LMFDB - Embedded newform 625.2.e.d.249.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [625,2,Mod(124,625)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("625.124"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(625, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.e (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-6,0,6,0,0,-14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 125)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			249.1
Root			$-0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	625.249
Dual form			625.2.e.d.374.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.951057 + 1.30902i) q^{2} +(-0.363271 + 0.118034i) q^{3} +(-0.190983 - 0.587785i) q^{4} +(0.190983 - 0.587785i) q^{6} -3.00000i q^{7} +(-2.12663 - 0.690983i) q^{8} +(-2.30902 + 1.67760i) q^{9} +(2.42705 + 1.76336i) q^{11} +(0.138757 + 0.190983i) q^{12} +(-2.85317 - 3.92705i) q^{13} +(3.92705 + 2.85317i) q^{14} +(3.92705 - 2.85317i) q^{16} +(4.02874 + 1.30902i) q^{17} -4.61803i q^{18} +(1.11803 - 3.44095i) q^{19} +(0.354102 + 1.08981i) q^{21} +(-4.61653 + 1.50000i) q^{22} +(0.726543 - 1.00000i) q^{23} +0.854102 q^{24} +7.85410 q^{26} +(1.31433 - 1.80902i) q^{27} +(-1.76336 + 0.572949i) q^{28} +(-2.07295 - 6.37988i) q^{29} +(1.57295 - 4.84104i) q^{31} +3.38197i q^{32} +(-1.08981 - 0.354102i) q^{33} +(-5.54508 + 4.02874i) q^{34} +(1.42705 + 1.03681i) q^{36} +(-2.17963 - 3.00000i) q^{37} +(3.44095 + 4.73607i) q^{38} +(1.50000 + 1.08981i) q^{39} +(2.42705 - 1.76336i) q^{41} +(-1.76336 - 0.572949i) q^{42} +9.00000i q^{43} +(0.572949 - 1.76336i) q^{44} +(0.618034 + 1.90211i) q^{46} +(7.91872 - 2.57295i) q^{47} +(-1.08981 + 1.50000i) q^{48} -2.00000 q^{49} -1.61803 q^{51} +(-1.76336 + 2.42705i) q^{52} +(4.39201 - 1.42705i) q^{53} +(1.11803 + 3.44095i) q^{54} +(-2.07295 + 6.37988i) q^{56} +1.38197i q^{57} +(10.3229 + 3.35410i) q^{58} +(3.35410 - 2.43690i) q^{59} +(4.92705 + 3.57971i) q^{61} +(4.84104 + 6.66312i) q^{62} +(5.03280 + 6.92705i) q^{63} +(3.42705 + 2.48990i) q^{64} +(1.50000 - 1.08981i) q^{66} +(-13.1760 - 4.28115i) q^{67} -2.61803i q^{68} +(-0.145898 + 0.449028i) q^{69} +(-0.927051 - 2.85317i) q^{71} +(6.06961 - 1.97214i) q^{72} +(-1.08981 + 1.50000i) q^{73} +6.00000 q^{74} -2.23607 q^{76} +(5.29007 - 7.28115i) q^{77} +(-2.85317 + 0.927051i) q^{78} +(-0.163119 - 0.502029i) q^{79} +(2.38197 - 7.33094i) q^{81} +4.85410i q^{82} +(-0.449028 - 0.145898i) q^{83} +(0.572949 - 0.416272i) q^{84} +(-11.7812 - 8.55951i) q^{86} +(1.50609 + 2.07295i) q^{87} +(-3.94298 - 5.42705i) q^{88} +(-10.8541 - 7.88597i) q^{89} +(-11.7812 + 8.55951i) q^{91} +(-0.726543 - 0.236068i) q^{92} +1.94427i q^{93} +(-4.16312 + 12.8128i) q^{94} +(-0.399187 - 1.22857i) q^{96} +(-7.46969 + 2.42705i) q^{97} +(1.90211 - 2.61803i) q^{98} -8.56231 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{4} + 6 q^{6} - 14 q^{9} + 6 q^{11} + 18 q^{14} + 18 q^{16} - 24 q^{21} - 20 q^{24} + 36 q^{26} - 30 q^{29} + 26 q^{31} - 22 q^{34} - 2 q^{36} + 12 q^{39} + 6 q^{41} + 18 q^{44} - 4 q^{46} - 16 q^{49}+ \cdots + 12 q^{99}+O(q^{100}) $ 8 * q - 6 * q^4 + 6 * q^6 - 14 * q^9 + 6 * q^11 + 18 * q^14 + 18 * q^16 - 24 * q^21 - 20 * q^24 + 36 * q^26 - 30 * q^29 + 26 * q^31 - 22 * q^34 - 2 * q^36 + 12 * q^39 + 6 * q^41 + 18 * q^44 - 4 * q^46 - 16 * q^49 - 4 * q^51 - 30 * q^56 + 26 * q^61 + 14 * q^64 + 12 * q^66 - 28 * q^69 + 6 * q^71 + 48 * q^74 + 30 * q^79 + 28 * q^81 + 18 * q^84 - 54 * q^86 - 60 * q^89 - 54 * q^91 - 2 * q^94 + 46 * q^96 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$	−0.951057	+	1.30902i	−0.672499	+	0.925615i	−0.999814	−	0.0193004i	$-0.993856\pi$
$2$	−0.951057	+	1.30902i	−0.672499	+	0.925615i	0.327315	+	0.944915i	$0.393856\pi$
$3$	−0.363271	+	0.118034i	−0.209735	+	0.0681470i	−0.412000	−	0.911184i	$-0.635170\pi$
$3$	−0.363271	+	0.118034i	−0.209735	+	0.0681470i	0.202265	+	0.979331i	$0.435170\pi$
$4$	−0.190983	−	0.587785i	−0.0954915	−	0.293893i
$5$		0			0
$5$		0			0
$6$	0.190983	−	0.587785i	0.0779685	−	0.239962i
$7$		−	3.00000i		−	1.13389i	−0.823754	−	0.566947i	$-0.808125\pi$
$7$		−	3.00000i		−	1.13389i	0.823754	−	0.566947i	$-0.191875\pi$
$8$	−2.12663	−	0.690983i	−0.751876	−	0.244299i
$9$	−2.30902	+	1.67760i	−0.769672	+	0.559200i
$10$		0			0
$11$	2.42705	+	1.76336i	0.731783	+	0.531672i	0.890127	−	0.455712i	$-0.150615\pi$
$11$	2.42705	+	1.76336i	0.731783	+	0.531672i	−0.158344	+	0.987384i	$0.550615\pi$
$12$	0.138757	+	0.190983i	0.0400558	+	0.0551320i
$13$	−2.85317	−	3.92705i	−0.791327	−	1.08917i	−0.993942	−	0.109909i	$-0.964944\pi$
$13$	−2.85317	−	3.92705i	−0.791327	−	1.08917i	0.202615	−	0.979259i	$-0.435056\pi$
$14$	3.92705	+	2.85317i	1.04955	+	0.762542i
$15$		0			0
$16$	3.92705	−	2.85317i	0.981763	−	0.713292i
$17$	4.02874	+	1.30902i	0.977113	+	0.317483i	0.753684	−	0.657237i	$-0.228275\pi$
$17$	4.02874	+	1.30902i	0.977113	+	0.317483i	0.223429	+	0.974720i	$0.428275\pi$
$18$		−	4.61803i		−	1.08848i
$19$	1.11803	−	3.44095i	0.256495	−	0.789409i	−0.737037	−	0.675852i	$-0.763776\pi$
$19$	1.11803	−	3.44095i	0.256495	−	0.789409i	0.993532	−	0.113557i	$-0.0362244\pi$
$20$		0			0
$21$	0.354102	+	1.08981i	0.0772714	+	0.237817i
$22$	−4.61653	+	1.50000i	−0.984247	+	0.319801i
$23$	0.726543	−	1.00000i	0.151495	−	0.208514i	−0.726524	−	0.687141i	$-0.758865\pi$
$23$	0.726543	−	1.00000i	0.151495	−	0.208514i	0.878018	+	0.478627i	$0.158865\pi$
$24$	0.854102			0.174343
$25$		0			0
$26$	7.85410			1.54032
$27$	1.31433	−	1.80902i	0.252942	−	0.348145i
$28$	−1.76336	+	0.572949i	−0.333243	+	0.108277i
$29$	−2.07295	−	6.37988i	−0.384937	−	1.18471i	−0.936526	−	0.350598i	$-0.885978\pi$
$29$	−2.07295	−	6.37988i	−0.384937	−	1.18471i	0.551589	−	0.834116i	$-0.314022\pi$
$30$		0			0
$31$	1.57295	−	4.84104i	0.282510	−	0.869476i	−0.704624	−	0.709581i	$-0.748884\pi$
$31$	1.57295	−	4.84104i	0.282510	−	0.869476i	0.987134	−	0.159895i	$-0.0511157\pi$
$32$			3.38197i			0.597853i
$33$	−1.08981	−	0.354102i	−0.189712	−	0.0616412i
$34$	−5.54508	+	4.02874i	−0.950974	+	0.690923i
$35$		0			0
$36$	1.42705	+	1.03681i	0.237842	+	0.172802i
$37$	−2.17963	−	3.00000i	−0.358329	−	0.493197i	0.591354	−	0.806412i	$-0.298594\pi$
$37$	−2.17963	−	3.00000i	−0.358329	−	0.493197i	−0.949682	+	0.313215i	$0.898594\pi$
$38$	3.44095	+	4.73607i	0.558197	+	0.768292i
$39$	1.50000	+	1.08981i	0.240192	+	0.174510i
$40$		0			0
$41$	2.42705	−	1.76336i	0.379042	−	0.275390i	−0.381909	−	0.924200i	$-0.624733\pi$
$41$	2.42705	−	1.76336i	0.379042	−	0.275390i	0.760950	+	0.648810i	$0.224733\pi$
$42$	−1.76336	−	0.572949i	−0.272092	−	0.0884080i
$43$			9.00000i			1.37249i	0.727372	+	0.686244i	$0.240742\pi$
$43$			9.00000i			1.37249i	−0.727372	+	0.686244i	$0.759258\pi$
$44$	0.572949	−	1.76336i	0.0863753	−	0.265836i
$45$		0			0
$46$	0.618034	+	1.90211i	0.0911241	+	0.280451i
$47$	7.91872	−	2.57295i	1.15506	−	0.375303i	0.332016	−	0.943274i	$-0.392271\pi$
$47$	7.91872	−	2.57295i	1.15506	−	0.375303i	0.823049	+	0.567971i	$0.192271\pi$
$48$	−1.08981	+	1.50000i	−0.157301	+	0.216506i
$49$	−2.00000			−0.285714
$50$		0			0
$51$	−1.61803			−0.226570
$52$	−1.76336	+	2.42705i	−0.244533	+	0.336571i
$53$	4.39201	−	1.42705i	0.603289	−	0.196021i	0.00858231	−	0.999963i	$-0.497268\pi$
$53$	4.39201	−	1.42705i	0.603289	−	0.196021i	0.594707	+	0.803943i	$0.297268\pi$
$54$	1.11803	+	3.44095i	0.152145	+	0.468255i
$55$		0			0
$56$	−2.07295	+	6.37988i	−0.277009	+	0.852547i
$57$			1.38197i			0.183046i
$58$	10.3229	+	3.35410i	1.35546	+	0.440415i
$59$	3.35410	−	2.43690i	0.436667	−	0.317257i	−0.347642	−	0.937627i	$-0.613018\pi$
$59$	3.35410	−	2.43690i	0.436667	−	0.317257i	0.784309	+	0.620370i	$0.213018\pi$
$60$		0			0
$61$	4.92705	+	3.57971i	0.630844	+	0.458335i	0.856693	−	0.515827i	$-0.172515\pi$
$61$	4.92705	+	3.57971i	0.630844	+	0.458335i	−0.225848	+	0.974162i	$0.572515\pi$
$62$	4.84104	+	6.66312i	0.614813	+	0.846217i
$63$	5.03280	+	6.92705i	0.634073	+	0.872726i
$64$	3.42705	+	2.48990i	0.428381	+	0.311237i
$65$		0			0
$66$	1.50000	−	1.08981i	0.184637	−	0.134147i
$67$	−13.1760	−	4.28115i	−1.60971	−	0.523026i	−0.640226	−	0.768186i	$-0.721159\pi$
$67$	−13.1760	−	4.28115i	−1.60971	−	0.523026i	−0.969483	+	0.245160i	$0.921159\pi$
$68$		−	2.61803i		−	0.317483i
$69$	−0.145898	+	0.449028i	−0.0175641	+	0.0540566i
$70$		0			0
$71$	−0.927051	−	2.85317i	−0.110021	−	0.338609i	0.880855	−	0.473386i	$-0.156968\pi$
$71$	−0.927051	−	2.85317i	−0.110021	−	0.338609i	−0.990876	+	0.134777i	$0.956968\pi$
$72$	6.06961	−	1.97214i	0.715310	−	0.232418i
$73$	−1.08981	+	1.50000i	−0.127553	+	0.175562i	−0.868017	−	0.496534i	$-0.834606\pi$
$73$	−1.08981	+	1.50000i	−0.127553	+	0.175562i	0.740464	+	0.672096i	$0.234606\pi$
$74$	6.00000			0.697486
$75$		0			0
$76$	−2.23607			−0.256495
$77$	5.29007	−	7.28115i	0.602859	−	0.829764i
$78$	−2.85317	+	0.927051i	−0.323058	+	0.104968i
$79$	−0.163119	−	0.502029i	−0.0183523	−	0.0564826i	0.941461	−	0.337122i	$-0.109453\pi$
$79$	−0.163119	−	0.502029i	−0.0183523	−	0.0564826i	−0.959813	+	0.280639i	$0.909453\pi$
$80$		0			0
$81$	2.38197	−	7.33094i	0.264663	−	0.814549i
$82$			4.85410i			0.536046i
$83$	−0.449028	−	0.145898i	−0.0492872	−	0.0160144i	0.284270	−	0.958744i	$-0.408249\pi$
$83$	−0.449028	−	0.145898i	−0.0492872	−	0.0160144i	−0.333557	+	0.942730i	$0.608249\pi$
$84$	0.572949	−	0.416272i	0.0625139	−	0.0454190i
$85$		0			0
$86$	−11.7812	−	8.55951i	−1.27039	−	0.922996i
$87$	1.50609	+	2.07295i	0.161469	+	0.222243i
$88$	−3.94298	−	5.42705i	−0.420323	−	0.578526i
$89$	−10.8541	−	7.88597i	−1.15053	−	0.835911i	−0.161981	−	0.986794i	$-0.551788\pi$
$89$	−10.8541	−	7.88597i	−1.15053	−	0.835911i	−0.988552	+	0.150883i	$0.951788\pi$
$90$		0			0
$91$	−11.7812	+	8.55951i	−1.23500	+	0.897280i
$92$	−0.726543	−	0.236068i	−0.0757473	−	0.0246118i
$93$			1.94427i			0.201612i
$94$	−4.16312	+	12.8128i	−0.429393	+	1.32154i
$95$		0			0
$96$	−0.399187	−	1.22857i	−0.0407418	−	0.125391i
$97$	−7.46969	+	2.42705i	−0.758433	+	0.246430i	−0.662606	−	0.748968i	$-0.730549\pi$
$97$	−7.46969	+	2.42705i	−0.758433	+	0.246430i	−0.0958268	+	0.995398i	$0.530549\pi$
$98$	1.90211	−	2.61803i	0.192142	−	0.264461i
$99$	−8.56231			−0.860544
$100$		0			0
$101$	−3.00000			−0.298511			−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000			−0.298511			−0.149256	+	0.988799i	$0.547688\pi$
$102$	1.53884	−	2.11803i	0.152368	−	0.209717i
$103$	12.0862	−	3.92705i	1.19089	−	0.386944i	0.354489	−	0.935060i	$-0.384655\pi$
$103$	12.0862	−	3.92705i	1.19089	−	0.386944i	0.836402	+	0.548116i	$0.184655\pi$
$104$	3.35410	+	10.3229i	0.328897	+	1.01224i
$105$		0			0
$106$	−2.30902	+	7.10642i	−0.224272	+	0.690237i
$107$			0.0901699i			0.00871706i	0.999991	+	0.00435853i	$0.00138737\pi$
$107$			0.0901699i			0.00871706i	−0.999991	+	0.00435853i	$0.998613\pi$
$108$	−1.31433	−	0.427051i	−0.126471	−	0.0410930i
$109$	4.30902	−	3.13068i	0.412729	−	0.299865i	−0.361977	−	0.932187i	$-0.617898\pi$
$109$	4.30902	−	3.13068i	0.412729	−	0.299865i	0.774706	+	0.632322i	$0.217898\pi$
$110$		0			0
$111$	1.14590	+	0.832544i	0.108764	+	0.0790215i
$112$	−8.55951	−	11.7812i	−0.808798	−	1.11321i
$113$	1.20833	+	1.66312i	0.113670	+	0.156453i	0.862061	−	0.506804i	$-0.169173\pi$
$113$	1.20833	+	1.66312i	0.113670	+	0.156453i	−0.748391	+	0.663258i	$0.769173\pi$
$114$	−1.80902	−	1.31433i	−0.169430	−	0.123098i
$115$		0			0
$116$	−3.35410	+	2.43690i	−0.311421	+	0.226260i
$117$	13.1760	+	4.28115i	1.21812	+	0.395793i
$118$			6.70820i			0.617540i
$119$	3.92705	−	12.0862i	0.359992	−	1.10794i
$120$		0			0
$121$	−0.618034	−	1.90211i	−0.0561849	−	0.172919i
$122$	−9.37181	+	3.04508i	−0.848484	+	0.275689i
$123$	−0.673542	+	0.927051i	−0.0607312	+	0.0835894i
$124$	−3.14590			−0.282510
$125$		0			0
$126$	−13.8541			−1.23422
$127$	−5.70634	+	7.85410i	−0.506356	+	0.696939i	−0.983299	−	0.181995i	$-0.941745\pi$
$127$	−5.70634	+	7.85410i	−0.506356	+	0.696939i	0.476944	+	0.878934i	$0.341745\pi$
$128$	−12.9515	+	4.20820i	−1.14476	+	0.371956i
$129$	−1.06231	−	3.26944i	−0.0935308	−	0.287858i
$130$		0			0
$131$	−3.79180	+	11.6699i	−0.331291	+	1.01961i	0.637230	+	0.770674i	$0.280080\pi$
$131$	−3.79180	+	11.6699i	−0.331291	+	1.01961i	−0.968520	+	0.248934i	$0.919920\pi$
$132$			0.708204i			0.0616412i
$133$	−10.3229	−	3.35410i	−0.895106	−	0.290838i
$134$	18.1353	−	13.1760i	1.56665	−	1.13824i
$135$		0			0
$136$	−7.66312	−	5.56758i	−0.657107	−	0.477416i
$137$	−3.30220	−	4.54508i	−0.282126	−	0.388313i	0.644311	−	0.764764i	$-0.277144\pi$
$137$	−3.30220	−	4.54508i	−0.282126	−	0.388313i	−0.926437	+	0.376451i	$0.877144\pi$
$138$	−0.449028	−	0.618034i	−0.0382238	−	0.0526105i
$139$	−9.89919	−	7.19218i	−0.839638	−	0.610033i	0.0826315	−	0.996580i	$-0.473668\pi$
$139$	−9.89919	−	7.19218i	−0.839638	−	0.610033i	−0.922270	+	0.386547i	$0.873668\pi$
$140$		0			0
$141$	−2.57295	+	1.86936i	−0.216681	+	0.157428i
$142$	4.61653	+	1.50000i	0.387410	+	0.125877i
$143$		−	14.5623i		−	1.21776i
$144$	−4.28115	+	13.1760i	−0.356763	+	1.09800i
$145$		0			0
$146$	−0.927051	−	2.85317i	−0.0767233	−	0.236130i
$147$	0.726543	−	0.236068i	0.0599242	−	0.0194706i
$148$	−1.34708	+	1.85410i	−0.110730	+	0.152406i
$149$	15.0000			1.22885			0.614424	−	0.788976i	$-0.289388\pi$
$149$	15.0000			1.22885			0.614424	+	0.788976i	$0.289388\pi$
$150$		0			0
$151$	−21.0902			−1.71629			−0.858147	−	0.513404i	$-0.828384\pi$
$151$	−21.0902			−1.71629			−0.858147	+	0.513404i	$0.828384\pi$
$152$	−4.75528	+	6.54508i	−0.385704	+	0.530876i
$153$	−11.4984	+	3.73607i	−0.929593	+	0.302043i
$154$	4.50000	+	13.8496i	0.362620	+	1.11603i
$155$		0			0
$156$	0.354102	−	1.08981i	0.0283508	−	0.0872549i
$157$		−	12.2705i		−	0.979293i	−0.871921	−	0.489647i	$-0.837126\pi$
$157$		−	12.2705i		−	0.979293i	0.871921	−	0.489647i	$-0.162874\pi$
$158$	0.812299	+	0.263932i	0.0646231	+	0.0209973i
$159$	−1.42705	+	1.03681i	−0.113173	+	0.0822246i
$160$		0			0
$161$	−3.00000	−	2.17963i	−0.236433	−	0.171779i
$162$	7.33094	+	10.0902i	0.575973	+	0.792759i
$163$	−11.6699	−	16.0623i	−0.914061	−	1.25810i	−0.965761	−	0.259434i	$-0.916464\pi$
$163$	−11.6699	−	16.0623i	−0.914061	−	1.25810i	0.0516999	−	0.998663i	$-0.483536\pi$
$164$	−1.50000	−	1.08981i	−0.117130	−	0.0851002i
$165$		0			0
$166$	0.618034	−	0.449028i	0.0479687	−	0.0348513i
$167$	8.78402	+	2.85410i	0.679728	+	0.220857i	0.628476	−	0.777829i	$-0.283679\pi$
$167$	8.78402	+	2.85410i	0.679728	+	0.220857i	0.0512518	+	0.998686i	$0.483679\pi$
$168$		−	2.56231i		−	0.197686i
$169$	−3.26393	+	10.0453i	−0.251072	+	0.772719i
$170$		0			0
$171$	3.19098	+	9.82084i	0.244021	+	0.751018i
$172$	5.29007	−	1.71885i	0.403364	−	0.131061i
$173$	0.0327561	−	0.0450850i	0.00249040	−	0.00342775i	−0.807770	−	0.589498i	$-0.799326\pi$
$173$	0.0327561	−	0.0450850i	0.00249040	−	0.00342775i	0.810260	+	0.586070i	$0.199326\pi$
$174$	−4.14590			−0.314300
$175$		0			0
$176$	14.5623			1.09768
$177$	−0.930812	+	1.28115i	−0.0699641	+	0.0962974i
$178$	20.6457	−	6.70820i	1.54746	−	0.502801i
$179$	−2.07295	−	6.37988i	−0.154939	−	0.476855i	0.843215	−	0.537576i	$-0.180660\pi$
$179$	−2.07295	−	6.37988i	−0.154939	−	0.476855i	−0.998155	+	0.0607213i	$0.980660\pi$
$180$		0			0
$181$	5.61803	−	17.2905i	0.417585	−	1.28520i	−0.492333	−	0.870407i	$-0.663856\pi$
$181$	5.61803	−	17.2905i	0.417585	−	1.28520i	0.909918	−	0.414788i	$-0.136144\pi$
$182$		−	23.5623i		−	1.74655i
$183$	−2.21238	−	0.718847i	−0.163544	−	0.0531387i
$184$	−2.23607	+	1.62460i	−0.164845	+	0.119767i
$185$		0			0
$186$	−2.54508	−	1.84911i	−0.186615	−	0.135584i
$187$	7.46969	+	10.2812i	0.546238	+	0.751832i
$188$	−3.02468	−	4.16312i	−0.220598	−	0.303627i
$189$	−5.42705	−	3.94298i	−0.394760	−	0.286810i
$190$		0			0
$191$	−9.70820	+	7.05342i	−0.702461	+	0.510368i	−0.880733	−	0.473614i	$-0.842949\pi$
$191$	−9.70820	+	7.05342i	−0.702461	+	0.510368i	0.178272	+	0.983981i	$0.442949\pi$
$192$	−1.53884	−	0.500000i	−0.111056	−	0.0360844i
$193$		−	15.2705i		−	1.09920i	−0.835429	−	0.549598i	$-0.814781\pi$
$193$		−	15.2705i		−	1.09920i	0.835429	−	0.549598i	$-0.185219\pi$
$194$	3.92705	−	12.0862i	0.281946	−	0.867740i
$195$		0			0
$196$	0.381966	+	1.17557i	0.0272833	+	0.0839693i
$197$	3.85723	−	1.25329i	0.274816	−	0.0892931i	−0.168367	−	0.985724i	$-0.553849\pi$
$197$	3.85723	−	1.25329i	0.274816	−	0.0892931i	0.443183	+	0.896431i	$0.353849\pi$
$198$	8.14324	−	11.2082i	0.578715	−	0.796532i
$199$	−16.1803			−1.14699			−0.573497	−	0.819208i	$-0.694414\pi$
$199$	−16.1803			−1.14699			−0.573497	+	0.819208i	$0.694414\pi$
$200$		0			0
$201$	5.29180			0.373255
$202$	2.85317	−	3.92705i	0.200748	−	0.276306i
$203$	−19.1396	+	6.21885i	−1.34334	+	0.436477i
$204$	0.309017	+	0.951057i	0.0216355	+	0.0665873i
$205$		0			0
$206$	−6.35410	+	19.5559i	−0.442711	+	1.36253i
$207$			3.52786i			0.245204i
$208$	−22.4091	−	7.28115i	−1.55379	−	0.504857i
$209$	8.78115	−	6.37988i	0.607405	−	0.441306i
$210$		0			0
$211$	3.38197	+	2.45714i	0.232824	+	0.169157i	0.698080	−	0.716019i	$-0.254038\pi$
$211$	3.38197	+	2.45714i	0.232824	+	0.169157i	−0.465256	+	0.885176i	$0.654038\pi$
$212$	−1.67760	−	2.30902i	−0.115218	−	0.158584i
$213$	0.673542	+	0.927051i	0.0461503	+	0.0635205i
$214$	−0.118034	−	0.0857567i	−0.00806864	−	0.00586221i
$215$		0			0
$216$	−4.04508	+	2.93893i	−0.275233	+	0.199969i
$217$	−14.5231	−	4.71885i	−0.985893	−	0.320336i
$218$			8.61803i			0.583687i
$219$	0.218847	−	0.673542i	0.0147883	−	0.0455137i
$220$		0			0
$221$	−6.35410	−	19.5559i	−0.427423	−	1.31547i
$222$	−2.17963	+	0.708204i	−0.146287	+	0.0475315i
$223$	−1.08981	+	1.50000i	−0.0729793	+	0.100447i	−0.843946	−	0.536428i	$-0.819773\pi$
$223$	−1.08981	+	1.50000i	−0.0729793	+	0.100447i	0.770967	+	0.636875i	$0.219773\pi$
$224$	10.1459			0.677901
$225$		0			0
$226$	−3.32624			−0.221258
$227$	−3.88998	+	5.35410i	−0.258187	+	0.355364i	−0.918358	−	0.395752i	$-0.870484\pi$
$227$	−3.88998	+	5.35410i	−0.258187	+	0.355364i	0.660170	+	0.751116i	$0.270484\pi$
$228$	0.812299	−	0.263932i	0.0537958	−	0.0174793i
$229$	0.427051	+	1.31433i	0.0282203	+	0.0868532i	0.964175	−	0.265268i	$-0.0854605\pi$
$229$	0.427051	+	1.31433i	0.0282203	+	0.0868532i	−0.935954	+	0.352121i	$0.885460\pi$
$230$		0			0
$231$	−1.06231	+	3.26944i	−0.0698946	+	0.215113i
$232$			15.0000i			0.984798i
$233$	25.5725	+	8.30902i	1.67531	+	0.544342i	0.983993	−	0.178208i	$-0.0570300\pi$
$233$	25.5725	+	8.30902i	1.67531	+	0.544342i	0.691319	+	0.722550i	$0.257030\pi$
$234$	−18.1353	+	13.1760i	−1.18554	+	0.861344i
$235$		0			0
$236$	−2.07295	−	1.50609i	−0.134937	−	0.0980378i
$237$	0.118513	+	0.163119i	0.00769824	+	0.0105957i
$238$	12.0862	+	16.6353i	0.783433	+	1.07830i
$239$	20.9164	+	15.1967i	1.35297	+	0.982990i	0.998858	+	0.0477873i	$0.0152170\pi$
$239$	20.9164	+	15.1967i	1.35297	+	0.982990i	0.354112	+	0.935203i	$0.384783\pi$
$240$		0			0
$241$	15.5172	−	11.2739i	0.999552	−	0.726217i	0.0375600	−	0.999294i	$-0.488041\pi$
$241$	15.5172	−	11.2739i	0.999552	−	0.726217i	0.961992	+	0.273077i	$0.0880415\pi$
$242$	3.07768	+	1.00000i	0.197841	+	0.0642824i
$243$			9.65248i			0.619207i
$244$	1.16312	−	3.57971i	0.0744611	−	0.229168i
$245$		0			0
$246$	−0.572949	−	1.76336i	−0.0365299	−	0.112427i
$247$	−16.7027	+	5.42705i	−1.06277	+	0.345315i
$248$	−6.69015	+	9.20820i	−0.424825	+	0.584722i
$249$	0.180340			0.0114286
$250$		0			0
$251$	6.27051			0.395791			0.197896	−	0.980223i	$-0.436589\pi$
$251$	6.27051			0.395791			0.197896	+	0.980223i	$0.436589\pi$
$252$	3.11044	−	4.28115i	0.195939	−	0.269687i
$253$	3.52671	−	1.14590i	0.221722	−	0.0720420i
$254$	−4.85410	−	14.9394i	−0.304573	−	0.937381i
$255$		0			0
$256$	4.19098	−	12.8985i	0.261936	−	0.806157i
$257$			29.3607i			1.83147i	0.401784	+	0.915734i	$0.368390\pi$
$257$			29.3607i			1.83147i	−0.401784	+	0.915734i	$0.631610\pi$
$258$	5.29007	+	1.71885i	0.329345	+	0.107011i
$259$	−9.00000	+	6.53888i	−0.559233	+	0.406306i
$260$		0			0
$261$	15.4894	+	11.2537i	0.958767	+	0.696585i
$262$	−11.6699	−	16.0623i	−0.720972	−	0.992333i
$263$	9.59632	+	13.2082i	0.591735	+	0.814453i	0.994920	−	0.100665i	$-0.0320972\pi$
$263$	9.59632	+	13.2082i	0.591735	+	0.814453i	−0.403186	+	0.915118i	$0.632097\pi$
$264$	2.07295	+	1.50609i	0.127581	+	0.0926932i
$265$		0			0
$266$	14.2082	−	10.3229i	0.871161	−	0.632935i
$267$	4.87380	+	1.58359i	0.298271	+	0.0969143i
$268$			8.56231i			0.523026i
$269$	−0.791796	+	2.43690i	−0.0482767	+	0.148580i	−0.972289	−	0.233783i	$-0.924890\pi$
$269$	−0.791796	+	2.43690i	−0.0482767	+	0.148580i	0.924012	+	0.382363i	$0.124890\pi$
$270$		0			0
$271$	6.20820	+	19.1069i	0.377122	+	1.16066i	0.942036	+	0.335511i	$0.108909\pi$
$271$	6.20820	+	19.1069i	0.377122	+	1.16066i	−0.564915	+	0.825149i	$0.691091\pi$
$272$	19.5559	−	6.35410i	1.18575	−	0.385274i
$273$	3.26944	−	4.50000i	0.197876	−	0.272352i
$274$	9.09017			0.549157
$275$		0			0
$276$	0.291796			0.0175641
$277$	3.11044	−	4.28115i	0.186888	−	0.257230i	−0.705284	−	0.708925i	$-0.749181\pi$
$277$	3.11044	−	4.28115i	0.186888	−	0.257230i	0.892172	+	0.451695i	$0.149181\pi$
$278$	18.8294	−	6.11803i	1.12931	−	0.366935i
$279$	4.48936	+	13.8168i	0.268771	+	0.827191i
$280$		0			0
$281$	3.70820	−	11.4127i	0.221213	−	0.680823i	−0.777441	−	0.628956i	$-0.783483\pi$
$281$	3.70820	−	11.4127i	0.221213	−	0.680823i	0.998654	−	0.0518675i	$-0.0165174\pi$
$282$		−	5.14590i		−	0.306434i
$283$	14.9394	+	4.85410i	0.888055	+	0.288546i	0.717298	−	0.696767i	$-0.245379\pi$
$283$	14.9394	+	4.85410i	0.888055	+	0.288546i	0.170757	+	0.985313i	$0.445379\pi$
$284$	−1.50000	+	1.08981i	−0.0890086	+	0.0646686i
$285$		0			0
$286$	19.0623	+	13.8496i	1.12718	+	0.818943i
$287$	−5.29007	−	7.28115i	−0.312263	−	0.429793i
$288$	−5.67358	−	7.80902i	−0.334319	−	0.460151i
$289$	0.763932	+	0.555029i	0.0449372	+	0.0326488i
$290$		0			0
$291$	2.42705	−	1.76336i	0.142276	−	0.103370i
$292$	1.08981	+	0.354102i	0.0637765	+	0.0207223i
$293$			21.3607i			1.24790i	0.781463	+	0.623952i	$0.214474\pi$
$293$			21.3607i			1.24790i	−0.781463	+	0.623952i	$0.785526\pi$
$294$	−0.381966	+	1.17557i	−0.0222767	+	0.0685607i
$295$		0			0
$296$	2.56231	+	7.88597i	0.148931	+	0.458363i
$297$	6.37988	−	2.07295i	0.370198	−	0.120285i
$298$	−14.2658	+	19.6353i	−0.826398	+	1.13744i
$299$	−6.00000			−0.346989
$300$		0			0
$301$	27.0000			1.55625
$302$	20.0579	−	27.6074i	1.15420	−	1.58863i
$303$	1.08981	−	0.354102i	0.0626082	−	0.0203426i
$304$	−5.42705	−	16.7027i	−0.311263	−	0.957968i
$305$		0			0
$306$	6.04508	−	18.6049i	0.345575	−	1.06357i
$307$			6.27051i			0.357877i	0.983860	+	0.178938i	$0.0572663\pi$
$307$			6.27051i			0.357877i	−0.983860	+	0.178938i	$0.942734\pi$
$308$	−5.29007	−	1.71885i	−0.301430	−	0.0979404i
$309$	−3.92705	+	2.85317i	−0.223402	+	0.162311i
$310$		0			0
$311$	−17.2082	−	12.5025i	−0.975788	−	0.708951i	−0.0190245	−	0.999819i	$-0.506056\pi$
$311$	−17.2082	−	12.5025i	−0.975788	−	0.708951i	−0.956763	+	0.290868i	$0.906056\pi$
$312$	−2.43690	−	3.35410i	−0.137962	−	0.189889i
$313$	11.4127	+	15.7082i	0.645083	+	0.887880i	0.998874	−	0.0474443i	$-0.0151076\pi$
$313$	11.4127	+	15.7082i	0.645083	+	0.887880i	−0.353791	+	0.935324i	$0.615108\pi$
$314$	16.0623	+	11.6699i	0.906448	+	0.658573i
$315$		0			0
$316$	−0.263932	+	0.191758i	−0.0148473	+	0.0107872i
$317$	−25.6255	−	8.32624i	−1.43927	−	0.467648i	−0.517602	−	0.855621i	$-0.673175\pi$
$317$	−25.6255	−	8.32624i	−1.43927	−	0.467648i	−0.921671	+	0.387973i	$0.873175\pi$
$318$		−	2.85410i		−	0.160050i
$319$	6.21885	−	19.1396i	0.348189	−	1.07161i
$320$		0			0
$321$	−0.0106431	−	0.0327561i	−0.000594041	−	0.00182827i
$322$	5.70634	−	1.85410i	0.318002	−	0.103325i
$323$	9.00854	−	12.3992i	0.501248	−	0.689909i
$324$	−4.76393			−0.264663
$325$		0			0
$326$	32.1246			1.77922
$327$	−1.19581	+	1.64590i	−0.0661287	+	0.0910184i
$328$	−6.37988	+	2.07295i	−0.352270	+	0.114459i
$329$	−7.71885	−	23.7562i	−0.425554	−	1.30972i
$330$		0			0
$331$	−6.51722	+	20.0579i	−0.358219	+	1.10248i	0.595901	+	0.803058i	$0.296795\pi$
$331$	−6.51722	+	20.0579i	−0.358219	+	1.10248i	−0.954119	+	0.299426i	$0.903205\pi$
$332$			0.291796i			0.0160144i
$333$	10.0656	+	3.27051i	0.551591	+	0.179223i
$334$	−12.0902	+	8.78402i	−0.661545	+	0.480640i
$335$		0			0
$336$	4.50000	+	3.26944i	0.245495	+	0.178363i
$337$	17.5353	+	24.1353i	0.955208	+	1.31473i	0.949175	+	0.314749i	$0.101920\pi$
$337$	17.5353	+	24.1353i	0.955208	+	1.31473i	0.00603323	+	0.999982i	$0.498080\pi$
$338$	−10.0453	−	13.8262i	−0.546395	−	0.752048i
$339$	−0.635255	−	0.461540i	−0.0345023	−	0.0250674i
$340$		0			0
$341$	12.3541	−	8.97578i	0.669012	−	0.486066i
$342$	−15.8904	−	5.16312i	−0.859257	−	0.279189i
$343$		−	15.0000i		−	0.809924i
$344$	6.21885	−	19.1396i	0.335298	−	1.03194i
$345$		0			0
$346$	0.0278640	+	0.0857567i	0.00149798	+	0.00461031i
$347$	−15.1639	+	4.92705i	−0.814041	+	0.264498i	−0.686308	−	0.727311i	$-0.740770\pi$
$347$	−15.1639	+	4.92705i	−0.814041	+	0.264498i	−0.127733	+	0.991809i	$0.540770\pi$
$348$	0.930812	−	1.28115i	0.0498968	−	0.0686770i
$349$	17.3607			0.929296			0.464648	−	0.885496i	$-0.346181\pi$
$349$	17.3607			0.929296			0.464648	+	0.885496i	$0.346181\pi$
$350$		0			0
$351$	−10.8541			−0.579349
$352$	−5.96361	+	8.20820i	−0.317861	+	0.437499i
$353$	3.69822	−	1.20163i	0.196837	−	0.0639561i	−0.208940	−	0.977929i	$-0.567001\pi$
$353$	3.69822	−	1.20163i	0.196837	−	0.0639561i	0.405776	+	0.913972i	$0.367001\pi$
$354$	−0.791796	−	2.43690i	−0.0420835	−	0.129520i
$355$		0			0
$356$	−2.56231	+	7.88597i	−0.135802	+	0.417955i
$357$			4.85410i			0.256906i
$358$	10.3229	+	3.35410i	0.545580	+	0.177270i
$359$	−8.78115	+	6.37988i	−0.463452	+	0.336717i	−0.794884	−	0.606762i	$-0.792468\pi$
$359$	−8.78115	+	6.37988i	−0.463452	+	0.336717i	0.331432	+	0.943479i	$0.392468\pi$
$360$		0			0
$361$	4.78115	+	3.47371i	0.251640	+	0.182827i
$362$	17.2905	+	23.7984i	0.908770	+	1.25081i
$363$	0.449028	+	0.618034i	0.0235679	+	0.0324384i
$364$	7.28115	+	5.29007i	0.381636	+	0.277275i
$365$		0			0
$366$	3.04508	−	2.21238i	0.159169	−	0.115643i
$367$	1.08981	+	0.354102i	0.0568878	+	0.0184840i	0.337323	−	0.941389i	$-0.390479\pi$
$367$	1.08981	+	0.354102i	0.0568878	+	0.0184840i	−0.280435	+	0.959873i	$0.590479\pi$
$368$		−	6.00000i		−	0.312772i
$369$	−2.64590	+	8.14324i	−0.137740	+	0.423920i
$370$		0			0
$371$	−4.28115	−	13.1760i	−0.222266	−	0.684066i
$372$	1.14281	−	0.371323i	0.0592522	−	0.0192522i
$373$	−1.08981	+	1.50000i	−0.0564284	+	0.0776671i	−0.836299	−	0.548274i	$-0.815285\pi$
$373$	−1.08981	+	1.50000i	−0.0564284	+	0.0776671i	0.779870	+	0.625941i	$0.215285\pi$
$374$	−20.5623			−1.06325
$375$		0			0
$376$	−18.6180			−0.960152
$377$	−19.1396	+	26.3435i	−0.985742	+	1.35676i
$378$	10.3229	−	3.35410i	0.530951	−	0.172516i
$379$	2.33688	+	7.19218i	0.120038	+	0.369437i	0.992964	−	0.118414i	$-0.0377809\pi$
$379$	2.33688	+	7.19218i	0.120038	+	0.369437i	−0.872927	+	0.487851i	$0.837781\pi$
$380$		0			0
$381$	1.14590	−	3.52671i	0.0587061	−	0.180679i
$382$		−	19.4164i		−	0.993430i
$383$	−33.7360	−	10.9615i	−1.72383	−	0.560106i	−0.731294	−	0.682062i	$-0.761083\pi$
$383$	−33.7360	−	10.9615i	−1.72383	−	0.560106i	−0.992535	+	0.121956i	$0.961083\pi$
$384$	4.20820	−	3.05744i	0.214749	−	0.156024i
$385$		0			0
$386$	19.9894	+	14.5231i	1.01743	+	0.739207i
$387$	−15.0984	−	20.7812i	−0.767494	−	1.05637i
$388$	2.85317	+	3.92705i	0.144848	+	0.199366i
$389$	1.28115	+	0.930812i	0.0649570	+	0.0471940i	0.619790	−	0.784768i	$-0.287218\pi$
$389$	1.28115	+	0.930812i	0.0649570	+	0.0471940i	−0.554833	+	0.831962i	$0.687218\pi$
$390$		0			0
$391$	4.23607	−	3.07768i	0.214227	−	0.155645i
$392$	4.25325	+	1.38197i	0.214822	+	0.0697998i
$393$		−	4.68692i		−	0.236424i
$394$	−2.02786	+	6.24112i	−0.102162	+	0.314423i
$395$		0			0
$396$	1.63525	+	5.03280i	0.0821747	+	0.252908i
$397$	15.6129	−	5.07295i	0.783591	−	0.254604i	0.110218	−	0.993907i	$-0.464845\pi$
$397$	15.6129	−	5.07295i	0.783591	−	0.254604i	0.673372	+	0.739303i	$0.264845\pi$
$398$	15.3884	−	21.1803i	0.771352	−	1.06167i
$399$	4.14590			0.207555
$400$		0			0
$401$	12.0000			0.599251			0.299626	−	0.954057i	$-0.403138\pi$
$401$	12.0000			0.599251			0.299626	+	0.954057i	$0.403138\pi$
$402$	−5.03280	+	6.92705i	−0.251013	+	0.345490i
$403$	−23.4989	+	7.63525i	−1.17056	+	0.380339i
$404$	0.572949	+	1.76336i	0.0285053	+	0.0877302i
$405$		0			0
$406$	10.0623	−	30.9686i	0.499384	−	1.53695i
$407$		−	11.1246i		−	0.551427i
$408$	3.44095	+	1.11803i	0.170353	+	0.0553509i
$409$	−18.4164	+	13.3803i	−0.910633	+	0.661613i	−0.941175	−	0.337920i	$-0.890277\pi$
$409$	−18.4164	+	13.3803i	−0.910633	+	0.661613i	0.0305421	+	0.999533i	$0.490277\pi$
$410$		0			0
$411$	1.73607	+	1.26133i	0.0856339	+	0.0622167i
$412$	−4.61653	−	6.35410i	−0.227440	−	0.313044i
$413$	−7.31069	−	10.0623i	−0.359736	−	0.495134i
$414$	−4.61803	−	3.35520i	−0.226964	−	0.164899i
$415$		0			0
$416$	13.2812	−	9.64932i	0.651162	−	0.473097i
$417$	4.44501	+	1.44427i	0.217673	+	0.0707263i
$418$			17.5623i			0.859000i
$419$	2.07295	−	6.37988i	0.101270	−	0.311678i	−0.887567	−	0.460679i	$-0.847606\pi$
$419$	2.07295	−	6.37988i	0.101270	−	0.311678i	0.988837	+	0.149001i	$0.0476059\pi$
$420$		0			0
$421$	2.75329	+	8.47375i	0.134187	+	0.412985i	0.995463	−	0.0951527i	$-0.0303339\pi$
$421$	2.75329	+	8.47375i	0.134187	+	0.412985i	−0.861276	+	0.508138i	$0.830334\pi$
$422$	−6.43288	+	2.09017i	−0.313148	+	0.101748i
$423$	−13.9681	+	19.2254i	−0.679152	+	0.934772i
$424$	−10.3262			−0.501486
$425$		0			0
$426$	−1.85410			−0.0898315
$427$	10.7391	−	14.7812i	0.519703	−	0.715310i
$428$	0.0530006	−	0.0172209i	0.00256188	−	0.000832405i
$429$	1.71885	+	5.29007i	0.0829867	+	0.255407i
$430$		0			0
$431$	−3.79180	+	11.6699i	−0.182644	+	0.562122i	−0.999900	−	0.0141540i	$-0.995495\pi$
$431$	−3.79180	+	11.6699i	−0.182644	+	0.562122i	0.817255	+	0.576276i	$0.195495\pi$
$432$		−	10.8541i		−	0.522218i
$433$	−13.5923	−	4.41641i	−0.653205	−	0.212239i	−0.0363780	−	0.999338i	$-0.511582\pi$
$433$	−13.5923	−	4.41641i	−0.653205	−	0.212239i	−0.616827	+	0.787099i	$0.711582\pi$
$434$	19.9894	−	14.5231i	0.959520	−	0.697132i
$435$		0			0
$436$	−2.66312	−	1.93487i	−0.127540	−	0.0926634i
$437$	−2.62866	−	3.61803i	−0.125746	−	0.173074i
$438$	0.673542	+	0.927051i	0.0321831	+	0.0442962i
$439$	24.3713	+	17.7068i	1.16318	+	0.845100i	0.990177	−	0.139822i	$-0.0446529\pi$
$439$	24.3713	+	17.7068i	1.16318	+	0.845100i	0.173003	+	0.984921i	$0.444653\pi$
$440$		0			0
$441$	4.61803	−	3.35520i	0.219906	−	0.159771i
$442$	31.6421	+	10.2812i	1.50506	+	0.489025i
$443$		−	7.18034i		−	0.341148i	−0.985345	−	0.170574i	$-0.945438\pi$
$443$		−	7.18034i		−	0.341148i	0.985345	−	0.170574i	$-0.0545622\pi$
$444$	0.270510	−	0.832544i	0.0128378	−	0.0395108i
$445$		0			0
$446$	−0.927051	−	2.85317i	−0.0438971	−	0.135101i
$447$	−5.44907	+	1.77051i	−0.257732	+	0.0837422i
$448$	7.46969	−	10.2812i	0.352910	−	0.485739i
$449$	39.2705			1.85329			0.926645	−	0.375938i	$-0.122679\pi$
$449$	39.2705			1.85329			0.926645	+	0.375938i	$0.122679\pi$
$450$		0			0
$451$	9.00000			0.423793
$452$	0.746787	−	1.02786i	0.0351259	−	0.0483467i
$453$	7.66145	−	2.48936i	0.359966	−	0.116960i
$454$	−3.30902	−	10.1841i	−0.155300	−	0.477964i
$455$		0			0
$456$	0.954915	−	2.93893i	0.0447180	−	0.137628i
$457$		−	18.0000i		−	0.842004i	−0.907060	−	0.421002i	$-0.861678\pi$
$457$		−	18.0000i		−	0.842004i	0.907060	−	0.421002i	$-0.138322\pi$
$458$	−2.12663	−	0.690983i	−0.0993708	−	0.0322875i
$459$	7.66312	−	5.56758i	0.357684	−	0.259872i
$460$		0			0
$461$	−29.3435	−	21.3193i	−1.36666	−	0.992937i	−0.997990	−	0.0633777i	$-0.979813\pi$
$461$	−29.3435	−	21.3193i	−1.36666	−	0.992937i	−0.368672	−	0.929560i	$-0.620187\pi$
$462$	−3.26944	−	4.50000i	−0.152108	−	0.209359i
$463$	−8.30224	−	11.4271i	−0.385838	−	0.531060i	0.571282	−	0.820754i	$-0.306446\pi$
$463$	−8.30224	−	11.4271i	−0.385838	−	0.531060i	−0.957119	+	0.289694i	$0.906446\pi$
$464$	−26.3435	−	19.1396i	−1.22296	−	0.888536i
$465$		0			0
$466$	−35.1976	+	25.5725i	−1.63050	+	1.18462i
$467$	37.3157	+	12.1246i	1.72677	+	0.561060i	0.992976	−	0.118317i	$-0.0377498\pi$
$467$	37.3157	+	12.1246i	1.72677	+	0.561060i	0.733790	+	0.679377i	$0.237750\pi$
$468$		−	8.56231i		−	0.395793i
$469$	−12.8435	+	39.5281i	−0.593056	+	1.82524i
$470$		0			0
$471$	1.44834	+	4.45752i	0.0667359	+	0.205392i
$472$	−8.81678	+	2.86475i	−0.405825	+	0.131861i
$473$	−15.8702	+	21.8435i	−0.729713	+	1.00436i
$474$	−0.326238			−0.0149846
$475$		0			0
$476$	−7.85410			−0.359992
$477$	−7.74721	+	10.6631i	−0.354720	+	0.488231i
$478$	−39.7854	+	12.9271i	−1.81974	+	0.591270i
$479$	10.0623	+	30.9686i	0.459758	+	1.41499i	0.865457	+	0.500984i	$0.167028\pi$
$479$	10.0623	+	30.9686i	0.459758	+	1.41499i	−0.405698	+	0.914007i	$0.632972\pi$
$480$		0			0
$481$	−5.56231	+	17.1190i	−0.253619	+	0.780560i
$482$			31.0344i			1.41358i
$483$	1.34708	+	0.437694i	0.0612944	+	0.0199158i
$484$	−1.00000	+	0.726543i	−0.0454545	+	0.0330247i
$485$		0			0
$486$	−12.6353	−	9.18005i	−0.573147	−	0.416416i
$487$	−2.17963	−	3.00000i	−0.0987684	−	0.135943i	0.756772	−	0.653679i	$-0.226775\pi$
$487$	−2.17963	−	3.00000i	−0.0987684	−	0.135943i	−0.855541	+	0.517736i	$0.826775\pi$
$488$	−8.00448	−	11.0172i	−0.362346	−	0.498726i
$489$	6.13525	+	4.45752i	0.277446	+	0.201576i
$490$		0			0
$491$	−29.3435	+	21.3193i	−1.32425	+	0.962125i	−0.324383	+	0.945926i	$0.605157\pi$
$491$	−29.3435	+	21.3193i	−1.32425	+	0.962125i	−0.999869	+	0.0161994i	$0.994843\pi$
$492$	0.673542	+	0.218847i	0.0303656	+	0.00986639i
$493$		−	28.4164i		−	1.27981i
$494$	8.78115	−	27.0256i	0.395083	−	1.21594i
$495$		0			0
$496$	−7.63525	−	23.4989i	−0.342833	−	1.05513i
$497$	−8.55951	+	2.78115i	−0.383946	+	0.124752i
$498$	−0.171513	+	0.236068i	−0.00768570	+	0.0105785i
$499$	−42.3607			−1.89632			−0.948162	−	0.317787i	$-0.897060\pi$
$499$	−42.3607			−1.89632			−0.948162	+	0.317787i	$0.897060\pi$
$500$		0			0
$501$	−3.52786			−0.157613
$502$	−5.96361	+	8.20820i	−0.266169	+	0.366350i
$503$	24.5357	−	7.97214i	1.09399	−	0.355460i	0.294205	−	0.955742i	$-0.404945\pi$
$503$	24.5357	−	7.97214i	1.09399	−	0.355460i	0.799788	+	0.600282i	$0.204945\pi$
$504$	−5.91641	−	18.2088i	−0.263538	−	0.811086i
$505$		0			0
$506$	−1.85410	+	5.70634i	−0.0824249	+	0.253678i
$507$		−	4.03444i		−	0.179176i
$508$	5.70634	+	1.85410i	0.253178	+	0.0822625i
$509$	10.8541	−	7.88597i	0.481100	−	0.349539i	−0.320652	−	0.947197i	$-0.603902\pi$
$509$	10.8541	−	7.88597i	0.481100	−	0.349539i	0.801751	+	0.597658i	$0.203902\pi$
$510$		0			0
$511$	4.50000	+	3.26944i	0.199068	+	0.144632i
$512$	−3.11044	−	4.28115i	−0.137463	−	0.189202i
$513$	−4.75528	−	6.54508i	−0.209951	−	0.288973i
$514$	−38.4336	−	27.9237i	−1.69523	−	1.23166i
$515$		0			0
$516$	−1.71885	+	1.24882i	−0.0756680	+	0.0549760i
$517$	23.7562	+	7.71885i	1.04480	+	0.339475i
$518$		−	18.0000i		−	0.790875i
$519$	−0.00657781	+	0.0202444i	−0.000288734	+	0.000888631i
$520$		0			0
$521$	1.93769	+	5.96361i	0.0848919	+	0.261270i	0.984488	−	0.175453i	$-0.0561389\pi$
$521$	1.93769	+	5.96361i	0.0848919	+	0.261270i	−0.899596	+	0.436723i	$0.856139\pi$
$522$	−29.4625	+	9.57295i	−1.28954	+	0.418997i
$523$	21.9928	−	30.2705i	0.961679	−	1.32364i	0.0155385	−	0.999879i	$-0.495054\pi$
$523$	21.9928	−	30.2705i	0.961679	−	1.32364i	0.946140	−	0.323758i	$-0.104946\pi$
$524$	7.58359			0.331291
$525$		0			0
$526$	−26.4164			−1.15181
$527$	12.6740	−	17.4443i	0.552088	−	0.759884i
$528$	−5.29007	+	1.71885i	−0.230221	+	0.0748032i
$529$	6.63525	+	20.4212i	0.288489	+	0.887879i
$530$		0			0
$531$	−3.65654	+	11.2537i	−0.158680	+	0.488368i
$532$			6.70820i			0.290838i
$533$	−13.8496	−	4.50000i	−0.599892	−	0.194917i
$534$	−6.70820	+	4.87380i	−0.290292	+	0.210910i
$535$		0			0
$536$	25.0623	+	18.2088i	1.08253	+	0.786502i
$537$	1.50609	+	2.07295i	0.0649924	+	0.0894544i
$538$	−2.43690	−	3.35410i	−0.105062	−	0.144606i
$539$	−4.85410	−	3.52671i	−0.209081	−	0.151906i
$540$		0			0
$541$	27.6525	−	20.0907i	1.18887	−	0.863767i	0.195728	−	0.980658i	$-0.437293\pi$
$541$	27.6525	−	20.0907i	1.18887	−	0.863767i	0.993145	+	0.116892i	$0.0372930\pi$
$542$	−30.9156	−	10.0451i	−1.32794	−	0.431473i
$543$			6.94427i			0.298007i
$544$	−4.42705	+	13.6251i	−0.189808	+	0.584170i
$545$		0			0
$546$	2.78115	+	8.55951i	0.119022	+	0.366313i
$547$	21.0620	−	6.84346i	0.900546	−	0.292605i	0.178084	−	0.984015i	$-0.443010\pi$
$547$	21.0620	−	6.84346i	0.900546	−	0.292605i	0.722462	+	0.691410i	$0.243010\pi$
$548$	−2.04087	+	2.80902i	−0.0871817	+	0.119995i
$549$	−17.3820			−0.741844
$550$		0			0
$551$	−24.2705			−1.03396
$552$	0.620541	−	0.854102i	0.0264120	−	0.0363530i
$553$	−1.50609	+	0.489357i	−0.0640453	+	0.0208096i
$554$	2.64590	+	8.14324i	0.112413	+	0.345973i
$555$		0			0
$556$	−2.33688	+	7.19218i	−0.0991058	+	0.305016i
$557$		−	40.3607i		−	1.71014i	−0.518515	−	0.855068i	$-0.673515\pi$
$557$		−	40.3607i		−	1.71014i	0.518515	−	0.855068i	$-0.326485\pi$
$558$	−22.3561	−	7.26393i	−0.946409	−	0.307507i
$559$	35.3435	−	25.6785i	1.49487	−	1.08609i
$560$		0			0
$561$	−3.92705	−	2.85317i	−0.165800	−	0.120461i
$562$	11.4127	+	15.7082i	0.481415	+	0.662611i
$563$	4.14725	+	5.70820i	0.174786	+	0.240572i	0.887418	−	0.460966i	$-0.152497\pi$
$563$	4.14725	+	5.70820i	0.174786	+	0.240572i	−0.712632	+	0.701538i	$0.752497\pi$
$564$	1.59017	+	1.15533i	0.0669582	+	0.0486480i
$565$		0			0
$566$	−20.5623	+	14.9394i	−0.864298	+	0.627949i
$567$	−21.9928	−	7.14590i	−0.923611	−	0.300100i
$568$			6.70820i			0.281470i
$569$	−8.29180	+	25.5195i	−0.347610	+	1.06983i	0.612561	+	0.790423i	$0.290139\pi$
$569$	−8.29180	+	25.5195i	−0.347610	+	1.06983i	−0.960172	+	0.279411i	$0.909861\pi$
$570$		0			0
$571$	−4.01722	−	12.3637i	−0.168115	−	0.517406i	0.831137	−	0.556068i	$-0.187691\pi$
$571$	−4.01722	−	12.3637i	−0.168115	−	0.517406i	−0.999252	+	0.0386617i	$0.987691\pi$
$572$	−8.55951	+	2.78115i	−0.357891	+	0.116286i
$573$	2.69417	−	3.70820i	0.112550	−	0.154912i
$574$	14.5623			0.607819
$575$		0			0
$576$	−12.0902			−0.503757
$577$	17.3763	−	23.9164i	0.723384	−	0.995653i	−0.276020	−	0.961152i	$-0.589016\pi$
$577$	17.3763	−	23.9164i	0.723384	−	0.995653i	0.999405	−	0.0345013i	$-0.0109843\pi$
$578$	−1.45309	+	0.472136i	−0.0604404	+	0.0196383i
$579$	1.80244	+	5.54734i	0.0749068	+	0.230539i
$580$		0			0
$581$	−0.437694	+	1.34708i	−0.0181586	+	0.0558865i
$582$			4.85410i			0.201209i
$583$	13.1760	+	4.28115i	0.545696	+	0.177307i
$584$	3.35410	−	2.43690i	0.138794	−	0.100840i
$585$		0			0
$586$	−27.9615	−	20.3152i	−1.15508	−	0.839214i
$587$	1.45309	+	2.00000i	0.0599752	+	0.0825488i	0.837951	−	0.545745i	$-0.183753\pi$
$587$	1.45309	+	2.00000i	0.0599752	+	0.0825488i	−0.777976	+	0.628294i	$0.783753\pi$
$588$	−0.277515	−	0.381966i	−0.0114445	−	0.0157520i
$589$	−14.8992	−	10.8249i	−0.613910	−	0.446032i
$590$		0			0
$591$	−1.25329	+	0.910568i	−0.0515534	+	0.0374557i
$592$	−17.1190	−	5.56231i	−0.703587	−	0.228609i
$593$			41.3607i			1.69848i	0.528007	+	0.849240i	$0.322939\pi$
$593$			41.3607i			1.69848i	−0.528007	+	0.849240i	$0.677061\pi$
$594$	−3.35410	+	10.3229i	−0.137620	+	0.423552i
$595$		0			0
$596$	−2.86475	−	8.81678i	−0.117345	−	0.361149i
$597$	5.87785	−	1.90983i	0.240564	−	0.0781641i
$598$	5.70634	−	7.85410i	0.233350	−	0.321178i
$599$	24.2705			0.991666			0.495833	−	0.868418i	$-0.334863\pi$
$599$	24.2705			0.991666			0.495833	+	0.868418i	$0.334863\pi$
$600$		0			0
$601$	−0.639320			−0.0260784			−0.0130392	−	0.999915i	$-0.504151\pi$
$601$	−0.639320			−0.0260784			−0.0130392	+	0.999915i	$0.504151\pi$
$602$	−25.6785	+	35.3435i	−1.04658	+	1.44049i
$603$	37.6057	−	12.2188i	1.53142	−	0.497590i
$604$	4.02786	+	12.3965i	0.163891	+	0.504406i
$605$		0			0
$606$	−0.572949	+	1.76336i	−0.0232745	+	0.0716314i
$607$			30.5410i			1.23962i	0.784751	+	0.619811i	$0.212791\pi$
$607$			30.5410i			1.23962i	−0.784751	+	0.619811i	$0.787209\pi$
$608$	11.6372	+	3.78115i	0.471950	+	0.153346i
$609$	6.21885	−	4.51826i	0.252000	−	0.183089i
$610$		0			0
$611$	−32.6976	−	23.7562i	−1.32280	−	0.961072i
$612$	4.39201	+	6.04508i	0.177537	+	0.244358i
$613$	2.59590	+	3.57295i	0.104847	+	0.144310i	0.858217	−	0.513288i	$-0.171573\pi$
$613$	2.59590	+	3.57295i	0.104847	+	0.144310i	−0.753369	+	0.657598i	$0.771573\pi$
$614$	−8.20820	−	5.96361i	−0.331256	−	0.240672i
$615$		0			0
$616$	−16.2812	+	11.8290i	−0.655986	+	0.476602i
$617$	−24.5030	−	7.96149i	−0.986452	−	0.320518i	−0.229013	−	0.973423i	$-0.573550\pi$
$617$	−24.5030	−	7.96149i	−0.986452	−	0.320518i	−0.757439	+	0.652906i	$0.773550\pi$
$618$		−	7.85410i		−	0.315938i
$619$	6.34346	−	19.5232i	0.254965	−	0.784702i	−0.738871	−	0.673846i	$-0.764641\pi$
$619$	6.34346	−	19.5232i	0.254965	−	0.784702i	0.993837	−	0.110856i	$-0.0353591\pi$
$620$		0			0
$621$	−0.854102	−	2.62866i	−0.0342739	−	0.105484i
$622$	32.7319	−	10.6353i	1.31243	−	0.426435i
$623$	−23.6579	+	32.5623i	−0.947834	+	1.30458i
$624$	9.00000			0.360288
$625$		0			0
$626$	−31.4164			−1.25565
$627$	−2.43690	+	3.35410i	−0.0973203	+	0.133950i
$628$	−7.21242	+	2.34346i	−0.287807	+	0.0935142i
$629$	−4.85410	−	14.9394i	−0.193546	−	0.595672i
$630$		0			0
$631$	0.618034	−	1.90211i	0.0246035	−	0.0757219i	−0.938001	−	0.346633i	$-0.887325\pi$
$631$	0.618034	−	1.90211i	0.0246035	−	0.0757219i	0.962604	+	0.270911i	$0.0873249\pi$
$632$			1.18034i			0.0469514i
$633$	−1.51860	−	0.493422i	−0.0603588	−	0.0196118i
$634$	35.2705	−	25.6255i	1.40077	−	1.01772i
$635$		0			0
$636$	0.881966	+	0.640786i	0.0349722	+	0.0254088i
$637$	5.70634	+	7.85410i	0.226093	+	0.311191i
$638$	19.1396	+	26.3435i	0.757746	+	1.04295i
$639$	6.92705	+	5.03280i	0.274030	+	0.199094i
$640$		0			0
$641$	7.06231	−	5.13107i	0.278944	−	0.202665i	−0.439513	−	0.898236i	$-0.644849\pi$
$641$	7.06231	−	5.13107i	0.278944	−	0.202665i	0.718457	+	0.695572i	$0.244849\pi$
$642$	0.0530006	+	0.0172209i	0.00209177	+	0.000679656i
$643$			18.2705i			0.720519i	0.932852	+	0.360259i	$0.117312\pi$
$643$			18.2705i			0.720519i	−0.932852	+	0.360259i	$0.882688\pi$
$644$	−0.708204	+	2.17963i	−0.0279071	+	0.0858894i
$645$		0			0
$646$	7.66312	+	23.5847i	0.301501	+	0.927926i
$647$	19.2456	−	6.25329i	0.756624	−	0.245842i	0.0947951	−	0.995497i	$-0.469780\pi$
$647$	19.2456	−	6.25329i	0.756624	−	0.245842i	0.661829	+	0.749655i	$0.269780\pi$
$648$	−10.1311	+	13.9443i	−0.397987	+	0.547783i
$649$	12.4377			0.488222
$650$		0			0
$651$	5.83282			0.228606
$652$	−7.21242	+	9.92705i	−0.282460	+	0.388773i
$653$	−4.42477	+	1.43769i	−0.173155	+	0.0562613i	−0.394311	−	0.918977i	$-0.629017\pi$
$653$	−4.42477	+	1.43769i	−0.173155	+	0.0562613i	0.221157	+	0.975238i	$0.429017\pi$
$654$	−1.01722	−	3.13068i	−0.0397765	−	0.122419i
$655$		0			0
$656$	4.50000	−	13.8496i	0.175695	−	0.540735i
$657$		−	5.29180i		−	0.206453i
$658$	38.4383	+	12.4894i	1.49848	+	0.486886i
$659$	−20.9164	+	15.1967i	−0.814788	+	0.591978i	−0.915215	−	0.402967i	$-0.867979\pi$
$659$	−20.9164	+	15.1967i	−0.814788	+	0.591978i	0.100427	+	0.994944i	$0.467979\pi$
$660$		0			0
$661$	−11.6180	−	8.44100i	−0.451889	−	0.328317i	0.338452	−	0.940984i	$-0.390097\pi$
$661$	−11.6180	−	8.44100i	−0.451889	−	0.328317i	−0.790341	+	0.612667i	$0.790097\pi$
$662$	−20.0579	−	27.6074i	−0.779574	−	1.07299i
$663$	4.61653	+	6.35410i	0.179291	+	0.246773i
$664$	0.854102	+	0.620541i	0.0331456	+	0.0240817i
$665$		0			0
$666$	−13.8541	+	10.0656i	−0.536836	+	0.390034i
$667$	−7.88597	−	2.56231i	−0.305346	−	0.0992129i
$668$		−	5.70820i		−	0.220857i
$669$	0.218847	−	0.673542i	0.00846112	−	0.0260406i
$670$		0			0
$671$	5.64590	+	17.3763i	0.217957	+	0.670804i
$672$	−3.68571	+	1.19756i	−0.142179	+	0.0461969i
$673$	18.6251	−	25.6353i	0.717945	−	0.988166i	−0.281645	−	0.959519i	$-0.590880\pi$
$673$	18.6251	−	25.6353i	0.717945	−	0.988166i	0.999590	−	0.0286477i	$-0.00912008\pi$
$674$	−48.2705			−1.85931
$675$		0			0
$676$	6.52786			0.251072
$677$	2.41665	−	3.32624i	0.0928795	−	0.127838i	−0.760048	−	0.649867i	$-0.774825\pi$
$677$	2.41665	−	3.32624i	0.0928795	−	0.127838i	0.852928	+	0.522029i	$0.174825\pi$
$678$	1.20833	−	0.392609i	0.0464055	−	0.0150781i
$679$	7.28115	+	22.4091i	0.279425	+	0.859982i
$680$		0			0
$681$	0.781153	−	2.40414i	0.0299338	−	0.0921269i
$682$			24.7082i			0.946126i
$683$	40.9609	+	13.3090i	1.56733	+	0.509255i	0.958753	−	0.284242i	$-0.0917418\pi$
$683$	40.9609	+	13.3090i	1.56733	+	0.509255i	0.608574	+	0.793497i	$0.291742\pi$
$684$	5.16312	−	3.75123i	0.197417	−	0.143432i
$685$		0			0
$686$	19.6353	+	14.2658i	0.749678	+	0.544673i
$687$	−0.310271	−	0.427051i	−0.0118376	−	0.0162930i
$688$	25.6785	+	35.3435i	0.978985	+	1.34746i
$689$	−18.1353	−	13.1760i	−0.690898	−	0.501967i
$690$		0			0
$691$	−20.8885	+	15.1764i	−0.794638	+	0.577338i	−0.909336	−	0.416062i	$-0.863410\pi$
$691$	−20.8885	+	15.1764i	−0.794638	+	0.577338i	0.114698	+	0.993400i	$0.463410\pi$
$692$	−0.0327561	−	0.0106431i	−0.00124520	−	0.000404591i
$693$			25.6869i			0.975765i
$694$	7.97214	−	24.5357i	0.302618	−	0.931363i
$695$		0			0
$696$	−1.77051	−	5.44907i	−0.0671110	−	0.206546i
$697$	12.0862	−	3.92705i	0.457798	−	0.148748i
$698$	−16.5110	+	22.7254i	−0.624950	+	0.860170i
$699$	−10.2705			−0.388466
$700$		0			0
$701$	2.72949			0.103091			0.0515457	−	0.998671i	$-0.483585\pi$
$701$	2.72949			0.103091			0.0515457	+	0.998671i	$0.483585\pi$
$702$	10.3229	−	14.2082i	0.389611	−	0.536254i
$703$	−12.7598	+	4.14590i	−0.481244	+	0.156366i
$704$	3.92705	+	12.0862i	0.148006	+	0.455517i
$705$		0			0
$706$	−1.94427	+	5.98385i	−0.0731736	+	0.225205i
$707$			9.00000i			0.338480i
$708$	0.930812	+	0.302439i	0.0349821	+	0.0113664i
$709$	−13.7812	+	10.0126i	−0.517562	+	0.376031i	−0.815685	−	0.578497i	$-0.803640\pi$
$709$	−13.7812	+	10.0126i	−0.517562	+	0.376031i	0.298123	+	0.954528i	$0.403640\pi$
$710$		0			0
$711$	1.21885	+	0.885544i	0.0457103	+	0.0332105i
$712$	17.6336	+	24.2705i	0.660846	+	0.909576i
$713$	−3.69822	−	5.09017i	−0.138500	−	0.190628i
$714$	−6.35410	−	4.61653i	−0.237796	−	0.172769i
$715$		0			0
$716$	−3.35410	+	2.43690i	−0.125349	+	0.0910711i
$717$	−9.39205	−	3.05166i	−0.350753	−	0.113966i
$718$		−	17.5623i		−	0.655419i
$719$	−14.6976	+	45.2344i	−0.548127	+	1.68696i	0.165311	+	0.986241i	$0.447137\pi$
$719$	−14.6976	+	45.2344i	−0.548127	+	1.68696i	−0.713438	+	0.700719i	$0.752863\pi$
$720$		0			0
$721$	−11.7812	−	36.2587i	−0.438753	−	1.35034i
$722$	−9.09429	+	2.95492i	−0.338455	+	0.109971i
$723$	−4.30625	+	5.92705i	−0.160151	+	0.220429i
$724$	−11.2361			−0.417585
$725$		0			0
$726$	−1.23607			−0.0458748
$727$	22.8254	−	31.4164i	0.846546	−	1.16517i	−0.138068	−	0.990423i	$-0.544089\pi$
$727$	22.8254	−	31.4164i	0.846546	−	1.16517i	0.984613	−	0.174747i	$-0.0559108\pi$
$728$	30.9686	−	10.0623i	1.14777	−	0.372934i
$729$	6.00658	+	18.4863i	0.222466	+	0.684679i
$730$		0			0
$731$	−11.7812	+	36.2587i	−0.435742	+	1.34108i
$732$			1.43769i			0.0531387i
$733$	−22.4091	−	7.28115i	−0.827698	−	0.268936i	−0.135623	−	0.990761i	$-0.543304\pi$
$733$	−22.4091	−	7.28115i	−0.827698	−	0.268936i	−0.692076	+	0.721825i	$0.743304\pi$
$734$	−1.50000	+	1.08981i	−0.0553660	+	0.0402258i
$735$		0			0
$736$	3.38197	+	2.45714i	0.124661	+	0.0905715i
$737$	−24.4297	−	33.6246i	−0.899880	−	1.23858i
$738$	−8.14324	−	11.2082i	−0.299757	−	0.412580i
$739$	14.3713	+	10.4414i	0.528658	+	0.384092i	0.819855	−	0.572571i	$-0.194054\pi$
$739$	14.3713	+	10.4414i	0.528658	+	0.384092i	−0.291198	+	0.956663i	$0.594054\pi$
$740$		0			0
$741$	5.42705	−	3.94298i	0.199368	−	0.144849i
$742$	21.3193	+	6.92705i	0.782655	+	0.254300i
$743$			25.9098i			0.950539i	0.879840	+	0.475270i	$0.157650\pi$
$743$			25.9098i			0.950539i	−0.879840	+	0.475270i	$0.842350\pi$
$744$	1.34346	−	4.13474i	0.0492536	−	0.151587i
$745$		0			0
$746$	−0.927051	−	2.85317i	−0.0339417	−	0.104462i
$747$	1.28157	−	0.416408i	0.0468903	−	0.0152356i
$748$	4.61653	−	6.35410i	0.168797	−	0.232329i
$749$	0.270510			0.00988421
$750$		0			0
$751$	−15.3607			−0.560519			−0.280260	−	0.959924i	$-0.590421\pi$
$751$	−15.3607			−0.560519			−0.280260	+	0.959924i	$0.590421\pi$
$752$	23.7562	−	32.6976i	0.866298	−	1.19236i
$753$	−2.27790	+	0.740133i	−0.0830111	+	0.0269720i
$754$	−16.2812	−	50.1082i	−0.592925	−	1.82483i
$755$		0			0
$756$	−1.28115	+	3.94298i	−0.0465951	+	0.143405i
$757$			27.0000i			0.981332i	0.871348	+	0.490666i	$0.163246\pi$
$757$			27.0000i			0.981332i	−0.871348	+	0.490666i	$0.836754\pi$
$758$	−11.6372	−	3.78115i	−0.422682	−	0.137338i
$759$	−1.14590	+	0.832544i	−0.0415935	+	0.0302194i
$760$		0			0
$761$	14.5623	+	10.5801i	0.527883	+	0.383530i	0.819565	−	0.572986i	$-0.194215\pi$
$761$	14.5623	+	10.5801i	0.527883	+	0.383530i	−0.291682	+	0.956515i	$0.594215\pi$
$762$	3.52671	+	4.85410i	0.127759	+	0.175846i
$763$	−9.39205	−	12.9271i	−0.340015	−	0.467991i
$764$	6.00000	+	4.35926i	0.217072	+	0.157712i
$765$		0			0
$766$	46.4336	−	33.7360i	1.67772	−	1.21893i
$767$	−19.1396	−	6.21885i	−0.691092	−	0.224550i
$768$			5.18034i			0.186929i
$769$	3.98278	−	12.2577i	0.143623	−	0.442025i	−0.853209	−	0.521570i	$-0.825347\pi$
$769$	3.98278	−	12.2577i	0.143623	−	0.442025i	0.996831	+	0.0795446i	$0.0253466\pi$
$770$		0			0
$771$	−3.46556	−	10.6659i	−0.124809	−	0.384123i
$772$	−8.97578	+	2.91641i	−0.323045	+	0.104964i
$773$	12.4822	−	17.1803i	0.448955	−	0.617934i	−0.523217	−	0.852199i	$-0.675268\pi$
$773$	12.4822	−	17.1803i	0.448955	−	0.617934i	0.972173	+	0.234265i	$0.0752684\pi$
$774$	41.5623			1.49393
$775$		0			0
$776$	17.5623			0.630450
$777$	2.49763	−	3.43769i	0.0896020	−	0.123327i
$778$	−2.43690	+	0.791796i	−0.0873670	+	0.0283873i
$779$	−3.35410	−	10.3229i	−0.120173	−	0.369855i
$780$		0			0
$781$	2.78115	−	8.55951i	0.0995175	−	0.306283i
$782$			8.47214i			0.302963i
$783$	−14.2658	−	4.63525i	−0.509820	−	0.165650i
$784$	−7.85410	+	5.70634i	−0.280504	+	0.203798i
$785$		0			0
$786$	6.13525	+	4.45752i	0.218837	+	0.158995i
$787$	6.63715	+	9.13525i	0.236589	+	0.325637i	0.910758	−	0.412940i	$-0.135498\pi$
$787$	6.63715	+	9.13525i	0.236589	+	0.325637i	−0.674169	+	0.738577i	$0.735498\pi$
$788$	−1.47333	−	2.02786i	−0.0524852	−	0.0722397i
$789$	−5.04508	−	3.66547i	−0.179610	−	0.130494i
$790$		0			0
$791$	4.98936	−	3.62498i	0.177401	−	0.128889i
$792$	18.2088	+	5.91641i	0.647023	+	0.210230i
$793$		−	29.5623i		−	1.04979i
$794$	−8.20820	+	25.2623i	−0.291298	+	0.896524i
$795$		0			0
$796$	3.09017	+	9.51057i	0.109528	+	0.337093i
$797$	−33.4912	+	10.8820i	−1.18632	+	0.385459i	−0.834711	−	0.550688i	$-0.814366\pi$
$797$	−33.4912	+	10.8820i	−1.18632	+	0.385459i	−0.351610	+	0.936147i	$0.614366\pi$
$798$	−3.94298	+	5.42705i	−0.139580	+	0.192116i
$799$	35.2705			1.24778
$800$		0			0
$801$	38.2918			1.35297
$802$	−11.4127	+	15.7082i	−0.402996	+	0.554676i
$803$	−5.29007	+	1.71885i	−0.186682	+	0.0606568i
$804$	−1.01064	−	3.11044i	−0.0356426	−	0.109697i
$805$		0			0
$806$	12.3541	−	38.0220i	0.435155	−	1.33927i
$807$		−	0.978714i		−	0.0344524i
$808$	6.37988	+	2.07295i	0.224443	+	0.0729261i
$809$	−4.14590	+	3.01217i	−0.145762	+	0.105902i	−0.658276	−	0.752776i	$-0.728714\pi$
$809$	−4.14590	+	3.01217i	−0.145762	+	0.105902i	0.512514	+	0.858679i	$0.328714\pi$
$810$		0			0
$811$	9.56231	+	6.94742i	0.335778	+	0.243957i	0.742878	−	0.669426i	$-0.233460\pi$
$811$	9.56231	+	6.94742i	0.335778	+	0.243957i	−0.407100	+	0.913383i	$0.633460\pi$
$812$	7.31069	+	10.0623i	0.256555	+	0.353118i
$813$	−4.51052	−	6.20820i	−0.158191	−	0.217731i
$814$	14.5623	+	10.5801i	0.510409	+	0.370834i
$815$		0			0
$816$	−6.35410	+	4.61653i	−0.222438	+	0.161611i
$817$	30.9686	+	10.0623i	1.08345	+	0.352036i
$818$		−	36.8328i		−	1.28783i
$819$	12.8435	−	39.5281i	0.448787	−	1.38122i
$820$		0			0
$821$	6.57295	+	20.2295i	0.229398	+	0.706013i	0.997815	+	0.0660645i	$0.0210443\pi$
$821$	6.57295	+	20.2295i	0.229398	+	0.706013i	−0.768418	+	0.639948i	$0.778956\pi$
$822$	−3.30220	+	1.07295i	−0.115177	+	0.0374234i
$823$	13.1760	−	18.1353i	0.459288	−	0.632155i	−0.515073	−	0.857146i	$-0.672235\pi$
$823$	13.1760	−	18.1353i	0.459288	−	0.632155i	0.974361	+	0.224991i	$0.0722353\pi$
$824$	−28.4164			−0.989932
$825$		0			0
$826$	20.1246			0.700225
$827$	−18.5846	+	25.5795i	−0.646250	+	0.889487i	−0.998930	−	0.0462570i	$-0.985271\pi$
$827$	−18.5846	+	25.5795i	−0.646250	+	0.889487i	0.352679	+	0.935744i	$0.385271\pi$
$828$	2.07363	−	0.673762i	0.0720635	−	0.0234149i
$829$	−1.93363	−	5.95110i	−0.0671577	−	0.206690i	0.911846	−	0.410532i	$-0.134657\pi$
$829$	−1.93363	−	5.95110i	−0.0671577	−	0.206690i	−0.979004	+	0.203842i	$0.934657\pi$
$830$		0			0
$831$	−0.624612	+	1.92236i	−0.0216675	+	0.0666858i
$832$		−	20.5623i		−	0.712870i
$833$	−8.05748	−	2.61803i	−0.279175	−	0.0907095i
$834$	−6.11803	+	4.44501i	−0.211850	+	0.153918i
$835$		0			0
$836$	−5.42705	−	3.94298i	−0.187698	−	0.136371i
$837$	−6.69015	−	9.20820i	−0.231245	−	0.318282i
$838$	6.37988	+	8.78115i	0.220389	+	0.303340i
$839$	23.7812	+	17.2780i	0.821017	+	0.596503i	0.917004	−	0.398879i	$-0.130601\pi$
$839$	23.7812	+	17.2780i	0.821017	+	0.596503i	−0.0959869	+	0.995383i	$0.530601\pi$
$840$		0			0
$841$	−12.9443	+	9.40456i	−0.446354	+	0.324295i
$842$	−13.7108	−	4.45492i	−0.472506	−	0.153527i
$843$			4.58359i			0.157867i
$844$	0.798374	−	2.45714i	0.0274812	−	0.0845783i
$845$		0			0
$846$	−11.8820	−	36.5689i	−0.408510	−	1.25727i
$847$	−5.70634	+	1.85410i	−0.196072	+	0.0637077i
$848$	13.1760	−	18.1353i	0.452467	−	0.622767i
$849$	−6.00000			−0.205919
$850$		0			0
$851$	−4.58359			−0.157124
$852$	0.416272	−	0.572949i	0.0142612	−	0.0196289i
$853$	−5.54734	+	1.80244i	−0.189937	+	0.0617143i	−0.402441	−	0.915446i	$-0.631838\pi$
$853$	−5.54734	+	1.80244i	−0.189937	+	0.0617143i	0.212504	+	0.977160i	$0.431838\pi$
$854$	9.13525	+	28.1154i	0.312602	+	0.962090i
$855$		0			0
$856$	0.0623059	−	0.191758i	0.00212957	−	0.00655415i
$857$		−	34.1803i		−	1.16758i	−0.811905	−	0.583789i	$-0.801569\pi$
$857$		−	34.1803i		−	1.16758i	0.811905	−	0.583789i	$-0.198431\pi$
$858$	−8.55951	−	2.78115i	−0.292217	−	0.0949470i
$859$	−20.3262	+	14.7679i	−0.693522	+	0.503873i	−0.877816	−	0.478998i	$-0.841000\pi$
$859$	−20.3262	+	14.7679i	−0.693522	+	0.503873i	0.184294	+	0.982871i	$0.441000\pi$
$860$		0			0
$861$	2.78115	+	2.02063i	0.0947814	+	0.0688627i
$862$	−11.6699	−	16.0623i	−0.397480	−	0.547084i
$863$	−3.97574	−	5.47214i	−0.135336	−	0.186274i	0.735970	−	0.677014i	$-0.236726\pi$
$863$	−3.97574	−	5.47214i	−0.135336	−	0.186274i	−0.871306	+	0.490740i	$0.836726\pi$
$864$	6.11803	+	4.44501i	0.208140	+	0.151222i
$865$		0			0
$866$	18.7082	−	13.5923i	0.635731	−	0.461885i
$867$	−0.343027	−	0.111456i	−0.0116498	−	0.00378525i
$868$			9.43769i			0.320336i
$869$	0.489357	−	1.50609i	0.0166003	−	0.0510905i
$870$		0			0
$871$	20.7812	+	63.9578i	0.704143	+	2.16713i
$872$	−11.3269	+	3.68034i	−0.383578	+	0.124632i
$873$	13.1760	−	18.1353i	0.445941	−	0.613785i
$874$	7.23607			0.244764
$875$		0			0
$876$	−0.437694			−0.0147883
$877$	−11.1554	+	15.3541i	−0.376691	+	0.518471i	−0.954704	−	0.297556i	$-0.903828\pi$
$877$	−11.1554	+	15.3541i	−0.376691	+	0.518471i	0.578013	+	0.816028i	$0.303828\pi$
$878$	−46.3570	+	15.0623i	−1.56447	+	0.508328i
$879$	−2.52129	−	7.75972i	−0.0850409	−	0.261729i
$880$		0			0
$881$	14.0729	−	43.3121i	0.474130	−	1.45922i	−0.372998	−	0.927832i	$-0.621670\pi$
$881$	14.0729	−	43.3121i	0.474130	−	1.45922i	0.847128	−	0.531389i	$-0.178330\pi$
$882$			9.23607i			0.310995i
$883$	−16.9600	−	5.51064i	−0.570750	−	0.185448i	0.00940251	−	0.999956i	$-0.497007\pi$
$883$	−16.9600	−	5.51064i	−0.570750	−	0.185448i	−0.580152	+	0.814508i	$0.697007\pi$
$884$	−10.2812	+	7.46969i	−0.345793	+	0.251233i
$885$		0			0
$886$	9.39919	+	6.82891i	0.315772	+	0.229422i
$887$	24.9645	+	34.3607i	0.838226	+	1.15372i	0.986336	+	0.164748i	$0.0526810\pi$
$887$	24.9645	+	34.3607i	0.838226	+	1.15372i	−0.148110	+	0.988971i	$0.547319\pi$
$888$	−1.86162	−	2.56231i	−0.0624720	−	0.0859854i
$889$	23.5623	+	17.1190i	0.790254	+	0.574153i
$890$		0			0
$891$	18.7082	−	13.5923i	0.626748	−	0.455359i
$892$	1.08981	+	0.354102i	0.0364897	+	0.0118562i
$893$		−	30.1246i		−	1.00808i
$894$	2.86475	−	8.81678i	0.0958114	−	0.294877i
$895$		0			0
$896$	12.6246	+	38.8546i	0.421759	+	1.29804i
$897$	2.17963	−	0.708204i	0.0727756	−	0.0236462i
$898$	−37.3485	+	51.4058i	−1.24633	+	1.71543i
$899$	−34.1459			−1.13883
$900$		0			0
$901$	19.5623			0.651715
$902$	−8.55951	+	11.7812i	−0.285000	+	0.392269i
$903$	−9.80832	+	3.18692i	−0.326401	+	0.106054i
$904$	−1.42047	−	4.37177i	−0.0472442	−	0.145403i
$905$		0			0
$906$	−4.02786	+	12.3965i	−0.133817	+	0.411846i
$907$		−	42.2705i		−	1.40357i	−0.712389	−	0.701785i	$-0.752387\pi$
$907$		−	42.2705i		−	1.40357i	0.712389	−	0.701785i	$-0.247613\pi$
$908$	3.88998	+	1.26393i	0.129094	+	0.0419451i
$909$	6.92705	−	5.03280i	0.229756	−	0.166927i
$910$		0			0
$911$	29.5623	+	21.4783i	0.979443	+	0.711607i	0.957584	−	0.288154i	$-0.0930416\pi$
$911$	29.5623	+	21.4783i	0.979443	+	0.711607i	0.0218589	+	0.999761i	$0.493042\pi$
$912$	3.94298	+	5.42705i	0.130565	+	0.179708i
$913$	−0.832544	−	1.14590i	−0.0275532	−	0.0379237i
$914$	23.5623	+	17.1190i	0.779372	+	0.566247i
$915$		0			0
$916$	0.690983	−	0.502029i	0.0228307	−	0.0165875i
$917$	35.0098	+	11.3754i	1.15613	+	0.375648i
$918$			15.3262i			0.505841i
$919$	7.43769	−	22.8909i	0.245347	−	0.755100i	−0.750232	−	0.661174i	$-0.770058\pi$
$919$	7.43769	−	22.8909i	0.245347	−	0.755100i	0.995579	−	0.0939258i	$-0.0299416\pi$
$920$		0			0
$921$	−0.740133	−	2.27790i	−0.0243882	−	0.0750592i
$922$	55.8146	−	18.1353i	1.83816	−	0.597253i
$923$	−8.55951	+	11.7812i	−0.281740	+	0.387781i
$924$	2.12461			0.0698946
$925$		0			0
$926$	22.8541			0.751032
$927$	−21.3193	+	29.3435i	−0.700217	+	0.963766i
$928$	21.5765	−	7.01064i	0.708285	−	0.230136i
$929$	−11.3435	−	34.9116i	−0.372167	−	1.14541i	−0.945370	−	0.325999i	$-0.894300\pi$
$929$	−11.3435	−	34.9116i	−0.372167	−	1.14541i	0.573203	−	0.819413i	$-0.305700\pi$
$930$		0			0
$931$	−2.23607	+	6.88191i	−0.0732842	+	0.225545i
$932$		−	16.6180i		−	0.544342i
$933$	7.72696	+	2.51064i	0.252969	+	0.0821948i
$934$	−51.3607	+	37.3157i	−1.68057	+	1.22101i
$935$		0			0
$936$	−25.0623	−	18.2088i	−0.819187	−	0.595174i
$937$	−5.54734	−	7.63525i	−0.181224	−	0.249433i	0.708734	−	0.705475i	$-0.249266\pi$
$937$	−5.54734	−	7.63525i	−0.181224	−	0.249433i	−0.889958	+	0.456043i	$0.849266\pi$
$938$	−39.5281	−	54.4058i	−1.29064	−	1.77641i
$939$	−6.00000	−	4.35926i	−0.195803	−	0.142259i
$940$		0			0
$941$	22.0623	−	16.0292i	0.719211	−	0.522537i	−0.166921	−	0.985970i	$-0.553383\pi$
$941$	22.0623	−	16.0292i	0.719211	−	0.522537i	0.886132	+	0.463433i	$0.153383\pi$
$942$	−7.21242	−	2.34346i	−0.234993	−	0.0763540i
$943$		−	3.70820i		−	0.120756i
$944$	6.21885	−	19.1396i	0.202406	−	0.622942i
$945$		0			0
$946$	−13.5000	−	41.5487i	−0.438923	−	1.35087i
$947$	21.4908	−	6.98278i	0.698357	−	0.226910i	0.0617423	−	0.998092i	$-0.480334\pi$
$947$	21.4908	−	6.98278i	0.698357	−	0.226910i	0.636614	+	0.771182i	$0.280334\pi$
$948$	0.0732450	−	0.100813i	0.00237889	−	0.00327426i
$949$	9.00000			0.292152
$950$		0			0
$951$	10.2918			0.333734
$952$	−16.7027	+	22.9894i	−0.541339	+	0.745089i
$953$	12.5150	−	4.06637i	0.405401	−	0.131723i	−0.0992165	−	0.995066i	$-0.531634\pi$
$953$	12.5150	−	4.06637i	0.405401	−	0.131723i	0.504617	+	0.863343i	$0.331634\pi$
$954$	−6.59017	−	20.2825i	−0.213365	−	0.656669i
$955$		0			0
$956$	4.93769	−	15.1967i	0.159696	−	0.491495i
$957$			7.68692i			0.248483i
$958$	−50.1082	−	16.2812i	−1.61892	−	0.526020i
$959$	−13.6353	+	9.90659i	−0.440305	+	0.319901i
$960$		0			0
$961$	4.11803	+	2.99193i	0.132840	+	0.0965138i
$962$	−17.1190	−	23.5623i	−0.551939	−	0.759679i
$963$	−0.151269	−	0.208204i	−0.00487458	−	0.00670928i
$964$	−9.59017	−	6.96767i	−0.308879	−	0.224413i
$965$		0			0
$966$	−1.85410	+	1.34708i	−0.0596548	+	0.0433417i
$967$	15.3557	+	4.98936i	0.493805	+	0.160447i	0.545324	−	0.838225i	$-0.316406\pi$
$967$	15.3557	+	4.98936i	0.493805	+	0.160447i	−0.0515196	+	0.998672i	$0.516406\pi$
$968$			4.47214i			0.143740i
$969$	−1.80902	+	5.56758i	−0.0581140	+	0.178856i
$970$		0			0
$971$	−15.9271	−	49.0184i	−0.511123	−	1.57308i	−0.790226	−	0.612815i	$-0.790037\pi$
$971$	−15.9271	−	49.0184i	−0.511123	−	1.57308i	0.279103	−	0.960261i	$-0.409963\pi$
$972$	5.67358	−	1.84346i	0.181980	−	0.0591290i
$973$	−21.5765	+	29.6976i	−0.691712	+	0.952060i
$974$	6.00000			0.192252
$975$		0			0
$976$	29.5623			0.946266
$977$	13.7436	−	18.9164i	0.439696	−	0.605190i	−0.530449	−	0.847717i	$-0.677976\pi$
$977$	13.7436	−	18.9164i	0.439696	−	0.605190i	0.970145	+	0.242528i	$0.0779765\pi$
$978$	−11.6699	+	3.79180i	−0.373164	+	0.121248i
$979$	−12.4377	−	38.2793i	−0.397510	−	1.22341i
$980$		0			0
$981$	−4.69756	+	14.4576i	−0.149982	+	0.461596i
$982$		−	58.6869i		−	1.87277i
$983$	5.00004	+	1.62461i	0.159477	+	0.0518171i	0.387667	−	0.921799i	$-0.373281\pi$
$983$	5.00004	+	1.62461i	0.159477	+	0.0518171i	−0.228191	+	0.973616i	$0.573281\pi$
$984$	2.07295	−	1.50609i	0.0660832	−	0.0480123i
$985$		0			0
$986$	37.1976	+	27.0256i	1.18461	+	0.860671i
$987$	5.60807	+	7.71885i	0.178507	+	0.245694i
$988$	6.37988	+	8.78115i	0.202971	+	0.279366i
$989$	9.00000	+	6.53888i	0.286183	+	0.207924i
$990$		0			0
$991$	21.6976	−	15.7642i	0.689246	−	0.500766i	−0.187166	−	0.982328i	$-0.559930\pi$
$991$	21.6976	−	15.7642i	0.689246	−	0.500766i	0.876412	+	0.481562i	$0.159930\pi$
$992$	16.3722	+	5.31966i	0.519819	+	0.168899i
$993$		−	8.05573i		−	0.255641i
$994$	4.50000	−	13.8496i	0.142731	−	0.439282i
$995$		0			0
$996$	−0.0344419	−	0.106001i	−0.00109133	−	0.00335877i
$997$	−50.2672	+	16.3328i	−1.59198	+	0.517265i	−0.965107	−	0.261856i	$-0.915665\pi$
$997$	−50.2672	+	16.3328i	−1.59198	+	0.517265i	−0.626873	+	0.779122i	$0.715665\pi$
$998$	40.2874	−	55.4508i	1.27528	−	1.75527i
$999$	−8.29180			−0.262341

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.e.d.249.1		8
5.2	odd	4		625.2.d.a.376.1		4
5.3	odd	4		625.2.d.j.376.1		4
5.4	even	2	inner	625.2.e.d.249.2		8
25.2	odd	20		625.2.d.a.251.1		4
25.3	odd	20		625.2.d.d.126.1		4
25.4	even	10		625.2.e.g.499.1		8
25.6	even	5		125.2.b.b.124.1		4
25.8	odd	20		125.2.a.a.1.1	✓	2
25.9	even	10		625.2.e.g.124.2		8
25.11	even	5	inner	625.2.e.d.374.2		8
25.12	odd	20		625.2.d.g.501.1		4
25.13	odd	20		625.2.d.d.501.1		4
25.14	even	10	inner	625.2.e.d.374.1		8
25.16	even	5		625.2.e.g.124.1		8
25.17	odd	20		125.2.a.b.1.2	yes	2
25.19	even	10		125.2.b.b.124.4		4
25.21	even	5		625.2.e.g.499.2		8
25.22	odd	20		625.2.d.g.126.1		4
25.23	odd	20		625.2.d.j.251.1		4
75.8	even	20		1125.2.a.d.1.2		2
75.17	even	20		1125.2.a.c.1.1		2
75.44	odd	10		1125.2.b.f.874.1		4
75.56	odd	10		1125.2.b.f.874.4		4
100.19	odd	10		2000.2.c.e.1249.3		4
100.31	odd	10		2000.2.c.e.1249.2		4
100.67	even	20		2000.2.a.a.1.2		2
100.83	even	20		2000.2.a.l.1.1		2
175.83	even	20		6125.2.a.d.1.1		2
175.167	even	20		6125.2.a.g.1.2		2
200.67	even	20		8000.2.a.u.1.1		2
200.83	even	20		8000.2.a.c.1.2		2
200.117	odd	20		8000.2.a.d.1.2		2
200.133	odd	20		8000.2.a.v.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.a.a.1.1	✓	2	25.8	odd	20
125.2.a.b.1.2	yes	2	25.17	odd	20
125.2.b.b.124.1		4	25.6	even	5
125.2.b.b.124.4		4	25.19	even	10
625.2.d.a.251.1		4	25.2	odd	20
625.2.d.a.376.1		4	5.2	odd	4
625.2.d.d.126.1		4	25.3	odd	20
625.2.d.d.501.1		4	25.13	odd	20
625.2.d.g.126.1		4	25.22	odd	20
625.2.d.g.501.1		4	25.12	odd	20
625.2.d.j.251.1		4	25.23	odd	20
625.2.d.j.376.1		4	5.3	odd	4
625.2.e.d.249.1		8	1.1	even	1	trivial
625.2.e.d.249.2		8	5.4	even	2	inner
625.2.e.d.374.1		8	25.14	even	10	inner
625.2.e.d.374.2		8	25.11	even	5	inner
625.2.e.g.124.1		8	25.16	even	5
625.2.e.g.124.2		8	25.9	even	10
625.2.e.g.499.1		8	25.4	even	10
625.2.e.g.499.2		8	25.21	even	5
1125.2.a.c.1.1		2	75.17	even	20
1125.2.a.d.1.2		2	75.8	even	20
1125.2.b.f.874.1		4	75.44	odd	10
1125.2.b.f.874.4		4	75.56	odd	10
2000.2.a.a.1.2		2	100.67	even	20
2000.2.a.l.1.1		2	100.83	even	20
2000.2.c.e.1249.2		4	100.31	odd	10
2000.2.c.e.1249.3		4	100.19	odd	10
6125.2.a.d.1.1		2	175.83	even	20
6125.2.a.g.1.2		2	175.167	even	20
8000.2.a.c.1.2		2	200.83	even	20
8000.2.a.d.1.2		2	200.117	odd	20
8000.2.a.u.1.1		2	200.67	even	20
8000.2.a.v.1.1		2	200.133	odd	20

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.e (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 1.30902i) q^{2} +(-0.363271 + 0.118034i) q^{3} +(-0.190983 - 0.587785i) q^{4} +(0.190983 - 0.587785i) q^{6} -3.00000i q^{7} +(-2.12663 - 0.690983i) q^{8} +(-2.30902 + 1.67760i) q^{9} +(2.42705 + 1.76336i) q^{11} +(0.138757 + 0.190983i) q^{12} +(-2.85317 - 3.92705i) q^{13} +(3.92705 + 2.85317i) q^{14} +(3.92705 - 2.85317i) q^{16} +(4.02874 + 1.30902i) q^{17} -4.61803i q^{18} +(1.11803 - 3.44095i) q^{19} +(0.354102 + 1.08981i) q^{21} +(-4.61653 + 1.50000i) q^{22} +(0.726543 - 1.00000i) q^{23} +0.854102 q^{24} +7.85410 q^{26} +(1.31433 - 1.80902i) q^{27} +(-1.76336 + 0.572949i) q^{28} +(-2.07295 - 6.37988i) q^{29} +(1.57295 - 4.84104i) q^{31} +3.38197i q^{32} +(-1.08981 - 0.354102i) q^{33} +(-5.54508 + 4.02874i) q^{34} +(1.42705 + 1.03681i) q^{36} +(-2.17963 - 3.00000i) q^{37} +(3.44095 + 4.73607i) q^{38} +(1.50000 + 1.08981i) q^{39} +(2.42705 - 1.76336i) q^{41} +(-1.76336 - 0.572949i) q^{42} +9.00000i q^{43} +(0.572949 - 1.76336i) q^{44} +(0.618034 + 1.90211i) q^{46} +(7.91872 - 2.57295i) q^{47} +(-1.08981 + 1.50000i) q^{48} -2.00000 q^{49} -1.61803 q^{51} +(-1.76336 + 2.42705i) q^{52} +(4.39201 - 1.42705i) q^{53} +(1.11803 + 3.44095i) q^{54} +(-2.07295 + 6.37988i) q^{56} +1.38197i q^{57} +(10.3229 + 3.35410i) q^{58} +(3.35410 - 2.43690i) q^{59} +(4.92705 + 3.57971i) q^{61} +(4.84104 + 6.66312i) q^{62} +(5.03280 + 6.92705i) q^{63} +(3.42705 + 2.48990i) q^{64} +(1.50000 - 1.08981i) q^{66} +(-13.1760 - 4.28115i) q^{67} -2.61803i q^{68} +(-0.145898 + 0.449028i) q^{69} +(-0.927051 - 2.85317i) q^{71} +(6.06961 - 1.97214i) q^{72} +(-1.08981 + 1.50000i) q^{73} +6.00000 q^{74} -2.23607 q^{76} +(5.29007 - 7.28115i) q^{77} +(-2.85317 + 0.927051i) q^{78} +(-0.163119 - 0.502029i) q^{79} +(2.38197 - 7.33094i) q^{81} +4.85410i q^{82} +(-0.449028 - 0.145898i) q^{83} +(0.572949 - 0.416272i) q^{84} +(-11.7812 - 8.55951i) q^{86} +(1.50609 + 2.07295i) q^{87} +(-3.94298 - 5.42705i) q^{88} +(-10.8541 - 7.88597i) q^{89} +(-11.7812 + 8.55951i) q^{91} +(-0.726543 - 0.236068i) q^{92} +1.94427i q^{93} +(-4.16312 + 12.8128i) q^{94} +(-0.399187 - 1.22857i) q^{96} +(-7.46969 + 2.42705i) q^{97} +(1.90211 - 2.61803i) q^{98} -8.56231 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{4} + 6 q^{6} - 14 q^{9} + 6 q^{11} + 18 q^{14} + 18 q^{16} - 24 q^{21} - 20 q^{24} + 36 q^{26} - 30 q^{29} + 26 q^{31} - 22 q^{34} - 2 q^{36} + 12 q^{39} + 6 q^{41} + 18 q^{44} - 4 q^{46} - 16 q^{49}+ \cdots + 12 q^{99}+O(q^{100}) \) 8 * q - 6 * q^4 + 6 * q^6 - 14 * q^9 + 6 * q^11 + 18 * q^14 + 18 * q^16 - 24 * q^21 - 20 * q^24 + 36 * q^26 - 30 * q^29 + 26 * q^31 - 22 * q^34 - 2 * q^36 + 12 * q^39 + 6 * q^41 + 18 * q^44 - 4 * q^46 - 16 * q^49 - 4 * q^51 - 30 * q^56 + 26 * q^61 + 14 * q^64 + 12 * q^66 - 28 * q^69 + 6 * q^71 + 48 * q^74 + 30 * q^79 + 28 * q^81 + 18 * q^84 - 54 * q^86 - 60 * q^89 - 54 * q^91 - 2 * q^94 + 46 * q^96 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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