LMFDB - Embedded newform 20.11.f.a.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,11,Mod(13,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("20.13");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	20.f (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:	$12.7071450535$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 75402 x^{8} + 1918432665 x^{6} + 20025190470928 x^{4} + \cdots + 13\!\cdots\!00 $ x^10 + 75402x^8 + 1918432665x^6 + 20025190470928x^4 + 87673968468747264x^2 + 130532036219814297600
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{22}\cdot 3^{2}\cdot 5^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.5
Root			$95.3750i$ of defining polynomial
Character	$\chi$	$=$	20.17
Dual form			20.11.f.a.13.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(217.737 - 217.737i) q^{3} +(-944.998 + 2978.69i) q^{5} +(21520.5 + 21520.5i) q^{7} -35770.2i q^{9} +O(q^{10})$	\(q+(217.737 - 217.737i) q^{3} +(-944.998 + 2978.69i) q^{5} +(21520.5 + 21520.5i) q^{7} -35770.2i q^{9} -85975.7 q^{11} +(415494. - 415494. i) q^{13} +(442811. + 854334. i) q^{15} +(1.81178e6 + 1.81178e6i) q^{17} -1.42225e6i q^{19} +9.37164e6 q^{21} +(-2.90015e6 + 2.90015e6i) q^{23} +(-7.97958e6 - 5.62971e6i) q^{25} +(5.06867e6 + 5.06867e6i) q^{27} -1.33457e7i q^{29} +4.49702e6 q^{31} +(-1.87201e7 + 1.87201e7i) q^{33} +(-8.44398e7 + 4.37661e7i) q^{35} +(-5.25338e6 - 5.25338e6i) q^{37} -1.80937e8i q^{39} -1.21276e8 q^{41} +(1.73566e7 - 1.73566e7i) q^{43} +(1.06548e8 + 3.38027e7i) q^{45} +(-2.68509e7 - 2.68509e7i) q^{47} +6.43789e8i q^{49} +7.88986e8 q^{51} +(1.97311e8 - 1.97311e8i) q^{53} +(8.12468e7 - 2.56095e8i) q^{55} +(-3.09677e8 - 3.09677e8i) q^{57} +2.66408e8i q^{59} -6.61822e8 q^{61} +(7.69792e8 - 7.69792e8i) q^{63} +(8.44989e8 + 1.63027e9i) q^{65} +(-1.44748e9 - 1.44748e9i) q^{67} +1.26294e9i q^{69} -1.11740e9 q^{71} +(1.83076e7 - 1.83076e7i) q^{73} +(-2.96325e9 + 5.11655e8i) q^{75} +(-1.85024e9 - 1.85024e9i) q^{77} -2.56459e9i q^{79} +4.31947e9 q^{81} +(8.98227e8 - 8.98227e8i) q^{83} +(-7.10887e9 + 3.68461e9i) q^{85} +(-2.90585e9 - 2.90585e9i) q^{87} +4.22207e9i q^{89} +1.78833e10 q^{91} +(9.79169e8 - 9.79169e8i) q^{93} +(4.23644e9 + 1.34402e9i) q^{95} +(5.59920e9 + 5.59920e9i) q^{97} +3.07536e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 62 q^{3} + 894 q^{5} + 22286 q^{7}+O(q^{10}) $ 10 * q + 62 * q^3 + 894 * q^5 + 22286 * q^7	$ 10 q + 62 q^{3} + 894 q^{5} + 22286 q^{7} - 201700 q^{11} + 239298 q^{13} + 213662 q^{15} + 1045442 q^{17} + 4578860 q^{21} - 4097986 q^{23} - 4233934 q^{25} - 4817488 q^{27} + 23221660 q^{31} + 31816220 q^{33} - 55388242 q^{35} - 87811974 q^{37} + 29776460 q^{41} + 156325470 q^{43} - 144135236 q^{45} - 450750018 q^{47} + 1632585820 q^{51} + 701393866 q^{53} - 1301185140 q^{55} - 2564330416 q^{57} + 2991488220 q^{61} + 3352397678 q^{63} - 2867494182 q^{65} - 6990333394 q^{67} + 9915200380 q^{71} + 8401915018 q^{73} - 10170758642 q^{75} - 19825815140 q^{77} + 26071184290 q^{81} + 16998617454 q^{83} - 24280829854 q^{85} - 36065578576 q^{87} + 52347612540 q^{91} + 26277966572 q^{93} - 23431125296 q^{95} - 48945511254 q^{97}+O(q^{100}) $ 10 * q + 62 * q^3 + 894 * q^5 + 22286 * q^7 - 201700 * q^11 + 239298 * q^13 + 213662 * q^15 + 1045442 * q^17 + 4578860 * q^21 - 4097986 * q^23 - 4233934 * q^25 - 4817488 * q^27 + 23221660 * q^31 + 31816220 * q^33 - 55388242 * q^35 - 87811974 * q^37 + 29776460 * q^41 + 156325470 * q^43 - 144135236 * q^45 - 450750018 * q^47 + 1632585820 * q^51 + 701393866 * q^53 - 1301185140 * q^55 - 2564330416 * q^57 + 2991488220 * q^61 + 3352397678 * q^63 - 2867494182 * q^65 - 6990333394 * q^67 + 9915200380 * q^71 + 8401915018 * q^73 - 10170758642 * q^75 - 19825815140 * q^77 + 26071184290 * q^81 + 16998617454 * q^83 - 24280829854 * q^85 - 36065578576 * q^87 + 52347612540 * q^91 + 26277966572 * q^93 - 23431125296 * q^95 - 48945511254 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	217.737	−	217.737i	0.896039	−	0.896039i	−0.0990442	−	0.995083i	$-0.531579\pi$
$3$	217.737	−	217.737i	0.896039	−	0.896039i	0.995083	+	0.0990442i	$0.0315785\pi$
$4$		0			0
$5$	−944.998	+	2978.69i	−0.302399	+	0.953181i
$5$	−944.998	+	2978.69i	−0.302399	+	0.953181i
$6$		0			0
$7$	21520.5	+	21520.5i	1.28045	+	1.28045i	0.940412	+	0.340037i	$0.110440\pi$
$7$	21520.5	+	21520.5i	1.28045	+	1.28045i	0.340037	+	0.940412i	$0.389560\pi$
$8$		0			0
$9$		−	35770.2i		−	0.605771i
$10$		0			0
$11$	−85975.7			−0.533841			−0.266921	−	0.963719i	$-0.586006\pi$
$11$	−85975.7			−0.533841			−0.266921	+	0.963719i	$0.586006\pi$
$12$		0			0
$13$	415494.	−	415494.i	1.11905	−	1.11905i	0.127166	−	0.991881i	$-0.459412\pi$
$13$	415494.	−	415494.i	1.11905	−	1.11905i	0.991881	−	0.127166i	$-0.0405881\pi$
$14$		0			0
$15$	442811.	+	854334.i	0.583126	+	1.12505i
$16$		0			0
$17$	1.81178e6	+	1.81178e6i	1.27603	+	1.27603i	0.942870	+	0.333162i	$0.108116\pi$
$17$	1.81178e6	+	1.81178e6i	1.27603	+	1.27603i	0.333162	+	0.942870i	$0.391884\pi$
$18$		0			0
$19$		−	1.42225e6i		−	0.574391i	−0.957872	−	0.287196i	$-0.907277\pi$
$19$		−	1.42225e6i		−	0.574391i	0.957872	−	0.287196i	$-0.0927230\pi$
$20$		0			0
$21$	9.37164e6			2.29466
$22$		0			0
$23$	−2.90015e6	+	2.90015e6i	−0.450589	+	0.450589i	−0.895550	−	0.444961i	$-0.853218\pi$
$23$	−2.90015e6	+	2.90015e6i	−0.450589	+	0.450589i	0.444961	+	0.895550i	$0.353218\pi$
$24$		0			0
$25$	−7.97958e6	−	5.62971e6i	−0.817109	−	0.576483i
$26$		0			0
$27$	5.06867e6	+	5.06867e6i	0.353244	+	0.353244i
$28$		0			0
$29$		−	1.33457e7i		−	0.650654i	−0.945602	−	0.325327i	$-0.894526\pi$
$29$		−	1.33457e7i		−	0.650654i	0.945602	−	0.325327i	$-0.105474\pi$
$30$		0			0
$31$	4.49702e6			0.157078			0.0785391	−	0.996911i	$-0.474974\pi$
$31$	4.49702e6			0.157078			0.0785391	+	0.996911i	$0.474974\pi$
$32$		0			0
$33$	−1.87201e7	+	1.87201e7i	−0.478342	+	0.478342i
$34$		0			0
$35$	−8.44398e7	+	4.37661e7i	−1.60771	+	0.833293i
$36$		0			0
$37$	−5.25338e6	−	5.25338e6i	−0.0757583	−	0.0757583i	0.668212	−	0.743971i	$-0.267060\pi$
$37$	−5.25338e6	−	5.25338e6i	−0.0757583	−	0.0757583i	−0.743971	+	0.668212i	$0.767060\pi$
$38$		0			0
$39$		−	1.80937e8i		−	2.00542i
$40$		0			0
$41$	−1.21276e8			−1.04678			−0.523390	−	0.852093i	$-0.675333\pi$
$41$	−1.21276e8			−1.04678			−0.523390	+	0.852093i	$0.675333\pi$
$42$		0			0
$43$	1.73566e7	−	1.73566e7i	0.118065	−	0.118065i	−0.645606	−	0.763671i	$-0.723395\pi$
$43$	1.73566e7	−	1.73566e7i	0.118065	−	0.118065i	0.763671	+	0.645606i	$0.223395\pi$
$44$		0			0
$45$	1.06548e8	+	3.38027e7i	0.577410	+	0.183185i
$46$		0			0
$47$	−2.68509e7	−	2.68509e7i	−0.117076	−	0.117076i	0.646141	−	0.763218i	$-0.276382\pi$
$47$	−2.68509e7	−	2.68509e7i	−0.117076	−	0.117076i	−0.763218	+	0.646141i	$0.776382\pi$
$48$		0			0
$49$			6.43789e8i			2.27910i
$50$		0			0
$51$	7.88986e8			2.28675
$52$		0			0
$53$	1.97311e8	−	1.97311e8i	0.471815	−	0.471815i	−0.430687	−	0.902502i	$-0.641729\pi$
$53$	1.97311e8	−	1.97311e8i	0.471815	−	0.471815i	0.902502	+	0.430687i	$0.141729\pi$
$54$		0			0
$55$	8.12468e7	−	2.56095e8i	0.161433	−	0.508848i
$56$		0			0
$57$	−3.09677e8	−	3.09677e8i	−0.514677	−	0.514677i
$58$		0			0
$59$			2.66408e8i			0.372638i	0.982489	+	0.186319i	$0.0596558\pi$
$59$			2.66408e8i			0.372638i	−0.982489	+	0.186319i	$0.940344\pi$
$60$		0			0
$61$	−6.61822e8			−0.783596			−0.391798	−	0.920051i	$-0.628147\pi$
$61$	−6.61822e8			−0.783596			−0.391798	+	0.920051i	$0.628147\pi$
$62$		0			0
$63$	7.69792e8	−	7.69792e8i	0.775659	−	0.775659i
$64$		0			0
$65$	8.44989e8	+	1.63027e9i	0.728256	+	1.40505i
$66$		0			0
$67$	−1.44748e9	−	1.44748e9i	−1.07211	−	1.07211i	−0.997189	−	0.0749212i	$-0.976129\pi$
$67$	−1.44748e9	−	1.44748e9i	−1.07211	−	1.07211i	−0.0749212	−	0.997189i	$-0.523871\pi$
$68$		0			0
$69$			1.26294e9i			0.807491i
$70$		0			0
$71$	−1.11740e9			−0.619320			−0.309660	−	0.950847i	$-0.600215\pi$
$71$	−1.11740e9			−0.619320			−0.309660	+	0.950847i	$0.600215\pi$
$72$		0			0
$73$	1.83076e7	−	1.83076e7i	0.00883113	−	0.00883113i	−0.702677	−	0.711509i	$-0.748012\pi$
$73$	1.83076e7	−	1.83076e7i	0.00883113	−	0.00883113i	0.711509	+	0.702677i	$0.248012\pi$
$74$		0			0
$75$	−2.96325e9	+	5.11655e8i	−1.24871	+	0.215611i
$76$		0			0
$77$	−1.85024e9	−	1.85024e9i	−0.683557	−	0.683557i
$78$		0			0
$79$		−	2.56459e9i		−	0.833457i	−0.909031	−	0.416729i	$-0.863177\pi$
$79$		−	2.56459e9i		−	0.833457i	0.909031	−	0.416729i	$-0.136823\pi$
$80$		0			0
$81$	4.31947e9			1.23881
$82$		0			0
$83$	8.98227e8	−	8.98227e8i	0.228032	−	0.228032i	−0.583838	−	0.811870i	$-0.698450\pi$
$83$	8.98227e8	−	8.98227e8i	0.228032	−	0.228032i	0.811870	+	0.583838i	$0.198450\pi$
$84$		0			0
$85$	−7.10887e9	+	3.68461e9i	−1.60216	+	0.830418i
$86$		0			0
$87$	−2.90585e9	−	2.90585e9i	−0.583011	−	0.583011i
$88$		0			0
$89$			4.22207e9i			0.756093i	0.925787	+	0.378047i	$0.123404\pi$
$89$			4.22207e9i			0.756093i	−0.925787	+	0.378047i	$0.876596\pi$
$90$		0			0
$91$	1.78833e10			2.86577
$92$		0			0
$93$	9.79169e8	−	9.79169e8i	0.140748	−	0.140748i
$94$		0			0
$95$	4.23644e9	+	1.34402e9i	0.547499	+	0.173696i
$96$		0			0
$97$	5.59920e9	+	5.59920e9i	0.652029	+	0.652029i	0.953481	−	0.301452i	$-0.0974714\pi$
$97$	5.59920e9	+	5.59920e9i	0.652029	+	0.652029i	−0.301452	+	0.953481i	$0.597471\pi$
$98$		0			0
$99$			3.07536e9i			0.323386i
$100$		0			0
$101$	−1.23153e9			−0.117176			−0.0585878	−	0.998282i	$-0.518660\pi$
$101$	−1.23153e9			−0.117176			−0.0585878	+	0.998282i	$0.518660\pi$
$102$		0			0
$103$	9.98910e9	−	9.98910e9i	0.861668	−	0.861668i	−0.129864	−	0.991532i	$-0.541454\pi$
$103$	9.98910e9	−	9.98910e9i	0.861668	−	0.861668i	0.991532	+	0.129864i	$0.0414539\pi$
$104$		0			0
$105$	−8.85618e9	+	2.79152e10i	−0.693905	+	2.18723i
$106$		0			0
$107$	−1.79677e10	−	1.79677e10i	−1.28107	−	1.28107i	−0.940057	−	0.341018i	$-0.889228\pi$
$107$	−1.79677e10	−	1.79677e10i	−1.28107	−	1.28107i	−0.341018	−	0.940057i	$-0.610772\pi$
$108$		0			0
$109$		−	2.07428e10i		−	1.34814i	−0.738669	−	0.674068i	$-0.764545\pi$
$109$		−	2.07428e10i		−	1.34814i	0.738669	−	0.674068i	$-0.235455\pi$
$110$		0			0
$111$	−2.28772e9			−0.135765
$112$		0			0
$113$	1.42629e10	−	1.42629e10i	0.774134	−	0.774134i	−0.204692	−	0.978826i	$-0.565619\pi$
$113$	1.42629e10	−	1.42629e10i	0.774134	−	0.774134i	0.978826	+	0.204692i	$0.0656194\pi$
$114$		0			0
$115$	−5.89801e9	−	1.13793e10i	−0.293236	−	0.565751i
$116$		0			0
$117$	−1.48623e10	−	1.48623e10i	−0.677887	−	0.677887i
$118$		0			0
$119$			7.79810e10i			3.26779i
$120$		0			0
$121$	−1.85456e10			−0.715014
$122$		0			0
$123$	−2.64063e10	+	2.64063e10i	−0.937955	+	0.937955i
$124$		0			0
$125$	2.43099e10	−	1.84487e10i	0.796586	−	0.604525i
$126$		0			0
$127$	−3.57139e10	−	3.57139e10i	−1.08098	−	1.08098i	−0.996418	−	0.0845637i	$-0.973050\pi$
$127$	−3.57139e10	−	3.57139e10i	−1.08098	−	1.08098i	−0.0845637	−	0.996418i	$-0.526950\pi$
$128$		0			0
$129$		−	7.55836e9i		−	0.211582i
$130$		0			0
$131$	2.03833e10			0.528346			0.264173	−	0.964475i	$-0.414901\pi$
$131$	2.03833e10			0.528346			0.264173	+	0.964475i	$0.414901\pi$
$132$		0			0
$133$	3.06075e10	−	3.06075e10i	0.735479	−	0.735479i
$134$		0			0
$135$	−1.98879e10	+	1.03081e10i	−0.443527	+	0.229885i
$136$		0			0
$137$	−2.55076e9	−	2.55076e9i	−0.0528526	−	0.0528526i	0.680186	−	0.733039i	$-0.261899\pi$
$137$	−2.55076e9	−	2.55076e9i	−0.0528526	−	0.0528526i	−0.733039	+	0.680186i	$0.761899\pi$
$138$		0			0
$139$		−	5.20961e10i		−	1.00399i	−0.864869	−	0.501997i	$-0.832599\pi$
$139$		−	5.20961e10i		−	1.00399i	0.864869	−	0.501997i	$-0.167401\pi$
$140$		0			0
$141$	−1.16929e10			−0.209810
$142$		0			0
$143$	−3.57224e10	+	3.57224e10i	−0.597394	+	0.597394i
$144$		0			0
$145$	3.97526e10	+	1.26116e10i	0.620191	+	0.196757i
$146$		0			0
$147$	1.40177e11	+	1.40177e11i	2.04216	+	2.04216i
$148$		0			0
$149$			1.19984e10i			0.163377i	0.996658	+	0.0816887i	$0.0260313\pi$
$149$			1.19984e10i			0.163377i	−0.996658	+	0.0816887i	$0.973969\pi$
$150$		0			0
$151$	6.80192e10			0.866457			0.433229	−	0.901284i	$-0.357374\pi$
$151$	6.80192e10			0.866457			0.433229	+	0.901284i	$0.357374\pi$
$152$		0			0
$153$	6.48078e10	−	6.48078e10i	0.772983	−	0.772983i
$154$		0			0
$155$	−4.24967e9	+	1.33952e10i	−0.0475004	+	0.149724i
$156$		0			0
$157$	3.73101e10	+	3.73101e10i	0.391136	+	0.391136i	0.875092	−	0.483956i	$-0.160801\pi$
$157$	3.73101e10	+	3.73101e10i	0.391136	+	0.391136i	−0.483956	+	0.875092i	$0.660801\pi$
$158$		0			0
$159$		−	8.59239e10i		−	0.845529i
$160$		0			0
$161$	−1.24825e11			−1.15391
$162$		0			0
$163$	−8.50673e10	+	8.50673e10i	−0.739307	+	0.739307i	−0.972444	−	0.233137i	$-0.925101\pi$
$163$	−8.50673e10	+	8.50673e10i	−0.739307	+	0.739307i	0.233137	+	0.972444i	$0.425101\pi$
$164$		0			0
$165$	−3.80710e10	−	7.34519e10i	−0.311297	−	0.600598i
$166$		0			0
$167$	4.38001e10	+	4.38001e10i	0.337204	+	0.337204i	0.855314	−	0.518110i	$-0.173364\pi$
$167$	4.38001e10	+	4.38001e10i	0.337204	+	0.337204i	−0.518110	+	0.855314i	$0.673364\pi$
$168$		0			0
$169$		−	2.07413e11i		−	1.50453i
$170$		0			0
$171$	−5.08741e10			−0.347950
$172$		0			0
$173$	−2.06473e11	+	2.06473e11i	−1.33240	+	1.33240i	−0.429177	+	0.903221i	$0.641196\pi$
$173$	−2.06473e11	+	2.06473e11i	−1.33240	+	1.33240i	−0.903221	+	0.429177i	$0.858804\pi$
$174$		0			0
$175$	−5.05704e10	−	2.92879e11i	−0.308110	−	1.78442i
$176$		0			0
$177$	5.80070e10	+	5.80070e10i	0.333898	+	0.333898i
$178$		0			0
$179$			4.02316e10i			0.218928i	0.993991	+	0.109464i	$0.0349135\pi$
$179$			4.02316e10i			0.218928i	−0.993991	+	0.109464i	$0.965087\pi$
$180$		0			0
$181$	3.81629e10			0.196448			0.0982241	−	0.995164i	$-0.468684\pi$
$181$	3.81629e10			0.196448			0.0982241	+	0.995164i	$0.468684\pi$
$182$		0			0
$183$	−1.44103e11	+	1.44103e11i	−0.702132	+	0.702132i
$184$		0			0
$185$	2.06126e10	−	1.06838e10i	0.0951207	−	0.0493022i
$186$		0			0
$187$	−1.55769e11	−	1.55769e11i	−0.681198	−	0.681198i
$188$		0			0
$189$			2.18161e11i			0.904623i
$190$		0			0
$191$	−3.39364e11			−1.33505			−0.667527	−	0.744586i	$-0.732647\pi$
$191$	−3.39364e11			−1.33505			−0.667527	+	0.744586i	$0.732647\pi$
$192$		0			0
$193$	2.17565e11	−	2.17565e11i	0.812463	−	0.812463i	−0.172540	−	0.985003i	$-0.555197\pi$
$193$	2.17565e11	−	2.17565e11i	0.812463	−	0.812463i	0.985003	+	0.172540i	$0.0551974\pi$
$194$		0			0
$195$	5.38957e11	+	1.70985e11i	1.91153	+	0.606438i
$196$		0			0
$197$	3.06071e11	+	3.06071e11i	1.03155	+	1.03155i	0.999486	+	0.0320646i	$0.0102082\pi$
$197$	3.06071e11	+	3.06071e11i	1.03155	+	1.03155i	0.0320646	+	0.999486i	$0.489792\pi$
$198$		0			0
$199$		−	1.32604e11i		−	0.424905i	−0.977171	−	0.212453i	$-0.931855\pi$
$199$		−	1.32604e11i		−	0.424905i	0.977171	−	0.212453i	$-0.0681451\pi$
$200$		0			0
$201$	−6.30343e11			−1.92131
$202$		0			0
$203$	2.87205e11	−	2.87205e11i	0.833129	−	0.833129i
$204$		0			0
$205$	1.14605e11	−	3.61244e11i	0.316545	−	0.997771i
$206$		0			0
$207$	1.03739e11	+	1.03739e11i	0.272954	+	0.272954i
$208$		0			0
$209$			1.22279e11i			0.306634i
$210$		0			0
$211$	2.11326e11			0.505291			0.252645	−	0.967559i	$-0.418699\pi$
$211$	2.11326e11			0.505291			0.252645	+	0.967559i	$0.418699\pi$
$212$		0			0
$213$	−2.43299e11	+	2.43299e11i	−0.554935	+	0.554935i
$214$		0			0
$215$	3.52980e10	+	6.81018e10i	0.0768347	+	0.148240i
$216$		0			0
$217$	9.67781e10	+	9.67781e10i	0.201131	+	0.201131i
$218$		0			0
$219$		−	7.97249e9i		−	0.0158261i
$220$		0			0
$221$	1.50557e12			2.85588
$222$		0			0
$223$	2.22052e11	−	2.22052e11i	0.402653	−	0.402653i	−0.476514	−	0.879167i	$-0.658100\pi$
$223$	2.22052e11	−	2.22052e11i	0.402653	−	0.402653i	0.879167	+	0.476514i	$0.158100\pi$
$224$		0			0
$225$	−2.01376e11	+	2.85431e11i	−0.349217	+	0.494981i
$226$		0			0
$227$	−2.15351e11	−	2.15351e11i	−0.357288	−	0.357288i	0.505525	−	0.862812i	$-0.331299\pi$
$227$	−2.15351e11	−	2.15351e11i	−0.357288	−	0.357288i	−0.862812	+	0.505525i	$0.831299\pi$
$228$		0			0
$229$			8.37787e11i			1.33032i	0.746701	+	0.665160i	$0.231637\pi$
$229$			8.37787e11i			1.33032i	−0.746701	+	0.665160i	$0.768363\pi$
$230$		0			0
$231$	−8.05733e11			−1.22499
$232$		0			0
$233$	−8.15420e11	+	8.15420e11i	−1.18741	+	1.18741i	−0.209632	+	0.977780i	$0.567227\pi$
$233$	−8.15420e11	+	8.15420e11i	−1.18741	+	1.18741i	−0.977780	+	0.209632i	$0.932773\pi$
$234$		0			0
$235$	1.05354e11	−	5.46064e10i	0.146999	−	0.0761911i
$236$		0			0
$237$	−5.58408e11	−	5.58408e11i	−0.746810	−	0.746810i
$238$		0			0
$239$		−	1.24196e12i		−	1.59264i	−0.604875	−	0.796320i	$-0.706777\pi$
$239$		−	1.24196e12i		−	1.59264i	0.604875	−	0.796320i	$-0.293223\pi$
$240$		0			0
$241$	−1.26315e11			−0.155371			−0.0776855	−	0.996978i	$-0.524753\pi$
$241$	−1.26315e11			−0.155371			−0.0776855	+	0.996978i	$0.524753\pi$
$242$		0			0
$243$	6.41211e11	−	6.41211e11i	0.756780	−	0.756780i
$244$		0			0
$245$	−1.91765e12	−	6.08379e11i	−2.17240	−	0.689198i
$246$		0			0
$247$	−5.90937e11	−	5.90937e11i	−0.642771	−	0.642771i
$248$		0			0
$249$		−	3.91155e11i		−	0.408651i
$250$		0			0
$251$	1.08444e12			1.08853			0.544263	−	0.838915i	$-0.316809\pi$
$251$	1.08444e12			1.08853			0.544263	+	0.838915i	$0.316809\pi$
$252$		0			0
$253$	2.49342e11	−	2.49342e11i	0.240543	−	0.240543i
$254$		0			0
$255$	−7.45590e11	+	2.35015e12i	−0.691511	+	2.17969i
$256$		0			0
$257$	2.07692e11	+	2.07692e11i	0.185248	+	0.185248i	0.793638	−	0.608390i	$-0.208184\pi$
$257$	2.07692e11	+	2.07692e11i	0.185248	+	0.185248i	−0.608390	+	0.793638i	$0.708184\pi$
$258$		0			0
$259$		−	2.26111e11i		−	0.194009i
$260$		0			0
$261$	−4.77376e11			−0.394147
$262$		0			0
$263$	−9.65428e11	+	9.65428e11i	−0.767257	+	0.767257i	−0.977623	−	0.210365i	$-0.932535\pi$
$263$	−9.65428e11	+	9.65428e11i	−0.767257	+	0.767257i	0.210365	+	0.977623i	$0.432535\pi$
$264$		0			0
$265$	4.01270e11	+	7.74187e11i	0.307049	+	0.592402i
$266$		0			0
$267$	9.19302e11	+	9.19302e11i	0.677489	+	0.677489i
$268$		0			0
$269$			1.01791e12i			0.722681i	0.932434	+	0.361341i	$0.117681\pi$
$269$			1.01791e12i			0.722681i	−0.932434	+	0.361341i	$0.882319\pi$
$270$		0			0
$271$	7.80267e11			0.533822			0.266911	−	0.963721i	$-0.413997\pi$
$271$	7.80267e11			0.533822			0.266911	+	0.963721i	$0.413997\pi$
$272$		0			0
$273$	3.89386e12	−	3.89386e12i	2.56784	−	2.56784i
$274$		0			0
$275$	6.86050e11	+	4.84018e11i	0.436207	+	0.307750i
$276$		0			0
$277$	−1.55085e12	−	1.55085e12i	−0.950977	−	0.950977i	0.0478763	−	0.998853i	$-0.484755\pi$
$277$	−1.55085e12	−	1.55085e12i	−0.950977	−	0.950977i	−0.998853	+	0.0478763i	$0.984755\pi$
$278$		0			0
$279$		−	1.60859e11i		−	0.0951535i
$280$		0			0
$281$	1.67374e12			0.955334			0.477667	−	0.878541i	$-0.341483\pi$
$281$	1.67374e12			0.955334			0.477667	+	0.878541i	$0.341483\pi$
$282$		0			0
$283$	−2.13571e12	+	2.13571e12i	−1.17655	+	1.17655i	−0.195935	+	0.980617i	$0.562774\pi$
$283$	−2.13571e12	+	2.13571e12i	−1.17655	+	1.17655i	−0.980617	+	0.195935i	$0.937226\pi$
$284$		0			0
$285$	1.21508e12	−	6.29788e11i	0.646218	−	0.334943i
$286$		0			0
$287$	−2.60992e12	−	2.60992e12i	−1.34035	−	1.34035i
$288$		0			0
$289$			4.54912e12i			2.25651i
$290$		0			0
$291$	2.43831e12			1.16849
$292$		0			0
$293$	1.39130e12	−	1.39130e12i	0.644292	−	0.644292i	−0.307315	−	0.951608i	$-0.599431\pi$
$293$	1.39130e12	−	1.39130e12i	0.644292	−	0.644292i	0.951608	+	0.307315i	$0.0994307\pi$
$294$		0			0
$295$	−7.93547e11	−	2.51755e11i	−0.355191	−	0.112685i
$296$		0			0
$297$	−4.35782e11	−	4.35782e11i	−0.188576	−	0.188576i
$298$		0			0
$299$			2.40999e12i			1.00846i
$300$		0			0
$301$	7.47045e11			0.302353
$302$		0			0
$303$	−2.68149e11	+	2.68149e11i	−0.104994	+	0.104994i
$304$		0			0
$305$	6.25420e11	−	1.97136e12i	0.236959	−	0.746909i
$306$		0			0
$307$	2.35024e12	+	2.35024e12i	0.861827	+	0.861827i	0.991550	−	0.129723i	$-0.0414089\pi$
$307$	2.35024e12	+	2.35024e12i	0.861827	+	0.861827i	−0.129723	+	0.991550i	$0.541409\pi$
$308$		0			0
$309$		−	4.35000e12i		−	1.54418i
$310$		0			0
$311$	−4.31700e12			−1.48382			−0.741908	−	0.670502i	$-0.766079\pi$
$311$	−4.31700e12			−1.48382			−0.741908	+	0.670502i	$0.766079\pi$
$312$		0			0
$313$	−1.25085e12	+	1.25085e12i	−0.416375	+	0.416375i	−0.883952	−	0.467577i	$-0.845127\pi$
$313$	−1.25085e12	+	1.25085e12i	−0.416375	+	0.416375i	0.467577	+	0.883952i	$0.345127\pi$
$314$		0			0
$315$	1.56552e12	+	3.02043e12i	0.504785	+	0.973902i
$316$		0			0
$317$	−2.25338e11	−	2.25338e11i	−0.0703943	−	0.0703943i	0.671033	−	0.741427i	$-0.265851\pi$
$317$	−2.25338e11	−	2.25338e11i	−0.0703943	−	0.0703943i	−0.741427	+	0.671033i	$0.765851\pi$
$318$		0			0
$319$			1.14740e12i			0.347346i
$320$		0			0
$321$	−7.82450e12			−2.29579
$322$		0			0
$323$	2.57681e12	−	2.57681e12i	0.732942	−	0.732942i
$324$		0			0
$325$	−5.65459e12	+	9.76358e11i	−1.55950	+	0.269273i
$326$		0			0
$327$	−4.51647e12	−	4.51647e12i	−1.20798	−	1.20798i
$328$		0			0
$329$		−	1.15569e12i		−	0.299820i
$330$		0			0
$331$	2.33946e12			0.588811			0.294406	−	0.955681i	$-0.404878\pi$
$331$	2.33946e12			0.588811			0.294406	+	0.955681i	$0.404878\pi$
$332$		0			0
$333$	−1.87914e11	+	1.87914e11i	−0.0458922	+	0.0458922i
$334$		0			0
$335$	5.67948e12	−	2.94374e12i	1.34612	−	0.697710i
$336$		0			0
$337$	4.07335e12	+	4.07335e12i	0.937135	+	0.937135i	0.998138	−	0.0610028i	$-0.0194299\pi$
$337$	4.07335e12	+	4.07335e12i	0.937135	+	0.937135i	−0.0610028	+	0.998138i	$0.519430\pi$
$338$		0			0
$339$		−	6.21114e12i		−	1.38731i
$340$		0			0
$341$	−3.86634e11			−0.0838549
$342$		0			0
$343$	−7.77566e12	+	7.77566e12i	−1.63782	+	1.63782i
$344$		0			0
$345$	−3.76191e12	−	1.19348e12i	−0.769686	−	0.244185i
$346$		0			0
$347$	1.14454e12	+	1.14454e12i	0.227500	+	0.227500i	0.811648	−	0.584147i	$-0.198571\pi$
$347$	1.14454e12	+	1.14454e12i	0.227500	+	0.227500i	−0.584147	+	0.811648i	$0.698571\pi$
$348$		0			0
$349$		−	4.04873e12i		−	0.781973i	−0.920396	−	0.390987i	$-0.872134\pi$
$349$		−	4.04873e12i		−	0.781973i	0.920396	−	0.390987i	$-0.127866\pi$
$350$		0			0
$351$	4.21201e12			0.790595
$352$		0			0
$353$	6.79465e11	−	6.79465e11i	0.123963	−	0.123963i	−0.642403	−	0.766367i	$-0.722063\pi$
$353$	6.79465e11	−	6.79465e11i	0.123963	−	0.123963i	0.766367	+	0.642403i	$0.222063\pi$
$354$		0			0
$355$	1.05594e12	−	3.32838e12i	0.187282	−	0.590324i
$356$		0			0
$357$	1.69794e13	+	1.69794e13i	2.92806	+	2.92806i
$358$		0			0
$359$		−	8.55204e11i		−	0.143416i	−0.997426	−	0.0717080i	$-0.977155\pi$
$359$		−	8.55204e11i		−	0.143416i	0.997426	−	0.0717080i	$-0.0228450\pi$
$360$		0			0
$361$	4.10827e12			0.670074
$362$		0			0
$363$	−4.03807e12	+	4.03807e12i	−0.640680	+	0.640680i
$364$		0			0
$365$	3.72320e10	+	7.18332e10i	0.00574714	+	0.0110882i
$366$		0			0
$367$	−1.77990e11	−	1.77990e11i	−0.0267341	−	0.0267341i	0.693613	−	0.720347i	$-0.256018\pi$
$367$	−1.77990e11	−	1.77990e11i	−0.0267341	−	0.0267341i	−0.720347	+	0.693613i	$0.756018\pi$
$368$		0			0
$369$			4.33806e12i			0.634109i
$370$		0			0
$371$	8.49246e12			1.20827
$372$		0			0
$373$	5.47010e12	−	5.47010e12i	0.757619	−	0.757619i	−0.218270	−	0.975888i	$-0.570041\pi$
$373$	5.47010e12	−	5.47010e12i	0.757619	−	0.757619i	0.975888	+	0.218270i	$0.0700412\pi$
$374$		0			0
$375$	1.27621e12	−	9.31013e12i	0.172094	−	1.25545i
$376$		0			0
$377$	−5.54504e12	−	5.54504e12i	−0.728112	−	0.728112i
$378$		0			0
$379$		−	1.23571e12i		−	0.158023i	−0.996874	−	0.0790116i	$-0.974824\pi$
$379$		−	1.23571e12i		−	0.158023i	0.996874	−	0.0790116i	$-0.0251764\pi$
$380$		0			0
$381$	−1.55525e13			−1.93720
$382$		0			0
$383$	−6.54041e12	+	6.54041e12i	−0.793617	+	0.793617i	−0.982080	−	0.188463i	$-0.939649\pi$
$383$	−6.54041e12	+	6.54041e12i	−0.793617	+	0.793617i	0.188463	+	0.982080i	$0.439649\pi$
$384$		0			0
$385$	7.25977e12	−	3.76282e12i	0.858260	−	0.444846i
$386$		0			0
$387$	−6.20848e11	−	6.20848e11i	−0.0715205	−	0.0715205i
$388$		0			0
$389$			1.27373e12i			0.142998i	0.997441	+	0.0714989i	$0.0227783\pi$
$389$			1.27373e12i			0.142998i	−0.997441	+	0.0714989i	$0.977222\pi$
$390$		0			0
$391$	−1.05089e13			−1.14993
$392$		0			0
$393$	4.43822e12	−	4.43822e12i	0.473419	−	0.473419i
$394$		0			0
$395$	7.63914e12	+	2.42354e12i	0.794436	+	0.252037i
$396$		0			0
$397$	5.79936e12	+	5.79936e12i	0.588068	+	0.588068i	0.937108	−	0.349040i	$-0.113492\pi$
$397$	5.79936e12	+	5.79936e12i	0.588068	+	0.588068i	−0.349040	+	0.937108i	$0.613492\pi$
$398$		0			0
$399$		−	1.33288e13i		−	1.31804i
$400$		0			0
$401$	−1.45777e13			−1.40594			−0.702968	−	0.711221i	$-0.748142\pi$
$401$	−1.45777e13			−1.40594			−0.702968	+	0.711221i	$0.748142\pi$
$402$		0			0
$403$	1.86849e12	−	1.86849e12i	0.175778	−	0.175778i
$404$		0			0
$405$	−4.08189e12	+	1.28664e13i	−0.374616	+	1.18081i
$406$		0			0
$407$	4.51663e11	+	4.51663e11i	0.0404429	+	0.0404429i
$408$		0			0
$409$			1.92886e13i			1.68532i	0.538442	+	0.842662i	$0.319013\pi$
$409$			1.92886e13i			1.68532i	−0.538442	+	0.842662i	$0.680987\pi$
$410$		0			0
$411$	−1.11079e12			−0.0947160
$412$		0			0
$413$	−5.73323e12	+	5.73323e12i	−0.477144	+	0.477144i
$414$		0			0
$415$	1.82672e12	+	3.52436e12i	0.148399	+	0.286313i
$416$		0			0
$417$	−1.13433e13	−	1.13433e13i	−0.899617	−	0.899617i
$418$		0			0
$419$		−	1.00227e13i		−	0.776093i	−0.921640	−	0.388047i	$-0.873150\pi$
$419$		−	1.00227e13i		−	0.776093i	0.921640	−	0.388047i	$-0.126850\pi$
$420$		0			0
$421$	−9.44730e12			−0.714327			−0.357164	−	0.934042i	$-0.616256\pi$
$421$	−9.44730e12			−0.714327			−0.357164	+	0.934042i	$0.616256\pi$
$422$		0			0
$423$	−9.60460e11	+	9.60460e11i	−0.0709214	+	0.0709214i
$424$		0			0
$425$	−4.25745e12	−	2.46571e13i	−0.307047	−	1.77827i
$426$		0			0
$427$	−1.42427e13	−	1.42427e13i	−1.00335	−	1.00335i
$428$		0			0
$429$			1.55562e13i			1.07058i
$430$		0			0
$431$	1.35809e13			0.913147			0.456573	−	0.889686i	$-0.349077\pi$
$431$	1.35809e13			0.913147			0.456573	+	0.889686i	$0.349077\pi$
$432$		0			0
$433$	6.10266e12	−	6.10266e12i	0.400940	−	0.400940i	−0.477624	−	0.878564i	$-0.658502\pi$
$433$	6.10266e12	−	6.10266e12i	0.400940	−	0.400940i	0.878564	+	0.477624i	$0.158502\pi$
$434$		0			0
$435$	1.14016e13	−	5.90961e12i	0.732017	−	0.379413i
$436$		0			0
$437$	4.12474e12	+	4.12474e12i	0.258815	+	0.258815i
$438$		0			0
$439$		−	3.09826e12i		−	0.190018i	−0.995476	−	0.0950091i	$-0.969712\pi$
$439$		−	3.09826e12i		−	0.190018i	0.995476	−	0.0950091i	$-0.0302880\pi$
$440$		0			0
$441$	2.30285e13			1.38061
$442$		0			0
$443$	−7.77163e12	+	7.77163e12i	−0.455505	+	0.455505i	−0.897177	−	0.441671i	$-0.854386\pi$
$443$	−7.77163e12	+	7.77163e12i	−0.455505	+	0.455505i	0.441671	+	0.897177i	$0.354386\pi$
$444$		0			0
$445$	−1.25762e13	−	3.98985e12i	−0.720694	−	0.228642i
$446$		0			0
$447$	2.61250e12	+	2.61250e12i	0.146392	+	0.146392i
$448$		0			0
$449$			1.92817e13i			1.05661i	0.849056	+	0.528303i	$0.177171\pi$
$449$			1.92817e13i			1.05661i	−0.849056	+	0.528303i	$0.822829\pi$
$450$		0			0
$451$	1.04268e13			0.558814
$452$		0			0
$453$	1.48103e13	−	1.48103e13i	0.776379	−	0.776379i
$454$		0			0
$455$	−1.68997e13	+	5.32689e13i	−0.866606	+	2.73160i
$456$		0			0
$457$	9.28044e11	+	9.28044e11i	0.0465573	+	0.0465573i	0.730002	−	0.683445i	$-0.239519\pi$
$457$	9.28044e11	+	9.28044e11i	0.0465573	+	0.0465573i	−0.683445	+	0.730002i	$0.739519\pi$
$458$		0			0
$459$			1.83667e13i			0.901502i
$460$		0			0
$461$	3.50051e13			1.68123			0.840614	−	0.541635i	$-0.182194\pi$
$461$	3.50051e13			1.68123			0.840614	+	0.541635i	$0.182194\pi$
$462$		0			0
$463$	1.82360e13	−	1.82360e13i	0.857086	−	0.857086i	−0.133908	−	0.990994i	$-0.542753\pi$
$463$	1.82360e13	−	1.82360e13i	0.857086	−	0.857086i	0.990994	+	0.133908i	$0.0427526\pi$
$464$		0			0
$465$	1.99133e12	+	3.84196e12i	0.0915964	+	0.176721i
$466$		0			0
$467$	1.75301e13	+	1.75301e13i	0.789224	+	0.789224i	0.981367	−	0.192143i	$-0.0615436\pi$
$467$	1.75301e13	+	1.75301e13i	0.789224	+	0.789224i	−0.192143	+	0.981367i	$0.561544\pi$
$468$		0			0
$469$		−	6.23012e13i		−	2.74557i
$470$		0			0
$471$	1.62476e13			0.700946
$472$		0			0
$473$	−1.49224e12	+	1.49224e12i	−0.0630281	+	0.0630281i
$474$		0			0
$475$	−8.00686e12	+	1.13490e13i	−0.331127	+	0.469341i
$476$		0			0
$477$	−7.05784e12	−	7.05784e12i	−0.285812	−	0.285812i
$478$		0			0
$479$		−	3.00857e13i		−	1.19312i	−0.802570	−	0.596559i	$-0.796534\pi$
$479$		−	3.00857e13i		−	1.19312i	0.802570	−	0.596559i	$-0.203466\pi$
$480$		0			0
$481$	−4.36550e12			−0.169554
$482$		0			0
$483$	−2.71791e13	+	2.71791e13i	−1.03395	+	1.03395i
$484$		0			0
$485$	−2.19695e13	+	1.13870e13i	−0.818675	+	0.424329i
$486$		0			0
$487$	−1.37449e13	−	1.37449e13i	−0.501762	−	0.501762i	0.410223	−	0.911985i	$-0.365451\pi$
$487$	−1.37449e13	−	1.37449e13i	−0.501762	−	0.501762i	−0.911985	+	0.410223i	$0.865451\pi$
$488$		0			0
$489$			3.70447e13i			1.32490i
$490$		0			0
$491$	−4.60818e13			−1.61481			−0.807406	−	0.589997i	$-0.799129\pi$
$491$	−4.60818e13			−1.61481			−0.807406	+	0.589997i	$0.799129\pi$
$492$		0			0
$493$	2.41794e13	−	2.41794e13i	0.830254	−	0.830254i
$494$		0			0
$495$	−9.16056e12	−	2.90621e12i	−0.308245	−	0.0977916i
$496$		0			0
$497$	−2.40469e13	−	2.40469e13i	−0.793008	−	0.793008i
$498$		0			0
$499$			1.73560e13i			0.560981i	0.959857	+	0.280490i	$0.0904971\pi$
$499$			1.73560e13i			0.560981i	−0.959857	+	0.280490i	$0.909503\pi$
$500$		0			0
$501$	1.90739e13			0.604296
$502$		0			0
$503$	1.11241e13	−	1.11241e13i	0.345480	−	0.345480i	−0.512943	−	0.858423i	$-0.671445\pi$
$503$	1.11241e13	−	1.11241e13i	0.345480	−	0.345480i	0.858423	+	0.512943i	$0.171445\pi$
$504$		0			0
$505$	1.16379e12	−	3.66834e12i	0.0354338	−	0.111690i
$506$		0			0
$507$	−4.51615e13	−	4.51615e13i	−1.34812	−	1.34812i
$508$		0			0
$509$		−	2.24241e13i		−	0.656335i	−0.944620	−	0.328167i	$-0.893569\pi$
$509$		−	2.24241e13i		−	0.656335i	0.944620	−	0.328167i	$-0.106431\pi$
$510$		0			0
$511$	7.87977e11			0.0226156
$512$		0			0
$513$	7.20892e12	−	7.20892e12i	0.202901	−	0.202901i
$514$		0			0
$515$	2.03148e13	+	3.91941e13i	0.560758	+	1.08189i
$516$		0			0
$517$	2.30852e12	+	2.30852e12i	0.0625001	+	0.0625001i
$518$		0			0
$519$			8.99140e13i			2.38776i
$520$		0			0
$521$	2.77245e12			0.0722229			0.0361115	−	0.999348i	$-0.488503\pi$
$521$	2.77245e12			0.0722229			0.0361115	+	0.999348i	$0.488503\pi$
$522$		0			0
$523$	−2.89110e12	+	2.89110e12i	−0.0738848	+	0.0738848i	−0.743083	−	0.669199i	$-0.766637\pi$
$523$	−2.89110e12	+	2.89110e12i	−0.0738848	+	0.0738848i	0.669199	+	0.743083i	$0.266637\pi$
$524$		0			0
$525$	−7.47818e13	−	5.27597e13i	−1.87499	−	1.32283i
$526$		0			0
$527$	8.14762e12	+	8.14762e12i	0.200437	+	0.200437i
$528$		0			0
$529$			2.46048e13i			0.593938i
$530$		0			0
$531$	9.52946e12			0.225733
$532$		0			0
$533$	−5.03895e13	+	5.03895e13i	−1.17140	+	1.17140i
$534$		0			0
$535$	7.04998e13	−	3.65409e13i	1.60849	−	0.833701i
$536$		0			0
$537$	8.75992e12	+	8.75992e12i	0.196168	+	0.196168i
$538$		0			0
$539$		−	5.53502e13i		−	1.21668i
$540$		0			0
$541$	3.12178e13			0.673621			0.336811	−	0.941572i	$-0.390652\pi$
$541$	3.12178e13			0.673621			0.336811	+	0.941572i	$0.390652\pi$
$542$		0			0
$543$	8.30948e12	−	8.30948e12i	0.176025	−	0.176025i
$544$		0			0
$545$	6.17863e13	+	1.96019e13i	1.28502	+	0.407676i
$546$		0			0
$547$	−2.61590e13	−	2.61590e13i	−0.534175	−	0.534175i	0.387637	−	0.921812i	$-0.373291\pi$
$547$	−2.61590e13	−	2.61590e13i	−0.534175	−	0.534175i	−0.921812	+	0.387637i	$0.873291\pi$
$548$		0			0
$549$			2.36735e13i			0.474680i
$550$		0			0
$551$	−1.89809e13			−0.373730
$552$		0			0
$553$	5.51914e13	−	5.51914e13i	1.06720	−	1.06720i
$554$		0			0
$555$	2.16189e12	−	6.81440e12i	0.0410552	−	0.129409i
$556$		0			0
$557$	−6.90965e12	−	6.90965e12i	−0.128878	−	0.128878i	0.639725	−	0.768604i	$-0.279048\pi$
$557$	−6.90965e12	−	6.90965e12i	−0.128878	−	0.128878i	−0.768604	+	0.639725i	$0.779048\pi$
$558$		0			0
$559$		−	1.44231e13i		−	0.264241i
$560$		0			0
$561$	−6.78336e13			−1.22076
$562$		0			0
$563$	7.11759e13	−	7.11759e13i	1.25832	−	1.25832i	0.306424	−	0.951895i	$-0.400867\pi$
$563$	7.11759e13	−	7.11759e13i	1.25832	−	1.25832i	0.951895	−	0.306424i	$-0.0991326\pi$
$564$		0			0
$565$	2.90064e13	+	5.59632e13i	0.503792	+	0.971987i
$566$		0			0
$567$	9.29572e13	+	9.29572e13i	1.58624	+	1.58624i
$568$		0			0
$569$			4.00303e13i			0.671162i	0.942011	+	0.335581i	$0.108933\pi$
$569$			4.00303e13i			0.671162i	−0.942011	+	0.335581i	$0.891067\pi$
$570$		0			0
$571$	−8.33761e13			−1.37360			−0.686801	−	0.726845i	$-0.740986\pi$
$571$	−8.33761e13			−1.37360			−0.686801	+	0.726845i	$0.740986\pi$
$572$		0			0
$573$	−7.38922e13	+	7.38922e13i	−1.19626	+	1.19626i
$574$		0			0
$575$	3.94690e13	−	6.81497e12i	0.627938	−	0.108424i
$576$		0			0
$577$	6.54321e13	+	6.54321e13i	1.02309	+	1.02309i	0.999727	+	0.0233582i	$0.00743581\pi$
$577$	6.54321e13	+	6.54321e13i	1.02309	+	1.02309i	0.0233582	+	0.999727i	$0.492564\pi$
$578$		0			0
$579$		−	9.47443e13i		−	1.45600i
$580$		0			0
$581$	3.86606e13			0.583967
$582$		0			0
$583$	−1.69639e13	+	1.69639e13i	−0.251874	+	0.251874i
$584$		0			0
$585$	5.83151e13	−	3.02254e13i	0.851141	−	0.441156i
$586$		0			0
$587$	4.87401e13	+	4.87401e13i	0.699353	+	0.699353i	0.964271	−	0.264918i	$-0.0853449\pi$
$587$	4.87401e13	+	4.87401e13i	0.699353	+	0.699353i	−0.264918	+	0.964271i	$0.585345\pi$
$588$		0			0
$589$		−	6.39588e12i		−	0.0902244i
$590$		0			0
$591$	1.33286e14			1.84862
$592$		0			0
$593$	−6.48145e13	+	6.48145e13i	−0.883891	+	0.883891i	−0.993928	−	0.110036i	$-0.964903\pi$
$593$	−6.48145e13	+	6.48145e13i	−0.883891	+	0.883891i	0.110036	+	0.993928i	$0.464903\pi$
$594$		0			0
$595$	−2.32281e14	−	7.36918e13i	−3.11479	−	0.988176i
$596$		0			0
$597$	−2.88729e13	−	2.88729e13i	−0.380732	−	0.380732i
$598$		0			0
$599$		−	3.90741e13i		−	0.506704i	−0.967374	−	0.253352i	$-0.918467\pi$
$599$		−	3.90741e13i		−	0.506704i	0.967374	−	0.253352i	$-0.0815331\pi$
$600$		0			0
$601$	−1.19366e14			−1.52232			−0.761162	−	0.648562i	$-0.775371\pi$
$601$	−1.19366e14			−1.52232			−0.761162	+	0.648562i	$0.775371\pi$
$602$		0			0
$603$	−5.17767e13	+	5.17767e13i	−0.649454	+	0.649454i
$604$		0			0
$605$	1.75256e13	−	5.52417e13i	0.216220	−	0.681538i
$606$		0			0
$607$	4.61189e12	+	4.61189e12i	0.0559674	+	0.0559674i	0.734537	−	0.678569i	$-0.237400\pi$
$607$	4.61189e12	+	4.61189e12i	0.0559674	+	0.0559674i	−0.678569	+	0.734537i	$0.737400\pi$
$608$		0			0
$609$		−	1.25071e14i		−	1.49303i
$610$		0			0
$611$	−2.23128e13			−0.262028
$612$		0			0
$613$	−2.54272e12	+	2.54272e12i	−0.0293762	+	0.0293762i	−0.721642	−	0.692266i	$-0.756612\pi$
$613$	−2.54272e12	+	2.54272e12i	−0.0293762	+	0.0293762i	0.692266	+	0.721642i	$0.256612\pi$
$614$		0			0
$615$	−5.37024e13	−	1.03610e14i	−0.610405	−	1.17768i
$616$		0			0
$617$	−8.20087e13	−	8.20087e13i	−0.917137	−	0.917137i	0.0796837	−	0.996820i	$-0.474609\pi$
$617$	−8.20087e13	−	8.20087e13i	−0.917137	−	0.917137i	−0.996820	+	0.0796837i	$0.974609\pi$
$618$		0			0
$619$			4.93259e12i			0.0542777i	0.999632	+	0.0271389i	$0.00863963\pi$
$619$			4.93259e12i			0.0542777i	−0.999632	+	0.0271389i	$0.991360\pi$
$620$		0			0
$621$	−2.93998e13			−0.318336
$622$		0			0
$623$	−9.08611e13	+	9.08611e13i	−0.968139	+	0.968139i
$624$		0			0
$625$	3.19801e13	+	8.98455e13i	0.335335	+	0.942099i
$626$		0			0
$627$	2.66247e13	+	2.66247e13i	0.274756	+	0.274756i
$628$		0			0
$629$		−	1.90360e13i		−	0.193340i
$630$		0			0
$631$	−3.76130e12			−0.0376003			−0.0188001	−	0.999823i	$-0.505985\pi$
$631$	−3.76130e12			−0.0376003			−0.0188001	+	0.999823i	$0.505985\pi$
$632$		0			0
$633$	4.60137e13	−	4.60137e13i	0.452760	−	0.452760i
$634$		0			0
$635$	1.40130e14	−	7.26311e13i	1.35726	−	0.703484i
$636$		0			0
$637$	2.67491e14	+	2.67491e14i	2.55042	+	2.55042i
$638$		0			0
$639$			3.99694e13i			0.375166i
$640$		0			0
$641$	−1.29655e14			−1.19812			−0.599061	−	0.800704i	$-0.704459\pi$
$641$	−1.29655e14			−1.19812			−0.599061	+	0.800704i	$0.704459\pi$
$642$		0			0
$643$	−9.65193e13	+	9.65193e13i	−0.878131	+	0.878131i	−0.993341	−	0.115210i	$-0.963246\pi$
$643$	−9.65193e13	+	9.65193e13i	−0.878131	+	0.878131i	0.115210	+	0.993341i	$0.463246\pi$
$644$		0			0
$645$	2.25140e13	+	7.14263e12i	0.201676	+	0.0639822i
$646$		0			0
$647$	−1.38565e14	−	1.38565e14i	−1.22217	−	1.22217i	−0.966857	−	0.255317i	$-0.917820\pi$
$647$	−1.38565e14	−	1.38565e14i	−1.22217	−	1.22217i	−0.255317	−	0.966857i	$-0.582180\pi$
$648$		0			0
$649$		−	2.29046e13i		−	0.198929i
$650$		0			0
$651$	4.21444e13			0.360442
$652$		0			0
$653$	−1.84848e13	+	1.84848e13i	−0.155685	+	0.155685i	−0.780652	−	0.624966i	$-0.785113\pi$
$653$	−1.84848e13	+	1.84848e13i	−0.155685	+	0.155685i	0.624966	+	0.780652i	$0.285113\pi$
$654$		0			0
$655$	−1.92622e13	+	6.07157e13i	−0.159772	+	0.503610i
$656$		0			0
$657$	−6.54865e11	−	6.54865e11i	−0.00534965	−	0.00534965i
$658$		0			0
$659$			7.92781e13i			0.637861i	0.947778	+	0.318930i	$0.103324\pi$
$659$			7.92781e13i			0.637861i	−0.947778	+	0.318930i	$0.896676\pi$
$660$		0			0
$661$	9.14633e13			0.724836			0.362418	−	0.932016i	$-0.381951\pi$
$661$	9.14633e13			0.724836			0.362418	+	0.932016i	$0.381951\pi$
$662$		0			0
$663$	3.27819e14	−	3.27819e14i	2.55898	−	2.55898i
$664$		0			0
$665$	6.22464e13	+	1.20094e14i	0.478637	+	0.923453i
$666$		0			0
$667$	3.87044e13	+	3.87044e13i	0.293178	+	0.293178i
$668$		0			0
$669$		−	9.66981e13i		−	0.721585i
$670$		0			0
$671$	5.69006e13			0.418316
$672$		0			0
$673$	−7.71224e12	+	7.71224e12i	−0.0558605	+	0.0558605i	−0.734485	−	0.678625i	$-0.762576\pi$
$673$	−7.71224e12	+	7.71224e12i	−0.0558605	+	0.0558605i	0.678625	+	0.734485i	$0.262576\pi$
$674$		0			0
$675$	−1.19107e13	−	6.89811e13i	−0.0850000	−	0.492279i
$676$		0			0
$677$	−1.23744e14	−	1.23744e14i	−0.870120	−	0.870120i	0.122365	−	0.992485i	$-0.460952\pi$
$677$	−1.23744e14	−	1.23744e14i	−0.870120	−	0.870120i	−0.992485	+	0.122365i	$0.960952\pi$
$678$		0			0
$679$			2.40995e14i			1.66978i
$680$		0			0
$681$	−9.37800e13			−0.640287
$682$		0			0
$683$	5.27727e13	−	5.27727e13i	0.355063	−	0.355063i	−0.506926	−	0.861989i	$-0.669218\pi$
$683$	5.27727e13	−	5.27727e13i	0.355063	−	0.355063i	0.861989	+	0.506926i	$0.169218\pi$
$684$		0			0
$685$	1.00084e13	−	5.18746e12i	0.0663607	−	0.0343955i
$686$		0			0
$687$	1.82418e14	+	1.82418e14i	1.19202	+	1.19202i
$688$		0			0
$689$		−	1.63963e14i		−	1.05597i
$690$		0			0
$691$	−1.74675e14			−1.10877			−0.554383	−	0.832262i	$-0.687046\pi$
$691$	−1.74675e14			−1.10877			−0.554383	+	0.832262i	$0.687046\pi$
$692$		0			0
$693$	−6.61834e13	+	6.61834e13i	−0.414079	+	0.414079i
$694$		0			0
$695$	1.55178e14	+	4.92307e13i	0.956988	+	0.303607i
$696$		0			0
$697$	−2.19726e14	−	2.19726e14i	−1.33572	−	1.33572i
$698$		0			0
$699$			3.55095e14i			2.12794i
$700$		0			0
$701$	2.74147e14			1.61955			0.809775	−	0.586741i	$-0.199589\pi$
$701$	2.74147e14			1.61955			0.809775	+	0.586741i	$0.199589\pi$
$702$		0			0
$703$	−7.47162e12	+	7.47162e12i	−0.0435149	+	0.0435149i
$704$		0			0
$705$	1.10497e13	−	3.48295e13i	0.0634463	−	0.199987i
$706$		0			0
$707$	−2.65031e13	−	2.65031e13i	−0.150037	−	0.150037i
$708$		0			0
$709$			1.99751e14i			1.11496i	0.830192	+	0.557478i	$0.188231\pi$
$709$			1.99751e14i			1.11496i	−0.830192	+	0.557478i	$0.811769\pi$
$710$		0			0
$711$	−9.17360e13			−0.504884
$712$		0			0
$713$	−1.30420e13	+	1.30420e13i	−0.0707778	+	0.0707778i
$714$		0			0
$715$	−7.26485e13	−	1.40164e14i	−0.388773	−	0.750076i
$716$		0			0
$717$	−2.70421e14	−	2.70421e14i	−1.42707	−	1.42707i
$718$		0			0
$719$		−	8.83356e13i		−	0.459718i	−0.973224	−	0.229859i	$-0.926174\pi$
$719$		−	8.83356e13i		−	0.459718i	0.973224	−	0.229859i	$-0.0738265\pi$
$720$		0			0
$721$	4.29941e14			2.20664
$722$		0			0
$723$	−2.75035e13	+	2.75035e13i	−0.139218	+	0.139218i
$724$		0			0
$725$	−7.51322e13	+	1.06493e14i	−0.375091	+	0.531655i
$726$		0			0
$727$	−2.18760e14	−	2.18760e14i	−1.07720	−	1.07720i	−0.996760	−	0.0804387i	$-0.974368\pi$
$727$	−2.18760e14	−	2.18760e14i	−1.07720	−	1.07720i	−0.0804387	−	0.996760i	$-0.525632\pi$
$728$		0			0
$729$		−	2.41706e13i		−	0.117395i
$730$		0			0
$731$	6.28927e13			0.301310
$732$		0			0
$733$	−4.20350e12	+	4.20350e12i	−0.0198651	+	0.0198651i	−0.716970	−	0.697104i	$-0.754471\pi$
$733$	−4.20350e12	+	4.20350e12i	−0.0198651	+	0.0198651i	0.697104	+	0.716970i	$0.254471\pi$
$734$		0			0
$735$	−5.50011e14	+	2.85077e14i	−2.56410	+	1.32900i
$736$		0			0
$737$	1.24448e14	+	1.24448e14i	0.572337	+	0.572337i
$738$		0			0
$739$			4.99681e13i			0.226710i	0.993555	+	0.113355i	$0.0361597\pi$
$739$			4.99681e13i			0.226710i	−0.993555	+	0.113355i	$0.963840\pi$
$740$		0			0
$741$	−2.57338e14			−1.15190
$742$		0			0
$743$	−1.97844e14	+	1.97844e14i	−0.873732	+	0.873732i	−0.992877	−	0.119145i	$-0.961985\pi$
$743$	−1.97844e14	+	1.97844e14i	−0.873732	+	0.873732i	0.119145	+	0.992877i	$0.461985\pi$
$744$		0			0
$745$	−3.57395e13	−	1.13385e13i	−0.155728	−	0.0494052i
$746$		0			0
$747$	−3.21297e13	−	3.21297e13i	−0.138135	−	0.138135i
$748$		0			0
$749$		−	7.73350e14i		−	3.28070i
$750$		0			0
$751$	−2.63524e14			−1.10311			−0.551557	−	0.834137i	$-0.685966\pi$
$751$	−2.63524e14			−1.10311			−0.551557	+	0.834137i	$0.685966\pi$
$752$		0			0
$753$	2.36124e14	−	2.36124e14i	0.975361	−	0.975361i
$754$		0			0
$755$	−6.42780e13	+	2.02608e14i	−0.262016	+	0.825891i
$756$		0			0
$757$	4.39851e13	+	4.39851e13i	0.176940	+	0.176940i	0.790021	−	0.613080i	$-0.210070\pi$
$757$	4.39851e13	+	4.39851e13i	0.176940	+	0.176940i	−0.613080	+	0.790021i	$0.710070\pi$
$758$		0			0
$759$		−	1.08582e14i		−	0.431072i
$760$		0			0
$761$	2.97643e14			1.16620			0.583099	−	0.812401i	$-0.301840\pi$
$761$	2.97643e14			1.16620			0.583099	+	0.812401i	$0.301840\pi$
$762$		0			0
$763$	4.46395e14	−	4.46395e14i	1.72622	−	1.72622i
$764$		0			0
$765$	1.31799e14	+	2.54286e14i	0.503043	+	0.970542i
$766$		0			0
$767$	1.10691e14	+	1.10691e14i	0.416999	+	0.416999i
$768$		0			0
$769$			3.41786e14i			1.27093i	0.772128	+	0.635467i	$0.219192\pi$
$769$			3.41786e14i			1.27093i	−0.772128	+	0.635467i	$0.780808\pi$
$770$		0			0
$771$	9.04447e13			0.331980
$772$		0			0
$773$	−1.53945e14	+	1.53945e14i	−0.557785	+	0.557785i	−0.928676	−	0.370891i	$-0.879052\pi$
$773$	−1.53945e14	+	1.53945e14i	−0.557785	+	0.557785i	0.370891	+	0.928676i	$0.379052\pi$
$774$		0			0
$775$	−3.58843e13	−	2.53169e13i	−0.128350	−	0.0905529i
$776$		0			0
$777$	−4.92328e13	−	4.92328e13i	−0.173840	−	0.173840i
$778$		0			0
$779$			1.72485e14i			0.601261i
$780$		0			0
$781$	9.60688e13			0.330619
$782$		0			0
$783$	6.76447e13	−	6.76447e13i	0.229840	−	0.229840i
$784$		0			0
$785$	−1.46393e14	+	7.58772e13i	−0.491103	+	0.254544i
$786$		0			0
$787$	2.72686e14	+	2.72686e14i	0.903212	+	0.903212i	0.995713	−	0.0925003i	$-0.0294859\pi$
$787$	2.72686e14	+	2.72686e14i	0.903212	+	0.903212i	−0.0925003	+	0.995713i	$0.529486\pi$
$788$		0			0
$789$			4.20420e14i			1.37498i
$790$		0			0
$791$	6.13890e14			1.98248
$792$		0			0
$793$	−2.74983e14	+	2.74983e14i	−0.876881	+	0.876881i
$794$		0			0
$795$	2.55941e14	+	8.11979e13i	0.805943	+	0.255687i
$796$		0			0
$797$	−2.45218e14	−	2.45218e14i	−0.762536	−	0.762536i	0.214244	−	0.976780i	$-0.431271\pi$
$797$	−2.45218e14	−	2.45218e14i	−0.762536	−	0.762536i	−0.976780	+	0.214244i	$0.931271\pi$
$798$		0			0
$799$		−	9.72958e13i		−	0.298786i
$800$		0			0
$801$	1.51024e14			0.458019
$802$		0			0
$803$	−1.57401e12	+	1.57401e12i	−0.00471442	+	0.00471442i
$804$		0			0
$805$	1.17960e14	−	3.71816e14i	0.348943	−	1.09989i
$806$		0			0
$807$	2.21637e14	+	2.21637e14i	0.647550	+	0.647550i
$808$		0			0
$809$		−	6.25564e13i		−	0.180522i	−0.995918	−	0.0902609i	$-0.971230\pi$
$809$		−	6.25564e13i		−	0.180522i	0.995918	−	0.0902609i	$-0.0287701\pi$
$810$		0			0
$811$	3.11979e12			0.00889243			0.00444621	−	0.999990i	$-0.498585\pi$
$811$	3.11979e12			0.00889243			0.00444621	+	0.999990i	$0.498585\pi$
$812$		0			0
$813$	1.69893e14	−	1.69893e14i	0.478326	−	0.478326i
$814$		0			0
$815$	−1.73001e14	−	3.33778e14i	−0.481128	−	0.928260i
$816$		0			0
$817$	−2.46854e13	−	2.46854e13i	−0.0678156	−	0.0678156i
$818$		0			0
$819$		−	6.39689e14i		−	1.73600i
$820$		0			0
$821$	−2.45644e14			−0.658551			−0.329276	−	0.944234i	$-0.606805\pi$
$821$	−2.45644e14			−0.658551			−0.329276	+	0.944234i	$0.606805\pi$
$822$		0			0
$823$	3.73327e14	−	3.73327e14i	0.988759	−	0.988759i	−0.0111784	−	0.999938i	$-0.503558\pi$
$823$	3.73327e14	−	3.73327e14i	0.988759	−	0.988759i	0.999938	+	0.0111784i	$0.00355826\pi$
$824$		0			0
$825$	2.54768e14	−	4.39898e13i	0.666614	−	0.115102i
$826$		0			0
$827$	−3.46998e14	−	3.46998e14i	−0.897015	−	0.897015i	0.0981559	−	0.995171i	$-0.468706\pi$
$827$	−3.46998e14	−	3.46998e14i	−0.897015	−	0.897015i	−0.995171	+	0.0981559i	$0.968706\pi$
$828$		0			0
$829$			3.01733e14i			0.770636i	0.922784	+	0.385318i	$0.125908\pi$
$829$			3.01733e14i			0.770636i	−0.922784	+	0.385318i	$0.874092\pi$
$830$		0			0
$831$	−6.75355e14			−1.70422
$832$		0			0
$833$	−1.16641e15	+	1.16641e15i	−2.90820	+	2.90820i
$834$		0			0
$835$	−1.71858e14	+	8.90761e13i	−0.423387	+	0.219446i
$836$		0			0
$837$	2.27939e13	+	2.27939e13i	0.0554870	+	0.0554870i
$838$		0			0
$839$			3.16450e14i			0.761195i	0.924741	+	0.380597i	$0.124282\pi$
$839$			3.16450e14i			0.761195i	−0.924741	+	0.380597i	$0.875718\pi$
$840$		0			0
$841$	2.42601e14			0.576650
$842$		0			0
$843$	3.64435e14	−	3.64435e14i	0.856016	−	0.856016i
$844$		0			0
$845$	6.17819e14	+	1.96005e14i	1.43409	+	0.454970i
$846$		0			0
$847$	−3.99111e14	−	3.99111e14i	−0.915538	−	0.915538i
$848$		0			0
$849$			9.30050e14i			2.10847i
$850$		0			0
$851$	3.04712e13			0.0682718
$852$		0			0
$853$	5.58415e14	−	5.58415e14i	1.23655	−	1.23655i	0.275150	−	0.961401i	$-0.411272\pi$
$853$	5.58415e14	−	5.58415e14i	1.23655	−	1.23655i	0.961401	−	0.275150i	$-0.0887276\pi$
$854$		0			0
$855$	4.80759e13	−	1.51538e14i	0.105220	−	0.331659i
$856$		0			0
$857$	5.63362e13	+	5.63362e13i	0.121866	+	0.121866i	0.765410	−	0.643543i	$-0.222536\pi$
$857$	5.63362e13	+	5.63362e13i	0.121866	+	0.121866i	−0.643543	+	0.765410i	$0.722536\pi$
$858$		0			0
$859$		−	4.41497e14i		−	0.943977i	−0.881605	−	0.471989i	$-0.843536\pi$
$859$		−	4.41497e14i		−	0.943977i	0.881605	−	0.471989i	$-0.156464\pi$
$860$		0			0
$861$	−1.13655e15			−2.40201
$862$		0			0
$863$	−3.93725e14	+	3.93725e14i	−0.822506	+	0.822506i	−0.986467	−	0.163961i	$-0.947573\pi$
$863$	−3.93725e14	+	3.93725e14i	−0.822506	+	0.822506i	0.163961	+	0.986467i	$0.447573\pi$
$864$		0			0
$865$	−4.19904e14	−	8.10138e14i	−0.867100	−	1.67293i
$866$		0			0
$867$	9.90513e14	+	9.90513e14i	2.02192	+	2.02192i
$868$		0			0
$869$			2.20493e14i			0.444934i
$870$		0			0
$871$	−1.20284e15			−2.39949
$872$		0			0
$873$	2.00284e14	−	2.00284e14i	0.394980	−	0.394980i
$874$		0			0
$875$	9.20185e14	+	1.26136e14i	1.79405	+	0.245924i
$876$		0			0
$877$	2.46549e13	+	2.46549e13i	0.0475232	+	0.0475232i	0.730469	−	0.682946i	$-0.239302\pi$
$877$	2.46549e13	+	2.46549e13i	0.0475232	+	0.0475232i	−0.682946	+	0.730469i	$0.739302\pi$
$878$		0			0
$879$		−	6.05876e14i		−	1.15462i
$880$		0			0
$881$	−9.94024e13			−0.187291			−0.0936455	−	0.995606i	$-0.529852\pi$
$881$	−9.94024e13			−0.187291			−0.0936455	+	0.995606i	$0.529852\pi$
$882$		0			0
$883$	−5.32335e14	+	5.32335e14i	−0.991703	+	0.991703i	−0.999966	−	0.00826295i	$-0.997370\pi$
$883$	−5.32335e14	+	5.32335e14i	−0.991703	+	0.991703i	0.00826295	+	0.999966i	$0.497370\pi$
$884$		0			0
$885$	−2.27601e14	+	1.17968e14i	−0.419236	+	0.217295i
$886$		0			0
$887$	−5.42475e14	−	5.42475e14i	−0.988011	−	0.988011i	0.0119179	−	0.999929i	$-0.496206\pi$
$887$	−5.42475e14	−	5.42475e14i	−0.988011	−	0.988011i	−0.999929	+	0.0119179i	$0.996206\pi$
$888$		0			0
$889$		−	1.53716e15i		−	2.76828i
$890$		0			0
$891$	−3.71369e14			−0.661329
$892$		0			0
$893$	−3.81886e13	+	3.81886e13i	−0.0672476	+	0.0672476i
$894$		0			0
$895$	−1.19837e14	−	3.80187e13i	−0.208678	−	0.0662037i
$896$		0			0
$897$	5.24745e14	+	5.24745e14i	0.903621	+	0.903621i
$898$		0			0
$899$		−	6.00156e13i		−	0.102204i
$900$		0			0
$901$	7.14969e14			1.20410
$902$		0			0
$903$	1.62660e14	−	1.62660e14i	0.270920	−	0.270920i
$904$		0			0
$905$	−3.60638e13	+	1.13675e14i	−0.0594058	+	0.187251i
$906$		0			0
$907$	6.86086e14	+	6.86086e14i	1.11774	+	1.11774i	0.992072	+	0.125671i	$0.0401085\pi$
$907$	6.86086e14	+	6.86086e14i	1.11774	+	1.11774i	0.125671	+	0.992072i	$0.459892\pi$
$908$		0			0
$909$			4.40519e13i			0.0709815i
$910$		0			0
$911$	1.00145e15			1.59601			0.798006	−	0.602650i	$-0.205888\pi$
$911$	1.00145e15			1.59601			0.798006	+	0.602650i	$0.205888\pi$
$912$		0			0
$913$	−7.72257e13	+	7.72257e13i	−0.121733	+	0.121733i
$914$		0			0
$915$	−2.93062e14	−	5.65417e14i	−0.456935	−	0.881584i
$916$		0			0
$917$	4.38660e14	+	4.38660e14i	0.676521	+	0.676521i
$918$		0			0
$919$			1.22010e15i			1.86130i	0.365907	+	0.930651i	$0.380759\pi$
$919$			1.22010e15i			1.86130i	−0.365907	+	0.930651i	$0.619241\pi$
$920$		0			0
$921$	1.02347e15			1.54446
$922$		0			0
$923$	−4.64272e14	+	4.64272e14i	−0.693048	+	0.693048i
$924$		0			0
$925$	1.23448e13	+	7.14949e13i	0.0182295	+	0.105576i
$926$		0			0
$927$	−3.57312e14	−	3.57312e14i	−0.521974	−	0.521974i
$928$		0			0
$929$		−	1.01149e15i		−	1.46178i	−0.682494	−	0.730891i	$-0.739105\pi$
$929$		−	1.01149e15i		−	1.46178i	0.682494	−	0.730891i	$-0.260895\pi$
$930$		0			0
$931$	9.15629e14			1.30910
$932$		0			0
$933$	−9.39972e14	+	9.39972e14i	−1.32956	+	1.32956i
$934$		0			0
$935$	6.11190e14	−	3.16787e14i	0.855299	−	0.443312i
$936$		0			0
$937$	6.71201e14	+	6.71201e14i	0.929297	+	0.929297i	0.997660	−	0.0683634i	$-0.0217777\pi$
$937$	6.71201e14	+	6.71201e14i	0.929297	+	0.929297i	−0.0683634	+	0.997660i	$0.521778\pi$
$938$		0			0
$939$			5.44715e14i			0.746176i
$940$		0			0
$941$	−5.08025e14			−0.688552			−0.344276	−	0.938868i	$-0.611876\pi$
$941$	−5.08025e14			−0.688552			−0.344276	+	0.938868i	$0.611876\pi$
$942$		0			0
$943$	3.51718e14	−	3.51718e14i	0.471668	−	0.471668i
$944$		0			0
$945$	−6.49834e14	−	2.06161e14i	−0.862270	−	0.273557i
$946$		0			0
$947$	2.44363e14	+	2.44363e14i	0.320838	+	0.320838i	0.849089	−	0.528250i	$-0.177152\pi$
$947$	2.44363e14	+	2.44363e14i	0.320838	+	0.320838i	−0.528250	+	0.849089i	$0.677152\pi$
$948$		0			0
$949$		−	1.52134e13i		−	0.0197649i
$950$		0			0
$951$	−9.81288e13			−0.126152
$952$		0			0
$953$	8.52044e14	−	8.52044e14i	1.08392	−	1.08392i	0.0877802	−	0.996140i	$-0.472023\pi$
$953$	8.52044e14	−	8.52044e14i	1.08392	−	1.08392i	0.996140	−	0.0877802i	$-0.0279773\pi$
$954$		0			0
$955$	3.20698e14	−	1.01086e15i	0.403719	−	1.27255i
$956$		0			0
$957$	2.49832e14	+	2.49832e14i	0.311235	+	0.311235i
$958$		0			0
$959$		−	1.09787e14i		−	0.135350i
$960$		0			0
$961$	−7.99405e14			−0.975326
$962$		0			0
$963$	−6.42709e14	+	6.42709e14i	−0.776038	+	0.776038i
$964$		0			0
$965$	4.42462e14	+	8.53659e14i	0.528736	+	1.02011i
$966$		0			0
$967$	−3.60625e14	−	3.60625e14i	−0.426505	−	0.426505i	0.460931	−	0.887436i	$-0.347515\pi$
$967$	−3.60625e14	−	3.60625e14i	−0.426505	−	0.426505i	−0.887436	+	0.460931i	$0.847515\pi$
$968$		0			0
$969$		−	1.12213e15i		−	1.31349i
$970$		0			0
$971$	−6.24070e14			−0.722999			−0.361499	−	0.932372i	$-0.617735\pi$
$971$	−6.24070e14			−0.722999			−0.361499	+	0.932372i	$0.617735\pi$
$972$		0			0
$973$	1.12113e15	−	1.12113e15i	1.28556	−	1.28556i
$974$		0			0
$975$	−1.01863e15	+	1.44381e15i	−1.15609	+	1.63865i
$976$		0			0
$977$	−8.73031e14	−	8.73031e14i	−0.980746	−	0.980746i	0.0190719	−	0.999818i	$-0.493929\pi$
$977$	−8.73031e14	−	8.73031e14i	−0.980746	−	0.980746i	−0.999818	+	0.0190719i	$0.993929\pi$
$978$		0			0
$979$		−	3.62995e14i		−	0.403634i
$980$		0			0
$981$	−7.41972e14			−0.816662
$982$		0			0
$983$	−6.81567e14	+	6.81567e14i	−0.742576	+	0.742576i	−0.973073	−	0.230497i	$-0.925965\pi$
$983$	−6.81567e14	+	6.81567e14i	−0.742576	+	0.742576i	0.230497	+	0.973073i	$0.425965\pi$
$984$		0			0
$985$	−1.20093e15	+	6.22454e14i	−1.29519	+	0.671315i
$986$		0			0
$987$	−2.51637e14	−	2.51637e14i	−0.268651	−	0.268651i
$988$		0			0
$989$			1.00673e14i			0.106398i
$990$		0			0
$991$	2.02924e14			0.212307			0.106154	−	0.994350i	$-0.466146\pi$
$991$	2.02924e14			0.212307			0.106154	+	0.994350i	$0.466146\pi$
$992$		0			0
$993$	5.09388e14	−	5.09388e14i	0.527598	−	0.527598i
$994$		0			0
$995$	3.94987e14	+	1.25311e14i	0.405012	+	0.128491i
$996$		0			0
$997$	−3.12150e14	−	3.12150e14i	−0.316874	−	0.316874i	0.530691	−	0.847565i	$-0.321932\pi$
$997$	−3.12150e14	−	3.12150e14i	−0.316874	−	0.316874i	−0.847565	+	0.530691i	$0.821932\pi$
$998$		0			0
$999$		−	5.32554e13i		−	0.0535224i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.11.f.a.17.5	yes	10
3.2	odd	2		180.11.l.a.37.4		10
4.3	odd	2		80.11.p.e.17.1		10
5.2	odd	4		100.11.f.b.93.1		10
5.3	odd	4	inner	20.11.f.a.13.5	✓	10
5.4	even	2		100.11.f.b.57.1		10
15.8	even	4		180.11.l.a.73.4		10
20.3	even	4		80.11.p.e.33.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.11.f.a.13.5	✓	10	5.3	odd	4	inner
20.11.f.a.17.5	yes	10	1.1	even	1	trivial
80.11.p.e.17.1		10	4.3	odd	2
80.11.p.e.33.1		10	20.3	even	4
100.11.f.b.57.1		10	5.4	even	2
100.11.f.b.93.1		10	5.2	odd	4
180.11.l.a.37.4		10	3.2	odd	2
180.11.l.a.73.4		10	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	20.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(217.737 - 217.737i) q^{3} +(-944.998 + 2978.69i) q^{5} +(21520.5 + 21520.5i) q^{7} -35770.2i q^{9} +O(q^{10})\)	\(q+(217.737 - 217.737i) q^{3} +(-944.998 + 2978.69i) q^{5} +(21520.5 + 21520.5i) q^{7} -35770.2i q^{9} -85975.7 q^{11} +(415494. - 415494. i) q^{13} +(442811. + 854334. i) q^{15} +(1.81178e6 + 1.81178e6i) q^{17} -1.42225e6i q^{19} +9.37164e6 q^{21} +(-2.90015e6 + 2.90015e6i) q^{23} +(-7.97958e6 - 5.62971e6i) q^{25} +(5.06867e6 + 5.06867e6i) q^{27} -1.33457e7i q^{29} +4.49702e6 q^{31} +(-1.87201e7 + 1.87201e7i) q^{33} +(-8.44398e7 + 4.37661e7i) q^{35} +(-5.25338e6 - 5.25338e6i) q^{37} -1.80937e8i q^{39} -1.21276e8 q^{41} +(1.73566e7 - 1.73566e7i) q^{43} +(1.06548e8 + 3.38027e7i) q^{45} +(-2.68509e7 - 2.68509e7i) q^{47} +6.43789e8i q^{49} +7.88986e8 q^{51} +(1.97311e8 - 1.97311e8i) q^{53} +(8.12468e7 - 2.56095e8i) q^{55} +(-3.09677e8 - 3.09677e8i) q^{57} +2.66408e8i q^{59} -6.61822e8 q^{61} +(7.69792e8 - 7.69792e8i) q^{63} +(8.44989e8 + 1.63027e9i) q^{65} +(-1.44748e9 - 1.44748e9i) q^{67} +1.26294e9i q^{69} -1.11740e9 q^{71} +(1.83076e7 - 1.83076e7i) q^{73} +(-2.96325e9 + 5.11655e8i) q^{75} +(-1.85024e9 - 1.85024e9i) q^{77} -2.56459e9i q^{79} +4.31947e9 q^{81} +(8.98227e8 - 8.98227e8i) q^{83} +(-7.10887e9 + 3.68461e9i) q^{85} +(-2.90585e9 - 2.90585e9i) q^{87} +4.22207e9i q^{89} +1.78833e10 q^{91} +(9.79169e8 - 9.79169e8i) q^{93} +(4.23644e9 + 1.34402e9i) q^{95} +(5.59920e9 + 5.59920e9i) q^{97} +3.07536e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 62 q^{3} + 894 q^{5} + 22286 q^{7}+O(q^{10}) \) 10 * q + 62 * q^3 + 894 * q^5 + 22286 * q^7	\( 10 q + 62 q^{3} + 894 q^{5} + 22286 q^{7} - 201700 q^{11} + 239298 q^{13} + 213662 q^{15} + 1045442 q^{17} + 4578860 q^{21} - 4097986 q^{23} - 4233934 q^{25} - 4817488 q^{27} + 23221660 q^{31} + 31816220 q^{33} - 55388242 q^{35} - 87811974 q^{37} + 29776460 q^{41} + 156325470 q^{43} - 144135236 q^{45} - 450750018 q^{47} + 1632585820 q^{51} + 701393866 q^{53} - 1301185140 q^{55} - 2564330416 q^{57} + 2991488220 q^{61} + 3352397678 q^{63} - 2867494182 q^{65} - 6990333394 q^{67} + 9915200380 q^{71} + 8401915018 q^{73} - 10170758642 q^{75} - 19825815140 q^{77} + 26071184290 q^{81} + 16998617454 q^{83} - 24280829854 q^{85} - 36065578576 q^{87} + 52347612540 q^{91} + 26277966572 q^{93} - 23431125296 q^{95} - 48945511254 q^{97}+O(q^{100}) \) 10 * q + 62 * q^3 + 894 * q^5 + 22286 * q^7 - 201700 * q^11 + 239298 * q^13 + 213662 * q^15 + 1045442 * q^17 + 4578860 * q^21 - 4097986 * q^23 - 4233934 * q^25 - 4817488 * q^27 + 23221660 * q^31 + 31816220 * q^33 - 55388242 * q^35 - 87811974 * q^37 + 29776460 * q^41 + 156325470 * q^43 - 144135236 * q^45 - 450750018 * q^47 + 1632585820 * q^51 + 701393866 * q^53 - 1301185140 * q^55 - 2564330416 * q^57 + 2991488220 * q^61 + 3352397678 * q^63 - 2867494182 * q^65 - 6990333394 * q^67 + 9915200380 * q^71 + 8401915018 * q^73 - 10170758642 * q^75 - 19825815140 * q^77 + 26071184290 * q^81 + 16998617454 * q^83 - 24280829854 * q^85 - 36065578576 * q^87 + 52347612540 * q^91 + 26277966572 * q^93 - 23431125296 * q^95 - 48945511254 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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