LMFDB - Embedded newform 784.3.s.g.129.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("784.129");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$21.3624527258$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.339738624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 $ x^8 - 4x^6 + 14x^4 - 8*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 7^{4} $
Twist minimal:	no (minimal twist has level 196)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			129.3
Root			$1.60021 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	784.129
Dual form			784.3.s.g.705.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.274552 + 0.158513i) q^{3} +(-4.91434 + 2.83730i) q^{5} +(-4.44975 - 7.70719i) q^{9} +O(q^{10})$	\(q+(0.274552 + 0.158513i) q^{3} +(-4.91434 + 2.83730i) q^{5} +(-4.44975 - 7.70719i) q^{9} +(-7.94975 + 13.7694i) q^{11} -20.1940i q^{13} -1.79899 q^{15} +(-0.823656 - 0.475538i) q^{17} +(27.5918 - 15.9301i) q^{19} +(13.0000 + 22.5167i) q^{23} +(3.60051 - 6.23626i) q^{25} -5.67459i q^{27} +27.7990 q^{29} +(13.1233 + 7.57675i) q^{31} +(-4.36524 + 2.52027i) q^{33} +(16.0000 + 27.7128i) q^{37} +(3.20101 - 5.54431i) q^{39} -17.3408i q^{41} +59.2965 q^{43} +(43.7352 + 25.2505i) q^{45} +(-66.1105 + 38.1689i) q^{47} +(-0.150758 - 0.261120i) q^{51} +(-12.8995 + 22.3426i) q^{53} -90.2232i q^{55} +10.1005 q^{57} +(59.2743 + 34.2220i) q^{59} +(46.9746 - 27.1208i) q^{61} +(57.2965 + 99.2404i) q^{65} +(43.6985 - 75.6880i) q^{67} +8.24266i q^{69} -16.4020 q^{71} +(60.9216 + 35.1731i) q^{73} +(1.97705 - 1.14145i) q^{75} +(20.1005 + 34.8151i) q^{79} +(-39.1482 + 67.8067i) q^{81} -71.5505i q^{83} +5.39697 q^{85} +(7.63227 + 4.40649i) q^{87} +(66.9617 - 38.6604i) q^{89} +(2.40202 + 4.16042i) q^{93} +(-90.3970 + 156.572i) q^{95} -128.328i q^{97} +141.497 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^9	$ 8 q + 4 q^{9} - 24 q^{11} + 144 q^{15} + 104 q^{23} + 108 q^{25} + 64 q^{29} + 128 q^{37} + 184 q^{39} - 80 q^{43} - 120 q^{51} - 24 q^{53} + 160 q^{57} - 96 q^{65} + 112 q^{67} - 448 q^{71} + 240 q^{79} - 36 q^{81} - 432 q^{85} + 336 q^{93} - 248 q^{95} + 736 q^{99}+O(q^{100}) $ 8 * q + 4 * q^9 - 24 * q^11 + 144 * q^15 + 104 * q^23 + 108 * q^25 + 64 * q^29 + 128 * q^37 + 184 * q^39 - 80 * q^43 - 120 * q^51 - 24 * q^53 + 160 * q^57 - 96 * q^65 + 112 * q^67 - 448 * q^71 + 240 * q^79 - 36 * q^81 - 432 * q^85 + 336 * q^93 - 248 * q^95 + 736 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.274552	+	0.158513i	0.0915173	+	0.0528376i	0.545060	−	0.838397i	$-0.316507\pi$
$3$	0.274552	+	0.158513i	0.0915173	+	0.0528376i	−0.453543	+	0.891234i	$0.649840\pi$
$4$		0			0
$5$	−4.91434	+	2.83730i	−0.982868	+	0.567459i	−0.903135	−	0.429357i	$-0.858740\pi$
$5$	−4.91434	+	2.83730i	−0.982868	+	0.567459i	−0.0797335	+	0.996816i	$0.525407\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−4.44975	−	7.70719i	−0.494416	−	0.856354i
$10$		0			0
$11$	−7.94975	+	13.7694i	−0.722704	+	1.25176i	0.237208	+	0.971459i	$0.423768\pi$
$11$	−7.94975	+	13.7694i	−0.722704	+	1.25176i	−0.959912	+	0.280302i	$0.909566\pi$
$12$		0			0
$13$		−	20.1940i		−	1.55339i	−0.629879	−	0.776694i	$-0.716895\pi$
$13$		−	20.1940i		−	1.55339i	0.629879	−	0.776694i	$-0.283105\pi$
$14$		0			0
$15$	−1.79899			−0.119933
$16$		0			0
$17$	−0.823656	−	0.475538i	−0.0484504	−	0.0279728i	0.475579	−	0.879673i	$-0.342239\pi$
$17$	−0.823656	−	0.475538i	−0.0484504	−	0.0279728i	−0.524030	+	0.851700i	$0.675572\pi$
$18$		0			0
$19$	27.5918	−	15.9301i	1.45220	−	0.838428i	0.453593	−	0.891209i	$-0.350142\pi$
$19$	27.5918	−	15.9301i	1.45220	−	0.838428i	0.998606	+	0.0527814i	$0.0168087\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	13.0000	+	22.5167i	0.565217	+	0.978985i	0.997029	+	0.0770216i	$0.0245410\pi$
$23$	13.0000	+	22.5167i	0.565217	+	0.978985i	−0.431812	+	0.901964i	$0.642126\pi$
$24$		0			0
$25$	3.60051	−	6.23626i	0.144020	−	0.249450i
$26$		0			0
$27$		−	5.67459i		−	0.210170i
$28$		0			0
$29$	27.7990			0.958586			0.479293	−	0.877655i	$-0.340893\pi$
$29$	27.7990			0.958586			0.479293	+	0.877655i	$0.340893\pi$
$30$		0			0
$31$	13.1233	+	7.57675i	0.423333	+	0.244411i	0.696502	−	0.717555i	$-0.254739\pi$
$31$	13.1233	+	7.57675i	0.423333	+	0.244411i	−0.273170	+	0.961966i	$0.588072\pi$
$32$		0			0
$33$	−4.36524	+	2.52027i	−0.132280	+	0.0763719i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	16.0000	+	27.7128i	0.432432	+	0.748995i	0.997082	−	0.0763357i	$-0.0243221\pi$
$37$	16.0000	+	27.7128i	0.432432	+	0.748995i	−0.564650	+	0.825331i	$0.690989\pi$
$38$		0			0
$39$	3.20101	−	5.54431i	0.0820772	−	0.142162i
$40$		0			0
$41$		−	17.3408i		−	0.422946i	−0.977384	−	0.211473i	$-0.932174\pi$
$41$		−	17.3408i		−	0.422946i	0.977384	−	0.211473i	$-0.0678261\pi$
$42$		0			0
$43$	59.2965			1.37899			0.689494	−	0.724292i	$-0.257833\pi$
$43$	59.2965			1.37899			0.689494	+	0.724292i	$0.257833\pi$
$44$		0			0
$45$	43.7352	+	25.2505i	0.971892	+	0.561122i
$46$		0			0
$47$	−66.1105	+	38.1689i	−1.40661	+	0.812104i	−0.995059	−	0.0992848i	$-0.968345\pi$
$47$	−66.1105	+	38.1689i	−1.40661	+	0.812104i	−0.411546	+	0.911389i	$0.635011\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−0.150758	−	0.261120i	−0.00295603	−	0.00512000i
$52$		0			0
$53$	−12.8995	+	22.3426i	−0.243387	+	0.421558i	−0.961677	−	0.274186i	$-0.911592\pi$
$53$	−12.8995	+	22.3426i	−0.243387	+	0.421558i	0.718290	+	0.695744i	$0.244925\pi$
$54$		0			0
$55$		−	90.2232i		−	1.64042i
$56$		0			0
$57$	10.1005			0.177202
$58$		0			0
$59$	59.2743	+	34.2220i	1.00465	+	0.580034i	0.909620	−	0.415441i	$-0.136373\pi$
$59$	59.2743	+	34.2220i	1.00465	+	0.580034i	0.0950280	+	0.995475i	$0.469706\pi$
$60$		0			0
$61$	46.9746	−	27.1208i	0.770075	−	0.444603i	−0.0628261	−	0.998024i	$-0.520011\pi$
$61$	46.9746	−	27.1208i	0.770075	−	0.444603i	0.832902	+	0.553421i	$0.186678\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	57.2965	+	99.2404i	0.881484	+	1.52678i
$66$		0			0
$67$	43.6985	−	75.6880i	0.652216	−	1.12967i	−0.330368	−	0.943852i	$-0.607173\pi$
$67$	43.6985	−	75.6880i	0.652216	−	1.12967i	0.982584	−	0.185819i	$-0.0594939\pi$
$68$		0			0
$69$			8.24266i			0.119459i
$70$		0			0
$71$	−16.4020			−0.231014			−0.115507	−	0.993307i	$-0.536849\pi$
$71$	−16.4020			−0.231014			−0.115507	+	0.993307i	$0.536849\pi$
$72$		0			0
$73$	60.9216	+	35.1731i	0.834542	+	0.481823i	0.855405	−	0.517959i	$-0.173308\pi$
$73$	60.9216	+	35.1731i	0.834542	+	0.481823i	−0.0208633	+	0.999782i	$0.506641\pi$
$74$		0			0
$75$	1.97705	−	1.14145i	0.0263607	−	0.0152194i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	20.1005	+	34.8151i	0.254437	+	0.440697i	0.964742	−	0.263196i	$-0.0847766\pi$
$79$	20.1005	+	34.8151i	0.254437	+	0.440697i	−0.710306	+	0.703893i	$0.751443\pi$
$80$		0			0
$81$	−39.1482	+	67.8067i	−0.483312	+	0.837120i
$82$		0			0
$83$		−	71.5505i		−	0.862055i	−0.902339	−	0.431027i	$-0.858151\pi$
$83$		−	71.5505i		−	0.862055i	0.902339	−	0.431027i	$-0.141849\pi$
$84$		0			0
$85$	5.39697			0.0634938
$86$		0			0
$87$	7.63227	+	4.40649i	0.0877272	+	0.0506493i
$88$		0			0
$89$	66.9617	−	38.6604i	0.752379	−	0.434386i	−0.0741740	−	0.997245i	$-0.523632\pi$
$89$	66.9617	−	38.6604i	0.752379	−	0.434386i	0.826553	+	0.562859i	$0.190299\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	2.40202	+	4.16042i	0.0258282	+	0.0447357i
$94$		0			0
$95$	−90.3970	+	156.572i	−0.951547	+	1.64813i
$96$		0			0
$97$		−	128.328i		−	1.32297i	−0.749957	−	0.661486i	$-0.769926\pi$
$97$		−	128.328i		−	1.32297i	0.749957	−	0.661486i	$-0.230074\pi$
$98$		0			0
$99$	141.497			1.42927
$100$		0			0
$101$	−86.8384	−	50.1362i	−0.859787	−	0.496398i	0.00415427	−	0.999991i	$-0.498678\pi$
$101$	−86.8384	−	50.1362i	−0.859787	−	0.496398i	−0.863941	+	0.503593i	$0.832011\pi$
$102$		0			0
$103$	42.6094	−	24.6005i	0.413683	−	0.238840i	−0.278688	−	0.960382i	$-0.589900\pi$
$103$	42.6094	−	24.6005i	0.413683	−	0.238840i	0.692371	+	0.721542i	$0.256566\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	14.7990	+	25.6326i	0.138308	+	0.239557i	0.926856	−	0.375416i	$-0.122500\pi$
$107$	14.7990	+	25.6326i	0.138308	+	0.239557i	−0.788548	+	0.614973i	$0.789167\pi$
$108$		0			0
$109$	5.59798	−	9.69599i	0.0513576	−	0.0889540i	−0.839204	−	0.543817i	$-0.816979\pi$
$109$	5.59798	−	9.69599i	0.0513576	−	0.0889540i	0.890561	+	0.454863i	$0.150312\pi$
$110$		0			0
$111$			10.1448i			0.0913947i
$112$		0			0
$113$	133.698			1.18317			0.591586	−	0.806242i	$-0.298502\pi$
$113$	133.698			1.18317			0.591586	+	0.806242i	$0.298502\pi$
$114$		0			0
$115$	−127.773	−	73.7697i	−1.11107	−	0.641476i
$116$		0			0
$117$	−155.639	+	89.8583i	−1.33025	+	0.768020i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−65.8970	−	114.137i	−0.544603	−	0.943280i
$122$		0			0
$123$	2.74874	−	4.76095i	0.0223475	−	0.0387069i
$124$		0			0
$125$		−	101.002i		−	0.808016i
$126$		0			0
$127$	−120.995			−0.952716			−0.476358	−	0.879251i	$-0.658043\pi$
$127$	−120.995			−0.952716			−0.476358	+	0.879251i	$0.658043\pi$
$128$		0			0
$129$	16.2800	+	9.39924i	0.126201	+	0.0728623i
$130$		0			0
$131$	110.037	−	63.5301i	0.839980	−	0.484963i	−0.0172774	−	0.999851i	$-0.505500\pi$
$131$	110.037	−	63.5301i	0.839980	−	0.484963i	0.857257	+	0.514888i	$0.172167\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	16.1005	+	27.8869i	0.119263	+	0.206570i
$136$		0			0
$137$	74.9497	−	129.817i	0.547078	−	0.947568i	−0.451394	−	0.892325i	$-0.649073\pi$
$137$	74.9497	−	129.817i	0.547078	−	0.947568i	0.998473	−	0.0552432i	$-0.0175934\pi$
$138$		0			0
$139$		−	14.2661i		−	0.102634i	−0.998682	−	0.0513171i	$-0.983658\pi$
$139$		−	14.2661i		−	0.102634i	0.998682	−	0.0513171i	$-0.0163419\pi$
$140$		0			0
$141$	−24.2010			−0.171638
$142$		0			0
$143$	278.059	+	160.537i	1.94447	+	1.12264i
$144$		0			0
$145$	−136.614	+	78.8740i	−0.942164	+	0.543958i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−25.3015	−	43.8235i	−0.169809	−	0.294118i	0.768544	−	0.639797i	$-0.220982\pi$
$149$	−25.3015	−	43.8235i	−0.169809	−	0.294118i	−0.938353	+	0.345680i	$0.887648\pi$
$150$		0			0
$151$	−20.8995	+	36.1990i	−0.138407	+	0.239728i	−0.926894	−	0.375324i	$-0.877532\pi$
$151$	−20.8995	+	36.1990i	−0.138407	+	0.239728i	0.788487	+	0.615052i	$0.210865\pi$
$152$		0			0
$153$			8.46410i			0.0553209i
$154$		0			0
$155$	−85.9899			−0.554774
$156$		0			0
$157$	124.067	+	71.6302i	0.790237	+	0.456243i	0.840046	−	0.542515i	$-0.182528\pi$
$157$	124.067	+	71.6302i	0.790237	+	0.456243i	−0.0498093	+	0.998759i	$0.515861\pi$
$158$		0			0
$159$	−7.08316	+	4.08947i	−0.0445482	+	0.0257199i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	57.1457	+	98.9793i	0.350587	+	0.607235i	0.986352	−	0.164648i	$-0.0526487\pi$
$163$	57.1457	+	98.9793i	0.350587	+	0.607235i	−0.635765	+	0.771882i	$0.719315\pi$
$164$		0			0
$165$	14.3015	−	24.7710i	0.0866758	−	0.150127i
$166$		0			0
$167$			290.895i			1.74189i	0.491382	+	0.870944i	$0.336492\pi$
$167$			290.895i			1.74189i	−0.491382	+	0.870944i	$0.663508\pi$
$168$		0			0
$169$	−238.799			−1.41301
$170$		0			0
$171$	−245.553	−	141.770i	−1.43598	−	0.829065i
$172$		0			0
$173$	184.027	−	106.248i	1.06374	−	0.614151i	0.137276	−	0.990533i	$-0.456165\pi$
$173$	184.027	−	106.248i	1.06374	−	0.614151i	0.926465	+	0.376382i	$0.122832\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	10.8492	+	18.7914i	0.0612952	+	0.106166i
$178$		0			0
$179$	11.8040	−	20.4452i	0.0659444	−	0.114219i	−0.831168	−	0.556021i	$-0.812327\pi$
$179$	11.8040	−	20.4452i	0.0659444	−	0.114219i	0.897113	+	0.441802i	$0.145661\pi$
$180$		0			0
$181$			156.384i			0.864002i	0.901873	+	0.432001i	$0.142192\pi$
$181$			156.384i			0.864002i	−0.901873	+	0.432001i	$0.857808\pi$
$182$		0			0
$183$	17.1960			0.0939670
$184$		0			0
$185$	−157.259	−	90.7935i	−0.850048	−	0.490776i
$186$		0			0
$187$	13.0957	−	7.56081i	0.0700306	−	0.0404322i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−122.794	−	212.685i	−0.642900	−	1.11354i	−0.984782	−	0.173793i	$-0.944398\pi$
$191$	−122.794	−	212.685i	−0.642900	−	1.11354i	0.341882	−	0.939743i	$-0.388936\pi$
$192$		0			0
$193$	−28.7487	+	49.7943i	−0.148957	+	0.258001i	−0.930842	−	0.365421i	$-0.880925\pi$
$193$	−28.7487	+	49.7943i	−0.148957	+	0.258001i	0.781885	+	0.623423i	$0.214258\pi$
$194$		0			0
$195$			36.3289i			0.186302i
$196$		0			0
$197$	174.402			0.885289			0.442645	−	0.896697i	$-0.354040\pi$
$197$	174.402			0.885289			0.442645	+	0.896697i	$0.354040\pi$
$198$		0			0
$199$	145.289	+	83.8827i	0.730096	+	0.421521i	0.818457	−	0.574568i	$-0.194830\pi$
$199$	145.289	+	83.8827i	0.730096	+	0.421521i	−0.0883615	+	0.996088i	$0.528163\pi$
$200$		0			0
$201$	23.9950	−	13.8535i	0.119378	−	0.0689230i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	49.2010	+	85.2186i	0.240005	+	0.415701i
$206$		0			0
$207$	115.693	−	200.387i	0.558905	−	0.968053i
$208$		0			0
$209$			506.562i			2.42374i
$210$		0			0
$211$	81.7889			0.387625			0.193813	−	0.981039i	$-0.437915\pi$
$211$	81.7889			0.387625			0.193813	+	0.981039i	$0.437915\pi$
$212$		0			0
$213$	−4.50321	−	2.59993i	−0.0211418	−	0.0122062i
$214$		0			0
$215$	−291.403	+	168.242i	−1.35536	+	0.782519i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	11.1508	+	19.3137i	0.0509167	+	0.0881903i
$220$		0			0
$221$	−9.60303	+	16.6329i	−0.0434526	+	0.0752622i
$222$		0			0
$223$		−	91.4275i		−	0.409989i	−0.978763	−	0.204994i	$-0.934282\pi$
$223$		−	91.4275i		−	0.409989i	0.978763	−	0.204994i	$-0.0657176\pi$
$224$		0			0
$225$	−64.0854			−0.284824
$226$		0			0
$227$	−318.308	−	183.775i	−1.40224	−	0.809582i	−0.407615	−	0.913154i	$-0.633639\pi$
$227$	−318.308	−	183.775i	−1.40224	−	0.809582i	−0.994622	+	0.103572i	$0.966973\pi$
$228$		0			0
$229$	−10.4606	+	6.03941i	−0.0456793	+	0.0263730i	−0.522666	−	0.852538i	$-0.675062\pi$
$229$	−10.4606	+	6.03941i	−0.0456793	+	0.0263730i	0.476986	+	0.878911i	$0.341729\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.849242	+	1.47093i	0.00364482	+	0.00631301i	0.867842	−	0.496840i	$-0.165506\pi$
$233$	0.849242	+	1.47093i	0.00364482	+	0.00631301i	−0.864197	+	0.503153i	$0.832173\pi$
$234$		0			0
$235$	216.593	−	375.150i	0.921672	−	1.59638i
$236$		0			0
$237$			12.7447i			0.0537753i
$238$		0			0
$239$	−201.397			−0.842665			−0.421333	−	0.906906i	$-0.638437\pi$
$239$	−201.397			−0.842665			−0.421333	+	0.906906i	$0.638437\pi$
$240$		0			0
$241$	−84.3675	−	48.7096i	−0.350072	−	0.202114i	0.314645	−	0.949210i	$-0.398115\pi$
$241$	−84.3675	−	48.7096i	−0.350072	−	0.202114i	−0.664717	+	0.747095i	$0.731448\pi$
$242$		0			0
$243$	−65.7255	+	37.9467i	−0.270475	+	0.156159i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−321.693	−	557.189i	−1.30240	−	2.25583i
$248$		0			0
$249$	11.3417	−	19.6443i	0.0455489	−	0.0788929i
$250$		0			0
$251$			77.2251i			0.307670i	0.988097	+	0.153835i	$0.0491624\pi$
$251$			77.2251i			0.307670i	−0.988097	+	0.153835i	$0.950838\pi$
$252$		0			0
$253$	−413.387			−1.63394
$254$		0			0
$255$	1.48175	+	0.855488i	0.00581078	+	0.00335486i
$256$		0			0
$257$	314.958	−	181.841i	1.22552	−	0.707553i	0.259429	−	0.965762i	$-0.416466\pi$
$257$	314.958	−	181.841i	1.22552	−	0.707553i	0.966089	+	0.258209i	$0.0831325\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−123.698	−	214.252i	−0.473941	−	0.820889i
$262$		0			0
$263$	−205.296	+	355.584i	−0.780595	+	1.35203i	0.151001	+	0.988534i	$0.451750\pi$
$263$	−205.296	+	355.584i	−0.780595	+	1.35203i	−0.931596	+	0.363496i	$0.881583\pi$
$264$		0			0
$265$		−	146.399i		−	0.552448i
$266$		0			0
$267$	24.5126			0.0918076
$268$		0			0
$269$	−266.611	−	153.928i	−0.991118	−	0.572222i	−0.0855095	−	0.996337i	$-0.527252\pi$
$269$	−266.611	−	153.928i	−0.991118	−	0.572222i	−0.905608	+	0.424115i	$0.860585\pi$
$270$		0			0
$271$	−154.513	+	89.2084i	−0.570160	+	0.329182i	−0.757213	−	0.653168i	$-0.773440\pi$
$271$	−154.513	+	89.2084i	−0.570160	+	0.329182i	0.187053	+	0.982350i	$0.440106\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	57.2462	+	99.1533i	0.208168	+	0.360558i
$276$		0			0
$277$	−48.0955	+	83.3038i	−0.173630	+	0.300736i	−0.939686	−	0.342038i	$-0.888883\pi$
$277$	−48.0955	+	83.3038i	−0.173630	+	0.300736i	0.766056	+	0.642773i	$0.222216\pi$
$278$		0			0
$279$		−	134.858i		−	0.483363i
$280$		0			0
$281$	−155.106			−0.551977			−0.275989	−	0.961161i	$-0.589005\pi$
$281$	−155.106			−0.551977			−0.275989	+	0.961161i	$0.589005\pi$
$282$		0			0
$283$	−271.278	−	156.622i	−0.958580	−	0.553436i	−0.0628440	−	0.998023i	$-0.520017\pi$
$283$	−271.278	−	156.622i	−0.958580	−	0.553436i	−0.895736	+	0.444587i	$0.853350\pi$
$284$		0			0
$285$	−49.6373	+	28.6581i	−0.174166	+	0.100555i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−144.048	−	249.498i	−0.498435	−	0.863315i
$290$		0			0
$291$	20.3417	−	35.2328i	0.0699026	−	0.121075i
$292$		0			0
$293$			202.543i			0.691271i	0.938369	+	0.345636i	$0.112337\pi$
$293$			202.543i			0.691271i	−0.938369	+	0.345636i	$0.887663\pi$
$294$		0			0
$295$	−388.392			−1.31658
$296$		0			0
$297$	78.1356	+	45.1116i	0.263083	+	0.151891i
$298$		0			0
$299$	454.702	−	262.522i	1.52074	−	0.878001i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−15.8944	−	27.5300i	−0.0524569	−	0.0908580i
$304$		0			0
$305$	−153.899	+	266.562i	−0.504589	+	0.873973i
$306$		0			0
$307$			378.772i			1.23378i	0.787047	+	0.616892i	$0.211609\pi$
$307$			378.772i			1.23378i	−0.787047	+	0.616892i	$0.788391\pi$
$308$		0			0
$309$	15.5980			0.0504789
$310$		0			0
$311$	178.235	+	102.904i	0.573104	+	0.330882i	0.758388	−	0.651803i	$-0.225987\pi$
$311$	178.235	+	102.904i	0.573104	+	0.330882i	−0.185284	+	0.982685i	$0.559321\pi$
$312$		0			0
$313$	−391.419	+	225.986i	−1.25054	+	0.721999i	−0.971217	−	0.238198i	$-0.923443\pi$
$313$	−391.419	+	225.986i	−1.25054	+	0.721999i	−0.279322	+	0.960197i	$0.590110\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	41.6934	+	72.2151i	0.131525	+	0.227808i	0.924265	−	0.381752i	$-0.124679\pi$
$317$	41.6934	+	72.2151i	0.131525	+	0.227808i	−0.792740	+	0.609560i	$0.791346\pi$
$318$		0			0
$319$	−220.995	+	382.774i	−0.692774	+	1.19992i
$320$		0			0
$321$			9.38331i			0.0292315i
$322$		0			0
$323$	−30.3015			−0.0938127
$324$		0			0
$325$	−125.935	−	72.7087i	−0.387493	−	0.223719i
$326$		0			0
$327$	3.07387	−	1.77470i	0.00940022	−	0.00542722i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	76.7437	+	132.924i	0.231854	+	0.401583i	0.958354	−	0.285584i	$-0.0921875\pi$
$331$	76.7437	+	132.924i	0.231854	+	0.401583i	−0.726500	+	0.687167i	$0.758854\pi$
$332$		0			0
$333$	142.392	−	246.630i	0.427603	−	0.740631i
$334$		0			0
$335$			495.942i			1.48042i
$336$		0			0
$337$	519.377			1.54118			0.770589	−	0.637333i	$-0.219962\pi$
$337$	519.377			1.54118			0.770589	+	0.637333i	$0.219962\pi$
$338$		0			0
$339$	36.7072	+	21.1929i	0.108281	+	0.0625159i
$340$		0			0
$341$	−208.654	+	120.466i	−0.611888	+	0.353274i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−23.3869	−	40.5072i	−0.0677880	−	0.117412i
$346$		0			0
$347$	42.2412	−	73.1638i	0.121732	−	0.210847i	−0.798719	−	0.601705i	$-0.794488\pi$
$347$	42.2412	−	73.1638i	0.121732	−	0.210847i	0.920451	+	0.390858i	$0.127822\pi$
$348$		0			0
$349$			187.959i			0.538565i	0.963061	+	0.269283i	$0.0867866\pi$
$349$			187.959i			0.538565i	−0.963061	+	0.269283i	$0.913213\pi$
$350$		0			0
$351$	−114.593			−0.326476
$352$		0			0
$353$	98.0951	+	56.6352i	0.277890	+	0.160440i	0.632468	−	0.774587i	$-0.282042\pi$
$353$	98.0951	+	56.6352i	0.277890	+	0.160440i	−0.354578	+	0.935026i	$0.615375\pi$
$354$		0			0
$355$	80.6051	−	46.5374i	0.227057	−	0.131091i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	330.588	+	572.595i	0.920858	+	1.59497i	0.798091	+	0.602537i	$0.205843\pi$
$359$	330.588	+	572.595i	0.920858	+	1.59497i	0.122766	+	0.992436i	$0.460823\pi$
$360$		0			0
$361$	327.038	−	566.446i	0.905921	−	1.56910i
$362$		0			0
$363$		−	41.7820i		−	0.115102i
$364$		0			0
$365$	−399.186			−1.09366
$366$		0			0
$367$	−76.1047	−	43.9391i	−0.207370	−	0.119725i	0.392719	−	0.919659i	$-0.371535\pi$
$367$	−76.1047	−	43.9391i	−0.207370	−	0.119725i	−0.600088	+	0.799934i	$0.704868\pi$
$368$		0			0
$369$	−133.649	+	77.1622i	−0.362192	+	0.209112i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−213.101	−	369.101i	−0.571315	−	0.989547i	−0.996431	−	0.0844079i	$-0.973100\pi$
$373$	−213.101	−	369.101i	−0.571315	−	0.989547i	0.425116	−	0.905139i	$-0.360233\pi$
$374$		0			0
$375$	16.0101	−	27.7303i	0.0426936	−	0.0739475i
$376$		0			0
$377$		−	561.374i		−	1.48905i
$378$		0			0
$379$	719.879			1.89942			0.949709	−	0.313134i	$-0.101379\pi$
$379$	719.879			1.89942			0.949709	+	0.313134i	$0.101379\pi$
$380$		0			0
$381$	−33.2194	−	19.1792i	−0.0871900	−	0.0503392i
$382$		0			0
$383$	209.148	−	120.752i	0.546078	−	0.315278i	−0.201461	−	0.979497i	$-0.564569\pi$
$383$	209.148	−	120.752i	0.546078	−	0.315278i	0.747539	+	0.664218i	$0.231235\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−263.854	−	457.009i	−0.681794	−	1.18090i
$388$		0			0
$389$	132.704	−	229.849i	0.341140	−	0.590872i	−0.643505	−	0.765442i	$-0.722520\pi$
$389$	132.704	−	229.849i	0.341140	−	0.590872i	0.984645	+	0.174570i	$0.0558536\pi$
$390$		0			0
$391$		−	24.7280i		−	0.0632429i
$392$		0			0
$393$	40.2813			0.102497
$394$		0			0
$395$	−197.562	−	114.062i	−0.500156	−	0.288765i
$396$		0			0
$397$	156.848	−	90.5561i	0.395083	−	0.228101i	−0.289277	−	0.957245i	$-0.593415\pi$
$397$	156.848	−	90.5561i	0.395083	−	0.228101i	0.684360	+	0.729144i	$0.260082\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	210.296	+	364.244i	0.524430	+	0.908340i	0.999595	+	0.0284430i	$0.00905492\pi$
$401$	210.296	+	364.244i	0.524430	+	0.908340i	−0.475165	+	0.879897i	$0.657612\pi$
$402$		0			0
$403$	153.005	−	265.013i	0.379665	−	0.657599i
$404$		0			0
$405$		−	444.301i		−	1.09704i
$406$		0			0
$407$	−508.784			−1.25008
$408$		0			0
$409$	−126.566	−	73.0727i	−0.309452	−	0.178662i	0.337229	−	0.941422i	$-0.390510\pi$
$409$	−126.566	−	73.0727i	−0.309452	−	0.178662i	−0.646681	+	0.762761i	$0.723844\pi$
$410$		0			0
$411$	41.1552	−	23.7610i	0.100134	−	0.0578126i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	203.010	+	351.624i	0.489181	+	0.847286i
$416$		0			0
$417$	2.26136	−	3.91680i	0.00542294	−	0.00939280i
$418$		0			0
$419$		−	521.905i		−	1.24560i	−0.782383	−	0.622798i	$-0.785996\pi$
$419$		−	521.905i		−	1.24560i	0.782383	−	0.622798i	$-0.214004\pi$
$420$		0			0
$421$	746.181			1.77240			0.886200	−	0.463302i	$-0.153335\pi$
$421$	746.181			1.77240			0.886200	+	0.463302i	$0.153335\pi$
$422$		0			0
$423$	588.350	+	339.684i	1.39090	+	0.803035i
$424$		0			0
$425$	−5.93116	+	3.42435i	−0.0139557	+	0.00805730i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	50.8944	+	88.1518i	0.118635	+	0.205482i
$430$		0			0
$431$	124.296	−	215.288i	0.288391	−	0.499508i	−0.685035	−	0.728510i	$-0.740213\pi$
$431$	124.296	−	215.288i	0.288391	−	0.499508i	0.973426	+	0.229003i	$0.0735464\pi$
$432$		0			0
$433$			494.357i			1.14170i	0.821054	+	0.570851i	$0.193387\pi$
$433$			494.357i			1.14170i	−0.821054	+	0.570851i	$0.806613\pi$
$434$		0			0
$435$	−50.0101			−0.114966
$436$		0			0
$437$	717.386	+	414.183i	1.64162	+	0.947788i
$438$		0			0
$439$	−567.484	+	327.637i	−1.29267	+	0.746325i	−0.979127	−	0.203247i	$-0.934850\pi$
$439$	−567.484	+	327.637i	−1.29267	+	0.746325i	−0.313546	+	0.949573i	$0.601517\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−19.6985	−	34.1188i	−0.0444661	−	0.0770176i	0.842936	−	0.538014i	$-0.180825\pi$
$443$	−19.6985	−	34.1188i	−0.0444661	−	0.0770176i	−0.887402	+	0.460997i	$0.847492\pi$
$444$		0			0
$445$	−219.382	+	379.980i	−0.492993	+	0.853889i
$446$		0			0
$447$		−	16.0424i		−	0.0358891i
$448$		0			0
$449$	−700.362			−1.55983			−0.779913	−	0.625888i	$-0.784737\pi$
$449$	−700.362			−1.55983			−0.779913	+	0.625888i	$0.784737\pi$
$450$		0			0
$451$	238.772	+	137.855i	0.529428	+	0.305665i
$452$		0			0
$453$	−11.4760	+	6.62567i	−0.0253333	+	0.0146262i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	176.739	+	306.120i	0.386737	+	0.669847i	0.992008	−	0.126171i	$-0.0402689\pi$
$457$	176.739	+	306.120i	0.386737	+	0.669847i	−0.605272	+	0.796019i	$0.706936\pi$
$458$		0			0
$459$	−2.69848	+	4.67391i	−0.00587905	+	0.0101828i
$460$		0			0
$461$			382.482i			0.829680i	0.909894	+	0.414840i	$0.136162\pi$
$461$			382.482i			0.829680i	−0.909894	+	0.414840i	$0.863838\pi$
$462$		0			0
$463$	309.005			0.667398			0.333699	−	0.942680i	$-0.391703\pi$
$463$	309.005			0.667398			0.333699	+	0.942680i	$0.391703\pi$
$464$		0			0
$465$	−23.6087	−	13.6305i	−0.0507714	−	0.0293129i
$466$		0			0
$467$	398.612	−	230.139i	0.853559	−	0.492803i	−0.00829089	−	0.999966i	$-0.502639\pi$
$467$	398.612	−	230.139i	0.853559	−	0.492803i	0.861850	+	0.507163i	$0.169306\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	22.7086	+	39.3324i	0.0482136	+	0.0835083i
$472$		0			0
$473$	−471.392	+	816.475i	−0.996600	+	1.72616i
$474$		0			0
$475$		−	229.426i		−	0.483002i
$476$		0			0
$477$	229.598			0.481337
$478$		0			0
$479$	−12.9577	−	7.48116i	−0.0270517	−	0.0156183i	0.486413	−	0.873729i	$-0.338305\pi$
$479$	−12.9577	−	7.48116i	−0.0270517	−	0.0156183i	−0.513465	+	0.858111i	$0.671638\pi$
$480$		0			0
$481$	559.633	−	323.105i	1.16348	−	0.671735i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	364.106	+	630.649i	0.750733	+	1.30031i
$486$		0			0
$487$	−218.688	+	378.779i	−0.449052	+	0.777781i	−0.998325	−	0.0578622i	$-0.981572\pi$
$487$	−218.688	+	378.779i	−0.449052	+	0.777781i	0.549272	+	0.835643i	$0.314905\pi$
$488$		0			0
$489$			36.2333i			0.0740967i
$490$		0			0
$491$	816.583			1.66310			0.831551	−	0.555449i	$-0.187454\pi$
$491$	816.583			1.66310			0.831551	+	0.555449i	$0.187454\pi$
$492$		0			0
$493$	−22.8968	−	13.2195i	−0.0464438	−	0.0268144i
$494$		0			0
$495$	−695.367	+	401.470i	−1.40478	+	0.811051i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−124.503	−	215.645i	−0.249504	−	0.432154i	0.713884	−	0.700264i	$-0.246934\pi$
$499$	−124.503	−	215.645i	−0.249504	−	0.432154i	−0.963388	+	0.268110i	$0.913601\pi$
$500$		0			0
$501$	−46.1106	+	79.8659i	−0.0920371	+	0.159413i
$502$		0			0
$503$		−	423.536i		−	0.842020i	−0.907056	−	0.421010i	$-0.861676\pi$
$503$		−	423.536i		−	0.842020i	0.907056	−	0.421010i	$-0.138324\pi$
$504$		0			0
$505$	569.005			1.12674
$506$		0			0
$507$	−65.5627	−	37.8527i	−0.129315	−	0.0746601i
$508$		0			0
$509$	671.289	−	387.569i	1.31884	−	0.761432i	0.335297	−	0.942112i	$-0.391163\pi$
$509$	671.289	−	387.569i	1.31884	−	0.761432i	0.983542	+	0.180680i	$0.0578299\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−90.3970	−	156.572i	−0.176212	−	0.305209i
$514$		0			0
$515$	−139.598	+	241.791i	−0.271064	+	0.469497i
$516$		0			0
$517$		−	1213.73i		−	2.34764i
$518$		0			0
$519$	67.3667			0.129801
$520$		0			0
$521$	441.194	+	254.723i	0.846821	+	0.488913i	0.859577	−	0.511006i	$-0.170727\pi$
$521$	441.194	+	254.723i	0.846821	+	0.488913i	−0.0127557	+	0.999919i	$0.504060\pi$
$522$		0			0
$523$	−457.391	+	264.075i	−0.874553	+	0.504923i	−0.868859	−	0.495060i	$-0.835146\pi$
$523$	−457.391	+	264.075i	−0.874553	+	0.504923i	−0.00569433	+	0.999984i	$0.501813\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−7.20606	−	12.4813i	−0.0136737	−	0.0236836i
$528$		0			0
$529$	−73.5000	+	127.306i	−0.138941	+	0.240654i
$530$		0			0
$531$		−	609.117i		−	1.14711i
$532$		0			0
$533$	−350.181			−0.657000
$534$		0			0
$535$	−145.455	−	83.9783i	−0.271878	−	0.156969i
$536$		0			0
$537$	6.48165	−	3.74218i	0.0120701	−	0.00696868i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	264.799	+	458.645i	0.489462	+	0.847773i	0.999926	−	0.0121257i	$-0.00385982\pi$
$541$	264.799	+	458.645i	0.489462	+	0.847773i	−0.510464	+	0.859899i	$0.670526\pi$
$542$		0			0
$543$	−24.7889	+	42.9356i	−0.0456517	+	0.0790711i
$544$		0			0
$545$			63.5325i			0.116573i
$546$		0			0
$547$	−16.9045			−0.0309041			−0.0154521	−	0.999881i	$-0.504919\pi$
$547$	−16.9045			−0.0309041			−0.0154521	+	0.999881i	$0.504919\pi$
$548$		0			0
$549$	−418.050	−	241.361i	−0.761476	−	0.439638i
$550$		0			0
$551$	767.024	−	442.841i	1.39206	−	0.803705i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−28.7838	−	49.8551i	−0.0518628	−	0.0898290i
$556$		0			0
$557$	−446.980	+	774.192i	−0.802477	+	1.38993i	0.115504	+	0.993307i	$0.463152\pi$
$557$	−446.980	+	774.192i	−0.802477	+	1.38993i	−0.917981	+	0.396624i	$0.870182\pi$
$558$		0			0
$559$		−	1197.43i		−	2.14210i
$560$		0			0
$561$	4.79394			0.00854535
$562$		0			0
$563$	84.1219	+	48.5678i	0.149417	+	0.0862661i	0.572845	−	0.819664i	$-0.305840\pi$
$563$	84.1219	+	48.5678i	0.149417	+	0.0862661i	−0.423427	+	0.905930i	$0.639173\pi$
$564$		0			0
$565$	−657.040	+	379.342i	−1.16290	+	0.671402i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−380.090	−	658.336i	−0.667997	−	1.15701i	−0.978463	−	0.206421i	$-0.933818\pi$
$569$	−380.090	−	658.336i	−0.667997	−	1.15701i	0.310466	−	0.950584i	$-0.399515\pi$
$570$		0			0
$571$	169.146	−	292.969i	0.296227	−	0.513080i	−0.679042	−	0.734099i	$-0.737605\pi$
$571$	169.146	−	292.969i	0.296227	−	0.513080i	0.975270	+	0.221019i	$0.0709381\pi$
$572$		0			0
$573$		−	77.8576i		−	0.135877i
$574$		0			0
$575$	187.226			0.325611
$576$		0			0
$577$	−209.039	−	120.689i	−0.362286	−	0.209166i	0.307797	−	0.951452i	$-0.400408\pi$
$577$	−209.039	−	120.689i	−0.362286	−	0.209166i	−0.670083	+	0.742286i	$0.733742\pi$
$578$		0			0
$579$	−15.7860	+	9.11408i	−0.0272643	+	0.0157411i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−205.095	−	355.236i	−0.351793	−	0.609324i
$584$		0			0
$585$	509.910	−	883.189i	0.871640	−	1.50973i
$586$		0			0
$587$			405.338i			0.690525i	0.938506	+	0.345263i	$0.112210\pi$
$587$			405.338i			0.690525i	−0.938506	+	0.345263i	$0.887790\pi$
$588$		0			0
$589$	482.794			0.819684
$590$		0			0
$591$	47.8824	+	27.6449i	0.0810193	+	0.0467765i
$592$		0			0
$593$	128.459	−	74.1656i	0.216625	−	0.125068i	−0.387762	−	0.921760i	$-0.626752\pi$
$593$	128.459	−	74.1656i	0.216625	−	0.125068i	0.604387	+	0.796691i	$0.293418\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	26.5929	+	46.0603i	0.0445443	+	0.0771529i
$598$		0			0
$599$	200.894	−	347.959i	0.335383	−	0.580900i	−0.648175	−	0.761491i	$-0.724468\pi$
$599$	200.894	−	347.959i	0.335383	−	0.580900i	0.983558	+	0.180591i	$0.0578009\pi$
$600$		0			0
$601$		−	782.716i		−	1.30236i	−0.758925	−	0.651178i	$-0.774275\pi$
$601$		−	782.716i		−	1.30236i	0.758925	−	0.651178i	$-0.225725\pi$
$602$		0			0
$603$	−777.789			−1.28987
$604$		0			0
$605$	647.680	+	373.939i	1.07055	+	0.618080i
$606$		0			0
$607$	113.772	−	65.6864i	0.187433	−	0.108215i	−0.403347	−	0.915047i	$-0.632153\pi$
$607$	113.772	−	65.6864i	0.187433	−	0.108215i	0.590781	+	0.806832i	$0.298820\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	770.784	+	1335.04i	1.26151	+	2.18500i
$612$		0			0
$613$	500.382	−	866.687i	0.816284	−	1.41384i	−0.0921190	−	0.995748i	$-0.529364\pi$
$613$	500.382	−	866.687i	0.816284	−	1.41384i	0.908403	−	0.418097i	$-0.137303\pi$
$614$		0			0
$615$			31.1959i			0.0507251i
$616$		0			0
$617$	738.563			1.19702			0.598511	−	0.801115i	$-0.295759\pi$
$617$	738.563			1.19702			0.598511	+	0.801115i	$0.295759\pi$
$618$		0			0
$619$	826.105	+	476.952i	1.33458	+	0.770520i	0.985998	−	0.166758i	$-0.0533300\pi$
$619$	826.105	+	476.952i	1.33458	+	0.770520i	0.348582	+	0.937278i	$0.386663\pi$
$620$		0			0
$621$	127.773	−	73.7697i	0.205753	−	0.118792i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	376.585	+	652.265i	0.602537	+	1.04362i
$626$		0			0
$627$	−80.2965	+	139.078i	−0.128065	+	0.221814i
$628$		0			0
$629$		−	30.4344i		−	0.0483854i
$630$		0			0
$631$	743.176			1.17777			0.588887	−	0.808215i	$-0.299566\pi$
$631$	743.176			1.17777			0.588887	+	0.808215i	$0.299566\pi$
$632$		0			0
$633$	22.4553	+	12.9646i	0.0354744	+	0.0204812i
$634$		0			0
$635$	594.611	−	343.299i	0.936395	−	0.540628i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	72.9848	+	126.413i	0.114217	+	0.197830i
$640$		0			0
$641$	−119.709	+	207.341i	−0.186753	+	0.323465i	−0.944166	−	0.329471i	$-0.893130\pi$
$641$	−119.709	+	207.341i	−0.186753	+	0.323465i	0.757413	+	0.652936i	$0.226463\pi$
$642$		0			0
$643$			812.453i			1.26353i	0.775158	+	0.631767i	$0.217670\pi$
$643$			812.453i			1.26353i	−0.775158	+	0.631767i	$0.782330\pi$
$644$		0			0
$645$	−106.674			−0.165386
$646$		0			0
$647$	−617.342	−	356.422i	−0.954160	−	0.550885i	−0.0597896	−	0.998211i	$-0.519043\pi$
$647$	−617.342	−	356.422i	−0.954160	−	0.550885i	−0.894371	+	0.447326i	$0.852376\pi$
$648$		0			0
$649$	−942.431	+	544.113i	−1.45213	+	0.838386i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−148.291	−	256.848i	−0.227093	−	0.393336i	0.729853	−	0.683604i	$-0.239589\pi$
$653$	−148.291	−	256.848i	−0.227093	−	0.393336i	−0.956945	+	0.290269i	$0.906255\pi$
$654$		0			0
$655$	−360.508	+	624.417i	−0.550393	+	0.953309i
$656$		0			0
$657$		−	626.045i		−	0.952885i
$658$		0			0
$659$	617.709			0.937342			0.468671	−	0.883373i	$-0.344733\pi$
$659$	617.709			0.937342			0.468671	+	0.883373i	$0.344733\pi$
$660$		0			0
$661$	−281.544	−	162.550i	−0.425937	−	0.245915i	0.271677	−	0.962388i	$-0.412422\pi$
$661$	−281.544	−	162.550i	−0.425937	−	0.245915i	−0.697614	+	0.716474i	$0.745755\pi$
$662$		0			0
$663$	−5.27306	+	3.04440i	−0.00795334	+	0.00459186i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	361.387	+	625.940i	0.541809	+	0.938441i
$668$		0			0
$669$	14.4924	−	25.1016i	0.0216628	−	0.0375211i
$670$		0			0
$671$			862.414i			1.28527i
$672$		0			0
$673$	−793.899			−1.17964			−0.589821	−	0.807534i	$-0.700802\pi$
$673$	−793.899			−1.17964			−0.589821	+	0.807534i	$0.700802\pi$
$674$		0			0
$675$	−35.3882	−	20.4314i	−0.0524270	−	0.0302687i
$676$		0			0
$677$	−297.029	+	171.490i	−0.438743	+	0.253309i	−0.703064	−	0.711126i	$-0.748185\pi$
$677$	−297.029	+	171.490i	−0.438743	+	0.253309i	0.264321	+	0.964435i	$0.414852\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−58.2614	−	100.912i	−0.0855527	−	0.148182i
$682$		0			0
$683$	−596.080	+	1032.44i	−0.872738	+	1.51163i	−0.0135858	+	0.999908i	$0.504325\pi$
$683$	−596.080	+	1032.44i	−0.872738	+	1.51163i	−0.859153	+	0.511719i	$0.829009\pi$
$684$		0			0
$685$			850.619i			1.24178i
$686$		0			0
$687$	−3.82929			−0.00557394
$688$		0			0
$689$	451.187	+	260.493i	0.654843	+	0.378074i
$690$		0			0
$691$	−271.032	+	156.481i	−0.392232	+	0.226455i	−0.683127	−	0.730300i	$-0.739380\pi$
$691$	−271.032	+	156.481i	−0.392232	+	0.226455i	0.290895	+	0.956755i	$0.406047\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	40.4773	+	70.1087i	0.0582407	+	0.100876i
$696$		0			0
$697$	−8.24621	+	14.2829i	−0.0118310	+	0.0204919i
$698$		0			0
$699$			0.538463i			0.000770333i
$700$		0			0
$701$	414.010			0.590599			0.295300	−	0.955405i	$-0.404581\pi$
$701$	414.010			0.590599			0.295300	+	0.955405i	$0.404581\pi$
$702$		0			0
$703$	882.937	+	509.764i	1.25596	+	0.725127i
$704$		0			0
$705$	118.932	−	68.6654i	0.168698	−	0.0973978i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−561.980	−	973.378i	−0.792637	−	1.37289i	−0.924329	−	0.381597i	$-0.875374\pi$
$709$	−561.980	−	973.378i	−0.792637	−	1.37289i	0.131691	−	0.991291i	$-0.457959\pi$
$710$		0			0
$711$	178.884	−	309.837i	0.251595	−	0.435776i
$712$		0			0
$713$			393.991i			0.552582i
$714$		0			0
$715$	−1821.97			−2.54821
$716$		0			0
$717$	−55.2939	−	31.9240i	−0.0771185	−	0.0445244i
$718$		0			0
$719$	940.262	−	542.860i	1.30774	−	0.755021i	0.326018	−	0.945364i	$-0.394293\pi$
$719$	940.262	−	542.860i	1.30774	−	0.755021i	0.981718	+	0.190342i	$0.0609598\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−15.4422	−	26.7466i	−0.0213585	−	0.0369939i
$724$		0			0
$725$	100.090	−	173.362i	0.138056	−	0.239120i
$726$		0			0
$727$			270.606i			0.372223i	0.982529	+	0.186111i	$0.0595885\pi$
$727$			270.606i			0.372223i	−0.982529	+	0.186111i	$0.940412\pi$
$728$		0			0
$729$	680.608			0.933619
$730$		0			0
$731$	−48.8399	−	28.1977i	−0.0668124	−	0.0385742i
$732$		0			0
$733$	−266.994	+	154.149i	−0.364249	+	0.210299i	−0.670943	−	0.741509i	$-0.734110\pi$
$733$	−266.994	+	154.149i	−0.364249	+	0.210299i	0.306694	+	0.951808i	$0.400777\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	694.784	+	1203.40i	0.942719	+	1.63284i
$738$		0			0
$739$	136.261	−	236.012i	0.184386	−	0.319366i	−0.758983	−	0.651110i	$-0.774304\pi$
$739$	136.261	−	236.012i	0.184386	−	0.319366i	0.943370	+	0.331744i	$0.107637\pi$
$740$		0			0
$741$		−	203.970i		−	0.275263i
$742$		0			0
$743$	225.196			0.303090			0.151545	−	0.988450i	$-0.451575\pi$
$743$	225.196			0.303090			0.151545	+	0.988450i	$0.451575\pi$
$744$		0			0
$745$	248.681	+	143.576i	0.333799	+	0.192719i
$746$		0			0
$747$	−551.453	+	318.382i	−0.738224	+	0.426214i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−255.693	−	442.874i	−0.340471	−	0.589712i	0.644050	−	0.764984i	$-0.277253\pi$
$751$	−255.693	−	442.874i	−0.340471	−	0.589712i	−0.984520	+	0.175271i	$0.943920\pi$
$752$		0			0
$753$	−12.2412	+	21.2023i	−0.0162565	+	0.0281571i
$754$		0			0
$755$		−	237.192i		−	0.314162i
$756$		0			0
$757$	−779.598			−1.02985			−0.514926	−	0.857235i	$-0.672181\pi$
$757$	−779.598			−1.02985			−0.514926	+	0.857235i	$0.672181\pi$
$758$		0			0
$759$	−113.496	−	65.5271i	−0.149534	−	0.0863334i
$760$		0			0
$761$	−168.899	+	97.5140i	−0.221944	+	0.128139i	−0.606850	−	0.794816i	$-0.707567\pi$
$761$	−168.899	+	97.5140i	−0.221944	+	0.128139i	0.384906	+	0.922956i	$0.374234\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−24.0152	−	41.5955i	−0.0313924	−	0.0543732i
$766$		0			0
$767$	691.080	−	1196.99i	0.901017	−	1.56061i
$768$		0			0
$769$		−	73.8956i		−	0.0960931i	−0.998845	−	0.0480465i	$-0.984700\pi$
$769$		−	73.8956i		−	0.0960931i	0.998845	−	0.0480465i	$-0.0152996\pi$
$770$		0			0
$771$	115.296			0.149541
$772$		0			0
$773$	−161.020	−	92.9649i	−0.208305	−	0.120265i	0.392218	−	0.919872i	$-0.371708\pi$
$773$	−161.020	−	92.9649i	−0.208305	−	0.120265i	−0.600523	+	0.799607i	$0.705041\pi$
$774$		0			0
$775$	94.5011	−	54.5602i	0.121937	−	0.0704003i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−276.241	−	478.464i	−0.354610	−	0.614202i
$780$		0			0
$781$	130.392	−	225.845i	0.166955	−	0.289175i
$782$		0			0
$783$		−	157.748i		−	0.201466i
$784$		0			0
$785$	−812.944			−1.03560
$786$		0			0
$787$	−618.085	−	356.852i	−0.785369	−	0.453433i	0.0529606	−	0.998597i	$-0.483134\pi$
$787$	−618.085	−	356.852i	−0.785369	−	0.453433i	−0.838330	+	0.545164i	$0.816468\pi$
$788$		0			0
$789$	−112.729	+	65.0842i	−0.142876	+	0.0824895i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−547.678	−	948.607i	−0.690641	−	1.19623i
$794$		0			0
$795$	23.2061	−	40.1941i	0.0291900	−	0.0505586i
$796$		0			0
$797$			908.540i			1.13995i	0.821662	+	0.569975i	$0.193047\pi$
$797$			908.540i			1.13995i	−0.821662	+	0.569975i	$0.806953\pi$
$798$		0			0
$799$	72.6030			0.0908674
$800$		0			0
$801$	−595.925	−	344.058i	−0.743977	−	0.429535i
$802$		0			0
$803$	−968.622	+	559.234i	−1.20625	+	0.696431i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−48.7990	−	84.5223i	−0.0604696	−	0.104736i
$808$		0			0
$809$	160.055	−	277.224i	0.197843	−	0.342675i	−0.749986	−	0.661454i	$-0.769940\pi$
$809$	160.055	−	277.224i	0.197843	−	0.342675i	0.947829	+	0.318779i	$0.103273\pi$
$810$		0			0
$811$		−	839.749i		−	1.03545i	−0.855547	−	0.517724i	$-0.826779\pi$
$811$		−	839.749i		−	1.03545i	0.855547	−	0.517724i	$-0.173221\pi$
$812$		0			0
$813$	−56.5626			−0.0695727
$814$		0			0
$815$	−561.667	−	324.279i	−0.689162	−	0.397888i
$816$		0			0
$817$	1636.10	−	944.600i	2.00256	−	1.15618i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−64.9798	−	112.548i	−0.0791471	−	0.137087i	0.823735	−	0.566975i	$-0.191886\pi$
$821$	−64.9798	−	112.548i	−0.0791471	−	0.137087i	−0.902882	+	0.429888i	$0.858553\pi$
$822$		0			0
$823$	400.482	−	693.656i	0.486613	−	0.842838i	−0.513269	−	0.858228i	$-0.671566\pi$
$823$	400.482	−	693.656i	0.486613	−	0.842838i	0.999882	+	0.0153898i	$0.00489893\pi$
$824$		0			0
$825$			36.2970i			0.0439964i
$826$		0			0
$827$	−289.156			−0.349644			−0.174822	−	0.984600i	$-0.555935\pi$
$827$	−289.156			−0.349644			−0.174822	+	0.984600i	$0.555935\pi$
$828$		0			0
$829$	−274.133	−	158.270i	−0.330679	−	0.190917i	0.325464	−	0.945555i	$-0.394480\pi$
$829$	−274.133	−	158.270i	−0.330679	−	0.190917i	−0.656142	+	0.754637i	$0.727813\pi$
$830$		0			0
$831$	−26.4094	+	15.2475i	−0.0317803	+	0.0183483i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−825.357	−	1429.56i	−0.988451	−	1.71205i
$836$		0			0
$837$	42.9949	−	74.4694i	0.0513679	−	0.0889718i
$838$		0			0
$839$			802.370i			0.956341i	0.878267	+	0.478171i	$0.158700\pi$
$839$			802.370i			0.956341i	−0.878267	+	0.478171i	$0.841300\pi$
$840$		0			0
$841$	−68.2162			−0.0811132
$842$		0			0
$843$	−42.5845	−	24.5862i	−0.0505155	−	0.0291651i
$844$		0			0
$845$	1173.54	−	677.544i	1.38880	−	0.801827i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−49.6533	−	86.0020i	−0.0584844	−	0.101298i
$850$		0			0
$851$	−416.000	+	720.533i	−0.488837	+	0.846690i
$852$		0			0
$853$		−	235.386i		−	0.275950i	−0.990436	−	0.137975i	$-0.955941\pi$
$853$		−	235.386i		−	0.275950i	0.990436	−	0.137975i	$-0.0440594\pi$
$854$		0			0
$855$	1608.97			1.88184
$856$		0			0
$857$	−1226.53	−	708.138i	−1.43119	−	0.826299i	−0.433980	−	0.900923i	$-0.642891\pi$
$857$	−1226.53	−	708.138i	−1.43119	−	0.826299i	−0.997212	+	0.0746237i	$0.976224\pi$
$858$		0			0
$859$	−1117.26	+	645.052i	−1.30065	+	0.750933i	−0.980516	−	0.196438i	$-0.937063\pi$
$859$	−1117.26	+	645.052i	−1.30065	+	0.750933i	−0.320138	+	0.947371i	$0.603729\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−186.080	−	322.301i	−0.215620	−	0.373465i	0.737844	−	0.674971i	$-0.235844\pi$
$863$	−186.080	−	322.301i	−0.215620	−	0.373465i	−0.953464	+	0.301506i	$0.902511\pi$
$864$		0			0
$865$	−602.915	+	1044.28i	−0.697011	+	1.20726i
$866$		0			0
$867$		−	91.3336i		−	0.105344i
$868$		0			0
$869$	−639.176			−0.735530
$870$		0			0
$871$	−1528.45	−	882.449i	−1.75482	−	1.01314i
$872$		0			0
$873$	−989.051	+	571.029i	−1.13293	+	0.654099i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	389.296	+	674.281i	0.443896	+	0.768850i	0.997975	−	0.0636144i	$-0.0202628\pi$
$877$	389.296	+	674.281i	0.443896	+	0.768850i	−0.554079	+	0.832464i	$0.686929\pi$
$878$		0			0
$879$	−32.1056	+	55.6085i	−0.0365251	+	0.0632633i
$880$		0			0
$881$			1206.76i			1.36976i	0.728657	+	0.684879i	$0.240145\pi$
$881$			1206.76i			1.36976i	−0.728657	+	0.684879i	$0.759855\pi$
$882$		0			0
$883$	−1132.77			−1.28287			−0.641435	−	0.767178i	$-0.721660\pi$
$883$	−1132.77			−1.28287			−0.641435	+	0.767178i	$0.721660\pi$
$884$		0			0
$885$	−106.634	−	61.5650i	−0.120490	−	0.0695650i
$886$		0			0
$887$	631.180	−	364.412i	0.711589	−	0.410836i	−0.100060	−	0.994981i	$-0.531903\pi$
$887$	631.180	−	364.412i	0.711589	−	0.410836i	0.811649	+	0.584145i	$0.198570\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−622.437	−	1078.09i	−0.698583	−	1.20998i
$892$		0			0
$893$	−1216.07	+	2106.30i	−1.36178	+	2.35867i
$894$		0			0
$895$			133.966i			0.149683i
$896$		0			0
$897$	166.453			0.185566
$898$		0			0
$899$	364.815	+	210.626i	0.405801	+	0.234289i
$900$		0			0
$901$	21.2495	−	12.2684i	0.0235843	−	0.0136164i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−443.709	−	768.526i	−0.490286	−	0.849200i
$906$		0			0
$907$	−4.80909	+	8.32959i	−0.00530220	+	0.00918367i	−0.868664	−	0.495401i	$-0.835021\pi$
$907$	−4.80909	+	8.32959i	−0.00530220	+	0.00918367i	0.863362	+	0.504585i	$0.168354\pi$
$908$		0			0
$909$			892.374i			0.981709i
$910$		0			0
$911$	−1015.41			−1.11461			−0.557304	−	0.830309i	$-0.688164\pi$
$911$	−1015.41			−1.11461			−0.557304	+	0.830309i	$0.688164\pi$
$912$		0			0
$913$	985.206	+	568.809i	1.07909	+	0.623011i
$914$		0			0
$915$	−84.5068	+	48.7900i	−0.0923572	+	0.0533224i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	241.508	+	418.303i	0.262794	+	0.455172i	0.966983	−	0.254840i	$-0.0820227\pi$
$919$	241.508	+	418.303i	0.262794	+	0.455172i	−0.704189	+	0.710012i	$0.748689\pi$
$920$		0			0
$921$	−60.0402	+	103.993i	−0.0651902	+	0.112913i
$922$		0			0
$923$			331.223i			0.358855i
$924$		0			0
$925$	230.432			0.249116
$926$		0			0
$927$	−379.202	−	218.932i	−0.409063	−	0.236173i
$928$		0			0
$929$	816.334	−	471.311i	0.878723	−	0.507331i	0.00848612	−	0.999964i	$-0.497299\pi$
$929$	816.334	−	471.311i	0.878723	−	0.507331i	0.870237	+	0.492633i	$0.163965\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	32.6232	+	56.5051i	0.0349660	+	0.0605628i
$934$		0			0
$935$	−42.9045	+	74.3129i	−0.0458872	+	0.0794790i
$936$		0			0
$937$			1489.44i			1.58958i	0.606882	+	0.794792i	$0.292420\pi$
$937$			1489.44i			1.58958i	−0.606882	+	0.794792i	$0.707580\pi$
$938$		0			0
$939$	−143.286			−0.152595
$940$		0			0
$941$	−951.382	−	549.281i	−1.01103	−	0.583720i	−0.0995389	−	0.995034i	$-0.531737\pi$
$941$	−951.382	−	549.281i	−1.01103	−	0.583720i	−0.911494	+	0.411314i	$0.865070\pi$
$942$		0			0
$943$	390.457	−	225.430i	0.414058	−	0.239057i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	152.452	+	264.055i	0.160984	+	0.278833i	0.935222	−	0.354062i	$-0.115200\pi$
$947$	152.452	+	264.055i	0.160984	+	0.278833i	−0.774238	+	0.632895i	$0.781866\pi$
$948$		0			0
$949$	710.286	−	1230.25i	0.748458	−	1.29637i
$950$		0			0
$951$			26.4357i			0.0277978i
$952$		0			0
$953$	−803.578			−0.843209			−0.421604	−	0.906780i	$-0.638533\pi$
$953$	−803.578			−0.843209			−0.421604	+	0.906780i	$0.638533\pi$
$954$		0			0
$955$	1206.90	+	696.806i	1.26377	+	0.729639i
$956$		0			0
$957$	−121.349	+	70.0610i	−0.126802	+	0.0732090i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−365.686	−	633.386i	−0.380526	−	0.659091i
$962$		0			0
$963$	131.704	−	228.117i	0.136764	−	0.236882i
$964$		0			0
$965$		−	326.275i		−	0.338109i
$966$		0			0
$967$	93.6182			0.0968130			0.0484065	−	0.998828i	$-0.484586\pi$
$967$	93.6182			0.0968130			0.0484065	+	0.998828i	$0.484586\pi$
$968$		0			0
$969$	−8.31934	−	4.80317i	−0.00858549	−	0.00495684i
$970$		0			0
$971$	−363.252	+	209.723i	−0.374100	+	0.215987i	−0.675248	−	0.737590i	$-0.735964\pi$
$971$	−363.252	+	209.723i	−0.374100	+	0.215987i	0.301148	+	0.953577i	$0.402630\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−23.0505	−	39.9246i	−0.0236415	−	0.0409484i
$976$		0			0
$977$	839.824	−	1454.62i	0.859595	−	1.48886i	−0.0127213	−	0.999919i	$-0.504049\pi$
$977$	839.824	−	1454.62i	0.859595	−	1.48886i	0.872316	−	0.488943i	$-0.162617\pi$
$978$		0			0
$979$			1229.36i			1.25573i
$980$		0			0
$981$	−99.6384			−0.101568
$982$		0			0
$983$	−230.673	−	133.179i	−0.234663	−	0.135483i	0.378059	−	0.925782i	$-0.376592\pi$
$983$	−230.673	−	133.179i	−0.234663	−	0.135483i	−0.612721	+	0.790299i	$0.709925\pi$
$984$		0			0
$985$	−857.071	+	494.830i	−0.870123	+	0.502366i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	770.854	+	1335.16i	0.779428	+	1.35001i
$990$		0			0
$991$	447.307	−	774.758i	0.451369	−	0.781794i	−0.547102	−	0.837066i	$-0.684269\pi$
$991$	447.307	−	774.758i	0.451369	−	0.781794i	0.998471	+	0.0552718i	$0.0176025\pi$
$992$		0			0
$993$			48.6594i			0.0490024i
$994$		0			0
$995$	−952.000			−0.956784
$996$		0			0
$997$	553.290	+	319.442i	0.554955	+	0.320403i	0.751118	−	0.660168i	$-0.229515\pi$
$997$	553.290	+	319.442i	0.554955	+	0.320403i	−0.196163	+	0.980571i	$0.562848\pi$
$998$		0			0
$999$	157.259	−	90.7935i	0.157416	−	0.0908844i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.3.s.g.129.3		8
4.3	odd	2		196.3.h.c.129.2		8
7.2	even	3	inner	784.3.s.g.705.2		8
7.3	odd	6		784.3.c.d.97.3		4
7.4	even	3		784.3.c.d.97.2		4
7.5	odd	6	inner	784.3.s.g.705.3		8
7.6	odd	2	inner	784.3.s.g.129.2		8
12.11	even	2		1764.3.z.k.325.3		8
28.3	even	6		196.3.b.b.97.2	✓	4
28.11	odd	6		196.3.b.b.97.3	yes	4
28.19	even	6		196.3.h.c.117.2		8
28.23	odd	6		196.3.h.c.117.3		8
28.27	even	2		196.3.h.c.129.3		8
84.11	even	6		1764.3.d.e.685.3		4
84.23	even	6		1764.3.z.k.901.2		8
84.47	odd	6		1764.3.z.k.901.3		8
84.59	odd	6		1764.3.d.e.685.2		4
84.83	odd	2		1764.3.z.k.325.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.3.b.b.97.2	✓	4	28.3	even	6
196.3.b.b.97.3	yes	4	28.11	odd	6
196.3.h.c.117.2		8	28.19	even	6
196.3.h.c.117.3		8	28.23	odd	6
196.3.h.c.129.2		8	4.3	odd	2
196.3.h.c.129.3		8	28.27	even	2
784.3.c.d.97.2		4	7.4	even	3
784.3.c.d.97.3		4	7.3	odd	6
784.3.s.g.129.2		8	7.6	odd	2	inner
784.3.s.g.129.3		8	1.1	even	1	trivial
784.3.s.g.705.2		8	7.2	even	3	inner
784.3.s.g.705.3		8	7.5	odd	6	inner
1764.3.d.e.685.2		4	84.59	odd	6
1764.3.d.e.685.3		4	84.11	even	6
1764.3.z.k.325.2		8	84.83	odd	2
1764.3.z.k.325.3		8	12.11	even	2
1764.3.z.k.901.2		8	84.23	even	6
1764.3.z.k.901.3		8	84.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.274552 + 0.158513i) q^{3} +(-4.91434 + 2.83730i) q^{5} +(-4.44975 - 7.70719i) q^{9} +O(q^{10})\)	\(q+(0.274552 + 0.158513i) q^{3} +(-4.91434 + 2.83730i) q^{5} +(-4.44975 - 7.70719i) q^{9} +(-7.94975 + 13.7694i) q^{11} -20.1940i q^{13} -1.79899 q^{15} +(-0.823656 - 0.475538i) q^{17} +(27.5918 - 15.9301i) q^{19} +(13.0000 + 22.5167i) q^{23} +(3.60051 - 6.23626i) q^{25} -5.67459i q^{27} +27.7990 q^{29} +(13.1233 + 7.57675i) q^{31} +(-4.36524 + 2.52027i) q^{33} +(16.0000 + 27.7128i) q^{37} +(3.20101 - 5.54431i) q^{39} -17.3408i q^{41} +59.2965 q^{43} +(43.7352 + 25.2505i) q^{45} +(-66.1105 + 38.1689i) q^{47} +(-0.150758 - 0.261120i) q^{51} +(-12.8995 + 22.3426i) q^{53} -90.2232i q^{55} +10.1005 q^{57} +(59.2743 + 34.2220i) q^{59} +(46.9746 - 27.1208i) q^{61} +(57.2965 + 99.2404i) q^{65} +(43.6985 - 75.6880i) q^{67} +8.24266i q^{69} -16.4020 q^{71} +(60.9216 + 35.1731i) q^{73} +(1.97705 - 1.14145i) q^{75} +(20.1005 + 34.8151i) q^{79} +(-39.1482 + 67.8067i) q^{81} -71.5505i q^{83} +5.39697 q^{85} +(7.63227 + 4.40649i) q^{87} +(66.9617 - 38.6604i) q^{89} +(2.40202 + 4.16042i) q^{93} +(-90.3970 + 156.572i) q^{95} -128.328i q^{97} +141.497 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^9	\( 8 q + 4 q^{9} - 24 q^{11} + 144 q^{15} + 104 q^{23} + 108 q^{25} + 64 q^{29} + 128 q^{37} + 184 q^{39} - 80 q^{43} - 120 q^{51} - 24 q^{53} + 160 q^{57} - 96 q^{65} + 112 q^{67} - 448 q^{71} + 240 q^{79} - 36 q^{81} - 432 q^{85} + 336 q^{93} - 248 q^{95} + 736 q^{99}+O(q^{100}) \) 8 * q + 4 * q^9 - 24 * q^11 + 144 * q^15 + 104 * q^23 + 108 * q^25 + 64 * q^29 + 128 * q^37 + 184 * q^39 - 80 * q^43 - 120 * q^51 - 24 * q^53 + 160 * q^57 - 96 * q^65 + 112 * q^67 - 448 * q^71 + 240 * q^79 - 36 * q^81 - 432 * q^85 + 336 * q^93 - 248 * q^95 + 736 * q^99

Introduction

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