LMFDB - Embedded newform 504.3.e.c.251.29

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			251.29
Character	$\chi$	$=$	504.251
Dual form			504.3.e.c.251.31

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.852241 - 1.80933i) q^{2} +(-2.54737 - 3.08398i) q^{4} +9.10939i q^{5} +(-0.958628 - 6.93405i) q^{7} +(-7.75091 + 1.98075i) q^{8} +(16.4819 + 7.76340i) q^{10} -9.66169i q^{11} -2.31922 q^{13} +(-13.3630 - 4.17501i) q^{14} +(-3.02182 + 15.7121i) q^{16} -21.8883 q^{17} -26.9198i q^{19} +(28.0931 - 23.2050i) q^{20} +(-17.4812 - 8.23410i) q^{22} +15.4172 q^{23} -57.9809 q^{25} +(-1.97653 + 4.19623i) q^{26} +(-18.9425 + 20.6200i) q^{28} -18.1366 q^{29} -45.9762 q^{31} +(25.8530 + 18.8579i) q^{32} +(-18.6541 + 39.6032i) q^{34} +(63.1649 - 8.73251i) q^{35} -32.3318i q^{37} +(-48.7069 - 22.9422i) q^{38} +(-18.0434 - 70.6061i) q^{40} -33.0463 q^{41} -60.5091 q^{43} +(-29.7964 + 24.6119i) q^{44} +(13.1391 - 27.8948i) q^{46} -29.4932i q^{47} +(-47.1621 + 13.2943i) q^{49} +(-49.4138 + 104.907i) q^{50} +(5.90790 + 7.15241i) q^{52} +65.7621 q^{53} +88.0121 q^{55} +(21.1648 + 51.8464i) q^{56} +(-15.4568 + 32.8152i) q^{58} +8.47268 q^{59} +74.9438 q^{61} +(-39.1828 + 83.1863i) q^{62} +(56.1533 - 30.7052i) q^{64} -21.1266i q^{65} +20.2120 q^{67} +(55.7575 + 67.5029i) q^{68} +(38.0318 - 121.729i) q^{70} +21.7110 q^{71} +100.202i q^{73} +(-58.4989 - 27.5545i) q^{74} +(-83.0201 + 68.5747i) q^{76} +(-66.9947 + 9.26197i) q^{77} +78.9852i q^{79} +(-143.127 - 27.5269i) q^{80} +(-28.1634 + 59.7918i) q^{82} -67.6265 q^{83} -199.389i q^{85} +(-51.5684 + 109.481i) q^{86} +(19.1374 + 74.8869i) q^{88} +130.927 q^{89} +(2.22326 + 16.0816i) q^{91} +(-39.2732 - 47.5461i) q^{92} +(-53.3629 - 25.1353i) q^{94} +245.223 q^{95} -175.267i q^{97} +(-16.1396 + 96.6619i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.855273\pi$
$11$		−	9.66169i		−	0.878336i	0.898405	−	0.439168i	$-0.144727\pi$
$12$		0			0
$13$	−2.31922			−0.178401			−0.0892006	−	0.996014i	$-0.528431\pi$
$13$	−2.31922			−0.178401			−0.0892006	+	0.996014i	$0.528431\pi$
$14$	−13.3630	−	4.17501i	−0.954499	−	0.298215i
$15$		0			0
$16$	−3.02182	+	15.7121i	−0.188864	+	0.982003i
$17$	−21.8883			−1.28755			−0.643773	−	0.765217i	$-0.722632\pi$
$17$	−21.8883			−1.28755			−0.643773	+	0.765217i	$0.722632\pi$
$18$		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
$28$	−18.9425	+	20.6200i	−0.676517	+	0.736427i
$29$	−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	$-0.765910\pi$
$31$	−45.9762			−1.48310			−0.741552	+	0.670896i	$0.765910\pi$
$32$	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	$-0.856071\pi$
$37$		−	32.3318i		−	0.873832i	0.899502	−	0.436916i	$-0.143929\pi$
$38$	−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	$-0.632034\pi$
$41$	−33.0463			−0.806007			−0.403004	+	0.915198i	$0.632034\pi$
$42$		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
$56$	21.1648	+	51.8464i	0.377943	+	0.925829i
$57$		0			0
$58$	−15.4568	+	32.8152i	−0.266496	+	0.565778i
$59$	8.47268			0.143605			0.0718024	−	0.997419i	$-0.477125\pi$
$59$	8.47268			0.143605			0.0718024	+	0.997419i	$0.477125\pi$
$60$		0			0
$61$	74.9438			1.22859			0.614294	−	0.789077i	$-0.289441\pi$
$61$	74.9438			1.22859			0.614294	+	0.789077i	$0.289441\pi$
$62$	−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
$70$	38.0318	−	121.729i	0.543311	−	1.73898i
$71$	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	$0.166632\pi$
$79$			78.9852i			0.999813i	−0.866079	+	0.499906i	$0.833368\pi$
$80$	−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	$-0.633560\pi$
$83$	−67.6265			−0.814777			−0.407388	+	0.913255i	$0.633560\pi$
$84$		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	$-0.236926\pi$
$89$	130.927			1.47109			0.735546	+	0.677474i	$0.236926\pi$
$90$		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	$-0.358965\pi$
$98$	−16.1396	+	96.6619i	−0.164690	+	0.986345i
$99$		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	$-0.634328\pi$
$103$	−84.3756			−0.819181			−0.409590	+	0.912270i	$0.634328\pi$
$104$	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	$-0.876874\pi$
$107$		−	80.7290i		−	0.754476i	0.926116	−	0.377238i	$-0.123126\pi$
$108$		0			0
$109$		−	100.232i		−	0.919557i	−0.888034	−	0.459778i	$-0.847929\pi$
$109$		−	100.232i		−	0.919557i	0.888034	−	0.459778i	$-0.152071\pi$
$110$	75.0076	−	159.243i	0.681887	−	1.44767i
$111$		0			0
$112$	111.845	+	5.89144i	0.998616	+	0.0526021i
$113$			14.6523i			0.129666i	0.997896	+	0.0648330i	$0.0206515\pi$
$113$			14.6523i			0.129666i	−0.997896	+	0.0648330i	$0.979349\pi$
$114$		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	$-0.971147\pi$
$127$		−	22.9919i		−	0.181039i	0.995895	−	0.0905193i	$-0.0288527\pi$
$128$	−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	$-0.701554\pi$
$131$	−155.033			−1.18345			−0.591727	+	0.806138i	$0.701554\pi$
$132$		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	$-0.923084\pi$
$137$		−	65.5667i		−	0.478589i	0.970947	−	0.239294i	$-0.0769161\pi$
$138$		0			0
$139$		−	149.873i		−	1.07823i	−0.842233	−	0.539113i	$-0.818760\pi$
$139$		−	149.873i		−	1.07823i	0.842233	−	0.539113i	$-0.181240\pi$
$140$	−187.835	−	172.554i	−1.34168	−	1.23253i
$141$		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	$0.0938636\pi$
$151$			87.7691i			0.581252i	−0.956837	+	0.290626i	$0.906136\pi$
$152$	53.3213	+	208.653i	0.350798	+	1.37272i
$153$		0			0
$154$	−40.3376	+	129.109i	−0.261933	+	0.838370i
$155$		−	418.815i		−	2.70203i
$156$		0			0
$157$	−12.9625			−0.0825635			−0.0412818	−	0.999148i	$-0.513144\pi$
$157$	−12.9625			−0.0825635			−0.0412818	+	0.999148i	$0.513144\pi$
$158$	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	$-0.901227\pi$
$179$		−	109.315i		−	0.610696i	0.952241	−	0.305348i	$-0.0987728\pi$
$180$		0			0
$181$	75.4317			0.416750			0.208375	−	0.978049i	$-0.433183\pi$
$181$	75.4317			0.416750			0.208375	+	0.978049i	$0.433183\pi$
$182$	30.9917	+	9.68275i	0.170284	+	0.0532019i
$183$		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
$196$	161.139	+	111.581i	0.822136	+	0.569291i
$197$	−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	$-0.592232\pi$
$199$	−113.715			−0.571434			−0.285717	+	0.958314i	$0.592232\pi$
$200$	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	$-0.328768\pi$
$223$	228.516			1.02474			0.512368	+	0.858766i	$0.328768\pi$
$224$	105.978	−	197.344i	0.473118	−	0.880999i
$225$		0			0
$226$	26.5108	+	12.4873i	0.117304	+	0.0552534i
$227$	182.563			0.804242			0.402121	−	0.915587i	$-0.368273\pi$
$227$	182.563			0.804242			0.402121	+	0.915587i	$0.368273\pi$
$228$		0			0
$229$	331.984			1.44971			0.724857	−	0.688900i	$-0.241906\pi$
$229$	331.984			1.44971			0.724857	+	0.688900i	$0.241906\pi$
$230$	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	$0.281168\pi$
$233$			360.147i			1.54570i	−0.634592	+	0.772848i	$0.718832\pi$
$234$		0			0
$235$	268.665			1.14325
$236$	−21.5830	−	26.1296i	−0.0914536	−	0.110718i
$237$		0			0
$238$	292.493	+	91.3837i	1.22896	+	0.383965i
$239$	−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	$-0.253777\pi$
$251$	350.730			1.39733			0.698666	+	0.715448i	$0.253777\pi$
$252$		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	$-0.748366\pi$
$257$	−361.582			−1.40694			−0.703468	+	0.710727i	$0.748366\pi$
$258$		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
$266$	−112.390	+	359.729i	−0.422520	+	1.35236i
$267$		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	$-0.769154\pi$
$271$	−405.606			−1.49670			−0.748350	+	0.663304i	$0.769154\pi$
$272$	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	$-0.982099\pi$
$277$		−	31.1395i		−	0.112417i	0.998419	−	0.0562084i	$-0.0179011\pi$
$278$	−271.171	−	127.728i	−0.975435	−	0.459455i
$279$		0			0
$280$	−472.289	+	192.799i	−1.68675	+	0.688567i
$281$		−	15.2327i		−	0.0542087i	−0.999633	−	0.0271044i	$-0.991371\pi$
$281$		−	15.2327i		−	0.0542087i	0.999633	−	0.0271044i	$-0.00862864\pi$
$282$		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	$-0.232096\pi$
$308$	199.224	+	183.016i	0.646831	+	0.594209i
$309$		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
$322$	−206.019	−	64.3667i	−0.639811	−	0.199897i
$323$			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	$0.0962823\pi$
$347$			206.734i			0.595777i	−0.954601	+	0.297888i	$0.903718\pi$
$348$		0			0
$349$	−618.655			−1.77265			−0.886325	−	0.463063i	$-0.846750\pi$
$349$	−618.655			−1.77265			−0.886325	+	0.463063i	$0.846750\pi$
$350$	774.798	+	242.071i	2.21371	+	0.691631i
$351$		0			0
$352$	182.200	−	249.784i	0.517613	−	0.709613i
$353$	−357.742			−1.01343			−0.506717	−	0.862113i	$-0.669141\pi$
$353$	−357.742			−1.01343			−0.506717	+	0.862113i	$0.669141\pi$
$354$		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
$364$	43.9317	−	47.8222i	0.120691	−	0.131380i
$365$	−912.779			−2.50077
$366$		0			0
$367$	45.1294			0.122968			0.0614842	−	0.998108i	$-0.480417\pi$
$367$	45.1294			0.122968			0.0614842	+	0.998108i	$0.480417\pi$
$368$	−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	$-0.768548\pi$
$373$		−	495.886i		−	1.32945i	0.747087	−	0.664726i	$-0.231452\pi$
$374$	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
$392$	339.216	−	196.459i	0.865348	−	0.501172i
$393$		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	$-0.494015\pi$
$397$	14.9294			0.0376056			0.0188028	+	0.999823i	$0.494015\pi$
$398$	−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	$0.00499671\pi$
$401$			12.5890i			0.0313940i	−0.999877	+	0.0156970i	$0.995003\pi$
$402$		0			0
$403$	106.629			0.264588
$404$	219.790	−	181.547i	0.544036	−	0.449374i
$405$		0			0
$406$	242.359	+	75.7205i	0.596944	+	0.186504i
$407$	−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	$-0.467284\pi$
$419$	85.9785			0.205199			0.102600	+	0.994723i	$0.467284\pi$
$420$		0			0
$421$			32.5132i			0.0772285i	0.999254	+	0.0386143i	$0.0122944\pi$
$421$			32.5132i			0.0772285i	−0.999254	+	0.0386143i	$0.987706\pi$
$422$	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	$-0.0913310\pi$
$434$	614.379	+	191.951i	1.41562	+	0.442283i
$435$		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	$-0.474783\pi$
$439$	69.4826			0.158275			0.0791374	+	0.996864i	$0.474783\pi$
$440$	−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	$0.247673\pi$
$443$			621.899i			1.40384i	−0.712258	+	0.701918i	$0.752327\pi$
$444$		0			0
$445$			1192.67i			2.68015i
$446$	194.751	−	413.462i	0.436661	−	0.927044i
$447$		0			0
$448$	−266.741	−	359.935i	−0.595405	−	0.803426i
$449$		−	777.572i		−	1.73179i	−0.500229	−	0.865893i	$-0.666751\pi$
$449$		−	777.572i		−	1.73179i	0.500229	−	0.865893i	$-0.333249\pi$
$450$		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	$-0.888510\pi$
$463$		−	317.745i		−	0.686275i	0.939285	−	0.343137i	$-0.111490\pi$
$464$	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	$-0.552197\pi$
$467$	−152.473			−0.326495			−0.163248	+	0.986585i	$0.552197\pi$
$468$		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
$476$	414.618	−	451.335i	0.871046	−	0.948184i
$477$		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	$0.0445538\pi$
$487$			135.886i			0.279027i	−0.990220	+	0.139513i	$0.955446\pi$
$488$	−580.883	+	148.445i	−1.19033	+	0.304190i
$489$		0			0
$490$	−880.530	−	147.022i	−1.79700	−	0.300044i
$491$		−	813.773i		−	1.65738i	−0.559708	−	0.828690i	$-0.689087\pi$
$491$		−	813.773i		−	1.65738i	0.559708	−	0.828690i	$-0.310913\pi$
$492$		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
$518$	−134.985	+	432.049i	−0.260590	+	0.834071i
$519$		0			0
$520$	41.8465	+	163.751i	0.0804741	+	0.314905i
$521$	−252.033			−0.483748			−0.241874	−	0.970308i	$-0.577762\pi$
$521$	−252.033			−0.483748			−0.241874	+	0.970308i	$0.577762\pi$
$522$		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
$532$	555.086	+	509.928i	1.04339	+	0.958511i
$533$	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	$-0.941694\pi$
$541$		−	197.089i		−	0.364305i	0.983270	−	0.182152i	$-0.0583065\pi$
$542$	−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
$560$	−53.6674	+	1018.84i	−0.0958346	+	1.81936i
$561$		0			0
$562$	−27.5609	−	12.9819i	−0.0490408	−	0.0230995i
$563$	−143.148			−0.254260			−0.127130	−	0.991886i	$-0.540576\pi$
$563$	−143.148			−0.254260			−0.127130	+	0.991886i	$0.540576\pi$
$564$		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	$-0.834137\pi$
$569$		−	566.510i		−	0.995625i	0.867285	−	0.497812i	$-0.165863\pi$
$570$		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
$574$	441.597	+	137.969i	0.769333	+	0.240363i
$575$	−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	$-0.499192\pi$
$587$	2.97914			0.00507520			0.00253760	+	0.999997i	$0.499192\pi$
$588$		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	$-0.664645\pi$
$593$	−586.465			−0.988979			−0.494490	+	0.869184i	$0.664645\pi$
$594$		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	$0.950738\pi$
$602$	808.582	+	252.626i	1.34316	+	0.419645i
$603$		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	$-0.630873\pi$
$607$	−485.191			−0.799326			−0.399663	+	0.916662i	$0.630873\pi$
$608$	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	$0.134958\pi$
$613$			504.370i			0.822790i	−0.911457	+	0.411395i	$0.865042\pi$
$614$	−740.143	−	348.626i	−1.20544	−	0.567795i
$615$		0			0
$616$	500.924	−	204.488i	0.813189	−	0.331961i
$617$			20.6090i			0.0334019i	0.999861	+	0.0167010i	$0.00531633\pi$
$617$			20.6090i			0.0334019i	−0.999861	+	0.0167010i	$0.994684\pi$
$618$		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	$-0.746214\pi$
$631$		−	902.920i		−	1.43094i	0.698646	−	0.715468i	$-0.253786\pi$
$632$	−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	$-0.941230\pi$
$641$		−	235.354i		−	0.367167i	0.983004	−	0.183584i	$-0.0587698\pi$
$642$		0			0
$643$		−	189.811i		−	0.295197i	−0.989047	−	0.147598i	$-0.952846\pi$
$643$		−	189.811i		−	0.295197i	0.989047	−	0.147598i	$-0.0471543\pi$
$644$	−292.039	+	317.901i	−0.453477	+	0.493635i
$645$		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
$658$	−123.134	+	394.117i	−0.187134	+	0.598961i
$659$		−	584.716i		−	0.887277i	−0.896206	−	0.443639i	$-0.853687\pi$
$659$		−	584.716i		−	0.887277i	0.896206	−	0.443639i	$-0.146313\pi$
$660$		0			0
$661$	−687.188			−1.03962			−0.519809	−	0.854282i	$-0.673997\pi$
$661$	−687.188			−1.03962			−0.519809	+	0.854282i	$0.673997\pi$
$662$	−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	$0.0488139\pi$
$683$			208.661i			0.305506i	−0.988264	+	0.152753i	$0.951186\pi$
$684$		0			0
$685$	597.272			0.871930
$686$	685.730	+	19.2499i	0.999606	+	0.0280611i
$687$		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
$700$	1098.30	−	1195.56i	1.56900	−	1.70795i
$701$	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	$-0.959023\pi$
$709$		−	182.040i		−	0.256756i	0.991725	−	0.128378i	$-0.0409771\pi$
$710$	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	$-0.663817\pi$
$727$	−715.698			−0.984453			−0.492227	+	0.870467i	$0.663817\pi$
$728$	−49.0858	−	120.243i	−0.0674256	−	0.165169i
$729$		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	$-0.626051\pi$
$733$	−565.483			−0.771464			−0.385732	+	0.922611i	$0.626051\pi$
$734$	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
$742$	−878.778	−	274.557i	−1.18434	−	0.370023i
$743$	−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	$0.00170749\pi$
$751$			8.05706i			0.0107284i	−0.999986	+	0.00536422i	$0.998293\pi$
$752$	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	$-0.957161\pi$
$757$		−	203.142i		−	0.268352i	0.990958	−	0.134176i	$-0.0428387\pi$
$758$	−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	$-0.836315\pi$
$761$	−1325.16			−1.74134			−0.870670	+	0.491867i	$0.836315\pi$
$762$		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	$-0.00567850\pi$
$770$	−1176.10	−	367.451i	−1.52741	−	0.477209i
$771$		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
$784$	−66.3661	−	781.186i	−0.0846507	−	0.996411i
$785$		−	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	$-0.912695\pi$
$809$		−	438.239i		−	0.541705i	0.962621	−	0.270852i	$-0.0873055\pi$
$810$		0			0
$811$		−	1406.16i		−	1.73386i	−0.498427	−	0.866931i	$-0.666089\pi$
$811$		−	1406.16i		−	1.73386i	0.498427	−	0.866931i	$-0.333911\pi$
$812$	343.552	−	373.976i	0.423094	−	0.460562i
$813$		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	$-0.772474\pi$
$823$		−	1078.89i		−	1.31092i	0.755229	−	0.655461i	$-0.227526\pi$
$824$	653.988	−	167.127i	0.793675	−	0.202824i
$825$		0			0
$826$	−113.220	−	35.3735i	−0.137071	−	0.0428251i
$827$		−	111.468i		−	0.134785i	−0.997727	−	0.0673927i	$-0.978532\pi$
$827$		−	111.468i		−	0.134785i	0.997727	−	0.0673927i	$-0.0214680\pi$
$828$		0			0
$829$	109.080			0.131580			0.0657900	−	0.997833i	$-0.479043\pi$
$829$	109.080			0.131580			0.0657900	+	0.997833i	$0.479043\pi$
$830$	−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	$-0.277000\pi$
$853$	1099.79			1.28932			0.644658	+	0.764471i	$0.277000\pi$
$854$	−1001.47	−	312.891i	−1.17269	−	0.366383i
$855$		0			0
$856$	159.904	+	625.723i	0.186803	+	0.730985i
$857$	616.955			0.719900			0.359950	−	0.932972i	$-0.382794\pi$
$857$	616.955			0.719900			0.359950	+	0.932972i	$0.382794\pi$
$858$		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
$868$	870.903	−	948.028i	1.00334	−	1.09220i
$869$	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	$0.0501427\pi$
$877$			275.163i			0.313754i	−0.987618	+	0.156877i	$0.949857\pi$
$878$	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	$-0.366256\pi$
$881$	718.744			0.815827			0.407914	+	0.913020i	$0.366256\pi$
$882$		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
$896$	−878.570	+	175.872i	−0.980547	+	0.196286i
$897$		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
$910$	−88.2039	+	282.315i	−0.0969273	+	0.310236i
$911$	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	$-0.818329\pi$
$919$		−	992.984i		−	1.08050i	0.841503	−	0.540252i	$-0.181671\pi$
$920$	−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	$-0.508060\pi$
$929$	−47.0391			−0.0506342			−0.0253171	+	0.999679i	$0.508060\pi$
$930$		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	$-0.415640\pi$
$938$	−270.092	−	84.3852i	−0.287945	−	0.0899629i
$939$		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	$0.203574\pi$
$947$			1130.40i			1.19366i	−0.802367	+	0.596831i	$0.796426\pi$
$948$		0			0
$949$		−	232.390i		−	0.244879i
$950$	2824.07	+	1330.21i	2.97271	+	1.40022i
$951$		0			0
$952$	−463.262	−	1134.83i	−0.486619	−	1.19205i
$953$			781.337i			0.819871i	0.912114	+	0.409936i	$0.134449\pi$
$953$			781.337i			0.819871i	−0.912114	+	0.409936i	$0.865551\pi$
$954$		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	$0.333081\pi$
$967$			1674.13i			1.73126i	−0.500685	+	0.865629i	$0.666919\pi$
$968$	−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	$-0.544715\pi$
$971$	−271.907			−0.280028			−0.140014	+	0.990150i	$0.544715\pi$
$972$		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	$0.316857\pi$
$977$			1639.40i			1.67799i	−0.544138	+	0.838995i	$0.683143\pi$
$978$		0			0
$979$		−	1264.98i		−	1.29211i
$980$	−1016.44	+	1467.87i	−1.03718	+	1.49783i
$981$		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	$-0.851973\pi$
$991$		−	888.843i		−	0.896916i	0.893804	−	0.448458i	$-0.148027\pi$
$992$	−1188.62	−	867.017i	−1.19821	−	0.874009i
$993$		0			0
$994$	−290.124	−	90.6436i	−0.291875	−	0.0911908i
$995$		−	1035.88i		−	1.04108i
$996$		0			0
$997$	43.3671			0.0434976			0.0217488	−	0.999763i	$-0.493077\pi$
$997$	43.3671			0.0434976			0.0217488	+	0.999763i	$0.493077\pi$
$998$	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.251.29	yes	48
3.2	odd	2	inner	504.3.e.c.251.19	yes	48
4.3	odd	2		2016.3.e.c.1007.8		48
7.6	odd	2	inner	504.3.e.c.251.30	yes	48
8.3	odd	2	inner	504.3.e.c.251.18	yes	48
8.5	even	2		2016.3.e.c.1007.33		48
12.11	even	2		2016.3.e.c.1007.5		48
21.20	even	2	inner	504.3.e.c.251.20	yes	48
24.5	odd	2		2016.3.e.c.1007.24		48
24.11	even	2	inner	504.3.e.c.251.32	yes	48
28.27	even	2		2016.3.e.c.1007.23		48
56.13	odd	2		2016.3.e.c.1007.6		48
56.27	even	2	inner	504.3.e.c.251.17	✓	48
84.83	odd	2		2016.3.e.c.1007.34		48
168.83	odd	2	inner	504.3.e.c.251.31	yes	48
168.125	even	2		2016.3.e.c.1007.7		48

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

\(f(q)\)	\(=\)	\(q+(0.852241 - 1.80933i) q^{2} +(-2.54737 - 3.08398i) q^{4} +9.10939i q^{5} +(-0.958628 - 6.93405i) q^{7} +(-7.75091 + 1.98075i) q^{8} +(16.4819 + 7.76340i) q^{10} -9.66169i q^{11} -2.31922 q^{13} +(-13.3630 - 4.17501i) q^{14} +(-3.02182 + 15.7121i) q^{16} -21.8883 q^{17} -26.9198i q^{19} +(28.0931 - 23.2050i) q^{20} +(-17.4812 - 8.23410i) q^{22} +15.4172 q^{23} -57.9809 q^{25} +(-1.97653 + 4.19623i) q^{26} +(-18.9425 + 20.6200i) q^{28} -18.1366 q^{29} -45.9762 q^{31} +(25.8530 + 18.8579i) q^{32} +(-18.6541 + 39.6032i) q^{34} +(63.1649 - 8.73251i) q^{35} -32.3318i q^{37} +(-48.7069 - 22.9422i) q^{38} +(-18.0434 - 70.6061i) q^{40} -33.0463 q^{41} -60.5091 q^{43} +(-29.7964 + 24.6119i) q^{44} +(13.1391 - 27.8948i) q^{46} -29.4932i q^{47} +(-47.1621 + 13.2943i) q^{49} +(-49.4138 + 104.907i) q^{50} +(5.90790 + 7.15241i) q^{52} +65.7621 q^{53} +88.0121 q^{55} +(21.1648 + 51.8464i) q^{56} +(-15.4568 + 32.8152i) q^{58} +8.47268 q^{59} +74.9438 q^{61} +(-39.1828 + 83.1863i) q^{62} +(56.1533 - 30.7052i) q^{64} -21.1266i q^{65} +20.2120 q^{67} +(55.7575 + 67.5029i) q^{68} +(38.0318 - 121.729i) q^{70} +21.7110 q^{71} +100.202i q^{73} +(-58.4989 - 27.5545i) q^{74} +(-83.0201 + 68.5747i) q^{76} +(-66.9947 + 9.26197i) q^{77} +78.9852i q^{79} +(-143.127 - 27.5269i) q^{80} +(-28.1634 + 59.7918i) q^{82} -67.6265 q^{83} -199.389i q^{85} +(-51.5684 + 109.481i) q^{86} +(19.1374 + 74.8869i) q^{88} +130.927 q^{89} +(2.22326 + 16.0816i) q^{91} +(-39.2732 - 47.5461i) q^{92} +(-53.3629 - 25.1353i) q^{94} +245.223 q^{95} -175.267i q^{97} +(-16.1396 + 96.6619i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 144 q^{22} - 336 q^{25} - 232 q^{28} - 384 q^{43} + 736 q^{46} + 368 q^{49} - 432 q^{58} + 480 q^{64} - 896 q^{67} + 264 q^{70} - 48 q^{88} - 576 q^{91}+O(q^{100}) \) 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

Varieties

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Database

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