LMFDB - Embedded newform 396.2.r.a.127.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [396,2,Mod(19,396)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(396, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("396.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$396 = 2^{2} \cdot 3^{2} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	396.r (of order $10$ , degree $4$ , 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:	$3.16207592004$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} - 5 x^{15} + 13 x^{14} - 25 x^{13} + 35 x^{12} - 30 x^{11} - 2 x^{10} + 60 x^{9} - 116 x^{8} + \cdots + 256$ x^16 - 5x^15 + 13x^14 - 25x^13 + 35x^12 - 30x^11 - 2x^10 + 60x^9 - 116x^8 + 120x^7 - 8x^6 - 240x^5 + 560x^4 - 800x^3 + 832x^2 - 640*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			127.2
Root			$0.656642 - 1.25253i$ of defining polynomial
Character	$\chi$	$=$	396.127
Dual form			396.2.r.a.343.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.656642 + 1.25253i) q^{2} +(-1.13764 + 1.64492i) q^{4} +(-0.529876 + 1.63079i) q^{5} +(-1.93399 + 1.40513i) q^{7} +(-2.80733 - 0.344804i) q^{8} +(-2.39055 + 0.407162i) q^{10} +(-2.65349 - 1.98973i) q^{11} +(-1.52988 + 0.497087i) q^{13} +(-3.02990 - 1.49971i) q^{14} +(-1.41153 - 3.74267i) q^{16} +(5.74986 + 1.86824i) q^{17} +(-1.07237 - 0.779122i) q^{19} +(-2.07971 - 2.72686i) q^{20} +(0.749794 - 4.63010i) q^{22} +7.25726i q^{23} +(1.66637 + 1.21069i) q^{25} +(-1.62719 - 1.58980i) q^{26} +(-0.111131 - 4.77980i) q^{28} +(0.318958 + 0.439008i) q^{29} +(-7.82777 + 2.54340i) q^{31} +(3.76092 - 4.22558i) q^{32} +(1.43557 + 8.42861i) q^{34} +(-1.26669 - 3.89848i) q^{35} +(-0.299076 + 0.217291i) q^{37} +(0.271708 - 1.85477i) q^{38} +(2.04984 - 4.39547i) q^{40} +(-2.99295 + 4.11944i) q^{41} +9.45922 q^{43} +(6.29167 - 2.10118i) q^{44} +(-9.08991 + 4.76542i) q^{46} +(2.35548 - 3.24205i) q^{47} +(-0.397175 + 1.22238i) q^{49} +(-0.422212 + 2.88217i) q^{50} +(0.922785 - 3.08203i) q^{52} +(0.765944 + 2.35733i) q^{53} +(4.65085 - 3.27297i) q^{55} +(5.91385 - 3.27781i) q^{56} +(-0.340428 + 0.687775i) q^{58} +(4.14490 + 5.70497i) q^{59} +(9.41156 + 3.05800i) q^{61} +(-8.32571 - 8.13438i) q^{62} +(7.76222 + 1.93596i) q^{64} -2.75830i q^{65} -4.79085i q^{67} +(-9.61440 + 7.33267i) q^{68} +(4.05119 - 4.14647i) q^{70} +(-3.34001 - 1.08524i) q^{71} +(-1.23553 - 1.70056i) q^{73} +(-0.468549 - 0.231918i) q^{74} +(2.50157 - 0.877601i) q^{76} +(7.92764 + 0.119627i) q^{77} +(0.797547 + 2.45460i) q^{79} +(6.85145 - 0.318767i) q^{80} +(-7.12500 - 1.04375i) q^{82} +(1.22709 - 3.77660i) q^{83} +(-6.09343 + 8.38688i) q^{85} +(6.21132 + 11.8479i) q^{86} +(6.76315 + 6.50075i) q^{88} +8.45225 q^{89} +(2.26030 - 3.11103i) q^{91} +(-11.9376 - 8.25618i) q^{92} +(5.60746 + 0.821443i) q^{94} +(1.83881 - 1.33597i) q^{95} +(-2.57295 - 7.91872i) q^{97} +(-1.79186 + 0.305193i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q + 5 q^{2} - q^{4} + 6 q^{5} + 5 q^{8} - 10 q^{13} - 8 q^{14} + 23 q^{16} + 10 q^{17} - 16 q^{20} + 17 q^{22} + 6 q^{25} + 4 q^{26} + 20 q^{28} + 10 q^{29} - 6 q^{34} + 18 q^{37} + 38 q^{38} - 40 q^{40}+ \cdots - 68 q^{97}+O(q^{100})$ 16 * q + 5 * q^2 - q^4 + 6 * q^5 + 5 * q^8 - 10 * q^13 - 8 * q^14 + 23 * q^16 + 10 * q^17 - 16 * q^20 + 17 * q^22 + 6 * q^25 + 4 * q^26 + 20 * q^28 + 10 * q^29 - 6 * q^34 + 18 * q^37 + 38 * q^38 - 40 * q^40 - 10 * q^41 + 28 * q^44 - 30 * q^46 + 6 * q^49 + 15 * q^50 - 10 * q^52 - 38 * q^53 + 12 * q^56 + 30 * q^58 - 10 * q^61 - 70 * q^62 + 23 * q^64 - 60 * q^68 + 12 * q^70 - 30 * q^73 - 40 * q^74 - 2 * q^77 + 28 * q^80 - 59 * q^82 - 50 * q^85 + 39 * q^86 - 53 * q^88 + 36 * q^89 - 36 * q^92 - 30 * q^94 - 68 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/396\mathbb{Z}\right)^\times$ .

$n$	$145$	$199$	$353$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$	$1$

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

)

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

$2$	0.656642	+	1.25253i	0.464316	+	0.885670i
$2$	0.656642	+	1.25253i	0.464316	+	0.885670i
$3$		0			0
$3$		0			0
$4$	−1.13764	+	1.64492i	−0.568822	+	0.822461i
$5$	−0.529876	+	1.63079i	−0.236968	+	0.729312i	0.759886	+	0.650056i	$0.225254\pi$
$5$	−0.529876	+	1.63079i	−0.236968	+	0.729312i	−0.996854	+	0.0792561i	$0.974746\pi$
$6$		0			0
$7$	−1.93399	+	1.40513i	−0.730981	+	0.531089i	−0.889874	−	0.456207i	$-0.849208\pi$
$7$	−1.93399	+	1.40513i	−0.730981	+	0.531089i	0.158893	+	0.987296i	$0.449208\pi$
$8$	−2.80733	−	0.344804i	−0.992542	−	0.121907i
$9$		0			0
$10$	−2.39055	+	0.407162i	−0.755957	+	0.128756i
$11$	−2.65349	−	1.98973i	−0.800056	−	0.599925i
$11$	−2.65349	−	1.98973i	−0.800056	−	0.599925i
$12$		0			0
$13$	−1.52988	+	0.497087i	−0.424311	+	0.137867i	−0.513386	−	0.858158i	$-0.671609\pi$
$13$	−1.52988	+	0.497087i	−0.424311	+	0.137867i	0.0890746	+	0.996025i	$0.471609\pi$
$14$	−3.02990	−	1.49971i	−0.809775	−	0.400815i
$15$		0			0
$16$	−1.41153	−	3.74267i	−0.352884	−	0.935667i
$17$	5.74986	+	1.86824i	1.39455	+	0.453115i	0.907423	−	0.420218i	$-0.138046\pi$
$17$	5.74986	+	1.86824i	1.39455	+	0.453115i	0.487123	+	0.873334i	$0.338046\pi$
$18$		0			0
$19$	−1.07237	−	0.779122i	−0.246018	−	0.178743i	0.457942	−	0.888982i	$-0.348587\pi$
$19$	−1.07237	−	0.779122i	−0.246018	−	0.178743i	−0.703960	+	0.710239i	$0.748587\pi$
$20$	−2.07971	−	2.72686i	−0.465038	−	0.609745i
$21$		0			0
$22$	0.749794	−	4.63010i	0.159857	−	0.987140i
$23$			7.25726i			1.51324i	0.653853	+	0.756622i	$0.273152\pi$
$23$			7.25726i			1.51324i	−0.653853	+	0.756622i	$0.726848\pi$
$24$		0			0
$25$	1.66637	+	1.21069i	0.333275	+	0.242138i
$26$	−1.62719	−	1.58980i	−0.319119	−	0.311786i
$27$		0			0
$28$	−0.111131	−	4.77980i	−0.0210018	−	0.903298i
$29$	0.318958	+	0.439008i	0.0592291	+	0.0815218i	0.837604	−	0.546278i	$-0.183956\pi$
$29$	0.318958	+	0.439008i	0.0592291	+	0.0815218i	−0.778375	+	0.627800i	$0.783956\pi$
$30$		0			0
$31$	−7.82777	+	2.54340i	−1.40591	+	0.456807i	−0.911097	−	0.412193i	$-0.864763\pi$
$31$	−7.82777	+	2.54340i	−1.40591	+	0.456807i	−0.494812	+	0.869000i	$0.664763\pi$
$32$	3.76092	−	4.22558i	0.664843	−	0.746983i
$33$		0			0
$34$	1.43557	+	8.42861i	0.246199	+	1.44550i
$35$	−1.26669	−	3.89848i	−0.214110	−	0.658964i
$36$		0			0
$37$	−0.299076	+	0.217291i	−0.0491678	+	0.0357225i	−0.612098	−	0.790782i	$-0.709674\pi$
$37$	−0.299076	+	0.217291i	−0.0491678	+	0.0357225i	0.562930	+	0.826505i	$0.309674\pi$
$38$	0.271708	−	1.85477i	0.0440769	−	0.300884i
$39$		0			0
$40$	2.04984	−	4.39547i	0.324108	−	0.694984i
$41$	−2.99295	+	4.11944i	−0.467420	+	0.643348i	−0.976027	−	0.217651i	$-0.930161\pi$
$41$	−2.99295	+	4.11944i	−0.467420	+	0.643348i	0.508607	+	0.860999i	$0.330161\pi$
$42$		0			0
$43$	9.45922			1.44252			0.721259	−	0.692666i	$-0.243564\pi$
$43$	9.45922			1.44252			0.721259	+	0.692666i	$0.243564\pi$
$44$	6.29167	−	2.10118i	0.948504	−	0.316765i
$45$		0			0
$46$	−9.08991	+	4.76542i	−1.34023	+	0.702623i
$47$	2.35548	−	3.24205i	0.343583	−	0.472901i	−0.601901	−	0.798571i	$-0.705590\pi$
$47$	2.35548	−	3.24205i	0.343583	−	0.472901i	0.945484	+	0.325670i	$0.105590\pi$
$48$		0			0
$49$	−0.397175	+	1.22238i	−0.0567393	+	0.174626i
$50$	−0.422212	+	2.88217i	−0.0597099	+	0.407600i
$51$		0			0
$52$	0.922785	−	3.08203i	0.127967	−	0.427401i
$53$	0.765944	+	2.35733i	0.105211	+	0.323805i	0.989780	−	0.142604i	$-0.0455476\pi$
$53$	0.765944	+	2.35733i	0.105211	+	0.323805i	−0.884569	+	0.466409i	$0.845548\pi$
$54$		0			0
$55$	4.65085	−	3.27297i	0.627120	−	0.441328i
$56$	5.91385	−	3.27781i	0.790272	−	0.438016i
$57$		0			0
$58$	−0.340428	+	0.687775i	−0.0447004	+	0.0903092i
$59$	4.14490	+	5.70497i	0.539620	+	0.742724i	0.988558	−	0.150839i	$-0.0481975\pi$
$59$	4.14490	+	5.70497i	0.539620	+	0.742724i	−0.448938	+	0.893563i	$0.648198\pi$
$60$		0			0
$61$	9.41156	+	3.05800i	1.20503	+	0.391537i	0.841608	−	0.540089i	$-0.181609\pi$
$61$	9.41156	+	3.05800i	1.20503	+	0.391537i	0.363419	+	0.931626i	$0.381609\pi$
$62$	−8.32571	−	8.13438i	−1.05737	−	1.03307i
$63$		0			0
$64$	7.76222	+	1.93596i	0.970277	+	0.241995i
$65$		−	2.75830i		−	0.342125i
$66$		0			0
$67$		−	4.79085i		−	0.585296i	−0.956220	−	0.292648i	$-0.905464\pi$
$67$		−	4.79085i		−	0.585296i	0.956220	−	0.292648i	$-0.0945364\pi$
$68$	−9.61440	+	7.33267i	−1.16592	+	0.889217i
$69$		0			0
$70$	4.05119	−	4.14647i	0.484210	−	0.495598i
$71$	−3.34001	−	1.08524i	−0.396387	−	0.128794i	0.104039	−	0.994573i	$-0.466823\pi$
$71$	−3.34001	−	1.08524i	−0.396387	−	0.128794i	−0.500426	+	0.865779i	$0.666823\pi$
$72$		0			0
$73$	−1.23553	−	1.70056i	−0.144607	−	0.199035i	0.730569	−	0.682839i	$-0.239255\pi$
$73$	−1.23553	−	1.70056i	−0.144607	−	0.199035i	−0.875177	+	0.483804i	$0.839255\pi$
$74$	−0.468549	−	0.231918i	−0.0544677	−	0.0269599i
$75$		0			0
$76$	2.50157	−	0.877601i	0.286950	−	0.100668i
$77$	7.92764	+	0.119627i	0.903439	+	0.0136328i
$78$		0			0
$79$	0.797547	+	2.45460i	0.0897311	+	0.276164i	0.985845	−	0.167661i	$-0.0536213\pi$
$79$	0.797547	+	2.45460i	0.0897311	+	0.276164i	−0.896114	+	0.443825i	$0.853621\pi$
$80$	6.85145	−	0.318767i	0.766015	−	0.0356392i
$81$		0			0
$82$	−7.12500	−	1.04375i	−0.786824	−	0.115263i
$83$	1.22709	−	3.77660i	0.134691	−	0.414536i	−0.860851	−	0.508857i	$-0.830068\pi$
$83$	1.22709	−	3.77660i	0.134691	−	0.414536i	0.995542	+	0.0943213i	$0.0300681\pi$
$84$		0			0
$85$	−6.09343	+	8.38688i	−0.660925	+	0.909685i
$86$	6.21132	+	11.8479i	0.669784	+	1.27759i
$87$		0			0
$88$	6.76315	+	6.50075i	0.720954	+	0.692983i
$89$	8.45225			0.895937			0.447969	−	0.894049i	$-0.352148\pi$
$89$	8.45225			0.895937			0.447969	+	0.894049i	$0.352148\pi$
$90$		0			0
$91$	2.26030	−	3.11103i	0.236944	−	0.326125i
$92$	−11.9376	−	8.25618i	−1.24458	−	0.860766i
$93$		0			0
$94$	5.60746	+	0.821443i	0.578365	+	0.0847254i
$95$	1.83881	−	1.33597i	0.188658	−	0.137068i
$96$		0			0
$97$	−2.57295	−	7.91872i	−0.261243	−	0.804024i	−0.992535	−	0.121960i	$-0.961082\pi$
$97$	−2.57295	−	7.91872i	−0.261243	−	0.804024i	0.731292	−	0.682065i	$-0.238918\pi$
$98$	−1.79186	+	0.305193i	−0.181005	+	0.0308291i
$99$		0			0
$100$	−3.88723	+	1.36372i	−0.388723	+	0.136372i
$101$	−8.58788	+	2.79037i	−0.854526	+	0.277652i	−0.703340	−	0.710853i	$-0.748309\pi$
$101$	−8.58788	+	2.79037i	−0.854526	+	0.277652i	−0.151185	+	0.988505i	$0.548309\pi$
$102$		0			0
$103$	5.28660	+	7.27638i	0.520904	+	0.716963i	0.985710	−	0.168450i	$-0.0538760\pi$
$103$	5.28660	+	7.27638i	0.520904	+	0.716963i	−0.464806	+	0.885412i	$0.653876\pi$
$104$	4.46627	−	0.867980i	0.437954	−	0.0851124i
$105$		0			0
$106$	−2.44967	+	2.50729i	−0.237933	+	0.243529i
$107$	2.49422	+	1.81216i	0.241126	+	0.175188i	0.701785	−	0.712389i	$-0.252387\pi$
$107$	2.49422	+	1.81216i	0.241126	+	0.175188i	−0.460659	+	0.887577i	$0.652387\pi$
$108$		0			0
$109$		−	9.68863i		−	0.928002i	−0.885835	−	0.464001i	$-0.846413\pi$
$109$		−	9.68863i		−	0.928002i	0.885835	−	0.464001i	$-0.153587\pi$
$110$	7.15342	+	3.67614i	0.682052	+	0.350506i
$111$		0			0
$112$	7.98883	+	5.25491i	0.754873	+	0.496542i
$113$	−8.70152	−	6.32202i	−0.818570	−	0.594726i	0.0977325	−	0.995213i	$-0.468841\pi$
$113$	−8.70152	−	6.32202i	−0.818570	−	0.594726i	−0.916303	+	0.400487i	$0.868841\pi$
$114$		0			0
$115$	−11.8351	−	3.84545i	−1.10363	−	0.358590i
$116$	−1.08500	+	0.0252263i	−0.100739	+	0.00234220i
$117$		0			0
$118$	−4.42391	+	8.93772i	−0.407254	+	0.822784i
$119$	−13.7453	+	4.46612i	−1.26003	+	0.409409i
$120$		0			0
$121$	3.08198	+	10.5594i	0.280180	+	0.959947i
$122$	2.34980	+	13.7962i	0.212740	+	1.24905i
$123$		0			0
$124$	4.72152	−	15.7695i	0.424005	−	1.41615i
$125$	−9.79353	+	7.11541i	−0.875960	+	0.636422i
$126$		0			0
$127$	−0.100873	+	0.310454i	−0.00895101	+	0.0275484i	−0.955432	−	0.295210i	$-0.904610\pi$
$127$	−0.100873	+	0.310454i	−0.00895101	+	0.0275484i	0.946481	+	0.322759i	$0.104610\pi$
$128$	2.67216	+	10.9936i	0.236187	+	0.971708i
$129$		0			0
$130$	3.45485	−	1.81122i	0.303010	−	0.158854i
$131$	10.8360			0.946745			0.473372	−	0.880862i	$-0.343037\pi$
$131$	10.8360			0.946745			0.473372	+	0.880862i	$0.343037\pi$
$132$		0			0
$133$	3.16872			0.274763
$134$	6.00067	−	3.14587i	0.518379	−	0.271762i
$135$		0			0
$136$	−15.4976	−	7.22735i	−1.32891	−	0.619740i
$137$	0.390122	−	1.20067i	0.0333304	−	0.102580i	−0.933007	−	0.359857i	$-0.882825\pi$
$137$	0.390122	−	1.20067i	0.0333304	−	0.102580i	0.966338	+	0.257277i	$0.0828253\pi$
$138$		0			0
$139$	8.13031	−	5.90702i	0.689604	−	0.501026i	−0.186926	−	0.982374i	$-0.559852\pi$
$139$	8.13031	−	5.90702i	0.689604	−	0.501026i	0.876530	+	0.481347i	$0.159852\pi$
$140$	7.85374	+	2.35147i	0.663763	+	0.198736i
$141$		0			0
$142$	−0.833905	−	4.89606i	−0.0699797	−	0.410869i
$143$	5.04857	+	1.72502i	0.422183	+	0.144253i
$144$		0			0
$145$	−0.884939	+	0.287534i	−0.0734902	+	0.0238784i
$146$	1.31869	−	2.66418i	0.109136	−	0.220490i
$147$		0			0
$148$	−0.0171855	−	0.739156i	−0.00141264	−	0.0607583i
$149$	−2.24743	−	0.730233i	−0.184116	−	0.0598230i	0.215508	−	0.976502i	$-0.430859\pi$
$149$	−2.24743	−	0.730233i	−0.184116	−	0.0598230i	−0.399624	+	0.916679i	$0.630859\pi$
$150$		0			0
$151$	15.4539	+	11.2279i	1.25762	+	0.913713i	0.998638	−	0.0521699i	$-0.0166137\pi$
$151$	15.4539	+	11.2279i	1.25762	+	0.913713i	0.258980	+	0.965883i	$0.416614\pi$
$152$	2.74185	+	2.55701i	0.222394	+	0.207401i
$153$		0			0
$154$	5.05579	+	10.0081i	0.407407	+	0.806479i
$155$		−	14.1131i		−	1.13359i
$156$		0			0
$157$	−7.93699	−	5.76656i	−0.633441	−	0.460222i	0.224150	−	0.974555i	$-0.428040\pi$
$157$	−7.93699	−	5.76656i	−0.633441	−	0.460222i	−0.857591	+	0.514333i	$0.828040\pi$
$158$	−2.55075	+	2.61074i	−0.202926	+	0.207699i
$159$		0			0
$160$	4.89821	+	8.37230i	0.387237	+	0.661889i
$161$	−10.1974	−	14.0355i	−0.803667	−	1.10615i
$162$		0			0
$163$	−13.5498	+	4.40261i	−1.06130	+	0.344839i	−0.787096	−	0.616831i	$-0.788416\pi$
$163$	−13.5498	+	4.40261i	−1.06130	+	0.344839i	−0.274209	+	0.961670i	$0.588416\pi$
$164$	−3.37125	−	9.60962i	−0.263250	−	0.750385i
$165$		0			0
$166$	5.53605	−	0.942909i	0.429681	−	0.0731839i
$167$	−0.0216699	−	0.0666932i	−0.00167687	−	0.00516088i	0.950215	−	0.311596i	$-0.100864\pi$
$167$	−0.0216699	−	0.0666932i	−0.00167687	−	0.00516088i	−0.951891	+	0.306435i	$0.900864\pi$
$168$		0			0
$169$	−8.42380	+	6.12025i	−0.647984	+	0.470788i
$170$	−14.5060	−	2.12500i	−1.11256	−	0.162980i
$171$		0			0
$172$	−10.7612	+	15.5597i	−0.820535	+	1.18641i
$173$	11.6546	−	16.0412i	0.886086	−	1.21959i	−0.0886112	−	0.996066i	$-0.528243\pi$
$173$	11.6546	−	16.0412i	0.886086	−	1.21959i	0.974698	−	0.223527i	$-0.0717571\pi$
$174$		0			0
$175$	−4.92393			−0.372214
$176$	−3.70140	+	12.7397i	−0.279003	+	0.960290i
$177$		0			0
$178$	5.55010	+	10.5867i	0.415998	+	0.793504i
$179$	2.02535	−	2.78765i	0.151382	−	0.208359i	−0.726590	−	0.687071i	$-0.758896\pi$
$179$	2.02535	−	2.78765i	0.151382	−	0.208359i	0.877972	+	0.478712i	$0.158896\pi$
$180$		0			0
$181$	4.87022	−	14.9890i	0.362001	−	1.11412i	−0.589837	−	0.807522i	$-0.700808\pi$
$181$	4.87022	−	14.9890i	0.362001	−	1.11412i	0.951838	−	0.306601i	$-0.0991918\pi$
$182$	5.38086	+	0.788249i	0.398856	+	0.0584289i
$183$		0			0
$184$	2.50234	−	20.3735i	0.184475	−	1.50196i
$185$	−0.195884	−	0.602867i	−0.0144016	−	0.0443237i
$186$		0			0
$187$	−11.5399	−	16.3980i	−0.843880	−	1.19914i
$188$	2.65321	+	7.56288i	0.193505	+	0.551580i
$189$		0			0
$190$	2.88078	+	1.42590i	0.208994	+	0.103446i
$191$	−4.18731	−	5.76334i	−0.302983	−	0.417020i	0.630194	−	0.776438i	$-0.282975\pi$
$191$	−4.18731	−	5.76334i	−0.302983	−	0.417020i	−0.933177	+	0.359417i	$0.882975\pi$
$192$		0			0
$193$	−16.0372	−	5.21080i	−1.15438	−	0.375081i	−0.331590	−	0.943424i	$-0.607585\pi$
$193$	−16.0372	−	5.21080i	−1.15438	−	0.375081i	−0.822792	+	0.568342i	$0.807585\pi$
$194$	8.22890	−	8.42245i	0.590801	−	0.604697i
$195$		0			0
$196$	−1.55887	−	2.04395i	−0.111348	−	0.145997i
$197$		−	24.6863i		−	1.75883i	−0.476058	−	0.879414i	$-0.657935\pi$
$197$		−	24.6863i		−	1.75883i	0.476058	−	0.879414i	$-0.342065\pi$
$198$		0			0
$199$			15.7596i			1.11717i	0.829449	+	0.558583i	$0.188655\pi$
$199$			15.7596i			1.11717i	−0.829449	+	0.558583i	$0.811345\pi$
$200$	−4.26061	−	3.97339i	−0.301271	−	0.280961i
$201$		0			0
$202$	−9.13417	−	8.92427i	−0.642678	−	0.627909i
$203$	−1.23373	−	0.400862i	−0.0865906	−	0.0281350i
$204$		0			0
$205$	−5.13205	−	7.06366i	−0.358438	−	0.493348i
$206$	−5.64245	+	11.3996i	−0.393128	+	0.794246i
$207$		0			0
$208$	4.01990	+	5.02416i	0.278730	+	0.348363i
$209$	1.29528	+	4.20111i	0.0895963	+	0.290597i
$210$		0			0
$211$	−7.38354	−	22.7242i	−0.508304	−	1.56440i	−0.795145	−	0.606419i	$-0.792605\pi$
$211$	−7.38354	−	22.7242i	−0.508304	−	1.56440i	0.286841	−	0.957978i	$-0.407395\pi$
$212$	−4.74900	−	1.42189i	−0.326163	−	0.0976556i
$213$		0			0
$214$	−0.631966	+	4.31402i	−0.0432003	+	0.294900i
$215$	−5.01221	+	15.4260i	−0.341830	+	1.05205i
$216$		0			0
$217$	11.5651	−	15.9179i	0.785087	−	1.08058i
$218$	12.1353	−	6.36196i	0.821904	−	0.430886i
$219$		0			0
$220$	0.0927799	+	11.3738i	0.00625522	+	0.766818i
$221$	−9.72525			−0.654191
$222$		0			0
$223$	−11.0894	+	15.2632i	−0.742600	+	1.02210i	0.255865	+	0.966712i	$0.417640\pi$
$223$	−11.0894	+	15.2632i	−0.742600	+	1.02210i	−0.998465	+	0.0553883i	$0.982360\pi$
$224$	−1.33611	+	13.4568i	−0.0892729	+	0.899121i
$225$		0			0
$226$	2.20472	−	15.0502i	0.146656	−	1.00112i
$227$	−9.11637	+	6.62343i	−0.605075	+	0.439612i	−0.847676	−	0.530514i	$-0.821999\pi$
$227$	−9.11637	+	6.62343i	−0.605075	+	0.439612i	0.242602	+	0.970126i	$0.421999\pi$
$228$		0			0
$229$	6.75257	+	20.7823i	0.446223	+	1.37333i	0.881137	+	0.472860i	$0.156778\pi$
$229$	6.75257	+	20.7823i	0.446223	+	1.37333i	−0.434915	+	0.900472i	$0.643222\pi$
$230$	−2.95488	−	17.3488i	−0.194839	−	1.14395i
$231$		0			0
$232$	−0.744050	−	1.34242i	−0.0488492	−	0.0881342i
$233$	−6.04225	+	1.96325i	−0.395841	+	0.128617i	−0.500172	−	0.865926i	$-0.666730\pi$
$233$	−6.04225	+	1.96325i	−0.395841	+	0.128617i	0.104331	+	0.994543i	$0.466730\pi$
$234$		0			0
$235$	4.03898	+	5.55919i	0.263474	+	0.362641i
$236$	−14.0997	+	0.327819i	−0.917809	+	0.0213392i
$237$		0			0
$238$	−14.6197	−	14.2837i	−0.947653	−	0.925876i
$239$	12.0990	+	8.79041i	0.782617	+	0.568605i	0.905763	−	0.423784i	$-0.139298\pi$
$239$	12.0990	+	8.79041i	0.782617	+	0.568605i	−0.123146	+	0.992389i	$0.539298\pi$
$240$		0			0
$241$		−	0.457365i		−	0.0294615i	−0.999891	−	0.0147307i	$-0.995311\pi$
$241$		−	0.457365i		−	0.0294615i	0.999891	−	0.0147307i	$-0.00468911\pi$
$242$	−11.2022	+	10.7940i	−0.720104	+	0.693866i
$243$		0			0
$244$	−15.7372	+	12.0024i	−1.00747	+	0.768373i
$245$	−1.78299	−	1.29542i	−0.113911	−	0.0827612i
$246$		0			0
$247$	2.02788	+	0.658899i	0.129031	+	0.0419248i
$248$	22.8521	−	4.44111i	1.45111	−	0.282011i
$249$		0			0
$250$	−15.3431	−	7.59437i	−0.970381	−	0.480310i
$251$	−12.0935	+	3.92941i	−0.763334	+	0.248022i	−0.664709	−	0.747103i	$-0.731444\pi$
$251$	−12.0935	+	3.92941i	−0.763334	+	0.248022i	−0.0986249	+	0.995125i	$0.531444\pi$
$252$		0			0
$253$	14.4400	−	19.2571i	0.907833	−	1.21068i
$254$	−0.455090	+	0.0775115i	−0.0285549	+	0.00486351i
$255$		0			0
$256$	−12.0151	+	10.5658i	−0.750946	+	0.660363i
$257$	−1.20619	+	0.876350i	−0.0752402	+	0.0546652i	−0.624770	−	0.780809i	$-0.714807\pi$
$257$	−1.20619	+	0.876350i	−0.0752402	+	0.0546652i	0.549529	+	0.835474i	$0.314807\pi$
$258$		0			0
$259$	0.273088	−	0.840480i	0.0169689	−	0.0522249i
$260$	4.53719	+	3.13797i	0.281385	+	0.194608i
$261$		0			0
$262$	7.11536	+	13.5724i	0.439589	+	0.838503i
$263$	14.7580			0.910017			0.455008	−	0.890487i	$-0.349636\pi$
$263$	14.7580			0.910017			0.455008	+	0.890487i	$0.349636\pi$
$264$		0			0
$265$	−4.25017			−0.261086
$266$	2.08071	+	3.96891i	0.127577	+	0.243349i
$267$		0			0
$268$	7.88058	+	5.45028i	0.481383	+	0.332929i
$269$	−4.06176	+	12.5008i	−0.247650	+	0.762189i	0.747539	+	0.664218i	$0.231235\pi$
$269$	−4.06176	+	12.5008i	−0.247650	+	0.762189i	−0.995189	+	0.0979710i	$0.968765\pi$
$270$		0			0
$271$	9.14409	−	6.64357i	0.555464	−	0.403568i	−0.274332	−	0.961635i	$-0.588457\pi$
$271$	9.14409	−	6.64357i	0.555464	−	0.403568i	0.829796	+	0.558067i	$0.188457\pi$
$272$	−1.12391	−	24.1569i	−0.0681471	−	1.46473i
$273$		0			0
$274$	1.76004	−	0.299773i	0.106328	−	0.0181100i
$275$	−2.01276	−	6.52818i	−0.121374	−	0.393664i
$276$		0			0
$277$	−1.50422	+	0.488750i	−0.0903796	+	0.0293661i	−0.353858	−	0.935299i	$-0.615130\pi$
$277$	−1.50422	+	0.488750i	−0.0903796	+	0.0293661i	0.263478	+	0.964665i	$0.415130\pi$
$278$	12.7374	+	6.30463i	0.763938	+	0.378127i
$279$		0			0
$280$	2.21182	+	11.3811i	0.132181	+	0.680150i
$281$	8.38361	+	2.72400i	0.500124	+	0.162500i	0.548206	−	0.836343i	$-0.315311\pi$
$281$	8.38361	+	2.72400i	0.500124	+	0.162500i	−0.0480820	+	0.998843i	$0.515311\pi$
$282$		0			0
$283$	16.4054	+	11.9192i	0.975201	+	0.708525i	0.956631	−	0.291302i	$-0.0940885\pi$
$283$	16.4054	+	11.9192i	0.975201	+	0.708525i	0.0185704	+	0.999828i	$0.494089\pi$
$284$	5.58487	−	4.25945i	0.331401	−	0.252752i
$285$		0			0
$286$	1.15447	+	7.45619i	0.0682652	+	0.440894i
$287$		−	12.1724i		−	0.718516i
$288$		0			0
$289$	15.8173	+	11.4919i	0.930427	+	0.675995i
$290$	−0.941232	−	0.919603i	−0.0552710	−	0.0540009i
$291$		0			0
$292$	4.20287	−	0.0977173i	0.245954	−	0.00571847i
$293$	8.20064	+	11.2872i	0.479087	+	0.659406i	0.978329	−	0.207056i	$-0.0663883\pi$
$293$	8.20064	+	11.2872i	0.479087	+	0.659406i	−0.499242	+	0.866462i	$0.666388\pi$
$294$		0			0
$295$	−11.4999	+	3.73654i	−0.669550	+	0.217550i
$296$	0.914528	−	0.506886i	0.0531558	−	0.0294621i
$297$		0			0
$298$	−0.561118	−	3.29446i	−0.0325047	−	0.190843i
$299$	−3.60749	−	11.1027i	−0.208627	−	0.642087i
$300$		0			0
$301$	−18.2941	+	13.2914i	−1.05445	+	0.766105i
$302$	−3.91558	+	26.7291i	−0.225316	+	1.53809i
$303$		0			0
$304$	−1.40231	+	5.11328i	−0.0804280	+	0.293267i
$305$	−9.97392	+	13.7279i	−0.571105	+	0.786059i
$306$		0			0
$307$	5.88829			0.336062			0.168031	−	0.985782i	$-0.446259\pi$
$307$	5.88829			0.336062			0.168031	+	0.985782i	$0.446259\pi$
$308$	−9.21561	+	12.9043i	−0.525108	+	0.735289i
$309$		0			0
$310$	17.6771	−	9.26727i	1.00399	−	0.526346i
$311$	−15.4196	+	21.2233i	−0.874366	+	1.20346i	0.103584	+	0.994621i	$0.466969\pi$
$311$	−15.4196	+	21.2233i	−0.874366	+	1.20346i	−0.977950	+	0.208840i	$0.933031\pi$
$312$		0			0
$313$	−5.29404	+	16.2934i	−0.299237	+	0.920955i	0.682529	+	0.730859i	$0.260880\pi$
$313$	−5.29404	+	16.2934i	−0.299237	+	0.920955i	−0.981765	+	0.190097i	$0.939120\pi$
$314$	2.01101	−	13.7279i	0.113488	−	0.774708i
$315$		0			0
$316$	−4.94495	−	1.48056i	−0.278175	−	0.0832877i
$317$	−0.246344	−	0.758169i	−0.0138361	−	0.0425830i	0.943900	−	0.330231i	$-0.107127\pi$
$317$	−0.246344	−	0.758169i	−0.0138361	−	0.0425830i	−0.957736	+	0.287648i	$0.907127\pi$
$318$		0			0
$319$	0.0271549	−	1.79954i	0.00152038	−	0.100755i
$320$	−7.27016	+	11.6327i	−0.406414	+	0.650290i
$321$		0			0
$322$	10.8838	−	21.9888i	0.606530	−	1.22539i
$323$	−4.71038	−	6.48329i	−0.262093	−	0.360740i
$324$		0			0
$325$	−3.15117	−	1.02388i	−0.174795	−	0.0567944i
$326$	−14.4118	−	14.0806i	−0.798194	−	0.779852i
$327$		0			0
$328$	9.82259	−	10.5326i	0.542362	−	0.581568i
$329$			9.57985i			0.528154i
$330$		0			0
$331$		−	21.2979i		−	1.17064i	−0.810803	−	0.585319i	$-0.800969\pi$
$331$		−	21.2979i		−	1.17064i	0.810803	−	0.585319i	$-0.199031\pi$
$332$	4.81622	+	6.31490i	0.264324	+	0.346575i
$333$		0			0
$334$	0.0693056	−	0.0709357i	0.00379223	−	0.00388143i
$335$	7.81288	+	2.53856i	0.426863	+	0.138696i
$336$		0			0
$337$	6.39268	+	8.79876i	0.348231	+	0.479299i	0.946823	−	0.321755i	$-0.104273\pi$
$337$	6.39268	+	8.79876i	0.348231	+	0.479299i	−0.598592	+	0.801054i	$0.704273\pi$
$338$	−13.1972	−	6.53222i	−0.717832	−	0.355306i
$339$		0			0
$340$	−6.86362	−	19.5645i	−0.372232	−	1.06103i
$341$	25.8315	+	8.82625i	1.39886	+	0.477968i
$342$		0			0
$343$	−6.12050	−	18.8370i	−0.330476	−	1.01710i
$344$	−26.5552	−	3.26158i	−1.43176	−	0.175853i
$345$		0			0
$346$	27.7450	+	4.06440i	1.49158	+	0.218504i
$347$	−0.198863	+	0.612038i	−0.0106755	+	0.0328559i	−0.956252	−	0.292543i	$-0.905499\pi$
$347$	−0.198863	+	0.612038i	−0.0106755	+	0.0328559i	0.945577	+	0.325399i	$0.105499\pi$
$348$		0			0
$349$	−10.1567	+	13.9796i	−0.543678	+	0.748309i	−0.989137	−	0.146993i	$-0.953040\pi$
$349$	−10.1567	+	13.9796i	−0.543678	+	0.748309i	0.445459	+	0.895302i	$0.353040\pi$
$350$	−3.23326	−	6.16736i	−0.172825	−	0.329659i
$351$		0			0
$352$	−18.3873	+	3.72931i	−0.980046	+	0.198773i
$353$	28.3825			1.51065			0.755324	−	0.655352i	$-0.227480\pi$
$353$	28.3825			1.51065			0.755324	+	0.655352i	$0.227480\pi$
$354$		0			0
$355$	3.53959	−	4.87182i	0.187862	−	0.258569i
$356$	−9.61565	+	13.9033i	−0.509629	+	0.736873i
$357$		0			0
$358$	4.82154	+	0.706313i	0.254826	+	0.0373298i
$359$	23.1001	−	16.7832i	1.21918	−	0.885785i	0.223147	−	0.974785i	$-0.428367\pi$
$359$	23.1001	−	16.7832i	1.21918	−	0.885785i	0.996032	+	0.0889996i	$0.0283670\pi$
$360$		0			0
$361$	−5.32838	−	16.3991i	−0.280441	−	0.863108i
$362$	21.9721	−	3.74232i	1.15483	−	0.196692i
$363$		0			0
$364$	2.54599	+	7.25726i	0.133446	+	0.380384i
$365$	3.42793	−	1.11380i	0.179426	−	0.0582990i
$366$		0			0
$367$	0.228900	+	0.315054i	0.0119485	+	0.0164457i	0.814949	−	0.579532i	$-0.196765\pi$
$367$	0.228900	+	0.315054i	0.0119485	+	0.0164457i	−0.803001	+	0.595978i	$0.796765\pi$
$368$	27.1615	−	10.2439i	1.41589	−	0.533999i
$369$		0			0
$370$	0.626482	−	0.641217i	0.0325692	−	0.0333353i
$371$	−4.79369	−	3.48282i	−0.248876	−	0.180819i
$372$		0			0
$373$			9.95150i			0.515269i	0.966242	+	0.257635i	$0.0829430\pi$
$373$			9.95150i			0.515269i	−0.966242	+	0.257635i	$0.917057\pi$
$374$	12.9614	−	25.2216i	0.670216	−	1.30418i
$375$		0			0
$376$	−7.73050	+	8.28932i	−0.398670	+	0.427489i
$377$	−0.706192	−	0.513078i	−0.0363707	−	0.0264249i
$378$		0			0
$379$	19.1280	+	6.21508i	0.982541	+	0.319247i	0.755868	−	0.654724i	$-0.227215\pi$
$379$	19.1280	+	6.21508i	0.982541	+	0.319247i	0.226673	+	0.973971i	$0.427215\pi$
$380$	0.105662	+	4.54456i	0.00542032	+	0.233131i
$381$		0			0
$382$	4.46917	−	9.02916i	0.228663	−	0.461972i
$383$	9.77842	−	3.17720i	0.499654	−	0.162347i	−0.0483380	−	0.998831i	$-0.515392\pi$
$383$	9.77842	−	3.17720i	0.499654	−	0.162347i	0.547992	+	0.836484i	$0.315392\pi$
$384$		0			0
$385$	−4.39576	+	12.8649i	−0.224029	+	0.655658i
$386$	−4.00402	−	23.5086i	−0.203799	−	1.19656i
$387$		0			0
$388$	15.9528	+	4.77638i	0.809880	+	0.242484i
$389$	−15.5977	+	11.3324i	−0.790836	+	0.574576i	−0.908212	−	0.418511i	$-0.862552\pi$
$389$	−15.5977	+	11.3324i	−0.790836	+	0.574576i	0.117375	+	0.993088i	$0.462552\pi$
$390$		0			0
$391$	−13.5583	+	41.7282i	−0.685674	+	2.11029i
$392$	1.53648	−	3.29467i	0.0776041	−	0.166406i
$393$		0			0
$394$	30.9203	−	16.2101i	1.55774	−	0.816651i
$395$	−4.42554			−0.222673
$396$		0			0
$397$	38.1030			1.91233			0.956167	−	0.292823i	$-0.0945945\pi$
$397$	38.1030			1.91233			0.956167	+	0.292823i	$0.0945945\pi$
$398$	−19.7393	+	10.3484i	−0.989440	+	0.518718i
$399$		0			0
$400$	2.17907	−	7.94562i	0.108954	−	0.397281i
$401$	1.28297	−	3.94858i	0.0640685	−	0.197183i	−0.913898	−	0.405943i	$-0.866943\pi$
$401$	1.28297	−	3.94858i	0.0640685	−	0.197183i	0.977967	+	0.208761i	$0.0669430\pi$
$402$		0			0
$403$	10.7112	−	7.78216i	0.533564	−	0.387657i
$404$	5.18000	−	17.3008i	0.257715	−	0.860748i
$405$		0			0
$406$	−0.308026	−	1.80850i	−0.0152871	−	0.0897542i
$407$	1.22594	+	0.0184994i	0.0607678	+	0.000916979i
$408$		0			0
$409$	10.7679	−	3.49869i	0.532437	−	0.172999i	−0.0304453	−	0.999536i	$-0.509693\pi$
$409$	10.7679	−	3.49869i	0.532437	−	0.172999i	0.562882	+	0.826537i	$0.309693\pi$
$410$	5.47750	−	11.0663i	0.270515	−	0.546527i
$411$		0			0
$412$	−17.9833	+	0.418115i	−0.885975	+	0.0205990i
$413$	−16.0324	−	5.20925i	−0.788904	−	0.256331i
$414$		0			0
$415$	5.50864	+	4.00226i	0.270409	+	0.196463i
$416$	−3.65326	+	8.33411i	−0.179116	+	0.408613i
$417$		0			0
$418$	−4.41147	+	4.38099i	−0.215772	+	0.214281i
$419$			21.2095i			1.03615i	0.855335	+	0.518075i	$0.173351\pi$
$419$			21.2095i			1.03615i	−0.855335	+	0.518075i	$0.826649\pi$
$420$		0			0
$421$	−20.0502	−	14.5673i	−0.977185	−	0.709966i	−0.0201071	−	0.999798i	$-0.506401\pi$
$421$	−20.0502	−	14.5673i	−0.977185	−	0.709966i	−0.957078	+	0.289832i	$0.906401\pi$
$422$	23.6143	−	24.1697i	1.14953	−	1.17656i
$423$		0			0
$424$	−1.33744	−	6.88192i	−0.0649518	−	0.334215i
$425$	7.31955	+	10.0745i	0.355050	+	0.488685i
$426$		0			0
$427$	−22.4988	+	7.31030i	−1.08879	+	0.353770i
$428$	−5.81840	+	2.04121i	−0.281243	+	0.0986657i
$429$		0			0
$430$	−22.6127	+	3.85143i	−1.09048	+	0.185732i
$431$	0.546129	+	1.68081i	0.0263061	+	0.0809619i	0.963348	−	0.268256i	$-0.0864473\pi$
$431$	0.546129	+	1.68081i	0.0263061	+	0.0809619i	−0.937042	+	0.349218i	$0.886447\pi$
$432$		0			0
$433$	26.6582	−	19.3684i	1.28111	−	0.930784i	0.281528	−	0.959553i	$-0.409159\pi$
$433$	26.6582	−	19.3684i	1.28111	−	0.930784i	0.999586	+	0.0287696i	$0.00915892\pi$
$434$	27.5317	+	4.03316i	1.32156	+	0.193598i
$435$		0			0
$436$	15.9370	+	11.0222i	0.763245	+	0.527868i
$437$	5.65429	−	7.78247i	0.270482	−	0.372286i
$438$		0			0
$439$	27.3520			1.30544			0.652719	−	0.757600i	$-0.273628\pi$
$439$	27.3520			1.30544			0.652719	+	0.757600i	$0.273628\pi$
$440$	−14.1850	+	7.58469i	−0.676243	+	0.361586i
$441$		0			0
$442$	−6.38600	−	12.1811i	−0.303751	−	0.579397i
$443$	0.996488	−	1.37155i	0.0473446	−	0.0651642i	−0.784688	−	0.619890i	$-0.787177\pi$
$443$	0.996488	−	1.37155i	0.0473446	−	0.0651642i	0.832033	+	0.554726i	$0.187177\pi$
$444$		0			0
$445$	−4.47865	+	13.7839i	−0.212308	+	0.653418i
$446$	−26.3993	−	3.86727i	−1.25004	−	0.183121i
$447$		0			0
$448$	−17.7324	+	7.16278i	−0.837775	+	0.338410i
$449$	5.72704	+	17.6260i	0.270276	+	0.831823i	0.990431	+	0.138010i	$0.0440705\pi$
$449$	5.72704	+	17.6260i	0.270276	+	0.831823i	−0.720155	+	0.693813i	$0.755929\pi$
$450$		0			0
$451$	16.1383	−	4.97573i	0.759923	−	0.234298i
$452$	20.2985	−	7.12111i	0.954759	−	0.334949i
$453$		0			0
$454$	−14.2822	−	7.06927i	−0.670297	−	0.331777i
$455$	3.87577	+	5.33454i	0.181699	+	0.250087i
$456$		0			0
$457$	10.3504	+	3.36303i	0.484169	+	0.157316i	0.540923	−	0.841072i	$-0.318075\pi$
$457$	10.3504	+	3.36303i	0.484169	+	0.157316i	−0.0567538	+	0.998388i	$0.518075\pi$
$458$	−21.5963	+	22.1043i	−1.00913	+	1.03287i
$459$		0			0
$460$	19.7896	−	15.0930i	0.922693	−	0.703716i
$461$			13.8278i			0.644024i	0.946736	+	0.322012i	$0.104359\pi$
$461$			13.8278i			0.644024i	−0.946736	+	0.322012i	$0.895641\pi$
$462$		0			0
$463$		−	37.3657i		−	1.73653i	−0.496099	−	0.868266i	$-0.665235\pi$
$463$		−	37.3657i		−	1.73653i	0.496099	−	0.868266i	$-0.334765\pi$
$464$	1.19284	−	1.81343i	0.0553763	−	0.0841864i
$465$		0			0
$466$	−6.42661	−	6.27893i	−0.297707	−	0.290866i
$467$	−13.1201	−	4.26296i	−0.607124	−	0.197266i	−0.0107086	−	0.999943i	$-0.503409\pi$
$467$	−13.1201	−	4.26296i	−0.607124	−	0.197266i	−0.596415	+	0.802676i	$0.703409\pi$
$468$		0			0
$469$	6.73176	+	9.26547i	0.310844	+	0.427840i
$470$	−4.31086	+	8.70933i	−0.198845	+	0.401731i
$471$		0			0
$472$	−9.66902	−	17.4449i	−0.445053	−	0.802968i
$473$	−25.0999	−	18.8213i	−1.15410	−	0.865402i
$474$		0			0
$475$	−0.843692	−	2.59662i	−0.0387113	−	0.119141i
$476$	8.29084	−	27.6908i	0.380010	−	1.26921i
$477$		0			0
$478$	−3.06554	+	20.9264i	−0.140214	+	0.957152i
$479$	−4.17392	+	12.8460i	−0.190711	+	0.586949i	−1.00000		0.000462487i	$-0.999853\pi$
$479$	−4.17392	+	12.8460i	−0.190711	+	0.586949i	0.809289	+	0.587411i	$0.199853\pi$
$480$		0			0
$481$	0.349536	−	0.481095i	0.0159375	−	0.0219361i
$482$	0.572862	−	0.300325i	0.0260931	−	0.0136794i
$483$		0			0
$484$	−20.8756	−	6.94324i	−0.948892	−	0.315602i
$485$	14.2771			0.648291
$486$		0			0
$487$	−21.0066	+	28.9132i	−0.951902	+	1.31018i	−0.00122483	+	0.999999i	$0.500390\pi$
$487$	−21.0066	+	28.9132i	−0.951902	+	1.31018i	−0.950677	+	0.310182i	$0.899610\pi$
$488$	−25.3670	−	11.8300i	−1.14831	−	0.535518i
$489$		0			0
$490$	0.451760	−	3.08387i	0.0204084	−	0.139315i
$491$	32.6427	−	23.7163i	1.47314	−	1.07030i	0.493455	−	0.869771i	$-0.335734\pi$
$491$	32.6427	−	23.7163i	1.47314	−	1.07030i	0.979688	−	0.200530i	$-0.0642663\pi$
$492$		0			0
$493$	1.01379	+	3.12013i	0.0456588	+	0.140523i
$494$	0.506304	+	2.97264i	0.0227797	+	0.133745i
$495$		0			0
$496$	20.5683	+	25.7067i	0.923542	+	1.15426i
$497$	7.98446	−	2.59431i	0.358152	−	0.116371i
$498$		0			0
$499$	2.39243	+	3.29289i	0.107100	+	0.147410i	0.859202	−	0.511636i	$-0.170960\pi$
$499$	2.39243	+	3.29289i	0.107100	+	0.147410i	−0.752103	+	0.659046i	$0.770960\pi$
$500$	−0.562755	−	24.2044i	−0.0251672	−	1.08245i
$501$		0			0
$502$	−12.8628	−	12.5672i	−0.574094	−	0.560901i
$503$	15.7894	+	11.4717i	0.704013	+	0.511496i	0.881237	−	0.472675i	$-0.156712\pi$
$503$	15.7894	+	11.4717i	0.704013	+	0.511496i	−0.177223	+	0.984171i	$0.556712\pi$
$504$		0			0
$505$		−	15.4836i		−	0.689010i
$506$	33.6018	+	5.44145i	1.49378	+	0.241902i
$507$		0			0
$508$	−0.395916	−	0.519114i	−0.0175659	−	0.0230320i
$509$	18.9874	+	13.7952i	0.841602	+	0.611459i	0.922818	−	0.385237i	$-0.125880\pi$
$509$	18.9874	+	13.7952i	0.841602	+	0.611459i	−0.0812160	+	0.996697i	$0.525880\pi$
$510$		0			0
$511$	4.77900	+	1.55279i	0.211410	+	0.0686914i
$512$	−21.1236	−	8.11133i	−0.933540	−	0.358473i
$513$		0			0
$514$	−1.88969	−	0.935339i	−0.0833505	−	0.0412560i
$515$	−14.6675	+	4.76576i	−0.646327	+	0.210004i
$516$		0			0
$517$	−12.7010	+	3.91596i	−0.558591	+	0.172224i
$518$	1.23204	−	0.209844i	0.0541329	−	0.00922000i
$519$		0			0
$520$	−0.951075	+	7.74347i	−0.0417074	+	0.339574i
$521$	16.5556	−	12.0284i	0.725315	−	0.526972i	−0.162763	−	0.986665i	$-0.552041\pi$
$521$	16.5556	−	12.0284i	0.725315	−	0.526972i	0.888078	+	0.459693i	$0.152041\pi$
$522$		0			0
$523$	−2.54447	+	7.83107i	−0.111262	+	0.342429i	−0.991149	−	0.132754i	$-0.957618\pi$
$523$	−2.54447	+	7.83107i	−0.111262	+	0.342429i	0.879887	+	0.475183i	$0.157618\pi$
$524$	−12.3275	+	17.8244i	−0.538529	+	0.778660i
$525$		0			0
$526$	9.69071	+	18.4848i	0.422535	+	0.805974i
$527$	−49.7602			−2.16759
$528$		0			0
$529$	−29.6679			−1.28991
$530$	−2.79084	−	5.32345i	−0.121226	−	0.231236i
$531$		0			0
$532$	−3.60488	+	5.21230i	−0.156291	+	0.225982i
$533$	2.53112	−	7.78999i	0.109635	−	0.337422i
$534$		0			0
$535$	−4.27688	+	3.10734i	−0.184906	+	0.134342i
$536$	−1.65191	+	13.4495i	−0.0713515	+	0.580930i
$537$		0			0
$538$	−18.3247	+	3.12110i	−0.790035	+	0.134560i
$539$	3.48610	−	2.45330i	0.150157	−	0.105671i
$540$		0			0
$541$	−20.9142	+	6.79544i	−0.899172	+	0.292159i	−0.721895	−	0.692002i	$-0.756729\pi$
$541$	−20.9142	+	6.79544i	−0.899172	+	0.292159i	−0.177277	+	0.984161i	$0.556729\pi$
$542$	14.3256	+	7.09076i	0.615339	+	0.304574i
$543$		0			0
$544$	29.5192	−	17.2702i	1.26562	−	0.740452i
$545$	15.8001	+	5.13377i	0.676803	+	0.219907i
$546$		0			0
$547$	−20.5153	−	14.9052i	−0.877170	−	0.637301i	0.0553316	−	0.998468i	$-0.482378\pi$
$547$	−20.5153	−	14.9052i	−0.877170	−	0.637301i	−0.932501	+	0.361167i	$0.882378\pi$
$548$	1.53119	+	2.00766i	0.0654093	+	0.0857629i
$549$		0			0
$550$	6.85506	−	6.80771i	0.292301	−	0.290282i
$551$		−	0.719286i		−	0.0306426i
$552$		0			0
$553$	−4.99148	−	3.62652i	−0.212259	−	0.154215i
$554$	−1.59990	−	1.56314i	−0.0679734	−	0.0664113i
$555$		0			0
$556$	0.467184	+	20.0938i	0.0198130	+	0.852167i
$557$	−2.66116	−	3.66277i	−0.112757	−	0.155197i	0.748908	−	0.662673i	$-0.230578\pi$
$557$	−2.66116	−	3.66277i	−0.112757	−	0.155197i	−0.861665	+	0.507477i	$0.830578\pi$
$558$		0			0
$559$	−14.4714	+	4.70205i	−0.612076	+	0.198876i
$560$	−12.8027	+	10.2437i	−0.541015	+	0.432874i
$561$		0			0
$562$	2.09315	+	12.2894i	0.0882940	+	0.518396i
$563$	−12.0512	−	37.0897i	−0.507896	−	1.56314i	−0.795847	−	0.605498i	$-0.792974\pi$
$563$	−12.0512	−	37.0897i	−0.507896	−	1.56314i	0.287951	−	0.957645i	$-0.407026\pi$
$564$		0			0
$565$	14.9206	−	10.8405i	0.627715	−	0.456062i
$566$	−4.15667	+	28.3749i	−0.174718	+	1.19269i
$567$		0			0
$568$	9.00233	+	4.19827i	0.377729	+	0.176155i
$569$	−20.6897	+	28.4769i	−0.867357	+	1.19381i	0.112408	+	0.993662i	$0.464144\pi$
$569$	−20.6897	+	28.4769i	−0.867357	+	1.19381i	−0.979765	+	0.200152i	$0.935856\pi$
$570$		0			0
$571$	−28.8320			−1.20658			−0.603291	−	0.797521i	$-0.706144\pi$
$571$	−28.8320			−1.20658			−0.603291	+	0.797521i	$0.706144\pi$
$572$	−8.58100	+	6.34205i	−0.358790	+	0.265174i
$573$		0			0
$574$	15.2463	−	7.99293i	0.636368	−	0.333619i
$575$	−8.78631	+	12.0933i	−0.366414	+	0.504326i
$576$		0			0
$577$	−1.76215	+	5.42333i	−0.0733591	+	0.225776i	−0.981013	−	0.193944i	$-0.937872\pi$
$577$	−1.76215	+	5.42333i	−0.0733591	+	0.225776i	0.907653	+	0.419720i	$0.137872\pi$
$578$	−4.00765	+	27.3576i	−0.166696	+	1.13793i
$579$		0			0
$580$	0.533774	−	1.78277i	0.0221638	−	0.0740254i
$581$	2.93342	+	9.02814i	0.121699	+	0.374551i
$582$		0			0
$583$	2.65803	−	7.77917i	0.110084	−	0.322180i
$584$	2.88217	+	5.20004i	0.119265	+	0.215179i
$585$		0			0
$586$	−8.75265	+	17.6832i	−0.361569	+	0.730485i
$587$	24.8378	+	34.1864i	1.02517	+	1.41102i	0.908517	+	0.417849i	$0.137216\pi$
$587$	24.8378	+	34.1864i	1.02517	+	1.41102i	0.116651	+	0.993173i	$0.462784\pi$
$588$		0			0
$589$	10.3759	+	3.37133i	0.427530	+	0.138913i
$590$	−12.2314	−	11.9504i	−0.503560	−	0.491988i
$591$		0			0
$592$	1.23540	+	0.812627i	0.0507748	+	0.0333988i
$593$		−	21.6694i		−	0.889855i	−0.895567	−	0.444927i	$-0.853229\pi$
$593$		−	21.6694i		−	0.889855i	0.895567	−	0.444927i	$-0.146771\pi$
$594$		0			0
$595$		−	24.7822i		−	1.01597i
$596$	3.75795	−	2.86610i	0.153932	−	0.117400i
$597$		0			0
$598$	11.5376	−	11.8090i	0.471808	−	0.482905i
$599$	−17.9158	−	5.82121i	−0.732021	−	0.237848i	−0.0807939	−	0.996731i	$-0.525746\pi$
$599$	−17.9158	−	5.82121i	−0.732021	−	0.237848i	−0.651227	+	0.758883i	$0.725746\pi$
$600$		0			0
$601$	8.90397	+	12.2553i	0.363200	+	0.499902i	0.951037	−	0.309077i	$-0.100020\pi$
$601$	8.90397	+	12.2553i	0.363200	+	0.499902i	−0.587837	+	0.808980i	$0.700020\pi$
$602$	−28.6605	−	14.1861i	−1.16811	−	0.578182i
$603$		0			0
$604$	−36.0500	+	12.6471i	−1.46685	+	0.514602i
$605$	−18.8533	−	0.569118i	−0.766495	−	0.0231379i
$606$		0			0
$607$	−2.09788	−	6.45662i	−0.0851505	−	0.262066i	0.899411	−	0.437103i	$-0.143996\pi$
$607$	−2.09788	−	6.45662i	−0.0851505	−	0.262066i	−0.984562	+	0.175037i	$0.943996\pi$
$608$	−7.32533	+	1.60116i	−0.297081	+	0.0649358i
$609$		0			0
$610$	−23.7439	−	3.47827i	−0.961361	−	0.140831i
$611$	−1.99202	+	6.13081i	−0.0805885	+	0.248026i
$612$		0			0
$613$	−5.26974	+	7.25318i	−0.212843	+	0.292953i	−0.902068	−	0.431594i	$-0.857951\pi$
$613$	−5.26974	+	7.25318i	−0.212843	+	0.292953i	0.689225	+	0.724547i	$0.257951\pi$
$614$	3.86650	+	7.37524i	0.156039	+	0.297640i
$615$		0			0
$616$	−22.2143	−	3.06932i	−0.895039	−	0.123666i
$617$	−41.7476			−1.68069			−0.840347	−	0.542049i	$-0.817649\pi$
$617$	−41.7476			−1.68069			−0.840347	+	0.542049i	$0.817649\pi$
$618$		0			0
$619$	−3.56169	+	4.90225i	−0.143157	+	0.197038i	−0.874574	−	0.484892i	$-0.838859\pi$
$619$	−3.56169	+	4.90225i	−0.143157	+	0.197038i	0.731418	+	0.681930i	$0.238859\pi$
$620$	23.2150	+	16.0557i	0.932337	+	0.644813i
$621$		0			0
$622$	−36.7079	−	5.37738i	−1.47185	−	0.215613i
$623$	−16.3466	+	11.8765i	−0.654913	+	0.475822i
$624$		0			0
$625$	−3.23190	−	9.94678i	−0.129276	−	0.397871i
$626$	−23.8841	+	4.06798i	−0.954603	+	0.162589i
$627$		0			0
$628$	18.5150	−	6.49544i	0.738829	−	0.259196i
$629$	−2.12560	+	0.690648i	−0.0847531	+	0.0275379i
$630$		0			0
$631$	9.43855	+	12.9911i	0.375743	+	0.517166i	0.954450	−	0.298369i	$-0.0964427\pi$
$631$	9.43855	+	12.9911i	0.375743	+	0.517166i	−0.578708	+	0.815535i	$0.696443\pi$
$632$	−1.39262	−	7.16587i	−0.0553956	−	0.285043i
$633$		0			0
$634$	0.787867	−	0.806397i	0.0312902	−	0.0320261i
$635$	−0.452836	−	0.329005i	−0.0179703	−	0.0130562i
$636$		0			0
$637$		−	2.06752i		−	0.0819181i
$638$	2.27180	−	1.14764i	0.0899416	−	0.0454356i
$639$		0			0
$640$	−19.3442	−	1.46753i	−0.764647	−	0.0580090i
$641$	−16.2489	−	11.8055i	−0.641793	−	0.466290i	0.218673	−	0.975798i	$-0.429827\pi$
$641$	−16.2489	−	11.8055i	−0.641793	−	0.466290i	−0.860466	+	0.509508i	$0.829827\pi$
$642$		0			0
$643$	4.15001	+	1.34842i	0.163660	+	0.0531764i	0.389701	−	0.920941i	$-0.372578\pi$
$643$	4.15001	+	1.34842i	0.163660	+	0.0531764i	−0.226041	+	0.974118i	$0.572578\pi$
$644$	34.6883	−	0.806507i	1.36691	−	0.0317808i
$645$		0			0
$646$	5.02745	−	10.1571i	0.197802	−	0.399625i
$647$	9.16047	−	2.97642i	0.360135	−	0.117015i	−0.123360	−	0.992362i	$-0.539367\pi$
$647$	9.16047	−	2.97642i	0.360135	−	0.117015i	0.483495	+	0.875347i	$0.339367\pi$
$648$		0			0
$649$	0.352882	−	23.3853i	0.0138518	−	0.917953i
$650$	−0.786755	−	4.61924i	−0.0308591	−	0.181181i
$651$		0			0
$652$	8.17294	−	27.2970i	0.320077	−	1.06903i
$653$	14.7817	−	10.7396i	0.578454	−	0.420272i	−0.259712	−	0.965686i	$-0.583628\pi$
$653$	14.7817	−	10.7396i	0.578454	−	0.420272i	0.838167	+	0.545414i	$0.183628\pi$
$654$		0			0
$655$	−5.74173	+	17.6712i	−0.224348	+	0.690472i
$656$	19.6423	+	5.38688i	0.766905	+	0.210322i
$657$		0			0
$658$	−11.9990	+	6.29053i	−0.467770	+	0.245230i
$659$	17.9779			0.700318			0.350159	−	0.936690i	$-0.386128\pi$
$659$	17.9779			0.700318			0.350159	+	0.936690i	$0.386128\pi$
$660$		0			0
$661$	2.57645			0.100212			0.0501062	−	0.998744i	$-0.484044\pi$
$661$	2.57645			0.100212			0.0501062	+	0.998744i	$0.484044\pi$
$662$	26.6761	−	13.9851i	1.03680	−	0.543545i
$663$		0			0
$664$	−4.74704	+	10.1791i	−0.184221	+	0.395024i
$665$	−1.67903	+	5.16752i	−0.0651100	+	0.200388i
$666$		0			0
$667$	−3.18600	+	2.31476i	−0.123362	+	0.0896280i
$668$	0.134358	+	0.0402278i	0.00519846	+	0.00155646i
$669$		0			0
$670$	1.95065	+	11.4528i	0.0753602	+	0.442459i
$671$	−18.8889	−	26.8408i	−0.729196	−	1.03618i
$672$		0			0
$673$	32.6554	−	10.6104i	1.25878	−	0.409001i	0.397717	−	0.917508i	$-0.369802\pi$
$673$	32.6554	−	10.6104i	1.25878	−	0.409001i	0.861058	+	0.508507i	$0.169802\pi$
$674$	−6.82298	+	13.7846i	−0.262812	+	0.530964i
$675$		0			0
$676$	−0.484048	−	20.8191i	−0.0186172	−	0.800736i
$677$	−16.4156	−	5.33375i	−0.630902	−	0.204993i	−0.0239275	−	0.999714i	$-0.507617\pi$
$677$	−16.4156	−	5.33375i	−0.630902	−	0.204993i	−0.606975	+	0.794721i	$0.707617\pi$
$678$		0			0
$679$	16.1029	+	11.6994i	0.617972	+	0.448983i
$680$	19.9981	−	21.4437i	0.766892	−	0.822329i
$681$		0			0
$682$	5.90696	+	38.1504i	0.226189	+	1.46085i
$683$		−	0.254052i		−	0.00972104i	−0.999988	−	0.00486052i	$-0.998453\pi$
$683$		−	0.254052i		−	0.00972104i	0.999988	−	0.00486052i	$-0.00154716\pi$
$684$		0			0
$685$	1.75133	+	1.27242i	0.0669148	+	0.0486165i
$686$	19.5748	−	20.0352i	0.747370	−	0.764949i
$687$		0			0
$688$	−13.3520	−	35.4027i	−0.509041	−	1.34972i
$689$	−2.34360	−	3.22569i	−0.0892840	−	0.122889i
$690$		0			0
$691$	−9.02104	+	2.93111i	−0.343176	+	0.111505i	−0.475534	−	0.879697i	$-0.657745\pi$
$691$	−9.02104	+	2.93111i	−0.343176	+	0.111505i	0.132358	+	0.991202i	$0.457745\pi$
$692$	13.1278	+	37.4202i	0.499043	+	1.42250i
$693$		0			0
$694$	−0.897175	+	0.152808i	−0.0340563	+	0.00580052i
$695$	5.32505	+	16.3888i	0.201991	+	0.621663i
$696$		0			0
$697$	−24.9051	+	18.0946i	−0.943349	+	0.685383i
$698$	−24.1791	−	3.54203i	−0.915193	−	0.134068i
$699$		0			0
$700$	5.60168	−	8.09949i	0.211724	−	0.306132i
$701$	5.04306	−	6.94118i	0.190474	−	0.262165i	−0.703090	−	0.711101i	$-0.748197\pi$
$701$	5.04306	−	6.94118i	0.190474	−	0.262165i	0.893564	+	0.448936i	$0.148197\pi$
$702$		0			0
$703$	0.490016			0.0184813
$704$	−16.7449	−	20.5817i	−0.631098	−	0.775703i
$705$		0			0
$706$	18.6371	+	35.5498i	0.701417	+	1.33793i
$707$	12.6881	−	17.4636i	0.477184	−	0.656787i
$708$		0			0
$709$	2.13737	−	6.57816i	0.0802708	−	0.247048i	−0.902865	−	0.429924i	$-0.858541\pi$
$709$	2.13737	−	6.57816i	0.0802708	−	0.247048i	0.983136	+	0.182875i	$0.0585405\pi$
$710$	8.42632	+	1.23438i	0.316234	+	0.0463256i
$711$		0			0
$712$	−23.7283	−	2.91437i	−0.889255	−	0.109221i
$713$	−18.4581	−	56.8082i	−0.691261	−	2.12748i
$714$		0			0
$715$	−5.48827	+	7.31912i	−0.205250	+	0.273720i
$716$	2.28135	+	6.50290i	0.0852580	+	0.243025i
$717$		0			0
$718$	36.1900	+	17.9130i	1.35060	+	0.668506i
$719$	−11.1867	−	15.3972i	−0.417195	−	0.574219i	0.547760	−	0.836636i	$-0.315481\pi$
$719$	−11.1867	−	15.3972i	−0.417195	−	0.574219i	−0.964955	+	0.262416i	$0.915481\pi$
$720$		0			0
$721$	−20.4485	−	6.64412i	−0.761542	−	0.247440i
$722$	17.0414	−	17.4422i	0.634216	−	0.649133i
$723$		0			0
$724$	19.1151	+	25.0633i	0.710409	+	0.931469i
$725$			1.11771i			0.0415108i
$726$		0			0
$727$			19.7014i			0.730685i	0.930873	+	0.365342i	$0.119048\pi$
$727$			19.7014i			0.730685i	−0.930873	+	0.365342i	$0.880952\pi$
$728$	−7.41811	+	7.95435i	−0.274933	+	0.294808i
$729$		0			0
$730$	3.64598	+	3.56220i	0.134944	+	0.131843i
$731$	54.3892	+	17.6721i	2.01166	+	0.653627i
$732$		0			0
$733$	−29.2902	−	40.3146i	−1.08186	−	1.48905i	−0.857457	−	0.514556i	$-0.827957\pi$
$733$	−29.2902	−	40.3146i	−1.08186	−	1.48905i	−0.224403	−	0.974496i	$-0.572043\pi$
$734$	−0.244308	+	0.493582i	−0.00901759	+	0.0182184i
$735$		0			0
$736$	30.6661	+	27.2940i	1.13037	+	1.00607i
$737$	−9.53248	+	12.7125i	−0.351133	+	0.468270i
$738$		0			0
$739$	−5.07527	−	15.6201i	−0.186697	−	0.574593i	0.813277	−	0.581877i	$-0.197682\pi$
$739$	−5.07527	−	15.6201i	−0.186697	−	0.574593i	−0.999973	+	0.00728362i	$0.997682\pi$
$740$	1.21452	+	0.363635i	0.0446465	+	0.0133675i
$741$		0			0
$742$	1.21459	−	8.29118i	0.0445888	−	0.304379i
$743$	0.924280	−	2.84464i	0.0339086	−	0.104360i	−0.932670	−	0.360731i	$-0.882527\pi$
$743$	0.924280	−	2.84464i	0.0339086	−	0.104360i	0.966578	+	0.256372i	$0.0825271\pi$
$744$		0			0
$745$	2.38172	−	3.27815i	0.0872593	−	0.120102i
$746$	−12.4645	+	6.53457i	−0.456358	+	0.239248i
$747$		0			0
$748$	40.1017	−	0.327124i	1.46626	−	0.0119609i
$749$	−7.37013			−0.269299
$750$		0			0
$751$	24.4608	−	33.6674i	0.892587	−	1.22854i	−0.0801854	−	0.996780i	$-0.525551\pi$
$751$	24.4608	−	33.6674i	0.892587	−	1.22854i	0.972773	−	0.231761i	$-0.0744488\pi$
$752$	−15.4588	−	4.23954i	−0.563723	−	0.154600i
$753$		0			0
$754$	0.178929	−	1.22143i	0.00651622	−	0.0444819i
$755$	−26.4990	+	19.2526i	−0.964397	+	0.700675i
$756$		0			0
$757$	−7.07412	−	21.7719i	−0.257113	−	0.791313i	−0.993406	−	0.114650i	$-0.963425\pi$
$757$	−7.07412	−	21.7719i	−0.257113	−	0.791313i	0.736293	−	0.676663i	$-0.236575\pi$
$758$	4.77572	+	28.0394i	0.173462	+	1.01844i
$759$		0			0
$760$	−5.62279	+	3.11649i	−0.203960	+	0.113047i
$761$	45.5970	−	14.8154i	1.65289	−	0.537056i	0.673526	−	0.739163i	$-0.264779\pi$
$761$	45.5970	−	14.8154i	1.65289	−	0.537056i	0.979363	+	0.202107i	$0.0647789\pi$
$762$		0			0
$763$	13.6138	+	18.7377i	0.492851	+	0.678352i
$764$	14.2439	−	0.331173i	0.515326	−	0.0119814i
$765$		0			0
$766$	10.4004	+	10.1614i	0.375783	+	0.367148i
$767$	−9.17705	−	6.66752i	−0.331364	−	0.240750i
$768$		0			0
$769$			43.0718i			1.55321i	0.629989	+	0.776604i	$0.283059\pi$
$769$			43.0718i			1.55321i	−0.629989	+	0.776604i	$0.716941\pi$
$770$	−19.0001	+	2.94186i	−0.684717	+	0.106017i
$771$		0			0
$772$	26.8160	−	20.4519i	0.965127	−	0.736080i
$773$	−10.3986	−	7.55502i	−0.374011	−	0.271735i	0.384861	−	0.922975i	$-0.374249\pi$
$773$	−10.3986	−	7.55502i	−0.374011	−	0.271735i	−0.758872	+	0.651239i	$0.774249\pi$
$774$		0			0
$775$	−16.1233	−	5.23877i	−0.579165	−	0.188182i
$776$	4.49271	+	23.1176i	0.161279	+	0.829875i
$777$		0			0
$778$	−24.4363	−	12.0952i	−0.876083	−	0.433635i
$779$	6.41909	−	2.08569i	0.229988	−	0.0747276i
$780$		0			0
$781$	6.70336	+	9.52537i	0.239865	+	0.340844i
$782$	−61.1687	+	10.4183i	−2.18739	+	0.372559i
$783$		0			0
$784$	5.13558	−	0.238935i	0.183414	−	0.00853340i
$785$	13.6097	−	9.88801i	0.485750	−	0.352918i
$786$		0			0
$787$	12.3196	−	37.9159i	0.439147	−	1.35156i	−0.449629	−	0.893215i	$-0.648444\pi$
$787$	12.3196	−	37.9159i	0.439147	−	1.35156i	0.888777	−	0.458341i	$-0.151556\pi$
$788$	40.6071	+	28.0842i	1.44657	+	1.00046i
$789$		0			0
$790$	−2.90599	−	5.54310i	−0.103391	−	0.197215i
$791$	25.7119			0.914211
$792$		0			0
$793$	−15.9186			−0.565287
$794$	25.0200	+	47.7250i	0.887927	+	1.69370i
$795$		0			0
$796$	−25.9232	−	17.9288i	−0.918825	−	0.635468i
$797$	8.31012	−	25.5759i	0.294360	−	0.905946i	−0.689076	−	0.724689i	$-0.741984\pi$
$797$	8.31012	−	25.5759i	0.294360	−	0.905946i	0.983436	−	0.181257i	$-0.0580165\pi$
$798$		0			0
$799$	19.6006	−	14.2407i	0.693420	−	0.503799i
$800$	11.3830	−	2.48808i	0.402449	−	0.0879668i
$801$		0			0
$802$	5.78815	−	0.985846i	0.204387	−	0.0348114i
$803$	−0.105188	+	6.97076i	−0.00371201	+	0.245993i
$804$		0			0
$805$	28.2923	−	9.19273i	0.997173	−	0.324001i
$806$	16.7808	+	8.30600i	0.591078	+	0.292566i
$807$		0			0
$808$	25.0711	−	4.87236i	0.882000	−	0.171409i
$809$	11.0316	+	3.58440i	0.387852	+	0.126021i	0.496451	−	0.868065i	$-0.334636\pi$
$809$	11.0316	+	3.58440i	0.387852	+	0.126021i	−0.108599	+	0.994086i	$0.534636\pi$
$810$		0			0
$811$	29.6177	+	21.5185i	1.04002	+	0.755616i	0.970289	−	0.241950i	$-0.0777869\pi$
$811$	29.6177	+	21.5185i	1.04002	+	0.755616i	0.0697279	+	0.997566i	$0.477787\pi$
$812$	2.06293	−	1.57334i	0.0723945	−	0.0552136i
$813$		0			0
$814$	0.781835	+	1.54767i	0.0274033	+	0.0542459i
$815$		−	24.4298i		−	0.855738i
$816$		0			0
$817$	−10.1438	−	7.36989i	−0.354886	−	0.257840i
$818$	11.4528	+	11.1896i	0.400439	+	0.391237i
$819$		0			0
$820$	17.4576	−	0.405892i	0.609646	−	0.0141744i
$821$	−18.6399	−	25.6556i	−0.650536	−	0.895386i	0.348586	−	0.937277i	$-0.386662\pi$
$821$	−18.6399	−	25.6556i	−0.650536	−	0.895386i	−0.999122	+	0.0418907i	$0.986662\pi$
$822$		0			0
$823$	17.5566	−	5.70447i	0.611983	−	0.198845i	0.0134055	−	0.999910i	$-0.495733\pi$
$823$	17.5566	−	5.70447i	0.611983	−	0.198845i	0.598578	+	0.801065i	$0.295733\pi$
$824$	−12.3323	−	22.2500i	−0.429616	−	0.775117i
$825$		0			0
$826$	−4.00284	−	23.5016i	−0.139276	−	0.817727i
$827$	5.85114	+	18.0080i	0.203464	+	0.626199i	0.999773	+	0.0213081i	$0.00678310\pi$
$827$	5.85114	+	18.0080i	0.203464	+	0.626199i	−0.796309	+	0.604890i	$0.793217\pi$
$828$		0			0
$829$	−6.62707	+	4.81485i	−0.230168	+	0.167227i	−0.696892	−	0.717176i	$-0.745434\pi$
$829$	−6.62707	+	4.81485i	−0.230168	+	0.167227i	0.466724	+	0.884403i	$0.345434\pi$
$830$	−1.39573	+	9.52777i	−0.0484467	+	0.330714i
$831$		0			0
$832$	−12.8376	+	0.896719i	−0.445063	+	0.0310881i
$833$	−4.56740	+	6.28649i	−0.158251	+	0.217814i
$834$		0			0
$835$	0.120245			0.00416125
$836$	−8.38406	−	2.64873i	−0.289969	−	0.0916084i
$837$		0			0
$838$	−26.5654	+	13.9270i	−0.917687	+	0.481101i
$839$	21.3596	−	29.3990i	0.737416	−	1.01497i	−0.261347	−	0.965245i	$-0.584167\pi$
$839$	21.3596	−	29.3990i	0.737416	−	1.01497i	0.998763	−	0.0497210i	$-0.0158332\pi$
$840$		0			0
$841$	8.87050	−	27.3006i	0.305879	−	0.941400i
$842$	5.08015	−	34.6788i	0.175073	−	1.19511i
$843$		0			0
$844$	45.7793	+	13.7067i	1.57579	+	0.471804i
$845$	−5.51727	−	16.9804i	−0.189800	−	0.584144i
$846$		0			0
$847$	−20.7979	−	16.0913i	−0.714623	−	0.552903i
$848$	7.74156	−	6.19413i	0.265846	−	0.212707i
$849$		0			0
$850$	−7.81225	+	15.7833i	−0.267958	+	0.541362i
$851$	−1.57694	−	2.17047i	−0.0540568	−	0.0744028i
$852$		0			0
$853$	−11.3089	−	3.67449i	−0.387210	−	0.125812i	0.108941	−	0.994048i	$-0.465254\pi$
$853$	−11.3089	−	3.67449i	−0.387210	−	0.125812i	−0.496152	+	0.868236i	$0.665254\pi$
$854$	−23.9300	−	23.3801i	−0.818867	−	0.800049i
$855$		0			0
$856$	−6.37728	−	5.94735i	−0.217971	−	0.203276i
$857$			35.7039i			1.21962i	0.792547	+	0.609811i	$0.208755\pi$
$857$			35.7039i			1.21962i	−0.792547	+	0.609811i	$0.791245\pi$
$858$		0			0
$859$			40.2518i			1.37337i	0.726953	+	0.686687i	$0.240936\pi$
$859$			40.2518i			1.37337i	−0.726953	+	0.686687i	$0.759064\pi$
$860$	−19.6725	−	25.7940i	−0.670825	−	0.879568i
$861$		0			0
$862$	−1.74665	+	1.78773i	−0.0594911	+	0.0608904i
$863$	17.2998	+	5.62104i	0.588891	+	0.191342i	0.588280	−	0.808657i	$-0.299805\pi$
$863$	17.2998	+	5.62104i	0.588891	+	0.191342i	0.000611565		1.00000i	$0.499805\pi$
$864$		0			0
$865$	19.9844	+	27.5062i	0.679490	+	0.935238i
$866$	41.7643	+	20.6721i	1.41921	+	0.702466i
$867$		0			0
$868$	13.0268	+	37.1325i	0.442160	+	1.26036i
$869$	2.76770	−	8.10014i	0.0938877	−	0.274779i
$870$		0			0
$871$	2.38147	+	7.32941i	0.0806930	+	0.248348i
$872$	−3.34068	+	27.1992i	−0.113130	+	0.921081i
$873$		0			0
$874$	13.4606	+	1.97186i	0.455311	+	0.0666991i
$875$	8.94254	−	27.5223i	0.302313	−	0.930424i
$876$		0			0
$877$	23.4777	−	32.3142i	0.792784	−	1.09117i	−0.200971	−	0.979597i	$-0.564410\pi$
$877$	23.4777	−	32.3142i	0.792784	−	1.09117i	0.993756	−	0.111577i	$-0.0355902\pi$
$878$	17.9604	+	34.2591i	0.606135	+	1.15619i
$879$		0			0
$880$	−18.8145	−	12.7867i	−0.634236	−	0.431038i
$881$	−21.8173			−0.735045			−0.367522	−	0.930015i	$-0.619794\pi$
$881$	−21.8173			−0.735045			−0.367522	+	0.930015i	$0.619794\pi$
$882$		0			0
$883$	−9.07011	+	12.4839i	−0.305234	+	0.420118i	−0.933887	−	0.357567i	$-0.883606\pi$
$883$	−9.07011	+	12.4839i	−0.305234	+	0.420118i	0.628654	+	0.777685i	$0.283606\pi$
$884$	11.0639	−	15.9973i	0.372118	−	0.538047i
$885$		0			0
$886$	2.37223	+	0.347512i	0.0796968	+	0.0116749i
$887$	−13.7001	+	9.95369i	−0.460004	+	0.334212i	−0.793533	−	0.608528i	$-0.791760\pi$
$887$	−13.7001	+	9.95369i	−0.460004	+	0.334212i	0.333529	+	0.942740i	$0.391760\pi$
$888$		0			0
$889$	−0.241141	−	0.742156i	−0.00808761	−	0.0248911i
$890$	−20.2055	+	3.44143i	−0.677290	+	0.115357i
$891$		0			0
$892$	−12.4910	−	35.6053i	−0.418231	−	1.19215i
$893$	−5.05190	+	1.64146i	−0.169055	+	0.0549294i
$894$		0			0
$895$	3.47290	+	4.78003i	0.116086	+	0.159779i
$896$	−20.6154	−	17.5069i	−0.688711	−	0.584863i
$897$		0			0
$898$	−18.3164	+	18.7472i	−0.611227	+	0.625603i
$899$	−3.61330	−	2.62522i	−0.120510	−	0.0875559i
$900$		0			0
$901$			14.9853i			0.499233i
$902$	16.8293	+	16.9464i	0.560355	+	0.564252i
$903$		0			0
$904$	22.2482	+	20.7483i	0.739964	+	0.690079i
$905$	21.8633	+	15.8846i	0.726761	+	0.528023i
$906$		0			0
$907$	23.7227	+	7.70798i	0.787700	+	0.255939i	0.675124	−	0.737704i	$-0.264090\pi$
$907$	23.7227	+	7.70798i	0.787700	+	0.255939i	0.112576	+	0.993643i	$0.464090\pi$
$908$	−0.523844	−	22.5308i	−0.0173844	−	0.747711i
$909$		0			0
$910$	−4.13666	+	8.35738i	−0.137129	+	0.277045i
$911$	−42.2349	+	13.7229i	−1.39930	+	0.454662i	−0.908966	−	0.416871i	$-0.863127\pi$
$911$	−42.2349	+	13.7229i	−1.39930	+	0.454662i	−0.490338	+	0.871532i	$0.663127\pi$
$912$		0			0
$913$	−10.7705	+	7.57958i	−0.356451	+	0.250848i
$914$	2.58419	+	15.1724i	0.0854773	+	0.501858i
$915$		0			0
$916$	−41.8672	−	12.5354i	−1.38333	−	0.414180i
$917$	−20.9567	+	15.2260i	−0.692052	+	0.502805i
$918$		0			0
$919$	14.9742	−	46.0859i	0.493954	−	1.52023i	−0.324626	−	0.945842i	$-0.605239\pi$
$919$	14.9742	−	46.0859i	0.493954	−	1.52023i	0.818580	−	0.574392i	$-0.194761\pi$
$920$	31.8991	+	14.8762i	1.05168	+	0.490455i
$921$		0			0
$922$	−17.3197	+	9.07990i	−0.570393	+	0.299031i
$923$	5.64926			0.185948
$924$		0			0
$925$	−0.761445			−0.0250362
$926$	46.8015	−	24.5359i	1.53799	−	0.806299i
$927$		0			0
$928$	3.05464	+	0.303292i	0.100273	+	0.00995606i
$929$	−6.91854	+	21.2931i	−0.226990	+	0.698603i	0.771094	+	0.636722i	$0.219710\pi$
$929$	−6.91854	+	21.2931i	−0.226990	+	0.698603i	−0.998084	+	0.0618814i	$0.980290\pi$
$930$		0			0
$931$	1.37830	−	1.00139i	0.0451720	−	0.0328194i
$932$	3.64454	−	12.1725i	0.119381	−	0.398723i
$933$		0			0
$934$	−3.27570	−	19.2324i	−0.107184	−	0.629305i
$935$	32.8564	−	10.1302i	1.07452	−	0.331294i
$936$		0			0
$937$	−34.2110	+	11.1158i	−1.11762	+	0.363138i	−0.808860	−	0.588001i	$-0.799915\pi$
$937$	−34.2110	+	11.1158i	−1.11762	+	0.363138i	−0.308763	+	0.951139i	$0.599915\pi$
$938$	−7.18489	+	14.5158i	−0.234595	+	0.473958i
$939$		0			0
$940$	−13.7393	+	0.319442i	−0.448128	+	0.0104190i
$941$	−47.1567	−	15.3221i	−1.53726	−	0.499487i	−0.586644	−	0.809845i	$-0.699551\pi$
$941$	−47.1567	−	15.3221i	−1.53726	−	0.499487i	−0.950620	+	0.310357i	$0.899551\pi$
$942$		0			0
$943$	−29.8959	−	21.7206i	−0.973543	−	0.707320i
$944$	15.5011	−	23.5658i	0.504519	−	0.767000i
$945$		0			0
$946$	7.09247	−	43.7971i	0.230596	−	1.42397i
$947$		−	45.1846i		−	1.46830i	−0.678985	−	0.734152i	$-0.737580\pi$
$947$		−	45.1846i		−	1.46830i	0.678985	−	0.734152i	$-0.262420\pi$
$948$		0			0
$949$	2.73553	+	1.98748i	0.0887989	+	0.0645162i
$950$	2.69833	−	2.76179i	0.0875453	−	0.0896044i
$951$		0			0
$952$	40.1276	−	7.79844i	1.30054	−	0.252749i
$953$	17.5119	+	24.1030i	0.567265	+	0.780774i	0.992227	−	0.124437i	$-0.0397126\pi$
$953$	17.5119	+	24.1030i	0.567265	+	0.780774i	−0.424962	+	0.905211i	$0.639713\pi$
$954$		0			0
$955$	11.6176	−	3.77477i	0.375935	−	0.122149i
$956$	−28.2239	+	9.90149i	−0.912825	+	0.320237i
$957$		0			0
$958$	−18.8307	+	3.20728i	−0.608393	+	0.103622i
$959$	0.932605	+	2.87026i	0.0301154	+	0.0926856i
$960$		0			0
$961$	29.7256	−	21.5969i	0.958889	−	0.696674i
$962$	0.832105	+	0.121896i	0.0268281	+	0.00393009i
$963$		0			0
$964$	0.752330	+	0.520319i	0.0242309	+	0.0167583i
$965$	16.9954	−	23.3922i	0.547103	−	0.753022i
$966$		0			0
$967$	2.10906			0.0678227			0.0339113	−	0.999425i	$-0.489204\pi$
$967$	2.10906			0.0678227			0.0339113	+	0.999425i	$0.489204\pi$
$968$	−5.01121	−	30.7065i	−0.161066	−	0.986944i
$969$		0			0
$970$	9.37496	+	17.8825i	0.301012	+	0.574172i
$971$	−33.7588	+	46.4651i	−1.08337	+	1.49113i	−0.227620	+	0.973750i	$0.573094\pi$
$971$	−33.7588	+	46.4651i	−1.08337	+	1.49113i	−0.855753	+	0.517385i	$0.826906\pi$
$972$		0			0
$973$	−7.42385	+	22.8483i	−0.237998	+	0.732481i
$974$	−50.0083	−	7.32579i	−1.60237	−	0.234733i
$975$		0			0
$976$	−1.83965	−	39.5408i	−0.0588859	−	1.26567i
$977$	−1.61602	−	4.97360i	−0.0517011	−	0.159120i	0.921872	−	0.387494i	$-0.126659\pi$
$977$	−1.61602	−	4.97360i	−0.0517011	−	0.159120i	−0.973573	+	0.228374i	$0.926659\pi$
$978$		0			0
$979$	−22.4279	−	16.8177i	−0.716800	−	0.537495i
$980$	4.15927	−	1.45916i	0.132863	−	0.0466110i
$981$		0			0
$982$	51.1398	+	25.3127i	1.63194	+	0.807760i
$983$	16.7859	+	23.1038i	0.535386	+	0.736896i	0.987939	−	0.154841i	$-0.0494867\pi$
$983$	16.7859	+	23.1038i	0.535386	+	0.736896i	−0.452553	+	0.891738i	$0.649487\pi$
$984$		0			0
$985$	40.2582	+	13.0807i	1.28273	+	0.416785i
$986$	−3.24234	+	3.31861i	−0.103257	+	0.105686i
$987$		0			0
$988$	−3.39085	+	2.58612i	−0.107877	+	0.0822753i
$989$			68.6481i			2.18288i
$990$		0			0
$991$			0.537995i			0.0170900i	0.999963	+	0.00854499i	$0.00271999\pi$
$991$			0.537995i			0.0170900i	−0.999963	+	0.00854499i	$0.997280\pi$
$992$	−18.6923	+	42.6423i	−0.593481	+	1.35390i
$993$		0			0
$994$	8.49236	+	8.29721i	0.269361	+	0.263172i
$995$	−25.7006	−	8.35062i	−0.814762	−	0.264732i
$996$		0			0
$997$	14.2814	+	19.6567i	0.452297	+	0.622534i	0.972889	−	0.231272i	$-0.0742887\pi$
$997$	14.2814	+	19.6567i	0.452297	+	0.622534i	−0.520592	+	0.853806i	$0.674289\pi$
$998$	−2.55347	+	5.15883i	−0.0808286	+	0.163300i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	396.2.r.a.127.2		16
3.2	odd	2		44.2.g.a.39.3	yes	16
4.3	odd	2	inner	396.2.r.a.127.1		16
11.2	odd	10	inner	396.2.r.a.343.1		16
12.11	even	2		44.2.g.a.39.4	yes	16
24.5	odd	2		704.2.u.c.127.2		16
24.11	even	2		704.2.u.c.127.3		16
33.2	even	10		44.2.g.a.35.4	yes	16
33.5	odd	10		484.2.g.j.403.4		16
33.8	even	10		484.2.c.d.483.15		16
33.14	odd	10		484.2.c.d.483.2		16
33.17	even	10		484.2.g.f.403.1		16
33.20	odd	10		484.2.g.i.475.1		16
33.26	odd	10		484.2.g.f.239.4		16
33.29	even	10		484.2.g.j.239.1		16
33.32	even	2		484.2.g.i.215.2		16
44.35	even	10	inner	396.2.r.a.343.2		16
132.35	odd	10		44.2.g.a.35.3	✓	16
132.47	even	10		484.2.c.d.483.16		16
132.59	even	10		484.2.g.f.239.1		16
132.71	even	10		484.2.g.j.403.1		16
132.83	odd	10		484.2.g.f.403.4		16
132.95	odd	10		484.2.g.j.239.4		16
132.107	odd	10		484.2.c.d.483.1		16
132.119	even	10		484.2.g.i.475.2		16
132.131	odd	2		484.2.g.i.215.1		16
264.35	odd	10		704.2.u.c.255.2		16
264.101	even	10		704.2.u.c.255.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.2.g.a.35.3	✓	16	132.35	odd	10
44.2.g.a.35.4	yes	16	33.2	even	10
44.2.g.a.39.3	yes	16	3.2	odd	2
44.2.g.a.39.4	yes	16	12.11	even	2
396.2.r.a.127.1		16	4.3	odd	2	inner
396.2.r.a.127.2		16	1.1	even	1	trivial
396.2.r.a.343.1		16	11.2	odd	10	inner
396.2.r.a.343.2		16	44.35	even	10	inner
484.2.c.d.483.1		16	132.107	odd	10
484.2.c.d.483.2		16	33.14	odd	10
484.2.c.d.483.15		16	33.8	even	10
484.2.c.d.483.16		16	132.47	even	10
484.2.g.f.239.1		16	132.59	even	10
484.2.g.f.239.4		16	33.26	odd	10
484.2.g.f.403.1		16	33.17	even	10
484.2.g.f.403.4		16	132.83	odd	10
484.2.g.i.215.1		16	132.131	odd	2
484.2.g.i.215.2		16	33.32	even	2
484.2.g.i.475.1		16	33.20	odd	10
484.2.g.i.475.2		16	132.119	even	10
484.2.g.j.239.1		16	33.29	even	10
484.2.g.j.239.4		16	132.95	odd	10
484.2.g.j.403.1		16	132.71	even	10
484.2.g.j.403.4		16	33.5	odd	10
704.2.u.c.127.2		16	24.5	odd	2
704.2.u.c.127.3		16	24.11	even	2
704.2.u.c.255.2		16	264.35	odd	10
704.2.u.c.255.3		16	264.101	even	10

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Classical	Maass
Hilbert	Bianchi

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	396.2.r.a.127.2

Level	$396$
Weight	$2$
Character	396.127
Analytic conductor	$3.162$
Analytic rank	$0$
Dimension	$16$
Inner twists	$4$