LMFDB - Embedded newform 125.2.d.b.76.4

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			76.4
Root			$-1.86824 + 0.357358i$ of defining polynomial
Character	$\chi$	$=$	125.76
Dual form			125.2.d.b.51.4

$q$-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 $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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	0.999919	+	0.0127610i	$0.00406207\pi$
$2$	1.86824	+	1.35736i	1.32105	+	0.959797i	0.321128	+	0.947036i	$0.395938\pi$
$3$	−0.146753	−	0.451659i	−0.0847279	−	0.260766i	0.899713	−	0.436482i	$-0.143776\pi$
$3$	−0.146753	−	0.451659i	−0.0847279	−	0.260766i	−0.984441	+	0.175716i	$0.943776\pi$
$4$	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	$-0.694498\pi$
$7$	−3.03582			−1.14743			−0.573716	+	0.819055i	$0.694498\pi$
$8$	−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	0.316503	−	0.948591i	$-0.397491\pi$
$11$	−1.61803	−	1.17557i	−0.487856	−	0.354448i	−0.804359	+	0.594144i	$0.797491\pi$
$12$	1.28046	−	0.930307i	0.369636	−	0.268556i
$13$	−1.15464	+	0.838893i	−0.320239	+	0.232667i	−0.736277	−	0.676680i	$-0.763418\pi$
$13$	−1.15464	+	0.838893i	−0.320239	+	0.232667i	0.416039	+	0.909347i	$0.363418\pi$
$14$	−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	$-0.972430\pi$
$17$	−0.574848	+	1.76920i	−0.139421	+	0.429094i	0.856830	+	0.515598i	$0.172430\pi$
$18$	6.40701			1.51015
$19$	0.279141	−	0.859107i	0.0640393	−	0.197093i	−0.913918	−	0.405900i	$-0.866958\pi$
$19$	0.279141	−	0.859107i	0.0640393	−	0.197093i	0.977957	+	0.208807i	$0.0669581\pi$
$20$		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	$-0.412836\pi$
$23$	−2.69348	−	1.95693i	−0.561629	−	0.408048i	−0.832055	+	0.554693i	$0.812836\pi$
$24$	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	0.998038	+	0.0626159i	$0.0199443\pi$
$29$	1.22466	+	3.76910i	0.227413	+	0.699905i	−0.770625	+	0.637289i	$0.780056\pi$
$30$		0			0
$31$	−1.99006	+	6.12477i	−0.357425	+	1.10004i	0.597165	+	0.802119i	$0.296294\pi$
$31$	−1.99006	+	6.12477i	−0.357425	+	1.10004i	−0.954590	+	0.297923i	$0.903706\pi$
$32$	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	$-0.598324\pi$
$37$	3.09062	−	2.24547i	0.508095	−	0.369153i	0.812100	+	0.583518i	$0.198324\pi$
$38$	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	−0.465851	−	0.884863i	$-0.654252\pi$
$41$	1.48391	−	1.07813i	0.231749	−	0.168375i	0.697599	+	0.716488i	$0.254252\pi$
$42$	−1.02882	+	3.16637i	−0.158750	+	0.488582i
$43$	3.59445			0.548149			0.274074	−	0.961708i	$-0.411629\pi$
$43$	3.59445			0.548149			0.274074	+	0.961708i	$0.411629\pi$
$44$	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	0.999055	+	0.0434750i	$0.0138429\pi$
$47$	1.48326	+	4.56502i	0.216356	+	0.665877i	−0.782698	+	0.622402i	$0.786157\pi$
$48$	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	0.922187	+	0.386745i	$0.126401\pi$
$53$	2.93712	+	9.03953i	0.403445	+	1.24168i	−0.518742	+	0.854931i	$0.673599\pi$
$54$	−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	−0.984398	−	0.175956i	$-0.943698\pi$
$59$	−8.61248	+	6.25734i	−1.12125	+	0.814636i	−0.136852	+	0.990592i	$0.543698\pi$
$60$		0			0
$61$	−11.5481	−	8.39016i	−1.47858	−	1.07425i	−0.978012	−	0.208551i	$-0.933125\pi$
$61$	−11.5481	−	8.39016i	−1.47858	−	1.07425i	−0.500566	−	0.865698i	$-0.666875\pi$
$62$	−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	−0.518494	−	0.855081i	$-0.673507\pi$
$67$	3.30345	−	10.1670i	0.403580	−	1.24209i	0.922075	−	0.387012i	$-0.126493\pi$
$68$	−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	0.868834	+	0.495104i	$0.164870\pi$
$71$	3.85030	+	11.8500i	0.456947	+	1.40634i	−0.411887	+	0.911235i	$0.635130\pi$
$72$	2.63868	+	8.12101i	0.310971	+	0.957070i
$73$	0.216518	+	0.157310i	0.0253415	+	0.0184117i	0.600384	−	0.799712i	$-0.295014\pi$
$73$	0.216518	+	0.157310i	0.0253415	+	0.0184117i	−0.575042	+	0.818124i	$0.695014\pi$
$74$	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	−0.982192	−	0.187881i	$-0.939838\pi$
$79$	−2.64882	−	8.15223i	−0.298015	−	0.917197i	0.684176	−	0.729316i	$-0.260162\pi$
$80$		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	−0.472100	−	0.881545i	$-0.656504\pi$
$83$	3.89923	−	12.0006i	0.427996	−	1.31724i	0.900096	−	0.435691i	$-0.143496\pi$
$84$	−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	0.773148	−	0.634226i	$-0.218681\pi$
$89$	3.85736	+	2.80253i	0.408879	+	0.297068i	−0.364269	+	0.931294i	$0.618681\pi$
$90$		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	0.976794	+	0.214180i	$0.0687079\pi$
$97$	3.07721	+	9.47067i	0.312443	+	0.961600i	−0.664351	+	0.747420i	$0.731292\pi$
$98$	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	−0.988793	−	0.149294i	$-0.952300\pi$
$103$	−2.80713	−	8.63947i	−0.276595	−	0.851272i	0.712198	−	0.701979i	$-0.247700\pi$
$104$	−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	$-0.587710\pi$
$107$	−5.62871			−0.544148			−0.272074	+	0.962276i	$0.587710\pi$
$108$	2.82424	−	8.69212i	0.271763	−	0.836400i
$109$	8.18158	−	5.94427i	0.783654	−	0.569358i	−0.122420	−	0.992478i	$-0.539065\pi$
$109$	8.18158	−	5.94427i	0.783654	−	0.569358i	0.906073	+	0.423121i	$0.139065\pi$
$110$		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	$-0.531916\pi$
$113$	8.66620	−	6.29636i	0.815247	−	0.592312i	0.915347	+	0.402666i	$0.131916\pi$
$114$	−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	$-0.468161\pi$
$127$	−9.19118	−	6.67779i	−0.815586	−	0.592558i	−0.915445	+	0.402444i	$0.868161\pi$
$128$	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	−0.783446	−	0.621459i	$-0.786540\pi$
$131$	2.46834	−	7.59677i	0.215660	−	0.663732i	0.999106	−	0.0422730i	$-0.0134599\pi$
$132$	−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	$-0.569403\pi$
$137$	7.55401	−	5.48831i	0.645382	−	0.468898i	0.861695	+	0.507426i	$0.169403\pi$
$138$	−2.95389	+	2.14612i	−0.251452	+	0.182690i
$139$	−14.4936	−	10.5302i	−1.22933	−	0.893160i	−0.232489	−	0.972599i	$-0.574687\pi$
$139$	−14.4936	−	10.5302i	−1.22933	−	0.893160i	−0.996840	+	0.0794393i	$0.974687\pi$
$140$		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	$-0.518671\pi$
$157$	−1.46908			−0.117245			−0.0586225	+	0.998280i	$0.518671\pi$
$158$	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	$-0.644119\pi$
$163$	3.60797	−	2.62134i	0.282598	−	0.205319i	0.720050	+	0.693922i	$0.244119\pi$
$164$	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	0.745370	+	0.666651i	$0.232273\pi$
$167$	−3.22418	+	9.92300i	−0.249494	+	0.767865i	−0.994865	+	0.101214i	$0.967727\pi$
$168$	−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	$-0.394256\pi$
$173$	−6.21017	−	4.51195i	−0.472151	−	0.343037i	−0.798279	+	0.602288i	$0.794256\pi$
$174$	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	0.954017	+	0.299752i	$0.0969040\pi$
$179$	4.79494	+	14.7573i	0.358391	+	1.10301i	−0.595626	+	0.803262i	$0.703096\pi$
$180$		0			0
$181$	−0.491509	+	1.51271i	−0.0365336	+	0.112439i	−0.967660	−	0.252257i	$-0.918827\pi$
$181$	−0.491509	+	1.51271i	−0.0365336	+	0.112439i	0.931127	+	0.364696i	$0.118827\pi$
$182$	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	−0.988661	−	0.150164i	$-0.952020\pi$
$191$	−15.9121	+	11.5608i	−1.15136	+	0.836511i	−0.162698	+	0.986676i	$0.552020\pi$
$192$	1.86997	−	5.75518i	0.134954	−	0.415344i
$193$	−13.1100			−0.943680			−0.471840	−	0.881684i	$-0.656410\pi$
$193$	−13.1100			−0.943680			−0.471840	+	0.881684i	$0.656410\pi$
$194$	−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	$-0.0610145\pi$
$197$	1.05977	+	3.26164i	0.0755055	+	0.232382i	−0.906180	+	0.422893i	$0.861015\pi$
$198$	−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	0.674438	−	0.738331i	$-0.264386\pi$
$211$	2.62418	+	1.90658i	0.180656	+	0.131254i	−0.493782	+	0.869586i	$0.664386\pi$
$212$	−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	0.939469	+	0.342633i	$0.111319\pi$
$223$	23.2307	+	16.8781i	1.55564	+	1.13024i	0.616175	+	0.787609i	$0.288681\pi$
$224$	−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	$-0.172833\pi$
$227$	9.48219	+	6.88921i	0.629355	+	0.457253i	−0.226822	+	0.973936i	$0.572833\pi$
$228$	−0.441805	−	1.35974i	−0.0292593	−	0.0900508i
$229$	−5.06828	−	15.5985i	−0.334921	−	1.03078i	−0.966761	−	0.255682i	$-0.917700\pi$
$229$	−5.06828	−	15.5985i	−0.334921	−	1.03078i	0.631840	−	0.775099i	$-0.282300\pi$
$230$		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	0.414407	+	0.910092i	$0.363989\pi$
$233$	−6.95739	+	21.4126i	−0.455794	+	1.40279i	−0.870201	+	0.492697i	$0.836011\pi$
$234$	−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	0.747663	−	0.664078i	$-0.231176\pi$
$239$	5.36647	+	3.89897i	0.347128	+	0.252204i	−0.400535	+	0.916281i	$0.631176\pi$
$240$		0			0
$241$	−21.2173	+	15.4153i	−1.36673	+	0.992986i	−0.368743	+	0.929531i	$0.620212\pi$
$241$	−21.2173	+	15.4153i	−1.36673	+	0.992986i	−0.997985	+	0.0634545i	$0.979788\pi$
$242$	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	$-0.565798\pi$
$257$	−6.58051			−0.410481			−0.205240	+	0.978712i	$0.565798\pi$
$258$	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	−0.353382	+	0.935479i	$0.614968\pi$
$263$	−21.9302	+	15.9332i	−1.35228	+	0.982486i	−0.998895	+	0.0470069i	$0.985032\pi$
$264$	−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	−0.941096	−	0.338138i	$-0.890203\pi$
$269$	0.311938	−	0.960046i	0.0190192	−	0.0585350i	0.960116	+	0.279603i	$0.0902029\pi$
$270$		0			0
$271$	1.93198	+	5.94603i	0.117360	+	0.361196i	0.992432	−	0.122796i	$-0.0391862\pi$
$271$	1.93198	+	5.94603i	0.117360	+	0.361196i	−0.875072	+	0.483992i	$0.839186\pi$
$272$	−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	$-0.565718\pi$
$277$	−19.9587	−	14.5009i	−1.19920	−	0.871272i	−0.994206	+	0.107491i	$0.965718\pi$
$278$	−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	−0.932675	−	0.360717i	$-0.882532\pi$
$281$	0.568255	−	1.74891i	0.0338993	−	0.104331i	0.966574	+	0.256386i	$0.0825319\pi$
$282$	5.26401			0.313467
$283$	2.67026	−	8.21823i	0.158731	−	0.488523i	−0.839789	−	0.542913i	$-0.817321\pi$
$283$	2.67026	−	8.21823i	0.158731	−	0.488523i	0.998520	+	0.0543898i	$0.0173214\pi$
$284$	−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	$-0.558833\pi$
$293$	−6.29156			−0.367557			−0.183779	+	0.982968i	$0.558833\pi$
$294$	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	$-0.195066\pi$
$307$	28.6661			1.63606			0.818030	+	0.575175i	$0.195066\pi$
$308$	−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	0.752844	−	0.658199i	$-0.228682\pi$
$311$	6.33985	+	4.60617i	0.359500	+	0.261192i	−0.393343	+	0.919392i	$0.628682\pi$
$312$	−1.68762	+	1.22613i	−0.0955426	+	0.0694158i
$313$	17.3205	−	12.5840i	0.979010	−	0.711292i	0.0215228	−	0.999768i	$-0.493149\pi$
$313$	17.3205	−	12.5840i	0.979010	−	0.711292i	0.957487	+	0.288476i	$0.0931486\pi$
$314$	−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	$-0.936010\pi$
$317$	−1.24220	+	3.82309i	−0.0697688	+	0.214726i	0.910093	+	0.414405i	$0.136010\pi$
$318$	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	−0.802161	−	0.597108i	$-0.796316\pi$
$331$	3.59815	−	11.0740i	0.197772	−	0.608681i	0.999933	−	0.0115724i	$-0.00368369\pi$
$332$	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	$-0.899509\pi$
$337$	−17.4220	+	12.6578i	−0.949037	+	0.689516i	0.00154181	+	0.999999i	$0.499509\pi$
$338$	−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	−0.993069	−	0.117529i	$-0.962503\pi$
$347$	−4.81981	−	14.8339i	−0.258741	−	0.796323i	0.734328	−	0.678794i	$-0.237497\pi$
$348$	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	$-0.168483\pi$
$353$	−2.47898	−	7.62953i	−0.131943	−	0.406079i	−0.995102	+	0.0988533i	$0.968483\pi$
$354$	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	−0.292226	−	0.956349i	$-0.594396\pi$
$359$	9.98547	−	7.25487i	0.527013	−	0.382897i	0.819239	+	0.573452i	$0.194396\pi$
$360$		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	0.461100	+	0.887348i	$0.347455\pi$
$367$	−8.30481	+	25.5596i	−0.433508	+	1.33420i	−0.894608	+	0.446852i	$0.852545\pi$
$368$	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	$-0.553821\pi$
$373$	−22.3604	−	16.2457i	−1.15778	−	0.841173i	−0.989495	+	0.144566i	$0.953821\pi$
$374$	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	0.919685	−	0.392656i	$-0.128444\pi$
$379$	−1.07372	−	3.30456i	−0.0551532	−	0.169744i	−0.974839	+	0.222912i	$0.928444\pi$
$380$		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	0.463723	+	0.885980i	$0.346513\pi$
$383$	−8.45837	+	26.0322i	−0.432203	+	1.33018i	−0.895926	+	0.444203i	$0.853487\pi$
$384$	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	0.341731	−	0.939798i	$-0.388987\pi$
$389$	−8.80576	−	6.39776i	−0.446470	−	0.324379i	−0.788200	+	0.615419i	$0.788987\pi$
$390$		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	−0.994485	−	0.104881i	$-0.966554\pi$
$397$	−5.01264	−	15.4273i	−0.251577	−	0.774275i	0.742908	−	0.669394i	$-0.233446\pi$
$398$	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	−0.624286	−	0.781196i	$-0.714610\pi$
$409$	−1.50142	+	1.09084i	−0.0742403	+	0.0539388i	0.550046	+	0.835134i	$0.314610\pi$
$410$		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	−0.782445	−	0.622720i	$-0.786028\pi$
$419$	4.43353	−	13.6450i	0.216592	−	0.666602i	0.999037	−	0.0438818i	$-0.0139725\pi$
$420$		0			0
$421$	4.77571	+	14.6981i	0.232754	+	0.716343i	0.997411	+	0.0719060i	$0.0229082\pi$
$421$	4.77571	+	14.6981i	0.232754	+	0.716343i	−0.764658	+	0.644437i	$0.777092\pi$
$422$	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	−0.813842	−	0.581087i	$-0.802628\pi$
$431$	3.86404	−	11.8923i	0.186124	−	0.572832i	0.999966	+	0.00825486i	$0.00262763\pi$
$432$	1.21133			0.0582801
$433$	6.95138	−	21.3941i	0.334062	−	1.02814i	−0.633120	−	0.774053i	$-0.718226\pi$
$433$	6.95138	−	21.3941i	0.334062	−	1.02814i	0.967182	−	0.254084i	$-0.0817738\pi$
$434$	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	0.327317	−	0.944915i	$-0.393855\pi$
$439$	−9.85186	−	7.15780i	−0.470204	−	0.341623i	−0.797521	+	0.603292i	$0.793855\pi$
$440$		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	$-0.336272\pi$
$443$	20.7101			0.983968			0.491984	+	0.870604i	$0.336272\pi$
$444$	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	$-0.436282\pi$
$457$	8.50150			0.397684			0.198842	+	0.980032i	$0.436282\pi$
$458$	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	0.273299	−	0.961929i	$-0.411885\pi$
$461$	−11.9614	−	8.69044i	−0.557097	−	0.404754i	−0.830395	+	0.557175i	$0.811885\pi$
$462$	5.38696	−	3.91385i	0.250624	−	0.182089i
$463$	−17.9538	+	13.0442i	−0.834384	+	0.606215i	−0.920796	−	0.390044i	$-0.872460\pi$
$463$	−17.9538	+	13.0442i	−0.834384	+	0.606215i	0.0864125	+	0.996259i	$0.472460\pi$
$464$	−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	−0.511182	−	0.859473i	$-0.670792\pi$
$467$	8.80741	−	27.1064i	0.407558	−	1.25434i	0.918740	−	0.394863i	$-0.129208\pi$
$468$	−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	0.956709	+	0.291045i	$0.0940030\pi$
$479$	7.74301	+	23.8305i	0.353787	+	1.08885i	−0.602922	+	0.797800i	$0.705997\pi$
$480$		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	$-0.710566\pi$
$487$	−1.18504	+	0.860980i	−0.0536992	+	0.0390147i	0.560612	+	0.828079i	$0.310566\pi$
$488$	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	−0.157706	−	0.987486i	$-0.550410\pi$
$491$	16.2359	−	11.7961i	0.732715	−	0.532348i	0.890421	+	0.455138i	$0.150410\pi$
$492$	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	0.991463	+	0.130391i	$0.0416233\pi$
$503$	5.96563	+	18.3603i	0.265994	+	0.818647i	−0.725468	+	0.688256i	$0.758377\pi$
$504$	−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	−0.382965	−	0.923763i	$-0.625097\pi$
$509$	8.51099	−	6.18360i	0.377243	−	0.274083i	0.760208	+	0.649680i	$0.225097\pi$
$510$		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	0.860187	−	0.509979i	$-0.170347\pi$
$521$	−3.09232	−	9.51719i	−0.135477	−	0.416956i	−0.995664	+	0.0930234i	$0.970347\pi$
$522$	7.84638	+	24.1487i	0.343427	+	1.05696i
$523$	18.4319	+	13.3915i	0.805970	+	0.585571i	0.912659	−	0.408721i	$-0.134025\pi$
$523$	18.4319	+	13.3915i	0.805970	+	0.585571i	−0.106690	+	0.994292i	$0.534025\pi$
$524$	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	−0.643019	−	0.765850i	$-0.722318\pi$
$541$	−2.63658	+	1.91559i	−0.113356	+	0.0823576i	0.529663	+	0.848208i	$0.322318\pi$
$542$	−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	$-0.00617949\pi$
$547$	4.19901	+	12.9232i	0.179537	+	0.552557i	−0.820275	+	0.571970i	$0.806179\pi$
$548$	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	$-0.300870\pi$
$557$	27.6399			1.17114			0.585571	+	0.810621i	$0.300870\pi$
$558$	−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	$-0.711132\pi$
$563$	−1.34236	+	0.975284i	−0.0565738	+	0.0411033i	0.559139	+	0.829074i	$0.311132\pi$
$564$	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	−0.765880	−	0.642983i	$-0.777697\pi$
$569$	5.52609	−	17.0076i	0.231666	−	0.712994i	0.997546	−	0.0700110i	$-0.0223034\pi$
$570$		0			0
$571$	−11.3942	−	35.0677i	−0.476832	−	1.46754i	−0.843472	−	0.537174i	$-0.819492\pi$
$571$	−11.3942	−	35.0677i	−0.476832	−	1.46754i	0.366640	−	0.930363i	$-0.380508\pi$
$572$	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	$-0.457506\pi$
$577$	−18.4567	−	13.4095i	−0.768361	−	0.558247i	−0.901463	+	0.432855i	$0.857506\pi$
$578$	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	$-0.773471\pi$
$587$	−8.96834	+	6.51588i	−0.370163	+	0.268939i	0.387116	+	0.922031i	$0.373471\pi$
$588$	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	$-0.573405\pi$
$593$	−11.1321			−0.457139			−0.228570	+	0.973528i	$0.573405\pi$
$594$	−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	$-0.261982\pi$
$607$	33.5066			1.35999			0.679996	+	0.733216i	$0.261982\pi$
$608$	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	$-0.891524\pi$
$613$	−22.6758	+	16.4750i	−0.915869	+	0.665418i	0.0266235	+	0.999646i	$0.491524\pi$
$614$	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	0.560528	+	0.828135i	$0.310598\pi$
$617$	−9.43191	+	29.0284i	−0.379714	+	1.16864i	−0.940243	+	0.340505i	$0.889402\pi$
$618$	−9.96234			−0.400744
$619$	−6.70477	+	20.6352i	−0.269488	+	0.829398i	0.721138	+	0.692792i	$0.243619\pi$
$619$	−6.70477	+	20.6352i	−0.269488	+	0.829398i	−0.990625	+	0.136606i	$0.956381\pi$
$620$		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	0.800262	+	0.599651i	$0.204694\pi$
$631$	−5.01463	+	15.4335i	−0.199629	+	0.614396i	−0.999891	+	0.0147456i	$0.995306\pi$
$632$	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	−0.174079	−	0.984732i	$-0.555695\pi$
$641$	17.9419	−	13.0356i	0.708663	−	0.514874i	0.882742	+	0.469858i	$0.155695\pi$
$642$	−1.90753	+	5.87078i	−0.0752843	+	0.231701i
$643$	13.2767			0.523583			0.261792	−	0.965124i	$-0.415687\pi$
$643$	13.2767			0.523583			0.261792	+	0.965124i	$0.415687\pi$
$644$	−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	$-0.0287953\pi$
$647$	3.48735	+	10.7329i	0.137102	+	0.421956i	−0.858809	+	0.512295i	$0.828795\pi$
$648$	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	0.895038	+	0.445989i	$0.147148\pi$
$653$	11.0669	+	34.0606i	0.433083	+	1.33289i	−0.461955	+	0.886903i	$0.652852\pi$
$654$	−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	−0.998403	−	0.0564876i	$-0.982010\pi$
$659$	−32.1710	+	23.3736i	−1.25320	+	0.910506i	−0.254801	+	0.966994i	$0.582010\pi$
$660$		0			0
$661$	5.05420	+	3.67209i	0.196586	+	0.142828i	0.681724	−	0.731610i	$-0.261231\pi$
$661$	5.05420	+	3.67209i	0.196586	+	0.142828i	−0.485138	+	0.874438i	$0.661231\pi$
$662$	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	$-0.594709\pi$
$673$	−33.5441	−	24.3712i	−1.29303	−	0.939440i	−0.999862	+	0.0166215i	$0.994709\pi$
$674$	−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	$-0.308804\pi$
$677$	−1.16430	−	0.845914i	−0.0447477	−	0.0325111i	−0.609934	+	0.792452i	$0.708804\pi$
$678$	−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	$-0.848090\pi$
$683$	2.62239	−	8.07088i	0.100343	−	0.308824i	0.988609	+	0.150505i	$0.0480900\pi$
$684$	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	0.348248	−	0.937402i	$-0.386777\pi$
$691$	35.4186	−	25.7331i	1.34739	−	0.978933i	0.999137	−	0.0415304i	$-0.0132233\pi$
$692$	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	−0.365644	−	0.930755i	$-0.619151\pi$
$709$	10.8256	−	7.86529i	0.406566	−	0.295387i	0.772210	+	0.635367i	$0.219151\pi$
$710$		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	−0.308154	−	0.951336i	$-0.599711\pi$
$719$	13.4159	−	41.2900i	0.500329	−	1.53986i	0.808483	−	0.588519i	$-0.200289\pi$
$720$		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	$-0.502570\pi$
$727$	−25.9274	−	18.8373i	−0.961593	−	0.698639i	−0.953520	+	0.301329i	$0.902570\pi$
$728$	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	$-0.948029\pi$
$733$	−2.51517	+	7.74091i	−0.0929001	+	0.285917i	0.893801	+	0.448465i	$0.148029\pi$
$734$	−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	0.688766	−	0.724984i	$-0.258153\pi$
$739$	5.76598	+	4.18923i	0.212105	+	0.154103i	−0.476661	+	0.879087i	$0.658153\pi$
$740$		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	$-0.631612\pi$
$743$	−21.9040			−0.803578			−0.401789	+	0.915732i	$0.631612\pi$
$744$	−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	$-0.811450\pi$
$757$	−45.6524			−1.65926			−0.829632	+	0.558311i	$0.811450\pi$
$758$	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	−0.179264	−	0.983801i	$-0.557372\pi$
$761$	−32.2844	−	23.4560i	−1.17031	−	0.850280i	−0.991046	+	0.133521i	$0.957372\pi$
$762$	−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	0.324198	+	0.945989i	$0.394906\pi$
$769$	−13.7024	+	42.1717i	−0.494122	+	1.52075i	−0.818320	+	0.574762i	$0.805094\pi$
$770$		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	$-0.543391\pi$
$773$	−31.1426	−	22.6264i	−1.12012	−	0.813816i	−0.984228	+	0.176907i	$0.943391\pi$
$774$	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	−0.572231	+	0.820093i	$0.693922\pi$
$787$	−42.8942	+	31.1645i	−1.52901	+	1.11089i	−0.956784	+	0.290801i	$0.906078\pi$
$788$	−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	$-0.0279190\pi$
$797$	3.91737	+	12.0564i	0.138760	+	0.427060i	−0.857396	+	0.514658i	$0.827919\pi$
$798$	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	0.198167	−	0.980168i	$-0.436501\pi$
$809$	33.8926	−	24.6244i	1.19160	−	0.865747i	0.993432	+	0.114421i	$0.0365013\pi$
$810$		0			0
$811$	27.9504	+	20.3072i	0.981472	+	0.713081i	0.958037	−	0.286644i	$-0.0925398\pi$
$811$	27.9504	+	20.3072i	0.981472	+	0.713081i	0.0234348	+	0.999725i	$0.492540\pi$
$812$	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	−0.997980	−	0.0635220i	$-0.979767\pi$
$821$	−6.53103	−	20.1004i	−0.227935	−	0.701511i	0.770046	−	0.637989i	$-0.220233\pi$
$822$	−3.16433	−	9.73882i	−0.110369	−	0.339680i
$823$	2.57036	+	1.86747i	0.0895970	+	0.0650960i	0.631682	−	0.775228i	$-0.282365\pi$
$823$	2.57036	+	1.86747i	0.0895970	+	0.0650960i	−0.542085	+	0.840324i	$0.682365\pi$
$824$	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	$-0.245807\pi$
$827$	7.88372	+	5.72786i	0.274144	+	0.199177i	−0.442215	+	0.896909i	$0.645807\pi$
$828$	−9.51307	−	29.2782i	−0.330602	−	1.01749i
$829$	7.24188	+	22.2882i	0.251521	+	0.774101i	0.994495	+	0.104782i	$0.0334144\pi$
$829$	7.24188	+	22.2882i	0.251521	+	0.774101i	−0.742974	+	0.669320i	$0.766586\pi$
$830$		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	−0.198634	−	0.980074i	$-0.563650\pi$
$839$	−34.5304	−	25.0878i	−1.19212	−	0.866126i	−0.993487	+	0.113948i	$0.963650\pi$
$840$		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	$-0.193777\pi$
$853$	−5.24124	−	16.1309i	−0.179456	−	0.552310i	−0.999809	+	0.0195480i	$0.993777\pi$
$854$	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	$-0.265637\pi$
$857$	39.3176			1.34306			0.671531	+	0.740976i	$0.265637\pi$
$858$	0.967343	−	2.97718i	0.0330246	−	0.101639i
$859$	−0.572020	+	0.415597i	−0.0195171	+	0.0141800i	−0.597501	−	0.801868i	$-0.703840\pi$
$859$	−0.572020	+	0.415597i	−0.0195171	+	0.0141800i	0.577984	+	0.816048i	$0.303840\pi$
$860$		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	$-0.695073\pi$
$863$	0.735728	−	0.534537i	0.0250445	−	0.0181959i	0.600237	+	0.799822i	$0.295073\pi$
$864$	−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	$-0.107589\pi$
$877$	27.2326	+	19.7856i	0.919578	+	0.668113i	−0.0238407	+	0.999716i	$0.507589\pi$
$878$	−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	0.792128	+	0.610355i	$0.208973\pi$
$881$	−6.15819	+	18.9529i	−0.207475	+	0.638541i	−0.999603	+	0.0281862i	$0.991027\pi$
$882$	14.1991			0.478109
$883$	−4.82317	+	14.8442i	−0.162313	+	0.499547i	−0.998828	−	0.0483963i	$-0.984589\pi$
$883$	−4.82317	+	14.8442i	−0.162313	+	0.499547i	0.836516	+	0.547943i	$0.184589\pi$
$884$	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	$-0.411468\pi$
$887$	37.9403	−	27.5652i	1.27391	−	0.925550i	0.999351	+	0.0360196i	$0.0114679\pi$
$888$	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	$-0.507581\pi$
$907$	−1.43447			−0.0476308			−0.0238154	+	0.999716i	$0.507581\pi$
$908$	−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	0.624824	−	0.780765i	$-0.285171\pi$
$911$	2.27438	+	1.65244i	0.0753537	+	0.0547476i	−0.549471	+	0.835513i	$0.685171\pi$
$912$	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	−0.945872	−	0.324540i	$-0.894790\pi$
$919$	0.306618	−	0.943673i	0.0101144	−	0.0311289i	0.955986	+	0.293411i	$0.0947905\pi$
$920$		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	0.965305	+	0.261127i	$0.0840940\pi$
$929$	10.2973	+	31.6918i	0.337843	+	1.03977i	−0.627461	+	0.778648i	$0.715906\pi$
$930$		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	$-0.629933\pi$
$937$	10.8146	−	7.85724i	0.353296	−	0.256685i	0.750251	+	0.661154i	$0.229933\pi$
$938$	−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	−0.559075	−	0.829117i	$-0.688844\pi$
$941$	1.73924	−	1.26363i	0.0566976	−	0.0411932i	0.615773	+	0.787924i	$0.288844\pi$
$942$	−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	−0.958495	−	0.285109i	$-0.907970\pi$
$947$	−10.7903	−	33.2093i	−0.350639	−	1.07916i	0.607856	−	0.794047i	$-0.292030\pi$
$948$	−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	$-0.0571892\pi$
$953$	2.55830	+	7.87364i	0.0828715	+	0.255052i	−0.901032	+	0.433752i	$0.857189\pi$
$954$	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	0.690856	+	0.722993i	$0.257234\pi$
$967$	−9.11201	+	28.0439i	−0.293023	+	0.901831i	−0.983878	+	0.178838i	$0.942766\pi$
$968$	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	0.999017	+	0.0443227i	$0.0141130\pi$
$971$	6.75716	+	20.7964i	0.216848	+	0.667388i	−0.782170	+	0.623065i	$0.785887\pi$
$972$	−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	$-0.228898\pi$
$977$	11.2034	+	8.13976i	0.358429	+	0.260414i	−0.393967	+	0.919124i	$0.628898\pi$
$978$	−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	$-0.914906\pi$
$983$	−0.907082	+	2.79171i	−0.0289314	+	0.0890418i	0.935548	+	0.353199i	$0.114906\pi$
$984$	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	−0.914540	−	0.404496i	$-0.867447\pi$
$991$	−25.5760	+	18.5821i	−0.812450	+	0.590279i	0.102090	+	0.994775i	$0.467447\pi$
$992$	−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	$-0.0386899\pi$
$997$	3.73554	+	11.4968i	0.118306	+	0.364108i	−0.874316	+	0.485356i	$0.838690\pi$
$998$	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.76.4		16
5.2	odd	4		25.2.e.a.9.1	✓	8
5.3	odd	4		125.2.e.b.49.2		8
5.4	even	2	inner	125.2.d.b.76.1		16
15.2	even	4		225.2.m.a.109.2		8
20.7	even	4		400.2.y.c.209.1		8
25.2	odd	20		125.2.e.b.74.2		8
25.3	odd	20		625.2.e.i.499.1		8
25.4	even	10		625.2.d.o.126.4		16
25.6	even	5		625.2.a.f.1.1		8
25.8	odd	20		625.2.b.c.624.8		8
25.9	even	10		625.2.d.o.501.4		16
25.11	even	5	inner	125.2.d.b.51.4		16
25.12	odd	20		625.2.e.i.124.1		8
25.13	odd	20		625.2.e.a.124.2		8
25.14	even	10	inner	125.2.d.b.51.1		16
25.16	even	5		625.2.d.o.501.1		16
25.17	odd	20		625.2.b.c.624.1		8
25.19	even	10		625.2.a.f.1.8		8
25.21	even	5		625.2.d.o.126.1		16
25.22	odd	20		625.2.e.a.499.2		8
25.23	odd	20		25.2.e.a.14.1	yes	8
75.23	even	20		225.2.m.a.64.2		8
75.44	odd	10		5625.2.a.x.1.1		8
75.56	odd	10		5625.2.a.x.1.8		8
100.19	odd	10		10000.2.a.bj.1.4		8
100.23	even	20		400.2.y.c.289.1		8
100.31	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	5.2	odd	4
25.2.e.a.14.1	yes	8	25.23	odd	20
125.2.d.b.51.1		16	25.14	even	10	inner
125.2.d.b.51.4		16	25.11	even	5	inner
125.2.d.b.76.1		16	5.4	even	2	inner
125.2.d.b.76.4		16	1.1	even	1	trivial
125.2.e.b.49.2		8	5.3	odd	4
125.2.e.b.74.2		8	25.2	odd	20
225.2.m.a.64.2		8	75.23	even	20
225.2.m.a.109.2		8	15.2	even	4
400.2.y.c.209.1		8	20.7	even	4
400.2.y.c.289.1		8	100.23	even	20
625.2.a.f.1.1		8	25.6	even	5
625.2.a.f.1.8		8	25.19	even	10
625.2.b.c.624.1		8	25.17	odd	20
625.2.b.c.624.8		8	25.8	odd	20
625.2.d.o.126.1		16	25.21	even	5
625.2.d.o.126.4		16	25.4	even	10
625.2.d.o.501.1		16	25.16	even	5
625.2.d.o.501.4		16	25.9	even	10
625.2.e.a.124.2		8	25.13	odd	20
625.2.e.a.499.2		8	25.22	odd	20
625.2.e.i.124.1		8	25.12	odd	20
625.2.e.i.499.1		8	25.3	odd	20
5625.2.a.x.1.1		8	75.44	odd	10
5625.2.a.x.1.8		8	75.56	odd	10
10000.2.a.bj.1.4		8	100.19	odd	10
10000.2.a.bj.1.5		8	100.31	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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