498i	$0.792574\pi$
$278$	27.7128	−	27.7128i	0.0996864	−	0.0996864i
$279$		0			0
$280$	3.95918	−	387.959i	0.0141399	−	1.38557i
$281$			371.938i			1.32362i	0.749670	+	0.661812i	$0.230212\pi$
$281$			371.938i			1.32362i	−0.749670	+	0.661812i	$0.769788\pi$
$282$		0			0
$283$		−	460.504i		−	1.62722i	−0.581409	−	0.813611i	$-0.697498\pi$
$283$		−	460.504i		−	1.62722i	0.581409	−	0.813611i	$-0.302502\pi$
$284$		−	164.049i		−	0.577637i
$285$		0			0
$286$	274.343	−	274.343i	0.959241	−	0.959241i
$287$	−305.470	−	311.769i	−1.06436	−	1.08630i
$288$		0			0
$289$	−241.000			−0.833910
$290$	180.133	−	180.133i	0.621149	−	0.621149i
$291$		0			0
$292$	117.576			0.402656
$293$			242.487i			0.827601i	0.910368	+	0.413801i	$0.135799\pi$
$293$			242.487i			0.827601i	−0.910368	+	0.413801i	$0.864201\pi$
$294$		0			0
$295$		−	480.000i		−	1.62712i
$296$	−147.078	−	147.078i	−0.496886	−	0.496886i
$297$		0			0
$298$	−214.000	−	214.000i	−0.718121	−	0.718121i
$299$	−803.672			−2.68786
$300$		0			0
$301$	−235.151	−	240.000i	−0.781233	−	0.797342i
$302$	14.1421	−	14.1421i	0.0468283	−	0.0468283i
$303$		0			0
$304$			156.767i			0.515682i
$305$			203.647i			0.667694i
$306$		0			0
$307$			303.737i			0.989370i	0.869072	+	0.494685i	$0.164717\pi$
$307$			303.737i			0.989370i	−0.869072	+	0.494685i	$0.835283\pi$
$308$	−193.990	−	197.990i	−0.629837	−	0.642824i
$309$		0			0
$310$	384.000	−	384.000i	1.23871	−	1.23871i
$311$		−	235.559i		−	0.757424i	−0.925515	−	0.378712i	$-0.876367\pi$
$311$		−	235.559i		−	0.757424i	0.925515	−	0.378712i	$-0.123633\pi$
$312$		0			0
$313$		−	333.131i		−	1.06432i	−0.846645	−	0.532158i	$-0.821381\pi$
$313$		−	333.131i		−	1.06432i	0.846645	−	0.532158i	$-0.178619\pi$
$314$	290.985	+	290.985i	0.926702	+	0.926702i
$315$		0			0
$316$	192.000			0.607595
$317$	222.032			0.700415			0.350207	−	0.936672i	$-0.386111\pi$
$317$	222.032			0.700415			0.350207	+	0.936672i	$0.386111\pi$
$318$		0			0
$319$		−	182.000i		−	0.570533i
$320$	443.405			1.38564
$321$		0			0
$322$	−5.85919	+	574.141i	−0.0181962	+	1.78305i
$323$		−	67.8823i		−	0.210162i
$324$		0			0
$325$	450.706			1.38679
$326$	−427.092	−	427.092i	−1.31010	−	1.31010i
$327$		0			0
$328$	352.727	−	352.727i	1.07539	−	1.07539i
$329$	138.564	−	135.765i	0.421167	−	0.412658i
$330$		0			0
$331$	144.000			0.435045			0.217523	−	0.976055i	$-0.430202\pi$
$331$	144.000			0.435045			0.217523	+	0.976055i	$0.430202\pi$
$332$			443.405i			1.33556i
$333$		0			0
$334$	−97.9796	+	97.9796i	−0.293352	+	0.293352i
$335$		−	96.9948i		−	0.289537i
$336$		0			0
$337$	−480.000			−1.42433			−0.712166	−	0.702011i	$-0.752286\pi$
$337$	−480.000			−1.42433			−0.712166	+	0.702011i	$0.752286\pi$
$338$	−304.056	−	304.056i	−0.899574	−	0.899574i
$339$		0			0
$340$	−192.000			−0.564706
$341$		−	387.979i		−	1.13777i
$342$		0			0
$343$	249.848	−	235.000i	0.728420	−	0.685131i
$344$	271.529	−	271.529i	0.789328	−	0.789328i
$345$		0			0
$346$	−421.312	+	421.312i	−1.21767	+	1.21767i
$347$		−	213.546i		−	0.615407i	−0.951482	−	0.307704i	$-0.900440\pi$
$347$		−	213.546i		−	0.615407i	0.951482	−	0.307704i	$-0.0995605\pi$
$348$		0			0
$349$	68.5857			0.196521			0.0982603	−	0.995161i	$-0.468672\pi$
$349$	68.5857			0.196521			0.0982603	+	0.995161i	$0.468672\pi$
$350$	3.28589	−	321.983i	0.00938824	−	0.919952i
$351$		0			0
$352$	224.000	−	224.000i	0.636364	−	0.636364i
$353$	−256.344			−0.726186			−0.363093	−	0.931753i	$-0.618279\pi$
$353$	−256.344			−0.726186			−0.363093	+	0.931753i	$0.618279\pi$
$354$		0			0
$355$		−	284.141i		−	0.800397i
$356$			581.969i			1.63474i
$357$		0			0
$358$	158.000	−	158.000i	0.441341	−	0.441341i
$359$	637.810			1.77663			0.888315	−	0.459234i	$-0.151876\pi$
$359$	637.810			1.77663			0.888315	+	0.459234i	$0.151876\pi$
$360$		0			0
$361$	265.000			0.734072
$362$	332.554	+	332.554i	0.918657	+	0.918657i
$363$		0			0
$364$	−391.918	+	384.000i	−1.07670	+	1.05495i
$365$	203.647			0.557936
$366$		0			0
$367$	−499.696			−1.36157			−0.680785	−	0.732484i	$-0.738361\pi$
$367$	−499.696			−1.36157			−0.680785	+	0.732484i	$0.738361\pi$
$368$	−656.195			−1.78314
$369$		0			0
$370$	−254.747	−	254.747i	−0.688505	−	0.688505i
$371$	256.344	+	261.630i	0.690953	+	0.705201i
$372$		0			0
$373$		−	576.000i		−	1.54424i	−0.635479	−	0.772118i	$-0.719197\pi$
$373$		−	576.000i		−	1.54424i	0.635479	−	0.772118i	$-0.280803\pi$
$374$	−96.9948	+	96.9948i	−0.259345	+	0.259345i
$375$		0			0
$376$	156.767	+	156.767i	0.416934	+	0.416934i
$377$	−360.267			−0.955614
$378$		0			0
$379$	48.0000			0.126649			0.0633245	−	0.997993i	$-0.479830\pi$
$379$	48.0000			0.126649			0.0633245	+	0.997993i	$0.479830\pi$
$380$			271.529i			0.714550i
$381$		0			0
$382$	−106.000	−	106.000i	−0.277487	−	0.277487i
$383$			221.703i			0.578858i	0.957200	+	0.289429i	$0.0934654\pi$
$383$			221.703i			0.578858i	−0.957200	+	0.289429i	$0.906535\pi$
$384$		0			0
$385$	−336.000	−	342.929i	−0.872727	−	0.890724i
$386$	475.176	+	475.176i	1.23103	+	1.23103i
$387$		0			0
$388$	666.261			1.71717
$389$	−188.090			−0.483523			−0.241761	−	0.970336i	$-0.577725\pi$
$389$	−188.090			−0.483523			−0.241761	+	0.970336i	$0.577725\pi$
$390$		0			0
$391$	284.141			0.726703
$392$	271.471	+	282.785i	0.692529	+	0.721390i
$393$		0			0
$394$	266.000	+	266.000i	0.675127	+	0.675127i
$395$	332.554			0.841908
$396$		0			0
$397$	−127.373			−0.320840			−0.160420	−	0.987049i	$-0.551285\pi$
$397$	−127.373			−0.320840			−0.160420	+	0.987049i	$0.551285\pi$
$398$	−124.708	−	124.708i	−0.313336	−	0.313336i
$399$		0			0
$400$	368.000			0.920000
$401$		−	137.179i		−	0.342092i	−0.985263	−	0.171046i	$-0.945285\pi$
$401$		−	137.179i		−	0.342092i	0.985263	−	0.171046i	$-0.0547146\pi$
$402$		0			0
$403$	−768.000			−1.90571
$404$	637.395			1.57771
$405$		0			0
$406$	−2.62653	+	257.373i	−0.00646929	+	0.633925i
$407$	−257.387			−0.632400
$408$		0			0
$409$		−	519.292i		−	1.26966i	−0.772651	−	0.634831i	$-0.781070\pi$
$409$		−	519.292i		−	1.26966i	0.772651	−	0.634831i	$-0.218930\pi$
$410$	610.940	−	610.940i	1.49010	−	1.49010i
$411$		0			0
$412$		−	391.918i		−	0.951258i
$413$	339.411	+	346.410i	0.821819	+	0.838766i
$414$		0			0
$415$			768.000i			1.85060i
$416$	−443.405	−	443.405i	−1.06588	−	1.06588i
$417$		0			0
$418$	137.171	+	137.171i	0.328161	+	0.328161i
$419$	−13.8564			−0.0330702			−0.0165351	−	0.999863i	$-0.505264\pi$
$419$	−13.8564			−0.0330702			−0.0165351	+	0.999863i	$0.505264\pi$
$420$		0			0
$421$		−	432.000i		−	1.02613i	−0.858350	−	0.513064i	$-0.828510\pi$
$421$		−	432.000i		−	1.02613i	0.858350	−	0.513064i	$-0.171490\pi$
$422$	−203.647	−	203.647i	−0.482575	−	0.482575i
$423$		0			0
$424$	−296.000	+	296.000i	−0.698113	+	0.698113i
$425$	−159.349			−0.374938
$426$		0			0
$427$	−144.000	−	146.969i	−0.337237	−	0.344191i
$428$	231.931			0.541895
$429$		0			0
$430$	470.302	−	470.302i	1.09373	−	1.09373i
$431$	−7.07107			−0.0164062			−0.00820309	−	0.999966i	$-0.502611\pi$
$431$	−7.07107			−0.0164062			−0.00820309	+	0.999966i	$0.502611\pi$
$432$		0			0
$433$			764.241i			1.76499i	0.470321	+	0.882495i	$0.344138\pi$
$433$			764.241i			1.76499i	−0.470321	+	0.882495i	$0.655862\pi$
$434$	−5.59913	+	548.657i	−0.0129012	+	1.26419i
$435$		0			0
$436$	−488.000			−1.11927
$437$		−	401.836i		−	0.919533i
$438$		0			0
$439$	−656.463			−1.49536			−0.747680	−	0.664059i	$-0.768832\pi$
$439$	−656.463			−1.49536			−0.747680	+	0.664059i	$0.768832\pi$
$440$	387.979	−	387.979i	0.881771	−	0.881771i
$441$		0			0
$442$	192.000	+	192.000i	0.434389	+	0.434389i
$443$			688.722i			1.55468i	0.629082	+	0.777339i	$0.283431\pi$
$443$			688.722i			1.55468i	−0.629082	+	0.777339i	$0.716569\pi$
$444$		0			0
$445$			1008.00i			2.26517i
$446$	−152.420	−	152.420i	−0.341750	−	0.341750i
$447$		0			0
$448$	−320.000	+	313.535i	−0.714286	+	0.699854i
$449$			270.115i			0.601592i	0.953689	+	0.300796i	$0.0972523\pi$
$449$			270.115i			0.601592i	−0.953689	+	0.300796i	$0.902748\pi$
$450$		0			0
$451$		−	617.271i		−	1.36867i
$452$	265.872			0.588213
$453$		0			0
$454$	235.151	+	235.151i	0.517954	+	0.517954i
$455$	−678.823	+	665.108i	−1.49192	+	1.46177i
$456$		0			0
$457$	96.0000			0.210066			0.105033	−	0.994469i	$-0.466505\pi$
$457$	96.0000			0.210066			0.105033	+	0.994469i	$0.466505\pi$
$458$	−110.851	−	110.851i	−0.242033	−	0.242033i
$459$		0			0
$460$	−1136.56			−2.47079
$461$		−	20.7846i		−	0.0450859i	−0.999746	−	0.0225430i	$-0.992824\pi$
$461$		−	20.7846i		−	0.0450859i	0.999746	−	0.0225430i	$-0.00717626\pi$
$462$		0			0
$463$		−	240.000i		−	0.518359i	−0.965829	−	0.259179i	$-0.916548\pi$
$463$		−	240.000i		−	0.518359i	0.965829	−	0.259179i	$-0.0834520\pi$
$464$	−294.156			−0.633958
$465$		0			0
$466$	142.000	−	142.000i	0.304721	−	0.304721i
$467$	152.420			0.326382			0.163191	−	0.986594i	$-0.447821\pi$
$467$	152.420			0.326382			0.163191	+	0.986594i	$0.447821\pi$
$468$		0			0
$469$	68.5857	+	70.0000i	0.146238	+	0.149254i
$470$	271.529	+	271.529i	0.577721	+	0.577721i
$471$		0			0
$472$	−391.918	+	391.918i	−0.830336	+	0.830336i
$473$		−	475.176i		−	1.00460i
$474$		0			0
$475$			225.353i			0.474427i
$476$	138.564	−	135.765i	0.291101	−	0.285220i
$477$		0			0
$478$	−374.000	−	374.000i	−0.782427	−	0.782427i
$479$			263.272i			0.549628i	0.961497	+	0.274814i	$0.0886162\pi$
$479$			263.272i			0.549628i	−0.961497	+	0.274814i	$0.911384\pi$
$480$		0			0
$481$			509.494i			1.05924i
$482$	318.697	−	318.697i	0.661198	−	0.661198i
$483$		0			0
$484$			92.0000i			0.190083i
$485$	1154.00			2.37938
$486$		0			0
$487$			278.000i			0.570842i	0.958402	+	0.285421i	$0.0921334\pi$
$487$			278.000i			0.570842i	−0.958402	+	0.285421i	$0.907867\pi$
$488$	166.277	−	166.277i	0.340731	−	0.340731i
$489$		0			0
$490$	470.202	+	489.798i	0.959596	+	0.999588i
$491$		−	77.7817i		−	0.158415i	−0.996858	−	0.0792075i	$-0.974761\pi$
$491$		−	77.7817i		−	0.158415i	0.996858	−	0.0792075i	$-0.0252390\pi$
$492$		0			0
$493$	127.373			0.258364
$494$	271.529	−	271.529i	0.549654	−	0.549654i
$495$		0			0
$496$	−627.069			−1.26425
$497$	200.918	+	205.061i	0.404261	+	0.412598i
$498$		0			0
$499$	−528.000			−1.05812			−0.529058	−	0.848586i	$-0.677455\pi$
$499$	−528.000			−1.05812			−0.529058	+	0.848586i	$0.677455\pi$
$500$	−55.4256			−0.110851
$501$		0			0
$502$	−19.5959	−	19.5959i	−0.0390357	−	0.0390357i
$503$		−	166.277i		−	0.330570i	−0.986246	−	0.165285i	$-0.947146\pi$
$503$		−	166.277i		−	0.330570i	0.986246	−	0.165285i	$-0.0528544\pi$
$504$		0			0
$505$	1104.00			2.18614
$506$	−574.171	+	574.171i	−1.13472	+	1.13472i
$507$		0			0
$508$	960.000			1.88976
$509$			644.323i			1.26586i	0.774209	+	0.632930i	$0.218148\pi$
$509$			644.323i			1.26586i	−0.774209	+	0.632930i	$0.781852\pi$
$510$		0			0
$511$	−146.969	+	144.000i	−0.287611	+	0.281800i
$512$	−362.039	−	362.039i	−0.707107	−	0.707107i
$513$		0			0
$514$	−342.929	−	342.929i	−0.667176	−	0.667176i
$515$		−	678.823i		−	1.31810i
$516$		0			0
$517$	274.343			0.530644
$518$	363.981	+	3.71448i	0.702666	+	0.00717081i
$519$		0			0
$520$	−768.000	−	768.000i	−1.47692	−	1.47692i
$521$	−187.061			−0.359043			−0.179522	−	0.983754i	$-0.557455\pi$
$521$	−187.061			−0.359043			−0.179522	+	0.983754i	$0.557455\pi$
$522$		0			0
$523$			548.686i			1.04911i	0.851376	+	0.524556i	$0.175769\pi$
$523$			548.686i			1.04911i	−0.851376	+	0.524556i	$0.824231\pi$
$524$		−	110.851i		−	0.211548i
$525$		0			0
$526$	−134.000	−	134.000i	−0.254753	−	0.254753i
$527$	271.529			0.515235
$528$		0			0
$529$	1153.00			2.17958
$530$	−512.687	+	512.687i	−0.967334	+	0.967334i
$531$		0			0
$532$	−192.000	−	195.959i	−0.360902	−	0.368344i
$533$	−1221.88			−2.29246
$534$		0			0
$535$	401.716			0.750872
$536$	−79.1960	+	79.1960i	−0.147754	+	0.147754i
$537$		0			0
$538$	421.312	−	421.312i	0.783108	−	0.783108i
$539$	484.974	+	9.89949i	0.899767	+	0.0183664i
$540$		0			0
$541$			432.000i			0.798521i	0.916837	+	0.399261i	$0.130733\pi$
$541$			432.000i			0.798521i	−0.916837	+	0.399261i	$0.869267\pi$
$542$	−360.267	−	360.267i	−0.664698	−	0.664698i
$543$		0			0
$544$	156.767	+	156.767i	0.288175	+	0.288175i
$545$	−845.241			−1.55090
$546$		0			0
$547$	658.000			1.20293			0.601463	−	0.798901i	$-0.294585\pi$
$547$	658.000			1.20293			0.601463	+	0.798901i	$0.294585\pi$
$548$	−141.421			−0.258068
$549$		0			0
$550$	322.000	−	322.000i	0.585455	−	0.585455i
$551$		−	180.133i		−	0.326921i
$552$		0			0
$553$	−240.000	+	235.151i	−0.433996	+	0.425228i
$554$	475.176	−	475.176i	0.857718	−	0.857718i
$555$		0			0
$556$	−78.3837			−0.140978
$557$	289.914			0.520492			0.260246	−	0.965542i	$-0.416196\pi$
$557$	289.914			0.520492			0.260246	+	0.965542i	$0.416196\pi$
$558$		0			0
$559$	−940.604			−1.68265
$560$	−554.256	+	543.058i	−0.989743	+	0.969746i
$561$		0			0
$562$	526.000	−	526.000i	0.935943	−	0.935943i
$563$		0			0			−	1.00000i	$-0.5\pi$
$563$		0			0				1.00000i	$0.5\pi$
$564$		0			0
$565$	460.504			0.815051
$566$	−651.251	+	651.251i	−1.15062	+	1.15062i
$567$		0			0
$568$	−232.000	+	232.000i	−0.408451	+	0.408451i
$569$			239.002i			0.420039i	0.977697	+	0.210019i	$0.0673527\pi$
$569$			239.002i			0.420039i	−0.977697	+	0.210019i	$0.932647\pi$
$570$		0			0
$571$	−130.000			−0.227671			−0.113835	−	0.993500i	$-0.536314\pi$
$571$	−130.000			−0.227671			−0.113835	+	0.993500i	$0.536314\pi$
$572$	−775.959			−1.35657
$573$		0			0
$574$	−8.90815	+	872.908i	−0.0155194	+	1.52075i
$575$	−943.280			−1.64049
$576$		0			0
$577$			78.3837i			0.135847i	0.997691	+	0.0679235i	$0.0216374\pi$
$577$			78.3837i			0.135847i	−0.997691	+	0.0679235i	$0.978363\pi$
$578$	340.825	+	340.825i	0.589663	+	0.589663i
$579$		0			0
$580$	−509.494			−0.878438
$581$	−543.058	−	554.256i	−0.934695	−	0.953969i
$582$		0			0
$583$			518.000i			0.888508i
$584$	−166.277	−	166.277i	−0.284721	−	0.284721i
$585$		0			0
$586$	342.929	−	342.929i	0.585202	−	0.585202i
$587$	−290.985			−0.495715			−0.247857	−	0.968797i	$-0.579726\pi$
$587$	−290.985			−0.495715			−0.247857	+	0.968797i	$0.579726\pi$
$588$		0			0
$589$		−	384.000i		−	0.651952i
$590$	−678.823	+	678.823i	−1.15055	+	1.15055i
$591$		0			0
$592$			416.000i			0.702703i
$593$	76.2102			0.128516			0.0642582	−	0.997933i	$-0.479532\pi$
$593$	76.2102			0.128516			0.0642582	+	0.997933i	$0.479532\pi$
$594$		0			0
$595$	240.000	−	235.151i	0.403361	−	0.395212i
$596$			605.283i			1.01558i
$597$		0			0
$598$	1136.56	+	1136.56i	1.90061	+	1.90061i
$599$	244.659			0.408446			0.204223	−	0.978924i	$-0.434533\pi$
$599$	244.659			0.408446			0.204223	+	0.978924i	$0.434533\pi$
$600$		0			0
$601$			842.624i			1.40204i	0.713143	+	0.701019i	$0.247271\pi$
$601$			842.624i			1.40204i	−0.713143	+	0.701019i	$0.752729\pi$
$602$	−6.85750	+	671.965i	−0.0113912	+	1.11622i
$603$		0			0
$604$	−40.0000			−0.0662252
$605$			159.349i			0.263386i
$606$		0			0
$607$	382.120			0.629523			0.314761	−	0.949171i	$-0.398075\pi$
$607$	382.120			0.629523			0.314761	+	0.949171i	$0.398075\pi$
$608$	221.703	−	221.703i	0.364642	−	0.364642i
$609$		0			0
$610$	288.000	−	288.000i	0.472131	−	0.472131i
$611$		−	543.058i		−	0.888802i
$612$		0			0
$613$		−	480.000i		−	0.783034i	−0.920171	−	0.391517i	$-0.871950\pi$
$613$		−	480.000i		−	0.783034i	0.920171	−	0.391517i	$-0.128050\pi$
$614$	429.549	−	429.549i	0.699591	−	0.699591i
$615$		0			0
$616$	−5.65715	+	554.343i	−0.00918368	+	0.899907i
$617$			442.649i			0.717421i	0.933449	+	0.358711i	$0.116783\pi$
$617$			442.649i			0.717421i	−0.933449	+	0.358711i	$0.883217\pi$
$618$		0			0
$619$			529.090i			0.854749i	0.904075	+	0.427375i	$0.140561\pi$
$619$			529.090i			0.854749i	−0.904075	+	0.427375i	$0.859439\pi$
$620$	−1086.12			−1.75180
$621$		0			0
$622$	−333.131	+	333.131i	−0.535580	+	0.535580i
$623$	−712.764	−	727.461i	−1.14408	−	1.16767i
$624$		0			0
$625$	−671.000			−1.07360
$626$	−471.118	+	471.118i	−0.752584	+	0.752584i
$627$		0			0
$628$		−	823.029i		−	1.31056i
$629$		−	180.133i		−	0.286380i
$630$		0			0
$631$		−	48.0000i		−	0.0760697i	−0.999276	−	0.0380349i	$-0.987890\pi$
$631$		−	48.0000i		−	0.0760697i	0.999276	−	0.0380349i	$-0.0121098\pi$
$632$	−271.529	−	271.529i	−0.429634	−	0.429634i
$633$		0			0
$634$	−314.000	−	314.000i	−0.495268	−	0.495268i
$635$	1662.77			2.61853
$636$		0			0
$637$	19.5959	−	960.000i	0.0307628	−	1.50706i
$638$	−257.387	+	257.387i	−0.403428	+	0.403428i
$639$		0			0
$640$	−627.069	−	627.069i	−0.979796	−	0.979796i
$641$			1.41421i			0.00220626i	0.999999	+	0.00110313i	$0.000351137\pi$
$641$			1.41421i			0.00220626i	−0.999999	+	0.00110313i	$0.999649\pi$
$642$		0			0
$643$		−	793.635i		−	1.23427i	−0.786858	−	0.617134i	$-0.788294\pi$
$643$		−	793.635i		−	1.23427i	0.786858	−	0.617134i	$-0.211706\pi$
$644$	820.244	−	803.672i	1.27367	−	1.24794i
$645$		0			0
$646$	−96.0000	+	96.0000i	−0.148607	+	0.148607i
$647$		−	1274.79i		−	1.97031i	−0.171672	−	0.985154i	$-0.554917\pi$
$647$		−	1274.79i		−	1.97031i	0.171672	−	0.985154i	$-0.445083\pi$
$648$		0			0
$649$			685.857i			1.05679i
$650$	−637.395	−	637.395i	−0.980607	−	0.980607i
$651$		0			0
$652$			1208.00i			1.85276i
$653$	1172.38			1.79538			0.897690	−	0.440628i	$-0.145244\pi$
$653$	1172.38			1.79538			0.897690	+	0.440628i	$0.145244\pi$
$654$		0			0
$655$		−	192.000i		−	0.293130i
$656$	−997.661			−1.52083
$657$		0			0
$658$	−387.959	−	3.95918i	−0.589604	−	0.00601699i
$659$		−	634.982i		−	0.963554i	−0.876294	−	0.481777i	$-0.839992\pi$
$659$		−	634.982i		−	0.963554i	0.876294	−	0.481777i	$-0.160008\pi$
$660$		0			0
$661$	−342.929			−0.518803			−0.259401	−	0.965770i	$-0.583525\pi$
$661$	−342.929			−0.518803			−0.259401	+	0.965770i	$0.583525\pi$
$662$	−203.647	−	203.647i	−0.307623	−	0.307623i
$663$		0			0
$664$	627.069	−	627.069i	0.944382	−	0.944382i
$665$	−332.554	−	339.411i	−0.500081	−	0.510393i
$666$		0			0
$667$	754.000			1.13043
$668$	277.128			0.414862
$669$		0			0
$670$	−137.171	+	137.171i	−0.204733	+	0.204733i
$671$		−	290.985i		−	0.433658i
$672$		0			0
$673$	912.000			1.35513			0.677563	−	0.735465i	$-0.263036\pi$
$673$	912.000			1.35513			0.677563	+	0.735465i	$0.263036\pi$
$674$	678.823	+	678.823i	1.00716	+	1.00716i
$675$		0			0
$676$			860.000i			1.27219i
$677$			256.344i			0.378646i	0.981915	+	0.189323i	$0.0606294\pi$
$677$			256.344i			0.378646i	−0.981915	+	0.189323i	$0.939371\pi$
$678$		0			0
$679$	−832.827	+	816.000i	−1.22655	+	1.20177i
$680$	271.529	+	271.529i	0.399307	+	0.399307i
$681$		0			0
$682$	−548.686	+	548.686i	−0.804524	+	0.804524i
$683$		−	1299.66i		−	1.90287i	−0.307845	−	0.951437i	$-0.599608\pi$
$683$		−	1299.66i		−	1.90287i	0.307845	−	0.951437i	$-0.400392\pi$
$684$		0			0
$685$	−244.949			−0.357590
$686$	−685.679	−	20.9982i	−0.999531	−	0.0306096i
$687$		0			0
$688$	−768.000			−1.11628
$689$	1025.37			1.48821
$690$		0			0
$691$			117.576i			0.170153i	0.996374	+	0.0850763i	$0.0271134\pi$
$691$			117.576i			0.170153i	−0.996374	+	0.0850763i	$0.972887\pi$
$692$	1191.65			1.72204
$693$		0			0
$694$	−302.000	+	302.000i	−0.435159	+	0.435159i
$695$	−135.765			−0.195345
$696$		0			0
$697$	432.000			0.619799
$698$	−96.9948	−	96.9948i	−0.138961	−	0.138961i
$699$		0			0
$700$	−460.000	+	450.706i	−0.657143	+	0.643866i
$701$	49.4975			0.0706098			0.0353049	−	0.999377i	$-0.488760\pi$
$701$	49.4975			0.0706098			0.0353049	+	0.999377i	$0.488760\pi$
$702$		0			0
$703$	−254.747			−0.362371
$704$	−633.568			−0.899954
$705$		0			0
$706$	362.524	+	362.524i	0.513491	+	0.513491i
$707$	−796.743	+	780.646i	−1.12694	+	1.10417i
$708$		0			0
$709$		−	502.000i		−	0.708039i	−0.935238	−	0.354020i	$-0.884815\pi$
$709$		−	502.000i		−	0.708039i	0.935238	−	0.354020i	$-0.115185\pi$
$710$	−401.836	+	401.836i	−0.565966	+	0.565966i
$711$		0			0
$712$	823.029	−	823.029i	1.15594	−	1.15594i
$713$	1607.34			2.25434
$714$		0			0
$715$	−1344.00			−1.87972
$716$	−446.891			−0.624150
$717$		0			0
$718$	−902.000	−	902.000i	−1.25627	−	1.25627i
$719$		−	1344.07i		−	1.86936i	−0.355487	−	0.934681i	$-0.615685\pi$
$719$		−	1344.07i		−	1.86936i	0.355487	−	0.934681i	$-0.384315\pi$
$720$		0			0
$721$	480.000	+	489.898i	0.665742	+	0.679470i
$722$	−374.767	−	374.767i	−0.519067	−	0.519067i
$723$		0			0
$724$		−	940.604i		−	1.29918i
$725$	−422.850			−0.583241
$726$		0			0
$727$	470.302			0.646908			0.323454	−	0.946244i	$-0.395156\pi$
$727$	470.302			0.646908			0.323454	+	0.946244i	$0.395156\pi$
$728$	1097.31	+	11.1983i	1.50730	+	0.0153822i
$729$		0			0
$730$	−288.000	−	288.000i	−0.394521	−	0.394521i
$731$	332.554			0.454930
$732$		0			0
$733$		0			0			−	1.00000i	$-0.5\pi$
$733$		0			0				1.00000i	$0.5\pi$
$734$	706.677	+	706.677i	0.962775	+	0.962775i
$735$		0			0
$736$	928.000	+	928.000i	1.26087	+	1.26087i
$737$			138.593i			0.188050i
$738$		0			0
$739$	274.000			0.370771			0.185386	−	0.982666i	$-0.440647\pi$
$739$	274.000			0.370771			0.185386	+	0.982666i	$0.440647\pi$
$740$			720.533i			0.973693i
$741$		0			0
$742$	7.47552	−	732.524i	0.0100748	−	0.987230i
$743$	298.399			0.401614			0.200807	−	0.979631i	$-0.435644\pi$
$743$	298.399			0.401614			0.200807	+	0.979631i	$0.435644\pi$
$744$		0			0
$745$			1048.38i			1.40722i
$746$	−814.587	+	814.587i	−1.09194	+	1.09194i
$747$		0			0
$748$	274.343			0.366769
$749$	−289.914	+	284.056i	−0.387068	+	0.379247i
$750$		0			0
$751$			1094.00i			1.45672i	0.685192	+	0.728362i	$0.259718\pi$
$751$			1094.00i			1.45672i	−0.685192	+	0.728362i	$0.740282\pi$
$752$		−	443.405i		−	0.589634i
$753$		0			0
$754$	509.494	+	509.494i	0.675721	+	0.675721i
$755$	−69.2820			−0.0917643
$756$		0			0
$757$			118.000i			0.155878i	0.996958	+	0.0779392i	$0.0248340\pi$
$757$			118.000i			0.155878i	−0.996958	+	0.0779392i	$0.975166\pi$
$758$	−67.8823	−	67.8823i	−0.0895544	−	0.0895544i
$759$		0			0
$760$	384.000	−	384.000i	0.505263	−	0.505263i
$761$	−547.328			−0.719222			−0.359611	−	0.933102i	$-0.617091\pi$
$761$	−547.328			−0.719222			−0.359611	+	0.933102i	$0.617091\pi$
$762$		0			0
$763$	610.000	−	597.675i	0.799476	−	0.783323i
$764$			299.813i			0.392426i
$765$		0			0
$766$	313.535	−	313.535i	0.409314	−	0.409314i
$767$	1357.65			1.77007
$768$		0			0
$769$		−	803.433i		−	1.04478i	−0.852708	−	0.522388i	$-0.825041\pi$
$769$		−	803.433i		−	1.04478i	0.852708	−	0.522388i	$-0.174959\pi$
$770$	−9.79847	+	960.150i	−0.0127253	+	1.24695i
$771$		0			0
$772$		−	1344.00i		−	1.74093i
$773$			561.184i			0.725982i	0.931793	+	0.362991i	$0.118245\pi$
$773$			561.184i			0.725982i	−0.931793	+	0.362991i	$0.881755\pi$
$774$		0			0
$775$	−901.412			−1.16311
$776$	−942.236	−	942.236i	−1.21422	−	1.21422i
$777$		0			0
$778$	266.000	+	266.000i	0.341902	+	0.341902i
$779$		−	610.940i		−	0.784262i
$780$		0			0
$781$			406.000i			0.519846i
$782$	−401.836	−	401.836i	−0.513857	−	0.513857i
$783$		0			0
$784$	16.0000	−	783.837i	0.0204082	−	0.999792i
$785$		−	1425.53i		−	1.81596i
$786$		0			0
$787$			823.029i			1.04578i	0.852400	+	0.522890i	$0.175146\pi$
$787$			823.029i			1.04578i	−0.852400	+	0.522890i	$0.824854\pi$
$788$		−	752.362i		−	0.954774i
$789$		0			0
$790$	−470.302	−	470.302i	−0.595319	−	0.595319i
$791$	−332.340	+	325.626i	−0.420152	+	0.411663i
$792$		0			0
$793$	−576.000			−0.726356
$794$	180.133	+	180.133i	0.226868	+	0.226868i
$795$		0			0
$796$			352.727i			0.443124i
$797$			630.466i			0.791050i	0.918455	+	0.395525i	$0.129437\pi$
$797$			630.466i			0.791050i	−0.918455	+	0.395525i	$0.870563\pi$
$798$		0			0
$799$			192.000i			0.240300i
$800$	−520.431	−	520.431i	−0.650538	−	0.650538i
$801$		0			0
$802$	−194.000	+	194.000i	−0.241895	+	0.241895i
$803$	−290.985			−0.362372
$804$		0			0
$805$	1420.70	−	1392.00i	1.76485	−	1.72919i
$806$	1086.12	+	1086.12i	1.34754	+	1.34754i
$807$		0			0
$808$	−901.412	−	901.412i	−1.11561	−	1.11561i
$809$			1458.05i			1.80229i	0.433516	+	0.901146i	$0.357273\pi$
$809$			1458.05i			1.80229i	−0.433516	+	0.901146i	$0.642727\pi$
$810$		0			0
$811$			293.939i			0.362440i	0.983443	+	0.181220i	$0.0580046\pi$
$811$			293.939i			0.362440i	−0.983443	+	0.181220i	$0.941995\pi$
$812$	367.696	−	360.267i	0.452827	−	0.443678i
$813$		0			0
$814$	364.000	+	364.000i	0.447174	+	0.447174i
$815$			2092.32i			2.56726i
$816$		0			0
$817$		−	470.302i		−	0.575645i
$818$	−734.390	+	734.390i	−0.897787	+	0.897787i
$819$		0			0
$820$	−1728.00			−2.10732
$821$	595.384			0.725194			0.362597	−	0.931946i	$-0.381890\pi$
$821$	595.384			0.725194			0.362597	+	0.931946i	$0.381890\pi$
$822$		0			0
$823$		−	1296.00i		−	1.57473i	−0.616489	−	0.787363i	$-0.711446\pi$
$823$		−	1296.00i		−	1.57473i	0.616489	−	0.787363i	$-0.288554\pi$
$824$	−554.256	+	554.256i	−0.672641	+	0.672641i
$825$		0			0
$826$	9.89795	−	969.898i	0.0119830	−	1.17421i
$827$		−	485.075i		−	0.586548i	−0.956028	−	0.293274i	$-0.905255\pi$
$827$		−	485.075i		−	0.586548i	0.956028	−	0.293274i	$-0.0947448\pi$
$828$		0			0
$829$	−293.939			−0.354570			−0.177285	−	0.984160i	$-0.556731\pi$
$829$	−293.939			−0.354570			−0.177285	+	0.984160i	$0.556731\pi$
$830$	1086.12	−	1086.12i	1.30857	−	1.30857i
$831$		0			0
$832$			1254.14i			1.50738i
$833$	−6.92820	+	339.411i	−0.00831717	+	0.407456i
$834$		0			0
$835$	480.000			0.574850
$836$		−	387.979i		−	0.464090i
$837$		0			0
$838$	19.5959	+	19.5959i	0.0233842	+	0.0233842i
$839$			1371.78i			1.63502i	0.575912	+	0.817511i	$0.304647\pi$
$839$			1371.78i			1.63502i	−0.575912	+	0.817511i	$0.695353\pi$
$840$		0			0
$841$	−503.000			−0.598098
$842$	−610.940	+	610.940i	−0.725582	+	0.725582i
$843$		0			0
$844$			576.000i			0.682464i
$845$			1489.56i			1.76280i
$846$		0			0
$847$	−112.677	−	115.000i	−0.133030	−	0.135773i
$848$	837.214			0.987281
$849$		0			0
$850$	225.353	+	225.353i	0.265121	+	0.265121i
$851$		−	1066.32i		−	1.25302i
$852$		0			0
$853$	1185.55			1.38986			0.694931	−	0.719076i	$-0.255435\pi$
$853$	1185.55			1.38986			0.694931	+	0.719076i	$0.255435\pi$
$854$	−4.19934	+	411.493i	−0.00491726	+	0.481842i
$855$		0			0
$856$	−328.000	−	328.000i	−0.383178	−	0.383178i
$857$	−519.615			−0.606319			−0.303159	−	0.952940i	$-0.598041\pi$
$857$	−519.615			−0.606319			−0.303159	+	0.952940i	$0.598041\pi$
$858$		0			0
$859$		−	1459.90i		−	1.69953i	−0.527162	−	0.849765i	$-0.676744\pi$
$859$		−	1459.90i		−	1.69953i	0.527162	−	0.849765i	$-0.323256\pi$
$860$	−1330.22			−1.54676
$861$		0			0
$862$	10.0000	+	10.0000i	0.0116009	+	0.0116009i
$863$	60.8112			0.0704649			0.0352324	−	0.999379i	$-0.488783\pi$
$863$	60.8112			0.0704649			0.0352324	+	0.999379i	$0.488783\pi$
$864$		0			0
$865$	2064.00			2.38613
$866$	1080.80	−	1080.80i	1.24804	−	1.24804i
$867$		0			0
$868$	783.837	−	768.000i	0.903038	−	0.884793i
$869$	−475.176			−0.546808
$870$		0			0
$871$	274.343			0.314975
$872$	690.136	+	690.136i	0.791441	+	0.791441i
$873$		0			0
$874$	−568.282	+	568.282i	−0.650208	+	0.650208i
$875$	69.2820	−	67.8823i	0.0791795	−	0.0775797i
$876$		0			0
$877$			672.000i			0.766249i	0.923697	+	0.383124i	$0.125152\pi$
$877$			672.000i			0.766249i	−0.923697	+	0.383124i	$0.874848\pi$
$878$	928.379	+	928.379i	1.05738	+	1.05738i
$879$		0			0
$880$	−1097.37			−1.24701
$881$	1364.86			1.54921			0.774606	−	0.632444i	$-0.217948\pi$
$881$	1364.86			1.54921			0.774606	+	0.632444i	$0.217948\pi$
$882$		0			0
$883$	−1392.00			−1.57644			−0.788222	−	0.615391i	$-0.788998\pi$
$883$	−1392.00			−1.57644			−0.788222	+	0.615391i	$0.788998\pi$
$884$		−	543.058i		−	0.614319i
$885$		0			0
$886$	974.000	−	974.000i	1.09932	−	1.09932i
$887$		−	956.092i		−	1.07789i	−0.842340	−	0.538947i	$-0.818822\pi$
$887$		−	956.092i		−	1.07789i	0.842340	−	0.538947i	$-0.181178\pi$
$888$		0			0
$889$	−1200.00	+	1175.76i	−1.34983	+	1.32256i
$890$	1425.53	−	1425.53i	1.60172	−	1.60172i
$891$		0			0
$892$			431.110i			0.483307i
$893$	271.529			0.304064
$894$		0			0
$895$	−774.039			−0.864848
$896$	895.953	+	9.14333i	0.999948	+	0.0102046i
$897$		0			0
$898$	382.000	−	382.000i	0.425390	−	0.425390i
$899$	720.533			0.801483
$900$		0			0
$901$	−362.524			−0.402358
$902$	−872.954	+	872.954i	−0.967798	+	0.967798i
$903$		0			0
$904$	−376.000	−	376.000i	−0.415929	−	0.415929i
$905$		−	1629.17i		−	1.80019i
$906$		0			0
$907$	−1392.00			−1.53473			−0.767365	−	0.641211i	$-0.778432\pi$
$907$	−1392.00			−1.53473			−0.767365	+	0.641211i	$0.778432\pi$
$908$		−	665.108i		−	0.732497i
$909$		0			0
$910$	1900.60	+	19.3959i	2.08858	+	0.0213142i
$911$	−875.398			−0.960920			−0.480460	−	0.877017i	$-0.659530\pi$
$911$	−875.398			−0.960920			−0.480460	+	0.877017i	$0.659530\pi$
$912$		0			0
$913$		−	1097.37i		−	1.20194i
$914$	−135.765	−	135.765i	−0.148539	−	0.148539i
$915$		0			0
$916$			313.535i			0.342287i
$917$	135.765	+	138.564i	0.148053	+	0.151106i
$918$		0			0
$919$			1738.00i			1.89119i	0.325352	+	0.945593i	$0.394517\pi$
$919$			1738.00i			1.89119i	−0.325352	+	0.945593i	$0.605483\pi$
$920$	1607.34	+	1607.34i	1.74711	+	1.74711i
$921$		0			0
$922$	−29.3939	+	29.3939i	−0.0318806	+	0.0318806i
$923$	803.672			0.870717
$924$		0			0
$925$			598.000i			0.646486i
$926$	−339.411	+	339.411i	−0.366535	+	0.366535i
$927$		0			0
$928$	416.000	+	416.000i	0.448276	+	0.448276i
$929$	−1600.41			−1.72273			−0.861364	−	0.507988i	$-0.830390\pi$
$929$	−1600.41			−1.72273			−0.861364	+	0.507988i	$0.830390\pi$
$930$		0			0
$931$	480.000	+	9.79796i	0.515575	+	0.0105241i
$932$	−401.637			−0.430941
$933$		0			0
$934$	−215.555	−	215.555i	−0.230787	−	0.230787i
$935$	475.176			0.508209
$936$		0			0
$937$		−	19.5959i		−	0.0209135i	−0.999945	−	0.0104567i	$-0.996671\pi$
$937$		−	19.5959i		−	0.0209135i	0.999945	−	0.0104567i	$-0.00332854\pi$
$938$	2.00010	−	195.990i	0.00213231	−	0.208944i
$939$		0			0
$940$		−	768.000i		−	0.817021i
$941$			284.056i			0.301866i	0.988544	+	0.150933i	$0.0482278\pi$
$941$			284.056i			0.301866i	−0.988544	+	0.150933i	$0.951772\pi$
$942$		0			0
$943$	2557.27			2.71184
$944$	1108.51			1.17427
$945$		0			0
$946$	−672.000	+	672.000i	−0.710359	+	0.710359i
$947$			1788.98i			1.88910i	0.328364	+	0.944551i	$0.393503\pi$
$947$			1788.98i			1.88910i	−0.328364	+	0.944551i	$0.606497\pi$
$948$		0			0
$949$			576.000i			0.606955i
$950$	318.697	−	318.697i	0.335471	−	0.335471i
$951$		0			0
$952$	−387.959	−	3.95918i	−0.407520	−	0.00415880i
$953$		−	32.5269i		−	0.0341311i	−0.999854	−	0.0170655i	$-0.994568\pi$
$953$		−	32.5269i		−	0.0341311i	0.999854	−	0.0170655i	$-0.00543239\pi$
$954$		0			0
$955$			519.292i			0.543761i
$956$			1057.83i			1.10652i
$957$		0			0
$958$	372.322	−	372.322i	0.388646	−	0.388646i
$959$	176.777	−	173.205i	0.184334	−	0.180610i
$960$		0			0
$961$	575.000			0.598335
$962$	720.533	−	720.533i	0.748995	−	0.748995i
$963$		0			0
$964$	−901.412			−0.935075
$965$		−	2327.88i		−	2.41231i
$966$		0			0
$967$		−	816.000i		−	0.843847i	−0.906631	−	0.421923i	$-0.861355\pi$
$967$		−	816.000i		−	0.843847i	0.906631	−	0.421923i	$-0.138645\pi$
$968$	130.108	−	130.108i	0.134409	−	0.134409i
$969$		0			0
$970$	−1632.00	−	1632.00i	−1.68247	−	1.68247i
$971$	1163.94			1.19870			0.599350	−	0.800487i	$-0.295426\pi$
$971$	1163.94			1.19870			0.599350	+	0.800487i	$0.295426\pi$
$972$		0			0
$973$	97.9796	−	96.0000i	0.100698	−	0.0986639i
$974$	393.151	−	393.151i	0.403646	−	0.403646i
$975$		0			0
$976$	−470.302			−0.481867
$977$			1424.11i			1.45764i	0.684706	+	0.728819i	$0.259931\pi$
$977$			1424.11i			1.45764i	−0.684706	+	0.728819i	$0.740069\pi$
$978$		0			0
$979$		−	1440.30i		−	1.47120i
$980$	27.7128	−	1357.65i	0.0282784	−	1.38535i
$981$		0			0
$982$	−110.000	+	110.000i	−0.112016	+	0.112016i
$983$		−	900.666i		−	0.916243i	−0.888890	−	0.458121i	$-0.848523\pi$
$983$		−	900.666i		−	0.916243i	0.888890	−	0.458121i	$-0.151477\pi$
$984$		0			0
$985$		−	1303.13i		−	1.32297i
$986$	−180.133	−	180.133i	−0.182691	−	0.182691i
$987$		0			0
$988$	−768.000			−0.777328
$989$	1968.59			1.99048
$990$		0			0
$991$		−	1306.00i		−	1.31786i	−0.752204	−	0.658930i	$-0.771009\pi$
$991$		−	1306.00i		−	1.31786i	0.752204	−	0.658930i	$-0.228991\pi$
$992$	886.810	+	886.810i	0.893962	+	0.893962i
$993$		0			0
$994$	5.85919	−	574.141i	0.00589456	−	0.577606i
$995$			610.940i			0.614010i
$996$		0			0
$997$	107.778			0.108102			0.0540509	−	0.998538i	$-0.482787\pi$
$997$	107.778			0.108102			0.0540509	+	0.998538i	$0.482787\pi$
$998$	746.705	+	746.705i	0.748201	+	0.748201i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.3.e.a.251.2	yes	8
3.2	odd	2	inner	504.3.e.a.251.7	yes	8
4.3	odd	2		2016.3.e.a.1007.8		8
7.6	odd	2	inner	504.3.e.a.251.1	✓	8
8.3	odd	2	inner	504.3.e.a.251.5	yes	8
8.5	even	2		2016.3.e.a.1007.1		8
12.11	even	2		2016.3.e.a.1007.4		8
21.20	even	2	inner	504.3.e.a.251.8	yes	8
24.5	odd	2		2016.3.e.a.1007.5		8
24.11	even	2	inner	504.3.e.a.251.4	yes	8
28.27	even	2		2016.3.e.a.1007.2		8
56.13	odd	2		2016.3.e.a.1007.7		8
56.27	even	2	inner	504.3.e.a.251.6	yes	8
84.83	odd	2		2016.3.e.a.1007.6		8
168.83	odd	2	inner	504.3.e.a.251.3	yes	8
168.125	even	2		2016.3.e.a.1007.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.3.e.a.251.1	✓	8	7.6	odd	2	inner
504.3.e.a.251.2	yes	8	1.1	even	1	trivial
504.3.e.a.251.3	yes	8	168.83	odd	2	inner
504.3.e.a.251.4	yes	8	24.11	even	2	inner
504.3.e.a.251.5	yes	8	8.3	odd	2	inner
504.3.e.a.251.6	yes	8	56.27	even	2	inner
504.3.e.a.251.7	yes	8	3.2	odd	2	inner
504.3.e.a.251.8	yes	8	21.20	even	2	inner
2016.3.e.a.1007.1		8	8.5	even	2
2016.3.e.a.1007.2		8	28.27	even	2
2016.3.e.a.1007.3		8	168.125	even	2
2016.3.e.a.1007.4		8	12.11	even	2
2016.3.e.a.1007.5		8	24.5	odd	2
2016.3.e.a.1007.6		8	84.83	odd	2
2016.3.e.a.1007.7		8	56.13	odd	2
2016.3.e.a.1007.8		8	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	504.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 - 1.41421i) q^{2} +4.00000i q^{4} +6.92820i q^{5} +(-4.89898 - 5.00000i) q^{7} +(5.65685 - 5.65685i) q^{8} +(9.79796 - 9.79796i) q^{10} -9.89949i q^{11} -19.5959 q^{13} +(-0.142865 + 13.9993i) q^{14} -16.0000 q^{16} +6.92820 q^{17} -9.79796i q^{19} -27.7128 q^{20} +(-14.0000 + 14.0000i) q^{22} +41.0122 q^{23} -23.0000 q^{25} +(27.7128 + 27.7128i) q^{26} +(20.0000 - 19.5959i) q^{28} +18.3848 q^{29} +39.1918 q^{31} +(22.6274 + 22.6274i) q^{32} +(-9.79796 - 9.79796i) q^{34} +(34.6410 - 33.9411i) q^{35} -26.0000i q^{37} +(-13.8564 + 13.8564i) q^{38} +(39.1918 + 39.1918i) q^{40} +62.3538 q^{41} +48.0000 q^{43} +39.5980 q^{44} +(-58.0000 - 58.0000i) q^{46} +27.7128i q^{47} +(-1.00000 + 48.9898i) q^{49} +(32.5269 + 32.5269i) q^{50} -78.3837i q^{52} -52.3259 q^{53} +68.5857 q^{55} +(-55.9971 - 0.571458i) q^{56} +(-26.0000 - 26.0000i) q^{58} -69.2820 q^{59} +29.3939 q^{61} +(-55.4256 - 55.4256i) q^{62} -64.0000i q^{64} -135.765i q^{65} -14.0000 q^{67} +27.7128i q^{68} +(-96.9898 - 0.989795i) q^{70} -41.0122 q^{71} -29.3939i q^{73} +(-36.7696 + 36.7696i) q^{74} +39.1918 q^{76} +(-49.4975 + 48.4974i) q^{77} -48.0000i q^{79} -110.851i q^{80} +(-88.1816 - 88.1816i) q^{82} +110.851 q^{83} +48.0000i q^{85} +(-67.8823 - 67.8823i) q^{86} +(-56.0000 - 56.0000i) q^{88} +145.492 q^{89} +(96.0000 + 97.9796i) q^{91} +164.049i q^{92} +(39.1918 - 39.1918i) q^{94} +67.8823 q^{95} -166.565i q^{97} +(70.6962 - 67.8678i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 128 q^{16} - 112 q^{22} - 184 q^{25} + 160 q^{28} + 384 q^{43} - 464 q^{46} - 8 q^{49} - 208 q^{58} - 112 q^{67} - 384 q^{70} - 448 q^{88} + 768 q^{91}+O(q^{100}) \) 8 * q - 128 * q^16 - 112 * q^22 - 184 * q^25 + 160 * q^28 + 384 * q^43 - 464 * q^46 - 8 * q^49 - 208 * q^58 - 112 * q^67 - 384 * q^70 - 448 * q^88 + 768 * q^91

Introduction

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