LMFDB - Embedded newform 192.4.k.a.143.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [192,4,Mod(47,192)] 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("192.47"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(192, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	192.k (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$11.3283667211$
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			143.11
Character	$\chi$	$=$	192.143
Dual form			192.4.k.a.47.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0749974 + 5.19561i) q^{3} +(-5.37662 + 5.37662i) q^{5} -14.8575 q^{7} +(-26.9888 + 0.779314i) q^{9} +(-30.0526 - 30.0526i) q^{11} +(61.5437 - 61.5437i) q^{13} +(-28.3380 - 27.5316i) q^{15} +48.8426i q^{17} +(-7.45581 - 7.45581i) q^{19} +(-1.11427 - 77.1939i) q^{21} -43.0756i q^{23} +67.1840i q^{25} +(-6.07310 - 140.165i) q^{27} +(-32.9665 - 32.9665i) q^{29} -173.357i q^{31} +(153.888 - 158.396i) q^{33} +(79.8832 - 79.8832i) q^{35} +(-177.539 - 177.539i) q^{37} +(324.373 + 315.141i) q^{39} -454.458 q^{41} +(-239.150 + 239.150i) q^{43} +(140.918 - 149.298i) q^{45} -30.4238 q^{47} -122.254 q^{49} +(-253.767 + 3.66306i) q^{51} +(235.743 - 235.743i) q^{53} +323.163 q^{55} +(38.1783 - 39.2967i) q^{57} +(-260.222 - 260.222i) q^{59} +(-388.869 + 388.869i) q^{61} +(400.986 - 11.5787i) q^{63} +661.793i q^{65} +(-334.013 - 334.013i) q^{67} +(223.804 - 3.23055i) q^{69} +522.443i q^{71} +689.751i q^{73} +(-349.062 + 5.03862i) q^{75} +(446.508 + 446.508i) q^{77} +692.930i q^{79} +(727.785 - 42.0654i) q^{81} +(677.176 - 677.176i) q^{83} +(-262.608 - 262.608i) q^{85} +(168.809 - 173.754i) q^{87} +261.949 q^{89} +(-914.386 + 914.386i) q^{91} +(900.694 - 13.0013i) q^{93} +80.1741 q^{95} -641.755 q^{97} +(834.504 + 787.663i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.0749974	+	5.19561i	0.0144332	+	0.999896i
$3$	0.0749974	+	5.19561i	0.0144332	+	0.999896i
$4$		0			0
$5$	−5.37662	+	5.37662i	−0.480899	+	0.480899i	−0.905419	−	0.424520i	$-0.860443\pi$
$5$	−5.37662	+	5.37662i	−0.480899	+	0.480899i	0.424520	+	0.905419i	$0.360443\pi$
$6$		0			0
$7$	−14.8575			−0.802231			−0.401115	−	0.916028i	$-0.631377\pi$
$7$	−14.8575			−0.802231			−0.401115	+	0.916028i	$0.631377\pi$
$8$		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	$-0.447916\pi$
$11$	−30.0526	−	30.0526i	−0.823746	−	0.823746i	−0.986643	+	0.162897i	$0.947916\pi$
$12$		0			0
$13$	61.5437	−	61.5437i	1.31301	−	1.31301i	0.393825	−	0.919185i	$-0.371151\pi$
$13$	61.5437	−	61.5437i	1.31301	−	1.31301i	0.919185	−	0.393825i	$-0.128849\pi$
$14$		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	0.660660	−	0.750685i	$-0.270277\pi$
$19$	−7.45581	−	7.45581i	−0.0900253	−	0.0900253i	−0.750685	+	0.660660i	$0.770277\pi$
$20$		0			0
$21$	−1.11427	−	77.1939i	−0.0115788	−	0.802147i
$22$		0			0
$23$		−	43.0756i		−	0.390516i	−0.980752	−	0.195258i	$-0.937446\pi$
$23$		−	43.0756i		−	0.390516i	0.980752	−	0.195258i	$-0.0625545\pi$
$24$		0			0
$25$			67.1840i			0.537472i
$26$		0			0
$27$	−6.07310	−	140.165i	−0.0432877	−	0.999063i
$28$		0			0
$29$	−32.9665	−	32.9665i	−0.211094	−	0.211094i	0.593638	−	0.804732i	$-0.297691\pi$
$29$	−32.9665	−	32.9665i	−0.211094	−	0.211094i	−0.804732	+	0.593638i	$0.797691\pi$
$30$		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	$-0.438353\pi$
$37$	−177.539	−	177.539i	−0.788842	−	0.788842i	−0.981304	+	0.192462i	$0.938353\pi$
$38$		0			0
$39$	324.373	+	315.141i	1.33182	+	1.29392i
$40$		0			0
$41$	−454.458			−1.73108			−0.865542	−	0.500837i	$-0.833026\pi$
$41$	−454.458			−1.73108			−0.865542	+	0.500837i	$0.833026\pi$
$42$		0			0
$43$	−239.150	+	239.150i	−0.848139	+	0.848139i	−0.989901	−	0.141762i	$-0.954723\pi$
$43$	−239.150	+	239.150i	−0.848139	+	0.848139i	0.141762	+	0.989901i	$0.454723\pi$
$44$		0			0
$45$	140.918	−	149.298i	0.466818	−	0.494579i
$46$		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
$51$	−253.767	+	3.66306i	−0.696755	+	0.0100575i
$52$		0			0
$53$	235.743	−	235.743i	0.610976	−	0.610976i	−0.332224	−	0.943200i	$-0.607799\pi$
$53$	235.743	−	235.743i	0.610976	−	0.610976i	0.943200	+	0.332224i	$0.107799\pi$
$54$		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	$-0.383085\pi$
$59$	−260.222	−	260.222i	−0.574204	−	0.574204i	−0.933300	+	0.359096i	$0.883085\pi$
$60$		0			0
$61$	−388.869	+	388.869i	−0.816222	+	0.816222i	−0.985558	−	0.169336i	$-0.945838\pi$
$61$	−388.869	+	388.869i	−0.816222	+	0.816222i	0.169336	+	0.985558i	$0.445838\pi$
$62$		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	0.333650	−	0.942697i	$-0.391720\pi$
$67$	−334.013	−	334.013i	−0.609047	−	0.609047i	−0.942697	+	0.333650i	$0.891720\pi$
$68$		0			0
$69$	223.804	−	3.23055i	0.390476	−	0.00563642i
$70$		0			0
$71$			522.443i			0.873275i	0.899637	+	0.436638i	$0.143831\pi$
$71$			522.443i			0.873275i	−0.899637	+	0.436638i	$0.856169\pi$
$72$		0			0
$73$			689.751i			1.10588i	0.833221	+	0.552940i	$0.186494\pi$
$73$			689.751i			1.10588i	−0.833221	+	0.552940i	$0.813506\pi$
$74$		0			0
$75$	−349.062	+	5.03862i	−0.537416	+	0.00775747i
$76$		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	$-0.531724\pi$
$83$	677.176	−	677.176i	0.895539	−	0.895539i	0.995038	+	0.0994989i	$0.0317240\pi$
$84$		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	$-0.450143\pi$
$89$	261.949			0.311983			0.155992	+	0.987758i	$0.450143\pi$
$90$		0			0
$91$	−914.386	+	914.386i	−1.05334	+	1.05334i
$92$		0			0
$93$	900.694	−	13.0013i	1.00428	−	0.0144965i
$94$		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
$99$	834.504	+	787.663i	0.847179	+	0.799627i
$100$		0			0
$101$	962.520	−	962.520i	0.948260	−	0.948260i	−0.0504657	−	0.998726i	$-0.516071\pi$
$101$	962.520	−	962.520i	0.948260	−	0.948260i	0.998726	+	0.0504657i	$0.0160705\pi$
$102$		0			0
$103$	−1478.65			−1.41452			−0.707262	−	0.706951i	$-0.750070\pi$
$103$	−1478.65			−1.41452			−0.707262	+	0.706951i	$0.750070\pi$
$104$		0			0
$105$	421.033	+	409.051i	0.391320	+	0.380184i
$106$		0			0
$107$	1484.78	+	1484.78i	1.34149	+	1.34149i	0.894580	+	0.446908i	$0.147475\pi$
$107$	1484.78	+	1484.78i	1.34149	+	1.34149i	0.446908	+	0.894580i	$0.352525\pi$
$108$		0			0
$109$	−103.806	+	103.806i	−0.0912181	+	0.0912181i	−0.751243	−	0.660025i	$-0.770546\pi$
$109$	−103.806	+	103.806i	−0.0912181	+	0.0912181i	0.660025	+	0.751243i	$0.270546\pi$
$110$		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
$117$	−1613.02	+	1708.95i	−1.27457	+	1.35036i
$118$		0			0
$119$		−	725.680i		−	0.559016i
$120$		0			0
$121$			475.322i			0.357116i
$122$		0			0
$123$	−34.0832	−	2361.19i	−0.0249852	−	1.73090i
$124$		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	−0.134364	+	0.990932i	$0.542899\pi$
$131$	−1687.23	+	1687.23i	−1.12530	+	1.12530i	−0.990932	+	0.134364i	$0.957101\pi$
$132$		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	$-0.545167\pi$
$137$	−453.548			−0.282841			−0.141420	+	0.989950i	$0.545167\pi$
$138$		0			0
$139$	1392.05	−	1392.05i	0.849439	−	0.849439i	−0.140624	−	0.990063i	$-0.544911\pi$
$139$	1392.05	−	1392.05i	0.849439	−	0.849439i	0.990063	+	0.140624i	$0.0449110\pi$
$140$		0			0
$141$	−2.28170	−	158.070i	−0.00136279	−	0.0944106i
$142$		0			0
$143$	−3699.10			−2.16318
$144$		0			0
$145$	354.497			0.203030
$146$		0			0
$147$	−9.16874	−	635.185i	−0.00514438	−	0.356389i
$148$		0			0
$149$	118.909	−	118.909i	0.0653785	−	0.0653785i	−0.673662	−	0.739040i	$-0.735279\pi$
$149$	118.909	−	118.909i	0.0653785	−	0.0653785i	0.739040	+	0.673662i	$0.235279\pi$
$150$		0			0
$151$	−289.153			−0.155834			−0.0779170	−	0.996960i	$-0.524827\pi$
$151$	−289.153			−0.155834			−0.0779170	+	0.996960i	$0.524827\pi$
$152$		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	$-0.829052\pi$
$157$	−683.842	+	683.842i	−0.347621	+	0.347621i	0.511602	+	0.859223i	$0.329052\pi$
$158$		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	0.698545	−	0.715566i	$-0.253831\pi$
$163$	−35.4216	−	35.4216i	−0.0170210	−	0.0170210i	−0.715566	+	0.698545i	$0.753831\pi$
$164$		0			0
$165$	24.2364	+	1679.03i	0.0114351	+	0.792195i
$166$		0			0
$167$		−	2091.54i		−	0.969150i	−0.874750	−	0.484575i	$-0.838974\pi$
$167$		−	2091.54i		−	0.969150i	0.874750	−	0.484575i	$-0.161026\pi$
$168$		0			0
$169$		−	5378.24i		−	2.44799i
$170$		0			0
$171$	207.034	+	195.413i	0.0925863	+	0.0873894i
$172$		0			0
$173$	−2566.01	−	2566.01i	−1.12769	−	1.12769i	−0.990552	−	0.137137i	$-0.956210\pi$
$173$	−2566.01	−	2566.01i	−1.12769	−	1.12769i	−0.137137	−	0.990552i	$-0.543790\pi$
$174$		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	$-0.629459\pi$
$179$	1252.13	−	1252.13i	0.522841	−	0.522841i	0.918429	+	0.395587i	$0.129459\pi$
$180$		0			0
$181$	1732.51	+	1732.51i	0.711474	+	0.711474i	0.966844	−	0.255370i	$-0.0821971\pi$
$181$	1732.51	+	1732.51i	0.711474	+	0.711474i	−0.255370	+	0.966844i	$0.582197\pi$
$182$		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
$189$	90.2312	+	2082.50i	0.0347267	+	0.801479i
$190$		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
$195$	−3438.42	+	49.6327i	−1.26272	+	0.0182270i
$196$		0			0
$197$	−780.741	+	780.741i	−0.282363	+	0.282363i	−0.834051	−	0.551688i	$-0.813984\pi$
$197$	−780.741	+	780.741i	−0.282363	+	0.282363i	0.551688	+	0.834051i	$0.313984\pi$
$198$		0			0
$199$	1640.08			0.584233			0.292116	−	0.956383i	$-0.405640\pi$
$199$	1640.08			0.584233			0.292116	+	0.956383i	$0.405640\pi$
$200$		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	0.774782	−	0.632229i	$-0.217860\pi$
$211$	436.919	+	436.919i	0.142553	+	0.142553i	−0.632229	+	0.774782i	$0.717860\pi$
$212$		0			0
$213$	−2714.41	+	39.1818i	−0.873185	+	0.0126042i
$214$		0			0
$215$		−	2571.63i		−	0.815739i
$216$		0			0
$217$			2575.65i			0.805745i
$218$		0			0
$219$	−3583.68	+	51.7295i	−1.10577	+	0.0159614i
$220$		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	$-0.681044\pi$
$227$	1039.61	−	1039.61i	0.303972	−	0.303972i	0.842566	+	0.538594i	$0.181044\pi$
$228$		0			0
$229$	1142.20	+	1142.20i	0.329601	+	0.329601i	0.852435	−	0.522834i	$-0.175125\pi$
$229$	1142.20	+	1142.20i	0.329601	+	0.329601i	−0.522834	+	0.852435i	$0.675125\pi$
$230$		0			0
$231$	−2286.39	+	2353.37i	−0.651228	+	0.670304i
$232$		0			0
$233$	−3480.39			−0.978575			−0.489287	−	0.872123i	$-0.662743\pi$
$233$	−3480.39			−0.978575			−0.489287	+	0.872123i	$0.662743\pi$
$234$		0			0
$235$	163.577	−	163.577i	0.0454067	−	0.0454067i
$236$		0			0
$237$	−3600.19	+	51.9679i	−0.986742	+	0.0142434i
$238$		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
$243$	273.138	+	3778.13i	0.0721061	+	0.997397i
$244$		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	$-0.0325164\pi$
$251$	3550.34	+	3550.34i	0.892811	+	0.892811i	−0.101976	+	0.994787i	$0.532516\pi$
$252$		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
$261$	915.417	+	864.034i	0.217099	+	0.204913i
$262$		0			0
$263$			2114.79i			0.495832i	0.968782	+	0.247916i	$0.0797457\pi$
$263$			2114.79i			0.495832i	−0.968782	+	0.247916i	$0.920254\pi$
$264$		0			0
$265$			2535.00i			0.587636i
$266$		0			0
$267$	19.6455	+	1360.98i	0.00450293	+	0.311951i
$268$		0			0
$269$	120.142	+	120.142i	0.0272312	+	0.0272312i	0.720591	−	0.693360i	$-0.243870\pi$
$269$	120.142	+	120.142i	0.0272312	+	0.0272312i	−0.693360	+	0.720591i	$0.743870\pi$
$270$		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	$-0.453031\pi$
$277$	−3882.29	−	3882.29i	−0.842110	−	0.842110i	−0.989133	+	0.147023i	$0.953031\pi$
$278$		0			0
$279$	135.099	+	4678.68i	0.0289899	+	1.00396i
$280$		0			0
$281$	−175.744			−0.0373097			−0.0186548	−	0.999826i	$-0.505938\pi$
$281$	−175.744			−0.0373097			−0.0186548	+	0.999826i	$0.505938\pi$
$282$		0			0
$283$	563.080	−	563.080i	0.118274	−	0.118274i	−0.645492	−	0.763767i	$-0.723348\pi$
$283$	563.080	−	563.080i	0.118274	−	0.118274i	0.763767	+	0.645492i	$0.223348\pi$
$284$		0			0
$285$	6.01285	+	416.553i	0.00124972	+	0.0865772i
$286$		0			0
$287$	6752.12			1.38873
$288$		0			0
$289$	2527.40			0.514432
$290$		0			0
$291$	−48.1300	−	3334.31i	−0.00969563	−	0.671687i
$292$		0			0
$293$	5718.53	−	5718.53i	1.14020	−	1.14020i	0.151792	−	0.988412i	$-0.451496\pi$
$293$	5718.53	−	5718.53i	1.14020	−	1.14020i	0.988412	−	0.151792i	$-0.0485045\pi$
$294$		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	0.605161	−	0.796103i	$-0.293109\pi$
$307$	−1027.09	−	1027.09i	−0.190942	−	0.190942i	−0.796103	+	0.605161i	$0.793109\pi$
$308$		0			0
$309$	−110.895	−	7682.51i	−0.0204162	−	1.41438i
$310$		0			0
$311$			3479.04i			0.634335i	0.948370	+	0.317168i	$0.102732\pi$
$311$			3479.04i			0.634335i	−0.948370	+	0.317168i	$0.897268\pi$
$312$		0			0
$313$			3308.25i			0.597424i	0.954343	+	0.298712i	$0.0965569\pi$
$313$			3308.25i			0.597424i	−0.954343	+	0.298712i	$0.903443\pi$
$314$		0			0
$315$	−2093.69	+	2218.20i	−0.374496	+	0.396767i
$316$		0			0
$317$	1297.15	+	1297.15i	0.229826	+	0.229826i	0.812620	−	0.582794i	$-0.198040\pi$
$317$	1297.15	+	1297.15i	0.229826	+	0.229826i	−0.582794	+	0.812620i	$0.698040\pi$
$318$		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	−0.968059	−	0.250721i	$-0.919332\pi$
$331$	−4319.83	+	4319.83i	−0.717339	+	0.717339i	0.250721	+	0.968059i	$0.419332\pi$
$332$		0			0
$333$	4929.90	+	4653.19i	0.811282	+	0.765745i
$334$		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
$339$	−283.363	+	4.09028i	−0.0453988	+	0.000655320i
$340$		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	$-0.486694\pi$
$347$	−6188.11	−	6188.11i	−0.957335	−	0.957335i	−0.999126	+	0.0417910i	$0.986694\pi$
$348$		0			0
$349$	−1274.05	+	1274.05i	−0.195411	+	0.195411i	−0.798030	−	0.602618i	$-0.794124\pi$
$349$	−1274.05	+	1274.05i	−0.195411	+	0.195411i	0.602618	+	0.798030i	$0.294124\pi$
$350$		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
$357$	3770.35	−	54.4241i	0.558958	−	0.00806842i
$358$		0			0
$359$		−	479.331i		−	0.0704683i	−0.999379	−	0.0352342i	$-0.988782\pi$
$359$		−	479.331i		−	0.0704683i	0.999379	−	0.0352342i	$-0.0112177\pi$
$360$		0			0
$361$		−	6747.82i		−	0.983791i
$362$		0			0
$363$	−2469.59	+	35.6479i	−0.357079	+	0.00515435i
$364$		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	−0.991720	−	0.128418i	$-0.959010\pi$
$373$	−8069.28	−	8069.28i	−1.12014	−	1.12014i	−0.128418	−	0.991720i	$-0.540990\pi$
$374$		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	−0.818471	−	0.574548i	$-0.805178\pi$
$379$	−1799.74	+	1799.74i	−0.243922	+	0.243922i	0.574548	+	0.818471i	$0.305178\pi$
$380$		0			0
$381$	−164.606	+	2.37604i	−0.0221339	+	0.000319497i
$382$		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
$387$	6267.98	−	6640.73i	0.823306	−	0.872266i
$388$		0			0
$389$	1661.54	−	1661.54i	0.216564	−	0.216564i	−0.590485	−	0.807049i	$-0.701064\pi$
$389$	1661.54	−	1661.54i	0.216564	−	0.216564i	0.807049	+	0.590485i	$0.201064\pi$
$390$		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	$-0.757371\pi$
$397$	−259.031	+	259.031i	−0.0327465	+	0.0327465i	0.690544	+	0.723290i	$0.257371\pi$
$398$		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
$405$	−3686.85	+	4139.19i	−0.452349	+	0.507847i
$406$		0			0
$407$			10671.0i			1.29961i
$408$		0			0
$409$			4138.32i			0.500311i	0.968206	+	0.250155i	$0.0804817\pi$
$409$			4138.32i			0.500311i	−0.968206	+	0.250155i	$0.919518\pi$
$410$		0			0
$411$	−34.0149	−	2356.46i	−0.00408231	−	0.282811i
$412$		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	$-0.819406\pi$
$419$	−2623.85	+	2623.85i	−0.305927	+	0.305927i	0.537401	+	0.843327i	$0.319406\pi$
$420$		0			0
$421$	−207.548	−	207.548i	−0.0240268	−	0.0240268i	0.694991	−	0.719018i	$-0.255408\pi$
$421$	−207.548	−	207.548i	−0.0240268	−	0.0240268i	−0.719018	+	0.694991i	$0.755408\pi$
$422$		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
$429$	−277.423	−	19219.1i	−0.0312217	−	2.16295i
$430$		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
$435$	26.5863	+	1841.83i	0.00293038	+	0.203009i
$436$		0			0
$437$	−321.163	+	321.163i	−0.0351564	+	0.0351564i
$438$		0			0
$439$	−1006.82			−0.109459			−0.0547297	−	0.998501i	$-0.517430\pi$
$439$	−1006.82			−0.109459			−0.0547297	+	0.998501i	$0.517430\pi$
$440$		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	$-0.159520\pi$
$443$	3697.94	+	3697.94i	0.396601	+	0.396601i	−0.480431	+	0.877032i	$0.659520\pi$
$444$		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
$453$	−21.6857	−	1502.33i	−0.00224919	−	0.155818i
$454$		0			0
$455$		−	9832.60i		−	1.01310i
$456$		0			0
$457$		−	1710.35i		−	0.175070i	−0.996161	−	0.0875349i	$-0.972101\pi$
$457$		−	1710.35i		−	0.175070i	0.996161	−	0.0875349i	$-0.0278989\pi$
$458$		0			0
$459$	6846.00	−	296.626i	0.696174	−	0.0301641i
$460$		0			0
$461$	−4945.52	−	4945.52i	−0.499644	−	0.499644i	0.411683	−	0.911327i	$-0.364941\pi$
$461$	−4945.52	−	4945.52i	−0.499644	−	0.499644i	−0.911327	+	0.411683i	$0.864941\pi$
$462$		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	$-0.871957\pi$
$467$	−5335.45	+	5335.45i	−0.528683	+	0.528683i	0.391497	+	0.920180i	$0.371957\pi$
$468$		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
$477$	−6178.68	+	6546.12i	−0.593087	+	0.628357i
$478$		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
$483$	−3325.17	+	47.9980i	−0.313251	+	0.00452171i
$484$		0			0
$485$	3450.47	−	3450.47i	0.323047	−	0.323047i
$486$		0			0
$487$	−18653.5			−1.73567			−0.867833	−	0.496856i	$-0.834488\pi$
$487$	−18653.5			−1.73567			−0.867833	+	0.496856i	$0.834488\pi$
$488$		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	$-0.337203\pi$
$491$	−4162.67	−	4162.67i	−0.382604	−	0.382604i	−0.872039	+	0.489436i	$0.837203\pi$
$492$		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	0.959816	−	0.280631i	$-0.0905439\pi$
$499$	7570.74	+	7570.74i	0.679184	+	0.679184i	−0.280631	+	0.959816i	$0.590544\pi$
$500$		0			0
$501$	10866.8	−	156.860i	0.969049	−	0.0139880i
$502$		0			0
$503$			10216.7i			0.905647i	0.891600	+	0.452823i	$0.149583\pi$
$503$			10216.7i			0.905647i	−0.891600	+	0.452823i	$0.850417\pi$
$504$		0			0
$505$			10350.2i			0.912035i
$506$		0			0
$507$	27943.3	−	403.354i	2.44774	−	0.0353325i
$508$		0			0
$509$	12175.7	+	12175.7i	1.06027	+	1.06027i	0.998063	+	0.0622119i	$0.0198155\pi$
$509$	12175.7	+	12175.7i	1.06027	+	1.06027i	0.0622119	+	0.998063i	$0.480185\pi$
$510$		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	$-0.509827\pi$
$521$	−734.120			−0.0617320			−0.0308660	+	0.999524i	$0.509827\pi$
$522$		0			0
$523$	−4289.83	+	4289.83i	−0.358664	+	0.358664i	−0.863320	−	0.504656i	$-0.831619\pi$
$523$	−4289.83	+	4289.83i	−0.358664	+	0.358664i	0.504656	+	0.863320i	$0.331619\pi$
$524$		0			0
$525$	5186.20	−	74.8615i	0.431132	−	0.00622328i
$526$		0			0
$527$	8467.19			0.699880
$528$		0			0
$529$	10311.5			0.847497
$530$		0			0
$531$	7225.86	+	6820.27i	0.590538	+	0.557391i
$532$		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	$-0.980404\pi$
$541$	−11785.3	+	11785.3i	−0.936583	+	0.936583i	0.0615231	+	0.998106i	$0.480404\pi$
$542$		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	0.192942	−	0.981210i	$-0.438197\pi$
$547$	−10084.5	−	10084.5i	−0.788268	−	0.788268i	−0.981210	+	0.192942i	$0.938197\pi$
$548$		0			0
$549$	10192.0	−	10798.1i	0.792323	−	0.839441i
$550$		0			0
$551$			491.585i			0.0380076i
$552$		0			0
$553$		−	10295.2i		−	0.791677i
$554$		0			0
$555$	143.178	+	9919.01i	0.0109506	+	0.758628i
$556$		0			0
$557$	−6502.22	−	6502.22i	−0.494628	−	0.494628i	0.415133	−	0.909761i	$-0.363735\pi$
$557$	−6502.22	−	6502.22i	−0.494628	−	0.494628i	−0.909761	+	0.415133i	$0.863735\pi$
$558$		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	$-0.856167\pi$
$563$	−6184.95	+	6184.95i	−0.462992	+	0.462992i	0.436643	+	0.899635i	$0.356167\pi$
$564$		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	$-0.125495\pi$
$569$	25063.0			1.84657			0.923284	+	0.384119i	$0.125495\pi$
$570$		0			0
$571$	−15682.4	+	15682.4i	−1.14937	+	1.14937i	−0.162692	+	0.986677i	$0.552018\pi$
$571$	−15682.4	+	15682.4i	−1.14937	+	1.14937i	−0.986677	+	0.162692i	$0.947982\pi$
$572$		0			0
$573$	−14.1343	−	979.183i	−0.00103048	−	0.0713891i
$574$		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
$579$	−6.34357	−	439.465i	−0.000455319	−	0.0315432i
$580$		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	$-0.300406\pi$
$587$	−3171.66	−	3171.66i	−0.223013	−	0.223013i	−0.809766	+	0.586753i	$0.800406\pi$
$588$		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
$597$	123.002	+	8521.23i	0.00843238	+	0.584172i
$598$		0			0
$599$		−	27598.5i		−	1.88255i	−0.337647	−	0.941273i	$-0.609631\pi$
$599$		−	27598.5i		−	1.88255i	0.337647	−	0.941273i	$-0.390369\pi$
$600$		0			0
$601$		−	12432.1i		−	0.843789i	−0.906645	−	0.421894i	$-0.861365\pi$
$601$		−	12432.1i		−	0.843789i	0.906645	−	0.421894i	$-0.138635\pi$
$602$		0			0
$603$	9274.88	+	8754.28i	0.626372	+	0.591214i
$604$		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	0.987006	+	0.160686i	$0.0513706\pi$
$613$	17418.7	+	17418.7i	1.14769	+	1.14769i	0.160686	+	0.987006i	$0.448629\pi$
$614$		0			0
$615$	12878.4	+	12511.9i	0.844405	+	0.820375i
$616$		0			0
$617$	−6194.64			−0.404193			−0.202096	−	0.979366i	$-0.564775\pi$
$617$	−6194.64			−0.404193			−0.202096	+	0.979366i	$0.564775\pi$
$618$		0			0
$619$	15342.7	−	15342.7i	0.996247	−	0.996247i	−0.00374578	−	0.999993i	$-0.501192\pi$
$619$	15342.7	−	15342.7i	0.996247	−	0.996247i	0.999993	+	0.00374578i	$0.00119232\pi$
$620$		0			0
$621$	−6037.67	+	261.602i	−0.390150	+	0.0169046i
$622$		0			0
$623$	−3891.91			−0.250282
$624$		0			0
$625$	2713.31			0.173652
$626$		0			0
$627$	−2328.33	+	33.6088i	−0.148301	+	0.00214068i
$628$		0			0
$629$	8671.44	−	8671.44i	0.549687	−	0.549687i
$630$		0			0
$631$	24841.9			1.56726			0.783631	−	0.621227i	$-0.213365\pi$
$631$	24841.9			1.56726			0.783631	+	0.621227i	$0.213365\pi$
$632$		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	0.203022	−	0.979174i	$-0.434924\pi$
$643$	−12655.0	−	12655.0i	−0.776152	−	0.776152i	−0.979174	+	0.203022i	$0.934924\pi$
$644$		0			0
$645$	13361.2	−	192.866i	0.815654	−	0.0117738i
$646$		0			0
$647$		−	8771.04i		−	0.532960i	−0.963840	−	0.266480i	$-0.914139\pi$
$647$		−	8771.04i		−	0.532960i	0.963840	−	0.266480i	$-0.0858607\pi$
$648$		0			0
$649$			15640.7i			0.945997i
$650$		0			0
$651$	−13382.1	+	193.167i	−0.805661	+	0.0116295i
$652$		0			0
$653$	21658.4	+	21658.4i	1.29794	+	1.29794i	0.929748	+	0.368197i	$0.120025\pi$
$653$	21658.4	+	21658.4i	1.29794	+	1.29794i	0.368197	+	0.929748i	$0.379975\pi$
$654$		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	$-0.623202\pi$
$659$	9280.25	−	9280.25i	0.548569	−	0.548569i	0.926027	+	0.377457i	$0.123202\pi$
$660$		0			0
$661$	−13336.7	−	13336.7i	−0.784776	−	0.784776i	0.195857	−	0.980632i	$-0.437251\pi$
$661$	−13336.7	−	13336.7i	−0.784776	−	0.784776i	−0.980632	+	0.195857i	$0.937251\pi$
$662$		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
$669$	−2340.04	+	33.7779i	−0.135234	+	0.00195206i
$670$		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
$675$	9416.82	−	408.015i	0.536968	−	0.0232659i
$676$		0			0
$677$	3185.15	−	3185.15i	0.180820	−	0.180820i	−0.610893	−	0.791713i	$-0.709189\pi$
$677$	3185.15	−	3185.15i	0.180820	−	0.180820i	0.791713	+	0.610893i	$0.209189\pi$
$678$		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	$-0.244655\pi$
$683$	423.850	+	423.850i	0.0237455	+	0.0237455i	−0.695134	+	0.718880i	$0.744655\pi$
$684$		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	0.535714	−	0.844399i	$-0.320042\pi$
$691$	−5607.03	−	5607.03i	−0.308685	−	0.308685i	−0.844399	+	0.535714i	$0.820042\pi$
$692$		0			0
$693$	−12398.7	−	11702.7i	−0.679633	−	0.641485i
$694$		0			0
$695$			14969.0i			0.816989i
$696$		0			0
$697$		−	22196.9i		−	1.20627i
$698$		0			0
$699$	−261.020	−	18082.7i	−0.0141240	−	0.978473i
$700$		0			0
$701$	−15985.1	−	15985.1i	−0.861267	−	0.861267i	0.130218	−	0.991485i	$-0.458432\pi$
$701$	−15985.1	−	15985.1i	−0.861267	−	0.861267i	−0.991485	+	0.130218i	$0.958432\pi$
$702$		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	$-0.292932\pi$
$709$	−3590.05	−	3590.05i	−0.190165	−	0.190165i	−0.795768	+	0.605602i	$0.792932\pi$
$710$		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
$717$	−239.686	−	16604.8i	−0.0124843	−	0.864876i
$718$		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
$723$	−19.1509	−	1326.72i	−0.000985105	−	0.0682454i
$724$		0			0
$725$	2214.82	−	2214.82i	0.113457	−	0.113457i
$726$		0			0
$727$	15850.3			0.808606			0.404303	−	0.914625i	$-0.367514\pi$
$727$	15850.3			0.808606			0.404303	+	0.914625i	$0.367514\pi$
$728$		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	$-0.561934\pi$
$733$	15633.8	−	15633.8i	0.787784	−	0.787784i	0.981131	+	0.193346i	$0.0619341\pi$
$734$		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	0.989174	+	0.146747i	$0.0468805\pi$
$739$	22820.0	+	22820.0i	1.13592	+	1.13592i	0.146747	+	0.989174i	$0.453120\pi$
$740$		0			0
$741$	−68.8263	−	4768.10i	−0.00341214	−	0.236384i
$742$		0			0
$743$			34196.9i			1.68851i	0.535941	+	0.844255i	$0.319957\pi$
$743$			34196.9i			1.68851i	−0.535941	+	0.844255i	$0.680043\pi$
$744$		0			0
$745$			1278.65i			0.0628809i
$746$		0			0
$747$	−17748.4	+	18803.9i	−0.869317	+	0.921014i
$748$		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	$-0.385865\pi$
$757$	−12194.0	−	12194.0i	−0.585468	−	0.585468i	−0.936401	+	0.350933i	$0.885865\pi$
$758$		0			0
$759$	−6822.98	−	6628.81i	−0.326296	−	0.317010i
$760$		0			0
$761$	−33960.5			−1.61770			−0.808848	−	0.588018i	$-0.799909\pi$
$761$	−33960.5			−1.61770			−0.808848	+	0.588018i	$0.799909\pi$
$762$		0			0
$763$	1542.29	−	1542.29i	0.0731780	−	0.0731780i
$764$		0			0
$765$	7292.11	+	6882.80i	0.344636	+	0.325292i
$766$		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
$771$	−37703.5	+	544.241i	−1.76117	+	0.0254220i
$772$		0			0
$773$	−2736.24	+	2736.24i	−0.127316	+	0.127316i	−0.767894	−	0.640577i	$-0.778695\pi$
$773$	−2736.24	+	2736.24i	−0.127316	+	0.127316i	0.640577	+	0.767894i	$0.278695\pi$
$774$		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	0.596554	−	0.802573i	$-0.296536\pi$
$787$	−4548.50	−	4548.50i	−0.206018	−	0.206018i	−0.802573	+	0.596554i	$0.796536\pi$
$788$		0			0
$789$	−10987.6	+	158.604i	−0.495780	+	0.00715647i
$790$		0			0
$791$		−	810.314i		−	0.0364241i
$792$		0			0
$793$			47864.8i			2.14342i
$794$		0			0
$795$	−13170.9	+	190.118i	−0.587575	+	0.00848150i
$796$		0			0
$797$	10333.6	+	10333.6i	0.459265	+	0.459265i	0.898414	−	0.439149i	$-0.144720\pi$
$797$	10333.6	+	10333.6i	0.459265	+	0.459265i	−0.439149	+	0.898414i	$0.644720\pi$
$798$		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	$-0.590708\pi$
$809$	−12937.6			−0.562252			−0.281126	+	0.959671i	$0.590708\pi$
$810$		0			0
$811$	−13303.5	+	13303.5i	−0.576015	+	0.576015i	−0.933803	−	0.357788i	$-0.883531\pi$
$811$	−13303.5	+	13303.5i	−0.576015	+	0.576015i	0.357788	+	0.933803i	$0.383531\pi$
$812$		0			0
$813$	4805.74	−	69.3697i	0.207312	−	0.00299250i
$814$		0			0
$815$	380.896			0.0163708
$816$		0			0
$817$	3566.11			0.152708
$818$		0			0
$819$	23965.5	−	25390.7i	1.02250	−	1.08330i
$820$		0			0
$821$	23606.7	−	23606.7i	1.00351	−	1.00351i	0.00351227	−	0.999994i	$-0.498882\pi$
$821$	23606.7	−	23606.7i	1.00351	−	1.00351i	0.999994	−	0.00351227i	$-0.00111799\pi$
$822$		0			0
$823$	13577.6			0.575071			0.287536	−	0.957770i	$-0.407164\pi$
$823$	13577.6			0.575071			0.287536	+	0.957770i	$0.407164\pi$
$824$		0			0
$825$	10641.7	+	10338.8i	0.449085	+	0.436304i
$826$		0			0
$827$	−28241.2	−	28241.2i	−1.18747	−	1.18747i	−0.977763	−	0.209711i	$-0.932748\pi$
$827$	−28241.2	−	28241.2i	−1.18747	−	1.18747i	−0.209711	−	0.977763i	$-0.567252\pi$
$828$		0			0
$829$	13869.8	−	13869.8i	0.581082	−	0.581082i	−0.354118	−	0.935201i	$-0.615219\pi$
$829$	13869.8	−	13869.8i	0.581082	−	0.581082i	0.935201	+	0.354118i	$0.115219\pi$
$830$		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
$837$	−24298.5	+	1052.81i	−1.00344	+	0.0434773i
$838$		0			0
$839$			15874.8i			0.653229i	0.945158	+	0.326615i	$0.105908\pi$
$839$			15874.8i			0.653229i	−0.945158	+	0.326615i	$0.894092\pi$
$840$		0			0
$841$		−	22215.4i		−	0.910878i
$842$		0			0
$843$	−13.1804	−	913.099i	−0.000538500	−	0.0373058i
$844$		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	$-0.272848\pi$
$853$	−2526.73	−	2526.73i	−0.101423	−	0.101423i	−0.755997	+	0.654575i	$0.772848\pi$
$854$		0			0
$855$	−2163.80	+	62.4808i	−0.0865501	+	0.00249918i
$856$		0			0
$857$	35121.3			1.39991			0.699954	−	0.714188i	$-0.253204\pi$
$857$	35121.3			1.39991			0.699954	+	0.714188i	$0.253204\pi$
$858$		0			0
$859$	−14337.3	+	14337.3i	−0.569480	+	0.569480i	−0.931983	−	0.362503i	$-0.881922\pi$
$859$	−14337.3	+	14337.3i	−0.569480	+	0.569480i	0.362503	+	0.931983i	$0.381922\pi$
$860$		0			0
$861$	506.391	+	35081.4i	0.0200439	+	1.38858i
$862$		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
$867$	189.549	+	13131.4i	0.00742492	+	0.514378i
$868$		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	$-0.774630\pi$
$877$	−2839.24	+	2839.24i	−0.109321	+	0.109321i	0.650331	+	0.759651i	$0.274630\pi$
$878$		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	0.158986	−	0.987281i	$-0.449177\pi$
$883$	−21733.3	−	21733.3i	−0.828294	−	0.828294i	−0.987281	+	0.158986i	$0.949177\pi$
$884$		0			0
$885$	209.860	+	14538.5i	0.00797103	+	0.552211i
$886$		0			0
$887$		−	32216.9i		−	1.21955i	−0.792575	−	0.609774i	$-0.791260\pi$
$887$		−	32216.9i		−	1.21955i	0.792575	−	0.609774i	$-0.208740\pi$
$888$		0			0
$889$		−	470.711i		−	0.0177583i
$890$		0			0
$891$	−23136.0	−	20607.7i	−0.869906	−	0.774841i
$892$		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	−0.817874	−	0.575398i	$-0.804847\pi$
$907$	−6623.37	+	6623.37i	−0.242476	+	0.242476i	0.575398	+	0.817874i	$0.304847\pi$
$908$		0			0
$909$	−25227.1	+	26727.3i	−0.920495	+	0.975235i
$910$		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
$915$	21726.0	−	313.609i	0.784959	−	0.0113307i
$916$		0			0
$917$	25068.0	−	25068.0i	0.902747	−	0.902747i
$918$		0			0
$919$	32283.9			1.15881			0.579407	−	0.815039i	$-0.303284\pi$
$919$	32283.9			1.15881			0.579407	+	0.815039i	$0.303284\pi$
$920$		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
$933$	−18075.7	+	260.919i	−0.634269	+	0.00915552i
$934$		0			0
$935$			15784.1i			0.552081i
$936$		0			0
$937$			13947.1i			0.486266i	0.969993	+	0.243133i	$0.0781751\pi$
$937$			13947.1i			0.486266i	−0.969993	+	0.243133i	$0.921825\pi$
$938$		0			0
$939$	−17188.4	+	248.110i	−0.597361	+	0.00862276i
$940$		0			0
$941$	−32438.8	−	32438.8i	−1.12378	−	1.12378i	−0.991169	−	0.132608i	$-0.957665\pi$
$941$	−32438.8	−	32438.8i	−1.12378	−	1.12378i	−0.132608	−	0.991169i	$-0.542335\pi$
$942$		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	$-0.633363\pi$
$947$	14766.0	−	14766.0i	0.506685	−	0.506685i	0.913507	+	0.406823i	$0.133363\pi$
$948$		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	$-0.656250\pi$
$953$	−27736.7			−0.942791			−0.471395	+	0.881922i	$0.656250\pi$
$954$		0			0
$955$	1013.30	−	1013.30i	0.0343345	−	0.0343345i
$956$		0			0
$957$	−10294.9	+	148.604i	−0.347740	+	0.00501954i
$958$		0			0
$959$	6738.59			0.226904
$960$		0			0
$961$	−261.548			−0.00877942
$962$		0			0
$963$	−41229.5	−	38915.3i	−1.37965	−	1.30221i
$964$		0			0
$965$	454.775	−	454.775i	0.0151707	−	0.0151707i
$966$		0			0
$967$	38161.5			1.26907			0.634535	−	0.772894i	$-0.281191\pi$
$967$	38161.5			1.26907			0.634535	+	0.772894i	$0.281191\pi$
$968$		0			0
$969$	1919.35	+	1864.73i	0.0636310	+	0.0618201i
$970$		0			0
$971$	40351.2	+	40351.2i	1.33361	+	1.33361i	0.902119	+	0.431488i	$0.142011\pi$
$971$	40351.2	+	40351.2i	1.33361	+	1.33361i	0.431488	+	0.902119i	$0.357989\pi$
$972$		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
$981$	2720.69	−	2882.48i	0.0885472	−	0.0938130i
$982$		0			0
$983$			11135.5i			0.361310i	0.983547	+	0.180655i	$0.0578217\pi$
$983$			11135.5i			0.361310i	−0.983547	+	0.180655i	$0.942178\pi$
$984$		0			0
$985$		−	8395.49i		−	0.271576i
$986$		0			0
$987$	33.9004	+	2348.53i	0.00109328	+	0.0757391i
$988$		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	−0.998139	−	0.0609797i	$-0.980578\pi$
$997$	−33341.7	−	33341.7i	−1.05912	−	1.05912i	−0.0609797	−	0.998139i	$-0.519422\pi$
$998$		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	192.4.k.a.143.11		44
3.2	odd	2	inner	192.4.k.a.143.22		44
4.3	odd	2		48.4.k.a.11.17	yes	44
8.3	odd	2		384.4.k.b.287.11		44
8.5	even	2		384.4.k.a.287.12		44
12.11	even	2		48.4.k.a.11.6	✓	44
16.3	odd	4	inner	192.4.k.a.47.22		44
16.5	even	4		384.4.k.b.95.22		44
16.11	odd	4		384.4.k.a.95.1		44
16.13	even	4		48.4.k.a.35.6	yes	44
24.5	odd	2		384.4.k.a.287.1		44
24.11	even	2		384.4.k.b.287.22		44
48.5	odd	4		384.4.k.b.95.11		44
48.11	even	4		384.4.k.a.95.12		44
48.29	odd	4		48.4.k.a.35.17	yes	44
48.35	even	4	inner	192.4.k.a.47.11		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.k.a.11.6	✓	44	12.11	even	2
48.4.k.a.11.17	yes	44	4.3	odd	2
48.4.k.a.35.6	yes	44	16.13	even	4
48.4.k.a.35.17	yes	44	48.29	odd	4
192.4.k.a.47.11		44	48.35	even	4	inner
192.4.k.a.47.22		44	16.3	odd	4	inner
192.4.k.a.143.11		44	1.1	even	1	trivial
192.4.k.a.143.22		44	3.2	odd	2	inner
384.4.k.a.95.1		44	16.11	odd	4
384.4.k.a.95.12		44	48.11	even	4
384.4.k.a.287.1		44	24.5	odd	2
384.4.k.a.287.12		44	8.5	even	2
384.4.k.b.95.11		44	48.5	odd	4
384.4.k.b.95.22		44	16.5	even	4
384.4.k.b.287.11		44	8.3	odd	2
384.4.k.b.287.22		44	24.11	even	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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	192.k (of order \(4\), degree \(2\), not minimal)

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

Varieties

Fields

Representations

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Database

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