LMFDB - Embedded newform 160.6.n.c.127.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,6,Mod(63,160)]

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, 0, 3]))

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

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

chi := DirichletCharacter("160.63");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	160.n (of order $4$, degree $2$, 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:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 1375 x^{14} + 743087 x^{12} + 198706725 x^{10} + 26872635188 x^{8} + 1612811892960 x^{6} + \cdots + 177426662425600 $ x^16 + 1375x^14 + 743087x^12 + 198706725x^10 + 26872635188x^8 + 1612811892960x^6 + 24971013117824x^4 + 124211190826240*x^2 + 177426662425600
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{41}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.8
Root			$-18.6675i$ of defining polynomial
Character	$\chi$	$=$	160.127
Dual form			160.6.n.c.63.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(17.6675 + 17.6675i) q^{3} +(55.7953 + 3.44692i) q^{5} +(-52.6478 + 52.6478i) q^{7} +381.282i q^{9} +O(q^{10})$	\(q+(17.6675 + 17.6675i) q^{3} +(55.7953 + 3.44692i) q^{5} +(-52.6478 + 52.6478i) q^{7} +381.282i q^{9} -126.754i q^{11} +(-788.215 + 788.215i) q^{13} +(924.866 + 1046.66i) q^{15} +(425.884 + 425.884i) q^{17} +182.630 q^{19} -1860.31 q^{21} +(846.687 + 846.687i) q^{23} +(3101.24 + 384.644i) q^{25} +(-2443.09 + 2443.09i) q^{27} +6177.24i q^{29} -7364.54i q^{31} +(2239.43 - 2239.43i) q^{33} +(-3118.97 + 2756.03i) q^{35} +(-5037.28 - 5037.28i) q^{37} -27851.6 q^{39} +19084.7 q^{41} +(-9237.55 - 9237.55i) q^{43} +(-1314.25 + 21273.7i) q^{45} +(-18589.3 + 18589.3i) q^{47} +11263.4i q^{49} +15048.6i q^{51} +(6808.95 - 6808.95i) q^{53} +(436.911 - 7072.28i) q^{55} +(3226.62 + 3226.62i) q^{57} +47009.8 q^{59} +14370.2 q^{61} +(-20073.6 - 20073.6i) q^{63} +(-46695.6 + 41261.8i) q^{65} +(-30347.8 + 30347.8i) q^{67} +29917.7i q^{69} -43994.2i q^{71} +(-29820.5 + 29820.5i) q^{73} +(47995.4 + 61586.8i) q^{75} +(6673.31 + 6673.31i) q^{77} +54115.9 q^{79} +6324.78 q^{81} +(4507.43 + 4507.43i) q^{83} +(22294.3 + 25230.3i) q^{85} +(-109136. + 109136. i) q^{87} -29233.7i q^{89} -82995.5i q^{91} +(130113. - 130113. i) q^{93} +(10189.9 + 629.511i) q^{95} +(-63973.4 - 63973.4i) q^{97} +48328.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 10 q^{3} - 42 q^{5} + 86 q^{7}+O(q^{10}) $ 16 * q - 10 * q^3 - 42 * q^5 + 86 * q^7	$ 16 q - 10 q^{3} - 42 q^{5} + 86 q^{7} + 536 q^{13} + 698 q^{15} - 1828 q^{17} - 2512 q^{19} - 4284 q^{21} + 7642 q^{23} + 9140 q^{25} + 12272 q^{27} + 11876 q^{33} - 10518 q^{35} - 7620 q^{37} - 11244 q^{39} - 21284 q^{41} - 20002 q^{43} + 686 q^{45} - 25298 q^{47} + 12852 q^{53} + 10584 q^{55} + 55848 q^{57} + 142704 q^{59} - 20564 q^{61} + 115282 q^{63} - 38256 q^{65} + 10506 q^{67} + 15432 q^{73} - 256226 q^{75} + 133852 q^{77} + 159344 q^{79} - 236116 q^{81} + 61222 q^{83} + 7056 q^{85} - 162176 q^{87} + 122180 q^{93} - 267512 q^{95} - 17344 q^{97} - 107332 q^{99}+O(q^{100}) $ 16 * q - 10 * q^3 - 42 * q^5 + 86 * q^7 + 536 * q^13 + 698 * q^15 - 1828 * q^17 - 2512 * q^19 - 4284 * q^21 + 7642 * q^23 + 9140 * q^25 + 12272 * q^27 + 11876 * q^33 - 10518 * q^35 - 7620 * q^37 - 11244 * q^39 - 21284 * q^41 - 20002 * q^43 + 686 * q^45 - 25298 * q^47 + 12852 * q^53 + 10584 * q^55 + 55848 * q^57 + 142704 * q^59 - 20564 * q^61 + 115282 * q^63 - 38256 * q^65 + 10506 * q^67 + 15432 * q^73 - 256226 * q^75 + 133852 * q^77 + 159344 * q^79 - 236116 * q^81 + 61222 * q^83 + 7056 * q^85 - 162176 * q^87 + 122180 * q^93 - 267512 * q^95 - 17344 * q^97 - 107332 * q^99

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
$3$	17.6675	+	17.6675i	1.13337	+	1.13337i	0.989613	+	0.143758i	$0.0459188\pi$
$3$	17.6675	+	17.6675i	1.13337	+	1.13337i	0.143758	+	0.989613i	$0.454081\pi$
$4$		0			0
$5$	55.7953	+	3.44692i	0.998097	+	0.0616603i
$5$	55.7953	+	3.44692i	0.998097	+	0.0616603i
$6$		0			0
$7$	−52.6478	+	52.6478i	−0.406102	+	0.406102i	−0.880377	−	0.474275i	$-0.842710\pi$
$7$	−52.6478	+	52.6478i	−0.406102	+	0.406102i	0.474275	+	0.880377i	$0.342710\pi$
$8$		0			0
$9$			381.282i			1.56906i
$10$		0			0
$11$		−	126.754i		−	0.315849i	−0.987451	−	0.157925i	$-0.949520\pi$
$11$		−	126.754i		−	0.315849i	0.987451	−	0.157925i	$-0.0504803\pi$
$12$		0			0
$13$	−788.215	+	788.215i	−1.29356	+	1.29356i	−0.360990	+	0.932570i	$0.617561\pi$
$13$	−788.215	+	788.215i	−1.29356	+	1.29356i	−0.932570	+	0.360990i	$0.882439\pi$
$14$		0			0
$15$	924.866	+	1046.66i	1.06133	+	1.20110i
$16$		0			0
$17$	425.884	+	425.884i	0.357412	+	0.357412i	0.862858	−	0.505446i	$-0.168672\pi$
$17$	425.884	+	425.884i	0.357412	+	0.357412i	−0.505446	+	0.862858i	$0.668672\pi$
$18$		0			0
$19$	182.630			0.116062			0.0580308	−	0.998315i	$-0.481518\pi$
$19$	182.630			0.116062			0.0580308	+	0.998315i	$0.481518\pi$
$20$		0			0
$21$	−1860.31			−0.920528
$22$		0			0
$23$	846.687	+	846.687i	0.333736	+	0.333736i	0.854004	−	0.520267i	$-0.174168\pi$
$23$	846.687	+	846.687i	0.333736	+	0.333736i	−0.520267	+	0.854004i	$0.674168\pi$
$24$		0			0
$25$	3101.24	+	384.644i	0.992396	+	0.123086i
$26$		0			0
$27$	−2443.09	+	2443.09i	−0.644956	+	0.644956i
$28$		0			0
$29$			6177.24i			1.36395i	0.731374	+	0.681977i	$0.238879\pi$
$29$			6177.24i			1.36395i	−0.731374	+	0.681977i	$0.761121\pi$
$30$		0			0
$31$		−	7364.54i		−	1.37639i	−0.725526	−	0.688195i	$-0.758403\pi$
$31$		−	7364.54i		−	1.37639i	0.725526	−	0.688195i	$-0.241597\pi$
$32$		0			0
$33$	2239.43	−	2239.43i	0.357974	−	0.357974i
$34$		0			0
$35$	−3118.97	+	2756.03i	−0.430369	+	0.380289i
$36$		0			0
$37$	−5037.28	−	5037.28i	−0.604912	−	0.604912i	0.336700	−	0.941612i	$-0.390689\pi$
$37$	−5037.28	−	5037.28i	−0.604912	−	0.604912i	−0.941612	+	0.336700i	$0.890689\pi$
$38$		0			0
$39$	−27851.6			−2.93217
$40$		0			0
$41$	19084.7			1.77307			0.886533	−	0.462665i	$-0.153107\pi$
$41$	19084.7			1.77307			0.886533	+	0.462665i	$0.153107\pi$
$42$		0			0
$43$	−9237.55	−	9237.55i	−0.761878	−	0.761878i	0.214783	−	0.976662i	$-0.431095\pi$
$43$	−9237.55	−	9237.55i	−0.761878	−	0.761878i	−0.976662	+	0.214783i	$0.931095\pi$
$44$		0			0
$45$	−1314.25	+	21273.7i	−0.0967488	+	1.56607i
$46$		0			0
$47$	−18589.3	+	18589.3i	−1.22749	+	1.22749i	−0.262584	+	0.964909i	$0.584575\pi$
$47$	−18589.3	+	18589.3i	−1.22749	+	1.22749i	−0.964909	+	0.262584i	$0.915425\pi$
$48$		0			0
$49$			11263.4i			0.670163i
$50$		0			0
$51$			15048.6i			0.810160i
$52$		0			0
$53$	6808.95	−	6808.95i	0.332959	−	0.332959i	−0.520750	−	0.853709i	$-0.674348\pi$
$53$	6808.95	−	6808.95i	0.332959	−	0.332959i	0.853709	+	0.520750i	$0.174348\pi$
$54$		0			0
$55$	436.911	−	7072.28i	0.0194754	−	0.315248i
$56$		0			0
$57$	3226.62	+	3226.62i	0.131541	+	0.131541i
$58$		0			0
$59$	47009.8			1.75816			0.879079	−	0.476676i	$-0.158158\pi$
$59$	47009.8			1.75816			0.879079	+	0.476676i	$0.158158\pi$
$60$		0			0
$61$	14370.2			0.494467			0.247233	−	0.968956i	$-0.420479\pi$
$61$	14370.2			0.494467			0.247233	+	0.968956i	$0.420479\pi$
$62$		0			0
$63$	−20073.6	−	20073.6i	−0.637198	−	0.637198i
$64$		0			0
$65$	−46695.6	+	41261.8i	−1.37086	+	1.21134i
$66$		0			0
$67$	−30347.8	+	30347.8i	−0.825924	+	0.825924i	−0.986950	−	0.161026i	$-0.948520\pi$
$67$	−30347.8	+	30347.8i	−0.825924	+	0.825924i	0.161026	+	0.986950i	$0.448520\pi$
$68$		0			0
$69$			29917.7i			0.756494i
$70$		0			0
$71$		−	43994.2i		−	1.03574i	−0.855460	−	0.517868i	$-0.826726\pi$
$71$		−	43994.2i		−	1.03574i	0.855460	−	0.517868i	$-0.173274\pi$
$72$		0			0
$73$	−29820.5	+	29820.5i	−0.654949	+	0.654949i	−0.954180	−	0.299232i	$-0.903270\pi$
$73$	−29820.5	+	29820.5i	−0.654949	+	0.654949i	0.299232	+	0.954180i	$0.403270\pi$
$74$		0			0
$75$	47995.4	+	61586.8i	0.985251	+	1.26426i
$76$		0			0
$77$	6673.31	+	6673.31i	0.128267	+	0.128267i
$78$		0			0
$79$	54115.9			0.975568			0.487784	−	0.872964i	$-0.337805\pi$
$79$	54115.9			0.975568			0.487784	+	0.872964i	$0.337805\pi$
$80$		0			0
$81$	6324.78			0.107111
$82$		0			0
$83$	4507.43	+	4507.43i	0.0718181	+	0.0718181i	0.742103	−	0.670285i	$-0.233828\pi$
$83$	4507.43	+	4507.43i	0.0718181	+	0.0718181i	−0.670285	+	0.742103i	$0.733828\pi$
$84$		0			0
$85$	22294.3	+	25230.3i	0.334694	+	0.378770i
$86$		0			0
$87$	−109136.	+	109136.i	−1.54587	+	1.54587i
$88$		0			0
$89$		−	29233.7i		−	0.391209i	−0.980683	−	0.195604i	$-0.937333\pi$
$89$		−	29233.7i		−	0.391209i	0.980683	−	0.195604i	$-0.0626668\pi$
$90$		0			0
$91$		−	82995.5i		−	1.05063i
$92$		0			0
$93$	130113.	−	130113.i	1.55996	−	1.55996i
$94$		0			0
$95$	10189.9	+	629.511i	0.115841	+	0.00715639i
$96$		0			0
$97$	−63973.4	−	63973.4i	−0.690351	−	0.690351i	0.271958	−	0.962309i	$-0.412329\pi$
$97$	−63973.4	−	63973.4i	−0.690351	−	0.690351i	−0.962309	+	0.271958i	$0.912329\pi$
$98$		0			0
$99$	48328.9			0.495586
$100$		0			0
$101$	−22842.8			−0.222815			−0.111408	−	0.993775i	$-0.535536\pi$
$101$	−22842.8			−0.222815			−0.111408	+	0.993775i	$0.535536\pi$
$102$		0			0
$103$	−139128.	−	139128.i	−1.29218	−	1.29218i	−0.933438	−	0.358738i	$-0.883207\pi$
$103$	−139128.	−	139128.i	−1.29218	−	1.29218i	−0.358738	−	0.933438i	$-0.616793\pi$
$104$		0			0
$105$	−103797.	−	6412.33i	−0.918776	−	0.0567601i
$106$		0			0
$107$	101354.	−	101354.i	0.855818	−	0.855818i	−0.135024	−	0.990842i	$-0.543111\pi$
$107$	101354.	−	101354.i	0.855818	−	0.855818i	0.990842	+	0.135024i	$0.0431112\pi$
$108$		0			0
$109$			27234.7i			0.219562i	0.993956	+	0.109781i	$0.0350149\pi$
$109$			27234.7i			0.219562i	−0.993956	+	0.109781i	$0.964985\pi$
$110$		0			0
$111$		−	177992.i		−	1.37118i
$112$		0			0
$113$	158778.	−	158778.i	1.16975	−	1.16975i	0.187484	−	0.982268i	$-0.439967\pi$
$113$	158778.	−	158778.i	1.16975	−	1.16975i	0.982268	−	0.187484i	$-0.0600332\pi$
$114$		0			0
$115$	44322.7	+	50159.7i	0.312523	+	0.353680i
$116$		0			0
$117$	−300532.	−	300532.i	−2.02967	−	2.02967i
$118$		0			0
$119$	−44843.7			−0.290291
$120$		0			0
$121$	144984.			0.900239
$122$		0			0
$123$	337178.	+	337178.i	2.00954	+	2.00954i
$124$		0			0
$125$	171709.	+	32151.0i	0.982918	+	0.184043i
$126$		0			0
$127$	192843.	−	192843.i	1.06095	−	1.06095i	0.0629291	−	0.998018i	$-0.479956\pi$
$127$	192843.	−	192843.i	1.06095	−	1.06095i	0.998018	−	0.0629291i	$-0.0200442\pi$
$128$		0			0
$129$		−	326409.i		−	1.72698i
$130$		0			0
$131$		−	66394.9i		−	0.338031i	−0.985613	−	0.169015i	$-0.945941\pi$
$131$		−	66394.9i		−	0.338031i	0.985613	−	0.169015i	$-0.0540588\pi$
$132$		0			0
$133$	−9615.06	+	9615.06i	−0.0471328	+	0.0471328i
$134$		0			0
$135$	−144734.	+	127892.i	−0.683497	+	0.603961i
$136$		0			0
$137$	125670.	+	125670.i	0.572045	+	0.572045i	0.932700	−	0.360654i	$-0.117447\pi$
$137$	125670.	+	125670.i	0.572045	+	0.572045i	−0.360654	+	0.932700i	$0.617447\pi$
$138$		0			0
$139$	293891.			1.29018			0.645089	−	0.764107i	$-0.276820\pi$
$139$	293891.			1.29018			0.645089	+	0.764107i	$0.276820\pi$
$140$		0			0
$141$	−656854.			−2.78241
$142$		0			0
$143$	99909.4	+	99909.4i	0.408570	+	0.408570i
$144$		0			0
$145$	−21292.4	+	344661.i	−0.0841019	+	1.36136i
$146$		0			0
$147$	−198997.	+	198997.i	−0.759543	+	0.759543i
$148$		0			0
$149$			313881.i			1.15824i	0.815242	+	0.579121i	$0.196604\pi$
$149$			313881.i			1.15824i	−0.815242	+	0.579121i	$0.803396\pi$
$150$		0			0
$151$		−	3773.26i		−	0.0134671i	−0.999977	−	0.00673355i	$-0.997857\pi$
$151$		−	3773.26i		−	0.0134671i	0.999977	−	0.00673355i	$-0.00214337\pi$
$152$		0			0
$153$	−162382.	+	162382.i	−0.560800	+	0.560800i
$154$		0			0
$155$	25385.0	−	410907.i	0.0848687	−	1.37377i
$156$		0			0
$157$	233723.	+	233723.i	0.756750	+	0.756750i	0.975729	−	0.218979i	$-0.0702728\pi$
$157$	233723.	+	233723.i	0.756750	+	0.756750i	−0.218979	+	0.975729i	$0.570273\pi$
$158$		0			0
$159$	240594.			0.754732
$160$		0			0
$161$	−89152.4			−0.271062
$162$		0			0
$163$	9013.04	+	9013.04i	0.0265707	+	0.0265707i	0.720267	−	0.693697i	$-0.244019\pi$
$163$	9013.04	+	9013.04i	0.0265707	+	0.0265707i	−0.693697	+	0.720267i	$0.744019\pi$
$164$		0			0
$165$	132669.	−	117230.i	0.379366	−	0.335220i
$166$		0			0
$167$	−143156.	+	143156.i	−0.397207	+	0.397207i	−0.877247	−	0.480040i	$-0.840622\pi$
$167$	−143156.	+	143156.i	−0.397207	+	0.397207i	0.480040	+	0.877247i	$0.340622\pi$
$168$		0			0
$169$		−	871273.i		−	2.34659i
$170$		0			0
$171$			69633.5i			0.182108i
$172$		0			0
$173$	−90907.6	+	90907.6i	−0.230932	+	0.230932i	−0.813082	−	0.582149i	$-0.802212\pi$
$173$	−90907.6	+	90907.6i	−0.230932	+	0.230932i	0.582149	+	0.813082i	$0.302212\pi$
$174$		0			0
$175$	−183524.	+	143023.i	−0.452999	+	0.353028i
$176$		0			0
$177$	830545.	+	830545.i	1.99265	+	1.99265i
$178$		0			0
$179$	−221965.			−0.517787			−0.258893	−	0.965906i	$-0.583358\pi$
$179$	−221965.			−0.517787			−0.258893	+	0.965906i	$0.583358\pi$
$180$		0			0
$181$	140962.			0.319819			0.159909	−	0.987132i	$-0.448880\pi$
$181$	140962.			0.319819			0.159909	+	0.987132i	$0.448880\pi$
$182$		0			0
$183$	253885.	+	253885.i	0.560415	+	0.560415i
$184$		0			0
$185$	−263694.	−	298420.i	−0.566462	−	0.641060i
$186$		0			0
$187$	53982.5	−	53982.5i	0.112888	−	0.112888i
$188$		0			0
$189$		−	257247.i		−	0.523836i
$190$		0			0
$191$		−	388949.i		−	0.771453i	−0.922613	−	0.385726i	$-0.873951\pi$
$191$		−	388949.i		−	0.771453i	0.922613	−	0.385726i	$-0.126049\pi$
$192$		0			0
$193$	−98208.1	+	98208.1i	−0.189782	+	0.189782i	−0.795602	−	0.605820i	$-0.792845\pi$
$193$	−98208.1	+	98208.1i	−0.189782	+	0.189782i	0.605820	+	0.795602i	$0.292845\pi$
$194$		0			0
$195$	−1.55399e6	−	96002.2i	−2.92659	−	0.180798i
$196$		0			0
$197$	60017.9	+	60017.9i	0.110183	+	0.110183i	0.760049	−	0.649866i	$-0.225175\pi$
$197$	60017.9	+	60017.9i	0.110183	+	0.110183i	−0.649866	+	0.760049i	$0.725175\pi$
$198$		0			0
$199$	−74339.7			−0.133072			−0.0665362	−	0.997784i	$-0.521195\pi$
$199$	−74339.7			−0.133072			−0.0665362	+	0.997784i	$0.521195\pi$
$200$		0			0
$201$	−1.07234e6			−1.87216
$202$		0			0
$203$	−325218.	−	325218.i	−0.553904	−	0.553904i
$204$		0			0
$205$	1.06484e6	+	65783.3i	1.76969	+	0.109328i
$206$		0			0
$207$	−322826.	+	322826.i	−0.523652	+	0.523652i
$208$		0			0
$209$		−	23149.1i		−	0.0366579i
$210$		0			0
$211$			143583.i			0.222023i	0.993819	+	0.111011i	$0.0354090\pi$
$211$			143583.i			0.222023i	−0.993819	+	0.111011i	$0.964591\pi$
$212$		0			0
$213$	777267.	−	777267.i	1.17387	−	1.17387i
$214$		0			0
$215$	−483571.	−	547253.i	−0.713451	−	0.807406i
$216$		0			0
$217$	387727.	+	387727.i	0.558954	+	0.558954i
$218$		0			0
$219$	−1.05371e6			−1.48460
$220$		0			0
$221$	−671376.			−0.924667
$222$		0			0
$223$	728700.	+	728700.i	0.981266	+	0.981266i	0.999828	−	0.0185618i	$-0.00590876\pi$
$223$	728700.	+	728700.i	0.981266	+	0.981266i	−0.0185618	+	0.999828i	$0.505909\pi$
$224$		0			0
$225$	−146658.	+	1.18244e6i	−0.193129	+	1.55713i
$226$		0			0
$227$	763824.	−	763824.i	0.983850	−	0.983850i	−0.0160217	−	0.999872i	$-0.505100\pi$
$227$	763824.	−	763824.i	0.983850	−	0.983850i	0.999872	+	0.0160217i	$0.00510008\pi$
$228$		0			0
$229$			724270.i			0.912666i	0.889809	+	0.456333i	$0.150837\pi$
$229$			724270.i			0.912666i	−0.889809	+	0.456333i	$0.849163\pi$
$230$		0			0
$231$			235802.i			0.290748i
$232$		0			0
$233$	−544324.	+	544324.i	−0.656853	+	0.656853i	−0.954634	−	0.297782i	$-0.903753\pi$
$233$	−544324.	+	544324.i	−0.656853	+	0.656853i	0.297782	+	0.954634i	$0.403753\pi$
$234$		0			0
$235$	−1.10127e6	+	973122.i	−1.30085	+	1.14947i
$236$		0			0
$237$	956094.	+	956094.i	1.10568	+	1.10568i
$238$		0			0
$239$	380807.			0.431231			0.215616	−	0.976478i	$-0.430824\pi$
$239$	380807.			0.431231			0.215616	+	0.976478i	$0.430824\pi$
$240$		0			0
$241$	431367.			0.478415			0.239207	−	0.970969i	$-0.423112\pi$
$241$	431367.			0.478415			0.239207	+	0.970969i	$0.423112\pi$
$242$		0			0
$243$	705414.	+	705414.i	0.766352	+	0.766352i
$244$		0			0
$245$	−38824.1	+	628447.i	−0.0413225	+	0.668888i
$246$		0			0
$247$	−143952.	+	143952.i	−0.150133	+	0.150133i
$248$		0			0
$249$			159270.i			0.162793i
$250$		0			0
$251$		−	611036.i		−	0.612185i	−0.952002	−	0.306093i	$-0.900978\pi$
$251$		−	611036.i		−	0.612185i	0.952002	−	0.306093i	$-0.0990217\pi$
$252$		0			0
$253$	107321.	−	107321.i	0.105410	−	0.105410i
$254$		0			0
$255$	−51871.3	+	839642.i	−0.0499548	+	0.808619i
$256$		0			0
$257$	−216982.	−	216982.i	−0.204923	−	0.204923i	0.597183	−	0.802105i	$-0.296287\pi$
$257$	−216982.	−	216982.i	−0.204923	−	0.204923i	−0.802105	+	0.597183i	$0.796287\pi$
$258$		0			0
$259$	530403.			0.491311
$260$		0			0
$261$	−2.35527e6			−2.14012
$262$		0			0
$263$	672935.	+	672935.i	0.599907	+	0.599907i	0.940288	−	0.340381i	$-0.110556\pi$
$263$	672935.	+	672935.i	0.599907	+	0.599907i	−0.340381	+	0.940288i	$0.610556\pi$
$264$		0			0
$265$	403378.	−	356438.i	0.352856	−	0.311795i
$266$		0			0
$267$	516486.	−	516486.i	0.443385	−	0.443385i
$268$		0			0
$269$			175979.i			0.148279i	0.997248	+	0.0741396i	$0.0236210\pi$
$269$			175979.i			0.148279i	−0.997248	+	0.0741396i	$0.976379\pi$
$270$		0			0
$271$		−	879491.i		−	0.727458i	−0.931505	−	0.363729i	$-0.881503\pi$
$271$		−	879491.i		−	0.727458i	0.931505	−	0.363729i	$-0.118497\pi$
$272$		0			0
$273$	1.46632e6	−	1.46632e6i	1.19076	−	1.19076i
$274$		0			0
$275$	48755.1	−	393094.i	0.0388766	−	0.313448i
$276$		0			0
$277$	−1.12427e6	−	1.12427e6i	−0.880379	−	0.880379i	0.113194	−	0.993573i	$-0.463892\pi$
$277$	−1.12427e6	−	1.12427e6i	−0.880379	−	0.880379i	−0.993573	+	0.113194i	$0.963892\pi$
$278$		0			0
$279$	2.80796e6			2.15964
$280$		0			0
$281$	−1.98398e6			−1.49889			−0.749447	−	0.662065i	$-0.769680\pi$
$281$	−1.98398e6			−1.49889			−0.749447	+	0.662065i	$0.769680\pi$
$282$		0			0
$283$	−81236.1	−	81236.1i	−0.0602952	−	0.0602952i	0.676316	−	0.736611i	$-0.263575\pi$
$283$	−81236.1	−	81236.1i	−0.0602952	−	0.0602952i	−0.736611	+	0.676316i	$0.763575\pi$
$284$		0			0
$285$	168908.	+	191152.i	0.123180	+	0.139401i
$286$		0			0
$287$	−1.00476e6	+	1.00476e6i	−0.720045	+	0.720045i
$288$		0			0
$289$		−	1.05710e6i		−	0.744514i
$290$		0			0
$291$		−	2.26050e6i		−	1.56485i
$292$		0			0
$293$	−733270.	+	733270.i	−0.498993	+	0.498993i	−0.911125	−	0.412131i	$-0.864785\pi$
$293$	−733270.	+	733270.i	−0.498993	+	0.498993i	0.412131	+	0.911125i	$0.364785\pi$
$294$		0			0
$295$	2.62293e6	+	162039.i	1.75481	+	0.108409i
$296$		0			0
$297$	309671.	+	309671.i	0.203709	+	0.203709i
$298$		0			0
$299$	−1.33474e6			−0.863416
$300$		0			0
$301$	972673.			0.618800
$302$		0			0
$303$	−403575.	−	403575.i	−0.252533	−	0.252533i
$304$		0			0
$305$	801788.	+	49532.8i	0.493526	+	0.0304890i
$306$		0			0
$307$	−1.76435e6	+	1.76435e6i	−1.06841	+	1.06841i	−0.0709334	+	0.997481i	$0.522598\pi$
$307$	−1.76435e6	+	1.76435e6i	−1.06841	+	1.06841i	−0.997481	+	0.0709334i	$0.977402\pi$
$308$		0			0
$309$		−	4.91609e6i		−	2.92903i
$310$		0			0
$311$		−	2.62297e6i		−	1.53778i	−0.639384	−	0.768888i	$-0.720811\pi$
$311$		−	2.62297e6i		−	1.53778i	0.639384	−	0.768888i	$-0.279189\pi$
$312$		0			0
$313$	1.63979e6	−	1.63979e6i	0.946078	−	0.946078i	−0.0525405	−	0.998619i	$-0.516732\pi$
$313$	1.63979e6	−	1.63979e6i	0.946078	−	0.946078i	0.998619	+	0.0525405i	$0.0167319\pi$
$314$		0			0
$315$	−1.05082e6	−	1.18921e6i	−0.596696	−	0.675275i
$316$		0			0
$317$	277809.	+	277809.i	0.155274	+	0.155274i	0.780469	−	0.625195i	$-0.214981\pi$
$317$	277809.	+	277809.i	0.155274	+	0.155274i	−0.625195	+	0.780469i	$0.714981\pi$
$318$		0			0
$319$	782990.			0.430804
$320$		0			0
$321$	3.58135e6			1.93992
$322$		0			0
$323$	77779.2	+	77779.2i	0.0414818	+	0.0414818i
$324$		0			0
$325$	−2.74762e6	+	2.14126e6i	−1.44294	+	1.12450i
$326$		0			0
$327$	−481169.	+	481169.i	−0.248845	+	0.248845i
$328$		0			0
$329$		−	1.95737e6i		−	0.996974i
$330$		0			0
$331$			1.46347e6i			0.734200i	0.930181	+	0.367100i	$0.119649\pi$
$331$			1.46347e6i			0.734200i	−0.930181	+	0.367100i	$0.880351\pi$
$332$		0			0
$333$	1.92062e6	−	1.92062e6i	0.949143	−	0.949143i
$334$		0			0
$335$	−1.79787e6	+	1.58866e6i	−0.875279	+	0.773425i
$336$		0			0
$337$	−2.31231e6	−	2.31231e6i	−1.10910	−	1.10910i	−0.993269	−	0.115833i	$-0.963046\pi$
$337$	−2.31231e6	−	2.31231e6i	−1.10910	−	1.10910i	−0.115833	−	0.993269i	$-0.536954\pi$
$338$		0			0
$339$	5.61041e6			2.65152
$340$		0			0
$341$	−933485.			−0.434732
$342$		0			0
$343$	−1.47785e6	−	1.47785e6i	−0.678256	−	0.678256i
$344$		0			0
$345$	−103124.	+	1.66927e6i	−0.0466457	+	0.755055i
$346$		0			0
$347$	63608.0	−	63608.0i	0.0283588	−	0.0283588i	−0.692785	−	0.721144i	$-0.743617\pi$
$347$	63608.0	−	63608.0i	0.0283588	−	0.0283588i	0.721144	+	0.692785i	$0.243617\pi$
$348$		0			0
$349$			124120.i			0.0545478i	0.999628	+	0.0272739i	$0.00868263\pi$
$349$			124120.i			0.0545478i	−0.999628	+	0.0272739i	$0.991317\pi$
$350$		0			0
$351$		−	3.85136e6i		−	1.66858i
$352$		0			0
$353$	−738449.	+	738449.i	−0.315416	+	0.315416i	−0.847003	−	0.531588i	$-0.821596\pi$
$353$	−738449.	+	738449.i	−0.315416	+	0.315416i	0.531588	+	0.847003i	$0.321596\pi$
$354$		0			0
$355$	151644.	−	2.45467e6i	0.0638639	−	1.03377i
$356$		0			0
$357$	−792276.	−	792276.i	−0.329007	−	0.329007i
$358$		0			0
$359$	1.18111e6			0.483674			0.241837	−	0.970317i	$-0.422250\pi$
$359$	1.18111e6			0.483674			0.241837	+	0.970317i	$0.422250\pi$
$360$		0			0
$361$	−2.44275e6			−0.986530
$362$		0			0
$363$	2.56151e6	+	2.56151e6i	1.02031	+	1.02031i
$364$		0			0
$365$	−1.76663e6	+	1.56105e6i	−0.694087	+	0.613318i
$366$		0			0
$367$	−2.49323e6	+	2.49323e6i	−0.966266	+	0.966266i	−0.999449	−	0.0331836i	$-0.989435\pi$
$367$	−2.49323e6	+	2.49323e6i	−0.966266	+	0.966266i	0.0331836	+	0.999449i	$0.489435\pi$
$368$		0			0
$369$			7.27663e6i			2.78205i
$370$		0			0
$371$			716952.i			0.270430i
$372$		0			0
$373$	738856.	−	738856.i	0.274971	−	0.274971i	−0.556126	−	0.831098i	$-0.687713\pi$
$373$	738856.	−	738856.i	0.274971	−	0.274971i	0.831098	+	0.556126i	$0.187713\pi$
$374$		0			0
$375$	2.46564e6	+	3.60169e6i	0.905422	+	1.32260i
$376$		0			0
$377$	−4.86900e6	−	4.86900e6i	−1.76436	−	1.76436i
$378$		0			0
$379$	−1.48357e6			−0.530531			−0.265265	−	0.964175i	$-0.585460\pi$
$379$	−1.48357e6			−0.530531			−0.265265	+	0.964175i	$0.585460\pi$
$380$		0			0
$381$	6.81410e6			2.40489
$382$		0			0
$383$	−1.85469e6	−	1.85469e6i	−0.646061	−	0.646061i	0.305978	−	0.952039i	$-0.401017\pi$
$383$	−1.85469e6	−	1.85469e6i	−0.646061	−	0.646061i	−0.952039	+	0.305978i	$0.901017\pi$
$384$		0			0
$385$	349337.	+	395342.i	0.120114	+	0.135932i
$386$		0			0
$387$	3.52211e6	−	3.52211e6i	1.19543	−	1.19543i
$388$		0			0
$389$		−	1.13185e6i		−	0.379241i	−0.981857	−	0.189620i	$-0.939274\pi$
$389$		−	1.13185e6i		−	0.379241i	0.981857	−	0.189620i	$-0.0607257\pi$
$390$		0			0
$391$			721181.i			0.238563i
$392$		0			0
$393$	1.17303e6	−	1.17303e6i	0.383115	−	0.383115i
$394$		0			0
$395$	3.01942e6	+	186533.i	0.973712	+	0.0601539i
$396$		0			0
$397$	2.88995e6	+	2.88995e6i	0.920266	+	0.920266i	0.997048	−	0.0767815i	$-0.0244644\pi$
$397$	2.88995e6	+	2.88995e6i	0.920266	+	0.920266i	−0.0767815	+	0.997048i	$0.524464\pi$
$398$		0			0
$399$	−339748.			−0.106838
$400$		0			0
$401$	−4.96166e6			−1.54087			−0.770435	−	0.637518i	$-0.779961\pi$
$401$	−4.96166e6			−1.54087			−0.770435	+	0.637518i	$0.779961\pi$
$402$		0			0
$403$	5.80484e6	+	5.80484e6i	1.78044	+	1.78044i
$404$		0			0
$405$	352893.	+	21801.0i	0.106907	+	0.00660448i
$406$		0			0
$407$	−638495.	+	638495.i	−0.191061	+	0.191061i
$408$		0			0
$409$			2.35258e6i			0.695403i	0.937605	+	0.347701i	$0.113038\pi$
$409$			2.35258e6i			0.695403i	−0.937605	+	0.347701i	$0.886962\pi$
$410$		0			0
$411$			4.44055e6i			1.29668i
$412$		0			0
$413$	−2.47496e6	+	2.47496e6i	−0.713991	+	0.713991i
$414$		0			0
$415$	235957.	+	267030.i	0.0672531	+	0.0761097i
$416$		0			0
$417$	5.19233e6	+	5.19233e6i	1.46225	+	1.46225i
$418$		0			0
$419$	−3.78569e6			−1.05344			−0.526720	−	0.850039i	$-0.676578\pi$
$419$	−3.78569e6			−1.05344			−0.526720	+	0.850039i	$0.676578\pi$
$420$		0			0
$421$	493431.			0.135682			0.0678409	−	0.997696i	$-0.478389\pi$
$421$	493431.			0.135682			0.0678409	+	0.997696i	$0.478389\pi$
$422$		0			0
$423$	−7.08777e6	−	7.08777e6i	−1.92601	−	1.92601i
$424$		0			0
$425$	1.15695e6	+	1.48458e6i	0.310702	+	0.398686i
$426$		0			0
$427$	−756557.	+	756557.i	−0.200804	+	0.200804i
$428$		0			0
$429$			3.53030e6i			0.926122i
$430$		0			0
$431$		−	6.01612e6i		−	1.56000i	−0.625782	−	0.779998i	$-0.715220\pi$
$431$		−	6.01612e6i		−	1.56000i	0.625782	−	0.779998i	$-0.284780\pi$
$432$		0			0
$433$	403708.	−	403708.i	0.103478	−	0.103478i	−0.653472	−	0.756950i	$-0.726688\pi$
$433$	403708.	−	403708.i	0.103478	−	0.103478i	0.756950	+	0.653472i	$0.226688\pi$
$434$		0			0
$435$	−6.46549e6	+	5.71312e6i	−1.63824	+	1.44761i
$436$		0			0
$437$	154631.	+	154631.i	0.0387339	+	0.0387339i
$438$		0			0
$439$	−5.33440e6			−1.32107			−0.660533	−	0.750797i	$-0.729670\pi$
$439$	−5.33440e6			−1.32107			−0.660533	+	0.750797i	$0.729670\pi$
$440$		0			0
$441$	−4.29454e6			−1.05153
$442$		0			0
$443$	−4.90768e6	−	4.90768e6i	−1.18814	−	1.18814i	−0.977582	−	0.210555i	$-0.932473\pi$
$443$	−4.90768e6	−	4.90768e6i	−1.18814	−	1.18814i	−0.210555	−	0.977582i	$-0.567527\pi$
$444$		0			0
$445$	100766.	−	1.63110e6i	0.0241221	−	0.390464i
$446$		0			0
$447$	−5.54549e6	+	5.54549e6i	−1.31272	+	1.31272i
$448$		0			0
$449$			2.34964e6i			0.550028i	0.961440	+	0.275014i	$0.0886825\pi$
$449$			2.34964e6i			0.550028i	−0.961440	+	0.275014i	$0.911317\pi$
$450$		0			0
$451$		−	2.41906e6i		−	0.560022i
$452$		0			0
$453$	66664.1	−	66664.1i	0.0152632	−	0.0152632i
$454$		0			0
$455$	286079.	−	4.63076e6i	0.0647824	−	1.04863i
$456$		0			0
$457$	−932235.	−	932235.i	−0.208802	−	0.208802i	0.594956	−	0.803758i	$-0.297169\pi$
$457$	−932235.	−	932235.i	−0.208802	−	0.208802i	−0.803758	+	0.594956i	$0.797169\pi$
$458$		0			0
$459$	−2.08095e6			−0.461030
$460$		0			0
$461$	2.63945e6			0.578444			0.289222	−	0.957262i	$-0.406603\pi$
$461$	2.63945e6			0.578444			0.289222	+	0.957262i	$0.406603\pi$
$462$		0			0
$463$	2.19784e6	+	2.19784e6i	0.476478	+	0.476478i	0.904003	−	0.427525i	$-0.140614\pi$
$463$	2.19784e6	+	2.19784e6i	0.476478	+	0.476478i	−0.427525	+	0.904003i	$0.640614\pi$
$464$		0			0
$465$	7.70819e6	−	6.81121e6i	1.65318	−	1.46080i
$466$		0			0
$467$	1.98654e6	−	1.98654e6i	0.421507	−	0.421507i	−0.464215	−	0.885722i	$-0.653664\pi$
$467$	1.98654e6	−	1.98654e6i	0.421507	−	0.421507i	0.885722	+	0.464215i	$0.153664\pi$
$468$		0			0
$469$		−	3.19549e6i		−	0.670818i
$470$		0			0
$471$			8.25861e6i			1.71536i
$472$		0			0
$473$	−1.17090e6	+	1.17090e6i	−0.240639	+	0.240639i
$474$		0			0
$475$	566379.	+	70247.5i	0.115179	+	0.0142856i
$476$		0			0
$477$	2.59613e6	+	2.59613e6i	0.522433	+	0.522433i
$478$		0			0
$479$	−1.44223e6			−0.287207			−0.143603	−	0.989635i	$-0.545869\pi$
$479$	−1.44223e6			−0.287207			−0.143603	+	0.989635i	$0.545869\pi$
$480$		0			0
$481$	7.94092e6			1.56498
$482$		0			0
$483$	−1.57510e6	−	1.57510e6i	−0.307214	−	0.307214i
$484$		0			0
$485$	−3.34891e6	−	3.78993e6i	−0.646470	−	0.731605i
$486$		0			0
$487$	−2.25125e6	+	2.25125e6i	−0.430132	+	0.430132i	−0.888673	−	0.458541i	$-0.848372\pi$
$487$	−2.25125e6	+	2.25125e6i	−0.430132	+	0.430132i	0.458541	+	0.888673i	$0.348372\pi$
$488$		0			0
$489$			318476.i			0.0602288i
$490$		0			0
$491$			7.62831e6i			1.42799i	0.700152	+	0.713994i	$0.253116\pi$
$491$			7.62831e6i			1.42799i	−0.700152	+	0.713994i	$0.746884\pi$
$492$		0			0
$493$	−2.63079e6	+	2.63079e6i	−0.487493	+	0.487493i
$494$		0			0
$495$	2.69653e6	+	166586.i	0.494643	+	0.0305580i
$496$		0			0
$497$	2.31619e6	+	2.31619e6i	0.420614	+	0.420614i
$498$		0			0
$499$	−2.96923e6			−0.533817			−0.266909	−	0.963722i	$-0.586002\pi$
$499$	−2.96923e6			−0.533817			−0.266909	+	0.963722i	$0.586002\pi$
$500$		0			0
$501$	−5.05840e6			−0.900366
$502$		0			0
$503$	−567671.	−	567671.i	−0.100041	−	0.100041i	0.655315	−	0.755356i	$-0.272536\pi$
$503$	−567671.	−	567671.i	−0.100041	−	0.100041i	−0.755356	+	0.655315i	$0.772536\pi$
$504$		0			0
$505$	−1.27452e6	−	78737.1i	−0.222391	−	0.0137389i
$506$		0			0
$507$	1.53932e7	−	1.53932e7i	2.65956	−	2.65956i
$508$		0			0
$509$		−	2.85991e6i		−	0.489281i	−0.969614	−	0.244641i	$-0.921330\pi$
$509$		−	2.85991e6i		−	0.489281i	0.969614	−	0.244641i	$-0.0786700\pi$
$510$		0			0
$511$		−	3.13996e6i		−	0.531951i
$512$		0			0
$513$	−446182.	+	446182.i	−0.0748546	+	0.0748546i
$514$		0			0
$515$	−7.28314e6	−	8.24226e6i	−1.21004	−	1.36939i
$516$		0			0
$517$	2.35627e6	+	2.35627e6i	0.387703	+	0.387703i
$518$		0			0
$519$	−3.21222e6			−0.523464
$520$		0			0
$521$	4.13972e6			0.668153			0.334077	−	0.942546i	$-0.391576\pi$
$521$	4.13972e6			0.668153			0.334077	+	0.942546i	$0.391576\pi$
$522$		0			0
$523$	5.29293e6	+	5.29293e6i	0.846140	+	0.846140i	0.989649	−	0.143509i	$-0.0458386\pi$
$523$	5.29293e6	+	5.29293e6i	0.846140	+	0.846140i	−0.143509	+	0.989649i	$0.545839\pi$
$524$		0			0
$525$	−5.76926e6	−	715557.i	−0.913528	−	0.113304i
$526$		0			0
$527$	3.13644e6	−	3.13644e6i	0.491938	−	0.491938i
$528$		0			0
$529$		−	5.00258e6i		−	0.777240i
$530$		0			0
$531$			1.79240e7i			2.75866i
$532$		0			0
$533$	−1.50428e7	+	1.50428e7i	−2.29357	+	2.29357i
$534$		0			0
$535$	6.00444e6	−	5.30572e6i	0.906960	−	0.801420i
$536$		0			0
$537$	−3.92156e6	−	3.92156e6i	−0.586845	−	0.586845i
$538$		0			0
$539$	1.42768e6			0.211670
$540$		0			0
$541$	3.33385e6			0.489725			0.244863	−	0.969558i	$-0.421257\pi$
$541$	3.33385e6			0.489725			0.244863	+	0.969558i	$0.421257\pi$
$542$		0			0
$543$	2.49044e6	+	2.49044e6i	0.362473	+	0.362473i
$544$		0			0
$545$	−93875.8	+	1.51957e6i	−0.0135382	+	0.219144i
$546$		0			0
$547$	−3.13742e6	+	3.13742e6i	−0.448337	+	0.448337i	−0.894801	−	0.446464i	$-0.852683\pi$
$547$	−3.13742e6	+	3.13742e6i	−0.448337	+	0.448337i	0.446464	+	0.894801i	$0.352683\pi$
$548$		0			0
$549$			5.47908e6i			0.775848i
$550$		0			0
$551$			1.12815e6i			0.158303i
$552$		0			0
$553$	−2.84908e6	+	2.84908e6i	−0.396180	+	0.396180i
$554$		0			0
$555$	613525.	−	9.93115e6i	0.0845474	−	1.36857i
$556$		0			0
$557$	−4.40791e6	−	4.40791e6i	−0.601998	−	0.601998i	0.338844	−	0.940842i	$-0.389964\pi$
$557$	−4.40791e6	−	4.40791e6i	−0.601998	−	0.601998i	−0.940842	+	0.338844i	$0.889964\pi$
$558$		0			0
$559$	1.45624e7			1.97107
$560$		0			0
$561$	1.90747e6			0.255888
$562$		0			0
$563$	7.23390e6	+	7.23390e6i	0.961837	+	0.961837i	0.999298	−	0.0374610i	$-0.0119270\pi$
$563$	7.23390e6	+	7.23390e6i	0.961837	+	0.961837i	−0.0374610	+	0.999298i	$0.511927\pi$
$564$		0			0
$565$	9.40635e6	−	8.31176e6i	1.23965	−	1.09540i
$566$		0			0
$567$	−332985.	+	332985.i	−0.0434978	+	0.0434978i
$568$		0			0
$569$			4.13369e6i			0.535251i	0.963523	+	0.267625i	$0.0862389\pi$
$569$			4.13369e6i			0.535251i	−0.963523	+	0.267625i	$0.913761\pi$
$570$		0			0
$571$			1.46263e7i			1.87735i	0.344805	+	0.938674i	$0.387945\pi$
$571$			1.46263e7i			1.87735i	−0.344805	+	0.938674i	$0.612055\pi$
$572$		0			0
$573$	6.87176e6	−	6.87176e6i	0.874342	−	0.874342i
$574$		0			0
$575$	2.30011e6	+	2.95145e6i	0.290120	+	0.372277i
$576$		0			0
$577$	5.95323e6	+	5.95323e6i	0.744412	+	0.744412i	0.973424	−	0.229012i	$-0.0735494\pi$
$577$	5.95323e6	+	5.95323e6i	0.744412	+	0.744412i	−0.229012	+	0.973424i	$0.573549\pi$
$578$		0			0
$579$	−3.47019e6			−0.430186
$580$		0			0
$581$	−474612.			−0.0583309
$582$		0			0
$583$	−863062.	−	863062.i	−0.105165	−	0.105165i
$584$		0			0
$585$	−1.57324e7	−	1.78042e7i	−1.90066	−	2.15096i
$586$		0			0
$587$	7.70795e6	−	7.70795e6i	0.923302	−	0.923302i	−0.0739594	−	0.997261i	$-0.523564\pi$
$587$	7.70795e6	−	7.70795e6i	0.923302	−	0.923302i	0.997261	+	0.0739594i	$0.0235635\pi$
$588$		0			0
$589$		−	1.34499e6i		−	0.159746i
$590$		0			0
$591$			2.12073e6i			0.249757i
$592$		0			0
$593$	−6.05514e6	+	6.05514e6i	−0.707111	+	0.707111i	−0.965927	−	0.258816i	$-0.916668\pi$
$593$	−6.05514e6	+	6.05514e6i	−0.707111	+	0.707111i	0.258816	+	0.965927i	$0.416668\pi$
$594$		0			0
$595$	−2.50207e6	−	154572.i	−0.289739	−	0.0178994i
$596$		0			0
$597$	−1.31340e6	−	1.31340e6i	−0.150820	−	0.150820i
$598$		0			0
$599$	−1.44521e7			−1.64575			−0.822873	−	0.568225i	$-0.807630\pi$
$599$	−1.44521e7			−1.64575			−0.822873	+	0.568225i	$0.807630\pi$
$600$		0			0
$601$	1.40388e6			0.158542			0.0792709	−	0.996853i	$-0.474741\pi$
$601$	1.40388e6			0.158542			0.0792709	+	0.996853i	$0.474741\pi$
$602$		0			0
$603$	−1.15711e7	−	1.15711e7i	−1.29592	−	1.29592i
$604$		0			0
$605$	8.08945e6	+	499749.i	0.898526	+	0.0555091i
$606$		0			0
$607$	9.99295e6	−	9.99295e6i	1.10083	−	1.10083i	0.106524	−	0.994310i	$-0.466028\pi$
$607$	9.99295e6	−	9.99295e6i	1.10083	−	1.10083i	0.994310	−	0.106524i	$-0.0339722\pi$
$608$		0			0
$609$		−	1.14916e7i		−	1.25556i
$610$		0			0
$611$		−	2.93048e7i		−	3.17567i
$612$		0			0
$613$	7.92200e6	−	7.92200e6i	0.851498	−	0.851498i	−0.138819	−	0.990318i	$-0.544331\pi$
$613$	7.92200e6	−	7.92200e6i	0.851498	−	0.851498i	0.990318	+	0.138819i	$0.0443308\pi$
$614$		0			0
$615$	1.76508e7	+	1.99752e7i	1.88181	+	2.12963i
$616$		0			0
$617$	−2.56228e6	−	2.56228e6i	−0.270966	−	0.270966i	0.558523	−	0.829489i	$-0.311368\pi$
$617$	−2.56228e6	−	2.56228e6i	−0.270966	−	0.270966i	−0.829489	+	0.558523i	$0.811368\pi$
$618$		0			0
$619$	−1.02661e7			−1.07691			−0.538455	−	0.842654i	$-0.680992\pi$
$619$	−1.02661e7			−1.07691			−0.538455	+	0.842654i	$0.680992\pi$
$620$		0			0
$621$	−4.13707e6			−0.430491
$622$		0			0
$623$	1.53909e6	+	1.53909e6i	0.158871	+	0.158871i
$624$		0			0
$625$	9.46972e6	+	2.38574e6i	0.969700	+	0.244300i
$626$		0			0
$627$	408987.	−	408987.i	0.0415471	−	0.0415471i
$628$		0			0
$629$		−	4.29059e6i		−	0.432405i
$630$		0			0
$631$			2.42221e6i			0.242180i	0.992642	+	0.121090i	$0.0386390\pi$
$631$			2.42221e6i			0.242180i	−0.992642	+	0.121090i	$0.961361\pi$
$632$		0			0
$633$	−2.53676e6	+	2.53676e6i	−0.251634	+	0.251634i
$634$		0			0
$635$	1.14244e7	−	1.00950e7i	1.12435	−	0.993510i
$636$		0			0
$637$	−8.87800e6	−	8.87800e6i	−0.866896	−	0.866896i
$638$		0			0
$639$	1.67742e7			1.62513
$640$		0			0
$641$	−9.07452e6			−0.872325			−0.436163	−	0.899868i	$-0.643663\pi$
$641$	−9.07452e6			−0.872325			−0.436163	+	0.899868i	$0.643663\pi$
$642$		0			0
$643$	−7.74038e6	−	7.74038e6i	−0.738303	−	0.738303i	0.233946	−	0.972250i	$-0.424836\pi$
$643$	−7.74038e6	−	7.74038e6i	−0.738303	−	0.738303i	−0.972250	+	0.233946i	$0.924836\pi$
$644$		0			0
$645$	1.12510e6	−	1.82121e7i	0.106486	−	1.72370i
$646$		0			0
$647$	683707.	−	683707.i	0.0642110	−	0.0642110i	−0.674272	−	0.738483i	$-0.735542\pi$
$647$	683707.	−	683707.i	0.0642110	−	0.0642110i	0.738483	+	0.674272i	$0.235542\pi$
$648$		0			0
$649$		−	5.95867e6i		−	0.555313i
$650$		0			0
$651$			1.37003e7i			1.26701i
$652$		0			0
$653$	1.18520e7	−	1.18520e7i	1.08770	−	1.08770i	0.0919388	−	0.995765i	$-0.470694\pi$
$653$	1.18520e7	−	1.18520e7i	1.08770	−	1.08770i	0.995765	−	0.0919388i	$-0.0293064\pi$
$654$		0			0
$655$	228858.	−	3.70453e6i	0.0208431	−	0.337388i
$656$		0			0
$657$	−1.13700e7	−	1.13700e7i	−1.02765	−	1.02765i
$658$		0			0
$659$	−1.10305e7			−0.989420			−0.494710	−	0.869058i	$-0.664726\pi$
$659$	−1.10305e7			−0.989420			−0.494710	+	0.869058i	$0.664726\pi$
$660$		0			0
$661$	1.25394e7			1.11628			0.558139	−	0.829747i	$-0.311516\pi$
$661$	1.25394e7			1.11628			0.558139	+	0.829747i	$0.311516\pi$
$662$		0			0
$663$	−1.18615e7	−	1.18615e7i	−1.04799	−	1.04799i
$664$		0			0
$665$	−569618.	+	503333.i	−0.0499493	+	0.0441369i
$666$		0			0
$667$	−5.23019e6	+	5.23019e6i	−0.455201	+	0.455201i
$668$		0			0
$669$			2.57486e7i			2.22428i
$670$		0			0
$671$		−	1.82148e6i		−	0.156177i
$672$		0			0
$673$	−1.00955e7	+	1.00955e7i	−0.859191	+	0.859191i	−0.991243	−	0.132052i	$-0.957843\pi$
$673$	−1.00955e7	+	1.00955e7i	−0.859191	+	0.859191i	0.132052	+	0.991243i	$0.457843\pi$
$674$		0			0
$675$	−8.51632e6	+	6.63688e6i	−0.719437	+	0.560667i
$676$		0			0
$677$	−6.31095e6	−	6.31095e6i	−0.529204	−	0.529204i	0.391131	−	0.920335i	$-0.372084\pi$
$677$	−6.31095e6	−	6.31095e6i	−0.529204	−	0.529204i	−0.920335	+	0.391131i	$0.872084\pi$
$678$		0			0
$679$	6.73611e6			0.560706
$680$		0			0
$681$	2.69897e7			2.23013
$682$		0			0
$683$	115205.	+	115205.i	0.00944977	+	0.00944977i	0.711816	−	0.702366i	$-0.247873\pi$
$683$	115205.	+	115205.i	0.00944977	+	0.00944977i	−0.702366	+	0.711816i	$0.747873\pi$
$684$		0			0
$685$	6.57863e6	+	7.44497e6i	0.535684	+	0.606229i
$686$		0			0
$687$	−1.27960e7	+	1.27960e7i	−1.03439	+	1.03439i
$688$		0			0
$689$			1.07338e7i			0.861404i
$690$		0			0
$691$			5.13607e6i			0.409200i	0.978846	+	0.204600i	$0.0655894\pi$
$691$			5.13607e6i			0.409200i	−0.978846	+	0.204600i	$0.934411\pi$
$692$		0			0
$693$	−2.54441e6	+	2.54441e6i	−0.201258	+	0.201258i
$694$		0			0
$695$	1.63978e7	+	1.01302e6i	1.28772	+	0.0795528i
$696$		0			0
$697$	8.12785e6	+	8.12785e6i	0.633715	+	0.633715i
$698$		0			0
$699$	−1.92337e7			−1.48892
$700$		0			0
$701$	−2.10359e6			−0.161684			−0.0808420	−	0.996727i	$-0.525761\pi$
$701$	−2.10359e6			−0.161684			−0.0808420	+	0.996727i	$0.525761\pi$
$702$		0			0
$703$	−919959.	−	919959.i	−0.0702070	−	0.0702070i
$704$		0			0
$705$	−3.66494e7	−	2.26412e6i	−2.77712	−	0.171564i
$706$		0			0
$707$	1.20262e6	−	1.20262e6i	0.0904857	−	0.0904857i
$708$		0			0
$709$			1.53118e7i			1.14396i	0.820269	+	0.571978i	$0.193824\pi$
$709$			1.53118e7i			1.14396i	−0.820269	+	0.571978i	$0.806176\pi$
$710$		0			0
$711$			2.06334e7i			1.53072i
$712$		0			0
$713$	6.23546e6	−	6.23546e6i	0.459351	−	0.459351i
$714$		0			0
$715$	5.23010e6	+	5.91886e6i	0.382600	+	0.432985i
$716$		0			0
$717$	6.72791e6	+	6.72791e6i	0.488745	+	0.488745i
$718$		0			0
$719$	8.69010e6			0.626906			0.313453	−	0.949604i	$-0.398514\pi$
$719$	8.69010e6			0.626906			0.313453	+	0.949604i	$0.398514\pi$
$720$		0			0
$721$	1.46496e7			1.04951
$722$		0			0
$723$	7.62118e6	+	7.62118e6i	0.542221	+	0.542221i
$724$		0			0
$725$	−2.37604e6	+	1.91571e7i	−0.167884	+	1.35358i
$726$		0			0
$727$	8.46369e6	−	8.46369e6i	0.593914	−	0.593914i	−0.344772	−	0.938686i	$-0.612044\pi$
$727$	8.46369e6	−	8.46369e6i	0.593914	−	0.593914i	0.938686	+	0.344772i	$0.112044\pi$
$728$		0			0
$729$			2.33889e7i			1.63001i
$730$		0			0
$731$		−	7.86825e6i		−	0.544609i
$732$		0			0
$733$	−1.56579e7	+	1.56579e7i	−1.07640	+	1.07640i	−0.0795729	+	0.996829i	$0.525356\pi$
$733$	−1.56579e7	+	1.56579e7i	−1.07640	+	1.07640i	−0.996829	+	0.0795729i	$0.974644\pi$
$734$		0			0
$735$	−1.17890e7	+	1.04172e7i	−0.804932	+	0.711264i
$736$		0			0
$737$	3.84670e6	+	3.84670e6i	0.260867	+	0.260867i
$738$		0			0
$739$	6.96566e6			0.469192			0.234596	−	0.972093i	$-0.424623\pi$
$739$	6.96566e6			0.469192			0.234596	+	0.972093i	$0.424623\pi$
$740$		0			0
$741$	−5.08654e6			−0.340312
$742$		0			0
$743$	−6.71433e6	−	6.71433e6i	−0.446201	−	0.446201i	0.447888	−	0.894090i	$-0.352176\pi$
$743$	−6.71433e6	−	6.71433e6i	−0.446201	−	0.446201i	−0.894090	+	0.447888i	$0.852176\pi$
$744$		0			0
$745$	−1.08192e6	+	1.75131e7i	−0.0714176	+	1.15604i
$746$		0			0
$747$	−1.71860e6	+	1.71860e6i	−0.112687	+	0.112687i
$748$		0			0
$749$			1.06721e7i			0.695099i
$750$		0			0
$751$		−	1.73970e7i		−	1.12558i	−0.826601	−	0.562789i	$-0.809728\pi$
$751$		−	1.73970e7i		−	1.12558i	0.826601	−	0.562789i	$-0.190272\pi$
$752$		0			0
$753$	1.07955e7	−	1.07955e7i	0.693833	−	0.693833i
$754$		0			0
$755$	13006.1	−	210530.i	0.000830386	−	0.0134415i
$756$		0			0
$757$	−2.16918e7	−	2.16918e7i	−1.37580	−	1.37580i	−0.851587	−	0.524213i	$-0.824359\pi$
$757$	−2.16918e7	−	2.16918e7i	−1.37580	−	1.37580i	−0.524213	−	0.851587i	$-0.675641\pi$
$758$		0			0
$759$	3.79219e6			0.238938
$760$		0			0
$761$	1.96872e7			1.23231			0.616157	−	0.787623i	$-0.288689\pi$
$761$	1.96872e7			1.23231			0.616157	+	0.787623i	$0.288689\pi$
$762$		0			0
$763$	−1.43385e6	−	1.43385e6i	−0.0891643	−	0.0891643i
$764$		0			0
$765$	−9.61985e6	+	8.50042e6i	−0.594313	+	0.525154i
$766$		0			0
$767$	−3.70538e7	+	3.70538e7i	−2.27428	+	2.27428i
$768$		0			0
$769$		−	2.75928e7i		−	1.68260i	−0.540569	−	0.841299i	$-0.681791\pi$
$769$		−	2.75928e7i		−	1.68260i	0.540569	−	0.841299i	$-0.318209\pi$
$770$		0			0
$771$		−	7.66705e6i		−	0.464507i
$772$		0			0
$773$	3.16964e6	−	3.16964e6i	0.190792	−	0.190792i	−0.605246	−	0.796038i	$-0.706925\pi$
$773$	3.16964e6	−	3.16964e6i	0.190792	−	0.190792i	0.796038	+	0.605246i	$0.206925\pi$
$774$		0			0
$775$	2.83273e6	−	2.28392e7i	0.169414	−	1.36592i
$776$		0			0
$777$	9.37090e6	+	9.37090e6i	0.556838	+	0.556838i
$778$		0			0
$779$	3.48543e6			0.205785
$780$		0			0
$781$	−5.57643e6			−0.327136
$782$		0			0
$783$	−1.50916e7	−	1.50916e7i	−0.879690	−	0.879690i
$784$		0			0
$785$	1.22350e7	+	1.38463e7i	0.708649	+	0.801972i
$786$		0			0
$787$	−3.86812e6	+	3.86812e6i	−0.222619	+	0.222619i	−0.809601	−	0.586981i	$-0.800316\pi$
$787$	−3.86812e6	+	3.86812e6i	−0.222619	+	0.222619i	0.586981	+	0.809601i	$0.300316\pi$
$788$		0			0
$789$			2.37782e7i			1.35983i
$790$		0			0
$791$			1.67186e7i			0.950076i
$792$		0			0
$793$	−1.13268e7	+	1.13268e7i	−0.639622	+	0.639622i
$794$		0			0
$795$	1.34240e7	+	829309.i	0.753296	+	0.0465370i
$796$		0			0
$797$	−8.96589e6	−	8.96589e6i	−0.499974	−	0.499974i	0.411456	−	0.911430i	$-0.365021\pi$
$797$	−8.96589e6	−	8.96589e6i	−0.499974	−	0.499974i	−0.911430	+	0.411456i	$0.865021\pi$
$798$		0			0
$799$	−1.58338e7			−0.877441
$800$		0			0
$801$	1.11463e7			0.613830
$802$		0			0
$803$	3.77986e6	+	3.77986e6i	0.206865	+	0.206865i
$804$		0			0
$805$	−4.97429e6	−	307301.i	−0.270546	−	0.0167138i
$806$		0			0
$807$	−3.10911e6	+	3.10911e6i	−0.168055	+	0.168055i
$808$		0			0
$809$		−	2.38416e7i		−	1.28075i	−0.768064	−	0.640373i	$-0.778780\pi$
$809$		−	2.38416e7i		−	1.28075i	0.768064	−	0.640373i	$-0.221220\pi$
$810$		0			0
$811$			2.52576e7i			1.34847i	0.738518	+	0.674234i	$0.235526\pi$
$811$			2.52576e7i			1.34847i	−0.738518	+	0.674234i	$0.764474\pi$
$812$		0			0
$813$	1.55384e7	−	1.55384e7i	0.824480	−	0.824480i
$814$		0			0
$815$	471818.	+	533953.i	0.0248817	+	0.0281584i
$816$		0			0
$817$	−1.68705e6	−	1.68705e6i	−0.0884248	−	0.0884248i
$818$		0			0
$819$	3.16447e7			1.64851
$820$		0			0
$821$	3.30250e7			1.70995			0.854977	−	0.518666i	$-0.173571\pi$
$821$	3.30250e7			1.70995			0.854977	+	0.518666i	$0.173571\pi$
$822$		0			0
$823$	−1.04816e6	−	1.04816e6i	−0.0539424	−	0.0539424i	0.679621	−	0.733563i	$-0.262144\pi$
$823$	−1.04816e6	−	1.04816e6i	−0.0539424	−	0.0539424i	−0.733563	+	0.679621i	$0.762144\pi$
$824$		0			0
$825$	7.80637e6	−	6.08361e6i	0.399314	−	0.311191i
$826$		0			0
$827$	−1.58868e7	+	1.58868e7i	−0.807742	+	0.807742i	−0.984292	−	0.176550i	$-0.943506\pi$
$827$	−1.58868e7	+	1.58868e7i	−0.807742	+	0.807742i	0.176550	+	0.984292i	$0.443506\pi$
$828$		0			0
$829$		−	2.53047e7i		−	1.27884i	−0.768859	−	0.639419i	$-0.779175\pi$
$829$		−	2.53047e7i		−	1.27884i	0.768859	−	0.639419i	$-0.220825\pi$
$830$		0			0
$831$		−	3.97260e7i		−	1.99559i
$832$		0			0
$833$	−4.79691e6	+	4.79691e6i	−0.239524	+	0.239524i
$834$		0			0
$835$	−8.48085e6	+	7.49396e6i	−0.420943	+	0.371959i
$836$		0			0
$837$	1.79922e7	+	1.79922e7i	0.887711	+	0.887711i
$838$		0			0
$839$	−2.80653e7			−1.37647			−0.688233	−	0.725490i	$-0.741613\pi$
$839$	−2.80653e7			−1.37647			−0.688233	+	0.725490i	$0.741613\pi$
$840$		0			0
$841$	−1.76472e7			−0.860369
$842$		0			0
$843$	−3.50519e7	−	3.50519e7i	−1.69880	−	1.69880i
$844$		0			0
$845$	3.00321e6	−	4.86130e7i	0.144692	−	2.34213i
$846$		0			0
$847$	−7.63311e6	+	7.63311e6i	−0.365589	+	0.365589i
$848$		0			0
$849$		−	2.87048e6i		−	0.136674i
$850$		0			0
$851$		−	8.53001e6i		−	0.403762i
$852$		0			0
$853$	−2.10361e7	+	2.10361e7i	−0.989905	+	0.989905i	−0.999950	−	0.0100448i	$-0.996803\pi$
$853$	−2.10361e7	+	2.10361e7i	−0.989905	+	0.989905i	0.0100448	+	0.999950i	$0.496803\pi$
$854$		0			0
$855$	−240021.	+	3.88522e6i	−0.0112288	+	0.181761i
$856$		0			0
$857$	1.03841e7	+	1.03841e7i	0.482968	+	0.482968i	0.906078	−	0.423110i	$-0.139062\pi$
$857$	1.03841e7	+	1.03841e7i	0.482968	+	0.482968i	−0.423110	+	0.906078i	$0.639062\pi$
$858$		0			0
$859$	−2.10934e7			−0.975358			−0.487679	−	0.873023i	$-0.662156\pi$
$859$	−2.10934e7			−0.975358			−0.487679	+	0.873023i	$0.662156\pi$
$860$		0			0
$861$	−3.55034e7			−1.63216
$862$		0			0
$863$	2.17573e7	+	2.17573e7i	0.994441	+	0.994441i	0.999985	−	0.00554382i	$-0.00176466\pi$
$863$	2.17573e7	+	2.17573e7i	0.994441	+	0.994441i	−0.00554382	+	0.999985i	$0.501765\pi$
$864$		0			0
$865$	−5.38557e6	+	4.75887e6i	−0.244732	+	0.216254i
$866$		0			0
$867$	1.86764e7	−	1.86764e7i	0.843810	−	0.843810i
$868$		0			0
$869$		−	6.85941e6i		−	0.308132i
$870$		0			0
$871$		−	4.78412e7i		−	2.13676i
$872$		0			0
$873$	2.43919e7	−	2.43919e7i	1.08320	−	1.08320i
$874$		0			0
$875$	−1.07328e7	+	7.34740e6i	−0.473905	+	0.324424i
$876$		0			0
$877$	3.30759e6	+	3.30759e6i	0.145216	+	0.145216i	0.775977	−	0.630761i	$-0.217257\pi$
$877$	3.30759e6	+	3.30759e6i	0.145216	+	0.145216i	−0.630761	+	0.775977i	$0.717257\pi$
$878$		0			0
$879$	−2.59101e7			−1.13109
$880$		0			0
$881$	−2.18920e7			−0.950265			−0.475133	−	0.879914i	$-0.657600\pi$
$881$	−2.18920e7			−0.950265			−0.475133	+	0.879914i	$0.657600\pi$
$882$		0			0
$883$	1.07511e7	+	1.07511e7i	0.464037	+	0.464037i	0.899976	−	0.435939i	$-0.143584\pi$
$883$	1.07511e7	+	1.07511e7i	0.464037	+	0.464037i	−0.435939	+	0.899976i	$0.643584\pi$
$884$		0			0
$885$	4.34777e7	+	4.92034e7i	1.86599	+	2.11172i
$886$		0			0
$887$	1.49586e7	−	1.49586e7i	0.638385	−	0.638385i	−0.311772	−	0.950157i	$-0.600923\pi$
$887$	1.49586e7	−	1.49586e7i	0.638385	−	0.638385i	0.950157	+	0.311772i	$0.100923\pi$
$888$		0			0
$889$			2.03055e7i			0.861705i
$890$		0			0
$891$		−	801691.i		−	0.0338308i
$892$		0			0
$893$	−3.39497e6	+	3.39497e6i	−0.142465	+	0.142465i
$894$		0			0
$895$	−1.23846e7	−	765094.i	−0.516802	−	0.0319269i
$896$		0			0
$897$	−2.35816e7	−	2.35816e7i	−0.978570	−	0.978570i
$898$		0			0
$899$	4.54926e7			1.87733
$900$		0			0
$901$	5.79965e6			0.238007
$902$		0			0
$903$	1.71847e7	+	1.71847e7i	0.701330	+	0.701330i
$904$		0			0
$905$	7.86499e6	+	485883.i	0.319210	+	0.0197201i
$906$		0			0
$907$	−5.85030e6	+	5.85030e6i	−0.236135	+	0.236135i	−0.815247	−	0.579113i	$-0.803399\pi$
$907$	−5.85030e6	+	5.85030e6i	−0.236135	+	0.236135i	0.579113	+	0.815247i	$0.303399\pi$
$908$		0			0
$909$		−	8.70953e6i		−	0.349611i
$910$		0			0
$911$			3.90512e7i			1.55897i	0.626420	+	0.779486i	$0.284519\pi$
$911$			3.90512e7i			1.55897i	−0.626420	+	0.779486i	$0.715481\pi$
$912$		0			0
$913$	571335.	−	571335.i	0.0226837	−	0.0226837i
$914$		0			0
$915$	1.32905e7	+	1.50407e7i	0.524793	+	0.593904i
$916$		0			0
$917$	3.49554e6	+	3.49554e6i	0.137275	+	0.137275i
$918$		0			0
$919$	7.28180e6			0.284413			0.142207	−	0.989837i	$-0.454580\pi$
$919$	7.28180e6			0.284413			0.142207	+	0.989837i	$0.454580\pi$
$920$		0			0
$921$	−6.23435e7			−2.42182
$922$		0			0
$923$	3.46769e7	+	3.46769e7i	1.33979	+	1.33979i
$924$		0			0
$925$	−1.36842e7	−	1.75594e7i	−0.525856	−	0.674768i
$926$		0			0
$927$	5.30470e7	−	5.30470e7i	2.02750	−	2.02750i
$928$		0			0
$929$			1.45942e7i			0.554805i	0.960754	+	0.277403i	$0.0894736\pi$
$929$			1.45942e7i			0.554805i	−0.960754	+	0.277403i	$0.910526\pi$
$930$		0			0
$931$			2.05704e6i			0.0777801i
$932$		0			0
$933$	4.63414e7	−	4.63414e7i	1.74287	−	1.74287i
$934$		0			0
$935$	3.19804e6	−	2.82590e6i	0.119634	−	0.105713i
$936$		0			0
$937$	2.28643e6	+	2.28643e6i	0.0850765	+	0.0850765i	0.748364	−	0.663288i	$-0.230839\pi$
$937$	2.28643e6	+	2.28643e6i	0.0850765	+	0.0850765i	−0.663288	+	0.748364i	$0.730839\pi$
$938$		0			0
$939$	5.79420e7			2.14452
$940$		0			0
$941$	−1.26003e7			−0.463880			−0.231940	−	0.972730i	$-0.574507\pi$
$941$	−1.26003e7			−0.463880			−0.231940	+	0.972730i	$0.574507\pi$
$942$		0			0
$943$	1.61587e7	+	1.61587e7i	0.591736	+	0.591736i
$944$		0			0
$945$	886708.	−	1.43532e7i	0.0322999	−	0.522839i
$946$		0			0
$947$	6.38078e6	−	6.38078e6i	0.231206	−	0.231206i	−0.581990	−	0.813196i	$-0.697726\pi$
$947$	6.38078e6	−	6.38078e6i	0.231206	−	0.231206i	0.813196	+	0.581990i	$0.197726\pi$
$948$		0			0
$949$		−	4.70099e7i		−	1.69443i
$950$		0			0
$951$			9.81639e6i			0.351966i
$952$		0			0
$953$	−3.52261e6	+	3.52261e6i	−0.125641	+	0.125641i	−0.767131	−	0.641490i	$-0.778317\pi$
$953$	−3.52261e6	+	3.52261e6i	−0.125641	+	0.125641i	0.641490	+	0.767131i	$0.278317\pi$
$954$		0			0
$955$	1.34068e6	−	2.17015e7i	0.0475680	−	0.769985i
$956$		0			0
$957$	1.38335e7	+	1.38335e7i	0.488260	+	0.488260i
$958$		0			0
$959$	−1.32325e7			−0.464617
$960$		0			0
$961$	−2.56073e7			−0.894450
$962$		0			0
$963$	3.86444e7	+	3.86444e7i	1.34283	+	1.34283i
$964$		0			0
$965$	−5.81807e6	+	5.14104e6i	−0.201123	+	0.177719i
$966$		0			0
$967$	1.25985e7	−	1.25985e7i	0.433265	−	0.433265i	−0.456473	−	0.889738i	$-0.650887\pi$
$967$	1.25985e7	−	1.25985e7i	0.433265	−	0.433265i	0.889738	+	0.456473i	$0.150887\pi$
$968$		0			0
$969$			2.74833e6i			0.0940284i
$970$		0			0
$971$		−	1.03947e7i		−	0.353804i	−0.984228	−	0.176902i	$-0.943392\pi$
$971$		−	1.03947e7i		−	0.353804i	0.984228	−	0.176902i	$-0.0566076\pi$
$972$		0			0
$973$	−1.54727e7	+	1.54727e7i	−0.523943	+	0.523943i
$974$		0			0
$975$	−8.63744e7	−	1.07129e7i	−2.90987	−	0.360909i
$976$		0			0
$977$	−3.98844e7	−	3.98844e7i	−1.33680	−	1.33680i	−0.899140	−	0.437661i	$-0.855807\pi$
$977$	−3.98844e7	−	3.98844e7i	−1.33680	−	1.33680i	−0.437661	−	0.899140i	$-0.644193\pi$
$978$		0			0
$979$	−3.70549e6			−0.123563
$980$		0			0
$981$	−1.03841e7			−0.344505
$982$		0			0
$983$	2.67850e6	+	2.67850e6i	0.0884113	+	0.0884113i	0.749929	−	0.661518i	$-0.230087\pi$
$983$	2.67850e6	+	2.67850e6i	0.0884113	+	0.0884113i	−0.661518	+	0.749929i	$0.730087\pi$
$984$		0			0
$985$	3.14184e6	+	3.55559e6i	0.103180	+	0.116767i
$986$		0			0
$987$	3.45819e7	−	3.45819e7i	1.12994	−	1.12994i
$988$		0			0
$989$		−	1.56426e7i		−	0.508533i
$990$		0			0
$991$			3.20336e6i			0.103615i	0.998657	+	0.0518073i	$0.0164982\pi$
$991$			3.20336e6i			0.103615i	−0.998657	+	0.0518073i	$0.983502\pi$
$992$		0			0
$993$	−2.58559e7	+	2.58559e7i	−0.832122	+	0.832122i
$994$		0			0
$995$	−4.14781e6	−	256243.i	−0.132819	−	0.00820529i
$996$		0			0
$997$	2.90973e7	+	2.90973e7i	0.927076	+	0.927076i	0.997516	−	0.0704402i	$-0.0224404\pi$
$997$	2.90973e7	+	2.90973e7i	0.927076	+	0.927076i	−0.0704402	+	0.997516i	$0.522440\pi$
$998$		0			0
$999$	2.46131e7			0.780283

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.6.n.c.127.8	yes	16
4.3	odd	2		160.6.n.d.127.1	yes	16
5.3	odd	4		160.6.n.d.63.1	yes	16
20.3	even	4	inner	160.6.n.c.63.8	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.6.n.c.63.8	✓	16	20.3	even	4	inner
160.6.n.c.127.8	yes	16	1.1	even	1	trivial
160.6.n.d.63.1	yes	16	5.3	odd	4
160.6.n.d.127.1	yes	16	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	160.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(17.6675 + 17.6675i) q^{3} +(55.7953 + 3.44692i) q^{5} +(-52.6478 + 52.6478i) q^{7} +381.282i q^{9} +O(q^{10})\)	\(q+(17.6675 + 17.6675i) q^{3} +(55.7953 + 3.44692i) q^{5} +(-52.6478 + 52.6478i) q^{7} +381.282i q^{9} -126.754i q^{11} +(-788.215 + 788.215i) q^{13} +(924.866 + 1046.66i) q^{15} +(425.884 + 425.884i) q^{17} +182.630 q^{19} -1860.31 q^{21} +(846.687 + 846.687i) q^{23} +(3101.24 + 384.644i) q^{25} +(-2443.09 + 2443.09i) q^{27} +6177.24i q^{29} -7364.54i q^{31} +(2239.43 - 2239.43i) q^{33} +(-3118.97 + 2756.03i) q^{35} +(-5037.28 - 5037.28i) q^{37} -27851.6 q^{39} +19084.7 q^{41} +(-9237.55 - 9237.55i) q^{43} +(-1314.25 + 21273.7i) q^{45} +(-18589.3 + 18589.3i) q^{47} +11263.4i q^{49} +15048.6i q^{51} +(6808.95 - 6808.95i) q^{53} +(436.911 - 7072.28i) q^{55} +(3226.62 + 3226.62i) q^{57} +47009.8 q^{59} +14370.2 q^{61} +(-20073.6 - 20073.6i) q^{63} +(-46695.6 + 41261.8i) q^{65} +(-30347.8 + 30347.8i) q^{67} +29917.7i q^{69} -43994.2i q^{71} +(-29820.5 + 29820.5i) q^{73} +(47995.4 + 61586.8i) q^{75} +(6673.31 + 6673.31i) q^{77} +54115.9 q^{79} +6324.78 q^{81} +(4507.43 + 4507.43i) q^{83} +(22294.3 + 25230.3i) q^{85} +(-109136. + 109136. i) q^{87} -29233.7i q^{89} -82995.5i q^{91} +(130113. - 130113. i) q^{93} +(10189.9 + 629.511i) q^{95} +(-63973.4 - 63973.4i) q^{97} +48328.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 10 q^{3} - 42 q^{5} + 86 q^{7}+O(q^{10}) \) 16 * q - 10 * q^3 - 42 * q^5 + 86 * q^7	\( 16 q - 10 q^{3} - 42 q^{5} + 86 q^{7} + 536 q^{13} + 698 q^{15} - 1828 q^{17} - 2512 q^{19} - 4284 q^{21} + 7642 q^{23} + 9140 q^{25} + 12272 q^{27} + 11876 q^{33} - 10518 q^{35} - 7620 q^{37} - 11244 q^{39} - 21284 q^{41} - 20002 q^{43} + 686 q^{45} - 25298 q^{47} + 12852 q^{53} + 10584 q^{55} + 55848 q^{57} + 142704 q^{59} - 20564 q^{61} + 115282 q^{63} - 38256 q^{65} + 10506 q^{67} + 15432 q^{73} - 256226 q^{75} + 133852 q^{77} + 159344 q^{79} - 236116 q^{81} + 61222 q^{83} + 7056 q^{85} - 162176 q^{87} + 122180 q^{93} - 267512 q^{95} - 17344 q^{97} - 107332 q^{99}+O(q^{100}) \) 16 * q - 10 * q^3 - 42 * q^5 + 86 * q^7 + 536 * q^13 + 698 * q^15 - 1828 * q^17 - 2512 * q^19 - 4284 * q^21 + 7642 * q^23 + 9140 * q^25 + 12272 * q^27 + 11876 * q^33 - 10518 * q^35 - 7620 * q^37 - 11244 * q^39 - 21284 * q^41 - 20002 * q^43 + 686 * q^45 - 25298 * q^47 + 12852 * q^53 + 10584 * q^55 + 55848 * q^57 + 142704 * q^59 - 20564 * q^61 + 115282 * q^63 - 38256 * q^65 + 10506 * q^67 + 15432 * q^73 - 256226 * q^75 + 133852 * q^77 + 159344 * q^79 - 236116 * q^81 + 61222 * q^83 + 7056 * q^85 - 162176 * q^87 + 122180 * q^93 - 267512 * q^95 - 17344 * q^97 - 107332 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more