LMFDB - Embedded newform 976.2.bw.c.625.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [976,2,Mod(225,976)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("976.225"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(976, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([0, 0, 28])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 976 = 2^{4} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	976.bw (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.79339923728$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 61)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			625.1
Character	$\chi$	$=$	976.625
Dual form			976.2.bw.c.545.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.09846 + 0.798080i) q^{3} +(2.01896 + 2.24228i) q^{5} +(2.42543 - 1.07987i) q^{7} +(-0.357362 + 1.09985i) q^{9} +2.81637 q^{11} +(3.25426 - 5.63654i) q^{13} +(-4.00727 - 0.851773i) q^{15} +(0.988198 - 0.210048i) q^{17} +(2.84524 + 1.26678i) q^{19} +(-1.80242 + 3.12188i) q^{21} +(0.957874 - 2.94803i) q^{23} +(-0.428988 + 4.08155i) q^{25} +(-1.74394 - 5.36731i) q^{27} +(-1.25301 - 2.17028i) q^{29} +(-0.444151 + 4.22582i) q^{31} +(-3.09368 + 2.24769i) q^{33} +(7.31821 + 3.25828i) q^{35} +(-5.69250 - 4.13585i) q^{37} +(0.923728 + 8.78869i) q^{39} +(8.51930 + 6.18964i) q^{41} +(-6.04008 - 1.28386i) q^{43} +(-3.18766 + 1.41924i) q^{45} +(-0.0929380 - 0.160973i) q^{47} +(0.0326575 - 0.0362698i) q^{49} +(-0.917864 + 1.01939i) q^{51} +(1.96750 + 6.05535i) q^{53} +(5.68613 + 6.31509i) q^{55} +(-4.13639 + 0.879216i) q^{57} +(0.425310 + 4.04655i) q^{59} +(-1.85551 - 7.58664i) q^{61} +(0.320936 + 3.05350i) q^{63} +(19.2089 - 4.08298i) q^{65} +(0.557122 + 0.618747i) q^{67} +(1.30058 + 4.00276i) q^{69} +(-4.21558 + 4.68187i) q^{71} +(-0.628481 + 0.697999i) q^{73} +(-2.78618 - 4.82580i) q^{75} +(6.83089 - 3.04131i) q^{77} +(11.6299 + 2.47200i) q^{79} +(3.39244 + 2.46475i) q^{81} +(0.517961 + 4.92807i) q^{83} +(2.46612 + 1.79174i) q^{85} +(3.10844 + 1.38397i) q^{87} +(-7.02573 + 5.10449i) q^{89} +(1.80624 - 17.1852i) q^{91} +(-2.88466 - 4.99637i) q^{93} +(2.90394 + 8.93742i) q^{95} +(-0.337747 + 3.21345i) q^{97} +(-1.00646 + 3.09757i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} + 2 q^{5} - q^{7} - 2 q^{9} + 18 q^{11} - 2 q^{15} - 24 q^{17} - 9 q^{19} - 3 q^{21} + 2 q^{23} + 28 q^{25} - 35 q^{27} - 4 q^{29} + 11 q^{31} - 35 q^{33} + 58 q^{35} - 14 q^{37} - 17 q^{39}+ \cdots + 31 q^{99}+O(q^{100}) $ 32 * q + 4 * q^3 + 2 * q^5 - q^7 - 2 * q^9 + 18 * q^11 - 2 * q^15 - 24 * q^17 - 9 * q^19 - 3 * q^21 + 2 * q^23 + 28 * q^25 - 35 * q^27 - 4 * q^29 + 11 * q^31 - 35 * q^33 + 58 * q^35 - 14 * q^37 - 17 * q^39 + 11 * q^41 - 40 * q^43 + 12 * q^45 - 40 * q^47 + q^49 + 9 * q^51 + 17 * q^53 + 60 * q^55 - 38 * q^57 + 11 * q^59 - 55 * q^61 + 58 * q^63 + 59 * q^65 + 13 * q^67 - 32 * q^69 - 63 * q^71 - 46 * q^73 - q^75 - 31 * q^77 + 49 * q^79 + 48 * q^81 - 39 * q^83 + 21 * q^85 - 17 * q^87 + 32 * q^89 - 70 * q^91 + 67 * q^93 - 47 * q^95 + 37 * q^97 + 31 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/976\mathbb{Z}\right)^\times$.

$n$	$245$	$367$	$673$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{15}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.09846	+	0.798080i	−0.634198	+	0.460772i	−0.857852	−	0.513897i	$-0.828201\pi$
$3$	−1.09846	+	0.798080i	−0.634198	+	0.460772i	0.223654	+	0.974669i	$0.428201\pi$
$4$		0			0
$5$	2.01896	+	2.24228i	0.902907	+	1.00278i	0.999972	+	0.00750126i	$0.00238775\pi$
$5$	2.01896	+	2.24228i	0.902907	+	1.00278i	−0.0970654	+	0.995278i	$0.530946\pi$
$6$		0			0
$7$	2.42543	−	1.07987i	0.916725	−	0.408152i	0.106528	−	0.994310i	$-0.466027\pi$
$7$	2.42543	−	1.07987i	0.916725	−	0.408152i	0.810197	+	0.586158i	$0.199360\pi$
$8$		0			0
$9$	−0.357362	+	1.09985i	−0.119121	+	0.366615i
$10$		0			0
$11$	2.81637			0.849167			0.424583	−	0.905389i	$-0.360421\pi$
$11$	2.81637			0.849167			0.424583	+	0.905389i	$0.360421\pi$
$12$		0			0
$13$	3.25426	−	5.63654i	0.902569	−	1.56329i	0.0784206	−	0.996920i	$-0.475012\pi$
$13$	3.25426	−	5.63654i	0.902569	−	1.56329i	0.824148	−	0.566374i	$-0.191654\pi$
$14$		0			0
$15$	−4.00727	−	0.851773i	−1.03467	−	0.219927i
$16$		0			0
$17$	0.988198	−	0.210048i	0.239673	−	0.0509441i	−0.0865089	−	0.996251i	$-0.527571\pi$
$17$	0.988198	−	0.210048i	0.239673	−	0.0509441i	0.326182	+	0.945307i	$0.394238\pi$
$18$		0			0
$19$	2.84524	+	1.26678i	0.652743	+	0.290620i	0.706266	−	0.707947i	$-0.250378\pi$
$19$	2.84524	+	1.26678i	0.652743	+	0.290620i	−0.0535227	+	0.998567i	$0.517045\pi$
$20$		0			0
$21$	−1.80242	+	3.12188i	−0.393320	+	0.681250i
$22$		0			0
$23$	0.957874	−	2.94803i	0.199730	−	0.614707i	−0.800158	−	0.599789i	$-0.795251\pi$
$23$	0.957874	−	2.94803i	0.199730	−	0.614707i	0.999889	−	0.0149182i	$-0.00474879\pi$
$24$		0			0
$25$	−0.428988	+	4.08155i	−0.0857976	+	0.816310i
$26$		0			0
$27$	−1.74394	−	5.36731i	−0.335622	−	1.03294i
$28$		0			0
$29$	−1.25301	−	2.17028i	−0.232678	−	0.403010i	0.725917	−	0.687782i	$-0.241415\pi$
$29$	−1.25301	−	2.17028i	−0.232678	−	0.403010i	−0.958595	+	0.284772i	$0.908082\pi$
$30$		0			0
$31$	−0.444151	+	4.22582i	−0.0797720	+	0.758979i	0.879386	+	0.476109i	$0.157953\pi$
$31$	−0.444151	+	4.22582i	−0.0797720	+	0.758979i	−0.959158	+	0.282870i	$0.908713\pi$
$32$		0			0
$33$	−3.09368	+	2.24769i	−0.538540	+	0.391272i
$34$		0			0
$35$	7.31821	+	3.25828i	1.23700	+	0.550749i
$36$		0			0
$37$	−5.69250	−	4.13585i	−0.935842	−	0.679929i	0.0115743	−	0.999933i	$-0.496316\pi$
$37$	−5.69250	−	4.13585i	−0.935842	−	0.679929i	−0.947416	+	0.320004i	$0.896316\pi$
$38$		0			0
$39$	0.923728	+	8.78869i	0.147915	+	1.40732i
$40$		0			0
$41$	8.51930	+	6.18964i	1.33049	+	0.966659i	0.999737	+	0.0229423i	$0.00730339\pi$
$41$	8.51930	+	6.18964i	1.33049	+	0.966659i	0.330755	+	0.943717i	$0.392697\pi$
$42$		0			0
$43$	−6.04008	−	1.28386i	−0.921103	−	0.195787i	−0.277128	−	0.960833i	$-0.589383\pi$
$43$	−6.04008	−	1.28386i	−0.921103	−	0.195787i	−0.643975	+	0.765046i	$0.722716\pi$
$44$		0			0
$45$	−3.18766	+	1.41924i	−0.475189	+	0.211568i
$46$		0			0
$47$	−0.0929380	−	0.160973i	−0.0135564	−	0.0234804i	0.859168	−	0.511694i	$-0.170982\pi$
$47$	−0.0929380	−	0.160973i	−0.0135564	−	0.0234804i	−0.872724	+	0.488214i	$0.837649\pi$
$48$		0			0
$49$	0.0326575	−	0.0362698i	0.00466535	−	0.00518140i
$50$		0			0
$51$	−0.917864	+	1.01939i	−0.128527	+	0.142743i
$52$		0			0
$53$	1.96750	+	6.05535i	0.270257	+	0.831766i	0.990435	+	0.137977i	$0.0440601\pi$
$53$	1.96750	+	6.05535i	0.270257	+	0.831766i	−0.720178	+	0.693789i	$0.755940\pi$
$54$		0			0
$55$	5.68613	+	6.31509i	0.766718	+	0.851527i
$56$		0			0
$57$	−4.13639	+	0.879216i	−0.547878	+	0.116455i
$58$		0			0
$59$	0.425310	+	4.04655i	0.0553706	+	0.526816i	0.986690	+	0.162613i	$0.0519921\pi$
$59$	0.425310	+	4.04655i	0.0553706	+	0.526816i	−0.931319	+	0.364204i	$0.881341\pi$
$60$		0			0
$61$	−1.85551	−	7.58664i	−0.237574	−	0.971369i
$61$	−1.85551	−	7.58664i	−0.237574	−	0.971369i
$62$		0			0
$63$	0.320936	+	3.05350i	0.0404341	+	0.384705i
$64$		0			0
$65$	19.2089	−	4.08298i	2.38257	−	0.506432i
$66$		0			0
$67$	0.557122	+	0.618747i	0.0680633	+	0.0755920i	0.776215	−	0.630469i	$-0.217137\pi$
$67$	0.557122	+	0.618747i	0.0680633	+	0.0755920i	−0.708151	+	0.706061i	$0.750471\pi$
$68$		0			0
$69$	1.30058	+	4.00276i	0.156571	+	0.481876i
$70$		0			0
$71$	−4.21558	+	4.68187i	−0.500297	+	0.555636i	−0.939410	−	0.342796i	$-0.888626\pi$
$71$	−4.21558	+	4.68187i	−0.500297	+	0.555636i	0.439113	+	0.898432i	$0.355293\pi$
$72$		0			0
$73$	−0.628481	+	0.697999i	−0.0735582	+	0.0816946i	−0.778800	−	0.627272i	$-0.784172\pi$
$73$	−0.628481	+	0.697999i	−0.0735582	+	0.0816946i	0.705242	+	0.708966i	$0.250838\pi$
$74$		0			0
$75$	−2.78618	−	4.82580i	−0.321720	−	0.557235i
$76$		0			0
$77$	6.83089	−	3.04131i	0.778452	−	0.346589i
$78$		0			0
$79$	11.6299	+	2.47200i	1.30846	+	0.278122i	0.808793	−	0.588094i	$-0.200121\pi$
$79$	11.6299	+	2.47200i	1.30846	+	0.278122i	0.499670	+	0.866216i	$0.333455\pi$
$80$		0			0
$81$	3.39244	+	2.46475i	0.376938	+	0.273862i
$82$		0			0
$83$	0.517961	+	4.92807i	0.0568536	+	0.540926i	0.985466	+	0.169874i	$0.0543362\pi$
$83$	0.517961	+	4.92807i	0.0568536	+	0.540926i	−0.928612	+	0.371052i	$0.878997\pi$
$84$		0			0
$85$	2.46612	+	1.79174i	0.267488	+	0.194341i
$86$		0			0
$87$	3.10844	+	1.38397i	0.333260	+	0.148377i
$88$		0			0
$89$	−7.02573	+	5.10449i	−0.744726	+	0.541075i	−0.894188	−	0.447693i	$-0.852246\pi$
$89$	−7.02573	+	5.10449i	−0.744726	+	0.541075i	0.149462	+	0.988768i	$0.452246\pi$
$90$		0			0
$91$	1.80624	−	17.1852i	0.189345	−	1.80150i
$92$		0			0
$93$	−2.88466	−	4.99637i	−0.299125	−	0.518100i
$94$		0			0
$95$	2.90394	+	8.93742i	0.297938	+	0.916960i
$96$		0			0
$97$	−0.337747	+	3.21345i	−0.0342930	+	0.326276i	0.963904	+	0.266251i	$0.0857849\pi$
$97$	−0.337747	+	3.21345i	−0.0342930	+	0.326276i	−0.998197	+	0.0600257i	$0.980882\pi$
$98$		0			0
$99$	−1.00646	+	3.09757i	−0.101153	+	0.311318i
$100$		0			0
$101$	−2.10851	+	3.65204i	−0.209804	+	0.363392i	−0.951653	−	0.307176i	$-0.900616\pi$
$101$	−2.10851	+	3.65204i	−0.209804	+	0.363392i	0.741848	+	0.670568i	$0.233949\pi$
$102$		0			0
$103$	−7.28194	−	3.24213i	−0.717511	−	0.319456i	0.0153057	−	0.999883i	$-0.495128\pi$
$103$	−7.28194	−	3.24213i	−0.717511	−	0.319456i	−0.732816	+	0.680427i	$0.761795\pi$
$104$		0			0
$105$	−10.6391	+	2.26142i	−1.03827	+	0.220692i
$106$		0			0
$107$	−8.22327	−	1.74791i	−0.794974	−	0.168977i	−0.207516	−	0.978232i	$-0.566538\pi$
$107$	−8.22327	−	1.74791i	−0.794974	−	0.168977i	−0.587458	+	0.809255i	$0.699871\pi$
$108$		0			0
$109$	−2.65351	+	4.59602i	−0.254160	+	0.440219i	−0.964667	−	0.263472i	$-0.915132\pi$
$109$	−2.65351	+	4.59602i	−0.254160	+	0.440219i	0.710507	+	0.703690i	$0.248466\pi$
$110$		0			0
$111$	9.55374			0.906801
$112$		0			0
$113$	−0.107514	+	0.330893i	−0.0101140	+	0.0311278i	−0.955986	−	0.293412i	$-0.905209\pi$
$113$	−0.107514	+	0.330893i	−0.0101140	+	0.0311278i	0.945872	+	0.324540i	$0.105209\pi$
$114$		0			0
$115$	8.54423	−	3.80414i	0.796753	−	0.354737i
$116$		0			0
$117$	5.03638	+	5.59347i	0.465613	+	0.517116i
$118$		0			0
$119$	2.16998	−	1.57658i	0.198921	−	0.144525i
$120$		0			0
$121$	−3.06808			−0.278916
$122$		0			0
$123$	−14.2980			−1.28920
$124$		0			0
$125$	2.18709	−	1.58902i	0.195619	−	0.142126i
$126$		0			0
$127$	3.66360	+	4.06884i	0.325092	+	0.361051i	0.883431	−	0.468562i	$-0.155228\pi$
$127$	3.66360	+	4.06884i	0.325092	+	0.361051i	−0.558339	+	0.829613i	$0.688561\pi$
$128$		0			0
$129$	7.65942	−	3.41020i	0.674375	−	0.300251i
$130$		0			0
$131$	4.02896	−	12.3999i	0.352012	−	1.08338i	−0.605709	−	0.795686i	$-0.707111\pi$
$131$	4.02896	−	12.3999i	0.352012	−	1.08338i	0.957722	−	0.287696i	$-0.0928894\pi$
$132$		0			0
$133$	8.26888			0.717003
$134$		0			0
$135$	8.51406	−	14.7468i	0.732774	−	1.26920i
$136$		0			0
$137$	−10.5832	−	2.24953i	−0.904185	−	0.192190i	−0.267720	−	0.963497i	$-0.586270\pi$
$137$	−10.5832	−	2.24953i	−0.904185	−	0.192190i	−0.636464	+	0.771306i	$0.719604\pi$
$138$		0			0
$139$	−18.1490	+	3.85769i	−1.53938	+	0.327205i	−0.897992	−	0.440011i	$-0.854974\pi$
$139$	−18.1490	+	3.85769i	−1.53938	+	0.327205i	−0.641388	+	0.767217i	$0.721641\pi$
$140$		0			0
$141$	0.230559	+	0.102651i	0.0194165	+	0.00864480i
$142$		0			0
$143$	9.16518	−	15.8746i	0.766431	−	1.32750i
$144$		0			0
$145$	2.33660	−	7.19130i	0.194044	−	0.597205i
$146$		0			0
$147$	−0.00692682	+	0.0659043i	−0.000571315	+	0.00543570i
$148$		0			0
$149$	−1.06602	−	3.28088i	−0.0873321	−	0.268780i	0.897848	−	0.440307i	$-0.145130\pi$
$149$	−1.06602	−	3.28088i	−0.0873321	−	0.268780i	−0.985180	+	0.171526i	$0.945130\pi$
$150$		0			0
$151$	−0.233510	−	0.404452i	−0.0190028	−	0.0329138i	0.856368	−	0.516367i	$-0.172716\pi$
$151$	−0.233510	−	0.404452i	−0.0190028	−	0.0329138i	−0.875370	+	0.483453i	$0.839382\pi$
$152$		0			0
$153$	−0.122124	+	1.16193i	−0.00987311	+	0.0939363i
$154$		0			0
$155$	−10.3722	+	7.53585i	−0.833115	+	0.605294i
$156$		0			0
$157$	10.1903	+	4.53701i	0.813273	+	0.362093i	0.770858	−	0.637007i	$-0.219828\pi$
$157$	10.1903	+	4.53701i	0.813273	+	0.362093i	0.0424156	+	0.999100i	$0.486495\pi$
$158$		0			0
$159$	−6.99389	−	5.08136i	−0.554651	−	0.402978i
$160$		0			0
$161$	−0.860237	−	8.18461i	−0.0677962	−	0.645038i
$162$		0			0
$163$	−18.4370	−	13.3953i	−1.44410	−	1.04920i	−0.987166	−	0.159697i	$-0.948948\pi$
$163$	−18.4370	−	13.3953i	−1.44410	−	1.04920i	−0.456932	−	0.889501i	$-0.651052\pi$
$164$		0			0
$165$	−11.2860	−	2.39890i	−0.878611	−	0.186754i
$166$		0			0
$167$	3.78099	−	1.68341i	0.292582	−	0.130266i	−0.255197	−	0.966889i	$-0.582140\pi$
$167$	3.78099	−	1.68341i	0.292582	−	0.130266i	0.547779	+	0.836623i	$0.315474\pi$
$168$		0			0
$169$	−14.6804	−	25.4272i	−1.12926	−	1.95594i
$170$		0			0
$171$	−2.41005	+	2.67663i	−0.184301	+	0.204687i
$172$		0			0
$173$	4.07628	−	4.52717i	0.309914	−	0.344194i	−0.567986	−	0.823038i	$-0.692277\pi$
$173$	4.07628	−	4.52717i	0.309914	−	0.344194i	0.877900	+	0.478844i	$0.158944\pi$
$174$		0			0
$175$	3.36706	+	10.3627i	0.254526	+	0.783350i
$176$		0			0
$177$	−3.69666	−	4.10556i	−0.277858	−	0.308593i
$178$		0			0
$179$	−12.2261	+	2.59873i	−0.913820	+	0.194239i	−0.640745	−	0.767754i	$-0.721374\pi$
$179$	−12.2261	+	2.59873i	−0.913820	+	0.194239i	−0.273076	+	0.961993i	$0.588041\pi$
$180$		0			0
$181$	0.658888	+	6.26890i	0.0489748	+	0.465964i	0.991334	+	0.131362i	$0.0419351\pi$
$181$	0.658888	+	6.26890i	0.0489748	+	0.465964i	−0.942360	+	0.334602i	$0.891398\pi$
$182$		0			0
$183$	8.09296	+	6.85279i	0.598249	+	0.506573i
$184$		0			0
$185$	−2.21920	−	21.1143i	−0.163159	−	1.55236i
$186$		0			0
$187$	2.78313	−	0.591572i	0.203522	−	0.0432600i
$188$		0			0
$189$	−10.0258	−	11.1348i	−0.729269	−	0.809935i
$190$		0			0
$191$	−7.52102	−	23.1473i	−0.544202	−	1.67488i	−0.722881	−	0.690973i	$-0.757182\pi$
$191$	−7.52102	−	23.1473i	−0.544202	−	1.67488i	0.178679	−	0.983907i	$-0.442818\pi$
$192$		0			0
$193$	−12.6517	+	14.0512i	−0.910693	+	1.01143i	0.0891885	+	0.996015i	$0.471573\pi$
$193$	−12.6517	+	14.0512i	−0.910693	+	1.01143i	−0.999881	+	0.0154120i	$0.995094\pi$
$194$		0			0
$195$	−17.8418	+	19.8153i	−1.27767	+	1.41900i
$196$		0			0
$197$	−7.72263	−	13.3760i	−0.550214	−	0.952999i	−0.998259	−	0.0589880i	$-0.981213\pi$
$197$	−7.72263	−	13.3760i	−0.550214	−	0.952999i	0.448044	−	0.894011i	$-0.352121\pi$
$198$		0			0
$199$	−1.65900	+	0.738636i	−0.117604	+	0.0523605i	−0.464695	−	0.885471i	$-0.653836\pi$
$199$	−1.65900	+	0.738636i	−0.117604	+	0.0523605i	0.347091	+	0.937831i	$0.387169\pi$
$200$		0			0
$201$	−1.10579	−	0.235043i	−0.0779963	−	0.0165786i
$202$		0			0
$203$	−5.38269	−	3.91076i	−0.377791	−	0.274481i
$204$		0			0
$205$	3.32122	+	31.5993i	0.231964	+	2.20699i
$206$		0			0
$207$	2.90007	+	2.10703i	0.201569	+	0.146449i
$208$		0			0
$209$	8.01325	+	3.56773i	0.554288	+	0.246785i
$210$		0			0
$211$	3.97709	−	2.88952i	0.273794	−	0.198923i	−0.442412	−	0.896812i	$-0.645877\pi$
$211$	3.97709	−	2.88952i	0.273794	−	0.198923i	0.716206	+	0.697889i	$0.245877\pi$
$212$		0			0
$213$	0.894146	−	8.50723i	0.0612659	−	0.582906i
$214$		0			0
$215$	−9.31590	−	16.1356i	−0.635339	−	1.10044i
$216$		0			0
$217$	3.48607	+	10.7290i	0.236650	+	0.728334i
$218$		0			0
$219$	0.133304	−	1.26831i	0.00900787	−	0.0857041i
$220$		0			0
$221$	2.03191	−	6.25356i	0.136681	−	0.420660i
$222$		0			0
$223$	−8.55445	+	14.8167i	−0.572848	+	0.992202i	0.423423	+	0.905932i	$0.360828\pi$
$223$	−8.55445	+	14.8167i	−0.572848	+	0.992202i	−0.996272	+	0.0862706i	$0.972505\pi$
$224$		0			0
$225$	−4.33577	−	1.93041i	−0.289052	−	0.128694i
$226$		0			0
$227$	−7.03985	+	1.49637i	−0.467251	+	0.0993173i	−0.435520	−	0.900179i	$-0.643435\pi$
$227$	−7.03985	+	1.49637i	−0.467251	+	0.0993173i	−0.0317312	+	0.999496i	$0.510102\pi$
$228$		0			0
$229$	−25.1839	−	5.35300i	−1.66420	−	0.353736i	−0.722806	−	0.691051i	$-0.757148\pi$
$229$	−25.1839	−	5.35300i	−1.66420	−	0.353736i	−0.941392	+	0.337315i	$0.890481\pi$
$230$		0			0
$231$	−5.07627	+	8.79236i	−0.333994	+	0.578495i
$232$		0			0
$233$	14.3075			0.937315			0.468657	−	0.883380i	$-0.344738\pi$
$233$	14.3075			0.937315			0.468657	+	0.883380i	$0.344738\pi$
$234$		0			0
$235$	0.173310	−	0.533392i	0.0113055	−	0.0347947i
$236$		0			0
$237$	−14.7478	+	6.56616i	−0.957975	+	0.426518i
$238$		0			0
$239$	18.0020	+	19.9933i	1.16446	+	1.29326i	0.948472	+	0.316861i	$0.102629\pi$
$239$	18.0020	+	19.9933i	1.16446	+	1.29326i	0.215983	+	0.976397i	$0.430704\pi$
$240$		0			0
$241$	6.68877	−	4.85968i	0.430862	−	0.313039i	−0.351132	−	0.936326i	$-0.614203\pi$
$241$	6.68877	−	4.85968i	0.430862	−	0.313039i	0.781993	+	0.623287i	$0.214203\pi$
$242$		0			0
$243$	11.2370			0.720855
$244$		0			0
$245$	0.147261			0.00940818
$246$		0			0
$247$	16.3994	−	11.9149i	1.04347	−	0.758126i
$248$		0			0
$249$	−4.50196	−	4.99993i	−0.285300	−	0.316858i
$250$		0			0
$251$	26.5759	−	11.8323i	1.67745	−	0.746851i	0.677518	−	0.735506i	$-0.263055\pi$
$251$	26.5759	−	11.8323i	1.67745	−	0.746851i	0.999936	−	0.0113449i	$-0.00361126\pi$
$252$		0			0
$253$	2.69772	−	8.30274i	0.169604	−	0.521989i
$254$		0			0
$255$	−4.13889			−0.259187
$256$		0			0
$257$	0.926109	−	1.60407i	0.0577691	−	0.100059i	−0.835695	−	0.549194i	$-0.814935\pi$
$257$	0.926109	−	1.60407i	0.0577691	−	0.100059i	0.893464	+	0.449135i	$0.148268\pi$
$258$		0			0
$259$	−18.2729	−	3.88403i	−1.13542	−	0.241342i
$260$		0			0
$261$	2.83475	−	0.602544i	0.175466	−	0.0372965i
$262$		0			0
$263$	13.1298	+	5.84575i	0.809616	+	0.360464i	0.769433	−	0.638728i	$-0.220539\pi$
$263$	13.1298	+	5.84575i	0.809616	+	0.360464i	0.0401836	+	0.999192i	$0.487206\pi$
$264$		0			0
$265$	−9.60550	+	16.6372i	−0.590061	+	1.02202i
$266$		0			0
$267$	3.64371	−	11.2142i	0.222992	−	0.686297i
$268$		0			0
$269$	−1.18446	+	11.2694i	−0.0722177	+	0.687106i	0.897189	+	0.441646i	$0.145605\pi$
$269$	−1.18446	+	11.2694i	−0.0722177	+	0.687106i	−0.969407	+	0.245459i	$0.921061\pi$
$270$		0			0
$271$	6.00085	+	18.4687i	0.364526	+	1.12189i	0.950278	+	0.311404i	$0.100799\pi$
$271$	6.00085	+	18.4687i	0.364526	+	1.12189i	−0.585752	+	0.810490i	$0.699201\pi$
$272$		0			0
$273$	11.7311	+	20.3188i	0.709997	+	1.22975i
$274$		0			0
$275$	−1.20819	+	11.4951i	−0.0728565	+	0.693183i
$276$		0			0
$277$	26.4318	−	19.2038i	1.58813	−	1.15384i	0.681583	−	0.731741i	$-0.261292\pi$
$277$	26.4318	−	19.2038i	1.58813	−	1.15384i	0.906547	−	0.422104i	$-0.138708\pi$
$278$		0			0
$279$	−4.48903	−	1.99864i	−0.268751	−	0.119656i
$280$		0			0
$281$	−0.000812221	0	0.000590113i	−4.84530e−5	0	3.52032e-5i	0.587761	−	0.809035i	$-0.300010\pi$
$281$	−0.000812221	0	0.000590113i	−4.84530e−5	0	3.52032e-5i	−0.587809	+	0.808999i	$0.700010\pi$
$282$		0			0
$283$	−2.63268	−	25.0482i	−0.156496	−	1.48896i	−0.737658	−	0.675175i	$-0.764068\pi$
$283$	−2.63268	−	25.0482i	−0.156496	−	1.48896i	0.581162	−	0.813788i	$-0.302598\pi$
$284$		0			0
$285$	−10.3227	−	7.49985i	−0.611461	−	0.444253i
$286$		0			0
$287$	27.3469	+	5.81277i	1.61424	+	0.343117i
$288$		0			0
$289$	−14.5979	+	6.49939i	−0.858698	+	0.382317i
$290$		0			0
$291$	−2.19359	−	3.79941i	−0.128590	−	0.222725i
$292$		0			0
$293$	−12.2260	+	13.5784i	−0.714253	+	0.793259i	−0.985577	−	0.169230i	$-0.945872\pi$
$293$	−12.2260	+	13.5784i	−0.714253	+	0.793259i	0.271323	+	0.962488i	$0.412539\pi$
$294$		0			0
$295$	−8.21483	+	9.12349i	−0.478286	+	0.531190i
$296$		0			0
$297$	−4.91159	−	15.1163i	−0.284999	−	0.877137i
$298$		0			0
$299$	−13.4995	−	14.9927i	−0.780698	−	0.867053i
$300$		0			0
$301$	−16.0362	+	3.40859i	−0.924309	+	0.196468i
$302$		0			0
$303$	−0.598505	−	5.69439i	−0.0343832	−	0.327134i
$304$		0			0
$305$	13.2652	−	19.4777i	0.759562	−	1.11529i
$306$		0			0
$307$	−2.01301	−	19.1525i	−0.114889	−	1.09309i	−0.888324	−	0.459217i	$-0.848130\pi$
$307$	−2.01301	−	19.1525i	−0.114889	−	1.09309i	0.773435	−	0.633875i	$-0.218537\pi$
$308$		0			0
$309$	10.5864	−	2.25021i	0.602240	−	0.128010i
$310$		0			0
$311$	0.455620	+	0.506017i	0.0258358	+	0.0286936i	0.755924	−	0.654659i	$-0.227188\pi$
$311$	0.455620	+	0.506017i	0.0258358	+	0.0286936i	−0.730088	+	0.683353i	$0.760521\pi$
$312$		0			0
$313$	−5.54059	−	17.0522i	−0.313173	−	0.963846i	−0.976500	−	0.215517i	$-0.930856\pi$
$313$	−5.54059	−	17.0522i	−0.313173	−	0.963846i	0.663327	−	0.748329i	$-0.269144\pi$
$314$		0			0
$315$	−6.19885	+	6.88452i	−0.349266	+	0.387899i
$316$		0			0
$317$	16.6234	−	18.4621i	0.933662	−	1.03694i	−0.0655738	−	0.997848i	$-0.520888\pi$
$317$	16.6234	−	18.4621i	0.933662	−	1.03694i	0.999236	−	0.0390889i	$-0.0124456\pi$
$318$		0			0
$319$	−3.52893	−	6.11229i	−0.197582	−	0.342223i
$320$		0			0
$321$	10.4279	−	4.64282i	0.582030	−	0.259137i
$322$		0			0
$323$	3.07775	+	0.654195i	0.171250	+	0.0364004i
$324$		0			0
$325$	21.6098	+	15.7004i	1.19869	+	0.870903i
$326$		0			0
$327$	−0.753205	−	7.16627i	−0.0416523	−	0.396296i
$328$		0			0
$329$	−0.399244	−	0.290068i	−0.0220111	−	0.0159920i
$330$		0			0
$331$	22.6996	+	10.1065i	1.24768	+	0.555505i	0.920976	−	0.389620i	$-0.127394\pi$
$331$	22.6996	+	10.1065i	1.24768	+	0.555505i	0.326709	+	0.945125i	$0.394060\pi$
$332$		0			0
$333$	6.58308	−	4.78289i	0.360750	−	0.262101i
$334$		0			0
$335$	−0.262598	+	2.49845i	−0.0143473	+	0.136505i
$336$		0			0
$337$	10.9034	+	18.8852i	0.593945	+	1.02874i	0.993695	+	0.112118i	$0.0357635\pi$
$337$	10.9034	+	18.8852i	0.593945	+	1.02874i	−0.399750	+	0.916624i	$0.630903\pi$
$338$		0			0
$339$	−0.145979	−	0.449278i	−0.00792851	−	0.0244014i
$340$		0			0
$341$	−1.25089	+	11.9015i	−0.0677397	+	0.644500i
$342$		0			0
$343$	−5.70295	+	17.5519i	−0.307930	+	0.947712i
$344$		0			0
$345$	−6.34952	+	10.9977i	−0.341846	+	0.592095i
$346$		0			0
$347$	7.78673	+	3.46688i	0.418014	+	0.186112i	0.604956	−	0.796259i	$-0.293191\pi$
$347$	7.78673	+	3.46688i	0.418014	+	0.186112i	−0.186942	+	0.982371i	$0.559858\pi$
$348$		0			0
$349$	−15.9732	+	3.39520i	−0.855024	+	0.181741i	−0.614514	−	0.788906i	$-0.710648\pi$
$349$	−15.9732	+	3.39520i	−0.855024	+	0.181741i	−0.240510	+	0.970647i	$0.577315\pi$
$350$		0			0
$351$	−35.9283	−	7.63679i	−1.91771	−	0.407622i
$352$		0			0
$353$	1.16347	−	2.01518i	0.0619251	−	0.107257i	−0.833401	−	0.552669i	$-0.813609\pi$
$353$	1.16347	−	2.01518i	0.0619251	−	0.107257i	0.895326	+	0.445412i	$0.146943\pi$
$354$		0			0
$355$	−19.0092			−1.00890
$356$		0			0
$357$	−1.12540	+	3.46363i	−0.0595625	+	0.183315i
$358$		0			0
$359$	−21.6747	+	9.65022i	−1.14395	+	0.509319i	−0.889123	−	0.457668i	$-0.848685\pi$
$359$	−21.6747	+	9.65022i	−1.14395	+	0.509319i	−0.254826	+	0.966987i	$0.582018\pi$
$360$		0			0
$361$	−6.22282	−	6.91114i	−0.327517	−	0.363744i
$362$		0			0
$363$	3.37017	−	2.44857i	0.176888	−	0.128517i
$364$		0			0
$365$	−2.83399			−0.148338
$366$		0			0
$367$	−14.0566			−0.733749			−0.366875	−	0.930270i	$-0.619572\pi$
$367$	−14.0566			−0.733749			−0.366875	+	0.930270i	$0.619572\pi$
$368$		0			0
$369$	−9.85212	+	7.15799i	−0.512881	+	0.372630i
$370$		0			0
$371$	11.3110	+	12.5622i	0.587239	+	0.652195i
$372$		0			0
$373$	32.2659	−	14.3657i	1.67067	−	0.743829i	0.670668	−	0.741757i	$-0.266007\pi$
$373$	32.2659	−	14.3657i	1.67067	−	0.743829i	0.999998	−	0.00207123i	$-0.000659292\pi$
$374$		0			0
$375$	−1.13428	+	3.49095i	−0.0585739	+	0.180272i
$376$		0			0
$377$	−16.3105			−0.840031
$378$		0			0
$379$	−1.42658	+	2.47091i	−0.0732785	+	0.126922i	−0.900336	−	0.435195i	$-0.856680\pi$
$379$	−1.42658	+	2.47091i	−0.0732785	+	0.126922i	0.827058	+	0.562117i	$0.190013\pi$
$380$		0			0
$381$	−7.27159	−	1.54563i	−0.372535	−	0.0791848i
$382$		0			0
$383$	17.0129	−	3.61620i	0.869318	−	0.184779i	0.248403	−	0.968657i	$-0.420094\pi$
$383$	17.0129	−	3.61620i	0.869318	−	0.184779i	0.620915	+	0.783878i	$0.286761\pi$
$384$		0			0
$385$	20.6108	+	9.17650i	1.05042	+	0.467678i
$386$		0			0
$387$	3.57054	−	6.18435i	0.181501	−	0.314368i
$388$		0			0
$389$	−8.22318	+	25.3084i	−0.416932	+	1.28318i	0.493579	+	0.869701i	$0.335688\pi$
$389$	−8.22318	+	25.3084i	−0.416932	+	1.28318i	−0.910511	+	0.413484i	$0.864312\pi$
$390$		0			0
$391$	0.327341	−	3.11444i	0.0165543	−	0.157504i
$392$		0			0
$393$	5.47043	+	16.8362i	0.275947	+	0.849276i
$394$		0			0
$395$	17.9373	+	31.0683i	0.902524	+	1.56322i
$396$		0			0
$397$	−1.05682	+	10.0550i	−0.0530403	+	0.504645i	0.935461	+	0.353431i	$0.114985\pi$
$397$	−1.05682	+	10.0550i	−0.0530403	+	0.504645i	−0.988501	+	0.151214i	$0.951682\pi$
$398$		0			0
$399$	−9.08306	+	6.59923i	−0.454722	+	0.330375i
$400$		0			0
$401$	26.9960	+	12.0194i	1.34811	+	0.600219i	0.948591	−	0.316504i	$-0.102509\pi$
$401$	26.9960	+	12.0194i	1.34811	+	0.600219i	0.399523	+	0.916723i	$0.369176\pi$
$402$		0			0
$403$	22.3736	+	16.2554i	1.11451	+	0.809738i
$404$		0			0
$405$	1.32253	+	12.5831i	0.0657172	+	0.625257i
$406$		0			0
$407$	−16.0322	−	11.6481i	−0.794686	−	0.577373i
$408$		0			0
$409$	−17.9004	−	3.80485i	−0.885117	−	0.188137i	−0.257145	−	0.966373i	$-0.582782\pi$
$409$	−17.9004	−	3.80485i	−0.885117	−	0.188137i	−0.627973	+	0.778235i	$0.716115\pi$
$410$		0			0
$411$	13.4206	−	5.97522i	0.661988	−	0.294736i
$412$		0			0
$413$	5.40130	+	9.35533i	0.265781	+	0.460346i
$414$		0			0
$415$	−10.0044	+	11.1110i	−0.491096	+	0.545417i
$416$		0			0
$417$	16.8573	−	18.7219i	0.825505	−	0.916816i
$418$		0			0
$419$	−7.68503	−	23.6521i	−0.375438	−	1.15548i	−0.943183	−	0.332275i	$-0.892184\pi$
$419$	−7.68503	−	23.6521i	−0.375438	−	1.15548i	0.567744	−	0.823205i	$-0.307816\pi$
$420$		0			0
$421$	6.64819	+	7.38356i	0.324013	+	0.359853i	0.883041	−	0.469296i	$-0.155492\pi$
$421$	6.64819	+	7.38356i	0.324013	+	0.359853i	−0.559028	+	0.829149i	$0.688826\pi$
$422$		0			0
$423$	0.210258	−	0.0446918i	0.0102231	−	0.00217299i
$424$		0			0
$425$	0.433396	+	4.12349i	0.0210228	+	0.200018i
$426$		0			0
$427$	−12.6930	−	16.3971i	−0.614257	−	0.793512i
$428$		0			0
$429$	2.60156	+	24.7522i	0.125604	+	1.19505i
$430$		0			0
$431$	24.3878	−	5.18379i	1.17472	−	0.249695i	0.421106	−	0.907011i	$-0.361642\pi$
$431$	24.3878	−	5.18379i	1.17472	−	0.249695i	0.753614	+	0.657317i	$0.228309\pi$
$432$		0			0
$433$	−6.16032	−	6.84173i	−0.296046	−	0.328792i	0.576710	−	0.816949i	$-0.304336\pi$
$433$	−6.16032	−	6.84173i	−0.296046	−	0.328792i	−0.872756	+	0.488156i	$0.837670\pi$
$434$		0			0
$435$	3.17257	+	9.76417i	0.152113	+	0.468156i
$436$		0			0
$437$	6.45990	−	7.17445i	0.309019	−	0.343200i
$438$		0			0
$439$	−3.42144	+	3.79989i	−0.163296	+	0.181359i	−0.819240	−	0.573451i	$-0.805604\pi$
$439$	−3.42144	+	3.79989i	−0.163296	+	0.181359i	0.655943	+	0.754810i	$0.272271\pi$
$440$		0			0
$441$	0.0282207	+	0.0488796i	0.00134384	+	0.00232760i
$442$		0			0
$443$	−33.0448	+	14.7125i	−1.57001	+	0.699012i	−0.993043	−	0.117756i	$-0.962430\pi$
$443$	−33.0448	+	14.7125i	−1.57001	+	0.699012i	−0.576965	+	0.816769i	$0.695763\pi$
$444$		0			0
$445$	−25.6304	−	5.44791i	−1.21500	−	0.258255i
$446$		0			0
$447$	3.78940	+	2.75316i	0.179232	+	0.130220i
$448$		0			0
$449$	−0.841664	−	8.00790i	−0.0397206	−	0.377916i	−0.996266	−	0.0863336i	$-0.972485\pi$
$449$	−0.841664	−	8.00790i	−0.0397206	−	0.377916i	0.956546	−	0.291582i	$-0.0941817\pi$
$450$		0			0
$451$	23.9935	+	17.4323i	1.12981	+	0.820854i
$452$		0			0
$453$	0.579288	+	0.257916i	0.0272173	+	0.0121179i
$454$		0			0
$455$	42.1807	−	30.6461i	1.97746	−	1.43671i
$456$		0			0
$457$	0.0867369	−	0.825246i	0.00405738	−	0.0386034i	−0.992306	−	0.123810i	$-0.960489\pi$
$457$	0.0867369	−	0.825246i	0.00405738	−	0.0386034i	0.996363	+	0.0852071i	$0.0271552\pi$
$458$		0			0
$459$	−2.85075	−	4.93765i	−0.133062	−	0.230470i
$460$		0			0
$461$	−10.6559	−	32.7954i	−0.496293	−	1.52743i	−0.814931	−	0.579557i	$-0.803225\pi$
$461$	−10.6559	−	32.7954i	−0.496293	−	1.52743i	0.318638	−	0.947876i	$-0.396775\pi$
$462$		0			0
$463$	−1.51858	+	14.4483i	−0.0705743	+	0.671470i	0.900852	+	0.434127i	$0.142943\pi$
$463$	−1.51858	+	14.4483i	−0.0705743	+	0.671470i	−0.971426	+	0.237343i	$0.923724\pi$
$464$		0			0
$465$	5.37927	−	16.5557i	0.249458	−	0.767752i
$466$		0			0
$467$	2.11107	−	3.65649i	0.0976889	−	0.169202i	−0.813039	−	0.582210i	$-0.802188\pi$
$467$	2.11107	−	3.65649i	0.0976889	−	0.169202i	0.910728	+	0.413007i	$0.135522\pi$
$468$		0			0
$469$	2.01942	+	0.899106i	0.0932484	+	0.0415168i
$470$		0			0
$471$	−14.8145	+	3.14893i	−0.682618	+	0.145095i
$472$		0			0
$473$	−17.0111	−	3.61582i	−0.782170	−	0.166255i
$474$		0			0
$475$	−6.39101	+	11.0696i	−0.293240	+	0.507906i
$476$		0			0
$477$	−7.36306			−0.337132
$478$		0			0
$479$	11.6583	−	35.8807i	0.532683	−	1.63943i	−0.215919	−	0.976411i	$-0.569275\pi$
$479$	11.6583	−	35.8807i	0.532683	−	1.63943i	0.748602	−	0.663020i	$-0.230725\pi$
$480$		0			0
$481$	−41.8367	+	18.6269i	−1.90759	+	0.849314i
$482$		0			0
$483$	7.47691	+	8.30395i	0.340211	+	0.377843i
$484$		0			0
$485$	−7.88736	+	5.73050i	−0.358147	+	0.260209i
$486$		0			0
$487$	−13.1516			−0.595956			−0.297978	−	0.954573i	$-0.596312\pi$
$487$	−13.1516			−0.595956			−0.297978	+	0.954573i	$0.596312\pi$
$488$		0			0
$489$	30.9429			1.39929
$490$		0			0
$491$	2.85528	−	2.07448i	0.128857	−	0.0936200i	−0.521490	−	0.853257i	$-0.674624\pi$
$491$	2.85528	−	2.07448i	0.128857	−	0.0936200i	0.650347	+	0.759637i	$0.274624\pi$
$492$		0			0
$493$	−1.69408	−	1.88147i	−0.0762976	−	0.0847371i
$494$		0			0
$495$	−8.97763	+	3.99710i	−0.403515	+	0.179656i
$496$		0			0
$497$	−5.16876	+	15.9078i	−0.231850	+	0.713562i
$498$		0			0
$499$	17.7432			0.794293			0.397146	−	0.917755i	$-0.370001\pi$
$499$	17.7432			0.794293			0.397146	+	0.917755i	$0.370001\pi$
$500$		0			0
$501$	−2.80979	+	4.86669i	−0.125532	+	0.217428i
$502$		0			0
$503$	12.2886	+	2.61202i	0.547921	+	0.116464i	0.473551	−	0.880767i	$-0.342972\pi$
$503$	12.2886	+	2.61202i	0.547921	+	0.116464i	0.0743702	+	0.997231i	$0.476305\pi$
$504$		0			0
$505$	−12.4459	+	2.64546i	−0.553836	+	0.117721i
$506$		0			0
$507$	36.4188	+	16.2147i	1.61741	+	0.720120i
$508$		0			0
$509$	5.28551	−	9.15477i	0.234276	−	0.405778i	−0.724786	−	0.688974i	$-0.758061\pi$
$509$	5.28551	−	9.15477i	0.234276	−	0.405778i	0.959062	+	0.283196i	$0.0913947\pi$
$510$		0			0
$511$	−0.770587	+	2.37162i	−0.0340888	+	0.104914i
$512$		0			0
$513$	1.83727	−	17.4805i	0.0811176	−	0.771782i
$514$		0			0
$515$	−7.43218	−	22.8739i	−0.327501	−	1.00794i
$516$		0			0
$517$	−0.261748	−	0.453360i	−0.0115116	−	0.0199388i
$518$		0			0
$519$	−0.864601	+	8.22613i	−0.0379518	+	0.361087i
$520$		0			0
$521$	10.6412	−	7.73128i	0.466199	−	0.338714i	−0.329759	−	0.944065i	$-0.606967\pi$
$521$	10.6412	−	7.73128i	0.466199	−	0.338714i	0.795958	+	0.605352i	$0.206967\pi$
$522$		0			0
$523$	9.45287	+	4.20869i	0.413345	+	0.184033i	0.602864	−	0.797844i	$-0.294026\pi$
$523$	9.45287	+	4.20869i	0.413345	+	0.184033i	−0.189519	+	0.981877i	$0.560693\pi$
$524$		0			0
$525$	−11.9689	−	8.69591i	−0.522365	−	0.379521i
$526$		0			0
$527$	0.448715	+	4.26924i	0.0195463	+	0.185971i
$528$		0			0
$529$	10.8340	+	7.87138i	0.471044	+	0.342234i
$530$		0			0
$531$	−4.60257	−	0.978307i	−0.199735	−	0.0424549i
$532$		0			0
$533$	62.6121	−	27.8767i	2.71203	−	1.20747i
$534$		0			0
$535$	−12.6831	−	21.9679i	−0.548340	−	0.949753i
$536$		0			0
$537$	11.3559	−	12.6120i	0.490043	−	0.544248i
$538$		0			0
$539$	0.0919754	−	0.102149i	0.00396166	−	0.00439987i
$540$		0			0
$541$	−3.47648	−	10.6995i	−0.149466	−	0.460008i	0.848093	−	0.529848i	$-0.177751\pi$
$541$	−3.47648	−	10.6995i	−0.149466	−	0.460008i	−0.997558	+	0.0698402i	$0.977751\pi$
$542$		0			0
$543$	−5.72685	−	6.36031i	−0.245763	−	0.272947i
$544$		0			0
$545$	−15.6629	+	3.32925i	−0.670925	+	0.142610i
$546$		0			0
$547$	0.728273	+	6.92905i	0.0311387	+	0.296265i	0.998997	+	0.0447700i	$0.0142555\pi$
$547$	0.728273	+	6.92905i	0.0311387	+	0.296265i	−0.967859	+	0.251495i	$0.919078\pi$
$548$		0			0
$549$	9.00722	+	0.670394i	0.384419	+	0.0286117i
$550$		0			0
$551$	−0.815845	−	7.76225i	−0.0347562	−	0.330683i
$552$		0			0
$553$	30.8768	−	6.56307i	1.31302	−	0.279090i
$554$		0			0
$555$	19.2886	+	21.4222i	0.818757	+	0.909321i
$556$		0			0
$557$	7.48423	+	23.0341i	0.317117	+	0.975985i	0.974874	+	0.222756i	$0.0715052\pi$
$557$	7.48423	+	23.0341i	0.317117	+	0.975985i	−0.657757	+	0.753230i	$0.728495\pi$
$558$		0			0
$559$	−26.8925	+	29.8671i	−1.13743	+	1.26324i
$560$		0			0
$561$	−2.58504	+	2.87098i	−0.109140	+	0.121213i
$562$		0			0
$563$	7.11363	+	12.3212i	0.299804	+	0.519275i	0.976091	−	0.217363i	$-0.0697455\pi$
$563$	7.11363	+	12.3212i	0.299804	+	0.519275i	−0.676287	+	0.736638i	$0.736412\pi$
$564$		0			0
$565$	−0.959021	+	0.426984i	−0.0403463	+	0.0179633i
$566$		0			0
$567$	10.8897	+	2.31468i	0.457326	+	0.0972076i
$568$		0			0
$569$	−18.9037	−	13.7343i	−0.792482	−	0.575772i	0.116217	−	0.993224i	$-0.462923\pi$
$569$	−18.9037	−	13.7343i	−0.792482	−	0.575772i	−0.908699	+	0.417452i	$0.862923\pi$
$570$		0			0
$571$	2.28192	+	21.7110i	0.0954954	+	0.908578i	0.932448	+	0.361303i	$0.117668\pi$
$571$	2.28192	+	21.7110i	0.0954954	+	0.908578i	−0.836953	+	0.547275i	$0.815665\pi$
$572$		0			0
$573$	26.7350	+	19.4241i	1.11687	+	0.811453i
$574$		0			0
$575$	11.6216	+	5.17428i	0.484655	+	0.215782i
$576$		0			0
$577$	7.82847	−	5.68772i	0.325904	−	0.236783i	−0.412787	−	0.910828i	$-0.635445\pi$
$577$	7.82847	−	5.68772i	0.325904	−	0.236783i	0.738690	+	0.674045i	$0.235445\pi$
$578$		0			0
$579$	2.68350	−	25.5318i	0.111523	−	1.06107i
$580$		0			0
$581$	6.57795	+	11.3933i	0.272899	+	0.472675i
$582$		0			0
$583$	5.54121	+	17.0541i	0.229493	+	0.706308i
$584$		0			0
$585$	−2.37388	+	22.5860i	−0.0981479	+	0.933815i
$586$		0			0
$587$	10.6052	−	32.6396i	0.437725	−	1.34718i	−0.452543	−	0.891742i	$-0.649483\pi$
$587$	10.6052	−	32.6396i	0.437725	−	1.34718i	0.890268	−	0.455437i	$-0.150517\pi$
$588$		0			0
$589$	−6.61691	+	11.4608i	−0.272645	+	0.472235i
$590$		0			0
$591$	19.1581	+	8.52975i	0.788060	+	0.350867i
$592$		0			0
$593$	−34.5383	+	7.34135i	−1.41832	+	0.301473i	−0.852358	−	0.522959i	$-0.824828\pi$
$593$	−34.5383	+	7.34135i	−1.41832	+	0.301473i	−0.565961	+	0.824432i	$0.691495\pi$
$594$		0			0
$595$	7.91623	+	1.68265i	0.324534	+	0.0689818i
$596$		0			0
$597$	1.23286	−	2.13538i	0.0504578	−	0.0873954i
$598$		0			0
$599$	18.5941			0.759733			0.379867	−	0.925041i	$-0.375970\pi$
$599$	18.5941			0.759733			0.379867	+	0.925041i	$0.375970\pi$
$600$		0			0
$601$	−2.77356	+	8.53615i	−0.113136	+	0.348197i	−0.991554	−	0.129697i	$-0.958600\pi$
$601$	−2.77356	+	8.53615i	−0.113136	+	0.348197i	0.878418	+	0.477894i	$0.158600\pi$
$602$		0			0
$603$	−0.879621	+	0.391632i	−0.0358209	+	0.0159485i
$604$		0			0
$605$	−6.19433	−	6.87950i	−0.251835	−	0.279691i
$606$		0			0
$607$	−26.9514	+	19.5813i	−1.09392	+	0.794781i	−0.980057	−	0.198716i	$-0.936323\pi$
$607$	−26.9514	+	19.5813i	−1.09392	+	0.794781i	−0.113865	+	0.993496i	$0.536323\pi$
$608$		0			0
$609$	9.03379			0.366068
$610$		0			0
$611$	−1.20978			−0.0489423
$612$		0			0
$613$	17.5992	−	12.7865i	0.710823	−	0.516443i	−0.172616	−	0.984989i	$-0.555222\pi$
$613$	17.5992	−	12.7865i	0.710823	−	0.516443i	0.883439	+	0.468546i	$0.155222\pi$
$614$		0			0
$615$	−28.8670	−	32.0601i	−1.16403	−	1.29279i
$616$		0			0
$617$	10.0955	−	4.49479i	0.406428	−	0.180953i	−0.193332	−	0.981133i	$-0.561929\pi$
$617$	10.0955	−	4.49479i	0.406428	−	0.180953i	0.599760	+	0.800180i	$0.295263\pi$
$618$		0			0
$619$	−1.89369	+	5.82818i	−0.0761139	+	0.234254i	−0.981874	−	0.189537i	$-0.939301\pi$
$619$	−1.89369	+	5.82818i	−0.0761139	+	0.234254i	0.905760	+	0.423792i	$0.139301\pi$
$620$		0			0
$621$	−17.4935			−0.701989
$622$		0			0
$623$	−11.5282	+	19.9674i	−0.461868	+	0.799978i
$624$		0			0
$625$	28.0504	+	5.96230i	1.12202	+	0.238492i
$626$		0			0
$627$	−11.6496	+	2.47620i	−0.465240	+	0.0988897i
$628$		0			0
$629$	−6.49404	−	2.89133i	−0.258934	−	0.115285i
$630$		0			0
$631$	−6.66789	+	11.5491i	−0.265444	+	0.459763i	−0.967680	−	0.252181i	$-0.918852\pi$
$631$	−6.66789	+	11.5491i	−0.265444	+	0.459763i	0.702236	+	0.711945i	$0.252185\pi$
$632$		0			0
$633$	−2.06261	+	6.34807i	−0.0819815	+	0.252313i
$634$		0			0
$635$	−1.72683	+	16.4297i	−0.0685270	+	0.651991i
$636$		0			0
$637$	−0.0981603	−	0.302106i	−0.00388925	−	0.0119699i
$638$		0			0
$639$	−3.64285	−	6.30961i	−0.144109	−	0.249604i
$640$		0			0
$641$	−1.19331	+	11.3536i	−0.0471329	+	0.448439i	0.945350	+	0.326057i	$0.105720\pi$
$641$	−1.19331	+	11.3536i	−0.0471329	+	0.448439i	−0.992483	+	0.122382i	$0.960947\pi$
$642$		0			0
$643$	16.8513	−	12.2432i	0.664551	−	0.482825i	−0.203646	−	0.979045i	$-0.565279\pi$
$643$	16.8513	−	12.2432i	0.664551	−	0.482825i	0.868197	+	0.496220i	$0.165279\pi$
$644$		0			0
$645$	23.1107	+	10.2895i	0.909983	+	0.405150i
$646$		0			0
$647$	31.4040	+	22.8163i	1.23462	+	0.897003i	0.997228	−	0.0744109i	$-0.0237076\pi$
$647$	31.4040	+	22.8163i	1.23462	+	0.897003i	0.237391	+	0.971414i	$0.423708\pi$
$648$		0			0
$649$	1.19783	+	11.3966i	0.0470189	+	0.447355i
$650$		0			0
$651$	−12.3920	−	9.00328i	−0.485679	−	0.352866i
$652$		0			0
$653$	−24.2297	−	5.15018i	−0.948181	−	0.201542i	−0.292232	−	0.956347i	$-0.594398\pi$
$653$	−24.2297	−	5.15018i	−0.948181	−	0.201542i	−0.655949	+	0.754805i	$0.727731\pi$
$654$		0			0
$655$	35.9384	−	16.0008i	1.40423	−	0.625202i
$656$		0			0
$657$	−0.543097	−	0.940671i	−0.0211882	−	0.0366991i
$658$		0			0
$659$	−7.95501	+	8.83494i	−0.309883	+	0.344160i	−0.877889	−	0.478864i	$-0.841049\pi$
$659$	−7.95501	+	8.83494i	−0.309883	+	0.344160i	0.568006	+	0.823025i	$0.307715\pi$
$660$		0			0
$661$	12.4595	−	13.8377i	0.484619	−	0.538224i	−0.450397	−	0.892828i	$-0.648718\pi$
$661$	12.4595	−	13.8377i	0.484619	−	0.538224i	0.935017	+	0.354604i	$0.115384\pi$
$662$		0			0
$663$	2.75887	+	8.49093i	0.107146	+	0.329761i
$664$		0			0
$665$	16.6945	+	18.5412i	0.647387	+	0.718996i
$666$		0			0
$667$	−7.59827	+	1.61506i	−0.294206	+	0.0625354i
$668$		0			0
$669$	−2.42820	−	23.1028i	−0.0938797	−	0.893205i
$670$		0			0
$671$	−5.22581	−	21.3668i	−0.201740	−	0.824854i
$672$		0			0
$673$	−1.11150	−	10.5753i	−0.0428454	−	0.407646i	−0.994834	−	0.101513i	$-0.967631\pi$
$673$	−1.11150	−	10.5753i	−0.0428454	−	0.407646i	0.951989	−	0.306133i	$-0.0990352\pi$
$674$		0			0
$675$	22.6551	−	4.81548i	0.871994	−	0.185348i
$676$		0			0
$677$	9.34109	+	10.3743i	0.359007	+	0.398718i	0.895409	−	0.445245i	$-0.146883\pi$
$677$	9.34109	+	10.3743i	0.359007	+	0.398718i	−0.536401	+	0.843963i	$0.680217\pi$
$678$		0			0
$679$	2.65092	+	8.15871i	0.101733	+	0.313102i
$680$		0			0
$681$	6.53879	−	7.26206i	0.250567	−	0.278283i
$682$		0			0
$683$	−28.7078	+	31.8833i	−1.09847	+	1.21998i	−0.124764	+	0.992186i	$0.539817\pi$
$683$	−28.7078	+	31.8833i	−1.09847	+	1.21998i	−0.973710	+	0.227792i	$0.926849\pi$
$684$		0			0
$685$	−16.3230	−	28.2723i	−0.623670	−	1.08023i
$686$		0			0
$687$	31.9357	−	14.2187i	1.21842	−	0.542477i
$688$		0			0
$689$	40.5340	+	8.61576i	1.54422	+	0.328235i
$690$		0			0
$691$	−29.6439	−	21.5376i	−1.12771	−	0.819328i	−0.142349	−	0.989817i	$-0.545465\pi$
$691$	−29.6439	−	21.5376i	−1.12771	−	0.819328i	−0.985360	+	0.170488i	$0.945465\pi$
$692$		0			0
$693$	0.903873	+	8.59977i	0.0343353	+	0.326678i
$694$		0			0
$695$	−45.2922	−	32.9067i	−1.71803	−	1.24822i
$696$		0			0
$697$	9.71888	+	4.32712i	0.368129	+	0.163901i
$698$		0			0
$699$	−15.7162	+	11.4185i	−0.594443	+	0.431888i
$700$		0			0
$701$	−3.21770	+	30.6143i	−0.121531	+	1.15629i	0.748446	+	0.663195i	$0.230800\pi$
$701$	−3.21770	+	30.6143i	−0.121531	+	1.15629i	−0.869977	+	0.493092i	$0.835867\pi$
$702$		0			0
$703$	−10.9573	−	18.9787i	−0.413264	−	0.715793i
$704$		0			0
$705$	0.235315	+	0.724227i	0.00886249	+	0.0272759i
$706$		0			0
$707$	−1.17030	+	11.1347i	−0.0440137	+	0.418762i
$708$		0			0
$709$	−7.33891	+	22.5869i	−0.275619	+	0.848267i	0.713436	+	0.700720i	$0.247138\pi$
$709$	−7.33891	+	22.5869i	−0.275619	+	0.848267i	−0.989055	+	0.147547i	$0.952862\pi$
$710$		0			0
$711$	−6.87489	+	11.9077i	−0.257829	+	0.446572i
$712$		0			0
$713$	12.0324	+	5.35717i	0.450617	+	0.200628i
$714$		0			0
$715$	54.0994	−	11.4992i	2.02320	−	0.430045i
$716$		0			0
$717$	−35.7308	−	7.59482i	−1.33439	−	0.283634i
$718$		0			0
$719$	3.08994	−	5.35193i	0.115235	−	0.199593i	−0.802638	−	0.596466i	$-0.796571\pi$
$719$	3.08994	−	5.35193i	0.115235	−	0.199593i	0.917874	+	0.396872i	$0.129904\pi$
$720$		0			0
$721$	−21.1629			−0.788146
$722$		0			0
$723$	−3.46896	+	10.6764i	−0.129012	+	0.397058i
$724$		0			0
$725$	9.39561	−	4.18320i	0.348944	−	0.155360i
$726$		0			0
$727$	−11.6891	−	12.9820i	−0.433524	−	0.481477i	0.486309	−	0.873787i	$-0.338343\pi$
$727$	−11.6891	−	12.9820i	−0.433524	−	0.481477i	−0.919833	+	0.392310i	$0.871676\pi$
$728$		0			0
$729$	−22.5208	+	16.3623i	−0.834103	+	0.606011i
$730$		0			0
$731$	−6.23846			−0.230738
$732$		0			0
$733$	−35.3097			−1.30419			−0.652097	−	0.758135i	$-0.726111\pi$
$733$	−35.3097			−1.30419			−0.652097	+	0.758135i	$0.726111\pi$
$734$		0			0
$735$	−0.161761	+	0.117526i	−0.00596665	+	0.00433502i
$736$		0			0
$737$	1.56906	+	1.74262i	0.0577971	+	0.0641902i
$738$		0			0
$739$	−29.5579	+	13.1600i	−1.08731	+	0.484100i	−0.870527	−	0.492121i	$-0.836222\pi$
$739$	−29.5579	+	13.1600i	−1.08731	+	0.484100i	−0.216779	+	0.976221i	$0.569555\pi$
$740$		0			0
$741$	−8.50513	+	26.1761i	−0.312444	+	0.961604i
$742$		0			0
$743$	25.9087			0.950497			0.475248	−	0.879852i	$-0.342358\pi$
$743$	25.9087			0.950497			0.475248	+	0.879852i	$0.342358\pi$
$744$		0			0
$745$	5.20441	−	9.01430i	0.190675	−	0.330258i
$746$		0			0
$747$	−5.60522	−	1.19143i	−0.205084	−	0.0435920i
$748$		0			0
$749$	−21.8324	+	4.64063i	−0.797740	+	0.169565i
$750$		0			0
$751$	−28.3998	−	12.6444i	−1.03632	−	0.461402i	−0.183182	−	0.983079i	$-0.558640\pi$
$751$	−28.3998	−	12.6444i	−1.03632	−	0.461402i	−0.853143	+	0.521678i	$0.825306\pi$
$752$		0			0
$753$	−19.7495	+	34.2071i	−0.719710	+	1.24657i
$754$		0			0
$755$	0.435447	−	1.34017i	0.0158475	−	0.0487737i
$756$		0			0
$757$	0.710198	−	6.75708i	0.0258126	−	0.245590i	−0.974006	−	0.226524i	$-0.927264\pi$
$757$	0.710198	−	6.75708i	0.0258126	−	0.245590i	0.999818	−	0.0190665i	$-0.00606942\pi$
$758$		0			0
$759$	3.66290	+	11.2733i	0.132955	+	0.409193i
$760$		0			0
$761$	−6.86043	−	11.8826i	−0.248690	−	0.430744i	0.714472	−	0.699664i	$-0.246667\pi$
$761$	−6.86043	−	11.8826i	−0.248690	−	0.430744i	−0.963163	+	0.268919i	$0.913333\pi$
$762$		0			0
$763$	−1.47280	+	14.0127i	−0.0533189	+	0.507295i
$764$		0			0
$765$	−2.85193	+	2.07205i	−0.103112	+	0.0749152i
$766$		0			0
$767$	24.1926	+	10.7712i	0.873545	+	0.388927i
$768$		0			0
$769$	20.6882	+	15.0309i	0.746037	+	0.542027i	0.894596	−	0.446876i	$-0.147464\pi$
$769$	20.6882	+	15.0309i	0.746037	+	0.542027i	−0.148559	+	0.988904i	$0.547464\pi$
$770$		0			0
$771$	0.262878	+	2.50112i	0.00946733	+	0.0900756i
$772$		0			0
$773$	−21.6539	−	15.7325i	−0.778838	−	0.565859i	0.125792	−	0.992057i	$-0.459853\pi$
$773$	−21.6539	−	15.7325i	−0.778838	−	0.565859i	−0.904630	+	0.426198i	$0.859853\pi$
$774$		0			0
$775$	−17.0574	−	3.62565i	−0.612718	−	0.130237i
$776$		0			0
$777$	23.1719	−	10.3168i	0.831287	−	0.370113i
$778$		0			0
$779$	16.3986	+	28.4031i	0.587539	+	1.01765i
$780$		0			0
$781$	−11.8726	+	13.1859i	−0.424835	+	0.471828i
$782$		0			0
$783$	−9.46336	+	10.5101i	−0.338193	+	0.375601i
$784$		0			0
$785$	10.4005	+	32.0095i	0.371211	+	1.14247i
$786$		0			0
$787$	26.4964	+	29.4272i	0.944494	+	1.04897i	0.998727	+	0.0504385i	$0.0160619\pi$
$787$	26.4964	+	29.4272i	0.944494	+	1.04897i	−0.0542332	+	0.998528i	$0.517271\pi$
$788$		0			0
$789$	−19.0879	+	4.05727i	−0.679549	+	0.144443i
$790$		0			0
$791$	0.0965547	+	0.918657i	0.00343309	+	0.0326637i
$792$		0			0
$793$	−48.8007	−	14.2302i	−1.73296	−	0.505329i
$794$		0			0
$795$	−2.72654	−	25.9413i	−0.0967005	−	0.920044i
$796$		0			0
$797$	28.6305	−	6.08560i	1.01414	−	0.215563i	0.329279	−	0.944233i	$-0.393194\pi$
$797$	28.6305	−	6.08560i	1.01414	−	0.215563i	0.684865	+	0.728670i	$0.259861\pi$
$798$		0			0
$799$	−0.125653	−	0.139552i	−0.00444529	−	0.00493700i
$800$		0			0
$801$	−3.10343	−	9.55137i	−0.109654	−	0.337481i
$802$		0			0
$803$	−1.77003	+	1.96582i	−0.0624632	+	0.0693724i
$804$		0			0
$805$	16.6154	−	18.4533i	0.585617	−	0.650393i
$806$		0			0
$807$	−7.69278	−	13.3243i	−0.270799	−	0.469037i
$808$		0			0
$809$	−47.5670	+	21.1782i	−1.67237	+	0.744585i	−0.672375	+	0.740211i	$0.734726\pi$
$809$	−47.5670	+	21.1782i	−1.67237	+	0.744585i	−0.999990	+	0.00437461i	$0.998608\pi$
$810$		0			0
$811$	−36.7646	−	7.81455i	−1.29098	−	0.274406i	−0.489276	−	0.872129i	$-0.662739\pi$
$811$	−36.7646	−	7.81455i	−1.29098	−	0.274406i	−0.801703	+	0.597723i	$0.796072\pi$
$812$		0			0
$813$	−21.3312	−	15.4980i	−0.748119	−	0.543540i
$814$		0			0
$815$	−7.18761	−	68.3855i	−0.251771	−	2.39544i
$816$		0			0
$817$	−15.5591	−	11.3044i	−0.544344	−	0.395489i
$818$		0			0
$819$	18.2556	+	8.12790i	0.637901	+	0.284012i
$820$		0			0
$821$	34.7911	−	25.2772i	1.21422	−	0.882182i	0.218612	−	0.975812i	$-0.429847\pi$
$821$	34.7911	−	25.2772i	1.21422	−	0.882182i	0.995607	+	0.0936298i	$0.0298470\pi$
$822$		0			0
$823$	3.83087	−	36.4483i	0.133536	−	1.27051i	−0.698429	−	0.715680i	$-0.746117\pi$
$823$	3.83087	−	36.4483i	0.133536	−	1.27051i	0.831965	−	0.554829i	$-0.187216\pi$
$824$		0			0
$825$	−7.84690	−	13.5912i	−0.273194	−	0.473186i
$826$		0			0
$827$	−12.3793	−	38.0995i	−0.430470	−	1.32485i	−0.897658	−	0.440693i	$-0.854733\pi$
$827$	−12.3793	−	38.0995i	−0.430470	−	1.32485i	0.467188	−	0.884158i	$-0.345267\pi$
$828$		0			0
$829$	−0.862470	+	8.20585i	−0.0299548	+	0.285001i	0.969282	+	0.245950i	$0.0791000\pi$
$829$	−0.862470	+	8.20585i	−0.0299548	+	0.285001i	−0.999237	+	0.0390507i	$0.987567\pi$
$830$		0			0
$831$	−13.7081	+	42.1893i	−0.475530	+	1.46353i
$832$		0			0
$833$	0.0246536	−	0.0427014i	0.000854198	−	0.00147951i
$834$		0			0
$835$	11.4083	+	5.07932i	0.394802	+	0.175777i
$836$		0			0
$837$	23.4558	−	4.98569i	0.810752	−	0.172331i
$838$		0			0
$839$	−34.4495	−	7.32246i	−1.18933	−	0.252800i	−0.429587	−	0.903025i	$-0.641341\pi$
$839$	−34.4495	−	7.32246i	−1.18933	−	0.252800i	−0.759741	+	0.650226i	$0.774674\pi$
$840$		0			0
$841$	11.3599	−	19.6760i	0.391722	−	0.678482i
$842$		0			0
$843$	0.00136315			4.69495e−5
$844$		0			0
$845$	27.3758	−	84.2540i	0.941756	−	2.89843i
$846$		0			0
$847$	−7.44139	+	3.31312i	−0.255689	+	0.113840i
$848$		0			0
$849$	22.8824	+	25.4135i	0.785322	+	0.872188i
$850$		0			0
$851$	−17.6453	+	12.8201i	−0.604873	+	0.439466i
$852$		0			0
$853$	−53.0410			−1.81609			−0.908045	−	0.418872i	$-0.862426\pi$
$853$	−53.0410			−1.81609			−0.908045	+	0.418872i	$0.862426\pi$
$854$		0			0
$855$	−10.8675			−0.371662
$856$		0			0
$857$	−24.0151	+	17.4480i	−0.820340	+	0.596012i	−0.916810	−	0.399324i	$-0.869245\pi$
$857$	−24.0151	+	17.4480i	−0.820340	+	0.596012i	0.0964702	+	0.995336i	$0.469245\pi$
$858$		0			0
$859$	−30.7976	−	34.2042i	−1.05080	−	1.16703i	−0.985588	−	0.169162i	$-0.945894\pi$
$859$	−30.7976	−	34.2042i	−1.05080	−	1.16703i	−0.0652131	−	0.997871i	$-0.520773\pi$
$860$		0			0
$861$	−34.6787	+	15.4399i	−1.18185	+	0.526192i
$862$		0			0
$863$	13.3450	−	41.0716i	0.454268	−	1.39809i	−0.417725	−	0.908574i	$-0.637172\pi$
$863$	13.3450	−	41.0716i	0.454268	−	1.39809i	0.871993	−	0.489519i	$-0.162828\pi$
$864$		0			0
$865$	18.3810			0.624974
$866$		0			0
$867$	10.8482	−	18.7896i	0.368423	−	0.638128i
$868$		0			0
$869$	32.7540	+	6.96207i	1.11110	+	0.236172i
$870$		0			0
$871$	5.30061	−	1.12668i	0.179604	−	0.0381761i
$872$		0			0
$873$	−3.41360	−	1.51983i	−0.115533	−	0.0514386i
$874$		0			0
$875$	3.58870	−	6.21581i	0.121320	−	0.210133i
$876$		0			0
$877$	11.1781	−	34.4026i	0.377457	−	1.16169i	−0.564348	−	0.825537i	$-0.690873\pi$
$877$	11.1781	−	34.4026i	0.377457	−	1.16169i	0.941806	−	0.336158i	$-0.109127\pi$
$878$		0			0
$879$	2.59321	−	24.6727i	0.0874668	−	0.832191i
$880$		0			0
$881$	−16.9600	−	52.1974i	−0.571396	−	1.75858i	−0.648136	−	0.761525i	$-0.724451\pi$
$881$	−16.9600	−	52.1974i	−0.571396	−	1.75858i	0.0767395	−	0.997051i	$-0.475549\pi$
$882$		0			0
$883$	−4.78399	−	8.28612i	−0.160994	−	0.278850i	0.774231	−	0.632903i	$-0.218137\pi$
$883$	−4.78399	−	8.28612i	−0.160994	−	0.278850i	−0.935226	+	0.354053i	$0.884803\pi$
$884$		0			0
$885$	1.74241	−	16.5779i	0.0585704	−	0.557260i
$886$		0			0
$887$	−18.4392	+	13.3969i	−0.619128	+	0.449823i	−0.852617	−	0.522537i	$-0.824986\pi$
$887$	−18.4392	+	13.3969i	−0.619128	+	0.449823i	0.233489	+	0.972359i	$0.424986\pi$
$888$		0			0
$889$	13.2796	+	5.91246i	0.445384	+	0.198298i
$890$		0			0
$891$	9.55437	+	6.94165i	0.320083	+	0.232554i
$892$		0			0
$893$	−0.0605128	−	0.575740i	−0.00202498	−	0.0192664i
$894$		0			0
$895$	−30.5111	−	22.1676i	−1.01987	−	0.740981i
$896$		0			0
$897$	26.7942	+	5.69527i	0.894631	+	0.190160i
$898$		0			0
$899$	9.72772	−	4.33106i	0.324438	−	0.144449i
$900$		0			0
$901$	3.21620	+	5.57061i	0.107147	+	0.185584i
$902$		0			0
$903$	14.8948	−	16.5423i	0.495668	−	0.550495i
$904$		0			0
$905$	−12.7264	+	14.1341i	−0.423039	+	0.469833i
$906$		0			0
$907$	10.2039	+	31.4045i	0.338816	+	1.04277i	0.964812	+	0.262942i	$0.0846928\pi$
$907$	10.2039	+	31.4045i	0.338816	+	1.04277i	−0.625996	+	0.779827i	$0.715307\pi$
$908$		0			0
$909$	−3.26319	−	3.62414i	−0.108233	−	0.120205i
$910$		0			0
$911$	−21.7634	+	4.62594i	−0.721052	+	0.153264i	−0.553800	−	0.832650i	$-0.686823\pi$
$911$	−21.7634	+	4.62594i	−0.721052	+	0.153264i	−0.167252	+	0.985914i	$0.553489\pi$
$912$		0			0
$913$	1.45877	+	13.8793i	0.0482782	+	0.459336i
$914$		0			0
$915$	0.973464	+	31.9822i	0.0321817	+	1.05730i
$916$		0			0
$917$	−3.61829	−	34.4257i	−0.119486	−	1.13684i
$918$		0			0
$919$	−10.2169	+	2.17168i	−0.337026	+	0.0716371i	−0.373316	−	0.927704i	$-0.621779\pi$
$919$	−10.2169	+	2.17168i	−0.337026	+	0.0716371i	0.0362901	+	0.999341i	$0.488446\pi$
$920$		0			0
$921$	17.4965	+	19.4318i	0.576529	+	0.640300i
$922$		0			0
$923$	12.6710	+	38.9973i	0.417071	+	1.28361i
$924$		0			0
$925$	19.3227	−	21.4600i	0.635326	−	0.705601i
$926$		0			0
$927$	6.16813	−	6.85040i	0.202588	−	0.224997i
$928$		0			0
$929$	1.39703	+	2.41972i	0.0458350	+	0.0793885i	0.888033	−	0.459780i	$-0.152072\pi$
$929$	1.39703	+	2.41972i	0.0458350	+	0.0793885i	−0.842198	+	0.539169i	$0.818738\pi$
$930$		0			0
$931$	0.138864	−	0.0618264i	0.00455110	−	0.00202628i
$932$		0			0
$933$	−0.904324	−	0.192220i	−0.0296062	−	0.00629300i
$934$		0			0
$935$	6.94549	+	5.04620i	0.227142	+	0.165028i
$936$		0			0
$937$	−5.30312	−	50.4558i	−0.173245	−	1.64832i	−0.643250	−	0.765656i	$-0.722414\pi$
$937$	−5.30312	−	50.4558i	−0.173245	−	1.64832i	0.470004	−	0.882664i	$-0.344252\pi$
$938$		0			0
$939$	19.6951	+	14.3094i	0.642727	+	0.466968i
$940$		0			0
$941$	19.8676	+	8.84565i	0.647667	+	0.288360i	0.704158	−	0.710043i	$-0.251325\pi$
$941$	19.8676	+	8.84565i	0.647667	+	0.288360i	−0.0564913	+	0.998403i	$0.517991\pi$
$942$		0			0
$943$	26.4077	−	19.1863i	0.859952	−	0.624792i
$944$		0			0
$945$	4.72563	−	44.9613i	0.153725	−	1.46259i
$946$		0			0
$947$	16.8117	+	29.1188i	0.546308	+	0.946232i	0.998523	+	0.0543239i	$0.0173004\pi$
$947$	16.8117	+	29.1188i	0.546308	+	0.946232i	−0.452216	+	0.891909i	$0.649366\pi$
$948$		0			0
$949$	1.88906	+	5.81393i	0.0613215	+	0.188728i
$950$		0			0
$951$	−3.52591	+	33.5468i	−0.114335	+	1.08783i
$952$		0			0
$953$	6.44518	−	19.8362i	0.208780	−	0.642559i	−0.790757	−	0.612130i	$-0.790313\pi$
$953$	6.44518	−	19.8362i	0.208780	−	0.642559i	0.999537	−	0.0304284i	$-0.00968716\pi$
$954$		0			0
$955$	36.7182	−	63.5977i	1.18817	−	2.05797i
$956$		0			0
$957$	8.75450	+	3.89776i	0.282993	+	0.125997i
$958$		0			0
$959$	−28.0980	+	5.97241i	−0.907331	+	0.192859i
$960$		0			0
$961$	12.6623	+	2.69146i	0.408461	+	0.0868212i
$962$		0			0
$963$	4.86111	−	8.41970i	0.156647	−	0.271321i
$964$		0			0
$965$	−57.0501			−1.83651
$966$		0			0
$967$	9.54730	−	29.3836i	0.307020	−	0.944912i	−0.671895	−	0.740646i	$-0.734519\pi$
$967$	9.54730	−	29.3836i	0.307020	−	0.944912i	0.978916	−	0.204265i	$-0.0654806\pi$
$968$		0			0
$969$	−3.90289	+	1.73768i	−0.125379	+	0.0558223i
$970$		0			0
$971$	9.45208	+	10.4976i	0.303332	+	0.336884i	0.875469	−	0.483274i	$-0.160552\pi$
$971$	9.45208	+	10.4976i	0.303332	+	0.336884i	−0.572138	+	0.820158i	$0.693886\pi$
$972$		0			0
$973$	−39.8533	+	28.9551i	−1.27764	+	0.928259i
$974$		0			0
$975$	−36.2677			−1.16150
$976$		0			0
$977$	20.7190			0.662859			0.331429	−	0.943480i	$-0.392469\pi$
$977$	20.7190			0.662859			0.331429	+	0.943480i	$0.392469\pi$
$978$		0			0
$979$	−19.7870	+	14.3761i	−0.632396	+	0.459463i
$980$		0			0
$981$	−4.10665	−	4.56089i	−0.131115	−	0.145618i
$982$		0			0
$983$	−43.1721	+	19.2214i	−1.37698	+	0.613069i	−0.955829	−	0.293924i	$-0.905039\pi$
$983$	−43.1721	+	19.2214i	−1.37698	+	0.613069i	−0.421147	+	0.906993i	$0.638372\pi$
$984$		0			0
$985$	14.4011	−	44.3219i	0.458856	−	1.41221i
$986$		0			0
$987$	0.670053			0.0213280
$988$		0			0
$989$	−9.57048	+	16.5766i	−0.304324	+	0.527104i
$990$		0			0
$991$	41.4537	+	8.81126i	1.31682	+	0.279899i	0.812168	−	0.583424i	$-0.198287\pi$
$991$	41.4537	+	8.81126i	1.31682	+	0.279899i	0.504653	+	0.863322i	$0.331621\pi$
$992$		0			0
$993$	−33.0005	+	7.01448i	−1.04724	+	0.222598i
$994$		0			0
$995$	−5.00569	−	2.22868i	−0.158691	−	0.0706539i
$996$		0			0
$997$	−5.76240	+	9.98077i	−0.182497	+	0.316094i	−0.942730	−	0.333556i	$-0.891751\pi$
$997$	−5.76240	+	9.98077i	−0.182497	+	0.316094i	0.760233	+	0.649650i	$0.225085\pi$
$998$		0			0
$999$	−12.2709	+	37.7661i	−0.388236	+	1.19487i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	976.2.bw.c.625.1		32
4.3	odd	2		61.2.i.a.15.1	✓	32
12.11	even	2		549.2.bl.b.442.4		32
61.57	even	15	inner	976.2.bw.c.545.1		32
244.39	odd	30		3721.2.a.l.1.1		16
244.83	odd	30		3721.2.a.j.1.16		16
244.179	odd	30		61.2.i.a.57.1	yes	32
732.179	even	30		549.2.bl.b.118.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.i.a.15.1	✓	32	4.3	odd	2
61.2.i.a.57.1	yes	32	244.179	odd	30
549.2.bl.b.118.4		32	732.179	even	30
549.2.bl.b.442.4		32	12.11	even	2
976.2.bw.c.545.1		32	61.57	even	15	inner
976.2.bw.c.625.1		32	1.1	even	1	trivial
3721.2.a.j.1.16		16	244.83	odd	30
3721.2.a.l.1.1		16	244.39	odd	30

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 976 = 2^{4} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	976.bw (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.09846 + 0.798080i) q^{3} +(2.01896 + 2.24228i) q^{5} +(2.42543 - 1.07987i) q^{7} +(-0.357362 + 1.09985i) q^{9} +2.81637 q^{11} +(3.25426 - 5.63654i) q^{13} +(-4.00727 - 0.851773i) q^{15} +(0.988198 - 0.210048i) q^{17} +(2.84524 + 1.26678i) q^{19} +(-1.80242 + 3.12188i) q^{21} +(0.957874 - 2.94803i) q^{23} +(-0.428988 + 4.08155i) q^{25} +(-1.74394 - 5.36731i) q^{27} +(-1.25301 - 2.17028i) q^{29} +(-0.444151 + 4.22582i) q^{31} +(-3.09368 + 2.24769i) q^{33} +(7.31821 + 3.25828i) q^{35} +(-5.69250 - 4.13585i) q^{37} +(0.923728 + 8.78869i) q^{39} +(8.51930 + 6.18964i) q^{41} +(-6.04008 - 1.28386i) q^{43} +(-3.18766 + 1.41924i) q^{45} +(-0.0929380 - 0.160973i) q^{47} +(0.0326575 - 0.0362698i) q^{49} +(-0.917864 + 1.01939i) q^{51} +(1.96750 + 6.05535i) q^{53} +(5.68613 + 6.31509i) q^{55} +(-4.13639 + 0.879216i) q^{57} +(0.425310 + 4.04655i) q^{59} +(-1.85551 - 7.58664i) q^{61} +(0.320936 + 3.05350i) q^{63} +(19.2089 - 4.08298i) q^{65} +(0.557122 + 0.618747i) q^{67} +(1.30058 + 4.00276i) q^{69} +(-4.21558 + 4.68187i) q^{71} +(-0.628481 + 0.697999i) q^{73} +(-2.78618 - 4.82580i) q^{75} +(6.83089 - 3.04131i) q^{77} +(11.6299 + 2.47200i) q^{79} +(3.39244 + 2.46475i) q^{81} +(0.517961 + 4.92807i) q^{83} +(2.46612 + 1.79174i) q^{85} +(3.10844 + 1.38397i) q^{87} +(-7.02573 + 5.10449i) q^{89} +(1.80624 - 17.1852i) q^{91} +(-2.88466 - 4.99637i) q^{93} +(2.90394 + 8.93742i) q^{95} +(-0.337747 + 3.21345i) q^{97} +(-1.00646 + 3.09757i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} + 2 q^{5} - q^{7} - 2 q^{9} + 18 q^{11} - 2 q^{15} - 24 q^{17} - 9 q^{19} - 3 q^{21} + 2 q^{23} + 28 q^{25} - 35 q^{27} - 4 q^{29} + 11 q^{31} - 35 q^{33} + 58 q^{35} - 14 q^{37} - 17 q^{39}+ \cdots + 31 q^{99}+O(q^{100}) \) 32 * q + 4 * q^3 + 2 * q^5 - q^7 - 2 * q^9 + 18 * q^11 - 2 * q^15 - 24 * q^17 - 9 * q^19 - 3 * q^21 + 2 * q^23 + 28 * q^25 - 35 * q^27 - 4 * q^29 + 11 * q^31 - 35 * q^33 + 58 * q^35 - 14 * q^37 - 17 * q^39 + 11 * q^41 - 40 * q^43 + 12 * q^45 - 40 * q^47 + q^49 + 9 * q^51 + 17 * q^53 + 60 * q^55 - 38 * q^57 + 11 * q^59 - 55 * q^61 + 58 * q^63 + 59 * q^65 + 13 * q^67 - 32 * q^69 - 63 * q^71 - 46 * q^73 - q^75 - 31 * q^77 + 49 * q^79 + 48 * q^81 - 39 * q^83 + 21 * q^85 - 17 * q^87 + 32 * q^89 - 70 * q^91 + 67 * q^93 - 47 * q^95 + 37 * q^97 + 31 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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