LMFDB - Embedded newform 160.6.o.a.47.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("160.47");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			47.15
Character	$\chi$	$=$	160.47
Dual form			160.6.o.a.143.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.12794 - 3.12794i) q^{3} +(34.4559 + 44.0204i) q^{5} +(-19.1929 + 19.1929i) q^{7} +223.432i q^{9} +O(q^{10})$	\(q+(3.12794 - 3.12794i) q^{3} +(34.4559 + 44.0204i) q^{5} +(-19.1929 + 19.1929i) q^{7} +223.432i q^{9} -648.221 q^{11} +(-392.250 - 392.250i) q^{13} +(245.469 + 29.9171i) q^{15} +(739.873 + 739.873i) q^{17} -1806.23i q^{19} +120.068i q^{21} +(-1662.57 - 1662.57i) q^{23} +(-750.584 + 3033.52i) q^{25} +(1458.97 + 1458.97i) q^{27} -7682.01 q^{29} -2500.39i q^{31} +(-2027.59 + 2027.59i) q^{33} +(-1506.19 - 183.570i) q^{35} +(4619.77 - 4619.77i) q^{37} -2453.86 q^{39} -1664.65 q^{41} +(-11387.6 + 11387.6i) q^{43} +(-9835.56 + 7698.55i) q^{45} +(-12902.6 + 12902.6i) q^{47} +16070.3i q^{49} +4628.55 q^{51} +(-12615.7 - 12615.7i) q^{53} +(-22335.0 - 28534.9i) q^{55} +(-5649.78 - 5649.78i) q^{57} +30075.1i q^{59} -22710.0i q^{61} +(-4288.31 - 4288.31i) q^{63} +(3751.66 - 30782.3i) q^{65} +(6337.59 + 6337.59i) q^{67} -10400.8 q^{69} +2950.81i q^{71} +(-10777.2 + 10777.2i) q^{73} +(7140.88 + 11836.4i) q^{75} +(12441.2 - 12441.2i) q^{77} -7474.95 q^{79} -45166.9 q^{81} +(-9875.91 + 9875.91i) q^{83} +(-7076.50 + 58062.5i) q^{85} +(-24028.8 + 24028.8i) q^{87} -226.889i q^{89} +15056.8 q^{91} +(-7821.06 - 7821.06i) q^{93} +(79511.0 - 62235.3i) q^{95} +(69631.7 + 69631.7i) q^{97} -144833. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{3}+O(q^{10}) $ 56 * q + 4 * q^3	$ 56 q + 4 q^{3} + 8 q^{11} - 408 q^{17} - 3120 q^{25} - 968 q^{27} - 976 q^{33} + 4780 q^{35} - 8 q^{41} - 1308 q^{43} - 20872 q^{51} + 968 q^{57} + 17680 q^{65} - 89252 q^{67} - 25184 q^{73} + 127740 q^{75} - 67792 q^{81} + 126444 q^{83} - 329432 q^{91} + 212576 q^{97}+O(q^{100}) $ 56 * q + 4 * q^3 + 8 * q^11 - 408 * q^17 - 3120 * q^25 - 968 * q^27 - 976 * q^33 + 4780 * q^35 - 8 * q^41 - 1308 * q^43 - 20872 * q^51 + 968 * q^57 + 17680 * q^65 - 89252 * q^67 - 25184 * q^73 + 127740 * q^75 - 67792 * q^81 + 126444 * q^83 - 329432 * q^91 + 212576 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	3.12794	−	3.12794i	0.200657	−	0.200657i	−0.599624	−	0.800282i	$-0.704683\pi$
$3$	3.12794	−	3.12794i	0.200657	−	0.200657i	0.800282	+	0.599624i	$0.204683\pi$
$4$		0			0
$5$	34.4559	+	44.0204i	0.616366	+	0.787460i
$5$	34.4559	+	44.0204i	0.616366	+	0.787460i
$6$		0			0
$7$	−19.1929	+	19.1929i	−0.148046	+	0.148046i	−0.777244	−	0.629199i	$-0.783383\pi$
$7$	−19.1929	+	19.1929i	−0.148046	+	0.148046i	0.629199	+	0.777244i	$0.283383\pi$
$8$		0			0
$9$			223.432i			0.919473i
$10$		0			0
$11$	−648.221			−1.61526			−0.807628	−	0.589692i	$-0.799249\pi$
$11$	−648.221			−1.61526			−0.807628	+	0.589692i	$0.799249\pi$
$12$		0			0
$13$	−392.250	−	392.250i	−0.643731	−	0.643731i	0.307740	−	0.951471i	$-0.400427\pi$
$13$	−392.250	−	392.250i	−0.643731	−	0.643731i	−0.951471	+	0.307740i	$0.900427\pi$
$14$		0			0
$15$	245.469	+	29.9171i	0.281688	+	0.0343313i
$16$		0			0
$17$	739.873	+	739.873i	0.620919	+	0.620919i	0.945766	−	0.324847i	$-0.105313\pi$
$17$	739.873	+	739.873i	0.620919	+	0.620919i	−0.324847	+	0.945766i	$0.605313\pi$
$18$		0			0
$19$		−	1806.23i		−	1.14786i	−0.818904	−	0.573931i	$-0.805418\pi$
$19$		−	1806.23i		−	1.14786i	0.818904	−	0.573931i	$-0.194582\pi$
$20$		0			0
$21$			120.068i			0.0594128i
$22$		0			0
$23$	−1662.57	−	1662.57i	−0.655331	−	0.655331i	0.298941	−	0.954272i	$-0.403367\pi$
$23$	−1662.57	−	1662.57i	−0.655331	−	0.655331i	−0.954272	+	0.298941i	$0.903367\pi$
$24$		0			0
$25$	−750.584	+	3033.52i	−0.240187	+	0.970727i
$26$		0			0
$27$	1458.97	+	1458.97i	0.385156	+	0.385156i
$28$		0			0
$29$	−7682.01			−1.69621			−0.848106	−	0.529827i	$-0.822257\pi$
$29$	−7682.01			−1.69621			−0.848106	+	0.529827i	$0.822257\pi$
$30$		0			0
$31$		−	2500.39i		−	0.467308i	−0.972320	−	0.233654i	$-0.924932\pi$
$31$		−	2500.39i		−	0.467308i	0.972320	−	0.233654i	$-0.0750683\pi$
$32$		0			0
$33$	−2027.59	+	2027.59i	−0.324113	+	0.324113i
$34$		0			0
$35$	−1506.19	−	183.570i	−0.207830	−	0.0253298i
$36$		0			0
$37$	4619.77	−	4619.77i	0.554774	−	0.554774i	−0.373041	−	0.927815i	$-0.621685\pi$
$37$	4619.77	−	4619.77i	0.554774	−	0.554774i	0.927815	+	0.373041i	$0.121685\pi$
$38$		0			0
$39$	−2453.86			−0.258338
$40$		0			0
$41$	−1664.65			−0.154654			−0.0773272	−	0.997006i	$-0.524639\pi$
$41$	−1664.65			−0.154654			−0.0773272	+	0.997006i	$0.524639\pi$
$42$		0			0
$43$	−11387.6	+	11387.6i	−0.939208	+	0.939208i	−0.998255	−	0.0590474i	$-0.981194\pi$
$43$	−11387.6	+	11387.6i	−0.939208	+	0.939208i	0.0590474	+	0.998255i	$0.481194\pi$
$44$		0			0
$45$	−9835.56	+	7698.55i	−0.724049	+	0.566732i
$46$		0			0
$47$	−12902.6	+	12902.6i	−0.851988	+	0.851988i	−0.990378	−	0.138390i	$-0.955807\pi$
$47$	−12902.6	+	12902.6i	−0.851988	+	0.851988i	0.138390	+	0.990378i	$0.455807\pi$
$48$		0			0
$49$			16070.3i			0.956165i
$50$		0			0
$51$	4628.55			0.249184
$52$		0			0
$53$	−12615.7	−	12615.7i	−0.616908	−	0.616908i	0.327829	−	0.944737i	$-0.393683\pi$
$53$	−12615.7	−	12615.7i	−0.616908	−	0.616908i	−0.944737	+	0.327829i	$0.893683\pi$
$54$		0			0
$55$	−22335.0	−	28534.9i	−0.995589	−	1.27195i
$56$		0			0
$57$	−5649.78	−	5649.78i	−0.230327	−	0.230327i
$58$		0			0
$59$			30075.1i			1.12481i	0.826863	+	0.562403i	$0.190123\pi$
$59$			30075.1i			1.12481i	−0.826863	+	0.562403i	$0.809877\pi$
$60$		0			0
$61$		−	22710.0i		−	0.781435i	−0.920511	−	0.390717i	$-0.872227\pi$
$61$		−	22710.0i		−	0.781435i	0.920511	−	0.390717i	$-0.127773\pi$
$62$		0			0
$63$	−4288.31	−	4288.31i	−0.136124	−	0.136124i
$64$		0			0
$65$	3751.66	−	30782.3i	0.110139	−	0.903686i
$66$		0			0
$67$	6337.59	+	6337.59i	0.172479	+	0.172479i	0.788068	−	0.615588i	$-0.211082\pi$
$67$	6337.59	+	6337.59i	0.172479	+	0.172479i	−0.615588	+	0.788068i	$0.711082\pi$
$68$		0			0
$69$	−10400.8			−0.262994
$70$		0			0
$71$			2950.81i			0.0694696i	0.999397	+	0.0347348i	$0.0110587\pi$
$71$			2950.81i			0.0694696i	−0.999397	+	0.0347348i	$0.988941\pi$
$72$		0			0
$73$	−10777.2	+	10777.2i	−0.236700	+	0.236700i	−0.815482	−	0.578782i	$-0.803528\pi$
$73$	−10777.2	+	10777.2i	−0.236700	+	0.236700i	0.578782	+	0.815482i	$0.303528\pi$
$74$		0			0
$75$	7140.88	+	11836.4i	0.146588	+	0.242979i
$76$		0			0
$77$	12441.2	−	12441.2i	0.239132	−	0.239132i
$78$		0			0
$79$	−7474.95			−0.134754			−0.0673768	−	0.997728i	$-0.521463\pi$
$79$	−7474.95			−0.134754			−0.0673768	+	0.997728i	$0.521463\pi$
$80$		0			0
$81$	−45166.9			−0.764905
$82$		0			0
$83$	−9875.91	+	9875.91i	−0.157356	+	0.157356i	−0.781394	−	0.624038i	$-0.785491\pi$
$83$	−9875.91	+	9875.91i	−0.157356	+	0.157356i	0.624038	+	0.781394i	$0.285491\pi$
$84$		0			0
$85$	−7076.50	+	58062.5i	−0.106236	+	0.871662i
$86$		0			0
$87$	−24028.8	+	24028.8i	−0.340357	+	0.340357i
$88$		0			0
$89$		−	226.889i		−	0.00303626i	−0.999999	−	0.00151813i	$-0.999517\pi$
$89$		−	226.889i		−	0.00303626i	0.999999	−	0.00151813i	$-0.000483236\pi$
$90$		0			0
$91$	15056.8			0.190603
$92$		0			0
$93$	−7821.06	−	7821.06i	−0.0937687	−	0.0937687i
$94$		0			0
$95$	79511.0	−	62235.3i	0.903895	−	0.707502i
$96$		0			0
$97$	69631.7	+	69631.7i	0.751411	+	0.751411i	0.974743	−	0.223331i	$-0.0716931\pi$
$97$	69631.7	+	69631.7i	0.751411	+	0.751411i	−0.223331	+	0.974743i	$0.571693\pi$
$98$		0			0
$99$		−	144833.i		−	1.48519i
$100$		0			0
$101$			62934.7i			0.613884i	0.951728	+	0.306942i	$0.0993058\pi$
$101$			62934.7i			0.613884i	−0.951728	+	0.306942i	$0.900694\pi$
$102$		0			0
$103$	141817.	+	141817.i	1.31715	+	1.31715i	0.916021	+	0.401131i	$0.131383\pi$
$103$	141817.	+	141817.i	1.31715	+	1.31715i	0.401131	+	0.916021i	$0.368617\pi$
$104$		0			0
$105$	−5285.45	+	4137.06i	−0.0467852	+	0.0366200i
$106$		0			0
$107$	−69303.7	−	69303.7i	−0.585190	−	0.585190i	0.351135	−	0.936325i	$-0.385796\pi$
$107$	−69303.7	−	69303.7i	−0.585190	−	0.585190i	−0.936325	+	0.351135i	$0.885796\pi$
$108$		0			0
$109$	162445.			1.30961			0.654804	−	0.755799i	$-0.272751\pi$
$109$	162445.			1.30961			0.654804	+	0.755799i	$0.272751\pi$
$110$		0			0
$111$		−	28900.7i		−	0.222639i
$112$		0			0
$113$	72741.9	−	72741.9i	0.535906	−	0.535906i	−0.386418	−	0.922324i	$-0.626288\pi$
$113$	72741.9	−	72741.9i	0.535906	−	0.535906i	0.922324	+	0.386418i	$0.126288\pi$
$114$		0			0
$115$	15901.6	−	130472.i	0.112124	−	0.919970i
$116$		0			0
$117$	87641.2	−	87641.2i	0.591893	−	0.591893i
$118$		0			0
$119$	−28400.6			−0.183849
$120$		0			0
$121$	259140.			1.60905
$122$		0			0
$123$	−5206.91	+	5206.91i	−0.0310325	+	0.0310325i
$124$		0			0
$125$	−159399.	+	71481.7i	−0.912451	+	0.409185i
$126$		0			0
$127$	46439.3	−	46439.3i	0.255492	−	0.255492i	−0.567726	−	0.823218i	$-0.692177\pi$
$127$	46439.3	−	46439.3i	0.255492	−	0.255492i	0.823218	+	0.567726i	$0.192177\pi$
$128$		0			0
$129$			71239.5i			0.376918i
$130$		0			0
$131$	154464.			0.786408			0.393204	−	0.919451i	$-0.371367\pi$
$131$	154464.			0.786408			0.393204	+	0.919451i	$0.371367\pi$
$132$		0			0
$133$	34666.8	+	34666.8i	0.169936	+	0.169936i
$134$		0			0
$135$	−13954.3	+	114494.i	−0.0658981	+	0.540692i
$136$		0			0
$137$	−209839.	−	209839.i	−0.955180	−	0.955180i	0.0438575	−	0.999038i	$-0.486035\pi$
$137$	−209839.	−	209839.i	−0.955180	−	0.955180i	−0.999038	+	0.0438575i	$0.986035\pi$
$138$		0			0
$139$			138092.i			0.606222i	0.952955	+	0.303111i	$0.0980253\pi$
$139$			138092.i			0.606222i	−0.952955	+	0.303111i	$0.901975\pi$
$140$		0			0
$141$			80717.2i			0.341915i
$142$		0			0
$143$	254265.	+	254265.i	1.03979	+	1.03979i
$144$		0			0
$145$	−264691.	−	338165.i	−1.04549	−	1.33570i
$146$		0			0
$147$	50266.8	+	50266.8i	0.191861	+	0.191861i
$148$		0			0
$149$	493486.			1.82100			0.910498	−	0.413514i	$-0.135699\pi$
$149$	493486.			1.82100			0.910498	+	0.413514i	$0.135699\pi$
$150$		0			0
$151$		−	490809.i		−	1.75174i	−0.482545	−	0.875871i	$-0.660288\pi$
$151$		−	490809.i		−	1.75174i	0.482545	−	0.875871i	$-0.339712\pi$
$152$		0			0
$153$	−165311.	+	165311.i	−0.570918	+	0.570918i
$154$		0			0
$155$	110068.	−	86153.1i	0.367986	−	0.288033i
$156$		0			0
$157$	−71767.6	+	71767.6i	−0.232369	+	0.232369i	−0.813681	−	0.581312i	$-0.802540\pi$
$157$	−71767.6	+	71767.6i	−0.232369	+	0.232369i	0.581312	+	0.813681i	$0.302540\pi$
$158$		0			0
$159$	−78922.0			−0.247574
$160$		0			0
$161$	63819.1			0.194038
$162$		0			0
$163$	−345655.	+	345655.i	−1.01900	+	1.01900i	−0.0191825	+	0.999816i	$0.506106\pi$
$163$	−345655.	+	345655.i	−1.01900	+	1.01900i	−0.999816	+	0.0191825i	$0.993894\pi$
$164$		0			0
$165$	−159118.	−	19392.9i	−0.454998	−	0.0554539i
$166$		0			0
$167$	−371161.	+	371161.i	−1.02984	+	1.02984i	−0.0303018	+	0.999541i	$0.509647\pi$
$167$	−371161.	+	371161.i	−1.02984	+	1.02984i	−0.999541	+	0.0303018i	$0.990353\pi$
$168$		0			0
$169$		−	63573.2i		−	0.171221i
$170$		0			0
$171$	403570.			1.05543
$172$		0			0
$173$	−289958.	−	289958.i	−0.736579	−	0.736579i	0.235335	−	0.971914i	$-0.424381\pi$
$173$	−289958.	−	289958.i	−0.736579	−	0.736579i	−0.971914	+	0.235335i	$0.924381\pi$
$174$		0			0
$175$	−43816.2	−	72627.9i	−0.108153	−	0.179270i
$176$		0			0
$177$	94073.1	+	94073.1i	0.225700	+	0.225700i
$178$		0			0
$179$			546325.i			1.27444i	0.770683	+	0.637218i	$0.219915\pi$
$179$			546325.i			1.27444i	−0.770683	+	0.637218i	$0.780085\pi$
$180$		0			0
$181$		−	272124.i		−	0.617406i	−0.951158	−	0.308703i	$-0.900105\pi$
$181$		−	272124.i		−	0.617406i	0.951158	−	0.308703i	$-0.0998949\pi$
$182$		0			0
$183$	−71035.5	−	71035.5i	−0.156800	−	0.156800i
$184$		0			0
$185$	362542.	+	44185.7i	0.778806	+	0.0949188i
$186$		0			0
$187$	−479601.	−	479601.i	−1.00294	−	1.00294i
$188$		0			0
$189$	−56003.7			−0.114041
$190$		0			0
$191$		−	83461.3i		−	0.165539i	−0.996569	−	0.0827697i	$-0.973623\pi$
$191$		−	83461.3i		−	0.165539i	0.996569	−	0.0827697i	$-0.0263766\pi$
$192$		0			0
$193$	38883.2	−	38883.2i	0.0751397	−	0.0751397i	−0.668538	−	0.743678i	$-0.733080\pi$
$193$	38883.2	−	38883.2i	0.0751397	−	0.0751397i	0.743678	+	0.668538i	$0.233080\pi$
$194$		0			0
$195$	−84550.1	−	108020.i	−0.159231	−	0.203431i
$196$		0			0
$197$	−386340.	+	386340.i	−0.709257	+	0.709257i	−0.966379	−	0.257122i	$-0.917226\pi$
$197$	−386340.	+	386340.i	−0.709257	+	0.709257i	0.257122	+	0.966379i	$0.417226\pi$
$198$		0			0
$199$	−297969.			−0.533382			−0.266691	−	0.963782i	$-0.585930\pi$
$199$	−297969.			−0.533382			−0.266691	+	0.963782i	$0.585930\pi$
$200$		0			0
$201$	39647.2			0.0692184
$202$		0			0
$203$	147440.	−	147440.i	0.251117	−	0.251117i
$204$		0			0
$205$	−57356.9	−	73278.3i	−0.0953237	−	0.121784i
$206$		0			0
$207$	371472.	−	371472.i	0.602559	−	0.602559i
$208$		0			0
$209$			1.17084e6i			1.85409i
$210$		0			0
$211$	−132172.			−0.204377			−0.102189	−	0.994765i	$-0.532584\pi$
$211$	−132172.			−0.204377			−0.102189	+	0.994765i	$0.532584\pi$
$212$		0			0
$213$	9229.93	+	9229.93i	0.0139396	+	0.0139396i
$214$		0			0
$215$	−893657.	−	108917.i	−1.31848	−	0.160693i
$216$		0			0
$217$	47989.7	+	47989.7i	0.0691829	+	0.0691829i
$218$		0			0
$219$			67420.6i			0.0949910i
$220$		0			0
$221$		−	580430.i		−	0.799409i
$222$		0			0
$223$	−143338.	−	143338.i	−0.193018	−	0.193018i	0.603981	−	0.796999i	$-0.293580\pi$
$223$	−143338.	−	143338.i	−0.193018	−	0.193018i	−0.796999	+	0.603981i	$0.793580\pi$
$224$		0			0
$225$	−677786.	−	167704.i	−0.892557	−	0.220845i
$226$		0			0
$227$	160750.	+	160750.i	0.207055	+	0.207055i	0.803015	−	0.595959i	$-0.203228\pi$
$227$	160750.	+	160750.i	0.207055	+	0.207055i	−0.595959	+	0.803015i	$0.703228\pi$
$228$		0			0
$229$	−1.00602e6			−1.26771			−0.633854	−	0.773453i	$-0.718528\pi$
$229$	−1.00602e6			−1.26771			−0.633854	+	0.773453i	$0.718528\pi$
$230$		0			0
$231$		−	77830.8i		−	0.0959670i
$232$		0			0
$233$	−1.09508e6	+	1.09508e6i	−1.32147	+	1.32147i	−0.408879	+	0.912589i	$0.634080\pi$
$233$	−1.09508e6	+	1.09508e6i	−1.32147	+	1.32147i	−0.912589	+	0.408879i	$0.865920\pi$
$234$		0			0
$235$	−1.01255e6	−	123407.i	−1.19604	−	0.145770i
$236$		0			0
$237$	−23381.2	+	23381.2i	−0.0270393	+	0.0270393i
$238$		0			0
$239$	1.17736e6			1.33326			0.666628	−	0.745390i	$-0.267737\pi$
$239$	1.17736e6			1.33326			0.666628	+	0.745390i	$0.267737\pi$
$240$		0			0
$241$	1.26027e6			1.39772			0.698859	−	0.715259i	$-0.253691\pi$
$241$	1.26027e6			1.39772			0.698859	+	0.715259i	$0.253691\pi$
$242$		0			0
$243$	−495809.	+	495809.i	−0.538640	+	0.538640i
$244$		0			0
$245$	−707419.	+	553715.i	−0.752942	+	0.589347i
$246$		0			0
$247$	−708494.	+	708494.i	−0.738914	+	0.738914i
$248$		0			0
$249$			61782.4i			0.0631490i
$250$		0			0
$251$	1.54897e6			1.55188			0.775942	−	0.630804i	$-0.217275\pi$
$251$	1.54897e6			1.55188			0.775942	+	0.630804i	$0.217275\pi$
$252$		0			0
$253$	1.07771e6	+	1.07771e6i	1.05853	+	1.05853i
$254$		0			0
$255$	159481.	+	203751.i	0.153588	+	0.196222i
$256$		0			0
$257$	−678258.	−	678258.i	−0.640564	−	0.640564i	0.310130	−	0.950694i	$-0.399627\pi$
$257$	−678258.	−	678258.i	−0.640564	−	0.640564i	−0.950694	+	0.310130i	$0.899627\pi$
$258$		0			0
$259$			177334.i			0.164264i
$260$		0			0
$261$		−	1.71641e6i		−	1.55962i
$262$		0			0
$263$	−280837.	−	280837.i	−0.250360	−	0.250360i	0.570758	−	0.821118i	$-0.306649\pi$
$263$	−280837.	−	280837.i	−0.250360	−	0.250360i	−0.821118	+	0.570758i	$0.806649\pi$
$264$		0			0
$265$	120662.	−	990031.i	0.105550	−	0.866032i
$266$		0			0
$267$	−709.695	−	709.695i	−0.000609247	−	0.000609247i
$268$		0			0
$269$	135326.			0.114025			0.0570124	−	0.998373i	$-0.481843\pi$
$269$	135326.			0.114025			0.0570124	+	0.998373i	$0.481843\pi$
$270$		0			0
$271$		−	1.40272e6i		−	1.16024i	−0.814532	−	0.580119i	$-0.803006\pi$
$271$		−	1.40272e6i		−	1.16024i	0.814532	−	0.580119i	$-0.196994\pi$
$272$		0			0
$273$	47096.8	−	47096.8i	0.0382459	−	0.0382459i
$274$		0			0
$275$	486544.	−	1.96639e6i	0.387963	−	1.56797i
$276$		0			0
$277$	306749.	−	306749.i	0.240206	−	0.240206i	−0.576729	−	0.816935i	$-0.695671\pi$
$277$	306749.	−	306749.i	0.240206	−	0.240206i	0.816935	+	0.576729i	$0.195671\pi$
$278$		0			0
$279$	558667.			0.429677
$280$		0			0
$281$	1.42850e6			1.07923			0.539615	−	0.841912i	$-0.318570\pi$
$281$	1.42850e6			1.07923			0.539615	+	0.841912i	$0.318570\pi$
$282$		0			0
$283$	−948370.	+	948370.i	−0.703901	+	0.703901i	−0.965246	−	0.261344i	$-0.915834\pi$
$283$	−948370.	+	948370.i	−0.703901	+	0.703901i	0.261344	+	0.965246i	$0.415834\pi$
$284$		0			0
$285$	54037.1	−	443373.i	0.0394076	−	0.323338i
$286$		0			0
$287$	31949.4	−	31949.4i	0.0228959	−	0.0228959i
$288$		0			0
$289$		−	325033.i		−	0.228919i
$290$		0			0
$291$	435607.			0.301552
$292$		0			0
$293$	1.76289e6	+	1.76289e6i	1.19966	+	1.19966i	0.974269	+	0.225387i	$0.0723646\pi$
$293$	1.76289e6	+	1.76289e6i	1.19966	+	1.19966i	0.225387	+	0.974269i	$0.427635\pi$
$294$		0			0
$295$	−1.32392e6	+	1.03626e6i	−0.885739	+	0.693291i
$296$		0			0
$297$	−945735.	−	945735.i	−0.622126	−	0.622126i
$298$		0			0
$299$			1.30429e6i			0.843714i
$300$		0			0
$301$		−	437123.i		−	0.278091i
$302$		0			0
$303$	196856.	+	196856.i	0.123180	+	0.123180i
$304$		0			0
$305$	999703.	−	782493.i	0.615349	−	0.481649i
$306$		0			0
$307$	123298.	+	123298.i	0.0746635	+	0.0746635i	0.743452	−	0.668789i	$-0.233187\pi$
$307$	123298.	+	123298.i	0.0746635	+	0.0746635i	−0.668789	+	0.743452i	$0.733187\pi$
$308$		0			0
$309$	887190.			0.528592
$310$		0			0
$311$			3.16561e6i			1.85591i	0.372693	+	0.927955i	$0.378435\pi$
$311$			3.16561e6i			1.85591i	−0.372693	+	0.927955i	$0.621565\pi$
$312$		0			0
$313$	531452.	−	531452.i	0.306622	−	0.306622i	−0.536976	−	0.843598i	$-0.680433\pi$
$313$	531452.	−	531452.i	0.306622	−	0.306622i	0.843598	+	0.536976i	$0.180433\pi$
$314$		0			0
$315$	41015.4	−	336530.i	0.0232901	−	0.191094i
$316$		0			0
$317$	−1.06483e6	+	1.06483e6i	−0.595159	+	0.595159i	−0.939020	−	0.343862i	$-0.888265\pi$
$317$	−1.06483e6	+	1.06483e6i	−0.595159	+	0.595159i	0.343862	+	0.939020i	$0.388265\pi$
$318$		0			0
$319$	4.97964e6			2.73982
$320$		0			0
$321$	−433555.			−0.234845
$322$		0			0
$323$	1.33638e6	−	1.33638e6i	0.712729	−	0.712729i
$324$		0			0
$325$	1.48431e6	−	895482.i	0.779502	−	0.470271i
$326$		0			0
$327$	508119.	−	508119.i	0.262782	−	0.262782i
$328$		0			0
$329$		−	495278.i		−	0.252266i
$330$		0			0
$331$	−99178.8			−0.0497564			−0.0248782	−	0.999690i	$-0.507920\pi$
$331$	−99178.8			−0.0497564			−0.0248782	+	0.999690i	$0.507920\pi$
$332$		0			0
$333$	1.03221e6	+	1.03221e6i	0.510100	+	0.510100i
$334$		0			0
$335$	−60615.7	+	497350.i	−0.0295103	+	0.242131i
$336$		0			0
$337$	−615804.	−	615804.i	−0.295371	−	0.295371i	0.543827	−	0.839198i	$-0.316975\pi$
$337$	−615804.	−	615804.i	−0.295371	−	0.295371i	−0.839198	+	0.543827i	$0.816975\pi$
$338$		0			0
$339$		−	455064.i		−	0.215067i
$340$		0			0
$341$			1.62080e6i			0.754822i
$342$		0			0
$343$	−631010.	−	631010.i	−0.289602	−	0.289602i
$344$		0			0
$345$	−358370.	−	457848.i	−0.162100	−	0.207097i
$346$		0			0
$347$	162825.	+	162825.i	0.0725937	+	0.0725937i	0.742471	−	0.669878i	$-0.233654\pi$
$347$	162825.	+	162825.i	0.0725937	+	0.0725937i	−0.669878	+	0.742471i	$0.733654\pi$
$348$		0			0
$349$	926819.			0.407316			0.203658	−	0.979042i	$-0.434717\pi$
$349$	926819.			0.407316			0.203658	+	0.979042i	$0.434717\pi$
$350$		0			0
$351$		−	1.14456e6i		−	0.495874i
$352$		0			0
$353$	−1.42444e6	+	1.42444e6i	−0.608427	+	0.608427i	−0.942535	−	0.334108i	$-0.891565\pi$
$353$	−1.42444e6	+	1.42444e6i	−0.608427	+	0.608427i	0.334108	+	0.942535i	$0.391565\pi$
$354$		0			0
$355$	−129896.	+	101673.i	−0.0547045	+	0.0428187i
$356$		0			0
$357$	−88835.3	+	88835.3i	−0.0368906	+	0.0368906i
$358$		0			0
$359$	−4.66887e6			−1.91195			−0.955974	−	0.293452i	$-0.905196\pi$
$359$	−4.66887e6			−1.91195			−0.955974	+	0.293452i	$0.905196\pi$
$360$		0			0
$361$	−786373.			−0.317585
$362$		0			0
$363$	810573.	−	810573.i	0.322868	−	0.322868i
$364$		0			0
$365$	−845752.	−	103078.i	−0.332285	−	0.0404980i
$366$		0			0
$367$	3.11370e6	−	3.11370e6i	1.20673	−	1.20673i	0.234655	−	0.972079i	$-0.424604\pi$
$367$	3.11370e6	−	3.11370e6i	1.20673	−	1.20673i	0.972079	−	0.234655i	$-0.0753960\pi$
$368$		0			0
$369$		−	371935.i		−	0.142201i
$370$		0			0
$371$	484263.			0.182661
$372$		0			0
$373$	−1.67420e6	−	1.67420e6i	−0.623070	−	0.623070i	0.323246	−	0.946315i	$-0.395226\pi$
$373$	−1.67420e6	−	1.67420e6i	−0.623070	−	0.623070i	−0.946315	+	0.323246i	$0.895226\pi$
$374$		0			0
$375$	−274999.	+	722179.i	−0.100984	+	0.265196i
$376$		0			0
$377$	3.01327e6	+	3.01327e6i	1.09190	+	1.09190i
$378$		0			0
$379$		−	1.27799e6i		−	0.457013i	−0.973542	−	0.228506i	$-0.926616\pi$
$379$		−	1.27799e6i		−	0.457013i	0.973542	−	0.228506i	$-0.0733842\pi$
$380$		0			0
$381$		−	290519.i		−	0.102532i
$382$		0			0
$383$	3.07991e6	+	3.07991e6i	1.07285	+	1.07285i	0.997129	+	0.0757254i	$0.0241272\pi$
$383$	3.07991e6	+	3.07991e6i	1.07285	+	1.07285i	0.0757254	+	0.997129i	$0.475873\pi$
$384$		0			0
$385$	976342.	+	118994.i	0.335699	+	0.0409141i
$386$		0			0
$387$	−2.54436e6	−	2.54436e6i	−0.863577	−	0.863577i
$388$		0			0
$389$	−1.71604e6			−0.574980			−0.287490	−	0.957784i	$-0.592821\pi$
$389$	−1.71604e6			−0.574980			−0.287490	+	0.957784i	$0.592821\pi$
$390$		0			0
$391$		−	2.46018e6i		−	0.813815i
$392$		0			0
$393$	483153.	−	483153.i	0.157799	−	0.157799i
$394$		0			0
$395$	−257556.	−	329050.i	−0.0830575	−	0.106113i
$396$		0			0
$397$	65868.8	−	65868.8i	0.0209751	−	0.0209751i	−0.696541	−	0.717517i	$-0.745279\pi$
$397$	65868.8	−	65868.8i	0.0209751	−	0.0209751i	0.717517	+	0.696541i	$0.245279\pi$
$398$		0			0
$399$	216871.			0.0681977
$400$		0			0
$401$	3.68346e6			1.14392			0.571959	−	0.820282i	$-0.306184\pi$
$401$	3.68346e6			1.14392			0.571959	+	0.820282i	$0.306184\pi$
$402$		0			0
$403$	−980777.	+	980777.i	−0.300821	+	0.300821i
$404$		0			0
$405$	−1.55626e6	−	1.98826e6i	−0.471461	−	0.602332i
$406$		0			0
$407$	−2.99463e6	+	2.99463e6i	−0.896103	+	0.896103i
$408$		0			0
$409$			2.74141e6i			0.810337i	0.914242	+	0.405168i	$0.132787\pi$
$409$			2.74141e6i			0.810337i	−0.914242	+	0.405168i	$0.867213\pi$
$410$		0			0
$411$	−1.31273e6			−0.383328
$412$		0			0
$413$	−577229.	−	577229.i	−0.166522	−	0.166522i
$414$		0			0
$415$	−775024.	−	94457.9i	−0.220900	−	0.0269227i
$416$		0			0
$417$	431943.	+	431943.i	0.121643	+	0.121643i
$418$		0			0
$419$			2.43743e6i			0.678263i	0.940739	+	0.339131i	$0.110133\pi$
$419$			2.43743e6i			0.678263i	−0.940739	+	0.339131i	$0.889867\pi$
$420$		0			0
$421$		−	695447.i		−	0.191231i	−0.995418	−	0.0956155i	$-0.969518\pi$
$421$		−	695447.i		−	0.191231i	0.995418	−	0.0956155i	$-0.0304819\pi$
$422$		0			0
$423$	−2.88286e6	−	2.88286e6i	−0.783380	−	0.783380i
$424$		0			0
$425$	−2.79976e6	+	1.68908e6i	−0.751879	+	0.453606i
$426$		0			0
$427$	435871.	+	435871.i	0.115688	+	0.115688i
$428$		0			0
$429$	1.59065e6			0.417283
$430$		0			0
$431$		−	1.52454e6i		−	0.395316i	−0.980271	−	0.197658i	$-0.936666\pi$
$431$		−	1.52454e6i		−	0.395316i	0.980271	−	0.197658i	$-0.0633336\pi$
$432$		0			0
$433$	−4.56566e6	+	4.56566e6i	−1.17026	+	1.17026i	−0.188117	+	0.982147i	$0.560238\pi$
$433$	−4.56566e6	+	4.56566e6i	−1.17026	+	1.17026i	−0.982147	+	0.188117i	$0.939762\pi$
$434$		0			0
$435$	−1.88569e6	−	229823.i	−0.477802	−	0.0582332i
$436$		0			0
$437$	−3.00299e6	+	3.00299e6i	−0.752229	+	0.752229i
$438$		0			0
$439$	−4.66021e6			−1.15410			−0.577051	−	0.816708i	$-0.695796\pi$
$439$	−4.66021e6			−1.15410			−0.577051	+	0.816708i	$0.695796\pi$
$440$		0			0
$441$	−3.59061e6			−0.879168
$442$		0			0
$443$	−3.39264e6	+	3.39264e6i	−0.821350	+	0.821350i	−0.986302	−	0.164951i	$-0.947253\pi$
$443$	−3.39264e6	+	3.39264e6i	−0.821350	+	0.821350i	0.164951	+	0.986302i	$0.447253\pi$
$444$		0			0
$445$	9987.75	−	7817.67i	0.00239093	−	0.00187145i
$446$		0			0
$447$	1.54359e6	−	1.54359e6i	0.365396	−	0.365396i
$448$		0			0
$449$		−	3.02340e6i		−	0.707749i	−0.935293	−	0.353874i	$-0.884864\pi$
$449$		−	3.02340e6i		−	0.707749i	0.935293	−	0.353874i	$-0.115136\pi$
$450$		0			0
$451$	1.07906e6			0.249807
$452$		0			0
$453$	−1.53522e6	−	1.53522e6i	−0.351500	−	0.351500i
$454$		0			0
$455$	518796.	+	662807.i	0.117481	+	0.150092i
$456$		0			0
$457$	−2.25695e6	−	2.25695e6i	−0.505512	−	0.505512i	0.407633	−	0.913146i	$-0.366354\pi$
$457$	−2.25695e6	−	2.25695e6i	−0.505512	−	0.505512i	−0.913146	+	0.407633i	$0.866354\pi$
$458$		0			0
$459$			2.15890e6i			0.478302i
$460$		0			0
$461$			149750.i			0.0328181i	0.999865	+	0.0164090i	$0.00522340\pi$
$461$			149750.i			0.0328181i	−0.999865	+	0.0164090i	$0.994777\pi$
$462$		0			0
$463$	504994.	+	504994.i	0.109480	+	0.109480i	0.759725	−	0.650245i	$-0.225334\pi$
$463$	504994.	+	504994.i	0.109480	+	0.109480i	−0.650245	+	0.759725i	$0.725334\pi$
$464$		0			0
$465$	74804.3	−	613767.i	0.0160433	−	0.131635i
$466$		0			0
$467$	6.16159e6	+	6.16159e6i	1.30738	+	1.30738i	0.923302	+	0.384076i	$0.125480\pi$
$467$	6.16159e6	+	6.16159e6i	1.30738	+	1.30738i	0.384076	+	0.923302i	$0.374520\pi$
$468$		0			0
$469$	−243273.			−0.0510696
$470$		0			0
$471$			448969.i			0.0932532i
$472$		0			0
$473$	7.38169e6	−	7.38169e6i	1.51706	−	1.51706i
$474$		0			0
$475$	5.47924e6	+	1.35573e6i	1.11426	+	0.275701i
$476$		0			0
$477$	2.81875e6	−	2.81875e6i	0.567231	−	0.567231i
$478$		0			0
$479$	−3.27963e6			−0.653110			−0.326555	−	0.945178i	$-0.605888\pi$
$479$	−3.27963e6			−0.653110			−0.326555	+	0.945178i	$0.605888\pi$
$480$		0			0
$481$	−3.62421e6			−0.714251
$482$		0			0
$483$	199622.	−	199622.i	0.0389351	−	0.0389351i
$484$		0			0
$485$	−665991.	+	5.46444e6i	−0.128562	+	1.05485i
$486$		0			0
$487$	−6.00351e6	+	6.00351e6i	−1.14705	+	1.14705i	−0.159922	+	0.987130i	$0.551124\pi$
$487$	−6.00351e6	+	6.00351e6i	−1.14705	+	1.14705i	−0.987130	+	0.159922i	$0.948876\pi$
$488$		0			0
$489$			2.16237e6i			0.408939i
$490$		0			0
$491$	−2.80758e6			−0.525568			−0.262784	−	0.964855i	$-0.584641\pi$
$491$	−2.80758e6			−0.525568			−0.262784	+	0.964855i	$0.584641\pi$
$492$		0			0
$493$	−5.68371e6	−	5.68371e6i	−1.05321	−	1.05321i
$494$		0			0
$495$	6.37562e6	−	4.99036e6i	1.16952	−	0.915417i
$496$		0			0
$497$	−56634.5	−	56634.5i	−0.0102847	−	0.0102847i
$498$		0			0
$499$		−	2.83578e6i		−	0.509826i	−0.966964	−	0.254913i	$-0.917953\pi$
$499$		−	2.83578e6i		−	0.509826i	0.966964	−	0.254913i	$-0.0820468\pi$
$500$		0			0
$501$			2.32193e6i			0.413291i
$502$		0			0
$503$	−1.49851e6	−	1.49851e6i	−0.264083	−	0.264083i	0.562628	−	0.826710i	$-0.309791\pi$
$503$	−1.49851e6	−	1.49851e6i	−0.264083	−	0.264083i	−0.826710	+	0.562628i	$0.809791\pi$
$504$		0			0
$505$	−2.77041e6	+	2.16847e6i	−0.483410	+	0.378377i
$506$		0			0
$507$	−198853.	−	198853.i	−0.0343568	−	0.0343568i
$508$		0			0
$509$	−3.58529e6			−0.613380			−0.306690	−	0.951809i	$-0.599222\pi$
$509$	−3.58529e6			−0.613380			−0.306690	+	0.951809i	$0.599222\pi$
$510$		0			0
$511$		−	413690.i		−	0.0700847i
$512$		0			0
$513$	2.63524e6	−	2.63524e6i	0.442106	−	0.442106i
$514$		0			0
$515$	−1.35641e6	+	1.11293e7i	−0.225357	+	1.84905i
$516$		0			0
$517$	8.36376e6	−	8.36376e6i	1.37618	−	1.37618i
$518$		0			0
$519$	−1.81394e6			−0.295600
$520$		0			0
$521$	−1.82322e6			−0.294269			−0.147135	−	0.989116i	$-0.547005\pi$
$521$	−1.82322e6			−0.294269			−0.147135	+	0.989116i	$0.547005\pi$
$522$		0			0
$523$	5.80194e6	−	5.80194e6i	0.927511	−	0.927511i	−0.0700335	−	0.997545i	$-0.522311\pi$
$523$	5.80194e6	−	5.80194e6i	0.927511	−	0.927511i	0.997545	+	0.0700335i	$0.0223106\pi$
$524$		0			0
$525$	−364230.	−	90121.4i	−0.0576736	−	0.0142702i
$526$		0			0
$527$	1.84997e6	−	1.84997e6i	0.290160	−	0.290160i
$528$		0			0
$529$		−	908056.i		−	0.141083i
$530$		0			0
$531$	−6.71975e6			−1.03423
$532$		0			0
$533$	652957.	+	652957.i	0.0995558	+	0.0995558i
$534$		0			0
$535$	662854.	−	5.43870e6i	0.100123	−	0.821505i
$536$		0			0
$537$	1.70887e6	+	1.70887e6i	0.255725	+	0.255725i
$538$		0			0
$539$		−	1.04171e7i		−	1.54445i
$540$		0			0
$541$			9.16864e6i			1.34683i	0.739266	+	0.673414i	$0.235173\pi$
$541$			9.16864e6i			1.34683i	−0.739266	+	0.673414i	$0.764827\pi$
$542$		0			0
$543$	−851188.	−	851188.i	−0.123887	−	0.123887i
$544$		0			0
$545$	5.59720e6	+	7.15091e6i	0.807197	+	1.03126i
$546$		0			0
$547$	−6.83419e6	−	6.83419e6i	−0.976605	−	0.976605i	0.0231275	−	0.999733i	$-0.492638\pi$
$547$	−6.83419e6	−	6.83419e6i	−0.976605	−	0.976605i	−0.999733	+	0.0231275i	$0.992638\pi$
$548$		0			0
$549$	5.07414e6			0.718508
$550$		0			0
$551$			1.38755e7i			1.94702i
$552$		0			0
$553$	143466.	−	143466.i	0.0199497	−	0.0199497i
$554$		0			0
$555$	1.27222e6	−	995799.i	0.175319	−	0.137227i
$556$		0			0
$557$	−1.90300e6	+	1.90300e6i	−0.259897	+	0.259897i	−0.825012	−	0.565115i	$-0.808832\pi$
$557$	−1.90300e6	+	1.90300e6i	−0.259897	+	0.259897i	0.565115	+	0.825012i	$0.308832\pi$
$558$		0			0
$559$	8.93358e6			1.20919
$560$		0			0
$561$	−3.00033e6			−0.402496
$562$		0			0
$563$	2.90513e6	−	2.90513e6i	0.386273	−	0.386273i	−0.487083	−	0.873356i	$-0.661939\pi$
$563$	2.90513e6	−	2.90513e6i	0.386273	−	0.386273i	0.873356	+	0.487083i	$0.161939\pi$
$564$		0			0
$565$	5.70851e6	+	695738.i	0.752319	+	0.0916906i
$566$		0			0
$567$	866883.	−	866883.i	0.113241	−	0.113241i
$568$		0			0
$569$		−	1.63994e6i		−	0.212348i	−0.994348	−	0.106174i	$-0.966140\pi$
$569$		−	1.63994e6i		−	0.212348i	0.994348	−	0.106174i	$-0.0338601\pi$
$570$		0			0
$571$	−3.51371e6			−0.450999			−0.225500	−	0.974243i	$-0.572401\pi$
$571$	−3.51371e6			−0.450999			−0.225500	+	0.974243i	$0.572401\pi$
$572$		0			0
$573$	−261062.	−	261062.i	−0.0332167	−	0.0332167i
$574$		0			0
$575$	6.29134e6	−	3.79555e6i	0.793549	−	0.478745i
$576$		0			0
$577$	1.30066e6	+	1.30066e6i	0.162639	+	0.162639i	0.783735	−	0.621096i	$-0.213312\pi$
$577$	1.30066e6	+	1.30066e6i	0.162639	+	0.162639i	−0.621096	+	0.783735i	$0.713312\pi$
$578$		0			0
$579$		−	243249.i		−	0.0301546i
$580$		0			0
$581$		−	379095.i		−	0.0465916i
$582$		0			0
$583$	8.17775e6	+	8.17775e6i	0.996466	+	0.996466i
$584$		0			0
$585$	6.87775e6	+	838242.i	0.830915	+	0.101270i
$586$		0			0
$587$	−2.17744e6	−	2.17744e6i	−0.260826	−	0.260826i	0.564563	−	0.825390i	$-0.309045\pi$
$587$	−2.17744e6	−	2.17744e6i	−0.260826	−	0.260826i	−0.825390	+	0.564563i	$0.809045\pi$
$588$		0			0
$589$	−4.51628e6			−0.536405
$590$		0			0
$591$			2.41689e6i			0.284635i
$592$		0			0
$593$	6.39982e6	−	6.39982e6i	0.747362	−	0.747362i	−0.226621	−	0.973983i	$-0.572768\pi$
$593$	6.39982e6	−	6.39982e6i	0.747362	−	0.747362i	0.973983	+	0.226621i	$0.0727680\pi$
$594$		0			0
$595$	−978568.	−	1.25021e6i	−0.113318	−	0.144773i
$596$		0			0
$597$	−932028.	+	932028.i	−0.107027	+	0.107027i
$598$		0			0
$599$	−1.52076e6			−0.173178			−0.0865890	−	0.996244i	$-0.527597\pi$
$599$	−1.52076e6			−0.173178			−0.0865890	+	0.996244i	$0.527597\pi$
$600$		0			0
$601$	−8.93347e6			−1.00887			−0.504434	−	0.863450i	$-0.668299\pi$
$601$	−8.93347e6			−1.00887			−0.504434	+	0.863450i	$0.668299\pi$
$602$		0			0
$603$	−1.41602e6	+	1.41602e6i	−0.158590	+	0.158590i
$604$		0			0
$605$	8.92889e6	+	1.14074e7i	0.991766	+	1.26707i
$606$		0			0
$607$	−1.52331e6	+	1.52331e6i	−0.167810	+	0.167810i	−0.786016	−	0.618206i	$-0.787860\pi$
$607$	−1.52331e6	+	1.52331e6i	−0.167810	+	0.167810i	0.618206	+	0.786016i	$0.287860\pi$
$608$		0			0
$609$		−	922367.i		−	0.100777i
$610$		0			0
$611$	1.01221e7			1.09690
$612$		0			0
$613$	−2.44300e6	−	2.44300e6i	−0.262587	−	0.262587i	0.563518	−	0.826104i	$-0.309448\pi$
$613$	−2.44300e6	−	2.44300e6i	−0.262587	−	0.262587i	−0.826104	+	0.563518i	$0.809448\pi$
$614$		0			0
$615$	−408619.	−	49801.3i	−0.0435643	−	0.00530950i
$616$		0			0
$617$	6.66745e6	+	6.66745e6i	0.705093	+	0.705093i	0.965499	−	0.260406i	$-0.0838564\pi$
$617$	6.66745e6	+	6.66745e6i	0.705093	+	0.705093i	−0.260406	+	0.965499i	$0.583856\pi$
$618$		0			0
$619$		−	7.26158e6i		−	0.761736i	−0.924629	−	0.380868i	$-0.875625\pi$
$619$		−	7.26158e6i		−	0.761736i	0.924629	−	0.380868i	$-0.124375\pi$
$620$		0			0
$621$		−	4.85128e6i		−	0.504810i
$622$		0			0
$623$	4354.66	+	4354.66i	0.000449505	+	0.000449505i
$624$		0			0
$625$	−8.63887e6	−	4.55382e6i	−0.884621	−	0.466312i
$626$		0			0
$627$	3.66231e6	+	3.66231e6i	0.372037	+	0.372037i
$628$		0			0
$629$	6.83609e6			0.688940
$630$		0			0
$631$		−	1.27725e7i		−	1.27704i	−0.769606	−	0.638519i	$-0.779548\pi$
$631$		−	1.27725e7i		−	1.27704i	0.769606	−	0.638519i	$-0.220452\pi$
$632$		0			0
$633$	−413424.	+	413424.i	−0.0410097	+	0.0410097i
$634$		0			0
$635$	3.64438e6	+	444168.i	0.358666	+	0.0437132i
$636$		0			0
$637$	6.30356e6	−	6.30356e6i	0.615513	−	0.615513i
$638$		0			0
$639$	−659304.			−0.0638754
$640$		0			0
$641$	2.59483e6			0.249439			0.124719	−	0.992192i	$-0.460197\pi$
$641$	2.59483e6			0.249439			0.124719	+	0.992192i	$0.460197\pi$
$642$		0			0
$643$	9.83511e6	−	9.83511e6i	0.938106	−	0.938106i	−0.0600871	−	0.998193i	$-0.519138\pi$
$643$	9.83511e6	−	9.83511e6i	0.938106	−	0.938106i	0.998193	+	0.0600871i	$0.0191378\pi$
$644$		0			0
$645$	−3.13599e6	+	2.45462e6i	−0.296808	+	0.232319i
$646$		0			0
$647$	6.28343e6	−	6.28343e6i	0.590114	−	0.590114i	−0.347548	−	0.937662i	$-0.612986\pi$
$647$	6.28343e6	−	6.28343e6i	0.590114	−	0.590114i	0.937662	+	0.347548i	$0.112986\pi$
$648$		0			0
$649$		−	1.94953e7i		−	1.81685i
$650$		0			0
$651$	300217.			0.0277641
$652$		0			0
$653$	532425.	+	532425.i	0.0488625	+	0.0488625i	0.731116	−	0.682253i	$-0.239000\pi$
$653$	532425.	+	532425.i	0.0488625	+	0.0488625i	−0.682253	+	0.731116i	$0.739000\pi$
$654$		0			0
$655$	5.32218e6	+	6.79955e6i	0.484715	+	0.619265i
$656$		0			0
$657$	−2.40797e6	−	2.40797e6i	−0.217639	−	0.217639i
$658$		0			0
$659$		−	3.54164e6i		−	0.317681i	−0.987304	−	0.158841i	$-0.949224\pi$
$659$		−	3.54164e6i		−	0.317681i	0.987304	−	0.158841i	$-0.0507756\pi$
$660$		0			0
$661$			1.14846e7i			1.02238i	0.859468	+	0.511189i	$0.170795\pi$
$661$			1.14846e7i			1.02238i	−0.859468	+	0.511189i	$0.829205\pi$
$662$		0			0
$663$	−1.81555e6	−	1.81555e6i	−0.160407	−	0.160407i
$664$		0			0
$665$	−331570.	+	2.72052e6i	−0.0290751	+	0.238560i
$666$		0			0
$667$	1.27719e7	+	1.27719e7i	1.11158	+	1.11158i
$668$		0			0
$669$	−896703.			−0.0774610
$670$		0			0
$671$			1.47211e7i			1.26222i
$672$		0			0
$673$	2.64129e6	−	2.64129e6i	0.224790	−	0.224790i	−0.585722	−	0.810512i	$-0.699189\pi$
$673$	2.64129e6	−	2.64129e6i	0.224790	−	0.224790i	0.810512	+	0.585722i	$0.199189\pi$
$674$		0			0
$675$	−5.52089e6	+	3.33074e6i	−0.466391	+	0.281372i
$676$		0			0
$677$	−4.45791e6	+	4.45791e6i	−0.373817	+	0.373817i	−0.868866	−	0.495048i	$-0.835150\pi$
$677$	−4.45791e6	+	4.45791e6i	−0.373817	+	0.373817i	0.495048	+	0.868866i	$0.335150\pi$
$678$		0			0
$679$	−2.67287e6			−0.222486
$680$		0			0
$681$	1.00563e6			0.0830942
$682$		0			0
$683$	−8.50766e6	+	8.50766e6i	−0.697844	+	0.697844i	−0.963945	−	0.266101i	$-0.914265\pi$
$683$	−8.50766e6	+	8.50766e6i	−0.697844	+	0.697844i	0.266101	+	0.963945i	$0.414265\pi$
$684$		0			0
$685$	2.00700e6	−	1.64674e7i	0.163426	−	1.34091i
$686$		0			0
$687$	−3.14677e6	+	3.14677e6i	−0.254375	+	0.254375i
$688$		0			0
$689$			9.89699e6i			0.794246i
$690$		0			0
$691$	−1.94961e7			−1.55329			−0.776643	−	0.629940i	$-0.783079\pi$
$691$	−1.94961e7			−1.55329			−0.776643	+	0.629940i	$0.783079\pi$
$692$		0			0
$693$	2.77977e6	+	2.77977e6i	0.219875	+	0.219875i
$694$		0			0
$695$	−6.07886e6	+	4.75809e6i	−0.477376	+	0.373655i
$696$		0			0
$697$	−1.23163e6	−	1.23163e6i	−0.0960279	−	0.0960279i
$698$		0			0
$699$			6.85069e6i			0.530324i
$700$		0			0
$701$			2.02740e6i			0.155828i	0.996960	+	0.0779139i	$0.0248259\pi$
$701$			2.02740e6i			0.155828i	−0.996960	+	0.0779139i	$0.975174\pi$
$702$		0			0
$703$	−8.34438e6	−	8.34438e6i	−0.636804	−	0.636804i
$704$		0			0
$705$	−3.55320e6	+	2.78118e6i	−0.269244	+	0.210745i
$706$		0			0
$707$	−1.20790e6	−	1.20790e6i	−0.0908829	−	0.0908829i
$708$		0			0
$709$	−2.16543e7			−1.61781			−0.808907	−	0.587937i	$-0.799940\pi$
$709$	−2.16543e7			−1.61781			−0.808907	+	0.587937i	$0.799940\pi$
$710$		0			0
$711$		−	1.67014e6i		−	0.123902i
$712$		0			0
$713$	−4.15707e6	+	4.15707e6i	−0.306241	+	0.306241i
$714$		0			0
$715$	−2.43191e6	+	1.99537e7i	−0.177902	+	1.45968i
$716$		0			0
$717$	3.68270e6	−	3.68270e6i	0.267528	−	0.267528i
$718$		0			0
$719$	−1.85327e7			−1.33695			−0.668477	−	0.743733i	$-0.733053\pi$
$719$	−1.85327e7			−1.33695			−0.668477	+	0.743733i	$0.733053\pi$
$720$		0			0
$721$	−5.44377e6			−0.389997
$722$		0			0
$723$	3.94203e6	−	3.94203e6i	0.280462	−	0.280462i
$724$		0			0
$725$	5.76600e6	−	2.33035e7i	0.407408	−	1.64656i
$726$		0			0
$727$	4.14363e6	−	4.14363e6i	0.290767	−	0.290767i	−0.546616	−	0.837383i	$-0.684084\pi$
$727$	4.14363e6	−	4.14363e6i	0.290767	−	0.290767i	0.837383	+	0.546616i	$0.184084\pi$
$728$		0			0
$729$		−	7.87383e6i		−	0.548741i
$730$		0			0
$731$	−1.68508e7			−1.16634
$732$		0			0
$733$	4.63493e6	+	4.63493e6i	0.318628	+	0.318628i	0.848240	−	0.529612i	$-0.177663\pi$
$733$	4.63493e6	+	4.63493e6i	0.318628	+	0.318628i	−0.529612	+	0.848240i	$0.677663\pi$
$734$		0			0
$735$	−480775.	+	3.94475e6i	−0.0328264	+	0.269340i
$736$		0			0
$737$	−4.10816e6	−	4.10816e6i	−0.278598	−	0.278598i
$738$		0			0
$739$			9.51962e6i			0.641222i	0.947211	+	0.320611i	$0.103888\pi$
$739$			9.51962e6i			0.641222i	−0.947211	+	0.320611i	$0.896112\pi$
$740$		0			0
$741$			4.43225e6i			0.296537i
$742$		0			0
$743$	−1.19265e7	−	1.19265e7i	−0.792579	−	0.792579i	0.189333	−	0.981913i	$-0.439367\pi$
$743$	−1.19265e7	−	1.19265e7i	−0.792579	−	0.792579i	−0.981913	+	0.189333i	$0.939367\pi$
$744$		0			0
$745$	1.70035e7	+	2.17234e7i	1.12240	+	1.43396i
$746$		0			0
$747$	−2.20659e6	−	2.20659e6i	−0.144684	−	0.144684i
$748$		0			0
$749$	2.66028e6			0.173270
$750$		0			0
$751$			619101.i			0.0400555i	0.999799	+	0.0200277i	$0.00637545\pi$
$751$			619101.i			0.0400555i	−0.999799	+	0.0200277i	$0.993625\pi$
$752$		0			0
$753$	4.84509e6	−	4.84509e6i	0.311397	−	0.311397i
$754$		0			0
$755$	2.16056e7	−	1.69113e7i	1.37943	−	1.07971i
$756$		0			0
$757$	−5.29958e6	+	5.29958e6i	−0.336126	+	0.336126i	−0.854907	−	0.518781i	$-0.826386\pi$
$757$	−5.29958e6	+	5.29958e6i	−0.336126	+	0.336126i	0.518781	+	0.854907i	$0.326386\pi$
$758$		0			0
$759$	6.74204e6			0.424802
$760$		0			0
$761$	−1.89611e7			−1.18686			−0.593432	−	0.804884i	$-0.702227\pi$
$761$	−1.89611e7			−1.18686			−0.593432	+	0.804884i	$0.702227\pi$
$762$		0			0
$763$	−3.11780e6	+	3.11780e6i	−0.193882	+	0.193882i
$764$		0			0
$765$	−1.29730e7	−	1.58112e6i	−0.801470	−	0.0976810i
$766$		0			0
$767$	1.17970e7	−	1.17970e7i	0.724072	−	0.724072i
$768$		0			0
$769$			5.44231e6i			0.331869i	0.986137	+	0.165935i	$0.0530641\pi$
$769$			5.44231e6i			0.331869i	−0.986137	+	0.165935i	$0.946936\pi$
$770$		0			0
$771$	−4.24310e6			−0.257067
$772$		0			0
$773$	−1.35362e7	−	1.35362e7i	−0.814792	−	0.814792i	0.170556	−	0.985348i	$-0.445444\pi$
$773$	−1.35362e7	−	1.35362e7i	−0.814792	−	0.814792i	−0.985348	+	0.170556i	$0.945444\pi$
$774$		0			0
$775$	7.58498e6	+	1.87675e6i	0.453628	+	0.112241i
$776$		0			0
$777$	554688.	+	554688.i	0.0329607	+	0.0329607i
$778$		0			0
$779$			3.00674e6i			0.177522i
$780$		0			0
$781$		−	1.91277e6i		−	0.112211i
$782$		0			0
$783$	−1.12078e7	−	1.12078e7i	−0.653306	−	0.653306i
$784$		0			0
$785$	−5.63205e6	−	686419.i	−0.326206	−	0.0397571i
$786$		0			0
$787$	1.00190e7	+	1.00190e7i	0.576615	+	0.576615i	0.933969	−	0.357354i	$-0.116321\pi$
$787$	1.00190e7	+	1.00190e7i	0.576615	+	0.576615i	−0.357354	+	0.933969i	$0.616321\pi$
$788$		0			0
$789$	−1.75688e6			−0.100473
$790$		0			0
$791$			2.79226e6i			0.158677i
$792$		0			0
$793$	−8.90799e6	+	8.90799e6i	−0.503034	+	0.503034i
$794$		0			0
$795$	−2.71933e6	−	3.47418e6i	−0.152596	−	0.194955i
$796$		0			0
$797$	−2.38772e7	+	2.38772e7i	−1.33149	+	1.33149i	−0.427453	+	0.904038i	$0.640589\pi$
$797$	−2.38772e7	+	2.38772e7i	−1.33149	+	1.33149i	−0.904038	+	0.427453i	$0.859411\pi$
$798$		0			0
$799$	−1.90926e7			−1.05803
$800$		0			0
$801$	50694.3			0.00279176
$802$		0			0
$803$	6.98599e6	−	6.98599e6i	0.382331	−	0.382331i
$804$		0			0
$805$	2.19894e6	+	2.80934e6i	0.119598	+	0.152797i
$806$		0			0
$807$	423290.	−	423290.i	0.0228799	−	0.0228799i
$808$		0			0
$809$			6.68830e6i			0.359290i	0.983732	+	0.179645i	$0.0574948\pi$
$809$			6.68830e6i			0.359290i	−0.983732	+	0.179645i	$0.942505\pi$
$810$		0			0
$811$	2.06080e7			1.10023			0.550115	−	0.835089i	$-0.314584\pi$
$811$	2.06080e7			1.10023			0.550115	+	0.835089i	$0.314584\pi$
$812$		0			0
$813$	−4.38761e6	−	4.38761e6i	−0.232810	−	0.232810i
$814$		0			0
$815$	−2.71257e7	−	3.30601e6i	−1.43050	−	0.174345i
$816$		0			0
$817$	2.05687e7	+	2.05687e7i	1.07808	+	1.07808i
$818$		0			0
$819$			3.36418e6i			0.175254i
$820$		0			0
$821$		−	1.74397e7i		−	0.902985i	−0.892275	−	0.451492i	$-0.850892\pi$
$821$		−	1.74397e7i		−	0.902985i	0.892275	−	0.451492i	$-0.149108\pi$
$822$		0			0
$823$	4.29034e6	+	4.29034e6i	0.220797	+	0.220797i	0.808834	−	0.588037i	$-0.200099\pi$
$823$	4.29034e6	+	4.29034e6i	0.220797	+	0.220797i	−0.588037	+	0.808834i	$0.700099\pi$
$824$		0			0
$825$	−4.62887e6	−	7.67263e6i	−0.236777	−	0.392473i
$826$		0			0
$827$	−1.22618e7	−	1.22618e7i	−0.623434	−	0.623434i	0.322974	−	0.946408i	$-0.395317\pi$
$827$	−1.22618e7	−	1.22618e7i	−0.623434	−	0.623434i	−0.946408	+	0.322974i	$0.895317\pi$
$828$		0			0
$829$	−1.66613e6			−0.0842021			−0.0421010	−	0.999113i	$-0.513405\pi$
$829$	−1.66613e6			−0.0842021			−0.0421010	+	0.999113i	$0.513405\pi$
$830$		0			0
$831$		−	1.91898e6i		−	0.0963980i
$832$		0			0
$833$	−1.18900e7	+	1.18900e7i	−0.593701	+	0.593701i
$834$		0			0
$835$	−2.91273e7	−	3.54996e6i	−1.44572	−	0.176200i
$836$		0			0
$837$	3.64799e6	−	3.64799e6i	0.179987	−	0.179987i
$838$		0			0
$839$	3.44947e7			1.69179			0.845896	−	0.533348i	$-0.179066\pi$
$839$	3.44947e7			1.69179			0.845896	+	0.533348i	$0.179066\pi$
$840$		0			0
$841$	3.85022e7			1.87713
$842$		0			0
$843$	4.46825e6	−	4.46825e6i	0.216555	−	0.216555i
$844$		0			0
$845$	2.79852e6	−	2.19047e6i	0.134830	−	0.105535i
$846$		0			0
$847$	−4.97364e6	+	4.97364e6i	−0.238213	+	0.238213i
$848$		0			0
$849$			5.93288e6i			0.282486i
$850$		0			0
$851$	−1.53614e7			−0.727121
$852$		0			0
$853$	2.02443e7	+	2.02443e7i	0.952642	+	0.952642i	0.998928	−	0.0462866i	$-0.0147387\pi$
$853$	2.02443e7	+	2.02443e7i	0.952642	+	0.952642i	−0.0462866	+	0.998928i	$0.514739\pi$
$854$		0			0
$855$	1.39054e7	+	1.77653e7i	0.650529	+	0.831107i
$856$		0			0
$857$	−1.43088e7	−	1.43088e7i	−0.665505	−	0.665505i	0.291167	−	0.956672i	$-0.405957\pi$
$857$	−1.43088e7	−	1.43088e7i	−0.665505	−	0.665505i	−0.956672	+	0.291167i	$0.905957\pi$
$858$		0			0
$859$		−	1.60807e7i		−	0.743571i	−0.928319	−	0.371785i	$-0.878746\pi$
$859$		−	1.60807e7i		−	0.743571i	0.928319	−	0.371785i	$-0.121254\pi$
$860$		0			0
$861$		−	199871.i		−	0.00918846i
$862$		0			0
$863$	6.83472e6	+	6.83472e6i	0.312387	+	0.312387i	0.845834	−	0.533446i	$-0.179103\pi$
$863$	6.83472e6	+	6.83472e6i	0.312387	+	0.312387i	−0.533446	+	0.845834i	$0.679103\pi$
$864$		0			0
$865$	2.77329e6	−	2.27548e7i	0.126025	−	1.03403i
$866$		0			0
$867$	−1.01668e6	−	1.01668e6i	−0.0459343	−	0.0459343i
$868$		0			0
$869$	4.84542e6			0.217662
$870$		0			0
$871$		−	4.97184e6i		−	0.222061i
$872$		0			0
$873$	−1.55580e7	+	1.55580e7i	−0.690903	+	0.690903i
$874$		0			0
$875$	1.68738e6	−	4.43126e6i	0.0745064	−	0.195662i
$876$		0			0
$877$	5.82980e6	−	5.82980e6i	0.255950	−	0.255950i	−0.567455	−	0.823405i	$-0.692072\pi$
$877$	5.82980e6	−	5.82980e6i	0.255950	−	0.255950i	0.823405	+	0.567455i	$0.192072\pi$
$878$		0			0
$879$	1.10284e7			0.481439
$880$		0			0
$881$	979191.			0.0425038			0.0212519	−	0.999774i	$-0.493235\pi$
$881$	979191.			0.0425038			0.0212519	+	0.999774i	$0.493235\pi$
$882$		0			0
$883$	−1.83879e7	+	1.83879e7i	−0.793653	+	0.793653i	−0.982086	−	0.188433i	$-0.939659\pi$
$883$	−1.83879e7	+	1.83879e7i	−0.793653	+	0.793653i	0.188433	+	0.982086i	$0.439659\pi$
$884$		0			0
$885$	−899759.	+	7.38250e6i	−0.0386161	+	0.316844i
$886$		0			0
$887$	1.72529e7	−	1.72529e7i	0.736297	−	0.736297i	−0.235562	−	0.971859i	$-0.575693\pi$
$887$	1.72529e7	−	1.72529e7i	0.736297	−	0.736297i	0.971859	+	0.235562i	$0.0756931\pi$
$888$		0			0
$889$			1.78261e6i			0.0756488i
$890$		0			0
$891$	2.92781e7			1.23552
$892$		0			0
$893$	2.33051e7	+	2.33051e7i	0.977964	+	0.977964i
$894$		0			0
$895$	−2.40494e7	+	1.88241e7i	−1.00357	+	0.785519i
$896$		0			0
$897$	4.07973e6	+	4.07973e6i	0.169297	+	0.169297i
$898$		0			0
$899$			1.92080e7i			0.792653i
$900$		0			0
$901$		−	1.86680e7i		−	0.766100i
$902$		0			0
$903$	−1.36729e6	−	1.36729e6i	−0.0558010	−	0.0558010i
$904$		0			0
$905$	1.19790e7	−	9.37629e6i	0.486183	−	0.380548i
$906$		0			0
$907$	−1.97949e7	−	1.97949e7i	−0.798980	−	0.798980i	0.183955	−	0.982935i	$-0.441110\pi$
$907$	−1.97949e7	−	1.97949e7i	−0.798980	−	0.798980i	−0.982935	+	0.183955i	$0.941110\pi$
$908$		0			0
$909$	−1.40616e7			−0.564450
$910$		0			0
$911$			3.84298e6i			0.153416i	0.997054	+	0.0767082i	$0.0244410\pi$
$911$			3.84298e6i			0.153416i	−0.997054	+	0.0767082i	$0.975559\pi$
$912$		0			0
$913$	6.40178e6	−	6.40178e6i	0.254170	−	0.254170i
$914$		0			0
$915$	679417.	−	5.57460e6i	0.0268277	−	0.220121i
$916$		0			0
$917$	−2.96461e6	+	2.96461e6i	−0.116424	+	0.116424i
$918$		0			0
$919$	2.06477e7			0.806459			0.403229	−	0.915099i	$-0.367888\pi$
$919$	2.06477e7			0.806459			0.403229	+	0.915099i	$0.367888\pi$
$920$		0			0
$921$	771334.			0.0299635
$922$		0			0
$923$	1.15745e6	−	1.15745e6i	0.0447197	−	0.0447197i
$924$		0			0
$925$	1.05466e7	+	1.74817e7i	0.405285	+	0.671784i
$926$		0			0
$927$	−3.16865e7	+	3.16865e7i	−1.21109	+	1.21109i
$928$		0			0
$929$		−	1.55025e7i		−	0.589335i	−0.955600	−	0.294668i	$-0.904791\pi$
$929$		−	1.55025e7i		−	0.589335i	0.955600	−	0.294668i	$-0.0952089\pi$
$930$		0			0
$931$	2.90266e7			1.09754
$932$		0			0
$933$	9.90184e6	+	9.90184e6i	0.372402	+	0.372402i
$934$		0			0
$935$	4.58713e6	−	3.76373e7i	0.171598	−	1.40796i
$936$		0			0
$937$	−1.92742e7	−	1.92742e7i	−0.717177	−	0.717177i	0.250849	−	0.968026i	$-0.419290\pi$
$937$	−1.92742e7	−	1.92742e7i	−0.717177	−	0.717177i	−0.968026	+	0.250849i	$0.919290\pi$
$938$		0			0
$939$		−	3.32470e6i		−	0.123052i
$940$		0			0
$941$		−	3.56736e7i		−	1.31333i	−0.754183	−	0.656664i	$-0.771967\pi$
$941$		−	3.56736e7i		−	1.31333i	0.754183	−	0.656664i	$-0.228033\pi$
$942$		0			0
$943$	2.76759e6	+	2.76759e6i	0.101350	+	0.101350i
$944$		0			0
$945$	−1.92966e6	−	2.46530e6i	−0.0702912	−	0.0898030i
$946$		0			0
$947$	2.34596e7	+	2.34596e7i	0.850052	+	0.850052i	0.990139	−	0.140087i	$-0.0447382\pi$
$947$	2.34596e7	+	2.34596e7i	0.850052	+	0.850052i	−0.140087	+	0.990139i	$0.544738\pi$
$948$		0			0
$949$	8.45469e6			0.304742
$950$		0			0
$951$			6.66145e6i			0.238846i
$952$		0			0
$953$	2.67137e7	−	2.67137e7i	0.952798	−	0.952798i	−0.0461367	−	0.998935i	$-0.514691\pi$
$953$	2.67137e7	−	2.67137e7i	0.952798	−	0.952798i	0.998935	+	0.0461367i	$0.0146910\pi$
$954$		0			0
$955$	3.67399e6	−	2.87573e6i	0.130356	−	0.102033i
$956$		0			0
$957$	1.55760e7	−	1.55760e7i	0.549764	−	0.549764i
$958$		0			0
$959$	8.05485e6			0.282820
$960$		0			0
$961$	2.23772e7			0.781623
$962$		0			0
$963$	1.54847e7	−	1.54847e7i	0.538067	−	0.538067i
$964$		0			0
$965$	3.05141e6	+	371898.i	0.105483	+	0.0128560i
$966$		0			0
$967$	1.09161e7	−	1.09161e7i	0.375407	−	0.375407i	−0.494035	−	0.869442i	$-0.664479\pi$
$967$	1.09161e7	−	1.09161e7i	0.375407	−	0.375407i	0.869442	+	0.494035i	$0.164479\pi$
$968$		0			0
$969$		−	8.36024e6i		−	0.286028i
$970$		0			0
$971$	1.97557e7			0.672427			0.336214	−	0.941786i	$-0.390854\pi$
$971$	1.97557e7			0.672427			0.336214	+	0.941786i	$0.390854\pi$
$972$		0			0
$973$	−2.65039e6	−	2.65039e6i	−0.0897485	−	0.0897485i
$974$		0			0
$975$	1.84183e6	−	7.44385e6i	0.0620495	−	0.250776i
$976$		0			0
$977$	−3.50337e7	−	3.50337e7i	−1.17422	−	1.17422i	−0.981194	−	0.193025i	$-0.938170\pi$
$977$	−3.50337e7	−	3.50337e7i	−1.17422	−	1.17422i	−0.193025	−	0.981194i	$-0.561830\pi$
$978$		0			0
$979$			147074.i			0.00490434i
$980$		0			0
$981$			3.62955e7i			1.20415i
$982$		0			0
$983$	3.24328e7	+	3.24328e7i	1.07054	+	1.07054i	0.997316	+	0.0732202i	$0.0233276\pi$
$983$	3.24328e7	+	3.24328e7i	1.07054	+	1.07054i	0.0732202	+	0.997316i	$0.476672\pi$
$984$		0			0
$985$	−3.03185e7	−	3.69513e6i	−0.995673	−	0.121350i
$986$		0			0
$987$	−1.54920e6	−	1.54920e6i	−0.0506190	−	0.0506190i
$988$		0			0
$989$	3.78654e7			1.23098
$990$		0			0
$991$		−	1.17192e7i		−	0.379066i	−0.981874	−	0.189533i	$-0.939303\pi$
$991$		−	1.17192e7i		−	0.379066i	0.981874	−	0.189533i	$-0.0606974\pi$
$992$		0			0
$993$	−310225.	+	310225.i	−0.00998398	+	0.00998398i
$994$		0			0
$995$	−1.02668e7	−	1.31167e7i	−0.328758	−	0.420017i
$996$		0			0
$997$	6.91501e6	−	6.91501e6i	0.220320	−	0.220320i	−0.588313	−	0.808633i	$-0.700208\pi$
$997$	6.91501e6	−	6.91501e6i	0.220320	−	0.220320i	0.808633	+	0.588313i	$0.200208\pi$
$998$		0			0
$999$	1.34802e7			0.427349

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.6.o.a.47.15		56
4.3	odd	2		40.6.k.a.27.12	yes	56
5.3	odd	4	inner	160.6.o.a.143.16		56
8.3	odd	2	inner	160.6.o.a.47.16		56
8.5	even	2		40.6.k.a.27.3	yes	56
20.3	even	4		40.6.k.a.3.3	✓	56
40.3	even	4	inner	160.6.o.a.143.15		56
40.13	odd	4		40.6.k.a.3.12	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.k.a.3.3	✓	56	20.3	even	4
40.6.k.a.3.12	yes	56	40.13	odd	4
40.6.k.a.27.3	yes	56	8.5	even	2
40.6.k.a.27.12	yes	56	4.3	odd	2
160.6.o.a.47.15		56	1.1	even	1	trivial
160.6.o.a.47.16		56	8.3	odd	2	inner
160.6.o.a.143.15		56	40.3	even	4	inner
160.6.o.a.143.16		56	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(3.12794 - 3.12794i) q^{3} +(34.4559 + 44.0204i) q^{5} +(-19.1929 + 19.1929i) q^{7} +223.432i q^{9} +O(q^{10})\)	\(q+(3.12794 - 3.12794i) q^{3} +(34.4559 + 44.0204i) q^{5} +(-19.1929 + 19.1929i) q^{7} +223.432i q^{9} -648.221 q^{11} +(-392.250 - 392.250i) q^{13} +(245.469 + 29.9171i) q^{15} +(739.873 + 739.873i) q^{17} -1806.23i q^{19} +120.068i q^{21} +(-1662.57 - 1662.57i) q^{23} +(-750.584 + 3033.52i) q^{25} +(1458.97 + 1458.97i) q^{27} -7682.01 q^{29} -2500.39i q^{31} +(-2027.59 + 2027.59i) q^{33} +(-1506.19 - 183.570i) q^{35} +(4619.77 - 4619.77i) q^{37} -2453.86 q^{39} -1664.65 q^{41} +(-11387.6 + 11387.6i) q^{43} +(-9835.56 + 7698.55i) q^{45} +(-12902.6 + 12902.6i) q^{47} +16070.3i q^{49} +4628.55 q^{51} +(-12615.7 - 12615.7i) q^{53} +(-22335.0 - 28534.9i) q^{55} +(-5649.78 - 5649.78i) q^{57} +30075.1i q^{59} -22710.0i q^{61} +(-4288.31 - 4288.31i) q^{63} +(3751.66 - 30782.3i) q^{65} +(6337.59 + 6337.59i) q^{67} -10400.8 q^{69} +2950.81i q^{71} +(-10777.2 + 10777.2i) q^{73} +(7140.88 + 11836.4i) q^{75} +(12441.2 - 12441.2i) q^{77} -7474.95 q^{79} -45166.9 q^{81} +(-9875.91 + 9875.91i) q^{83} +(-7076.50 + 58062.5i) q^{85} +(-24028.8 + 24028.8i) q^{87} -226.889i q^{89} +15056.8 q^{91} +(-7821.06 - 7821.06i) q^{93} +(79511.0 - 62235.3i) q^{95} +(69631.7 + 69631.7i) q^{97} -144833. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{3}+O(q^{10}) \) 56 * q + 4 * q^3	\( 56 q + 4 q^{3} + 8 q^{11} - 408 q^{17} - 3120 q^{25} - 968 q^{27} - 976 q^{33} + 4780 q^{35} - 8 q^{41} - 1308 q^{43} - 20872 q^{51} + 968 q^{57} + 17680 q^{65} - 89252 q^{67} - 25184 q^{73} + 127740 q^{75} - 67792 q^{81} + 126444 q^{83} - 329432 q^{91} + 212576 q^{97}+O(q^{100}) \) 56 * q + 4 * q^3 + 8 * q^11 - 408 * q^17 - 3120 * q^25 - 968 * q^27 - 976 * q^33 + 4780 * q^35 - 8 * q^41 - 1308 * q^43 - 20872 * q^51 + 968 * q^57 + 17680 * q^65 - 89252 * q^67 - 25184 * q^73 + 127740 * q^75 - 67792 * q^81 + 126444 * q^83 - 329432 * q^91 + 212576 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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