LMFDB - Embedded newform 855.2.da.b.289.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(199,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 8]))

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

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

chi := DirichletCharacter("855.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.da (of order $18$, degree $6$, 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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			289.4
Character	$\chi$	$=$	855.289
Dual form			855.2.da.b.784.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0854197 + 0.234689i) q^{2} +(1.48431 + 1.24548i) q^{4} +(1.06599 - 1.96562i) q^{5} +(3.42983 + 1.98021i) q^{7} +(-0.851670 + 0.491712i) q^{8} +O(q^{10})$	\(q+(-0.0854197 + 0.234689i) q^{2} +(1.48431 + 1.24548i) q^{4} +(1.06599 - 1.96562i) q^{5} +(3.42983 + 1.98021i) q^{7} +(-0.851670 + 0.491712i) q^{8} +(0.370253 + 0.418078i) q^{10} +(1.56732 + 2.71468i) q^{11} +(-2.61887 - 0.461777i) q^{13} +(-0.757709 + 0.635793i) q^{14} +(0.630280 + 3.57450i) q^{16} +(0.772000 - 2.12105i) q^{17} +(3.76831 - 2.19085i) q^{19} +(4.03040 - 1.58992i) q^{20} +(-0.770986 + 0.135946i) q^{22} +(-4.87838 + 5.81383i) q^{23} +(-2.72734 - 4.19066i) q^{25} +(0.332077 - 0.575174i) q^{26} +(2.62460 + 7.21103i) q^{28} +(-1.28051 + 0.466066i) q^{29} +(-0.447237 + 0.774637i) q^{31} +(-2.82970 - 0.498952i) q^{32} +(0.431843 + 0.362360i) q^{34} +(7.54850 - 4.63087i) q^{35} -6.62537i q^{37} +(0.192280 + 1.07152i) q^{38} +(0.0586502 + 2.19822i) q^{40} +(-1.08295 - 6.14171i) q^{41} +(-1.13925 - 1.35771i) q^{43} +(-1.05470 + 5.98149i) q^{44} +(-0.947730 - 1.64152i) q^{46} +(-0.0603191 - 0.165725i) q^{47} +(4.34248 + 7.52140i) q^{49} +(1.21647 - 0.282112i) q^{50} +(-3.31207 - 3.94717i) q^{52} +(4.35505 - 5.19015i) q^{53} +(7.00678 - 0.186946i) q^{55} -3.89478 q^{56} -0.340331i q^{58} +(7.34459 + 2.67321i) q^{59} +(-0.796232 - 0.668118i) q^{61} +(-0.143596 - 0.171131i) q^{62} +(-3.27083 + 5.66524i) q^{64} +(-3.69936 + 4.65545i) q^{65} +(5.20252 + 14.2938i) q^{67} +(3.78762 - 2.18678i) q^{68} +(0.442021 + 2.16712i) q^{70} +(-7.99569 + 6.70918i) q^{71} +(-4.11762 + 0.726048i) q^{73} +(1.55490 + 0.565937i) q^{74} +(8.32199 + 1.44147i) q^{76} +12.4145i q^{77} +(-1.94633 - 11.0382i) q^{79} +(7.69798 + 2.57148i) q^{80} +(1.53390 + 0.270467i) q^{82} +(11.4785 + 6.62712i) q^{83} +(-3.34625 - 3.77848i) q^{85} +(0.415955 - 0.151395i) q^{86} +(-2.66968 - 1.54134i) q^{88} +(0.257827 - 1.46221i) q^{89} +(-8.06785 - 6.76973i) q^{91} +(-14.4820 + 2.55357i) q^{92} +0.0440463 q^{94} +(-0.289409 - 9.74250i) q^{95} +(5.26246 - 14.4585i) q^{97} +(-2.13612 + 0.376656i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 18 q^{4} + 6 q^{5}+O(q^{10}) $ 48 * q - 18 * q^4 + 6 * q^5	$ 48 q - 18 q^{4} + 6 q^{5} - 15 q^{10} + 12 q^{11} - 6 q^{14} - 42 q^{16} + 12 q^{19} - 42 q^{20} + 12 q^{25} - 12 q^{26} - 42 q^{31} - 36 q^{34} - 6 q^{35} + 66 q^{40} - 6 q^{41} + 6 q^{44} - 6 q^{46} + 12 q^{49} + 18 q^{50} - 36 q^{56} + 36 q^{59} + 48 q^{61} + 18 q^{65} - 123 q^{70} + 24 q^{71} - 84 q^{74} + 66 q^{76} + 48 q^{79} + 39 q^{80} - 84 q^{85} + 42 q^{86} + 12 q^{89} - 30 q^{91} - 72 q^{94} + 63 q^{95}+O(q^{100}) $ 48 * q - 18 * q^4 + 6 * q^5 - 15 * q^10 + 12 * q^11 - 6 * q^14 - 42 * q^16 + 12 * q^19 - 42 * q^20 + 12 * q^25 - 12 * q^26 - 42 * q^31 - 36 * q^34 - 6 * q^35 + 66 * q^40 - 6 * q^41 + 6 * q^44 - 6 * q^46 + 12 * q^49 + 18 * q^50 - 36 * q^56 + 36 * q^59 + 48 * q^61 + 18 * q^65 - 123 * q^70 + 24 * q^71 - 84 * q^74 + 66 * q^76 + 48 * q^79 + 39 * q^80 - 84 * q^85 + 42 * q^86 + 12 * q^89 - 30 * q^91 - 72 * q^94 + 63 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{9}\right)$

Coefficient data

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

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

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

$2$	−0.0854197	+	0.234689i	−0.0604009	+	0.165950i	−0.966223	−	0.257709i	$-0.917032\pi$
$2$	−0.0854197	+	0.234689i	−0.0604009	+	0.165950i	0.905822	+	0.423659i	$0.139255\pi$
$3$		0			0
$3$		0			0
$4$	1.48431	+	1.24548i	0.742153	+	0.622741i
$5$	1.06599	−	1.96562i	0.476724	−	0.879053i
$5$	1.06599	−	1.96562i	0.476724	−	0.879053i
$6$		0			0
$7$	3.42983	+	1.98021i	1.29635	+	0.748450i	0.979772	−	0.200115i	$-0.0641317\pi$
$7$	3.42983	+	1.98021i	1.29635	+	0.748450i	0.316581	+	0.948565i	$0.397465\pi$
$8$	−0.851670	+	0.491712i	−0.301111	+	0.173846i
$9$		0			0
$10$	0.370253	+	0.418078i	0.117084	+	0.132208i
$11$	1.56732	+	2.71468i	0.472565	+	0.818507i	0.999507	−	0.0313941i	$-0.00999470\pi$
$11$	1.56732	+	2.71468i	0.472565	+	0.818507i	−0.526942	+	0.849901i	$0.676661\pi$
$12$		0			0
$13$	−2.61887	−	0.461777i	−0.726343	−	0.128074i	−0.201762	−	0.979435i	$-0.564667\pi$
$13$	−2.61887	−	0.461777i	−0.726343	−	0.128074i	−0.524581	+	0.851361i	$0.675778\pi$
$14$	−0.757709	+	0.635793i	−0.202506	+	0.169923i
$15$		0			0
$16$	0.630280	+	3.57450i	0.157570	+	0.893624i
$17$	0.772000	−	2.12105i	0.187238	−	0.514431i	−0.810186	−	0.586173i	$-0.800634\pi$
$17$	0.772000	−	2.12105i	0.187238	−	0.514431i	0.997423	+	0.0717425i	$0.0228560\pi$
$18$		0			0
$19$	3.76831	−	2.19085i	0.864510	−	0.502615i
$19$	3.76831	−	2.19085i	0.864510	−	0.502615i
$20$	4.03040	−	1.58992i	0.901224	−	0.355517i
$21$		0			0
$22$	−0.770986	+	0.135946i	−0.164375	+	0.0289837i
$23$	−4.87838	+	5.81383i	−1.01721	+	1.21227i	−0.0401766	+	0.999193i	$0.512792\pi$
$23$	−4.87838	+	5.81383i	−1.01721	+	1.21227i	−0.977036	+	0.213074i	$0.931652\pi$
$24$		0			0
$25$	−2.72734	−	4.19066i	−0.545468	−	0.838132i
$26$	0.332077	−	0.575174i	0.0651256	−	0.112801i
$27$		0			0
$28$	2.62460	+	7.21103i	0.496003	+	1.36276i
$29$	−1.28051	+	0.466066i	−0.237784	+	0.0865462i	−0.458164	−	0.888868i	$-0.651493\pi$
$29$	−1.28051	+	0.466066i	−0.237784	+	0.0865462i	0.220380	+	0.975414i	$0.429270\pi$
$30$		0			0
$31$	−0.447237	+	0.774637i	−0.0803261	+	0.139129i	−0.903390	−	0.428820i	$-0.858930\pi$
$31$	−0.447237	+	0.774637i	−0.0803261	+	0.139129i	0.823064	+	0.567949i	$0.192263\pi$
$32$	−2.82970	−	0.498952i	−0.500225	−	0.0882032i
$33$		0			0
$34$	0.431843	+	0.362360i	0.0740605	+	0.0621441i
$35$	7.54850	−	4.63087i	1.27593	−	0.782759i
$36$		0			0
$37$		−	6.62537i		−	1.08920i	−0.838695	−	0.544602i	$-0.816681\pi$
$37$		−	6.62537i		−	1.08920i	0.838695	−	0.544602i	$-0.183319\pi$
$38$	0.192280	+	1.07152i	0.0311919	+	0.173824i
$39$		0			0
$40$	0.0586502	+	2.19822i	0.00927341	+	0.347569i
$41$	−1.08295	−	6.14171i	−0.169128	−	0.959174i	−0.944705	−	0.327921i	$-0.893652\pi$
$41$	−1.08295	−	6.14171i	−0.169128	−	0.959174i	0.775577	−	0.631253i	$-0.217459\pi$
$42$		0			0
$43$	−1.13925	−	1.35771i	−0.173735	−	0.207049i	0.672150	−	0.740415i	$-0.265371\pi$
$43$	−1.13925	−	1.35771i	−0.173735	−	0.207049i	−0.845884	+	0.533366i	$0.820927\pi$
$44$	−1.05470	+	5.98149i	−0.159002	+	0.901744i
$45$		0			0
$46$	−0.947730	−	1.64152i	−0.139735	−	0.242028i
$47$	−0.0603191	−	0.165725i	−0.00879844	−	0.0241735i	0.935216	−	0.354079i	$-0.115205\pi$
$47$	−0.0603191	−	0.165725i	−0.00879844	−	0.0241735i	−0.944014	+	0.329905i	$0.892983\pi$
$48$		0			0
$49$	4.34248	+	7.52140i	0.620355	+	1.07449i
$50$	1.21647	−	0.282112i	0.172035	−	0.0398966i
$51$		0			0
$52$	−3.31207	−	3.94717i	−0.459301	−	0.547374i
$53$	4.35505	−	5.19015i	0.598212	−	0.712921i	−0.378950	−	0.925417i	$-0.623715\pi$
$53$	4.35505	−	5.19015i	0.598212	−	0.712921i	0.977162	+	0.212496i	$0.0681592\pi$
$54$		0			0
$55$	7.00678	−	0.186946i	0.944795	−	0.0252078i
$56$	−3.89478			−0.520462
$57$		0			0
$58$		−	0.340331i		−	0.0446877i
$59$	7.34459	+	2.67321i	0.956184	+	0.348023i	0.772537	−	0.634970i	$-0.218987\pi$
$59$	7.34459	+	2.67321i	0.956184	+	0.348023i	0.183647	+	0.982992i	$0.441210\pi$
$60$		0			0
$61$	−0.796232	−	0.668118i	−0.101947	−	0.0855437i	0.590389	−	0.807119i	$-0.298974\pi$
$61$	−0.796232	−	0.668118i	−0.101947	−	0.0855437i	−0.692337	+	0.721575i	$0.743419\pi$
$62$	−0.143596	−	0.171131i	−0.0182367	−	0.0217336i
$63$		0			0
$64$	−3.27083	+	5.66524i	−0.408853	+	0.708155i
$65$	−3.69936	+	4.65545i	−0.458849	+	0.577438i
$66$		0			0
$67$	5.20252	+	14.2938i	0.635589	+	1.74627i	0.665157	+	0.746703i	$0.268364\pi$
$67$	5.20252	+	14.2938i	0.635589	+	1.74627i	−0.0295684	+	0.999563i	$0.509413\pi$
$68$	3.78762	−	2.18678i	0.459316	−	0.265186i
$69$		0			0
$70$	0.442021	+	2.16712i	0.0528316	+	0.259020i
$71$	−7.99569	+	6.70918i	−0.948914	+	0.796233i	−0.979114	−	0.203311i	$-0.934830\pi$
$71$	−7.99569	+	6.70918i	−0.948914	+	0.796233i	0.0302004	+	0.999544i	$0.490385\pi$
$72$		0			0
$73$	−4.11762	+	0.726048i	−0.481931	+	0.0849775i	−0.409336	−	0.912384i	$-0.634239\pi$
$73$	−4.11762	+	0.726048i	−0.481931	+	0.0849775i	−0.0725959	+	0.997361i	$0.523128\pi$
$74$	1.55490	+	0.565937i	0.180753	+	0.0657889i
$75$		0			0
$76$	8.32199	+	1.44147i	0.954598	+	0.165348i
$77$			12.4145i			1.41477i
$78$		0			0
$79$	−1.94633	−	11.0382i	−0.218979	−	1.24189i	−0.873867	−	0.486165i	$-0.838396\pi$
$79$	−1.94633	−	11.0382i	−0.218979	−	1.24189i	0.654889	−	0.755725i	$-0.272716\pi$
$80$	7.69798	+	2.57148i	0.860660	+	0.287500i
$81$		0			0
$82$	1.53390	+	0.270467i	0.169390	+	0.0298681i
$83$	11.4785	+	6.62712i	1.25993	+	0.727421i	0.973061	−	0.230549i	$-0.0740523\pi$
$83$	11.4785	+	6.62712i	1.25993	+	0.727421i	0.286869	+	0.957970i	$0.407386\pi$
$84$		0			0
$85$	−3.34625	−	3.77848i	−0.362951	−	0.409833i
$86$	0.415955	−	0.151395i	0.0448535	−	0.0163253i
$87$		0			0
$88$	−2.66968	−	1.54134i	−0.284589	−	0.164308i
$89$	0.257827	−	1.46221i	0.0273296	−	0.154994i	−0.968089	−	0.250607i	$-0.919370\pi$
$89$	0.257827	−	1.46221i	0.0273296	−	0.154994i	0.995419	+	0.0956127i	$0.0304810\pi$
$90$		0			0
$91$	−8.06785	−	6.76973i	−0.845740	−	0.709660i
$92$	−14.4820	+	2.55357i	−1.50986	+	0.266228i
$93$		0			0
$94$	0.0440463			0.00454303
$95$	−0.289409	−	9.74250i	−0.0296927	−	0.999559i
$96$		0			0
$97$	5.26246	−	14.4585i	0.534322	−	1.46804i	−0.319557	−	0.947567i	$-0.603534\pi$
$97$	5.26246	−	14.4585i	0.534322	−	1.46804i	0.853879	−	0.520471i	$-0.174244\pi$
$98$	−2.13612	+	0.376656i	−0.215781	+	0.0380480i
$99$		0			0
$100$	1.17117	−	9.61707i	0.117117	−	0.961707i
$101$	−1.02858	+	5.83337i	−0.102348	+	0.580442i	0.889899	+	0.456158i	$0.150775\pi$
$101$	−1.02858	+	5.83337i	−0.102348	+	0.580442i	−0.992247	+	0.124284i	$0.960336\pi$
$102$		0			0
$103$	−4.33650	+	2.50368i	−0.427288	+	0.246695i	−0.698191	−	0.715912i	$-0.746011\pi$
$103$	−4.33650	+	2.50368i	−0.427288	+	0.246695i	0.270902	+	0.962607i	$0.412678\pi$
$104$	2.45747	−	0.894447i	0.240975	−	0.0877077i
$105$		0			0
$106$	0.846062	+	1.46542i	0.0821768	+	0.142334i
$107$	−2.44085	−	1.40922i	−0.235966	−	0.136235i	0.377355	−	0.926069i	$-0.376834\pi$
$107$	−2.44085	−	1.40922i	−0.235966	−	0.136235i	−0.613321	+	0.789834i	$0.710167\pi$
$108$		0			0
$109$	−5.16898	+	4.33729i	−0.495098	+	0.415437i	−0.855849	−	0.517225i	$-0.826965\pi$
$109$	−5.16898	+	4.33729i	−0.495098	+	0.415437i	0.360751	+	0.932662i	$0.382520\pi$
$110$	−0.554644	+	1.66038i	−0.0528832	+	0.158311i
$111$		0			0
$112$	−4.91651	+	13.5080i	−0.464566	+	1.27639i
$113$		−	7.76636i		−	0.730598i	−0.930890	−	0.365299i	$-0.880967\pi$
$113$		−	7.76636i		−	0.730598i	0.930890	−	0.365299i	$-0.119033\pi$
$114$		0			0
$115$	6.22750	+	15.7865i	0.580717	+	1.47210i
$116$	−2.48114	−	0.903060i	−0.230368	−	0.0838471i
$117$		0			0
$118$	−1.25475	+	1.49535i	−0.115509	+	0.137658i
$119$	6.84796	−	5.74612i	0.627752	−	0.526746i
$120$		0			0
$121$	0.587002	−	1.01672i	0.0533638	−	0.0924288i
$122$	0.224814	−	0.129796i	0.0203537	−	0.0117512i
$123$		0			0
$124$	−1.62863	+	0.592774i	−0.146255	+	0.0532326i
$125$	−11.1446	+	0.893733i	−0.996800	+	0.0799379i
$126$		0			0
$127$	1.65693	+	0.292162i	0.147029	+	0.0259251i	0.246678	−	0.969097i	$-0.420661\pi$
$127$	1.65693	+	0.292162i	0.147029	+	0.0259251i	−0.0996493	+	0.995023i	$0.531772\pi$
$128$	−4.74409	−	5.65378i	−0.419322	−	0.499728i
$129$		0			0
$130$	−0.776585	−	1.26587i	−0.0681110	−	0.111024i
$131$	−7.21678	−	2.62669i	−0.630533	−	0.229495i	0.00693025	−	0.999976i	$-0.497794\pi$
$131$	−7.21678	−	2.62669i	−0.630533	−	0.229495i	−0.637463	+	0.770481i	$0.720016\pi$
$132$		0			0
$133$	17.2630	−	0.0521804i	1.49689	−	0.00452462i
$134$	−3.79899			−0.328183
$135$		0			0
$136$	0.385458	+	2.18604i	0.0330527	+	0.187451i
$137$	6.23168	−	7.42662i	0.532408	−	0.634499i	−0.431060	−	0.902323i	$-0.641860\pi$
$137$	6.23168	−	7.42662i	0.532408	−	0.634499i	0.963468	+	0.267824i	$0.0863046\pi$
$138$		0			0
$139$	1.11197	−	6.30632i	0.0943165	−	0.534895i	−0.900638	−	0.434570i	$-0.856900\pi$
$139$	1.11197	−	6.30632i	0.0943165	−	0.534895i	0.994955	−	0.100326i	$-0.0319884\pi$
$140$	16.9720	+	2.52790i	1.43439	+	0.213646i
$141$		0			0
$142$	−0.891580	−	2.44960i	−0.0748197	−	0.205565i
$143$	−2.85103	−	7.83314i	−0.238415	−	0.655040i
$144$		0			0
$145$	−0.448893	+	3.01381i	−0.0372786	+	0.250283i
$146$	0.181331	−	1.02838i	0.0150071	−	0.0851093i
$147$		0			0
$148$	8.25177	−	9.83408i	0.678291	−	0.808356i
$149$	−0.337776	−	1.91562i	−0.0276716	−	0.156934i	0.967841	−	0.251563i	$-0.0809446\pi$
$149$	−0.337776	−	1.91562i	−0.0276716	−	0.156934i	−0.995513	+	0.0946292i	$0.969833\pi$
$150$		0			0
$151$	−16.7168			−1.36040			−0.680199	−	0.733028i	$-0.738107\pi$
$151$	−16.7168			−1.36040			−0.680199	+	0.733028i	$0.738107\pi$
$152$	−2.13209	+	3.71881i	−0.172936	+	0.301635i
$153$		0			0
$154$	−2.91355	−	1.06045i	−0.234781	−	0.0854531i
$155$	1.04589	+	1.70485i	0.0840083	+	0.136937i
$156$		0			0
$157$	−6.30587	−	7.51504i	−0.503263	−	0.599766i	0.453276	−	0.891370i	$-0.350255\pi$
$157$	−6.30587	−	7.51504i	−0.503263	−	0.599766i	−0.956539	+	0.291605i	$0.905811\pi$
$158$	2.75679	+	0.486096i	0.219318	+	0.0386717i
$159$		0			0
$160$	−3.99718	+	5.03024i	−0.316005	+	0.397676i
$161$	−28.2446	+	10.2802i	−2.22599	+	0.810193i
$162$		0			0
$163$	4.38712	−	2.53291i	0.343626	−	0.198393i	−0.318248	−	0.948007i	$-0.603095\pi$
$163$	4.38712	−	2.53291i	0.343626	−	0.198393i	0.661874	+	0.749615i	$0.269761\pi$
$164$	6.04195	−	10.4650i	0.471797	−	0.817177i
$165$		0			0
$166$	−2.53580	+	2.12779i	−0.196816	+	0.165149i
$167$	12.9593	−	15.4443i	1.00282	−	1.19512i	0.0220890	−	0.999756i	$-0.492968\pi$
$167$	12.9593	−	15.4443i	1.00282	−	1.19512i	0.980732	−	0.195359i	$-0.0625873\pi$
$168$		0			0
$169$	−5.57078	−	2.02760i	−0.428522	−	0.155969i
$170$	1.17260	−	0.462570i	0.0899344	−	0.0354775i
$171$		0			0
$172$		−	3.43418i		−	0.261854i
$173$	−0.666513	+	1.83123i	−0.0506741	+	0.139226i	−0.962448	−	0.271467i	$-0.912491\pi$
$173$	−0.666513	+	1.83123i	−0.0506741	+	0.139226i	0.911774	+	0.410693i	$0.134713\pi$
$174$		0			0
$175$	−1.05592	−	19.7740i	−0.0798200	−	1.49477i
$176$	−8.71577	+	7.31340i	−0.656976	+	0.551268i
$177$		0			0
$178$	0.321141	+	0.185411i	0.0240705	+	0.0138971i
$179$	−8.63549	−	14.9571i	−0.645447	−	1.11795i	−0.984198	−	0.177071i	$-0.943338\pi$
$179$	−8.63549	−	14.9571i	−0.645447	−	1.11795i	0.338752	−	0.940876i	$-0.389995\pi$
$180$		0			0
$181$	−13.5671	+	4.93801i	−1.00843	+	0.367039i	−0.792830	−	0.609442i	$-0.791393\pi$
$181$	−13.5671	+	4.93801i	−1.00843	+	0.367039i	−0.215601	+	0.976481i	$0.569171\pi$
$182$	2.27793	−	1.31516i	0.168852	−	0.0974865i
$183$		0			0
$184$	1.29604	−	7.35022i	0.0955455	−	0.541866i
$185$	−13.0230	−	7.06256i	−0.957468	−	0.519250i
$186$		0			0
$187$	6.96796	−	1.22864i	0.509547	−	0.0898469i
$188$	0.116876	−	0.321113i	0.00852404	−	0.0234196i
$189$		0			0
$190$	2.31118	+	0.764281i	0.167670	+	0.0554467i
$191$	8.05176			0.582605			0.291302	−	0.956631i	$-0.405911\pi$
$191$	8.05176			0.582605			0.291302	+	0.956631i	$0.405911\pi$
$192$		0			0
$193$	6.04326	−	1.06559i	0.435004	−	0.0767029i	0.0481417	−	0.998841i	$-0.484670\pi$
$193$	6.04326	−	1.06559i	0.435004	−	0.0767029i	0.386862	+	0.922138i	$0.373559\pi$
$194$	2.94373	+	2.47008i	0.211347	+	0.177342i
$195$		0			0
$196$	−2.92219	+	16.5725i	−0.208728	+	1.18375i
$197$	−15.0827	−	8.70798i	−1.07460	−	0.620418i	−0.145162	−	0.989408i	$-0.546370\pi$
$197$	−15.0827	−	8.70798i	−1.07460	−	0.620418i	−0.929433	+	0.368990i	$0.879704\pi$
$198$		0			0
$199$	0.00995808	−	0.00362445i	0.000705910	−	0.000256930i	−0.341667	−	0.939821i	$-0.610992\pi$
$199$	0.00995808	−	0.00362445i	0.000705910	−	0.000256930i	0.342373	+	0.939564i	$0.388769\pi$
$200$	4.38339	+	2.22799i	0.309953	+	0.157543i
$201$		0			0
$202$	−1.28117	−	0.739681i	−0.0901425	−	0.0520438i
$203$	−5.31482	−	0.937147i	−0.373027	−	0.0657748i
$204$		0			0
$205$	−13.2267	−	4.41832i	−0.923792	−	0.308589i
$206$	−0.217163	−	1.23159i	−0.0151305	−	0.0858091i
$207$		0			0
$208$		−	9.65218i		−	0.669258i
$209$	11.8536	+	6.79600i	0.819932	+	0.470089i
$210$		0			0
$211$	−25.4903	−	9.27771i	−1.75482	−	0.638704i	−0.754970	−	0.655759i	$-0.772349\pi$
$211$	−25.4903	−	9.27771i	−1.75482	−	0.638704i	−0.999855	+	0.0170552i	$0.994571\pi$
$212$	12.9285	−	2.27964i	0.887930	−	0.156566i
$213$		0			0
$214$	0.539226	−	0.452464i	0.0368607	−	0.0309298i
$215$	−3.88318	+	0.792042i	−0.264831	+	0.0540168i
$216$		0			0
$217$	−3.06789	+	1.77125i	−0.208262	+	0.120240i
$218$	−0.576380	−	1.58359i	−0.0390374	−	0.107254i
$219$		0			0
$220$	10.6331	+	8.44933i	0.716880	+	0.569654i
$221$	−3.00122	+	5.19826i	−0.201884	+	0.349673i
$222$		0			0
$223$	−4.91760	−	5.86057i	−0.329307	−	0.392453i	0.575832	−	0.817568i	$-0.304678\pi$
$223$	−4.91760	−	5.86057i	−0.329307	−	0.392453i	−0.905139	+	0.425115i	$0.860234\pi$
$224$	−8.71736	−	7.31473i	−0.582453	−	0.488736i
$225$		0			0
$226$	1.82268	+	0.663401i	0.121243	+	0.0441288i
$227$			25.9617i			1.72314i	0.507638	+	0.861571i	$0.330519\pi$
$227$			25.9617i			1.72314i	−0.507638	+	0.861571i	$0.669481\pi$
$228$		0			0
$229$	6.42130			0.424332			0.212166	−	0.977234i	$-0.431948\pi$
$229$	6.42130			0.424332			0.212166	+	0.977234i	$0.431948\pi$
$230$	−4.23687	+	0.113043i	−0.279371	+	0.00745383i
$231$		0			0
$232$	0.861398	−	1.02657i	0.0565536	−	0.0673979i
$233$	12.2743	+	14.6280i	0.804117	+	0.958309i	0.999750	−	0.0223680i	$-0.00712055\pi$
$233$	12.2743	+	14.6280i	0.804117	+	0.958309i	−0.195633	+	0.980677i	$0.562676\pi$
$234$		0			0
$235$	−0.390053	−	0.0580966i	−0.0254442	−	0.00378980i
$236$	7.57219	+	13.1154i	0.492908	+	0.853741i
$237$		0			0
$238$	0.763600	+	2.09797i	0.0494968	+	0.135991i
$239$	4.19589	+	7.26749i	0.271409	+	0.470095i	0.969223	−	0.246184i	$-0.0791769\pi$
$239$	4.19589	+	7.26749i	0.271409	+	0.470095i	−0.697813	+	0.716279i	$0.745844\pi$
$240$		0			0
$241$	−1.49631	+	8.48598i	−0.0963856	+	0.546630i	0.897928	+	0.440142i	$0.145072\pi$
$241$	−1.49631	+	8.48598i	−0.0963856	+	0.546630i	−0.994314	+	0.106488i	$0.966039\pi$
$242$	0.188471	+	0.224611i	0.0121154	+	0.0144385i
$243$		0			0
$244$	−0.349724	−	1.98338i	−0.0223888	−	0.126973i
$245$	19.4133	−	0.517961i	1.24027	−	0.0330913i
$246$		0			0
$247$	−10.8804	+	3.99742i	−0.692303	+	0.254350i
$248$		−	0.879647i		−	0.0558576i
$249$		0			0
$250$	0.742216	−	2.69185i	0.0469419	−	0.170247i
$251$	−22.4159	−	18.8092i	−1.41488	−	1.18723i	−0.954016	−	0.299755i	$-0.903095\pi$
$251$	−22.4159	−	18.8092i	−1.41488	−	1.18723i	−0.460864	−	0.887471i	$-0.652460\pi$
$252$		0			0
$253$	−23.4287	−	4.13111i	−1.47295	−	0.259721i
$254$	−0.210102	+	0.363907i	−0.0131829	+	0.0228335i
$255$		0			0
$256$	−10.5622	+	3.84432i	−0.660136	+	0.240270i
$257$	1.87450	+	5.15016i	0.116928	+	0.321258i	0.984326	−	0.176357i	$-0.0564314\pi$
$257$	1.87450	+	5.15016i	0.116928	+	0.321258i	−0.867398	+	0.497615i	$0.834209\pi$
$258$		0			0
$259$	13.1196	−	22.7239i	0.815214	−	1.41199i
$260$	−11.2893	+	2.30264i	−0.700130	+	0.142804i
$261$		0			0
$262$	1.23291	−	1.46933i	0.0761695	−	0.0907753i
$263$	−0.559648	+	0.0986810i	−0.0345094	+	0.00608493i	−0.190876	−	0.981614i	$-0.561133\pi$
$263$	−0.559648	+	0.0986810i	−0.0345094	+	0.00608493i	0.156367	+	0.987699i	$0.450022\pi$
$264$		0			0
$265$	−5.55944	−	14.0930i	−0.341514	−	0.865727i
$266$	−1.46236	+	4.05589i	−0.0896628	+	0.248683i
$267$		0			0
$268$	−10.0805	+	27.6960i	−0.615766	+	1.69180i
$269$	−0.771539	−	4.37561i	−0.0470416	−	0.266786i	0.952211	−	0.305441i	$-0.0988038\pi$
$269$	−0.771539	−	4.37561i	−0.0470416	−	0.266786i	−0.999253	+	0.0386549i	$0.987693\pi$
$270$		0			0
$271$	13.6096	−	11.4198i	0.826722	−	0.693702i	−0.127814	−	0.991798i	$-0.540796\pi$
$271$	13.6096	−	11.4198i	0.826722	−	0.693702i	0.954536	+	0.298096i	$0.0963515\pi$
$272$	8.06827	+	1.42265i	0.489211	+	0.0862611i
$273$		0			0
$274$	1.21064	+	2.09689i	0.0731373	+	0.126677i
$275$	7.10168	−	13.9720i	0.428247	−	0.842542i
$276$		0			0
$277$	−7.01870	+	4.05225i	−0.421713	+	0.243476i	−0.695810	−	0.718226i	$-0.744954\pi$
$277$	−7.01870	+	4.05225i	−0.421713	+	0.243476i	0.274097	+	0.961702i	$0.411621\pi$
$278$	1.38504	+	0.799652i	0.0830691	+	0.0479600i
$279$		0			0
$280$	−4.15178	+	7.65566i	−0.248117	+	0.457513i
$281$	−5.40233	−	4.53309i	−0.322276	−	0.270422i	0.467268	−	0.884116i	$-0.345238\pi$
$281$	−5.40233	−	4.53309i	−0.322276	−	0.270422i	−0.789544	+	0.613694i	$0.789683\pi$
$282$		0			0
$283$	0.444154	−	1.22030i	0.0264022	−	0.0725395i	−0.925791	−	0.378035i	$-0.876600\pi$
$283$	0.444154	−	1.22030i	0.0264022	−	0.0725395i	0.952194	+	0.305496i	$0.0988221\pi$
$284$	−20.2242			−1.20009
$285$		0			0
$286$	2.08188			0.123104
$287$	8.44756	−	23.2095i	0.498644	−	1.37001i
$288$		0			0
$289$	9.11988	+	7.65248i	0.536463	+	0.450146i
$290$	−0.668963	−	0.362789i	−0.0392829	−	0.0213037i
$291$		0			0
$292$	−7.01609	−	4.05074i	−0.410586	−	0.237052i
$293$	−12.9469	+	7.47489i	−0.756365	+	0.436688i	−0.827989	−	0.560744i	$-0.810515\pi$
$293$	−12.9469	+	7.47489i	−0.756365	+	0.436688i	0.0716238	+	0.997432i	$0.477182\pi$
$294$		0			0
$295$	13.0838	−	11.5871i	0.761766	−	0.674626i
$296$	3.25777	+	5.64263i	0.189354	+	0.327971i
$297$		0			0
$298$	0.478427	+	0.0843596i	0.0277146	+	0.00488682i
$299$	15.4605	−	12.9729i	0.894105	−	0.750243i
$300$		0			0
$301$	−1.21889	−	6.91268i	−0.0702558	−	0.398440i
$302$	1.42795	−	3.92326i	0.0821692	−	0.225758i
$303$		0			0
$304$	10.2063	+	12.0890i	0.585370	+	0.693350i
$305$	−2.16204	+	0.852886i	−0.123798	+	0.0488361i
$306$		0			0
$307$	4.93754	−	0.870621i	0.281800	−	0.0496890i	−0.0309616	−	0.999521i	$-0.509857\pi$
$307$	4.93754	−	0.870621i	0.281800	−	0.0496890i	0.312762	+	0.949832i	$0.398746\pi$
$308$	−15.4621	+	18.4270i	−0.881032	+	1.04997i
$309$		0			0
$310$	−0.489450	+	0.0998318i	−0.0277989	+	0.00567006i
$311$	−8.37214	+	14.5010i	−0.474741	+	0.822275i	−0.999582	−	0.0289254i	$-0.990791\pi$
$311$	−8.37214	+	14.5010i	−0.474741	+	0.822275i	0.524841	+	0.851200i	$0.324125\pi$
$312$		0			0
$313$	−1.96271	−	5.39250i	−0.110939	−	0.304802i	0.871783	−	0.489893i	$-0.162964\pi$
$313$	−1.96271	−	5.39250i	−0.110939	−	0.304802i	−0.982721	+	0.185091i	$0.940742\pi$
$314$	2.30234	−	0.837984i	0.129929	−	0.0472902i
$315$		0			0
$316$	10.8589	−	18.8081i	0.610859	−	1.05804i
$317$	7.82563	+	1.37987i	0.439531	+	0.0775012i	0.389035	−	0.921223i	$-0.372809\pi$
$317$	7.82563	+	1.37987i	0.439531	+	0.0775012i	0.0504963	+	0.998724i	$0.483920\pi$
$318$		0			0
$319$	−3.27218	−	2.74569i	−0.183207	−	0.153729i
$320$	7.64906	+	12.4683i	0.427595	+	0.696998i
$321$		0			0
$322$		−	7.50683i		−	0.418339i
$323$	−1.73777	−	9.68412i	−0.0966921	−	0.538839i
$324$		0			0
$325$	5.20739	+	12.2342i	0.288854	+	0.678631i
$326$	0.219698	+	1.24597i	0.0121679	+	0.0690078i
$327$		0			0
$328$	3.94227	+	4.69821i	0.217675	+	0.259415i
$329$	0.121287	−	0.687854i	0.00668678	−	0.0379226i
$330$		0			0
$331$	10.4088	+	18.0286i	0.572121	+	0.990943i	0.996348	+	0.0853872i	$0.0272127\pi$
$331$	10.4088	+	18.0286i	0.572121	+	0.990943i	−0.424226	+	0.905556i	$0.639454\pi$
$332$	8.78367	+	24.1329i	0.482067	+	1.32447i
$333$		0			0
$334$	2.51762	+	4.36065i	0.137758	+	0.238604i
$335$	33.6420	+	5.01083i	1.83806	+	0.273771i
$336$		0			0
$337$	17.5878	+	20.9603i	0.958069	+	1.14178i	0.989826	+	0.142286i	$0.0454454\pi$
$337$	17.5878	+	20.9603i	0.958069	+	1.14178i	−0.0317566	+	0.999496i	$0.510110\pi$
$338$	0.951710	−	1.13420i	0.0517662	−	0.0616925i
$339$		0			0
$340$	−0.260834	−	9.77610i	−0.0141457	−	0.530184i
$341$	−2.80386			−0.151837
$342$		0			0
$343$			6.67319i			0.360318i
$344$	1.63787	+	0.596137i	0.0883082	+	0.0321415i
$345$		0			0
$346$	−0.372836	−	0.312846i	−0.0200438	−	0.0168187i
$347$	−12.9842	−	15.4740i	−0.697031	−	0.830689i	0.295156	−	0.955449i	$-0.404628\pi$
$347$	−12.9842	−	15.4740i	−0.697031	−	0.830689i	−0.992187	+	0.124760i	$0.960184\pi$
$348$		0			0
$349$	−7.81199	+	13.5308i	−0.418166	+	0.724285i	−0.995755	−	0.0920429i	$-0.970660\pi$
$349$	−7.81199	+	13.5308i	−0.418166	+	0.724285i	0.577589	+	0.816328i	$0.303994\pi$
$350$	4.73092	+	1.44127i	0.252878	+	0.0770393i
$351$		0			0
$352$	−3.08055	−	8.46375i	−0.164194	−	0.451120i
$353$	−3.98149	+	2.29871i	−0.211913	+	0.122348i	−0.602200	−	0.798345i	$-0.705709\pi$
$353$	−3.98149	+	2.29871i	−0.211913	+	0.122348i	0.390287	+	0.920693i	$0.372376\pi$
$354$		0			0
$355$	4.66441	+	22.8684i	0.247561	+	1.21373i
$356$	2.20385	−	1.84925i	0.116804	−	0.0980100i
$357$		0			0
$358$	4.24791	−	0.749020i	0.224509	−	0.0395870i
$359$	10.1771	+	3.70416i	0.537126	+	0.195498i	0.596317	−	0.802749i	$-0.296630\pi$
$359$	10.1771	+	3.70416i	0.537126	+	0.195498i	−0.0591913	+	0.998247i	$0.518852\pi$
$360$		0			0
$361$	9.40035	−	16.5116i	0.494755	−	0.869032i
$362$		−	3.60584i		−	0.189519i
$363$		0			0
$364$	−3.54359	−	20.0967i	−0.185735	−	1.05335i
$365$	−2.96220	+	8.86765i	−0.155049	+	0.464154i
$366$		0			0
$367$	−6.56116	−	1.15691i	−0.342490	−	0.0603902i	−0.000242048	−	1.00000i	$-0.500077\pi$
$367$	−6.56116	−	1.15691i	−0.342490	−	0.0603902i	−0.342248	+	0.939610i	$0.611188\pi$
$368$	−23.8562	−	13.7734i	−1.24359	−	0.717989i
$369$		0			0
$370$	2.76992	−	2.45306i	0.144001	−	0.127529i
$371$	25.2147	−	9.17739i	1.30908	−	0.476466i
$372$		0			0
$373$	15.6934	+	9.06058i	0.812573	+	0.469139i	0.847849	−	0.530238i	$-0.177898\pi$
$373$	15.6934	+	9.06058i	0.812573	+	0.469139i	−0.0352756	+	0.999378i	$0.511231\pi$
$374$	−0.306853	+	1.74025i	−0.0158670	+	0.0899862i
$375$		0			0
$376$	0.132861	+	0.111484i	0.00685179	+	0.00574933i
$377$	3.56869	−	0.629256i	0.183797	−	0.0324083i
$378$		0			0
$379$	−31.9277			−1.64002			−0.820008	−	0.572352i	$-0.806031\pi$
$379$	−31.9277			−1.64002			−0.820008	+	0.572352i	$0.806031\pi$
$380$	11.7045	−	14.8213i	0.600429	−	0.760317i
$381$		0			0
$382$	−0.687779	+	1.88966i	−0.0351898	+	0.0966833i
$383$	13.5753	−	2.39369i	0.693666	−	0.122312i	0.184310	−	0.982868i	$-0.440995\pi$
$383$	13.5753	−	2.39369i	0.693666	−	0.122312i	0.509356	+	0.860556i	$0.329884\pi$
$384$		0			0
$385$	24.4023	+	13.2337i	1.24365	+	0.674453i
$386$	−0.266132	+	1.50931i	−0.0135458	+	0.0768218i
$387$		0			0
$388$	25.8189	−	14.9065i	1.31076	−	0.756765i
$389$	23.1934	−	8.44172i	1.17595	−	0.428012i	0.321182	−	0.947017i	$-0.395920\pi$
$389$	23.1934	−	8.44172i	1.17595	−	0.428012i	0.854771	+	0.519005i	$0.173698\pi$
$390$		0			0
$391$	8.56532	+	14.8356i	0.433167	+	0.750267i
$392$	−7.39673	−	4.27050i	−0.373591	−	0.215693i
$393$		0			0
$394$	3.33202	−	2.79590i	0.167865	−	0.140855i
$395$	−23.7716	−	7.94080i	−1.19608	−	0.399545i
$396$		0			0
$397$	−6.11117	+	16.7903i	−0.306711	+	0.842681i	0.686582	+	0.727053i	$0.259110\pi$
$397$	−6.11117	+	16.7903i	−0.306711	+	0.842681i	−0.993293	+	0.115628i	$0.963112\pi$
$398$			0.00264665i			0.000132665i
$399$		0			0
$400$	13.2605	−	12.3902i	0.663025	−	0.619508i
$401$	−21.5491	−	7.84324i	−1.07611	−	0.391673i	−0.257653	−	0.966238i	$-0.582949\pi$
$401$	−21.5491	−	7.84324i	−1.07611	−	0.391673i	−0.818459	+	0.574565i	$0.805171\pi$
$402$		0			0
$403$	1.52896	−	1.82215i	0.0761631	−	0.0907676i
$404$	−8.79208	+	7.37743i	−0.437422	+	0.367041i
$405$		0			0
$406$	0.673929	−	1.16728i	0.0334465	−	0.0579311i
$407$	17.9858	−	10.3841i	0.891521	−	0.514720i
$408$		0			0
$409$	23.6619	−	8.61222i	1.17001	−	0.425847i	0.317343	−	0.948311i	$-0.397209\pi$
$409$	23.6619	−	8.61222i	1.17001	−	0.425847i	0.852662	+	0.522464i	$0.174987\pi$
$410$	2.16675	−	2.72674i	0.107008	−	0.134664i
$411$		0			0
$412$	−9.55499	−	1.68480i	−0.470741	−	0.0830043i
$413$	19.8972	+	23.7125i	0.979075	+	1.16682i
$414$		0			0
$415$	25.2624	−	15.4980i	1.24008	−	0.760766i
$416$	7.18020	+	2.61338i	0.352038	+	0.128131i
$417$		0			0
$418$	−2.60748	+	2.20140i	−0.127536	+	0.107674i
$419$	0.249578			0.0121927			0.00609635	−	0.999981i	$-0.498059\pi$
$419$	0.249578			0.0121927			0.00609635	+	0.999981i	$0.498059\pi$
$420$		0			0
$421$	5.23866	+	29.7099i	0.255316	+	1.44797i	0.795259	+	0.606270i	$0.207335\pi$
$421$	5.23866	+	29.7099i	0.255316	+	1.44797i	−0.539943	+	0.841702i	$0.681554\pi$
$422$	4.35475	−	5.18979i	0.211986	−	0.252635i
$423$		0			0
$424$	−1.15701	+	6.56172i	−0.0561893	+	0.318666i
$425$	−10.9941	+	2.54965i	−0.533293	+	0.123676i
$426$		0			0
$427$	−1.40792	−	3.86824i	−0.0681342	−	0.187197i
$428$	−1.86781	−	5.13175i	−0.0902838	−	0.248053i
$429$		0			0
$430$	0.145817	−	0.978995i	0.00703191	−	0.0472113i
$431$	−2.67705	+	15.1823i	−0.128949	+	0.731307i	0.849935	+	0.526888i	$0.176641\pi$
$431$	−2.67705	+	15.1823i	−0.128949	+	0.731307i	−0.978884	+	0.204418i	$0.934470\pi$
$432$		0			0
$433$	−8.05915	+	9.60452i	−0.387298	+	0.461564i	−0.924104	−	0.382142i	$-0.875186\pi$
$433$	−8.05915	+	9.60452i	−0.387298	+	0.461564i	0.536806	+	0.843706i	$0.319631\pi$
$434$	−0.153634	−	0.871299i	−0.00737465	−	0.0418237i
$435$		0			0
$436$	−13.0744			−0.626148
$437$	−5.64604	+	32.5961i	−0.270087	+	1.55928i
$438$		0			0
$439$	23.7964	+	8.66118i	1.13574	+	0.413375i	0.840373	−	0.542008i	$-0.182336\pi$
$439$	23.7964	+	8.66118i	1.13574	+	0.413375i	0.295367	+	0.955384i	$0.404558\pi$
$440$	−5.87555	+	3.60454i	−0.280106	+	0.171840i
$441$		0			0
$442$	−0.963611	−	1.14839i	−0.0458343	−	0.0546232i
$443$	−7.30468	−	1.28801i	−0.347056	−	0.0611953i	−0.00259666	−	0.999997i	$-0.500827\pi$
$443$	−7.30468	−	1.28801i	−0.347056	−	0.0611953i	−0.344459	+	0.938801i	$0.611938\pi$
$444$		0			0
$445$	−2.59931	−	2.06549i	−0.123219	−	0.0979135i
$446$	1.79547	−	0.653498i	0.0850180	−	0.0309440i
$447$		0			0
$448$	−22.4368	+	12.9539i	−1.06004	+	0.612013i
$449$	−12.0290	+	20.8349i	−0.567684	+	0.983257i	0.429110	+	0.903252i	$0.358827\pi$
$449$	−12.0290	+	20.8349i	−0.567684	+	0.983257i	−0.996794	+	0.0800054i	$0.974506\pi$
$450$		0			0
$451$	14.9755	−	12.5659i	0.705166	−	0.591705i
$452$	9.67286	−	11.5277i	0.454973	−	0.542216i
$453$		0			0
$454$	−6.09293	−	2.21765i	−0.285955	−	0.104079i
$455$	−21.9069	+	8.64189i	−1.02701	+	0.405138i
$456$		0			0
$457$			6.39908i			0.299337i	0.988736	+	0.149668i	$0.0478206\pi$
$457$			6.39908i			0.299337i	−0.988736	+	0.149668i	$0.952179\pi$
$458$	−0.548506	+	1.50701i	−0.0256300	+	0.0704178i
$459$		0			0
$460$	−10.4183	+	31.1883i	−0.485756	+	1.45416i
$461$	11.6823	−	9.80258i	0.544097	−	0.456552i	−0.328839	−	0.944386i	$-0.606657\pi$
$461$	11.6823	−	9.80258i	0.544097	−	0.456552i	0.872936	+	0.487834i	$0.162213\pi$
$462$		0			0
$463$	−31.5491	−	18.2149i	−1.46621	−	0.846518i	−0.466927	−	0.884296i	$-0.654639\pi$
$463$	−31.5491	−	18.2149i	−1.46621	−	0.846518i	−0.999286	+	0.0377774i	$0.987972\pi$
$464$	−2.47303	−	4.28341i	−0.114807	−	0.198852i
$465$		0			0
$466$	−4.48149	+	1.63113i	−0.207601	+	0.0755605i
$467$	−24.4191	+	14.0984i	−1.12998	+	0.652395i	−0.943930	−	0.330146i	$-0.892902\pi$
$467$	−24.4191	+	14.0984i	−1.12998	+	0.652395i	−0.186050	+	0.982540i	$0.559569\pi$
$468$		0			0
$469$	−10.4610	+	59.3274i	−0.483045	+	2.73948i
$470$	0.0469528	−	0.0865784i	0.00216577	−	0.00399356i
$471$		0			0
$472$	−7.56962	+	1.33473i	−0.348420	+	0.0614359i
$473$	1.90017	−	5.22069i	0.0873701	−	0.240047i
$474$		0			0
$475$	−19.4586	−	9.81651i	−0.892821	−	0.450412i
$476$	17.3212			0.793914
$477$		0			0
$478$	−2.06401	+	0.363941i	−0.0944057	+	0.0166463i
$479$	22.5455	+	18.9179i	1.03013	+	0.864383i	0.990867	−	0.134846i	$-0.0430540\pi$
$479$	22.5455	+	18.9179i	1.03013	+	0.864383i	0.0392648	+	0.999229i	$0.487498\pi$
$480$		0			0
$481$	−3.05944	+	17.3509i	−0.139498	+	0.791135i
$482$	−1.86375	−	1.07604i	−0.0848915	−	0.0490121i
$483$		0			0
$484$	2.13759	−	0.778020i	0.0971633	−	0.0353646i
$485$	−22.8102	−	25.7566i	−1.03576	−	1.16955i
$486$		0			0
$487$	−2.35574	−	1.36008i	−0.106749	−	0.0616313i	0.445675	−	0.895195i	$-0.352964\pi$
$487$	−2.35574	−	1.36008i	−0.106749	−	0.0616313i	−0.552424	+	0.833563i	$0.686297\pi$
$488$	1.00665	+	0.177499i	0.0455689	+	0.00803502i
$489$		0			0
$490$	−1.53672	+	4.60032i	−0.0694218	+	0.207821i
$491$	−3.29287	−	18.6748i	−0.148605	−	0.842781i	−0.964402	−	0.264442i	$-0.914812\pi$
$491$	−3.29287	−	18.6748i	−0.148605	−	0.842781i	0.815796	−	0.578339i	$-0.196299\pi$
$492$		0			0
$493$			3.07582i			0.138528i
$494$	−0.00875052	−	2.89496i	−0.000393705	−	0.130251i
$495$		0			0
$496$	−3.05082	−	1.11041i	−0.136986	−	0.0498588i
$497$	−40.7095	+	7.17817i	−1.82607	+	0.321985i
$498$		0			0
$499$	4.61421	−	3.87179i	0.206561	−	0.173325i	−0.533638	−	0.845713i	$-0.679176\pi$
$499$	4.61421	−	3.87179i	0.206561	−	0.173325i	0.740199	+	0.672388i	$0.234731\pi$
$500$	−17.6551	−	12.5538i	−0.789559	−	0.561421i
$501$		0			0
$502$	6.32907	−	3.65409i	0.282480	−	0.163090i
$503$	−6.36795	−	17.4958i	−0.283933	−	0.780099i	−0.996884	−	0.0788848i	$-0.974864\pi$
$503$	−6.36795	−	17.4958i	−0.283933	−	0.780099i	0.712951	−	0.701214i	$-0.247358\pi$
$504$		0			0
$505$	10.3697	+	8.24010i	0.461448	+	0.366680i
$506$	2.97080	−	5.14557i	0.132068	−	0.228749i
$507$		0			0
$508$	2.09551	+	2.49733i	0.0929733	+	0.110801i
$509$	20.0405	+	16.8160i	0.888281	+	0.745356i	0.967865	−	0.251472i	$-0.0809147\pi$
$509$	20.0405	+	16.8160i	0.888281	+	0.745356i	−0.0795838	+	0.996828i	$0.525359\pi$
$510$		0			0
$511$	−15.5605	−	5.66355i	−0.688355	−	0.250541i
$512$		−	17.5682i		−	0.776411i
$513$		0			0
$514$	−1.36880			−0.0603754
$515$	0.298633	+	11.1928i	0.0131593	+	0.493215i
$516$		0			0
$517$	0.355352	−	0.423492i	0.0156284	−	0.0186252i
$518$	4.21236	+	5.02010i	0.185081	+	0.220570i
$519$		0			0
$520$	0.861490	−	5.78393i	0.0377789	−	0.253642i
$521$	−1.53459	−	2.65798i	−0.0672315	−	0.116448i	0.830450	−	0.557093i	$-0.188083\pi$
$521$	−1.53459	−	2.65798i	−0.0672315	−	0.116448i	−0.897682	+	0.440645i	$0.854750\pi$
$522$		0			0
$523$	3.93883	+	10.8219i	0.172233	+	0.473207i	0.995535	−	0.0943977i	$-0.0300925\pi$
$523$	3.93883	+	10.8219i	0.172233	+	0.473207i	−0.823301	+	0.567604i	$0.807870\pi$
$524$	−7.44042	−	12.8872i	−0.325036	−	0.562979i
$525$		0			0
$526$	0.0246456	−	0.139772i	0.00107460	−	0.00609436i
$527$	1.29778	+	1.54663i	0.0565321	+	0.0673724i
$528$		0			0
$529$	−6.00809	−	34.0735i	−0.261221	−	1.48146i
$530$	3.78236	−	0.100916i	0.164295	−	0.00438352i
$531$		0			0
$532$	25.6886	+	21.4233i	1.11374	+	0.928818i
$533$			16.5844i			0.718350i
$534$		0			0
$535$	−5.37192	+	3.29557i	−0.232248	+	0.142480i
$536$	−11.4593	−	9.61547i	−0.494965	−	0.415325i
$537$		0			0
$538$	1.09281	+	0.192692i	0.0471145	+	0.00830756i
$539$	−13.6121	+	23.5769i	−0.586316	+	1.01553i
$540$		0			0
$541$	28.0468	−	10.2082i	1.20583	−	0.438885i	0.340573	−	0.940218i	$-0.389379\pi$
$541$	28.0468	−	10.2082i	1.20583	−	0.438885i	0.865255	+	0.501333i	$0.167157\pi$
$542$	1.51757	+	4.16949i	0.0651852	+	0.179095i
$543$		0			0
$544$	−3.24283	+	5.61675i	−0.139035	+	0.240816i
$545$	3.01540	+	14.7838i	0.129166	+	0.633266i
$546$		0			0
$547$	0.756420	−	0.901466i	0.0323422	−	0.0385439i	−0.749631	−	0.661856i	$-0.769769\pi$
$547$	0.756420	−	0.901466i	0.0323422	−	0.0385439i	0.781973	+	0.623312i	$0.214213\pi$
$548$	18.4994	−	3.26195i	0.790257	−	0.139344i
$549$		0			0
$550$	2.67244	+	2.86017i	0.113953	+	0.121958i
$551$	−3.80426	+	4.56168i	−0.162067	+	0.194334i
$552$		0			0
$553$	15.1823	−	41.7131i	0.645619	−	1.77382i
$554$	−0.351482	−	1.99335i	−0.0149330	−	0.0846894i
$555$		0			0
$556$	9.50492	−	7.97557i	0.403098	−	0.338240i
$557$	45.2840	+	7.98479i	1.91874	+	0.338326i	0.998583	−	0.0532132i	$-0.0169463\pi$
$557$	45.2840	+	7.98479i	1.91874	+	0.338326i	0.920161	+	0.391540i	$0.128057\pi$
$558$		0			0
$559$	2.35660	+	4.08175i	0.0996734	+	0.172639i
$560$	21.3107	+	24.0634i	0.900541	+	1.01686i
$561$		0			0
$562$	1.52533	−	0.880650i	0.0643422	−	0.0371480i
$563$	−20.5465	−	11.8625i	−0.865930	−	0.499945i	6.33160e−5	−	1.00000i	$-0.499980\pi$
$563$	−20.5465	−	11.8625i	−0.865930	−	0.499945i	−0.865994	+	0.500055i	$0.833313\pi$
$564$		0			0
$565$	−15.2657	−	8.27885i	−0.642234	−	0.348294i
$566$	0.248452	+	0.208476i	0.0104432	+	0.00876290i
$567$		0			0
$568$	3.51071	−	9.64559i	0.147306	−	0.404720i
$569$	7.42753			0.311378			0.155689	−	0.987806i	$-0.450240\pi$
$569$	7.42753			0.311378			0.155689	+	0.987806i	$0.450240\pi$
$570$		0			0
$571$	35.2355			1.47456			0.737279	−	0.675588i	$-0.236110\pi$
$571$	35.2355			1.47456			0.737279	+	0.675588i	$0.236110\pi$
$572$	5.52423	−	15.1777i	0.230980	−	0.634611i
$573$		0			0
$574$	4.72542	+	3.96509i	0.197235	+	0.165500i
$575$	37.6688	+	4.58733i	1.57090	+	0.191305i
$576$		0			0
$577$	−27.3387	−	15.7840i	−1.13812	−	0.657096i	−0.192159	−	0.981364i	$-0.561549\pi$
$577$	−27.3387	−	15.7840i	−1.13812	−	0.657096i	−0.945965	+	0.324268i	$0.894882\pi$
$578$	−2.57497	+	1.48666i	−0.107105	+	0.0618369i
$579$		0			0
$580$	−4.41994	+	3.91433i	−0.183528	+	0.162534i
$581$	26.2462	+	45.4598i	1.08888	+	1.88599i
$582$		0			0
$583$	20.9154	+	3.68794i	0.866226	+	0.152739i
$584$	3.14985	−	2.64304i	0.130342	−	0.109370i
$585$		0			0
$586$	−0.648353	−	3.67699i	−0.0267832	−	0.151895i
$587$	−12.7295	+	34.9741i	−0.525405	+	1.44354i	0.339022	+	0.940778i	$0.389904\pi$
$587$	−12.7295	+	34.9741i	−0.525405	+	1.44354i	−0.864427	+	0.502759i	$0.832318\pi$
$588$		0			0
$589$	0.0117851	+	3.89890i	0.000485597	+	0.160651i
$590$	1.60175	+	4.06038i	0.0659428	+	0.167163i
$591$		0			0
$592$	23.6823	−	4.17584i	0.973339	−	0.171626i
$593$	24.1232	−	28.7489i	0.990621	−	1.18058i	0.00706438	−	0.999975i	$-0.497751\pi$
$593$	24.1232	−	28.7489i	0.990621	−	1.18058i	0.983556	−	0.180601i	$-0.0578042\pi$
$594$		0			0
$595$	−3.99486	−	19.5858i	−0.163773	−	0.802940i
$596$	1.88451	−	3.26406i	0.0771924	−	0.133701i
$597$		0			0
$598$	1.72396	+	4.73655i	0.0704981	+	0.193692i
$599$	−2.00274	+	0.728937i	−0.0818297	+	0.0297836i	−0.382611	−	0.923910i	$-0.624975\pi$
$599$	−2.00274	+	0.728937i	−0.0818297	+	0.0297836i	0.300781	+	0.953693i	$0.402753\pi$
$600$		0			0
$601$	0.0426707	−	0.0739079i	0.00174058	−	0.00301477i	−0.865154	−	0.501507i	$-0.832779\pi$
$601$	0.0426707	−	0.0739079i	0.00174058	−	0.00301477i	0.866894	+	0.498492i	$0.166113\pi$
$602$	1.72645	+	0.304419i	0.0703647	+	0.0124072i
$603$		0			0
$604$	−24.8129	−	20.8205i	−1.00962	−	0.847175i
$605$	−1.37275	−	2.23763i	−0.0558100	−	0.0909727i
$606$		0			0
$607$			21.0800i			0.855610i	0.903871	+	0.427805i	$0.140713\pi$
$607$			21.0800i			0.855610i	−0.903871	+	0.427805i	$0.859287\pi$
$608$	−11.7563	+	4.31924i	−0.476782	+	0.175168i
$609$		0			0
$610$	−0.0154818	−	0.580260i	−0.000626839	−	0.0234940i
$611$	0.0814395	+	0.461866i	0.00329469	+	0.0186851i
$612$		0			0
$613$	11.4993	+	13.7043i	0.464452	+	0.553512i	0.946530	−	0.322616i	$-0.104562\pi$
$613$	11.4993	+	13.7043i	0.464452	+	0.553512i	−0.482078	+	0.876128i	$0.660118\pi$
$614$	−0.217438	+	1.23315i	−0.00877509	+	0.0497660i
$615$		0			0
$616$	−6.10437	−	10.5731i	−0.245952	−	0.426002i
$617$	−0.521668	−	1.43327i	−0.0210016	−	0.0577013i	0.928749	−	0.370710i	$-0.120885\pi$
$617$	−0.521668	−	1.43327i	−0.0210016	−	0.0577013i	−0.949750	+	0.313008i	$0.898663\pi$
$618$		0			0
$619$	5.90606	+	10.2296i	0.237384	+	0.411162i	0.959963	−	0.280127i	$-0.0903766\pi$
$619$	5.90606	+	10.2296i	0.237384	+	0.411162i	−0.722579	+	0.691289i	$0.757043\pi$
$620$	−0.570933	+	3.83317i	−0.0229292	+	0.153944i
$621$		0			0
$622$	−2.68807	−	3.20352i	−0.107782	−	0.128449i
$623$	3.77979	−	4.50458i	0.151434	−	0.180472i
$624$		0			0
$625$	−10.1232	+	22.8587i	−0.404929	+	0.914348i
$626$	1.43321			0.0572827
$627$		0			0
$628$		−	19.0085i		−	0.758520i
$629$	−14.0528	−	5.11478i	−0.560320	−	0.203940i
$630$		0			0
$631$	6.14404	+	5.15546i	0.244590	+	0.205236i	0.756839	−	0.653602i	$-0.226743\pi$
$631$	6.14404	+	5.15546i	0.244590	+	0.205236i	−0.512248	+	0.858837i	$0.671187\pi$
$632$	7.08522	+	8.44384i	0.281835	+	0.335878i
$633$		0			0
$634$	−0.992303	+	1.71872i	−0.0394094	+	0.0682591i
$635$	2.34055	−	2.94546i	0.0928817	−	0.116887i
$636$		0			0
$637$	−7.89917	−	21.7028i	−0.312977	−	0.859896i
$638$	0.923892	−	0.533409i	0.0365772	−	0.0211179i
$639$		0			0
$640$	−16.1703	+	3.29822i	−0.639189	+	0.130374i
$641$	32.1747	−	26.9978i	1.27082	−	1.06635i	0.276384	−	0.961047i	$-0.410864\pi$
$641$	32.1747	−	26.9978i	1.27082	−	1.06635i	0.994440	−	0.105301i	$-0.0335807\pi$
$642$		0			0
$643$	12.5650	−	2.21554i	0.495514	−	0.0873724i	0.0796938	−	0.996819i	$-0.474606\pi$
$643$	12.5650	−	2.21554i	0.495514	−	0.0873724i	0.415820	+	0.909447i	$0.363495\pi$
$644$	−54.7275	−	19.9192i	−2.15656	−	0.784925i
$645$		0			0
$646$	2.42120	+	0.419380i	0.0952607	+	0.0165003i
$647$		−	44.1646i		−	1.73629i	−0.496311	−	0.868145i	$-0.665312\pi$
$647$		−	44.1646i		−	1.73629i	0.496311	−	0.868145i	$-0.334688\pi$
$648$		0			0
$649$	4.25442	+	24.1280i	0.167001	+	0.947107i
$650$	−3.31604	+	0.177075i	−0.130066	+	0.00694546i
$651$		0			0
$652$	9.66652	+	1.70447i	0.378570	+	0.0667522i
$653$	18.8561	+	10.8866i	0.737895	+	0.426024i	0.821304	−	0.570491i	$-0.193247\pi$
$653$	18.8561	+	10.8866i	0.737895	+	0.426024i	−0.0834083	+	0.996515i	$0.526581\pi$
$654$		0			0
$655$	−12.8561	+	11.3854i	−0.502329	+	0.444866i
$656$	21.2709	−	7.74199i	0.830491	−	0.302274i
$657$		0			0
$658$	0.151071	+	0.0872211i	0.00588937	+	0.00340023i
$659$	−7.15120	+	40.5565i	−0.278571	+	1.57986i	0.448813	+	0.893626i	$0.351847\pi$
$659$	−7.15120	+	40.5565i	−0.278571	+	1.57986i	−0.727384	+	0.686230i	$0.759264\pi$
$660$		0			0
$661$	−10.4302	−	8.75199i	−0.405688	−	0.340413i	0.416999	−	0.908907i	$-0.363082\pi$
$661$	−10.4302	−	8.75199i	−0.405688	−	0.340413i	−0.822687	+	0.568494i	$0.807526\pi$
$662$	−5.12024	+	0.902836i	−0.199004	+	0.0350897i
$663$		0			0
$664$	−13.0345			−0.505838
$665$	18.2996	−	33.9882i	0.709628	−	1.31801i
$666$		0			0
$667$	3.53717	−	9.71828i	0.136960	−	0.376293i
$668$	38.4711	−	6.78350i	1.48849	−	0.262462i
$669$		0			0
$670$	−4.04968	+	7.46739i	−0.156453	+	0.288490i
$671$	0.565776	−	3.20867i	0.0218415	−	0.123869i
$672$		0			0
$673$	−13.8873	+	8.01782i	−0.535315	+	0.309064i	−0.743178	−	0.669094i	$-0.766682\pi$
$673$	−13.8873	+	8.01782i	−0.535315	+	0.309064i	0.207863	+	0.978158i	$0.433349\pi$
$674$	−6.42150	+	2.33724i	−0.247347	+	0.0900269i
$675$		0			0
$676$	−5.74341	−	9.94788i	−0.220900	−	0.382611i
$677$	−18.8980	−	10.9107i	−0.726308	−	0.419334i	0.0907621	−	0.995873i	$-0.471070\pi$
$677$	−18.8980	−	10.9107i	−0.726308	−	0.419334i	−0.817070	+	0.576539i	$0.804403\pi$
$678$		0			0
$679$	46.6802	−	39.1694i	1.79142	−	1.50318i
$680$	4.70782	+	1.57263i	0.180537	+	0.0603075i
$681$		0			0
$682$	0.239505	−	0.658034i	0.00917111	−	0.0251974i
$683$		−	13.5921i		−	0.520088i	−0.965597	−	0.260044i	$-0.916263\pi$
$683$		−	13.5921i		−	0.520088i	0.965597	−	0.260044i	$-0.0837370\pi$
$684$		0			0
$685$	−7.95505	−	20.1658i	−0.303947	−	0.770496i
$686$	−1.56612	−	0.570022i	−0.0597948	−	0.0217635i
$687$		0			0
$688$	4.13508	−	4.92800i	0.157649	−	0.187878i
$689$	−13.8020	+	11.5812i	−0.525814	+	0.441210i
$690$		0			0
$691$	−9.07292	+	15.7148i	−0.345150	+	0.597818i	−0.985381	−	0.170365i	$-0.945505\pi$
$691$	−9.07292	+	15.7148i	−0.345150	+	0.597818i	0.640231	+	0.768183i	$0.278839\pi$
$692$	−3.27007	+	1.88798i	−0.124310	+	0.0717701i
$693$		0			0
$694$	4.74069	−	1.72547i	0.179954	−	0.0654979i
$695$	−11.2105	−	8.90818i	−0.425238	−	0.337907i
$696$		0			0
$697$	−13.8629	−	2.44441i	−0.525096	−	0.0925885i
$698$	−2.50822	−	2.98918i	−0.0949375	−	0.113142i
$699$		0			0
$700$	23.0608	−	30.6657i	0.871615	−	1.15906i
$701$	−25.2540	−	9.19171i	−0.953831	−	0.347166i	−0.182218	−	0.983258i	$-0.558328\pi$
$701$	−25.2540	−	9.19171i	−0.953831	−	0.347166i	−0.771613	+	0.636092i	$0.780550\pi$
$702$		0			0
$703$	−14.5152	−	24.9665i	−0.547451	−	0.941628i
$704$	−20.5058			−0.772840
$705$		0			0
$706$	−0.199385	−	1.13077i	−0.00750394	−	0.0425569i
$707$	−15.0792	+	17.9707i	−0.567110	+	0.675856i
$708$		0			0
$709$	−3.59200	+	20.3713i	−0.134901	+	0.765059i	0.840028	+	0.542542i	$0.182538\pi$
$709$	−3.59200	+	20.3713i	−0.134901	+	0.765059i	−0.974929	+	0.222516i	$0.928573\pi$
$710$	−5.76539	−	0.858729i	−0.216371	−	0.0322275i
$711$		0			0
$712$	0.499402	+	1.37210i	0.0187159	+	0.0514215i
$713$	−2.32181	−	6.37913i	−0.0869526	−	0.238900i
$714$		0			0
$715$	−18.4362	−	2.74598i	−0.689473	−	0.102694i
$716$	5.81108	−	32.9563i	0.217170	−	1.23163i
$717$		0			0
$718$	−1.73865	+	2.07204i	−0.0648858	+	0.0773279i
$719$	−5.05336	−	28.6590i	−0.188458	−	1.06880i	−0.921431	−	0.388542i	$-0.872979\pi$
$719$	−5.05336	−	28.6590i	−0.188458	−	1.06880i	0.732972	−	0.680258i	$-0.238132\pi$
$720$		0			0
$721$	−19.8313			−0.738556
$722$	3.07211	+	3.61658i	0.114332	+	0.134595i
$723$		0			0
$724$	−26.2879	−	9.56800i	−0.976981	−	0.355592i
$725$	5.44550	+	4.09504i	0.202241	+	0.152086i
$726$		0			0
$727$	6.98125	+	8.31993i	0.258920	+	0.308569i	0.879807	−	0.475331i	$-0.157672\pi$
$727$	6.98125	+	8.31993i	0.258920	+	0.308569i	−0.620887	+	0.783900i	$0.713227\pi$
$728$	10.1999	+	1.79852i	0.378034	+	0.0666575i
$729$		0			0
$730$	−1.82811	−	1.45267i	−0.0676613	−	0.0537656i
$731$	−3.75928	+	1.36827i	−0.139042	+	0.0506072i
$732$		0			0
$733$	−42.8524	+	24.7409i	−1.58279	+	0.913825i	−0.588342	+	0.808613i	$0.700219\pi$
$733$	−42.8524	+	24.7409i	−1.58279	+	0.913825i	−0.994450	+	0.105212i	$0.966448\pi$
$734$	0.831966	−	1.44101i	0.0307084	−	0.0531886i
$735$		0			0
$736$	16.7052	−	14.0173i	0.615761	−	0.516685i
$737$	−30.6491	+	36.5262i	−1.12897	+	1.34546i
$738$		0			0
$739$	−29.6052	−	10.7754i	−1.08904	−	0.396379i	−0.265777	−	0.964035i	$-0.585628\pi$
$739$	−29.6052	−	10.7754i	−1.08904	−	0.396379i	−0.823266	+	0.567655i	$0.807851\pi$
$740$	−10.5338	−	26.7029i	−0.387230	−	0.981617i
$741$		0			0
$742$			6.70153i			0.246021i
$743$	−12.1988	+	33.5159i	−0.447531	+	1.22958i	0.486907	+	0.873454i	$0.338125\pi$
$743$	−12.1988	+	33.5159i	−0.447531	+	1.22958i	−0.934438	+	0.356127i	$0.884097\pi$
$744$		0			0
$745$	−4.12545	−	1.37809i	−0.151145	−	0.0504892i
$746$	−3.46694	+	2.90911i	−0.126934	+	0.106510i
$747$		0			0
$748$	11.8728	+	6.85478i	0.434114	+	0.250636i
$749$	−5.58113	−	9.66680i	−0.203930	−	0.353217i
$750$		0			0
$751$	1.97358	−	0.718325i	0.0720170	−	0.0262120i	−0.305760	−	0.952108i	$-0.598911\pi$
$751$	1.97358	−	0.718325i	0.0720170	−	0.0262120i	0.377777	+	0.925896i	$0.376688\pi$
$752$	0.554367	−	0.320064i	0.0202157	−	0.0116715i
$753$		0			0
$754$	−0.157157	+	0.891282i	−0.00572333	+	0.0324586i
$755$	−17.8199	+	32.8590i	−0.648534	+	1.19586i
$756$		0			0
$757$	−1.14058	+	0.201115i	−0.0414550	+	0.00730963i	−0.194337	−	0.980935i	$-0.562256\pi$
$757$	−1.14058	+	0.201115i	−0.0414550	+	0.00730963i	0.152882	+	0.988244i	$0.451144\pi$
$758$	2.72726	−	7.49307i	0.0990584	−	0.272161i
$759$		0			0
$760$	5.03698	+	8.15509i	0.182711	+	0.295816i
$761$	44.6406			1.61822			0.809111	−	0.587656i	$-0.199949\pi$
$761$	44.6406			1.61822			0.809111	+	0.587656i	$0.199949\pi$
$762$		0			0
$763$	−26.3175	+	4.64048i	−0.952756	+	0.167997i
$764$	11.9513	+	10.0283i	0.432382	+	0.362812i
$765$		0			0
$766$	−0.597826	+	3.39044i	−0.0216003	+	0.122502i
$767$	−18.0001	−	10.3923i	−0.649945	−	0.375246i
$768$		0			0
$769$	27.9589	−	10.1762i	1.00822	−	0.366963i	0.215473	−	0.976510i	$-0.430871\pi$
$769$	27.9589	−	10.1762i	1.00822	−	0.366963i	0.792750	+	0.609546i	$0.208648\pi$
$770$	−5.19024	+	4.59652i	−0.187043	+	0.165647i
$771$		0			0
$772$	10.2972	+	5.94511i	0.370605	+	0.213969i
$773$	−13.4537	−	2.37225i	−0.483895	−	0.0853237i	−0.0736214	−	0.997286i	$-0.523456\pi$
$773$	−13.4537	−	2.37225i	−0.483895	−	0.0853237i	−0.410274	+	0.911963i	$0.634567\pi$
$774$		0			0
$775$	4.46601	−	0.238483i	0.160424	−	0.00856655i
$776$	2.62753	+	14.9015i	0.0943230	+	0.534932i
$777$		0			0
$778$			6.16433i			0.221002i
$779$	−17.5364	−	20.7713i	−0.628308	−	0.744209i
$780$		0			0
$781$	−30.7451	−	11.1903i	−1.10015	−	0.400421i
$782$	−4.21339	+	0.742935i	−0.150671	+	0.0265673i
$783$		0			0
$784$	−24.1482	+	20.2628i	−0.862437	+	0.723671i
$785$	−21.4937	+	4.38401i	−0.767143	+	0.156472i
$786$		0			0
$787$	43.3003	−	24.9994i	1.54349	−	0.891134i	0.544875	−	0.838517i	$-0.316577\pi$
$787$	43.3003	−	24.9994i	1.54349	−	0.891134i	0.998615	−	0.0526166i	$-0.0167561\pi$
$788$	−11.5417	−	31.7105i	−0.411155	−	1.12964i
$789$		0			0
$790$	3.89418	−	4.90063i	0.138549	−	0.174357i
$791$	15.3791	−	26.6373i	0.546816	−	0.947113i
$792$		0			0
$793$	1.77670	+	2.11739i	0.0630926	+	0.0751908i
$794$	−3.41848	−	2.86845i	−0.121317	−	0.101797i
$795$		0			0
$796$	0.0192950	+	0.00702281i	0.000683894	+	0.000248917i
$797$		−	11.0649i		−	0.391939i	−0.980610	−	0.195969i	$-0.937215\pi$
$797$		−	11.0649i		−	0.391939i	0.980610	−	0.195969i	$-0.0627853\pi$
$798$		0			0
$799$	−0.398078			−0.0140830
$800$	5.62662	+	13.2191i	0.198931	+	0.467366i
$801$		0			0
$802$	3.68144	−	4.38737i	0.129996	−	0.154923i
$803$	−8.42463	−	10.0401i	−0.297299	−	0.354307i
$804$		0			0
$805$	−9.90142	+	66.4768i	−0.348979	+	2.34300i
$806$	0.297034	+	0.514478i	0.0104626	+	0.0181217i
$807$		0			0
$808$	−1.99233	−	5.47387i	−0.0700898	−	0.192570i
$809$	−3.02713	−	5.24315i	−0.106428	−	0.184339i	0.807893	−	0.589330i	$-0.200608\pi$
$809$	−3.02713	−	5.24315i	−0.106428	−	0.184339i	−0.914321	+	0.404991i	$0.867275\pi$
$810$		0			0
$811$	1.21038	−	6.86438i	0.0425021	−	0.241041i	−0.956154	−	0.292864i	$-0.905392\pi$
$811$	1.21038	−	6.86438i	0.0425021	−	0.241041i	0.998656	+	0.0518223i	$0.0165030\pi$
$812$	−6.72163	−	8.01052i	−0.235883	−	0.281114i
$813$		0			0
$814$	0.900689	+	5.10806i	0.0315691	+	0.179038i
$815$	−0.302119	−	11.3235i	−0.0105828	−	0.396644i
$816$		0			0
$817$	−7.26761	−	2.62034i	−0.254261	−	0.0916742i
$818$			6.28883i			0.219884i
$819$		0			0
$820$	−14.1295	−	23.0317i	−0.493425	−	0.804303i
$821$	−7.39489	−	6.20505i	−0.258084	−	0.216558i	0.504560	−	0.863376i	$-0.331655\pi$
$821$	−7.39489	−	6.20505i	−0.258084	−	0.216558i	−0.762644	+	0.646819i	$0.776099\pi$
$822$		0			0
$823$	−14.2747	−	2.51702i	−0.497585	−	0.0877377i	−0.0807771	−	0.996732i	$-0.525740\pi$
$823$	−14.2747	−	2.51702i	−0.497585	−	0.0877377i	−0.416808	+	0.908994i	$0.636851\pi$
$824$	2.46218	−	4.26462i	0.0857742	−	0.148565i
$825$		0			0
$826$	−7.26467	+	2.64412i	−0.252770	+	0.0920009i
$827$	9.47450	+	26.0310i	0.329461	+	0.905186i	0.988248	+	0.152857i	$0.0488474\pi$
$827$	9.47450	+	26.0310i	0.329461	+	0.905186i	−0.658788	+	0.752329i	$0.728930\pi$
$828$		0			0
$829$	−16.1035	+	27.8921i	−0.559299	+	0.968734i	0.438256	+	0.898850i	$0.355596\pi$
$829$	−16.1035	+	27.8921i	−0.559299	+	0.968734i	−0.997555	+	0.0698842i	$0.977737\pi$
$830$	1.47930	+	7.25263i	0.0513472	+	0.251742i
$831$		0			0
$832$	11.1819	−	13.3261i	0.387664	−	0.462000i
$833$	19.3057	−	3.40411i	0.668902	−	0.117946i
$834$		0			0
$835$	−16.5432	−	41.9365i	−0.572501	−	1.45127i
$836$	9.13011	+	24.8508i	0.315772	+	0.859483i
$837$		0			0
$838$	−0.0213189	+	0.0585733i	−0.000736450	+	0.00202338i
$839$	7.84640	+	44.4992i	0.270888	+	1.53628i	0.751728	+	0.659473i	$0.229221\pi$
$839$	7.84640	+	44.4992i	0.270888	+	1.53628i	−0.480840	+	0.876808i	$0.659668\pi$
$840$		0			0
$841$	−20.7928	+	17.4472i	−0.716994	+	0.601629i
$842$	−7.42006	−	1.30836i	−0.255712	−	0.0450890i
$843$		0			0
$844$	−26.2802	−	45.5187i	−0.904602	−	1.56682i
$845$	−9.92388	+	8.78866i	−0.341392	+	0.302339i
$846$		0			0
$847$	4.02663	−	2.32478i	0.138357	−	0.0798803i
$848$	21.2971	+	12.2959i	0.731344	+	0.422242i
$849$		0			0
$850$	0.340741	−	2.79799i	0.0116873	−	0.0959701i
$851$	38.5187	+	32.3211i	1.32041	+	1.10795i
$852$		0			0
$853$	14.2994	−	39.2873i	0.489603	−	1.34517i	−0.411438	−	0.911438i	$-0.634973\pi$
$853$	14.2994	−	39.2873i	0.489603	−	1.34517i	0.901041	−	0.433735i	$-0.142804\pi$
$854$	1.02810			0.0351808
$855$		0			0
$856$	2.77173			0.0947358
$857$	14.5281	−	39.9155i	0.496269	−	1.36349i	−0.398586	−	0.917131i	$-0.630499\pi$
$857$	14.5281	−	39.9155i	0.496269	−	1.36349i	0.894855	−	0.446357i	$-0.147279\pi$
$858$		0			0
$859$	−1.74555	−	1.46469i	−0.0595574	−	0.0499746i	0.612523	−	0.790453i	$-0.290155\pi$
$859$	−1.74555	−	1.46469i	−0.0595574	−	0.0499746i	−0.672080	+	0.740478i	$0.734599\pi$
$860$	−6.75030	−	3.66079i	−0.230183	−	0.124832i
$861$		0			0
$862$	−3.33445	−	1.92514i	−0.113572	−	0.0655707i
$863$	−36.0986	+	20.8416i	−1.22881	+	0.709455i	−0.966781	−	0.255604i	$-0.917726\pi$
$863$	−36.0986	+	20.8416i	−1.22881	+	0.709455i	−0.262031	+	0.965060i	$0.584392\pi$
$864$		0			0
$865$	2.88901	+	3.26218i	0.0982294	+	0.110918i
$866$	−1.56566	−	2.71181i	−0.0532034	−	0.0921510i
$867$		0			0
$868$	−6.75975	−	1.19193i	−0.229441	−	0.0404566i
$869$	26.9146	−	22.5840i	0.913014	−	0.766110i
$870$		0			0
$871$	−7.02415	−	39.8360i	−0.238004	−	1.34979i
$872$	2.26957	−	6.23559i	0.0768573	−	0.211164i
$873$		0			0
$874$	−7.16766	−	4.10941i	−0.242450	−	0.139003i
$875$	−39.9937	−	19.0032i	−1.35203	−	0.642427i
$876$		0			0
$877$	−5.26252	+	0.927924i	−0.177703	+	0.0313338i	−0.261791	−	0.965125i	$-0.584313\pi$
$877$	−5.26252	+	0.927924i	−0.177703	+	0.0313338i	0.0840887	+	0.996458i	$0.473202\pi$
$878$	−4.06536	+	4.84491i	−0.137199	+	0.163508i
$879$		0			0
$880$	5.08448	+	24.9279i	0.171398	+	0.840319i
$881$	9.59945	−	16.6267i	0.323414	−	0.560169i	−0.657776	−	0.753213i	$-0.728503\pi$
$881$	9.59945	−	16.6267i	0.323414	−	0.560169i	0.981190	+	0.193044i	$0.0618362\pi$
$882$		0			0
$883$	9.81908	+	26.9777i	0.330438	+	0.907872i	0.987998	+	0.154469i	$0.0493668\pi$
$883$	9.81908	+	26.9777i	0.330438	+	0.907872i	−0.657559	+	0.753403i	$0.728411\pi$
$884$	−10.9291	+	3.97785i	−0.367584	+	0.133790i
$885$		0			0
$886$	0.926246	−	1.60430i	0.0311178	−	0.0538977i
$887$	10.0399	+	1.77030i	0.337107	+	0.0594410i	0.339639	−	0.940556i	$-0.389695\pi$
$887$	10.0399	+	1.77030i	0.337107	+	0.0594410i	−0.00253260	+	0.999997i	$0.500806\pi$
$888$		0			0
$889$	5.10445	+	4.28314i	0.171198	+	0.143652i
$890$	0.706779	−	0.433596i	0.0236913	−	0.0145342i
$891$		0			0
$892$		−	14.8237i		−	0.496333i
$893$	−0.590380	−	0.492355i	−0.0197563	−	0.0164760i
$894$		0			0
$895$	−38.6053	+	1.03002i	−1.29043	+	0.0344298i
$896$	−5.07571	−	28.7858i	−0.169568	−	0.961666i
$897$		0			0
$898$	−3.86219	−	4.60278i	−0.128883	−	0.153597i
$899$	0.211657	−	1.20037i	0.00705917	−	0.0400345i
$900$		0			0
$901$	−7.64648	−	13.2441i	−0.254741	−	0.441224i
$902$	1.66988	+	4.58795i	0.0556008	+	0.152762i
$903$		0			0
$904$	3.81882	+	6.61438i	0.127012	+	0.219991i
$905$	−4.75606	+	31.9316i	−0.158097	+	1.06144i
$906$		0			0
$907$	25.1233	+	29.9408i	0.834205	+	0.994167i	0.999968	+	0.00800118i	$0.00254688\pi$
$907$	25.1233	+	29.9408i	0.834205	+	0.994167i	−0.165763	+	0.986166i	$0.553009\pi$
$908$	−32.3349	+	38.5352i	−1.07307	+	1.27883i
$909$		0			0
$910$	−0.156870	−	5.87950i	−0.00520018	−	0.194904i
$911$	−36.6728			−1.21502			−0.607512	−	0.794310i	$-0.707832\pi$
$911$	−36.6728			−1.21502			−0.607512	+	0.794310i	$0.707832\pi$
$912$		0			0
$913$			41.5473i			1.37502i
$914$	−1.50179	−	0.546608i	−0.0496749	−	0.0180802i
$915$		0			0
$916$	9.53118	+	7.99761i	0.314919	+	0.264248i
$917$	−19.5509	−	23.2999i	−0.645628	−	0.769429i
$918$		0			0
$919$	−10.2427	+	17.7409i	−0.337877	+	0.585219i	−0.984033	−	0.177985i	$-0.943042\pi$
$919$	−10.2427	+	17.7409i	−0.337877	+	0.585219i	0.646157	+	0.763205i	$0.276375\pi$
$920$	−13.0662	−	10.3828i	−0.430780	−	0.342310i
$921$		0			0
$922$	1.30266	+	3.57903i	0.0429008	+	0.117869i
$923$	24.0378	−	13.8782i	0.791213	−	0.456807i
$924$		0			0
$925$	−27.7646	+	18.0696i	−0.912896	+	0.594126i
$926$	6.96975	−	5.84832i	0.229040	−	0.192188i
$927$		0			0
$928$	3.85599	−	0.679915i	0.126579	−	0.0223193i
$929$	−16.3391	−	5.94695i	−0.536069	−	0.195113i	0.0597774	−	0.998212i	$-0.480961\pi$
$929$	−16.3391	−	5.94695i	−0.536069	−	0.195113i	−0.595846	+	0.803099i	$0.703183\pi$
$930$		0			0
$931$	32.8421	+	18.8293i	1.07636	+	0.617104i
$932$			36.9998i			1.21197i
$933$		0			0
$934$	−1.22286	−	6.93516i	−0.0400131	−	0.226926i
$935$	5.01271	−	15.0061i	0.163933	−	0.490751i
$936$		0			0
$937$	32.7030	+	5.76643i	1.06836	+	0.188381i	0.680064	−	0.733153i	$-0.261952\pi$
$937$	32.7030	+	5.76643i	1.06836	+	0.188381i	0.388298	+	0.921534i	$0.373063\pi$
$938$	−13.0299	−	7.52282i	−0.425441	−	0.245629i
$939$		0			0
$940$	−0.506600	−	0.572037i	−0.0165235	−	0.0186578i
$941$	−34.5608	+	12.5791i	−1.12665	+	0.410067i	−0.837075	−	0.547089i	$-0.815736\pi$
$941$	−34.5608	+	12.5791i	−1.12665	+	0.410067i	−0.289574	+	0.957156i	$0.593514\pi$
$942$		0			0
$943$	40.9899	+	23.6655i	1.33481	+	0.770655i
$944$	−4.92624	+	27.9381i	−0.160335	+	0.909307i
$945$		0			0
$946$	1.06292	+	0.891899i	0.0345586	+	0.0289981i
$947$	34.4566	−	6.07563i	1.11969	−	0.197432i	0.416985	−	0.908913i	$-0.363087\pi$
$947$	34.4566	−	6.07563i	1.11969	−	0.197432i	0.702705	+	0.711482i	$0.251975\pi$
$948$		0			0
$949$	11.1188			0.360931
$950$	3.96597	−	3.72819i	0.128673	−	0.120958i
$951$		0			0
$952$	−3.00677	+	8.26103i	−0.0974499	+	0.267741i
$953$	−53.0797	+	9.35937i	−1.71942	+	0.303180i	−0.944410	−	0.328771i	$-0.893366\pi$
$953$	−53.0797	+	9.35937i	−1.71942	+	0.303180i	−0.775009	+	0.631950i	$0.782255\pi$
$954$		0			0
$955$	8.58307	−	15.8267i	0.277742	−	0.512140i
$956$	−2.82354	+	16.0131i	−0.0913198	+	0.517900i
$957$		0			0
$958$	−6.36566	+	3.67522i	−0.205665	+	0.118741i
$959$	36.0799	−	13.1320i	1.16508	−	0.424055i
$960$		0			0
$961$	15.1000	+	26.1539i	0.487095	+	0.843674i
$962$	−3.81074	−	2.20013i	−0.122863	−	0.0709350i
$963$		0			0
$964$	−12.7901	+	10.7322i	−0.411942	+	0.345660i
$965$	4.34750	−	13.0147i	0.139951	−	0.418957i
$966$		0			0
$967$	17.0610	−	46.8747i	0.548645	−	1.50739i	−0.286896	−	0.957962i	$-0.592623\pi$
$967$	17.0610	−	46.8747i	0.548645	−	1.50739i	0.835541	−	0.549428i	$-0.185154\pi$
$968$			1.15454i			0.0371084i
$969$		0			0
$970$	7.99323	−	3.15318i	0.256647	−	0.101243i
$971$	12.9739	+	4.72213i	0.416354	+	0.151540i	0.541698	−	0.840573i	$-0.317781\pi$
$971$	12.9739	+	4.72213i	0.416354	+	0.151540i	−0.125345	+	0.992113i	$0.540004\pi$
$972$		0			0
$973$	16.3017	−	19.4277i	0.522610	−	0.622822i
$974$	0.520423	−	0.436687i	0.0166754	−	0.0139923i
$975$		0			0
$976$	1.88634	−	3.26723i	0.0603801	−	0.104581i
$977$	27.4039	−	15.8217i	0.876729	−	0.506180i	0.00715070	−	0.999974i	$-0.497724\pi$
$977$	27.4039	−	15.8217i	0.876729	−	0.506180i	0.869579	+	0.493795i	$0.164391\pi$
$978$		0			0
$979$	4.37353	−	1.59184i	0.139779	−	0.0508753i
$980$	29.4604	+	23.4100i	0.941076	+	0.747807i
$981$		0			0
$982$	4.66404	+	0.822396i	0.148836	+	0.0262437i
$983$	25.8335	+	30.7872i	0.823961	+	0.981958i	0.999997	−	0.00242541i	$-0.000772031\pi$
$983$	25.8335	+	30.7872i	0.823961	+	0.981958i	−0.176036	+	0.984384i	$0.556328\pi$
$984$		0			0
$985$	−33.1945	+	20.3642i	−1.05767	+	0.648858i
$986$	−0.721861	−	0.262736i	−0.0229887	−	0.00836721i
$987$		0			0
$988$	−21.1285	−	7.61792i	−0.672189	−	0.242358i
$989$	13.4512			0.427724
$990$		0			0
$991$	−3.38192	−	19.1798i	−0.107430	−	0.609268i	−0.990222	−	0.139503i	$-0.955450\pi$
$991$	−3.38192	−	19.1798i	−0.107430	−	0.609268i	0.882791	−	0.469765i	$-0.155661\pi$
$992$	1.65205	−	1.96884i	0.0524527	−	0.0625107i
$993$		0			0
$994$	1.79275	−	10.1672i	0.0568627	−	0.322484i
$995$	0.00349090	−	0.0234374i	0.000110669	−	0.000743017i
$996$		0			0
$997$	4.83705	+	13.2897i	0.153191	+	0.420889i	0.992420	−	0.122889i	$-0.0392158\pi$
$997$	4.83705	+	13.2897i	0.153191	+	0.420889i	−0.839229	+	0.543777i	$0.816994\pi$
$998$	0.514520	+	1.41363i	0.0162868	+	0.0447477i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.da.b.289.4		48
3.2	odd	2		95.2.p.a.4.5	yes	48
5.4	even	2	inner	855.2.da.b.289.5		48
15.2	even	4		475.2.l.f.251.5		48
15.8	even	4		475.2.l.f.251.4		48
15.14	odd	2		95.2.p.a.4.4	✓	48
19.5	even	9	inner	855.2.da.b.784.5		48
57.5	odd	18		95.2.p.a.24.4	yes	48
57.29	even	18		1805.2.b.l.1084.11		24
57.47	odd	18		1805.2.b.k.1084.14		24
95.24	even	18	inner	855.2.da.b.784.4		48
285.29	even	18		1805.2.b.l.1084.14		24
285.47	even	36		9025.2.a.cu.1.11		24
285.62	even	36		475.2.l.f.176.5		48
285.104	odd	18		1805.2.b.k.1084.11		24
285.119	odd	18		95.2.p.a.24.5	yes	48
285.143	odd	36		9025.2.a.ct.1.11		24
285.218	even	36		9025.2.a.cu.1.14		24
285.233	even	36		475.2.l.f.176.4		48
285.257	odd	36		9025.2.a.ct.1.14		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.4.4	✓	48	15.14	odd	2
95.2.p.a.4.5	yes	48	3.2	odd	2
95.2.p.a.24.4	yes	48	57.5	odd	18
95.2.p.a.24.5	yes	48	285.119	odd	18
475.2.l.f.176.4		48	285.233	even	36
475.2.l.f.176.5		48	285.62	even	36
475.2.l.f.251.4		48	15.8	even	4
475.2.l.f.251.5		48	15.2	even	4
855.2.da.b.289.4		48	1.1	even	1	trivial
855.2.da.b.289.5		48	5.4	even	2	inner
855.2.da.b.784.4		48	95.24	even	18	inner
855.2.da.b.784.5		48	19.5	even	9	inner
1805.2.b.k.1084.11		24	285.104	odd	18
1805.2.b.k.1084.14		24	57.47	odd	18
1805.2.b.l.1084.11		24	57.29	even	18
1805.2.b.l.1084.14		24	285.29	even	18
9025.2.a.ct.1.11		24	285.143	odd	36
9025.2.a.ct.1.14		24	285.257	odd	36
9025.2.a.cu.1.11		24	285.47	even	36
9025.2.a.cu.1.14		24	285.218	even	36

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.da (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0854197 + 0.234689i) q^{2} +(1.48431 + 1.24548i) q^{4} +(1.06599 - 1.96562i) q^{5} +(3.42983 + 1.98021i) q^{7} +(-0.851670 + 0.491712i) q^{8} +O(q^{10})\)	\(q+(-0.0854197 + 0.234689i) q^{2} +(1.48431 + 1.24548i) q^{4} +(1.06599 - 1.96562i) q^{5} +(3.42983 + 1.98021i) q^{7} +(-0.851670 + 0.491712i) q^{8} +(0.370253 + 0.418078i) q^{10} +(1.56732 + 2.71468i) q^{11} +(-2.61887 - 0.461777i) q^{13} +(-0.757709 + 0.635793i) q^{14} +(0.630280 + 3.57450i) q^{16} +(0.772000 - 2.12105i) q^{17} +(3.76831 - 2.19085i) q^{19} +(4.03040 - 1.58992i) q^{20} +(-0.770986 + 0.135946i) q^{22} +(-4.87838 + 5.81383i) q^{23} +(-2.72734 - 4.19066i) q^{25} +(0.332077 - 0.575174i) q^{26} +(2.62460 + 7.21103i) q^{28} +(-1.28051 + 0.466066i) q^{29} +(-0.447237 + 0.774637i) q^{31} +(-2.82970 - 0.498952i) q^{32} +(0.431843 + 0.362360i) q^{34} +(7.54850 - 4.63087i) q^{35} -6.62537i q^{37} +(0.192280 + 1.07152i) q^{38} +(0.0586502 + 2.19822i) q^{40} +(-1.08295 - 6.14171i) q^{41} +(-1.13925 - 1.35771i) q^{43} +(-1.05470 + 5.98149i) q^{44} +(-0.947730 - 1.64152i) q^{46} +(-0.0603191 - 0.165725i) q^{47} +(4.34248 + 7.52140i) q^{49} +(1.21647 - 0.282112i) q^{50} +(-3.31207 - 3.94717i) q^{52} +(4.35505 - 5.19015i) q^{53} +(7.00678 - 0.186946i) q^{55} -3.89478 q^{56} -0.340331i q^{58} +(7.34459 + 2.67321i) q^{59} +(-0.796232 - 0.668118i) q^{61} +(-0.143596 - 0.171131i) q^{62} +(-3.27083 + 5.66524i) q^{64} +(-3.69936 + 4.65545i) q^{65} +(5.20252 + 14.2938i) q^{67} +(3.78762 - 2.18678i) q^{68} +(0.442021 + 2.16712i) q^{70} +(-7.99569 + 6.70918i) q^{71} +(-4.11762 + 0.726048i) q^{73} +(1.55490 + 0.565937i) q^{74} +(8.32199 + 1.44147i) q^{76} +12.4145i q^{77} +(-1.94633 - 11.0382i) q^{79} +(7.69798 + 2.57148i) q^{80} +(1.53390 + 0.270467i) q^{82} +(11.4785 + 6.62712i) q^{83} +(-3.34625 - 3.77848i) q^{85} +(0.415955 - 0.151395i) q^{86} +(-2.66968 - 1.54134i) q^{88} +(0.257827 - 1.46221i) q^{89} +(-8.06785 - 6.76973i) q^{91} +(-14.4820 + 2.55357i) q^{92} +0.0440463 q^{94} +(-0.289409 - 9.74250i) q^{95} +(5.26246 - 14.4585i) q^{97} +(-2.13612 + 0.376656i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 18 q^{4} + 6 q^{5}+O(q^{10}) \) 48 * q - 18 * q^4 + 6 * q^5	\( 48 q - 18 q^{4} + 6 q^{5} - 15 q^{10} + 12 q^{11} - 6 q^{14} - 42 q^{16} + 12 q^{19} - 42 q^{20} + 12 q^{25} - 12 q^{26} - 42 q^{31} - 36 q^{34} - 6 q^{35} + 66 q^{40} - 6 q^{41} + 6 q^{44} - 6 q^{46} + 12 q^{49} + 18 q^{50} - 36 q^{56} + 36 q^{59} + 48 q^{61} + 18 q^{65} - 123 q^{70} + 24 q^{71} - 84 q^{74} + 66 q^{76} + 48 q^{79} + 39 q^{80} - 84 q^{85} + 42 q^{86} + 12 q^{89} - 30 q^{91} - 72 q^{94} + 63 q^{95}+O(q^{100}) \) 48 * q - 18 * q^4 + 6 * q^5 - 15 * q^10 + 12 * q^11 - 6 * q^14 - 42 * q^16 + 12 * q^19 - 42 * q^20 + 12 * q^25 - 12 * q^26 - 42 * q^31 - 36 * q^34 - 6 * q^35 + 66 * q^40 - 6 * q^41 + 6 * q^44 - 6 * q^46 + 12 * q^49 + 18 * q^50 - 36 * q^56 + 36 * q^59 + 48 * q^61 + 18 * q^65 - 123 * q^70 + 24 * q^71 - 84 * q^74 + 66 * q^76 + 48 * q^79 + 39 * q^80 - 84 * q^85 + 42 * q^86 + 12 * q^89 - 30 * q^91 - 72 * q^94 + 63 * q^95

Introduction

L-functions

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