LMFDB - Embedded newform 760.2.p.i.379.52

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [760,2,Mod(379,760)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(760, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("760.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 760 = 2^{3} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	760.p (of order $2$, degree $1$, 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:	$6.06863055362$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.52
Character	$\chi$	$=$	760.379
Dual form			760.2.p.i.379.50

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.39359 + 0.240666i) q^{2} +0.258346 q^{3} +(1.88416 + 0.670777i) q^{4} +(1.58207 + 1.58020i) q^{5} +(0.360027 + 0.0621750i) q^{6} -1.26592 q^{7} +(2.46430 + 1.38824i) q^{8} -2.93326 q^{9} +(1.82445 + 2.58290i) q^{10} +2.83314 q^{11} +(0.486765 + 0.173292i) q^{12} +3.39679i q^{13} +(-1.76416 - 0.304663i) q^{14} +(0.408722 + 0.408239i) q^{15} +(3.10012 + 2.52770i) q^{16} -6.36655i q^{17} +(-4.08774 - 0.705935i) q^{18} +(2.57960 + 3.51364i) q^{19} +(1.92092 + 4.03857i) q^{20} -0.327045 q^{21} +(3.94822 + 0.681840i) q^{22} +3.56413 q^{23} +(0.636643 + 0.358645i) q^{24} +(0.00591838 + 5.00000i) q^{25} +(-0.817492 + 4.73372i) q^{26} -1.53283 q^{27} +(-2.38519 - 0.849149i) q^{28} -3.46592 q^{29} +(0.471340 + 0.667281i) q^{30} -6.48912 q^{31} +(3.71194 + 4.26866i) q^{32} +0.731930 q^{33} +(1.53221 - 8.87233i) q^{34} +(-2.00278 - 2.00041i) q^{35} +(-5.52673 - 1.96756i) q^{36} -6.08243i q^{37} +(2.74928 + 5.51738i) q^{38} +0.877547i q^{39} +(1.70501 + 6.09040i) q^{40} -6.80813i q^{41} +(-0.455764 - 0.0787085i) q^{42} -0.877151i q^{43} +(5.33809 + 1.90041i) q^{44} +(-4.64063 - 4.63514i) q^{45} +(4.96692 + 0.857765i) q^{46} +11.4036 q^{47} +(0.800902 + 0.653021i) q^{48} -5.39745 q^{49} +(-1.19508 + 6.96935i) q^{50} -1.64477i q^{51} +(-2.27849 + 6.40010i) q^{52} -11.8970i q^{53} +(-2.13613 - 0.368900i) q^{54} +(4.48224 + 4.47694i) q^{55} +(-3.11961 - 1.75740i) q^{56} +(0.666429 + 0.907734i) q^{57} +(-4.83005 - 0.834128i) q^{58} +7.80036i q^{59} +(0.496261 + 1.04335i) q^{60} -6.24640i q^{61} +(-9.04315 - 1.56171i) q^{62} +3.71326 q^{63} +(4.14559 + 6.84208i) q^{64} +(-5.36762 + 5.37398i) q^{65} +(1.02001 + 0.176151i) q^{66} +1.66931 q^{67} +(4.27053 - 11.9956i) q^{68} +0.920778 q^{69} +(-2.30961 - 3.26974i) q^{70} -16.1930 q^{71} +(-7.22844 - 4.07206i) q^{72} +2.02240i q^{73} +(1.46383 - 8.47639i) q^{74} +(0.00152899 + 1.29173i) q^{75} +(2.50351 + 8.35060i) q^{76} -3.58652 q^{77} +(-0.211196 + 1.22294i) q^{78} -2.67496 q^{79} +(0.910333 + 8.89783i) q^{80} +8.40377 q^{81} +(1.63848 - 9.48770i) q^{82} -7.93457i q^{83} +(-0.616204 - 0.219374i) q^{84} +(10.0604 - 10.0724i) q^{85} +(0.211100 - 1.22239i) q^{86} -0.895405 q^{87} +(6.98172 + 3.93307i) q^{88} +13.1568i q^{89} +(-5.35159 - 7.57631i) q^{90} -4.30006i q^{91} +(6.71539 + 2.39074i) q^{92} -1.67644 q^{93} +(15.8919 + 2.74446i) q^{94} +(-1.47115 + 9.63513i) q^{95} +(0.958965 + 1.10279i) q^{96} +8.92672 q^{97} +(-7.52181 - 1.29898i) q^{98} -8.31033 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 16 q^{4} - 8 q^{6} + 88 q^{9} + 32 q^{11} + 48 q^{16} - 56 q^{19} + 4 q^{20} - 32 q^{24} + 80 q^{25} + 24 q^{26} + 24 q^{30} + 48 q^{35} - 96 q^{36} + 104 q^{44} - 72 q^{49} + 104 q^{54} + 16 q^{64}+ \cdots - 272 q^{99}+O(q^{100}) $ 56 * q + 16 * q^4 - 8 * q^6 + 88 * q^9 + 32 * q^11 + 48 * q^16 - 56 * q^19 + 4 * q^20 - 32 * q^24 + 80 * q^25 + 24 * q^26 + 24 * q^30 + 48 * q^35 - 96 * q^36 + 104 * q^44 - 72 * q^49 + 104 * q^54 + 16 * q^64 - 24 * q^66 + 64 * q^74 + 88 * q^76 + 128 * q^80 - 168 * q^81 - 96 * q^96 - 272 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/760\mathbb{Z}\right)^\times$.

$n$	$191$	$381$	$401$	$457$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	1.39359	+	0.240666i	0.985414	+	0.170177i
$2$	1.39359	+	0.240666i	0.985414	+	0.170177i
$3$	0.258346			0.149156			0.0745780	−	0.997215i	$-0.476239\pi$
$3$	0.258346			0.149156			0.0745780	+	0.997215i	$0.476239\pi$
$4$	1.88416	+	0.670777i	0.942080	+	0.335388i
$5$	1.58207	+	1.58020i	0.707525	+	0.706688i
$5$	1.58207	+	1.58020i	0.707525	+	0.706688i
$6$	0.360027	+	0.0621750i	0.146980	+	0.0253828i
$7$	−1.26592			−0.478472			−0.239236	−	0.970961i	$-0.576897\pi$
$7$	−1.26592			−0.478472			−0.239236	+	0.970961i	$0.576897\pi$
$8$	2.46430	+	1.38824i	0.871263	+	0.490816i
$9$	−2.93326			−0.977752
$10$	1.82445	+	2.58290i	0.576943	+	0.816784i
$11$	2.83314			0.854224			0.427112	−	0.904199i	$-0.359531\pi$
$11$	2.83314			0.854224			0.427112	+	0.904199i	$0.359531\pi$
$12$	0.486765	+	0.173292i	0.140517	+	0.0500252i
$13$			3.39679i			0.942101i	0.882106	+	0.471050i	$0.156125\pi$
$13$			3.39679i			0.942101i	−0.882106	+	0.471050i	$0.843875\pi$
$14$	−1.76416	−	0.304663i	−0.471493	−	0.0814247i
$15$	0.408722	+	0.408239i	0.105532	+	0.105407i
$16$	3.10012	+	2.52770i	0.775029	+	0.631926i
$17$		−	6.36655i		−	1.54412i	−0.635553	−	0.772058i	$-0.719228\pi$
$17$		−	6.36655i		−	1.54412i	0.635553	−	0.772058i	$-0.280772\pi$
$18$	−4.08774	−	0.705935i	−0.963491	−	0.166391i
$19$	2.57960	+	3.51364i	0.591801	+	0.806084i
$19$	2.57960	+	3.51364i	0.591801	+	0.806084i
$20$	1.92092	+	4.03857i	0.429530	+	0.903053i
$21$	−0.327045			−0.0713670
$22$	3.94822	+	0.681840i	0.841764	+	0.145369i
$23$	3.56413			0.743173			0.371586	−	0.928398i	$-0.378814\pi$
$23$	3.56413			0.743173			0.371586	+	0.928398i	$0.378814\pi$
$24$	0.636643	+	0.358645i	0.129954	+	0.0732082i
$25$	0.00591838	+	5.00000i	0.00118368	+	0.999999i
$26$	−0.817492	+	4.73372i	−0.160323	+	0.928359i
$27$	−1.53283			−0.294994
$28$	−2.38519	−	0.849149i	−0.450759	−	0.160474i
$29$	−3.46592			−0.643604			−0.321802	−	0.946807i	$-0.604289\pi$
$29$	−3.46592			−0.643604			−0.321802	+	0.946807i	$0.604289\pi$
$30$	0.471340	+	0.667281i	0.0860545	+	0.121828i
$31$	−6.48912			−1.16548			−0.582741	−	0.812658i	$-0.698020\pi$
$31$	−6.48912			−1.16548			−0.582741	+	0.812658i	$0.698020\pi$
$32$	3.71194	+	4.26866i	0.656185	+	0.754600i
$33$	0.731930			0.127413
$34$	1.53221	−	8.87233i	0.262772	−	1.52159i
$35$	−2.00278	−	2.00041i	−0.338531	−	0.338130i
$36$	−5.52673	−	1.96756i	−0.921121	−	0.327927i
$37$		−	6.08243i		−	0.999946i	−0.866041	−	0.499973i	$-0.833343\pi$
$37$		−	6.08243i		−	0.999946i	0.866041	−	0.499973i	$-0.166657\pi$
$38$	2.74928	+	5.51738i	0.445992	+	0.895037i
$39$			0.877547i			0.140520i
$40$	1.70501	+	6.09040i	0.269587	+	0.962976i
$41$		−	6.80813i		−	1.06325i	−0.846980	−	0.531625i	$-0.821581\pi$
$41$		−	6.80813i		−	1.06325i	0.846980	−	0.531625i	$-0.178419\pi$
$42$	−0.455764	−	0.0787085i	−0.0703260	−	0.0121450i
$43$		−	0.877151i		−	0.133764i	−0.997761	−	0.0668822i	$-0.978695\pi$
$43$		−	0.877151i		−	0.133764i	0.997761	−	0.0668822i	$-0.0213052\pi$
$44$	5.33809	+	1.90041i	0.804747	+	0.286497i
$45$	−4.64063	−	4.63514i	−0.691784	−	0.690966i
$46$	4.96692	+	0.857765i	0.732332	+	0.126471i
$47$	11.4036			1.66339			0.831694	−	0.555235i	$-0.187372\pi$
$47$	11.4036			1.66339			0.831694	+	0.555235i	$0.187372\pi$
$48$	0.800902	+	0.653021i	0.115600	+	0.0942555i
$49$	−5.39745			−0.771065
$50$	−1.19508	+	6.96935i	−0.169010	+	0.985614i
$51$		−	1.64477i		−	0.230314i
$52$	−2.27849	+	6.40010i	−0.315970	+	0.887534i
$53$		−	11.8970i		−	1.63418i	−0.576509	−	0.817091i	$-0.695585\pi$
$53$		−	11.8970i		−	1.63418i	0.576509	−	0.817091i	$-0.304415\pi$
$54$	−2.13613	−	0.368900i	−0.290691	−	0.0502010i
$55$	4.48224	+	4.47694i	0.604385	+	0.603670i
$56$	−3.11961	−	1.75740i	−0.416875	−	0.234842i
$57$	0.666429	+	0.907734i	0.0882706	+	0.120232i
$58$	−4.83005	−	0.834128i	−0.634216	−	0.109526i
$59$			7.80036i			1.01552i	0.861498	+	0.507760i	$0.169526\pi$
$59$			7.80036i			1.01552i	−0.861498	+	0.507760i	$0.830474\pi$
$60$	0.496261	+	1.04335i	0.0640670	+	0.134696i
$61$		−	6.24640i		−	0.799770i	−0.916565	−	0.399885i	$-0.869050\pi$
$61$		−	6.24640i		−	0.799770i	0.916565	−	0.399885i	$-0.130950\pi$
$62$	−9.04315	−	1.56171i	−1.14848	−	0.198337i
$63$	3.71326			0.467827
$64$	4.14559	+	6.84208i	0.518199	+	0.855260i
$65$	−5.36762	+	5.37398i	−0.665772	+	0.666560i
$66$	1.02001	+	0.176151i	0.125554	+	0.0216826i
$67$	1.66931			0.203939			0.101970	−	0.994788i	$-0.467486\pi$
$67$	1.66931			0.203939			0.101970	+	0.994788i	$0.467486\pi$
$68$	4.27053	−	11.9956i	0.517878	−	1.45468i
$69$	0.920778			0.110849
$70$	−2.30961	−	3.26974i	−0.276051	−	0.390808i
$71$	−16.1930			−1.92176			−0.960878	−	0.276972i	$-0.910669\pi$
$71$	−16.1930			−1.92176			−0.960878	+	0.276972i	$0.910669\pi$
$72$	−7.22844	−	4.07206i	−0.851880	−	0.479897i
$73$			2.02240i			0.236704i	0.992972	+	0.118352i	$0.0377612\pi$
$73$			2.02240i			0.236704i	−0.992972	+	0.118352i	$0.962239\pi$
$74$	1.46383	−	8.47639i	0.170167	−	0.985360i
$75$	0.00152899	+	1.29173i	0.000176552	+	0.149156i
$76$	2.50351	+	8.35060i	0.287172	+	0.957879i
$77$	−3.58652			−0.408722
$78$	−0.211196	+	1.22294i	−0.0239132	+	0.138470i
$79$	−2.67496			−0.300957			−0.150479	−	0.988613i	$-0.548081\pi$
$79$	−2.67496			−0.300957			−0.150479	+	0.988613i	$0.548081\pi$
$80$	0.910333	+	8.89783i	0.101778	+	0.994807i
$81$	8.40377			0.933752
$82$	1.63848	−	9.48770i	0.180940	−	1.04774i
$83$		−	7.93457i		−	0.870932i	−0.900205	−	0.435466i	$-0.856584\pi$
$83$		−	7.93457i		−	0.870932i	0.900205	−	0.435466i	$-0.143416\pi$
$84$	−0.616204	−	0.219374i	−0.0672334	−	0.0239357i
$85$	10.0604	−	10.0724i	1.09121	−	1.09250i
$86$	0.211100	−	1.22239i	0.0227635	−	0.131813i
$87$	−0.895405			−0.0959975
$88$	6.98172	+	3.93307i	0.744254	+	0.419267i
$89$			13.1568i			1.39462i	0.716771	+	0.697308i	$0.245619\pi$
$89$			13.1568i			1.39462i	−0.716771	+	0.697308i	$0.754381\pi$
$90$	−5.35159	−	7.57631i	−0.564108	−	0.798613i
$91$		−	4.30006i		−	0.450769i
$92$	6.71539	+	2.39074i	0.700128	+	0.249252i
$93$	−1.67644			−0.173839
$94$	15.8919	+	2.74446i	1.63912	+	0.283069i
$95$	−1.47115	+	9.63513i	−0.150936	+	0.988543i
$96$	0.958965	+	1.10279i	0.0978740	+	0.112553i
$97$	8.92672			0.906371			0.453186	−	0.891416i	$-0.350287\pi$
$97$	8.92672			0.906371			0.453186	+	0.891416i	$0.350287\pi$
$98$	−7.52181	−	1.29898i	−0.759817	−	0.131217i
$99$	−8.31033			−0.835220
$100$	−3.34273	+	9.42476i	−0.334273	+	0.942476i
$101$		−	10.7056i		−	1.06525i	−0.846351	−	0.532625i	$-0.821205\pi$
$101$		−	10.7056i		−	1.06525i	0.846351	−	0.532625i	$-0.178795\pi$
$102$	0.395840	−	2.29213i	0.0391940	−	0.226955i
$103$		−	2.38512i		−	0.235013i	−0.993072	−	0.117507i	$-0.962510\pi$
$103$		−	2.38512i		−	0.235013i	0.993072	−	0.117507i	$-0.0374901\pi$
$104$	−4.71556	+	8.37073i	−0.462398	+	0.820818i
$105$	−0.517409	−	0.516797i	−0.0504939	−	0.0504342i
$106$	2.86321	−	16.5795i	0.278099	−	1.61034i
$107$	3.43479			0.332054			0.166027	−	0.986121i	$-0.446906\pi$
$107$	3.43479			0.332054			0.166027	+	0.986121i	$0.446906\pi$
$108$	−2.88810	−	1.02819i	−0.277908	−	0.0989375i
$109$	10.0322			0.960908			0.480454	−	0.877020i	$-0.340472\pi$
$109$	10.0322			0.960908			0.480454	+	0.877020i	$0.340472\pi$
$110$	5.16894	+	7.31772i	0.492839	+	0.697717i
$111$		−	1.57137i		−	0.149148i
$112$	−3.92449	−	3.19986i	−0.370830	−	0.302359i
$113$	−12.4513			−1.17132			−0.585660	−	0.810557i	$-0.699165\pi$
$113$	−12.4513			−1.17132			−0.585660	+	0.810557i	$0.699165\pi$
$114$	0.710264	+	1.42539i	0.0665224	+	0.133500i
$115$	5.63872	+	5.63205i	0.525813	+	0.525191i
$116$	−6.53034	−	2.32486i	−0.606327	−	0.215857i
$117$		−	9.96367i		−	0.921142i
$118$	−1.87728	+	10.8705i	−0.172818	+	1.00071i
$119$			8.05953i			0.738816i
$120$	0.440483	+	1.57343i	0.0402105	+	0.143634i
$121$	−2.97331			−0.270301
$122$	1.50330	−	8.70489i	0.136102	−	0.788104i
$123$		−	1.75885i		−	0.158590i
$124$	−12.2265	−	4.35275i	−1.09798	−	0.390889i
$125$	−7.89165	+	7.91972i	−0.705850	+	0.708361i
$126$	5.17475	+	0.893656i	0.461003	+	0.0796132i
$127$		−	15.7250i		−	1.39537i	−0.716406	−	0.697683i	$-0.754214\pi$
$127$		−	15.7250i		−	1.39537i	0.716406	−	0.697683i	$-0.245786\pi$
$128$	4.13058	+	10.5327i	0.365095	+	0.930970i
$129$		−	0.226608i		−	0.0199518i
$130$	−8.77357	+	6.19729i	−0.769493	+	0.543539i
$131$	1.19527			0.104431			0.0522157	−	0.998636i	$-0.483372\pi$
$131$	1.19527			0.104431			0.0522157	+	0.998636i	$0.483372\pi$
$132$	1.37907	+	0.490962i	0.120033	+	0.0427327i
$133$	−3.26556	−	4.44798i	−0.283160	−	0.385689i
$134$	2.32633	+	0.401747i	0.200965	+	0.0347057i
$135$	−2.42505	−	2.42219i	−0.208715	−	0.208469i
$136$	8.83829	−	15.6891i	0.757877	−	1.34533i
$137$		−	15.7323i		−	1.34410i	−0.740506	−	0.672050i	$-0.765414\pi$
$137$		−	15.7323i		−	1.34410i	0.740506	−	0.672050i	$-0.234586\pi$
$138$	1.28318	+	0.221600i	0.109232	+	0.0188638i
$139$	−11.5489			−0.979569			−0.489784	−	0.871844i	$-0.662924\pi$
$139$	−11.5489			−0.979569			−0.489784	+	0.871844i	$0.662924\pi$
$140$	−2.43172	−	5.11250i	−0.205518	−	0.432085i
$141$	2.94607			0.248104
$142$	−22.5663	−	3.89710i	−1.89372	−	0.327038i
$143$			9.62359i			0.804765i
$144$	−9.09344	−	7.41440i	−0.757787	−	0.617867i
$145$	−5.48334	−	5.47685i	−0.455366	−	0.454828i
$146$	−0.486724	+	2.81839i	−0.0402815	+	0.233252i
$147$	−1.39441			−0.115009
$148$	4.07996	−	11.4603i	0.335370	−	0.942029i
$149$		−	10.4075i		−	0.852612i	−0.904579	−	0.426306i	$-0.859815\pi$
$149$		−	10.4075i		−	0.852612i	0.904579	−	0.426306i	$-0.140185\pi$
$150$	−0.308744	+	1.80050i	−0.0252089	+	0.147010i
$151$	18.8692			1.53556			0.767778	−	0.640716i	$-0.221363\pi$
$151$	18.8692			1.53556			0.767778	+	0.640716i	$0.221363\pi$
$152$	1.47915	+	12.2398i	0.119975	+	0.992777i
$153$			18.6747i			1.50976i
$154$	−4.99813	−	0.863154i	−0.402761	−	0.0695549i
$155$	−10.2663	−	10.2541i	−0.824607	−	0.823632i
$156$	−0.588639	+	1.65344i	−0.0471288	+	0.132381i
$157$	−16.4356			−1.31171			−0.655854	−	0.754888i	$-0.727691\pi$
$157$	−16.4356			−1.31171			−0.655854	+	0.754888i	$0.727691\pi$
$158$	−3.72779	−	0.643773i	−0.296567	−	0.0512158i
$159$		−	3.07355i		−	0.243748i
$160$	−0.872777	+	12.6190i	−0.0689991	+	0.997617i
$161$	−4.51190			−0.355587
$162$	11.7114	+	2.02250i	0.920132	+	0.158903i
$163$			12.2060i			0.956049i	0.878346	+	0.478025i	$0.158647\pi$
$163$			12.2060i			0.956049i	−0.878346	+	0.478025i	$0.841353\pi$
$164$	4.56673	−	12.8276i	0.356602	−	1.00167i
$165$	1.15797	+	1.15660i	0.0901477	+	0.0900410i
$166$	1.90958	−	11.0575i	0.148212	−	0.858228i
$167$			17.3005i			1.33875i	0.742923	+	0.669377i	$0.233439\pi$
$167$			17.3005i			1.33875i	−0.742923	+	0.669377i	$0.766561\pi$
$168$	−0.805937	−	0.454016i	−0.0621794	−	0.0350281i
$169$	1.46180			0.112446
$170$	16.4442	−	11.6155i	1.26121	−	0.890867i
$171$	−7.56663	−	10.3064i	−0.578635	−	0.788151i
$172$	0.588373	−	1.65269i	0.0448630	−	0.126017i
$173$			7.90043i			0.600659i	0.953836	+	0.300329i	$0.0970966\pi$
$173$			7.90043i			0.600659i	−0.953836	+	0.300329i	$0.902903\pi$
$174$	−1.24782	−	0.215493i	−0.0945972	−	0.0163365i
$175$	−0.00749218	−	6.32959i	−0.000566355	−	0.478472i
$176$	8.78307	+	7.16134i	0.662049	+	0.539806i
$177$			2.01519i			0.151471i
$178$	−3.16639	+	18.3351i	−0.237331	+	1.37427i
$179$		−	8.15538i		−	0.609562i	−0.952423	−	0.304781i	$-0.901417\pi$
$179$		−	8.15538i		−	0.609562i	0.952423	−	0.304781i	$-0.0985832\pi$
$180$	−5.63454	−	11.8462i	−0.419974	−	0.882962i
$181$	−17.8284			−1.32517			−0.662586	−	0.748986i	$-0.730541\pi$
$181$	−17.8284			−1.32517			−0.662586	+	0.748986i	$0.730541\pi$
$182$	1.03488	−	5.99250i	0.0767103	−	0.444194i
$183$		−	1.61373i		−	0.119290i
$184$	8.78310	+	4.94786i	0.647499	+	0.364761i
$185$	9.61148	−	9.62286i	0.706650	−	0.707487i
$186$	−2.33626	−	0.403461i	−0.171303	−	0.0295832i
$187$		−	18.0373i		−	1.31902i
$188$	21.4862	+	7.64928i	1.56704	+	0.557881i
$189$	1.94044			0.141146
$190$	−4.36902	+	13.0733i	−0.316962	+	0.948438i
$191$			3.46078i			0.250413i	0.992131	+	0.125207i	$0.0399594\pi$
$191$			3.46078i			0.250413i	−0.992131	+	0.125207i	$0.960041\pi$
$192$	1.07100	+	1.76762i	0.0772925	+	0.127567i
$193$	−17.6215			−1.26842			−0.634212	−	0.773159i	$-0.718675\pi$
$193$	−17.6215			−1.26842			−0.634212	+	0.773159i	$0.718675\pi$
$194$	12.4401	+	2.14836i	0.893151	+	0.154243i
$195$	−1.38670	+	1.38835i	−0.0993038	+	0.0994215i
$196$	−10.1697	−	3.62049i	−0.726404	−	0.258606i
$197$	−5.06945			−0.361184			−0.180592	−	0.983558i	$-0.557801\pi$
$197$	−5.06945			−0.361184			−0.180592	+	0.983558i	$0.557801\pi$
$198$	−11.5812	−	2.00001i	−0.823037	−	0.142135i
$199$		−	8.88628i		−	0.629932i	−0.949103	−	0.314966i	$-0.898007\pi$
$199$		−	8.88628i		−	0.629932i	0.949103	−	0.314966i	$-0.101993\pi$
$200$	−6.92660	+	12.3297i	−0.489785	+	0.871843i
$201$	0.431261			0.0304188
$202$	2.57648	−	14.9192i	0.181281	−	1.04971i
$203$	4.38756			0.307947
$204$	1.10327	−	3.09901i	0.0772447	−	0.216974i
$205$	10.7582	−	10.7710i	0.751387	−	0.752277i
$206$	0.574018	−	3.32387i	0.0399937	−	0.231585i
$207$	−10.4545			−0.726639
$208$	−8.58608	+	10.5305i	−0.595338	+	0.730156i
$209$	7.30837	+	9.95464i	0.505530	+	0.688577i
$210$	−0.596678	−	0.844723i	−0.0411747	−	0.0582914i
$211$			21.3887i			1.47246i	0.676733	+	0.736228i	$0.263395\pi$
$211$			21.3887i			1.47246i	−0.676733	+	0.736228i	$0.736605\pi$
$212$	7.98025	−	22.4159i	0.548086	−	1.53953i
$213$	−4.18339			−0.286641
$214$	4.78668	+	0.826638i	0.327210	+	0.0565078i
$215$	1.38608	−	1.38772i	0.0945297	−	0.0946416i
$216$	−3.77736	−	2.12794i	−0.257017	−	0.144788i
$217$	8.21470			0.557650
$218$	13.9807	+	2.41440i	0.946892	+	0.163524i
$219$			0.522479i			0.0353059i
$220$	5.44223	+	11.4418i	0.366915	+	0.771409i
$221$	21.6259			1.45471
$222$	0.378175	−	2.18984i	0.0253815	−	0.146972i
$223$			4.33931i			0.290582i	0.989389	+	0.145291i	$0.0464118\pi$
$223$			4.33931i			0.290582i	−0.989389	+	0.145291i	$0.953588\pi$
$224$	−4.69902	−	5.40377i	−0.313966	−	0.361055i
$225$	−0.0173601	−	14.6663i	−0.00115734	−	0.977752i
$226$	−17.3520	−	2.99661i	−1.15424	−	0.199331i
$227$	−7.50030			−0.497813			−0.248906	−	0.968528i	$-0.580071\pi$
$227$	−7.50030			−0.497813			−0.248906	+	0.968528i	$0.580071\pi$
$228$	0.646771	+	2.15734i	0.0428334	+	0.142873i
$229$			0.338427i			0.0223639i	0.999937	+	0.0111819i	$0.00355939\pi$
$229$			0.338427i			0.0223639i	−0.999937	+	0.0111819i	$0.996441\pi$
$230$	6.50259	+	9.20579i	0.428768	+	0.607012i
$231$	−0.926563			−0.0609634
$232$	−8.54107	−	4.81152i	−0.560749	−	0.315891i
$233$			22.9496i			1.50348i	0.659459	+	0.751741i	$0.270785\pi$
$233$			22.9496i			1.50348i	−0.659459	+	0.751741i	$0.729215\pi$
$234$	2.39792	−	13.8852i	0.156757	−	0.907705i
$235$	18.0414	+	18.0200i	1.17689	+	1.17550i
$236$	−5.23230	+	14.6971i	−0.340594	+	0.956701i
$237$	−0.691066			−0.0448896
$238$	−1.93965	+	11.2316i	−0.125729	+	0.728039i
$239$			27.8657i			1.80248i	0.433316	+	0.901242i	$0.357343\pi$
$239$			27.8657i			1.80248i	−0.433316	+	0.901242i	$0.642657\pi$
$240$	0.235181	+	2.29872i	0.0151808	+	0.148381i
$241$		−	12.9409i		−	0.833600i	−0.908998	−	0.416800i	$-0.863152\pi$
$241$		−	12.9409i		−	0.833600i	0.908998	−	0.416800i	$-0.136848\pi$
$242$	−4.14356	−	0.715575i	−0.266358	−	0.0459989i
$243$	6.76958			0.434268
$244$	4.18994	−	11.7692i	0.268234	−	0.753447i
$245$	−8.53917	−	8.52907i	−0.545548	−	0.544902i
$246$	0.423295	−	2.45111i	0.0269883	−	0.156277i
$247$	−11.9351	+	8.76237i	−0.759413	+	0.557536i
$248$	−15.9912	−	9.00845i	−1.01544	−	0.572037i
$249$		−	2.04986i		−	0.129905i
$250$	−12.9037	+	9.13755i	−0.816101	+	0.577910i
$251$	18.6666			1.17822			0.589112	−	0.808051i	$-0.299478\pi$
$251$	18.6666			1.17822			0.589112	+	0.808051i	$0.299478\pi$
$252$	6.99638	+	2.49077i	0.440731	+	0.156904i
$253$	10.0977			0.634836
$254$	3.78447	−	21.9141i	0.237459	−	1.37501i
$255$	2.59907	−	2.60215i	0.162760	−	0.162953i
$256$	3.22144	+	15.6723i	0.201340	+	0.979521i
$257$	14.0960			0.879281			0.439641	−	0.898174i	$-0.355106\pi$
$257$	14.0960			0.879281			0.439641	+	0.898174i	$0.355106\pi$
$258$	0.0545369	−	0.315798i	0.00339532	−	0.0196607i
$259$			7.69986i			0.478446i
$260$	−13.7182	+	6.52496i	−0.850767	+	0.404661i
$261$	10.1664			0.629286
$262$	1.66571	+	0.287661i	0.102908	+	0.0177718i
$263$	9.76231			0.601970			0.300985	−	0.953629i	$-0.402685\pi$
$263$	9.76231			0.601970			0.300985	+	0.953629i	$0.402685\pi$
$264$	1.80370	+	1.01609i	0.111010	+	0.0625362i
$265$	18.7997	−	18.8220i	1.15486	−	1.15622i
$266$	−3.48036	−	6.98455i	−0.213395	−	0.428250i
$267$			3.39900i			0.208015i
$268$	3.14526	+	1.11974i	0.192127	+	0.0683989i
$269$	17.3225			1.05617			0.528087	−	0.849190i	$-0.322909\pi$
$269$	17.3225			1.05617			0.528087	+	0.849190i	$0.322909\pi$
$270$	−2.79658	−	3.95915i	−0.170195	−	0.240946i
$271$			7.60484i			0.461961i	0.972958	+	0.230980i	$0.0741934\pi$
$271$			7.60484i			0.461961i	−0.972958	+	0.230980i	$0.925807\pi$
$272$	16.0927	−	19.7370i	0.975766	−	1.19673i
$273$		−	1.11090i		−	0.0672349i
$274$	3.78622	−	21.9243i	0.228734	−	1.32449i
$275$	0.0167676	+	14.1657i	0.00101112	+	0.854224i
$276$	1.73489	+	0.617637i	0.104428	+	0.0371774i
$277$	−6.73071			−0.404409			−0.202205	−	0.979343i	$-0.564811\pi$
$277$	−6.73071			−0.404409			−0.202205	+	0.979343i	$0.564811\pi$
$278$	−16.0944	−	2.77944i	−0.965280	−	0.166700i
$279$	19.0343			1.13955
$280$	−2.15841	−	7.70994i	−0.128990	−	0.460757i
$281$			1.13819i			0.0678990i	0.999424	+	0.0339495i	$0.0108085\pi$
$281$			1.13819i			0.0678990i	−0.999424	+	0.0339495i	$0.989191\pi$
$282$	4.10561	+	0.709020i	0.244485	+	0.0422215i
$283$		−	18.7657i		−	1.11550i	−0.830007	−	0.557752i	$-0.811664\pi$
$283$		−	18.7657i		−	1.11550i	0.830007	−	0.557752i	$-0.188336\pi$
$284$	−30.5102	−	10.8619i	−1.81045	−	0.644535i
$285$	−0.380065	+	2.48920i	−0.0225131	+	0.147447i
$286$	−2.31607	+	13.4113i	−0.136952	+	0.793027i
$287$			8.61853i			0.508736i
$288$	−10.8881	−	12.5211i	−0.641587	−	0.737812i
$289$	−23.5330			−1.38429
$290$	−6.32340	−	8.95211i	−0.371323	−	0.525686i
$291$	2.30618			0.135191
$292$	−1.35658	+	3.81053i	−0.0793879	+	0.222994i
$293$			15.7782i			0.921772i	0.887459	+	0.460886i	$0.152468\pi$
$293$			15.7782i			0.921772i	−0.887459	+	0.460886i	$0.847532\pi$
$294$	−1.94323	−	0.335587i	−0.113331	−	0.0195718i
$295$	−12.3262	+	12.3408i	−0.717656	+	0.718506i
$296$	8.44386	−	14.9890i	0.490790	−	0.871216i
$297$	−4.34273			−0.251991
$298$	2.50472	−	14.5037i	0.145095	−	0.840176i
$299$			12.1066i			0.700144i
$300$	−0.863581	+	2.43485i	−0.0498588	+	0.140576i
$301$			1.11040i			0.0640025i
$302$	26.2959	+	4.54118i	1.51316	+	0.261315i
$303$		−	2.76576i		−	0.158889i
$304$	−0.884378	+	17.4132i	−0.0507225	+	0.998713i
$305$	9.87058	−	9.88227i	0.565188	−	0.565857i
$306$	−4.49437	+	26.0248i	−0.256926	+	1.48774i
$307$	23.7035			1.35283			0.676416	−	0.736520i	$-0.263532\pi$
$307$	23.7035			1.35283			0.676416	+	0.736520i	$0.263532\pi$
$308$	−6.75758	−	2.40576i	−0.385049	−	0.137081i
$309$		−	0.616187i		−	0.0350536i
$310$	−11.8391	−	16.7607i	−0.672416	−	0.951947i
$311$			34.2107i			1.93991i	0.243287	+	0.969954i	$0.421774\pi$
$311$			34.2107i			1.93991i	−0.243287	+	0.969954i	$0.578226\pi$
$312$	−1.21824	+	2.16254i	−0.0689695	+	0.122430i
$313$		−	1.98923i		−	0.112438i	−0.998418	−	0.0562189i	$-0.982096\pi$
$313$		−	1.98923i		−	0.112438i	0.998418	−	0.0562189i	$-0.0179045\pi$
$314$	−22.9045	−	3.95550i	−1.29257	−	0.223222i
$315$	5.87466	+	5.86771i	0.330999	+	0.330608i
$316$	−5.04006	−	1.79430i	−0.283526	−	0.100938i
$317$		−	2.31382i		−	0.129957i	−0.997887	−	0.0649784i	$-0.979302\pi$
$317$		−	2.31382i		−	0.129957i	0.997887	−	0.0649784i	$-0.0206979\pi$
$318$	0.739698	−	4.28325i	0.0414802	−	0.240193i
$319$	−9.81943			−0.549782
$320$	−4.25324	+	17.3756i	−0.237764	+	0.971323i
$321$	0.887364			0.0495278
$322$	−6.28771	−	1.08586i	−0.350401	−	0.0605126i
$323$	22.3698	−	16.4231i	1.24469	−	0.913808i
$324$	15.8340	+	5.63706i	0.879669	+	0.313170i
$325$	−16.9840	+	0.0201035i	−0.942100	+	0.00111514i
$326$	−2.93757	+	17.0101i	−0.162697	+	0.942104i
$327$	2.59177			0.143325
$328$	9.45130	−	16.7773i	0.521861	−	0.926371i
$329$	−14.4360			−0.795884
$330$	1.33537	+	1.89050i	0.0735099	+	0.104069i
$331$		−	15.8426i		−	0.870788i	−0.900240	−	0.435394i	$-0.856609\pi$
$331$		−	15.8426i		−	0.870788i	0.900240	−	0.435394i	$-0.143391\pi$
$332$	5.32232	−	14.9500i	0.292100	−	0.820487i
$333$			17.8413i			0.977699i
$334$	−4.16364	+	24.1097i	−0.227824	+	1.31923i
$335$	2.64098	+	2.63786i	0.144292	+	0.144121i
$336$	−1.01388	−	0.826671i	−0.0553115	−	0.0450986i
$337$	−13.5306			−0.737060			−0.368530	−	0.929616i	$-0.620139\pi$
$337$	−13.5306			−0.737060			−0.368530	+	0.929616i	$0.620139\pi$
$338$	2.03714	+	0.351804i	0.110806	+	0.0191356i
$339$	−3.21674			−0.174709
$340$	25.7118	−	12.2296i	1.39442	−	0.663244i
$341$	−18.3846			−0.995582
$342$	−8.06434	−	16.1839i	−0.436070	−	0.875125i
$343$	15.6942			0.847405
$344$	1.21769	−	2.16157i	0.0656537	−	0.116544i
$345$	1.45674	+	1.45502i	0.0784282	+	0.0783354i
$346$	−1.90137	+	11.0099i	−0.102218	+	0.591897i
$347$			12.7659i			0.685310i	0.939461	+	0.342655i	$0.111326\pi$
$347$			12.7659i			0.685310i	−0.939461	+	0.342655i	$0.888674\pi$
$348$	−1.68709	−	0.600617i	−0.0904373	−	0.0321964i
$349$			34.7739i			1.86141i	0.365777	+	0.930703i	$0.380803\pi$
$349$			34.7739i			1.86141i	−0.365777	+	0.930703i	$0.619197\pi$
$350$	1.51287	−	8.82262i	0.0808665	−	0.471589i
$351$		−	5.20671i		−	0.277914i
$352$	10.5165	+	12.0937i	0.560529	+	0.644597i
$353$			21.5755i			1.14835i	0.818734	+	0.574173i	$0.194676\pi$
$353$			21.5755i			1.14835i	−0.818734	+	0.574173i	$0.805324\pi$
$354$	−0.484988	+	2.80834i	−0.0257768	+	0.149262i
$355$	−25.6185	−	25.5882i	−1.35969	−	1.35808i
$356$	−8.82527	+	24.7895i	−0.467738	+	1.31384i
$357$			2.08215i			0.110199i
$358$	1.96272	−	11.3652i	0.103733	−	0.600670i
$359$		−	10.7320i		−	0.566414i	−0.959059	−	0.283207i	$-0.908602\pi$
$359$		−	10.7320i		−	0.566414i	0.959059	−	0.283207i	$-0.0913983\pi$
$360$	−5.00125	−	17.8647i	−0.263589	−	0.941552i
$361$	−5.69134	+	18.1276i	−0.299544	+	0.954082i
$362$	−24.8453	−	4.29068i	−1.30584	−	0.225513i
$363$	−0.768143			−0.0403170
$364$	2.88438	−	8.10200i	0.151183	−	0.424660i
$365$	−3.19581	+	3.19959i	−0.167276	+	0.167474i
$366$	0.388370	−	2.24887i	0.0203004	−	0.117550i
$367$	10.8547			0.566610			0.283305	−	0.959030i	$-0.408569\pi$
$367$	10.8547			0.566610			0.283305	+	0.959030i	$0.408569\pi$
$368$	11.0492	+	9.00906i	0.575980	+	0.469630i
$369$			19.9700i			1.03960i
$370$	15.7103	−	11.0971i	0.816740	−	0.576912i
$371$			15.0607i			0.781910i
$372$	−3.15868	−	1.12452i	−0.163770	−	0.0583034i
$373$		−	17.8817i		−	0.925880i	−0.886390	−	0.462940i	$-0.846795\pi$
$373$		−	17.8817i		−	0.925880i	0.886390	−	0.462940i	$-0.153205\pi$
$374$	4.34097	−	25.1366i	0.224466	−	1.29978i
$375$	−2.03877	+	2.04603i	−0.105282	+	0.105656i
$376$	28.1020	+	15.8309i	1.44925	+	0.816418i
$377$		−	11.7730i		−	0.606340i
$378$	2.70417	+	0.466998i	0.139087	+	0.0240198i
$379$			28.5443i			1.46622i	0.680108	+	0.733112i	$0.261933\pi$
$379$			28.5443i			1.46622i	−0.680108	+	0.733112i	$0.738067\pi$
$380$	−9.23490	+	17.1673i	−0.473740	+	0.880665i
$381$		−	4.06248i		−	0.208127i
$382$	−0.832892	+	4.82290i	−0.0426145	+	0.246761i
$383$			9.33603i			0.477049i	0.971137	+	0.238524i	$0.0766637\pi$
$383$			9.33603i			0.477049i	−0.971137	+	0.238524i	$0.923336\pi$
$384$	1.06712	+	2.72109i	0.0544561	+	0.138860i
$385$	−5.67415	−	5.66743i	−0.289181	−	0.288839i
$386$	−24.5571	−	4.24090i	−1.24992	−	0.215856i
$387$			2.57291i			0.130788i
$388$	16.8194	+	5.98784i	0.853874	+	0.303986i
$389$		−	6.20496i		−	0.314604i	−0.987551	−	0.157302i	$-0.949720\pi$
$389$		−	6.20496i		−	0.314604i	0.987551	−	0.157302i	$-0.0502796\pi$
$390$	−2.26662	+	1.60105i	−0.114775	+	0.0810721i
$391$		−	22.6912i		−	1.14754i
$392$	−13.3010	−	7.49295i	−0.671800	−	0.378451i
$393$	0.308793			0.0155766
$394$	−7.06472	−	1.22005i	−0.355915	−	0.0614650i
$395$	−4.23199	−	4.22699i	−0.212935	−	0.212683i
$396$	−15.6580	−	5.57438i	−0.786844	−	0.280123i
$397$	6.06521			0.304404			0.152202	−	0.988349i	$-0.451364\pi$
$397$	6.06521			0.304404			0.152202	+	0.988349i	$0.451364\pi$
$398$	2.13863	−	12.3838i	0.107200	−	0.620743i
$399$	−0.843644	−	1.14912i	−0.0422350	−	0.0575278i
$400$	−12.6202	+	15.5155i	−0.631008	+	0.775777i
$401$		−	31.9497i		−	1.59549i	−0.602993	−	0.797746i	$-0.706026\pi$
$401$		−	31.9497i		−	1.59549i	0.602993	−	0.797746i	$-0.293974\pi$
$402$	0.600998	+	0.103790i	0.0299751	+	0.00517656i
$403$		−	22.0422i		−	1.09800i
$404$	7.18110	−	20.1711i	0.357273	−	1.00355i
$405$	13.2954	+	13.2797i	0.660653	+	0.659872i
$406$	6.11444	+	1.05594i	0.303455	+	0.0524053i
$407$		−	17.2324i		−	0.854178i
$408$	2.28333	−	4.05322i	0.113042	−	0.200664i
$409$			18.6694i			0.923140i	0.887104	+	0.461570i	$0.152714\pi$
$409$			18.6694i			0.923140i	−0.887104	+	0.461570i	$0.847286\pi$
$410$	17.5847	−	12.4211i	0.868446	−	0.613435i
$411$		−	4.06437i		−	0.200481i
$412$	1.59989	−	4.49395i	0.0788207	−	0.221401i
$413$		−	9.87462i		−	0.485898i
$414$	−14.5693	−	2.51604i	−0.716040	−	0.123657i
$415$	12.5382	−	12.5531i	0.615477	−	0.616206i
$416$	−14.4998	+	12.6087i	−0.710909	+	0.618193i
$417$	−2.98362			−0.146109
$418$	7.78909	+	15.6315i	0.380977	+	0.764562i
$419$	−5.03419			−0.245936			−0.122968	−	0.992411i	$-0.539241\pi$
$419$	−5.03419			−0.245936			−0.122968	+	0.992411i	$0.539241\pi$
$420$	−0.628226	−	1.32079i	−0.0306543	−	0.0644481i
$421$	−0.685583			−0.0334133			−0.0167066	−	0.999860i	$-0.505318\pi$
$421$	−0.685583			−0.0334133			−0.0167066	+	0.999860i	$0.505318\pi$
$422$	−5.14752	+	29.8069i	−0.250578	+	1.45098i
$423$	−33.4497			−1.62638
$424$	16.5159	−	29.3179i	0.802083	−	1.42380i
$425$	31.8327	−	0.0376796i	1.54411	−	0.00182773i
$426$	−5.82992	−	1.00680i	−0.282460	−	0.0487796i
$427$			7.90743i			0.382667i
$428$	6.47170	+	2.30398i	0.312821	+	0.111367i
$429$			2.48622i			0.120036i
$430$	2.26559	−	1.60032i	0.109257	−	0.0771744i
$431$	25.7307			1.23940			0.619701	−	0.784838i	$-0.287254\pi$
$431$	25.7307			1.23940			0.619701	+	0.784838i	$0.287254\pi$
$432$	−4.75196	−	3.87454i	−0.228629	−	0.186414i
$433$	−14.9829			−0.720031			−0.360015	−	0.932946i	$-0.617229\pi$
$433$	−14.9829			−0.720031			−0.360015	+	0.932946i	$0.617229\pi$
$434$	11.4479	+	1.97700i	0.549516	+	0.0948989i
$435$	−1.41660	−	1.41492i	−0.0679206	−	0.0678403i
$436$	18.9022	+	6.72935i	0.905252	+	0.322277i
$437$	9.19403	+	12.5231i	0.439810	+	0.599060i
$438$	−0.125743	+	0.728120i	−0.00600823	+	0.0347909i
$439$	10.9574			0.522967			0.261483	−	0.965208i	$-0.415788\pi$
$439$	10.9574			0.522967			0.261483	+	0.965208i	$0.415788\pi$
$440$	4.83055	+	17.2550i	0.230287	+	0.822597i
$441$	15.8321			0.753910
$442$	30.1375	+	5.20461i	1.43349	+	0.247558i
$443$		−	20.5245i		−	0.975151i	−0.873081	−	0.487575i	$-0.837881\pi$
$443$		−	20.5245i		−	0.975151i	0.873081	−	0.487575i	$-0.162119\pi$
$444$	1.05404	−	2.96071i	0.0500225	−	0.140509i
$445$	−20.7904	+	20.8150i	−0.985559	+	0.986726i
$446$	−1.04432	+	6.04720i	−0.0494502	+	0.286343i
$447$		−	2.68872i		−	0.127172i
$448$	−5.24798	−	8.66151i	−0.247944	−	0.409218i
$449$		−	14.7788i		−	0.697456i	−0.937224	−	0.348728i	$-0.886614\pi$
$449$		−	14.7788i		−	0.697456i	0.937224	−	0.348728i	$-0.113386\pi$
$450$	3.50548	−	20.4429i	0.165250	−	0.963687i
$451$		−	19.2884i		−	0.908254i
$452$	−23.4603	−	8.35205i	−1.10348	−	0.392847i
$453$	4.87478			0.229037
$454$	−10.4523	−	1.80507i	−0.490551	−	0.0847160i
$455$	6.79497	−	6.80302i	0.318553	−	0.318930i
$456$	0.382132	+	3.16209i	0.0178950	+	0.148079i
$457$		−	0.894681i		−	0.0418514i	−0.999781	−	0.0209257i	$-0.993339\pi$
$457$		−	0.894681i		−	0.0418514i	0.999781	−	0.0209257i	$-0.00666135\pi$
$458$	−0.0814478	+	0.471627i	−0.00380581	+	0.0220377i
$459$			9.75885i			0.455504i
$460$	6.84640	+	14.3940i	0.319215	+	0.671124i
$461$			35.1230i			1.63584i	0.575331	+	0.817921i	$0.304873\pi$
$461$			35.1230i			1.63584i	−0.575331	+	0.817921i	$0.695127\pi$
$462$	−1.29125	−	0.222992i	−0.0600742	−	0.0103745i
$463$	−39.4988			−1.83566			−0.917832	−	0.396970i	$-0.870062\pi$
$463$	−39.4988			−1.83566			−0.917832	+	0.396970i	$0.870062\pi$
$464$	−10.7447	−	8.76080i	−0.498812	−	0.406710i
$465$	−2.65225	−	2.64911i	−0.122995	−	0.122850i
$466$	−5.52320	+	31.9823i	−0.255857	+	1.48155i
$467$			1.64539i			0.0761395i	0.999275	+	0.0380698i	$0.0121209\pi$
$467$			1.64539i			0.0761395i	−0.999275	+	0.0380698i	$0.987879\pi$
$468$	6.68340	−	18.7731i	0.308940	−	0.867789i
$469$	−2.11322			−0.0975792
$470$	20.8054	+	29.4544i	0.959680	+	1.35863i
$471$	−4.24608			−0.195649
$472$	−10.8288	+	19.2225i	−0.498434	+	0.884786i
$473$		−	2.48509i		−	0.114265i
$474$	−0.963059	−	0.166316i	−0.0442348	−	0.00763915i
$475$	−17.5529	+	12.9188i	−0.805383	+	0.592754i
$476$	−5.40615	+	15.1854i	−0.247790	+	0.696024i
$477$			34.8970i			1.59782i
$478$	−6.70633	+	38.8333i	−0.306740	+	1.77619i
$479$			16.7454i			0.765118i	0.923931	+	0.382559i	$0.124957\pi$
$479$			16.7454i			0.765118i	−0.923931	+	0.382559i	$0.875043\pi$
$480$	−0.225478	+	3.26006i	−0.0102916	+	0.148801i
$481$	20.6608			0.942050
$482$	3.11445	−	18.0343i	0.141859	−	0.821441i
$483$	−1.16563			−0.0530380
$484$	−5.60220	−	1.99443i	−0.254645	−	0.0906559i
$485$	14.1227	+	14.1060i	0.641280	+	0.640522i
$486$	9.43398	+	1.62921i	0.427934	+	0.0739023i
$487$		−	17.3149i		−	0.784615i	−0.919834	−	0.392308i	$-0.871677\pi$
$487$		−	17.3149i		−	0.784615i	0.919834	−	0.392308i	$-0.128323\pi$
$488$	8.67149	−	15.3930i	0.392540	−	0.696810i
$489$			3.15337i			0.142600i
$490$	−9.84741	−	13.9411i	−0.444860	−	0.629793i
$491$	−15.2044			−0.686164			−0.343082	−	0.939305i	$-0.611471\pi$
$491$	−15.2044			−0.686164			−0.343082	+	0.939305i	$0.611471\pi$
$492$	1.17980	−	3.31396i	0.0531893	−	0.149405i
$493$			22.0659i			0.993799i
$494$	−18.7414	+	9.33873i	−0.843215	+	0.420169i
$495$	−13.1476	−	13.1320i	−0.590939	−	0.590240i
$496$	−20.1170	−	16.4026i	−0.903282	−	0.736497i
$497$	20.4990			0.919506
$498$	0.493332	−	2.85666i	0.0221067	−	0.128010i
$499$	22.8249			1.02178			0.510892	−	0.859645i	$-0.329315\pi$
$499$	22.8249			1.02178			0.510892	+	0.859645i	$0.329315\pi$
$500$	−20.1815	+	9.62848i	−0.902543	+	0.430599i
$501$			4.46951i			0.199683i
$502$	26.0135	+	4.49241i	1.16104	+	0.200506i
$503$	−5.72316			−0.255183			−0.127591	−	0.991827i	$-0.540725\pi$
$503$	−5.72316			−0.255183			−0.127591	+	0.991827i	$0.540725\pi$
$504$	9.15061	+	5.15489i	0.407601	+	0.229617i
$505$	16.9171	−	16.9371i	0.752800	−	0.753692i
$506$	14.0720	+	2.43017i	0.625576	+	0.108034i
$507$	0.377649			0.0167720
$508$	10.5480	−	29.6284i	0.467990	−	1.31455i
$509$	19.9910			0.886084			0.443042	−	0.896501i	$-0.353899\pi$
$509$	19.9910			0.886084			0.443042	+	0.896501i	$0.353899\pi$
$510$	4.24828	−	3.00081i	0.188117	−	0.132878i
$511$		−	2.56020i		−	0.113256i
$512$	0.717559	+	22.6160i	0.0317119	+	0.999497i
$513$	−3.95409	−	5.38582i	−0.174577	−	0.237790i
$514$	19.6439	+	3.39242i	0.866456	+	0.149633i
$515$	3.76898	−	3.77344i	0.166081	−	0.166278i
$516$	0.152004	−	0.426966i	0.00669159	−	0.0187961i
$517$	32.3080			1.42091
$518$	−1.85309	+	10.7304i	−0.0814203	+	0.471467i
$519$			2.04104i			0.0895919i
$520$	−20.6878	+	5.79158i	−0.907221	+	0.253978i
$521$			22.5450i			0.987715i	0.869543	+	0.493858i	$0.164414\pi$
$521$			22.5450i			0.987715i	−0.869543	+	0.493858i	$0.835586\pi$
$522$	14.1678	+	2.44671i	0.620107	+	0.107090i
$523$	43.1323			1.88604			0.943022	−	0.332731i	$-0.107970\pi$
$523$	43.1323			1.88604			0.943022	+	0.332731i	$0.107970\pi$
$524$	2.25208	+	0.801760i	0.0983826	+	0.0350251i
$525$	−0.00193557	−	1.63522i	−8.44753e−5	−	0.0713669i
$526$	13.6046	+	2.34945i	0.593189	+	0.102441i
$527$			41.3133i			1.79964i
$528$	2.26907	+	1.85010i	0.0987485	+	0.0805153i
$529$	−10.2970			−0.447694
$530$	30.7288	−	21.7056i	1.33477	−	0.942830i
$531$		−	22.8805i		−	0.992928i
$532$	−3.16924	−	10.5712i	−0.137404	−	0.458318i
$533$	23.1258			1.00169
$534$	−0.818024	+	4.73680i	−0.0353993	+	0.204981i
$535$	5.43410	+	5.42767i	0.234937	+	0.234659i
$536$	4.11370	+	2.31741i	0.177685	+	0.100097i
$537$		−	2.10691i		−	0.0909198i
$538$	24.1404	+	4.16895i	1.04077	+	0.179736i
$539$	−15.2917			−0.658662
$540$	−2.94444	−	6.19046i	−0.126709	−	0.266395i
$541$			4.22591i			0.181686i	0.995865	+	0.0908430i	$0.0289561\pi$
$541$			4.22591i			0.181686i	−0.995865	+	0.0908430i	$0.971044\pi$
$542$	−1.83023	+	10.5980i	−0.0786149	+	0.455223i
$543$	−4.60588			−0.197657
$544$	27.1766	−	23.6323i	1.16519	−	1.01323i
$545$	15.8716	+	15.8529i	0.679867	+	0.679062i
$546$	0.267356	−	1.54814i	0.0114418	−	0.0662542i
$547$	−43.3273			−1.85254			−0.926271	−	0.376858i	$-0.877005\pi$
$547$	−43.3273			−1.85254			−0.926271	+	0.376858i	$0.877005\pi$
$548$	10.5529	−	29.6421i	0.450795	−	1.26625i
$549$			18.3223i			0.781977i
$550$	−3.38583	+	19.7451i	−0.144372	+	0.841936i
$551$	−8.94067	−	12.1780i	−0.380885	−	0.518799i
$552$	2.26908	+	1.27826i	0.0965784	+	0.0544063i
$553$	3.38629			0.144000
$554$	−9.37982	−	1.61985i	−0.398510	−	0.0688210i
$555$	2.48308	−	2.48603i	0.105401	−	0.105526i
$556$	−21.7601	−	7.74677i	−0.922832	−	0.328536i
$557$	−6.39998			−0.271176			−0.135588	−	0.990765i	$-0.543292\pi$
$557$	−6.39998			−0.271176			−0.135588	+	0.990765i	$0.543292\pi$
$558$	26.5259	+	4.58090i	1.12293	+	0.193925i
$559$	2.97950			0.126020
$560$	−1.15241	−	11.2639i	−0.0486981	−	0.475987i
$561$		−	4.65987i		−	0.196740i
$562$	−0.273925	+	1.58617i	−0.0115548	+	0.0669086i
$563$	−5.70125			−0.240279			−0.120140	−	0.992757i	$-0.538334\pi$
$563$	−5.70125			−0.240279			−0.120140	+	0.992757i	$0.538334\pi$
$564$	5.55088	+	1.97616i	0.233734	+	0.0832113i
$565$	−19.6989	−	19.6756i	−0.828739	−	0.827758i
$566$	4.51626	−	26.1516i	0.189833	−	1.09923i
$567$	−10.6385			−0.446774
$568$	−39.9045	−	22.4797i	−1.67436	−	0.943229i
$569$		−	22.9385i		−	0.961632i	−0.876822	−	0.480816i	$-0.840341\pi$
$569$		−	22.9385i		−	0.961632i	0.876822	−	0.480816i	$-0.159659\pi$
$570$	−1.12872	+	3.37744i	−0.0472767	+	0.141465i
$571$	−15.5374			−0.650218			−0.325109	−	0.945676i	$-0.605401\pi$
$571$	−15.5374			−0.650218			−0.325109	+	0.945676i	$0.605401\pi$
$572$	−6.45529	+	18.1324i	−0.269909	+	0.758153i
$573$			0.894079i			0.0373507i
$574$	−2.07419	+	12.0107i	−0.0865749	+	0.501315i
$575$	0.0210939	+	17.8206i	0.000879675	+	0.743172i
$576$	−12.1601	−	20.0696i	−0.506670	−	0.836233i
$577$			13.1651i			0.548070i	0.961720	+	0.274035i	$0.0883584\pi$
$577$			13.1651i			0.548070i	−0.961720	+	0.274035i	$0.911642\pi$
$578$	−32.7952	−	5.66358i	−1.36410	−	0.235574i
$579$	−4.55244			−0.189193
$580$	−6.65774	−	13.9974i	−0.276447	−	0.581208i
$581$			10.0445i			0.416716i
$582$	3.21386	+	0.555019i	0.133219	+	0.0230063i
$583$		−	33.7059i		−	1.39596i
$584$	−2.80758	+	4.98382i	−0.116178	+	0.206232i
$585$	15.7446	−	15.7633i	0.650960	−	0.651731i
$586$	−3.79727	+	21.9883i	−0.156864	+	0.908326i
$587$			15.3667i			0.634251i	0.948384	+	0.317126i	$0.102718\pi$
$587$			15.3667i			0.634251i	−0.948384	+	0.317126i	$0.897282\pi$
$588$	−2.62729	−	0.935337i	−0.108348	−	0.0385727i
$589$	−16.7393	−	22.8004i	−0.689732	−	0.939476i
$590$	−20.1475	+	14.2314i	−0.829461	+	0.585898i
$591$	−1.30967			−0.0538727
$592$	15.3746	−	18.8562i	0.631891	−	0.774987i
$593$			18.7079i			0.768242i	0.923283	+	0.384121i	$0.125495\pi$
$593$			18.7079i			0.768242i	−0.923283	+	0.384121i	$0.874505\pi$
$594$	−6.05196	−	1.04515i	−0.248315	−	0.0428829i
$595$	−12.7357	+	12.7508i	−0.522112	+	0.522731i
$596$	6.98108	−	19.6093i	0.285956	−	0.803229i
$597$		−	2.29573i		−	0.0939581i
$598$	−2.91365	+	16.8716i	−0.119148	+	0.689931i
$599$	−19.9380			−0.814645			−0.407323	−	0.913284i	$-0.633538\pi$
$599$	−19.9380			−0.814645			−0.407323	+	0.913284i	$0.633538\pi$
$600$	−1.78946	+	3.18533i	−0.0730543	+	0.130041i
$601$		−	10.7515i		−	0.438562i	−0.975662	−	0.219281i	$-0.929629\pi$
$601$		−	10.7515i		−	0.438562i	0.975662	−	0.219281i	$-0.0703711\pi$
$602$	−0.267236	+	1.54744i	−0.0108917	+	0.0630689i
$603$	−4.89653			−0.199402
$604$	35.5526	+	12.6570i	1.44662	+	0.515008i
$605$	−4.70400	−	4.69844i	−0.191245	−	0.191019i
$606$	0.665623	−	3.85432i	0.0270391	−	0.156571i
$607$		−	40.5699i		−	1.64668i	−0.567548	−	0.823340i	$-0.692108\pi$
$607$		−	40.5699i		−	1.64668i	0.567548	−	0.823340i	$-0.307892\pi$
$608$	−5.42321	+	24.0539i	−0.219940	+	0.975513i
$609$	1.13351			0.0459321
$610$	16.1338	−	11.3963i	0.653239	−	0.461422i
$611$			38.7357i			1.56708i
$612$	−12.5266	+	35.1862i	−0.506357	+	1.42232i
$613$	−12.5598			−0.507286			−0.253643	−	0.967298i	$-0.581629\pi$
$613$	−12.5598			−0.507286			−0.253643	+	0.967298i	$0.581629\pi$
$614$	33.0329	+	5.70463i	1.33310	+	0.230220i
$615$	2.77934	−	2.78263i	0.112074	−	0.112207i
$616$	−8.83829	−	4.97895i	−0.356105	−	0.200608i
$617$			6.62936i			0.266888i	0.991056	+	0.133444i	$0.0426036\pi$
$617$			6.62936i			0.266888i	−0.991056	+	0.133444i	$0.957396\pi$
$618$	0.148295	−	0.858709i	0.00596530	−	0.0345423i
$619$	−12.5313			−0.503677			−0.251839	−	0.967769i	$-0.581035\pi$
$619$	−12.5313			−0.503677			−0.251839	+	0.967769i	$0.581035\pi$
$620$	−12.4651	−	26.2068i	−0.500609	−	1.05249i
$621$	−5.46321			−0.219231
$622$	−8.23334	+	47.6755i	−0.330127	+	1.91161i
$623$		−	16.6554i		−	0.667285i
$624$	−2.21818	+	2.72050i	−0.0887982	+	0.108907i
$625$	−24.9999	+	0.0591837i	−0.999997	+	0.00236735i
$626$	0.478739	−	2.77216i	0.0191343	−	0.110798i
$627$	1.88809	+	2.57174i	0.0754029	+	0.102705i
$628$	−30.9674	−	11.0247i	−1.23573	−	0.439932i
$629$	−38.7241			−1.54403
$630$	6.77468	+	9.59098i	0.269910	+	0.382114i
$631$		−	40.3979i		−	1.60822i	−0.594484	−	0.804108i	$-0.702644\pi$
$631$		−	40.3979i		−	1.60822i	0.594484	−	0.804108i	$-0.297356\pi$
$632$	−6.59193	−	3.71349i	−0.262213	−	0.147715i
$633$			5.52567i			0.219626i
$634$	0.556857	−	3.22450i	0.0221156	−	0.128061i
$635$	24.8487	−	24.8781i	0.986089	−	0.987257i
$636$	2.06166	−	5.79105i	0.0817503	−	0.229630i
$637$		−	18.3340i		−	0.726421i
$638$	−13.6842	−	2.36320i	−0.541763	−	0.0935600i
$639$	47.4983			1.87900
$640$	−10.1090	+	23.1907i	−0.399592	+	0.916693i
$641$			39.9052i			1.57616i	0.615572	+	0.788081i	$0.288925\pi$
$641$			39.9052i			1.57616i	−0.615572	+	0.788081i	$0.711075\pi$
$642$	1.23662	+	0.213558i	0.0488054	+	0.00842848i
$643$		−	3.03293i		−	0.119607i	−0.998210	−	0.0598035i	$-0.980953\pi$
$643$		−	3.03293i		−	0.119607i	0.998210	−	0.0598035i	$-0.0190474\pi$
$644$	−8.50113	−	3.02648i	−0.334992	−	0.119260i
$645$	0.358087	−	0.358511i	0.0140997	−	0.0141164i
$646$	35.1267	−	17.5034i	1.38204	−	0.688663i
$647$	34.1972			1.34443			0.672216	−	0.740355i	$-0.265343\pi$
$647$	34.1972			1.34443			0.672216	+	0.740355i	$0.265343\pi$
$648$	20.7094	+	11.6664i	0.813544	+	0.458301i
$649$			22.0995i			0.867482i
$650$	−23.6734	−	4.05944i	−0.928548	−	0.159224i
$651$	2.12223			0.0831769
$652$	−8.18752	+	22.9981i	−0.320648	+	0.900675i
$653$	−27.9899			−1.09533			−0.547664	−	0.836698i	$-0.684483\pi$
$653$	−27.9899			−1.09533			−0.547664	+	0.836698i	$0.684483\pi$
$654$	3.61185	+	0.623751i	0.141235	+	0.0243906i
$655$	1.89101	+	1.88877i	0.0738878	+	0.0738004i
$656$	17.2089	−	21.1060i	0.671895	−	0.824050i
$657$		−	5.93223i		−	0.231438i
$658$	−20.1178	−	3.47426i	−0.784275	−	0.135441i
$659$		−	38.0941i		−	1.48394i	−0.670436	−	0.741968i	$-0.733893\pi$
$659$		−	38.0941i		−	1.48394i	0.670436	−	0.741968i	$-0.266107\pi$
$660$	1.40598	+	2.95595i	0.0547276	+	0.115060i
$661$	35.3736			1.37587			0.687937	−	0.725771i	$-0.258517\pi$
$661$	35.3736			1.37587			0.687937	+	0.725771i	$0.258517\pi$
$662$	3.81278	−	22.0780i	0.148188	−	0.858087i
$663$	5.58695			0.216979
$664$	11.0151	−	19.5532i	0.427467	−	0.758811i
$665$	1.86235	−	12.1973i	0.0722189	−	0.472990i
$666$	−4.29380	+	24.8634i	−0.166381	+	0.963438i
$667$	−12.3530			−0.478309
$668$	−11.6048	+	32.5969i	−0.449002	+	1.26121i
$669$			1.12104i			0.0433420i
$670$	3.04559	+	4.31167i	0.117661	+	0.166574i
$671$		−	17.6969i		−	0.683182i
$672$	−1.21397	−	1.39604i	−0.0468300	−	0.0538535i
$673$	−4.67684			−0.180279			−0.0901394	−	0.995929i	$-0.528731\pi$
$673$	−4.67684			−0.180279			−0.0901394	+	0.995929i	$0.528731\pi$
$674$	−18.8561	−	3.25636i	−0.726309	−	0.125430i
$675$	−0.00907188	−	7.66416i	−0.000349177	−	0.294993i
$676$	2.75426	+	0.980538i	0.105933	+	0.0377130i
$677$		−	26.8419i		−	1.03162i	−0.856704	−	0.515809i	$-0.827491\pi$
$677$		−	26.8419i		−	1.03162i	0.856704	−	0.515809i	$-0.172509\pi$
$678$	−4.48281	−	0.774160i	−0.172161	−	0.0297314i
$679$	−11.3005			−0.433673
$680$	38.7748	−	10.8551i	1.48695	−	0.416273i
$681$	−1.93767			−0.0742517
$682$	−25.6205	−	4.42455i	−0.981060	−	0.169425i
$683$	16.6100			0.635564			0.317782	−	0.948164i	$-0.397062\pi$
$683$	16.6100			0.635564			0.317782	+	0.948164i	$0.397062\pi$
$684$	−7.34343	−	24.4944i	−0.280783	−	0.936569i
$685$	24.8602	−	24.8896i	0.949859	−	0.950984i
$686$	21.8711	+	3.77705i	0.835044	+	0.144208i
$687$			0.0874311i			0.00333571i
$688$	2.21718	−	2.71927i	0.0845291	−	0.103671i
$689$	40.4117			1.53956
$690$	1.67992	+	2.37828i	0.0639534	+	0.0905394i
$691$	5.78792			0.220183			0.110092	−	0.993921i	$-0.464886\pi$
$691$	5.78792			0.220183			0.110092	+	0.993921i	$0.464886\pi$
$692$	−5.29943	+	14.8857i	−0.201454	+	0.565869i
$693$	10.5202			0.399629
$694$	−3.07232	+	17.7904i	−0.116624	+	0.675313i
$695$	−18.2713	−	18.2497i	−0.693069	−	0.692250i
$696$	−2.20655	−	1.24303i	−0.0836390	−	0.0471171i
$697$	−43.3443			−1.64178
$698$	−8.36890	+	48.4604i	−0.316767	+	1.83425i
$699$			5.92894i			0.224253i
$700$	4.23162	−	11.9310i	0.159940	−	0.450948i
$701$			2.45989i			0.0929089i	0.998920	+	0.0464544i	$0.0147922\pi$
$701$			2.45989i			0.0929089i	−0.998920	+	0.0464544i	$0.985208\pi$
$702$	1.25308	−	7.25600i	0.0472944	−	0.273860i
$703$	21.3715	−	15.6902i	0.806041	−	0.591768i
$704$	11.7450	+	19.3846i	0.442658	+	0.730584i
$705$	4.66091	+	4.65540i	0.175540	+	0.175332i
$706$	−5.19248	+	30.0672i	−0.195421	+	1.13160i
$707$			13.5525i			0.509693i
$708$	−1.35174	+	3.79694i	−0.0508016	+	0.142698i
$709$		−	19.5279i		−	0.733386i	−0.930342	−	0.366693i	$-0.880490\pi$
$709$		−	19.5279i		−	0.733386i	0.930342	−	0.366693i	$-0.119510\pi$
$710$	−29.5434	−	41.8249i	−1.10874	−	1.56966i
$711$	7.84636			0.294261
$712$	−18.2648	+	32.4223i	−0.684501	+	1.21508i
$713$	−23.1281			−0.866154
$714$	−0.501101	+	2.90165i	−0.0187533	+	0.108591i
$715$	−15.2072	+	15.2252i	−0.568718	+	0.569392i
$716$	5.47044	−	15.3660i	0.204440	−	0.574256i
$717$			7.19899i			0.268851i
$718$	2.58283	−	14.9560i	0.0963903	−	0.558152i
$719$		−	37.6639i		−	1.40463i	−0.711868	−	0.702313i	$-0.752151\pi$
$719$		−	37.6639i		−	1.40463i	0.711868	−	0.702313i	$-0.247849\pi$
$720$	−2.67024	−	26.0996i	−0.0995140	−	0.972675i
$721$			3.01937i			0.112447i
$722$	−12.2940	+	23.8926i	−0.457537	+	0.889191i
$723$		−	3.34324i		−	0.124336i
$724$	−33.5915	−	11.9589i	−1.24842	−	0.444447i
$725$	−0.0205126	−	17.3296i	−0.000761818	−	0.643604i
$726$	−1.07047	−	0.184866i	−0.0397290	−	0.00686101i
$727$	−26.3342			−0.976681			−0.488340	−	0.872653i	$-0.662398\pi$
$727$	−26.3342			−0.976681			−0.488340	+	0.872653i	$0.662398\pi$
$728$	5.96951	−	10.5967i	0.221245	−	0.392738i
$729$	−23.4624			−0.868979
$730$	−5.22366	+	3.68978i	−0.193336	+	0.136565i
$731$	−5.58443			−0.206548
$732$	1.08245	−	3.04053i	0.0400086	−	0.112381i
$733$	19.7382			0.729046			0.364523	−	0.931194i	$-0.381232\pi$
$733$	19.7382			0.729046			0.364523	+	0.931194i	$0.381232\pi$
$734$	15.1269	+	2.61235i	0.558345	+	0.0964237i
$735$	−2.20606	−	2.20345i	−0.0813717	−	0.0812754i
$736$	13.2299	+	15.2141i	0.487659	+	0.560798i
$737$	4.72940			0.174210
$738$	−4.80610	+	27.8299i	−0.176915	+	1.02443i
$739$	−12.1551			−0.447131			−0.223566	−	0.974689i	$-0.571770\pi$
$739$	−12.1551			−0.447131			−0.223566	+	0.974689i	$0.571770\pi$
$740$	24.5643	−	11.6838i	0.903003	−	0.429507i
$741$	−3.08339	+	2.26372i	−0.113271	+	0.0831598i
$742$	−3.62459	+	20.9883i	−0.133063	+	0.770505i
$743$		−	16.6057i		−	0.609204i	−0.952480	−	0.304602i	$-0.901477\pi$
$743$		−	16.6057i		−	0.609204i	0.952480	−	0.304602i	$-0.0985235\pi$
$744$	−4.13125	−	2.32729i	−0.151459	−	0.0853228i
$745$	16.4459	−	16.4654i	0.602531	−	0.603245i
$746$	4.30352	−	24.9197i	0.157563	−	0.912375i
$747$			23.2741i			0.851556i
$748$	12.0990	−	33.9852i	0.442384	−	1.24262i
$749$	−4.34817			−0.158879
$750$	−3.33361	+	2.36065i	−0.121726	+	0.0861987i
$751$	−23.7806			−0.867767			−0.433884	−	0.900969i	$-0.642857\pi$
$751$	−23.7806			−0.867767			−0.433884	+	0.900969i	$0.642857\pi$
$752$	35.3525	+	28.8249i	1.28917	+	1.05114i
$753$	4.82243			0.175739
$754$	2.83336	−	16.4067i	0.103185	−	0.597496i
$755$	29.8525	+	29.8172i	1.08644	+	1.08516i
$756$	3.65610	+	1.30160i	0.132971	+	0.0473388i
$757$	32.7868			1.19166			0.595829	−	0.803111i	$-0.296824\pi$
$757$	32.7868			1.19166			0.595829	+	0.803111i	$0.296824\pi$
$758$	−6.86964	+	39.7789i	−0.249517	+	1.44484i
$759$	2.60869			0.0946896
$760$	−17.0012	+	21.7016i	−0.616699	+	0.787199i
$761$	−38.6598			−1.40142			−0.700708	−	0.713449i	$-0.747132\pi$
$761$	−38.6598			−1.40142			−0.700708	+	0.713449i	$0.747132\pi$
$762$	0.977701	−	5.66142i	0.0354184	−	0.205091i
$763$	−12.6999			−0.459768
$764$	−2.32141	+	6.52067i	−0.0839858	+	0.235909i
$765$	−29.5099	+	29.5448i	−1.06693	+	1.06819i
$766$	−2.24686	+	13.0105i	−0.0811825	+	0.470090i
$767$	−26.4962			−0.956723
$768$	0.832247	+	4.04888i	0.0300311	+	0.146102i
$769$	7.22987			0.260716			0.130358	−	0.991467i	$-0.458387\pi$
$769$	7.22987			0.260716			0.130358	+	0.991467i	$0.458387\pi$
$770$	−6.54345	−	9.26363i	−0.235810	−	0.333838i
$771$	3.64163			0.131150
$772$	−33.2017	−	11.8201i	−1.19496	−	0.425415i
$773$		−	32.9647i		−	1.18566i	−0.805328	−	0.592829i	$-0.798011\pi$
$773$		−	32.9647i		−	1.18566i	0.805328	−	0.592829i	$-0.201989\pi$
$774$	−0.619212	+	3.58557i	−0.0222571	+	0.128881i
$775$	−0.0384051	−	32.4456i	−0.00137955	−	1.16548i
$776$	21.9982	+	12.3924i	0.789688	+	0.444862i
$777$			1.98923i			0.0713631i
$778$	1.49332	−	8.64714i	0.0535382	−	0.310015i
$779$	23.9213	−	17.5622i	0.857070	−	0.629232i
$780$	−3.54404	+	1.68570i	−0.126897	+	0.0603576i
$781$	−45.8771			−1.64161
$782$	5.46100	−	31.6221i	0.195285	−	1.13081i
$783$	5.31267			0.189859
$784$	−16.7327	−	13.6432i	−0.597597	−	0.487255i
$785$	−26.0024	−	25.9717i	−0.928066	−	0.926968i
$786$	0.430330	+	0.0743160i	0.0153494	+	0.00265076i
$787$	−7.61457			−0.271430			−0.135715	−	0.990748i	$-0.543333\pi$
$787$	−7.61457			−0.271430			−0.135715	+	0.990748i	$0.543333\pi$
$788$	−9.55166	−	3.40047i	−0.340264	−	0.121137i
$789$	2.52205			0.0897874
$790$	−4.88035	−	6.90916i	−0.173635	−	0.245817i
$791$	15.7623			0.560444
$792$	−20.4792	−	11.5367i	−0.727696	−	0.409939i
$793$	21.2177			0.753464
$794$	8.45238	+	1.45969i	0.299964	+	0.0518024i
$795$	4.85682	−	4.86258i	0.172254	−	0.172458i
$796$	5.96071	−	16.7432i	0.211272	−	0.593446i
$797$			18.9980i			0.672943i	0.941694	+	0.336472i	$0.109234\pi$
$797$			18.9980i			0.672943i	−0.941694	+	0.336472i	$0.890766\pi$
$798$	−0.899136	−	1.80443i	−0.0318291	−	0.0638761i
$799$		−	72.6016i		−	2.56846i
$800$	−21.3213	+	18.5850i	−0.753823	+	0.657078i
$801$		−	38.5922i		−	1.36359i
$802$	7.68921	−	44.5246i	0.271515	−	1.57222i
$803$			5.72975i			0.202199i
$804$	0.812564	+	0.289280i	0.0286569	+	0.0102021i
$805$	−7.13816	−	7.12971i	−0.251587	−	0.251289i
$806$	5.30481	−	30.7177i	0.186854	−	1.08198i
$807$	4.47521			0.157535
$808$	14.8620	−	26.3820i	0.522842	−	0.928114i
$809$	−7.73249			−0.271860			−0.135930	−	0.990718i	$-0.543402\pi$
$809$	−7.73249			−0.271860			−0.135930	+	0.990718i	$0.543402\pi$
$810$	15.3323	+	21.7061i	0.538722	+	0.762674i
$811$			13.9763i			0.490776i	0.969425	+	0.245388i	$0.0789153\pi$
$811$			13.9763i			0.490776i	−0.969425	+	0.245388i	$0.921085\pi$
$812$	8.26687	+	2.94308i	0.290110	+	0.103282i
$813$			1.96468i			0.0689043i
$814$	4.14725	−	24.0148i	0.145361	−	0.841718i
$815$	−19.2880	+	19.3108i	−0.675629	+	0.676429i
$816$	4.15749	−	5.09898i	0.145541	−	0.178500i
$817$	3.08199	−	2.26270i	0.107825	−	0.0791618i
$818$	−4.49308	+	26.0173i	−0.157097	+	0.909675i
$819$			12.6132i			0.440740i
$820$	27.4951	−	13.0778i	0.960171	−	0.456698i
$821$		−	31.9595i		−	1.11539i	−0.830045	−	0.557696i	$-0.811685\pi$
$821$		−	31.9595i		−	1.11539i	0.830045	−	0.557696i	$-0.188315\pi$
$822$	0.978155	−	5.66404i	0.0341171	−	0.197556i
$823$	−28.4590			−0.992018			−0.496009	−	0.868317i	$-0.665202\pi$
$823$	−28.4590			−0.992018			−0.496009	+	0.868317i	$0.665202\pi$
$824$	3.31112	−	5.87767i	0.115348	−	0.204758i
$825$	0.00433184	+	3.65965i	0.000150815	+	0.127413i
$826$	2.37648	−	13.7611i	0.0826884	−	0.478811i
$827$	−53.4173			−1.85750			−0.928750	−	0.370707i	$-0.879116\pi$
$827$	−53.4173			−1.85750			−0.928750	+	0.370707i	$0.879116\pi$
$828$	−19.6980	−	7.01265i	−0.684552	−	0.243706i
$829$	4.49611			0.156156			0.0780781	−	0.996947i	$-0.475122\pi$
$829$	4.49611			0.156156			0.0780781	+	0.996947i	$0.475122\pi$
$830$	20.4942	−	14.4763i	0.711363	−	0.502478i
$831$	−1.73885			−0.0603201
$832$	−23.2411	+	14.0817i	−0.805741	+	0.488196i
$833$			34.3631i			1.19061i
$834$	−4.15793	−	0.718056i	−0.143977	−	0.0248642i
$835$	−27.3383	+	27.3707i	−0.946081	+	0.947202i
$836$	7.09279	+	23.6584i	0.245309	+	0.818243i
$837$	9.94674			0.343810
$838$	−7.01557	−	1.21156i	−0.242349	−	0.0418526i
$839$	−32.4057			−1.11877			−0.559385	−	0.828908i	$-0.688962\pi$
$839$	−32.4057			−1.11877			−0.559385	+	0.828908i	$0.688962\pi$
$840$	−0.557616	−	1.99183i	−0.0192396	−	0.0687247i
$841$	−16.9874			−0.585773
$842$	−0.955418	−	0.164996i	−0.0329259	−	0.00568615i
$843$			0.294048i			0.0101275i
$844$	−14.3470	+	40.2997i	−0.493845	+	1.38717i
$845$	2.31267	+	2.30993i	0.0795582	+	0.0794641i
$846$	−46.6150	−	8.05021i	−1.60266	−	0.276772i
$847$	3.76397			0.129332
$848$	30.0721	−	36.8821i	1.03268	−	1.26654i
$849$		−	4.84804i		−	0.166384i
$850$	44.3707	+	7.60854i	1.52190	+	0.260971i
$851$		−	21.6786i		−	0.743132i
$852$	−7.88218	−	2.80612i	−0.270039	−	0.0961362i
$853$	29.7549			1.01879			0.509395	−	0.860533i	$-0.329869\pi$
$853$	29.7549			1.01879			0.509395	+	0.860533i	$0.329869\pi$
$854$	−1.90305	+	11.0197i	−0.0651210	+	0.377086i
$855$	4.31525	−	28.2623i	0.147578	−	0.966551i
$856$	8.46437	+	4.76831i	0.289306	+	0.162977i
$857$	6.41431			0.219109			0.109554	−	0.993981i	$-0.465058\pi$
$857$	6.41431			0.219109			0.109554	+	0.993981i	$0.465058\pi$
$858$	−0.598347	+	3.46475i	−0.0204272	+	0.118285i
$859$	−58.0660			−1.98119			−0.990594	−	0.136834i	$-0.956307\pi$
$859$	−58.0660			−1.98119			−0.990594	+	0.136834i	$0.956307\pi$
$860$	3.54244	−	1.68494i	0.120796	−	0.0574558i
$861$			2.22656i			0.0758810i
$862$	35.8579	+	6.19249i	1.22132	+	0.210917i
$863$			6.39820i			0.217797i	0.994053	+	0.108899i	$0.0347324\pi$
$863$			6.39820i			0.217797i	−0.994053	+	0.108899i	$0.965268\pi$
$864$	−5.68979	−	6.54314i	−0.193571	−	0.222602i
$865$	−12.4843	+	12.4991i	−0.424478	+	0.424981i
$866$	−20.8799	−	3.60587i	−0.709528	−	0.122532i
$867$	−6.07964			−0.206475
$868$	15.4778	+	5.51023i	0.525351	+	0.187029i
$869$	−7.57855			−0.257085
$870$	−1.63363	−	2.31274i	−0.0553851	−	0.0784092i
$871$			5.67032i			0.192131i
$872$	24.7223	+	13.9270i	0.837204	+	0.471629i
$873$	−26.1844			−0.886207
$874$	9.79879	+	19.6647i	0.331449	+	0.665167i
$875$	9.99017	−	10.0257i	0.337730	−	0.338931i
$876$	−0.350467	+	0.984435i	−0.0118412	+	0.0332610i
$877$		−	10.2675i		−	0.346707i	−0.984860	−	0.173354i	$-0.944540\pi$
$877$		−	10.2675i		−	0.346707i	0.984860	−	0.173354i	$-0.0554604\pi$
$878$	15.2700	+	2.63707i	0.515339	+	0.0889967i
$879$			4.07623i			0.137488i
$880$	2.57910	+	25.2088i	0.0869415	+	0.849788i
$881$	0.867365			0.0292223			0.0146111	−	0.999893i	$-0.495349\pi$
$881$	0.867365			0.0292223			0.0146111	+	0.999893i	$0.495349\pi$
$882$	22.0634	+	3.81025i	0.742913	+	0.128298i
$883$		−	51.4058i		−	1.72994i	−0.501820	−	0.864972i	$-0.667336\pi$
$883$		−	51.4058i		−	1.72994i	0.501820	−	0.864972i	$-0.332664\pi$
$884$	40.7466	+	14.5061i	1.37046	+	0.487894i
$885$	−3.18441	+	3.18818i	−0.107043	+	0.107170i
$886$	4.93956	−	28.6027i	0.165948	−	0.960927i
$887$			2.42756i			0.0815093i	0.999169	+	0.0407547i	$0.0129762\pi$
$887$			2.42756i			0.0815093i	−0.999169	+	0.0407547i	$0.987024\pi$
$888$	2.18144	−	3.87234i	0.0732042	−	0.129947i
$889$			19.9065i			0.667644i
$890$	−33.9827	+	24.0040i	−1.13910	+	0.804615i
$891$	23.8091			0.797634
$892$	−2.91071	+	8.17595i	−0.0974577	+	0.273751i
$893$	29.4167	+	40.0682i	0.984394	+	1.34083i
$894$	0.647084	−	3.74697i	0.0216417	−	0.125317i
$895$	12.8871	−	12.9024i	0.430770	−	0.431280i
$896$	−5.22897	−	13.3336i	−0.174688	−	0.445443i
$897$			3.12769i			0.104431i
$898$	3.55676	−	20.5956i	0.118691	−	0.687283i
$899$	22.4908			0.750109
$900$	9.80509	−	27.6453i	0.326836	−	0.921508i
$901$	−75.7430			−2.52336
$902$	4.64206	−	26.8800i	0.154564	−	0.895006i
$903$			0.286868i			0.00954636i
$904$	−30.6838	−	17.2854i	−1.02053	−	0.574903i
$905$	−28.2058	−	28.1724i	−0.937592	−	0.936483i
$906$	6.79343	+	1.17319i	0.225696	+	0.0389768i
$907$	5.13704			0.170573			0.0852863	−	0.996356i	$-0.472820\pi$
$907$	5.13704			0.170573			0.0852863	+	0.996356i	$0.472820\pi$
$908$	−14.1318	−	5.03103i	−0.468979	−	0.166961i
$909$			31.4024i			1.04155i
$910$	11.1066	−	7.84527i	0.368181	−	0.260068i
$911$	7.40739			0.245418			0.122709	−	0.992443i	$-0.460842\pi$
$911$	7.40739			0.245418			0.122709	+	0.992443i	$0.460842\pi$
$912$	−0.228475	+	4.49861i	−0.00756557	+	0.148964i
$913$		−	22.4797i		−	0.743971i
$914$	0.215319	−	1.24681i	0.00712213	−	0.0412410i
$915$	2.55002	−	2.55304i	0.0843011	−	0.0844010i
$916$	−0.227009	+	0.637650i	−0.00750058	+	0.0210686i
$917$	−1.51311			−0.0499675
$918$	−2.34862	+	13.5998i	−0.0775161	+	0.448860i
$919$			36.8760i			1.21643i	0.793773	+	0.608214i	$0.208114\pi$
$919$			36.8760i			1.21643i	−0.793773	+	0.608214i	$0.791886\pi$
$920$	6.07690	+	21.7070i	0.200349	+	0.715658i
$921$	6.12370			0.201783
$922$	−8.45291	+	48.9469i	−0.278382	+	1.61198i
$923$		−	55.0043i		−	1.81049i
$924$	−1.74579	−	0.621517i	−0.0574324	−	0.0204464i
$925$	30.4121	−	0.0359981i	0.999945	−	0.00118361i
$926$	−55.0449	−	9.50601i	−1.80889	−	0.312387i
$927$			6.99618i			0.229785i
$928$	−12.8653	−	14.7948i	−0.422324	−	0.485664i
$929$	15.2559			0.500529			0.250265	−	0.968177i	$-0.419482\pi$
$929$	15.2559			0.500529			0.250265	+	0.968177i	$0.419482\pi$
$930$	−3.05858	−	4.33007i	−0.100295	−	0.141989i
$931$	−13.9233	−	18.9647i	−0.456316	−	0.621543i
$932$	−15.3941	+	43.2408i	−0.504250	+	1.41640i
$933$			8.83818i			0.289349i
$934$	−0.395989	+	2.29299i	−0.0129572	+	0.0750289i
$935$	28.5026	−	28.5364i	0.932136	−	0.933240i
$936$	13.8319	−	24.5535i	0.452111	−	0.802557i
$937$		−	20.7943i		−	0.679321i	−0.940548	−	0.339661i	$-0.889688\pi$
$937$		−	20.7943i		−	0.679321i	0.940548	−	0.339661i	$-0.110312\pi$
$938$	−2.94495	−	0.508579i	−0.0961559	−	0.0166057i
$939$		−	0.513908i		−	0.0167708i
$940$	21.9054	+	46.0543i	0.714475	+	1.50213i
$941$	51.8985			1.69184			0.845921	−	0.533308i	$-0.179051\pi$
$941$	51.8985			1.69184			0.845921	+	0.533308i	$0.179051\pi$
$942$	−5.91728	−	1.02189i	−0.192795	−	0.0332949i
$943$		−	24.2651i		−	0.790179i
$944$	−19.7170	+	24.1820i	−0.641733	+	0.787058i
$945$	3.06992	+	3.06629i	0.0998645	+	0.0997464i
$946$	0.598077	−	3.46319i	0.0194452	−	0.112598i
$947$			49.6458i			1.61327i	0.591049	+	0.806636i	$0.298714\pi$
$947$			49.6458i			1.61327i	−0.591049	+	0.806636i	$0.701286\pi$
$948$	−1.30208	−	0.463551i	−0.0422895	−	0.0150554i
$949$	−6.86969			−0.222999
$950$	−27.5706	+	13.7790i	−0.894509	+	0.447051i
$951$		−	0.597765i		−	0.0193838i
$952$	−11.1885	+	19.8611i	−0.362623	+	0.643703i
$953$	−44.8642			−1.45329			−0.726647	−	0.687011i	$-0.758922\pi$
$953$	−44.8642			−1.45329			−0.726647	+	0.687011i	$0.758922\pi$
$954$	−8.39852	+	48.6320i	−0.271912	+	1.57452i
$955$	−5.46874	+	5.47522i	−0.176964	+	0.177174i
$956$	−18.6917	+	52.5035i	−0.604532	+	1.69808i
$957$	−2.53681			−0.0820033
$958$	−4.03006	+	23.3362i	−0.130205	+	0.753958i
$959$			19.9158i			0.643114i
$960$	−1.09881	+	4.48890i	−0.0354639	+	0.144879i
$961$	11.1087			0.358346
$962$	28.7925	+	4.97234i	0.928309	+	0.160315i
$963$	−10.0751			−0.324667
$964$	8.68049	−	24.3828i	0.279580	−	0.785318i
$965$	−27.8785	−	27.8456i	−0.897442	−	0.896380i
$966$	−1.62440	−	0.280527i	−0.0522643	−	0.00902582i
$967$	14.7567			0.474544			0.237272	−	0.971443i	$-0.423747\pi$
$967$	14.7567			0.474544			0.237272	+	0.971443i	$0.423747\pi$
$968$	−7.32715	−	4.12767i	−0.235503	−	0.132668i
$969$	5.77913	−	4.24285i	0.185653	−	0.136300i
$970$	16.2864	+	23.0568i	0.522925	+	0.740310i
$971$			19.7765i			0.634657i	0.948316	+	0.317329i	$0.102786\pi$
$971$			19.7765i			0.634657i	−0.948316	+	0.317329i	$0.897214\pi$
$972$	12.7550	+	4.54088i	0.409116	+	0.145649i
$973$	14.6200			0.468696
$974$	4.16712	−	24.1299i	0.133523	−	0.773170i
$975$	−4.38773	+	0.00519365i	−0.140520	+	0.000166330i
$976$	15.7890	−	19.3646i	0.505395	−	0.619845i
$977$	36.2137			1.15858			0.579289	−	0.815122i	$-0.303330\pi$
$977$	36.2137			1.15858			0.579289	+	0.815122i	$0.303330\pi$
$978$	−0.758910	+	4.39449i	−0.0242673	+	0.140520i
$979$			37.2750i			1.19132i
$980$	−10.3681	−	21.7980i	−0.331195	−	0.696312i
$981$	−29.4269			−0.939530
$982$	−21.1886	−	3.65918i	−0.676156	−	0.116769i
$983$			50.5807i			1.61327i	0.591048	+	0.806637i	$0.298714\pi$
$983$			50.5807i			1.61327i	−0.591048	+	0.806637i	$0.701286\pi$
$984$	2.44170	−	4.33434i	0.0778387	−	0.138174i
$985$	−8.02025	−	8.01077i	−0.255547	−	0.255244i
$986$	−5.31052	+	30.7507i	−0.169121	+	0.979303i
$987$	−3.72949			−0.118711
$988$	−28.3652	+	8.50390i	−0.902419	+	0.270545i
$989$		−	3.12628i		−	0.0994100i
$990$	−15.1618	−	21.4647i	−0.481874	−	0.682194i
$991$	−25.3500			−0.805271			−0.402635	−	0.915360i	$-0.631906\pi$
$991$	−25.3500			−0.805271			−0.402635	+	0.915360i	$0.631906\pi$
$992$	−24.0873	−	27.6999i	−0.764772	−	0.879472i
$993$		−	4.09287i		−	0.129883i
$994$	28.5671	+	4.93341i	0.906094	+	0.156478i
$995$	14.0421	−	14.0588i	0.445165	−	0.445693i
$996$	1.37500	−	3.86227i	0.0435685	−	0.122381i
$997$	39.4379			1.24901			0.624505	−	0.781021i	$-0.285301\pi$
$997$	39.4379			1.24901			0.624505	+	0.781021i	$0.285301\pi$
$998$	31.8085	+	5.49319i	1.00688	+	0.173884i
$999$			9.32335i			0.294978i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	760.2.p.i.379.52	yes	56
5.4	even	2	inner	760.2.p.i.379.5	✓	56
8.3	odd	2	inner	760.2.p.i.379.49	yes	56
19.18	odd	2	inner	760.2.p.i.379.6	yes	56
40.19	odd	2	inner	760.2.p.i.379.8	yes	56
95.94	odd	2	inner	760.2.p.i.379.51	yes	56
152.75	even	2	inner	760.2.p.i.379.7	yes	56
760.379	even	2	inner	760.2.p.i.379.50	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
760.2.p.i.379.5	✓	56	5.4	even	2	inner
760.2.p.i.379.6	yes	56	19.18	odd	2	inner
760.2.p.i.379.7	yes	56	152.75	even	2	inner
760.2.p.i.379.8	yes	56	40.19	odd	2	inner
760.2.p.i.379.49	yes	56	8.3	odd	2	inner
760.2.p.i.379.50	yes	56	760.379	even	2	inner
760.2.p.i.379.51	yes	56	95.94	odd	2	inner
760.2.p.i.379.52	yes	56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39359 + 0.240666i) q^{2} +0.258346 q^{3} +(1.88416 + 0.670777i) q^{4} +(1.58207 + 1.58020i) q^{5} +(0.360027 + 0.0621750i) q^{6} -1.26592 q^{7} +(2.46430 + 1.38824i) q^{8} -2.93326 q^{9} +(1.82445 + 2.58290i) q^{10} +2.83314 q^{11} +(0.486765 + 0.173292i) q^{12} +3.39679i q^{13} +(-1.76416 - 0.304663i) q^{14} +(0.408722 + 0.408239i) q^{15} +(3.10012 + 2.52770i) q^{16} -6.36655i q^{17} +(-4.08774 - 0.705935i) q^{18} +(2.57960 + 3.51364i) q^{19} +(1.92092 + 4.03857i) q^{20} -0.327045 q^{21} +(3.94822 + 0.681840i) q^{22} +3.56413 q^{23} +(0.636643 + 0.358645i) q^{24} +(0.00591838 + 5.00000i) q^{25} +(-0.817492 + 4.73372i) q^{26} -1.53283 q^{27} +(-2.38519 - 0.849149i) q^{28} -3.46592 q^{29} +(0.471340 + 0.667281i) q^{30} -6.48912 q^{31} +(3.71194 + 4.26866i) q^{32} +0.731930 q^{33} +(1.53221 - 8.87233i) q^{34} +(-2.00278 - 2.00041i) q^{35} +(-5.52673 - 1.96756i) q^{36} -6.08243i q^{37} +(2.74928 + 5.51738i) q^{38} +0.877547i q^{39} +(1.70501 + 6.09040i) q^{40} -6.80813i q^{41} +(-0.455764 - 0.0787085i) q^{42} -0.877151i q^{43} +(5.33809 + 1.90041i) q^{44} +(-4.64063 - 4.63514i) q^{45} +(4.96692 + 0.857765i) q^{46} +11.4036 q^{47} +(0.800902 + 0.653021i) q^{48} -5.39745 q^{49} +(-1.19508 + 6.96935i) q^{50} -1.64477i q^{51} +(-2.27849 + 6.40010i) q^{52} -11.8970i q^{53} +(-2.13613 - 0.368900i) q^{54} +(4.48224 + 4.47694i) q^{55} +(-3.11961 - 1.75740i) q^{56} +(0.666429 + 0.907734i) q^{57} +(-4.83005 - 0.834128i) q^{58} +7.80036i q^{59} +(0.496261 + 1.04335i) q^{60} -6.24640i q^{61} +(-9.04315 - 1.56171i) q^{62} +3.71326 q^{63} +(4.14559 + 6.84208i) q^{64} +(-5.36762 + 5.37398i) q^{65} +(1.02001 + 0.176151i) q^{66} +1.66931 q^{67} +(4.27053 - 11.9956i) q^{68} +0.920778 q^{69} +(-2.30961 - 3.26974i) q^{70} -16.1930 q^{71} +(-7.22844 - 4.07206i) q^{72} +2.02240i q^{73} +(1.46383 - 8.47639i) q^{74} +(0.00152899 + 1.29173i) q^{75} +(2.50351 + 8.35060i) q^{76} -3.58652 q^{77} +(-0.211196 + 1.22294i) q^{78} -2.67496 q^{79} +(0.910333 + 8.89783i) q^{80} +8.40377 q^{81} +(1.63848 - 9.48770i) q^{82} -7.93457i q^{83} +(-0.616204 - 0.219374i) q^{84} +(10.0604 - 10.0724i) q^{85} +(0.211100 - 1.22239i) q^{86} -0.895405 q^{87} +(6.98172 + 3.93307i) q^{88} +13.1568i q^{89} +(-5.35159 - 7.57631i) q^{90} -4.30006i q^{91} +(6.71539 + 2.39074i) q^{92} -1.67644 q^{93} +(15.8919 + 2.74446i) q^{94} +(-1.47115 + 9.63513i) q^{95} +(0.958965 + 1.10279i) q^{96} +8.92672 q^{97} +(-7.52181 - 1.29898i) q^{98} -8.31033 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 16 q^{4} - 8 q^{6} + 88 q^{9} + 32 q^{11} + 48 q^{16} - 56 q^{19} + 4 q^{20} - 32 q^{24} + 80 q^{25} + 24 q^{26} + 24 q^{30} + 48 q^{35} - 96 q^{36} + 104 q^{44} - 72 q^{49} + 104 q^{54} + 16 q^{64}+ \cdots - 272 q^{99}+O(q^{100}) \) 56 * q + 16 * q^4 - 8 * q^6 + 88 * q^9 + 32 * q^11 + 48 * q^16 - 56 * q^19 + 4 * q^20 - 32 * q^24 + 80 * q^25 + 24 * q^26 + 24 * q^30 + 48 * q^35 - 96 * q^36 + 104 * q^44 - 72 * q^49 + 104 * q^54 + 16 * q^64 - 24 * q^66 + 64 * q^74 + 88 * q^76 + 128 * q^80 - 168 * q^81 - 96 * q^96 - 272 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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