LMFDB - Embedded newform 160.6.n.b.63.1

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:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 4 x^{13} + 8 x^{12} - 4626 x^{11} + 149441 x^{10} - 2113414 x^{9} + 17958066 x^{8} + \cdots + 69451154208 $ x^14 - 4x^13 + 8x^12 - 4626x^11 + 149441x^10 - 2113414x^9 + 17958066x^8 - 97717112x^7 + 355171384x^6 - 910571904x^5 + 2428303248x^4 - 9166992192x^3 + 32237484304x^2 - 66916821408*x + 69451154208
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{31}\cdot 5^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			63.1
Root			$-15.8126 - 15.8126i$ of defining polynomial
Character	$\chi$	$=$	160.63
Dual form			160.6.n.b.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-16.5519 + 16.5519i) q^{3} +(13.9288 - 54.1386i) q^{5} +(-2.15894 - 2.15894i) q^{7} -304.928i q^{9} +O(q^{10})$	\(q+(-16.5519 + 16.5519i) q^{3} +(13.9288 - 54.1386i) q^{5} +(-2.15894 - 2.15894i) q^{7} -304.928i q^{9} +255.685i q^{11} +(111.516 + 111.516i) q^{13} +(665.546 + 1126.64i) q^{15} +(998.711 - 998.711i) q^{17} +1946.41 q^{19} +71.4691 q^{21} +(-1615.69 + 1615.69i) q^{23} +(-2736.97 - 1508.18i) q^{25} +(1025.02 + 1025.02i) q^{27} +5843.34i q^{29} +1607.74i q^{31} +(-4232.06 - 4232.06i) q^{33} +(-146.954 + 86.8106i) q^{35} +(-11348.6 + 11348.6i) q^{37} -3691.59 q^{39} -8433.98 q^{41} +(-13638.6 + 13638.6i) q^{43} +(-16508.4 - 4247.29i) q^{45} +(-12797.4 - 12797.4i) q^{47} -16797.7i q^{49} +33061.0i q^{51} +(2038.79 + 2038.79i) q^{53} +(13842.4 + 3561.40i) q^{55} +(-32216.6 + 32216.6i) q^{57} +27506.9 q^{59} +9598.42 q^{61} +(-658.322 + 658.322i) q^{63} +(7590.61 - 4484.03i) q^{65} +(37401.5 + 37401.5i) q^{67} -53485.4i q^{69} +60089.5i q^{71} +(25054.5 + 25054.5i) q^{73} +(70265.1 - 20338.9i) q^{75} +(552.010 - 552.010i) q^{77} -49267.4 q^{79} +40165.4 q^{81} +(-44679.8 + 44679.8i) q^{83} +(-40157.9 - 67979.7i) q^{85} +(-96718.2 - 96718.2i) q^{87} -20469.3i q^{89} -481.514i q^{91} +(-26611.1 - 26611.1i) q^{93} +(27111.2 - 105376. i) q^{95} +(-100982. + 100982. i) q^{97} +77965.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 10 q^{3} + 42 q^{5} + 66 q^{7}+O(q^{10}) $ 14 * q + 10 * q^3 + 42 * q^5 + 66 * q^7	$ 14 q + 10 q^{3} + 42 q^{5} + 66 q^{7} - 414 q^{13} + 278 q^{15} + 1222 q^{17} + 5672 q^{19} + 5924 q^{21} + 2902 q^{23} - 4466 q^{25} - 2168 q^{27} - 2444 q^{33} - 2618 q^{35} - 1790 q^{37} - 11076 q^{39} + 11644 q^{41} - 3982 q^{43} + 14704 q^{45} - 1278 q^{47} + 5882 q^{53} + 65608 q^{55} - 14552 q^{57} - 8504 q^{59} + 20564 q^{61} + 19422 q^{63} + 40798 q^{65} + 107926 q^{67} - 16418 q^{73} + 66586 q^{75} - 13348 q^{77} - 146544 q^{79} + 173806 q^{81} - 36398 q^{83} - 66262 q^{85} + 124384 q^{87} - 306620 q^{93} + 173768 q^{95} - 60314 q^{97} - 388628 q^{99}+O(q^{100}) $ 14 * q + 10 * q^3 + 42 * q^5 + 66 * q^7 - 414 * q^13 + 278 * q^15 + 1222 * q^17 + 5672 * q^19 + 5924 * q^21 + 2902 * q^23 - 4466 * q^25 - 2168 * q^27 - 2444 * q^33 - 2618 * q^35 - 1790 * q^37 - 11076 * q^39 + 11644 * q^41 - 3982 * q^43 + 14704 * q^45 - 1278 * q^47 + 5882 * q^53 + 65608 * q^55 - 14552 * q^57 - 8504 * q^59 + 20564 * q^61 + 19422 * q^63 + 40798 * q^65 + 107926 * q^67 - 16418 * q^73 + 66586 * q^75 - 13348 * q^77 - 146544 * q^79 + 173806 * q^81 - 36398 * q^83 - 66262 * q^85 + 124384 * q^87 - 306620 * q^93 + 173768 * q^95 - 60314 * q^97 - 388628 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−16.5519	+	16.5519i	−1.06180	+	1.06180i	−0.0638422	+	0.997960i	$0.520335\pi$
$3$	−16.5519	+	16.5519i	−1.06180	+	1.06180i	−0.997960	+	0.0638422i	$0.979665\pi$
$4$		0			0
$5$	13.9288	−	54.1386i	0.249167	−	0.968461i
$5$	13.9288	−	54.1386i	0.249167	−	0.968461i
$6$		0			0
$7$	−2.15894	−	2.15894i	−0.0166531	−	0.0166531i	0.698731	−	0.715384i	$-0.253748\pi$
$7$	−2.15894	−	2.15894i	−0.0166531	−	0.0166531i	−0.715384	+	0.698731i	$0.753748\pi$
$8$		0			0
$9$		−	304.928i		−	1.25485i
$10$		0			0
$11$			255.685i			0.637124i	0.947902	+	0.318562i	$0.103200\pi$
$11$			255.685i			0.637124i	−0.947902	+	0.318562i	$0.896800\pi$
$12$		0			0
$13$	111.516	+	111.516i	0.183012	+	0.183012i	0.792667	−	0.609655i	$-0.208692\pi$
$13$	111.516	+	111.516i	0.183012	+	0.183012i	−0.609655	+	0.792667i	$0.708692\pi$
$14$		0			0
$15$	665.546	+	1126.64i	0.763748	+	1.29288i
$16$		0			0
$17$	998.711	−	998.711i	0.838142	−	0.838142i	−0.150473	−	0.988614i	$-0.548080\pi$
$17$	998.711	−	998.711i	0.838142	−	0.838142i	0.988614	+	0.150473i	$0.0480795\pi$
$18$		0			0
$19$	1946.41			1.23694			0.618471	−	0.785807i	$-0.287752\pi$
$19$	1946.41			1.23694			0.618471	+	0.785807i	$0.287752\pi$
$20$		0			0
$21$	71.4691			0.0353647
$22$		0			0
$23$	−1615.69	+	1615.69i	−0.636853	+	0.636853i	−0.949778	−	0.312925i	$-0.898691\pi$
$23$	−1615.69	+	1615.69i	−0.636853	+	0.636853i	0.312925	+	0.949778i	$0.398691\pi$
$24$		0			0
$25$	−2736.97	−	1508.18i	−0.875832	−	0.482616i
$26$		0			0
$27$	1025.02	+	1025.02i	0.270598	+	0.270598i
$28$		0			0
$29$			5843.34i			1.29023i	0.764087	+	0.645114i	$0.223190\pi$
$29$			5843.34i			1.29023i	−0.764087	+	0.645114i	$0.776810\pi$
$30$		0			0
$31$			1607.74i			0.300477i	0.988650	+	0.150238i	$0.0480041\pi$
$31$			1607.74i			0.300477i	−0.988650	+	0.150238i	$0.951996\pi$
$32$		0			0
$33$	−4232.06	−	4232.06i	−0.676499	−	0.676499i
$34$		0			0
$35$	−146.954	+	86.8106i	−0.0202773	+	0.0119785i
$36$		0			0
$37$	−11348.6	+	11348.6i	−1.36282	+	1.36282i	−0.492511	+	0.870306i	$0.663921\pi$
$37$	−11348.6	+	11348.6i	−1.36282	+	1.36282i	−0.870306	+	0.492511i	$0.836079\pi$
$38$		0			0
$39$	−3691.59			−0.388644
$40$		0			0
$41$	−8433.98			−0.783561			−0.391781	−	0.920059i	$-0.628141\pi$
$41$	−8433.98			−0.783561			−0.391781	+	0.920059i	$0.628141\pi$
$42$		0			0
$43$	−13638.6	+	13638.6i	−1.12486	+	1.12486i	−0.133861	+	0.991000i	$0.542738\pi$
$43$	−13638.6	+	13638.6i	−1.12486	+	1.12486i	−0.991000	+	0.133861i	$0.957262\pi$
$44$		0			0
$45$	−16508.4	−	4247.29i	−1.21527	−	0.312666i
$46$		0			0
$47$	−12797.4	−	12797.4i	−0.845043	−	0.845043i	0.144467	−	0.989510i	$-0.453853\pi$
$47$	−12797.4	−	12797.4i	−0.845043	−	0.845043i	−0.989510	+	0.144467i	$0.953853\pi$
$48$		0			0
$49$		−	16797.7i		−	0.999445i
$50$		0			0
$51$			33061.0i			1.77988i
$52$		0			0
$53$	2038.79	+	2038.79i	0.0996973	+	0.0996973i	0.755196	−	0.655499i	$-0.227542\pi$
$53$	2038.79	+	2038.79i	0.0996973	+	0.0996973i	−0.655499	+	0.755196i	$0.727542\pi$
$54$		0			0
$55$	13842.4	+	3561.40i	0.617029	+	0.158750i
$56$		0			0
$57$	−32216.6	+	32216.6i	−1.31339	+	1.31339i
$58$		0			0
$59$	27506.9			1.02875			0.514376	−	0.857565i	$-0.328023\pi$
$59$	27506.9			1.02875			0.514376	+	0.857565i	$0.328023\pi$
$60$		0			0
$61$	9598.42			0.330275			0.165137	−	0.986271i	$-0.447193\pi$
$61$	9598.42			0.330275			0.165137	+	0.986271i	$0.447193\pi$
$62$		0			0
$63$	−658.322	+	658.322i	−0.0208972	+	0.0208972i
$64$		0			0
$65$	7590.61	−	4484.03i	0.222840	−	0.131639i
$66$		0			0
$67$	37401.5	+	37401.5i	1.01789	+	1.01789i	0.999837	+	0.0180552i	$0.00574746\pi$
$67$	37401.5	+	37401.5i	1.01789	+	1.01789i	0.0180552	+	0.999837i	$0.494253\pi$
$68$		0			0
$69$		−	53485.4i		−	1.35242i
$70$		0			0
$71$			60089.5i			1.41466i	0.706883	+	0.707331i	$0.250101\pi$
$71$			60089.5i			1.41466i	−0.706883	+	0.707331i	$0.749899\pi$
$72$		0			0
$73$	25054.5	+	25054.5i	0.550274	+	0.550274i	0.926520	−	0.376246i	$-0.122785\pi$
$73$	25054.5	+	25054.5i	0.550274	+	0.550274i	−0.376246	+	0.926520i	$0.622785\pi$
$74$		0			0
$75$	70265.1	−	20338.9i	1.44240	−	0.417517i
$76$		0			0
$77$	552.010	−	552.010i	0.0106101	−	0.0106101i
$78$		0			0
$79$	−49267.4			−0.888161			−0.444080	−	0.895987i	$-0.646470\pi$
$79$	−49267.4			−0.888161			−0.444080	+	0.895987i	$0.646470\pi$
$80$		0			0
$81$	40165.4			0.680205
$82$		0			0
$83$	−44679.8	+	44679.8i	−0.711895	+	0.711895i	−0.966931	−	0.255036i	$-0.917913\pi$
$83$	−44679.8	+	44679.8i	−0.711895	+	0.711895i	0.255036	+	0.966931i	$0.417913\pi$
$84$		0			0
$85$	−40157.9	−	67979.7i	−0.602870	−	1.02054i
$86$		0			0
$87$	−96718.2	−	96718.2i	−1.36997	−	1.36997i
$88$		0			0
$89$		−	20469.3i		−	0.273922i	−0.990576	−	0.136961i	$-0.956266\pi$
$89$		−	20469.3i		−	0.273922i	0.990576	−	0.136961i	$-0.0437335\pi$
$90$		0			0
$91$		−	481.514i		−	0.00609544i
$92$		0			0
$93$	−26611.1	−	26611.1i	−0.319047	−	0.319047i
$94$		0			0
$95$	27111.2	−	105376.i	0.308205	−	1.19793i
$96$		0			0
$97$	−100982.	+	100982.i	−1.08972	+	1.08972i	−0.0941648	+	0.995557i	$0.530018\pi$
$97$	−100982.	+	100982.i	−1.08972	+	1.08972i	−0.995557	+	0.0941648i	$0.969982\pi$
$98$		0			0
$99$	77965.5			0.799493
$100$		0			0
$101$	167690.			1.63570			0.817852	−	0.575429i	$-0.195165\pi$
$101$	167690.			1.63570			0.817852	+	0.575429i	$0.195165\pi$
$102$		0			0
$103$	−82074.1	+	82074.1i	−0.762277	+	0.762277i	−0.976734	−	0.214456i	$-0.931202\pi$
$103$	−82074.1	+	82074.1i	−0.762277	+	0.762277i	0.214456	+	0.976734i	$0.431202\pi$
$104$		0			0
$105$	995.481	−	3869.23i	0.00881170	−	0.0342493i
$106$		0			0
$107$	−91100.8	−	91100.8i	−0.769241	−	0.769241i	0.208732	−	0.977973i	$-0.433066\pi$
$107$	−91100.8	−	91100.8i	−0.769241	−	0.769241i	−0.977973	+	0.208732i	$0.933066\pi$
$108$		0			0
$109$			188806.i			1.52212i	0.648680	+	0.761062i	$0.275322\pi$
$109$			188806.i			1.52212i	−0.648680	+	0.761062i	$0.724678\pi$
$110$		0			0
$111$		−	375680.i		−	2.89408i
$112$		0			0
$113$	130082.	+	130082.i	0.958343	+	0.958343i	0.999166	−	0.0408237i	$-0.0129982\pi$
$113$	130082.	+	130082.i	0.958343	+	0.958343i	−0.0408237	+	0.999166i	$0.512998\pi$
$114$		0			0
$115$	64966.6	+	109976.i	0.458084	+	0.775449i
$116$		0			0
$117$	34004.4	−	34004.4i	0.229652	−	0.229652i
$118$		0			0
$119$	−4312.32			−0.0279154
$120$		0			0
$121$	95676.1			0.594074
$122$		0			0
$123$	139598.	−	139598.i	0.831987	−	0.831987i
$124$		0			0
$125$	−119773.	+	127169.i	−0.685623	+	0.727957i
$126$		0			0
$127$	−118771.	−	118771.i	−0.653431	−	0.653431i	0.300387	−	0.953818i	$-0.402884\pi$
$127$	−118771.	−	118771.i	−0.653431	−	0.653431i	−0.953818	+	0.300387i	$0.902884\pi$
$128$		0			0
$129$		−	451489.i		−	2.38876i
$130$		0			0
$131$			53985.4i			0.274852i	0.990512	+	0.137426i	$0.0438829\pi$
$131$			53985.4i			0.274852i	−0.990512	+	0.137426i	$0.956117\pi$
$132$		0			0
$133$	−4202.18	−	4202.18i	−0.0205990	−	0.0205990i
$134$		0			0
$135$	69770.7	−	41215.9i	0.329487	−	0.194639i
$136$		0			0
$137$	101234.	−	101234.i	0.460813	−	0.460813i	−0.438109	−	0.898922i	$-0.644351\pi$
$137$	101234.	−	101234.i	0.460813	−	0.460813i	0.898922	+	0.438109i	$0.144351\pi$
$138$		0			0
$139$	−92974.7			−0.408157			−0.204079	−	0.978954i	$-0.565420\pi$
$139$	−92974.7			−0.408157			−0.204079	+	0.978954i	$0.565420\pi$
$140$		0			0
$141$	423643.			1.79454
$142$		0			0
$143$	−28513.0	+	28513.0i	−0.116601	+	0.116601i
$144$		0			0
$145$	316350.	+	81391.0i	1.24953	+	0.321482i
$146$		0			0
$147$	278033.	+	278033.i	1.06121	+	1.06121i
$148$		0			0
$149$			209067.i			0.771470i	0.922610	+	0.385735i	$0.126052\pi$
$149$			209067.i			0.771470i	−0.922610	+	0.385735i	$0.873948\pi$
$150$		0			0
$151$			37816.8i			0.134972i	0.997720	+	0.0674858i	$0.0214977\pi$
$151$			37816.8i			0.134972i	−0.997720	+	0.0674858i	$0.978502\pi$
$152$		0			0
$153$	−304535.	−	304535.i	−1.05174	−	1.05174i
$154$		0			0
$155$	87040.7	+	22393.9i	0.291000	+	0.0748688i
$156$		0			0
$157$	250564.	−	250564.i	0.811277	−	0.811277i	−0.173548	−	0.984825i	$-0.555523\pi$
$157$	250564.	−	250564.i	0.811277	−	0.811277i	0.984825	+	0.173548i	$0.0555232\pi$
$158$		0			0
$159$	−67491.6			−0.211718
$160$		0			0
$161$	6976.37			0.0212112
$162$		0			0
$163$	−114285.	+	114285.i	−0.336915	+	0.336915i	−0.855205	−	0.518290i	$-0.826569\pi$
$163$	−114285.	+	114285.i	−0.336915	+	0.336915i	0.518290	+	0.855205i	$0.326569\pi$
$164$		0			0
$165$	−288066.	+	170170.i	−0.823724	+	0.486602i
$166$		0			0
$167$	351508.	+	351508.i	0.975313	+	0.975313i	0.999703	−	0.0243893i	$-0.00776413\pi$
$167$	351508.	+	351508.i	0.975313	+	0.975313i	−0.0243893	+	0.999703i	$0.507764\pi$
$168$		0			0
$169$		−	346421.i		−	0.933013i
$170$		0			0
$171$		−	593514.i		−	1.55217i
$172$		0			0
$173$	−264889.	−	264889.i	−0.672898	−	0.672898i	0.285485	−	0.958383i	$-0.407845\pi$
$173$	−264889.	−	264889.i	−0.672898	−	0.672898i	−0.958383	+	0.285485i	$0.907845\pi$
$174$		0			0
$175$	2652.91	+	9165.04i	0.00654828	+	0.0226224i
$176$		0			0
$177$	−455290.	+	455290.i	−1.09233	+	1.09233i
$178$		0			0
$179$	−584607.			−1.36374			−0.681870	−	0.731473i	$-0.738833\pi$
$179$	−584607.			−1.36374			−0.681870	+	0.731473i	$0.738833\pi$
$180$		0			0
$181$	−224651.			−0.509698			−0.254849	−	0.966981i	$-0.582026\pi$
$181$	−224651.			−0.509698			−0.254849	+	0.966981i	$0.582026\pi$
$182$		0			0
$183$	−158872.	+	158872.i	−0.350686	+	0.350686i
$184$		0			0
$185$	456324.	+	772469.i	0.980266	+	1.65940i
$186$		0			0
$187$	255355.	+	255355.i	0.534000	+	0.534000i
$188$		0			0
$189$		−	4425.94i		−	0.00901261i
$190$		0			0
$191$		−	17886.3i		−	0.0354761i	−0.999843	−	0.0177381i	$-0.994354\pi$
$191$		−	17886.3i		−	0.0354761i	0.999843	−	0.0177381i	$-0.00564650\pi$
$192$		0			0
$193$	42336.3	+	42336.3i	0.0818125	+	0.0818125i	0.746829	−	0.665016i	$-0.231575\pi$
$193$	42336.3	+	42336.3i	0.0818125	+	0.0818125i	−0.665016	+	0.746829i	$0.731575\pi$
$194$		0			0
$195$	−51419.6	+	199858.i	−0.0968372	+	0.376387i
$196$		0			0
$197$	−209419.	+	209419.i	−0.384459	+	0.384459i	−0.872706	−	0.488247i	$-0.837637\pi$
$197$	−209419.	+	209419.i	−0.384459	+	0.384459i	0.488247	+	0.872706i	$0.337637\pi$
$198$		0			0
$199$	−447716.			−0.801438			−0.400719	−	0.916201i	$-0.631240\pi$
$199$	−447716.			−0.801438			−0.400719	+	0.916201i	$0.631240\pi$
$200$		0			0
$201$	−1.23813e6			−2.16160
$202$		0			0
$203$	12615.4	−	12615.4i	0.0214863	−	0.0214863i
$204$		0			0
$205$	−117476.	+	456604.i	−0.195237	+	0.758848i
$206$		0			0
$207$	492670.	+	492670.i	0.799153	+	0.799153i
$208$		0			0
$209$			497667.i			0.788085i
$210$		0			0
$211$		−	1.13095e6i		−	1.74879i	−0.485216	−	0.874394i	$-0.661259\pi$
$211$		−	1.13095e6i		−	1.74879i	0.485216	−	0.874394i	$-0.338741\pi$
$212$		0			0
$213$	−994592.	−	994592.i	−1.50209	−	1.50209i
$214$		0			0
$215$	548405.	+	928345.i	0.809106	+	1.36966i
$216$		0			0
$217$	3471.02	−	3471.02i	0.00500388	−	0.00500388i
$218$		0			0
$219$	−829398.			−1.16857
$220$		0			0
$221$	222744.			0.306779
$222$		0			0
$223$	−274750.	+	274750.i	−0.369978	+	0.369978i	−0.867469	−	0.497491i	$-0.834255\pi$
$223$	−274750.	+	274750.i	−0.369978	+	0.369978i	0.497491	+	0.867469i	$0.334255\pi$
$224$		0			0
$225$	−459885.	+	834580.i	−0.605610	+	1.09904i
$226$		0			0
$227$	488532.	+	488532.i	0.629258	+	0.629258i	0.947881	−	0.318624i	$-0.103221\pi$
$227$	488532.	+	488532.i	0.629258	+	0.629258i	−0.318624	+	0.947881i	$0.603221\pi$
$228$		0			0
$229$		−	342575.i		−	0.431685i	−0.976428	−	0.215843i	$-0.930750\pi$
$229$		−	342575.i		−	0.431685i	0.976428	−	0.215843i	$-0.0692498\pi$
$230$		0			0
$231$			18273.6i			0.0225317i
$232$		0			0
$233$	−452353.	−	452353.i	−0.545868	−	0.545868i	0.379375	−	0.925243i	$-0.376139\pi$
$233$	−452353.	−	452353.i	−0.545868	−	0.545868i	−0.925243	+	0.379375i	$0.876139\pi$
$234$		0			0
$235$	−871089.	+	514582.i	−1.02895	+	0.607834i
$236$		0			0
$237$	815466.	−	815466.i	0.943051	−	0.943051i
$238$		0			0
$239$	467505.			0.529409			0.264704	−	0.964330i	$-0.414726\pi$
$239$	467505.			0.529409			0.264704	+	0.964330i	$0.414726\pi$
$240$		0			0
$241$	1.38008e6			1.53060			0.765298	−	0.643676i	$-0.222592\pi$
$241$	1.38008e6			1.53060			0.765298	+	0.643676i	$0.222592\pi$
$242$		0			0
$243$	−913893.	+	913893.i	−0.992841	+	0.992841i
$244$		0			0
$245$	−909403.	−	233972.i	−0.967923	−	0.249028i
$246$		0			0
$247$	217055.	+	217055.i	0.226375	+	0.226375i
$248$		0			0
$249$		−	1.47907e6i		−	1.51178i
$250$		0			0
$251$		−	368447.i		−	0.369140i	−0.982819	−	0.184570i	$-0.940911\pi$
$251$		−	368447.i		−	0.369140i	0.982819	−	0.184570i	$-0.0590893\pi$
$252$		0			0
$253$	−413108.	−	413108.i	−0.405754	−	0.405754i
$254$		0			0
$255$	1.78988e6	+	460502.i	1.72374	+	0.443487i
$256$		0			0
$257$	−75698.4	+	75698.4i	−0.0714915	+	0.0714915i	−0.741948	−	0.670457i	$-0.766098\pi$
$257$	−75698.4	+	75698.4i	−0.0714915	+	0.0714915i	0.670457	+	0.741948i	$0.266098\pi$
$258$		0			0
$259$	49001.9			0.0453904
$260$		0			0
$261$	1.78180e6			1.61904
$262$		0			0
$263$	487680.	−	487680.i	0.434756	−	0.434756i	−0.455487	−	0.890243i	$-0.650535\pi$
$263$	487680.	−	487680.i	0.434756	−	0.434756i	0.890243	+	0.455487i	$0.150535\pi$
$264$		0			0
$265$	138775.	−	81979.4i	0.121394	−	0.0717117i
$266$		0			0
$267$	338804.	+	338804.i	0.290851	+	0.290851i
$268$		0			0
$269$			1.45194e6i			1.22340i	0.791091	+	0.611698i	$0.209513\pi$
$269$			1.45194e6i			1.22340i	−0.791091	+	0.611698i	$0.790487\pi$
$270$		0			0
$271$			444992.i			0.368069i	0.982920	+	0.184034i	$0.0589157\pi$
$271$			444992.i			0.368069i	−0.982920	+	0.184034i	$0.941084\pi$
$272$		0			0
$273$	7969.94	+	7969.94i	0.00647215	+	0.00647215i
$274$		0			0
$275$	385618.	−	699804.i	0.307486	−	0.558013i
$276$		0			0
$277$	−519577.	+	519577.i	−0.406865	+	0.406865i	−0.880644	−	0.473779i	$-0.842890\pi$
$277$	−519577.	+	519577.i	−0.406865	+	0.406865i	0.473779	+	0.880644i	$0.342890\pi$
$278$		0			0
$279$	490244.			0.377053
$280$		0			0
$281$	1.04138e6			0.786763			0.393381	−	0.919375i	$-0.371305\pi$
$281$	1.04138e6			0.786763			0.393381	+	0.919375i	$0.371305\pi$
$282$		0			0
$283$	448357.	−	448357.i	0.332780	−	0.332780i	−0.520861	−	0.853641i	$-0.674389\pi$
$283$	448357.	−	448357.i	0.332780	−	0.332780i	0.853641	+	0.520861i	$0.174389\pi$
$284$		0			0
$285$	1.29542e6	+	2.19290e6i	0.944712	+	1.59922i
$286$		0			0
$287$	18208.5	+	18208.5i	0.0130488	+	0.0130488i
$288$		0			0
$289$		−	574989.i		−	0.404963i
$290$		0			0
$291$		−	3.34289e6i		−	2.31414i
$292$		0			0
$293$	518007.	+	518007.i	0.352506	+	0.352506i	0.861041	−	0.508535i	$-0.169813\pi$
$293$	518007.	+	518007.i	0.352506	+	0.352506i	−0.508535	+	0.861041i	$0.669813\pi$
$294$		0			0
$295$	383139.	−	1.48918e6i	0.256331	−	0.996307i
$296$		0			0
$297$	−262083.	+	262083.i	−0.172404	+	0.172404i
$298$		0			0
$299$	−360351.			−0.233103
$300$		0			0
$301$	58890.0			0.0374649
$302$		0			0
$303$	−2.77559e6	+	2.77559e6i	−1.73679	+	1.73679i
$304$		0			0
$305$	133695.	−	519645.i	0.0822934	−	0.319858i
$306$		0			0
$307$	−1.73933e6	−	1.73933e6i	−1.05326	−	1.05326i	−0.998500	−	0.0547590i	$-0.982561\pi$
$307$	−1.73933e6	−	1.73933e6i	−1.05326	−	1.05326i	−0.0547590	−	0.998500i	$-0.517439\pi$
$308$		0			0
$309$		−	2.71696e6i		−	1.61878i
$310$		0			0
$311$		−	1.01730e6i		−	0.596413i	−0.954501	−	0.298207i	$-0.903612\pi$
$311$		−	1.01730e6i		−	0.596413i	0.954501	−	0.298207i	$-0.0963884\pi$
$312$		0			0
$313$	−1.40539e6	−	1.40539e6i	−0.810839	−	0.810839i	0.173921	−	0.984760i	$-0.444356\pi$
$313$	−1.40539e6	−	1.40539e6i	−0.810839	−	0.810839i	−0.984760	+	0.173921i	$0.944356\pi$
$314$		0			0
$315$	26471.0	+	44810.3i	0.0150312	+	0.0254450i
$316$		0			0
$317$	−2.34064e6	+	2.34064e6i	−1.30824	+	1.30824i	−0.385555	+	0.922685i	$0.625990\pi$
$317$	−2.34064e6	+	2.34064e6i	−1.30824	+	1.30824i	−0.922685	+	0.385555i	$0.874010\pi$
$318$		0			0
$319$	−1.49406e6			−0.822034
$320$		0			0
$321$	3.01577e6			1.63356
$322$		0			0
$323$	1.94390e6	−	1.94390e6i	1.03673	−	1.03673i
$324$		0			0
$325$	−137031.	−	473402.i	−0.0719631	−	0.248612i
$326$		0			0
$327$	−3.12509e6	−	3.12509e6i	−1.61619	−	1.61619i
$328$		0			0
$329$			55257.9i			0.0281452i
$330$		0			0
$331$			592772.i			0.297384i	0.988884	+	0.148692i	$0.0475063\pi$
$331$			592772.i			0.297384i	−0.988884	+	0.148692i	$0.952494\pi$
$332$		0			0
$333$	3.46050e6	+	3.46050e6i	1.71013	+	1.71013i
$334$		0			0
$335$	2.54582e6	−	1.50390e6i	1.23941	−	0.732164i
$336$		0			0
$337$	226356.	−	226356.i	0.108572	−	0.108572i	−0.650734	−	0.759306i	$-0.725539\pi$
$337$	226356.	−	226356.i	0.108572	−	0.108572i	0.759306	+	0.650734i	$0.225539\pi$
$338$		0			0
$339$	−4.30620e6			−2.03514
$340$		0			0
$341$	−411075.			−0.191441
$342$		0			0
$343$	−72550.6	+	72550.6i	−0.0332971	+	0.0332971i
$344$		0			0
$345$	−2.89562e6	−	744989.i	−1.30977	−	0.336979i
$346$		0			0
$347$	1.68068e6	+	1.68068e6i	0.749312	+	0.749312i	0.974350	−	0.225038i	$-0.0722507\pi$
$347$	1.68068e6	+	1.68068e6i	0.749312	+	0.749312i	−0.225038	+	0.974350i	$0.572251\pi$
$348$		0			0
$349$		−	2.90392e6i		−	1.27621i	−0.769951	−	0.638103i	$-0.779719\pi$
$349$		−	2.90392e6i		−	1.27621i	0.769951	−	0.638103i	$-0.220281\pi$
$350$		0			0
$351$			228613.i			0.0990451i
$352$		0			0
$353$	2.50898e6	+	2.50898e6i	1.07167	+	1.07167i	0.997225	+	0.0744409i	$0.0237172\pi$
$353$	2.50898e6	+	2.50898e6i	1.07167	+	1.07167i	0.0744409	+	0.997225i	$0.476283\pi$
$354$		0			0
$355$	3.25316e6	+	836977.i	1.37004	+	0.352486i
$356$		0			0
$357$	71376.9	−	71376.9i	0.0296406	−	0.0296406i
$358$		0			0
$359$	3.85795e6			1.57987			0.789933	−	0.613193i	$-0.210115\pi$
$359$	3.85795e6			1.57987			0.789933	+	0.613193i	$0.210115\pi$
$360$		0			0
$361$	1.31240e6			0.530027
$362$		0			0
$363$	−1.58362e6	+	1.58362e6i	−0.630789	+	0.630789i
$364$		0			0
$365$	1.70540e6	−	1.00744e6i	0.670029	−	0.395809i
$366$		0			0
$367$	−974922.	−	974922.i	−0.377837	−	0.377837i	0.492484	−	0.870321i	$-0.336089\pi$
$367$	−974922.	−	974922.i	−0.377837	−	0.377837i	−0.870321	+	0.492484i	$0.836089\pi$
$368$		0			0
$369$			2.57176e6i			0.983250i
$370$		0			0
$371$		−	8803.28i		−	0.00332055i
$372$		0			0
$373$	−2.95423e6	−	2.95423e6i	−1.09944	−	1.09944i	−0.994476	−	0.104968i	$-0.966526\pi$
$373$	−2.95423e6	−	2.95423e6i	−1.09944	−	1.09944i	−0.104968	−	0.994476i	$-0.533474\pi$
$374$		0			0
$375$	−122409.	−	4.08735e6i	−0.0449505	−	1.50094i
$376$		0			0
$377$	−651626.	+	651626.i	−0.236127	+	0.236127i
$378$		0			0
$379$	1.93723e6			0.692760			0.346380	−	0.938094i	$-0.387411\pi$
$379$	1.93723e6			0.692760			0.346380	+	0.938094i	$0.387411\pi$
$380$		0			0
$381$	3.93175e6			1.38763
$382$		0			0
$383$	−456982.	+	456982.i	−0.159185	+	0.159185i	−0.782206	−	0.623020i	$-0.785905\pi$
$383$	−456982.	+	456982.i	−0.159185	+	0.159185i	0.623020	+	0.782206i	$0.285905\pi$
$384$		0			0
$385$	−22196.2	−	37573.9i	−0.00763179	−	0.0129192i
$386$		0			0
$387$	4.15879e6	+	4.15879e6i	1.41153	+	1.41153i
$388$		0			0
$389$		−	2.78550e6i		−	0.933317i	−0.884438	−	0.466658i	$-0.845458\pi$
$389$		−	2.78550e6i		−	0.933317i	0.884438	−	0.466658i	$-0.154542\pi$
$390$		0			0
$391$			3.22722e6i			1.06755i
$392$		0			0
$393$	−893559.	−	893559.i	−0.291838	−	0.291838i
$394$		0			0
$395$	−686237.	+	2.66727e6i	−0.221300	+	0.860149i
$396$		0			0
$397$	−965661.	+	965661.i	−0.307502	+	0.307502i	−0.843940	−	0.536438i	$-0.819770\pi$
$397$	−965661.	+	965661.i	−0.307502	+	0.307502i	0.536438	+	0.843940i	$0.319770\pi$
$398$		0			0
$399$	139108.			0.0437441
$400$		0			0
$401$	2.13461e6			0.662916			0.331458	−	0.943470i	$-0.392460\pi$
$401$	2.13461e6			0.662916			0.331458	+	0.943470i	$0.392460\pi$
$402$		0			0
$403$	−179289.	+	179289.i	−0.0549908	+	0.0549908i
$404$		0			0
$405$	559458.	−	2.17450e6i	0.169484	−	0.658752i
$406$		0			0
$407$	−2.90166e6	−	2.90166e6i	−0.868283	−	0.868283i
$408$		0			0
$409$			1.60900e6i			0.475608i	0.971313	+	0.237804i	$0.0764275\pi$
$409$			1.60900e6i			0.475608i	−0.971313	+	0.237804i	$0.923572\pi$
$410$		0			0
$411$			3.35122e6i			0.978585i
$412$		0			0
$413$	−59385.8	−	59385.8i	−0.0171320	−	0.0171320i
$414$		0			0
$415$	1.79656e6	+	3.04124e6i	0.512062	+	0.866823i
$416$		0			0
$417$	1.53890e6	−	1.53890e6i	0.433382	−	0.433382i
$418$		0			0
$419$	5.37383e6			1.49537			0.747685	−	0.664053i	$-0.231165\pi$
$419$	5.37383e6			1.49537			0.747685	+	0.664053i	$0.231165\pi$
$420$		0			0
$421$	−5.58822e6			−1.53663			−0.768313	−	0.640074i	$-0.778904\pi$
$421$	−5.58822e6			−1.53663			−0.768313	+	0.640074i	$0.778904\pi$
$422$		0			0
$423$	−3.90230e6	+	3.90230e6i	−1.06040	+	1.06040i
$424$		0			0
$425$	−4.23968e6	+	1.22722e6i	−1.13857	+	0.329571i
$426$		0			0
$427$	−20722.5	−	20722.5i	−0.00550011	−	0.00550011i
$428$		0			0
$429$		−	943885.i		−	0.247614i
$430$		0			0
$431$		−	2.59273e6i		−	0.672302i	−0.941808	−	0.336151i	$-0.890875\pi$
$431$		−	2.59273e6i		−	0.672302i	0.941808	−	0.336151i	$-0.109125\pi$
$432$		0			0
$433$	−1.81191e6	−	1.81191e6i	−0.464428	−	0.464428i	0.435676	−	0.900104i	$-0.356509\pi$
$433$	−1.81191e6	−	1.81191e6i	−0.464428	−	0.464428i	−0.900104	+	0.435676i	$0.856509\pi$
$434$		0			0
$435$	−6.58336e6	+	3.88901e6i	−1.66811	+	0.985409i
$436$		0			0
$437$	−3.14479e6	+	3.14479e6i	−0.787750	+	0.787750i
$438$		0			0
$439$	−3.09173e6			−0.765669			−0.382834	−	0.923817i	$-0.625052\pi$
$439$	−3.09173e6			−0.765669			−0.382834	+	0.923817i	$0.625052\pi$
$440$		0			0
$441$	−5.12208e6			−1.25415
$442$		0			0
$443$	3.50150e6	−	3.50150e6i	0.847705	−	0.847705i	−0.142141	−	0.989846i	$-0.545399\pi$
$443$	3.50150e6	−	3.50150e6i	0.847705	−	0.847705i	0.989846	+	0.142141i	$0.0453986\pi$
$444$		0			0
$445$	−1.10818e6	−	285113.i	−0.265283	−	0.0682522i
$446$		0			0
$447$	−3.46044e6	−	3.46044e6i	−0.819149	−	0.819149i
$448$		0			0
$449$			7.60289e6i			1.77977i	0.456190	+	0.889883i	$0.349214\pi$
$449$			7.60289e6i			1.77977i	−0.456190	+	0.889883i	$0.650786\pi$
$450$		0			0
$451$		−	2.15644e6i		−	0.499225i
$452$		0			0
$453$	−625938.	−	625938.i	−0.143313	−	0.143313i
$454$		0			0
$455$	−26068.5	−	6706.92i	−0.00590319	−	0.00151878i
$456$		0			0
$457$	1.09632e6	−	1.09632e6i	0.245553	−	0.245553i	−0.573590	−	0.819143i	$-0.694450\pi$
$457$	1.09632e6	−	1.09632e6i	0.245553	−	0.245553i	0.819143	+	0.573590i	$0.194450\pi$
$458$		0			0
$459$	2.04740e6			0.453599
$460$		0			0
$461$	−3.67309e6			−0.804969			−0.402484	−	0.915427i	$-0.631853\pi$
$461$	−3.67309e6			−0.804969			−0.402484	+	0.915427i	$0.631853\pi$
$462$		0			0
$463$	−1.59149e6	+	1.59149e6i	−0.345026	+	0.345026i	−0.858253	−	0.513227i	$-0.828450\pi$
$463$	−1.59149e6	+	1.59149e6i	−0.345026	+	0.345026i	0.513227	+	0.858253i	$0.328450\pi$
$464$		0			0
$465$	−1.81135e6	+	1.07002e6i	−0.388480	+	0.229489i
$466$		0			0
$467$	4.91174e6	+	4.91174e6i	1.04218	+	1.04218i	0.999070	+	0.0431100i	$0.0137266\pi$
$467$	4.91174e6	+	4.91174e6i	1.04218	+	1.04218i	0.0431100	+	0.999070i	$0.486273\pi$
$468$		0			0
$469$		−	161495.i		−	0.0339022i
$470$		0			0
$471$			8.29460e6i			1.72283i
$472$		0			0
$473$	−3.48719e6	−	3.48719e6i	−0.716675	−	0.716675i
$474$		0			0
$475$	−5.32727e6	−	2.93552e6i	−1.08335	−	0.596968i
$476$		0			0
$477$	621685.	−	621685.i	0.125105	−	0.125105i
$478$		0			0
$479$	−3.25161e6			−0.647530			−0.323765	−	0.946138i	$-0.604949\pi$
$479$	−3.25161e6			−0.647530			−0.323765	+	0.946138i	$0.604949\pi$
$480$		0			0
$481$	−2.53110e6			−0.498823
$482$		0			0
$483$	−115472.	+	115472.i	−0.0225221	+	0.0225221i
$484$		0			0
$485$	4.06047e6	+	6.87360e6i	0.783830	+	1.32687i
$486$		0			0
$487$	−1.81453e6	−	1.81453e6i	−0.346690	−	0.346690i	0.512185	−	0.858875i	$-0.328836\pi$
$487$	−1.81453e6	−	1.81453e6i	−0.346690	−	0.346690i	−0.858875	+	0.512185i	$0.828836\pi$
$488$		0			0
$489$		−	3.78326e6i		−	0.715474i
$490$		0			0
$491$			2.04842e6i			0.383456i	0.981448	+	0.191728i	$0.0614092\pi$
$491$			2.04842e6i			0.383456i	−0.981448	+	0.191728i	$0.938591\pi$
$492$		0			0
$493$	5.83581e6	+	5.83581e6i	1.08139	+	1.08139i
$494$		0			0
$495$	1.08597e6	−	4.22094e6i	0.199207	−	0.774278i
$496$		0			0
$497$	129730.	−	129730.i	0.0235586	−	0.0235586i
$498$		0			0
$499$	−1.07626e7			−1.93493			−0.967467	−	0.252995i	$-0.918584\pi$
$499$	−1.07626e7			−1.93493			−0.967467	+	0.252995i	$0.918584\pi$
$500$		0			0
$501$	−1.16362e7			−2.07118
$502$		0			0
$503$	6.61394e6	−	6.61394e6i	1.16558	−	1.16558i	0.182340	−	0.983236i	$-0.441633\pi$
$503$	6.61394e6	−	6.61394e6i	1.16558	−	1.16558i	0.983236	−	0.182340i	$-0.0583671\pi$
$504$		0			0
$505$	2.33573e6	−	9.07852e6i	0.407563	−	1.58411i
$506$		0			0
$507$	5.73392e6	+	5.73392e6i	0.990676	+	0.990676i
$508$		0			0
$509$			9.31007e6i			1.59279i	0.604777	+	0.796395i	$0.293262\pi$
$509$			9.31007e6i			1.59279i	−0.604777	+	0.796395i	$0.706738\pi$
$510$		0			0
$511$		−	108183.i		−	0.0183276i
$512$		0			0
$513$	1.99511e6	+	1.99511e6i	0.334714	+	0.334714i
$514$		0			0
$515$	3.30018e6	+	5.58657e6i	0.548302	+	0.928170i
$516$		0			0
$517$	3.27212e6	−	3.27212e6i	0.538397	−	0.538397i
$518$		0			0
$519$	8.76882e6			1.42897
$520$		0			0
$521$	−126938.			−0.0204879			−0.0102440	−	0.999948i	$-0.503261\pi$
$521$	−126938.			−0.0204879			−0.0102440	+	0.999948i	$0.503261\pi$
$522$		0			0
$523$	7.33758e6	−	7.33758e6i	1.17300	−	1.17300i	0.191511	−	0.981490i	$-0.438661\pi$
$523$	7.33758e6	−	7.33758e6i	1.17300	−	1.17300i	0.981490	−	0.191511i	$-0.0613388\pi$
$524$		0			0
$525$	−195609.	−	107788.i	−0.0309735	−	0.0170676i
$526$		0			0
$527$	1.60567e6	+	1.60567e6i	0.251842	+	0.251842i
$528$		0			0
$529$			1.21542e6i			0.188838i
$530$		0			0
$531$		−	8.38761e6i		−	1.29093i
$532$		0			0
$533$	−940524.	−	940524.i	−0.143401	−	0.143401i
$534$		0			0
$535$	−6.20100e6	+	3.66314e6i	−0.936649	+	0.553311i
$536$		0			0
$537$	9.67634e6	−	9.67634e6i	1.44802	−	1.44802i
$538$		0			0
$539$	4.29492e6			0.636770
$540$		0			0
$541$	4.43492e6			0.651468			0.325734	−	0.945462i	$-0.394389\pi$
$541$	4.43492e6			0.651468			0.325734	+	0.945462i	$0.394389\pi$
$542$		0			0
$543$	3.71840e6	−	3.71840e6i	0.541198	−	0.541198i
$544$		0			0
$545$	1.02217e7	+	2.62985e6i	1.47412	+	0.379262i
$546$		0			0
$547$	8.43075e6	+	8.43075e6i	1.20475	+	1.20475i	0.972704	+	0.232049i	$0.0745428\pi$
$547$	8.43075e6	+	8.43075e6i	1.20475	+	1.20475i	0.232049	+	0.972704i	$0.425457\pi$
$548$		0			0
$549$		−	2.92683e6i		−	0.414444i
$550$		0			0
$551$			1.13735e7i			1.59594i
$552$		0			0
$553$	106365.	+	106365.i	0.0147907	+	0.0147907i
$554$		0			0
$555$	−2.03388e7	−	5.23279e6i	−2.80281	−	0.721109i
$556$		0			0
$557$	5.80705e6	−	5.80705e6i	0.793081	−	0.793081i	−0.188913	−	0.981994i	$-0.560496\pi$
$557$	5.80705e6	−	5.80705e6i	0.793081	−	0.793081i	0.981994	+	0.188913i	$0.0604963\pi$
$558$		0			0
$559$	−3.04185e6			−0.411725
$560$		0			0
$561$	−8.45321e6			−1.13400
$562$		0			0
$563$	−4.54116e6	+	4.54116e6i	−0.603804	+	0.603804i	−0.941320	−	0.337516i	$-0.890413\pi$
$563$	−4.54116e6	+	4.54116e6i	−0.603804	+	0.603804i	0.337516	+	0.941320i	$0.390413\pi$
$564$		0			0
$565$	8.85434e6	−	5.23056e6i	1.16690	−	0.689330i
$566$		0			0
$567$	−86714.9	−	86714.9i	−0.0113276	−	0.0113276i
$568$		0			0
$569$		−	1.81256e6i		−	0.234700i	−0.993091	−	0.117350i	$-0.962560\pi$
$569$		−	1.81256e6i		−	0.234700i	0.993091	−	0.117350i	$-0.0374399\pi$
$570$		0			0
$571$		−	6.42241e6i		−	0.824342i	−0.911107	−	0.412171i	$-0.864771\pi$
$571$		−	6.42241e6i		−	0.824342i	0.911107	−	0.412171i	$-0.135229\pi$
$572$		0			0
$573$	296051.	+	296051.i	0.0376686	+	0.0376686i
$574$		0			0
$575$	6.85885e6	−	1.98536e6i	0.865131	−	0.250421i
$576$		0			0
$577$	1.17171e6	−	1.17171e6i	0.146515	−	0.146515i	−0.630044	−	0.776559i	$-0.716963\pi$
$577$	1.17171e6	−	1.17171e6i	0.146515	−	0.146515i	0.776559	+	0.630044i	$0.216963\pi$
$578$		0			0
$579$	−1.40149e6			−0.173737
$580$		0			0
$581$	192922.			0.0237106
$582$		0			0
$583$	−521289.	+	521289.i	−0.0635195	+	0.0635195i
$584$		0			0
$585$	−1.36731e6	−	2.31459e6i	−0.165187	−	0.279630i
$586$		0			0
$587$	−1.03287e7	−	1.03287e7i	−1.23723	−	1.23723i	−0.961129	−	0.276099i	$-0.910958\pi$
$587$	−1.03287e7	−	1.03287e7i	−1.23723	−	1.23723i	−0.276099	−	0.961129i	$-0.589042\pi$
$588$		0			0
$589$			3.12931e6i			0.371673i
$590$		0			0
$591$		−	6.93254e6i		−	0.816438i
$592$		0			0
$593$	5.28605e6	+	5.28605e6i	0.617297	+	0.617297i	0.944837	−	0.327540i	$-0.106220\pi$
$593$	5.28605e6	+	5.28605e6i	0.617297	+	0.617297i	−0.327540	+	0.944837i	$0.606220\pi$
$594$		0			0
$595$	−60065.6	+	233463.i	−0.00695558	+	0.0270350i
$596$		0			0
$597$	7.41053e6	−	7.41053e6i	0.850968	−	0.850968i
$598$		0			0
$599$	1.31419e7			1.49655			0.748274	−	0.663389i	$-0.230883\pi$
$599$	1.31419e7			1.49655			0.748274	+	0.663389i	$0.230883\pi$
$600$		0			0
$601$	563134.			0.0635954			0.0317977	−	0.999494i	$-0.489877\pi$
$601$	563134.			0.0635954			0.0317977	+	0.999494i	$0.489877\pi$
$602$		0			0
$603$	1.14048e7	−	1.14048e7i	1.27730	−	1.27730i
$604$		0			0
$605$	1.33266e6	−	5.17977e6i	0.148023	−	0.575337i
$606$		0			0
$607$	−8.33422e6	−	8.33422e6i	−0.918107	−	0.918107i	0.0787849	−	0.996892i	$-0.474896\pi$
$607$	−8.33422e6	−	8.33422e6i	−0.918107	−	0.918107i	−0.996892	+	0.0787849i	$0.974896\pi$
$608$		0			0
$609$			417618.i			0.0456285i
$610$		0			0
$611$		−	2.85424e6i		−	0.309305i
$612$		0			0
$613$	−3.43809e6	−	3.43809e6i	−0.369544	−	0.369544i	0.497767	−	0.867311i	$-0.334154\pi$
$613$	−3.43809e6	−	3.43809e6i	−0.369544	−	0.369544i	−0.867311	+	0.497767i	$0.834154\pi$
$614$		0			0
$615$	−5.61320e6	−	9.50208e6i	−0.598443	−	1.01305i
$616$		0			0
$617$	−1.28154e7	+	1.28154e7i	−1.35525	+	1.35525i	−0.475568	+	0.879679i	$0.657757\pi$
$617$	−1.28154e7	+	1.28154e7i	−1.35525	+	1.35525i	−0.879679	+	0.475568i	$0.842243\pi$
$618$		0			0
$619$	−6.06861e6			−0.636594			−0.318297	−	0.947991i	$-0.603111\pi$
$619$	−6.06861e6			−0.636594			−0.318297	+	0.947991i	$0.603111\pi$
$620$		0			0
$621$	−3.31224e6			−0.344662
$622$		0			0
$623$	−44192.0	+	44192.0i	−0.00456166	+	0.00456166i
$624$		0			0
$625$	5.21644e6	+	8.25568e6i	0.534163	+	0.845381i
$626$		0			0
$627$	−8.23732e6	−	8.23732e6i	−0.836791	−	0.836791i
$628$		0			0
$629$			2.26679e7i			2.28447i
$630$		0			0
$631$			1.63004e7i			1.62976i	0.579627	+	0.814882i	$0.303198\pi$
$631$			1.63004e7i			1.62976i	−0.579627	+	0.814882i	$0.696802\pi$
$632$		0			0
$633$	1.87193e7	+	1.87193e7i	1.85687	+	1.85687i
$634$		0			0
$635$	−8.08441e6	+	4.77574e6i	−0.795635	+	0.470009i
$636$		0			0
$637$	1.87321e6	−	1.87321e6i	0.182910	−	0.182910i
$638$		0			0
$639$	1.83230e7			1.77518
$640$		0			0
$641$	−1.89780e6			−0.182434			−0.0912170	−	0.995831i	$-0.529076\pi$
$641$	−1.89780e6			−0.182434			−0.0912170	+	0.995831i	$0.529076\pi$
$642$		0			0
$643$	1.27382e7	−	1.27382e7i	1.21501	−	1.21501i	0.245655	−	0.969357i	$-0.420997\pi$
$643$	1.27382e7	−	1.27382e7i	1.21501	−	1.21501i	0.969357	−	0.245655i	$-0.0790029\pi$
$644$		0			0
$645$	−2.44430e7	−	6.28871e6i	−2.31342	−	0.595199i
$646$		0			0
$647$	−1.46429e6	−	1.46429e6i	−0.137520	−	0.137520i	0.634996	−	0.772516i	$-0.281002\pi$
$647$	−1.46429e6	−	1.46429e6i	−0.137520	−	0.137520i	−0.772516	+	0.634996i	$0.781002\pi$
$648$		0			0
$649$			7.03309e6i			0.655443i
$650$		0			0
$651$			114904.i			0.0106263i
$652$		0			0
$653$	1.34304e6	+	1.34304e6i	0.123256	+	0.123256i	0.766044	−	0.642788i	$-0.222223\pi$
$653$	1.34304e6	+	1.34304e6i	0.123256	+	0.123256i	−0.642788	+	0.766044i	$0.722223\pi$
$654$		0			0
$655$	2.92269e6	+	751954.i	0.266183	+	0.0684838i
$656$		0			0
$657$	7.63983e6	−	7.63983e6i	0.690511	−	0.690511i
$658$		0			0
$659$	−1.40391e7			−1.25929			−0.629643	−	0.776885i	$-0.716799\pi$
$659$	−1.40391e7			−1.25929			−0.629643	+	0.776885i	$0.716799\pi$
$660$		0			0
$661$	1.44204e7			1.28373			0.641866	−	0.766817i	$-0.278161\pi$
$661$	1.44204e7			1.28373			0.641866	+	0.766817i	$0.278161\pi$
$662$		0			0
$663$	−3.68683e6	+	3.68683e6i	−0.325739	+	0.325739i
$664$		0			0
$665$	−286032.	+	168969.i	−0.0250819	+	0.0148167i
$666$		0			0
$667$	−9.44104e6	−	9.44104e6i	−0.821685	−	0.821685i
$668$		0			0
$669$		−	9.09525e6i		−	0.785686i
$670$		0			0
$671$			2.45417e6i			0.210426i
$672$		0			0
$673$	−8.05670e6	−	8.05670e6i	−0.685677	−	0.685677i	0.275597	−	0.961273i	$-0.411125\pi$
$673$	−8.05670e6	−	8.05670e6i	−0.685677	−	0.685677i	−0.961273	+	0.275597i	$0.911125\pi$
$674$		0			0
$675$	−1.25955e6	−	4.35138e6i	−0.106403	−	0.367593i
$676$		0			0
$677$	5.78497e6	−	5.78497e6i	0.485098	−	0.485098i	−0.421657	−	0.906755i	$-0.638552\pi$
$677$	5.78497e6	−	5.78497e6i	0.485098	−	0.485098i	0.906755	+	0.421657i	$0.138552\pi$
$678$		0			0
$679$	436030.			0.0362946
$680$		0			0
$681$	−1.61722e7			−1.33629
$682$		0			0
$683$	6.59840e6	−	6.59840e6i	0.541236	−	0.541236i	−0.382655	−	0.923891i	$-0.624990\pi$
$683$	6.59840e6	−	6.59840e6i	0.541236	−	0.541236i	0.923891	+	0.382655i	$0.124990\pi$
$684$		0			0
$685$	−4.07060e6	−	6.89074e6i	−0.331460	−	0.561099i
$686$		0			0
$687$	5.67025e6	+	5.67025e6i	0.458364	+	0.458364i
$688$		0			0
$689$			454716.i			0.0364916i
$690$		0			0
$691$			1.60816e6i			0.128125i	0.997946	+	0.0640626i	$0.0204057\pi$
$691$			1.60816e6i			0.128125i	−0.997946	+	0.0640626i	$0.979594\pi$
$692$		0			0
$693$	−168323.	−	168323.i	−0.0133141	−	0.0133141i
$694$		0			0
$695$	−1.29503e6	+	5.03352e6i	−0.101699	+	0.395284i
$696$		0			0
$697$	−8.42311e6	+	8.42311e6i	−0.656735	+	0.656735i
$698$		0			0
$699$	1.49746e7			1.15921
$700$		0			0
$701$	1.89009e6			0.145274			0.0726368	−	0.997358i	$-0.476859\pi$
$701$	1.89009e6			0.145274			0.0726368	+	0.997358i	$0.476859\pi$
$702$		0			0
$703$	−2.20890e7	+	2.20890e7i	−1.68573	+	1.68573i
$704$		0			0
$705$	5.90085e6	−	2.29354e7i	0.447139	−	1.73794i
$706$		0			0
$707$	−362034.	−	362034.i	−0.0272396	−	0.0272396i
$708$		0			0
$709$			2.56522e6i			0.191650i	0.995398	+	0.0958249i	$0.0305489\pi$
$709$			2.56522e6i			0.191650i	−0.995398	+	0.0958249i	$0.969451\pi$
$710$		0			0
$711$			1.50230e7i			1.11451i
$712$		0			0
$713$	−2.59761e6	−	2.59761e6i	−0.191359	−	0.191359i
$714$		0			0
$715$	1.14650e6	+	1.94081e6i	0.0838704	+	0.141977i
$716$		0			0
$717$	−7.73807e6	+	7.73807e6i	−0.562127	+	0.562127i
$718$		0			0
$719$	1.28532e6			0.0927231			0.0463616	−	0.998925i	$-0.485237\pi$
$719$	1.28532e6			0.0927231			0.0463616	+	0.998925i	$0.485237\pi$
$720$		0			0
$721$	354387.			0.0253886
$722$		0			0
$723$	−2.28428e7	+	2.28428e7i	−1.62519	+	1.62519i
$724$		0			0
$725$	8.81278e6	−	1.59931e7i	0.622685	−	1.13002i
$726$		0			0
$727$	−2.51635e6	−	2.51635e6i	−0.176577	−	0.176577i	0.613285	−	0.789862i	$-0.289848\pi$
$727$	−2.51635e6	−	2.51635e6i	−0.176577	−	0.176577i	−0.789862	+	0.613285i	$0.789848\pi$
$728$		0			0
$729$		−	2.04931e7i		−	1.42820i
$730$		0			0
$731$			2.72420e7i			1.88559i
$732$		0			0
$733$	6.19797e6	+	6.19797e6i	0.426078	+	0.426078i	0.887290	−	0.461212i	$-0.152585\pi$
$733$	6.19797e6	+	6.19797e6i	0.426078	+	0.426078i	−0.461212	+	0.887290i	$0.652585\pi$
$734$		0			0
$735$	1.89250e7	−	1.11796e7i	1.29216	−	0.763324i
$736$		0			0
$737$	−9.56300e6	+	9.56300e6i	−0.648523	+	0.648523i
$738$		0			0
$739$	1.66087e7			1.11873			0.559363	−	0.828923i	$-0.311046\pi$
$739$	1.66087e7			1.11873			0.559363	+	0.828923i	$0.311046\pi$
$740$		0			0
$741$	−7.18534e6			−0.480731
$742$		0			0
$743$	1.70625e7	−	1.70625e7i	1.13389	−	1.13389i	0.144361	−	0.989525i	$-0.453887\pi$
$743$	1.70625e7	−	1.70625e7i	1.13389	−	1.13389i	0.989525	−	0.144361i	$-0.0461128\pi$
$744$		0			0
$745$	1.13186e7	+	2.91206e6i	0.747138	+	0.192225i
$746$		0			0
$747$	1.36241e7	+	1.36241e7i	0.893320	+	0.893320i
$748$		0			0
$749$			393363.i			0.0256206i
$750$		0			0
$751$			2.01562e7i			1.30409i	0.758179	+	0.652047i	$0.226089\pi$
$751$			2.01562e7i			1.30409i	−0.758179	+	0.652047i	$0.773911\pi$
$752$		0			0
$753$	6.09849e6	+	6.09849e6i	0.391954	+	0.391954i
$754$		0			0
$755$	2.04735e6	+	526744.i	0.130715	+	0.0336304i
$756$		0			0
$757$	−1.27967e7	+	1.27967e7i	−0.811633	+	0.811633i	−0.984879	−	0.173246i	$-0.944574\pi$
$757$	−1.27967e7	+	1.27967e7i	−0.811633	+	0.811633i	0.173246	+	0.984879i	$0.444574\pi$
$758$		0			0
$759$	1.36754e7			0.861660
$760$		0			0
$761$	−1.56925e6			−0.0982272			−0.0491136	−	0.998793i	$-0.515640\pi$
$761$	−1.56925e6			−0.0982272			−0.0491136	+	0.998793i	$0.515640\pi$
$762$		0			0
$763$	407622.	−	407622.i	0.0253481	−	0.0253481i
$764$		0			0
$765$	−2.07289e7	+	1.22453e7i	−1.28063	+	0.756510i
$766$		0			0
$767$	3.06746e6	+	3.06746e6i	0.188274	+	0.188274i
$768$		0			0
$769$		−	2.88122e7i		−	1.75696i	−0.477783	−	0.878478i	$-0.658560\pi$
$769$		−	2.88122e7i		−	1.75696i	0.477783	−	0.878478i	$-0.341440\pi$
$770$		0			0
$771$		−	2.50590e6i		−	0.151820i
$772$		0			0
$773$	1.17155e7	+	1.17155e7i	0.705201	+	0.705201i	0.965522	−	0.260321i	$-0.0838284\pi$
$773$	1.17155e7	+	1.17155e7i	0.705201	+	0.705201i	−0.260321	+	0.965522i	$0.583828\pi$
$774$		0			0
$775$	2.42475e6	−	4.40034e6i	0.145015	−	0.263167i
$776$		0			0
$777$	−811073.	+	811073.i	−0.0481956	+	0.0481956i
$778$		0			0
$779$	−1.64160e7			−0.969220
$780$		0			0
$781$	−1.53640e7			−0.901314
$782$		0			0
$783$	−5.98956e6	+	5.98956e6i	−0.349133	+	0.349133i
$784$		0			0
$785$	−1.00751e7	−	1.70552e7i	−0.583547	−	0.987833i
$786$		0			0
$787$	2.61369e6	+	2.61369e6i	0.150424	+	0.150424i	0.778308	−	0.627883i	$-0.216078\pi$
$787$	2.61369e6	+	2.61369e6i	0.150424	+	0.150424i	−0.627883	+	0.778308i	$0.716078\pi$
$788$		0			0
$789$			1.61440e7i			0.923250i
$790$		0			0
$791$		−	561679.i		−	0.0319188i
$792$		0			0
$793$	1.07038e6	+	1.07038e6i	0.0604441	+	0.0604441i
$794$		0			0
$795$	−940080.	+	3.65390e6i	−0.0527530	+	0.205040i
$796$		0			0
$797$	−4.52543e6	+	4.52543e6i	−0.252356	+	0.252356i	−0.821936	−	0.569580i	$-0.807106\pi$
$797$	−4.52543e6	+	4.52543e6i	−0.252356	+	0.252356i	0.569580	+	0.821936i	$0.307106\pi$
$798$		0			0
$799$	−2.55619e7			−1.41653
$800$		0			0
$801$	−6.24165e6			−0.343730
$802$		0			0
$803$	−6.40607e6	+	6.40607e6i	−0.350593	+	0.350593i
$804$		0			0
$805$	97172.8	−	377691.i	0.00528512	−	0.0205422i
$806$		0			0
$807$	−2.40323e7	−	2.40323e7i	−1.29901	−	1.29901i
$808$		0			0
$809$		−	3.71301e6i		−	0.199459i	−0.995015	−	0.0997297i	$-0.968202\pi$
$809$		−	3.71301e6i		−	0.199459i	0.995015	−	0.0997297i	$-0.0317978\pi$
$810$		0			0
$811$			2.34173e7i			1.25021i	0.780539	+	0.625107i	$0.214945\pi$
$811$			2.34173e7i			1.25021i	−0.780539	+	0.625107i	$0.785055\pi$
$812$		0			0
$813$	−7.36544e6	−	7.36544e6i	−0.390816	−	0.390816i
$814$		0			0
$815$	4.59537e6	+	7.77909e6i	0.242341	+	0.410237i
$816$		0			0
$817$	−2.65463e7	+	2.65463e7i	−1.39139	+	1.39139i
$818$		0			0
$819$	−146827.			−0.00764885
$820$		0			0
$821$	2.80546e7			1.45260			0.726300	−	0.687377i	$-0.241238\pi$
$821$	2.80546e7			1.45260			0.726300	+	0.687377i	$0.241238\pi$
$822$		0			0
$823$	1.24663e7	−	1.24663e7i	0.641561	−	0.641561i	−0.309378	−	0.950939i	$-0.600121\pi$
$823$	1.24663e7	−	1.24663e7i	0.641561	−	0.641561i	0.950939	+	0.309378i	$0.100121\pi$
$824$		0			0
$825$	5.20036e6	+	1.79657e7i	0.266010	+	0.918989i
$826$		0			0
$827$	−2.15743e6	−	2.15743e6i	−0.109691	−	0.109691i	0.650131	−	0.759822i	$-0.274714\pi$
$827$	−2.15743e6	−	2.15743e6i	−0.109691	−	0.109691i	−0.759822	+	0.650131i	$0.774714\pi$
$828$		0			0
$829$			2.15226e7i			1.08770i	0.839184	+	0.543848i	$0.183033\pi$
$829$			2.15226e7i			1.08770i	−0.839184	+	0.543848i	$0.816967\pi$
$830$		0			0
$831$		−	1.71999e7i		−	0.864020i
$832$		0			0
$833$	−1.67760e7	−	1.67760e7i	−0.837677	−	0.837677i
$834$		0			0
$835$	2.39263e7	−	1.41341e7i	1.18757	−	0.701537i
$836$		0			0
$837$	−1.64797e6	+	1.64797e6i	−0.0813084	+	0.0813084i
$838$		0			0
$839$	−8.19583e6			−0.401965			−0.200982	−	0.979595i	$-0.564413\pi$
$839$	−8.19583e6			−0.401965			−0.200982	+	0.979595i	$0.564413\pi$
$840$		0			0
$841$	−1.36335e7			−0.664687
$842$		0			0
$843$	−1.72368e7	+	1.72368e7i	−0.835386	+	0.835386i
$844$		0			0
$845$	−1.87548e7	−	4.82525e6i	−0.903587	−	0.232476i
$846$		0			0
$847$	−206559.	−	206559.i	−0.00989319	−	0.00989319i
$848$		0			0
$849$			1.48423e7i			0.706694i
$850$		0			0
$851$		−	3.66716e7i		−	1.73583i
$852$		0			0
$853$	−1.35799e7	−	1.35799e7i	−0.639034	−	0.639034i	0.311283	−	0.950317i	$-0.399241\pi$
$853$	−1.35799e7	−	1.35799e7i	−0.639034	−	0.639034i	−0.950317	+	0.311283i	$0.899241\pi$
$854$		0			0
$855$	−3.21320e7	−	8.26696e6i	−1.50322	−	0.386750i
$856$		0			0
$857$	2.21901e7	−	2.21901e7i	1.03206	−	1.03206i	0.0325950	−	0.999469i	$-0.489623\pi$
$857$	2.21901e7	−	2.21901e7i	1.03206	−	1.03206i	0.999469	−	0.0325950i	$-0.0103771\pi$
$858$		0			0
$859$	2.20106e7			1.01777			0.508884	−	0.860835i	$-0.330058\pi$
$859$	2.20106e7			1.01777			0.508884	+	0.860835i	$0.330058\pi$
$860$		0			0
$861$	−602769.			−0.0277104
$862$		0			0
$863$	−8.57998e6	+	8.57998e6i	−0.392157	+	0.392157i	−0.875455	−	0.483299i	$-0.839438\pi$
$863$	−8.57998e6	+	8.57998e6i	−0.392157	+	0.392157i	0.483299	+	0.875455i	$0.339438\pi$
$864$		0			0
$865$	−1.80303e7	+	1.06511e7i	−0.819339	+	0.484011i
$866$		0			0
$867$	9.51714e6	+	9.51714e6i	0.429990	+	0.429990i
$868$		0			0
$869$		−	1.25969e7i		−	0.565868i
$870$		0			0
$871$			8.34173e6i			0.372572i
$872$		0			0
$873$	3.07923e7	+	3.07923e7i	1.36743	+	1.36743i
$874$		0			0
$875$	533134.	−	15966.4i	0.0235405	−	0.000704997i
$876$		0			0
$877$	1.95582e7	−	1.95582e7i	0.858675	−	0.858675i	−0.132507	−	0.991182i	$-0.542303\pi$
$877$	1.95582e7	−	1.95582e7i	0.858675	−	0.858675i	0.991182	+	0.132507i	$0.0423026\pi$
$878$		0			0
$879$	−1.71479e7			−0.748583
$880$		0			0
$881$	1.63267e7			0.708695			0.354347	−	0.935114i	$-0.384703\pi$
$881$	1.63267e7			0.708695			0.354347	+	0.935114i	$0.384703\pi$
$882$		0			0
$883$	2.66296e7	−	2.66296e7i	1.14938	−	1.14938i	0.162701	−	0.986675i	$-0.447979\pi$
$883$	2.66296e7	−	2.66296e7i	1.14938	−	1.14938i	0.986675	−	0.162701i	$-0.0520207\pi$
$884$		0			0
$885$	1.83071e7	+	3.09904e7i	0.785708	+	1.33005i
$886$		0			0
$887$	−1.96242e7	−	1.96242e7i	−0.837497	−	0.837497i	0.151032	−	0.988529i	$-0.451740\pi$
$887$	−1.96242e7	−	1.96242e7i	−0.837497	−	0.837497i	−0.988529	+	0.151032i	$0.951740\pi$
$888$		0			0
$889$			512838.i			0.0217634i
$890$		0			0
$891$			1.02697e7i			0.433375i
$892$		0			0
$893$	−2.49090e7	−	2.49090e7i	−1.04527	−	1.04527i
$894$		0			0
$895$	−8.14290e6	+	3.16498e7i	−0.339799	+	1.32073i
$896$		0			0
$897$	5.96448e6	−	5.96448e6i	0.247509	−	0.247509i
$898$		0			0
$899$	−9.39456e6			−0.387684
$900$		0			0
$901$	4.07233e6			0.167121
$902$		0			0
$903$	−974738.	+	974738.i	−0.0397804	+	0.0397804i
$904$		0			0
$905$	−3.12913e6	+	1.21623e7i	−0.127000	+	0.493622i
$906$		0			0
$907$	7.72965e6	+	7.72965e6i	0.311991	+	0.311991i	0.845680	−	0.533690i	$-0.179195\pi$
$907$	7.72965e6	+	7.72965e6i	0.311991	+	0.311991i	−0.533690	+	0.845680i	$0.679195\pi$
$908$		0			0
$909$		−	5.11335e7i		−	2.05256i
$910$		0			0
$911$		−	4.22203e7i		−	1.68549i	−0.538316	−	0.842743i	$-0.680939\pi$
$911$		−	4.22203e7i		−	1.68549i	0.538316	−	0.842743i	$-0.319061\pi$
$912$		0			0
$913$	−1.14240e7	−	1.14240e7i	−0.453565	−	0.453565i
$914$		0			0
$915$	6.38819e6	+	1.08140e7i	0.252247	+	0.427005i
$916$		0			0
$917$	116551.	−	116551.i	0.00457714	−	0.00457714i
$918$		0			0
$919$	−1.08434e7			−0.423524			−0.211762	−	0.977321i	$-0.567920\pi$
$919$	−1.08434e7			−0.423524			−0.211762	+	0.977321i	$0.567920\pi$
$920$		0			0
$921$	5.75781e7			2.23670
$922$		0			0
$923$	−6.70094e6	+	6.70094e6i	−0.258900	+	0.258900i
$924$		0			0
$925$	4.81765e7	−	1.39451e7i	1.85132	−	0.535881i
$926$		0			0
$927$	2.50267e7	+	2.50267e7i	0.956542	+	0.956542i
$928$		0			0
$929$			1.23730e7i			0.470364i	0.971951	+	0.235182i	$0.0755686\pi$
$929$			1.23730e7i			0.470364i	−0.971951	+	0.235182i	$0.924431\pi$
$930$		0			0
$931$		−	3.26951e7i		−	1.23626i
$932$		0			0
$933$	1.68382e7	+	1.68382e7i	0.633273	+	0.633273i
$934$		0			0
$935$	1.73814e7	−	1.02678e7i	0.650213	−	0.384103i
$936$		0			0
$937$	6.41736e6	−	6.41736e6i	0.238785	−	0.238785i	−0.577562	−	0.816347i	$-0.695996\pi$
$937$	6.41736e6	−	6.41736e6i	0.238785	−	0.238785i	0.816347	+	0.577562i	$0.195996\pi$
$938$		0			0
$939$	4.65235e7			1.72190
$940$		0			0
$941$	−9.23235e6			−0.339890			−0.169945	−	0.985454i	$-0.554359\pi$
$941$	−9.23235e6			−0.339890			−0.169945	+	0.985454i	$0.554359\pi$
$942$		0			0
$943$	1.36267e7	−	1.36267e7i	0.499013	−	0.499013i
$944$		0			0
$945$	−239614.	−	61648.1i	−0.00872836	−	0.00224564i
$946$		0			0
$947$	9.45749e6	+	9.45749e6i	0.342690	+	0.342690i	0.857378	−	0.514688i	$-0.172092\pi$
$947$	9.45749e6	+	9.45749e6i	0.342690	+	0.342690i	−0.514688	+	0.857378i	$0.672092\pi$
$948$		0			0
$949$			5.58797e6i			0.201413i
$950$		0			0
$951$		−	7.74840e7i		−	2.77818i
$952$		0			0
$953$	−2.10031e7	−	2.10031e7i	−0.749119	−	0.749119i	0.225195	−	0.974314i	$-0.427698\pi$
$953$	−2.10031e7	−	2.10031e7i	−0.749119	−	0.749119i	−0.974314	+	0.225195i	$0.927698\pi$
$954$		0			0
$955$	−968337.	−	249135.i	−0.0343572	−	0.00883947i
$956$		0			0
$957$	2.47294e7	−	2.47294e7i	0.872838	−	0.872838i
$958$		0			0
$959$	−437117.			−0.0153480
$960$		0			0
$961$	2.60443e7			0.909714
$962$		0			0
$963$	−2.77792e7	+	2.77792e7i	−0.965281	+	0.965281i
$964$		0			0
$965$	2.88172e6	−	1.70233e6i	0.0996171	−	0.0588472i
$966$		0			0
$967$	2.08082e7	+	2.08082e7i	0.715595	+	0.715595i	0.967700	−	0.252105i	$-0.0811227\pi$
$967$	2.08082e7	+	2.08082e7i	0.715595	+	0.715595i	−0.252105	+	0.967700i	$0.581123\pi$
$968$		0			0
$969$			6.43502e7i			2.20161i
$970$		0			0
$971$			2.28152e7i			0.776562i	0.921541	+	0.388281i	$0.126931\pi$
$971$			2.28152e7i			0.776562i	−0.921541	+	0.388281i	$0.873069\pi$
$972$		0			0
$973$	200727.	+	200727.i	0.00679711	+	0.00679711i
$974$		0			0
$975$	1.01038e7	+	5.56757e6i	0.340387	+	0.187566i
$976$		0			0
$977$	7.29946e6	−	7.29946e6i	0.244655	−	0.244655i	−0.574118	−	0.818773i	$-0.694655\pi$
$977$	7.29946e6	−	7.29946e6i	0.244655	−	0.244655i	0.818773	+	0.574118i	$0.194655\pi$
$978$		0			0
$979$	5.23368e6			0.174522
$980$		0			0
$981$	5.75723e7			1.91003
$982$		0			0
$983$	6.02463e6	−	6.02463e6i	0.198860	−	0.198860i	−0.600651	−	0.799511i	$-0.705092\pi$
$983$	6.02463e6	−	6.02463e6i	0.198860	−	0.198860i	0.799511	+	0.600651i	$0.205092\pi$
$984$		0			0
$985$	8.42067e6	+	1.42546e7i	0.276539	+	0.468127i
$986$		0			0
$987$	−914622.	−	914622.i	−0.0298847	−	0.0298847i
$988$		0			0
$989$		−	4.40716e7i		−	1.43274i
$990$		0			0
$991$		−	4.94029e7i		−	1.59797i	−0.601352	−	0.798984i	$-0.705371\pi$
$991$		−	4.94029e7i		−	1.59797i	0.601352	−	0.798984i	$-0.294629\pi$
$992$		0			0
$993$	−9.81148e6	−	9.81148e6i	−0.315763	−	0.315763i
$994$		0			0
$995$	−6.23616e6	+	2.42387e7i	−0.199692	+	0.776161i
$996$		0			0
$997$	−2.07170e7	+	2.07170e7i	−0.660070	+	0.660070i	−0.955396	−	0.295327i	$-0.904572\pi$
$997$	−2.07170e7	+	2.07170e7i	−0.660070	+	0.660070i	0.295327	+	0.955396i	$0.404572\pi$
$998$		0			0
$999$	−2.32651e7			−0.737551

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.6.n.b.63.1	yes	14
4.3	odd	2		160.6.n.a.63.7	✓	14
5.2	odd	4		160.6.n.a.127.7	yes	14
20.7	even	4	inner	160.6.n.b.127.1	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.6.n.a.63.7	✓	14	4.3	odd	2
160.6.n.a.127.7	yes	14	5.2	odd	4
160.6.n.b.63.1	yes	14	1.1	even	1	trivial
160.6.n.b.127.1	yes	14	20.7	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.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-16.5519 + 16.5519i) q^{3} +(13.9288 - 54.1386i) q^{5} +(-2.15894 - 2.15894i) q^{7} -304.928i q^{9} +O(q^{10})\)	\(q+(-16.5519 + 16.5519i) q^{3} +(13.9288 - 54.1386i) q^{5} +(-2.15894 - 2.15894i) q^{7} -304.928i q^{9} +255.685i q^{11} +(111.516 + 111.516i) q^{13} +(665.546 + 1126.64i) q^{15} +(998.711 - 998.711i) q^{17} +1946.41 q^{19} +71.4691 q^{21} +(-1615.69 + 1615.69i) q^{23} +(-2736.97 - 1508.18i) q^{25} +(1025.02 + 1025.02i) q^{27} +5843.34i q^{29} +1607.74i q^{31} +(-4232.06 - 4232.06i) q^{33} +(-146.954 + 86.8106i) q^{35} +(-11348.6 + 11348.6i) q^{37} -3691.59 q^{39} -8433.98 q^{41} +(-13638.6 + 13638.6i) q^{43} +(-16508.4 - 4247.29i) q^{45} +(-12797.4 - 12797.4i) q^{47} -16797.7i q^{49} +33061.0i q^{51} +(2038.79 + 2038.79i) q^{53} +(13842.4 + 3561.40i) q^{55} +(-32216.6 + 32216.6i) q^{57} +27506.9 q^{59} +9598.42 q^{61} +(-658.322 + 658.322i) q^{63} +(7590.61 - 4484.03i) q^{65} +(37401.5 + 37401.5i) q^{67} -53485.4i q^{69} +60089.5i q^{71} +(25054.5 + 25054.5i) q^{73} +(70265.1 - 20338.9i) q^{75} +(552.010 - 552.010i) q^{77} -49267.4 q^{79} +40165.4 q^{81} +(-44679.8 + 44679.8i) q^{83} +(-40157.9 - 67979.7i) q^{85} +(-96718.2 - 96718.2i) q^{87} -20469.3i q^{89} -481.514i q^{91} +(-26611.1 - 26611.1i) q^{93} +(27111.2 - 105376. i) q^{95} +(-100982. + 100982. i) q^{97} +77965.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 10 q^{3} + 42 q^{5} + 66 q^{7}+O(q^{10}) \) 14 * q + 10 * q^3 + 42 * q^5 + 66 * q^7	\( 14 q + 10 q^{3} + 42 q^{5} + 66 q^{7} - 414 q^{13} + 278 q^{15} + 1222 q^{17} + 5672 q^{19} + 5924 q^{21} + 2902 q^{23} - 4466 q^{25} - 2168 q^{27} - 2444 q^{33} - 2618 q^{35} - 1790 q^{37} - 11076 q^{39} + 11644 q^{41} - 3982 q^{43} + 14704 q^{45} - 1278 q^{47} + 5882 q^{53} + 65608 q^{55} - 14552 q^{57} - 8504 q^{59} + 20564 q^{61} + 19422 q^{63} + 40798 q^{65} + 107926 q^{67} - 16418 q^{73} + 66586 q^{75} - 13348 q^{77} - 146544 q^{79} + 173806 q^{81} - 36398 q^{83} - 66262 q^{85} + 124384 q^{87} - 306620 q^{93} + 173768 q^{95} - 60314 q^{97} - 388628 q^{99}+O(q^{100}) \) 14 * q + 10 * q^3 + 42 * q^5 + 66 * q^7 - 414 * q^13 + 278 * q^15 + 1222 * q^17 + 5672 * q^19 + 5924 * q^21 + 2902 * q^23 - 4466 * q^25 - 2168 * q^27 - 2444 * q^33 - 2618 * q^35 - 1790 * q^37 - 11076 * q^39 + 11644 * q^41 - 3982 * q^43 + 14704 * q^45 - 1278 * q^47 + 5882 * q^53 + 65608 * q^55 - 14552 * q^57 - 8504 * q^59 + 20564 * q^61 + 19422 * q^63 + 40798 * q^65 + 107926 * q^67 - 16418 * q^73 + 66586 * q^75 - 13348 * q^77 - 146544 * q^79 + 173806 * q^81 - 36398 * q^83 - 66262 * q^85 + 124384 * q^87 - 306620 * q^93 + 173768 * q^95 - 60314 * q^97 - 388628 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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