LMFDB - Embedded newform 625.2.d.p.376.4

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} + 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			376.4
Root			$-1.63097i$ of defining polynomial
Character	$\chi$	$=$	625.376
Dual form			625.2.d.p.251.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.15604 + 1.56645i) q^{2} +(-0.234569 - 0.721930i) q^{3} +(1.57669 + 4.85257i) q^{4} +(0.625130 - 1.92395i) q^{6} +2.04213 q^{7} +(-2.55484 + 7.86300i) q^{8} +(1.96089 - 1.42467i) q^{9} +O(q^{10})$	\(q+(2.15604 + 1.56645i) q^{2} +(-0.234569 - 0.721930i) q^{3} +(1.57669 + 4.85257i) q^{4} +(0.625130 - 1.92395i) q^{6} +2.04213 q^{7} +(-2.55484 + 7.86300i) q^{8} +(1.96089 - 1.42467i) q^{9} +(-1.09110 - 0.792729i) q^{11} +(3.13337 - 2.27653i) q^{12} +(1.06761 - 0.775663i) q^{13} +(4.40291 + 3.19890i) q^{14} +(-9.56969 + 6.95279i) q^{16} +(-1.26301 + 3.88713i) q^{17} +6.45944 q^{18} +(-1.51010 + 4.64762i) q^{19} +(-0.479021 - 1.47427i) q^{21} +(-1.11068 - 3.41831i) q^{22} +(-2.21361 - 1.60828i) q^{23} +6.27582 q^{24} +3.51685 q^{26} +(-3.33081 - 2.41997i) q^{27} +(3.21981 + 9.90957i) q^{28} +(-1.42739 - 4.39306i) q^{29} +(2.21172 - 6.80697i) q^{31} -14.9886 q^{32} +(-0.316357 + 0.973647i) q^{33} +(-8.81211 + 6.40237i) q^{34} +(10.0050 + 7.26908i) q^{36} +(-6.99508 + 5.08223i) q^{37} +(-10.5361 + 7.65495i) q^{38} +(-0.810403 - 0.588793i) q^{39} +(8.17073 - 5.93639i) q^{41} +(1.27660 - 3.92896i) q^{42} -2.43460 q^{43} +(2.12644 - 6.54452i) q^{44} +(-2.25333 - 6.93505i) q^{46} +(-2.33985 - 7.20133i) q^{47} +(7.26419 + 5.27774i) q^{48} -2.82971 q^{49} +3.10250 q^{51} +(5.44725 + 3.95766i) q^{52} +(0.191975 + 0.590839i) q^{53} +(-3.39058 - 10.4351i) q^{54} +(-5.21732 + 16.0573i) q^{56} +3.70948 q^{57} +(3.80402 - 11.7076i) q^{58} +(9.17521 - 6.66618i) q^{59} +(-0.523849 - 0.380599i) q^{61} +(15.4314 - 11.2115i) q^{62} +(4.00439 - 2.90936i) q^{63} +(-13.1766 - 9.57336i) q^{64} +(-2.20725 + 1.60366i) q^{66} +(-3.38029 + 10.4035i) q^{67} -20.8539 q^{68} +(-0.641823 + 1.97533i) q^{69} +(-0.912311 - 2.80781i) q^{71} +(6.19241 + 19.0583i) q^{72} +(10.9533 + 7.95802i) q^{73} -23.0428 q^{74} -24.9339 q^{76} +(-2.22816 - 1.61886i) q^{77} +(-0.824945 - 2.53892i) q^{78} +(0.583824 + 1.79683i) q^{79} +(1.28123 - 3.94323i) q^{81} +26.9155 q^{82} +(-0.733857 + 2.25858i) q^{83} +(6.39875 - 4.64896i) q^{84} +(-5.24909 - 3.81368i) q^{86} +(-2.83666 + 2.06096i) q^{87} +(9.02081 - 6.55400i) q^{88} +(-5.93723 - 4.31365i) q^{89} +(2.18020 - 1.58400i) q^{91} +(4.31411 - 13.2775i) q^{92} -5.43296 q^{93} +(6.23574 - 19.1916i) q^{94} +(3.51586 + 10.8207i) q^{96} +(-1.79204 - 5.51532i) q^{97} +(-6.10097 - 4.43261i) q^{98} -3.26890 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}+O(q^{10}) $ 16 * q + 5 * q^3 - 8 * q^4 - 3 * q^6 - 20 * q^7 + 10 * q^8 + 3 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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 $

$2$	2.15604	+	1.56645i	1.52455	+	1.10765i	0.959173	+	0.282818i	$0.0912694\pi$
$2$	2.15604	+	1.56645i	1.52455	+	1.10765i	0.565377	+	0.824832i	$0.308731\pi$
$3$	−0.234569	−	0.721930i	−0.135429	−	0.416807i	0.860228	−	0.509910i	$-0.170321\pi$
$3$	−0.234569	−	0.721930i	−0.135429	−	0.416807i	−0.995656	+	0.0931033i	$0.970321\pi$
$4$	1.57669	+	4.85257i	0.788347	+	2.42628i
$5$		0			0
$5$		0			0
$6$	0.625130	−	1.92395i	0.255208	−	0.785451i
$7$	2.04213			0.771852			0.385926	−	0.922530i	$-0.373882\pi$
$7$	2.04213			0.771852			0.385926	+	0.922530i	$0.373882\pi$
$8$	−2.55484	+	7.86300i	−0.903273	+	2.77999i
$9$	1.96089	−	1.42467i	0.653630	−	0.474890i
$10$		0			0
$11$	−1.09110	−	0.792729i	−0.328979	−	0.239017i	0.411019	−	0.911627i	$-0.365173\pi$
$11$	−1.09110	−	0.792729i	−0.328979	−	0.239017i	−0.739997	+	0.672610i	$0.765173\pi$
$12$	3.13337	−	2.27653i	0.904526	−	0.657177i
$13$	1.06761	−	0.775663i	0.296101	−	0.215130i	−0.429808	−	0.902920i	$-0.641419\pi$
$13$	1.06761	−	0.775663i	0.296101	−	0.215130i	0.725910	+	0.687790i	$0.241419\pi$
$14$	4.40291	+	3.19890i	1.17673	+	0.854943i
$15$		0			0
$16$	−9.56969	+	6.95279i	−2.39242	+	1.73820i
$17$	−1.26301	+	3.88713i	−0.306324	+	0.942768i	0.672856	+	0.739774i	$0.265067\pi$
$17$	−1.26301	+	3.88713i	−0.306324	+	0.942768i	−0.979180	+	0.202995i	$0.934933\pi$
$18$	6.45944			1.52250
$19$	−1.51010	+	4.64762i	−0.346442	+	1.06624i	0.614366	+	0.789021i	$0.289412\pi$
$19$	−1.51010	+	4.64762i	−0.346442	+	1.06624i	−0.960807	+	0.277216i	$0.910588\pi$
$20$		0			0
$21$	−0.479021	−	1.47427i	−0.104531	−	0.321713i
$22$	−1.11068	−	3.41831i	−0.236797	−	0.728787i
$23$	−2.21361	−	1.60828i	−0.461570	−	0.335350i	0.332577	−	0.943076i	$-0.392082\pi$
$23$	−2.21361	−	1.60828i	−0.461570	−	0.335350i	−0.794147	+	0.607726i	$0.792082\pi$
$24$	6.27582			1.28105
$25$		0			0
$26$	3.51685			0.689711
$27$	−3.33081	−	2.41997i	−0.641015	−	0.465724i
$28$	3.21981	+	9.90957i	0.608488	+	1.87273i
$29$	−1.42739	−	4.39306i	−0.265060	−	0.815771i	−0.991680	−	0.128731i	$-0.958910\pi$
$29$	−1.42739	−	4.39306i	−0.265060	−	0.815771i	0.726619	−	0.687040i	$-0.241090\pi$
$30$		0			0
$31$	2.21172	−	6.80697i	0.397236	−	1.22257i	−0.529970	−	0.848016i	$-0.677797\pi$
$31$	2.21172	−	6.80697i	0.397236	−	1.22257i	0.927206	−	0.374551i	$-0.122203\pi$
$32$	−14.9886			−2.64963
$33$	−0.316357	+	0.973647i	−0.0550707	+	0.169490i
$34$	−8.81211	+	6.40237i	−1.51126	+	1.09800i
$35$		0			0
$36$	10.0050	+	7.26908i	1.66751	+	1.21151i
$37$	−6.99508	+	5.08223i	−1.14998	+	0.835513i	−0.988479	−	0.151359i	$-0.951635\pi$
$37$	−6.99508	+	5.08223i	−1.14998	+	0.835513i	−0.161506	+	0.986872i	$0.551635\pi$
$38$	−10.5361	+	7.65495i	−1.70919	+	1.24180i
$39$	−0.810403	−	0.588793i	−0.129768	−	0.0942823i
$40$		0			0
$41$	8.17073	−	5.93639i	1.27605	−	0.927108i	0.276628	−	0.960977i	$-0.410783\pi$
$41$	8.17073	−	5.93639i	1.27605	−	0.927108i	0.999426	+	0.0338695i	$0.0107830\pi$
$42$	1.27660	−	3.92896i	0.196983	−	0.606252i
$43$	−2.43460			−0.371272			−0.185636	−	0.982619i	$-0.559435\pi$
$43$	−2.43460			−0.371272			−0.185636	+	0.982619i	$0.559435\pi$
$44$	2.12644	−	6.54452i	0.320573	−	0.986623i
$45$		0			0
$46$	−2.25333	−	6.93505i	−0.332236	−	1.02252i
$47$	−2.33985	−	7.20133i	−0.341303	−	1.05042i	−0.963534	−	0.267588i	$-0.913774\pi$
$47$	−2.33985	−	7.20133i	−0.341303	−	1.05042i	0.622231	−	0.782834i	$-0.286226\pi$
$48$	7.26419	+	5.27774i	1.04849	+	0.761776i
$49$	−2.82971			−0.404244
$50$		0			0
$51$	3.10250			0.434437
$52$	5.44725	+	3.95766i	0.755398	+	0.548829i
$53$	0.191975	+	0.590839i	0.0263698	+	0.0811579i	0.963375	−	0.268157i	$-0.0864145\pi$
$53$	0.191975	+	0.590839i	0.0263698	+	0.0811579i	−0.937006	+	0.349315i	$0.886414\pi$
$54$	−3.39058	−	10.4351i	−0.461399	−	1.42004i
$55$		0			0
$56$	−5.21732	+	16.0573i	−0.697193	+	2.14574i
$57$	3.70948			0.491333
$58$	3.80402	−	11.7076i	0.499492	−	1.53728i
$59$	9.17521	−	6.66618i	1.19451	−	0.867862i	0.200777	−	0.979637i	$-0.435653\pi$
$59$	9.17521	−	6.66618i	1.19451	−	0.867862i	0.993734	+	0.111775i	$0.0356535\pi$
$60$		0			0
$61$	−0.523849	−	0.380599i	−0.0670720	−	0.0487307i	0.553744	−	0.832687i	$-0.313199\pi$
$61$	−0.523849	−	0.380599i	−0.0670720	−	0.0487307i	−0.620816	+	0.783956i	$0.713199\pi$
$62$	15.4314	−	11.2115i	1.95978	−	1.42387i
$63$	4.00439	−	2.90936i	0.504506	−	0.366545i
$64$	−13.1766	−	9.57336i	−1.64708	−	1.19667i
$65$		0			0
$66$	−2.20725	+	1.60366i	−0.271694	+	0.197397i
$67$	−3.38029	+	10.4035i	−0.412969	+	1.27099i	0.501087	+	0.865397i	$0.332934\pi$
$67$	−3.38029	+	10.4035i	−0.412969	+	1.27099i	−0.914055	+	0.405590i	$0.867066\pi$
$68$	−20.8539			−2.52891
$69$	−0.641823	+	1.97533i	−0.0772664	+	0.237802i
$70$		0			0
$71$	−0.912311	−	2.80781i	−0.108271	−	0.333225i	0.882213	−	0.470851i	$-0.156053\pi$
$71$	−0.912311	−	2.80781i	−0.108271	−	0.333225i	−0.990484	+	0.137625i	$0.956053\pi$
$72$	6.19241	+	19.0583i	0.729783	+	2.24604i
$73$	10.9533	+	7.95802i	1.28198	+	0.931415i	0.999611	−	0.0278896i	$-0.00887869\pi$
$73$	10.9533	+	7.95802i	1.28198	+	0.931415i	0.282372	+	0.959305i	$0.408879\pi$
$74$	−23.0428			−2.67867
$75$		0			0
$76$	−24.9339			−2.86011
$77$	−2.22816	−	1.61886i	−0.253923	−	0.184486i
$78$	−0.824945	−	2.53892i	−0.0934067	−	0.287476i
$79$	0.583824	+	1.79683i	0.0656853	+	0.202159i	0.978513	−	0.206187i	$-0.0661057\pi$
$79$	0.583824	+	1.79683i	0.0656853	+	0.202159i	−0.912827	+	0.408346i	$0.866106\pi$
$80$		0			0
$81$	1.28123	−	3.94323i	0.142359	−	0.438137i
$82$	26.9155			2.97232
$83$	−0.733857	+	2.25858i	−0.0805513	+	0.247911i	−0.983220	−	0.182425i	$-0.941605\pi$
$83$	−0.733857	+	2.25858i	−0.0805513	+	0.247911i	0.902668	+	0.430337i	$0.141605\pi$
$84$	6.39875	−	4.64896i	0.698161	−	0.507243i
$85$		0			0
$86$	−5.24909	−	3.81368i	−0.566024	−	0.411240i
$87$	−2.83666	+	2.06096i	−0.304122	+	0.220958i
$88$	9.02081	−	6.55400i	0.961622	−	0.698659i
$89$	−5.93723	−	4.31365i	−0.629345	−	0.457246i	0.226828	−	0.973935i	$-0.427164\pi$
$89$	−5.93723	−	4.31365i	−0.629345	−	0.457246i	−0.856173	+	0.516689i	$0.827164\pi$
$90$		0			0
$91$	2.18020	−	1.58400i	0.228547	−	0.166049i
$92$	4.31411	−	13.2775i	0.449777	−	1.38427i
$93$	−5.43296			−0.563371
$94$	6.23574	−	19.1916i	0.643167	−	1.97946i
$95$		0			0
$96$	3.51586	+	10.8207i	0.358836	+	1.10438i
$97$	−1.79204	−	5.51532i	−0.181954	−	0.559996i	0.817929	−	0.575319i	$-0.195122\pi$
$97$	−1.79204	−	5.51532i	−0.181954	−	0.559996i	−0.999883	+	0.0153235i	$0.995122\pi$
$98$	−6.10097	−	4.43261i	−0.616291	−	0.447761i
$99$	−3.26890			−0.328537
$100$		0			0
$101$	11.5536			1.14962			0.574812	−	0.818285i	$-0.305075\pi$
$101$	11.5536			1.14962			0.574812	+	0.818285i	$0.305075\pi$
$102$	6.68912	+	4.85993i	0.662321	+	0.481205i
$103$	−3.58680	−	11.0390i	−0.353418	−	1.08771i	−0.956921	−	0.290348i	$-0.906229\pi$
$103$	−3.58680	−	11.0390i	−0.353418	−	1.08771i	0.603503	−	0.797361i	$-0.293771\pi$
$104$	3.37147	+	10.3763i	0.330599	+	1.01748i
$105$		0			0
$106$	−0.511616	+	1.57459i	−0.0496925	+	0.152938i
$107$	−10.1703			−0.983204			−0.491602	−	0.870820i	$-0.663588\pi$
$107$	−10.1703			−0.983204			−0.491602	+	0.870820i	$0.663588\pi$
$108$	6.49142	−	19.9785i	0.624637	−	1.92244i
$109$	−0.966573	+	0.702257i	−0.0925809	+	0.0672640i	−0.633113	−	0.774060i	$-0.718223\pi$
$109$	−0.966573	+	0.702257i	−0.0925809	+	0.0672640i	0.540532	+	0.841324i	$0.318223\pi$
$110$		0			0
$111$	5.30985	+	3.85783i	0.503988	+	0.366169i
$112$	−19.5425	+	14.1985i	−1.84660	+	1.34163i
$113$	3.62647	−	2.63479i	0.341150	−	0.247860i	−0.403997	−	0.914760i	$-0.632379\pi$
$113$	3.62647	−	2.63479i	0.341150	−	0.247860i	0.745147	+	0.666900i	$0.232379\pi$
$114$	7.99780	+	5.81074i	0.749062	+	0.544226i
$115$		0			0
$116$	19.0671	−	13.8530i	1.77033	−	1.28622i
$117$	0.988400	−	3.04198i	0.0913776	−	0.281231i
$118$	30.2244			2.78238
$119$	−2.57922	+	7.93803i	−0.236437	+	0.727678i
$120$		0			0
$121$	−2.83711	−	8.73173i	−0.257919	−	0.793794i
$122$	−0.533249	−	1.64117i	−0.0482781	−	0.148585i
$123$	−6.20226	−	4.50621i	−0.559239	−	0.406311i
$124$	36.5185			3.27946
$125$		0			0
$126$	13.1910			1.17515
$127$	−3.37914	−	2.45509i	−0.299850	−	0.217854i	0.427679	−	0.903931i	$-0.359331\pi$
$127$	−3.37914	−	2.45509i	−0.299850	−	0.217854i	−0.727529	+	0.686077i	$0.759331\pi$
$128$	−4.14959	−	12.7711i	−0.366776	−	1.12882i
$129$	0.571082	+	1.75761i	0.0502809	+	0.154749i
$130$		0			0
$131$	1.04730	−	3.22327i	0.0915032	−	0.281618i	−0.894823	−	0.446420i	$-0.852699\pi$
$131$	1.04730	−	3.22327i	0.0915032	−	0.281618i	0.986327	+	0.164802i	$0.0526986\pi$
$132$	−5.22349			−0.454646
$133$	−3.08383	+	9.49104i	−0.267402	+	0.822978i
$134$	−23.5846	+	17.1352i	−2.03740	+	1.48026i
$135$		0			0
$136$	−27.3377	−	19.8620i	−2.34419	−	1.70315i
$137$	−6.74394	+	4.89976i	−0.576174	+	0.418615i	−0.837343	−	0.546678i	$-0.815892\pi$
$137$	−6.74394	+	4.89976i	−0.576174	+	0.418615i	0.261169	+	0.965293i	$0.415892\pi$
$138$	−4.47806	+	3.25350i	−0.381198	+	0.276956i
$139$	2.77780	+	2.01819i	0.235610	+	0.171181i	0.699325	−	0.714804i	$-0.253484\pi$
$139$	2.77780	+	2.01819i	0.235610	+	0.171181i	−0.463715	+	0.885984i	$0.653484\pi$
$140$		0			0
$141$	−4.65000	+	3.37842i	−0.391601	+	0.284514i
$142$	2.43132	−	7.48284i	0.204032	−	0.627946i
$143$	−1.77976			−0.148831
$144$	−8.85968	+	27.2673i	−0.738307	+	2.27228i
$145$		0			0
$146$	11.1498	+	34.3156i	0.922765	+	2.83998i
$147$	0.663763	+	2.04285i	0.0547463	+	0.168492i
$148$	−35.6910	−	25.9310i	−2.93378	−	2.13151i
$149$	9.96023			0.815974			0.407987	−	0.912988i	$-0.366231\pi$
$149$	9.96023			0.815974			0.407987	+	0.912988i	$0.366231\pi$
$150$		0			0
$151$	−21.0404			−1.71225			−0.856123	−	0.516772i	$-0.827134\pi$
$151$	−21.0404			−1.71225			−0.856123	+	0.516772i	$0.827134\pi$
$152$	−32.6862	−	23.7479i	−2.65120	−	1.92621i
$153$	3.06127	+	9.42161i	0.247489	+	0.761692i
$154$	−2.26815	−	6.98063i	−0.182772	−	0.562516i
$155$		0			0
$156$	1.57940	−	4.86088i	0.126453	−	0.389182i
$157$	−7.80843			−0.623181			−0.311590	−	0.950217i	$-0.600862\pi$
$157$	−7.80843			−0.623181			−0.311590	+	0.950217i	$0.600862\pi$
$158$	−1.55590	+	4.78856i	−0.123781	+	0.380957i
$159$	0.381513	−	0.277185i	0.0302559	−	0.0219822i
$160$		0			0
$161$	−4.52048	−	3.28432i	−0.356264	−	0.258841i
$162$	8.93928	−	6.49477i	0.702336	−	0.510277i
$163$	−9.44814	+	6.86447i	−0.740035	+	0.537667i	−0.892722	−	0.450608i	$-0.851207\pi$
$163$	−9.44814	+	6.86447i	−0.740035	+	0.537667i	0.152687	+	0.988275i	$0.451207\pi$
$164$	41.6895	+	30.2892i	3.25540	+	2.36519i
$165$		0			0
$166$	−5.12019	+	3.72004i	−0.397404	+	0.288731i
$167$	−2.32133	+	7.14431i	−0.179630	+	0.552844i	−0.999815	−	0.0192551i	$-0.993871\pi$
$167$	−2.32133	+	7.14431i	−0.179630	+	0.552844i	0.820185	+	0.572099i	$0.193871\pi$
$168$	12.8160			0.988779
$169$	−3.47909	+	10.7075i	−0.267622	+	0.823656i
$170$		0			0
$171$	3.66018	+	11.2649i	0.279901	+	0.861447i
$172$	−3.83861	−	11.8140i	−0.292692	−	0.900812i
$173$	4.29897	+	3.12338i	0.326844	+	0.237466i	0.739090	−	0.673606i	$-0.235256\pi$
$173$	4.29897	+	3.12338i	0.326844	+	0.237466i	−0.412246	+	0.911073i	$0.635256\pi$
$174$	−9.34436			−0.708394
$175$		0			0
$176$	15.9532			1.20251
$177$	−6.96474	−	5.06018i	−0.523502	−	0.380346i
$178$	−6.04377	−	18.6008i	−0.453000	−	1.39419i
$179$	0.403805	+	1.24279i	0.0301818	+	0.0928901i	0.965013	−	0.262203i	$-0.0844491\pi$
$179$	0.403805	+	1.24279i	0.0301818	+	0.0928901i	−0.934831	+	0.355093i	$0.884449\pi$
$180$		0			0
$181$	−6.23062	+	19.1759i	−0.463118	+	1.42533i	0.398215	+	0.917292i	$0.369630\pi$
$181$	−6.23062	+	19.1759i	−0.463118	+	1.42533i	−0.861334	+	0.508040i	$0.830370\pi$
$182$	7.18186			0.532355
$183$	−0.151887	+	0.467459i	−0.0112278	+	0.0345556i
$184$	18.3014	−	13.2967i	1.34919	−	0.980247i
$185$		0			0
$186$	−11.7137	−	8.51048i	−0.858888	−	0.624019i
$187$	4.45951	−	3.24002i	0.326111	−	0.236934i
$188$	31.2557	−	22.7086i	2.27956	−	1.65619i
$189$	−6.80194	−	4.94190i	−0.494769	−	0.359470i
$190$		0			0
$191$	−17.2286	+	12.5173i	−1.24662	+	0.905721i	−0.998021	−	0.0628858i	$-0.979970\pi$
$191$	−17.2286	+	12.5173i	−1.24662	+	0.905721i	−0.248597	+	0.968607i	$0.579970\pi$
$192$	−3.82047	+	11.7582i	−0.275719	+	0.848576i
$193$	7.99352			0.575386			0.287693	−	0.957723i	$-0.407112\pi$
$193$	7.99352			0.575386			0.287693	+	0.957723i	$0.407112\pi$
$194$	4.77580	−	14.6984i	0.342882	−	1.05528i
$195$		0			0
$196$	−4.46159	−	13.7314i	−0.318685	−	0.980811i
$197$	6.70611	+	20.6393i	0.477790	+	1.47049i	0.842157	+	0.539232i	$0.181285\pi$
$197$	6.70611	+	20.6393i	0.477790	+	1.47049i	−0.364367	+	0.931255i	$0.618715\pi$
$198$	−7.04788	−	5.12059i	−0.500871	−	0.363904i
$199$	9.34240			0.662265			0.331133	−	0.943584i	$-0.392569\pi$
$199$	9.34240			0.662265			0.331133	+	0.943584i	$0.392569\pi$
$200$		0			0
$201$	8.30350			0.585684
$202$	24.9100	+	18.0982i	1.75266	+	1.27338i
$203$	−2.91492	−	8.97120i	−0.204587	−	0.629655i
$204$	4.89170	+	15.0551i	0.342487	+	1.05407i
$205$		0			0
$206$	9.55887	−	29.4192i	0.665998	−	2.04973i
$207$	−6.63192			−0.460951
$208$	−4.82367	+	14.8457i	−0.334461	+	1.02937i
$209$	5.33198	−	3.87391i	0.368821	−	0.267964i
$210$		0			0
$211$	5.56723	+	4.04483i	0.383264	+	0.278457i	0.762690	−	0.646765i	$-0.223878\pi$
$211$	5.56723	+	4.04483i	0.383264	+	0.278457i	−0.379426	+	0.925222i	$0.623878\pi$
$212$	−2.56440	+	1.86314i	−0.176124	+	0.127961i
$213$	−1.81304	+	1.31725i	−0.124227	+	0.0902565i
$214$	−21.9277	−	15.9314i	−1.49894	−	1.08905i
$215$		0			0
$216$	27.5379	−	20.0075i	1.87372	−	1.36134i
$217$	4.51661	−	13.9007i	0.306608	−	0.943641i
$218$	−3.18402			−0.215649
$219$	3.17583	−	9.77421i	0.214603	−	0.660480i
$220$		0			0
$221$	1.66671	+	5.12961i	0.112115	+	0.345055i
$222$	5.40513	+	16.6353i	0.362768	+	1.11649i
$223$	6.88875	+	5.00497i	0.461305	+	0.335158i	0.794043	−	0.607862i	$-0.207972\pi$
$223$	6.88875	+	5.00497i	0.461305	+	0.335158i	−0.332738	+	0.943019i	$0.607972\pi$
$224$	−30.6086			−2.04512
$225$		0			0
$226$	11.9461			0.794643
$227$	16.9761	+	12.3338i	1.12674	+	0.818625i	0.985217	−	0.171310i	$-0.0547999\pi$
$227$	16.9761	+	12.3338i	1.12674	+	0.818625i	0.141524	+	0.989935i	$0.454800\pi$
$228$	5.84872	+	18.0005i	0.387341	+	1.19211i
$229$	9.19724	+	28.3062i	0.607771	+	1.87053i	0.476488	+	0.879181i	$0.341910\pi$
$229$	9.19724	+	28.3062i	0.607771	+	1.87053i	0.131283	+	0.991345i	$0.458090\pi$
$230$		0			0
$231$	−0.646042	+	1.98831i	−0.0425064	+	0.130821i
$232$	38.1894			2.50726
$233$	0.701943	−	2.16036i	0.0459858	−	0.141530i	−0.925427	−	0.378925i	$-0.876294\pi$
$233$	0.701943	−	2.16036i	0.0459858	−	0.141530i	0.971413	+	0.237395i	$0.0762937\pi$
$234$	6.89616	−	5.01035i	0.450816	−	0.327537i
$235$		0			0
$236$	46.8146	+	34.0128i	3.04737	+	2.21404i
$237$	1.16024	−	0.842960i	0.0753654	−	0.0547562i
$238$	−17.9955	+	13.0745i	−1.16647	+	0.847492i
$239$	−12.4838	−	9.06999i	−0.807508	−	0.586689i	0.105599	−	0.994409i	$-0.466324\pi$
$239$	−12.4838	−	9.06999i	−0.807508	−	0.586689i	−0.913107	+	0.407720i	$0.866324\pi$
$240$		0			0
$241$	3.91713	−	2.84596i	0.252324	−	0.183324i	−0.454432	−	0.890781i	$-0.650158\pi$
$241$	3.91713	−	2.84596i	0.252324	−	0.183324i	0.706756	+	0.707457i	$0.250158\pi$
$242$	7.56094	−	23.2702i	0.486035	−	1.49586i
$243$	−15.4986			−0.994235
$244$	1.02093	−	3.14210i	0.0653584	−	0.201152i
$245$		0			0
$246$	−6.31356	−	19.4311i	−0.402538	−	1.23888i
$247$	1.99279	+	6.13318i	0.126798	+	0.390245i
$248$	47.8726	+	34.7815i	3.03991	+	2.20862i
$249$	1.80268			0.114240
$250$		0			0
$251$	−17.8293			−1.12537			−0.562687	−	0.826670i	$-0.690232\pi$
$251$	−17.8293			−1.12537			−0.562687	+	0.826670i	$0.690232\pi$
$252$	20.4316	+	14.8444i	1.28707	+	0.935109i
$253$	1.14034	+	3.50959i	0.0716923	+	0.220646i
$254$	−3.43977	−	10.5865i	−0.215831	−	0.664258i
$255$		0			0
$256$	0.992687	−	3.05518i	0.0620430	−	0.190949i
$257$	−5.88929			−0.367364			−0.183682	−	0.982986i	$-0.558802\pi$
$257$	−5.88929			−0.367364			−0.183682	+	0.982986i	$0.558802\pi$
$258$	−1.52194	+	4.68405i	−0.0947518	+	0.291616i
$259$	−14.2849	+	10.3786i	−0.887618	+	0.644892i
$260$		0			0
$261$	−9.05763	−	6.58075i	−0.560653	−	0.407338i
$262$	7.30713	−	5.30894i	0.451436	−	0.327987i
$263$	19.1553	−	13.9172i	1.18117	−	0.858168i	0.188865	−	0.982003i	$-0.439519\pi$
$263$	19.1553	−	13.9172i	1.18117	−	0.858168i	0.992303	+	0.123835i	$0.0395192\pi$
$264$	−6.84754	−	4.97503i	−0.421437	−	0.306192i
$265$		0			0
$266$	−21.5161	+	15.6324i	−1.31924	+	0.958484i
$267$	−1.72146	+	5.29812i	−0.105352	+	0.324240i
$268$	−55.8132			−3.40934
$269$	4.24776	−	13.0733i	0.258991	−	0.797091i	−0.734027	−	0.679121i	$-0.762361\pi$
$269$	4.24776	−	13.0733i	0.258991	−	0.797091i	0.993017	−	0.117970i	$-0.0376388\pi$
$270$		0			0
$271$	2.31726	+	7.13180i	0.140764	+	0.433226i	0.996442	−	0.0842822i	$-0.0268597\pi$
$271$	2.31726	+	7.13180i	0.140764	+	0.433226i	−0.855678	+	0.517508i	$0.826860\pi$
$272$	−14.9398	−	45.9801i	−0.905860	−	2.78795i
$273$	−1.65495	−	1.20239i	−0.100162	−	0.0727720i
$274$	−22.2155			−1.34209
$275$		0			0
$276$	−10.5974			−0.637887
$277$	2.29597	+	1.66812i	0.137952	+	0.100228i	0.654621	−	0.755957i	$-0.272828\pi$
$277$	2.29597	+	1.66812i	0.137952	+	0.100228i	−0.516669	+	0.856185i	$0.672828\pi$
$278$	2.82764	+	8.70259i	0.169591	+	0.521947i
$279$	−5.36075	−	16.4987i	−0.320940	−	0.987750i
$280$		0			0
$281$	−7.09532	+	21.8372i	−0.423272	+	1.30270i	0.481368	+	0.876519i	$0.340140\pi$
$281$	−7.09532	+	21.8372i	−0.423272	+	1.30270i	−0.904640	+	0.426177i	$0.859860\pi$
$282$	−15.3177			−0.912158
$283$	7.76395	−	23.8950i	0.461519	−	1.42041i	−0.401789	−	0.915732i	$-0.631612\pi$
$283$	7.76395	−	23.8950i	0.461519	−	1.42041i	0.863308	−	0.504677i	$-0.168388\pi$
$284$	12.1866	−	8.85410i	0.723143	−	0.525394i
$285$		0			0
$286$	−3.83723	−	2.78791i	−0.226900	−	0.164853i
$287$	16.6857	−	12.1229i	0.984925	−	0.715590i
$288$	−29.3910	+	21.3538i	−1.73188	+	1.25828i
$289$	0.238675	+	0.173407i	0.0140397	+	0.0102004i
$290$		0			0
$291$	−3.56132	+	2.58745i	−0.208768	+	0.151679i
$292$	−21.3468	+	65.6988i	−1.24923	+	3.84473i
$293$	28.8755			1.68692			0.843461	−	0.537190i	$-0.180514\pi$
$293$	28.8755			1.68692			0.843461	+	0.537190i	$0.180514\pi$
$294$	−1.76894	+	5.44423i	−0.103167	+	0.317514i
$295$		0			0
$296$	−22.0902	−	67.9866i	−1.28397	−	3.95164i
$297$	1.71586	+	5.28086i	0.0995640	+	0.306427i
$298$	21.4747	+	15.6022i	1.24399	+	0.903814i
$299$	−3.61076			−0.208816
$300$		0			0
$301$	−4.97176			−0.286567
$302$	−45.3640	−	32.9589i	−2.61041	−	1.89657i
$303$	−2.71012	−	8.34088i	−0.155692	−	0.479171i
$304$	−17.8627	−	54.9757i	−1.02450	−	3.15308i
$305$		0			0
$306$	−8.15831	+	25.1087i	−0.466380	+	1.43537i
$307$	−23.9526			−1.36704			−0.683522	−	0.729930i	$-0.739553\pi$
$307$	−23.9526			−1.36704			−0.683522	+	0.729930i	$0.739553\pi$
$308$	4.34247	−	13.3648i	0.247435	−	0.761527i
$309$	−7.12806	+	5.17884i	−0.405501	+	0.294614i
$310$		0			0
$311$	7.99984	+	5.81222i	0.453629	+	0.329581i	0.791027	−	0.611781i	$-0.209547\pi$
$311$	7.99984	+	5.81222i	0.453629	+	0.329581i	−0.337398	+	0.941362i	$0.609547\pi$
$312$	6.70013	−	4.86793i	0.379320	−	0.275592i
$313$	−15.1922	+	11.0378i	−0.858712	+	0.623891i	−0.927534	−	0.373738i	$-0.878076\pi$
$313$	−15.1922	+	11.0378i	−0.858712	+	0.623891i	0.0688221	+	0.997629i	$0.478076\pi$
$314$	−16.8353	−	12.2316i	−0.950070	−	0.690267i
$315$		0			0
$316$	−7.79870	+	5.66609i	−0.438711	+	0.318742i
$317$	7.99793	−	24.6151i	0.449208	−	1.38252i	−0.428594	−	0.903497i	$-0.640991\pi$
$317$	7.99793	−	24.6151i	0.449208	−	1.38252i	0.877802	−	0.479024i	$-0.159009\pi$
$318$	1.25676			0.0704754
$319$	−1.92508	+	5.92480i	−0.107784	+	0.331725i
$320$		0			0
$321$	2.38565	+	7.34228i	0.133154	+	0.409806i
$322$	−4.60160	−	14.1623i	−0.256437	−	0.789232i
$323$	−16.1587	−	11.7399i	−0.899092	−	0.653228i
$324$	21.1549			1.17527
$325$		0			0
$326$	−31.1234			−1.72377
$327$	0.733709	+	0.533071i	0.0405742	+	0.0294789i
$328$	25.8028	+	79.4130i	1.42472	+	4.38485i
$329$	−4.77828	−	14.7060i	−0.263435	−	0.810770i
$330$		0			0
$331$	0.400929	−	1.23393i	0.0220371	−	0.0678231i	−0.939433	−	0.342732i	$-0.888648\pi$
$331$	0.400929	−	1.23393i	0.0220371	−	0.0678231i	0.961470	+	0.274909i	$0.0886477\pi$
$332$	−12.1170			−0.665006
$333$	−6.47610	+	19.9314i	−0.354888	+	1.09223i
$334$	−16.1961	+	11.7672i	−0.886212	+	0.643871i
$335$		0			0
$336$	14.8344	+	10.7778i	0.809283	+	0.587979i
$337$	−9.12322	+	6.62841i	−0.496974	+	0.361073i	−0.807860	−	0.589375i	$-0.799374\pi$
$337$	−9.12322	+	6.62841i	−0.496974	+	0.361073i	0.310886	+	0.950447i	$0.399374\pi$
$338$	−24.2739	+	17.6360i	−1.32033	+	0.959273i
$339$	−2.75279	−	2.00002i	−0.149511	−	0.108626i
$340$		0			0
$341$	−7.80928	+	5.67378i	−0.422896	+	0.307252i
$342$	−9.75443	+	30.0210i	−0.527459	+	1.62335i
$343$	−20.0735			−1.08387
$344$	6.22001	−	19.1432i	0.335360	−	1.03213i
$345$		0			0
$346$	4.37611	+	13.4683i	0.235261	+	0.724059i
$347$	−0.665933	−	2.04953i	−0.0357492	−	0.110025i	0.931590	−	0.363512i	$-0.118422\pi$
$347$	−0.665933	−	2.04953i	−0.0357492	−	0.110025i	−0.967339	+	0.253487i	$0.918422\pi$
$348$	−14.4735	−	10.5156i	−0.775860	−	0.563695i
$349$	5.60904			0.300245			0.150122	−	0.988667i	$-0.452033\pi$
$349$	5.60904			0.300245			0.150122	+	0.988667i	$0.452033\pi$
$350$		0			0
$351$	−5.43309			−0.289997
$352$	16.3540	+	11.8819i	0.871672	+	0.633307i
$353$	5.71587	+	17.5916i	0.304225	+	0.936308i	0.979965	+	0.199168i	$0.0638240\pi$
$353$	5.71587	+	17.5916i	0.304225	+	0.936308i	−0.675740	+	0.737140i	$0.736176\pi$
$354$	−7.08972	−	21.8199i	−0.376814	−	1.15971i
$355$		0			0
$356$	11.5711	−	35.6121i	0.613266	−	1.88744i
$357$	6.33571			0.335321
$358$	−1.07615	+	3.31204i	−0.0568761	+	0.175047i
$359$	−9.09737	+	6.60963i	−0.480141	+	0.348843i	−0.801380	−	0.598155i	$-0.795901\pi$
$359$	−9.09737	+	6.60963i	−0.480141	+	0.348843i	0.321239	+	0.946998i	$0.395901\pi$
$360$		0			0
$361$	−3.94866	−	2.86887i	−0.207824	−	0.150993i
$362$	−43.4716	+	31.5840i	−2.28482	+	1.66002i
$363$	−5.63820	+	4.09639i	−0.295929	+	0.215005i
$364$	11.1240	+	8.08205i	0.583056	+	0.423615i
$365$		0			0
$366$	−1.05973	+	0.769937i	−0.0553929	+	0.0402453i
$367$	8.82789	−	27.1695i	0.460812	−	1.41823i	−0.403362	−	0.915041i	$-0.632158\pi$
$367$	8.82789	−	27.1695i	0.460812	−	1.41823i	0.864174	−	0.503193i	$-0.167842\pi$
$368$	32.3656			1.68718
$369$	7.56452	−	23.2812i	0.393793	−	1.21197i
$370$		0			0
$371$	0.392038	+	1.20657i	0.0203536	+	0.0626419i
$372$	−8.56612	−	26.3638i	−0.444132	−	1.36690i
$373$	11.3948	+	8.27884i	0.590003	+	0.428662i	0.842316	−	0.538983i	$-0.181191\pi$
$373$	11.3948	+	8.27884i	0.590003	+	0.428662i	−0.252314	+	0.967646i	$0.581191\pi$
$374$	14.6902			0.759613
$375$		0			0
$376$	62.6020			3.22845
$377$	−4.93144	−	3.58290i	−0.253982	−	0.184529i
$378$	−6.92400	−	21.3099i	−0.356132	−	1.09606i
$379$	6.79538	+	20.9140i	0.349055	+	1.07428i	0.959377	+	0.282128i	$0.0910403\pi$
$379$	6.79538	+	20.9140i	0.349055	+	1.07428i	−0.610322	+	0.792154i	$0.708960\pi$
$380$		0			0
$381$	−0.979760	+	3.01539i	−0.0501946	+	0.154483i
$382$	−56.7534			−2.90376
$383$	4.55603	−	14.0220i	0.232802	−	0.716491i	−0.764603	−	0.644501i	$-0.777065\pi$
$383$	4.55603	−	14.0220i	0.232802	−	0.716491i	0.997405	−	0.0719898i	$-0.0229349\pi$
$384$	−8.24650	+	5.99143i	−0.420828	+	0.305749i
$385$		0			0
$386$	17.2344	+	12.5215i	0.877205	+	0.637327i
$387$	−4.77397	+	3.46850i	−0.242675	+	0.176314i
$388$	23.9380	−	17.3919i	1.21527	−	0.882942i
$389$	11.5340	+	8.37991i	0.584795	+	0.424879i	0.840450	−	0.541890i	$-0.182291\pi$
$389$	11.5340	+	8.37991i	0.584795	+	0.424879i	−0.255654	+	0.966768i	$0.582291\pi$
$390$		0			0
$391$	9.04742	−	6.57333i	0.457548	−	0.332428i
$392$	7.22946	−	22.2500i	0.365143	−	1.12379i
$393$	−2.57264			−0.129772
$394$	−17.8719	+	55.0039i	−0.900371	+	2.77106i
$395$		0			0
$396$	−5.15406	−	15.8626i	−0.259001	−	0.797124i
$397$	1.69670	+	5.22192i	0.0851551	+	0.262080i	0.984563	−	0.175029i	$-0.0560021\pi$
$397$	1.69670	+	5.22192i	0.0851551	+	0.262080i	−0.899408	+	0.437110i	$0.856002\pi$
$398$	20.1426	+	14.6344i	1.00966	+	0.733559i
$399$	7.57525			0.379237
$400$		0			0
$401$	26.7528			1.33597			0.667985	−	0.744175i	$-0.267157\pi$
$401$	26.7528			1.33597			0.667985	+	0.744175i	$0.267157\pi$
$402$	17.9027	+	13.0071i	0.892904	+	0.648733i
$403$	−2.91867	−	8.98273i	−0.145389	−	0.447462i
$404$	18.2165	+	56.0645i	0.906303	+	2.78931i
$405$		0			0
$406$	7.76830	−	23.9084i	0.385534	−	1.18655i
$407$	11.6612			0.578022
$408$	−7.92640	+	24.3950i	−0.392415	+	1.20773i
$409$	−4.15340	+	3.01762i	−0.205372	+	0.149212i	−0.685718	−	0.727868i	$-0.740511\pi$
$409$	−4.15340	+	3.01762i	−0.205372	+	0.149212i	0.480345	+	0.877080i	$0.340511\pi$
$410$		0			0
$411$	5.11921	+	3.71932i	0.252512	+	0.183461i
$412$	47.9124	−	34.8104i	2.36047	−	1.71498i
$413$	18.7370	−	13.6132i	0.921985	−	0.669861i
$414$	−14.2987	−	10.3886i	−0.702743	−	0.510572i
$415$		0			0
$416$	−16.0019	+	11.6261i	−0.784560	+	0.570016i
$417$	0.805405	−	2.47878i	0.0394409	−	0.121386i
$418$	17.5643			0.859096
$419$	9.84269	−	30.2927i	0.480847	−	1.47989i	−0.357060	−	0.934081i	$-0.616221\pi$
$419$	9.84269	−	30.2927i	0.480847	−	1.47989i	0.837907	−	0.545813i	$-0.183779\pi$
$420$		0			0
$421$	0.951909	+	2.92968i	0.0463932	+	0.142784i	0.971570	−	0.236753i	$-0.0760833\pi$
$421$	0.951909	+	2.92968i	0.0463932	+	0.142784i	−0.925177	+	0.379537i	$0.876083\pi$
$422$	5.66713	+	17.4416i	0.275871	+	0.849045i
$423$	−14.8477	−	10.7875i	−0.721920	−	0.524506i
$424$	−5.13623			−0.249437
$425$		0			0
$426$	−5.97240			−0.289364
$427$	−1.06977	−	0.777231i	−0.0517697	−	0.0376129i
$428$	−16.0355	−	49.3523i	−0.775106	−	2.38553i
$429$	0.417477	+	1.28486i	0.0201560	+	0.0620337i
$430$		0			0
$431$	7.21465	−	22.2044i	0.347517	−	1.06955i	−0.612705	−	0.790312i	$-0.709919\pi$
$431$	7.21465	−	22.2044i	0.347517	−	1.06955i	0.960222	−	0.279237i	$-0.0900815\pi$
$432$	48.7004			2.34310
$433$	−2.53831	+	7.81212i	−0.121984	+	0.375427i	−0.993339	−	0.115225i	$-0.963241\pi$
$433$	−2.53831	+	7.81212i	−0.121984	+	0.375427i	0.871356	+	0.490651i	$0.163241\pi$
$434$	31.5128	−	22.8954i	1.51266	−	1.09901i
$435$		0			0
$436$	−4.93174	−	3.58312i	−0.236187	−	0.171600i
$437$	10.8175	−	7.85936i	0.517470	−	0.375964i
$438$	22.1581	−	16.0988i	1.05875	−	0.769230i
$439$	19.6686	+	14.2901i	0.938731	+	0.682028i	0.948115	−	0.317928i	$-0.102987\pi$
$439$	19.6686	+	14.2901i	0.938731	+	0.682028i	−0.00938352	+	0.999956i	$0.502987\pi$
$440$		0			0
$441$	−5.54875	+	4.03140i	−0.264226	+	0.191972i
$442$	−4.44180	+	13.6705i	−0.211275	+	0.650238i
$443$	−0.0631363			−0.00299970			−0.00149985	−	0.999999i	$-0.500477\pi$
$443$	−0.0631363			−0.00299970			−0.00149985	+	0.999999i	$0.500477\pi$
$444$	−10.3484	+	31.8490i	−0.491112	+	1.51149i
$445$		0			0
$446$	7.01236	+	21.5818i	0.332045	+	1.02193i
$447$	−2.33636	−	7.19059i	−0.110506	−	0.340103i
$448$	−26.9083	−	19.5500i	−1.27130	−	0.923653i
$449$	−11.5711			−0.546074			−0.273037	−	0.962004i	$-0.588028\pi$
$449$	−11.5711			−0.546074			−0.273037	+	0.962004i	$0.588028\pi$
$450$		0			0
$451$	−13.6210			−0.641389
$452$	18.5033	+	13.4435i	0.870323	+	0.632327i
$453$	4.93544	+	15.1897i	0.231887	+	0.713676i
$454$	17.2807	+	53.1845i	0.811023	+	2.49607i
$455$		0			0
$456$	−9.47715	+	29.1677i	−0.443808	+	1.36590i
$457$	41.3967			1.93646			0.968228	−	0.250071i	$-0.0804539\pi$
$457$	41.3967			1.93646			0.968228	+	0.250071i	$0.0804539\pi$
$458$	−24.5108	+	75.4364i	−1.14531	+	3.52491i
$459$	13.6136	−	9.89086i	0.635428	−	0.461666i
$460$		0			0
$461$	−23.7614	−	17.2637i	−1.10668	−	0.804049i	−0.124541	−	0.992214i	$-0.539746\pi$
$461$	−23.7614	−	17.2637i	−1.10668	−	0.804049i	−0.982137	+	0.188166i	$0.939746\pi$
$462$	−4.50750	+	3.27489i	−0.209708	+	0.152362i
$463$	−24.7155	+	17.9569i	−1.14863	+	0.834527i	−0.988298	−	0.152536i	$-0.951256\pi$
$463$	−24.7155	+	17.9569i	−1.14863	+	0.834527i	−0.160330	+	0.987063i	$0.551256\pi$
$464$	44.2037	+	32.1159i	2.05211	+	1.49094i
$465$		0			0
$466$	4.89752	−	3.55826i	0.226873	−	0.164833i
$467$	−10.1095	+	31.1137i	−0.467810	+	1.43977i	0.387605	+	0.921826i	$0.373303\pi$
$467$	−10.1095	+	31.1137i	−0.467810	+	1.43977i	−0.855414	+	0.517944i	$0.826697\pi$
$468$	16.3198			0.754384
$469$	−6.90300	+	21.2452i	−0.318751	+	0.981014i
$470$		0			0
$471$	1.83162	+	5.63714i	0.0843966	+	0.259746i
$472$	28.9749	+	89.1756i	1.33368	+	4.10464i
$473$	2.65638	+	1.92998i	0.122141	+	0.0887404i
$474$	3.82197			0.175549
$475$		0			0
$476$	−42.5864			−1.95195
$477$	1.21819	+	0.885069i	0.0557772	+	0.0405245i
$478$	−12.7078	−	39.1105i	−0.581240	−	1.78887i
$479$	−3.81181	−	11.7315i	−0.174166	−	0.536028i	0.825428	−	0.564507i	$-0.190934\pi$
$479$	−3.81181	−	11.7315i	−0.174166	−	0.536028i	−0.999594	+	0.0284789i	$0.990934\pi$
$480$		0			0
$481$	−3.52592	+	10.8517i	−0.160768	+	0.494793i
$482$	12.9036			0.587741
$483$	−1.31069	+	4.03387i	−0.0596383	+	0.183548i
$484$	37.8980	−	27.5345i	1.72264	−	1.25157i
$485$		0			0
$486$	−33.4156	−	24.2779i	−1.51576	−	1.10127i
$487$	28.5552	−	20.7466i	1.29396	−	0.940117i	0.294083	−	0.955780i	$-0.404986\pi$
$487$	28.5552	−	20.7466i	1.29396	−	0.940117i	0.999877	+	0.0156629i	$0.00498588\pi$
$488$	4.33100	−	3.14665i	0.196055	−	0.142442i
$489$	7.17192	+	5.21070i	0.324325	+	0.235636i
$490$		0			0
$491$	−12.3906	+	9.00227i	−0.559178	+	0.406267i	−0.831158	−	0.556036i	$-0.812322\pi$
$491$	−12.3906	+	9.00227i	−0.559178	+	0.406267i	0.271980	+	0.962303i	$0.412322\pi$
$492$	12.0876	−	37.2018i	0.544951	−	1.67719i
$493$	18.8792			0.850278
$494$	−5.31081	+	16.3450i	−0.238945	+	0.735396i
$495$		0			0
$496$	26.1619	+	80.5182i	1.17471	+	3.61537i
$497$	−1.86306	−	5.73390i	−0.0835696	−	0.257201i
$498$	3.88665	+	2.82381i	0.174165	+	0.126538i
$499$	−35.1777			−1.57477			−0.787386	−	0.616461i	$-0.788566\pi$
$499$	−35.1777			−1.57477			−0.787386	+	0.616461i	$0.788566\pi$
$500$		0			0
$501$	5.70221			0.254756
$502$	−38.4406	−	27.9288i	−1.71569	−	1.24652i
$503$	−2.26662	−	6.97595i	−0.101064	−	0.311042i	0.887723	−	0.460378i	$-0.152286\pi$
$503$	−2.26662	−	6.97595i	−0.101064	−	0.311042i	−0.988786	+	0.149336i	$0.952286\pi$
$504$	12.6457	+	38.9195i	0.563284	+	1.73361i
$505$		0			0
$506$	−3.03901	+	9.35310i	−0.135100	+	0.415796i
$507$	8.54617			0.379549
$508$	6.58561	−	20.2684i	0.292189	−	0.899266i
$509$	−4.61704	+	3.35447i	−0.204647	+	0.148684i	−0.685388	−	0.728178i	$-0.740367\pi$
$509$	−4.61704	+	3.35447i	−0.204647	+	0.148684i	0.480742	+	0.876862i	$0.340367\pi$
$510$		0			0
$511$	22.3680	+	16.2513i	0.989502	+	0.718915i
$512$	−14.8015	+	10.7539i	−0.654139	+	0.475260i
$513$	16.2770	−	11.8259i	0.718647	−	0.522128i
$514$	−12.6975	−	9.22530i	−0.560065	−	0.406911i
$515$		0			0
$516$	−7.62849	+	5.54242i	−0.335826	+	0.243992i
$517$	−3.15569	+	9.71223i	−0.138787	+	0.427143i
$518$	−47.0563			−2.06753
$519$	1.24646	−	3.83620i	0.0547135	−	0.168391i
$520$		0			0
$521$	−10.2254	−	31.4706i	−0.447983	−	1.37875i	−0.879179	−	0.476492i	$-0.841908\pi$
$521$	−10.2254	−	31.4706i	−0.447983	−	1.37875i	0.431196	−	0.902258i	$-0.358092\pi$
$522$	−9.22016	−	28.3767i	−0.403555	−	1.24202i
$523$	−25.4613	−	18.4987i	−1.11335	−	0.808894i	−0.130159	−	0.991493i	$-0.541549\pi$
$523$	−25.4613	−	18.4987i	−1.11335	−	0.808894i	−0.983187	+	0.182600i	$0.941549\pi$
$524$	17.2924			0.755421
$525$		0			0
$526$	63.1002			2.75130
$527$	23.6662	+	17.1945i	1.03091	+	0.749003i
$528$	−3.74212	−	11.5171i	−0.162855	−	0.501216i
$529$	−4.79389	−	14.7541i	−0.208430	−	0.641481i
$530$		0			0
$531$	8.49447	−	26.1433i	0.368629	−	1.13452i
$532$	−50.9182			−2.20758
$533$	4.11851	−	12.6755i	0.178393	−	0.549036i
$534$	−12.0108	+	8.72636i	−0.519758	+	0.377627i
$535$		0			0
$536$	−73.1664	−	53.1585i	−3.16031	−	2.29610i
$537$	0.802484	−	0.583039i	0.0346297	−	0.0251600i
$538$	29.6370	−	21.5326i	1.27774	−	0.928335i
$539$	3.08749	+	2.24319i	0.132988	+	0.0966212i
$540$		0			0
$541$	18.5070	−	13.4461i	0.795678	−	0.578094i	−0.113965	−	0.993485i	$-0.536355\pi$
$541$	18.5070	−	13.4461i	0.795678	−	0.578094i	0.909643	+	0.415391i	$0.136355\pi$
$542$	−6.17553	+	19.0063i	−0.265262	+	0.816392i
$543$	15.3052			0.656808
$544$	18.9307	−	58.2626i	0.811646	−	2.49799i
$545$		0			0
$546$	−1.68464	−	5.18480i	−0.0720961	−	0.221889i
$547$	−5.48653	−	16.8858i	−0.234587	−	0.721984i	−0.997176	−	0.0751011i	$-0.976072\pi$
$547$	−5.48653	−	16.8858i	−0.234587	−	0.721984i	0.762589	−	0.646883i	$-0.223928\pi$
$548$	−34.4095	−	25.0000i	−1.46990	−	1.06795i
$549$	−1.56944			−0.0669820
$550$		0			0
$551$	22.5728			0.961634
$552$	−13.8922	−	10.0933i	−0.591293	−	0.429600i
$553$	1.19224	+	3.66935i	0.0506994	+	0.156037i
$554$	2.33717	+	7.19307i	0.0992968	+	0.305604i
$555$		0			0
$556$	−5.41366	+	16.6615i	−0.229590	+	0.706606i
$557$	2.27448			0.0963727			0.0481864	−	0.998838i	$-0.484656\pi$
$557$	2.27448			0.0963727			0.0481864	+	0.998838i	$0.484656\pi$
$558$	14.2865	−	43.9692i	0.604794	−	1.86136i
$559$	−2.59920	+	1.88843i	−0.109934	+	0.0798719i
$560$		0			0
$561$	−3.38513	−	2.45944i	−0.142920	−	0.103838i
$562$	−49.5047	+	35.9673i	−2.08823	+	1.51719i
$563$	−0.321745	+	0.233761i	−0.0135599	+	0.00985187i	−0.594545	−	0.804063i	$-0.702668\pi$
$563$	−0.321745	+	0.233761i	−0.0135599	+	0.00985187i	0.580985	+	0.813915i	$0.302668\pi$
$564$	−23.7256	−	17.2377i	−0.999030	−	0.725838i
$565$		0			0
$566$	54.1698	−	39.3567i	2.27693	−	1.65428i
$567$	2.61644	−	8.05258i	0.109880	−	0.338177i
$568$	24.4086			1.02416
$569$	−3.45717	+	10.6401i	−0.144932	+	0.446055i	−0.997002	−	0.0773726i	$-0.975347\pi$
$569$	−3.45717	+	10.6401i	−0.144932	+	0.446055i	0.852070	+	0.523427i	$0.175347\pi$
$570$		0			0
$571$	−5.84424	−	17.9867i	−0.244574	−	0.752721i	−0.995706	−	0.0925696i	$-0.970492\pi$
$571$	−5.84424	−	17.9867i	−0.244574	−	0.752721i	0.751132	−	0.660152i	$-0.229508\pi$
$572$	−2.80613	−	8.63639i	−0.117330	−	0.361106i
$573$	13.0779	+	9.50168i	0.546339	+	0.396938i
$574$	54.9649			2.29419
$575$		0			0
$576$	−39.4768			−1.64486
$577$	−4.86874	−	3.53735i	−0.202688	−	0.147262i	0.481811	−	0.876275i	$-0.339979\pi$
$577$	−4.86874	−	3.53735i	−0.202688	−	0.147262i	−0.684499	+	0.729013i	$0.739979\pi$
$578$	0.242958	+	0.747747i	0.0101057	+	0.0311022i
$579$	−1.87504	−	5.77077i	−0.0779238	−	0.239825i
$580$		0			0
$581$	−1.49863	+	4.61231i	−0.0621737	+	0.191351i
$582$	−11.7315			−0.486285
$583$	0.258911	−	0.796847i	0.0107230	−	0.0330020i
$584$	−90.5577	+	65.7940i	−3.74731	+	2.72258i
$585$		0			0
$586$	62.2567	+	45.2321i	2.57180	+	1.86852i
$587$	−13.2133	+	9.60006i	−0.545373	+	0.396237i	−0.826077	−	0.563558i	$-0.809432\pi$
$587$	−13.2133	+	9.60006i	−0.545373	+	0.396237i	0.280703	+	0.959795i	$0.409432\pi$
$588$	−8.86653	+	6.44191i	−0.365650	+	0.265660i
$589$	28.2963	+	20.5585i	1.16593	+	0.847097i
$590$		0			0
$591$	13.3271	−	9.68268i	0.548202	−	0.398292i
$592$	31.6052	−	97.2707i	1.29896	−	3.99780i
$593$	−8.40604			−0.345195			−0.172597	−	0.984992i	$-0.555216\pi$
$593$	−8.40604			−0.345195			−0.172597	+	0.984992i	$0.555216\pi$
$594$	−4.57278	+	14.0736i	−0.187623	+	0.577445i
$595$		0			0
$596$	15.7042	+	48.3327i	0.643271	+	1.97978i
$597$	−2.19144	−	6.74456i	−0.0896897	−	0.276037i
$598$	−7.78494	−	5.65609i	−0.318350	−	0.231295i
$599$	13.1918			0.539001			0.269501	−	0.963000i	$-0.413141\pi$
$599$	13.1918			0.539001			0.269501	+	0.963000i	$0.413141\pi$
$600$		0			0
$601$	−6.06690			−0.247474			−0.123737	−	0.992315i	$-0.539488\pi$
$601$	−6.06690			−0.247474			−0.123737	+	0.992315i	$0.539488\pi$
$602$	−10.7193	−	7.78804i	−0.436886	−	0.317417i
$603$	8.19314	+	25.2159i	0.333650	+	1.02687i
$604$	−33.1743	−	102.100i	−1.34984	−	4.15440i
$605$		0			0
$606$	7.22250	−	22.2286i	0.293394	−	0.902973i
$607$	14.9141			0.605345			0.302672	−	0.953095i	$-0.402121\pi$
$607$	14.9141			0.605345			0.302672	+	0.953095i	$0.402121\pi$
$608$	22.6343	−	69.6613i	0.917943	−	2.82514i
$609$	−5.79283	+	4.20874i	−0.234737	+	0.170547i
$610$		0			0
$611$	−8.08385	−	5.87326i	−0.327038	−	0.237607i
$612$	−40.8923	+	29.7100i	−1.65297	+	1.20096i
$613$	−29.5107	+	21.4408i	−1.19193	+	0.865985i	−0.993467	−	0.114124i	$-0.963594\pi$
$613$	−29.5107	+	21.4408i	−1.19193	+	0.865985i	−0.198460	+	0.980109i	$0.563594\pi$
$614$	−51.6427	−	37.5206i	−2.08413	−	1.51421i
$615$		0			0
$616$	18.4217	−	13.3841i	0.742230	−	0.539261i
$617$	−5.01661	+	15.4395i	−0.201961	+	0.621572i	0.797864	+	0.602838i	$0.205964\pi$
$617$	−5.01661	+	15.4395i	−0.201961	+	0.621572i	−0.999825	+	0.0187338i	$0.994036\pi$
$618$	−23.4808			−0.944537
$619$	−3.10131	+	9.54484i	−0.124652	+	0.383639i	−0.993838	−	0.110847i	$-0.964644\pi$
$619$	−3.10131	+	9.54484i	−0.124652	+	0.383639i	0.869186	+	0.494486i	$0.164644\pi$
$620$		0			0
$621$	3.48112	+	10.7138i	0.139692	+	0.429929i
$622$	8.14339	+	25.0628i	0.326520	+	1.00493i
$623$	−12.1246	−	8.80903i	−0.485761	−	0.352926i
$624$	11.8491			0.474342
$625$		0			0
$626$	−50.0451			−2.00020
$627$	−4.04741	−	2.94062i	−0.161638	−	0.117437i
$628$	−12.3115	−	37.8909i	−0.491283	−	1.51201i
$629$	−10.9205	−	33.6097i	−0.435427	−	1.34011i
$630$		0			0
$631$	8.88672	−	27.3505i	0.353775	−	1.08881i	−0.602942	−	0.797785i	$-0.706005\pi$
$631$	8.88672	−	27.3505i	0.353775	−	1.08881i	0.956716	−	0.291022i	$-0.0939952\pi$
$632$	−15.6200			−0.621330
$633$	1.61418	−	4.96794i	0.0641580	−	0.197458i
$634$	55.8023	−	40.5427i	2.21619	−	1.61016i
$635$		0			0
$636$	1.94659	+	1.41428i	0.0771873	+	0.0560799i
$637$	−3.02102	+	2.19490i	−0.119697	+	0.0869652i
$638$	−13.4315	+	9.75855i	−0.531758	+	0.386345i
$639$	−5.78914	−	4.20606i	−0.229015	−	0.166389i
$640$		0			0
$641$	14.7595	−	10.7234i	0.582963	−	0.423548i	−0.256828	−	0.966457i	$-0.582677\pi$
$641$	14.7595	−	10.7234i	0.582963	−	0.423548i	0.839791	+	0.542909i	$0.182677\pi$
$642$	−6.35779	+	19.5673i	−0.250922	+	0.772258i
$643$	33.9734			1.33978			0.669890	−	0.742461i	$-0.266341\pi$
$643$	33.9734			1.33978			0.669890	+	0.742461i	$0.266341\pi$
$644$	8.80997	−	27.1143i	0.347162	−	1.06845i
$645$		0			0
$646$	−16.4486	−	50.6236i	−0.647162	−	1.99176i
$647$	−14.6390	−	45.0542i	−0.575518	−	1.77126i	−0.634408	−	0.772999i	$-0.718756\pi$
$647$	−14.6390	−	45.0542i	−0.575518	−	1.77126i	0.0588895	−	0.998265i	$-0.481244\pi$
$648$	27.7322	+	20.1487i	1.08943	+	0.791514i
$649$	−15.2955			−0.600402
$650$		0			0
$651$	−11.0948			−0.434840
$652$	−48.2071	−	35.0245i	−1.88794	−	1.37167i
$653$	11.5560	+	35.5657i	0.452220	+	1.39179i	0.874368	+	0.485264i	$0.161277\pi$
$653$	11.5560	+	35.5657i	0.452220	+	1.39179i	−0.422147	+	0.906527i	$0.638723\pi$
$654$	0.746875	+	2.29864i	0.0292051	+	0.0898841i
$655$		0			0
$656$	−36.9170	+	113.619i	−1.44137	+	4.43607i
$657$	32.8157			1.28026
$658$	12.7342	−	39.1918i	0.496430	−	1.52785i
$659$	7.67072	−	5.57311i	0.298809	−	0.217097i	−0.428271	−	0.903650i	$-0.640877\pi$
$659$	7.67072	−	5.57311i	0.298809	−	0.217097i	0.727080	+	0.686553i	$0.240877\pi$
$660$		0			0
$661$	7.10389	+	5.16128i	0.276309	+	0.200750i	0.717306	−	0.696758i	$-0.245375\pi$
$661$	7.10389	+	5.16128i	0.276309	+	0.200750i	−0.440997	+	0.897509i	$0.645375\pi$
$662$	2.79732	−	2.03237i	0.108721	−	0.0789904i
$663$	3.31226	−	2.40650i	0.128637	−	0.0934606i
$664$	−15.8843	−	11.5406i	−0.616431	−	0.447863i
$665$		0			0
$666$	−45.1843	+	32.8283i	−1.75086	+	1.27207i
$667$	−3.90560	+	12.0202i	−0.151225	+	0.465424i
$668$	−38.3283			−1.48297
$669$	1.99735	−	6.14721i	0.0772220	−	0.237665i
$670$		0			0
$671$	0.269859	+	0.830541i	0.0104178	+	0.0320627i
$672$	7.17984	+	22.0973i	0.276969	+	0.852421i
$673$	38.8538	+	28.2289i	1.49770	+	1.08814i	0.971285	+	0.237919i	$0.0764651\pi$
$673$	38.8538	+	28.2289i	1.49770	+	1.08814i	0.526418	+	0.850226i	$0.323535\pi$
$674$	−30.0531			−1.15760
$675$		0			0
$676$	−57.4444			−2.20940
$677$	−12.4711	−	9.06078i	−0.479303	−	0.348234i	0.321753	−	0.946824i	$-0.395728\pi$
$677$	−12.4711	−	9.06078i	−0.479303	−	0.348234i	−0.801056	+	0.598590i	$0.795728\pi$
$678$	−2.80219	−	8.62425i	−0.107617	−	0.331213i
$679$	−3.65957	−	11.2630i	−0.140441	−	0.432234i
$680$		0			0
$681$	4.92210	−	15.1487i	0.188615	−	0.580499i
$682$	−25.7248			−0.985055
$683$	8.59751	−	26.4604i	0.328975	−	1.01248i	−0.640640	−	0.767842i	$-0.721331\pi$
$683$	8.59751	−	26.4604i	0.328975	−	1.01248i	0.969614	−	0.244638i	$-0.0786692\pi$
$684$	−48.8926	+	35.5225i	−1.86945	+	1.35824i
$685$		0			0
$686$	−43.2793	−	31.4443i	−1.65241	−	1.20055i
$687$	18.2777	−	13.2795i	0.697338	−	0.506646i
$688$	23.2983	−	16.9272i	0.888240	−	0.645344i
$689$	0.663246	+	0.481877i	0.0252677	+	0.0183580i
$690$		0			0
$691$	16.2824	−	11.8298i	0.619411	−	0.450028i	−0.233305	−	0.972404i	$-0.574954\pi$
$691$	16.2824	−	11.8298i	0.619411	−	0.450028i	0.852716	+	0.522375i	$0.174954\pi$
$692$	−8.37826	+	25.7856i	−0.318494	+	0.980223i
$693$	−6.67552			−0.253582
$694$	1.77472	−	5.46203i	0.0673675	−	0.207336i
$695$		0			0
$696$	−8.95807	−	27.5701i	−0.339555	−	1.04504i
$697$	12.7558	+	39.2584i	0.483162	+	1.48702i
$698$	12.0933	+	8.78630i	0.457738	+	0.332566i
$699$	−1.72428			−0.0652184
$700$		0			0
$701$	31.6216			1.19433			0.597166	−	0.802118i	$-0.296293\pi$
$701$	31.6216			1.19433			0.597166	+	0.802118i	$0.296293\pi$
$702$	−11.7140	−	8.51069i	−0.442115	−	0.321215i
$703$	−13.0570	−	40.1852i	−0.492453	−	1.51561i
$704$	6.78788	+	20.8910i	0.255828	+	0.787358i
$705$		0			0
$706$	−15.2329	+	46.8819i	−0.573296	+	1.76442i
$707$	23.5939			0.887340
$708$	13.5736	−	41.7752i	0.510127	−	1.57001i
$709$	3.85098	−	2.79790i	0.144627	−	0.105077i	−0.513119	−	0.858317i	$-0.671510\pi$
$709$	3.85098	−	2.79790i	0.144627	−	0.105077i	0.657746	+	0.753240i	$0.271510\pi$
$710$		0			0
$711$	3.70470	+	2.69162i	0.138937	+	0.100944i
$712$	49.0869	−	35.6637i	1.83961	−	1.33655i
$713$	−15.8434	+	11.5109i	−0.593341	+	0.431087i
$714$	13.6600	+	9.92460i	0.511214	+	0.371419i
$715$		0			0
$716$	−5.39402	+	3.91899i	−0.201584	+	0.146459i
$717$	−3.61959	+	11.1400i	−0.135176	+	0.416029i
$718$	−29.9680			−1.11840
$719$	−7.12986	+	21.9435i	−0.265899	+	0.818353i	0.725586	+	0.688132i	$0.241569\pi$
$719$	−7.12986	+	21.9435i	−0.265899	+	0.818353i	−0.991485	+	0.130221i	$0.958431\pi$
$720$		0			0
$721$	−7.32471	−	22.5431i	−0.272786	−	0.839550i
$722$	−4.01951	−	12.3708i	−0.149591	−	0.460393i
$723$	−2.97342	−	2.16032i	−0.110583	−	0.0803431i
$724$	−102.876			−3.82336
$725$		0			0
$726$	−18.5730			−0.689309
$727$	12.6050	+	9.15810i	0.467495	+	0.339655i	0.796464	−	0.604686i	$-0.206701\pi$
$727$	12.6050	+	9.15810i	0.467495	+	0.339655i	−0.328969	+	0.944341i	$0.606701\pi$
$728$	6.88497	+	21.1897i	0.255174	+	0.785344i
$729$	−0.208202	−	0.640779i	−0.00771118	−	0.0237326i
$730$		0			0
$731$	3.07491	−	9.46360i	0.113730	−	0.350024i
$732$	−2.50786			−0.0926931
$733$	−5.32175	+	16.3787i	−0.196563	+	0.604960i	0.803391	+	0.595451i	$0.203027\pi$
$733$	−5.32175	+	16.3787i	−0.196563	+	0.604960i	−0.999955	+	0.00950846i	$0.996973\pi$
$734$	61.5930	−	44.7499i	2.27344	−	1.65175i
$735$		0			0
$736$	33.1789	+	24.1059i	1.22299	+	0.888555i
$737$	11.9354	−	8.67156i	0.439645	−	0.319421i
$738$	52.7784	−	38.3457i	1.94280	−	1.41153i
$739$	22.2381	+	16.1569i	0.818043	+	0.594343i	0.916151	−	0.400833i	$-0.131279\pi$
$739$	22.2381	+	16.1569i	0.818043	+	0.594343i	−0.0981086	+	0.995176i	$0.531279\pi$
$740$		0			0
$741$	3.96028	−	2.87731i	0.145485	−	0.105701i
$742$	−1.04479	+	3.21552i	−0.0383553	+	0.118045i
$743$	−48.4801			−1.77856			−0.889280	−	0.457362i	$-0.848794\pi$
$743$	−48.4801			−1.77856			−0.889280	+	0.457362i	$0.848794\pi$
$744$	13.8803	−	42.7193i	0.508878	−	1.56617i
$745$		0			0
$746$	11.5993	+	35.6990i	0.424681	+	1.30703i
$747$	1.77872	+	5.47433i	0.0650799	+	0.200295i
$748$	22.7537	+	16.5315i	0.831958	+	0.604453i
$749$	−20.7691			−0.758888
$750$		0			0
$751$	3.29720			0.120316			0.0601582	−	0.998189i	$-0.480839\pi$
$751$	3.29720			0.120316			0.0601582	+	0.998189i	$0.480839\pi$
$752$	72.4610	+	52.6460i	2.64238	+	1.91980i
$753$	4.18220	+	12.8715i	0.152408	+	0.469063i
$754$	−5.01993	−	15.4497i	−0.182815	−	0.562647i
$755$		0			0
$756$	13.2563	−	40.7987i	0.482128	−	1.48384i
$757$	35.7934			1.30093			0.650466	−	0.759535i	$-0.274574\pi$
$757$	35.7934			1.30093			0.650466	+	0.759535i	$0.274574\pi$
$758$	−18.1098	+	55.7362i	−0.657777	+	2.02443i
$759$	2.26619	−	1.64649i	0.0822576	−	0.0597636i
$760$		0			0
$761$	0.537277	+	0.390354i	0.0194763	+	0.0141503i	0.597481	−	0.801883i	$-0.296168\pi$
$761$	0.537277	+	0.390354i	0.0194763	+	0.0141503i	−0.578005	+	0.816034i	$0.696168\pi$
$762$	−6.83588	+	4.96656i	−0.247638	+	0.179919i
$763$	−1.97387	+	1.43410i	−0.0714588	+	0.0519179i
$764$	−87.9054	−	63.8670i	−3.18030	−	2.31063i
$765$		0			0
$766$	31.7878	−	23.0952i	1.14854	−	0.834463i
$767$	4.62482	−	14.2337i	0.166993	−	0.513951i
$768$	−2.43848			−0.0879911
$769$	7.94452	−	24.4507i	0.286487	−	0.881716i	−0.699462	−	0.714669i	$-0.746577\pi$
$769$	7.94452	−	24.4507i	0.286487	−	0.881716i	0.985949	−	0.167046i	$-0.0534229\pi$
$770$		0			0
$771$	1.38145	+	4.25166i	0.0497516	+	0.153120i
$772$	12.6033	+	38.7891i	0.453604	+	1.39605i
$773$	−31.1842	−	22.6567i	−1.12162	−	0.814904i	−0.137165	−	0.990548i	$-0.543799\pi$
$773$	−31.1842	−	22.6567i	−1.12162	−	0.814904i	−0.984454	+	0.175644i	$0.943799\pi$
$774$	−15.7261			−0.565264
$775$		0			0
$776$	47.9453			1.72114
$777$	10.8434	+	7.87818i	0.389004	+	0.282628i
$778$	11.7409	+	36.1349i	0.420933	+	1.29550i
$779$	15.2514	+	46.9390i	0.546439	+	1.68177i
$780$		0			0
$781$	−1.23041	+	3.78681i	−0.0440275	+	0.135503i
$782$	29.8034			1.06577
$783$	−5.87673	+	18.0867i	−0.210017	+	0.646366i
$784$	27.0794	−	19.6744i	0.967123	−	0.702656i
$785$		0			0
$786$	−5.54671	−	4.02992i	−0.197845	−	0.143743i
$787$	−29.3116	+	21.2962i	−1.04485	+	0.759126i	−0.971226	−	0.238160i	$-0.923456\pi$
$787$	−29.3116	+	21.2962i	−1.04485	+	0.759126i	−0.0736214	+	0.997286i	$0.523456\pi$
$788$	−89.5800	+	65.0837i	−3.19115	+	2.31851i
$789$	−14.5405	−	10.5643i	−0.517654	−	0.376098i
$790$		0			0
$791$	7.40573	−	5.38058i	0.263317	−	0.191311i
$792$	8.35153	−	25.7034i	0.296759	−	0.913329i
$793$	−0.854482			−0.0303436
$794$	−4.52174	+	13.9165i	−0.160470	+	0.493877i
$795$		0			0
$796$	14.7301	+	45.3346i	0.522095	+	1.60684i
$797$	−10.4533	−	32.1719i	−0.370275	−	1.13959i	−0.946612	−	0.322376i	$-0.895518\pi$
$797$	−10.4533	−	32.1719i	−0.370275	−	1.13959i	0.576337	−	0.817212i	$-0.304482\pi$
$798$	16.3325	+	11.8663i	0.578165	+	0.420062i
$799$	30.9478			1.09485
$800$		0			0
$801$	−17.7878			−0.628501
$802$	57.6801	+	41.9070i	2.03675	+	1.47979i
$803$	−5.64254	−	17.3660i	−0.199121	−	0.612831i
$804$	13.0921	+	40.2933i	0.461722	+	1.42103i
$805$		0			0
$806$	7.77828	−	23.9391i	0.273978	−	0.843218i
$807$	−10.4344			−0.367308
$808$	−29.5176	+	90.8458i	−1.03842	+	3.19594i
$809$	1.18448	−	0.860572i	0.0416439	−	0.0302561i	−0.566769	−	0.823877i	$-0.691807\pi$
$809$	1.18448	−	0.860572i	0.0416439	−	0.0302561i	0.608413	+	0.793621i	$0.291807\pi$
$810$		0			0
$811$	32.9177	+	23.9161i	1.15590	+	0.839808i	0.989254	−	0.146210i	$-0.0467075\pi$
$811$	32.9177	+	23.9161i	1.15590	+	0.839808i	0.166642	+	0.986017i	$0.446707\pi$
$812$	38.9374	−	28.2897i	1.36644	−	0.992774i
$813$	4.60510	−	3.34580i	0.161508	−	0.117342i
$814$	25.1419	+	18.2667i	0.881224	+	0.640247i
$815$		0			0
$816$	−29.6900	+	21.5710i	−1.03936	+	0.755137i
$817$	3.67649	−	11.3151i	0.128624	−	0.395865i
$818$	−13.6819			−0.478375
$819$	2.01844	−	6.21212i	0.0705300	−	0.217069i
$820$		0			0
$821$	−9.25608	−	28.4873i	−0.323040	−	0.994214i	−0.972318	−	0.233663i	$-0.924929\pi$
$821$	−9.25608	−	28.4873i	−0.323040	−	0.994214i	0.649278	−	0.760551i	$-0.275071\pi$
$822$	5.21107	+	16.0380i	0.181757	+	0.559390i
$823$	15.3203	+	11.1308i	0.534030	+	0.387996i	0.821863	−	0.569685i	$-0.192935\pi$
$823$	15.3203	+	11.1308i	0.534030	+	0.387996i	−0.287833	+	0.957681i	$0.592935\pi$
$824$	95.9636			3.34305
$825$		0			0
$826$	61.7221			2.14759
$827$	16.3938	+	11.9108i	0.570069	+	0.414179i	0.835130	−	0.550052i	$-0.185392\pi$
$827$	16.3938	+	11.9108i	0.570069	+	0.414179i	−0.265061	+	0.964232i	$0.585392\pi$
$828$	−10.4565	−	32.1819i	−0.363389	−	1.11840i
$829$	5.14205	+	15.8256i	0.178591	+	0.549646i	0.999779	−	0.0210110i	$-0.00668850\pi$
$829$	5.14205	+	15.8256i	0.178591	+	0.549646i	−0.821188	+	0.570657i	$0.806689\pi$
$830$		0			0
$831$	0.665702	−	2.04882i	0.0230930	−	0.0710728i
$832$	−21.4932			−0.745142
$833$	3.57394	−	10.9995i	0.123830	−	0.381109i
$834$	5.61939	−	4.08272i	0.194583	−	0.141373i
$835$		0			0
$836$	27.2053	+	19.7658i	0.940915	+	0.683615i
$837$	−23.8395	+	17.3204i	−0.824014	+	0.598681i
$838$	68.6734	−	49.8941i	2.37228	−	1.72356i
$839$	5.77368	+	4.19482i	0.199330	+	0.144821i	0.682973	−	0.730444i	$-0.260687\pi$
$839$	5.77368	+	4.19482i	0.199330	+	0.144821i	−0.483643	+	0.875265i	$0.660687\pi$
$840$		0			0
$841$	6.19993	−	4.50452i	0.213791	−	0.155328i
$842$	−2.53685	+	7.80762i	−0.0874256	+	0.269068i
$843$	17.4293			0.600295
$844$	−10.8500	+	33.3928i	−0.373472	+	1.14943i
$845$		0			0
$846$	−15.1141	−	46.5165i	−0.519635	−	1.59927i
$847$	−5.79375	−	17.8313i	−0.199075	−	0.612691i
$848$	−5.94512	−	4.31938i	−0.204156	−	0.148328i
$849$	−19.0717			−0.654539
$850$		0			0
$851$	23.6581			0.810988
$852$	−9.25066	−	6.72100i	−0.316922	−	0.230258i
$853$	−9.83454	−	30.2676i	−0.336728	−	1.03634i	−0.965864	−	0.259048i	$-0.916591\pi$
$853$	−9.83454	−	30.2676i	−0.336728	−	1.03634i	0.629136	−	0.777295i	$-0.283409\pi$
$854$	−1.08896	−	3.35148i	−0.0372636	−	0.114685i
$855$		0			0
$856$	25.9836	−	79.9693i	0.888102	−	2.73330i
$857$	−43.1535			−1.47409			−0.737047	−	0.675842i	$-0.763780\pi$
$857$	−43.1535			−1.47409			−0.737047	+	0.675842i	$0.763780\pi$
$858$	−1.11258	+	3.42417i	−0.0379829	+	0.116899i
$859$	−24.9917	+	18.1576i	−0.852707	+	0.619528i	−0.925891	−	0.377791i	$-0.876684\pi$
$859$	−24.9917	+	18.1576i	−0.852707	+	0.619528i	0.0731840	+	0.997318i	$0.476684\pi$
$860$		0			0
$861$	−12.6658	−	9.20225i	−0.431650	−	0.313612i
$862$	50.3373	−	36.5722i	1.71449	−	1.24565i
$863$	30.8972	−	22.4481i	1.05175	−	0.764143i	0.0792075	−	0.996858i	$-0.474761\pi$
$863$	30.8972	−	22.4481i	1.05175	−	0.764143i	0.972545	+	0.232715i	$0.0747610\pi$
$864$	49.9241	+	36.2720i	1.69845	+	1.23400i
$865$		0			0
$866$	−17.7100	+	12.8671i	−0.601812	+	0.437242i
$867$	0.0692023	−	0.212983i	0.00235023	−	0.00723327i
$868$	74.5754			2.53125
$869$	0.787387	−	2.42333i	0.0267103	−	0.0822057i
$870$		0			0
$871$	4.46076	+	13.7288i	0.151147	+	0.465183i
$872$	−3.05240	−	9.39432i	−0.103367	−	0.318132i
$873$	−11.3715	−	8.26187i	−0.384867	−	0.279622i
$874$	35.6343			1.20535
$875$		0			0
$876$	52.4373			1.77169
$877$	−25.6658	−	18.6473i	−0.866674	−	0.629675i	0.0630186	−	0.998012i	$-0.479927\pi$
$877$	−25.6658	−	18.6473i	−0.866674	−	0.629675i	−0.929692	+	0.368337i	$0.879927\pi$
$878$	20.0215	+	61.6200i	0.675694	+	2.07957i
$879$	−6.77330	−	20.8461i	−0.228458	−	0.703121i
$880$		0			0
$881$	−11.8789	+	36.5595i	−0.400210	+	1.23172i	0.524619	+	0.851337i	$0.324208\pi$
$881$	−11.8789	+	36.5595i	−0.400210	+	1.23172i	−0.924829	+	0.380383i	$0.875792\pi$
$882$	−18.2783			−0.615464
$883$	3.75447	−	11.5551i	0.126348	−	0.388859i	−0.867796	−	0.496920i	$-0.834464\pi$
$883$	3.75447	−	11.5551i	0.126348	−	0.388859i	0.994144	+	0.108061i	$0.0344642\pi$
$884$	−22.2639	+	16.1756i	−0.748815	+	0.544046i
$885$		0			0
$886$	−0.136124	−	0.0989002i	−0.00457319	−	0.00332262i
$887$	19.6131	−	14.2498i	0.658544	−	0.478460i	−0.207627	−	0.978208i	$-0.566574\pi$
$887$	19.6131	−	14.2498i	0.658544	−	0.478460i	0.866171	+	0.499748i	$0.166574\pi$
$888$	−43.8999	+	31.8952i	−1.47318	+	1.07033i
$889$	−6.90064	−	5.01361i	−0.231440	−	0.168151i
$890$		0			0
$891$	−4.52386	+	3.28678i	−0.151555	+	0.110111i
$892$	−13.4255	+	41.3194i	−0.449519	+	1.38348i
$893$	37.0025			1.23824
$894$	6.22644	−	19.1630i	0.208243	−	0.640907i
$895$		0			0
$896$	−8.47400	−	26.0803i	−0.283097	−	0.871282i
$897$	0.846974	+	2.60672i	0.0282796	+	0.0870358i
$898$	−24.9477	−	18.1256i	−0.832517	−	0.604859i
$899$	−33.0604			−1.10263
$900$		0			0
$901$	−2.53913			−0.0845908
$902$	−29.3675	−	21.3367i	−0.977830	−	0.710435i
$903$	1.16622	+	3.58926i	0.0388095	+	0.119443i
$904$	11.4523	+	35.2464i	0.380896	+	1.17228i
$905$		0			0
$906$	−13.1530	+	40.4808i	−0.436980	+	1.34489i
$907$	−32.5046			−1.07930			−0.539649	−	0.841890i	$-0.681443\pi$
$907$	−32.5046			−1.07930			−0.539649	+	0.841890i	$0.681443\pi$
$908$	−33.0847	+	101.824i	−1.09795	+	3.37915i
$909$	22.6553	−	16.4600i	0.751429	−	0.545945i
$910$		0			0
$911$	−35.7794	−	25.9953i	−1.18542	−	0.861261i	−0.192651	−	0.981267i	$-0.561709\pi$
$911$	−35.7794	−	25.9953i	−1.18542	−	0.861261i	−0.992773	+	0.120006i	$0.961709\pi$
$912$	−35.4986	+	25.7913i	−1.17548	+	0.854034i
$913$	2.59115	−	1.88258i	0.0857547	−	0.0623044i
$914$	89.2529	+	64.8460i	2.95222	+	2.14492i
$915$		0			0
$916$	−122.856	+	89.2604i	−4.05929	+	2.94925i
$917$	2.13873	−	6.58232i	0.0706270	−	0.217367i
$918$	44.8450			1.48011
$919$	−12.2969	+	37.8460i	−0.405637	+	1.24842i	0.514724	+	0.857356i	$0.327894\pi$
$919$	−12.2969	+	37.8460i	−0.405637	+	1.24842i	−0.920362	+	0.391068i	$0.872106\pi$
$920$		0			0
$921$	5.61854	+	17.2921i	0.185137	+	0.569793i
$922$	−24.1878	−	74.4423i	−0.796582	−	2.45163i
$923$	−3.15190	−	2.28999i	−0.103746	−	0.0753760i
$924$	−10.6670			−0.350920
$925$		0			0
$926$	−81.4163			−2.67551
$927$	−22.7603	−	16.5363i	−0.747547	−	0.543124i
$928$	21.3946	+	65.8458i	0.702312	+	2.16149i
$929$	−2.05379	−	6.32093i	−0.0673828	−	0.207383i	0.911696	−	0.410866i	$-0.134774\pi$
$929$	−2.05379	−	6.32093i	−0.0673828	−	0.207383i	−0.979078	+	0.203483i	$0.934774\pi$
$930$		0			0
$931$	4.27316	−	13.1514i	0.140047	−	0.431020i
$932$	11.5900			0.379644
$933$	2.31950	−	7.13870i	0.0759371	−	0.233710i
$934$	−70.5346	+	51.2464i	−2.30796	+	1.67683i
$935$		0			0
$936$	21.3939	+	15.5436i	0.699281	+	0.508057i
$937$	−0.185738	+	0.134947i	−0.00606781	+	0.00440852i	−0.590815	−	0.806807i	$-0.701194\pi$
$937$	−0.185738	+	0.134947i	−0.00606781	+	0.00440852i	0.584747	+	0.811216i	$0.301194\pi$
$938$	−48.1628	+	34.9924i	−1.57257	+	1.14254i
$939$	11.5321	+	8.37857i	0.376336	+	0.273424i
$940$		0			0
$941$	−22.9337	+	16.6623i	−0.747618	+	0.543176i	−0.895088	−	0.445890i	$-0.852887\pi$
$941$	−22.9337	+	16.6623i	−0.747618	+	0.543176i	0.147470	+	0.989067i	$0.452887\pi$
$942$	−4.88129	+	15.0231i	−0.159041	+	0.489478i
$943$	−27.6342			−0.899894
$944$	−41.4554	+	127.587i	−1.34926	+	4.15259i
$945$		0			0
$946$	2.70405	+	8.32221i	0.0879162	+	0.270578i
$947$	14.8339	+	45.6542i	0.482038	+	1.48356i	0.836225	+	0.548386i	$0.184758\pi$
$947$	14.8339	+	45.6542i	0.482038	+	1.48356i	−0.354187	+	0.935175i	$0.615242\pi$
$948$	5.91986	+	4.30103i	0.192268	+	0.139691i
$949$	17.8666			0.579973
$950$		0			0
$951$	−19.6464			−0.637080
$952$	−55.8272	−	40.5608i	−1.80937	−	1.31458i
$953$	−8.30900	−	25.5725i	−0.269155	−	0.828374i	−0.990707	−	0.136014i	$-0.956571\pi$
$953$	−8.30900	−	25.5725i	−0.269155	−	0.828374i	0.721552	−	0.692360i	$-0.243429\pi$
$954$	1.24005	+	3.81649i	0.0401482	+	0.123563i
$955$		0			0
$956$	24.3296	−	74.8789i	0.786877	−	2.42176i
$957$	4.72886			0.152862
$958$	10.1585	−	31.2647i	0.328207	−	1.01012i
$959$	−13.7720	+	10.0059i	−0.444721	+	0.323109i
$960$		0			0
$961$	−16.3636	−	11.8888i	−0.527857	−	0.383511i
$962$	−24.6007	+	17.8734i	−0.793157	+	0.576262i
$963$	−19.9429	+	14.4894i	−0.642652	+	0.466914i
$964$	19.9863	+	14.5209i	0.643716	+	0.467687i
$965$		0			0
$966$	−9.14477	+	6.64407i	−0.294228	+	0.213769i
$967$	−1.16813	+	3.59515i	−0.0375647	+	0.115612i	−0.968080	−	0.250640i	$-0.919359\pi$
$967$	−1.16813	+	3.59515i	−0.0375647	+	0.115612i	0.930516	+	0.366252i	$0.119359\pi$
$968$	75.9059			2.43971
$969$	−4.68510	+	14.4193i	−0.150507	+	0.463213i
$970$		0			0
$971$	3.48802	+	10.7350i	0.111936	+	0.344503i	0.991296	−	0.131655i	$-0.0420290\pi$
$971$	3.48802	+	10.7350i	0.111936	+	0.344503i	−0.879360	+	0.476158i	$0.842029\pi$
$972$	−24.4366	−	75.2080i	−0.783803	−	2.41230i
$973$	5.67262	+	4.12140i	0.181856	+	0.132126i
$974$	94.0648			3.01403
$975$		0			0
$976$	7.65930			0.245168
$977$	−16.4067	−	11.9201i	−0.524896	−	0.381359i	0.293549	−	0.955944i	$-0.405164\pi$
$977$	−16.4067	−	11.9201i	−0.524896	−	0.381359i	−0.818445	+	0.574585i	$0.805164\pi$
$978$	7.30061	+	22.4690i	0.233448	+	0.718478i
$979$	3.05855	+	9.41323i	0.0977515	+	0.300848i
$980$		0			0
$981$	−0.894860	+	2.75410i	−0.0285707	+	0.0879315i
$982$	−40.8162			−1.30250
$983$	−8.74910	+	26.9270i	−0.279053	+	0.858837i	0.709065	+	0.705143i	$0.249117\pi$
$983$	−8.74910	+	26.9270i	−0.279053	+	0.858837i	−0.988118	+	0.153694i	$0.950883\pi$
$984$	51.2781	−	37.2557i	1.63469	−	1.18767i
$985$		0			0
$986$	40.7044	+	29.5735i	1.29629	+	0.941811i
$987$	−9.49590	+	6.89917i	−0.302258	+	0.219603i
$988$	−26.6196	+	19.3403i	−0.846883	+	0.615297i
$989$	5.38925	+	3.91552i	0.171368	+	0.124506i
$990$		0			0
$991$	−19.3040	+	14.0252i	−0.613211	+	0.445524i	−0.850544	−	0.525905i	$-0.823727\pi$
$991$	−19.3040	+	14.0252i	−0.613211	+	0.445524i	0.237333	+	0.971428i	$0.423727\pi$
$992$	−33.1505	+	102.027i	−1.05253	+	3.23935i
$993$	−0.984859			−0.0312536
$994$	4.96507	−	15.2809i	0.157482	−	0.484681i
$995$		0			0
$996$	2.84227	+	8.74762i	0.0900609	+	0.277179i
$997$	4.22488	+	13.0028i	0.133803	+	0.411804i	0.995402	−	0.0957860i	$-0.0305364\pi$
$997$	4.22488	+	13.0028i	0.133803	+	0.411804i	−0.861599	+	0.507590i	$0.830536\pi$
$998$	−75.8446	−	55.1043i	−2.40082	−	1.74430i
$999$	35.5982			1.12628

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.d.p.376.4		16
5.2	odd	4		625.2.e.k.249.1		32
5.3	odd	4		625.2.e.k.249.8		32
5.4	even	2		625.2.d.n.376.1		16
25.2	odd	20		625.2.e.k.374.8		32
25.3	odd	20		625.2.e.j.499.1		32
25.4	even	10		625.2.d.m.126.4		16
25.6	even	5		625.2.a.e.1.1	✓	8
25.8	odd	20		625.2.b.d.624.16		16
25.9	even	10		625.2.d.m.501.4		16
25.11	even	5	inner	625.2.d.p.251.4		16
25.12	odd	20		625.2.e.j.124.1		32
25.13	odd	20		625.2.e.j.124.8		32
25.14	even	10		625.2.d.n.251.1		16
25.16	even	5		625.2.d.q.501.1		16
25.17	odd	20		625.2.b.d.624.1		16
25.19	even	10		625.2.a.g.1.8	yes	8
25.21	even	5		625.2.d.q.126.1		16
25.22	odd	20		625.2.e.j.499.8		32
25.23	odd	20		625.2.e.k.374.1		32
75.44	odd	10		5625.2.a.s.1.1		8
75.56	odd	10		5625.2.a.be.1.8		8
100.19	odd	10		10000.2.a.be.1.4		8
100.31	odd	10		10000.2.a.bn.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
625.2.a.e.1.1	✓	8	25.6	even	5
625.2.a.g.1.8	yes	8	25.19	even	10
625.2.b.d.624.1		16	25.17	odd	20
625.2.b.d.624.16		16	25.8	odd	20
625.2.d.m.126.4		16	25.4	even	10
625.2.d.m.501.4		16	25.9	even	10
625.2.d.n.251.1		16	25.14	even	10
625.2.d.n.376.1		16	5.4	even	2
625.2.d.p.251.4		16	25.11	even	5	inner
625.2.d.p.376.4		16	1.1	even	1	trivial
625.2.d.q.126.1		16	25.21	even	5
625.2.d.q.501.1		16	25.16	even	5
625.2.e.j.124.1		32	25.12	odd	20
625.2.e.j.124.8		32	25.13	odd	20
625.2.e.j.499.1		32	25.3	odd	20
625.2.e.j.499.8		32	25.22	odd	20
625.2.e.k.249.1		32	5.2	odd	4
625.2.e.k.249.8		32	5.3	odd	4
625.2.e.k.374.1		32	25.23	odd	20
625.2.e.k.374.8		32	25.2	odd	20
5625.2.a.s.1.1		8	75.44	odd	10
5625.2.a.be.1.8		8	75.56	odd	10
10000.2.a.be.1.4		8	100.19	odd	10
10000.2.a.bn.1.5		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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(2.15604 + 1.56645i) q^{2} +(-0.234569 - 0.721930i) q^{3} +(1.57669 + 4.85257i) q^{4} +(0.625130 - 1.92395i) q^{6} +2.04213 q^{7} +(-2.55484 + 7.86300i) q^{8} +(1.96089 - 1.42467i) q^{9} +O(q^{10})\)	\(q+(2.15604 + 1.56645i) q^{2} +(-0.234569 - 0.721930i) q^{3} +(1.57669 + 4.85257i) q^{4} +(0.625130 - 1.92395i) q^{6} +2.04213 q^{7} +(-2.55484 + 7.86300i) q^{8} +(1.96089 - 1.42467i) q^{9} +(-1.09110 - 0.792729i) q^{11} +(3.13337 - 2.27653i) q^{12} +(1.06761 - 0.775663i) q^{13} +(4.40291 + 3.19890i) q^{14} +(-9.56969 + 6.95279i) q^{16} +(-1.26301 + 3.88713i) q^{17} +6.45944 q^{18} +(-1.51010 + 4.64762i) q^{19} +(-0.479021 - 1.47427i) q^{21} +(-1.11068 - 3.41831i) q^{22} +(-2.21361 - 1.60828i) q^{23} +6.27582 q^{24} +3.51685 q^{26} +(-3.33081 - 2.41997i) q^{27} +(3.21981 + 9.90957i) q^{28} +(-1.42739 - 4.39306i) q^{29} +(2.21172 - 6.80697i) q^{31} -14.9886 q^{32} +(-0.316357 + 0.973647i) q^{33} +(-8.81211 + 6.40237i) q^{34} +(10.0050 + 7.26908i) q^{36} +(-6.99508 + 5.08223i) q^{37} +(-10.5361 + 7.65495i) q^{38} +(-0.810403 - 0.588793i) q^{39} +(8.17073 - 5.93639i) q^{41} +(1.27660 - 3.92896i) q^{42} -2.43460 q^{43} +(2.12644 - 6.54452i) q^{44} +(-2.25333 - 6.93505i) q^{46} +(-2.33985 - 7.20133i) q^{47} +(7.26419 + 5.27774i) q^{48} -2.82971 q^{49} +3.10250 q^{51} +(5.44725 + 3.95766i) q^{52} +(0.191975 + 0.590839i) q^{53} +(-3.39058 - 10.4351i) q^{54} +(-5.21732 + 16.0573i) q^{56} +3.70948 q^{57} +(3.80402 - 11.7076i) q^{58} +(9.17521 - 6.66618i) q^{59} +(-0.523849 - 0.380599i) q^{61} +(15.4314 - 11.2115i) q^{62} +(4.00439 - 2.90936i) q^{63} +(-13.1766 - 9.57336i) q^{64} +(-2.20725 + 1.60366i) q^{66} +(-3.38029 + 10.4035i) q^{67} -20.8539 q^{68} +(-0.641823 + 1.97533i) q^{69} +(-0.912311 - 2.80781i) q^{71} +(6.19241 + 19.0583i) q^{72} +(10.9533 + 7.95802i) q^{73} -23.0428 q^{74} -24.9339 q^{76} +(-2.22816 - 1.61886i) q^{77} +(-0.824945 - 2.53892i) q^{78} +(0.583824 + 1.79683i) q^{79} +(1.28123 - 3.94323i) q^{81} +26.9155 q^{82} +(-0.733857 + 2.25858i) q^{83} +(6.39875 - 4.64896i) q^{84} +(-5.24909 - 3.81368i) q^{86} +(-2.83666 + 2.06096i) q^{87} +(9.02081 - 6.55400i) q^{88} +(-5.93723 - 4.31365i) q^{89} +(2.18020 - 1.58400i) q^{91} +(4.31411 - 13.2775i) q^{92} -5.43296 q^{93} +(6.23574 - 19.1916i) q^{94} +(3.51586 + 10.8207i) q^{96} +(-1.79204 - 5.51532i) q^{97} +(-6.10097 - 4.43261i) q^{98} -3.26890 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{3} - 8 q^{4} - 3 q^{6} - 20 q^{7} + 10 q^{8} + 3 q^{9}+O(q^{10}) \) 16 * q + 5 * q^3 - 8 * q^4 - 3 * q^6 - 20 * q^7 + 10 * q^8 + 3 * q^9	\( 16 q + 5 q^{3} - 8 q^{4} - 3 q^{6} - 20 q^{7} + 10 q^{8} + 3 q^{9} + 2 q^{11} + 25 q^{12} + 5 q^{13} + 9 q^{14} - 14 q^{16} - 10 q^{17} + 10 q^{18} + 7 q^{21} - 40 q^{22} + 15 q^{23} + 10 q^{24} + 22 q^{26} + 20 q^{27} + 30 q^{28} - 10 q^{29} + 17 q^{31} - 60 q^{32} + 5 q^{33} - q^{34} - 4 q^{36} - 15 q^{37} - 15 q^{38} - 9 q^{39} + 12 q^{41} - 45 q^{42} + 49 q^{44} - 33 q^{46} + 25 q^{47} - 20 q^{48} - 8 q^{49} - 28 q^{51} + 20 q^{52} - 30 q^{54} - 35 q^{56} + 20 q^{57} + 5 q^{58} + 20 q^{59} - 23 q^{61} + 15 q^{62} + 10 q^{63} - 28 q^{64} - 26 q^{66} - 80 q^{68} + 6 q^{69} + 22 q^{71} + 5 q^{72} + 40 q^{73} - 36 q^{74} - 20 q^{76} - 40 q^{77} - 25 q^{78} + 75 q^{79} + 11 q^{81} + 90 q^{82} + 25 q^{83} - 31 q^{84} + 17 q^{86} - 20 q^{87} + 5 q^{89} + 22 q^{91} + 60 q^{92} + 80 q^{93} - 51 q^{94} - 28 q^{96} + 40 q^{97} + 15 q^{98} - 44 q^{99}+O(q^{100}) \) 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

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