LMFDB - Embedded newform 384.4.k.b.95.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [384,4,Mod(95,384)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("384.95"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(384, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	384.k (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [44,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$22.6567334422$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			95.22
Character	$\chi$	$=$	384.95
Dual form			384.4.k.b.287.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(5.19561 - 0.0749974i) q^{3} +(-5.37662 - 5.37662i) q^{5} +14.8575 q^{7} +(26.9888 - 0.779314i) q^{9} +(30.0526 - 30.0526i) q^{11} +(-61.5437 - 61.5437i) q^{13} +(-28.3380 - 27.5316i) q^{15} +48.8426i q^{17} +(-7.45581 + 7.45581i) q^{19} +(77.1939 - 1.11427i) q^{21} +43.0756i q^{23} -67.1840i q^{25} +(140.165 - 6.07310i) q^{27} +(-32.9665 + 32.9665i) q^{29} -173.357i q^{31} +(153.888 - 158.396i) q^{33} +(-79.8832 - 79.8832i) q^{35} +(177.539 - 177.539i) q^{37} +(-324.373 - 315.141i) q^{39} +454.458 q^{41} +(-239.150 - 239.150i) q^{43} +(-149.298 - 140.918i) q^{45} -30.4238 q^{47} -122.254 q^{49} +(3.66306 + 253.767i) q^{51} +(235.743 + 235.743i) q^{53} -323.163 q^{55} +(-38.1783 + 39.2967i) q^{57} +(260.222 - 260.222i) q^{59} +(388.869 + 388.869i) q^{61} +(400.986 - 11.5787i) q^{63} +661.793i q^{65} +(-334.013 + 334.013i) q^{67} +(3.23055 + 223.804i) q^{69} -522.443i q^{71} -689.751i q^{73} +(-5.03862 - 349.062i) q^{75} +(446.508 - 446.508i) q^{77} +692.930i q^{79} +(727.785 - 42.0654i) q^{81} +(-677.176 - 677.176i) q^{83} +(262.608 - 262.608i) q^{85} +(-168.809 + 173.754i) q^{87} -261.949 q^{89} +(-914.386 - 914.386i) q^{91} +(-13.0013 - 900.694i) q^{93} +80.1741 q^{95} -641.755 q^{97} +(787.663 - 834.504i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{3} - 8 q^{7} + 4 q^{13} - 20 q^{19} + 56 q^{21} + 134 q^{27} - 4 q^{33} + 4 q^{37} + 596 q^{39} + 436 q^{43} + 252 q^{45} + 972 q^{49} + 648 q^{51} + 280 q^{55} + 916 q^{61} + 1636 q^{67} - 52 q^{69}+ \cdots - 1196 q^{99}+O(q^{100}) $ 44 * q + 2 * q^3 - 8 * q^7 + 4 * q^13 - 20 * q^19 + 56 * q^21 + 134 * q^27 - 4 * q^33 + 4 * q^37 + 596 * q^39 + 436 * q^43 + 252 * q^45 + 972 * q^49 + 648 * q^51 + 280 * q^55 + 916 * q^61 + 1636 * q^67 - 52 * q^69 - 1454 * q^75 - 4 * q^81 - 736 * q^85 + 1284 * q^87 - 424 * q^91 + 2084 * q^93 - 8 * q^97 - 1196 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	5.19561	−	0.0749974i	0.999896	−	0.0144332i
$3$	5.19561	−	0.0749974i	0.999896	−	0.0144332i
$4$		0			0
$5$	−5.37662	−	5.37662i	−0.480899	−	0.480899i	0.424520	−	0.905419i	$-0.360443\pi$
$5$	−5.37662	−	5.37662i	−0.480899	−	0.480899i	−0.905419	+	0.424520i	$0.860443\pi$
$6$		0			0
$7$	14.8575			0.802231			0.401115	−	0.916028i	$-0.368623\pi$
$7$	14.8575			0.802231			0.401115	+	0.916028i	$0.368623\pi$
$8$		0			0
$9$	26.9888	−	0.779314i	0.999583	−	0.0288635i
$10$		0			0
$11$	30.0526	−	30.0526i	0.823746	−	0.823746i	−0.162897	−	0.986643i	$-0.552084\pi$
$11$	30.0526	−	30.0526i	0.823746	−	0.823746i	0.986643	+	0.162897i	$0.0520837\pi$
$12$		0			0
$13$	−61.5437	−	61.5437i	−1.31301	−	1.31301i	−0.919185	−	0.393825i	$-0.871151\pi$
$13$	−61.5437	−	61.5437i	−1.31301	−	1.31301i	−0.393825	−	0.919185i	$-0.628849\pi$
$14$		0			0
$15$	−28.3380	−	27.5316i	−0.487790	−	0.473908i
$16$		0			0
$17$			48.8426i			0.696827i	0.937341	+	0.348414i	$0.113280\pi$
$17$			48.8426i			0.696827i	−0.937341	+	0.348414i	$0.886720\pi$
$18$		0			0
$19$	−7.45581	+	7.45581i	−0.0900253	+	0.0900253i	−0.750685	−	0.660660i	$-0.770277\pi$
$19$	−7.45581	+	7.45581i	−0.0900253	+	0.0900253i	0.660660	+	0.750685i	$0.270277\pi$
$20$		0			0
$21$	77.1939	−	1.11427i	0.802147	−	0.0115788i
$22$		0			0
$23$			43.0756i			0.390516i	0.980752	+	0.195258i	$0.0625545\pi$
$23$			43.0756i			0.390516i	−0.980752	+	0.195258i	$0.937446\pi$
$24$		0			0
$25$		−	67.1840i		−	0.537472i
$26$		0			0
$27$	140.165	−	6.07310i	0.999063	−	0.0432877i
$28$		0			0
$29$	−32.9665	+	32.9665i	−0.211094	+	0.211094i	−0.804732	−	0.593638i	$-0.797691\pi$
$29$	−32.9665	+	32.9665i	−0.211094	+	0.211094i	0.593638	+	0.804732i	$0.297691\pi$
$30$		0			0
$31$		−	173.357i		−	1.00438i	−0.864757	−	0.502190i	$-0.832528\pi$
$31$		−	173.357i		−	1.00438i	0.864757	−	0.502190i	$-0.167472\pi$
$32$		0			0
$33$	153.888	−	158.396i	0.811771	−	0.835550i
$34$		0			0
$35$	−79.8832	−	79.8832i	−0.385792	−	0.385792i
$36$		0			0
$37$	177.539	−	177.539i	0.788842	−	0.788842i	−0.192462	−	0.981304i	$-0.561647\pi$
$37$	177.539	−	177.539i	0.788842	−	0.788842i	0.981304	+	0.192462i	$0.0616472\pi$
$38$		0			0
$39$	−324.373	−	315.141i	−1.33182	−	1.29392i
$40$		0			0
$41$	454.458			1.73108			0.865542	−	0.500837i	$-0.166974\pi$
$41$	454.458			1.73108			0.865542	+	0.500837i	$0.166974\pi$
$42$		0			0
$43$	−239.150	−	239.150i	−0.848139	−	0.848139i	0.141762	−	0.989901i	$-0.454723\pi$
$43$	−239.150	−	239.150i	−0.848139	−	0.848139i	−0.989901	+	0.141762i	$0.954723\pi$
$44$		0			0
$45$	−149.298	−	140.918i	−0.494579	−	0.466818i
$46$		0			0
$47$	−30.4238			−0.0944205			−0.0472102	−	0.998885i	$-0.515033\pi$
$47$	−30.4238			−0.0944205			−0.0472102	+	0.998885i	$0.515033\pi$
$48$		0			0
$49$	−122.254			−0.356426
$50$		0			0
$51$	3.66306	+	253.767i	0.0100575	+	0.696755i
$52$		0			0
$53$	235.743	+	235.743i	0.610976	+	0.610976i	0.943200	−	0.332224i	$-0.107799\pi$
$53$	235.743	+	235.743i	0.610976	+	0.610976i	−0.332224	+	0.943200i	$0.607799\pi$
$54$		0			0
$55$	−323.163			−0.792278
$56$		0			0
$57$	−38.1783	+	39.2967i	−0.0887166	+	0.0913153i
$58$		0			0
$59$	260.222	−	260.222i	0.574204	−	0.574204i	−0.359096	−	0.933300i	$-0.616915\pi$
$59$	260.222	−	260.222i	0.574204	−	0.574204i	0.933300	+	0.359096i	$0.116915\pi$
$60$		0			0
$61$	388.869	+	388.869i	0.816222	+	0.816222i	0.985558	−	0.169336i	$-0.0541623\pi$
$61$	388.869	+	388.869i	0.816222	+	0.816222i	−0.169336	+	0.985558i	$0.554162\pi$
$62$		0			0
$63$	400.986	−	11.5787i	0.801896	−	0.0231552i
$64$		0			0
$65$			661.793i			1.26285i
$66$		0			0
$67$	−334.013	+	334.013i	−0.609047	+	0.609047i	−0.942697	−	0.333650i	$-0.891720\pi$
$67$	−334.013	+	334.013i	−0.609047	+	0.609047i	0.333650	+	0.942697i	$0.391720\pi$
$68$		0			0
$69$	3.23055	+	223.804i	0.00563642	+	0.390476i
$70$		0			0
$71$		−	522.443i		−	0.873275i	−0.899637	−	0.436638i	$-0.856169\pi$
$71$		−	522.443i		−	0.873275i	0.899637	−	0.436638i	$-0.143831\pi$
$72$		0			0
$73$		−	689.751i		−	1.10588i	−0.833221	−	0.552940i	$-0.813506\pi$
$73$		−	689.751i		−	1.10588i	0.833221	−	0.552940i	$-0.186494\pi$
$74$		0			0
$75$	−5.03862	−	349.062i	−0.00775747	−	0.537416i
$76$		0			0
$77$	446.508	−	446.508i	0.660835	−	0.660835i
$78$		0			0
$79$			692.930i			0.986844i	0.869790	+	0.493422i	$0.164254\pi$
$79$			692.930i			0.986844i	−0.869790	+	0.493422i	$0.835746\pi$
$80$		0			0
$81$	727.785	−	42.0654i	0.998334	−	0.0577029i
$82$		0			0
$83$	−677.176	−	677.176i	−0.895539	−	0.895539i	0.0994989	−	0.995038i	$-0.468276\pi$
$83$	−677.176	−	677.176i	−0.895539	−	0.895539i	−0.995038	+	0.0994989i	$0.968276\pi$
$84$		0			0
$85$	262.608	−	262.608i	0.335104	−	0.335104i
$86$		0			0
$87$	−168.809	+	173.754i	−0.208025	+	0.214119i
$88$		0			0
$89$	−261.949			−0.311983			−0.155992	−	0.987758i	$-0.549857\pi$
$89$	−261.949			−0.311983			−0.155992	+	0.987758i	$0.549857\pi$
$90$		0			0
$91$	−914.386	−	914.386i	−1.05334	−	1.05334i
$92$		0			0
$93$	−13.0013	−	900.694i	−0.0144965	−	1.00428i
$94$		0			0
$95$	80.1741			0.0865862
$96$		0			0
$97$	−641.755			−0.671757			−0.335878	−	0.941905i	$-0.609033\pi$
$97$	−641.755			−0.671757			−0.335878	+	0.941905i	$0.609033\pi$
$98$		0			0
$99$	787.663	−	834.504i	0.799627	−	0.847179i
$100$		0			0
$101$	962.520	+	962.520i	0.948260	+	0.948260i	0.998726	−	0.0504657i	$-0.0160705\pi$
$101$	962.520	+	962.520i	0.948260	+	0.948260i	−0.0504657	+	0.998726i	$0.516071\pi$
$102$		0			0
$103$	1478.65			1.41452			0.707262	−	0.706951i	$-0.249930\pi$
$103$	1478.65			1.41452			0.707262	+	0.706951i	$0.249930\pi$
$104$		0			0
$105$	−421.033	−	409.051i	−0.391320	−	0.380184i
$106$		0			0
$107$	−1484.78	+	1484.78i	−1.34149	+	1.34149i	−0.446908	+	0.894580i	$0.647475\pi$
$107$	−1484.78	+	1484.78i	−1.34149	+	1.34149i	−0.894580	+	0.446908i	$0.852525\pi$
$108$		0			0
$109$	103.806	+	103.806i	0.0912181	+	0.0912181i	0.751243	−	0.660025i	$-0.229454\pi$
$109$	103.806	+	103.806i	0.0912181	+	0.0912181i	−0.660025	+	0.751243i	$0.729454\pi$
$110$		0			0
$111$	909.107	−	935.736i	0.777375	−	0.800146i
$112$		0			0
$113$			54.5390i			0.0454035i	0.999742	+	0.0227017i	$0.00722681\pi$
$113$			54.5390i			0.0454035i	−0.999742	+	0.0227017i	$0.992773\pi$
$114$		0			0
$115$	231.601	−	231.601i	0.187799	−	0.187799i
$116$		0			0
$117$	−1708.95	−	1613.02i	−1.35036	−	1.27457i
$118$		0			0
$119$			725.680i			0.559016i
$120$		0			0
$121$		−	475.322i		−	0.357116i
$122$		0			0
$123$	2361.19	−	34.0832i	1.73090	−	0.0249852i
$124$		0			0
$125$	−1033.30	+	1033.30i	−0.739369	+	0.739369i
$126$		0			0
$127$			31.6817i			0.0221362i	0.999939	+	0.0110681i	$0.00352315\pi$
$127$			31.6817i			0.0221362i	−0.999939	+	0.0110681i	$0.996477\pi$
$128$		0			0
$129$	−1260.46	−	1224.59i	−0.860292	−	0.835810i
$130$		0			0
$131$	1687.23	+	1687.23i	1.12530	+	1.12530i	0.990932	+	0.134364i	$0.0428990\pi$
$131$	1687.23	+	1687.23i	1.12530	+	1.12530i	0.134364	+	0.990932i	$0.457101\pi$
$132$		0			0
$133$	−110.775	+	110.775i	−0.0722211	+	0.0722211i
$134$		0			0
$135$	−786.264	−	720.958i	−0.501265	−	0.459631i
$136$		0			0
$137$	453.548			0.282841			0.141420	−	0.989950i	$-0.454833\pi$
$137$	453.548			0.282841			0.141420	+	0.989950i	$0.454833\pi$
$138$		0			0
$139$	1392.05	+	1392.05i	0.849439	+	0.849439i	0.990063	−	0.140624i	$-0.0449110\pi$
$139$	1392.05	+	1392.05i	0.849439	+	0.849439i	−0.140624	+	0.990063i	$0.544911\pi$
$140$		0			0
$141$	−158.070	+	2.28170i	−0.0944106	+	0.00136279i
$142$		0			0
$143$	−3699.10			−2.16318
$144$		0			0
$145$	354.497			0.203030
$146$		0			0
$147$	−635.185	+	9.16874i	−0.356389	+	0.00514438i
$148$		0			0
$149$	118.909	+	118.909i	0.0653785	+	0.0653785i	0.739040	−	0.673662i	$-0.235279\pi$
$149$	118.909	+	118.909i	0.0653785	+	0.0653785i	−0.673662	+	0.739040i	$0.735279\pi$
$150$		0			0
$151$	289.153			0.155834			0.0779170	−	0.996960i	$-0.475173\pi$
$151$	289.153			0.155834			0.0779170	+	0.996960i	$0.475173\pi$
$152$		0			0
$153$	38.0637	+	1318.20i	0.0201129	+	0.696537i
$154$		0			0
$155$	−932.072	+	932.072i	−0.483005	+	0.483005i
$156$		0			0
$157$	683.842	+	683.842i	0.347621	+	0.347621i	0.859223	−	0.511602i	$-0.170948\pi$
$157$	683.842	+	683.842i	0.347621	+	0.347621i	−0.511602	+	0.859223i	$0.670948\pi$
$158$		0			0
$159$	1242.51	+	1207.15i	0.619731	+	0.602094i
$160$		0			0
$161$			639.996i			0.313284i
$162$		0			0
$163$	−35.4216	+	35.4216i	−0.0170210	+	0.0170210i	−0.715566	−	0.698545i	$-0.753831\pi$
$163$	−35.4216	+	35.4216i	−0.0170210	+	0.0170210i	0.698545	+	0.715566i	$0.253831\pi$
$164$		0			0
$165$	−1679.03	+	24.2364i	−0.792195	+	0.0114351i
$166$		0			0
$167$			2091.54i			0.969150i	0.874750	+	0.484575i	$0.161026\pi$
$167$			2091.54i			0.969150i	−0.874750	+	0.484575i	$0.838974\pi$
$168$		0			0
$169$			5378.24i			2.44799i
$170$		0			0
$171$	−195.413	+	207.034i	−0.0873894	+	0.0925863i
$172$		0			0
$173$	−2566.01	+	2566.01i	−1.12769	+	1.12769i	−0.137137	+	0.990552i	$0.543790\pi$
$173$	−2566.01	+	2566.01i	−1.12769	+	1.12769i	−0.990552	+	0.137137i	$0.956210\pi$
$174$		0			0
$175$		−	998.188i		−	0.431177i
$176$		0			0
$177$	1332.50	−	1371.53i	0.565857	−	0.582432i
$178$		0			0
$179$	−1252.13	−	1252.13i	−0.522841	−	0.522841i	0.395587	−	0.918429i	$-0.370541\pi$
$179$	−1252.13	−	1252.13i	−0.522841	−	0.522841i	−0.918429	+	0.395587i	$0.870541\pi$
$180$		0			0
$181$	−1732.51	+	1732.51i	−0.711474	+	0.711474i	−0.966844	−	0.255370i	$-0.917803\pi$
$181$	−1732.51	+	1732.51i	−0.711474	+	0.711474i	0.255370	+	0.966844i	$0.417803\pi$
$182$		0			0
$183$	2049.58	+	1991.25i	0.827918	+	0.804357i
$184$		0			0
$185$	−1909.11			−0.758707
$186$		0			0
$187$	1467.85	+	1467.85i	0.574009	+	0.574009i
$188$		0			0
$189$	2082.50	−	90.2312i	0.801479	−	0.0347267i
$190$		0			0
$191$	−188.463			−0.0713965			−0.0356983	−	0.999363i	$-0.511366\pi$
$191$	−188.463			−0.0713965			−0.0356983	+	0.999363i	$0.511366\pi$
$192$		0			0
$193$	−84.5839			−0.0315465			−0.0157733	−	0.999876i	$-0.505021\pi$
$193$	−84.5839			−0.0315465			−0.0157733	+	0.999876i	$0.505021\pi$
$194$		0			0
$195$	49.6327	+	3438.42i	0.0182270	+	1.26272i
$196$		0			0
$197$	−780.741	−	780.741i	−0.282363	−	0.282363i	0.551688	−	0.834051i	$-0.313984\pi$
$197$	−780.741	−	780.741i	−0.282363	−	0.282363i	−0.834051	+	0.551688i	$0.813984\pi$
$198$		0			0
$199$	−1640.08			−0.584233			−0.292116	−	0.956383i	$-0.594360\pi$
$199$	−1640.08			−0.584233			−0.292116	+	0.956383i	$0.594360\pi$
$200$		0			0
$201$	−1710.35	+	1760.45i	−0.600193	+	0.617774i
$202$		0			0
$203$	−489.801	+	489.801i	−0.169346	+	0.169346i
$204$		0			0
$205$	−2443.45	−	2443.45i	−0.832477	−	0.832477i
$206$		0			0
$207$	33.5694	+	1162.56i	0.0112717	+	0.390354i
$208$		0			0
$209$			448.134i			0.148316i
$210$		0			0
$211$	436.919	−	436.919i	0.142553	−	0.142553i	−0.632229	−	0.774782i	$-0.717860\pi$
$211$	436.919	−	436.919i	0.142553	−	0.142553i	0.774782	+	0.632229i	$0.217860\pi$
$212$		0			0
$213$	−39.1818	−	2714.41i	−0.0126042	−	0.873185i
$214$		0			0
$215$			2571.63i			0.815739i
$216$		0			0
$217$		−	2575.65i		−	0.805745i
$218$		0			0
$219$	−51.7295	−	3583.68i	−0.0159614	−	1.10577i
$220$		0			0
$221$	3005.95	−	3005.95i	0.914942	−	0.914942i
$222$		0			0
$223$			450.388i			0.135248i	0.997711	+	0.0676239i	$0.0215418\pi$
$223$			450.388i			0.135248i	−0.997711	+	0.0676239i	$0.978458\pi$
$224$		0			0
$225$	−52.3575	−	1813.21i	−0.0155133	−	0.537248i
$226$		0			0
$227$	−1039.61	−	1039.61i	−0.303972	−	0.303972i	0.538594	−	0.842566i	$-0.318956\pi$
$227$	−1039.61	−	1039.61i	−0.303972	−	0.303972i	−0.842566	+	0.538594i	$0.818956\pi$
$228$		0			0
$229$	−1142.20	+	1142.20i	−0.329601	+	0.329601i	−0.852435	−	0.522834i	$-0.824875\pi$
$229$	−1142.20	+	1142.20i	−0.329601	+	0.329601i	0.522834	+	0.852435i	$0.324875\pi$
$230$		0			0
$231$	2286.39	−	2353.37i	0.651228	−	0.670304i
$232$		0			0
$233$	3480.39			0.978575			0.489287	−	0.872123i	$-0.337257\pi$
$233$	3480.39			0.978575			0.489287	+	0.872123i	$0.337257\pi$
$234$		0			0
$235$	163.577	+	163.577i	0.0454067	+	0.0454067i
$236$		0			0
$237$	51.9679	+	3600.19i	0.0142434	+	0.986742i
$238$		0			0
$239$	−3195.92			−0.864966			−0.432483	−	0.901642i	$-0.642363\pi$
$239$	−3195.92			−0.864966			−0.432483	+	0.901642i	$0.642363\pi$
$240$		0			0
$241$	−255.355			−0.0682525			−0.0341262	−	0.999418i	$-0.510865\pi$
$241$	−255.355			−0.0682525			−0.0341262	+	0.999418i	$0.510865\pi$
$242$		0			0
$243$	3778.13	−	273.138i	0.997397	−	0.0721061i
$244$		0			0
$245$	657.313	+	657.313i	0.171405	+	0.171405i
$246$		0			0
$247$	917.716			0.236408
$248$		0			0
$249$	−3569.13	−	3467.56i	−0.908371	−	0.882520i
$250$		0			0
$251$	−3550.34	+	3550.34i	−0.892811	+	0.892811i	−0.994787	−	0.101976i	$-0.967484\pi$
$251$	−3550.34	+	3550.34i	−0.892811	+	0.892811i	0.101976	+	0.994787i	$0.467484\pi$
$252$		0			0
$253$	1294.53	+	1294.53i	0.321686	+	0.321686i
$254$		0			0
$255$	1344.71	−	1384.10i	0.330232	−	0.339905i
$256$		0			0
$257$			7256.80i			1.76135i	0.473721	+	0.880675i	$0.342911\pi$
$257$			7256.80i			1.76135i	−0.473721	+	0.880675i	$0.657089\pi$
$258$		0			0
$259$	2637.78	−	2637.78i	0.632834	−	0.632834i
$260$		0			0
$261$	−864.034	+	915.417i	−0.204913	+	0.217099i
$262$		0			0
$263$		−	2114.79i		−	0.495832i	−0.968782	−	0.247916i	$-0.920254\pi$
$263$		−	2114.79i		−	0.495832i	0.968782	−	0.247916i	$-0.0797457\pi$
$264$		0			0
$265$		−	2535.00i		−	0.587636i
$266$		0			0
$267$	−1360.98	+	19.6455i	−0.311951	+	0.00450293i
$268$		0			0
$269$	120.142	−	120.142i	0.0272312	−	0.0272312i	−0.693360	−	0.720591i	$-0.743870\pi$
$269$	120.142	−	120.142i	0.0272312	−	0.0272312i	0.720591	+	0.693360i	$0.243870\pi$
$270$		0			0
$271$		−	924.962i		−	0.207334i	−0.994612	−	0.103667i	$-0.966942\pi$
$271$		−	924.962i		−	0.207334i	0.994612	−	0.103667i	$-0.0330576\pi$
$272$		0			0
$273$	−4819.37	−	4682.22i	−1.06843	−	1.03802i
$274$		0			0
$275$	−2019.06	−	2019.06i	−0.442741	−	0.442741i
$276$		0			0
$277$	3882.29	−	3882.29i	0.842110	−	0.842110i	−0.147023	−	0.989133i	$-0.546969\pi$
$277$	3882.29	−	3882.29i	0.842110	−	0.842110i	0.989133	+	0.147023i	$0.0469692\pi$
$278$		0			0
$279$	−135.099	−	4678.68i	−0.0289899	−	1.00396i
$280$		0			0
$281$	175.744			0.0373097			0.0186548	−	0.999826i	$-0.494062\pi$
$281$	175.744			0.0373097			0.0186548	+	0.999826i	$0.494062\pi$
$282$		0			0
$283$	563.080	+	563.080i	0.118274	+	0.118274i	0.763767	−	0.645492i	$-0.223348\pi$
$283$	563.080	+	563.080i	0.118274	+	0.118274i	−0.645492	+	0.763767i	$0.723348\pi$
$284$		0			0
$285$	416.553	−	6.01285i	0.0865772	−	0.00124972i
$286$		0			0
$287$	6752.12			1.38873
$288$		0			0
$289$	2527.40			0.514432
$290$		0			0
$291$	−3334.31	+	48.1300i	−0.671687	+	0.00969563i
$292$		0			0
$293$	5718.53	+	5718.53i	1.14020	+	1.14020i	0.988412	+	0.151792i	$0.0485045\pi$
$293$	5718.53	+	5718.53i	1.14020	+	1.14020i	0.151792	+	0.988412i	$0.451496\pi$
$294$		0			0
$295$	−2798.23			−0.552268
$296$		0			0
$297$	4029.80	−	4394.83i	0.787316	−	0.858632i
$298$		0			0
$299$	2651.03	−	2651.03i	0.512752	−	0.512752i
$300$		0			0
$301$	−3553.17	−	3553.17i	−0.680403	−	0.680403i
$302$		0			0
$303$	5073.06	+	4928.69i	0.961848	+	0.934475i
$304$		0			0
$305$		−	4181.60i		−	0.785041i
$306$		0			0
$307$	−1027.09	+	1027.09i	−0.190942	+	0.190942i	−0.796103	−	0.605161i	$-0.793109\pi$
$307$	−1027.09	+	1027.09i	−0.190942	+	0.190942i	0.605161	+	0.796103i	$0.293109\pi$
$308$		0			0
$309$	7682.51	−	110.895i	1.41438	−	0.0204162i
$310$		0			0
$311$		−	3479.04i		−	0.634335i	−0.948370	−	0.317168i	$-0.897268\pi$
$311$		−	3479.04i		−	0.634335i	0.948370	−	0.317168i	$-0.102732\pi$
$312$		0			0
$313$		−	3308.25i		−	0.597424i	−0.954343	−	0.298712i	$-0.903443\pi$
$313$		−	3308.25i		−	0.597424i	0.954343	−	0.298712i	$-0.0965569\pi$
$314$		0			0
$315$	−2218.20	−	2093.69i	−0.396767	−	0.374496i
$316$		0			0
$317$	1297.15	−	1297.15i	0.229826	−	0.229826i	−0.582794	−	0.812620i	$-0.698040\pi$
$317$	1297.15	−	1297.15i	0.229826	−	0.229826i	0.812620	+	0.582794i	$0.198040\pi$
$318$		0			0
$319$			1981.46i			0.347776i
$320$		0			0
$321$	−7602.99	+	7825.70i	−1.32199	+	1.36071i
$322$		0			0
$323$	−364.161	−	364.161i	−0.0627321	−	0.0627321i
$324$		0			0
$325$	−4134.75	+	4134.75i	−0.705707	+	0.705707i
$326$		0			0
$327$	547.119	+	531.548i	0.0925252	+	0.0898920i
$328$		0			0
$329$	−452.022			−0.0757470
$330$		0			0
$331$	−4319.83	−	4319.83i	−0.717339	−	0.717339i	0.250721	−	0.968059i	$-0.419332\pi$
$331$	−4319.83	−	4319.83i	−0.717339	−	0.717339i	−0.968059	+	0.250721i	$0.919332\pi$
$332$		0			0
$333$	4653.19	−	4929.90i	0.765745	−	0.811282i
$334$		0			0
$335$	3591.71			0.585780
$336$		0			0
$337$	9925.19			1.60433			0.802165	−	0.597102i	$-0.203681\pi$
$337$	9925.19			1.60433			0.802165	+	0.597102i	$0.203681\pi$
$338$		0			0
$339$	4.09028	+	283.363i	0.000655320	+	0.0453988i
$340$		0			0
$341$	−5209.83	−	5209.83i	−0.827355	−	0.827355i
$342$		0			0
$343$	−6912.52			−1.08817
$344$		0			0
$345$	1185.94	−	1220.68i	0.185069	−	0.190490i
$346$		0			0
$347$	6188.11	−	6188.11i	0.957335	−	0.957335i	−0.0417910	−	0.999126i	$-0.513306\pi$
$347$	6188.11	−	6188.11i	0.957335	−	0.957335i	0.999126	+	0.0417910i	$0.0133063\pi$
$348$		0			0
$349$	1274.05	+	1274.05i	0.195411	+	0.195411i	0.798030	−	0.602618i	$-0.205876\pi$
$349$	1274.05	+	1274.05i	0.195411	+	0.195411i	−0.602618	+	0.798030i	$0.705876\pi$
$350$		0			0
$351$	−9000.00	−	8252.48i	−1.36862	−	1.25494i
$352$		0			0
$353$			1359.26i			0.204947i	0.994736	+	0.102473i	$0.0326756\pi$
$353$			1359.26i			0.204947i	−0.994736	+	0.102473i	$0.967324\pi$
$354$		0			0
$355$	−2808.97	+	2808.97i	−0.419957	+	0.419957i
$356$		0			0
$357$	54.4241	+	3770.35i	0.00806842	+	0.558958i
$358$		0			0
$359$			479.331i			0.0704683i	0.999379	+	0.0352342i	$0.0112177\pi$
$359$			479.331i			0.0704683i	−0.999379	+	0.0352342i	$0.988782\pi$
$360$		0			0
$361$			6747.82i			0.983791i
$362$		0			0
$363$	−35.6479	−	2469.59i	−0.00515435	−	0.357079i
$364$		0			0
$365$	−3708.53	+	3708.53i	−0.531817	+	0.531817i
$366$		0			0
$367$		−	6512.69i		−	0.926320i	−0.886275	−	0.463160i	$-0.846715\pi$
$367$		−	6512.69i		−	0.926320i	0.886275	−	0.463160i	$-0.153285\pi$
$368$		0			0
$369$	12265.3	−	354.166i	1.73036	−	0.0499651i
$370$		0			0
$371$	3502.55	+	3502.55i	0.490144	+	0.490144i
$372$		0			0
$373$	8069.28	−	8069.28i	1.12014	−	1.12014i	0.128418	−	0.991720i	$-0.459010\pi$
$373$	8069.28	−	8069.28i	1.12014	−	1.12014i	0.991720	−	0.128418i	$-0.0409898\pi$
$374$		0			0
$375$	−5291.13	+	5446.12i	−0.728620	+	0.749963i
$376$		0			0
$377$	4057.76			0.554338
$378$		0			0
$379$	−1799.74	−	1799.74i	−0.243922	−	0.243922i	0.574548	−	0.818471i	$-0.305178\pi$
$379$	−1799.74	−	1799.74i	−0.243922	−	0.243922i	−0.818471	+	0.574548i	$0.805178\pi$
$380$		0			0
$381$	2.37604	+	164.606i	0.000319497	+	0.0221339i
$382$		0			0
$383$	−12267.5			−1.63666			−0.818332	−	0.574746i	$-0.805101\pi$
$383$	−12267.5			−1.63666			−0.818332	+	0.574746i	$0.805101\pi$
$384$		0			0
$385$	−4801.40			−0.635590
$386$		0			0
$387$	−6640.73	−	6267.98i	−0.872266	−	0.823306i
$388$		0			0
$389$	1661.54	+	1661.54i	0.216564	+	0.216564i	0.807049	−	0.590485i	$-0.201064\pi$
$389$	1661.54	+	1661.54i	0.216564	+	0.216564i	−0.590485	+	0.807049i	$0.701064\pi$
$390$		0			0
$391$	−2103.92			−0.272122
$392$		0			0
$393$	8892.71	+	8639.64i	1.14142	+	1.10894i
$394$		0			0
$395$	3725.62	−	3725.62i	0.474573	−	0.474573i
$396$		0			0
$397$	259.031	+	259.031i	0.0327465	+	0.0327465i	0.723290	−	0.690544i	$-0.242629\pi$
$397$	259.031	+	259.031i	0.0327465	+	0.0327465i	−0.690544	+	0.723290i	$0.742629\pi$
$398$		0			0
$399$	−567.236	+	583.851i	−0.0711712	+	0.0732559i
$400$		0			0
$401$		−	5120.78i		−	0.637705i	−0.947804	−	0.318852i	$-0.896703\pi$
$401$		−	5120.78i		−	0.637705i	0.947804	−	0.318852i	$-0.103297\pi$
$402$		0			0
$403$	−10669.0	+	10669.0i	−1.31876	+	1.31876i
$404$		0			0
$405$	−4139.19	−	3686.85i	−0.507847	−	0.452349i
$406$		0			0
$407$		−	10671.0i		−	1.29961i
$408$		0			0
$409$		−	4138.32i		−	0.500311i	−0.968206	−	0.250155i	$-0.919518\pi$
$409$		−	4138.32i		−	0.500311i	0.968206	−	0.250155i	$-0.0804817\pi$
$410$		0			0
$411$	2356.46	−	34.0149i	0.282811	−	0.00408231i
$412$		0			0
$413$	3866.26	−	3866.26i	0.460644	−	0.460644i
$414$		0			0
$415$			7281.83i			0.861327i
$416$		0			0
$417$	7336.94	+	7128.14i	0.861610	+	0.837090i
$418$		0			0
$419$	2623.85	+	2623.85i	0.305927	+	0.305927i	0.843327	−	0.537401i	$-0.180594\pi$
$419$	2623.85	+	2623.85i	0.305927	+	0.305927i	−0.537401	+	0.843327i	$0.680594\pi$
$420$		0			0
$421$	207.548	−	207.548i	0.0240268	−	0.0240268i	−0.694991	−	0.719018i	$-0.744592\pi$
$421$	207.548	−	207.548i	0.0240268	−	0.0240268i	0.719018	+	0.694991i	$0.244592\pi$
$422$		0			0
$423$	−821.099	+	23.7097i	−0.0943811	+	0.00272530i
$424$		0			0
$425$	3281.44			0.374525
$426$		0			0
$427$	5777.63	+	5777.63i	0.654799	+	0.654799i
$428$		0			0
$429$	−19219.1	+	277.423i	−2.16295	+	0.0312217i
$430$		0			0
$431$	11772.7			1.31571			0.657855	−	0.753145i	$-0.271464\pi$
$431$	11772.7			1.31571			0.657855	+	0.753145i	$0.271464\pi$
$432$		0			0
$433$	−4268.67			−0.473763			−0.236881	−	0.971539i	$-0.576125\pi$
$433$	−4268.67			−0.473763			−0.236881	+	0.971539i	$0.576125\pi$
$434$		0			0
$435$	1841.83	−	26.5863i	0.203009	−	0.00293038i
$436$		0			0
$437$	−321.163	−	321.163i	−0.0351564	−	0.0351564i
$438$		0			0
$439$	1006.82			0.109459			0.0547297	−	0.998501i	$-0.482570\pi$
$439$	1006.82			0.109459			0.0547297	+	0.998501i	$0.482570\pi$
$440$		0			0
$441$	−3299.49	+	95.2744i	−0.356277	+	0.0102877i
$442$		0			0
$443$	−3697.94	+	3697.94i	−0.396601	+	0.396601i	−0.877032	−	0.480431i	$-0.840480\pi$
$443$	−3697.94	+	3697.94i	−0.396601	+	0.396601i	0.480431	+	0.877032i	$0.340480\pi$
$444$		0			0
$445$	1408.40	+	1408.40i	0.150032	+	0.150032i
$446$		0			0
$447$	626.722	+	608.886i	0.0663153	+	0.0644281i
$448$		0			0
$449$		−	11582.4i		−	1.21738i	−0.793407	−	0.608692i	$-0.791695\pi$
$449$		−	11582.4i		−	1.21738i	0.793407	−	0.608692i	$-0.208305\pi$
$450$		0			0
$451$	13657.7	−	13657.7i	1.42597	−	1.42597i
$452$		0			0
$453$	1502.33	−	21.6857i	0.155818	−	0.00224919i
$454$		0			0
$455$			9832.60i			1.01310i
$456$		0			0
$457$			1710.35i			0.175070i	0.996161	+	0.0875349i	$0.0278989\pi$
$457$			1710.35i			0.175070i	−0.996161	+	0.0875349i	$0.972101\pi$
$458$		0			0
$459$	296.626	+	6846.00i	0.0301641	+	0.696174i
$460$		0			0
$461$	−4945.52	+	4945.52i	−0.499644	+	0.499644i	−0.911327	−	0.411683i	$-0.864941\pi$
$461$	−4945.52	+	4945.52i	−0.499644	+	0.499644i	0.411683	+	0.911327i	$0.364941\pi$
$462$		0			0
$463$		−	5550.67i		−	0.557152i	−0.960414	−	0.278576i	$-0.910138\pi$
$463$		−	5550.67i		−	0.557152i	0.960414	−	0.278576i	$-0.0898624\pi$
$464$		0			0
$465$	−4772.78	+	4912.59i	−0.475984	+	0.489926i
$466$		0			0
$467$	5335.45	+	5335.45i	0.528683	+	0.528683i	0.920180	−	0.391497i	$-0.128043\pi$
$467$	5335.45	+	5335.45i	0.528683	+	0.528683i	−0.391497	+	0.920180i	$0.628043\pi$
$468$		0			0
$469$	−4962.60	+	4962.60i	−0.488596	+	0.488596i
$470$		0			0
$471$	3604.26	+	3501.69i	0.352602	+	0.342568i
$472$		0			0
$473$	−14374.2			−1.39730
$474$		0			0
$475$	500.912	+	500.912i	0.0483861	+	0.0483861i
$476$		0			0
$477$	6546.12	+	6178.68i	0.628357	+	0.593087i
$478$		0			0
$479$	3196.65			0.304924			0.152462	−	0.988309i	$-0.451280\pi$
$479$	3196.65			0.304924			0.152462	+	0.988309i	$0.451280\pi$
$480$		0			0
$481$	−21852.7			−2.07152
$482$		0			0
$483$	47.9980	+	3325.17i	0.00452171	+	0.313251i
$484$		0			0
$485$	3450.47	+	3450.47i	0.323047	+	0.323047i
$486$		0			0
$487$	18653.5			1.73567			0.867833	−	0.496856i	$-0.165512\pi$
$487$	18653.5			1.73567			0.867833	+	0.496856i	$0.165512\pi$
$488$		0			0
$489$	−181.380	+	186.693i	−0.0167736	+	0.0172649i
$490$		0			0
$491$	4162.67	−	4162.67i	0.382604	−	0.382604i	−0.489436	−	0.872039i	$-0.662797\pi$
$491$	4162.67	−	4162.67i	0.382604	−	0.382604i	0.872039	+	0.489436i	$0.162797\pi$
$492$		0			0
$493$	−1610.17	−	1610.17i	−0.147096	−	0.147096i
$494$		0			0
$495$	−8721.76	+	251.845i	−0.791948	+	0.0228679i
$496$		0			0
$497$		−	7762.20i		−	0.700568i
$498$		0			0
$499$	7570.74	−	7570.74i	0.679184	−	0.679184i	−0.280631	−	0.959816i	$-0.590544\pi$
$499$	7570.74	−	7570.74i	0.679184	−	0.679184i	0.959816	+	0.280631i	$0.0905439\pi$
$500$		0			0
$501$	156.860	+	10866.8i	0.0139880	+	0.969049i
$502$		0			0
$503$		−	10216.7i		−	0.905647i	−0.891600	−	0.452823i	$-0.850417\pi$
$503$		−	10216.7i		−	0.905647i	0.891600	−	0.452823i	$-0.149583\pi$
$504$		0			0
$505$		−	10350.2i		−	0.912035i
$506$		0			0
$507$	403.354	+	27943.3i	0.0353325	+	2.44774i
$508$		0			0
$509$	12175.7	−	12175.7i	1.06027	−	1.06027i	0.0622119	−	0.998063i	$-0.480185\pi$
$509$	12175.7	−	12175.7i	1.06027	−	1.06027i	0.998063	−	0.0622119i	$-0.0198155\pi$
$510$		0			0
$511$		−	10248.0i		−	0.887171i
$512$		0			0
$513$	−999.761	+	1090.32i	−0.0860439	+	0.0938379i
$514$		0			0
$515$	−7950.15	−	7950.15i	−0.680244	−	0.680244i
$516$		0			0
$517$	−914.314	+	914.314i	−0.0777785	+	0.0777785i
$518$		0			0
$519$	−13139.5	+	13524.4i	−1.11130	+	1.14385i
$520$		0			0
$521$	734.120			0.0617320			0.0308660	−	0.999524i	$-0.490173\pi$
$521$	734.120			0.0617320			0.0308660	+	0.999524i	$0.490173\pi$
$522$		0			0
$523$	−4289.83	−	4289.83i	−0.358664	−	0.358664i	0.504656	−	0.863320i	$-0.331619\pi$
$523$	−4289.83	−	4289.83i	−0.358664	−	0.358664i	−0.863320	+	0.504656i	$0.831619\pi$
$524$		0			0
$525$	−74.8615	−	5186.20i	−0.00622328	−	0.431132i
$526$		0			0
$527$	8467.19			0.699880
$528$		0			0
$529$	10311.5			0.847497
$530$		0			0
$531$	6820.27	−	7225.86i	0.557391	−	0.590538i
$532$		0			0
$533$	−27969.0	−	27969.0i	−2.27293	−	2.27293i
$534$		0			0
$535$	15966.2			1.29024
$536$		0			0
$537$	−6599.49	−	6411.68i	−0.530333	−	0.515241i
$538$		0			0
$539$	−3674.06	+	3674.06i	−0.293605	+	0.293605i
$540$		0			0
$541$	11785.3	+	11785.3i	0.936583	+	0.936583i	0.998106	−	0.0615231i	$-0.0195958\pi$
$541$	11785.3	+	11785.3i	0.936583	+	0.936583i	−0.0615231	+	0.998106i	$0.519596\pi$
$542$		0			0
$543$	−8871.54	+	9131.41i	−0.701131	+	0.721669i
$544$		0			0
$545$		−	1116.25i		−	0.0877334i
$546$		0			0
$547$	−10084.5	+	10084.5i	−0.788268	+	0.788268i	−0.981210	−	0.192942i	$-0.938197\pi$
$547$	−10084.5	+	10084.5i	−0.788268	+	0.788268i	0.192942	+	0.981210i	$0.438197\pi$
$548$		0			0
$549$	10798.1	+	10192.0i	0.839441	+	0.792323i
$550$		0			0
$551$		−	491.585i		−	0.0380076i
$552$		0			0
$553$			10295.2i			0.791677i
$554$		0			0
$555$	−9919.01	+	143.178i	−0.758628	+	0.0109506i
$556$		0			0
$557$	−6502.22	+	6502.22i	−0.494628	+	0.494628i	−0.909761	−	0.415133i	$-0.863735\pi$
$557$	−6502.22	+	6502.22i	−0.494628	+	0.494628i	0.415133	+	0.909761i	$0.363735\pi$
$558$		0			0
$559$			29436.3i			2.22723i
$560$		0			0
$561$	7736.45	+	7516.28i	0.582234	+	0.565664i
$562$		0			0
$563$	6184.95	+	6184.95i	0.462992	+	0.462992i	0.899635	−	0.436643i	$-0.143833\pi$
$563$	6184.95	+	6184.95i	0.462992	+	0.462992i	−0.436643	+	0.899635i	$0.643833\pi$
$564$		0			0
$565$	293.235	−	293.235i	0.0218345	−	0.0218345i
$566$		0			0
$567$	10813.1	−	624.988i	0.800894	−	0.0462911i
$568$		0			0
$569$	−25063.0			−1.84657			−0.923284	−	0.384119i	$-0.874505\pi$
$569$	−25063.0			−1.84657			−0.923284	+	0.384119i	$0.874505\pi$
$570$		0			0
$571$	−15682.4	−	15682.4i	−1.14937	−	1.14937i	−0.986677	−	0.162692i	$-0.947982\pi$
$571$	−15682.4	−	15682.4i	−1.14937	−	1.14937i	−0.162692	−	0.986677i	$-0.552018\pi$
$572$		0			0
$573$	−979.183	+	14.1343i	−0.0713891	+	0.00103048i
$574$		0			0
$575$	2893.99			0.209892
$576$		0			0
$577$	−1972.54			−0.142319			−0.0711593	−	0.997465i	$-0.522670\pi$
$577$	−1972.54			−0.142319			−0.0711593	+	0.997465i	$0.522670\pi$
$578$		0			0
$579$	−439.465	+	6.34357i	−0.0315432	+	0.000455319i
$580$		0			0
$581$	−10061.2	−	10061.2i	−0.718429	−	0.718429i
$582$		0			0
$583$	14169.4			1.00658
$584$		0			0
$585$	515.745	+	17861.0i	0.0364503	+	1.26233i
$586$		0			0
$587$	3171.66	−	3171.66i	0.223013	−	0.223013i	−0.586753	−	0.809766i	$-0.699594\pi$
$587$	3171.66	−	3171.66i	0.223013	−	0.223013i	0.809766	+	0.586753i	$0.199594\pi$
$588$		0			0
$589$	1292.52	+	1292.52i	0.0904196	+	0.0904196i
$590$		0			0
$591$	−4114.98	−	3997.87i	−0.286409	−	0.278258i
$592$		0			0
$593$			2763.19i			0.191350i	0.995413	+	0.0956752i	$0.0305010\pi$
$593$			2763.19i			0.191350i	−0.995413	+	0.0956752i	$0.969499\pi$
$594$		0			0
$595$	3901.70	−	3901.70i	0.268830	−	0.268830i
$596$		0			0
$597$	−8521.23	+	123.002i	−0.584172	+	0.00843238i
$598$		0			0
$599$			27598.5i			1.88255i	0.337647	+	0.941273i	$0.390369\pi$
$599$			27598.5i			1.88255i	−0.337647	+	0.941273i	$0.609631\pi$
$600$		0			0
$601$			12432.1i			0.843789i	0.906645	+	0.421894i	$0.138635\pi$
$601$			12432.1i			0.843789i	−0.906645	+	0.421894i	$0.861365\pi$
$602$		0			0
$603$	−8754.28	+	9274.88i	−0.591214	+	0.626372i
$604$		0			0
$605$	−2555.62	+	2555.62i	−0.171737	+	0.171737i
$606$		0			0
$607$			13691.9i			0.915545i	0.889069	+	0.457772i	$0.151353\pi$
$607$			13691.9i			0.915545i	−0.889069	+	0.457772i	$0.848647\pi$
$608$		0			0
$609$	−2508.08	+	2581.55i	−0.166884	+	0.171773i
$610$		0			0
$611$	1872.39	+	1872.39i	0.123975	+	0.123975i
$612$		0			0
$613$	−17418.7	+	17418.7i	−1.14769	+	1.14769i	−0.160686	+	0.987006i	$0.551371\pi$
$613$	−17418.7	+	17418.7i	−1.14769	+	1.14769i	−0.987006	+	0.160686i	$0.948629\pi$
$614$		0			0
$615$	−12878.4	−	12511.9i	−0.844405	−	0.820375i
$616$		0			0
$617$	6194.64			0.404193			0.202096	−	0.979366i	$-0.435225\pi$
$617$	6194.64			0.404193			0.202096	+	0.979366i	$0.435225\pi$
$618$		0			0
$619$	15342.7	+	15342.7i	0.996247	+	0.996247i	0.999993	−	0.00374578i	$-0.00119232\pi$
$619$	15342.7	+	15342.7i	0.996247	+	0.996247i	−0.00374578	+	0.999993i	$0.501192\pi$
$620$		0			0
$621$	261.602	+	6037.67i	0.0169046	+	0.390150i
$622$		0			0
$623$	−3891.91			−0.250282
$624$		0			0
$625$	2713.31			0.173652
$626$		0			0
$627$	33.6088	+	2328.33i	0.00214068	+	0.148301i
$628$		0			0
$629$	8671.44	+	8671.44i	0.549687	+	0.549687i
$630$		0			0
$631$	−24841.9			−1.56726			−0.783631	−	0.621227i	$-0.786635\pi$
$631$	−24841.9			−1.56726			−0.783631	+	0.621227i	$0.786635\pi$
$632$		0			0
$633$	2237.30	−	2302.83i	0.140481	−	0.144596i
$634$		0			0
$635$	170.340	−	170.340i	0.0106453	−	0.0106453i
$636$		0			0
$637$	7523.96	+	7523.96i	0.467991	+	0.467991i
$638$		0			0
$639$	−407.147	−	14100.1i	−0.0252058	−	0.872912i
$640$		0			0
$641$			13544.6i			0.834600i	0.908769	+	0.417300i	$0.137024\pi$
$641$			13544.6i			0.834600i	−0.908769	+	0.417300i	$0.862976\pi$
$642$		0			0
$643$	−12655.0	+	12655.0i	−0.776152	+	0.776152i	−0.979174	−	0.203022i	$-0.934924\pi$
$643$	−12655.0	+	12655.0i	−0.776152	+	0.776152i	0.203022	+	0.979174i	$0.434924\pi$
$644$		0			0
$645$	192.866	+	13361.2i	0.0117738	+	0.815654i
$646$		0			0
$647$			8771.04i			0.532960i	0.963840	+	0.266480i	$0.0858607\pi$
$647$			8771.04i			0.532960i	−0.963840	+	0.266480i	$0.914139\pi$
$648$		0			0
$649$		−	15640.7i		−	0.945997i
$650$		0			0
$651$	−193.167	−	13382.1i	−0.0116295	−	0.805661i
$652$		0			0
$653$	21658.4	−	21658.4i	1.29794	−	1.29794i	0.368197	−	0.929748i	$-0.379975\pi$
$653$	21658.4	−	21658.4i	1.29794	−	1.29794i	0.929748	−	0.368197i	$-0.120025\pi$
$654$		0			0
$655$		−	18143.1i		−	1.08231i
$656$		0			0
$657$	−537.533	−	18615.5i	−0.0319196	−	1.10542i
$658$		0			0
$659$	−9280.25	−	9280.25i	−0.548569	−	0.548569i	0.377457	−	0.926027i	$-0.376798\pi$
$659$	−9280.25	−	9280.25i	−0.548569	−	0.548569i	−0.926027	+	0.377457i	$0.876798\pi$
$660$		0			0
$661$	13336.7	−	13336.7i	0.784776	−	0.784776i	−0.195857	−	0.980632i	$-0.562749\pi$
$661$	13336.7	−	13336.7i	0.784776	−	0.784776i	0.980632	+	0.195857i	$0.0627488\pi$
$662$		0			0
$663$	15392.3	−	15843.2i	0.901641	−	0.928052i
$664$		0			0
$665$	1191.19			0.0694621
$666$		0			0
$667$	−1420.05	−	1420.05i	−0.0824357	−	0.0824357i
$668$		0			0
$669$	33.7779	+	2340.04i	0.00195206	+	0.135234i
$670$		0			0
$671$	23373.1			1.34472
$672$		0			0
$673$	−15820.7			−0.906156			−0.453078	−	0.891471i	$-0.649674\pi$
$673$	−15820.7			−0.906156			−0.453078	+	0.891471i	$0.649674\pi$
$674$		0			0
$675$	−408.015	−	9416.82i	−0.0232659	−	0.536968i
$676$		0			0
$677$	3185.15	+	3185.15i	0.180820	+	0.180820i	0.791713	−	0.610893i	$-0.209189\pi$
$677$	3185.15	+	3185.15i	0.180820	+	0.180820i	−0.610893	+	0.791713i	$0.709189\pi$
$678$		0			0
$679$	−9534.89			−0.538904
$680$		0			0
$681$	−5479.40	−	5323.46i	−0.308328	−	0.299553i
$682$		0			0
$683$	−423.850	+	423.850i	−0.0237455	+	0.0237455i	−0.718880	−	0.695134i	$-0.755345\pi$
$683$	−423.850	+	423.850i	−0.0237455	+	0.0237455i	0.695134	+	0.718880i	$0.255345\pi$
$684$		0			0
$685$	−2438.55	−	2438.55i	−0.136018	−	0.136018i
$686$		0			0
$687$	−5848.76	+	6020.08i	−0.324810	+	0.334324i
$688$		0			0
$689$		−	29016.9i		−	1.60444i
$690$		0			0
$691$	−5607.03	+	5607.03i	−0.308685	+	0.308685i	−0.844399	−	0.535714i	$-0.820042\pi$
$691$	−5607.03	+	5607.03i	−0.308685	+	0.308685i	0.535714	+	0.844399i	$0.320042\pi$
$692$		0			0
$693$	11702.7	−	12398.7i	0.641485	−	0.679633i
$694$		0			0
$695$		−	14969.0i		−	0.816989i
$696$		0			0
$697$			22196.9i			1.20627i
$698$		0			0
$699$	18082.7	−	261.020i	0.978473	−	0.0141240i
$700$		0			0
$701$	−15985.1	+	15985.1i	−0.861267	+	0.861267i	−0.991485	−	0.130218i	$-0.958432\pi$
$701$	−15985.1	+	15985.1i	−0.861267	+	0.861267i	0.130218	+	0.991485i	$0.458432\pi$
$702$		0			0
$703$			2647.39i			0.142032i
$704$		0			0
$705$	862.150	+	837.614i	0.0460574	+	0.0447466i
$706$		0			0
$707$	14300.7	+	14300.7i	0.760723	+	0.760723i
$708$		0			0
$709$	3590.05	−	3590.05i	0.190165	−	0.190165i	−0.605602	−	0.795768i	$-0.707068\pi$
$709$	3590.05	−	3590.05i	0.190165	−	0.190165i	0.795768	+	0.605602i	$0.207068\pi$
$710$		0			0
$711$	540.010	+	18701.3i	0.0284838	+	0.986433i
$712$		0			0
$713$	7467.44			0.392227
$714$		0			0
$715$	19888.6	+	19888.6i	1.04027	+	1.04027i
$716$		0			0
$717$	−16604.8	+	239.686i	−0.864876	+	0.0124843i
$718$		0			0
$719$	−5996.91			−0.311053			−0.155526	−	0.987832i	$-0.549707\pi$
$719$	−5996.91			−0.311053			−0.155526	+	0.987832i	$0.549707\pi$
$720$		0			0
$721$	21969.1			1.13477
$722$		0			0
$723$	−1326.72	+	19.1509i	−0.0682454	+	0.000985105i
$724$		0			0
$725$	2214.82	+	2214.82i	0.113457	+	0.113457i
$726$		0			0
$727$	−15850.3			−0.808606			−0.404303	−	0.914625i	$-0.632486\pi$
$727$	−15850.3			−0.808606			−0.404303	+	0.914625i	$0.632486\pi$
$728$		0			0
$729$	19609.2	−	1702.47i	0.996252	−	0.0864943i
$730$		0			0
$731$	11680.7	−	11680.7i	0.591007	−	0.591007i
$732$		0			0
$733$	−15633.8	−	15633.8i	−0.787784	−	0.787784i	0.193346	−	0.981131i	$-0.438066\pi$
$733$	−15633.8	−	15633.8i	−0.787784	−	0.787784i	−0.981131	+	0.193346i	$0.938066\pi$
$734$		0			0
$735$	3464.44	+	3365.85i	0.173861	+	0.168913i
$736$		0			0
$737$			20075.9i			1.00340i
$738$		0			0
$739$	22820.0	−	22820.0i	1.13592	−	1.13592i	0.146747	−	0.989174i	$-0.453120\pi$
$739$	22820.0	−	22820.0i	1.13592	−	1.13592i	0.989174	−	0.146747i	$-0.0468805\pi$
$740$		0			0
$741$	4768.10	−	68.8263i	0.236384	−	0.00341214i
$742$		0			0
$743$		−	34196.9i		−	1.68851i	−0.535941	−	0.844255i	$-0.680043\pi$
$743$		−	34196.9i		−	1.68851i	0.535941	−	0.844255i	$-0.319957\pi$
$744$		0			0
$745$		−	1278.65i		−	0.0628809i
$746$		0			0
$747$	−18803.9	−	17748.4i	−0.921014	−	0.869317i
$748$		0			0
$749$	−22060.2	+	22060.2i	−1.07618	+	1.07618i
$750$		0			0
$751$		−	36702.6i		−	1.78335i	−0.452675	−	0.891676i	$-0.649530\pi$
$751$		−	36702.6i		−	1.78335i	0.452675	−	0.891676i	$-0.350470\pi$
$752$		0			0
$753$	−18179.9	+	18712.5i	−0.879832	+	0.905604i
$754$		0			0
$755$	−1554.66	−	1554.66i	−0.0749404	−	0.0749404i
$756$		0			0
$757$	12194.0	−	12194.0i	0.585468	−	0.585468i	−0.350933	−	0.936401i	$-0.614135\pi$
$757$	12194.0	−	12194.0i	0.585468	−	0.585468i	0.936401	+	0.350933i	$0.114135\pi$
$758$		0			0
$759$	6822.98	+	6628.81i	0.326296	+	0.317010i
$760$		0			0
$761$	33960.5			1.61770			0.808848	−	0.588018i	$-0.200091\pi$
$761$	33960.5			1.61770			0.808848	+	0.588018i	$0.200091\pi$
$762$		0			0
$763$	1542.29	+	1542.29i	0.0731780	+	0.0731780i
$764$		0			0
$765$	6882.80	−	7292.11i	0.325292	−	0.344636i
$766$		0			0
$767$	−32030.0			−1.50787
$768$		0			0
$769$	21884.2			1.02622			0.513112	−	0.858322i	$-0.328493\pi$
$769$	21884.2			1.02622			0.513112	+	0.858322i	$0.328493\pi$
$770$		0			0
$771$	544.241	+	37703.5i	0.0254220	+	1.76117i
$772$		0			0
$773$	−2736.24	−	2736.24i	−0.127316	−	0.127316i	0.640577	−	0.767894i	$-0.278695\pi$
$773$	−2736.24	−	2736.24i	−0.127316	−	0.127316i	−0.767894	+	0.640577i	$0.778695\pi$
$774$		0			0
$775$	−11646.8			−0.539826
$776$		0			0
$777$	13507.1	−	13902.7i	0.623634	−	0.641901i
$778$		0			0
$779$	−3388.36	+	3388.36i	−0.155841	+	0.155841i
$780$		0			0
$781$	−15700.8	−	15700.8i	−0.719358	−	0.719358i
$782$		0			0
$783$	−4420.53	+	4820.95i	−0.201759	+	0.220034i
$784$		0			0
$785$		−	7353.51i		−	0.334341i
$786$		0			0
$787$	−4548.50	+	4548.50i	−0.206018	+	0.206018i	−0.802573	−	0.596554i	$-0.796536\pi$
$787$	−4548.50	+	4548.50i	−0.206018	+	0.206018i	0.596554	+	0.802573i	$0.296536\pi$
$788$		0			0
$789$	−158.604	−	10987.6i	−0.00715647	−	0.495780i
$790$		0			0
$791$			810.314i			0.0364241i
$792$		0			0
$793$		−	47864.8i		−	2.14342i
$794$		0			0
$795$	−190.118	−	13170.9i	−0.00848150	−	0.587575i
$796$		0			0
$797$	10333.6	−	10333.6i	0.459265	−	0.459265i	−0.439149	−	0.898414i	$-0.644720\pi$
$797$	10333.6	−	10333.6i	0.459265	−	0.459265i	0.898414	+	0.439149i	$0.144720\pi$
$798$		0			0
$799$		−	1485.97i		−	0.0657948i
$800$		0			0
$801$	−7069.67	+	204.140i	−0.311853	+	0.00900492i
$802$		0			0
$803$	−20728.8	−	20728.8i	−0.910965	−	0.910965i
$804$		0			0
$805$	3441.01	−	3441.01i	0.150658	−	0.150658i
$806$		0			0
$807$	615.202	−	633.223i	0.0268354	−	0.0276214i
$808$		0			0
$809$	12937.6			0.562252			0.281126	−	0.959671i	$-0.409292\pi$
$809$	12937.6			0.562252			0.281126	+	0.959671i	$0.409292\pi$
$810$		0			0
$811$	−13303.5	−	13303.5i	−0.576015	−	0.576015i	0.357788	−	0.933803i	$-0.383531\pi$
$811$	−13303.5	−	13303.5i	−0.576015	−	0.576015i	−0.933803	+	0.357788i	$0.883531\pi$
$812$		0			0
$813$	−69.3697	−	4805.74i	−0.00299250	−	0.207312i
$814$		0			0
$815$	380.896			0.0163708
$816$		0			0
$817$	3566.11			0.152708
$818$		0			0
$819$	−25390.7	−	23965.5i	−1.08330	−	1.02250i
$820$		0			0
$821$	23606.7	+	23606.7i	1.00351	+	1.00351i	0.999994	+	0.00351227i	$0.00111799\pi$
$821$	23606.7	+	23606.7i	1.00351	+	1.00351i	0.00351227	+	0.999994i	$0.498882\pi$
$822$		0			0
$823$	−13577.6			−0.575071			−0.287536	−	0.957770i	$-0.592836\pi$
$823$	−13577.6			−0.575071			−0.287536	+	0.957770i	$0.592836\pi$
$824$		0			0
$825$	−10641.7	−	10338.8i	−0.449085	−	0.436304i
$826$		0			0
$827$	28241.2	−	28241.2i	1.18747	−	1.18747i	0.209711	−	0.977763i	$-0.432748\pi$
$827$	28241.2	−	28241.2i	1.18747	−	1.18747i	0.977763	−	0.209711i	$-0.0672523\pi$
$828$		0			0
$829$	−13869.8	−	13869.8i	−0.581082	−	0.581082i	0.354118	−	0.935201i	$-0.384781\pi$
$829$	−13869.8	−	13869.8i	−0.581082	−	0.581082i	−0.935201	+	0.354118i	$0.884781\pi$
$830$		0			0
$831$	19879.7	−	20462.1i	0.829868	−	0.854177i
$832$		0			0
$833$		−	5971.21i		−	0.248367i
$834$		0			0
$835$	11245.4	−	11245.4i	0.466064	−	0.466064i
$836$		0			0
$837$	−1052.81	−	24298.5i	−0.0434773	−	1.00344i
$838$		0			0
$839$		−	15874.8i		−	0.653229i	−0.945158	−	0.326615i	$-0.894092\pi$
$839$		−	15874.8i		−	0.653229i	0.945158	−	0.326615i	$-0.105908\pi$
$840$		0			0
$841$			22215.4i			0.910878i
$842$		0			0
$843$	913.099	−	13.1804i	0.0373058	−	0.000538500i
$844$		0			0
$845$	28916.7	−	28916.7i	1.17724	−	1.17724i
$846$		0			0
$847$		−	7062.10i		−	0.286490i
$848$		0			0
$849$	2967.77	+	2883.31i	0.119969	+	0.116555i
$850$		0			0
$851$	7647.57	+	7647.57i	0.308056	+	0.308056i
$852$		0			0
$853$	2526.73	−	2526.73i	0.101423	−	0.101423i	−0.654575	−	0.755997i	$-0.727152\pi$
$853$	2526.73	−	2526.73i	0.101423	−	0.101423i	0.755997	+	0.654575i	$0.227152\pi$
$854$		0			0
$855$	2163.80	−	62.4808i	0.0865501	−	0.00249918i
$856$		0			0
$857$	−35121.3			−1.39991			−0.699954	−	0.714188i	$-0.746796\pi$
$857$	−35121.3			−1.39991			−0.699954	+	0.714188i	$0.746796\pi$
$858$		0			0
$859$	−14337.3	−	14337.3i	−0.569480	−	0.569480i	0.362503	−	0.931983i	$-0.381922\pi$
$859$	−14337.3	−	14337.3i	−0.569480	−	0.569480i	−0.931983	+	0.362503i	$0.881922\pi$
$860$		0			0
$861$	35081.4	−	506.391i	1.38858	−	0.0200439i
$862$		0			0
$863$	4109.05			0.162079			0.0810393	−	0.996711i	$-0.474176\pi$
$863$	4109.05			0.162079			0.0810393	+	0.996711i	$0.474176\pi$
$864$		0			0
$865$	27592.9			1.08461
$866$		0			0
$867$	13131.4	−	189.549i	0.514378	−	0.00742492i
$868$		0			0
$869$	20824.4	+	20824.4i	0.812910	+	0.812910i
$870$		0			0
$871$	41112.7			1.59937
$872$		0			0
$873$	−17320.2	+	500.129i	−0.671477	+	0.0193892i
$874$		0			0
$875$	−15352.3	+	15352.3i	−0.593144	+	0.593144i
$876$		0			0
$877$	2839.24	+	2839.24i	0.109321	+	0.109321i	0.759651	−	0.650331i	$-0.225370\pi$
$877$	2839.24	+	2839.24i	0.109321	+	0.109321i	−0.650331	+	0.759651i	$0.725370\pi$
$878$		0			0
$879$	30140.1	+	29282.4i	1.15654	+	1.12363i
$880$		0			0
$881$			25816.2i			0.987254i	0.869674	+	0.493627i	$0.164329\pi$
$881$			25816.2i			0.987254i	−0.869674	+	0.493627i	$0.835671\pi$
$882$		0			0
$883$	−21733.3	+	21733.3i	−0.828294	+	0.828294i	−0.987281	−	0.158986i	$-0.949177\pi$
$883$	−21733.3	+	21733.3i	−0.828294	+	0.828294i	0.158986	+	0.987281i	$0.449177\pi$
$884$		0			0
$885$	−14538.5	+	209.860i	−0.552211	+	0.00797103i
$886$		0			0
$887$			32216.9i			1.21955i	0.792575	+	0.609774i	$0.208740\pi$
$887$			32216.9i			1.21955i	−0.792575	+	0.609774i	$0.791260\pi$
$888$		0			0
$889$			470.711i			0.0177583i
$890$		0			0
$891$	20607.7	−	23136.0i	0.774841	−	0.869906i
$892$		0			0
$893$	226.834	−	226.834i	0.00850023	−	0.00850023i
$894$		0			0
$895$			13464.4i			0.502868i
$896$		0			0
$897$	13574.9	−	13972.5i	0.505298	−	0.520099i
$898$		0			0
$899$	5714.97	+	5714.97i	0.212019	+	0.212019i
$900$		0			0
$901$	−11514.3	+	11514.3i	−0.425745	+	0.425745i
$902$		0			0
$903$	−18727.4	−	18194.4i	−0.690153	−	0.670512i
$904$		0			0
$905$	18630.1			0.684294
$906$		0			0
$907$	−6623.37	−	6623.37i	−0.242476	−	0.242476i	0.575398	−	0.817874i	$-0.304847\pi$
$907$	−6623.37	−	6623.37i	−0.242476	−	0.242476i	−0.817874	+	0.575398i	$0.804847\pi$
$908$		0			0
$909$	26727.3	+	25227.1i	0.975235	+	0.920495i
$910$		0			0
$911$	−13826.3			−0.502838			−0.251419	−	0.967878i	$-0.580897\pi$
$911$	−13826.3			−0.502838			−0.251419	+	0.967878i	$0.580897\pi$
$912$		0			0
$913$	−40701.8			−1.47539
$914$		0			0
$915$	−313.609	−	21726.0i	−0.0113307	−	0.784959i
$916$		0			0
$917$	25068.0	+	25068.0i	0.902747	+	0.902747i
$918$		0			0
$919$	−32283.9			−1.15881			−0.579407	−	0.815039i	$-0.696716\pi$
$919$	−32283.9			−1.15881			−0.579407	+	0.815039i	$0.696716\pi$
$920$		0			0
$921$	−5259.35	+	5413.41i	−0.188167	+	0.193678i
$922$		0			0
$923$	−32153.0	+	32153.0i	−1.14662	+	1.14662i
$924$		0			0
$925$	−11927.8	−	11927.8i	−0.423981	−	0.423981i
$926$		0			0
$927$	39907.0	−	1152.34i	1.41394	−	0.0408281i
$928$		0			0
$929$			19418.8i			0.685801i	0.939372	+	0.342901i	$0.111409\pi$
$929$			19418.8i			0.685801i	−0.939372	+	0.342901i	$0.888591\pi$
$930$		0			0
$931$	911.504	−	911.504i	0.0320874	−	0.0320874i
$932$		0			0
$933$	−260.919	−	18075.7i	−0.00915552	−	0.634269i
$934$		0			0
$935$		−	15784.1i		−	0.552081i
$936$		0			0
$937$		−	13947.1i		−	0.486266i	−0.969993	−	0.243133i	$-0.921825\pi$
$937$		−	13947.1i		−	0.486266i	0.969993	−	0.243133i	$-0.0781751\pi$
$938$		0			0
$939$	−248.110	−	17188.4i	−0.00862276	−	0.597361i
$940$		0			0
$941$	−32438.8	+	32438.8i	−1.12378	+	1.12378i	−0.132608	+	0.991169i	$0.542335\pi$
$941$	−32438.8	+	32438.8i	−1.12378	+	1.12378i	−0.991169	+	0.132608i	$0.957665\pi$
$942$		0			0
$943$			19576.0i			0.676016i
$944$		0			0
$945$	−11681.9	−	10711.7i	−0.402130	−	0.368730i
$946$		0			0
$947$	−14766.0	−	14766.0i	−0.506685	−	0.506685i	0.406823	−	0.913507i	$-0.366637\pi$
$947$	−14766.0	−	14766.0i	−0.506685	−	0.506685i	−0.913507	+	0.406823i	$0.866637\pi$
$948$		0			0
$949$	−42449.8	+	42449.8i	−1.45203	+	1.45203i
$950$		0			0
$951$	6642.18	−	6836.75i	0.226485	−	0.233120i
$952$		0			0
$953$	27736.7			0.942791			0.471395	−	0.881922i	$-0.343750\pi$
$953$	27736.7			0.942791			0.471395	+	0.881922i	$0.343750\pi$
$954$		0			0
$955$	1013.30	+	1013.30i	0.0343345	+	0.0343345i
$956$		0			0
$957$	148.604	+	10294.9i	0.00501954	+	0.347740i
$958$		0			0
$959$	6738.59			0.226904
$960$		0			0
$961$	−261.548			−0.00877942
$962$		0			0
$963$	−38915.3	+	41229.5i	−1.30221	+	1.37965i
$964$		0			0
$965$	454.775	+	454.775i	0.0151707	+	0.0151707i
$966$		0			0
$967$	−38161.5			−1.26907			−0.634535	−	0.772894i	$-0.718809\pi$
$967$	−38161.5			−1.26907			−0.634535	+	0.772894i	$0.718809\pi$
$968$		0			0
$969$	−1919.35	−	1864.73i	−0.0636310	−	0.0618201i
$970$		0			0
$971$	−40351.2	+	40351.2i	−1.33361	+	1.33361i	−0.431488	+	0.902119i	$0.642011\pi$
$971$	−40351.2	+	40351.2i	−1.33361	+	1.33361i	−0.902119	+	0.431488i	$0.857989\pi$
$972$		0			0
$973$	20682.4	+	20682.4i	0.681446	+	0.681446i
$974$		0			0
$975$	−21172.5	+	21792.6i	−0.695447	+	0.715819i
$976$		0			0
$977$			37478.8i			1.22728i	0.789586	+	0.613640i	$0.210296\pi$
$977$			37478.8i			1.22728i	−0.789586	+	0.613640i	$0.789704\pi$
$978$		0			0
$979$	−7872.25	+	7872.25i	−0.256995	+	0.256995i
$980$		0			0
$981$	2882.48	+	2720.69i	0.0938130	+	0.0885472i
$982$		0			0
$983$		−	11135.5i		−	0.361310i	−0.983547	−	0.180655i	$-0.942178\pi$
$983$		−	11135.5i		−	0.361310i	0.983547	−	0.180655i	$-0.0578217\pi$
$984$		0			0
$985$			8395.49i			0.271576i
$986$		0			0
$987$	−2348.53	+	33.9004i	−0.0757391	+	0.00109328i
$988$		0			0
$989$	10301.5	−	10301.5i	0.331212	−	0.331212i
$990$		0			0
$991$			39321.0i			1.26042i	0.776427	+	0.630208i	$0.217030\pi$
$991$			39321.0i			1.26042i	−0.776427	+	0.630208i	$0.782970\pi$
$992$		0			0
$993$	−22768.1	−	22120.2i	−0.727617	−	0.706910i
$994$		0			0
$995$	8818.09	+	8818.09i	0.280957	+	0.280957i
$996$		0			0
$997$	33341.7	−	33341.7i	1.05912	−	1.05912i	0.0609797	−	0.998139i	$-0.480578\pi$
$997$	33341.7	−	33341.7i	1.05912	−	1.05912i	0.998139	−	0.0609797i	$-0.0194225\pi$
$998$		0			0
$999$	23806.4	−	25962.8i	0.753956	−	0.822250i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.4.k.b.95.22		44
3.2	odd	2	inner	384.4.k.b.95.11		44
4.3	odd	2		384.4.k.a.95.1		44
8.3	odd	2		192.4.k.a.47.22		44
8.5	even	2		48.4.k.a.35.6	yes	44
12.11	even	2		384.4.k.a.95.12		44
16.3	odd	4		48.4.k.a.11.17	yes	44
16.5	even	4		384.4.k.a.287.12		44
16.11	odd	4	inner	384.4.k.b.287.11		44
16.13	even	4		192.4.k.a.143.11		44
24.5	odd	2		48.4.k.a.35.17	yes	44
24.11	even	2		192.4.k.a.47.11		44
48.5	odd	4		384.4.k.a.287.1		44
48.11	even	4	inner	384.4.k.b.287.22		44
48.29	odd	4		192.4.k.a.143.22		44
48.35	even	4		48.4.k.a.11.6	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.k.a.11.6	✓	44	48.35	even	4
48.4.k.a.11.17	yes	44	16.3	odd	4
48.4.k.a.35.6	yes	44	8.5	even	2
48.4.k.a.35.17	yes	44	24.5	odd	2
192.4.k.a.47.11		44	24.11	even	2
192.4.k.a.47.22		44	8.3	odd	2
192.4.k.a.143.11		44	16.13	even	4
192.4.k.a.143.22		44	48.29	odd	4
384.4.k.a.95.1		44	4.3	odd	2
384.4.k.a.95.12		44	12.11	even	2
384.4.k.a.287.1		44	48.5	odd	4
384.4.k.a.287.12		44	16.5	even	4
384.4.k.b.95.11		44	3.2	odd	2	inner
384.4.k.b.95.22		44	1.1	even	1	trivial
384.4.k.b.287.11		44	16.11	odd	4	inner
384.4.k.b.287.22		44	48.11	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	384.k (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(5.19561 - 0.0749974i) q^{3} +(-5.37662 - 5.37662i) q^{5} +14.8575 q^{7} +(26.9888 - 0.779314i) q^{9} +(30.0526 - 30.0526i) q^{11} +(-61.5437 - 61.5437i) q^{13} +(-28.3380 - 27.5316i) q^{15} +48.8426i q^{17} +(-7.45581 + 7.45581i) q^{19} +(77.1939 - 1.11427i) q^{21} +43.0756i q^{23} -67.1840i q^{25} +(140.165 - 6.07310i) q^{27} +(-32.9665 + 32.9665i) q^{29} -173.357i q^{31} +(153.888 - 158.396i) q^{33} +(-79.8832 - 79.8832i) q^{35} +(177.539 - 177.539i) q^{37} +(-324.373 - 315.141i) q^{39} +454.458 q^{41} +(-239.150 - 239.150i) q^{43} +(-149.298 - 140.918i) q^{45} -30.4238 q^{47} -122.254 q^{49} +(3.66306 + 253.767i) q^{51} +(235.743 + 235.743i) q^{53} -323.163 q^{55} +(-38.1783 + 39.2967i) q^{57} +(260.222 - 260.222i) q^{59} +(388.869 + 388.869i) q^{61} +(400.986 - 11.5787i) q^{63} +661.793i q^{65} +(-334.013 + 334.013i) q^{67} +(3.23055 + 223.804i) q^{69} -522.443i q^{71} -689.751i q^{73} +(-5.03862 - 349.062i) q^{75} +(446.508 - 446.508i) q^{77} +692.930i q^{79} +(727.785 - 42.0654i) q^{81} +(-677.176 - 677.176i) q^{83} +(262.608 - 262.608i) q^{85} +(-168.809 + 173.754i) q^{87} -261.949 q^{89} +(-914.386 - 914.386i) q^{91} +(-13.0013 - 900.694i) q^{93} +80.1741 q^{95} -641.755 q^{97} +(787.663 - 834.504i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{3} - 8 q^{7} + 4 q^{13} - 20 q^{19} + 56 q^{21} + 134 q^{27} - 4 q^{33} + 4 q^{37} + 596 q^{39} + 436 q^{43} + 252 q^{45} + 972 q^{49} + 648 q^{51} + 280 q^{55} + 916 q^{61} + 1636 q^{67} - 52 q^{69}+ \cdots - 1196 q^{99}+O(q^{100}) \) 44 * q + 2 * q^3 - 8 * q^7 + 4 * q^13 - 20 * q^19 + 56 * q^21 + 134 * q^27 - 4 * q^33 + 4 * q^37 + 596 * q^39 + 436 * q^43 + 252 * q^45 + 972 * q^49 + 648 * q^51 + 280 * q^55 + 916 * q^61 + 1636 * q^67 - 52 * q^69 - 1454 * q^75 - 4 * q^81 - 736 * q^85 + 1284 * q^87 - 424 * q^91 + 2084 * q^93 - 8 * q^97 - 1196 * q^99

Introduction

L-functions

Modular forms

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Database

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