LMFDB - Embedded newform 640.2.l.a.481.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [640,2,Mod(161,640)] 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("640.161"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(640, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.l (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$5.11042572936$
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			481.6
Root			$-0.530822 + 1.31081i$ of defining polynomial
Character	$\chi$	$=$	640.481
Dual form			640.2.l.a.161.6

$q$-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 $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.37027	−	1.37027i	0.791125	−	0.791125i	−0.190552	−	0.981677i	$-0.561028\pi$
$3$	1.37027	−	1.37027i	0.791125	−	0.791125i	0.981677	+	0.190552i	$0.0610278\pi$
$4$		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	$0.0916285\pi$
$11$	4.12175	+	4.12175i	1.24275	+	1.24275i	0.283900	+	0.958854i	$0.408371\pi$
$12$		0			0
$13$	1.37919	−	1.37919i	0.382519	−	0.382519i	−0.489490	−	0.872009i	$-0.662817\pi$
$13$	1.37919	−	1.37919i	0.382519	−	0.382519i	0.872009	+	0.489490i	$0.162817\pi$
$14$		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	−0.739886	−	0.672732i	$-0.765121\pi$
$19$	−0.292715	+	0.292715i	−0.0671535	+	0.0671535i	0.672732	+	0.739886i	$0.265121\pi$
$20$		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	$-0.482517\pi$
$29$	5.67267	−	5.67267i	1.05339	−	1.05339i	0.998492	−	0.0548963i	$-0.0174828\pi$
$30$		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	0.472403	−	0.881382i	$-0.343387\pi$
$37$	−2.48772	−	2.48772i	−0.408979	−	0.408979i	−0.881382	+	0.472403i	$0.843387\pi$
$38$		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	0.416845	−	0.908978i	$-0.363136\pi$
$43$	−3.22713	−	3.22713i	−0.492133	−	0.492133i	−0.908978	+	0.416845i	$0.863136\pi$
$44$		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	0.0102143	−	0.999948i	$-0.496749\pi$
$53$	−7.20537	−	7.20537i	−0.989733	−	0.989733i	−0.999948	+	0.0102143i	$0.996749\pi$
$54$		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	0.153459	−	0.988155i	$-0.450959\pi$
$59$	−6.41142	−	6.41142i	−0.834695	−	0.834695i	−0.988155	+	0.153459i	$0.950959\pi$
$60$		0			0
$61$	3.82618	−	3.82618i	0.489892	−	0.489892i	−0.418380	−	0.908272i	$-0.637402\pi$
$61$	3.82618	−	3.82618i	0.489892	−	0.489892i	0.908272	+	0.418380i	$0.137402\pi$
$62$		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	−0.261463	−	0.965213i	$-0.584205\pi$
$67$	5.76044	−	5.76044i	0.703750	−	0.703750i	0.965213	+	0.261463i	$0.0842050\pi$
$68$		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	−0.734869	−	0.678209i	$-0.762756\pi$
$83$	−0.516191	+	0.516191i	−0.0566594	+	0.0566594i	0.678209	+	0.734869i	$0.262756\pi$
$84$		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	$0.0336491\pi$
$101$	11.0542	+	11.0542i	1.09993	+	1.09993i	0.105515	+	0.994418i	$0.466351\pi$
$102$		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	0.721161	−	0.692768i	$-0.243609\pi$
$107$	0.293704	+	0.293704i	0.0283934	+	0.0283934i	−0.692768	+	0.721161i	$0.743609\pi$
$108$		0			0
$109$	−10.4135	+	10.4135i	−0.997429	+	0.997429i	−0.999997	−	0.00256817i	$-0.999183\pi$
$109$	−10.4135	+	10.4135i	−0.997429	+	0.997429i	0.00256817	+	0.999997i	$0.499183\pi$
$110$		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	−0.408564	−	0.912730i	$-0.633970\pi$
$131$	5.77044	−	5.77044i	0.504166	−	0.504166i	0.912730	+	0.408564i	$0.133970\pi$
$132$		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	0.884078	−	0.467340i	$-0.154788\pi$
$139$	4.91327	+	4.91327i	0.416738	+	0.416738i	−0.467340	+	0.884078i	$0.654788\pi$
$140$		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	0.183029	−	0.983107i	$-0.441410\pi$
$149$	−9.76620	−	9.76620i	−0.800078	−	0.800078i	−0.983107	+	0.183029i	$0.941410\pi$
$150$		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	−0.508732	−	0.860925i	$-0.669886\pi$
$157$	4.41296	−	4.41296i	0.352192	−	0.352192i	0.860925	+	0.508732i	$0.169886\pi$
$158$		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	−0.833556	−	0.552435i	$-0.813699\pi$
$163$	−3.58912	+	3.58912i	−0.281122	+	0.281122i	0.552435	+	0.833556i	$0.313699\pi$
$164$		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	−0.371584	−	0.928400i	$-0.621185\pi$
$173$	7.32377	−	7.32377i	0.556816	−	0.556816i	0.928400	+	0.371584i	$0.121185\pi$
$174$		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	−0.424800	−	0.905287i	$-0.639655\pi$
$179$	6.42849	−	6.42849i	0.480488	−	0.480488i	0.905287	+	0.424800i	$0.139655\pi$
$180$		0			0
$181$	3.67884	+	3.67884i	0.273446	+	0.273446i	0.830486	−	0.557040i	$-0.188063\pi$
$181$	3.67884	+	3.67884i	0.273446	+	0.273446i	−0.557040	+	0.830486i	$0.688063\pi$
$182$		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	0.214989	−	0.976616i	$-0.431028\pi$
$197$	−10.6900	−	10.6900i	−0.761627	−	0.761627i	−0.976616	+	0.214989i	$0.931028\pi$
$198$		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	$0.672444\pi$
$211$	−19.9359	+	19.9359i	−1.37244	+	1.37244i	−0.856809	+	0.515634i	$0.827556\pi$
$212$		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	−0.184079	−	0.982911i	$-0.558930\pi$
$227$	12.0356	−	12.0356i	0.798832	−	0.798832i	0.982911	+	0.184079i	$0.0589303\pi$
$228$		0			0
$229$	−6.70809	−	6.70809i	−0.443283	−	0.443283i	0.449831	−	0.893114i	$-0.351484\pi$
$229$	−6.70809	−	6.70809i	−0.443283	−	0.443283i	−0.893114	+	0.449831i	$0.851484\pi$
$230$		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	0.795734	−	0.605647i	$-0.207086\pi$
$251$	3.01154	+	3.01154i	0.190087	+	0.190087i	−0.605647	+	0.795734i	$0.707086\pi$
$252$		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	−0.840544	−	0.541744i	$-0.817764\pi$
$269$	−4.90068	+	4.90068i	−0.298800	+	0.298800i	0.541744	+	0.840544i	$0.317764\pi$
$270$		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	0.948011	−	0.318236i	$-0.103091\pi$
$277$	10.4815	+	10.4815i	0.629775	+	0.629775i	−0.318236	+	0.948011i	$0.603091\pi$
$278$		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	0.616153	−	0.787626i	$-0.288690\pi$
$283$	−2.88462	−	2.88462i	−0.171473	−	0.171473i	−0.787626	+	0.616153i	$0.788690\pi$
$284$		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	0.583150	−	0.812364i	$-0.301820\pi$
$293$	−3.92351	−	3.92351i	−0.229214	−	0.229214i	−0.812364	+	0.583150i	$0.801820\pi$
$294$		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	−0.712691	−	0.701478i	$-0.752524\pi$
$307$	−0.196482	+	0.196482i	−0.0112138	+	0.0112138i	0.701478	+	0.712691i	$0.252524\pi$
$308$		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	−0.490265	−	0.871574i	$-0.663100\pi$
$317$	6.78901	−	6.78901i	0.381309	−	0.381309i	0.871574	+	0.490265i	$0.163100\pi$
$318$		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	0.754637	−	0.656143i	$-0.227813\pi$
$331$	1.79195	+	1.79195i	0.0984944	+	0.0984944i	−0.656143	+	0.754637i	$0.727813\pi$
$332$		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	0.959888	−	0.280385i	$-0.0904622\pi$
$347$	12.6577	+	12.6577i	0.679502	+	0.679502i	−0.280385	+	0.959888i	$0.590462\pi$
$348$		0			0
$349$	16.3020	−	16.3020i	0.872627	−	0.872627i	−0.120131	−	0.992758i	$-0.538331\pi$
$349$	16.3020	−	16.3020i	0.872627	−	0.872627i	0.992758	+	0.120131i	$0.0383314\pi$
$350$		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	0.999908	−	0.0135655i	$-0.00431817\pi$
$373$	19.0494	+	19.0494i	0.986342	+	0.986342i	−0.0135655	+	0.999908i	$0.504318\pi$
$374$		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	0.577655	−	0.816281i	$-0.303968\pi$
$379$	−4.64554	−	4.64554i	−0.238625	−	0.238625i	−0.816281	+	0.577655i	$0.803968\pi$
$380$		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	0.729633	−	0.683839i	$-0.239691\pi$
$389$	0.903192	+	0.903192i	0.0457937	+	0.0457937i	−0.683839	+	0.729633i	$0.739691\pi$
$390$		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	−0.809850	−	0.586637i	$-0.800451\pi$
$397$	−4.44748	+	4.44748i	−0.223212	+	0.223212i	0.586637	+	0.809850i	$0.300451\pi$
$398$		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	−0.502412	−	0.864628i	$-0.667554\pi$
$419$	7.41439	−	7.41439i	0.362217	−	0.362217i	0.864628	+	0.502412i	$0.167554\pi$
$420$		0			0
$421$	10.3279	+	10.3279i	0.503351	+	0.503351i	0.912478	−	0.409127i	$-0.134167\pi$
$421$	10.3279	+	10.3279i	0.503351	+	0.503351i	−0.409127	+	0.912478i	$0.634167\pi$
$422$		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	0.502350	−	0.864664i	$-0.332469\pi$
$443$	−7.62584	−	7.62584i	−0.362315	−	0.362315i	−0.864664	+	0.502350i	$0.832469\pi$
$444$		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	$-0.478116\pi$
$461$	22.8952	−	22.8952i	1.06634	−	1.06634i	0.997638	−	0.0686980i	$-0.0218845\pi$
$462$		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	$0.529944\pi$
$467$	−23.5446	+	23.5446i	−1.08951	+	1.08951i	−0.995578	+	0.0939334i	$0.970056\pi$
$468$		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	$-0.872781\pi$
$491$	−29.0344	−	29.0344i	−1.31030	−	1.31030i	−0.389113	−	0.921190i	$-0.627219\pi$
$492$		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	−0.861451	−	0.507841i	$-0.830444\pi$
$499$	−7.89904	+	7.89904i	−0.353610	+	0.353610i	0.507841	+	0.861451i	$0.330444\pi$
$500$		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	−0.606628	−	0.794986i	$-0.707478\pi$
$509$	4.24956	−	4.24956i	0.188358	−	0.188358i	0.794986	+	0.606628i	$0.207478\pi$
$510$		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	0.598701	−	0.800973i	$-0.295684\pi$
$523$	−4.62580	−	4.62580i	−0.202272	−	0.202272i	−0.800973	+	0.598701i	$0.795684\pi$
$524$		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	$0.510595\pi$
$541$	−24.0206	+	24.0206i	−1.03272	+	1.03272i	−0.999446	+	0.0332788i	$0.989405\pi$
$542$		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	−0.600943	−	0.799292i	$-0.705208\pi$
$547$	4.63900	−	4.63900i	0.198349	−	0.198349i	0.799292	+	0.600943i	$0.205208\pi$
$548$		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	−0.934171	−	0.356826i	$-0.883859\pi$
$557$	−13.6258	+	13.6258i	−0.577345	+	0.577345i	0.356826	+	0.934171i	$0.383859\pi$
$558$		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	$-0.434269\pi$
$563$	28.0885	−	28.0885i	1.18379	−	1.18379i	0.978755	−	0.205035i	$-0.0657308\pi$
$564$		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	0.854278	−	0.519816i	$-0.174000\pi$
$571$	7.99217	+	7.99217i	0.334462	+	0.334462i	−0.519816	+	0.854278i	$0.674000\pi$
$572$		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	0.715925	−	0.698178i	$-0.246005\pi$
$587$	0.429976	+	0.429976i	0.0177470	+	0.0177470i	−0.698178	+	0.715925i	$0.746005\pi$
$588$		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	0.587633	−	0.809127i	$-0.300060\pi$
$613$	−5.48393	−	5.48393i	−0.221494	−	0.221494i	−0.809127	+	0.587633i	$0.800060\pi$
$614$		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	0.880288	−	0.474439i	$-0.157349\pi$
$619$	10.0974	+	10.0974i	0.405849	+	0.405849i	−0.474439	+	0.880288i	$0.657349\pi$
$620$		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	$0.554588\pi$
$643$	−29.3128	+	29.3128i	−1.15598	+	1.15598i	−0.985331	+	0.170653i	$0.945412\pi$
$644$		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	−0.422995	−	0.906132i	$-0.639021\pi$
$653$	12.3460	−	12.3460i	0.483137	−	0.483137i	0.906132	+	0.422995i	$0.139021\pi$
$654$		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	−0.215470	−	0.976510i	$-0.569128\pi$
$659$	19.5367	−	19.5367i	0.761040	−	0.761040i	0.976510	+	0.215470i	$0.0691284\pi$
$660$		0			0
$661$	−26.4901	−	26.4901i	−1.03035	−	1.03035i	−0.999525	−	0.0308210i	$-0.990188\pi$
$661$	−26.4901	−	26.4901i	−1.03035	−	1.03035i	−0.0308210	−	0.999525i	$-0.509812\pi$
$662$		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	0.942234	−	0.334956i	$-0.108721\pi$
$677$	15.8009	+	15.8009i	0.607278	+	0.607278i	−0.334956	+	0.942234i	$0.608721\pi$
$678$		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	0.0372032	−	0.999308i	$-0.488155\pi$
$683$	−25.1439	−	25.1439i	−0.962105	−	0.962105i	−0.999308	+	0.0372032i	$0.988155\pi$
$684$		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	$0.512072\pi$
$691$	−27.2647	+	27.2647i	−1.03720	+	1.03720i	−0.999281	+	0.0379162i	$0.987928\pi$
$692$		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	−0.903289	−	0.429032i	$-0.858855\pi$
$701$	−12.5566	+	12.5566i	−0.474257	+	0.474257i	0.429032	+	0.903289i	$0.358855\pi$
$702$		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	0.281586	−	0.959536i	$-0.409140\pi$
$709$	−18.0518	−	18.0518i	−0.677950	−	0.677950i	−0.959536	+	0.281586i	$0.909140\pi$
$710$		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	−0.525715	−	0.850661i	$-0.676202\pi$
$733$	8.79758	−	8.79758i	0.324946	−	0.324946i	0.850661	+	0.525715i	$0.176202\pi$
$734$		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	−0.815594	−	0.578625i	$-0.803590\pi$
$739$	−6.44190	+	6.44190i	−0.236969	+	0.236969i	0.578625	+	0.815594i	$0.303590\pi$
$740$		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	0.223980	−	0.974594i	$-0.428095\pi$
$757$	−20.6521	−	20.6521i	−0.750614	−	0.750614i	−0.974594	+	0.223980i	$0.928095\pi$
$758$		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	0.878260	−	0.478184i	$-0.158705\pi$
$773$	11.1233	+	11.1233i	0.400076	+	0.400076i	−0.478184	+	0.878260i	$0.658705\pi$
$774$		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	−0.562430	−	0.826845i	$-0.690133\pi$
$787$	7.41779	−	7.41779i	0.264416	−	0.264416i	0.826845	+	0.562430i	$0.190133\pi$
$788$		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	−0.549840	−	0.835270i	$-0.685311\pi$
$797$	8.05803	−	8.05803i	0.285430	−	0.285430i	0.835270	+	0.549840i	$0.185311\pi$
$798$		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	0.497018	−	0.867741i	$-0.334428\pi$
$811$	−10.5575	−	10.5575i	−0.370723	−	0.370723i	−0.867741	+	0.497018i	$0.834428\pi$
$812$		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	0.990251	−	0.139294i	$-0.0444833\pi$
$821$	24.3826	+	24.3826i	0.850957	+	0.850957i	−0.139294	+	0.990251i	$0.544483\pi$
$822$		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	0.683942	−	0.729537i	$-0.260264\pi$
$827$	−1.31121	−	1.31121i	−0.0455952	−	0.0455952i	−0.729537	+	0.683942i	$0.760264\pi$
$828$		0			0
$829$	20.8346	−	20.8346i	0.723617	−	0.723617i	−0.245723	−	0.969340i	$-0.579025\pi$
$829$	20.8346	−	20.8346i	0.723617	−	0.723617i	0.969340	+	0.245723i	$0.0790255\pi$
$830$		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	0.0254034	−	0.999677i	$-0.491913\pi$
$853$	−28.4548	−	28.4548i	−0.974274	−	0.974274i	−0.999677	+	0.0254034i	$0.991913\pi$
$854$		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	$0.0789982\pi$
$859$	35.6101	+	35.6101i	1.21500	+	1.21500i	0.245640	+	0.969361i	$0.421002\pi$
$860$		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	−0.0110076	−	0.999939i	$-0.503504\pi$
$877$	29.2864	−	29.2864i	0.988932	−	0.988932i	0.999939	+	0.0110076i	$0.00350389\pi$
$878$		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	−0.993771	−	0.111444i	$-0.964453\pi$
$883$	−26.2186	+	26.2186i	−0.882327	+	0.882327i	0.111444	+	0.993771i	$0.464453\pi$
$884$		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	0.883222	−	0.468955i	$-0.155369\pi$
$907$	12.4762	+	12.4762i	0.414267	+	0.414267i	−0.468955	+	0.883222i	$0.655369\pi$
$908$		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	−0.720164	−	0.693804i	$-0.755933\pi$
$941$	−0.808622	+	0.808622i	−0.0263603	+	0.0263603i	0.693804	+	0.720164i	$0.255933\pi$
$942$		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	−0.924484	−	0.381220i	$-0.875504\pi$
$947$	−16.7181	+	16.7181i	−0.543265	+	0.543265i	0.381220	+	0.924484i	$0.375504\pi$
$948$		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	0.890770	−	0.454454i	$-0.150166\pi$
$971$	13.5960	+	13.5960i	0.436316	+	0.436316i	−0.454454	+	0.890770i	$0.650166\pi$
$972$		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	$0.0198710\pi$
$997$	33.4837	+	33.4837i	1.06044	+	1.06044i	0.0623860	+	0.998052i	$0.480129\pi$
$998$		0			0
$999$		−	15.3039i		−	0.484193i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.l.a.481.6		16
4.3	odd	2		640.2.l.b.481.3		16
8.3	odd	2		80.2.l.a.21.2	✓	16
8.5	even	2		320.2.l.a.241.3		16
16.3	odd	4		640.2.l.b.161.3		16
16.5	even	4		320.2.l.a.81.3		16
16.11	odd	4		80.2.l.a.61.2	yes	16
16.13	even	4	inner	640.2.l.a.161.6		16
24.5	odd	2		2880.2.t.c.2161.8		16
24.11	even	2		720.2.t.c.181.7		16
32.3	odd	8		5120.2.a.s.1.3		8
32.13	even	8		5120.2.a.t.1.3		8
32.19	odd	8		5120.2.a.v.1.6		8
32.29	even	8		5120.2.a.u.1.6		8
40.3	even	4		400.2.q.h.149.5		16
40.13	odd	4		1600.2.q.g.49.3		16
40.19	odd	2		400.2.l.h.101.7		16
40.27	even	4		400.2.q.g.149.4		16
40.29	even	2		1600.2.l.i.1201.6		16
40.37	odd	4		1600.2.q.h.49.6		16
48.5	odd	4		2880.2.t.c.721.5		16
48.11	even	4		720.2.t.c.541.7		16
80.27	even	4		400.2.q.h.349.5		16
80.37	odd	4		1600.2.q.g.849.3		16
80.43	even	4		400.2.q.g.349.4		16
80.53	odd	4		1600.2.q.h.849.6		16
80.59	odd	4		400.2.l.h.301.7		16
80.69	even	4		1600.2.l.i.401.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.2	✓	16	8.3	odd	2
80.2.l.a.61.2	yes	16	16.11	odd	4
320.2.l.a.81.3		16	16.5	even	4
320.2.l.a.241.3		16	8.5	even	2
400.2.l.h.101.7		16	40.19	odd	2
400.2.l.h.301.7		16	80.59	odd	4
400.2.q.g.149.4		16	40.27	even	4
400.2.q.g.349.4		16	80.43	even	4
400.2.q.h.149.5		16	40.3	even	4
400.2.q.h.349.5		16	80.27	even	4
640.2.l.a.161.6		16	16.13	even	4	inner
640.2.l.a.481.6		16	1.1	even	1	trivial
640.2.l.b.161.3		16	16.3	odd	4
640.2.l.b.481.3		16	4.3	odd	2
720.2.t.c.181.7		16	24.11	even	2
720.2.t.c.541.7		16	48.11	even	4
1600.2.l.i.401.6		16	80.69	even	4
1600.2.l.i.1201.6		16	40.29	even	2
1600.2.q.g.49.3		16	40.13	odd	4
1600.2.q.g.849.3		16	80.37	odd	4
1600.2.q.h.49.6		16	40.37	odd	4
1600.2.q.h.849.6		16	80.53	odd	4
2880.2.t.c.721.5		16	48.5	odd	4
2880.2.t.c.2161.8		16	24.5	odd	2
5120.2.a.s.1.3		8	32.3	odd	8
5120.2.a.t.1.3		8	32.13	even	8
5120.2.a.u.1.6		8	32.29	even	8
5120.2.a.v.1.6		8	32.19	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more