LMFDB - Embedded newform 320.2.l.a.241.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [320,2,Mod(81,320)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(320, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("320.81"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	320.l (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.55521286468$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 $ x^16 - 4x^15 + 4x^14 + 7x^12 - 8x^11 - 28x^10 + 28x^9 + 17x^8 + 56x^7 - 112x^6 - 64x^5 + 112x^4 + 256x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			241.3
Root			$-0.530822 + 1.31081i$ of defining polynomial
Character	$\chi$	$=$	320.241
Dual form			320.2.l.a.81.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37027 + 1.37027i) q^{3} +(-0.707107 - 0.707107i) q^{5} +2.73482i q^{7} -0.755274i q^{9} +(-4.12175 - 4.12175i) q^{11} +(-1.37919 + 1.37919i) q^{13} +1.93785 q^{15} -4.94921 q^{17} +(0.292715 - 0.292715i) q^{19} +(-3.74744 - 3.74744i) q^{21} +1.64818i q^{23} +1.00000i q^{25} +(-3.07588 - 3.07588i) q^{27} +(-5.67267 + 5.67267i) q^{29} -3.95550 q^{31} +11.2958 q^{33} +(1.93381 - 1.93381i) q^{35} +(2.48772 + 2.48772i) q^{37} -3.77973i q^{39} -8.40843i q^{41} +(3.22713 + 3.22713i) q^{43} +(-0.534060 + 0.534060i) q^{45} +5.19809 q^{47} -0.479225 q^{49} +(6.78176 - 6.78176i) q^{51} +(7.20537 + 7.20537i) q^{53} +5.82903i q^{55} +0.802198i q^{57} +(6.41142 + 6.41142i) q^{59} +(-3.82618 + 3.82618i) q^{61} +2.06554 q^{63} +1.95047 q^{65} +(-5.76044 + 5.76044i) q^{67} +(-2.25846 - 2.25846i) q^{69} +7.92245i q^{71} +4.36276i q^{73} +(-1.37027 - 1.37027i) q^{75} +(11.2722 - 11.2722i) q^{77} +5.56087 q^{79} +10.6954 q^{81} +(0.516191 - 0.516191i) q^{83} +(3.49962 + 3.49962i) q^{85} -15.5462i q^{87} -6.42236i q^{89} +(-3.77184 - 3.77184i) q^{91} +(5.42011 - 5.42011i) q^{93} -0.413962 q^{95} -9.44534 q^{97} +(-3.11305 + 3.11305i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{11} + 8 q^{15} + 8 q^{19} - 24 q^{27} - 16 q^{29} - 16 q^{37} - 8 q^{43} + 40 q^{47} - 16 q^{49} + 32 q^{51} + 16 q^{53} + 8 q^{59} + 16 q^{61} - 40 q^{63} - 40 q^{67} + 16 q^{69} + 16 q^{77}+ \cdots + 8 q^{99}+O(q^{100}) $ 16 * q + 8 * q^11 + 8 * q^15 + 8 * q^19 - 24 * q^27 - 16 * q^29 - 16 * q^37 - 8 * q^43 + 40 * q^47 - 16 * q^49 + 32 * q^51 + 16 * q^53 + 8 * q^59 + 16 * q^61 - 40 * q^63 - 40 * q^67 + 16 * q^69 + 16 * q^77 - 16 * q^79 - 16 * q^81 - 40 * q^83 - 16 * q^85 - 32 * q^91 - 48 * q^93 - 32 * q^95 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−1.37027	+	1.37027i	−0.791125	+	0.791125i	−0.981677	−	0.190552i	$-0.938972\pi$
$3$	−1.37027	+	1.37027i	−0.791125	+	0.791125i	0.190552	+	0.981677i	$0.438972\pi$
$4$		0			0
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$		0			0
$7$			2.73482i			1.03366i	0.856087	+	0.516832i	$0.172889\pi$
$7$			2.73482i			1.03366i	−0.856087	+	0.516832i	$0.827111\pi$
$8$		0			0
$9$		−	0.755274i		−	0.251758i
$10$		0			0
$11$	−4.12175	−	4.12175i	−1.24275	−	1.24275i	−0.958854	−	0.283900i	$-0.908371\pi$
$11$	−4.12175	−	4.12175i	−1.24275	−	1.24275i	−0.283900	−	0.958854i	$-0.591629\pi$
$12$		0			0
$13$	−1.37919	+	1.37919i	−0.382519	+	0.382519i	−0.872009	−	0.489490i	$-0.837183\pi$
$13$	−1.37919	+	1.37919i	−0.382519	+	0.382519i	0.489490	+	0.872009i	$0.337183\pi$
$14$		0			0
$15$	1.93785			0.500352
$16$		0			0
$17$	−4.94921			−1.20036			−0.600180	−	0.799865i	$-0.704905\pi$
$17$	−4.94921			−1.20036			−0.600180	+	0.799865i	$0.704905\pi$
$18$		0			0
$19$	0.292715	−	0.292715i	0.0671535	−	0.0671535i	−0.672732	−	0.739886i	$-0.734879\pi$
$19$	0.292715	−	0.292715i	0.0671535	−	0.0671535i	0.739886	+	0.672732i	$0.234879\pi$
$20$		0			0
$21$	−3.74744	−	3.74744i	−0.817757	−	0.817757i
$22$		0			0
$23$			1.64818i			0.343670i	0.985126	+	0.171835i	$0.0549696\pi$
$23$			1.64818i			0.343670i	−0.985126	+	0.171835i	$0.945030\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	−3.07588	−	3.07588i	−0.591953	−	0.591953i
$28$		0			0
$29$	−5.67267	+	5.67267i	−1.05339	+	1.05339i	−0.0548963	+	0.998492i	$0.517483\pi$
$29$	−5.67267	+	5.67267i	−1.05339	+	1.05339i	−0.998492	+	0.0548963i	$0.982517\pi$
$30$		0			0
$31$	−3.95550			−0.710430			−0.355215	−	0.934785i	$-0.615592\pi$
$31$	−3.95550			−0.710430			−0.355215	+	0.934785i	$0.615592\pi$
$32$		0			0
$33$	11.2958			1.96635
$34$		0			0
$35$	1.93381	−	1.93381i	0.326873	−	0.326873i
$36$		0			0
$37$	2.48772	+	2.48772i	0.408979	+	0.408979i	0.881382	−	0.472403i	$-0.156613\pi$
$37$	2.48772	+	2.48772i	0.408979	+	0.408979i	−0.472403	+	0.881382i	$0.656613\pi$
$38$		0			0
$39$		−	3.77973i		−	0.605241i
$40$		0			0
$41$		−	8.40843i		−	1.31318i	−0.754250	−	0.656588i	$-0.771999\pi$
$41$		−	8.40843i		−	1.31318i	0.754250	−	0.656588i	$-0.228001\pi$
$42$		0			0
$43$	3.22713	+	3.22713i	0.492133	+	0.492133i	0.908978	−	0.416845i	$-0.136864\pi$
$43$	3.22713	+	3.22713i	0.492133	+	0.492133i	−0.416845	+	0.908978i	$0.636864\pi$
$44$		0			0
$45$	−0.534060	+	0.534060i	−0.0796129	+	0.0796129i
$46$		0			0
$47$	5.19809			0.758219			0.379109	−	0.925352i	$-0.376230\pi$
$47$	5.19809			0.758219			0.379109	+	0.925352i	$0.376230\pi$
$48$		0			0
$49$	−0.479225			−0.0684607
$50$		0			0
$51$	6.78176	−	6.78176i	0.949636	−	0.949636i
$52$		0			0
$53$	7.20537	+	7.20537i	0.989733	+	0.989733i	0.999948	−	0.0102143i	$-0.00325138\pi$
$53$	7.20537	+	7.20537i	0.989733	+	0.989733i	−0.0102143	+	0.999948i	$0.503251\pi$
$54$		0			0
$55$			5.82903i			0.785987i
$56$		0			0
$57$			0.802198i			0.106254i
$58$		0			0
$59$	6.41142	+	6.41142i	0.834695	+	0.834695i	0.988155	−	0.153459i	$-0.0490414\pi$
$59$	6.41142	+	6.41142i	0.834695	+	0.834695i	−0.153459	+	0.988155i	$0.549041\pi$
$60$		0			0
$61$	−3.82618	+	3.82618i	−0.489892	+	0.489892i	−0.908272	−	0.418380i	$-0.862598\pi$
$61$	−3.82618	+	3.82618i	−0.489892	+	0.489892i	0.418380	+	0.908272i	$0.362598\pi$
$62$		0			0
$63$	2.06554			0.260233
$64$		0			0
$65$	1.95047			0.241926
$66$		0			0
$67$	−5.76044	+	5.76044i	−0.703750	+	0.703750i	−0.965213	−	0.261463i	$-0.915795\pi$
$67$	−5.76044	+	5.76044i	−0.703750	+	0.703750i	0.261463	+	0.965213i	$0.415795\pi$
$68$		0			0
$69$	−2.25846	−	2.25846i	−0.271886	−	0.271886i
$70$		0			0
$71$			7.92245i			0.940222i	0.882607	+	0.470111i	$0.155786\pi$
$71$			7.92245i			0.940222i	−0.882607	+	0.470111i	$0.844214\pi$
$72$		0			0
$73$			4.36276i			0.510622i	0.966859	+	0.255311i	$0.0821779\pi$
$73$			4.36276i			0.510622i	−0.966859	+	0.255311i	$0.917822\pi$
$74$		0			0
$75$	−1.37027	−	1.37027i	−0.158225	−	0.158225i
$76$		0			0
$77$	11.2722	−	11.2722i	1.28459	−	1.28459i
$78$		0			0
$79$	5.56087			0.625647			0.312824	−	0.949811i	$-0.398725\pi$
$79$	5.56087			0.625647			0.312824	+	0.949811i	$0.398725\pi$
$80$		0			0
$81$	10.6954			1.18838
$82$		0			0
$83$	0.516191	−	0.516191i	0.0566594	−	0.0566594i	−0.678209	−	0.734869i	$-0.737244\pi$
$83$	0.516191	−	0.516191i	0.0566594	−	0.0566594i	0.734869	+	0.678209i	$0.237244\pi$
$84$		0			0
$85$	3.49962	+	3.49962i	0.379587	+	0.379587i
$86$		0			0
$87$		−	15.5462i		−	1.66672i
$88$		0			0
$89$		−	6.42236i		−	0.680768i	−0.940286	−	0.340384i	$-0.889443\pi$
$89$		−	6.42236i		−	0.680768i	0.940286	−	0.340384i	$-0.110557\pi$
$90$		0			0
$91$	−3.77184	−	3.77184i	−0.395396	−	0.395396i
$92$		0			0
$93$	5.42011	−	5.42011i	0.562039	−	0.562039i
$94$		0			0
$95$	−0.413962			−0.0424716
$96$		0			0
$97$	−9.44534			−0.959029			−0.479515	−	0.877534i	$-0.659187\pi$
$97$	−9.44534			−0.959029			−0.479515	+	0.877534i	$0.659187\pi$
$98$		0			0
$99$	−3.11305	+	3.11305i	−0.312873	+	0.312873i
$100$		0			0
$101$	−11.0542	−	11.0542i	−1.09993	−	1.09993i	−0.994418	−	0.105515i	$-0.966351\pi$
$101$	−11.0542	−	11.0542i	−1.09993	−	1.09993i	−0.105515	−	0.994418i	$-0.533649\pi$
$102$		0			0
$103$			5.46824i			0.538801i	0.963028	+	0.269401i	$0.0868256\pi$
$103$			5.46824i			0.538801i	−0.963028	+	0.269401i	$0.913174\pi$
$104$		0			0
$105$			5.29967i			0.517195i
$106$		0			0
$107$	−0.293704	−	0.293704i	−0.0283934	−	0.0283934i	0.692768	−	0.721161i	$-0.256391\pi$
$107$	−0.293704	−	0.293704i	−0.0283934	−	0.0283934i	−0.721161	+	0.692768i	$0.756391\pi$
$108$		0			0
$109$	10.4135	−	10.4135i	0.997429	−	0.997429i	−0.00256817	−	0.999997i	$-0.500817\pi$
$109$	10.4135	−	10.4135i	0.997429	−	0.997429i	0.999997	+	0.00256817i	$0.000817475\pi$
$110$		0			0
$111$	−6.81770			−0.647107
$112$		0			0
$113$	−17.4145			−1.63822			−0.819108	−	0.573639i	$-0.805531\pi$
$113$	−17.4145			−1.63822			−0.819108	+	0.573639i	$0.805531\pi$
$114$		0			0
$115$	1.16544	−	1.16544i	0.108678	−	0.108678i
$116$		0			0
$117$	1.04167	+	1.04167i	0.0963022	+	0.0963022i
$118$		0			0
$119$		−	13.5352i		−	1.24077i
$120$		0			0
$121$			22.9776i			2.08888i
$122$		0			0
$123$	11.5218	+	11.5218i	1.03889	+	1.03889i
$124$		0			0
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$		0			0
$127$	−10.9793			−0.974254			−0.487127	−	0.873331i	$-0.661955\pi$
$127$	−10.9793			−0.974254			−0.487127	+	0.873331i	$0.661955\pi$
$128$		0			0
$129$	−8.84407			−0.778677
$130$		0			0
$131$	−5.77044	+	5.77044i	−0.504166	+	0.504166i	−0.912730	−	0.408564i	$-0.866030\pi$
$131$	−5.77044	+	5.77044i	−0.504166	+	0.504166i	0.408564	+	0.912730i	$0.366030\pi$
$132$		0			0
$133$	0.800523	+	0.800523i	0.0694142	+	0.0694142i
$134$		0			0
$135$			4.34995i			0.374384i
$136$		0			0
$137$		−	7.18832i		−	0.614139i	−0.951687	−	0.307070i	$-0.900652\pi$
$137$		−	7.18832i		−	0.614139i	0.951687	−	0.307070i	$-0.0993484\pi$
$138$		0			0
$139$	−4.91327	−	4.91327i	−0.416738	−	0.416738i	0.467340	−	0.884078i	$-0.345212\pi$
$139$	−4.91327	−	4.91327i	−0.416738	−	0.416738i	−0.884078	+	0.467340i	$0.845212\pi$
$140$		0			0
$141$	−7.12278	+	7.12278i	−0.599846	+	0.599846i
$142$		0			0
$143$	11.3694			0.950754
$144$		0			0
$145$	8.02237			0.666221
$146$		0			0
$147$	0.656667	−	0.656667i	0.0541609	−	0.0541609i
$148$		0			0
$149$	9.76620	+	9.76620i	0.800078	+	0.800078i	0.983107	−	0.183029i	$-0.0585903\pi$
$149$	9.76620	+	9.76620i	0.800078	+	0.800078i	−0.183029	+	0.983107i	$0.558590\pi$
$150$		0			0
$151$		−	1.90755i		−	0.155234i	−0.996983	−	0.0776169i	$-0.975269\pi$
$151$		−	1.90755i		−	0.155234i	0.996983	−	0.0776169i	$-0.0247311\pi$
$152$		0			0
$153$			3.73801i			0.302201i
$154$		0			0
$155$	2.79696	+	2.79696i	0.224658	+	0.224658i
$156$		0			0
$157$	−4.41296	+	4.41296i	−0.352192	+	0.352192i	−0.860925	−	0.508732i	$-0.830114\pi$
$157$	−4.41296	+	4.41296i	−0.352192	+	0.352192i	0.508732	+	0.860925i	$0.330114\pi$
$158$		0			0
$159$	−19.7466			−1.56601
$160$		0			0
$161$	−4.50748			−0.355240
$162$		0			0
$163$	3.58912	−	3.58912i	0.281122	−	0.281122i	−0.552435	−	0.833556i	$-0.686301\pi$
$163$	3.58912	−	3.58912i	0.281122	−	0.281122i	0.833556	+	0.552435i	$0.186301\pi$
$164$		0			0
$165$	−7.98734	−	7.98734i	−0.621814	−	0.621814i
$166$		0			0
$167$		−	17.5993i		−	1.36188i	−0.732341	−	0.680938i	$-0.761572\pi$
$167$		−	17.5993i		−	1.36188i	0.732341	−	0.680938i	$-0.238428\pi$
$168$		0			0
$169$			9.19566i			0.707359i
$170$		0			0
$171$	−0.221080	−	0.221080i	−0.0169064	−	0.0169064i
$172$		0			0
$173$	−7.32377	+	7.32377i	−0.556816	+	0.556816i	−0.928400	−	0.371584i	$-0.878815\pi$
$173$	−7.32377	+	7.32377i	−0.556816	+	0.556816i	0.371584	+	0.928400i	$0.378815\pi$
$174$		0			0
$175$	−2.73482			−0.206733
$176$		0			0
$177$	−17.5707			−1.32070
$178$		0			0
$179$	−6.42849	+	6.42849i	−0.480488	+	0.480488i	−0.905287	−	0.424800i	$-0.860345\pi$
$179$	−6.42849	+	6.42849i	−0.480488	+	0.480488i	0.424800	+	0.905287i	$0.360345\pi$
$180$		0			0
$181$	−3.67884	−	3.67884i	−0.273446	−	0.273446i	0.557040	−	0.830486i	$-0.311937\pi$
$181$	−3.67884	−	3.67884i	−0.273446	−	0.273446i	−0.830486	+	0.557040i	$0.811937\pi$
$182$		0			0
$183$		−	10.4858i		−	0.775131i
$184$		0			0
$185$		−	3.51817i		−	0.258661i
$186$		0			0
$187$	20.3994	+	20.3994i	1.49175	+	1.49175i
$188$		0			0
$189$	8.41196	−	8.41196i	0.611880	−	0.611880i
$190$		0			0
$191$	5.39093			0.390074			0.195037	−	0.980796i	$-0.437517\pi$
$191$	5.39093			0.390074			0.195037	+	0.980796i	$0.437517\pi$
$192$		0			0
$193$	−3.53818			−0.254684			−0.127342	−	0.991859i	$-0.540645\pi$
$193$	−3.53818			−0.254684			−0.127342	+	0.991859i	$0.540645\pi$
$194$		0			0
$195$	−2.67267	+	2.67267i	−0.191394	+	0.191394i
$196$		0			0
$197$	10.6900	+	10.6900i	0.761627	+	0.761627i	0.976616	−	0.214989i	$-0.0689716\pi$
$197$	10.6900	+	10.6900i	0.761627	+	0.761627i	−0.214989	+	0.976616i	$0.568972\pi$
$198$		0			0
$199$			15.6543i			1.10971i	0.831948	+	0.554853i	$0.187226\pi$
$199$			15.6543i			1.10971i	−0.831948	+	0.554853i	$0.812774\pi$
$200$		0			0
$201$		−	15.7867i		−	1.11351i
$202$		0			0
$203$	−15.5137	−	15.5137i	−1.08885	−	1.08885i
$204$		0			0
$205$	−5.94566	+	5.94566i	−0.415263	+	0.415263i
$206$		0			0
$207$	1.24483			0.0865218
$208$		0			0
$209$	−2.41300			−0.166911
$210$		0			0
$211$	19.9359	−	19.9359i	1.37244	−	1.37244i	0.515634	−	0.856809i	$-0.327556\pi$
$211$	19.9359	−	19.9359i	1.37244	−	1.37244i	0.856809	−	0.515634i	$-0.172444\pi$
$212$		0			0
$213$	−10.8559	−	10.8559i	−0.743833	−	0.743833i
$214$		0			0
$215$		−	4.56385i		−	0.311252i
$216$		0			0
$217$		−	10.8176i		−	0.734345i
$218$		0			0
$219$	−5.97815	−	5.97815i	−0.403966	−	0.403966i
$220$		0			0
$221$	6.82591	−	6.82591i	0.459161	−	0.459161i
$222$		0			0
$223$	−21.2173			−1.42081			−0.710406	−	0.703792i	$-0.751489\pi$
$223$	−21.2173			−1.42081			−0.710406	+	0.703792i	$0.751489\pi$
$224$		0			0
$225$	0.755274			0.0503516
$226$		0			0
$227$	−12.0356	+	12.0356i	−0.798832	+	0.798832i	−0.982911	−	0.184079i	$-0.941070\pi$
$227$	−12.0356	+	12.0356i	−0.798832	+	0.798832i	0.184079	+	0.982911i	$0.441070\pi$
$228$		0			0
$229$	6.70809	+	6.70809i	0.443283	+	0.443283i	0.893114	−	0.449831i	$-0.148516\pi$
$229$	6.70809	+	6.70809i	0.443283	+	0.443283i	−0.449831	+	0.893114i	$0.648516\pi$
$230$		0			0
$231$			30.8920i			2.03254i
$232$		0			0
$233$		−	5.40431i		−	0.354048i	−0.984207	−	0.177024i	$-0.943353\pi$
$233$		−	5.40431i		−	0.354048i	0.984207	−	0.177024i	$-0.0566470\pi$
$234$		0			0
$235$	−3.67560	−	3.67560i	−0.239770	−	0.239770i
$236$		0			0
$237$	−7.61989	+	7.61989i	−0.494965	+	0.494965i
$238$		0			0
$239$	1.86569			0.120681			0.0603406	−	0.998178i	$-0.480781\pi$
$239$	1.86569			0.120681			0.0603406	+	0.998178i	$0.480781\pi$
$240$		0			0
$241$	16.3740			1.05474			0.527369	−	0.849636i	$-0.323178\pi$
$241$	16.3740			1.05474			0.527369	+	0.849636i	$0.323178\pi$
$242$		0			0
$243$	−5.42792	+	5.42792i	−0.348201	+	0.348201i
$244$		0			0
$245$	0.338863	+	0.338863i	0.0216492	+	0.0216492i
$246$		0			0
$247$			0.807421i			0.0513750i
$248$		0			0
$249$			1.41464i			0.0896493i
$250$		0			0
$251$	−3.01154	−	3.01154i	−0.190087	−	0.190087i	0.605647	−	0.795734i	$-0.292914\pi$
$251$	−3.01154	−	3.01154i	−0.190087	−	0.190087i	−0.795734	+	0.605647i	$0.792914\pi$
$252$		0			0
$253$	6.79340	−	6.79340i	0.427098	−	0.427098i
$254$		0			0
$255$	−9.59085			−0.600602
$256$		0			0
$257$	22.7407			1.41853			0.709263	−	0.704944i	$-0.249028\pi$
$257$	22.7407			1.41853			0.709263	+	0.704944i	$0.249028\pi$
$258$		0			0
$259$	−6.80346	+	6.80346i	−0.422747	+	0.422747i
$260$		0			0
$261$	4.28442	+	4.28442i	0.265199	+	0.265199i
$262$		0			0
$263$		−	12.0300i		−	0.741805i	−0.928672	−	0.370902i	$-0.879048\pi$
$263$		−	12.0300i		−	0.741805i	0.928672	−	0.370902i	$-0.120952\pi$
$264$		0			0
$265$		−	10.1899i		−	0.625962i
$266$		0			0
$267$	8.80035	+	8.80035i	0.538573	+	0.538573i
$268$		0			0
$269$	4.90068	−	4.90068i	0.298800	−	0.298800i	−0.541744	−	0.840544i	$-0.682236\pi$
$269$	4.90068	−	4.90068i	0.298800	−	0.298800i	0.840544	+	0.541744i	$0.182236\pi$
$270$		0			0
$271$	4.14616			0.251862			0.125931	−	0.992039i	$-0.459808\pi$
$271$	4.14616			0.251862			0.125931	+	0.992039i	$0.459808\pi$
$272$		0			0
$273$	10.3369			0.625615
$274$		0			0
$275$	4.12175	−	4.12175i	0.248551	−	0.248551i
$276$		0			0
$277$	−10.4815	−	10.4815i	−0.629775	−	0.629775i	0.318236	−	0.948011i	$-0.396909\pi$
$277$	−10.4815	−	10.4815i	−0.629775	−	0.629775i	−0.948011	+	0.318236i	$0.896909\pi$
$278$		0			0
$279$			2.98749i			0.178856i
$280$		0			0
$281$		−	3.51927i		−	0.209942i	−0.994475	−	0.104971i	$-0.966525\pi$
$281$		−	3.51927i		−	0.209942i	0.994475	−	0.104971i	$-0.0334750\pi$
$282$		0			0
$283$	2.88462	+	2.88462i	0.171473	+	0.171473i	0.787626	−	0.616153i	$-0.211310\pi$
$283$	2.88462	+	2.88462i	0.171473	+	0.171473i	−0.616153	+	0.787626i	$0.711310\pi$
$284$		0			0
$285$	0.567240	−	0.567240i	0.0336004	−	0.0336004i
$286$		0			0
$287$	22.9955			1.35738
$288$		0			0
$289$	7.49472			0.440866
$290$		0			0
$291$	12.9427	−	12.9427i	0.758712	−	0.758712i
$292$		0			0
$293$	3.92351	+	3.92351i	0.229214	+	0.229214i	0.812364	−	0.583150i	$-0.198180\pi$
$293$	3.92351	+	3.92351i	0.229214	+	0.229214i	−0.583150	+	0.812364i	$0.698180\pi$
$294$		0			0
$295$		−	9.06711i		−	0.527908i
$296$		0			0
$297$			25.3560i			1.47130i
$298$		0			0
$299$	−2.27316	−	2.27316i	−0.131460	−	0.131460i
$300$		0			0
$301$	−8.82561	+	8.82561i	−0.508700	+	0.508700i
$302$		0			0
$303$	30.2944			1.74037
$304$		0			0
$305$	5.41103			0.309835
$306$		0			0
$307$	0.196482	−	0.196482i	0.0112138	−	0.0112138i	−0.701478	−	0.712691i	$-0.747476\pi$
$307$	0.196482	−	0.196482i	0.0112138	−	0.0112138i	0.712691	+	0.701478i	$0.247476\pi$
$308$		0			0
$309$	−7.49296	−	7.49296i	−0.426259	−	0.426259i
$310$		0			0
$311$		−	2.52927i		−	0.143422i	−0.997425	−	0.0717110i	$-0.977154\pi$
$311$		−	2.52927i		−	0.143422i	0.997425	−	0.0717110i	$-0.0228459\pi$
$312$		0			0
$313$		−	3.84874i		−	0.217543i	−0.994067	−	0.108772i	$-0.965308\pi$
$313$		−	3.84874i		−	0.217543i	0.994067	−	0.108772i	$-0.0346917\pi$
$314$		0			0
$315$	−1.46056	−	1.46056i	−0.0822930	−	0.0822930i
$316$		0			0
$317$	−6.78901	+	6.78901i	−0.381309	+	0.381309i	−0.871574	−	0.490265i	$-0.836900\pi$
$317$	−6.78901	+	6.78901i	−0.381309	+	0.381309i	0.490265	+	0.871574i	$0.336900\pi$
$318$		0			0
$319$	46.7627			2.61821
$320$		0			0
$321$	0.804906			0.0449255
$322$		0			0
$323$	−1.44871	+	1.44871i	−0.0806085	+	0.0806085i
$324$		0			0
$325$	−1.37919	−	1.37919i	−0.0765038	−	0.0765038i
$326$		0			0
$327$			28.5385i			1.57818i
$328$		0			0
$329$			14.2158i			0.783743i
$330$		0			0
$331$	−1.79195	−	1.79195i	−0.0984944	−	0.0984944i	0.656143	−	0.754637i	$-0.272187\pi$
$331$	−1.79195	−	1.79195i	−0.0984944	−	0.0984944i	−0.754637	+	0.656143i	$0.772187\pi$
$332$		0			0
$333$	1.87891	−	1.87891i	0.102964	−	0.102964i
$334$		0			0
$335$	8.14650			0.445091
$336$		0			0
$337$	16.1071			0.877411			0.438706	−	0.898631i	$-0.355437\pi$
$337$	16.1071			0.877411			0.438706	+	0.898631i	$0.355437\pi$
$338$		0			0
$339$	23.8625	−	23.8625i	1.29603	−	1.29603i
$340$		0			0
$341$	16.3036	+	16.3036i	0.882889	+	0.882889i
$342$		0			0
$343$			17.8331i			0.962898i
$344$		0			0
$345$			3.19394i			0.171956i
$346$		0			0
$347$	−12.6577	−	12.6577i	−0.679502	−	0.679502i	0.280385	−	0.959888i	$-0.409538\pi$
$347$	−12.6577	−	12.6577i	−0.679502	−	0.679502i	−0.959888	+	0.280385i	$0.909538\pi$
$348$		0			0
$349$	−16.3020	+	16.3020i	−0.872627	+	0.872627i	−0.992758	−	0.120131i	$-0.961669\pi$
$349$	−16.3020	+	16.3020i	−0.872627	+	0.872627i	0.120131	+	0.992758i	$0.461669\pi$
$350$		0			0
$351$	8.48445			0.452866
$352$		0			0
$353$	−13.2637			−0.705954			−0.352977	−	0.935632i	$-0.614831\pi$
$353$	−13.2637			−0.705954			−0.352977	+	0.935632i	$0.614831\pi$
$354$		0			0
$355$	5.60202	−	5.60202i	0.297324	−	0.297324i
$356$		0			0
$357$	18.5469	+	18.5469i	0.981604	+	0.981604i
$358$		0			0
$359$			13.3561i			0.704906i	0.935830	+	0.352453i	$0.114652\pi$
$359$			13.3561i			0.704906i	−0.935830	+	0.352453i	$0.885348\pi$
$360$		0			0
$361$			18.8286i			0.990981i
$362$		0			0
$363$	−31.4855	−	31.4855i	−1.65256	−	1.65256i
$364$		0			0
$365$	3.08494	−	3.08494i	0.161473	−	0.161473i
$366$		0			0
$367$	−11.8938			−0.620852			−0.310426	−	0.950598i	$-0.600472\pi$
$367$	−11.8938			−0.620852			−0.310426	+	0.950598i	$0.600472\pi$
$368$		0			0
$369$	−6.35067			−0.330603
$370$		0			0
$371$	−19.7054	+	19.7054i	−1.02305	+	1.02305i
$372$		0			0
$373$	−19.0494	−	19.0494i	−0.986342	−	0.986342i	0.0135655	−	0.999908i	$-0.495682\pi$
$373$	−19.0494	−	19.0494i	−0.986342	−	0.986342i	−0.999908	+	0.0135655i	$0.995682\pi$
$374$		0			0
$375$			1.93785i			0.100070i
$376$		0			0
$377$		−	15.6474i		−	0.805882i
$378$		0			0
$379$	4.64554	+	4.64554i	0.238625	+	0.238625i	0.816281	−	0.577655i	$-0.196032\pi$
$379$	4.64554	+	4.64554i	0.238625	+	0.238625i	−0.577655	+	0.816281i	$0.696032\pi$
$380$		0			0
$381$	15.0446	−	15.0446i	0.770757	−	0.770757i
$382$		0			0
$383$	−38.5131			−1.96793			−0.983964	−	0.178366i	$-0.942919\pi$
$383$	−38.5131			−1.96793			−0.983964	+	0.178366i	$0.942919\pi$
$384$		0			0
$385$	−15.9413			−0.812446
$386$		0			0
$387$	2.43737	−	2.43737i	0.123898	−	0.123898i
$388$		0			0
$389$	−0.903192	−	0.903192i	−0.0457937	−	0.0457937i	0.683839	−	0.729633i	$-0.260309\pi$
$389$	−0.903192	−	0.903192i	−0.0457937	−	0.0457937i	−0.729633	+	0.683839i	$0.760309\pi$
$390$		0			0
$391$		−	8.15722i		−	0.412528i
$392$		0			0
$393$		−	15.8141i		−	0.797716i
$394$		0			0
$395$	−3.93213	−	3.93213i	−0.197847	−	0.197847i
$396$		0			0
$397$	4.44748	−	4.44748i	0.223212	−	0.223212i	−0.586637	−	0.809850i	$-0.699549\pi$
$397$	4.44748	−	4.44748i	0.223212	−	0.223212i	0.809850	+	0.586637i	$0.199549\pi$
$398$		0			0
$399$	−2.19386			−0.109831
$400$		0			0
$401$	27.3379			1.36519			0.682596	−	0.730796i	$-0.260851\pi$
$401$	27.3379			1.36519			0.682596	+	0.730796i	$0.260851\pi$
$402$		0			0
$403$	5.45540	−	5.45540i	0.271753	−	0.271753i
$404$		0			0
$405$	−7.56278	−	7.56278i	−0.375797	−	0.375797i
$406$		0			0
$407$		−	20.5075i		−	1.01652i
$408$		0			0
$409$		−	38.6889i		−	1.91304i	−0.291661	−	0.956522i	$-0.594208\pi$
$409$		−	38.6889i		−	1.91304i	0.291661	−	0.956522i	$-0.405792\pi$
$410$		0			0
$411$	9.84993	+	9.84993i	0.485861	+	0.485861i
$412$		0			0
$413$	−17.5341	+	17.5341i	−0.862794	+	0.862794i
$414$		0			0
$415$	−0.730005			−0.0358345
$416$		0			0
$417$	13.4650			0.659384
$418$		0			0
$419$	−7.41439	+	7.41439i	−0.362217	+	0.362217i	−0.864628	−	0.502412i	$-0.832446\pi$
$419$	−7.41439	+	7.41439i	−0.362217	+	0.362217i	0.502412	+	0.864628i	$0.332446\pi$
$420$		0			0
$421$	−10.3279	−	10.3279i	−0.503351	−	0.503351i	0.409127	−	0.912478i	$-0.365833\pi$
$421$	−10.3279	−	10.3279i	−0.503351	−	0.503351i	−0.912478	+	0.409127i	$0.865833\pi$
$422$		0			0
$423$		−	3.92598i		−	0.190888i
$424$		0			0
$425$		−	4.94921i		−	0.240072i
$426$		0			0
$427$	−10.4639	−	10.4639i	−0.506383	−	0.506383i
$428$		0			0
$429$	−15.5791	+	15.5791i	−0.752165	+	0.752165i
$430$		0			0
$431$	14.8644			0.715991			0.357995	−	0.933723i	$-0.383460\pi$
$431$	14.8644			0.715991			0.357995	+	0.933723i	$0.383460\pi$
$432$		0			0
$433$	−4.96284			−0.238499			−0.119249	−	0.992864i	$-0.538049\pi$
$433$	−4.96284			−0.238499			−0.119249	+	0.992864i	$0.538049\pi$
$434$		0			0
$435$	−10.9928	+	10.9928i	−0.527064	+	0.527064i
$436$		0			0
$437$	0.482449	+	0.482449i	0.0230787	+	0.0230787i
$438$		0			0
$439$		−	13.7348i		−	0.655527i	−0.944760	−	0.327763i	$-0.893705\pi$
$439$		−	13.7348i		−	0.655527i	0.944760	−	0.327763i	$-0.106295\pi$
$440$		0			0
$441$			0.361946i			0.0172355i
$442$		0			0
$443$	7.62584	+	7.62584i	0.362315	+	0.362315i	0.864664	−	0.502350i	$-0.167531\pi$
$443$	7.62584	+	7.62584i	0.362315	+	0.362315i	−0.502350	+	0.864664i	$0.667531\pi$
$444$		0			0
$445$	−4.54129	+	4.54129i	−0.215278	+	0.215278i
$446$		0			0
$447$	−26.7646			−1.26592
$448$		0			0
$449$	−15.8544			−0.748215			−0.374108	−	0.927385i	$-0.622051\pi$
$449$	−15.8544			−0.748215			−0.374108	+	0.927385i	$0.622051\pi$
$450$		0			0
$451$	−34.6574	+	34.6574i	−1.63195	+	1.63195i
$452$		0			0
$453$	2.61385	+	2.61385i	0.122809	+	0.122809i
$454$		0			0
$455$			5.33418i			0.250070i
$456$		0			0
$457$			14.1978i			0.664144i	0.943254	+	0.332072i	$0.107748\pi$
$457$			14.1978i			0.664144i	−0.943254	+	0.332072i	$0.892252\pi$
$458$		0			0
$459$	15.2232	+	15.2232i	0.710557	+	0.710557i
$460$		0			0
$461$	−22.8952	+	22.8952i	−1.06634	+	1.06634i	−0.0686980	+	0.997638i	$0.521884\pi$
$461$	−22.8952	+	22.8952i	−1.06634	+	1.06634i	−0.997638	+	0.0686980i	$0.978116\pi$
$462$		0			0
$463$	−25.0175			−1.16266			−0.581330	−	0.813668i	$-0.697467\pi$
$463$	−25.0175			−1.16266			−0.581330	+	0.813668i	$0.697467\pi$
$464$		0			0
$465$	−7.66519			−0.355465
$466$		0			0
$467$	23.5446	−	23.5446i	1.08951	−	1.08951i	0.0939334	−	0.995578i	$-0.470056\pi$
$467$	23.5446	−	23.5446i	1.08951	−	1.08951i	0.995578	−	0.0939334i	$-0.0299441\pi$
$468$		0			0
$469$	−15.7538	−	15.7538i	−0.727441	−	0.727441i
$470$		0			0
$471$		−	12.0939i		−	0.557256i
$472$		0			0
$473$		−	26.6028i		−	1.22320i
$474$		0			0
$475$	0.292715	+	0.292715i	0.0134307	+	0.0134307i
$476$		0			0
$477$	5.44203	−	5.44203i	0.249173	−	0.249173i
$478$		0			0
$479$	−39.3416			−1.79756			−0.898781	−	0.438398i	$-0.855546\pi$
$479$	−39.3416			−1.79756			−0.898781	+	0.438398i	$0.855546\pi$
$480$		0			0
$481$	−6.86209			−0.312884
$482$		0			0
$483$	6.17647	−	6.17647i	0.281039	−	0.281039i
$484$		0			0
$485$	6.67886	+	6.67886i	0.303272	+	0.303272i
$486$		0			0
$487$			25.6970i			1.16444i	0.813030	+	0.582222i	$0.197816\pi$
$487$			25.6970i			1.16444i	−0.813030	+	0.582222i	$0.802184\pi$
$488$		0			0
$489$			9.83612i			0.444805i
$490$		0			0
$491$	29.0344	+	29.0344i	1.31030	+	1.31030i	0.921190	+	0.389113i	$0.127219\pi$
$491$	29.0344	+	29.0344i	1.31030	+	1.31030i	0.389113	+	0.921190i	$0.372781\pi$
$492$		0			0
$493$	28.0753	−	28.0753i	1.26445	−	1.26445i
$494$		0			0
$495$	4.40252			0.197879
$496$		0			0
$497$	−21.6665			−0.971873
$498$		0			0
$499$	7.89904	−	7.89904i	0.353610	−	0.353610i	−0.507841	−	0.861451i	$-0.669556\pi$
$499$	7.89904	−	7.89904i	0.353610	−	0.353610i	0.861451	+	0.507841i	$0.169556\pi$
$500$		0			0
$501$	24.1158	+	24.1158i	1.07741	+	1.07741i
$502$		0			0
$503$			9.53668i			0.425220i	0.977137	+	0.212610i	$0.0681963\pi$
$503$			9.53668i			0.425220i	−0.977137	+	0.212610i	$0.931804\pi$
$504$		0			0
$505$			15.6330i			0.695658i
$506$		0			0
$507$	−12.6005	−	12.6005i	−0.559609	−	0.559609i
$508$		0			0
$509$	−4.24956	+	4.24956i	−0.188358	+	0.188358i	−0.794986	−	0.606628i	$-0.792522\pi$
$509$	−4.24956	+	4.24956i	−0.188358	+	0.188358i	0.606628	+	0.794986i	$0.292522\pi$
$510$		0			0
$511$	−11.9313			−0.527812
$512$		0			0
$513$	−1.80071			−0.0795035
$514$		0			0
$515$	3.86663	−	3.86663i	0.170384	−	0.170384i
$516$		0			0
$517$	−21.4252	−	21.4252i	−0.942280	−	0.942280i
$518$		0			0
$519$		−	20.0711i		−	0.881022i
$520$		0			0
$521$			9.71766i			0.425739i	0.977081	+	0.212869i	$0.0682809\pi$
$521$			9.71766i			0.425739i	−0.977081	+	0.212869i	$0.931719\pi$
$522$		0			0
$523$	4.62580	+	4.62580i	0.202272	+	0.202272i	0.800973	−	0.598701i	$-0.204316\pi$
$523$	4.62580	+	4.62580i	0.202272	+	0.202272i	−0.598701	+	0.800973i	$0.704316\pi$
$524$		0			0
$525$	3.74744	−	3.74744i	0.163551	−	0.163551i
$526$		0			0
$527$	19.5766			0.852772
$528$		0			0
$529$	20.2835			0.881891
$530$		0			0
$531$	4.84238	−	4.84238i	0.210141	−	0.210141i
$532$		0			0
$533$	11.5968	+	11.5968i	0.502314	+	0.502314i
$534$		0			0
$535$			0.415360i			0.0179576i
$536$		0			0
$537$		−	17.6175i		−	0.760252i
$538$		0			0
$539$	1.97524	+	1.97524i	0.0850798	+	0.0850798i
$540$		0			0
$541$	24.0206	−	24.0206i	1.03272	−	1.03272i	0.0332788	−	0.999446i	$-0.489405\pi$
$541$	24.0206	−	24.0206i	1.03272	−	1.03272i	0.999446	−	0.0332788i	$-0.0105949\pi$
$542$		0			0
$543$	10.0820			0.432660
$544$		0			0
$545$	−14.7269			−0.630829
$546$		0			0
$547$	−4.63900	+	4.63900i	−0.198349	+	0.198349i	−0.799292	−	0.600943i	$-0.794792\pi$
$547$	−4.63900	+	4.63900i	−0.198349	+	0.198349i	0.600943	+	0.799292i	$0.294792\pi$
$548$		0			0
$549$	2.88981	+	2.88981i	0.123334	+	0.123334i
$550$		0			0
$551$			3.32096i			0.141477i
$552$		0			0
$553$			15.2080i			0.646709i
$554$		0			0
$555$	4.82084	+	4.82084i	0.204633	+	0.204633i
$556$		0			0
$557$	13.6258	−	13.6258i	0.577345	−	0.577345i	−0.356826	−	0.934171i	$-0.616141\pi$
$557$	13.6258	−	13.6258i	0.577345	−	0.577345i	0.934171	+	0.356826i	$0.116141\pi$
$558$		0			0
$559$	−8.90166			−0.376500
$560$		0			0
$561$	−55.9054			−2.36033
$562$		0			0
$563$	−28.0885	+	28.0885i	−1.18379	+	1.18379i	−0.205035	+	0.978755i	$0.565731\pi$
$563$	−28.0885	+	28.0885i	−1.18379	+	1.18379i	−0.978755	+	0.205035i	$0.934269\pi$
$564$		0			0
$565$	12.3139	+	12.3139i	0.518050	+	0.518050i
$566$		0			0
$567$			29.2499i			1.22838i
$568$		0			0
$569$			42.3770i			1.77654i	0.459326	+	0.888268i	$0.348091\pi$
$569$			42.3770i			1.77654i	−0.459326	+	0.888268i	$0.651909\pi$
$570$		0			0
$571$	−7.99217	−	7.99217i	−0.334462	−	0.334462i	0.519816	−	0.854278i	$-0.326000\pi$
$571$	−7.99217	−	7.99217i	−0.334462	−	0.334462i	−0.854278	+	0.519816i	$0.826000\pi$
$572$		0			0
$573$	−7.38702	+	7.38702i	−0.308597	+	0.308597i
$574$		0			0
$575$	−1.64818			−0.0687341
$576$		0			0
$577$	−20.4651			−0.851972			−0.425986	−	0.904730i	$-0.640073\pi$
$577$	−20.4651			−0.851972			−0.425986	+	0.904730i	$0.640073\pi$
$578$		0			0
$579$	4.84826	−	4.84826i	0.201487	−	0.201487i
$580$		0			0
$581$	1.41169	+	1.41169i	0.0585667	+	0.0585667i
$582$		0			0
$583$		−	59.3974i		−	2.45999i
$584$		0			0
$585$		−	1.47314i		−	0.0609069i
$586$		0			0
$587$	−0.429976	−	0.429976i	−0.0177470	−	0.0177470i	0.698178	−	0.715925i	$-0.253995\pi$
$587$	−0.429976	−	0.429976i	−0.0177470	−	0.0177470i	−0.715925	+	0.698178i	$0.753995\pi$
$588$		0			0
$589$	−1.15784	+	1.15784i	−0.0477079	+	0.0477079i
$590$		0			0
$591$	−29.2962			−1.20509
$592$		0			0
$593$	37.9620			1.55891			0.779455	−	0.626458i	$-0.215496\pi$
$593$	37.9620			1.55891			0.779455	+	0.626458i	$0.215496\pi$
$594$		0			0
$595$	−9.57083	+	9.57083i	−0.392366	+	0.392366i
$596$		0			0
$597$	−21.4507	−	21.4507i	−0.877917	−	0.877917i
$598$		0			0
$599$			13.7108i			0.560207i	0.959970	+	0.280104i	$0.0903688\pi$
$599$			13.7108i			0.560207i	−0.959970	+	0.280104i	$0.909631\pi$
$600$		0			0
$601$		−	2.84070i		−	0.115875i	−0.998320	−	0.0579373i	$-0.981548\pi$
$601$		−	2.84070i		−	0.115875i	0.998320	−	0.0579373i	$-0.0184523\pi$
$602$		0			0
$603$	4.35072	+	4.35072i	0.177175	+	0.177175i
$604$		0			0
$605$	16.2476	−	16.2476i	0.660561	−	0.660561i
$606$		0			0
$607$	42.8562			1.73948			0.869740	−	0.493510i	$-0.164287\pi$
$607$	42.8562			1.73948			0.869740	+	0.493510i	$0.164287\pi$
$608$		0			0
$609$	42.5159			1.72283
$610$		0			0
$611$	−7.16916	+	7.16916i	−0.290033	+	0.290033i
$612$		0			0
$613$	5.48393	+	5.48393i	0.221494	+	0.221494i	0.809127	−	0.587633i	$-0.199940\pi$
$613$	5.48393	+	5.48393i	0.221494	+	0.221494i	−0.587633	+	0.809127i	$0.699940\pi$
$614$		0			0
$615$		−	16.2943i		−	0.657049i
$616$		0			0
$617$			22.2539i			0.895908i	0.894057	+	0.447954i	$0.147847\pi$
$617$			22.2539i			0.895908i	−0.894057	+	0.447954i	$0.852153\pi$
$618$		0			0
$619$	−10.0974	−	10.0974i	−0.405849	−	0.405849i	0.474439	−	0.880288i	$-0.342651\pi$
$619$	−10.0974	−	10.0974i	−0.405849	−	0.405849i	−0.880288	+	0.474439i	$0.842651\pi$
$620$		0			0
$621$	5.06962	−	5.06962i	0.203437	−	0.203437i
$622$		0			0
$623$	17.5640			0.703685
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	3.30646	−	3.30646i	0.132047	−	0.132047i
$628$		0			0
$629$	−12.3123	−	12.3123i	−0.490922	−	0.490922i
$630$		0			0
$631$		−	49.5996i		−	1.97453i	−0.159086	−	0.987265i	$-0.550855\pi$
$631$		−	49.5996i		−	1.97453i	0.159086	−	0.987265i	$-0.449145\pi$
$632$		0			0
$633$			54.6351i			2.17155i
$634$		0			0
$635$	7.76353	+	7.76353i	0.308086	+	0.308086i
$636$		0			0
$637$	0.660942	−	0.660942i	0.0261875	−	0.0261875i
$638$		0			0
$639$	5.98362			0.236709
$640$		0			0
$641$	−42.5379			−1.68015			−0.840074	−	0.542472i	$-0.817488\pi$
$641$	−42.5379			−1.68015			−0.840074	+	0.542472i	$0.817488\pi$
$642$		0			0
$643$	29.3128	−	29.3128i	1.15598	−	1.15598i	0.170653	−	0.985331i	$-0.445412\pi$
$643$	29.3128	−	29.3128i	1.15598	−	1.15598i	0.985331	−	0.170653i	$-0.0545878\pi$
$644$		0			0
$645$	6.25370	+	6.25370i	0.246239	+	0.246239i
$646$		0			0
$647$		−	4.35345i		−	0.171152i	−0.996332	−	0.0855759i	$-0.972727\pi$
$647$		−	4.35345i		−	0.171152i	0.996332	−	0.0855759i	$-0.0272730\pi$
$648$		0			0
$649$		−	52.8525i		−	2.07464i
$650$		0			0
$651$	14.8230	+	14.8230i	0.580959	+	0.580959i
$652$		0			0
$653$	−12.3460	+	12.3460i	−0.483137	+	0.483137i	−0.906132	−	0.422995i	$-0.860979\pi$
$653$	−12.3460	+	12.3460i	−0.483137	+	0.483137i	0.422995	+	0.906132i	$0.360979\pi$
$654$		0			0
$655$	8.16063			0.318862
$656$		0			0
$657$	3.29508			0.128553
$658$		0			0
$659$	−19.5367	+	19.5367i	−0.761040	+	0.761040i	−0.976510	−	0.215470i	$-0.930872\pi$
$659$	−19.5367	+	19.5367i	−0.761040	+	0.761040i	0.215470	+	0.976510i	$0.430872\pi$
$660$		0			0
$661$	26.4901	+	26.4901i	1.03035	+	1.03035i	0.999525	+	0.0308210i	$0.00981219\pi$
$661$	26.4901	+	26.4901i	1.03035	+	1.03035i	0.0308210	+	0.999525i	$0.490188\pi$
$662$		0			0
$663$			18.7067i			0.726507i
$664$		0			0
$665$		−	1.13211i		−	0.0439014i
$666$		0			0
$667$	−9.34961	−	9.34961i	−0.362018	−	0.362018i
$668$		0			0
$669$	29.0734	−	29.0734i	1.12404	−	1.12404i
$670$		0			0
$671$	31.5411			1.21763
$672$		0			0
$673$	−11.5260			−0.444295			−0.222148	−	0.975013i	$-0.571307\pi$
$673$	−11.5260			−0.444295			−0.222148	+	0.975013i	$0.571307\pi$
$674$		0			0
$675$	3.07588	−	3.07588i	0.118391	−	0.118391i
$676$		0			0
$677$	−15.8009	−	15.8009i	−0.607278	−	0.607278i	0.334956	−	0.942234i	$-0.391279\pi$
$677$	−15.8009	−	15.8009i	−0.607278	−	0.607278i	−0.942234	+	0.334956i	$0.891279\pi$
$678$		0			0
$679$		−	25.8313i		−	0.991314i
$680$		0			0
$681$		−	32.9841i		−	1.26395i
$682$		0			0
$683$	25.1439	+	25.1439i	0.962105	+	0.962105i	0.999308	−	0.0372032i	$-0.0118449\pi$
$683$	25.1439	+	25.1439i	0.962105	+	0.962105i	−0.0372032	+	0.999308i	$0.511845\pi$
$684$		0			0
$685$	−5.08291	+	5.08291i	−0.194208	+	0.194208i
$686$		0			0
$687$	−18.3838			−0.701385
$688$		0			0
$689$	−19.8752			−0.757183
$690$		0			0
$691$	27.2647	−	27.2647i	1.03720	−	1.03720i	0.0379162	−	0.999281i	$-0.487928\pi$
$691$	27.2647	−	27.2647i	1.03720	−	1.03720i	0.999281	−	0.0379162i	$-0.0120720\pi$
$692$		0			0
$693$	−8.51363	−	8.51363i	−0.323406	−	0.323406i
$694$		0			0
$695$			6.94841i			0.263568i
$696$		0			0
$697$			41.6151i			1.57628i
$698$		0			0
$699$	7.40536	+	7.40536i	0.280096	+	0.280096i
$700$		0			0
$701$	12.5566	−	12.5566i	0.474257	−	0.474257i	−0.429032	−	0.903289i	$-0.641145\pi$
$701$	12.5566	−	12.5566i	0.474257	−	0.474257i	0.903289	+	0.429032i	$0.141145\pi$
$702$		0			0
$703$	1.45639			0.0549288
$704$		0			0
$705$	10.0731			0.379376
$706$		0			0
$707$	30.2312	−	30.2312i	1.13696	−	1.13696i
$708$		0			0
$709$	18.0518	+	18.0518i	0.677950	+	0.677950i	0.959536	−	0.281586i	$-0.0908604\pi$
$709$	18.0518	+	18.0518i	0.677950	+	0.677950i	−0.281586	+	0.959536i	$0.590860\pi$
$710$		0			0
$711$		−	4.19999i		−	0.157512i
$712$		0			0
$713$		−	6.51940i		−	0.244154i
$714$		0			0
$715$	−8.03935	−	8.03935i	−0.300655	−	0.300655i
$716$		0			0
$717$	−2.55649	+	2.55649i	−0.0954739	+	0.0954739i
$718$		0			0
$719$	1.68053			0.0626731			0.0313366	−	0.999509i	$-0.490024\pi$
$719$	1.68053			0.0626731			0.0313366	+	0.999509i	$0.490024\pi$
$720$		0			0
$721$	−14.9546			−0.556939
$722$		0			0
$723$	−22.4367	+	22.4367i	−0.834431	+	0.834431i
$724$		0			0
$725$	−5.67267	−	5.67267i	−0.210678	−	0.210678i
$726$		0			0
$727$			15.5235i			0.575735i	0.957670	+	0.287867i	$0.0929462\pi$
$727$			15.5235i			0.575735i	−0.957670	+	0.287867i	$0.907054\pi$
$728$		0			0
$729$			17.2107i			0.637435i
$730$		0			0
$731$	−15.9718	−	15.9718i	−0.590737	−	0.590737i
$732$		0			0
$733$	−8.79758	+	8.79758i	−0.324946	+	0.324946i	−0.850661	−	0.525715i	$-0.823798\pi$
$733$	−8.79758	+	8.79758i	−0.324946	+	0.324946i	0.525715	+	0.850661i	$0.323798\pi$
$734$		0			0
$735$	−0.928667			−0.0342544
$736$		0			0
$737$	47.4862			1.74918
$738$		0			0
$739$	6.44190	−	6.44190i	0.236969	−	0.236969i	−0.578625	−	0.815594i	$-0.696410\pi$
$739$	6.44190	−	6.44190i	0.236969	−	0.236969i	0.815594	+	0.578625i	$0.196410\pi$
$740$		0			0
$741$	−1.10638	−	1.10638i	−0.0406440	−	0.0406440i
$742$		0			0
$743$			34.8920i			1.28006i	0.768348	+	0.640032i	$0.221079\pi$
$743$			34.8920i			1.28006i	−0.768348	+	0.640032i	$0.778921\pi$
$744$		0			0
$745$		−	13.8115i		−	0.506014i
$746$		0			0
$747$	−0.389866	−	0.389866i	−0.0142645	−	0.0142645i
$748$		0			0
$749$	0.803225	−	0.803225i	0.0293492	−	0.0293492i
$750$		0			0
$751$	−17.4058			−0.635148			−0.317574	−	0.948234i	$-0.602868\pi$
$751$	−17.4058			−0.635148			−0.317574	+	0.948234i	$0.602868\pi$
$752$		0			0
$753$	8.25325			0.300765
$754$		0			0
$755$	−1.34884	+	1.34884i	−0.0490893	+	0.0490893i
$756$		0			0
$757$	20.6521	+	20.6521i	0.750614	+	0.750614i	0.974594	−	0.223980i	$-0.0719050\pi$
$757$	20.6521	+	20.6521i	0.750614	+	0.750614i	−0.223980	+	0.974594i	$0.571905\pi$
$758$		0			0
$759$			18.6176i			0.675776i
$760$		0			0
$761$		−	8.36636i		−	0.303280i	−0.988436	−	0.151640i	$-0.951545\pi$
$761$		−	8.36636i		−	0.303280i	0.988436	−	0.151640i	$-0.0484555\pi$
$762$		0			0
$763$	28.4789	+	28.4789i	1.03101	+	1.03101i
$764$		0			0
$765$	2.64318	−	2.64318i	0.0955642	−	0.0955642i
$766$		0			0
$767$	−17.6851			−0.638574
$768$		0			0
$769$	45.1264			1.62730			0.813650	−	0.581356i	$-0.197477\pi$
$769$	45.1264			1.62730			0.813650	+	0.581356i	$0.197477\pi$
$770$		0			0
$771$	−31.1609	+	31.1609i	−1.12223	+	1.12223i
$772$		0			0
$773$	−11.1233	−	11.1233i	−0.400076	−	0.400076i	0.478184	−	0.878260i	$-0.341295\pi$
$773$	−11.1233	−	11.1233i	−0.400076	−	0.400076i	−0.878260	+	0.478184i	$0.841295\pi$
$774$		0			0
$775$		−	3.95550i		−	0.142086i
$776$		0			0
$777$		−	18.6452i		−	0.668891i
$778$		0			0
$779$	−2.46128	−	2.46128i	−0.0881844	−	0.0881844i
$780$		0			0
$781$	32.6544	−	32.6544i	1.16846	−	1.16846i
$782$		0			0
$783$	34.8969			1.24711
$784$		0			0
$785$	6.24086			0.222746
$786$		0			0
$787$	−7.41779	+	7.41779i	−0.264416	+	0.264416i	−0.826845	−	0.562430i	$-0.809867\pi$
$787$	−7.41779	+	7.41779i	−0.264416	+	0.264416i	0.562430	+	0.826845i	$0.309867\pi$
$788$		0			0
$789$	16.4844	+	16.4844i	0.586860	+	0.586860i
$790$		0			0
$791$		−	47.6254i		−	1.69337i
$792$		0			0
$793$		−	10.5541i		−	0.374786i
$794$		0			0
$795$	13.9629	+	13.9629i	0.495215	+	0.495215i
$796$		0			0
$797$	−8.05803	+	8.05803i	−0.285430	+	0.285430i	−0.835270	−	0.549840i	$-0.814689\pi$
$797$	−8.05803	+	8.05803i	−0.285430	+	0.285430i	0.549840	+	0.835270i	$0.314689\pi$
$798$		0			0
$799$	−25.7264			−0.910136
$800$		0			0
$801$	−4.85064			−0.171389
$802$		0			0
$803$	17.9822	−	17.9822i	0.634578	−	0.634578i
$804$		0			0
$805$	3.18727	+	3.18727i	0.112337	+	0.112337i
$806$		0			0
$807$			13.4305i			0.472776i
$808$		0			0
$809$			20.1500i			0.708436i	0.935163	+	0.354218i	$0.115253\pi$
$809$			20.1500i			0.708436i	−0.935163	+	0.354218i	$0.884747\pi$
$810$		0			0
$811$	10.5575	+	10.5575i	0.370723	+	0.370723i	0.867741	−	0.497018i	$-0.165572\pi$
$811$	10.5575	+	10.5575i	0.370723	+	0.370723i	−0.497018	+	0.867741i	$0.665572\pi$
$812$		0			0
$813$	−5.68136	+	5.68136i	−0.199254	+	0.199254i
$814$		0			0
$815$	−5.07578			−0.177797
$816$		0			0
$817$	1.88926			0.0660969
$818$		0			0
$819$	−2.84877	+	2.84877i	−0.0995441	+	0.0995441i
$820$		0			0
$821$	−24.3826	−	24.3826i	−0.850957	−	0.850957i	0.139294	−	0.990251i	$-0.455517\pi$
$821$	−24.3826	−	24.3826i	−0.850957	−	0.850957i	−0.990251	+	0.139294i	$0.955517\pi$
$822$		0			0
$823$			32.5617i			1.13503i	0.823363	+	0.567515i	$0.192095\pi$
$823$			32.5617i			1.13503i	−0.823363	+	0.567515i	$0.807905\pi$
$824$		0			0
$825$			11.2958i			0.393270i
$826$		0			0
$827$	1.31121	+	1.31121i	0.0455952	+	0.0455952i	0.729537	−	0.683942i	$-0.239736\pi$
$827$	1.31121	+	1.31121i	0.0455952	+	0.0455952i	−0.683942	+	0.729537i	$0.739736\pi$
$828$		0			0
$829$	−20.8346	+	20.8346i	−0.723617	+	0.723617i	−0.969340	−	0.245723i	$-0.920975\pi$
$829$	−20.8346	+	20.8346i	−0.723617	+	0.723617i	0.245723	+	0.969340i	$0.420975\pi$
$830$		0			0
$831$	28.7251			0.996462
$832$		0			0
$833$	2.37179			0.0821775
$834$		0			0
$835$	−12.4446	+	12.4446i	−0.430663	+	0.430663i
$836$		0			0
$837$	12.1666	+	12.1666i	0.420541	+	0.420541i
$838$		0			0
$839$			54.2029i			1.87129i	0.352939	+	0.935646i	$0.385182\pi$
$839$			54.2029i			1.87129i	−0.352939	+	0.935646i	$0.614818\pi$
$840$		0			0
$841$		−	35.3584i		−	1.21925i
$842$		0			0
$843$	4.82234	+	4.82234i	0.166090	+	0.166090i
$844$		0			0
$845$	6.50232	−	6.50232i	0.223686	−	0.223686i
$846$		0			0
$847$	−62.8396			−2.15920
$848$		0			0
$849$	−7.90541			−0.271313
$850$		0			0
$851$	−4.10023	+	4.10023i	−0.140554	+	0.140554i
$852$		0			0
$853$	28.4548	+	28.4548i	0.974274	+	0.974274i	0.999677	−	0.0254034i	$-0.00808702\pi$
$853$	28.4548	+	28.4548i	0.974274	+	0.974274i	−0.0254034	+	0.999677i	$0.508087\pi$
$854$		0			0
$855$			0.312655i			0.0106926i
$856$		0			0
$857$		−	28.9592i		−	0.989228i	−0.869113	−	0.494614i	$-0.835309\pi$
$857$		−	28.9592i		−	0.989228i	0.869113	−	0.494614i	$-0.164691\pi$
$858$		0			0
$859$	−35.6101	−	35.6101i	−1.21500	−	1.21500i	−0.969361	−	0.245640i	$-0.921002\pi$
$859$	−35.6101	−	35.6101i	−1.21500	−	1.21500i	−0.245640	−	0.969361i	$-0.578998\pi$
$860$		0			0
$861$	−31.5100	+	31.5100i	−1.07386	+	1.07386i
$862$		0			0
$863$	31.8081			1.08276			0.541380	−	0.840778i	$-0.317902\pi$
$863$	31.8081			1.08276			0.541380	+	0.840778i	$0.317902\pi$
$864$		0			0
$865$	10.3574			0.352161
$866$		0			0
$867$	−10.2698	+	10.2698i	−0.348780	+	0.348780i
$868$		0			0
$869$	−22.9205	−	22.9205i	−0.777526	−	0.777526i
$870$		0			0
$871$		−	15.8895i		−	0.538396i
$872$		0			0
$873$			7.13382i			0.241443i
$874$		0			0
$875$	1.93381	+	1.93381i	0.0653746	+	0.0653746i
$876$		0			0
$877$	−29.2864	+	29.2864i	−0.988932	+	0.988932i	−0.999939	−	0.0110076i	$-0.996496\pi$
$877$	−29.2864	+	29.2864i	−0.988932	+	0.988932i	0.0110076	+	0.999939i	$0.496496\pi$
$878$		0			0
$879$	−10.7525			−0.362673
$880$		0			0
$881$	−6.72061			−0.226423			−0.113212	−	0.993571i	$-0.536114\pi$
$881$	−6.72061			−0.226423			−0.113212	+	0.993571i	$0.536114\pi$
$882$		0			0
$883$	26.2186	−	26.2186i	0.882327	−	0.882327i	−0.111444	−	0.993771i	$-0.535547\pi$
$883$	26.2186	−	26.2186i	0.882327	−	0.882327i	0.993771	+	0.111444i	$0.0355474\pi$
$884$		0			0
$885$	12.4244	+	12.4244i	0.417641	+	0.417641i
$886$		0			0
$887$			10.4628i			0.351307i	0.984452	+	0.175654i	$0.0562039\pi$
$887$			10.4628i			0.351307i	−0.984452	+	0.175654i	$0.943796\pi$
$888$		0			0
$889$		−	30.0263i		−	1.00705i
$890$		0			0
$891$	−44.0837	−	44.0837i	−1.47686	−	1.47686i
$892$		0			0
$893$	1.52156	−	1.52156i	0.0509171	−	0.0509171i
$894$		0			0
$895$	9.09126			0.303887
$896$		0			0
$897$	6.22969			0.208003
$898$		0			0
$899$	22.4383	−	22.4383i	0.748358	−	0.748358i
$900$		0			0
$901$	−35.6609	−	35.6609i	−1.18804	−	1.18804i
$902$		0			0
$903$		−	24.1869i		−	0.804890i
$904$		0			0
$905$			5.20267i			0.172943i
$906$		0			0
$907$	−12.4762	−	12.4762i	−0.414267	−	0.414267i	0.468955	−	0.883222i	$-0.344631\pi$
$907$	−12.4762	−	12.4762i	−0.414267	−	0.414267i	−0.883222	+	0.468955i	$0.844631\pi$
$908$		0			0
$909$	−8.34894	+	8.34894i	−0.276917	+	0.276917i
$910$		0			0
$911$	−49.3786			−1.63599			−0.817994	−	0.575227i	$-0.804914\pi$
$911$	−49.3786			−1.63599			−0.817994	+	0.575227i	$0.804914\pi$
$912$		0			0
$913$	−4.25522			−0.140827
$914$		0			0
$915$	−7.41457	+	7.41457i	−0.245118	+	0.245118i
$916$		0			0
$917$	−15.7811	−	15.7811i	−0.521138	−	0.521138i
$918$		0			0
$919$			26.6465i			0.878988i	0.898246	+	0.439494i	$0.144842\pi$
$919$			26.6465i			0.878988i	−0.898246	+	0.439494i	$0.855158\pi$
$920$		0			0
$921$			0.538466i			0.0177431i
$922$		0			0
$923$	−10.9266	−	10.9266i	−0.359653	−	0.359653i
$924$		0			0
$925$	−2.48772	+	2.48772i	−0.0817958	+	0.0817958i
$926$		0			0
$927$	4.13002			0.135648
$928$		0			0
$929$	−29.5531			−0.969606			−0.484803	−	0.874623i	$-0.661109\pi$
$929$	−29.5531			−0.969606			−0.484803	+	0.874623i	$0.661109\pi$
$930$		0			0
$931$	−0.140276	+	0.140276i	−0.00459737	+	0.00459737i
$932$		0			0
$933$	3.46579	+	3.46579i	0.113465	+	0.113465i
$934$		0			0
$935$		−	28.8491i		−	0.943468i
$936$		0			0
$937$		−	30.5505i		−	0.998042i	−0.866590	−	0.499021i	$-0.833693\pi$
$937$		−	30.5505i		−	0.998042i	0.866590	−	0.499021i	$-0.166307\pi$
$938$		0			0
$939$	5.27380	+	5.27380i	0.172104	+	0.172104i
$940$		0			0
$941$	0.808622	−	0.808622i	0.0263603	−	0.0263603i	−0.693804	−	0.720164i	$-0.744067\pi$
$941$	0.808622	−	0.808622i	0.0263603	−	0.0263603i	0.720164	+	0.693804i	$0.244067\pi$
$942$		0			0
$943$	13.8586			0.451299
$944$		0			0
$945$	−11.8963			−0.386987
$946$		0			0
$947$	16.7181	−	16.7181i	0.543265	−	0.543265i	−0.381220	−	0.924484i	$-0.624496\pi$
$947$	16.7181	−	16.7181i	0.543265	−	0.543265i	0.924484	+	0.381220i	$0.124496\pi$
$948$		0			0
$949$	−6.01708	−	6.01708i	−0.195323	−	0.195323i
$950$		0			0
$951$		−	18.6055i		−	0.603326i
$952$		0			0
$953$		−	5.39705i		−	0.174828i	−0.996172	−	0.0874138i	$-0.972140\pi$
$953$		−	5.39705i		−	0.174828i	0.996172	−	0.0874138i	$-0.0278603\pi$
$954$		0			0
$955$	−3.81196	−	3.81196i	−0.123352	−	0.123352i
$956$		0			0
$957$	−64.0774	+	64.0774i	−2.07133	+	2.07133i
$958$		0			0
$959$	19.6587			0.634813
$960$		0			0
$961$	−15.3540			−0.495290
$962$		0			0
$963$	−0.221827	+	0.221827i	−0.00714827	+	0.00714827i
$964$		0			0
$965$	2.50187	+	2.50187i	0.0805381	+	0.0805381i
$966$		0			0
$967$		−	14.0430i		−	0.451593i	−0.974175	−	0.225796i	$-0.927502\pi$
$967$		−	14.0430i		−	0.451593i	0.974175	−	0.225796i	$-0.0724984\pi$
$968$		0			0
$969$		−	3.97025i		−	0.127543i
$970$		0			0
$971$	−13.5960	−	13.5960i	−0.436316	−	0.436316i	0.454454	−	0.890770i	$-0.349834\pi$
$971$	−13.5960	−	13.5960i	−0.436316	−	0.436316i	−0.890770	+	0.454454i	$0.849834\pi$
$972$		0			0
$973$	13.4369	−	13.4369i	0.430767	−	0.430767i
$974$		0			0
$975$	3.77973			0.121048
$976$		0			0
$977$	44.9303			1.43745			0.718724	−	0.695295i	$-0.244726\pi$
$977$	44.9303			1.43745			0.718724	+	0.695295i	$0.244726\pi$
$978$		0			0
$979$	−26.4713	+	26.4713i	−0.846028	+	0.846028i
$980$		0			0
$981$	−7.86502	−	7.86502i	−0.251111	−	0.251111i
$982$		0			0
$983$			55.7813i			1.77915i	0.456791	+	0.889574i	$0.348999\pi$
$983$			55.7813i			1.77915i	−0.456791	+	0.889574i	$0.651001\pi$
$984$		0			0
$985$		−	15.1179i		−	0.481696i
$986$		0			0
$987$	−19.4795	−	19.4795i	−0.620039	−	0.620039i
$988$		0			0
$989$	−5.31891	+	5.31891i	−0.169131	+	0.169131i
$990$		0			0
$991$	46.1815			1.46700			0.733502	−	0.679688i	$-0.237885\pi$
$991$	46.1815			1.46700			0.733502	+	0.679688i	$0.237885\pi$
$992$		0			0
$993$	4.91090			0.155843
$994$		0			0
$995$	11.0693	−	11.0693i	0.350920	−	0.350920i
$996$		0			0
$997$	−33.4837	−	33.4837i	−1.06044	−	1.06044i	−0.998052	−	0.0623860i	$-0.980129\pi$
$997$	−33.4837	−	33.4837i	−1.06044	−	1.06044i	−0.0623860	−	0.998052i	$-0.519871\pi$
$998$		0			0
$999$		−	15.3039i		−	0.484193i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.2.l.a.241.3		16
3.2	odd	2		2880.2.t.c.2161.8		16
4.3	odd	2		80.2.l.a.21.2	✓	16
5.2	odd	4		1600.2.q.h.49.6		16
5.3	odd	4		1600.2.q.g.49.3		16
5.4	even	2		1600.2.l.i.1201.6		16
8.3	odd	2		640.2.l.b.481.3		16
8.5	even	2		640.2.l.a.481.6		16
12.11	even	2		720.2.t.c.181.7		16
16.3	odd	4		80.2.l.a.61.2	yes	16
16.5	even	4		640.2.l.a.161.6		16
16.11	odd	4		640.2.l.b.161.3		16
16.13	even	4	inner	320.2.l.a.81.3		16
20.3	even	4		400.2.q.h.149.5		16
20.7	even	4		400.2.q.g.149.4		16
20.19	odd	2		400.2.l.h.101.7		16
32.3	odd	8		5120.2.a.v.1.6		8
32.13	even	8		5120.2.a.u.1.6		8
32.19	odd	8		5120.2.a.s.1.3		8
32.29	even	8		5120.2.a.t.1.3		8
48.29	odd	4		2880.2.t.c.721.5		16
48.35	even	4		720.2.t.c.541.7		16
80.3	even	4		400.2.q.g.349.4		16
80.13	odd	4		1600.2.q.h.849.6		16
80.19	odd	4		400.2.l.h.301.7		16
80.29	even	4		1600.2.l.i.401.6		16
80.67	even	4		400.2.q.h.349.5		16
80.77	odd	4		1600.2.q.g.849.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.2	✓	16	4.3	odd	2
80.2.l.a.61.2	yes	16	16.3	odd	4
320.2.l.a.81.3		16	16.13	even	4	inner
320.2.l.a.241.3		16	1.1	even	1	trivial
400.2.l.h.101.7		16	20.19	odd	2
400.2.l.h.301.7		16	80.19	odd	4
400.2.q.g.149.4		16	20.7	even	4
400.2.q.g.349.4		16	80.3	even	4
400.2.q.h.149.5		16	20.3	even	4
400.2.q.h.349.5		16	80.67	even	4
640.2.l.a.161.6		16	16.5	even	4
640.2.l.a.481.6		16	8.5	even	2
640.2.l.b.161.3		16	16.11	odd	4
640.2.l.b.481.3		16	8.3	odd	2
720.2.t.c.181.7		16	12.11	even	2
720.2.t.c.541.7		16	48.35	even	4
1600.2.l.i.401.6		16	80.29	even	4
1600.2.l.i.1201.6		16	5.4	even	2
1600.2.q.g.49.3		16	5.3	odd	4
1600.2.q.g.849.3		16	80.77	odd	4
1600.2.q.h.49.6		16	5.2	odd	4
1600.2.q.h.849.6		16	80.13	odd	4
2880.2.t.c.721.5		16	48.29	odd	4
2880.2.t.c.2161.8		16	3.2	odd	2
5120.2.a.s.1.3		8	32.19	odd	8
5120.2.a.t.1.3		8	32.29	even	8
5120.2.a.u.1.6		8	32.13	even	8
5120.2.a.v.1.6		8	32.3	odd	8

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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	320.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.37027 + 1.37027i) q^{3} +(-0.707107 - 0.707107i) q^{5} +2.73482i q^{7} -0.755274i q^{9} +(-4.12175 - 4.12175i) q^{11} +(-1.37919 + 1.37919i) q^{13} +1.93785 q^{15} -4.94921 q^{17} +(0.292715 - 0.292715i) q^{19} +(-3.74744 - 3.74744i) q^{21} +1.64818i q^{23} +1.00000i q^{25} +(-3.07588 - 3.07588i) q^{27} +(-5.67267 + 5.67267i) q^{29} -3.95550 q^{31} +11.2958 q^{33} +(1.93381 - 1.93381i) q^{35} +(2.48772 + 2.48772i) q^{37} -3.77973i q^{39} -8.40843i q^{41} +(3.22713 + 3.22713i) q^{43} +(-0.534060 + 0.534060i) q^{45} +5.19809 q^{47} -0.479225 q^{49} +(6.78176 - 6.78176i) q^{51} +(7.20537 + 7.20537i) q^{53} +5.82903i q^{55} +0.802198i q^{57} +(6.41142 + 6.41142i) q^{59} +(-3.82618 + 3.82618i) q^{61} +2.06554 q^{63} +1.95047 q^{65} +(-5.76044 + 5.76044i) q^{67} +(-2.25846 - 2.25846i) q^{69} +7.92245i q^{71} +4.36276i q^{73} +(-1.37027 - 1.37027i) q^{75} +(11.2722 - 11.2722i) q^{77} +5.56087 q^{79} +10.6954 q^{81} +(0.516191 - 0.516191i) q^{83} +(3.49962 + 3.49962i) q^{85} -15.5462i q^{87} -6.42236i q^{89} +(-3.77184 - 3.77184i) q^{91} +(5.42011 - 5.42011i) q^{93} -0.413962 q^{95} -9.44534 q^{97} +(-3.11305 + 3.11305i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{11} + 8 q^{15} + 8 q^{19} - 24 q^{27} - 16 q^{29} - 16 q^{37} - 8 q^{43} + 40 q^{47} - 16 q^{49} + 32 q^{51} + 16 q^{53} + 8 q^{59} + 16 q^{61} - 40 q^{63} - 40 q^{67} + 16 q^{69} + 16 q^{77}+ \cdots + 8 q^{99}+O(q^{100}) \) 16 * q + 8 * q^11 + 8 * q^15 + 8 * q^19 - 24 * q^27 - 16 * q^29 - 16 * q^37 - 8 * q^43 + 40 * q^47 - 16 * q^49 + 32 * q^51 + 16 * q^53 + 8 * q^59 + 16 * q^61 - 40 * q^63 - 40 * q^67 + 16 * q^69 + 16 * q^77 - 16 * q^79 - 16 * q^81 - 40 * q^83 - 16 * q^85 - 32 * q^91 - 48 * q^93 - 32 * q^95 + 8 * q^99

Introduction

L-functions

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