LMFDB - Embedded newform 1620.2.e.b.971.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1620,2,Mod(971,1620)] 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("1620.971"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1620, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1620.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(16)] == traces)

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

Self dual:	no
Analytic conductor:	$12.9357651274$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			971.18
Character	$\chi$	$=$	1620.971
Dual form			1620.2.e.b.971.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.499529 + 1.32305i) q^{2} +(-1.50094 - 1.32181i) q^{4} -1.00000i q^{5} -1.20913i q^{7} +(2.49858 - 1.32555i) q^{8} +(1.32305 + 0.499529i) q^{10} -3.04322 q^{11} -5.07917 q^{13} +(1.59974 + 0.603996i) q^{14} +(0.505654 + 3.96791i) q^{16} +2.23944i q^{17} -2.53835i q^{19} +(-1.32181 + 1.50094i) q^{20} +(1.52017 - 4.02634i) q^{22} +6.96134 q^{23} -1.00000 q^{25} +(2.53719 - 6.72001i) q^{26} +(-1.59824 + 1.81484i) q^{28} +5.59345i q^{29} +3.27657i q^{31} +(-5.50235 - 1.31308i) q^{32} +(-2.96289 - 1.11866i) q^{34} -1.20913 q^{35} -10.3514 q^{37} +(3.35837 + 1.26798i) q^{38} +(-1.32555 - 2.49858i) q^{40} +4.27480i q^{41} +4.31983i q^{43} +(4.56769 + 4.02254i) q^{44} +(-3.47739 + 9.21023i) q^{46} +10.3014 q^{47} +5.53800 q^{49} +(0.499529 - 1.32305i) q^{50} +(7.62354 + 6.71368i) q^{52} +9.42683i q^{53} +3.04322i q^{55} +(-1.60276 - 3.02112i) q^{56} +(-7.40044 - 2.79409i) q^{58} +8.92669 q^{59} -2.65793 q^{61} +(-4.33508 - 1.63674i) q^{62} +(4.48585 - 6.62398i) q^{64} +5.07917i q^{65} +14.4173i q^{67} +(2.96010 - 3.36126i) q^{68} +(0.603996 - 1.59974i) q^{70} +3.49303 q^{71} +5.10052 q^{73} +(5.17084 - 13.6955i) q^{74} +(-3.35521 + 3.80992i) q^{76} +3.67965i q^{77} +3.76977i q^{79} +(3.96791 - 0.505654i) q^{80} +(-5.65579 - 2.13538i) q^{82} +0.572344 q^{83} +2.23944 q^{85} +(-5.71536 - 2.15788i) q^{86} +(-7.60373 + 4.03392i) q^{88} +2.40129i q^{89} +6.14138i q^{91} +(-10.4486 - 9.20155i) q^{92} +(-5.14586 + 13.6293i) q^{94} -2.53835 q^{95} -11.6511 q^{97} +(-2.76639 + 7.32708i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{25} + 12 q^{34} + 12 q^{40} - 12 q^{46} - 48 q^{49} + 36 q^{52} + 36 q^{58} - 48 q^{64} - 24 q^{73} - 12 q^{76} - 36 q^{82} - 36 q^{94} + 24 q^{97}+O(q^{100}) $ 48 * q - 48 * q^25 + 12 * q^34 + 12 * q^40 - 12 * q^46 - 48 * q^49 + 36 * q^52 + 36 * q^58 - 48 * q^64 - 24 * q^73 - 12 * q^76 - 36 * q^82 - 36 * q^94 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−0.499529	+	1.32305i	−0.353220	+	0.935540i
$2$	−0.499529	+	1.32305i	−0.353220	+	0.935540i
$3$		0			0
$3$		0			0
$4$	−1.50094	−	1.32181i	−0.750471	−	0.660903i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$		−	1.20913i		−	0.457008i	−0.973543	−	0.228504i	$-0.926617\pi$
$7$		−	1.20913i		−	0.457008i	0.973543	−	0.228504i	$-0.0733835\pi$
$8$	2.49858	−	1.32555i	0.883383	−	0.468651i
$9$		0			0
$10$	1.32305	+	0.499529i	0.418386	+	0.157965i
$11$	−3.04322			−0.917564			−0.458782	−	0.888549i	$-0.651714\pi$
$11$	−3.04322			−0.917564			−0.458782	+	0.888549i	$0.651714\pi$
$12$		0			0
$13$	−5.07917			−1.40871			−0.704354	−	0.709849i	$-0.748763\pi$
$13$	−5.07917			−1.40871			−0.704354	+	0.709849i	$0.748763\pi$
$14$	1.59974	+	0.603996i	0.427550	+	0.161425i
$15$		0			0
$16$	0.505654	+	3.96791i	0.126413	+	0.991978i
$17$			2.23944i			0.543143i	0.962418	+	0.271572i	$0.0875434\pi$
$17$			2.23944i			0.543143i	−0.962418	+	0.271572i	$0.912457\pi$
$18$		0			0
$19$		−	2.53835i		−	0.582337i	−0.956672	−	0.291169i	$-0.905956\pi$
$19$		−	2.53835i		−	0.582337i	0.956672	−	0.291169i	$-0.0940441\pi$
$20$	−1.32181	+	1.50094i	−0.295565	+	0.335621i
$21$		0			0
$22$	1.52017	−	4.02634i	0.324102	−	0.858418i
$23$	6.96134			1.45154			0.725770	−	0.687937i	$-0.241484\pi$
$23$	6.96134			1.45154			0.725770	+	0.687937i	$0.241484\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	2.53719	−	6.72001i	0.497584	−	1.31790i
$27$		0			0
$28$	−1.59824	+	1.81484i	−0.302038	+	0.342972i
$29$			5.59345i			1.03868i	0.854568	+	0.519339i	$0.173822\pi$
$29$			5.59345i			1.03868i	−0.854568	+	0.519339i	$0.826178\pi$
$30$		0			0
$31$			3.27657i			0.588489i	0.955730	+	0.294245i	$0.0950680\pi$
$31$			3.27657i			0.588489i	−0.955730	+	0.294245i	$0.904932\pi$
$32$	−5.50235	−	1.31308i	−0.972687	−	0.232122i
$33$		0			0
$34$	−2.96289	−	1.11866i	−0.508132	−	0.191849i
$35$	−1.20913			−0.204380
$36$		0			0
$37$	−10.3514			−1.70176			−0.850882	−	0.525356i	$-0.823932\pi$
$37$	−10.3514			−1.70176			−0.850882	+	0.525356i	$0.823932\pi$
$38$	3.35837	+	1.26798i	0.544800	+	0.205693i
$39$		0			0
$40$	−1.32555	−	2.49858i	−0.209587	−	0.395061i
$41$			4.27480i			0.667611i	0.942642	+	0.333806i	$0.108333\pi$
$41$			4.27480i			0.667611i	−0.942642	+	0.333806i	$0.891667\pi$
$42$		0			0
$43$			4.31983i			0.658767i	0.944196	+	0.329384i	$0.106841\pi$
$43$			4.31983i			0.658767i	−0.944196	+	0.329384i	$0.893159\pi$
$44$	4.56769	+	4.02254i	0.688605	+	0.606421i
$45$		0			0
$46$	−3.47739	+	9.21023i	−0.512713	+	1.35797i
$47$	10.3014			1.50262			0.751308	−	0.659951i	$-0.229423\pi$
$47$	10.3014			1.50262			0.751308	+	0.659951i	$0.229423\pi$
$48$		0			0
$49$	5.53800			0.791143
$50$	0.499529	−	1.32305i	0.0706440	−	0.187108i
$51$		0			0
$52$	7.62354	+	6.71368i	1.05719	+	0.931020i
$53$			9.42683i			1.29487i	0.762119	+	0.647437i	$0.224159\pi$
$53$			9.42683i			1.29487i	−0.762119	+	0.647437i	$0.775841\pi$
$54$		0			0
$55$			3.04322i			0.410347i
$56$	−1.60276	−	3.02112i	−0.214178	−	0.403714i
$57$		0			0
$58$	−7.40044	−	2.79409i	−0.971725	−	0.366882i
$59$	8.92669			1.16216			0.581078	−	0.813848i	$-0.302631\pi$
$59$	8.92669			1.16216			0.581078	+	0.813848i	$0.302631\pi$
$60$		0			0
$61$	−2.65793			−0.340313			−0.170156	−	0.985417i	$-0.554427\pi$
$61$	−2.65793			−0.340313			−0.170156	+	0.985417i	$0.554427\pi$
$62$	−4.33508	−	1.63674i	−0.550555	−	0.207866i
$63$		0			0
$64$	4.48585	−	6.62398i	0.560732	−	0.827998i
$65$			5.07917i			0.629993i
$66$		0			0
$67$			14.4173i			1.76136i	0.473714	+	0.880679i	$0.342913\pi$
$67$			14.4173i			1.76136i	−0.473714	+	0.880679i	$0.657087\pi$
$68$	2.96010	−	3.36126i	0.358965	−	0.407613i
$69$		0			0
$70$	0.603996	−	1.59974i	0.0721913	−	0.191206i
$71$	3.49303			0.414546			0.207273	−	0.978283i	$-0.433541\pi$
$71$	3.49303			0.414546			0.207273	+	0.978283i	$0.433541\pi$
$72$		0			0
$73$	5.10052			0.596970			0.298485	−	0.954414i	$-0.403519\pi$
$73$	5.10052			0.596970			0.298485	+	0.954414i	$0.403519\pi$
$74$	5.17084	−	13.6955i	0.601098	−	1.59207i
$75$		0			0
$76$	−3.35521	+	3.80992i	−0.384869	+	0.437027i
$77$			3.67965i			0.419335i
$78$		0			0
$79$			3.76977i			0.424132i	0.977255	+	0.212066i	$0.0680192\pi$
$79$			3.76977i			0.424132i	−0.977255	+	0.212066i	$0.931981\pi$
$80$	3.96791	−	0.505654i	0.443626	−	0.0565338i
$81$		0			0
$82$	−5.65579	−	2.13538i	−0.624577	−	0.235814i
$83$	0.572344			0.0628230			0.0314115	−	0.999507i	$-0.490000\pi$
$83$	0.572344			0.0628230			0.0314115	+	0.999507i	$0.490000\pi$
$84$		0			0
$85$	2.23944			0.242901
$86$	−5.71536	−	2.15788i	−0.616303	−	0.232690i
$87$		0			0
$88$	−7.60373	+	4.03392i	−0.810561	+	0.430018i
$89$			2.40129i			0.254536i	0.991868	+	0.127268i	$0.0406208\pi$
$89$			2.40129i			0.254536i	−0.991868	+	0.127268i	$0.959379\pi$
$90$		0			0
$91$			6.14138i			0.643791i
$92$	−10.4486	−	9.20155i	−1.08934	−	0.959328i
$93$		0			0
$94$	−5.14586	+	13.6293i	−0.530755	+	1.40576i
$95$	−2.53835			−0.260429
$96$		0			0
$97$	−11.6511			−1.18299			−0.591496	−	0.806308i	$-0.701462\pi$
$97$	−11.6511			−1.18299			−0.591496	+	0.806308i	$0.701462\pi$
$98$	−2.76639	+	7.32708i	−0.279448	+	0.740146i
$99$		0			0
$100$	1.50094	+	1.32181i	0.150094	+	0.132181i
$101$			4.77766i			0.475395i	0.971339	+	0.237698i	$0.0763927\pi$
$101$			4.77766i			0.475395i	−0.971339	+	0.237698i	$0.923607\pi$
$102$		0			0
$103$			9.45891i			0.932014i	0.884781	+	0.466007i	$0.154308\pi$
$103$			9.45891i			0.932014i	−0.884781	+	0.466007i	$0.845692\pi$
$104$	−12.6907	+	6.73267i	−1.24443	+	0.660193i
$105$		0			0
$106$	−12.4722	−	4.70897i	−1.21141	−	0.457376i
$107$	−18.3014			−1.76926			−0.884630	−	0.466294i	$-0.845589\pi$
$107$	−18.3014			−1.76926			−0.884630	+	0.466294i	$0.845589\pi$
$108$		0			0
$109$	−10.2589			−0.982625			−0.491312	−	0.870983i	$-0.663483\pi$
$109$	−10.2589			−0.982625			−0.491312	+	0.870983i	$0.663483\pi$
$110$	−4.02634	−	1.52017i	−0.383896	−	0.144943i
$111$		0			0
$112$	4.79772	−	0.611402i	0.453342	−	0.0577720i
$113$			6.13462i			0.577096i	0.957465	+	0.288548i	$0.0931725\pi$
$113$			6.13462i			0.577096i	−0.957465	+	0.288548i	$0.906827\pi$
$114$		0			0
$115$		−	6.96134i		−	0.649149i
$116$	7.39346	−	8.39545i	0.686466	−	0.779498i
$117$		0			0
$118$	−4.45914	+	11.8105i	−0.410497	+	1.08724i
$119$	2.70777			0.248221
$120$		0			0
$121$	−1.73884			−0.158076
$122$	1.32771	−	3.51658i	0.120205	−	0.318376i
$123$		0			0
$124$	4.33099	−	4.91794i	0.388934	−	0.441644i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$		−	9.41213i		−	0.835192i	−0.908633	−	0.417596i	$-0.862873\pi$
$127$		−	9.41213i		−	0.835192i	0.908633	−	0.417596i	$-0.137127\pi$
$128$	6.52307	+	9.24389i	0.576563	+	0.817053i
$129$		0			0
$130$	−6.72001	−	2.53719i	−0.589384	−	0.222526i
$131$	−2.13260			−0.186327			−0.0931633	−	0.995651i	$-0.529698\pi$
$131$	−2.13260			−0.186327			−0.0931633	+	0.995651i	$0.529698\pi$
$132$		0			0
$133$	−3.06920			−0.266133
$134$	−19.0749	−	7.20187i	−1.64782	−	0.622147i
$135$		0			0
$136$	2.96848	+	5.59542i	0.254545	+	0.479803i
$137$		−	16.4869i		−	1.40857i	−0.709918	−	0.704285i	$-0.751268\pi$
$137$		−	16.4869i		−	1.40857i	0.709918	−	0.704285i	$-0.248732\pi$
$138$		0			0
$139$		−	20.1007i		−	1.70492i	−0.522792	−	0.852460i	$-0.675110\pi$
$139$		−	20.1007i		−	1.70492i	0.522792	−	0.852460i	$-0.324890\pi$
$140$	1.81484	+	1.59824i	0.153382	+	0.135076i
$141$		0			0
$142$	−1.74487	+	4.62146i	−0.146426	+	0.387824i
$143$	15.4570			1.29258
$144$		0			0
$145$	5.59345			0.464511
$146$	−2.54785	+	6.74826i	−0.210862	+	0.558490i
$147$		0			0
$148$	15.5369	+	13.6826i	1.27713	+	1.12470i
$149$			1.88370i			0.154319i	0.997019	+	0.0771594i	$0.0245850\pi$
$149$			1.88370i			0.154319i	−0.997019	+	0.0771594i	$0.975415\pi$
$150$		0			0
$151$		−	6.18825i		−	0.503593i	−0.967780	−	0.251796i	$-0.918979\pi$
$151$		−	6.18825i		−	0.503593i	0.967780	−	0.251796i	$-0.0810214\pi$
$152$	−3.36470	−	6.34228i	−0.272913	−	0.514427i
$153$		0			0
$154$	−4.86837	−	1.83809i	−0.392304	−	0.148117i
$155$	3.27657			0.263180
$156$		0			0
$157$	−2.20024			−0.175598			−0.0877991	−	0.996138i	$-0.527983\pi$
$157$	−2.20024			−0.175598			−0.0877991	+	0.996138i	$0.527983\pi$
$158$	−4.98761	−	1.88311i	−0.396793	−	0.149812i
$159$		0			0
$160$	−1.31308	+	5.50235i	−0.103808	+	0.434999i
$161$		−	8.41717i		−	0.663366i
$162$		0			0
$163$			15.3649i			1.20347i	0.798694	+	0.601737i	$0.205525\pi$
$163$			15.3649i			1.20347i	−0.798694	+	0.601737i	$0.794475\pi$
$164$	5.65046	−	6.41622i	0.441227	−	0.501023i
$165$		0			0
$166$	−0.285903	+	0.757242i	−0.0221903	+	0.0587734i
$167$	−22.2247			−1.71980			−0.859901	−	0.510461i	$-0.829475\pi$
$167$	−22.2247			−1.71980			−0.859901	+	0.510461i	$0.829475\pi$
$168$		0			0
$169$	12.7979			0.984457
$170$	−1.11866	+	2.96289i	−0.0857975	+	0.227244i
$171$		0			0
$172$	5.70997	−	6.48381i	0.435381	−	0.494386i
$173$			15.4106i			1.17165i	0.810438	+	0.585825i	$0.199229\pi$
$173$			15.4106i			1.17165i	−0.810438	+	0.585825i	$0.800771\pi$
$174$		0			0
$175$			1.20913i			0.0914017i
$176$	−1.53881	−	12.0752i	−0.115992	−	0.910203i
$177$		0			0
$178$	−3.17703	−	1.19951i	−0.238129	−	0.0899073i
$179$	12.8229			0.958425			0.479212	−	0.877699i	$-0.340922\pi$
$179$	12.8229			0.958425			0.479212	+	0.877699i	$0.340922\pi$
$180$		0			0
$181$	17.3649			1.29072			0.645360	−	0.763879i	$-0.276707\pi$
$181$	17.3649			1.29072			0.645360	+	0.763879i	$0.276707\pi$
$182$	−8.12537	−	3.06779i	−0.602293	−	0.227400i
$183$		0			0
$184$	17.3935	−	9.22758i	1.28227	−	0.680266i
$185$			10.3514i			0.761052i
$186$		0			0
$187$		−	6.81509i		−	0.498369i
$188$	−15.4618	−	13.6165i	−1.12767	−	0.993085i
$189$		0			0
$190$	1.26798	−	3.35837i	0.0919889	−	0.243642i
$191$	−17.8286			−1.29003			−0.645017	−	0.764169i	$-0.723150\pi$
$191$	−17.8286			−1.29003			−0.645017	+	0.764169i	$0.723150\pi$
$192$		0			0
$193$	−4.88362			−0.351530			−0.175765	−	0.984432i	$-0.556240\pi$
$193$	−4.88362			−0.351530			−0.175765	+	0.984432i	$0.556240\pi$
$194$	5.82007	−	15.4151i	0.417856	−	1.10674i
$195$		0			0
$196$	−8.31222	−	7.32017i	−0.593730	−	0.522869i
$197$			16.8173i			1.19818i	0.800682	+	0.599090i	$0.204471\pi$
$197$			16.8173i			1.19818i	−0.800682	+	0.599090i	$0.795529\pi$
$198$		0			0
$199$		−	5.91492i		−	0.419297i	−0.977777	−	0.209649i	$-0.932768\pi$
$199$		−	5.91492i		−	0.419297i	0.977777	−	0.209649i	$-0.0672320\pi$
$200$	−2.49858	+	1.32555i	−0.176677	+	0.0937303i
$201$		0			0
$202$	−6.32110	−	2.38658i	−0.444751	−	0.167919i
$203$	6.76321			0.474685
$204$		0			0
$205$	4.27480			0.298565
$206$	−12.5146	−	4.72500i	−0.871937	−	0.329206i
$207$		0			0
$208$	−2.56830	−	20.1537i	−0.178080	−	1.39741i
$209$			7.72475i			0.534332i
$210$		0			0
$211$		−	27.6534i		−	1.90374i	−0.306507	−	0.951868i	$-0.599160\pi$
$211$		−	27.6534i		−	1.90374i	0.306507	−	0.951868i	$-0.400840\pi$
$212$	12.4604	−	14.1491i	0.855787	−	0.971766i
$213$		0			0
$214$	9.14206	−	24.2137i	0.624938	−	1.65521i
$215$	4.31983			0.294610
$216$		0			0
$217$	3.96180			0.268945
$218$	5.12462	−	13.5731i	0.347083	−	0.919285i
$219$		0			0
$220$	4.02254	−	4.56769i	0.271200	−	0.307954i
$221$		−	11.3745i		−	0.765130i
$222$		0			0
$223$			23.9473i			1.60363i	0.597572	+	0.801815i	$0.296132\pi$
$223$			23.9473i			1.60363i	−0.597572	+	0.801815i	$0.703868\pi$
$224$	−1.58768	+	6.65306i	−0.106082	+	0.444526i
$225$		0			0
$226$	−8.11643	−	3.06442i	−0.539897	−	0.203842i
$227$	6.91958			0.459269			0.229634	−	0.973277i	$-0.426247\pi$
$227$	6.91958			0.459269			0.229634	+	0.973277i	$0.426247\pi$
$228$		0			0
$229$	−15.3167			−1.01216			−0.506080	−	0.862487i	$-0.668906\pi$
$229$	−15.3167			−1.01216			−0.506080	+	0.862487i	$0.668906\pi$
$230$	9.21023	+	3.47739i	0.607305	+	0.229292i
$231$		0			0
$232$	7.41438	+	13.9757i	0.486778	+	0.917551i
$233$			6.61050i			0.433068i	0.976275	+	0.216534i	$0.0694753\pi$
$233$			6.61050i			0.433068i	−0.976275	+	0.216534i	$0.930525\pi$
$234$		0			0
$235$		−	10.3014i		−	0.671991i
$236$	−13.3984	−	11.7994i	−0.872165	−	0.768073i
$237$		0			0
$238$	−1.35261	+	3.58253i	−0.0876767	+	0.232221i
$239$	−8.22119			−0.531785			−0.265892	−	0.964003i	$-0.585667\pi$
$239$	−8.22119			−0.531785			−0.265892	+	0.964003i	$0.585667\pi$
$240$		0			0
$241$	14.6155			0.941470			0.470735	−	0.882275i	$-0.343989\pi$
$241$	14.6155			0.941470			0.470735	+	0.882275i	$0.343989\pi$
$242$	0.868600	−	2.30058i	0.0558357	−	0.147887i
$243$		0			0
$244$	3.98940	+	3.51327i	0.255395	+	0.224914i
$245$		−	5.53800i		−	0.353810i
$246$		0			0
$247$			12.8927i			0.820343i
$248$	4.34324	+	8.18679i	0.275796	+	0.519861i
$249$		0			0
$250$	−1.32305	−	0.499529i	−0.0836773	−	0.0315930i
$251$	2.39191			0.150976			0.0754880	−	0.997147i	$-0.475949\pi$
$251$	2.39191			0.150976			0.0754880	+	0.997147i	$0.475949\pi$
$252$		0			0
$253$	−21.1849			−1.33188
$254$	12.4528	+	4.70163i	0.781355	+	0.295007i
$255$		0			0
$256$	−15.4886	+	4.01278i	−0.968039	+	0.250799i
$257$			8.44949i			0.527065i	0.964651	+	0.263532i	$0.0848876\pi$
$257$			8.44949i			0.527065i	−0.964651	+	0.263532i	$0.915112\pi$
$258$		0			0
$259$			12.5162i			0.777721i
$260$	6.71368	−	7.62354i	0.416365	−	0.472792i
$261$		0			0
$262$	1.06530	−	2.82155i	0.0658143	−	0.174316i
$263$	6.46324			0.398540			0.199270	−	0.979945i	$-0.436143\pi$
$263$	6.46324			0.398540			0.199270	+	0.979945i	$0.436143\pi$
$264$		0			0
$265$	9.42683			0.579086
$266$	1.53315	−	4.06071i	0.0940036	−	0.248978i
$267$		0			0
$268$	19.0569	−	21.6396i	1.16409	−	1.32185i
$269$		−	6.14888i		−	0.374904i	−0.982274	−	0.187452i	$-0.939977\pi$
$269$		−	6.14888i		−	0.374904i	0.982274	−	0.187452i	$-0.0600229\pi$
$270$		0			0
$271$		−	0.446839i		−	0.0271436i	−0.999908	−	0.0135718i	$-0.995680\pi$
$271$		−	0.446839i		−	0.0271436i	0.999908	−	0.0135718i	$-0.00432016\pi$
$272$	−8.88588	+	1.13238i	−0.538786	+	0.0686606i
$273$		0			0
$274$	21.8130	+	8.23567i	1.31777	+	0.497535i
$275$	3.04322			0.183513
$276$		0			0
$277$	6.83247			0.410524			0.205262	−	0.978707i	$-0.434195\pi$
$277$	6.83247			0.410524			0.205262	+	0.978707i	$0.434195\pi$
$278$	26.5943	+	10.0409i	1.59502	+	0.602212i
$279$		0			0
$280$	−3.02112	+	1.60276i	−0.180546	+	0.0957832i
$281$			3.29157i			0.196359i	0.995169	+	0.0981794i	$0.0313019\pi$
$281$			3.29157i			0.196359i	−0.995169	+	0.0981794i	$0.968698\pi$
$282$		0			0
$283$		−	23.4374i		−	1.39321i	−0.717457	−	0.696603i	$-0.754694\pi$
$283$		−	23.4374i		−	1.39321i	0.717457	−	0.696603i	$-0.245306\pi$
$284$	−5.24283	−	4.61711i	−0.311105	−	0.273975i
$285$		0			0
$286$	−7.72122	+	20.4504i	−0.456565	+	1.20926i
$287$	5.16879			0.305104
$288$		0			0
$289$	11.9849			0.704996
$290$	−2.79409	+	7.40044i	−0.164075	+	0.434569i
$291$		0			0
$292$	−7.65558	−	6.74190i	−0.448009	−	0.394540i
$293$			27.9131i			1.63070i	0.578970	+	0.815349i	$0.303455\pi$
$293$			27.9131i			1.63070i	−0.578970	+	0.815349i	$0.696545\pi$
$294$		0			0
$295$		−	8.92669i		−	0.519732i
$296$	−25.8639	+	13.7213i	−1.50331	+	0.797535i
$297$		0			0
$298$	−2.49224	−	0.940963i	−0.144371	−	0.0545085i
$299$	−35.3578			−2.04480
$300$		0			0
$301$	5.22323			0.301062
$302$	8.18739	+	3.09121i	0.471131	+	0.177879i
$303$		0			0
$304$	10.0719	−	1.28353i	0.577666	−	0.0736153i
$305$			2.65793i			0.152193i
$306$		0			0
$307$			22.5939i			1.28950i	0.764393	+	0.644750i	$0.223039\pi$
$307$			22.5939i			1.28950i	−0.764393	+	0.644750i	$0.776961\pi$
$308$	4.86378	−	5.52293i	0.277140	−	0.314698i
$309$		0			0
$310$	−1.63674	+	4.33508i	−0.0929606	+	0.246216i
$311$	−5.89086			−0.334040			−0.167020	−	0.985953i	$-0.553414\pi$
$311$	−5.89086			−0.334040			−0.167020	+	0.985953i	$0.553414\pi$
$312$		0			0
$313$	7.76738			0.439038			0.219519	−	0.975608i	$-0.429551\pi$
$313$	7.76738			0.439038			0.219519	+	0.975608i	$0.429551\pi$
$314$	1.09908	−	2.91104i	0.0620249	−	0.164279i
$315$		0			0
$316$	4.98291	−	5.65820i	0.280310	−	0.318299i
$317$			11.7709i			0.661120i	0.943785	+	0.330560i	$0.107238\pi$
$317$			11.7709i			0.661120i	−0.943785	+	0.330560i	$0.892762\pi$
$318$		0			0
$319$		−	17.0221i		−	0.953054i
$320$	−6.62398	−	4.48585i	−0.370292	−	0.250767i
$321$		0			0
$322$	11.1364	+	4.20462i	0.620606	+	0.234314i
$323$	5.68447			0.316293
$324$		0			0
$325$	5.07917			0.281742
$326$	−20.3286	−	7.67523i	−1.12590	−	0.425091i
$327$		0			0
$328$	5.66644	+	10.6809i	0.312877	+	0.589757i
$329$		−	12.4558i		−	0.686709i
$330$		0			0
$331$			4.32394i			0.237665i	0.992914	+	0.118833i	$0.0379152\pi$
$331$			4.32394i			0.237665i	−0.992914	+	0.118833i	$0.962085\pi$
$332$	−0.859056	−	0.756529i	−0.0471468	−	0.0415199i
$333$		0			0
$334$	11.1019	−	29.4045i	0.607469	−	1.60894i
$335$	14.4173			0.787703
$336$		0			0
$337$	7.77010			0.423264			0.211632	−	0.977349i	$-0.432122\pi$
$337$	7.77010			0.423264			0.211632	+	0.977349i	$0.432122\pi$
$338$	−6.39294	+	16.9324i	−0.347730	+	0.920999i
$339$		0			0
$340$	−3.36126	−	2.96010i	−0.182290	−	0.160534i
$341$		−	9.97131i		−	0.539977i
$342$		0			0
$343$		−	15.1601i		−	0.818568i
$344$	5.72613	+	10.7935i	0.308732	+	0.581944i
$345$		0			0
$346$	−20.3891	−	7.69806i	−1.09613	−	0.413850i
$347$	11.2661			0.604798			0.302399	−	0.953181i	$-0.402212\pi$
$347$	11.2661			0.604798			0.302399	+	0.953181i	$0.402212\pi$
$348$		0			0
$349$	−22.2806			−1.19265			−0.596326	−	0.802742i	$-0.703374\pi$
$349$	−22.2806			−1.19265			−0.596326	+	0.802742i	$0.703374\pi$
$350$	−1.59974	−	0.603996i	−0.0855100	−	0.0322849i
$351$		0			0
$352$	16.7448	+	3.99598i	0.892502	+	0.212986i
$353$			22.0645i			1.17438i	0.809451	+	0.587188i	$0.199765\pi$
$353$			22.0645i			1.17438i	−0.809451	+	0.587188i	$0.800235\pi$
$354$		0			0
$355$		−	3.49303i		−	0.185391i
$356$	3.17404	−	3.60420i	0.168224	−	0.191022i
$357$		0			0
$358$	−6.40538	+	16.9653i	−0.338535	+	0.896645i
$359$	−1.70332			−0.0898978			−0.0449489	−	0.998989i	$-0.514313\pi$
$359$	−1.70332			−0.0898978			−0.0449489	+	0.998989i	$0.514313\pi$
$360$		0			0
$361$	12.5568			0.660883
$362$	−8.67425	+	22.9746i	−0.455908	+	1.20752i
$363$		0			0
$364$	8.11771	−	9.21785i	0.425484	−	0.483147i
$365$		−	5.10052i		−	0.266973i
$366$		0			0
$367$		−	9.42151i		−	0.491799i	−0.969295	−	0.245900i	$-0.920917\pi$
$367$		−	9.42151i		−	0.491799i	0.969295	−	0.245900i	$-0.0790833\pi$
$368$	3.52003	+	27.6220i	0.183494	+	1.43990i
$369$		0			0
$370$	−13.6955	−	5.17084i	−0.711995	−	0.268819i
$371$	11.3983			0.591769
$372$		0			0
$373$	14.5855			0.755210			0.377605	−	0.925967i	$-0.376748\pi$
$373$	14.5855			0.755210			0.377605	+	0.925967i	$0.376748\pi$
$374$	9.01673	+	3.40433i	0.466244	+	0.176034i
$375$		0			0
$376$	25.7390	−	13.6550i	1.32739	−	0.704203i
$377$		−	28.4101i		−	1.46319i
$378$		0			0
$379$			9.46065i			0.485961i	0.970031	+	0.242980i	$0.0781251\pi$
$379$			9.46065i			0.485961i	−0.970031	+	0.242980i	$0.921875\pi$
$380$	3.80992	+	3.35521i	0.195445	+	0.172119i
$381$		0			0
$382$	8.90590	−	23.5882i	0.455666	−	1.20688i
$383$	−6.86013			−0.350536			−0.175268	−	0.984521i	$-0.556079\pi$
$383$	−6.86013			−0.350536			−0.175268	+	0.984521i	$0.556079\pi$
$384$		0			0
$385$	3.67965			0.187532
$386$	2.43951	−	6.46129i	0.124168	−	0.328871i
$387$		0			0
$388$	17.4876	+	15.4005i	0.887801	+	0.781843i
$389$		−	8.21735i		−	0.416636i	−0.978061	−	0.208318i	$-0.933201\pi$
$389$		−	8.21735i		−	0.416636i	0.978061	−	0.208318i	$-0.0667989\pi$
$390$		0			0
$391$			15.5895i			0.788394i
$392$	13.8372	−	7.34088i	0.698883	−	0.370770i
$393$		0			0
$394$	−22.2501	−	8.40070i	−1.12095	−	0.423221i
$395$	3.76977			0.189678
$396$		0			0
$397$	−7.07936			−0.355303			−0.177651	−	0.984093i	$-0.556850\pi$
$397$	−7.07936			−0.355303			−0.177651	+	0.984093i	$0.556850\pi$
$398$	7.82575	+	2.95467i	0.392269	+	0.148104i
$399$		0			0
$400$	−0.505654	−	3.96791i	−0.0252827	−	0.198396i
$401$		−	17.6923i		−	0.883511i	−0.897136	−	0.441755i	$-0.854356\pi$
$401$		−	17.6923i		−	0.883511i	0.897136	−	0.441755i	$-0.145644\pi$
$402$		0			0
$403$		−	16.6422i		−	0.829009i
$404$	6.31514	−	7.17099i	0.314190	−	0.356770i
$405$		0			0
$406$	−3.37842	+	8.94810i	−0.167668	+	0.444087i
$407$	31.5016			1.56148
$408$		0			0
$409$	−22.7084			−1.12286			−0.561428	−	0.827526i	$-0.689748\pi$
$409$	−22.7084			−1.12286			−0.561428	+	0.827526i	$0.689748\pi$
$410$	−2.13538	+	5.65579i	−0.105459	+	0.279319i
$411$		0			0
$412$	12.5028	−	14.1973i	0.615971	−	0.699449i
$413$		−	10.7935i		−	0.531115i
$414$		0			0
$415$		−	0.572344i		−	0.0280953i
$416$	27.9473	+	6.66934i	1.37023	+	0.326992i
$417$		0			0
$418$	−10.2203	−	3.85873i	−0.499889	−	0.188737i
$419$	26.3609			1.28782			0.643908	−	0.765103i	$-0.277312\pi$
$419$	26.3609			1.28782			0.643908	+	0.765103i	$0.277312\pi$
$420$		0			0
$421$	17.1554			0.836101			0.418050	−	0.908424i	$-0.362714\pi$
$421$	17.1554			0.836101			0.418050	+	0.908424i	$0.362714\pi$
$422$	36.5869	+	13.8137i	1.78102	+	0.672438i
$423$		0			0
$424$	12.4957	+	23.5537i	0.606845	+	1.14387i
$425$		−	2.23944i		−	0.108629i
$426$		0			0
$427$			3.21378i			0.155526i
$428$	27.4693	+	24.1909i	1.32778	+	1.16931i
$429$		0			0
$430$	−2.15788	+	5.71536i	−0.104062	+	0.275619i
$431$	−12.5816			−0.606037			−0.303018	−	0.952985i	$-0.597994\pi$
$431$	−12.5816			−0.606037			−0.303018	+	0.952985i	$0.597994\pi$
$432$		0			0
$433$	−11.7433			−0.564346			−0.282173	−	0.959364i	$-0.591055\pi$
$433$	−11.7433			−0.564346			−0.282173	+	0.959364i	$0.591055\pi$
$434$	−1.97903	+	5.24167i	−0.0949966	+	0.251608i
$435$		0			0
$436$	15.3980	+	13.5603i	0.737431	+	0.649420i
$437$		−	17.6703i		−	0.845286i
$438$		0			0
$439$			1.68284i			0.0803176i	0.999193	+	0.0401588i	$0.0127864\pi$
$439$			1.68284i			0.0803176i	−0.999193	+	0.0401588i	$0.987214\pi$
$440$	4.03392	+	7.60373i	0.192310	+	0.362494i
$441$		0			0
$442$	15.0490	+	5.68188i	0.715810	+	0.270259i
$443$	−0.759020			−0.0360621			−0.0180311	−	0.999837i	$-0.505740\pi$
$443$	−0.759020			−0.0360621			−0.0180311	+	0.999837i	$0.505740\pi$
$444$		0			0
$445$	2.40129			0.113832
$446$	−31.6836	−	11.9624i	−1.50026	−	0.566434i
$447$		0			0
$448$	−8.00926	−	5.42398i	−0.378402	−	0.256259i
$449$			17.4579i			0.823887i	0.911209	+	0.411943i	$0.135150\pi$
$449$			17.4579i			0.823887i	−0.911209	+	0.411943i	$0.864850\pi$
$450$		0			0
$451$		−	13.0091i		−	0.612576i
$452$	8.10878	−	9.20770i	0.381405	−	0.433094i
$453$		0			0
$454$	−3.45653	+	9.15498i	−0.162223	+	0.429665i
$455$	6.14138			0.287912
$456$		0			0
$457$	−34.8638			−1.63086			−0.815430	−	0.578855i	$-0.803500\pi$
$457$	−34.8638			−1.63086			−0.815430	+	0.578855i	$0.803500\pi$
$458$	7.65116	−	20.2649i	0.357515	−	0.946916i
$459$		0			0
$460$	−9.20155	+	10.4486i	−0.429025	+	0.487167i
$461$		−	31.2815i		−	1.45692i	−0.685086	−	0.728462i	$-0.740235\pi$
$461$		−	31.2815i		−	1.45692i	0.685086	−	0.728462i	$-0.259765\pi$
$462$		0			0
$463$			10.2827i			0.477879i	0.971034	+	0.238940i	$0.0767998\pi$
$463$			10.2827i			0.477879i	−0.971034	+	0.238940i	$0.923200\pi$
$464$	−22.1943	+	2.82835i	−1.03035	+	0.131303i
$465$		0			0
$466$	−8.74605	−	3.30214i	−0.405153	−	0.152968i
$467$	2.90585			0.134467			0.0672333	−	0.997737i	$-0.478583\pi$
$467$	2.90585			0.134467			0.0672333	+	0.997737i	$0.478583\pi$
$468$		0			0
$469$	17.4324			0.804955
$470$	13.6293	+	5.14586i	0.628674	+	0.237361i
$471$		0			0
$472$	22.3041	−	11.8327i	1.02663	−	0.544646i
$473$		−	13.1462i		−	0.604461i
$474$		0			0
$475$			2.53835i			0.116467i
$476$	−4.06421	−	3.57915i	−0.186283	−	0.164050i
$477$		0			0
$478$	4.10672	−	10.8771i	0.187837	−	0.497506i
$479$	−18.8555			−0.861528			−0.430764	−	0.902465i	$-0.641756\pi$
$479$	−18.8555			−0.861528			−0.430764	+	0.902465i	$0.641756\pi$
$480$		0			0
$481$	52.5767			2.39729
$482$	−7.30088	+	19.3371i	−0.332546	+	0.880783i
$483$		0			0
$484$	2.60990	+	2.29841i	0.118632	+	0.104473i
$485$			11.6511i			0.529050i
$486$		0			0
$487$		−	11.5696i		−	0.524268i	−0.965031	−	0.262134i	$-0.915574\pi$
$487$		−	11.5696i		−	0.524268i	0.965031	−	0.262134i	$-0.0844263\pi$
$488$	−6.64106	+	3.52321i	−0.300627	+	0.159488i
$489$		0			0
$490$	7.32708	+	2.76639i	0.331004	+	0.124973i
$491$	1.49523			0.0674790			0.0337395	−	0.999431i	$-0.489258\pi$
$491$	1.49523			0.0674790			0.0337395	+	0.999431i	$0.489258\pi$
$492$		0			0
$493$	−12.5262			−0.564151
$494$	−17.0577	−	6.44028i	−0.767464	−	0.289762i
$495$		0			0
$496$	−13.0011	+	1.65681i	−0.583768	+	0.0743930i
$497$		−	4.22352i		−	0.189451i
$498$		0			0
$499$			31.4785i			1.40917i	0.709618	+	0.704586i	$0.248867\pi$
$499$			31.4785i			1.40917i	−0.709618	+	0.704586i	$0.751133\pi$
$500$	1.32181	−	1.50094i	0.0591130	−	0.0671242i
$501$		0			0
$502$	−1.19483	+	3.16463i	−0.0533278	+	0.141244i
$503$	−1.90449			−0.0849171			−0.0424585	−	0.999098i	$-0.513519\pi$
$503$	−1.90449			−0.0849171			−0.0424585	+	0.999098i	$0.513519\pi$
$504$		0			0
$505$	4.77766			0.212603
$506$	10.5825	−	28.0287i	0.470447	−	1.24603i
$507$		0			0
$508$	−12.4410	+	14.1271i	−0.551981	+	0.626787i
$509$			31.4341i			1.39329i	0.717414	+	0.696647i	$0.245326\pi$
$509$			31.4341i			1.39329i	−0.717414	+	0.696647i	$0.754674\pi$
$510$		0			0
$511$		−	6.16719i		−	0.272820i
$512$	2.42789	−	22.4968i	0.107299	−	0.994227i
$513$		0			0
$514$	−11.1791	−	4.22076i	−0.493090	−	0.186170i
$515$	9.45891			0.416809
$516$		0			0
$517$	−31.3494			−1.37875
$518$	−16.5596	−	6.25222i	−0.727589	−	0.274707i
$519$		0			0
$520$	6.73267	+	12.6907i	0.295247	+	0.556525i
$521$			23.2742i			1.01966i	0.860275	+	0.509831i	$0.170292\pi$
$521$			23.2742i			1.01966i	−0.860275	+	0.509831i	$0.829708\pi$
$522$		0			0
$523$		−	10.8804i		−	0.475769i	−0.971293	−	0.237884i	$-0.923546\pi$
$523$		−	10.8804i		−	0.475769i	0.971293	−	0.237884i	$-0.0764539\pi$
$524$	3.20092	+	2.81889i	0.139833	+	0.123144i
$525$		0			0
$526$	−3.22857	+	8.55121i	−0.140773	+	0.372851i
$527$	−7.33767			−0.319634
$528$		0			0
$529$	25.4603			1.10697
$530$	−4.70897	+	12.4722i	−0.204545	+	0.541758i
$531$		0			0
$532$	4.60669	+	4.05689i	0.199725	+	0.175888i
$533$		−	21.7124i		−	0.940469i
$534$		0			0
$535$			18.3014i			0.791237i
$536$	19.1108	+	36.0229i	0.825463	+	1.55595i
$537$		0			0
$538$	8.13530	+	3.07154i	0.350738	+	0.132424i
$539$	−16.8533			−0.725925
$540$		0			0
$541$	−6.53795			−0.281088			−0.140544	−	0.990074i	$-0.544885\pi$
$541$	−6.53795			−0.281088			−0.140544	+	0.990074i	$0.544885\pi$
$542$	0.591192	+	0.223209i	0.0253939	+	0.00958765i
$543$		0			0
$544$	2.94055	−	12.3222i	0.126075	−	0.528308i
$545$			10.2589i			0.439443i
$546$		0			0
$547$		−	26.5771i		−	1.13636i	−0.822906	−	0.568178i	$-0.807649\pi$
$547$		−	26.5771i		−	1.13636i	0.822906	−	0.568178i	$-0.192351\pi$
$548$	−21.7925	+	24.7458i	−0.930928	+	1.05709i
$549$		0			0
$550$	−1.52017	+	4.02634i	−0.0648204	+	0.171684i
$551$	14.1981			0.604861
$552$		0			0
$553$	4.55814			0.193832
$554$	−3.41302	+	9.03973i	−0.145005	+	0.384061i
$555$		0			0
$556$	−26.5693	+	30.1700i	−1.12679	+	1.27949i
$557$			8.68248i			0.367889i	0.982937	+	0.183944i	$0.0588866\pi$
$557$			8.68248i			0.367889i	−0.982937	+	0.183944i	$0.941113\pi$
$558$		0			0
$559$		−	21.9411i		−	0.928010i
$560$	−0.611402	−	4.79772i	−0.0258364	−	0.202741i
$561$		0			0
$562$	−4.35493	−	1.64424i	−0.183702	−	0.0693579i
$563$	31.6649			1.33451			0.667257	−	0.744827i	$-0.267468\pi$
$563$	31.6649			1.33451			0.667257	+	0.744827i	$0.267468\pi$
$564$		0			0
$565$	6.13462			0.258085
$566$	31.0089	+	11.7076i	1.30340	+	0.492109i
$567$		0			0
$568$	8.72762	−	4.63017i	0.366203	−	0.194278i
$569$		−	32.2966i		−	1.35395i	−0.736008	−	0.676973i	$-0.763291\pi$
$569$		−	32.2966i		−	1.35395i	0.736008	−	0.676973i	$-0.236709\pi$
$570$		0			0
$571$			14.6930i			0.614884i	0.951567	+	0.307442i	$0.0994729\pi$
$571$			14.6930i			0.614884i	−0.951567	+	0.307442i	$0.900527\pi$
$572$	−23.2001	−	20.4312i	−0.970043	−	0.854270i
$573$		0			0
$574$	−2.58196	+	6.83859i	−0.107769	+	0.285437i
$575$	−6.96134			−0.290308
$576$		0			0
$577$	−22.4886			−0.936214			−0.468107	−	0.883672i	$-0.655064\pi$
$577$	−22.4886			−0.936214			−0.468107	+	0.883672i	$0.655064\pi$
$578$	−5.98682	+	15.8567i	−0.249019	+	0.659552i
$579$		0			0
$580$	−8.39545	−	7.39346i	−0.348602	−	0.306997i
$581$		−	0.692039i		−	0.0287106i
$582$		0			0
$583$		−	28.6879i		−	1.18813i
$584$	12.7441	−	6.76097i	0.527354	−	0.279771i
$585$		0			0
$586$	−36.9305	−	13.9434i	−1.52558	−	0.575996i
$587$	−34.4969			−1.42384			−0.711919	−	0.702262i	$-0.752174\pi$
$587$	−34.4969			−1.42384			−0.711919	+	0.702262i	$0.752174\pi$
$588$		0			0
$589$	8.31708			0.342699
$590$	11.8105	+	4.45914i	0.486230	+	0.183580i
$591$		0			0
$592$	−5.23424	−	41.0736i	−0.215126	−	1.68811i
$593$			11.5133i			0.472794i	0.971656	+	0.236397i	$0.0759667\pi$
$593$			11.5133i			0.472794i	−0.971656	+	0.236397i	$0.924033\pi$
$594$		0			0
$595$		−	2.70777i		−	0.111008i
$596$	2.48989	−	2.82733i	0.101990	−	0.115812i
$597$		0			0
$598$	17.6623	−	46.7803i	0.722263	−	1.91299i
$599$	−35.6121			−1.45507			−0.727535	−	0.686071i	$-0.759334\pi$
$599$	−35.6121			−1.45507			−0.727535	+	0.686071i	$0.759334\pi$
$600$		0			0
$601$	40.8274			1.66539			0.832693	−	0.553735i	$-0.186798\pi$
$601$	40.8274			1.66539			0.832693	+	0.553735i	$0.186798\pi$
$602$	−2.60916	+	6.91062i	−0.106341	+	0.281656i
$603$		0			0
$604$	−8.17968	+	9.28821i	−0.332826	+	0.377932i
$605$			1.73884i			0.0706938i
$606$		0			0
$607$			2.19423i			0.0890609i	0.999008	+	0.0445304i	$0.0141792\pi$
$607$			2.19423i			0.0890609i	−0.999008	+	0.0445304i	$0.985821\pi$
$608$	−3.33305	+	13.9669i	−0.135173	+	0.566432i
$609$		0			0
$610$	−3.51658	−	1.32771i	−0.142382	−	0.0537575i
$611$	−52.3227			−2.11675
$612$		0			0
$613$	38.7673			1.56580			0.782899	−	0.622149i	$-0.213740\pi$
$613$	38.7673			1.56580			0.782899	+	0.622149i	$0.213740\pi$
$614$	−29.8929	−	11.2863i	−1.20638	−	0.455478i
$615$		0			0
$616$	4.87754	+	9.19391i	0.196522	+	0.370433i
$617$		−	14.8556i		−	0.598062i	−0.954243	−	0.299031i	$-0.903337\pi$
$617$		−	14.8556i		−	0.598062i	0.954243	−	0.299031i	$-0.0966634\pi$
$618$		0			0
$619$		−	14.2470i		−	0.572637i	−0.958135	−	0.286318i	$-0.907569\pi$
$619$		−	14.2470i		−	0.572637i	0.958135	−	0.286318i	$-0.0924315\pi$
$620$	−4.91794	−	4.33099i	−0.197509	−	0.173937i
$621$		0			0
$622$	2.94266	−	7.79393i	0.117990	−	0.312508i
$623$	2.90347			0.116325
$624$		0			0
$625$	1.00000			0.0400000
$626$	−3.88003	+	10.2767i	−0.155077	+	0.410738i
$627$		0			0
$628$	3.30243	+	2.90829i	0.131781	+	0.116053i
$629$		−	23.1814i		−	0.924302i
$630$		0			0
$631$		−	38.8200i		−	1.54540i	−0.634772	−	0.772700i	$-0.718906\pi$
$631$		−	38.8200i		−	1.54540i	0.634772	−	0.772700i	$-0.281094\pi$
$632$	4.99700	+	9.41909i	0.198770	+	0.374671i
$633$		0			0
$634$	−15.5735	−	5.87991i	−0.618504	−	0.233521i
$635$	−9.41213			−0.373509
$636$		0			0
$637$	−28.1284			−1.11449
$638$	22.5211	+	8.50302i	0.891620	+	0.336638i
$639$		0			0
$640$	9.24389	−	6.52307i	0.365397	−	0.257847i
$641$		−	19.1212i		−	0.755243i	−0.925960	−	0.377621i	$-0.876742\pi$
$641$		−	19.1212i		−	0.755243i	0.925960	−	0.377621i	$-0.123258\pi$
$642$		0			0
$643$		−	6.57189i		−	0.259170i	−0.991568	−	0.129585i	$-0.958635\pi$
$643$		−	6.57189i		−	0.259170i	0.991568	−	0.129585i	$-0.0413645\pi$
$644$	−11.1259	+	12.6337i	−0.438421	+	0.497837i
$645$		0			0
$646$	−2.83956	+	7.52086i	−0.111721	+	0.295904i
$647$	−12.7191			−0.500040			−0.250020	−	0.968241i	$-0.580437\pi$
$647$	−12.7191			−0.500040			−0.250020	+	0.968241i	$0.580437\pi$
$648$		0			0
$649$	−27.1658			−1.06635
$650$	−2.53719	+	6.72001i	−0.0995168	+	0.263581i
$651$		0			0
$652$	20.3095	−	23.0619i	0.795380	−	0.903173i
$653$		−	44.0821i		−	1.72506i	−0.506002	−	0.862532i	$-0.668877\pi$
$653$		−	44.0821i		−	1.72506i	0.506002	−	0.862532i	$-0.331123\pi$
$654$		0			0
$655$			2.13260i			0.0833278i
$656$	−16.9620	+	2.16157i	−0.662256	+	0.0843951i
$657$		0			0
$658$	16.4796	+	6.22201i	0.642444	+	0.242559i
$659$	21.7858			0.848656			0.424328	−	0.905509i	$-0.360510\pi$
$659$	21.7858			0.848656			0.424328	+	0.905509i	$0.360510\pi$
$660$		0			0
$661$	20.5513			0.799353			0.399676	−	0.916656i	$-0.369123\pi$
$661$	20.5513			0.799353			0.399676	+	0.916656i	$0.369123\pi$
$662$	−5.72080	−	2.15993i	−0.222345	−	0.0839481i
$663$		0			0
$664$	1.43005	−	0.758669i	0.0554968	−	0.0294421i
$665$			3.06920i			0.119018i
$666$		0			0
$667$			38.9379i			1.50768i
$668$	33.3580	+	29.3768i	1.29066	+	1.13662i
$669$		0			0
$670$	−7.20187	+	19.0749i	−0.278233	+	0.736928i
$671$	8.08865			0.312259
$672$		0			0
$673$	−2.17749			−0.0839359			−0.0419680	−	0.999119i	$-0.513363\pi$
$673$	−2.17749			−0.0839359			−0.0419680	+	0.999119i	$0.513363\pi$
$674$	−3.88139	+	10.2803i	−0.149505	+	0.395981i
$675$		0			0
$676$	−19.2090	−	16.9164i	−0.738807	−	0.650631i
$677$		−	2.22672i		−	0.0855798i	−0.999084	−	0.0427899i	$-0.986375\pi$
$677$		−	2.22672i		−	0.0855798i	0.999084	−	0.0427899i	$-0.0136246\pi$
$678$		0			0
$679$			14.0877i			0.540637i
$680$	5.59542	−	2.96848i	0.214575	−	0.113836i
$681$		0			0
$682$	13.1926	+	4.98095i	0.505170	+	0.190731i
$683$	−12.9800			−0.496665			−0.248333	−	0.968675i	$-0.579883\pi$
$683$	−12.9800			−0.496665			−0.248333	+	0.968675i	$0.579883\pi$
$684$		0			0
$685$	−16.4869			−0.629931
$686$	20.0576	+	7.57290i	0.765803	+	0.289135i
$687$		0			0
$688$	−17.1407	+	2.18434i	−0.653482	+	0.0832770i
$689$		−	47.8805i		−	1.82410i
$690$		0			0
$691$			27.9275i			1.06241i	0.847243	+	0.531205i	$0.178261\pi$
$691$			27.9275i			1.06241i	−0.847243	+	0.531205i	$0.821739\pi$
$692$	20.3699	−	23.1305i	0.774347	−	0.879289i
$693$		0			0
$694$	−5.62776	+	14.9057i	−0.213627	+	0.565813i
$695$	−20.1007			−0.762464
$696$		0			0
$697$	−9.57314			−0.362608
$698$	11.1298	−	29.4784i	0.421269	−	1.11577i
$699$		0			0
$700$	1.59824	−	1.81484i	0.0604077	−	0.0685943i
$701$		−	31.0643i		−	1.17328i	−0.809847	−	0.586641i	$-0.800450\pi$
$701$		−	31.0643i		−	1.17328i	0.809847	−	0.586641i	$-0.199550\pi$
$702$		0			0
$703$			26.2756i			0.991001i
$704$	−13.6514	+	20.1582i	−0.514507	+	0.759741i
$705$		0			0
$706$	−29.1925	−	11.0219i	−1.09868	−	0.414813i
$707$	5.77682			0.217260
$708$		0			0
$709$	−43.4478			−1.63172			−0.815859	−	0.578251i	$-0.803735\pi$
$709$	−43.4478			−1.63172			−0.815859	+	0.578251i	$0.803735\pi$
$710$	4.62146	+	1.74487i	0.173440	+	0.0654837i
$711$		0			0
$712$	3.18302	+	5.99982i	0.119289	+	0.224853i
$713$			22.8093i			0.854216i
$714$		0			0
$715$		−	15.4570i		−	0.578059i
$716$	−19.2464	−	16.9493i	−0.719270	−	0.633426i
$717$		0			0
$718$	0.850858	−	2.25358i	0.0317537	−	0.0841030i
$719$	12.6495			0.471747			0.235874	−	0.971784i	$-0.424205\pi$
$719$	12.6495			0.471747			0.235874	+	0.971784i	$0.424205\pi$
$720$		0			0
$721$	11.4371			0.425938
$722$	−6.27247	+	16.6133i	−0.233437	+	0.618283i
$723$		0			0
$724$	−26.0636	−	22.9530i	−0.968648	−	0.853041i
$725$		−	5.59345i		−	0.207736i
$726$		0			0
$727$			50.1181i			1.85878i	0.369103	+	0.929389i	$0.379665\pi$
$727$			50.1181i			1.85878i	−0.369103	+	0.929389i	$0.620335\pi$
$728$	8.14068	+	15.3448i	0.301714	+	0.568714i
$729$		0			0
$730$	6.74826	+	2.54785i	0.249764	+	0.0943003i
$731$	−9.67397			−0.357805
$732$		0			0
$733$	−29.4655			−1.08833			−0.544166	−	0.838978i	$-0.683154\pi$
$733$	−29.4655			−1.08833			−0.544166	+	0.838978i	$0.683154\pi$
$734$	12.4652	+	4.70632i	0.460098	+	0.173713i
$735$		0			0
$736$	−38.3037	−	9.14079i	−1.41189	−	0.336934i
$737$		−	43.8751i		−	1.61616i
$738$		0			0
$739$			45.3131i			1.66687i	0.552618	+	0.833435i	$0.313629\pi$
$739$			45.3131i			1.66687i	−0.552618	+	0.833435i	$0.686371\pi$
$740$	13.6826	−	15.5369i	0.502982	−	0.571148i
$741$		0			0
$742$	−5.69376	+	15.0805i	−0.209025	+	0.553623i
$743$	−8.07559			−0.296265			−0.148132	−	0.988968i	$-0.547326\pi$
$743$	−8.07559			−0.296265			−0.148132	+	0.988968i	$0.547326\pi$
$744$		0			0
$745$	1.88370			0.0690135
$746$	−7.28589	+	19.2974i	−0.266756	+	0.706530i
$747$		0			0
$748$	−9.00823	+	10.2291i	−0.329373	+	0.374011i
$749$			22.1287i			0.808567i
$750$		0			0
$751$		−	11.2164i		−	0.409291i	−0.978836	−	0.204646i	$-0.934396\pi$
$751$		−	11.2164i		−	0.409291i	0.978836	−	0.204646i	$-0.0656042\pi$
$752$	5.20895	+	40.8751i	0.189951	+	1.49056i
$753$		0			0
$754$	37.5881	+	14.1917i	1.36888	+	0.516829i
$755$	−6.18825			−0.225214
$756$		0			0
$757$	−26.9148			−0.978236			−0.489118	−	0.872218i	$-0.662681\pi$
$757$	−26.9148			−0.978236			−0.489118	+	0.872218i	$0.662681\pi$
$758$	−12.5169	−	4.72587i	−0.454636	−	0.171651i
$759$		0			0
$760$	−6.34228	+	3.36470i	−0.230059	+	0.122051i
$761$			7.78903i			0.282352i	0.989985	+	0.141176i	$0.0450884\pi$
$761$			7.78903i			0.282352i	−0.989985	+	0.141176i	$0.954912\pi$
$762$		0			0
$763$			12.4044i			0.449068i
$764$	26.7597	+	23.5660i	0.968132	+	0.852587i
$765$		0			0
$766$	3.42683	−	9.07632i	0.123816	−	0.327941i
$767$	−45.3402			−1.63714
$768$		0			0
$769$	6.72981			0.242683			0.121342	−	0.992611i	$-0.461280\pi$
$769$	6.72981			0.242683			0.121342	+	0.992611i	$0.461280\pi$
$770$	−1.83809	+	4.86837i	−0.0662401	+	0.175444i
$771$		0			0
$772$	7.33003	+	6.45520i	0.263813	+	0.232328i
$773$		−	16.5270i		−	0.594435i	−0.954810	−	0.297217i	$-0.903941\pi$
$773$		−	16.5270i		−	0.594435i	0.954810	−	0.297217i	$-0.0960586\pi$
$774$		0			0
$775$		−	3.27657i		−	0.117698i
$776$	−29.1113	+	15.4441i	−1.04503	+	0.554411i
$777$		0			0
$778$	10.8720	+	4.10480i	0.389780	+	0.147164i
$779$	10.8509			0.388775
$780$		0			0
$781$	−10.6300			−0.380372
$782$	−20.6257	−	7.78740i	−0.737574	−	0.278477i
$783$		0			0
$784$	2.80031	+	21.9743i	0.100011	+	0.784796i
$785$			2.20024i			0.0785299i
$786$		0			0
$787$		−	2.75942i		−	0.0983628i	−0.998790	−	0.0491814i	$-0.984339\pi$
$787$		−	2.75942i		−	0.0983628i	0.998790	−	0.0491814i	$-0.0156612\pi$
$788$	22.2292	−	25.2417i	0.791881	−	0.899199i
$789$		0			0
$790$	−1.88311	+	4.98761i	−0.0669980	+	0.177451i
$791$	7.41755			0.263738
$792$		0			0
$793$	13.5001			0.479401
$794$	3.53634	−	9.36637i	0.125500	−	0.332400i
$795$		0			0
$796$	−7.81838	+	8.87795i	−0.277115	+	0.314670i
$797$			5.24247i			0.185698i	0.995680	+	0.0928488i	$0.0295973\pi$
$797$			5.24247i			0.185698i	−0.995680	+	0.0928488i	$0.970403\pi$
$798$		0			0
$799$			23.0694i			0.816136i
$800$	5.50235	+	1.31308i	0.194537	+	0.0464243i
$801$		0			0
$802$	23.4079	+	8.83781i	0.826560	+	0.312074i
$803$	−15.5220			−0.547759
$804$		0			0
$805$	−8.41717			−0.296666
$806$	22.0186	+	8.31328i	0.775571	+	0.292823i
$807$		0			0
$808$	6.33301	+	11.9374i	0.222795	+	0.419956i
$809$		−	47.1813i		−	1.65881i	−0.558650	−	0.829403i	$-0.688681\pi$
$809$		−	47.1813i		−	1.65881i	0.558650	−	0.829403i	$-0.311319\pi$
$810$		0			0
$811$		−	18.8666i		−	0.662495i	−0.943544	−	0.331247i	$-0.892531\pi$
$811$		−	18.8666i		−	0.662495i	0.943544	−	0.331247i	$-0.107469\pi$
$812$	−10.1512	−	8.93966i	−0.356237	−	0.313721i
$813$		0			0
$814$	−15.7360	+	41.6784i	−0.551546	+	1.46083i
$815$	15.3649			0.538210
$816$		0			0
$817$	10.9652			0.383625
$818$	11.3435	−	30.0444i	0.396615	−	1.05048i
$819$		0			0
$820$	−6.41622	−	5.65046i	−0.224064	−	0.197323i
$821$		−	1.29788i		−	0.0452962i	−0.999743	−	0.0226481i	$-0.992790\pi$
$821$		−	1.29788i		−	0.0452962i	0.999743	−	0.0226481i	$-0.00720973\pi$
$822$		0			0
$823$		−	6.67062i		−	0.232523i	−0.993219	−	0.116262i	$-0.962909\pi$
$823$		−	6.67062i		−	0.232523i	0.993219	−	0.116262i	$-0.0370911\pi$
$824$	12.5382	+	23.6339i	0.436790	+	0.823325i
$825$		0			0
$826$	14.2804	+	5.39168i	0.496880	+	0.187601i
$827$	37.4924			1.30374			0.651869	−	0.758331i	$-0.273985\pi$
$827$	37.4924			1.30374			0.651869	+	0.758331i	$0.273985\pi$
$828$		0			0
$829$	−22.9261			−0.796255			−0.398127	−	0.917330i	$-0.630340\pi$
$829$	−22.9261			−0.796255			−0.398127	+	0.917330i	$0.630340\pi$
$830$	0.757242	+	0.285903i	0.0262843	+	0.00992382i
$831$		0			0
$832$	−22.7844	+	33.6443i	−0.789907	+	1.16641i
$833$			12.4020i			0.429704i
$834$		0			0
$835$			22.2247i			0.769119i
$836$	10.2106	−	11.5944i	0.353142	−	0.401001i
$837$		0			0
$838$	−13.1680	+	34.8769i	−0.454882	+	1.20480i
$839$	18.2210			0.629057			0.314529	−	0.949248i	$-0.398154\pi$
$839$	18.2210			0.629057			0.314529	+	0.949248i	$0.398154\pi$
$840$		0			0
$841$	−2.28670			−0.0788518
$842$	−8.56959	+	22.6975i	−0.295328	+	0.782206i
$843$		0			0
$844$	−36.5524	+	41.5061i	−1.25819	+	1.42870i
$845$		−	12.7979i		−	0.440263i
$846$		0			0
$847$			2.10248i			0.0722422i
$848$	−37.4048	+	4.76671i	−1.28449	+	0.163690i
$849$		0			0
$850$	2.96289	+	1.11866i	0.101626	+	0.0383698i
$851$	−72.0599			−2.47018
$852$		0			0
$853$	−1.95096			−0.0667994			−0.0333997	−	0.999442i	$-0.510633\pi$
$853$	−1.95096			−0.0667994			−0.0333997	+	0.999442i	$0.510633\pi$
$854$	−4.25201	−	1.60538i	−0.145501	−	0.0549349i
$855$		0			0
$856$	−45.7275	+	24.2593i	−1.56293	+	0.829166i
$857$		−	13.0233i		−	0.444868i	−0.974948	−	0.222434i	$-0.928600\pi$
$857$		−	13.0233i		−	0.444868i	0.974948	−	0.222434i	$-0.0714002\pi$
$858$		0			0
$859$		−	4.04184i		−	0.137906i	−0.997620	−	0.0689530i	$-0.978034\pi$
$859$		−	4.04184i		−	0.137906i	0.997620	−	0.0689530i	$-0.0219658\pi$
$860$	−6.48381	−	5.70997i	−0.221096	−	0.194709i
$861$		0			0
$862$	6.28489	−	16.6462i	0.214064	−	0.566972i
$863$	10.6258			0.361705			0.180853	−	0.983510i	$-0.442114\pi$
$863$	10.6258			0.361705			0.180853	+	0.983510i	$0.442114\pi$
$864$		0			0
$865$	15.4106			0.523978
$866$	5.86611	−	15.5370i	0.199338	−	0.527969i
$867$		0			0
$868$	−5.94643	−	5.23673i	−0.201835	−	0.177746i
$869$		−	11.4722i		−	0.389168i
$870$		0			0
$871$		−	73.2281i		−	2.48124i
$872$	−25.6327	+	13.5986i	−0.868034	+	0.460508i
$873$		0			0
$874$	23.3788	+	8.82684i	0.790799	+	0.298572i
$875$	1.20913			0.0408761
$876$		0			0
$877$	−53.1060			−1.79326			−0.896631	−	0.442779i	$-0.853992\pi$
$877$	−53.1060			−1.79326			−0.896631	+	0.442779i	$0.853992\pi$
$878$	−2.22649	−	0.840628i	−0.0751404	−	0.0283698i
$879$		0			0
$880$	−12.0752	+	1.53881i	−0.407055	+	0.0518734i
$881$		−	10.8244i		−	0.364685i	−0.983235	−	0.182342i	$-0.941632\pi$
$881$		−	10.8244i		−	0.364685i	0.983235	−	0.182342i	$-0.0583679\pi$
$882$		0			0
$883$		−	21.6083i		−	0.727178i	−0.931559	−	0.363589i	$-0.881551\pi$
$883$		−	21.6083i		−	0.727178i	0.931559	−	0.363589i	$-0.118449\pi$
$884$	−15.0349	+	17.0724i	−0.505677	+	0.574208i
$885$		0			0
$886$	0.379152	−	1.00422i	0.0127379	−	0.0337376i
$887$	0.528051			0.0177302			0.00886511	−	0.999961i	$-0.497178\pi$
$887$	0.528051			0.0177302			0.00886511	+	0.999961i	$0.497178\pi$
$888$		0			0
$889$	−11.3805			−0.381690
$890$	−1.19951	+	3.17703i	−0.0402078	+	0.106494i
$891$		0			0
$892$	31.6537	−	35.9435i	1.05984	−	1.20348i
$893$		−	26.1486i		−	0.875030i
$894$		0			0
$895$		−	12.8229i		−	0.428621i
$896$	11.1771	−	7.88724i	0.373400	−	0.263494i
$897$		0			0
$898$	−23.0977	−	8.72070i	−0.770779	−	0.291013i
$899$	−18.3273			−0.611251
$900$		0			0
$901$	−21.1108			−0.703302
$902$	17.2118	+	6.49844i	0.573090	+	0.216374i
$903$		0			0
$904$	8.13172	+	15.3279i	0.270457	+	0.509797i
$905$		−	17.3649i		−	0.577227i
$906$		0			0
$907$			47.3294i			1.57155i	0.618515	+	0.785773i	$0.287735\pi$
$907$			47.3294i			1.57155i	−0.618515	+	0.785773i	$0.712265\pi$
$908$	−10.3859	−	9.14635i	−0.344668	−	0.303532i
$909$		0			0
$910$	−3.06779	+	8.12537i	−0.101696	+	0.269353i
$911$	−37.6319			−1.24680			−0.623401	−	0.781902i	$-0.714250\pi$
$911$	−37.6319			−1.24680			−0.623401	+	0.781902i	$0.714250\pi$
$912$		0			0
$913$	−1.74177			−0.0576441
$914$	17.4155	−	46.1267i	0.576053	−	1.52574i
$915$		0			0
$916$	22.9896	+	20.2458i	0.759596	+	0.668939i
$917$			2.57860i			0.0851528i
$918$		0			0
$919$			42.9157i			1.41566i	0.706383	+	0.707830i	$0.250326\pi$
$919$			42.9157i			1.41566i	−0.706383	+	0.707830i	$0.749674\pi$
$920$	−9.22758	−	17.3935i	−0.304224	−	0.573447i
$921$		0			0
$922$	41.3871	+	15.6260i	1.36301	+	0.514615i
$923$	−17.7417			−0.583974
$924$		0			0
$925$	10.3514			0.340353
$926$	−13.6046	−	5.13652i	−0.447075	−	0.168797i
$927$		0			0
$928$	7.34464	−	30.7771i	0.241100	−	1.01031i
$929$			29.0533i			0.953209i	0.879118	+	0.476605i	$0.158133\pi$
$929$			29.0533i			0.953209i	−0.879118	+	0.476605i	$0.841867\pi$
$930$		0			0
$931$		−	14.0574i		−	0.460712i
$932$	8.73781	−	9.92198i	0.286216	−	0.325005i
$933$		0			0
$934$	−1.45156	+	3.84459i	−0.0474963	+	0.125799i
$935$	−6.81509			−0.222877
$936$		0			0
$937$	51.0143			1.66656			0.833282	−	0.552848i	$-0.186459\pi$
$937$	51.0143			1.66656			0.833282	+	0.552848i	$0.186459\pi$
$938$	−8.70801	+	23.0641i	−0.284326	+	0.753068i
$939$		0			0
$940$	−13.6165	+	15.4618i	−0.444121	+	0.504310i
$941$			8.71487i			0.284097i	0.989860	+	0.142048i	$0.0453688\pi$
$941$			8.71487i			0.284097i	−0.989860	+	0.142048i	$0.954631\pi$
$942$		0			0
$943$			29.7583i			0.969065i
$944$	4.51382	+	35.4203i	0.146912	+	1.15283i
$945$		0			0
$946$	17.3931	+	6.56689i	0.565498	+	0.213508i
$947$	−38.1607			−1.24006			−0.620028	−	0.784580i	$-0.712879\pi$
$947$	−38.1607			−1.24006			−0.620028	+	0.784580i	$0.712879\pi$
$948$		0			0
$949$	−25.9064			−0.840957
$950$	−3.35837	−	1.26798i	−0.108960	−	0.0411387i
$951$		0			0
$952$	6.76560	−	3.58928i	0.219274	−	0.116329i
$953$			40.4395i			1.30996i	0.755645	+	0.654982i	$0.227324\pi$
$953$			40.4395i			1.30996i	−0.755645	+	0.654982i	$0.772676\pi$
$954$		0			0
$955$			17.8286i			0.576920i
$956$	12.3395	+	10.8668i	0.399089	+	0.351458i
$957$		0			0
$958$	9.41884	−	24.9468i	0.304309	−	0.805994i
$959$	−19.9348			−0.643728
$960$		0			0
$961$	20.2641			0.653680
$962$	−26.2636	+	69.5617i	−0.846771	+	2.24276i
$963$		0			0
$964$	−21.9371	−	19.3189i	−0.706546	−	0.622220i
$965$			4.88362i			0.157209i
$966$		0			0
$967$		−	16.8302i		−	0.541224i	−0.962689	−	0.270612i	$-0.912774\pi$
$967$		−	16.8302i		−	0.541224i	0.962689	−	0.270612i	$-0.0872260\pi$
$968$	−4.34463	+	2.30491i	−0.139642	+	0.0740826i
$969$		0			0
$970$	−15.4151	−	5.82007i	−0.494947	−	0.186871i
$971$	34.0951			1.09416			0.547082	−	0.837079i	$-0.315738\pi$
$971$	34.0951			1.09416			0.547082	+	0.837079i	$0.315738\pi$
$972$		0			0
$973$	−24.3044			−0.779163
$974$	15.3072	+	5.77934i	0.490474	+	0.185182i
$975$		0			0
$976$	−1.34399	−	10.5464i	−0.0430201	−	0.337583i
$977$			0.863887i			0.0276382i	0.999905	+	0.0138191i	$0.00439889\pi$
$977$			0.863887i			0.0276382i	−0.999905	+	0.0138191i	$0.995601\pi$
$978$		0			0
$979$		−	7.30764i		−	0.233553i
$980$	−7.32017	+	8.31222i	−0.233834	+	0.265524i
$981$		0			0
$982$	−0.746913	+	1.97828i	−0.0238349	+	0.0631293i
$983$	36.8214			1.17442			0.587209	−	0.809435i	$-0.300226\pi$
$983$	36.8214			1.17442			0.587209	+	0.809435i	$0.300226\pi$
$984$		0			0
$985$	16.8173			0.535842
$986$	6.25719	−	16.5728i	0.199269	−	0.527786i
$987$		0			0
$988$	17.0417	−	19.3512i	0.542168	−	0.615644i
$989$			30.0718i			0.956227i
$990$		0			0
$991$			35.9773i			1.14286i	0.820652	+	0.571428i	$0.193610\pi$
$991$			35.9773i			1.14286i	−0.820652	+	0.571428i	$0.806390\pi$
$992$	4.30239	−	18.0288i	0.136601	−	0.572416i
$993$		0			0
$994$	5.58795	+	2.10977i	0.177239	+	0.0669179i
$995$	−5.91492			−0.187515
$996$		0			0
$997$	−33.4645			−1.05983			−0.529915	−	0.848051i	$-0.677776\pi$
$997$	−33.4645			−1.05983			−0.529915	+	0.848051i	$0.677776\pi$
$998$	−41.6478	−	15.7244i	−1.31834	−	0.497748i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.2.e.b.971.18		48
3.2	odd	2	inner	1620.2.e.b.971.31		48
4.3	odd	2	inner	1620.2.e.b.971.32		48
9.2	odd	6		180.2.q.a.131.1	yes	48
9.4	even	3		180.2.q.a.11.8	yes	48
9.5	odd	6		540.2.q.a.251.17		48
9.7	even	3		540.2.q.a.71.24		48
12.11	even	2	inner	1620.2.e.b.971.17		48
36.7	odd	6		540.2.q.a.71.17		48
36.11	even	6		180.2.q.a.131.8	yes	48
36.23	even	6		540.2.q.a.251.24		48
36.31	odd	6		180.2.q.a.11.1	✓	48
45.2	even	12		900.2.o.b.599.11		48
45.4	even	6		900.2.r.f.551.17		48
45.13	odd	12		900.2.o.b.299.6		48
45.22	odd	12		900.2.o.c.299.19		48
45.29	odd	6		900.2.r.f.851.24		48
45.38	even	12		900.2.o.c.599.14		48
180.47	odd	12		900.2.o.b.599.6		48
180.67	even	12		900.2.o.c.299.14		48
180.83	odd	12		900.2.o.c.599.19		48
180.103	even	12		900.2.o.b.299.11		48
180.119	even	6		900.2.r.f.851.17		48
180.139	odd	6		900.2.r.f.551.24		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.q.a.11.1	✓	48	36.31	odd	6
180.2.q.a.11.8	yes	48	9.4	even	3
180.2.q.a.131.1	yes	48	9.2	odd	6
180.2.q.a.131.8	yes	48	36.11	even	6
540.2.q.a.71.17		48	36.7	odd	6
540.2.q.a.71.24		48	9.7	even	3
540.2.q.a.251.17		48	9.5	odd	6
540.2.q.a.251.24		48	36.23	even	6
900.2.o.b.299.6		48	45.13	odd	12
900.2.o.b.299.11		48	180.103	even	12
900.2.o.b.599.6		48	180.47	odd	12
900.2.o.b.599.11		48	45.2	even	12
900.2.o.c.299.14		48	180.67	even	12
900.2.o.c.299.19		48	45.22	odd	12
900.2.o.c.599.14		48	45.38	even	12
900.2.o.c.599.19		48	180.83	odd	12
900.2.r.f.551.17		48	45.4	even	6
900.2.r.f.551.24		48	180.139	odd	6
900.2.r.f.851.17		48	180.119	even	6
900.2.r.f.851.24		48	45.29	odd	6
1620.2.e.b.971.17		48	12.11	even	2	inner
1620.2.e.b.971.18		48	1.1	even	1	trivial
1620.2.e.b.971.31		48	3.2	odd	2	inner
1620.2.e.b.971.32		48	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1620.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.499529 + 1.32305i) q^{2} +(-1.50094 - 1.32181i) q^{4} -1.00000i q^{5} -1.20913i q^{7} +(2.49858 - 1.32555i) q^{8} +(1.32305 + 0.499529i) q^{10} -3.04322 q^{11} -5.07917 q^{13} +(1.59974 + 0.603996i) q^{14} +(0.505654 + 3.96791i) q^{16} +2.23944i q^{17} -2.53835i q^{19} +(-1.32181 + 1.50094i) q^{20} +(1.52017 - 4.02634i) q^{22} +6.96134 q^{23} -1.00000 q^{25} +(2.53719 - 6.72001i) q^{26} +(-1.59824 + 1.81484i) q^{28} +5.59345i q^{29} +3.27657i q^{31} +(-5.50235 - 1.31308i) q^{32} +(-2.96289 - 1.11866i) q^{34} -1.20913 q^{35} -10.3514 q^{37} +(3.35837 + 1.26798i) q^{38} +(-1.32555 - 2.49858i) q^{40} +4.27480i q^{41} +4.31983i q^{43} +(4.56769 + 4.02254i) q^{44} +(-3.47739 + 9.21023i) q^{46} +10.3014 q^{47} +5.53800 q^{49} +(0.499529 - 1.32305i) q^{50} +(7.62354 + 6.71368i) q^{52} +9.42683i q^{53} +3.04322i q^{55} +(-1.60276 - 3.02112i) q^{56} +(-7.40044 - 2.79409i) q^{58} +8.92669 q^{59} -2.65793 q^{61} +(-4.33508 - 1.63674i) q^{62} +(4.48585 - 6.62398i) q^{64} +5.07917i q^{65} +14.4173i q^{67} +(2.96010 - 3.36126i) q^{68} +(0.603996 - 1.59974i) q^{70} +3.49303 q^{71} +5.10052 q^{73} +(5.17084 - 13.6955i) q^{74} +(-3.35521 + 3.80992i) q^{76} +3.67965i q^{77} +3.76977i q^{79} +(3.96791 - 0.505654i) q^{80} +(-5.65579 - 2.13538i) q^{82} +0.572344 q^{83} +2.23944 q^{85} +(-5.71536 - 2.15788i) q^{86} +(-7.60373 + 4.03392i) q^{88} +2.40129i q^{89} +6.14138i q^{91} +(-10.4486 - 9.20155i) q^{92} +(-5.14586 + 13.6293i) q^{94} -2.53835 q^{95} -11.6511 q^{97} +(-2.76639 + 7.32708i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{25} + 12 q^{34} + 12 q^{40} - 12 q^{46} - 48 q^{49} + 36 q^{52} + 36 q^{58} - 48 q^{64} - 24 q^{73} - 12 q^{76} - 36 q^{82} - 36 q^{94} + 24 q^{97}+O(q^{100}) \) 48 * q - 48 * q^25 + 12 * q^34 + 12 * q^40 - 12 * q^46 - 48 * q^49 + 36 * q^52 + 36 * q^58 - 48 * q^64 - 24 * q^73 - 12 * q^76 - 36 * q^82 - 36 * q^94 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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