LMFDB - Embedded newform 504.3.e.c.251.32

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,3,Mod(251,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.251"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	504.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:	$13.7330053238$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.32
Character	$\chi$	$=$	504.251
Dual form			504.3.e.c.251.30

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.852241 + 1.80933i) q^{2} +(-2.54737 + 3.08398i) q^{4} +9.10939i q^{5} +(0.958628 + 6.93405i) q^{7} +(-7.75091 - 1.98075i) q^{8} +(-16.4819 + 7.76340i) q^{10} +9.66169i q^{11} +2.31922 q^{13} +(-11.7290 + 7.64396i) q^{14} +(-3.02182 - 15.7121i) q^{16} +21.8883 q^{17} -26.9198i q^{19} +(-28.0931 - 23.2050i) q^{20} +(-17.4812 + 8.23410i) q^{22} +15.4172 q^{23} -57.9809 q^{25} +(1.97653 + 4.19623i) q^{26} +(-23.8264 - 14.7072i) q^{28} -18.1366 q^{29} +45.9762 q^{31} +(25.8530 - 18.8579i) q^{32} +(18.6541 + 39.6032i) q^{34} +(-63.1649 + 8.73251i) q^{35} +32.3318i q^{37} +(48.7069 - 22.9422i) q^{38} +(18.0434 - 70.6061i) q^{40} +33.0463 q^{41} -60.5091 q^{43} +(-29.7964 - 24.6119i) q^{44} +(13.1391 + 27.8948i) q^{46} -29.4932i q^{47} +(-47.1621 + 13.2943i) q^{49} +(-49.4138 - 104.907i) q^{50} +(-5.90790 + 7.15241i) q^{52} +65.7621 q^{53} -88.0121 q^{55} +(6.30435 - 55.6440i) q^{56} +(-15.4568 - 32.8152i) q^{58} -8.47268 q^{59} -74.9438 q^{61} +(39.1828 + 83.1863i) q^{62} +(56.1533 + 30.7052i) q^{64} +21.1266i q^{65} +20.2120 q^{67} +(-55.7575 + 67.5029i) q^{68} +(-69.6318 - 106.844i) q^{70} +21.7110 q^{71} +100.202i q^{73} +(-58.4989 + 27.5545i) q^{74} +(83.0201 + 68.5747i) q^{76} +(-66.9947 + 9.26197i) q^{77} -78.9852i q^{79} +(143.127 - 27.5269i) q^{80} +(28.1634 + 59.7918i) q^{82} +67.6265 q^{83} +199.389i q^{85} +(-51.5684 - 109.481i) q^{86} +(19.1374 - 74.8869i) q^{88} -130.927 q^{89} +(2.22326 + 16.0816i) q^{91} +(-39.2732 + 47.5461i) q^{92} +(53.3629 - 25.1353i) q^{94} +245.223 q^{95} -175.267i q^{97} +(-64.2473 - 74.0019i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 144 q^{22} - 336 q^{25} - 232 q^{28} - 384 q^{43} + 736 q^{46} + 368 q^{49} - 432 q^{58} + 480 q^{64} - 896 q^{67} + 264 q^{70} - 48 q^{88} - 576 q^{91}+O(q^{100}) $ 48 * q + 144 * q^22 - 336 * q^25 - 232 * q^28 - 384 * q^43 + 736 * q^46 + 368 * q^49 - 432 * q^58 + 480 * q^64 - 896 * q^67 + 264 * q^70 - 48 * q^88 - 576 * q^91

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	0.852241	+	1.80933i	0.426121	+	0.904666i
$2$	0.852241	+	1.80933i	0.426121	+	0.904666i
$3$		0			0
$3$		0			0
$4$	−2.54737	+	3.08398i	−0.636842	+	0.770994i
$5$			9.10939i			1.82188i	0.412542	+	0.910939i	$0.364641\pi$
$5$			9.10939i			1.82188i	−0.412542	+	0.910939i	$0.635359\pi$
$6$		0			0
$7$	0.958628	+	6.93405i	0.136947	+	0.990578i
$7$	0.958628	+	6.93405i	0.136947	+	0.990578i
$8$	−7.75091	−	1.98075i	−0.968864	−	0.247593i
$9$		0			0
$10$	−16.4819	+	7.76340i	−1.64819	+	0.776340i
$11$			9.66169i			0.878336i	0.898405	+	0.439168i	$0.144727\pi$
$11$			9.66169i			0.878336i	−0.898405	+	0.439168i	$0.855273\pi$
$12$		0			0
$13$	2.31922			0.178401			0.0892006	−	0.996014i	$-0.471569\pi$
$13$	2.31922			0.178401			0.0892006	+	0.996014i	$0.471569\pi$
$14$	−11.7290	+	7.64396i	−0.837787	+	0.545997i
$15$		0			0
$16$	−3.02182	−	15.7121i	−0.188864	−	0.982003i
$17$	21.8883			1.28755			0.643773	−	0.765217i	$-0.277368\pi$
$17$	21.8883			1.28755			0.643773	+	0.765217i	$0.277368\pi$
$18$		0			0
$19$		−	26.9198i		−	1.41683i	−0.705795	−	0.708416i	$-0.749410\pi$
$19$		−	26.9198i		−	1.41683i	0.705795	−	0.708416i	$-0.250590\pi$
$20$	−28.0931	−	23.2050i	−1.40466	−	1.16025i
$21$		0			0
$22$	−17.4812	+	8.23410i	−0.794601	+	0.374277i
$23$	15.4172			0.670311			0.335156	−	0.942163i	$-0.391211\pi$
$23$	15.4172			0.670311			0.335156	+	0.942163i	$0.391211\pi$
$24$		0			0
$25$	−57.9809			−2.31924
$26$	1.97653	+	4.19623i	0.0760205	+	0.161394i
$27$		0			0
$28$	−23.8264	−	14.7072i	−0.850944	−	0.525257i
$29$	−18.1366			−0.625400			−0.312700	−	0.949852i	$-0.601233\pi$
$29$	−18.1366			−0.625400			−0.312700	+	0.949852i	$0.601233\pi$
$30$		0			0
$31$	45.9762			1.48310			0.741552	−	0.670896i	$-0.234090\pi$
$31$	45.9762			1.48310			0.741552	+	0.670896i	$0.234090\pi$
$32$	25.8530	−	18.8579i	0.807907	−	0.589311i
$33$		0			0
$34$	18.6541	+	39.6032i	0.548650	+	1.16480i
$35$	−63.1649	+	8.73251i	−1.80471	+	0.249500i
$36$		0			0
$37$			32.3318i			0.873832i	0.899502	+	0.436916i	$0.143929\pi$
$37$			32.3318i			0.873832i	−0.899502	+	0.436916i	$0.856071\pi$
$38$	48.7069	−	22.9422i	1.28176	−	0.603742i
$39$		0			0
$40$	18.0434	−	70.6061i	0.451085	−	1.76515i
$41$	33.0463			0.806007			0.403004	−	0.915198i	$-0.367966\pi$
$41$	33.0463			0.806007			0.403004	+	0.915198i	$0.367966\pi$
$42$		0			0
$43$	−60.5091			−1.40719			−0.703594	−	0.710602i	$-0.748423\pi$
$43$	−60.5091			−1.40719			−0.703594	+	0.710602i	$0.748423\pi$
$44$	−29.7964	−	24.6119i	−0.677192	−	0.559361i
$45$		0			0
$46$	13.1391	+	27.8948i	0.285633	+	0.606408i
$47$		−	29.4932i		−	0.627514i	−0.949503	−	0.313757i	$-0.898412\pi$
$47$		−	29.4932i		−	0.627514i	0.949503	−	0.313757i	$-0.101588\pi$
$48$		0			0
$49$	−47.1621	+	13.2943i	−0.962491	+	0.271313i
$50$	−49.4138	−	104.907i	−0.988275	−	2.09814i
$51$		0			0
$52$	−5.90790	+	7.15241i	−0.113613	+	0.137546i
$53$	65.7621			1.24079			0.620397	−	0.784288i	$-0.286971\pi$
$53$	65.7621			1.24079			0.620397	+	0.784288i	$0.286971\pi$
$54$		0			0
$55$	−88.0121			−1.60022
$56$	6.30435	−	55.6440i	0.112578	−	0.993643i
$57$		0			0
$58$	−15.4568	−	32.8152i	−0.266496	−	0.565778i
$59$	−8.47268			−0.143605			−0.0718024	−	0.997419i	$-0.522875\pi$
$59$	−8.47268			−0.143605			−0.0718024	+	0.997419i	$0.522875\pi$
$60$		0			0
$61$	−74.9438			−1.22859			−0.614294	−	0.789077i	$-0.710559\pi$
$61$	−74.9438			−1.22859			−0.614294	+	0.789077i	$0.710559\pi$
$62$	39.1828	+	83.1863i	0.631981	+	1.34171i
$63$		0			0
$64$	56.1533	+	30.7052i	0.877395	+	0.479768i
$65$			21.1266i			0.325025i
$66$		0			0
$67$	20.2120			0.301671			0.150836	−	0.988559i	$-0.451804\pi$
$67$	20.2120			0.301671			0.150836	+	0.988559i	$0.451804\pi$
$68$	−55.7575	+	67.5029i	−0.819963	+	0.992690i
$69$		0			0
$70$	−69.6318	−	106.844i	−0.994740	−	1.52635i
$71$	21.7110			0.305789			0.152894	−	0.988243i	$-0.451141\pi$
$71$	21.7110			0.305789			0.152894	+	0.988243i	$0.451141\pi$
$72$		0			0
$73$			100.202i			1.37263i	0.727304	+	0.686315i	$0.240773\pi$
$73$			100.202i			1.37263i	−0.727304	+	0.686315i	$0.759227\pi$
$74$	−58.4989	+	27.5545i	−0.790526	+	0.372358i
$75$		0			0
$76$	83.0201	+	68.5747i	1.09237	+	0.902299i
$77$	−66.9947	+	9.26197i	−0.870061	+	0.120285i
$78$		0			0
$79$		−	78.9852i		−	0.999813i	−0.866079	−	0.499906i	$-0.833368\pi$
$79$		−	78.9852i		−	0.999813i	0.866079	−	0.499906i	$-0.166632\pi$
$80$	143.127	−	27.5269i	1.78909	−	0.344087i
$81$		0			0
$82$	28.1634	+	59.7918i	0.343456	+	0.729168i
$83$	67.6265			0.814777			0.407388	−	0.913255i	$-0.366440\pi$
$83$	67.6265			0.814777			0.407388	+	0.913255i	$0.366440\pi$
$84$		0			0
$85$			199.389i			2.34575i
$86$	−51.5684	−	109.481i	−0.599632	−	1.27304i
$87$		0			0
$88$	19.1374	−	74.8869i	0.217470	−	0.850988i
$89$	−130.927			−1.47109			−0.735546	−	0.677474i	$-0.763074\pi$
$89$	−130.927			−1.47109			−0.735546	+	0.677474i	$0.763074\pi$
$90$		0			0
$91$	2.22326	+	16.0816i	0.0244315	+	0.176720i
$92$	−39.2732	+	47.5461i	−0.426882	+	0.516806i
$93$		0			0
$94$	53.3629	−	25.1353i	0.567691	−	0.267397i
$95$	245.223			2.58129
$96$		0			0
$97$		−	175.267i		−	1.80688i	−0.428719	−	0.903438i	$-0.641035\pi$
$97$		−	175.267i		−	1.80688i	0.428719	−	0.903438i	$-0.358965\pi$
$98$	−64.2473	−	74.0019i	−0.655585	−	0.755121i
$99$		0			0
$100$	147.699	−	178.812i	1.47699	−	1.78812i
$101$			71.2685i			0.705629i	0.935693	+	0.352815i	$0.114775\pi$
$101$			71.2685i			0.705629i	−0.935693	+	0.352815i	$0.885225\pi$
$102$		0			0
$103$	84.3756			0.819181			0.409590	−	0.912270i	$-0.365672\pi$
$103$	84.3756			0.819181			0.409590	+	0.912270i	$0.365672\pi$
$104$	−17.9760	−	4.59378i	−0.172847	−	0.0441710i
$105$		0			0
$106$	56.0452	+	118.986i	0.528728	+	1.12251i
$107$			80.7290i			0.754476i	0.926116	+	0.377238i	$0.123126\pi$
$107$			80.7290i			0.754476i	−0.926116	+	0.377238i	$0.876874\pi$
$108$		0			0
$109$			100.232i			0.919557i	0.888034	+	0.459778i	$0.152071\pi$
$109$			100.232i			0.919557i	−0.888034	+	0.459778i	$0.847929\pi$
$110$	−75.0076	−	159.243i	−0.681887	−	1.44767i
$111$		0			0
$112$	106.051	−	36.0155i	0.946887	−	0.321567i
$113$		−	14.6523i		−	0.129666i	−0.997896	−	0.0648330i	$-0.979349\pi$
$113$		−	14.6523i		−	0.129666i	0.997896	−	0.0648330i	$-0.0206515\pi$
$114$		0			0
$115$			140.441i			1.22122i
$116$	46.2006	−	55.9329i	0.398281	−	0.482180i
$117$		0			0
$118$	−7.22077	−	15.3299i	−0.0611930	−	0.129914i
$119$	20.9827	+	151.774i	0.176325	+	1.27541i
$120$		0			0
$121$	27.6517			0.228526
$122$	−63.8702	−	135.598i	−0.523527	−	1.11146i
$123$		0			0
$124$	−117.118	+	141.790i	−0.944503	+	1.14346i
$125$		−	300.436i		−	2.40349i
$126$		0			0
$127$			22.9919i			0.181039i	0.995895	+	0.0905193i	$0.0288527\pi$
$127$			22.9919i			0.181039i	−0.995895	+	0.0905193i	$0.971147\pi$
$128$	−7.69973	+	127.768i	−0.0601541	+	0.998189i
$129$		0			0
$130$	−38.2251	+	18.0050i	−0.294039	+	0.138500i
$131$	155.033			1.18345			0.591727	−	0.806138i	$-0.298446\pi$
$131$	155.033			1.18345			0.591727	+	0.806138i	$0.298446\pi$
$132$		0			0
$133$	186.663	−	25.8061i	1.40348	−	0.194031i
$134$	17.2255	+	36.5702i	0.128548	+	0.272912i
$135$		0			0
$136$	−169.654	−	43.3551i	−1.24746	−	0.318788i
$137$			65.5667i			0.478589i	0.970947	+	0.239294i	$0.0769161\pi$
$137$			65.5667i			0.478589i	−0.970947	+	0.239294i	$0.923084\pi$
$138$		0			0
$139$		−	149.873i		−	1.07823i	−0.842233	−	0.539113i	$-0.818760\pi$
$139$		−	149.873i		−	1.07823i	0.842233	−	0.539113i	$-0.181240\pi$
$140$	133.974	−	217.044i	0.956954	−	1.55031i
$141$		0			0
$142$	18.5030	+	39.2824i	0.130303	+	0.276637i
$143$			22.4076i			0.156696i
$144$		0			0
$145$		−	165.213i		−	1.13940i
$146$	−181.299	+	85.3963i	−1.24177	+	0.584906i
$147$		0			0
$148$	−99.7104	−	82.3610i	−0.673719	−	0.556493i
$149$	−63.7340			−0.427745			−0.213873	−	0.976862i	$-0.568608\pi$
$149$	−63.7340			−0.427745			−0.213873	+	0.976862i	$0.568608\pi$
$150$		0			0
$151$		−	87.7691i		−	0.581252i	−0.956837	−	0.290626i	$-0.906136\pi$
$151$		−	87.7691i		−	0.581252i	0.956837	−	0.290626i	$-0.0938636\pi$
$152$	−53.3213	+	208.653i	−0.350798	+	1.37272i
$153$		0			0
$154$	−73.8536	−	113.322i	−0.479569	−	0.735858i
$155$			418.815i			2.70203i
$156$		0			0
$157$	12.9625			0.0825635			0.0412818	−	0.999148i	$-0.486856\pi$
$157$	12.9625			0.0825635			0.0412818	+	0.999148i	$0.486856\pi$
$158$	142.911	−	67.3145i	0.904497	−	0.426041i
$159$		0			0
$160$	171.784	+	235.505i	1.07365	+	1.47191i
$161$	14.7793	+	106.903i	0.0917969	+	0.663996i
$162$		0			0
$163$	129.380			0.793745			0.396872	−	0.917874i	$-0.370096\pi$
$163$	129.380			0.793745			0.396872	+	0.917874i	$0.370096\pi$
$164$	−84.1811	+	101.914i	−0.513300	+	0.621427i
$165$		0			0
$166$	57.6341	+	122.359i	0.347193	+	0.737101i
$167$			189.489i			1.13466i	0.823489	+	0.567332i	$0.192024\pi$
$167$			189.489i			1.13466i	−0.823489	+	0.567332i	$0.807976\pi$
$168$		0			0
$169$	−163.621			−0.968173
$170$	−360.761	+	169.927i	−2.12212	+	0.999573i
$171$		0			0
$172$	154.139	−	186.609i	0.896157	−	1.08493i
$173$			309.161i			1.78706i	0.449008	+	0.893528i	$0.351778\pi$
$173$			309.161i			1.78706i	−0.449008	+	0.893528i	$0.648222\pi$
$174$		0			0
$175$	−55.5821	−	402.043i	−0.317612	−	2.29739i
$176$	151.805	−	29.1959i	0.862529	−	0.165886i
$177$		0			0
$178$	−111.582	−	236.891i	−0.626863	−	1.33085i
$179$			109.315i			0.610696i	0.952241	+	0.305348i	$0.0987728\pi$
$179$			109.315i			0.610696i	−0.952241	+	0.305348i	$0.901227\pi$
$180$		0			0
$181$	−75.4317			−0.416750			−0.208375	−	0.978049i	$-0.566817\pi$
$181$	−75.4317			−0.416750			−0.208375	+	0.978049i	$0.566817\pi$
$182$	−27.2021	+	17.7280i	−0.149462	+	0.0974066i
$183$		0			0
$184$	−119.497	−	30.5375i	−0.649440	−	0.165964i
$185$	−294.523			−1.59201
$186$		0			0
$187$			211.478i			1.13090i
$188$	90.9562	+	75.1300i	0.483810	+	0.399627i
$189$		0			0
$190$	208.989	+	443.690i	1.09994	+	2.33521i
$191$	204.357			1.06993			0.534966	−	0.844874i	$-0.320324\pi$
$191$	204.357			1.06993			0.534966	+	0.844874i	$0.320324\pi$
$192$		0			0
$193$	−114.368			−0.592579			−0.296290	−	0.955098i	$-0.595749\pi$
$193$	−114.368			−0.592579			−0.296290	+	0.955098i	$0.595749\pi$
$194$	317.116	−	149.370i	1.63462	−	0.769947i
$195$		0			0
$196$	79.1398	−	179.312i	0.403774	−	0.914859i
$197$	−227.241			−1.15351			−0.576753	−	0.816919i	$-0.695680\pi$
$197$	−227.241			−1.15351			−0.576753	+	0.816919i	$0.695680\pi$
$198$		0			0
$199$	113.715			0.571434			0.285717	−	0.958314i	$-0.407768\pi$
$199$	113.715			0.571434			0.285717	+	0.958314i	$0.407768\pi$
$200$	449.405	+	114.846i	2.24703	+	0.574228i
$201$		0			0
$202$	−128.948	+	60.7380i	−0.638359	+	0.300683i
$203$	−17.3863	−	125.760i	−0.0856466	−	0.619508i
$204$		0			0
$205$			301.032i			1.46845i
$206$	71.9084	+	152.664i	0.349070	+	0.741085i
$207$		0			0
$208$	−7.00825	−	36.4397i	−0.0336935	−	0.175191i
$209$	260.091			1.24445
$210$		0			0
$211$	389.006			1.84363			0.921815	−	0.387630i	$-0.126706\pi$
$211$	389.006			1.84363			0.921815	+	0.387630i	$0.126706\pi$
$212$	−167.520	+	202.809i	−0.790191	+	0.956645i
$213$		0			0
$214$	−146.066	+	68.8006i	−0.682549	+	0.321498i
$215$		−	551.201i		−	2.56373i
$216$		0			0
$217$	44.0741	+	318.801i	0.203106	+	1.46913i
$218$	−181.352	+	85.4216i	−0.831892	+	0.391842i
$219$		0			0
$220$	224.199	−	271.427i	1.01909	−	1.23376i
$221$	50.7636			0.229700
$222$		0			0
$223$	−228.516			−1.02474			−0.512368	−	0.858766i	$-0.671232\pi$
$223$	−228.516			−1.02474			−0.512368	+	0.858766i	$0.671232\pi$
$224$	155.545	+	161.188i	0.694399	+	0.719591i
$225$		0			0
$226$	26.5108	−	12.4873i	0.117304	−	0.0552534i
$227$	−182.563			−0.804242			−0.402121	−	0.915587i	$-0.631727\pi$
$227$	−182.563			−0.804242			−0.402121	+	0.915587i	$0.631727\pi$
$228$		0			0
$229$	−331.984			−1.44971			−0.724857	−	0.688900i	$-0.758094\pi$
$229$	−331.984			−1.44971			−0.724857	+	0.688900i	$0.758094\pi$
$230$	−254.104	+	119.689i	−1.10480	+	0.520389i
$231$		0			0
$232$	140.575	+	35.9240i	0.605928	+	0.154845i
$233$		−	360.147i		−	1.54570i	−0.634592	−	0.772848i	$-0.718832\pi$
$233$		−	360.147i		−	1.54570i	0.634592	−	0.772848i	$-0.281168\pi$
$234$		0			0
$235$	268.665			1.14325
$236$	21.5830	−	26.1296i	0.0914536	−	0.110718i
$237$		0			0
$238$	−256.728	+	167.313i	−1.07869	+	0.702996i
$239$	−333.265			−1.39442			−0.697208	−	0.716869i	$-0.745575\pi$
$239$	−333.265			−1.39442			−0.697208	+	0.716869i	$0.745575\pi$
$240$		0			0
$241$		−	331.691i		−	1.37631i	−0.725564	−	0.688155i	$-0.758421\pi$
$241$		−	331.691i		−	1.37631i	0.725564	−	0.688155i	$-0.241579\pi$
$242$	23.5659	+	50.0311i	0.0973797	+	0.206740i
$243$		0			0
$244$	190.910	−	231.125i	0.782416	−	0.947234i
$245$	−121.103	−	429.618i	−0.494299	−	1.75354i
$246$		0			0
$247$		−	62.4329i		−	0.252765i
$248$	−356.358	−	91.0672i	−1.43693	−	0.367206i
$249$		0			0
$250$	543.589	−	256.044i	2.17436	−	1.02418i
$251$	−350.730			−1.39733			−0.698666	−	0.715448i	$-0.746223\pi$
$251$	−350.730			−1.39733			−0.698666	+	0.715448i	$0.746223\pi$
$252$		0			0
$253$			148.956i			0.588758i
$254$	−41.6000	+	19.5947i	−0.163780	+	0.0771443i
$255$		0			0
$256$	−237.737	+	94.9580i	−0.928661	+	0.370930i
$257$	361.582			1.40694			0.703468	−	0.710727i	$-0.251634\pi$
$257$	361.582			1.40694			0.703468	+	0.710727i	$0.251634\pi$
$258$		0			0
$259$	−224.190	+	30.9941i	−0.865599	+	0.119668i
$260$	−65.1541	−	53.8174i	−0.250593	−	0.206990i
$261$		0			0
$262$	132.125	+	280.505i	0.504295	+	1.07063i
$263$	255.224			0.970434			0.485217	−	0.874394i	$-0.338741\pi$
$263$	255.224			0.970434			0.485217	+	0.874394i	$0.338741\pi$
$264$		0			0
$265$			599.053i			2.26058i
$266$	205.774	+	315.743i	0.773586	+	1.18700i
$267$		0			0
$268$	−51.4874	+	62.3333i	−0.192117	+	0.232587i
$269$			141.207i			0.524934i	0.964941	+	0.262467i	$0.0845360\pi$
$269$			141.207i			0.524934i	−0.964941	+	0.262467i	$0.915464\pi$
$270$		0			0
$271$	405.606			1.49670			0.748350	−	0.663304i	$-0.230846\pi$
$271$	405.606			1.49670			0.748350	+	0.663304i	$0.230846\pi$
$272$	−66.1424	−	343.910i	−0.243171	−	1.26437i
$273$		0			0
$274$	−118.632	+	55.8786i	−0.432963	+	0.203937i
$275$		−	560.194i		−	2.03707i
$276$		0			0
$277$			31.1395i			0.112417i	0.998419	+	0.0562084i	$0.0179011\pi$
$277$			31.1395i			0.112417i	−0.998419	+	0.0562084i	$0.982099\pi$
$278$	271.171	−	127.728i	0.975435	−	0.459455i
$279$		0			0
$280$	506.883	+	57.4288i	1.81030	+	0.205103i
$281$			15.2327i			0.0542087i	0.999633	+	0.0271044i	$0.00862864\pi$
$281$			15.2327i			0.0542087i	−0.999633	+	0.0271044i	$0.991371\pi$
$282$		0			0
$283$		−	222.494i		−	0.786199i	−0.919496	−	0.393100i	$-0.871403\pi$
$283$		−	222.494i		−	0.786199i	0.919496	−	0.393100i	$-0.128597\pi$
$284$	−55.3060	+	66.9563i	−0.194739	+	0.235761i
$285$		0			0
$286$	−40.5427	+	19.0967i	−0.141758	+	0.0667715i
$287$	31.6791	+	229.145i	0.110380	+	0.798414i
$288$		0			0
$289$	190.097			0.657773
$290$	298.926	−	140.802i	1.03078	−	0.485523i
$291$		0			0
$292$	−309.021	−	255.252i	−1.05829	−	0.874149i
$293$			64.2745i			0.219367i	0.993967	+	0.109683i	$0.0349837\pi$
$293$			64.2745i			0.219367i	−0.993967	+	0.109683i	$0.965016\pi$
$294$		0			0
$295$		−	77.1809i		−	0.261630i
$296$	64.0410	−	250.601i	0.216355	−	0.846624i
$297$		0			0
$298$	−54.3168	−	115.316i	−0.182271	−	0.386967i
$299$	35.7557			0.119584
$300$		0			0
$301$	−58.0057	−	419.573i	−0.192710	−	1.39393i
$302$	158.803	−	74.8004i	0.525839	−	0.247684i
$303$		0			0
$304$	−422.966	+	81.3468i	−1.39133	+	0.267588i
$305$		−	682.692i		−	2.23834i
$306$		0			0
$307$		−	409.069i		−	1.33247i	−0.745740	−	0.666237i	$-0.767904\pi$
$307$		−	409.069i		−	1.33247i	0.745740	−	0.666237i	$-0.232096\pi$
$308$	142.096	−	230.204i	0.461352	−	0.747414i
$309$		0			0
$310$	−757.776	+	356.932i	−2.44444	+	1.15139i
$311$		−	117.035i		−	0.376318i	−0.982139	−	0.188159i	$-0.939748\pi$
$311$		−	117.035i		−	0.376318i	0.982139	−	0.188159i	$-0.0602520\pi$
$312$		0			0
$313$		−	6.47974i		−	0.0207021i	−0.999946	−	0.0103510i	$-0.996705\pi$
$313$		−	6.47974i		−	0.0207021i	0.999946	−	0.0103510i	$-0.00329489\pi$
$314$	11.0472	+	23.4534i	0.0351820	+	0.0746924i
$315$		0			0
$316$	243.589	+	201.205i	0.770850	+	0.636723i
$317$	−403.391			−1.27253			−0.636263	−	0.771472i	$-0.719521\pi$
$317$	−403.391			−1.27253			−0.636263	+	0.771472i	$0.719521\pi$
$318$		0			0
$319$		−	175.230i		−	0.549311i
$320$	−279.705	+	511.522i	−0.874079	+	1.59851i
$321$		0			0
$322$	−180.828	+	117.848i	−0.561578	+	0.365988i
$323$		−	589.228i		−	1.82424i
$324$		0			0
$325$	−134.470			−0.413755
$326$	110.263	+	234.092i	0.338231	+	0.718074i
$327$		0			0
$328$	−256.139	−	65.4563i	−0.780912	−	0.199562i
$329$	204.507	−	28.2730i	0.621602	−	0.0859360i
$330$		0			0
$331$	−87.5977			−0.264646			−0.132323	−	0.991207i	$-0.542244\pi$
$331$	−87.5977			−0.264646			−0.132323	+	0.991207i	$0.542244\pi$
$332$	−172.270	+	208.558i	−0.518884	+	0.628188i
$333$		0			0
$334$	−342.848	+	161.490i	−1.02649	+	0.483504i
$335$			184.119i			0.549608i
$336$		0			0
$337$	254.014			0.753752			0.376876	−	0.926264i	$-0.376998\pi$
$337$	254.014			0.753752			0.376876	+	0.926264i	$0.376998\pi$
$338$	−139.445	−	296.045i	−0.412559	−	0.875873i
$339$		0			0
$340$	−614.910	−	507.917i	−1.80856	−	1.49387i
$341$			444.208i			1.30266i
$342$		0			0
$343$	−137.394	−	314.280i	−0.400567	−	0.916267i
$344$	469.001	+	119.853i	1.36337	+	0.348410i
$345$		0			0
$346$	−559.374	+	263.479i	−1.61669	+	0.761501i
$347$		−	206.734i		−	0.595777i	−0.954601	−	0.297888i	$-0.903718\pi$
$347$		−	206.734i		−	0.595777i	0.954601	−	0.297888i	$-0.0962823\pi$
$348$		0			0
$349$	618.655			1.77265			0.886325	−	0.463063i	$-0.153250\pi$
$349$	618.655			1.77265			0.886325	+	0.463063i	$0.153250\pi$
$350$	680.059	−	443.204i	1.94303	−	1.26630i
$351$		0			0
$352$	182.200	+	249.784i	0.517613	+	0.709613i
$353$	357.742			1.01343			0.506717	−	0.862113i	$-0.330859\pi$
$353$	357.742			1.01343			0.506717	+	0.862113i	$0.330859\pi$
$354$		0			0
$355$			197.774i			0.557110i
$356$	333.520	−	403.776i	0.936854	−	1.13420i
$357$		0			0
$358$	−197.786	+	93.1624i	−0.552476	+	0.260230i
$359$	−54.1360			−0.150797			−0.0753983	−	0.997153i	$-0.524023\pi$
$359$	−54.1360			−0.150797			−0.0753983	+	0.997153i	$0.524023\pi$
$360$		0			0
$361$	−363.676			−1.00741
$362$	−64.2861	−	136.481i	−0.177586	−	0.377020i
$363$		0			0
$364$	−55.2586	−	34.1092i	−0.151809	−	0.0937065i
$365$	−912.779			−2.50077
$366$		0			0
$367$	−45.1294			−0.122968			−0.0614842	−	0.998108i	$-0.519583\pi$
$367$	−45.1294			−0.122968			−0.0614842	+	0.998108i	$0.519583\pi$
$368$	−46.5879	−	242.235i	−0.126597	−	0.658248i
$369$		0			0
$370$	−251.004	−	532.889i	−0.678390	−	1.44024i
$371$	63.0414	+	455.998i	0.169923	+	1.22910i
$372$		0			0
$373$			495.886i			1.32945i	0.747087	+	0.664726i	$0.231452\pi$
$373$			495.886i			1.32945i	−0.747087	+	0.664726i	$0.768548\pi$
$374$	−382.634	+	180.230i	−1.02308	+	0.481899i
$375$		0			0
$376$	−58.4185	+	228.599i	−0.155368	+	0.607976i
$377$	−42.0627			−0.111572
$378$		0			0
$379$	−427.550			−1.12810			−0.564050	−	0.825741i	$-0.690757\pi$
$379$	−427.550			−1.12810			−0.564050	+	0.825741i	$0.690757\pi$
$380$	−624.674	+	756.262i	−1.64388	+	1.99016i
$381$		0			0
$382$	174.162	+	369.750i	0.455920	+	0.967932i
$383$		−	77.1824i		−	0.201521i	−0.994911	−	0.100760i	$-0.967872\pi$
$383$		−	77.1824i		−	0.201521i	0.994911	−	0.100760i	$-0.0321275\pi$
$384$		0			0
$385$	−84.3708	−	610.280i	−0.219145	−	1.58514i
$386$	−97.4689	−	206.929i	−0.252510	−	0.536086i
$387$		0			0
$388$	540.519	+	446.470i	1.39309	+	1.15070i
$389$	510.843			1.31322			0.656610	−	0.754230i	$-0.271990\pi$
$389$	510.843			1.31322			0.656610	+	0.754230i	$0.271990\pi$
$390$		0			0
$391$	337.455			0.863056
$392$	391.882	−	9.62719i	0.999698	−	0.0245592i
$393$		0			0
$394$	−193.664	−	411.154i	−0.491533	−	1.04354i
$395$	719.507			1.82154
$396$		0			0
$397$	−14.9294			−0.0376056			−0.0188028	−	0.999823i	$-0.505985\pi$
$397$	−14.9294			−0.0376056			−0.0188028	+	0.999823i	$0.505985\pi$
$398$	96.9129	+	205.749i	0.243500	+	0.516957i
$399$		0			0
$400$	175.208	+	910.999i	0.438020	+	2.27750i
$401$		−	12.5890i		−	0.0313940i	−0.999877	−	0.0156970i	$-0.995003\pi$
$401$		−	12.5890i		−	0.0313940i	0.999877	−	0.0156970i	$-0.00499671\pi$
$402$		0			0
$403$	106.629			0.264588
$404$	−219.790	−	181.547i	−0.544036	−	0.449374i
$405$		0			0
$406$	212.725	−	138.635i	0.523952	−	0.341467i
$407$	−312.380			−0.767518
$408$		0			0
$409$			122.775i			0.300183i	0.988672	+	0.150091i	$0.0479568\pi$
$409$			122.775i			0.300183i	−0.988672	+	0.150091i	$0.952043\pi$
$410$	−544.666	+	256.552i	−1.32845	+	0.625736i
$411$		0			0
$412$	−214.936	+	260.212i	−0.521689	+	0.631584i
$413$	−8.12215	−	58.7500i	−0.0196662	−	0.142252i
$414$		0			0
$415$			616.036i			1.48442i
$416$	59.9587	−	43.7356i	0.144132	−	0.105134i
$417$		0			0
$418$	221.660	+	470.591i	0.530288	+	1.12582i
$419$	−85.9785			−0.205199			−0.102600	−	0.994723i	$-0.532716\pi$
$419$	−85.9785			−0.205199			−0.102600	+	0.994723i	$0.532716\pi$
$420$		0			0
$421$		−	32.5132i		−	0.0772285i	−0.999254	−	0.0386143i	$-0.987706\pi$
$421$		−	32.5132i		−	0.0772285i	0.999254	−	0.0386143i	$-0.0122944\pi$
$422$	331.527	+	703.841i	0.785609	+	1.66787i
$423$		0			0
$424$	−509.716	−	130.258i	−1.20216	−	0.307212i
$425$	−1269.10			−2.98612
$426$		0			0
$427$	−71.8432	−	519.664i	−0.168251	−	1.21701i
$428$	−248.966	−	205.647i	−0.581697	−	0.480483i
$429$		0			0
$430$	997.306	−	469.756i	2.31932	−	1.09246i
$431$	−769.964			−1.78646			−0.893230	−	0.449600i	$-0.851566\pi$
$431$	−769.964			−1.78646			−0.893230	+	0.449600i	$0.851566\pi$
$432$		0			0
$433$		−	245.082i		−	0.566008i	−0.959119	−	0.283004i	$-0.908669\pi$
$433$		−	245.082i		−	0.566008i	0.959119	−	0.283004i	$-0.0913310\pi$
$434$	−539.256	+	351.440i	−1.24253	+	0.809770i
$435$		0			0
$436$	−309.112	−	255.327i	−0.708973	−	0.585613i
$437$		−	415.027i		−	0.949718i
$438$		0			0
$439$	−69.4826			−0.158275			−0.0791374	−	0.996864i	$-0.525217\pi$
$439$	−69.4826			−0.158275			−0.0791374	+	0.996864i	$0.525217\pi$
$440$	682.174	+	174.330i	1.55040	+	0.396204i
$441$		0			0
$442$	43.2629	+	91.8483i	0.0978798	+	0.207802i
$443$		−	621.899i		−	1.40384i	−0.712258	−	0.701918i	$-0.752327\pi$
$443$		−	621.899i		−	1.40384i	0.712258	−	0.701918i	$-0.247673\pi$
$444$		0			0
$445$		−	1192.67i		−	2.68015i
$446$	−194.751	−	413.462i	−0.436661	−	0.927044i
$447$		0			0
$448$	−159.081	+	418.804i	−0.355092	+	0.934831i
$449$			777.572i			1.73179i	0.500229	+	0.865893i	$0.333249\pi$
$449$			777.572i			1.73179i	−0.500229	+	0.865893i	$0.666751\pi$
$450$		0			0
$451$			319.283i			0.707945i
$452$	45.1872	+	37.3247i	0.0999717	+	0.0825768i
$453$		0			0
$454$	−155.588	−	330.317i	−0.342704	−	0.727571i
$455$	−146.493	+	20.2526i	−0.321963	+	0.0445112i
$456$		0			0
$457$	746.303			1.63305			0.816524	−	0.577312i	$-0.195898\pi$
$457$	746.303			1.63305			0.816524	+	0.577312i	$0.195898\pi$
$458$	−282.931	−	600.670i	−0.617753	−	1.31151i
$459$		0			0
$460$	−433.116	−	357.755i	−0.941557	−	0.777727i
$461$		−	289.301i		−	0.627550i	−0.949497	−	0.313775i	$-0.898406\pi$
$461$		−	289.301i		−	0.627550i	0.949497	−	0.313775i	$-0.101594\pi$
$462$		0			0
$463$			317.745i			0.686275i	0.939285	+	0.343137i	$0.111490\pi$
$463$			317.745i			0.686275i	−0.939285	+	0.343137i	$0.888510\pi$
$464$	54.8056	+	284.963i	0.118115	+	0.614145i
$465$		0			0
$466$	651.626	−	306.932i	1.39834	−	0.658653i
$467$	152.473			0.326495			0.163248	−	0.986585i	$-0.447803\pi$
$467$	152.473			0.326495			0.163248	+	0.986585i	$0.447803\pi$
$468$		0			0
$469$	19.3758	+	140.151i	0.0413129	+	0.298829i
$470$	228.967	+	486.104i	0.487164	+	1.03426i
$471$		0			0
$472$	65.6710	+	16.7822i	0.139134	+	0.0355556i
$473$		−	584.621i		−	1.23598i
$474$		0			0
$475$			1560.84i			3.28597i
$476$	−521.519	−	321.915i	−1.09563	−	0.676292i
$477$		0			0
$478$	−284.023	−	602.988i	−0.594189	−	1.26148i
$479$		−	413.409i		−	0.863067i	−0.902097	−	0.431533i	$-0.857973\pi$
$479$		−	413.409i		−	0.863067i	0.902097	−	0.431533i	$-0.142027\pi$
$480$		0			0
$481$			74.9844i			0.155893i
$482$	600.139	−	282.681i	1.24510	−	0.586474i
$483$		0			0
$484$	−70.4390	+	85.2771i	−0.145535	+	0.176192i
$485$	1596.57			3.29191
$486$		0			0
$487$		−	135.886i		−	0.279027i	−0.990220	−	0.139513i	$-0.955446\pi$
$487$		−	135.886i		−	0.279027i	0.990220	−	0.139513i	$-0.0445538\pi$
$488$	580.883	+	148.445i	1.19033	+	0.304190i
$489$		0			0
$490$	674.112	−	585.254i	1.37574	−	1.19440i
$491$			813.773i			1.65738i	0.559708	+	0.828690i	$0.310913\pi$
$491$			813.773i			1.65738i	−0.559708	+	0.828690i	$0.689087\pi$
$492$		0			0
$493$	−396.979			−0.805231
$494$	112.962	−	53.2079i	0.228668	−	0.107708i
$495$		0			0
$496$	−138.932	−	722.381i	−0.280104	−	1.45641i
$497$	20.8128	+	150.545i	0.0418768	+	0.302908i
$498$		0			0
$499$	91.2098			0.182785			0.0913925	−	0.995815i	$-0.470868\pi$
$499$	91.2098			0.182785			0.0913925	+	0.995815i	$0.470868\pi$
$500$	926.538	+	765.322i	1.85308	+	1.53064i
$501$		0			0
$502$	−298.907	−	634.588i	−0.595432	−	1.26412i
$503$			546.674i			1.08683i	0.839465	+	0.543414i	$0.182869\pi$
$503$			546.674i			1.08683i	−0.839465	+	0.543414i	$0.817131\pi$
$504$		0			0
$505$	−649.213			−1.28557
$506$	−269.511	+	126.946i	−0.532630	+	0.250882i
$507$		0			0
$508$	−70.9065	−	58.5689i	−0.139580	−	0.115293i
$509$		−	366.160i		−	0.719372i	−0.933073	−	0.359686i	$-0.882884\pi$
$509$		−	366.160i		−	0.719372i	0.933073	−	0.359686i	$-0.117116\pi$
$510$		0			0
$511$	−694.806	+	96.0564i	−1.35970	+	0.187977i
$512$	−374.420	−	349.219i	−0.731289	−	0.682068i
$513$		0			0
$514$	308.156	+	654.223i	0.599524	+	1.27281i
$515$			768.610i			1.49245i
$516$		0			0
$517$	284.954			0.551168
$518$	−247.143	−	379.220i	−0.477110	−	0.732085i
$519$		0			0
$520$	41.8465	−	163.751i	0.0804741	−	0.314905i
$521$	252.033			0.483748			0.241874	−	0.970308i	$-0.422238\pi$
$521$	252.033			0.483748			0.241874	+	0.970308i	$0.422238\pi$
$522$		0			0
$523$		−	335.060i		−	0.640651i	−0.947308	−	0.320325i	$-0.896208\pi$
$523$		−	335.060i		−	0.640651i	0.947308	−	0.320325i	$-0.103792\pi$
$524$	−394.925	+	478.117i	−0.753674	+	0.912437i
$525$		0			0
$526$	217.512	+	461.785i	0.413522	+	0.877919i
$527$	1006.34			1.90956
$528$		0			0
$529$	−291.311			−0.550683
$530$	−1083.89	+	510.537i	−2.04507	+	0.963278i
$531$		0			0
$532$	−395.915	+	641.403i	−0.744201	+	1.20564i
$533$	76.6415			0.143793
$534$		0			0
$535$	−735.392			−1.37456
$536$	−156.661	−	40.0348i	−0.292279	−	0.0746918i
$537$		0			0
$538$	−255.491	+	120.343i	−0.474890	+	0.223685i
$539$	−128.446	−	455.665i	−0.238304	−	0.845390i
$540$		0			0
$541$			197.089i			0.364305i	0.983270	+	0.182152i	$0.0583065\pi$
$541$			197.089i			0.364305i	−0.983270	+	0.182152i	$0.941694\pi$
$542$	345.674	+	733.876i	0.637775	+	1.35401i
$543$		0			0
$544$	565.878	−	412.768i	1.04022	−	0.758764i
$545$	−913.049			−1.67532
$546$		0			0
$547$	296.822			0.542637			0.271318	−	0.962490i	$-0.412540\pi$
$547$	296.822			0.542637			0.271318	+	0.962490i	$0.412540\pi$
$548$	−202.206	−	167.023i	−0.368989	−	0.304786i
$549$		0			0
$550$	1013.58	−	477.421i	1.84287	−	0.868037i
$551$			488.234i			0.886087i
$552$		0			0
$553$	547.687	−	75.7174i	0.990393	−	0.136921i
$554$	−56.3417	+	26.5383i	−0.101700	+	0.0479032i
$555$		0			0
$556$	462.206	+	381.783i	0.831306	+	0.686660i
$557$	−64.7524			−0.116252			−0.0581261	−	0.998309i	$-0.518513\pi$
$557$	−64.7524			−0.116252			−0.0581261	+	0.998309i	$0.518513\pi$
$558$		0			0
$559$	−140.334			−0.251044
$560$	328.079	+	966.063i	0.585855	+	1.72511i
$561$		0			0
$562$	−27.5609	+	12.9819i	−0.0490408	+	0.0230995i
$563$	143.148			0.254260			0.127130	−	0.991886i	$-0.459424\pi$
$563$	143.148			0.254260			0.127130	+	0.991886i	$0.459424\pi$
$564$		0			0
$565$	133.473			0.236236
$566$	402.566	−	189.619i	0.711248	−	0.335016i
$567$		0			0
$568$	−168.280	−	43.0040i	−0.296268	−	0.0757113i
$569$			566.510i			0.995625i	0.867285	+	0.497812i	$0.165863\pi$
$569$			566.510i			0.995625i	−0.867285	+	0.497812i	$0.834137\pi$
$570$		0			0
$571$	788.303			1.38057			0.690283	−	0.723539i	$-0.257486\pi$
$571$	788.303			1.38057			0.690283	+	0.723539i	$0.257486\pi$
$572$	−69.1044	−	57.0803i	−0.120812	−	0.0997908i
$573$		0			0
$574$	−387.601	+	252.605i	−0.675263	+	0.440078i
$575$	−893.901			−1.55461
$576$		0			0
$577$			273.614i			0.474200i	0.971485	+	0.237100i	$0.0761970\pi$
$577$			273.614i			0.474200i	−0.971485	+	0.237100i	$0.923803\pi$
$578$	162.008	+	343.948i	0.280291	+	0.595065i
$579$		0			0
$580$	509.514	+	420.859i	0.878473	+	0.725620i
$581$	64.8286	+	468.925i	0.111581	+	0.807100i
$582$		0			0
$583$			635.374i			1.08983i
$584$	198.475	−	776.657i	0.339854	−	1.32989i
$585$		0			0
$586$	−116.294	+	54.7774i	−0.198454	+	0.0934767i
$587$	−2.97914			−0.00507520			−0.00253760	−	0.999997i	$-0.500808\pi$
$587$	−2.97914			−0.00507520			−0.00253760	+	0.999997i	$0.500808\pi$
$588$		0			0
$589$		−	1237.67i		−	2.10131i
$590$	139.646	−	65.7768i	0.236688	−	0.111486i
$591$		0			0
$592$	507.998	−	97.7008i	0.858106	−	0.165035i
$593$	586.465			0.988979			0.494490	−	0.869184i	$-0.335355\pi$
$593$	586.465			0.988979			0.494490	+	0.869184i	$0.335355\pi$
$594$		0			0
$595$	−1382.57	+	191.140i	−2.32365	+	0.321243i
$596$	162.354	−	196.554i	0.272406	−	0.329789i
$597$		0			0
$598$	30.4725	+	64.6940i	0.0509574	+	0.108184i
$599$	−44.6708			−0.0745757			−0.0372878	−	0.999305i	$-0.511872\pi$
$599$	−44.6708			−0.0745757			−0.0372878	+	0.999305i	$0.511872\pi$
$600$		0			0
$601$			185.280i			0.308286i	0.988049	+	0.154143i	$0.0492617\pi$
$601$			185.280i			0.308286i	−0.988049	+	0.154143i	$0.950738\pi$
$602$	709.713	−	462.529i	1.17892	−	0.768321i
$603$		0			0
$604$	270.678	+	223.580i	0.448142	+	0.370166i
$605$			251.890i			0.416347i
$606$		0			0
$607$	485.191			0.799326			0.399663	−	0.916662i	$-0.369127\pi$
$607$	485.191			0.799326			0.399663	+	0.916662i	$0.369127\pi$
$608$	−507.652	−	695.958i	−0.834954	−	1.14467i
$609$		0			0
$610$	1235.22	−	581.819i	2.02495	−	0.953801i
$611$		−	68.4010i		−	0.111949i
$612$		0			0
$613$		−	504.370i		−	0.822790i	−0.911457	−	0.411395i	$-0.865042\pi$
$613$		−	504.370i		−	0.822790i	0.911457	−	0.411395i	$-0.134958\pi$
$614$	740.143	−	348.626i	1.20544	−	0.567795i
$615$		0			0
$616$	537.615	+	60.9107i	0.872752	+	0.0988810i
$617$		−	20.6090i		−	0.0334019i	−0.999861	−	0.0167010i	$-0.994684\pi$
$617$		−	20.6090i		−	0.0334019i	0.999861	−	0.0167010i	$-0.00531633\pi$
$618$		0			0
$619$		−	925.741i		−	1.49554i	−0.663957	−	0.747771i	$-0.731124\pi$
$619$		−	925.741i		−	1.49554i	0.663957	−	0.747771i	$-0.268876\pi$
$620$	−1291.62	−	1066.88i	−2.08325	−	1.72077i
$621$		0			0
$622$	211.755	−	99.7419i	0.340442	−	0.160357i
$623$	−125.510	−	907.856i	−0.201461	−	1.45723i
$624$		0			0
$625$	1287.27			2.05962
$626$	11.7240	−	5.52231i	0.0187285	−	0.00882158i
$627$		0			0
$628$	−33.0202	+	39.9760i	−0.0525799	+	0.0636560i
$629$			707.687i			1.12510i
$630$		0			0
$631$			902.920i			1.43094i	0.698646	+	0.715468i	$0.253786\pi$
$631$			902.920i			1.43094i	−0.698646	+	0.715468i	$0.746214\pi$
$632$	−156.450	+	612.208i	−0.247547	+	0.968683i
$633$		0			0
$634$	−343.787	−	729.869i	−0.542250	−	1.15121i
$635$	−209.442			−0.329830
$636$		0			0
$637$	−109.379	+	30.8325i	−0.171710	+	0.0484026i
$638$	317.050	−	149.339i	0.496944	−	0.234073i
$639$		0			0
$640$	−1163.89	−	70.1398i	−1.81858	−	0.109593i
$641$			235.354i			0.367167i	0.983004	+	0.183584i	$0.0587698\pi$
$641$			235.354i			0.367167i	−0.983004	+	0.183584i	$0.941230\pi$
$642$		0			0
$643$		−	189.811i		−	0.295197i	−0.989047	−	0.147598i	$-0.952846\pi$
$643$		−	189.811i		−	0.295197i	0.989047	−	0.147598i	$-0.0471543\pi$
$644$	−367.336	−	226.743i	−0.570397	−	0.352086i
$645$		0			0
$646$	1066.11	−	502.165i	1.65032	−	0.777345i
$647$		−	9.78084i		−	0.0151172i	−0.999971	−	0.00755861i	$-0.997594\pi$
$647$		−	9.78084i		−	0.0151172i	0.999971	−	0.00755861i	$-0.00240600\pi$
$648$		0			0
$649$		−	81.8605i		−	0.126133i
$650$	−114.601	−	243.302i	−0.176310	−	0.374310i
$651$		0			0
$652$	−329.580	+	399.006i	−0.505490	+	0.611972i
$653$	700.168			1.07223			0.536117	−	0.844144i	$-0.319891\pi$
$653$	700.168			1.07223			0.536117	+	0.844144i	$0.319891\pi$
$654$		0			0
$655$			1412.25i			2.15611i
$656$	−99.8600	−	519.225i	−0.152226	−	0.791502i
$657$		0			0
$658$	225.444	+	345.926i	0.342621	+	0.525723i
$659$			584.716i			0.887277i	0.896206	+	0.443639i	$0.146313\pi$
$659$			584.716i			0.887277i	−0.896206	+	0.443639i	$0.853687\pi$
$660$		0			0
$661$	687.188			1.03962			0.519809	−	0.854282i	$-0.326003\pi$
$661$	687.188			1.03962			0.519809	+	0.854282i	$0.326003\pi$
$662$	−74.6544	−	158.493i	−0.112771	−	0.239416i
$663$		0			0
$664$	−524.167	−	133.951i	−0.789408	−	0.201733i
$665$	235.078	+	1700.39i	0.353500	+	2.55697i
$666$		0			0
$667$	−279.615			−0.419213
$668$	−584.379	−	482.698i	−0.874819	−	0.722602i
$669$		0			0
$670$	−333.132	+	156.914i	−0.497212	+	0.234200i
$671$		−	724.084i		−	1.07911i
$672$		0			0
$673$	−394.412			−0.586050			−0.293025	−	0.956105i	$-0.594662\pi$
$673$	−394.412			−0.586050			−0.293025	+	0.956105i	$0.594662\pi$
$674$	216.482	+	459.596i	0.321189	+	0.681894i
$675$		0			0
$676$	416.804	−	504.604i	0.616574	−	0.746456i
$677$		−	115.342i		−	0.170372i	−0.996365	−	0.0851858i	$-0.972852\pi$
$677$		−	115.342i		−	0.170372i	0.996365	−	0.0851858i	$-0.0271484\pi$
$678$		0			0
$679$	1215.31	−	168.016i	1.78985	−	0.247446i
$680$	394.939	−	1545.44i	0.580792	−	2.27271i
$681$		0			0
$682$	−803.720	+	378.573i	−1.17848	+	0.555092i
$683$		−	208.661i		−	0.305506i	−0.988264	−	0.152753i	$-0.951186\pi$
$683$		−	208.661i		−	0.305506i	0.988264	−	0.152753i	$-0.0488139\pi$
$684$		0			0
$685$	−597.272			−0.871930
$686$	451.543	−	516.434i	0.658226	−	0.752820i
$687$		0			0
$688$	182.848	+	950.723i	0.265767	+	1.38186i
$689$	152.517			0.221359
$690$		0			0
$691$		−	755.615i		−	1.09351i	−0.837293	−	0.546755i	$-0.815863\pi$
$691$		−	755.615i		−	1.09351i	0.837293	−	0.546755i	$-0.184137\pi$
$692$	−953.444	−	787.546i	−1.37781	−	1.13807i
$693$		0			0
$694$	374.051	−	176.188i	0.538979	−	0.253873i
$695$	1365.26			1.96440
$696$		0			0
$697$	723.327			1.03777
$698$	527.244	+	1119.35i	0.755363	+	1.60366i
$699$		0			0
$700$	1381.48	+	852.737i	1.97354	+	1.21820i
$701$	611.239			0.871953			0.435977	−	0.899958i	$-0.356403\pi$
$701$	611.239			0.871953			0.435977	+	0.899958i	$0.356403\pi$
$702$		0			0
$703$	870.365			1.23807
$704$	−296.664	+	542.536i	−0.421398	+	0.770648i
$705$		0			0
$706$	304.883	+	647.274i	0.431845	+	0.916819i
$707$	−494.179	+	68.3200i	−0.698981	+	0.0966336i
$708$		0			0
$709$			182.040i			0.256756i	0.991725	+	0.128378i	$0.0409771\pi$
$709$			182.040i			0.256756i	−0.991725	+	0.128378i	$0.959023\pi$
$710$	−357.839	+	168.551i	−0.503999	+	0.237396i
$711$		0			0
$712$	1014.81	+	259.334i	1.42529	+	0.364233i
$713$	708.822			0.994141
$714$		0			0
$715$	−204.119			−0.285481
$716$	−337.124	−	278.465i	−0.470843	−	0.388917i
$717$		0			0
$718$	−46.1369	−	97.9500i	−0.0642575	−	0.136421i
$719$			927.993i			1.29067i	0.763899	+	0.645336i	$0.223283\pi$
$719$			927.993i			1.29067i	−0.763899	+	0.645336i	$0.776717\pi$
$720$		0			0
$721$	80.8848	+	585.065i	0.112184	+	0.811463i
$722$	−309.940	−	658.012i	−0.429280	−	0.911373i
$723$		0			0
$724$	192.153	−	232.630i	0.265404	−	0.321312i
$725$	1051.58			1.45045
$726$		0			0
$727$	715.698			0.984453			0.492227	−	0.870467i	$-0.336183\pi$
$727$	715.698			0.984453			0.492227	+	0.870467i	$0.336183\pi$
$728$	14.6212	−	129.050i	0.0200840	−	0.177267i
$729$		0			0
$730$	−777.908	−	1651.52i	−1.06563	−	2.26236i
$731$	−1324.44			−1.81182
$732$		0			0
$733$	565.483			0.771464			0.385732	−	0.922611i	$-0.373949\pi$
$733$	565.483			0.771464			0.385732	+	0.922611i	$0.373949\pi$
$734$	−38.4611	−	81.6541i	−0.0523994	−	0.111245i
$735$		0			0
$736$	398.580	−	290.736i	0.541549	−	0.395021i
$737$			195.282i			0.264969i
$738$		0			0
$739$	104.108			0.140876			0.0704382	−	0.997516i	$-0.477560\pi$
$739$	104.108			0.140876			0.0704382	+	0.997516i	$0.477560\pi$
$740$	750.258	−	908.301i	1.01386	−	1.22743i
$741$		0			0
$742$	−771.325	+	502.683i	−1.03952	+	0.677470i
$743$	−1159.59			−1.56068			−0.780341	−	0.625354i	$-0.784955\pi$
$743$	−1159.59			−1.56068			−0.780341	+	0.625354i	$0.784955\pi$
$744$		0			0
$745$		−	580.578i		−	0.779299i
$746$	−897.222	+	422.614i	−1.20271	+	0.566507i
$747$		0			0
$748$	−652.193	−	538.712i	−0.871915	−	0.720203i
$749$	−559.779	+	77.3890i	−0.747368	+	0.103323i
$750$		0			0
$751$		−	8.05706i		−	0.0107284i	−0.999986	−	0.00536422i	$-0.998293\pi$
$751$		−	8.05706i		−	0.0107284i	0.999986	−	0.00536422i	$-0.00170749\pi$
$752$	−463.398	+	89.1230i	−0.616221	+	0.118515i
$753$		0			0
$754$	−35.8476	−	76.1054i	−0.0475432	−	0.100936i
$755$	799.522			1.05897
$756$		0			0
$757$			203.142i			0.268352i	0.990958	+	0.134176i	$0.0428387\pi$
$757$			203.142i			0.268352i	−0.990958	+	0.134176i	$0.957161\pi$
$758$	−364.376	−	773.580i	−0.480707	−	1.02055i
$759$		0			0
$760$	−1900.70	−	485.725i	−2.50092	−	0.639111i
$761$	1325.16			1.74134			0.870670	−	0.491867i	$-0.163685\pi$
$761$	1325.16			1.74134			0.870670	+	0.491867i	$0.163685\pi$
$762$		0			0
$763$	−695.012	+	96.0849i	−0.910893	+	0.125930i
$764$	−520.573	+	630.232i	−0.681378	+	0.824911i
$765$		0			0
$766$	139.649	−	65.7780i	0.182309	−	0.0858721i
$767$	−19.6500			−0.0256193
$768$		0			0
$769$		−	27.4357i		−	0.0356772i	−0.999841	−	0.0178386i	$-0.994322\pi$
$769$		−	27.4357i		−	0.0356772i	0.999841	−	0.0178386i	$-0.00567850\pi$
$770$	1032.30	−	672.761i	1.34064	−	0.873716i
$771$		0			0
$772$	291.337	−	352.707i	0.377379	−	0.456875i
$773$			127.533i			0.164985i	0.996592	+	0.0824925i	$0.0262880\pi$
$773$			127.533i			0.164985i	−0.996592	+	0.0824925i	$0.973712\pi$
$774$		0			0
$775$	−2665.74			−3.43967
$776$	−347.159	+	1358.48i	−0.447370	+	1.75062i
$777$		0			0
$778$	435.361	+	924.284i	0.559590	+	1.18803i
$779$		−	889.600i		−	1.14198i
$780$		0			0
$781$			209.765i			0.268585i
$782$	287.593	+	610.568i	0.367766	+	0.780778i
$783$		0			0
$784$	351.397	+	700.840i	0.448210	+	0.893928i
$785$			118.080i			0.150421i
$786$		0			0
$787$		−	151.856i		−	0.192956i	−0.995335	−	0.0964781i	$-0.969242\pi$
$787$		−	151.856i		−	0.192956i	0.995335	−	0.0964781i	$-0.0307578\pi$
$788$	578.866	−	700.805i	0.734601	−	0.889346i
$789$		0			0
$790$	613.194	+	1301.83i	0.776194	+	1.64788i
$791$	101.599	−	14.0461i	0.128444	−	0.0177573i
$792$		0			0
$793$	−173.811			−0.219182
$794$	−12.7235	−	27.0123i	−0.0160245	−	0.0340205i
$795$		0			0
$796$	−289.675	+	350.695i	−0.363913	+	0.440572i
$797$			1136.09i			1.42545i	0.701443	+	0.712726i	$0.252540\pi$
$797$			1136.09i			1.42545i	−0.701443	+	0.712726i	$0.747460\pi$
$798$		0			0
$799$		−	645.554i		−	0.807953i
$800$	−1498.98	+	1093.40i	−1.87373	+	1.36675i
$801$		0			0
$802$	22.7776	−	10.7288i	0.0284011	−	0.0133776i
$803$	−968.122			−1.20563
$804$		0			0
$805$	−973.823	+	134.630i	−1.20972	+	0.167243i
$806$	90.8735	+	192.927i	0.112746	+	0.239363i
$807$		0			0
$808$	141.165	−	552.396i	0.174709	−	0.683659i
$809$			438.239i			0.541705i	0.962621	+	0.270852i	$0.0873055\pi$
$809$			438.239i			0.541705i	−0.962621	+	0.270852i	$0.912695\pi$
$810$		0			0
$811$		−	1406.16i		−	1.73386i	−0.498427	−	0.866931i	$-0.666089\pi$
$811$		−	1406.16i		−	1.73386i	0.498427	−	0.866931i	$-0.333911\pi$
$812$	432.130	+	266.739i	0.532180	+	0.328496i
$813$		0			0
$814$	−266.223	−	565.199i	−0.327055	−	0.694347i
$815$			1178.58i			1.44611i
$816$		0			0
$817$			1628.89i			1.99375i
$818$	−222.140	+	104.634i	−0.271565	+	0.127914i
$819$		0			0
$820$	−928.374	−	766.839i	−1.13216	−	0.935169i
$821$	592.105			0.721200			0.360600	−	0.932721i	$-0.382572\pi$
$821$	592.105			0.721200			0.360600	+	0.932721i	$0.382572\pi$
$822$		0			0
$823$			1078.89i			1.31092i	0.755229	+	0.655461i	$0.227526\pi$
$823$			1078.89i			1.31092i	−0.755229	+	0.655461i	$0.772474\pi$
$824$	−653.988	−	167.127i	−0.793675	−	0.202824i
$825$		0			0
$826$	99.3762	−	64.7648i	0.120310	−	0.0784078i
$827$			111.468i			0.134785i	0.997727	+	0.0673927i	$0.0214680\pi$
$827$			111.468i			0.134785i	−0.997727	+	0.0673927i	$0.978532\pi$
$828$		0			0
$829$	−109.080			−0.131580			−0.0657900	−	0.997833i	$-0.520957\pi$
$829$	−109.080			−0.131580			−0.0657900	+	0.997833i	$0.520957\pi$
$830$	−1114.61	+	525.011i	−1.34291	+	0.632543i
$831$		0			0
$832$	130.232	+	71.2120i	0.156528	+	0.0855913i
$833$	−1032.30	+	290.990i	−1.23925	+	0.349328i
$834$		0			0
$835$	−1726.13			−2.06722
$836$	−662.548	+	802.115i	−0.792521	+	0.959467i
$837$		0			0
$838$	−73.2744	−	155.564i	−0.0874397	−	0.185637i
$839$		−	1297.65i		−	1.54667i	−0.633999	−	0.773334i	$-0.718588\pi$
$839$		−	1297.65i		−	1.54667i	0.633999	−	0.773334i	$-0.281412\pi$
$840$		0			0
$841$	−512.064			−0.608875
$842$	58.8272	−	27.7091i	0.0698661	−	0.0329087i
$843$		0			0
$844$	−990.942	+	1199.69i	−1.17410	+	1.42143i
$845$		−	1490.49i		−	1.76389i
$846$		0			0
$847$	26.5076	+	191.738i	0.0312959	+	0.226373i
$848$	−198.721	−	1033.26i	−0.234341	−	1.21846i
$849$		0			0
$850$	−1081.58	−	2296.23i	−1.27245	−	2.70145i
$851$			498.464i			0.585739i
$852$		0			0
$853$	−1099.79			−1.28932			−0.644658	−	0.764471i	$-0.723000\pi$
$853$	−1099.79			−1.28932			−0.644658	+	0.764471i	$0.723000\pi$
$854$	879.018	−	572.868i	1.02929	−	0.670805i
$855$		0			0
$856$	159.904	−	625.723i	0.186803	−	0.730985i
$857$	−616.955			−0.719900			−0.359950	−	0.932972i	$-0.617206\pi$
$857$	−616.955			−0.719900			−0.359950	+	0.932972i	$0.617206\pi$
$858$		0			0
$859$			1202.72i			1.40014i	0.714075	+	0.700069i	$0.246848\pi$
$859$			1202.72i			1.40014i	−0.714075	+	0.700069i	$0.753152\pi$
$860$	1699.89	+	1404.11i	1.97662	+	1.63269i
$861$		0			0
$862$	−656.195	−	1393.12i	−0.761247	−	1.61615i
$863$	−481.815			−0.558303			−0.279151	−	0.960247i	$-0.590053\pi$
$863$	−481.815			−0.558303			−0.279151	+	0.960247i	$0.590053\pi$
$864$		0			0
$865$	−2816.26			−3.25580
$866$	443.434	−	208.869i	0.512049	−	0.241188i
$867$		0			0
$868$	−1095.45	−	676.181i	−1.26204	−	0.779011i
$869$	763.131			0.878171
$870$		0			0
$871$	46.8760			0.0538186
$872$	198.534	−	776.887i	0.227676	−	0.890926i
$873$		0			0
$874$	750.922	−	353.703i	0.859178	−	0.404695i
$875$	2083.24	−	288.006i	2.38084	−	0.329150i
$876$		0			0
$877$		−	275.163i		−	0.313754i	−0.987618	−	0.156877i	$-0.949857\pi$
$877$		−	275.163i		−	0.313754i	0.987618	−	0.156877i	$-0.0501427\pi$
$878$	−59.2159	−	125.717i	−0.0674441	−	0.143186i
$879$		0			0
$880$	265.957	+	1382.85i	0.302224	+	1.57142i
$881$	−718.744			−0.815827			−0.407914	−	0.913020i	$-0.633744\pi$
$881$	−718.744			−0.815827			−0.407914	+	0.913020i	$0.633744\pi$
$882$		0			0
$883$	−1561.31			−1.76819			−0.884095	−	0.467308i	$-0.845224\pi$
$883$	−1561.31			−1.76819			−0.884095	+	0.467308i	$0.845224\pi$
$884$	−129.314	+	156.554i	−0.146283	+	0.177097i
$885$		0			0
$886$	1125.22	−	530.008i	1.27000	−	0.598203i
$887$		−	983.157i		−	1.10841i	−0.832381	−	0.554204i	$-0.813023\pi$
$887$		−	983.157i		−	1.10841i	0.832381	−	0.554204i	$-0.186977\pi$
$888$		0			0
$889$	−159.427	+	22.0407i	−0.179333	+	0.0247927i
$890$	2157.93	−	1016.44i	2.42464	−	1.14207i
$891$		0			0
$892$	582.115	−	704.738i	0.652595	−	0.790065i
$893$	−793.950			−0.889082
$894$		0			0
$895$	−995.789			−1.11261
$896$	−893.332	+	69.0918i	−0.997022	+	0.0771114i
$897$		0			0
$898$	−1406.89	+	662.679i	−1.56669	+	0.737950i
$899$	−833.852			−0.927533
$900$		0			0
$901$	1439.42			1.59758
$902$	−577.690	+	272.106i	−0.640454	+	0.301670i
$903$		0			0
$904$	−29.0224	+	113.568i	−0.0321044	+	0.125629i
$905$		−	687.137i		−	0.759267i
$906$		0			0
$907$	1121.27			1.23624			0.618119	−	0.786085i	$-0.287895\pi$
$907$	1121.27			1.23624			0.618119	+	0.786085i	$0.287895\pi$
$908$	465.055	−	563.020i	0.512175	−	0.620066i
$909$		0			0
$910$	−161.491	−	247.795i	−0.177463	−	0.272302i
$911$	1308.23			1.43604			0.718020	−	0.696022i	$-0.245048\pi$
$911$	1308.23			1.43604			0.718020	+	0.696022i	$0.245048\pi$
$912$		0			0
$913$			653.386i			0.715647i
$914$	636.030	+	1350.31i	0.695876	+	1.47736i
$915$		0			0
$916$	845.687	−	1023.83i	0.923239	−	1.11772i
$917$	148.618	+	1075.00i	0.162070	+	1.17230i
$918$		0			0
$919$			992.984i			1.08050i	0.841503	+	0.540252i	$0.181671\pi$
$919$			992.984i			1.08050i	−0.841503	+	0.540252i	$0.818329\pi$
$920$	278.178	−	1088.54i	0.302367	−	1.18320i
$921$		0			0
$922$	523.441	−	246.554i	0.567724	−	0.267412i
$923$	50.3525			0.0545531
$924$		0			0
$925$		−	1874.63i		−	2.02662i
$926$	−574.907	+	270.796i	−0.620850	+	0.292436i
$927$		0			0
$928$	−468.886	+	342.019i	−0.505265	+	0.368555i
$929$	47.0391			0.0506342			0.0253171	−	0.999679i	$-0.491940\pi$
$929$	47.0391			0.0506342			0.0253171	+	0.999679i	$0.491940\pi$
$930$		0			0
$931$	357.881	+	1269.59i	0.384405	+	1.36369i
$932$	1110.68	+	917.427i	1.19172	+	0.984364i
$933$		0			0
$934$	129.944	+	275.875i	0.139126	+	0.295369i
$935$	−1926.43			−2.06036
$936$		0			0
$937$		−	1808.57i		−	1.93017i	−0.261932	−	0.965086i	$-0.584360\pi$
$937$		−	1808.57i		−	1.93017i	0.261932	−	0.965086i	$-0.415640\pi$
$938$	−237.067	+	154.500i	−0.252736	+	0.164712i
$939$		0			0
$940$	−684.388	+	828.555i	−0.728072	+	0.881442i
$941$		−	628.185i		−	0.667572i	−0.942649	−	0.333786i	$-0.891674\pi$
$941$		−	628.185i		−	0.667572i	0.942649	−	0.333786i	$-0.108326\pi$
$942$		0			0
$943$	509.480			0.540276
$944$	25.6029	+	133.123i	0.0271217	+	0.141020i
$945$		0			0
$946$	1057.77	−	498.238i	1.11815	−	0.526679i
$947$		−	1130.40i		−	1.19366i	−0.802367	−	0.596831i	$-0.796426\pi$
$947$		−	1130.40i		−	1.19366i	0.802367	−	0.596831i	$-0.203574\pi$
$948$		0			0
$949$			232.390i			0.244879i
$950$	−2824.07	+	1330.21i	−2.97271	+	1.40022i
$951$		0			0
$952$	137.991	−	1217.95i	0.144949	−	1.27936i
$953$		−	781.337i		−	0.819871i	−0.912114	−	0.409936i	$-0.865551\pi$
$953$		−	781.337i		−	0.819871i	0.912114	−	0.409936i	$-0.134449\pi$
$954$		0			0
$955$			1861.57i			1.94929i
$956$	848.950	−	1027.78i	0.888023	−	1.07509i
$957$		0			0
$958$	747.994	−	352.324i	0.780787	−	0.367771i
$959$	−454.643	+	62.8540i	−0.474080	+	0.0655412i
$960$		0			0
$961$	1152.81			1.19960
$962$	−135.672	+	63.9048i	−0.141031	+	0.0664291i
$963$		0			0
$964$	1022.93	+	844.939i	1.06113	+	0.876493i
$965$		−	1041.82i		−	1.07961i
$966$		0			0
$967$		−	1674.13i		−	1.73126i	−0.500685	−	0.865629i	$-0.666919\pi$
$967$		−	1674.13i		−	1.73126i	0.500685	−	0.865629i	$-0.333081\pi$
$968$	−214.326	−	54.7709i	−0.221411	−	0.0565815i
$969$		0			0
$970$	1360.67	+	2888.73i	1.40275	+	2.97808i
$971$	271.907			0.280028			0.140014	−	0.990150i	$-0.455285\pi$
$971$	271.907			0.280028			0.140014	+	0.990150i	$0.455285\pi$
$972$		0			0
$973$	1039.23	−	143.673i	1.06807	−	0.147660i
$974$	245.863	−	115.808i	0.252426	−	0.118899i
$975$		0			0
$976$	226.467	+	1177.52i	0.232036	+	1.20648i
$977$		−	1639.40i		−	1.67799i	−0.544138	−	0.838995i	$-0.683143\pi$
$977$		−	1639.40i		−	1.67799i	0.544138	−	0.838995i	$-0.316857\pi$
$978$		0			0
$979$		−	1264.98i		−	1.29211i
$980$	1633.43	+	720.915i	1.66676	+	0.735627i
$981$		0			0
$982$	−1472.39	+	693.531i	−1.49938	+	0.706244i
$983$			824.584i			0.838844i	0.907791	+	0.419422i	$0.137767\pi$
$983$			824.584i			0.838844i	−0.907791	+	0.419422i	$0.862233\pi$
$984$		0			0
$985$		−	2070.02i		−	2.10155i
$986$	−338.322	−	718.267i	−0.343126	−	0.728466i
$987$		0			0
$988$	192.542	+	159.040i	0.194880	+	0.160971i
$989$	−932.878			−0.943254
$990$		0			0
$991$			888.843i			0.896916i	0.893804	+	0.448458i	$0.148027\pi$
$991$			888.843i			0.896916i	−0.893804	+	0.448458i	$0.851973\pi$
$992$	1188.62	−	867.017i	1.19821	−	0.874009i
$993$		0			0
$994$	−254.649	+	165.958i	−0.256186	+	0.166960i
$995$			1035.88i			1.04108i
$996$		0			0
$997$	−43.3671			−0.0434976			−0.0217488	−	0.999763i	$-0.506923\pi$
$997$	−43.3671			−0.0434976			−0.0217488	+	0.999763i	$0.506923\pi$
$998$	77.7327	+	165.029i	0.0778885	+	0.165360i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.3.e.c.251.32	yes	48
3.2	odd	2	inner	504.3.e.c.251.18	yes	48
4.3	odd	2		2016.3.e.c.1007.24		48
7.6	odd	2	inner	504.3.e.c.251.31	yes	48
8.3	odd	2	inner	504.3.e.c.251.19	yes	48
8.5	even	2		2016.3.e.c.1007.5		48
12.11	even	2		2016.3.e.c.1007.33		48
21.20	even	2	inner	504.3.e.c.251.17	✓	48
24.5	odd	2		2016.3.e.c.1007.8		48
24.11	even	2	inner	504.3.e.c.251.29	yes	48
28.27	even	2		2016.3.e.c.1007.7		48
56.13	odd	2		2016.3.e.c.1007.34		48
56.27	even	2	inner	504.3.e.c.251.20	yes	48
84.83	odd	2		2016.3.e.c.1007.6		48
168.83	odd	2	inner	504.3.e.c.251.30	yes	48
168.125	even	2		2016.3.e.c.1007.23		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.3.e.c.251.17	✓	48	21.20	even	2	inner
504.3.e.c.251.18	yes	48	3.2	odd	2	inner
504.3.e.c.251.19	yes	48	8.3	odd	2	inner
504.3.e.c.251.20	yes	48	56.27	even	2	inner
504.3.e.c.251.29	yes	48	24.11	even	2	inner
504.3.e.c.251.30	yes	48	168.83	odd	2	inner
504.3.e.c.251.31	yes	48	7.6	odd	2	inner
504.3.e.c.251.32	yes	48	1.1	even	1	trivial
2016.3.e.c.1007.5		48	8.5	even	2
2016.3.e.c.1007.6		48	84.83	odd	2
2016.3.e.c.1007.7		48	28.27	even	2
2016.3.e.c.1007.8		48	24.5	odd	2
2016.3.e.c.1007.23		48	168.125	even	2
2016.3.e.c.1007.24		48	4.3	odd	2
2016.3.e.c.1007.33		48	12.11	even	2
2016.3.e.c.1007.34		48	56.13	odd	2

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.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.852241 + 1.80933i) q^{2} +(-2.54737 + 3.08398i) q^{4} +9.10939i q^{5} +(0.958628 + 6.93405i) q^{7} +(-7.75091 - 1.98075i) q^{8} +(-16.4819 + 7.76340i) q^{10} +9.66169i q^{11} +2.31922 q^{13} +(-11.7290 + 7.64396i) q^{14} +(-3.02182 - 15.7121i) q^{16} +21.8883 q^{17} -26.9198i q^{19} +(-28.0931 - 23.2050i) q^{20} +(-17.4812 + 8.23410i) q^{22} +15.4172 q^{23} -57.9809 q^{25} +(1.97653 + 4.19623i) q^{26} +(-23.8264 - 14.7072i) q^{28} -18.1366 q^{29} +45.9762 q^{31} +(25.8530 - 18.8579i) q^{32} +(18.6541 + 39.6032i) q^{34} +(-63.1649 + 8.73251i) q^{35} +32.3318i q^{37} +(48.7069 - 22.9422i) q^{38} +(18.0434 - 70.6061i) q^{40} +33.0463 q^{41} -60.5091 q^{43} +(-29.7964 - 24.6119i) q^{44} +(13.1391 + 27.8948i) q^{46} -29.4932i q^{47} +(-47.1621 + 13.2943i) q^{49} +(-49.4138 - 104.907i) q^{50} +(-5.90790 + 7.15241i) q^{52} +65.7621 q^{53} -88.0121 q^{55} +(6.30435 - 55.6440i) q^{56} +(-15.4568 - 32.8152i) q^{58} -8.47268 q^{59} -74.9438 q^{61} +(39.1828 + 83.1863i) q^{62} +(56.1533 + 30.7052i) q^{64} +21.1266i q^{65} +20.2120 q^{67} +(-55.7575 + 67.5029i) q^{68} +(-69.6318 - 106.844i) q^{70} +21.7110 q^{71} +100.202i q^{73} +(-58.4989 + 27.5545i) q^{74} +(83.0201 + 68.5747i) q^{76} +(-66.9947 + 9.26197i) q^{77} -78.9852i q^{79} +(143.127 - 27.5269i) q^{80} +(28.1634 + 59.7918i) q^{82} +67.6265 q^{83} +199.389i q^{85} +(-51.5684 - 109.481i) q^{86} +(19.1374 - 74.8869i) q^{88} -130.927 q^{89} +(2.22326 + 16.0816i) q^{91} +(-39.2732 + 47.5461i) q^{92} +(53.3629 - 25.1353i) q^{94} +245.223 q^{95} -175.267i q^{97} +(-64.2473 - 74.0019i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 144 q^{22} - 336 q^{25} - 232 q^{28} - 384 q^{43} + 736 q^{46} + 368 q^{49} - 432 q^{58} + 480 q^{64} - 896 q^{67} + 264 q^{70} - 48 q^{88} - 576 q^{91}+O(q^{100}) \) 48 * q + 144 * q^22 - 336 * q^25 - 232 * q^28 - 384 * q^43 + 736 * q^46 + 368 * q^49 - 432 * q^58 + 480 * q^64 - 896 * q^67 + 264 * q^70 - 48 * q^88 - 576 * q^91

Introduction

L-functions

Modular forms

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Database

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