LMFDB - Embedded newform 1300.2.ba.b.849.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1300,2,Mod(49,1300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1300, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("1300.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1300 = 2^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1300.ba (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:	$10.3805522628$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			849.4
Root			$-1.27597 + 0.609843i$ of defining polynomial
Character	$\chi$	$=$	1300.849
Dual form			1300.2.ba.b.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38581 + 0.800098i) q^{3} +(2.16612 + 3.75184i) q^{7} +(-0.219687 - 0.380509i) q^{9} +O(q^{10})$	$q+(1.38581 + 0.800098i) q^{3} +(2.16612 + 3.75184i) q^{7} +(-0.219687 - 0.380509i) q^{9} +(1.50000 + 0.866025i) q^{11} +(1.81988 + 3.11256i) q^{13} +(-6.49837 + 3.75184i) q^{17} +(-4.65213 + 2.68591i) q^{19} +6.93244i q^{21} +(1.00530 + 0.580411i) q^{23} -5.50367i q^{27} +(-1.01236 + 1.75347i) q^{29} -7.86488i q^{31} +(1.38581 + 2.40029i) q^{33} +(4.76632 - 8.25551i) q^{37} +(0.0316594 + 5.76950i) q^{39} +(6.69615 + 3.86603i) q^{41} +(3.62479 - 2.09277i) q^{43} +3.46410 q^{47} +(-5.88418 + 10.1917i) q^{49} -12.0073 q^{51} +12.6471i q^{53} -8.59596 q^{57} +(-5.49674 + 3.17354i) q^{59} +(-1.85154 - 3.20696i) q^{61} +(0.951738 - 1.64846i) q^{63} +(2.63022 - 4.55568i) q^{67} +(0.928771 + 1.60868i) q^{69} +(-10.8377 + 6.25714i) q^{71} +5.23898 q^{73} +7.50367i q^{77} +8.16719 q^{79} +(3.74441 - 6.48552i) q^{81} +0.456760 q^{83} +(-2.80589 + 1.61998i) q^{87} +(11.4967 + 6.63765i) q^{89} +(-7.73572 + 13.5701i) q^{91} +(6.29268 - 10.8992i) q^{93} +(-1.40511 - 2.43371i) q^{97} -0.761018i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{3} + 6 q^{7} + 4 q^{9}+O(q^{10}) $ 8 * q - 6 * q^3 + 6 * q^7 + 4 * q^9	$ 8 q - 6 q^{3} + 6 q^{7} + 4 q^{9} + 12 q^{11} - 18 q^{17} - 6 q^{23} - 6 q^{33} + 18 q^{37} + 4 q^{39} + 12 q^{41} + 18 q^{43} + 4 q^{49} - 36 q^{57} + 24 q^{59} - 4 q^{61} - 12 q^{63} - 18 q^{67} + 24 q^{69} - 36 q^{71} + 48 q^{73} + 16 q^{79} + 8 q^{81} + 72 q^{83} + 18 q^{87} + 24 q^{89} + 48 q^{93} - 6 q^{97}+O(q^{100}) $ 8 * q - 6 * q^3 + 6 * q^7 + 4 * q^9 + 12 * q^11 - 18 * q^17 - 6 * q^23 - 6 * q^33 + 18 * q^37 + 4 * q^39 + 12 * q^41 + 18 * q^43 + 4 * q^49 - 36 * q^57 + 24 * q^59 - 4 * q^61 - 12 * q^63 - 18 * q^67 + 24 * q^69 - 36 * q^71 + 48 * q^73 + 16 * q^79 + 8 * q^81 + 72 * q^83 + 18 * q^87 + 24 * q^89 + 48 * q^93 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times$.

$n$	$301$	$651$	$677$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	1.38581	+	0.800098i	0.800098	+	0.461937i	0.843505	−	0.537121i	$-0.180488\pi$
$3$	1.38581	+	0.800098i	0.800098	+	0.461937i	−0.0434075	+	0.999057i	$0.513821\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.16612	+	3.75184i	0.818718	+	1.41806i	0.906627	+	0.421932i	$0.138648\pi$
$7$	2.16612	+	3.75184i	0.818718	+	1.41806i	−0.0879098	+	0.996128i	$0.528019\pi$
$8$		0			0
$9$	−0.219687	−	0.380509i	−0.0732290	−	0.126836i
$10$		0			0
$11$	1.50000	+	0.866025i	0.452267	+	0.261116i	0.708787	−	0.705422i	$-0.249243\pi$
$11$	1.50000	+	0.866025i	0.452267	+	0.261116i	−0.256520	+	0.966539i	$0.582576\pi$
$12$		0			0
$13$	1.81988	+	3.11256i	0.504745	+	0.863269i
$13$	1.81988	+	3.11256i	0.504745	+	0.863269i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−6.49837	+	3.75184i	−1.57609	+	0.909954i	−0.580688	+	0.814126i	$0.697216\pi$
$17$	−6.49837	+	3.75184i	−1.57609	+	0.909954i	−0.995398	+	0.0958278i	$0.969450\pi$
$18$		0			0
$19$	−4.65213	+	2.68591i	−1.06727	+	0.616190i	−0.927435	−	0.373985i	$-0.877991\pi$
$19$	−4.65213	+	2.68591i	−1.06727	+	0.616190i	−0.139837	+	0.990175i	$0.544658\pi$
$20$		0			0
$21$			6.93244i			1.51278i
$22$		0			0
$23$	1.00530	+	0.580411i	0.209620	+	0.121024i	0.601135	−	0.799148i	$-0.294716\pi$
$23$	1.00530	+	0.580411i	0.209620	+	0.121024i	−0.391515	+	0.920172i	$0.628049\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	5.50367i		−	1.05918i
$28$		0			0
$29$	−1.01236	+	1.75347i	−0.187991	+	0.325610i	−0.944580	−	0.328280i	$-0.893531\pi$
$29$	−1.01236	+	1.75347i	−0.187991	+	0.325610i	0.756589	+	0.653891i	$0.226864\pi$
$30$		0			0
$31$		−	7.86488i		−	1.41257i	−0.707925	−	0.706287i	$-0.750369\pi$
$31$		−	7.86488i		−	1.41257i	0.707925	−	0.706287i	$-0.249631\pi$
$32$		0			0
$33$	1.38581	+	2.40029i	0.241239	+	0.417837i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.76632	−	8.25551i	0.783578	−	1.35720i	−0.146267	−	0.989245i	$-0.546726\pi$
$37$	4.76632	−	8.25551i	0.783578	−	1.35720i	0.929845	−	0.367952i	$-0.119941\pi$
$38$		0			0
$39$	0.0316594	+	5.76950i	0.00506956	+	0.923860i
$40$		0			0
$41$	6.69615	+	3.86603i	1.04576	+	0.603772i	0.921460	−	0.388473i	$-0.126997\pi$
$41$	6.69615	+	3.86603i	1.04576	+	0.603772i	0.124303	+	0.992244i	$0.460331\pi$
$42$		0			0
$43$	3.62479	−	2.09277i	0.552776	−	0.319145i	−0.197465	−	0.980310i	$-0.563271\pi$
$43$	3.62479	−	2.09277i	0.552776	−	0.319145i	0.750241	+	0.661165i	$0.229938\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.46410			0.505291			0.252646	−	0.967559i	$-0.418699\pi$
$47$	3.46410			0.505291			0.252646	+	0.967559i	$0.418699\pi$
$48$		0			0
$49$	−5.88418	+	10.1917i	−0.840597	+	1.45596i
$50$		0			0
$51$	−12.0073			−1.68136
$52$		0			0
$53$			12.6471i			1.73721i	0.495502	+	0.868607i	$0.334984\pi$
$53$			12.6471i			1.73721i	−0.495502	+	0.868607i	$0.665016\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−8.59596			−1.13856
$58$		0			0
$59$	−5.49674	+	3.17354i	−0.715615	+	0.413160i	−0.813136	−	0.582073i	$-0.802242\pi$
$59$	−5.49674	+	3.17354i	−0.715615	+	0.413160i	0.0975219	+	0.995233i	$0.468908\pi$
$60$		0			0
$61$	−1.85154	−	3.20696i	−0.237066	−	0.410610i	0.722805	−	0.691052i	$-0.242852\pi$
$61$	−1.85154	−	3.20696i	−0.237066	−	0.410610i	−0.959871	+	0.280442i	$0.909519\pi$
$62$		0			0
$63$	0.951738	−	1.64846i	0.119908	−	0.207686i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.63022	−	4.55568i	0.321333	−	0.556565i	−0.659430	−	0.751766i	$-0.729202\pi$
$67$	2.63022	−	4.55568i	0.321333	−	0.556565i	0.980763	+	0.195200i	$0.0625358\pi$
$68$		0			0
$69$	0.928771	+	1.60868i	0.111811	+	0.193662i
$70$		0			0
$71$	−10.8377	+	6.25714i	−1.28620	+	0.742586i	−0.977974	−	0.208729i	$-0.933067\pi$
$71$	−10.8377	+	6.25714i	−1.28620	+	0.742586i	−0.308222	+	0.951314i	$0.599734\pi$
$72$		0			0
$73$	5.23898			0.613177			0.306588	−	0.951842i	$-0.400813\pi$
$73$	5.23898			0.613177			0.306588	+	0.951842i	$0.400813\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			7.50367i			0.855123i
$78$		0			0
$79$	8.16719			0.918880			0.459440	−	0.888209i	$-0.348050\pi$
$79$	8.16719			0.918880			0.459440	+	0.888209i	$0.348050\pi$
$80$		0			0
$81$	3.74441	−	6.48552i	0.416046	−	0.720613i
$82$		0			0
$83$	0.456760			0.0501359			0.0250679	−	0.999686i	$-0.492020\pi$
$83$	0.456760			0.0501359			0.0250679	+	0.999686i	$0.492020\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−2.80589	+	1.61998i	−0.300823	+	0.173680i
$88$		0			0
$89$	11.4967	+	6.63765i	1.21865	+	0.703589i	0.964630	−	0.263609i	$-0.0849130\pi$
$89$	11.4967	+	6.63765i	1.21865	+	0.703589i	0.254022	+	0.967198i	$0.418246\pi$
$90$		0			0
$91$	−7.73572	+	13.5701i	−0.810924	+	1.42253i
$92$		0			0
$93$	6.29268	−	10.8992i	0.652520	−	1.13020i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−1.40511	−	2.43371i	−0.142667	−	0.247106i	0.785833	−	0.618439i	$-0.212234\pi$
$97$	−1.40511	−	2.43371i	−0.142667	−	0.247106i	−0.928500	+	0.371332i	$0.878901\pi$
$98$		0			0
$99$		−	0.761018i		−	0.0764852i
$100$		0			0
$101$	−3.31988	+	5.75021i	−0.330341	+	0.572167i	−0.982579	−	0.185847i	$-0.940497\pi$
$101$	−3.31988	+	5.75021i	−0.330341	+	0.572167i	0.652238	+	0.758014i	$0.273830\pi$
$102$		0			0
$103$		−	7.37605i		−	0.726784i	−0.931636	−	0.363392i	$-0.881619\pi$
$103$		−	7.37605i		−	0.726784i	0.931636	−	0.363392i	$-0.118381\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.85317	+	3.95668i	0.662521	+	0.382507i	0.793237	−	0.608913i	$-0.208394\pi$
$107$	6.85317	+	3.95668i	0.662521	+	0.382507i	−0.130716	+	0.991420i	$0.541728\pi$
$108$		0			0
$109$		−	9.18301i		−	0.879572i	−0.898102	−	0.439786i	$-0.855054\pi$
$109$		−	9.18301i		−	0.879572i	0.898102	−	0.439786i	$-0.144946\pi$
$110$		0			0
$111$	13.2104	−	7.62704i	1.25388	−	0.723927i
$112$		0			0
$113$	5.00204	−	2.88793i	0.470552	−	0.271674i	−0.245919	−	0.969291i	$-0.579090\pi$
$113$	5.00204	−	2.88793i	0.470552	−	0.271674i	0.716471	+	0.697617i	$0.245756\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.784552	−	1.37627i	0.0725319	−	0.127236i
$118$		0			0
$119$	−28.1525	−	16.2539i	−2.58074	−	1.48999i
$120$		0			0
$121$	−4.00000	−	6.92820i	−0.363636	−	0.629837i
$122$		0			0
$123$	6.18640	+	10.7152i	0.557809	+	0.966153i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	16.4266	+	9.48389i	1.45762	+	0.841559i	0.998894	−	0.0470176i	$-0.0149717\pi$
$127$	16.4266	+	9.48389i	1.45762	+	0.841559i	0.458729	+	0.888576i	$0.348305\pi$
$128$		0			0
$129$	6.69770			0.589699
$130$		0			0
$131$	−1.34637			−0.117633			−0.0588165	−	0.998269i	$-0.518733\pi$
$131$	−1.34637			−0.117633			−0.0588165	+	0.998269i	$0.518733\pi$
$132$		0			0
$133$	−20.1542	−	11.6360i	−1.74759	−	1.00897i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.18640	−	10.7152i	−0.528540	−	0.915457i	−0.999446	−	0.0332744i	$-0.989406\pi$
$137$	−6.18640	−	10.7152i	−0.528540	−	0.915457i	0.470907	−	0.882183i	$-0.343927\pi$
$138$		0			0
$139$	4.38418	+	7.59362i	0.371861	+	0.644083i	0.989852	−	0.142103i	$-0.0453864\pi$
$139$	4.38418	+	7.59362i	0.371861	+	0.644083i	−0.617991	+	0.786185i	$0.712053\pi$
$140$		0			0
$141$	4.80059	+	2.77162i	0.404282	+	0.233413i
$142$		0			0
$143$	0.0342681	+	6.24490i	0.00286565	+	0.522225i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−16.3087	+	9.41584i	−1.34512	+	0.776605i
$148$		0			0
$149$	−4.10443	+	2.36970i	−0.336248	+	0.194133i	−0.658612	−	0.752483i	$-0.728856\pi$
$149$	−4.10443	+	2.36970i	−0.336248	+	0.194133i	0.322363	+	0.946616i	$0.395523\pi$
$150$		0			0
$151$			1.56063i			0.127002i	0.997982	+	0.0635010i	$0.0202266\pi$
$151$			1.56063i			0.127002i	−0.997982	+	0.0635010i	$0.979773\pi$
$152$		0			0
$153$	2.85521	+	1.64846i	0.230830	+	0.133270i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		−	9.15332i		−	0.730515i	−0.930907	−	0.365257i	$-0.880981\pi$
$157$		−	9.15332i		−	0.730515i	0.930907	−	0.365257i	$-0.119019\pi$
$158$		0			0
$159$	−10.1189	+	17.5265i	−0.802483	+	1.38994i
$160$		0			0
$161$			5.02897i			0.396338i
$162$		0			0
$163$	−1.32151	−	2.28893i	−0.103509	−	0.179283i	0.809619	−	0.586956i	$-0.199674\pi$
$163$	−1.32151	−	2.28893i	−0.103509	−	0.179283i	−0.913128	+	0.407673i	$0.866340\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−4.45435	+	7.71515i	−0.344688	+	0.597017i	−0.985297	−	0.170850i	$-0.945349\pi$
$167$	−4.45435	+	7.71515i	−0.344688	+	0.597017i	0.640609	+	0.767867i	$0.278682\pi$
$168$		0			0
$169$	−6.37605	+	11.3290i	−0.490466	+	0.871460i
$170$		0			0
$171$	2.04402	+	1.18012i	0.156310	+	0.0902458i
$172$		0			0
$173$	11.9580	−	6.90396i	0.909151	−	0.524899i	0.0289933	−	0.999580i	$-0.490770\pi$
$173$	11.9580	−	6.90396i	0.909151	−	0.524899i	0.880158	+	0.474681i	$0.157437\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−10.1566			−0.763416
$178$		0			0
$179$	12.1751	−	21.0879i	0.910009	−	1.57618i	0.0959612	−	0.995385i	$-0.469408\pi$
$179$	12.1751	−	21.0879i	0.910009	−	1.57618i	0.814048	−	0.580797i	$-0.197259\pi$
$180$		0			0
$181$	24.8336			1.84587			0.922935	−	0.384956i	$-0.125783\pi$
$181$	24.8336			1.84587			0.922935	+	0.384956i	$0.125783\pi$
$182$		0			0
$183$		−	5.92566i		−	0.438037i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−12.9967			−0.950416
$188$		0			0
$189$	20.6489	−	11.9216i	1.50198	−	0.867171i
$190$		0			0
$191$	−2.98438	−	5.16909i	−0.215942	−	0.374022i	0.737622	−	0.675214i	$-0.235949\pi$
$191$	−2.98438	−	5.16909i	−0.215942	−	0.374022i	−0.953564	+	0.301192i	$0.902615\pi$
$192$		0			0
$193$	−4.52636	+	7.83988i	−0.325814	+	0.564327i	−0.981677	−	0.190553i	$-0.938972\pi$
$193$	−4.52636	+	7.83988i	−0.325814	+	0.564327i	0.655862	+	0.754880i	$0.272305\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.69452	−	9.86320i	0.405718	−	0.702724i	−0.588687	−	0.808361i	$-0.700355\pi$
$197$	5.69452	−	9.86320i	0.405718	−	0.702724i	0.994405	+	0.105637i	$0.0336882\pi$
$198$		0			0
$199$	−5.38863	−	9.33339i	−0.381990	−	0.661626i	0.609357	−	0.792896i	$-0.291428\pi$
$199$	−5.38863	−	9.33339i	−0.381990	−	0.661626i	−0.991347	+	0.131270i	$0.958094\pi$
$200$		0			0
$201$	7.28998	−	4.20887i	0.514196	−	0.296871i
$202$		0			0
$203$	−8.77162			−0.615647
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	0.510035i		−	0.0354499i
$208$		0			0
$209$	−9.30426			−0.643589
$210$		0			0
$211$	1.61256	−	2.79304i	0.111013	−	0.192280i	−0.805166	−	0.593050i	$-0.797924\pi$
$211$	1.61256	−	2.79304i	0.111013	−	0.192280i	0.916179	+	0.400769i	$0.131257\pi$
$212$		0			0
$213$	−20.0253			−1.37211
$214$		0			0
$215$		0			0
$216$		0			0
$217$	29.5078	−	17.0363i	2.00312	−	1.15650i
$218$		0			0
$219$	7.26023	+	4.19170i	0.490601	+	0.283249i
$220$		0			0
$221$	−23.5041	−	13.3987i	−1.58106	−	0.901292i
$222$		0			0
$223$	−8.48968	+	14.7046i	−0.568511	+	0.984690i	0.428203	+	0.903683i	$0.359147\pi$
$223$	−8.48968	+	14.7046i	−0.568511	+	0.984690i	−0.996714	+	0.0810069i	$0.974186\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.20026	+	2.07891i	0.0796641	+	0.137982i	0.903105	−	0.429420i	$-0.141282\pi$
$227$	1.20026	+	2.07891i	0.0796641	+	0.137982i	−0.823441	+	0.567402i	$0.807949\pi$
$228$		0			0
$229$		−	7.35671i		−	0.486145i	−0.970008	−	0.243073i	$-0.921845\pi$
$229$		−	7.35671i		−	0.486145i	0.970008	−	0.243073i	$-0.0781553\pi$
$230$		0			0
$231$	−6.00367	+	10.3987i	−0.395013	+	0.684182i
$232$		0			0
$233$			3.37410i			0.221045i	0.993874	+	0.110522i	$0.0352523\pi$
$233$			3.37410i			0.221045i	−0.993874	+	0.110522i	$0.964748\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	11.3182	+	6.53455i	0.735194	+	0.424464i
$238$		0			0
$239$		−	23.7807i		−	1.53824i	−0.639103	−	0.769121i	$-0.720694\pi$
$239$		−	23.7807i		−	1.53824i	0.639103	−	0.769121i	$-0.279306\pi$
$240$		0			0
$241$	19.3307	−	11.1606i	1.24520	−	0.718918i	0.275054	−	0.961429i	$-0.411304\pi$
$241$	19.3307	−	11.1606i	1.24520	−	0.718918i	0.970149	+	0.242511i	$0.0779709\pi$
$242$		0			0
$243$	−3.92086	+	2.26371i	−0.251523	+	0.145217i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−16.8264	−	9.59199i	−1.07064	−	0.610324i
$248$		0			0
$249$	0.632982	+	0.365452i	0.0401136	+	0.0231596i
$250$		0			0
$251$	−2.31119	−	4.00310i	−0.145881	−	0.252673i	0.783820	−	0.620988i	$-0.213268\pi$
$251$	−2.31119	−	4.00310i	−0.145881	−	0.252673i	−0.929701	+	0.368314i	$0.879935\pi$
$252$		0			0
$253$	1.00530	+	1.74123i	0.0632028	+	0.109470i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	18.9347	+	10.9320i	1.18111	+	0.681916i	0.956272	−	0.292479i	$-0.0944801\pi$
$257$	18.9347	+	10.9320i	1.18111	+	0.681916i	0.224842	+	0.974395i	$0.427813\pi$
$258$		0			0
$259$	41.2977			2.56612
$260$		0			0
$261$	0.889612			0.0550656
$262$		0			0
$263$	−17.4756	−	10.0895i	−1.07759	−	0.622146i	−0.147344	−	0.989085i	$-0.547072\pi$
$263$	−17.4756	−	10.0895i	−1.07759	−	0.622146i	−0.930245	+	0.366939i	$0.880406\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	10.6215	+	18.3970i	0.650027	+	1.12588i
$268$		0			0
$269$	3.64344	+	6.31062i	0.222144	+	0.384765i	0.955459	−	0.295124i	$-0.0953611\pi$
$269$	3.64344	+	6.31062i	0.222144	+	0.384765i	−0.733315	+	0.679889i	$0.762028\pi$
$270$		0			0
$271$	−4.23650	−	2.44595i	−0.257349	−	0.148581i	0.365775	−	0.930703i	$-0.380804\pi$
$271$	−4.23650	−	2.44595i	−0.257349	−	0.148581i	−0.623125	+	0.782122i	$0.714137\pi$
$272$		0			0
$273$	−21.5776	+	12.6162i	−1.30594	+	0.763569i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−7.62153	+	4.40029i	−0.457933	+	0.264388i	−0.711175	−	0.703015i	$-0.751837\pi$
$277$	−7.62153	+	4.40029i	−0.457933	+	0.264388i	0.253241	+	0.967403i	$0.418503\pi$
$278$		0			0
$279$	−2.99266	+	1.72781i	−0.179166	+	0.103441i
$280$		0			0
$281$		−	12.6085i		−	0.752161i	−0.926587	−	0.376081i	$-0.877272\pi$
$281$		−	12.6085i		−	0.752161i	0.926587	−	0.376081i	$-0.122728\pi$
$282$		0			0
$283$	18.1007	+	10.4505i	1.07598	+	0.621216i	0.929808	−	0.368044i	$-0.119972\pi$
$283$	18.1007	+	10.4505i	1.07598	+	0.621216i	0.146169	+	0.989260i	$0.453306\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			33.4972i			1.97727i
$288$		0			0
$289$	19.6525	−	34.0392i	1.15603	−	2.00231i
$290$		0			0
$291$		−	4.49689i		−	0.263612i
$292$		0			0
$293$	0.346241	+	0.599706i	0.0202276	+	0.0350352i	0.875962	−	0.482380i	$-0.160228\pi$
$293$	0.346241	+	0.599706i	0.0202276	+	0.0350352i	−0.855734	+	0.517415i	$0.826894\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	4.76632	−	8.25551i	0.276570	−	0.479033i
$298$		0			0
$299$	0.0229665	+	4.18534i	0.00132819	+	0.242044i
$300$		0			0
$301$	15.7035	+	9.06642i	0.905134	+	0.522580i
$302$		0			0
$303$	−9.20145	+	5.31246i	−0.528610	+	0.305193i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−8.83168			−0.504051			−0.252025	−	0.967721i	$-0.581097\pi$
$307$	−8.83168			−0.504051			−0.252025	+	0.967721i	$0.581097\pi$
$308$		0			0
$309$	5.90157	−	10.2218i	0.335728	−	0.581499i
$310$		0			0
$311$	−11.3958			−0.646198			−0.323099	−	0.946365i	$-0.604725\pi$
$311$	−11.3958			−0.646198			−0.323099	+	0.946365i	$0.604725\pi$
$312$		0			0
$313$			3.38496i			0.191329i	0.995414	+	0.0956647i	$0.0304977\pi$
$313$			3.38496i			0.191329i	−0.995414	+	0.0956647i	$0.969502\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.557104			0.0312901			0.0156450	−	0.999878i	$-0.495020\pi$
$317$	0.557104			0.0312901			0.0156450	+	0.999878i	$0.495020\pi$
$318$		0			0
$319$	−3.03709	+	1.75347i	−0.170044	+	0.0981752i
$320$		0			0
$321$	6.33146	+	10.9664i	0.353388	+	0.612086i
$322$		0			0
$323$	20.1542	−	34.9080i	1.12141	−	1.94234i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	7.34730	−	12.7259i	0.406307	−	0.703744i
$328$		0			0
$329$	7.50367	+	12.9967i	0.413691	+	0.716533i
$330$		0			0
$331$	3.43266	−	1.98185i	0.188676	−	0.108932i	−0.402687	−	0.915338i	$-0.631924\pi$
$331$	3.43266	−	1.98185i	0.188676	−	0.108932i	0.591363	+	0.806406i	$0.298590\pi$
$332$		0			0
$333$	−4.18839			−0.229522
$334$		0			0
$335$		0			0
$336$		0			0
$337$			16.7243i			0.911030i	0.890228	+	0.455515i	$0.150545\pi$
$337$			16.7243i			0.911030i	−0.890228	+	0.455515i	$0.849455\pi$
$338$		0			0
$339$	9.24251			0.501984
$340$		0			0
$341$	6.81119	−	11.7973i	0.368847	−	0.638861i
$342$		0			0
$343$	−20.6577			−1.11541
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.56521	−	3.79043i	0.352439	−	0.203481i	−0.313320	−	0.949648i	$-0.601441\pi$
$347$	6.56521	−	3.79043i	0.352439	−	0.203481i	0.665759	+	0.746167i	$0.268108\pi$
$348$		0			0
$349$	−23.6733	−	13.6678i	−1.26720	−	0.731621i	−0.292746	−	0.956190i	$-0.594569\pi$
$349$	−23.6733	−	13.6678i	−1.26720	−	0.731621i	−0.974458	+	0.224569i	$0.927903\pi$
$350$		0			0
$351$	17.1305	−	10.0160i	0.914359	−	0.534616i
$352$		0			0
$353$	13.0461	−	22.5964i	0.694372	−	1.20269i	−0.276020	−	0.961152i	$-0.589016\pi$
$353$	13.0461	−	22.5964i	0.694372	−	1.20269i	0.970392	−	0.241536i	$-0.0776511\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−26.0094	−	45.0496i	−1.37656	−	2.38428i
$358$		0			0
$359$		−	0.694176i		−	0.0366372i	−0.999832	−	0.0183186i	$-0.994169\pi$
$359$		−	0.694176i		−	0.0366372i	0.999832	−	0.0183186i	$-0.00583132\pi$
$360$		0			0
$361$	4.92820	−	8.53590i	0.259379	−	0.449258i
$362$		0			0
$363$		−	12.8016i		−	0.671908i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−19.7643	−	11.4109i	−1.03169	−	0.595644i	−0.114218	−	0.993456i	$-0.536436\pi$
$367$	−19.7643	−	11.4109i	−1.03169	−	0.595644i	−0.917467	+	0.397812i	$0.869770\pi$
$368$		0			0
$369$		−	3.39726i		−	0.176854i
$370$		0			0
$371$	−47.4499	+	27.3952i	−2.46347	+	1.42229i
$372$		0			0
$373$	6.82540	−	3.94065i	0.353406	−	0.204039i	−0.312779	−	0.949826i	$-0.601260\pi$
$373$	6.82540	−	3.94065i	0.353406	−	0.204039i	0.666184	+	0.745787i	$0.267926\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−7.30015	+	0.0400587i	−0.375977	+	0.00206313i
$378$		0			0
$379$	−26.9703	−	15.5713i	−1.38537	−	0.799843i	−0.392580	−	0.919718i	$-0.628417\pi$
$379$	−26.9703	−	15.5713i	−1.38537	−	0.799843i	−0.992789	+	0.119875i	$0.961751\pi$
$380$		0			0
$381$	15.1761	+	26.2857i	0.777494	+	1.34666i
$382$		0			0
$383$	−17.2561	−	29.8885i	−0.881747	−	1.52723i	−0.849397	−	0.527754i	$-0.823034\pi$
$383$	−17.2561	−	29.8885i	−0.881747	−	1.52723i	−0.0323495	−	0.999477i	$-0.510299\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.59264	−	0.919510i	−0.0809584	−	0.0467413i
$388$		0			0
$389$	6.18414			0.313548			0.156774	−	0.987634i	$-0.449891\pi$
$389$	6.18414			0.313548			0.156774	+	0.987634i	$0.449891\pi$
$390$		0			0
$391$	−8.71043			−0.440505
$392$		0			0
$393$	−1.86582	−	1.07723i	−0.0941179	−	0.0543390i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	11.3281	+	19.6209i	0.568543	+	0.984745i	0.996710	+	0.0810459i	$0.0258260\pi$
$397$	11.3281	+	19.6209i	0.568543	+	0.984745i	−0.428167	+	0.903699i	$0.640841\pi$
$398$		0			0
$399$	−18.6199	−	32.2506i	−0.932161	−	1.61455i
$400$		0			0
$401$	3.35847	+	1.93902i	0.167714	+	0.0968298i	0.581508	−	0.813541i	$-0.302463\pi$
$401$	3.35847	+	1.93902i	0.167714	+	0.0968298i	−0.413793	+	0.910371i	$0.635796\pi$
$402$		0			0
$403$	24.4799	−	14.3132i	1.21943	−	0.712990i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	14.2990	−	8.25551i	0.708773	−	0.409210i
$408$		0			0
$409$	−12.0037	+	6.93032i	−0.593543	+	0.342682i	−0.766497	−	0.642248i	$-0.778002\pi$
$409$	−12.0037	+	6.93032i	−0.593543	+	0.342682i	0.172954	+	0.984930i	$0.444669\pi$
$410$		0			0
$411$		−	19.7989i		−	0.976607i
$412$		0			0
$413$	−23.8132	−	13.7486i	−1.17177	−	0.676523i
$414$		0			0
$415$		0			0
$416$		0			0
$417$			14.0311i			0.687106i
$418$		0			0
$419$	−15.1751	+	26.2840i	−0.741352	+	1.28406i	0.210528	+	0.977588i	$0.432482\pi$
$419$	−15.1751	+	26.2840i	−0.741352	+	1.28406i	−0.951880	+	0.306471i	$0.900852\pi$
$420$		0			0
$421$			0.608516i			0.0296573i	0.999890	+	0.0148286i	$0.00472027\pi$
$421$			0.608516i			0.0296573i	−0.999890	+	0.0148286i	$0.995280\pi$
$422$		0			0
$423$	−0.761018	−	1.31812i	−0.0370019	−	0.0640892i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	8.02134	−	13.8934i	0.388180	−	0.672347i
$428$		0			0
$429$	−4.94905	+	8.68167i	−0.238942	+	0.419155i
$430$		0			0
$431$	−34.0819	−	19.6772i	−1.64167	−	0.947818i	−0.980240	−	0.197810i	$-0.936617\pi$
$431$	−34.0819	−	19.6772i	−1.64167	−	0.947818i	−0.661429	−	0.750008i	$-0.730050\pi$
$432$		0			0
$433$	5.56810	−	3.21474i	0.267586	−	0.154491i	−0.360204	−	0.932873i	$-0.617293\pi$
$433$	5.56810	−	3.21474i	0.267586	−	0.154491i	0.627790	+	0.778383i	$0.283960\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−6.23572			−0.298295
$438$		0			0
$439$	−0.735722	+	1.27431i	−0.0351141	+	0.0608194i	−0.883048	−	0.469282i	$-0.844513\pi$
$439$	−0.735722	+	1.27431i	−0.0351141	+	0.0608194i	0.847934	+	0.530101i	$0.177846\pi$
$440$		0			0
$441$	5.17071			0.246224
$442$		0			0
$443$			16.9193i			0.803860i	0.915670	+	0.401930i	$0.131660\pi$
$443$			16.9193i			0.803860i	−0.915670	+	0.401930i	$0.868340\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−7.58396			−0.358709
$448$		0			0
$449$	7.89557	−	4.55851i	0.372615	−	0.215129i	−0.301985	−	0.953313i	$-0.597649\pi$
$449$	7.89557	−	4.55851i	0.372615	−	0.215129i	0.674600	+	0.738183i	$0.264316\pi$
$450$		0			0
$451$	6.69615	+	11.5981i	0.315310	+	0.546132i
$452$		0			0
$453$	−1.24865	+	2.16273i	−0.0586669	+	0.101614i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	8.77811	−	15.2041i	0.410623	−	0.711220i	−0.584335	−	0.811512i	$-0.698645\pi$
$457$	8.77811	−	15.2041i	0.410623	−	0.711220i	0.994958	+	0.100293i	$0.0319779\pi$
$458$		0			0
$459$	20.6489	+	35.7649i	0.963807	+	1.66936i
$460$		0			0
$461$	−13.2973	+	7.67722i	−0.619318	+	0.357564i	−0.776604	−	0.629990i	$-0.783059\pi$
$461$	−13.2973	+	7.67722i	−0.619318	+	0.357564i	0.157285	+	0.987553i	$0.449726\pi$
$462$		0			0
$463$	−18.8614			−0.876562			−0.438281	−	0.898838i	$-0.644412\pi$
$463$	−18.8614			−0.876562			−0.438281	+	0.898838i	$0.644412\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			32.9302i			1.52383i	0.647679	+	0.761913i	$0.275740\pi$
$467$			32.9302i			1.52383i	−0.647679	+	0.761913i	$0.724260\pi$
$468$		0			0
$469$	22.7896			1.05232
$470$		0			0
$471$	7.32355	−	12.6848i	0.337452	−	0.584483i
$472$		0			0
$473$	7.24958			0.333336
$474$		0			0
$475$		0			0
$476$		0			0
$477$	4.81234	−	2.77840i	0.220342	−	0.127214i
$478$		0			0
$479$	14.9368	+	8.62378i	0.682481	+	0.394031i	0.800789	−	0.598946i	$-0.204414\pi$
$479$	14.9368	+	8.62378i	0.682481	+	0.394031i	−0.118308	+	0.992977i	$0.537747\pi$
$480$		0			0
$481$	34.3699	−	0.188601i	1.56713	−	0.00859944i
$482$		0			0
$483$	−4.02367	+	6.96919i	−0.183083	+	0.317109i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−8.98720	−	15.5663i	−0.407249	−	0.705376i	0.587331	−	0.809346i	$-0.300178\pi$
$487$	−8.98720	−	15.5663i	−0.407249	−	0.705376i	−0.994580	+	0.103971i	$0.966845\pi$
$488$		0			0
$489$		−	4.22936i		−	0.191258i
$490$		0			0
$491$	13.0977	−	22.6858i	0.591089	−	1.02380i	−0.402997	−	0.915201i	$-0.632032\pi$
$491$	13.0977	−	22.6858i	0.591089	−	1.02380i	0.994086	−	0.108595i	$-0.0346350\pi$
$492$		0			0
$493$		−	15.1929i		−	0.684253i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−46.9515	−	27.1075i	−2.10606	−	1.21594i
$498$		0			0
$499$			18.3428i			0.821139i	0.911829	+	0.410569i	$0.134670\pi$
$499$			18.3428i			0.821139i	−0.911829	+	0.410569i	$0.865330\pi$
$500$		0			0
$501$	−12.3458	+	7.12783i	−0.551568	+	0.318448i
$502$		0			0
$503$	12.3462	−	7.12811i	0.550492	−	0.317827i	−0.198829	−	0.980034i	$-0.563714\pi$
$503$	12.3462	−	7.12811i	0.550492	−	0.317827i	0.749320	+	0.662208i	$0.230380\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−17.9003	+	10.5984i	−0.794980	+	0.470690i
$508$		0			0
$509$	−27.5380	−	15.8991i	−1.22060	−	0.704714i	−0.255555	−	0.966795i	$-0.582258\pi$
$509$	−27.5380	−	15.8991i	−1.22060	−	0.704714i	−0.965046	+	0.262081i	$0.915591\pi$
$510$		0			0
$511$	11.3483	+	19.6558i	0.502018	+	0.869521i
$512$		0			0
$513$	14.7824	+	25.6038i	0.652657	+	1.13043i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	5.19615	+	3.00000i	0.228527	+	0.131940i
$518$		0			0
$519$	22.0954			0.969880
$520$		0			0
$521$	−45.1676			−1.97883			−0.989414	−	0.145122i	$-0.953642\pi$
$521$	−45.1676			−1.97883			−0.989414	+	0.145122i	$0.953642\pi$
$522$		0			0
$523$	22.6159	+	13.0573i	0.988924	+	0.570955i	0.904952	−	0.425513i	$-0.139906\pi$
$523$	22.6159	+	13.0573i	0.988924	+	0.570955i	0.0839712	+	0.996468i	$0.473240\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	29.5078	+	51.1089i	1.28538	+	2.22634i
$528$		0			0
$529$	−10.8262	−	18.7516i	−0.470706	−	0.815287i
$530$		0			0
$531$	2.41512	+	1.39437i	0.104807	+	0.0605106i
$532$		0			0
$533$	0.152976	+	27.8779i	0.00662615	+	1.20753i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	33.7447	−	19.4825i	1.45619	−	0.840733i
$538$		0			0
$539$	−17.6525	+	10.1917i	−0.760349	+	0.438988i
$540$		0			0
$541$			31.4750i			1.35321i	0.736344	+	0.676607i	$0.236550\pi$
$541$			31.4750i			1.35321i	−0.736344	+	0.676607i	$0.763450\pi$
$542$		0			0
$543$	34.4147	+	19.8693i	1.47688	+	0.852675i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	5.70391i		−	0.243881i	−0.992537	−	0.121941i	$-0.961088\pi$
$547$		−	5.70391i		−	0.243881i	0.992537	−	0.121941i	$-0.0389118\pi$
$548$		0			0
$549$	−0.813519	+	1.40906i	−0.0347201	+	0.0601370i
$550$		0			0
$551$		−	10.8765i		−	0.463353i
$552$		0			0
$553$	17.6911	+	30.6419i	0.752303	+	1.30303i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−10.4360	+	18.0757i	−0.442187	+	0.765890i	−0.997851	−	0.0655165i	$-0.979130\pi$
$557$	−10.4360	+	18.0757i	−0.442187	+	0.765890i	0.555665	+	0.831406i	$0.312464\pi$
$558$		0			0
$559$	13.1106	+	7.47378i	0.554519	+	0.316107i
$560$		0			0
$561$	−18.0110	−	10.3987i	−0.760426	−	0.439032i
$562$		0			0
$563$	−28.7793	+	16.6157i	−1.21290	+	0.700270i	−0.963391	−	0.268102i	$-0.913604\pi$
$563$	−28.7793	+	16.6157i	−1.21290	+	0.700270i	−0.249513	+	0.968372i	$0.580270\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	32.4435			1.36250
$568$		0			0
$569$	20.0336	−	34.6992i	0.839851	−	1.45466i	−0.0501680	−	0.998741i	$-0.515976\pi$
$569$	20.0336	−	34.6992i	0.839851	−	1.45466i	0.890019	−	0.455924i	$-0.150691\pi$
$570$		0			0
$571$	−4.53590			−0.189821			−0.0949107	−	0.995486i	$-0.530257\pi$
$571$	−4.53590			−0.189821			−0.0949107	+	0.995486i	$0.530257\pi$
$572$		0			0
$573$		−	9.55117i		−	0.399006i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	35.2706			1.46834			0.734168	−	0.678968i	$-0.237573\pi$
$577$	35.2706			1.46834			0.734168	+	0.678968i	$0.237573\pi$
$578$		0			0
$579$	−12.5453	+	7.24306i	−0.521367	+	0.301011i
$580$		0			0
$581$	0.989397	+	1.71369i	0.0410471	+	0.0710957i
$582$		0			0
$583$	−10.9527	+	18.9707i	−0.453615	+	0.785684i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	20.5832	−	35.6511i	0.849558	−	1.47148i	−0.0320457	−	0.999486i	$-0.510202\pi$
$587$	20.5832	−	35.6511i	0.849558	−	1.47148i	0.881603	−	0.471991i	$-0.156464\pi$
$588$		0			0
$589$	21.1244	+	36.5885i	0.870414	+	1.50760i
$590$		0			0
$591$	15.7831	−	9.11235i	0.649228	−	0.374832i
$592$		0			0
$593$	9.39726			0.385899			0.192950	−	0.981209i	$-0.438195\pi$
$593$	9.39726			0.385899			0.192950	+	0.981209i	$0.438195\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		−	17.2457i		−	0.705821i
$598$		0			0
$599$	−21.7881			−0.890239			−0.445119	−	0.895471i	$-0.646839\pi$
$599$	−21.7881			−0.890239			−0.445119	+	0.895471i	$0.646839\pi$
$600$		0			0
$601$	−12.5481	+	21.7340i	−0.511848	+	0.886547i	0.488058	+	0.872811i	$0.337706\pi$
$601$	−12.5481	+	21.7340i	−0.511848	+	0.886547i	−0.999906	+	0.0137352i	$0.995628\pi$
$602$		0			0
$603$	−2.31130			−0.0941236
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−29.4254	+	16.9888i	−1.19434	+	0.689552i	−0.959288	−	0.282431i	$-0.908859\pi$
$607$	−29.4254	+	16.9888i	−1.19434	+	0.689552i	−0.235052	+	0.971983i	$0.575526\pi$
$608$		0			0
$609$	−12.1558	−	7.01815i	−0.492578	−	0.284390i
$610$		0			0
$611$	6.30426	+	10.7822i	0.255043	+	0.436202i
$612$		0			0
$613$	10.7235	−	18.5736i	0.433118	−	0.750182i	−0.564022	−	0.825760i	$-0.690747\pi$
$613$	10.7235	−	18.5736i	0.433118	−	0.750182i	0.997140	+	0.0755778i	$0.0240801\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	17.0372	+	29.5092i	0.685890	+	1.18800i	0.973156	+	0.230146i	$0.0739203\pi$
$617$	17.0372	+	29.5092i	0.685890	+	1.18800i	−0.287266	+	0.957851i	$0.592746\pi$
$618$		0			0
$619$			26.9791i			1.08438i	0.840256	+	0.542191i	$0.182405\pi$
$619$			26.9791i			1.08438i	−0.840256	+	0.542191i	$0.817595\pi$
$620$		0			0
$621$	3.19439	−	5.53285i	0.128186	−	0.222026i
$622$		0			0
$623$			57.5118i			2.30416i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−12.8939	−	7.44432i	−0.514934	−	0.297297i
$628$		0			0
$629$			71.5298i			2.85208i
$630$		0			0
$631$	−32.8863	+	18.9869i	−1.30918	+	0.755857i	−0.981960	−	0.189090i	$-0.939446\pi$
$631$	−32.8863	+	18.9869i	−1.30918	+	0.755857i	−0.327223	+	0.944947i	$0.606113\pi$
$632$		0			0
$633$	4.46940	−	2.58041i	0.177643	−	0.102562i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−42.4308	+	0.232834i	−1.68117	+	0.00922521i
$638$		0			0
$639$	4.76179	+	2.74922i	0.188374	+	0.108758i
$640$		0			0
$641$	−4.12590	−	7.14627i	−0.162963	−	0.282261i	0.772967	−	0.634446i	$-0.218772\pi$
$641$	−4.12590	−	7.14627i	−0.162963	−	0.282261i	−0.935930	+	0.352186i	$0.885439\pi$
$642$		0			0
$643$	−24.0750	−	41.6992i	−0.949427	−	1.64446i	−0.746636	−	0.665233i	$-0.768332\pi$
$643$	−24.0750	−	41.6992i	−0.949427	−	1.64446i	−0.202791	−	0.979222i	$-0.565001\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.88709	−	1.08951i	−0.0741893	−	0.0428332i	0.462446	−	0.886647i	$-0.346972\pi$
$647$	−1.88709	−	1.08951i	−0.0741893	−	0.0428332i	−0.536636	+	0.843814i	$0.680305\pi$
$648$		0			0
$649$	−10.9935			−0.431532
$650$		0			0
$651$	54.5229			2.13692
$652$		0			0
$653$	29.3308	+	16.9341i	1.14780	+	0.662684i	0.948351	−	0.317224i	$-0.102751\pi$
$653$	29.3308	+	16.9341i	1.14780	+	0.662684i	0.199451	+	0.979908i	$0.436084\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−1.15094	−	1.99348i	−0.0449023	−	0.0777730i
$658$		0			0
$659$	13.2246	+	22.9056i	0.515155	+	0.892275i	0.999845	+	0.0175892i	$0.00559912\pi$
$659$	13.2246	+	22.9056i	0.515155	+	0.892275i	−0.484690	+	0.874686i	$0.661068\pi$
$660$		0			0
$661$	−26.3259	−	15.1993i	−1.02396	−	0.591182i	−0.108710	−	0.994074i	$-0.534672\pi$
$661$	−26.3259	−	15.1993i	−1.02396	−	0.591182i	−0.915248	+	0.402891i	$0.868005\pi$
$662$		0			0
$663$	−21.8520	−	37.3736i	−0.848660	−	1.45147i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−2.03546	+	1.17517i	−0.0788134	+	0.0455029i
$668$		0			0
$669$	−23.5302	+	13.5851i	−0.909729	+	0.525232i
$670$		0			0
$671$		−	6.41393i		−	0.247607i
$672$		0			0
$673$	31.5192	+	18.1976i	1.21498	+	0.701467i	0.963839	−	0.266485i	$-0.0858622\pi$
$673$	31.5192	+	18.1976i	1.21498	+	0.701467i	0.251137	+	0.967952i	$0.419196\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			36.0043i			1.38376i	0.722013	+	0.691880i	$0.243217\pi$
$677$			36.0043i			1.38376i	−0.722013	+	0.691880i	$0.756783\pi$
$678$		0			0
$679$	6.08726	−	10.5435i	0.233608	−	0.404620i
$680$		0			0
$681$			3.84130i			0.147199i
$682$		0			0
$683$	6.41478	+	11.1107i	0.245455	+	0.425140i	0.962259	−	0.272134i	$-0.0877294\pi$
$683$	6.41478	+	11.1107i	0.245455	+	0.425140i	−0.716805	+	0.697274i	$0.754396\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	5.88609	−	10.1950i	0.224568	−	0.388964i
$688$		0			0
$689$	−39.3649	+	23.0162i	−1.49968	+	0.876849i
$690$		0			0
$691$	28.5608	+	16.4896i	1.08650	+	0.627294i	0.932644	−	0.360799i	$-0.117496\pi$
$691$	28.5608	+	16.4896i	1.08650	+	0.627294i	0.153861	+	0.988092i	$0.450829\pi$
$692$		0			0
$693$	2.85521	−	1.64846i	0.108461	−	0.0626197i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−58.0188			−2.19762
$698$		0			0
$699$	−2.69961	+	4.67586i	−0.102109	+	0.176857i
$700$		0			0
$701$	40.7352			1.53855			0.769273	−	0.638921i	$-0.220619\pi$
$701$	40.7352			1.53855			0.769273	+	0.638921i	$0.220619\pi$
$702$		0			0
$703$			51.2076i			1.93133i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−28.7651			−1.08182
$708$		0			0
$709$	15.2932	−	8.82956i	0.574350	−	0.331601i	−0.184535	−	0.982826i	$-0.559078\pi$
$709$	15.2932	−	8.82956i	0.574350	−	0.331601i	0.758885	+	0.651225i	$0.225745\pi$
$710$		0			0
$711$	−1.79422	−	3.10769i	−0.0672886	−	0.116547i
$712$		0			0
$713$	4.56487	−	7.90658i	0.170956	−	0.296104i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	19.0269	−	32.9555i	0.710571	−	1.23074i
$718$		0			0
$719$	−24.7836	−	42.9265i	−0.924273	−	1.60089i	−0.792727	−	0.609577i	$-0.791339\pi$
$719$	−24.7836	−	42.9265i	−0.924273	−	1.60089i	−0.131546	−	0.991310i	$-0.541994\pi$
$720$		0			0
$721$	27.6737	−	15.9774i	1.03062	−	0.595031i
$722$		0			0
$723$	35.7183			1.32838
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	36.4738i		−	1.35274i	−0.736562	−	0.676370i	$-0.763552\pi$
$727$		−	36.4738i		−	1.35274i	0.736562	−	0.676370i	$-0.236448\pi$
$728$		0			0
$729$	−29.7112			−1.10042
$730$		0			0
$731$	−15.7035	+	27.1993i	−0.580815	+	1.00600i
$732$		0			0
$733$	−28.8491			−1.06556			−0.532782	−	0.846252i	$-0.678854\pi$
$733$	−28.8491			−1.06556			−0.532782	+	0.846252i	$0.678854\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	7.89067	−	4.55568i	0.290657	−	0.167811i
$738$		0			0
$739$	−17.1330	−	9.89173i	−0.630247	−	0.363873i	0.150601	−	0.988595i	$-0.451879\pi$
$739$	−17.1330	−	9.89173i	−0.630247	−	0.363873i	−0.780848	+	0.624721i	$0.785213\pi$
$740$		0			0
$741$	−15.6436	−	26.7554i	−0.574683	−	0.982885i
$742$		0			0
$743$	−13.2003	+	22.8635i	−0.484271	+	0.838781i	−0.999837	−	0.0180685i	$-0.994248\pi$
$743$	−13.2003	+	22.8635i	−0.484271	+	0.838781i	0.515566	+	0.856850i	$0.327582\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.100344	−	0.173801i	−0.00367140	−	0.00635905i
$748$		0			0
$749$			34.2826i			1.25266i
$750$		0			0
$751$	−6.90171	+	11.9541i	−0.251847	+	0.436212i	−0.964034	−	0.265778i	$-0.914371\pi$
$751$	−6.90171	+	11.9541i	−0.251847	+	0.436212i	0.712187	+	0.701990i	$0.247705\pi$
$752$		0			0
$753$		−	7.39671i		−	0.269551i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	4.48739	+	2.59080i	0.163097	+	0.0941642i	0.579327	−	0.815095i	$-0.303315\pi$
$757$	4.48739	+	2.59080i	0.163097	+	0.0941642i	−0.416230	+	0.909259i	$0.636649\pi$
$758$		0			0
$759$			3.21736i			0.116783i
$760$		0			0
$761$	0.00743288	−	0.00429137i	0.000269442	−	0.000155562i	−0.499865	−	0.866103i	$-0.666617\pi$
$761$	0.00743288	−	0.00429137i	0.000269442	−	0.000155562i	0.500135	+	0.865948i	$0.333284\pi$
$762$		0			0
$763$	34.4531	−	19.8915i	1.24729	−	0.720121i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−19.8813	−	11.3335i	−0.717871	−	0.409227i
$768$		0			0
$769$	−10.2610	−	5.92417i	−0.370020	−	0.213631i	0.303447	−	0.952848i	$-0.401862\pi$
$769$	−10.2610	−	5.92417i	−0.370020	−	0.213631i	−0.673467	+	0.739217i	$0.735196\pi$
$770$		0			0
$771$	17.4933	+	30.2992i	0.630005	+	1.09120i
$772$		0			0
$773$	10.5229	+	18.2262i	0.378482	+	0.655550i	0.990842	−	0.135030i	$-0.0431129\pi$
$773$	10.5229	+	18.2262i	0.378482	+	0.655550i	−0.612360	+	0.790579i	$0.709780\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	57.2308	+	33.0422i	2.05314	+	1.18538i
$778$		0			0
$779$	−41.5352			−1.48815
$780$		0			0
$781$	−21.6754			−0.775605
$782$		0			0
$783$	9.65050	+	5.57172i	0.344881	+	0.199117i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−2.50587	−	4.34029i	−0.0893246	−	0.154715i	0.817901	−	0.575359i	$-0.195138\pi$
$787$	−2.50587	−	4.34029i	−0.0893246	−	0.154715i	−0.907226	+	0.420644i	$0.861804\pi$
$788$		0			0
$789$	−16.1452	−	27.9643i	−0.574784	−	0.995556i
$790$		0			0
$791$	21.6701	+	12.5112i	0.770499	+	0.444848i
$792$		0			0
$793$	6.61228	−	11.5993i	0.234809	−	0.411904i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−35.2096	+	20.3283i	−1.24719	+	0.720065i	−0.970548	−	0.240909i	$-0.922555\pi$
$797$	−35.2096	+	20.3283i	−1.24719	+	0.720065i	−0.276641	+	0.960973i	$0.589221\pi$
$798$		0			0
$799$	−22.5110	+	12.9967i	−0.796382	+	0.459792i
$800$		0			0
$801$		−	5.83281i		−	0.206092i
$802$		0			0
$803$	7.85847	+	4.53709i	0.277320	+	0.160110i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			11.6604i			0.410466i
$808$		0			0
$809$	2.70676	−	4.68824i	0.0951644	−	0.164830i	−0.814513	−	0.580146i	$-0.802996\pi$
$809$	2.70676	−	4.68824i	0.0951644	−	0.164830i	0.909677	+	0.415316i	$0.136329\pi$
$810$		0			0
$811$			0.616994i			0.0216656i	0.999941	+	0.0108328i	$0.00344825\pi$
$811$			0.616994i			0.0216656i	−0.999941	+	0.0108328i	$0.996552\pi$
$812$		0			0
$813$	−3.91399	−	6.77924i	−0.137270	−	0.237758i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−11.2420	+	19.4717i	−0.393308	+	0.681229i
$818$		0			0
$819$	6.86297	−	0.0376597i	0.239812	−	0.00131594i
$820$		0			0
$821$	−19.8377	−	11.4533i	−0.692340	−	0.399723i	0.112148	−	0.993691i	$-0.464227\pi$
$821$	−19.8377	−	11.4533i	−0.692340	−	0.399723i	−0.804488	+	0.593969i	$0.797560\pi$
$822$		0			0
$823$	8.36456	−	4.82928i	0.291570	−	0.168338i	−0.347080	−	0.937836i	$-0.612827\pi$
$823$	8.36456	−	4.82928i	0.291570	−	0.168338i	0.638650	+	0.769498i	$0.279493\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	21.2602			0.739289			0.369645	−	0.929173i	$-0.379479\pi$
$827$	21.2602			0.739289			0.369645	+	0.929173i	$0.379479\pi$
$828$		0			0
$829$	11.9948	−	20.7755i	0.416595	−	0.721564i	−0.578999	−	0.815328i	$-0.696557\pi$
$829$	11.9948	−	20.7755i	0.416595	−	0.721564i	0.995594	+	0.0937639i	$0.0298899\pi$
$830$		0			0
$831$	−14.0827			−0.488522
$832$		0			0
$833$		−	88.3059i		−	3.05962i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−43.2857			−1.49617
$838$		0			0
$839$	18.4511	−	10.6527i	0.637003	−	0.367774i	−0.146456	−	0.989217i	$-0.546787\pi$
$839$	18.4511	−	10.6527i	0.637003	−	0.367774i	0.783459	+	0.621443i	$0.213453\pi$
$840$		0			0
$841$	12.4502	+	21.5644i	0.429319	+	0.743602i
$842$		0			0
$843$	10.0880	−	17.4730i	0.347451	−	0.601802i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	17.3290	−	30.0147i	0.595431	−	1.03132i
$848$		0			0
$849$	16.7228	+	28.9647i	0.573925	+	0.994067i
$850$		0			0
$851$	9.58317	−	5.53285i	0.328507	−	0.189664i
$852$		0			0
$853$	−12.1098			−0.414631			−0.207315	−	0.978274i	$-0.566473\pi$
$853$	−12.1098			−0.414631			−0.207315	+	0.978274i	$0.566473\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			35.4491i			1.21092i	0.795876	+	0.605459i	$0.207010\pi$
$857$			35.4491i			1.21092i	−0.795876	+	0.605459i	$0.792990\pi$
$858$		0			0
$859$	47.4600			1.61931			0.809657	−	0.586904i	$-0.199653\pi$
$859$	47.4600			1.61931			0.809657	+	0.586904i	$0.199653\pi$
$860$		0			0
$861$	−26.8010	+	46.4207i	−0.913376	+	1.58201i
$862$		0			0
$863$	18.7268			0.637467			0.318733	−	0.947844i	$-0.396743\pi$
$863$	18.7268			0.637467			0.318733	+	0.947844i	$0.396743\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	54.4694	−	31.4479i	1.84988	−	1.06803i
$868$		0			0
$869$	12.2508	+	7.07299i	0.415579	+	0.239935i
$870$		0			0
$871$	18.9665	−	0.104077i	0.642657	−	0.00352650i
$872$		0			0
$873$	−0.617367	+	1.06931i	−0.0208947	+	0.0361907i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.907583	+	1.57198i	0.0306469	+	0.0530820i	0.880942	−	0.473224i	$-0.156910\pi$
$877$	0.907583	+	1.57198i	0.0306469	+	0.0530820i	−0.850295	+	0.526306i	$0.823577\pi$
$878$		0			0
$879$			1.10811i			0.0373755i
$880$		0			0
$881$	−25.1718	+	43.5989i	−0.848061	+	1.46888i	0.0348758	+	0.999392i	$0.488896\pi$
$881$	−25.1718	+	43.5989i	−0.848061	+	1.46888i	−0.882936	+	0.469493i	$0.844437\pi$
$882$		0			0
$883$		−	4.42003i		−	0.148746i	−0.997230	−	0.0743729i	$-0.976304\pi$
$883$		−	4.42003i		−	0.148746i	0.997230	−	0.0743729i	$-0.0236955\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.33076	−	1.34567i	−0.0782594	−	0.0451831i	0.460360	−	0.887732i	$-0.347720\pi$
$887$	−2.33076	−	1.34567i	−0.0782594	−	0.0451831i	−0.538619	+	0.842549i	$0.681054\pi$
$888$		0			0
$889$			82.1731i			2.75600i
$890$		0			0
$891$	11.2332	−	6.48552i	0.376328	−	0.217273i
$892$		0			0
$893$	−16.1154	+	9.30426i	−0.539283	+	0.311355i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−3.31685	+	5.81846i	−0.110747	+	0.194273i
$898$		0			0
$899$	13.7908	+	7.96213i	0.459949	+	0.265552i
$900$		0			0
$901$	−47.4499	−	82.1856i	−1.58078	−	2.73800i
$902$		0			0
$903$	14.5080	+	25.1287i	0.482797	+	0.836230i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	12.4722	+	7.20083i	0.414133	+	0.239100i	0.692564	−	0.721356i	$-0.256481\pi$
$907$	12.4722	+	7.20083i	0.414133	+	0.239100i	−0.278431	+	0.960456i	$0.589814\pi$
$908$		0			0
$909$	2.91734			0.0967620
$910$		0			0
$911$	−8.88723			−0.294447			−0.147223	−	0.989103i	$-0.547034\pi$
$911$	−8.88723			−0.294447			−0.147223	+	0.989103i	$0.547034\pi$
$912$		0			0
$913$	0.685139	+	0.395565i	0.0226748	+	0.0130913i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−2.91641	−	5.05137i	−0.0963083	−	0.166811i
$918$		0			0
$919$	−21.4873	−	37.2171i	−0.708802	−	1.22768i	−0.965302	−	0.261136i	$-0.915903\pi$
$919$	−21.4873	−	37.2171i	−0.708802	−	1.22768i	0.256500	−	0.966544i	$-0.417431\pi$
$920$		0			0
$921$	−12.2390	−	7.06621i	−0.403290	−	0.232839i
$922$		0			0
$923$	−39.1990	−	22.3457i	−1.29025	−	0.735517i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−2.80665	+	1.62042i	−0.0921826	+	0.0532217i
$928$		0			0
$929$	25.7537	−	14.8689i	0.844952	−	0.487833i	−0.0139925	−	0.999902i	$-0.504454\pi$
$929$	25.7537	−	14.8689i	0.844952	−	0.487833i	0.858944	+	0.512069i	$0.171121\pi$
$930$		0			0
$931$		−	63.2175i		−	2.07187i
$932$		0			0
$933$	−15.7925	−	9.11778i	−0.517022	−	0.298503i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			17.1355i			0.559793i	0.960030	+	0.279896i	$0.0903001\pi$
$937$			17.1355i			0.559793i	−0.960030	+	0.279896i	$0.909700\pi$
$938$		0			0
$939$	−2.70830	+	4.69092i	−0.0883821	+	0.153082i
$940$		0			0
$941$			23.5767i			0.768580i	0.923212	+	0.384290i	$0.125554\pi$
$941$			23.5767i			0.768580i	−0.923212	+	0.384290i	$0.874446\pi$
$942$		0			0
$943$	4.48777	+	7.77304i	0.146142	+	0.253125i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−8.81360	+	15.2656i	−0.286404	+	0.496066i	−0.972949	−	0.231022i	$-0.925793\pi$
$947$	−8.81360	+	15.2656i	−0.286404	+	0.496066i	0.686545	+	0.727087i	$0.259126\pi$
$948$		0			0
$949$	9.53433	+	16.3066i	0.309498	+	0.529336i
$950$		0			0
$951$	0.772040	+	0.445737i	0.0250351	+	0.0144540i
$952$		0			0
$953$	−50.8903	+	29.3816i	−1.64850	+	0.951762i	−0.670831	+	0.741610i	$0.734063\pi$
$953$	−50.8903	+	29.3816i	−1.64850	+	0.951762i	−0.977669	+	0.210152i	$0.932604\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−5.61178			−0.181403
$958$		0			0
$959$	26.8010	−	46.4207i	0.865449	−	1.49900i
$960$		0			0
$961$	−30.8564			−0.995368
$962$		0			0
$963$		−	3.47692i		−	0.112042i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−2.92168			−0.0939550			−0.0469775	−	0.998896i	$-0.514959\pi$
$967$	−2.92168			−0.0939550			−0.0469775	+	0.998896i	$0.514959\pi$
$968$		0			0
$969$	55.8597	−	32.2506i	1.79447	−	1.03604i
$970$		0			0
$971$	5.00693	+	8.67226i	0.160680	+	0.278306i	0.935113	−	0.354350i	$-0.115298\pi$
$971$	5.00693	+	8.67226i	0.160680	+	0.278306i	−0.774433	+	0.632656i	$0.781965\pi$
$972$		0			0
$973$	−18.9933	+	32.8974i	−0.608899	+	1.05464i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	13.2650	−	22.9757i	0.424386	−	0.735058i	−0.571977	−	0.820270i	$-0.693823\pi$
$977$	13.2650	−	22.9757i	0.424386	−	0.735058i	0.996363	+	0.0852116i	$0.0271566\pi$
$978$		0			0
$979$	11.4967	+	19.9129i	0.367437	+	0.636420i
$980$		0			0
$981$	−3.49421	+	2.01739i	−0.111562	+	0.0644102i
$982$		0			0
$983$	4.69317			0.149689			0.0748445	−	0.997195i	$-0.476154\pi$
$983$	4.69317			0.149689			0.0748445	+	0.997195i	$0.476154\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$			24.0147i			0.764396i
$988$		0			0
$989$	4.85868			0.154497
$990$		0			0
$991$	11.4601	−	19.8494i	0.364041	−	0.630537i	−0.624581	−	0.780960i	$-0.714730\pi$
$991$	11.4601	−	19.8494i	0.364041	−	0.630537i	0.988622	+	0.150423i	$0.0480636\pi$
$992$		0			0
$993$	6.34268			0.201279
$994$		0			0
$995$		0			0
$996$		0			0
$997$	42.8186	−	24.7213i	1.35608	−	0.782932i	0.366985	−	0.930227i	$-0.380390\pi$
$997$	42.8186	−	24.7213i	1.35608	−	0.782932i	0.989093	+	0.147295i	$0.0470568\pi$
$998$		0			0
$999$	−45.4356	−	26.2323i	−1.43752	−	0.829952i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1300.2.ba.b.849.4		8
5.2	odd	4		1300.2.y.b.901.3		8
5.3	odd	4		260.2.x.a.121.2	yes	8
5.4	even	2		1300.2.ba.c.849.1		8
13.10	even	6		1300.2.ba.c.49.1		8
15.8	even	4		2340.2.dj.d.901.4		8
20.3	even	4		1040.2.da.c.641.3		8
65.23	odd	12		260.2.x.a.101.2	✓	8
65.33	even	12		3380.2.a.q.1.3		4
65.43	odd	12		3380.2.f.i.3041.6		8
65.48	odd	12		3380.2.f.i.3041.5		8
65.49	even	6	inner	1300.2.ba.b.49.4		8
65.58	even	12		3380.2.a.p.1.3		4
65.62	odd	12		1300.2.y.b.101.3		8
195.23	even	12		2340.2.dj.d.361.2		8
260.23	even	12		1040.2.da.c.881.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.x.a.101.2	✓	8	65.23	odd	12
260.2.x.a.121.2	yes	8	5.3	odd	4
1040.2.da.c.641.3		8	20.3	even	4
1040.2.da.c.881.3		8	260.23	even	12
1300.2.y.b.101.3		8	65.62	odd	12
1300.2.y.b.901.3		8	5.2	odd	4
1300.2.ba.b.49.4		8	65.49	even	6	inner
1300.2.ba.b.849.4		8	1.1	even	1	trivial
1300.2.ba.c.49.1		8	13.10	even	6
1300.2.ba.c.849.1		8	5.4	even	2
2340.2.dj.d.361.2		8	195.23	even	12
2340.2.dj.d.901.4		8	15.8	even	4
3380.2.a.p.1.3		4	65.58	even	12
3380.2.a.q.1.3		4	65.33	even	12
3380.2.f.i.3041.5		8	65.48	odd	12
3380.2.f.i.3041.6		8	65.43	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:	\( N \)	\(=\)	\( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1300.ba (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.38581 + 0.800098i) q^{3} +(2.16612 + 3.75184i) q^{7} +(-0.219687 - 0.380509i) q^{9} +O(q^{10})\)	\(q+(1.38581 + 0.800098i) q^{3} +(2.16612 + 3.75184i) q^{7} +(-0.219687 - 0.380509i) q^{9} +(1.50000 + 0.866025i) q^{11} +(1.81988 + 3.11256i) q^{13} +(-6.49837 + 3.75184i) q^{17} +(-4.65213 + 2.68591i) q^{19} +6.93244i q^{21} +(1.00530 + 0.580411i) q^{23} -5.50367i q^{27} +(-1.01236 + 1.75347i) q^{29} -7.86488i q^{31} +(1.38581 + 2.40029i) q^{33} +(4.76632 - 8.25551i) q^{37} +(0.0316594 + 5.76950i) q^{39} +(6.69615 + 3.86603i) q^{41} +(3.62479 - 2.09277i) q^{43} +3.46410 q^{47} +(-5.88418 + 10.1917i) q^{49} -12.0073 q^{51} +12.6471i q^{53} -8.59596 q^{57} +(-5.49674 + 3.17354i) q^{59} +(-1.85154 - 3.20696i) q^{61} +(0.951738 - 1.64846i) q^{63} +(2.63022 - 4.55568i) q^{67} +(0.928771 + 1.60868i) q^{69} +(-10.8377 + 6.25714i) q^{71} +5.23898 q^{73} +7.50367i q^{77} +8.16719 q^{79} +(3.74441 - 6.48552i) q^{81} +0.456760 q^{83} +(-2.80589 + 1.61998i) q^{87} +(11.4967 + 6.63765i) q^{89} +(-7.73572 + 13.5701i) q^{91} +(6.29268 - 10.8992i) q^{93} +(-1.40511 - 2.43371i) q^{97} -0.761018i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{3} + 6 q^{7} + 4 q^{9}+O(q^{10}) \) 8 * q - 6 * q^3 + 6 * q^7 + 4 * q^9	\( 8 q - 6 q^{3} + 6 q^{7} + 4 q^{9} + 12 q^{11} - 18 q^{17} - 6 q^{23} - 6 q^{33} + 18 q^{37} + 4 q^{39} + 12 q^{41} + 18 q^{43} + 4 q^{49} - 36 q^{57} + 24 q^{59} - 4 q^{61} - 12 q^{63} - 18 q^{67} + 24 q^{69} - 36 q^{71} + 48 q^{73} + 16 q^{79} + 8 q^{81} + 72 q^{83} + 18 q^{87} + 24 q^{89} + 48 q^{93} - 6 q^{97}+O(q^{100}) \) 8 * q - 6 * q^3 + 6 * q^7 + 4 * q^9 + 12 * q^11 - 18 * q^17 - 6 * q^23 - 6 * q^33 + 18 * q^37 + 4 * q^39 + 12 * q^41 + 18 * q^43 + 4 * q^49 - 36 * q^57 + 24 * q^59 - 4 * q^61 - 12 * q^63 - 18 * q^67 + 24 * q^69 - 36 * q^71 + 48 * q^73 + 16 * q^79 + 8 * q^81 + 72 * q^83 + 18 * q^87 + 24 * q^89 + 48 * q^93 - 6 * q^97

Introduction

L-functions

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