LMFDB - Embedded newform 160.5.p.f.33.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [160,5,Mod(33,160)] 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("160.33"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(160, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 3])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	160.p (of order $4$, degree $2$, 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:	$16.5391940934$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			33.1
Root			$-2.09327 + 0.657043i$ of defining polynomial
Character	$\chi$	$=$	160.33
Dual form			160.5.p.f.97.1

$q$-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 $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−11.8869	−	11.8869i	−1.32076	−	1.32076i	−0.913159	−	0.407604i	$-0.866364\pi$
$3$	−11.8869	−	11.8869i	−1.32076	−	1.32076i	−0.407604	−	0.913159i	$-0.633636\pi$
$4$		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	$-0.645983\pi$
$7$	22.2437	−	22.2437i	0.453952	−	0.453952i	0.896664	+	0.442712i	$0.145983\pi$
$8$		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	$-0.0458294\pi$
$13$	143.003	+	143.003i	0.846173	+	0.846173i	−0.143480	+	0.989653i	$0.545829\pi$
$14$		0			0
$15$	−322.483	−	269.493i	−1.43326	−	1.19775i
$16$		0			0
$17$	115.384	−	115.384i	0.399254	−	0.399254i	−0.478716	−	0.877970i	$-0.658898\pi$
$17$	115.384	−	115.384i	0.399254	−	0.399254i	0.877970	+	0.478716i	$0.158898\pi$
$18$		0			0
$19$			296.302i			0.820780i	0.911910	+	0.410390i	$0.134607\pi$
$19$			296.302i			0.820780i	−0.911910	+	0.410390i	$0.865393\pi$
$20$		0			0
$21$	−528.815			−1.19913
$22$		0			0
$23$	−350.657	−	350.657i	−0.662867	−	0.662867i	0.293188	−	0.956055i	$-0.405284\pi$
$23$	−350.657	−	350.657i	−0.662867	−	0.662867i	−0.956055	+	0.293188i	$0.905284\pi$
$24$		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	$-0.445950\pi$
$31$	324.793			0.337974			0.168987	+	0.985618i	$0.445950\pi$
$32$		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	0.0910056	−	0.995850i	$-0.470992\pi$
$37$	1487.91	−	1487.91i	1.08686	−	1.08686i	0.995850	−	0.0910056i	$-0.0290081\pi$
$38$		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	0.567073	−	0.823668i	$-0.308076\pi$
$43$	−474.444	−	474.444i	−0.256595	−	0.256595i	−0.823668	+	0.567073i	$0.808076\pi$
$44$		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	$-0.845667\pi$
$47$	−924.838	+	924.838i	−0.418668	+	0.418668i	0.466076	+	0.884745i	$0.345667\pi$
$48$		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	$-0.0970719\pi$
$53$	1835.97	+	1835.97i	0.653604	+	0.653604i	−0.300255	+	0.953859i	$0.597072\pi$
$54$		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	$-0.993836\pi$
$59$		−	134.802i		−	0.0387251i	0.999813	−	0.0193625i	$-0.00616367\pi$
$60$		0			0
$61$	−2417.52			−0.649697			−0.324849	−	0.945766i	$-0.605313\pi$
$61$	−2417.52			−0.649697			−0.324849	+	0.945766i	$0.605313\pi$
$62$		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	−0.835652	−	0.549259i	$-0.814910\pi$
$67$	−1285.62	+	1285.62i	−0.286393	+	0.286393i	0.549259	+	0.835652i	$0.314910\pi$
$68$		0			0
$69$			8336.42i			1.75098i
$70$		0			0
$71$	−4587.66			−0.910069			−0.455034	−	0.890474i	$-0.650373\pi$
$71$	−4587.66			−0.910069			−0.455034	+	0.890474i	$0.650373\pi$
$72$		0			0
$73$	−3061.83	−	3061.83i	−0.574559	−	0.574559i	0.358840	−	0.933399i	$-0.383172\pi$
$73$	−3061.83	−	3061.83i	−0.574559	−	0.574559i	−0.933399	+	0.358840i	$0.883172\pi$
$74$		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	0.791250	−	0.611493i	$-0.209431\pi$
$83$	1238.34	+	1238.34i	0.179757	+	0.179757i	−0.611493	+	0.791250i	$0.709431\pi$
$84$		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	$-0.678434\pi$
$89$		−	13417.5i		−	1.69391i	0.531666	−	0.846954i	$-0.321566\pi$
$90$		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	0.0825919	−	0.996583i	$-0.473680\pi$
$97$	10154.0	−	10154.0i	1.07918	−	1.07918i	0.996583	−	0.0825919i	$-0.0263198\pi$
$98$		0			0
$99$			42904.4i			4.37755i
$100$		0			0
$101$	9511.87			0.932445			0.466222	−	0.884668i	$-0.345615\pi$
$101$	9511.87			0.932445			0.466222	+	0.884668i	$0.345615\pi$
$102$		0			0
$103$	130.280	+	130.280i	0.0122801	+	0.0122801i	0.713220	−	0.700940i	$-0.247236\pi$
$103$	130.280	+	130.280i	0.0122801	+	0.0122801i	−0.700940	+	0.713220i	$0.747236\pi$
$104$		0			0
$105$	−13167.7	+	1178.70i	−1.19435	+	0.106911i
$106$		0			0
$107$	11690.4	−	11690.4i	1.02108	−	1.02108i	0.0213109	−	0.999773i	$-0.493216\pi$
$107$	11690.4	−	11690.4i	1.02108	−	1.02108i	0.999773	−	0.0213109i	$-0.00678397\pi$
$108$		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	0.753179	−	0.657816i	$-0.228519\pi$
$113$	1217.69	+	1217.69i	0.0953633	+	0.0953633i	−0.657816	+	0.753179i	$0.728519\pi$
$114$		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	$-0.977596\pi$
$127$	−14954.8	+	14954.8i	−0.927199	+	0.927199i	0.0703251	+	0.997524i	$0.477596\pi$
$128$		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	−0.198396	+	0.980122i	$0.563573\pi$
$137$	−22119.6	+	22119.6i	−1.17852	+	1.17852i	−0.980122	+	0.198396i	$0.936427\pi$
$138$		0			0
$139$		−	16817.7i		−	0.870436i	−0.900325	−	0.435218i	$-0.856671\pi$
$139$		−	16817.7i		−	0.870436i	0.900325	−	0.435218i	$-0.143329\pi$
$140$		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	$-0.733751\pi$
$151$	−30558.2			−1.34021			−0.670106	+	0.742265i	$0.733751\pi$
$152$		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	$-0.698229\pi$
$157$	5644.63	−	5644.63i	0.229000	−	0.229000i	0.812275	+	0.583275i	$0.198229\pi$
$158$		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	0.270314	−	0.962772i	$-0.412873\pi$
$163$	−18397.9	−	18397.9i	−0.692458	−	0.692458i	−0.962772	+	0.270314i	$0.912873\pi$
$164$		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	$-0.708777\pi$
$167$	5093.57	−	5093.57i	0.182637	−	0.182637i	0.792504	+	0.609867i	$0.208777\pi$
$168$		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	$-0.173667\pi$
$173$	10053.1	+	10053.1i	0.335899	+	0.335899i	−0.518923	+	0.854821i	$0.673667\pi$
$174$		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	$0.103465\pi$
$179$			20464.7i			0.638705i	−0.947636	+	0.319352i	$0.896535\pi$
$180$		0			0
$181$	−17956.1			−0.548093			−0.274046	−	0.961717i	$-0.588362\pi$
$181$	−17956.1			−0.548093			−0.274046	+	0.961717i	$0.588362\pi$
$182$		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	$-0.258300\pi$
$191$	50229.3			1.37686			0.688431	+	0.725302i	$0.258300\pi$
$192$		0			0
$193$	−23236.7	−	23236.7i	−0.623821	−	0.623821i	0.322685	−	0.946506i	$-0.395414\pi$
$193$	−23236.7	−	23236.7i	−0.623821	−	0.623821i	−0.946506	+	0.322685i	$0.895414\pi$
$194$		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	$-0.969040\pi$
$197$	−34856.9	+	34856.9i	−0.898164	+	0.898164i	0.0971093	+	0.995274i	$0.469040\pi$
$198$		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	−0.971477	−	0.237133i	$-0.923792\pi$
$223$	−60103.0	−	60103.0i	−1.20861	−	1.20861i	−0.237133	−	0.971477i	$-0.576208\pi$
$224$		0			0
$225$	22377.7	+	123994.i	0.442029	+	2.44926i
$226$		0			0
$227$	23306.2	−	23306.2i	0.452293	−	0.452293i	−0.443822	−	0.896115i	$-0.646378\pi$
$227$	23306.2	−	23306.2i	0.452293	−	0.452293i	0.896115	+	0.443822i	$0.146378\pi$
$228$		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	0.755389	−	0.655277i	$-0.227448\pi$
$233$	5434.95	+	5434.95i	0.100112	+	0.100112i	−0.655277	+	0.755389i	$0.727448\pi$
$234$		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	−0.590045	−	0.807370i	$-0.700890\pi$
$257$	14354.1	−	14354.1i	0.217326	−	0.217326i	0.807370	+	0.590045i	$0.200890\pi$
$258$		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	$-0.0437852\pi$
$263$	59031.1	+	59031.1i	0.853432	+	0.853432i	−0.137122	+	0.990554i	$0.543785\pi$
$264$		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	$-0.506044\pi$
$271$	−2788.66			−0.0379714			−0.0189857	+	0.999820i	$0.506044\pi$
$272$		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	$-0.957155\pi$
$277$	−65738.2	+	65738.2i	−0.856758	+	0.856758i	0.134197	+	0.990955i	$0.457155\pi$
$278$		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	0.988342	−	0.152248i	$-0.0486513\pi$
$283$	66961.9	+	66961.9i	0.836094	+	0.836094i	−0.152248	+	0.988342i	$0.548651\pi$
$284$		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	−0.888531	−	0.458817i	$-0.848273\pi$
$293$	−115668.	−	115668.i	−1.34735	−	1.34735i	−0.458817	−	0.888531i	$-0.651727\pi$
$294$		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	−0.528767	−	0.848767i	$-0.677345\pi$
$307$	30159.7	−	30159.7i	0.320000	−	0.320000i	0.848767	+	0.528767i	$0.177345\pi$
$308$		0			0
$309$		−	3097.24i		−	0.0324383i
$310$		0			0
$311$	39594.0			0.409363			0.204681	−	0.978829i	$-0.434384\pi$
$311$	39594.0			0.409363			0.204681	+	0.978829i	$0.434384\pi$
$312$		0			0
$313$	−37570.1	−	37570.1i	−0.383490	−	0.383490i	0.488868	−	0.872358i	$-0.337410\pi$
$313$	−37570.1	−	37570.1i	−0.383490	−	0.383490i	−0.872358	+	0.488868i	$0.837410\pi$
$314$		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	$-0.872364\pi$
$317$	−53295.0	+	53295.0i	−0.530356	+	0.530356i	0.390322	+	0.920678i	$0.372364\pi$
$318$		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	−0.710135	−	0.704066i	$-0.751366\pi$
$337$	−689.307	+	689.307i	−0.00606950	+	0.00606950i	0.704066	+	0.710135i	$0.251366\pi$
$338$		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	−0.820873	−	0.571111i	$-0.806513\pi$
$347$	−30073.5	+	30073.5i	−0.249762	+	0.249762i	0.571111	+	0.820873i	$0.306513\pi$
$348$		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	0.387098	−	0.922039i	$-0.373478\pi$
$353$	−66658.5	−	66658.5i	−0.534941	−	0.534941i	−0.922039	+	0.387098i	$0.873478\pi$
$354$		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	$-0.768220\pi$
$367$	−10896.8	+	10896.8i	−0.0809030	+	0.0809030i	0.665497	+	0.746400i	$0.268220\pi$
$368$		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	$-0.245342\pi$
$373$	2879.15	+	2879.15i	0.0206941	+	0.0206941i	−0.696684	+	0.717378i	$0.745342\pi$
$374$		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	$-0.664236\pi$
$379$		−	249883.i		−	1.73964i	0.493372	−	0.869818i	$-0.335764\pi$
$380$		0			0
$381$	355531.			2.44922
$382$		0			0
$383$	10909.7	+	10909.7i	0.0743732	+	0.0743732i	0.743315	−	0.668942i	$-0.233252\pi$
$383$	10909.7	+	10909.7i	0.0743732	+	0.0743732i	−0.668942	+	0.743315i	$0.733252\pi$
$384$		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	$-0.919307\pi$
$397$	−113044.	+	113044.i	−0.717240	+	0.717240i	0.250799	+	0.968039i	$0.419307\pi$
$398$		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	$-0.867609\pi$
$409$		−	135173.i		−	0.808060i	0.914746	−	0.404030i	$-0.132391\pi$
$410$		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	$0.0523409\pi$
$419$			57476.5i			0.327388i	−0.986511	+	0.163694i	$0.947659\pi$
$420$		0			0
$421$	−217580.			−1.22759			−0.613796	−	0.789465i	$-0.710358\pi$
$421$	−217580.			−1.22759			−0.613796	+	0.789465i	$0.710358\pi$
$422$		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	$-0.426693\pi$
$431$	84807.6			0.456541			0.228271	+	0.973598i	$0.426693\pi$
$432$		0			0
$433$	−40613.6	−	40613.6i	−0.216618	−	0.216618i	0.590453	−	0.807072i	$-0.298949\pi$
$433$	−40613.6	−	40613.6i	−0.216618	−	0.216618i	−0.807072	+	0.590453i	$0.798949\pi$
$434$		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	0.946788	−	0.321859i	$-0.104308\pi$
$443$	122642.	+	122642.i	0.624929	+	0.624929i	−0.321859	+	0.946788i	$0.604308\pi$
$444$		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	$0.203996\pi$
$449$			241072.i			1.19579i	−0.801575	+	0.597894i	$0.796004\pi$
$450$		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	−0.699161	−	0.714965i	$-0.746443\pi$
$457$	3300.64	−	3300.64i	0.0158039	−	0.0158039i	0.714965	+	0.699161i	$0.246443\pi$
$458$		0			0
$459$		−	330806.i		−	1.57018i
$460$		0			0
$461$	278003.			1.30812			0.654061	−	0.756442i	$-0.273064\pi$
$461$	278003.			1.30812			0.654061	+	0.756442i	$0.273064\pi$
$462$		0			0
$463$	−288618.	−	288618.i	−1.34636	−	1.34636i	−0.889579	−	0.456781i	$-0.849002\pi$
$463$	−288618.	−	288618.i	−1.34636	−	1.34636i	−0.456781	−	0.889579i	$-0.650998\pi$
$464$		0			0
$465$	−104740.	−	87529.5i	−0.484405	−	0.404808i
$466$		0			0
$467$	−218636.	+	218636.i	−1.00251	+	1.00251i	−0.00251206	+	0.999997i	$0.500800\pi$
$467$	−218636.	+	218636.i	−1.00251	+	1.00251i	−0.999997	+	0.00251206i	$0.999200\pi$
$468$		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	$-0.829944\pi$
$487$	−83355.2	+	83355.2i	−0.351459	+	0.351459i	0.509193	+	0.860652i	$0.329944\pi$
$488$		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	$0.209874\pi$
$499$			305073.i			1.22519i	−0.790397	+	0.612594i	$0.790126\pi$
$500$		0			0
$501$	−121093.			−0.482441
$502$		0			0
$503$	113631.	+	113631.i	0.449120	+	0.449120i	0.895062	−	0.445942i	$-0.147131\pi$
$503$	113631.	+	113631.i	0.449120	+	0.449120i	−0.445942	+	0.895062i	$0.647131\pi$
$504$		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	−0.957330	−	0.288997i	$-0.906678\pi$
$523$	−340907.	−	340907.i	−1.24633	−	1.24633i	−0.288997	−	0.957330i	$-0.593322\pi$
$524$		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	$-0.342864\pi$
$541$	277374.			0.947700			0.473850	+	0.880606i	$0.342864\pi$
$542$		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	−0.994889	−	0.100979i	$-0.967803\pi$
$547$	−267466.	+	267466.i	−0.893910	+	0.893910i	0.100979	+	0.994889i	$0.467803\pi$
$548$		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	$-0.712157\pi$
$557$	52040.5	−	52040.5i	0.167738	−	0.167738i	0.785984	+	0.618246i	$0.212157\pi$
$558$		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	0.101135	−	0.994873i	$-0.467753\pi$
$563$	−283287.	−	283287.i	−0.893738	−	0.893738i	−0.994873	+	0.101135i	$0.967753\pi$
$564$		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	$-0.878227\pi$
$569$		−	241718.i		−	0.746595i	0.927712	−	0.373298i	$-0.121773\pi$
$570$		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	−0.165834	−	0.986154i	$-0.553032\pi$
$577$	273108.	−	273108.i	0.820320	−	0.820320i	0.986154	+	0.165834i	$0.0530315\pi$
$578$		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	−0.404401	−	0.914582i	$-0.632520\pi$
$587$	175793.	−	175793.i	0.510181	−	0.510181i	0.914582	+	0.404401i	$0.132520\pi$
$588$		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	0.0877563	−	0.996142i	$-0.472030\pi$
$593$	−319433.	−	319433.i	−0.908386	−	0.908386i	−0.996142	+	0.0877563i	$0.972030\pi$
$594$		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	$-0.717862\pi$
$607$	52520.3	−	52520.3i	0.142544	−	0.142544i	0.774778	+	0.632234i	$0.217862\pi$
$608$		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	−0.963302	−	0.268420i	$-0.913499\pi$
$613$	−462843.	−	462843.i	−1.23172	−	1.23172i	−0.268420	−	0.963302i	$-0.586501\pi$
$614$		0			0
$615$	257941.	+	215556.i	0.681978	+	0.569916i
$616$		0			0
$617$	−242154.	+	242154.i	−0.636094	+	0.636094i	−0.949590	−	0.313496i	$-0.898500\pi$
$617$	−242154.	+	242154.i	−0.636094	+	0.636094i	0.313496	+	0.949590i	$0.398500\pi$
$618$		0			0
$619$			265002.i			0.691620i	0.938305	+	0.345810i	$0.112396\pi$
$619$			265002.i			0.691620i	−0.938305	+	0.345810i	$0.887604\pi$
$620$		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	$-0.484204\pi$
$631$	39501.6			0.0992102			0.0496051	+	0.998769i	$0.484204\pi$
$632$		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	0.691710	−	0.722175i	$-0.256858\pi$
$643$	−12595.9	−	12595.9i	−0.0304654	−	0.0304654i	−0.722175	+	0.691710i	$0.756858\pi$
$644$		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	$-0.845378\pi$
$647$	−174745.	+	174745.i	−0.417441	+	0.417441i	0.466879	+	0.884321i	$0.345378\pi$
$648$		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	$-0.201663\pi$
$653$	91222.0	+	91222.0i	0.213931	+	0.213931i	−0.592004	+	0.805935i	$0.701663\pi$
$654$		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	$-0.810438\pi$
$659$		−	487216.i		−	1.12189i	0.827852	−	0.560946i	$-0.189562\pi$
$660$		0			0
$661$	122005.			0.279238			0.139619	−	0.990205i	$-0.455412\pi$
$661$	122005.			0.279238			0.139619	+	0.990205i	$0.455412\pi$
$662$		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	0.640285	−	0.768137i	$-0.278816\pi$
$673$	−57907.9	−	57907.9i	−0.127852	−	0.127852i	−0.768137	+	0.640285i	$0.778816\pi$
$674$		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	$-0.629532\pi$
$677$	239495.	−	239495.i	0.522540	−	0.522540i	0.918338	+	0.395798i	$0.129532\pi$
$678$		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	0.936928	−	0.349523i	$-0.113656\pi$
$683$	274018.	+	274018.i	0.587405	+	0.587405i	−0.349523	+	0.936928i	$0.613656\pi$
$684$		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	$-0.600693\pi$
$701$	−305736.			−0.622172			−0.311086	+	0.950382i	$0.600693\pi$
$702$		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	$-0.663979\pi$
$727$	199545.	−	199545.i	0.377548	−	0.377548i	0.870217	+	0.492669i	$0.163979\pi$
$728$		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	$-0.446875\pi$
$733$	−440566.	−	440566.i	−0.819980	−	0.819980i	−0.986105	+	0.166125i	$0.946875\pi$
$734$		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	$-0.847931\pi$
$739$		−	502182.i		−	0.919543i	0.888037	−	0.459771i	$-0.152069\pi$
$740$		0			0
$741$	1.00734e6			1.83460
$742$		0			0
$743$	−67600.2	−	67600.2i	−0.122453	−	0.122453i	0.643224	−	0.765678i	$-0.277596\pi$
$743$	−67600.2	−	67600.2i	−0.122453	−	0.122453i	−0.765678	+	0.643224i	$0.777596\pi$
$744$		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	$-0.852023\pi$
$751$	−1.00829e6			−1.78775			−0.893873	+	0.448319i	$0.852023\pi$
$752$		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	$-0.977367\pi$
$757$	−530890.	+	530890.i	−0.926431	+	0.926431i	0.0710427	+	0.997473i	$0.477367\pi$
$758$		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	$0.147664\pi$
$769$			529196.i			0.894878i	−0.894314	+	0.447439i	$0.852336\pi$
$770$		0			0
$771$	−341251.			−0.574071
$772$		0			0
$773$	154197.	+	154197.i	0.258057	+	0.258057i	0.824263	−	0.566206i	$-0.191589\pi$
$773$	154197.	+	154197.i	0.258057	+	0.258057i	−0.566206	+	0.824263i	$0.691589\pi$
$774$		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	−0.992368	−	0.123313i	$-0.960648\pi$
$787$	−538266.	+	538266.i	−0.869055	+	0.869055i	0.123313	+	0.992368i	$0.460648\pi$
$788$		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	$-0.988890\pi$
$797$	−612655.	+	612655.i	−0.964494	+	0.964494i	0.0348973	+	0.999391i	$0.488890\pi$
$798$		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	$-0.925212\pi$
$809$		−	304723.i		−	0.465596i	0.972525	−	0.232798i	$-0.0747880\pi$
$810$		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	$-0.564406\pi$
$821$	−270912.			−0.401922			−0.200961	+	0.979599i	$0.564406\pi$
$822$		0			0
$823$	698746.	+	698746.i	1.03162	+	1.03162i	0.999483	+	0.0321369i	$0.0102313\pi$
$823$	698746.	+	698746.i	1.03162	+	1.03162i	0.0321369	+	0.999483i	$0.489769\pi$
$824$		0			0
$825$	−1.83681e6	−	1.27518e6i	−2.69872	−	1.87354i
$826$		0			0
$827$	−796692.	+	796692.i	−1.16487	+	1.16487i	−0.181480	+	0.983395i	$0.558089\pi$
$827$	−796692.	+	796692.i	−1.16487	+	1.16487i	−0.983395	+	0.181480i	$0.941911\pi$
$828$		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	0.976875	+	0.213810i	$0.0685874\pi$
$853$	866353.	+	866353.i	1.19069	+	1.19069i	0.213810	+	0.976875i	$0.431413\pi$
$854$		0			0
$855$	−1.48738e6	+	133141.i	−2.03465	+	0.182130i
$856$		0			0
$857$	−688481.	+	688481.i	−0.937411	+	0.937411i	−0.998153	−	0.0607421i	$-0.980653\pi$
$857$	−688481.	+	688481.i	−0.937411	+	0.937411i	0.0607421	+	0.998153i	$0.480653\pi$
$858$		0			0
$859$		−	204193.i		−	0.276729i	−0.990381	−	0.138364i	$-0.955816\pi$
$859$		−	204193.i		−	0.276729i	0.990381	−	0.138364i	$-0.0441845\pi$
$860$		0			0
$861$	422977.			0.570573
$862$		0			0
$863$	−186718.	−	186718.i	−0.250706	−	0.250706i	0.570554	−	0.821260i	$-0.306729\pi$
$863$	−186718.	−	186718.i	−0.250706	−	0.250706i	−0.821260	+	0.570554i	$0.806729\pi$
$864$		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	$-0.828021\pi$
$877$	−263947.	+	263947.i	−0.343176	+	0.343176i	0.514384	+	0.857560i	$0.328021\pi$
$878$		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	0.654947	−	0.755675i	$-0.272691\pi$
$883$	−78535.9	−	78535.9i	−0.100727	−	0.100727i	−0.755675	+	0.654947i	$0.772691\pi$
$884$		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	$-0.712716\pi$
$887$	130030.	−	130030.i	0.165270	−	0.165270i	0.784897	+	0.619626i	$0.212716\pi$
$888$		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	−0.785068	−	0.619410i	$-0.787372\pi$
$907$	−136278.	+	136278.i	−0.165658	+	0.165658i	0.619410	+	0.785068i	$0.287372\pi$
$908$		0			0
$909$			1.91755e6i			2.32070i
$910$		0			0
$911$	−536004.			−0.645849			−0.322924	−	0.946425i	$-0.604666\pi$
$911$	−536004.			−0.645849			−0.322924	+	0.946425i	$0.604666\pi$
$912$		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	$-0.887032\pi$
$929$		−	599808.i		−	0.694994i	0.937681	−	0.347497i	$-0.112968\pi$
$930$		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	−0.668102	−	0.744070i	$-0.732893\pi$
$937$	66697.5	−	66697.5i	0.0759679	−	0.0759679i	0.744070	+	0.668102i	$0.232893\pi$
$938$		0			0
$939$			893183.i			1.01300i
$940$		0			0
$941$	1.05842e6			1.19531			0.597653	−	0.801755i	$-0.296100\pi$
$941$	1.05842e6			1.19531			0.597653	+	0.801755i	$0.296100\pi$
$942$		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	−0.825363	−	0.564602i	$-0.809030\pi$
$947$	−233853.	+	233853.i	−0.260761	+	0.260761i	0.564602	+	0.825363i	$0.309030\pi$
$948$		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	0.948106	−	0.317954i	$-0.102996\pi$
$953$	572309.	+	572309.i	0.630152	+	0.630152i	−0.317954	+	0.948106i	$0.602996\pi$
$954$		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	$-0.976875\pi$
$967$	−864750.	+	864750.i	−0.924778	+	0.924778i	0.0725841	+	0.997362i	$0.476875\pi$
$968$		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	−0.264356	−	0.964425i	$-0.585159\pi$
$977$	668236.	−	668236.i	0.700069	−	0.700069i	0.964425	+	0.264356i	$0.0851594\pi$
$978$		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	$-0.413690\pi$
$983$	−672172.	−	672172.i	−0.695622	−	0.695622i	−0.963463	+	0.267841i	$0.913690\pi$
$984$		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	$-0.736989\pi$
$991$	−1.33096e6			−1.35524			−0.677621	+	0.735411i	$0.736989\pi$
$992$		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	$-0.638451\pi$
$997$	482609.	−	482609.i	0.485518	−	0.485518i	0.906889	+	0.421371i	$0.138451\pi$
$998$		0			0
$999$		−	4.26582e6i		−	4.27436i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.5.p.e.33.6	✓	12	4.3	odd	2
160.5.p.e.97.6	yes	12	20.7	even	4
160.5.p.f.33.1	yes	12	1.1	even	1	trivial
160.5.p.f.97.1	yes	12	5.2	odd	4	inner
320.5.p.r.193.1		12	8.3	odd	2
320.5.p.r.257.1		12	40.27	even	4
320.5.p.s.193.6		12	8.5	even	2
320.5.p.s.257.6		12	40.37	odd	4

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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	160.p (of order \(4\), degree \(2\), 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

Varieties

Fields

Representations

Groups

Database

Properties

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