LMFDB - Embedded newform 1300.2.y.d.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1300,2,Mod(101,1300)]

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, 0, 5]))

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

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

chi := DirichletCharacter("1300.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1300 = 2^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1300.y (of order $6$, degree $2$, 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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 19x^{8} + 120x^{6} + 301x^{4} + 271x^{2} + 75 $ x^10 + 19x^8 + 120x^6 + 301x^4 + 271x^2 + 75
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.1
Root			$-1.84944i$ of defining polynomial
Character	$\chi$	$=$	1300.101
Dual form			1300.2.y.d.901.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20373 - 2.08492i) q^{3} +(2.70233 + 1.56019i) q^{7} +(-1.39793 + 2.42129i) q^{9} +O(q^{10})$	$q+(-1.20373 - 2.08492i) q^{3} +(2.70233 + 1.56019i) q^{7} +(-1.39793 + 2.42129i) q^{9} +(5.43560 - 3.13825i) q^{11} +(-0.478014 + 3.57372i) q^{13} +(-3.44806 + 5.97221i) q^{17} +(-0.745730 - 0.430548i) q^{19} -7.51219i q^{21} +(4.12980 + 7.15303i) q^{23} -0.491460 q^{27} +(3.25386 + 5.63585i) q^{29} +7.77672i q^{31} +(-13.0860 - 7.55520i) q^{33} +(5.43560 - 3.13825i) q^{37} +(8.02633 - 3.30518i) q^{39} +(0.630624 - 0.364091i) q^{41} +(-3.23327 + 5.60019i) q^{43} -1.80852i q^{47} +(1.36839 + 2.37011i) q^{49} +16.6021 q^{51} -1.89694 q^{53} +2.07305i q^{57} +(-5.36517 - 3.09758i) q^{59} +(2.98754 - 5.17458i) q^{61} +(-7.55533 + 4.36207i) q^{63} +(8.27247 - 4.77611i) q^{67} +(9.94233 - 17.2206i) q^{69} +(5.53920 + 3.19806i) q^{71} -10.4463i q^{73} +19.5850 q^{77} -7.60798 q^{79} +(4.78537 + 8.28851i) q^{81} -3.59429i q^{83} +(7.83353 - 13.5681i) q^{87} +(7.09019 - 4.09352i) q^{89} +(-6.86744 + 8.91158i) q^{91} +(16.2138 - 9.36106i) q^{93} +(-11.7011 - 6.75563i) q^{97} +17.5482i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{3} - 8 q^{9}+O(q^{10}) $ 10 * q + q^3 - 8 * q^9	$ 10 q + q^{3} - 8 q^{9} + 3 q^{11} + 4 q^{13} - 12 q^{17} - 12 q^{19} - 3 q^{23} - 14 q^{27} + 3 q^{29} - 30 q^{33} + 3 q^{37} + 16 q^{39} + 12 q^{41} - 8 q^{43} + 19 q^{49} - 24 q^{51} - 24 q^{53} - 6 q^{59} + q^{61} + 24 q^{63} + 48 q^{67} + 45 q^{71} + 24 q^{77} + 16 q^{79} + 7 q^{81} + 21 q^{87} + 12 q^{89} - 3 q^{91} + 93 q^{93} - 15 q^{97}+O(q^{100}) $ 10 * q + q^3 - 8 * q^9 + 3 * q^11 + 4 * q^13 - 12 * q^17 - 12 * q^19 - 3 * q^23 - 14 * q^27 + 3 * q^29 - 30 * q^33 + 3 * q^37 + 16 * q^39 + 12 * q^41 - 8 * q^43 + 19 * q^49 - 24 * q^51 - 24 * q^53 - 6 * q^59 + q^61 + 24 * q^63 + 48 * q^67 + 45 * q^71 + 24 * q^77 + 16 * q^79 + 7 * q^81 + 21 * q^87 + 12 * q^89 - 3 * q^91 + 93 * q^93 - 15 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$301$	$651$	$677$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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
$3$	−1.20373	−	2.08492i	−0.694974	−	1.20373i	−0.970190	−	0.242347i	$-0.922083\pi$
$3$	−1.20373	−	2.08492i	−0.694974	−	1.20373i	0.275216	−	0.961382i	$-0.411251\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.70233	+	1.56019i	1.02138	+	0.589696i	0.914505	−	0.404576i	$-0.132581\pi$
$7$	2.70233	+	1.56019i	1.02138	+	0.589696i	0.106880	+	0.994272i	$0.465914\pi$
$8$		0			0
$9$	−1.39793	+	2.42129i	−0.465977	+	0.807095i
$10$		0			0
$11$	5.43560	−	3.13825i	1.63890	−	0.946217i	0.657681	−	0.753296i	$-0.271537\pi$
$11$	5.43560	−	3.13825i	1.63890	−	0.946217i	0.981214	−	0.192920i	$-0.0617959\pi$
$12$		0			0
$13$	−0.478014	+	3.57372i	−0.132577	+	0.991173i
$13$	−0.478014	+	3.57372i	−0.132577	+	0.991173i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.44806	+	5.97221i	−0.836277	+	1.44847i	0.0567094	+	0.998391i	$0.481939\pi$
$17$	−3.44806	+	5.97221i	−0.836277	+	1.44847i	−0.892986	+	0.450084i	$0.851394\pi$
$18$		0			0
$19$	−0.745730	−	0.430548i	−0.171082	−	0.0987744i	0.412014	−	0.911178i	$-0.364826\pi$
$19$	−0.745730	−	0.430548i	−0.171082	−	0.0987744i	−0.583096	+	0.812403i	$0.698159\pi$
$20$		0			0
$21$		−	7.51219i		−	1.63929i
$22$		0			0
$23$	4.12980	+	7.15303i	0.861123	+	1.49151i	0.870846	+	0.491556i	$0.163572\pi$
$23$	4.12980	+	7.15303i	0.861123	+	1.49151i	−0.00972253	+	0.999953i	$0.503095\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.491460			−0.0945816
$28$		0			0
$29$	3.25386	+	5.63585i	0.604226	+	1.04655i	0.992173	+	0.124869i	$0.0398511\pi$
$29$	3.25386	+	5.63585i	0.604226	+	1.04655i	−0.387947	+	0.921682i	$0.626816\pi$
$30$		0			0
$31$			7.77672i			1.39674i	0.715737	+	0.698370i	$0.246091\pi$
$31$			7.77672i			1.39674i	−0.715737	+	0.698370i	$0.753909\pi$
$32$		0			0
$33$	−13.0860	−	7.55520i	−2.27798	−	1.31519i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	5.43560	−	3.13825i	0.893607	−	0.515924i	0.0184867	−	0.999829i	$-0.494115\pi$
$37$	5.43560	−	3.13825i	0.893607	−	0.515924i	0.875121	+	0.483905i	$0.160782\pi$
$38$		0			0
$39$	8.02633	−	3.30518i	1.28524	−	0.529252i
$40$		0			0
$41$	0.630624	−	0.364091i	0.0984870	−	0.0568615i	−0.449948	−	0.893055i	$-0.648557\pi$
$41$	0.630624	−	0.364091i	0.0984870	−	0.0568615i	0.548435	+	0.836194i	$0.315224\pi$
$42$		0			0
$43$	−3.23327	+	5.60019i	−0.493070	+	0.854022i	−0.999968	−	0.00798418i	$-0.997459\pi$
$43$	−3.23327	+	5.60019i	−0.493070	+	0.854022i	0.506899	+	0.862006i	$0.330792\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	1.80852i		−	0.263800i	−0.991263	−	0.131900i	$-0.957892\pi$
$47$		−	1.80852i		−	0.263800i	0.991263	−	0.131900i	$-0.0421078\pi$
$48$		0			0
$49$	1.36839	+	2.37011i	0.195484	+	0.338588i
$50$		0			0
$51$	16.6021			2.32476
$52$		0			0
$53$	−1.89694			−0.260565			−0.130282	−	0.991477i	$-0.541588\pi$
$53$	−1.89694			−0.260565			−0.130282	+	0.991477i	$0.541588\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			2.07305i			0.274582i
$58$		0			0
$59$	−5.36517	−	3.09758i	−0.698486	−	0.403271i	0.108297	−	0.994119i	$-0.465460\pi$
$59$	−5.36517	−	3.09758i	−0.698486	−	0.403271i	−0.806783	+	0.590848i	$0.798793\pi$
$60$		0			0
$61$	2.98754	−	5.17458i	0.382516	−	0.662537i	−0.608905	−	0.793243i	$-0.708391\pi$
$61$	2.98754	−	5.17458i	0.382516	−	0.662537i	0.991421	+	0.130706i	$0.0417245\pi$
$62$		0			0
$63$	−7.55533	+	4.36207i	−0.951882	+	0.549569i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	8.27247	−	4.77611i	1.01064	−	0.583495i	0.0992633	−	0.995061i	$-0.468351\pi$
$67$	8.27247	−	4.77611i	1.01064	−	0.583495i	0.911380	+	0.411566i	$0.135018\pi$
$68$		0			0
$69$	9.94233	−	17.2206i	1.19692	−	2.07312i
$70$		0			0
$71$	5.53920	+	3.19806i	0.657382	+	0.379540i	0.791279	−	0.611456i	$-0.209416\pi$
$71$	5.53920	+	3.19806i	0.657382	+	0.379540i	−0.133897	+	0.990995i	$0.542749\pi$
$72$		0			0
$73$		−	10.4463i		−	1.22265i	−0.791379	−	0.611325i	$-0.790637\pi$
$73$		−	10.4463i		−	1.22265i	0.791379	−	0.611325i	$-0.209363\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	19.5850			2.23192
$78$		0			0
$79$	−7.60798			−0.855964			−0.427982	−	0.903787i	$-0.640775\pi$
$79$	−7.60798			−0.855964			−0.427982	+	0.903787i	$0.640775\pi$
$80$		0			0
$81$	4.78537	+	8.28851i	0.531708	+	0.920946i
$82$		0			0
$83$		−	3.59429i		−	0.394525i	−0.980351	−	0.197262i	$-0.936795\pi$
$83$		−	3.59429i		−	0.394525i	0.980351	−	0.197262i	$-0.0632051\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	7.83353	−	13.5681i	0.839843	−	1.45465i
$88$		0			0
$89$	7.09019	−	4.09352i	0.751559	−	0.433913i	−0.0746980	−	0.997206i	$-0.523799\pi$
$89$	7.09019	−	4.09352i	0.751559	−	0.433913i	0.826257	+	0.563293i	$0.190466\pi$
$90$		0			0
$91$	−6.86744	+	8.91158i	−0.719903	+	0.934188i
$92$		0			0
$93$	16.2138	−	9.36106i	1.68130	−	0.970697i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−11.7011	−	6.75563i	−1.18807	−	0.685930i	−0.230199	−	0.973143i	$-0.573938\pi$
$97$	−11.7011	−	6.75563i	−1.18807	−	0.685930i	−0.957867	+	0.287213i	$0.907271\pi$
$98$		0			0
$99$			17.5482i			1.76366i
$100$		0			0
$101$	0.650798	+	1.12722i	0.0647568	+	0.112162i	0.896586	−	0.442869i	$-0.146039\pi$
$101$	0.650798	+	1.12722i	0.0647568	+	0.112162i	−0.831829	+	0.555032i	$0.812706\pi$
$102$		0			0
$103$	−0.658375			−0.0648716			−0.0324358	−	0.999474i	$-0.510326\pi$
$103$	−0.658375			−0.0648716			−0.0324358	+	0.999474i	$0.510326\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.48098	+	6.02923i	0.336519	+	0.582867i	0.983775	−	0.179405i	$-0.0574172\pi$
$107$	3.48098	+	6.02923i	0.336519	+	0.582867i	−0.647257	+	0.762272i	$0.724084\pi$
$108$		0			0
$109$		−	9.74832i		−	0.933720i	−0.884331	−	0.466860i	$-0.845385\pi$
$109$		−	9.74832i		−	0.933720i	0.884331	−	0.466860i	$-0.154615\pi$
$110$		0			0
$111$	−13.0860	−	7.55520i	−1.24207	−	0.717108i
$112$		0			0
$113$	−2.79293	+	4.83750i	−0.262737	+	0.455074i	−0.966968	−	0.254897i	$-0.917958\pi$
$113$	−2.79293	+	4.83750i	−0.262737	+	0.455074i	0.704231	+	0.709971i	$0.251292\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−7.98478	−	6.15322i	−0.738193	−	0.568866i
$118$		0			0
$119$	−18.6356	+	10.7593i	−1.70832	+	0.986299i
$120$		0			0
$121$	14.1972	−	24.5902i	1.29065	−	2.23548i
$122$		0			0
$123$	−1.51820	−	0.876534i	−0.136892	−	0.0790344i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−2.61020	−	4.52100i	−0.231618	−	0.401174i	0.726667	−	0.686990i	$-0.241069\pi$
$127$	−2.61020	−	4.52100i	−0.231618	−	0.401174i	−0.958284	+	0.285817i	$0.907735\pi$
$128$		0			0
$129$	15.5679			1.37068
$130$		0			0
$131$	−8.47049			−0.740070			−0.370035	−	0.929018i	$-0.620654\pi$
$131$	−8.47049			−0.740070			−0.370035	+	0.929018i	$0.620654\pi$
$132$		0			0
$133$	−1.34347	−	2.32696i	−0.116494	−	0.201773i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.97900	−	2.87463i	−0.425385	−	0.245596i	0.271994	−	0.962299i	$-0.412317\pi$
$137$	−4.97900	−	2.87463i	−0.425385	−	0.245596i	−0.697379	+	0.716703i	$0.745650\pi$
$138$		0			0
$139$	11.0870	−	19.2032i	0.940385	−	1.62880i	0.175648	−	0.984453i	$-0.443798\pi$
$139$	11.0870	−	19.2032i	0.940385	−	1.62880i	0.764737	−	0.644342i	$-0.222869\pi$
$140$		0			0
$141$	−3.77062	+	2.17697i	−0.317544	+	0.183334i
$142$		0			0
$143$	8.61693	+	20.9255i	0.720584	+	1.74988i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	3.29433	−	5.70595i	0.271712	−	0.470619i
$148$		0			0
$149$	−0.718989	−	0.415108i	−0.0589019	−	0.0340070i	0.470260	−	0.882528i	$-0.344160\pi$
$149$	−0.718989	−	0.415108i	−0.0589019	−	0.0340070i	−0.529162	+	0.848521i	$0.677494\pi$
$150$		0			0
$151$			23.3283i			1.89843i	0.314625	+	0.949216i	$0.398121\pi$
$151$			23.3283i			1.89843i	−0.314625	+	0.949216i	$0.601879\pi$
$152$		0			0
$153$	−9.64029	−	16.6975i	−0.779371	−	1.34991i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−5.37023			−0.428591			−0.214296	−	0.976769i	$-0.568746\pi$
$157$	−5.37023			−0.428591			−0.214296	+	0.976769i	$0.568746\pi$
$158$		0			0
$159$	2.28340	+	3.95497i	0.181086	+	0.313649i
$160$		0			0
$161$			25.7731i			2.03121i
$162$		0			0
$163$	10.4219	+	6.01709i	0.816307	+	0.471295i	0.849141	−	0.528166i	$-0.177120\pi$
$163$	10.4219	+	6.01709i	0.816307	+	0.471295i	−0.0328342	+	0.999461i	$0.510453\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	9.24493	−	5.33757i	0.715395	−	0.413033i	−0.0976607	−	0.995220i	$-0.531136\pi$
$167$	9.24493	−	5.33757i	0.715395	−	0.413033i	0.813055	+	0.582187i	$0.197803\pi$
$168$		0			0
$169$	−12.5430	−	3.41658i	−0.964847	−	0.262814i
$170$		0			0
$171$	2.08496	−	1.20375i	0.159441	−	0.0920531i
$172$		0			0
$173$	−1.92132	+	3.32782i	−0.146075	+	0.253009i	−0.929774	−	0.368132i	$-0.879997\pi$
$173$	−1.92132	+	3.32782i	−0.146075	+	0.253009i	0.783698	+	0.621141i	$0.213331\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			14.9146i			1.12105i
$178$		0			0
$179$	8.08484	+	14.0034i	0.604289	+	1.04666i	0.992163	+	0.124947i	$0.0398762\pi$
$179$	8.08484	+	14.0034i	0.604289	+	1.04666i	−0.387874	+	0.921712i	$0.626790\pi$
$180$		0			0
$181$	8.98019			0.667492			0.333746	−	0.942663i	$-0.391687\pi$
$181$	8.98019			0.667492			0.333746	+	0.942663i	$0.391687\pi$
$182$		0			0
$183$	−14.3848			−1.06335
$184$		0			0
$185$		0			0
$186$		0			0
$187$			43.2834i			3.16520i
$188$		0			0
$189$	−1.32809	−	0.766772i	−0.0966042	−	0.0557744i
$190$		0			0
$191$	7.25542	−	12.5668i	0.524984	−	0.909298i	−0.474593	−	0.880205i	$-0.657405\pi$
$191$	7.25542	−	12.5668i	0.524984	−	0.909298i	0.999577	−	0.0290931i	$-0.00926193\pi$
$192$		0			0
$193$	−7.49023	+	4.32448i	−0.539158	+	0.311283i	−0.744738	−	0.667357i	$-0.767425\pi$
$193$	−7.49023	+	4.32448i	−0.539158	+	0.311283i	0.205579	+	0.978640i	$0.434092\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3.76578	+	2.17417i	−0.268301	+	0.154903i	−0.628115	−	0.778120i	$-0.716173\pi$
$197$	−3.76578	+	2.17417i	−0.268301	+	0.154903i	0.359814	+	0.933024i	$0.382840\pi$
$198$		0			0
$199$	−5.50575	+	9.53623i	−0.390292	+	0.676005i	−0.992488	−	0.122343i	$-0.960959\pi$
$199$	−5.50575	+	9.53623i	−0.390292	+	0.676005i	0.602196	+	0.798348i	$0.294293\pi$
$200$		0			0
$201$	−19.9156	−	11.4983i	−1.40474	−	0.811027i
$202$		0			0
$203$			20.3066i			1.42524i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−23.0927			−1.60505
$208$		0			0
$209$	−5.40466			−0.373848
$210$		0			0
$211$	−0.407584	−	0.705957i	−0.0280593	−	0.0486001i	0.851655	−	0.524103i	$-0.175599\pi$
$211$	−0.407584	−	0.705957i	−0.0280593	−	0.0486001i	−0.879714	+	0.475503i	$0.842266\pi$
$212$		0			0
$213$		−	15.3984i		−	1.05508i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−12.1332	+	21.0152i	−0.823652	+	1.42661i
$218$		0			0
$219$	−21.7798	+	12.5746i	−1.47174	+	0.849710i
$220$		0			0
$221$	−19.6948	−	15.1772i	−1.32482	−	1.02093i
$222$		0			0
$223$	14.2938	−	8.25250i	0.957181	−	0.552628i	0.0618764	−	0.998084i	$-0.480292\pi$
$223$	14.2938	−	8.25250i	0.957181	−	0.552628i	0.895304	+	0.445455i	$0.146958\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−11.9432	−	6.89541i	−0.792698	−	0.457664i	0.0482138	−	0.998837i	$-0.484647\pi$
$227$	−11.9432	−	6.89541i	−0.792698	−	0.457664i	−0.840911	+	0.541173i	$0.817980\pi$
$228$		0			0
$229$		−	15.6881i		−	1.03670i	−0.855169	−	0.518349i	$-0.826547\pi$
$229$		−	15.6881i		−	1.03670i	0.855169	−	0.518349i	$-0.173453\pi$
$230$		0			0
$231$	−23.5751	−	40.8333i	−1.55113	−	2.68663i
$232$		0			0
$233$	−14.6517			−0.959865			−0.479932	−	0.877306i	$-0.659339\pi$
$233$	−14.6517			−0.959865			−0.479932	+	0.877306i	$0.659339\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	9.15794	+	15.8620i	0.594872	+	1.03035i
$238$		0			0
$239$			11.8041i			0.763543i	0.924257	+	0.381772i	$0.124686\pi$
$239$			11.8041i			0.763543i	−0.924257	+	0.381772i	$0.875314\pi$
$240$		0			0
$241$	−2.10573	−	1.21574i	−0.135642	−	0.0783129i	0.430643	−	0.902522i	$-0.358287\pi$
$241$	−2.10573	−	1.21574i	−0.135642	−	0.0783129i	−0.566285	+	0.824209i	$0.691620\pi$
$242$		0			0
$243$	10.7834	−	18.6774i	0.691756	−	1.19816i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.89513	−	2.45923i	0.120584	−	0.156477i
$248$		0			0
$249$	−7.49382	+	4.32656i	−0.474901	+	0.274184i
$250$		0			0
$251$	−13.5535	+	23.4753i	−0.855488	+	1.48175i	0.0207031	+	0.999786i	$0.493410\pi$
$251$	−13.5535	+	23.4753i	−0.855488	+	1.48175i	−0.876191	+	0.481963i	$0.839924\pi$
$252$		0			0
$253$	44.8959	+	25.9207i	2.82258	+	1.62962i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−10.7142	−	18.5576i	−0.668336	−	1.15759i	−0.978369	−	0.206867i	$-0.933673\pi$
$257$	−10.7142	−	18.5576i	−0.668336	−	1.15759i	0.310033	−	0.950726i	$-0.399660\pi$
$258$		0			0
$259$	19.5850			1.21696
$260$		0			0
$261$	−18.1947			−1.12622
$262$		0			0
$263$	2.46358	+	4.26704i	0.151911	+	0.263117i	0.931930	−	0.362639i	$-0.118124\pi$
$263$	2.46358	+	4.26704i	0.151911	+	0.263117i	−0.780019	+	0.625756i	$0.784791\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−17.0693	−	9.85499i	−1.04463	−	0.603116i
$268$		0			0
$269$	−14.2285	+	24.6445i	−0.867529	+	1.50260i	−0.00301506	+	0.999995i	$0.500960\pi$
$269$	−14.2285	+	24.6445i	−0.867529	+	1.50260i	−0.864514	+	0.502609i	$0.832374\pi$
$270$		0			0
$271$	25.3053	−	14.6100i	1.53719	−	0.887496i	0.538186	−	0.842826i	$-0.319110\pi$
$271$	25.3053	−	14.6100i	1.53719	−	0.887496i	0.999002	−	0.0446697i	$-0.0142235\pi$
$272$		0			0
$273$	26.8465	+	3.59093i	1.62482	+	0.217333i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−5.85144	+	10.1350i	−0.351579	+	0.608953i	−0.986526	−	0.163603i	$-0.947688\pi$
$277$	−5.85144	+	10.1350i	−0.351579	+	0.608953i	0.634947	+	0.772555i	$0.281022\pi$
$278$		0			0
$279$	−18.8296	−	10.8713i	−1.12730	−	0.650848i
$280$		0			0
$281$			3.39279i			0.202397i	0.994866	+	0.101199i	$0.0322677\pi$
$281$			3.39279i			0.202397i	−0.994866	+	0.101199i	$0.967732\pi$
$282$		0			0
$283$	−7.38588	−	12.7927i	−0.439045	−	0.760449i	0.558571	−	0.829457i	$-0.311350\pi$
$283$	−7.38588	−	12.7927i	−0.439045	−	0.760449i	−0.997616	+	0.0690082i	$0.978017\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.27220			0.134124
$288$		0			0
$289$	−15.2782	−	26.4626i	−0.898719	−	1.55663i
$290$		0			0
$291$			32.5278i			1.90681i
$292$		0			0
$293$	−10.6546	−	6.15143i	−0.622448	−	0.359370i	0.155374	−	0.987856i	$-0.450342\pi$
$293$	−10.6546	−	6.15143i	−0.622448	−	0.359370i	−0.777821	+	0.628485i	$0.783675\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−2.67138	+	1.54232i	−0.155009	+	0.0894947i
$298$		0			0
$299$	−27.5370	+	11.3395i	−1.59251	+	0.655782i
$300$		0			0
$301$	−17.4747	+	10.0890i	−1.00723	+	0.581523i
$302$		0			0
$303$	1.56677	−	2.71373i	0.0900086	−	0.155899i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	8.72544i		−	0.497987i	−0.968505	−	0.248994i	$-0.919900\pi$
$307$		−	8.72544i		−	0.497987i	0.968505	−	0.248994i	$-0.0800998\pi$
$308$		0			0
$309$	0.792505	+	1.37266i	0.0450841	+	0.0780879i
$310$		0			0
$311$	−15.6001			−0.884599			−0.442299	−	0.896867i	$-0.645837\pi$
$311$	−15.6001			−0.884599			−0.442299	+	0.896867i	$0.645837\pi$
$312$		0			0
$313$	23.6416			1.33630			0.668152	−	0.744024i	$-0.267085\pi$
$313$	23.6416			1.33630			0.668152	+	0.744024i	$0.267085\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	10.9687i		−	0.616064i	−0.951376	−	0.308032i	$-0.900330\pi$
$317$		−	10.9687i		−	0.616064i	0.951376	−	0.308032i	$-0.0996704\pi$
$318$		0			0
$319$	35.3734	+	20.4228i	1.98053	+	1.14346i
$320$		0			0
$321$	8.38031	−	14.5151i	0.467743	−	0.810155i
$322$		0			0
$323$	5.14264	−	2.96911i	0.286144	−	0.165206i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−20.3245	+	11.7343i	−1.12395	+	0.648911i
$328$		0			0
$329$	2.82164	−	4.88722i	0.155562	−	0.269441i
$330$		0			0
$331$	−0.629124	−	0.363225i	−0.0345798	−	0.0199646i	0.482610	−	0.875835i	$-0.339689\pi$
$331$	−0.629124	−	0.363225i	−0.0345798	−	0.0199646i	−0.517190	+	0.855870i	$0.673022\pi$
$332$		0			0
$333$			17.5482i			0.961635i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−5.18228			−0.282297			−0.141148	−	0.989988i	$-0.545079\pi$
$337$	−5.18228			−0.282297			−0.141148	+	0.989988i	$0.545079\pi$
$338$		0			0
$339$	13.4477			0.730381
$340$		0			0
$341$	24.4053	+	42.2711i	1.32162	+	2.28911i
$342$		0			0
$343$		−	13.3029i		−	0.718289i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	18.2763	−	31.6554i	0.981122	−	1.69935i	0.323079	−	0.946372i	$-0.395282\pi$
$347$	18.2763	−	31.6554i	0.981122	−	1.69935i	0.658043	−	0.752981i	$-0.271385\pi$
$348$		0			0
$349$	18.8743	−	10.8971i	1.01032	−	0.583308i	0.0990343	−	0.995084i	$-0.468425\pi$
$349$	18.8743	−	10.8971i	1.01032	−	0.583308i	0.911285	+	0.411776i	$0.135091\pi$
$350$		0			0
$351$	0.234925	−	1.75634i	0.0125394	−	0.0937467i
$352$		0			0
$353$	13.0690	−	7.54540i	0.695594	−	0.401601i	−0.110110	−	0.993919i	$-0.535120\pi$
$353$	13.0690	−	7.54540i	0.695594	−	0.401601i	0.805704	+	0.592318i	$0.201787\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	44.8644	+	25.9025i	2.37447	+	1.37090i
$358$		0			0
$359$		−	15.5267i		−	0.819469i	−0.912205	−	0.409735i	$-0.865621\pi$
$359$		−	15.5267i		−	0.819469i	0.912205	−	0.409735i	$-0.134379\pi$
$360$		0			0
$361$	−9.12926	−	15.8123i	−0.480487	−	0.832228i
$362$		0			0
$363$	−68.3582			−3.58788
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−5.99971	−	10.3918i	−0.313183	−	0.542448i	0.665867	−	0.746070i	$-0.268062\pi$
$367$	−5.99971	−	10.3918i	−0.313183	−	0.542448i	−0.979049	+	0.203622i	$0.934728\pi$
$368$		0			0
$369$			2.03589i			0.105984i
$370$		0			0
$371$	−5.12615	−	2.95959i	−0.266137	−	0.153654i
$372$		0			0
$373$	12.4298	−	21.5291i	0.643593	−	1.11474i	−0.341032	−	0.940052i	$-0.610776\pi$
$373$	12.4298	−	21.5291i	0.643593	−	1.11474i	0.984625	−	0.174683i	$-0.0558902\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−21.6964	+	8.93438i	−1.11742	+	0.460144i
$378$		0			0
$379$	−6.88212	+	3.97339i	−0.353511	+	0.204099i	−0.666230	−	0.745746i	$-0.732093\pi$
$379$	−6.88212	+	3.97339i	−0.353511	+	0.204099i	0.312720	+	0.949845i	$0.398760\pi$
$380$		0			0
$381$	−6.28395	+	10.8841i	−0.321936	+	0.557610i
$382$		0			0
$383$	17.2702	+	9.97098i	0.882469	+	0.509493i	0.871472	−	0.490446i	$-0.163166\pi$
$383$	17.2702	+	9.97098i	0.882469	+	0.509493i	0.0109970	+	0.999940i	$0.496499\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−9.03978	−	15.6574i	−0.459518	−	0.795908i
$388$		0			0
$389$	5.16183			0.261715			0.130858	−	0.991401i	$-0.458227\pi$
$389$	5.16183			0.261715			0.130858	+	0.991401i	$0.458227\pi$
$390$		0			0
$391$	−56.9592			−2.88055
$392$		0			0
$393$	10.1962	+	17.6603i	0.514329	+	0.890844i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	19.5850	+	11.3074i	0.982945	+	0.567504i	0.903158	−	0.429308i	$-0.141243\pi$
$397$	19.5850	+	11.3074i	0.982945	+	0.567504i	0.0797871	+	0.996812i	$0.474576\pi$
$398$		0			0
$399$	−3.23435	+	5.60207i	−0.161920	+	0.280454i
$400$		0			0
$401$	14.3746	−	8.29917i	0.717833	−	0.414441i	−0.0961217	−	0.995370i	$-0.530644\pi$
$401$	14.3746	−	8.29917i	0.717833	−	0.414441i	0.813955	+	0.580929i	$0.197310\pi$
$402$		0			0
$403$	−27.7918	−	3.71738i	−1.38441	−	0.185176i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	19.6972	−	34.1165i	0.976353	−	1.69109i
$408$		0			0
$409$	−17.0763	−	9.85901i	−0.844369	−	0.487497i	0.0143779	−	0.999897i	$-0.495423\pi$
$409$	−17.0763	−	9.85901i	−0.844369	−	0.487497i	−0.858747	+	0.512400i	$0.828757\pi$
$410$		0			0
$411$			13.8411i			0.682731i
$412$		0			0
$413$	−9.66564	−	16.7414i	−0.475615	−	0.823789i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−53.3829			−2.61417
$418$		0			0
$419$	0.322441	+	0.558484i	0.0157523	+	0.0272837i	0.873794	−	0.486296i	$-0.161652\pi$
$419$	0.322441	+	0.558484i	0.0157523	+	0.0272837i	−0.858042	+	0.513580i	$0.828319\pi$
$420$		0			0
$421$		−	1.14482i		−	0.0557950i	−0.999611	−	0.0278975i	$-0.991119\pi$
$421$		−	1.14482i		−	0.0557950i	0.999611	−	0.0278975i	$-0.00888120\pi$
$422$		0			0
$423$	4.37895	+	2.52819i	0.212912	+	0.122925i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	16.1466	−	9.32227i	0.781391	−	0.451136i
$428$		0			0
$429$	33.2555	−	43.1542i	1.60559	−	2.08351i
$430$		0			0
$431$	−19.0432	+	10.9946i	−0.917278	+	0.529591i	−0.882766	−	0.469814i	$-0.844321\pi$
$431$	−19.0432	+	10.9946i	−0.917278	+	0.529591i	−0.0345122	+	0.999404i	$0.510988\pi$
$432$		0			0
$433$	−13.7683	+	23.8473i	−0.661661	+	1.14603i	0.318518	+	0.947917i	$0.396815\pi$
$433$	−13.7683	+	23.8473i	−0.661661	+	1.14603i	−0.980179	+	0.198113i	$0.936519\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	7.11230i		−	0.340228i
$438$		0			0
$439$	−10.7249	−	18.5761i	−0.511872	−	0.886588i	−0.999905	−	0.0137633i	$-0.995619\pi$
$439$	−10.7249	−	18.5761i	−0.511872	−	0.886588i	0.488033	−	0.872825i	$-0.337714\pi$
$440$		0			0
$441$	−7.65163			−0.364363
$442$		0			0
$443$	−2.96360			−0.140805			−0.0704023	−	0.997519i	$-0.522428\pi$
$443$	−2.96360			−0.140805			−0.0704023	+	0.997519i	$0.522428\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			1.99871i			0.0945359i
$448$		0			0
$449$	−23.0337	−	13.2985i	−1.08703	−	0.627596i	−0.154244	−	0.988033i	$-0.549294\pi$
$449$	−23.0337	−	13.2985i	−1.08703	−	0.627596i	−0.932784	+	0.360437i	$0.882628\pi$
$450$		0			0
$451$	2.28521	−	3.95811i	0.107607	−	0.186380i
$452$		0			0
$453$	48.6377	−	28.0810i	2.28520	−	1.31936i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	6.85144	−	3.95568i	0.320497	−	0.185039i	−0.331117	−	0.943590i	$-0.607426\pi$
$457$	6.85144	−	3.95568i	0.320497	−	0.185039i	0.651614	+	0.758551i	$0.274092\pi$
$458$		0			0
$459$	1.69458	−	2.93511i	0.0790964	−	0.136999i
$460$		0			0
$461$	8.91164	+	5.14514i	0.415056	+	0.239633i	0.692960	−	0.720976i	$-0.256306\pi$
$461$	8.91164	+	5.14514i	0.415056	+	0.239633i	−0.277904	+	0.960609i	$0.589640\pi$
$462$		0			0
$463$		−	16.9348i		−	0.787026i	−0.919319	−	0.393513i	$-0.871260\pi$
$463$		−	16.9348i		−	0.787026i	0.919319	−	0.393513i	$-0.128740\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	26.8077			1.24051			0.620255	−	0.784400i	$-0.287029\pi$
$467$	26.8077			1.24051			0.620255	+	0.784400i	$0.287029\pi$
$468$		0			0
$469$	29.8066			1.37634
$470$		0			0
$471$	6.46431	+	11.1965i	0.297860	+	0.515908i
$472$		0			0
$473$			40.5872i			1.86620i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	2.65179	−	4.59303i	0.121417	−	0.210300i
$478$		0			0
$479$	−14.9474	+	8.62988i	−0.682964	+	0.394309i	−0.800971	−	0.598703i	$-0.795683\pi$
$479$	−14.9474	+	8.62988i	−0.682964	+	0.394309i	0.118007	+	0.993013i	$0.462350\pi$
$480$		0			0
$481$	8.61693	+	20.9255i	0.392898	+	0.954119i
$482$		0			0
$483$	53.7349	−	31.0238i	2.44502	−	1.41163i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−10.3749	−	5.98994i	−0.470131	−	0.271430i	0.246164	−	0.969228i	$-0.420830\pi$
$487$	−10.3749	−	5.98994i	−0.470131	−	0.271430i	−0.716294	+	0.697798i	$0.754163\pi$
$488$		0			0
$489$		−	28.9718i		−	1.31015i
$490$		0			0
$491$	7.93099	+	13.7369i	0.357920	+	0.619936i	0.987613	−	0.156908i	$-0.0501526\pi$
$491$	7.93099	+	13.7369i	0.357920	+	0.619936i	−0.629693	+	0.776844i	$0.716819\pi$
$492$		0			0
$493$	−44.8780			−2.02120
$494$		0			0
$495$		0			0
$496$		0			0
$497$	9.97916	+	17.2844i	0.447626	+	0.775311i
$498$		0			0
$499$			24.0268i			1.07559i	0.843077	+	0.537793i	$0.180742\pi$
$499$			24.0268i			1.07559i	−0.843077	+	0.537793i	$0.819258\pi$
$500$		0			0
$501$	−22.2568	−	12.8500i	−0.994361	−	0.574094i
$502$		0			0
$503$	−11.8996	+	20.6108i	−0.530578	+	0.918989i	0.468785	+	0.883312i	$0.344692\pi$
$503$	−11.8996	+	20.6108i	−0.530578	+	0.918989i	−0.999363	+	0.0356763i	$0.988641\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	7.97509	+	30.2638i	0.354186	+	1.34406i
$508$		0			0
$509$	−18.7070	+	10.8005i	−0.829172	+	0.478723i	−0.853569	−	0.520980i	$-0.825567\pi$
$509$	−18.7070	+	10.8005i	−0.829172	+	0.478723i	0.0243972	+	0.999702i	$0.492233\pi$
$510$		0			0
$511$	16.2983	−	28.2294i	0.720993	−	1.24880i
$512$		0			0
$513$	0.366497	+	0.211597i	0.0161812	+	0.00934224i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−5.67559	−	9.83040i	−0.249612	−	0.432341i
$518$		0			0
$519$	9.25098			0.406073
$520$		0			0
$521$	19.7262			0.864218			0.432109	−	0.901821i	$-0.357770\pi$
$521$	19.7262			0.864218			0.432109	+	0.901821i	$0.357770\pi$
$522$		0			0
$523$	5.81545	+	10.0727i	0.254292	+	0.440447i	0.964703	−	0.263340i	$-0.0848242\pi$
$523$	5.81545	+	10.0727i	0.254292	+	0.440447i	−0.710411	+	0.703787i	$0.751491\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−46.4442	−	26.8146i	−2.02314	−	1.16806i
$528$		0			0
$529$	−22.6105	+	39.1626i	−0.983066	+	1.70272i
$530$		0			0
$531$	15.0003	−	8.66041i	0.650956	−	0.375830i
$532$		0			0
$533$	0.999714	+	2.42772i	0.0433024	+	0.105156i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	19.4639	−	33.7125i	0.839930	−	1.45480i
$538$		0			0
$539$	14.8760	+	8.58866i	0.640755	+	0.369940i
$540$		0			0
$541$			0.198507i			0.00853450i	0.999991	+	0.00426725i	$0.00135831\pi$
$541$			0.198507i			0.00853450i	−0.999991	+	0.00426725i	$0.998642\pi$
$542$		0			0
$543$	−10.8097	−	18.7230i	−0.463889	−	0.803480i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	33.4453			1.43002			0.715009	−	0.699116i	$-0.246423\pi$
$547$	33.4453			1.43002			0.715009	+	0.699116i	$0.246423\pi$
$548$		0			0
$549$	8.35275	+	14.4674i	0.356487	+	0.617453i
$550$		0			0
$551$		−	5.60376i		−	0.238728i
$552$		0			0
$553$	−20.5592	−	11.8699i	−0.874268	−	0.504759i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−2.71076	+	1.56506i	−0.114858	+	0.0663136i	−0.556329	−	0.830962i	$-0.687790\pi$
$557$	−2.71076	+	1.56506i	−0.114858	+	0.0663136i	0.441470	+	0.897276i	$0.354457\pi$
$558$		0			0
$559$	−18.4680	−	14.2318i	−0.781113	−	0.601941i
$560$		0			0
$561$	90.2425	−	52.1015i	3.81004	−	2.19973i
$562$		0			0
$563$	−4.67626	+	8.09953i	−0.197081	+	0.341354i	−0.947581	−	0.319516i	$-0.896480\pi$
$563$	−4.67626	+	8.09953i	−0.197081	+	0.341354i	0.750500	+	0.660871i	$0.229813\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$			29.8644i			1.25419i
$568$		0			0
$569$	19.0882	+	33.0618i	0.800220	+	1.38602i	0.919471	+	0.393158i	$0.128617\pi$
$569$	19.0882	+	33.0618i	0.800220	+	1.38602i	−0.119251	+	0.992864i	$0.538049\pi$
$570$		0			0
$571$	17.3279			0.725152			0.362576	−	0.931954i	$-0.381897\pi$
$571$	17.3279			0.725152			0.362576	+	0.931954i	$0.381897\pi$
$572$		0			0
$573$	−34.9343			−1.45940
$574$		0			0
$575$		0			0
$576$		0			0
$577$			10.9310i			0.455064i	0.973771	+	0.227532i	$0.0730656\pi$
$577$			10.9310i			0.455064i	−0.973771	+	0.227532i	$0.926934\pi$
$578$		0			0
$579$	18.0324	+	10.4110i	0.749402	+	0.432667i
$580$		0			0
$581$	5.60778	−	9.71296i	0.232650	−	0.402962i
$582$		0			0
$583$	−10.3110	+	5.95306i	−0.427038	+	0.246551i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	7.49665	−	4.32820i	0.309420	−	0.178644i	−0.337247	−	0.941416i	$-0.609496\pi$
$587$	7.49665	−	4.32820i	0.309420	−	0.178644i	0.646667	+	0.762772i	$0.276162\pi$
$588$		0			0
$589$	3.34825	−	5.79933i	0.137962	−	0.238957i
$590$		0			0
$591$	9.06596	+	5.23423i	0.372924	+	0.215308i
$592$		0			0
$593$		−	19.3598i		−	0.795013i	−0.917599	−	0.397507i	$-0.869876\pi$
$593$		−	19.3598i		−	0.795013i	0.917599	−	0.397507i	$-0.130124\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	26.5097			1.08497
$598$		0			0
$599$	33.0812			1.35166			0.675831	−	0.737056i	$-0.263785\pi$
$599$	33.0812			1.35166			0.675831	+	0.737056i	$0.263785\pi$
$600$		0			0
$601$	−0.127830	−	0.221408i	−0.00521428	−	0.00903141i	0.863406	−	0.504509i	$-0.168326\pi$
$601$	−0.127830	−	0.221408i	−0.00521428	−	0.00903141i	−0.868621	+	0.495478i	$0.834993\pi$
$602$		0			0
$603$			26.7067i			1.08758i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−3.95957	+	6.85817i	−0.160714	+	0.278365i	−0.935125	−	0.354318i	$-0.884713\pi$
$607$	−3.95957	+	6.85817i	−0.160714	+	0.278365i	0.774411	+	0.632683i	$0.218046\pi$
$608$		0			0
$609$	42.3375	−	24.4436i	1.71560	−	0.990504i
$610$		0			0
$611$	6.46316	+	0.864498i	0.261471	+	0.0349739i
$612$		0			0
$613$	8.52940	−	4.92445i	0.344499	−	0.198897i	−0.317761	−	0.948171i	$-0.602931\pi$
$613$	8.52940	−	4.92445i	0.344499	−	0.198897i	0.662260	+	0.749274i	$0.269597\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	24.4573	+	14.1205i	0.984616	+	0.568468i	0.903660	−	0.428250i	$-0.140870\pi$
$617$	24.4573	+	14.1205i	0.984616	+	0.568468i	0.0809551	+	0.996718i	$0.474203\pi$
$618$		0			0
$619$			11.3380i			0.455713i	0.973695	+	0.227856i	$0.0731717\pi$
$619$			11.3380i			0.455713i	−0.973695	+	0.227856i	$0.926828\pi$
$620$		0			0
$621$	−2.02963	−	3.51543i	−0.0814464	−	0.141069i
$622$		0			0
$623$	25.5467			1.02351
$624$		0			0
$625$		0			0
$626$		0			0
$627$	6.50575	+	11.2683i	0.259814	+	0.450012i
$628$		0			0
$629$			43.2834i			1.72582i
$630$		0			0
$631$	7.00860	+	4.04642i	0.279008	+	0.161085i	0.632974	−	0.774173i	$-0.281834\pi$
$631$	7.00860	+	4.04642i	0.279008	+	0.161085i	−0.353966	+	0.935258i	$0.615167\pi$
$632$		0			0
$633$	−0.981242	+	1.69956i	−0.0390009	+	0.0675515i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−9.12424	+	3.75729i	−0.361516	+	0.148869i
$638$		0			0
$639$	−15.4868	+	8.94132i	−0.612649	+	0.353713i
$640$		0			0
$641$	−11.5303	+	19.9710i	−0.455418	+	0.788808i	−0.998712	−	0.0507348i	$-0.983844\pi$
$641$	−11.5303	+	19.9710i	−0.455418	+	0.788808i	0.543294	+	0.839543i	$0.317177\pi$
$642$		0			0
$643$	−15.3234	−	8.84700i	−0.604298	−	0.348891i	0.166433	−	0.986053i	$-0.446775\pi$
$643$	−15.3234	−	8.84700i	−0.604298	−	0.348891i	−0.770730	+	0.637161i	$0.780108\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	22.4728	+	38.9240i	0.883496	+	1.53026i	0.847428	+	0.530910i	$0.178150\pi$
$647$	22.4728	+	38.9240i	0.883496	+	1.53026i	0.0360677	+	0.999349i	$0.488517\pi$
$648$		0			0
$649$	−38.8839			−1.52633
$650$		0			0
$651$	58.4202			2.28967
$652$		0			0
$653$	−0.865172	−	1.49852i	−0.0338568	−	0.0586417i	0.848601	−	0.529034i	$-0.177446\pi$
$653$	−0.865172	−	1.49852i	−0.0338568	−	0.0586417i	−0.882457	+	0.470392i	$0.844112\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	25.2936	+	14.6032i	0.986795	+	0.569727i
$658$		0			0
$659$	5.35651	−	9.27774i	0.208660	−	0.361410i	−0.742633	−	0.669699i	$-0.766423\pi$
$659$	5.35651	−	9.27774i	0.208660	−	0.361410i	0.951293	+	0.308289i	$0.0997565\pi$
$660$		0			0
$661$	−6.80837	+	3.93081i	−0.264815	+	0.152891i	−0.626529	−	0.779398i	$-0.715525\pi$
$661$	−6.80837	+	3.93081i	−0.264815	+	0.152891i	0.361714	+	0.932289i	$0.382192\pi$
$662$		0			0
$663$	−7.93604	+	59.3314i	−0.308210	+	2.30424i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−26.8756	+	46.5499i	−1.04063	+	1.80242i
$668$		0			0
$669$	−34.4116	−	19.8676i	−1.33043	−	0.768124i
$670$		0			0
$671$		−	37.5026i		−	1.44777i
$672$		0			0
$673$	−17.5452	−	30.3892i	−0.676319	−	1.17142i	−0.976082	−	0.217405i	$-0.930241\pi$
$673$	−17.5452	−	30.3892i	−0.676319	−	1.17142i	0.299763	−	0.954014i	$-0.403093\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−25.7519			−0.989725			−0.494863	−	0.868971i	$-0.664782\pi$
$677$	−25.7519			−0.989725			−0.494863	+	0.868971i	$0.664782\pi$
$678$		0			0
$679$	−21.0801	−	36.5119i	−0.808981	−	1.40120i
$680$		0			0
$681$			33.2008i			1.27226i
$682$		0			0
$683$	−20.9818	−	12.1138i	−0.802846	−	0.463523i	0.0416192	−	0.999134i	$-0.486748\pi$
$683$	−20.9818	−	12.1138i	−0.802846	−	0.463523i	−0.844465	+	0.535610i	$0.820082\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−32.7084	+	18.8842i	−1.24790	+	0.720477i
$688$		0			0
$689$	0.906763	−	6.77914i	0.0345449	−	0.258265i
$690$		0			0
$691$	41.7879	−	24.1263i	1.58969	−	0.917806i	0.596329	−	0.802740i	$-0.296625\pi$
$691$	41.7879	−	24.1263i	1.58969	−	0.917806i	0.993358	−	0.115066i	$-0.0367079\pi$
$692$		0			0
$693$	−27.3785	+	47.4210i	−1.04002	+	1.80137i
$694$		0			0
$695$		0			0
$696$		0			0
$697$			5.02163i			0.190208i
$698$		0			0
$699$	17.6367	+	30.5476i	0.667081	+	1.15542i
$700$		0			0
$701$	−26.0605			−0.984293			−0.492147	−	0.870512i	$-0.663788\pi$
$701$	−26.0605			−0.984293			−0.492147	+	0.870512i	$0.663788\pi$
$702$		0			0
$703$	−5.40466			−0.203840
$704$		0			0
$705$		0			0
$706$		0			0
$707$			4.06148i			0.152748i
$708$		0			0
$709$	37.4415	+	21.6168i	1.40614	+	0.811838i	0.995014	−	0.0997387i	$-0.0318007\pi$
$709$	37.4415	+	21.6168i	1.40614	+	0.811838i	0.411131	+	0.911576i	$0.365134\pi$
$710$		0			0
$711$	10.6354	−	18.4211i	0.398859	−	0.690844i
$712$		0			0
$713$	−55.6271	+	32.1163i	−2.08325	+	1.20276i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	24.6106	−	14.2089i	0.919100	−	0.530642i
$718$		0			0
$719$	−4.80510	+	8.32268i	−0.179200	+	0.310384i	−0.941607	−	0.336714i	$-0.890684\pi$
$719$	−4.80510	+	8.32268i	−0.179200	+	0.310384i	0.762407	+	0.647098i	$0.224018\pi$
$720$		0			0
$721$	−1.77915	−	1.02719i	−0.0662588	−	0.0382546i
$722$		0			0
$723$			5.85371i			0.217702i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−39.6920			−1.47210			−0.736048	−	0.676929i	$-0.763310\pi$
$727$	−39.6920			−1.47210			−0.736048	+	0.676929i	$0.763310\pi$
$728$		0			0
$729$	−23.2090			−0.859591
$730$		0			0
$731$	−22.2970	−	38.6196i	−0.824686	−	1.42840i
$732$		0			0
$733$			34.4457i			1.27228i	0.771574	+	0.636140i	$0.219470\pi$
$733$			34.4457i			1.27228i	−0.771574	+	0.636140i	$0.780530\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	29.9772	−	51.9221i	1.10423	−	1.91258i
$738$		0			0
$739$	−1.20391	+	0.695077i	−0.0442865	+	0.0255688i	−0.521980	−	0.852958i	$-0.674806\pi$
$739$	−1.20391	+	0.695077i	−0.0442865	+	0.0255688i	0.477693	+	0.878527i	$0.341473\pi$
$740$		0			0
$741$	−7.40851	−	0.990947i	−0.272159	−	0.0364033i
$742$		0			0
$743$	12.6173	−	7.28458i	0.462883	−	0.267245i	−0.250373	−	0.968149i	$-0.580553\pi$
$743$	12.6173	−	7.28458i	0.462883	−	0.267245i	0.713256	+	0.700904i	$0.247220\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	8.70281	+	5.02457i	0.318419	+	0.183839i
$748$		0			0
$749$			21.7239i			0.793775i
$750$		0			0
$751$	−16.7590	−	29.0275i	−0.611546	−	1.05923i	−0.990980	−	0.134009i	$-0.957215\pi$
$751$	−16.7590	−	29.0275i	−0.611546	−	1.05923i	0.379435	−	0.925219i	$-0.376119\pi$
$752$		0			0
$753$	65.2589			2.37817
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−12.5621	−	21.7581i	−0.456576	−	0.790813i	0.542201	−	0.840249i	$-0.317591\pi$
$757$	−12.5621	−	21.7581i	−0.456576	−	0.790813i	−0.998777	+	0.0494358i	$0.984258\pi$
$758$		0			0
$759$		−	124.806i		−	4.53017i
$760$		0			0
$761$	−13.2403	−	7.64430i	−0.479961	−	0.277106i	0.240439	−	0.970664i	$-0.422709\pi$
$761$	−13.2403	−	7.64430i	−0.479961	−	0.277106i	−0.720400	+	0.693559i	$0.756042\pi$
$762$		0			0
$763$	15.2092	−	26.3432i	0.550611	−	0.953687i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	13.6345	−	17.6930i	0.492315	−	0.638856i
$768$		0			0
$769$	23.9409	−	13.8223i	0.863329	−	0.498443i	−0.00179636	−	0.999998i	$-0.500572\pi$
$769$	23.9409	−	13.8223i	0.863329	−	0.498443i	0.865126	+	0.501555i	$0.167238\pi$
$770$		0			0
$771$	−25.7941	+	44.6767i	−0.928952	+	1.60899i
$772$		0			0
$773$	−19.6814	−	11.3630i	−0.707889	−	0.408700i	0.102390	−	0.994744i	$-0.467351\pi$
$773$	−19.6814	−	11.3630i	−0.707889	−	0.408700i	−0.810279	+	0.586044i	$0.800684\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−23.5751	−	40.8333i	−0.845752	−	1.46488i
$778$		0			0
$779$	−0.627034			−0.0224658
$780$		0			0
$781$	40.1452			1.43651
$782$		0			0
$783$	−1.59914	−	2.76980i	−0.0571487	−	0.0989845i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	0.00695942	+	0.00401802i	0.000248077	+	0.000143227i	0.500124	−	0.865954i	$-0.333288\pi$
$787$	0.00695942	+	0.00401802i	0.000248077	+	0.000143227i	−0.499876	+	0.866097i	$0.666621\pi$
$788$		0			0
$789$	5.93096	−	10.2727i	0.211148	−	0.365719i
$790$		0			0
$791$	−15.0948	+	8.71501i	−0.536711	+	0.309870i
$792$		0			0
$793$	17.0644	+	13.1502i	0.605975	+	0.466976i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−11.9632	+	20.7209i	−0.423759	+	0.733972i	−0.996304	−	0.0859012i	$-0.972623\pi$
$797$	−11.9632	+	20.7209i	−0.423759	+	0.733972i	0.572544	+	0.819874i	$0.305956\pi$
$798$		0			0
$799$	10.8009	+	6.23589i	0.382108	+	0.220610i
$800$		0			0
$801$			22.8898i			0.808773i
$802$		0			0
$803$	−32.7832	−	56.7821i	−1.15689	−	2.00380i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	68.5092			2.41164
$808$		0			0
$809$	26.5978	+	46.0687i	0.935128	+	1.61969i	0.774406	+	0.632689i	$0.218049\pi$
$809$	26.5978	+	46.0687i	0.935128	+	1.61969i	0.160721	+	0.987000i	$0.448618\pi$
$810$		0			0
$811$			15.4030i			0.540871i	0.962738	+	0.270436i	$0.0871677\pi$
$811$			15.4030i			0.540871i	−0.962738	+	0.270436i	$0.912832\pi$
$812$		0			0
$813$	−60.9215	−	35.1730i	−2.13661	−	1.23357i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	4.82230	−	2.78416i	0.168711	−	0.0974053i
$818$		0			0
$819$	−11.9773	−	29.0858i	−0.418520	−	1.01634i
$820$		0			0
$821$	26.8681	−	15.5123i	0.937703	−	0.541383i	0.0484631	−	0.998825i	$-0.484568\pi$
$821$	26.8681	−	15.5123i	0.937703	−	0.541383i	0.889239	+	0.457442i	$0.151234\pi$
$822$		0			0
$823$	−4.01402	+	6.95248i	−0.139920	+	0.242348i	−0.927466	−	0.373907i	$-0.878018\pi$
$823$	−4.01402	+	6.95248i	−0.139920	+	0.242348i	0.787546	+	0.616256i	$0.211351\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			12.1775i			0.423454i	0.977329	+	0.211727i	$0.0679088\pi$
$827$			12.1775i			0.423454i	−0.977329	+	0.211727i	$0.932091\pi$
$828$		0			0
$829$	−3.25960	−	5.64579i	−0.113210	−	0.196086i	0.803853	−	0.594829i	$-0.202780\pi$
$829$	−3.25960	−	5.64579i	−0.113210	−	0.196086i	−0.917063	+	0.398742i	$0.869447\pi$
$830$		0			0
$831$	28.1742			0.977352
$832$		0			0
$833$	−18.8731			−0.653914
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	3.82195i		−	0.132106i
$838$		0			0
$839$	49.0774	+	28.3349i	1.69434	+	0.978229i	0.950936	+	0.309387i	$0.100124\pi$
$839$	49.0774	+	28.3349i	1.69434	+	0.978229i	0.743405	+	0.668841i	$0.233209\pi$
$840$		0			0
$841$	−6.67519	+	11.5618i	−0.230179	+	0.398682i
$842$		0			0
$843$	7.07370	−	4.08400i	0.243631	−	0.140661i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	76.7309	−	44.3006i	2.63650	−	1.52219i
$848$		0			0
$849$	−17.7812	+	30.7980i	−0.610250	+	1.05698i
$850$		0			0
$851$	44.8959	+	25.9207i	1.53901	+	0.888549i
$852$		0			0
$853$		−	25.1466i		−	0.861002i	−0.902590	−	0.430501i	$-0.858337\pi$
$853$		−	25.1466i		−	0.861002i	0.902590	−	0.430501i	$-0.141663\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−8.79926			−0.300577			−0.150289	−	0.988642i	$-0.548020\pi$
$857$	−8.79926			−0.300577			−0.150289	+	0.988642i	$0.548020\pi$
$858$		0			0
$859$	45.5772			1.55507			0.777537	−	0.628837i	$-0.216469\pi$
$859$	45.5772			1.55507			0.777537	+	0.628837i	$0.216469\pi$
$860$		0			0
$861$	−2.73512	−	4.73737i	−0.0932126	−	0.161449i
$862$		0			0
$863$			41.0390i			1.39698i	0.715618	+	0.698492i	$0.246145\pi$
$863$			41.0390i			1.39698i	−0.715618	+	0.698492i	$0.753855\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−36.7817	+	63.7077i	−1.24917	+	2.16363i
$868$		0			0
$869$	−41.3539	+	23.8757i	−1.40284	+	0.809928i
$870$		0			0
$871$	13.1142	+	31.8466i	0.444356	+	1.07908i
$872$		0			0
$873$	32.7146	−	18.8878i	1.10722	−	0.639255i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−44.6614	−	25.7853i	−1.50811	−	0.870707i	−0.999955	−	0.00943944i	$-0.996995\pi$
$877$	−44.6614	−	25.7853i	−1.50811	−	0.870707i	−0.508153	−	0.861267i	$-0.669671\pi$
$878$		0			0
$879$			29.6186i			0.999012i
$880$		0			0
$881$	−8.67658	−	15.0283i	−0.292322	−	0.506316i	0.682037	−	0.731318i	$-0.261094\pi$
$881$	−8.67658	−	15.0283i	−0.292322	−	0.506316i	−0.974358	+	0.225002i	$0.927761\pi$
$882$		0			0
$883$	35.5857			1.19755			0.598777	−	0.800916i	$-0.295654\pi$
$883$	35.5857			1.19755			0.598777	+	0.800916i	$0.295654\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−6.80960	−	11.7946i	−0.228644	−	0.396023i	0.728762	−	0.684767i	$-0.240096\pi$
$887$	−6.80960	−	11.7946i	−0.228644	−	0.396023i	−0.957406	+	0.288744i	$0.906763\pi$
$888$		0			0
$889$		−	16.2896i		−	0.546336i
$890$		0			0
$891$	52.0228	+	30.0354i	1.74283	+	1.00622i
$892$		0			0
$893$	−0.778655	+	1.34867i	−0.0260567	+	0.0451315i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	56.7892	+	43.7628i	1.89614	+	1.46120i
$898$		0			0
$899$	−43.8284	+	25.3043i	−1.46176	+	0.843947i
$900$		0			0
$901$	6.54076	−	11.3289i	0.217904	−	0.377421i
$902$		0			0
$903$	42.0697	+	24.2890i	1.39999	+	0.808286i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	7.91839	+	13.7151i	0.262926	+	0.455401i	0.967018	−	0.254708i	$-0.0819792\pi$
$907$	7.91839	+	13.7151i	0.262926	+	0.455401i	−0.704092	+	0.710108i	$0.748646\pi$
$908$		0			0
$909$	−3.63908			−0.120701
$910$		0			0
$911$	−18.0798			−0.599009			−0.299504	−	0.954095i	$-0.596821\pi$
$911$	−18.0798			−0.599009			−0.299504	+	0.954095i	$0.596821\pi$
$912$		0			0
$913$	−11.2798	−	19.5371i	−0.373306	−	0.646585i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−22.8900	−	13.2156i	−0.755896	−	0.436417i
$918$		0			0
$919$	12.2836	−	21.2758i	0.405197	−	0.701822i	−0.589147	−	0.808026i	$-0.700536\pi$
$919$	12.2836	−	21.2758i	0.405197	−	0.701822i	0.994344	+	0.106203i	$0.0338695\pi$
$920$		0			0
$921$	−18.1919	+	10.5031i	−0.599442	+	0.346088i
$922$		0			0
$923$	−14.0768	+	18.2669i	−0.463343	+	0.601261i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	0.920362	−	1.59411i	0.0302286	−	0.0523576i
$928$		0			0
$929$	29.4502	+	17.0031i	0.966231	+	0.557854i	0.898085	−	0.439822i	$-0.144958\pi$
$929$	29.4502	+	17.0031i	0.966231	+	0.557854i	0.0681458	+	0.997675i	$0.478292\pi$
$930$		0			0
$931$		−	2.35662i		−	0.0772351i
$932$		0			0
$933$	18.7783	+	32.5249i	0.614773	+	1.06482i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	2.95329			0.0964799			0.0482400	−	0.998836i	$-0.484639\pi$
$937$	2.95329			0.0964799			0.0482400	+	0.998836i	$0.484639\pi$
$938$		0			0
$939$	−28.4581	−	49.2910i	−0.928697	−	1.60855i
$940$		0			0
$941$		−	45.6985i		−	1.48973i	−0.667217	−	0.744864i	$-0.732514\pi$
$941$		−	45.6985i		−	1.48973i	0.667217	−	0.744864i	$-0.267486\pi$
$942$		0			0
$943$	5.20871	+	3.00725i	0.169619	+	0.0979295i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	43.0286	−	24.8426i	1.39824	−	0.807275i	0.404033	−	0.914744i	$-0.367608\pi$
$947$	43.0286	−	24.8426i	1.39824	−	0.807275i	0.994208	+	0.107469i	$0.0342748\pi$
$948$		0			0
$949$	37.3323	+	4.99349i	1.21186	+	0.162096i
$950$		0			0
$951$	−22.8689	+	13.2034i	−0.741575	+	0.428148i
$952$		0			0
$953$	25.3032	−	43.8265i	0.819652	−	1.41968i	−0.0862877	−	0.996270i	$-0.527500\pi$
$953$	25.3032	−	43.8265i	0.819652	−	1.41968i	0.905939	−	0.423408i	$-0.139166\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	98.3342i		−	3.17869i
$958$		0			0
$959$	−8.96994	−	15.5364i	−0.289654	−	0.501696i
$960$		0			0
$961$	−29.4773			−0.950881
$962$		0			0
$963$	−19.4646			−0.627239
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	54.6224i		−	1.75654i	−0.478166	−	0.878269i	$-0.658698\pi$
$967$		−	54.6224i		−	1.75654i	0.478166	−	0.878269i	$-0.341302\pi$
$968$		0			0
$969$	−12.3807	−	7.14800i	−0.397725	−	0.229627i
$970$		0			0
$971$	−6.62505	+	11.4749i	−0.212608	+	0.368248i	−0.952530	−	0.304445i	$-0.901529\pi$
$971$	−6.62505	+	11.4749i	−0.212608	+	0.368248i	0.739922	+	0.672693i	$0.234862\pi$
$972$		0			0
$973$	59.9213	−	34.5956i	1.92099	−	1.10908i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.12304	−	2.95779i	0.163901	−	0.0946281i	−0.415806	−	0.909453i	$-0.636500\pi$
$977$	5.12304	−	2.95779i	0.163901	−	0.0946281i	0.579707	+	0.814825i	$0.303167\pi$
$978$		0			0
$979$	25.6930	−	44.5015i	0.821151	−	1.42228i
$980$		0			0
$981$	23.6035	+	13.6275i	0.753601	+	0.435092i
$982$		0			0
$983$			59.7254i			1.90494i	0.304625	+	0.952472i	$0.401469\pi$
$983$			59.7254i			1.90494i	−0.304625	+	0.952472i	$0.598531\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−13.5860			−0.432446
$988$		0			0
$989$	−53.4111			−1.69837
$990$		0			0
$991$	−19.0250	−	32.9523i	−0.604349	−	1.04676i	−0.992154	−	0.125022i	$-0.960100\pi$
$991$	−19.0250	−	32.9523i	−0.604349	−	1.04676i	0.387805	−	0.921741i	$-0.373233\pi$
$992$		0			0
$993$			1.74890i			0.0554996i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	10.3716	−	17.9642i	0.328473	−	0.568931i	−0.653736	−	0.756722i	$-0.726799\pi$
$997$	10.3716	−	17.9642i	0.328473	−	0.568931i	0.982209	+	0.187791i	$0.0601328\pi$
$998$		0			0
$999$	−2.67138	+	1.54232i	−0.0845188	+	0.0487970i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1300.2.y.d.101.1	yes	10
5.2	odd	4		1300.2.ba.d.49.2		20
5.3	odd	4		1300.2.ba.d.49.9		20
5.4	even	2		1300.2.y.c.101.5	✓	10
13.4	even	6	inner	1300.2.y.d.901.1	yes	10
65.4	even	6		1300.2.y.c.901.5	yes	10
65.17	odd	12		1300.2.ba.d.849.9		20
65.43	odd	12		1300.2.ba.d.849.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1300.2.y.c.101.5	✓	10	5.4	even	2
1300.2.y.c.901.5	yes	10	65.4	even	6
1300.2.y.d.101.1	yes	10	1.1	even	1	trivial
1300.2.y.d.901.1	yes	10	13.4	even	6	inner
1300.2.ba.d.49.2		20	5.2	odd	4
1300.2.ba.d.49.9		20	5.3	odd	4
1300.2.ba.d.849.2		20	65.43	odd	12
1300.2.ba.d.849.9		20	65.17	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.y (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20373 - 2.08492i) q^{3} +(2.70233 + 1.56019i) q^{7} +(-1.39793 + 2.42129i) q^{9} +O(q^{10})\)	\(q+(-1.20373 - 2.08492i) q^{3} +(2.70233 + 1.56019i) q^{7} +(-1.39793 + 2.42129i) q^{9} +(5.43560 - 3.13825i) q^{11} +(-0.478014 + 3.57372i) q^{13} +(-3.44806 + 5.97221i) q^{17} +(-0.745730 - 0.430548i) q^{19} -7.51219i q^{21} +(4.12980 + 7.15303i) q^{23} -0.491460 q^{27} +(3.25386 + 5.63585i) q^{29} +7.77672i q^{31} +(-13.0860 - 7.55520i) q^{33} +(5.43560 - 3.13825i) q^{37} +(8.02633 - 3.30518i) q^{39} +(0.630624 - 0.364091i) q^{41} +(-3.23327 + 5.60019i) q^{43} -1.80852i q^{47} +(1.36839 + 2.37011i) q^{49} +16.6021 q^{51} -1.89694 q^{53} +2.07305i q^{57} +(-5.36517 - 3.09758i) q^{59} +(2.98754 - 5.17458i) q^{61} +(-7.55533 + 4.36207i) q^{63} +(8.27247 - 4.77611i) q^{67} +(9.94233 - 17.2206i) q^{69} +(5.53920 + 3.19806i) q^{71} -10.4463i q^{73} +19.5850 q^{77} -7.60798 q^{79} +(4.78537 + 8.28851i) q^{81} -3.59429i q^{83} +(7.83353 - 13.5681i) q^{87} +(7.09019 - 4.09352i) q^{89} +(-6.86744 + 8.91158i) q^{91} +(16.2138 - 9.36106i) q^{93} +(-11.7011 - 6.75563i) q^{97} +17.5482i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{3} - 8 q^{9}+O(q^{10}) \) 10 * q + q^3 - 8 * q^9	\( 10 q + q^{3} - 8 q^{9} + 3 q^{11} + 4 q^{13} - 12 q^{17} - 12 q^{19} - 3 q^{23} - 14 q^{27} + 3 q^{29} - 30 q^{33} + 3 q^{37} + 16 q^{39} + 12 q^{41} - 8 q^{43} + 19 q^{49} - 24 q^{51} - 24 q^{53} - 6 q^{59} + q^{61} + 24 q^{63} + 48 q^{67} + 45 q^{71} + 24 q^{77} + 16 q^{79} + 7 q^{81} + 21 q^{87} + 12 q^{89} - 3 q^{91} + 93 q^{93} - 15 q^{97}+O(q^{100}) \) 10 * q + q^3 - 8 * q^9 + 3 * q^11 + 4 * q^13 - 12 * q^17 - 12 * q^19 - 3 * q^23 - 14 * q^27 + 3 * q^29 - 30 * q^33 + 3 * q^37 + 16 * q^39 + 12 * q^41 - 8 * q^43 + 19 * q^49 - 24 * q^51 - 24 * q^53 - 6 * q^59 + q^61 + 24 * q^63 + 48 * q^67 + 45 * q^71 + 24 * q^77 + 16 * q^79 + 7 * q^81 + 21 * q^87 + 12 * q^89 - 3 * q^91 + 93 * q^93 - 15 * q^97

Introduction

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