LMFDB - Embedded newform 504.3.by.a.73.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,3,Mod(73,504)] 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("504.73"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	504.by (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$13.7330053238$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.126303473664.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 9x^{6} + 2x^{5} + 92x^{4} + 14x^{3} - 441x^{2} - 686x + 2401 $ x^8 - 2x^7 - 9x^6 + 2x^5 + 92x^4 + 14x^3 - 441x^2 - 686*x + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			73.1
Root			$-1.43536 + 2.22255i$ of defining polynomial
Character	$\chi$	$=$	504.73
Dual form			504.3.by.a.145.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.79369 + 4.49969i) q^{5} +(-6.97403 + 0.602461i) q^{7} +(-2.31967 + 4.01778i) q^{11} -15.7769i q^{13} +(8.01512 + 4.62753i) q^{17} +(23.8573 - 13.7740i) q^{19} +(2.82843 + 4.89898i) q^{23} +(27.9944 - 48.4878i) q^{25} +14.6969 q^{29} +(8.63587 + 4.98592i) q^{31} +(51.6425 - 36.0764i) q^{35} +(25.4246 + 44.0367i) q^{37} -70.2028i q^{41} -49.9937 q^{43} +(14.3163 - 8.26552i) q^{47} +(48.2741 - 8.40315i) q^{49} +(-4.28137 + 7.41555i) q^{53} -41.7512i q^{55} +(-85.0212 - 49.0870i) q^{59} +(-30.0000 + 17.3205i) q^{61} +(70.9913 + 122.961i) q^{65} +(-5.19046 + 8.99014i) q^{67} -93.3690 q^{71} +(107.866 + 62.2765i) q^{73} +(13.7569 - 29.4176i) q^{77} +(-55.3705 - 95.9046i) q^{79} -136.246i q^{83} -83.2899 q^{85} +(138.839 - 80.1585i) q^{89} +(9.50498 + 110.029i) q^{91} +(-123.958 + 214.701i) q^{95} -129.419i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{5} - 4 q^{7} - 14 q^{11} - 12 q^{17} + 78 q^{19} - 6 q^{25} + 4 q^{29} - 24 q^{31} + 156 q^{35} + 50 q^{37} - 20 q^{43} - 12 q^{47} + 220 q^{49} + 50 q^{53} + 186 q^{59} - 240 q^{61} + 148 q^{65}+ \cdots - 144 q^{95}+O(q^{100}) $ 8 * q - 6 * q^5 - 4 * q^7 - 14 * q^11 - 12 * q^17 + 78 * q^19 - 6 * q^25 + 4 * q^29 - 24 * q^31 + 156 * q^35 + 50 * q^37 - 20 * q^43 - 12 * q^47 + 220 * q^49 + 50 * q^53 + 186 * q^59 - 240 * q^61 + 148 * q^65 + 34 * q^67 - 424 * q^71 + 294 * q^73 - 126 * q^77 - 40 * q^79 - 232 * q^85 + 132 * q^89 - 378 * q^91 - 144 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−7.79369	+	4.49969i	−1.55874	+	0.899938i	−0.561361	+	0.827571i	$0.689722\pi$
$5$	−7.79369	+	4.49969i	−1.55874	+	0.899938i	−0.997378	+	0.0723670i	$0.976945\pi$
$6$		0			0
$7$	−6.97403	+	0.602461i	−0.996289	+	0.0860658i
$7$	−6.97403	+	0.602461i	−0.996289	+	0.0860658i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.31967	+	4.01778i	−0.210879	+	0.365253i	−0.951990	−	0.306130i	$-0.900966\pi$
$11$	−2.31967	+	4.01778i	−0.210879	+	0.365253i	0.741111	+	0.671383i	$0.234299\pi$
$12$		0			0
$13$		−	15.7769i		−	1.21361i	−0.794851	−	0.606805i	$-0.792451\pi$
$13$		−	15.7769i		−	1.21361i	0.794851	−	0.606805i	$-0.207549\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	8.01512	+	4.62753i	0.471478	+	0.272208i	0.716858	−	0.697219i	$-0.245580\pi$
$17$	8.01512	+	4.62753i	0.471478	+	0.272208i	−0.245380	+	0.969427i	$0.578913\pi$
$18$		0			0
$19$	23.8573	−	13.7740i	1.25565	−	0.724948i	0.283422	−	0.958995i	$-0.408530\pi$
$19$	23.8573	−	13.7740i	1.25565	−	0.724948i	0.972225	+	0.234047i	$0.0751969\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.82843	+	4.89898i	0.122975	+	0.212999i	0.920940	−	0.389705i	$-0.127423\pi$
$23$	2.82843	+	4.89898i	0.122975	+	0.212999i	−0.797965	+	0.602704i	$0.794090\pi$
$24$		0			0
$25$	27.9944	−	48.4878i	1.11978	−	1.93951i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	14.6969			0.506789			0.253395	−	0.967363i	$-0.418453\pi$
$29$	14.6969			0.506789			0.253395	+	0.967363i	$0.418453\pi$
$30$		0			0
$31$	8.63587	+	4.98592i	0.278577	+	0.160836i	0.632779	−	0.774333i	$-0.281914\pi$
$31$	8.63587	+	4.98592i	0.278577	+	0.160836i	−0.354202	+	0.935169i	$0.615248\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	51.6425	−	36.0764i	1.47550	−	1.03075i
$36$		0			0
$37$	25.4246	+	44.0367i	0.687151	+	1.19018i	0.972756	+	0.231832i	$0.0744721\pi$
$37$	25.4246	+	44.0367i	0.687151	+	1.19018i	−0.285605	+	0.958347i	$0.592195\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	70.2028i		−	1.71226i	−0.516758	−	0.856132i	$-0.672861\pi$
$41$		−	70.2028i		−	1.71226i	0.516758	−	0.856132i	$-0.327139\pi$
$42$		0			0
$43$	−49.9937			−1.16264			−0.581322	−	0.813674i	$-0.697464\pi$
$43$	−49.9937			−1.16264			−0.581322	+	0.813674i	$0.697464\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	14.3163	−	8.26552i	0.304602	−	0.175862i	−0.339906	−	0.940459i	$-0.610395\pi$
$47$	14.3163	−	8.26552i	0.304602	−	0.175862i	0.644508	+	0.764597i	$0.277062\pi$
$48$		0			0
$49$	48.2741	−	8.40315i	0.985185	−	0.171493i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−4.28137	+	7.41555i	−0.0807806	+	0.139916i	−0.903585	−	0.428408i	$-0.859075\pi$
$53$	−4.28137	+	7.41555i	−0.0807806	+	0.139916i	0.822805	+	0.568324i	$0.192408\pi$
$54$		0			0
$55$		−	41.7512i		−	0.759112i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−85.0212	−	49.0870i	−1.44104	−	0.831983i	−0.443118	−	0.896463i	$-0.646128\pi$
$59$	−85.0212	−	49.0870i	−1.44104	−	0.831983i	−0.997919	+	0.0644804i	$0.979461\pi$
$60$		0			0
$61$	−30.0000	+	17.3205i	−0.491803	+	0.283943i	−0.725322	−	0.688409i	$-0.758309\pi$
$61$	−30.0000	+	17.3205i	−0.491803	+	0.283943i	0.233519	+	0.972352i	$0.424976\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	70.9913	+	122.961i	1.09217	+	1.89170i
$66$		0			0
$67$	−5.19046	+	8.99014i	−0.0774696	+	0.134181i	−0.902158	−	0.431407i	$-0.858017\pi$
$67$	−5.19046	+	8.99014i	−0.0774696	+	0.134181i	0.824688	+	0.565588i	$0.191351\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−93.3690			−1.31506			−0.657528	−	0.753430i	$-0.728398\pi$
$71$	−93.3690			−1.31506			−0.657528	+	0.753430i	$0.728398\pi$
$72$		0			0
$73$	107.866	+	62.2765i	1.47762	+	0.853103i	0.999680	−	0.0252907i	$-0.00805113\pi$
$73$	107.866	+	62.2765i	1.47762	+	0.853103i	0.477938	+	0.878394i	$0.341384\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	13.7569	−	29.4176i	0.178661	−	0.382047i
$78$		0			0
$79$	−55.3705	−	95.9046i	−0.700893	−	1.21398i	−0.968153	−	0.250358i	$-0.919452\pi$
$79$	−55.3705	−	95.9046i	−0.700893	−	1.21398i	0.267261	−	0.963624i	$-0.413882\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	136.246i		−	1.64151i	−0.571277	−	0.820757i	$-0.693552\pi$
$83$		−	136.246i		−	1.64151i	0.571277	−	0.820757i	$-0.306448\pi$
$84$		0			0
$85$	−83.2899			−0.979881
$86$		0			0
$87$		0			0
$88$		0			0
$89$	138.839	−	80.1585i	1.55998	−	0.900658i	0.562728	−	0.826642i	$-0.309752\pi$
$89$	138.839	−	80.1585i	1.55998	−	0.900658i	0.997257	−	0.0740153i	$-0.0235814\pi$
$90$		0			0
$91$	9.50498	+	110.029i	0.104450	+	1.20911i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−123.958	+	214.701i	−1.30482	+	2.26001i
$96$		0			0
$97$		−	129.419i		−	1.33421i	−0.744962	−	0.667107i	$-0.767532\pi$
$97$		−	129.419i		−	1.33421i	0.744962	−	0.667107i	$-0.232468\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−32.4031	−	18.7080i	−0.320823	−	0.185227i	0.330936	−	0.943653i	$-0.392635\pi$
$101$	−32.4031	−	18.7080i	−0.320823	−	0.185227i	−0.651759	+	0.758426i	$0.725969\pi$
$102$		0			0
$103$	131.312	−	75.8130i	1.27487	−	0.736049i	0.298972	−	0.954262i	$-0.403356\pi$
$103$	131.312	−	75.8130i	1.27487	−	0.736049i	0.975901	+	0.218213i	$0.0700228\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	34.4845	+	59.7289i	0.322285	+	0.558214i	0.980959	−	0.194214i	$-0.0622157\pi$
$107$	34.4845	+	59.7289i	0.322285	+	0.558214i	−0.658674	+	0.752428i	$0.728882\pi$
$108$		0			0
$109$	29.0570	−	50.3282i	0.266578	−	0.461726i	−0.701398	−	0.712770i	$-0.747440\pi$
$109$	29.0570	−	50.3282i	0.266578	−	0.461726i	0.967976	+	0.251044i	$0.0807737\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	123.136			1.08970			0.544849	−	0.838534i	$-0.316587\pi$
$113$	123.136			1.08970			0.544849	+	0.838534i	$0.316587\pi$
$114$		0			0
$115$	−44.0878	−	25.4541i	−0.383372	−	0.221340i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−58.6856	−	27.4437i	−0.493156	−	0.230620i
$120$		0			0
$121$	49.7383	+	86.1492i	0.411060	+	0.711977i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			278.881i			2.23105i
$126$		0			0
$127$	−34.1002			−0.268505			−0.134253	−	0.990947i	$-0.542863\pi$
$127$	−34.1002			−0.268505			−0.134253	+	0.990947i	$0.542863\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−42.9691	+	24.8082i	−0.328008	+	0.189376i	−0.654956	−	0.755667i	$-0.727313\pi$
$131$	−42.9691	+	24.8082i	−0.328008	+	0.189376i	0.326948	+	0.945042i	$0.393980\pi$
$132$		0			0
$133$	−158.083	+	110.433i	−1.18859	+	0.830327i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	52.8342	−	91.5115i	0.385651	−	0.667967i	−0.606208	−	0.795306i	$-0.707310\pi$
$137$	52.8342	−	91.5115i	0.385651	−	0.667967i	0.991859	+	0.127339i	$0.0406436\pi$
$138$		0			0
$139$			108.092i			0.777644i	0.921313	+	0.388822i	$0.127118\pi$
$139$			108.092i			0.777644i	−0.921313	+	0.388822i	$0.872882\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	63.3882	+	36.5972i	0.443274	+	0.255925i
$144$		0			0
$145$	−114.543	+	66.1314i	−0.789952	+	0.456079i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−27.5987	−	47.8023i	−0.185226	−	0.320821i	0.758427	−	0.651759i	$-0.225968\pi$
$149$	−27.5987	−	47.8023i	−0.185226	−	0.320821i	−0.943653	+	0.330937i	$0.892635\pi$
$150$		0			0
$151$	54.0409	−	93.6017i	0.357887	−	0.619879i	−0.629721	−	0.776822i	$-0.716831\pi$
$151$	54.0409	−	93.6017i	0.357887	−	0.619879i	0.987608	+	0.156943i	$0.0501640\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−89.7405			−0.578971
$156$		0			0
$157$	−146.196	−	84.4060i	−0.931182	−	0.537618i	−0.0439967	−	0.999032i	$-0.514009\pi$
$157$	−146.196	−	84.4060i	−0.931182	−	0.537618i	−0.887185	+	0.461414i	$0.847342\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−22.6770	−	32.4616i	−0.140851	−	0.201625i
$162$		0			0
$163$	67.4557	+	116.837i	0.413838	+	0.716789i	0.995306	−	0.0967806i	$-0.0308545\pi$
$163$	67.4557	+	116.837i	0.413838	+	0.716789i	−0.581467	+	0.813570i	$0.697521\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			36.1722i			0.216600i	0.994118	+	0.108300i	$0.0345407\pi$
$167$			36.1722i			0.216600i	−0.994118	+	0.108300i	$0.965459\pi$
$168$		0			0
$169$	−79.9113			−0.472848
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−224.748	+	129.758i	−1.29912	+	0.750047i	−0.980252	−	0.197753i	$-0.936636\pi$
$173$	−224.748	+	129.758i	−1.29912	+	0.750047i	−0.318867	+	0.947799i	$0.603302\pi$
$174$		0			0
$175$	−166.022	+	355.021i	−0.948697	+	2.02869i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−14.9891	+	25.9618i	−0.0837378	+	0.145038i	−0.904853	−	0.425725i	$-0.860019\pi$
$179$	−14.9891	+	25.9618i	−0.0837378	+	0.145038i	0.821115	+	0.570763i	$0.193352\pi$
$180$		0			0
$181$		−	61.8216i		−	0.341556i	−0.985310	−	0.170778i	$-0.945372\pi$
$181$		−	61.8216i		−	0.341556i	0.985310	−	0.170778i	$-0.0546281\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−396.303	−	228.805i	−2.14218	−	1.23679i
$186$		0			0
$187$	−37.1848	+	21.4687i	−0.198849	+	0.114806i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−43.6857	−	75.6659i	−0.228721	−	0.396156i	0.728708	−	0.684824i	$-0.240121\pi$
$191$	−43.6857	−	75.6659i	−0.228721	−	0.396156i	−0.957429	+	0.288668i	$0.906788\pi$
$192$		0			0
$193$	−4.19168	+	7.26020i	−0.0217185	+	0.0376176i	−0.876680	−	0.481073i	$-0.840247\pi$
$193$	−4.19168	+	7.26020i	−0.0217185	+	0.0376176i	0.854962	+	0.518691i	$0.173580\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	253.870			1.28868			0.644340	−	0.764739i	$-0.277132\pi$
$197$	253.870			1.28868			0.644340	+	0.764739i	$0.277132\pi$
$198$		0			0
$199$	−179.618	−	103.702i	−0.902602	−	0.521118i	−0.0245587	−	0.999698i	$-0.507818\pi$
$199$	−179.618	−	103.702i	−0.902602	−	0.521118i	−0.878044	+	0.478581i	$0.841151\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−102.496	+	8.85429i	−0.504909	+	0.0436172i
$204$		0			0
$205$	315.891	+	547.139i	1.54093	+	2.66897i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			127.805i			0.611505i
$210$		0			0
$211$	−155.940			−0.739051			−0.369525	−	0.929221i	$-0.620480\pi$
$211$	−155.940			−0.739051			−0.369525	+	0.929221i	$0.620480\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	389.635	−	224.956i	1.81226	−	1.04631i
$216$		0			0
$217$	−63.2306	−	29.5692i	−0.291385	−	0.136264i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	73.0082	−	126.454i	0.330354	−	0.572190i
$222$		0			0
$223$			241.512i			1.08301i	0.840696	+	0.541507i	$0.182146\pi$
$223$			241.512i			1.08301i	−0.840696	+	0.541507i	$0.817854\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	123.555	+	71.3342i	0.544293	+	0.314248i	0.746817	−	0.665030i	$-0.231581\pi$
$227$	123.555	+	71.3342i	0.544293	+	0.314248i	−0.202524	+	0.979277i	$0.564914\pi$
$228$		0			0
$229$	279.606	−	161.431i	1.22099	−	0.704938i	0.255859	−	0.966714i	$-0.417642\pi$
$229$	279.606	−	161.431i	1.22099	−	0.704938i	0.965129	+	0.261777i	$0.0843084\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	32.3671	+	56.0615i	0.138915	+	0.240607i	0.927086	−	0.374849i	$-0.122305\pi$
$233$	32.3671	+	56.0615i	0.138915	+	0.240607i	−0.788171	+	0.615456i	$0.788972\pi$
$234$		0			0
$235$	−74.3846	+	128.838i	−0.316530	+	0.548246i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	81.7863			0.342202			0.171101	−	0.985253i	$-0.445268\pi$
$239$	81.7863			0.342202			0.171101	+	0.985253i	$0.445268\pi$
$240$		0			0
$241$	27.7057	+	15.9959i	0.114961	+	0.0663730i	0.556378	−	0.830929i	$-0.312191\pi$
$241$	27.7057	+	15.9959i	0.114961	+	0.0663730i	−0.441417	+	0.897302i	$0.645524\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−338.422	+	282.710i	−1.38131	+	1.15392i
$246$		0			0
$247$	−217.312	−	376.395i	−0.879804	−	1.52387i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	251.044i		−	1.00018i	−0.865975	−	0.500088i	$-0.833301\pi$
$251$		−	251.044i		−	1.00018i	0.865975	−	0.500088i	$-0.166699\pi$
$252$		0			0
$253$	−26.2440			−0.103731
$254$		0			0
$255$		0			0
$256$		0			0
$257$	117.871	−	68.0529i	0.458642	−	0.264797i	−0.252831	−	0.967510i	$-0.581362\pi$
$257$	117.871	−	68.0529i	0.458642	−	0.264797i	0.711473	+	0.702713i	$0.248028\pi$
$258$		0			0
$259$	−203.842	−	291.795i	−0.787035	−	1.12662i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	78.5656	−	136.080i	0.298728	−	0.517413i	−0.677117	−	0.735875i	$-0.736771\pi$
$263$	78.5656	−	136.080i	0.298728	−	0.517413i	0.975845	+	0.218463i	$0.0701042\pi$
$264$		0			0
$265$		−	77.0594i		−	0.290790i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−40.5367	−	23.4039i	−0.150694	−	0.0870032i	0.422757	−	0.906243i	$-0.361062\pi$
$269$	−40.5367	−	23.4039i	−0.150694	−	0.0870032i	−0.573451	+	0.819240i	$0.694396\pi$
$270$		0			0
$271$	306.591	−	177.010i	1.13133	−	0.653175i	0.187062	−	0.982348i	$-0.440103\pi$
$271$	306.591	−	177.010i	1.13133	−	0.653175i	0.944270	+	0.329173i	$0.106770\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	129.876	+	224.951i	0.472275	+	0.818004i
$276$		0			0
$277$	63.8828	−	110.648i	0.230624	−	0.399452i	−0.727368	−	0.686248i	$-0.759257\pi$
$277$	63.8828	−	110.648i	0.230624	−	0.399452i	0.957992	+	0.286795i	$0.0925900\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	23.9203			0.0851256			0.0425628	−	0.999094i	$-0.486448\pi$
$281$	23.9203			0.0851256			0.0425628	+	0.999094i	$0.486448\pi$
$282$		0			0
$283$	94.6113	+	54.6239i	0.334316	+	0.193017i	0.657756	−	0.753232i	$-0.271506\pi$
$283$	94.6113	+	54.6239i	0.334316	+	0.193017i	−0.323440	+	0.946249i	$0.604839\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	42.2944	+	489.596i	0.147367	+	1.70591i
$288$		0			0
$289$	−101.672	−	176.101i	−0.351806	−	0.609346i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			233.340i			0.796384i	0.917302	+	0.398192i	$0.130362\pi$
$293$			233.340i			0.796384i	−0.917302	+	0.398192i	$0.869638\pi$
$294$		0			0
$295$	883.505			2.99493
$296$		0			0
$297$		0			0
$298$		0			0
$299$	77.2908	−	44.6239i	0.258498	−	0.149244i
$300$		0			0
$301$	348.657	−	30.1192i	1.15833	−	0.100064i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	155.874	−	269.981i	0.511062	−	0.885185i
$306$		0			0
$307$		−	355.416i		−	1.15771i	−0.815432	−	0.578854i	$-0.803500\pi$
$307$		−	355.416i		−	1.15771i	0.815432	−	0.578854i	$-0.196500\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−230.408	−	133.026i	−0.740863	−	0.427737i	0.0815201	−	0.996672i	$-0.474023\pi$
$311$	−230.408	−	133.026i	−0.740863	−	0.427737i	−0.822383	+	0.568934i	$0.807356\pi$
$312$		0			0
$313$	221.913	−	128.122i	0.708988	−	0.409335i	−0.101698	−	0.994815i	$-0.532428\pi$
$313$	221.913	−	128.122i	0.708988	−	0.409335i	0.810686	+	0.585481i	$0.199094\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−178.699	−	309.516i	−0.563719	−	0.976390i	−0.997168	−	0.0752120i	$-0.976037\pi$
$317$	−178.699	−	309.516i	−0.563719	−	0.976390i	0.433448	−	0.901178i	$-0.357297\pi$
$318$		0			0
$319$	−34.0919	+	59.0489i	−0.106871	+	0.185106i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	254.959			0.789346
$324$		0			0
$325$	−764.988	−	441.666i	−2.35381	−	1.35897i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−94.8626	+	66.2690i	−0.288336	+	0.201425i
$330$		0			0
$331$	236.800	+	410.149i	0.715407	+	1.23912i	0.962802	+	0.270206i	$0.0870919\pi$
$331$	236.800	+	410.149i	0.715407	+	1.23912i	−0.247396	+	0.968915i	$0.579575\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		−	93.4219i		−	0.278871i
$336$		0			0
$337$	−401.285			−1.19076			−0.595378	−	0.803446i	$-0.702998\pi$
$337$	−401.285			−1.19076			−0.595378	+	0.803446i	$0.702998\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−40.0647	+	23.1314i	−0.117492	+	0.0678339i
$342$		0			0
$343$	−331.602	+	87.6870i	−0.966770	+	0.255647i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−78.0363	+	135.163i	−0.224889	+	0.389518i	−0.956286	−	0.292433i	$-0.905535\pi$
$347$	−78.0363	+	135.163i	−0.224889	+	0.389518i	0.731397	+	0.681951i	$0.238868\pi$
$348$		0			0
$349$			123.443i			0.353706i	0.984237	+	0.176853i	$0.0565917\pi$
$349$			123.443i			0.353706i	−0.984237	+	0.176853i	$0.943408\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	94.5733	+	54.6019i	0.267913	+	0.154680i	0.627939	−	0.778263i	$-0.283899\pi$
$353$	94.5733	+	54.6019i	0.267913	+	0.154680i	−0.360026	+	0.932942i	$0.617232\pi$
$354$		0			0
$355$	727.689	−	420.132i	2.04983	−	1.18347i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	147.053	+	254.704i	0.409619	+	0.709481i	0.994847	−	0.101388i	$-0.0323283\pi$
$359$	147.053	+	254.704i	0.409619	+	0.709481i	−0.585228	+	0.810869i	$0.698995\pi$
$360$		0			0
$361$	198.947	−	344.587i	0.551100	−	0.954534i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1120.90			−3.07096
$366$		0			0
$367$	−237.563	−	137.157i	−0.647311	−	0.373725i	0.140114	−	0.990135i	$-0.455253\pi$
$367$	−237.563	−	137.157i	−0.647311	−	0.373725i	−0.787425	+	0.616410i	$0.788586\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	25.3908	−	54.2956i	0.0684389	−	0.146349i
$372$		0			0
$373$	−41.8256	−	72.4440i	−0.112133	−	0.194220i	0.804497	−	0.593957i	$-0.202435\pi$
$373$	−41.8256	−	72.4440i	−0.112133	−	0.194220i	−0.916630	+	0.399737i	$0.869102\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	231.872i		−	0.615044i
$378$		0			0
$379$	77.2239			0.203757			0.101878	−	0.994797i	$-0.467515\pi$
$379$	77.2239			0.203757			0.101878	+	0.994797i	$0.467515\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.16581	+	1.82778i	−0.00826584	+	0.00477228i	−0.504127	−	0.863629i	$-0.668186\pi$
$383$	−3.16581	+	1.82778i	−0.00826584	+	0.00477228i	0.495861	+	0.868402i	$0.334852\pi$
$384$		0			0
$385$	25.1534	+	291.174i	0.0653336	+	0.756295i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	143.199	−	248.028i	0.368120	−	0.637603i	−0.621151	−	0.783691i	$-0.713335\pi$
$389$	143.199	−	248.028i	0.368120	−	0.637603i	0.989272	+	0.146087i	$0.0466681\pi$
$390$		0			0
$391$			52.3546i			0.133899i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	863.082	+	498.301i	2.18502	+	1.26152i
$396$		0			0
$397$	172.816	−	99.7752i	0.435304	−	0.251323i	−0.266300	−	0.963890i	$-0.585801\pi$
$397$	172.816	−	99.7752i	0.435304	−	0.251323i	0.701604	+	0.712567i	$0.252468\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−259.828	−	450.036i	−0.647951	−	1.12228i	−0.983611	−	0.180301i	$-0.942293\pi$
$401$	−259.828	−	450.036i	−0.647951	−	1.12228i	0.335661	−	0.941983i	$-0.391041\pi$
$402$		0			0
$403$	78.6625	−	136.247i	0.195192	−	0.338083i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−235.906			−0.579622
$408$		0			0
$409$	−484.787	−	279.892i	−1.18530	−	0.684332i	−0.228064	−	0.973646i	$-0.573239\pi$
$409$	−484.787	−	279.892i	−1.18530	−	0.684332i	−0.957234	+	0.289314i	$0.906573\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	622.513	+	291.112i	1.50730	+	0.704872i
$414$		0			0
$415$	613.064	+	1061.86i	1.47726	+	2.55869i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	659.099i		−	1.57303i	−0.617572	−	0.786514i	$-0.711884\pi$
$419$		−	659.099i		−	1.57303i	0.617572	−	0.786514i	$-0.288116\pi$
$420$		0			0
$421$	−90.2042			−0.214262			−0.107131	−	0.994245i	$-0.534166\pi$
$421$	−90.2042			−0.214262			−0.107131	+	0.994245i	$0.534166\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	448.758	−	259.090i	1.05590	−	0.609624i
$426$		0			0
$427$	198.786	−	138.867i	0.465541	−	0.325217i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	325.863	−	564.411i	0.756063	−	1.30954i	−0.188782	−	0.982019i	$-0.560454\pi$
$431$	325.863	−	564.411i	0.756063	−	1.30954i	0.944844	−	0.327520i	$-0.106213\pi$
$432$		0			0
$433$		−	320.857i		−	0.741008i	−0.928831	−	0.370504i	$-0.879185\pi$
$433$		−	320.857i		−	0.741008i	0.928831	−	0.370504i	$-0.120815\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	134.957	+	77.9176i	0.308827	+	0.178301i
$438$		0			0
$439$	−289.465	+	167.123i	−0.659375	+	0.380690i	−0.792039	−	0.610471i	$-0.790980\pi$
$439$	−289.465	+	167.123i	−0.659375	+	0.380690i	0.132664	+	0.991161i	$0.457647\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	56.2101	+	97.3587i	0.126885	+	0.219771i	0.922468	−	0.386073i	$-0.126169\pi$
$443$	56.2101	+	97.3587i	0.126885	+	0.219771i	−0.795583	+	0.605844i	$0.792835\pi$
$444$		0			0
$445$	−721.377	+	1249.46i	−1.62107	+	2.80778i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	496.635			1.10609			0.553045	−	0.833151i	$-0.313466\pi$
$449$	496.635			1.10609			0.553045	+	0.833151i	$0.313466\pi$
$450$		0			0
$451$	282.060	+	162.847i	0.625409	+	0.361080i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−569.174	−	814.760i	−1.25093	−	1.79068i
$456$		0			0
$457$	394.112	+	682.622i	0.862390	+	1.49370i	0.869616	+	0.493729i	$0.164366\pi$
$457$	394.112	+	682.622i	0.862390	+	1.49370i	−0.00722631	+	0.999974i	$0.502300\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	422.078i		−	0.915570i	−0.889063	−	0.457785i	$-0.848643\pi$
$461$		−	422.078i		−	0.915570i	0.889063	−	0.457785i	$-0.151357\pi$
$462$		0			0
$463$	−7.47288			−0.0161401			−0.00807006	−	0.999967i	$-0.502569\pi$
$463$	−7.47288			−0.0161401			−0.00807006	+	0.999967i	$0.502569\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−375.896	+	217.024i	−0.804916	+	0.464719i	−0.845187	−	0.534470i	$-0.820511\pi$
$467$	−375.896	+	217.024i	−0.804916	+	0.464719i	0.0402710	+	0.999189i	$0.487178\pi$
$468$		0			0
$469$	30.7822	−	65.8245i	0.0656337	−	0.140351i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	115.969	−	200.864i	0.245177	−	0.424659i
$474$		0			0
$475$		−	1542.38i		−	3.24712i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	466.274	+	269.204i	0.973433	+	0.562012i	0.900281	−	0.435309i	$-0.143361\pi$
$479$	466.274	+	269.204i	0.973433	+	0.562012i	0.0731516	+	0.997321i	$0.476694\pi$
$480$		0			0
$481$	694.763	−	401.122i	1.44441	−	0.833933i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	582.344	+	1008.65i	1.20071	+	2.07969i
$486$		0			0
$487$	−31.4524	+	54.4772i	−0.0645841	+	0.111863i	−0.896509	−	0.443025i	$-0.853905\pi$
$487$	−31.4524	+	54.4772i	−0.0645841	+	0.111863i	0.831925	+	0.554888i	$0.187239\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−824.426			−1.67908			−0.839538	−	0.543301i	$-0.817174\pi$
$491$	−824.426			−1.67908			−0.839538	+	0.543301i	$0.817174\pi$
$492$		0			0
$493$	117.797	+	68.0103i	0.238940	+	0.137952i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	651.158	−	56.2512i	1.31018	−	0.113181i
$498$		0			0
$499$	122.027	+	211.358i	0.244544	+	0.423562i	0.962003	−	0.273038i	$-0.0880285\pi$
$499$	122.027	+	211.358i	0.244544	+	0.423562i	−0.717459	+	0.696600i	$0.754695\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	152.196i		−	0.302577i	−0.988490	−	0.151289i	$-0.951658\pi$
$503$		−	152.196i		−	0.302577i	0.988490	−	0.151289i	$-0.0483423\pi$
$504$		0			0
$505$	336.720			0.666773
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−612.043	+	353.363i	−1.20244	+	0.694231i	−0.961098	−	0.276209i	$-0.910922\pi$
$509$	−612.043	+	353.363i	−1.20244	+	0.694231i	−0.241345	+	0.970439i	$0.577589\pi$
$510$		0			0
$511$	−789.780	−	369.333i	−1.54556	−	0.722765i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−682.270	+	1181.73i	−1.32480	+	2.29461i
$516$		0			0
$517$			76.6931i			0.148342i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−769.852	−	444.474i	−1.47764	−	0.853117i	−0.477962	−	0.878381i	$-0.658624\pi$
$521$	−769.852	−	444.474i	−1.47764	−	0.853117i	−0.999681	+	0.0252634i	$0.991958\pi$
$522$		0			0
$523$	−814.987	+	470.533i	−1.55829	+	0.899681i	−0.560873	+	0.827902i	$0.689534\pi$
$523$	−814.987	+	470.533i	−1.55829	+	0.899681i	−0.997421	+	0.0717789i	$0.977132\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	46.1450	+	79.9256i	0.0875618	+	0.151661i
$528$		0			0
$529$	248.500	−	430.415i	0.469754	−	0.813638i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1107.58			−2.07802
$534$		0			0
$535$	−537.523	−	310.339i	−1.00472	−	0.580073i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−78.2178	+	213.447i	−0.145116	+	0.396006i
$540$		0			0
$541$	−265.064	−	459.104i	−0.489951	−	0.848621i	0.509982	−	0.860185i	$-0.329652\pi$
$541$	−265.064	−	459.104i	−0.489951	−	0.848621i	−0.999933	+	0.0115644i	$0.996319\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$			522.990i			0.959614i
$546$		0			0
$547$	−1063.97			−1.94510			−0.972548	−	0.232701i	$-0.925244\pi$
$547$	−1063.97			−1.94510			−0.972548	+	0.232701i	$0.925244\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	350.628	−	202.435i	0.636348	−	0.367396i
$552$		0			0
$553$	443.934	+	635.482i	0.802774	+	1.14915i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−11.8294	+	20.4892i	−0.0212378	+	0.0367849i	−0.876449	−	0.481495i	$-0.840094\pi$
$557$	−11.8294	+	20.4892i	−0.0212378	+	0.0367849i	0.855211	+	0.518280i	$0.173427\pi$
$558$		0			0
$559$			788.746i			1.41100i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−53.2634	−	30.7516i	−0.0946064	−	0.0546210i	0.451950	−	0.892043i	$-0.350728\pi$
$563$	−53.2634	−	30.7516i	−0.0946064	−	0.0546210i	−0.546557	+	0.837422i	$0.684062\pi$
$564$		0			0
$565$	−959.682	+	554.073i	−1.69855	+	0.980660i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	340.735	+	590.171i	0.598832	+	1.03721i	0.992994	+	0.118166i	$0.0377016\pi$
$569$	340.735	+	590.171i	0.598832	+	1.03721i	−0.394162	+	0.919041i	$0.628965\pi$
$570$		0			0
$571$	−182.474	+	316.054i	−0.319569	+	0.553509i	−0.980398	−	0.197027i	$-0.936871\pi$
$571$	−182.474	+	316.054i	−0.319569	+	0.553509i	0.660829	+	0.750536i	$0.270205\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	316.721			0.550819
$576$		0			0
$577$	272.457	+	157.303i	0.472196	+	0.272622i	0.717158	−	0.696910i	$-0.245442\pi$
$577$	272.457	+	157.303i	0.472196	+	0.272622i	−0.244963	+	0.969533i	$0.578776\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	82.0827	+	950.181i	0.141278	+	1.63542i
$582$		0			0
$583$	−19.8627	−	34.4032i	−0.0340699	−	0.0590107i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	190.516i		−	0.324560i	−0.986745	−	0.162280i	$-0.948115\pi$
$587$		−	190.516i		−	0.324560i	0.986745	−	0.162280i	$-0.0518847\pi$
$588$		0			0
$589$	274.705			0.466392
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−115.462	+	66.6622i	−0.194709	+	0.112415i	−0.594185	−	0.804328i	$-0.702525\pi$
$593$	−115.462	+	66.6622i	−0.194709	+	0.112415i	0.399476	+	0.916744i	$0.369192\pi$
$594$		0			0
$595$	580.866	−	50.1789i	0.976245	−	0.0843342i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−136.021	+	235.595i	−0.227080	+	0.393313i	−0.956941	−	0.290281i	$-0.906251\pi$
$599$	−136.021	+	235.595i	−0.227080	+	0.393313i	0.729862	+	0.683595i	$0.239584\pi$
$600$		0			0
$601$			661.949i			1.10141i	0.834699	+	0.550706i	$0.185642\pi$
$601$			661.949i			1.10141i	−0.834699	+	0.550706i	$0.814358\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−775.290	−	447.614i	−1.28147	−	0.739858i
$606$		0			0
$607$	63.0330	−	36.3921i	0.103844	−	0.0599541i	−0.447179	−	0.894445i	$-0.647571\pi$
$607$	63.0330	−	36.3921i	0.103844	−	0.0599541i	0.551022	+	0.834491i	$0.314238\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−130.404	−	225.867i	−0.213428	−	0.369668i
$612$		0			0
$613$	46.2649	−	80.1332i	0.0754730	−	0.130723i	−0.825819	−	0.563935i	$-0.809287\pi$
$613$	46.2649	−	80.1332i	0.0754730	−	0.130723i	0.901292	+	0.433212i	$0.142620\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−128.000			−0.207455			−0.103728	−	0.994606i	$-0.533077\pi$
$617$	−128.000			−0.207455			−0.103728	+	0.994606i	$0.533077\pi$
$618$		0			0
$619$	−210.386	−	121.467i	−0.339881	−	0.196230i	0.320338	−	0.947303i	$-0.396203\pi$
$619$	−210.386	−	121.467i	−0.339881	−	0.196230i	−0.660219	+	0.751073i	$0.729537\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−919.972	+	642.673i	−1.47668	+	1.03158i
$624$		0			0
$625$	−555.017	−	961.317i	−0.888027	−	1.53811i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			470.612i			0.748191i
$630$		0			0
$631$	−179.943			−0.285171			−0.142586	−	0.989782i	$-0.545542\pi$
$631$	−179.943			−0.285171			−0.142586	+	0.989782i	$0.545542\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	265.766	−	153.440i	0.418530	−	0.241638i
$636$		0			0
$637$	−132.576	−	761.616i	−0.208125	−	1.19563i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−130.466	+	225.974i	−0.203535	+	0.352533i	−0.949665	−	0.313267i	$-0.898577\pi$
$641$	−130.466	+	225.974i	−0.203535	+	0.352533i	0.746130	+	0.665801i	$0.231910\pi$
$642$		0			0
$643$			845.112i			1.31433i	0.753748	+	0.657163i	$0.228244\pi$
$643$			845.112i			1.31433i	−0.753748	+	0.657163i	$0.771756\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	42.5096	+	24.5429i	0.0657026	+	0.0379334i	0.532491	−	0.846435i	$-0.321256\pi$
$647$	42.5096	+	24.5429i	0.0657026	+	0.0379334i	−0.466789	+	0.884369i	$0.654589\pi$
$648$		0			0
$649$	394.442	−	227.731i	0.607768	−	0.350895i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	268.628	+	465.278i	0.411376	+	0.712523i	0.995040	−	0.0994713i	$-0.0317152\pi$
$653$	268.628	+	465.278i	0.411376	+	0.712523i	−0.583665	+	0.811995i	$0.698382\pi$
$654$		0			0
$655$	223.258	−	386.695i	0.340853	−	0.590374i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	687.009			1.04250			0.521251	−	0.853403i	$-0.325465\pi$
$659$	687.009			1.04250			0.521251	+	0.853403i	$0.325465\pi$
$660$		0			0
$661$	15.1793	+	8.76380i	0.0229642	+	0.0132584i	0.511438	−	0.859320i	$-0.329113\pi$
$661$	15.1793	+	8.76380i	0.0229642	+	0.0132584i	−0.488474	+	0.872578i	$0.662446\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	735.135	−	1572.01i	1.10547	−	2.36392i
$666$		0			0
$667$	41.5691	+	71.9997i	0.0623224	+	0.107946i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		−	160.711i		−	0.239510i
$672$		0			0
$673$	−238.854			−0.354909			−0.177455	−	0.984129i	$-0.556786\pi$
$673$	−238.854			−0.354909			−0.177455	+	0.984129i	$0.556786\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	598.044	−	345.281i	0.883374	−	0.510016i	0.0116048	−	0.999933i	$-0.496306\pi$
$677$	598.044	−	345.281i	0.883374	−	0.510016i	0.871769	+	0.489916i	$0.162973\pi$
$678$		0			0
$679$	77.9697	+	902.570i	0.114830	+	1.32926i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	363.772	−	630.072i	0.532609	−	0.922507i	−0.466665	−	0.884434i	$-0.654545\pi$
$683$	363.772	−	630.072i	0.532609	−	0.922507i	0.999275	−	0.0380728i	$-0.0121219\pi$
$684$		0			0
$685$			950.950i			1.38825i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	116.995	+	67.5469i	0.169804	+	0.0980361i
$690$		0			0
$691$	−258.027	+	148.972i	−0.373412	+	0.215589i	−0.674948	−	0.737865i	$-0.735834\pi$
$691$	−258.027	+	148.972i	−0.373412	+	0.215589i	0.301536	+	0.953455i	$0.402501\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−486.383	−	842.439i	−0.699831	−	1.21214i
$696$		0			0
$697$	324.866	−	562.684i	0.466091	−	0.807294i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	621.118			0.886046			0.443023	−	0.896510i	$-0.353906\pi$
$701$	621.118			0.886046			0.443023	+	0.896510i	$0.353906\pi$
$702$		0			0
$703$	1213.12	+	700.397i	1.72564	+	0.996297i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	237.251	+	110.948i	0.335574	+	0.156928i
$708$		0			0
$709$	214.245	+	371.083i	0.302179	+	0.523390i	0.976629	−	0.214931i	$-0.0689526\pi$
$709$	214.245	+	371.083i	0.302179	+	0.523390i	−0.674450	+	0.738320i	$0.735619\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			56.4093i			0.0791154i
$714$		0			0
$715$	−658.705			−0.921265
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−149.222	+	86.1534i	−0.207541	+	0.119824i	−0.600168	−	0.799874i	$-0.704900\pi$
$719$	−149.222	+	86.1534i	−0.207541	+	0.119824i	0.392627	+	0.919698i	$0.371566\pi$
$720$		0			0
$721$	−870.099	+	607.832i	−1.20679	+	0.843040i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	411.431	−	712.620i	0.567491	−	0.982923i
$726$		0			0
$727$		−	1320.20i		−	1.81596i	−0.419010	−	0.907981i	$-0.637623\pi$
$727$		−	1320.20i		−	1.81596i	0.419010	−	0.907981i	$-0.362377\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−400.705	−	231.347i	−0.548161	−	0.316481i
$732$		0			0
$733$	484.152	−	279.525i	0.660508	−	0.381344i	−0.131963	−	0.991255i	$-0.542128\pi$
$733$	484.152	−	279.525i	0.660508	−	0.381344i	0.792470	+	0.609910i	$0.208795\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−24.0803	−	41.7083i	−0.0326734	−	0.0565920i
$738$		0			0
$739$	−571.142	+	989.248i	−0.772858	+	1.33863i	0.163132	+	0.986604i	$0.447840\pi$
$739$	−571.142	+	989.248i	−0.772858	+	1.33863i	−0.935990	+	0.352026i	$0.885493\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1392.95			1.87477			0.937383	−	0.348301i	$-0.113241\pi$
$743$	1392.95			1.87477			0.937383	+	0.348301i	$0.113241\pi$
$744$		0			0
$745$	430.192	+	248.371i	0.577438	+	0.333384i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−276.480	−	395.776i	−0.369132	−	0.528405i
$750$		0			0
$751$	−695.732	−	1205.04i	−0.926408	−	1.60459i	−0.789281	−	0.614032i	$-0.789547\pi$
$751$	−695.732	−	1205.04i	−0.926408	−	1.60459i	−0.137127	−	0.990554i	$-0.543787\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			972.670i			1.28830i
$756$		0			0
$757$	139.507			0.184289			0.0921446	−	0.995746i	$-0.470628\pi$
$757$	139.507			0.184289			0.0921446	+	0.995746i	$0.470628\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−643.482	+	371.514i	−0.845574	+	0.488192i	−0.859155	−	0.511716i	$-0.829010\pi$
$761$	−643.482	+	371.514i	−0.845574	+	0.488192i	0.0135813	+	0.999908i	$0.495677\pi$
$762$		0			0
$763$	−172.323	+	368.496i	−0.225850	+	0.482956i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−774.442	+	1341.37i	−1.00970	+	1.74886i
$768$		0			0
$769$			157.528i			0.204848i	0.994741	+	0.102424i	$0.0326598\pi$
$769$			157.528i			0.204848i	−0.994741	+	0.102424i	$0.967340\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	355.723	+	205.377i	0.460184	+	0.265688i	0.712122	−	0.702056i	$-0.247734\pi$
$773$	355.723	+	205.377i	0.460184	+	0.265688i	−0.251937	+	0.967744i	$0.581068\pi$
$774$		0			0
$775$	483.513	−	279.156i	0.623888	−	0.360202i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−966.974	−	1674.85i	−1.24130	−	2.15000i
$780$		0			0
$781$	216.585	−	375.136i	0.277318	−	0.480328i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1519.20			1.93529
$786$		0			0
$787$	937.533	+	541.285i	1.19127	+	0.687783i	0.958596	−	0.284771i	$-0.0919174\pi$
$787$	937.533	+	541.285i	1.19127	+	0.687783i	0.232679	+	0.972554i	$0.425251\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−858.752	+	74.1845i	−1.08565	+	0.0937857i
$792$		0			0
$793$	273.264	+	473.308i	0.344596	+	0.596857i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	569.370i		−	0.714392i	−0.934029	−	0.357196i	$-0.883733\pi$
$797$		−	569.370i		−	0.714392i	0.934029	−	0.357196i	$-0.116267\pi$
$798$		0			0
$799$	152.996			0.191484
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−500.427	+	288.922i	−0.623197	+	0.359803i
$804$		0			0
$805$	322.805	+	150.956i	0.400999	+	0.187523i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−539.238	+	933.987i	−0.666548	+	1.15450i	0.312315	+	0.949979i	$0.398896\pi$
$809$	−539.238	+	933.987i	−0.666548	+	1.15450i	−0.978863	+	0.204517i	$0.934438\pi$
$810$		0			0
$811$		−	1159.86i		−	1.43016i	−0.699041	−	0.715082i	$-0.746390\pi$
$811$		−	1159.86i		−	1.43016i	0.699041	−	0.715082i	$-0.253610\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−1051.46	−	607.059i	−1.29013	−	0.744858i
$816$		0			0
$817$	−1192.71	+	688.614i	−1.45987	+	0.842857i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−418.519	−	724.896i	−0.509767	−	0.882943i	−0.999936	−	0.0113155i	$-0.996398\pi$
$821$	−418.519	−	724.896i	−0.509767	−	0.882943i	0.490168	−	0.871628i	$-0.336935\pi$
$822$		0			0
$823$	−272.266	+	471.578i	−0.330821	+	0.572999i	−0.982673	−	0.185347i	$-0.940659\pi$
$823$	−272.266	+	471.578i	−0.330821	+	0.572999i	0.651852	+	0.758346i	$0.273992\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−888.956			−1.07492			−0.537458	−	0.843290i	$-0.680615\pi$
$827$	−888.956			−1.07492			−0.537458	+	0.843290i	$0.680615\pi$
$828$		0			0
$829$	−776.384	−	448.246i	−0.936531	−	0.540707i	−0.0476600	−	0.998864i	$-0.515176\pi$
$829$	−776.384	−	448.246i	−0.936531	−	0.540707i	−0.888871	+	0.458157i	$0.848510\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	425.808	+	156.038i	0.511175	+	0.187320i
$834$		0			0
$835$	−162.764	−	281.915i	−0.194927	−	0.337623i
$836$		0			0
$837$		0			0
$838$		0			0
$839$			183.658i			0.218901i	0.993992	+	0.109450i	$0.0349091\pi$
$839$			183.658i			0.218901i	−0.993992	+	0.109450i	$0.965091\pi$
$840$		0			0
$841$	−625.002			−0.743165
$842$		0			0
$843$		0			0
$844$		0			0
$845$	622.804	−	359.576i	0.737046	−	0.425534i
$846$		0			0
$847$	−398.778	−	570.842i	−0.470812	−	0.673957i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−143.823	+	249.109i	−0.169005	+	0.292725i
$852$		0			0
$853$			1013.43i			1.18808i	0.804435	+	0.594041i	$0.202468\pi$
$853$			1013.43i			1.18808i	−0.804435	+	0.594041i	$0.797532\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	361.130	+	208.498i	0.421388	+	0.243289i	0.695671	−	0.718360i	$-0.255107\pi$
$857$	361.130	+	208.498i	0.421388	+	0.243289i	−0.274283	+	0.961649i	$0.588440\pi$
$858$		0			0
$859$	440.723	−	254.451i	0.513065	−	0.296218i	−0.221028	−	0.975267i	$-0.570941\pi$
$859$	440.723	−	254.451i	0.513065	−	0.296218i	0.734092	+	0.679049i	$0.237608\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	147.576	+	255.610i	0.171004	+	0.296188i	0.938771	−	0.344541i	$-0.111966\pi$
$863$	147.576	+	255.610i	0.171004	+	0.296188i	−0.767767	+	0.640729i	$0.778632\pi$
$864$		0			0
$865$	1167.74	−	2022.59i	1.34999	−	2.33825i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	513.765			0.591214
$870$		0			0
$871$	141.837	+	81.8895i	0.162844	+	0.0940178i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−168.015	−	1944.92i	−0.192017	−	2.22277i
$876$		0			0
$877$	−154.304	−	267.262i	−0.175945	−	0.304746i	0.764543	−	0.644573i	$-0.222965\pi$
$877$	−154.304	−	267.262i	−0.175945	−	0.304746i	−0.940488	+	0.339827i	$0.889631\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			1262.47i			1.43300i	0.697589	+	0.716499i	$0.254256\pi$
$881$			1262.47i			1.43300i	−0.697589	+	0.716499i	$0.745744\pi$
$882$		0			0
$883$	441.944			0.500502			0.250251	−	0.968181i	$-0.419487\pi$
$883$	441.944			0.500502			0.250251	+	0.968181i	$0.419487\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	196.588	−	113.500i	0.221633	−	0.127960i	−0.385073	−	0.922886i	$-0.625824\pi$
$887$	196.588	−	113.500i	0.221633	−	0.127960i	0.606706	+	0.794926i	$0.292490\pi$
$888$		0			0
$889$	237.816	−	20.5440i	0.267509	−	0.0231091i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	227.699	−	394.386i	0.254982	−	0.441642i
$894$		0			0
$895$		−	269.785i		−	0.301435i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	126.920	+	73.2775i	0.141180	+	0.0815100i
$900$		0			0
$901$	−68.6314	+	39.6244i	−0.0761725	+	0.0439782i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	278.178	+	481.819i	0.307379	+	0.532396i
$906$		0			0
$907$	656.392	−	1136.90i	0.723695	−	1.25348i	−0.235814	−	0.971798i	$-0.575775\pi$
$907$	656.392	−	1136.90i	0.723695	−	1.25348i	0.959509	−	0.281679i	$-0.0908912\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1305.51			1.43305			0.716527	−	0.697560i	$-0.245731\pi$
$911$	1305.51			1.43305			0.716527	+	0.697560i	$0.245731\pi$
$912$		0			0
$913$	547.406	+	316.045i	0.599568	+	0.346161i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	284.721	−	198.900i	0.310492	−	0.216903i
$918$		0			0
$919$	−697.970	−	1208.92i	−0.759489	−	1.31547i	−0.943112	−	0.332476i	$-0.892116\pi$
$919$	−697.970	−	1208.92i	−0.759489	−	1.31547i	0.183623	−	0.982997i	$-0.441217\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			1473.08i			1.59596i
$924$		0			0
$925$	2846.99			3.07782
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−735.473	+	424.625i	−0.791682	+	0.457078i	−0.840554	−	0.541727i	$-0.817771\pi$
$929$	−735.473	+	424.625i	−0.791682	+	0.457078i	0.0488721	+	0.998805i	$0.484437\pi$
$930$		0			0
$931$	1035.94	−	865.405i	1.11272	−	0.929543i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	193.205	−	334.641i	0.206636	−	0.357904i
$936$		0			0
$937$		−	522.446i		−	0.557573i	−0.960353	−	0.278787i	$-0.910068\pi$
$937$		−	522.446i		−	0.557573i	0.960353	−	0.278787i	$-0.0899322\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1114.74	+	643.596i	1.18463	+	0.683949i	0.957082	−	0.289817i	$-0.0935944\pi$
$941$	1114.74	+	643.596i	1.18463	+	0.683949i	0.227552	+	0.973766i	$0.426928\pi$
$942$		0			0
$943$	343.922	−	198.563i	0.364711	−	0.210566i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	126.835	+	219.685i	0.133934	+	0.231980i	0.925190	−	0.379505i	$-0.123906\pi$
$947$	126.835	+	219.685i	0.133934	+	0.231980i	−0.791256	+	0.611485i	$0.790572\pi$
$948$		0			0
$949$	982.532	−	1701.80i	1.03533	−	1.79325i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−338.890			−0.355603			−0.177801	−	0.984066i	$-0.556898\pi$
$953$	−338.890			−0.355603			−0.177801	+	0.984066i	$0.556898\pi$
$954$		0			0
$955$	680.946	+	393.144i	0.713032	+	0.411669i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−313.335	+	670.034i	−0.326731	+	0.698680i
$960$		0			0
$961$	−430.781	−	746.135i	−0.448263	−	0.776415i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		−	75.4450i		−	0.0781814i
$966$		0			0
$967$	283.286			0.292954			0.146477	−	0.989214i	$-0.453207\pi$
$967$	283.286			0.292954			0.146477	+	0.989214i	$0.453207\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1334.53	−	770.494i	1.37439	−	0.793506i	0.382915	−	0.923784i	$-0.374920\pi$
$971$	1334.53	−	770.494i	1.37439	−	0.793506i	0.991477	+	0.130278i	$0.0415870\pi$
$972$		0			0
$973$	−65.1215	−	753.840i	−0.0669285	−	0.774758i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	540.764	−	936.630i	0.553494	−	0.958680i	−0.444525	−	0.895766i	$-0.646628\pi$
$977$	540.764	−	936.630i	0.553494	−	0.958680i	0.998019	−	0.0629132i	$-0.0200391\pi$
$978$		0			0
$979$			743.765i			0.759719i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−34.9710	−	20.1905i	−0.0355758	−	0.0205397i	0.482107	−	0.876113i	$-0.339872\pi$
$983$	−34.9710	−	20.1905i	−0.0355758	−	0.0205397i	−0.517682	+	0.855573i	$0.673205\pi$
$984$		0			0
$985$	−1978.58	+	1142.34i	−2.00871	+	1.15973i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−141.403	−	244.918i	−0.142976	−	0.247642i
$990$		0			0
$991$	329.050	−	569.931i	0.332038	−	0.575107i	−0.650873	−	0.759186i	$-0.725597\pi$
$991$	329.050	−	569.931i	0.332038	−	0.575107i	0.982911	+	0.184080i	$0.0589304\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1866.52			1.87589
$996$		0			0
$997$	824.469	+	476.007i	0.826950	+	0.477440i	0.852807	−	0.522226i	$-0.174898\pi$
$997$	824.469	+	476.007i	0.826950	+	0.477440i	−0.0258573	+	0.999666i	$0.508232\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.3.by.a.73.1		8
3.2	odd	2		168.3.z.a.73.4	✓	8
4.3	odd	2		1008.3.cg.n.577.1		8
7.3	odd	6		3528.3.f.f.2449.8		8
7.4	even	3		3528.3.f.f.2449.1		8
7.5	odd	6	inner	504.3.by.a.145.1		8
12.11	even	2		336.3.bh.h.241.4		8
21.2	odd	6		1176.3.z.d.313.1		8
21.5	even	6		168.3.z.a.145.4	yes	8
21.11	odd	6		1176.3.f.a.97.8		8
21.17	even	6		1176.3.f.a.97.1		8
21.20	even	2		1176.3.z.d.913.1		8
28.19	even	6		1008.3.cg.n.145.1		8
84.11	even	6		2352.3.f.k.97.4		8
84.47	odd	6		336.3.bh.h.145.4		8
84.59	odd	6		2352.3.f.k.97.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.3.z.a.73.4	✓	8	3.2	odd	2
168.3.z.a.145.4	yes	8	21.5	even	6
336.3.bh.h.145.4		8	84.47	odd	6
336.3.bh.h.241.4		8	12.11	even	2
504.3.by.a.73.1		8	1.1	even	1	trivial
504.3.by.a.145.1		8	7.5	odd	6	inner
1008.3.cg.n.145.1		8	28.19	even	6
1008.3.cg.n.577.1		8	4.3	odd	2
1176.3.f.a.97.1		8	21.17	even	6
1176.3.f.a.97.8		8	21.11	odd	6
1176.3.z.d.313.1		8	21.2	odd	6
1176.3.z.d.913.1		8	21.20	even	2
2352.3.f.k.97.4		8	84.11	even	6
2352.3.f.k.97.5		8	84.59	odd	6
3528.3.f.f.2449.1		8	7.4	even	3
3528.3.f.f.2449.8		8	7.3	odd	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	504.by (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.79369 + 4.49969i) q^{5} +(-6.97403 + 0.602461i) q^{7} +(-2.31967 + 4.01778i) q^{11} -15.7769i q^{13} +(8.01512 + 4.62753i) q^{17} +(23.8573 - 13.7740i) q^{19} +(2.82843 + 4.89898i) q^{23} +(27.9944 - 48.4878i) q^{25} +14.6969 q^{29} +(8.63587 + 4.98592i) q^{31} +(51.6425 - 36.0764i) q^{35} +(25.4246 + 44.0367i) q^{37} -70.2028i q^{41} -49.9937 q^{43} +(14.3163 - 8.26552i) q^{47} +(48.2741 - 8.40315i) q^{49} +(-4.28137 + 7.41555i) q^{53} -41.7512i q^{55} +(-85.0212 - 49.0870i) q^{59} +(-30.0000 + 17.3205i) q^{61} +(70.9913 + 122.961i) q^{65} +(-5.19046 + 8.99014i) q^{67} -93.3690 q^{71} +(107.866 + 62.2765i) q^{73} +(13.7569 - 29.4176i) q^{77} +(-55.3705 - 95.9046i) q^{79} -136.246i q^{83} -83.2899 q^{85} +(138.839 - 80.1585i) q^{89} +(9.50498 + 110.029i) q^{91} +(-123.958 + 214.701i) q^{95} -129.419i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{5} - 4 q^{7} - 14 q^{11} - 12 q^{17} + 78 q^{19} - 6 q^{25} + 4 q^{29} - 24 q^{31} + 156 q^{35} + 50 q^{37} - 20 q^{43} - 12 q^{47} + 220 q^{49} + 50 q^{53} + 186 q^{59} - 240 q^{61} + 148 q^{65}+ \cdots - 144 q^{95}+O(q^{100}) \) 8 * q - 6 * q^5 - 4 * q^7 - 14 * q^11 - 12 * q^17 + 78 * q^19 - 6 * q^25 + 4 * q^29 - 24 * q^31 + 156 * q^35 + 50 * q^37 - 20 * q^43 - 12 * q^47 + 220 * q^49 + 50 * q^53 + 186 * q^59 - 240 * q^61 + 148 * q^65 + 34 * q^67 - 424 * q^71 + 294 * q^73 - 126 * q^77 - 40 * q^79 - 232 * q^85 + 132 * q^89 - 378 * q^91 - 144 * q^95

Introduction

L-functions

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