LMFDB - Embedded newform 625.2.d.j.376.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [625,2,Mod(126,625)] 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("625.126"); 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([4])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [4,3,4,3,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 125)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			376.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	625.376
Dual form			625.2.d.j.251.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.30902 + 0.951057i) q^{2} +(-0.118034 - 0.363271i) q^{3} +(0.190983 + 0.587785i) q^{4} +(0.190983 - 0.587785i) q^{6} -3.00000 q^{7} +(0.690983 - 2.12663i) q^{8} +(2.30902 - 1.67760i) q^{9} +(2.42705 + 1.76336i) q^{11} +(0.190983 - 0.138757i) q^{12} +(3.92705 - 2.85317i) q^{13} +(-3.92705 - 2.85317i) q^{14} +(3.92705 - 2.85317i) q^{16} +(1.30902 - 4.02874i) q^{17} +4.61803 q^{18} +(-1.11803 + 3.44095i) q^{19} +(0.354102 + 1.08981i) q^{21} +(1.50000 + 4.61653i) q^{22} +(1.00000 + 0.726543i) q^{23} -0.854102 q^{24} +7.85410 q^{26} +(-1.80902 - 1.31433i) q^{27} +(-0.572949 - 1.76336i) q^{28} +(2.07295 + 6.37988i) q^{29} +(1.57295 - 4.84104i) q^{31} +3.38197 q^{32} +(0.354102 - 1.08981i) q^{33} +(5.54508 - 4.02874i) q^{34} +(1.42705 + 1.03681i) q^{36} +(-3.00000 + 2.17963i) q^{37} +(-4.73607 + 3.44095i) q^{38} +(-1.50000 - 1.08981i) q^{39} +(2.42705 - 1.76336i) q^{41} +(-0.572949 + 1.76336i) q^{42} -9.00000 q^{43} +(-0.572949 + 1.76336i) q^{44} +(0.618034 + 1.90211i) q^{46} +(-2.57295 - 7.91872i) q^{47} +(-1.50000 - 1.08981i) q^{48} +2.00000 q^{49} -1.61803 q^{51} +(2.42705 + 1.76336i) q^{52} +(1.42705 + 4.39201i) q^{53} +(-1.11803 - 3.44095i) q^{54} +(-2.07295 + 6.37988i) q^{56} +1.38197 q^{57} +(-3.35410 + 10.3229i) q^{58} +(-3.35410 + 2.43690i) q^{59} +(4.92705 + 3.57971i) q^{61} +(6.66312 - 4.84104i) q^{62} +(-6.92705 + 5.03280i) q^{63} +(-3.42705 - 2.48990i) q^{64} +(1.50000 - 1.08981i) q^{66} +(-4.28115 + 13.1760i) q^{67} +2.61803 q^{68} +(0.145898 - 0.449028i) q^{69} +(-0.927051 - 2.85317i) q^{71} +(-1.97214 - 6.06961i) q^{72} +(-1.50000 - 1.08981i) q^{73} -6.00000 q^{74} -2.23607 q^{76} +(-7.28115 - 5.29007i) q^{77} +(-0.927051 - 2.85317i) q^{78} +(0.163119 + 0.502029i) q^{79} +(2.38197 - 7.33094i) q^{81} +4.85410 q^{82} +(0.145898 - 0.449028i) q^{83} +(-0.572949 + 0.416272i) q^{84} +(-11.7812 - 8.55951i) q^{86} +(2.07295 - 1.50609i) q^{87} +(5.42705 - 3.94298i) q^{88} +(10.8541 + 7.88597i) q^{89} +(-11.7812 + 8.55951i) q^{91} +(-0.236068 + 0.726543i) q^{92} -1.94427 q^{93} +(4.16312 - 12.8128i) q^{94} +(-0.399187 - 1.22857i) q^{96} +(2.42705 + 7.46969i) q^{97} +(2.61803 + 1.90211i) q^{98} +8.56231 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} + 4 q^{3} + 3 q^{4} + 3 q^{6} - 12 q^{7} + 5 q^{8} + 7 q^{9} + 3 q^{11} + 3 q^{12} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 3 q^{17} + 14 q^{18} - 12 q^{21} + 6 q^{22} + 4 q^{23} + 10 q^{24} + 18 q^{26}+ \cdots - 6 q^{99}+O(q^{100}) $ 4 * q + 3 * q^2 + 4 * q^3 + 3 * q^4 + 3 * q^6 - 12 * q^7 + 5 * q^8 + 7 * q^9 + 3 * q^11 + 3 * q^12 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 3 * q^17 + 14 * q^18 - 12 * q^21 + 6 * q^22 + 4 * q^23 + 10 * q^24 + 18 * q^26 - 5 * q^27 - 9 * q^28 + 15 * q^29 + 13 * q^31 + 18 * q^32 - 12 * q^33 + 11 * q^34 - q^36 - 12 * q^37 - 10 * q^38 - 6 * q^39 + 3 * q^41 - 9 * q^42 - 36 * q^43 - 9 * q^44 - 2 * q^46 - 17 * q^47 - 6 * q^48 + 8 * q^49 - 2 * q^51 + 3 * q^52 - q^53 - 15 * q^56 + 10 * q^57 + 13 * q^61 + 11 * q^62 - 21 * q^63 - 7 * q^64 + 6 * q^66 + 3 * q^67 + 6 * q^68 + 14 * q^69 + 3 * q^71 + 10 * q^72 - 6 * q^73 - 24 * q^74 - 9 * q^77 + 3 * q^78 - 15 * q^79 + 14 * q^81 + 6 * q^82 + 14 * q^83 - 9 * q^84 - 27 * q^86 + 15 * q^87 + 15 * q^88 + 30 * q^89 - 27 * q^91 + 8 * q^92 + 28 * q^93 + q^94 + 23 * q^96 + 3 * q^97 + 6 * q^98 - 6 * q^99

Character values

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

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

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 $

$2$	1.30902	+	0.951057i	0.925615	+	0.672499i	0.944915	−	0.327315i	$-0.106144\pi$
$2$	1.30902	+	0.951057i	0.925615	+	0.672499i	−0.0193004	+	0.999814i	$0.506144\pi$
$3$	−0.118034	−	0.363271i	−0.0681470	−	0.209735i	0.911184	−	0.412000i	$-0.135170\pi$
$3$	−0.118034	−	0.363271i	−0.0681470	−	0.209735i	−0.979331	+	0.202265i	$0.935170\pi$
$4$	0.190983	+	0.587785i	0.0954915	+	0.293893i
$5$		0			0
$5$		0			0
$6$	0.190983	−	0.587785i	0.0779685	−	0.239962i
$7$	−3.00000			−1.13389			−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000			−1.13389			−0.566947	+	0.823754i	$0.691875\pi$
$8$	0.690983	−	2.12663i	0.244299	−	0.751876i
$9$	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	$0.550615\pi$
$12$	0.190983	−	0.138757i	0.0551320	−	0.0400558i
$13$	3.92705	−	2.85317i	1.08917	−	0.791327i	0.109909	−	0.993942i	$-0.464944\pi$
$13$	3.92705	−	2.85317i	1.08917	−	0.791327i	0.979259	+	0.202615i	$0.0649439\pi$
$14$	−3.92705	−	2.85317i	−1.04955	−	0.762542i
$15$		0			0
$16$	3.92705	−	2.85317i	0.981763	−	0.713292i
$17$	1.30902	−	4.02874i	0.317483	−	0.977113i	−0.657237	−	0.753684i	$-0.728275\pi$
$17$	1.30902	−	4.02874i	0.317483	−	0.977113i	0.974720	−	0.223429i	$-0.0717251\pi$
$18$	4.61803			1.08848
$19$	−1.11803	+	3.44095i	−0.256495	+	0.789409i	0.737037	+	0.675852i	$0.236224\pi$
$19$	−1.11803	+	3.44095i	−0.256495	+	0.789409i	−0.993532	+	0.113557i	$0.963776\pi$
$20$		0			0
$21$	0.354102	+	1.08981i	0.0772714	+	0.237817i
$22$	1.50000	+	4.61653i	0.319801	+	0.984247i
$23$	1.00000	+	0.726543i	0.208514	+	0.151495i	0.687141	−	0.726524i	$-0.258865\pi$
$23$	1.00000	+	0.726543i	0.208514	+	0.151495i	−0.478627	+	0.878018i	$0.658865\pi$
$24$	−0.854102			−0.174343
$25$		0			0
$26$	7.85410			1.54032
$27$	−1.80902	−	1.31433i	−0.348145	−	0.252942i
$28$	−0.572949	−	1.76336i	−0.108277	−	0.333243i
$29$	2.07295	+	6.37988i	0.384937	+	1.18471i	0.936526	+	0.350598i	$0.114022\pi$
$29$	2.07295	+	6.37988i	0.384937	+	1.18471i	−0.551589	+	0.834116i	$0.685978\pi$
$30$		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	$-0.0511157\pi$
$32$	3.38197			0.597853
$33$	0.354102	−	1.08981i	0.0616412	−	0.189712i
$34$	5.54508	−	4.02874i	0.950974	−	0.690923i
$35$		0			0
$36$	1.42705	+	1.03681i	0.237842	+	0.172802i
$37$	−3.00000	+	2.17963i	−0.493197	+	0.358329i	−0.806412	−	0.591354i	$-0.798594\pi$
$37$	−3.00000	+	2.17963i	−0.493197	+	0.358329i	0.313215	+	0.949682i	$0.398594\pi$
$38$	−4.73607	+	3.44095i	−0.768292	+	0.558197i
$39$	−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	$0.224733\pi$
$42$	−0.572949	+	1.76336i	−0.0884080	+	0.272092i
$43$	−9.00000			−1.37249			−0.686244	−	0.727372i	$-0.740742\pi$
$43$	−9.00000			−1.37249			−0.686244	+	0.727372i	$0.740742\pi$
$44$	−0.572949	+	1.76336i	−0.0863753	+	0.265836i
$45$		0			0
$46$	0.618034	+	1.90211i	0.0911241	+	0.280451i
$47$	−2.57295	−	7.91872i	−0.375303	−	1.15506i	−0.943274	−	0.332016i	$-0.892271\pi$
$47$	−2.57295	−	7.91872i	−0.375303	−	1.15506i	0.567971	−	0.823049i	$-0.307729\pi$
$48$	−1.50000	−	1.08981i	−0.216506	−	0.157301i
$49$	2.00000			0.285714
$50$		0			0
$51$	−1.61803			−0.226570
$52$	2.42705	+	1.76336i	0.336571	+	0.244533i
$53$	1.42705	+	4.39201i	0.196021	+	0.603289i	0.999963	+	0.00858231i	$0.00273187\pi$
$53$	1.42705	+	4.39201i	0.196021	+	0.603289i	−0.803943	+	0.594707i	$0.797268\pi$
$54$	−1.11803	−	3.44095i	−0.152145	−	0.468255i
$55$		0			0
$56$	−2.07295	+	6.37988i	−0.277009	+	0.852547i
$57$	1.38197			0.183046
$58$	−3.35410	+	10.3229i	−0.440415	+	1.35546i
$59$	−3.35410	+	2.43690i	−0.436667	+	0.317257i	−0.784309	−	0.620370i	$-0.786982\pi$
$59$	−3.35410	+	2.43690i	−0.436667	+	0.317257i	0.347642	+	0.937627i	$0.386982\pi$
$60$		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	$0.572515\pi$
$62$	6.66312	−	4.84104i	0.846217	−	0.614813i
$63$	−6.92705	+	5.03280i	−0.872726	+	0.634073i
$64$	−3.42705	−	2.48990i	−0.428381	−	0.311237i
$65$		0			0
$66$	1.50000	−	1.08981i	0.184637	−	0.134147i
$67$	−4.28115	+	13.1760i	−0.523026	+	1.60971i	0.245160	+	0.969483i	$0.421159\pi$
$67$	−4.28115	+	13.1760i	−0.523026	+	1.60971i	−0.768186	+	0.640226i	$0.778841\pi$
$68$	2.61803			0.317483
$69$	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	$0.956968\pi$
$72$	−1.97214	−	6.06961i	−0.232418	−	0.715310i
$73$	−1.50000	−	1.08981i	−0.175562	−	0.127553i	0.496534	−	0.868017i	$-0.334606\pi$
$73$	−1.50000	−	1.08981i	−0.175562	−	0.127553i	−0.672096	+	0.740464i	$0.734606\pi$
$74$	−6.00000			−0.697486
$75$		0			0
$76$	−2.23607			−0.256495
$77$	−7.28115	−	5.29007i	−0.829764	−	0.602859i
$78$	−0.927051	−	2.85317i	−0.104968	−	0.323058i
$79$	0.163119	+	0.502029i	0.0183523	+	0.0564826i	0.959813	−	0.280639i	$-0.0905465\pi$
$79$	0.163119	+	0.502029i	0.0183523	+	0.0564826i	−0.941461	+	0.337122i	$0.890547\pi$
$80$		0			0
$81$	2.38197	−	7.33094i	0.264663	−	0.814549i
$82$	4.85410			0.536046
$83$	0.145898	−	0.449028i	0.0160144	−	0.0492872i	−0.942730	−	0.333557i	$-0.891751\pi$
$83$	0.145898	−	0.449028i	0.0160144	−	0.0492872i	0.958744	+	0.284270i	$0.0917511\pi$
$84$	−0.572949	+	0.416272i	−0.0625139	+	0.0454190i
$85$		0			0
$86$	−11.7812	−	8.55951i	−1.27039	−	0.922996i
$87$	2.07295	−	1.50609i	0.222243	−	0.161469i
$88$	5.42705	−	3.94298i	0.578526	−	0.420323i
$89$	10.8541	+	7.88597i	1.15053	+	0.835911i	0.988552	−	0.150883i	$-0.0482117\pi$
$89$	10.8541	+	7.88597i	1.15053	+	0.835911i	0.161981	+	0.986794i	$0.448212\pi$
$90$		0			0
$91$	−11.7812	+	8.55951i	−1.23500	+	0.897280i
$92$	−0.236068	+	0.726543i	−0.0246118	+	0.0757473i
$93$	−1.94427			−0.201612
$94$	4.16312	−	12.8128i	0.429393	−	1.32154i
$95$		0			0
$96$	−0.399187	−	1.22857i	−0.0407418	−	0.125391i
$97$	2.42705	+	7.46969i	0.246430	+	0.758433i	0.995398	+	0.0958268i	$0.0305495\pi$
$97$	2.42705	+	7.46969i	0.246430	+	0.758433i	−0.748968	+	0.662606i	$0.769451\pi$
$98$	2.61803	+	1.90211i	0.264461	+	0.192142i
$99$	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	$0.547688\pi$
$102$	−2.11803	−	1.53884i	−0.209717	−	0.152368i
$103$	3.92705	+	12.0862i	0.386944	+	1.19089i	0.935060	+	0.354489i	$0.115345\pi$
$103$	3.92705	+	12.0862i	0.386944	+	1.19089i	−0.548116	+	0.836402i	$0.684655\pi$
$104$	−3.35410	−	10.3229i	−0.328897	−	1.01224i
$105$		0			0
$106$	−2.30902	+	7.10642i	−0.224272	+	0.690237i
$107$	0.0901699			0.00871706			0.00435853	−	0.999991i	$-0.498613\pi$
$107$	0.0901699			0.00871706			0.00435853	+	0.999991i	$0.498613\pi$
$108$	0.427051	−	1.31433i	0.0410930	−	0.126471i
$109$	−4.30902	+	3.13068i	−0.412729	+	0.299865i	−0.774706	−	0.632322i	$-0.782102\pi$
$109$	−4.30902	+	3.13068i	−0.412729	+	0.299865i	0.361977	+	0.932187i	$0.382102\pi$
$110$		0			0
$111$	1.14590	+	0.832544i	0.108764	+	0.0790215i
$112$	−11.7812	+	8.55951i	−1.11321	+	0.808798i
$113$	−1.66312	+	1.20833i	−0.156453	+	0.113670i	−0.663258	−	0.748391i	$-0.730827\pi$
$113$	−1.66312	+	1.20833i	−0.156453	+	0.113670i	0.506804	+	0.862061i	$0.330827\pi$
$114$	1.80902	+	1.31433i	0.169430	+	0.123098i
$115$		0			0
$116$	−3.35410	+	2.43690i	−0.311421	+	0.226260i
$117$	4.28115	−	13.1760i	0.395793	−	1.21812i
$118$	−6.70820			−0.617540
$119$	−3.92705	+	12.0862i	−0.359992	+	1.10794i
$120$		0			0
$121$	−0.618034	−	1.90211i	−0.0561849	−	0.172919i
$122$	3.04508	+	9.37181i	0.275689	+	0.848484i
$123$	−0.927051	−	0.673542i	−0.0835894	−	0.0607312i
$124$	3.14590			0.282510
$125$		0			0
$126$	−13.8541			−1.23422
$127$	7.85410	+	5.70634i	0.696939	+	0.506356i	0.878934	−	0.476944i	$-0.158255\pi$
$127$	7.85410	+	5.70634i	0.696939	+	0.506356i	−0.181995	+	0.983299i	$0.558255\pi$
$128$	−4.20820	−	12.9515i	−0.371956	−	1.14476i
$129$	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	$0.919920\pi$
$132$	0.708204			0.0616412
$133$	3.35410	−	10.3229i	0.290838	−	0.895106i
$134$	−18.1353	+	13.1760i	−1.56665	+	1.13824i
$135$		0			0
$136$	−7.66312	−	5.56758i	−0.657107	−	0.477416i
$137$	−4.54508	+	3.30220i	−0.388313	+	0.282126i	−0.764764	−	0.644311i	$-0.777144\pi$
$137$	−4.54508	+	3.30220i	−0.388313	+	0.282126i	0.376451	+	0.926437i	$0.377144\pi$
$138$	0.618034	−	0.449028i	0.0526105	−	0.0382238i
$139$	9.89919	+	7.19218i	0.839638	+	0.610033i	0.922270	−	0.386547i	$-0.126332\pi$
$139$	9.89919	+	7.19218i	0.839638	+	0.610033i	−0.0826315	+	0.996580i	$0.526332\pi$
$140$		0			0
$141$	−2.57295	+	1.86936i	−0.216681	+	0.157428i
$142$	1.50000	−	4.61653i	0.125877	−	0.387410i
$143$	14.5623			1.21776
$144$	4.28115	−	13.1760i	0.356763	−	1.09800i
$145$		0			0
$146$	−0.927051	−	2.85317i	−0.0767233	−	0.236130i
$147$	−0.236068	−	0.726543i	−0.0194706	−	0.0599242i
$148$	−1.85410	−	1.34708i	−0.152406	−	0.110730i
$149$	−15.0000			−1.22885			−0.614424	−	0.788976i	$-0.710612\pi$
$149$	−15.0000			−1.22885			−0.614424	+	0.788976i	$0.710612\pi$
$150$		0			0
$151$	−21.0902			−1.71629			−0.858147	−	0.513404i	$-0.828384\pi$
$151$	−21.0902			−1.71629			−0.858147	+	0.513404i	$0.828384\pi$
$152$	6.54508	+	4.75528i	0.530876	+	0.385704i
$153$	−3.73607	−	11.4984i	−0.302043	−	0.929593i
$154$	−4.50000	−	13.8496i	−0.362620	−	1.11603i
$155$		0			0
$156$	0.354102	−	1.08981i	0.0283508	−	0.0872549i
$157$	−12.2705			−0.979293			−0.489647	−	0.871921i	$-0.662874\pi$
$157$	−12.2705			−0.979293			−0.489647	+	0.871921i	$0.662874\pi$
$158$	−0.263932	+	0.812299i	−0.0209973	+	0.0646231i
$159$	1.42705	−	1.03681i	0.113173	−	0.0822246i
$160$		0			0
$161$	−3.00000	−	2.17963i	−0.236433	−	0.171779i
$162$	10.0902	−	7.33094i	0.792759	−	0.575973i
$163$	16.0623	−	11.6699i	1.25810	−	0.914061i	0.259434	−	0.965761i	$-0.416464\pi$
$163$	16.0623	−	11.6699i	1.25810	−	0.914061i	0.998663	+	0.0516999i	$0.0164639\pi$
$164$	1.50000	+	1.08981i	0.117130	+	0.0851002i
$165$		0			0
$166$	0.618034	−	0.449028i	0.0479687	−	0.0348513i
$167$	2.85410	−	8.78402i	0.220857	−	0.679728i	−0.777829	−	0.628476i	$-0.783679\pi$
$167$	2.85410	−	8.78402i	0.220857	−	0.679728i	0.998686	−	0.0512518i	$-0.0163211\pi$
$168$	2.56231			0.197686
$169$	3.26393	−	10.0453i	0.251072	−	0.772719i
$170$		0			0
$171$	3.19098	+	9.82084i	0.244021	+	0.751018i
$172$	−1.71885	−	5.29007i	−0.131061	−	0.403364i
$173$	0.0450850	+	0.0327561i	0.00342775	+	0.00249040i	0.589498	−	0.807770i	$-0.299326\pi$
$173$	0.0450850	+	0.0327561i	0.00342775	+	0.00249040i	−0.586070	+	0.810260i	$0.699326\pi$
$174$	4.14590			0.314300
$175$		0			0
$176$	14.5623			1.09768
$177$	1.28115	+	0.930812i	0.0962974	+	0.0699641i
$178$	6.70820	+	20.6457i	0.502801	+	1.54746i
$179$	2.07295	+	6.37988i	0.154939	+	0.476855i	0.998155	−	0.0607213i	$-0.0193401\pi$
$179$	2.07295	+	6.37988i	0.154939	+	0.476855i	−0.843215	+	0.537576i	$0.819340\pi$
$180$		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	$-0.136144\pi$
$182$	−23.5623			−1.74655
$183$	0.718847	−	2.21238i	0.0531387	−	0.163544i
$184$	2.23607	−	1.62460i	0.164845	−	0.119767i
$185$		0			0
$186$	−2.54508	−	1.84911i	−0.186615	−	0.135584i
$187$	10.2812	−	7.46969i	0.751832	−	0.546238i
$188$	4.16312	−	3.02468i	0.303627	−	0.220598i
$189$	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	$0.442949\pi$
$192$	−0.500000	+	1.53884i	−0.0360844	+	0.111056i
$193$	15.2705			1.09920			0.549598	−	0.835429i	$-0.314781\pi$
$193$	15.2705			1.09920			0.549598	+	0.835429i	$0.314781\pi$
$194$	−3.92705	+	12.0862i	−0.281946	+	0.867740i
$195$		0			0
$196$	0.381966	+	1.17557i	0.0272833	+	0.0839693i
$197$	−1.25329	−	3.85723i	−0.0892931	−	0.274816i	0.896431	−	0.443183i	$-0.146151\pi$
$197$	−1.25329	−	3.85723i	−0.0892931	−	0.274816i	−0.985724	+	0.168367i	$0.946151\pi$
$198$	11.2082	+	8.14324i	0.796532	+	0.578715i
$199$	16.1803			1.14699			0.573497	−	0.819208i	$-0.305586\pi$
$199$	16.1803			1.14699			0.573497	+	0.819208i	$0.305586\pi$
$200$		0			0
$201$	5.29180			0.373255
$202$	−3.92705	−	2.85317i	−0.276306	−	0.200748i
$203$	−6.21885	−	19.1396i	−0.436477	−	1.34334i
$204$	−0.309017	−	0.951057i	−0.0216355	−	0.0665873i
$205$		0			0
$206$	−6.35410	+	19.5559i	−0.442711	+	1.36253i
$207$	3.52786			0.245204
$208$	7.28115	−	22.4091i	0.504857	−	1.55379i
$209$	−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	$0.654038\pi$
$212$	−2.30902	+	1.67760i	−0.158584	+	0.115218i
$213$	−0.927051	+	0.673542i	−0.0635205	+	0.0461503i
$214$	0.118034	+	0.0857567i	0.00806864	+	0.00586221i
$215$		0			0
$216$	−4.04508	+	2.93893i	−0.275233	+	0.199969i
$217$	−4.71885	+	14.5231i	−0.320336	+	0.985893i
$218$	−8.61803			−0.583687
$219$	−0.218847	+	0.673542i	−0.0147883	+	0.0455137i
$220$		0			0
$221$	−6.35410	−	19.5559i	−0.427423	−	1.31547i
$222$	0.708204	+	2.17963i	0.0475315	+	0.146287i
$223$	−1.50000	−	1.08981i	−0.100447	−	0.0729793i	0.536428	−	0.843946i	$-0.319773\pi$
$223$	−1.50000	−	1.08981i	−0.100447	−	0.0729793i	−0.636875	+	0.770967i	$0.719773\pi$
$224$	−10.1459			−0.677901
$225$		0			0
$226$	−3.32624			−0.221258
$227$	5.35410	+	3.88998i	0.355364	+	0.258187i	0.751116	−	0.660170i	$-0.229516\pi$
$227$	5.35410	+	3.88998i	0.355364	+	0.258187i	−0.395752	+	0.918358i	$0.629516\pi$
$228$	0.263932	+	0.812299i	0.0174793	+	0.0537958i
$229$	−0.427051	−	1.31433i	−0.0282203	−	0.0868532i	0.935954	−	0.352121i	$-0.114540\pi$
$229$	−0.427051	−	1.31433i	−0.0282203	−	0.0868532i	−0.964175	+	0.265268i	$0.914540\pi$
$230$		0			0
$231$	−1.06231	+	3.26944i	−0.0698946	+	0.215113i
$232$	15.0000			0.984798
$233$	−8.30902	+	25.5725i	−0.544342	+	1.67531i	0.178208	+	0.983993i	$0.442970\pi$
$233$	−8.30902	+	25.5725i	−0.544342	+	1.67531i	−0.722550	+	0.691319i	$0.757030\pi$
$234$	18.1353	−	13.1760i	1.18554	−	0.861344i
$235$		0			0
$236$	−2.07295	−	1.50609i	−0.134937	−	0.0980378i
$237$	0.163119	−	0.118513i	0.0105957	−	0.00769824i
$238$	−16.6353	+	12.0862i	−1.07830	+	0.783433i
$239$	−20.9164	−	15.1967i	−1.35297	−	0.982990i	−0.998858	−	0.0477873i	$-0.984783\pi$
$239$	−20.9164	−	15.1967i	−1.35297	−	0.982990i	−0.354112	−	0.935203i	$-0.615217\pi$
$240$		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	$0.0880415\pi$
$242$	1.00000	−	3.07768i	0.0642824	−	0.197841i
$243$	−9.65248			−0.619207
$244$	−1.16312	+	3.57971i	−0.0744611	+	0.229168i
$245$		0			0
$246$	−0.572949	−	1.76336i	−0.0365299	−	0.112427i
$247$	5.42705	+	16.7027i	0.345315	+	1.06277i
$248$	−9.20820	−	6.69015i	−0.584722	−	0.424825i
$249$	−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	$0.436589\pi$
$252$	−4.28115	−	3.11044i	−0.269687	−	0.195939i
$253$	1.14590	+	3.52671i	0.0720420	+	0.221722i
$254$	4.85410	+	14.9394i	0.304573	+	0.937381i
$255$		0			0
$256$	4.19098	−	12.8985i	0.261936	−	0.806157i
$257$	29.3607			1.83147			0.915734	−	0.401784i	$-0.131610\pi$
$257$	29.3607			1.83147			0.915734	+	0.401784i	$0.131610\pi$
$258$	−1.71885	+	5.29007i	−0.107011	+	0.329345i
$259$	9.00000	−	6.53888i	0.559233	−	0.406306i
$260$		0			0
$261$	15.4894	+	11.2537i	0.958767	+	0.696585i
$262$	−16.0623	+	11.6699i	−0.992333	+	0.720972i
$263$	−13.2082	+	9.59632i	−0.814453	+	0.591735i	−0.915118	−	0.403186i	$-0.867903\pi$
$263$	−13.2082	+	9.59632i	−0.814453	+	0.591735i	0.100665	+	0.994920i	$0.467903\pi$
$264$	−2.07295	−	1.50609i	−0.127581	−	0.0926932i
$265$		0			0
$266$	14.2082	−	10.3229i	0.871161	−	0.632935i
$267$	1.58359	−	4.87380i	0.0969143	−	0.298271i
$268$	−8.56231			−0.523026
$269$	0.791796	−	2.43690i	0.0482767	−	0.148580i	−0.924012	−	0.382363i	$-0.875110\pi$
$269$	0.791796	−	2.43690i	0.0482767	−	0.148580i	0.972289	+	0.233783i	$0.0751104\pi$
$270$		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	$0.691091\pi$
$272$	−6.35410	−	19.5559i	−0.385274	−	1.18575i
$273$	4.50000	+	3.26944i	0.272352	+	0.197876i
$274$	−9.09017			−0.549157
$275$		0			0
$276$	0.291796			0.0175641
$277$	−4.28115	−	3.11044i	−0.257230	−	0.186888i	0.451695	−	0.892172i	$-0.350819\pi$
$277$	−4.28115	−	3.11044i	−0.257230	−	0.186888i	−0.708925	+	0.705284i	$0.750819\pi$
$278$	6.11803	+	18.8294i	0.366935	+	1.12931i
$279$	−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	$-0.0165174\pi$
$282$	−5.14590			−0.306434
$283$	−4.85410	+	14.9394i	−0.288546	+	0.888055i	0.696767	+	0.717298i	$0.254621\pi$
$283$	−4.85410	+	14.9394i	−0.288546	+	0.888055i	−0.985313	+	0.170757i	$0.945379\pi$
$284$	1.50000	−	1.08981i	0.0890086	−	0.0646686i
$285$		0			0
$286$	19.0623	+	13.8496i	1.12718	+	0.818943i
$287$	−7.28115	+	5.29007i	−0.429793	+	0.312263i
$288$	7.80902	−	5.67358i	0.460151	−	0.334319i
$289$	−0.763932	−	0.555029i	−0.0449372	−	0.0326488i
$290$		0			0
$291$	2.42705	−	1.76336i	0.142276	−	0.103370i
$292$	0.354102	−	1.08981i	0.0207223	−	0.0637765i
$293$	−21.3607			−1.24790			−0.623952	−	0.781463i	$-0.714474\pi$
$293$	−21.3607			−1.24790			−0.623952	+	0.781463i	$0.714474\pi$
$294$	0.381966	−	1.17557i	0.0222767	−	0.0685607i
$295$		0			0
$296$	2.56231	+	7.88597i	0.148931	+	0.458363i
$297$	−2.07295	−	6.37988i	−0.120285	−	0.370198i
$298$	−19.6353	−	14.2658i	−1.13744	−	0.826398i
$299$	6.00000			0.346989
$300$		0			0
$301$	27.0000			1.55625
$302$	−27.6074	−	20.0579i	−1.58863	−	1.15420i
$303$	0.354102	+	1.08981i	0.0203426	+	0.0626082i
$304$	5.42705	+	16.7027i	0.311263	+	0.957968i
$305$		0			0
$306$	6.04508	−	18.6049i	0.345575	−	1.06357i
$307$	6.27051			0.357877			0.178938	−	0.983860i	$-0.442734\pi$
$307$	6.27051			0.357877			0.178938	+	0.983860i	$0.442734\pi$
$308$	1.71885	−	5.29007i	0.0979404	−	0.301430i
$309$	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	$0.906056\pi$
$312$	−3.35410	+	2.43690i	−0.189889	+	0.137962i
$313$	−15.7082	+	11.4127i	−0.887880	+	0.645083i	−0.935324	−	0.353791i	$-0.884892\pi$
$313$	−15.7082	+	11.4127i	−0.887880	+	0.645083i	0.0474443	+	0.998874i	$0.484892\pi$
$314$	−16.0623	−	11.6699i	−0.906448	−	0.658573i
$315$		0			0
$316$	−0.263932	+	0.191758i	−0.0148473	+	0.0107872i
$317$	−8.32624	+	25.6255i	−0.467648	+	1.43927i	0.387973	+	0.921671i	$0.373175\pi$
$317$	−8.32624	+	25.6255i	−0.467648	+	1.43927i	−0.855621	+	0.517602i	$0.826825\pi$
$318$	2.85410			0.160050
$319$	−6.21885	+	19.1396i	−0.348189	+	1.07161i
$320$		0			0
$321$	−0.0106431	−	0.0327561i	−0.000594041	−	0.00182827i
$322$	−1.85410	−	5.70634i	−0.103325	−	0.318002i
$323$	12.3992	+	9.00854i	0.689909	+	0.501248i
$324$	4.76393			0.264663
$325$		0			0
$326$	32.1246			1.77922
$327$	1.64590	+	1.19581i	0.0910184	+	0.0661287i
$328$	−2.07295	−	6.37988i	−0.114459	−	0.352270i
$329$	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	$0.903205\pi$
$332$	0.291796			0.0160144
$333$	−3.27051	+	10.0656i	−0.179223	+	0.551591i
$334$	12.0902	−	8.78402i	0.661545	−	0.480640i
$335$		0			0
$336$	4.50000	+	3.26944i	0.245495	+	0.178363i
$337$	24.1353	−	17.5353i	1.31473	−	0.955208i	0.314749	−	0.949175i	$-0.398080\pi$
$337$	24.1353	−	17.5353i	1.31473	−	0.955208i	0.999982	−	0.00603323i	$-0.00192045\pi$
$338$	13.8262	−	10.0453i	0.752048	−	0.546395i
$339$	0.635255	+	0.461540i	0.0345023	+	0.0250674i
$340$		0			0
$341$	12.3541	−	8.97578i	0.669012	−	0.486066i
$342$	−5.16312	+	15.8904i	−0.279189	+	0.859257i
$343$	15.0000			0.809924
$344$	−6.21885	+	19.1396i	−0.335298	+	1.03194i
$345$		0			0
$346$	0.0278640	+	0.0857567i	0.00149798	+	0.00461031i
$347$	4.92705	+	15.1639i	0.264498	+	0.814041i	0.991809	+	0.127733i	$0.0407699\pi$
$347$	4.92705	+	15.1639i	0.264498	+	0.814041i	−0.727311	+	0.686308i	$0.759230\pi$
$348$	1.28115	+	0.930812i	0.0686770	+	0.0498968i
$349$	−17.3607			−0.929296			−0.464648	−	0.885496i	$-0.653819\pi$
$349$	−17.3607			−0.929296			−0.464648	+	0.885496i	$0.653819\pi$
$350$		0			0
$351$	−10.8541			−0.579349
$352$	8.20820	+	5.96361i	0.437499	+	0.317861i
$353$	1.20163	+	3.69822i	0.0639561	+	0.196837i	0.977929	−	0.208940i	$-0.0670012\pi$
$353$	1.20163	+	3.69822i	0.0639561	+	0.196837i	−0.913972	+	0.405776i	$0.867001\pi$
$354$	0.791796	+	2.43690i	0.0420835	+	0.129520i
$355$		0			0
$356$	−2.56231	+	7.88597i	−0.135802	+	0.417955i
$357$	4.85410			0.256906
$358$	−3.35410	+	10.3229i	−0.177270	+	0.545580i
$359$	8.78115	−	6.37988i	0.463452	−	0.336717i	−0.331432	−	0.943479i	$-0.607532\pi$
$359$	8.78115	−	6.37988i	0.463452	−	0.336717i	0.794884	+	0.606762i	$0.207532\pi$
$360$		0			0
$361$	4.78115	+	3.47371i	0.251640	+	0.182827i
$362$	23.7984	−	17.2905i	1.25081	−	0.908770i
$363$	−0.618034	+	0.449028i	−0.0324384	+	0.0235679i
$364$	−7.28115	−	5.29007i	−0.381636	−	0.277275i
$365$		0			0
$366$	3.04508	−	2.21238i	0.159169	−	0.115643i
$367$	0.354102	−	1.08981i	0.0184840	−	0.0568878i	−0.941389	−	0.337323i	$-0.890479\pi$
$367$	0.354102	−	1.08981i	0.0184840	−	0.0568878i	0.959873	+	0.280435i	$0.0904787\pi$
$368$	6.00000			0.312772
$369$	2.64590	−	8.14324i	0.137740	−	0.423920i
$370$		0			0
$371$	−4.28115	−	13.1760i	−0.222266	−	0.684066i
$372$	−0.371323	−	1.14281i	−0.0192522	−	0.0592522i
$373$	−1.50000	−	1.08981i	−0.0776671	−	0.0564284i	0.548274	−	0.836299i	$-0.315285\pi$
$373$	−1.50000	−	1.08981i	−0.0776671	−	0.0564284i	−0.625941	+	0.779870i	$0.715285\pi$
$374$	20.5623			1.06325
$375$		0			0
$376$	−18.6180			−0.960152
$377$	26.3435	+	19.1396i	1.35676	+	0.985742i
$378$	3.35410	+	10.3229i	0.172516	+	0.530951i
$379$	−2.33688	−	7.19218i	−0.120038	−	0.369437i	0.872927	−	0.487851i	$-0.162219\pi$
$379$	−2.33688	−	7.19218i	−0.120038	−	0.369437i	−0.992964	+	0.118414i	$0.962219\pi$
$380$		0			0
$381$	1.14590	−	3.52671i	0.0587061	−	0.180679i
$382$	−19.4164			−0.993430
$383$	10.9615	−	33.7360i	0.560106	−	1.72383i	−0.121956	−	0.992535i	$-0.538917\pi$
$383$	10.9615	−	33.7360i	0.560106	−	1.72383i	0.682062	−	0.731294i	$-0.261083\pi$
$384$	−4.20820	+	3.05744i	−0.214749	+	0.156024i
$385$		0			0
$386$	19.9894	+	14.5231i	1.01743	+	0.739207i
$387$	−20.7812	+	15.0984i	−1.05637	+	0.767494i
$388$	−3.92705	+	2.85317i	−0.199366	+	0.144848i
$389$	−1.28115	−	0.930812i	−0.0649570	−	0.0471940i	0.554833	−	0.831962i	$-0.312782\pi$
$389$	−1.28115	−	0.930812i	−0.0649570	−	0.0471940i	−0.619790	+	0.784768i	$0.712782\pi$
$390$		0			0
$391$	4.23607	−	3.07768i	0.214227	−	0.155645i
$392$	1.38197	−	4.25325i	0.0697998	−	0.214822i
$393$	4.68692			0.236424
$394$	2.02786	−	6.24112i	0.102162	−	0.314423i
$395$		0			0
$396$	1.63525	+	5.03280i	0.0821747	+	0.252908i
$397$	−5.07295	−	15.6129i	−0.254604	−	0.783591i	−0.993907	−	0.110218i	$-0.964845\pi$
$397$	−5.07295	−	15.6129i	−0.254604	−	0.783591i	0.739303	−	0.673372i	$-0.235155\pi$
$398$	21.1803	+	15.3884i	1.06167	+	0.771352i
$399$	−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	$0.403138\pi$
$402$	6.92705	+	5.03280i	0.345490	+	0.251013i
$403$	−7.63525	−	23.4989i	−0.380339	−	1.17056i
$404$	−0.572949	−	1.76336i	−0.0285053	−	0.0877302i
$405$		0			0
$406$	10.0623	−	30.9686i	0.499384	−	1.53695i
$407$	−11.1246			−0.551427
$408$	−1.11803	+	3.44095i	−0.0553509	+	0.170353i
$409$	18.4164	−	13.3803i	0.910633	−	0.661613i	−0.0305421	−	0.999533i	$-0.509723\pi$
$409$	18.4164	−	13.3803i	0.910633	−	0.661613i	0.941175	+	0.337920i	$0.109723\pi$
$410$		0			0
$411$	1.73607	+	1.26133i	0.0856339	+	0.0622167i
$412$	−6.35410	+	4.61653i	−0.313044	+	0.227440i
$413$	10.0623	−	7.31069i	0.495134	−	0.359736i
$414$	4.61803	+	3.35520i	0.226964	+	0.164899i
$415$		0			0
$416$	13.2812	−	9.64932i	0.651162	−	0.473097i
$417$	1.44427	−	4.44501i	0.0707263	−	0.217673i
$418$	−17.5623			−0.859000
$419$	−2.07295	+	6.37988i	−0.101270	+	0.311678i	−0.988837	−	0.149001i	$-0.952394\pi$
$419$	−2.07295	+	6.37988i	−0.101270	+	0.311678i	0.887567	+	0.460679i	$0.152394\pi$
$420$		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	$0.830334\pi$
$422$	2.09017	+	6.43288i	0.101748	+	0.313148i
$423$	−19.2254	−	13.9681i	−0.934772	−	0.679152i
$424$	10.3262			0.501486
$425$		0			0
$426$	−1.85410			−0.0898315
$427$	−14.7812	−	10.7391i	−0.715310	−	0.519703i
$428$	0.0172209	+	0.0530006i	0.000832405	+	0.00256188i
$429$	−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	$0.195495\pi$
$432$	−10.8541			−0.522218
$433$	4.41641	−	13.5923i	0.212239	−	0.653205i	−0.787099	−	0.616827i	$-0.788418\pi$
$433$	4.41641	−	13.5923i	0.212239	−	0.653205i	0.999338	−	0.0363780i	$-0.0115820\pi$
$434$	−19.9894	+	14.5231i	−0.959520	+	0.697132i
$435$		0			0
$436$	−2.66312	−	1.93487i	−0.127540	−	0.0926634i
$437$	−3.61803	+	2.62866i	−0.173074	+	0.125746i
$438$	−0.927051	+	0.673542i	−0.0442962	+	0.0321831i
$439$	−24.3713	−	17.7068i	−1.16318	−	0.845100i	−0.173003	−	0.984921i	$-0.555347\pi$
$439$	−24.3713	−	17.7068i	−1.16318	−	0.845100i	−0.990177	+	0.139822i	$0.955347\pi$
$440$		0			0
$441$	4.61803	−	3.35520i	0.219906	−	0.159771i
$442$	10.2812	−	31.6421i	0.489025	−	1.50506i
$443$	7.18034			0.341148			0.170574	−	0.985345i	$-0.445438\pi$
$443$	7.18034			0.341148			0.170574	+	0.985345i	$0.445438\pi$
$444$	−0.270510	+	0.832544i	−0.0128378	+	0.0395108i
$445$		0			0
$446$	−0.927051	−	2.85317i	−0.0438971	−	0.135101i
$447$	1.77051	+	5.44907i	0.0837422	+	0.257732i
$448$	10.2812	+	7.46969i	0.485739	+	0.352910i
$449$	−39.2705			−1.85329			−0.926645	−	0.375938i	$-0.877321\pi$
$449$	−39.2705			−1.85329			−0.926645	+	0.375938i	$0.877321\pi$
$450$		0			0
$451$	9.00000			0.423793
$452$	−1.02786	−	0.746787i	−0.0483467	−	0.0351259i
$453$	2.48936	+	7.66145i	0.116960	+	0.359966i
$454$	3.30902	+	10.1841i	0.155300	+	0.477964i
$455$		0			0
$456$	0.954915	−	2.93893i	0.0447180	−	0.137628i
$457$	−18.0000			−0.842004			−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000			−0.842004			−0.421002	+	0.907060i	$0.638322\pi$
$458$	0.690983	−	2.12663i	0.0322875	−	0.0993708i
$459$	−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	$-0.620187\pi$
$462$	−4.50000	+	3.26944i	−0.209359	+	0.152108i
$463$	11.4271	−	8.30224i	0.531060	−	0.385838i	−0.289694	−	0.957119i	$-0.593554\pi$
$463$	11.4271	−	8.30224i	0.531060	−	0.385838i	0.820754	+	0.571282i	$0.193554\pi$
$464$	26.3435	+	19.1396i	1.22296	+	0.888536i
$465$		0			0
$466$	−35.1976	+	25.5725i	−1.63050	+	1.18462i
$467$	12.1246	−	37.3157i	0.561060	−	1.72677i	−0.118317	−	0.992976i	$-0.537750\pi$
$467$	12.1246	−	37.3157i	0.561060	−	1.72677i	0.679377	−	0.733790i	$-0.262250\pi$
$468$	8.56231			0.395793
$469$	12.8435	−	39.5281i	0.593056	−	1.82524i
$470$		0			0
$471$	1.44834	+	4.45752i	0.0667359	+	0.205392i
$472$	2.86475	+	8.81678i	0.131861	+	0.405825i
$473$	−21.8435	−	15.8702i	−1.00436	−	0.729713i
$474$	0.326238			0.0149846
$475$		0			0
$476$	−7.85410			−0.359992
$477$	10.6631	+	7.74721i	0.488231	+	0.354720i
$478$	−12.9271	−	39.7854i	−0.591270	−	1.81974i
$479$	−10.0623	−	30.9686i	−0.459758	−	1.41499i	−0.865457	−	0.500984i	$-0.832972\pi$
$479$	−10.0623	−	30.9686i	−0.459758	−	1.41499i	0.405698	−	0.914007i	$-0.367028\pi$
$480$		0			0
$481$	−5.56231	+	17.1190i	−0.253619	+	0.780560i
$482$	31.0344			1.41358
$483$	−0.437694	+	1.34708i	−0.0199158	+	0.0612944i
$484$	1.00000	−	0.726543i	0.0454545	−	0.0330247i
$485$		0			0
$486$	−12.6353	−	9.18005i	−0.573147	−	0.416416i
$487$	−3.00000	+	2.17963i	−0.135943	+	0.0987684i	−0.653679	−	0.756772i	$-0.726775\pi$
$487$	−3.00000	+	2.17963i	−0.135943	+	0.0987684i	0.517736	+	0.855541i	$0.326775\pi$
$488$	11.0172	−	8.00448i	0.498726	−	0.362346i
$489$	−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	$0.994843\pi$
$492$	0.218847	−	0.673542i	0.00986639	−	0.0303656i
$493$	28.4164			1.27981
$494$	−8.78115	+	27.0256i	−0.395083	+	1.21594i
$495$		0			0
$496$	−7.63525	−	23.4989i	−0.342833	−	1.05513i
$497$	2.78115	+	8.55951i	0.124752	+	0.383946i
$498$	−0.236068	−	0.171513i	−0.0105785	−	0.00768570i
$499$	42.3607			1.89632			0.948162	−	0.317787i	$-0.102940\pi$
$499$	42.3607			1.89632			0.948162	+	0.317787i	$0.102940\pi$
$500$		0			0
$501$	−3.52786			−0.157613
$502$	8.20820	+	5.96361i	0.366350	+	0.266169i
$503$	7.97214	+	24.5357i	0.355460	+	1.09399i	0.955742	+	0.294205i	$0.0950549\pi$
$503$	7.97214	+	24.5357i	0.355460	+	1.09399i	−0.600282	+	0.799788i	$0.704945\pi$
$504$	5.91641	+	18.2088i	0.263538	+	0.811086i
$505$		0			0
$506$	−1.85410	+	5.70634i	−0.0824249	+	0.253678i
$507$	−4.03444			−0.179176
$508$	−1.85410	+	5.70634i	−0.0822625	+	0.253178i
$509$	−10.8541	+	7.88597i	−0.481100	+	0.349539i	−0.801751	−	0.597658i	$-0.796098\pi$
$509$	−10.8541	+	7.88597i	−0.481100	+	0.349539i	0.320652	+	0.947197i	$0.396098\pi$
$510$		0			0
$511$	4.50000	+	3.26944i	0.199068	+	0.144632i
$512$	−4.28115	+	3.11044i	−0.189202	+	0.137463i
$513$	6.54508	−	4.75528i	0.288973	−	0.209951i
$514$	38.4336	+	27.9237i	1.69523	+	1.23166i
$515$		0			0
$516$	−1.71885	+	1.24882i	−0.0756680	+	0.0549760i
$517$	7.71885	−	23.7562i	0.339475	−	1.04480i
$518$	18.0000			0.790875
$519$	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	$0.856139\pi$
$522$	9.57295	+	29.4625i	0.418997	+	1.28954i
$523$	30.2705	+	21.9928i	1.32364	+	0.961679i	0.999879	+	0.0155385i	$0.00494627\pi$
$523$	30.2705	+	21.9928i	1.32364	+	0.961679i	0.323758	+	0.946140i	$0.395054\pi$
$524$	−7.58359			−0.331291
$525$		0			0
$526$	−26.4164			−1.15181
$527$	−17.4443	−	12.6740i	−0.759884	−	0.552088i
$528$	−1.71885	−	5.29007i	−0.0748032	−	0.230221i
$529$	−6.63525	−	20.4212i	−0.288489	−	0.887879i
$530$		0			0
$531$	−3.65654	+	11.2537i	−0.158680	+	0.488368i
$532$	6.70820			0.290838
$533$	4.50000	−	13.8496i	0.194917	−	0.599892i
$534$	6.70820	−	4.87380i	0.290292	−	0.210910i
$535$		0			0
$536$	25.0623	+	18.2088i	1.08253	+	0.786502i
$537$	2.07295	−	1.50609i	0.0894544	−	0.0649924i
$538$	3.35410	−	2.43690i	0.144606	−	0.105062i
$539$	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	$0.0372930\pi$
$542$	−10.0451	+	30.9156i	−0.431473	+	1.32794i
$543$	−6.94427			−0.298007
$544$	4.42705	−	13.6251i	0.189808	−	0.584170i
$545$		0			0
$546$	2.78115	+	8.55951i	0.119022	+	0.366313i
$547$	−6.84346	−	21.0620i	−0.292605	−	0.900546i	−0.984015	−	0.178084i	$-0.943010\pi$
$547$	−6.84346	−	21.0620i	−0.292605	−	0.900546i	0.691410	−	0.722462i	$-0.256990\pi$
$548$	−2.80902	−	2.04087i	−0.119995	−	0.0871817i
$549$	17.3820			0.741844
$550$		0			0
$551$	−24.2705			−1.03396
$552$	−0.854102	−	0.620541i	−0.0363530	−	0.0264120i
$553$	−0.489357	−	1.50609i	−0.0208096	−	0.0640453i
$554$	−2.64590	−	8.14324i	−0.112413	−	0.345973i
$555$		0			0
$556$	−2.33688	+	7.19218i	−0.0991058	+	0.305016i
$557$	−40.3607			−1.71014			−0.855068	−	0.518515i	$-0.826485\pi$
$557$	−40.3607			−1.71014			−0.855068	+	0.518515i	$0.826485\pi$
$558$	7.26393	−	22.3561i	0.307507	−	0.946409i
$559$	−35.3435	+	25.6785i	−1.49487	+	1.08609i
$560$		0			0
$561$	−3.92705	−	2.85317i	−0.165800	−	0.120461i
$562$	15.7082	−	11.4127i	0.662611	−	0.481415i
$563$	−5.70820	+	4.14725i	−0.240572	+	0.174786i	−0.701538	−	0.712632i	$-0.747503\pi$
$563$	−5.70820	+	4.14725i	−0.240572	+	0.174786i	0.460966	+	0.887418i	$0.347503\pi$
$564$	−1.59017	−	1.15533i	−0.0669582	−	0.0486480i
$565$		0			0
$566$	−20.5623	+	14.9394i	−0.864298	+	0.627949i
$567$	−7.14590	+	21.9928i	−0.300100	+	0.923611i
$568$	−6.70820			−0.281470
$569$	8.29180	−	25.5195i	0.347610	−	1.06983i	−0.612561	−	0.790423i	$-0.709861\pi$
$569$	8.29180	−	25.5195i	0.347610	−	1.06983i	0.960172	−	0.279411i	$-0.0901392\pi$
$570$		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	$0.987691\pi$
$572$	2.78115	+	8.55951i	0.116286	+	0.357891i
$573$	3.70820	+	2.69417i	0.154912	+	0.112550i
$574$	−14.5623			−0.607819
$575$		0			0
$576$	−12.0902			−0.503757
$577$	−23.9164	−	17.3763i	−0.995653	−	0.723384i	−0.0345013	−	0.999405i	$-0.510984\pi$
$577$	−23.9164	−	17.3763i	−0.995653	−	0.723384i	−0.961152	+	0.276020i	$0.910984\pi$
$578$	−0.472136	−	1.45309i	−0.0196383	−	0.0604404i
$579$	−1.80244	−	5.54734i	−0.0749068	−	0.230539i
$580$		0			0
$581$	−0.437694	+	1.34708i	−0.0181586	+	0.0558865i
$582$	4.85410			0.201209
$583$	−4.28115	+	13.1760i	−0.177307	+	0.545696i
$584$	−3.35410	+	2.43690i	−0.138794	+	0.100840i
$585$		0			0
$586$	−27.9615	−	20.3152i	−1.15508	−	0.839214i
$587$	2.00000	−	1.45309i	0.0825488	−	0.0599752i	−0.545745	−	0.837951i	$-0.683753\pi$
$587$	2.00000	−	1.45309i	0.0825488	−	0.0599752i	0.628294	+	0.777976i	$0.283753\pi$
$588$	0.381966	−	0.277515i	0.0157520	−	0.0114445i
$589$	14.8992	+	10.8249i	0.613910	+	0.446032i
$590$		0			0
$591$	−1.25329	+	0.910568i	−0.0515534	+	0.0374557i
$592$	−5.56231	+	17.1190i	−0.228609	+	0.703587i
$593$	−41.3607			−1.69848			−0.849240	−	0.528007i	$-0.822939\pi$
$593$	−41.3607			−1.69848			−0.849240	+	0.528007i	$0.822939\pi$
$594$	3.35410	−	10.3229i	0.137620	−	0.423552i
$595$		0			0
$596$	−2.86475	−	8.81678i	−0.117345	−	0.361149i
$597$	−1.90983	−	5.87785i	−0.0781641	−	0.240564i
$598$	7.85410	+	5.70634i	0.321178	+	0.233350i
$599$	−24.2705			−0.991666			−0.495833	−	0.868418i	$-0.665137\pi$
$599$	−24.2705			−0.991666			−0.495833	+	0.868418i	$0.665137\pi$
$600$		0			0
$601$	−0.639320			−0.0260784			−0.0130392	−	0.999915i	$-0.504151\pi$
$601$	−0.639320			−0.0260784			−0.0130392	+	0.999915i	$0.504151\pi$
$602$	35.3435	+	25.6785i	1.44049	+	1.04658i
$603$	12.2188	+	37.6057i	0.497590	+	1.53142i
$604$	−4.02786	−	12.3965i	−0.163891	−	0.504406i
$605$		0			0
$606$	−0.572949	+	1.76336i	−0.0232745	+	0.0716314i
$607$	30.5410			1.23962			0.619811	−	0.784751i	$-0.287209\pi$
$607$	30.5410			1.23962			0.619811	+	0.784751i	$0.287209\pi$
$608$	−3.78115	+	11.6372i	−0.153346	+	0.471950i
$609$	−6.21885	+	4.51826i	−0.252000	+	0.183089i
$610$		0			0
$611$	−32.6976	−	23.7562i	−1.32280	−	0.961072i
$612$	6.04508	−	4.39201i	0.244358	−	0.177537i
$613$	−3.57295	+	2.59590i	−0.144310	+	0.104847i	−0.657598	−	0.753369i	$-0.728427\pi$
$613$	−3.57295	+	2.59590i	−0.144310	+	0.104847i	0.513288	+	0.858217i	$0.328427\pi$
$614$	8.20820	+	5.96361i	0.331256	+	0.240672i
$615$		0			0
$616$	−16.2812	+	11.8290i	−0.655986	+	0.476602i
$617$	−7.96149	+	24.5030i	−0.320518	+	0.986452i	0.652906	+	0.757439i	$0.273550\pi$
$617$	−7.96149	+	24.5030i	−0.320518	+	0.986452i	−0.973423	+	0.229013i	$0.926450\pi$
$618$	7.85410			0.315938
$619$	−6.34346	+	19.5232i	−0.254965	+	0.784702i	0.738871	+	0.673846i	$0.235359\pi$
$619$	−6.34346	+	19.5232i	−0.254965	+	0.784702i	−0.993837	+	0.110856i	$0.964641\pi$
$620$		0			0
$621$	−0.854102	−	2.62866i	−0.0342739	−	0.105484i
$622$	−10.6353	−	32.7319i	−0.426435	−	1.31243i
$623$	−32.5623	−	23.6579i	−1.30458	−	0.947834i
$624$	−9.00000			−0.360288
$625$		0			0
$626$	−31.4164			−1.25565
$627$	3.35410	+	2.43690i	0.133950	+	0.0973203i
$628$	−2.34346	−	7.21242i	−0.0935142	−	0.287807i
$629$	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	$0.0873249\pi$
$632$	1.18034			0.0469514
$633$	0.493422	−	1.51860i	0.0196118	−	0.0603588i
$634$	−35.2705	+	25.6255i	−1.40077	+	1.01772i
$635$		0			0
$636$	0.881966	+	0.640786i	0.0349722	+	0.0254088i
$637$	7.85410	−	5.70634i	0.311191	−	0.226093i
$638$	−26.3435	+	19.1396i	−1.04295	+	0.757746i
$639$	−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	$0.244849\pi$
$642$	0.0172209	−	0.0530006i	0.000679656	−	0.00209177i
$643$	−18.2705			−0.720519			−0.360259	−	0.932852i	$-0.617312\pi$
$643$	−18.2705			−0.720519			−0.360259	+	0.932852i	$0.617312\pi$
$644$	0.708204	−	2.17963i	0.0279071	−	0.0858894i
$645$		0			0
$646$	7.66312	+	23.5847i	0.301501	+	0.927926i
$647$	−6.25329	−	19.2456i	−0.245842	−	0.756624i	−0.995497	−	0.0947951i	$-0.969780\pi$
$647$	−6.25329	−	19.2456i	−0.245842	−	0.756624i	0.749655	−	0.661829i	$-0.230220\pi$
$648$	−13.9443	−	10.1311i	−0.547783	−	0.397987i
$649$	−12.4377			−0.488222
$650$		0			0
$651$	5.83282			0.228606
$652$	9.92705	+	7.21242i	0.388773	+	0.282460i
$653$	−1.43769	−	4.42477i	−0.0562613	−	0.173155i	0.918977	−	0.394311i	$-0.129017\pi$
$653$	−1.43769	−	4.42477i	−0.0562613	−	0.173155i	−0.975238	+	0.221157i	$0.929017\pi$
$654$	1.01722	+	3.13068i	0.0397765	+	0.122419i
$655$		0			0
$656$	4.50000	−	13.8496i	0.175695	−	0.540735i
$657$	−5.29180			−0.206453
$658$	−12.4894	+	38.4383i	−0.486886	+	1.49848i
$659$	20.9164	−	15.1967i	0.814788	−	0.591978i	−0.100427	−	0.994944i	$-0.532021\pi$
$659$	20.9164	−	15.1967i	0.814788	−	0.591978i	0.915215	+	0.402967i	$0.132021\pi$
$660$		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	$0.790097\pi$
$662$	−27.6074	+	20.0579i	−1.07299	+	0.779574i
$663$	−6.35410	+	4.61653i	−0.246773	+	0.179291i
$664$	−0.854102	−	0.620541i	−0.0331456	−	0.0240817i
$665$		0			0
$666$	−13.8541	+	10.0656i	−0.536836	+	0.390034i
$667$	−2.56231	+	7.88597i	−0.0992129	+	0.305346i
$668$	5.70820			0.220857
$669$	−0.218847	+	0.673542i	−0.00846112	+	0.0260406i
$670$		0			0
$671$	5.64590	+	17.3763i	0.217957	+	0.670804i
$672$	1.19756	+	3.68571i	0.0461969	+	0.142179i
$673$	25.6353	+	18.6251i	0.988166	+	0.717945i	0.959519	−	0.281645i	$-0.0908799\pi$
$673$	25.6353	+	18.6251i	0.988166	+	0.717945i	0.0286477	+	0.999590i	$0.490880\pi$
$674$	48.2705			1.85931
$675$		0			0
$676$	6.52786			0.251072
$677$	−3.32624	−	2.41665i	−0.127838	−	0.0928795i	0.522029	−	0.852928i	$-0.325175\pi$
$677$	−3.32624	−	2.41665i	−0.127838	−	0.0928795i	−0.649867	+	0.760048i	$0.725175\pi$
$678$	0.392609	+	1.20833i	0.0150781	+	0.0464055i
$679$	−7.28115	−	22.4091i	−0.279425	−	0.859982i
$680$		0			0
$681$	0.781153	−	2.40414i	0.0299338	−	0.0921269i
$682$	24.7082			0.946126
$683$	−13.3090	+	40.9609i	−0.509255	+	1.56733i	0.284242	+	0.958753i	$0.408258\pi$
$683$	−13.3090	+	40.9609i	−0.509255	+	1.56733i	−0.793497	+	0.608574i	$0.791742\pi$
$684$	−5.16312	+	3.75123i	−0.197417	+	0.143432i
$685$		0			0
$686$	19.6353	+	14.2658i	0.749678	+	0.544673i
$687$	−0.427051	+	0.310271i	−0.0162930	+	0.0118376i
$688$	−35.3435	+	25.6785i	−1.34746	+	0.978985i
$689$	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	$0.463410\pi$
$692$	−0.0106431	+	0.0327561i	−0.000404591	+	0.00124520i
$693$	−25.6869			−0.975765
$694$	−7.97214	+	24.5357i	−0.302618	+	0.931363i
$695$		0			0
$696$	−1.77051	−	5.44907i	−0.0671110	−	0.206546i
$697$	−3.92705	−	12.0862i	−0.148748	−	0.457798i
$698$	−22.7254	−	16.5110i	−0.860170	−	0.624950i
$699$	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	$0.483585\pi$
$702$	−14.2082	−	10.3229i	−0.536254	−	0.389611i
$703$	−4.14590	−	12.7598i	−0.156366	−	0.481244i
$704$	−3.92705	−	12.0862i	−0.148006	−	0.455517i
$705$		0			0
$706$	−1.94427	+	5.98385i	−0.0731736	+	0.225205i
$707$	9.00000			0.338480
$708$	−0.302439	+	0.930812i	−0.0113664	+	0.0349821i
$709$	13.7812	−	10.0126i	0.517562	−	0.376031i	−0.298123	−	0.954528i	$-0.596360\pi$
$709$	13.7812	−	10.0126i	0.517562	−	0.376031i	0.815685	+	0.578497i	$0.196360\pi$
$710$		0			0
$711$	1.21885	+	0.885544i	0.0457103	+	0.0332105i
$712$	24.2705	−	17.6336i	0.909576	−	0.660846i
$713$	5.09017	−	3.69822i	0.190628	−	0.138500i
$714$	6.35410	+	4.61653i	0.237796	+	0.172769i
$715$		0			0
$716$	−3.35410	+	2.43690i	−0.125349	+	0.0910711i
$717$	−3.05166	+	9.39205i	−0.113966	+	0.350753i
$718$	17.5623			0.655419
$719$	14.6976	−	45.2344i	0.548127	−	1.68696i	−0.165311	−	0.986241i	$-0.552863\pi$
$719$	14.6976	−	45.2344i	0.548127	−	1.68696i	0.713438	−	0.700719i	$-0.247137\pi$
$720$		0			0
$721$	−11.7812	−	36.2587i	−0.438753	−	1.35034i
$722$	2.95492	+	9.09429i	0.109971	+	0.338455i
$723$	−5.92705	−	4.30625i	−0.220429	−	0.160151i
$724$	11.2361			0.417585
$725$		0			0
$726$	−1.23607			−0.0458748
$727$	−31.4164	−	22.8254i	−1.16517	−	0.846546i	−0.174747	−	0.984613i	$-0.555911\pi$
$727$	−31.4164	−	22.8254i	−1.16517	−	0.846546i	−0.990423	+	0.138068i	$0.955911\pi$
$728$	10.0623	+	30.9686i	0.372934	+	1.14777i
$729$	−6.00658	−	18.4863i	−0.222466	−	0.684679i
$730$		0			0
$731$	−11.7812	+	36.2587i	−0.435742	+	1.34108i
$732$	1.43769			0.0531387
$733$	7.28115	−	22.4091i	0.268936	−	0.827698i	−0.721825	−	0.692076i	$-0.756696\pi$
$733$	7.28115	−	22.4091i	0.268936	−	0.827698i	0.990761	−	0.135623i	$-0.0433035\pi$
$734$	1.50000	−	1.08981i	0.0553660	−	0.0402258i
$735$		0			0
$736$	3.38197	+	2.45714i	0.124661	+	0.0905715i
$737$	−33.6246	+	24.4297i	−1.23858	+	0.899880i
$738$	11.2082	−	8.14324i	0.412580	−	0.299757i
$739$	−14.3713	−	10.4414i	−0.528658	−	0.384092i	0.291198	−	0.956663i	$-0.405946\pi$
$739$	−14.3713	−	10.4414i	−0.528658	−	0.384092i	−0.819855	+	0.572571i	$0.805946\pi$
$740$		0			0
$741$	5.42705	−	3.94298i	0.199368	−	0.144849i
$742$	6.92705	−	21.3193i	0.254300	−	0.782655i
$743$	−25.9098			−0.950539			−0.475270	−	0.879840i	$-0.657650\pi$
$743$	−25.9098			−0.950539			−0.475270	+	0.879840i	$0.657650\pi$
$744$	−1.34346	+	4.13474i	−0.0492536	+	0.151587i
$745$		0			0
$746$	−0.927051	−	2.85317i	−0.0339417	−	0.104462i
$747$	−0.416408	−	1.28157i	−0.0152356	−	0.0468903i
$748$	6.35410	+	4.61653i	0.232329	+	0.168797i
$749$	−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	$0.590421\pi$
$752$	−32.6976	−	23.7562i	−1.19236	−	0.866298i
$753$	−0.740133	−	2.27790i	−0.0269720	−	0.0830111i
$754$	16.2812	+	50.1082i	0.592925	+	1.82483i
$755$		0			0
$756$	−1.28115	+	3.94298i	−0.0465951	+	0.143405i
$757$	27.0000			0.981332			0.490666	−	0.871348i	$-0.336754\pi$
$757$	27.0000			0.981332			0.490666	+	0.871348i	$0.336754\pi$
$758$	3.78115	−	11.6372i	0.137338	−	0.422682i
$759$	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	$0.594215\pi$
$762$	4.85410	−	3.52671i	0.175846	−	0.127759i
$763$	12.9271	−	9.39205i	0.467991	−	0.340015i
$764$	−6.00000	−	4.35926i	−0.217072	−	0.157712i
$765$		0			0
$766$	46.4336	−	33.7360i	1.67772	−	1.21893i
$767$	−6.21885	+	19.1396i	−0.224550	+	0.691092i
$768$	−5.18034			−0.186929
$769$	−3.98278	+	12.2577i	−0.143623	+	0.442025i	−0.996831	−	0.0795446i	$-0.974653\pi$
$769$	−3.98278	+	12.2577i	−0.143623	+	0.442025i	0.853209	+	0.521570i	$0.174653\pi$
$770$		0			0
$771$	−3.46556	−	10.6659i	−0.124809	−	0.384123i
$772$	2.91641	+	8.97578i	0.104964	+	0.323045i
$773$	17.1803	+	12.4822i	0.617934	+	0.448955i	0.852199	−	0.523217i	$-0.175268\pi$
$773$	17.1803	+	12.4822i	0.617934	+	0.448955i	−0.234265	+	0.972173i	$0.575268\pi$
$774$	−41.5623			−1.49393
$775$		0			0
$776$	17.5623			0.630450
$777$	−3.43769	−	2.49763i	−0.123327	−	0.0896020i
$778$	−0.791796	−	2.43690i	−0.0283873	−	0.0873670i
$779$	3.35410	+	10.3229i	0.120173	+	0.369855i
$780$		0			0
$781$	2.78115	−	8.55951i	0.0995175	−	0.306283i
$782$	8.47214			0.302963
$783$	4.63525	−	14.2658i	0.165650	−	0.509820i
$784$	7.85410	−	5.70634i	0.280504	−	0.203798i
$785$		0			0
$786$	6.13525	+	4.45752i	0.218837	+	0.158995i
$787$	9.13525	−	6.63715i	0.325637	−	0.236589i	−0.412940	−	0.910758i	$-0.635498\pi$
$787$	9.13525	−	6.63715i	0.325637	−	0.236589i	0.738577	+	0.674169i	$0.235498\pi$
$788$	2.02786	−	1.47333i	0.0722397	−	0.0524852i
$789$	5.04508	+	3.66547i	0.179610	+	0.130494i
$790$		0			0
$791$	4.98936	−	3.62498i	0.177401	−	0.128889i
$792$	5.91641	−	18.2088i	0.210230	−	0.647023i
$793$	29.5623			1.04979
$794$	8.20820	−	25.2623i	0.291298	−	0.896524i
$795$		0			0
$796$	3.09017	+	9.51057i	0.109528	+	0.337093i
$797$	10.8820	+	33.4912i	0.385459	+	1.18632i	0.936147	+	0.351610i	$0.114366\pi$
$797$	10.8820	+	33.4912i	0.385459	+	1.18632i	−0.550688	+	0.834711i	$0.685634\pi$
$798$	−5.42705	−	3.94298i	−0.192116	−	0.139580i
$799$	−35.2705			−1.24778
$800$		0			0
$801$	38.2918			1.35297
$802$	15.7082	+	11.4127i	0.554676	+	0.402996i
$803$	−1.71885	−	5.29007i	−0.0606568	−	0.186682i
$804$	1.01064	+	3.11044i	0.0356426	+	0.109697i
$805$		0			0
$806$	12.3541	−	38.0220i	0.435155	−	1.33927i
$807$	−0.978714			−0.0344524
$808$	−2.07295	+	6.37988i	−0.0729261	+	0.224443i
$809$	4.14590	−	3.01217i	0.145762	−	0.105902i	−0.512514	−	0.858679i	$-0.671286\pi$
$809$	4.14590	−	3.01217i	0.145762	−	0.105902i	0.658276	+	0.752776i	$0.271286\pi$
$810$		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	$0.633460\pi$
$812$	10.0623	−	7.31069i	0.353118	−	0.256555i
$813$	6.20820	−	4.51052i	0.217731	−	0.158191i
$814$	−14.5623	−	10.5801i	−0.510409	−	0.370834i
$815$		0			0
$816$	−6.35410	+	4.61653i	−0.222438	+	0.161611i
$817$	10.0623	−	30.9686i	0.352036	−	1.08345i
$818$	36.8328			1.28783
$819$	−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	$0.778956\pi$
$822$	1.07295	+	3.30220i	0.0374234	+	0.115177i
$823$	18.1353	+	13.1760i	0.632155	+	0.459288i	0.857146	−	0.515073i	$-0.172235\pi$
$823$	18.1353	+	13.1760i	0.632155	+	0.459288i	−0.224991	+	0.974361i	$0.572235\pi$
$824$	28.4164			0.989932
$825$		0			0
$826$	20.1246			0.700225
$827$	25.5795	+	18.5846i	0.889487	+	0.646250i	0.935744	−	0.352679i	$-0.114729\pi$
$827$	25.5795	+	18.5846i	0.889487	+	0.646250i	−0.0462570	+	0.998930i	$0.514729\pi$
$828$	0.673762	+	2.07363i	0.0234149	+	0.0720635i
$829$	1.93363	+	5.95110i	0.0671577	+	0.206690i	0.979004	−	0.203842i	$-0.0653429\pi$
$829$	1.93363	+	5.95110i	0.0671577	+	0.206690i	−0.911846	+	0.410532i	$0.865343\pi$
$830$		0			0
$831$	−0.624612	+	1.92236i	−0.0216675	+	0.0666858i
$832$	−20.5623			−0.712870
$833$	2.61803	−	8.05748i	0.0907095	−	0.279175i
$834$	6.11803	−	4.44501i	0.211850	−	0.153918i
$835$		0			0
$836$	−5.42705	−	3.94298i	−0.187698	−	0.136371i
$837$	−9.20820	+	6.69015i	−0.318282	+	0.231245i
$838$	−8.78115	+	6.37988i	−0.303340	+	0.220389i
$839$	−23.7812	−	17.2780i	−0.821017	−	0.596503i	0.0959869	−	0.995383i	$-0.469399\pi$
$839$	−23.7812	−	17.2780i	−0.821017	−	0.596503i	−0.917004	+	0.398879i	$0.869399\pi$
$840$		0			0
$841$	−12.9443	+	9.40456i	−0.446354	+	0.324295i
$842$	−4.45492	+	13.7108i	−0.153527	+	0.472506i
$843$	−4.58359			−0.157867
$844$	−0.798374	+	2.45714i	−0.0274812	+	0.0845783i
$845$		0			0
$846$	−11.8820	−	36.5689i	−0.408510	−	1.25727i
$847$	1.85410	+	5.70634i	0.0637077	+	0.196072i
$848$	18.1353	+	13.1760i	0.622767	+	0.452467i
$849$	6.00000			0.205919
$850$		0			0
$851$	−4.58359			−0.157124
$852$	−0.572949	−	0.416272i	−0.0196289	−	0.0142612i
$853$	−1.80244	−	5.54734i	−0.0617143	−	0.189937i	0.915446	−	0.402441i	$-0.131838\pi$
$853$	−1.80244	−	5.54734i	−0.0617143	−	0.189937i	−0.977160	+	0.212504i	$0.931838\pi$
$854$	−9.13525	−	28.1154i	−0.312602	−	0.962090i
$855$		0			0
$856$	0.0623059	−	0.191758i	0.00212957	−	0.00655415i
$857$	−34.1803			−1.16758			−0.583789	−	0.811905i	$-0.698431\pi$
$857$	−34.1803			−1.16758			−0.583789	+	0.811905i	$0.698431\pi$
$858$	2.78115	−	8.55951i	0.0949470	−	0.292217i
$859$	20.3262	−	14.7679i	0.693522	−	0.503873i	−0.184294	−	0.982871i	$-0.559000\pi$
$859$	20.3262	−	14.7679i	0.693522	−	0.503873i	0.877816	+	0.478998i	$0.159000\pi$
$860$		0			0
$861$	2.78115	+	2.02063i	0.0947814	+	0.0688627i
$862$	−16.0623	+	11.6699i	−0.547084	+	0.397480i
$863$	5.47214	−	3.97574i	0.186274	−	0.135336i	−0.490740	−	0.871306i	$-0.663274\pi$
$863$	5.47214	−	3.97574i	0.186274	−	0.135336i	0.677014	+	0.735970i	$0.263274\pi$
$864$	−6.11803	−	4.44501i	−0.208140	−	0.151222i
$865$		0			0
$866$	18.7082	−	13.5923i	0.635731	−	0.461885i
$867$	−0.111456	+	0.343027i	−0.00378525	+	0.0116498i
$868$	−9.43769			−0.320336
$869$	−0.489357	+	1.50609i	−0.0166003	+	0.0510905i
$870$		0			0
$871$	20.7812	+	63.9578i	0.704143	+	2.16713i
$872$	3.68034	+	11.3269i	0.124632	+	0.383578i
$873$	18.1353	+	13.1760i	0.613785	+	0.445941i
$874$	−7.23607			−0.244764
$875$		0			0
$876$	−0.437694			−0.0147883
$877$	15.3541	+	11.1554i	0.518471	+	0.376691i	0.816028	−	0.578013i	$-0.196172\pi$
$877$	15.3541	+	11.1554i	0.518471	+	0.376691i	−0.297556	+	0.954704i	$0.596172\pi$
$878$	−15.0623	−	46.3570i	−0.508328	−	1.56447i
$879$	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	$-0.178330\pi$
$882$	9.23607			0.310995
$883$	5.51064	−	16.9600i	0.185448	−	0.570750i	−0.814508	−	0.580152i	$-0.802993\pi$
$883$	5.51064	−	16.9600i	0.185448	−	0.570750i	0.999956	+	0.00940251i	$0.00299296\pi$
$884$	10.2812	−	7.46969i	0.345793	−	0.251233i
$885$		0			0
$886$	9.39919	+	6.82891i	0.315772	+	0.229422i
$887$	34.3607	−	24.9645i	1.15372	−	0.838226i	0.164748	−	0.986336i	$-0.447319\pi$
$887$	34.3607	−	24.9645i	1.15372	−	0.838226i	0.988971	+	0.148110i	$0.0473190\pi$
$888$	2.56231	−	1.86162i	0.0859854	−	0.0624720i
$889$	−23.5623	−	17.1190i	−0.790254	−	0.574153i
$890$		0			0
$891$	18.7082	−	13.5923i	0.626748	−	0.455359i
$892$	0.354102	−	1.08981i	0.0118562	−	0.0364897i
$893$	30.1246			1.00808
$894$	−2.86475	+	8.81678i	−0.0958114	+	0.294877i
$895$		0			0
$896$	12.6246	+	38.8546i	0.421759	+	1.29804i
$897$	−0.708204	−	2.17963i	−0.0236462	−	0.0727756i
$898$	−51.4058	−	37.3485i	−1.71543	−	1.24633i
$899$	34.1459			1.13883
$900$		0			0
$901$	19.5623			0.651715
$902$	11.7812	+	8.55951i	0.392269	+	0.285000i
$903$	−3.18692	−	9.80832i	−0.106054	−	0.326401i
$904$	1.42047	+	4.37177i	0.0472442	+	0.145403i
$905$		0			0
$906$	−4.02786	+	12.3965i	−0.133817	+	0.411846i
$907$	−42.2705			−1.40357			−0.701785	−	0.712389i	$-0.747613\pi$
$907$	−42.2705			−1.40357			−0.701785	+	0.712389i	$0.747613\pi$
$908$	−1.26393	+	3.88998i	−0.0419451	+	0.129094i
$909$	−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	$0.493042\pi$
$912$	5.42705	−	3.94298i	0.179708	−	0.130565i
$913$	1.14590	−	0.832544i	0.0379237	−	0.0275532i
$914$	−23.5623	−	17.1190i	−0.779372	−	0.566247i
$915$		0			0
$916$	0.690983	−	0.502029i	0.0228307	−	0.0165875i
$917$	11.3754	−	35.0098i	0.375648	−	1.15613i
$918$	−15.3262			−0.505841
$919$	−7.43769	+	22.8909i	−0.245347	+	0.755100i	0.750232	+	0.661174i	$0.229942\pi$
$919$	−7.43769	+	22.8909i	−0.245347	+	0.755100i	−0.995579	+	0.0939258i	$0.970058\pi$
$920$		0			0
$921$	−0.740133	−	2.27790i	−0.0243882	−	0.0750592i
$922$	−18.1353	−	55.8146i	−0.597253	−	1.83816i
$923$	−11.7812	−	8.55951i	−0.387781	−	0.281740i
$924$	−2.12461			−0.0698946
$925$		0			0
$926$	22.8541			0.751032
$927$	29.3435	+	21.3193i	0.963766	+	0.700217i
$928$	7.01064	+	21.5765i	0.230136	+	0.708285i
$929$	11.3435	+	34.9116i	0.372167	+	1.14541i	0.945370	+	0.325999i	$0.105700\pi$
$929$	11.3435	+	34.9116i	0.372167	+	1.14541i	−0.573203	+	0.819413i	$0.694300\pi$
$930$		0			0
$931$	−2.23607	+	6.88191i	−0.0732842	+	0.225545i
$932$	−16.6180			−0.544342
$933$	−2.51064	+	7.72696i	−0.0821948	+	0.252969i
$934$	51.3607	−	37.3157i	1.68057	−	1.22101i
$935$		0			0
$936$	−25.0623	−	18.2088i	−0.819187	−	0.595174i
$937$	−7.63525	+	5.54734i	−0.249433	+	0.181224i	−0.705475	−	0.708734i	$-0.749266\pi$
$937$	−7.63525	+	5.54734i	−0.249433	+	0.181224i	0.456043	+	0.889958i	$0.349266\pi$
$938$	54.4058	−	39.5281i	1.77641	−	1.29064i
$939$	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	$0.153383\pi$
$942$	−2.34346	+	7.21242i	−0.0763540	+	0.234993i
$943$	3.70820			0.120756
$944$	−6.21885	+	19.1396i	−0.202406	+	0.622942i
$945$		0			0
$946$	−13.5000	−	41.5487i	−0.438923	−	1.35087i
$947$	−6.98278	−	21.4908i	−0.226910	−	0.698357i	−0.998092	−	0.0617423i	$-0.980334\pi$
$947$	−6.98278	−	21.4908i	−0.226910	−	0.698357i	0.771182	−	0.636614i	$-0.219666\pi$
$948$	0.100813	+	0.0732450i	0.00327426	+	0.00237889i
$949$	−9.00000			−0.292152
$950$		0			0
$951$	10.2918			0.333734
$952$	22.9894	+	16.7027i	0.745089	+	0.541339i
$953$	4.06637	+	12.5150i	0.131723	+	0.405401i	0.995066	−	0.0992165i	$-0.0316336\pi$
$953$	4.06637	+	12.5150i	0.131723	+	0.405401i	−0.863343	+	0.504617i	$0.831634\pi$
$954$	6.59017	+	20.2825i	0.213365	+	0.656669i
$955$		0			0
$956$	4.93769	−	15.1967i	0.159696	−	0.491495i
$957$	7.68692			0.248483
$958$	16.2812	−	50.1082i	0.526020	−	1.61892i
$959$	13.6353	−	9.90659i	0.440305	−	0.319901i
$960$		0			0
$961$	4.11803	+	2.99193i	0.132840	+	0.0965138i
$962$	−23.5623	+	17.1190i	−0.759679	+	0.551939i
$963$	0.208204	−	0.151269i	0.00670928	−	0.00487458i
$964$	9.59017	+	6.96767i	0.308879	+	0.224413i
$965$		0			0
$966$	−1.85410	+	1.34708i	−0.0596548	+	0.0433417i
$967$	4.98936	−	15.3557i	0.160447	−	0.493805i	−0.838225	−	0.545324i	$-0.816406\pi$
$967$	4.98936	−	15.3557i	0.160447	−	0.493805i	0.998672	+	0.0515196i	$0.0164065\pi$
$968$	−4.47214			−0.143740
$969$	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	$-0.409963\pi$
$972$	−1.84346	−	5.67358i	−0.0591290	−	0.181980i
$973$	−29.6976	−	21.5765i	−0.952060	−	0.691712i
$974$	−6.00000			−0.192252
$975$		0			0
$976$	29.5623			0.946266
$977$	−18.9164	−	13.7436i	−0.605190	−	0.439696i	0.242528	−	0.970145i	$-0.422024\pi$
$977$	−18.9164	−	13.7436i	−0.605190	−	0.439696i	−0.847717	+	0.530449i	$0.822024\pi$
$978$	−3.79180	−	11.6699i	−0.121248	−	0.373164i
$979$	12.4377	+	38.2793i	0.397510	+	1.22341i
$980$		0			0
$981$	−4.69756	+	14.4576i	−0.149982	+	0.461596i
$982$	−58.6869			−1.87277
$983$	−1.62461	+	5.00004i	−0.0518171	+	0.159477i	−0.973616	−	0.228191i	$-0.926719\pi$
$983$	−1.62461	+	5.00004i	−0.0518171	+	0.159477i	0.921799	+	0.387667i	$0.126719\pi$
$984$	−2.07295	+	1.50609i	−0.0660832	+	0.0480123i
$985$		0			0
$986$	37.1976	+	27.0256i	1.18461	+	0.860671i
$987$	7.71885	−	5.60807i	0.245694	−	0.178507i
$988$	−8.78115	+	6.37988i	−0.279366	+	0.202971i
$989$	−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	$0.159930\pi$
$992$	5.31966	−	16.3722i	0.168899	−	0.519819i
$993$	8.05573			0.255641
$994$	−4.50000	+	13.8496i	−0.142731	+	0.439282i
$995$		0			0
$996$	−0.0344419	−	0.106001i	−0.00109133	−	0.00335877i
$997$	16.3328	+	50.2672i	0.517265	+	1.59198i	0.779122	+	0.626873i	$0.215665\pi$
$997$	16.3328	+	50.2672i	0.517265	+	1.59198i	−0.261856	+	0.965107i	$0.584335\pi$
$998$	55.4508	+	40.2874i	1.75527	+	1.27528i
$999$	8.29180			0.262341

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.a.a.1.1	✓	2	25.6	even	5
125.2.a.b.1.2	yes	2	25.19	even	10
125.2.b.b.124.1		4	25.17	odd	20
125.2.b.b.124.4		4	25.8	odd	20
625.2.d.a.251.1		4	25.14	even	10
625.2.d.a.376.1		4	5.4	even	2
625.2.d.d.126.1		4	25.21	even	5
625.2.d.d.501.1		4	25.16	even	5
625.2.d.g.126.1		4	25.4	even	10
625.2.d.g.501.1		4	25.9	even	10
625.2.d.j.251.1		4	25.11	even	5	inner
625.2.d.j.376.1		4	1.1	even	1	trivial
625.2.e.d.249.1		8	5.2	odd	4
625.2.e.d.249.2		8	5.3	odd	4
625.2.e.d.374.1		8	25.23	odd	20
625.2.e.d.374.2		8	25.2	odd	20
625.2.e.g.124.1		8	25.12	odd	20
625.2.e.g.124.2		8	25.13	odd	20
625.2.e.g.499.1		8	25.3	odd	20
625.2.e.g.499.2		8	25.22	odd	20
1125.2.a.c.1.1		2	75.44	odd	10
1125.2.a.d.1.2		2	75.56	odd	10
1125.2.b.f.874.1		4	75.8	even	20
1125.2.b.f.874.4		4	75.17	even	20
2000.2.a.a.1.2		2	100.19	odd	10
2000.2.a.l.1.1		2	100.31	odd	10
2000.2.c.e.1249.2		4	100.67	even	20
2000.2.c.e.1249.3		4	100.83	even	20
6125.2.a.d.1.1		2	175.6	odd	10
6125.2.a.g.1.2		2	175.69	odd	10
8000.2.a.c.1.2		2	200.131	odd	10
8000.2.a.d.1.2		2	200.69	even	10
8000.2.a.u.1.1		2	200.19	odd	10
8000.2.a.v.1.1		2	200.181	even	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(1.30902 + 0.951057i) q^{2} +(-0.118034 - 0.363271i) q^{3} +(0.190983 + 0.587785i) q^{4} +(0.190983 - 0.587785i) q^{6} -3.00000 q^{7} +(0.690983 - 2.12663i) q^{8} +(2.30902 - 1.67760i) q^{9} +(2.42705 + 1.76336i) q^{11} +(0.190983 - 0.138757i) q^{12} +(3.92705 - 2.85317i) q^{13} +(-3.92705 - 2.85317i) q^{14} +(3.92705 - 2.85317i) q^{16} +(1.30902 - 4.02874i) q^{17} +4.61803 q^{18} +(-1.11803 + 3.44095i) q^{19} +(0.354102 + 1.08981i) q^{21} +(1.50000 + 4.61653i) q^{22} +(1.00000 + 0.726543i) q^{23} -0.854102 q^{24} +7.85410 q^{26} +(-1.80902 - 1.31433i) q^{27} +(-0.572949 - 1.76336i) q^{28} +(2.07295 + 6.37988i) q^{29} +(1.57295 - 4.84104i) q^{31} +3.38197 q^{32} +(0.354102 - 1.08981i) q^{33} +(5.54508 - 4.02874i) q^{34} +(1.42705 + 1.03681i) q^{36} +(-3.00000 + 2.17963i) q^{37} +(-4.73607 + 3.44095i) q^{38} +(-1.50000 - 1.08981i) q^{39} +(2.42705 - 1.76336i) q^{41} +(-0.572949 + 1.76336i) q^{42} -9.00000 q^{43} +(-0.572949 + 1.76336i) q^{44} +(0.618034 + 1.90211i) q^{46} +(-2.57295 - 7.91872i) q^{47} +(-1.50000 - 1.08981i) q^{48} +2.00000 q^{49} -1.61803 q^{51} +(2.42705 + 1.76336i) q^{52} +(1.42705 + 4.39201i) q^{53} +(-1.11803 - 3.44095i) q^{54} +(-2.07295 + 6.37988i) q^{56} +1.38197 q^{57} +(-3.35410 + 10.3229i) q^{58} +(-3.35410 + 2.43690i) q^{59} +(4.92705 + 3.57971i) q^{61} +(6.66312 - 4.84104i) q^{62} +(-6.92705 + 5.03280i) q^{63} +(-3.42705 - 2.48990i) q^{64} +(1.50000 - 1.08981i) q^{66} +(-4.28115 + 13.1760i) q^{67} +2.61803 q^{68} +(0.145898 - 0.449028i) q^{69} +(-0.927051 - 2.85317i) q^{71} +(-1.97214 - 6.06961i) q^{72} +(-1.50000 - 1.08981i) q^{73} -6.00000 q^{74} -2.23607 q^{76} +(-7.28115 - 5.29007i) q^{77} +(-0.927051 - 2.85317i) q^{78} +(0.163119 + 0.502029i) q^{79} +(2.38197 - 7.33094i) q^{81} +4.85410 q^{82} +(0.145898 - 0.449028i) q^{83} +(-0.572949 + 0.416272i) q^{84} +(-11.7812 - 8.55951i) q^{86} +(2.07295 - 1.50609i) q^{87} +(5.42705 - 3.94298i) q^{88} +(10.8541 + 7.88597i) q^{89} +(-11.7812 + 8.55951i) q^{91} +(-0.236068 + 0.726543i) q^{92} -1.94427 q^{93} +(4.16312 - 12.8128i) q^{94} +(-0.399187 - 1.22857i) q^{96} +(2.42705 + 7.46969i) q^{97} +(2.61803 + 1.90211i) q^{98} +8.56231 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} + 4 q^{3} + 3 q^{4} + 3 q^{6} - 12 q^{7} + 5 q^{8} + 7 q^{9} + 3 q^{11} + 3 q^{12} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 3 q^{17} + 14 q^{18} - 12 q^{21} + 6 q^{22} + 4 q^{23} + 10 q^{24} + 18 q^{26}+ \cdots - 6 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 + 4 * q^3 + 3 * q^4 + 3 * q^6 - 12 * q^7 + 5 * q^8 + 7 * q^9 + 3 * q^11 + 3 * q^12 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 3 * q^17 + 14 * q^18 - 12 * q^21 + 6 * q^22 + 4 * q^23 + 10 * q^24 + 18 * q^26 - 5 * q^27 - 9 * q^28 + 15 * q^29 + 13 * q^31 + 18 * q^32 - 12 * q^33 + 11 * q^34 - q^36 - 12 * q^37 - 10 * q^38 - 6 * q^39 + 3 * q^41 - 9 * q^42 - 36 * q^43 - 9 * q^44 - 2 * q^46 - 17 * q^47 - 6 * q^48 + 8 * q^49 - 2 * q^51 + 3 * q^52 - q^53 - 15 * q^56 + 10 * q^57 + 13 * q^61 + 11 * q^62 - 21 * q^63 - 7 * q^64 + 6 * q^66 + 3 * q^67 + 6 * q^68 + 14 * q^69 + 3 * q^71 + 10 * q^72 - 6 * q^73 - 24 * q^74 - 9 * q^77 + 3 * q^78 - 15 * q^79 + 14 * q^81 + 6 * q^82 + 14 * q^83 - 9 * q^84 - 27 * q^86 + 15 * q^87 + 15 * q^88 + 30 * q^89 - 27 * q^91 + 8 * q^92 + 28 * q^93 + q^94 + 23 * q^96 + 3 * q^97 + 6 * q^98 - 6 * q^99

Introduction

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