LMFDB - Embedded newform 625.2.d.p.126.4

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 = [16,0,5,-8,0,-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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 25x^{14} + 239x^{12} + 1165x^{10} + 3166x^{8} + 4820x^{6} + 3809x^{4} + 1205x^{2} + 1 $ x^16 + 25x^14 + 239x^12 + 1165x^10 + 3166x^8 + 4820x^6 + 3809x^4 + 1205*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			126.4
Root			$0.991969i$ of defining polynomial
Character	$\chi$	$=$	625.126
Dual form			625.2.d.p.501.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.520202 + 1.60102i) q^{2} +(0.574677 - 0.417528i) q^{3} +(-0.674615 + 0.490137i) q^{4} +(0.967418 + 0.702870i) q^{6} -4.59110 q^{7} +(1.58816 + 1.15387i) q^{8} +(-0.771126 + 2.37328i) q^{9} +(1.20974 + 3.72319i) q^{11} +(-0.183041 + 0.563341i) q^{12} +(-0.177048 + 0.544898i) q^{13} +(-2.38830 - 7.35044i) q^{14} +(-1.53656 + 4.72903i) q^{16} +(0.188186 + 0.136725i) q^{17} -4.20081 q^{18} +(4.49012 + 3.26227i) q^{19} +(-2.63840 + 1.91691i) q^{21} +(-5.33158 + 3.87362i) q^{22} +(-1.52428 - 4.69124i) q^{23} +1.39445 q^{24} -0.964492 q^{26} +(1.20628 + 3.71256i) q^{27} +(3.09723 - 2.25027i) q^{28} +(-3.34174 + 2.42792i) q^{29} +(2.82777 + 2.05449i) q^{31} -4.44444 q^{32} +(2.24974 + 1.63453i) q^{33} +(-0.121005 + 0.372415i) q^{34} +(-0.643019 - 1.97901i) q^{36} +(-1.67378 + 5.15138i) q^{37} +(-2.88717 + 8.88581i) q^{38} +(0.125764 + 0.387063i) q^{39} +(3.22079 - 9.91257i) q^{41} +(-4.44152 - 3.22695i) q^{42} +1.38833 q^{43} +(-2.64098 - 1.91878i) q^{44} +(6.71783 - 4.88079i) q^{46} +(-0.744634 + 0.541008i) q^{47} +(1.09148 + 3.35922i) q^{48} +14.0782 q^{49} +0.165233 q^{51} +(-0.147635 - 0.454374i) q^{52} +(-0.996044 + 0.723668i) q^{53} +(-5.31636 + 3.86256i) q^{54} +(-7.29141 - 5.29752i) q^{56} +3.94246 q^{57} +(-5.62552 - 4.08718i) q^{58} +(1.39299 - 4.28718i) q^{59} +(-3.60276 - 11.0881i) q^{61} +(-1.81827 + 5.59606i) q^{62} +(3.54032 - 10.8960i) q^{63} +(0.761103 + 2.34244i) q^{64} +(-1.44660 + 4.45216i) q^{66} +(2.39022 + 1.73660i) q^{67} -0.193968 q^{68} +(-2.83469 - 2.05952i) q^{69} +(-2.59331 + 1.88415i) q^{71} +(-3.96312 + 2.87938i) q^{72} +(-3.18047 - 9.78847i) q^{73} -9.11816 q^{74} -4.62806 q^{76} +(-5.55402 - 17.0935i) q^{77} +(-0.554272 + 0.402702i) q^{78} +(7.77877 - 5.65161i) q^{79} +(-3.81318 - 2.77044i) q^{81} +17.5457 q^{82} +(8.48125 + 6.16199i) q^{83} +(0.840358 - 2.58636i) q^{84} +(0.722211 + 2.22274i) q^{86} +(-0.906701 + 2.79054i) q^{87} +(-2.37480 + 7.30889i) q^{88} +(2.24293 + 6.90303i) q^{89} +(0.812846 - 2.50168i) q^{91} +(3.32765 + 2.41768i) q^{92} +2.48286 q^{93} +(-1.25352 - 0.910739i) q^{94} +(-2.55412 + 1.85568i) q^{96} +(6.73079 - 4.89020i) q^{97} +(7.32353 + 22.5395i) q^{98} -9.76903 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 5 q^{3} - 8 q^{4} - 3 q^{6} - 20 q^{7} + 10 q^{8} + 3 q^{9} + 2 q^{11} + 25 q^{12} + 5 q^{13} + 9 q^{14} - 14 q^{16} - 10 q^{17} + 10 q^{18} + 7 q^{21} - 40 q^{22} + 15 q^{23} + 10 q^{24} + 22 q^{26}+ \cdots - 44 q^{99}+O(q^{100}) $ 16 * q + 5 * q^3 - 8 * q^4 - 3 * q^6 - 20 * q^7 + 10 * q^8 + 3 * q^9 + 2 * q^11 + 25 * q^12 + 5 * q^13 + 9 * q^14 - 14 * q^16 - 10 * q^17 + 10 * q^18 + 7 * q^21 - 40 * q^22 + 15 * q^23 + 10 * q^24 + 22 * q^26 + 20 * q^27 + 30 * q^28 - 10 * q^29 + 17 * q^31 - 60 * q^32 + 5 * q^33 - q^34 - 4 * q^36 - 15 * q^37 - 15 * q^38 - 9 * q^39 + 12 * q^41 - 45 * q^42 + 49 * q^44 - 33 * q^46 + 25 * q^47 - 20 * q^48 - 8 * q^49 - 28 * q^51 + 20 * q^52 - 30 * q^54 - 35 * q^56 + 20 * q^57 + 5 * q^58 + 20 * q^59 - 23 * q^61 + 15 * q^62 + 10 * q^63 - 28 * q^64 - 26 * q^66 - 80 * q^68 + 6 * q^69 + 22 * q^71 + 5 * q^72 + 40 * q^73 - 36 * q^74 - 20 * q^76 - 40 * q^77 - 25 * q^78 + 75 * q^79 + 11 * q^81 + 90 * q^82 + 25 * q^83 - 31 * q^84 + 17 * q^86 - 20 * q^87 + 5 * q^89 + 22 * q^91 + 60 * q^92 + 80 * q^93 - 51 * q^94 - 28 * q^96 + 40 * q^97 + 15 * q^98 - 44 * q^99

Character values

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

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

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 $

$2$	0.520202	+	1.60102i	0.367839	+	1.13209i	0.948184	+	0.317721i	$0.102917\pi$
$2$	0.520202	+	1.60102i	0.367839	+	1.13209i	−0.580346	+	0.814370i	$0.697083\pi$
$3$	0.574677	−	0.417528i	0.331790	−	0.241060i	−0.409400	−	0.912355i	$-0.634262\pi$
$3$	0.574677	−	0.417528i	0.331790	−	0.241060i	0.741190	+	0.671295i	$0.234262\pi$
$4$	−0.674615	+	0.490137i	−0.337308	+	0.245068i
$5$		0			0
$5$		0			0
$6$	0.967418	+	0.702870i	0.394947	+	0.286946i
$7$	−4.59110			−1.73527			−0.867637	−	0.497198i	$-0.834362\pi$
$7$	−4.59110			−1.73527			−0.867637	+	0.497198i	$0.834362\pi$
$8$	1.58816	+	1.15387i	0.561500	+	0.407953i
$9$	−0.771126	+	2.37328i	−0.257042	+	0.791094i
$10$		0			0
$11$	1.20974	+	3.72319i	0.364749	+	1.12258i	0.950138	+	0.311830i	$0.100942\pi$
$11$	1.20974	+	3.72319i	0.364749	+	1.12258i	−0.585389	+	0.810753i	$0.699058\pi$
$12$	−0.183041	+	0.563341i	−0.0528393	+	0.162623i
$13$	−0.177048	+	0.544898i	−0.0491043	+	0.151127i	−0.972602	−	0.232476i	$-0.925317\pi$
$13$	−0.177048	+	0.544898i	−0.0491043	+	0.151127i	0.923498	+	0.383604i	$0.125317\pi$
$14$	−2.38830	−	7.35044i	−0.638301	−	1.96449i
$15$		0			0
$16$	−1.53656	+	4.72903i	−0.384139	+	1.18226i
$17$	0.188186	+	0.136725i	0.0456419	+	0.0331608i	0.610372	−	0.792115i	$-0.291020\pi$
$17$	0.188186	+	0.136725i	0.0456419	+	0.0331608i	−0.564730	+	0.825275i	$0.691020\pi$
$18$	−4.20081			−0.990140
$19$	4.49012	+	3.26227i	1.03010	+	0.748415i	0.968330	−	0.249675i	$-0.0803238\pi$
$19$	4.49012	+	3.26227i	1.03010	+	0.748415i	0.0617752	+	0.998090i	$0.480324\pi$
$20$		0			0
$21$	−2.63840	+	1.91691i	−0.575747	+	0.418305i
$22$	−5.33158	+	3.87362i	−1.13670	+	0.825858i
$23$	−1.52428	−	4.69124i	−0.317834	−	0.978192i	−0.974572	−	0.224073i	$-0.928064\pi$
$23$	−1.52428	−	4.69124i	−0.317834	−	0.978192i	0.656738	−	0.754118i	$-0.271936\pi$
$24$	1.39445			0.284641
$25$		0			0
$26$	−0.964492			−0.189152
$27$	1.20628	+	3.71256i	0.232149	+	0.714482i
$28$	3.09723	−	2.25027i	0.585321	−	0.425261i
$29$	−3.34174	+	2.42792i	−0.620546	+	0.450853i	−0.853112	−	0.521727i	$-0.825288\pi$
$29$	−3.34174	+	2.42792i	−0.620546	+	0.450853i	0.232566	+	0.972581i	$0.425288\pi$
$30$		0			0
$31$	2.82777	+	2.05449i	0.507882	+	0.368998i	0.812020	−	0.583630i	$-0.198368\pi$
$31$	2.82777	+	2.05449i	0.507882	+	0.368998i	−0.304138	+	0.952628i	$0.598368\pi$
$32$	−4.44444			−0.785674
$33$	2.24974	+	1.63453i	0.391630	+	0.284536i
$34$	−0.121005	+	0.372415i	−0.0207522	+	0.0638686i
$35$		0			0
$36$	−0.643019	−	1.97901i	−0.107170	−	0.329835i
$37$	−1.67378	+	5.15138i	−0.275169	+	0.846882i	0.714006	+	0.700139i	$0.246879\pi$
$37$	−1.67378	+	5.15138i	−0.275169	+	0.846882i	−0.989175	+	0.146742i	$0.953121\pi$
$38$	−2.88717	+	8.88581i	−0.468361	+	1.44147i
$39$	0.125764	+	0.387063i	0.0201384	+	0.0619797i
$40$		0			0
$41$	3.22079	−	9.91257i	0.503003	−	1.54808i	−0.301100	−	0.953593i	$-0.597354\pi$
$41$	3.22079	−	9.91257i	0.503003	−	1.54808i	0.804103	−	0.594491i	$-0.202646\pi$
$42$	−4.44152	−	3.22695i	−0.685341	−	0.497929i
$43$	1.38833			0.211718			0.105859	−	0.994381i	$-0.466241\pi$
$43$	1.38833			0.211718			0.105859	+	0.994381i	$0.466241\pi$
$44$	−2.64098	−	1.91878i	−0.398142	−	0.289267i
$45$		0			0
$46$	6.71783	−	4.88079i	0.990491	−	0.719634i
$47$	−0.744634	+	0.541008i	−0.108616	+	0.0789142i	−0.640767	−	0.767735i	$-0.721384\pi$
$47$	−0.744634	+	0.541008i	−0.108616	+	0.0789142i	0.532151	+	0.846649i	$0.321384\pi$
$48$	1.09148	+	3.35922i	0.157541	+	0.484862i
$49$	14.0782			2.01118
$50$		0			0
$51$	0.165233			0.0231373
$52$	−0.147635	−	0.454374i	−0.0204733	−	0.0630103i
$53$	−0.996044	+	0.723668i	−0.136817	+	0.0994034i	−0.654089	−	0.756418i	$-0.726948\pi$
$53$	−0.996044	+	0.723668i	−0.136817	+	0.0994034i	0.517272	+	0.855821i	$0.326948\pi$
$54$	−5.31636	+	3.86256i	−0.723466	+	0.525628i
$55$		0			0
$56$	−7.29141	−	5.29752i	−0.974356	−	0.707911i
$57$	3.94246			0.522191
$58$	−5.62552	−	4.08718i	−0.738668	−	0.536673i
$59$	1.39299	−	4.28718i	0.181352	−	0.558143i	−0.818515	−	0.574485i	$-0.805202\pi$
$59$	1.39299	−	4.28718i	0.181352	−	0.558143i	0.999866	+	0.0163426i	$0.00520224\pi$
$60$		0			0
$61$	−3.60276	−	11.0881i	−0.461286	−	1.41969i	−0.863594	−	0.504187i	$-0.831792\pi$
$61$	−3.60276	−	11.0881i	−0.461286	−	1.41969i	0.402309	−	0.915504i	$-0.368208\pi$
$62$	−1.81827	+	5.59606i	−0.230921	+	0.710700i
$63$	3.54032	−	10.8960i	0.446038	−	1.37277i
$64$	0.761103	+	2.34244i	0.0951379	+	0.292804i
$65$		0			0
$66$	−1.44660	+	4.45216i	−0.178064	+	0.548023i
$67$	2.39022	+	1.73660i	0.292012	+	0.212159i	0.724140	−	0.689653i	$-0.242237\pi$
$67$	2.39022	+	1.73660i	0.292012	+	0.212159i	−0.432128	+	0.901812i	$0.642237\pi$
$68$	−0.193968			−0.0235220
$69$	−2.83469	−	2.05952i	−0.341257	−	0.247938i
$70$		0			0
$71$	−2.59331	+	1.88415i	−0.307770	+	0.223608i	−0.730939	−	0.682443i	$-0.760918\pi$
$71$	−2.59331	+	1.88415i	−0.307770	+	0.223608i	0.423169	+	0.906051i	$0.360918\pi$
$72$	−3.96312	+	2.87938i	−0.467058	+	0.339338i
$73$	−3.18047	−	9.78847i	−0.372245	−	1.14565i	−0.945318	−	0.326149i	$-0.894249\pi$
$73$	−3.18047	−	9.78847i	−0.372245	−	1.14565i	0.573073	−	0.819504i	$-0.305751\pi$
$74$	−9.11816			−1.05996
$75$		0			0
$76$	−4.62806			−0.530875
$77$	−5.55402	−	17.0935i	−0.632940	−	1.94799i
$78$	−0.554272	+	0.402702i	−0.0627589	+	0.0455970i
$79$	7.77877	−	5.65161i	0.875180	−	0.635856i	−0.0567919	−	0.998386i	$-0.518087\pi$
$79$	7.77877	−	5.65161i	0.875180	−	0.635856i	0.931972	+	0.362531i	$0.118087\pi$
$80$		0			0
$81$	−3.81318	−	2.77044i	−0.423687	−	0.307827i
$82$	17.5457			1.93759
$83$	8.48125	+	6.16199i	0.930938	+	0.676366i	0.946222	−	0.323517i	$-0.104865\pi$
$83$	8.48125	+	6.16199i	0.930938	+	0.676366i	−0.0152844	+	0.999883i	$0.504865\pi$
$84$	0.840358	−	2.58636i	0.0916906	−	0.282195i
$85$		0			0
$86$	0.722211	+	2.22274i	0.0778780	+	0.239684i
$87$	−0.906701	+	2.79054i	−0.0972086	+	0.299177i
$88$	−2.37480	+	7.30889i	−0.253155	+	0.779130i
$89$	2.24293	+	6.90303i	0.237750	+	0.731720i	0.996745	+	0.0806230i	$0.0256910\pi$
$89$	2.24293	+	6.90303i	0.237750	+	0.731720i	−0.758994	+	0.651097i	$0.774309\pi$
$90$		0			0
$91$	0.812846	−	2.50168i	0.0852094	−	0.262248i
$92$	3.32765	+	2.41768i	0.346932	+	0.252061i
$93$	2.48286			0.257461
$94$	−1.25352	−	0.910739i	−0.129291	−	0.0939356i
$95$		0			0
$96$	−2.55412	+	1.85568i	−0.260679	+	0.189394i
$97$	6.73079	−	4.89020i	0.683408	−	0.496525i	−0.191079	−	0.981575i	$-0.561199\pi$
$97$	6.73079	−	4.89020i	0.683408	−	0.496525i	0.874487	+	0.485050i	$0.161199\pi$
$98$	7.32353	+	22.5395i	0.739788	+	2.27683i
$99$	−9.76903			−0.981824
$100$		0			0
$101$	−3.56513			−0.354744			−0.177372	−	0.984144i	$-0.556760\pi$
$101$	−3.56513			−0.354744			−0.177372	+	0.984144i	$0.556760\pi$
$102$	0.0859547	+	0.264541i	0.00851078	+	0.0261935i
$103$	0.323059	−	0.234716i	0.0318320	−	0.0231273i	−0.571756	−	0.820424i	$-0.693737\pi$
$103$	0.323059	−	0.234716i	0.0318320	−	0.0231273i	0.603587	+	0.797297i	$0.293737\pi$
$104$	−0.909920	+	0.661095i	−0.0892250	+	0.0648257i
$105$		0			0
$106$	−1.67675	−	1.21823i	−0.162860	−	0.118325i
$107$	−1.64372			−0.158904			−0.0794522	−	0.996839i	$-0.525317\pi$
$107$	−1.64372			−0.158904			−0.0794522	+	0.996839i	$0.525317\pi$
$108$	−2.63344	−	1.91331i	−0.253403	−	0.184108i
$109$	0.0231501	−	0.0712488i	0.00221738	−	0.00682440i	−0.949942	−	0.312427i	$-0.898858\pi$
$109$	0.0231501	−	0.0712488i	0.00221738	−	0.00682440i	0.952159	+	0.305603i	$0.0988580\pi$
$110$		0			0
$111$	1.18896	+	3.65923i	0.112851	+	0.347319i
$112$	7.05449	−	21.7115i	0.666587	−	2.05154i
$113$	4.36729	−	13.4411i	0.410840	−	1.26444i	−0.505079	−	0.863073i	$-0.668537\pi$
$113$	4.36729	−	13.4411i	0.410840	−	1.26444i	0.915919	−	0.401363i	$-0.131463\pi$
$114$	2.05088	+	6.31195i	0.192082	+	0.591168i
$115$		0			0
$116$	1.06438	−	3.27582i	0.0988251	−	0.304152i
$117$	−1.15667	−	0.840370i	−0.106934	−	0.0776922i
$118$	7.58848			0.698576
$119$	−0.863983	−	0.627721i	−0.0792012	−	0.0575431i
$120$		0			0
$121$	−3.49946	+	2.54251i	−0.318133	+	0.231137i
$122$	15.8782	−	11.5362i	1.43754	−	1.04443i
$123$	−2.28786	−	7.04130i	−0.206289	−	0.634892i
$124$	−2.91464			−0.261742
$125$		0			0
$126$	19.2864			1.71817
$127$	3.65025	+	11.2343i	0.323907	+	0.996883i	0.971932	+	0.235264i	$0.0755954\pi$
$127$	3.65025	+	11.2343i	0.323907	+	0.996883i	−0.648025	+	0.761619i	$0.724405\pi$
$128$	−10.5456	+	7.66184i	−0.932109	+	0.677217i
$129$	0.797840	−	0.579665i	0.0702459	−	0.0510366i
$130$		0			0
$131$	13.5407	+	9.83791i	1.18306	+	0.859542i	0.992513	−	0.122136i	$-0.0389744\pi$
$131$	13.5407	+	9.83791i	1.18306	+	0.859542i	0.190545	+	0.981678i	$0.438974\pi$
$132$	−2.31885			−0.201830
$133$	−20.6146	−	14.9774i	−1.78751	−	1.29871i
$134$	−1.53692	+	4.73017i	−0.132770	+	0.408624i
$135$		0			0
$136$	0.141107	+	0.434284i	0.0120999	+	0.0372395i
$137$	3.22062	−	9.91204i	0.275156	−	0.846843i	−0.714022	−	0.700123i	$-0.753128\pi$
$137$	3.22062	−	9.91204i	0.275156	−	0.846843i	0.989178	−	0.146720i	$-0.0468715\pi$
$138$	1.82272	−	5.60976i	0.155160	−	0.477535i
$139$	2.05803	+	6.33397i	0.174560	+	0.537241i	0.999613	−	0.0278147i	$-0.00885484\pi$
$139$	2.05803	+	6.33397i	0.174560	+	0.537241i	−0.825053	+	0.565055i	$0.808855\pi$
$140$		0			0
$141$	−0.202038	+	0.621811i	−0.0170147	+	0.0523659i
$142$	−4.36561	−	3.17180i	−0.366354	−	0.266172i
$143$	−2.24294			−0.187564
$144$	−10.0385	−	7.29336i	−0.836538	−	0.607780i
$145$		0			0
$146$	14.0170	−	10.1840i	1.16006	−	0.842831i
$147$	8.09044	−	5.87805i	0.667289	−	0.484814i
$148$	−1.39572	−	4.29558i	−0.114727	−	0.353095i
$149$	−12.0316			−0.985667			−0.492834	−	0.870124i	$-0.664039\pi$
$149$	−12.0316			−0.985667			−0.492834	+	0.870124i	$0.664039\pi$
$150$		0			0
$151$	−1.54218			−0.125501			−0.0627505	−	0.998029i	$-0.519987\pi$
$151$	−1.54218			−0.125501			−0.0627505	+	0.998029i	$0.519987\pi$
$152$	3.36682	+	10.3620i	0.273085	+	0.840469i
$153$	−0.469603	+	0.341187i	−0.0379652	+	0.0275833i
$154$	24.4778	−	17.7842i	1.97248	−	1.43309i
$155$		0			0
$156$	−0.274556	−	0.199477i	−0.0219821	−	0.0159709i
$157$	−9.82482			−0.784106			−0.392053	−	0.919943i	$-0.628235\pi$
$157$	−9.82482			−0.784106			−0.392053	+	0.919943i	$0.628235\pi$
$158$	13.0949	+	9.51397i	1.04177	+	0.756891i
$159$	−0.270252	+	0.831751i	−0.0214324	+	0.0659622i
$160$		0			0
$161$	6.99812	+	21.5380i	0.551529	+	1.69743i
$162$	2.45190	−	7.54617i	0.192639	−	0.592883i
$163$	−1.72465	+	5.30792i	−0.135085	+	0.415748i	−0.995603	−	0.0936712i	$-0.970140\pi$
$163$	−1.72465	+	5.30792i	−0.135085	+	0.415748i	0.860518	+	0.509419i	$0.170140\pi$
$164$	2.68572	+	8.26580i	0.209720	+	0.645450i
$165$		0			0
$166$	−5.45349	+	16.7841i	−0.423273	+	1.30270i
$167$	17.6857	+	12.8494i	1.36856	+	0.994318i	0.997848	+	0.0655703i	$0.0208867\pi$
$167$	17.6857	+	12.8494i	1.36856	+	0.994318i	0.370713	+	0.928747i	$0.379113\pi$
$168$	−6.40207			−0.493930
$169$	10.2517	+	7.44826i	0.788589	+	0.572943i
$170$		0			0
$171$	−11.2047	+	8.14071i	−0.856847	+	0.622536i
$172$	−0.936586	+	0.680470i	−0.0714140	+	0.0518853i
$173$	7.24291	+	22.2914i	0.550668	+	1.69478i	0.707117	+	0.707096i	$0.249995\pi$
$173$	7.24291	+	22.2914i	0.550668	+	1.69478i	−0.156449	+	0.987686i	$0.550005\pi$
$174$	−4.93937			−0.374453
$175$		0			0
$176$	−19.4659			−1.46730
$177$	−0.989495	−	3.04535i	−0.0743750	−	0.228903i
$178$	−9.88511	+	7.18195i	−0.740920	+	0.538310i
$179$	5.11196	−	3.71406i	0.382086	−	0.277602i	−0.380119	−	0.924938i	$-0.624117\pi$
$179$	5.11196	−	3.71406i	0.382086	−	0.277602i	0.762205	+	0.647336i	$0.224117\pi$
$180$		0			0
$181$	10.7904	+	7.83972i	0.802047	+	0.582722i	0.911514	−	0.411269i	$-0.134914\pi$
$181$	10.7904	+	7.83972i	0.802047	+	0.582722i	−0.109467	+	0.993990i	$0.534914\pi$
$182$	4.42808			0.328231
$183$	−6.70003	−	4.86786i	−0.495280	−	0.359842i
$184$	2.99227	−	9.20926i	0.220593	−	0.678916i
$185$		0			0
$186$	1.29159	+	3.97511i	0.0947040	+	0.291469i
$187$	−0.281398	+	0.866054i	−0.0205779	+	0.0633322i
$188$	0.237174	−	0.729945i	0.0172977	−	0.0532367i
$189$	−5.53817	−	17.0447i	−0.402843	−	1.23982i
$190$		0			0
$191$	−0.859323	+	2.64472i	−0.0621784	+	0.191365i	−0.977320	−	0.211766i	$-0.932078\pi$
$191$	−0.859323	+	2.64472i	−0.0621784	+	0.191365i	0.915142	+	0.403132i	$0.132078\pi$
$192$	1.41542	+	1.02836i	0.102149	+	0.0742157i
$193$	22.5667			1.62438			0.812192	−	0.583391i	$-0.198274\pi$
$193$	22.5667			1.62438			0.812192	+	0.583391i	$0.198274\pi$
$194$	11.3307	+	8.23222i	0.813495	+	0.591039i
$195$		0			0
$196$	−9.49739	+	6.90026i	−0.678385	+	0.492876i
$197$	−1.02892	+	0.747558i	−0.0733079	+	0.0532613i	−0.623836	−	0.781556i	$-0.714427\pi$
$197$	−1.02892	+	0.747558i	−0.0733079	+	0.0532613i	0.550528	+	0.834817i	$0.314427\pi$
$198$	−5.08187	−	15.6404i	−0.361153	−	1.11151i
$199$	−8.62648			−0.611515			−0.305757	−	0.952109i	$-0.598910\pi$
$199$	−8.62648			−0.611515			−0.305757	+	0.952109i	$0.598910\pi$
$200$		0			0
$201$	2.09868			0.148030
$202$	−1.85459	−	5.70784i	−0.130488	−	0.401602i
$203$	15.3423	−	11.1468i	1.07682	−	0.782354i
$204$	−0.111469	+	0.0809868i	−0.00780438	+	0.00567021i
$205$		0			0
$206$	0.543841	+	0.395124i	0.0378912	+	0.0275296i
$207$	12.3091			0.855538
$208$	−2.30480	−	1.67453i	−0.159809	−	0.116108i
$209$	−6.71415	+	20.6640i	−0.464428	+	1.42936i
$210$		0			0
$211$	−6.49912	−	20.0022i	−0.447418	−	1.37701i	−0.879810	−	0.475325i	$-0.842330\pi$
$211$	−6.49912	−	20.0022i	−0.447418	−	1.37701i	0.432392	−	0.901686i	$-0.357670\pi$
$212$	0.317250	−	0.976395i	0.0217888	−	0.0670591i
$213$	−0.703633	+	2.16556i	−0.0482121	+	0.148382i
$214$	−0.855067	−	2.63162i	−0.0584511	−	0.179894i
$215$		0			0
$216$	−2.36803	+	7.28803i	−0.161124	+	0.495888i
$217$	−12.9826	−	9.43239i	−0.881315	−	0.640313i
$218$	0.126113			0.00854148
$219$	−5.91470	−	4.29728i	−0.399678	−	0.290383i
$220$		0			0
$221$	−0.107819	+	0.0783354i	−0.00725272	+	0.00526941i
$222$	−5.24000	+	3.80708i	−0.351686	+	0.255515i
$223$	−1.95774	−	6.02530i	−0.131100	−	0.403484i	0.863863	−	0.503726i	$-0.168038\pi$
$223$	−1.95774	−	6.02530i	−0.131100	−	0.403484i	−0.994963	+	0.100243i	$0.968038\pi$
$224$	20.4049			1.36336
$225$		0			0
$226$	23.7914			1.58258
$227$	−3.48028	−	10.7112i	−0.230994	−	0.710926i	−0.997628	−	0.0688416i	$-0.978070\pi$
$227$	−3.48028	−	10.7112i	−0.230994	−	0.710926i	0.766634	−	0.642085i	$-0.221930\pi$
$228$	−2.65964	+	1.93234i	−0.176139	+	0.127973i
$229$	−12.1683	+	8.84079i	−0.804104	+	0.584216i	−0.912115	−	0.409934i	$-0.865552\pi$
$229$	−12.1683	+	8.84079i	−0.804104	+	0.584216i	0.108011	+	0.994150i	$0.465552\pi$
$230$		0			0
$231$	−10.3288	−	7.50431i	−0.679585	−	0.493747i
$232$	−8.10872			−0.532363
$233$	6.33257	+	4.60088i	0.414861	+	0.301414i	0.775567	−	0.631266i	$-0.217464\pi$
$233$	6.33257	+	4.60088i	0.414861	+	0.301414i	−0.360706	+	0.932680i	$0.617464\pi$
$234$	0.743745	−	2.28901i	0.0486201	−	0.149637i
$235$		0			0
$236$	1.16157	+	3.57495i	0.0756119	+	0.232709i
$237$	2.11058	−	6.49570i	0.137097	−	0.421941i
$238$	0.555546	−	1.70979i	0.0360107	−	0.110830i
$239$	2.70046	+	8.31115i	0.174678	+	0.537603i	0.999619	−	0.0276159i	$-0.00879153\pi$
$239$	2.70046	+	8.31115i	0.174678	+	0.537603i	−0.824941	+	0.565219i	$0.808792\pi$
$240$		0			0
$241$	−0.185686	+	0.571482i	−0.0119611	+	0.0368124i	−0.956859	−	0.290553i	$-0.906161\pi$
$241$	−0.185686	+	0.571482i	−0.0119611	+	0.0368124i	0.944898	+	0.327365i	$0.106161\pi$
$242$	−5.89102	−	4.28008i	−0.378689	−	0.275134i
$243$	−15.0589			−0.966031
$244$	7.86518	+	5.71439i	0.503517	+	0.365826i
$245$		0			0
$246$	10.0831	−	7.32580i	0.642875	−	0.467076i
$247$	−2.57257	+	1.86908i	−0.163689	+	0.118927i
$248$	2.12034	+	6.52573i	0.134642	+	0.414384i
$249$	7.44678			0.471921
$250$		0			0
$251$	−14.1908			−0.895712			−0.447856	−	0.894106i	$-0.647812\pi$
$251$	−14.1908			−0.895712			−0.447856	+	0.894106i	$0.647812\pi$
$252$	2.95217	+	9.08584i	0.185969	+	0.572354i
$253$	15.6224	−	11.3503i	0.982171	−	0.713589i
$254$	−16.0875	+	11.6882i	−1.00942	+	0.733384i
$255$		0			0
$256$	−13.7674	−	10.0026i	−0.860463	−	0.625163i
$257$	−17.6859			−1.10322			−0.551609	−	0.834103i	$-0.685986\pi$
$257$	−17.6859			−1.10322			−0.551609	+	0.834103i	$0.685986\pi$
$258$	1.34309	+	0.975813i	0.0836173	+	0.0607515i
$259$	7.68452	−	23.6505i	0.477493	−	1.46957i
$260$		0			0
$261$	−3.18523	−	9.80313i	−0.197161	−	0.606799i
$262$	−8.70676	+	26.7967i	−0.537906	+	1.65550i
$263$	−7.51987	+	23.1438i	−0.463695	+	1.42711i	0.396922	+	0.917852i	$0.370078\pi$
$263$	−7.51987	+	23.1438i	−0.463695	+	1.42711i	−0.860617	+	0.509254i	$0.829922\pi$
$264$	1.68692	+	5.19180i	0.103823	+	0.319533i
$265$		0			0
$266$	13.2553	−	40.7957i	0.812736	−	2.50134i
$267$	4.17117	+	3.03053i	0.255271	+	0.185466i
$268$	−2.46365			−0.150491
$269$	−24.2558	−	17.6229i	−1.47890	−	1.07449i	−0.977908	−	0.209037i	$-0.932967\pi$
$269$	−24.2558	−	17.6229i	−1.47890	−	1.07449i	−0.500996	−	0.865449i	$-0.667033\pi$
$270$		0			0
$271$	22.4083	−	16.2806i	1.36121	−	0.988974i	0.362838	−	0.931852i	$-0.381808\pi$
$271$	22.4083	−	16.2806i	1.36121	−	0.988974i	0.998367	−	0.0571213i	$-0.0181922\pi$
$272$	−0.935738	+	0.679854i	−0.0567375	+	0.0412222i
$273$	−0.577397	−	1.77705i	−0.0349457	−	0.107552i
$274$	17.5447			1.05992
$275$		0			0
$276$	2.92177			0.175870
$277$	0.708908	+	2.18179i	0.0425941	+	0.131091i	0.970092	−	0.242737i	$-0.0780451\pi$
$277$	0.708908	+	2.18179i	0.0425941	+	0.131091i	−0.927498	+	0.373828i	$0.878045\pi$
$278$	−9.07021	+	6.58990i	−0.543995	+	0.395236i
$279$	−7.05646	+	5.12682i	−0.422459	+	0.306934i
$280$		0			0
$281$	1.30922	+	0.951204i	0.0781015	+	0.0567441i	0.626151	−	0.779702i	$-0.284629\pi$
$281$	1.30922	+	0.951204i	0.0781015	+	0.0567441i	−0.548049	+	0.836446i	$0.684629\pi$
$282$	−1.10063			−0.0655416
$283$	10.5109	+	7.63662i	0.624808	+	0.453950i	0.854598	−	0.519291i	$-0.173804\pi$
$283$	10.5109	+	7.63662i	0.624808	+	0.453950i	−0.229789	+	0.973240i	$0.573804\pi$
$284$	0.825997	−	2.54216i	0.0490139	−	0.150849i
$285$		0			0
$286$	−1.16678	−	3.59098i	−0.0689932	−	0.212339i
$287$	−14.7870	+	45.5096i	−0.872848	+	2.68635i
$288$	3.42723	−	10.5479i	0.201951	−	0.621542i
$289$	−5.23657	−	16.1165i	−0.308033	−	0.948029i
$290$		0			0
$291$	1.82624	−	5.62058i	0.107056	−	0.329484i
$292$	6.94328	+	5.04459i	0.406325	+	0.295212i
$293$	−11.7009			−0.683572			−0.341786	−	0.939778i	$-0.611032\pi$
$293$	−11.7009			−0.683572			−0.341786	+	0.939778i	$0.611032\pi$
$294$	13.6195	+	9.89517i	0.794308	+	0.577098i
$295$		0			0
$296$	−8.60224	+	6.24990i	−0.499995	+	0.363268i
$297$	−12.3633	+	8.98244i	−0.717389	+	0.521214i
$298$	−6.25887	−	19.2628i	−0.362566	−	1.11586i
$299$	2.82612			0.163439
$300$		0			0
$301$	−6.37395			−0.367388
$302$	−0.802247	−	2.46906i	−0.0461641	−	0.142079i
$303$	−2.04880	+	1.48854i	−0.117701	+	0.0855144i
$304$	−22.3267	+	16.2213i	−1.28052	+	0.930355i
$305$		0			0
$306$	−0.790535	−	0.574358i	−0.0451919	−	0.0328338i
$307$	26.5673			1.51628			0.758138	−	0.652094i	$-0.226109\pi$
$307$	26.5673			1.51628			0.758138	+	0.652094i	$0.226109\pi$
$308$	12.1250	+	8.80933i	0.690886	+	0.501958i
$309$	0.0876543	−	0.269772i	0.00498648	−	0.0153468i
$310$		0			0
$311$	−4.16895	−	12.8307i	−0.236399	−	0.727563i	−0.996933	−	0.0782636i	$-0.975062\pi$
$311$	−4.16895	−	12.8307i	−0.236399	−	0.727563i	0.760533	−	0.649299i	$-0.224938\pi$
$312$	−0.246885	+	0.759833i	−0.0139771	+	0.0430171i
$313$	5.25155	−	16.1626i	0.296835	−	0.913564i	−0.685764	−	0.727824i	$-0.740532\pi$
$313$	5.25155	−	16.1626i	0.296835	−	0.913564i	0.982599	−	0.185740i	$-0.0594683\pi$
$314$	−5.11089	−	15.7297i	−0.288424	−	0.887679i
$315$		0			0
$316$	−2.47762	+	7.62532i	−0.139377	+	0.428958i
$317$	−13.5882	−	9.87237i	−0.763187	−	0.554488i	0.136699	−	0.990613i	$-0.456351\pi$
$317$	−13.5882	−	9.87237i	−0.763187	−	0.554488i	−0.899886	+	0.436125i	$0.856351\pi$
$318$	−1.47224			−0.0825588
$319$	−13.0822	−	9.50479i	−0.732464	−	0.532166i
$320$		0			0
$321$	−0.944608	+	0.686298i	−0.0527229	+	0.0383054i
$322$	−30.8423	+	22.4082i	−1.71877	+	1.24876i
$323$	0.398945	+	1.22783i	0.0221979	+	0.0683182i
$324$	3.93033			0.218351
$325$		0			0
$326$	−9.39524			−0.520354
$327$	−0.0164445	−	0.0506109i	−0.000909382	−	0.00279879i
$328$	16.5529	−	12.0264i	0.913982	−	0.664047i
$329$	3.41869	−	2.48383i	0.188479	−	0.136938i
$330$		0			0
$331$	−10.3832	−	7.54386i	−0.570714	−	0.414648i	0.264650	−	0.964344i	$-0.414743\pi$
$331$	−10.3832	−	7.54386i	−0.570714	−	0.414648i	−0.835365	+	0.549696i	$0.814743\pi$
$332$	−8.74180			−0.479768
$333$	−10.9350	−	7.94473i	−0.599233	−	0.435368i
$334$	−11.3720	+	34.9994i	−0.622249	+	1.91508i
$335$		0			0
$336$	−5.01109	−	15.4225i	−0.273377	−	0.841369i
$337$	6.56274	−	20.1980i	0.357495	−	1.10026i	−0.597053	−	0.802202i	$-0.703662\pi$
$337$	6.56274	−	20.1980i	0.357495	−	1.10026i	0.954548	−	0.298056i	$-0.0963382\pi$
$338$	−6.59187	+	20.2877i	−0.358550	+	1.10350i
$339$	−3.10226	−	9.54778i	−0.168492	−	0.518564i
$340$		0			0
$341$	−4.22841	+	13.0137i	−0.228981	+	0.704731i
$342$	−18.8622	−	13.7042i	−1.01995	−	0.741036i
$343$	−32.4969			−1.75467
$344$	2.20489	+	1.60194i	0.118879	+	0.0863710i
$345$		0			0
$346$	−31.9211	+	23.1921i	−1.71609	+	1.24681i
$347$	−23.1606	+	16.8272i	−1.24333	+	0.903331i	−0.997815	−	0.0660623i	$-0.978956\pi$
$347$	−23.1606	+	16.8272i	−1.24333	+	0.903331i	−0.245513	+	0.969393i	$0.578956\pi$
$348$	−0.756071	−	2.32695i	−0.0405297	−	0.124738i
$349$	19.9124			1.06588			0.532942	−	0.846152i	$-0.321086\pi$
$349$	19.9124			1.06588			0.532942	+	0.846152i	$0.321086\pi$
$350$		0			0
$351$	−2.23654			−0.119377
$352$	−5.37660	−	16.5475i	−0.286574	−	0.881984i
$353$	−19.9759	+	14.5133i	−1.06321	+	0.772467i	−0.974679	−	0.223607i	$-0.928217\pi$
$353$	−19.9759	+	14.5133i	−1.06321	+	0.772467i	−0.0885298	+	0.996074i	$0.528217\pi$
$354$	4.36093	−	3.16840i	0.231781	−	0.168399i
$355$		0			0
$356$	−4.89655	−	3.55755i	−0.259516	−	0.188550i
$357$	−0.758602			−0.0401495
$358$	8.60552	+	6.25228i	0.454816	+	0.330443i
$359$	6.64419	−	20.4487i	0.350667	−	1.07924i	−0.607812	−	0.794081i	$-0.707953\pi$
$359$	6.64419	−	20.4487i	0.350667	−	1.07924i	0.958479	−	0.285162i	$-0.0920473\pi$
$360$		0			0
$361$	3.64751	+	11.2259i	0.191974	+	0.590835i
$362$	−6.93832	+	21.3539i	−0.364670	+	1.12234i
$363$	−0.949494	+	2.92224i	−0.0498355	+	0.153378i
$364$	0.677808	+	2.08608i	0.0355268	+	0.109340i
$365$		0			0
$366$	4.30816	−	13.2591i	0.225191	−	0.693066i
$367$	0.925379	+	0.672327i	0.0483044	+	0.0350952i	0.611675	−	0.791109i	$-0.290496\pi$
$367$	0.925379	+	0.672327i	0.0483044	+	0.0350952i	−0.563371	+	0.826204i	$0.690496\pi$
$368$	24.5272			1.27857
$369$	21.0417	+	15.2877i	1.09539	+	0.795845i
$370$		0			0
$371$	4.57294	−	3.32244i	0.237415	−	0.172492i
$372$	−1.67498	+	1.21694i	−0.0868435	+	0.0630955i
$373$	3.56590	+	10.9747i	0.184636	+	0.568250i	0.999942	−	0.0107800i	$-0.00343146\pi$
$373$	3.56590	+	10.9747i	0.184636	+	0.568250i	−0.815306	+	0.579030i	$0.803431\pi$
$374$	−1.53295			−0.0792671
$375$		0			0
$376$	−1.80685			−0.0931812
$377$	−0.731318	−	2.25077i	−0.0376648	−	0.115920i
$378$	24.4080	−	17.7334i	1.25541	−	0.912110i
$379$	−17.0745	+	12.4054i	−0.877059	+	0.637221i	−0.932472	−	0.361243i	$-0.882352\pi$
$379$	−17.0745	+	12.4054i	−0.877059	+	0.637221i	0.0554129	+	0.998464i	$0.482352\pi$
$380$		0			0
$381$	6.78835	+	4.93202i	0.347778	+	0.252675i
$382$	−4.68127			−0.239515
$383$	0.694241	+	0.504395i	0.0354740	+	0.0257734i	0.605381	−	0.795936i	$-0.293021\pi$
$383$	0.694241	+	0.504395i	0.0354740	+	0.0257734i	−0.569907	+	0.821709i	$0.693021\pi$
$384$	−2.86130	+	8.80617i	−0.146015	+	0.449388i
$385$		0			0
$386$	11.7392	+	36.1296i	0.597511	+	1.83895i
$387$	−1.07057	+	3.29489i	−0.0544204	+	0.167489i
$388$	−2.14382	+	6.59801i	−0.108836	+	0.334963i
$389$	−10.4864	−	32.2738i	−0.531681	−	1.63634i	−0.750714	−	0.660627i	$-0.770290\pi$
$389$	−10.4864	−	32.2738i	−0.531681	−	1.63634i	0.219034	−	0.975717i	$-0.429710\pi$
$390$		0			0
$391$	0.354564	−	1.09124i	0.0179311	−	0.0551862i
$392$	22.3585	+	16.2444i	1.12927	+	0.820466i
$393$	11.8891			0.599728
$394$	−1.73210	−	1.25845i	−0.0872621	−	0.0633996i
$395$		0			0
$396$	6.59034	−	4.78816i	0.331177	−	0.240614i
$397$	21.7048	−	15.7695i	1.08933	−	0.791446i	0.110046	−	0.993926i	$-0.464900\pi$
$397$	21.7048	−	15.7695i	1.08933	−	0.791446i	0.979286	+	0.202480i	$0.0649001\pi$
$398$	−4.48751	−	13.8112i	−0.224939	−	0.692290i
$399$	−18.1002			−0.906145
$400$		0			0
$401$	3.79757			0.189642			0.0948208	−	0.995494i	$-0.469772\pi$
$401$	3.79757			0.189642			0.0948208	+	0.995494i	$0.469772\pi$
$402$	1.09174	+	3.36003i	0.0544510	+	0.167583i
$403$	−1.62014	+	1.17710i	−0.0807049	+	0.0586355i
$404$	2.40509	−	1.74740i	0.119658	−	0.0869365i
$405$		0			0
$406$	25.8274	+	18.7647i	1.28179	+	0.931276i
$407$	−21.2044			−1.05106
$408$	0.262417	+	0.190657i	0.0129916	+	0.00943892i
$409$	−4.38043	+	13.4816i	−0.216598	+	0.666621i	0.782438	+	0.622728i	$0.213976\pi$
$409$	−4.38043	+	13.4816i	−0.216598	+	0.666621i	−0.999036	+	0.0438924i	$0.986024\pi$
$410$		0			0
$411$	−2.28773	−	7.04092i	−0.112846	−	0.347303i
$412$	−0.102898	+	0.316686i	−0.00506940	+	0.0156020i
$413$	−6.39535	+	19.6829i	−0.314695	+	0.968531i
$414$	6.40320	+	19.7070i	0.314700	+	0.968547i
$415$		0			0
$416$	0.786879	−	2.42177i	0.0385799	−	0.118737i
$417$	3.82731	+	2.78071i	0.187424	+	0.136172i
$418$	−36.5762			−1.78900
$419$	15.8542	+	11.5187i	0.774528	+	0.562727i	0.903332	−	0.428943i	$-0.141114\pi$
$419$	15.8542	+	11.5187i	0.774528	+	0.562727i	−0.128804	+	0.991670i	$0.541114\pi$
$420$		0			0
$421$	20.8597	−	15.1555i	1.01664	−	0.738632i	0.0510485	−	0.998696i	$-0.483744\pi$
$421$	20.8597	−	15.1555i	1.01664	−	0.738632i	0.965591	+	0.260064i	$0.0837437\pi$
$422$	28.6431	−	20.8104i	1.39432	−	1.01304i
$423$	−0.709759	−	2.18441i	−0.0345096	−	0.106210i
$424$	−2.41689			−0.117375
$425$		0			0
$426$	−3.83313			−0.185716
$427$	16.5406	+	50.9068i	0.800457	+	2.46355i
$428$	1.10888	−	0.805647i	0.0535996	−	0.0389424i
$429$	−1.28896	+	0.936488i	−0.0622318	+	0.0452141i
$430$		0			0
$431$	−7.62525	−	5.54007i	−0.367296	−	0.266856i	0.388793	−	0.921325i	$-0.372892\pi$
$431$	−7.62525	−	5.54007i	−0.367296	−	0.266856i	−0.756089	+	0.654469i	$0.772892\pi$
$432$	−19.4103			−0.933881
$433$	1.41708	+	1.02957i	0.0681006	+	0.0494780i	0.621315	−	0.783561i	$-0.286599\pi$
$433$	1.41708	+	1.02957i	0.0681006	+	0.0494780i	−0.553214	+	0.833039i	$0.686599\pi$
$434$	8.34787	−	25.6921i	0.400710	−	1.23326i
$435$		0			0
$436$	0.0193042	+	0.0594123i	0.000924504	+	0.00284533i
$437$	8.45989	−	26.0369i	0.404691	−	1.24551i
$438$	3.80318	−	11.7050i	0.181723	−	0.559286i
$439$	8.67814	+	26.7086i	0.414185	+	1.27473i	0.912978	+	0.408009i	$0.133777\pi$
$439$	8.67814	+	26.7086i	0.414185	+	1.27473i	−0.498793	+	0.866721i	$0.666223\pi$
$440$		0			0
$441$	−10.8561	+	33.4116i	−0.516957	+	1.59103i
$442$	−0.181504	−	0.131871i	−0.00863328	−	0.00627244i
$443$	29.9110			1.42111			0.710557	−	0.703640i	$-0.248443\pi$
$443$	29.9110			1.42111			0.710557	+	0.703640i	$0.248443\pi$
$444$	−2.59561	−	1.88582i	−0.123182	−	0.0894972i
$445$		0			0
$446$	8.62819	−	6.26875i	0.408557	−	0.296834i
$447$	−6.91429	+	5.02352i	−0.327035	+	0.237605i
$448$	−3.49431	−	10.7544i	−0.165090	−	0.508096i
$449$	6.29974			0.297303			0.148652	−	0.988890i	$-0.452507\pi$
$449$	6.29974			0.297303			0.148652	+	0.988890i	$0.452507\pi$
$450$		0			0
$451$	40.8026			1.92132
$452$	3.64175	+	11.2082i	0.171294	+	0.527188i
$453$	−0.886258	+	0.643904i	−0.0416400	+	0.0302532i
$454$	15.3384	−	11.1440i	0.719865	−	0.523012i
$455$		0			0
$456$	6.26126	+	4.54907i	0.293210	+	0.213030i
$457$	−19.1809			−0.897243			−0.448622	−	0.893722i	$-0.648085\pi$
$457$	−19.1809			−0.897243			−0.448622	+	0.893722i	$0.648085\pi$
$458$	−20.4842	−	14.8827i	−0.957166	−	0.695422i
$459$	−0.280595	+	0.863583i	−0.0130971	+	0.0403086i
$460$		0			0
$461$	2.18509	+	6.72502i	0.101770	+	0.313215i	0.988959	−	0.148191i	$-0.0473450\pi$
$461$	2.18509	+	6.72502i	0.101770	+	0.313215i	−0.887189	+	0.461406i	$0.847345\pi$
$462$	6.64147	−	20.4403i	0.308989	−	0.950971i
$463$	2.97225	−	9.14766i	0.138132	−	0.425128i	−0.857932	−	0.513764i	$-0.828251\pi$
$463$	2.97225	−	9.14766i	0.138132	−	0.425128i	0.996064	+	0.0886360i	$0.0282508\pi$
$464$	−6.34693	−	19.5339i	−0.294649	−	0.906836i
$465$		0			0
$466$	−4.07188	+	12.5320i	−0.188626	+	0.580531i
$467$	−15.5509	−	11.2984i	−0.719611	−	0.522828i	0.166649	−	0.986016i	$-0.446705\pi$
$467$	−15.5509	−	11.2984i	−0.719611	−	0.522828i	−0.886260	+	0.463188i	$0.846705\pi$
$468$	1.19220			0.0551096
$469$	−10.9737	−	7.97289i	−0.506720	−	0.368154i
$470$		0			0
$471$	−5.64610	+	4.10213i	−0.260159	+	0.189016i
$472$	7.15912	−	5.20140i	0.329525	−	0.239414i
$473$	1.67951	+	5.16900i	0.0772239	+	0.237671i
$474$	11.4977			0.528105
$475$		0			0
$476$	0.890525			0.0408172
$477$	−0.949393	−	2.92193i	−0.0434697	−	0.133786i
$478$	−11.9015	+	8.64696i	−0.544363	+	0.395503i
$479$	30.7423	−	22.3356i	1.40465	−	1.02054i	0.410579	−	0.911825i	$-0.365327\pi$
$479$	30.7423	−	22.3356i	1.40465	−	1.02054i	0.994073	−	0.108714i	$-0.0346734\pi$
$480$		0			0
$481$	−2.51063	−	1.82408i	−0.114475	−	0.0831710i
$482$	−1.01155			−0.0460747
$483$	13.0144	+	9.45549i	0.592174	+	0.430240i
$484$	1.11461	−	3.43043i	0.0506642	−	0.155928i
$485$		0			0
$486$	−7.83369	−	24.1096i	−0.355344	−	1.09364i
$487$	5.17572	−	15.9292i	0.234534	−	0.721823i	−0.762648	−	0.646813i	$-0.776101\pi$
$487$	5.17572	−	15.9292i	0.234534	−	0.721823i	0.997183	−	0.0750094i	$-0.0238987\pi$
$488$	7.07248	−	21.7669i	0.320156	−	0.985339i
$489$	1.22509	+	3.77043i	0.0554003	+	0.170505i
$490$		0			0
$491$	−2.76587	+	8.51248i	−0.124822	+	0.384163i	−0.993869	−	0.110567i	$-0.964733\pi$
$491$	−2.76587	+	8.51248i	−0.124822	+	0.384163i	0.869047	+	0.494730i	$0.164733\pi$
$492$	4.99462	+	3.62880i	0.225175	+	0.163599i
$493$	−0.960829			−0.0432736
$494$	−4.33069	−	3.14643i	−0.194847	−	0.141565i
$495$		0			0
$496$	−14.0608	+	10.2158i	−0.631348	+	0.458701i
$497$	11.9062	−	8.65034i	0.534065	−	0.388021i
$498$	3.87383	+	11.9224i	0.173591	+	0.534257i
$499$	−36.3310			−1.62640			−0.813200	−	0.581985i	$-0.802276\pi$
$499$	−36.3310			−1.62640			−0.813200	+	0.581985i	$0.802276\pi$
$500$		0			0
$501$	15.5286			0.693765
$502$	−7.38206	−	22.7197i	−0.329478	−	1.01403i
$503$	9.94645	−	7.22652i	0.443490	−	0.322215i	−0.343530	−	0.939142i	$-0.611623\pi$
$503$	9.94645	−	7.22652i	0.443490	−	0.322215i	0.787020	+	0.616927i	$0.211623\pi$
$504$	18.1951	−	13.2195i	0.810475	−	0.588844i
$505$		0			0
$506$	26.2989	+	19.1073i	1.16913	+	0.849422i
$507$	9.00125			0.399759
$508$	−7.96886	−	5.78971i	−0.353561	−	0.256877i
$509$	−9.61945	+	29.6056i	−0.426375	+	1.31225i	0.475297	+	0.879825i	$0.342341\pi$
$509$	−9.61945	+	29.6056i	−0.426375	+	1.31225i	−0.901672	+	0.432421i	$0.857659\pi$
$510$		0			0
$511$	14.6018	+	44.9399i	0.645948	+	1.98802i
$512$	0.796386	−	2.45102i	0.0351956	−	0.108321i
$513$	−6.69499	+	20.6051i	−0.295591	+	0.909736i
$514$	−9.20026	−	28.3155i	−0.405806	−	1.24894i
$515$		0			0
$516$	−0.254120	+	0.782101i	−0.0111870	+	0.0344301i
$517$	−2.91508	−	2.11793i	−0.128205	−	0.0931466i
$518$	41.8624			1.83933
$519$	13.4696	+	9.78624i	0.591250	+	0.429568i
$520$		0			0
$521$	−13.1198	+	9.53206i	−0.574787	+	0.417607i	−0.836841	−	0.547446i	$-0.815600\pi$
$521$	−13.1198	+	9.53206i	−0.574787	+	0.417607i	0.262054	+	0.965053i	$0.415600\pi$
$522$	14.0380	−	10.1992i	0.614428	−	0.446408i
$523$	9.45381	+	29.0958i	0.413386	+	1.27227i	0.913686	+	0.406420i	$0.133223\pi$
$523$	9.45381	+	29.0958i	0.413386	+	1.27227i	−0.500300	+	0.865852i	$0.666777\pi$
$524$	−13.9567			−0.609701
$525$		0			0
$526$	−40.9655			−1.78618
$527$	0.251246	+	0.773255i	0.0109444	+	0.0336835i
$528$	−11.1866	+	8.12755i	−0.486835	+	0.353706i
$529$	−1.07695	+	0.782451i	−0.0468240	+	0.0340196i
$530$		0			0
$531$	9.10051	+	6.61191i	0.394928	+	0.286932i
$532$	21.2479			0.921214
$533$	4.83110	+	3.51000i	0.209258	+	0.152035i
$534$	−2.68208	+	8.25461i	−0.116065	+	0.357212i
$535$		0			0
$536$	1.79225	+	5.51599i	0.0774135	+	0.238254i
$537$	1.38701	−	4.26877i	0.0598538	−	0.184211i
$538$	15.5966	−	48.0015i	0.672419	−	2.06949i
$539$	17.0310	+	52.4159i	0.733575	+	2.25771i
$540$		0			0
$541$	5.65545	−	17.4057i	0.243147	−	0.748329i	−0.752789	−	0.658262i	$-0.771292\pi$
$541$	5.65545	−	17.4057i	0.243147	−	0.748329i	0.995936	−	0.0900672i	$-0.0287082\pi$
$542$	37.7223	+	27.4069i	1.62031	+	1.17723i
$543$	9.47432			0.406582
$544$	−0.836383	−	0.607668i	−0.0358596	−	0.0260536i
$545$		0			0
$546$	2.54472	−	1.84885i	0.108904	−	0.0791233i
$547$	−5.30394	+	3.85354i	−0.226780	+	0.164765i	−0.695373	−	0.718649i	$-0.744761\pi$
$547$	−5.30394	+	3.85354i	−0.226780	+	0.164765i	0.468593	+	0.883414i	$0.344761\pi$
$548$	2.68558	+	8.26536i	0.114722	+	0.353078i
$549$	29.0935			1.24168
$550$		0			0
$551$	−22.9254			−0.976653
$552$	−2.12553	−	6.54171i	−0.0904686	−	0.278434i
$553$	−35.7131	+	25.9471i	−1.51868	+	1.10338i
$554$	−3.12432	+	2.26995i	−0.132739	+	0.0964409i
$555$		0			0
$556$	−4.49289	−	3.26428i	−0.190541	−	0.138436i
$557$	35.5383			1.50581			0.752904	−	0.658131i	$-0.228653\pi$
$557$	35.5383			1.50581			0.752904	+	0.658131i	$0.228653\pi$
$558$	−11.8789	−	8.63054i	−0.502875	−	0.365360i
$559$	−0.245800	+	0.756496i	−0.0103963	+	0.0319964i
$560$		0			0
$561$	0.199888	+	0.615193i	0.00843930	+	0.0259735i
$562$	−0.841836	+	2.59090i	−0.0355107	+	0.109291i
$563$	−11.8193	+	36.3760i	−0.498123	+	1.53306i	0.313911	+	0.949453i	$0.398361\pi$
$563$	−11.8193	+	36.3760i	−0.498123	+	1.53306i	−0.812033	+	0.583611i	$0.801639\pi$
$564$	−0.168474	−	0.518509i	−0.00709403	−	0.0218332i
$565$		0			0
$566$	−6.75857	+	20.8007i	−0.284084	+	0.874320i
$567$	17.5067	+	12.7194i	0.735213	+	0.534164i
$568$	−6.29266			−0.264034
$569$	−6.11534	−	4.44305i	−0.256368	−	0.186262i	0.452176	−	0.891929i	$-0.350648\pi$
$569$	−6.11534	−	4.44305i	−0.256368	−	0.186262i	−0.708544	+	0.705666i	$0.750648\pi$
$570$		0			0
$571$	−18.6286	+	13.5345i	−0.779583	+	0.566400i	−0.904854	−	0.425723i	$-0.860020\pi$
$571$	−18.6286	+	13.5345i	−0.779583	+	0.566400i	0.125271	+	0.992123i	$0.460020\pi$
$572$	1.51312	−	1.09935i	0.0632667	−	0.0459659i
$573$	0.610412	+	1.87865i	0.0255003	+	0.0784819i
$574$	−80.5540			−3.36226
$575$		0			0
$576$	−6.14617			−0.256090
$577$	−6.89626	−	21.2245i	−0.287095	−	0.883587i	−0.985763	−	0.168141i	$-0.946223\pi$
$577$	−6.89626	−	21.2245i	−0.287095	−	0.883587i	0.698668	−	0.715446i	$-0.253777\pi$
$578$	23.0787	−	16.7677i	0.959949	−	0.697444i
$579$	12.9685	−	9.42220i	0.538954	−	0.391573i
$580$		0			0
$581$	−38.9383	−	28.2903i	−1.61543	−	1.17368i
$582$	9.94866			0.412385
$583$	−3.89930	−	2.83301i	−0.161493	−	0.117331i
$584$	6.24349	−	19.2155i	0.258358	−	0.795143i
$585$		0			0
$586$	−6.08682	−	18.7333i	−0.251444	−	0.773866i
$587$	6.51365	−	20.0470i	0.268847	−	0.827426i	−0.721935	−	0.691961i	$-0.756747\pi$
$587$	6.51365	−	20.0470i	0.268847	−	0.827426i	0.990782	−	0.135465i	$-0.0432529\pi$
$588$	−2.57689	+	7.93085i	−0.106269	+	0.327063i
$589$	5.99472	+	18.4499i	0.247008	+	0.760213i
$590$		0			0
$591$	−0.279174	+	0.859209i	−0.0114837	+	0.0353431i
$592$	−21.7892	−	15.8308i	−0.895530	−	0.650641i
$593$	−34.3547			−1.41078			−0.705390	−	0.708819i	$-0.749228\pi$
$593$	−34.3547			−1.41078			−0.705390	+	0.708819i	$0.749228\pi$
$594$	−20.8124	−	15.1211i	−0.853945	−	0.620427i
$595$		0			0
$596$	8.11670	−	5.89713i	0.332473	−	0.241556i
$597$	−4.95744	+	3.60179i	−0.202895	+	0.147412i
$598$	1.47015	+	4.52467i	0.0601190	+	0.185027i
$599$	0.498231			0.0203572			0.0101786	−	0.999948i	$-0.496760\pi$
$599$	0.498231			0.0203572			0.0101786	+	0.999948i	$0.496760\pi$
$600$		0			0
$601$	27.8635			1.13657			0.568287	−	0.822830i	$-0.307606\pi$
$601$	27.8635			1.13657			0.568287	+	0.822830i	$0.307606\pi$
$602$	−3.31574	−	10.2048i	−0.135140	−	0.415917i
$603$	−5.96459	+	4.33353i	−0.242897	+	0.176475i
$604$	1.04038	−	0.755880i	0.0423325	−	0.0307563i
$605$		0			0
$606$	−3.44897	−	2.50582i	−0.140105	−	0.101792i
$607$	14.1000			0.572303			0.286152	−	0.958184i	$-0.407624\pi$
$607$	14.1000			0.572303			0.286152	+	0.958184i	$0.407624\pi$
$608$	−19.9561	−	14.4989i	−0.809326	−	0.588010i
$609$	4.16276	−	12.8117i	0.168684	−	0.519155i
$610$		0			0
$611$	−0.162958	−	0.501534i	−0.00659258	−	0.0202899i
$612$	0.149573	−	0.460340i	0.00604615	−	0.0186081i
$613$	9.83468	−	30.2680i	0.397219	−	1.22251i	−0.530001	−	0.847997i	$-0.677808\pi$
$613$	9.83468	−	30.2680i	0.397219	−	1.22251i	0.927220	−	0.374518i	$-0.122192\pi$
$614$	13.8204	+	42.5348i	0.557745	+	1.71656i
$615$		0			0
$616$	10.9030	−	33.5559i	0.439293	−	1.35200i
$617$	−27.4793	−	19.9649i	−1.10627	−	0.803755i	−0.124201	−	0.992257i	$-0.539637\pi$
$617$	−27.4793	−	19.9649i	−1.10627	−	0.803755i	−0.982073	+	0.188502i	$0.939637\pi$
$618$	0.477508			0.0192082
$619$	−0.912910	−	0.663268i	−0.0366929	−	0.0266590i	0.569288	−	0.822138i	$-0.307219\pi$
$619$	−0.912910	−	0.663268i	−0.0366929	−	0.0266590i	−0.605981	+	0.795479i	$0.707219\pi$
$620$		0			0
$621$	15.5778	−	11.3179i	0.625116	−	0.454173i
$622$	18.3735	−	13.3491i	0.736710	−	0.535251i
$623$	−10.2975	−	31.6925i	−0.412562	−	1.26974i
$624$	−2.02368			−0.0810119
$625$		0			0
$626$	28.6085			1.14343
$627$	4.76933	+	14.6785i	0.190469	+	0.586203i
$628$	6.62797	−	4.81550i	0.264485	−	0.192159i
$629$	−1.01931	+	0.740571i	−0.0406425	+	0.0295285i
$630$		0			0
$631$	−26.5197	−	19.2677i	−1.05573	−	0.767034i	−0.0824380	−	0.996596i	$-0.526271\pi$
$631$	−26.5197	−	19.2677i	−1.05573	−	0.767034i	−0.973294	+	0.229562i	$0.926271\pi$
$632$	18.8751			0.750813
$633$	−12.0864	−	8.78127i	−0.480391	−	0.349024i
$634$	8.73726	−	26.8905i	0.347001	−	1.06796i
$635$		0			0
$636$	−0.225355	−	0.693573i	−0.00893593	−	0.0275020i
$637$	−2.49252	+	7.67120i	−0.0987574	+	0.303944i
$638$	8.41194	−	25.8893i	0.333032	−	1.02497i
$639$	−2.47185	−	7.60758i	−0.0977850	−	0.300951i
$640$		0			0
$641$	9.39802	−	28.9241i	0.371199	−	1.14243i	−0.574808	−	0.818288i	$-0.694923\pi$
$641$	9.39802	−	28.9241i	0.371199	−	1.14243i	0.946007	−	0.324146i	$-0.105077\pi$
$642$	−1.59016	−	1.15532i	−0.0627587	−	0.0455969i
$643$	−1.06932			−0.0421700			−0.0210850	−	0.999778i	$-0.506712\pi$
$643$	−1.06932			−0.0421700			−0.0210850	+	0.999778i	$0.506712\pi$
$644$	−15.2776	−	11.0998i	−0.602022	−	0.437394i
$645$		0			0
$646$	−1.75824	+	1.27744i	−0.0691771	+	0.0502601i
$647$	24.7300	−	17.9674i	0.972237	−	0.706372i	0.0162768	−	0.999868i	$-0.494819\pi$
$647$	24.7300	−	17.9674i	0.972237	−	0.706372i	0.955960	+	0.293496i	$0.0948187\pi$
$648$	−2.85923	−	8.79981i	−0.112321	−	0.345689i
$649$	17.6471			0.692709
$650$		0			0
$651$	−11.3991			−0.446765
$652$	−1.43813	−	4.42611i	−0.0563216	−	0.173340i
$653$	−26.9808	+	19.6027i	−1.05584	+	0.767114i	−0.973315	−	0.229475i	$-0.926299\pi$
$653$	−26.9808	+	19.6027i	−1.05584	+	0.767114i	−0.0825273	+	0.996589i	$0.526299\pi$
$654$	0.0724745	−	0.0526558i	0.00283398	−	0.00205901i
$655$		0			0
$656$	41.9280	+	30.4624i	1.63701	+	1.18936i
$657$	25.6833			1.00200
$658$	5.75506	+	4.18130i	0.224356	+	0.163004i
$659$	−3.12572	+	9.61998i	−0.121761	+	0.374741i	−0.993297	−	0.115590i	$-0.963124\pi$
$659$	−3.12572	+	9.61998i	−0.121761	+	0.374741i	0.871536	+	0.490331i	$0.163124\pi$
$660$		0			0
$661$	−9.52955	−	29.3290i	−0.370657	−	1.14076i	−0.946362	−	0.323107i	$-0.895273\pi$
$661$	−9.52955	−	29.3290i	−0.370657	−	1.14076i	0.575706	−	0.817657i	$-0.304727\pi$
$662$	6.67648	−	20.5481i	0.259489	−	0.798624i
$663$	−0.0292542	+	0.0900351i	−0.00113614	+	0.00349667i
$664$	6.35948	+	19.5725i	0.246796	+	0.759558i
$665$		0			0
$666$	7.03125	−	21.6400i	0.272455	−	0.838532i
$667$	16.4837	+	11.9761i	0.638251	+	0.463717i
$668$	−18.2290			−0.705302
$669$	−3.64079	−	2.64519i	−0.140761	−	0.102269i
$670$		0			0
$671$	36.9248	−	26.8275i	1.42547	−	1.03566i
$672$	11.7262	−	8.51961i	0.452349	−	0.328651i
$673$	9.52544	+	29.3163i	0.367179	+	1.13006i	0.948606	+	0.316461i	$0.102495\pi$
$673$	9.52544	+	29.3163i	0.367179	+	1.13006i	−0.581427	+	0.813599i	$0.697505\pi$
$674$	35.7514			1.37709
$675$		0			0
$676$	−10.5666			−0.406407
$677$	−12.7476	−	39.2331i	−0.489930	−	1.50785i	−0.824712	−	0.565553i	$-0.808663\pi$
$677$	−12.7476	−	39.2331i	−0.489930	−	1.50785i	0.334782	−	0.942296i	$-0.391337\pi$
$678$	13.6724	−	9.93356i	0.525084	−	0.381496i
$679$	−30.9017	+	22.4514i	−1.18590	+	0.861607i
$680$		0			0
$681$	−6.47225	−	4.70237i	−0.248017	−	0.180195i
$682$	−23.0348			−0.882048
$683$	18.0827	+	13.1379i	0.691915	+	0.502706i	0.877289	−	0.479962i	$-0.159350\pi$
$683$	18.0827	+	13.1379i	0.691915	+	0.502706i	−0.185374	+	0.982668i	$0.559350\pi$
$684$	3.56882	−	10.9837i	0.136457	−	0.419972i
$685$		0			0
$686$	−16.9050	−	52.0282i	−0.645435	−	1.98644i
$687$	−3.30157	+	10.1612i	−0.125963	+	0.387674i
$688$	−2.13324	+	6.56544i	−0.0813291	+	0.250305i
$689$	−0.217978	−	0.670866i	−0.00830428	−	0.0255580i
$690$		0			0
$691$	2.83956	−	8.73927i	0.108022	−	0.332457i	−0.882406	−	0.470489i	$-0.844078\pi$
$691$	2.83956	−	8.73927i	0.108022	−	0.332457i	0.990428	+	0.138032i	$0.0440776\pi$
$692$	−15.8120	−	11.4881i	−0.601082	−	0.436712i
$693$	44.8506			1.70373
$694$	−38.9889	−	28.3271i	−1.48000	−	1.07528i
$695$		0			0
$696$	−4.65990	+	3.38561i	−0.176633	+	0.128331i
$697$	1.96141	−	1.42505i	0.0742937	−	0.0539775i
$698$	10.3585	+	31.8801i	0.392073	+	1.20668i
$699$	5.56018			0.210305
$700$		0			0
$701$	−35.9929			−1.35943			−0.679717	−	0.733475i	$-0.737897\pi$
$701$	−35.9929			−1.35943			−0.679717	+	0.733475i	$0.737897\pi$
$702$	−1.16345	−	3.58073i	−0.0439116	−	0.135146i
$703$	−24.3207	+	17.6700i	−0.917271	+	0.666437i
$704$	−7.80059	+	5.66746i	−0.293996	+	0.213600i
$705$		0			0
$706$	−33.6276	−	24.4319i	−1.26559	−	0.919506i
$707$	16.3679			0.615578
$708$	2.16017	+	1.56945i	0.0811841	+	0.0589837i
$709$	6.25640	−	19.2552i	0.234964	−	0.723145i	−0.762162	−	0.647386i	$-0.775862\pi$
$709$	6.25640	−	19.2552i	0.234964	−	0.723145i	0.997126	−	0.0757586i	$-0.0241378\pi$
$710$		0			0
$711$	7.41445	+	22.8193i	0.278063	+	0.855791i
$712$	−4.40304	+	13.5512i	−0.165011	+	0.507852i
$713$	5.32783	−	16.3974i	0.199529	−	0.614086i
$714$	−0.394627	−	1.21454i	−0.0147685	−	0.0454529i
$715$		0			0
$716$	−1.62821	+	5.01112i	−0.0608491	+	0.187274i
$717$	5.02202	+	3.64871i	0.187551	+	0.136264i
$718$	36.1951			1.35079
$719$	29.9551	+	21.7637i	1.11714	+	0.811647i	0.983773	−	0.179420i	$-0.0574220\pi$
$719$	29.9551	+	21.7637i	1.11714	+	0.811647i	0.133364	+	0.991067i	$0.457422\pi$
$720$		0			0
$721$	−1.48320	+	1.07761i	−0.0552372	+	0.0401322i
$722$	−16.0754	+	11.6794i	−0.598264	+	0.434664i
$723$	0.131900	+	0.405947i	0.00490542	+	0.0150973i
$724$	−11.1219			−0.413343
$725$		0			0
$726$	−5.17249			−0.191969
$727$	3.73261	+	11.4878i	0.138435	+	0.426059i	0.996108	−	0.0881356i	$-0.0280909\pi$
$727$	3.73261	+	11.4878i	0.138435	+	0.426059i	−0.857673	+	0.514195i	$0.828091\pi$
$728$	4.17754	−	3.03516i	0.154830	−	0.112490i
$729$	2.78552	−	2.02380i	0.103167	−	0.0749555i
$730$		0			0
$731$	0.261264	+	0.189820i	0.00966320	+	0.00702073i
$732$	6.90586			0.255248
$733$	36.0916	+	26.2221i	1.33307	+	0.968534i	0.999668	+	0.0257496i	$0.00819725\pi$
$733$	36.0916	+	26.2221i	1.33307	+	0.968534i	0.333404	+	0.942784i	$0.391803\pi$
$734$	−0.595024	+	1.83130i	−0.0219627	+	0.0675943i
$735$		0			0
$736$	6.77456	+	20.8500i	0.249714	+	0.768540i
$737$	−3.57413	+	11.0001i	−0.131655	+	0.405192i
$738$	−13.5299	+	41.6408i	−0.498043	+	1.53282i
$739$	−4.52596	−	13.9295i	−0.166490	−	0.512404i	0.832653	−	0.553795i	$-0.186821\pi$
$739$	−4.52596	−	13.9295i	−0.166490	−	0.512404i	−0.999143	+	0.0413910i	$0.986821\pi$
$740$		0			0
$741$	−0.698004	+	2.14824i	−0.0256418	+	0.0789174i
$742$	7.69813	+	5.59302i	0.282607	+	0.205326i
$743$	−24.4397			−0.896604			−0.448302	−	0.893882i	$-0.647971\pi$
$743$	−24.4397			−0.896604			−0.448302	+	0.893882i	$0.647971\pi$
$744$	3.94318	+	2.86489i	0.144564	+	0.105032i
$745$		0			0
$746$	−15.7157	+	11.4182i	−0.575394	+	0.418048i
$747$	−21.1642	+	15.3767i	−0.774359	+	0.562605i
$748$	−0.234650	−	0.722177i	−0.00857964	−	0.0264054i
$749$	7.54648			0.275743
$750$		0			0
$751$	31.2863			1.14165			0.570826	−	0.821071i	$-0.306623\pi$
$751$	31.2863			1.14165			0.570826	+	0.821071i	$0.306623\pi$
$752$	−1.41427	−	4.35269i	−0.0515733	−	0.158726i
$753$	−8.15510	+	5.92503i	−0.297189	+	0.215920i
$754$	3.22308	−	2.34171i	0.117378	−	0.0852800i
$755$		0			0
$756$	12.0904	+	8.78418i	0.439723	+	0.319478i
$757$	11.3251			0.411617			0.205808	−	0.978592i	$-0.434018\pi$
$757$	11.3251			0.411617			0.205808	+	0.978592i	$0.434018\pi$
$758$	−28.7434	−	20.8833i	−1.04401	−	0.758516i
$759$	4.23876	−	13.0456i	0.153857	−	0.473524i
$760$		0			0
$761$	−12.7728	−	39.3108i	−0.463015	−	1.42501i	−0.861462	−	0.507822i	$-0.830451\pi$
$761$	−12.7728	−	39.3108i	−0.463015	−	1.42501i	0.398447	−	0.917191i	$-0.369549\pi$
$762$	−4.36494	+	13.4339i	−0.158125	+	0.486659i
$763$	−0.106285	+	0.327111i	−0.00384776	+	0.0118422i
$764$	−0.716564	−	2.20536i	−0.0259244	−	0.0797870i
$765$		0			0
$766$	−0.446401	+	1.37388i	−0.0161291	+	0.0496403i
$767$	2.08945	+	1.51807i	0.0754455	+	0.0548144i
$768$	−12.0882			−0.436195
$769$	−18.3235	−	13.3128i	−0.660762	−	0.480072i	0.206158	−	0.978519i	$-0.433904\pi$
$769$	−18.3235	−	13.3128i	−0.660762	−	0.480072i	−0.866920	+	0.498447i	$0.833904\pi$
$770$		0			0
$771$	−10.1637	+	7.38436i	−0.366037	+	0.265941i
$772$	−15.2238	+	11.0607i	−0.547917	+	0.398085i
$773$	−5.20820	−	16.0292i	−0.187326	−	0.576530i	0.812655	−	0.582746i	$-0.198022\pi$
$773$	−5.20820	−	16.0292i	−0.187326	−	0.576530i	−0.999981	+	0.00621531i	$0.998022\pi$
$774$	−5.83210			−0.209630
$775$		0			0
$776$	16.3322			0.586292
$777$	−5.45862	−	16.7999i	−0.195827	−	0.602694i
$778$	46.2158	−	33.5778i	1.65692	−	1.20382i
$779$	46.7992	−	34.0016i	1.67675	−	1.21823i
$780$		0			0
$781$	−10.1523	−	7.37606i	−0.363277	−	0.263936i
$782$	1.93153			0.0690715
$783$	−13.0449	−	9.47766i	−0.466186	−	0.338704i
$784$	−21.6320	+	66.5765i	−0.772572	+	2.37773i
$785$		0			0
$786$	6.18476	+	19.0347i	0.220603	+	0.678947i
$787$	−6.21393	+	19.1245i	−0.221503	+	0.681716i	0.777125	+	0.629346i	$0.216677\pi$
$787$	−6.21393	+	19.1245i	−0.221503	+	0.681716i	−0.998628	+	0.0523693i	$0.983323\pi$
$788$	0.327723	−	1.00863i	0.0116746	−	0.0359309i
$789$	5.34166	+	16.4400i	0.190168	+	0.585278i
$790$		0			0
$791$	−20.0507	+	61.7097i	−0.712920	+	2.19414i
$792$	−15.5148	−	11.2722i	−0.551294	−	0.400539i
$793$	6.67976			0.237205
$794$	36.5381	+	26.5465i	1.29669	+	0.942099i
$795$		0			0
$796$	5.81955	−	4.22815i	0.206269	−	0.149863i
$797$	−43.8266	+	31.8419i	−1.55242	+	1.12790i	−0.610521	+	0.792000i	$0.709040\pi$
$797$	−43.8266	+	31.8419i	−1.55242	+	1.12790i	−0.941898	+	0.335898i	$0.890960\pi$
$798$	−9.41579	−	28.9788i	−0.333315	−	1.02584i
$799$	−0.214100			−0.00757430
$800$		0			0
$801$	−18.1124			−0.639971
$802$	1.97550	+	6.07998i	0.0697575	+	0.214691i
$803$	32.5967	−	23.6829i	1.15031	−	0.835752i
$804$	−1.41580	+	1.02864i	−0.0499315	+	0.0362774i
$805$		0			0
$806$	−2.72736	−	1.98154i	−0.0960671	−	0.0697969i
$807$	−21.2973			−0.749701
$808$	−5.66200	−	4.11368i	−0.199189	−	0.144719i
$809$	4.73927	−	14.5860i	0.166624	−	0.512815i	−0.832528	−	0.553982i	$-0.813108\pi$
$809$	4.73927	−	14.5860i	0.166624	−	0.512815i	0.999152	+	0.0411669i	$0.0131075\pi$
$810$		0			0
$811$	3.57428	+	11.0005i	0.125510	+	0.386279i	0.993994	−	0.109438i	$-0.0349051\pi$
$811$	3.57428	+	11.0005i	0.125510	+	0.386279i	−0.868484	+	0.495717i	$0.834905\pi$
$812$	−4.88667	+	15.0396i	−0.171489	+	0.527788i
$813$	6.07994	−	18.7121i	0.213233	−	0.656263i
$814$	−11.0306	−	33.9486i	−0.386621	−	1.18990i
$815$		0			0
$816$	−0.253890	+	0.781393i	−0.00888793	+	0.0273542i
$817$	6.23376	+	4.52909i	0.218092	+	0.158453i
$818$	−23.8630			−0.834349
$819$	5.31039	+	3.85822i	0.185560	+	0.134817i
$820$		0			0
$821$	−26.9949	+	19.6129i	−0.942128	+	0.684496i	−0.948932	−	0.315480i	$-0.897834\pi$
$821$	−26.9949	+	19.6129i	−0.942128	+	0.684496i	0.00680360	+	0.999977i	$0.497834\pi$
$822$	10.0826	−	7.32541i	0.351670	−	0.255503i
$823$	−9.26497	−	28.5146i	−0.322956	−	0.993958i	−0.972355	−	0.233509i	$-0.924979\pi$
$823$	−9.26497	−	28.5146i	−0.322956	−	0.993958i	0.649398	−	0.760449i	$-0.275021\pi$
$824$	0.783901			0.0273085
$825$		0			0
$826$	−34.8395			−1.21222
$827$	7.63982	+	23.5130i	0.265663	+	0.817626i	0.991540	+	0.129801i	$0.0414340\pi$
$827$	7.63982	+	23.5130i	0.265663	+	0.817626i	−0.725877	+	0.687824i	$0.758566\pi$
$828$	−8.30388	+	6.03312i	−0.288580	+	0.209665i
$829$	0.171031	−	0.124261i	0.00594015	−	0.00431577i	−0.584811	−	0.811169i	$-0.698831\pi$
$829$	0.171031	−	0.124261i	0.00594015	−	0.00431577i	0.590751	+	0.806854i	$0.298831\pi$
$830$		0			0
$831$	1.31835	+	0.957839i	0.0457331	+	0.0332271i
$832$	−1.41114			−0.0489225
$833$	2.64933	+	1.92485i	0.0917939	+	0.0666922i
$834$	−2.46098	+	7.57413i	−0.0852169	+	0.262271i
$835$		0			0
$836$	−5.59873	−	17.2311i	−0.193636	−	0.595951i
$837$	−4.21634	+	12.9766i	−0.145738	+	0.448535i
$838$	−10.1943	+	31.3749i	−0.352157	+	1.08383i
$839$	−1.70489	−	5.24712i	−0.0588594	−	0.181151i	0.917304	−	0.398188i	$-0.130361\pi$
$839$	−1.70489	−	5.24712i	−0.0588594	−	0.181151i	−0.976163	+	0.217037i	$0.930361\pi$
$840$		0			0
$841$	−3.68903	+	11.3537i	−0.127208	+	0.391506i
$842$	35.1154	+	25.5129i	1.21016	+	0.879231i
$843$	1.14953			0.0395920
$844$	14.1882	+	10.3084i	0.488379	+	0.354828i
$845$		0			0
$846$	3.12807	−	2.27267i	0.107545	−	0.0781361i
$847$	16.0664	−	11.6729i	0.552047	−	0.401086i
$848$	−1.89177	−	5.82228i	−0.0649638	−	0.199938i
$849$	9.22888			0.316734
$850$		0			0
$851$	26.7177			0.915871
$852$	−0.586739	−	1.80580i	−0.0201013	−	0.0618656i
$853$	1.24545	−	0.904870i	0.0426433	−	0.0309822i	−0.566259	−	0.824227i	$-0.691610\pi$
$853$	1.24545	−	0.904870i	0.0426433	−	0.0309822i	0.608903	+	0.793245i	$0.291610\pi$
$854$	−72.8983	+	52.9637i	−2.49453	+	1.81238i
$855$		0			0
$856$	−2.61049	−	1.89663i	−0.0892247	−	0.0648255i
$857$	−45.3407			−1.54881			−0.774404	−	0.632691i	$-0.781950\pi$
$857$	−45.3407			−1.54881			−0.774404	+	0.632691i	$0.781950\pi$
$858$	−2.16986	−	1.57649i	−0.0740777	−	0.0538206i
$859$	−6.73547	+	20.7296i	−0.229811	+	0.707286i	0.767956	+	0.640502i	$0.221274\pi$
$859$	−6.73547	+	20.7296i	−0.229811	+	0.707286i	−0.997767	+	0.0667839i	$0.978726\pi$
$860$		0			0
$861$	10.5038	+	32.3273i	0.357968	+	1.10171i
$862$	4.90308	−	15.0901i	0.167000	−	0.513972i
$863$	−3.95176	+	12.1623i	−0.134519	+	0.414008i	−0.995515	−	0.0946043i	$-0.969841\pi$
$863$	−3.95176	+	12.1623i	−0.134519	+	0.414008i	0.860996	+	0.508613i	$0.169841\pi$
$864$	−5.36126	−	16.5003i	−0.182394	−	0.561350i
$865$		0			0
$866$	−0.911192	+	2.80436i	−0.0309636	+	0.0952960i
$867$	−9.73842	−	7.07538i	−0.330734	−	0.240292i
$868$	13.3814			0.454194
$869$	30.4522	+	22.1248i	1.03302	+	0.750534i
$870$		0			0
$871$	−1.36945	+	0.994964i	−0.0464021	+	0.0337131i
$872$	0.118978	−	0.0864424i	0.00402909	−	0.00292731i
$873$	6.41555	+	19.7450i	0.217133	+	0.668268i
$874$	46.0863			1.55889
$875$		0			0
$876$	6.09640			0.205978
$877$	2.95216	+	9.08583i	0.0996875	+	0.306807i	0.988447	−	0.151567i	$-0.0484321\pi$
$877$	2.95216	+	9.08583i	0.0996875	+	0.306807i	−0.888759	+	0.458374i	$0.848432\pi$
$878$	−38.2465	+	27.7877i	−1.29076	+	0.937790i
$879$	−6.72423	+	4.88544i	−0.226803	+	0.164782i
$880$		0			0
$881$	31.6595	+	23.0020i	1.06664	+	0.774956i	0.975305	−	0.220864i	$-0.0708877\pi$
$881$	31.6595	+	23.0020i	1.06664	+	0.774956i	0.0913314	+	0.995821i	$0.470888\pi$
$882$	−59.1400			−1.99135
$883$	28.3361	+	20.5874i	0.953586	+	0.692821i	0.951652	−	0.307177i	$-0.0993844\pi$
$883$	28.3361	+	20.5874i	0.953586	+	0.692821i	0.00193394	+	0.999998i	$0.499384\pi$
$884$	0.0343416	−	0.105692i	0.00115503	−	0.00355482i
$885$		0			0
$886$	15.5598	+	47.8880i	0.522741	+	1.60883i
$887$	11.2000	−	34.4699i	0.376058	−	1.15739i	−0.566705	−	0.823921i	$-0.691782\pi$
$887$	11.2000	−	34.4699i	0.376058	−	1.15739i	0.942762	−	0.333465i	$-0.108218\pi$
$888$	−2.33401	+	7.18335i	−0.0783243	+	0.241057i
$889$	−16.7587	−	51.5779i	−0.562068	−	1.72987i
$890$		0			0
$891$	5.70191	−	17.5487i	0.191021	−	0.587903i
$892$	4.27394	+	3.10520i	0.143102	+	0.103970i
$893$	−5.10841			−0.170946
$894$	−11.6396	−	8.45665i	−0.389286	−	0.282833i
$895$		0			0
$896$	48.4160	−	35.1763i	1.61747	−	1.17516i
$897$	1.62411	−	1.17998i	0.0542273	−	0.0393985i
$898$	3.27714	+	10.0860i	0.109360	+	0.336574i
$899$	−14.4378			−0.481528
$900$		0			0
$901$	−0.286386			−0.00954089
$902$	21.2256	+	65.3258i	0.706736	+	2.17511i
$903$	−3.66297	+	2.66130i	−0.121896	+	0.0885625i
$904$	22.4452	−	16.3074i	0.746517	−	0.542377i
$905$		0			0
$906$	−1.49194	−	1.08395i	−0.0495662	−	0.0360120i
$907$	−40.8532			−1.35651			−0.678255	−	0.734827i	$-0.737263\pi$
$907$	−40.8532			−1.35651			−0.678255	+	0.734827i	$0.737263\pi$
$908$	7.59779	+	5.52012i	0.252142	+	0.183192i
$909$	2.74917	−	8.46106i	0.0911841	−	0.280636i
$910$		0			0
$911$	3.93897	+	12.1229i	0.130504	+	0.401650i	0.994864	−	0.101224i	$-0.0322759\pi$
$911$	3.93897	+	12.1229i	0.130504	+	0.401650i	−0.864360	+	0.502874i	$0.832276\pi$
$912$	−6.05781	+	18.6440i	−0.200594	+	0.617365i
$913$	−12.6821	+	39.0316i	−0.419718	+	1.29176i
$914$	−9.97794	−	30.7089i	−0.330041	−	1.01576i
$915$		0			0
$916$	3.87573	−	11.9283i	0.128058	−	0.394121i
$917$	−62.1669	−	45.1669i	−2.05293	−	1.49154i
$918$	−1.52858			−0.0504506
$919$	−7.82486	−	5.68509i	−0.258118	−	0.187534i	0.451199	−	0.892423i	$-0.350997\pi$
$919$	−7.82486	−	5.68509i	−0.258118	−	0.187534i	−0.709317	+	0.704890i	$0.750997\pi$
$920$		0			0
$921$	15.2676	−	11.0926i	0.503086	−	0.365513i
$922$	−9.63019	+	6.99674i	−0.317153	+	0.230425i
$923$	−0.567529	−	1.74668i	−0.0186805	−	0.0574925i
$924$	10.6461			0.350231
$925$		0			0
$926$	16.1917			0.532094
$927$	0.307928	+	0.947706i	0.0101137	+	0.0311268i
$928$	14.8522	−	10.7907i	0.487547	−	0.354223i
$929$	−8.83405	+	6.41831i	−0.289836	+	0.210578i	−0.723196	−	0.690643i	$-0.757328\pi$
$929$	−8.83405	+	6.41831i	−0.289836	+	0.210578i	0.433360	+	0.901221i	$0.357328\pi$
$930$		0			0
$931$	63.2130	+	45.9269i	2.07172	+	1.50519i
$932$	−6.52711			−0.213803
$933$	−7.75297	−	5.63287i	−0.253821	−	0.184412i
$934$	9.99933	−	30.7748i	0.327188	−	1.00698i
$935$		0			0
$936$	−0.867303	−	2.66928i	−0.0283487	−	0.0872483i
$937$	4.92778	−	15.1661i	0.160984	−	0.495456i	−0.837734	−	0.546078i	$-0.816120\pi$
$937$	4.92778	−	15.1661i	0.160984	−	0.495456i	0.998718	+	0.0506216i	$0.0161202\pi$
$938$	7.05618	−	21.7167i	0.230392	−	0.709075i
$939$	−3.73039	−	11.4809i	−0.121737	−	0.374667i
$940$		0			0
$941$	1.83155	−	5.63692i	0.0597067	−	0.183758i	−0.916755	−	0.399451i	$-0.869201\pi$
$941$	1.83155	−	5.63692i	0.0597067	−	0.183758i	0.976461	+	0.215692i	$0.0692009\pi$
$942$	−9.50470	−	6.90557i	−0.309680	−	0.224996i
$943$	−51.4117			−1.67419
$944$	18.1338	+	13.1750i	0.590205	+	0.428809i
$945$		0			0
$946$	−7.40197	+	5.37785i	−0.240659	+	0.174849i
$947$	0.801236	−	0.582132i	0.0260367	−	0.0189168i	−0.574691	−	0.818371i	$-0.694878\pi$
$947$	0.801236	−	0.582132i	0.0260367	−	0.0189168i	0.600727	+	0.799454i	$0.294878\pi$
$948$	1.75995	+	5.41657i	0.0571606	+	0.175922i
$949$	5.89681			0.191418
$950$		0			0
$951$	−11.9308			−0.386882
$952$	−0.647839	−	1.99384i	−0.0209966	−	0.0646208i
$953$	43.3627	−	31.5049i	1.40466	−	1.02054i	0.410584	−	0.911823i	$-0.365325\pi$
$953$	43.3627	−	31.5049i	1.40466	−	1.02054i	0.994072	−	0.108720i	$-0.0346750\pi$
$954$	4.18419	−	3.03999i	0.135468	−	0.0984234i
$955$		0			0
$956$	−5.89537	−	4.28324i	−0.190670	−	0.138530i
$957$	−11.4866			−0.371308
$958$	51.7519	+	37.6000i	1.67203	+	1.21480i
$959$	−14.7862	+	45.5072i	−0.477471	+	1.46950i
$960$		0			0
$961$	−5.80420	−	17.8635i	−0.187232	−	0.576242i
$962$	1.61435	−	4.96846i	0.0520488	−	0.160190i
$963$	1.26751	−	3.90101i	0.0408451	−	0.125708i
$964$	−0.154838	−	0.476542i	−0.00498699	−	0.0153484i
$965$		0			0
$966$	−8.36831	+	25.7550i	−0.269246	+	0.828654i
$967$	24.0561	+	17.4778i	0.773592	+	0.562047i	0.903049	−	0.429538i	$-0.141323\pi$
$967$	24.0561	+	17.4778i	0.773592	+	0.562047i	−0.129457	+	0.991585i	$0.541323\pi$
$968$	−8.49141			−0.272924
$969$	0.741917	+	0.539034i	0.0238338	+	0.0173163i
$970$		0			0
$971$	−49.0399	+	35.6296i	−1.57376	+	1.14341i	−0.650330	+	0.759652i	$0.725369\pi$
$971$	−49.0399	+	35.6296i	−1.57376	+	1.14341i	−0.923435	+	0.383755i	$0.874631\pi$
$972$	10.1590	−	7.38094i	0.325850	−	0.236744i
$973$	−9.44864	−	29.0799i	−0.302910	−	0.932260i
$974$	28.1954			0.903440
$975$		0			0
$976$	57.9720			1.85564
$977$	13.7553	+	42.3343i	0.440070	+	1.35440i	0.887801	+	0.460227i	$0.152232\pi$
$977$	13.7553	+	42.3343i	0.440070	+	1.35440i	−0.447731	+	0.894168i	$0.647768\pi$
$978$	−5.39923	+	3.92277i	−0.172648	+	0.125436i
$979$	−22.9879	+	16.7017i	−0.734697	+	0.533789i
$980$		0			0
$981$	0.151242	+	0.109884i	0.00482878	+	0.00350831i
$982$	−15.0675			−0.480822
$983$	−30.9369	−	22.4769i	−0.986732	−	0.716903i	−0.0275293	−	0.999621i	$-0.508764\pi$
$983$	−30.9369	−	22.4769i	−0.986732	−	0.716903i	−0.959203	+	0.282718i	$0.908764\pi$
$984$	4.49123	−	13.8226i	0.143175	−	0.440648i
$985$		0			0
$986$	−0.499825	−	1.53830i	−0.0159177	−	0.0489896i
$987$	0.927580	−	2.85480i	0.0295252	−	0.0908692i
$988$	0.819389	−	2.52182i	0.0260682	−	0.0802298i
$989$	−2.11619	−	6.51298i	−0.0672911	−	0.207101i
$990$		0			0
$991$	7.01721	−	21.5968i	0.222909	−	0.686044i	−0.775588	−	0.631239i	$-0.782547\pi$
$991$	7.01721	−	21.5968i	0.222909	−	0.686044i	0.998497	−	0.0548043i	$-0.0174535\pi$
$992$	−12.5678	−	9.13108i	−0.399030	−	0.289912i
$993$	−9.11678			−0.289312
$994$	20.0430	+	14.5621i	0.635725	+	0.461881i
$995$		0			0
$996$	−5.02371	+	3.64994i	−0.159182	+	0.115653i
$997$	−16.6887	+	12.1251i	−0.528538	+	0.384005i	−0.819811	−	0.572635i	$-0.805921\pi$
$997$	−16.6887	+	12.1251i	−0.528538	+	0.384005i	0.291273	+	0.956640i	$0.405921\pi$
$998$	−18.8995	−	58.1666i	−0.598253	−	1.84123i
$999$	−21.1439			−0.668962

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.d.p.126.4		16
5.2	odd	4		625.2.e.k.499.3		32
5.3	odd	4		625.2.e.k.499.6		32
5.4	even	2		625.2.d.n.126.1		16
25.2	odd	20		625.2.b.d.624.12		16
25.3	odd	20		625.2.e.k.124.3		32
25.4	even	10		625.2.d.n.501.1		16
25.6	even	5		625.2.d.q.376.1		16
25.8	odd	20		625.2.e.j.249.3		32
25.9	even	10		625.2.d.m.251.4		16
25.11	even	5		625.2.a.e.1.7	✓	8
25.12	odd	20		625.2.e.j.374.3		32
25.13	odd	20		625.2.e.j.374.6		32
25.14	even	10		625.2.a.g.1.2	yes	8
25.16	even	5		625.2.d.q.251.1		16
25.17	odd	20		625.2.e.j.249.6		32
25.19	even	10		625.2.d.m.376.4		16
25.21	even	5	inner	625.2.d.p.501.4		16
25.22	odd	20		625.2.e.k.124.6		32
25.23	odd	20		625.2.b.d.624.5		16
75.11	odd	10		5625.2.a.be.1.2		8
75.14	odd	10		5625.2.a.s.1.7		8
100.11	odd	10		10000.2.a.bn.1.4		8
100.39	odd	10		10000.2.a.be.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
625.2.a.e.1.7	✓	8	25.11	even	5
625.2.a.g.1.2	yes	8	25.14	even	10
625.2.b.d.624.5		16	25.23	odd	20
625.2.b.d.624.12		16	25.2	odd	20
625.2.d.m.251.4		16	25.9	even	10
625.2.d.m.376.4		16	25.19	even	10
625.2.d.n.126.1		16	5.4	even	2
625.2.d.n.501.1		16	25.4	even	10
625.2.d.p.126.4		16	1.1	even	1	trivial
625.2.d.p.501.4		16	25.21	even	5	inner
625.2.d.q.251.1		16	25.16	even	5
625.2.d.q.376.1		16	25.6	even	5
625.2.e.j.249.3		32	25.8	odd	20
625.2.e.j.249.6		32	25.17	odd	20
625.2.e.j.374.3		32	25.12	odd	20
625.2.e.j.374.6		32	25.13	odd	20
625.2.e.k.124.3		32	25.3	odd	20
625.2.e.k.124.6		32	25.22	odd	20
625.2.e.k.499.3		32	5.2	odd	4
625.2.e.k.499.6		32	5.3	odd	4
5625.2.a.s.1.7		8	75.14	odd	10
5625.2.a.be.1.2		8	75.11	odd	10
10000.2.a.be.1.5		8	100.39	odd	10
10000.2.a.bn.1.4		8	100.11	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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+(0.520202 + 1.60102i) q^{2} +(0.574677 - 0.417528i) q^{3} +(-0.674615 + 0.490137i) q^{4} +(0.967418 + 0.702870i) q^{6} -4.59110 q^{7} +(1.58816 + 1.15387i) q^{8} +(-0.771126 + 2.37328i) q^{9} +(1.20974 + 3.72319i) q^{11} +(-0.183041 + 0.563341i) q^{12} +(-0.177048 + 0.544898i) q^{13} +(-2.38830 - 7.35044i) q^{14} +(-1.53656 + 4.72903i) q^{16} +(0.188186 + 0.136725i) q^{17} -4.20081 q^{18} +(4.49012 + 3.26227i) q^{19} +(-2.63840 + 1.91691i) q^{21} +(-5.33158 + 3.87362i) q^{22} +(-1.52428 - 4.69124i) q^{23} +1.39445 q^{24} -0.964492 q^{26} +(1.20628 + 3.71256i) q^{27} +(3.09723 - 2.25027i) q^{28} +(-3.34174 + 2.42792i) q^{29} +(2.82777 + 2.05449i) q^{31} -4.44444 q^{32} +(2.24974 + 1.63453i) q^{33} +(-0.121005 + 0.372415i) q^{34} +(-0.643019 - 1.97901i) q^{36} +(-1.67378 + 5.15138i) q^{37} +(-2.88717 + 8.88581i) q^{38} +(0.125764 + 0.387063i) q^{39} +(3.22079 - 9.91257i) q^{41} +(-4.44152 - 3.22695i) q^{42} +1.38833 q^{43} +(-2.64098 - 1.91878i) q^{44} +(6.71783 - 4.88079i) q^{46} +(-0.744634 + 0.541008i) q^{47} +(1.09148 + 3.35922i) q^{48} +14.0782 q^{49} +0.165233 q^{51} +(-0.147635 - 0.454374i) q^{52} +(-0.996044 + 0.723668i) q^{53} +(-5.31636 + 3.86256i) q^{54} +(-7.29141 - 5.29752i) q^{56} +3.94246 q^{57} +(-5.62552 - 4.08718i) q^{58} +(1.39299 - 4.28718i) q^{59} +(-3.60276 - 11.0881i) q^{61} +(-1.81827 + 5.59606i) q^{62} +(3.54032 - 10.8960i) q^{63} +(0.761103 + 2.34244i) q^{64} +(-1.44660 + 4.45216i) q^{66} +(2.39022 + 1.73660i) q^{67} -0.193968 q^{68} +(-2.83469 - 2.05952i) q^{69} +(-2.59331 + 1.88415i) q^{71} +(-3.96312 + 2.87938i) q^{72} +(-3.18047 - 9.78847i) q^{73} -9.11816 q^{74} -4.62806 q^{76} +(-5.55402 - 17.0935i) q^{77} +(-0.554272 + 0.402702i) q^{78} +(7.77877 - 5.65161i) q^{79} +(-3.81318 - 2.77044i) q^{81} +17.5457 q^{82} +(8.48125 + 6.16199i) q^{83} +(0.840358 - 2.58636i) q^{84} +(0.722211 + 2.22274i) q^{86} +(-0.906701 + 2.79054i) q^{87} +(-2.37480 + 7.30889i) q^{88} +(2.24293 + 6.90303i) q^{89} +(0.812846 - 2.50168i) q^{91} +(3.32765 + 2.41768i) q^{92} +2.48286 q^{93} +(-1.25352 - 0.910739i) q^{94} +(-2.55412 + 1.85568i) q^{96} +(6.73079 - 4.89020i) q^{97} +(7.32353 + 22.5395i) q^{98} -9.76903 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{3} - 8 q^{4} - 3 q^{6} - 20 q^{7} + 10 q^{8} + 3 q^{9} + 2 q^{11} + 25 q^{12} + 5 q^{13} + 9 q^{14} - 14 q^{16} - 10 q^{17} + 10 q^{18} + 7 q^{21} - 40 q^{22} + 15 q^{23} + 10 q^{24} + 22 q^{26}+ \cdots - 44 q^{99}+O(q^{100}) \) 16 * q + 5 * q^3 - 8 * q^4 - 3 * q^6 - 20 * q^7 + 10 * q^8 + 3 * q^9 + 2 * q^11 + 25 * q^12 + 5 * q^13 + 9 * q^14 - 14 * q^16 - 10 * q^17 + 10 * q^18 + 7 * q^21 - 40 * q^22 + 15 * q^23 + 10 * q^24 + 22 * q^26 + 20 * q^27 + 30 * q^28 - 10 * q^29 + 17 * q^31 - 60 * q^32 + 5 * q^33 - q^34 - 4 * q^36 - 15 * q^37 - 15 * q^38 - 9 * q^39 + 12 * q^41 - 45 * q^42 + 49 * q^44 - 33 * q^46 + 25 * q^47 - 20 * q^48 - 8 * q^49 - 28 * q^51 + 20 * q^52 - 30 * q^54 - 35 * q^56 + 20 * q^57 + 5 * q^58 + 20 * q^59 - 23 * q^61 + 15 * q^62 + 10 * q^63 - 28 * q^64 - 26 * q^66 - 80 * q^68 + 6 * q^69 + 22 * q^71 + 5 * q^72 + 40 * q^73 - 36 * q^74 - 20 * q^76 - 40 * q^77 - 25 * q^78 + 75 * q^79 + 11 * q^81 + 90 * q^82 + 25 * q^83 - 31 * q^84 + 17 * q^86 - 20 * q^87 + 5 * q^89 + 22 * q^91 + 60 * q^92 + 80 * q^93 - 51 * q^94 - 28 * q^96 + 40 * q^97 + 15 * q^98 - 44 * q^99

Introduction

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