LMFDB - Embedded newform 125.2.d.b.51.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(26,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("125.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.d (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 $ x^16 + x^14 - 4x^12 - 49x^10 + 11x^8 + 395x^6 + 900x^4 + 1125x^2 + 625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			51.1
Root			$1.86824 + 0.357358i$ of defining polynomial
Character	$\chi$	$=$	125.51
Dual form			125.2.d.b.76.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.86824 + 1.35736i) q^{2} +(0.146753 - 0.451659i) q^{3} +(1.02988 - 3.16963i) q^{4} +(0.338893 + 1.04301i) q^{6} +3.03582 q^{7} +(0.951057 + 2.92705i) q^{8} +(2.24459 + 1.63079i) q^{9} +O(q^{10})$	\(q+(-1.86824 + 1.35736i) q^{2} +(0.146753 - 0.451659i) q^{3} +(1.02988 - 3.16963i) q^{4} +(0.338893 + 1.04301i) q^{6} +3.03582 q^{7} +(0.951057 + 2.92705i) q^{8} +(2.24459 + 1.63079i) q^{9} +(-1.61803 + 1.17557i) q^{11} +(-1.28046 - 0.930307i) q^{12} +(1.15464 + 0.838893i) q^{13} +(-5.67164 + 4.12069i) q^{14} +(-0.357358 - 0.259635i) q^{16} +(0.574848 + 1.76920i) q^{17} -6.40701 q^{18} +(0.279141 + 0.859107i) q^{19} +(0.445515 - 1.37116i) q^{21} +(1.42721 - 4.39250i) q^{22} +(2.69348 - 1.95693i) q^{23} +1.46160 q^{24} -3.29582 q^{26} +(2.21858 - 1.61189i) q^{27} +(3.12652 - 9.62243i) q^{28} +(1.22466 - 3.76910i) q^{29} +(-1.99006 - 6.12477i) q^{31} -5.13532 q^{32} +(0.293506 + 0.903319i) q^{33} +(-3.47539 - 2.52502i) q^{34} +(7.48066 - 5.43502i) q^{36} +(-3.09062 - 2.24547i) q^{37} +(-1.68762 - 1.22613i) q^{38} +(0.548341 - 0.398393i) q^{39} +(1.48391 + 1.07813i) q^{41} +(1.02882 + 3.16637i) q^{42} -3.59445 q^{43} +(2.05975 + 6.33927i) q^{44} +(-2.37582 + 7.31203i) q^{46} +(-1.48326 + 4.56502i) q^{47} +(-0.169710 + 0.123302i) q^{48} +2.21619 q^{49} +0.883436 q^{51} +(3.84812 - 2.79582i) q^{52} +(-2.93712 + 9.03953i) q^{53} +(-1.95693 + 6.02280i) q^{54} +(2.88723 + 8.88599i) q^{56} +0.428989 q^{57} +(2.82807 + 8.70390i) q^{58} +(-8.61248 - 6.25734i) q^{59} +(-11.5481 + 8.39016i) q^{61} +(12.0314 + 8.74134i) q^{62} +(6.81417 + 4.95078i) q^{63} +(10.3087 - 7.48973i) q^{64} +(-1.77447 - 1.28923i) q^{66} +(-3.30345 - 10.1670i) q^{67} +6.19974 q^{68} +(-0.488588 - 1.50372i) q^{69} +(3.85030 - 11.8500i) q^{71} +(-2.63868 + 8.12101i) q^{72} +(-0.216518 + 0.157310i) q^{73} +8.82193 q^{74} +3.01054 q^{76} +(-4.91206 + 3.56882i) q^{77} +(-0.483672 + 1.48859i) q^{78} +(-2.64882 + 8.15223i) q^{79} +(2.16963 + 6.67743i) q^{81} -4.23572 q^{82} +(-3.89923 - 12.0006i) q^{83} +(-3.88723 - 2.82424i) q^{84} +(6.71531 - 4.87896i) q^{86} +(-1.52263 - 1.10626i) q^{87} +(-4.97980 - 3.61803i) q^{88} +(3.85736 - 2.80253i) q^{89} +(3.50527 + 2.54673i) q^{91} +(-3.42879 - 10.5527i) q^{92} -3.05836 q^{93} +(-3.42527 - 10.5419i) q^{94} +(-0.753624 + 2.31942i) q^{96} +(-3.07721 + 9.47067i) q^{97} +(-4.14037 + 3.00816i) q^{98} -5.54893 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} - 18 q^{6} - 2 q^{9}+O(q^{10}) $ 16 * q + 2 * q^4 - 18 * q^6 - 2 * q^9	$ 16 q + 2 q^{4} - 18 q^{6} - 2 q^{9} - 8 q^{11} - 26 q^{14} + 6 q^{16} + 10 q^{19} - 8 q^{21} + 40 q^{24} + 12 q^{26} + 10 q^{29} - 18 q^{31} - 26 q^{34} + 46 q^{36} + 6 q^{39} - 8 q^{41} + 4 q^{44} - 38 q^{46} - 28 q^{49} - 8 q^{51} + 10 q^{54} + 20 q^{56} - 18 q^{61} - 8 q^{64} + 24 q^{66} - 34 q^{69} + 12 q^{71} + 24 q^{74} - 40 q^{76} - 30 q^{79} + 56 q^{81} - 36 q^{84} - 18 q^{86} + 50 q^{89} + 12 q^{91} + 54 q^{94} + 32 q^{96} + 16 q^{99}+O(q^{100}) $ 16 * q + 2 * q^4 - 18 * q^6 - 2 * q^9 - 8 * q^11 - 26 * q^14 + 6 * q^16 + 10 * q^19 - 8 * q^21 + 40 * q^24 + 12 * q^26 + 10 * q^29 - 18 * q^31 - 26 * q^34 + 46 * q^36 + 6 * q^39 - 8 * q^41 + 4 * q^44 - 38 * q^46 - 28 * q^49 - 8 * q^51 + 10 * q^54 + 20 * q^56 - 18 * q^61 - 8 * q^64 + 24 * q^66 - 34 * q^69 + 12 * q^71 + 24 * q^74 - 40 * q^76 - 30 * q^79 + 56 * q^81 - 36 * q^84 - 18 * q^86 + 50 * q^89 + 12 * q^91 + 54 * q^94 + 32 * q^96 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−1.86824	+	1.35736i	−1.32105	+	0.959797i	−0.321128	+	0.947036i	$0.604062\pi$
$2$	−1.86824	+	1.35736i	−1.32105	+	0.959797i	−0.999919	+	0.0127610i	$0.995938\pi$
$3$	0.146753	−	0.451659i	0.0847279	−	0.260766i	−0.899713	−	0.436482i	$-0.856224\pi$
$3$	0.146753	−	0.451659i	0.0847279	−	0.260766i	0.984441	+	0.175716i	$0.0562242\pi$
$4$	1.02988	−	3.16963i	0.514938	−	1.58482i
$5$		0			0
$5$		0			0
$6$	0.338893	+	1.04301i	0.138353	+	0.425805i
$7$	3.03582			1.14743			0.573716	−	0.819055i	$-0.305502\pi$
$7$	3.03582			1.14743			0.573716	+	0.819055i	$0.305502\pi$
$8$	0.951057	+	2.92705i	0.336249	+	1.03487i
$9$	2.24459	+	1.63079i	0.748197	+	0.543597i
$10$		0			0
$11$	−1.61803	+	1.17557i	−0.487856	+	0.354448i	−0.804359	−	0.594144i	$-0.797491\pi$
$11$	−1.61803	+	1.17557i	−0.487856	+	0.354448i	0.316503	+	0.948591i	$0.397491\pi$
$12$	−1.28046	−	0.930307i	−0.369636	−	0.268556i
$13$	1.15464	+	0.838893i	0.320239	+	0.232667i	0.736277	−	0.676680i	$-0.236582\pi$
$13$	1.15464	+	0.838893i	0.320239	+	0.232667i	−0.416039	+	0.909347i	$0.636582\pi$
$14$	−5.67164	+	4.12069i	−1.51581	+	1.10130i
$15$		0			0
$16$	−0.357358	−	0.259635i	−0.0893394	−	0.0649089i
$17$	0.574848	+	1.76920i	0.139421	+	0.429094i	0.996251	−	0.0865044i	$-0.0275697\pi$
$17$	0.574848	+	1.76920i	0.139421	+	0.429094i	−0.856830	+	0.515598i	$0.827570\pi$
$18$	−6.40701			−1.51015
$19$	0.279141	+	0.859107i	0.0640393	+	0.197093i	0.977957	−	0.208807i	$-0.0669581\pi$
$19$	0.279141	+	0.859107i	0.0640393	+	0.197093i	−0.913918	+	0.405900i	$0.866958\pi$
$20$		0			0
$21$	0.445515	−	1.37116i	0.0972194	−	0.299211i
$22$	1.42721	−	4.39250i	0.304282	−	0.936484i
$23$	2.69348	−	1.95693i	0.561629	−	0.408048i	−0.270426	−	0.962741i	$-0.587164\pi$
$23$	2.69348	−	1.95693i	0.561629	−	0.408048i	0.832055	+	0.554693i	$0.187164\pi$
$24$	1.46160			0.298348
$25$		0			0
$26$	−3.29582			−0.646364
$27$	2.21858	−	1.61189i	0.426965	−	0.310208i
$28$	3.12652	−	9.62243i	0.590856	−	1.81847i
$29$	1.22466	−	3.76910i	0.227413	−	0.699905i	−0.770625	−	0.637289i	$-0.780056\pi$
$29$	1.22466	−	3.76910i	0.227413	−	0.699905i	0.998038	−	0.0626159i	$-0.0199443\pi$
$30$		0			0
$31$	−1.99006	−	6.12477i	−0.357425	−	1.10004i	−0.954590	−	0.297923i	$-0.903706\pi$
$31$	−1.99006	−	6.12477i	−0.357425	−	1.10004i	0.597165	−	0.802119i	$-0.296294\pi$
$32$	−5.13532			−0.907805
$33$	0.293506	+	0.903319i	0.0510929	+	0.157248i
$34$	−3.47539	−	2.52502i	−0.596025	−	0.433037i
$35$		0			0
$36$	7.48066	−	5.43502i	1.24678	−	0.905836i
$37$	−3.09062	−	2.24547i	−0.508095	−	0.369153i	0.304005	−	0.952670i	$-0.401676\pi$
$37$	−3.09062	−	2.24547i	−0.508095	−	0.369153i	−0.812100	+	0.583518i	$0.801676\pi$
$38$	−1.68762	−	1.22613i	−0.273768	−	0.198904i
$39$	0.548341	−	0.398393i	0.0878048	−	0.0637939i
$40$		0			0
$41$	1.48391	+	1.07813i	0.231749	+	0.168375i	0.697599	−	0.716488i	$-0.254252\pi$
$41$	1.48391	+	1.07813i	0.231749	+	0.168375i	−0.465851	+	0.884863i	$0.654252\pi$
$42$	1.02882	+	3.16637i	0.158750	+	0.488582i
$43$	−3.59445			−0.548149			−0.274074	−	0.961708i	$-0.588371\pi$
$43$	−3.59445			−0.548149			−0.274074	+	0.961708i	$0.588371\pi$
$44$	2.05975	+	6.33927i	0.310519	+	0.955680i
$45$		0			0
$46$	−2.37582	+	7.31203i	−0.350296	+	1.07810i
$47$	−1.48326	+	4.56502i	−0.216356	+	0.665877i	0.782698	+	0.622402i	$0.213843\pi$
$47$	−1.48326	+	4.56502i	−0.216356	+	0.665877i	−0.999055	+	0.0434750i	$0.986157\pi$
$48$	−0.169710	+	0.123302i	−0.0244955	+	0.0177971i
$49$	2.21619			0.316598
$50$		0			0
$51$	0.883436			0.123706
$52$	3.84812	−	2.79582i	0.533638	−	0.387711i
$53$	−2.93712	+	9.03953i	−0.403445	+	1.24168i	0.518742	+	0.854931i	$0.326401\pi$
$53$	−2.93712	+	9.03953i	−0.403445	+	1.24168i	−0.922187	+	0.386745i	$0.873599\pi$
$54$	−1.95693	+	6.02280i	−0.266304	+	0.819600i
$55$		0			0
$56$	2.88723	+	8.88599i	0.385823	+	1.18744i
$57$	0.428989			0.0568209
$58$	2.82807	+	8.70390i	0.371343	+	1.14288i
$59$	−8.61248	−	6.25734i	−1.12125	−	0.814636i	−0.136852	−	0.990592i	$-0.543698\pi$
$59$	−8.61248	−	6.25734i	−1.12125	−	0.814636i	−0.984398	+	0.175956i	$0.943698\pi$
$60$		0			0
$61$	−11.5481	+	8.39016i	−1.47858	+	1.07425i	−0.500566	+	0.865698i	$0.666875\pi$
$61$	−11.5481	+	8.39016i	−1.47858	+	1.07425i	−0.978012	+	0.208551i	$0.933125\pi$
$62$	12.0314	+	8.74134i	1.52799	+	1.11015i
$63$	6.81417	+	4.95078i	0.858505	+	0.623740i
$64$	10.3087	−	7.48973i	1.28859	−	0.936217i
$65$		0			0
$66$	−1.77447	−	1.28923i	−0.218422	−	0.158693i
$67$	−3.30345	−	10.1670i	−0.403580	−	1.24209i	−0.922075	−	0.387012i	$-0.873507\pi$
$67$	−3.30345	−	10.1670i	−0.403580	−	1.24209i	0.518494	−	0.855081i	$-0.326493\pi$
$68$	6.19974			0.751828
$69$	−0.488588	−	1.50372i	−0.0588191	−	0.181027i
$70$		0			0
$71$	3.85030	−	11.8500i	0.456947	−	1.40634i	−0.411887	−	0.911235i	$-0.635130\pi$
$71$	3.85030	−	11.8500i	0.456947	−	1.40634i	0.868834	−	0.495104i	$-0.164870\pi$
$72$	−2.63868	+	8.12101i	−0.310971	+	0.957070i
$73$	−0.216518	+	0.157310i	−0.0253415	+	0.0184117i	−0.600384	−	0.799712i	$-0.704986\pi$
$73$	−0.216518	+	0.157310i	−0.0253415	+	0.0184117i	0.575042	+	0.818124i	$0.304986\pi$
$74$	8.82193			1.02553
$75$		0			0
$76$	3.01054			0.345332
$77$	−4.91206	+	3.56882i	−0.559781	+	0.406704i
$78$	−0.483672	+	1.48859i	−0.0547650	+	0.168549i
$79$	−2.64882	+	8.15223i	−0.298015	+	0.917197i	0.684176	+	0.729316i	$0.260162\pi$
$79$	−2.64882	+	8.15223i	−0.298015	+	0.917197i	−0.982192	+	0.187881i	$0.939838\pi$
$80$		0			0
$81$	2.16963	+	6.67743i	0.241070	+	0.741937i
$82$	−4.23572			−0.467757
$83$	−3.89923	−	12.0006i	−0.427996	−	1.31724i	−0.900096	−	0.435691i	$-0.856504\pi$
$83$	−3.89923	−	12.0006i	−0.427996	−	1.31724i	0.472100	−	0.881545i	$-0.343496\pi$
$84$	−3.88723	−	2.82424i	−0.424132	−	0.308150i
$85$		0			0
$86$	6.71531	−	4.87896i	0.724130	−	0.526112i
$87$	−1.52263	−	1.10626i	−0.163243	−	0.118603i
$88$	−4.97980	−	3.61803i	−0.530848	−	0.385684i
$89$	3.85736	−	2.80253i	0.408879	−	0.297068i	−0.364269	−	0.931294i	$-0.618681\pi$
$89$	3.85736	−	2.80253i	0.408879	−	0.297068i	0.773148	+	0.634226i	$0.218681\pi$
$90$		0			0
$91$	3.50527	+	2.54673i	0.367452	+	0.266969i
$92$	−3.42879	−	10.5527i	−0.357476	−	1.10020i
$93$	−3.05836			−0.317137
$94$	−3.42527	−	10.5419i	−0.353289	−	1.08731i
$95$		0			0
$96$	−0.753624	+	2.31942i	−0.0769164	+	0.236724i
$97$	−3.07721	+	9.47067i	−0.312443	+	0.961600i	0.664351	+	0.747420i	$0.268708\pi$
$97$	−3.07721	+	9.47067i	−0.312443	+	0.961600i	−0.976794	+	0.214180i	$0.931292\pi$
$98$	−4.14037	+	3.00816i	−0.418241	+	0.303870i
$99$	−5.54893			−0.557689
$100$		0			0
$101$	9.34612			0.929974			0.464987	−	0.885318i	$-0.346059\pi$
$101$	9.34612			0.929974			0.464987	+	0.885318i	$0.346059\pi$
$102$	−1.65047	+	1.19914i	−0.163421	+	0.118732i
$103$	2.80713	−	8.63947i	0.276595	−	0.851272i	−0.712198	−	0.701979i	$-0.752300\pi$
$103$	2.80713	−	8.63947i	0.276595	−	0.851272i	0.988793	−	0.149294i	$-0.0476999\pi$
$104$	−1.35736	+	4.17752i	−0.133100	+	0.409639i
$105$		0			0
$106$	−6.78262	−	20.8748i	−0.658787	−	2.02754i
$107$	5.62871			0.544148			0.272074	−	0.962276i	$-0.412290\pi$
$107$	5.62871			0.544148			0.272074	+	0.962276i	$0.412290\pi$
$108$	−2.82424	−	8.69212i	−0.271763	−	0.836400i
$109$	8.18158	+	5.94427i	0.783654	+	0.569358i	0.906073	−	0.423121i	$-0.139065\pi$
$109$	8.18158	+	5.94427i	0.783654	+	0.569358i	−0.122420	+	0.992478i	$0.539065\pi$
$110$		0			0
$111$	−1.46774	+	1.06638i	−0.139312	+	0.101216i
$112$	−1.08487	−	0.788206i	−0.102511	−	0.0744784i
$113$	−8.66620	−	6.29636i	−0.815247	−	0.592312i	0.100100	−	0.994977i	$-0.468084\pi$
$113$	−8.66620	−	6.29636i	−0.815247	−	0.592312i	−0.915347	+	0.402666i	$0.868084\pi$
$114$	−0.801455	+	0.582291i	−0.0750631	+	0.0545366i
$115$		0			0
$116$	−10.6854	−	7.76342i	−0.992118	−	0.720816i
$117$	1.22363	+	3.76594i	0.113125	+	0.348162i
$118$	24.5836			2.26311
$119$	1.74513	+	5.37097i	0.159976	+	0.492356i
$120$		0			0
$121$	−2.16312	+	6.65740i	−0.196647	+	0.605218i
$122$	10.1861	−	31.3497i	0.922209	−	2.83827i
$123$	0.704715	−	0.512006i	0.0635420	−	0.0461660i
$124$	−21.4628			−1.92742
$125$		0			0
$126$	−19.4505			−1.73279
$127$	9.19118	−	6.67779i	0.815586	−	0.592558i	−0.0998589	−	0.995002i	$-0.531839\pi$
$127$	9.19118	−	6.67779i	0.815586	−	0.592558i	0.915445	+	0.402444i	$0.131839\pi$
$128$	−5.91917	+	18.2173i	−0.523185	+	1.61020i
$129$	−0.527497	+	1.62347i	−0.0464435	+	0.142938i
$130$		0			0
$131$	2.46834	+	7.59677i	0.215660	+	0.663732i	0.999106	+	0.0422730i	$0.0134599\pi$
$131$	2.46834	+	7.59677i	0.215660	+	0.663732i	−0.783446	+	0.621459i	$0.786540\pi$
$132$	3.16546			0.275518
$133$	0.847421	+	2.60809i	0.0734807	+	0.226150i
$134$	19.9719	+	14.5104i	1.72531	+	1.25351i
$135$		0			0
$136$	−4.63182	+	3.36522i	−0.397176	+	0.288565i
$137$	−7.55401	−	5.48831i	−0.645382	−	0.468898i	0.216313	−	0.976324i	$-0.430597\pi$
$137$	−7.55401	−	5.48831i	−0.645382	−	0.468898i	−0.861695	+	0.507426i	$0.830597\pi$
$138$	2.95389	+	2.14612i	0.251452	+	0.182690i
$139$	−14.4936	+	10.5302i	−1.22933	+	0.893160i	−0.996840	−	0.0794393i	$-0.974687\pi$
$139$	−14.4936	+	10.5302i	−1.22933	+	0.893160i	−0.232489	+	0.972599i	$0.574687\pi$
$140$		0			0
$141$	1.84416	+	1.33986i	0.155306	+	0.112837i
$142$	8.89141	+	27.3649i	0.746151	+	2.29642i
$143$	−2.85442			−0.238699
$144$	−0.378710	−	1.16555i	−0.0315592	−	0.0971292i
$145$		0			0
$146$	0.190983	−	0.587785i	0.0158059	−	0.0486455i
$147$	0.325232	−	1.00096i	0.0268247	−	0.0825579i
$148$	−10.3003	+	7.48358i	−0.846676	+	0.615146i
$149$	−6.31395			−0.517259			−0.258629	−	0.965977i	$-0.583271\pi$
$149$	−6.31395			−0.517259			−0.258629	+	0.965977i	$0.583271\pi$
$150$		0			0
$151$	4.71947			0.384065			0.192033	−	0.981389i	$-0.438492\pi$
$151$	4.71947			0.384065			0.192033	+	0.981389i	$0.438492\pi$
$152$	−2.24917	+	1.63412i	−0.182432	+	0.132545i
$153$	−1.59490	+	4.90859i	−0.128940	+	0.396836i
$154$	4.33275	−	13.3348i	0.349143	−	1.07455i
$155$		0			0
$156$	−0.698036	−	2.14833i	−0.0558876	−	0.172004i
$157$	1.46908			0.117245			0.0586225	−	0.998280i	$-0.481329\pi$
$157$	1.46908			0.117245			0.0586225	+	0.998280i	$0.481329\pi$
$158$	−6.11685	−	18.8257i	−0.486630	−	1.49769i
$159$	3.65176	+	2.65316i	0.289603	+	0.210409i
$160$		0			0
$161$	8.17691	−	5.94087i	0.644431	−	0.468206i
$162$	−13.1171	−	9.53010i	−1.03057	−	0.748756i
$163$	−3.60797	−	2.62134i	−0.282598	−	0.205319i	0.437452	−	0.899242i	$-0.355881\pi$
$163$	−3.60797	−	2.62134i	−0.282598	−	0.205319i	−0.720050	+	0.693922i	$0.755881\pi$
$164$	4.94552	−	3.59313i	0.386180	−	0.280576i
$165$		0			0
$166$	23.5738	+	17.1274i	1.82968	+	1.32934i
$167$	3.22418	+	9.92300i	0.249494	+	0.767865i	0.994865	+	0.101214i	$0.0322728\pi$
$167$	3.22418	+	9.92300i	0.249494	+	0.767865i	−0.745370	+	0.666651i	$0.767727\pi$
$168$	4.43715			0.342334
$169$	−3.38778	−	10.4265i	−0.260598	−	0.802038i
$170$		0			0
$171$	−0.774467	+	2.38357i	−0.0592250	+	0.182276i
$172$	−3.70184	+	11.3931i	−0.282263	+	0.868715i
$173$	6.21017	−	4.51195i	0.472151	−	0.343037i	−0.326128	−	0.945326i	$-0.605744\pi$
$173$	6.21017	−	4.51195i	0.472151	−	0.343037i	0.798279	+	0.602288i	$0.205744\pi$
$174$	4.34623			0.329486
$175$		0			0
$176$	0.883436			0.0665915
$177$	−4.09009	+	2.97163i	−0.307430	+	0.223361i
$178$	−3.40244	+	10.4716i	−0.255023	+	0.784882i
$179$	4.79494	−	14.7573i	0.358391	−	1.10301i	−0.595626	−	0.803262i	$-0.703096\pi$
$179$	4.79494	−	14.7573i	0.358391	−	1.10301i	0.954017	−	0.299752i	$-0.0969040\pi$
$180$		0			0
$181$	−0.491509	−	1.51271i	−0.0365336	−	0.112439i	0.931127	−	0.364696i	$-0.118827\pi$
$181$	−0.491509	−	1.51271i	−0.0365336	−	0.112439i	−0.967660	+	0.252257i	$0.918827\pi$
$182$	−10.0055			−0.741658
$183$	2.09478	+	6.44707i	0.154851	+	0.476581i
$184$	8.28968	+	6.02280i	0.611123	+	0.444007i
$185$		0			0
$186$	5.71375	−	4.15129i	0.418953	−	0.304387i
$187$	−3.00994	−	2.18685i	−0.220109	−	0.159918i
$188$	12.9419	+	9.40281i	0.943882	+	0.685770i
$189$	6.73519	−	4.89340i	0.489913	−	0.355943i
$190$		0			0
$191$	−15.9121	−	11.5608i	−1.15136	−	0.836511i	−0.162698	−	0.986676i	$-0.552020\pi$
$191$	−15.9121	−	11.5608i	−1.15136	−	0.836511i	−0.988661	+	0.150164i	$0.952020\pi$
$192$	−1.86997	−	5.75518i	−0.134954	−	0.415344i
$193$	13.1100			0.943680			0.471840	−	0.881684i	$-0.343590\pi$
$193$	13.1100			0.943680			0.471840	+	0.881684i	$0.343590\pi$
$194$	−7.10611	−	21.8704i	−0.510189	−	1.57020i
$195$		0			0
$196$	2.28240	−	7.02449i	0.163028	−	0.501750i
$197$	−1.05977	+	3.26164i	−0.0755055	+	0.232382i	−0.981685	−	0.190511i	$-0.938985\pi$
$197$	−1.05977	+	3.26164i	−0.0755055	+	0.232382i	0.906180	+	0.422893i	$0.138985\pi$
$198$	10.3668	−	7.53189i	0.736733	−	0.535268i
$199$	17.6959			1.25443			0.627215	−	0.778846i	$-0.284195\pi$
$199$	17.6959			1.25443			0.627215	+	0.778846i	$0.284195\pi$
$200$		0			0
$201$	−5.07680			−0.358090
$202$	−17.4608	+	12.6860i	−1.22854	+	0.892586i
$203$	3.71783	−	11.4423i	0.260941	−	0.803093i
$204$	0.909830	−	2.80017i	0.0637008	−	0.196051i
$205$		0			0
$206$	6.48244	+	19.9509i	0.451653	+	1.39005i
$207$	9.23710			0.642023
$208$	−0.194812	−	0.599570i	−0.0135078	−	0.0415727i
$209$	−1.46160	−	1.06192i	−0.101101	−	0.0734542i
$210$		0			0
$211$	2.62418	−	1.90658i	0.180656	−	0.131254i	−0.493782	−	0.869586i	$-0.664386\pi$
$211$	2.62418	−	1.90658i	0.180656	−	0.131254i	0.674438	+	0.738331i	$0.264386\pi$
$212$	25.6271	+	18.6192i	1.76008	+	1.27877i
$213$	−4.78713	−	3.47805i	−0.328009	−	0.238312i
$214$	−10.5158	+	7.64018i	−0.718845	+	0.522272i
$215$		0			0
$216$	6.82808	+	4.96089i	0.464592	+	0.337546i
$217$	−6.04145	−	18.5937i	−0.410121	−	1.26222i
$218$	−23.3537			−1.58171
$219$	0.0392757	+	0.120878i	0.00265401	+	0.00816819i
$220$		0			0
$221$	−0.820429	+	2.52502i	−0.0551880	+	0.169851i
$222$	1.29465	−	3.98451i	0.0868909	−	0.267423i
$223$	−23.2307	+	16.8781i	−1.55564	+	1.13024i	−0.616175	+	0.787609i	$0.711319\pi$
$223$	−23.2307	+	16.8781i	−1.55564	+	1.13024i	−0.939469	+	0.342633i	$0.888681\pi$
$224$	−15.5899			−1.04164
$225$		0			0
$226$	24.7370			1.64548
$227$	−9.48219	+	6.88921i	−0.629355	+	0.457253i	−0.856177	−	0.516683i	$-0.827167\pi$
$227$	−9.48219	+	6.88921i	−0.629355	+	0.457253i	0.226822	+	0.973936i	$0.427167\pi$
$228$	0.441805	−	1.35974i	0.0292593	−	0.0900508i
$229$	−5.06828	+	15.5985i	−0.334921	+	1.03078i	0.631840	+	0.775099i	$0.282300\pi$
$229$	−5.06828	+	15.5985i	−0.334921	+	1.03078i	−0.966761	+	0.255682i	$0.917700\pi$
$230$		0			0
$231$	0.891031	+	2.74231i	0.0586255	+	0.180431i
$232$	12.1971			0.800777
$233$	6.95739	+	21.4126i	0.455794	+	1.40279i	0.870201	+	0.492697i	$0.163989\pi$
$233$	6.95739	+	21.4126i	0.455794	+	1.40279i	−0.414407	+	0.910092i	$0.636011\pi$
$234$	−7.39777	−	5.37479i	−0.483607	−	0.351361i
$235$		0			0
$236$	−28.7032	+	20.8541i	−1.86842	+	1.35749i
$237$	3.29331	+	2.39273i	0.213923	+	0.155424i
$238$	−10.5507	−	7.66550i	−0.683897	−	0.496880i
$239$	5.36647	−	3.89897i	0.347128	−	0.252204i	−0.400535	−	0.916281i	$-0.631176\pi$
$239$	5.36647	−	3.89897i	0.347128	−	0.252204i	0.747663	+	0.664078i	$0.231176\pi$
$240$		0			0
$241$	−21.2173	−	15.4153i	−1.36673	−	0.992986i	−0.997985	−	0.0634545i	$-0.979788\pi$
$241$	−21.2173	−	15.4153i	−1.36673	−	0.992986i	−0.368743	−	0.929531i	$-0.620212\pi$
$242$	−4.99524	−	15.3738i	−0.321106	−	0.988262i
$243$	11.5613			0.741655
$244$	14.7006	+	45.2439i	0.941112	+	2.89645i
$245$		0			0
$246$	−0.621604	+	1.91310i	−0.0396320	+	0.121975i
$247$	−0.398393	+	1.22613i	−0.0253491	+	0.0780166i
$248$	16.0349	−	11.6500i	1.01821	−	0.739776i
$249$	−5.99241			−0.379753
$250$		0			0
$251$	−10.9121			−0.688766			−0.344383	−	0.938829i	$-0.611912\pi$
$251$	−10.9121			−0.688766			−0.344383	+	0.938829i	$0.611912\pi$
$252$	22.7099	−	16.4997i	1.43059	−	1.03938i
$253$	−2.05763	+	6.33275i	−0.129362	+	0.398137i
$254$	−8.10722	+	24.9514i	−0.508692	+	1.56559i
$255$		0			0
$256$	−5.79381	−	17.8315i	−0.362113	−	1.11447i
$257$	6.58051			0.410481			0.205240	−	0.978712i	$-0.434202\pi$
$257$	6.58051			0.410481			0.205240	+	0.978712i	$0.434202\pi$
$258$	−1.21814	−	3.74903i	−0.0758378	−	0.233405i
$259$	−9.38256	−	6.81683i	−0.583004	−	0.423577i
$260$		0			0
$261$	8.89547	−	6.46294i	0.550616	−	0.400046i
$262$	−14.9230	−	10.8422i	−0.921945	−	0.669832i
$263$	21.9302	+	15.9332i	1.35228	+	0.982486i	0.998895	+	0.0470069i	$0.0149683\pi$
$263$	21.9302	+	15.9332i	1.35228	+	0.982486i	0.353382	+	0.935479i	$0.385032\pi$
$264$	−2.36492	+	1.71821i	−0.145551	+	0.105749i
$265$		0			0
$266$	−5.12330	−	3.72230i	−0.314130	−	0.228229i
$267$	−0.699712	−	2.15349i	−0.0428217	−	0.131792i
$268$	−35.6277			−2.17631
$269$	0.311938	+	0.960046i	0.0190192	+	0.0585350i	0.960116	−	0.279603i	$-0.0902029\pi$
$269$	0.311938	+	0.960046i	0.0190192	+	0.0585350i	−0.941096	+	0.338138i	$0.890203\pi$
$270$		0			0
$271$	1.93198	−	5.94603i	0.117360	−	0.361196i	−0.875072	−	0.483992i	$-0.839186\pi$
$271$	1.93198	−	5.94603i	0.117360	−	0.361196i	0.992432	+	0.122796i	$0.0391862\pi$
$272$	0.253921	−	0.781488i	0.0153962	−	0.0473847i
$273$	1.66466	−	1.20945i	0.100750	−	0.0731991i
$274$	21.5623			1.30263
$275$		0			0
$276$	−5.26943			−0.317182
$277$	19.9587	−	14.5009i	1.19920	−	0.871272i	0.204997	−	0.978763i	$-0.434282\pi$
$277$	19.9587	−	14.5009i	1.19920	−	0.871272i	0.994206	+	0.107491i	$0.0342816\pi$
$278$	12.7843	−	39.3459i	0.766749	−	2.35981i
$279$	5.52135	−	16.9930i	0.330555	−	1.01734i
$280$		0			0
$281$	0.568255	+	1.74891i	0.0338993	+	0.104331i	0.966574	−	0.256386i	$-0.0825319\pi$
$281$	0.568255	+	1.74891i	0.0338993	+	0.104331i	−0.932675	+	0.360717i	$0.882532\pi$
$282$	−5.26401			−0.313467
$283$	−2.67026	−	8.21823i	−0.158731	−	0.488523i	0.839789	−	0.542913i	$-0.182679\pi$
$283$	−2.67026	−	8.21823i	−0.158731	−	0.488523i	−0.998520	+	0.0543898i	$0.982679\pi$
$284$	−33.5949	−	24.4081i	−1.99349	−	1.44835i
$285$		0			0
$286$	5.33275	−	3.87447i	0.315332	−	0.229102i
$287$	4.50489	+	3.27300i	0.265915	+	0.193199i
$288$	−11.5267	−	8.37463i	−0.679217	−	0.493480i
$289$	10.9537	−	7.95831i	0.644334	−	0.468136i
$290$		0			0
$291$	3.82593	+	2.77970i	0.224280	+	0.162949i
$292$	0.275627	+	0.848293i	0.0161299	+	0.0496426i
$293$	6.29156			0.367557			0.183779	−	0.982968i	$-0.441167\pi$
$293$	6.29156			0.367557			0.183779	+	0.982968i	$0.441167\pi$
$294$	0.751050	+	2.31149i	0.0438021	+	0.134809i
$295$		0			0
$296$	3.63324	−	11.1820i	0.211178	−	0.649939i
$297$	−1.69484	+	5.21619i	−0.0983447	+	0.302674i
$298$	11.7960	−	8.57029i	0.683323	−	0.496463i
$299$	4.75164			0.274795
$300$		0			0
$301$	−10.9121			−0.628963
$302$	−8.81712	+	6.40601i	−0.507368	+	0.368625i
$303$	1.37157	−	4.22126i	0.0787947	−	0.242505i
$304$	0.123302	−	0.379483i	0.00707183	−	0.0217649i
$305$		0			0
$306$	−3.68305	−	11.3353i	−0.210546	−	0.647994i
$307$	−28.6661			−1.63606			−0.818030	−	0.575175i	$-0.804934\pi$
$307$	−28.6661			−1.63606			−0.818030	+	0.575175i	$0.804934\pi$
$308$	6.25303	+	19.2449i	0.356300	+	1.09658i
$309$	−3.49014	−	2.53574i	−0.198547	−	0.144253i
$310$		0			0
$311$	6.33985	−	4.60617i	0.359500	−	0.261192i	−0.393343	−	0.919392i	$-0.628682\pi$
$311$	6.33985	−	4.60617i	0.359500	−	0.261192i	0.752844	+	0.658199i	$0.228682\pi$
$312$	1.68762	+	1.22613i	0.0955426	+	0.0694158i
$313$	−17.3205	−	12.5840i	−0.979010	−	0.711292i	−0.0215228	−	0.999768i	$-0.506851\pi$
$313$	−17.3205	−	12.5840i	−0.979010	−	0.711292i	−0.957487	+	0.288476i	$0.906851\pi$
$314$	−2.74459	+	1.99406i	−0.154886	+	0.112531i
$315$		0			0
$316$	23.1116	+	16.7916i	1.30013	+	0.944599i
$317$	1.24220	+	3.82309i	0.0697688	+	0.214726i	0.979861	−	0.199679i	$-0.0639898\pi$
$317$	1.24220	+	3.82309i	0.0697688	+	0.214726i	−0.910093	+	0.414405i	$0.863990\pi$
$318$	−10.4237			−0.584530
$319$	2.44931	+	7.53821i	0.137135	+	0.422059i
$320$		0			0
$321$	0.826031	−	2.54226i	0.0461046	−	0.141895i
$322$	−7.21256	+	22.1980i	−0.401940	+	1.23705i
$323$	−1.35947	+	0.987712i	−0.0756429	+	0.0549578i
$324$	23.3995			1.29997
$325$		0			0
$326$	10.2987			0.570390
$327$	3.88546	−	2.82295i	0.214866	−	0.156109i
$328$	−1.74445	+	5.36885i	−0.0963209	+	0.296445i
$329$	−4.50292	+	13.8586i	−0.248254	+	0.764047i
$330$		0			0
$331$	3.59815	+	11.0740i	0.197772	+	0.608681i	0.999933	+	0.0115724i	$0.00368369\pi$
$331$	3.59815	+	11.0740i	0.197772	+	0.608681i	−0.802161	+	0.597108i	$0.796316\pi$
$332$	−42.0532			−2.30797
$333$	−3.27529	−	10.0803i	−0.179485	−	0.552398i
$334$	−19.4926	−	14.1622i	−1.06659	−	0.774922i
$335$		0			0
$336$	−0.515209	+	0.374321i	−0.0281069	+	0.0204209i
$337$	17.4220	+	12.6578i	0.949037	+	0.689516i	0.950579	−	0.310483i	$-0.100491\pi$
$337$	17.4220	+	12.6578i	0.949037	+	0.689516i	−0.00154181	+	0.999999i	$0.500491\pi$
$338$	20.4817	+	14.8808i	1.11406	+	0.809409i
$339$	−4.11560	+	2.99016i	−0.223529	+	0.162403i
$340$		0			0
$341$	10.4201	+	7.57063i	0.564279	+	0.409973i
$342$	−1.78846	−	5.50431i	−0.0967087	−	0.297639i
$343$	−14.5228			−0.784157
$344$	−3.41853	−	10.5211i	−0.184315	−	0.567262i
$345$		0			0
$346$	−5.47777	+	16.8588i	−0.294487	+	0.906337i
$347$	4.81981	−	14.8339i	0.258741	−	0.796323i	−0.734328	−	0.678794i	$-0.762503\pi$
$347$	4.81981	−	14.8339i	0.258741	−	0.796323i	0.993069	−	0.117529i	$-0.0374972\pi$
$348$	−5.07454	+	3.68687i	−0.272024	+	0.197637i
$349$	5.56598			0.297940			0.148970	−	0.988842i	$-0.452404\pi$
$349$	5.56598			0.297940			0.148970	+	0.988842i	$0.452404\pi$
$350$		0			0
$351$	3.91385			0.208906
$352$	8.30912	−	6.03693i	0.442878	−	0.321769i
$353$	2.47898	−	7.62953i	0.131943	−	0.406079i	−0.863159	−	0.504932i	$-0.831517\pi$
$353$	2.47898	−	7.62953i	0.131943	−	0.406079i	0.995102	+	0.0988533i	$0.0315175\pi$
$354$	3.60773	−	11.1034i	0.191748	−	0.590141i
$355$		0			0
$356$	−4.91040	−	15.1127i	−0.260251	−	0.800970i
$357$	2.68195			0.141944
$358$	11.0728	+	34.0787i	0.585218	+	1.80112i
$359$	9.98547	+	7.25487i	0.527013	+	0.382897i	0.819239	−	0.573452i	$-0.194396\pi$
$359$	9.98547	+	7.25487i	0.527013	+	0.382897i	−0.292226	+	0.956349i	$0.594396\pi$
$360$		0			0
$361$	14.7112	−	10.6883i	0.774272	−	0.562542i
$362$	2.97155	+	2.15895i	0.156181	+	0.113472i
$363$	2.68943	+	1.95399i	0.141159	+	0.102558i
$364$	11.6822	−	8.48760i	0.612312	−	0.444871i
$365$		0			0
$366$	−12.6645	−	9.20132i	−0.661986	−	0.480961i
$367$	8.30481	+	25.5596i	0.433508	+	1.33420i	0.894608	+	0.446852i	$0.147455\pi$
$367$	8.30481	+	25.5596i	0.433508	+	1.33420i	−0.461100	+	0.887348i	$0.652545\pi$
$368$	−1.47062			−0.0766615
$369$	1.57258	+	4.83991i	0.0818653	+	0.251956i
$370$		0			0
$371$	−8.91657	+	27.4424i	−0.462925	+	1.42474i
$372$	−3.14973	+	9.69387i	−0.163306	+	0.502604i
$373$	22.3604	−	16.2457i	1.15778	−	0.841173i	0.168280	−	0.985739i	$-0.446179\pi$
$373$	22.3604	−	16.2457i	1.15778	−	0.841173i	0.989495	+	0.144566i	$0.0461787\pi$
$374$	8.59164			0.444263
$375$		0			0
$376$	−14.7727			−0.761845
$377$	4.57591	−	3.32459i	0.235671	−	0.171225i
$378$	−5.94087	+	18.2841i	−0.305566	+	0.940434i
$379$	−1.07372	+	3.30456i	−0.0551532	+	0.169744i	−0.974839	−	0.222912i	$-0.928444\pi$
$379$	−1.07372	+	3.30456i	−0.0551532	+	0.169744i	0.919685	+	0.392656i	$0.128444\pi$
$380$		0			0
$381$	−1.66725	−	5.13127i	−0.0854159	−	0.262883i
$382$	45.4198			2.32388
$383$	8.45837	+	26.0322i	0.432203	+	1.33018i	0.895926	+	0.444203i	$0.146513\pi$
$383$	8.45837	+	26.0322i	0.432203	+	1.33018i	−0.463723	+	0.885980i	$0.653487\pi$
$384$	7.35937	+	5.34689i	0.375556	+	0.272858i
$385$		0			0
$386$	−24.4927	+	17.7950i	−1.24665	+	0.905741i
$387$	−8.06808	−	5.86180i	−0.410123	−	0.297972i
$388$	26.8494	+	19.5072i	1.36307	+	0.990329i
$389$	−8.80576	+	6.39776i	−0.446470	+	0.324379i	−0.788200	−	0.615419i	$-0.788987\pi$
$389$	−8.80576	+	6.39776i	−0.446470	+	0.324379i	0.341731	+	0.939798i	$0.388987\pi$
$390$		0			0
$391$	5.01054	+	3.64037i	0.253394	+	0.184101i
$392$	2.10772	+	6.48689i	0.106456	+	0.327637i
$393$	3.79339			0.191351
$394$	−2.44730	−	7.53202i	−0.123293	−	0.379458i
$395$		0			0
$396$	−5.71472	+	17.5881i	−0.287175	+	0.883835i
$397$	5.01264	−	15.4273i	0.251577	−	0.774275i	−0.742908	−	0.669394i	$-0.766554\pi$
$397$	5.01264	−	15.4273i	0.251577	−	0.774275i	0.994485	−	0.104881i	$-0.0334461\pi$
$398$	−33.0603	+	24.0197i	−1.65716	+	1.20400i
$399$	1.30233			0.0651981
$400$		0			0
$401$	3.78686			0.189107			0.0945534	−	0.995520i	$-0.469858\pi$
$401$	3.78686			0.189107			0.0945534	+	0.995520i	$0.469858\pi$
$402$	9.48469	−	6.89103i	0.473053	−	0.343693i
$403$	2.84023	−	8.74134i	0.141482	−	0.435437i
$404$	9.62535	−	29.6238i	0.478879	−	1.47384i
$405$		0			0
$406$	8.58550	+	26.4234i	0.426091	+	1.31137i
$407$	7.64044			0.378722
$408$	0.840198	+	2.58586i	0.0415960	+	0.128019i
$409$	−1.50142	−	1.09084i	−0.0742403	−	0.0539388i	0.550046	−	0.835134i	$-0.314610\pi$
$409$	−1.50142	−	1.09084i	−0.0742403	−	0.0539388i	−0.624286	+	0.781196i	$0.714610\pi$
$410$		0			0
$411$	−3.58742	+	2.60641i	−0.176954	+	0.128565i
$412$	−24.4930	−	17.7952i	−1.20668	−	0.876705i
$413$	−26.1459	−	18.9961i	−1.28656	−	0.934738i
$414$	−17.2571	+	12.5380i	−0.848142	+	0.616211i
$415$		0			0
$416$	−5.92943	−	4.30798i	−0.290714	−	0.211216i
$417$	2.62909	+	8.09150i	0.128747	+	0.396242i
$418$	4.17202			0.204060
$419$	4.43353	+	13.6450i	0.216592	+	0.666602i	0.999037	+	0.0438818i	$0.0139725\pi$
$419$	4.43353	+	13.6450i	0.216592	+	0.666602i	−0.782445	+	0.622720i	$0.786028\pi$
$420$		0			0
$421$	4.77571	−	14.6981i	0.232754	−	0.716343i	−0.764658	−	0.644437i	$-0.777092\pi$
$421$	4.77571	−	14.6981i	0.232754	−	0.716343i	0.997411	−	0.0719060i	$-0.0229082\pi$
$422$	−2.31469	+	7.12390i	−0.112678	+	0.346786i
$423$	−10.7739	+	7.82771i	−0.523846	+	0.380596i
$424$	−29.2525			−1.42063
$425$		0			0
$426$	13.6645			0.662046
$427$	−35.0578	+	25.4710i	−1.69657	+	1.23263i
$428$	5.79688	−	17.8410i	0.280203	−	0.862375i
$429$	−0.418895	+	1.28923i	−0.0202244	+	0.0622444i
$430$		0			0
$431$	3.86404	+	11.8923i	0.186124	+	0.572832i	0.999966	−	0.00825486i	$-0.00262763\pi$
$431$	3.86404	+	11.8923i	0.186124	+	0.572832i	−0.813842	+	0.581087i	$0.802628\pi$
$432$	−1.21133			−0.0582801
$433$	−6.95138	−	21.3941i	−0.334062	−	1.02814i	−0.967182	−	0.254084i	$-0.918226\pi$
$433$	−6.95138	−	21.3941i	−0.334062	−	1.02814i	0.633120	−	0.774053i	$-0.281774\pi$
$434$	36.5252	+	26.5371i	1.75326	+	1.27382i
$435$		0			0
$436$	27.2672	−	19.8108i	1.30586	−	0.948763i
$437$	2.43307	+	1.76773i	0.116390	+	0.0845620i
$438$	−0.237451	−	0.172519i	−0.0113459	−	0.00824326i
$439$	−9.85186	+	7.15780i	−0.470204	+	0.341623i	−0.797521	−	0.603292i	$-0.793855\pi$
$439$	−9.85186	+	7.15780i	−0.470204	+	0.341623i	0.327317	+	0.944915i	$0.393855\pi$
$440$		0			0
$441$	4.97443	+	3.61414i	0.236878	+	0.172102i
$442$	−1.89460	−	5.83096i	−0.0901167	−	0.277351i
$443$	−20.7101			−0.983968			−0.491984	−	0.870604i	$-0.663728\pi$
$443$	−20.7101			−0.983968			−0.491984	+	0.870604i	$0.663728\pi$
$444$	1.86843	+	5.75045i	0.0886720	+	0.272904i
$445$		0			0
$446$	20.4910	−	63.0648i	0.970277	−	2.98621i
$447$	−0.926591	+	2.85176i	−0.0438263	+	0.134883i
$448$	31.2954	−	22.7375i	1.47857	−	1.07424i
$449$	−25.9539			−1.22484			−0.612420	−	0.790533i	$-0.709804\pi$
$449$	−25.9539			−1.22484			−0.612420	+	0.790533i	$0.709804\pi$
$450$		0			0
$451$	−3.66844			−0.172740
$452$	−28.8823	+	20.9842i	−1.35851	+	0.987013i
$453$	0.692597	−	2.13159i	0.0325411	−	0.100151i
$454$	8.36390	−	25.7414i	0.392537	−	1.20811i
$455$		0			0
$456$	0.407993	+	1.25567i	0.0191060	+	0.0588022i
$457$	−8.50150			−0.397684			−0.198842	−	0.980032i	$-0.563718\pi$
$457$	−8.50150			−0.397684			−0.198842	+	0.980032i	$0.563718\pi$
$458$	−11.7040	−	36.0213i	−0.546894	−	1.68317i
$459$	4.12710	+	2.99851i	0.192636	+	0.139959i
$460$		0			0
$461$	−11.9614	+	8.69044i	−0.557097	+	0.404754i	−0.830395	−	0.557175i	$-0.811885\pi$
$461$	−11.9614	+	8.69044i	−0.557097	+	0.404754i	0.273299	+	0.961929i	$0.411885\pi$
$462$	−5.38696	−	3.91385i	−0.250624	−	0.182089i
$463$	17.9538	+	13.0442i	0.834384	+	0.606215i	0.920796	−	0.390044i	$-0.127540\pi$
$463$	17.9538	+	13.0442i	0.834384	+	0.606215i	−0.0864125	+	0.996259i	$0.527540\pi$
$464$	−1.41623	+	1.02895i	−0.0657470	+	0.0477680i
$465$		0			0
$466$	−42.0627	−	30.5603i	−1.94852	−	1.41568i
$467$	−8.80741	−	27.1064i	−0.407558	−	1.25434i	−0.918740	−	0.394863i	$-0.870792\pi$
$467$	−8.80741	−	27.1064i	−0.407558	−	1.25434i	0.511182	−	0.859473i	$-0.329208\pi$
$468$	13.1968			0.610024
$469$	−10.0287	−	30.8651i	−0.463081	−	1.42522i
$470$		0			0
$471$	0.215591	−	0.663522i	0.00993393	−	0.0305735i
$472$	10.1246	−	31.1603i	0.466022	−	1.43427i
$473$	5.81595	−	4.22553i	0.267418	−	0.194290i
$474$	−9.40048			−0.431779
$475$		0			0
$476$	18.8213			0.862671
$477$	−21.3342	+	15.5002i	−0.976827	+	0.709707i
$478$	−4.73358	+	14.5684i	−0.216509	+	0.666345i
$479$	7.74301	−	23.8305i	0.353787	−	1.08885i	−0.602922	−	0.797800i	$-0.705997\pi$
$479$	7.74301	−	23.8305i	0.353787	−	1.08885i	0.956709	−	0.291045i	$-0.0940030\pi$
$480$		0			0
$481$	−1.68484	−	5.18540i	−0.0768220	−	0.236434i
$482$	60.5632			2.75858
$483$	−1.48326	−	4.56502i	−0.0674909	−	0.207716i
$484$	18.8738	+	13.7126i	0.857898	+	0.623299i
$485$		0			0
$486$	−21.5992	+	15.6928i	−0.979761	+	0.711838i
$487$	1.18504	+	0.860980i	0.0536992	+	0.0390147i	0.614311	−	0.789064i	$-0.289434\pi$
$487$	1.18504	+	0.860980i	0.0536992	+	0.0390147i	−0.560612	+	0.828079i	$0.689434\pi$
$488$	−35.5413	−	25.8222i	−1.60888	−	1.16892i
$489$	−1.71343	+	1.24488i	−0.0774842	+	0.0562955i
$490$		0			0
$491$	16.2359	+	11.7961i	0.732715	+	0.532348i	0.890421	−	0.455138i	$-0.150410\pi$
$491$	16.2359	+	11.7961i	0.732715	+	0.532348i	−0.157706	+	0.987486i	$0.550410\pi$
$492$	−0.897100	−	2.76099i	−0.0404444	−	0.124475i
$493$	7.37229			0.332031
$494$	−0.919998	−	2.83146i	−0.0413927	−	0.127394i
$495$		0			0
$496$	−0.879045	+	2.70542i	−0.0394703	+	0.121477i
$497$	11.6888	−	35.9745i	0.524315	−	1.61368i
$498$	11.1953	−	8.13384i	0.501672	−	0.364486i
$499$	0.624999			0.0279788			0.0139894	−	0.999902i	$-0.495547\pi$
$499$	0.624999			0.0279788			0.0139894	+	0.999902i	$0.495547\pi$
$500$		0			0
$501$	4.95498			0.221372
$502$	20.3865	−	14.8116i	0.909892	−	0.661075i
$503$	−5.96563	+	18.3603i	−0.265994	+	0.818647i	0.725468	+	0.688256i	$0.241623\pi$
$503$	−5.96563	+	18.3603i	−0.265994	+	0.818647i	−0.991463	+	0.130391i	$0.958377\pi$
$504$	−8.01054	+	24.6539i	−0.356818	+	1.09817i
$505$		0			0
$506$	−4.75164	−	14.6241i	−0.211236	−	0.650119i
$507$	−5.20639			−0.231224
$508$	−11.7003	−	36.0100i	−0.519119	−	1.59768i
$509$	8.51099	+	6.18360i	0.377243	+	0.274083i	0.760208	−	0.649680i	$-0.225097\pi$
$509$	8.51099	+	6.18360i	0.377243	+	0.274083i	−0.382965	+	0.923763i	$0.625097\pi$
$510$		0			0
$511$	−0.657310	+	0.477563i	−0.0290777	+	0.0211262i
$512$	4.03481	+	2.93146i	0.178315	+	0.129554i
$513$	2.00408	+	1.45605i	0.0884824	+	0.0642862i
$514$	−12.2940	+	8.93210i	−0.542264	+	0.393978i
$515$		0			0
$516$	4.60254	+	3.34394i	0.202616	+	0.147209i
$517$	−2.96653	−	9.13004i	−0.130468	−	0.401539i
$518$	26.7818			1.17672
$519$	−1.12650	−	3.46703i	−0.0494481	−	0.152186i
$520$		0			0
$521$	−3.09232	+	9.51719i	−0.135477	+	0.416956i	−0.995664	−	0.0930234i	$-0.970347\pi$
$521$	−3.09232	+	9.51719i	−0.135477	+	0.416956i	0.860187	+	0.509979i	$0.170347\pi$
$522$	−7.84638	+	24.1487i	−0.343427	+	1.05696i
$523$	−18.4319	+	13.3915i	−0.805970	+	0.585571i	−0.912659	−	0.408721i	$-0.865975\pi$
$523$	−18.4319	+	13.3915i	−0.805970	+	0.585571i	0.106690	+	0.994292i	$0.465975\pi$
$524$	26.6210			1.16295
$525$		0			0
$526$	−62.5981			−2.72941
$527$	9.69196	−	7.04162i	0.422188	−	0.306738i
$528$	0.129647	−	0.399012i	0.00564216	−	0.0173648i
$529$	−3.68213	+	11.3324i	−0.160092	+	0.492714i
$530$		0			0
$531$	−9.12710	−	28.0903i	−0.396082	−	1.21902i
$532$	9.13943			0.396245
$533$	0.808950	+	2.48969i	0.0350395	+	0.107841i
$534$	4.23029	+	3.07349i	0.183063	+	0.133003i
$535$		0			0
$536$	26.6175	−	19.3387i	1.14970	−	0.835306i
$537$	−5.96161	−	4.33136i	−0.257262	−	0.186912i
$538$	−1.88590	−	1.37019i	−0.0813070	−	0.0590730i
$539$	−3.58586	+	2.60528i	−0.154454	+	0.112217i
$540$		0			0
$541$	−2.63658	−	1.91559i	−0.113356	−	0.0823576i	0.529663	−	0.848208i	$-0.322318\pi$
$541$	−2.63658	−	1.91559i	−0.113356	−	0.0823576i	−0.643019	+	0.765850i	$0.722318\pi$
$542$	4.46148	+	13.7310i	0.191637	+	0.589798i
$543$	−0.755360			−0.0324156
$544$	−2.95203	−	9.08540i	−0.126567	−	0.389533i
$545$		0			0
$546$	−1.46834	+	4.51908i	−0.0628391	+	0.193399i
$547$	−4.19901	+	12.9232i	−0.179537	+	0.552557i	−0.999812	−	0.0194122i	$-0.993821\pi$
$547$	−4.19901	+	12.9232i	−0.179537	+	0.552557i	0.820275	+	0.571970i	$0.193821\pi$
$548$	−25.1756	+	18.2911i	−1.07545	+	0.781359i
$549$	−39.6033			−1.69023
$550$		0			0
$551$	3.57992			0.152510
$552$	3.93679	−	2.86025i	0.167561	−	0.121740i
$553$	−8.04133	+	24.7487i	−0.341952	+	1.05242i
$554$	−17.6049	+	54.1822i	−0.747959	+	2.30198i
$555$		0			0
$556$	18.4503	+	56.7841i	0.782466	+	2.40818i
$557$	−27.6399			−1.17114			−0.585571	−	0.810621i	$-0.699130\pi$
$557$	−27.6399			−1.17114			−0.585571	+	0.810621i	$0.699130\pi$
$558$	12.7503	+	39.2414i	0.539764	+	1.66122i
$559$	−4.15029	−	3.01536i	−0.175539	−	0.127536i
$560$		0			0
$561$	−1.42943	+	1.03854i	−0.0603506	+	0.0438473i
$562$	−3.43554	−	2.49606i	−0.144919	−	0.105290i
$563$	1.34236	+	0.975284i	0.0565738	+	0.0411033i	0.615713	−	0.787971i	$-0.288868\pi$
$563$	1.34236	+	0.975284i	0.0565738	+	0.0411033i	−0.559139	+	0.829074i	$0.688868\pi$
$564$	6.14612	−	4.46542i	0.258799	−	0.188028i
$565$		0			0
$566$	16.1438	+	11.7291i	0.678574	+	0.493013i
$567$	6.58660	+	20.2715i	0.276611	+	0.851322i
$568$	38.3475			1.60902
$569$	5.52609	+	17.0076i	0.231666	+	0.712994i	0.997546	+	0.0700110i	$0.0223034\pi$
$569$	5.52609	+	17.0076i	0.231666	+	0.712994i	−0.765880	+	0.642983i	$0.777697\pi$
$570$		0			0
$571$	−11.3942	+	35.0677i	−0.476832	+	1.46754i	0.366640	+	0.930363i	$0.380508\pi$
$571$	−11.3942	+	35.0677i	−0.476832	+	1.46754i	−0.843472	+	0.537174i	$0.819492\pi$
$572$	−2.93970	+	9.04746i	−0.122915	+	0.378293i
$573$	−7.55670	+	5.49027i	−0.315686	+	0.229359i
$574$	−12.8589			−0.536718
$575$		0			0
$576$	35.3531			1.47305
$577$	18.4567	−	13.4095i	0.768361	−	0.558247i	−0.133103	−	0.991102i	$-0.542494\pi$
$577$	18.4567	−	13.4095i	0.768361	−	0.558247i	0.901463	+	0.432855i	$0.142494\pi$
$578$	−9.66184	+	29.7361i	−0.401880	+	1.23686i
$579$	1.92394	−	5.92127i	0.0799560	−	0.246079i
$580$		0			0
$581$	−11.8373	−	36.4316i	−0.491096	−	1.51144i
$582$	−10.9208			−0.452682
$583$	−5.87425	−	18.0791i	−0.243286	−	0.748759i
$584$	−0.666375	−	0.484149i	−0.0275748	−	0.0200342i
$585$		0			0
$586$	−11.7542	+	8.53990i	−0.485560	+	0.352780i
$587$	8.96834	+	6.51588i	0.370163	+	0.268939i	0.757278	−	0.653092i	$-0.226529\pi$
$587$	8.96834	+	6.51588i	0.370163	+	0.268939i	−0.387116	+	0.922031i	$0.626529\pi$
$588$	−2.83773	−	2.06173i	−0.117026	−	0.0850244i
$589$	4.70633	−	3.41935i	0.193921	−	0.140892i
$590$		0			0
$591$	1.31762	+	0.957311i	0.0541998	+	0.0393785i
$592$	0.521454	+	1.60487i	0.0214316	+	0.0659597i
$593$	11.1321			0.457139			0.228570	−	0.973528i	$-0.426595\pi$
$593$	11.1321			0.457139			0.228570	+	0.973528i	$0.426595\pi$
$594$	−3.91385	−	12.0456i	−0.160587	−	0.494237i
$595$		0			0
$596$	−6.50259	+	20.0129i	−0.266356	+	0.819760i
$597$	2.59693	−	7.99253i	0.106285	−	0.327112i
$598$	−8.87722	+	6.44968i	−0.363017	+	0.263747i
$599$	36.2736			1.48210			0.741049	−	0.671451i	$-0.234329\pi$
$599$	36.2736			1.48210			0.741049	+	0.671451i	$0.234329\pi$
$600$		0			0
$601$	−15.1051			−0.616150			−0.308075	−	0.951362i	$-0.599685\pi$
$601$	−15.1051			−0.616150			−0.308075	+	0.951362i	$0.599685\pi$
$602$	20.3865	−	14.8116i	0.830890	−	0.603677i
$603$	9.16531	−	28.2079i	0.373240	−	1.14872i
$604$	4.86047	−	14.9590i	0.197770	−	0.608673i
$605$		0			0
$606$	3.16734	+	9.74806i	0.128664	+	0.395988i
$607$	−33.5066			−1.35999			−0.679996	−	0.733216i	$-0.738018\pi$
$607$	−33.5066			−1.35999			−0.679996	+	0.733216i	$0.738018\pi$
$608$	−1.43348	−	4.41179i	−0.0581352	−	0.178922i
$609$	−4.62243	−	3.35839i	−0.187310	−	0.136089i
$610$		0			0
$611$	−5.54220	+	4.02664i	−0.224213	+	0.162900i
$612$	13.9159	+	10.1105i	0.562516	+	0.408692i
$613$	22.6758	+	16.4750i	0.915869	+	0.665418i	0.942492	−	0.334228i	$-0.108476\pi$
$613$	22.6758	+	16.4750i	0.915869	+	0.665418i	−0.0266235	+	0.999646i	$0.508476\pi$
$614$	53.5552	−	38.9102i	2.16131	−	1.57029i
$615$		0			0
$616$	−15.1178	−	10.9837i	−0.609112	−	0.442545i
$617$	9.43191	+	29.0284i	0.379714	+	1.16864i	0.940243	+	0.340505i	$0.110598\pi$
$617$	9.43191	+	29.0284i	0.379714	+	1.16864i	−0.560528	+	0.828135i	$0.689402\pi$
$618$	9.96234			0.400744
$619$	−6.70477	−	20.6352i	−0.269488	−	0.829398i	−0.990625	−	0.136606i	$-0.956381\pi$
$619$	−6.70477	−	20.6352i	−0.269488	−	0.829398i	0.721138	−	0.692792i	$-0.243619\pi$
$620$		0			0
$621$	2.82134	−	8.68318i	0.113216	−	0.348444i
$622$	−5.59216	+	17.2109i	−0.224225	+	0.690094i
$623$	11.7102	−	8.50798i	0.469161	−	0.340865i
$624$	−0.299391			−0.0119852
$625$		0			0
$626$	49.4399			1.97601
$627$	−0.694118	+	0.504306i	−0.0277204	+	0.0201401i
$628$	1.51297	−	4.65643i	0.0603740	−	0.185812i
$629$	2.19604	−	6.75873i	0.0875620	−	0.269488i
$630$		0			0
$631$	−5.01463	−	15.4335i	−0.199629	−	0.614396i	−0.999891	−	0.0147456i	$-0.995306\pi$
$631$	−5.01463	−	15.4335i	−0.199629	−	0.614396i	0.800262	−	0.599651i	$-0.204694\pi$
$632$	−26.3812			−1.04939
$633$	−0.476017	−	1.46503i	−0.0189200	−	0.0582297i
$634$	−7.51003	−	5.45635i	−0.298261	−	0.216699i
$635$		0			0
$636$	12.1704	−	8.84231i	0.482588	−	0.350620i
$637$	2.55889	+	1.85914i	0.101387	+	0.0736619i
$638$	−14.8080	−	10.7586i	−0.586253	−	0.425937i
$639$	27.9673	−	20.3194i	1.10637	−	0.803823i
$640$		0			0
$641$	17.9419	+	13.0356i	0.708663	+	0.514874i	0.882742	−	0.469858i	$-0.155695\pi$
$641$	17.9419	+	13.0356i	0.708663	+	0.514874i	−0.174079	+	0.984732i	$0.555695\pi$
$642$	1.90753	+	5.87078i	0.0752843	+	0.231701i
$643$	−13.2767			−0.523583			−0.261792	−	0.965124i	$-0.584313\pi$
$643$	−13.2767			−0.523583			−0.261792	+	0.965124i	$0.584313\pi$
$644$	−10.4092	−	32.0362i	−0.410179	−	1.26240i
$645$		0			0
$646$	1.19914	−	3.69057i	0.0471795	−	0.145204i
$647$	−3.48735	+	10.7329i	−0.137102	+	0.421956i	−0.995911	−	0.0903397i	$-0.971205\pi$
$647$	−3.48735	+	10.7329i	−0.137102	+	0.421956i	0.858809	+	0.512295i	$0.171205\pi$
$648$	−17.4818	+	12.7012i	−0.686748	+	0.498952i
$649$	21.2912			0.835754
$650$		0			0
$651$	−9.28462			−0.363893
$652$	−12.0245	+	8.73627i	−0.470914	+	0.342139i
$653$	−11.0669	+	34.0606i	−0.433083	+	1.33289i	0.461955	+	0.886903i	$0.347148\pi$
$653$	−11.0669	+	34.0606i	−0.433083	+	1.33289i	−0.895038	+	0.445989i	$0.852852\pi$
$654$	−3.42722	+	10.5479i	−0.134015	+	0.412456i
$655$		0			0
$656$	−0.250368	−	0.770554i	−0.00977523	−	0.0300851i
$657$	−0.742534			−0.0289690
$658$	−10.3985	−	32.0032i	−0.405375	−	1.24762i
$659$	−32.1710	−	23.3736i	−1.25320	−	0.910506i	−0.254801	−	0.966994i	$-0.582010\pi$
$659$	−32.1710	−	23.3736i	−1.25320	−	0.910506i	−0.998403	+	0.0564876i	$0.982010\pi$
$660$		0			0
$661$	5.05420	−	3.67209i	0.196586	−	0.142828i	−0.485138	−	0.874438i	$-0.661231\pi$
$661$	5.05420	−	3.67209i	0.196586	−	0.142828i	0.681724	+	0.731610i	$0.261231\pi$
$662$	−21.7536	−	15.8049i	−0.845476	−	0.614274i
$663$	1.02005	+	0.741109i	0.0396154	+	0.0287823i
$664$	31.4180	−	22.8265i	1.21925	−	0.885839i
$665$		0			0
$666$	19.8016	+	14.3867i	0.767298	+	0.557474i
$667$	−4.07728	−	12.5486i	−0.157873	−	0.485882i
$668$	34.7728			1.34540
$669$	4.21398	+	12.9693i	0.162922	+	0.501422i
$670$		0			0
$671$	8.82193	−	27.1511i	0.340567	−	1.04816i
$672$	−2.28786	+	7.04132i	−0.0882563	+	0.271625i
$673$	33.5441	−	24.3712i	1.29303	−	0.939440i	0.293166	−	0.956061i	$-0.405291\pi$
$673$	33.5441	−	24.3712i	1.29303	−	0.939440i	0.999862	+	0.0166215i	$0.00529102\pi$
$674$	−49.7297			−1.91552
$675$		0			0
$676$	−36.5372			−1.40528
$677$	1.16430	−	0.845914i	0.0447477	−	0.0325111i	−0.565187	−	0.824963i	$-0.691196\pi$
$677$	1.16430	−	0.845914i	0.0447477	−	0.0325111i	0.609934	+	0.792452i	$0.291196\pi$
$678$	3.63023	−	11.1727i	0.139418	−	0.429084i
$679$	−9.34183	+	28.7512i	−0.358507	+	1.10337i
$680$		0			0
$681$	1.72004	+	5.29373i	0.0659120	+	0.202856i
$682$	−29.7433			−1.13893
$683$	−2.62239	−	8.07088i	−0.100343	−	0.308824i	0.888266	−	0.459329i	$-0.151910\pi$
$683$	−2.62239	−	8.07088i	−0.100343	−	0.308824i	−0.988609	+	0.150505i	$0.951910\pi$
$684$	6.75742	+	4.90955i	0.258376	+	0.187721i
$685$		0			0
$686$	27.1321	−	19.7126i	1.03591	−	0.752631i
$687$	6.30145	+	4.57827i	0.240415	+	0.174672i
$688$	1.28450	+	0.933247i	0.0489713	+	0.0355797i
$689$	−10.9745	+	7.97345i	−0.418096	+	0.303764i
$690$		0			0
$691$	35.4186	+	25.7331i	1.34739	+	0.978933i	0.999137	+	0.0415304i	$0.0132233\pi$
$691$	35.4186	+	25.7331i	1.34739	+	0.978933i	0.348248	+	0.937402i	$0.386777\pi$
$692$	−7.90553	−	24.3307i	−0.300523	−	0.924915i
$693$	−16.8456			−0.639910
$694$	11.1303	+	34.2554i	0.422499	+	1.30032i
$695$		0			0
$696$	1.78996	−	5.50893i	0.0678482	−	0.208815i
$697$	−1.05440	+	3.24510i	−0.0399381	+	0.122917i
$698$	−10.3986	+	7.55503i	−0.393593	+	0.285962i
$699$	10.6922			0.404418
$700$		0			0
$701$	0.840795			0.0317564			0.0158782	−	0.999874i	$-0.494946\pi$
$701$	0.840795			0.0317564			0.0158782	+	0.999874i	$0.494946\pi$
$702$	−7.31203	+	5.31250i	−0.275975	+	0.200507i
$703$	1.06638	−	3.28198i	0.0402192	−	0.123782i
$704$	−7.87517	+	24.2373i	−0.296807	+	0.913477i
$705$		0			0
$706$	5.72466	+	17.6187i	0.215450	+	0.663088i
$707$	28.3731			1.06708
$708$	5.20668	+	16.0245i	0.195679	+	0.602238i
$709$	10.8256	+	7.86529i	0.406566	+	0.295387i	0.772210	−	0.635367i	$-0.219151\pi$
$709$	10.8256	+	7.86529i	0.406566	+	0.295387i	−0.365644	+	0.930755i	$0.619151\pi$
$710$		0			0
$711$	−19.2401	+	13.9787i	−0.721560	+	0.524244i
$712$	11.8717	+	8.62531i	0.444912	+	0.323247i
$713$	−17.3459	−	12.6025i	−0.649610	−	0.471969i
$714$	−5.01054	+	3.64037i	−0.187515	+	0.136237i
$715$		0			0
$716$	−41.8371	−	30.3964i	−1.56353	−	1.13597i
$717$	−0.973461	−	2.99601i	−0.0363546	−	0.111888i
$718$	−28.5027			−1.06371
$719$	13.4159	+	41.2900i	0.500329	+	1.53986i	0.808483	+	0.588519i	$0.200289\pi$
$719$	13.4159	+	41.2900i	0.500329	+	1.53986i	−0.308154	+	0.951336i	$0.599711\pi$
$720$		0			0
$721$	8.52195	−	26.2279i	0.317374	−	0.976776i
$722$	−12.9762	+	39.9367i	−0.482924	+	1.48629i
$723$	−10.0762	+	7.32076i	−0.374737	+	0.272262i
$724$	−5.30093			−0.197007
$725$		0			0
$726$	−7.67677			−0.284912
$727$	25.9274	−	18.8373i	0.961593	−	0.698639i	0.00807318	−	0.999967i	$-0.497430\pi$
$727$	25.9274	−	18.8373i	0.961593	−	0.698639i	0.953520	+	0.301329i	$0.0974302\pi$
$728$	−4.12069	+	12.6822i	−0.152723	+	0.470033i
$729$	−4.81224	+	14.8106i	−0.178231	+	0.548539i
$730$		0			0
$731$	−2.06626	−	6.35930i	−0.0764235	−	0.235207i
$732$	22.5922			0.835032
$733$	2.51517	+	7.74091i	0.0929001	+	0.285917i	0.986701	−	0.162547i	$-0.0519711\pi$
$733$	2.51517	+	7.74091i	0.0929001	+	0.285917i	−0.893801	+	0.448465i	$0.851971\pi$
$734$	−50.2089	−	36.4789i	−1.85324	−	1.34646i
$735$		0			0
$736$	−13.8319	+	10.0494i	−0.509850	+	0.370427i
$737$	17.2971	+	12.5671i	0.637146	+	0.462914i
$738$	−9.50745	−	6.90757i	−0.349974	−	0.254271i
$739$	5.76598	−	4.18923i	0.212105	−	0.154103i	−0.476661	−	0.879087i	$-0.658153\pi$
$739$	5.76598	−	4.18923i	0.212105	−	0.154103i	0.688766	+	0.724984i	$0.258153\pi$
$740$		0			0
$741$	0.495326	+	0.359876i	0.0181963	+	0.0132204i
$742$	−20.5908	−	63.3720i	−0.755912	−	2.32646i
$743$	21.9040			0.803578			0.401789	−	0.915732i	$-0.368388\pi$
$743$	21.9040			0.803578			0.401789	+	0.915732i	$0.368388\pi$
$744$	−2.90867	−	8.95197i	−0.106637	−	0.328195i
$745$		0			0
$746$	−19.7233	+	60.7020i	−0.722120	+	2.22246i
$747$	10.8183	−	33.2953i	0.395820	−	1.21821i
$748$	−10.0314	+	7.28823i	−0.366784	+	0.266484i
$749$	17.0877			0.624373
$750$		0			0
$751$	9.21909			0.336409			0.168205	−	0.985752i	$-0.446203\pi$
$751$	9.21909			0.336409			0.168205	+	0.985752i	$0.446203\pi$
$752$	1.71530	−	1.24624i	0.0625504	−	0.0454456i
$753$	−1.60138	+	4.92855i	−0.0583577	+	0.179606i
$754$	−4.03625	+	12.4223i	−0.146991	+	0.452393i
$755$		0			0
$756$	−8.57388	−	26.3877i	−0.311829	−	0.959711i
$757$	45.6524			1.65926			0.829632	−	0.558311i	$-0.188550\pi$
$757$	45.6524			1.65926			0.829632	+	0.558311i	$0.188550\pi$
$758$	−2.47951	−	7.63114i	−0.0900598	−	0.277176i
$759$	2.55828	+	1.85870i	0.0928597	+	0.0674666i
$760$		0			0
$761$	−32.2844	+	23.4560i	−1.17031	+	0.850280i	−0.991046	−	0.133521i	$-0.957372\pi$
$761$	−32.2844	+	23.4560i	−1.17031	+	0.850280i	−0.179264	+	0.983801i	$0.557372\pi$
$762$	10.0798	+	7.32340i	0.365153	+	0.265299i
$763$	24.8378	+	18.0457i	0.899188	+	0.653299i
$764$	−53.0310	+	38.5293i	−1.91860	+	1.39394i
$765$		0			0
$766$	−51.1373	−	37.1534i	−1.84767	−	1.34241i
$767$	−4.69506	−	14.4499i	−0.169529	−	0.521756i
$768$	−8.90403			−0.321296
$769$	−13.7024	−	42.1717i	−0.494122	−	1.52075i	−0.818320	−	0.574762i	$-0.805094\pi$
$769$	−13.7024	−	42.1717i	−0.494122	−	1.52075i	0.324198	−	0.945989i	$-0.394906\pi$
$770$		0			0
$771$	0.965710	−	2.97215i	0.0347792	−	0.107039i
$772$	13.5017	−	41.5540i	0.485937	−	1.49556i
$773$	31.1426	−	22.6264i	1.12012	−	0.813816i	0.135894	−	0.990723i	$-0.456609\pi$
$773$	31.1426	−	22.6264i	1.12012	−	0.813816i	0.984228	+	0.176907i	$0.0566093\pi$
$774$	23.0297			0.827785
$775$		0			0
$776$	−30.6477			−1.10019
$777$	−4.45580	+	3.23733i	−0.159851	+	0.116139i
$778$	7.76725	−	23.9051i	0.278469	−	0.857041i
$779$	−0.512006	+	1.57579i	−0.0183445	+	0.0564586i
$780$		0			0
$781$	7.70061	+	23.7000i	0.275549	+	0.848054i
$782$	−14.3022			−0.511445
$783$	−3.35839	−	10.3361i	−0.120019	−	0.369381i
$784$	−0.791971	−	0.575400i	−0.0282847	−	0.0205500i
$785$		0			0
$786$	−7.08697	+	5.14898i	−0.252784	+	0.183658i
$787$	42.8942	+	31.1645i	1.52901	+	1.11089i	0.956784	+	0.290801i	$0.0939218\pi$
$787$	42.8942	+	31.1645i	1.52901	+	1.11089i	0.572231	+	0.820093i	$0.306078\pi$
$788$	9.24676	+	6.71817i	0.329402	+	0.239325i
$789$	10.4147	−	7.56674i	0.370774	−	0.269383i
$790$		0			0
$791$	−26.3090	−	19.1146i	−0.935440	−	0.679637i
$792$	−5.27735	−	16.2420i	−0.187522	−	0.577135i
$793$	−20.3723			−0.723440
$794$	11.5756	+	35.6259i	0.410801	+	1.26432i
$795$		0			0
$796$	18.2246	−	56.0896i	0.645954	−	1.98804i
$797$	−3.91737	+	12.0564i	−0.138760	+	0.427060i	−0.996156	−	0.0875977i	$-0.972081\pi$
$797$	−3.91737	+	12.0564i	−0.138760	+	0.427060i	0.857396	+	0.514658i	$0.172081\pi$
$798$	−2.43307	+	1.76773i	−0.0861298	+	0.0625769i
$799$	−8.92908			−0.315888
$800$		0			0
$801$	13.2285			0.467407
$802$	−7.07477	+	5.14012i	−0.249819	+	0.181504i
$803$	0.165405	−	0.509065i	0.00583702	−	0.0179645i
$804$	−5.22847	+	16.0916i	−0.184394	+	0.567507i
$805$		0			0
$806$	6.55888	+	20.1861i	0.231027	+	0.711027i
$807$	0.479392			0.0168754
$808$	8.88869	+	27.3566i	0.312703	+	0.962401i
$809$	33.8926	+	24.6244i	1.19160	+	0.865747i	0.993432	−	0.114421i	$-0.0365013\pi$
$809$	33.8926	+	24.6244i	1.19160	+	0.865747i	0.198167	+	0.980168i	$0.436501\pi$
$810$		0			0
$811$	27.9504	−	20.3072i	0.981472	−	0.713081i	0.0234348	−	0.999725i	$-0.492540\pi$
$811$	27.9504	−	20.3072i	0.981472	−	0.713081i	0.958037	+	0.286644i	$0.0925398\pi$
$812$	−32.4390	−	23.5683i	−1.13839	−	0.827086i
$813$	−2.40206	−	1.74520i	−0.0842439	−	0.0612068i
$814$	−14.2742	+	10.3708i	−0.500310	+	0.363496i
$815$		0			0
$816$	−0.315703	−	0.229371i	−0.0110518	−	0.00802961i
$817$	−1.00336	−	3.08802i	−0.0351031	−	0.108036i
$818$	4.28568			0.149845
$819$	3.71472	+	11.4327i	0.129803	+	0.399491i
$820$		0			0
$821$	−6.53103	+	20.1004i	−0.227935	+	0.701511i	0.770046	+	0.637989i	$0.220233\pi$
$821$	−6.53103	+	20.1004i	−0.227935	+	0.701511i	−0.997980	+	0.0635220i	$0.979767\pi$
$822$	3.16433	−	9.73882i	0.110369	−	0.339680i
$823$	−2.57036	+	1.86747i	−0.0895970	+	0.0650960i	−0.631682	−	0.775228i	$-0.717635\pi$
$823$	−2.57036	+	1.86747i	−0.0895970	+	0.0650960i	0.542085	+	0.840324i	$0.317635\pi$
$824$	27.9579			0.973960
$825$		0			0
$826$	74.6315			2.59676
$827$	−7.88372	+	5.72786i	−0.274144	+	0.199177i	−0.716359	−	0.697732i	$-0.754193\pi$
$827$	−7.88372	+	5.72786i	−0.274144	+	0.199177i	0.442215	+	0.896909i	$0.354193\pi$
$828$	9.51307	−	29.2782i	0.330602	−	1.01749i
$829$	7.24188	−	22.2882i	0.251521	−	0.774101i	−0.742974	−	0.669320i	$-0.766586\pi$
$829$	7.24188	−	22.2882i	0.251521	−	0.774101i	0.994495	−	0.104782i	$-0.0334144\pi$
$830$		0			0
$831$	−3.62045	−	11.1426i	−0.125592	−	0.386532i
$832$	18.1859			0.630484
$833$	1.27397	+	3.92087i	0.0441404	+	0.135850i
$834$	−15.8948	−	11.5483i	−0.550393	−	0.399884i
$835$		0			0
$836$	−4.87115	+	3.53910i	−0.168472	+	0.122402i
$837$	−14.2876	−	10.3805i	−0.493850	−	0.358803i
$838$	−26.8041	−	19.4743i	−0.925931	−	0.672728i
$839$	−34.5304	+	25.0878i	−1.19212	+	0.866126i	−0.993487	−	0.113948i	$-0.963650\pi$
$839$	−34.5304	+	25.0878i	−1.19212	+	0.866126i	−0.198634	+	0.980074i	$0.563650\pi$
$840$		0			0
$841$	10.7551	+	7.81406i	0.370866	+	0.269450i
$842$	11.0284	+	33.9420i	0.380065	+	1.16972i
$843$	0.873305			0.0300782
$844$	−3.34057	−	10.2812i	−0.114987	−	0.353894i
$845$		0			0
$846$	9.50329	−	29.2481i	0.326730	−	1.00557i
$847$	−6.56683	+	20.2106i	−0.225639	+	0.694446i
$848$	3.39659	−	2.46776i	0.116639	−	0.0847434i
$849$	−4.10371			−0.140839
$850$		0			0
$851$	−12.7187			−0.435993
$852$	−15.9543	+	11.5915i	−0.546585	+	0.397117i
$853$	5.24124	−	16.1309i	0.179456	−	0.552310i	−0.820352	−	0.571858i	$-0.806223\pi$
$853$	5.24124	−	16.1309i	0.179456	−	0.552310i	0.999809	+	0.0195480i	$0.00622272\pi$
$854$	30.9232	−	95.1719i	1.05817	−	3.25672i
$855$		0			0
$856$	5.35323	+	16.4755i	0.182969	+	0.563122i
$857$	−39.3176			−1.34306			−0.671531	−	0.740976i	$-0.734363\pi$
$857$	−39.3176			−1.34306			−0.671531	+	0.740976i	$0.734363\pi$
$858$	−0.967343	−	2.97718i	−0.0330246	−	0.101639i
$859$	−0.572020	−	0.415597i	−0.0195171	−	0.0141800i	0.577984	−	0.816048i	$-0.303840\pi$
$859$	−0.572020	−	0.415597i	−0.0195171	−	0.0141800i	−0.597501	+	0.801868i	$0.703840\pi$
$860$		0			0
$861$	2.13939	−	1.55436i	0.0729101	−	0.0529723i
$862$	−23.3611	−	16.9728i	−0.795681	−	0.578096i
$863$	−0.735728	−	0.534537i	−0.0250445	−	0.0181959i	0.575193	−	0.818018i	$-0.304927\pi$
$863$	−0.735728	−	0.534537i	−0.0250445	−	0.0181959i	−0.600237	+	0.799822i	$0.704927\pi$
$864$	−11.3931	+	8.27757i	−0.387601	+	0.281609i
$865$		0			0
$866$	42.0264	+	30.5339i	1.42811	+	1.03759i
$867$	−1.98696	−	6.11524i	−0.0674807	−	0.207684i
$868$	−65.1571			−2.21158
$869$	−5.29764	−	16.3045i	−0.179710	−	0.553091i
$870$		0			0
$871$	4.71472	−	14.5104i	0.159752	−	0.491666i
$872$	−9.61803	+	29.6012i	−0.325708	+	1.00242i
$873$	−22.3517	+	16.2395i	−0.756492	+	0.549624i
$874$	−6.94501			−0.234918
$875$		0			0
$876$	0.423589			0.0143117
$877$	−27.2326	+	19.7856i	−0.919578	+	0.668113i	−0.943419	−	0.331603i	$-0.892411\pi$
$877$	−27.2326	+	19.7856i	−0.919578	+	0.668113i	0.0238407	+	0.999716i	$0.492411\pi$
$878$	8.68997	−	26.7450i	0.293272	−	0.902600i
$879$	0.923306	−	2.84164i	0.0311423	−	0.0958463i
$880$		0			0
$881$	−6.15819	−	18.9529i	−0.207475	−	0.638541i	−0.999603	−	0.0281862i	$-0.991027\pi$
$881$	−6.15819	−	18.9529i	−0.207475	−	0.638541i	0.792128	−	0.610355i	$-0.208973\pi$
$882$	−14.1991			−0.478109
$883$	4.82317	+	14.8442i	0.162313	+	0.499547i	0.998828	−	0.0483963i	$-0.0154110\pi$
$883$	4.82317	+	14.8442i	0.162313	+	0.499547i	−0.836516	+	0.547943i	$0.815411\pi$
$884$	7.15845	+	5.20091i	0.240765	+	0.174926i
$885$		0			0
$886$	38.6916	−	28.1111i	1.29987	−	0.944410i
$887$	−37.9403	−	27.5652i	−1.27391	−	0.925550i	−0.274560	−	0.961570i	$-0.588532\pi$
$887$	−37.9403	−	27.5652i	−1.27391	−	0.925550i	−0.999351	+	0.0360196i	$0.988532\pi$
$888$	−4.51725	−	3.28198i	−0.151589	−	0.110136i
$889$	27.9028	−	20.2725i	0.935828	−	0.679919i
$890$		0			0
$891$	−11.3603	−	8.25376i	−0.380585	−	0.276511i
$892$	29.5726	+	91.0152i	0.990165	+	3.04742i
$893$	−4.33588			−0.145095
$894$	−2.13975	−	6.58549i	−0.0715641	−	0.220252i
$895$		0			0
$896$	−17.9695	+	55.3045i	−0.600319	+	1.84759i
$897$	0.697318	−	2.14612i	0.0232828	−	0.0716570i
$898$	48.4882	−	35.2287i	1.61807	−	1.17560i
$899$	−25.5220			−0.851208
$900$		0			0
$901$	−17.6811			−0.589044
$902$	6.85353	−	4.97938i	0.228198	−	0.165795i
$903$	−1.60138	+	4.92855i	−0.0532907	+	0.164012i
$904$	10.1877	−	31.3546i	0.338839	−	1.04284i
$905$		0			0
$906$	1.59940	+	4.92244i	0.0531364	+	0.163537i
$907$	1.43447			0.0476308			0.0238154	−	0.999716i	$-0.492419\pi$
$907$	1.43447			0.0476308			0.0238154	+	0.999716i	$0.492419\pi$
$908$	12.0708	+	37.1501i	0.400583	+	1.23287i
$909$	20.9782	+	15.2416i	0.695804	+	0.505531i
$910$		0			0
$911$	2.27438	−	1.65244i	0.0753537	−	0.0547476i	−0.549471	−	0.835513i	$-0.685171\pi$
$911$	2.27438	−	1.65244i	0.0753537	−	0.0547476i	0.624824	+	0.780765i	$0.285171\pi$
$912$	−0.153302	−	0.111381i	−0.00507635	−	0.00368818i
$913$	20.4166	+	14.8335i	0.675692	+	0.490919i
$914$	15.8829	−	11.5396i	0.525359	−	0.381695i
$915$		0			0
$916$	44.2220	+	32.1291i	1.46114	+	1.06158i
$917$	7.49342	+	23.0624i	0.247455	+	0.761587i
$918$	−11.7805			−0.388814
$919$	0.306618	+	0.943673i	0.0101144	+	0.0311289i	0.955986	−	0.293411i	$-0.0947905\pi$
$919$	0.306618	+	0.943673i	0.0101144	+	0.0311289i	−0.945872	+	0.324540i	$0.894790\pi$
$920$		0			0
$921$	−4.20684	+	12.9473i	−0.138620	+	0.426629i
$922$	10.5507	−	32.4717i	0.347469	−	1.06940i
$923$	14.3866	−	10.4525i	0.473541	−	0.344048i
$924$	9.60977			0.316138
$925$		0			0
$926$	−51.2477			−1.68410
$927$	20.3900	−	14.8142i	0.669697	−	0.486563i
$928$	−6.28900	+	19.3556i	−0.206447	+	0.635377i
$929$	10.2973	−	31.6918i	0.337843	−	1.03977i	−0.627461	−	0.778648i	$-0.715906\pi$
$929$	10.2973	−	31.6918i	0.337843	−	1.03977i	0.965305	−	0.261127i	$-0.0840940\pi$
$930$		0			0
$931$	0.618628	+	1.90394i	0.0202747	+	0.0623992i
$932$	75.0355			2.45787
$933$	−1.15003	−	3.53943i	−0.0376503	−	0.115876i
$934$	53.2475	+	38.6866i	1.74231	+	1.26586i
$935$		0			0
$936$	−9.85937	+	7.16325i	−0.322264	+	0.234138i
$937$	−10.8146	−	7.85724i	−0.353296	−	0.256685i	0.396954	−	0.917838i	$-0.370067\pi$
$937$	−10.8146	−	7.85724i	−0.353296	−	0.256685i	−0.750251	+	0.661154i	$0.770067\pi$
$938$	60.6309	+	44.0509i	1.97967	+	1.43831i
$939$	−8.22553	+	5.97620i	−0.268430	+	0.195026i
$940$		0			0
$941$	1.73924	+	1.26363i	0.0566976	+	0.0411932i	0.615773	−	0.787924i	$-0.288844\pi$
$941$	1.73924	+	1.26363i	0.0566976	+	0.0411932i	−0.559075	+	0.829117i	$0.688844\pi$
$942$	0.497860	+	1.53226i	0.0162212	+	0.0499236i
$943$	6.10671			0.198862
$944$	1.45311	+	4.47221i	0.0472947	+	0.145558i
$945$		0			0
$946$	−5.13004	+	15.7886i	−0.166792	+	0.513333i
$947$	10.7903	−	33.2093i	0.350639	−	1.07916i	−0.607856	−	0.794047i	$-0.707970\pi$
$947$	10.7903	−	33.2093i	0.350639	−	1.07916i	0.958495	−	0.285109i	$-0.0920299\pi$
$948$	10.9758	−	7.97436i	0.356476	−	0.258995i
$949$	−0.381966			−0.0123991
$950$		0			0
$951$	1.90903			0.0619046
$952$	−14.0614	+	10.2162i	−0.455732	+	0.331108i
$953$	−2.55830	+	7.87364i	−0.0828715	+	0.255052i	−0.983904	−	0.178700i	$-0.942811\pi$
$953$	−2.55830	+	7.87364i	−0.0828715	+	0.255052i	0.901032	+	0.433752i	$0.142811\pi$
$954$	18.8182	−	57.9164i	0.609261	−	1.87511i
$955$		0			0
$956$	−6.83151	−	21.0252i	−0.220947	−	0.680004i
$957$	3.76415			0.121678
$958$	17.8807	+	55.0313i	0.577701	+	1.77798i
$959$	−22.9326	−	16.6615i	−0.740532	−	0.538028i
$960$		0			0
$961$	−8.47296	+	6.15597i	−0.273321	+	0.198580i
$962$	10.1861	+	7.40066i	0.328414	+	0.238607i
$963$	12.6342	+	9.17926i	0.407130	+	0.295797i
$964$	−70.7120	+	51.3753i	−2.27748	+	1.65469i
$965$		0			0
$966$	8.96746	+	6.51524i	0.288523	+	0.209624i
$967$	9.11201	+	28.0439i	0.293023	+	0.901831i	0.983878	+	0.178838i	$0.0572339\pi$
$967$	9.11201	+	28.0439i	0.293023	+	0.901831i	−0.690856	+	0.722993i	$0.742766\pi$
$968$	−21.5438			−0.692443
$969$	0.246603	+	0.758967i	0.00792204	+	0.0243815i
$970$		0			0
$971$	6.75716	−	20.7964i	0.216848	−	0.667388i	−0.782170	−	0.623065i	$-0.785887\pi$
$971$	6.75716	−	20.7964i	0.216848	−	0.667388i	0.999017	−	0.0443227i	$-0.0141130\pi$
$972$	11.9067	−	36.6449i	0.381906	−	1.17539i
$973$	−43.9998	+	31.9678i	−1.41057	+	1.02484i
$974$	−3.38260			−0.108385
$975$		0			0
$976$	6.30517			0.201823
$977$	−11.2034	+	8.13976i	−0.358429	+	0.260414i	−0.752397	−	0.658710i	$-0.771102\pi$
$977$	−11.2034	+	8.13976i	−0.358429	+	0.260414i	0.393967	+	0.919124i	$0.371102\pi$
$978$	1.51136	−	4.65149i	0.0483279	−	0.148738i
$979$	−2.94676	+	9.06919i	−0.0941788	+	0.289853i
$980$		0			0
$981$	8.67045	+	26.6849i	0.276826	+	0.851983i
$982$	−46.3440			−1.47890
$983$	0.907082	+	2.79171i	0.0289314	+	0.0890418i	0.964480	−	0.264157i	$-0.0850938\pi$
$983$	0.907082	+	2.79171i	0.0289314	+	0.0890418i	−0.935548	+	0.353199i	$0.885094\pi$
$984$	2.16889	+	1.57579i	0.0691417	+	0.0502344i
$985$		0			0
$986$	−13.7732	+	10.0068i	−0.438629	+	0.318682i
$987$	5.59853	+	4.06757i	0.178203	+	0.129472i
$988$	3.47608	+	2.52552i	0.110589	+	0.0803474i
$989$	−9.68158	+	7.03408i	−0.307856	+	0.223671i
$990$		0			0
$991$	−25.5760	−	18.5821i	−0.812450	−	0.590279i	0.102090	−	0.994775i	$-0.467447\pi$
$991$	−25.5760	−	18.5821i	−0.812450	−	0.590279i	−0.914540	+	0.404496i	$0.867447\pi$
$992$	10.2196	+	31.4526i	0.324472	+	0.998623i
$993$	5.52970			0.175480
$994$	26.9927	+	83.0750i	0.856156	+	2.63498i
$995$		0			0
$996$	−6.17144	+	18.9937i	−0.195549	+	0.601839i
$997$	−3.73554	+	11.4968i	−0.118306	+	0.364108i	−0.992622	−	0.121249i	$-0.961310\pi$
$997$	−3.73554	+	11.4968i	−0.118306	+	0.364108i	0.874316	+	0.485356i	$0.161310\pi$
$998$	−1.16765	+	0.848347i	−0.0369613	+	0.0268540i
$999$	−10.4762			−0.331453

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.d.b.51.1		16
5.2	odd	4		25.2.e.a.14.1	yes	8
5.3	odd	4		125.2.e.b.74.2		8
5.4	even	2	inner	125.2.d.b.51.4		16
15.2	even	4		225.2.m.a.64.2		8
20.7	even	4		400.2.y.c.289.1		8
25.2	odd	20		625.2.e.i.499.1		8
25.3	odd	20		625.2.b.c.624.1		8
25.4	even	10		625.2.a.f.1.1		8
25.6	even	5		625.2.d.o.501.4		16
25.8	odd	20		625.2.e.i.124.1		8
25.9	even	10	inner	125.2.d.b.76.4		16
25.11	even	5		625.2.d.o.126.4		16
25.12	odd	20		125.2.e.b.49.2		8
25.13	odd	20		25.2.e.a.9.1	✓	8
25.14	even	10		625.2.d.o.126.1		16
25.16	even	5	inner	125.2.d.b.76.1		16
25.17	odd	20		625.2.e.a.124.2		8
25.19	even	10		625.2.d.o.501.1		16
25.21	even	5		625.2.a.f.1.8		8
25.22	odd	20		625.2.b.c.624.8		8
25.23	odd	20		625.2.e.a.499.2		8
75.29	odd	10		5625.2.a.x.1.8		8
75.38	even	20		225.2.m.a.109.2		8
75.71	odd	10		5625.2.a.x.1.1		8
100.63	even	20		400.2.y.c.209.1		8
100.71	odd	10		10000.2.a.bj.1.4		8
100.79	odd	10		10000.2.a.bj.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.e.a.9.1	✓	8	25.13	odd	20
25.2.e.a.14.1	yes	8	5.2	odd	4
125.2.d.b.51.1		16	1.1	even	1	trivial
125.2.d.b.51.4		16	5.4	even	2	inner
125.2.d.b.76.1		16	25.16	even	5	inner
125.2.d.b.76.4		16	25.9	even	10	inner
125.2.e.b.49.2		8	25.12	odd	20
125.2.e.b.74.2		8	5.3	odd	4
225.2.m.a.64.2		8	15.2	even	4
225.2.m.a.109.2		8	75.38	even	20
400.2.y.c.209.1		8	100.63	even	20
400.2.y.c.289.1		8	20.7	even	4
625.2.a.f.1.1		8	25.4	even	10
625.2.a.f.1.8		8	25.21	even	5
625.2.b.c.624.1		8	25.3	odd	20
625.2.b.c.624.8		8	25.22	odd	20
625.2.d.o.126.1		16	25.14	even	10
625.2.d.o.126.4		16	25.11	even	5
625.2.d.o.501.1		16	25.19	even	10
625.2.d.o.501.4		16	25.6	even	5
625.2.e.a.124.2		8	25.17	odd	20
625.2.e.a.499.2		8	25.23	odd	20
625.2.e.i.124.1		8	25.8	odd	20
625.2.e.i.499.1		8	25.2	odd	20
5625.2.a.x.1.1		8	75.71	odd	10
5625.2.a.x.1.8		8	75.29	odd	10
10000.2.a.bj.1.4		8	100.71	odd	10
10000.2.a.bj.1.5		8	100.79	odd	10

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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.86824 + 1.35736i) q^{2} +(0.146753 - 0.451659i) q^{3} +(1.02988 - 3.16963i) q^{4} +(0.338893 + 1.04301i) q^{6} +3.03582 q^{7} +(0.951057 + 2.92705i) q^{8} +(2.24459 + 1.63079i) q^{9} +O(q^{10})\)	\(q+(-1.86824 + 1.35736i) q^{2} +(0.146753 - 0.451659i) q^{3} +(1.02988 - 3.16963i) q^{4} +(0.338893 + 1.04301i) q^{6} +3.03582 q^{7} +(0.951057 + 2.92705i) q^{8} +(2.24459 + 1.63079i) q^{9} +(-1.61803 + 1.17557i) q^{11} +(-1.28046 - 0.930307i) q^{12} +(1.15464 + 0.838893i) q^{13} +(-5.67164 + 4.12069i) q^{14} +(-0.357358 - 0.259635i) q^{16} +(0.574848 + 1.76920i) q^{17} -6.40701 q^{18} +(0.279141 + 0.859107i) q^{19} +(0.445515 - 1.37116i) q^{21} +(1.42721 - 4.39250i) q^{22} +(2.69348 - 1.95693i) q^{23} +1.46160 q^{24} -3.29582 q^{26} +(2.21858 - 1.61189i) q^{27} +(3.12652 - 9.62243i) q^{28} +(1.22466 - 3.76910i) q^{29} +(-1.99006 - 6.12477i) q^{31} -5.13532 q^{32} +(0.293506 + 0.903319i) q^{33} +(-3.47539 - 2.52502i) q^{34} +(7.48066 - 5.43502i) q^{36} +(-3.09062 - 2.24547i) q^{37} +(-1.68762 - 1.22613i) q^{38} +(0.548341 - 0.398393i) q^{39} +(1.48391 + 1.07813i) q^{41} +(1.02882 + 3.16637i) q^{42} -3.59445 q^{43} +(2.05975 + 6.33927i) q^{44} +(-2.37582 + 7.31203i) q^{46} +(-1.48326 + 4.56502i) q^{47} +(-0.169710 + 0.123302i) q^{48} +2.21619 q^{49} +0.883436 q^{51} +(3.84812 - 2.79582i) q^{52} +(-2.93712 + 9.03953i) q^{53} +(-1.95693 + 6.02280i) q^{54} +(2.88723 + 8.88599i) q^{56} +0.428989 q^{57} +(2.82807 + 8.70390i) q^{58} +(-8.61248 - 6.25734i) q^{59} +(-11.5481 + 8.39016i) q^{61} +(12.0314 + 8.74134i) q^{62} +(6.81417 + 4.95078i) q^{63} +(10.3087 - 7.48973i) q^{64} +(-1.77447 - 1.28923i) q^{66} +(-3.30345 - 10.1670i) q^{67} +6.19974 q^{68} +(-0.488588 - 1.50372i) q^{69} +(3.85030 - 11.8500i) q^{71} +(-2.63868 + 8.12101i) q^{72} +(-0.216518 + 0.157310i) q^{73} +8.82193 q^{74} +3.01054 q^{76} +(-4.91206 + 3.56882i) q^{77} +(-0.483672 + 1.48859i) q^{78} +(-2.64882 + 8.15223i) q^{79} +(2.16963 + 6.67743i) q^{81} -4.23572 q^{82} +(-3.89923 - 12.0006i) q^{83} +(-3.88723 - 2.82424i) q^{84} +(6.71531 - 4.87896i) q^{86} +(-1.52263 - 1.10626i) q^{87} +(-4.97980 - 3.61803i) q^{88} +(3.85736 - 2.80253i) q^{89} +(3.50527 + 2.54673i) q^{91} +(-3.42879 - 10.5527i) q^{92} -3.05836 q^{93} +(-3.42527 - 10.5419i) q^{94} +(-0.753624 + 2.31942i) q^{96} +(-3.07721 + 9.47067i) q^{97} +(-4.14037 + 3.00816i) q^{98} -5.54893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} - 18 q^{6} - 2 q^{9}+O(q^{10}) \) 16 * q + 2 * q^4 - 18 * q^6 - 2 * q^9	\( 16 q + 2 q^{4} - 18 q^{6} - 2 q^{9} - 8 q^{11} - 26 q^{14} + 6 q^{16} + 10 q^{19} - 8 q^{21} + 40 q^{24} + 12 q^{26} + 10 q^{29} - 18 q^{31} - 26 q^{34} + 46 q^{36} + 6 q^{39} - 8 q^{41} + 4 q^{44} - 38 q^{46} - 28 q^{49} - 8 q^{51} + 10 q^{54} + 20 q^{56} - 18 q^{61} - 8 q^{64} + 24 q^{66} - 34 q^{69} + 12 q^{71} + 24 q^{74} - 40 q^{76} - 30 q^{79} + 56 q^{81} - 36 q^{84} - 18 q^{86} + 50 q^{89} + 12 q^{91} + 54 q^{94} + 32 q^{96} + 16 q^{99}+O(q^{100}) \) 16 * q + 2 * q^4 - 18 * q^6 - 2 * q^9 - 8 * q^11 - 26 * q^14 + 6 * q^16 + 10 * q^19 - 8 * q^21 + 40 * q^24 + 12 * q^26 + 10 * q^29 - 18 * q^31 - 26 * q^34 + 46 * q^36 + 6 * q^39 - 8 * q^41 + 4 * q^44 - 38 * q^46 - 28 * q^49 - 8 * q^51 + 10 * q^54 + 20 * q^56 - 18 * q^61 - 8 * q^64 + 24 * q^66 - 34 * q^69 + 12 * q^71 + 24 * q^74 - 40 * q^76 - 30 * q^79 + 56 * q^81 - 36 * q^84 - 18 * q^86 + 50 * q^89 + 12 * q^91 + 54 * q^94 + 32 * q^96 + 16 * q^99

Introduction

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