LMFDB - Embedded newform 625.2.e.a.499.1

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			499.1
Root			$1.66637 + 0.917186i$ of defining polynomial
Character	$\chi$	$=$	625.499
Dual form			625.2.e.a.124.1

$q$-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 $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

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	−0.664315	−	0.747453i	$-0.731276\pi$
$2$	−1.07822	+	0.350334i	−0.762414	+	0.247723i	−0.0980998	+	0.995177i	$0.531276\pi$
$3$	−1.52988	−	2.10569i	−0.883274	−	1.21572i	−0.975503	−	0.219985i	$-0.929399\pi$
$3$	−1.52988	−	2.10569i	−0.883274	−	1.21572i	0.0922289	−	0.995738i	$-0.470601\pi$
$4$	−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	$0.0245170\pi$
$7$			0.407162i			0.153893i	−0.997035	+	0.0769463i	$0.975483\pi$
$8$	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	0.999969	−	0.00788181i	$-0.00250889\pi$
$11$	0.618034	+	1.90211i	0.186344	+	0.573509i	−0.813625	+	0.581390i	$0.802509\pi$
$12$	1.76920	+	0.574848i	0.510724	+	0.165944i
$13$	0.666375	+	0.216518i	0.184819	+	0.0600513i	0.399964	−	0.916531i	$-0.369023\pi$
$13$	0.666375	+	0.216518i	0.184819	+	0.0600513i	−0.215145	+	0.976582i	$0.569023\pi$
$14$	−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	−0.681159	−	0.732135i	$-0.738524\pi$
$17$	0.930307	−	1.28046i	0.225632	−	0.310556i	0.906792	+	0.421579i	$0.138524\pi$
$18$		−	4.27913i		−	1.00860i
$19$	4.00527	+	2.91000i	0.918871	+	0.667599i	0.943243	−	0.332104i	$-0.107758\pi$
$19$	4.00527	+	2.91000i	0.918871	+	0.667599i	−0.0243714	+	0.999703i	$0.507758\pi$
$20$		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	−0.187454	−	0.982273i	$-0.560024\pi$
$23$	1.14264	−	0.371267i	0.238257	−	0.0774145i	0.425712	+	0.904859i	$0.360024\pi$
$24$	−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	−0.0912574	−	0.995827i	$-0.529089\pi$
$29$	4.45693	−	3.23815i	0.827631	−	0.601309i	0.918888	+	0.394519i	$0.129089\pi$
$30$		0			0
$31$	−6.63709	−	4.82213i	−1.19206	−	0.866080i	−0.198577	−	0.980085i	$-0.563632\pi$
$31$	−6.63709	−	4.82213i	−1.19206	−	0.866080i	−0.993480	+	0.114005i	$0.963632\pi$
$32$			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	−0.121324	−	0.992613i	$-0.538714\pi$
$37$	−4.88398	−	1.58690i	−0.802921	−	0.260885i	−0.681597	+	0.731728i	$0.738714\pi$
$38$	−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	−0.611562	−	0.791196i	$-0.709459\pi$
$41$	2.22992	−	6.86300i	0.348256	−	1.07182i	0.959818	−	0.280624i	$-0.0905414\pi$
$42$	−0.706192	+	0.971990i	−0.108968	+	0.149981i
$43$		−	9.16531i		−	1.39770i	−0.715270	−	0.698848i	$-0.753696\pi$
$43$		−	9.16531i		−	1.39770i	0.715270	−	0.698848i	$-0.246304\pi$
$44$	−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	0.860103	−	0.510120i	$-0.170399\pi$
$47$	0.748388	+	1.03007i	0.109164	+	0.150251i	−0.750940	+	0.660371i	$0.770399\pi$
$48$	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	0.553106	−	0.833111i	$-0.313442\pi$
$53$	−2.98593	−	4.10978i	−0.410149	−	0.564521i	−0.963255	+	0.268590i	$0.913442\pi$
$54$	−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	−0.730994	−	0.682383i	$-0.760943\pi$
$59$	2.00852	−	6.18160i	0.261487	−	0.804776i	0.992482	−	0.122392i	$-0.0390566\pi$
$60$		0			0
$61$	−2.91097	−	8.95903i	−0.372711	−	1.14709i	−0.945010	−	0.327041i	$-0.893948\pi$
$61$	−2.91097	−	8.95903i	−0.372711	−	1.14709i	0.572299	−	0.820045i	$-0.306052\pi$
$62$	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	−0.905202	−	0.424982i	$-0.860280\pi$
$67$	−1.81140	+	2.49317i	−0.221297	+	0.304590i	0.683905	+	0.729571i	$0.260280\pi$
$68$			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	−0.866413	−	0.499328i	$-0.833580\pi$
$71$	−5.55503	+	4.03596i	−0.659260	+	0.478981i	0.207153	+	0.978309i	$0.433580\pi$
$72$	6.82808	+	9.39804i	0.804696	+	1.10757i
$73$	0.518464	−	0.168459i	0.0606817	−	0.0197167i	−0.278519	−	0.960431i	$-0.589843\pi$
$73$	0.518464	−	0.168459i	0.0606817	−	0.0197167i	0.339201	+	0.940714i	$0.389843\pi$
$74$	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	−0.309670	−	0.950844i	$-0.600219\pi$
$79$	4.43470	−	3.22200i	0.498942	−	0.362503i	0.808613	+	0.588341i	$0.200219\pi$
$80$		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	−0.839284	−	0.543693i	$-0.817026\pi$
$83$	−0.572582	+	0.788091i	−0.0628490	+	0.0865043i	0.776435	+	0.630197i	$0.217026\pi$
$84$	−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	0.981290	−	0.192535i	$-0.0616709\pi$
$89$	0.700383	+	2.15556i	0.0742404	+	0.228488i	−0.907050	+	0.421024i	$0.861671\pi$
$90$		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	−0.967762	−	0.251865i	$-0.918956\pi$
$97$	−8.94518	−	12.3120i	−0.908245	−	1.25009i	0.0595168	−	0.998227i	$-0.481044\pi$
$98$	−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	0.999996	−	0.00282822i	$-0.000900250\pi$
$103$	6.98539	+	9.61456i	0.688290	+	0.947351i	−0.311706	+	0.950179i	$0.600900\pi$
$104$	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	$0.0116178\pi$
$107$			0.754919i			0.0729808i	−0.999334	+	0.0364904i	$0.988382\pi$
$108$	−0.846822	+	1.16555i	−0.0814855	+	0.112155i
$109$	2.82983	−	8.70932i	0.271048	−	0.834201i	−0.719190	−	0.694814i	$-0.755487\pi$
$109$	2.82983	−	8.70932i	0.271048	−	0.834201i	0.990238	−	0.139387i	$-0.0445133\pi$
$110$		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	0.820675	−	0.571395i	$-0.193598\pi$
$113$	12.2115	+	3.96774i	1.14876	+	0.373254i	0.328082	+	0.944649i	$0.393598\pi$
$114$	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	−0.593073	−	0.805149i	$-0.702085\pi$
$127$	−6.75742	+	2.19562i	−0.599624	+	0.194830i	−0.00655135	+	0.999979i	$0.502085\pi$
$128$	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	0.499943	−	0.866058i	$-0.333354\pi$
$131$	−1.93699	−	1.40731i	−0.169236	−	0.122957i	−0.669179	+	0.743101i	$0.733354\pi$
$132$			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	0.952861	−	0.303408i	$-0.0981246\pi$
$137$	18.0885	+	5.87730i	1.54540	+	0.502132i	0.592542	+	0.805540i	$0.298125\pi$
$138$	3.37169	+	1.09553i	0.287017	+	0.0932576i
$139$	2.08114	+	6.40508i	0.176520	+	0.543272i	0.999700	−	0.0245087i	$-0.00780215\pi$
$139$	2.08114	+	6.40508i	0.176520	+	0.543272i	−0.823180	+	0.567781i	$0.807802\pi$
$140$		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	$-0.964562\pi$
$157$		−	2.78418i		−	0.222202i	0.993809	−	0.111101i	$-0.0354376\pi$
$158$	−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	−0.803314	−	0.595556i	$-0.796932\pi$
$163$	−23.0226	−	7.48049i	−1.80327	−	0.585917i	−0.999954	+	0.00963930i	$0.996932\pi$
$164$	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	−0.113731	−	0.993512i	$-0.536280\pi$
$167$	11.1951	−	15.4087i	0.866300	−	1.19236i	0.980030	−	0.198848i	$-0.0637199\pi$
$168$		−	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	0.211955	−	0.977279i	$-0.432017\pi$
$173$	12.5987	−	4.09356i	0.957861	−	0.311228i	0.745906	+	0.666052i	$0.232017\pi$
$174$	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	−0.892469	−	0.451108i	$-0.851029\pi$
$179$	−9.89021	+	7.18566i	−0.739229	+	0.537081i	0.153241	+	0.988189i	$0.451029\pi$
$180$		0			0
$181$	−8.83187	−	6.41673i	−0.656468	−	0.476952i	0.209000	−	0.977916i	$-0.432979\pi$
$181$	−8.83187	−	6.41673i	−0.656468	−	0.476952i	−0.865468	+	0.500964i	$0.832979\pi$
$182$		−	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	−0.932000	−	0.362459i	$-0.881937\pi$
$191$	0.484424	−	1.49090i	0.0350517	−	0.107878i	0.967052	+	0.254581i	$0.0819374\pi$
$192$	−12.9282	+	17.7942i	−0.933014	+	1.28418i
$193$			1.65786i			0.119335i	0.998218	+	0.0596675i	$0.0190040\pi$
$193$			1.65786i			0.119335i	−0.998218	+	0.0596675i	$0.980996\pi$
$194$	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	0.990846	−	0.134997i	$-0.0431024\pi$
$197$	7.80760	+	10.7462i	0.556268	+	0.765638i	−0.434578	+	0.900634i	$0.643102\pi$
$198$	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	0.854141	−	0.520041i	$-0.174083\pi$
$211$	−2.07060	−	6.37266i	−0.142546	−	0.438712i	−0.996687	+	0.0813294i	$0.974083\pi$
$212$	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	0.0483465	−	0.998831i	$-0.484605\pi$
$223$	10.0733	−	3.27301i	0.674558	−	0.219177i	0.626211	+	0.779654i	$0.284605\pi$
$224$	−1.55545			−0.103928
$225$		0			0
$226$	−14.5566			−0.968293
$227$	18.6514	−	6.06020i	1.23794	−	0.402230i	0.384353	−	0.923186i	$-0.374425\pi$
$227$	18.6514	−	6.06020i	1.23794	−	0.402230i	0.853583	+	0.520956i	$0.174425\pi$
$228$	5.41331	+	7.45079i	0.358505	+	0.493440i
$229$	7.15088	−	5.19542i	0.472544	−	0.343323i	−0.325888	−	0.945408i	$-0.605663\pi$
$229$	7.15088	−	5.19542i	0.472544	−	0.343323i	0.798432	+	0.602085i	$0.205663\pi$
$230$		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	−0.541043	−	0.840995i	$-0.681971\pi$
$233$	6.50233	−	8.94969i	0.425982	−	0.586313i	0.967025	+	0.254681i	$0.0819706\pi$
$234$	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	−0.972809	−	0.231609i	$-0.925601\pi$
$239$	−4.97686	−	15.3172i	−0.321926	−	0.990788i	0.650882	−	0.759179i	$-0.274399\pi$
$240$		0			0
$241$	1.85062	−	5.69562i	0.119209	−	0.366887i	−0.873593	−	0.486658i	$-0.838216\pi$
$241$	1.85062	−	5.69562i	0.119209	−	0.366887i	0.992802	+	0.119771i	$0.0382159\pi$
$242$	−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	$0.263223\pi$
$257$			23.5935i			1.47172i	−0.677132	+	0.735862i	$0.736777\pi$
$258$	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	0.107733	−	0.994180i	$-0.465641\pi$
$263$	−6.31621	−	2.05226i	−0.389474	−	0.126548i	−0.497207	+	0.867632i	$0.665641\pi$
$264$	−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	0.217609	−	0.976036i	$-0.430174\pi$
$269$	−10.5527	−	7.66701i	−0.643411	−	0.467466i	−0.861020	+	0.508570i	$0.830174\pi$
$270$		0			0
$271$	9.58586	−	6.96454i	0.582300	−	0.423066i	−0.257253	−	0.966344i	$-0.582817\pi$
$271$	9.58586	−	6.96454i	0.582300	−	0.423066i	0.839552	+	0.543279i	$0.182817\pi$
$272$	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	0.218538	−	0.975828i	$-0.429871\pi$
$277$	16.1260	−	5.23965i	0.968917	−	0.314820i	0.750379	+	0.661008i	$0.229871\pi$
$278$	−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	0.703476	−	0.710719i	$-0.251630\pi$
$281$	4.10575	+	2.98300i	0.244928	+	0.177951i	−0.458548	+	0.888670i	$0.651630\pi$
$282$			3.75704i			0.223728i
$283$	6.95047	−	9.56650i	0.413162	−	0.568669i	−0.550824	−	0.834622i	$-0.685686\pi$
$283$	6.95047	−	9.56650i	0.413162	−	0.568669i	0.963986	+	0.265952i	$0.0856864\pi$
$284$	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	$-0.807834\pi$
$293$		−	19.4348i		−	1.13540i	0.823237	−	0.567698i	$-0.192166\pi$
$294$	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	$-0.741697\pi$
$307$		−	25.4169i		−	1.45062i	0.688423	−	0.725310i	$-0.258303\pi$
$308$	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	0.988445	+	0.151578i	$0.0484356\pi$
$311$	4.90032	+	15.0816i	0.277872	+	0.855201i	−0.710573	+	0.703623i	$0.751564\pi$
$312$	−5.33802	−	1.73443i	−0.302206	−	0.0981926i
$313$	6.67303	+	2.16820i	0.377182	+	0.122554i	0.491471	−	0.870894i	$-0.336459\pi$
$313$	6.67303	+	2.16820i	0.377182	+	0.122554i	−0.114290	+	0.993447i	$0.536459\pi$
$314$	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	−0.968019	−	0.250879i	$-0.919280\pi$
$317$	−7.66100	+	10.5445i	−0.430285	+	0.592236i	0.537734	+	0.843115i	$0.319280\pi$
$318$		−	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	0.906350	−	0.422527i	$-0.138857\pi$
$331$	14.2742	+	10.3708i	0.784580	+	0.570031i	−0.121770	+	0.992558i	$0.538857\pi$
$332$		−	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	−0.416211	−	0.909268i	$-0.636642\pi$
$337$	−23.6333	−	7.67892i	−1.28739	−	0.418297i	−0.871176	+	0.490971i	$0.836642\pi$
$338$	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	0.965375	−	0.260868i	$-0.0840087\pi$
$347$	7.80431	+	10.7417i	0.418957	+	0.576645i	−0.546417	+	0.837513i	$0.684009\pi$
$348$	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	0.990531	−	0.137288i	$-0.0438387\pi$
$353$	10.4063	+	14.3230i	0.553871	+	0.762338i	−0.436660	+	0.899627i	$0.643839\pi$
$354$	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	0.221829	+	0.975086i	$0.428797\pi$
$359$	−10.0568	+	30.9515i	−0.530775	+	1.63356i	−0.752605	+	0.658473i	$0.771203\pi$
$360$		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	−0.0925399	+	0.995709i	$0.529499\pi$
$367$	−19.3664	+	26.6556i	−1.01092	+	1.39141i	−0.918379	+	0.395702i	$0.870501\pi$
$368$			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	−0.393121	−	0.919487i	$-0.628605\pi$
$373$	−3.29681	+	1.07120i	−0.170703	+	0.0554646i	0.222419	+	0.974951i	$0.428605\pi$
$374$	−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	−0.627137	−	0.778909i	$-0.715773\pi$
$379$	−1.56029	+	1.13362i	−0.0801469	+	0.0582301i	0.546990	+	0.837139i	$0.315773\pi$
$380$		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	−0.876609	−	0.481203i	$-0.840200\pi$
$383$	−2.89780	+	3.98848i	−0.148071	+	0.203802i	0.728538	+	0.685005i	$0.240200\pi$
$384$	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	−0.999486	−	0.0320593i	$-0.989793\pi$
$389$	−4.13650	−	12.7308i	−0.209729	−	0.645479i	0.789757	−	0.613420i	$-0.210207\pi$
$390$		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	0.839399	−	0.543515i	$-0.182907\pi$
$397$	1.25719	+	1.73038i	0.0630968	+	0.0868452i	−0.776302	+	0.630361i	$0.782907\pi$
$398$	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	0.785338	+	0.619067i	$0.212489\pi$
$409$	−4.32570	+	13.3131i	−0.213892	+	0.658292i	−0.999230	+	0.0392250i	$0.987511\pi$
$410$		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	0.996211	−	0.0869710i	$-0.0277187\pi$
$419$	25.0003	+	18.1638i	1.22134	+	0.887357i	0.225132	+	0.974328i	$0.427719\pi$
$420$		0			0
$421$	6.66609	−	4.84320i	0.324885	−	0.236043i	−0.413372	−	0.910562i	$-0.635649\pi$
$421$	6.66609	−	4.84320i	0.324885	−	0.236043i	0.738257	+	0.674519i	$0.235649\pi$
$422$	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	−0.0842309	−	0.996446i	$-0.526843\pi$
$431$	−21.9633	−	15.9573i	−1.05794	−	0.768636i	−0.973705	+	0.227810i	$0.926843\pi$
$432$			4.15198i			0.199762i
$433$	−12.6318	+	17.3862i	−0.607045	+	0.835526i	−0.996330	−	0.0855913i	$-0.972722\pi$
$433$	−12.6318	+	17.3862i	−0.607045	+	0.835526i	0.389285	+	0.921117i	$0.372722\pi$
$434$	−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	0.939729	+	0.341921i	$0.111078\pi$
$439$	7.97128	+	24.5331i	0.380448	+	1.17090i	−0.559280	+	0.828979i	$0.688922\pi$
$440$		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	$-0.975895\pi$
$443$		−	3.18479i		−	0.151314i	0.997134	−	0.0756570i	$-0.0241054\pi$
$444$	−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	$0.203638\pi$
$457$			25.5245i			1.19399i	−0.802246	+	0.596994i	$0.796362\pi$
$458$	−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	−0.996496	−	0.0836412i	$-0.973345\pi$
$461$	−5.14179	−	15.8248i	−0.239477	−	0.737034i	0.757019	−	0.653393i	$-0.226655\pi$
$462$	−2.28528	−	0.742534i	−0.106321	−	0.0345458i
$463$	−16.9457	−	5.50599i	−0.787534	−	0.255885i	−0.112480	−	0.993654i	$-0.535880\pi$
$463$	−16.9457	−	5.50599i	−0.787534	−	0.255885i	−0.675054	+	0.737769i	$0.735880\pi$
$464$	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	−0.957562	−	0.288227i	$-0.906934\pi$
$467$	−8.37479	+	11.5269i	−0.387539	+	0.533402i	0.570023	+	0.821629i	$0.306934\pi$
$468$		−	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	−0.532727	−	0.846287i	$-0.678833\pi$
$479$	2.35314	−	1.70966i	0.107518	−	0.0781162i	0.640245	+	0.768171i	$0.278833\pi$
$480$		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	−0.0827414	−	0.996571i	$-0.526368\pi$
$487$	−16.2300	−	5.27344i	−0.735450	−	0.238962i	−0.652709	+	0.757609i	$0.726368\pi$
$488$	−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	−0.469703	−	0.882824i	$-0.655639\pi$
$491$	9.51057	−	29.2705i	0.429206	−	1.32096i	0.898909	−	0.438135i	$-0.144361\pi$
$492$	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	0.768205	−	0.640204i	$-0.221150\pi$
$503$	−1.75056	−	2.40944i	−0.0780536	−	0.107432i	−0.846259	+	0.532772i	$0.821150\pi$
$504$	−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	−0.301385	−	0.953503i	$-0.597449\pi$
$509$	11.3458	−	34.9189i	0.502895	−	1.54775i	0.804280	−	0.594250i	$-0.202551\pi$
$510$		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	−0.631214	−	0.775608i	$-0.717443\pi$
$521$	−2.02286	+	1.46969i	−0.0886229	+	0.0643883i	0.542591	+	0.839997i	$0.317443\pi$
$522$	−13.8564	−	19.0718i	−0.606480	−	0.834749i
$523$	−40.0640	+	13.0176i	−1.75188	+	0.569220i	−0.996308	−	0.0858485i	$-0.972640\pi$
$523$	−40.0640	+	13.0176i	−1.75188	+	0.569220i	−0.755570	+	0.655068i	$0.772640\pi$
$524$	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	0.587654	+	0.809112i	$0.300052\pi$
$541$	−8.45136	+	26.0106i	−0.363352	+	1.11828i	−0.951006	+	0.309171i	$0.899948\pi$
$542$	−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	0.984115	−	0.177534i	$-0.0568119\pi$
$547$	11.9551	+	16.4547i	0.511162	+	0.703554i	−0.472953	+	0.881088i	$0.656812\pi$
$548$	−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	$-0.795677\pi$
$557$		−	28.2605i		−	1.19744i	0.800960	−	0.598718i	$-0.204323\pi$
$558$	−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	0.556374	−	0.830932i	$-0.312192\pi$
$563$	12.2928	+	3.99418i	0.518081	+	0.168335i	−0.0382934	+	0.999267i	$0.512192\pi$
$564$	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	0.534250	−	0.845326i	$-0.320594\pi$
$569$	−2.49536	−	1.81298i	−0.104611	−	0.0760043i	−0.638861	+	0.769322i	$0.720594\pi$
$570$		0			0
$571$	3.33935	−	2.42618i	0.139747	−	0.101532i	−0.515715	−	0.856760i	$-0.672474\pi$
$571$	3.33935	−	2.42618i	0.139747	−	0.101532i	0.655463	+	0.755228i	$0.272474\pi$
$572$	−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	−0.180480	−	0.983579i	$-0.557765\pi$
$577$	6.04463	−	1.96402i	0.251641	−	0.0817632i	0.432121	+	0.901815i	$0.357765\pi$
$578$	−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	0.692380	−	0.721533i	$-0.256562\pi$
$587$	20.0711	+	6.52148i	0.828421	+	0.269170i	0.136041	+	0.990703i	$0.456562\pi$
$588$	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	$0.146650\pi$
$593$			21.6529i			0.889177i	−0.895735	+	0.444589i	$0.853350\pi$
$594$	−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	$0.103021\pi$
$607$			15.6708i			0.636059i	−0.948081	+	0.318029i	$0.896979\pi$
$608$	−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	0.930318	−	0.366754i	$-0.119531\pi$
$613$	36.3308	+	11.8046i	1.46739	+	0.476783i	0.537070	+	0.843538i	$0.319531\pi$
$614$	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	−0.623239	−	0.782031i	$-0.714184\pi$
$617$	7.77744	−	10.7047i	0.313108	−	0.430956i	0.936347	+	0.351075i	$0.114184\pi$
$618$			35.0678i			1.41064i
$619$	4.89021	+	3.55294i	0.196554	+	0.142805i	0.681709	−	0.731623i	$-0.261237\pi$
$619$	4.89021	+	3.55294i	0.196554	+	0.142805i	−0.485155	+	0.874428i	$0.661237\pi$
$620$		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	0.995842	−	0.0910970i	$-0.0290373\pi$
$631$	30.5691	+	22.2097i	1.21694	+	0.884156i	0.221094	+	0.975253i	$0.429037\pi$
$632$		−	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	0.739345	+	0.673326i	$0.235135\pi$
$641$	−6.44517	+	19.8362i	−0.254569	+	0.783482i	−0.993914	+	0.110156i	$0.964865\pi$
$642$	−1.30935	+	1.80217i	−0.0516760	+	0.0711259i
$643$			37.5552i			1.48103i	0.672039	+	0.740516i	$0.265419\pi$
$643$			37.5552i			1.48103i	−0.672039	+	0.740516i	$0.734581\pi$
$644$	−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	0.998228	−	0.0594998i	$-0.0189506\pi$
$647$	16.1055	+	22.1673i	0.633171	+	0.871485i	−0.365057	+	0.930985i	$0.618951\pi$
$648$	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	0.987146	−	0.159821i	$-0.0510916\pi$
$653$	13.5462	+	18.6447i	0.530103	+	0.729624i	−0.457044	+	0.889444i	$0.651092\pi$
$654$	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	0.748799	+	0.662797i	$0.230631\pi$
$659$	−6.32981	+	19.4811i	−0.246574	+	0.758878i	−0.995374	+	0.0960808i	$0.969369\pi$
$660$		0			0
$661$	4.32314	+	13.3053i	0.168151	+	0.517515i	0.999255	−	0.0386024i	$-0.0122906\pi$
$661$	4.32314	+	13.3053i	0.168151	+	0.517515i	−0.831104	+	0.556117i	$0.812291\pi$
$662$	−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	−0.161649	−	0.986848i	$-0.551681\pi$
$673$	7.46172	−	2.42446i	0.287628	−	0.0934561i	0.449278	+	0.893392i	$0.351681\pi$
$674$	28.1720			1.08514
$675$		0			0
$676$	8.94042			0.343862
$677$	−13.6936	+	4.44932i	−0.526287	+	0.171001i	−0.560097	−	0.828427i	$-0.689236\pi$
$677$	−13.6936	+	4.44932i	−0.526287	+	0.171001i	0.0338094	+	0.999428i	$0.489236\pi$
$678$	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	−0.642348	−	0.766413i	$-0.722040\pi$
$683$	7.44957	−	10.2535i	0.285050	−	0.392338i	0.927398	+	0.374075i	$0.122040\pi$
$684$	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	−0.911591	−	0.411098i	$-0.865145\pi$
$691$	1.77540	−	5.46411i	0.0675392	−	0.207864i	0.979130	+	0.203234i	$0.0651452\pi$
$692$	−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	−0.661949	−	0.749549i	$-0.730270\pi$
$709$	8.36497	−	25.7447i	0.314153	−	0.966864i	0.976102	−	0.217315i	$-0.0697297\pi$
$710$		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	0.306506	−	0.951869i	$-0.400840\pi$
$719$	−13.5159	−	9.81991i	−0.504060	−	0.366221i	−0.810565	+	0.585648i	$0.800840\pi$
$720$		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	−0.508011	−	0.861350i	$-0.669619\pi$
$727$	−11.1279	+	3.61568i	−0.412712	+	0.134098i	0.0952994	+	0.995449i	$0.469619\pi$
$728$	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	0.258098	+	0.966119i	$0.416904\pi$
$733$	−20.0481	+	27.5938i	−0.740493	+	1.01920i	−0.998590	+	0.0530818i	$0.983096\pi$
$734$	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	0.913078	−	0.407785i	$-0.133699\pi$
$739$	−1.77536	−	5.46398i	−0.0653075	−	0.200996i	−0.978386	+	0.206789i	$0.933699\pi$
$740$		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	$-0.767009\pi$
$743$		−	36.4348i		−	1.33666i	0.743863	−	0.668332i	$-0.232991\pi$
$744$	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	$-0.967939\pi$
$757$		−	5.53316i		−	0.201106i	0.994932	−	0.100553i	$-0.0320612\pi$
$758$	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	−0.999518	−	0.0310389i	$-0.990118\pi$
$761$	−5.76925	−	17.7559i	−0.209135	−	0.643652i	0.790383	−	0.612613i	$-0.209882\pi$
$762$	−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	0.379321	−	0.925265i	$-0.376158\pi$
$769$	−10.6332	−	7.72544i	−0.383441	−	0.278587i	−0.762763	+	0.646679i	$0.776158\pi$
$770$		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	0.211381	−	0.977404i	$-0.432204\pi$
$773$	26.6045	−	8.64431i	0.956896	−	0.310914i	0.745514	+	0.666489i	$0.232204\pi$
$774$	−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	0.814028	−	0.580825i	$-0.197270\pi$
$787$	31.7339	+	10.3110i	1.13119	+	0.367546i	0.317162	+	0.948371i	$0.397270\pi$
$788$	−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	−0.995429	−	0.0955049i	$-0.969553\pi$
$797$	−21.9824	−	30.2561i	−0.778655	−	1.07173i	0.216774	−	0.976222i	$-0.430447\pi$
$798$	−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	0.584876	+	0.811123i	$0.301143\pi$
$809$	−10.3835	+	31.9571i	−0.365064	+	1.12355i	−0.949941	+	0.312430i	$0.898857\pi$
$810$		0			0
$811$	−11.7444	−	36.1454i	−0.412400	−	1.26924i	−0.914556	−	0.404460i	$-0.867459\pi$
$811$	−11.7444	−	36.1454i	−0.412400	−	1.26924i	0.502155	−	0.864778i	$-0.332541\pi$
$812$	−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	−0.881228	−	0.472691i	$-0.843283\pi$
$821$	−20.1714	+	14.6554i	−0.703987	+	0.511477i	0.177241	+	0.984167i	$0.443283\pi$
$822$	32.9877	+	45.4036i	1.15058	+	1.58363i
$823$	−24.2144	+	7.86775i	−0.844062	+	0.274252i	−0.698957	−	0.715164i	$-0.746352\pi$
$823$	−24.2144	+	7.86775i	−0.844062	+	0.274252i	−0.145105	+	0.989416i	$0.546352\pi$
$824$	36.5760			1.27418
$825$		0			0
$826$	−3.00027			−0.104393
$827$	30.7559	−	9.99321i	1.06949	−	0.347498i	0.279200	−	0.960233i	$-0.409931\pi$
$827$	30.7559	−	9.99321i	1.06949	−	0.347498i	0.790288	+	0.612735i	$0.209931\pi$
$828$	−1.90507	−	2.62211i	−0.0662058	−	0.0911245i
$829$	20.2102	−	14.6836i	0.701930	−	0.509982i	−0.178630	−	0.983916i	$-0.557167\pi$
$829$	20.2102	−	14.6836i	0.701930	−	0.509982i	0.880560	+	0.473934i	$0.157167\pi$
$830$		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	−0.999650	−	0.0264480i	$-0.991580\pi$
$839$	−5.98027	−	18.4054i	−0.206462	−	0.635424i	0.793188	−	0.608976i	$-0.208420\pi$
$840$		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	0.449374	−	0.893344i	$-0.351647\pi$
$853$	−15.7454	−	21.6716i	−0.539111	−	0.742022i	−0.988485	+	0.151321i	$0.951647\pi$
$854$	−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	$0.301404\pi$
$857$			47.5186i			1.62320i	−0.584210	+	0.811602i	$0.698596\pi$
$858$	−2.43051	+	3.34531i	−0.0829764	+	0.114207i
$859$	−3.56266	+	10.9647i	−0.121556	+	0.374112i	−0.993258	−	0.115925i	$-0.963017\pi$
$859$	−3.56266	+	10.9647i	−0.121556	+	0.374112i	0.871702	+	0.490037i	$0.163017\pi$
$860$		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	0.585610	−	0.810593i	$-0.300855\pi$
$863$	17.1245	+	5.56407i	0.582923	+	0.189403i	−0.00268645	+	0.999996i	$0.500855\pi$
$864$	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	−0.570401	−	0.821366i	$-0.693212\pi$
$877$	−16.2605	+	5.28336i	−0.549078	+	0.178406i	0.0213227	+	0.999773i	$0.493212\pi$
$878$	−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	0.969607	−	0.244667i	$-0.0786787\pi$
$881$	30.7662	+	22.3530i	1.03654	+	0.753090i	0.0669326	+	0.997757i	$0.478679\pi$
$882$		−	29.2445i		−	0.984714i
$883$	−21.6595	+	29.8118i	−0.728900	+	1.00325i	0.270281	+	0.962782i	$0.412884\pi$
$883$	−21.6595	+	29.8118i	−0.728900	+	1.00325i	−0.999181	+	0.0404637i	$0.987116\pi$
$884$	−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	−0.209642	−	0.977778i	$-0.567230\pi$
$887$	−28.4116	−	9.23150i	−0.953970	−	0.309964i	−0.744328	+	0.667815i	$0.767230\pi$
$888$	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	$-0.743211\pi$
$907$		−	43.4897i		−	1.44405i	0.691866	−	0.722026i	$-0.256789\pi$
$908$	−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	−0.994865	−	0.101215i	$-0.967727\pi$
$911$	−7.53045	−	23.1763i	−0.249495	−	0.767866i	0.745370	−	0.666651i	$-0.232273\pi$
$912$	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	0.995644	−	0.0932366i	$-0.0297213\pi$
$919$	36.8219	+	26.7527i	1.21464	+	0.882489i	0.218998	+	0.975725i	$0.429721\pi$
$920$		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	−0.461342	−	0.887222i	$-0.652632\pi$
$929$	7.31185	−	5.31237i	0.239894	−	0.174293i	0.701236	+	0.712929i	$0.252632\pi$
$930$		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	0.776949	−	0.629564i	$-0.216766\pi$
$937$	31.6961	+	10.2987i	1.03546	+	0.336443i	0.258516	+	0.966007i	$0.416766\pi$
$938$	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	0.687996	+	0.725715i	$0.258491\pi$
$941$	−9.05452	+	27.8669i	−0.295169	+	0.908436i	−0.983165	+	0.182722i	$0.941509\pi$
$942$	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	−0.852998	−	0.521914i	$-0.825218\pi$
$947$	−33.4130	−	45.9891i	−1.08578	−	1.49444i	−0.232779	−	0.972530i	$-0.574782\pi$
$948$	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	0.950833	−	0.309703i	$-0.100229\pi$
$953$	11.1896	+	15.4011i	0.362465	+	0.498890i	−0.588368	+	0.808593i	$0.700229\pi$
$954$	−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	−0.925089	−	0.379750i	$-0.876010\pi$
$967$	−8.64663	+	11.9011i	−0.278057	+	0.382713i	0.647032	+	0.762463i	$0.276010\pi$
$968$		−	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	0.0446263	−	0.999004i	$-0.485790\pi$
$971$	31.4265	−	22.8327i	1.00853	−	0.732737i	0.963899	+	0.266267i	$0.0857903\pi$
$972$	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	−0.998838	−	0.0481892i	$-0.984655\pi$
$977$	−55.5934	+	18.0634i	−1.77859	+	0.577899i	−0.779752	+	0.626088i	$0.784655\pi$
$978$	−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	−0.458894	−	0.888491i	$-0.651754\pi$
$983$	16.5517	−	22.7815i	0.527918	−	0.726616i	0.986811	+	0.161875i	$0.0517541\pi$
$984$	−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	−0.549393	−	0.835564i	$-0.685141\pi$
$991$	12.1579	−	37.4181i	0.386208	−	1.18862i	0.935601	−	0.353060i	$-0.114859\pi$
$992$	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	0.992416	+	0.122926i	$0.0392279\pi$
$997$	25.3440	+	34.8830i	0.802652	+	1.10476i	−0.189763	+	0.981830i	$0.560772\pi$
$998$	−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.499.1		8
5.2	odd	4		625.2.d.o.126.2		16
5.3	odd	4		625.2.d.o.126.3		16
5.4	even	2		625.2.e.i.499.2		8
25.2	odd	20		625.2.a.f.1.3		8
25.3	odd	20		625.2.d.o.501.3		16
25.4	even	10	inner	625.2.e.a.124.1		8
25.6	even	5		25.2.e.a.9.2	✓	8
25.8	odd	20		125.2.d.b.76.2		16
25.9	even	10		25.2.e.a.14.2	yes	8
25.11	even	5		625.2.b.c.624.6		8
25.12	odd	20		125.2.d.b.51.3		16
25.13	odd	20		125.2.d.b.51.2		16
25.14	even	10		625.2.b.c.624.3		8
25.16	even	5		125.2.e.b.74.1		8
25.17	odd	20		125.2.d.b.76.3		16
25.19	even	10		125.2.e.b.49.1		8
25.21	even	5		625.2.e.i.124.2		8
25.22	odd	20		625.2.d.o.501.2		16
25.23	odd	20		625.2.a.f.1.6		8
75.2	even	20		5625.2.a.x.1.6		8
75.23	even	20		5625.2.a.x.1.3		8
75.56	odd	10		225.2.m.a.109.1		8
75.59	odd	10		225.2.m.a.64.1		8
100.23	even	20		10000.2.a.bj.1.8		8
100.27	even	20		10000.2.a.bj.1.1		8
100.31	odd	10		400.2.y.c.209.2		8
100.59	odd	10		400.2.y.c.289.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.e.a.9.2	✓	8	25.6	even	5
25.2.e.a.14.2	yes	8	25.9	even	10
125.2.d.b.51.2		16	25.13	odd	20
125.2.d.b.51.3		16	25.12	odd	20
125.2.d.b.76.2		16	25.8	odd	20
125.2.d.b.76.3		16	25.17	odd	20
125.2.e.b.49.1		8	25.19	even	10
125.2.e.b.74.1		8	25.16	even	5
225.2.m.a.64.1		8	75.59	odd	10
225.2.m.a.109.1		8	75.56	odd	10
400.2.y.c.209.2		8	100.31	odd	10
400.2.y.c.289.2		8	100.59	odd	10
625.2.a.f.1.3		8	25.2	odd	20
625.2.a.f.1.6		8	25.23	odd	20
625.2.b.c.624.3		8	25.14	even	10
625.2.b.c.624.6		8	25.11	even	5
625.2.d.o.126.2		16	5.2	odd	4
625.2.d.o.126.3		16	5.3	odd	4
625.2.d.o.501.2		16	25.22	odd	20
625.2.d.o.501.3		16	25.3	odd	20
625.2.e.a.124.1		8	25.4	even	10	inner
625.2.e.a.499.1		8	1.1	even	1	trivial
625.2.e.i.124.2		8	25.21	even	5
625.2.e.i.499.2		8	5.4	even	2
5625.2.a.x.1.3		8	75.23	even	20
5625.2.a.x.1.6		8	75.2	even	20
10000.2.a.bj.1.1		8	100.27	even	20
10000.2.a.bj.1.8		8	100.23	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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