LMFDB - Embedded newform 784.3.s.f.705.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,3,Mod(129,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("784.129");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	784.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$21.3624527258$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.339738624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 $ x^8 - 4x^6 + 14x^4 - 8*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			705.1
Root			$0.662827 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	784.705
Dual form			784.3.s.f.129.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.20041 + 1.84776i) q^{3} +(-0.549104 - 0.317025i) q^{5} +(2.32843 - 4.03295i) q^{9} +O(q^{10})$	\(q+(-3.20041 + 1.84776i) q^{3} +(-0.549104 - 0.317025i) q^{5} +(2.32843 - 4.03295i) q^{9} +(6.65685 + 11.5300i) q^{11} -21.5391i q^{13} +2.34315 q^{15} +(5.30262 - 3.06147i) q^{17} +(-17.1003 - 9.87285i) q^{19} +(-14.3137 + 24.7921i) q^{23} +(-12.2990 - 21.3025i) q^{25} -16.0502i q^{27} +37.3137 q^{29} +(18.1043 - 10.4525i) q^{31} +(-42.6094 - 24.6005i) q^{33} +(11.9706 - 20.7336i) q^{37} +(39.7990 + 68.9339i) q^{39} +70.1061i q^{41} +46.0000 q^{43} +(-2.55710 + 1.47634i) q^{45} +(-0.909785 - 0.525265i) q^{47} +(-11.3137 + 19.5959i) q^{51} +(7.68629 + 13.3130i) q^{53} -8.44157i q^{55} +72.9706 q^{57} +(12.8959 - 7.44543i) q^{59} +(75.1626 + 43.3951i) q^{61} +(-6.82843 + 11.8272i) q^{65} +(12.3137 + 21.3280i) q^{67} -105.793i q^{69} +45.0294 q^{71} +(-44.8058 + 25.8686i) q^{73} +(78.7237 + 45.4511i) q^{75} +(-16.8579 + 29.1987i) q^{79} +(50.6127 + 87.6638i) q^{81} +77.3883i q^{83} -3.88225 q^{85} +(-119.419 + 68.9467i) q^{87} +(68.2127 + 39.3826i) q^{89} +(-38.6274 + 66.9046i) q^{93} +(6.25988 + 10.8424i) q^{95} +90.1781i q^{97} +62.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^9	$ 8 q - 4 q^{9} + 8 q^{11} + 64 q^{15} - 24 q^{23} + 60 q^{25} + 208 q^{29} - 40 q^{37} + 160 q^{39} + 368 q^{43} + 152 q^{53} + 448 q^{57} - 32 q^{65} + 8 q^{67} + 496 q^{71} - 248 q^{79} + 156 q^{81} + 512 q^{85} - 128 q^{93} + 480 q^{95} + 496 q^{99}+O(q^{100}) $ 8 * q - 4 * q^9 + 8 * q^11 + 64 * q^15 - 24 * q^23 + 60 * q^25 + 208 * q^29 - 40 * q^37 + 160 * q^39 + 368 * q^43 + 152 * q^53 + 448 * q^57 - 32 * q^65 + 8 * q^67 + 496 * q^71 - 248 * q^79 + 156 * q^81 + 512 * q^85 - 128 * q^93 + 480 * q^95 + 496 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−3.20041	+	1.84776i	−1.06680	+	0.615920i	−0.927307	−	0.374303i	$-0.877882\pi$
$3$	−3.20041	+	1.84776i	−1.06680	+	0.615920i	−0.139498	+	0.990222i	$0.544549\pi$
$4$		0			0
$5$	−0.549104	−	0.317025i	−0.109821	−	0.0634051i	0.444084	−	0.895985i	$-0.353529\pi$
$5$	−0.549104	−	0.317025i	−0.109821	−	0.0634051i	−0.553904	+	0.832580i	$0.686863\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	2.32843	−	4.03295i	0.258714	−	0.448106i
$10$		0			0
$11$	6.65685	+	11.5300i	0.605169	+	1.04818i	0.992025	+	0.126043i	$0.0402276\pi$
$11$	6.65685	+	11.5300i	0.605169	+	1.04818i	−0.386856	+	0.922140i	$0.626439\pi$
$12$		0			0
$13$		−	21.5391i		−	1.65685i	−0.560100	−	0.828425i	$-0.689237\pi$
$13$		−	21.5391i		−	1.65685i	0.560100	−	0.828425i	$-0.310763\pi$
$14$		0			0
$15$	2.34315			0.156210
$16$		0			0
$17$	5.30262	−	3.06147i	0.311919	−	0.180086i	−0.335866	−	0.941910i	$-0.609029\pi$
$17$	5.30262	−	3.06147i	0.311919	−	0.180086i	0.647785	+	0.761823i	$0.275696\pi$
$18$		0			0
$19$	−17.1003	−	9.87285i	−0.900014	−	0.519623i	−0.0228094	−	0.999740i	$-0.507261\pi$
$19$	−17.1003	−	9.87285i	−0.900014	−	0.519623i	−0.877205	+	0.480116i	$0.840594\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−14.3137	+	24.7921i	−0.622335	+	1.07792i	0.366715	+	0.930333i	$0.380483\pi$
$23$	−14.3137	+	24.7921i	−0.622335	+	1.07792i	−0.989050	+	0.147583i	$0.952851\pi$
$24$		0			0
$25$	−12.2990	−	21.3025i	−0.491960	−	0.852099i
$26$		0			0
$27$		−	16.0502i		−	0.594451i
$28$		0			0
$29$	37.3137			1.28668			0.643340	−	0.765581i	$-0.277548\pi$
$29$	37.3137			1.28668			0.643340	+	0.765581i	$0.277548\pi$
$30$		0			0
$31$	18.1043	−	10.4525i	0.584009	−	0.337178i	−0.178716	−	0.983901i	$-0.557194\pi$
$31$	18.1043	−	10.4525i	0.584009	−	0.337178i	0.762725	+	0.646723i	$0.223861\pi$
$32$		0			0
$33$	−42.6094	−	24.6005i	−1.29119	−	0.745470i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	11.9706	−	20.7336i	0.323529	−	0.560368i	−0.657685	−	0.753293i	$-0.728464\pi$
$37$	11.9706	−	20.7336i	0.323529	−	0.560368i	0.981213	+	0.192925i	$0.0617974\pi$
$38$		0			0
$39$	39.7990	+	68.9339i	1.02049	+	1.76754i
$40$		0			0
$41$			70.1061i			1.70990i	0.518707	+	0.854952i	$0.326413\pi$
$41$			70.1061i			1.70990i	−0.518707	+	0.854952i	$0.673587\pi$
$42$		0			0
$43$	46.0000			1.06977			0.534884	−	0.844926i	$-0.320355\pi$
$43$	46.0000			1.06977			0.534884	+	0.844926i	$0.320355\pi$
$44$		0			0
$45$	−2.55710	+	1.47634i	−0.0568244	+	0.0328076i
$46$		0			0
$47$	−0.909785	−	0.525265i	−0.0193571	−	0.0111758i	0.490290	−	0.871559i	$-0.336891\pi$
$47$	−0.909785	−	0.525265i	−0.0193571	−	0.0111758i	−0.509647	+	0.860383i	$0.670224\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−11.3137	+	19.5959i	−0.221837	+	0.384234i
$52$		0			0
$53$	7.68629	+	13.3130i	0.145024	+	0.251190i	0.929382	−	0.369119i	$-0.120341\pi$
$53$	7.68629	+	13.3130i	0.145024	+	0.251190i	−0.784358	+	0.620309i	$0.787007\pi$
$54$		0			0
$55$		−	8.44157i		−	0.153483i
$56$		0			0
$57$	72.9706			1.28019
$58$		0			0
$59$	12.8959	−	7.44543i	0.218574	−	0.126194i	−0.386716	−	0.922199i	$-0.626391\pi$
$59$	12.8959	−	7.44543i	0.218574	−	0.126194i	0.605290	+	0.796005i	$0.293057\pi$
$60$		0			0
$61$	75.1626	+	43.3951i	1.23217	+	0.711396i	0.967483	−	0.252938i	$-0.0813967\pi$
$61$	75.1626	+	43.3951i	1.23217	+	0.711396i	0.264691	+	0.964333i	$0.414730\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−6.82843	+	11.8272i	−0.105053	+	0.181957i
$66$		0			0
$67$	12.3137	+	21.3280i	0.183787	+	0.318328i	0.943167	−	0.332319i	$-0.107831\pi$
$67$	12.3137	+	21.3280i	0.183787	+	0.318328i	−0.759380	+	0.650647i	$0.774498\pi$
$68$		0			0
$69$		−	105.793i		−	1.53323i
$70$		0			0
$71$	45.0294			0.634217			0.317109	−	0.948389i	$-0.397288\pi$
$71$	45.0294			0.634217			0.317109	+	0.948389i	$0.397288\pi$
$72$		0			0
$73$	−44.8058	+	25.8686i	−0.613778	+	0.354365i	−0.774443	−	0.632644i	$-0.781970\pi$
$73$	−44.8058	+	25.8686i	−0.613778	+	0.354365i	0.160665	+	0.987009i	$0.448636\pi$
$74$		0			0
$75$	78.7237	+	45.4511i	1.04965	+	0.606015i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−16.8579	+	29.1987i	−0.213391	+	0.369604i	−0.952774	−	0.303682i	$-0.901784\pi$
$79$	−16.8579	+	29.1987i	−0.213391	+	0.369604i	0.739383	+	0.673285i	$0.235117\pi$
$80$		0			0
$81$	50.6127	+	87.6638i	0.624848	+	1.08227i
$82$		0			0
$83$			77.3883i			0.932389i	0.884682	+	0.466195i	$0.154375\pi$
$83$			77.3883i			0.932389i	−0.884682	+	0.466195i	$0.845625\pi$
$84$		0			0
$85$	−3.88225			−0.0456735
$86$		0			0
$87$	−119.419	+	68.9467i	−1.37264	+	0.792491i
$88$		0			0
$89$	68.2127	+	39.3826i	0.766434	+	0.442501i	0.831601	−	0.555373i	$-0.187425\pi$
$89$	68.2127	+	39.3826i	0.766434	+	0.442501i	−0.0651668	+	0.997874i	$0.520758\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−38.6274	+	66.9046i	−0.415349	+	0.719405i
$94$		0			0
$95$	6.25988	+	10.8424i	0.0658935	+	0.114131i
$96$		0			0
$97$			90.1781i			0.929671i	0.885397	+	0.464836i	$0.153887\pi$
$97$			90.1781i			0.929671i	−0.885397	+	0.464836i	$0.846113\pi$
$98$		0			0
$99$	62.0000			0.626263
$100$		0			0
$101$	112.281	−	64.8254i	1.11169	−	0.641836i	0.172425	−	0.985023i	$-0.444840\pi$
$101$	112.281	−	64.8254i	1.11169	−	0.641836i	0.939267	+	0.343187i	$0.111506\pi$
$102$		0			0
$103$	29.8077	+	17.2095i	0.289395	+	0.167082i	0.637669	−	0.770310i	$-0.279899\pi$
$103$	29.8077	+	17.2095i	0.289395	+	0.167082i	−0.348274	+	0.937393i	$0.613232\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	74.9411	−	129.802i	0.700384	−	1.21310i	−0.267947	−	0.963434i	$-0.586345\pi$
$107$	74.9411	−	129.802i	0.700384	−	1.21310i	0.968332	−	0.249668i	$-0.0803214\pi$
$108$		0			0
$109$	33.6274	+	58.2444i	0.308508	+	0.534352i	0.978036	−	0.208435i	$-0.0668369\pi$
$109$	33.6274	+	58.2444i	0.308508	+	0.534352i	−0.669528	+	0.742787i	$0.733504\pi$
$110$		0			0
$111$			88.4749i			0.797071i
$112$		0			0
$113$	70.2843			0.621985			0.310992	−	0.950412i	$-0.399339\pi$
$113$	70.2843			0.621985			0.310992	+	0.950412i	$0.399339\pi$
$114$		0			0
$115$	15.7194	−	9.07562i	0.136691	−	0.0789184i
$116$		0			0
$117$	−86.8660	−	50.1521i	−0.742445	−	0.428651i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−28.1274	+	48.7181i	−0.232458	+	0.402629i
$122$		0			0
$123$	−129.539	−	224.368i	−1.05316	−	1.82413i
$124$		0			0
$125$			31.4476i			0.251581i
$126$		0			0
$127$	93.7645			0.738303			0.369152	−	0.929369i	$-0.379648\pi$
$127$	93.7645			0.738303			0.369152	+	0.929369i	$0.379648\pi$
$128$		0			0
$129$	−147.219	+	84.9969i	−1.14123	+	0.658891i
$130$		0			0
$131$	−126.636	−	73.1131i	−0.966684	−	0.558116i	−0.0684606	−	0.997654i	$-0.521809\pi$
$131$	−126.636	−	73.1131i	−0.966684	−	0.558116i	−0.898224	+	0.439538i	$0.855142\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−5.08831	+	8.81321i	−0.0376912	+	0.0652831i
$136$		0			0
$137$	74.8823	+	129.700i	0.546586	+	0.946714i	0.998505	+	0.0546556i	$0.0174061\pi$
$137$	74.8823	+	129.700i	0.546586	+	0.946714i	−0.451919	+	0.892059i	$0.649261\pi$
$138$		0			0
$139$		−	120.249i		−	0.865100i	−0.901610	−	0.432550i	$-0.857614\pi$
$139$		−	120.249i		−	0.865100i	0.901610	−	0.432550i	$-0.142386\pi$
$140$		0			0
$141$	3.88225			0.0275337
$142$		0			0
$143$	248.346	−	143.382i	1.73668	−	1.00267i
$144$		0			0
$145$	−20.4891	−	11.8294i	−0.141304	−	0.0815820i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−16.8823	+	29.2409i	−0.113304	+	0.196248i	−0.917100	−	0.398656i	$-0.869477\pi$
$149$	−16.8823	+	29.2409i	−0.113304	+	0.196248i	0.803797	+	0.594904i	$0.202810\pi$
$150$		0			0
$151$	72.3137	+	125.251i	0.478899	+	0.829477i	0.999707	−	0.0241966i	$-0.00770277\pi$
$151$	72.3137	+	125.251i	0.478899	+	0.829477i	−0.520808	+	0.853674i	$0.674369\pi$
$152$		0			0
$153$		−	28.5136i		−	0.186363i
$154$		0			0
$155$	−13.2548			−0.0855151
$156$		0			0
$157$	111.560	−	64.4089i	0.710570	−	0.410248i	−0.100702	−	0.994917i	$-0.532109\pi$
$157$	111.560	−	64.4089i	0.710570	−	0.410248i	0.811272	+	0.584669i	$0.198775\pi$
$158$		0			0
$159$	−49.1986	−	28.4048i	−0.309425	−	0.178647i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	28.7157	−	49.7371i	0.176170	−	0.305136i	−0.764395	−	0.644748i	$-0.776962\pi$
$163$	28.7157	−	49.7371i	0.176170	−	0.305136i	0.940566	+	0.339612i	$0.110296\pi$
$164$		0			0
$165$	15.5980	+	27.0165i	0.0945332	+	0.163736i
$166$		0			0
$167$		−	229.122i		−	1.37199i	−0.727607	−	0.685994i	$-0.759367\pi$
$167$		−	229.122i		−	1.37199i	0.727607	−	0.685994i	$-0.240633\pi$
$168$		0			0
$169$	−294.931			−1.74515
$170$		0			0
$171$	−79.6335	+	45.9764i	−0.465693	+	0.268868i
$172$		0			0
$173$	−106.790	−	61.6552i	−0.617282	−	0.356388i	0.158528	−	0.987355i	$-0.449325\pi$
$173$	−106.790	−	61.6552i	−0.617282	−	0.356388i	−0.775810	+	0.630966i	$0.782659\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−27.5147	+	47.6569i	−0.155450	+	0.269248i
$178$		0			0
$179$	−135.971	−	235.508i	−0.759612	−	1.31569i	−0.943049	−	0.332655i	$-0.892055\pi$
$179$	−135.971	−	235.508i	−0.759612	−	1.31569i	0.183436	−	0.983032i	$-0.441278\pi$
$180$		0			0
$181$			30.6333i			0.169245i	0.996413	+	0.0846225i	$0.0269684\pi$
$181$			30.6333i			0.169245i	−0.996413	+	0.0846225i	$0.973032\pi$
$182$		0			0
$183$	−320.735			−1.75265
$184$		0			0
$185$	−13.1462	+	7.58994i	−0.0710604	+	0.0410267i
$186$		0			0
$187$	70.5975	+	40.7595i	0.377527	+	0.217965i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−34.7990	+	60.2736i	−0.182194	+	0.315569i	−0.942627	−	0.333847i	$-0.891653\pi$
$191$	−34.7990	+	60.2736i	−0.182194	+	0.315569i	0.760434	+	0.649416i	$0.224986\pi$
$192$		0			0
$193$	−139.711	−	241.986i	−0.723890	−	1.25381i	−0.959429	−	0.281949i	$-0.909019\pi$
$193$	−139.711	−	241.986i	−0.723890	−	1.25381i	0.235540	−	0.971865i	$-0.424314\pi$
$194$		0			0
$195$		−	50.4692i		−	0.258816i
$196$		0			0
$197$	102.451			0.520055			0.260027	−	0.965601i	$-0.416268\pi$
$197$	102.451			0.520055			0.260027	+	0.965601i	$0.416268\pi$
$198$		0			0
$199$	−140.253	+	80.9750i	−0.704788	+	0.406910i	−0.809128	−	0.587632i	$-0.800060\pi$
$199$	−140.253	+	80.9750i	−0.704788	+	0.406910i	0.104340	+	0.994542i	$0.466727\pi$
$200$		0			0
$201$	−78.8179	−	45.5055i	−0.392129	−	0.226396i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	22.2254	−	38.4955i	0.108417	−	0.187783i
$206$		0			0
$207$	66.6569	+	115.453i	0.322014	+	0.557744i
$208$		0			0
$209$		−	262.888i		−	1.25784i
$210$		0			0
$211$	51.0193			0.241798			0.120899	−	0.992665i	$-0.461422\pi$
$211$	51.0193			0.241798			0.120899	+	0.992665i	$0.461422\pi$
$212$		0			0
$213$	−144.113	+	83.2036i	−0.676586	+	0.390627i
$214$		0			0
$215$	−25.2588	−	14.5832i	−0.117483	−	0.0678287i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	95.5980	−	165.581i	0.436520	−	0.756076i
$220$		0			0
$221$	−65.9411	−	114.213i	−0.298376	−	0.516803i
$222$		0			0
$223$			221.296i			0.992358i	0.868220	+	0.496179i	$0.165264\pi$
$223$			221.296i			0.992358i	−0.868220	+	0.496179i	$0.834736\pi$
$224$		0			0
$225$	−114.549			−0.509108
$226$		0			0
$227$	−87.5093	+	50.5235i	−0.385504	+	0.222571i	−0.680210	−	0.733017i	$-0.738111\pi$
$227$	−87.5093	+	50.5235i	−0.385504	+	0.222571i	0.294706	+	0.955588i	$0.404778\pi$
$228$		0			0
$229$	147.391	+	85.0964i	0.643630	+	0.371600i	0.786011	−	0.618212i	$-0.212143\pi$
$229$	147.391	+	85.0964i	0.643630	+	0.371600i	−0.142382	+	0.989812i	$0.545476\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	225.510	−	390.594i	0.967853	−	1.67637i	0.266105	−	0.963944i	$-0.414263\pi$
$233$	225.510	−	390.594i	0.967853	−	1.67637i	0.701747	−	0.712426i	$-0.252404\pi$
$234$		0			0
$235$	0.333044	+	0.576850i	0.00141721	+	0.00245468i
$236$		0			0
$237$		−	124.597i		−	0.525726i
$238$		0			0
$239$	−219.137			−0.916892			−0.458446	−	0.888722i	$-0.651594\pi$
$239$	−219.137			−0.916892			−0.458446	+	0.888722i	$0.651594\pi$
$240$		0			0
$241$	281.792	−	162.693i	1.16926	−	0.675074i	0.215757	−	0.976447i	$-0.430778\pi$
$241$	281.792	−	162.693i	1.16926	−	0.675074i	0.953506	+	0.301373i	$0.0974449\pi$
$242$		0			0
$243$	−198.864	−	114.814i	−0.818372	−	0.472487i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−212.652	+	368.324i	−0.860938	+	1.49119i
$248$		0			0
$249$	−142.995	−	247.675i	−0.574277	−	0.994677i
$250$		0			0
$251$			260.063i			1.03611i	0.855348	+	0.518054i	$0.173343\pi$
$251$			260.063i			1.03611i	−0.855348	+	0.518054i	$0.826657\pi$
$252$		0			0
$253$	−381.137			−1.50647
$254$		0			0
$255$	12.4248	−	7.17346i	0.0487247	−	0.0281312i
$256$		0			0
$257$	159.832	+	92.2792i	0.621915	+	0.359063i	0.777614	−	0.628742i	$-0.216430\pi$
$257$	159.832	+	92.2792i	0.621915	+	0.359063i	−0.155699	+	0.987805i	$0.549763\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	86.8823	−	150.484i	0.332882	−	0.576569i
$262$		0			0
$263$	123.426	+	213.781i	0.469302	+	0.812855i	0.999384	−	0.0350915i	$-0.0111723\pi$
$263$	123.426	+	213.781i	0.469302	+	0.812855i	−0.530082	+	0.847946i	$0.677839\pi$
$264$		0			0
$265$		−	9.74700i		−	0.0367811i
$266$		0			0
$267$	−291.078			−1.09018
$268$		0			0
$269$	−91.0704	+	52.5795i	−0.338552	+	0.195463i	−0.659631	−	0.751589i	$-0.729288\pi$
$269$	−91.0704	+	52.5795i	−0.338552	+	0.195463i	0.321080	+	0.947052i	$0.395954\pi$
$270$		0			0
$271$	62.1887	+	35.9047i	0.229479	+	0.132489i	0.610331	−	0.792146i	$-0.291036\pi$
$271$	62.1887	+	35.9047i	0.229479	+	0.132489i	−0.380853	+	0.924636i	$0.624370\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	163.745	−	283.615i	0.595437	−	1.03133i
$276$		0			0
$277$	−201.049	−	348.227i	−0.725808	−	1.25714i	−0.958641	−	0.284619i	$-0.908133\pi$
$277$	−201.049	−	348.227i	−0.725808	−	1.25714i	0.232833	−	0.972517i	$-0.425201\pi$
$278$		0			0
$279$		−	97.3516i		−	0.348930i
$280$		0			0
$281$	321.529			1.14423			0.572116	−	0.820173i	$-0.306123\pi$
$281$	321.529			1.14423			0.572116	+	0.820173i	$0.306123\pi$
$282$		0			0
$283$	420.508	−	242.781i	1.48590	−	0.857882i	0.486024	−	0.873945i	$-0.338447\pi$
$283$	420.508	−	242.781i	1.48590	−	0.857882i	0.999871	+	0.0160633i	$0.00511333\pi$
$284$		0			0
$285$	−40.0684	−	23.1335i	−0.140591	−	0.0811702i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−125.755	+	217.814i	−0.435138	+	0.753681i
$290$		0			0
$291$	−166.627	−	288.607i	−0.572603	−	0.991777i
$292$		0			0
$293$			480.218i			1.63897i	0.573100	+	0.819485i	$0.305741\pi$
$293$			480.218i			1.63897i	−0.573100	+	0.819485i	$0.694259\pi$
$294$		0			0
$295$	−9.44156			−0.0320053
$296$		0			0
$297$	185.059	−	106.844i	0.623093	−	0.359743i
$298$		0			0
$299$	533.998	+	308.304i	1.78595	+	1.03112i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−239.563	+	414.936i	−0.790639	+	1.36943i
$304$		0			0
$305$	−27.5147	−	47.6569i	−0.0902122	−	0.156252i
$306$		0			0
$307$			13.1876i			0.0429564i	0.999769	+	0.0214782i	$0.00683725\pi$
$307$			13.1876i			0.0429564i	−0.999769	+	0.0214782i	$0.993163\pi$
$308$		0			0
$309$	−127.196			−0.411637
$310$		0			0
$311$	−340.530	+	196.605i	−1.09495	+	0.632171i	−0.934891	−	0.354936i	$-0.884503\pi$
$311$	−340.530	+	196.605i	−1.09495	+	0.632171i	−0.160062	+	0.987107i	$0.551169\pi$
$312$		0			0
$313$	−191.992	−	110.847i	−0.613394	−	0.354143i	0.160898	−	0.986971i	$-0.448561\pi$
$313$	−191.992	−	110.847i	−0.613394	−	0.354143i	−0.774293	+	0.632828i	$0.781894\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	47.2843	−	81.8988i	0.149162	−	0.258356i	−0.781756	−	0.623584i	$-0.785676\pi$
$317$	47.2843	−	81.8988i	0.149162	−	0.258356i	0.930918	+	0.365229i	$0.119009\pi$
$318$		0			0
$319$	248.392	+	430.227i	0.778658	+	1.34868i
$320$		0			0
$321$			553.893i			1.72552i
$322$		0			0
$323$	−120.902			−0.374308
$324$		0			0
$325$	−458.835	+	264.909i	−1.41180	+	0.815104i
$326$		0			0
$327$	−215.243	−	124.271i	−0.658236	−	0.380033i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−95.1665	+	164.833i	−0.287512	+	0.497986i	−0.973215	−	0.229896i	$-0.926162\pi$
$331$	−95.1665	+	164.833i	−0.287512	+	0.497986i	0.685703	+	0.727881i	$0.259495\pi$
$332$		0			0
$333$	−55.7452	−	96.5535i	−0.167403	−	0.289950i
$334$		0			0
$335$		−	15.6150i		−	0.0466120i
$336$		0			0
$337$	−430.735			−1.27815			−0.639073	−	0.769146i	$-0.720682\pi$
$337$	−430.735			−1.27815			−0.639073	+	0.769146i	$0.720682\pi$
$338$		0			0
$339$	−224.939	+	129.868i	−0.663536	+	0.383093i
$340$		0			0
$341$	241.035	+	139.162i	0.706847	+	0.408098i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−33.5391	+	58.0914i	−0.0972148	+	0.168381i
$346$		0			0
$347$	−125.627	−	217.593i	−0.362039	−	0.627069i	0.626258	−	0.779616i	$-0.284586\pi$
$347$	−125.627	−	217.593i	−0.362039	−	0.627069i	−0.988296	+	0.152547i	$0.951253\pi$
$348$		0			0
$349$			78.3487i			0.224495i	0.993680	+	0.112247i	$0.0358049\pi$
$349$			78.3487i			0.224495i	−0.993680	+	0.112247i	$0.964195\pi$
$350$		0			0
$351$	−345.706			−0.984916
$352$		0			0
$353$	−38.0281	+	21.9555i	−0.107728	+	0.0621970i	−0.552896	−	0.833250i	$-0.686477\pi$
$353$	−38.0281	+	21.9555i	−0.107728	+	0.0621970i	0.445168	+	0.895447i	$0.353144\pi$
$354$		0			0
$355$	−24.7258	−	14.2755i	−0.0696503	−	0.0402126i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	273.215	−	473.223i	0.761045	−	1.31817i	−0.181267	−	0.983434i	$-0.558020\pi$
$359$	273.215	−	473.223i	0.761045	−	1.31817i	0.942312	−	0.334735i	$-0.108647\pi$
$360$		0			0
$361$	14.4462	+	25.0215i	0.0400171	+	0.0693117i
$362$		0			0
$363$		−	207.891i		−	0.572702i
$364$		0			0
$365$	32.8040			0.0898741
$366$		0			0
$367$	416.996	−	240.753i	1.13623	−	0.656002i	0.190734	−	0.981642i	$-0.438913\pi$
$367$	416.996	−	240.753i	1.13623	−	0.656002i	0.945494	+	0.325640i	$0.105580\pi$
$368$		0			0
$369$	282.735	+	163.237i	0.766218	+	0.442376i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	216.421	−	374.853i	0.580218	−	1.00497i	−0.415235	−	0.909714i	$-0.636301\pi$
$373$	216.421	−	374.853i	0.580218	−	1.00497i	0.995453	−	0.0952531i	$-0.0303660\pi$
$374$		0			0
$375$	−58.1076	−	100.645i	−0.154954	−	0.268388i
$376$		0			0
$377$		−	803.702i		−	2.13184i
$378$		0			0
$379$	512.607			1.35253			0.676263	−	0.736660i	$-0.263598\pi$
$379$	512.607			1.35253			0.676263	+	0.736660i	$0.263598\pi$
$380$		0			0
$381$	−300.085	+	173.254i	−0.787625	+	0.454735i
$382$		0			0
$383$	564.559	+	325.948i	1.47405	+	0.851040i	0.999573	−	0.0292301i	$-0.00930557\pi$
$383$	564.559	+	325.948i	1.47405	+	0.851040i	0.474472	+	0.880270i	$0.342639\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	107.108	−	185.516i	0.276764	−	0.479369i
$388$		0			0
$389$	261.676	+	453.236i	0.672689	+	1.16513i	0.977139	+	0.212604i	$0.0681943\pi$
$389$	261.676	+	453.236i	0.672689	+	1.16513i	−0.304449	+	0.952529i	$0.598472\pi$
$390$		0			0
$391$			175.284i			0.448296i
$392$		0			0
$393$	540.382			1.37502
$394$		0			0
$395$	18.5134	−	10.6887i	0.0468695	−	0.0270601i
$396$		0			0
$397$	13.7276	+	7.92563i	0.0345783	+	0.0199638i	0.517190	−	0.855871i	$-0.326978\pi$
$397$	13.7276	+	7.92563i	0.0345783	+	0.0199638i	−0.482611	+	0.875835i	$0.660312\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5.88730	+	10.1971i	−0.0146816	+	0.0254292i	−0.873273	−	0.487232i	$-0.838007\pi$
$401$	−5.88730	+	10.1971i	−0.0146816	+	0.0254292i	0.858591	+	0.512661i	$0.171340\pi$
$402$		0			0
$403$	−225.137	−	389.949i	−0.558653	−	0.967615i
$404$		0			0
$405$		−	64.1820i		−	0.158474i
$406$		0			0
$407$	318.745			0.783158
$408$		0			0
$409$	426.503	−	246.241i	1.04279	−	0.602057i	0.122171	−	0.992509i	$-0.461014\pi$
$409$	426.503	−	246.241i	1.04279	−	0.602057i	0.920623	+	0.390452i	$0.127681\pi$
$410$		0			0
$411$	−479.308	−	276.729i	−1.16620	−	0.673306i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	24.5341	−	42.4942i	0.0591182	−	0.102396i
$416$		0			0
$417$	222.191	+	384.846i	0.532832	+	0.922892i
$418$		0			0
$419$		−	276.946i		−	0.660970i	−0.943811	−	0.330485i	$-0.892788\pi$
$419$		−	276.946i		−	0.660970i	0.943811	−	0.330485i	$-0.107212\pi$
$420$		0			0
$421$	14.3532			0.0340932			0.0170466	−	0.999855i	$-0.494574\pi$
$421$	14.3532			0.0340932			0.0170466	+	0.999855i	$0.494574\pi$
$422$		0			0
$423$	−4.23674	+	2.44608i	−0.0100159	+	0.00578270i
$424$		0			0
$425$	−130.434	−	75.3059i	−0.306903	−	0.177190i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−529.872	+	917.765i	−1.23513	+	2.13931i
$430$		0			0
$431$	125.235	+	216.914i	0.290570	+	0.503281i	0.973945	−	0.226786i	$-0.0728219\pi$
$431$	125.235	+	216.914i	0.290570	+	0.503281i	−0.683375	+	0.730068i	$0.739489\pi$
$432$		0			0
$433$		−	656.534i		−	1.51625i	−0.652112	−	0.758123i	$-0.726117\pi$
$433$		−	656.534i		−	1.51625i	0.652112	−	0.758123i	$-0.273883\pi$
$434$		0			0
$435$	87.4315			0.200992
$436$		0			0
$437$	489.537	−	282.634i	1.12022	−	0.646760i
$438$		0			0
$439$	−308.650	−	178.199i	−0.703075	−	0.405921i	0.105417	−	0.994428i	$-0.466382\pi$
$439$	−308.650	−	178.199i	−0.703075	−	0.405921i	−0.808492	+	0.588508i	$0.799716\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	126.892	−	219.784i	0.286439	−	0.496126i	−0.686518	−	0.727112i	$-0.740862\pi$
$443$	126.892	−	219.784i	0.286439	−	0.496126i	0.972957	+	0.230986i	$0.0741952\pi$
$444$		0			0
$445$	−24.9706	−	43.2503i	−0.0561136	−	0.0971916i
$446$		0			0
$447$		−	124.777i		−	0.279144i
$448$		0			0
$449$	−107.921			−0.240358			−0.120179	−	0.992752i	$-0.538347\pi$
$449$	−107.921			−0.240358			−0.120179	+	0.992752i	$0.538347\pi$
$450$		0			0
$451$	−808.324	+	466.686i	−1.79229	+	1.03478i
$452$		0			0
$453$	−462.867	−	267.237i	−1.02178	−	0.589926i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−71.9949	+	124.699i	−0.157538	+	0.272864i	−0.933980	−	0.357324i	$-0.883689\pi$
$457$	−71.9949	+	124.699i	−0.157538	+	0.272864i	0.776442	+	0.630189i	$0.217022\pi$
$458$		0			0
$459$	−49.1371	−	85.1079i	−0.107052	−	0.185420i
$460$		0			0
$461$			380.728i			0.825875i	0.910759	+	0.412938i	$0.135497\pi$
$461$			380.728i			0.825875i	−0.910759	+	0.412938i	$0.864503\pi$
$462$		0			0
$463$	227.990			0.492419			0.246209	−	0.969217i	$-0.420815\pi$
$463$	227.990			0.492419			0.246209	+	0.969217i	$0.420815\pi$
$464$		0			0
$465$	42.4209	−	24.4917i	0.0912278	−	0.0526704i
$466$		0			0
$467$	−435.539	−	251.458i	−0.932631	−	0.538455i	−0.0449884	−	0.998988i	$-0.514325\pi$
$467$	−435.539	−	251.458i	−0.932631	−	0.538455i	−0.887643	+	0.460533i	$0.847658\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−238.024	+	412.270i	−0.505360	+	0.875309i
$472$		0			0
$473$	306.215	+	530.380i	0.647390	+	1.12131i
$474$		0			0
$475$			485.704i			1.02254i
$476$		0			0
$477$	71.5879			0.150079
$478$		0			0
$479$	184.149	−	106.318i	0.384444	−	0.221959i	−0.295306	−	0.955403i	$-0.595422\pi$
$479$	184.149	−	106.318i	0.384444	−	0.221959i	0.679750	+	0.733444i	$0.262088\pi$
$480$		0			0
$481$	−446.583	−	257.835i	−0.928446	−	0.536039i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	28.5887	−	49.5172i	0.0589459	−	0.102097i
$486$		0			0
$487$	−60.7056	−	105.145i	−0.124652	−	0.215904i	0.796945	−	0.604052i	$-0.206448\pi$
$487$	−60.7056	−	105.145i	−0.124652	−	0.215904i	−0.921597	+	0.388148i	$0.873115\pi$
$488$		0			0
$489$			212.239i			0.434027i
$490$		0			0
$491$	130.353			0.265485			0.132743	−	0.991151i	$-0.457622\pi$
$491$	130.353			0.265485			0.132743	+	0.991151i	$0.457622\pi$
$492$		0			0
$493$	197.860	−	114.235i	0.401339	−	0.231713i
$494$		0			0
$495$	−34.0444	−	19.6556i	−0.0687767	−	0.0397082i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	78.9899	−	136.815i	0.158296	−	0.274177i	−0.775958	−	0.630785i	$-0.782733\pi$
$499$	78.9899	−	136.815i	0.158296	−	0.274177i	0.934254	+	0.356607i	$0.116067\pi$
$500$		0			0
$501$	423.362	+	733.285i	0.845035	+	1.46364i
$502$		0			0
$503$			323.502i			0.643146i	0.946885	+	0.321573i	$0.104212\pi$
$503$			323.502i			0.643146i	−0.946885	+	0.321573i	$0.895788\pi$
$504$		0			0
$505$	−82.2052			−0.162783
$506$		0			0
$507$	943.901	−	544.961i	1.86174	−	1.07487i
$508$		0			0
$509$	−437.969	−	252.862i	−0.860450	−	0.496781i	0.00371263	−	0.999993i	$-0.498818\pi$
$509$	−437.969	−	252.862i	−0.860450	−	0.496781i	−0.864163	+	0.503212i	$0.832152\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−158.461	+	274.462i	−0.308891	+	0.535014i
$514$		0			0
$515$	−10.9117	−	18.8996i	−0.0211877	−	0.0366982i
$516$		0			0
$517$		−	13.9864i		−	0.0270531i
$518$		0			0
$519$	455.696			0.878026
$520$		0			0
$521$	−716.925	+	413.917i	−1.37606	+	0.794466i	−0.991682	−	0.128712i	$-0.958916\pi$
$521$	−716.925	+	413.917i	−1.37606	+	0.794466i	−0.384373	+	0.923178i	$0.625582\pi$
$522$		0			0
$523$	98.9920	+	57.1531i	0.189277	+	0.109279i	0.591644	−	0.806199i	$-0.298479\pi$
$523$	98.9920	+	57.1531i	0.189277	+	0.109279i	−0.402367	+	0.915479i	$0.631812\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	64.0000	−	110.851i	0.121442	−	0.210344i
$528$		0			0
$529$	−145.265	−	251.605i	−0.274602	−	0.475625i
$530$		0			0
$531$		−	69.3446i		−	0.130592i
$532$		0			0
$533$	1510.02			2.83306
$534$		0			0
$535$	−82.3009	+	47.5165i	−0.153834	+	0.0888158i
$536$		0			0
$537$	870.324	+	502.482i	1.62071	+	0.935720i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−264.549	+	458.213i	−0.489000	+	0.846974i	−0.999920	−	0.0126550i	$-0.995972\pi$
$541$	−264.549	+	458.213i	−0.489000	+	0.846974i	0.510920	+	0.859629i	$0.329305\pi$
$542$		0			0
$543$	−56.6030	−	98.0393i	−0.104241	−	0.180551i
$544$		0			0
$545$		−	42.6430i		−	0.0782440i
$546$		0			0
$547$	281.314			0.514285			0.257142	−	0.966374i	$-0.417219\pi$
$547$	281.314			0.514285			0.257142	+	0.966374i	$0.417219\pi$
$548$		0			0
$549$	350.021	−	202.085i	0.637561	−	0.368096i
$550$		0			0
$551$	−638.075	−	368.392i	−1.15803	−	0.668589i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	28.0488	−	48.5819i	0.0505383	−	0.0875350i
$556$		0			0
$557$	99.2355	+	171.881i	0.178161	+	0.308583i	0.941251	−	0.337709i	$-0.109652\pi$
$557$	99.2355	+	171.881i	0.178161	+	0.308583i	−0.763090	+	0.646292i	$0.776319\pi$
$558$		0			0
$559$		−	990.797i		−	1.77244i
$560$		0			0
$561$	−301.255			−0.536996
$562$		0			0
$563$	85.1245	−	49.1467i	0.151198	−	0.0872942i	−0.422492	−	0.906367i	$-0.638845\pi$
$563$	85.1245	−	49.1467i	0.151198	−	0.0872942i	0.573690	+	0.819072i	$0.305511\pi$
$564$		0			0
$565$	−38.5934	−	22.2819i	−0.0683069	−	0.0394370i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	354.515	−	614.038i	0.623049	−	1.07915i	−0.365866	−	0.930668i	$-0.619227\pi$
$569$	354.515	−	614.038i	0.623049	−	1.07915i	0.988915	−	0.148484i	$-0.0474395\pi$
$570$		0			0
$571$	231.059	+	400.206i	0.404657	+	0.700886i	0.994281	−	0.106792i	$-0.0340578\pi$
$571$	231.059	+	400.206i	0.404657	+	0.700886i	−0.589625	+	0.807677i	$0.700724\pi$
$572$		0			0
$573$		−	257.201i		−	0.448867i
$574$		0			0
$575$	704.177			1.22465
$576$		0			0
$577$	−507.985	+	293.285i	−0.880391	+	0.508294i	−0.870787	−	0.491660i	$-0.836390\pi$
$577$	−507.985	+	293.285i	−0.880391	+	0.508294i	−0.00960341	+	0.999954i	$0.503057\pi$
$578$		0			0
$579$	894.264	+	516.303i	1.54450	+	0.891716i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−102.333	+	177.246i	−0.175528	+	0.304024i
$584$		0			0
$585$	31.7990	+	55.0775i	0.0543572	+	0.0941495i
$586$		0			0
$587$		−	441.613i		−	0.752322i	−0.926554	−	0.376161i	$-0.877244\pi$
$587$		−	441.613i		−	0.752322i	0.926554	−	0.376161i	$-0.122756\pi$
$588$		0			0
$589$	−412.784			−0.700821
$590$		0			0
$591$	−327.885	+	189.304i	−0.554797	+	0.320312i
$592$		0			0
$593$	−75.3672	−	43.5133i	−0.127095	−	0.0733782i	0.435105	−	0.900380i	$-0.356711\pi$
$593$	−75.3672	−	43.5133i	−0.127095	−	0.0733782i	−0.562199	+	0.827002i	$0.690045\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	299.245	−	518.307i	0.501247	−	0.868186i
$598$		0			0
$599$	242.054	+	419.250i	0.404097	+	0.699916i	0.994216	−	0.107400i	$-0.0342526\pi$
$599$	242.054	+	419.250i	0.404097	+	0.699916i	−0.590119	+	0.807316i	$0.700919\pi$
$600$		0			0
$601$			904.895i			1.50565i	0.658221	+	0.752825i	$0.271309\pi$
$601$			904.895i			1.50565i	−0.658221	+	0.752825i	$0.728691\pi$
$602$		0			0
$603$	114.686			0.190193
$604$		0			0
$605$	30.8898	−	17.8342i	0.0510574	−	0.0294780i
$606$		0			0
$607$	814.913	+	470.490i	1.34253	+	0.775107i	0.987177	−	0.159627i	$-0.0510291\pi$
$607$	814.913	+	470.490i	1.34253	+	0.775107i	0.355348	+	0.934734i	$0.384362\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−11.3137	+	19.5959i	−0.0185167	+	0.0320719i
$612$		0			0
$613$	−120.314	−	208.389i	−0.196270	−	0.339950i	0.751046	−	0.660250i	$-0.229550\pi$
$613$	−120.314	−	208.389i	−0.196270	−	0.339950i	−0.947316	+	0.320300i	$0.896216\pi$
$614$		0			0
$615$			164.269i			0.267104i
$616$		0			0
$617$	781.716			1.26696			0.633481	−	0.773758i	$-0.281625\pi$
$617$	781.716			1.26696			0.633481	+	0.773758i	$0.281625\pi$
$618$		0			0
$619$	8.65912	−	4.99935i	0.0139889	−	0.00807649i	−0.492989	−	0.870035i	$-0.664096\pi$
$619$	8.65912	−	4.99935i	0.0139889	−	0.00807649i	0.506978	+	0.861959i	$0.330762\pi$
$620$		0			0
$621$	397.917	+	229.738i	0.640768	+	0.369948i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−297.505	+	515.294i	−0.476008	+	0.824470i
$626$		0			0
$627$	485.754	+	841.351i	0.774728	+	1.34187i
$628$		0			0
$629$		−	146.590i		−	0.233052i
$630$		0			0
$631$	−908.538			−1.43984			−0.719919	−	0.694058i	$-0.755821\pi$
$631$	−908.538			−1.43984			−0.719919	+	0.694058i	$0.755821\pi$
$632$		0			0
$633$	−163.283	+	94.2714i	−0.257951	+	0.148928i
$634$		0			0
$635$	−51.4865	−	29.7257i	−0.0810810	−	0.0468122i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	104.848	−	181.602i	0.164081	−	0.284197i
$640$		0			0
$641$	−96.7300	−	167.541i	−0.150905	−	0.261375i	0.780656	−	0.624962i	$-0.214885\pi$
$641$	−96.7300	−	167.541i	−0.150905	−	0.261375i	−0.931560	+	0.363587i	$0.881552\pi$
$642$		0			0
$643$		−	362.412i		−	0.563627i	−0.959469	−	0.281814i	$-0.909064\pi$
$643$		−	362.412i		−	0.563627i	0.959469	−	0.281814i	$-0.0909360\pi$
$644$		0			0
$645$	107.785			0.167108
$646$		0			0
$647$	−311.444	+	179.812i	−0.481366	+	0.277917i	−0.720986	−	0.692950i	$-0.756311\pi$
$647$	−311.444	+	179.812i	−0.481366	+	0.277917i	0.239619	+	0.970867i	$0.422977\pi$
$648$		0			0
$649$	171.692	+	99.1263i	0.264548	+	0.152737i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	357.843	−	619.802i	0.547998	−	0.949160i	−0.450414	−	0.892820i	$-0.648723\pi$
$653$	357.843	−	619.802i	0.547998	−	0.949160i	0.998412	−	0.0563404i	$-0.0179432\pi$
$654$		0			0
$655$	46.3574	+	80.2934i	0.0707747	+	0.122585i
$656$		0			0
$657$			240.933i			0.366717i
$658$		0			0
$659$	390.431			0.592459			0.296230	−	0.955117i	$-0.404271\pi$
$659$	390.431			0.592459			0.296230	+	0.955117i	$0.404271\pi$
$660$		0			0
$661$	−303.520	+	175.237i	−0.459183	+	0.265109i	−0.711700	−	0.702483i	$-0.752075\pi$
$661$	−303.520	+	175.237i	−0.459183	+	0.265109i	0.252518	+	0.967592i	$0.418741\pi$
$662$		0			0
$663$	422.078	+	243.687i	0.636618	+	0.367551i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−534.098	+	925.084i	−0.800746	+	1.38693i
$668$		0			0
$669$	−408.902	−	708.238i	−0.611213	−	1.05865i
$670$		0			0
$671$			1155.50i			1.72206i
$672$		0			0
$673$	487.214			0.723944			0.361972	−	0.932189i	$-0.382104\pi$
$673$	487.214			0.723944			0.361972	+	0.932189i	$0.382104\pi$
$674$		0			0
$675$	−341.908	+	197.401i	−0.506531	+	0.292446i
$676$		0			0
$677$	391.220	+	225.871i	0.577873	+	0.333635i	0.760288	−	0.649586i	$-0.225058\pi$
$677$	391.220	+	225.871i	0.577873	+	0.333635i	−0.182414	+	0.983222i	$0.558391\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	186.711	−	323.392i	0.274171	−	0.474879i
$682$		0			0
$683$	−112.373	−	194.635i	−0.164528	−	0.284971i	0.771960	−	0.635672i	$-0.219277\pi$
$683$	−112.373	−	194.635i	−0.164528	−	0.284971i	−0.936488	+	0.350701i	$0.885943\pi$
$684$		0			0
$685$		−	94.9583i		−	0.138625i
$686$		0			0
$687$	−628.950			−0.915503
$688$		0			0
$689$	286.751	−	165.555i	0.416184	−	0.240284i
$690$		0			0
$691$	48.5715	+	28.0427i	0.0702915	+	0.0405828i	0.534734	−	0.845021i	$-0.320412\pi$
$691$	48.5715	+	28.0427i	0.0702915	+	0.0405828i	−0.464442	+	0.885603i	$0.653745\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−38.1219	+	66.0291i	−0.0548517	+	0.0950059i
$696$		0			0
$697$	214.627	+	371.746i	0.307930	+	0.533351i
$698$		0			0
$699$			1666.75i			2.38448i
$700$		0			0
$701$	−769.647			−1.09793			−0.548963	−	0.835846i	$-0.684977\pi$
$701$	−769.647			−1.09793			−0.548963	+	0.835846i	$0.684977\pi$
$702$		0			0
$703$	−409.400	+	236.367i	−0.582361	+	0.336226i
$704$		0			0
$705$	−2.13176	−	1.23077i	−0.00302377	−	0.00174578i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−232.980	+	403.533i	−0.328603	+	0.569158i	−0.982235	−	0.187655i	$-0.939911\pi$
$709$	−232.980	+	403.533i	−0.328603	+	0.569158i	0.653632	+	0.756813i	$0.273245\pi$
$710$		0			0
$711$	78.5046	+	135.974i	0.110414	+	0.191243i
$712$		0			0
$713$			598.456i			0.839350i
$714$		0			0
$715$	−181.823			−0.254298
$716$		0			0
$717$	701.329	−	404.913i	0.978144	−	0.564732i
$718$		0			0
$719$	−910.957	−	525.942i	−1.26698	−	0.731490i	−0.292563	−	0.956246i	$-0.594508\pi$
$719$	−910.957	−	525.942i	−1.26698	−	0.731490i	−0.974415	+	0.224756i	$0.927842\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−601.235	+	1041.37i	−0.831583	+	1.44034i
$724$		0			0
$725$	−458.921	−	794.874i	−0.632994	−	1.09638i
$726$		0			0
$727$			161.080i			0.221568i	0.993845	+	0.110784i	$0.0353361\pi$
$727$			161.080i			0.221568i	−0.993845	+	0.110784i	$0.964664\pi$
$728$		0			0
$729$	−62.4315			−0.0856399
$730$		0			0
$731$	243.920	−	140.828i	0.333680	−	0.192650i
$732$		0			0
$733$	1245.95	+	719.349i	1.69979	+	0.981376i	0.945945	+	0.324327i	$0.105138\pi$
$733$	1245.95	+	719.349i	1.69979	+	0.981376i	0.753848	+	0.657049i	$0.228195\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−163.941	+	283.954i	−0.222444	+	0.385284i
$738$		0			0
$739$	568.696	+	985.010i	0.769547	+	1.33290i	0.937809	+	0.347153i	$0.112851\pi$
$739$	568.696	+	985.010i	0.769547	+	1.33290i	−0.168261	+	0.985742i	$0.553815\pi$
$740$		0			0
$741$		−	1571.72i		−	2.12108i
$742$		0			0
$743$	745.882			1.00388			0.501940	−	0.864903i	$-0.332620\pi$
$743$	745.882			1.00388			0.501940	+	0.864903i	$0.332620\pi$
$744$		0			0
$745$	18.5402	−	10.7042i	0.0248862	−	0.0143681i
$746$		0			0
$747$	312.103	+	180.193i	0.417809	+	0.241222i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−76.9411	+	133.266i	−0.102452	+	0.177451i	−0.912694	−	0.408643i	$-0.866002\pi$
$751$	−76.9411	+	133.266i	−0.102452	+	0.177451i	0.810243	+	0.586095i	$0.199335\pi$
$752$		0			0
$753$	−480.534	−	832.309i	−0.638159	−	1.10532i
$754$		0			0
$755$		−	91.7011i		−	0.121458i
$756$		0			0
$757$	−119.137			−0.157381			−0.0786903	−	0.996899i	$-0.525074\pi$
$757$	−119.137			−0.157381			−0.0786903	+	0.996899i	$0.525074\pi$
$758$		0			0
$759$	1219.80	−	704.250i	1.60711	−	0.927865i
$760$		0			0
$761$	−1199.62	−	692.600i	−1.57637	−	0.910119i	−0.995360	−	0.0962239i	$-0.969324\pi$
$761$	−1199.62	−	692.600i	−1.57637	−	0.910119i	−0.581012	−	0.813895i	$-0.697343\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−9.03954	+	15.6569i	−0.0118164	+	0.0204666i
$766$		0			0
$767$	−160.368	−	277.765i	−0.209084	−	0.362144i
$768$		0			0
$769$			55.9020i			0.0726945i	0.999339	+	0.0363472i	$0.0115722\pi$
$769$			55.9020i			0.0726945i	−0.999339	+	0.0363472i	$0.988428\pi$
$770$		0			0
$771$	−682.039			−0.884616
$772$		0			0
$773$	155.676	−	89.8797i	0.201392	−	0.116274i	−0.395912	−	0.918288i	$-0.629572\pi$
$773$	155.676	−	89.8797i	0.201392	−	0.116274i	0.597305	+	0.802014i	$0.296238\pi$
$774$		0			0
$775$	−445.328	−	257.110i	−0.574617	−	0.331755i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	692.146	−	1198.83i	0.888506	−	1.53894i
$780$		0			0
$781$	299.754	+	519.190i	0.383808	+	0.664776i
$782$		0			0
$783$		−	598.892i		−	0.764868i
$784$		0			0
$785$	−81.6771			−0.104047
$786$		0			0
$787$	−180.448	+	104.182i	−0.229286	+	0.132378i	−0.610242	−	0.792215i	$-0.708928\pi$
$787$	−180.448	+	104.182i	−0.229286	+	0.132378i	0.380957	+	0.924593i	$0.375595\pi$
$788$		0			0
$789$	−790.031	−	456.125i	−1.00131	−	0.578105i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	934.690	−	1618.93i	1.17868	−	2.04153i
$794$		0			0
$795$	18.0101	+	31.1944i	0.0226542	+	0.0392383i
$796$		0			0
$797$		−	237.327i		−	0.297776i	−0.988854	−	0.148888i	$-0.952431\pi$
$797$		−	237.327i		−	0.297776i	0.988854	−	0.148888i	$-0.0475694\pi$
$798$		0			0
$799$	−6.43232			−0.00805047
$800$		0			0
$801$	317.656	−	183.399i	0.396575	−	0.228963i
$802$		0			0
$803$	−596.531	−	344.407i	−0.742878	−	0.428901i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	194.309	−	336.552i	0.240779	−	0.417041i
$808$		0			0
$809$	−256.897	−	444.958i	−0.317548	−	0.550010i	0.662428	−	0.749126i	$-0.269526\pi$
$809$	−256.897	−	444.958i	−0.317548	−	0.550010i	−0.979976	+	0.199116i	$0.936193\pi$
$810$		0			0
$811$		−	452.373i		−	0.557797i	−0.960321	−	0.278898i	$-0.910031\pi$
$811$		−	452.373i		−	0.557797i	0.960321	−	0.278898i	$-0.0899692\pi$
$812$		0			0
$813$	−265.373			−0.326412
$814$		0			0
$815$	−31.5358	+	18.2072i	−0.0386943	+	0.0223402i
$816$		0			0
$817$	−786.612	−	454.151i	−0.962806	−	0.555876i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	720.519	−	1247.98i	0.877611	−	1.52007i	0.0236566	−	0.999720i	$-0.492469\pi$
$821$	720.519	−	1247.98i	0.877611	−	1.52007i	0.853955	−	0.520347i	$-0.174197\pi$
$822$		0			0
$823$	−801.828	−	1388.81i	−0.974275	−	1.68749i	−0.682307	−	0.731066i	$-0.739023\pi$
$823$	−801.828	−	1388.81i	−0.974275	−	1.68749i	−0.291968	−	0.956428i	$-0.594310\pi$
$824$		0			0
$825$			1210.25i			1.46697i
$826$		0			0
$827$	−933.549			−1.12884			−0.564419	−	0.825488i	$-0.690900\pi$
$827$	−933.549			−1.12884			−0.564419	+	0.825488i	$0.690900\pi$
$828$		0			0
$829$	−362.699	+	209.404i	−0.437514	+	0.252599i	−0.702543	−	0.711642i	$-0.747952\pi$
$829$	−362.699	+	209.404i	−0.437514	+	0.252599i	0.265029	+	0.964241i	$0.414619\pi$
$830$		0			0
$831$	1286.88	+	742.979i	1.54859	+	0.894079i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−72.6375	+	125.812i	−0.0869910	+	0.150673i
$836$		0			0
$837$	−167.765	−	290.577i	−0.200435	−	0.347164i
$838$		0			0
$839$		−	995.689i		−	1.18676i	−0.804924	−	0.593378i	$-0.797794\pi$
$839$		−	995.689i		−	1.18676i	0.804924	−	0.593378i	$-0.202206\pi$
$840$		0			0
$841$	551.313			0.655544
$842$		0			0
$843$	−1029.03	+	594.108i	−1.22067	+	0.704755i
$844$		0			0
$845$	161.948	+	93.5006i	0.191654	+	0.110652i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−897.200	+	1554.00i	−1.05677	+	1.83038i
$850$		0			0
$851$	342.686	+	593.550i	0.402687	+	0.697474i
$852$		0			0
$853$		−	315.117i		−	0.369422i	−0.982793	−	0.184711i	$-0.940865\pi$
$853$		−	315.117i		−	0.369422i	0.982793	−	0.184711i	$-0.0591349\pi$
$854$		0			0
$855$	58.3027			0.0681903
$856$		0			0
$857$	−189.042	+	109.144i	−0.220586	+	0.127355i	−0.606222	−	0.795296i	$-0.707316\pi$
$857$	−189.042	+	109.144i	−0.220586	+	0.127355i	0.385636	+	0.922651i	$0.373982\pi$
$858$		0			0
$859$	−1248.60	−	720.879i	−1.45355	−	0.839208i	−0.454870	−	0.890558i	$-0.650314\pi$
$859$	−1248.60	−	720.879i	−1.45355	−	0.839208i	−0.998681	+	0.0513505i	$0.983647\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	437.437	−	757.662i	0.506879	−	0.877940i	−0.493089	−	0.869979i	$-0.664132\pi$
$863$	437.437	−	757.662i	0.506879	−	0.877940i	0.999968	−	0.00796139i	$-0.00253422\pi$
$864$		0			0
$865$	39.0925	+	67.7102i	0.0451936	+	0.0782777i
$866$		0			0
$867$		−	929.459i		−	1.07204i
$868$		0			0
$869$	−448.881			−0.516549
$870$		0			0
$871$	459.384	−	265.226i	0.527422	−	0.304507i
$872$		0			0
$873$	363.684	+	209.973i	0.416591	+	0.240519i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−851.323	+	1474.53i	−0.970722	+	1.68134i	−0.277336	+	0.960773i	$0.589451\pi$
$877$	−851.323	+	1474.53i	−0.970722	+	1.68134i	−0.693386	+	0.720566i	$0.743882\pi$
$878$		0			0
$879$	−887.328	−	1536.90i	−1.00947	−	1.74846i
$880$		0			0
$881$			1018.58i			1.15617i	0.815978	+	0.578083i	$0.196199\pi$
$881$			1018.58i			1.15617i	−0.815978	+	0.578083i	$0.803801\pi$
$882$		0			0
$883$	−1646.04			−1.86414			−0.932071	−	0.362276i	$-0.882000\pi$
$883$	−1646.04			−1.86414			−0.932071	+	0.362276i	$0.882000\pi$
$884$		0			0
$885$	30.2169	−	17.4457i	0.0341434	−	0.0197127i
$886$		0			0
$887$	596.343	+	344.299i	0.672314	+	0.388161i	0.796953	−	0.604041i	$-0.206444\pi$
$887$	596.343	+	344.299i	0.672314	+	0.388161i	−0.124639	+	0.992202i	$0.539777\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−673.843	+	1167.13i	−0.756277	+	1.30991i
$892$		0			0
$893$	10.3717	+	17.9643i	0.0116145	+	0.0201168i
$894$		0			0
$895$			172.424i			0.192653i
$896$		0			0
$897$	−2278.68			−2.54034
$898$		0			0
$899$	675.537	−	390.022i	0.751432	−	0.433839i
$900$		0			0
$901$	81.5149	+	47.0627i	0.0904716	+	0.0522338i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	9.71154	−	16.8209i	0.0107310	−	0.0185866i
$906$		0			0
$907$	−106.009	−	183.613i	−0.116879	−	0.202440i	0.801650	−	0.597793i	$-0.203956\pi$
$907$	−106.009	−	183.613i	−0.116879	−	0.202440i	−0.918529	+	0.395353i	$0.870622\pi$
$908$		0			0
$909$		−	603.765i		−	0.664208i
$910$		0			0
$911$	601.882			0.660683			0.330342	−	0.943861i	$-0.392836\pi$
$911$	601.882			0.660683			0.330342	+	0.943861i	$0.392836\pi$
$912$		0			0
$913$	−892.288	+	515.163i	−0.977314	+	0.564253i
$914$		0			0
$915$	176.117	+	101.681i	0.192477	+	0.111127i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	559.171	−	968.512i	0.608456	−	1.05388i	−0.383039	−	0.923732i	$-0.625123\pi$
$919$	559.171	−	968.512i	0.608456	−	1.05388i	0.991495	−	0.130144i	$-0.0415440\pi$
$920$		0			0
$921$	−24.3675	−	42.2058i	−0.0264577	−	0.0458261i
$922$		0			0
$923$		−	969.892i		−	1.05080i
$924$		0			0
$925$	−588.903			−0.636652
$926$		0			0
$927$	138.810	−	80.1421i	0.149741	−	0.0864532i
$928$		0			0
$929$	348.062	+	200.954i	0.374663	+	0.216312i	0.675494	−	0.737366i	$-0.263931\pi$
$929$	348.062	+	200.954i	0.374663	+	0.216312i	−0.300831	+	0.953678i	$0.597264\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	726.558	−	1258.44i	0.778734	−	1.34881i
$934$		0			0
$935$	−25.8436	−	44.7624i	−0.0276402	−	0.0478742i
$936$		0			0
$937$		−	1597.84i		−	1.70527i	−0.522507	−	0.852635i	$-0.675003\pi$
$937$		−	1597.84i		−	1.70527i	0.522507	−	0.852635i	$-0.324997\pi$
$938$		0			0
$939$	819.273			0.872496
$940$		0			0
$941$	−1331.70	+	768.857i	−1.41520	+	0.817064i	−0.995872	−	0.0907721i	$-0.971067\pi$
$941$	−1331.70	+	768.857i	−1.41520	+	0.817064i	−0.419325	+	0.907836i	$0.637733\pi$
$942$		0			0
$943$	−1738.07	−	1003.48i	−1.84313	−	1.06413i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−160.137	+	277.366i	−0.169099	+	0.292889i	−0.938103	−	0.346355i	$-0.887419\pi$
$947$	−160.137	+	277.366i	−0.169099	+	0.292889i	0.769004	+	0.639244i	$0.220753\pi$
$948$		0			0
$949$	557.186	+	965.074i	0.587129	+	1.01694i
$950$		0			0
$951$			349.480i			0.367487i
$952$		0			0
$953$	−734.861			−0.771103			−0.385552	−	0.922686i	$-0.625989\pi$
$953$	−734.861			−0.771103			−0.385552	+	0.922686i	$0.625989\pi$
$954$		0			0
$955$	38.2165	−	22.0643i	0.0400173	−	0.0231040i
$956$		0			0
$957$	−1589.91	−	917.937i	−1.66135	−	0.959182i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−261.990	+	453.781i	−0.272623	+	0.472196i
$962$		0			0
$963$	−348.990	−	604.468i	−0.362399	−	0.627693i
$964$		0			0
$965$			177.167i			0.183593i
$966$		0			0
$967$	−1446.98			−1.49636			−0.748179	−	0.663497i	$-0.769072\pi$
$967$	−1446.98			−1.49636			−0.748179	+	0.663497i	$0.769072\pi$
$968$		0			0
$969$	386.935	−	223.397i	0.399314	−	0.230544i
$970$		0			0
$971$	836.653	+	483.042i	0.861641	+	0.497469i	0.864561	−	0.502527i	$-0.167596\pi$
$971$	836.653	+	483.042i	0.861641	+	0.497469i	−0.00292046	+	0.999996i	$0.500930\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	978.975	−	1695.63i	1.00408	−	1.73911i
$976$		0			0
$977$	304.803	+	527.935i	0.311979	+	0.540363i	0.978791	−	0.204863i	$-0.0656749\pi$
$977$	304.803	+	527.935i	0.311979	+	0.540363i	−0.666812	+	0.745226i	$0.732342\pi$
$978$		0			0
$979$			1048.66i			1.07115i
$980$		0			0
$981$	313.196			0.319262
$982$		0			0
$983$	−1106.15	+	638.635i	−1.12528	+	0.649679i	−0.942743	−	0.333520i	$-0.891763\pi$
$983$	−1106.15	+	638.635i	−1.12528	+	0.649679i	−0.182534	+	0.983199i	$0.558430\pi$
$984$		0			0
$985$	−56.2561	−	32.4795i	−0.0571128	−	0.0329741i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−658.431	+	1140.44i	−0.665754	+	1.15312i
$990$		0			0
$991$	−834.994	−	1446.25i	−0.842577	−	1.45939i	−0.887709	−	0.460406i	$-0.847704\pi$
$991$	−834.994	−	1446.25i	−0.842577	−	1.45939i	0.0451314	−	0.998981i	$-0.485629\pi$
$992$		0			0
$993$		−	703.379i		−	0.708338i
$994$		0			0
$995$	102.685			0.103201
$996$		0			0
$997$	684.118	−	394.976i	0.686177	−	0.396164i	−0.116001	−	0.993249i	$-0.537008\pi$
$997$	684.118	−	394.976i	0.686177	−	0.396164i	0.802178	+	0.597085i	$0.203674\pi$
$998$		0			0
$999$	−332.778	−	192.130i	−0.333111	−	0.192322i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.3.s.f.705.1		8
4.3	odd	2		392.3.o.b.313.4		8
7.2	even	3		112.3.c.c.97.1		4
7.3	odd	6	inner	784.3.s.f.129.1		8
7.4	even	3	inner	784.3.s.f.129.4		8
7.5	odd	6		112.3.c.c.97.4		4
7.6	odd	2	inner	784.3.s.f.705.4		8
21.2	odd	6		1008.3.f.h.433.2		4
21.5	even	6		1008.3.f.h.433.3		4
28.3	even	6		392.3.o.b.129.4		8
28.11	odd	6		392.3.o.b.129.1		8
28.19	even	6		56.3.c.a.41.1	✓	4
28.23	odd	6		56.3.c.a.41.4	yes	4
28.27	even	2		392.3.o.b.313.1		8
56.5	odd	6		448.3.c.e.321.1		4
56.19	even	6		448.3.c.f.321.4		4
56.37	even	6		448.3.c.e.321.4		4
56.51	odd	6		448.3.c.f.321.1		4
84.23	even	6		504.3.f.a.433.2		4
84.47	odd	6		504.3.f.a.433.3		4
140.19	even	6		1400.3.f.a.601.4		4
140.23	even	12		1400.3.p.a.1049.2		8
140.47	odd	12		1400.3.p.a.1049.1		8
140.79	odd	6		1400.3.f.a.601.1		4
140.103	odd	12		1400.3.p.a.1049.8		8
140.107	even	12		1400.3.p.a.1049.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.c.a.41.1	✓	4	28.19	even	6
56.3.c.a.41.4	yes	4	28.23	odd	6
112.3.c.c.97.1		4	7.2	even	3
112.3.c.c.97.4		4	7.5	odd	6
392.3.o.b.129.1		8	28.11	odd	6
392.3.o.b.129.4		8	28.3	even	6
392.3.o.b.313.1		8	28.27	even	2
392.3.o.b.313.4		8	4.3	odd	2
448.3.c.e.321.1		4	56.5	odd	6
448.3.c.e.321.4		4	56.37	even	6
448.3.c.f.321.1		4	56.51	odd	6
448.3.c.f.321.4		4	56.19	even	6
504.3.f.a.433.2		4	84.23	even	6
504.3.f.a.433.3		4	84.47	odd	6
784.3.s.f.129.1		8	7.3	odd	6	inner
784.3.s.f.129.4		8	7.4	even	3	inner
784.3.s.f.705.1		8	1.1	even	1	trivial
784.3.s.f.705.4		8	7.6	odd	2	inner
1008.3.f.h.433.2		4	21.2	odd	6
1008.3.f.h.433.3		4	21.5	even	6
1400.3.f.a.601.1		4	140.79	odd	6
1400.3.f.a.601.4		4	140.19	even	6
1400.3.p.a.1049.1		8	140.47	odd	12
1400.3.p.a.1049.2		8	140.23	even	12
1400.3.p.a.1049.7		8	140.107	even	12
1400.3.p.a.1049.8		8	140.103	odd	12

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	784.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.20041 + 1.84776i) q^{3} +(-0.549104 - 0.317025i) q^{5} +(2.32843 - 4.03295i) q^{9} +O(q^{10})\)	\(q+(-3.20041 + 1.84776i) q^{3} +(-0.549104 - 0.317025i) q^{5} +(2.32843 - 4.03295i) q^{9} +(6.65685 + 11.5300i) q^{11} -21.5391i q^{13} +2.34315 q^{15} +(5.30262 - 3.06147i) q^{17} +(-17.1003 - 9.87285i) q^{19} +(-14.3137 + 24.7921i) q^{23} +(-12.2990 - 21.3025i) q^{25} -16.0502i q^{27} +37.3137 q^{29} +(18.1043 - 10.4525i) q^{31} +(-42.6094 - 24.6005i) q^{33} +(11.9706 - 20.7336i) q^{37} +(39.7990 + 68.9339i) q^{39} +70.1061i q^{41} +46.0000 q^{43} +(-2.55710 + 1.47634i) q^{45} +(-0.909785 - 0.525265i) q^{47} +(-11.3137 + 19.5959i) q^{51} +(7.68629 + 13.3130i) q^{53} -8.44157i q^{55} +72.9706 q^{57} +(12.8959 - 7.44543i) q^{59} +(75.1626 + 43.3951i) q^{61} +(-6.82843 + 11.8272i) q^{65} +(12.3137 + 21.3280i) q^{67} -105.793i q^{69} +45.0294 q^{71} +(-44.8058 + 25.8686i) q^{73} +(78.7237 + 45.4511i) q^{75} +(-16.8579 + 29.1987i) q^{79} +(50.6127 + 87.6638i) q^{81} +77.3883i q^{83} -3.88225 q^{85} +(-119.419 + 68.9467i) q^{87} +(68.2127 + 39.3826i) q^{89} +(-38.6274 + 66.9046i) q^{93} +(6.25988 + 10.8424i) q^{95} +90.1781i q^{97} +62.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^9	\( 8 q - 4 q^{9} + 8 q^{11} + 64 q^{15} - 24 q^{23} + 60 q^{25} + 208 q^{29} - 40 q^{37} + 160 q^{39} + 368 q^{43} + 152 q^{53} + 448 q^{57} - 32 q^{65} + 8 q^{67} + 496 q^{71} - 248 q^{79} + 156 q^{81} + 512 q^{85} - 128 q^{93} + 480 q^{95} + 496 q^{99}+O(q^{100}) \) 8 * q - 4 * q^9 + 8 * q^11 + 64 * q^15 - 24 * q^23 + 60 * q^25 + 208 * q^29 - 40 * q^37 + 160 * q^39 + 368 * q^43 + 152 * q^53 + 448 * q^57 - 32 * q^65 + 8 * q^67 + 496 * q^71 - 248 * q^79 + 156 * q^81 + 512 * q^85 - 128 * q^93 + 480 * q^95 + 496 * q^99

Introduction

L-functions

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