LMFDB - Embedded newform 224.2.p.a.31.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(31,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("224.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.p (of order $6$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.2353561680715186176.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 2 x^{14} + 41 x^{12} - 92 x^{11} + 66 x^{10} - 104 x^{9} + 291 x^{8} - 388 x^{7} + \cdots + 4 $ x^16 - 4x^15 + 2x^14 + 41x^12 - 92x^11 + 66x^10 - 104x^9 + 291x^8 - 388x^7 + 366x^6 - 344x^5 + 286x^4 - 184x^3 + 84x^2 - 24x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{20} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.3
Root			$-1.57391 - 1.48605i$ of defining polynomial
Character	$\chi$	$=$	224.31
Dual form			224.2.p.a.159.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.376846 + 0.652717i) q^{3} +(1.00367 - 0.579471i) q^{5} +(-0.286555 + 2.63019i) q^{7} +(1.21597 + 2.10613i) q^{9} +O(q^{10})$	\(q+(-0.376846 + 0.652717i) q^{3} +(1.00367 - 0.579471i) q^{5} +(-0.286555 + 2.63019i) q^{7} +(1.21597 + 2.10613i) q^{9} +(1.47390 + 0.850956i) q^{11} -3.51537i q^{13} +0.873485i q^{15} +(4.54440 + 2.62371i) q^{17} +(0.663401 + 1.14904i) q^{19} +(-1.60878 - 1.17821i) q^{21} +(-1.84798 + 1.06693i) q^{23} +(-1.82843 + 3.16693i) q^{25} -4.09402 q^{27} -2.43195 q^{29} +(4.27183 - 7.39903i) q^{31} +(-1.11087 + 0.641359i) q^{33} +(1.23651 + 2.80590i) q^{35} +(-3.21965 - 5.57659i) q^{37} +(2.29454 + 1.32475i) q^{39} -3.51537i q^{41} -12.2677i q^{43} +(2.44088 + 1.40924i) q^{45} +(-4.84494 - 8.39168i) q^{47} +(-6.83577 - 1.50738i) q^{49} +(-3.42508 + 1.97747i) q^{51} +(-6.04807 + 10.4756i) q^{53} +1.97242 q^{55} -1.00000 q^{57} +(3.13853 - 5.43609i) q^{59} +(2.64425 - 1.52666i) q^{61} +(-5.88796 + 2.59472i) q^{63} +(-2.03706 - 3.52828i) q^{65} +(11.4448 + 6.60766i) q^{67} -1.60827i q^{69} +10.2530i q^{71} +(-2.10352 - 1.21447i) q^{73} +(-1.37807 - 2.38689i) q^{75} +(-2.66053 + 3.63279i) q^{77} +(4.10905 - 2.37236i) q^{79} +(-2.10511 + 3.64615i) q^{81} -16.9737 q^{83} +6.08146 q^{85} +(0.916470 - 1.58737i) q^{87} +(6.59615 - 3.80829i) q^{89} +(9.24609 + 1.00735i) q^{91} +(3.21965 + 5.57659i) q^{93} +(1.33167 + 0.768843i) q^{95} -12.0646i q^{97} +4.13896i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^9	$ 16 q - 8 q^{9} - 24 q^{21} + 16 q^{25} + 16 q^{29} + 24 q^{33} - 8 q^{37} - 24 q^{45} - 32 q^{49} - 8 q^{53} - 16 q^{57} - 24 q^{61} + 8 q^{65} - 24 q^{73} + 64 q^{77} - 48 q^{81} - 16 q^{85} - 72 q^{89} + 8 q^{93}+O(q^{100}) $ 16 * q - 8 * q^9 - 24 * q^21 + 16 * q^25 + 16 * q^29 + 24 * q^33 - 8 * q^37 - 24 * q^45 - 32 * q^49 - 8 * q^53 - 16 * q^57 - 24 * q^61 + 8 * q^65 - 24 * q^73 + 64 * q^77 - 48 * q^81 - 16 * q^85 - 72 * q^89 + 8 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	−0.376846	+	0.652717i	−0.217572	+	0.376846i	−0.954065	−	0.299599i	$-0.903147\pi$
$3$	−0.376846	+	0.652717i	−0.217572	+	0.376846i	0.736493	+	0.676445i	$0.236480\pi$
$4$		0			0
$5$	1.00367	−	0.579471i	0.448856	−	0.259147i	−0.258491	−	0.966014i	$-0.583225\pi$
$5$	1.00367	−	0.579471i	0.448856	−	0.259147i	0.707347	+	0.706866i	$0.249892\pi$
$6$		0			0
$7$	−0.286555	+	2.63019i	−0.108307	+	0.994117i
$7$	−0.286555	+	2.63019i	−0.108307	+	0.994117i
$8$		0			0
$9$	1.21597	+	2.10613i	0.405325	+	0.702043i
$10$		0			0
$11$	1.47390	+	0.850956i	0.444397	+	0.256573i	0.705461	−	0.708749i	$-0.250740\pi$
$11$	1.47390	+	0.850956i	0.444397	+	0.256573i	−0.261064	+	0.965322i	$0.584073\pi$
$12$		0			0
$13$		−	3.51537i		−	0.974989i	−0.873126	−	0.487494i	$-0.837911\pi$
$13$		−	3.51537i		−	0.974989i	0.873126	−	0.487494i	$-0.162089\pi$
$14$		0			0
$15$			0.873485i			0.225533i
$16$		0			0
$17$	4.54440	+	2.62371i	1.10218	+	0.636343i	0.936793	−	0.349885i	$-0.113779\pi$
$17$	4.54440	+	2.62371i	1.10218	+	0.636343i	0.165387	+	0.986229i	$0.447113\pi$
$18$		0			0
$19$	0.663401	+	1.14904i	0.152195	+	0.263609i	0.932034	−	0.362371i	$-0.118033\pi$
$19$	0.663401	+	1.14904i	0.152195	+	0.263609i	−0.779839	+	0.625980i	$0.784699\pi$
$20$		0			0
$21$	−1.60878	−	1.17821i	−0.351065	−	0.257108i
$22$		0			0
$23$	−1.84798	+	1.06693i	−0.385330	+	0.222470i	−0.680135	−	0.733087i	$-0.738079\pi$
$23$	−1.84798	+	1.06693i	−0.385330	+	0.222470i	0.294805	+	0.955558i	$0.404745\pi$
$24$		0			0
$25$	−1.82843	+	3.16693i	−0.365685	+	0.633386i
$26$		0			0
$27$	−4.09402			−0.787894
$28$		0			0
$29$	−2.43195			−0.451601			−0.225801	−	0.974174i	$-0.572500\pi$
$29$	−2.43195			−0.451601			−0.225801	+	0.974174i	$0.572500\pi$
$30$		0			0
$31$	4.27183	−	7.39903i	0.767244	−	1.32891i	−0.171808	−	0.985130i	$-0.554961\pi$
$31$	4.27183	−	7.39903i	0.767244	−	1.32891i	0.939052	−	0.343775i	$-0.111706\pi$
$32$		0			0
$33$	−1.11087	+	0.641359i	−0.193377	+	0.111646i
$34$		0			0
$35$	1.23651	+	2.80590i	0.209008	+	0.474283i
$36$		0			0
$37$	−3.21965	−	5.57659i	−0.529307	−	0.916786i	−0.999416	−	0.0341778i	$-0.989119\pi$
$37$	−3.21965	−	5.57659i	−0.529307	−	0.916786i	0.470109	−	0.882608i	$-0.344215\pi$
$38$		0			0
$39$	2.29454	+	1.32475i	0.367421	+	0.212130i
$40$		0			0
$41$		−	3.51537i		−	0.549009i	−0.961586	−	0.274504i	$-0.911486\pi$
$41$		−	3.51537i		−	0.549009i	0.961586	−	0.274504i	$-0.0885138\pi$
$42$		0			0
$43$		−	12.2677i		−	1.87081i	−0.353578	−	0.935405i	$-0.615035\pi$
$43$		−	12.2677i		−	1.87081i	0.353578	−	0.935405i	$-0.384965\pi$
$44$		0			0
$45$	2.44088	+	1.40924i	0.363865	+	0.210078i
$46$		0			0
$47$	−4.84494	−	8.39168i	−0.706707	−	1.22405i	−0.966072	−	0.258273i	$-0.916846\pi$
$47$	−4.84494	−	8.39168i	−0.706707	−	1.22405i	0.259365	−	0.965779i	$-0.416487\pi$
$48$		0			0
$49$	−6.83577	−	1.50738i	−0.976539	−	0.215341i
$50$		0			0
$51$	−3.42508	+	1.97747i	−0.479607	+	0.276901i
$52$		0			0
$53$	−6.04807	+	10.4756i	−0.830767	+	1.43893i	0.0666641	+	0.997775i	$0.478764\pi$
$53$	−6.04807	+	10.4756i	−0.830767	+	1.43893i	−0.897431	+	0.441155i	$0.854569\pi$
$54$		0			0
$55$	1.97242			0.265961
$56$		0			0
$57$	−1.00000			−0.132453
$58$		0			0
$59$	3.13853	−	5.43609i	0.408601	−	0.707718i	−0.586132	−	0.810216i	$-0.699350\pi$
$59$	3.13853	−	5.43609i	0.408601	−	0.707718i	0.994733	+	0.102497i	$0.0326834\pi$
$60$		0			0
$61$	2.64425	−	1.52666i	0.338561	−	0.195469i	−0.321074	−	0.947054i	$-0.604044\pi$
$61$	2.64425	−	1.52666i	0.338561	−	0.195469i	0.659636	+	0.751585i	$0.270711\pi$
$62$		0			0
$63$	−5.88796	+	2.59472i	−0.741813	+	0.326904i
$64$		0			0
$65$	−2.03706	−	3.52828i	−0.252666	−	0.437630i
$66$		0			0
$67$	11.4448	+	6.60766i	1.39820	+	0.807254i	0.994205	−	0.107505i	$-0.0342861\pi$
$67$	11.4448	+	6.60766i	1.39820	+	0.807254i	0.404000	+	0.914759i	$0.367619\pi$
$68$		0			0
$69$		−	1.60827i		−	0.193613i
$70$		0			0
$71$			10.2530i			1.21681i	0.793626	+	0.608405i	$0.208190\pi$
$71$			10.2530i			1.21681i	−0.793626	+	0.608405i	$0.791810\pi$
$72$		0			0
$73$	−2.10352	−	1.21447i	−0.246198	−	0.142143i	0.371824	−	0.928303i	$-0.378733\pi$
$73$	−2.10352	−	1.21447i	−0.246198	−	0.142143i	−0.618022	+	0.786161i	$0.712066\pi$
$74$		0			0
$75$	−1.37807	−	2.38689i	−0.159126	−	0.275614i
$76$		0			0
$77$	−2.66053	+	3.63279i	−0.303195	+	0.413994i
$78$		0			0
$79$	4.10905	−	2.37236i	0.462305	−	0.266912i	−0.250708	−	0.968063i	$-0.580663\pi$
$79$	4.10905	−	2.37236i	0.462305	−	0.266912i	0.713013	+	0.701151i	$0.247330\pi$
$80$		0			0
$81$	−2.10511	+	3.64615i	−0.233901	+	0.405128i
$82$		0			0
$83$	−16.9737			−1.86311			−0.931554	−	0.363604i	$-0.881546\pi$
$83$	−16.9737			−1.86311			−0.931554	+	0.363604i	$0.881546\pi$
$84$		0			0
$85$	6.08146			0.659627
$86$		0			0
$87$	0.916470	−	1.58737i	0.0982559	−	0.170184i
$88$		0			0
$89$	6.59615	−	3.80829i	0.699190	−	0.403678i	−0.107855	−	0.994167i	$-0.534398\pi$
$89$	6.59615	−	3.80829i	0.699190	−	0.403678i	0.807046	+	0.590489i	$0.201065\pi$
$90$		0			0
$91$	9.24609	+	1.00735i	0.969253	+	0.105599i
$92$		0			0
$93$	3.21965	+	5.57659i	0.333862	+	0.578266i
$94$		0			0
$95$	1.33167	+	0.768843i	0.136627	+	0.0788816i
$96$		0			0
$97$		−	12.0646i		−	1.22497i	−0.790482	−	0.612486i	$-0.790170\pi$
$97$		−	12.0646i		−	1.22497i	0.790482	−	0.612486i	$-0.209830\pi$
$98$		0			0
$99$			4.13896i			0.415981i
$100$		0			0
$101$	14.0851	+	8.13205i	1.40152	+	0.809170i	0.994549	−	0.104270i	$-0.0332507\pi$
$101$	14.0851	+	8.13205i	1.40152	+	0.809170i	0.406974	+	0.913440i	$0.366584\pi$
$102$		0			0
$103$	−1.04302	−	1.80656i	−0.102771	−	0.178005i	0.810054	−	0.586355i	$-0.199438\pi$
$103$	−1.04302	−	1.80656i	−0.102771	−	0.178005i	−0.912825	+	0.408350i	$0.866104\pi$
$104$		0			0
$105$	−2.29743	−	0.250301i	−0.224206	−	0.0244269i
$106$		0			0
$107$	−3.50312	+	2.02253i	−0.338660	+	0.195525i	−0.659679	−	0.751547i	$-0.729308\pi$
$107$	−3.50312	+	2.02253i	−0.338660	+	0.195525i	0.321019	+	0.947073i	$0.395975\pi$
$108$		0			0
$109$	1.17525	−	2.03559i	0.112568	−	0.194974i	−0.804237	−	0.594309i	$-0.797426\pi$
$109$	1.17525	−	2.03559i	0.112568	−	0.194974i	0.916805	+	0.399335i	$0.130759\pi$
$110$		0			0
$111$	4.85325			0.460650
$112$		0			0
$113$	4.44664			0.418305			0.209152	−	0.977883i	$-0.432930\pi$
$113$	4.44664			0.418305			0.209152	+	0.977883i	$0.432930\pi$
$114$		0			0
$115$	−1.23651	+	2.14170i	−0.115305	+	0.199714i
$116$		0			0
$117$	7.40383	−	4.27460i	0.684484	−	0.395187i
$118$		0			0
$119$	−8.20307	+	11.2008i	−0.751974	+	1.02677i
$120$		0			0
$121$	−4.05175	−	7.01783i	−0.368341	−	0.637985i
$122$		0			0
$123$	2.29454	+	1.32475i	0.206892	+	0.119449i
$124$		0			0
$125$			10.0328i			0.897360i
$126$		0			0
$127$			4.95401i			0.439598i	0.975545	+	0.219799i	$0.0705401\pi$
$127$			4.95401i			0.439598i	−0.975545	+	0.219799i	$0.929460\pi$
$128$		0			0
$129$	8.00735	+	4.62304i	0.705007	+	0.407036i
$130$		0			0
$131$	9.43681	+	16.3450i	0.824498	+	1.42807i	0.902302	+	0.431104i	$0.141876\pi$
$131$	9.43681	+	16.3450i	0.824498	+	1.42807i	−0.0778040	+	0.996969i	$0.524791\pi$
$132$		0			0
$133$	−3.21230	+	1.41560i	−0.278542	+	0.122748i
$134$		0			0
$135$	−4.10905	+	2.37236i	−0.353651	+	0.204181i
$136$		0			0
$137$	4.53706	−	7.85841i	0.387627	−	0.671389i	−0.604503	−	0.796603i	$-0.706628\pi$
$137$	4.53706	−	7.85841i	0.387627	−	0.671389i	0.992130	+	0.125214i	$0.0399616\pi$
$138$		0			0
$139$	−12.0904			−1.02549			−0.512747	−	0.858540i	$-0.671372\pi$
$139$	−12.0904			−1.02549			−0.512747	+	0.858540i	$0.671372\pi$
$140$		0			0
$141$	7.30319			0.615040
$142$		0			0
$143$	2.99143	−	5.18130i	0.250156	−	0.433282i
$144$		0			0
$145$	−2.44088	+	1.40924i	−0.202704	+	0.117031i
$146$		0			0
$147$	3.55993	−	3.89377i	0.293618	−	0.321153i
$148$		0			0
$149$	0.996327	+	1.72569i	0.0816223	+	0.141374i	0.903947	−	0.427645i	$-0.140657\pi$
$149$	0.996327	+	1.72569i	0.0816223	+	0.141374i	−0.822325	+	0.569019i	$0.807323\pi$
$150$		0			0
$151$	4.45242	+	2.57060i	0.362332	+	0.209193i	0.670103	−	0.742268i	$-0.266250\pi$
$151$	4.45242	+	2.57060i	0.362332	+	0.209193i	−0.307771	+	0.951460i	$0.599583\pi$
$152$		0			0
$153$			12.7615i			1.03170i
$154$		0			0
$155$		−	9.90161i		−	0.795316i
$156$		0			0
$157$	−10.4372	−	6.02592i	−0.832980	−	0.480921i	0.0218920	−	0.999760i	$-0.493031\pi$
$157$	−10.4372	−	6.02592i	−0.832980	−	0.480921i	−0.854872	+	0.518839i	$0.826364\pi$
$158$		0			0
$159$	−4.55839	−	7.89536i	−0.361504	−	0.626143i
$160$		0			0
$161$	−2.27668	−	5.16626i	−0.179428	−	0.407158i
$162$		0			0
$163$	3.59802	−	2.07732i	0.281819	−	0.162708i	−0.352428	−	0.935839i	$-0.614644\pi$
$163$	3.59802	−	2.07732i	0.281819	−	0.162708i	0.634247	+	0.773131i	$0.281310\pi$
$164$		0			0
$165$	−0.743298	+	1.28743i	−0.0578657	+	0.100226i
$166$		0			0
$167$	12.1371			0.939195			0.469598	−	0.882881i	$-0.344399\pi$
$167$	12.1371			0.939195			0.469598	+	0.882881i	$0.344399\pi$
$168$		0			0
$169$	0.642163			0.0493971
$170$		0			0
$171$	−1.61336	+	2.79441i	−0.123376	+	0.213694i
$172$		0			0
$173$	−13.2625	+	7.65709i	−1.00833	+	0.582157i	−0.910701	−	0.413066i	$-0.864458\pi$
$173$	−13.2625	+	7.65709i	−1.00833	+	0.582157i	−0.0976251	+	0.995223i	$0.531125\pi$
$174$		0			0
$175$	−7.80567	−	5.71660i	−0.590053	−	0.432135i
$176$		0			0
$177$	2.36548	+	4.09714i	0.177801	+	0.307960i
$178$		0			0
$179$	−9.07222	−	5.23785i	−0.678089	−	0.391495i	0.121046	−	0.992647i	$-0.461375\pi$
$179$	−9.07222	−	5.23785i	−0.678089	−	0.391495i	−0.799135	+	0.601152i	$0.794709\pi$
$180$		0			0
$181$		−	18.1199i		−	1.34684i	−0.739258	−	0.673422i	$-0.764824\pi$
$181$		−	18.1199i		−	1.34684i	0.739258	−	0.673422i	$-0.235176\pi$
$182$		0			0
$183$			2.30126i			0.170114i
$184$		0			0
$185$	−6.46294	−	3.73138i	−0.475165	−	0.274337i
$186$		0			0
$187$	4.46533	+	7.73417i	0.326537	+	0.565579i
$188$		0			0
$189$	1.17316	−	10.7680i	0.0853348	−	0.783259i
$190$		0			0
$191$	8.43282	−	4.86869i	0.610177	−	0.352286i	−0.162857	−	0.986650i	$-0.552071\pi$
$191$	8.43282	−	4.86869i	0.610177	−	0.352286i	0.773035	+	0.634364i	$0.218738\pi$
$192$		0			0
$193$	−9.15527	+	15.8574i	−0.659011	+	1.14144i	0.321862	+	0.946787i	$0.395691\pi$
$193$	−9.15527	+	15.8574i	−0.659011	+	1.14144i	−0.980872	+	0.194653i	$0.937642\pi$
$194$		0			0
$195$	3.07063			0.219892
$196$		0			0
$197$	−14.6096			−1.04089			−0.520444	−	0.853896i	$-0.674233\pi$
$197$	−14.6096			−1.04089			−0.520444	+	0.853896i	$0.674233\pi$
$198$		0			0
$199$	1.45335	−	2.51727i	0.103025	−	0.178445i	−0.809905	−	0.586562i	$-0.800481\pi$
$199$	1.45335	−	2.51727i	0.103025	−	0.178445i	0.912930	+	0.408117i	$0.133815\pi$
$200$		0			0
$201$	−8.62586	+	4.98014i	−0.608421	+	0.351272i
$202$		0			0
$203$	0.696886	−	6.39648i	0.0489118	−	0.448945i
$204$		0			0
$205$	−2.03706	−	3.52828i	−0.142274	−	0.246426i
$206$		0			0
$207$	−4.49418	−	2.59472i	−0.312367	−	0.180345i
$208$		0			0
$209$			2.25810i			0.156196i
$210$		0			0
$211$		−	19.5814i		−	1.34804i	−0.738713	−	0.674021i	$-0.764566\pi$
$211$		−	19.5814i		−	1.34804i	0.738713	−	0.674021i	$-0.235434\pi$
$212$		0			0
$213$	−6.69232	−	3.86381i	−0.458550	−	0.264744i
$214$		0			0
$215$	−7.10879	−	12.3128i	−0.484815	−	0.839725i
$216$		0			0
$217$	18.2367	+	13.3559i	1.23799	+	0.906661i
$218$		0			0
$219$	1.58541	−	0.915335i	0.107132	−	0.0618526i
$220$		0			0
$221$	9.22332	−	15.9753i	0.620428	−	1.07461i
$222$		0			0
$223$	−3.48955			−0.233677			−0.116839	−	0.993151i	$-0.537276\pi$
$223$	−3.48955			−0.233677			−0.116839	+	0.993151i	$0.537276\pi$
$224$		0			0
$225$	−8.89328			−0.592885
$226$		0			0
$227$	−1.52517	+	2.64167i	−0.101229	+	0.175334i	−0.912191	−	0.409765i	$-0.865611\pi$
$227$	−1.52517	+	2.64167i	−0.101229	+	0.175334i	0.810962	+	0.585099i	$0.198944\pi$
$228$		0			0
$229$	−6.40015	+	3.69513i	−0.422934	+	0.244181i	−0.696332	−	0.717720i	$-0.745186\pi$
$229$	−6.40015	+	3.69513i	−0.422934	+	0.244181i	0.273398	+	0.961901i	$0.411852\pi$
$230$		0			0
$231$	−1.36857	−	3.10557i	−0.0900454	−	0.204332i
$232$		0			0
$233$	3.94088	+	6.82580i	0.258176	+	0.447173i	0.965753	−	0.259462i	$-0.0835453\pi$
$233$	3.94088	+	6.82580i	0.258176	+	0.447173i	−0.707578	+	0.706636i	$0.750212\pi$
$234$		0			0
$235$	−9.72547	−	5.61500i	−0.634420	−	0.366282i
$236$		0			0
$237$			3.57606i			0.232290i
$238$		0			0
$239$			13.2604i			0.857742i	0.903366	+	0.428871i	$0.141089\pi$
$239$			13.2604i			0.857742i	−0.903366	+	0.428871i	$0.858911\pi$
$240$		0			0
$241$	−2.60349	−	1.50313i	−0.167706	−	0.0968250i	0.413798	−	0.910369i	$-0.364202\pi$
$241$	−2.60349	−	1.50313i	−0.167706	−	0.0968250i	−0.581504	+	0.813544i	$0.697535\pi$
$242$		0			0
$243$	−7.72763	−	13.3846i	−0.495728	−	0.858625i
$244$		0			0
$245$	−7.73437	+	2.44821i	−0.494130	+	0.156410i
$246$		0			0
$247$	4.03932	−	2.33210i	0.257016	−	0.148388i
$248$		0			0
$249$	6.39648	−	11.0790i	0.405360	−	0.702105i
$250$		0			0
$251$	20.4166			1.28868			0.644342	−	0.764738i	$-0.277132\pi$
$251$	20.4166			1.28868			0.644342	+	0.764738i	$0.277132\pi$
$252$		0			0
$253$	−3.63164			−0.228319
$254$		0			0
$255$	−2.29177	+	3.96947i	−0.143516	+	0.248578i
$256$		0			0
$257$	17.8402	−	10.3001i	1.11284	−	0.642501i	0.173279	−	0.984873i	$-0.444564\pi$
$257$	17.8402	−	10.3001i	1.11284	−	0.642501i	0.939564	+	0.342372i	$0.111230\pi$
$258$		0			0
$259$	15.5901	−	6.87028i	0.968721	−	0.426898i
$260$		0			0
$261$	−2.95719	−	5.12200i	−0.183045	−	0.317044i
$262$		0			0
$263$	−23.3281	−	13.4685i	−1.43848	−	0.830504i	−0.440731	−	0.897639i	$-0.645281\pi$
$263$	−23.3281	−	13.4685i	−1.43848	−	0.830504i	−0.997744	+	0.0671351i	$0.978614\pi$
$264$		0			0
$265$			14.0187i			0.861164i
$266$		0			0
$267$			5.74055i			0.351316i
$268$		0			0
$269$	−16.5260	−	9.54130i	−1.00761	−	0.581743i	−0.0971180	−	0.995273i	$-0.530962\pi$
$269$	−16.5260	−	9.54130i	−1.00761	−	0.581743i	−0.910491	+	0.413530i	$0.864296\pi$
$270$		0			0
$271$	11.0216	+	19.0899i	0.669512	+	1.15963i	0.978041	+	0.208414i	$0.0668300\pi$
$271$	11.0216	+	19.0899i	0.669512	+	1.15963i	−0.308529	+	0.951215i	$0.599837\pi$
$272$		0			0
$273$	−4.14186	+	5.65546i	−0.250677	+	0.342284i
$274$		0			0
$275$	−5.38984	+	3.11182i	−0.325019	+	0.187650i
$276$		0			0
$277$	2.05542	−	3.56009i	0.123498	−	0.213905i	−0.797647	−	0.603125i	$-0.793922\pi$
$277$	2.05542	−	3.56009i	0.123498	−	0.213905i	0.921145	+	0.389220i	$0.127255\pi$
$278$		0			0
$279$	20.7777			1.24393
$280$		0			0
$281$	−7.73096			−0.461191			−0.230595	−	0.973050i	$-0.574067\pi$
$281$	−7.73096			−0.461191			−0.230595	+	0.973050i	$0.574067\pi$
$282$		0			0
$283$	−14.2866	+	24.7452i	−0.849252	+	1.47095i	0.0326251	+	0.999468i	$0.489613\pi$
$283$	−14.2866	+	24.7452i	−0.849252	+	1.47095i	−0.881877	+	0.471480i	$0.843720\pi$
$284$		0			0
$285$	−1.00367	+	0.579471i	−0.0594525	+	0.0343249i
$286$		0			0
$287$	9.24609	+	1.00735i	0.545779	+	0.0594617i
$288$		0			0
$289$	5.26772	+	9.12396i	0.309866	+	0.536704i
$290$		0			0
$291$	7.87475	+	4.54649i	0.461626	+	0.266520i
$292$		0			0
$293$			6.78319i			0.396278i	0.980174	+	0.198139i	$0.0634898\pi$
$293$			6.78319i			0.396278i	−0.980174	+	0.198139i	$0.936510\pi$
$294$		0			0
$295$		−	7.27474i		−	0.423551i
$296$		0			0
$297$	−6.03417	−	3.48383i	−0.350138	−	0.202152i
$298$		0			0
$299$	3.75066	+	6.49633i	0.216906	+	0.375692i
$300$		0			0
$301$	32.2664	+	3.51537i	1.85980	+	0.202623i
$302$		0			0
$303$	−10.6159	+	6.12907i	−0.609865	+	0.352106i
$304$		0			0
$305$	1.76931	−	3.06453i	0.101310	−	0.175474i
$306$		0			0
$307$	−13.4842			−0.769582			−0.384791	−	0.923004i	$-0.625726\pi$
$307$	−13.4842			−0.769582			−0.384791	+	0.923004i	$0.625726\pi$
$308$		0			0
$309$	1.57222			0.0894407
$310$		0			0
$311$	−6.58207	+	11.4005i	−0.373235	+	0.646462i	−0.990061	−	0.140637i	$-0.955085\pi$
$311$	−6.58207	+	11.4005i	−0.373235	+	0.646462i	0.616826	+	0.787100i	$0.288418\pi$
$312$		0			0
$313$	−12.9853	+	7.49706i	−0.733971	+	0.423759i	−0.819873	−	0.572545i	$-0.805956\pi$
$313$	−12.9853	+	7.49706i	−0.733971	+	0.423759i	0.0859018	+	0.996304i	$0.472623\pi$
$314$		0			0
$315$	−4.40602	+	6.01615i	−0.248251	+	0.338972i
$316$		0			0
$317$	5.60878	+	9.71469i	0.315020	+	0.545631i	0.979442	−	0.201727i	$-0.0646553\pi$
$317$	5.60878	+	9.71469i	0.315020	+	0.545631i	−0.664421	+	0.747358i	$0.731322\pi$
$318$		0			0
$319$	−3.58445	−	2.06948i	−0.200690	−	0.115869i
$320$		0			0
$321$		−	3.04873i		−	0.170163i
$322$		0			0
$323$			6.96229i			0.387392i
$324$		0			0
$325$	11.1329	+	6.42760i	0.617544	+	0.356539i
$326$		0			0
$327$	0.885774	+	1.53421i	0.0489834	+	0.0848417i
$328$		0			0
$329$	23.4600	−	10.3384i	1.29339	−	0.569976i
$330$		0			0
$331$	−9.03875	+	5.21853i	−0.496815	+	0.286836i	−0.727397	−	0.686217i	$-0.759270\pi$
$331$	−9.03875	+	5.21853i	−0.496815	+	0.286836i	0.230583	+	0.973053i	$0.425937\pi$
$332$		0			0
$333$	7.83001	−	13.5620i	0.429082	−	0.743192i
$334$		0			0
$335$	15.3158			0.836791
$336$		0			0
$337$	19.2543			1.04885			0.524424	−	0.851457i	$-0.324281\pi$
$337$	19.2543			1.04885			0.524424	+	0.851457i	$0.324281\pi$
$338$		0			0
$339$	−1.67570	+	2.90240i	−0.0910115	+	0.157636i
$340$		0			0
$341$	12.5925	−	7.27028i	0.681922	−	0.393708i
$342$		0			0
$343$	5.92353	−	17.5474i	0.319840	−	0.947471i
$344$		0			0
$345$	−0.931948	−	1.61418i	−0.0501744	−	0.0869046i
$346$		0			0
$347$	11.0680	+	6.39010i	0.594160	+	0.343038i	0.766741	−	0.641957i	$-0.221877\pi$
$347$	11.0680	+	6.39010i	0.594160	+	0.343038i	−0.172581	+	0.984995i	$0.555211\pi$
$348$		0			0
$349$			14.8521i			0.795016i	0.917599	+	0.397508i	$0.130125\pi$
$349$			14.8521i			0.795016i	−0.917599	+	0.397508i	$0.869875\pi$
$350$		0			0
$351$			14.3920i			0.768188i
$352$		0			0
$353$	−0.229378	−	0.132432i	−0.0122086	−	0.00704862i	0.493883	−	0.869528i	$-0.335577\pi$
$353$	−0.229378	−	0.132432i	−0.0122086	−	0.00704862i	−0.506092	+	0.862480i	$0.668910\pi$
$354$		0			0
$355$	5.94133	+	10.2907i	0.315333	+	0.546173i
$356$		0			0
$357$	−4.21965	−	9.57526i	−0.223327	−	0.506776i
$358$		0			0
$359$	8.80965	−	5.08625i	0.464955	−	0.268442i	−0.249170	−	0.968460i	$-0.580158\pi$
$359$	8.80965	−	5.08625i	0.464955	−	0.268442i	0.714126	+	0.700018i	$0.246825\pi$
$360$		0			0
$361$	8.61980	−	14.9299i	0.453674	−	0.785786i
$362$		0			0
$363$	6.10754			0.320563
$364$		0			0
$365$	−2.81500			−0.147344
$366$		0			0
$367$	−16.4313	+	28.4599i	−0.857707	+	1.48559i	0.0164037	+	0.999865i	$0.494778\pi$
$367$	−16.4313	+	28.4599i	−0.857707	+	1.48559i	−0.874111	+	0.485727i	$0.838555\pi$
$368$		0			0
$369$	7.40383	−	4.27460i	0.385428	−	0.222527i
$370$		0			0
$371$	−25.8196	−	18.9094i	−1.34049	−	0.981727i
$372$		0			0
$373$	9.04807	+	15.6717i	0.468492	+	0.811451i	0.999351	−	0.0360084i	$-0.0114643\pi$
$373$	9.04807	+	15.6717i	0.468492	+	0.811451i	−0.530860	+	0.847460i	$0.678131\pi$
$374$		0			0
$375$	−6.54857	−	3.78082i	−0.338167	−	0.195241i
$376$		0			0
$377$			8.54920i			0.440306i
$378$		0			0
$379$			12.1096i			0.622027i	0.950405	+	0.311014i	$0.100668\pi$
$379$			12.1096i			0.622027i	−0.950405	+	0.311014i	$0.899332\pi$
$380$		0			0
$381$	−3.23357	−	1.86690i	−0.165661	−	0.0956442i
$382$		0			0
$383$	2.88269	+	4.99296i	0.147298	+	0.255128i	0.930228	−	0.366982i	$-0.119609\pi$
$383$	2.88269	+	4.99296i	0.147298	+	0.255128i	−0.782930	+	0.622110i	$0.786276\pi$
$384$		0			0
$385$	−0.565205	+	5.18783i	−0.0288055	+	0.264396i
$386$		0			0
$387$	25.8374	−	14.9172i	1.31339	−	0.758285i
$388$		0			0
$389$	−6.42828	+	11.1341i	−0.325926	+	0.564521i	−0.981699	−	0.190437i	$-0.939010\pi$
$389$	−6.42828	+	11.1341i	−0.325926	+	0.564521i	0.655773	+	0.754958i	$0.272343\pi$
$390$		0			0
$391$	−11.1973			−0.566270
$392$		0			0
$393$	−14.2249			−0.717552
$394$		0			0
$395$	2.74943	−	4.76215i	0.138339	−	0.239610i
$396$		0			0
$397$	−16.7628	+	9.67798i	−0.841299	+	0.485724i	−0.857706	−	0.514141i	$-0.828111\pi$
$397$	−16.7628	+	9.67798i	−0.841299	+	0.485724i	0.0164067	+	0.999865i	$0.494777\pi$
$398$		0			0
$399$	0.286555	−	2.63019i	0.0143457	−	0.131674i
$400$		0			0
$401$	−14.2159	−	24.6227i	−0.709911	−	1.22960i	−0.964890	−	0.262655i	$-0.915402\pi$
$401$	−14.2159	−	24.6227i	−0.709911	−	1.22960i	0.254979	−	0.966946i	$-0.417931\pi$
$402$		0			0
$403$	−26.0103	−	15.0171i	−1.29567	−	0.748054i
$404$		0			0
$405$			4.87939i			0.242459i
$406$		0			0
$407$		−	10.9591i		−	0.543223i
$408$		0			0
$409$	−26.7147	−	15.4237i	−1.32095	−	0.762654i	−0.337074	−	0.941478i	$-0.609437\pi$
$409$	−26.7147	−	15.4237i	−1.32095	−	0.762654i	−0.983881	+	0.178825i	$0.942771\pi$
$410$		0			0
$411$	3.41954	+	5.92282i	0.168674	+	0.292151i
$412$		0			0
$413$	13.3986	+	9.81265i	0.659300	+	0.482849i
$414$		0			0
$415$	−17.0361	+	9.83577i	−0.836267	+	0.482819i
$416$		0			0
$417$	4.55622	−	7.89160i	0.223119	−	0.386453i
$418$		0			0
$419$	30.5826			1.49406			0.747028	−	0.664792i	$-0.231480\pi$
$419$	30.5826			1.49406			0.747028	+	0.664792i	$0.231480\pi$
$420$		0			0
$421$	32.7015			1.59377			0.796887	−	0.604128i	$-0.206478\pi$
$421$	32.7015			1.59377			0.796887	+	0.604128i	$0.206478\pi$
$422$		0			0
$423$	11.7826	−	20.4081i	0.572892	−	0.992278i
$424$		0			0
$425$	−16.6182	+	9.59453i	−0.806102	+	0.465403i
$426$		0			0
$427$	3.25767	+	7.39234i	0.157650	+	0.357740i
$428$		0			0
$429$	2.25462	+	3.90511i	0.108854	+	0.188540i
$430$		0			0
$431$	0.586041	+	0.338351i	0.0282286	+	0.0162978i	0.514048	−	0.857761i	$-0.328145\pi$
$431$	0.586041	+	0.338351i	0.0282286	+	0.0162978i	−0.485819	+	0.874059i	$0.661479\pi$
$432$		0			0
$433$		−	12.1162i		−	0.582268i	−0.956682	−	0.291134i	$-0.905967\pi$
$433$		−	12.1162i		−	0.582268i	0.956682	−	0.291134i	$-0.0940326\pi$
$434$		0			0
$435$		−	2.12427i		−	0.101851i
$436$		0			0
$437$	−2.45190	−	1.41560i	−0.117290	−	0.0677175i
$438$		0			0
$439$	5.47486	+	9.48273i	0.261301	+	0.452586i	0.966588	−	0.256336i	$-0.0825153\pi$
$439$	5.47486	+	9.48273i	0.261301	+	0.452586i	−0.705287	+	0.708922i	$0.749182\pi$
$440$		0			0
$441$	−5.13738	−	16.2300i	−0.244637	−	0.772855i
$442$		0			0
$443$	3.17662	−	1.83402i	0.150926	−	0.0871370i	−0.422635	−	0.906300i	$-0.638895\pi$
$443$	3.17662	−	1.83402i	0.150926	−	0.0871370i	0.573561	+	0.819163i	$0.305562\pi$
$444$		0			0
$445$	4.41358	−	7.64455i	0.209224	−	0.362386i
$446$		0			0
$447$	−1.50185			−0.0710350
$448$		0			0
$449$	−14.3904			−0.679125			−0.339562	−	0.940584i	$-0.610279\pi$
$449$	−14.3904			−0.679125			−0.339562	+	0.940584i	$0.610279\pi$
$450$		0			0
$451$	2.99143	−	5.18130i	0.140861	−	0.243978i
$452$		0			0
$453$	−3.35575	+	1.93744i	−0.157667	+	0.0910290i
$454$		0			0
$455$	9.86377	−	4.34679i	0.462421	−	0.203781i
$456$		0			0
$457$	5.68626	+	9.84890i	0.265992	+	0.460712i	0.967823	−	0.251632i	$-0.0809671\pi$
$457$	5.68626	+	9.84890i	0.265992	+	0.460712i	−0.701831	+	0.712344i	$0.747634\pi$
$458$		0			0
$459$	−18.6049	−	10.7415i	−0.868400	−	0.501371i
$460$		0			0
$461$			26.1261i			1.21681i	0.793626	+	0.608406i	$0.208191\pi$
$461$			26.1261i			1.21681i	−0.793626	+	0.608406i	$0.791809\pi$
$462$		0			0
$463$		−	17.7470i		−	0.824772i	−0.911009	−	0.412386i	$-0.864696\pi$
$463$		−	17.7470i		−	0.824772i	0.911009	−	0.412386i	$-0.135304\pi$
$464$		0			0
$465$	6.46294	+	3.73138i	0.299712	+	0.173039i
$466$		0			0
$467$	−13.8708	−	24.0249i	−0.641862	−	1.11174i	−0.985017	−	0.172459i	$-0.944829\pi$
$467$	−13.8708	−	24.0249i	−0.641862	−	1.11174i	0.343154	−	0.939279i	$-0.388505\pi$
$468$		0			0
$469$	−20.6589	+	28.2085i	−0.953941	+	1.30255i
$470$		0			0
$471$	7.86644	−	4.54169i	0.362467	−	0.209270i
$472$		0			0
$473$	10.4393	−	18.0814i	0.479999	−	0.831383i
$474$		0			0
$475$	−4.85192			−0.222621
$476$		0			0
$477$	−29.4172			−1.34692
$478$		0			0
$479$	−1.67293	+	2.89760i	−0.0764382	+	0.132395i	−0.901711	−	0.432340i	$-0.857688\pi$
$479$	−1.67293	+	2.89760i	−0.0764382	+	0.132395i	0.825273	+	0.564735i	$0.191021\pi$
$480$		0			0
$481$	−19.6038	+	11.3183i	−0.893856	+	0.516068i
$482$		0			0
$483$	4.23006	+	0.460858i	0.192475	+	0.0209698i
$484$		0			0
$485$	−6.99107	−	12.1089i	−0.317448	−	0.549836i
$486$		0			0
$487$	1.25363	+	0.723784i	0.0568075	+	0.0327978i	0.528135	−	0.849161i	$-0.322892\pi$
$487$	1.25363	+	0.723784i	0.0568075	+	0.0327978i	−0.471327	+	0.881958i	$0.656225\pi$
$488$		0			0
$489$			3.13132i			0.141603i
$490$		0			0
$491$			16.1390i			0.728341i	0.931332	+	0.364171i	$0.118647\pi$
$491$			16.1390i			0.728341i	−0.931332	+	0.364171i	$0.881353\pi$
$492$		0			0
$493$	−11.0517	−	6.38073i	−0.497746	−	0.287374i
$494$		0			0
$495$	2.39841	+	4.15416i	0.107800	+	0.186716i
$496$		0			0
$497$	−26.9674	−	2.93805i	−1.20965	−	0.131790i
$498$		0			0
$499$	3.59802	−	2.07732i	0.161070	−	0.0929936i	−0.417299	−	0.908769i	$-0.637023\pi$
$499$	3.59802	−	2.07732i	0.161070	−	0.0929936i	0.578368	+	0.815776i	$0.303690\pi$
$500$		0			0
$501$	−4.57381	+	7.92207i	−0.204343	+	0.353932i
$502$		0			0
$503$	−30.4579			−1.35805			−0.679025	−	0.734115i	$-0.737597\pi$
$503$	−30.4579			−1.35805			−0.679025	+	0.734115i	$0.737597\pi$
$504$		0			0
$505$	18.8492			0.838776
$506$		0			0
$507$	−0.241996	+	0.419150i	−0.0107474	+	0.0186151i
$508$		0			0
$509$	11.3216	−	6.53650i	0.501819	−	0.289725i	−0.227645	−	0.973744i	$-0.573103\pi$
$509$	11.3216	−	6.53650i	0.501819	−	0.289725i	0.729464	+	0.684019i	$0.239769\pi$
$510$		0			0
$511$	3.79705	−	5.18464i	0.167972	−	0.229355i
$512$		0			0
$513$	−2.71597	−	4.70420i	−0.119913	−	0.207696i
$514$		0			0
$515$	−2.09369	−	1.20879i	−0.0922591	−	0.0532658i
$516$		0			0
$517$		−	16.4913i		−	0.725288i
$518$		0			0
$519$		−	11.5422i		−	0.506645i
$520$		0			0
$521$	−18.0102	−	10.3982i	−0.789043	−	0.455554i	0.0505828	−	0.998720i	$-0.483892\pi$
$521$	−18.0102	−	10.3982i	−0.789043	−	0.455554i	−0.839625	+	0.543166i	$0.817225\pi$
$522$		0			0
$523$	−5.76420	−	9.98389i	−0.252051	−	0.436565i	0.712039	−	0.702139i	$-0.247772\pi$
$523$	−5.76420	−	9.98389i	−0.252051	−	0.436565i	−0.964090	+	0.265575i	$0.914438\pi$
$524$		0			0
$525$	6.67286	−	2.94061i	0.291227	−	0.128339i
$526$		0			0
$527$	38.8258	−	22.4161i	1.69128	−	0.976461i
$528$		0			0
$529$	−9.22332	+	15.9753i	−0.401014	+	0.694576i
$530$		0			0
$531$	15.2655			0.662465
$532$		0			0
$533$	−12.3578			−0.535277
$534$		0			0
$535$	−2.34399	+	4.05992i	−0.101340	+	0.175525i
$536$		0			0
$537$	6.83766	−	3.94772i	0.295067	−	0.170357i
$538$		0			0
$539$	−8.79252	−	8.03868i	−0.378721	−	0.346250i
$540$		0			0
$541$	−3.66787	−	6.35294i	−0.157694	−	0.273134i	0.776343	−	0.630311i	$-0.217073\pi$
$541$	−3.66787	−	6.35294i	−0.157694	−	0.273134i	−0.934037	+	0.357177i	$0.883739\pi$
$542$		0			0
$543$	11.8272	+	6.82843i	0.507553	+	0.293036i
$544$		0			0
$545$		−	2.72408i		−	0.116687i
$546$		0			0
$547$			3.09746i			0.132438i	0.997805	+	0.0662190i	$0.0210936\pi$
$547$			3.09746i			0.132438i	−0.997805	+	0.0662190i	$0.978906\pi$
$548$		0			0
$549$	6.43068	+	3.71275i	0.274455	+	0.158456i
$550$		0			0
$551$	−1.61336	−	2.79441i	−0.0687313	−	0.119046i
$552$		0			0
$553$	5.06229	+	11.4874i	0.215271	+	0.488494i
$554$		0			0
$555$	4.87107	−	2.81231i	0.206765	−	0.119376i
$556$		0			0
$557$	7.26405	−	12.5817i	0.307788	−	0.533104i	−0.670090	−	0.742279i	$-0.733745\pi$
$557$	7.26405	−	12.5817i	0.307788	−	0.533104i	0.977878	+	0.209176i	$0.0670781\pi$
$558$		0			0
$559$	−43.1256			−1.82402
$560$		0			0
$561$	−6.73096			−0.284182
$562$		0			0
$563$	9.91713	−	17.1770i	0.417957	−	0.723923i	−0.577777	−	0.816195i	$-0.696080\pi$
$563$	9.91713	−	17.1770i	0.417957	−	0.723923i	0.995734	+	0.0922719i	$0.0294129\pi$
$564$		0			0
$565$	4.46297	−	2.57670i	0.187759	−	0.108402i
$566$		0			0
$567$	−8.98684	−	6.58165i	−0.377412	−	0.276403i
$568$		0			0
$569$	16.6390	+	28.8195i	0.697542	+	1.20818i	0.969316	+	0.245817i	$0.0790561\pi$
$569$	16.6390	+	28.8195i	0.697542	+	1.20818i	−0.271775	+	0.962361i	$0.587611\pi$
$570$		0			0
$571$	6.06298	+	3.50046i	0.253728	+	0.146490i	0.621470	−	0.783438i	$-0.286536\pi$
$571$	6.06298	+	3.50046i	0.253728	+	0.146490i	−0.367742	+	0.929928i	$0.619869\pi$
$572$		0			0
$573$			7.33899i			0.306591i
$574$		0			0
$575$		−	7.80322i		−	0.325417i
$576$		0			0
$577$	24.1658	+	13.9521i	1.00604	+	0.580835i	0.910028	−	0.414546i	$-0.136060\pi$
$577$	24.1658	+	13.9521i	1.00604	+	0.580835i	0.0960069	+	0.995381i	$0.469393\pi$
$578$		0			0
$579$	−6.90025	−	11.9516i	−0.286765	−	0.496691i
$580$		0			0
$581$	4.86390	−	44.6441i	0.201788	−	1.85215i
$582$		0			0
$583$	−17.8285	+	10.2933i	−0.738381	+	0.426305i
$584$		0			0
$585$	4.95401	−	8.58060i	0.204823	−	0.354764i
$586$		0			0
$587$	13.4842			0.556551			0.278276	−	0.960501i	$-0.410237\pi$
$587$	13.4842			0.556551			0.278276	+	0.960501i	$0.410237\pi$
$588$		0			0
$589$	11.3357			0.467081
$590$		0			0
$591$	5.50555	−	9.53590i	0.226468	−	0.392254i
$592$		0			0
$593$	16.7412	−	9.66553i	0.687478	−	0.396916i	−0.115189	−	0.993344i	$-0.536747\pi$
$593$	16.7412	−	9.66553i	0.687478	−	0.396916i	0.802667	+	0.596428i	$0.203414\pi$
$594$		0			0
$595$	−1.74267	+	15.9954i	−0.0714425	+	0.655746i
$596$		0			0
$597$	1.09538	+	1.89725i	0.0448308	+	0.0776491i
$598$		0			0
$599$	24.7487	+	14.2887i	1.01120	+	0.583819i	0.911544	−	0.411203i	$-0.134891\pi$
$599$	24.7487	+	14.2887i	1.01120	+	0.583819i	0.0996601	+	0.995022i	$0.468224\pi$
$600$		0			0
$601$			7.82137i			0.319040i	0.987195	+	0.159520i	$0.0509947\pi$
$601$			7.82137i			0.319040i	−0.987195	+	0.159520i	$0.949005\pi$
$602$		0			0
$603$			32.1390i			1.30880i
$604$		0			0
$605$	−8.13326	−	4.69574i	−0.330664	−	0.190909i
$606$		0			0
$607$	11.9025	+	20.6157i	0.483106	+	0.836764i	0.999812	−	0.0193990i	$-0.00617529\pi$
$607$	11.9025	+	20.6157i	0.483106	+	0.836764i	−0.516706	+	0.856163i	$0.672842\pi$
$608$		0			0
$609$	3.91247	+	2.86536i	0.158541	+	0.116110i
$610$		0			0
$611$	−29.4999	+	17.0318i	−1.19344	+	0.689032i
$612$		0			0
$613$	−17.9062	+	31.0145i	−0.723225	+	1.25266i	0.236475	+	0.971637i	$0.424008\pi$
$613$	−17.9062	+	31.0145i	−0.723225	+	1.25266i	−0.959700	+	0.281025i	$0.909326\pi$
$614$		0			0
$615$	3.07063			0.123820
$616$		0			0
$617$	12.7751			0.514306			0.257153	−	0.966371i	$-0.417216\pi$
$617$	12.7751			0.514306			0.257153	+	0.966371i	$0.417216\pi$
$618$		0			0
$619$	−3.66590	+	6.34953i	−0.147345	+	0.255209i	−0.930245	−	0.366938i	$-0.880406\pi$
$619$	−3.66590	+	6.34953i	−0.147345	+	0.255209i	0.782900	+	0.622147i	$0.213739\pi$
$620$		0			0
$621$	7.56565	−	4.36803i	0.303599	−	0.175283i
$622$		0			0
$623$	8.12635	+	18.4404i	0.325576	+	0.738799i
$624$		0			0
$625$	−3.32843	−	5.76500i	−0.133137	−	0.230600i
$626$		0			0
$627$	−1.47390	−	0.850956i	−0.0588619	−	0.0339839i
$628$		0			0
$629$		−	33.7897i		−	1.34728i
$630$		0			0
$631$		−	34.3891i		−	1.36901i	−0.729009	−	0.684504i	$-0.760019\pi$
$631$		−	34.3891i		−	1.36901i	0.729009	−	0.684504i	$-0.239981\pi$
$632$		0			0
$633$	12.7811	+	7.37919i	0.508004	+	0.293296i
$634$		0			0
$635$	2.87071	+	4.97221i	0.113920	+	0.197316i
$636$		0			0
$637$	−5.29902	+	24.0303i	−0.209955	+	0.952114i
$638$		0			0
$639$	−21.5942	+	12.4674i	−0.854253	+	0.493203i
$640$		0			0
$641$	−24.1096	+	41.7590i	−0.952270	+	1.64938i	−0.211775	+	0.977318i	$0.567924\pi$
$641$	−24.1096	+	41.7590i	−0.952270	+	1.64938i	−0.740495	+	0.672062i	$0.765409\pi$
$642$		0			0
$643$	4.30600			0.169812			0.0849060	−	0.996389i	$-0.472941\pi$
$643$	4.30600			0.169812			0.0849060	+	0.996389i	$0.472941\pi$
$644$		0			0
$645$	10.7157			0.421929
$646$		0			0
$647$	−18.6725	+	32.3417i	−0.734091	+	1.27148i	0.221031	+	0.975267i	$0.429058\pi$
$647$	−18.6725	+	32.3417i	−0.734091	+	1.27148i	−0.955121	+	0.296215i	$0.904275\pi$
$648$		0			0
$649$	9.25174	−	5.34150i	0.363163	−	0.209672i
$650$		0			0
$651$	−15.5901	+	6.87028i	−0.611024	+	0.269267i
$652$		0			0
$653$	−13.2730	−	22.9895i	−0.519412	−	0.899648i	−0.999745	−	0.0225618i	$-0.992818\pi$
$653$	−13.2730	−	22.9895i	−0.519412	−	0.899648i	0.480334	−	0.877086i	$-0.340516\pi$
$654$		0			0
$655$	18.9429	+	10.9367i	0.740162	+	0.427333i
$656$		0			0
$657$		−	5.90705i		−	0.230456i
$658$		0			0
$659$			30.3597i			1.18265i	0.806435	+	0.591323i	$0.201394\pi$
$659$			30.3597i			1.18265i	−0.806435	+	0.591323i	$0.798606\pi$
$660$		0			0
$661$	26.8659	+	15.5111i	1.04496	+	0.603310i	0.921235	−	0.389006i	$-0.127182\pi$
$661$	26.8659	+	15.5111i	1.04496	+	0.603310i	0.123728	+	0.992316i	$0.460515\pi$
$662$		0			0
$663$	6.95154	+	12.0404i	0.269976	+	0.467612i
$664$		0			0
$665$	−2.40380	+	3.28224i	−0.0932153	+	0.127280i
$666$		0			0
$667$	4.49418	−	2.59472i	0.174016	−	0.100468i
$668$		0			0
$669$	1.31502	−	2.27769i	0.0508417	−	0.0880604i
$670$		0			0
$671$	5.19648			0.200608
$672$		0			0
$673$	24.9527			0.961856			0.480928	−	0.876760i	$-0.340300\pi$
$673$	24.9527			0.961856			0.480928	+	0.876760i	$0.340300\pi$
$674$		0			0
$675$	7.48561	−	12.9655i	0.288121	−	0.499041i
$676$		0			0
$677$	3.36337	−	1.94184i	0.129265	−	0.0746311i	−0.433973	−	0.900926i	$-0.642889\pi$
$677$	3.36337	−	1.94184i	0.129265	−	0.0746311i	0.563238	+	0.826295i	$0.309555\pi$
$678$		0			0
$679$	31.7321	+	3.45716i	1.21777	+	0.132674i
$680$		0			0
$681$	−1.14951	−	1.99101i	−0.0440493	−	0.0762956i
$682$		0			0
$683$	16.2323	+	9.37171i	0.621111	+	0.358598i	0.777301	−	0.629129i	$-0.216588\pi$
$683$	16.2323	+	9.37171i	0.621111	+	0.358598i	−0.156191	+	0.987727i	$0.549921\pi$
$684$		0			0
$685$		−	10.5164i		−	0.401810i
$686$		0			0
$687$		−	5.56998i		−	0.212508i
$688$		0			0
$689$	36.8255	+	21.2612i	1.40294	+	0.809988i
$690$		0			0
$691$	0.541729	+	0.938302i	0.0206083	+	0.0356947i	0.876146	−	0.482046i	$-0.160106\pi$
$691$	0.541729	+	0.938302i	0.0206083	+	0.0356947i	−0.855537	+	0.517741i	$0.826773\pi$
$692$		0			0
$693$	−10.8862	−	1.18604i	−0.413534	−	0.0450539i
$694$		0			0
$695$	−12.1348	+	7.00603i	−0.460299	+	0.265754i
$696$		0			0
$697$	9.22332	−	15.9753i	0.349358	−	0.605106i
$698$		0			0
$699$	−5.94042			−0.224687
$700$		0			0
$701$	9.31371			0.351774			0.175887	−	0.984410i	$-0.443721\pi$
$701$	9.31371			0.351774			0.175887	+	0.984410i	$0.443721\pi$
$702$		0			0
$703$	4.27183	−	7.39903i	0.161115	−	0.279060i
$704$		0			0
$705$	7.33001	−	4.23199i	0.276064	−	0.159386i
$706$		0			0
$707$	−25.4250	+	34.7163i	−0.956205	+	1.30564i
$708$		0			0
$709$	−19.6516	−	34.0376i	−0.738031	−	1.27831i	−0.953381	−	0.301770i	$-0.902422\pi$
$709$	−19.6516	−	34.0376i	−0.738031	−	1.27831i	0.215349	−	0.976537i	$-0.430911\pi$
$710$		0			0
$711$	9.99301	+	5.76946i	0.374767	+	0.216372i
$712$		0			0
$713$			18.2310i			0.682756i
$714$		0			0
$715$		−	6.93378i		−	0.259309i
$716$		0			0
$717$	−8.65527	−	4.99712i	−0.323237	−	0.186621i
$718$		0			0
$719$	−16.6488	−	28.8365i	−0.620895	−	1.07542i	−0.989319	−	0.145764i	$-0.953436\pi$
$719$	−16.6488	−	28.8365i	−0.620895	−	1.07542i	0.368425	−	0.929658i	$-0.379897\pi$
$720$		0			0
$721$	5.05046	−	2.22565i	0.188089	−	0.0828875i
$722$		0			0
$723$	1.96223	−	1.13290i	0.0729762	−	0.0421329i
$724$		0			0
$725$	4.44664	−	7.70181i	0.165144	−	0.286038i
$726$		0			0
$727$	−15.7046			−0.582452			−0.291226	−	0.956654i	$-0.594063\pi$
$727$	−15.7046			−0.582452			−0.291226	+	0.956654i	$0.594063\pi$
$728$		0			0
$729$	−0.982135			−0.0363754
$730$		0			0
$731$	32.1870	−	55.7494i	1.19048	−	2.06197i
$732$		0			0
$733$	3.95927	−	2.28589i	0.146239	−	0.0844311i	−0.425095	−	0.905149i	$-0.639759\pi$
$733$	3.95927	−	2.28589i	0.146239	−	0.0844311i	0.571334	+	0.820718i	$0.306426\pi$
$734$		0			0
$735$	1.31668	−	5.97095i	0.0485664	−	0.220242i
$736$		0			0
$737$	11.2457	+	19.4780i	0.414239	+	0.717483i
$738$		0			0
$739$	18.3539	+	10.5966i	0.675158	+	0.389803i	0.798028	−	0.602620i	$-0.205877\pi$
$739$	18.3539	+	10.5966i	0.675158	+	0.389803i	−0.122870	+	0.992423i	$0.539210\pi$
$740$		0			0
$741$			3.51537i			0.129140i
$742$		0			0
$743$			18.7112i			0.686447i	0.939254	+	0.343223i	$0.111519\pi$
$743$			18.7112i			0.686447i	−0.939254	+	0.343223i	$0.888481\pi$
$744$		0			0
$745$	1.99997	+	1.15468i	0.0732733	+	0.0423044i
$746$		0			0
$747$	−20.6396	−	35.7488i	−0.755163	−	1.30798i
$748$		0			0
$749$	−4.31579	−	9.79344i	−0.157696	−	0.357844i
$750$		0			0
$751$	−43.2420	+	24.9658i	−1.57792	+	0.911014i	−0.582773	+	0.812635i	$0.698032\pi$
$751$	−43.2420	+	24.9658i	−1.57792	+	0.911014i	−0.995149	+	0.0983790i	$0.968634\pi$
$752$		0			0
$753$	−7.69391	+	13.3262i	−0.280382	+	0.485635i
$754$		0			0
$755$	5.95836			0.216847
$756$		0			0
$757$	−24.3373			−0.884556			−0.442278	−	0.896878i	$-0.645830\pi$
$757$	−24.3373			−0.884556			−0.442278	+	0.896878i	$0.645830\pi$
$758$		0			0
$759$	1.36857	−	2.37043i	0.0496760	−	0.0860413i
$760$		0			0
$761$	−25.5964	+	14.7781i	−0.927870	+	0.535706i	−0.886137	−	0.463423i	$-0.846621\pi$
$761$	−25.5964	+	14.7781i	−0.927870	+	0.535706i	−0.0417324	+	0.999129i	$0.513288\pi$
$762$		0			0
$763$	5.01720	+	3.67442i	0.181635	+	0.133023i
$764$		0			0
$765$	7.39489	+	12.8083i	0.267363	+	0.463086i
$766$		0			0
$767$	−19.1099	−	11.0331i	−0.690017	−	0.398382i
$768$		0			0
$769$		−	51.5243i		−	1.85801i	−0.370063	−	0.929007i	$-0.620664\pi$
$769$		−	51.5243i		−	1.85801i	0.370063	−	0.929007i	$-0.379336\pi$
$770$		0			0
$771$			15.5262i			0.559161i
$772$		0			0
$773$	37.3957	+	21.5904i	1.34503	+	0.776553i	0.987540	−	0.157365i	$-0.0502999\pi$
$773$	37.3957	+	21.5904i	1.34503	+	0.776553i	0.357488	+	0.933918i	$0.383633\pi$
$774$		0			0
$775$	15.6215	+	27.0572i	0.561140	+	0.971922i
$776$		0			0
$777$	−1.39072	+	12.7649i	−0.0498918	+	0.457940i
$778$		0			0
$779$	4.03932	−	2.33210i	0.144724	−	0.0835562i
$780$		0			0
$781$	−8.72488	+	15.1119i	−0.312201	+	0.540748i
$782$		0			0
$783$	9.95644			0.355814
$784$		0			0
$785$	−13.9674			−0.498518
$786$		0			0
$787$	0.0937231	−	0.162333i	0.00334087	−	0.00578655i	−0.864350	−	0.502890i	$-0.832270\pi$
$787$	0.0937231	−	0.162333i	0.00334087	−	0.00578655i	0.867691	+	0.497104i	$0.165603\pi$
$788$		0			0
$789$	17.5822	−	10.1511i	0.625944	−	0.361389i
$790$		0			0
$791$	−1.27420	+	11.6955i	−0.0453055	+	0.415844i
$792$		0			0
$793$	−5.36677	−	9.29552i	−0.190580	−	0.330094i
$794$		0			0
$795$	−9.15026	−	5.28290i	−0.324526	−	0.187365i
$796$		0			0
$797$		−	28.9136i		−	1.02417i	−0.858934	−	0.512086i	$-0.828873\pi$
$797$		−	28.9136i		−	1.02417i	0.858934	−	0.512086i	$-0.171127\pi$
$798$		0			0
$799$		−	50.8469i		−	1.79883i
$800$		0			0
$801$	16.0415	+	9.26156i	0.566798	+	0.327241i
$802$		0			0
$803$	−2.06692	−	3.58001i	−0.0729400	−	0.126336i
$804$		0			0
$805$	−5.27874	−	3.86597i	−0.186051	−	0.136257i
$806$		0			0
$807$	12.4555	−	7.19120i	0.438455	−	0.253142i
$808$		0			0
$809$	−17.2958	+	29.9572i	−0.608089	+	1.05324i	0.383467	+	0.923555i	$0.374730\pi$
$809$	−17.2958	+	29.9572i	−0.608089	+	1.05324i	−0.991555	+	0.129686i	$0.958603\pi$
$810$		0			0
$811$	−15.5799			−0.547086			−0.273543	−	0.961860i	$-0.588196\pi$
$811$	−15.5799			−0.547086			−0.273543	+	0.961860i	$0.588196\pi$
$812$		0			0
$813$	−16.6137			−0.582669
$814$		0			0
$815$	2.40749	−	4.16990i	0.0843307	−	0.146065i
$816$		0			0
$817$	14.0961	−	8.13841i	0.493162	−	0.284727i
$818$		0			0
$819$	9.12140	+	20.6984i	0.318728	+	0.723259i
$820$		0			0
$821$	14.0538	+	24.3420i	0.490482	+	0.849540i	0.999940	−	0.0109556i	$-0.00348735\pi$
$821$	14.0538	+	24.3420i	0.490482	+	0.849540i	−0.509458	+	0.860496i	$0.670154\pi$
$822$		0			0
$823$	21.2591	+	12.2740i	0.741047	+	0.427844i	0.822450	−	0.568838i	$-0.192607\pi$
$823$	21.2591	+	12.2740i	0.741047	+	0.427844i	−0.0814028	+	0.996681i	$0.525940\pi$
$824$		0			0
$825$		−	4.69071i		−	0.163310i
$826$		0			0
$827$		−	27.2945i		−	0.949124i	−0.880222	−	0.474562i	$-0.842607\pi$
$827$		−	27.2945i		−	0.949124i	0.880222	−	0.474562i	$-0.157393\pi$
$828$		0			0
$829$	−33.0359	−	19.0733i	−1.14738	−	0.662443i	−0.199136	−	0.979972i	$-0.563814\pi$
$829$	−33.0359	−	19.0733i	−1.14738	−	0.662443i	−0.948249	+	0.317529i	$0.897147\pi$
$830$		0			0
$831$	1.54915	+	2.68321i	0.0537396	+	0.0930796i
$832$		0			0
$833$	−27.1096	−	24.7853i	−0.939290	−	0.858758i
$834$		0			0
$835$	12.1817	−	7.03308i	0.421564	−	0.243390i
$836$		0			0
$837$	−17.4890	+	30.2918i	−0.604507	+	1.04704i
$838$		0			0
$839$	−55.9292			−1.93089			−0.965444	−	0.260609i	$-0.916077\pi$
$839$	−55.9292			−1.93089			−0.965444	+	0.260609i	$0.916077\pi$
$840$		0			0
$841$	−23.0856			−0.796056
$842$		0			0
$843$	2.91338	−	5.04613i	0.100342	−	0.173798i
$844$		0			0
$845$	0.644521	−	0.372114i	0.0221722	−	0.0128011i
$846$		0			0
$847$	19.6193	−	8.64586i	0.674126	−	0.297075i
$848$		0			0
$849$	−10.7677	−	18.6502i	−0.369547	−	0.640075i
$850$		0			0
$851$	11.8997	+	6.87028i	0.407915	+	0.235510i
$852$		0			0
$853$		−	40.4997i		−	1.38668i	−0.720609	−	0.693342i	$-0.756138\pi$
$853$		−	40.4997i		−	1.38668i	0.720609	−	0.693342i	$-0.243862\pi$
$854$		0			0
$855$			3.73957i			0.127891i
$856$		0			0
$857$	−13.2365	−	7.64207i	−0.452149	−	0.261048i	0.256589	−	0.966521i	$-0.417401\pi$
$857$	−13.2365	−	7.64207i	−0.452149	−	0.261048i	−0.708737	+	0.705473i	$0.750735\pi$
$858$		0			0
$859$	−21.5705	−	37.3611i	−0.735975	−	1.27475i	−0.954294	−	0.298868i	$-0.903391\pi$
$859$	−21.5705	−	37.3611i	−0.735975	−	1.27475i	0.218320	−	0.975877i	$-0.429942\pi$
$860$		0			0
$861$	−4.14186	+	5.65546i	−0.141154	+	0.192738i
$862$		0			0
$863$	39.2807	−	22.6787i	1.33713	−	0.771993i	0.350750	−	0.936469i	$-0.385927\pi$
$863$	39.2807	−	22.6787i	1.33713	−	0.771993i	0.986381	+	0.164476i	$0.0525934\pi$
$864$		0			0
$865$	−8.87412	+	15.3704i	−0.301729	+	0.522610i
$866$		0			0
$867$	−7.94048			−0.269673
$868$		0			0
$869$	8.07511			0.273929
$870$		0			0
$871$	23.2284	−	40.2327i	0.787063	−	1.36323i
$872$		0			0
$873$	25.4095	−	14.6702i	0.859983	−	0.496511i
$874$		0			0
$875$	−26.3881	−	2.87494i	−0.892081	−	0.0971908i
$876$		0			0
$877$	16.6132	+	28.7750i	0.560989	+	0.971661i	0.997410	+	0.0719188i	$0.0229122\pi$
$877$	16.6132	+	28.7750i	0.560989	+	0.971661i	−0.436422	+	0.899742i	$0.643754\pi$
$878$		0			0
$879$	−4.42750	−	2.55622i	−0.149336	−	0.0862191i
$880$		0			0
$881$			22.4056i			0.754864i	0.926037	+	0.377432i	$0.123193\pi$
$881$			22.4056i			0.754864i	−0.926037	+	0.377432i	$0.876807\pi$
$882$		0			0
$883$		−	4.55462i		−	0.153275i	−0.997059	−	0.0766376i	$-0.975582\pi$
$883$		−	4.55462i		−	0.153275i	0.997059	−	0.0766376i	$-0.0244184\pi$
$884$		0			0
$885$	4.74834	+	2.74146i	0.159614	+	0.0921530i
$886$		0			0
$887$	−11.8499	−	20.5246i	−0.397879	−	0.689147i	0.595585	−	0.803293i	$-0.296920\pi$
$887$	−11.8499	−	20.5246i	−0.397879	−	0.689147i	−0.993464	+	0.114145i	$0.963587\pi$
$888$		0			0
$889$	−13.0300	−	1.41959i	−0.437012	−	0.0476117i
$890$		0			0
$891$	−6.20543	+	3.58271i	−0.207890	+	0.120025i
$892$		0			0
$893$	6.42828	−	11.1341i	0.215114	−	0.372588i
$894$		0			0
$895$	−12.1407			−0.405819
$896$		0			0
$897$	−5.65368			−0.188771
$898$		0			0
$899$	−10.3889	+	17.9941i	−0.346488	+	0.600135i
$900$		0			0
$901$	−54.9697	+	31.7368i	−1.83131	+	1.05731i
$902$		0			0
$903$	−14.4540	+	19.7361i	−0.480999	+	0.656775i
$904$		0			0
$905$	−10.5000	−	18.1865i	−0.349031	−	0.604539i
$906$		0			0
$907$	22.6362	+	13.0690i	0.751621	+	0.433949i	0.826279	−	0.563261i	$-0.190453\pi$
$907$	22.6362	+	13.0690i	0.751621	+	0.433949i	−0.0746582	+	0.997209i	$0.523787\pi$
$908$		0			0
$909$			39.5535i			1.31191i
$910$		0			0
$911$		−	42.5016i		−	1.40814i	−0.710131	−	0.704070i	$-0.751364\pi$
$911$		−	42.5016i		−	1.40814i	0.710131	−	0.704070i	$-0.248636\pi$
$912$		0			0
$913$	−25.0176	−	14.4439i	−0.827960	−	0.478023i
$914$		0			0
$915$	1.33351	+	2.30971i	0.0440846	+	0.0763568i
$916$		0			0
$917$	−45.6947	+	20.1368i	−1.50897	+	0.664977i
$918$		0			0
$919$	17.2342	−	9.95015i	0.568502	−	0.328225i	−0.188049	−	0.982160i	$-0.560216\pi$
$919$	17.2342	−	9.95015i	0.568502	−	0.328225i	0.756551	+	0.653935i	$0.226883\pi$
$920$		0			0
$921$	5.08146	−	8.80134i	0.167440	−	0.290014i
$922$		0			0
$923$	36.0432			1.18638
$924$		0			0
$925$	23.5476			0.774239
$926$		0			0
$927$	2.53656	−	4.39345i	0.0833115	−	0.144300i
$928$		0			0
$929$	−2.40671	+	1.38951i	−0.0789616	+	0.0455885i	−0.538961	−	0.842331i	$-0.681183\pi$
$929$	−2.40671	+	1.38951i	−0.0789616	+	0.0455885i	0.459999	+	0.887919i	$0.347850\pi$
$930$		0			0
$931$	−2.80281	−	8.85460i	−0.0918583	−	0.290198i
$932$		0			0
$933$	−4.96086	−	8.59246i	−0.162411	−	0.281304i
$934$		0			0
$935$	8.96346	+	5.17505i	0.293136	+	0.169242i
$936$		0			0
$937$		−	41.9794i		−	1.37141i	−0.727881	−	0.685703i	$-0.759495\pi$
$937$		−	41.9794i		−	1.37141i	0.727881	−	0.685703i	$-0.240505\pi$
$938$		0			0
$939$		−	11.3009i		−	0.368792i
$940$		0			0
$941$	36.1295	+	20.8594i	1.17779	+	0.679996i	0.955502	−	0.294986i	$-0.0953149\pi$
$941$	36.1295	+	20.8594i	1.17779	+	0.679996i	0.222286	+	0.974982i	$0.428648\pi$
$942$		0			0
$943$	3.75066	+	6.49633i	0.122138	+	0.211550i
$944$		0			0
$945$	−5.06229	−	11.4874i	−0.164676	−	0.373685i
$946$		0			0
$947$	−32.5648	+	18.8013i	−1.05821	+	0.610959i	−0.924937	−	0.380120i	$-0.875883\pi$
$947$	−32.5648	+	18.8013i	−1.05821	+	0.610959i	−0.133275	+	0.991079i	$0.542549\pi$
$948$		0			0
$949$	−4.26931	+	7.39466i	−0.138588	+	0.240041i
$950$		0			0
$951$	−8.45459			−0.274159
$952$		0			0
$953$	−10.1808			−0.329788			−0.164894	−	0.986311i	$-0.552728\pi$
$953$	−10.1808			−0.329788			−0.164894	+	0.986311i	$0.552728\pi$
$954$		0			0
$955$	5.64253	−	9.77315i	0.182588	−	0.316252i
$956$		0			0
$957$	2.70157	−	1.55975i	0.0873294	−	0.0504196i
$958$		0			0
$959$	19.3690	+	14.1852i	0.625457	+	0.458063i
$960$		0			0
$961$	−20.9971	−	36.3680i	−0.677326	−	1.17316i
$962$		0			0
$963$	−8.51941	−	4.91869i	−0.274534	−	0.158502i
$964$		0			0
$965$			21.2208i			0.683123i
$966$		0			0
$967$			24.0102i			0.772116i	0.922474	+	0.386058i	$0.126164\pi$
$967$			24.0102i			0.772116i	−0.922474	+	0.386058i	$0.873836\pi$
$968$		0			0
$969$	−4.54440	−	2.62371i	−0.145987	−	0.0842857i
$970$		0			0
$971$	10.5105	+	18.2048i	0.337299	+	0.584219i	0.983924	−	0.178590i	$-0.0571534\pi$
$971$	10.5105	+	18.2048i	0.337299	+	0.584219i	−0.646625	+	0.762808i	$0.723820\pi$
$972$		0			0
$973$	3.46456	−	31.8000i	0.111069	−	1.01946i
$974$		0			0
$975$	−8.39080	+	4.84443i	−0.268721	+	0.155146i
$976$		0			0
$977$	−2.27668	+	3.94333i	−0.0728375	+	0.126158i	−0.900144	−	0.435593i	$-0.856539\pi$
$977$	−2.27668	+	3.94333i	−0.0728375	+	0.126158i	0.827306	+	0.561751i	$0.189872\pi$
$978$		0			0
$979$	12.9627			0.414291
$980$		0			0
$981$	5.71627			0.182507
$982$		0			0
$983$	−9.18651	+	15.9115i	−0.293004	+	0.507498i	−0.974519	−	0.224306i	$-0.927988\pi$
$983$	−9.18651	+	15.9115i	−0.293004	+	0.507498i	0.681514	+	0.731805i	$0.261322\pi$
$984$		0			0
$985$	−14.6632	+	8.46581i	−0.467209	+	0.269743i
$986$		0			0
$987$	−2.09276	+	19.2088i	−0.0666134	+	0.611422i
$988$		0			0
$989$	13.0888	+	22.6705i	0.416200	+	0.720879i
$990$		0			0
$991$	−6.10229	−	3.52316i	−0.193846	−	0.111917i	0.399936	−	0.916543i	$-0.369032\pi$
$991$	−6.10229	−	3.52316i	−0.193846	−	0.111917i	−0.593782	+	0.804626i	$0.702366\pi$
$992$		0			0
$993$		−	7.86632i		−	0.249630i
$994$		0			0
$995$		−	3.36869i		−	0.106795i
$996$		0			0
$997$	19.7772	+	11.4184i	0.626350	+	0.361623i	0.779337	−	0.626605i	$-0.215556\pi$
$997$	19.7772	+	11.4184i	0.626350	+	0.361623i	−0.152987	+	0.988228i	$0.548889\pi$
$998$		0			0
$999$	13.1813	+	22.8307i	0.417038	+	0.722330i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.p.a.31.3	✓	16
3.2	odd	2		2016.2.cs.b.703.3		16
4.3	odd	2	inner	224.2.p.a.31.6	yes	16
7.2	even	3		1568.2.p.b.607.3		16
7.3	odd	6		1568.2.f.b.1567.5		16
7.4	even	3		1568.2.f.b.1567.12		16
7.5	odd	6	inner	224.2.p.a.159.6	yes	16
7.6	odd	2		1568.2.p.b.31.6		16
8.3	odd	2		448.2.p.e.255.3		16
8.5	even	2		448.2.p.e.255.6		16
12.11	even	2		2016.2.cs.b.703.4		16
21.5	even	6		2016.2.cs.b.1279.4		16
28.3	even	6		1568.2.f.b.1567.11		16
28.11	odd	6		1568.2.f.b.1567.6		16
28.19	even	6	inner	224.2.p.a.159.3	yes	16
28.23	odd	6		1568.2.p.b.607.6		16
28.27	even	2		1568.2.p.b.31.3		16
56.3	even	6		3136.2.f.j.3135.6		16
56.5	odd	6		448.2.p.e.383.3		16
56.11	odd	6		3136.2.f.j.3135.11		16
56.19	even	6		448.2.p.e.383.6		16
56.45	odd	6		3136.2.f.j.3135.12		16
56.53	even	6		3136.2.f.j.3135.5		16
84.47	odd	6		2016.2.cs.b.1279.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.p.a.31.3	✓	16	1.1	even	1	trivial
224.2.p.a.31.6	yes	16	4.3	odd	2	inner
224.2.p.a.159.3	yes	16	28.19	even	6	inner
224.2.p.a.159.6	yes	16	7.5	odd	6	inner
448.2.p.e.255.3		16	8.3	odd	2
448.2.p.e.255.6		16	8.5	even	2
448.2.p.e.383.3		16	56.5	odd	6
448.2.p.e.383.6		16	56.19	even	6
1568.2.f.b.1567.5		16	7.3	odd	6
1568.2.f.b.1567.6		16	28.11	odd	6
1568.2.f.b.1567.11		16	28.3	even	6
1568.2.f.b.1567.12		16	7.4	even	3
1568.2.p.b.31.3		16	28.27	even	2
1568.2.p.b.31.6		16	7.6	odd	2
1568.2.p.b.607.3		16	7.2	even	3
1568.2.p.b.607.6		16	28.23	odd	6
2016.2.cs.b.703.3		16	3.2	odd	2
2016.2.cs.b.703.4		16	12.11	even	2
2016.2.cs.b.1279.3		16	84.47	odd	6
2016.2.cs.b.1279.4		16	21.5	even	6
3136.2.f.j.3135.5		16	56.53	even	6
3136.2.f.j.3135.6		16	56.3	even	6
3136.2.f.j.3135.11		16	56.11	odd	6
3136.2.f.j.3135.12		16	56.45	odd	6

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.376846 + 0.652717i) q^{3} +(1.00367 - 0.579471i) q^{5} +(-0.286555 + 2.63019i) q^{7} +(1.21597 + 2.10613i) q^{9} +O(q^{10})\)	\(q+(-0.376846 + 0.652717i) q^{3} +(1.00367 - 0.579471i) q^{5} +(-0.286555 + 2.63019i) q^{7} +(1.21597 + 2.10613i) q^{9} +(1.47390 + 0.850956i) q^{11} -3.51537i q^{13} +0.873485i q^{15} +(4.54440 + 2.62371i) q^{17} +(0.663401 + 1.14904i) q^{19} +(-1.60878 - 1.17821i) q^{21} +(-1.84798 + 1.06693i) q^{23} +(-1.82843 + 3.16693i) q^{25} -4.09402 q^{27} -2.43195 q^{29} +(4.27183 - 7.39903i) q^{31} +(-1.11087 + 0.641359i) q^{33} +(1.23651 + 2.80590i) q^{35} +(-3.21965 - 5.57659i) q^{37} +(2.29454 + 1.32475i) q^{39} -3.51537i q^{41} -12.2677i q^{43} +(2.44088 + 1.40924i) q^{45} +(-4.84494 - 8.39168i) q^{47} +(-6.83577 - 1.50738i) q^{49} +(-3.42508 + 1.97747i) q^{51} +(-6.04807 + 10.4756i) q^{53} +1.97242 q^{55} -1.00000 q^{57} +(3.13853 - 5.43609i) q^{59} +(2.64425 - 1.52666i) q^{61} +(-5.88796 + 2.59472i) q^{63} +(-2.03706 - 3.52828i) q^{65} +(11.4448 + 6.60766i) q^{67} -1.60827i q^{69} +10.2530i q^{71} +(-2.10352 - 1.21447i) q^{73} +(-1.37807 - 2.38689i) q^{75} +(-2.66053 + 3.63279i) q^{77} +(4.10905 - 2.37236i) q^{79} +(-2.10511 + 3.64615i) q^{81} -16.9737 q^{83} +6.08146 q^{85} +(0.916470 - 1.58737i) q^{87} +(6.59615 - 3.80829i) q^{89} +(9.24609 + 1.00735i) q^{91} +(3.21965 + 5.57659i) q^{93} +(1.33167 + 0.768843i) q^{95} -12.0646i q^{97} +4.13896i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^9	\( 16 q - 8 q^{9} - 24 q^{21} + 16 q^{25} + 16 q^{29} + 24 q^{33} - 8 q^{37} - 24 q^{45} - 32 q^{49} - 8 q^{53} - 16 q^{57} - 24 q^{61} + 8 q^{65} - 24 q^{73} + 64 q^{77} - 48 q^{81} - 16 q^{85} - 72 q^{89} + 8 q^{93}+O(q^{100}) \) 16 * q - 8 * q^9 - 24 * q^21 + 16 * q^25 + 16 * q^29 + 24 * q^33 - 8 * q^37 - 24 * q^45 - 32 * q^49 - 8 * q^53 - 16 * q^57 - 24 * q^61 + 8 * q^65 - 24 * q^73 + 64 * q^77 - 48 * q^81 - 16 * q^85 - 72 * q^89 + 8 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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