LMFDB - Embedded newform 625.2.d.n.251.1

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			251.1
Root			$1.63097i$ of defining polynomial
Character	$\chi$	$=$	625.251
Dual form			625.2.d.n.376.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.15604 + 1.56645i) q^{2} +(0.234569 - 0.721930i) q^{3} +(1.57669 - 4.85257i) q^{4} +(0.625130 + 1.92395i) q^{6} -2.04213 q^{7} +(2.55484 + 7.86300i) q^{8} +(1.96089 + 1.42467i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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	−0.565377	+	0.824832i	$0.691269\pi$
$2$	−2.15604	+	1.56645i	−1.52455	+	1.10765i	−0.959173	+	0.282818i	$0.908731\pi$
$3$	0.234569	−	0.721930i	0.135429	−	0.416807i	−0.860228	−	0.509910i	$-0.829679\pi$
$3$	0.234569	−	0.721930i	0.135429	−	0.416807i	0.995656	+	0.0931033i	$0.0296787\pi$
$4$	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	$-0.626118\pi$
$7$	−2.04213			−0.771852			−0.385926	+	0.922530i	$0.626118\pi$
$8$	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	−0.739997	−	0.672610i	$-0.765173\pi$
$11$	−1.09110	+	0.792729i	−0.328979	+	0.239017i	0.411019	+	0.911627i	$0.365173\pi$
$12$	−3.13337	−	2.27653i	−0.904526	−	0.657177i
$13$	−1.06761	−	0.775663i	−0.296101	−	0.215130i	0.429808	−	0.902920i	$-0.358581\pi$
$13$	−1.06761	−	0.775663i	−0.296101	−	0.215130i	−0.725910	+	0.687790i	$0.758581\pi$
$14$	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	0.979180	+	0.202995i	$0.0650674\pi$
$17$	1.26301	+	3.88713i	0.306324	+	0.942768i	−0.672856	+	0.739774i	$0.734933\pi$
$18$	−6.45944			−1.52250
$19$	−1.51010	−	4.64762i	−0.346442	−	1.06624i	−0.960807	−	0.277216i	$-0.910588\pi$
$19$	−1.51010	−	4.64762i	−0.346442	−	1.06624i	0.614366	−	0.789021i	$-0.289412\pi$
$20$		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	$-0.607918\pi$
$23$	2.21361	−	1.60828i	0.461570	−	0.335350i	0.794147	+	0.607726i	$0.207918\pi$
$24$	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	0.726619	+	0.687040i	$0.241090\pi$
$29$	−1.42739	+	4.39306i	−0.265060	+	0.815771i	−0.991680	+	0.128731i	$0.958910\pi$
$30$		0			0
$31$	2.21172	+	6.80697i	0.397236	+	1.22257i	0.927206	+	0.374551i	$0.122203\pi$
$31$	2.21172	+	6.80697i	0.397236	+	1.22257i	−0.529970	+	0.848016i	$0.677797\pi$
$32$	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	$-0.0483649\pi$
$37$	6.99508	+	5.08223i	1.14998	+	0.835513i	0.161506	+	0.986872i	$0.448365\pi$
$38$	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	0.999426	−	0.0338695i	$-0.0107830\pi$
$41$	8.17073	+	5.93639i	1.27605	+	0.927108i	0.276628	+	0.960977i	$0.410783\pi$
$42$	−1.27660	−	3.92896i	−0.196983	−	0.606252i
$43$	2.43460			0.371272			0.185636	−	0.982619i	$-0.440565\pi$
$43$	2.43460			0.371272			0.185636	+	0.982619i	$0.440565\pi$
$44$	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	−0.622231	−	0.782834i	$-0.713774\pi$
$47$	2.33985	−	7.20133i	0.341303	−	1.05042i	0.963534	−	0.267588i	$-0.0862265\pi$
$48$	−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	$-0.913586\pi$
$53$	−0.191975	+	0.590839i	−0.0263698	+	0.0811579i	0.937006	+	0.349315i	$0.113586\pi$
$54$	−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	0.993734	−	0.111775i	$-0.0356535\pi$
$59$	9.17521	+	6.66618i	1.19451	+	0.867862i	0.200777	+	0.979637i	$0.435653\pi$
$60$		0			0
$61$	−0.523849	+	0.380599i	−0.0670720	+	0.0487307i	−0.620816	−	0.783956i	$-0.713199\pi$
$61$	−0.523849	+	0.380599i	−0.0670720	+	0.0487307i	0.553744	+	0.832687i	$0.313199\pi$
$62$	−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	0.914055	+	0.405590i	$0.132934\pi$
$67$	3.38029	+	10.4035i	0.412969	+	1.27099i	−0.501087	+	0.865397i	$0.667066\pi$
$68$	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	−0.990484	−	0.137625i	$-0.956053\pi$
$71$	−0.912311	+	2.80781i	−0.108271	+	0.333225i	0.882213	+	0.470851i	$0.156053\pi$
$72$	−6.19241	+	19.0583i	−0.729783	+	2.24604i
$73$	−10.9533	+	7.95802i	−1.28198	+	0.931415i	−0.999611	−	0.0278896i	$-0.991121\pi$
$73$	−10.9533	+	7.95802i	−1.28198	+	0.931415i	−0.282372	+	0.959305i	$0.591121\pi$
$74$	−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	−0.912827	−	0.408346i	$-0.866106\pi$
$79$	0.583824	−	1.79683i	0.0656853	−	0.202159i	0.978513	+	0.206187i	$0.0661057\pi$
$80$		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	$-0.0583948\pi$
$83$	0.733857	+	2.25858i	0.0805513	+	0.247911i	−0.902668	+	0.430337i	$0.858395\pi$
$84$	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	−0.856173	−	0.516689i	$-0.827164\pi$
$89$	−5.93723	+	4.31365i	−0.629345	+	0.457246i	0.226828	+	0.973935i	$0.427164\pi$
$90$		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	$-0.804878\pi$
$97$	1.79204	−	5.51532i	0.181954	−	0.559996i	0.999883	+	0.0153235i	$0.00487782\pi$
$98$	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	−0.603503	−	0.797361i	$-0.706229\pi$
$103$	3.58680	−	11.0390i	0.353418	−	1.08771i	0.956921	−	0.290348i	$-0.0937711\pi$
$104$	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	$-0.336412\pi$
$107$	10.1703			0.983204			0.491602	+	0.870820i	$0.336412\pi$
$108$	−6.49142	−	19.9785i	−0.624637	−	1.92244i
$109$	−0.966573	−	0.702257i	−0.0925809	−	0.0672640i	0.540532	−	0.841324i	$-0.318223\pi$
$109$	−0.966573	−	0.702257i	−0.0925809	−	0.0672640i	−0.633113	+	0.774060i	$0.718223\pi$
$110$		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	$-0.367621\pi$
$113$	−3.62647	−	2.63479i	−0.341150	−	0.247860i	−0.745147	+	0.666900i	$0.767621\pi$
$114$	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	$-0.640669\pi$
$127$	3.37914	−	2.45509i	0.299850	−	0.217854i	0.727529	+	0.686077i	$0.240669\pi$
$128$	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	0.986327	−	0.164802i	$-0.0526986\pi$
$131$	1.04730	+	3.22327i	0.0915032	+	0.281618i	−0.894823	+	0.446420i	$0.852699\pi$
$132$	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	$-0.184108\pi$
$137$	6.74394	+	4.89976i	0.576174	+	0.418615i	−0.261169	+	0.965293i	$0.584108\pi$
$138$	4.47806	+	3.25350i	0.381198	+	0.276956i
$139$	2.77780	−	2.01819i	0.235610	−	0.171181i	−0.463715	−	0.885984i	$-0.653484\pi$
$139$	2.77780	−	2.01819i	0.235610	−	0.171181i	0.699325	+	0.714804i	$0.253484\pi$
$140$		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	$-0.399138\pi$
$157$	7.80843			0.623181			0.311590	+	0.950217i	$0.399138\pi$
$158$	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	$-0.148793\pi$
$163$	9.44814	+	6.86447i	0.740035	+	0.537667i	−0.152687	+	0.988275i	$0.548793\pi$
$164$	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	$-0.00612946\pi$
$167$	2.32133	+	7.14431i	0.179630	+	0.552844i	−0.820185	+	0.572099i	$0.806129\pi$
$168$	−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	$-0.764744\pi$
$173$	−4.29897	+	3.12338i	−0.326844	+	0.237466i	0.412246	+	0.911073i	$0.364744\pi$
$174$	−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	−0.934831	−	0.355093i	$-0.884449\pi$
$179$	0.403805	−	1.24279i	0.0301818	−	0.0928901i	0.965013	+	0.262203i	$0.0844491\pi$
$180$		0			0
$181$	−6.23062	−	19.1759i	−0.463118	−	1.42533i	−0.861334	−	0.508040i	$-0.830370\pi$
$181$	−6.23062	−	19.1759i	−0.463118	−	1.42533i	0.398215	−	0.917292i	$-0.369630\pi$
$182$	−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	−0.248597	−	0.968607i	$-0.579970\pi$
$191$	−17.2286	−	12.5173i	−1.24662	−	0.905721i	−0.998021	+	0.0628858i	$0.979970\pi$
$192$	3.82047	+	11.7582i	0.275719	+	0.848576i
$193$	−7.99352			−0.575386			−0.287693	−	0.957723i	$-0.592888\pi$
$193$	−7.99352			−0.575386			−0.287693	+	0.957723i	$0.592888\pi$
$194$	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	0.364367	+	0.931255i	$0.381285\pi$
$197$	−6.70611	+	20.6393i	−0.477790	+	1.47049i	−0.842157	+	0.539232i	$0.818715\pi$
$198$	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	−0.379426	−	0.925222i	$-0.623878\pi$
$211$	5.56723	−	4.04483i	0.383264	−	0.278457i	0.762690	+	0.646765i	$0.223878\pi$
$212$	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	$-0.792028\pi$
$223$	−6.88875	+	5.00497i	−0.461305	+	0.335158i	0.332738	+	0.943019i	$0.392028\pi$
$224$	−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	$-0.945200\pi$
$227$	−16.9761	+	12.3338i	−1.12674	+	0.818625i	−0.141524	+	0.989935i	$0.545200\pi$
$228$	−5.84872	+	18.0005i	−0.387341	+	1.19211i
$229$	9.19724	−	28.3062i	0.607771	−	1.87053i	0.131283	−	0.991345i	$-0.458090\pi$
$229$	9.19724	−	28.3062i	0.607771	−	1.87053i	0.476488	−	0.879181i	$-0.341910\pi$
$230$		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	$-0.123706\pi$
$233$	−0.701943	−	2.16036i	−0.0459858	−	0.141530i	−0.971413	+	0.237395i	$0.923706\pi$
$234$	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	−0.913107	−	0.407720i	$-0.866324\pi$
$239$	−12.4838	+	9.06999i	−0.807508	+	0.586689i	0.105599	+	0.994409i	$0.466324\pi$
$240$		0			0
$241$	3.91713	+	2.84596i	0.252324	+	0.183324i	0.706756	−	0.707457i	$-0.250158\pi$
$241$	3.91713	+	2.84596i	0.252324	+	0.183324i	−0.454432	+	0.890781i	$0.650158\pi$
$242$	−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	$-0.441198\pi$
$257$	5.88929			0.367364			0.183682	+	0.982986i	$0.441198\pi$
$258$	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	$-0.560481\pi$
$263$	−19.1553	−	13.9172i	−1.18117	−	0.858168i	−0.992303	+	0.123835i	$0.960481\pi$
$264$	−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	0.993017	+	0.117970i	$0.0376388\pi$
$269$	4.24776	+	13.0733i	0.258991	+	0.797091i	−0.734027	+	0.679121i	$0.762361\pi$
$270$		0			0
$271$	2.31726	−	7.13180i	0.140764	−	0.433226i	−0.855678	−	0.517508i	$-0.826860\pi$
$271$	2.31726	−	7.13180i	0.140764	−	0.433226i	0.996442	+	0.0842822i	$0.0268597\pi$
$272$	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	$-0.727172\pi$
$277$	−2.29597	+	1.66812i	−0.137952	+	0.100228i	0.516669	+	0.856185i	$0.327172\pi$
$278$	−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	−0.904640	−	0.426177i	$-0.859860\pi$
$281$	−7.09532	−	21.8372i	−0.423272	−	1.30270i	0.481368	−	0.876519i	$-0.340140\pi$
$282$	15.3177			0.912158
$283$	−7.76395	−	23.8950i	−0.461519	−	1.42041i	−0.863308	−	0.504677i	$-0.831612\pi$
$283$	−7.76395	−	23.8950i	−0.461519	−	1.42041i	0.401789	−	0.915732i	$-0.368388\pi$
$284$	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	$-0.819486\pi$
$293$	−28.8755			−1.68692			−0.843461	+	0.537190i	$0.819486\pi$
$294$	−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	$-0.260447\pi$
$307$	23.9526			1.36704			0.683522	+	0.729930i	$0.260447\pi$
$308$	−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	−0.337398	−	0.941362i	$-0.609547\pi$
$311$	7.99984	−	5.81222i	0.453629	−	0.329581i	0.791027	+	0.611781i	$0.209547\pi$
$312$	−6.70013	−	4.86793i	−0.379320	−	0.275592i
$313$	15.1922	+	11.0378i	0.858712	+	0.623891i	0.927534	−	0.373738i	$-0.121924\pi$
$313$	15.1922	+	11.0378i	0.858712	+	0.623891i	−0.0688221	+	0.997629i	$0.521924\pi$
$314$	−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	−0.877802	−	0.479024i	$-0.840991\pi$
$317$	−7.99793	−	24.6151i	−0.449208	−	1.38252i	0.428594	−	0.903497i	$-0.359009\pi$
$318$	−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	0.961470	−	0.274909i	$-0.0886477\pi$
$331$	0.400929	+	1.23393i	0.0220371	+	0.0678231i	−0.939433	+	0.342732i	$0.888648\pi$
$332$	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	$-0.200626\pi$
$337$	9.12322	+	6.62841i	0.496974	+	0.361073i	−0.310886	+	0.950447i	$0.600626\pi$
$338$	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	$-0.881578\pi$
$347$	0.665933	−	2.04953i	0.0357492	−	0.110025i	0.967339	+	0.253487i	$0.0815776\pi$
$348$	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	0.675740	+	0.737140i	$0.263824\pi$
$353$	−5.71587	+	17.5916i	−0.304225	+	0.936308i	−0.979965	+	0.199168i	$0.936176\pi$
$354$	−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	0.321239	−	0.946998i	$-0.395901\pi$
$359$	−9.09737	−	6.60963i	−0.480141	−	0.348843i	−0.801380	+	0.598155i	$0.795901\pi$
$360$		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	−0.864174	−	0.503193i	$-0.832158\pi$
$367$	−8.82789	−	27.1695i	−0.460812	−	1.41823i	0.403362	−	0.915041i	$-0.367842\pi$
$368$	−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	$-0.818809\pi$
$373$	−11.3948	+	8.27884i	−0.590003	+	0.428662i	0.252314	+	0.967646i	$0.418809\pi$
$374$	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	−0.610322	−	0.792154i	$-0.708960\pi$
$379$	6.79538	−	20.9140i	0.349055	−	1.07428i	0.959377	−	0.282128i	$-0.0910403\pi$
$380$		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	−0.997405	−	0.0719898i	$-0.977065\pi$
$383$	−4.55603	−	14.0220i	−0.232802	−	0.716491i	0.764603	−	0.644501i	$-0.222935\pi$
$384$	−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	−0.255654	−	0.966768i	$-0.582291\pi$
$389$	11.5340	−	8.37991i	0.584795	−	0.424879i	0.840450	+	0.541890i	$0.182291\pi$
$390$		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	$-0.943998\pi$
$397$	−1.69670	+	5.22192i	−0.0851551	+	0.262080i	0.899408	+	0.437110i	$0.143998\pi$
$398$	−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	0.480345	−	0.877080i	$-0.340511\pi$
$409$	−4.15340	−	3.01762i	−0.205372	−	0.149212i	−0.685718	+	0.727868i	$0.740511\pi$
$410$		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	0.837907	+	0.545813i	$0.183779\pi$
$419$	9.84269	+	30.2927i	0.480847	+	1.47989i	−0.357060	+	0.934081i	$0.616221\pi$
$420$		0			0
$421$	0.951909	−	2.92968i	0.0463932	−	0.142784i	−0.925177	−	0.379537i	$-0.876083\pi$
$421$	0.951909	−	2.92968i	0.0463932	−	0.142784i	0.971570	+	0.236753i	$0.0760833\pi$
$422$	−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	0.960222	+	0.279237i	$0.0900815\pi$
$431$	7.21465	+	22.2044i	0.347517	+	1.06955i	−0.612705	+	0.790312i	$0.709919\pi$
$432$	−48.7004			−2.34310
$433$	2.53831	+	7.81212i	0.121984	+	0.375427i	0.993339	−	0.115225i	$-0.0367588\pi$
$433$	2.53831	+	7.81212i	0.121984	+	0.375427i	−0.871356	+	0.490651i	$0.836759\pi$
$434$	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	−0.00938352	−	0.999956i	$-0.502987\pi$
$439$	19.6686	−	14.2901i	0.938731	−	0.682028i	0.948115	+	0.317928i	$0.102987\pi$
$440$		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	$-0.499523\pi$
$443$	0.0631363			0.00299970			0.00149985	+	0.999999i	$0.499523\pi$
$444$	−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	$-0.919546\pi$
$457$	−41.3967			−1.93646			−0.968228	+	0.250071i	$0.919546\pi$
$458$	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	−0.982137	−	0.188166i	$-0.939746\pi$
$461$	−23.7614	+	17.2637i	−1.10668	+	0.804049i	−0.124541	+	0.992214i	$0.539746\pi$
$462$	4.50750	+	3.27489i	0.209708	+	0.152362i
$463$	24.7155	+	17.9569i	1.14863	+	0.834527i	0.988298	−	0.152536i	$-0.0487441\pi$
$463$	24.7155	+	17.9569i	1.14863	+	0.834527i	0.160330	+	0.987063i	$0.448744\pi$
$464$	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	0.855414	+	0.517944i	$0.173303\pi$
$467$	10.1095	+	31.1137i	0.467810	+	1.43977i	−0.387605	+	0.921826i	$0.626697\pi$
$468$	−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	−0.999594	−	0.0284789i	$-0.990934\pi$
$479$	−3.81181	+	11.7315i	−0.174166	+	0.536028i	0.825428	+	0.564507i	$0.190934\pi$
$480$		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	$-0.595014\pi$
$487$	−28.5552	−	20.7466i	−1.29396	−	0.940117i	−0.999877	+	0.0156629i	$0.995014\pi$
$488$	−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	0.271980	−	0.962303i	$-0.412322\pi$
$491$	−12.3906	−	9.00227i	−0.559178	−	0.406267i	−0.831158	+	0.556036i	$0.812322\pi$
$492$	−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	$-0.847714\pi$
$503$	2.26662	−	6.97595i	0.101064	−	0.311042i	0.988786	+	0.149336i	$0.0477137\pi$
$504$	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	0.480742	−	0.876862i	$-0.340367\pi$
$509$	−4.61704	−	3.35447i	−0.204647	−	0.148684i	−0.685388	+	0.728178i	$0.740367\pi$
$510$		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	0.431196	+	0.902258i	$0.358092\pi$
$521$	−10.2254	+	31.4706i	−0.447983	+	1.37875i	−0.879179	+	0.476492i	$0.841908\pi$
$522$	9.22016	−	28.3767i	0.403555	−	1.24202i
$523$	25.4613	−	18.4987i	1.11335	−	0.808894i	0.130159	−	0.991493i	$-0.458451\pi$
$523$	25.4613	−	18.4987i	1.11335	−	0.808894i	0.983187	+	0.182600i	$0.0584512\pi$
$524$	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	0.909643	−	0.415391i	$-0.136355\pi$
$541$	18.5070	+	13.4461i	0.795678	+	0.578094i	−0.113965	+	0.993485i	$0.536355\pi$
$542$	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	−0.762589	−	0.646883i	$-0.776072\pi$
$547$	5.48653	−	16.8858i	0.234587	−	0.721984i	0.997176	−	0.0751011i	$-0.0239279\pi$
$548$	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	$-0.515344\pi$
$557$	−2.27448			−0.0963727			−0.0481864	+	0.998838i	$0.515344\pi$
$558$	−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	$-0.297332\pi$
$563$	0.321745	+	0.233761i	0.0135599	+	0.00985187i	−0.580985	+	0.813915i	$0.697332\pi$
$564$	−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	0.852070	−	0.523427i	$-0.175347\pi$
$569$	−3.45717	−	10.6401i	−0.144932	−	0.446055i	−0.997002	+	0.0773726i	$0.975347\pi$
$570$		0			0
$571$	−5.84424	+	17.9867i	−0.244574	+	0.752721i	0.751132	+	0.660152i	$0.229508\pi$
$571$	−5.84424	+	17.9867i	−0.244574	+	0.752721i	−0.995706	+	0.0925696i	$0.970492\pi$
$572$	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	$-0.660021\pi$
$577$	4.86874	−	3.53735i	0.202688	−	0.147262i	0.684499	+	0.729013i	$0.260021\pi$
$578$	−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	$-0.190568\pi$
$587$	13.2133	+	9.60006i	0.545373	+	0.396237i	−0.280703	+	0.959795i	$0.590568\pi$
$588$	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	$-0.444784\pi$
$593$	8.40604			0.345195			0.172597	+	0.984992i	$0.444784\pi$
$594$	−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	$-0.597879\pi$
$607$	−14.9141			−0.605345			−0.302672	+	0.953095i	$0.597879\pi$
$608$	−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	$-0.0364061\pi$
$613$	29.5107	+	21.4408i	1.19193	+	0.865985i	0.198460	+	0.980109i	$0.436406\pi$
$614$	−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	0.999825	+	0.0187338i	$0.00596351\pi$
$617$	5.01661	+	15.4395i	0.201961	+	0.621572i	−0.797864	+	0.602838i	$0.794036\pi$
$618$	23.4808			0.944537
$619$	−3.10131	−	9.54484i	−0.124652	−	0.383639i	0.869186	−	0.494486i	$-0.164644\pi$
$619$	−3.10131	−	9.54484i	−0.124652	−	0.383639i	−0.993838	+	0.110847i	$0.964644\pi$
$620$		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	0.956716	+	0.291022i	$0.0939952\pi$
$631$	8.88672	+	27.3505i	0.353775	+	1.08881i	−0.602942	+	0.797785i	$0.706005\pi$
$632$	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	0.839791	−	0.542909i	$-0.182677\pi$
$641$	14.7595	+	10.7234i	0.582963	+	0.423548i	−0.256828	+	0.966457i	$0.582677\pi$
$642$	6.35779	+	19.5673i	0.250922	+	0.772258i
$643$	−33.9734			−1.33978			−0.669890	−	0.742461i	$-0.733659\pi$
$643$	−33.9734			−1.33978			−0.669890	+	0.742461i	$0.733659\pi$
$644$	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	−0.0588895	−	0.998265i	$-0.518756\pi$
$647$	14.6390	−	45.0542i	0.575518	−	1.77126i	0.634408	−	0.772999i	$-0.281244\pi$
$648$	−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	0.422147	+	0.906527i	$0.361277\pi$
$653$	−11.5560	+	35.5657i	−0.452220	+	1.39179i	−0.874368	+	0.485264i	$0.838723\pi$
$654$	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	0.727080	−	0.686553i	$-0.240877\pi$
$659$	7.67072	+	5.57311i	0.298809	+	0.217097i	−0.428271	+	0.903650i	$0.640877\pi$
$660$		0			0
$661$	7.10389	−	5.16128i	0.276309	−	0.200750i	−0.440997	−	0.897509i	$-0.645375\pi$
$661$	7.10389	−	5.16128i	0.276309	−	0.200750i	0.717306	+	0.696758i	$0.245375\pi$
$662$	−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	−0.526418	+	0.850226i	$0.676465\pi$
$673$	−38.8538	+	28.2289i	−1.49770	+	1.08814i	−0.971285	+	0.237919i	$0.923535\pi$
$674$	−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	$-0.604272\pi$
$677$	12.4711	−	9.06078i	0.479303	−	0.348234i	0.801056	+	0.598590i	$0.204272\pi$
$678$	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	−0.969614	−	0.244638i	$-0.921331\pi$
$683$	−8.59751	−	26.4604i	−0.328975	−	1.01248i	0.640640	−	0.767842i	$-0.278669\pi$
$684$	−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	0.852716	−	0.522375i	$-0.174954\pi$
$691$	16.2824	+	11.8298i	0.619411	+	0.450028i	−0.233305	+	0.972404i	$0.574954\pi$
$692$	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	0.657746	−	0.753240i	$-0.271510\pi$
$709$	3.85098	+	2.79790i	0.144627	+	0.105077i	−0.513119	+	0.858317i	$0.671510\pi$
$710$		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	−0.991485	−	0.130221i	$-0.958431\pi$
$719$	−7.12986	−	21.9435i	−0.265899	−	0.818353i	0.725586	−	0.688132i	$-0.241569\pi$
$720$		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	$-0.793299\pi$
$727$	−12.6050	+	9.15810i	−0.467495	+	0.339655i	0.328969	+	0.944341i	$0.393299\pi$
$728$	−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	0.999955	+	0.00950846i	$0.00302668\pi$
$733$	5.32175	+	16.3787i	0.196563	+	0.604960i	−0.803391	+	0.595451i	$0.796973\pi$
$734$	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	−0.0981086	−	0.995176i	$-0.531279\pi$
$739$	22.2381	−	16.1569i	0.818043	−	0.594343i	0.916151	+	0.400833i	$0.131279\pi$
$740$		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	$-0.151206\pi$
$743$	48.4801			1.77856			0.889280	+	0.457362i	$0.151206\pi$
$744$	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	$-0.725426\pi$
$757$	−35.7934			−1.30093			−0.650466	+	0.759535i	$0.725426\pi$
$758$	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	−0.578005	−	0.816034i	$-0.696168\pi$
$761$	0.537277	−	0.390354i	0.0194763	−	0.0141503i	0.597481	+	0.801883i	$0.296168\pi$
$762$	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	0.985949	+	0.167046i	$0.0534229\pi$
$769$	7.94452	+	24.4507i	0.286487	+	0.881716i	−0.699462	+	0.714669i	$0.746577\pi$
$770$		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	$-0.456201\pi$
$773$	31.1842	−	22.6567i	1.12162	−	0.814904i	0.984454	+	0.175644i	$0.0562008\pi$
$774$	−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	$-0.0765444\pi$
$787$	29.3116	+	21.2962i	1.04485	+	0.759126i	0.0736214	+	0.997286i	$0.476544\pi$
$788$	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	−0.576337	−	0.817212i	$-0.695518\pi$
$797$	10.4533	−	32.1719i	0.370275	−	1.13959i	0.946612	−	0.322376i	$-0.104482\pi$
$798$	−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	0.608413	−	0.793621i	$-0.291807\pi$
$809$	1.18448	+	0.860572i	0.0416439	+	0.0302561i	−0.566769	+	0.823877i	$0.691807\pi$
$810$		0			0
$811$	32.9177	−	23.9161i	1.15590	−	0.839808i	0.166642	−	0.986017i	$-0.446707\pi$
$811$	32.9177	−	23.9161i	1.15590	−	0.839808i	0.989254	+	0.146210i	$0.0467075\pi$
$812$	−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	0.649278	+	0.760551i	$0.275071\pi$
$821$	−9.25608	+	28.4873i	−0.323040	+	0.994214i	−0.972318	+	0.233663i	$0.924929\pi$
$822$	−5.21107	+	16.0380i	−0.181757	+	0.559390i
$823$	−15.3203	+	11.1308i	−0.534030	+	0.387996i	−0.821863	−	0.569685i	$-0.807065\pi$
$823$	−15.3203	+	11.1308i	−0.534030	+	0.387996i	0.287833	+	0.957681i	$0.407065\pi$
$824$	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	$-0.814608\pi$
$827$	−16.3938	+	11.9108i	−0.570069	+	0.414179i	0.265061	+	0.964232i	$0.414608\pi$
$828$	10.4565	−	32.1819i	0.363389	−	1.11840i
$829$	5.14205	−	15.8256i	0.178591	−	0.549646i	−0.821188	−	0.570657i	$-0.806689\pi$
$829$	5.14205	−	15.8256i	0.178591	−	0.549646i	0.999779	+	0.0210110i	$0.00668850\pi$
$830$		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	−0.483643	−	0.875265i	$-0.660687\pi$
$839$	5.77368	−	4.19482i	0.199330	−	0.144821i	0.682973	+	0.730444i	$0.260687\pi$
$840$		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	−0.629136	−	0.777295i	$-0.716591\pi$
$853$	9.83454	−	30.2676i	0.336728	−	1.03634i	0.965864	−	0.259048i	$-0.0834088\pi$
$854$	−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	$-0.236220\pi$
$857$	43.1535			1.47409			0.737047	+	0.675842i	$0.236220\pi$
$858$	1.11258	+	3.42417i	0.0379829	+	0.116899i
$859$	−24.9917	−	18.1576i	−0.852707	−	0.619528i	0.0731840	−	0.997318i	$-0.476684\pi$
$859$	−24.9917	−	18.1576i	−0.852707	−	0.619528i	−0.925891	+	0.377791i	$0.876684\pi$
$860$		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	$-0.525239\pi$
$863$	−30.8972	−	22.4481i	−1.05175	−	0.764143i	−0.972545	+	0.232715i	$0.925239\pi$
$864$	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	$-0.520073\pi$
$877$	25.6658	−	18.6473i	0.866674	−	0.629675i	0.929692	+	0.368337i	$0.120073\pi$
$878$	−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	−0.924829	−	0.380383i	$-0.875792\pi$
$881$	−11.8789	−	36.5595i	−0.400210	−	1.23172i	0.524619	−	0.851337i	$-0.324208\pi$
$882$	18.2783			0.615464
$883$	−3.75447	−	11.5551i	−0.126348	−	0.388859i	0.867796	−	0.496920i	$-0.165536\pi$
$883$	−3.75447	−	11.5551i	−0.126348	−	0.388859i	−0.994144	+	0.108061i	$0.965536\pi$
$884$	−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	$-0.433426\pi$
$887$	−19.6131	−	14.2498i	−0.658544	−	0.478460i	−0.866171	+	0.499748i	$0.833426\pi$
$888$	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	$-0.318557\pi$
$907$	32.5046			1.07930			0.539649	+	0.841890i	$0.318557\pi$
$908$	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	−0.992773	−	0.120006i	$-0.961709\pi$
$911$	−35.7794	+	25.9953i	−1.18542	+	0.861261i	−0.192651	+	0.981267i	$0.561709\pi$
$912$	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	−0.920362	−	0.391068i	$-0.872106\pi$
$919$	−12.2969	−	37.8460i	−0.405637	−	1.24842i	0.514724	−	0.857356i	$-0.327894\pi$
$920$		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	−0.979078	−	0.203483i	$-0.934774\pi$
$929$	−2.05379	+	6.32093i	−0.0673828	+	0.207383i	0.911696	+	0.410866i	$0.134774\pi$
$930$		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	$-0.298806\pi$
$937$	0.185738	+	0.134947i	0.00606781	+	0.00440852i	−0.584747	+	0.811216i	$0.698806\pi$
$938$	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	0.147470	−	0.989067i	$-0.452887\pi$
$941$	−22.9337	−	16.6623i	−0.747618	−	0.543176i	−0.895088	+	0.445890i	$0.852887\pi$
$942$	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	0.354187	+	0.935175i	$0.384758\pi$
$947$	−14.8339	+	45.6542i	−0.482038	+	1.48356i	−0.836225	+	0.548386i	$0.815242\pi$
$948$	−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	−0.721552	−	0.692360i	$-0.756571\pi$
$953$	8.30900	−	25.5725i	0.269155	−	0.828374i	0.990707	−	0.136014i	$-0.0434291\pi$
$954$	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	$-0.0806409\pi$
$967$	1.16813	+	3.59515i	0.0375647	+	0.115612i	−0.930516	+	0.366252i	$0.880641\pi$
$968$	−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	−0.879360	−	0.476158i	$-0.842029\pi$
$971$	3.48802	−	10.7350i	0.111936	−	0.344503i	0.991296	+	0.131655i	$0.0420290\pi$
$972$	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	$-0.594836\pi$
$977$	16.4067	−	11.9201i	0.524896	−	0.381359i	0.818445	+	0.574585i	$0.194836\pi$
$978$	−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	0.988118	+	0.153694i	$0.0491171\pi$
$983$	8.74910	+	26.9270i	0.279053	+	0.858837i	−0.709065	+	0.705143i	$0.750883\pi$
$984$	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	0.237333	−	0.971428i	$-0.423727\pi$
$991$	−19.3040	−	14.0252i	−0.613211	−	0.445524i	−0.850544	+	0.525905i	$0.823727\pi$
$992$	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	$-0.969464\pi$
$997$	−4.22488	+	13.0028i	−0.133803	+	0.411804i	0.861599	+	0.507590i	$0.169464\pi$
$998$	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.n.251.1		16
5.2	odd	4		625.2.e.k.374.1		32
5.3	odd	4		625.2.e.k.374.8		32
5.4	even	2		625.2.d.p.251.4		16
25.2	odd	20		625.2.e.j.499.1		32
25.3	odd	20		625.2.b.d.624.1		16
25.4	even	10		625.2.a.e.1.1	✓	8
25.6	even	5		625.2.d.m.501.4		16
25.8	odd	20		625.2.e.j.124.1		32
25.9	even	10		625.2.d.p.376.4		16
25.11	even	5		625.2.d.m.126.4		16
25.12	odd	20		625.2.e.k.249.8		32
25.13	odd	20		625.2.e.k.249.1		32
25.14	even	10		625.2.d.q.126.1		16
25.16	even	5	inner	625.2.d.n.376.1		16
25.17	odd	20		625.2.e.j.124.8		32
25.19	even	10		625.2.d.q.501.1		16
25.21	even	5		625.2.a.g.1.8	yes	8
25.22	odd	20		625.2.b.d.624.16		16
25.23	odd	20		625.2.e.j.499.8		32
75.29	odd	10		5625.2.a.be.1.8		8
75.71	odd	10		5625.2.a.s.1.1		8
100.71	odd	10		10000.2.a.be.1.4		8
100.79	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	25.4	even	10
625.2.a.g.1.8	yes	8	25.21	even	5
625.2.b.d.624.1		16	25.3	odd	20
625.2.b.d.624.16		16	25.22	odd	20
625.2.d.m.126.4		16	25.11	even	5
625.2.d.m.501.4		16	25.6	even	5
625.2.d.n.251.1		16	1.1	even	1	trivial
625.2.d.n.376.1		16	25.16	even	5	inner
625.2.d.p.251.4		16	5.4	even	2
625.2.d.p.376.4		16	25.9	even	10
625.2.d.q.126.1		16	25.14	even	10
625.2.d.q.501.1		16	25.19	even	10
625.2.e.j.124.1		32	25.8	odd	20
625.2.e.j.124.8		32	25.17	odd	20
625.2.e.j.499.1		32	25.2	odd	20
625.2.e.j.499.8		32	25.23	odd	20
625.2.e.k.249.1		32	25.13	odd	20
625.2.e.k.249.8		32	25.12	odd	20
625.2.e.k.374.1		32	5.2	odd	4
625.2.e.k.374.8		32	5.3	odd	4
5625.2.a.s.1.1		8	75.71	odd	10
5625.2.a.be.1.8		8	75.29	odd	10
10000.2.a.be.1.4		8	100.71	odd	10
10000.2.a.bn.1.5		8	100.79	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

Introduction

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