LMFDB - Embedded newform 625.2.d.o.501.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(126,625)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 $ x^16 + x^14 - 4x^12 - 49x^10 + 11x^8 + 395x^6 + 900x^4 + 1125x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			501.4
Root			$0.917186 + 1.66637i$ of defining polynomial
Character	$\chi$	$=$	625.501
Dual form			625.2.d.o.126.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.713605 - 2.19625i) q^{2} +(-0.384204 - 0.279141i) q^{3} +(-2.69625 - 1.95894i) q^{4} +(-0.887234 + 0.644613i) q^{6} +3.03582 q^{7} +(-2.48990 + 1.80902i) q^{8} +(-0.857358 - 2.63868i) q^{9} +(0.618034 - 1.90211i) q^{11} +(0.489091 + 1.50527i) q^{12} +(-0.441032 - 1.35736i) q^{13} +(2.16637 - 6.66742i) q^{14} +(0.136498 + 0.420099i) q^{16} +(-1.50497 + 1.09343i) q^{17} -6.40701 q^{18} +(-0.730800 + 0.530958i) q^{19} +(-1.16637 - 0.847421i) q^{21} +(-3.73648 - 2.71472i) q^{22} +(-1.02882 + 3.16637i) q^{23} +1.46160 q^{24} -3.29582 q^{26} +(-0.847421 + 2.60809i) q^{27} +(-8.18532 - 5.94699i) q^{28} +(-3.20619 - 2.32943i) q^{29} +(5.21004 - 3.78532i) q^{31} -5.13532 q^{32} +(-0.768409 + 0.558282i) q^{33} +(1.32748 + 4.08557i) q^{34} +(-2.85736 + 8.79404i) q^{36} +(1.18051 + 3.63324i) q^{37} +(0.644613 + 1.98391i) q^{38} +(-0.209447 + 0.644613i) q^{39} +(-0.566805 - 1.74445i) q^{41} +(-2.69348 + 1.95693i) q^{42} -3.59445 q^{43} +(-5.39250 + 3.91788i) q^{44} +(6.21998 + 4.51908i) q^{46} +(3.88324 + 2.82134i) q^{47} +(0.0648235 - 0.199506i) q^{48} +2.21619 q^{49} +0.883436 q^{51} +(-1.46985 + 4.52373i) q^{52} +(7.68949 + 5.58674i) q^{53} +(5.12330 + 3.72230i) q^{54} +(-7.55888 + 5.49184i) q^{56} +0.428989 q^{57} +(-7.40398 + 5.37930i) q^{58} +(3.28968 + 10.1246i) q^{59} +(4.41097 - 13.5756i) q^{61} +(-4.59559 - 14.1438i) q^{62} +(-2.60278 - 8.01054i) q^{63} +(-3.93759 + 12.1186i) q^{64} +(0.677786 + 2.08601i) q^{66} +(8.64854 - 6.28353i) q^{67} +6.19974 q^{68} +(1.27914 - 0.929350i) q^{69} +(-10.0802 - 7.32371i) q^{71} +(6.90814 + 5.01906i) q^{72} +(0.0827026 - 0.254532i) q^{73} +8.82193 q^{74} +3.01054 q^{76} +(1.87624 - 5.77447i) q^{77} +(1.26627 + 0.919998i) q^{78} +(6.93470 + 5.03835i) q^{79} +(-5.68017 + 4.12688i) q^{81} -4.23572 q^{82} +(10.2083 - 7.41677i) q^{83} +(1.48479 + 4.56972i) q^{84} +(-2.56502 + 7.89432i) q^{86} +(0.581593 + 1.78996i) q^{87} +(1.90211 + 5.85410i) q^{88} +(-1.47338 + 4.53460i) q^{89} +(-1.33889 - 4.12069i) q^{91} +(8.97669 - 6.52195i) q^{92} -3.05836 q^{93} +(8.96746 - 6.51524i) q^{94} +(1.97301 + 1.43348i) q^{96} +(8.05623 + 5.85319i) q^{97} +(1.58148 - 4.86730i) q^{98} -5.54893 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{4} + 12 q^{6} - 2 q^{9} - 8 q^{11} + 14 q^{14} - 4 q^{16} - 20 q^{19} + 2 q^{21} + 40 q^{24} + 12 q^{26} - 30 q^{29} + 2 q^{31} + 24 q^{34} - 34 q^{36} - 24 q^{39} - 18 q^{41} - 16 q^{44} + 32 q^{46}+ \cdots + 16 q^{99}+O(q^{100}) $ 16 * q - 8 * q^4 + 12 * q^6 - 2 * q^9 - 8 * q^11 + 14 * q^14 - 4 * q^16 - 20 * q^19 + 2 * q^21 + 40 * q^24 + 12 * q^26 - 30 * q^29 + 2 * q^31 + 24 * q^34 - 34 * q^36 - 24 * q^39 - 18 * q^41 - 16 * q^44 + 32 * q^46 - 28 * q^49 - 8 * q^51 + 20 * q^54 - 30 * q^56 - 30 * q^59 + 12 * q^61 + 52 * q^64 - 36 * q^66 + 26 * q^69 - 58 * q^71 + 24 * q^74 - 40 * q^76 + 20 * q^79 - 24 * q^81 + 54 * q^84 + 32 * q^86 - 80 * q^89 + 2 * q^91 + 14 * q^94 + 22 * q^96 + 16 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.713605	−	2.19625i	0.504595	−	1.55298i	−0.296855	−	0.954922i	$-0.595938\pi$
$2$	0.713605	−	2.19625i	0.504595	−	1.55298i	0.801450	−	0.598061i	$-0.204062\pi$
$3$	−0.384204	−	0.279141i	−0.221821	−	0.161162i	0.471325	−	0.881959i	$-0.343776\pi$
$3$	−0.384204	−	0.279141i	−0.221821	−	0.161162i	−0.693146	+	0.720797i	$0.743776\pi$
$4$	−2.69625	−	1.95894i	−1.34813	−	0.979470i
$5$		0			0
$5$		0			0
$6$	−0.887234	+	0.644613i	−0.362212	+	0.263162i
$7$	3.03582			1.14743			0.573716	−	0.819055i	$-0.305502\pi$
$7$	3.03582			1.14743			0.573716	+	0.819055i	$0.305502\pi$
$8$	−2.48990	+	1.80902i	−0.880312	+	0.639584i
$9$	−0.857358	−	2.63868i	−0.285786	−	0.879558i
$10$		0			0
$11$	0.618034	−	1.90211i	0.186344	−	0.573509i	−0.813625	−	0.581390i	$-0.802509\pi$
$11$	0.618034	−	1.90211i	0.186344	−	0.573509i	0.999969	+	0.00788181i	$0.00250889\pi$
$12$	0.489091	+	1.50527i	0.141188	+	0.434533i
$13$	−0.441032	−	1.35736i	−0.122320	−	0.376463i	0.871083	−	0.491136i	$-0.163418\pi$
$13$	−0.441032	−	1.35736i	−0.122320	−	0.376463i	−0.993403	+	0.114673i	$0.963418\pi$
$14$	2.16637	−	6.66742i	0.578988	−	1.78194i
$15$		0			0
$16$	0.136498	+	0.420099i	0.0341246	+	0.105025i
$17$	−1.50497	+	1.09343i	−0.365009	+	0.265195i	−0.755138	−	0.655565i	$-0.772430\pi$
$17$	−1.50497	+	1.09343i	−0.365009	+	0.265195i	0.390129	+	0.920760i	$0.372430\pi$
$18$	−6.40701			−1.51015
$19$	−0.730800	+	0.530958i	−0.167657	+	0.121810i	−0.668450	−	0.743757i	$-0.733042\pi$
$19$	−0.730800	+	0.530958i	−0.167657	+	0.121810i	0.500793	+	0.865567i	$0.333042\pi$
$20$		0			0
$21$	−1.16637	−	0.847421i	−0.254524	−	0.184922i
$22$	−3.73648	−	2.71472i	−0.796621	−	0.578779i
$23$	−1.02882	+	3.16637i	−0.214523	+	0.660235i	0.784664	+	0.619922i	$0.212836\pi$
$23$	−1.02882	+	3.16637i	−0.214523	+	0.660235i	−0.999187	+	0.0403132i	$0.987164\pi$
$24$	1.46160			0.298348
$25$		0			0
$26$	−3.29582			−0.646364
$27$	−0.847421	+	2.60809i	−0.163086	+	0.501928i
$28$	−8.18532	−	5.94699i	−1.54688	−	1.12387i
$29$	−3.20619	−	2.32943i	−0.595375	−	0.432565i	0.248859	−	0.968540i	$-0.419944\pi$
$29$	−3.20619	−	2.32943i	−0.595375	−	0.432565i	−0.844234	+	0.535974i	$0.819944\pi$
$30$		0			0
$31$	5.21004	−	3.78532i	0.935751	−	0.679863i	−0.0116431	−	0.999932i	$-0.503706\pi$
$31$	5.21004	−	3.78532i	0.935751	−	0.679863i	0.947394	+	0.320069i	$0.103706\pi$
$32$	−5.13532			−0.907805
$33$	−0.768409	+	0.558282i	−0.133763	+	0.0971844i
$34$	1.32748	+	4.08557i	0.227661	+	0.700669i
$35$		0			0
$36$	−2.85736	+	8.79404i	−0.476226	+	1.46567i
$37$	1.18051	+	3.63324i	0.194075	+	0.597301i	0.999986	+	0.00526493i	$0.00167589\pi$
$37$	1.18051	+	3.63324i	0.194075	+	0.597301i	−0.805911	+	0.592037i	$0.798324\pi$
$38$	0.644613	+	1.98391i	0.104570	+	0.321833i
$39$	−0.209447	+	0.644613i	−0.0335384	+	0.103221i
$40$		0			0
$41$	−0.566805	−	1.74445i	−0.0885201	−	0.272437i	0.896991	−	0.442049i	$-0.145748\pi$
$41$	−0.566805	−	1.74445i	−0.0885201	−	0.272437i	−0.985511	+	0.169613i	$0.945748\pi$
$42$	−2.69348	+	1.95693i	−0.415613	+	0.301960i
$43$	−3.59445			−0.548149			−0.274074	−	0.961708i	$-0.588371\pi$
$43$	−3.59445			−0.548149			−0.274074	+	0.961708i	$0.588371\pi$
$44$	−5.39250	+	3.91788i	−0.812950	+	0.590643i
$45$		0			0
$46$	6.21998	+	4.51908i	0.917086	+	0.666302i
$47$	3.88324	+	2.82134i	0.566428	+	0.411534i	0.833806	−	0.552057i	$-0.186157\pi$
$47$	3.88324	+	2.82134i	0.566428	+	0.411534i	−0.267378	+	0.963592i	$0.586157\pi$
$48$	0.0648235	−	0.199506i	0.00935647	−	0.0287962i
$49$	2.21619			0.316598
$50$		0			0
$51$	0.883436			0.123706
$52$	−1.46985	+	4.52373i	−0.203831	+	0.627329i
$53$	7.68949	+	5.58674i	1.05623	+	0.767398i	0.973388	−	0.229165i	$-0.0735995\pi$
$53$	7.68949	+	5.58674i	1.05623	+	0.767398i	0.0828447	+	0.996562i	$0.473599\pi$
$54$	5.12330	+	3.72230i	0.697193	+	0.506540i
$55$		0			0
$56$	−7.55888	+	5.49184i	−1.01010	+	0.733879i
$57$	0.428989			0.0568209
$58$	−7.40398	+	5.37930i	−0.972190	+	0.706337i
$59$	3.28968	+	10.1246i	0.428279	+	1.31811i	0.899819	+	0.436263i	$0.143698\pi$
$59$	3.28968	+	10.1246i	0.428279	+	1.31811i	−0.471540	+	0.881845i	$0.656302\pi$
$60$		0			0
$61$	4.41097	−	13.5756i	0.564766	−	1.73817i	−0.103879	−	0.994590i	$-0.533125\pi$
$61$	4.41097	−	13.5756i	0.564766	−	1.73817i	0.668645	−	0.743582i	$-0.266875\pi$
$62$	−4.59559	−	14.1438i	−0.583641	−	1.79626i
$63$	−2.60278	−	8.01054i	−0.327920	−	1.00923i
$64$	−3.93759	+	12.1186i	−0.492198	+	1.51483i
$65$		0			0
$66$	0.677786	+	2.08601i	0.0834297	+	0.256770i
$67$	8.64854	−	6.28353i	1.05659	−	0.767656i	0.0831333	−	0.996538i	$-0.473507\pi$
$67$	8.64854	−	6.28353i	1.05659	−	0.767656i	0.973454	+	0.228883i	$0.0735073\pi$
$68$	6.19974			0.751828
$69$	1.27914	−	0.929350i	0.153990	−	0.111881i
$70$		0			0
$71$	−10.0802	−	7.32371i	−1.19630	−	0.869165i	−0.202387	−	0.979306i	$-0.564870\pi$
$71$	−10.0802	−	7.32371i	−1.19630	−	0.869165i	−0.993916	+	0.110141i	$0.964870\pi$
$72$	6.90814	+	5.01906i	0.814132	+	0.591502i
$73$	0.0827026	−	0.254532i	0.00967961	−	0.0297908i	−0.946100	−	0.323874i	$-0.895014\pi$
$73$	0.0827026	−	0.254532i	0.00967961	−	0.0297908i	0.955780	+	0.294084i	$0.0950144\pi$
$74$	8.82193			1.02553
$75$		0			0
$76$	3.01054			0.345332
$77$	1.87624	−	5.77447i	0.213817	−	0.658062i
$78$	1.26627	+	0.919998i	0.143377	+	0.104169i
$79$	6.93470	+	5.03835i	0.780214	+	0.566859i	0.905043	−	0.425319i	$-0.139838\pi$
$79$	6.93470	+	5.03835i	0.780214	+	0.566859i	−0.124829	+	0.992178i	$0.539838\pi$
$80$		0			0
$81$	−5.68017	+	4.12688i	−0.631129	+	0.458542i
$82$	−4.23572			−0.467757
$83$	10.2083	−	7.41677i	1.12051	−	0.814097i	0.136222	−	0.990678i	$-0.456504\pi$
$83$	10.2083	−	7.41677i	1.12051	−	0.814097i	0.984286	+	0.176582i	$0.0565039\pi$
$84$	1.48479	+	4.56972i	0.162004	+	0.498597i
$85$		0			0
$86$	−2.56502	+	7.89432i	−0.276593	+	0.851266i
$87$	0.581593	+	1.78996i	0.0623533	+	0.191904i
$88$	1.90211	+	5.85410i	0.202766	+	0.624049i
$89$	−1.47338	+	4.53460i	−0.156178	+	0.480666i	−0.998278	−	0.0586546i	$-0.981319\pi$
$89$	−1.47338	+	4.53460i	−0.156178	+	0.480666i	0.842100	+	0.539321i	$0.181319\pi$
$90$		0			0
$91$	−1.33889	−	4.12069i	−0.140354	−	0.431966i
$92$	8.97669	−	6.52195i	0.935885	−	0.679960i
$93$	−3.05836			−0.317137
$94$	8.96746	−	6.51524i	0.924923	−	0.671996i
$95$		0			0
$96$	1.97301	+	1.43348i	0.201370	+	0.146304i
$97$	8.05623	+	5.85319i	0.817986	+	0.594302i	0.916135	−	0.400870i	$-0.131292\pi$
$97$	8.05623	+	5.85319i	0.817986	+	0.594302i	−0.0981488	+	0.995172i	$0.531292\pi$
$98$	1.58148	−	4.86730i	0.159754	−	0.491671i
$99$	−5.54893			−0.557689
$100$		0			0
$101$	9.34612			0.929974			0.464987	−	0.885318i	$-0.346059\pi$
$101$	9.34612			0.929974			0.464987	+	0.885318i	$0.346059\pi$
$102$	0.630425	−	1.94025i	0.0624213	−	0.192113i
$103$	−7.34917	−	5.33949i	−0.724136	−	0.526115i	0.163567	−	0.986532i	$-0.447700\pi$
$103$	−7.34917	−	5.33949i	−0.724136	−	0.526115i	−0.887703	+	0.460417i	$0.847700\pi$
$104$	3.55361	+	2.58185i	0.348460	+	0.253171i
$105$		0			0
$106$	17.7571	−	12.9013i	1.72473	−	1.25309i
$107$	5.62871			0.544148			0.272074	−	0.962276i	$-0.412290\pi$
$107$	5.62871			0.544148			0.272074	+	0.962276i	$0.412290\pi$
$108$	7.39396	−	5.37202i	0.711484	−	0.516923i
$109$	−3.12509	−	9.61803i	−0.299329	−	0.921240i	−0.981733	−	0.190265i	$-0.939065\pi$
$109$	−3.12509	−	9.61803i	−0.299329	−	0.921240i	0.682404	−	0.730975i	$-0.260935\pi$
$110$		0			0
$111$	0.560629	−	1.72544i	0.0532125	−	0.163771i
$112$	0.414384	+	1.27534i	0.0391556	+	0.120509i
$113$	3.31019	+	10.1877i	0.311397	+	0.958381i	0.977212	+	0.212264i	$0.0680838\pi$
$113$	3.31019	+	10.1877i	0.311397	+	0.958381i	−0.665815	+	0.746116i	$0.731916\pi$
$114$	0.306129	−	0.942167i	0.0286716	−	0.0882420i
$115$		0			0
$116$	4.08147	+	12.5615i	0.378955	+	1.16630i
$117$	−3.20350	+	2.32748i	−0.296164	+	0.215176i
$118$	24.5836			2.26311
$119$	−4.56882	+	3.31944i	−0.418823	+	0.304293i
$120$		0			0
$121$	5.66312	+	4.11450i	0.514829	+	0.374045i
$122$	−26.6676	−	19.3752i	−2.41437	−	1.75415i
$123$	−0.269177	+	0.828443i	−0.0242709	+	0.0746982i
$124$	−21.4628			−1.92742
$125$		0			0
$126$	−19.4505			−1.73279
$127$	−3.51072	+	10.8049i	−0.311526	+	0.958779i	0.665635	+	0.746278i	$0.268161\pi$
$127$	−3.51072	+	10.8049i	−0.311526	+	0.958779i	−0.977161	+	0.212501i	$0.931839\pi$
$128$	15.4966	+	11.2589i	1.36972	+	0.995158i
$129$	1.38100	+	1.00336i	0.121591	+	0.0883408i
$130$		0			0
$131$	−6.46219	+	4.69506i	−0.564605	+	0.410209i	−0.833141	−	0.553060i	$-0.813460\pi$
$131$	−6.46219	+	4.69506i	−0.564605	+	0.410209i	0.268537	+	0.963269i	$0.413460\pi$
$132$	3.16546			0.275518
$133$	−2.21858	+	1.61189i	−0.192375	+	0.139769i
$134$	−7.62857	−	23.4783i	−0.659008	−	2.02822i
$135$		0			0
$136$	1.76920	−	5.44504i	0.151708	−	0.466908i
$137$	2.88537	+	8.88027i	0.246514	+	0.758692i	0.995384	+	0.0959750i	$0.0305969\pi$
$137$	2.88537	+	8.88027i	0.246514	+	0.758692i	−0.748870	+	0.662717i	$0.769403\pi$
$138$	−1.12828	−	3.47250i	−0.0960460	−	0.295599i
$139$	5.53605	−	17.0382i	0.469562	−	1.44516i	−0.383592	−	0.923503i	$-0.625313\pi$
$139$	5.53605	−	17.0382i	0.469562	−	1.44516i	0.853154	−	0.521660i	$-0.174687\pi$
$140$		0			0
$141$	−0.704407	−	2.16794i	−0.0593217	−	0.182574i
$142$	−23.2780	+	16.9125i	−1.95345	+	1.41926i
$143$	−2.85442			−0.238699
$144$	0.991477	−	0.720350i	0.0826231	−	0.0600292i
$145$		0			0
$146$	−0.500000	−	0.363271i	−0.0413803	−	0.0300645i
$147$	−0.851468	−	0.618628i	−0.0702279	−	0.0510236i
$148$	3.93435	−	12.1087i	0.323402	−	0.995328i
$149$	−6.31395			−0.517259			−0.258629	−	0.965977i	$-0.583271\pi$
$149$	−6.31395			−0.517259			−0.258629	+	0.965977i	$0.583271\pi$
$150$		0			0
$151$	4.71947			0.384065			0.192033	−	0.981389i	$-0.438492\pi$
$151$	4.71947			0.384065			0.192033	+	0.981389i	$0.438492\pi$
$152$	0.859107	−	2.64406i	0.0696828	−	0.214462i
$153$	4.17549	+	3.03367i	0.337569	+	0.245258i
$154$	−11.3433	−	8.24138i	−0.914068	−	0.664109i
$155$		0			0
$156$	1.82748	−	1.32774i	0.146316	−	0.106305i
$157$	1.46908			0.117245			0.0586225	−	0.998280i	$-0.481329\pi$
$157$	1.46908			0.117245			0.0586225	+	0.998280i	$0.481329\pi$
$158$	16.0141	−	11.6349i	1.27402	−	0.925626i
$159$	−1.39485	−	4.29290i	−0.110619	−	0.340449i
$160$		0			0
$161$	−3.12330	+	9.61253i	−0.246151	+	0.757574i
$162$	5.01027	+	15.4200i	0.393644	+	1.21151i
$163$	1.37812	+	4.24142i	0.107943	+	0.332214i	0.990410	−	0.138160i	$-0.0441190\pi$
$163$	1.37812	+	4.24142i	0.107943	+	0.332214i	−0.882467	+	0.470374i	$0.844119\pi$
$164$	−1.88902	+	5.81380i	−0.147508	+	0.453982i
$165$		0			0
$166$	−9.00439	−	27.7127i	−0.698876	−	2.15092i
$167$	−8.44101	+	6.13275i	−0.653185	+	0.474567i	−0.864355	−	0.502883i	$-0.832273\pi$
$167$	−8.44101	+	6.13275i	−0.653185	+	0.474567i	0.211170	+	0.977449i	$0.432273\pi$
$168$	4.43715			0.342334
$169$	8.86931	−	6.44393i	0.682255	−	0.495687i
$170$		0			0
$171$	2.02758	+	1.47312i	0.155053	+	0.112653i
$172$	9.69155	+	7.04132i	0.738973	+	0.536896i
$173$	−2.37207	+	7.30049i	−0.180345	+	0.555046i	−0.999837	−	0.0180448i	$-0.994256\pi$
$173$	−2.37207	+	7.30049i	−0.180345	+	0.555046i	0.819492	+	0.573091i	$0.194256\pi$
$174$	4.34623			0.329486
$175$		0			0
$176$	0.883436			0.0665915
$177$	1.56228	−	4.80819i	0.117428	−	0.361406i
$178$	8.90770	+	6.47182i	0.667660	+	0.485084i
$179$	−12.5533	−	9.12053i	−0.938280	−	0.681700i	0.00972631	−	0.999953i	$-0.496904\pi$
$179$	−12.5533	−	9.12053i	−0.938280	−	0.681700i	−0.948006	+	0.318253i	$0.896904\pi$
$180$		0			0
$181$	1.28679	−	0.934906i	0.0956462	−	0.0694910i	−0.538934	−	0.842348i	$-0.681173\pi$
$181$	1.28679	−	0.934906i	0.0956462	−	0.0694910i	0.634580	+	0.772857i	$0.281173\pi$
$182$	−10.0055			−0.741658
$183$	−5.48421	+	3.98451i	−0.405404	+	0.294543i
$184$	−3.16637	−	9.74510i	−0.233428	−	0.718418i
$185$		0			0
$186$	−2.18246	+	6.71692i	−0.160026	+	0.492509i
$187$	1.14970	+	3.53840i	0.0840741	+	0.258753i
$188$	−4.94335	−	15.2141i	−0.360531	−	1.10960i
$189$	−2.57261	+	7.91769i	−0.187130	+	0.575927i
$190$		0			0
$191$	6.07788	+	18.7058i	0.439780	+	1.35350i	0.888108	+	0.459635i	$0.152020\pi$
$191$	6.07788	+	18.7058i	0.439780	+	1.35350i	−0.448328	+	0.893869i	$0.647980\pi$
$192$	4.89565	−	3.55690i	0.353313	−	0.256697i
$193$	13.1100			0.943680			0.471840	−	0.881684i	$-0.343590\pi$
$193$	13.1100			0.943680			0.471840	+	0.881684i	$0.343590\pi$
$194$	18.6040	−	13.5166i	1.33569	−	0.970437i
$195$		0			0
$196$	−5.97539	−	4.34138i	−0.426814	−	0.310098i
$197$	2.77451	+	2.01580i	0.197676	+	0.143620i	0.682220	−	0.731147i	$-0.261015\pi$
$197$	2.77451	+	2.01580i	0.197676	+	0.143620i	−0.484544	+	0.874767i	$0.661015\pi$
$198$	−3.95975	+	12.1869i	−0.281407	+	0.866082i
$199$	17.6959			1.25443			0.627215	−	0.778846i	$-0.284195\pi$
$199$	17.6959			1.25443			0.627215	+	0.778846i	$0.284195\pi$
$200$		0			0
$201$	−5.07680			−0.358090
$202$	6.66944	−	20.5264i	0.469260	−	1.44423i
$203$	−9.73341	−	7.07174i	−0.683152	−	0.496339i
$204$	−2.38197	−	1.73060i	−0.166771	−	0.121166i
$205$		0			0
$206$	−16.9713	+	12.3303i	−1.18244	+	0.859096i
$207$	9.23710			0.642023
$208$	0.510024	−	0.370554i	0.0353638	−	0.0256933i
$209$	0.558282	+	1.71821i	0.0386172	+	0.118851i
$210$		0			0
$211$	−1.00235	+	3.08491i	−0.0690044	+	0.212374i	−0.979612	−	0.200898i	$-0.935614\pi$
$211$	−1.00235	+	3.08491i	−0.0690044	+	0.212374i	0.910608	+	0.413272i	$0.135614\pi$
$212$	−9.78869	−	30.1265i	−0.672290	−	2.06910i
$213$	1.82852	+	5.62761i	0.125288	+	0.385597i
$214$	4.01668	−	12.3621i	0.274575	−	0.845054i
$215$		0			0
$216$	−2.60809	−	8.02688i	−0.177458	−	0.546160i
$217$	15.8167	−	11.4915i	1.07371	−	0.780096i
$218$	−23.3537			−1.58171
$219$	−0.102825	+	0.0747068i	−0.00694828	+	0.00504822i
$220$		0			0
$221$	2.14791	+	1.56055i	0.144484	+	0.104974i
$222$	−3.38943	−	2.46256i	−0.227483	−	0.165276i
$223$	8.87335	−	27.3094i	0.594203	−	1.82877i	0.0355515	−	0.999368i	$-0.488681\pi$
$223$	8.87335	−	27.3094i	0.594203	−	1.82877i	0.558652	−	0.829402i	$-0.311319\pi$
$224$	−15.5899			−1.04164
$225$		0			0
$226$	24.7370			1.64548
$227$	3.62187	−	11.1470i	0.240392	−	0.739851i	−0.755968	−	0.654609i	$-0.772833\pi$
$227$	3.62187	−	11.1470i	0.240392	−	0.739851i	0.996360	−	0.0852426i	$-0.0271665\pi$
$228$	−1.15666	−	0.840364i	−0.0766018	−	0.0556544i
$229$	13.2689	+	9.64043i	0.876835	+	0.637058i	0.932412	−	0.361397i	$-0.117700\pi$
$229$	13.2689	+	9.64043i	0.876835	+	0.637058i	−0.0555774	+	0.998454i	$0.517700\pi$
$230$		0			0
$231$	−2.33275	+	1.69484i	−0.153484	+	0.111512i
$232$	12.1971			0.800777
$233$	−18.2147	+	13.2337i	−1.19328	+	0.866971i	−0.993607	−	0.112891i	$-0.963989\pi$
$233$	−18.2147	+	13.2337i	−1.19328	+	0.866971i	−0.199676	+	0.979862i	$0.563989\pi$
$234$	2.82570	+	8.69660i	0.184722	+	0.568514i
$235$		0			0
$236$	10.9637	−	33.7427i	0.713674	−	2.19646i
$237$	−1.25793	−	3.87152i	−0.0817114	−	0.251482i
$238$	4.02999	+	12.4030i	0.261226	+	0.803969i
$239$	−2.04981	+	6.30867i	−0.132591	+	0.408074i	−0.995208	−	0.0977848i	$-0.968824\pi$
$239$	−2.04981	+	6.30867i	−0.132591	+	0.408074i	0.862616	+	0.505859i	$0.168824\pi$
$240$		0			0
$241$	8.10430	+	24.9425i	0.522044	+	1.60668i	0.770089	+	0.637936i	$0.220212\pi$
$241$	8.10430	+	24.9425i	0.522044	+	1.60668i	−0.248045	+	0.968748i	$0.579788\pi$
$242$	13.0777	−	9.50150i	0.840666	−	0.610780i
$243$	11.5613			0.741655
$244$	−38.4868	+	27.9623i	−2.46386	+	1.79010i
$245$		0			0
$246$	1.62738	+	1.18236i	0.103758	+	0.0753846i
$247$	1.04301	+	0.757788i	0.0663649	+	0.0482169i
$248$	−6.12477	+	18.8501i	−0.388923	+	1.19698i
$249$	−5.99241			−0.379753
$250$		0			0
$251$	−10.9121			−0.688766			−0.344383	−	0.938829i	$-0.611912\pi$
$251$	−10.9121			−0.688766			−0.344383	+	0.938829i	$0.611912\pi$
$252$	−8.67441	+	26.6971i	−0.546437	+	1.68176i
$253$	5.38696	+	3.91385i	0.338675	+	0.246062i
$254$	21.2250	+	15.4208i	1.33177	+	0.967590i
$255$		0			0
$256$	15.1684	−	11.0205i	0.948024	−	0.688780i
$257$	6.58051			0.410481			0.205240	−	0.978712i	$-0.434202\pi$
$257$	6.58051			0.410481			0.205240	+	0.978712i	$0.434202\pi$
$258$	3.18912	−	2.31703i	0.198546	−	0.144252i
$259$	3.58382	+	11.0299i	0.222688	+	0.685362i
$260$		0			0
$261$	−3.39777	+	10.4573i	−0.210317	+	0.647288i
$262$	5.70007	+	17.5430i	0.352152	+	1.08381i
$263$	−8.37660	−	25.7805i	−0.516524	−	1.58970i	−0.780493	−	0.625165i	$-0.785032\pi$
$263$	−8.37660	−	25.7805i	−0.516524	−	1.58970i	0.263969	−	0.964531i	$-0.414968\pi$
$264$	0.903319	−	2.78013i	0.0555954	−	0.171105i
$265$		0			0
$266$	1.95693	+	6.02280i	0.119987	+	0.369282i
$267$	1.83187	−	1.33093i	0.112109	−	0.0814517i
$268$	−35.6277			−2.17631
$269$	−0.816664	+	0.593341i	−0.0497929	+	0.0361766i	−0.612403	−	0.790546i	$-0.709797\pi$
$269$	−0.816664	+	0.593341i	−0.0497929	+	0.0361766i	0.562610	+	0.826722i	$0.309797\pi$
$270$		0			0
$271$	−5.05800	−	3.67485i	−0.307252	−	0.223231i	0.423465	−	0.905913i	$-0.360814\pi$
$271$	−5.05800	−	3.67485i	−0.307252	−	0.223231i	−0.730716	+	0.682681i	$0.760814\pi$
$272$	−0.664773	−	0.482986i	−0.0403078	−	0.0292853i
$273$	−0.635844	+	1.95693i	−0.0384830	+	0.118439i
$274$	21.5623			1.30263
$275$		0			0
$276$	−5.26943			−0.317182
$277$	−7.62355	+	23.4629i	−0.458055	+	1.40975i	0.409456	+	0.912330i	$0.365718\pi$
$277$	−7.62355	+	23.4629i	−0.458055	+	1.40975i	−0.867511	+	0.497418i	$0.834282\pi$
$278$	−33.4696	−	24.3171i	−2.00738	−	1.45844i
$279$	−14.4551	−	10.5022i	−0.865404	−	0.628753i
$280$		0			0
$281$	−1.48771	+	1.08089i	−0.0887495	+	0.0644803i	−0.631275	−	0.775559i	$-0.717468\pi$
$281$	−1.48771	+	1.08089i	−0.0887495	+	0.0644803i	0.542526	+	0.840039i	$0.317468\pi$
$282$	−5.26401			−0.313467
$283$	6.99084	−	5.07915i	0.415563	−	0.301924i	−0.360287	−	0.932841i	$-0.617321\pi$
$283$	6.99084	−	5.07915i	0.415563	−	0.301924i	0.775850	+	0.630918i	$0.217321\pi$
$284$	12.8321	+	39.4931i	0.761445	+	2.34349i
$285$		0			0
$286$	−2.03693	+	6.26902i	−0.120446	+	0.370695i
$287$	−1.72072	−	5.29582i	−0.101571	−	0.312602i
$288$	4.40280	+	13.5504i	0.259438	+	0.798467i
$289$	−4.18393	+	12.8768i	−0.246114	+	0.757460i
$290$		0			0
$291$	−1.46137	−	4.49765i	−0.0856672	−	0.263657i
$292$	−0.721601	+	0.524274i	−0.0422285	+	0.0306808i
$293$	6.29156			0.367557			0.183779	−	0.982968i	$-0.441167\pi$
$293$	6.29156			0.367557			0.183779	+	0.982968i	$0.441167\pi$
$294$	−1.96627	+	1.42858i	−0.114675	+	0.0833166i
$295$		0			0
$296$	−9.51195	−	6.91084i	−0.552871	−	0.401684i
$297$	4.43715	+	3.22378i	0.257470	+	0.187063i
$298$	−4.50567	+	13.8670i	−0.261006	+	0.803295i
$299$	4.75164			0.274795
$300$		0			0
$301$	−10.9121			−0.628963
$302$	3.36784	−	10.3651i	0.193797	−	0.596447i
$303$	−3.59082	−	2.60888i	−0.206287	−	0.149876i
$304$	−0.322808	−	0.234534i	−0.0185143	−	0.0134514i
$305$		0			0
$306$	9.64236	−	7.00558i	0.551217	−	0.400483i
$307$	−28.6661			−1.63606			−0.818030	−	0.575175i	$-0.804934\pi$
$307$	−28.6661			−1.63606			−0.818030	+	0.575175i	$0.804934\pi$
$308$	−16.3706	+	11.8940i	−0.932804	+	0.677722i
$309$	1.33312	+	4.10291i	0.0758383	+	0.233406i
$310$		0			0
$311$	−2.42161	+	7.45295i	−0.137317	+	0.422618i	−0.995943	−	0.0899842i	$-0.971318\pi$
$311$	−2.42161	+	7.45295i	−0.137317	+	0.422618i	0.858626	+	0.512602i	$0.171318\pi$
$312$	−0.644613	−	1.98391i	−0.0364940	−	0.112317i
$313$	6.61582	+	20.3614i	0.373949	+	1.15090i	0.944185	+	0.329415i	$0.106851\pi$
$313$	6.61582	+	20.3614i	0.373949	+	1.15090i	−0.570237	+	0.821480i	$0.693149\pi$
$314$	1.04834	−	3.22646i	0.0591613	−	0.182080i
$315$		0			0
$316$	−8.82785	−	27.1693i	−0.496605	−	1.52839i
$317$	−3.25211	+	2.36280i	−0.182657	+	0.132708i	−0.675356	−	0.737491i	$-0.736010\pi$
$317$	−3.25211	+	2.36280i	−0.182657	+	0.132708i	0.492699	+	0.870200i	$0.336010\pi$
$318$	−10.4237			−0.584530
$319$	−6.41238	+	4.65887i	−0.359025	+	0.260847i
$320$		0			0
$321$	−2.16258	−	1.57120i	−0.120703	−	0.0876961i
$322$	18.8827	+	13.7191i	1.05229	+	0.764536i
$323$	0.519271	−	1.59815i	0.0288930	−	0.0889235i
$324$	23.3995			1.29997
$325$		0			0
$326$	10.2987			0.570390
$327$	−1.48411	+	4.56763i	−0.0820716	+	0.252590i
$328$	4.56702	+	3.31813i	0.252171	+	0.183213i
$329$	11.7888	+	8.56506i	0.649938	+	0.472207i
$330$		0			0
$331$	−9.42008	+	6.84409i	−0.517775	+	0.376185i	−0.815765	−	0.578384i	$-0.803684\pi$
$331$	−9.42008	+	6.84409i	−0.517775	+	0.376185i	0.297990	+	0.954569i	$0.403684\pi$
$332$	−42.0532			−2.30797
$333$	8.57483	−	6.22998i	0.469898	−	0.341401i
$334$	7.44552	+	22.9149i	0.407400	+	1.25385i
$335$		0			0
$336$	0.196792	−	0.605664i	0.0107359	−	0.0330417i
$337$	−6.65461	−	20.4808i	−0.362500	−	1.11566i	−0.951532	−	0.307550i	$-0.900491\pi$
$337$	−6.65461	−	20.4808i	−0.362500	−	1.11566i	0.589032	−	0.808110i	$-0.299509\pi$
$338$	−7.82330	−	24.0777i	−0.425532	−	1.30965i
$339$	1.57202	−	4.83818i	0.0853804	−	0.262774i
$340$		0			0
$341$	−3.98012	−	12.2495i	−0.215535	−	0.663350i
$342$	4.68224	−	3.40185i	0.253187	−	0.183951i
$343$	−14.5228			−0.784157
$344$	8.94982	−	6.50243i	0.482542	−	0.350587i
$345$		0			0
$346$	14.3410	+	10.4193i	0.770976	+	0.560147i
$347$	−12.6184	−	9.16782i	−0.677393	−	0.492155i	0.195099	−	0.980784i	$-0.437497\pi$
$347$	−12.6184	−	9.16782i	−0.677393	−	0.492155i	−0.872492	+	0.488629i	$0.837497\pi$
$348$	1.93830	−	5.96548i	0.103904	−	0.319783i
$349$	5.56598			0.297940			0.148970	−	0.988842i	$-0.452404\pi$
$349$	5.56598			0.297940			0.148970	+	0.988842i	$0.452404\pi$
$350$		0			0
$351$	3.91385			0.208906
$352$	−3.17380	+	9.76796i	−0.169164	+	0.520634i
$353$	−6.49007	−	4.71531i	−0.345431	−	0.250971i	0.401519	−	0.915851i	$-0.368483\pi$
$353$	−6.49007	−	4.71531i	−0.345431	−	0.250971i	−0.746950	+	0.664880i	$0.768483\pi$
$354$	−9.44515	−	6.86230i	−0.502004	−	0.364727i
$355$		0			0
$356$	12.8556	−	9.34014i	0.681346	−	0.495027i
$357$	2.68195			0.141944
$358$	−28.9891	+	21.0618i	−1.53212	+	1.11315i
$359$	−3.81411	−	11.7386i	−0.201301	−	0.619541i	−0.999845	−	0.0176044i	$-0.994396\pi$
$359$	−3.81411	−	11.7386i	−0.201301	−	0.619541i	0.798544	−	0.601936i	$-0.205604\pi$
$360$		0			0
$361$	−5.61917	+	17.2940i	−0.295746	+	0.910212i
$362$	−1.13503	−	3.49326i	−0.0596558	−	0.183602i
$363$	−1.02727	−	3.16162i	−0.0539178	−	0.165942i
$364$	−4.46219	+	13.7332i	−0.233883	+	0.719816i
$365$		0			0
$366$	4.83742	+	14.8881i	0.252856	+	0.778211i
$367$	−21.7423	+	15.7967i	−1.13494	+	0.824581i	−0.986406	−	0.164327i	$-0.947455\pi$
$367$	−21.7423	+	15.7967i	−1.13494	+	0.824581i	−0.148532	+	0.988908i	$0.547455\pi$
$368$	−1.47062			−0.0766615
$369$	−4.11707	+	2.99123i	−0.214326	+	0.155717i
$370$		0			0
$371$	23.3439	+	16.9603i	1.21195	+	0.880536i
$372$	8.24610	+	5.99114i	0.427540	+	0.310626i
$373$	−8.54089	+	26.2862i	−0.442231	+	1.36105i	0.443262	+	0.896392i	$0.353821\pi$
$373$	−8.54089	+	26.2862i	−0.442231	+	1.36105i	−0.885492	+	0.464654i	$0.846179\pi$
$374$	8.59164			0.444263
$375$		0			0
$376$	−14.7727			−0.761845
$377$	−1.74784	+	5.37930i	−0.0900184	+	0.277048i
$378$	15.5534	+	11.3002i	0.799981	+	0.581220i
$379$	2.81103	+	2.04233i	0.144393	+	0.104908i	0.657637	−	0.753335i	$-0.271556\pi$
$379$	2.81103	+	2.04233i	0.144393	+	0.104908i	−0.513244	+	0.858243i	$0.671556\pi$
$380$		0			0
$381$	4.36492	−	3.17130i	0.223622	−	0.162471i
$382$	45.4198			2.32388
$383$	−22.1443	+	16.0888i	−1.13152	+	0.822098i	−0.985916	−	0.167244i	$-0.946513\pi$
$383$	−22.1443	+	16.0888i	−1.13152	+	0.822098i	−0.145606	+	0.989343i	$0.546513\pi$
$384$	−2.81103	−	8.65146i	−0.143450	−	0.441493i
$385$		0			0
$386$	9.35538	−	28.7929i	0.476176	−	1.46552i
$387$	3.08173	+	9.48459i	0.156653	+	0.482129i
$388$	−10.2556	−	31.5634i	−0.520647	−	1.60239i
$389$	3.36350	−	10.3518i	0.170536	−	0.524857i	−0.828865	−	0.559448i	$-0.811013\pi$
$389$	3.36350	−	10.3518i	0.170536	−	0.524857i	0.999402	+	0.0345916i	$0.0110130\pi$
$390$		0			0
$391$	−1.91385	−	5.89024i	−0.0967878	−	0.297882i
$392$	−5.51808	+	4.00912i	−0.278705	+	0.202491i
$393$	3.79339			0.191351
$394$	6.40712	−	4.65504i	0.322786	−	0.234518i
$395$		0			0
$396$	14.9613	+	10.8700i	0.751835	+	0.546240i
$397$	−13.1233	−	9.53460i	−0.658637	−	0.478528i	0.207565	−	0.978221i	$-0.433446\pi$
$397$	−13.1233	−	9.53460i	−0.658637	−	0.478528i	−0.866202	+	0.499693i	$0.833446\pi$
$398$	12.6279	−	38.8647i	0.632979	−	1.94811i
$399$	1.30233			0.0651981
$400$		0			0
$401$	3.78686			0.189107			0.0945534	−	0.995520i	$-0.469858\pi$
$401$	3.78686			0.189107			0.0945534	+	0.995520i	$0.469858\pi$
$402$	−3.62283	+	11.1499i	−0.180690	+	0.556108i
$403$	−7.43582	−	5.40244i	−0.370405	−	0.269115i
$404$	−25.1995	−	18.3085i	−1.25372	−	0.910882i
$405$		0			0
$406$	−22.4771	+	16.3306i	−1.11552	+	0.810473i
$407$	7.64044			0.378722
$408$	−2.19967	+	1.59815i	−0.108900	+	0.0791203i
$409$	0.573491	+	1.76502i	0.0283573	+	0.0872748i	0.964234	−	0.265054i	$-0.0853898\pi$
$409$	0.573491	+	1.76502i	0.0283573	+	0.0872748i	−0.935876	+	0.352329i	$0.885390\pi$
$410$		0			0
$411$	1.37027	−	4.21726i	0.0675905	−	0.208022i
$412$	9.35547	+	28.7932i	0.460911	+	1.41854i
$413$	9.98686	+	30.7364i	0.491421	+	1.51244i
$414$	6.59164	−	20.2870i	0.323961	−	0.997051i
$415$		0			0
$416$	2.26484	+	6.97046i	0.111043	+	0.341755i
$417$	−6.88304	+	5.00082i	−0.337064	+	0.244891i
$418$	4.17202			0.204060
$419$	−11.6071	+	8.43307i	−0.567045	+	0.411983i	−0.834031	−	0.551718i	$-0.813972\pi$
$419$	−11.6071	+	8.43307i	−0.567045	+	0.411983i	0.266985	+	0.963701i	$0.413972\pi$
$420$		0			0
$421$	−12.5030	−	9.08394i	−0.609358	−	0.442724i	0.239830	−	0.970815i	$-0.422908\pi$
$421$	−12.5030	−	9.08394i	−0.609358	−	0.442724i	−0.849188	+	0.528091i	$0.822908\pi$
$422$	6.05995	+	4.40281i	0.294994	+	0.214325i
$423$	4.11527	−	12.6655i	0.200091	−	0.615818i
$424$	−29.2525			−1.42063
$425$		0			0
$426$	13.6645			0.662046
$427$	13.3909	−	41.2129i	0.648030	−	1.99443i
$428$	−15.1764	−	11.0263i	−0.733580	−	0.532977i
$429$	1.09668	+	0.796785i	0.0529483	+	0.0384692i
$430$		0			0
$431$	−10.1162	+	7.34985i	−0.487280	+	0.354030i	−0.804137	−	0.594444i	$-0.797372\pi$
$431$	−10.1162	+	7.34985i	−0.487280	+	0.354030i	0.316857	+	0.948473i	$0.397372\pi$
$432$	−1.21133			−0.0582801
$433$	18.1989	−	13.2223i	0.874586	−	0.635424i	−0.0572279	−	0.998361i	$-0.518226\pi$
$433$	18.1989	−	13.2223i	0.874586	−	0.635424i	0.931813	+	0.362937i	$0.118226\pi$
$434$	−13.9514	−	42.9379i	−0.669688	−	2.06109i
$435$		0			0
$436$	−10.4151	+	32.0545i	−0.498794	+	1.53513i
$437$	−0.929350	−	2.86025i	−0.0444569	−	0.136824i
$438$	0.0906984	+	0.279141i	0.00433374	+	0.0133379i
$439$	3.76308	−	11.5816i	0.179602	−	0.552758i	−0.820212	−	0.572060i	$-0.806145\pi$
$439$	3.76308	−	11.5816i	0.179602	−	0.552758i	0.999814	+	0.0193023i	$0.00614450\pi$
$440$		0			0
$441$	−1.90006	−	5.84779i	−0.0904792	−	0.278466i
$442$	4.96011	−	3.60373i	0.235929	−	0.171412i
$443$	−20.7101			−0.983968			−0.491984	−	0.870604i	$-0.663728\pi$
$443$	−20.7101			−0.983968			−0.491984	+	0.870604i	$0.663728\pi$
$444$	−4.89162	+	3.55397i	−0.232146	+	0.168664i
$445$		0			0
$446$	−53.6461	−	38.9762i	−2.54022	−	1.84558i
$447$	2.42585	+	1.76248i	0.114739	+	0.0833625i
$448$	−11.9538	+	36.7900i	−0.564764	+	1.73816i
$449$	−25.9539			−1.22484			−0.612420	−	0.790533i	$-0.709804\pi$
$449$	−25.9539			−1.22484			−0.612420	+	0.790533i	$0.709804\pi$
$450$		0			0
$451$	−3.66844			−0.172740
$452$	11.0320	−	33.9531i	0.518904	−	1.59702i
$453$	−1.81324	−	1.31740i	−0.0851936	−	0.0618968i
$454$	−21.8970	−	15.9091i	−1.02768	−	0.746650i
$455$		0			0
$456$	−1.06814	+	0.776048i	−0.0500202	+	0.0363418i
$457$	−8.50150			−0.397684			−0.198842	−	0.980032i	$-0.563718\pi$
$457$	−8.50150			−0.397684			−0.198842	+	0.980032i	$0.563718\pi$
$458$	30.6416	−	22.2624i	1.43179	−	1.04025i
$459$	−1.57641	−	4.85170i	−0.0735806	−	0.226458i
$460$		0			0
$461$	4.56884	−	14.0614i	0.212792	−	0.654906i	−0.786511	−	0.617576i	$-0.788115\pi$
$461$	4.56884	−	14.0614i	0.212792	−	0.654906i	0.999303	−	0.0373301i	$-0.0118853\pi$
$462$	2.05763	+	6.33275i	0.0957298	+	0.294626i
$463$	−6.85774	−	21.1060i	−0.318706	−	0.980877i	−0.974202	−	0.225678i	$-0.927540\pi$
$463$	−6.85774	−	21.1060i	−0.318706	−	0.980877i	0.655496	−	0.755199i	$-0.272460\pi$
$464$	0.540953	−	1.66488i	0.0251131	−	0.0772902i
$465$		0			0
$466$	16.0665	+	49.4477i	0.744267	+	2.29062i
$467$	23.0581	−	16.7527i	1.06700	−	0.775222i	0.0916308	−	0.995793i	$-0.470792\pi$
$467$	23.0581	−	16.7527i	1.06700	−	0.775222i	0.975371	+	0.220571i	$0.0707920\pi$
$468$	13.1968			0.610024
$469$	26.2554	−	19.0757i	1.21236	−	0.880832i
$470$		0			0
$471$	−0.564426	−	0.410079i	−0.0260074	−	0.0188955i
$472$	−26.5065	−	19.2581i	−1.22006	−	0.886426i
$473$	−2.22149	+	6.83706i	−0.102144	+	0.314368i
$474$	−9.40048			−0.431779
$475$		0			0
$476$	18.8213			0.862671
$477$	8.14895	−	25.0799i	0.373115	−	1.14833i
$478$	12.3927	+	9.00380i	0.566827	+	0.411824i
$479$	−20.2715	−	14.7281i	−0.926227	−	0.672943i	0.0188390	−	0.999823i	$-0.494003\pi$
$479$	−20.2715	−	14.7281i	−0.926227	−	0.672943i	−0.945066	+	0.326879i	$0.894003\pi$
$480$		0			0
$481$	4.41097	−	3.20475i	0.201123	−	0.146124i
$482$	60.5632			2.75858
$483$	3.88324	−	2.82134i	0.176693	−	0.128375i
$484$	−7.20913	−	22.1874i	−0.327688	−	1.00852i
$485$		0			0
$486$	8.25017	−	25.3914i	0.374235	−	1.15178i
$487$	−0.452644	−	1.39310i	−0.0205113	−	0.0631272i	0.940277	−	0.340410i	$-0.110566\pi$
$487$	−0.452644	−	1.39310i	−0.0205113	−	0.0631272i	−0.960788	+	0.277283i	$0.910566\pi$
$488$	13.5756	+	41.7813i	0.614537	+	1.89135i
$489$	0.654474	−	2.01426i	0.0295963	−	0.0910881i
$490$		0			0
$491$	−6.20155	−	19.0864i	−0.279872	−	0.861358i	−0.987889	−	0.155162i	$-0.950410\pi$
$491$	−6.20155	−	19.0864i	−0.279872	−	0.861358i	0.708017	−	0.706195i	$-0.249590\pi$
$492$	2.34864	−	1.70639i	0.105885	−	0.0769298i
$493$	7.37229			0.332031
$494$	2.40859	−	1.74994i	0.108367	−	0.0787335i
$495$		0			0
$496$	2.30137	+	1.67204i	0.103335	+	0.0750770i
$497$	−30.6017	−	22.2335i	−1.37268	−	0.997307i
$498$	−4.27621	+	13.1608i	−0.191622	+	0.589751i
$499$	0.624999			0.0279788			0.0139894	−	0.999902i	$-0.495547\pi$
$499$	0.624999			0.0279788			0.0139894	+	0.999902i	$0.495547\pi$
$500$		0			0
$501$	4.95498			0.221372
$502$	−7.78693	+	23.9657i	−0.347548	+	1.06964i
$503$	15.6182	+	11.3473i	0.696382	+	0.505951i	0.878752	−	0.477279i	$-0.158377\pi$
$503$	15.6182	+	11.3473i	0.696382	+	0.505951i	−0.182370	+	0.983230i	$0.558377\pi$
$504$	20.9719	+	15.2369i	0.934161	+	0.678707i
$505$		0			0
$506$	12.4400	−	9.03816i	0.553024	−	0.401795i
$507$	−5.20639			−0.231224
$508$	30.6319	−	22.2554i	1.35907	−	0.987423i
$509$	−3.25091	−	10.0053i	−0.144094	−	0.443476i	0.852799	−	0.522239i	$-0.174903\pi$
$509$	−3.25091	−	10.0053i	−0.144094	−	0.443476i	−0.996893	+	0.0787629i	$0.974903\pi$
$510$		0			0
$511$	0.251070	−	0.772714i	0.0111067	−	0.0341828i
$512$	−1.54116	−	4.74321i	−0.0681103	−	0.209622i
$513$	−0.765491	−	2.35594i	−0.0337973	−	0.104017i
$514$	4.69588	−	14.4524i	0.207127	−	0.637470i
$515$		0			0
$516$	−1.75801	−	5.41061i	−0.0773923	−	0.238189i
$517$	7.76648	−	5.64267i	0.341569	−	0.248165i
$518$	26.7818			1.17672
$519$	2.94923	−	2.14274i	0.129457	−	0.0940558i
$520$		0			0
$521$	8.09580	+	5.88195i	0.354684	+	0.257693i	0.750831	−	0.660494i	$-0.229653\pi$
$521$	8.09580	+	5.88195i	0.354684	+	0.257693i	−0.396148	+	0.918187i	$0.629653\pi$
$522$	20.5421	+	14.9247i	0.899103	+	0.653237i
$523$	7.04035	−	21.6680i	0.307853	−	0.947474i	−0.670744	−	0.741689i	$-0.734025\pi$
$523$	7.04035	−	21.6680i	0.307853	−	0.947474i	0.978597	−	0.205785i	$-0.0659748\pi$
$524$	26.6210			1.16295
$525$		0			0
$526$	−62.5981			−2.72941
$527$	−3.70200	+	11.3936i	−0.161262	+	0.496312i
$528$	−0.339420	−	0.246603i	−0.0147714	−	0.0107320i
$529$	9.63993	+	7.00382i	0.419127	+	0.304514i
$530$		0			0
$531$	23.8951	−	17.3608i	1.03696	−	0.753393i
$532$	9.13943			0.396245
$533$	−2.11786	+	1.53871i	−0.0917346	+	0.0666491i
$534$	−1.61583	−	4.97301i	−0.0699237	−	0.215203i
$535$		0			0
$536$	−10.1670	+	31.2907i	−0.439146	+	1.35155i
$537$	2.27713	+	7.00829i	0.0982655	+	0.302430i
$538$	0.720350	+	2.21701i	0.0310565	+	0.0955821i
$539$	1.36968	−	4.21544i	0.0589962	−	0.181572i
$540$		0			0
$541$	1.00709	+	3.09949i	0.0432980	+	0.133257i	0.970369	−	0.241629i	$-0.0776817\pi$
$541$	1.00709	+	3.09949i	0.0432980	+	0.133257i	−0.927071	+	0.374886i	$0.877682\pi$
$542$	−11.6803	+	8.48624i	−0.501712	+	0.364515i
$543$	−0.755360			−0.0324156
$544$	7.72851	−	5.61509i	0.331357	−	0.240745i
$545$		0			0
$546$	3.84416	+	2.79295i	0.164515	+	0.119527i
$547$	10.9932	+	7.98700i	0.470033	+	0.341499i	0.797454	−	0.603379i	$-0.206179\pi$
$547$	10.9932	+	7.98700i	0.470033	+	0.341499i	−0.327421	+	0.944879i	$0.606179\pi$
$548$	9.61622	−	29.5957i	0.410785	−	1.26427i
$549$	−39.6033			−1.69023
$550$		0			0
$551$	3.57992			0.152510
$552$	−1.50372	+	4.62798i	−0.0640026	+	0.196980i
$553$	21.0525	+	15.2955i	0.895242	+	0.650432i
$554$	46.0901	+	33.4865i	1.95818	+	1.42270i
$555$		0			0
$556$	−48.3034	+	35.0945i	−2.04852	+	1.48834i
$557$	−27.6399			−1.17114			−0.585571	−	0.810621i	$-0.699130\pi$
$557$	−27.6399			−1.17114			−0.585571	+	0.810621i	$0.699130\pi$
$558$	−33.3808	+	24.2525i	−1.41312	+	1.02669i
$559$	1.58527	+	4.87896i	0.0670498	+	0.206358i
$560$		0			0
$561$	0.545994	−	1.68040i	0.0230519	−	0.0709464i
$562$	1.31226	+	4.03871i	0.0553543	+	0.170363i
$563$	−0.512737	−	1.57804i	−0.0216093	−	0.0665065i	0.939670	−	0.342081i	$-0.111132\pi$
$563$	−0.512737	−	1.57804i	−0.0216093	−	0.0665065i	−0.961280	+	0.275575i	$0.911132\pi$
$564$	−2.34761	+	7.22520i	−0.0988522	+	0.304236i
$565$		0			0
$566$	−6.16637	−	18.9781i	−0.259192	−	0.797711i
$567$	−17.2439	+	12.5285i	−0.724178	+	0.526146i
$568$	38.3475			1.60902
$569$	−14.4675	+	10.5113i	−0.606509	+	0.440655i	−0.848183	−	0.529703i	$-0.822303\pi$
$569$	−14.4675	+	10.5113i	−0.606509	+	0.440655i	0.241674	+	0.970357i	$0.422303\pi$
$570$		0			0
$571$	29.8303	+	21.6730i	1.24836	+	0.906987i	0.998126	−	0.0611975i	$-0.0194920\pi$
$571$	29.8303	+	21.6730i	1.24836	+	0.906987i	0.250235	+	0.968185i	$0.419492\pi$
$572$	7.69623	+	5.59164i	0.321796	+	0.233798i
$573$	2.88640	−	8.88344i	0.120581	−	0.371111i
$574$	−12.8589			−0.536718
$575$		0			0
$576$	35.3531			1.47305
$577$	−7.04982	+	21.6971i	−0.293488	+	0.903262i	0.690238	+	0.723583i	$0.257506\pi$
$577$	−7.04982	+	21.6971i	−0.293488	+	0.903262i	−0.983725	+	0.179679i	$0.942494\pi$
$578$	25.2950	+	18.3779i	1.05213	+	0.764421i
$579$	−5.03693	−	3.65954i	−0.209328	−	0.152085i
$580$		0			0
$581$	30.9906	−	22.5160i	1.28571	−	0.934120i
$582$	−10.9208			−0.452682
$583$	15.3790	−	11.1735i	0.636932	−	0.462758i
$584$	0.254532	+	0.783370i	0.0105326	+	0.0324161i
$585$		0			0
$586$	4.48969	−	13.8179i	0.185467	−	0.570810i
$587$	−3.42560	−	10.5429i	−0.141390	−	0.435153i	0.855139	−	0.518398i	$-0.173471\pi$
$587$	−3.42560	−	10.5429i	−0.141390	−	0.435153i	−0.996529	+	0.0832455i	$0.973471\pi$
$588$	1.08392	+	3.33595i	0.0447000	+	0.137572i
$589$	−1.79766	+	5.53262i	−0.0740712	+	0.227968i
$590$		0			0
$591$	−0.503288	−	1.54896i	−0.0207025	−	0.0637157i
$592$	−1.36518	+	0.991864i	−0.0561087	+	0.0407654i
$593$	11.1321			0.457139			0.228570	−	0.973528i	$-0.426595\pi$
$593$	11.1321			0.457139			0.228570	+	0.973528i	$0.426595\pi$
$594$	10.2466	−	7.44459i	0.420423	−	0.305455i
$595$		0			0
$596$	17.0240	+	12.3687i	0.697330	+	0.506640i
$597$	−6.79885	−	4.93965i	−0.278258	−	0.202167i
$598$	3.39080	−	10.4358i	0.138660	−	0.426752i
$599$	36.2736			1.48210			0.741049	−	0.671451i	$-0.234329\pi$
$599$	36.2736			1.48210			0.741049	+	0.671451i	$0.234329\pi$
$600$		0			0
$601$	−15.1051			−0.616150			−0.308075	−	0.951362i	$-0.599685\pi$
$601$	−15.1051			−0.616150			−0.308075	+	0.951362i	$0.599685\pi$
$602$	−7.78693	+	23.9657i	−0.317372	+	0.976769i
$603$	−23.9951	−	17.4335i	−0.977156	−	0.709945i
$604$	−12.7249	−	9.24517i	−0.517768	−	0.376181i
$605$		0			0
$606$	−8.29219	+	6.02463i	−0.336847	+	0.244734i
$607$	−33.5066			−1.35999			−0.679996	−	0.733216i	$-0.738018\pi$
$607$	−33.5066			−1.35999			−0.679996	+	0.733216i	$0.738018\pi$
$608$	3.75289	−	2.72664i	0.152200	−	0.110580i
$609$	1.76561	+	5.43399i	0.0715461	+	0.220196i
$610$		0			0
$611$	2.11693	−	6.51524i	0.0856418	−	0.263579i
$612$	−5.31539	−	16.3591i	−0.214862	−	0.661277i
$613$	−8.66140	−	26.6571i	−0.349831	−	1.07667i	−0.958947	−	0.283587i	$-0.908476\pi$
$613$	−8.66140	−	26.6571i	−0.349831	−	1.07667i	0.609116	−	0.793081i	$-0.291524\pi$
$614$	−20.4563	+	62.9579i	−0.825548	+	2.54078i
$615$		0			0
$616$	5.77447	+	17.7720i	0.232660	+	0.716054i
$617$	−24.6931	+	17.9406i	−0.994105	+	0.722260i	−0.960816	−	0.277186i	$-0.910598\pi$
$617$	−24.6931	+	17.9406i	−0.994105	+	0.722260i	−0.0332890	+	0.999446i	$0.510598\pi$
$618$	9.96234			0.400744
$619$	17.5533	−	12.7532i	0.705528	−	0.512596i	−0.176200	−	0.984354i	$-0.556381\pi$
$619$	17.5533	−	12.7532i	0.705528	−	0.512596i	0.881728	+	0.471758i	$0.156381\pi$
$620$		0			0
$621$	−7.38636	−	5.36650i	−0.296404	−	0.215350i
$622$	14.6405	+	10.6369i	0.587029	+	0.426502i
$623$	−4.47291	+	13.7662i	−0.179203	+	0.551531i
$624$	−0.299391			−0.0119852
$625$		0			0
$626$	49.4399			1.97601
$627$	0.265130	−	0.815985i	0.0105883	−	0.0325873i
$628$	−3.96100	−	2.87783i	−0.158061	−	0.114838i
$629$	−5.74932	−	4.17712i	−0.229240	−	0.166553i
$630$		0			0
$631$	13.1285	−	9.53840i	0.522637	−	0.379718i	−0.294960	−	0.955510i	$-0.595306\pi$
$631$	13.1285	−	9.53840i	0.522637	−	0.379718i	0.817596	+	0.575792i	$0.195306\pi$
$632$	−26.3812			−1.04939
$633$	1.24623	−	0.905439i	0.0495332	−	0.0359880i
$634$	2.86857	+	8.82857i	0.113926	+	0.350627i
$635$		0			0
$636$	−4.64868	+	14.3072i	−0.184332	+	0.567316i
$637$	−0.977409	−	3.00816i	−0.0387264	−	0.119187i
$638$	5.65614	+	17.4078i	0.223929	+	0.689181i
$639$	−10.6825	+	32.8775i	−0.422595	+	1.30061i
$640$		0			0
$641$	−6.85321	−	21.0920i	−0.270685	−	0.833084i	−0.990329	−	0.138740i	$-0.955695\pi$
$641$	−6.85321	−	21.0920i	−0.270685	−	0.833084i	0.719643	−	0.694344i	$-0.244305\pi$
$642$	−4.99398	+	3.62834i	−0.197097	+	0.143199i
$643$	−13.2767			−0.523583			−0.261792	−	0.965124i	$-0.584313\pi$
$643$	−13.2767			−0.523583			−0.261792	+	0.965124i	$0.584313\pi$
$644$	27.2516	−	19.7994i	1.07386	−	0.780207i
$645$		0			0
$646$	−3.13939	−	2.28090i	−0.123518	−	0.0897407i
$647$	9.12999	+	6.63333i	0.358937	+	0.260783i	0.752609	−	0.658468i	$-0.228795\pi$
$647$	9.12999	+	6.63333i	0.358937	+	0.260783i	−0.393672	+	0.919251i	$0.628795\pi$
$648$	6.67743	−	20.5510i	0.262314	−	0.807321i
$649$	21.2912			0.835754
$650$		0			0
$651$	−9.28462			−0.363893
$652$	4.59293	−	14.1356i	0.179873	−	0.553592i
$653$	28.9736	+	21.0506i	1.13383	+	0.823773i	0.986247	−	0.165277i	$-0.0528520\pi$
$653$	28.9736	+	21.0506i	1.13383	+	0.823773i	0.147579	+	0.989050i	$0.452852\pi$
$654$	8.97259	+	6.51897i	0.350856	+	0.254912i
$655$		0			0
$656$	0.655472	−	0.476228i	0.0255919	−	0.0185936i
$657$	−0.742534			−0.0289690
$658$	27.2236	−	19.7791i	1.06129	−	0.771069i
$659$	12.2882	+	37.8193i	0.478681	+	1.47323i	0.840928	+	0.541147i	$0.182010\pi$
$659$	12.2882	+	37.8193i	0.478681	+	1.47323i	−0.362247	+	0.932082i	$0.617990\pi$
$660$		0			0
$661$	−1.93053	+	5.94157i	−0.0750890	+	0.231100i	−0.981555	−	0.191178i	$-0.938769\pi$
$661$	−1.93053	+	5.94157i	−0.0750890	+	0.231100i	0.906466	+	0.422278i	$0.138769\pi$
$662$	8.30912	+	25.5728i	0.322943	+	0.993917i
$663$	−0.389624	−	1.19914i	−0.0151317	−	0.0465707i
$664$	−12.0006	+	36.9340i	−0.465713	+	1.43332i
$665$		0			0
$666$	−7.56355	−	23.2782i	−0.293082	−	0.902012i
$667$	10.6744	−	7.75544i	0.413316	−	0.300292i
$668$	34.7728			1.34540
$669$	−11.0323	+	8.01546i	−0.426535	+	0.309896i
$670$		0			0
$671$	−23.0961	−	16.7803i	−0.891616	−	0.647797i
$672$	5.98970	+	4.35178i	0.231058	+	0.167873i
$673$	−12.8127	+	39.4334i	−0.493893	+	1.52005i	0.324782	+	0.945789i	$0.394709\pi$
$673$	−12.8127	+	39.4334i	−0.493893	+	1.52005i	−0.818675	+	0.574257i	$0.805291\pi$
$674$	−49.7297			−1.91552
$675$		0			0
$676$	−36.5372			−1.40528
$677$	−0.444723	+	1.36872i	−0.0170921	+	0.0526041i	−0.959239	−	0.282597i	$-0.908804\pi$
$677$	−0.444723	+	1.36872i	−0.0170921	+	0.0526041i	0.942147	+	0.335201i	$0.108804\pi$
$678$	−9.50406	−	6.90510i	−0.365001	−	0.265189i
$679$	24.4572	+	17.7692i	0.938583	+	0.681920i
$680$		0			0
$681$	−4.50312	+	3.27171i	−0.172560	+	0.125372i
$682$	−29.7433			−1.13893
$683$	6.86550	−	4.98808i	0.262701	−	0.190864i	−0.448636	−	0.893715i	$-0.648090\pi$
$683$	6.86550	−	4.98808i	0.262701	−	0.190864i	0.711337	+	0.702851i	$0.248090\pi$
$684$	−2.58111	−	7.94382i	−0.0986910	−	0.303740i
$685$		0			0
$686$	−10.3635	+	31.8957i	−0.395682	+	1.21778i
$687$	−2.40694	−	7.40779i	−0.0918304	−	0.282625i
$688$	−0.490637	−	1.51003i	−0.0187054	−	0.0575692i
$689$	4.19189	−	12.9013i	0.159698	−	0.491501i
$690$		0			0
$691$	−13.5287	−	41.6370i	−0.514655	−	1.58395i	−0.783908	−	0.620877i	$-0.786777\pi$
$691$	−13.5287	−	41.6370i	−0.514655	−	1.58395i	0.269253	−	0.963070i	$-0.413223\pi$
$692$	20.6969	−	15.0372i	0.786780	−	0.571629i
$693$	−16.8456			−0.639910
$694$	−29.1394	+	21.1710i	−1.10612	+	0.803641i
$695$		0			0
$696$	−4.68617	−	3.40470i	−0.177629	−	0.129055i
$697$	2.76045	+	2.00558i	0.104559	+	0.0759668i
$698$	3.97191	−	12.2243i	0.150339	−	0.462696i
$699$	10.6922			0.404418
$700$		0			0
$701$	0.840795			0.0317564			0.0158782	−	0.999874i	$-0.494946\pi$
$701$	0.840795			0.0317564			0.0158782	+	0.999874i	$0.494946\pi$
$702$	2.79295	−	8.59580i	0.105413	−	0.324428i
$703$	−2.79182	−	2.02837i	−0.105295	−	0.0765015i
$704$	20.6175	+	14.9795i	0.777050	+	0.564560i
$705$		0			0
$706$	−14.9873	+	10.8889i	−0.564056	+	0.409811i
$707$	28.3731			1.06708
$708$	−13.6313	+	9.90369i	−0.512294	+	0.372203i
$709$	−4.13503	−	12.7263i	−0.155294	−	0.477947i	0.842896	−	0.538076i	$-0.180849\pi$
$709$	−4.13503	−	12.7263i	−0.155294	−	0.477947i	−0.998191	+	0.0601294i	$0.980849\pi$
$710$		0			0
$711$	7.34906	−	22.6181i	0.275611	−	0.848244i
$712$	−4.53460	−	13.9561i	−0.169941	−	0.523025i
$713$	6.62555	+	20.3913i	0.248129	+	0.763662i
$714$	1.91385	−	5.89024i	0.0716242	−	0.220437i
$715$		0			0
$716$	15.9803	+	49.1824i	0.597214	+	1.83803i
$717$	2.54855	−	1.85163i	0.0951775	−	0.0691505i
$718$	−28.5027			−1.06371
$719$	−35.1233	+	25.5186i	−1.30988	+	0.951683i	−0.309880	+	0.950776i	$0.600289\pi$
$719$	−35.1233	+	25.5186i	−1.30988	+	0.951683i	−1.00000		0.000907154i	$0.999711\pi$
$720$		0			0
$721$	−22.3107	−	16.2097i	−0.830896	−	0.603681i
$722$	33.9721	+	24.6822i	1.26431	+	0.918577i
$723$	3.84875	−	11.8452i	0.143137	−	0.440529i
$724$	−5.30093			−0.197007
$725$		0			0
$726$	−7.67677			−0.284912
$727$	−9.90338	+	30.4795i	−0.367296	+	1.13042i	0.581235	+	0.813736i	$0.302570\pi$
$727$	−9.90338	+	30.4795i	−0.367296	+	1.13042i	−0.948531	+	0.316685i	$0.897430\pi$
$728$	10.7881	+	7.83802i	0.399834	+	0.290496i
$729$	12.5986	+	9.15342i	0.466615	+	0.339016i
$730$		0			0
$731$	5.40955	−	3.93027i	0.200079	−	0.145366i
$732$	22.5922			0.835032
$733$	−6.58481	+	4.78415i	−0.243216	+	0.176706i	−0.702715	−	0.711472i	$-0.748029\pi$
$733$	−6.58481	+	4.78415i	−0.243216	+	0.176706i	0.459499	+	0.888178i	$0.348029\pi$
$734$	19.1781	+	59.0241i	0.707877	+	2.17862i
$735$		0			0
$736$	5.28331	−	16.2603i	0.194745	−	0.599364i
$737$	−6.60690	−	20.3339i	−0.243368	−	0.749010i
$738$	3.63152	+	11.1767i	0.133678	+	0.411419i
$739$	−2.20241	+	6.77831i	−0.0810169	+	0.249344i	−0.983358	−	0.181678i	$-0.941847\pi$
$739$	−2.20241	+	6.77831i	−0.0810169	+	0.249344i	0.902341	+	0.431023i	$0.141847\pi$
$740$		0			0
$741$	−0.189198	−	0.582291i	−0.00695036	−	0.0213910i
$742$	53.9074	−	39.1660i	1.97900	−	1.43783i
$743$	21.9040			0.803578			0.401789	−	0.915732i	$-0.368388\pi$
$743$	21.9040			0.803578			0.401789	+	0.915732i	$0.368388\pi$
$744$	7.61500	−	5.53262i	0.279179	−	0.202836i
$745$		0			0
$746$	51.6362	+	37.5159i	1.89054	+	1.37355i
$747$	−28.3226	−	20.5776i	−1.03627	−	0.752895i
$748$	3.83165	−	11.7926i	0.140099	−	0.431180i
$749$	17.0877			0.624373
$750$		0			0
$751$	9.21909			0.336409			0.168205	−	0.985752i	$-0.446203\pi$
$751$	9.21909			0.336409			0.168205	+	0.985752i	$0.446203\pi$
$752$	−0.655185	+	2.01645i	−0.0238921	+	0.0735325i
$753$	4.19248	+	3.04601i	0.152782	+	0.111003i
$754$	10.5670	+	7.67740i	0.384829	+	0.279594i
$755$		0			0
$756$	22.4467	−	16.3085i	0.816379	−	0.593134i
$757$	45.6524			1.65926			0.829632	−	0.558311i	$-0.188550\pi$
$757$	45.6524			1.65926			0.829632	+	0.558311i	$0.188550\pi$
$758$	6.49144	−	4.71631i	0.235780	−	0.171304i
$759$	−0.977177	−	3.00744i	−0.0354693	−	0.109163i
$760$		0			0
$761$	12.3316	−	37.9526i	0.447019	−	1.37578i	−0.433236	−	0.901280i	$-0.642628\pi$
$761$	12.3316	−	37.9526i	0.447019	−	1.37578i	0.880255	−	0.474501i	$-0.157372\pi$
$762$	−3.85014	−	11.8495i	−0.139476	−	0.429263i
$763$	−9.48719	−	29.1986i	−0.343459	−	1.05706i
$764$	20.2561	−	62.3417i	0.732838	−	2.25544i
$765$		0			0
$766$	19.5327	+	60.1155i	0.705745	+	2.17206i
$767$	12.2918	−	8.93053i	0.443832	−	0.322463i
$768$	−8.90403			−0.321296
$769$	35.8734	−	26.0636i	1.29363	−	0.939876i	0.293757	−	0.955880i	$-0.405094\pi$
$769$	35.8734	−	26.0636i	1.29363	−	0.939876i	0.999872	+	0.0160040i	$0.00509446\pi$
$770$		0			0
$771$	−2.52826	−	1.83689i	−0.0910531	−	0.0661539i
$772$	−35.3479	−	25.6818i	−1.27220	−	0.924307i
$773$	−11.8954	+	36.6103i	−0.427848	+	1.31678i	0.472392	+	0.881389i	$0.343391\pi$
$773$	−11.8954	+	36.6103i	−0.427848	+	1.31678i	−0.900240	+	0.435393i	$0.856609\pi$
$774$	23.0297			0.827785
$775$		0			0
$776$	−30.6477			−1.10019
$777$	1.70197	−	5.23811i	0.0610577	−	0.187916i
$778$	−20.3349	−	14.7742i	−0.729042	−	0.529680i
$779$	1.34045	+	0.973893i	0.0480265	+	0.0348933i
$780$		0			0
$781$	−20.1605	+	14.6474i	−0.721398	+	0.524126i
$782$	−14.3022			−0.511445
$783$	8.79238	−	6.38803i	0.314214	−	0.228290i
$784$	0.302506	+	0.931017i	0.0108038	+	0.0332506i
$785$		0			0
$786$	2.70698	−	8.33123i	0.0965548	−	0.297165i
$787$	−16.3841	−	50.4252i	−0.584031	−	1.79746i	−0.603126	−	0.797646i	$-0.706078\pi$
$787$	−16.3841	−	50.4252i	−0.584031	−	1.79746i	0.0190942	−	0.999818i	$-0.493922\pi$
$788$	−3.53195	−	10.8702i	−0.125820	−	0.387236i
$789$	−3.97807	+	12.2433i	−0.141623	+	0.435871i
$790$		0			0
$791$	10.0491	+	30.9281i	0.357306	+	1.09968i
$792$	13.8163	−	10.0381i	0.490940	−	0.356689i
$793$	−20.3723			−0.723440
$794$	−30.3052	+	22.0180i	−1.07549	+	0.781390i
$795$		0			0
$796$	−47.7126	−	34.6653i	−1.69113	−	1.22868i
$797$	10.2558	+	7.45127i	0.363279	+	0.263938i	0.754418	−	0.656394i	$-0.227919\pi$
$797$	10.2558	+	7.45127i	0.363279	+	0.263938i	−0.391139	+	0.920331i	$0.627919\pi$
$798$	0.929350	−	2.86025i	0.0328986	−	0.101252i
$799$	−8.92908			−0.315888
$800$		0			0
$801$	13.2285			0.467407
$802$	2.70232	−	8.31689i	0.0954223	−	0.293680i
$803$	−0.433036	−	0.314619i	−0.0152815	−	0.0111027i
$804$	13.6883	+	9.94515i	0.482750	+	0.350738i
$805$		0			0
$806$	−17.1714	+	12.4757i	−0.604835	+	0.439439i
$807$	0.479392			0.0168754
$808$	−23.2709	+	16.9073i	−0.818667	+	0.594796i
$809$	−12.9458	−	39.8431i	−0.455150	−	1.40081i	−0.870959	−	0.491356i	$-0.836501\pi$
$809$	−12.9458	−	39.8431i	−0.455150	−	1.40081i	0.415808	−	0.909452i	$-0.363499\pi$
$810$		0			0
$811$	−10.6761	+	32.8577i	−0.374889	+	1.15379i	0.568665	+	0.822569i	$0.307460\pi$
$811$	−10.6761	+	32.8577i	−0.374889	+	1.15379i	−0.943554	+	0.331220i	$0.892540\pi$
$812$	12.3906	+	38.1344i	0.434825	+	1.33825i
$813$	0.917505	+	2.82379i	0.0321783	+	0.0990346i
$814$	5.45225	−	16.7803i	0.191101	−	0.588150i
$815$		0			0
$816$	0.120588	+	0.371131i	0.00422141	+	0.0129922i
$817$	2.62683	−	1.90850i	0.0919011	−	0.0667700i
$818$	4.28568			0.149845
$819$	−9.72525	+	7.06581i	−0.339828	+	0.246899i
$820$		0			0
$821$	17.0985	+	12.4228i	0.596740	+	0.433557i	0.844720	−	0.535208i	$-0.179767\pi$
$821$	17.0985	+	12.4228i	0.596740	+	0.433557i	−0.247980	+	0.968765i	$0.579767\pi$
$822$	−8.28433	−	6.01892i	−0.288949	−	0.209934i
$823$	0.981789	−	3.02164i	0.0342230	−	0.105328i	−0.932486	−	0.361207i	$-0.882365\pi$
$823$	0.981789	−	3.02164i	0.0342230	−	0.105328i	0.966709	+	0.255879i	$0.0823649\pi$
$824$	27.9579			0.973960
$825$		0			0
$826$	74.6315			2.59676
$827$	3.01131	−	9.26787i	0.104714	−	0.322275i	−0.884949	−	0.465687i	$-0.845807\pi$
$827$	3.01131	−	9.26787i	0.104714	−	0.322275i	0.989663	+	0.143412i	$0.0458073\pi$
$828$	−24.9055	−	18.0949i	−0.865527	−	0.628842i
$829$	−18.9595	−	13.7749i	−0.658490	−	0.478421i	0.207663	−	0.978200i	$-0.433414\pi$
$829$	−18.9595	−	13.7749i	−0.658490	−	0.478421i	−0.866153	+	0.499780i	$0.833414\pi$
$830$		0			0
$831$	9.47845	−	6.88650i	0.328804	−	0.238890i
$832$	18.1859			0.630484
$833$	−3.33530	+	2.42323i	−0.115561	+	0.0839601i
$834$	6.07128	+	18.6855i	0.210231	+	0.647026i
$835$		0			0
$836$	1.86061	−	5.72638i	0.0643507	−	0.198051i
$837$	5.45736	+	16.7960i	0.188634	+	0.580556i
$838$	10.2382	+	31.5101i	0.353674	+	1.08850i
$839$	13.1894	−	40.5929i	0.455350	−	1.40142i	−0.415375	−	0.909650i	$-0.636350\pi$
$839$	13.1894	−	40.5929i	0.455350	−	1.40142i	0.870724	−	0.491771i	$-0.163650\pi$
$840$		0			0
$841$	−4.10809	−	12.6434i	−0.141658	−	0.435980i
$842$	−28.8728	+	20.9773i	−0.995022	+	0.722926i
$843$	0.873305			0.0300782
$844$	8.74573	−	6.35414i	0.301040	−	0.218719i
$845$		0			0
$846$	−24.8799	−	18.0763i	−0.855390	−	0.621477i
$847$	17.1922	+	12.4909i	0.590731	+	0.429191i
$848$	−1.29738	+	3.99293i	−0.0445522	+	0.137118i
$849$	−4.10371			−0.140839
$850$		0			0
$851$	−12.7187			−0.435993
$852$	6.09400	−	18.7554i	0.208777	−	0.642550i
$853$	−13.7217	−	9.96942i	−0.469823	−	0.341347i	0.327549	−	0.944834i	$-0.393777\pi$
$853$	−13.7217	−	9.96942i	−0.469823	−	0.341347i	−0.797372	+	0.603488i	$0.793777\pi$
$854$	−80.9581	−	58.8195i	−2.77033	−	2.01276i
$855$		0			0
$856$	−14.0149	+	10.1824i	−0.479020	+	0.348029i
$857$	−39.3176			−1.34306			−0.671531	−	0.740976i	$-0.734363\pi$
$857$	−39.3176			−1.34306			−0.671531	+	0.740976i	$0.734363\pi$
$858$	2.53254	−	1.84000i	0.0864594	−	0.0628164i
$859$	0.218492	+	0.672450i	0.00745486	+	0.0229437i	0.954715	−	0.297523i	$-0.0961604\pi$
$859$	0.218492	+	0.672450i	0.00745486	+	0.0229437i	−0.947260	+	0.320466i	$0.896160\pi$
$860$		0			0
$861$	−0.817173	+	2.51500i	−0.0278492	+	0.0857110i
$862$	8.92314	+	27.4626i	0.303923	+	0.935380i
$863$	0.281023	+	0.864900i	0.00956613	+	0.0294415i	0.955726	−	0.294259i	$-0.0950729\pi$
$863$	0.281023	+	0.864900i	0.00956613	+	0.0294415i	−0.946160	+	0.323701i	$0.895073\pi$
$864$	4.35178	−	13.3934i	0.148050	−	0.455652i
$865$		0			0
$866$	−16.0526	−	49.4050i	−0.545491	−	1.67885i
$867$	5.20193	−	3.77942i	0.176667	−	0.128356i
$868$	−65.1571			−2.21158
$869$	13.8694	−	10.0767i	0.470487	−	0.341829i
$870$		0			0
$871$	−12.3433	−	8.96792i	−0.418236	−	0.303866i
$872$	25.1803	+	18.2946i	0.852713	+	0.619533i
$873$	8.53761	−	26.2761i	0.288954	−	0.889310i
$874$	−6.94501			−0.234918
$875$		0			0
$876$	0.423589			0.0143117
$877$	10.4019	−	32.0138i	0.351248	−	1.08103i	−0.606906	−	0.794774i	$-0.707589\pi$
$877$	10.4019	−	32.0138i	0.351248	−	1.08103i	0.958153	−	0.286255i	$-0.0924106\pi$
$878$	−22.7506	−	16.5293i	−0.767797	−	0.557837i
$879$	−2.41725	−	1.75623i	−0.0815317	−	0.0592363i
$880$		0			0
$881$	16.1223	−	11.7136i	0.543175	−	0.394640i	−0.282088	−	0.959389i	$-0.591027\pi$
$881$	16.1223	−	11.7136i	0.543175	−	0.394640i	0.825263	+	0.564749i	$0.191027\pi$
$882$	−14.1991			−0.478109
$883$	−12.6272	+	9.17421i	−0.424940	+	0.308737i	−0.779622	−	0.626250i	$-0.784589\pi$
$883$	−12.6272	+	9.17421i	−0.424940	+	0.308737i	0.354683	+	0.934987i	$0.384589\pi$
$884$	−2.73428	−	8.41526i	−0.0919639	−	0.283036i
$885$		0			0
$886$	−14.7789	+	45.4846i	−0.496505	+	1.52809i
$887$	14.4919	+	44.6015i	0.486591	+	1.49757i	0.829664	+	0.558263i	$0.188532\pi$
$887$	14.4919	+	44.6015i	0.486591	+	1.49757i	−0.343073	+	0.939309i	$0.611468\pi$
$888$	1.72544	+	5.31035i	0.0579019	+	0.178204i
$889$	−10.6579	+	32.8017i	−0.357455	+	1.10013i
$890$		0			0
$891$	4.33926	+	13.3549i	0.145371	+	0.447405i
$892$	−77.4222	+	56.2505i	−2.59229	+	1.88341i
$893$	−4.33588			−0.145095
$894$	5.60195	−	4.07005i	0.187357	−	0.136123i
$895$		0			0
$896$	47.0448	+	34.1800i	1.57166	+	1.14187i
$897$	−1.82560	−	1.32638i	−0.0609551	−	0.0442865i
$898$	−18.5208	+	57.0013i	−0.618048	+	1.90216i
$899$	−25.5220			−0.851208
$900$		0			0
$901$	−17.6811			−0.589044
$902$	−2.61782	+	8.05681i	−0.0871638	+	0.268262i
$903$	4.19248	+	3.04601i	0.139517	+	0.101365i
$904$	−26.6718	−	19.3782i	−0.887091	−	0.644510i
$905$		0			0
$906$	−4.18728	+	3.04223i	−0.139113	+	0.101071i
$907$	1.43447			0.0476308			0.0238154	−	0.999716i	$-0.492419\pi$
$907$	1.43447			0.0476308			0.0238154	+	0.999716i	$0.492419\pi$
$908$	−31.6018	+	22.9600i	−1.04874	+	0.761955i
$909$	−8.01297	−	24.6614i	−0.265773	−	0.817966i
$910$		0			0
$911$	−0.868737	+	2.67370i	−0.0287825	+	0.0885835i	−0.964416	−	0.264390i	$-0.914829\pi$
$911$	−0.868737	+	2.67370i	−0.0287825	+	0.0885835i	0.935633	+	0.352973i	$0.114829\pi$
$912$	0.0585563	+	0.180218i	0.00193899	+	0.00596761i
$913$	−7.79846	−	24.0012i	−0.258091	−	0.794323i
$914$	−6.06672	+	18.6714i	−0.200669	+	0.617596i
$915$		0			0
$916$	−16.8913	−	51.9860i	−0.558104	−	1.71767i
$917$	−19.6180	+	14.2533i	−0.647845	+	0.470687i
$918$	−11.7805			−0.388814
$919$	−0.802736	+	0.583222i	−0.0264798	+	0.0192387i	−0.600946	−	0.799289i	$-0.705210\pi$
$919$	−0.802736	+	0.583222i	−0.0264798	+	0.0192387i	0.574467	+	0.818528i	$0.305210\pi$
$920$		0			0
$921$	11.0136	+	8.00188i	0.362912	+	0.263671i
$922$	−27.6221	−	20.0686i	−0.909685	−	0.660925i
$923$	−5.49519	+	16.9125i	−0.180877	+	0.556681i
$924$	9.60977			0.316138
$925$		0			0
$926$	−51.2477			−1.68410
$927$	−7.78830	+	23.9699i	−0.255801	+	0.787276i
$928$	16.4648	+	11.9624i	0.540484	+	0.392685i
$929$	−26.9587	−	19.5866i	−0.884485	−	0.642616i	0.0499493	−	0.998752i	$-0.484094\pi$
$929$	−26.9587	−	19.5866i	−0.884485	−	0.642616i	−0.934434	+	0.356136i	$0.884094\pi$
$930$		0			0
$931$	−1.61959	+	1.17670i	−0.0530799	+	0.0385648i
$932$	75.0355			2.45787
$933$	3.01081	−	2.18749i	0.0985697	−	0.0716150i
$934$	−20.3387	−	62.5962i	−0.665504	−	2.04821i
$935$		0			0
$936$	3.76594	−	11.5904i	0.123094	−	0.378844i
$937$	4.13079	+	12.7133i	0.134947	+	0.415325i	0.995582	−	0.0938984i	$-0.0299329\pi$
$937$	4.13079	+	12.7133i	0.134947	+	0.415325i	−0.860635	+	0.509223i	$0.829933\pi$
$938$	−23.1589	−	71.2759i	−0.756166	−	2.32724i
$939$	3.14187	−	9.66969i	0.102531	−	0.315559i
$940$		0			0
$941$	−0.664330	−	2.04460i	−0.0216565	−	0.0666520i	0.939644	−	0.342153i	$-0.111156\pi$
$941$	−0.664330	−	2.04460i	−0.0216565	−	0.0666520i	−0.961301	+	0.275501i	$0.911156\pi$
$942$	−1.30341	+	0.946986i	−0.0424675	+	0.0308545i
$943$	6.10671			0.198862
$944$	−3.80429	+	2.76398i	−0.123819	+	0.0899599i
$945$		0			0
$946$	13.4306	+	9.75792i	0.436667	+	0.317257i
$947$	−28.2495	−	20.5245i	−0.917985	−	0.666955i	0.0250363	−	0.999687i	$-0.492030\pi$
$947$	−28.2495	−	20.5245i	−0.917985	−	0.666955i	−0.943022	+	0.332731i	$0.892030\pi$
$948$	−4.19237	+	12.9028i	−0.136162	+	0.419063i
$949$	−0.381966			−0.0123991
$950$		0			0
$951$	1.90903			0.0619046
$952$	5.37097	−	16.5301i	0.174074	−	0.535745i
$953$	6.69772	+	4.86618i	0.216960	+	0.157631i	0.690957	−	0.722896i	$-0.257189\pi$
$953$	6.69772	+	4.86618i	0.216960	+	0.157631i	−0.473997	+	0.880526i	$0.657189\pi$
$954$	−49.2666	−	35.7943i	−1.59507	−	1.15888i
$955$		0			0
$956$	17.8851	−	12.9943i	0.578446	−	0.420266i
$957$	3.76415			0.121678
$958$	−46.8124	+	34.0112i	−1.51244	+	1.09885i
$959$	8.75947	+	26.9589i	0.282858	+	0.870547i
$960$		0			0
$961$	3.23638	−	9.96056i	0.104399	−	0.321308i
$962$	−3.89076	−	11.9745i	−0.125443	−	0.386074i
$963$	−4.82582	−	14.8523i	−0.155510	−	0.478610i
$964$	27.0096	−	83.1270i	0.869920	−	2.67734i
$965$		0			0
$966$	−3.42527	−	10.5419i	−0.110206	−	0.339180i
$967$	−23.8556	+	17.3321i	−0.767143	+	0.557362i	−0.901093	−	0.433626i	$-0.857234\pi$
$967$	−23.8556	+	17.3321i	−0.767143	+	0.557362i	0.133950	+	0.990988i	$0.457234\pi$
$968$	−21.5438			−0.692443
$969$	−0.645616	+	0.469067i	−0.0207402	+	0.0150686i
$970$		0			0
$971$	−17.6905	−	12.8529i	−0.567714	−	0.412469i	0.266560	−	0.963818i	$-0.414113\pi$
$971$	−17.6905	−	12.8529i	−0.567714	−	0.412469i	−0.834274	+	0.551350i	$0.814113\pi$
$972$	−31.1721	−	22.6478i	−0.999844	−	0.726429i
$973$	16.8064	−	51.7249i	0.538790	−	1.65822i
$974$	−3.38260			−0.108385
$975$		0			0
$976$	6.30517			0.201823
$977$	4.27933	−	13.1704i	0.136908	−	0.421359i	−0.858974	−	0.512019i	$-0.828898\pi$
$977$	4.27933	−	13.1704i	0.136908	−	0.421359i	0.995882	+	0.0906602i	$0.0288977\pi$
$978$	−3.95679	−	2.87478i	−0.126524	−	0.0919252i
$979$	7.71472	+	5.60507i	0.246563	+	0.179139i
$980$		0			0
$981$	−22.6995	+	16.4922i	−0.724740	+	0.526555i
$982$	−46.3440			−1.47890
$983$	−2.37477	+	1.72537i	−0.0757434	+	0.0550308i	−0.625013	−	0.780615i	$-0.714906\pi$
$983$	−2.37477	+	1.72537i	−0.0757434	+	0.0550308i	0.549269	+	0.835646i	$0.314906\pi$
$984$	−0.828443	−	2.54968i	−0.0264098	−	0.0812810i
$985$		0			0
$986$	5.26090	−	16.1914i	0.167541	−	0.515639i
$987$	−2.13845	−	6.58147i	−0.0680676	−	0.209491i
$988$	−1.32774	−	4.08637i	−0.0422411	−	0.130005i
$989$	3.69804	−	11.3814i	0.117591	−	0.361907i
$990$		0			0
$991$	9.76918	+	30.0664i	0.310328	+	0.955092i	0.977635	+	0.210309i	$0.0674470\pi$
$991$	9.76918	+	30.0664i	0.310328	+	0.955092i	−0.667307	+	0.744783i	$0.732553\pi$
$992$	−26.7552	+	19.4388i	−0.849479	+	0.617183i
$993$	5.52970			0.175480
$994$	−70.6678	+	51.3432i	−2.24145	+	1.62851i
$995$		0			0
$996$	16.1570	+	11.7388i	0.511955	+	0.371957i
$997$	9.77977	+	7.10542i	0.309728	+	0.225031i	0.731780	−	0.681541i	$-0.238690\pi$
$997$	9.77977	+	7.10542i	0.309728	+	0.225031i	−0.422052	+	0.906572i	$0.638690\pi$
$998$	0.446002	−	1.37265i	0.0141180	−	0.0434506i
$999$	−10.4762			−0.331453

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.d.o.501.4		16
5.2	odd	4		625.2.e.a.124.2		8
5.3	odd	4		625.2.e.i.124.1		8
5.4	even	2	inner	625.2.d.o.501.1		16
25.2	odd	20		125.2.e.b.49.2		8
25.3	odd	20		125.2.e.b.74.2		8
25.4	even	10		125.2.d.b.51.4		16
25.6	even	5	inner	625.2.d.o.126.4		16
25.8	odd	20		625.2.e.a.499.2		8
25.9	even	10		625.2.a.f.1.1		8
25.11	even	5		125.2.d.b.76.1		16
25.12	odd	20		625.2.b.c.624.8		8
25.13	odd	20		625.2.b.c.624.1		8
25.14	even	10		125.2.d.b.76.4		16
25.16	even	5		625.2.a.f.1.8		8
25.17	odd	20		625.2.e.i.499.1		8
25.19	even	10	inner	625.2.d.o.126.1		16
25.21	even	5		125.2.d.b.51.1		16
25.22	odd	20		25.2.e.a.14.1	yes	8
25.23	odd	20		25.2.e.a.9.1	✓	8
75.23	even	20		225.2.m.a.109.2		8
75.41	odd	10		5625.2.a.x.1.1		8
75.47	even	20		225.2.m.a.64.2		8
75.59	odd	10		5625.2.a.x.1.8		8
100.23	even	20		400.2.y.c.209.1		8
100.47	even	20		400.2.y.c.289.1		8
100.59	odd	10		10000.2.a.bj.1.5		8
100.91	odd	10		10000.2.a.bj.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.e.a.9.1	✓	8	25.23	odd	20
25.2.e.a.14.1	yes	8	25.22	odd	20
125.2.d.b.51.1		16	25.21	even	5
125.2.d.b.51.4		16	25.4	even	10
125.2.d.b.76.1		16	25.11	even	5
125.2.d.b.76.4		16	25.14	even	10
125.2.e.b.49.2		8	25.2	odd	20
125.2.e.b.74.2		8	25.3	odd	20
225.2.m.a.64.2		8	75.47	even	20
225.2.m.a.109.2		8	75.23	even	20
400.2.y.c.209.1		8	100.23	even	20
400.2.y.c.289.1		8	100.47	even	20
625.2.a.f.1.1		8	25.9	even	10
625.2.a.f.1.8		8	25.16	even	5
625.2.b.c.624.1		8	25.13	odd	20
625.2.b.c.624.8		8	25.12	odd	20
625.2.d.o.126.1		16	25.19	even	10	inner
625.2.d.o.126.4		16	25.6	even	5	inner
625.2.d.o.501.1		16	5.4	even	2	inner
625.2.d.o.501.4		16	1.1	even	1	trivial
625.2.e.a.124.2		8	5.2	odd	4
625.2.e.a.499.2		8	25.8	odd	20
625.2.e.i.124.1		8	5.3	odd	4
625.2.e.i.499.1		8	25.17	odd	20
5625.2.a.x.1.1		8	75.41	odd	10
5625.2.a.x.1.8		8	75.59	odd	10
10000.2.a.bj.1.4		8	100.91	odd	10
10000.2.a.bj.1.5		8	100.59	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.713605 - 2.19625i) q^{2} +(-0.384204 - 0.279141i) q^{3} +(-2.69625 - 1.95894i) q^{4} +(-0.887234 + 0.644613i) q^{6} +3.03582 q^{7} +(-2.48990 + 1.80902i) q^{8} +(-0.857358 - 2.63868i) q^{9} +(0.618034 - 1.90211i) q^{11} +(0.489091 + 1.50527i) q^{12} +(-0.441032 - 1.35736i) q^{13} +(2.16637 - 6.66742i) q^{14} +(0.136498 + 0.420099i) q^{16} +(-1.50497 + 1.09343i) q^{17} -6.40701 q^{18} +(-0.730800 + 0.530958i) q^{19} +(-1.16637 - 0.847421i) q^{21} +(-3.73648 - 2.71472i) q^{22} +(-1.02882 + 3.16637i) q^{23} +1.46160 q^{24} -3.29582 q^{26} +(-0.847421 + 2.60809i) q^{27} +(-8.18532 - 5.94699i) q^{28} +(-3.20619 - 2.32943i) q^{29} +(5.21004 - 3.78532i) q^{31} -5.13532 q^{32} +(-0.768409 + 0.558282i) q^{33} +(1.32748 + 4.08557i) q^{34} +(-2.85736 + 8.79404i) q^{36} +(1.18051 + 3.63324i) q^{37} +(0.644613 + 1.98391i) q^{38} +(-0.209447 + 0.644613i) q^{39} +(-0.566805 - 1.74445i) q^{41} +(-2.69348 + 1.95693i) q^{42} -3.59445 q^{43} +(-5.39250 + 3.91788i) q^{44} +(6.21998 + 4.51908i) q^{46} +(3.88324 + 2.82134i) q^{47} +(0.0648235 - 0.199506i) q^{48} +2.21619 q^{49} +0.883436 q^{51} +(-1.46985 + 4.52373i) q^{52} +(7.68949 + 5.58674i) q^{53} +(5.12330 + 3.72230i) q^{54} +(-7.55888 + 5.49184i) q^{56} +0.428989 q^{57} +(-7.40398 + 5.37930i) q^{58} +(3.28968 + 10.1246i) q^{59} +(4.41097 - 13.5756i) q^{61} +(-4.59559 - 14.1438i) q^{62} +(-2.60278 - 8.01054i) q^{63} +(-3.93759 + 12.1186i) q^{64} +(0.677786 + 2.08601i) q^{66} +(8.64854 - 6.28353i) q^{67} +6.19974 q^{68} +(1.27914 - 0.929350i) q^{69} +(-10.0802 - 7.32371i) q^{71} +(6.90814 + 5.01906i) q^{72} +(0.0827026 - 0.254532i) q^{73} +8.82193 q^{74} +3.01054 q^{76} +(1.87624 - 5.77447i) q^{77} +(1.26627 + 0.919998i) q^{78} +(6.93470 + 5.03835i) q^{79} +(-5.68017 + 4.12688i) q^{81} -4.23572 q^{82} +(10.2083 - 7.41677i) q^{83} +(1.48479 + 4.56972i) q^{84} +(-2.56502 + 7.89432i) q^{86} +(0.581593 + 1.78996i) q^{87} +(1.90211 + 5.85410i) q^{88} +(-1.47338 + 4.53460i) q^{89} +(-1.33889 - 4.12069i) q^{91} +(8.97669 - 6.52195i) q^{92} -3.05836 q^{93} +(8.96746 - 6.51524i) q^{94} +(1.97301 + 1.43348i) q^{96} +(8.05623 + 5.85319i) q^{97} +(1.58148 - 4.86730i) q^{98} -5.54893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{4} + 12 q^{6} - 2 q^{9} - 8 q^{11} + 14 q^{14} - 4 q^{16} - 20 q^{19} + 2 q^{21} + 40 q^{24} + 12 q^{26} - 30 q^{29} + 2 q^{31} + 24 q^{34} - 34 q^{36} - 24 q^{39} - 18 q^{41} - 16 q^{44} + 32 q^{46}+ \cdots + 16 q^{99}+O(q^{100}) \) 16 * q - 8 * q^4 + 12 * q^6 - 2 * q^9 - 8 * q^11 + 14 * q^14 - 4 * q^16 - 20 * q^19 + 2 * q^21 + 40 * q^24 + 12 * q^26 - 30 * q^29 + 2 * q^31 + 24 * q^34 - 34 * q^36 - 24 * q^39 - 18 * q^41 - 16 * q^44 + 32 * q^46 - 28 * q^49 - 8 * q^51 + 20 * q^54 - 30 * q^56 - 30 * q^59 + 12 * q^61 + 52 * q^64 - 36 * q^66 + 26 * q^69 - 58 * q^71 + 24 * q^74 - 40 * q^76 + 20 * q^79 - 24 * q^81 + 54 * q^84 + 32 * q^86 - 80 * q^89 + 2 * q^91 + 14 * q^94 + 22 * q^96 + 16 * q^99

Introduction

L-functions

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