LMFDB - Embedded newform 160.6.o.a.47.2

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			47.2
Character	$\chi$	$=$	160.47
Dual form			160.6.o.a.143.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-20.2357 + 20.2357i) q^{3} +(6.76469 - 55.4909i) q^{5} +(-37.6042 + 37.6042i) q^{7} -575.965i q^{9} +O(q^{10})$	\(q+(-20.2357 + 20.2357i) q^{3} +(6.76469 - 55.4909i) q^{5} +(-37.6042 + 37.6042i) q^{7} -575.965i q^{9} +216.161 q^{11} +(749.126 + 749.126i) q^{13} +(986.008 + 1259.78i) q^{15} +(595.235 + 595.235i) q^{17} -1625.40i q^{19} -1521.89i q^{21} +(-1137.10 - 1137.10i) q^{23} +(-3033.48 - 750.757i) q^{25} +(6737.77 + 6737.77i) q^{27} -2510.57 q^{29} +4278.50i q^{31} +(-4374.17 + 4374.17i) q^{33} +(1832.31 + 2341.07i) q^{35} +(-3549.84 + 3549.84i) q^{37} -30318.1 q^{39} +4205.26 q^{41} +(-5595.71 + 5595.71i) q^{43} +(-31960.8 - 3896.22i) q^{45} +(2274.28 - 2274.28i) q^{47} +13978.8i q^{49} -24090.0 q^{51} +(-4390.22 - 4390.22i) q^{53} +(1462.26 - 11995.0i) q^{55} +(32891.0 + 32891.0i) q^{57} +2415.05i q^{59} +49477.1i q^{61} +(21658.7 + 21658.7i) q^{63} +(46637.3 - 36502.1i) q^{65} +(8120.59 + 8120.59i) q^{67} +46019.8 q^{69} +23377.1i q^{71} +(-6337.57 + 6337.57i) q^{73} +(76576.6 - 46192.4i) q^{75} +(-8128.57 + 8128.57i) q^{77} -28845.4 q^{79} -132727. q^{81} +(-39161.8 + 39161.8i) q^{83} +(37056.7 - 29003.6i) q^{85} +(50803.0 - 50803.0i) q^{87} -79616.6i q^{89} -56340.6 q^{91} +(-86578.3 - 86578.3i) q^{93} +(-90194.8 - 10995.3i) q^{95} +(85618.4 + 85618.4i) q^{97} -124501. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−20.2357	+	20.2357i	−1.29812	+	1.29812i	−0.368486	+	0.929633i	$0.620124\pi$
$3$	−20.2357	+	20.2357i	−1.29812	+	1.29812i	−0.929633	+	0.368486i	$0.879876\pi$
$4$		0			0
$5$	6.76469	−	55.4909i	0.121010	−	0.992651i
$5$	6.76469	−	55.4909i	0.121010	−	0.992651i
$6$		0			0
$7$	−37.6042	+	37.6042i	−0.290062	+	0.290062i	−0.837105	−	0.547043i	$-0.815754\pi$
$7$	−37.6042	+	37.6042i	−0.290062	+	0.290062i	0.547043	+	0.837105i	$0.315754\pi$
$8$		0			0
$9$		−	575.965i		−	2.37023i
$10$		0			0
$11$	216.161			0.538637			0.269318	−	0.963051i	$-0.413202\pi$
$11$	216.161			0.538637			0.269318	+	0.963051i	$0.413202\pi$
$12$		0			0
$13$	749.126	+	749.126i	1.22941	+	1.22941i	0.964187	+	0.265222i	$0.0854452\pi$
$13$	749.126	+	749.126i	1.22941	+	1.22941i	0.265222	+	0.964187i	$0.414555\pi$
$14$		0			0
$15$	986.008	+	1259.78i	1.13149	+	1.44567i
$16$		0			0
$17$	595.235	+	595.235i	0.499536	+	0.499536i	0.911293	−	0.411758i	$-0.135085\pi$
$17$	595.235	+	595.235i	0.499536	+	0.499536i	−0.411758	+	0.911293i	$0.635085\pi$
$18$		0			0
$19$		−	1625.40i		−	1.03294i	−0.856305	−	0.516471i	$-0.827245\pi$
$19$		−	1625.40i		−	1.03294i	0.856305	−	0.516471i	$-0.172755\pi$
$20$		0			0
$21$		−	1521.89i		−	0.753071i
$22$		0			0
$23$	−1137.10	−	1137.10i	−0.448206	−	0.448206i	0.446552	−	0.894758i	$-0.352652\pi$
$23$	−1137.10	−	1137.10i	−0.448206	−	0.448206i	−0.894758	+	0.446552i	$0.852652\pi$
$24$		0			0
$25$	−3033.48	−	750.757i	−0.970713	−	0.240242i
$26$		0			0
$27$	6737.77	+	6737.77i	1.77872	+	1.77872i
$28$		0			0
$29$	−2510.57			−0.554340			−0.277170	−	0.960821i	$-0.589397\pi$
$29$	−2510.57			−0.554340			−0.277170	+	0.960821i	$0.589397\pi$
$30$		0			0
$31$			4278.50i			0.799627i	0.916597	+	0.399813i	$0.130925\pi$
$31$			4278.50i			0.799627i	−0.916597	+	0.399813i	$0.869075\pi$
$32$		0			0
$33$	−4374.17	+	4374.17i	−0.699215	+	0.699215i
$34$		0			0
$35$	1832.31	+	2341.07i	0.252830	+	0.323031i
$36$		0			0
$37$	−3549.84	+	3549.84i	−0.426290	+	0.426290i	−0.887362	−	0.461073i	$-0.847465\pi$
$37$	−3549.84	+	3549.84i	−0.426290	+	0.426290i	0.461073	+	0.887362i	$0.347465\pi$
$38$		0			0
$39$	−30318.1			−3.19184
$40$		0			0
$41$	4205.26			0.390691			0.195346	−	0.980734i	$-0.437417\pi$
$41$	4205.26			0.390691			0.195346	+	0.980734i	$0.437417\pi$
$42$		0			0
$43$	−5595.71	+	5595.71i	−0.461513	+	0.461513i	−0.899151	−	0.437638i	$-0.855815\pi$
$43$	−5595.71	+	5595.71i	−0.461513	+	0.461513i	0.437638	+	0.899151i	$0.355815\pi$
$44$		0			0
$45$	−31960.8	−	3896.22i	−2.35281	−	0.286822i
$46$		0			0
$47$	2274.28	−	2274.28i	0.150175	−	0.150175i	−0.628021	−	0.778196i	$-0.716135\pi$
$47$	2274.28	−	2274.28i	0.150175	−	0.150175i	0.778196	+	0.628021i	$0.216135\pi$
$48$		0			0
$49$			13978.8i			0.831728i
$50$		0			0
$51$	−24090.0			−1.29691
$52$		0			0
$53$	−4390.22	−	4390.22i	−0.214683	−	0.214683i	0.591571	−	0.806253i	$-0.298508\pi$
$53$	−4390.22	−	4390.22i	−0.214683	−	0.214683i	−0.806253	+	0.591571i	$0.798508\pi$
$54$		0			0
$55$	1462.26	−	11995.0i	0.0651807	−	0.534679i
$56$		0			0
$57$	32891.0	+	32891.0i	1.34088	+	1.34088i
$58$		0			0
$59$			2415.05i			0.0903225i	0.998980	+	0.0451612i	$0.0143802\pi$
$59$			2415.05i			0.0903225i	−0.998980	+	0.0451612i	$0.985620\pi$
$60$		0			0
$61$			49477.1i			1.70247i	0.524785	+	0.851235i	$0.324146\pi$
$61$			49477.1i			1.70247i	−0.524785	+	0.851235i	$0.675854\pi$
$62$		0			0
$63$	21658.7	+	21658.7i	0.687513	+	0.687513i
$64$		0			0
$65$	46637.3	−	36502.1i	1.36915	−	1.07160i
$66$		0			0
$67$	8120.59	+	8120.59i	0.221004	+	0.221004i	0.808921	−	0.587917i	$-0.200052\pi$
$67$	8120.59	+	8120.59i	0.221004	+	0.221004i	−0.587917	+	0.808921i	$0.700052\pi$
$68$		0			0
$69$	46019.8			1.16365
$70$		0			0
$71$			23377.1i			0.550358i	0.961393	+	0.275179i	$0.0887371\pi$
$71$			23377.1i			0.550358i	−0.961393	+	0.275179i	$0.911263\pi$
$72$		0			0
$73$	−6337.57	+	6337.57i	−0.139192	+	0.139192i	−0.773270	−	0.634077i	$-0.781380\pi$
$73$	−6337.57	+	6337.57i	−0.139192	+	0.139192i	0.634077	+	0.773270i	$0.281380\pi$
$74$		0			0
$75$	76576.6	−	46192.4i	1.57196	−	0.948238i
$76$		0			0
$77$	−8128.57	+	8128.57i	−0.156238	+	0.156238i
$78$		0			0
$79$	−28845.4			−0.520006			−0.260003	−	0.965608i	$-0.583724\pi$
$79$	−28845.4			−0.520006			−0.260003	+	0.965608i	$0.583724\pi$
$80$		0			0
$81$	−132727.			−2.24775
$82$		0			0
$83$	−39161.8	+	39161.8i	−0.623976	+	0.623976i	−0.946546	−	0.322570i	$-0.895453\pi$
$83$	−39161.8	+	39161.8i	−0.623976	+	0.623976i	0.322570	+	0.946546i	$0.395453\pi$
$84$		0			0
$85$	37056.7	−	29003.6i	0.556314	−	0.435416i
$86$		0			0
$87$	50803.0	−	50803.0i	0.719600	−	0.719600i
$88$		0			0
$89$		−	79616.6i		−	1.06544i	−0.846292	−	0.532719i	$-0.821170\pi$
$89$		−	79616.6i		−	1.06544i	0.846292	−	0.532719i	$-0.178830\pi$
$90$		0			0
$91$	−56340.6			−0.713210
$92$		0			0
$93$	−86578.3	−	86578.3i	−1.03801	−	1.03801i
$94$		0			0
$95$	−90194.8	−	10995.3i	−1.02535	−	0.124997i
$96$		0			0
$97$	85618.4	+	85618.4i	0.923928	+	0.923928i	0.997304	−	0.0733766i	$-0.0233775\pi$
$97$	85618.4	+	85618.4i	0.923928	+	0.923928i	−0.0733766	+	0.997304i	$0.523378\pi$
$98$		0			0
$99$		−	124501.i		−	1.27669i
$100$		0			0
$101$			107653.i			1.05008i	0.851078	+	0.525040i	$0.175950\pi$
$101$			107653.i			1.05008i	−0.851078	+	0.525040i	$0.824050\pi$
$102$		0			0
$103$	106389.	+	106389.i	0.988103	+	0.988103i	0.999930	−	0.0118275i	$-0.00376488\pi$
$103$	106389.	+	106389.i	0.988103	+	0.988103i	−0.0118275	+	0.999930i	$0.503765\pi$
$104$		0			0
$105$	−84451.2	−	10295.1i	−0.747537	−	0.0911294i
$106$		0			0
$107$	125310.	+	125310.i	1.05810	+	1.05810i	0.998205	+	0.0598911i	$0.0190753\pi$
$107$	125310.	+	125310.i	1.05810	+	1.05810i	0.0598911	+	0.998205i	$0.480925\pi$
$108$		0			0
$109$	−118547.			−0.955703			−0.477851	−	0.878441i	$-0.658584\pi$
$109$	−118547.			−0.955703			−0.477851	+	0.878441i	$0.658584\pi$
$110$		0			0
$111$		−	143667.i		−	1.10675i
$112$		0			0
$113$	30437.7	−	30437.7i	0.224241	−	0.224241i	−0.586040	−	0.810282i	$-0.699314\pi$
$113$	30437.7	−	30437.7i	0.224241	−	0.224241i	0.810282	+	0.586040i	$0.199314\pi$
$114$		0			0
$115$	−70790.6	+	55406.4i	−0.499150	+	0.390675i
$116$		0			0
$117$	431470.	−	431470.i	2.91398	−	2.91398i
$118$		0			0
$119$	−44766.7			−0.289793
$120$		0			0
$121$	−114325.			−0.709870
$122$		0			0
$123$	−85096.3	+	85096.3i	−0.507164	+	0.507164i
$124$		0			0
$125$	−62180.7	+	163252.i	−0.355943	+	0.934508i
$126$		0			0
$127$	−86885.2	+	86885.2i	−0.478010	+	0.478010i	−0.904495	−	0.426485i	$-0.859752\pi$
$127$	−86885.2	+	86885.2i	−0.478010	+	0.478010i	0.426485	+	0.904495i	$0.359752\pi$
$128$		0			0
$129$		−	226466.i		−	1.19820i
$130$		0			0
$131$	98703.6			0.502522			0.251261	−	0.967919i	$-0.419155\pi$
$131$	98703.6			0.502522			0.251261	+	0.967919i	$0.419155\pi$
$132$		0			0
$133$	61121.8	+	61121.8i	0.299617	+	0.299617i
$134$		0			0
$135$	419464.	−	328306.i	1.98089	−	1.55040i
$136$		0			0
$137$	−42728.3	−	42728.3i	−0.194498	−	0.194498i	0.603139	−	0.797636i	$-0.293917\pi$
$137$	−42728.3	−	42728.3i	−0.194498	−	0.194498i	−0.797636	+	0.603139i	$0.793917\pi$
$138$		0			0
$139$		−	324652.i		−	1.42522i	−0.701563	−	0.712608i	$-0.747514\pi$
$139$		−	324652.i		−	1.42522i	0.701563	−	0.712608i	$-0.252486\pi$
$140$		0			0
$141$			92043.0i			0.389891i
$142$		0			0
$143$	161932.	+	161932.i	0.662205	+	0.662205i
$144$		0			0
$145$	−16983.2	+	139313.i	−0.0670810	+	0.550267i
$146$		0			0
$147$	−282871.	−	282871.i	−1.07968	−	1.07968i
$148$		0			0
$149$	380526.			1.40417			0.702084	−	0.712094i	$-0.252253\pi$
$149$	380526.			1.40417			0.702084	+	0.712094i	$0.252253\pi$
$150$		0			0
$151$			239937.i			0.856358i	0.903694	+	0.428179i	$0.140845\pi$
$151$			239937.i			0.856358i	−0.903694	+	0.428179i	$0.859155\pi$
$152$		0			0
$153$	342835.	−	342835.i	1.18401	−	1.18401i
$154$		0			0
$155$	237418.	+	28942.7i	0.793750	+	0.0967632i
$156$		0			0
$157$	−351633.	+	351633.i	−1.13852	+	1.13852i	−0.149803	+	0.988716i	$0.547864\pi$
$157$	−351633.	+	351633.i	−1.13852	+	1.13852i	−0.988716	+	0.149803i	$0.952136\pi$
$158$		0			0
$159$	177678.			0.557367
$160$		0			0
$161$	85519.2			0.260015
$162$		0			0
$163$	446785.	−	446785.i	1.31713	−	1.31713i	0.401096	−	0.916036i	$-0.368629\pi$
$163$	446785.	−	446785.i	1.31713	−	1.31713i	0.916036	−	0.401096i	$-0.131371\pi$
$164$		0			0
$165$	213137.	+	272316.i	0.609464	+	0.778689i
$166$		0			0
$167$	−41932.4	+	41932.4i	−0.116348	+	0.116348i	−0.762884	−	0.646536i	$-0.776217\pi$
$167$	−41932.4	+	41932.4i	−0.116348	+	0.116348i	0.646536	+	0.762884i	$0.276217\pi$
$168$		0			0
$169$			751086.i			2.02289i
$170$		0			0
$171$	−936173.			−2.44831
$172$		0			0
$173$	−259889.	−	259889.i	−0.660197	−	0.660197i	0.295229	−	0.955426i	$-0.404604\pi$
$173$	−259889.	−	259889.i	−0.660197	−	0.660197i	−0.955426	+	0.295229i	$0.904604\pi$
$174$		0			0
$175$	142303.	−	85839.9i	0.351252	−	0.211882i
$176$		0			0
$177$	−48870.1	−	48870.1i	−0.117249	−	0.117249i
$178$		0			0
$179$			502124.i			1.17133i	0.810554	+	0.585664i	$0.199166\pi$
$179$			502124.i			1.17133i	−0.810554	+	0.585664i	$0.800834\pi$
$180$		0			0
$181$		−	598511.i		−	1.35792i	−0.734173	−	0.678962i	$-0.762430\pi$
$181$		−	598511.i		−	1.35792i	0.734173	−	0.678962i	$-0.237570\pi$
$182$		0			0
$183$	−1.00120e6	−	1.00120e6i	−2.21001	−	2.21001i
$184$		0			0
$185$	172970.	+	220998.i	0.371572	+	0.474743i
$186$		0			0
$187$	128667.	+	128667.i	0.269068	+	0.269068i
$188$		0			0
$189$	−506737.			−1.03188
$190$		0			0
$191$			631806.i			1.25314i	0.779364	+	0.626571i	$0.215542\pi$
$191$			631806.i			1.25314i	−0.779364	+	0.626571i	$0.784458\pi$
$192$		0			0
$193$	150856.	−	150856.i	0.291520	−	0.291520i	−0.546160	−	0.837681i	$-0.683911\pi$
$193$	150856.	−	150856.i	0.291520	−	0.291520i	0.837681	+	0.546160i	$0.183911\pi$
$194$		0			0
$195$	−205093.	+	1.68238e6i	−0.386246	+	3.16838i
$196$		0			0
$197$	−533876.	+	533876.i	−0.980111	+	0.980111i	−0.999806	−	0.0196952i	$-0.993730\pi$
$197$	−533876.	+	533876.i	−0.980111	+	0.980111i	0.0196952	+	0.999806i	$0.493730\pi$
$198$		0			0
$199$	−655627.			−1.17361			−0.586806	−	0.809728i	$-0.699615\pi$
$199$	−655627.			−1.17361			−0.586806	+	0.809728i	$0.699615\pi$
$200$		0			0
$201$	−328651.			−0.573779
$202$		0			0
$203$	94407.8	−	94407.8i	0.160793	−	0.160793i
$204$		0			0
$205$	28447.3	−	233354.i	0.0472777	−	0.387820i
$206$		0			0
$207$	−654928.	+	654928.i	−1.06235	+	1.06235i
$208$		0			0
$209$		−	351348.i		−	0.556380i
$210$		0			0
$211$	1.19605e6			1.84945			0.924723	−	0.380640i	$-0.124296\pi$
$211$	1.19605e6			1.84945			0.924723	+	0.380640i	$0.124296\pi$
$212$		0			0
$213$	−473052.	−	473052.i	−0.714430	−	0.714430i
$214$		0			0
$215$	272658.	+	348364.i	0.402274	+	0.513969i
$216$		0			0
$217$	−160890.	−	160890.i	−0.231941	−	0.231941i
$218$		0			0
$219$		−	256490.i		−	0.361377i
$220$		0			0
$221$			891813.i			1.22827i
$222$		0			0
$223$	234103.	+	234103.i	0.315242	+	0.315242i	0.846936	−	0.531694i	$-0.178444\pi$
$223$	234103.	+	234103.i	0.315242	+	0.315242i	−0.531694	+	0.846936i	$0.678444\pi$
$224$		0			0
$225$	−432410.	+	1.74718e6i	−0.569429	+	2.30081i
$226$		0			0
$227$	−366296.	−	366296.i	−0.471810	−	0.471810i	0.430690	−	0.902500i	$-0.358270\pi$
$227$	−366296.	−	366296.i	−0.471810	−	0.471810i	−0.902500	+	0.430690i	$0.858270\pi$
$228$		0			0
$229$	−630028.			−0.793910			−0.396955	−	0.917838i	$-0.629933\pi$
$229$	−630028.			−0.793910			−0.396955	+	0.917838i	$0.629933\pi$
$230$		0			0
$231$		−	328974.i		−	0.405632i
$232$		0			0
$233$	93978.0	−	93978.0i	0.113406	−	0.113406i	−0.648127	−	0.761533i	$-0.724447\pi$
$233$	93978.0	−	93978.0i	0.113406	−	0.113406i	0.761533	+	0.648127i	$0.224447\pi$
$234$		0			0
$235$	−110817.	−	141586.i	−0.130899	−	0.167245i
$236$		0			0
$237$	583706.	−	583706.i	0.675030	−	0.675030i
$238$		0			0
$239$	−1.10101e6			−1.24680			−0.623401	−	0.781902i	$-0.714249\pi$
$239$	−1.10101e6			−1.24680			−0.623401	+	0.781902i	$0.714249\pi$
$240$		0			0
$241$	−505381.			−0.560501			−0.280251	−	0.959927i	$-0.590418\pi$
$241$	−505381.			−0.560501			−0.280251	+	0.959927i	$0.590418\pi$
$242$		0			0
$243$	1.04855e6	−	1.04855e6i	1.13913	−	1.13913i
$244$		0			0
$245$	775699.	+	94562.6i	0.825616	+	0.100648i
$246$		0			0
$247$	1.21763e6	−	1.21763e6i	1.26991	−	1.26991i
$248$		0			0
$249$		−	1.58493e6i		−	1.61999i
$250$		0			0
$251$	−274571.			−0.275087			−0.137543	−	0.990496i	$-0.543921\pi$
$251$	−274571.			−0.275087			−0.137543	+	0.990496i	$0.543921\pi$
$252$		0			0
$253$	−245796.	−	245796.i	−0.241420	−	0.241420i
$254$		0			0
$255$	−162961.	+	1.33677e6i	−0.156940	+	1.28738i
$256$		0			0
$257$	8431.75	+	8431.75i	0.00796315	+	0.00796315i	0.711077	−	0.703114i	$-0.248208\pi$
$257$	8431.75	+	8431.75i	0.00796315	+	0.00796315i	−0.703114	+	0.711077i	$0.748208\pi$
$258$		0			0
$259$		−	266978.i		−	0.247301i
$260$		0			0
$261$			1.44600e6i			1.31391i
$262$		0			0
$263$	699032.	+	699032.i	0.623171	+	0.623171i	0.946341	−	0.323170i	$-0.104748\pi$
$263$	699032.	+	699032.i	0.623171	+	0.623171i	−0.323170	+	0.946341i	$0.604748\pi$
$264$		0			0
$265$	−273316.	+	213919.i	−0.239084	+	0.187126i
$266$		0			0
$267$	1.61110e6	+	1.61110e6i	1.38307	+	1.38307i
$268$		0			0
$269$	1.31287e6			1.10622			0.553111	−	0.833107i	$-0.313440\pi$
$269$	1.31287e6			1.10622			0.553111	+	0.833107i	$0.313440\pi$
$270$		0			0
$271$		−	238446.i		−	0.197227i	−0.995126	−	0.0986137i	$-0.968559\pi$
$271$		−	238446.i		−	0.197227i	0.995126	−	0.0986137i	$-0.0314408\pi$
$272$		0			0
$273$	1.14009e6	−	1.14009e6i	0.925832	−	0.925832i
$274$		0			0
$275$	−655720.	−	162285.i	−0.522862	−	0.129403i
$276$		0			0
$277$	−371505.	+	371505.i	−0.290915	+	0.290915i	−0.837442	−	0.546527i	$-0.815950\pi$
$277$	−371505.	+	371505.i	−0.290915	+	0.290915i	0.546527	+	0.837442i	$0.315950\pi$
$278$		0			0
$279$	2.46427e6			1.89530
$280$		0			0
$281$	732527.			0.553424			0.276712	−	0.960953i	$-0.410755\pi$
$281$	732527.			0.553424			0.276712	+	0.960953i	$0.410755\pi$
$282$		0			0
$283$	−894094.	+	894094.i	−0.663616	+	0.663616i	−0.956231	−	0.292614i	$-0.905475\pi$
$283$	−894094.	+	894094.i	−0.663616	+	0.663616i	0.292614	+	0.956231i	$0.405475\pi$
$284$		0			0
$285$	2.04765e6	−	1.60266e6i	1.49329	−	1.16877i
$286$		0			0
$287$	−158136.	+	158136.i	−0.113325	+	0.113325i
$288$		0			0
$289$		−	711247.i		−	0.500928i
$290$		0			0
$291$	−3.46509e6			−2.39874
$292$		0			0
$293$	537669.	+	537669.i	0.365886	+	0.365886i	0.865974	−	0.500088i	$-0.166699\pi$
$293$	537669.	+	537669.i	0.365886	+	0.365886i	−0.500088	+	0.865974i	$0.666699\pi$
$294$		0			0
$295$	134013.	+	16337.1i	0.0896587	+	0.0109300i
$296$		0			0
$297$	1.45645e6	+	1.45645e6i	0.958083	+	0.958083i
$298$		0			0
$299$		−	1.70366e6i		−	1.10206i
$300$		0			0
$301$		−	420844.i		−	0.267735i
$302$		0			0
$303$	−2.17843e6	−	2.17843e6i	−1.36313	−	1.36313i
$304$		0			0
$305$	2.74553e6	+	334697.i	1.68996	+	0.206017i
$306$		0			0
$307$	−1.17244e6	−	1.17244e6i	−0.709978	−	0.709978i	0.256552	−	0.966530i	$-0.417413\pi$
$307$	−1.17244e6	−	1.17244e6i	−0.709978	−	0.709978i	−0.966530	+	0.256552i	$0.917413\pi$
$308$		0			0
$309$	−4.30569e6			−2.56535
$310$		0			0
$311$		−	1.77536e6i		−	1.04085i	−0.853909	−	0.520423i	$-0.825774\pi$
$311$		−	1.77536e6i		−	1.04085i	0.853909	−	0.520423i	$-0.174226\pi$
$312$		0			0
$313$	−1.58502e6	+	1.58502e6i	−0.914478	+	0.914478i	−0.996621	−	0.0821427i	$-0.973824\pi$
$313$	−1.58502e6	+	1.58502e6i	−0.914478	+	0.914478i	0.0821427	+	0.996621i	$0.473824\pi$
$314$		0			0
$315$	1.34838e6	−	1.05535e6i	0.765657	−	0.599265i
$316$		0			0
$317$	357408.	−	357408.i	0.199764	−	0.199764i	−0.600135	−	0.799899i	$-0.704887\pi$
$317$	357408.	−	357408.i	0.199764	−	0.199764i	0.799899	+	0.600135i	$0.204887\pi$
$318$		0			0
$319$	−542687.			−0.298588
$320$		0			0
$321$	−5.07145e6			−2.74707
$322$		0			0
$323$	967494.	−	967494.i	0.515991	−	0.515991i
$324$		0			0
$325$	−1.71005e6	−	2.83487e6i	−0.898047	−	1.48876i
$326$		0			0
$327$	2.39887e6	−	2.39887e6i	1.24062	−	1.24062i
$328$		0			0
$329$			171045.i			0.0871204i
$330$		0			0
$331$	−2.66692e6			−1.33795			−0.668976	−	0.743284i	$-0.733267\pi$
$331$	−2.66692e6			−1.33795			−0.668976	+	0.743284i	$0.733267\pi$
$332$		0			0
$333$	2.04459e6	+	2.04459e6i	1.01040	+	1.01040i
$334$		0			0
$335$	505552.	−	395685.i	0.246124	−	0.192636i
$336$		0			0
$337$	−96732.1	−	96732.1i	−0.0463976	−	0.0463976i	0.683527	−	0.729925i	$-0.260445\pi$
$337$	−96732.1	−	96732.1i	−0.0463976	−	0.0463976i	−0.729925	+	0.683527i	$0.760445\pi$
$338$		0			0
$339$			1.23186e6i			0.582184i
$340$		0			0
$341$			924846.i			0.430708i
$342$		0			0
$343$	−1.15768e6	−	1.15768e6i	−0.531315	−	0.531315i
$344$		0			0
$345$	311310.	−	2.55368e6i	0.140814	−	1.15510i
$346$		0			0
$347$	1.79535e6	+	1.79535e6i	0.800433	+	0.800433i	0.983163	−	0.182730i	$-0.0584935\pi$
$347$	1.79535e6	+	1.79535e6i	0.800433	+	0.800433i	−0.182730	+	0.983163i	$0.558493\pi$
$348$		0			0
$349$	3.53895e6			1.55529			0.777645	−	0.628704i	$-0.216414\pi$
$349$	3.53895e6			1.55529			0.777645	+	0.628704i	$0.216414\pi$
$350$		0			0
$351$			1.00949e7i			4.37354i
$352$		0			0
$353$	824286.	−	824286.i	0.352080	−	0.352080i	−0.508803	−	0.860883i	$-0.669912\pi$
$353$	824286.	−	824286.i	0.352080	−	0.352080i	0.860883	+	0.508803i	$0.169912\pi$
$354$		0			0
$355$	1.29722e6	+	158139.i	0.546314	+	0.0665991i
$356$		0			0
$357$	905884.	−	905884.i	0.376186	−	0.376186i
$358$		0			0
$359$	919001.			0.376340			0.188170	−	0.982137i	$-0.439744\pi$
$359$	919001.			0.376340			0.188170	+	0.982137i	$0.439744\pi$
$360$		0			0
$361$	−165820.			−0.0669684
$362$		0			0
$363$	2.31345e6	−	2.31345e6i	0.921496	−	0.921496i
$364$		0			0
$365$	308806.	+	394549.i	0.121326	+	0.155013i
$366$		0			0
$367$	1.76897e6	−	1.76897e6i	0.685576	−	0.685576i	−0.275675	−	0.961251i	$-0.588901\pi$
$367$	1.76897e6	−	1.76897e6i	0.685576	−	0.685576i	0.961251	+	0.275675i	$0.0889014\pi$
$368$		0			0
$369$		−	2.42208e6i		−	0.926027i
$370$		0			0
$371$	330182.			0.124543
$372$		0			0
$373$	942636.	+	942636.i	0.350810	+	0.350810i	0.860411	−	0.509601i	$-0.170207\pi$
$373$	942636.	+	942636.i	0.350810	+	0.350810i	−0.509601	+	0.860411i	$0.670207\pi$
$374$		0			0
$375$	−2.04524e6	−	4.56178e6i	−0.751046	−	1.67516i
$376$		0			0
$377$	−1.88073e6	−	1.88073e6i	−0.681511	−	0.681511i
$378$		0			0
$379$		−	1.50545e6i		−	0.538356i	−0.963090	−	0.269178i	$-0.913248\pi$
$379$		−	1.50545e6i		−	0.538356i	0.963090	−	0.269178i	$-0.0867519\pi$
$380$		0			0
$381$		−	3.51636e6i		−	1.24103i
$382$		0			0
$383$	3.70372e6	+	3.70372e6i	1.29015	+	1.29015i	0.934691	+	0.355461i	$0.115676\pi$
$383$	3.70372e6	+	3.70372e6i	1.29015	+	1.29015i	0.355461	+	0.934691i	$0.384324\pi$
$384$		0			0
$385$	396074.	+	506049.i	0.136184	+	0.173997i
$386$		0			0
$387$	3.22293e6	+	3.22293e6i	1.09389	+	1.09389i
$388$		0			0
$389$	74329.1			0.0249049			0.0124525	−	0.999922i	$-0.496036\pi$
$389$	74329.1			0.0249049			0.0124525	+	0.999922i	$0.496036\pi$
$390$		0			0
$391$		−	1.35368e6i		−	0.447790i
$392$		0			0
$393$	−1.99733e6	+	1.99733e6i	−0.652333	+	0.652333i
$394$		0			0
$395$	−195130.	+	1.60066e6i	−0.0629262	+	0.516185i
$396$		0			0
$397$	1.96596e6	−	1.96596e6i	0.626034	−	0.626034i	−0.321034	−	0.947068i	$-0.604030\pi$
$397$	1.96596e6	−	1.96596e6i	0.626034	−	0.626034i	0.947068	+	0.321034i	$0.104030\pi$
$398$		0			0
$399$	−2.47368e6			−0.777878
$400$		0			0
$401$	33988.7			0.0105554			0.00527769	−	0.999986i	$-0.498320\pi$
$401$	33988.7			0.0105554			0.00527769	+	0.999986i	$0.498320\pi$
$402$		0			0
$403$	−3.20514e6	+	3.20514e6i	−0.983068	+	0.983068i
$404$		0			0
$405$	−897859.	+	7.36516e6i	−0.272001	+	2.23123i
$406$		0			0
$407$	−767339.	+	767339.i	−0.229615	+	0.229615i
$408$		0			0
$409$			62227.0i			0.0183938i	0.999958	+	0.00919689i	$0.00292750\pi$
$409$			62227.0i			0.0183938i	−0.999958	+	0.00919689i	$0.997072\pi$
$410$		0			0
$411$	1.72927e6			0.504962
$412$		0			0
$413$	−90816.0	−	90816.0i	−0.0261991	−	0.0261991i
$414$		0			0
$415$	1.90821e6	+	2.43804e6i	0.543883	+	0.694898i
$416$		0			0
$417$	6.56954e6	+	6.56954e6i	1.85010	+	1.85010i
$418$		0			0
$419$		−	4.72650e6i		−	1.31524i	−0.753351	−	0.657619i	$-0.771564\pi$
$419$		−	4.72650e6i		−	1.31524i	0.753351	−	0.657619i	$-0.228436\pi$
$420$		0			0
$421$		−	1.56815e6i		−	0.431203i	−0.976481	−	0.215601i	$-0.930829\pi$
$421$		−	1.56815e6i		−	0.431203i	0.976481	−	0.215601i	$-0.0691712\pi$
$422$		0			0
$423$	−1.30990e6	−	1.30990e6i	−0.355950	−	0.355950i
$424$		0			0
$425$	−1.35876e6	−	2.25251e6i	−0.364896	−	0.604915i
$426$		0			0
$427$	−1.86054e6	−	1.86054e6i	−0.493822	−	0.493822i
$428$		0			0
$429$	−6.55361e6			−1.71924
$430$		0			0
$431$		−	61939.2i		−	0.0160610i	−0.999968	−	0.00803050i	$-0.997444\pi$
$431$		−	61939.2i		−	0.0160610i	0.999968	−	0.00803050i	$-0.00255622\pi$
$432$		0			0
$433$	−970583.	+	970583.i	−0.248779	+	0.248779i	−0.820469	−	0.571691i	$-0.806288\pi$
$433$	−970583.	+	970583.i	−0.248779	+	0.248779i	0.571691	+	0.820469i	$0.306288\pi$
$434$		0			0
$435$	−2.47544e6	−	3.16277e6i	−0.627233	−	0.801391i
$436$		0			0
$437$	−1.84823e6	+	1.84823e6i	−0.462971	+	0.462971i
$438$		0			0
$439$	−2.03528e6			−0.504037			−0.252019	−	0.967722i	$-0.581094\pi$
$439$	−2.03528e6			−0.504037			−0.252019	+	0.967722i	$0.581094\pi$
$440$		0			0
$441$	8.05133e6			1.97138
$442$		0			0
$443$	−2.21815e6	+	2.21815e6i	−0.537009	+	0.537009i	−0.922649	−	0.385640i	$-0.873981\pi$
$443$	−2.21815e6	+	2.21815e6i	−0.537009	+	0.537009i	0.385640	+	0.922649i	$0.373981\pi$
$444$		0			0
$445$	−4.41800e6	−	538581.i	−1.05761	−	0.128929i
$446$		0			0
$447$	−7.70021e6	+	7.70021e6i	−1.82278	+	1.82278i
$448$		0			0
$449$		−	1.71409e6i		−	0.401252i	−0.979668	−	0.200626i	$-0.935702\pi$
$449$		−	1.71409e6i		−	0.401252i	0.979668	−	0.200626i	$-0.0642977\pi$
$450$		0			0
$451$	909015.			0.210441
$452$		0			0
$453$	−4.85529e6	−	4.85529e6i	−1.11165	−	1.11165i
$454$		0			0
$455$	−381126.	+	3.12639e6i	−0.0863059	+	0.707969i
$456$		0			0
$457$	−3.18338e6	−	3.18338e6i	−0.713014	−	0.713014i	0.254151	−	0.967165i	$-0.418204\pi$
$457$	−3.18338e6	−	3.18338e6i	−0.713014	−	0.713014i	−0.967165	+	0.254151i	$0.918204\pi$
$458$		0			0
$459$			8.02112e6i			1.77707i
$460$		0			0
$461$			7.10532e6i			1.55715i	0.627550	+	0.778576i	$0.284058\pi$
$461$			7.10532e6i			1.55715i	−0.627550	+	0.778576i	$0.715942\pi$
$462$		0			0
$463$	−5.60927e6	−	5.60927e6i	−1.21606	−	1.21606i	−0.969001	−	0.247057i	$-0.920537\pi$
$463$	−5.60927e6	−	5.60927e6i	−1.21606	−	1.21606i	−0.247057	−	0.969001i	$-0.579463\pi$
$464$		0			0
$465$	−5.38998e6	+	4.21863e6i	−1.15599	+	0.904772i
$466$		0			0
$467$	2.69763e6	+	2.69763e6i	0.572387	+	0.572387i	0.932795	−	0.360408i	$-0.117363\pi$
$467$	2.69763e6	+	2.69763e6i	0.572387	+	0.572387i	−0.360408	+	0.932795i	$0.617363\pi$
$468$		0			0
$469$	−610736.			−0.128210
$470$		0			0
$471$		−	1.42311e7i		−	2.95587i
$472$		0			0
$473$	−1.20958e6	+	1.20958e6i	−0.248588	+	0.248588i
$474$		0			0
$475$	−1.22028e6	+	4.93061e6i	−0.248156	+	1.00269i
$476$		0			0
$477$	−2.52861e6	+	2.52861e6i	−0.508846	+	0.508846i
$478$		0			0
$479$	574945.			0.114495			0.0572477	−	0.998360i	$-0.481768\pi$
$479$	574945.			0.114495			0.0572477	+	0.998360i	$0.481768\pi$
$480$		0			0
$481$	−5.31856e6			−1.04817
$482$		0			0
$483$	−1.73054e6	+	1.73054e6i	−0.337531	+	0.337531i
$484$		0			0
$485$	5.33023e6	−	4.17186e6i	1.02894	−	0.805333i
$486$		0			0
$487$	−992613.	+	992613.i	−0.189652	+	0.189652i	−0.795546	−	0.605894i	$-0.792816\pi$
$487$	−992613.	+	992613.i	−0.189652	+	0.189652i	0.605894	+	0.795546i	$0.292816\pi$
$488$		0			0
$489$			1.80820e7i			3.41959i
$490$		0			0
$491$	8.60252e6			1.61036			0.805178	−	0.593033i	$-0.202070\pi$
$491$	8.60252e6			1.61036			0.805178	+	0.593033i	$0.202070\pi$
$492$		0			0
$493$	−1.49438e6	−	1.49438e6i	−0.276913	−	0.276913i
$494$		0			0
$495$	−6.90869e6	−	842213.i	−1.26731	−	0.154493i
$496$		0			0
$497$	−879078.	−	879078.i	−0.159638	−	0.159638i
$498$		0			0
$499$			2.71053e6i			0.487308i	0.969862	+	0.243654i	$0.0783461\pi$
$499$			2.71053e6i			0.487308i	−0.969862	+	0.243654i	$0.921654\pi$
$500$		0			0
$501$		−	1.69706e6i		−	0.302067i
$502$		0			0
$503$	6.45342e6	+	6.45342e6i	1.13729	+	1.13729i	0.988935	+	0.148351i	$0.0473966\pi$
$503$	6.45342e6	+	6.45342e6i	1.13729	+	1.13729i	0.148351	+	0.988935i	$0.452603\pi$
$504$		0			0
$505$	5.97375e6	+	728238.i	1.04236	+	0.127071i
$506$		0			0
$507$	−1.51987e7	−	1.51987e7i	−2.62596	−	2.62596i
$508$		0			0
$509$	−69830.0			−0.0119467			−0.00597334	−	0.999982i	$-0.501901\pi$
$509$	−69830.0			−0.0119467			−0.00597334	+	0.999982i	$0.501901\pi$
$510$		0			0
$511$		−	476639.i		−	0.0807490i
$512$		0			0
$513$	1.09516e7	−	1.09516e7i	1.83731	−	1.83731i
$514$		0			0
$515$	6.62328e6	−	5.18391e6i	1.10041	−	0.861271i
$516$		0			0
$517$	491610.	−	491610.i	0.0808900	−	0.0808900i
$518$		0			0
$519$	1.05181e7			1.71403
$520$		0			0
$521$	1.06115e7			1.71271			0.856354	−	0.516389i	$-0.172724\pi$
$521$	1.06115e7			1.71271			0.856354	+	0.516389i	$0.172724\pi$
$522$		0			0
$523$	942699.	−	942699.i	0.150702	−	0.150702i	−0.627730	−	0.778431i	$-0.716016\pi$
$523$	942699.	−	942699.i	0.150702	−	0.150702i	0.778431	+	0.627730i	$0.216016\pi$
$524$		0			0
$525$	−1.14257e6	+	4.61663e6i	−0.180919	+	0.731016i
$526$		0			0
$527$	−2.54671e6	+	2.54671e6i	−0.399442	+	0.399442i
$528$		0			0
$529$		−	3.85037e6i		−	0.598223i
$530$		0			0
$531$	1.39098e6			0.214085
$532$		0			0
$533$	3.15027e6	+	3.15027e6i	0.480319	+	0.480319i
$534$		0			0
$535$	7.80122e6	−	6.10586e6i	1.17836	−	0.922280i
$536$		0			0
$537$	−1.01608e7	−	1.01608e7i	−1.52052	−	1.52052i
$538$		0			0
$539$			3.02169e6i			0.447999i
$540$		0			0
$541$			1.27997e6i			0.188021i	0.995571	+	0.0940106i	$0.0299687\pi$
$541$			1.27997e6i			0.188021i	−0.995571	+	0.0940106i	$0.970031\pi$
$542$		0			0
$543$	1.21113e7	+	1.21113e7i	1.76275	+	1.76275i
$544$		0			0
$545$	−801931.	+	6.57826e6i	−0.115650	+	0.948679i
$546$		0			0
$547$	−449946.	−	449946.i	−0.0642972	−	0.0642972i	0.674227	−	0.738524i	$-0.264477\pi$
$547$	−449946.	−	449946.i	−0.0642972	−	0.0642972i	−0.738524	+	0.674227i	$0.764477\pi$
$548$		0			0
$549$	2.84971e7			4.03524
$550$		0			0
$551$			4.08067e6i			0.572601i
$552$		0			0
$553$	1.08471e6	−	1.08471e6i	0.150834	−	0.150834i
$554$		0			0
$555$	−7.97221e6	−	971862.i	−1.09862	−	0.133928i
$556$		0			0
$557$	−5.75258e6	+	5.75258e6i	−0.785643	+	0.785643i	−0.980777	−	0.195134i	$-0.937486\pi$
$557$	−5.75258e6	+	5.75258e6i	−0.785643	+	0.785643i	0.195134	+	0.980777i	$0.437486\pi$
$558$		0			0
$559$	−8.38378e6			−1.13478
$560$		0			0
$561$	−5.20732e6			−0.698565
$562$		0			0
$563$	2.82733e6	−	2.82733e6i	0.375929	−	0.375929i	−0.493702	−	0.869631i	$-0.664357\pi$
$563$	2.82733e6	−	2.82733e6i	0.375929	−	0.375929i	0.869631	+	0.493702i	$0.164357\pi$
$564$		0			0
$565$	−1.48311e6	−	1.89492e6i	−0.195458	−	0.249729i
$566$		0			0
$567$	4.99110e6	−	4.99110e6i	0.651987	−	0.651987i
$568$		0			0
$569$		−	1.28127e6i		−	0.165905i	−0.996553	−	0.0829527i	$-0.973565\pi$
$569$		−	1.28127e6i		−	0.165905i	0.996553	−	0.0829527i	$-0.0264351\pi$
$570$		0			0
$571$	1.04567e7			1.34216			0.671078	−	0.741387i	$-0.265832\pi$
$571$	1.04567e7			1.34216			0.671078	+	0.741387i	$0.265832\pi$
$572$		0			0
$573$	−1.27850e7	−	1.27850e7i	−1.62673	−	1.62673i
$574$		0			0
$575$	2.59567e6	+	4.30304e6i	0.327401	+	0.542758i
$576$		0			0
$577$	−4.92804e6	−	4.92804e6i	−0.616219	−	0.616219i	0.328341	−	0.944559i	$-0.393511\pi$
$577$	−4.92804e6	−	4.92804e6i	−0.616219	−	0.616219i	−0.944559	+	0.328341i	$0.893511\pi$
$578$		0			0
$579$			6.10534e6i			0.756856i
$580$		0			0
$581$		−	2.94530e6i		−	0.361984i
$582$		0			0
$583$	−948996.	−	948996.i	−0.115636	−	0.115636i
$584$		0			0
$585$	−2.10239e7	−	2.68614e7i	−2.53994	−	3.24519i
$586$		0			0
$587$	−5.93935e6	−	5.93935e6i	−0.711448	−	0.711448i	0.255390	−	0.966838i	$-0.417796\pi$
$587$	−5.93935e6	−	5.93935e6i	−0.711448	−	0.711448i	−0.966838	+	0.255390i	$0.917796\pi$
$588$		0			0
$589$	6.95427e6			0.825968
$590$		0			0
$591$		−	2.16067e7i		−	2.54460i
$592$		0			0
$593$	−3.52475e6	+	3.52475e6i	−0.411615	+	0.411615i	−0.882301	−	0.470686i	$-0.844007\pi$
$593$	−3.52475e6	+	3.52475e6i	−0.411615	+	0.411615i	0.470686	+	0.882301i	$0.344007\pi$
$594$		0			0
$595$	−302833.	+	2.48414e6i	−0.0350680	+	0.287663i
$596$		0			0
$597$	1.32671e7	−	1.32671e7i	1.52349	−	1.52349i
$598$		0			0
$599$	−9.42763e6			−1.07358			−0.536792	−	0.843715i	$-0.680364\pi$
$599$	−9.42763e6			−1.07358			−0.536792	+	0.843715i	$0.680364\pi$
$600$		0			0
$601$	1.52233e7			1.71918			0.859590	−	0.510984i	$-0.170719\pi$
$601$	1.52233e7			1.71918			0.859590	+	0.510984i	$0.170719\pi$
$602$		0			0
$603$	4.67717e6	−	4.67717e6i	0.523830	−	0.523830i
$604$		0			0
$605$	−773375.	+	6.34401e6i	−0.0859017	+	0.704654i
$606$		0			0
$607$	−6.68075e6	+	6.68075e6i	−0.735958	+	0.735958i	−0.971793	−	0.235835i	$-0.924218\pi$
$607$	−6.68075e6	+	6.68075e6i	−0.735958	+	0.735958i	0.235835	+	0.971793i	$0.424218\pi$
$608$		0			0
$609$			3.82081e6i			0.417458i
$610$		0			0
$611$	3.40744e6			0.369254
$612$		0			0
$613$	7.77154e6	+	7.77154e6i	0.835326	+	0.835326i	0.988240	−	0.152914i	$-0.0488657\pi$
$613$	7.77154e6	+	7.77154e6i	0.835326	+	0.835326i	−0.152914	+	0.988240i	$0.548866\pi$
$614$		0			0
$615$	4.14642e6	+	5.29772e6i	0.442065	+	0.564809i
$616$		0			0
$617$	4.99746e6	+	4.99746e6i	0.528490	+	0.528490i	0.920122	−	0.391632i	$-0.128089\pi$
$617$	4.99746e6	+	4.99746e6i	0.528490	+	0.528490i	−0.391632	+	0.920122i	$0.628089\pi$
$618$		0			0
$619$		−	3.77207e6i		−	0.395688i	−0.980234	−	0.197844i	$-0.936606\pi$
$619$		−	3.77207e6i		−	0.395688i	0.980234	−	0.197844i	$-0.0633940\pi$
$620$		0			0
$621$		−	1.53230e7i		−	1.59446i
$622$		0			0
$623$	2.99392e6	+	2.99392e6i	0.309044	+	0.309044i
$624$		0			0
$625$	8.63835e6	+	4.55481e6i	0.884567	+	0.466413i
$626$		0			0
$627$	7.10977e6	+	7.10977e6i	0.722248	+	0.722248i
$628$		0			0
$629$	−4.22598e6			−0.425894
$630$		0			0
$631$			3.35353e6i			0.335297i	0.985847	+	0.167648i	$0.0536173\pi$
$631$			3.35353e6i			0.335297i	−0.985847	+	0.167648i	$0.946383\pi$
$632$		0			0
$633$	−2.42028e7	+	2.42028e7i	−2.40080	+	2.40080i
$634$		0			0
$635$	4.23359e6	+	5.40909e6i	0.416653	+	0.532341i
$636$		0			0
$637$	−1.04719e7	+	1.04719e7i	−1.02253	+	1.02253i
$638$		0			0
$639$	1.34644e7			1.30447
$640$		0			0
$641$	−2.39034e6			−0.229781			−0.114891	−	0.993378i	$-0.536652\pi$
$641$	−2.39034e6			−0.229781			−0.114891	+	0.993378i	$0.536652\pi$
$642$		0			0
$643$	−1.37541e7	+	1.37541e7i	−1.31191	+	1.31191i	−0.391903	+	0.920006i	$0.628183\pi$
$643$	−1.37541e7	+	1.37541e7i	−1.31191	+	1.31191i	−0.920006	+	0.391903i	$0.871817\pi$
$644$		0			0
$645$	−1.25668e7	−	1.53197e6i	−1.18939	−	0.144994i
$646$		0			0
$647$	7.34613e6	−	7.34613e6i	0.689919	−	0.689919i	−0.272295	−	0.962214i	$-0.587783\pi$
$647$	7.34613e6	−	7.34613e6i	0.689919	−	0.689919i	0.962214	+	0.272295i	$0.0877826\pi$
$648$		0			0
$649$			522040.i			0.0486510i
$650$		0			0
$651$	6.51142e6			0.602175
$652$		0			0
$653$	1.16302e7	+	1.16302e7i	1.06735	+	1.06735i	0.997562	+	0.0697839i	$0.0222310\pi$
$653$	1.16302e7	+	1.16302e7i	1.06735	+	1.06735i	0.0697839	+	0.997562i	$0.477769\pi$
$654$		0			0
$655$	667699.	−	5.47715e6i	0.0608103	−	0.498829i
$656$		0			0
$657$	3.65022e6	+	3.65022e6i	0.329918	+	0.329918i
$658$		0			0
$659$		−	1.68904e7i		−	1.51505i	−0.652807	−	0.757524i	$-0.726409\pi$
$659$		−	1.68904e7i		−	1.51505i	0.652807	−	0.757524i	$-0.273591\pi$
$660$		0			0
$661$		−	1.97068e7i		−	1.75433i	−0.480186	−	0.877167i	$-0.659431\pi$
$661$		−	1.97068e7i		−	1.75433i	0.480186	−	0.877167i	$-0.340569\pi$
$662$		0			0
$663$	−1.80464e7	−	1.80464e7i	−1.59444	−	1.59444i
$664$		0			0
$665$	3.80517e6	−	2.97823e6i	0.333672	−	0.261159i
$666$		0			0
$667$	2.85475e6	+	2.85475e6i	0.248459	+	0.248459i
$668$		0			0
$669$	−9.47445e6			−0.818443
$670$		0			0
$671$			1.06950e7i			0.917013i
$672$		0			0
$673$	7.59203e6	−	7.59203e6i	0.646130	−	0.646130i	−0.305925	−	0.952055i	$-0.598966\pi$
$673$	7.59203e6	−	7.59203e6i	0.646130	−	0.646130i	0.952055	+	0.305925i	$0.0989658\pi$
$674$		0			0
$675$	−1.53805e7	−	2.54973e7i	−1.29930	−	2.15395i
$676$		0			0
$677$	−1.15807e7	+	1.15807e7i	−0.971098	+	0.971098i	−0.999594	−	0.0284964i	$-0.990928\pi$
$677$	−1.15807e7	+	1.15807e7i	−0.971098	+	0.971098i	0.0284964	+	0.999594i	$0.490928\pi$
$678$		0			0
$679$	−6.43923e6			−0.535993
$680$		0			0
$681$	1.48245e7			1.22493
$682$		0			0
$683$	−1.53865e7	+	1.53865e7i	−1.26209	+	1.26209i	−0.312006	+	0.950080i	$0.601001\pi$
$683$	−1.53865e7	+	1.53865e7i	−1.26209	+	1.26209i	−0.950080	+	0.312006i	$0.898999\pi$
$684$		0			0
$685$	−2.66008e6	+	2.08199e6i	−0.216605	+	0.169532i
$686$		0			0
$687$	1.27490e7	−	1.27490e7i	1.03059	−	1.03059i
$688$		0			0
$689$		−	6.57766e6i		−	0.527866i
$690$		0			0
$691$	−1.58695e7			−1.26435			−0.632177	−	0.774824i	$-0.717838\pi$
$691$	−1.58695e7			−1.26435			−0.632177	+	0.774824i	$0.717838\pi$
$692$		0			0
$693$	4.68177e6	+	4.68177e6i	0.370320	+	0.370320i
$694$		0			0
$695$	−1.80152e7	−	2.19617e6i	−1.41474	−	0.172466i
$696$		0			0
$697$	2.50312e6	+	2.50312e6i	0.195164	+	0.195164i
$698$		0			0
$699$			3.80342e6i			0.294429i
$700$		0			0
$701$			1.38044e6i			0.106101i	0.998592	+	0.0530507i	$0.0168945\pi$
$701$			1.38044e6i			0.106101i	−0.998592	+	0.0530507i	$0.983105\pi$
$702$		0			0
$703$	5.76991e6	+	5.76991e6i	0.440332	+	0.440332i
$704$		0			0
$705$	5.10755e6	+	622643.i	0.387026	+	0.0471809i
$706$		0			0
$707$	−4.04820e6	−	4.04820e6i	−0.304588	−	0.304588i
$708$		0			0
$709$	−1.02298e7			−0.764275			−0.382138	−	0.924105i	$-0.624812\pi$
$709$	−1.02298e7			−0.764275			−0.382138	+	0.924105i	$0.624812\pi$
$710$		0			0
$711$			1.66139e7i			1.23253i
$712$		0			0
$713$	4.86507e6	−	4.86507e6i	0.358398	−	0.358398i
$714$		0			0
$715$	1.00812e7	−	7.89033e6i	0.737473	−	0.577205i
$716$		0			0
$717$	2.22797e7	−	2.22797e7i	1.61850	−	1.61850i
$718$		0			0
$719$	1.60502e7			1.15787			0.578935	−	0.815374i	$-0.303469\pi$
$719$	1.60502e7			1.15787			0.578935	+	0.815374i	$0.303469\pi$
$720$		0			0
$721$	−8.00132e6			−0.573223
$722$		0			0
$723$	1.02267e7	−	1.02267e7i	0.727598	−	0.727598i
$724$		0			0
$725$	7.61574e6	+	1.88482e6i	0.538105	+	0.133176i
$726$		0			0
$727$	−8.85038e6	+	8.85038e6i	−0.621049	+	0.621049i	−0.945800	−	0.324751i	$-0.894720\pi$
$727$	−8.85038e6	+	8.85038e6i	−0.621049	+	0.621049i	0.324751	+	0.945800i	$0.394720\pi$
$728$		0			0
$729$			1.01834e7i			0.709699i
$730$		0			0
$731$	−6.66153e6			−0.461084
$732$		0			0
$733$	1.71914e7	+	1.71914e7i	1.18182	+	1.18182i	0.979273	+	0.202544i	$0.0649209\pi$
$733$	1.71914e7	+	1.71914e7i	1.18182	+	1.18182i	0.202544	+	0.979273i	$0.435079\pi$
$734$		0			0
$735$	−1.76103e7	+	1.37833e7i	−1.20240	+	0.941095i
$736$		0			0
$737$	1.75536e6	+	1.75536e6i	0.119041	+	0.119041i
$738$		0			0
$739$			2.24498e7i			1.51218i	0.654470	+	0.756088i	$0.272892\pi$
$739$			2.24498e7i			1.51218i	−0.654470	+	0.756088i	$0.727108\pi$
$740$		0			0
$741$			4.92791e7i			3.29698i
$742$		0			0
$743$	1.01205e7	+	1.01205e7i	0.672555	+	0.672555i	0.958304	−	0.285749i	$-0.0922424\pi$
$743$	1.01205e7	+	1.01205e7i	0.672555	+	0.672555i	−0.285749	+	0.958304i	$0.592242\pi$
$744$		0			0
$745$	2.57414e6	−	2.11157e7i	0.169919	−	1.39385i
$746$		0			0
$747$	2.25558e7	+	2.25558e7i	1.47896	+	1.47896i
$748$		0			0
$749$	−9.42434e6			−0.613827
$750$		0			0
$751$		−	2.04566e6i		−	0.132353i	−0.997808	−	0.0661766i	$-0.978920\pi$
$751$		−	2.04566e6i		−	0.132353i	0.997808	−	0.0661766i	$-0.0210801\pi$
$752$		0			0
$753$	5.55613e6	−	5.55613e6i	0.357096	−	0.357096i
$754$		0			0
$755$	1.33143e7	+	1.62310e6i	0.850065	+	0.103628i
$756$		0			0
$757$	−1.12903e6	+	1.12903e6i	−0.0716090	+	0.0716090i	−0.742004	−	0.670395i	$-0.766125\pi$
$757$	−1.12903e6	+	1.12903e6i	−0.0716090	+	0.0716090i	0.670395	+	0.742004i	$0.266125\pi$
$758$		0			0
$759$	9.94770e6			0.626785
$760$		0			0
$761$	8.12519e6			0.508595			0.254297	−	0.967126i	$-0.418156\pi$
$761$	8.12519e6			0.508595			0.254297	+	0.967126i	$0.418156\pi$
$762$		0			0
$763$	4.45785e6	−	4.45785e6i	0.277213	−	0.277213i
$764$		0			0
$765$	−1.67050e7	−	2.13434e7i	−1.03203	−	1.31859i
$766$		0			0
$767$	−1.80918e6	+	1.80918e6i	−0.111043	+	0.111043i
$768$		0			0
$769$		−	7.89386e6i		−	0.481364i	−0.970604	−	0.240682i	$-0.922629\pi$
$769$		−	7.89386e6i		−	0.481364i	0.970604	−	0.240682i	$-0.0773711\pi$
$770$		0			0
$771$	−341244.			−0.0206742
$772$		0			0
$773$	−1.74653e7	−	1.74653e7i	−1.05130	−	1.05130i	−0.998611	−	0.0526894i	$-0.983221\pi$
$773$	−1.74653e7	−	1.74653e7i	−1.05130	−	1.05130i	−0.0526894	−	0.998611i	$-0.516779\pi$
$774$		0			0
$775$	3.21211e6	−	1.29787e7i	0.192104	−	0.776208i
$776$		0			0
$777$	5.40248e6	+	5.40248e6i	0.321026	+	0.321026i
$778$		0			0
$779$		−	6.83523e6i		−	0.403561i
$780$		0			0
$781$			5.05323e6i			0.296443i
$782$		0			0
$783$	−1.69156e7	−	1.69156e7i	−0.986015	−	0.986015i
$784$		0			0
$785$	1.71337e7	+	2.18911e7i	0.992380	+	1.26792i
$786$		0			0
$787$	−6.99225e6	−	6.99225e6i	−0.402421	−	0.402421i	0.476665	−	0.879085i	$-0.341846\pi$
$787$	−6.99225e6	−	6.99225e6i	−0.402421	−	0.402421i	−0.879085	+	0.476665i	$0.841846\pi$
$788$		0			0
$789$	−2.82908e7			−1.61790
$790$		0			0
$791$			2.28917e6i			0.130088i
$792$		0			0
$793$	−3.70645e7	+	3.70645e7i	−2.09303	+	2.09303i
$794$		0			0
$795$	1.20194e6	−	9.85952e6i	0.0674472	−	0.553271i
$796$		0			0
$797$	9.48068e6	−	9.48068e6i	0.528681	−	0.528681i	−0.391498	−	0.920179i	$-0.628043\pi$
$797$	9.48068e6	−	9.48068e6i	0.528681	−	0.528681i	0.920179	+	0.391498i	$0.128043\pi$
$798$		0			0
$799$	2.70746e6			0.150036
$800$		0			0
$801$	−4.58564e7			−2.52533
$802$		0			0
$803$	−1.36994e6	+	1.36994e6i	−0.0749742	+	0.0749742i
$804$		0			0
$805$	578511.	−	4.74554e6i	0.0314646	−	0.258105i
$806$		0			0
$807$	−2.65669e7	+	2.65669e7i	−1.43601	+	1.43601i
$808$		0			0
$809$			2.13643e7i			1.14767i	0.818970	+	0.573836i	$0.194545\pi$
$809$			2.13643e7i			1.14767i	−0.818970	+	0.573836i	$0.805455\pi$
$810$		0			0
$811$	5.33992e6			0.285091			0.142545	−	0.989788i	$-0.454471\pi$
$811$	5.33992e6			0.285091			0.142545	+	0.989788i	$0.454471\pi$
$812$		0			0
$813$	4.82512e6	+	4.82512e6i	0.256025	+	0.256025i
$814$		0			0
$815$	−2.17701e7	−	2.78148e7i	−1.14807	−	1.46684i
$816$		0			0
$817$	9.09526e6	+	9.09526e6i	0.476716	+	0.476716i
$818$		0			0
$819$			3.24502e7i			1.69047i
$820$		0			0
$821$		−	3.13838e7i		−	1.62498i	−0.582978	−	0.812488i	$-0.698112\pi$
$821$		−	3.13838e7i		−	1.62498i	0.582978	−	0.812488i	$-0.301888\pi$
$822$		0			0
$823$	1.21481e7	+	1.21481e7i	0.625184	+	0.625184i	0.946852	−	0.321668i	$-0.104244\pi$
$823$	1.21481e7	+	1.21481e7i	0.625184	+	0.625184i	−0.321668	+	0.946852i	$0.604244\pi$
$824$		0			0
$825$	1.65529e7	−	9.98501e6i	0.846718	−	0.510756i
$826$		0			0
$827$	1.21744e7	+	1.21744e7i	0.618990	+	0.618990i	0.945272	−	0.326282i	$-0.105796\pi$
$827$	1.21744e7	+	1.21744e7i	0.618990	+	0.618990i	−0.326282	+	0.945272i	$0.605796\pi$
$828$		0			0
$829$	−8.58099e6			−0.433662			−0.216831	−	0.976209i	$-0.569572\pi$
$829$	−8.58099e6			−0.433662			−0.216831	+	0.976209i	$0.569572\pi$
$830$		0			0
$831$		−	1.50353e7i		−	0.755284i
$832$		0			0
$833$	−8.32070e6	+	8.32070e6i	−0.415478	+	0.415478i
$834$		0			0
$835$	2.04321e6	+	2.61053e6i	0.101414	+	0.129572i
$836$		0			0
$837$	−2.88276e7	+	2.88276e7i	−1.42231	+	1.42231i
$838$		0			0
$839$	−1.30510e7			−0.640087			−0.320043	−	0.947403i	$-0.603697\pi$
$839$	−1.30510e7			−0.640087			−0.320043	+	0.947403i	$0.603697\pi$
$840$		0			0
$841$	−1.42082e7			−0.692707
$842$		0			0
$843$	−1.48232e7	+	1.48232e7i	−0.718411	+	0.718411i
$844$		0			0
$845$	4.16785e7	+	5.08087e6i	2.00803	+	0.244791i
$846$		0			0
$847$	4.29911e6	−	4.29911e6i	0.205907	−	0.205907i
$848$		0			0
$849$		−	3.61852e7i		−	1.72291i
$850$		0			0
$851$	8.07303e6			0.382131
$852$		0			0
$853$	−1.13258e7	−	1.13258e7i	−0.532960	−	0.532960i	0.388492	−	0.921452i	$-0.372996\pi$
$853$	−1.13258e7	−	1.13258e7i	−0.532960	−	0.532960i	−0.921452	+	0.388492i	$0.872996\pi$
$854$		0			0
$855$	−6.33292e6	+	5.19491e7i	−0.296271	+	2.43031i
$856$		0			0
$857$	−2.70697e7	−	2.70697e7i	−1.25901	−	1.25901i	−0.951564	−	0.307451i	$-0.900524\pi$
$857$	−2.70697e7	−	2.70697e7i	−1.25901	−	1.25901i	−0.307451	−	0.951564i	$-0.599476\pi$
$858$		0			0
$859$		−	1.44224e7i		−	0.666893i	−0.942769	−	0.333446i	$-0.891788\pi$
$859$		−	1.44224e7i		−	0.666893i	0.942769	−	0.333446i	$-0.108212\pi$
$860$		0			0
$861$		−	6.39996e6i		−	0.294218i
$862$		0			0
$863$	−2.06672e7	−	2.06672e7i	−0.944614	−	0.944614i	0.0539306	−	0.998545i	$-0.482825\pi$
$863$	−2.06672e7	−	2.06672e7i	−0.944614	−	0.944614i	−0.998545	+	0.0539306i	$0.982825\pi$
$864$		0			0
$865$	−1.61796e7	+	1.26634e7i	−0.735236	+	0.575455i
$866$		0			0
$867$	1.43926e7	+	1.43926e7i	0.650265	+	0.650265i
$868$		0			0
$869$	−6.23525e6			−0.280095
$870$		0			0
$871$			1.21667e7i			0.543409i
$872$		0			0
$873$	4.93132e7	−	4.93132e7i	2.18992	−	2.18992i
$874$		0			0
$875$	−3.80070e6	−	8.47721e6i	−0.167820	−	0.374311i
$876$		0			0
$877$	−3.95359e6	+	3.95359e6i	−0.173577	+	0.173577i	−0.788549	−	0.614972i	$-0.789167\pi$
$877$	−3.95359e6	+	3.95359e6i	−0.173577	+	0.173577i	0.614972	+	0.788549i	$0.289167\pi$
$878$		0			0
$879$	−2.17602e7			−0.949928
$880$		0			0
$881$	1.48955e7			0.646572			0.323286	−	0.946301i	$-0.395212\pi$
$881$	1.48955e7			0.646572			0.323286	+	0.946301i	$0.395212\pi$
$882$		0			0
$883$	2.54781e7	−	2.54781e7i	1.09968	−	1.09968i	0.105230	−	0.994448i	$-0.466442\pi$
$883$	2.54781e7	−	2.54781e7i	1.09968	−	1.09968i	0.994448	−	0.105230i	$-0.0335579\pi$
$884$		0			0
$885$	−3.04244e6	+	2.38126e6i	−0.130576	+	0.102199i
$886$		0			0
$887$	2.81679e7	−	2.81679e7i	1.20211	−	1.20211i	0.228593	−	0.973522i	$-0.426588\pi$
$887$	2.81679e7	−	2.81679e7i	1.20211	−	1.20211i	0.973522	−	0.228593i	$-0.0734124\pi$
$888$		0			0
$889$		−	6.53450e6i		−	0.277305i
$890$		0			0
$891$	−2.86905e7			−1.21072
$892$		0			0
$893$	−3.69660e6	−	3.69660e6i	−0.155122	−	0.155122i
$894$		0			0
$895$	2.78633e7	+	3.39671e6i	1.16272	+	0.141743i
$896$		0			0
$897$	3.44747e7	+	3.44747e7i	1.43060	+	1.43060i
$898$		0			0
$899$		−	1.07415e7i		−	0.443265i
$900$		0			0
$901$		−	5.22643e6i		−	0.214483i
$902$		0			0
$903$	8.51607e6	+	8.51607e6i	0.347552	+	0.347552i
$904$		0			0
$905$	−3.32119e7	−	4.04874e6i	−1.34795	−	0.164323i
$906$		0			0
$907$	−2.35411e7	−	2.35411e7i	−0.950187	−	0.950187i	0.0486295	−	0.998817i	$-0.484515\pi$
$907$	−2.35411e7	−	2.35411e7i	−0.950187	−	0.950187i	−0.998817	+	0.0486295i	$0.984515\pi$
$908$		0			0
$909$	6.20043e7			2.48893
$910$		0			0
$911$			7.50503e6i			0.299610i	0.988716	+	0.149805i	$0.0478646\pi$
$911$			7.50503e6i			0.299610i	−0.988716	+	0.149805i	$0.952135\pi$
$912$		0			0
$913$	−8.46527e6	+	8.46527e6i	−0.336096	+	0.336096i
$914$		0			0
$915$	−6.23304e7	+	4.87848e7i	−2.46120	+	1.92633i
$916$		0			0
$917$	−3.71167e6	+	3.71167e6i	−0.145763	+	0.145763i
$918$		0			0
$919$	3.13540e7			1.22463			0.612313	−	0.790615i	$-0.290239\pi$
$919$	3.13540e7			1.22463			0.612313	+	0.790615i	$0.290239\pi$
$920$		0			0
$921$	4.74503e7			1.84327
$922$		0			0
$923$	−1.75124e7	+	1.75124e7i	−0.676615	+	0.676615i
$924$		0			0
$925$	1.34334e7	−	8.10330e6i	0.516218	−	0.311392i
$926$		0			0
$927$	6.12761e7	−	6.12761e7i	2.34203	−	2.34203i
$928$		0			0
$929$		−	3.89072e7i		−	1.47908i	−0.673113	−	0.739539i	$-0.735043\pi$
$929$		−	3.89072e7i		−	1.47908i	0.673113	−	0.739539i	$-0.264957\pi$
$930$		0			0
$931$	2.27212e7			0.859126
$932$		0			0
$933$	3.59257e7	+	3.59257e7i	1.35114	+	1.35114i
$934$		0			0
$935$	8.01023e6	−	6.26945e6i	0.299651	−	0.234531i
$936$		0			0
$937$	−7.90706e6	−	7.90706e6i	−0.294216	−	0.294216i	0.544527	−	0.838743i	$-0.316709\pi$
$937$	−7.90706e6	−	7.90706e6i	−0.294216	−	0.294216i	−0.838743	+	0.544527i	$0.816709\pi$
$938$		0			0
$939$		−	6.41478e7i		−	2.37420i
$940$		0			0
$941$		−	2.66221e7i		−	0.980097i	−0.871695	−	0.490048i	$-0.836979\pi$
$941$		−	2.66221e7i		−	0.980097i	0.871695	−	0.490048i	$-0.163021\pi$
$942$		0			0
$943$	−4.78179e6	−	4.78179e6i	−0.175110	−	0.175110i
$944$		0			0
$945$	−3.42792e6	+	2.81193e7i	−0.124868	+	1.02429i
$946$		0			0
$947$	−2.53694e7	−	2.53694e7i	−0.919254	−	0.919254i	0.0777209	−	0.996975i	$-0.475236\pi$
$947$	−2.53694e7	−	2.53694e7i	−0.919254	−	0.919254i	−0.996975	+	0.0777209i	$0.975236\pi$
$948$		0			0
$949$	−9.49528e6			−0.342249
$950$		0			0
$951$			1.44648e7i			0.518634i
$952$		0			0
$953$	−1.51059e7	+	1.51059e7i	−0.538784	+	0.538784i	−0.923172	−	0.384388i	$-0.874412\pi$
$953$	−1.51059e7	+	1.51059e7i	−0.538784	+	0.538784i	0.384388	+	0.923172i	$0.374412\pi$
$954$		0			0
$955$	3.50595e7	+	4.27397e6i	1.24393	+	0.151643i
$956$		0			0
$957$	1.09816e7	−	1.09816e7i	0.387603	−	0.387603i
$958$		0			0
$959$	3.21353e6			0.112833
$960$		0			0
$961$	1.03236e7			0.360597
$962$		0			0
$963$	7.21740e7	−	7.21740e7i	2.50793	−	2.50793i
$964$		0			0
$965$	−7.35063e6	−	9.39162e6i	−0.254101	−	0.324655i
$966$		0			0
$967$	−2.00058e7	+	2.00058e7i	−0.688001	+	0.688001i	−0.961790	−	0.273789i	$-0.911723\pi$
$967$	−2.00058e7	+	2.00058e7i	−0.688001	+	0.688001i	0.273789	+	0.961790i	$0.411723\pi$
$968$		0			0
$969$			3.91558e7i			1.33964i
$970$		0			0
$971$	−2.93517e7			−0.999044			−0.499522	−	0.866301i	$-0.666491\pi$
$971$	−2.93517e7			−0.999044			−0.499522	+	0.866301i	$0.666491\pi$
$972$		0			0
$973$	1.22083e7	+	1.22083e7i	0.413401	+	0.413401i
$974$		0			0
$975$	9.19694e7	+	2.27616e7i	3.09836	+	0.766815i
$976$		0			0
$977$	−3.70837e7	−	3.70837e7i	−1.24293	−	1.24293i	−0.958780	−	0.284150i	$-0.908289\pi$
$977$	−3.70837e7	−	3.70837e7i	−1.24293	−	1.24293i	−0.284150	−	0.958780i	$-0.591711\pi$
$978$		0			0
$979$		−	1.72100e7i		−	0.573885i
$980$		0			0
$981$			6.82787e7i			2.26523i
$982$		0			0
$983$	−1.41592e6	−	1.41592e6i	−0.0467363	−	0.0467363i	0.683352	−	0.730089i	$-0.260521\pi$
$983$	−1.41592e6	−	1.41592e6i	−0.0467363	−	0.0467363i	−0.730089	+	0.683352i	$0.760521\pi$
$984$		0			0
$985$	2.60138e7	+	3.32368e7i	0.854305	+	1.09151i
$986$		0			0
$987$	−3.46120e6	−	3.46120e6i	−0.113093	−	0.113093i
$988$		0			0
$989$	1.27257e7			0.413706
$990$		0			0
$991$		−	1.80706e7i		−	0.584504i	−0.956341	−	0.292252i	$-0.905595\pi$
$991$		−	1.80706e7i		−	0.584504i	0.956341	−	0.292252i	$-0.0944047\pi$
$992$		0			0
$993$	5.39670e7	−	5.39670e7i	1.73682	−	1.73682i
$994$		0			0
$995$	−4.43511e6	+	3.63813e7i	−0.142019	+	1.16499i
$996$		0			0
$997$	3.51549e7	−	3.51549e7i	1.12008	−	1.12008i	0.128349	−	0.991729i	$-0.459032\pi$
$997$	3.51549e7	−	3.51549e7i	1.12008	−	1.12008i	0.991729	−	0.128349i	$-0.0409678\pi$
$998$		0			0
$999$	−4.78361e7			−1.51650

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.6.o.a.47.2		56
4.3	odd	2		40.6.k.a.27.17	yes	56
5.3	odd	4	inner	160.6.o.a.143.1		56
8.3	odd	2	inner	160.6.o.a.47.1		56
8.5	even	2		40.6.k.a.27.26	yes	56
20.3	even	4		40.6.k.a.3.26	yes	56
40.3	even	4	inner	160.6.o.a.143.2		56
40.13	odd	4		40.6.k.a.3.17	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.k.a.3.17	✓	56	40.13	odd	4
40.6.k.a.3.26	yes	56	20.3	even	4
40.6.k.a.27.17	yes	56	4.3	odd	2
40.6.k.a.27.26	yes	56	8.5	even	2
160.6.o.a.47.1		56	8.3	odd	2	inner
160.6.o.a.47.2		56	1.1	even	1	trivial
160.6.o.a.143.1		56	5.3	odd	4	inner
160.6.o.a.143.2		56	40.3	even	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)

\(f(q)\)	\(=\)	\(q+(-20.2357 + 20.2357i) q^{3} +(6.76469 - 55.4909i) q^{5} +(-37.6042 + 37.6042i) q^{7} -575.965i q^{9} +O(q^{10})\)	\(q+(-20.2357 + 20.2357i) q^{3} +(6.76469 - 55.4909i) q^{5} +(-37.6042 + 37.6042i) q^{7} -575.965i q^{9} +216.161 q^{11} +(749.126 + 749.126i) q^{13} +(986.008 + 1259.78i) q^{15} +(595.235 + 595.235i) q^{17} -1625.40i q^{19} -1521.89i q^{21} +(-1137.10 - 1137.10i) q^{23} +(-3033.48 - 750.757i) q^{25} +(6737.77 + 6737.77i) q^{27} -2510.57 q^{29} +4278.50i q^{31} +(-4374.17 + 4374.17i) q^{33} +(1832.31 + 2341.07i) q^{35} +(-3549.84 + 3549.84i) q^{37} -30318.1 q^{39} +4205.26 q^{41} +(-5595.71 + 5595.71i) q^{43} +(-31960.8 - 3896.22i) q^{45} +(2274.28 - 2274.28i) q^{47} +13978.8i q^{49} -24090.0 q^{51} +(-4390.22 - 4390.22i) q^{53} +(1462.26 - 11995.0i) q^{55} +(32891.0 + 32891.0i) q^{57} +2415.05i q^{59} +49477.1i q^{61} +(21658.7 + 21658.7i) q^{63} +(46637.3 - 36502.1i) q^{65} +(8120.59 + 8120.59i) q^{67} +46019.8 q^{69} +23377.1i q^{71} +(-6337.57 + 6337.57i) q^{73} +(76576.6 - 46192.4i) q^{75} +(-8128.57 + 8128.57i) q^{77} -28845.4 q^{79} -132727. q^{81} +(-39161.8 + 39161.8i) q^{83} +(37056.7 - 29003.6i) q^{85} +(50803.0 - 50803.0i) q^{87} -79616.6i q^{89} -56340.6 q^{91} +(-86578.3 - 86578.3i) q^{93} +(-90194.8 - 10995.3i) q^{95} +(85618.4 + 85618.4i) q^{97} -124501. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{3}+O(q^{10}) \) 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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