LMFDB - Embedded newform 625.2.e.a.124.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(124,625)]

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([1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("625.124");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.e (of order $10$, 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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			124.1
Root			$1.66637 - 0.917186i$ of defining polynomial
Character	$\chi$	$=$	625.124
Dual form			625.2.e.a.499.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07822 - 0.350334i) q^{2} +(-1.52988 + 2.10569i) q^{3} +(-0.578217 - 0.420099i) q^{4} +(2.38723 - 1.73443i) q^{6} -0.407162i q^{7} +(1.80902 + 2.48990i) q^{8} +(-1.16637 - 3.58973i) q^{9} +O(q^{10})$	\(q+(-1.07822 - 0.350334i) q^{2} +(-1.52988 + 2.10569i) q^{3} +(-0.578217 - 0.420099i) q^{4} +(2.38723 - 1.73443i) q^{6} -0.407162i q^{7} +(1.80902 + 2.48990i) q^{8} +(-1.16637 - 3.58973i) q^{9} +(0.618034 - 1.90211i) q^{11} +(1.76920 - 0.574848i) q^{12} +(0.666375 - 0.216518i) q^{13} +(-0.142642 + 0.439008i) q^{14} +(-0.636498 - 1.95894i) q^{16} +(0.930307 + 1.28046i) q^{17} +4.27913i q^{18} +(4.00527 - 2.91000i) q^{19} +(0.857358 + 0.622907i) q^{21} +(-1.33275 + 1.83437i) q^{22} +(1.14264 + 0.371267i) q^{23} -8.01054 q^{24} -0.794350 q^{26} +(1.91711 + 0.622907i) q^{27} +(-0.171048 + 0.235428i) q^{28} +(4.45693 + 3.23815i) q^{29} +(-6.63709 + 4.82213i) q^{31} -3.82022i q^{32} +(3.05975 + 4.21139i) q^{33} +(-0.554485 - 1.70653i) q^{34} +(-0.833625 + 2.56564i) q^{36} +(-4.88398 + 1.58690i) q^{37} +(-5.33802 + 1.73443i) q^{38} +(-0.563549 + 1.73443i) q^{39} +(2.22992 + 6.86300i) q^{41} +(-0.706192 - 0.971990i) q^{42} +9.16531i q^{43} +(-1.15643 + 0.840198i) q^{44} +(-1.10195 - 0.800613i) q^{46} +(0.748388 - 1.03007i) q^{47} +(5.09869 + 1.65667i) q^{48} +6.83422 q^{49} -4.11950 q^{51} +(-0.476268 - 0.154749i) q^{52} +(-2.98593 + 4.10978i) q^{53} +(-1.84883 - 1.34326i) q^{54} +(1.01379 - 0.736562i) q^{56} +12.8858i q^{57} +(-3.67110 - 5.05284i) q^{58} +(2.00852 + 6.18160i) q^{59} +(-2.91097 + 8.95903i) q^{61} +(8.84558 - 2.87410i) q^{62} +(-1.46160 + 0.474903i) q^{63} +(-2.61135 + 8.03690i) q^{64} +(-1.82368 - 5.61272i) q^{66} +(-1.81140 - 2.49317i) q^{67} -1.13120i q^{68} +(-2.52988 + 1.83806i) q^{69} +(-5.55503 - 4.03596i) q^{71} +(6.82808 - 9.39804i) q^{72} +(0.518464 + 0.168459i) q^{73} +5.82193 q^{74} -3.53840 q^{76} +(-0.774467 - 0.251640i) q^{77} +(1.21526 - 1.67266i) q^{78} +(4.43470 + 3.22200i) q^{79} +(4.91623 - 3.57185i) q^{81} -8.18102i q^{82} +(-0.572582 - 0.788091i) q^{83} +(-0.234056 - 0.720350i) q^{84} +(3.21092 - 9.88219i) q^{86} +(-13.6371 + 4.43096i) q^{87} +(5.85410 - 1.90211i) q^{88} +(0.700383 - 2.15556i) q^{89} +(-0.0881579 - 0.271322i) q^{91} +(-0.504726 - 0.694696i) q^{92} -21.3529i q^{93} +(-1.16779 + 0.848451i) q^{94} +(8.04421 + 5.84446i) q^{96} +(-8.94518 + 12.3120i) q^{97} +(-7.36877 - 2.39426i) q^{98} -7.54893 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9}+O(q^{10}) $ 8 * q - 5 * q^3 + 4 * q^4 + 6 * q^6 + 10 * q^8 + q^9	$ 8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9} - 4 q^{11} + 10 q^{12} - 5 q^{13} - 7 q^{14} - 2 q^{16} + 15 q^{17} + 10 q^{19} + q^{21} + 10 q^{22} + 15 q^{23} - 20 q^{24} + 6 q^{26} - 5 q^{27} - 20 q^{28} + 15 q^{29} + q^{31} + 10 q^{33} - 12 q^{34} - 17 q^{36} - 5 q^{37} + 12 q^{39} - 9 q^{41} + 5 q^{42} + 8 q^{44} + 16 q^{46} - 15 q^{47} - 5 q^{48} + 14 q^{49} - 4 q^{51} - 20 q^{52} + 35 q^{53} - 10 q^{54} - 15 q^{56} - 20 q^{58} + 15 q^{59} + 6 q^{61} + 45 q^{62} - 20 q^{63} - 26 q^{64} - 18 q^{66} - 13 q^{69} - 29 q^{71} + 5 q^{72} + 10 q^{73} - 12 q^{74} - 20 q^{76} + 20 q^{77} - 25 q^{78} - 10 q^{79} - 12 q^{81} + 15 q^{83} - 27 q^{84} + 16 q^{86} - 55 q^{87} + 20 q^{88} + 40 q^{89} + q^{91} - 5 q^{92} - 7 q^{94} + 11 q^{96} - 10 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100}) $ 8 * q - 5 * q^3 + 4 * q^4 + 6 * q^6 + 10 * q^8 + q^9 - 4 * q^11 + 10 * q^12 - 5 * q^13 - 7 * q^14 - 2 * q^16 + 15 * q^17 + 10 * q^19 + q^21 + 10 * q^22 + 15 * q^23 - 20 * q^24 + 6 * q^26 - 5 * q^27 - 20 * q^28 + 15 * q^29 + q^31 + 10 * q^33 - 12 * q^34 - 17 * q^36 - 5 * q^37 + 12 * q^39 - 9 * q^41 + 5 * q^42 + 8 * q^44 + 16 * q^46 - 15 * q^47 - 5 * q^48 + 14 * q^49 - 4 * q^51 - 20 * q^52 + 35 * q^53 - 10 * q^54 - 15 * q^56 - 20 * q^58 + 15 * q^59 + 6 * q^61 + 45 * q^62 - 20 * q^63 - 26 * q^64 - 18 * q^66 - 13 * q^69 - 29 * q^71 + 5 * q^72 + 10 * q^73 - 12 * q^74 - 20 * q^76 + 20 * q^77 - 25 * q^78 - 10 * q^79 - 12 * q^81 + 15 * q^83 - 27 * q^84 + 16 * q^86 - 55 * q^87 + 20 * q^88 + 40 * q^89 + q^91 - 5 * q^92 - 7 * q^94 + 11 * q^96 - 10 * q^97 - 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.07822	−	0.350334i	−0.762414	−	0.247723i	−0.0980998	−	0.995177i	$-0.531276\pi$
$2$	−1.07822	−	0.350334i	−0.762414	−	0.247723i	−0.664315	+	0.747453i	$0.731276\pi$
$3$	−1.52988	+	2.10569i	−0.883274	+	1.21572i	0.0922289	+	0.995738i	$0.470601\pi$
$3$	−1.52988	+	2.10569i	−0.883274	+	1.21572i	−0.975503	+	0.219985i	$0.929399\pi$
$4$	−0.578217	−	0.420099i	−0.289108	−	0.210049i
$5$		0			0
$5$		0			0
$6$	2.38723	−	1.73443i	0.974584	−	0.708077i
$7$		−	0.407162i		−	0.153893i	−0.997035	−	0.0769463i	$-0.975483\pi$
$7$		−	0.407162i		−	0.153893i	0.997035	−	0.0769463i	$-0.0245170\pi$
$8$	1.80902	+	2.48990i	0.639584	+	0.880312i
$9$	−1.16637	−	3.58973i	−0.388792	−	1.19658i
$10$		0			0
$11$	0.618034	−	1.90211i	0.186344	−	0.573509i	−0.813625	−	0.581390i	$-0.802509\pi$
$11$	0.618034	−	1.90211i	0.186344	−	0.573509i	0.999969	+	0.00788181i	$0.00250889\pi$
$12$	1.76920	−	0.574848i	0.510724	−	0.165944i
$13$	0.666375	−	0.216518i	0.184819	−	0.0600513i	−0.215145	−	0.976582i	$-0.569023\pi$
$13$	0.666375	−	0.216518i	0.184819	−	0.0600513i	0.399964	+	0.916531i	$0.369023\pi$
$14$	−0.142642	+	0.439008i	−0.0381228	+	0.117330i
$15$		0			0
$16$	−0.636498	−	1.95894i	−0.159125	−	0.489735i
$17$	0.930307	+	1.28046i	0.225632	+	0.310556i	0.906792	−	0.421579i	$-0.138524\pi$
$17$	0.930307	+	1.28046i	0.225632	+	0.310556i	−0.681159	+	0.732135i	$0.738524\pi$
$18$			4.27913i			1.00860i
$19$	4.00527	−	2.91000i	0.918871	−	0.667599i	−0.0243714	−	0.999703i	$-0.507758\pi$
$19$	4.00527	−	2.91000i	0.918871	−	0.667599i	0.943243	+	0.332104i	$0.107758\pi$
$20$		0			0
$21$	0.857358	+	0.622907i	0.187091	+	0.135929i
$22$	−1.33275	+	1.83437i	−0.284143	+	0.391089i
$23$	1.14264	+	0.371267i	0.238257	+	0.0774145i	0.425712	−	0.904859i	$-0.360024\pi$
$23$	1.14264	+	0.371267i	0.238257	+	0.0774145i	−0.187454	+	0.982273i	$0.560024\pi$
$24$	−8.01054			−1.63514
$25$		0			0
$26$	−0.794350			−0.155785
$27$	1.91711	+	0.622907i	0.368948	+	0.119878i
$28$	−0.171048	+	0.235428i	−0.0323251	+	0.0444916i
$29$	4.45693	+	3.23815i	0.827631	+	0.601309i	0.918888	−	0.394519i	$-0.129089\pi$
$29$	4.45693	+	3.23815i	0.827631	+	0.601309i	−0.0912574	+	0.995827i	$0.529089\pi$
$30$		0			0
$31$	−6.63709	+	4.82213i	−1.19206	+	0.866080i	−0.993480	−	0.114005i	$-0.963632\pi$
$31$	−6.63709	+	4.82213i	−1.19206	+	0.866080i	−0.198577	+	0.980085i	$0.563632\pi$
$32$		−	3.82022i		−	0.675325i
$33$	3.05975	+	4.21139i	0.532634	+	0.733108i
$34$	−0.554485	−	1.70653i	−0.0950933	−	0.292667i
$35$		0			0
$36$	−0.833625	+	2.56564i	−0.138938	+	0.427606i
$37$	−4.88398	+	1.58690i	−0.802921	+	0.260885i	−0.681597	−	0.731728i	$-0.738714\pi$
$37$	−4.88398	+	1.58690i	−0.802921	+	0.260885i	−0.121324	+	0.992613i	$0.538714\pi$
$38$	−5.33802	+	1.73443i	−0.865941	+	0.281361i
$39$	−0.563549	+	1.73443i	−0.0902401	+	0.277731i
$40$		0			0
$41$	2.22992	+	6.86300i	0.348256	+	1.07182i	0.959818	+	0.280624i	$0.0905414\pi$
$41$	2.22992	+	6.86300i	0.348256	+	1.07182i	−0.611562	+	0.791196i	$0.709459\pi$
$42$	−0.706192	−	0.971990i	−0.108968	−	0.149981i
$43$			9.16531i			1.39770i	0.715270	+	0.698848i	$0.246304\pi$
$43$			9.16531i			1.39770i	−0.715270	+	0.698848i	$0.753696\pi$
$44$	−1.15643	+	0.840198i	−0.174339	+	0.126665i
$45$		0			0
$46$	−1.10195	−	0.800613i	−0.162473	−	0.118044i
$47$	0.748388	−	1.03007i	0.109164	−	0.150251i	−0.750940	−	0.660371i	$-0.770399\pi$
$47$	0.748388	−	1.03007i	0.109164	−	0.150251i	0.860103	+	0.510120i	$0.170399\pi$
$48$	5.09869	+	1.65667i	0.735933	+	0.239119i
$49$	6.83422			0.976317
$50$		0			0
$51$	−4.11950			−0.576846
$52$	−0.476268	−	0.154749i	−0.0660465	−	0.0214598i
$53$	−2.98593	+	4.10978i	−0.410149	+	0.564521i	−0.963255	−	0.268590i	$-0.913442\pi$
$53$	−2.98593	+	4.10978i	−0.410149	+	0.564521i	0.553106	+	0.833111i	$0.313442\pi$
$54$	−1.84883	−	1.34326i	−0.251594	−	0.182794i
$55$		0			0
$56$	1.01379	−	0.736562i	0.135473	−	0.0984273i
$57$			12.8858i			1.70677i
$58$	−3.67110	−	5.05284i	−0.482039	−	0.663470i
$59$	2.00852	+	6.18160i	0.261487	+	0.804776i	0.992482	+	0.122392i	$0.0390566\pi$
$59$	2.00852	+	6.18160i	0.261487	+	0.804776i	−0.730994	+	0.682383i	$0.760943\pi$
$60$		0			0
$61$	−2.91097	+	8.95903i	−0.372711	+	1.14709i	0.572299	+	0.820045i	$0.306052\pi$
$61$	−2.91097	+	8.95903i	−0.372711	+	1.14709i	−0.945010	+	0.327041i	$0.893948\pi$
$62$	8.84558	−	2.87410i	1.12339	−	0.365011i
$63$	−1.46160	+	0.474903i	−0.184144	+	0.0598321i
$64$	−2.61135	+	8.03690i	−0.326419	+	1.00461i
$65$		0			0
$66$	−1.82368	−	5.61272i	−0.224480	−	0.690878i
$67$	−1.81140	−	2.49317i	−0.221297	−	0.304590i	0.683905	−	0.729571i	$-0.260280\pi$
$67$	−1.81140	−	2.49317i	−0.221297	−	0.304590i	−0.905202	+	0.424982i	$0.860280\pi$
$68$		−	1.13120i		−	0.137178i
$69$	−2.52988	+	1.83806i	−0.304561	+	0.221277i
$70$		0			0
$71$	−5.55503	−	4.03596i	−0.659260	−	0.478981i	0.207153	−	0.978309i	$-0.433580\pi$
$71$	−5.55503	−	4.03596i	−0.659260	−	0.478981i	−0.866413	+	0.499328i	$0.833580\pi$
$72$	6.82808	−	9.39804i	0.804696	−	1.10757i
$73$	0.518464	+	0.168459i	0.0606817	+	0.0197167i	0.339201	−	0.940714i	$-0.389843\pi$
$73$	0.518464	+	0.168459i	0.0606817	+	0.0197167i	−0.278519	+	0.960431i	$0.589843\pi$
$74$	5.82193			0.676786
$75$		0			0
$76$	−3.53840			−0.405882
$77$	−0.774467	−	0.251640i	−0.0882587	−	0.0286770i
$78$	1.21526	−	1.67266i	0.137601	−	0.189391i
$79$	4.43470	+	3.22200i	0.498942	+	0.362503i	0.808613	−	0.588341i	$-0.200219\pi$
$79$	4.43470	+	3.22200i	0.498942	+	0.362503i	−0.309670	+	0.950844i	$0.600219\pi$
$80$		0			0
$81$	4.91623	−	3.57185i	0.546248	−	0.396873i
$82$		−	8.18102i		−	0.903442i
$83$	−0.572582	−	0.788091i	−0.0628490	−	0.0865043i	0.776435	−	0.630197i	$-0.217026\pi$
$83$	−0.572582	−	0.788091i	−0.0628490	−	0.0865043i	−0.839284	+	0.543693i	$0.817026\pi$
$84$	−0.234056	−	0.720350i	−0.0255376	−	0.0785966i
$85$		0			0
$86$	3.21092	−	9.88219i	0.346242	−	1.06562i
$87$	−13.6371	+	4.43096i	−1.46205	+	0.475049i
$88$	5.85410	−	1.90211i	0.624049	−	0.202766i
$89$	0.700383	−	2.15556i	0.0742404	−	0.228488i	−0.907050	−	0.421024i	$-0.861671\pi$
$89$	0.700383	−	2.15556i	0.0742404	−	0.228488i	0.981290	+	0.192535i	$0.0616709\pi$
$90$		0			0
$91$	−0.0881579	−	0.271322i	−0.00924146	−	0.0284423i
$92$	−0.504726	−	0.694696i	−0.0526213	−	0.0724270i
$93$		−	21.3529i		−	2.21420i
$94$	−1.16779	+	0.848451i	−0.120449	+	0.0875110i
$95$		0			0
$96$	8.04421	+	5.84446i	0.821009	+	0.596498i
$97$	−8.94518	+	12.3120i	−0.908245	+	1.25009i	0.0595168	+	0.998227i	$0.481044\pi$
$97$	−8.94518	+	12.3120i	−0.908245	+	1.25009i	−0.967762	+	0.251865i	$0.918956\pi$
$98$	−7.36877	−	2.39426i	−0.744358	−	0.241857i
$99$	−7.54893			−0.758696
$100$		0			0
$101$	18.3965			1.83052			0.915261	−	0.402861i	$-0.131984\pi$
$101$	18.3965			1.83052			0.915261	+	0.402861i	$0.131984\pi$
$102$	4.44172	+	1.44320i	0.439796	+	0.142898i
$103$	6.98539	−	9.61456i	0.688290	−	0.947351i	−0.311706	−	0.950179i	$-0.600900\pi$
$103$	6.98539	−	9.61456i	0.688290	−	0.947351i	0.999996	+	0.00282822i	$0.000900250\pi$
$104$	1.74459	+	1.26752i	0.171071	+	0.124291i
$105$		0			0
$106$	4.65927	−	3.38516i	0.452548	−	0.328796i
$107$		−	0.754919i		−	0.0729808i	−0.999334	−	0.0364904i	$-0.988382\pi$
$107$		−	0.754919i		−	0.0729808i	0.999334	−	0.0364904i	$-0.0116178\pi$
$108$	−0.846822	−	1.16555i	−0.0814855	−	0.112155i
$109$	2.82983	+	8.70932i	0.271048	+	0.834201i	0.990238	+	0.139387i	$0.0445133\pi$
$109$	2.82983	+	8.70932i	0.271048	+	0.834201i	−0.719190	+	0.694814i	$0.755487\pi$
$110$		0			0
$111$	4.13035	−	12.7119i	0.392036	−	1.20656i
$112$	−0.797605	+	0.259158i	−0.0753666	+	0.0244881i
$113$	12.2115	−	3.96774i	1.14876	−	0.373254i	0.328082	−	0.944649i	$-0.393598\pi$
$113$	12.2115	−	3.96774i	1.14876	−	0.373254i	0.820675	+	0.571395i	$0.193598\pi$
$114$	4.51433	−	13.8937i	0.422806	−	1.30126i
$115$		0			0
$116$	−1.21673	−	3.74470i	−0.112970	−	0.347687i
$117$	−1.55448	−	2.13956i	−0.143712	−	0.197803i
$118$		−	7.36876i		−	0.678349i
$119$	0.521353	−	0.378785i	0.0477923	−	0.0347232i
$120$		0			0
$121$	5.66312	+	4.11450i	0.514829	+	0.374045i
$122$	6.27730	−	8.63997i	0.568320	−	0.782226i
$123$	−17.8629	−	5.80400i	−1.61064	−	0.523329i
$124$	5.86345			0.526553
$125$		0			0
$126$	1.74230			0.155216
$127$	−6.75742	−	2.19562i	−0.599624	−	0.194830i	−0.00655135	−	0.999979i	$-0.502085\pi$
$127$	−6.75742	−	2.19562i	−0.599624	−	0.194830i	−0.593073	+	0.805149i	$0.702085\pi$
$128$	1.14026	−	1.56944i	0.100786	−	0.138720i
$129$	−19.2993	−	14.0218i	−1.69921	−	1.23455i
$130$		0			0
$131$	−1.93699	+	1.40731i	−0.169236	+	0.122957i	−0.669179	−	0.743101i	$-0.733354\pi$
$131$	−1.93699	+	1.40731i	−0.169236	+	0.122957i	0.499943	+	0.866058i	$0.333354\pi$
$132$		−	3.72049i		−	0.323827i
$133$	−1.18484	−	1.63079i	−0.102739	−	0.141408i
$134$	1.07963	+	3.32277i	0.0932662	+	0.287044i
$135$		0			0
$136$	−1.50527	+	4.63274i	−0.129076	+	0.397254i
$137$	18.0885	−	5.87730i	1.54540	−	0.502132i	0.592542	−	0.805540i	$-0.298125\pi$
$137$	18.0885	−	5.87730i	1.54540	−	0.502132i	0.952861	+	0.303408i	$0.0981246\pi$
$138$	3.37169	−	1.09553i	0.287017	−	0.0932576i
$139$	2.08114	−	6.40508i	0.176520	−	0.543272i	−0.823180	−	0.567781i	$-0.807802\pi$
$139$	2.08114	−	6.40508i	0.176520	−	0.543272i	0.999700	+	0.0245087i	$0.00780215\pi$
$140$		0			0
$141$	1.02407	+	3.15175i	0.0862420	+	0.265426i
$142$	4.57559	+	6.29776i	0.383975	+	0.528496i
$143$		−	1.40134i		−	0.117186i
$144$	−6.28968	+	4.56972i	−0.524140	+	0.380810i
$145$		0			0
$146$	−0.500000	−	0.363271i	−0.0413803	−	0.0300645i
$147$	−10.4555	+	14.3908i	−0.862356	+	1.18693i
$148$	3.49065	+	1.13418i	0.286930	+	0.0932292i
$149$	0.720492			0.0590250			0.0295125	−	0.999564i	$-0.490605\pi$
$149$	0.720492			0.0590250			0.0295125	+	0.999564i	$0.490605\pi$
$150$		0			0
$151$	−15.5178			−1.26282			−0.631412	−	0.775447i	$-0.717524\pi$
$151$	−15.5178			−1.26282			−0.631412	+	0.775447i	$0.717524\pi$
$152$	14.4912	+	4.70847i	1.17539	+	0.381908i
$153$	3.51141	−	4.83304i	0.283881	−	0.390728i
$154$	0.746886	+	0.542644i	0.0601858	+	0.0437275i
$155$		0			0
$156$	1.05448	−	0.766128i	0.0844263	−	0.0613393i
$157$			2.78418i			0.222202i	0.993809	+	0.111101i	$0.0354376\pi$
$157$			2.78418i			0.222202i	−0.993809	+	0.111101i	$0.964562\pi$
$158$	−3.65279	−	5.02763i	−0.290600	−	0.399977i
$159$	−4.08583	−	12.5749i	−0.324027	−	0.997254i
$160$		0			0
$161$	0.151166	−	0.465240i	0.0119135	−	0.0366661i
$162$	−6.55211	+	2.12891i	−0.514782	+	0.167263i
$163$	−23.0226	+	7.48049i	−1.80327	+	0.585917i	−0.999954	−	0.00963930i	$-0.996932\pi$
$163$	−23.0226	+	7.48049i	−1.80327	+	0.585917i	−0.803314	+	0.595556i	$0.796932\pi$
$164$	1.59376	−	4.90509i	0.124452	−	0.383023i
$165$		0			0
$166$	0.341272	+	1.05033i	0.0264879	+	0.0815213i
$167$	11.1951	+	15.4087i	0.866300	+	1.19236i	0.980030	+	0.198848i	$0.0637199\pi$
$167$	11.1951	+	15.4087i	0.866300	+	1.19236i	−0.113731	+	0.993512i	$0.536280\pi$
$168$			3.26158i			0.251637i
$169$	−10.1200	+	7.35264i	−0.778465	+	0.565588i
$170$		0			0
$171$	−15.1178	−	10.9837i	−1.15608	−	0.839944i
$172$	3.85034	−	5.29953i	0.293585	−	0.404086i
$173$	12.5987	+	4.09356i	0.957861	+	0.311228i	0.745906	−	0.666052i	$-0.232017\pi$
$173$	12.5987	+	4.09356i	0.957861	+	0.311228i	0.211955	+	0.977279i	$0.432017\pi$
$174$	16.2561			1.23237
$175$		0			0
$176$	−4.11950			−0.310519
$177$	−16.0893	−	5.22775i	−1.20935	−	0.392941i
$178$	−1.51033	+	2.07879i	−0.113204	+	0.155812i
$179$	−9.89021	−	7.18566i	−0.739229	−	0.537081i	0.153241	−	0.988189i	$-0.451029\pi$
$179$	−9.89021	−	7.18566i	−0.739229	−	0.537081i	−0.892469	+	0.451108i	$0.851029\pi$
$180$		0			0
$181$	−8.83187	+	6.41673i	−0.656468	+	0.476952i	−0.865468	−	0.500964i	$-0.832979\pi$
$181$	−8.83187	+	6.41673i	−0.656468	+	0.476952i	0.209000	+	0.977916i	$0.432979\pi$
$182$			0.323429i			0.0239741i
$183$	−14.4116	−	19.8358i	−1.06533	−	1.46631i
$184$	1.14264	+	3.51669i	0.0842367	+	0.259254i
$185$		0			0
$186$	−7.48066	+	23.0231i	−0.548509	+	1.68814i
$187$	3.01054	−	0.978182i	0.220152	−	0.0715318i
$188$	−0.865461	+	0.281205i	−0.0631202	+	0.0205090i
$189$	0.253624	−	0.780573i	0.0184484	−	0.0567784i
$190$		0			0
$191$	0.484424	+	1.49090i	0.0350517	+	0.107878i	0.967052	−	0.254581i	$-0.0819374\pi$
$191$	0.484424	+	1.49090i	0.0350517	+	0.107878i	−0.932000	+	0.362459i	$0.881937\pi$
$192$	−12.9282	−	17.7942i	−0.933014	−	1.28418i
$193$		−	1.65786i		−	0.119335i	−0.998218	−	0.0596675i	$-0.980996\pi$
$193$		−	1.65786i		−	0.119335i	0.998218	−	0.0596675i	$-0.0190040\pi$
$194$	13.9581	−	10.1412i	1.00214	−	0.728095i
$195$		0			0
$196$	−3.95166	−	2.87105i	−0.282261	−	0.205075i
$197$	7.80760	−	10.7462i	0.556268	−	0.765638i	−0.434578	−	0.900634i	$-0.643102\pi$
$197$	7.80760	−	10.7462i	0.556268	−	0.765638i	0.990846	+	0.134997i	$0.0431024\pi$
$198$	8.13939	+	2.64465i	0.578441	+	0.187947i
$199$	−12.1025			−0.857921			−0.428960	−	0.903323i	$-0.641120\pi$
$199$	−12.1025			−0.857921			−0.428960	+	0.903323i	$0.641120\pi$
$200$		0			0
$201$	8.02107			0.565763
$202$	−19.8354	−	6.44493i	−1.39562	−	0.453463i
$203$	1.31845	−	1.81469i	0.0925370	−	0.127366i
$204$	2.38197	+	1.73060i	0.166771	+	0.121166i
$205$		0			0
$206$	−10.9001	+	7.91936i	−0.759443	+	0.551768i
$207$		−	4.53482i		−	0.315192i
$208$	−0.848293	−	1.16757i	−0.0588185	−	0.0809567i
$209$	−3.05975	−	9.41695i	−0.211647	−	0.651384i
$210$		0			0
$211$	−2.07060	+	6.37266i	−0.142546	+	0.438712i	−0.996687	−	0.0813294i	$-0.974083\pi$
$211$	−2.07060	+	6.37266i	−0.142546	+	0.438712i	0.854141	+	0.520041i	$0.174083\pi$
$212$	3.45303	−	1.12196i	0.237155	−	0.0770562i
$213$	16.9970	−	5.52266i	1.16462	−	0.378407i
$214$	−0.264474	+	0.813966i	−0.0180790	+	0.0556416i
$215$		0			0
$216$	1.91711	+	5.90026i	0.130443	+	0.401462i
$217$	1.96339	+	2.70237i	0.133283	+	0.183449i
$218$		−	10.3819i		−	0.703152i
$219$	−1.14791	+	0.834005i	−0.0775686	+	0.0563569i
$220$		0			0
$221$	0.897175	+	0.651836i	0.0603505	+	0.0438472i
$222$	−8.90683	+	12.2592i	−0.597788	+	0.822784i
$223$	10.0733	+	3.27301i	0.674558	+	0.219177i	0.626211	−	0.779654i	$-0.284605\pi$
$223$	10.0733	+	3.27301i	0.674558	+	0.219177i	0.0483465	+	0.998831i	$0.484605\pi$
$224$	−1.55545			−0.103928
$225$		0			0
$226$	−14.5566			−0.968293
$227$	18.6514	+	6.06020i	1.23794	+	0.402230i	0.853583	−	0.520956i	$-0.174425\pi$
$227$	18.6514	+	6.06020i	1.23794	+	0.402230i	0.384353	+	0.923186i	$0.374425\pi$
$228$	5.41331	−	7.45079i	0.358505	−	0.493440i
$229$	7.15088	+	5.19542i	0.472544	+	0.343323i	0.798432	−	0.602085i	$-0.205663\pi$
$229$	7.15088	+	5.19542i	0.472544	+	0.343323i	−0.325888	+	0.945408i	$0.605663\pi$
$230$		0			0
$231$	1.71472	−	1.24581i	0.112820	−	0.0819685i
$232$			16.9552i			1.11316i
$233$	6.50233	+	8.94969i	0.425982	+	0.586313i	0.967025	−	0.254681i	$-0.0819706\pi$
$233$	6.50233	+	8.94969i	0.425982	+	0.586313i	−0.541043	+	0.840995i	$0.681971\pi$
$234$	0.926509	+	2.85150i	0.0605678	+	0.186409i
$235$		0			0
$236$	1.43552	−	4.41808i	0.0934445	−	0.287593i
$237$	−13.5691	+	4.40886i	−0.881406	+	0.286386i
$238$	−0.694833	+	0.225765i	−0.0450393	+	0.0146342i
$239$	−4.97686	+	15.3172i	−0.321926	+	0.990788i	0.650882	+	0.759179i	$0.274399\pi$
$239$	−4.97686	+	15.3172i	−0.321926	+	0.990788i	−0.972809	+	0.231609i	$0.925601\pi$
$240$		0			0
$241$	1.85062	+	5.69562i	0.119209	+	0.366887i	0.992802	−	0.119771i	$-0.0382159\pi$
$241$	1.85062	+	5.69562i	0.119209	+	0.366887i	−0.873593	+	0.486658i	$0.838216\pi$
$242$	−4.66462	−	6.42030i	−0.299853	−	0.412713i
$243$			21.8639i			1.40257i
$244$	5.44685	−	3.95737i	0.348699	−	0.253344i
$245$		0			0
$246$	17.2267	+	12.5159i	1.09834	+	0.797988i
$247$	2.03894	−	2.80636i	0.129735	−	0.178565i
$248$	−24.0132	−	7.80237i	−1.52484	−	0.495451i
$249$	2.53546			0.160678
$250$		0			0
$251$	3.73176			0.235547			0.117773	−	0.993041i	$-0.462424\pi$
$251$	3.73176			0.235547			0.117773	+	0.993041i	$0.462424\pi$
$252$	1.04463	+	0.339420i	0.0658054	+	0.0213815i
$253$	1.41238	−	1.94398i	0.0887958	−	0.122217i
$254$	6.51676	+	4.73471i	0.408898	+	0.297082i
$255$		0			0
$256$	11.8939	−	8.64144i	0.743370	−	0.540090i
$257$		−	23.5935i		−	1.47172i	−0.677132	−	0.735862i	$-0.736777\pi$
$257$		−	23.5935i		−	1.47172i	0.677132	−	0.735862i	$-0.263223\pi$
$258$	15.8966	+	21.8797i	0.989676	+	1.36217i
$259$	0.646125	+	1.98857i	0.0401482	+	0.123564i
$260$		0			0
$261$	6.42563	−	19.7761i	0.397737	−	1.22411i
$262$	2.58152	−	0.838788i	0.159487	−	0.0518205i
$263$	−6.31621	+	2.05226i	−0.389474	+	0.126548i	−0.497207	−	0.867632i	$-0.665641\pi$
$263$	−6.31621	+	2.05226i	−0.389474	+	0.126548i	0.107733	+	0.994180i	$0.465641\pi$
$264$	−4.95078	+	15.2369i	−0.304700	+	0.937769i
$265$		0			0
$266$	0.706192	+	2.17344i	0.0432994	+	0.133262i
$267$	3.46744	+	4.77252i	0.212204	+	0.292074i
$268$			2.20256i			0.134543i
$269$	−10.5527	+	7.66701i	−0.643411	+	0.467466i	−0.861020	−	0.508570i	$-0.830174\pi$
$269$	−10.5527	+	7.66701i	−0.643411	+	0.467466i	0.217609	+	0.976036i	$0.430174\pi$
$270$		0			0
$271$	9.58586	+	6.96454i	0.582300	+	0.423066i	0.839552	−	0.543279i	$-0.182817\pi$
$271$	9.58586	+	6.96454i	0.582300	+	0.423066i	−0.257253	+	0.966344i	$0.582817\pi$
$272$	1.91620	−	2.63742i	0.116187	−	0.159917i
$273$	0.706192	+	0.229456i	0.0427407	+	0.0138873i
$274$	−21.5623			−1.30263
$275$		0			0
$276$	2.23498			0.134530
$277$	16.1260	+	5.23965i	0.968917	+	0.314820i	0.750379	−	0.661008i	$-0.229871\pi$
$277$	16.1260	+	5.23965i	0.968917	+	0.314820i	0.218538	+	0.975828i	$0.429871\pi$
$278$	−4.48783	+	6.17697i	−0.269162	+	0.370470i
$279$	25.0515	+	18.2010i	1.49979	+	1.08966i
$280$		0			0
$281$	4.10575	−	2.98300i	0.244928	−	0.177951i	−0.458548	−	0.888670i	$-0.651630\pi$
$281$	4.10575	−	2.98300i	0.244928	−	0.177951i	0.703476	+	0.710719i	$0.251630\pi$
$282$		−	3.75704i		−	0.223728i
$283$	6.95047	+	9.56650i	0.413162	+	0.568669i	0.963986	−	0.265952i	$-0.0856864\pi$
$283$	6.95047	+	9.56650i	0.413162	+	0.568669i	−0.550824	+	0.834622i	$0.685686\pi$
$284$	1.51650	+	4.66732i	0.0899880	+	0.276955i
$285$		0			0
$286$	−0.490935	+	1.51094i	−0.0290296	+	0.0893439i
$287$	2.79435	−	0.907939i	0.164945	−	0.0535940i
$288$	−13.7136	+	4.45580i	−0.808079	+	0.262561i
$289$	4.47919	−	13.7855i	0.263482	−	0.810913i
$290$		0			0
$291$	−12.2403	−	37.6716i	−0.717536	−	2.20835i
$292$	−0.229015	−	0.315212i	−0.0134021	−	0.0184464i
$293$			19.4348i			1.13540i	0.823237	+	0.567698i	$0.192166\pi$
$293$			19.4348i			1.13540i	−0.823237	+	0.567698i	$0.807834\pi$
$294$	16.3149	−	11.8535i	0.951503	−	0.691307i
$295$		0			0
$296$	−12.7864	−	9.28988i	−0.743196	−	0.539963i
$297$	2.36968	−	3.26158i	0.137503	−	0.189256i
$298$	−0.776846	−	0.252413i	−0.0450015	−	0.0146219i
$299$	0.841814			0.0486834
$300$		0			0
$301$	3.73176			0.215095
$302$	16.7316	+	5.43643i	0.962795	+	0.312831i
$303$	−28.1444	+	38.7374i	−1.61685	+	2.22541i
$304$	−8.24986	−	5.99387i	−0.473162	−	0.343772i
$305$		0			0
$306$	−5.47924	+	3.98090i	−0.313227	+	0.227573i
$307$			25.4169i			1.45062i	0.688423	+	0.725310i	$0.258303\pi$
$307$			25.4169i			1.45062i	−0.688423	+	0.725310i	$0.741697\pi$
$308$	0.342096	+	0.470855i	0.0194927	+	0.0268295i
$309$	9.55854	+	29.4182i	0.543766	+	1.67354i
$310$		0			0
$311$	4.90032	−	15.0816i	0.277872	−	0.855201i	−0.710573	−	0.703623i	$-0.751564\pi$
$311$	4.90032	−	15.0816i	0.277872	−	0.855201i	0.988445	−	0.151578i	$-0.0484356\pi$
$312$	−5.33802	+	1.73443i	−0.302206	+	0.0981926i
$313$	6.67303	−	2.16820i	0.377182	−	0.122554i	−0.114290	−	0.993447i	$-0.536459\pi$
$313$	6.67303	−	2.16820i	0.377182	−	0.122554i	0.491471	+	0.870894i	$0.336459\pi$
$314$	0.975392	−	3.00195i	0.0550445	−	0.169410i
$315$		0			0
$316$	−1.21066	−	3.72602i	−0.0681049	−	0.209605i
$317$	−7.66100	−	10.5445i	−0.430285	−	0.592236i	0.537734	−	0.843115i	$-0.319280\pi$
$317$	−7.66100	−	10.5445i	−0.430285	−	0.592236i	−0.968019	+	0.250879i	$0.919280\pi$
$318$			14.9899i			0.840590i
$319$	8.91385	−	6.47629i	0.499080	−	0.362603i
$320$		0			0
$321$	1.58963	+	1.15493i	0.0887244	+	0.0644620i
$322$	−0.325979	+	0.448671i	−0.0181661	+	0.0250035i
$323$	7.45225	+	2.42138i	0.414654	+	0.134729i
$324$	−4.34318			−0.241288
$325$		0			0
$326$	27.4440			1.51998
$327$	−22.6684	−	7.36542i	−1.25357	−	0.407309i
$328$	−13.0542	+	17.9676i	−0.720798	+	0.992093i
$329$	−0.419404	−	0.304715i	−0.0231225	−	0.0167995i
$330$		0			0
$331$	14.2742	−	10.3708i	0.784580	−	0.570031i	−0.121770	−	0.992558i	$-0.538857\pi$
$331$	14.2742	−	10.3708i	0.784580	−	0.570031i	0.906350	+	0.422527i	$0.138857\pi$
$332$			0.696229i			0.0382105i
$333$	11.3931	+	15.6813i	0.624338	+	0.859327i
$334$	−6.67252	−	20.5359i	−0.365104	−	1.12367i
$335$		0			0
$336$	0.674531	−	2.07599i	0.0367987	−	0.113255i
$337$	−23.6333	+	7.67892i	−1.28739	+	0.418297i	−0.871176	−	0.490971i	$-0.836642\pi$
$337$	−23.6333	+	7.67892i	−1.28739	+	0.418297i	−0.416211	+	0.909268i	$0.636642\pi$
$338$	13.4875	−	4.38235i	0.733622	−	0.238368i
$339$	−10.3272	+	31.7838i	−0.560895	+	1.72626i
$340$		0			0
$341$	5.07029	+	15.6047i	0.274571	+	0.845044i
$342$	12.4523	+	17.1391i	0.673341	+	0.926774i
$343$		−	5.63276i		−	0.304141i
$344$	−22.8207	+	16.5802i	−1.23041	+	0.893944i
$345$		0			0
$346$	−12.1500	−	8.82750i	−0.653188	−	0.474569i
$347$	7.80431	−	10.7417i	0.418957	−	0.576645i	−0.546417	−	0.837513i	$-0.684009\pi$
$347$	7.80431	−	10.7417i	0.418957	−	0.576645i	0.965375	+	0.260868i	$0.0840087\pi$
$348$	9.74664	+	3.16687i	0.522475	+	0.169762i
$349$	18.1283			0.970385			0.485192	−	0.874407i	$-0.338750\pi$
$349$	18.1283			0.970385			0.485192	+	0.874407i	$0.338750\pi$
$350$		0			0
$351$	1.41238			0.0753875
$352$	−7.26649	−	2.36102i	−0.387305	−	0.125843i
$353$	10.4063	−	14.3230i	0.553871	−	0.762338i	−0.436660	−	0.899627i	$-0.643839\pi$
$353$	10.4063	−	14.3230i	0.553871	−	0.762338i	0.990531	+	0.137288i	$0.0438387\pi$
$354$	15.5163	+	11.2733i	0.824684	+	0.599168i
$355$		0			0
$356$	−1.31052	+	0.952148i	−0.0694574	+	0.0504638i
$357$			1.67730i			0.0887723i
$358$	8.14641	+	11.2126i	0.430551	+	0.592603i
$359$	−10.0568	−	30.9515i	−0.530775	−	1.63356i	−0.752605	−	0.658473i	$-0.771203\pi$
$359$	−10.0568	−	30.9515i	−0.530775	−	1.63356i	0.221829	−	0.975086i	$-0.428797\pi$
$360$		0			0
$361$	1.70276	−	5.24056i	0.0896190	−	0.275819i
$362$	11.7707	−	3.82452i	0.618653	−	0.201012i
$363$	−17.3277	+	5.63012i	−0.909471	+	0.295505i
$364$	−0.0630078	+	0.193918i	−0.00330250	+	0.0101641i
$365$		0			0
$366$	8.58963	+	26.4362i	0.448987	+	1.38184i
$367$	−19.3664	−	26.6556i	−1.01092	−	1.39141i	−0.918379	−	0.395702i	$-0.870501\pi$
$367$	−19.3664	−	26.6556i	−1.01092	−	1.39141i	−0.0925399	−	0.995709i	$-0.529499\pi$
$368$		−	2.47468i		−	0.129002i
$369$	22.0354	−	16.0097i	1.14712	−	0.833429i
$370$		0			0
$371$	1.67334	+	1.21575i	0.0868756	+	0.0631188i
$372$	−8.97035	+	12.3466i	−0.465091	+	0.640143i
$373$	−3.29681	−	1.07120i	−0.170703	−	0.0554646i	0.222419	−	0.974951i	$-0.428605\pi$
$373$	−3.29681	−	1.07120i	−0.170703	−	0.0554646i	−0.393121	+	0.919487i	$0.628605\pi$
$374$	−3.58870			−0.185567
$375$		0			0
$376$	3.91861			0.202087
$377$	3.67110	+	1.19281i	0.189071	+	0.0614330i
$378$	−0.546923	+	0.752774i	−0.0281307	+	0.0387185i
$379$	−1.56029	−	1.13362i	−0.0801469	−	0.0582301i	0.546990	−	0.837139i	$-0.315773\pi$
$379$	−1.56029	−	1.13362i	−0.0801469	−	0.0582301i	−0.627137	+	0.778909i	$0.715773\pi$
$380$		0			0
$381$	14.9613	−	10.8700i	0.766492	−	0.556889i
$382$		−	1.77723i		−	0.0909309i
$383$	−2.89780	−	3.98848i	−0.148071	−	0.203802i	0.728538	−	0.685005i	$-0.240200\pi$
$383$	−2.89780	−	3.98848i	−0.148071	−	0.203802i	−0.876609	+	0.481203i	$0.840200\pi$
$384$	1.56029	+	4.80209i	0.0796234	+	0.245056i
$385$		0			0
$386$	−0.580803	+	1.78753i	−0.0295621	+	0.0909827i
$387$	32.9010	−	10.6902i	1.67245	−	0.543413i
$388$	10.3445	−	3.36113i	0.525163	−	0.170636i
$389$	−4.13650	+	12.7308i	−0.209729	+	0.645479i	0.789757	+	0.613420i	$0.210207\pi$
$389$	−4.13650	+	12.7308i	−0.209729	+	0.645479i	−0.999486	+	0.0320593i	$0.989793\pi$
$390$		0			0
$391$	0.587616	+	1.80850i	0.0297170	+	0.0914596i
$392$	12.3632	+	17.0165i	0.624437	+	0.859464i
$393$		−	6.23172i		−	0.314349i
$394$	−12.1831	+	8.85151i	−0.613773	+	0.445932i
$395$		0			0
$396$	4.36492	+	3.17130i	0.219345	+	0.159364i
$397$	1.25719	−	1.73038i	0.0630968	−	0.0868452i	−0.776302	−	0.630361i	$-0.782907\pi$
$397$	1.25719	−	1.73038i	0.0630968	−	0.0868452i	0.839399	+	0.543515i	$0.182907\pi$
$398$	13.0491	+	4.23990i	0.654091	+	0.212527i
$399$	5.24660			0.262659
$400$		0			0
$401$	−26.8213			−1.33939			−0.669696	−	0.742635i	$-0.733576\pi$
$401$	−26.8213			−1.33939			−0.669696	+	0.742635i	$0.733576\pi$
$402$	−8.64845	−	2.81005i	−0.431346	−	0.140153i
$403$	−3.37871	+	4.65040i	−0.168306	+	0.231653i
$404$	−10.6372	−	7.72836i	−0.529219	−	0.384500i
$405$		0			0
$406$	−2.05732	+	1.49473i	−0.102103	+	0.0741823i
$407$			10.2706i			0.509097i
$408$	−7.45225	−	10.2571i	−0.368942	−	0.507804i
$409$	−4.32570	−	13.3131i	−0.213892	−	0.658292i	−0.999230	−	0.0392250i	$-0.987511\pi$
$409$	−4.32570	−	13.3131i	−0.213892	−	0.658292i	0.785338	−	0.619067i	$-0.212489\pi$
$410$		0			0
$411$	−15.2973	+	47.0803i	−0.754561	+	2.32230i
$412$	−8.07813	+	2.62474i	−0.397981	+	0.129312i
$413$	2.51691	−	0.817793i	0.123849	−	0.0402410i
$414$	−1.58870	+	4.88951i	−0.0780803	+	0.240307i
$415$		0			0
$416$	−0.827147	−	2.54570i	−0.0405542	−	0.124813i
$417$	10.3033	+	14.1812i	0.504553	+	0.694457i
$418$			11.2254i			0.549055i
$419$	25.0003	−	18.1638i	1.22134	−	0.887357i	0.225132	−	0.974328i	$-0.427719\pi$
$419$	25.0003	−	18.1638i	1.22134	−	0.887357i	0.996211	+	0.0869710i	$0.0277187\pi$
$420$		0			0
$421$	6.66609	+	4.84320i	0.324885	+	0.236043i	0.738257	−	0.674519i	$-0.235649\pi$
$421$	6.66609	+	4.84320i	0.324885	+	0.236043i	−0.413372	+	0.910562i	$0.635649\pi$
$422$	4.46512	−	6.14570i	0.217358	−	0.299168i
$423$	−4.57057	−	1.48507i	−0.222229	−	0.0722065i
$424$	−15.6345			−0.759279
$425$		0			0
$426$	−20.2612			−0.981660
$427$	3.64777	+	1.18523i	0.176528	+	0.0573575i
$428$	−0.317141	+	0.436507i	−0.0153296	+	0.0210993i
$429$	2.95078	+	2.14387i	0.142465	+	0.103507i
$430$		0			0
$431$	−21.9633	+	15.9573i	−1.05794	+	0.768636i	−0.973705	−	0.227810i	$-0.926843\pi$
$431$	−21.9633	+	15.9573i	−1.05794	+	0.768636i	−0.0842309	+	0.996446i	$0.526843\pi$
$432$		−	4.15198i		−	0.199762i
$433$	−12.6318	−	17.3862i	−0.607045	−	0.835526i	0.389285	−	0.921117i	$-0.372722\pi$
$433$	−12.6318	−	17.3862i	−0.607045	−	0.835526i	−0.996330	+	0.0855913i	$0.972722\pi$
$434$	−1.17022	−	3.60158i	−0.0561726	−	0.172881i
$435$		0			0
$436$	2.02252	−	6.22468i	0.0968612	−	0.298108i
$437$	5.65697	−	1.83806i	0.270610	−	0.0879265i
$438$	1.52988	−	0.497087i	0.0731003	−	0.0237517i
$439$	7.97128	−	24.5331i	0.380448	−	1.17090i	−0.559280	−	0.828979i	$-0.688922\pi$
$439$	7.97128	−	24.5331i	0.380448	−	1.17090i	0.939729	−	0.341921i	$-0.111078\pi$
$440$		0			0
$441$	−7.97126	−	24.5330i	−0.379584	−	1.16824i
$442$	−0.738989	−	1.01713i	−0.0351501	−	0.0483800i
$443$			3.18479i			0.151314i	0.997134	+	0.0756570i	$0.0241054\pi$
$443$			3.18479i			0.151314i	−0.997134	+	0.0756570i	$0.975895\pi$
$444$	−7.72851	+	5.61509i	−0.366779	+	0.266480i
$445$		0			0
$446$	−9.71455	−	7.05803i	−0.459997	−	0.334207i
$447$	−1.10226	+	1.51714i	−0.0521353	+	0.0717580i
$448$	3.27232	+	1.06324i	0.154602	+	0.0502334i
$449$	−36.0785			−1.70265			−0.851325	−	0.524639i	$-0.824200\pi$
$449$	−36.0785			−1.70265			−0.851325	+	0.524639i	$0.824200\pi$
$450$		0			0
$451$	14.4324			0.679594
$452$	−8.72771	−	2.83581i	−0.410517	−	0.133385i
$453$	23.7404	−	32.6758i	1.11542	−	1.53524i
$454$	−17.9871	−	13.0684i	−0.844179	−	0.613332i
$455$		0			0
$456$	−32.0843	+	23.3106i	−1.50249	+	1.09162i
$457$		−	25.5245i		−	1.19399i	−0.802246	−	0.596994i	$-0.796362\pi$
$457$		−	25.5245i		−	1.19399i	0.802246	−	0.596994i	$-0.203638\pi$
$458$	−5.89007	−	8.10699i	−0.275225	−	0.378815i
$459$	0.985894	+	3.03427i	0.0460176	+	0.141628i
$460$		0			0
$461$	−5.14179	+	15.8248i	−0.239477	+	0.737034i	0.757019	+	0.653393i	$0.226655\pi$
$461$	−5.14179	+	15.8248i	−0.239477	+	0.737034i	−0.996496	+	0.0836412i	$0.973345\pi$
$462$	−2.28528	+	0.742534i	−0.106321	+	0.0345458i
$463$	−16.9457	+	5.50599i	−0.787534	+	0.255885i	−0.675054	−	0.737769i	$-0.735880\pi$
$463$	−16.9457	+	5.50599i	−0.787534	+	0.255885i	−0.112480	+	0.993654i	$0.535880\pi$
$464$	3.50651	−	10.7919i	0.162786	−	0.501003i
$465$		0			0
$466$	−3.87554	−	11.9277i	−0.179531	−	0.552539i
$467$	−8.37479	−	11.5269i	−0.387539	−	0.533402i	0.570023	−	0.821629i	$-0.306934\pi$
$467$	−8.37479	−	11.5269i	−0.387539	−	0.533402i	−0.957562	+	0.288227i	$0.906934\pi$
$468$			1.89017i			0.0873731i
$469$	−1.01512	+	0.737531i	−0.0468741	+	0.0340560i
$470$		0			0
$471$	−5.86263	−	4.25945i	−0.270136	−	0.196265i
$472$	−11.7581	+	16.1836i	−0.541210	+	0.744912i
$473$	17.4335	+	5.66447i	0.801591	+	0.260453i
$474$	16.1750			0.742941
$475$		0			0
$476$	−0.460582			−0.0211107
$477$	18.2357	+	5.92514i	0.834955	+	0.271293i
$478$	10.7323	−	14.7717i	0.490883	−	0.675642i
$479$	2.35314	+	1.70966i	0.107518	+	0.0781162i	0.640245	−	0.768171i	$-0.278833\pi$
$479$	2.35314	+	1.70966i	0.107518	+	0.0781162i	−0.532727	+	0.846287i	$0.678833\pi$
$480$		0			0
$481$	−2.91097	+	2.11494i	−0.132729	+	0.0964330i
$482$		−	6.78945i		−	0.309251i
$483$	0.748388	+	1.03007i	0.0340529	+	0.0468697i
$484$	−1.54601	−	4.75814i	−0.0702734	−	0.216279i
$485$		0			0
$486$	7.65966	−	23.5740i	0.347449	−	1.06934i
$487$	−16.2300	+	5.27344i	−0.735450	+	0.238962i	−0.652709	−	0.757609i	$-0.726368\pi$
$487$	−16.2300	+	5.27344i	−0.735450	+	0.238962i	−0.0827414	+	0.996571i	$0.526368\pi$
$488$	−27.5731	+	8.95903i	−1.24817	+	0.405556i
$489$	19.4701	−	59.9227i	0.880467	−	2.70980i
$490$		0			0
$491$	9.51057	+	29.2705i	0.429206	+	1.32096i	0.898909	+	0.438135i	$0.144361\pi$
$491$	9.51057	+	29.2705i	0.429206	+	1.32096i	−0.469703	+	0.882824i	$0.655639\pi$
$492$	7.89036	+	10.8602i	0.355725	+	0.489613i
$493$			8.71937i			0.392701i
$494$	−3.18158	+	2.31156i	−0.143146	+	0.104002i
$495$		0			0
$496$	13.6708	+	9.93239i	0.613836	+	0.445978i
$497$	−1.64329	+	2.26179i	−0.0737116	+	0.101455i
$498$	−2.73377	−	0.888257i	−0.122503	−	0.0398037i
$499$	11.8824			0.531927			0.265964	−	0.963983i	$-0.414310\pi$
$499$	11.8824			0.531927			0.265964	+	0.963983i	$0.414310\pi$
$500$		0			0
$501$	−49.5730			−2.21476
$502$	−4.02365	−	1.30736i	−0.179584	−	0.0583504i
$503$	−1.75056	+	2.40944i	−0.0780536	+	0.107432i	−0.846259	−	0.532772i	$-0.821150\pi$
$503$	−1.75056	+	2.40944i	−0.0780536	+	0.107432i	0.768205	+	0.640204i	$0.221150\pi$
$504$	−3.82652	−	2.78013i	−0.170447	−	0.123837i
$505$		0			0
$506$	−2.20390	+	1.60123i	−0.0979752	+	0.0711831i
$507$		−	32.5584i		−	1.44597i
$508$	2.98488	+	4.10833i	0.132432	+	0.182278i
$509$	11.3458	+	34.9189i	0.502895	+	1.54775i	0.804280	+	0.594250i	$0.202551\pi$
$509$	11.3458	+	34.9189i	0.502895	+	1.54775i	−0.301385	+	0.953503i	$0.597449\pi$
$510$		0			0
$511$	0.0685902	−	0.211099i	0.00303425	−	0.00933846i
$512$	−19.5416	+	6.34944i	−0.863624	+	0.280608i
$513$	9.49119	−	3.08388i	0.419046	−	0.136156i
$514$	−8.26561	+	25.4389i	−0.364580	+	1.12206i
$515$		0			0
$516$	5.26866	+	16.2153i	0.231940	+	0.713837i
$517$	−1.49678	−	2.06014i	−0.0658282	−	0.0906047i
$518$		−	2.37047i		−	0.104152i
$519$	−27.8942	+	20.2663i	−1.22442	+	0.889594i
$520$		0			0
$521$	−2.02286	−	1.46969i	−0.0886229	−	0.0643883i	0.542591	−	0.839997i	$-0.317443\pi$
$521$	−2.02286	−	1.46969i	−0.0886229	−	0.0643883i	−0.631214	+	0.775608i	$0.717443\pi$
$522$	−13.8564	+	19.0718i	−0.606480	+	0.834749i
$523$	−40.0640	−	13.0176i	−1.75188	−	0.569220i	−0.755570	−	0.655068i	$-0.772640\pi$
$523$	−40.0640	−	13.0176i	−1.75188	−	0.569220i	−0.996308	+	0.0858485i	$0.972640\pi$
$524$	1.71121			0.0747545
$525$		0			0
$526$	7.52922			0.328290
$527$	−12.3491	−	4.01245i	−0.537934	−	0.174785i
$528$	6.30233	−	8.67441i	0.274274	−	0.377505i
$529$	−17.4396	−	12.6706i	−0.758243	−	0.550896i
$530$		0			0
$531$	19.8476	−	14.4201i	0.861312	−	0.625780i
$532$			1.44070i			0.0624623i
$533$	2.97193	+	4.09051i	0.128729	+	0.177180i
$534$	−2.06668	−	6.36058i	−0.0894339	−	0.275249i
$535$		0			0
$536$	2.93090	−	9.02038i	0.126596	−	0.389621i
$537$	30.2616	−	9.83258i	1.30588	−	0.424307i
$538$	14.0641	−	4.56972i	0.606348	−	0.197014i
$539$	4.22378	−	12.9995i	0.181931	−	0.559926i
$540$		0			0
$541$	−8.45136	−	26.0106i	−0.363352	−	1.11828i	−0.951006	−	0.309171i	$-0.899948\pi$
$541$	−8.45136	−	26.0106i	−0.363352	−	1.11828i	0.587654	−	0.809112i	$-0.300052\pi$
$542$	−7.89572	−	10.8675i	−0.339150	−	0.466800i
$543$		−	28.4140i		−	1.21936i
$544$	4.89162	−	3.55397i	0.209727	−	0.152375i
$545$		0			0
$546$	−0.681042	−	0.494806i	−0.0291459	−	0.0211757i
$547$	11.9551	−	16.4547i	0.511162	−	0.703554i	−0.472953	−	0.881088i	$-0.656812\pi$
$547$	11.9551	−	16.4547i	0.511162	−	0.703554i	0.984115	+	0.177534i	$0.0568119\pi$
$548$	−12.9281	−	4.20059i	−0.552261	−	0.179441i
$549$	35.5558			1.51748
$550$		0			0
$551$	27.2742			1.16192
$552$	−9.15318	−	2.97405i	−0.389585	−	0.126584i
$553$	1.31187	−	1.80564i	0.0557865	−	0.0767836i
$554$	−15.5517	−	11.2990i	−0.660728	−	0.480047i
$555$		0			0
$556$	−3.89412	+	2.82924i	−0.165147	+	0.119987i
$557$			28.2605i			1.19744i	0.800960	+	0.598718i	$0.204323\pi$
$557$			28.2605i			1.19744i	−0.800960	+	0.598718i	$0.795677\pi$
$558$	−20.6345	−	28.4010i	−0.873529	−	1.20231i
$559$	1.98446	+	6.10753i	0.0839336	+	0.258321i
$560$		0			0
$561$	−2.54599	+	7.83576i	−0.107492	+	0.330826i
$562$	−5.47193	+	1.77794i	−0.230819	+	0.0749978i
$563$	12.2928	−	3.99418i	0.518081	−	0.168335i	−0.0382934	−	0.999267i	$-0.512192\pi$
$563$	12.2928	−	3.99418i	0.518081	−	0.168335i	0.556374	+	0.830932i	$0.312192\pi$
$564$	0.731916	−	2.25261i	0.0308192	−	0.0948518i
$565$		0			0
$566$	−4.14264	−	12.7497i	−0.174128	−	0.535912i
$567$	−1.45432	−	2.00170i	−0.0610757	−	0.0840635i
$568$		−	21.1326i		−	0.886703i
$569$	−2.49536	+	1.81298i	−0.104611	+	0.0760043i	−0.638861	−	0.769322i	$-0.720594\pi$
$569$	−2.49536	+	1.81298i	−0.104611	+	0.0760043i	0.534250	+	0.845326i	$0.320594\pi$
$570$		0			0
$571$	3.33935	+	2.42618i	0.139747	+	0.101532i	0.655463	−	0.755228i	$-0.272474\pi$
$571$	3.33935	+	2.42618i	0.139747	+	0.101532i	−0.515715	+	0.856760i	$0.672474\pi$
$572$	−0.588700	+	0.810275i	−0.0246148	+	0.0338793i
$573$	−3.88050	−	1.26085i	−0.162110	−	0.0526727i
$574$	−3.33100			−0.139033
$575$		0			0
$576$	31.8961			1.32901
$577$	6.04463	+	1.96402i	0.251641	+	0.0817632i	0.432121	−	0.901815i	$-0.357765\pi$
$577$	6.04463	+	1.96402i	0.251641	+	0.0817632i	−0.180480	+	0.983579i	$0.557765\pi$
$578$	−9.65907	+	13.2946i	−0.401764	+	0.552981i
$579$	3.49094	+	2.53631i	0.145078	+	0.105406i
$580$		0			0
$581$	−0.320880	+	0.233133i	−0.0133124	+	0.00967200i
$582$			44.9063i			1.86143i
$583$	5.97185	+	8.21955i	0.247329	+	0.340419i
$584$	0.518464	+	1.59567i	0.0214542	+	0.0660293i
$585$		0			0
$586$	6.80868	−	20.9550i	0.281264	−	0.865642i
$587$	20.0711	−	6.52148i	0.828421	−	0.269170i	0.136041	−	0.990703i	$-0.456562\pi$
$587$	20.0711	−	6.52148i	0.828421	−	0.269170i	0.692380	+	0.721533i	$0.256562\pi$
$588$	12.0911	−	3.92864i	0.498629	−	0.162014i
$589$	−12.5509	+	38.6278i	−0.517153	+	1.59163i
$590$		0			0
$591$	10.6836	+	32.8808i	0.439466	+	1.35254i
$592$	6.21729	+	8.55736i	0.255529	+	0.351705i
$593$		−	21.6529i		−	0.889177i	−0.895735	−	0.444589i	$-0.853350\pi$
$593$		−	21.6529i		−	0.889177i	0.895735	−	0.444589i	$-0.146650\pi$
$594$	−3.69767	+	2.68651i	−0.151717	+	0.110229i
$595$		0			0
$596$	−0.416600	−	0.302678i	−0.0170646	−	0.0123982i
$597$	18.5153	−	25.4841i	0.757779	−	1.04299i
$598$	−0.907658	−	0.294916i	−0.0371169	−	0.0120600i
$599$	3.38501			0.138308			0.0691539	−	0.997606i	$-0.477970\pi$
$599$	3.38501			0.138308			0.0691539	+	0.997606i	$0.477970\pi$
$600$		0			0
$601$	28.8265			1.17586			0.587928	−	0.808913i	$-0.299944\pi$
$601$	28.8265			1.17586			0.587928	+	0.808913i	$0.299944\pi$
$602$	−4.02365	−	1.30736i	−0.163992	−	0.0532841i
$603$	−6.83706	+	9.41040i	−0.278426	+	0.383221i
$604$	8.97268	+	6.51903i	0.365093	+	0.265256i
$605$		0			0
$606$	43.9168	−	31.9074i	1.78400	−	1.29615i
$607$		−	15.6708i		−	0.636059i	−0.948081	−	0.318029i	$-0.896979\pi$
$607$		−	15.6708i		−	0.636059i	0.948081	−	0.318029i	$-0.103021\pi$
$608$	−11.1168	−	15.3010i	−0.450847	−	0.620537i
$609$	1.80412	+	5.55250i	0.0731065	+	0.224999i
$610$		0			0
$611$	0.275678	−	0.848451i	0.0111528	−	0.0343247i
$612$	−4.06071	+	1.31941i	−0.164145	+	0.0533338i
$613$	36.3308	−	11.8046i	1.46739	−	0.476783i	0.537070	−	0.843538i	$-0.319531\pi$
$613$	36.3308	−	11.8046i	1.46739	−	0.476783i	0.930318	+	0.366754i	$0.119531\pi$
$614$	8.90440	−	27.4049i	0.359352	−	1.10597i
$615$		0			0
$616$	−0.774467	−	2.38357i	−0.0312042	−	0.0960366i
$617$	7.77744	+	10.7047i	0.313108	+	0.430956i	0.936347	−	0.351075i	$-0.114184\pi$
$617$	7.77744	+	10.7047i	0.313108	+	0.430956i	−0.623239	+	0.782031i	$0.714184\pi$
$618$		−	35.0678i		−	1.41064i
$619$	4.89021	−	3.55294i	0.196554	−	0.142805i	−0.485155	−	0.874428i	$-0.661237\pi$
$619$	4.89021	−	3.55294i	0.196554	−	0.142805i	0.681709	+	0.731623i	$0.261237\pi$
$620$		0			0
$621$	1.95931	+	1.42352i	0.0786243	+	0.0571239i
$622$	−10.5672	+	14.5445i	−0.423707	+	0.583182i
$623$	−0.877660	−	0.285169i	−0.0351627	−	0.0114250i
$624$	3.75634			0.150374
$625$		0			0
$626$	−7.95456			−0.317928
$627$	24.5103	+	7.96386i	0.978845	+	0.318046i
$628$	1.16963	−	1.60986i	0.0466733	−	0.0642403i
$629$	−6.57556	−	4.77742i	−0.262185	−	0.190488i
$630$		0			0
$631$	30.5691	−	22.2097i	1.21694	−	0.884156i	0.221094	−	0.975253i	$-0.429037\pi$
$631$	30.5691	−	22.2097i	1.21694	−	0.884156i	0.995842	+	0.0910970i	$0.0290373\pi$
$632$			16.8706i			0.671076i
$633$	−10.2511	−	14.1094i	−0.407445	−	0.560800i
$634$	4.56614	+	14.0531i	0.181344	+	0.558121i
$635$		0			0
$636$	−2.92021	+	8.98747i	−0.115794	+	0.356376i
$637$	4.55415	−	1.47973i	0.180442	−	0.0586292i
$638$	−11.8799	+	3.86002i	−0.470331	+	0.152820i
$639$	−8.00878	+	24.6485i	−0.316823	+	0.975080i
$640$		0			0
$641$	−6.44517	−	19.8362i	−0.254569	−	0.783482i	−0.993914	−	0.110156i	$-0.964865\pi$
$641$	−6.44517	−	19.8362i	−0.254569	−	0.783482i	0.739345	−	0.673326i	$-0.235135\pi$
$642$	−1.30935	−	1.80217i	−0.0516760	−	0.0711259i
$643$		−	37.5552i		−	1.48103i	−0.672039	−	0.740516i	$-0.734581\pi$
$643$		−	37.5552i		−	1.48103i	0.672039	−	0.740516i	$-0.265419\pi$
$644$	−0.282853	+	0.205505i	−0.0111460	+	0.00809803i
$645$		0			0
$646$	−7.18685	−	5.22155i	−0.282763	−	0.205439i
$647$	16.1055	−	22.1673i	0.633171	−	0.871485i	−0.365057	−	0.930985i	$-0.618951\pi$
$647$	16.1055	−	22.1673i	0.633171	−	0.871485i	0.998228	+	0.0594998i	$0.0189506\pi$
$648$	17.7871	+	5.77938i	0.698743	+	0.227035i
$649$	12.9994			0.510272
$650$		0			0
$651$	−8.69410			−0.340749
$652$	16.4546	+	5.34642i	0.644411	+	0.209382i
$653$	13.5462	−	18.6447i	0.530103	−	0.729624i	−0.457044	−	0.889444i	$-0.651092\pi$
$653$	13.5462	−	18.6447i	0.530103	−	0.729624i	0.987146	+	0.159821i	$0.0510916\pi$
$654$	21.8611	+	15.8830i	0.854838	+	0.621076i
$655$		0			0
$656$	12.0249	−	8.73658i	0.469492	−	0.341106i
$657$		−	2.05763i		−	0.0802760i
$658$	0.345457	+	0.475480i	0.0134673	+	0.0185361i
$659$	−6.32981	−	19.4811i	−0.246574	−	0.758878i	−0.995374	−	0.0960808i	$-0.969369\pi$
$659$	−6.32981	−	19.4811i	−0.246574	−	0.758878i	0.748799	−	0.662797i	$-0.230631\pi$
$660$		0			0
$661$	4.32314	−	13.3053i	0.168151	−	0.517515i	−0.831104	−	0.556117i	$-0.812291\pi$
$661$	4.32314	−	13.3053i	0.168151	−	0.517515i	0.999255	+	0.0386024i	$0.0122906\pi$
$662$	−19.0239	+	6.18124i	−0.739385	+	0.240241i
$663$	−2.74513	+	0.891948i	−0.106612	+	0.0346404i
$664$	0.926457	−	2.85134i	0.0359535	−	0.110654i
$665$		0			0
$666$	−6.79055	−	20.8992i	−0.263129	−	0.809826i
$667$	3.89046	+	5.35475i	0.150639	+	0.207337i
$668$		−	13.6126i		−	0.526687i
$669$	−22.3028	+	16.2040i	−0.862278	+	0.626482i
$670$		0			0
$671$	15.2420	+	11.0740i	0.588411	+	0.427506i
$672$	2.37964	−	3.27529i	0.0917966	−	0.126347i
$673$	7.46172	+	2.42446i	0.287628	+	0.0934561i	0.449278	−	0.893392i	$-0.351681\pi$
$673$	7.46172	+	2.42446i	0.287628	+	0.0934561i	−0.161649	+	0.986848i	$0.551681\pi$
$674$	28.1720			1.08514
$675$		0			0
$676$	8.94042			0.343862
$677$	−13.6936	−	4.44932i	−0.526287	−	0.171001i	0.0338094	−	0.999428i	$-0.489236\pi$
$677$	−13.6936	−	4.44932i	−0.526287	−	0.171001i	−0.560097	+	0.828427i	$0.689236\pi$
$678$	22.2698	−	30.6518i	0.855268	−	1.17718i
$679$	5.01297	+	3.64213i	0.192380	+	0.139772i
$680$		0			0
$681$	−41.2953	+	30.0028i	−1.58244	+	1.14971i
$682$		−	18.6016i		−	0.712291i
$683$	7.44957	+	10.2535i	0.285050	+	0.392338i	0.927398	−	0.374075i	$-0.122040\pi$
$683$	7.44957	+	10.2535i	0.285050	+	0.392338i	−0.642348	+	0.766413i	$0.722040\pi$
$684$	4.12710	+	12.7019i	0.157804	+	0.485669i
$685$		0			0
$686$	−1.97335	+	6.07334i	−0.0753427	+	0.231881i
$687$	−21.8799	+	7.10922i	−0.834771	+	0.271234i
$688$	17.9543	−	5.83371i	0.684501	−	0.222408i
$689$	−1.09990	+	3.38516i	−0.0419030	+	0.128964i
$690$		0			0
$691$	1.77540	+	5.46411i	0.0675392	+	0.207864i	0.979130	−	0.203234i	$-0.0651452\pi$
$691$	1.77540	+	5.46411i	0.0675392	+	0.207864i	−0.911591	+	0.411098i	$0.865145\pi$
$692$	−5.56507	−	7.65966i	−0.211552	−	0.291177i
$693$			3.07364i			0.116758i
$694$	−12.1779	+	8.84778i	−0.462268	+	0.335857i
$695$		0			0
$696$	−35.7024	−	25.9393i	−1.35329	−	0.983226i
$697$	−6.71326	+	9.24002i	−0.254283	+	0.349991i
$698$	−19.5462	−	6.35095i	−0.739835	−	0.240387i
$699$	−28.7931			−1.08905
$700$		0			0
$701$	−30.5834			−1.15512			−0.577560	−	0.816348i	$-0.695995\pi$
$701$	−30.5834			−1.15512			−0.577560	+	0.816348i	$0.695995\pi$
$702$	−1.52286	−	0.494806i	−0.0574765	−	0.0186752i
$703$	−14.9438	+	20.5683i	−0.563615	+	0.775749i
$704$	13.6732	+	9.93416i	0.515328	+	0.374408i
$705$		0			0
$706$	−16.2381	+	11.7977i	−0.611128	+	0.444011i
$707$		−	7.49036i		−	0.281704i
$708$	7.10696	+	9.78189i	0.267096	+	0.367626i
$709$	8.36497	+	25.7447i	0.314153	+	0.966864i	0.976102	+	0.217315i	$0.0697297\pi$
$709$	8.36497	+	25.7447i	0.314153	+	0.966864i	−0.661949	+	0.749549i	$0.730270\pi$
$710$		0			0
$711$	6.39358	−	19.6774i	0.239778	−	0.737961i
$712$	6.63412	−	2.15556i	0.248624	−	0.0807829i
$713$	−9.37412	+	3.04584i	−0.351064	+	0.114067i
$714$	0.587616	−	1.80850i	0.0219910	−	0.0676813i
$715$		0			0
$716$	2.70000	+	8.30973i	0.100904	+	0.310549i
$717$	−24.6394	−	33.9132i	−0.920174	−	1.26651i
$718$			36.8957i			1.37693i
$719$	−13.5159	+	9.81991i	−0.504060	+	0.366221i	−0.810565	−	0.585648i	$-0.800840\pi$
$719$	−13.5159	+	9.81991i	−0.504060	+	0.366221i	0.306506	+	0.951869i	$0.400840\pi$
$720$		0			0
$721$	−3.91468	−	2.84418i	−0.145790	−	0.105923i
$722$	−3.67189	+	5.05393i	−0.136654	+	0.188088i
$723$	−14.8245	−	4.81676i	−0.551327	−	0.179137i
$724$	7.80240			0.289974
$725$		0			0
$726$	20.6555			0.766597
$727$	−11.1279	−	3.61568i	−0.412712	−	0.134098i	0.0952994	−	0.995449i	$-0.469619\pi$
$727$	−11.1279	−	3.61568i	−0.412712	−	0.134098i	−0.508011	+	0.861350i	$0.669619\pi$
$728$	0.516085	−	0.710330i	0.0191274	−	0.0263266i
$729$	−31.2899	−	22.7335i	−1.15889	−	0.841980i
$730$		0			0
$731$	−11.7358	+	8.52655i	−0.434064	+	0.315366i
$732$			17.5237i			0.647694i
$733$	−20.0481	−	27.5938i	−0.740493	−	1.01920i	−0.998590	−	0.0530818i	$-0.983096\pi$
$733$	−20.0481	−	27.5938i	−0.740493	−	1.01920i	0.258098	−	0.966119i	$-0.416904\pi$
$734$	11.5428	+	35.5252i	0.426054	+	1.31126i
$735$		0			0
$736$	1.41832	−	4.36514i	0.0522800	−	0.160901i
$737$	−5.86180	+	1.90461i	−0.215922	+	0.0701574i
$738$	−29.3677	+	9.54213i	−1.08104	+	0.351251i
$739$	−1.77536	+	5.46398i	−0.0653075	+	0.200996i	−0.978386	−	0.206789i	$-0.933699\pi$
$739$	−1.77536	+	5.46398i	−0.0653075	+	0.200996i	0.913078	+	0.407785i	$0.133699\pi$
$740$		0			0
$741$	2.79001	+	8.58677i	0.102494	+	0.315443i
$742$	−1.37831	−	1.89708i	−0.0505992	−	0.0696438i
$743$			36.4348i			1.33666i	0.743863	+	0.668332i	$0.232991\pi$
$743$			36.4348i			1.33666i	−0.743863	+	0.668332i	$0.767009\pi$
$744$	53.1667	−	38.6278i	1.94918	−	1.41617i
$745$		0			0
$746$	3.17940	+	2.30997i	0.116406	+	0.0845740i
$747$	−2.16119	+	2.97463i	−0.0790739	+	0.108836i
$748$	−2.15167	−	0.699122i	−0.0786730	−	0.0255624i
$749$	−0.307374			−0.0112312
$750$		0			0
$751$	1.48912			0.0543387			0.0271693	−	0.999631i	$-0.491351\pi$
$751$	1.48912			0.0543387			0.0271693	+	0.999631i	$0.491351\pi$
$752$	−2.49419	−	0.810412i	−0.0909538	−	0.0295527i
$753$	−5.70913	+	7.85795i	−0.208052	+	0.286360i
$754$	−3.54036	−	2.57222i	−0.128932	−	0.0936748i
$755$		0			0
$756$	−0.474567	+	0.344793i	−0.0172599	+	0.0125400i
$757$			5.53316i			0.201106i	0.994932	+	0.100553i	$0.0320612\pi$
$757$			5.53316i			0.201106i	−0.994932	+	0.100553i	$0.967939\pi$
$758$	1.28519	+	1.76891i	0.0466802	+	0.0642498i
$759$	1.93265	+	5.94810i	0.0701509	+	0.215902i
$760$		0			0
$761$	−5.76925	+	17.7559i	−0.209135	+	0.643652i	0.790383	+	0.612613i	$0.209882\pi$
$761$	−5.76925	+	17.7559i	−0.209135	+	0.643652i	−0.999518	+	0.0310389i	$0.990118\pi$
$762$	−19.9397	+	6.47880i	−0.722339	+	0.234702i
$763$	3.54610	−	1.15220i	0.128377	−	0.0417123i
$764$	0.346225	−	1.06557i	0.0125260	−	0.0385510i
$765$		0			0
$766$	1.72716	+	5.31564i	0.0624047	+	0.192062i
$767$	2.67686	+	3.68438i	0.0966557	+	0.133035i
$768$			38.2653i			1.38078i
$769$	−10.6332	+	7.72544i	−0.383441	+	0.278587i	−0.762763	−	0.646679i	$-0.776158\pi$
$769$	−10.6332	+	7.72544i	−0.383441	+	0.278587i	0.379321	+	0.925265i	$0.376158\pi$
$770$		0			0
$771$	49.6807	+	36.0952i	1.78921	+	1.29994i
$772$	−0.696463	+	0.958599i	−0.0250663	+	0.0345007i
$773$	26.6045	+	8.64431i	0.956896	+	0.310914i	0.745514	−	0.666489i	$-0.232204\pi$
$773$	26.6045	+	8.64431i	0.956896	+	0.310914i	0.211381	+	0.977404i	$0.432204\pi$
$774$	−39.2195			−1.40972
$775$		0			0
$776$	−46.8376			−1.68137
$777$	−5.17581	−	1.68172i	−0.185681	−	0.0603314i
$778$	8.92008	−	12.2774i	0.319800	−	0.440168i
$779$	28.9028	+	20.9991i	1.03555	+	0.752370i
$780$		0			0
$781$	−11.1101	+	8.07193i	−0.397549	+	0.288836i
$782$		−	2.15581i		−	0.0770917i
$783$	6.52735	+	8.98413i	0.233269	+	0.321067i
$784$	−4.34997	−	13.3878i	−0.155356	−	0.478137i
$785$		0			0
$786$	−2.18318	+	6.71914i	−0.0778715	+	0.239664i
$787$	31.7339	−	10.3110i	1.13119	−	0.367546i	0.317162	−	0.948371i	$-0.397270\pi$
$787$	31.7339	−	10.3110i	1.13119	−	0.367546i	0.814028	+	0.580825i	$0.197270\pi$
$788$	−9.02897	+	2.93369i	−0.321644	+	0.104508i
$789$	5.34159	−	16.4397i	0.190166	−	0.585269i
$790$		0			0
$791$	−1.61551	−	4.97204i	−0.0574410	−	0.176785i
$792$	−13.6562	−	18.7961i	−0.485250	−	0.667890i
$793$			6.60035i			0.234385i
$794$	−1.96174	+	1.42529i	−0.0696195	+	0.0505815i
$795$		0			0
$796$	6.99784	+	5.08423i	0.248032	+	0.180206i
$797$	−21.9824	+	30.2561i	−0.778655	+	1.07173i	0.216774	+	0.976222i	$0.430447\pi$
$797$	−21.9824	+	30.2561i	−0.778655	+	1.07173i	−0.995429	+	0.0955049i	$0.969553\pi$
$798$	−5.65697	−	1.83806i	−0.200255	−	0.0650667i
$799$	2.01519			0.0712923
$800$		0			0
$801$	−8.55478			−0.302268
$802$	28.9192	+	9.39641i	1.02117	+	0.331799i
$803$	0.640857	−	0.882064i	0.0226154	−	0.0311274i
$804$	−4.63792	−	3.36964i	−0.163567	−	0.118838i
$805$		0			0
$806$	5.27217	−	3.83046i	0.185704	−	0.134922i
$807$		−	33.9504i		−	1.19511i
$808$	33.2796	+	45.8055i	1.17077	+	1.61143i
$809$	−10.3835	−	31.9571i	−0.365064	−	1.12355i	−0.949941	−	0.312430i	$-0.898857\pi$
$809$	−10.3835	−	31.9571i	−0.365064	−	1.12355i	0.584876	−	0.811123i	$-0.301143\pi$
$810$		0			0
$811$	−11.7444	+	36.1454i	−0.412400	+	1.26924i	0.502155	+	0.864778i	$0.332541\pi$
$811$	−11.7444	+	36.1454i	−0.412400	+	1.26924i	−0.914556	+	0.404460i	$0.867459\pi$
$812$	−1.52470	+	0.495404i	−0.0535064	+	0.0173853i
$813$	−29.3304	+	9.53001i	−1.02866	+	0.334232i
$814$	3.59815	−	11.0740i	0.126115	−	0.388143i
$815$		0			0
$816$	2.62206	+	8.06987i	0.0917904	+	0.282502i
$817$	26.6710	+	36.7095i	0.933101	+	1.28430i
$818$			15.8699i			0.554877i
$819$	−0.871148	+	0.632926i	−0.0304404	+	0.0221162i
$820$		0			0
$821$	−20.1714	−	14.6554i	−0.703987	−	0.511477i	0.177241	−	0.984167i	$-0.443283\pi$
$821$	−20.1714	−	14.6554i	−0.703987	−	0.511477i	−0.881228	+	0.472691i	$0.843283\pi$
$822$	32.9877	−	45.4036i	1.15058	−	1.58363i
$823$	−24.2144	−	7.86775i	−0.844062	−	0.274252i	−0.145105	−	0.989416i	$-0.546352\pi$
$823$	−24.2144	−	7.86775i	−0.844062	−	0.274252i	−0.698957	+	0.715164i	$0.746352\pi$
$824$	36.5760			1.27418
$825$		0			0
$826$	−3.00027			−0.104393
$827$	30.7559	+	9.99321i	1.06949	+	0.347498i	0.790288	−	0.612735i	$-0.209931\pi$
$827$	30.7559	+	9.99321i	1.06949	+	0.347498i	0.279200	+	0.960233i	$0.409931\pi$
$828$	−1.90507	+	2.62211i	−0.0662058	+	0.0911245i
$829$	20.2102	+	14.6836i	0.701930	+	0.509982i	0.880560	−	0.473934i	$-0.157167\pi$
$829$	20.2102	+	14.6836i	0.701930	+	0.509982i	−0.178630	+	0.983916i	$0.557167\pi$
$830$		0			0
$831$	−35.7039	+	25.9404i	−1.23855	+	0.899862i
$832$			5.92099i			0.205273i
$833$	6.35792	+	8.75093i	0.220289	+	0.303202i
$834$	−6.14099	−	18.9000i	−0.212645	−	0.654454i
$835$		0			0
$836$	−2.18685	+	6.73044i	−0.0756338	+	0.232777i
$837$	−15.7278	+	5.11026i	−0.543631	+	0.176637i
$838$	−33.3191	+	10.8260i	−1.15099	+	0.373979i
$839$	−5.98027	+	18.4054i	−0.206462	+	0.635424i	0.793188	+	0.608976i	$0.208420\pi$
$839$	−5.98027	+	18.4054i	−0.206462	+	0.635424i	−0.999650	+	0.0264480i	$0.991580\pi$
$840$		0			0
$841$	0.417110	+	1.28373i	0.0143831	+	0.0442666i
$842$	−5.49075	−	7.55738i	−0.189224	−	0.260444i
$843$			13.2091i			0.454944i
$844$	3.87440	−	2.81492i	0.133362	−	0.0968935i
$845$		0			0
$846$	4.40779	+	3.20245i	0.151543	+	0.110103i
$847$	1.67526	−	2.30580i	0.0575628	−	0.0792284i
$848$	9.95134	+	3.23339i	0.341731	+	0.111035i
$849$	−30.7775			−1.05628
$850$		0			0
$851$	−6.16980			−0.211498
$852$	−12.1480	−	3.94713i	−0.416184	−	0.135226i
$853$	−15.7454	+	21.6716i	−0.539111	+	0.742022i	−0.988485	−	0.151321i	$-0.951647\pi$
$853$	−15.7454	+	21.6716i	−0.539111	+	0.742022i	0.449374	+	0.893344i	$0.351647\pi$
$854$	−3.51786	−	2.55588i	−0.120379	−	0.0874603i
$855$		0			0
$856$	1.87967	−	1.36566i	0.0642459	−	0.0466773i
$857$		−	47.5186i		−	1.62320i	−0.584210	−	0.811602i	$-0.698596\pi$
$857$		−	47.5186i		−	1.62320i	0.584210	−	0.811602i	$-0.301404\pi$
$858$	−2.43051	−	3.34531i	−0.0829764	−	0.114207i
$859$	−3.56266	−	10.9647i	−0.121556	−	0.374112i	0.871702	−	0.490037i	$-0.163017\pi$
$859$	−3.56266	−	10.9647i	−0.121556	−	0.374112i	−0.993258	+	0.115925i	$0.963017\pi$
$860$		0			0
$861$	−2.36317	+	7.27308i	−0.0805365	+	0.247866i
$862$	29.2716	−	9.51092i	0.996995	−	0.323943i
$863$	17.1245	−	5.56407i	0.582923	−	0.189403i	−0.00268645	−	0.999996i	$-0.500855\pi$
$863$	17.1245	−	5.56407i	0.582923	−	0.189403i	0.585610	+	0.810593i	$0.300855\pi$
$864$	2.37964	−	7.32378i	0.0809570	−	0.249160i
$865$		0			0
$866$	7.52885	+	23.1714i	0.255841	+	0.787396i
$867$	22.1755	+	30.5219i	0.753119	+	1.03658i
$868$		−	2.38737i		−	0.0810327i
$869$	8.86940	−	6.44399i	0.300874	−	0.218597i
$870$		0			0
$871$	−1.74689	−	1.26919i	−0.0591910	−	0.0430048i
$872$	−16.5661	+	22.8013i	−0.560999	+	0.772149i
$873$	54.6302	+	17.7504i	1.84895	+	0.600760i
$874$	−6.74338			−0.228098
$875$		0			0
$876$	1.01411			0.0342635
$877$	−16.2605	−	5.28336i	−0.549078	−	0.178406i	0.0213227	−	0.999773i	$-0.493212\pi$
$877$	−16.2605	−	5.28336i	−0.549078	−	0.178406i	−0.570401	+	0.821366i	$0.693212\pi$
$878$	−17.1895	+	23.6594i	−0.580119	+	0.798465i
$879$	−40.9238	−	29.7329i	−1.38033	−	1.00287i
$880$		0			0
$881$	30.7662	−	22.3530i	1.03654	−	0.753090i	0.0669326	−	0.997757i	$-0.478679\pi$
$881$	30.7662	−	22.3530i	1.03654	−	0.753090i	0.969607	+	0.244667i	$0.0786787\pi$
$882$			29.2445i			0.984714i
$883$	−21.6595	−	29.8118i	−0.728900	−	1.00325i	−0.999181	−	0.0404637i	$-0.987116\pi$
$883$	−21.6595	−	29.8118i	−0.728900	−	1.00325i	0.270281	−	0.962782i	$-0.412884\pi$
$884$	−0.244926	−	0.753805i	−0.00823775	−	0.0253532i
$885$		0			0
$886$	1.11574	−	3.43389i	0.0374840	−	0.115364i
$887$	−28.4116	+	9.23150i	−0.953970	+	0.309964i	−0.744328	−	0.667815i	$-0.767230\pi$
$887$	−28.4116	+	9.23150i	−0.953970	+	0.309964i	−0.209642	+	0.977778i	$0.567230\pi$
$888$	39.1233	−	12.7119i	1.31289	−	0.426584i
$889$	−0.893972	+	2.75136i	−0.0299828	+	0.0922777i
$890$		0			0
$891$	−3.75567	−	11.5588i	−0.125820	−	0.387233i
$892$	−4.44956	−	6.12429i	−0.148982	−	0.205056i
$893$		−	6.30351i		−	0.210939i
$894$	1.71998	−	1.24964i	0.0575248	−	0.0417942i
$895$		0			0
$896$	−0.639015	−	0.464271i	−0.0213480	−	0.0155102i
$897$	−1.28787	+	1.77260i	−0.0430008	+	0.0591855i
$898$	38.9004	+	12.6395i	1.29812	+	0.421786i
$899$	−45.1958			−1.50736
$900$		0			0
$901$	−8.04022			−0.267859
$902$	−15.5612	−	5.05615i	−0.518132	−	0.168351i
$903$	−5.70913	+	7.85795i	−0.189988	+	0.261496i
$904$	31.9700	+	23.2276i	1.06331	+	0.772538i
$905$		0			0
$906$	−37.0447	+	26.9146i	−1.23073	+	0.894177i
$907$			43.4897i			1.44405i	0.691866	+	0.722026i	$0.256789\pi$
$907$			43.4897i			1.44405i	−0.691866	+	0.722026i	$0.743211\pi$
$908$	−8.23866	−	11.3395i	−0.273410	−	0.376316i
$909$	−21.4572	−	66.0386i	−0.711692	−	2.19036i
$910$		0			0
$911$	−7.53045	+	23.1763i	−0.249495	+	0.767866i	0.745370	+	0.666651i	$0.232273\pi$
$911$	−7.53045	+	23.1763i	−0.249495	+	0.767866i	−0.994865	+	0.101215i	$0.967727\pi$
$912$	25.2425	−	8.20179i	0.835863	−	0.271589i
$913$	−1.85291	+	0.602048i	−0.0613225	+	0.0199249i
$914$	−8.94211	+	27.5210i	−0.295779	+	0.910313i
$915$		0			0
$916$	−1.95217	−	6.00816i	−0.0645015	−	0.198515i
$917$	0.573001	+	0.788669i	0.0189222	+	0.0260441i
$918$		−	3.61699i		−	0.119379i
$919$	36.8219	−	26.7527i	1.21464	−	0.882489i	0.218998	−	0.975725i	$-0.429721\pi$
$919$	36.8219	−	26.7527i	1.21464	−	0.882489i	0.995644	+	0.0932366i	$0.0297213\pi$
$920$		0			0
$921$	−53.5202	−	38.8847i	−1.76355	−	1.28130i
$922$	11.0879	−	15.2612i	0.365161	−	0.502601i
$923$	−4.57559	−	1.48670i	−0.150607	−	0.0489353i
$924$	−1.51484			−0.0498346
$925$		0			0
$926$	20.2001			0.663816
$927$	−42.6613	−	13.8615i	−1.40118	−	0.455271i
$928$	12.3704	−	17.0264i	0.406079	−	0.558920i
$929$	7.31185	+	5.31237i	0.239894	+	0.174293i	0.701236	−	0.712929i	$-0.252632\pi$
$929$	7.31185	+	5.31237i	0.239894	+	0.174293i	−0.461342	+	0.887222i	$0.652632\pi$
$930$		0			0
$931$	27.3729	−	19.8876i	0.897110	−	0.651788i
$932$		−	7.90648i		−	0.258985i
$933$	24.2604	+	33.3916i	0.794251	+	1.09319i
$934$	4.99157	+	15.3625i	0.163329	+	0.502676i
$935$		0			0
$936$	2.51521	−	7.74102i	0.0822122	−	0.253023i
$937$	31.6961	−	10.2987i	1.03546	−	0.336443i	0.258516	−	0.966007i	$-0.416766\pi$
$937$	31.6961	−	10.2987i	1.03546	−	0.336443i	0.776949	+	0.629564i	$0.216766\pi$
$938$	1.35291	−	0.439586i	0.0441739	−	0.0143530i
$939$	−5.64334	+	17.3684i	−0.184164	+	0.566797i
$940$		0			0
$941$	−9.05452	−	27.8669i	−0.295169	−	0.908436i	−0.983165	−	0.182722i	$-0.941509\pi$
$941$	−9.05452	−	27.8669i	−0.295169	−	0.908436i	0.687996	−	0.725715i	$-0.258491\pi$
$942$	4.82895	+	6.64648i	0.157336	+	0.216554i
$943$			8.66985i			0.282329i
$944$	10.8310	−	7.86916i	0.352518	−	0.256119i
$945$		0			0
$946$	−16.8126	−	12.2151i	−0.546624	−	0.397146i
$947$	−33.4130	+	45.9891i	−1.08578	+	1.49444i	−0.232779	+	0.972530i	$0.574782\pi$
$947$	−33.4130	+	45.9891i	−1.08578	+	1.49444i	−0.852998	+	0.521914i	$0.825218\pi$
$948$	9.69802	+	3.15108i	0.314977	+	0.102342i
$949$	0.381966			0.0123991
$950$		0			0
$951$	33.9238			1.10005
$952$	1.88627	+	0.612887i	0.0611344	+	0.0198638i
$953$	11.1896	−	15.4011i	0.362465	−	0.498890i	−0.588368	−	0.808593i	$-0.700229\pi$
$953$	11.1896	−	15.4011i	0.362465	−	0.498890i	0.950833	+	0.309703i	$0.100229\pi$
$954$	−17.5863	−	12.7772i	−0.569376	−	0.413676i
$955$		0			0
$956$	9.31245	−	6.76589i	0.301186	−	0.218824i
$957$			28.6778i			0.927021i
$958$	−1.93824	−	2.66777i	−0.0626219	−	0.0861916i
$959$	−2.39301	−	7.36493i	−0.0772743	−	0.237826i
$960$		0			0
$961$	11.2185	−	34.5271i	0.361888	−	1.11378i
$962$	3.87959	−	1.26055i	0.125083	−	0.0406419i
$963$	−2.70996	+	0.880518i	−0.0873271	+	0.0283743i
$964$	1.32267	−	4.07075i	0.0426002	−	0.131110i
$965$		0			0
$966$	−0.446057	−	1.37282i	−0.0143517	−	0.0441698i
$967$	−8.64663	−	11.9011i	−0.278057	−	0.382713i	0.647032	−	0.762463i	$-0.276010\pi$
$967$	−8.64663	−	11.9011i	−0.278057	−	0.382713i	−0.925089	+	0.379750i	$0.876010\pi$
$968$			21.5438i			0.692443i
$969$	−16.4997	+	11.9877i	−0.530047	+	0.385102i
$970$		0			0
$971$	31.4265	+	22.8327i	1.00853	+	0.732737i	0.963899	−	0.266267i	$-0.0857903\pi$
$971$	31.4265	+	22.8327i	1.00853	+	0.732737i	0.0446263	+	0.999004i	$0.485790\pi$
$972$	9.18499	−	12.6421i	0.294609	−	0.405494i
$973$	−2.60790	−	0.847359i	−0.0836055	−	0.0271651i
$974$	19.3469			0.619914
$975$		0			0
$976$	19.4030			0.621076
$977$	−55.5934	−	18.0634i	−1.77859	−	0.577899i	−0.779752	−	0.626088i	$-0.784655\pi$
$977$	−55.5934	−	18.0634i	−1.77859	−	0.577899i	−0.998838	+	0.0481892i	$0.984655\pi$
$978$	−41.9859	+	57.7886i	−1.34256	+	1.84788i
$979$	−3.66725	−	2.66441i	−0.117206	−	0.0851550i
$980$		0			0
$981$	27.9635	−	20.3166i	0.892805	−	0.648661i
$982$		−	34.8918i		−	1.11344i
$983$	16.5517	+	22.7815i	0.527918	+	0.726616i	0.986811	−	0.161875i	$-0.0517541\pi$
$983$	16.5517	+	22.7815i	0.527918	+	0.726616i	−0.458894	+	0.888491i	$0.651754\pi$
$984$	−17.8629	−	54.9763i	−0.569448	−	1.75258i
$985$		0			0
$986$	3.05469	−	9.40137i	0.0972812	−	0.299401i
$987$	1.28327	−	0.416961i	0.0408470	−	0.0132720i
$988$	−2.35790	+	0.766128i	−0.0750148	+	0.0243738i
$989$	−3.40278	+	10.4727i	−0.108202	+	0.333012i
$990$		0			0
$991$	12.1579	+	37.4181i	0.386208	+	1.18862i	0.935601	+	0.353060i	$0.114859\pi$
$991$	12.1579	+	37.4181i	0.386208	+	1.18862i	−0.549393	+	0.835564i	$0.685141\pi$
$992$	18.4216	+	25.3551i	0.584886	+	0.805026i
$993$			45.9231i			1.45733i
$994$	2.56420	−	1.86300i	0.0813316	−	0.0590909i
$995$		0			0
$996$	−1.46604	−	1.06514i	−0.0464534	−	0.0337504i
$997$	25.3440	−	34.8830i	0.802652	−	1.10476i	−0.189763	−	0.981830i	$-0.560772\pi$
$997$	25.3440	−	34.8830i	0.802652	−	1.10476i	0.992416	−	0.122926i	$-0.0392279\pi$
$998$	−12.8118	−	4.16279i	−0.405549	−	0.131771i
$999$	−10.3516			−0.327511

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.e.a.124.1		8
5.2	odd	4		625.2.d.o.501.3		16
5.3	odd	4		625.2.d.o.501.2		16
5.4	even	2		625.2.e.i.124.2		8
25.2	odd	20		125.2.d.b.76.2		16
25.3	odd	20		125.2.d.b.51.3		16
25.4	even	10		125.2.e.b.74.1		8
25.6	even	5		625.2.e.i.499.2		8
25.8	odd	20		625.2.d.o.126.2		16
25.9	even	10		625.2.b.c.624.6		8
25.11	even	5		125.2.e.b.49.1		8
25.12	odd	20		625.2.a.f.1.6		8
25.13	odd	20		625.2.a.f.1.3		8
25.14	even	10		25.2.e.a.9.2	✓	8
25.16	even	5		625.2.b.c.624.3		8
25.17	odd	20		625.2.d.o.126.3		16
25.19	even	10	inner	625.2.e.a.499.1		8
25.21	even	5		25.2.e.a.14.2	yes	8
25.22	odd	20		125.2.d.b.51.2		16
25.23	odd	20		125.2.d.b.76.3		16
75.14	odd	10		225.2.m.a.109.1		8
75.38	even	20		5625.2.a.x.1.6		8
75.62	even	20		5625.2.a.x.1.3		8
75.71	odd	10		225.2.m.a.64.1		8
100.39	odd	10		400.2.y.c.209.2		8
100.63	even	20		10000.2.a.bj.1.1		8
100.71	odd	10		400.2.y.c.289.2		8
100.87	even	20		10000.2.a.bj.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.e.a.9.2	✓	8	25.14	even	10
25.2.e.a.14.2	yes	8	25.21	even	5
125.2.d.b.51.2		16	25.22	odd	20
125.2.d.b.51.3		16	25.3	odd	20
125.2.d.b.76.2		16	25.2	odd	20
125.2.d.b.76.3		16	25.23	odd	20
125.2.e.b.49.1		8	25.11	even	5
125.2.e.b.74.1		8	25.4	even	10
225.2.m.a.64.1		8	75.71	odd	10
225.2.m.a.109.1		8	75.14	odd	10
400.2.y.c.209.2		8	100.39	odd	10
400.2.y.c.289.2		8	100.71	odd	10
625.2.a.f.1.3		8	25.13	odd	20
625.2.a.f.1.6		8	25.12	odd	20
625.2.b.c.624.3		8	25.16	even	5
625.2.b.c.624.6		8	25.9	even	10
625.2.d.o.126.2		16	25.8	odd	20
625.2.d.o.126.3		16	25.17	odd	20
625.2.d.o.501.2		16	5.3	odd	4
625.2.d.o.501.3		16	5.2	odd	4
625.2.e.a.124.1		8	1.1	even	1	trivial
625.2.e.a.499.1		8	25.19	even	10	inner
625.2.e.i.124.2		8	5.4	even	2
625.2.e.i.499.2		8	25.6	even	5
5625.2.a.x.1.3		8	75.62	even	20
5625.2.a.x.1.6		8	75.38	even	20
10000.2.a.bj.1.1		8	100.63	even	20
10000.2.a.bj.1.8		8	100.87	even	20

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.e (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.07822 - 0.350334i) q^{2} +(-1.52988 + 2.10569i) q^{3} +(-0.578217 - 0.420099i) q^{4} +(2.38723 - 1.73443i) q^{6} -0.407162i q^{7} +(1.80902 + 2.48990i) q^{8} +(-1.16637 - 3.58973i) q^{9} +O(q^{10})\)	\(q+(-1.07822 - 0.350334i) q^{2} +(-1.52988 + 2.10569i) q^{3} +(-0.578217 - 0.420099i) q^{4} +(2.38723 - 1.73443i) q^{6} -0.407162i q^{7} +(1.80902 + 2.48990i) q^{8} +(-1.16637 - 3.58973i) q^{9} +(0.618034 - 1.90211i) q^{11} +(1.76920 - 0.574848i) q^{12} +(0.666375 - 0.216518i) q^{13} +(-0.142642 + 0.439008i) q^{14} +(-0.636498 - 1.95894i) q^{16} +(0.930307 + 1.28046i) q^{17} +4.27913i q^{18} +(4.00527 - 2.91000i) q^{19} +(0.857358 + 0.622907i) q^{21} +(-1.33275 + 1.83437i) q^{22} +(1.14264 + 0.371267i) q^{23} -8.01054 q^{24} -0.794350 q^{26} +(1.91711 + 0.622907i) q^{27} +(-0.171048 + 0.235428i) q^{28} +(4.45693 + 3.23815i) q^{29} +(-6.63709 + 4.82213i) q^{31} -3.82022i q^{32} +(3.05975 + 4.21139i) q^{33} +(-0.554485 - 1.70653i) q^{34} +(-0.833625 + 2.56564i) q^{36} +(-4.88398 + 1.58690i) q^{37} +(-5.33802 + 1.73443i) q^{38} +(-0.563549 + 1.73443i) q^{39} +(2.22992 + 6.86300i) q^{41} +(-0.706192 - 0.971990i) q^{42} +9.16531i q^{43} +(-1.15643 + 0.840198i) q^{44} +(-1.10195 - 0.800613i) q^{46} +(0.748388 - 1.03007i) q^{47} +(5.09869 + 1.65667i) q^{48} +6.83422 q^{49} -4.11950 q^{51} +(-0.476268 - 0.154749i) q^{52} +(-2.98593 + 4.10978i) q^{53} +(-1.84883 - 1.34326i) q^{54} +(1.01379 - 0.736562i) q^{56} +12.8858i q^{57} +(-3.67110 - 5.05284i) q^{58} +(2.00852 + 6.18160i) q^{59} +(-2.91097 + 8.95903i) q^{61} +(8.84558 - 2.87410i) q^{62} +(-1.46160 + 0.474903i) q^{63} +(-2.61135 + 8.03690i) q^{64} +(-1.82368 - 5.61272i) q^{66} +(-1.81140 - 2.49317i) q^{67} -1.13120i q^{68} +(-2.52988 + 1.83806i) q^{69} +(-5.55503 - 4.03596i) q^{71} +(6.82808 - 9.39804i) q^{72} +(0.518464 + 0.168459i) q^{73} +5.82193 q^{74} -3.53840 q^{76} +(-0.774467 - 0.251640i) q^{77} +(1.21526 - 1.67266i) q^{78} +(4.43470 + 3.22200i) q^{79} +(4.91623 - 3.57185i) q^{81} -8.18102i q^{82} +(-0.572582 - 0.788091i) q^{83} +(-0.234056 - 0.720350i) q^{84} +(3.21092 - 9.88219i) q^{86} +(-13.6371 + 4.43096i) q^{87} +(5.85410 - 1.90211i) q^{88} +(0.700383 - 2.15556i) q^{89} +(-0.0881579 - 0.271322i) q^{91} +(-0.504726 - 0.694696i) q^{92} -21.3529i q^{93} +(-1.16779 + 0.848451i) q^{94} +(8.04421 + 5.84446i) q^{96} +(-8.94518 + 12.3120i) q^{97} +(-7.36877 - 2.39426i) q^{98} -7.54893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9}+O(q^{10}) \) 8 * q - 5 * q^3 + 4 * q^4 + 6 * q^6 + 10 * q^8 + q^9	\( 8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9} - 4 q^{11} + 10 q^{12} - 5 q^{13} - 7 q^{14} - 2 q^{16} + 15 q^{17} + 10 q^{19} + q^{21} + 10 q^{22} + 15 q^{23} - 20 q^{24} + 6 q^{26} - 5 q^{27} - 20 q^{28} + 15 q^{29} + q^{31} + 10 q^{33} - 12 q^{34} - 17 q^{36} - 5 q^{37} + 12 q^{39} - 9 q^{41} + 5 q^{42} + 8 q^{44} + 16 q^{46} - 15 q^{47} - 5 q^{48} + 14 q^{49} - 4 q^{51} - 20 q^{52} + 35 q^{53} - 10 q^{54} - 15 q^{56} - 20 q^{58} + 15 q^{59} + 6 q^{61} + 45 q^{62} - 20 q^{63} - 26 q^{64} - 18 q^{66} - 13 q^{69} - 29 q^{71} + 5 q^{72} + 10 q^{73} - 12 q^{74} - 20 q^{76} + 20 q^{77} - 25 q^{78} - 10 q^{79} - 12 q^{81} + 15 q^{83} - 27 q^{84} + 16 q^{86} - 55 q^{87} + 20 q^{88} + 40 q^{89} + q^{91} - 5 q^{92} - 7 q^{94} + 11 q^{96} - 10 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 5 * q^3 + 4 * q^4 + 6 * q^6 + 10 * q^8 + q^9 - 4 * q^11 + 10 * q^12 - 5 * q^13 - 7 * q^14 - 2 * q^16 + 15 * q^17 + 10 * q^19 + q^21 + 10 * q^22 + 15 * q^23 - 20 * q^24 + 6 * q^26 - 5 * q^27 - 20 * q^28 + 15 * q^29 + q^31 + 10 * q^33 - 12 * q^34 - 17 * q^36 - 5 * q^37 + 12 * q^39 - 9 * q^41 + 5 * q^42 + 8 * q^44 + 16 * q^46 - 15 * q^47 - 5 * q^48 + 14 * q^49 - 4 * q^51 - 20 * q^52 + 35 * q^53 - 10 * q^54 - 15 * q^56 - 20 * q^58 + 15 * q^59 + 6 * q^61 + 45 * q^62 - 20 * q^63 - 26 * q^64 - 18 * q^66 - 13 * q^69 - 29 * q^71 + 5 * q^72 + 10 * q^73 - 12 * q^74 - 20 * q^76 + 20 * q^77 - 25 * q^78 - 10 * q^79 - 12 * q^81 + 15 * q^83 - 27 * q^84 + 16 * q^86 - 55 * q^87 + 20 * q^88 + 40 * q^89 + q^91 - 5 * q^92 - 7 * q^94 + 11 * q^96 - 10 * q^97 - 40 * q^98 - 8 * q^99

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