LMFDB - Embedded newform 160.6.o.a.47.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,6,Mod(47,160)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 1]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("160.47");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	160.o (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$25.6614111701$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.9
Character	$\chi$	$=$	160.47
Dual form			160.6.o.a.143.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.0657 + 10.0657i) q^{3} +(-23.9125 + 50.5291i) q^{5} +(96.6855 - 96.6855i) q^{7} +40.3635i q^{9} +O(q^{10})$	\(q+(-10.0657 + 10.0657i) q^{3} +(-23.9125 + 50.5291i) q^{5} +(96.6855 - 96.6855i) q^{7} +40.3635i q^{9} +283.587 q^{11} +(699.519 + 699.519i) q^{13} +(-267.915 - 749.307i) q^{15} +(399.025 + 399.025i) q^{17} +338.083i q^{19} +1946.41i q^{21} +(594.687 + 594.687i) q^{23} +(-1981.38 - 2416.56i) q^{25} +(-2852.25 - 2852.25i) q^{27} -5582.41 q^{29} -144.182i q^{31} +(-2854.50 + 2854.50i) q^{33} +(2573.44 + 7197.43i) q^{35} +(-11418.4 + 11418.4i) q^{37} -14082.3 q^{39} +11892.0 q^{41} +(8345.23 - 8345.23i) q^{43} +(-2039.53 - 965.191i) q^{45} +(-17955.5 + 17955.5i) q^{47} -1889.19i q^{49} -8032.92 q^{51} +(-3977.21 - 3977.21i) q^{53} +(-6781.27 + 14329.4i) q^{55} +(-3403.04 - 3403.04i) q^{57} +17288.6i q^{59} +6236.61i q^{61} +(3902.56 + 3902.56i) q^{63} +(-52073.3 + 18618.8i) q^{65} +(-39565.2 - 39565.2i) q^{67} -11971.9 q^{69} +50088.5i q^{71} +(42184.8 - 42184.8i) q^{73} +(44268.3 + 4380.30i) q^{75} +(27418.7 - 27418.7i) q^{77} +22093.6 q^{79} +47611.5 q^{81} +(-51337.5 + 51337.5i) q^{83} +(-29704.0 + 10620.7i) q^{85} +(56190.8 - 56190.8i) q^{87} +78727.1i q^{89} +135267. q^{91} +(1451.29 + 1451.29i) q^{93} +(-17083.0 - 8084.41i) q^{95} +(-9943.42 - 9943.42i) q^{97} +11446.5i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{3}+O(q^{10}) $ 56 * q + 4 * q^3	$ 56 q + 4 q^{3} + 8 q^{11} - 408 q^{17} - 3120 q^{25} - 968 q^{27} - 976 q^{33} + 4780 q^{35} - 8 q^{41} - 1308 q^{43} - 20872 q^{51} + 968 q^{57} + 17680 q^{65} - 89252 q^{67} - 25184 q^{73} + 127740 q^{75} - 67792 q^{81} + 126444 q^{83} - 329432 q^{91} + 212576 q^{97}+O(q^{100}) $ 56 * q + 4 * q^3 + 8 * q^11 - 408 * q^17 - 3120 * q^25 - 968 * q^27 - 976 * q^33 + 4780 * q^35 - 8 * q^41 - 1308 * q^43 - 20872 * q^51 + 968 * q^57 + 17680 * q^65 - 89252 * q^67 - 25184 * q^73 + 127740 * q^75 - 67792 * q^81 + 126444 * q^83 - 329432 * q^91 + 212576 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$

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
$3$	−10.0657	+	10.0657i	−0.645715	+	0.645715i	−0.951954	−	0.306240i	$-0.900929\pi$
$3$	−10.0657	+	10.0657i	−0.645715	+	0.645715i	0.306240	+	0.951954i	$0.400929\pi$
$4$		0			0
$5$	−23.9125	+	50.5291i	−0.427760	+	0.903892i
$5$	−23.9125	+	50.5291i	−0.427760	+	0.903892i
$6$		0			0
$7$	96.6855	−	96.6855i	0.745790	−	0.745790i	−0.227896	−	0.973686i	$-0.573185\pi$
$7$	96.6855	−	96.6855i	0.745790	−	0.745790i	0.973686	+	0.227896i	$0.0731845\pi$
$8$		0			0
$9$			40.3635i			0.166105i
$10$		0			0
$11$	283.587			0.706650			0.353325	−	0.935501i	$-0.385051\pi$
$11$	283.587			0.706650			0.353325	+	0.935501i	$0.385051\pi$
$12$		0			0
$13$	699.519	+	699.519i	1.14800	+	1.14800i	0.986946	+	0.161052i	$0.0514886\pi$
$13$	699.519	+	699.519i	1.14800	+	1.14800i	0.161052	+	0.986946i	$0.448511\pi$
$14$		0			0
$15$	−267.915	−	749.307i	−0.307446	−	0.859868i
$16$		0			0
$17$	399.025	+	399.025i	0.334871	+	0.334871i	0.854433	−	0.519562i	$-0.173905\pi$
$17$	399.025	+	399.025i	0.334871	+	0.334871i	−0.519562	+	0.854433i	$0.673905\pi$
$18$		0			0
$19$			338.083i			0.214852i	0.994213	+	0.107426i	$0.0342609\pi$
$19$			338.083i			0.214852i	−0.994213	+	0.107426i	$0.965739\pi$
$20$		0			0
$21$			1946.41i			0.963135i
$22$		0			0
$23$	594.687	+	594.687i	0.234406	+	0.234406i	0.814529	−	0.580123i	$-0.196995\pi$
$23$	594.687	+	594.687i	0.234406	+	0.234406i	−0.580123	+	0.814529i	$0.696995\pi$
$24$		0			0
$25$	−1981.38	−	2416.56i	−0.634043	−	0.773298i
$26$		0			0
$27$	−2852.25	−	2852.25i	−0.752971	−	0.752971i
$28$		0			0
$29$	−5582.41			−1.23261			−0.616306	−	0.787507i	$-0.711372\pi$
$29$	−5582.41			−1.23261			−0.616306	+	0.787507i	$0.711372\pi$
$30$		0			0
$31$		−	144.182i		−	0.0269468i	−0.999909	−	0.0134734i	$-0.995711\pi$
$31$		−	144.182i		−	0.0269468i	0.999909	−	0.0134734i	$-0.00428884\pi$
$32$		0			0
$33$	−2854.50	+	2854.50i	−0.456294	+	0.456294i
$34$		0			0
$35$	2573.44	+	7197.43i	0.355095	+	0.993133i
$36$		0			0
$37$	−11418.4	+	11418.4i	−1.37120	+	1.37120i	−0.512523	+	0.858674i	$0.671289\pi$
$37$	−11418.4	+	11418.4i	−1.37120	+	1.37120i	−0.858674	+	0.512523i	$0.828711\pi$
$38$		0			0
$39$	−14082.3			−1.48256
$40$		0			0
$41$	11892.0			1.10483			0.552413	−	0.833570i	$-0.313707\pi$
$41$	11892.0			1.10483			0.552413	+	0.833570i	$0.313707\pi$
$42$		0			0
$43$	8345.23	−	8345.23i	0.688283	−	0.688283i	−0.273569	−	0.961852i	$-0.588204\pi$
$43$	8345.23	−	8345.23i	0.688283	−	0.688283i	0.961852	+	0.273569i	$0.0882042\pi$
$44$		0			0
$45$	−2039.53	−	965.191i	−0.150141	−	0.0710530i
$46$		0			0
$47$	−17955.5	+	17955.5i	−1.18564	+	1.18564i	−0.207383	+	0.978260i	$0.566495\pi$
$47$	−17955.5	+	17955.5i	−1.18564	+	1.18564i	−0.978260	+	0.207383i	$0.933505\pi$
$48$		0			0
$49$		−	1889.19i		−	0.112405i
$50$		0			0
$51$	−8032.92			−0.432462
$52$		0			0
$53$	−3977.21	−	3977.21i	−0.194486	−	0.194486i	0.603145	−	0.797631i	$-0.293914\pi$
$53$	−3977.21	−	3977.21i	−0.194486	−	0.194486i	−0.797631	+	0.603145i	$0.793914\pi$
$54$		0			0
$55$	−6781.27	+	14329.4i	−0.302276	+	0.638735i
$56$		0			0
$57$	−3403.04	−	3403.04i	−0.138733	−	0.138733i
$58$		0			0
$59$			17288.6i			0.646590i	0.946298	+	0.323295i	$0.104791\pi$
$59$			17288.6i			0.646590i	−0.946298	+	0.323295i	$0.895209\pi$
$60$		0			0
$61$			6236.61i			0.214597i	0.994227	+	0.107299i	$0.0342201\pi$
$61$			6236.61i			0.214597i	−0.994227	+	0.107299i	$0.965780\pi$
$62$		0			0
$63$	3902.56	+	3902.56i	0.123879	+	0.123879i
$64$		0			0
$65$	−52073.3	+	18618.8i	−1.52873	+	0.546599i
$66$		0			0
$67$	−39565.2	−	39565.2i	−1.07678	−	1.07678i	−0.996796	−	0.0799829i	$-0.974513\pi$
$67$	−39565.2	−	39565.2i	−1.07678	−	1.07678i	−0.0799829	−	0.996796i	$-0.525487\pi$
$68$		0			0
$69$	−11971.9			−0.302719
$70$		0			0
$71$			50088.5i			1.17921i	0.807691	+	0.589606i	$0.200717\pi$
$71$			50088.5i			1.17921i	−0.807691	+	0.589606i	$0.799283\pi$
$72$		0			0
$73$	42184.8	−	42184.8i	0.926508	−	0.926508i	−0.0709703	−	0.997478i	$-0.522610\pi$
$73$	42184.8	−	42184.8i	0.926508	−	0.926508i	0.997478	+	0.0709703i	$0.0226096\pi$
$74$		0			0
$75$	44268.3	+	4380.30i	0.908741	+	0.0899189i
$76$		0			0
$77$	27418.7	−	27418.7i	0.527012	−	0.527012i
$78$		0			0
$79$	22093.6			0.398290			0.199145	−	0.979970i	$-0.436184\pi$
$79$	22093.6			0.398290			0.199145	+	0.979970i	$0.436184\pi$
$80$		0			0
$81$	47611.5			0.806304
$82$		0			0
$83$	−51337.5	+	51337.5i	−0.817974	+	0.817974i	−0.985814	−	0.167840i	$-0.946321\pi$
$83$	−51337.5	+	51337.5i	−0.817974	+	0.817974i	0.167840	+	0.985814i	$0.446321\pi$
$84$		0			0
$85$	−29704.0	+	10620.7i	−0.445932	+	0.159443i
$86$		0			0
$87$	56190.8	−	56190.8i	0.795916	−	0.795916i
$88$		0			0
$89$			78727.1i			1.05354i	0.850009	+	0.526768i	$0.176596\pi$
$89$			78727.1i			1.05354i	−0.850009	+	0.526768i	$0.823404\pi$
$90$		0			0
$91$	135267.			1.71233
$92$		0			0
$93$	1451.29	+	1451.29i	0.0173999	+	0.0173999i
$94$		0			0
$95$	−17083.0	−	8084.41i	−0.194203	−	0.0919050i
$96$		0			0
$97$	−9943.42	−	9943.42i	−0.107302	−	0.107302i	0.651418	−	0.758719i	$-0.274175\pi$
$97$	−9943.42	−	9943.42i	−0.107302	−	0.107302i	−0.758719	+	0.651418i	$0.774175\pi$
$98$		0			0
$99$			11446.5i			0.117378i
$100$		0			0
$101$			34886.7i			0.340296i	0.985419	+	0.170148i	$0.0544246\pi$
$101$			34886.7i			0.340296i	−0.985419	+	0.170148i	$0.945575\pi$
$102$		0			0
$103$	−74849.2	−	74849.2i	−0.695175	−	0.695175i	0.268191	−	0.963366i	$-0.413574\pi$
$103$	−74849.2	−	74849.2i	−0.695175	−	0.695175i	−0.963366	+	0.268191i	$0.913574\pi$
$104$		0			0
$105$	−98350.6	−	46543.7i	−0.870570	−	0.411991i
$106$		0			0
$107$	−117317.	−	117317.i	−0.990608	−	0.990608i	0.00934815	−	0.999956i	$-0.497024\pi$
$107$	−117317.	−	117317.i	−0.990608	−	0.990608i	−0.999956	+	0.00934815i	$0.997024\pi$
$108$		0			0
$109$	111201.			0.896486			0.448243	−	0.893912i	$-0.352050\pi$
$109$	111201.			0.896486			0.448243	+	0.893912i	$0.352050\pi$
$110$		0			0
$111$		−	229868.i		−	1.77080i
$112$		0			0
$113$	66036.6	−	66036.6i	0.486506	−	0.486506i	−0.420696	−	0.907202i	$-0.638214\pi$
$113$	66036.6	−	66036.6i	0.486506	−	0.486506i	0.907202	+	0.420696i	$0.138214\pi$
$114$		0			0
$115$	−44269.5	+	15828.6i	−0.312148	+	0.111608i
$116$		0			0
$117$	−28235.0	+	28235.0i	−0.190688	+	0.190688i
$118$		0			0
$119$	77159.8			0.499487
$120$		0			0
$121$	−80629.6			−0.500646
$122$		0			0
$123$	−119701.	+	119701.i	−0.713403	+	0.713403i
$124$		0			0
$125$	169486.	−	42331.7i	0.970196	−	0.242321i
$126$		0			0
$127$	78416.4	−	78416.4i	0.431418	−	0.431418i	−0.457693	−	0.889110i	$-0.651324\pi$
$127$	78416.4	−	78416.4i	0.431418	−	0.431418i	0.889110	+	0.457693i	$0.151324\pi$
$128$		0			0
$129$			168001.i			0.888870i
$130$		0			0
$131$	309770.			1.57711			0.788554	−	0.614966i	$-0.210830\pi$
$131$	309770.			1.57711			0.788554	+	0.614966i	$0.210830\pi$
$132$		0			0
$133$	32687.7	+	32687.7i	0.160234	+	0.160234i
$134$		0			0
$135$	212326.	−	75917.3i	1.00270	−	0.358514i
$136$		0			0
$137$	61997.1	+	61997.1i	0.282208	+	0.282208i	0.833989	−	0.551781i	$-0.186051\pi$
$137$	61997.1	+	61997.1i	0.282208	+	0.282208i	−0.551781	+	0.833989i	$0.686051\pi$
$138$		0			0
$139$		−	114337.i		−	0.501938i	−0.967995	−	0.250969i	$-0.919251\pi$
$139$		−	114337.i		−	0.501938i	0.967995	−	0.250969i	$-0.0807492\pi$
$140$		0			0
$141$		−	361470.i		−	1.53117i
$142$		0			0
$143$	198374.	+	198374.i	0.811232	+	0.811232i
$144$		0			0
$145$	133489.	−	282074.i	0.527262	−	1.11415i
$146$		0			0
$147$	19016.0	+	19016.0i	0.0725815	+	0.0725815i
$148$		0			0
$149$	−63562.8			−0.234551			−0.117276	−	0.993099i	$-0.537416\pi$
$149$	−63562.8			−0.234551			−0.117276	+	0.993099i	$0.537416\pi$
$150$		0			0
$151$			397853.i			1.41998i	0.704214	+	0.709988i	$0.251300\pi$
$151$			397853.i			1.41998i	−0.704214	+	0.709988i	$0.748700\pi$
$152$		0			0
$153$	−16106.0	+	16106.0i	−0.0556237	+	0.0556237i
$154$		0			0
$155$	7285.39	+	3447.75i	0.0243570	+	0.0115267i
$156$		0			0
$157$	283821.	−	283821.i	0.918958	−	0.918958i	−0.0779961	−	0.996954i	$-0.524852\pi$
$157$	283821.	−	283821.i	0.918958	−	0.918958i	0.996954	+	0.0779961i	$0.0248522\pi$
$158$		0			0
$159$	80066.8			0.251165
$160$		0			0
$161$	114995.			0.349635
$162$		0			0
$163$	−298452.	+	298452.i	−0.879843	+	0.879843i	−0.993518	−	0.113675i	$-0.963738\pi$
$163$	−298452.	+	298452.i	−0.879843	+	0.879843i	0.113675	+	0.993518i	$0.463738\pi$
$164$		0			0
$165$	−75977.1	−	212493.i	−0.217256	−	0.607625i
$166$		0			0
$167$	−234469.	+	234469.i	−0.650570	+	0.650570i	−0.953130	−	0.302560i	$-0.902159\pi$
$167$	−234469.	+	234469.i	−0.650570	+	0.650570i	0.302560	+	0.953130i	$0.402159\pi$
$168$		0			0
$169$			607360.i			1.63580i
$170$		0			0
$171$	−13646.2			−0.0356879
$172$		0			0
$173$	131530.	+	131530.i	0.334126	+	0.334126i	0.854151	−	0.520025i	$-0.174077\pi$
$173$	131530.	+	131530.i	0.334126	+	0.334126i	−0.520025	+	0.854151i	$0.674077\pi$
$174$		0			0
$175$	−425217.	−	42074.8i	−1.04958	−	0.103855i
$176$		0			0
$177$	−174022.	−	174022.i	−0.417513	−	0.417513i
$178$		0			0
$179$		−	370114.i		−	0.863383i	−0.902021	−	0.431691i	$-0.857917\pi$
$179$		−	370114.i		−	0.863383i	0.902021	−	0.431691i	$-0.142083\pi$
$180$		0			0
$181$			473727.i			1.07481i	0.843324	+	0.537405i	$0.180595\pi$
$181$			473727.i			1.07481i	−0.843324	+	0.537405i	$0.819405\pi$
$182$		0			0
$183$	−62775.9	−	62775.9i	−0.138569	−	0.138569i
$184$		0			0
$185$	−303918.	−	850002.i	−0.652871	−	1.82596i
$186$		0			0
$187$	113158.	+	113158.i	0.236636	+	0.236636i
$188$		0			0
$189$	−551543.			−1.12312
$190$		0			0
$191$		−	287004.i		−	0.569252i	−0.958639	−	0.284626i	$-0.908131\pi$
$191$		−	287004.i		−	0.569252i	0.958639	−	0.284626i	$-0.0918695\pi$
$192$		0			0
$193$	−391702.	+	391702.i	−0.756941	+	0.756941i	−0.975765	−	0.218823i	$-0.929778\pi$
$193$	−391702.	+	391702.i	−0.756941	+	0.756941i	0.218823	+	0.975765i	$0.429778\pi$
$194$		0			0
$195$	336743.	−	711566.i	0.634179	−	1.34007i
$196$		0			0
$197$	−686198.	+	686198.i	−1.25975	+	1.25975i	−0.308535	+	0.951213i	$0.599839\pi$
$197$	−686198.	+	686198.i	−1.25975	+	1.25975i	−0.951213	+	0.308535i	$0.900161\pi$
$198$		0			0
$199$	−775467.			−1.38813			−0.694066	−	0.719912i	$-0.744182\pi$
$199$	−775467.			−1.38813			−0.694066	+	0.719912i	$0.744182\pi$
$200$		0			0
$201$	796503.			1.39058
$202$		0			0
$203$	−539738.	+	539738.i	−0.919270	+	0.919270i
$204$		0			0
$205$	−284367.	+	600891.i	−0.472601	+	0.998645i
$206$		0			0
$207$	−24003.6	+	24003.6i	−0.0389360	+	0.0389360i
$208$		0			0
$209$			95875.8i			0.151825i
$210$		0			0
$211$	307476.			0.475450			0.237725	−	0.971333i	$-0.423598\pi$
$211$	307476.			0.475450			0.237725	+	0.971333i	$0.423598\pi$
$212$		0			0
$213$	−504176.	−	504176.i	−0.761435	−	0.761435i
$214$		0			0
$215$	222122.	+	621233.i	0.327714	+	0.916554i
$216$		0			0
$217$	−13940.3	−	13940.3i	−0.0200966	−	0.0200966i
$218$		0			0
$219$			849240.i			1.19652i
$220$		0			0
$221$			558251.i			0.768862i
$222$		0			0
$223$	−836770.	−	836770.i	−1.12679	−	1.12679i	−0.990696	−	0.136097i	$-0.956544\pi$
$223$	−836770.	−	836770.i	−1.12679	−	1.12679i	−0.136097	−	0.990696i	$-0.543456\pi$
$224$		0			0
$225$	97540.6	−	79975.5i	0.128448	−	0.105318i
$226$		0			0
$227$	79173.7	+	79173.7i	0.101980	+	0.101980i	0.756256	−	0.654276i	$-0.227026\pi$
$227$	79173.7	+	79173.7i	0.101980	+	0.101980i	−0.654276	+	0.756256i	$0.727026\pi$
$228$		0			0
$229$	686727.			0.865357			0.432679	−	0.901548i	$-0.357568\pi$
$229$	686727.			0.865357			0.432679	+	0.901548i	$0.357568\pi$
$230$		0			0
$231$			551977.i			0.680599i
$232$		0			0
$233$	−566816.	+	566816.i	−0.683994	+	0.683994i	−0.960898	−	0.276903i	$-0.910692\pi$
$233$	−566816.	+	566816.i	−0.683994	+	0.683994i	0.276903	+	0.960898i	$0.410692\pi$
$234$		0			0
$235$	−477916.	−	1.33664e6i	−0.564523	−	1.57886i
$236$		0			0
$237$	−222388.	+	222388.i	−0.257182	+	0.257182i
$238$		0			0
$239$	764329.			0.865537			0.432769	−	0.901505i	$-0.357537\pi$
$239$	764329.			0.865537			0.432769	+	0.901505i	$0.357537\pi$
$240$		0			0
$241$	257789.			0.285905			0.142952	−	0.989730i	$-0.454340\pi$
$241$	257789.			0.285905			0.142952	+	0.989730i	$0.454340\pi$
$242$		0			0
$243$	213854.	−	213854.i	0.232328	−	0.232328i
$244$		0			0
$245$	95459.0	+	45175.2i	0.101602	+	0.0480823i
$246$		0			0
$247$	−236495.	+	236495.i	−0.246650	+	0.246650i
$248$		0			0
$249$		−	1.03350e6i		−	1.05636i
$250$		0			0
$251$	818014.			0.819552			0.409776	−	0.912186i	$-0.365607\pi$
$251$	818014.			0.819552			0.409776	+	0.912186i	$0.365607\pi$
$252$		0			0
$253$	168645.	+	168645.i	0.165643	+	0.165643i
$254$		0			0
$255$	192087.	−	405897.i	0.184990	−	0.390899i
$256$		0			0
$257$	212976.	+	212976.i	0.201140	+	0.201140i	0.800488	−	0.599348i	$-0.204574\pi$
$257$	212976.	+	212976.i	0.201140	+	0.201140i	−0.599348	+	0.800488i	$0.704574\pi$
$258$		0			0
$259$			2.20798e6i			2.04525i
$260$		0			0
$261$		−	225325.i		−	0.204743i
$262$		0			0
$263$	1.19052e6	+	1.19052e6i	1.06132	+	1.06132i	0.997993	+	0.0633261i	$0.0201708\pi$
$263$	1.19052e6	+	1.19052e6i	1.06132	+	1.06132i	0.0633261	+	0.997993i	$0.479829\pi$
$264$		0			0
$265$	296070.	−	105860.i	0.258988	−	0.0926012i
$266$		0			0
$267$	−792444.	−	792444.i	−0.680284	−	0.680284i
$268$		0			0
$269$	−507577.			−0.427682			−0.213841	−	0.976868i	$-0.568598\pi$
$269$	−507577.			−0.427682			−0.213841	+	0.976868i	$0.568598\pi$
$270$		0			0
$271$		−	680345.i		−	0.562737i	−0.959600	−	0.281369i	$-0.909212\pi$
$271$		−	680345.i		−	0.562737i	0.959600	−	0.281369i	$-0.0907884\pi$
$272$		0			0
$273$	−1.36155e6	+	1.36155e6i	−1.10568	+	1.10568i
$274$		0			0
$275$	−561894.	−	685303.i	−0.448046	−	0.546451i
$276$		0			0
$277$	1.29751e6	−	1.29751e6i	1.01604	−	1.01604i	0.0161744	−	0.999869i	$-0.494851\pi$
$277$	1.29751e6	−	1.29751e6i	1.01604	−	1.01604i	0.999869	−	0.0161744i	$-0.00514869\pi$
$278$		0			0
$279$	5819.68			0.00447599
$280$		0			0
$281$	1.38793e6			1.04858			0.524289	−	0.851541i	$-0.324331\pi$
$281$	1.38793e6			1.04858			0.524289	+	0.851541i	$0.324331\pi$
$282$		0			0
$283$	506188.	−	506188.i	0.375704	−	0.375704i	−0.493846	−	0.869550i	$-0.664409\pi$
$283$	506188.	−	506188.i	0.375704	−	0.375704i	0.869550	+	0.493846i	$0.164409\pi$
$284$		0			0
$285$	253328.	−	90577.4i	0.184744	−	0.0660553i
$286$		0			0
$287$	1.14978e6	−	1.14978e6i	0.823969	−	0.823969i
$288$		0			0
$289$		−	1.10142e6i		−	0.775723i
$290$		0			0
$291$	200175.			0.138573
$292$		0			0
$293$	358870.	+	358870.i	0.244212	+	0.244212i	0.818590	−	0.574378i	$-0.194756\pi$
$293$	358870.	+	358870.i	0.244212	+	0.244212i	−0.574378	+	0.818590i	$0.694756\pi$
$294$		0			0
$295$	−873577.	−	413413.i	−0.584448	−	0.276585i
$296$		0			0
$297$	−808860.	−	808860.i	−0.532087	−	0.532087i
$298$		0			0
$299$			831990.i			0.538196i
$300$		0			0
$301$		−	1.61373e6i		−	1.02663i
$302$		0			0
$303$	−351159.	−	351159.i	−0.219734	−	0.219734i
$304$		0			0
$305$	−315131.	−	149133.i	−0.193973	−	0.0917961i
$306$		0			0
$307$	−800065.	−	800065.i	−0.484484	−	0.484484i	0.422076	−	0.906560i	$-0.361301\pi$
$307$	−800065.	−	800065.i	−0.484484	−	0.484484i	−0.906560	+	0.422076i	$0.861301\pi$
$308$		0			0
$309$	1.50682e6			0.897770
$310$		0			0
$311$			1.39145e6i			0.815766i	0.913034	+	0.407883i	$0.133733\pi$
$311$			1.39145e6i			0.815766i	−0.913034	+	0.407883i	$0.866267\pi$
$312$		0			0
$313$	−731178.	+	731178.i	−0.421854	+	0.421854i	−0.885842	−	0.463987i	$-0.846418\pi$
$313$	−731178.	+	731178.i	−0.421854	+	0.421854i	0.463987	+	0.885842i	$0.346418\pi$
$314$		0			0
$315$	−290513.	+	103873.i	−0.164964	+	0.0589829i
$316$		0			0
$317$	415835.	−	415835.i	0.232420	−	0.232420i	−0.581282	−	0.813702i	$-0.697449\pi$
$317$	415835.	−	415835.i	0.232420	−	0.232420i	0.813702	+	0.581282i	$0.197449\pi$
$318$		0			0
$319$	−1.58310e6			−0.871025
$320$		0			0
$321$	2.36176e6			1.27930
$322$		0			0
$323$	−134903.	+	134903.i	−0.0719477	+	0.0719477i
$324$		0			0
$325$	304411.	−	3.07644e6i	0.159864	−	1.61562i
$326$		0			0
$327$	−1.11932e6	+	1.11932e6i	−0.578874	+	0.578874i
$328$		0			0
$329$			3.47208e6i			1.76848i
$330$		0			0
$331$	2.46277e6			1.23553			0.617765	−	0.786363i	$-0.288038\pi$
$331$	2.46277e6			1.23553			0.617765	+	0.786363i	$0.288038\pi$
$332$		0			0
$333$	−460885.	−	460885.i	−0.227762	−	0.227762i
$334$		0			0
$335$	2.94530e6	−	1.05309e6i	1.43390	−	0.512690i
$336$		0			0
$337$	−1.44346e6	−	1.44346e6i	−0.692355	−	0.692355i	0.270395	−	0.962749i	$-0.412846\pi$
$337$	−1.44346e6	−	1.44346e6i	−0.692355	−	0.692355i	−0.962749	+	0.270395i	$0.912846\pi$
$338$		0			0
$339$			1.32941e6i			0.628289i
$340$		0			0
$341$		−	40888.1i		−	0.0190419i
$342$		0			0
$343$	1.44234e6	+	1.44234e6i	0.661959	+	0.661959i
$344$		0			0
$345$	286278.	−	604929.i	0.129491	−	0.273625i
$346$		0			0
$347$	966813.	+	966813.i	0.431041	+	0.431041i	0.888982	−	0.457941i	$-0.151413\pi$
$347$	966813.	+	966813.i	0.431041	+	0.431041i	−0.457941	+	0.888982i	$0.651413\pi$
$348$		0			0
$349$	−1.77134e6			−0.778462			−0.389231	−	0.921140i	$-0.627259\pi$
$349$	−1.77134e6			−0.778462			−0.389231	+	0.921140i	$0.627259\pi$
$350$		0			0
$351$		−	3.99041e6i		−	1.72882i
$352$		0			0
$353$	1.32730e6	−	1.32730e6i	0.566932	−	0.566932i	−0.364336	−	0.931268i	$-0.618704\pi$
$353$	1.32730e6	−	1.32730e6i	0.566932	−	0.566932i	0.931268	+	0.364336i	$0.118704\pi$
$354$		0			0
$355$	−2.53093e6	−	1.19774e6i	−1.06588	−	0.504420i
$356$		0			0
$357$	−776668.	+	776668.i	−0.322526	+	0.322526i
$358$		0			0
$359$	3.44839e6			1.41215			0.706074	−	0.708138i	$-0.250465\pi$
$359$	3.44839e6			1.41215			0.706074	+	0.708138i	$0.250465\pi$
$360$		0			0
$361$	2.36180e6			0.953839
$362$		0			0
$363$	811593.	−	811593.i	0.323275	−	0.323275i
$364$		0			0
$365$	1.12282e6	+	3.14031e6i	0.441141	+	1.23379i
$366$		0			0
$367$	2.52705e6	−	2.52705e6i	0.979374	−	0.979374i	−0.0204173	−	0.999792i	$-0.506499\pi$
$367$	2.52705e6	−	2.52705e6i	0.979374	−	0.979374i	0.999792	+	0.0204173i	$0.00649947\pi$
$368$		0			0
$369$			480001.i			0.183517i
$370$		0			0
$371$	−769077.			−0.290092
$372$		0			0
$373$	268402.	+	268402.i	0.0998882	+	0.0998882i	0.755285	−	0.655397i	$-0.227499\pi$
$373$	268402.	+	268402.i	0.0998882	+	0.0998882i	−0.655397	+	0.755285i	$0.727499\pi$
$374$		0			0
$375$	−1.27990e6	+	2.13210e6i	−0.470000	+	0.782940i
$376$		0			0
$377$	−3.90500e6	−	3.90500e6i	−1.41504	−	1.41504i
$378$		0			0
$379$		−	847168.i		−	0.302951i	−0.988461	−	0.151475i	$-0.951598\pi$
$379$		−	847168.i		−	0.302951i	0.988461	−	0.151475i	$-0.0484024\pi$
$380$		0			0
$381$			1.57863e6i			0.557145i
$382$		0			0
$383$	−2.32473e6	−	2.32473e6i	−0.809795	−	0.809795i	0.174807	−	0.984603i	$-0.444070\pi$
$383$	−2.32473e6	−	2.32473e6i	−0.809795	−	0.809795i	−0.984603	+	0.174807i	$0.944070\pi$
$384$		0			0
$385$	729794.	+	2.04109e6i	0.250928	+	0.701797i
$386$		0			0
$387$	336842.	+	336842.i	0.114327	+	0.114327i
$388$		0			0
$389$	3.52032e6			1.17953			0.589764	−	0.807575i	$-0.299221\pi$
$389$	3.52032e6			1.17953			0.589764	+	0.807575i	$0.299221\pi$
$390$		0			0
$391$			474590.i			0.156992i
$392$		0			0
$393$	−3.11805e6	+	3.11805e6i	−1.01836	+	1.01836i
$394$		0			0
$395$	−528314.	+	1.11637e6i	−0.170372	+	0.360011i
$396$		0			0
$397$	−239629.	+	239629.i	−0.0763067	+	0.0763067i	−0.744230	−	0.667923i	$-0.767183\pi$
$397$	−239629.	+	239629.i	−0.0763067	+	0.0763067i	0.667923	+	0.744230i	$0.267183\pi$
$398$		0			0
$399$	−658050.			−0.206931
$400$		0			0
$401$	−1.56689e6			−0.486607			−0.243303	−	0.969950i	$-0.578231\pi$
$401$	−1.56689e6			−0.486607			−0.243303	+	0.969950i	$0.578231\pi$
$402$		0			0
$403$	100858.	−	100858.i	0.0309348	−	0.0309348i
$404$		0			0
$405$	−1.13851e6	+	2.40577e6i	−0.344905	+	0.728812i
$406$		0			0
$407$	−3.23810e6	+	3.23810e6i	−0.968955	+	0.968955i
$408$		0			0
$409$			220244.i			0.0651022i	0.999470	+	0.0325511i	$0.0103632\pi$
$409$			220244.i			0.0651022i	−0.999470	+	0.0325511i	$0.989637\pi$
$410$		0			0
$411$	−1.24809e6			−0.364452
$412$		0			0
$413$	1.67156e6	+	1.67156e6i	0.482220	+	0.482220i
$414$		0			0
$415$	−1.36643e6	−	3.82165e6i	−0.389464	−	1.08926i
$416$		0			0
$417$	1.15088e6	+	1.15088e6i	0.324109	+	0.324109i
$418$		0			0
$419$		−	3.95300e6i		−	1.10000i	−0.835165	−	0.549999i	$-0.814628\pi$
$419$		−	3.95300e6i		−	1.10000i	0.835165	−	0.549999i	$-0.185372\pi$
$420$		0			0
$421$			1.92105e6i			0.528244i	0.964489	+	0.264122i	$0.0850821\pi$
$421$			1.92105e6i			0.528244i	−0.964489	+	0.264122i	$0.914918\pi$
$422$		0			0
$423$	−724748.	−	724748.i	−0.196941	−	0.196941i
$424$		0			0
$425$	173644.	−	1.75489e6i	0.0466324	−	0.471278i
$426$		0			0
$427$	602990.	+	602990.i	0.160045	+	0.160045i
$428$		0			0
$429$	−3.99355e6			−1.04765
$430$		0			0
$431$			5.12491e6i			1.32890i	0.747331	+	0.664451i	$0.231335\pi$
$431$			5.12491e6i			1.32890i	−0.747331	+	0.664451i	$0.768665\pi$
$432$		0			0
$433$	4.93044e6	−	4.93044e6i	1.26376	−	1.26376i	0.314510	−	0.949254i	$-0.398160\pi$
$433$	4.93044e6	−	4.93044e6i	1.26376	−	1.26376i	0.949254	−	0.314510i	$-0.101840\pi$
$434$		0			0
$435$	1.49561e6	+	4.18294e6i	0.378962	+	1.05988i
$436$		0			0
$437$	−201054.	+	201054.i	−0.0503626	+	0.0503626i
$438$		0			0
$439$	−2.70879e6			−0.670833			−0.335417	−	0.942070i	$-0.608877\pi$
$439$	−2.70879e6			−0.670833			−0.335417	+	0.942070i	$0.608877\pi$
$440$		0			0
$441$	76254.2			0.0186710
$442$		0			0
$443$	−940341.	+	940341.i	−0.227654	+	0.227654i	−0.811712	−	0.584058i	$-0.801464\pi$
$443$	−940341.	+	940341.i	−0.227654	+	0.227654i	0.584058	+	0.811712i	$0.301464\pi$
$444$		0			0
$445$	−3.97801e6	−	1.88256e6i	−0.952283	−	0.450660i
$446$		0			0
$447$	639804.	−	639804.i	0.151453	−	0.151453i
$448$		0			0
$449$			2.66405e6i			0.623630i	0.950143	+	0.311815i	$0.100937\pi$
$449$			2.66405e6i			0.623630i	−0.950143	+	0.311815i	$0.899063\pi$
$450$		0			0
$451$	3.37240e6			0.780725
$452$		0			0
$453$	−4.00467e6	−	4.00467e6i	−0.916899	−	0.916899i
$454$		0			0
$455$	−3.23457e6	+	6.83491e6i	−0.732466	+	1.54776i
$456$		0			0
$457$	4.92890e6	+	4.92890e6i	1.10398	+	1.10398i	0.993926	+	0.110049i	$0.0351007\pi$
$457$	4.92890e6	+	4.92890e6i	1.10398	+	1.10398i	0.110049	+	0.993926i	$0.464899\pi$
$458$		0			0
$459$		−	2.27624e6i		−	0.504296i
$460$		0			0
$461$			1.34239e6i			0.294189i	0.989122	+	0.147095i	$0.0469922\pi$
$461$			1.34239e6i			0.294189i	−0.989122	+	0.147095i	$0.953008\pi$
$462$		0			0
$463$	−66298.4	−	66298.4i	−0.0143731	−	0.0143731i	0.699884	−	0.714257i	$-0.253235\pi$
$463$	−66298.4	−	66298.4i	−0.0143731	−	0.0143731i	−0.714257	+	0.699884i	$0.753235\pi$
$464$		0			0
$465$	−108037.	+	38628.5i	−0.0231706	+	0.00828467i
$466$		0			0
$467$	493248.	+	493248.i	0.104658	+	0.104658i	0.757497	−	0.652839i	$-0.226422\pi$
$467$	493248.	+	493248.i	0.104658	+	0.104658i	−0.652839	+	0.757497i	$0.726422\pi$
$468$		0			0
$469$	−7.65077e6			−1.60610
$470$		0			0
$471$			5.71371e6i			1.18677i
$472$		0			0
$473$	2.36660e6	−	2.36660e6i	0.486375	−	0.486375i
$474$		0			0
$475$	816996.	−	669872.i	0.166145	−	0.136225i
$476$		0			0
$477$	160534.	−	160534.i	0.0323051	−	0.0323051i
$478$		0			0
$479$	−2.01091e6			−0.400456			−0.200228	−	0.979749i	$-0.564168\pi$
$479$	−2.01091e6			−0.400456			−0.200228	+	0.979749i	$0.564168\pi$
$480$		0			0
$481$	−1.59747e7			−3.14826
$482$		0			0
$483$	−1.15751e6	+	1.15751e6i	−0.225765	+	0.225765i
$484$		0			0
$485$	740204.	−	264660.i	0.142889	−	0.0510898i
$486$		0			0
$487$	−2.94894e6	+	2.94894e6i	−0.563435	+	0.563435i	−0.930281	−	0.366847i	$-0.880437\pi$
$487$	−2.94894e6	+	2.94894e6i	−0.563435	+	0.563435i	0.366847	+	0.930281i	$0.380437\pi$
$488$		0			0
$489$		−	6.00825e6i		−	1.13625i
$490$		0			0
$491$	−5.11456e6			−0.957425			−0.478712	−	0.877972i	$-0.658896\pi$
$491$	−5.11456e6			−0.957425			−0.478712	+	0.877972i	$0.658896\pi$
$492$		0			0
$493$	−2.22752e6	−	2.22752e6i	−0.412766	−	0.412766i
$494$		0			0
$495$	−578384.	−	273715.i	−0.106097	−	0.0502095i
$496$		0			0
$497$	4.84283e6	+	4.84283e6i	0.879445	+	0.879445i
$498$		0			0
$499$		−	22809.7i		−	0.00410079i	−0.999998	−	0.00205040i	$-0.999347\pi$
$499$		−	22809.7i		−	0.00410079i	0.999998	−	0.00205040i	$-0.000652662\pi$
$500$		0			0
$501$		−	4.72019e6i		−	0.840165i
$502$		0			0
$503$	5.18776e6	+	5.18776e6i	0.914240	+	0.914240i	0.996602	−	0.0823624i	$-0.0262465\pi$
$503$	5.18776e6	+	5.18776e6i	0.914240	+	0.914240i	−0.0823624	+	0.996602i	$0.526247\pi$
$504$		0			0
$505$	−1.76280e6	−	834229.i	−0.307591	−	0.145565i
$506$		0			0
$507$	−6.11350e6	−	6.11350e6i	−1.05626	−	1.05626i
$508$		0			0
$509$	1.15335e7			1.97318			0.986589	−	0.163222i	$-0.0521887\pi$
$509$	1.15335e7			1.97318			0.986589	+	0.163222i	$0.0521887\pi$
$510$		0			0
$511$		−	8.15733e6i		−	1.38196i
$512$		0			0
$513$	964297.	−	964297.i	0.161777	−	0.161777i
$514$		0			0
$515$	5.57190e6	−	1.99223e6i	0.925732	−	0.330995i
$516$		0			0
$517$	−5.09195e6	+	5.09195e6i	−0.837834	+	0.837834i
$518$		0			0
$519$	−2.64789e6			−0.431500
$520$		0			0
$521$	736346.			0.118847			0.0594234	−	0.998233i	$-0.481074\pi$
$521$	736346.			0.118847			0.0594234	+	0.998233i	$0.481074\pi$
$522$		0			0
$523$	−5.83896e6	+	5.83896e6i	−0.933430	+	0.933430i	−0.997918	−	0.0644887i	$-0.979458\pi$
$523$	−5.83896e6	+	5.83896e6i	−0.933430	+	0.933430i	0.0644887	+	0.997918i	$0.479458\pi$
$524$		0			0
$525$	4.70362e6	−	3.85660e6i	0.744790	−	0.610669i
$526$		0			0
$527$	57532.1	−	57532.1i	0.00902369	−	0.00902369i
$528$		0			0
$529$		−	5.72904e6i		−	0.890107i
$530$		0			0
$531$	−697827.			−0.107402
$532$		0			0
$533$	8.31866e6	+	8.31866e6i	1.26834	+	1.26834i
$534$		0			0
$535$	8.73328e6	−	3.12258e6i	1.31915	−	0.471661i
$536$		0			0
$537$	3.72546e6	+	3.72546e6i	0.557499	+	0.557499i
$538$		0			0
$539$		−	535749.i		−	0.0794308i
$540$		0			0
$541$		−	5.66802e6i		−	0.832604i	−0.909226	−	0.416302i	$-0.863326\pi$
$541$		−	5.66802e6i		−	0.832604i	0.909226	−	0.416302i	$-0.136674\pi$
$542$		0			0
$543$	−4.76839e6	−	4.76839e6i	−0.694021	−	0.694021i
$544$		0			0
$545$	−2.65910e6	+	5.61890e6i	−0.383481	+	0.810327i
$546$		0			0
$547$	3.64899e6	+	3.64899e6i	0.521440	+	0.521440i	0.918006	−	0.396566i	$-0.129798\pi$
$547$	3.64899e6	+	3.64899e6i	0.521440	+	0.521440i	−0.396566	+	0.918006i	$0.629798\pi$
$548$		0			0
$549$	−251731.			−0.0356456
$550$		0			0
$551$		−	1.88732e6i		−	0.264829i
$552$		0			0
$553$	2.13613e6	−	2.13613e6i	0.297040	−	0.297040i
$554$		0			0
$555$	1.16150e7	+	5.49671e6i	1.60062	+	0.757479i
$556$		0			0
$557$	1.61980e6	−	1.61980e6i	0.221219	−	0.221219i	−0.587793	−	0.809012i	$-0.700003\pi$
$557$	1.61980e6	−	1.61980e6i	0.221219	−	0.221219i	0.809012	+	0.587793i	$0.200003\pi$
$558$		0			0
$559$	1.16753e7			1.58030
$560$		0			0
$561$	−2.27803e6			−0.305599
$562$		0			0
$563$	6.15791e6	−	6.15791e6i	0.818771	−	0.818771i	−0.167159	−	0.985930i	$-0.553459\pi$
$563$	6.15791e6	−	6.15791e6i	0.818771	−	0.818771i	0.985930	+	0.167159i	$0.0534592\pi$
$564$		0			0
$565$	1.75767e6	+	4.91587e6i	0.231641	+	0.647857i
$566$		0			0
$567$	4.60334e6	−	4.60334e6i	0.601334	−	0.601334i
$568$		0			0
$569$			4.23310e6i			0.548123i	0.961712	+	0.274061i	$0.0883672\pi$
$569$			4.23310e6i			0.548123i	−0.961712	+	0.274061i	$0.911633\pi$
$570$		0			0
$571$	−6.05998e6			−0.777823			−0.388912	−	0.921275i	$-0.627149\pi$
$571$	−6.05998e6			−0.777823			−0.388912	+	0.921275i	$0.627149\pi$
$572$		0			0
$573$	2.88890e6	+	2.88890e6i	0.367575	+	0.367575i
$574$		0			0
$575$	258791.	−	2.61540e6i	0.0326422	−	0.329889i
$576$		0			0
$577$	6.43951e6	+	6.43951e6i	0.805217	+	0.805217i	0.983906	−	0.178689i	$-0.0571855\pi$
$577$	6.43951e6	+	6.43951e6i	0.805217	+	0.805217i	−0.178689	+	0.983906i	$0.557185\pi$
$578$		0			0
$579$		−	7.88550e6i		−	0.977536i
$580$		0			0
$581$			9.92719e6i			1.22007i
$582$		0			0
$583$	−1.12788e6	−	1.12788e6i	−0.137434	−	0.137434i
$584$		0			0
$585$	−751520.	−	2.10186e6i	−0.0907927	−	0.253930i
$586$		0			0
$587$	9.09859e6	+	9.09859e6i	1.08988	+	1.08988i	0.995540	+	0.0943400i	$0.0300741\pi$
$587$	9.09859e6	+	9.09859e6i	1.08988	+	1.08988i	0.0943400	+	0.995540i	$0.469926\pi$
$588$		0			0
$589$	48745.5			0.00578956
$590$		0			0
$591$		−	1.38141e7i		−	1.62688i
$592$		0			0
$593$	3.99751e6	−	3.99751e6i	0.466823	−	0.466823i	−0.434061	−	0.900884i	$-0.642920\pi$
$593$	3.99751e6	−	3.99751e6i	0.466823	−	0.466823i	0.900884	+	0.434061i	$0.142920\pi$
$594$		0			0
$595$	−1.84508e6	+	3.89882e6i	−0.213660	+	0.451482i
$596$		0			0
$597$	7.80561e6	−	7.80561e6i	0.896337	−	0.896337i
$598$		0			0
$599$	448071.			0.0510246			0.0255123	−	0.999675i	$-0.491878\pi$
$599$	448071.			0.0510246			0.0255123	+	0.999675i	$0.491878\pi$
$600$		0			0
$601$	−3.18693e6			−0.359903			−0.179952	−	0.983675i	$-0.557594\pi$
$601$	−3.18693e6			−0.359903			−0.179952	+	0.983675i	$0.557594\pi$
$602$		0			0
$603$	1.59699e6	−	1.59699e6i	0.178858	−	0.178858i
$604$		0			0
$605$	1.92806e6	−	4.07414e6i	0.214156	−	0.452531i
$606$		0			0
$607$	5.74029e6	−	5.74029e6i	0.632357	−	0.632357i	−0.316302	−	0.948659i	$-0.602441\pi$
$607$	5.74029e6	−	5.74029e6i	0.632357	−	0.632357i	0.948659	+	0.316302i	$0.102441\pi$
$608$		0			0
$609$		−	1.08657e7i		−	1.18717i
$610$		0			0
$611$	−2.51205e7			−2.72223
$612$		0			0
$613$	−4.84512e6	−	4.84512e6i	−0.520779	−	0.520779i	0.397028	−	0.917807i	$-0.370042\pi$
$613$	−4.84512e6	−	4.84512e6i	−0.520779	−	0.520779i	−0.917807	+	0.397028i	$0.870042\pi$
$614$		0			0
$615$	−3.18604e6	−	8.91074e6i	−0.339674	−	0.950005i
$616$		0			0
$617$	−7.13817e6	−	7.13817e6i	−0.754874	−	0.754874i	0.220511	−	0.975384i	$-0.429228\pi$
$617$	−7.13817e6	−	7.13817e6i	−0.754874	−	0.754874i	−0.975384	+	0.220511i	$0.929228\pi$
$618$		0			0
$619$		−	8.04378e6i		−	0.843789i	−0.906645	−	0.421894i	$-0.861365\pi$
$619$		−	8.04378e6i		−	0.843789i	0.906645	−	0.421894i	$-0.138635\pi$
$620$		0			0
$621$		−	3.39239e6i		−	0.353002i
$622$		0			0
$623$	7.61178e6	+	7.61178e6i	0.785717	+	0.785717i
$624$		0			0
$625$	−1.91386e6	+	9.57625e6i	−0.195979	+	0.980608i
$626$		0			0
$627$	−965057.	−	965057.i	−0.0980357	−	0.0980357i
$628$		0			0
$629$	−9.11242e6			−0.918348
$630$		0			0
$631$			1.34627e7i			1.34604i	0.739622	+	0.673022i	$0.235004\pi$
$631$			1.34627e7i			1.34604i	−0.739622	+	0.673022i	$0.764996\pi$
$632$		0			0
$633$	−3.09496e6	+	3.09496e6i	−0.307005	+	0.307005i
$634$		0			0
$635$	2.08718e6	+	5.83745e6i	0.205412	+	0.574498i
$636$		0			0
$637$	1.32152e6	−	1.32152e6i	0.129041	−	0.129041i
$638$		0			0
$639$	−2.02175e6			−0.195873
$640$		0			0
$641$	−2.67079e6			−0.256741			−0.128370	−	0.991726i	$-0.540975\pi$
$641$	−2.67079e6			−0.256741			−0.128370	+	0.991726i	$0.540975\pi$
$642$		0			0
$643$	4.33127e6	−	4.33127e6i	0.413131	−	0.413131i	−0.469697	−	0.882828i	$-0.655637\pi$
$643$	4.33127e6	−	4.33127e6i	0.413131	−	0.413131i	0.882828	+	0.469697i	$0.155637\pi$
$644$		0			0
$645$	−8.48895e6	−	4.01733e6i	−0.803442	−	0.380223i
$646$		0			0
$647$	2.01146e6	−	2.01146e6i	0.188908	−	0.188908i	−0.606316	−	0.795224i	$-0.707353\pi$
$647$	2.01146e6	−	2.01146e6i	0.188908	−	0.188908i	0.795224	+	0.606316i	$0.207353\pi$
$648$		0			0
$649$			4.90281e6i			0.456913i
$650$		0			0
$651$	280638.			0.0259534
$652$		0			0
$653$	−3.78586e6	−	3.78586e6i	−0.347441	−	0.347441i	0.511714	−	0.859156i	$-0.329011\pi$
$653$	−3.78586e6	−	3.78586e6i	−0.347441	−	0.347441i	−0.859156	+	0.511714i	$0.829011\pi$
$654$		0			0
$655$	−7.40738e6	+	1.56524e7i	−0.674623	+	1.42554i
$656$		0			0
$657$	1.70273e6	+	1.70273e6i	0.153897	+	0.153897i
$658$		0			0
$659$			3.51951e6i			0.315696i	0.987463	+	0.157848i	$0.0504556\pi$
$659$			3.51951e6i			0.315696i	−0.987463	+	0.157848i	$0.949544\pi$
$660$		0			0
$661$		−	1.09747e7i		−	0.976991i	−0.872566	−	0.488496i	$-0.837546\pi$
$661$		−	1.09747e7i		−	0.976991i	0.872566	−	0.488496i	$-0.162454\pi$
$662$		0			0
$663$	−5.61918e6	−	5.61918e6i	−0.496466	−	0.496466i
$664$		0			0
$665$	−2.43333e6	+	870037.i	−0.213376	+	0.0762928i
$666$		0			0
$667$	−3.31979e6	−	3.31979e6i	−0.288932	−	0.288932i
$668$		0			0
$669$	1.68453e7			1.45517
$670$		0			0
$671$			1.76862e6i			0.151645i
$672$		0			0
$673$	1.14860e7	−	1.14860e7i	0.977532	−	0.977532i	−0.0222213	−	0.999753i	$-0.507074\pi$
$673$	1.14860e7	−	1.14860e7i	0.977532	−	0.977532i	0.999753	+	0.0222213i	$0.00707384\pi$
$674$		0			0
$675$	−1.24122e6	+	1.25440e7i	−0.104855	+	1.05969i
$676$		0			0
$677$	1.56904e6	−	1.56904e6i	0.131571	−	0.131571i	−0.638254	−	0.769826i	$-0.720343\pi$
$677$	1.56904e6	−	1.56904e6i	0.131571	−	0.131571i	0.769826	+	0.638254i	$0.220343\pi$
$678$		0			0
$679$	−1.92277e6			−0.160049
$680$		0			0
$681$	−1.59388e6			−0.131700
$682$		0			0
$683$	8.69137e6	−	8.69137e6i	0.712913	−	0.712913i	−0.254231	−	0.967144i	$-0.581822\pi$
$683$	8.69137e6	−	8.69137e6i	0.712913	−	0.712913i	0.967144	+	0.254231i	$0.0818223\pi$
$684$		0			0
$685$	−4.61516e6	+	1.65015e6i	−0.375803	+	0.134369i
$686$		0			0
$687$	−6.91239e6	+	6.91239e6i	−0.558774	+	0.558774i
$688$		0			0
$689$		−	5.56427e6i		−	0.446539i
$690$		0			0
$691$	1.40891e7			1.12250			0.561252	−	0.827645i	$-0.310320\pi$
$691$	1.40891e7			1.12250			0.561252	+	0.827645i	$0.310320\pi$
$692$		0			0
$693$	1.10671e6	+	1.10671e6i	0.0875392	+	0.0875392i
$694$		0			0
$695$	5.77735e6	+	2.73409e6i	0.453698	+	0.214709i
$696$		0			0
$697$	4.74519e6	+	4.74519e6i	0.369974	+	0.369974i
$698$		0			0
$699$		−	1.14108e7i		−	0.883331i
$700$		0			0
$701$			1.15723e7i			0.889457i	0.895665	+	0.444729i	$0.146700\pi$
$701$			1.15723e7i			0.889457i	−0.895665	+	0.444729i	$0.853300\pi$
$702$		0			0
$703$	−3.86035e6	−	3.86035e6i	−0.294604	−	0.294604i
$704$		0			0
$705$	1.82648e7	+	8.64365e6i	1.38402	+	0.654975i
$706$		0			0
$707$	3.37304e6	+	3.37304e6i	0.253789	+	0.253789i
$708$		0			0
$709$	9.95975e6			0.744103			0.372051	−	0.928212i	$-0.378655\pi$
$709$	9.95975e6			0.744103			0.372051	+	0.928212i	$0.378655\pi$
$710$		0			0
$711$			891775.i			0.0661578i
$712$		0			0
$713$	85743.2	−	85743.2i	0.00631649	−	0.00631649i
$714$		0			0
$715$	−1.47673e7	+	5.28005e6i	−1.08028	+	0.386254i
$716$		0			0
$717$	−7.69351e6	+	7.69351e6i	−0.558890	+	0.558890i
$718$		0			0
$719$	3.73997e6			0.269803			0.134901	−	0.990859i	$-0.456928\pi$
$719$	3.73997e6			0.269803			0.134901	+	0.990859i	$0.456928\pi$
$720$		0			0
$721$	−1.44737e7			−1.03691
$722$		0			0
$723$	−2.59482e6	+	2.59482e6i	−0.184613	+	0.184613i
$724$		0			0
$725$	1.10609e7	+	1.34902e7i	0.781529	+	0.953176i
$726$		0			0
$727$	−4.69069e6	+	4.69069e6i	−0.329155	+	0.329155i	−0.852265	−	0.523110i	$-0.824772\pi$
$727$	−4.69069e6	+	4.69069e6i	−0.329155	+	0.329155i	0.523110	+	0.852265i	$0.324772\pi$
$728$		0			0
$729$			1.58748e7i			1.10634i
$730$		0			0
$731$	6.65991e6			0.460972
$732$		0			0
$733$	−5.58662e6	−	5.58662e6i	−0.384051	−	0.384051i	0.488508	−	0.872559i	$-0.337541\pi$
$733$	−5.58662e6	−	5.58662e6i	−0.384051	−	0.384051i	−0.872559	+	0.488508i	$0.837541\pi$
$734$		0			0
$735$	−1.41558e6	+	506142.i	−0.0966533	+	0.0345584i
$736$		0			0
$737$	−1.12202e7	−	1.12202e7i	−0.760905	−	0.760905i
$738$		0			0
$739$			1.60299e7i			1.07974i	0.841749	+	0.539870i	$0.181527\pi$
$739$			1.60299e7i			1.07974i	−0.841749	+	0.539870i	$0.818473\pi$
$740$		0			0
$741$		−	4.76098e6i		−	0.318531i
$742$		0			0
$743$	−269940.	−	269940.i	−0.0179389	−	0.0179389i	0.698080	−	0.716019i	$-0.254038\pi$
$743$	−269940.	−	269940.i	−0.0179389	−	0.0179389i	−0.716019	+	0.698080i	$0.754038\pi$
$744$		0			0
$745$	1.51995e6	−	3.21177e6i	0.100332	−	0.212009i
$746$		0			0
$747$	−2.07216e6	−	2.07216e6i	−0.135869	−	0.135869i
$748$		0			0
$749$	−2.26857e7			−1.47757
$750$		0			0
$751$			1.18503e7i			0.766707i	0.923602	+	0.383353i	$0.125231\pi$
$751$			1.18503e7i			0.766707i	−0.923602	+	0.383353i	$0.874769\pi$
$752$		0			0
$753$	−8.23388e6	+	8.23388e6i	−0.529197	+	0.529197i
$754$		0			0
$755$	−2.01032e7	−	9.51367e6i	−1.28350	−	0.607408i
$756$		0			0
$757$	−1.72173e6	+	1.72173e6i	−0.109201	+	0.109201i	−0.759596	−	0.650395i	$-0.774603\pi$
$757$	−1.72173e6	+	1.72173e6i	−0.109201	+	0.109201i	0.650395	+	0.759596i	$0.274603\pi$
$758$		0			0
$759$	−3.39507e6			−0.213916
$760$		0			0
$761$	1.62361e7			1.01629			0.508147	−	0.861271i	$-0.330331\pi$
$761$	1.62361e7			1.01629			0.508147	+	0.861271i	$0.330331\pi$
$762$		0			0
$763$	1.07516e7	−	1.07516e7i	0.668590	−	0.668590i
$764$		0			0
$765$	−428688.	−	1.19896e6i	−0.0264842	−	0.0740714i
$766$		0			0
$767$	−1.20937e7	+	1.20937e7i	−0.742284	+	0.742284i
$768$		0			0
$769$		−	1.91198e7i		−	1.16592i	−0.812502	−	0.582958i	$-0.801895\pi$
$769$		−	1.91198e7i		−	1.16592i	0.812502	−	0.582958i	$-0.198105\pi$
$770$		0			0
$771$	−4.28751e6			−0.259758
$772$		0			0
$773$	1.13423e6	+	1.13423e6i	0.0682737	+	0.0682737i	0.740419	−	0.672145i	$-0.234627\pi$
$773$	1.13423e6	+	1.13423e6i	0.0682737	+	0.0682737i	−0.672145	+	0.740419i	$0.734627\pi$
$774$		0			0
$775$	−348424.	+	285680.i	−0.0208379	+	0.0170854i
$776$		0			0
$777$	−2.22249e7	−	2.22249e7i	−1.32065	−	1.32065i
$778$		0			0
$779$			4.02047e6i			0.237374i
$780$		0			0
$781$			1.42044e7i			0.833290i
$782$		0			0
$783$	1.59224e7	+	1.59224e7i	0.928121	+	0.928121i
$784$		0			0
$785$	7.55436e6	+	2.11281e7i	0.437546	+	1.22373i
$786$		0			0
$787$	−5.19263e6	−	5.19263e6i	−0.298848	−	0.298848i	0.541715	−	0.840563i	$-0.317775\pi$
$787$	−5.19263e6	−	5.19263e6i	−0.298848	−	0.298848i	−0.840563	+	0.541715i	$0.817775\pi$
$788$		0			0
$789$	−2.39668e7			−1.37062
$790$		0			0
$791$		−	1.27696e7i		−	0.725663i
$792$		0			0
$793$	−4.36263e6	+	4.36263e6i	−0.246357	+	0.246357i
$794$		0			0
$795$	−1.91460e6	+	4.04570e6i	−0.107438	+	0.227026i
$796$		0			0
$797$	−1.09058e7	+	1.09058e7i	−0.608154	+	0.608154i	−0.942463	−	0.334309i	$-0.891497\pi$
$797$	−1.09058e7	+	1.09058e7i	−0.608154	+	0.608154i	0.334309	+	0.942463i	$0.391497\pi$
$798$		0			0
$799$	−1.43294e7			−0.794075
$800$		0			0
$801$	−3.17770e6			−0.174997
$802$		0			0
$803$	1.19631e7	−	1.19631e7i	0.654717	−	0.654717i
$804$		0			0
$805$	−2.74983e6	+	5.81061e6i	−0.149560	+	0.316033i
$806$		0			0
$807$	5.10912e6	−	5.10912e6i	0.276161	−	0.276161i
$808$		0			0
$809$		−	6.21861e6i		−	0.334058i	−0.985952	−	0.167029i	$-0.946583\pi$
$809$		−	6.21861e6i		−	0.334058i	0.985952	−	0.167029i	$-0.0534174\pi$
$810$		0			0
$811$	7.23689e6			0.386367			0.193183	−	0.981163i	$-0.438119\pi$
$811$	7.23689e6			0.386367			0.193183	+	0.981163i	$0.438119\pi$
$812$		0			0
$813$	6.84814e6	+	6.84814e6i	0.363368	+	0.363368i
$814$		0			0
$815$	−7.94378e6	−	2.22172e7i	−0.418922	−	1.17164i
$816$		0			0
$817$	2.82138e6	+	2.82138e6i	0.147879	+	0.147879i
$818$		0			0
$819$			5.45983e6i			0.284426i
$820$		0			0
$821$		−	9.66191e6i		−	0.500271i	−0.968211	−	0.250135i	$-0.919525\pi$
$821$		−	9.66191e6i		−	0.500271i	0.968211	−	0.250135i	$-0.0804751\pi$
$822$		0			0
$823$	−1.66712e7	−	1.66712e7i	−0.857961	−	0.857961i	0.133137	−	0.991098i	$-0.457495\pi$
$823$	−1.66712e7	−	1.66712e7i	−0.857961	−	0.857961i	−0.991098	+	0.133137i	$0.957495\pi$
$824$		0			0
$825$	1.25539e7	+	1.24220e6i	0.642161	+	0.0635411i
$826$		0			0
$827$	1.31048e7	+	1.31048e7i	0.666297	+	0.666297i	0.956857	−	0.290560i	$-0.0938415\pi$
$827$	1.31048e7	+	1.31048e7i	0.666297	+	0.666297i	−0.290560	+	0.956857i	$0.593841\pi$
$828$		0			0
$829$	7.86602e6			0.397529			0.198764	−	0.980047i	$-0.436307\pi$
$829$	7.86602e6			0.397529			0.198764	+	0.980047i	$0.436307\pi$
$830$		0			0
$831$			2.61207e7i			1.31215i
$832$		0			0
$833$	753833.	−	753833.i	0.0376411	−	0.0376411i
$834$		0			0
$835$	−6.24077e6	−	1.74542e7i	−0.309758	−	0.866333i
$836$		0			0
$837$	−411243.	+	411243.i	−0.0202901	+	0.0202901i
$838$		0			0
$839$	−7.46126e6			−0.365938			−0.182969	−	0.983119i	$-0.558571\pi$
$839$	−7.46126e6			−0.365938			−0.182969	+	0.983119i	$0.558571\pi$
$840$		0			0
$841$	1.06521e7			0.519333
$842$		0			0
$843$	−1.39704e7	+	1.39704e7i	−0.677082	+	0.677082i
$844$		0			0
$845$	−3.06894e7	−	1.45235e7i	−1.47859	−	0.699729i
$846$		0			0
$847$	−7.79572e6	+	7.79572e6i	−0.373377	+	0.373377i
$848$		0			0
$849$			1.01903e7i			0.485195i
$850$		0			0
$851$	−1.35807e7			−0.642834
$852$		0			0
$853$	1.59287e7	+	1.59287e7i	0.749562	+	0.749562i	0.974397	−	0.224835i	$-0.0721844\pi$
$853$	1.59287e7	+	1.59287e7i	0.749562	+	0.749562i	−0.224835	+	0.974397i	$0.572184\pi$
$854$		0			0
$855$	326315.	−	689530.i	0.0152659	−	0.0322581i
$856$		0			0
$857$	4.57402e6	+	4.57402e6i	0.212738	+	0.212738i	0.805430	−	0.592691i	$-0.201935\pi$
$857$	4.57402e6	+	4.57402e6i	0.212738	+	0.212738i	−0.592691	+	0.805430i	$0.701935\pi$
$858$		0			0
$859$			1.72334e7i			0.796872i	0.917196	+	0.398436i	$0.130447\pi$
$859$			1.72334e7i			0.796872i	−0.917196	+	0.398436i	$0.869553\pi$
$860$		0			0
$861$			2.31467e7i			1.06410i
$862$		0			0
$863$	1.12321e6	+	1.12321e6i	0.0513373	+	0.0513373i	0.732309	−	0.680972i	$-0.238443\pi$
$863$	1.12321e6	+	1.12321e6i	0.0513373	+	0.0513373i	−0.680972	+	0.732309i	$0.738443\pi$
$864$		0			0
$865$	−9.79132e6	+	3.50089e6i	−0.444940	+	0.159088i
$866$		0			0
$867$	1.10865e7	+	1.10865e7i	0.500896	+	0.500896i
$868$		0			0
$869$	6.26546e6			0.281451
$870$		0			0
$871$		−	5.53532e7i		−	2.47228i
$872$		0			0
$873$	401351.	−	401351.i	0.0178233	−	0.0178233i
$874$		0			0
$875$	1.22940e7	−	2.04797e7i	0.542842	−	0.904283i
$876$		0			0
$877$	−5.11686e6	+	5.11686e6i	−0.224649	+	0.224649i	−0.810453	−	0.585804i	$-0.800779\pi$
$877$	−5.11686e6	+	5.11686e6i	−0.224649	+	0.224649i	0.585804	+	0.810453i	$0.300779\pi$
$878$		0			0
$879$	−7.22455e6			−0.315383
$880$		0			0
$881$	3.96052e6			0.171915			0.0859573	−	0.996299i	$-0.472605\pi$
$881$	3.96052e6			0.171915			0.0859573	+	0.996299i	$0.472605\pi$
$882$		0			0
$883$	1.32476e7	−	1.32476e7i	0.571790	−	0.571790i	−0.360838	−	0.932628i	$-0.617509\pi$
$883$	1.32476e7	−	1.32476e7i	0.571790	−	0.571790i	0.932628	+	0.360838i	$0.117509\pi$
$884$		0			0
$885$	1.29545e7	−	4.63187e6i	0.555982	−	0.198792i
$886$		0			0
$887$	2.58340e7	−	2.58340e7i	1.10251	−	1.10251i	0.108401	−	0.994107i	$-0.465427\pi$
$887$	2.58340e7	−	2.58340e7i	1.10251	−	1.10251i	0.994107	−	0.108401i	$-0.0345730\pi$
$888$		0			0
$889$		−	1.51635e7i		−	0.643494i
$890$		0			0
$891$	1.35020e7			0.569775
$892$		0			0
$893$	−6.07046e6	−	6.07046e6i	−0.254738	−	0.254738i
$894$		0			0
$895$	1.87016e7	+	8.85036e6i	0.780405	+	0.369321i
$896$		0			0
$897$	−8.37456e6	−	8.37456e6i	−0.347521	−	0.347521i
$898$		0			0
$899$			804882.i			0.0332149i
$900$		0			0
$901$		−	3.17401e6i		−	0.130256i
$902$		0			0
$903$	1.62433e7	+	1.62433e7i	0.662910	+	0.662910i
$904$		0			0
$905$	−2.39370e7	−	1.13280e7i	−0.971513	−	0.459761i
$906$		0			0
$907$	−1.97512e7	−	1.97512e7i	−0.797214	−	0.797214i	0.185441	−	0.982655i	$-0.440629\pi$
$907$	−1.97512e7	−	1.97512e7i	−0.797214	−	0.797214i	−0.982655	+	0.185441i	$0.940629\pi$
$908$		0			0
$909$	−1.40815e6			−0.0565248
$910$		0			0
$911$			1.40853e7i			0.562304i	0.959663	+	0.281152i	$0.0907165\pi$
$911$			1.40853e7i			0.562304i	−0.959663	+	0.281152i	$0.909284\pi$
$912$		0			0
$913$	−1.45586e7	+	1.45586e7i	−0.578021	+	0.578021i
$914$		0			0
$915$	4.67314e6	−	1.67088e6i	0.184525	−	0.0659771i
$916$		0			0
$917$	2.99503e7	−	2.99503e7i	1.17619	−	1.17619i
$918$		0			0
$919$	2.47354e7			0.966116			0.483058	−	0.875588i	$-0.339526\pi$
$919$	2.47354e7			0.966116			0.483058	+	0.875588i	$0.339526\pi$
$920$		0			0
$921$	1.61064e7			0.625677
$922$		0			0
$923$	−3.50378e7	+	3.50378e7i	−1.35373	+	1.35373i
$924$		0			0
$925$	5.02173e7	+	4.96895e6i	1.92974	+	0.190946i
$926$		0			0
$927$	3.02117e6	−	3.02117e6i	0.115472	−	0.115472i
$928$		0			0
$929$			1.69900e7i			0.645884i	0.946419	+	0.322942i	$0.104672\pi$
$929$			1.69900e7i			0.645884i	−0.946419	+	0.322942i	$0.895328\pi$
$930$		0			0
$931$	638702.			0.0241504
$932$		0			0
$933$	−1.40059e7	−	1.40059e7i	−0.526752	−	0.526752i
$934$		0			0
$935$	−8.42367e6	+	3.01189e6i	−0.315117	+	0.112670i
$936$		0			0
$937$	2.16683e7	+	2.16683e7i	0.806260	+	0.806260i	0.984066	−	0.177806i	$-0.0568998\pi$
$937$	2.16683e7	+	2.16683e7i	0.806260	+	0.806260i	−0.177806	+	0.984066i	$0.556900\pi$
$938$		0			0
$939$		−	1.47196e7i		−	0.544795i
$940$		0			0
$941$		−	5.14995e7i		−	1.89596i	−0.318331	−	0.947980i	$-0.603122\pi$
$941$		−	5.14995e7i		−	1.89596i	0.318331	−	0.947980i	$-0.396878\pi$
$942$		0			0
$943$	7.07200e6	+	7.07200e6i	0.258978	+	0.258978i
$944$		0			0
$945$	1.31888e7	−	2.78690e7i	0.480424	−	1.01518i
$946$		0			0
$947$	1.45885e7	+	1.45885e7i	0.528610	+	0.528610i	0.920158	−	0.391548i	$-0.128060\pi$
$947$	1.45885e7	+	1.45885e7i	0.528610	+	0.528610i	−0.391548	+	0.920158i	$0.628060\pi$
$948$		0			0
$949$	5.90182e7			2.12726
$950$		0			0
$951$			8.37134e6i			0.300154i
$952$		0			0
$953$	−1.66848e7	+	1.66848e7i	−0.595097	+	0.595097i	−0.939004	−	0.343907i	$-0.888250\pi$
$953$	−1.66848e7	+	1.66848e7i	−0.595097	+	0.595097i	0.343907	+	0.939004i	$0.388250\pi$
$954$		0			0
$955$	1.45021e7	+	6.86299e6i	0.514543	+	0.243503i
$956$		0			0
$957$	1.59350e7	−	1.59350e7i	0.562434	−	0.562434i
$958$		0			0
$959$	1.19884e7			0.420936
$960$		0			0
$961$	2.86084e7			0.999274
$962$		0			0
$963$	4.73532e6	−	4.73532e6i	0.164545	−	0.164545i
$964$		0			0
$965$	−1.04258e7	−	2.91589e7i	−0.360404	−	1.00798i
$966$		0			0
$967$	−7.09186e6	+	7.09186e6i	−0.243890	+	0.243890i	−0.818457	−	0.574567i	$-0.805170\pi$
$967$	−7.09186e6	+	7.09186e6i	−0.243890	+	0.243890i	0.574567	+	0.818457i	$0.305170\pi$
$968$		0			0
$969$		−	2.71579e6i		−	0.0929153i
$970$		0			0
$971$	−2.60523e7			−0.886742			−0.443371	−	0.896338i	$-0.646218\pi$
$971$	−2.60523e7			−0.886742			−0.443371	+	0.896338i	$0.646218\pi$
$972$		0			0
$973$	−1.10547e7	−	1.10547e7i	−0.374340	−	0.374340i
$974$		0			0
$975$	2.79024e7	+	3.40306e7i	0.940006	+	1.14646i
$976$		0			0
$977$	−2.40458e6	−	2.40458e6i	−0.0805939	−	0.0805939i	0.665661	−	0.746255i	$-0.268150\pi$
$977$	−2.40458e6	−	2.40458e6i	−0.0805939	−	0.0805939i	−0.746255	+	0.665661i	$0.768150\pi$
$978$		0			0
$979$			2.23260e7i			0.744481i
$980$		0			0
$981$			4.48847e6i			0.148911i
$982$		0			0
$983$	−2.99200e7	−	2.99200e7i	−0.987591	−	0.987591i	0.0123328	−	0.999924i	$-0.496074\pi$
$983$	−2.99200e7	−	2.99200e7i	−0.987591	−	0.987591i	−0.999924	+	0.0123328i	$0.996074\pi$
$984$		0			0
$985$	−1.82643e7	−	5.10817e7i	−0.599807	−	1.67755i
$986$		0			0
$987$	−3.49489e7	−	3.49489e7i	−1.14193	−	1.14193i
$988$		0			0
$989$	9.92561e6			0.322676
$990$		0			0
$991$			3.78149e7i			1.22315i	0.791187	+	0.611574i	$0.209463\pi$
$991$			3.78149e7i			1.22315i	−0.791187	+	0.611574i	$0.790537\pi$
$992$		0			0
$993$	−2.47895e7	+	2.47895e7i	−0.797800	+	0.797800i
$994$		0			0
$995$	1.85434e7	−	3.91837e7i	0.593787	−	1.25472i
$996$		0			0
$997$	1.28781e6	−	1.28781e6i	0.0410312	−	0.0410312i	−0.686294	−	0.727325i	$-0.740763\pi$
$997$	1.28781e6	−	1.28781e6i	0.0410312	−	0.0410312i	0.727325	+	0.686294i	$0.240763\pi$
$998$		0			0
$999$	6.51361e7			2.06494

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.6.o.a.47.9		56
4.3	odd	2		40.6.k.a.27.7	yes	56
5.3	odd	4	inner	160.6.o.a.143.10		56
8.3	odd	2	inner	160.6.o.a.47.10		56
8.5	even	2		40.6.k.a.27.9	yes	56
20.3	even	4		40.6.k.a.3.9	yes	56
40.3	even	4	inner	160.6.o.a.143.9		56
40.13	odd	4		40.6.k.a.3.7	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.k.a.3.7	✓	56	40.13	odd	4
40.6.k.a.3.9	yes	56	20.3	even	4
40.6.k.a.27.7	yes	56	4.3	odd	2
40.6.k.a.27.9	yes	56	8.5	even	2
160.6.o.a.47.9		56	1.1	even	1	trivial
160.6.o.a.47.10		56	8.3	odd	2	inner
160.6.o.a.143.9		56	40.3	even	4	inner
160.6.o.a.143.10		56	5.3	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	160.o (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-10.0657 + 10.0657i) q^{3} +(-23.9125 + 50.5291i) q^{5} +(96.6855 - 96.6855i) q^{7} +40.3635i q^{9} +O(q^{10})\)	\(q+(-10.0657 + 10.0657i) q^{3} +(-23.9125 + 50.5291i) q^{5} +(96.6855 - 96.6855i) q^{7} +40.3635i q^{9} +283.587 q^{11} +(699.519 + 699.519i) q^{13} +(-267.915 - 749.307i) q^{15} +(399.025 + 399.025i) q^{17} +338.083i q^{19} +1946.41i q^{21} +(594.687 + 594.687i) q^{23} +(-1981.38 - 2416.56i) q^{25} +(-2852.25 - 2852.25i) q^{27} -5582.41 q^{29} -144.182i q^{31} +(-2854.50 + 2854.50i) q^{33} +(2573.44 + 7197.43i) q^{35} +(-11418.4 + 11418.4i) q^{37} -14082.3 q^{39} +11892.0 q^{41} +(8345.23 - 8345.23i) q^{43} +(-2039.53 - 965.191i) q^{45} +(-17955.5 + 17955.5i) q^{47} -1889.19i q^{49} -8032.92 q^{51} +(-3977.21 - 3977.21i) q^{53} +(-6781.27 + 14329.4i) q^{55} +(-3403.04 - 3403.04i) q^{57} +17288.6i q^{59} +6236.61i q^{61} +(3902.56 + 3902.56i) q^{63} +(-52073.3 + 18618.8i) q^{65} +(-39565.2 - 39565.2i) q^{67} -11971.9 q^{69} +50088.5i q^{71} +(42184.8 - 42184.8i) q^{73} +(44268.3 + 4380.30i) q^{75} +(27418.7 - 27418.7i) q^{77} +22093.6 q^{79} +47611.5 q^{81} +(-51337.5 + 51337.5i) q^{83} +(-29704.0 + 10620.7i) q^{85} +(56190.8 - 56190.8i) q^{87} +78727.1i q^{89} +135267. q^{91} +(1451.29 + 1451.29i) q^{93} +(-17083.0 - 8084.41i) q^{95} +(-9943.42 - 9943.42i) q^{97} +11446.5i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{3}+O(q^{10}) \) 56 * q + 4 * q^3	\( 56 q + 4 q^{3} + 8 q^{11} - 408 q^{17} - 3120 q^{25} - 968 q^{27} - 976 q^{33} + 4780 q^{35} - 8 q^{41} - 1308 q^{43} - 20872 q^{51} + 968 q^{57} + 17680 q^{65} - 89252 q^{67} - 25184 q^{73} + 127740 q^{75} - 67792 q^{81} + 126444 q^{83} - 329432 q^{91} + 212576 q^{97}+O(q^{100}) \) 56 * q + 4 * q^3 + 8 * q^11 - 408 * q^17 - 3120 * q^25 - 968 * q^27 - 976 * q^33 + 4780 * q^35 - 8 * q^41 - 1308 * q^43 - 20872 * q^51 + 968 * q^57 + 17680 * q^65 - 89252 * q^67 - 25184 * q^73 + 127740 * q^75 - 67792 * q^81 + 126444 * q^83 - 329432 * q^91 + 212576 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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