LMFDB - Embedded newform 320.5.p.r.257.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [320,5,Mod(193,320)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("320.193"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(320, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 3])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	320.p (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,-24,0,-48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$33.0783881868$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 10 x^{10} + 68 x^{9} - 52 x^{8} - 784 x^{7} + 960 x^{6} + 3824 x^{5} - 13583 x^{4} + \cdots + 348466 $ x^12 - 4x^11 - 10x^10 + 68x^9 - 52x^8 - 784x^7 + 960x^6 + 3824x^5 - 13583x^4 - 8828x^3 + 191418x^2 + 478524*x + 348466
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{24}\cdot 5^{5} $
Twist minimal:	no (minimal twist has level 160)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			257.1
Root			$-2.09327 - 0.657043i$ of defining polynomial
Character	$\chi$	$=$	320.257
Dual form			320.5.p.r.193.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-11.8869 + 11.8869i) q^{3} +(-24.9004 - 2.22894i) q^{5} +(-22.2437 - 22.2437i) q^{7} -201.595i q^{9} +212.824 q^{11} +(-143.003 + 143.003i) q^{13} +(322.483 - 269.493i) q^{15} +(115.384 + 115.384i) q^{17} -296.302i q^{19} +528.815 q^{21} +(350.657 - 350.657i) q^{23} +(615.064 + 111.003i) q^{25} +(1433.50 + 1433.50i) q^{27} -23.8085i q^{29} -324.793 q^{31} +(-2529.81 + 2529.81i) q^{33} +(504.297 + 603.457i) q^{35} +(-1487.91 - 1487.91i) q^{37} -3399.72i q^{39} -799.859 q^{41} +(-474.444 + 474.444i) q^{43} +(-449.344 + 5019.81i) q^{45} +(924.838 + 924.838i) q^{47} -1411.44i q^{49} -2743.12 q^{51} +(-1835.97 + 1835.97i) q^{53} +(-5299.42 - 474.374i) q^{55} +(3522.10 + 3522.10i) q^{57} +134.802i q^{59} +2417.52 q^{61} +(-4484.21 + 4484.21i) q^{63} +(3879.59 - 3242.10i) q^{65} +(-1285.62 - 1285.62i) q^{67} +8336.42i q^{69} +4587.66 q^{71} +(-3061.83 + 3061.83i) q^{73} +(-8630.66 + 5991.70i) q^{75} +(-4734.00 - 4734.00i) q^{77} +4493.29i q^{79} -17750.4 q^{81} +(1238.34 - 1238.34i) q^{83} +(-2615.94 - 3130.31i) q^{85} +(283.009 + 283.009i) q^{87} +13417.5i q^{89} +6361.83 q^{91} +(3860.77 - 3860.77i) q^{93} +(-660.440 + 7378.04i) q^{95} +(10154.0 + 10154.0i) q^{97} -42904.4i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{5} - 48 q^{7} + 320 q^{11} - 260 q^{13} + 592 q^{15} - 60 q^{17} + 400 q^{21} + 176 q^{23} + 836 q^{25} + 2208 q^{27} + 480 q^{31} - 3120 q^{33} + 2208 q^{35} + 500 q^{37} + 2160 q^{41} + 3744 q^{43}+ \cdots + 36460 q^{97}+O(q^{100}) $ 12 * q - 24 * q^5 - 48 * q^7 + 320 * q^11 - 260 * q^13 + 592 * q^15 - 60 * q^17 + 400 * q^21 + 176 * q^23 + 836 * q^25 + 2208 * q^27 + 480 * q^31 - 3120 * q^33 + 2208 * q^35 + 500 * q^37 + 2160 * q^41 + 3744 * q^43 + 3116 * q^45 - 1264 * q^47 - 16960 * q^51 - 7020 * q^53 - 8256 * q^55 + 1760 * q^57 - 2928 * q^61 - 15504 * q^63 + 5196 * q^65 + 2400 * q^67 + 31200 * q^71 - 340 * q^73 + 1472 * q^75 + 6960 * q^77 - 27676 * q^81 + 25952 * q^83 + 7292 * q^85 - 27744 * q^87 - 66240 * q^91 + 2640 * q^93 + 3552 * q^95 + 36460 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	−11.8869	+	11.8869i	−1.32076	+	1.32076i	−0.407604	+	0.913159i	$0.633636\pi$
$3$	−11.8869	+	11.8869i	−1.32076	+	1.32076i	−0.913159	+	0.407604i	$0.866364\pi$
$4$		0			0
$5$	−24.9004	−	2.22894i	−0.996018	−	0.0891577i
$5$	−24.9004	−	2.22894i	−0.996018	−	0.0891577i
$6$		0			0
$7$	−22.2437	−	22.2437i	−0.453952	−	0.453952i	0.442712	−	0.896664i	$-0.354017\pi$
$7$	−22.2437	−	22.2437i	−0.453952	−	0.453952i	−0.896664	+	0.442712i	$0.854017\pi$
$8$		0			0
$9$		−	201.595i		−	2.48883i
$10$		0			0
$11$	212.824			1.75888			0.879440	−	0.476010i	$-0.157918\pi$
$11$	212.824			1.75888			0.879440	+	0.476010i	$0.157918\pi$
$12$		0			0
$13$	−143.003	+	143.003i	−0.846173	+	0.846173i	−0.989653	−	0.143480i	$-0.954171\pi$
$13$	−143.003	+	143.003i	−0.846173	+	0.846173i	0.143480	+	0.989653i	$0.454171\pi$
$14$		0			0
$15$	322.483	−	269.493i	1.43326	−	1.19775i
$16$		0			0
$17$	115.384	+	115.384i	0.399254	+	0.399254i	0.877970	−	0.478716i	$-0.158898\pi$
$17$	115.384	+	115.384i	0.399254	+	0.399254i	−0.478716	+	0.877970i	$0.658898\pi$
$18$		0			0
$19$		−	296.302i		−	0.820780i	−0.911910	−	0.410390i	$-0.865393\pi$
$19$		−	296.302i		−	0.820780i	0.911910	−	0.410390i	$-0.134607\pi$
$20$		0			0
$21$	528.815			1.19913
$22$		0			0
$23$	350.657	−	350.657i	0.662867	−	0.662867i	−0.293188	−	0.956055i	$-0.594716\pi$
$23$	350.657	−	350.657i	0.662867	−	0.662867i	0.956055	+	0.293188i	$0.0947161\pi$
$24$		0			0
$25$	615.064	+	111.003i	0.984102	+	0.177605i
$26$		0			0
$27$	1433.50	+	1433.50i	1.96639	+	1.96639i
$28$		0			0
$29$		−	23.8085i		−	0.0283098i	−0.999900	−	0.0141549i	$-0.995494\pi$
$29$		−	23.8085i		−	0.0283098i	0.999900	−	0.0141549i	$-0.00450579\pi$
$30$		0			0
$31$	−324.793			−0.337974			−0.168987	−	0.985618i	$-0.554050\pi$
$31$	−324.793			−0.337974			−0.168987	+	0.985618i	$0.554050\pi$
$32$		0			0
$33$	−2529.81	+	2529.81i	−2.32306	+	2.32306i
$34$		0			0
$35$	504.297	+	603.457i	0.411671	+	0.492618i
$36$		0			0
$37$	−1487.91	−	1487.91i	−1.08686	−	1.08686i	−0.995850	−	0.0910056i	$-0.970992\pi$
$37$	−1487.91	−	1487.91i	−1.08686	−	1.08686i	−0.0910056	−	0.995850i	$-0.529008\pi$
$38$		0			0
$39$		−	3399.72i		−	2.23519i
$40$		0			0
$41$	−799.859			−0.475823			−0.237912	−	0.971287i	$-0.576463\pi$
$41$	−799.859			−0.475823			−0.237912	+	0.971287i	$0.576463\pi$
$42$		0			0
$43$	−474.444	+	474.444i	−0.256595	+	0.256595i	−0.823668	−	0.567073i	$-0.808076\pi$
$43$	−474.444	+	474.444i	−0.256595	+	0.256595i	0.567073	+	0.823668i	$0.308076\pi$
$44$		0			0
$45$	−449.344	+	5019.81i	−0.221898	+	2.47892i
$46$		0			0
$47$	924.838	+	924.838i	0.418668	+	0.418668i	0.884745	−	0.466076i	$-0.154333\pi$
$47$	924.838	+	924.838i	0.418668	+	0.418668i	−0.466076	+	0.884745i	$0.654333\pi$
$48$		0			0
$49$		−	1411.44i		−	0.587854i
$50$		0			0
$51$	−2743.12			−1.05464
$52$		0			0
$53$	−1835.97	+	1835.97i	−0.653604	+	0.653604i	−0.953859	−	0.300255i	$-0.902928\pi$
$53$	−1835.97	+	1835.97i	−0.653604	+	0.653604i	0.300255	+	0.953859i	$0.402928\pi$
$54$		0			0
$55$	−5299.42	−	474.374i	−1.75187	−	0.156818i
$56$		0			0
$57$	3522.10	+	3522.10i	1.08406	+	1.08406i
$58$		0			0
$59$			134.802i			0.0387251i	0.999813	+	0.0193625i	$0.00616367\pi$
$59$			134.802i			0.0387251i	−0.999813	+	0.0193625i	$0.993836\pi$
$60$		0			0
$61$	2417.52			0.649697			0.324849	−	0.945766i	$-0.394687\pi$
$61$	2417.52			0.649697			0.324849	+	0.945766i	$0.394687\pi$
$62$		0			0
$63$	−4484.21	+	4484.21i	−1.12981	+	1.12981i
$64$		0			0
$65$	3879.59	−	3242.10i	0.918246	−	0.767360i
$66$		0			0
$67$	−1285.62	−	1285.62i	−0.286393	−	0.286393i	0.549259	−	0.835652i	$-0.314910\pi$
$67$	−1285.62	−	1285.62i	−0.286393	−	0.286393i	−0.835652	+	0.549259i	$0.814910\pi$
$68$		0			0
$69$			8336.42i			1.75098i
$70$		0			0
$71$	4587.66			0.910069			0.455034	−	0.890474i	$-0.349627\pi$
$71$	4587.66			0.910069			0.455034	+	0.890474i	$0.349627\pi$
$72$		0			0
$73$	−3061.83	+	3061.83i	−0.574559	+	0.574559i	−0.933399	−	0.358840i	$-0.883172\pi$
$73$	−3061.83	+	3061.83i	−0.574559	+	0.574559i	0.358840	+	0.933399i	$0.383172\pi$
$74$		0			0
$75$	−8630.66	+	5991.70i	−1.53434	+	1.06519i
$76$		0			0
$77$	−4734.00	−	4734.00i	−0.798448	−	0.798448i
$78$		0			0
$79$			4493.29i			0.719963i	0.932959	+	0.359981i	$0.117217\pi$
$79$			4493.29i			0.719963i	−0.932959	+	0.359981i	$0.882783\pi$
$80$		0			0
$81$	−17750.4			−2.70544
$82$		0			0
$83$	1238.34	−	1238.34i	0.179757	−	0.179757i	−0.611493	−	0.791250i	$-0.709431\pi$
$83$	1238.34	−	1238.34i	0.179757	−	0.179757i	0.791250	+	0.611493i	$0.209431\pi$
$84$		0			0
$85$	−2615.94	−	3130.31i	−0.362067	−	0.433260i
$86$		0			0
$87$	283.009	+	283.009i	0.0373905	+	0.0373905i
$88$		0			0
$89$			13417.5i			1.69391i	0.531666	+	0.846954i	$0.321566\pi$
$89$			13417.5i			1.69391i	−0.531666	+	0.846954i	$0.678434\pi$
$90$		0			0
$91$	6361.83			0.768244
$92$		0			0
$93$	3860.77	−	3860.77i	0.446384	−	0.446384i
$94$		0			0
$95$	−660.440	+	7378.04i	−0.0731789	+	0.817512i
$96$		0			0
$97$	10154.0	+	10154.0i	1.07918	+	1.07918i	0.996583	+	0.0825919i	$0.0263198\pi$
$97$	10154.0	+	10154.0i	1.07918	+	1.07918i	0.0825919	+	0.996583i	$0.473680\pi$
$98$		0			0
$99$		−	42904.4i		−	4.37755i
$100$		0			0
$101$	−9511.87			−0.932445			−0.466222	−	0.884668i	$-0.654385\pi$
$101$	−9511.87			−0.932445			−0.466222	+	0.884668i	$0.654385\pi$
$102$		0			0
$103$	−130.280	+	130.280i	−0.0122801	+	0.0122801i	−0.713220	−	0.700940i	$-0.752764\pi$
$103$	−130.280	+	130.280i	−0.0122801	+	0.0122801i	0.700940	+	0.713220i	$0.252764\pi$
$104$		0			0
$105$	−13167.7	−	1178.70i	−1.19435	−	0.106911i
$106$		0			0
$107$	11690.4	+	11690.4i	1.02108	+	1.02108i	0.999773	+	0.0213109i	$0.00678397\pi$
$107$	11690.4	+	11690.4i	1.02108	+	1.02108i	0.0213109	+	0.999773i	$0.493216\pi$
$108$		0			0
$109$			7318.36i			0.615972i	0.951391	+	0.307986i	$0.0996549\pi$
$109$			7318.36i			0.615972i	−0.951391	+	0.307986i	$0.900345\pi$
$110$		0			0
$111$	35373.1			2.87096
$112$		0			0
$113$	1217.69	−	1217.69i	0.0953633	−	0.0953633i	−0.657816	−	0.753179i	$-0.728519\pi$
$113$	1217.69	−	1217.69i	0.0953633	−	0.0953633i	0.753179	+	0.657816i	$0.228519\pi$
$114$		0			0
$115$	−9513.10	+	7949.91i	−0.719327	+	0.601128i
$116$		0			0
$117$	28828.7	+	28828.7i	2.10598	+	2.10598i
$118$		0			0
$119$		−	5133.14i		−	0.362484i
$120$		0			0
$121$	30653.2			2.09366
$122$		0			0
$123$	9507.81	−	9507.81i	0.628450	−	0.628450i
$124$		0			0
$125$	−15067.9	−	4134.97i	−0.964348	−	0.264638i
$126$		0			0
$127$	14954.8	+	14954.8i	0.927199	+	0.927199i	0.997524	−	0.0703251i	$-0.0224037\pi$
$127$	14954.8	+	14954.8i	0.927199	+	0.927199i	−0.0703251	+	0.997524i	$0.522404\pi$
$128$		0			0
$129$		−	11279.3i		−	0.677802i
$130$		0			0
$131$	5241.05			0.305404			0.152702	−	0.988272i	$-0.451202\pi$
$131$	5241.05			0.305404			0.152702	+	0.988272i	$0.451202\pi$
$132$		0			0
$133$	−6590.84	+	6590.84i	−0.372595	+	0.372595i
$134$		0			0
$135$	−32499.5	−	38889.9i	−1.78324	−	2.13388i
$136$		0			0
$137$	−22119.6	−	22119.6i	−1.17852	−	1.17852i	−0.980122	−	0.198396i	$-0.936427\pi$
$137$	−22119.6	−	22119.6i	−1.17852	−	1.17852i	−0.198396	−	0.980122i	$-0.563573\pi$
$138$		0			0
$139$			16817.7i			0.870436i	0.900325	+	0.435218i	$0.143329\pi$
$139$			16817.7i			0.870436i	−0.900325	+	0.435218i	$0.856671\pi$
$140$		0			0
$141$	−21986.9			−1.10592
$142$		0			0
$143$	−30434.6	+	30434.6i	−1.48832	+	1.48832i
$144$		0			0
$145$	−53.0678	+	592.842i	−0.00252403	+	0.0281970i
$146$		0			0
$147$	16777.6	+	16777.6i	0.776416	+	0.776416i
$148$		0			0
$149$		−	41393.7i		−	1.86450i	−0.361817	−	0.932249i	$-0.617844\pi$
$149$		−	41393.7i		−	1.86450i	0.361817	−	0.932249i	$-0.382156\pi$
$150$		0			0
$151$	30558.2			1.34021			0.670106	−	0.742265i	$-0.266249\pi$
$151$	30558.2			1.34021			0.670106	+	0.742265i	$0.266249\pi$
$152$		0			0
$153$	23260.9	−	23260.9i	0.993674	−	0.993674i
$154$		0			0
$155$	8087.50	+	723.946i	0.336628	+	0.0301330i
$156$		0			0
$157$	−5644.63	−	5644.63i	−0.229000	−	0.229000i	0.583275	−	0.812275i	$-0.301771\pi$
$157$	−5644.63	−	5644.63i	−0.229000	−	0.229000i	−0.812275	+	0.583275i	$0.801771\pi$
$158$		0			0
$159$		−	43647.9i		−	1.72651i
$160$		0			0
$161$	−15599.8			−0.601820
$162$		0			0
$163$	−18397.9	+	18397.9i	−0.692458	+	0.692458i	−0.962772	−	0.270314i	$-0.912873\pi$
$163$	−18397.9	+	18397.9i	−0.692458	+	0.692458i	0.270314	+	0.962772i	$0.412873\pi$
$164$		0			0
$165$	68632.3	−	57354.7i	2.52093	−	2.10669i
$166$		0			0
$167$	−5093.57	−	5093.57i	−0.182637	−	0.182637i	0.609867	−	0.792504i	$-0.291223\pi$
$167$	−5093.57	−	5093.57i	−0.182637	−	0.182637i	−0.792504	+	0.609867i	$0.791223\pi$
$168$		0			0
$169$		−	12338.8i		−	0.432017i
$170$		0			0
$171$	−59733.0			−2.04278
$172$		0			0
$173$	−10053.1	+	10053.1i	−0.335899	+	0.335899i	−0.854821	−	0.518923i	$-0.826333\pi$
$173$	−10053.1	+	10053.1i	−0.335899	+	0.335899i	0.518923	+	0.854821i	$0.326333\pi$
$174$		0			0
$175$	−11212.2	−	16150.4i	−0.366111	−	0.527360i
$176$		0			0
$177$	−1602.37	−	1602.37i	−0.0511466	−	0.0511466i
$178$		0			0
$179$		−	20464.7i		−	0.638705i	−0.947636	−	0.319352i	$-0.896535\pi$
$179$		−	20464.7i		−	0.638705i	0.947636	−	0.319352i	$-0.103465\pi$
$180$		0			0
$181$	17956.1			0.548093			0.274046	−	0.961717i	$-0.411638\pi$
$181$	17956.1			0.548093			0.274046	+	0.961717i	$0.411638\pi$
$182$		0			0
$183$	−28736.8	+	28736.8i	−0.858096	+	0.858096i
$184$		0			0
$185$	33733.0	+	40366.0i	0.985626	+	1.17943i
$186$		0			0
$187$	24556.6	+	24556.6i	0.702239	+	0.702239i
$188$		0			0
$189$		−	63772.5i		−	1.78529i
$190$		0			0
$191$	−50229.3			−1.37686			−0.688431	−	0.725302i	$-0.741700\pi$
$191$	−50229.3			−1.37686			−0.688431	+	0.725302i	$0.741700\pi$
$192$		0			0
$193$	−23236.7	+	23236.7i	−0.623821	+	0.623821i	−0.946506	−	0.322685i	$-0.895414\pi$
$193$	−23236.7	+	23236.7i	−0.623821	+	0.623821i	0.322685	+	0.946506i	$0.395414\pi$
$194$		0			0
$195$	−7577.78	+	84654.5i	−0.199284	+	2.22629i
$196$		0			0
$197$	34856.9	+	34856.9i	0.898164	+	0.898164i	0.995274	−	0.0971093i	$-0.0309596\pi$
$197$	34856.9	+	34856.9i	0.898164	+	0.898164i	−0.0971093	+	0.995274i	$0.530960\pi$
$198$		0			0
$199$			52040.7i			1.31412i	0.753836	+	0.657062i	$0.228201\pi$
$199$			52040.7i			1.31412i	−0.753836	+	0.657062i	$0.771799\pi$
$200$		0			0
$201$	30564.0			0.756515
$202$		0			0
$203$	−529.589	+	529.589i	−0.0128513	+	0.0128513i
$204$		0			0
$205$	19916.8	+	1782.84i	0.473928	+	0.0424233i
$206$		0			0
$207$	−70690.7	−	70690.7i	−1.64976	−	1.64976i
$208$		0			0
$209$		−	63060.2i		−	1.44365i
$210$		0			0
$211$	−31911.9			−0.716783			−0.358392	−	0.933571i	$-0.616675\pi$
$211$	−31911.9			−0.716783			−0.358392	+	0.933571i	$0.616675\pi$
$212$		0			0
$213$	−54532.9	+	54532.9i	−1.20199	+	1.20199i
$214$		0			0
$215$	12871.4	−	10756.4i	0.278451	−	0.232696i
$216$		0			0
$217$	7224.60	+	7224.60i	0.153424	+	0.153424i
$218$		0			0
$219$		−	72791.0i		−	1.51771i
$220$		0			0
$221$	−33000.7			−0.675675
$222$		0			0
$223$	60103.0	−	60103.0i	1.20861	−	1.20861i	0.237133	−	0.971477i	$-0.423792\pi$
$223$	60103.0	−	60103.0i	1.20861	−	1.20861i	0.971477	−	0.237133i	$-0.0762076\pi$
$224$		0			0
$225$	22377.7	−	123994.i	0.442029	−	2.44926i
$226$		0			0
$227$	23306.2	+	23306.2i	0.452293	+	0.452293i	0.896115	−	0.443822i	$-0.146378\pi$
$227$	23306.2	+	23306.2i	0.452293	+	0.452293i	−0.443822	+	0.896115i	$0.646378\pi$
$228$		0			0
$229$			15094.1i			0.287830i	0.989590	+	0.143915i	$0.0459692\pi$
$229$			15094.1i			0.287830i	−0.989590	+	0.143915i	$0.954031\pi$
$230$		0			0
$231$	112545.			2.10912
$232$		0			0
$233$	5434.95	−	5434.95i	0.100112	−	0.100112i	−0.655277	−	0.755389i	$-0.727448\pi$
$233$	5434.95	−	5434.95i	0.100112	−	0.100112i	0.755389	+	0.655277i	$0.227448\pi$
$234$		0			0
$235$	−20967.5	−	25090.3i	−0.379674	−	0.454329i
$236$		0			0
$237$	−53411.1	−	53411.1i	−0.950900	−	0.950900i
$238$		0			0
$239$			84679.4i			1.48246i	0.671253	+	0.741228i	$0.265756\pi$
$239$			84679.4i			1.48246i	−0.671253	+	0.741228i	$0.734244\pi$
$240$		0			0
$241$	−39990.5			−0.688530			−0.344265	−	0.938873i	$-0.611872\pi$
$241$	−39990.5			−0.688530			−0.344265	+	0.938873i	$0.611872\pi$
$242$		0			0
$243$	94883.0	−	94883.0i	1.60685	−	1.60685i
$244$		0			0
$245$	−3146.02	+	35145.4i	−0.0524118	+	0.585513i
$246$		0			0
$247$	42372.1	+	42372.1i	0.694522	+	0.694522i
$248$		0			0
$249$			29440.0i			0.474832i
$250$		0			0
$251$	92601.1			1.46983			0.734917	−	0.678157i	$-0.237221\pi$
$251$	92601.1			1.46983			0.734917	+	0.678157i	$0.237221\pi$
$252$		0			0
$253$	74628.3	−	74628.3i	1.16590	−	1.16590i
$254$		0			0
$255$	68304.8	+	6114.25i	1.05044	+	0.0940292i
$256$		0			0
$257$	14354.1	+	14354.1i	0.217326	+	0.217326i	0.807370	−	0.590045i	$-0.200890\pi$
$257$	14354.1	+	14354.1i	0.217326	+	0.217326i	−0.590045	+	0.807370i	$0.700890\pi$
$258$		0			0
$259$			66193.0i			0.986762i
$260$		0			0
$261$	−4799.68			−0.0704581
$262$		0			0
$263$	−59031.1	+	59031.1i	−0.853432	+	0.853432i	−0.990554	−	0.137122i	$-0.956215\pi$
$263$	−59031.1	+	59031.1i	−0.853432	+	0.853432i	0.137122	+	0.990554i	$0.456215\pi$
$264$		0			0
$265$	49808.8	−	41624.2i	0.709274	−	0.592727i
$266$		0			0
$267$	−159491.	−	159491.i	−2.23725	−	2.23725i
$268$		0			0
$269$			55004.2i			0.760137i	0.924958	+	0.380068i	$0.124100\pi$
$269$			55004.2i			0.760137i	−0.924958	+	0.380068i	$0.875900\pi$
$270$		0			0
$271$	2788.66			0.0379714			0.0189857	−	0.999820i	$-0.493956\pi$
$271$	2788.66			0.0379714			0.0189857	+	0.999820i	$0.493956\pi$
$272$		0			0
$273$	−75622.2	+	75622.2i	−1.01467	+	1.01467i
$274$		0			0
$275$	130901.	+	23624.2i	1.73092	+	0.312386i
$276$		0			0
$277$	65738.2	+	65738.2i	0.856758	+	0.856758i	0.990955	−	0.134197i	$-0.0428454\pi$
$277$	65738.2	+	65738.2i	0.856758	+	0.856758i	−0.134197	+	0.990955i	$0.542845\pi$
$278$		0			0
$279$			65476.7i			0.841160i
$280$		0			0
$281$	−107677.			−1.36368			−0.681839	−	0.731503i	$-0.738819\pi$
$281$	−107677.			−1.36368			−0.681839	+	0.731503i	$0.738819\pi$
$282$		0			0
$283$	66961.9	−	66961.9i	0.836094	−	0.836094i	−0.152248	−	0.988342i	$-0.548651\pi$
$283$	66961.9	−	66961.9i	0.836094	−	0.836094i	0.988342	+	0.152248i	$0.0486513\pi$
$284$		0			0
$285$	−79851.2	−	95552.3i	−0.983087	−	1.17639i
$286$		0			0
$287$	17791.8	+	17791.8i	0.216001	+	0.216001i
$288$		0			0
$289$		−	56893.9i		−	0.681193i
$290$		0			0
$291$	−241398.			−2.85067
$292$		0			0
$293$	115668.	−	115668.i	1.34735	−	1.34735i	0.458817	−	0.888531i	$-0.348273\pi$
$293$	115668.	−	115668.i	1.34735	−	1.34735i	0.888531	−	0.458817i	$-0.151727\pi$
$294$		0			0
$295$	300.466	−	3356.63i	0.00345264	−	0.0385709i
$296$		0			0
$297$	305083.	+	305083.i	3.45864	+	3.45864i
$298$		0			0
$299$			100290.i			1.12180i
$300$		0			0
$301$	21106.8			0.232964
$302$		0			0
$303$	113066.	−	113066.i	1.23154	−	1.23154i
$304$		0			0
$305$	−60197.4	−	5388.52i	−0.647110	−	0.0579255i
$306$		0			0
$307$	30159.7	+	30159.7i	0.320000	+	0.320000i	0.848767	−	0.528767i	$-0.177345\pi$
$307$	30159.7	+	30159.7i	0.320000	+	0.320000i	−0.528767	+	0.848767i	$0.677345\pi$
$308$		0			0
$309$		−	3097.24i		−	0.0324383i
$310$		0			0
$311$	−39594.0			−0.409363			−0.204681	−	0.978829i	$-0.565616\pi$
$311$	−39594.0			−0.409363			−0.204681	+	0.978829i	$0.565616\pi$
$312$		0			0
$313$	−37570.1	+	37570.1i	−0.383490	+	0.383490i	−0.872358	−	0.488868i	$-0.837410\pi$
$313$	−37570.1	+	37570.1i	−0.383490	+	0.383490i	0.488868	+	0.872358i	$0.337410\pi$
$314$		0			0
$315$	121654.	−	101664.i	1.22604	−	1.02458i
$316$		0			0
$317$	53295.0	+	53295.0i	0.530356	+	0.530356i	0.920678	−	0.390322i	$-0.127636\pi$
$317$	53295.0	+	53295.0i	0.530356	+	0.530356i	−0.390322	+	0.920678i	$0.627636\pi$
$318$		0			0
$319$		−	5067.03i		−	0.0497935i
$320$		0			0
$321$	−277924.			−2.69722
$322$		0			0
$323$	34188.6	−	34188.6i	0.327700	−	0.327700i
$324$		0			0
$325$	−103830.	+	72082.2i	−0.983005	+	0.682435i
$326$		0			0
$327$	−86992.4	−	86992.4i	−0.813552	−	0.813552i
$328$		0			0
$329$		−	41143.6i		−	0.380111i
$330$		0			0
$331$	−71328.5			−0.651039			−0.325519	−	0.945535i	$-0.605539\pi$
$331$	−71328.5			−0.651039			−0.325519	+	0.945535i	$0.605539\pi$
$332$		0			0
$333$	−299955.	+	299955.i	−2.70500	+	2.70500i
$334$		0			0
$335$	29146.9	+	34878.0i	0.259718	+	0.310787i
$336$		0			0
$337$	−689.307	−	689.307i	−0.00606950	−	0.00606950i	0.704066	−	0.710135i	$-0.251366\pi$
$337$	−689.307	−	689.307i	−0.00606950	−	0.00606950i	−0.710135	+	0.704066i	$0.751366\pi$
$338$		0			0
$339$			28949.1i			0.251905i
$340$		0			0
$341$	−69124.0			−0.594456
$342$		0			0
$343$	−84802.6	+	84802.6i	−0.720810	+	0.720810i
$344$		0			0
$345$	18581.4	−	207580.i	0.156113	−	1.74401i
$346$		0			0
$347$	−30073.5	−	30073.5i	−0.249762	−	0.249762i	0.571111	−	0.820873i	$-0.306513\pi$
$347$	−30073.5	−	30073.5i	−0.249762	−	0.249762i	−0.820873	+	0.571111i	$0.806513\pi$
$348$		0			0
$349$			128085.i			1.05160i	0.850610	+	0.525798i	$0.176233\pi$
$349$			128085.i			1.05160i	−0.850610	+	0.525798i	$0.823767\pi$
$350$		0			0
$351$	−409989.			−3.32781
$352$		0			0
$353$	−66658.5	+	66658.5i	−0.534941	+	0.534941i	−0.922039	−	0.387098i	$-0.873478\pi$
$353$	−66658.5	+	66658.5i	−0.534941	+	0.534941i	0.387098	+	0.922039i	$0.373478\pi$
$354$		0			0
$355$	−114235.	−	10225.6i	−0.906445	−	0.0811397i
$356$		0			0
$357$	61017.0	+	61017.0i	0.478756	+	0.478756i
$358$		0			0
$359$			144282.i			1.11950i	0.828662	+	0.559749i	$0.189102\pi$
$359$			144282.i			1.11950i	−0.828662	+	0.559749i	$0.810898\pi$
$360$		0			0
$361$	42526.3			0.326320
$362$		0			0
$363$	−364371.	+	364371.i	−2.76522	+	2.76522i
$364$		0			0
$365$	83065.5	−	69416.2i	0.623498	−	0.521045i
$366$		0			0
$367$	10896.8	+	10896.8i	0.0809030	+	0.0809030i	0.746400	−	0.665497i	$-0.231780\pi$
$367$	10896.8	+	10896.8i	0.0809030	+	0.0809030i	−0.665497	+	0.746400i	$0.731780\pi$
$368$		0			0
$369$			161248.i			1.18424i
$370$		0			0
$371$	81677.5			0.593410
$372$		0			0
$373$	−2879.15	+	2879.15i	−0.0206941	+	0.0206941i	−0.717378	−	0.696684i	$-0.754658\pi$
$373$	−2879.15	+	2879.15i	−0.0206941	+	0.0206941i	0.696684	+	0.717378i	$0.254658\pi$
$374$		0			0
$375$	228262.	−	129959.i	1.62320	−	0.924150i
$376$		0			0
$377$	3404.69	+	3404.69i	0.0239550	+	0.0239550i
$378$		0			0
$379$			249883.i			1.73964i	0.493372	+	0.869818i	$0.335764\pi$
$379$			249883.i			1.73964i	−0.493372	+	0.869818i	$0.664236\pi$
$380$		0			0
$381$	−355531.			−2.44922
$382$		0			0
$383$	−10909.7	+	10909.7i	−0.0743732	+	0.0743732i	−0.743315	−	0.668942i	$-0.766748\pi$
$383$	−10909.7	+	10909.7i	−0.0743732	+	0.0743732i	0.668942	+	0.743315i	$0.266748\pi$
$384$		0			0
$385$	107327.	+	128430.i	0.724080	+	0.866456i
$386$		0			0
$387$	95645.7	+	95645.7i	0.638621	+	0.638621i
$388$		0			0
$389$			98799.1i			0.652911i	0.945213	+	0.326455i	$0.105854\pi$
$389$			98799.1i			0.652911i	−0.945213	+	0.326455i	$0.894146\pi$
$390$		0			0
$391$	80920.6			0.529304
$392$		0			0
$393$	−62299.6	+	62299.6i	−0.403367	+	0.403367i
$394$		0			0
$395$	10015.3	−	111885.i	0.0641903	−	0.717096i
$396$		0			0
$397$	113044.	+	113044.i	0.717240	+	0.717240i	0.968039	−	0.250799i	$-0.0806933\pi$
$397$	113044.	+	113044.i	0.717240	+	0.717240i	−0.250799	+	0.968039i	$0.580693\pi$
$398$		0			0
$399$		−	156689.i		−	0.984220i
$400$		0			0
$401$	241590.			1.50242			0.751209	−	0.660064i	$-0.229471\pi$
$401$	241590.			1.50242			0.751209	+	0.660064i	$0.229471\pi$
$402$		0			0
$403$	46446.5	−	46446.5i	0.285985	−	0.285985i
$404$		0			0
$405$	441992.	+	39564.6i	2.69466	+	0.241211i
$406$		0			0
$407$	−316663.	−	316663.i	−1.91165	−	1.91165i
$408$		0			0
$409$			135173.i			0.808060i	0.914746	+	0.404030i	$0.132391\pi$
$409$			135173.i			0.808060i	−0.914746	+	0.404030i	$0.867609\pi$
$410$		0			0
$411$	525865.			3.11308
$412$		0			0
$413$	2998.49	−	2998.49i	0.0175793	−	0.0175793i
$414$		0			0
$415$	−33595.5	+	28075.1i	−0.195067	+	0.163014i
$416$		0			0
$417$	−199910.	−	199910.i	−1.14964	−	1.14964i
$418$		0			0
$419$		−	57476.5i		−	0.327388i	−0.986511	−	0.163694i	$-0.947659\pi$
$419$		−	57476.5i		−	0.327388i	0.986511	−	0.163694i	$-0.0523409\pi$
$420$		0			0
$421$	217580.			1.22759			0.613796	−	0.789465i	$-0.289642\pi$
$421$	217580.			1.22759			0.613796	+	0.789465i	$0.289642\pi$
$422$		0			0
$423$	186443.	−	186443.i	1.04199	−	1.04199i
$424$		0			0
$425$	58160.7	+	83776.8i	0.321997	+	0.463816i
$426$		0			0
$427$	−53774.6	−	53774.6i	−0.294932	−	0.294932i
$428$		0			0
$429$		−	723543.i		−	3.93142i
$430$		0			0
$431$	−84807.6			−0.456541			−0.228271	−	0.973598i	$-0.573307\pi$
$431$	−84807.6			−0.456541			−0.228271	+	0.973598i	$0.573307\pi$
$432$		0			0
$433$	−40613.6	+	40613.6i	−0.216618	+	0.216618i	−0.807072	−	0.590453i	$-0.798949\pi$
$433$	−40613.6	+	40613.6i	−0.216618	+	0.216618i	0.590453	+	0.807072i	$0.298949\pi$
$434$		0			0
$435$	−6416.23	−	7677.85i	−0.0339079	−	0.0405752i
$436$		0			0
$437$	−103900.	−	103900.i	−0.544068	−	0.544068i
$438$		0			0
$439$		−	153018.i		−	0.793989i	−0.917821	−	0.396995i	$-0.870053\pi$
$439$		−	153018.i		−	0.793989i	0.917821	−	0.396995i	$-0.129947\pi$
$440$		0			0
$441$	−284539.			−1.46307
$442$		0			0
$443$	122642.	−	122642.i	0.624929	−	0.624929i	−0.321859	−	0.946788i	$-0.604308\pi$
$443$	122642.	−	122642.i	0.624929	−	0.624929i	0.946788	+	0.321859i	$0.104308\pi$
$444$		0			0
$445$	29906.7	−	334100.i	0.151025	−	1.68716i
$446$		0			0
$447$	492042.	+	492042.i	2.46256	+	2.46256i
$448$		0			0
$449$		−	241072.i		−	1.19579i	−0.801575	−	0.597894i	$-0.796004\pi$
$449$		−	241072.i		−	1.19579i	0.801575	−	0.597894i	$-0.203996\pi$
$450$		0			0
$451$	−170229.			−0.836916
$452$		0			0
$453$	−363241.	+	363241.i	−1.77010	+	1.77010i
$454$		0			0
$455$	−158412.	−	14180.2i	−0.765185	−	0.0684949i
$456$		0			0
$457$	3300.64	+	3300.64i	0.0158039	+	0.0158039i	0.714965	−	0.699161i	$-0.246443\pi$
$457$	3300.64	+	3300.64i	0.0158039	+	0.0158039i	−0.699161	+	0.714965i	$0.746443\pi$
$458$		0			0
$459$			330806.i			1.57018i
$460$		0			0
$461$	−278003.			−1.30812			−0.654061	−	0.756442i	$-0.726936\pi$
$461$	−278003.			−1.30812			−0.654061	+	0.756442i	$0.726936\pi$
$462$		0			0
$463$	288618.	−	288618.i	1.34636	−	1.34636i	0.456781	−	0.889579i	$-0.349002\pi$
$463$	288618.	−	288618.i	1.34636	−	1.34636i	0.889579	−	0.456781i	$-0.150998\pi$
$464$		0			0
$465$	−104740.	+	87529.5i	−0.484405	+	0.404808i
$466$		0			0
$467$	−218636.	−	218636.i	−1.00251	−	1.00251i	−0.999997	−	0.00251206i	$-0.999200\pi$
$467$	−218636.	−	218636.i	−1.00251	−	1.00251i	−0.00251206	−	0.999997i	$-0.500800\pi$
$468$		0			0
$469$			57193.8i			0.260018i
$470$		0			0
$471$	134194.			0.604911
$472$		0			0
$473$	−100973.	+	100973.i	−0.451320	+	0.451320i
$474$		0			0
$475$	32890.5	−	182244.i	0.145775	−	0.807731i
$476$		0			0
$477$	370123.	+	370123.i	1.62671	+	1.62671i
$478$		0			0
$479$		−	176726.i		−	0.770245i	−0.922866	−	0.385122i	$-0.874159\pi$
$479$		−	176726.i		−	0.770245i	0.922866	−	0.385122i	$-0.125841\pi$
$480$		0			0
$481$	425551.			1.83934
$482$		0			0
$483$	185433.	−	185433.i	0.794862	−	0.794862i
$484$		0			0
$485$	−230205.	−	275471.i	−0.978661	−	1.17109i
$486$		0			0
$487$	83355.2	+	83355.2i	0.351459	+	0.351459i	0.860652	−	0.509193i	$-0.170056\pi$
$487$	83355.2	+	83355.2i	0.351459	+	0.351459i	−0.509193	+	0.860652i	$0.670056\pi$
$488$		0			0
$489$		−	437387.i		−	1.82915i
$490$		0			0
$491$	323055.			1.34002			0.670012	−	0.742350i	$-0.266289\pi$
$491$	323055.			1.34002			0.670012	+	0.742350i	$0.266289\pi$
$492$		0			0
$493$	2747.13	−	2747.13i	0.0113028	−	0.0113028i
$494$		0			0
$495$	−95631.4	+	1.06834e6i	−0.390292	+	4.36012i
$496$		0			0
$497$	−102046.	−	102046.i	−0.413128	−	0.413128i
$498$		0			0
$499$		−	305073.i		−	1.22519i	−0.790397	−	0.612594i	$-0.790126\pi$
$499$		−	305073.i		−	1.22519i	0.790397	−	0.612594i	$-0.209874\pi$
$500$		0			0
$501$	121093.			0.482441
$502$		0			0
$503$	−113631.	+	113631.i	−0.449120	+	0.449120i	−0.895062	−	0.445942i	$-0.852869\pi$
$503$	−113631.	+	113631.i	−0.449120	+	0.449120i	0.445942	+	0.895062i	$0.352869\pi$
$504$		0			0
$505$	236850.	+	21201.4i	0.928732	+	0.0831347i
$506$		0			0
$507$	146670.	+	146670.i	0.570592	+	0.570592i
$508$		0			0
$509$			287113.i			1.10820i	0.832451	+	0.554098i	$0.186937\pi$
$509$			287113.i			1.10820i	−0.832451	+	0.554098i	$0.813063\pi$
$510$		0			0
$511$	136213.			0.521645
$512$		0			0
$513$	424748.	−	424748.i	1.61397	−	1.61397i
$514$		0			0
$515$	3534.41	−	2953.64i	0.0133261	−	0.0111364i
$516$		0			0
$517$	196828.	+	196828.i	0.736387	+	0.736387i
$518$		0			0
$519$		−	239000.i		−	0.887285i
$520$		0			0
$521$	22942.8			0.0845222			0.0422611	−	0.999107i	$-0.486544\pi$
$521$	22942.8			0.0845222			0.0422611	+	0.999107i	$0.486544\pi$
$522$		0			0
$523$	−340907.	+	340907.i	−1.24633	+	1.24633i	−0.288997	+	0.957330i	$0.593322\pi$
$523$	−340907.	+	340907.i	−1.24633	+	1.24633i	−0.957330	+	0.288997i	$0.906678\pi$
$524$		0			0
$525$	325255.	+	58700.2i	1.18006	+	0.212971i
$526$		0			0
$527$	−37476.1	−	37476.1i	−0.134938	−	0.134938i
$528$		0			0
$529$			33920.8i			0.121214i
$530$		0			0
$531$	27175.4			0.0963801
$532$		0			0
$533$	114382.	−	114382.i	0.402629	−	0.402629i
$534$		0			0
$535$	−265039.	−	317153.i	−0.925980	−	1.10805i
$536$		0			0
$537$	243262.	+	243262.i	0.843578	+	0.843578i
$538$		0			0
$539$		−	300388.i		−	1.03396i
$540$		0			0
$541$	−277374.			−0.947700			−0.473850	−	0.880606i	$-0.657136\pi$
$541$	−277374.			−0.947700			−0.473850	+	0.880606i	$0.657136\pi$
$542$		0			0
$543$	−213441.	+	213441.i	−0.723900	+	0.723900i
$544$		0			0
$545$	16312.2	−	182230.i	0.0549187	−	0.613519i
$546$		0			0
$547$	−267466.	−	267466.i	−0.893910	−	0.893910i	0.100979	−	0.994889i	$-0.467803\pi$
$547$	−267466.	−	267466.i	−0.893910	−	0.893910i	−0.994889	+	0.100979i	$0.967803\pi$
$548$		0			0
$549$		−	487361.i		−	1.61698i
$550$		0			0
$551$	−7054.50			−0.0232361
$552$		0			0
$553$	99947.2	−	99947.2i	0.326829	−	0.326829i
$554$		0			0
$555$	−880805.	−	78844.6i	−2.85952	−	0.255968i
$556$		0			0
$557$	−52040.5	−	52040.5i	−0.167738	−	0.167738i	0.618246	−	0.785984i	$-0.287843\pi$
$557$	−52040.5	−	52040.5i	−0.167738	−	0.167738i	−0.785984	+	0.618246i	$0.787843\pi$
$558$		0			0
$559$		−	135694.i		−	0.434248i
$560$		0			0
$561$	−583802.			−1.85498
$562$		0			0
$563$	−283287.	+	283287.i	−0.893738	+	0.893738i	−0.994873	−	0.101135i	$-0.967753\pi$
$563$	−283287.	+	283287.i	−0.893738	+	0.893738i	0.101135	+	0.994873i	$0.467753\pi$
$564$		0			0
$565$	−33035.3	+	27606.9i	−0.103486	+	0.0864812i
$566$		0			0
$567$	394834.	+	394834.i	1.22814	+	1.22814i
$568$		0			0
$569$			241718.i			0.746595i	0.927712	+	0.373298i	$0.121773\pi$
$569$			241718.i			0.746595i	−0.927712	+	0.373298i	$0.878227\pi$
$570$		0			0
$571$	420399.			1.28940			0.644702	−	0.764434i	$-0.276981\pi$
$571$	420399.			1.28940			0.644702	+	0.764434i	$0.276981\pi$
$572$		0			0
$573$	597069.	−	597069.i	1.81851	−	1.81851i
$574$		0			0
$575$	254600.	−	176752.i	0.770057	−	0.534600i
$576$		0			0
$577$	273108.	+	273108.i	0.820320	+	0.820320i	0.986154	−	0.165834i	$-0.0530315\pi$
$577$	273108.	+	273108.i	0.820320	+	0.820320i	−0.165834	+	0.986154i	$0.553032\pi$
$578$		0			0
$579$		−	552423.i		−	1.64784i
$580$		0			0
$581$	−55090.6			−0.163202
$582$		0			0
$583$	−390740.	+	390740.i	−1.14961	+	1.14961i
$584$		0			0
$585$	−653591.	−	782106.i	−1.90983	−	2.28536i
$586$		0			0
$587$	175793.	+	175793.i	0.510181	+	0.510181i	0.914582	−	0.404401i	$-0.132520\pi$
$587$	175793.	+	175793.i	0.510181	+	0.510181i	−0.404401	+	0.914582i	$0.632520\pi$
$588$		0			0
$589$			96236.8i			0.277403i
$590$		0			0
$591$	−828678.			−2.37252
$592$		0			0
$593$	−319433.	+	319433.i	−0.908386	+	0.908386i	−0.996142	−	0.0877563i	$-0.972030\pi$
$593$	−319433.	+	319433.i	−0.908386	+	0.908386i	0.0877563	+	0.996142i	$0.472030\pi$
$594$		0			0
$595$	−11441.5	+	127817.i	−0.0323183	+	0.361041i
$596$		0			0
$597$	−618600.	−	618600.i	−1.73565	−	1.73565i
$598$		0			0
$599$			392811.i			1.09479i	0.836875	+	0.547394i	$0.184380\pi$
$599$			392811.i			1.09479i	−0.836875	+	0.547394i	$0.815620\pi$
$600$		0			0
$601$	382579.			1.05919			0.529593	−	0.848252i	$-0.322344\pi$
$601$	382579.			1.05919			0.529593	+	0.848252i	$0.322344\pi$
$602$		0			0
$603$	−259174.	+	259174.i	−0.712783	+	0.712783i
$604$		0			0
$605$	−763279.	−	68324.3i	−2.08532	−	0.186666i
$606$		0			0
$607$	−52520.3	−	52520.3i	−0.142544	−	0.142544i	0.632234	−	0.774778i	$-0.282138\pi$
$607$	−52520.3	−	52520.3i	−0.142544	−	0.142544i	−0.774778	+	0.632234i	$0.782138\pi$
$608$		0			0
$609$		−	12590.3i		−	0.0339470i
$610$		0			0
$611$	−264510.			−0.708532
$612$		0			0
$613$	462843.	−	462843.i	1.23172	−	1.23172i	0.268420	−	0.963302i	$-0.413499\pi$
$613$	462843.	−	462843.i	1.23172	−	1.23172i	0.963302	−	0.268420i	$-0.0865014\pi$
$614$		0			0
$615$	−257941.	+	215556.i	−0.681978	+	0.569916i
$616$		0			0
$617$	−242154.	−	242154.i	−0.636094	−	0.636094i	0.313496	−	0.949590i	$-0.398500\pi$
$617$	−242154.	−	242154.i	−0.636094	−	0.636094i	−0.949590	+	0.313496i	$0.898500\pi$
$618$		0			0
$619$		−	265002.i		−	0.691620i	−0.938305	−	0.345810i	$-0.887604\pi$
$619$		−	265002.i		−	0.691620i	0.938305	−	0.345810i	$-0.112396\pi$
$620$		0			0
$621$	1.00533e6			2.60691
$622$		0			0
$623$	298453.	−	298453.i	0.768954	−	0.768954i
$624$		0			0
$625$	365982.	+	136548.i	0.936913	+	0.349564i
$626$		0			0
$627$	749588.	+	749588.i	1.90672	+	1.90672i
$628$		0			0
$629$		−	343362.i		−	0.867863i
$630$		0			0
$631$	−39501.6			−0.0992102			−0.0496051	−	0.998769i	$-0.515796\pi$
$631$	−39501.6			−0.0992102			−0.0496051	+	0.998769i	$0.515796\pi$
$632$		0			0
$633$	379333.	−	379333.i	0.946701	−	0.946701i
$634$		0			0
$635$	−339048.	−	405714.i	−0.840840	−	1.00617i
$636$		0			0
$637$	201840.	+	201840.i	0.497426	+	0.497426i
$638$		0			0
$639$		−	924849.i		−	2.26501i
$640$		0			0
$641$	−213812.			−0.520375			−0.260188	−	0.965558i	$-0.583784\pi$
$641$	−213812.			−0.520375			−0.260188	+	0.965558i	$0.583784\pi$
$642$		0			0
$643$	−12595.9	+	12595.9i	−0.0304654	+	0.0304654i	−0.722175	−	0.691710i	$-0.756858\pi$
$643$	−12595.9	+	12595.9i	−0.0304654	+	0.0304654i	0.691710	+	0.722175i	$0.256858\pi$
$644$		0			0
$645$	−25141.0	+	280860.i	−0.0604313	+	0.675103i
$646$		0			0
$647$	174745.	+	174745.i	0.417441	+	0.417441i	0.884321	−	0.466879i	$-0.154622\pi$
$647$	174745.	+	174745.i	0.417441	+	0.417441i	−0.466879	+	0.884321i	$0.654622\pi$
$648$		0			0
$649$			28689.2i			0.0681127i
$650$		0			0
$651$	−171756.			−0.405274
$652$		0			0
$653$	−91222.0	+	91222.0i	−0.213931	+	0.213931i	−0.805935	−	0.592004i	$-0.798337\pi$
$653$	−91222.0	+	91222.0i	−0.213931	+	0.213931i	0.592004	+	0.805935i	$0.298337\pi$
$654$		0			0
$655$	−130504.	−	11682.0i	−0.304188	−	0.0272292i
$656$		0			0
$657$	617249.	+	617249.i	1.42998	+	1.42998i
$658$		0			0
$659$			487216.i			1.12189i	0.827852	+	0.560946i	$0.189562\pi$
$659$			487216.i			1.12189i	−0.827852	+	0.560946i	$0.810438\pi$
$660$		0			0
$661$	−122005.			−0.279238			−0.139619	−	0.990205i	$-0.544588\pi$
$661$	−122005.			−0.279238			−0.139619	+	0.990205i	$0.544588\pi$
$662$		0			0
$663$	392274.	−	392274.i	0.892407	−	0.892407i
$664$		0			0
$665$	178805.	−	149424.i	0.404331	−	0.337892i
$666$		0			0
$667$	−8348.61	−	8348.61i	−0.0187656	−	0.0187656i
$668$		0			0
$669$			1.42887e6i			3.19257i
$670$		0			0
$671$	514508.			1.14274
$672$		0			0
$673$	−57907.9	+	57907.9i	−0.127852	+	0.127852i	−0.768137	−	0.640285i	$-0.778816\pi$
$673$	−57907.9	+	57907.9i	−0.127852	+	0.127852i	0.640285	+	0.768137i	$0.278816\pi$
$674$		0			0
$675$	722569.	+	1.04082e6i	1.58589	+	2.28437i
$676$		0			0
$677$	−239495.	−	239495.i	−0.522540	−	0.522540i	0.395798	−	0.918338i	$-0.370468\pi$
$677$	−239495.	−	239495.i	−0.522540	−	0.522540i	−0.918338	+	0.395798i	$0.870468\pi$
$678$		0			0
$679$		−	451723.i		−	0.979789i
$680$		0			0
$681$	−554075.			−1.19474
$682$		0			0
$683$	274018.	−	274018.i	0.587405	−	0.587405i	−0.349523	−	0.936928i	$-0.613656\pi$
$683$	274018.	−	274018.i	0.587405	−	0.587405i	0.936928	+	0.349523i	$0.113656\pi$
$684$		0			0
$685$	501484.	+	600091.i	1.06875	+	1.27890i
$686$		0			0
$687$	−179422.	−	179422.i	−0.380155	−	0.380155i
$688$		0			0
$689$		−	525100.i		−	1.10612i
$690$		0			0
$691$	431064.			0.902787			0.451393	−	0.892325i	$-0.350927\pi$
$691$	431064.			0.902787			0.451393	+	0.892325i	$0.350927\pi$
$692$		0			0
$693$	−954350.	+	954350.i	−1.98720	+	1.98720i
$694$		0			0
$695$	37485.7	−	418768.i	0.0776061	−	0.866970i
$696$		0			0
$697$	−92291.2	−	92291.2i	−0.189974	−	0.189974i
$698$		0			0
$699$			129209.i			0.264447i
$700$		0			0
$701$	305736.			0.622172			0.311086	−	0.950382i	$-0.399307\pi$
$701$	305736.			0.622172			0.311086	+	0.950382i	$0.399307\pi$
$702$		0			0
$703$	−440869.	+	440869.i	−0.892070	+	0.892070i
$704$		0			0
$705$	547482.	+	49007.5i	1.10152	+	0.0986016i
$706$		0			0
$707$	211579.	+	211579.i	0.423286	+	0.423286i
$708$		0			0
$709$			695518.i			1.38362i	0.722081	+	0.691809i	$0.243186\pi$
$709$			695518.i			1.38362i	−0.722081	+	0.691809i	$0.756814\pi$
$710$		0			0
$711$	905825.			1.79186
$712$		0			0
$713$	−113891.	+	113891.i	−0.224032	+	0.224032i
$714$		0			0
$715$	825671.	−	689997.i	1.61508	−	1.34969i
$716$		0			0
$717$	−1.00657e6	−	1.00657e6i	−1.95797	−	1.95797i
$718$		0			0
$719$		−	585333.i		−	1.13226i	−0.824317	−	0.566129i	$-0.808441\pi$
$719$		−	585333.i		−	1.13226i	0.824317	−	0.566129i	$-0.191559\pi$
$720$		0			0
$721$	5795.81			0.0111492
$722$		0			0
$723$	475361.	−	475361.i	0.909384	−	0.909384i
$724$		0			0
$725$	2642.82	−	14643.8i	0.00502797	−	0.0278597i
$726$		0			0
$727$	−199545.	−	199545.i	−0.377548	−	0.377548i	0.492669	−	0.870217i	$-0.336021\pi$
$727$	−199545.	−	199545.i	−0.377548	−	0.377548i	−0.870217	+	0.492669i	$0.836021\pi$
$728$		0			0
$729$			817943.i			1.53910i
$730$		0			0
$731$	−109487.			−0.204893
$732$		0			0
$733$	440566.	−	440566.i	0.819980	−	0.819980i	−0.166125	−	0.986105i	$-0.553125\pi$
$733$	440566.	−	440566.i	0.819980	−	0.819980i	0.986105	+	0.166125i	$0.0531255\pi$
$734$		0			0
$735$	−380373.	−	455165.i	−0.704100	−	0.842548i
$736$		0			0
$737$	−273611.	−	273611.i	−0.503731	−	0.503731i
$738$		0			0
$739$			502182.i			0.919543i	0.888037	+	0.459771i	$0.152069\pi$
$739$			502182.i			0.919543i	−0.888037	+	0.459771i	$0.847931\pi$
$740$		0			0
$741$	−1.00734e6			−1.83460
$742$		0			0
$743$	67600.2	−	67600.2i	0.122453	−	0.122453i	−0.643224	−	0.765678i	$-0.722404\pi$
$743$	67600.2	−	67600.2i	0.122453	−	0.122453i	0.765678	+	0.643224i	$0.222404\pi$
$744$		0			0
$745$	−92264.3	+	1.03072e6i	−0.166234	+	1.85707i
$746$		0			0
$747$	−249644.	−	249644.i	−0.447383	−	0.447383i
$748$		0			0
$749$		−	520074.i		−	0.927047i
$750$		0			0
$751$	1.00829e6			1.78775			0.893873	−	0.448319i	$-0.147977\pi$
$751$	1.00829e6			1.78775			0.893873	+	0.448319i	$0.147977\pi$
$752$		0			0
$753$	−1.10074e6	+	1.10074e6i	−1.94130	+	1.94130i
$754$		0			0
$755$	−760912.	−	68112.5i	−1.33487	−	0.119490i
$756$		0			0
$757$	530890.	+	530890.i	0.926431	+	0.926431i	0.997473	−	0.0710427i	$-0.0226327\pi$
$757$	530890.	+	530890.i	0.926431	+	0.926431i	−0.0710427	+	0.997473i	$0.522633\pi$
$758$		0			0
$759$			1.77419e6i			3.07976i
$760$		0			0
$761$	−750812.			−1.29647			−0.648234	−	0.761441i	$-0.724492\pi$
$761$	−750812.			−1.29647			−0.648234	+	0.761441i	$0.724492\pi$
$762$		0			0
$763$	162787.	−	162787.i	0.279622	−	0.279622i
$764$		0			0
$765$	−631054.	+	527360.i	−1.07831	+	0.901123i
$766$		0			0
$767$	−19277.1	−	19277.1i	−0.0327681	−	0.0327681i
$768$		0			0
$769$		−	529196.i		−	0.894878i	−0.894314	−	0.447439i	$-0.852336\pi$
$769$		−	529196.i		−	0.894878i	0.894314	−	0.447439i	$-0.147664\pi$
$770$		0			0
$771$	−341251.			−0.574071
$772$		0			0
$773$	−154197.	+	154197.i	−0.258057	+	0.258057i	−0.824263	−	0.566206i	$-0.808411\pi$
$773$	−154197.	+	154197.i	−0.258057	+	0.258057i	0.566206	+	0.824263i	$0.308411\pi$
$774$		0			0
$775$	−199769.	−	36053.2i	−0.332601	−	0.0600261i
$776$		0			0
$777$	−786827.	−	786827.i	−1.30328	−	1.30328i
$778$		0			0
$779$			237000.i			0.390546i
$780$		0			0
$781$	976365.			1.60070
$782$		0			0
$783$	34129.4	−	34129.4i	0.0556680	−	0.0556680i
$784$		0			0
$785$	127972.	+	153135.i	0.207671	+	0.248506i
$786$		0			0
$787$	−538266.	−	538266.i	−0.869055	−	0.869055i	0.123313	−	0.992368i	$-0.460648\pi$
$787$	−538266.	−	538266.i	−0.869055	−	0.869055i	−0.992368	+	0.123313i	$0.960648\pi$
$788$		0			0
$789$		−	1.40339e6i		−	2.25436i
$790$		0			0
$791$	−54172.0			−0.0865808
$792$		0			0
$793$	−345714.	+	345714.i	−0.549756	+	0.549756i
$794$		0			0
$795$	−97288.7	+	1.08685e6i	−0.153932	+	1.71963i
$796$		0			0
$797$	612655.	+	612655.i	0.964494	+	0.964494i	0.999391	−	0.0348973i	$-0.0111104\pi$
$797$	612655.	+	612655.i	0.964494	+	0.964494i	−0.0348973	+	0.999391i	$0.511110\pi$
$798$		0			0
$799$			213424.i			0.334310i
$800$		0			0
$801$	2.70489e6			4.21585
$802$		0			0
$803$	−651631.	+	651631.i	−1.01058	+	1.01058i
$804$		0			0
$805$	388441.	+	34771.0i	0.599424	+	0.0536569i
$806$		0			0
$807$	−653828.	−	653828.i	−1.00396	−	1.00396i
$808$		0			0
$809$			304723.i			0.465596i	0.972525	+	0.232798i	$0.0747880\pi$
$809$			304723.i			0.465596i	−0.972525	+	0.232798i	$0.925212\pi$
$810$		0			0
$811$	517570.			0.786914			0.393457	−	0.919343i	$-0.371279\pi$
$811$	517570.			0.786914			0.393457	+	0.919343i	$0.371279\pi$
$812$		0			0
$813$	−33148.4	+	33148.4i	−0.0501513	+	0.0501513i
$814$		0			0
$815$	499124.	−	417108.i	0.751439	−	0.627963i
$816$		0			0
$817$	140579.	+	140579.i	0.210608	+	0.210608i
$818$		0			0
$819$		−	1.28251e6i		−	1.91203i
$820$		0			0
$821$	270912.			0.401922			0.200961	−	0.979599i	$-0.435594\pi$
$821$	270912.			0.401922			0.200961	+	0.979599i	$0.435594\pi$
$822$		0			0
$823$	−698746.	+	698746.i	−1.03162	+	1.03162i	−0.0321369	+	0.999483i	$0.510231\pi$
$823$	−698746.	+	698746.i	−1.03162	+	1.03162i	−0.999483	+	0.0321369i	$0.989769\pi$
$824$		0			0
$825$	−1.83681e6	+	1.27518e6i	−2.69872	+	1.87354i
$826$		0			0
$827$	−796692.	−	796692.i	−1.16487	−	1.16487i	−0.983395	−	0.181480i	$-0.941911\pi$
$827$	−796692.	−	796692.i	−1.16487	−	1.16487i	−0.181480	−	0.983395i	$-0.558089\pi$
$828$		0			0
$829$		−	72341.1i		−	0.105263i	−0.998614	−	0.0526315i	$-0.983239\pi$
$829$		−	72341.1i		−	0.105263i	0.998614	−	0.0526315i	$-0.0167609\pi$
$830$		0			0
$831$	−1.56284e6			−2.26315
$832$		0			0
$833$	162858.	−	162858.i	0.234703	−	0.234703i
$834$		0			0
$835$	115479.	+	138185.i	0.165626	+	0.198193i
$836$		0			0
$837$	−465590.	−	465590.i	−0.664589	−	0.664589i
$838$		0			0
$839$			1.20946e6i			1.71818i	0.511823	+	0.859091i	$0.328970\pi$
$839$			1.20946e6i			1.71818i	−0.511823	+	0.859091i	$0.671030\pi$
$840$		0			0
$841$	706714.			0.999199
$842$		0			0
$843$	1.27995e6	−	1.27995e6i	1.80109	−	1.80109i
$844$		0			0
$845$	−27502.6	+	307242.i	−0.0385177	+	0.430296i
$846$		0			0
$847$	−681840.	−	681840.i	−0.950421	−	0.950421i
$848$		0			0
$849$			1.59193e6i			2.20856i
$850$		0			0
$851$	−1.04349e6			−1.44088
$852$		0			0
$853$	−866353.	+	866353.i	−1.19069	+	1.19069i	−0.213810	+	0.976875i	$0.568587\pi$
$853$	−866353.	+	866353.i	−1.19069	+	1.19069i	−0.976875	+	0.213810i	$0.931413\pi$
$854$		0			0
$855$	1.48738e6	+	133141.i	2.03465	+	0.182130i
$856$		0			0
$857$	−688481.	−	688481.i	−0.937411	−	0.937411i	0.0607421	−	0.998153i	$-0.480653\pi$
$857$	−688481.	−	688481.i	−0.937411	−	0.937411i	−0.998153	+	0.0607421i	$0.980653\pi$
$858$		0			0
$859$			204193.i			0.276729i	0.990381	+	0.138364i	$0.0441845\pi$
$859$			204193.i			0.276729i	−0.990381	+	0.138364i	$0.955816\pi$
$860$		0			0
$861$	−422977.			−0.570573
$862$		0			0
$863$	186718.	−	186718.i	0.250706	−	0.250706i	−0.570554	−	0.821260i	$-0.693271\pi$
$863$	186718.	−	186718.i	0.250706	−	0.250706i	0.821260	+	0.570554i	$0.193271\pi$
$864$		0			0
$865$	272735.	−	227919.i	0.364509	−	0.304613i
$866$		0			0
$867$	676290.	+	676290.i	0.899694	+	0.899694i
$868$		0			0
$869$			956282.i			1.26633i
$870$		0			0
$871$	367695.			0.484676
$872$		0			0
$873$	2.04699e6	−	2.04699e6i	2.68588	−	2.68588i
$874$		0			0
$875$	243189.	+	427143.i	0.317635	+	0.557901i
$876$		0			0
$877$	263947.	+	263947.i	0.343176	+	0.343176i	0.857560	−	0.514384i	$-0.171979\pi$
$877$	263947.	+	263947.i	0.343176	+	0.343176i	−0.514384	+	0.857560i	$0.671979\pi$
$878$		0			0
$879$			2.74987e6i			3.55905i
$880$		0			0
$881$	−25475.7			−0.0328227			−0.0164114	−	0.999865i	$-0.505224\pi$
$881$	−25475.7			−0.0328227			−0.0164114	+	0.999865i	$0.505224\pi$
$882$		0			0
$883$	−78535.9	+	78535.9i	−0.100727	+	0.100727i	−0.755675	−	0.654947i	$-0.772691\pi$
$883$	−78535.9	+	78535.9i	−0.100727	+	0.100727i	0.654947	+	0.755675i	$0.272691\pi$
$884$		0			0
$885$	36328.2	+	43471.4i	0.0463828	+	0.0555031i
$886$		0			0
$887$	−130030.	−	130030.i	−0.165270	−	0.165270i	0.619626	−	0.784897i	$-0.287284\pi$
$887$	−130030.	−	130030.i	−0.165270	−	0.165270i	−0.784897	+	0.619626i	$0.787284\pi$
$888$		0			0
$889$		−	665299.i		−	0.841809i
$890$		0			0
$891$	−3.77771e6			−4.75854
$892$		0			0
$893$	274031.	−	274031.i	0.343635	−	0.343635i
$894$		0			0
$895$	−45614.8	+	509581.i	−0.0569455	+	0.636161i
$896$		0			0
$897$	−1.19213e6	−	1.19213e6i	−1.48163	−	1.48163i
$898$		0			0
$899$			7732.85i			0.00956798i
$900$		0			0
$901$	−423685.			−0.521907
$902$		0			0
$903$	−250893.	+	250893.i	−0.307690	+	0.307690i
$904$		0			0
$905$	−447114.	−	40023.0i	−0.545910	−	0.0488667i
$906$		0			0
$907$	−136278.	−	136278.i	−0.165658	−	0.165658i	0.619410	−	0.785068i	$-0.287372\pi$
$907$	−136278.	−	136278.i	−0.165658	−	0.165658i	−0.785068	+	0.619410i	$0.787372\pi$
$908$		0			0
$909$			1.91755e6i			2.32070i
$910$		0			0
$911$	536004.			0.645849			0.322924	−	0.946425i	$-0.395334\pi$
$911$	536004.			0.645849			0.322924	+	0.946425i	$0.395334\pi$
$912$		0			0
$913$	263550.	−	263550.i	0.316170	−	0.316170i
$914$		0			0
$915$	779611.	−	651505.i	0.931184	−	0.778172i
$916$		0			0
$917$	−116580.	−	116580.i	−0.138639	−	0.138639i
$918$		0			0
$919$		−	503315.i		−	0.595949i	−0.954574	−	0.297974i	$-0.903689\pi$
$919$		−	503315.i		−	0.595949i	0.954574	−	0.297974i	$-0.0963110\pi$
$920$		0			0
$921$	−717008.			−0.845288
$922$		0			0
$923$	−656050.	+	656050.i	−0.770076	+	0.770076i
$924$		0			0
$925$	−749994.	−	1.08032e6i	−0.876546	−	1.26261i
$926$		0			0
$927$	26263.8	+	26263.8i	0.0305631	+	0.0305631i
$928$		0			0
$929$			599808.i			0.694994i	0.937681	+	0.347497i	$0.112968\pi$
$929$			599808.i			0.694994i	−0.937681	+	0.347497i	$0.887032\pi$
$930$		0			0
$931$	−418212.			−0.482499
$932$		0			0
$933$	470648.	−	470648.i	0.540671	−	0.540671i
$934$		0			0
$935$	−556735.	−	666205.i	−0.636832	−	0.762053i
$936$		0			0
$937$	66697.5	+	66697.5i	0.0759679	+	0.0759679i	0.744070	−	0.668102i	$-0.232893\pi$
$937$	66697.5	+	66697.5i	0.0759679	+	0.0759679i	−0.668102	+	0.744070i	$0.732893\pi$
$938$		0			0
$939$		−	893183.i		−	1.01300i
$940$		0			0
$941$	−1.05842e6			−1.19531			−0.597653	−	0.801755i	$-0.703900\pi$
$941$	−1.05842e6			−1.19531			−0.597653	+	0.801755i	$0.703900\pi$
$942$		0			0
$943$	−280476.	+	280476.i	−0.315408	+	0.315408i
$944$		0			0
$945$	−142145.	+	1.58796e6i	−0.159173	+	1.77818i
$946$		0			0
$947$	−233853.	−	233853.i	−0.260761	−	0.260761i	0.564602	−	0.825363i	$-0.309030\pi$
$947$	−233853.	−	233853.i	−0.260761	−	0.260761i	−0.825363	+	0.564602i	$0.809030\pi$
$948$		0			0
$949$		−	875702.i		−	0.972353i
$950$		0			0
$951$	−1.26702e6			−1.40095
$952$		0			0
$953$	572309.	−	572309.i	0.630152	−	0.630152i	−0.317954	−	0.948106i	$-0.602996\pi$
$953$	572309.	−	572309.i	0.630152	−	0.630152i	0.948106	+	0.317954i	$0.102996\pi$
$954$		0			0
$955$	1.25073e6	+	111958.i	1.37138	+	0.122758i
$956$		0			0
$957$	60231.1	+	60231.1i	0.0657653	+	0.0657653i
$958$		0			0
$959$			984042.i			1.06998i
$960$		0			0
$961$	−818030.			−0.885773
$962$		0			0
$963$	2.35672e6	−	2.35672e6i	2.54130	−	2.54130i
$964$		0			0
$965$	630398.	−	526811.i	0.676955	−	0.565718i
$966$		0			0
$967$	864750.	+	864750.i	0.924778	+	0.924778i	0.997362	−	0.0725841i	$-0.0231246\pi$
$967$	864750.	+	864750.i	0.924778	+	0.924778i	−0.0725841	+	0.997362i	$0.523125\pi$
$968$		0			0
$969$			812790.i			0.865627i
$970$		0			0
$971$	1.46781e6			1.55679			0.778397	−	0.627773i	$-0.216033\pi$
$971$	1.46781e6			1.55679			0.778397	+	0.627773i	$0.216033\pi$
$972$		0			0
$973$	374087.	−	374087.i	0.395137	−	0.395137i
$974$		0			0
$975$	377380.	−	2.09104e6i	0.396981	−	2.19965i
$976$		0			0
$977$	668236.	+	668236.i	0.700069	+	0.700069i	0.964425	−	0.264356i	$-0.0851594\pi$
$977$	668236.	+	668236.i	0.700069	+	0.700069i	−0.264356	+	0.964425i	$0.585159\pi$
$978$		0			0
$979$			2.85556e6i			2.97938i
$980$		0			0
$981$	1.47535e6			1.53305
$982$		0			0
$983$	672172.	−	672172.i	0.695622	−	0.695622i	−0.267841	−	0.963463i	$-0.586310\pi$
$983$	672172.	−	672172.i	0.695622	−	0.695622i	0.963463	+	0.267841i	$0.0863102\pi$
$984$		0			0
$985$	−790257.	−	945645.i	−0.814509	−	0.974666i
$986$		0			0
$987$	489068.	+	489068.i	0.502037	+	0.502037i
$988$		0			0
$989$			332734.i			0.340177i
$990$		0			0
$991$	1.33096e6			1.35524			0.677621	−	0.735411i	$-0.263011\pi$
$991$	1.33096e6			1.35524			0.677621	+	0.735411i	$0.263011\pi$
$992$		0			0
$993$	847872.	−	847872.i	0.859868	−	0.859868i
$994$		0			0
$995$	115996.	−	1.29584e6i	0.117164	−	1.30889i
$996$		0			0
$997$	−482609.	−	482609.i	−0.485518	−	0.485518i	0.421371	−	0.906889i	$-0.361549\pi$
$997$	−482609.	−	482609.i	−0.485518	−	0.485518i	−0.906889	+	0.421371i	$0.861549\pi$
$998$		0			0
$999$		−	4.26582e6i		−	4.27436i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.5.p.r.257.1		12
4.3	odd	2		320.5.p.s.257.6		12
5.3	odd	4	inner	320.5.p.r.193.1		12
8.3	odd	2		160.5.p.f.97.1	yes	12
8.5	even	2		160.5.p.e.97.6	yes	12
20.3	even	4		320.5.p.s.193.6		12
40.3	even	4		160.5.p.f.33.1	yes	12
40.13	odd	4		160.5.p.e.33.6	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.5.p.e.33.6	✓	12	40.13	odd	4
160.5.p.e.97.6	yes	12	8.5	even	2
160.5.p.f.33.1	yes	12	40.3	even	4
160.5.p.f.97.1	yes	12	8.3	odd	2
320.5.p.r.193.1		12	5.3	odd	4	inner
320.5.p.r.257.1		12	1.1	even	1	trivial
320.5.p.s.193.6		12	20.3	even	4
320.5.p.s.257.6		12	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	320.p (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-11.8869 + 11.8869i) q^{3} +(-24.9004 - 2.22894i) q^{5} +(-22.2437 - 22.2437i) q^{7} -201.595i q^{9} +212.824 q^{11} +(-143.003 + 143.003i) q^{13} +(322.483 - 269.493i) q^{15} +(115.384 + 115.384i) q^{17} -296.302i q^{19} +528.815 q^{21} +(350.657 - 350.657i) q^{23} +(615.064 + 111.003i) q^{25} +(1433.50 + 1433.50i) q^{27} -23.8085i q^{29} -324.793 q^{31} +(-2529.81 + 2529.81i) q^{33} +(504.297 + 603.457i) q^{35} +(-1487.91 - 1487.91i) q^{37} -3399.72i q^{39} -799.859 q^{41} +(-474.444 + 474.444i) q^{43} +(-449.344 + 5019.81i) q^{45} +(924.838 + 924.838i) q^{47} -1411.44i q^{49} -2743.12 q^{51} +(-1835.97 + 1835.97i) q^{53} +(-5299.42 - 474.374i) q^{55} +(3522.10 + 3522.10i) q^{57} +134.802i q^{59} +2417.52 q^{61} +(-4484.21 + 4484.21i) q^{63} +(3879.59 - 3242.10i) q^{65} +(-1285.62 - 1285.62i) q^{67} +8336.42i q^{69} +4587.66 q^{71} +(-3061.83 + 3061.83i) q^{73} +(-8630.66 + 5991.70i) q^{75} +(-4734.00 - 4734.00i) q^{77} +4493.29i q^{79} -17750.4 q^{81} +(1238.34 - 1238.34i) q^{83} +(-2615.94 - 3130.31i) q^{85} +(283.009 + 283.009i) q^{87} +13417.5i q^{89} +6361.83 q^{91} +(3860.77 - 3860.77i) q^{93} +(-660.440 + 7378.04i) q^{95} +(10154.0 + 10154.0i) q^{97} -42904.4i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{5} - 48 q^{7} + 320 q^{11} - 260 q^{13} + 592 q^{15} - 60 q^{17} + 400 q^{21} + 176 q^{23} + 836 q^{25} + 2208 q^{27} + 480 q^{31} - 3120 q^{33} + 2208 q^{35} + 500 q^{37} + 2160 q^{41} + 3744 q^{43}+ \cdots + 36460 q^{97}+O(q^{100}) \) 12 * q - 24 * q^5 - 48 * q^7 + 320 * q^11 - 260 * q^13 + 592 * q^15 - 60 * q^17 + 400 * q^21 + 176 * q^23 + 836 * q^25 + 2208 * q^27 + 480 * q^31 - 3120 * q^33 + 2208 * q^35 + 500 * q^37 + 2160 * q^41 + 3744 * q^43 + 3116 * q^45 - 1264 * q^47 - 16960 * q^51 - 7020 * q^53 - 8256 * q^55 + 1760 * q^57 - 2928 * q^61 - 15504 * q^63 + 5196 * q^65 + 2400 * q^67 + 31200 * q^71 - 340 * q^73 + 1472 * q^75 + 6960 * q^77 - 27676 * q^81 + 25952 * q^83 + 7292 * q^85 - 27744 * q^87 - 66240 * q^91 + 2640 * q^93 + 3552 * q^95 + 36460 * q^97

Introduction

L-functions

Modular forms

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Database

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