LMFDB - Embedded newform 625.2.d.p.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 = [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			376.1
Root			$-0.0288455i$ of defining polynomial
Character	$\chi$	$=$	625.376
Dual form			625.2.d.p.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+(-1.62909 - 1.18361i) q^{2} +(-0.934982 - 2.87758i) q^{3} +(0.634989 + 1.95429i) q^{4} +(-1.88274 + 5.79449i) q^{6} -0.369971 q^{7} +(0.0341417 - 0.105077i) q^{8} +(-4.97921 + 3.61761i) q^{9} +(1.41281 + 1.02647i) q^{11} +(5.02993 - 3.65446i) q^{12} +(0.903043 - 0.656099i) q^{13} +(0.602718 + 0.437900i) q^{14} +(3.14486 - 2.28487i) q^{16} +(-1.69588 + 5.21940i) q^{17} +12.3934 q^{18} +(-1.15949 + 3.56855i) q^{19} +(0.345917 + 1.06462i) q^{21} +(-1.08667 - 3.34442i) q^{22} +(5.86229 + 4.25920i) q^{23} -0.334290 q^{24} -2.24770 q^{26} +(7.72199 + 5.61035i) q^{27} +(-0.234928 - 0.723033i) q^{28} +(1.29566 + 3.98762i) q^{29} +(0.0944614 - 0.290722i) q^{31} -8.04862 q^{32} +(1.63279 - 5.02520i) q^{33} +(8.94046 - 6.49562i) q^{34} +(-10.2316 - 7.43371i) q^{36} +(-7.45878 + 5.41912i) q^{37} +(6.11267 - 4.44111i) q^{38} +(-2.73230 - 1.98514i) q^{39} +(3.38688 - 2.46071i) q^{41} +(0.696562 - 2.14380i) q^{42} -7.17118 q^{43} +(-1.10890 + 3.41284i) q^{44} +(-4.50900 - 13.8773i) q^{46} +(-0.250388 - 0.770615i) q^{47} +(-9.51528 - 6.91325i) q^{48} -6.86312 q^{49} +16.6048 q^{51} +(1.85563 + 1.34820i) q^{52} +(1.20983 + 3.72347i) q^{53} +(-5.93940 - 18.2796i) q^{54} +(-0.0126314 + 0.0388756i) q^{56} +11.3529 q^{57} +(2.60903 - 8.02976i) q^{58} +(1.50265 - 1.09174i) q^{59} +(-7.83835 - 5.69490i) q^{61} +(-0.497987 + 0.361809i) q^{62} +(1.84217 - 1.33841i) q^{63} +(6.82224 + 4.95665i) q^{64} +(-8.60781 + 6.25394i) q^{66} +(3.85346 - 11.8597i) q^{67} -11.2771 q^{68} +(6.77506 - 20.8515i) q^{69} +(3.60830 + 11.1052i) q^{71} +(0.210130 + 0.646713i) q^{72} +(2.77604 + 2.01691i) q^{73} +18.5652 q^{74} -7.71026 q^{76} +(-0.522699 - 0.379763i) q^{77} +(2.10156 + 6.46794i) q^{78} +(1.75937 + 5.41480i) q^{79} +(3.21864 - 9.90596i) q^{81} -8.43005 q^{82} +(-2.20444 + 6.78456i) q^{83} +(-1.86093 + 1.35205i) q^{84} +(11.6825 + 8.48784i) q^{86} +(10.2633 - 7.45671i) q^{87} +(0.156094 - 0.113409i) q^{88} +(-1.23779 - 0.899307i) q^{89} +(-0.334100 + 0.242738i) q^{91} +(-4.60125 + 14.1612i) q^{92} -0.924896 q^{93} +(-0.504199 + 1.55176i) q^{94} +(7.52531 + 23.1605i) q^{96} +(-1.97691 - 6.08430i) q^{97} +(11.1807 + 8.12323i) q^{98} -10.7480 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 $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.62909	−	1.18361i	−1.15194	−	0.836936i	−0.163205	−	0.986592i	$-0.552183\pi$
$2$	−1.62909	−	1.18361i	−1.15194	−	0.836936i	−0.988738	+	0.149657i	$0.952183\pi$
$3$	−0.934982	−	2.87758i	−0.539812	−	1.66137i	−0.733016	−	0.680212i	$-0.761888\pi$
$3$	−0.934982	−	2.87758i	−0.539812	−	1.66137i	0.193204	−	0.981159i	$-0.438112\pi$
$4$	0.634989	+	1.95429i	0.317494	+	0.977147i
$5$		0			0
$5$		0			0
$6$	−1.88274	+	5.79449i	−0.768627	+	2.36559i
$7$	−0.369971			−0.139836			−0.0699180	−	0.997553i	$-0.522274\pi$
$7$	−0.369971			−0.139836			−0.0699180	+	0.997553i	$0.522274\pi$
$8$	0.0341417	−	0.105077i	0.0120709	−	0.0371504i
$9$	−4.97921	+	3.61761i	−1.65974	+	1.20587i
$10$		0			0
$11$	1.41281	+	1.02647i	0.425978	+	0.309491i	0.780039	−	0.625731i	$-0.215199\pi$
$11$	1.41281	+	1.02647i	0.425978	+	0.309491i	−0.354061	+	0.935222i	$0.615199\pi$
$12$	5.02993	−	3.65446i	1.45202	−	1.05495i
$13$	0.903043	−	0.656099i	0.250459	−	0.181969i	−0.455471	−	0.890251i	$-0.650529\pi$
$13$	0.903043	−	0.656099i	0.250459	−	0.181969i	0.705930	+	0.708281i	$0.250529\pi$
$14$	0.602718	+	0.437900i	0.161083	+	0.117034i
$15$		0			0
$16$	3.14486	−	2.28487i	0.786214	−	0.571218i
$17$	−1.69588	+	5.21940i	−0.411312	+	1.26589i	0.504196	+	0.863590i	$0.331789\pi$
$17$	−1.69588	+	5.21940i	−0.411312	+	1.26589i	−0.915508	+	0.402300i	$0.868211\pi$
$18$	12.3934			2.92116
$19$	−1.15949	+	3.56855i	−0.266005	+	0.818681i	0.725455	+	0.688270i	$0.241630\pi$
$19$	−1.15949	+	3.56855i	−0.266005	+	0.818681i	−0.991460	+	0.130411i	$0.958370\pi$
$20$		0			0
$21$	0.345917	+	1.06462i	0.0754852	+	0.232319i
$22$	−1.08667	−	3.34442i	−0.231678	−	0.713032i
$23$	5.86229	+	4.25920i	1.22237	+	0.888106i	0.996295	−	0.0860037i	$-0.0274097\pi$
$23$	5.86229	+	4.25920i	1.22237	+	0.888106i	0.226078	+	0.974109i	$0.427410\pi$
$24$	−0.334290			−0.0682366
$25$		0			0
$26$	−2.24770			−0.440811
$27$	7.72199	+	5.61035i	1.48610	+	1.07971i
$28$	−0.234928	−	0.723033i	−0.0443972	−	0.136640i
$29$	1.29566	+	3.98762i	0.240598	+	0.740483i	0.996329	+	0.0856020i	$0.0272814\pi$
$29$	1.29566	+	3.98762i	0.240598	+	0.740483i	−0.755732	+	0.654881i	$0.772719\pi$
$30$		0			0
$31$	0.0944614	−	0.290722i	0.0169658	−	0.0522153i	−0.942215	−	0.335008i	$-0.891261\pi$
$31$	0.0944614	−	0.290722i	0.0169658	−	0.0522153i	0.959181	+	0.282793i	$0.0912609\pi$
$32$	−8.04862			−1.42281
$33$	1.63279	−	5.02520i	0.284231	−	0.874774i
$34$	8.94046	−	6.49562i	1.53328	−	1.11399i
$35$		0			0
$36$	−10.2316	−	7.43371i	−1.70527	−	1.23895i
$37$	−7.45878	+	5.41912i	−1.22622	+	0.890898i	−0.996601	−	0.0823830i	$-0.973747\pi$
$37$	−7.45878	+	5.41912i	−1.22622	+	0.890898i	−0.229616	+	0.973281i	$0.573747\pi$
$38$	6.11267	−	4.44111i	0.991606	−	0.720444i
$39$	−2.73230	−	1.98514i	−0.437519	−	0.317876i
$40$		0			0
$41$	3.38688	−	2.46071i	0.528941	−	0.384298i	−0.291020	−	0.956717i	$-0.593995\pi$
$41$	3.38688	−	2.46071i	0.528941	−	0.384298i	0.819962	+	0.572419i	$0.193995\pi$
$42$	0.696562	−	2.14380i	0.107482	−	0.330795i
$43$	−7.17118			−1.09359			−0.546797	−	0.837265i	$-0.684153\pi$
$43$	−7.17118			−1.09359			−0.546797	+	0.837265i	$0.684153\pi$
$44$	−1.10890	+	3.41284i	−0.167173	+	0.514505i
$45$		0			0
$46$	−4.50900	−	13.8773i	−0.664816	−	2.04609i
$47$	−0.250388	−	0.770615i	−0.0365229	−	0.112406i	0.931133	−	0.364680i	$-0.118822\pi$
$47$	−0.250388	−	0.770615i	−0.0365229	−	0.112406i	−0.967656	+	0.252274i	$0.918822\pi$
$48$	−9.51528	−	6.91325i	−1.37341	−	0.997842i
$49$	−6.86312			−0.980446
$50$		0			0
$51$	16.6048			2.32514
$52$	1.85563	+	1.34820i	0.257330	+	0.186961i
$53$	1.20983	+	3.72347i	0.166183	+	0.511457i	0.999121	−	0.0419076i	$-0.0133435\pi$
$53$	1.20983	+	3.72347i	0.166183	+	0.511457i	−0.832939	+	0.553365i	$0.813343\pi$
$54$	−5.93940	−	18.2796i	−0.808249	−	2.48754i
$55$		0			0
$56$	−0.0126314	+	0.0388756i	−0.00168795	+	0.00519497i
$57$	11.3529			1.50372
$58$	2.60903	−	8.02976i	0.342582	−	1.05436i
$59$	1.50265	−	1.09174i	0.195629	−	0.142132i	−0.485659	−	0.874148i	$-0.661420\pi$
$59$	1.50265	−	1.09174i	0.195629	−	0.142132i	0.681288	+	0.732016i	$0.261420\pi$
$60$		0			0
$61$	−7.83835	−	5.69490i	−1.00360	−	0.729157i	−0.0407418	−	0.999170i	$-0.512972\pi$
$61$	−7.83835	−	5.69490i	−1.00360	−	0.729157i	−0.962857	+	0.270013i	$0.912972\pi$
$62$	−0.497987	+	0.361809i	−0.0632444	+	0.0459498i
$63$	1.84217	−	1.33841i	0.232091	−	0.168624i
$64$	6.82224	+	4.95665i	0.852780	+	0.619581i
$65$		0			0
$66$	−8.60781	+	6.25394i	−1.05955	+	0.769807i
$67$	3.85346	−	11.8597i	0.470775	−	1.44890i	−0.380796	−	0.924659i	$-0.624350\pi$
$67$	3.85346	−	11.8597i	0.470775	−	1.44890i	0.851572	−	0.524238i	$-0.175650\pi$
$68$	−11.2771			−1.36755
$69$	6.77506	−	20.8515i	0.815621	−	2.51022i
$70$		0			0
$71$	3.60830	+	11.1052i	0.428227	+	1.31795i	0.899871	+	0.436157i	$0.143661\pi$
$71$	3.60830	+	11.1052i	0.428227	+	1.31795i	−0.471644	+	0.881789i	$0.656339\pi$
$72$	0.210130	+	0.646713i	0.0247641	+	0.0762159i
$73$	2.77604	+	2.01691i	0.324910	+	0.236061i	0.738268	−	0.674508i	$-0.235644\pi$
$73$	2.77604	+	2.01691i	0.324910	+	0.236061i	−0.413358	+	0.910569i	$0.635644\pi$
$74$	18.5652			2.15816
$75$		0			0
$76$	−7.71026			−0.884427
$77$	−0.522699	−	0.379763i	−0.0595671	−	0.0432780i
$78$	2.10156	+	6.46794i	0.237955	+	0.732350i
$79$	1.75937	+	5.41480i	0.197945	+	0.609212i	0.999930	+	0.0118675i	$0.00377764\pi$
$79$	1.75937	+	5.41480i	0.197945	+	0.609212i	−0.801984	+	0.597345i	$0.796222\pi$
$80$		0			0
$81$	3.21864	−	9.90596i	0.357627	−	1.10066i
$82$	−8.43005			−0.930943
$83$	−2.20444	+	6.78456i	−0.241969	+	0.744703i	0.754152	+	0.656700i	$0.228048\pi$
$83$	−2.20444	+	6.78456i	−0.241969	+	0.744703i	−0.996120	+	0.0880023i	$0.971952\pi$
$84$	−1.86093	+	1.35205i	−0.203044	+	0.147520i
$85$		0			0
$86$	11.6825	+	8.48784i	1.25976	+	0.915268i
$87$	10.2633	−	7.45671i	1.10034	−	0.799443i
$88$	0.156094	−	0.113409i	0.0166397	−	0.0120894i
$89$	−1.23779	−	0.899307i	−0.131205	−	0.0953263i	0.520247	−	0.854016i	$-0.325840\pi$
$89$	−1.23779	−	0.899307i	−0.131205	−	0.0953263i	−0.651452	+	0.758690i	$0.725840\pi$
$90$		0			0
$91$	−0.334100	+	0.242738i	−0.0350232	+	0.0254458i
$92$	−4.60125	+	14.1612i	−0.479714	+	1.47641i
$93$	−0.924896			−0.0959072
$94$	−0.504199	+	1.55176i	−0.0520042	+	0.160052i
$95$		0			0
$96$	7.52531	+	23.1605i	0.768049	+	2.36381i
$97$	−1.97691	−	6.08430i	−0.200725	−	0.617767i	−0.999862	−	0.0166186i	$-0.994710\pi$
$97$	−1.97691	−	6.08430i	−0.200725	−	0.617767i	0.799137	−	0.601149i	$-0.205290\pi$
$98$	11.1807	+	8.12323i	1.12942	+	0.820570i
$99$	−10.7480			−1.08022
$100$		0			0
$101$	−12.2487			−1.21879			−0.609396	−	0.792866i	$-0.708588\pi$
$101$	−12.2487			−1.21879			−0.609396	+	0.792866i	$0.708588\pi$
$102$	−27.0508	−	19.6536i	−2.67843	−	1.94599i
$103$	2.36933	+	7.29204i	0.233457	+	0.718506i	0.997322	+	0.0731305i	$0.0232990\pi$
$103$	2.36933	+	7.29204i	0.233457	+	0.718506i	−0.763866	+	0.645375i	$0.776701\pi$
$104$	−0.0381097	−	0.117290i	−0.00373696	−	0.0115012i
$105$		0			0
$106$	2.43619	−	7.49783i	0.236624	−	0.728254i
$107$	0.758003			0.0732789			0.0366394	−	0.999329i	$-0.488335\pi$
$107$	0.758003			0.0732789			0.0366394	+	0.999329i	$0.488335\pi$
$108$	−6.06091	+	18.6536i	−0.583211	+	1.79494i
$109$	2.64419	−	1.92111i	0.253267	−	0.184009i	−0.453906	−	0.891049i	$-0.649970\pi$
$109$	2.64419	−	1.92111i	0.253267	−	0.184009i	0.707174	+	0.707040i	$0.249970\pi$
$110$		0			0
$111$	22.5678	+	16.3965i	2.14204	+	1.55628i
$112$	−1.16351	+	0.845337i	−0.109941	+	0.0798768i
$113$	0.686012	−	0.498417i	0.0645346	−	0.0468871i	−0.555050	−	0.831817i	$-0.687301\pi$
$113$	0.686012	−	0.498417i	0.0645346	−	0.0468871i	0.619585	+	0.784930i	$0.287301\pi$
$114$	−18.4949	−	13.4373i	−1.73221	−	1.25852i
$115$		0			0
$116$	−6.97027	+	5.06419i	−0.647173	+	0.470199i
$117$	−2.12293	+	6.53372i	−0.196265	+	0.604042i
$118$	−3.74015			−0.344309
$119$	0.627429	−	1.93103i	0.0575163	−	0.177017i
$120$		0			0
$121$	−2.45679	−	7.56122i	−0.223344	−	0.687384i
$122$	6.02890	+	18.5550i	0.545831	+	1.67989i
$123$	−10.2476	−	7.44528i	−0.923990	−	0.671318i
$124$	0.628139			0.0564086
$125$		0			0
$126$	−4.58521			−0.408483
$127$	11.5872	+	8.41857i	1.02819	+	0.747027i	0.967947	−	0.251156i	$-0.0808109\pi$
$127$	11.5872	+	8.41857i	1.02819	+	0.747027i	0.0602479	+	0.998183i	$0.480811\pi$
$128$	−0.273031	−	0.840302i	−0.0241327	−	0.0742729i
$129$	6.70492	+	20.6356i	0.590335	+	1.81686i
$130$		0			0
$131$	−5.13789	+	15.8128i	−0.448899	+	1.38157i	0.429251	+	0.903185i	$0.358778\pi$
$131$	−5.13789	+	15.8128i	−0.448899	+	1.38157i	−0.878150	+	0.478385i	$0.841222\pi$
$132$	10.8575			0.945025
$133$	0.428978	−	1.32026i	0.0371972	−	0.114481i
$134$	−20.3149	+	14.7596i	−1.75494	+	1.27504i
$135$		0			0
$136$	0.490539	+	0.356398i	0.0420634	+	0.0305609i
$137$	−2.48521	+	1.80561i	−0.212326	+	0.154264i	−0.688865	−	0.724889i	$-0.741891\pi$
$137$	−2.48521	+	1.80561i	−0.212326	+	0.154264i	0.476540	+	0.879153i	$0.341891\pi$
$138$	−35.7171	+	25.9500i	−3.04044	+	2.20901i
$139$	12.7178	+	9.23999i	1.07871	+	0.783726i	0.977457	−	0.211135i	$-0.0677161\pi$
$139$	12.7178	+	9.23999i	1.07871	+	0.783726i	0.101249	+	0.994861i	$0.467716\pi$
$140$		0			0
$141$	−1.98340	+	1.44102i	−0.167032	+	0.121356i
$142$	7.26593	−	22.3622i	0.609743	−	1.87660i
$143$	1.94929			0.163008
$144$	−7.39313	+	22.7537i	−0.616094	+	1.89614i
$145$		0			0
$146$	−2.13520	−	6.57146i	−0.176710	−	0.543858i
$147$	6.41689	+	19.7492i	0.529256	+	1.62888i
$148$	−15.3268	−	11.1356i	−1.25986	−	0.915339i
$149$	14.8504			1.21660			0.608298	−	0.793709i	$-0.291853\pi$
$149$	14.8504			1.21660			0.608298	+	0.793709i	$0.291853\pi$
$150$		0			0
$151$	−0.712013			−0.0579428			−0.0289714	−	0.999580i	$-0.509223\pi$
$151$	−0.712013			−0.0579428			−0.0289714	+	0.999580i	$0.509223\pi$
$152$	0.335386	+	0.243672i	0.0272034	+	0.0197644i
$153$	−10.4376	−	32.1235i	−0.843828	−	2.59703i
$154$	0.402036	+	1.23734i	0.0323970	+	0.0997076i
$155$		0			0
$156$	2.14456	−	6.60027i	0.171702	−	0.528444i
$157$	22.0704			1.76141			0.880704	−	0.473667i	$-0.157070\pi$
$157$	22.0704			1.76141			0.880704	+	0.473667i	$0.157070\pi$
$158$	3.54280	−	10.9036i	0.281850	−	0.867445i
$159$	9.58340	−	6.96275i	0.760013	−	0.552182i
$160$		0			0
$161$	−2.16888	−	1.57578i	−0.170932	−	0.124189i
$162$	−16.9682	+	12.3281i	−1.33315	+	0.968589i
$163$	−10.6482	+	7.73637i	−0.834031	+	0.605959i	−0.920697	−	0.390278i	$-0.872379\pi$
$163$	−10.6482	+	7.73637i	−0.834031	+	0.605959i	0.0866658	+	0.996237i	$0.472379\pi$
$164$	6.95958	+	5.05643i	0.543452	+	0.394841i
$165$		0			0
$166$	11.6215	−	8.44350i	0.902002	−	0.655343i
$167$	−3.21628	+	9.89870i	−0.248883	+	0.765984i	0.746090	+	0.665845i	$0.231929\pi$
$167$	−3.21628	+	9.89870i	−0.248883	+	0.765984i	−0.994973	+	0.100139i	$0.968071\pi$
$168$	0.123678			0.00954194
$169$	−3.63220	+	11.1788i	−0.279400	+	0.859905i
$170$		0			0
$171$	−7.13626	−	21.9631i	−0.545723	−	1.67956i
$172$	−4.55362	−	14.0146i	−0.347210	−	1.06860i
$173$	−7.43686	−	5.40320i	−0.565414	−	0.410797i	0.268022	−	0.963413i	$-0.413630\pi$
$173$	−7.43686	−	5.40320i	−0.565414	−	0.410797i	−0.833436	+	0.552615i	$0.813630\pi$
$174$	−25.5457			−1.93661
$175$		0			0
$176$	6.78842			0.511697
$177$	−4.54652	−	3.30324i	−0.341737	−	0.248287i
$178$	0.952050	+	2.93011i	0.0713592	+	0.219621i
$179$	−6.70175	−	20.6259i	−0.500913	−	1.54165i	−0.807535	−	0.589819i	$-0.799199\pi$
$179$	−6.70175	−	20.6259i	−0.500913	−	1.54165i	0.306623	−	0.951831i	$-0.400801\pi$
$180$		0			0
$181$	3.32749	−	10.2410i	0.247331	−	0.761205i	−0.747914	−	0.663796i	$-0.768944\pi$
$181$	3.32749	−	10.2410i	0.247331	−	0.761205i	0.995244	−	0.0974094i	$-0.0310556\pi$
$182$	0.831586			0.0616413
$183$	−9.05880	+	27.8801i	−0.669645	+	2.06096i
$184$	0.647694	−	0.470577i	0.0477486	−	0.0346914i
$185$		0			0
$186$	1.50674	+	1.09471i	0.110480	+	0.0802682i
$187$	−7.75349	+	5.63324i	−0.566992	+	0.411944i
$188$	1.34702	−	0.978664i	0.0982412	−	0.0713764i
$189$	−2.85692	−	2.07567i	−0.207810	−	0.150983i
$190$		0			0
$191$	3.10615	−	2.25675i	0.224753	−	0.163293i	−0.469711	−	0.882820i	$-0.655642\pi$
$191$	3.10615	−	2.25675i	0.224753	−	0.163293i	0.694464	+	0.719528i	$0.255642\pi$
$192$	7.88447	−	24.2659i	0.569013	−	1.75124i
$193$	10.5334			0.758208			0.379104	−	0.925354i	$-0.376232\pi$
$193$	10.5334			0.758208			0.379104	+	0.925354i	$0.376232\pi$
$194$	−3.98084	+	12.2518i	−0.285808	+	0.879627i
$195$		0			0
$196$	−4.35801	−	13.4126i	−0.311286	−	0.958040i
$197$	2.98295	+	9.18057i	0.212526	+	0.654088i	0.999320	+	0.0368724i	$0.0117395\pi$
$197$	2.98295	+	9.18057i	0.212526	+	0.654088i	−0.786794	+	0.617216i	$0.788260\pi$
$198$	17.5096	+	12.7214i	1.24435	+	0.904073i
$199$	−15.8462			−1.12331			−0.561654	−	0.827372i	$-0.689835\pi$
$199$	−15.8462			−1.12331			−0.561654	+	0.827372i	$0.689835\pi$
$200$		0			0
$201$	−37.7302			−2.66129
$202$	19.9543	+	14.4976i	1.40398	+	1.02005i
$203$	−0.479356	−	1.47531i	−0.0336442	−	0.103546i
$204$	10.5439	+	32.4508i	0.738220	+	2.27201i
$205$		0			0
$206$	4.77104	−	14.6838i	0.332414	−	1.02307i
$207$	−44.5978			−3.09976
$208$	1.34084	−	4.12667i	0.0929703	−	0.286133i
$209$	−5.30113	+	3.85150i	−0.366687	+	0.266414i
$210$		0			0
$211$	−5.86623	−	4.26207i	−0.403848	−	0.293413i	0.367258	−	0.930119i	$-0.380296\pi$
$211$	−5.86623	−	4.26207i	−0.403848	−	0.293413i	−0.771107	+	0.636706i	$0.780296\pi$
$212$	−6.50852	+	4.72872i	−0.447007	+	0.324770i
$213$	28.5824	−	20.7663i	1.95843	−	1.42289i
$214$	−1.23486	−	0.897176i	−0.0844131	−	0.0613297i
$215$		0			0
$216$	0.853162	−	0.619859i	0.0580503	−	0.0421760i
$217$	−0.0349480	+	0.107559i	−0.00237243	+	0.00730158i
$218$	−6.58147			−0.445753
$219$	3.20827	−	9.87403i	0.216795	−	0.667225i
$220$		0			0
$221$	1.89298	+	5.82601i	0.127336	+	0.391900i
$222$	−17.3581	−	53.4227i	−1.16500	−	3.58550i
$223$	18.4984	+	13.4399i	1.23875	+	0.900003i	0.997514	−	0.0704644i	$-0.0224481\pi$
$223$	18.4984	+	13.4399i	1.23875	+	0.900003i	0.241233	+	0.970467i	$0.422448\pi$
$224$	2.97776			0.198960
$225$		0			0
$226$	−1.70751			−0.113582
$227$	−0.538335	−	0.391123i	−0.0357305	−	0.0259597i	0.569777	−	0.821800i	$-0.307030\pi$
$227$	−0.538335	−	0.391123i	−0.0357305	−	0.0259597i	−0.605507	+	0.795840i	$0.707030\pi$
$228$	7.20895	+	22.1869i	0.477424	+	1.46936i
$229$	−7.25362	−	22.3243i	−0.479332	−	1.47523i	−0.840025	−	0.542548i	$-0.817459\pi$
$229$	−7.25362	−	22.3243i	−0.479332	−	1.47523i	0.360692	−	0.932685i	$-0.382541\pi$
$230$		0			0
$231$	−0.604084	+	1.85918i	−0.0397458	+	0.122325i
$232$	0.463245			0.0304135
$233$	−5.50954	+	16.9566i	−0.360942	+	1.11087i	0.591541	+	0.806275i	$0.298520\pi$
$233$	−5.50954	+	16.9566i	−0.360942	+	1.11087i	−0.952483	+	0.304591i	$0.901480\pi$
$234$	11.1918	−	8.13132i	0.731631	−	0.531561i
$235$		0			0
$236$	3.08775	+	2.24338i	0.200995	+	0.146032i
$237$	13.9365	−	10.1255i	0.905274	−	0.657720i
$238$	−3.30771	+	2.40320i	−0.214407	+	0.155776i
$239$	19.3117	+	14.0308i	1.24917	+	0.907575i	0.998173	−	0.0604129i	$-0.0192417\pi$
$239$	19.3117	+	14.0308i	1.24917	+	0.907575i	0.250997	+	0.967988i	$0.419242\pi$
$240$		0			0
$241$	3.40859	−	2.47649i	0.219567	−	0.159524i	−0.472565	−	0.881296i	$-0.656672\pi$
$241$	3.40859	−	2.47649i	0.219567	−	0.159524i	0.692132	+	0.721771i	$0.256672\pi$
$242$	−4.94716	+	15.2258i	−0.318016	+	0.978752i
$243$	−2.87982			−0.184741
$244$	6.15224	−	18.9347i	0.393857	−	1.21217i
$245$		0			0
$246$	7.88194	+	24.2581i	0.502534	+	1.54664i
$247$	1.29425	+	3.98329i	0.0823511	+	0.253451i
$248$	−0.0273232	−	0.0198515i	−0.00173503	−	0.00126057i
$249$	21.5842			1.36784
$250$		0			0
$251$	19.5741			1.23551			0.617755	−	0.786371i	$-0.288042\pi$
$251$	19.5741			1.23551			0.617755	+	0.786371i	$0.288042\pi$
$252$	3.78541	+	2.75026i	0.238458	+	0.173250i
$253$	3.91037	+	12.0349i	0.245843	+	0.756627i
$254$	−8.91231	−	27.4293i	−0.559208	−	1.72106i
$255$		0			0
$256$	4.66193	−	14.3480i	0.291371	−	0.896747i
$257$	18.4169			1.14881			0.574407	−	0.818570i	$-0.305233\pi$
$257$	18.4169			1.14881			0.574407	+	0.818570i	$0.305233\pi$
$258$	13.5015	−	41.5533i	0.840566	−	2.58700i
$259$	2.75954	−	2.00492i	0.171469	−	0.124580i
$260$		0			0
$261$	−20.8770	−	15.1680i	−1.29226	−	0.938879i
$262$	27.0862	−	19.6793i	1.67339	−	1.21579i
$263$	−3.49860	+	2.54188i	−0.215733	+	0.156739i	−0.690404	−	0.723424i	$-0.742567\pi$
$263$	−3.49860	+	2.54188i	−0.215733	+	0.156739i	0.474671	+	0.880163i	$0.342567\pi$
$264$	−0.472288	−	0.343137i	−0.0290673	−	0.0211186i
$265$		0			0
$266$	−2.26151	+	1.64309i	−0.138662	+	0.100744i
$267$	−1.43051	+	4.40267i	−0.0875461	+	0.269439i
$268$	25.6243			1.56526
$269$	1.46442	−	4.50701i	0.0892870	−	0.274797i	−0.896436	−	0.443174i	$-0.853852\pi$
$269$	1.46442	−	4.50701i	0.0892870	−	0.274797i	0.985723	+	0.168377i	$0.0538525\pi$
$270$		0			0
$271$	3.07944	+	9.47755i	0.187063	+	0.575720i	0.999978	−	0.00666226i	$-0.00212068\pi$
$271$	3.07944	+	9.47755i	0.187063	+	0.575720i	−0.812915	+	0.582382i	$0.802121\pi$
$272$	6.59234	+	20.2891i	0.399719	+	1.23021i
$273$	1.01087	+	0.734443i	0.0611809	+	0.0444505i
$274$	6.18577			0.373696
$275$		0			0
$276$	45.0520			2.71181
$277$	−14.2462	−	10.3504i	−0.855969	−	0.621898i	0.0708162	−	0.997489i	$-0.477440\pi$
$277$	−14.2462	−	10.3504i	−0.855969	−	0.621898i	−0.926785	+	0.375591i	$0.877440\pi$
$278$	−9.78191	−	30.1056i	−0.586680	−	1.80561i
$279$	0.581377	+	1.78929i	0.0348061	+	0.107122i
$280$		0			0
$281$	−7.87882	+	24.2485i	−0.470011	+	1.44655i	0.382558	+	0.923931i	$0.375043\pi$
$281$	−7.87882	+	24.2485i	−0.470011	+	1.44655i	−0.852569	+	0.522614i	$0.824957\pi$
$282$	4.93674			0.293979
$283$	4.97531	−	15.3124i	0.295751	−	0.910229i	−0.687217	−	0.726453i	$-0.741168\pi$
$283$	4.97531	−	15.3124i	0.295751	−	0.910229i	0.982968	−	0.183777i	$-0.0588324\pi$
$284$	−19.4116	+	14.1034i	−1.15187	+	0.836881i
$285$		0			0
$286$	−3.17558	−	2.30719i	−0.187776	−	0.136427i
$287$	−1.25305	+	0.910392i	−0.0739650	+	0.0537387i
$288$	40.0758	−	29.1168i	2.36149	−	1.71572i
$289$	−10.6128	−	7.71064i	−0.624281	−	0.453567i
$290$		0			0
$291$	−15.6597	+	11.3774i	−0.917987	+	0.666957i
$292$	−2.17888	+	6.70591i	−0.127509	+	0.392433i
$293$	−24.9049			−1.45496			−0.727481	−	0.686128i	$-0.759309\pi$
$293$	−24.9049			−1.45496			−0.727481	+	0.686128i	$0.759309\pi$
$294$	12.9215	−	39.7683i	0.753598	−	2.31933i
$295$		0			0
$296$	0.314771	+	0.968766i	0.0182957	+	0.0563084i
$297$	5.15086	+	15.8527i	0.298883	+	0.919868i
$298$	−24.1927	−	17.5771i	−1.40145	−	1.01821i
$299$	8.08836			0.467762
$300$		0			0
$301$	2.65313			0.152924
$302$	1.15994	+	0.842742i	0.0667468	+	0.0484944i
$303$	11.4523	+	35.2466i	0.657919	+	2.02487i
$304$	4.50724	+	13.8718i	0.258508	+	0.795605i
$305$		0			0
$306$	−21.0178	+	64.6862i	−1.20151	+	3.69786i
$307$	−1.74743			−0.0997311			−0.0498655	−	0.998756i	$-0.515879\pi$
$307$	−1.74743			−0.0997311			−0.0498655	+	0.998756i	$0.515879\pi$
$308$	0.410261	−	1.26265i	0.0233768	−	0.0719464i
$309$	18.7681	−	13.6358i	1.06768	−	0.775716i
$310$		0			0
$311$	−14.8262	−	10.7719i	−0.840718	−	0.610818i	0.0818529	−	0.996644i	$-0.473916\pi$
$311$	−14.8262	−	10.7719i	−0.840718	−	0.610818i	−0.922571	+	0.385827i	$0.873916\pi$
$312$	−0.301878	+	0.219327i	−0.0170905	+	0.0124170i
$313$	2.67589	−	1.94415i	0.151250	−	0.109890i	−0.509587	−	0.860419i	$-0.670202\pi$
$313$	2.67589	−	1.94415i	0.151250	−	0.109890i	0.660837	+	0.750530i	$0.270202\pi$
$314$	−35.9547	−	26.1226i	−2.02904	−	1.47419i
$315$		0			0
$316$	−9.46493	+	6.87667i	−0.532444	+	0.386843i
$317$	0.308721	−	0.950146i	0.0173395	−	0.0533655i	−0.942012	−	0.335578i	$-0.891068\pi$
$317$	0.308721	−	0.950146i	0.0173395	−	0.0533655i	0.959352	+	0.282213i	$0.0910684\pi$
$318$	−23.8534			−1.33763
$319$	−2.26264	+	6.96370i	−0.126684	+	0.389892i
$320$		0			0
$321$	−0.708719	−	2.18121i	−0.0395568	−	0.121743i
$322$	1.66820	+	5.13420i	0.0929653	+	0.286118i
$323$	−16.6593	−	12.1037i	−0.926948	−	0.673467i
$324$	21.4030			1.18905
$325$		0			0
$326$	26.5037			1.46790
$327$	−8.00042	−	5.81265i	−0.442424	−	0.321440i
$328$	−0.142931	−	0.439896i	−0.00789204	−	0.0242892i
$329$	0.0926364	+	0.285106i	0.00510721	+	0.0157184i
$330$		0			0
$331$	−4.38833	+	13.5059i	−0.241205	+	0.742351i	0.755033	+	0.655687i	$0.227621\pi$
$331$	−4.38833	+	13.5059i	−0.241205	+	0.742351i	−0.996238	+	0.0866646i	$0.972379\pi$
$332$	−14.6588			−0.804508
$333$	17.5346	−	53.9660i	0.960890	−	2.95732i
$334$	16.9558	−	12.3191i	0.927779	−	0.674071i
$335$		0			0
$336$	3.52038	+	2.55771i	0.192052	+	0.139534i
$337$	10.6410	−	7.73114i	0.579652	−	0.421142i	−0.258947	−	0.965892i	$-0.583375\pi$
$337$	10.6410	−	7.73114i	0.579652	−	0.421142i	0.838599	+	0.544750i	$0.183375\pi$
$338$	19.1484	−	13.9122i	1.04154	−	0.756722i
$339$	−2.07564	−	1.50804i	−0.112733	−	0.0819056i
$340$		0			0
$341$	0.431872	−	0.313774i	0.0233872	−	0.0169918i
$342$	−14.3701	+	44.2265i	−0.777044	+	2.39150i
$343$	5.12896			0.276938
$344$	−0.244836	+	0.753527i	−0.0132007	+	0.0406275i
$345$		0			0
$346$	5.72009	+	17.6046i	0.307514	+	0.946430i
$347$	−4.18639	−	12.8844i	−0.224737	−	0.691670i	−0.998318	−	0.0579727i	$-0.981536\pi$
$347$	−4.18639	−	12.8844i	−0.224737	−	0.691670i	0.773581	−	0.633698i	$-0.218464\pi$
$348$	21.0897	+	15.3226i	1.13053	+	0.821375i
$349$	−32.0976			−1.71814			−0.859072	−	0.511854i	$-0.828959\pi$
$349$	−32.0976			−1.71814			−0.859072	+	0.511854i	$0.828959\pi$
$350$		0			0
$351$	10.6542			0.568681
$352$	−11.3712	−	8.26163i	−0.606085	−	0.440347i
$353$	−5.65879	−	17.4160i	−0.301187	−	0.926958i	−0.981073	−	0.193640i	$-0.937971\pi$
$353$	−5.65879	−	17.4160i	−0.301187	−	0.926958i	0.679886	−	0.733318i	$-0.262029\pi$
$354$	3.49697	+	10.7626i	0.185862	+	0.572024i
$355$		0			0
$356$	0.971528	−	2.99006i	0.0514909	−	0.158473i
$357$	−6.14332			−0.325139
$358$	−13.4951	+	41.5337i	−0.713239	+	2.19513i
$359$	11.6793	−	8.48553i	0.616412	−	0.447849i	−0.235255	−	0.971934i	$-0.575592\pi$
$359$	11.6793	−	8.48553i	0.616412	−	0.447849i	0.851666	+	0.524085i	$0.175592\pi$
$360$		0			0
$361$	3.98122	+	2.89253i	0.209538	+	0.152238i
$362$	−17.5421	+	12.7451i	−0.921990	+	0.669865i
$363$	−19.4609	+	14.1392i	−1.02143	+	0.742116i
$364$	−0.686531	−	0.498794i	−0.0359840	−	0.0261439i
$365$		0			0
$366$	47.7567	−	34.6973i	2.49628	−	1.81365i
$367$	−3.21780	+	9.90337i	−0.167968	+	0.516952i	−0.999243	−	0.0389099i	$-0.987611\pi$
$367$	−3.21780	+	9.90337i	−0.167968	+	0.516952i	0.831275	+	0.555861i	$0.187611\pi$
$368$	28.1678			1.46835
$369$	−7.96209	+	24.5048i	−0.414490	+	1.27567i
$370$		0			0
$371$	−0.447602	−	1.37758i	−0.0232383	−	0.0715202i
$372$	−0.587299	−	1.80752i	−0.0304500	−	0.0937155i
$373$	8.10835	+	5.89106i	0.419834	+	0.305028i	0.777571	−	0.628795i	$-0.216451\pi$
$373$	8.10835	+	5.89106i	0.419834	+	0.305028i	−0.357737	+	0.933822i	$0.616451\pi$
$374$	19.2987			0.997912
$375$		0			0
$376$	−0.0895228			−0.00461679
$377$	3.78631	+	2.75092i	0.195005	+	0.141679i
$378$	2.19741	+	6.76292i	0.113022	+	0.347847i
$379$	4.41879	+	13.5996i	0.226978	+	0.698566i	0.998085	+	0.0618604i	$0.0197034\pi$
$379$	4.41879	+	13.5996i	0.226978	+	0.698566i	−0.771107	+	0.636706i	$0.780297\pi$
$380$		0			0
$381$	13.3913	−	41.2142i	0.686057	−	2.11147i
$382$	−7.73131			−0.395568
$383$	−1.55653	+	4.79051i	−0.0795351	+	0.244784i	−0.982916	−	0.184056i	$-0.941077\pi$
$383$	−1.55653	+	4.79051i	−0.0795351	+	0.244784i	0.903381	+	0.428839i	$0.141077\pi$
$384$	−2.16276	+	1.57133i	−0.110368	+	0.0801868i
$385$		0			0
$386$	−17.1598	−	12.4673i	−0.873412	−	0.634571i
$387$	35.7068	−	25.9425i	1.81508	−	1.31873i
$388$	10.6352	−	7.72693i	0.539921	−	0.392275i
$389$	−8.19745	−	5.95580i	−0.415627	−	0.301971i	0.360249	−	0.932856i	$-0.382692\pi$
$389$	−8.19745	−	5.95580i	−0.415627	−	0.301971i	−0.775876	+	0.630885i	$0.782692\pi$
$390$		0			0
$391$	−32.1722	+	23.3745i	−1.62702	+	1.18210i
$392$	−0.234318	+	0.721158i	−0.0118349	+	0.0364240i
$393$	50.3064			2.53762
$394$	6.00667	−	18.4866i	0.302612	−	0.931343i
$395$		0			0
$396$	−6.82488	−	21.0048i	−0.342963	−	1.05553i
$397$	−6.07772	−	18.7053i	−0.305032	−	0.938792i	−0.979665	−	0.200639i	$-0.935698\pi$
$397$	−6.07772	−	18.7053i	−0.305032	−	0.938792i	0.674633	−	0.738153i	$-0.264302\pi$
$398$	25.8150	+	18.7557i	1.29399	+	0.940137i
$399$	−4.20024			−0.210275
$400$		0			0
$401$	−23.0931			−1.15321			−0.576606	−	0.817022i	$-0.695623\pi$
$401$	−23.0931			−1.15321			−0.576606	+	0.817022i	$0.695623\pi$
$402$	61.4661	+	44.6577i	3.06565	+	2.22732i
$403$	−0.105440	−	0.324511i	−0.00525234	−	0.0161650i
$404$	−7.77780	−	23.9376i	−0.386960	−	1.19094i
$405$		0			0
$406$	−0.965265	+	2.97078i	−0.0479053	+	0.147437i
$407$	−16.1004			−0.798066
$408$	0.566917	−	1.74479i	0.0280666	−	0.0863800i
$409$	−31.2554	+	22.7084i	−1.54548	+	1.12286i	−0.598701	+	0.800973i	$0.704316\pi$
$409$	−31.2554	+	22.7084i	−1.54548	+	1.12286i	−0.946779	+	0.321884i	$0.895684\pi$
$410$		0			0
$411$	7.51941	+	5.46317i	0.370905	+	0.269478i
$412$	−12.7463	+	9.26073i	−0.627965	+	0.456243i
$413$	−0.555938	+	0.403913i	−0.0273559	+	0.0198752i
$414$	72.6539	+	52.7862i	3.57074	+	2.59430i
$415$		0			0
$416$	−7.26825	+	5.28069i	−0.356355	+	0.258907i
$417$	14.6979	−	45.2356i	0.719760	−	2.21519i
$418$	13.1947			0.645373
$419$	−3.33402	+	10.2610i	−0.162877	+	0.501285i	−0.998874	−	0.0474503i	$-0.984890\pi$
$419$	−3.33402	+	10.2610i	−0.162877	+	0.501285i	0.835996	+	0.548735i	$0.184890\pi$
$420$		0			0
$421$	10.0292	+	30.8666i	0.488791	+	1.50434i	0.826414	+	0.563062i	$0.190377\pi$
$421$	10.0292	+	30.8666i	0.488791	+	1.50434i	−0.337623	+	0.941281i	$0.609623\pi$
$422$	4.51203	+	13.8866i	0.219642	+	0.675990i
$423$	4.03452	+	2.93125i	0.196165	+	0.142522i
$424$	0.432557			0.0210068
$425$		0			0
$426$	−71.1426			−3.44687
$427$	2.89997	+	2.10695i	0.140339	+	0.101962i
$428$	0.481323	+	1.48136i	0.0232656	+	0.0716043i
$429$	−1.82255	−	5.60924i	−0.0879936	−	0.270816i
$430$		0			0
$431$	4.26198	−	13.1170i	0.205292	−	0.631824i	−0.794409	−	0.607383i	$-0.792219\pi$
$431$	4.26198	−	13.1170i	0.205292	−	0.631824i	0.999701	−	0.0244412i	$-0.00778064\pi$
$432$	37.1035			1.78514
$433$	6.52397	−	20.0787i	0.313522	−	0.964922i	−0.662836	−	0.748764i	$-0.730647\pi$
$433$	6.52397	−	20.0787i	0.313522	−	0.964922i	0.976358	−	0.216158i	$-0.0693525\pi$
$434$	0.184241	−	0.133859i	0.00884385	−	0.00642543i
$435$		0			0
$436$	5.43345	+	3.94763i	0.260215	+	0.189057i
$437$	−21.9964	+	15.9814i	−1.05223	+	0.764492i
$438$	−16.9135	+	12.2884i	−0.808159	+	0.587162i
$439$	−29.4043	−	21.3634i	−1.40339	−	1.01962i	−0.994243	−	0.107153i	$-0.965827\pi$
$439$	−29.4043	−	21.3634i	−1.40339	−	1.01962i	−0.409146	−	0.912469i	$-0.634173\pi$
$440$		0			0
$441$	34.1730	−	24.8281i	1.62728	−	1.18229i
$442$	3.81185	−	11.7317i	0.181311	−	0.558018i
$443$	−6.38810			−0.303508			−0.151754	−	0.988418i	$-0.548492\pi$
$443$	−6.38810			−0.303508			−0.151754	+	0.988418i	$0.548492\pi$
$444$	−17.7132	+	54.5157i	−0.840632	+	2.58720i
$445$		0			0
$446$	−14.2281	−	43.7897i	−0.673722	−	2.07350i
$447$	−13.8849	−	42.7333i	−0.656733	−	2.02122i
$448$	−2.52403	−	1.83382i	−0.119249	−	0.0866397i
$449$	−35.1628			−1.65943			−0.829717	−	0.558185i	$-0.811498\pi$
$449$	−35.1628			−1.65943			−0.829717	+	0.558185i	$0.811498\pi$
$450$		0			0
$451$	7.31084			0.344254
$452$	1.40966	+	1.02418i	0.0663050	+	0.0481734i
$453$	0.665719	+	2.04887i	0.0312782	+	0.0962644i
$454$	0.414062	+	1.27435i	0.0194329	+	0.0598083i
$455$		0			0
$456$	0.387606	−	1.19293i	0.0181513	−	0.0558640i
$457$	−22.2994			−1.04312			−0.521561	−	0.853214i	$-0.674650\pi$
$457$	−22.2994			−1.04312			−0.521561	+	0.853214i	$0.674650\pi$
$458$	−14.6064	+	44.9538i	−0.682512	+	2.10056i
$459$	−42.3783	+	30.7896i	−1.97805	+	1.43714i
$460$		0			0
$461$	1.52533	+	1.10822i	0.0710416	+	0.0516147i	0.622739	−	0.782429i	$-0.286020\pi$
$461$	1.52533	+	1.10822i	0.0710416	+	0.0516147i	−0.551698	+	0.834044i	$0.686020\pi$
$462$	3.18464	−	2.31378i	0.148163	−	0.107647i
$463$	−10.4486	+	7.59134i	−0.485587	+	0.352800i	−0.803485	−	0.595325i	$-0.797023\pi$
$463$	−10.4486	+	7.59134i	−0.485587	+	0.352800i	0.317898	+	0.948125i	$0.397023\pi$
$464$	13.1859	+	9.58009i	0.612138	+	0.444745i
$465$		0			0
$466$	29.0455	−	21.1028i	1.34551	−	0.977569i
$467$	0.809055	−	2.49002i	0.0374386	−	0.115224i	−0.930591	−	0.366062i	$-0.880706\pi$
$467$	0.809055	−	2.49002i	0.0374386	−	0.115224i	0.968029	+	0.250837i	$0.0807060\pi$
$468$	−14.1168			−0.652551
$469$	−1.42567	+	4.38776i	−0.0658314	+	0.202608i
$470$		0			0
$471$	−20.6354	−	63.5093i	−0.950829	−	2.92635i
$472$	−0.0634140	−	0.195168i	−0.00291887	−	0.00898335i
$473$	−10.1315	−	7.36097i	−0.465847	−	0.338458i
$474$	−34.6885			−1.59329
$475$		0			0
$476$	4.17221			0.191233
$477$	−19.4940	−	14.1632i	−0.892571	−	0.648491i
$478$	−14.8537	−	45.7149i	−0.679391	−	2.09095i
$479$	2.08066	+	6.40362i	0.0950678	+	0.292589i	0.987271	−	0.159045i	$-0.0508414\pi$
$479$	2.08066	+	6.40362i	0.0950678	+	0.292589i	−0.892204	+	0.451634i	$0.850841\pi$
$480$		0			0
$481$	−3.18012	+	9.78740i	−0.145001	+	0.446267i
$482$	−8.48409			−0.386440
$483$	−2.50658	+	7.71445i	−0.114053	+	0.351020i
$484$	13.2168	−	9.60258i	0.600765	−	0.436481i
$485$		0			0
$486$	4.69150	+	3.40858i	0.212811	+	0.154616i
$487$	−4.49648	+	3.26688i	−0.203755	+	0.148037i	−0.684984	−	0.728559i	$-0.740191\pi$
$487$	−4.49648	+	3.26688i	−0.203755	+	0.148037i	0.481229	+	0.876595i	$0.340191\pi$
$488$	−0.866019	+	0.629200i	−0.0392028	+	0.0284825i
$489$	32.2179	+	23.4077i	1.45694	+	1.05853i
$490$		0			0
$491$	4.49165	−	3.26338i	0.202706	−	0.147274i	−0.481802	−	0.876280i	$-0.660017\pi$
$491$	4.49165	−	3.26338i	0.202706	−	0.147274i	0.684507	+	0.729006i	$0.260017\pi$
$492$	8.04319	−	24.7544i	0.362615	−	1.11601i
$493$	−23.0103			−1.03633
$494$	2.60619	−	8.02103i	0.117258	−	0.360883i
$495$		0			0
$496$	−0.367196	−	1.13011i	−0.0164876	−	0.0507435i
$497$	−1.33497	−	4.10861i	−0.0598815	−	0.184296i
$498$	−35.1627	−	25.5472i	−1.57568	−	1.14480i
$499$	19.2580			0.862107			0.431054	−	0.902326i	$-0.358142\pi$
$499$	19.2580			0.862107			0.431054	+	0.902326i	$0.358142\pi$
$500$		0			0
$501$	31.4914			1.40693
$502$	−31.8881	−	23.1681i	−1.42324	−	1.03404i
$503$	−9.62789	−	29.6316i	−0.429286	−	1.32121i	−0.898830	−	0.438298i	$-0.855581\pi$
$503$	−9.62789	−	29.6316i	−0.429286	−	1.32121i	0.469543	−	0.882909i	$-0.344419\pi$
$504$	−0.0777421	−	0.239265i	−0.00346291	−	0.0106577i
$505$		0			0
$506$	7.87420	−	24.2343i	0.350051	−	1.07735i
$507$	35.5638			1.57944
$508$	−9.09464	+	27.9904i	−0.403510	+	1.24187i
$509$	17.1714	−	12.4758i	0.761109	−	0.552978i	−0.138141	−	0.990413i	$-0.544113\pi$
$509$	17.1714	−	12.4758i	0.761109	−	0.552978i	0.899250	+	0.437434i	$0.144113\pi$
$510$		0			0
$511$	−1.02705	−	0.746198i	−0.0454342	−	0.0330099i
$512$	−26.0067	+	18.8949i	−1.14934	+	0.835046i
$513$	−28.9744	+	21.0511i	−1.27925	+	0.929430i
$514$	−30.0028	−	21.7983i	−1.32337	−	0.961483i
$515$		0			0
$516$	−36.0705	+	26.2068i	−1.58792	+	1.15369i
$517$	0.437260	−	1.34575i	0.0192307	−	0.0591859i
$518$	−6.86858			−0.301788
$519$	−8.59479	+	26.4520i	−0.377269	+	1.16112i
$520$		0			0
$521$	7.41935	+	22.8344i	0.325048	+	1.00039i	0.971419	+	0.237371i	$0.0762856\pi$
$521$	7.41935	+	22.8344i	0.325048	+	1.00039i	−0.646372	+	0.763023i	$0.723714\pi$
$522$	16.0576	+	49.4203i	0.702824	+	2.16307i
$523$	18.4609	+	13.4127i	0.807240	+	0.586494i	0.913029	−	0.407894i	$-0.133737\pi$
$523$	18.4609	+	13.4127i	0.807240	+	0.586494i	−0.105789	+	0.994389i	$0.533737\pi$
$524$	−34.1654			−1.49252
$525$		0			0
$526$	8.70813			0.379692
$527$	1.35720	+	0.986063i	0.0591205	+	0.0429536i
$528$	−6.34705	−	19.5342i	−0.276220	−	0.850118i
$529$	9.11826	+	28.0631i	0.396446	+	1.22014i
$530$		0			0
$531$	−3.53253	+	10.8720i	−0.153299	+	0.471805i
$532$	2.85257			0.123675
$533$	1.44402	−	4.44425i	0.0625477	−	0.192502i
$534$	7.54147	−	5.47920i	0.326351	−	0.237108i
$535$		0			0
$536$	−1.11462	−	0.809822i	−0.0481445	−	0.0349790i
$537$	−53.0866	+	38.5696i	−2.29085	+	1.66440i
$538$	−7.72019	+	5.60904i	−0.332841	+	0.241823i
$539$	−9.69628	−	7.04476i	−0.417648	−	0.303439i
$540$		0			0
$541$	−22.2538	+	16.1683i	−0.956766	+	0.695131i	−0.952397	−	0.304859i	$-0.901391\pi$
$541$	−22.2538	+	16.1683i	−0.956766	+	0.695131i	−0.00436851	+	0.999990i	$0.501391\pi$
$542$	6.20098	−	19.0847i	0.266355	−	0.819756i
$543$	−32.5803			−1.39816
$544$	13.6495	−	42.0089i	0.585219	−	1.80112i
$545$		0			0
$546$	−0.777518	−	2.39295i	−0.0332747	−	0.102409i
$547$	−0.0751603	−	0.231320i	−0.00321362	−	0.00989052i	0.949437	−	0.313958i	$-0.101655\pi$
$547$	−0.0751603	−	0.231320i	−0.00321362	−	0.00989052i	−0.952650	+	0.304068i	$0.901655\pi$
$548$	−5.10677	−	3.71029i	−0.218151	−	0.158496i
$549$	59.6308			2.54498
$550$		0			0
$551$	−15.7323			−0.670220
$552$	−1.95970	−	1.42381i	−0.0834106	−	0.0606013i
$553$	−0.650918	−	2.00332i	−0.0276799	−	0.0851898i
$554$	10.9575	+	33.7237i	0.465539	+	1.43278i
$555$		0			0
$556$	−9.98203	+	30.7215i	−0.423333	+	1.30288i
$557$	−27.7280			−1.17487			−0.587436	−	0.809271i	$-0.699862\pi$
$557$	−27.7280			−1.17487			−0.587436	+	0.809271i	$0.699862\pi$
$558$	1.17070	−	3.60305i	0.0495597	−	0.152529i
$559$	−6.47588	+	4.70500i	−0.273900	+	0.199000i
$560$		0			0
$561$	23.4595	+	17.0443i	0.990460	+	0.719611i
$562$	41.5360	−	30.1777i	1.75209	−	1.27297i
$563$	−10.0358	+	7.29143i	−0.422958	+	0.307297i	−0.778827	−	0.627239i	$-0.784185\pi$
$563$	−10.0358	+	7.29143i	−0.422958	+	0.307297i	0.355869	+	0.934536i	$0.384185\pi$
$564$	−4.07562	−	2.96111i	−0.171614	−	0.124685i
$565$		0			0
$566$	−26.2291	+	19.0566i	−1.10249	+	0.801007i
$567$	−1.19080	+	3.66492i	−0.0500091	+	0.153912i
$568$	1.29010			0.0541313
$569$	−8.22214	+	25.3052i	−0.344690	+	1.06085i	0.617059	+	0.786917i	$0.288324\pi$
$569$	−8.22214	+	25.3052i	−0.344690	+	1.06085i	−0.961749	+	0.273931i	$0.911676\pi$
$570$		0			0
$571$	3.99309	+	12.2895i	0.167106	+	0.514298i	0.999185	−	0.0403581i	$-0.0128499\pi$
$571$	3.99309	+	12.2895i	0.167106	+	0.514298i	−0.832080	+	0.554656i	$0.812850\pi$
$572$	1.23778	+	3.80949i	0.0517541	+	0.159283i
$573$	−9.39817	−	6.82817i	−0.392614	−	0.285251i
$574$	3.11888			0.130179
$575$		0			0
$576$	−51.9006			−2.16253
$577$	−22.9301	−	16.6597i	−0.954593	−	0.693552i	−0.00270417	−	0.999996i	$-0.500861\pi$
$577$	−22.9301	−	16.6597i	−0.954593	−	0.693552i	−0.951889	+	0.306444i	$0.900861\pi$
$578$	8.16286	+	25.1227i	0.339530	+	1.04497i
$579$	−9.84850	−	30.3106i	−0.409290	−	1.25966i
$580$		0			0
$581$	0.815579	−	2.51009i	0.0338359	−	0.104136i
$582$	38.9775			1.61567
$583$	−2.11276	+	6.50239i	−0.0875014	+	0.269302i
$584$	0.306710	−	0.222838i	0.0126917	−	0.00922108i
$585$		0			0
$586$	40.5725	+	29.4776i	1.67603	+	1.21771i
$587$	6.78673	−	4.93085i	0.280118	−	0.203518i	−0.438851	−	0.898560i	$-0.644614\pi$
$587$	6.78673	−	4.93085i	0.280118	−	0.203518i	0.718969	+	0.695042i	$0.244614\pi$
$588$	−34.5210	+	25.0810i	−1.42362	+	1.03432i
$589$	0.927929	+	0.674180i	0.0382346	+	0.0277791i
$590$		0			0
$591$	23.6288	−	17.1673i	0.971959	−	0.706170i
$592$	−11.0748	+	34.0847i	−0.455171	+	1.40087i
$593$	30.9031			1.26904			0.634518	−	0.772908i	$-0.281199\pi$
$593$	30.9031			1.26904			0.634518	+	0.772908i	$0.281199\pi$
$594$	10.3721	−	31.9221i	0.425574	−	1.30978i
$595$		0			0
$596$	9.42986	+	29.0221i	0.386262	+	1.18879i
$597$	14.8159	+	45.5987i	0.606376	+	1.86623i
$598$	−13.1767	−	9.57343i	−0.538835	−	0.391487i
$599$	32.6384			1.33357			0.666784	−	0.745251i	$-0.267671\pi$
$599$	32.6384			1.33357			0.666784	+	0.745251i	$0.267671\pi$
$600$		0			0
$601$	16.9351			0.690796			0.345398	−	0.938456i	$-0.387744\pi$
$601$	16.9351			0.690796			0.345398	+	0.938456i	$0.387744\pi$
$602$	−4.32220	−	3.14026i	−0.176160	−	0.127987i
$603$	23.7167	+	72.9925i	0.965819	+	2.97248i
$604$	−0.452120	−	1.39148i	−0.0183965	−	0.0566186i
$605$		0			0
$606$	23.0612	−	70.9751i	0.936797	−	2.88317i
$607$	36.3044			1.47355			0.736775	−	0.676138i	$-0.236348\pi$
$607$	36.3044			1.47355			0.736775	+	0.676138i	$0.236348\pi$
$608$	9.33230	−	28.7219i	0.378475	−	1.16483i
$609$	−3.79712	+	2.75877i	−0.153867	+	0.111791i
$610$		0			0
$611$	−0.731711	−	0.531619i	−0.0296019	−	0.0215070i
$612$	56.1511	−	40.7962i	2.26977	−	1.64909i
$613$	24.9129	−	18.1003i	1.00622	−	0.731064i	0.0428102	−	0.999083i	$-0.486369\pi$
$613$	24.9129	−	18.1003i	1.00622	−	0.731064i	0.963414	+	0.268019i	$0.0863689\pi$
$614$	2.84673	+	2.06827i	0.114884	+	0.0834685i
$615$		0			0
$616$	−0.0577503	+	0.0419580i	−0.00232682	+	0.00169054i
$617$	−10.9157	+	33.5949i	−0.439448	+	1.35248i	0.449011	+	0.893526i	$0.351776\pi$
$617$	−10.9157	+	33.5949i	−0.439448	+	1.35248i	−0.888459	+	0.458955i	$0.848224\pi$
$618$	−46.7145			−1.87913
$619$	1.22092	−	3.75761i	0.0490729	−	0.151031i	−0.923517	−	0.383557i	$-0.874699\pi$
$619$	1.22092	−	3.75761i	0.0490729	−	0.151031i	0.972590	+	0.232526i	$0.0746990\pi$
$620$		0			0
$621$	21.3729	+	65.7791i	0.857666	+	2.63962i
$622$	11.4036	+	35.0968i	0.457245	+	1.40725i
$623$	0.457947	+	0.332718i	0.0183472	+	0.0133301i
$624$	−13.1285			−0.525560
$625$		0			0
$626$	−6.66037			−0.266202
$627$	16.0394	+	11.6533i	0.640554	+	0.465390i
$628$	14.0144	+	43.1320i	0.559237	+	1.72116i
$629$	−15.6353	−	48.1206i	−0.623421	−	1.91869i
$630$		0			0
$631$	4.18001	−	12.8648i	0.166404	−	0.512138i	−0.832733	−	0.553674i	$-0.813225\pi$
$631$	4.18001	−	12.8648i	0.166404	−	0.512138i	0.999137	+	0.0415364i	$0.0132252\pi$
$632$	0.629040			0.0250219
$633$	−6.77961	+	20.8655i	−0.269465	+	0.829329i
$634$	−1.62753	+	1.18247i	−0.0646376	+	0.0469620i
$635$		0			0
$636$	19.6926	+	14.3075i	0.780863	+	0.567330i
$637$	−6.19769	+	4.50289i	−0.245562	+	0.178411i
$638$	11.9283	−	8.66644i	0.472247	−	0.343108i
$639$	−58.1408	−	42.2418i	−2.30002	−	1.67106i
$640$		0			0
$641$	29.2273	−	21.2349i	1.15441	−	0.838727i	0.165348	−	0.986235i	$-0.447125\pi$
$641$	29.2273	−	21.2349i	1.15441	−	0.838727i	0.989061	+	0.147508i	$0.0471253\pi$
$642$	−1.42713	+	4.39224i	−0.0563242	+	0.173348i
$643$	7.35135			0.289909			0.144954	−	0.989438i	$-0.453696\pi$
$643$	7.35135			0.289909			0.144954	+	0.989438i	$0.453696\pi$
$644$	1.70233	−	5.23924i	0.0670813	−	0.206455i
$645$		0			0
$646$	12.8136	+	39.4361i	0.504143	+	1.55159i
$647$	−13.5042	−	41.5615i	−0.530903	−	1.63395i	−0.752338	−	0.658777i	$-0.771074\pi$
$647$	−13.5042	−	41.5615i	−0.530903	−	1.63395i	0.221435	−	0.975175i	$-0.428926\pi$
$648$	−0.931001	−	0.676412i	−0.0365732	−	0.0265720i
$649$	3.24359			0.127322
$650$		0			0
$651$	0.342185			0.0134113
$652$	−21.8806	−	15.8972i	−0.856912	−	0.622583i
$653$	11.0766	+	34.0902i	0.433459	+	1.33405i	0.894657	+	0.446754i	$0.147420\pi$
$653$	11.0766	+	34.0902i	0.433459	+	1.33405i	−0.461198	+	0.887297i	$0.652580\pi$
$654$	6.15355	+	18.9387i	0.240623	+	0.740561i
$655$		0			0
$656$	5.02883	−	15.4771i	0.196343	−	0.604281i
$657$	−21.1189			−0.823925
$658$	0.186539	−	0.574109i	0.00727205	−	0.0223811i
$659$	−0.0552680	+	0.0401545i	−0.00215294	+	0.00156420i	−0.588861	−	0.808234i	$-0.700424\pi$
$659$	−0.0552680	+	0.0401545i	−0.00215294	+	0.00156420i	0.586708	+	0.809798i	$0.300424\pi$
$660$		0			0
$661$	21.3235	+	15.4924i	0.829388	+	0.602585i	0.919386	−	0.393357i	$-0.128686\pi$
$661$	21.3235	+	15.4924i	0.829388	+	0.602585i	−0.0899985	+	0.995942i	$0.528686\pi$
$662$	23.1347	−	16.8083i	0.899154	−	0.653274i
$663$	14.9949	−	10.8944i	0.582353	−	0.423104i
$664$	0.637640	+	0.463273i	0.0247452	+	0.0179785i
$665$		0			0
$666$	−92.4399	+	67.1615i	−3.58197	+	2.60246i
$667$	−9.38858	+	28.8951i	−0.363527	+	1.11882i
$668$	−21.3873			−0.827498
$669$	21.3787	−	65.7968i	0.826547	−	2.54385i
$670$		0			0
$671$	−5.22848	−	16.0916i	−0.201843	−	0.621210i
$672$	−2.78415	−	8.56873i	−0.107401	−	0.330546i
$673$	−4.10740	−	2.98420i	−0.158329	−	0.115032i	0.505800	−	0.862651i	$-0.331197\pi$
$673$	−4.10740	−	2.98420i	−0.158329	−	0.115032i	−0.664129	+	0.747618i	$0.731197\pi$
$674$	−26.4858			−1.02019
$675$		0			0
$676$	−24.1530			−0.928962
$677$	31.1883	+	22.6596i	1.19866	+	0.870879i	0.994152	−	0.107985i	$-0.0344399\pi$
$677$	31.1883	+	22.6596i	1.19866	+	0.870879i	0.204510	+	0.978865i	$0.434440\pi$
$678$	1.59649	+	4.91348i	0.0613127	+	0.188701i
$679$	0.731400	+	2.25102i	0.0280686	+	0.0863861i
$680$		0			0
$681$	−0.622154	+	1.91479i	−0.0238410	+	0.0733750i
$682$	−1.07494			−0.0411618
$683$	−11.3141	+	34.8213i	−0.432923	+	1.33240i	0.462277	+	0.886735i	$0.347032\pi$
$683$	−11.3141	+	34.8213i	−0.432923	+	1.33240i	−0.895200	+	0.445664i	$0.852968\pi$
$684$	38.3910	−	27.8927i	1.46792	−	1.06650i
$685$		0			0
$686$	−8.35555	−	6.07066i	−0.319016	−	0.231779i
$687$	−57.4580	+	41.7457i	−2.19216	+	1.59270i
$688$	−22.5523	+	16.3852i	−0.859799	+	0.624680i
$689$	3.53549	+	2.56868i	0.134691	+	0.0978590i
$690$		0			0
$691$	−23.7664	+	17.2673i	−0.904115	+	0.656878i	−0.939520	−	0.342495i	$-0.888728\pi$
$691$	−23.7664	+	17.2673i	−0.904115	+	0.656878i	0.0354046	+	0.999373i	$0.488728\pi$
$692$	5.83711	−	17.9648i	0.221894	−	0.682919i
$693$	3.97647			0.151053
$694$	−8.43001	+	25.9449i	−0.319999	+	0.984855i
$695$		0			0
$696$	−0.433125	−	1.33302i	−0.0164176	−	0.0505281i
$697$	7.09967	+	21.8505i	0.268919	+	0.827648i
$698$	52.2900	+	37.9909i	1.97920	+	1.43798i
$699$	53.9454			2.04040
$700$		0			0
$701$	−0.566147			−0.0213831			−0.0106915	−	0.999943i	$-0.503403\pi$
$701$	−0.566147			−0.0213831			−0.0106915	+	0.999943i	$0.503403\pi$
$702$	−17.3567	−	12.6104i	−0.655088	−	0.475949i
$703$	−10.6900	−	32.9004i	−0.403181	−	1.24086i
$704$	4.55069	+	14.0056i	0.171511	+	0.527856i
$705$		0			0
$706$	−11.3949	+	35.0700i	−0.428854	+	1.31988i
$707$	4.53167			0.170431
$708$	3.56852	−	10.9828i	0.134113	−	0.412758i
$709$	−0.531732	+	0.386326i	−0.0199696	+	0.0145088i	−0.597725	−	0.801701i	$-0.703929\pi$
$709$	−0.531732	+	0.386326i	−0.0199696	+	0.0145088i	0.577756	+	0.816210i	$0.303929\pi$
$710$		0			0
$711$	−28.3489	−	20.5967i	−1.06317	−	0.772437i
$712$	−0.136757	+	0.0993597i	−0.00512518	+	0.00372366i
$713$	1.79201	−	1.30197i	0.0671112	−	0.0487591i
$714$	10.0080	+	7.27126i	0.374541	+	0.272120i
$715$		0			0
$716$	36.0535	−	26.1944i	1.34738	−	0.978931i
$717$	22.3186	−	68.6894i	0.833502	−	2.56525i
$718$	−29.0702			−1.08489
$719$	10.8481	−	33.3870i	0.404566	−	1.24513i	−0.516692	−	0.856172i	$-0.672837\pi$
$719$	10.8481	−	33.3870i	0.404566	−	1.24513i	0.921257	−	0.388954i	$-0.127163\pi$
$720$		0			0
$721$	−0.876583	−	2.69785i	−0.0326457	−	0.100473i
$722$	−3.06217	−	9.42439i	−0.113962	−	0.350739i
$723$	−10.3133	−	7.49301i	−0.383554	−	0.278668i
$724$	22.1268			0.822336
$725$		0			0
$726$	48.4389			1.79774
$727$	−33.3461	−	24.2273i	−1.23674	−	0.898542i	−0.239361	−	0.970931i	$-0.576938\pi$
$727$	−33.3461	−	24.2273i	−1.23674	−	0.898542i	−0.997377	+	0.0723882i	$0.976938\pi$
$728$	0.0140995	+	0.0433938i	0.000522562	+	0.00160828i
$729$	−6.96334	−	21.4310i	−0.257901	−	0.793739i
$730$		0			0
$731$	12.1615	−	37.4292i	0.449809	−	1.38437i
$732$	−60.2382			−2.22647
$733$	12.3941	−	38.1452i	0.457787	−	1.40892i	−0.410045	−	0.912065i	$-0.634487\pi$
$733$	12.3941	−	38.1452i	0.457787	−	1.40892i	0.867832	−	0.496858i	$-0.165513\pi$
$734$	16.9638	−	12.3249i	0.626144	−	0.454920i
$735$		0			0
$736$	−47.1834	−	34.2807i	−1.73920	−	1.26360i
$737$	17.6178	−	12.8001i	0.648961	−	0.471498i
$738$	41.9750	−	30.4966i	1.54512	−	1.12260i
$739$	23.0921	+	16.7774i	0.849457	+	0.617167i	0.924996	−	0.379976i	$-0.124068\pi$
$739$	23.0921	+	16.7774i	0.849457	+	0.617167i	−0.0755391	+	0.997143i	$0.524068\pi$
$740$		0			0
$741$	10.2521	−	7.44861i	0.376621	−	0.273632i
$742$	−0.901322	+	2.77398i	−0.0330886	+	0.101836i
$743$	−29.6851			−1.08904			−0.544520	−	0.838748i	$-0.683288\pi$
$743$	−29.6851			−1.08904			−0.544520	+	0.838748i	$0.683288\pi$
$744$	−0.0315775	+	0.0971855i	−0.00115769	+	0.00356299i
$745$		0			0
$746$	−6.23657	−	19.1942i	−0.228337	−	0.702749i
$747$	−13.5675	−	41.7566i	−0.496410	−	1.52779i
$748$	−15.9324	−	11.5756i	−0.582546	−	0.423245i
$749$	−0.280439			−0.0102470
$750$		0			0
$751$	45.2113			1.64978			0.824892	−	0.565290i	$-0.191236\pi$
$751$	45.2113			1.64978			0.824892	+	0.565290i	$0.191236\pi$
$752$	−2.54819	−	1.85137i	−0.0929230	−	0.0675125i
$753$	−18.3015	−	56.3261i	−0.666943	−	2.05264i
$754$	−2.91225	−	8.96300i	−0.106058	−	0.326413i
$755$		0			0
$756$	2.24236	−	6.90128i	0.0815539	−	0.250997i
$757$	−5.69813			−0.207102			−0.103551	−	0.994624i	$-0.533020\pi$
$757$	−5.69813			−0.207102			−0.103551	+	0.994624i	$0.533020\pi$
$758$	8.89798	−	27.3852i	0.323189	−	0.994674i
$759$	30.9752	−	22.5048i	1.12433	−	0.816873i
$760$		0			0
$761$	33.6796	+	24.4697i	1.22088	+	0.887025i	0.996173	−	0.0874009i	$-0.0278561\pi$
$761$	33.6796	+	24.4697i	1.22088	+	0.887025i	0.224711	+	0.974425i	$0.427856\pi$
$762$	−70.5970	+	51.2917i	−2.55746	+	1.85810i
$763$	−0.978273	+	0.710757i	−0.0354159	+	0.0257311i
$764$	6.38272	+	4.63732i	0.230919	+	0.167772i
$765$		0			0
$766$	8.20582	−	5.96188i	0.296488	−	0.215411i
$767$	0.640669	−	1.97178i	0.0231332	−	0.0711967i
$768$	−45.6462			−1.64712
$769$	−4.92142	+	15.1466i	−0.177471	+	0.546200i	−0.999738	−	0.0229027i	$-0.992709\pi$
$769$	−4.92142	+	15.1466i	−0.177471	+	0.546200i	0.822267	+	0.569102i	$0.192709\pi$
$770$		0			0
$771$	−17.2195	−	52.9960i	−0.620144	−	1.90861i
$772$	6.68857	+	20.5853i	0.240727	+	0.740881i
$773$	−38.6969	−	28.1149i	−1.39183	−	1.01122i	−0.995662	−	0.0930462i	$-0.970340\pi$
$773$	−38.6969	−	28.1149i	−1.39183	−	1.01122i	−0.396169	−	0.918178i	$-0.629660\pi$
$774$	−88.8755			−3.19456
$775$		0			0
$776$	−0.706817			−0.0253732
$777$	−8.34943	−	6.06622i	−0.299534	−	0.217624i
$778$	6.30510	+	19.4051i	0.226049	+	0.695706i
$779$	4.85410	+	14.9394i	0.173916	+	0.535259i
$780$		0			0
$781$	−6.30128	+	19.3933i	−0.225477	+	0.693948i
$782$	80.0778			2.86358
$783$	−12.3669	+	38.0615i	−0.441958	+	1.36021i
$784$	−21.5835	+	15.6813i	−0.770840	+	0.560048i
$785$		0			0
$786$	−81.9538	−	59.5429i	−2.92319	−	2.12383i
$787$	32.8106	−	23.8383i	1.16957	−	0.849743i	0.178613	−	0.983919i	$-0.442839\pi$
$787$	32.8106	−	23.8383i	1.16957	−	0.849743i	0.990957	+	0.134177i	$0.0428390\pi$
$788$	−16.0474	+	11.6591i	−0.571665	+	0.415339i
$789$	10.5856	+	7.69088i	0.376857	+	0.273802i
$790$		0			0
$791$	−0.253805	+	0.184400i	−0.00902426	+	0.00655651i
$792$	−0.366956	+	1.12937i	−0.0130392	+	0.0401306i
$793$	−10.8148			−0.384044
$794$	−12.2385	+	37.6663i	−0.434329	+	1.33673i
$795$		0			0
$796$	−10.0622	−	30.9682i	−0.356644	−	1.09764i
$797$	−8.60045	−	26.4695i	−0.304644	−	0.937596i	−0.979810	−	0.199931i	$-0.935928\pi$
$797$	−8.60045	−	26.4695i	−0.304644	−	0.937596i	0.675166	−	0.737665i	$-0.264072\pi$
$798$	6.84258	+	4.97143i	0.242225	+	0.175987i
$799$	4.44678			0.157316
$800$		0			0
$801$	9.41656			0.332718
$802$	37.6207	+	27.3331i	1.32843	+	0.965164i
$803$	1.85172	+	5.69901i	0.0653458	+	0.201114i
$804$	−23.9583	−	73.7360i	−0.844943	−	2.60047i
$805$		0			0
$806$	−0.212321	+	0.653458i	−0.00747870	+	0.0230171i
$807$	−14.3385			−0.504738
$808$	−0.418191	+	1.28706i	−0.0147119	+	0.0452786i
$809$	6.67201	−	4.84750i	0.234575	−	0.170429i	−0.464288	−	0.885684i	$-0.653690\pi$
$809$	6.67201	−	4.84750i	0.234575	−	0.170429i	0.698863	+	0.715255i	$0.253690\pi$
$810$		0			0
$811$	14.8503	+	10.7894i	0.521465	+	0.378867i	0.817156	−	0.576417i	$-0.195550\pi$
$811$	14.8503	+	10.7894i	0.521465	+	0.378867i	−0.295690	+	0.955284i	$0.595550\pi$
$812$	2.57880	−	1.87361i	0.0904981	−	0.0657507i
$813$	24.3932	−	17.7227i	0.855506	−	0.621561i
$814$	26.2290	+	19.0565i	0.919327	+	0.667930i
$815$		0			0
$816$	52.2198	−	37.9399i	1.82806	−	1.32816i
$817$	8.31491	−	25.5907i	0.290902	−	0.895304i
$818$	77.7957			2.72006
$819$	0.785424	−	2.41729i	0.0274449	−	0.0844669i
$820$		0			0
$821$	−4.90209	−	15.0871i	−0.171084	−	0.526543i	0.828349	−	0.560213i	$-0.189281\pi$
$821$	−4.90209	−	15.0871i	−0.171084	−	0.526543i	−0.999433	+	0.0336695i	$0.989281\pi$
$822$	−5.78358	−	17.8000i	−0.201725	−	0.620847i
$823$	−26.2692	−	19.0857i	−0.915685	−	0.665284i	0.0267610	−	0.999642i	$-0.491481\pi$
$823$	−26.2692	−	19.0857i	−0.915685	−	0.665284i	−0.942446	+	0.334358i	$0.891481\pi$
$824$	0.847120			0.0295108
$825$		0			0
$826$	1.38375			0.0481468
$827$	23.2953	+	16.9250i	0.810057	+	0.588541i	0.913847	−	0.406058i	$-0.133097\pi$
$827$	23.2953	+	16.9250i	0.810057	+	0.588541i	−0.103790	+	0.994599i	$0.533097\pi$
$828$	−28.3191	−	87.1572i	−0.984156	−	3.02892i
$829$	−2.65515	−	8.17171i	−0.0922172	−	0.283815i	0.894301	−	0.447465i	$-0.147673\pi$
$829$	−2.65515	−	8.17171i	−0.0922172	−	0.283815i	−0.986518	+	0.163650i	$0.947673\pi$
$830$		0			0
$831$	−16.4643	+	50.6719i	−0.571141	+	1.75779i
$832$	9.41283			0.326331
$833$	11.6391	−	35.8213i	0.403270	−	1.24114i
$834$	−77.4854	+	56.2964i	−2.68310	+	1.94939i
$835$		0			0
$836$	−10.8931	−	7.91432i	−0.376746	−	0.273722i
$837$	2.36049	−	1.71499i	0.0815903	−	0.0592788i
$838$	17.5765	−	12.7700i	0.607168	−	0.441134i
$839$	38.0676	+	27.6577i	1.31424	+	0.954850i	0.999985	+	0.00551066i	$0.00175411\pi$
$839$	38.0676	+	27.6577i	1.31424	+	0.954850i	0.314253	+	0.949339i	$0.398246\pi$
$840$		0			0
$841$	9.23907	−	6.71258i	0.318589	−	0.231468i
$842$	20.1954	−	62.1551i	0.695979	−	2.14200i
$843$	77.1436			2.65697
$844$	4.60435	−	14.1707i	0.158488	−	0.487776i
$845$		0			0
$846$	−3.10317	−	9.55056i	−0.106689	−	0.328355i
$847$	0.908942	+	2.79744i	0.0312316	+	0.0961210i
$848$	12.3124	+	8.94546i	0.422809	+	0.307188i
$849$	−48.7145			−1.67188
$850$		0			0
$851$	−66.8067			−2.29011
$852$	58.7331	+	42.6721i	2.01216	+	1.46192i
$853$	5.77526	+	17.7744i	0.197741	+	0.608585i	0.999934	+	0.0115193i	$0.00366680\pi$
$853$	5.77526	+	17.7744i	0.197741	+	0.608585i	−0.802192	+	0.597066i	$0.796333\pi$
$854$	−2.23052	−	6.86483i	−0.0763268	−	0.234910i
$855$		0			0
$856$	0.0258795	−	0.0796489i	0.000884543	−	0.00272234i
$857$	−3.06228			−0.104606			−0.0523028	−	0.998631i	$-0.516656\pi$
$857$	−3.06228			−0.104606			−0.0523028	+	0.998631i	$0.516656\pi$
$858$	−3.67002	+	11.2952i	−0.125292	+	0.385610i
$859$	−13.7261	+	9.97258i	−0.468328	+	0.340260i	−0.796789	−	0.604257i	$-0.793470\pi$
$859$	−13.7261	+	9.97258i	−0.468328	+	0.340260i	0.328462	+	0.944517i	$0.393470\pi$
$860$		0			0
$861$	3.79130	+	2.75454i	0.129207	+	0.0938745i
$862$	−22.4685	+	16.3243i	−0.765281	+	0.556009i
$863$	−17.7150	+	12.8707i	−0.603025	+	0.438124i	−0.846951	−	0.531670i	$-0.821565\pi$
$863$	−17.7150	+	12.8707i	−0.603025	+	0.438124i	0.243926	+	0.969794i	$0.421565\pi$
$864$	−62.1514	−	45.1556i	−2.11443	−	1.53622i
$865$		0			0
$866$	−34.3935	+	24.9883i	−1.16874	+	0.849137i
$867$	−12.2652	+	37.7484i	−0.416548	+	1.28200i
$868$	−0.232393			−0.00788795
$869$	−3.07245	+	9.45601i	−0.104226	+	0.320773i
$870$		0			0
$871$	−4.30132	−	13.2381i	−0.145745	−	0.448556i
$872$	−0.111588	−	0.343434i	−0.00377886	−	0.0116301i
$873$	31.8541	+	23.1434i	1.07810	+	0.783284i
$874$	54.7499			1.85194
$875$		0			0
$876$	21.3340			0.720808
$877$	37.8879	+	27.5272i	1.27938	+	0.929527i	0.999534	−	0.0305170i	$-0.00971537\pi$
$877$	37.8879	+	27.5272i	1.27938	+	0.929527i	0.279850	+	0.960044i	$0.409715\pi$
$878$	22.6164	+	69.6061i	0.763266	+	2.34909i
$879$	23.2857	+	71.6659i	0.785406	+	2.41723i
$880$		0			0
$881$	0.00869502	−	0.0267605i	0.000292943	−	0.000901585i	−0.950910	−	0.309468i	$-0.899849\pi$
$881$	0.00869502	−	0.0267605i	0.000292943	−	0.000901585i	0.951203	+	0.308566i	$0.0998491\pi$
$882$	−85.0576			−2.86404
$883$	9.04544	−	27.8390i	0.304403	−	0.936857i	−0.675496	−	0.737364i	$-0.736070\pi$
$883$	9.04544	−	27.8390i	0.304403	−	0.936857i	0.979899	−	0.199493i	$-0.0639297\pi$
$884$	−10.1837	+	7.39890i	−0.342515	+	0.248852i
$885$		0			0
$886$	10.4068	+	7.56099i	0.349624	+	0.254016i
$887$	16.0830	−	11.6850i	0.540014	−	0.392343i	−0.284076	−	0.958802i	$-0.591687\pi$
$887$	16.0830	−	11.6850i	0.540014	−	0.392343i	0.824090	+	0.566458i	$0.191687\pi$
$888$	2.49340	−	1.81156i	0.0836729	−	0.0607919i
$889$	−4.28692	−	3.11463i	−0.143779	−	0.104461i
$890$		0			0
$891$	14.7155	−	10.6914i	0.492986	−	0.358175i
$892$	−14.5192	+	44.6856i	−0.486140	+	1.49618i
$893$	3.04030			0.101740
$894$	−27.9596	+	86.0508i	−0.935108	+	2.87797i
$895$		0			0
$896$	0.101014	+	0.310888i	0.00337462	+	0.0103860i
$897$	−7.56247	−	23.2749i	−0.252504	−	0.777126i
$898$	57.2834	+	41.6188i	1.91157	+	1.38884i
$899$	1.28168			0.0427465
$900$		0			0
$901$	−21.4860			−0.715801
$902$	−11.9100	−	8.65316i	−0.396561	−	0.288119i
$903$	−2.48063	−	7.63459i	−0.0825501	−	0.254063i
$904$	−0.0289507	−	0.0891010i	−0.000962885	−	0.00296346i
$905$		0			0
$906$	1.34054	−	4.12575i	0.0445364	−	0.137069i
$907$	14.2958			0.474685			0.237343	−	0.971426i	$-0.423724\pi$
$907$	14.2958			0.474685			0.237343	+	0.971426i	$0.423724\pi$
$908$	0.422533	−	1.30042i	0.0140223	−	0.0431561i
$909$	60.9890	−	44.3111i	2.02288	−	1.46971i
$910$		0			0
$911$	−15.6953	−	11.4033i	−0.520009	−	0.377808i	0.296599	−	0.955002i	$-0.404148\pi$
$911$	−15.6953	−	11.4033i	−0.520009	−	0.377808i	−0.816607	+	0.577194i	$0.804148\pi$
$912$	35.7031	−	25.9399i	1.18225	−	0.858954i
$913$	−10.0786	+	7.32251i	−0.333552	+	0.242340i
$914$	36.3278	+	26.3937i	1.20162	+	0.873025i
$915$		0			0
$916$	39.0224	−	28.3514i	1.28934	−	0.936757i
$917$	1.90087	−	5.85028i	0.0627723	−	0.193193i
$918$	105.481			3.48139
$919$	1.32851	−	4.08873i	0.0438234	−	0.134875i	−0.926751	−	0.375676i	$-0.877410\pi$
$919$	1.32851	−	4.08873i	0.0438234	−	0.134875i	0.970574	+	0.240802i	$0.0774104\pi$
$920$		0			0
$921$	1.63381	+	5.02836i	0.0538360	+	0.165690i
$922$	−1.17321	−	3.61077i	−0.0386376	−	0.118914i
$923$	10.5446	+	7.66108i	0.347079	+	0.252167i
$924$	−4.01697			−0.132149
$925$		0			0
$926$	26.0069			0.854639
$927$	−38.1771	−	27.7373i	−1.25390	−	0.911013i
$928$	−10.4283	−	32.0949i	−0.342324	−	1.05357i
$929$	13.2975	+	40.9256i	0.436277	+	1.34272i	0.891772	+	0.452485i	$0.149462\pi$
$929$	13.2975	+	40.9256i	0.436277	+	1.34272i	−0.455495	+	0.890239i	$0.650538\pi$
$930$		0			0
$931$	7.95773	−	24.4914i	0.260804	−	0.802672i
$932$	−36.6368			−1.20008
$933$	−17.1347	+	52.7352i	−0.560965	+	1.72647i
$934$	−4.26522	+	3.09887i	−0.139562	+	0.101398i
$935$		0			0
$936$	0.614064	+	0.446144i	0.0200713	+	0.0145827i
$937$	13.7378	−	9.98109i	0.448794	−	0.326068i	−0.340325	−	0.940308i	$-0.610537\pi$
$937$	13.7378	−	9.98109i	0.448794	−	0.326068i	0.789119	+	0.614240i	$0.210537\pi$
$938$	7.51593	−	5.46064i	0.245404	−	0.178296i
$939$	−8.09634	−	5.88233i	−0.264214	−	0.191963i
$940$		0			0
$941$	14.5985	−	10.6064i	0.475898	−	0.345760i	−0.323837	−	0.946113i	$-0.604973\pi$
$941$	14.5985	−	10.6064i	0.475898	−	0.345760i	0.799735	+	0.600353i	$0.204973\pi$
$942$	−41.5529	+	127.887i	−1.35387	+	4.16677i
$943$	30.3355			0.987860
$944$	2.23114	−	6.86673i	0.0726173	−	0.223493i
$945$		0			0
$946$	7.79268	+	23.9834i	0.253362	+	0.779768i
$947$	−2.22762	−	6.85590i	−0.0723879	−	0.222787i	0.908317	−	0.418284i	$-0.137368\pi$
$947$	−2.22762	−	6.85590i	−0.0723879	−	0.222787i	−0.980704	+	0.195497i	$0.937368\pi$
$948$	28.6377	+	20.8065i	0.930109	+	0.675764i
$949$	3.83017			0.124333
$950$		0			0
$951$	−3.02277			−0.0980200
$952$	−0.181486	−	0.131857i	−0.00588198	−	0.00427351i
$953$	−4.26444	−	13.1246i	−0.138139	−	0.425147i	0.857926	−	0.513773i	$-0.171753\pi$
$953$	−4.26444	−	13.1246i	−0.138139	−	0.425147i	−0.996065	+	0.0886255i	$0.971753\pi$
$954$	14.9939	+	46.1465i	0.485446	+	1.49405i
$955$		0			0
$956$	−15.1575	+	46.6501i	−0.490230	+	1.50877i
$957$	22.1541			0.716141
$958$	4.18977	−	12.8948i	0.135365	−	0.416611i
$959$	0.919456	−	0.668024i	0.0296908	−	0.0215716i
$960$		0			0
$961$	25.0039	+	18.1664i	0.806578	+	0.586014i
$962$	16.7651	−	12.1806i	0.540530	−	0.392718i
$963$	−3.77426	+	2.74216i	−0.121624	+	0.0883648i
$964$	7.00420	+	5.08885i	0.225590	+	0.163901i
$965$		0			0
$966$	13.2143	−	9.60076i	0.425164	−	0.308900i
$967$	−4.60299	+	14.1666i	−0.148022	+	0.455566i	−0.997387	−	0.0722402i	$-0.976985\pi$
$967$	−4.60299	+	14.1666i	−0.148022	+	0.455566i	0.849365	+	0.527806i	$0.176985\pi$
$968$	−0.878391			−0.0282326
$969$	−19.2532	+	59.2551i	−0.618501	+	1.90355i
$970$		0			0
$971$	12.2970	+	37.8461i	0.394628	+	1.21454i	0.929251	+	0.369449i	$0.120454\pi$
$971$	12.2970	+	37.8461i	0.394628	+	1.21454i	−0.534623	+	0.845091i	$0.679546\pi$
$972$	−1.82866	−	5.62803i	−0.0586542	−	0.180519i
$973$	−4.70521	−	3.41853i	−0.150842	−	0.109593i
$974$	11.1919			0.358611
$975$		0			0
$976$	−37.6626			−1.20555
$977$	25.0493	+	18.1994i	0.801399	+	0.582251i	0.911324	−	0.411689i	$-0.135061\pi$
$977$	25.0493	+	18.1994i	0.801399	+	0.582251i	−0.109925	+	0.993940i	$0.535061\pi$
$978$	−24.7805	−	76.2665i	−0.792393	−	2.43873i
$979$	−0.825653	−	2.54110i	−0.0263880	−	0.0812138i
$980$		0			0
$981$	−6.21613	+	19.1313i	−0.198466	+	0.610815i
$982$	−11.1799			−0.356764
$983$	8.57673	−	26.3965i	0.273555	−	0.841916i	−0.716043	−	0.698056i	$-0.754049\pi$
$983$	8.57673	−	26.3965i	0.273555	−	0.841916i	0.989598	−	0.143860i	$-0.0459515\pi$
$984$	−1.13220	+	0.822590i	−0.0360932	+	0.0262232i
$985$		0			0
$986$	37.4859	+	27.2351i	1.19379	+	0.867342i
$987$	0.733800	−	0.533137i	0.0233571	−	0.0169699i
$988$	−6.96269	+	5.05869i	−0.221513	+	0.160938i
$989$	−42.0395	−	30.5435i	−1.33678	−	0.971227i
$990$		0			0
$991$	−12.1498	+	8.82736i	−0.385952	+	0.280410i	−0.763795	−	0.645459i	$-0.776666\pi$
$991$	−12.1498	+	8.82736i	−0.385952	+	0.280410i	0.377843	+	0.925870i	$0.376666\pi$
$992$	−0.760284	+	2.33991i	−0.0241390	+	0.0742923i
$993$	42.9673			1.36353
$994$	−2.68819	+	8.27339i	−0.0852641	+	0.262416i
$995$		0			0
$996$	13.7057	+	42.1819i	0.434283	+	1.33659i
$997$	5.53566	+	17.0370i	0.175316	+	0.539568i	0.999648	−	0.0265394i	$-0.00844875\pi$
$997$	5.53566	+	17.0370i	0.175316	+	0.539568i	−0.824332	+	0.566107i	$0.808449\pi$
$998$	−31.3731	−	22.7939i	−0.993099	−	0.721528i
$999$	−87.9999			−2.78419

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.d.p.376.1		16
5.2	odd	4		625.2.e.k.249.7		32
5.3	odd	4		625.2.e.k.249.2		32
5.4	even	2		625.2.d.n.376.4		16
25.2	odd	20		625.2.e.k.374.2		32
25.3	odd	20		625.2.e.j.499.7		32
25.4	even	10		625.2.d.m.126.1		16
25.6	even	5		625.2.a.e.1.8	✓	8
25.8	odd	20		625.2.b.d.624.4		16
25.9	even	10		625.2.d.m.501.1		16
25.11	even	5	inner	625.2.d.p.251.1		16
25.12	odd	20		625.2.e.j.124.7		32
25.13	odd	20		625.2.e.j.124.2		32
25.14	even	10		625.2.d.n.251.4		16
25.16	even	5		625.2.d.q.501.4		16
25.17	odd	20		625.2.b.d.624.13		16
25.19	even	10		625.2.a.g.1.1	yes	8
25.21	even	5		625.2.d.q.126.4		16
25.22	odd	20		625.2.e.j.499.2		32
25.23	odd	20		625.2.e.k.374.7		32
75.44	odd	10		5625.2.a.s.1.8		8
75.56	odd	10		5625.2.a.be.1.1		8
100.19	odd	10		10000.2.a.be.1.2		8
100.31	odd	10		10000.2.a.bn.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
625.2.a.e.1.8	✓	8	25.6	even	5
625.2.a.g.1.1	yes	8	25.19	even	10
625.2.b.d.624.4		16	25.8	odd	20
625.2.b.d.624.13		16	25.17	odd	20
625.2.d.m.126.1		16	25.4	even	10
625.2.d.m.501.1		16	25.9	even	10
625.2.d.n.251.4		16	25.14	even	10
625.2.d.n.376.4		16	5.4	even	2
625.2.d.p.251.1		16	25.11	even	5	inner
625.2.d.p.376.1		16	1.1	even	1	trivial
625.2.d.q.126.4		16	25.21	even	5
625.2.d.q.501.4		16	25.16	even	5
625.2.e.j.124.2		32	25.13	odd	20
625.2.e.j.124.7		32	25.12	odd	20
625.2.e.j.499.2		32	25.22	odd	20
625.2.e.j.499.7		32	25.3	odd	20
625.2.e.k.249.2		32	5.3	odd	4
625.2.e.k.249.7		32	5.2	odd	4
625.2.e.k.374.2		32	25.2	odd	20
625.2.e.k.374.7		32	25.23	odd	20
5625.2.a.s.1.8		8	75.44	odd	10
5625.2.a.be.1.1		8	75.56	odd	10
10000.2.a.be.1.2		8	100.19	odd	10
10000.2.a.bn.1.7		8	100.31	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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+(-1.62909 - 1.18361i) q^{2} +(-0.934982 - 2.87758i) q^{3} +(0.634989 + 1.95429i) q^{4} +(-1.88274 + 5.79449i) q^{6} -0.369971 q^{7} +(0.0341417 - 0.105077i) q^{8} +(-4.97921 + 3.61761i) q^{9} +(1.41281 + 1.02647i) q^{11} +(5.02993 - 3.65446i) q^{12} +(0.903043 - 0.656099i) q^{13} +(0.602718 + 0.437900i) q^{14} +(3.14486 - 2.28487i) q^{16} +(-1.69588 + 5.21940i) q^{17} +12.3934 q^{18} +(-1.15949 + 3.56855i) q^{19} +(0.345917 + 1.06462i) q^{21} +(-1.08667 - 3.34442i) q^{22} +(5.86229 + 4.25920i) q^{23} -0.334290 q^{24} -2.24770 q^{26} +(7.72199 + 5.61035i) q^{27} +(-0.234928 - 0.723033i) q^{28} +(1.29566 + 3.98762i) q^{29} +(0.0944614 - 0.290722i) q^{31} -8.04862 q^{32} +(1.63279 - 5.02520i) q^{33} +(8.94046 - 6.49562i) q^{34} +(-10.2316 - 7.43371i) q^{36} +(-7.45878 + 5.41912i) q^{37} +(6.11267 - 4.44111i) q^{38} +(-2.73230 - 1.98514i) q^{39} +(3.38688 - 2.46071i) q^{41} +(0.696562 - 2.14380i) q^{42} -7.17118 q^{43} +(-1.10890 + 3.41284i) q^{44} +(-4.50900 - 13.8773i) q^{46} +(-0.250388 - 0.770615i) q^{47} +(-9.51528 - 6.91325i) q^{48} -6.86312 q^{49} +16.6048 q^{51} +(1.85563 + 1.34820i) q^{52} +(1.20983 + 3.72347i) q^{53} +(-5.93940 - 18.2796i) q^{54} +(-0.0126314 + 0.0388756i) q^{56} +11.3529 q^{57} +(2.60903 - 8.02976i) q^{58} +(1.50265 - 1.09174i) q^{59} +(-7.83835 - 5.69490i) q^{61} +(-0.497987 + 0.361809i) q^{62} +(1.84217 - 1.33841i) q^{63} +(6.82224 + 4.95665i) q^{64} +(-8.60781 + 6.25394i) q^{66} +(3.85346 - 11.8597i) q^{67} -11.2771 q^{68} +(6.77506 - 20.8515i) q^{69} +(3.60830 + 11.1052i) q^{71} +(0.210130 + 0.646713i) q^{72} +(2.77604 + 2.01691i) q^{73} +18.5652 q^{74} -7.71026 q^{76} +(-0.522699 - 0.379763i) q^{77} +(2.10156 + 6.46794i) q^{78} +(1.75937 + 5.41480i) q^{79} +(3.21864 - 9.90596i) q^{81} -8.43005 q^{82} +(-2.20444 + 6.78456i) q^{83} +(-1.86093 + 1.35205i) q^{84} +(11.6825 + 8.48784i) q^{86} +(10.2633 - 7.45671i) q^{87} +(0.156094 - 0.113409i) q^{88} +(-1.23779 - 0.899307i) q^{89} +(-0.334100 + 0.242738i) q^{91} +(-4.60125 + 14.1612i) q^{92} -0.924896 q^{93} +(-0.504199 + 1.55176i) q^{94} +(7.52531 + 23.1605i) q^{96} +(-1.97691 - 6.08430i) q^{97} +(11.1807 + 8.12323i) q^{98} -10.7480 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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