LMFDB - Embedded newform 384.3.m.a.271.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,3,Mod(79,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("384.79");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	384.m (of order $8$, degree $4$, 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:	$10.4632421514$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			271.2
Character	$\chi$	$=$	384.271
Dual form			384.3.m.a.367.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.60021 + 0.662827i) q^{3} +(-7.00900 - 2.90322i) q^{5} +(-2.35957 + 2.35957i) q^{7} +(2.12132 - 2.12132i) q^{9} +O(q^{10})$	\(q+(-1.60021 + 0.662827i) q^{3} +(-7.00900 - 2.90322i) q^{5} +(-2.35957 + 2.35957i) q^{7} +(2.12132 - 2.12132i) q^{9} +(-12.1899 - 5.04924i) q^{11} +(23.4042 - 9.69435i) q^{13} +13.1402 q^{15} +25.7007i q^{17} +(2.32569 + 5.61471i) q^{19} +(2.21181 - 5.33978i) q^{21} +(23.2058 + 23.2058i) q^{23} +(23.0197 + 23.0197i) q^{25} +(-1.98848 + 4.80062i) q^{27} +(-1.15484 - 2.78802i) q^{29} -28.2967i q^{31} +22.8532 q^{33} +(23.3885 - 9.68784i) q^{35} +(34.9633 + 14.4823i) q^{37} +(-31.0259 + 31.0259i) q^{39} +(10.1415 - 10.1415i) q^{41} +(22.8453 + 9.46285i) q^{43} +(-21.0270 + 8.70966i) q^{45} +11.2848 q^{47} +37.8649i q^{49} +(-17.0351 - 41.1265i) q^{51} +(1.71282 - 4.13510i) q^{53} +(70.7802 + 70.7802i) q^{55} +(-7.44317 - 7.44317i) q^{57} +(-14.3649 + 34.6800i) q^{59} +(-0.574221 - 1.38629i) q^{61} +10.0108i q^{63} -192.185 q^{65} +(-2.88669 + 1.19571i) q^{67} +(-52.5156 - 21.7527i) q^{69} +(82.7570 - 82.7570i) q^{71} +(6.80099 - 6.80099i) q^{73} +(-52.0942 - 21.5781i) q^{75} +(40.6770 - 16.8490i) q^{77} +58.6268 q^{79} -9.00000i q^{81} +(6.99463 + 16.8865i) q^{83} +(74.6149 - 180.136i) q^{85} +(3.69595 + 3.69595i) q^{87} +(85.6528 + 85.6528i) q^{89} +(-32.3494 + 78.0983i) q^{91} +(18.7558 + 45.2806i) q^{93} -46.1055i q^{95} +19.1537 q^{97} +(-36.5698 + 15.1477i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q - 128 q^{23} + 192 q^{35} + 192 q^{43} + 192 q^{51} + 320 q^{53} + 256 q^{55} + 256 q^{59} + 64 q^{61} - 64 q^{67} - 192 q^{69} - 512 q^{71} - 384 q^{75} - 448 q^{77} - 512 q^{79} - 192 q^{91}+O(q^{100}) $ 64 * q - 128 * q^23 + 192 * q^35 + 192 * q^43 + 192 * q^51 + 320 * q^53 + 256 * q^55 + 256 * q^59 + 64 * q^61 - 64 * q^67 - 192 * q^69 - 512 * q^71 - 384 * q^75 - 448 * q^77 - 512 * q^79 - 192 * q^91

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$e\left(\frac{1}{8}\right)$	$1$

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
$3$	−1.60021	+	0.662827i	−0.533402	+	0.220942i
$3$	−1.60021	+	0.662827i	−0.533402	+	0.220942i
$4$		0			0
$5$	−7.00900	−	2.90322i	−1.40180	−	0.580644i	−0.451581	−	0.892230i	$-0.649140\pi$
$5$	−7.00900	−	2.90322i	−1.40180	−	0.580644i	−0.950218	+	0.311586i	$0.899140\pi$
$6$		0			0
$7$	−2.35957	+	2.35957i	−0.337081	+	0.337081i	−0.855268	−	0.518187i	$-0.826607\pi$
$7$	−2.35957	+	2.35957i	−0.337081	+	0.337081i	0.518187	+	0.855268i	$0.326607\pi$
$8$		0			0
$9$	2.12132	−	2.12132i	0.235702	−	0.235702i
$10$		0			0
$11$	−12.1899	−	5.04924i	−1.10818	−	0.459022i	−0.247867	−	0.968794i	$-0.579730\pi$
$11$	−12.1899	−	5.04924i	−1.10818	−	0.459022i	−0.860310	+	0.509772i	$0.829730\pi$
$12$		0			0
$13$	23.4042	−	9.69435i	1.80033	−	0.745719i	0.814010	−	0.580850i	$-0.197280\pi$
$13$	23.4042	−	9.69435i	1.80033	−	0.745719i	0.986315	−	0.164869i	$-0.0527202\pi$
$14$		0			0
$15$	13.1402			0.876011
$16$		0			0
$17$			25.7007i			1.51181i	0.654682	+	0.755904i	$0.272802\pi$
$17$			25.7007i			1.51181i	−0.654682	+	0.755904i	$0.727198\pi$
$18$		0			0
$19$	2.32569	+	5.61471i	0.122405	+	0.295511i	0.973190	−	0.230002i	$-0.0738733\pi$
$19$	2.32569	+	5.61471i	0.122405	+	0.295511i	−0.850785	+	0.525513i	$0.823873\pi$
$20$		0			0
$21$	2.21181	−	5.33978i	0.105324	−	0.254275i
$22$		0			0
$23$	23.2058	+	23.2058i	1.00895	+	1.00895i	0.999960	+	0.00898919i	$0.00286139\pi$
$23$	23.2058	+	23.2058i	1.00895	+	1.00895i	0.00898919	+	0.999960i	$0.497139\pi$
$24$		0			0
$25$	23.0197	+	23.0197i	0.920786	+	0.920786i
$26$		0			0
$27$	−1.98848	+	4.80062i	−0.0736475	+	0.177801i
$28$		0			0
$29$	−1.15484	−	2.78802i	−0.0398219	−	0.0961386i	0.902717	−	0.430234i	$-0.141569\pi$
$29$	−1.15484	−	2.78802i	−0.0398219	−	0.0961386i	−0.942539	+	0.334096i	$0.891569\pi$
$30$		0			0
$31$		−	28.2967i		−	0.912798i	−0.889775	−	0.456399i	$-0.849139\pi$
$31$		−	28.2967i		−	0.912798i	0.889775	−	0.456399i	$-0.150861\pi$
$32$		0			0
$33$	22.8532			0.692521
$34$		0			0
$35$	23.3885	−	9.68784i	0.668244	−	0.276796i
$36$		0			0
$37$	34.9633	+	14.4823i	0.944953	+	0.391412i	0.801332	−	0.598220i	$-0.204125\pi$
$37$	34.9633	+	14.4823i	0.944953	+	0.391412i	0.143621	+	0.989633i	$0.454125\pi$
$38$		0			0
$39$	−31.0259	+	31.0259i	−0.795537	+	0.795537i
$40$		0			0
$41$	10.1415	−	10.1415i	0.247353	−	0.247353i	−0.572531	−	0.819883i	$-0.694038\pi$
$41$	10.1415	−	10.1415i	0.247353	−	0.247353i	0.819883	+	0.572531i	$0.194038\pi$
$42$		0			0
$43$	22.8453	+	9.46285i	0.531287	+	0.220066i	0.632167	−	0.774832i	$-0.282166\pi$
$43$	22.8453	+	9.46285i	0.531287	+	0.220066i	−0.100880	+	0.994899i	$0.532166\pi$
$44$		0			0
$45$	−21.0270	+	8.70966i	−0.467266	+	0.193548i
$46$		0			0
$47$	11.2848			0.240102			0.120051	−	0.992768i	$-0.461694\pi$
$47$	11.2848			0.240102			0.120051	+	0.992768i	$0.461694\pi$
$48$		0			0
$49$			37.8649i			0.772753i
$50$		0			0
$51$	−17.0351	−	41.1265i	−0.334023	−	0.806402i
$52$		0			0
$53$	1.71282	−	4.13510i	0.0323173	−	0.0780208i	−0.906897	−	0.421353i	$-0.861556\pi$
$53$	1.71282	−	4.13510i	0.0323173	−	0.0780208i	0.939214	+	0.343332i	$0.111556\pi$
$54$		0			0
$55$	70.7802	+	70.7802i	1.28691	+	1.28691i
$56$		0			0
$57$	−7.44317	−	7.44317i	−0.130582	−	0.130582i
$58$		0			0
$59$	−14.3649	+	34.6800i	−0.243473	+	0.587797i	−0.997623	−	0.0689057i	$-0.978049\pi$
$59$	−14.3649	+	34.6800i	−0.243473	+	0.587797i	0.754150	+	0.656702i	$0.228049\pi$
$60$		0			0
$61$	−0.574221	−	1.38629i	−0.00941347	−	0.0227261i	0.919103	−	0.394018i	$-0.128915\pi$
$61$	−0.574221	−	1.38629i	−0.00941347	−	0.0227261i	−0.928516	+	0.371291i	$0.878915\pi$
$62$		0			0
$63$			10.0108i			0.158901i
$64$		0			0
$65$	−192.185			−2.95669
$66$		0			0
$67$	−2.88669	+	1.19571i	−0.0430849	+	0.0178464i	−0.404122	−	0.914705i	$-0.632423\pi$
$67$	−2.88669	+	1.19571i	−0.0430849	+	0.0178464i	0.361037	+	0.932552i	$0.382423\pi$
$68$		0			0
$69$	−52.5156	−	21.7527i	−0.761095	−	0.315256i
$70$		0			0
$71$	82.7570	−	82.7570i	1.16559	−	1.16559i	0.182360	−	0.983232i	$-0.441626\pi$
$71$	82.7570	−	82.7570i	1.16559	−	1.16559i	0.983232	−	0.182360i	$-0.0583736\pi$
$72$		0			0
$73$	6.80099	−	6.80099i	0.0931643	−	0.0931643i	−0.658989	−	0.752153i	$-0.729015\pi$
$73$	6.80099	−	6.80099i	0.0931643	−	0.0931643i	0.752153	+	0.658989i	$0.229015\pi$
$74$		0			0
$75$	−52.0942	−	21.5781i	−0.694590	−	0.287709i
$76$		0			0
$77$	40.6770	−	16.8490i	0.528273	−	0.218818i
$78$		0			0
$79$	58.6268			0.742111			0.371056	−	0.928611i	$-0.378996\pi$
$79$	58.6268			0.742111			0.371056	+	0.928611i	$0.378996\pi$
$80$		0			0
$81$		−	9.00000i		−	0.111111i
$82$		0			0
$83$	6.99463	+	16.8865i	0.0842726	+	0.203452i	0.960398	−	0.278631i	$-0.0898805\pi$
$83$	6.99463	+	16.8865i	0.0842726	+	0.203452i	−0.876126	+	0.482083i	$0.839880\pi$
$84$		0			0
$85$	74.6149	−	180.136i	0.877823	−	2.11925i
$86$		0			0
$87$	3.69595	+	3.69595i	0.0424822	+	0.0424822i
$88$		0			0
$89$	85.6528	+	85.6528i	0.962391	+	0.962391i	0.999318	−	0.0369265i	$-0.0117567\pi$
$89$	85.6528	+	85.6528i	0.962391	+	0.962391i	−0.0369265	+	0.999318i	$0.511757\pi$
$90$		0			0
$91$	−32.3494	+	78.0983i	−0.355488	+	0.858223i
$92$		0			0
$93$	18.7558	+	45.2806i	0.201676	+	0.486888i
$94$		0			0
$95$		−	46.1055i		−	0.485321i
$96$		0			0
$97$	19.1537			0.197461			0.0987305	−	0.995114i	$-0.468522\pi$
$97$	19.1537			0.197461			0.0987305	+	0.995114i	$0.468522\pi$
$98$		0			0
$99$	−36.5698	+	15.1477i	−0.369392	+	0.153007i
$100$		0			0
$101$	12.1412	+	5.02904i	0.120210	+	0.0497924i	0.441978	−	0.897026i	$-0.354277\pi$
$101$	12.1412	+	5.02904i	0.120210	+	0.0497924i	−0.321768	+	0.946819i	$0.604277\pi$
$102$		0			0
$103$	2.43859	−	2.43859i	0.0236756	−	0.0236756i	−0.695170	−	0.718845i	$-0.744671\pi$
$103$	2.43859	−	2.43859i	0.0236756	−	0.0236756i	0.718845	+	0.695170i	$0.244671\pi$
$104$		0			0
$105$	−31.0051	+	31.0051i	−0.295287	+	0.295287i
$106$		0			0
$107$	−153.093	−	63.4133i	−1.43078	−	0.592648i	−0.473235	−	0.880936i	$-0.656914\pi$
$107$	−153.093	−	63.4133i	−1.43078	−	0.592648i	−0.957544	+	0.288288i	$0.906914\pi$
$108$		0			0
$109$	−152.961	+	63.3585i	−1.40331	+	0.581271i	−0.950609	−	0.310391i	$-0.899540\pi$
$109$	−152.961	+	63.3585i	−1.40331	+	0.581271i	−0.452703	+	0.891662i	$0.649540\pi$
$110$		0			0
$111$	−65.5477			−0.590520
$112$		0			0
$113$		−	78.9572i		−	0.698736i	−0.936986	−	0.349368i	$-0.886396\pi$
$113$		−	78.9572i		−	0.698736i	0.936986	−	0.349368i	$-0.113604\pi$
$114$		0			0
$115$	−95.2779	−	230.021i	−0.828503	−	2.00018i
$116$		0			0
$117$	29.0831	−	70.2127i	0.248573	−	0.600109i
$118$		0			0
$119$	−60.6426	−	60.6426i	−0.509602	−	0.509602i
$120$		0			0
$121$	37.5400	+	37.5400i	0.310248	+	0.310248i
$122$		0			0
$123$	−9.50639	+	22.9505i	−0.0772877	+	0.186589i
$124$		0			0
$125$	−21.9330	−	52.9509i	−0.175464	−	0.423607i
$126$		0			0
$127$		−	2.13791i		−	0.0168340i	−0.999965	−	0.00841698i	$-0.997321\pi$
$127$		−	2.13791i		−	0.0168340i	0.999965	−	0.00841698i	$-0.00267924\pi$
$128$		0			0
$129$	−42.8295			−0.332012
$130$		0			0
$131$	−25.8459	+	10.7057i	−0.197297	+	0.0817232i	−0.479144	−	0.877736i	$-0.659053\pi$
$131$	−25.8459	+	10.7057i	−0.197297	+	0.0817232i	0.281847	+	0.959459i	$0.409053\pi$
$132$		0			0
$133$	−18.7359	−	7.76067i	−0.140871	−	0.0583509i
$134$		0			0
$135$	27.8745	−	27.8745i	0.206478	−	0.206478i
$136$		0			0
$137$	−110.083	+	110.083i	−0.803527	+	0.803527i	−0.983645	−	0.180118i	$-0.942352\pi$
$137$	−110.083	+	110.083i	−0.803527	+	0.803527i	0.180118	+	0.983645i	$0.442352\pi$
$138$		0			0
$139$	28.9934	+	12.0094i	0.208585	+	0.0863989i	0.484530	−	0.874775i	$-0.338991\pi$
$139$	28.9934	+	12.0094i	0.208585	+	0.0863989i	−0.275945	+	0.961174i	$0.588991\pi$
$140$		0			0
$141$	−18.0580	+	7.47988i	−0.128071	+	0.0530488i
$142$		0			0
$143$	−334.246			−2.33738
$144$		0			0
$145$			22.8939i			0.157889i
$146$		0			0
$147$	−25.0979	−	60.5917i	−0.170734	−	0.412188i
$148$		0			0
$149$	56.7824	−	137.085i	0.381090	−	0.920033i	−0.610665	−	0.791889i	$-0.709098\pi$
$149$	56.7824	−	137.085i	0.381090	−	0.920033i	0.991756	−	0.128144i	$-0.0409020\pi$
$150$		0			0
$151$	189.419	+	189.419i	1.25443	+	1.25443i	0.953713	+	0.300718i	$0.0972264\pi$
$151$	189.419	+	189.419i	1.25443	+	1.25443i	0.300718	+	0.953713i	$0.402774\pi$
$152$		0			0
$153$	54.5195	+	54.5195i	0.356337	+	0.356337i
$154$		0			0
$155$	−82.1516	+	198.332i	−0.530011	+	1.27956i
$156$		0			0
$157$	81.6229	+	197.055i	0.519891	+	1.25513i	0.937970	+	0.346717i	$0.112703\pi$
$157$	81.6229	+	197.055i	0.519891	+	1.25513i	−0.418079	+	0.908411i	$0.637297\pi$
$158$		0			0
$159$			7.75232i			0.0487567i
$160$		0			0
$161$	−109.511			−0.680195
$162$		0			0
$163$	158.728	−	65.7474i	0.973792	−	0.403358i	0.161670	−	0.986845i	$-0.448312\pi$
$163$	158.728	−	65.7474i	0.973792	−	0.403358i	0.812123	+	0.583487i	$0.198312\pi$
$164$		0			0
$165$	−160.178	−	66.3479i	−0.970776	−	0.402108i
$166$		0			0
$167$	−41.5433	+	41.5433i	−0.248762	+	0.248762i	−0.820463	−	0.571700i	$-0.806284\pi$
$167$	−41.5433	+	41.5433i	−0.248762	+	0.248762i	0.571700	+	0.820463i	$0.306284\pi$
$168$		0			0
$169$	334.277	−	334.277i	1.97797	−	1.97797i
$170$		0			0
$171$	16.8441	+	6.97707i	0.0985037	+	0.0408016i
$172$		0			0
$173$	91.1085	−	37.7384i	0.526639	−	0.218141i	−0.103492	−	0.994630i	$-0.533002\pi$
$173$	91.1085	−	37.7384i	0.526639	−	0.218141i	0.630130	+	0.776489i	$0.283002\pi$
$174$		0			0
$175$	−108.633			−0.620759
$176$		0			0
$177$		−	65.0166i		−	0.367326i
$178$		0			0
$179$	125.736	+	303.554i	0.702436	+	1.69583i	0.718088	+	0.695952i	$0.245017\pi$
$179$	125.736	+	303.554i	0.702436	+	1.69583i	−0.0156525	+	0.999877i	$0.504983\pi$
$180$		0			0
$181$	−76.2312	+	184.038i	−0.421167	+	1.01679i	0.560837	+	0.827926i	$0.310479\pi$
$181$	−76.2312	+	184.038i	−0.421167	+	1.01679i	−0.982004	+	0.188861i	$0.939521\pi$
$182$		0			0
$183$	1.83775	+	1.83775i	0.0100423	+	0.0100423i
$184$		0			0
$185$	−203.012	−	203.012i	−1.09736	−	1.09736i
$186$		0			0
$187$	129.769	−	313.291i	0.693953	−	1.67535i
$188$		0			0
$189$	−6.63542	−	16.0193i	−0.0351081	−	0.0847583i
$190$		0			0
$191$		−	201.527i		−	1.05511i	−0.849520	−	0.527556i	$-0.823108\pi$
$191$		−	201.527i		−	1.05511i	0.849520	−	0.527556i	$-0.176892\pi$
$192$		0			0
$193$	2.68950			0.0139352			0.00696761	−	0.999976i	$-0.497782\pi$
$193$	2.68950			0.0139352			0.00696761	+	0.999976i	$0.497782\pi$
$194$		0			0
$195$	307.536	−	127.385i	1.57711	−	0.653259i
$196$		0			0
$197$	−6.97702	−	2.88997i	−0.0354163	−	0.0146699i	0.364905	−	0.931045i	$-0.381101\pi$
$197$	−6.97702	−	2.88997i	−0.0354163	−	0.0146699i	−0.400321	+	0.916375i	$0.631101\pi$
$198$		0			0
$199$	−178.829	+	178.829i	−0.898639	+	0.898639i	−0.995316	−	0.0966766i	$-0.969179\pi$
$199$	−178.829	+	178.829i	−0.898639	+	0.898639i	0.0966766	+	0.995316i	$0.469179\pi$
$200$		0			0
$201$	3.82675	−	3.82675i	0.0190386	−	0.0190386i
$202$		0			0
$203$	9.30342	+	3.85360i	0.0458297	+	0.0189833i
$204$		0			0
$205$	−100.524	+	41.6385i	−0.490362	+	0.203115i
$206$		0			0
$207$	98.4540			0.475623
$208$		0			0
$209$		−	80.1860i		−	0.383665i
$210$		0			0
$211$	111.432	+	269.022i	0.528116	+	1.27498i	0.932756	+	0.360508i	$0.117397\pi$
$211$	111.432	+	269.022i	0.528116	+	1.27498i	−0.404640	+	0.914476i	$0.632603\pi$
$212$		0			0
$213$	−77.5747	+	187.282i	−0.364200	+	0.879258i
$214$		0			0
$215$	−132.650	−	132.650i	−0.616977	−	0.616977i
$216$		0			0
$217$	66.7680	+	66.7680i	0.307687	+	0.307687i
$218$		0			0
$219$	−6.37511	+	15.3909i	−0.0291101	+	0.0702780i
$220$		0			0
$221$	249.152	+	601.506i	1.12738	+	2.72175i
$222$		0			0
$223$		−	303.282i		−	1.36001i	−0.733208	−	0.680005i	$-0.761978\pi$
$223$		−	303.282i		−	1.36001i	0.733208	−	0.680005i	$-0.238022\pi$
$224$		0			0
$225$	97.6641			0.434063
$226$		0			0
$227$	345.922	−	143.286i	1.52389	−	0.631214i	0.545520	−	0.838098i	$-0.316332\pi$
$227$	345.922	−	143.286i	1.52389	−	0.631214i	0.978365	+	0.206884i	$0.0663323\pi$
$228$		0			0
$229$	−115.129	−	47.6879i	−0.502746	−	0.208244i	0.116873	−	0.993147i	$-0.462713\pi$
$229$	−115.129	−	47.6879i	−0.502746	−	0.208244i	−0.619619	+	0.784903i	$0.712713\pi$
$230$		0			0
$231$	−53.9236	+	53.9236i	−0.233436	+	0.233436i
$232$		0			0
$233$	23.5752	−	23.5752i	0.101181	−	0.101181i	−0.654704	−	0.755885i	$-0.727207\pi$
$233$	23.5752	−	23.5752i	0.101181	−	0.101181i	0.755885	+	0.654704i	$0.227207\pi$
$234$		0			0
$235$	−79.0952	−	32.7623i	−0.336575	−	0.139414i
$236$		0			0
$237$	−93.8149	+	38.8594i	−0.395844	+	0.163964i
$238$		0			0
$239$	381.999			1.59832			0.799161	−	0.601118i	$-0.205278\pi$
$239$	381.999			1.59832			0.799161	+	0.601118i	$0.205278\pi$
$240$		0			0
$241$			262.698i			1.09003i	0.838425	+	0.545017i	$0.183477\pi$
$241$			262.698i			1.09003i	−0.838425	+	0.545017i	$0.816523\pi$
$242$		0			0
$243$	5.96544	+	14.4019i	0.0245492	+	0.0592669i
$244$		0			0
$245$	109.930	−	265.395i	0.448695	−	1.08324i
$246$		0			0
$247$	108.862	+	108.862i	0.440737	+	0.440737i
$248$		0			0
$249$	−22.3857	−	22.3857i	−0.0899024	−	0.0899024i
$250$		0			0
$251$	−150.886	+	364.271i	−0.601140	+	1.45128i	0.271270	+	0.962503i	$0.412556\pi$
$251$	−150.886	+	364.271i	−0.601140	+	1.45128i	−0.872409	+	0.488776i	$0.837444\pi$
$252$		0			0
$253$	−165.706	−	400.050i	−0.654964	−	1.58122i
$254$		0			0
$255$			337.712i			1.32436i
$256$		0			0
$257$	232.141			0.903273			0.451636	−	0.892202i	$-0.350840\pi$
$257$	232.141			0.903273			0.451636	+	0.892202i	$0.350840\pi$
$258$		0			0
$259$	−116.670	+	48.3263i	−0.450463	+	0.186588i
$260$		0			0
$261$	−8.36406	−	3.46451i	−0.0320462	−	0.0132740i
$262$		0			0
$263$	51.8767	−	51.8767i	0.197250	−	0.197250i	−0.601570	−	0.798820i	$-0.705458\pi$
$263$	51.8767	−	51.8767i	0.197250	−	0.197250i	0.798820	+	0.601570i	$0.205458\pi$
$264$		0			0
$265$	−24.0102	+	24.0102i	−0.0906047	+	0.0906047i
$266$		0			0
$267$	−193.835	−	80.2892i	−0.725975	−	0.300709i
$268$		0			0
$269$	157.161	−	65.0980i	0.584240	−	0.242000i	−0.0709304	−	0.997481i	$-0.522597\pi$
$269$	157.161	−	65.0980i	0.584240	−	0.242000i	0.655170	+	0.755481i	$0.272597\pi$
$270$		0			0
$271$	−312.143			−1.15182			−0.575910	−	0.817513i	$-0.695352\pi$
$271$	−312.143			−1.15182			−0.575910	+	0.817513i	$0.695352\pi$
$272$		0			0
$273$		−	146.415i		−	0.536320i
$274$		0			0
$275$	−164.377	−	396.840i	−0.597733	−	1.44306i
$276$		0			0
$277$	−118.178	+	285.308i	−0.426636	+	1.02999i	0.553710	+	0.832709i	$0.313211\pi$
$277$	−118.178	+	285.308i	−0.426636	+	1.02999i	−0.980347	+	0.197282i	$0.936789\pi$
$278$		0			0
$279$	−60.0264	−	60.0264i	−0.215148	−	0.215148i
$280$		0			0
$281$	97.5918	+	97.5918i	0.347302	+	0.347302i	0.859104	−	0.511802i	$-0.171022\pi$
$281$	97.5918	+	97.5918i	0.347302	+	0.347302i	−0.511802	+	0.859104i	$0.671022\pi$
$282$		0			0
$283$	−18.5403	+	44.7603i	−0.0655135	+	0.158164i	−0.953245	−	0.302197i	$-0.902280\pi$
$283$	−18.5403	+	44.7603i	−0.0655135	+	0.158164i	0.887732	+	0.460361i	$0.152280\pi$
$284$		0			0
$285$	30.5600	+	73.7783i	0.107228	+	0.258871i
$286$		0			0
$287$			47.8589i			0.166756i
$288$		0			0
$289$	−371.528			−1.28556
$290$		0			0
$291$	−30.6499	+	12.6956i	−0.105326	+	0.0436275i
$292$		0			0
$293$	161.620	+	66.9453i	0.551605	+	0.228482i	0.641036	−	0.767511i	$-0.278505\pi$
$293$	161.620	+	66.9453i	0.551605	+	0.228482i	−0.0894312	+	0.995993i	$0.528505\pi$
$294$		0			0
$295$	201.367	−	201.367i	0.682602	−	0.682602i
$296$		0			0
$297$	48.4790	−	48.4790i	0.163229	−	0.163229i
$298$		0			0
$299$	768.080	+	318.149i	2.56883	+	1.06404i
$300$		0			0
$301$	−76.2333	+	31.5769i	−0.253267	+	0.104907i
$302$		0			0
$303$	−22.7618			−0.0751213
$304$		0			0
$305$			11.3836i			0.0373233i
$306$		0			0
$307$	105.523	+	254.755i	0.343724	+	0.829822i	0.997333	+	0.0729899i	$0.0232541\pi$
$307$	105.523	+	254.755i	0.343724	+	0.829822i	−0.653609	+	0.756832i	$0.726746\pi$
$308$		0			0
$309$	−2.28588	+	5.51861i	−0.00739768	+	0.0178596i
$310$		0			0
$311$	43.9499	+	43.9499i	0.141318	+	0.141318i	0.774227	−	0.632909i	$-0.218139\pi$
$311$	43.9499	+	43.9499i	0.141318	+	0.141318i	−0.632909	+	0.774227i	$0.718139\pi$
$312$		0			0
$313$	−121.839	−	121.839i	−0.389261	−	0.389261i	0.485163	−	0.874424i	$-0.338760\pi$
$313$	−121.839	−	121.839i	−0.389261	−	0.389261i	−0.874424	+	0.485163i	$0.838760\pi$
$314$		0			0
$315$	29.0635	−	70.1656i	0.0922652	−	0.222748i
$316$		0			0
$317$	1.63885	+	3.95654i	0.00516988	+	0.0124812i	0.926443	−	0.376434i	$-0.122850\pi$
$317$	1.63885	+	3.95654i	0.00516988	+	0.0124812i	−0.921274	+	0.388915i	$0.872850\pi$
$318$		0			0
$319$			39.8168i			0.124818i
$320$		0			0
$321$	287.013			0.894122
$322$		0			0
$323$	−144.302	+	59.7720i	−0.446756	+	0.185053i
$324$		0			0
$325$	761.918	+	315.597i	2.34436	+	0.971067i
$326$		0			0
$327$	202.773	−	202.773i	0.620102	−	0.620102i
$328$		0			0
$329$	−26.6273	+	26.6273i	−0.0809339	+	0.0809339i
$330$		0			0
$331$	481.638	+	199.501i	1.45510	+	0.602722i	0.963406	−	0.268046i	$-0.0863779\pi$
$331$	481.638	+	199.501i	1.45510	+	0.602722i	0.491694	+	0.870768i	$0.336378\pi$
$332$		0			0
$333$	104.890	−	43.4468i	0.314984	−	0.130471i
$334$		0			0
$335$	23.7042			0.0707588
$336$		0			0
$337$		−	321.444i		−	0.953840i	−0.878947	−	0.476920i	$-0.841753\pi$
$337$		−	321.444i		−	0.953840i	0.878947	−	0.476920i	$-0.158247\pi$
$338$		0			0
$339$	52.3350	+	126.348i	0.154380	+	0.372707i
$340$		0			0
$341$	−142.877	+	344.936i	−0.418994	+	1.01154i
$342$		0			0
$343$	−204.963	−	204.963i	−0.597561	−	0.597561i
$344$		0			0
$345$	304.928	+	304.928i	0.883851	+	0.883851i
$346$		0			0
$347$	19.7482	−	47.6765i	0.0569113	−	0.137396i	−0.892866	−	0.450322i	$-0.851309\pi$
$347$	19.7482	−	47.6765i	0.0569113	−	0.137396i	0.949778	+	0.312926i	$0.101309\pi$
$348$		0			0
$349$	−67.7422	−	163.544i	−0.194104	−	0.468608i	0.796623	−	0.604476i	$-0.206618\pi$
$349$	−67.7422	−	163.544i	−0.194104	−	0.468608i	−0.990727	+	0.135868i	$0.956618\pi$
$350$		0			0
$351$			131.632i			0.375020i
$352$		0			0
$353$	325.836			0.923047			0.461524	−	0.887128i	$-0.347303\pi$
$353$	325.836			0.923047			0.461524	+	0.887128i	$0.347303\pi$
$354$		0			0
$355$	−820.305	+	339.782i	−2.31072	+	0.957131i
$356$		0			0
$357$	137.236	+	56.8451i	0.384415	+	0.159230i
$358$		0			0
$359$	−151.423	+	151.423i	−0.421790	+	0.421790i	−0.885820	−	0.464030i	$-0.846403\pi$
$359$	−151.423	+	151.423i	−0.421790	+	0.421790i	0.464030	+	0.885820i	$0.346403\pi$
$360$		0			0
$361$	229.149	−	229.149i	0.634763	−	0.634763i
$362$		0			0
$363$	−84.9544	−	35.1893i	−0.234034	−	0.0969401i
$364$		0			0
$365$	−67.4129	+	27.9233i	−0.184693	+	0.0765023i
$366$		0			0
$367$	−169.180			−0.460980			−0.230490	−	0.973075i	$-0.574033\pi$
$367$	−169.180			−0.460980			−0.230490	+	0.973075i	$0.574033\pi$
$368$		0			0
$369$		−	43.0266i		−	0.116603i
$370$		0			0
$371$	5.71555	+	13.7986i	0.0154058	+	0.0371929i
$372$		0			0
$373$	81.3001	−	196.276i	0.217963	−	0.526209i	−0.776642	−	0.629942i	$-0.783079\pi$
$373$	81.3001	−	196.276i	0.217963	−	0.526209i	0.994605	+	0.103733i	$0.0330787\pi$
$374$		0			0
$375$	70.1946	+	70.1946i	0.187186	+	0.187186i
$376$		0			0
$377$	−54.0561	−	54.0561i	−0.143385	−	0.143385i
$378$		0			0
$379$	176.519	−	426.154i	0.465749	−	1.12442i	−0.500252	−	0.865880i	$-0.666759\pi$
$379$	176.519	−	426.154i	0.465749	−	1.12442i	0.966001	−	0.258538i	$-0.0832406\pi$
$380$		0			0
$381$	1.41707	+	3.42110i	0.00371933	+	0.00897927i
$382$		0			0
$383$		−	111.777i		−	0.291847i	−0.989296	−	0.145923i	$-0.953385\pi$
$383$		−	111.777i		−	0.291847i	0.989296	−	0.145923i	$-0.0466153\pi$
$384$		0			0
$385$	−334.021			−0.867587
$386$		0			0
$387$	68.5360	−	28.3885i	0.177096	−	0.0733554i
$388$		0			0
$389$	−345.181	−	142.979i	−0.887355	−	0.367554i	−0.108010	−	0.994150i	$-0.534448\pi$
$389$	−345.181	−	142.979i	−0.887355	−	0.367554i	−0.779345	+	0.626595i	$0.784448\pi$
$390$		0			0
$391$	−596.407	+	596.407i	−1.52534	+	1.52534i
$392$		0			0
$393$	34.2628	−	34.2628i	0.0871826	−	0.0871826i
$394$		0			0
$395$	−410.915	−	170.206i	−1.04029	−	0.430902i
$396$		0			0
$397$	−507.186	+	210.083i	−1.27755	+	0.529177i	−0.915250	−	0.402886i	$-0.868007\pi$
$397$	−507.186	+	210.083i	−1.27755	+	0.529177i	−0.362296	+	0.932063i	$0.618007\pi$
$398$		0			0
$399$	35.1253			0.0880333
$400$		0			0
$401$		−	445.754i		−	1.11160i	−0.831314	−	0.555802i	$-0.812411\pi$
$401$		−	445.754i		−	1.11160i	0.831314	−	0.555802i	$-0.187589\pi$
$402$		0			0
$403$	−274.318	−	662.263i	−0.680691	−	1.64333i
$404$		0			0
$405$	−26.1290	+	63.0810i	−0.0645160	+	0.155755i
$406$		0			0
$407$	−353.076	−	353.076i	−0.867508	−	0.867508i
$408$		0			0
$409$	−380.306	−	380.306i	−0.929845	−	0.929845i	0.0678508	−	0.997695i	$-0.478386\pi$
$409$	−380.306	−	380.306i	−0.929845	−	0.929845i	−0.997695	+	0.0678508i	$0.978386\pi$
$410$		0			0
$411$	103.190	−	249.122i	0.251070	−	0.606136i
$412$		0			0
$413$	−47.9348	−	115.725i	−0.116065	−	0.280205i
$414$		0			0
$415$		−	138.665i		−	0.334131i
$416$		0			0
$417$	−54.3555			−0.130349
$418$		0			0
$419$	−130.080	+	53.8808i	−0.310453	+	0.128594i	−0.532470	−	0.846449i	$-0.678736\pi$
$419$	−130.080	+	53.8808i	−0.310453	+	0.128594i	0.222017	+	0.975043i	$0.428736\pi$
$420$		0			0
$421$	−127.092	−	52.6432i	−0.301881	−	0.125043i	0.226601	−	0.973988i	$-0.427239\pi$
$421$	−127.092	−	52.6432i	−0.301881	−	0.125043i	−0.528482	+	0.848944i	$0.677239\pi$
$422$		0			0
$423$	23.9387	−	23.9387i	0.0565927	−	0.0565927i
$424$		0			0
$425$	−591.622	+	591.622i	−1.39205	+	1.39205i
$426$		0			0
$427$	4.62596	+	1.91614i	0.0108336	+	0.00448744i
$428$		0			0
$429$	534.862	−	221.547i	1.24676	−	0.516427i
$430$		0			0
$431$	331.894			0.770055			0.385027	−	0.922905i	$-0.374192\pi$
$431$	331.894			0.770055			0.385027	+	0.922905i	$0.374192\pi$
$432$		0			0
$433$			806.945i			1.86361i	0.362955	+	0.931807i	$0.381768\pi$
$433$			806.945i			1.86361i	−0.362955	+	0.931807i	$0.618232\pi$
$434$		0			0
$435$	−15.1747	−	36.6350i	−0.0348844	−	0.0842185i
$436$		0			0
$437$	−76.3245	+	184.264i	−0.174656	+	0.421656i
$438$		0			0
$439$	−164.097	−	164.097i	−0.373797	−	0.373797i	0.495061	−	0.868858i	$-0.335146\pi$
$439$	−164.097	−	164.097i	−0.373797	−	0.373797i	−0.868858	+	0.495061i	$0.835146\pi$
$440$		0			0
$441$	80.3236	+	80.3236i	0.182140	+	0.182140i
$442$		0			0
$443$	220.439	−	532.187i	0.497606	−	1.20133i	−0.453164	−	0.891427i	$-0.649705\pi$
$443$	220.439	−	532.187i	0.497606	−	1.20133i	0.950770	−	0.309899i	$-0.100295\pi$
$444$		0			0
$445$	−351.671	−	849.009i	−0.790272	−	1.90789i
$446$		0			0
$447$			257.001i			0.574946i
$448$		0			0
$449$	−543.417			−1.21028			−0.605141	−	0.796118i	$-0.706883\pi$
$449$	−543.417			−1.21028			−0.605141	+	0.796118i	$0.706883\pi$
$450$		0			0
$451$	−174.830	+	72.4172i	−0.387651	+	0.160570i
$452$		0			0
$453$	−428.662	−	177.558i	−0.946273	−	0.391959i
$454$		0			0
$455$	453.473	−	453.473i	0.996644	−	0.996644i
$456$		0			0
$457$	−201.086	+	201.086i	−0.440013	+	0.440013i	−0.892016	−	0.452003i	$-0.850709\pi$
$457$	−201.086	+	201.086i	−0.440013	+	0.440013i	0.452003	+	0.892016i	$0.350709\pi$
$458$		0			0
$459$	−123.379	−	51.1054i	−0.268801	−	0.111341i
$460$		0			0
$461$	32.1175	−	13.3035i	0.0696692	−	0.0288579i	−0.347577	−	0.937652i	$-0.612995\pi$
$461$	32.1175	−	13.3035i	0.0696692	−	0.0288579i	0.417246	+	0.908794i	$0.362995\pi$
$462$		0			0
$463$	41.6305			0.0899146			0.0449573	−	0.998989i	$-0.485685\pi$
$463$	41.6305			0.0899146			0.0449573	+	0.998989i	$0.485685\pi$
$464$		0			0
$465$		−	371.824i		−	0.799621i
$466$		0			0
$467$	215.784	+	520.948i	0.462064	+	1.11552i	0.967549	+	0.252685i	$0.0813136\pi$
$467$	215.784	+	520.948i	0.462064	+	1.11552i	−0.505485	+	0.862835i	$0.668686\pi$
$468$		0			0
$469$	3.98999	−	9.63268i	0.00850744	−	0.0205388i
$470$		0			0
$471$	−261.227	−	261.227i	−0.554622	−	0.554622i
$472$		0			0
$473$	−230.703	−	230.703i	−0.487745	−	0.487745i
$474$		0			0
$475$	−75.7122	+	182.785i	−0.159394	+	0.384811i
$476$		0			0
$477$	−5.13845	−	12.4053i	−0.0107724	−	0.0260069i
$478$		0			0
$479$			662.316i			1.38270i	0.722518	+	0.691352i	$0.242985\pi$
$479$			662.316i			1.38270i	−0.722518	+	0.691352i	$0.757015\pi$
$480$		0			0
$481$	958.685			1.99311
$482$		0			0
$483$	175.241	−	72.5871i	0.362817	−	0.150284i
$484$		0			0
$485$	−134.248	−	55.6075i	−0.276801	−	0.114655i
$486$		0			0
$487$	309.360	−	309.360i	0.635236	−	0.635236i	−0.314140	−	0.949377i	$-0.601716\pi$
$487$	309.360	−	309.360i	0.635236	−	0.635236i	0.949377	+	0.314140i	$0.101716\pi$
$488$		0			0
$489$	−210.419	+	210.419i	−0.430304	+	0.430304i
$490$		0			0
$491$	−249.104	−	103.182i	−0.507340	−	0.210147i	0.114306	−	0.993446i	$-0.463536\pi$
$491$	−249.104	−	103.182i	−0.507340	−	0.210147i	−0.621646	+	0.783299i	$0.713536\pi$
$492$		0			0
$493$	71.6541	−	29.6801i	0.145343	−	0.0602031i
$494$		0			0
$495$	300.295			0.606657
$496$		0			0
$497$			390.541i			0.785797i
$498$		0			0
$499$	−203.686	−	491.742i	−0.408189	−	0.985455i	−0.985614	−	0.169012i	$-0.945942\pi$
$499$	−203.686	−	491.742i	−0.408189	−	0.985455i	0.577425	−	0.816444i	$-0.304058\pi$
$500$		0			0
$501$	38.9419	−	94.0139i	0.0777282	−	0.187653i
$502$		0			0
$503$	−135.286	−	135.286i	−0.268959	−	0.268959i	0.559722	−	0.828681i	$-0.310908\pi$
$503$	−135.286	−	135.286i	−0.268959	−	0.268959i	−0.828681	+	0.559722i	$0.810908\pi$
$504$		0			0
$505$	−70.4970	−	70.4970i	−0.139598	−	0.139598i
$506$		0			0
$507$	−313.344	+	756.480i	−0.618036	+	1.49207i
$508$		0			0
$509$	−294.504	−	710.995i	−0.578593	−	1.39685i	−0.894076	−	0.447915i	$-0.852167\pi$
$509$	−294.504	−	710.995i	−0.578593	−	1.39685i	0.315483	−	0.948931i	$-0.397833\pi$
$510$		0			0
$511$			32.0948i			0.0628078i
$512$		0			0
$513$	−31.5787			−0.0615569
$514$		0			0
$515$	−24.1718	+	10.0123i	−0.0469356	+	0.0194414i
$516$		0			0
$517$	−137.561	−	56.9797i	−0.266076	−	0.110212i
$518$		0			0
$519$	−120.778	+	120.778i	−0.232714	+	0.232714i
$520$		0			0
$521$	−328.950	+	328.950i	−0.631382	+	0.631382i	−0.948415	−	0.317033i	$-0.897313\pi$
$521$	−328.950	+	328.950i	−0.631382	+	0.631382i	0.317033	+	0.948415i	$0.397313\pi$
$522$		0			0
$523$	−375.998	−	155.744i	−0.718926	−	0.297789i	−0.00693327	−	0.999976i	$-0.502207\pi$
$523$	−375.998	−	155.744i	−0.718926	−	0.297789i	−0.711992	+	0.702187i	$0.752207\pi$
$524$		0			0
$525$	173.835	−	72.0047i	0.331114	−	0.137152i
$526$		0			0
$527$	727.247			1.37998
$528$		0			0
$529$			548.020i			1.03596i
$530$		0			0
$531$	43.0948	+	104.040i	0.0811578	+	0.195932i
$532$		0			0
$533$	139.038	−	335.668i	0.260860	−	0.629771i
$534$		0			0
$535$	888.928	+	888.928i	1.66155	+	1.66155i
$536$		0			0
$537$	−402.407	−	402.407i	−0.749361	−	0.749361i
$538$		0			0
$539$	191.189	−	461.571i	0.354711	−	0.856347i
$540$		0			0
$541$	−180.025	−	434.619i	−0.332764	−	0.803362i	−0.998371	−	0.0570600i	$-0.981827\pi$
$541$	−180.025	−	434.619i	−0.332764	−	0.803362i	0.665607	−	0.746302i	$-0.268173\pi$
$542$		0			0
$543$		−	345.028i		−	0.635410i
$544$		0			0
$545$	1256.05			2.30467
$546$		0			0
$547$	−842.270	+	348.880i	−1.53980	+	0.637805i	−0.981436	−	0.191791i	$-0.938570\pi$
$547$	−842.270	+	348.880i	−1.53980	+	0.637805i	−0.558363	+	0.829597i	$0.688570\pi$
$548$		0			0
$549$	−4.15888	−	1.72266i	−0.00757537	−	0.00313782i
$550$		0			0
$551$	12.9681	−	12.9681i	0.0235356	−	0.0235356i
$552$		0			0
$553$	−138.334	+	138.334i	−0.250151	+	0.250151i
$554$		0			0
$555$	459.423	+	190.299i	0.827790	+	0.342882i
$556$		0			0
$557$	838.978	−	347.516i	1.50624	−	0.623907i	0.531465	−	0.847080i	$-0.321642\pi$
$557$	838.978	−	347.516i	1.50624	−	0.623907i	0.974779	+	0.223173i	$0.0716415\pi$
$558$		0			0
$559$	626.414			1.12060
$560$		0			0
$561$			587.344i			1.04696i
$562$		0			0
$563$	10.7574	+	25.9706i	0.0191073	+	0.0461290i	0.933145	−	0.359500i	$-0.117053\pi$
$563$	10.7574	+	25.9706i	0.0191073	+	0.0461290i	−0.914038	+	0.405629i	$0.867053\pi$
$564$		0			0
$565$	−229.230	+	553.410i	−0.405717	+	0.979487i
$566$		0			0
$567$	21.2361	+	21.2361i	0.0374534	+	0.0374534i
$568$		0			0
$569$	319.628	+	319.628i	0.561736	+	0.561736i	0.929800	−	0.368064i	$-0.119979\pi$
$569$	319.628	+	319.628i	0.561736	+	0.561736i	−0.368064	+	0.929800i	$0.619979\pi$
$570$		0			0
$571$	249.558	−	602.487i	0.437055	−	1.05514i	−0.539906	−	0.841725i	$-0.681540\pi$
$571$	249.558	−	602.487i	0.437055	−	1.05514i	0.976961	−	0.213418i	$-0.0684597\pi$
$572$		0			0
$573$	133.577	+	322.484i	0.233119	+	0.562799i
$574$		0			0
$575$			1068.38i			1.85805i
$576$		0			0
$577$	−618.173			−1.07136			−0.535678	−	0.844422i	$-0.679944\pi$
$577$	−618.173			−1.07136			−0.535678	+	0.844422i	$0.679944\pi$
$578$		0			0
$579$	−4.30375	+	1.78267i	−0.00743308	+	0.00307888i
$580$		0			0
$581$	−56.3491	−	23.3406i	−0.0969865	−	0.0401731i
$582$		0			0
$583$	−41.7583	+	41.7583i	−0.0716265	+	0.0716265i
$584$		0			0
$585$	−407.686	+	407.686i	−0.696899	+	0.696899i
$586$		0			0
$587$	−917.045	−	379.852i	−1.56226	−	0.647108i	−0.576777	−	0.816901i	$-0.695690\pi$
$587$	−917.045	−	379.852i	−1.56226	−	0.647108i	−0.985480	+	0.169793i	$0.945690\pi$
$588$		0			0
$589$	158.878	−	65.8094i	0.269742	−	0.111731i
$590$		0			0
$591$	13.0802			0.0221324
$592$		0			0
$593$			304.459i			0.513421i	0.966488	+	0.256711i	$0.0826387\pi$
$593$			304.459i			0.513421i	−0.966488	+	0.256711i	$0.917361\pi$
$594$		0			0
$595$	248.985	+	601.102i	0.418462	+	1.01026i
$596$		0			0
$597$	167.631	−	404.696i	0.280789	−	0.677884i
$598$		0			0
$599$	277.512	+	277.512i	0.463293	+	0.463293i	0.899733	−	0.436441i	$-0.143761\pi$
$599$	277.512	+	277.512i	0.463293	+	0.463293i	−0.436441	+	0.899733i	$0.643761\pi$
$600$		0			0
$601$	−239.556	−	239.556i	−0.398596	−	0.398596i	0.479141	−	0.877738i	$-0.340948\pi$
$601$	−239.556	−	239.556i	−0.398596	−	0.398596i	−0.877738	+	0.479141i	$0.840948\pi$
$602$		0			0
$603$	−3.58712	+	8.66007i	−0.00594879	+	0.0143616i
$604$		0			0
$605$	−154.131	−	372.105i	−0.254762	−	0.615050i
$606$		0			0
$607$		−	596.668i		−	0.982978i	−0.870884	−	0.491489i	$-0.836453\pi$
$607$		−	596.668i		−	0.982978i	0.870884	−	0.491489i	$-0.163547\pi$
$608$		0			0
$609$	−17.4417			−0.0286398
$610$		0			0
$611$	264.112	−	109.399i	0.432263	−	0.179049i
$612$		0			0
$613$	582.048	+	241.092i	0.949507	+	0.393299i	0.803046	−	0.595917i	$-0.203211\pi$
$613$	582.048	+	241.092i	0.949507	+	0.393299i	0.146462	+	0.989216i	$0.453211\pi$
$614$		0			0
$615$	133.260	−	133.260i	0.216684	−	0.216684i
$616$		0			0
$617$	650.951	−	650.951i	1.05503	−	1.05503i	0.0566309	−	0.998395i	$-0.481964\pi$
$617$	650.951	−	650.951i	1.05503	−	1.05503i	0.998395	−	0.0566309i	$-0.0180358\pi$
$618$		0			0
$619$	−279.093	−	115.604i	−0.450878	−	0.186760i	0.145677	−	0.989332i	$-0.453464\pi$
$619$	−279.093	−	115.604i	−0.450878	−	0.186760i	−0.596554	+	0.802573i	$0.703464\pi$
$620$		0			0
$621$	−157.547	+	65.2580i	−0.253698	+	0.105085i
$622$		0			0
$623$	−404.207			−0.648807
$624$		0			0
$625$		−	379.059i		−	0.606494i
$626$		0			0
$627$	53.1495	+	128.314i	0.0847679	+	0.204648i
$628$		0			0
$629$	−372.205	+	898.582i	−0.591741	+	1.42859i
$630$		0			0
$631$	−761.197	−	761.197i	−1.20633	−	1.20633i	−0.972206	−	0.234128i	$-0.924777\pi$
$631$	−761.197	−	761.197i	−1.20633	−	1.20633i	−0.234128	−	0.972206i	$-0.575223\pi$
$632$		0			0
$633$	−356.630	−	356.630i	−0.563396	−	0.563396i
$634$		0			0
$635$	−6.20683	+	14.9846i	−0.00977454	+	0.0235978i
$636$		0			0
$637$	367.076	+	886.199i	0.576257	+	1.39121i
$638$		0			0
$639$		−	351.108i		−	0.549465i
$640$		0			0
$641$	19.6688			0.0306845			0.0153422	−	0.999882i	$-0.495116\pi$
$641$	19.6688			0.0306845			0.0153422	+	0.999882i	$0.495116\pi$
$642$		0			0
$643$	−361.198	+	149.613i	−0.561739	+	0.232680i	−0.645440	−	0.763811i	$-0.723326\pi$
$643$	−361.198	+	149.613i	−0.561739	+	0.232680i	0.0837010	+	0.996491i	$0.473326\pi$
$644$		0			0
$645$	300.192	+	124.343i	0.465413	+	0.192781i
$646$		0			0
$647$	−322.306	+	322.306i	−0.498154	+	0.498154i	−0.910863	−	0.412709i	$-0.864583\pi$
$647$	−322.306	+	322.306i	−0.498154	+	0.498154i	0.412709	+	0.910863i	$0.364583\pi$
$648$		0			0
$649$	350.215	−	350.215i	0.539623	−	0.539623i
$650$		0			0
$651$	−151.098	−	62.5869i	−0.232102	−	0.0961397i
$652$		0			0
$653$	−268.367	+	111.161i	−0.410976	+	0.170232i	−0.578586	−	0.815622i	$-0.696395\pi$
$653$	−268.367	+	111.161i	−0.410976	+	0.170232i	0.167610	+	0.985853i	$0.446395\pi$
$654$		0			0
$655$	212.235			0.324023
$656$		0			0
$657$		−	28.8542i		−	0.0439181i
$658$		0			0
$659$	51.5747	+	124.512i	0.0782621	+	0.188941i	0.958168	−	0.286207i	$-0.0923944\pi$
$659$	51.5747	+	124.512i	0.0782621	+	0.188941i	−0.879906	+	0.475148i	$0.842394\pi$
$660$		0			0
$661$	46.4357	−	112.106i	0.0702507	−	0.169600i	−0.884854	−	0.465868i	$-0.845742\pi$
$661$	46.4357	−	112.106i	0.0702507	−	0.169600i	0.955105	+	0.296268i	$0.0957421\pi$
$662$		0			0
$663$	−797.389	−	797.389i	−1.20270	−	1.20270i
$664$		0			0
$665$	108.789	+	108.789i	0.163592	+	0.163592i
$666$		0			0
$667$	37.8994	−	91.4972i	0.0568206	−	0.137177i
$668$		0			0
$669$	201.024	+	485.314i	0.300484	+	0.725432i
$670$		0			0
$671$			19.7982i			0.0295055i
$672$		0			0
$673$	744.919			1.10686			0.553432	−	0.832895i	$-0.313318\pi$
$673$	744.919			1.10686			0.553432	+	0.832895i	$0.313318\pi$
$674$		0			0
$675$	−156.283	+	64.7344i	−0.231530	+	0.0959029i
$676$		0			0
$677$	433.679	+	179.636i	0.640589	+	0.265341i	0.679245	−	0.733912i	$-0.262307\pi$
$677$	433.679	+	179.636i	0.640589	+	0.265341i	−0.0386554	+	0.999253i	$0.512307\pi$
$678$		0			0
$679$	−45.1945	+	45.1945i	−0.0665603	+	0.0665603i
$680$		0			0
$681$	−458.573	+	458.573i	−0.673382	+	0.673382i
$682$		0			0
$683$	−175.528	−	72.7059i	−0.256995	−	0.106451i	0.250466	−	0.968125i	$-0.419416\pi$
$683$	−175.528	−	72.7059i	−0.256995	−	0.106451i	−0.507461	+	0.861674i	$0.669416\pi$
$684$		0			0
$685$	1091.17	−	451.977i	1.59295	−	0.659820i
$686$		0			0
$687$	215.839			0.314176
$688$		0			0
$689$		−	113.384i		−	0.164563i
$690$		0			0
$691$	489.503	+	1181.77i	0.708399	+	1.71023i	0.703964	+	0.710235i	$0.251411\pi$
$691$	489.503	+	1181.77i	0.708399	+	1.71023i	0.00443406	+	0.999990i	$0.498589\pi$
$692$		0			0
$693$	50.5469	−	122.031i	0.0729392	−	0.176091i
$694$		0			0
$695$	−168.348	−	168.348i	−0.242228	−	0.242228i
$696$		0			0
$697$	260.643	+	260.643i	0.373950	+	0.373950i
$698$		0			0
$699$	−22.0989	+	53.3515i	−0.0316151	+	0.0763255i
$700$		0			0
$701$	126.775	+	306.062i	0.180849	+	0.436607i	0.988142	−	0.153543i	$-0.0490685\pi$
$701$	126.775	+	306.062i	0.180849	+	0.436607i	−0.807293	+	0.590150i	$0.799068\pi$
$702$		0			0
$703$			229.990i			0.327155i
$704$		0			0
$705$	148.284			0.210332
$706$		0			0
$707$	−40.5142	+	16.7815i	−0.0573044	+	0.0237363i
$708$		0			0
$709$	384.057	+	159.082i	0.541688	+	0.224375i	0.636714	−	0.771100i	$-0.280293\pi$
$709$	384.057	+	159.082i	0.541688	+	0.224375i	−0.0950254	+	0.995475i	$0.530293\pi$
$710$		0			0
$711$	124.366	−	124.366i	0.174917	−	0.174917i
$712$		0			0
$713$	656.649	−	656.649i	0.920966	−	0.920966i
$714$		0			0
$715$	2342.73	+	970.389i	3.27654	+	1.35719i
$716$		0			0
$717$	−611.277	+	253.199i	−0.852548	+	0.353137i
$718$		0			0
$719$	−597.352			−0.830810			−0.415405	−	0.909637i	$-0.636360\pi$
$719$	−597.352			−0.830810			−0.415405	+	0.909637i	$0.636360\pi$
$720$		0			0
$721$			11.5080i			0.0159612i
$722$		0			0
$723$	−174.123	−	420.371i	−0.240835	−	0.581426i
$724$		0			0
$725$	37.5953	−	90.7631i	0.0518556	−	0.125191i
$726$		0			0
$727$	890.023	+	890.023i	1.22424	+	1.22424i	0.966110	+	0.258131i	$0.0831065\pi$
$727$	890.023	+	890.023i	1.22424	+	1.22424i	0.258131	+	0.966110i	$0.416894\pi$
$728$		0			0
$729$	−19.0919	−	19.0919i	−0.0261891	−	0.0261891i
$730$		0			0
$731$	−243.202	+	587.142i	−0.332698	+	0.803204i
$732$		0			0
$733$	265.446	+	640.844i	0.362137	+	0.874276i	0.994987	+	0.100002i	$0.0318848\pi$
$733$	265.446	+	640.844i	0.362137	+	0.874276i	−0.632850	+	0.774274i	$0.718115\pi$
$734$		0			0
$735$			497.551i			0.676941i
$736$		0			0
$737$	41.2260			0.0559376
$738$		0			0
$739$	1201.59	−	497.716i	1.62597	−	0.673499i	0.631199	−	0.775621i	$-0.282563\pi$
$739$	1201.59	−	497.716i	1.62597	−	0.673499i	0.994772	+	0.102121i	$0.0325630\pi$
$740$		0			0
$741$	−246.358	−	102.045i	−0.332467	−	0.137713i
$742$		0			0
$743$	212.173	−	212.173i	0.285563	−	0.285563i	−0.549760	−	0.835323i	$-0.685281\pi$
$743$	212.173	−	212.173i	0.285563	−	0.285563i	0.835323	+	0.549760i	$0.185281\pi$
$744$		0			0
$745$	−795.976	+	795.976i	−1.06842	+	1.06842i
$746$		0			0
$747$	50.6596	+	20.9839i	0.0678174	+	0.0280909i
$748$		0			0
$749$	510.862	−	211.606i	0.682058	−	0.282518i
$750$		0			0
$751$	106.499			0.141810			0.0709050	−	0.997483i	$-0.477411\pi$
$751$	106.499			0.141810			0.0709050	+	0.997483i	$0.477411\pi$
$752$		0			0
$753$		−	682.920i		−	0.906933i
$754$		0			0
$755$	−777.712	−	1877.56i	−1.03008	−	2.48684i
$756$		0			0
$757$	436.588	−	1054.02i	0.576734	−	1.39236i	−0.318993	−	0.947757i	$-0.603345\pi$
$757$	436.588	−	1054.02i	0.576734	−	1.39236i	0.895728	−	0.444603i	$-0.146655\pi$
$758$		0			0
$759$	530.327	+	530.327i	0.698719	+	0.698719i
$760$		0			0
$761$	867.382	+	867.382i	1.13979	+	1.13979i	0.988487	+	0.151306i	$0.0483479\pi$
$761$	867.382	+	867.382i	1.13979	+	1.13979i	0.151306	+	0.988487i	$0.451652\pi$
$762$		0			0
$763$	211.423	−	510.420i	0.277094	−	0.668965i
$764$		0			0
$765$	−223.845	−	540.409i	−0.292608	−	0.706417i
$766$		0			0
$767$			950.918i			1.23979i
$768$		0			0
$769$	−363.245			−0.472360			−0.236180	−	0.971709i	$-0.575896\pi$
$769$	−363.245			−0.472360			−0.236180	+	0.971709i	$0.575896\pi$
$770$		0			0
$771$	−371.474	+	153.869i	−0.481808	+	0.199571i
$772$		0			0
$773$	−987.768	−	409.147i	−1.27784	−	0.529298i	−0.362499	−	0.931984i	$-0.618077\pi$
$773$	−987.768	−	409.147i	−1.27784	−	0.529298i	−0.915338	+	0.402686i	$0.868077\pi$
$774$		0			0
$775$	651.381	−	651.381i	0.840491	−	0.840491i
$776$		0			0
$777$	154.664	−	154.664i	0.199053	−	0.199053i
$778$		0			0
$779$	80.5273	+	33.3555i	0.103373	+	0.0428183i
$780$		0			0
$781$	−1426.66	+	590.943i	−1.82671	+	0.756650i
$782$		0			0
$783$	15.6806			0.0200263
$784$		0			0
$785$		−	1618.13i		−	2.06131i
$786$		0			0
$787$	−136.007	−	328.349i	−0.172817	−	0.417216i	0.813612	−	0.581409i	$-0.197498\pi$
$787$	−136.007	−	328.349i	−0.172817	−	0.417216i	−0.986428	+	0.164193i	$0.947498\pi$
$788$		0			0
$789$	−48.6282	+	117.399i	−0.0616326	+	0.148794i
$790$		0			0
$791$	186.305	+	186.305i	0.235531	+	0.235531i
$792$		0			0
$793$	−26.8784	−	26.8784i	−0.0338946	−	0.0338946i
$794$		0			0
$795$	22.5067	−	54.3360i	0.0283103	−	0.0683471i
$796$		0			0
$797$	65.5848	+	158.336i	0.0822896	+	0.198665i	0.959669	−	0.281133i	$-0.0907102\pi$
$797$	65.5848	+	158.336i	0.0822896	+	0.198665i	−0.877379	+	0.479797i	$0.840710\pi$
$798$		0			0
$799$			290.028i			0.362989i
$800$		0			0
$801$	363.394			0.453676
$802$		0			0
$803$	−117.244	+	48.5639i	−0.146007	+	0.0604781i
$804$		0			0
$805$	767.564	+	317.936i	0.953496	+	0.394951i
$806$		0			0
$807$	−208.341	+	208.341i	−0.258167	+	0.258167i
$808$		0			0
$809$	−594.060	+	594.060i	−0.734314	+	0.734314i	−0.971471	−	0.237157i	$-0.923784\pi$
$809$	−594.060	+	594.060i	−0.734314	+	0.734314i	0.237157	+	0.971471i	$0.423784\pi$
$810$		0			0
$811$	583.898	+	241.859i	0.719973	+	0.298223i	0.712424	−	0.701749i	$-0.247597\pi$
$811$	583.898	+	241.859i	0.719973	+	0.298223i	0.00754873	+	0.999972i	$0.497597\pi$
$812$		0			0
$813$	499.493	−	206.897i	0.614383	−	0.254486i
$814$		0			0
$815$	−1303.40			−1.59927
$816$		0			0
$817$			150.278i			0.183938i
$818$		0			0
$819$	97.0481	+	234.295i	0.118496	+	0.286074i
$820$		0			0
$821$	−252.315	+	609.143i	−0.307327	+	0.741952i	0.692463	+	0.721453i	$0.256525\pi$
$821$	−252.315	+	609.143i	−0.307327	+	0.741952i	−0.999790	+	0.0204989i	$0.993475\pi$
$822$		0			0
$823$	−384.849	−	384.849i	−0.467617	−	0.467617i	0.433525	−	0.901142i	$-0.357270\pi$
$823$	−384.849	−	384.849i	−0.467617	−	0.467617i	−0.901142	+	0.433525i	$0.857270\pi$
$824$		0			0
$825$	526.073	+	526.073i	0.637664	+	0.637664i
$826$		0			0
$827$	−186.532	+	450.328i	−0.225553	+	0.544533i	−0.995627	−	0.0934222i	$-0.970219\pi$
$827$	−186.532	+	450.328i	−0.225553	+	0.544533i	0.770074	+	0.637955i	$0.220219\pi$
$828$		0			0
$829$	−454.707	−	1097.76i	−0.548500	−	1.32420i	−0.918594	−	0.395202i	$-0.870674\pi$
$829$	−454.707	−	1097.76i	−0.548500	−	1.32420i	0.370094	−	0.928994i	$-0.379326\pi$
$830$		0			0
$831$		−	534.883i		−	0.643662i
$832$		0			0
$833$	−973.156			−1.16825
$834$		0			0
$835$	411.786	−	170.568i	0.493157	−	0.204272i
$836$		0			0
$837$	135.842	+	56.2675i	0.162296	+	0.0672252i
$838$		0			0
$839$	376.677	−	376.677i	0.448959	−	0.448959i	−0.446049	−	0.895008i	$-0.647169\pi$
$839$	376.677	−	376.677i	0.448959	−	0.448959i	0.895008	+	0.446049i	$0.147169\pi$
$840$		0			0
$841$	588.237	−	588.237i	0.699450	−	0.699450i
$842$		0			0
$843$	−220.854	−	91.4805i	−0.261985	−	0.108518i
$844$		0			0
$845$	−3313.42	+	1372.47i	−3.92121	+	1.62422i
$846$		0			0
$847$	−177.156			−0.209157
$848$		0			0
$849$		−	83.9148i		−	0.0988395i
$850$		0			0
$851$	475.279	+	1147.42i	0.558494	+	1.34832i
$852$		0			0
$853$	−26.3732	+	63.6706i	−0.0309182	+	0.0746431i	−0.938584	−	0.345049i	$-0.887862\pi$
$853$	−26.3732	+	63.6706i	−0.0309182	+	0.0746431i	0.907666	+	0.419693i	$0.137862\pi$
$854$		0			0
$855$	−97.8045	−	97.8045i	−0.114391	−	0.114391i
$856$		0			0
$857$	147.757	+	147.757i	0.172412	+	0.172412i	0.788038	−	0.615626i	$-0.211097\pi$
$857$	147.757	+	147.757i	0.172412	+	0.172412i	−0.615626	+	0.788038i	$0.711097\pi$
$858$		0			0
$859$	−579.032	+	1397.91i	−0.674076	+	1.62736i	0.100540	+	0.994933i	$0.467943\pi$
$859$	−579.032	+	1397.91i	−0.674076	+	1.62736i	−0.774616	+	0.632431i	$0.782057\pi$
$860$		0			0
$861$	−31.7222	−	76.5841i	−0.0368434	−	0.0889478i
$862$		0			0
$863$		−	405.553i		−	0.469934i	−0.972003	−	0.234967i	$-0.924502\pi$
$863$		−	405.553i		−	0.469934i	0.972003	−	0.234967i	$-0.0754982\pi$
$864$		0			0
$865$	−748.142			−0.864904
$866$		0			0
$867$	594.522	−	246.259i	0.685723	−	0.284036i
$868$		0			0
$869$	−714.657	−	296.021i	−0.822390	−	0.340645i
$870$		0			0
$871$	−55.9692	+	55.9692i	−0.0642585	+	0.0642585i
$872$		0			0
$873$	40.6312	−	40.6312i	0.0465420	−	0.0465420i
$874$		0			0
$875$	176.693	+	73.1888i	0.201935	+	0.0836444i
$876$		0			0
$877$	1246.79	−	516.439i	1.42166	−	0.588870i	0.466381	−	0.884584i	$-0.345558\pi$
$877$	1246.79	−	516.439i	1.42166	−	0.588870i	0.955276	+	0.295714i	$0.0955576\pi$
$878$		0			0
$879$	−302.999			−0.344709
$880$		0			0
$881$			579.161i			0.657391i	0.944436	+	0.328695i	$0.106609\pi$
$881$			579.161i			0.657391i	−0.944436	+	0.328695i	$0.893391\pi$
$882$		0			0
$883$	251.441	+	607.032i	0.284758	+	0.687466i	0.999934	−	0.0114783i	$-0.00365372\pi$
$883$	251.441	+	607.032i	0.284758	+	0.687466i	−0.715177	+	0.698944i	$0.753654\pi$
$884$		0			0
$885$	−188.758	+	455.701i	−0.213285	+	0.514917i
$886$		0			0
$887$	482.450	+	482.450i	0.543912	+	0.543912i	0.924673	−	0.380761i	$-0.124338\pi$
$887$	482.450	+	482.450i	0.543912	+	0.543912i	−0.380761	+	0.924673i	$0.624338\pi$
$888$		0			0
$889$	5.04454	+	5.04454i	0.00567440	+	0.00567440i
$890$		0			0
$891$	−45.4432	+	109.710i	−0.0510024	+	0.123131i
$892$		0			0
$893$	26.2450	+	63.3610i	0.0293897	+	0.0709529i
$894$		0			0
$895$		−	2492.64i		−	2.78508i
$896$		0			0
$897$	−1439.96			−1.60531
$898$		0			0
$899$	−78.8918	+	32.6780i	−0.0877550	+	0.0363493i
$900$		0			0
$901$	106.275	+	44.0206i	0.117953	+	0.0488575i
$902$		0			0
$903$	101.059	−	101.059i	0.111915	−	0.111915i
$904$		0			0
$905$	1068.61	−	1068.61i	1.18078	−	1.18078i
$906$		0			0
$907$	−902.707	−	373.913i	−0.995267	−	0.412253i	−0.175208	−	0.984532i	$-0.556060\pi$
$907$	−902.707	−	373.913i	−0.995267	−	0.412253i	−0.820059	+	0.572278i	$0.806060\pi$
$908$		0			0
$909$	36.4235	−	15.0871i	0.0400699	−	0.0165975i
$910$		0			0
$911$	340.128			0.373356			0.186678	−	0.982421i	$-0.440228\pi$
$911$	340.128			0.373356			0.186678	+	0.982421i	$0.440228\pi$
$912$		0			0
$913$		−	241.163i		−	0.264144i
$914$		0			0
$915$	−7.54537	−	18.2161i	−0.00824630	−	0.0199083i
$916$		0			0
$917$	35.7243	−	86.2461i	0.0389578	−	0.0940524i
$918$		0			0
$919$	−862.460	−	862.460i	−0.938477	−	0.938477i	0.0597374	−	0.998214i	$-0.480974\pi$
$919$	−862.460	−	862.460i	−0.938477	−	0.938477i	−0.998214	+	0.0597374i	$0.980974\pi$
$920$		0			0
$921$	−337.718	−	337.718i	−0.366686	−	0.366686i
$922$		0			0
$923$	1134.59	−	2739.14i	1.22924	−	2.96765i
$924$		0			0
$925$	471.466	+	1138.22i	0.509693	+	1.23051i
$926$		0			0
$927$		−	10.3461i		−	0.0111608i
$928$		0			0
$929$	615.216			0.662234			0.331117	−	0.943590i	$-0.392574\pi$
$929$	615.216			0.662234			0.331117	+	0.943590i	$0.392574\pi$
$930$		0			0
$931$	−212.601	+	88.0620i	−0.228357	+	0.0945886i
$932$		0			0
$933$	−99.4601	−	41.1977i	−0.106602	−	0.0441562i
$934$		0			0
$935$	−1819.10	+	1819.10i	−1.94557	+	1.94557i
$936$		0			0
$937$	414.108	−	414.108i	0.441951	−	0.441951i	−0.450716	−	0.892667i	$-0.648831\pi$
$937$	414.108	−	414.108i	0.441951	−	0.441951i	0.892667	+	0.450716i	$0.148831\pi$
$938$		0			0
$939$	275.725	+	114.209i	0.293637	+	0.121628i
$940$		0			0
$941$	270.294	−	111.960i	0.287241	−	0.118979i	−0.234410	−	0.972138i	$-0.575316\pi$
$941$	270.294	−	111.960i	0.287241	−	0.118979i	0.521652	+	0.853158i	$0.325316\pi$
$942$		0			0
$943$	470.682			0.499132
$944$		0			0
$945$			131.543i			0.139199i
$946$		0			0
$947$	−524.154	−	1265.42i	−0.553489	−	1.33624i	−0.914843	−	0.403811i	$-0.867685\pi$
$947$	−524.154	−	1265.42i	−0.553489	−	1.33624i	0.361354	−	0.932429i	$-0.382315\pi$
$948$		0			0
$949$	93.2408	−	225.103i	0.0982517	−	0.237201i
$950$		0			0
$951$	−5.24500	−	5.24500i	−0.00551525	−	0.00551525i
$952$		0			0
$953$	−923.672	−	923.672i	−0.969226	−	0.969226i	0.0303144	−	0.999540i	$-0.490349\pi$
$953$	−923.672	−	923.672i	−0.969226	−	0.969226i	−0.999540	+	0.0303144i	$0.990349\pi$
$954$		0			0
$955$	−585.076	+	1412.50i	−0.612645	+	1.47906i
$956$		0			0
$957$	−26.3917	−	63.7152i	−0.0275775	−	0.0665780i
$958$		0			0
$959$		−	519.497i		−	0.541707i
$960$		0			0
$961$	160.295			0.166801
$962$		0			0
$963$	−459.280	+	190.240i	−0.476926	+	0.197549i
$964$		0			0
$965$	−18.8507	−	7.80821i	−0.0195344	−	0.00809141i
$966$		0			0
$967$	−1286.99	+	1286.99i	−1.33091	+	1.33091i	−0.426344	+	0.904561i	$0.640199\pi$
$967$	−1286.99	+	1286.99i	−1.33091	+	1.33091i	−0.904561	+	0.426344i	$0.859801\pi$
$968$		0			0
$969$	191.295	−	191.295i	0.197415	−	0.197415i
$970$		0			0
$971$	729.976	+	302.366i	0.751778	+	0.311397i	0.725467	−	0.688257i	$-0.241624\pi$
$971$	729.976	+	302.366i	0.751778	+	0.311397i	0.0263112	+	0.999654i	$0.491624\pi$
$972$		0			0
$973$	−96.7488	+	40.0747i	−0.0994335	+	0.0411867i
$974$		0			0
$975$	−1428.41			−1.46504
$976$		0			0
$977$			346.223i			0.354374i	0.984177	+	0.177187i	$0.0566997\pi$
$977$			346.223i			0.354374i	−0.984177	+	0.177187i	$0.943300\pi$
$978$		0			0
$979$	−611.622	−	1476.59i	−0.624741	−	1.50826i
$980$		0			0
$981$	−190.076	+	458.883i	−0.193757	+	0.467771i
$982$		0			0
$983$	185.696	+	185.696i	0.188908	+	0.188908i	0.795224	−	0.606316i	$-0.207353\pi$
$983$	185.696	+	185.696i	0.188908	+	0.188908i	−0.606316	+	0.795224i	$0.707353\pi$
$984$		0			0
$985$	40.5116	+	40.5116i	0.0411286	+	0.0411286i
$986$		0			0
$987$	24.9598	−	60.2584i	0.0252886	−	0.0610520i
$988$		0			0
$989$	310.552	+	749.738i	0.314006	+	0.758077i
$990$		0			0
$991$			692.209i			0.698496i	0.937030	+	0.349248i	$0.113563\pi$
$991$			692.209i			0.698496i	−0.937030	+	0.349248i	$0.886437\pi$
$992$		0			0
$993$	−902.955			−0.909320
$994$		0			0
$995$	1772.59	−	734.232i	1.78150	−	0.737922i
$996$		0			0
$997$	−637.716	−	264.150i	−0.639635	−	0.264945i	0.0392058	−	0.999231i	$-0.487517\pi$
$997$	−637.716	−	264.150i	−0.639635	−	0.264945i	−0.678840	+	0.734286i	$0.737517\pi$
$998$		0			0
$999$	−139.048	+	139.048i	−0.139187	+	0.139187i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.3.m.a.271.2		64
4.3	odd	2		96.3.m.a.91.12	yes	64
12.11	even	2		288.3.u.b.91.5		64
32.13	even	8		96.3.m.a.19.12	✓	64
32.19	odd	8	inner	384.3.m.a.367.2		64
96.77	odd	8		288.3.u.b.19.5		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.3.m.a.19.12	✓	64	32.13	even	8
96.3.m.a.91.12	yes	64	4.3	odd	2
288.3.u.b.19.5		64	96.77	odd	8
288.3.u.b.91.5		64	12.11	even	2
384.3.m.a.271.2		64	1.1	even	1	trivial
384.3.m.a.367.2		64	32.19	odd	8	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	384.m (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.60021 + 0.662827i) q^{3} +(-7.00900 - 2.90322i) q^{5} +(-2.35957 + 2.35957i) q^{7} +(2.12132 - 2.12132i) q^{9} +O(q^{10})\)	\(q+(-1.60021 + 0.662827i) q^{3} +(-7.00900 - 2.90322i) q^{5} +(-2.35957 + 2.35957i) q^{7} +(2.12132 - 2.12132i) q^{9} +(-12.1899 - 5.04924i) q^{11} +(23.4042 - 9.69435i) q^{13} +13.1402 q^{15} +25.7007i q^{17} +(2.32569 + 5.61471i) q^{19} +(2.21181 - 5.33978i) q^{21} +(23.2058 + 23.2058i) q^{23} +(23.0197 + 23.0197i) q^{25} +(-1.98848 + 4.80062i) q^{27} +(-1.15484 - 2.78802i) q^{29} -28.2967i q^{31} +22.8532 q^{33} +(23.3885 - 9.68784i) q^{35} +(34.9633 + 14.4823i) q^{37} +(-31.0259 + 31.0259i) q^{39} +(10.1415 - 10.1415i) q^{41} +(22.8453 + 9.46285i) q^{43} +(-21.0270 + 8.70966i) q^{45} +11.2848 q^{47} +37.8649i q^{49} +(-17.0351 - 41.1265i) q^{51} +(1.71282 - 4.13510i) q^{53} +(70.7802 + 70.7802i) q^{55} +(-7.44317 - 7.44317i) q^{57} +(-14.3649 + 34.6800i) q^{59} +(-0.574221 - 1.38629i) q^{61} +10.0108i q^{63} -192.185 q^{65} +(-2.88669 + 1.19571i) q^{67} +(-52.5156 - 21.7527i) q^{69} +(82.7570 - 82.7570i) q^{71} +(6.80099 - 6.80099i) q^{73} +(-52.0942 - 21.5781i) q^{75} +(40.6770 - 16.8490i) q^{77} +58.6268 q^{79} -9.00000i q^{81} +(6.99463 + 16.8865i) q^{83} +(74.6149 - 180.136i) q^{85} +(3.69595 + 3.69595i) q^{87} +(85.6528 + 85.6528i) q^{89} +(-32.3494 + 78.0983i) q^{91} +(18.7558 + 45.2806i) q^{93} -46.1055i q^{95} +19.1537 q^{97} +(-36.5698 + 15.1477i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q - 128 q^{23} + 192 q^{35} + 192 q^{43} + 192 q^{51} + 320 q^{53} + 256 q^{55} + 256 q^{59} + 64 q^{61} - 64 q^{67} - 192 q^{69} - 512 q^{71} - 384 q^{75} - 448 q^{77} - 512 q^{79} - 192 q^{91}+O(q^{100}) \) 64 * q - 128 * q^23 + 192 * q^35 + 192 * q^43 + 192 * q^51 + 320 * q^53 + 256 * q^55 + 256 * q^59 + 64 * q^61 - 64 * q^67 - 192 * q^69 - 512 * q^71 - 384 * q^75 - 448 * q^77 - 512 * q^79 - 192 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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