LMFDB - Embedded newform 80.6.n.d.47.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,6,Mod(47,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("80.47");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	80.n (of order $4$, degree $2$, 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:	$12.8307055850$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 271 x^{18} + 109637 x^{16} + 25993614 x^{14} + 5522961902 x^{12} + 881545050522 x^{10} + \cdots + 57\!\cdots\!24 $ x^20 + 271x^18 + 109637x^16 + 25993614x^14 + 5522961902x^12 + 881545050522x^10 + 133816049059481x^8 + 14779507781220031x^6 + 824105698447750789x^4 + 12044868290803250652*x^2 + 579398322543528055824
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{65}\cdot 3^{4}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.6
Root			$1.99079 - 10.4027i$ of defining polynomial
Character	$\chi$	$=$	80.47
Dual form			80.6.n.d.63.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.839817 + 0.839817i) q^{3} +(3.71634 + 55.7780i) q^{5} +(-99.3589 + 99.3589i) q^{7} -241.589i q^{9} +O(q^{10})$	\(q+(0.839817 + 0.839817i) q^{3} +(3.71634 + 55.7780i) q^{5} +(-99.3589 + 99.3589i) q^{7} -241.589i q^{9} -637.781i q^{11} +(-640.389 + 640.389i) q^{13} +(-43.7223 + 49.9644i) q^{15} +(648.760 + 648.760i) q^{17} -2506.12 q^{19} -166.887 q^{21} +(-2801.60 - 2801.60i) q^{23} +(-3097.38 + 414.580i) q^{25} +(406.966 - 406.966i) q^{27} +4955.21i q^{29} -1961.18i q^{31} +(535.619 - 535.619i) q^{33} +(-5911.30 - 5172.79i) q^{35} +(-1897.88 - 1897.88i) q^{37} -1075.62 q^{39} -5828.95 q^{41} +(10692.1 + 10692.1i) q^{43} +(13475.4 - 897.828i) q^{45} +(-8309.52 + 8309.52i) q^{47} -2937.38i q^{49} +1089.68i q^{51} +(7437.17 - 7437.17i) q^{53} +(35574.2 - 2370.21i) q^{55} +(-2104.68 - 2104.68i) q^{57} +16738.4 q^{59} +23742.5 q^{61} +(24004.1 + 24004.1i) q^{63} +(-38099.5 - 33339.7i) q^{65} +(-4154.05 + 4154.05i) q^{67} -4705.66i q^{69} +12276.0i q^{71} +(36092.8 - 36092.8i) q^{73} +(-2949.40 - 2253.06i) q^{75} +(63369.2 + 63369.2i) q^{77} -64330.4 q^{79} -58022.7 q^{81} +(62856.9 + 62856.9i) q^{83} +(-33775.5 + 38597.6i) q^{85} +(-4161.47 + 4161.47i) q^{87} +24423.5i q^{89} -127257. i q^{91} +(1647.03 - 1647.03i) q^{93} +(-9313.60 - 139787. i) q^{95} +(-89666.0 - 89666.0i) q^{97} -154081. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 44 q^{5}+O(q^{10}) $ 20 * q - 44 * q^5	$ 20 q - 44 q^{5} + 804 q^{13} - 2236 q^{17} - 4520 q^{21} + 948 q^{25} - 11096 q^{33} + 44260 q^{37} - 6760 q^{41} - 92816 q^{45} + 182452 q^{53} - 34288 q^{57} - 41080 q^{61} - 155772 q^{65} + 264372 q^{73} + 399304 q^{77} - 520220 q^{81} - 344796 q^{85} + 713496 q^{93} + 374772 q^{97}+O(q^{100}) $ 20 * q - 44 * q^5 + 804 * q^13 - 2236 * q^17 - 4520 * q^21 + 948 * q^25 - 11096 * q^33 + 44260 * q^37 - 6760 * q^41 - 92816 * q^45 + 182452 * q^53 - 34288 * q^57 - 41080 * q^61 - 155772 * q^65 + 264372 * q^73 + 399304 * q^77 - 520220 * q^81 - 344796 * q^85 + 713496 * q^93 + 374772 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.839817	+	0.839817i	0.0538743	+	0.0538743i	0.733531	−	0.679656i	$-0.237871\pi$
$3$	0.839817	+	0.839817i	0.0538743	+	0.0538743i	−0.679656	+	0.733531i	$0.737871\pi$
$4$		0			0
$5$	3.71634	+	55.7780i	0.0664799	+	0.997788i
$5$	3.71634	+	55.7780i	0.0664799	+	0.997788i
$6$		0			0
$7$	−99.3589	+	99.3589i	−0.766411	+	0.766411i	−0.977473	−	0.211062i	$-0.932308\pi$
$7$	−99.3589	+	99.3589i	−0.766411	+	0.766411i	0.211062	+	0.977473i	$0.432308\pi$
$8$		0			0
$9$		−	241.589i		−	0.994195i
$10$		0			0
$11$		−	637.781i		−	1.58924i	−0.607107	−	0.794620i	$-0.707670\pi$
$11$		−	637.781i		−	1.58924i	0.607107	−	0.794620i	$-0.292330\pi$
$12$		0			0
$13$	−640.389	+	640.389i	−1.05096	+	1.05096i	−0.0523281	+	0.998630i	$0.516664\pi$
$13$	−640.389	+	640.389i	−1.05096	+	1.05096i	−0.998630	+	0.0523281i	$0.983336\pi$
$14$		0			0
$15$	−43.7223	+	49.9644i	−0.0501736	+	0.0573367i
$16$		0			0
$17$	648.760	+	648.760i	0.544455	+	0.544455i	0.924832	−	0.380377i	$-0.124206\pi$
$17$	648.760	+	648.760i	0.544455	+	0.544455i	−0.380377	+	0.924832i	$0.624206\pi$
$18$		0			0
$19$	−2506.12			−1.59264			−0.796321	−	0.604874i	$-0.793224\pi$
$19$	−2506.12			−1.59264			−0.796321	+	0.604874i	$0.793224\pi$
$20$		0			0
$21$	−166.887			−0.0825797
$22$		0			0
$23$	−2801.60	−	2801.60i	−1.10430	−	1.10430i	−0.993886	−	0.110413i	$-0.964783\pi$
$23$	−2801.60	−	2801.60i	−1.10430	−	1.10430i	−0.110413	−	0.993886i	$-0.535217\pi$
$24$		0			0
$25$	−3097.38	+	414.580i	−0.991161	+	0.132666i
$26$		0			0
$27$	406.966	−	406.966i	0.107436	−	0.107436i
$28$		0			0
$29$			4955.21i			1.09413i	0.837091	+	0.547063i	$0.184254\pi$
$29$			4955.21i			1.09413i	−0.837091	+	0.547063i	$0.815746\pi$
$30$		0			0
$31$		−	1961.18i		−	0.366533i	−0.983063	−	0.183267i	$-0.941333\pi$
$31$		−	1961.18i		−	0.366533i	0.983063	−	0.183267i	$-0.0586672\pi$
$32$		0			0
$33$	535.619	−	535.619i	0.0856192	−	0.0856192i
$34$		0			0
$35$	−5911.30	−	5172.79i	−0.815666	−	0.713765i
$36$		0			0
$37$	−1897.88	−	1897.88i	−0.227911	−	0.227911i	0.583909	−	0.811819i	$-0.301523\pi$
$37$	−1897.88	−	1897.88i	−0.227911	−	0.227911i	−0.811819	+	0.583909i	$0.801523\pi$
$38$		0			0
$39$	−1075.62			−0.113239
$40$		0			0
$41$	−5828.95			−0.541540			−0.270770	−	0.962644i	$-0.587278\pi$
$41$	−5828.95			−0.541540			−0.270770	+	0.962644i	$0.587278\pi$
$42$		0			0
$43$	10692.1	+	10692.1i	0.881844	+	0.881844i	0.993722	−	0.111878i	$-0.0356865\pi$
$43$	10692.1	+	10692.1i	0.881844	+	0.881844i	−0.111878	+	0.993722i	$0.535686\pi$
$44$		0			0
$45$	13475.4	−	897.828i	0.991996	−	0.0660940i
$46$		0			0
$47$	−8309.52	+	8309.52i	−0.548695	+	0.548695i	−0.926063	−	0.377368i	$-0.876829\pi$
$47$	−8309.52	+	8309.52i	−0.548695	+	0.548695i	0.377368	+	0.926063i	$0.376829\pi$
$48$		0			0
$49$		−	2937.38i		−	0.174771i
$50$		0			0
$51$			1089.68i			0.0586642i
$52$		0			0
$53$	7437.17	−	7437.17i	0.363679	−	0.363679i	−0.501487	−	0.865165i	$-0.667213\pi$
$53$	7437.17	−	7437.17i	0.363679	−	0.363679i	0.865165	+	0.501487i	$0.167213\pi$
$54$		0			0
$55$	35574.2	−	2370.21i	1.58572	−	0.105653i
$56$		0			0
$57$	−2104.68	−	2104.68i	−0.0858025	−	0.0858025i
$58$		0			0
$59$	16738.4			0.626014			0.313007	−	0.949751i	$-0.398664\pi$
$59$	16738.4			0.626014			0.313007	+	0.949751i	$0.398664\pi$
$60$		0			0
$61$	23742.5			0.816961			0.408481	−	0.912767i	$-0.366059\pi$
$61$	23742.5			0.816961			0.408481	+	0.912767i	$0.366059\pi$
$62$		0			0
$63$	24004.1	+	24004.1i	0.761962	+	0.761962i
$64$		0			0
$65$	−38099.5	−	33339.7i	−1.11850	−	0.978765i
$66$		0			0
$67$	−4154.05	+	4154.05i	−0.113054	+	0.113054i	−0.761371	−	0.648317i	$-0.775473\pi$
$67$	−4154.05	+	4154.05i	−0.113054	+	0.113054i	0.648317	+	0.761371i	$0.275473\pi$
$68$		0			0
$69$		−	4705.66i		−	0.118987i
$70$		0			0
$71$			12276.0i			0.289008i	0.989504	+	0.144504i	$0.0461587\pi$
$71$			12276.0i			0.289008i	−0.989504	+	0.144504i	$0.953841\pi$
$72$		0			0
$73$	36092.8	−	36092.8i	0.792709	−	0.792709i	−0.189225	−	0.981934i	$-0.560598\pi$
$73$	36092.8	−	36092.8i	0.792709	−	0.792709i	0.981934	+	0.189225i	$0.0605976\pi$
$74$		0			0
$75$	−2949.40	−	2253.06i	−0.0605454	−	0.0462508i
$76$		0			0
$77$	63369.2	+	63369.2i	1.21801	+	1.21801i
$78$		0			0
$79$	−64330.4			−1.15971			−0.579854	−	0.814721i	$-0.696890\pi$
$79$	−64330.4			−1.15971			−0.579854	+	0.814721i	$0.696890\pi$
$80$		0			0
$81$	−58022.7			−0.982619
$82$		0			0
$83$	62856.9	+	62856.9i	1.00152	+	1.00152i	0.999999	+	0.00151672i	$0.000482787\pi$
$83$	62856.9	+	62856.9i	1.00152	+	1.00152i	0.00151672	+	0.999999i	$0.499517\pi$
$84$		0			0
$85$	−33775.5	+	38597.6i	−0.507055	+	0.579446i
$86$		0			0
$87$	−4161.47	+	4161.47i	−0.0589453	+	0.0589453i
$88$		0			0
$89$			24423.5i			0.326838i	0.986557	+	0.163419i	$0.0522523\pi$
$89$			24423.5i			0.326838i	−0.986557	+	0.163419i	$0.947748\pi$
$90$		0			0
$91$		−	127257.i		−	1.61093i
$92$		0			0
$93$	1647.03	−	1647.03i	0.0197467	−	0.0197467i
$94$		0			0
$95$	−9313.60	−	139787.i	−0.105879	−	1.58912i
$96$		0			0
$97$	−89666.0	−	89666.0i	−0.967605	−	0.967605i	0.0318862	−	0.999492i	$-0.489849\pi$
$97$	−89666.0	−	89666.0i	−0.967605	−	0.967605i	−0.999492	+	0.0318862i	$0.989849\pi$
$98$		0			0
$99$	−154081.			−1.58002
$100$		0			0
$101$	31536.0			0.307612			0.153806	−	0.988101i	$-0.450847\pi$
$101$	31536.0			0.307612			0.153806	+	0.988101i	$0.450847\pi$
$102$		0			0
$103$	−4384.20	−	4384.20i	−0.0407190	−	0.0407190i	0.686454	−	0.727173i	$-0.259166\pi$
$103$	−4384.20	−	4384.20i	−0.0407190	−	0.0407190i	−0.727173	+	0.686454i	$0.759166\pi$
$104$		0			0
$105$	−620.207	−	9308.61i	−0.00548989	−	0.0823970i
$106$		0			0
$107$	−150691.	+	150691.i	−1.27241	+	1.27241i	−0.327589	+	0.944820i	$0.606236\pi$
$107$	−150691.	+	150691.i	−1.27241	+	1.27241i	−0.944820	+	0.327589i	$0.893764\pi$
$108$		0			0
$109$			201206.i			1.62209i	0.584984	+	0.811045i	$0.301101\pi$
$109$			201206.i			1.62209i	−0.584984	+	0.811045i	$0.698899\pi$
$110$		0			0
$111$		−	3187.75i		−	0.0245571i
$112$		0			0
$113$	−25930.0	+	25930.0i	−0.191032	+	0.191032i	−0.796142	−	0.605110i	$-0.793129\pi$
$113$	−25930.0	+	25930.0i	−0.191032	+	0.191032i	0.605110	+	0.796142i	$0.293129\pi$
$114$		0			0
$115$	145856.	−	166679.i	1.02844	−	1.17527i
$116$		0			0
$117$	154711.	+	154711.i	1.04486	+	1.04486i
$118$		0			0
$119$	−128920.			−0.834552
$120$		0			0
$121$	−245713.			−1.52569
$122$		0			0
$123$	−4895.25	−	4895.25i	−0.0291751	−	0.0291751i
$124$		0			0
$125$	−34635.4	−	171225.i	−0.198264	−	0.980149i
$126$		0			0
$127$	−46278.8	+	46278.8i	−0.254609	+	0.254609i	−0.822857	−	0.568248i	$-0.807621\pi$
$127$	−46278.8	+	46278.8i	−0.254609	+	0.254609i	0.568248	+	0.822857i	$0.307621\pi$
$128$		0			0
$129$			17958.8i			0.0950175i
$130$		0			0
$131$		−	83739.0i		−	0.426333i	−0.977016	−	0.213167i	$-0.931622\pi$
$131$		−	83739.0i		−	0.426333i	0.977016	−	0.213167i	$-0.0683777\pi$
$132$		0			0
$133$	249006.	−	249006.i	1.22062	−	1.22062i
$134$		0			0
$135$	24212.2	+	21187.4i	0.114341	+	0.100056i
$136$		0			0
$137$	29275.6	+	29275.6i	0.133261	+	0.133261i	0.770591	−	0.637330i	$-0.219961\pi$
$137$	29275.6	+	29275.6i	0.133261	+	0.133261i	−0.637330	+	0.770591i	$0.719961\pi$
$138$		0			0
$139$	56681.4			0.248830			0.124415	−	0.992230i	$-0.460295\pi$
$139$	56681.4			0.248830			0.124415	+	0.992230i	$0.460295\pi$
$140$		0			0
$141$	−13957.0			−0.0591211
$142$		0			0
$143$	408428.	+	408428.i	1.67023	+	1.67023i
$144$		0			0
$145$	−276392.	+	18415.3i	−1.09171	+	0.0727374i
$146$		0			0
$147$	2466.86	−	2466.86i	0.00941568	−	0.00941568i
$148$		0			0
$149$			30050.0i			0.110886i	0.998462	+	0.0554432i	$0.0176572\pi$
$149$			30050.0i			0.110886i	−0.998462	+	0.0554432i	$0.982343\pi$
$150$		0			0
$151$		−	255984.i		−	0.913631i	−0.889561	−	0.456816i	$-0.848990\pi$
$151$		−	255984.i		−	0.913631i	0.889561	−	0.456816i	$-0.151010\pi$
$152$		0			0
$153$	156734.	−	156734.i	0.541294	−	0.541294i
$154$		0			0
$155$	109391.	−	7288.42i	0.365723	−	0.0243671i
$156$		0			0
$157$	30035.3	+	30035.3i	0.0972486	+	0.0972486i	0.754057	−	0.656809i	$-0.228094\pi$
$157$	30035.3	+	30035.3i	0.0972486	+	0.0972486i	−0.656809	+	0.754057i	$0.728094\pi$
$158$		0			0
$159$	12491.7			0.0391859
$160$		0			0
$161$	556728.			1.69269
$162$		0			0
$163$	397588.	+	397588.i	1.17210	+	1.17210i	0.981708	+	0.190391i	$0.0609755\pi$
$163$	397588.	+	397588.i	1.17210	+	1.17210i	0.190391	+	0.981708i	$0.439024\pi$
$164$		0			0
$165$	31866.3	+	27885.2i	0.0911218	+	0.0797379i
$166$		0			0
$167$	−162249.	+	162249.i	−0.450185	+	0.450185i	−0.895416	−	0.445231i	$-0.853122\pi$
$167$	−162249.	+	162249.i	−0.450185	+	0.450185i	0.445231	+	0.895416i	$0.353122\pi$
$168$		0			0
$169$		−	448903.i		−	1.20903i
$170$		0			0
$171$			605453.i			1.58340i
$172$		0			0
$173$	−158564.	+	158564.i	−0.402800	+	0.402800i	−0.879219	−	0.476419i	$-0.841935\pi$
$173$	−158564.	+	158564.i	−0.402800	+	0.402800i	0.476419	+	0.879219i	$0.341935\pi$
$174$		0			0
$175$	266560.	−	348944.i	0.657960	−	0.861313i
$176$		0			0
$177$	14057.2	+	14057.2i	0.0337261	+	0.0337261i
$178$		0			0
$179$	−509602.			−1.18877			−0.594386	−	0.804180i	$-0.702605\pi$
$179$	−509602.			−1.18877			−0.594386	+	0.804180i	$0.702605\pi$
$180$		0			0
$181$	−356971.			−0.809910			−0.404955	−	0.914337i	$-0.632713\pi$
$181$	−356971.			−0.809910			−0.404955	+	0.914337i	$0.632713\pi$
$182$		0			0
$183$	19939.3	+	19939.3i	0.0440132	+	0.0440132i
$184$		0			0
$185$	98807.0	−	112913.i	0.212255	−	0.242558i
$186$		0			0
$187$	413767.	−	413767.i	0.865270	−	0.865270i
$188$		0			0
$189$			80871.5i			0.164680i
$190$		0			0
$191$		−	296067.i		−	0.587227i	−0.955924	−	0.293614i	$-0.905142\pi$
$191$		−	296067.i		−	0.587227i	0.955924	−	0.293614i	$-0.0948579\pi$
$192$		0			0
$193$	10953.8	−	10953.8i	0.0211676	−	0.0211676i	−0.696444	−	0.717611i	$-0.745235\pi$
$193$	10953.8	−	10953.8i	0.0211676	−	0.0211676i	0.717611	+	0.696444i	$0.245235\pi$
$194$		0			0
$195$	−3997.37	−	59995.9i	−0.00752813	−	0.112989i
$196$		0			0
$197$	−153834.	−	153834.i	−0.282415	−	0.282415i	0.551656	−	0.834071i	$-0.313996\pi$
$197$	−153834.	−	153834.i	−0.282415	−	0.282415i	−0.834071	+	0.551656i	$0.813996\pi$
$198$		0			0
$199$	415211.			0.743252			0.371626	−	0.928383i	$-0.378800\pi$
$199$	415211.			0.743252			0.371626	+	0.928383i	$0.378800\pi$
$200$		0			0
$201$	−6977.28			−0.0121814
$202$		0			0
$203$	−492345.	−	492345.i	−0.838550	−	0.838550i
$204$		0			0
$205$	−21662.4	−	325127.i	−0.0360016	−	0.540342i
$206$		0			0
$207$	−676837.	+	676837.i	−1.09789	+	1.09789i
$208$		0			0
$209$			1.59836e6i			2.53109i
$210$		0			0
$211$		−	673870.i		−	1.04200i	−0.853555	−	0.521002i	$-0.825558\pi$
$211$		−	673870.i		−	1.04200i	0.853555	−	0.521002i	$-0.174442\pi$
$212$		0			0
$213$	−10309.6	+	10309.6i	−0.0155701	+	0.0155701i
$214$		0			0
$215$	−556649.	+	636120.i	−0.821269	+	0.938518i
$216$		0			0
$217$	194861.	+	194861.i	0.280915	+	0.280915i
$218$		0			0
$219$	60622.7			0.0854132
$220$		0			0
$221$	−830917.			−1.14440
$222$		0			0
$223$	−916244.	−	916244.i	−1.23381	−	1.23381i	−0.962488	−	0.271323i	$-0.912539\pi$
$223$	−916244.	−	916244.i	−1.23381	−	1.23381i	−0.271323	−	0.962488i	$-0.587461\pi$
$224$		0			0
$225$	100158.	+	748294.i	0.131896	+	0.985407i
$226$		0			0
$227$	−317650.	+	317650.i	−0.409152	+	0.409152i	−0.881443	−	0.472291i	$-0.843427\pi$
$227$	−317650.	+	317650.i	−0.409152	+	0.409152i	0.472291	+	0.881443i	$0.343427\pi$
$228$		0			0
$229$		−	1.15003e6i		−	1.44917i	−0.689183	−	0.724587i	$-0.742030\pi$
$229$		−	1.15003e6i		−	1.44917i	0.689183	−	0.724587i	$-0.257970\pi$
$230$		0			0
$231$			106437.i			0.131239i
$232$		0			0
$233$	290928.	−	290928.i	0.351071	−	0.351071i	−0.509437	−	0.860508i	$-0.670146\pi$
$233$	290928.	−	290928.i	0.351071	−	0.351071i	0.860508	+	0.509437i	$0.170146\pi$
$234$		0			0
$235$	−494370.	−	432608.i	−0.583959	−	0.511004i
$236$		0			0
$237$	−54025.7	−	54025.7i	−0.0624784	−	0.0624784i
$238$		0			0
$239$	−152082.			−0.172220			−0.0861101	−	0.996286i	$-0.527444\pi$
$239$	−152082.			−0.172220			−0.0861101	+	0.996286i	$0.527444\pi$
$240$		0			0
$241$	43181.5			0.0478912			0.0239456	−	0.999713i	$-0.492377\pi$
$241$	43181.5			0.0478912			0.0239456	+	0.999713i	$0.492377\pi$
$242$		0			0
$243$	−147621.	−	147621.i	−0.160374	−	0.160374i
$244$		0			0
$245$	163841.	−	10916.3i	0.174385	−	0.0116188i
$246$		0			0
$247$	1.60489e6	−	1.60489e6i	1.67380	−	1.67380i
$248$		0			0
$249$			105577.i			0.107912i
$250$		0			0
$251$			547660.i			0.548689i	0.961631	+	0.274345i	$0.0884609\pi$
$251$			547660.i			0.548689i	−0.961631	+	0.274345i	$0.911539\pi$
$252$		0			0
$253$	−1.78681e6	+	1.78681e6i	−1.75500	+	1.75500i
$254$		0			0
$255$	−60780.2	+	4049.62i	−0.0585344	+	0.00389999i
$256$		0			0
$257$	−226438.	−	226438.i	−0.213853	−	0.213853i	0.592049	−	0.805902i	$-0.298319\pi$
$257$	−226438.	−	226438.i	−0.213853	−	0.213853i	−0.805902	+	0.592049i	$0.798319\pi$
$258$		0			0
$259$	377143.			0.349347
$260$		0			0
$261$	1.19713e6			1.08778
$262$		0			0
$263$	21617.3	+	21617.3i	0.0192714	+	0.0192714i	0.716677	−	0.697405i	$-0.245662\pi$
$263$	21617.3	+	21617.3i	0.0192714	+	0.0192714i	−0.697405	+	0.716677i	$0.745662\pi$
$264$		0			0
$265$	442470.	+	387191.i	0.387051	+	0.338697i
$266$		0			0
$267$	−20511.3	+	20511.3i	−0.0176082	+	0.0176082i
$268$		0			0
$269$		−	1.78124e6i		−	1.50087i	−0.660947	−	0.750433i	$-0.729845\pi$
$269$		−	1.78124e6i		−	1.50087i	0.660947	−	0.750433i	$-0.270155\pi$
$270$		0			0
$271$			1.45155e6i			1.20063i	0.799765	+	0.600314i	$0.204958\pi$
$271$			1.45155e6i			1.20063i	−0.799765	+	0.600314i	$0.795042\pi$
$272$		0			0
$273$	106872.	−	106872.i	0.0867878	−	0.0867878i
$274$		0			0
$275$	264411.	+	1.97545e6i	0.210838	+	1.57519i
$276$		0			0
$277$	−831788.	−	831788.i	−0.651348	−	0.651348i	0.301969	−	0.953318i	$-0.402356\pi$
$277$	−831788.	−	831788.i	−0.651348	−	0.651348i	−0.953318	+	0.301969i	$0.902356\pi$
$278$		0			0
$279$	−473801.			−0.364406
$280$		0			0
$281$	2.43146e6			1.83696			0.918482	−	0.395463i	$-0.129416\pi$
$281$	2.43146e6			1.83696			0.918482	+	0.395463i	$0.129416\pi$
$282$		0			0
$283$	−141203.	−	141203.i	−0.104804	−	0.104804i	0.652760	−	0.757565i	$-0.273611\pi$
$283$	−141203.	−	141203.i	−0.104804	−	0.104804i	−0.757565	+	0.652760i	$0.773611\pi$
$284$		0			0
$285$	109573.	−	125217.i	0.0799085	−	0.0913168i
$286$		0			0
$287$	579158.	−	579158.i	0.415042	−	0.415042i
$288$		0			0
$289$		−	578078.i		−	0.407138i
$290$		0			0
$291$		−	150606.i		−	0.104258i
$292$		0			0
$293$	540576.	−	540576.i	0.367864	−	0.367864i	−0.498834	−	0.866698i	$-0.666238\pi$
$293$	540576.	−	540576.i	0.367864	−	0.367864i	0.866698	+	0.498834i	$0.166238\pi$
$294$		0			0
$295$	62205.6	+	933636.i	0.0416174	+	0.624629i
$296$		0			0
$297$	−259555.	−	259555.i	−0.170741	−	0.170741i
$298$		0			0
$299$	3.58823e6			2.32114
$300$		0			0
$301$	−2.12471e6			−1.35171
$302$		0			0
$303$	26484.5	+	26484.5i	0.0165724	+	0.0165724i
$304$		0			0
$305$	88235.1	+	1.32431e6i	0.0543115	+	0.815154i
$306$		0			0
$307$	779170.	−	779170.i	0.471831	−	0.471831i	−0.430676	−	0.902507i	$-0.641725\pi$
$307$	779170.	−	779170.i	0.471831	−	0.471831i	0.902507	+	0.430676i	$0.141725\pi$
$308$		0			0
$309$		−	7363.86i		−	0.00438742i
$310$		0			0
$311$			1.56490e6i			0.917459i	0.888576	+	0.458730i	$0.151695\pi$
$311$			1.56490e6i			0.917459i	−0.888576	+	0.458730i	$0.848305\pi$
$312$		0			0
$313$	684828.	−	684828.i	0.395112	−	0.395112i	−0.481393	−	0.876505i	$-0.659869\pi$
$313$	684828.	−	684828.i	0.395112	−	0.395112i	0.876505	+	0.481393i	$0.159869\pi$
$314$		0			0
$315$	−1.24969e6	+	1.42811e6i	−0.709621	+	0.810932i
$316$		0			0
$317$	1.90957e6	+	1.90957e6i	1.06730	+	1.06730i	0.997565	+	0.0697372i	$0.0222161\pi$
$317$	1.90957e6	+	1.90957e6i	1.06730	+	1.06730i	0.0697372	+	0.997565i	$0.477784\pi$
$318$		0			0
$319$	3.16034e6			1.73883
$320$		0			0
$321$	−253105.			−0.137100
$322$		0			0
$323$	−1.62587e6	−	1.62587e6i	−0.867122	−	0.867122i
$324$		0			0
$325$	1.71803e6	−	2.24902e6i	0.902242	−	1.18109i
$326$		0			0
$327$	−168976.	+	168976.i	−0.0873890	+	0.0873890i
$328$		0			0
$329$		−	1.65125e6i		−	0.841052i
$330$		0			0
$331$		−	740425.i		−	0.371459i	−0.982601	−	0.185730i	$-0.940535\pi$
$331$		−	740425.i		−	0.371459i	0.982601	−	0.185730i	$-0.0594649\pi$
$332$		0			0
$333$	−458508.	+	458508.i	−0.226588	+	0.226588i
$334$		0			0
$335$	−247142.	−	216267.i	−0.120319	−	0.105288i
$336$		0			0
$337$	−2.17170e6	−	2.17170e6i	−1.04166	−	1.04166i	−0.999094	−	0.0425641i	$-0.986447\pi$
$337$	−2.17170e6	−	2.17170e6i	−1.04166	−	1.04166i	−0.0425641	−	0.999094i	$-0.513553\pi$
$338$		0			0
$339$	−43553.0			−0.0205835
$340$		0			0
$341$	−1.25080e6			−0.582510
$342$		0			0
$343$	−1.37807e6	−	1.37807e6i	−0.632464	−	0.632464i
$344$		0			0
$345$	262473.	−	17487.8i	0.118723	−	0.00791022i
$346$		0			0
$347$	−706412.	+	706412.i	−0.314945	+	0.314945i	−0.846822	−	0.531877i	$-0.821487\pi$
$347$	−706412.	+	706412.i	−0.314945	+	0.314945i	0.531877	+	0.846822i	$0.321487\pi$
$348$		0			0
$349$			3.03307e6i			1.33297i	0.745520	+	0.666483i	$0.232201\pi$
$349$			3.03307e6i			1.33297i	−0.745520	+	0.666483i	$0.767799\pi$
$350$		0			0
$351$			521234.i			0.225821i
$352$		0			0
$353$	−2.72516e6	+	2.72516e6i	−1.16401	+	1.16401i	−0.180418	+	0.983590i	$0.557745\pi$
$353$	−2.72516e6	+	2.72516e6i	−1.16401	+	1.16401i	−0.983590	+	0.180418i	$0.942255\pi$
$354$		0			0
$355$	−684730.	+	45621.7i	−0.288369	+	0.0192132i
$356$		0			0
$357$	−108269.	−	108269.i	−0.0449609	−	0.0449609i
$358$		0			0
$359$	−2.47478e6			−1.01345			−0.506723	−	0.862109i	$-0.669143\pi$
$359$	−2.47478e6			−1.01345			−0.506723	+	0.862109i	$0.669143\pi$
$360$		0			0
$361$	3.80455e6			1.53651
$362$		0			0
$363$	−206354.	−	206354.i	−0.0821953	−	0.0821953i
$364$		0			0
$365$	2.14732e6	+	1.87905e6i	0.843654	+	0.738256i
$366$		0			0
$367$	405936.	−	405936.i	0.157323	−	0.157323i	−0.624056	−	0.781379i	$-0.714516\pi$
$367$	405936.	−	405936.i	0.157323	−	0.157323i	0.781379	+	0.624056i	$0.214516\pi$
$368$		0			0
$369$			1.40821e6i			0.538397i
$370$		0			0
$371$			1.47790e6i			0.557455i
$372$		0			0
$373$	−378559.	+	378559.i	−0.140884	+	0.140884i	−0.774031	−	0.633147i	$-0.781763\pi$
$373$	−378559.	+	378559.i	−0.140884	+	0.140884i	0.633147	+	0.774031i	$0.281763\pi$
$374$		0			0
$375$	114710.	−	172885.i	0.0421235	−	0.0634862i
$376$		0			0
$377$	−3.17326e6	−	3.17326e6i	−1.14988	−	1.14988i
$378$		0			0
$379$	−3.91279e6			−1.39923			−0.699614	−	0.714521i	$-0.746645\pi$
$379$	−3.91279e6			−1.39923			−0.699614	+	0.714521i	$0.746645\pi$
$380$		0			0
$381$	−77731.5			−0.0274337
$382$		0			0
$383$	−2.53247e6	−	2.53247e6i	−0.882161	−	0.882161i	0.111593	−	0.993754i	$-0.464405\pi$
$383$	−2.53247e6	−	2.53247e6i	−0.882161	−	0.882161i	−0.993754	+	0.111593i	$0.964405\pi$
$384$		0			0
$385$	−3.29911e6	+	3.77011e6i	−1.13434	+	1.29629i
$386$		0			0
$387$	2.58310e6	−	2.58310e6i	0.876725	−	0.876725i
$388$		0			0
$389$		−	3.01392e6i		−	1.00985i	−0.863163	−	0.504925i	$-0.831520\pi$
$389$		−	3.01392e6i		−	1.00985i	0.863163	−	0.504925i	$-0.168480\pi$
$390$		0			0
$391$		−	3.63513e6i		−	1.20248i
$392$		0			0
$393$	70325.4	−	70325.4i	0.0229684	−	0.0229684i
$394$		0			0
$395$	−239074.	−	3.58822e6i	−0.0770972	−	1.15714i
$396$		0			0
$397$	3.43650e6	+	3.43650e6i	1.09431	+	1.09431i	0.995063	+	0.0992459i	$0.0316430\pi$
$397$	3.43650e6	+	3.43650e6i	1.09431	+	1.09431i	0.0992459	+	0.995063i	$0.468357\pi$
$398$		0			0
$399$	418238.			0.131520
$400$		0			0
$401$	−4.30306e6			−1.33634			−0.668169	−	0.744009i	$-0.732922\pi$
$401$	−4.30306e6			−1.33634			−0.668169	+	0.744009i	$0.732922\pi$
$402$		0			0
$403$	1.25592e6	+	1.25592e6i	0.385211	+	0.385211i
$404$		0			0
$405$	−215632.	−	3.23639e6i	−0.0653244	−	0.980445i
$406$		0			0
$407$	−1.21043e6	+	1.21043e6i	−0.362205	+	0.362205i
$408$		0			0
$409$		−	452926.i		−	0.133881i	−0.997757	−	0.0669405i	$-0.978676\pi$
$409$		−	452926.i		−	0.133881i	0.997757	−	0.0669405i	$-0.0213238\pi$
$410$		0			0
$411$			49172.2i			0.0143587i
$412$		0			0
$413$	−1.66311e6	+	1.66311e6i	−0.479784	+	0.479784i
$414$		0			0
$415$	−3.27244e6	+	3.73963e6i	−0.932719	+	1.06588i
$416$		0			0
$417$	47602.0	+	47602.0i	0.0134056	+	0.0134056i
$418$		0			0
$419$	448753.			0.124874			0.0624370	−	0.998049i	$-0.480113\pi$
$419$	448753.			0.124874			0.0624370	+	0.998049i	$0.480113\pi$
$420$		0			0
$421$	3.61031e6			0.992748			0.496374	−	0.868109i	$-0.334664\pi$
$421$	3.61031e6			0.992748			0.496374	+	0.868109i	$0.334664\pi$
$422$		0			0
$423$	2.00749e6	+	2.00749e6i	0.545510	+	0.545510i
$424$		0			0
$425$	−2.27842e6	−	1.74049e6i	−0.611873	−	0.467412i
$426$		0			0
$427$	−2.35903e6	+	2.35903e6i	−0.626128	+	0.626128i
$428$		0			0
$429$			686009.i			0.179964i
$430$		0			0
$431$		−	3.33480e6i		−	0.864722i	−0.901701	−	0.432361i	$-0.857681\pi$
$431$		−	3.33480e6i		−	0.864722i	0.901701	−	0.432361i	$-0.142319\pi$
$432$		0			0
$433$	4.26797e6	−	4.26797e6i	1.09396	−	1.09396i	0.0988602	−	0.995101i	$-0.468480\pi$
$433$	4.26797e6	−	4.26797e6i	1.09396	−	1.09396i	0.995101	−	0.0988602i	$-0.0315197\pi$
$434$		0			0
$435$	−247584.	−	216653.i	−0.0627336	−	0.0548962i
$436$		0			0
$437$	7.02115e6	+	7.02115e6i	1.75875	+	1.75875i
$438$		0			0
$439$	985119.			0.243965			0.121982	−	0.992532i	$-0.461075\pi$
$439$	985119.			0.243965			0.121982	+	0.992532i	$0.461075\pi$
$440$		0			0
$441$	−709641.			−0.173757
$442$		0			0
$443$	941343.	+	941343.i	0.227897	+	0.227897i	0.811814	−	0.583917i	$-0.198481\pi$
$443$	941343.	+	941343.i	0.227897	+	0.227897i	−0.583917	+	0.811814i	$0.698481\pi$
$444$		0			0
$445$	−1.36229e6	+	90766.0i	−0.326115	+	0.0217282i
$446$		0			0
$447$	−25236.5	+	25236.5i	−0.00597393	+	0.00597393i
$448$		0			0
$449$			2.05024e6i			0.479941i	0.970780	+	0.239971i	$0.0771378\pi$
$449$			2.05024e6i			0.479941i	−0.970780	+	0.239971i	$0.922862\pi$
$450$		0			0
$451$			3.71759e6i			0.860638i
$452$		0			0
$453$	214980.	−	214980.i	0.0492213	−	0.0492213i
$454$		0			0
$455$	7.09813e6	−	472929.i	1.60737	−	0.107095i
$456$		0			0
$457$	−5.54554e6	−	5.54554e6i	−1.24209	−	1.24209i	−0.959132	−	0.282958i	$-0.908684\pi$
$457$	−5.54554e6	−	5.54554e6i	−1.24209	−	1.24209i	−0.282958	−	0.959132i	$-0.591316\pi$
$458$		0			0
$459$	528047.			0.116988
$460$		0			0
$461$	−3.71258e6			−0.813624			−0.406812	−	0.913512i	$-0.633360\pi$
$461$	−3.71258e6			−0.813624			−0.406812	+	0.913512i	$0.633360\pi$
$462$		0			0
$463$	4.14889e6	+	4.14889e6i	0.899455	+	0.899455i	0.995388	−	0.0959328i	$-0.0305834\pi$
$463$	4.14889e6	+	4.14889e6i	0.899455	+	0.899455i	−0.0959328	+	0.995388i	$0.530583\pi$
$464$		0			0
$465$	97989.3	+	85747.4i	0.0210158	+	0.0183903i
$466$		0			0
$467$	599788.	−	599788.i	0.127264	−	0.127264i	−0.640606	−	0.767870i	$-0.721317\pi$
$467$	599788.	−	599788.i	0.127264	−	0.127264i	0.767870	+	0.640606i	$0.221317\pi$
$468$		0			0
$469$		−	825483.i		−	0.173291i
$470$		0			0
$471$			50448.4i			0.0104784i
$472$		0			0
$473$	6.81922e6	−	6.81922e6i	1.40146	−	1.40146i
$474$		0			0
$475$	7.76241e6	−	1.03899e6i	1.57857	−	0.211289i
$476$		0			0
$477$	−1.79674e6	−	1.79674e6i	−0.361568	−	0.361568i
$478$		0			0
$479$	−130460.			−0.0259799			−0.0129900	−	0.999916i	$-0.504135\pi$
$479$	−130460.			−0.0259799			−0.0129900	+	0.999916i	$0.504135\pi$
$480$		0			0
$481$	2.43077e6			0.479049
$482$		0			0
$483$	467550.	+	467550.i	0.0911927	+	0.0911927i
$484$		0			0
$485$	4.66816e6	−	5.33462e6i	0.901138	−	1.02979i
$486$		0			0
$487$	−5.53566e6	+	5.53566e6i	−1.05766	+	1.05766i	−0.0594298	+	0.998232i	$0.518928\pi$
$487$	−5.53566e6	+	5.53566e6i	−1.05766	+	1.05766i	−0.998232	+	0.0594298i	$0.981072\pi$
$488$		0			0
$489$			667803.i			0.126292i
$490$		0			0
$491$		−	2.06198e6i		−	0.385993i	−0.981199	−	0.192997i	$-0.938179\pi$
$491$		−	2.06198e6i		−	0.385993i	0.981199	−	0.192997i	$-0.0618206\pi$
$492$		0			0
$493$	−3.21474e6	+	3.21474e6i	−0.595702	+	0.595702i
$494$		0			0
$495$	−572618.	−	8.59434e6i	−0.105039	−	1.57652i
$496$		0			0
$497$	−1.21973e6	−	1.21973e6i	−0.221499	−	0.221499i
$498$		0			0
$499$	−3.96927e6			−0.713608			−0.356804	−	0.934179i	$-0.616134\pi$
$499$	−3.96927e6			−0.713608			−0.356804	+	0.934179i	$0.616134\pi$
$500$		0			0
$501$	−272519.			−0.0485068
$502$		0			0
$503$	7.68593e6	+	7.68593e6i	1.35449	+	1.35449i	0.880564	+	0.473928i	$0.157164\pi$
$503$	7.68593e6	+	7.68593e6i	1.35449	+	1.35449i	0.473928	+	0.880564i	$0.342836\pi$
$504$		0			0
$505$	117199.	+	1.75902e6i	0.0204500	+	0.306932i
$506$		0			0
$507$	376996.	−	376996.i	0.0651354	−	0.0651354i
$508$		0			0
$509$		−	149834.i		−	0.0256340i	−0.999918	−	0.0128170i	$-0.995920\pi$
$509$		−	149834.i		−	0.0256340i	0.999918	−	0.0128170i	$-0.00407988\pi$
$510$		0			0
$511$			7.17229e6i			1.21508i
$512$		0			0
$513$	−1.01991e6	+	1.01991e6i	−0.171107	+	0.171107i
$514$		0			0
$515$	228249.	−	260835.i	0.0379220	−	0.0433360i
$516$		0			0
$517$	5.29965e6	+	5.29965e6i	0.872009	+	0.872009i
$518$		0			0
$519$	−266330.			−0.0434011
$520$		0			0
$521$	1.13714e6			0.183536			0.0917678	−	0.995780i	$-0.470748\pi$
$521$	1.13714e6			0.183536			0.0917678	+	0.995780i	$0.470748\pi$
$522$		0			0
$523$	4.86949e6	+	4.86949e6i	0.778447	+	0.778447i	0.979567	−	0.201119i	$-0.0644579\pi$
$523$	4.86949e6	+	4.86949e6i	0.778447	+	0.778447i	−0.201119	+	0.979567i	$0.564458\pi$
$524$		0			0
$525$	516911.	−	69187.9i	0.0818498	−	0.0109555i
$526$		0			0
$527$	1.27234e6	−	1.27234e6i	0.199561	−	0.199561i
$528$		0			0
$529$			9.26159e6i			1.43895i
$530$		0			0
$531$		−	4.04382e6i		−	0.622380i
$532$		0			0
$533$	3.73280e6	−	3.73280e6i	0.569136	−	0.569136i
$534$		0			0
$535$	−8.96524e6	−	7.84521e6i	−1.35418	−	1.18500i
$536$		0			0
$537$	−427972.	−	427972.i	−0.0640442	−	0.0640442i
$538$		0			0
$539$	−1.87341e6			−0.277754
$540$		0			0
$541$	−6.42771e6			−0.944198			−0.472099	−	0.881546i	$-0.656503\pi$
$541$	−6.42771e6			−0.944198			−0.472099	+	0.881546i	$0.656503\pi$
$542$		0			0
$543$	−299790.	−	299790.i	−0.0436333	−	0.0436333i
$544$		0			0
$545$	−1.12229e7	+	747751.i	−1.61850	+	0.107836i
$546$		0			0
$547$	−6.88980e6	+	6.88980e6i	−0.984551	+	0.984551i	−0.999882	−	0.0153314i	$-0.995120\pi$
$547$	−6.88980e6	+	6.88980e6i	−0.984551	+	0.984551i	0.0153314	+	0.999882i	$0.495120\pi$
$548$		0			0
$549$		−	5.73593e6i		−	0.812219i
$550$		0			0
$551$		−	1.24184e7i		−	1.74255i
$552$		0			0
$553$	6.39179e6	−	6.39179e6i	0.888812	−	0.888812i
$554$		0			0
$555$	177806.	−	11846.8i	0.0245027	−	0.00163255i
$556$		0			0
$557$	−626234.	−	626234.i	−0.0855261	−	0.0855261i	0.663049	−	0.748576i	$-0.269262\pi$
$557$	−626234.	−	626234.i	−0.0855261	−	0.0855261i	−0.748576	+	0.663049i	$0.769262\pi$
$558$		0			0
$559$	−1.36942e7			−1.85356
$560$		0			0
$561$	694977.			0.0932316
$562$		0			0
$563$	−3.78102e6	−	3.78102e6i	−0.502733	−	0.502733i	0.409553	−	0.912286i	$-0.365685\pi$
$563$	−3.78102e6	−	3.78102e6i	−0.502733	−	0.502733i	−0.912286	+	0.409553i	$0.865685\pi$
$564$		0			0
$565$	−1.54269e6	−	1.34996e6i	−0.203309	−	0.177910i
$566$		0			0
$567$	5.76507e6	−	5.76507e6i	0.753090	−	0.753090i
$568$		0			0
$569$			5.86991e6i			0.760065i	0.924973	+	0.380032i	$0.124087\pi$
$569$			5.86991e6i			0.760065i	−0.924973	+	0.380032i	$0.875913\pi$
$570$		0			0
$571$		−	3.63228e6i		−	0.466218i	−0.972451	−	0.233109i	$-0.925110\pi$
$571$		−	3.63228e6i		−	0.466218i	0.972451	−	0.233109i	$-0.0748899\pi$
$572$		0			0
$573$	248642.	−	248642.i	0.0316365	−	0.0316365i
$574$		0			0
$575$	9.83910e6	+	7.51613e6i	1.24104	+	0.948035i
$576$		0			0
$577$	7.85335e6	+	7.85335e6i	0.982009	+	0.982009i	0.999841	−	0.0178322i	$-0.00567647\pi$
$577$	7.85335e6	+	7.85335e6i	0.982009	+	0.982009i	−0.0178322	+	0.999841i	$0.505676\pi$
$578$		0			0
$579$	18398.4			0.00228078
$580$		0			0
$581$	−1.24908e7			−1.53514
$582$		0			0
$583$	−4.74328e6	−	4.74328e6i	−0.577973	−	0.577973i
$584$		0			0
$585$	−8.05452e6	+	9.20444e6i	−0.973084	+	1.11201i
$586$		0			0
$587$	−4.62105e6	+	4.62105e6i	−0.553535	+	0.553535i	−0.927459	−	0.373924i	$-0.878012\pi$
$587$	−4.62105e6	+	4.62105e6i	−0.553535	+	0.553535i	0.373924	+	0.927459i	$0.378012\pi$
$588$		0			0
$589$			4.91496e6i			0.583757i
$590$		0			0
$591$		−	258386.i		−	0.0304298i
$592$		0			0
$593$	−6.65088e6	+	6.65088e6i	−0.776681	+	0.776681i	−0.979265	−	0.202584i	$-0.935066\pi$
$593$	−6.65088e6	+	6.65088e6i	−0.776681	+	0.776681i	0.202584	+	0.979265i	$0.435066\pi$
$594$		0			0
$595$	−479111.	−	7.19091e6i	−0.0554809	−	0.832706i
$596$		0			0
$597$	348701.	+	348701.i	0.0400422	+	0.0400422i
$598$		0			0
$599$	−4.31406e6			−0.491269			−0.245634	−	0.969363i	$-0.578996\pi$
$599$	−4.31406e6			−0.491269			−0.245634	+	0.969363i	$0.578996\pi$
$600$		0			0
$601$	1.43695e7			1.62277			0.811384	−	0.584513i	$-0.198714\pi$
$601$	1.43695e7			1.62277			0.811384	+	0.584513i	$0.198714\pi$
$602$		0			0
$603$	1.00357e6	+	1.00357e6i	0.112397	+	0.112397i
$604$		0			0
$605$	−913154.	−	1.37054e7i	−0.101427	−	1.52231i
$606$		0			0
$607$	−997962.	+	997962.i	−0.109937	+	0.109937i	−0.759935	−	0.649999i	$-0.774769\pi$
$607$	−997962.	+	997962.i	−0.109937	+	0.109937i	0.649999	+	0.759935i	$0.274769\pi$
$608$		0			0
$609$		−	826959.i		−	0.0903526i
$610$		0			0
$611$		−	1.06426e7i		−	1.15331i
$612$		0			0
$613$	−6.18198e6	+	6.18198e6i	−0.664472	+	0.664472i	−0.956431	−	0.291959i	$-0.905693\pi$
$613$	−6.18198e6	+	6.18198e6i	−0.664472	+	0.664472i	0.291959	+	0.956431i	$0.405693\pi$
$614$		0			0
$615$	254855.	−	291240.i	0.0271710	−	0.0310501i
$616$		0			0
$617$	−274155.	−	274155.i	−0.0289924	−	0.0289924i	0.692462	−	0.721454i	$-0.256526\pi$
$617$	−274155.	−	274155.i	−0.0289924	−	0.0289924i	−0.721454	+	0.692462i	$0.756526\pi$
$618$		0			0
$619$	−1.04395e7			−1.09510			−0.547549	−	0.836774i	$-0.684439\pi$
$619$	−1.04395e7			−1.09510			−0.547549	+	0.836774i	$0.684439\pi$
$620$		0			0
$621$	−2.28031e6			−0.237283
$622$		0			0
$623$	−2.42669e6	−	2.42669e6i	−0.250492	−	0.250492i
$624$		0			0
$625$	9.42187e6	−	2.56822e6i	0.964800	−	0.262986i
$626$		0			0
$627$	−1.34233e6	+	1.34233e6i	−0.136361	+	0.136361i
$628$		0			0
$629$		−	2.46254e6i		−	0.248174i
$630$		0			0
$631$			1.95332e7i			1.95299i	0.215544	+	0.976494i	$0.430848\pi$
$631$			1.95332e7i			1.95299i	−0.215544	+	0.976494i	$0.569152\pi$
$632$		0			0
$633$	565927.	−	565927.i	0.0561373	−	0.0561373i
$634$		0			0
$635$	−2.75333e6	−	2.40935e6i	−0.270972	−	0.237119i
$636$		0			0
$637$	1.88107e6	+	1.88107e6i	0.183677	+	0.183677i
$638$		0			0
$639$	2.96574e6			0.287330
$640$		0			0
$641$	1.16310e7			1.11808			0.559038	−	0.829142i	$-0.311171\pi$
$641$	1.16310e7			1.11808			0.559038	+	0.829142i	$0.311171\pi$
$642$		0			0
$643$	8.86995e6	+	8.86995e6i	0.846045	+	0.846045i	0.989637	−	0.143592i	$-0.0458653\pi$
$643$	8.86995e6	+	8.86995e6i	0.846045	+	0.846045i	−0.143592	+	0.989637i	$0.545865\pi$
$644$		0			0
$645$	−1.00171e6	+	66741.1i	−0.0948073	+	0.00631675i
$646$		0			0
$647$	−7.82351e6	+	7.82351e6i	−0.734752	+	0.734752i	−0.971557	−	0.236805i	$-0.923900\pi$
$647$	−7.82351e6	+	7.82351e6i	−0.734752	+	0.734752i	0.236805	+	0.971557i	$0.423900\pi$
$648$		0			0
$649$		−	1.06754e7i		−	0.994887i
$650$		0			0
$651$			327295.i			0.0302682i
$652$		0			0
$653$	−5.80259e6	+	5.80259e6i	−0.532524	+	0.532524i	−0.921323	−	0.388799i	$-0.872890\pi$
$653$	−5.80259e6	+	5.80259e6i	−0.532524	+	0.532524i	0.388799	+	0.921323i	$0.372890\pi$
$654$		0			0
$655$	4.67079e6	−	311202.i	0.425390	−	0.0283426i
$656$		0			0
$657$	−8.71964e6	−	8.71964e6i	−0.788107	−	0.788107i
$658$		0			0
$659$	1.87531e7			1.68213			0.841065	−	0.540934i	$-0.181929\pi$
$659$	1.87531e7			1.68213			0.841065	+	0.540934i	$0.181929\pi$
$660$		0			0
$661$	−1.79645e7			−1.59923			−0.799615	−	0.600513i	$-0.794963\pi$
$661$	−1.79645e7			−1.59923			−0.799615	+	0.600513i	$0.794963\pi$
$662$		0			0
$663$	−697819.	−	697819.i	−0.0616536	−	0.0616536i
$664$		0			0
$665$	1.48144e7	+	1.29637e7i	1.29907	+	1.13677i
$666$		0			0
$667$	1.38825e7	−	1.38825e7i	1.20824	−	1.20824i
$668$		0			0
$669$		−	1.53895e6i		−	0.132941i
$670$		0			0
$671$		−	1.51425e7i		−	1.29835i
$672$		0			0
$673$	1.23479e7	−	1.23479e7i	1.05089	−	1.05089i	0.0522545	−	0.998634i	$-0.483359\pi$
$673$	1.23479e7	−	1.23479e7i	1.05089	−	1.05089i	0.998634	−	0.0522545i	$-0.0166407\pi$
$674$		0			0
$675$	−1.09181e6	+	1.42925e6i	−0.0922332	+	0.120739i
$676$		0			0
$677$	−5.66444e6	−	5.66444e6i	−0.474991	−	0.474991i	0.428535	−	0.903525i	$-0.359030\pi$
$677$	−5.66444e6	−	5.66444e6i	−0.474991	−	0.474991i	−0.903525	+	0.428535i	$0.859030\pi$
$678$		0			0
$679$	1.78182e7			1.48317
$680$		0			0
$681$	−533536.			−0.0440855
$682$		0			0
$683$	2.21820e6	+	2.21820e6i	0.181948	+	0.181948i	0.792204	−	0.610256i	$-0.208933\pi$
$683$	2.21820e6	+	2.21820e6i	0.181948	+	0.181948i	−0.610256	+	0.792204i	$0.708933\pi$
$684$		0			0
$685$	−1.52413e6	+	1.74173e6i	−0.124107	+	0.141826i
$686$		0			0
$687$	965815.	−	965815.i	0.0780732	−	0.0780732i
$688$		0			0
$689$			9.52536e6i			0.764422i
$690$		0			0
$691$			1.63246e7i			1.30061i	0.759674	+	0.650304i	$0.225358\pi$
$691$			1.63246e7i			1.30061i	−0.759674	+	0.650304i	$0.774642\pi$
$692$		0			0
$693$	1.53093e7	−	1.53093e7i	1.21094	−	1.21094i
$694$		0			0
$695$	210647.	+	3.16157e6i	0.0165422	+	0.248280i
$696$		0			0
$697$	−3.78159e6	−	3.78159e6i	−0.294844	−	0.294844i
$698$		0			0
$699$	488652.			0.0378274
$700$		0			0
$701$	1.64161e7			1.26175			0.630876	−	0.775884i	$-0.282696\pi$
$701$	1.64161e7			1.26175			0.630876	+	0.775884i	$0.282696\pi$
$702$		0			0
$703$	4.75633e6	+	4.75633e6i	0.362981	+	0.362981i
$704$		0			0
$705$	−51868.8	−	778491.i	−0.00393037	−	0.0589903i
$706$		0			0
$707$	−3.13338e6	+	3.13338e6i	−0.235757	+	0.235757i
$708$		0			0
$709$		−	2.37201e6i		−	0.177215i	−0.996067	−	0.0886077i	$-0.971758\pi$
$709$		−	2.37201e6i		−	0.177215i	0.996067	−	0.0886077i	$-0.0282417\pi$
$710$		0			0
$711$			1.55415e7i			1.15298i
$712$		0			0
$713$	−5.49445e6	+	5.49445e6i	−0.404762	+	0.404762i
$714$		0			0
$715$	−2.12634e7	+	2.42991e7i	−1.55549	+	1.77757i
$716$		0			0
$717$	−127721.	−	127721.i	−0.00927824	−	0.00927824i
$718$		0			0
$719$	8.62894e6			0.622494			0.311247	−	0.950329i	$-0.399253\pi$
$719$	8.62894e6			0.622494			0.311247	+	0.950329i	$0.399253\pi$
$720$		0			0
$721$	871219.			0.0624150
$722$		0			0
$723$	36264.6	+	36264.6i	0.00258010	+	0.00258010i
$724$		0			0
$725$	−2.05433e6	−	1.53482e7i	−0.145153	−	1.08446i
$726$		0			0
$727$	1.16170e7	−	1.16170e7i	0.815187	−	0.815187i	−0.170219	−	0.985406i	$-0.554448\pi$
$727$	1.16170e7	−	1.16170e7i	0.815187	−	0.815187i	0.985406	+	0.170219i	$0.0544475\pi$
$728$		0			0
$729$			1.38516e7i			0.965339i
$730$		0			0
$731$			1.38732e7i			0.960249i
$732$		0			0
$733$	−7.58933e6	+	7.58933e6i	−0.521727	+	0.521727i	−0.918093	−	0.396366i	$-0.870271\pi$
$733$	−7.58933e6	+	7.58933e6i	−0.521727	+	0.521727i	0.396366	+	0.918093i	$0.370271\pi$
$734$		0			0
$735$	146765.	+	128429.i	0.0100208	+	0.00876890i
$736$		0			0
$737$	2.64937e6	+	2.64937e6i	0.179669	+	0.179669i
$738$		0			0
$739$	1.89099e6			0.127373			0.0636867	−	0.997970i	$-0.479714\pi$
$739$	1.89099e6			0.127373			0.0636867	+	0.997970i	$0.479714\pi$
$740$		0			0
$741$	2.69563e6			0.180350
$742$		0			0
$743$	−1.86435e7	−	1.86435e7i	−1.23895	−	1.23895i	−0.960430	−	0.278523i	$-0.910155\pi$
$743$	−1.86435e7	−	1.86435e7i	−1.23895	−	1.23895i	−0.278523	−	0.960430i	$-0.589845\pi$
$744$		0			0
$745$	−1.67613e6	+	111676.i	−0.110641	+	0.00737172i
$746$		0			0
$747$	1.51856e7	−	1.51856e7i	0.995702	−	0.995702i
$748$		0			0
$749$		−	2.99449e7i		−	1.95038i
$750$		0			0
$751$		−	4.60302e6i		−	0.297813i	−0.988851	−	0.148906i	$-0.952425\pi$
$751$		−	4.60302e6i		−	0.297813i	0.988851	−	0.148906i	$-0.0475753\pi$
$752$		0			0
$753$	−459934.	+	459934.i	−0.0295602	+	0.0295602i
$754$		0			0
$755$	1.42783e7	−	951325.i	0.911610	−	0.0607381i
$756$		0			0
$757$	6.60445e6	+	6.60445e6i	0.418887	+	0.418887i	0.884820	−	0.465933i	$-0.154281\pi$
$757$	6.60445e6	+	6.60445e6i	0.418887	+	0.418887i	−0.465933	+	0.884820i	$0.654281\pi$
$758$		0			0
$759$	−3.00118e6			−0.189098
$760$		0			0
$761$	−7.76470e6			−0.486030			−0.243015	−	0.970023i	$-0.578136\pi$
$761$	−7.76470e6			−0.486030			−0.243015	+	0.970023i	$0.578136\pi$
$762$		0			0
$763$	−1.99916e7	−	1.99916e7i	−1.24319	−	1.24319i
$764$		0			0
$765$	9.32476e6	+	8.15981e6i	0.576082	+	0.504112i
$766$		0			0
$767$	−1.07191e7	+	1.07191e7i	−0.657915	+	0.657915i
$768$		0			0
$769$		−	1.03998e7i		−	0.634172i	−0.948397	−	0.317086i	$-0.897296\pi$
$769$		−	1.03998e7i		−	0.634172i	0.948397	−	0.317086i	$-0.102704\pi$
$770$		0			0
$771$		−	380332.i		−	0.0230424i
$772$		0			0
$773$	−2.28295e7	+	2.28295e7i	−1.37419	+	1.37419i	−0.520068	+	0.854125i	$0.674093\pi$
$773$	−2.28295e7	+	2.28295e7i	−1.37419	+	1.37419i	−0.854125	+	0.520068i	$0.825907\pi$
$774$		0			0
$775$	813067.	+	6.07452e6i	0.0486264	+	0.363294i
$776$		0			0
$777$	316731.	+	316731.i	0.0188208	+	0.0188208i
$778$		0			0
$779$	1.46081e7			0.862480
$780$		0			0
$781$	7.82938e6			0.459303
$782$		0			0
$783$	2.01661e6	+	2.01661e6i	0.117548	+	0.117548i
$784$		0			0
$785$	−1.56369e6	+	1.78693e6i	−0.0905683	+	0.103498i
$786$		0			0
$787$	5.72096e6	−	5.72096e6i	0.329255	−	0.329255i	−0.523048	−	0.852303i	$-0.675205\pi$
$787$	5.72096e6	−	5.72096e6i	0.329255	−	0.329255i	0.852303	+	0.523048i	$0.175205\pi$
$788$		0			0
$789$			36309.2i			0.00207646i
$790$		0			0
$791$		−	5.15276e6i		−	0.292818i
$792$		0			0
$793$	−1.52044e7	+	1.52044e7i	−0.858592	+	0.858592i
$794$		0			0
$795$	46423.5	+	696764.i	0.00260507	+	0.0390992i
$796$		0			0
$797$	4.79102e6	+	4.79102e6i	0.267167	+	0.267167i	0.827957	−	0.560791i	$-0.189503\pi$
$797$	4.79102e6	+	4.79102e6i	0.267167	+	0.267167i	−0.560791	+	0.827957i	$0.689503\pi$
$798$		0			0
$799$	−1.07818e7			−0.597479
$800$		0			0
$801$	5.90046e6			0.324941
$802$		0			0
$803$	−2.30193e7	−	2.30193e7i	−1.25980	−	1.25980i
$804$		0			0
$805$	2.06899e6	+	3.10532e7i	0.112530	+	1.68895i
$806$		0			0
$807$	1.49592e6	−	1.49592e6i	0.0808580	−	0.0808580i
$808$		0			0
$809$		−	1.42552e7i		−	0.765778i	−0.923794	−	0.382889i	$-0.874929\pi$
$809$		−	1.42552e7i		−	0.765778i	0.923794	−	0.382889i	$-0.125071\pi$
$810$		0			0
$811$		−	2.56090e7i		−	1.36723i	−0.729843	−	0.683614i	$-0.760407\pi$
$811$		−	2.56090e7i		−	1.36723i	0.729843	−	0.683614i	$-0.239593\pi$
$812$		0			0
$813$	−1.21904e6	+	1.21904e6i	−0.0646830	+	0.0646830i
$814$		0			0
$815$	−2.06991e7	+	2.36543e7i	−1.09159	+	1.24743i
$816$		0			0
$817$	−2.67957e7	−	2.67957e7i	−1.40446	−	1.40446i
$818$		0			0
$819$	−3.07439e7			−1.60158
$820$		0			0
$821$	2.31917e6			0.120081			0.0600406	−	0.998196i	$-0.480877\pi$
$821$	2.31917e6			0.120081			0.0600406	+	0.998196i	$0.480877\pi$
$822$		0			0
$823$	−4.90869e6	−	4.90869e6i	−0.252619	−	0.252619i	0.569425	−	0.822044i	$-0.307166\pi$
$823$	−4.90869e6	−	4.90869e6i	−0.252619	−	0.252619i	−0.822044	+	0.569425i	$0.807166\pi$
$824$		0			0
$825$	−1.43696e6	+	1.88107e6i	−0.0735037	+	0.0962211i
$826$		0			0
$827$	−2.02142e7	+	2.02142e7i	−1.02776	+	1.02776i	−0.0281570	+	0.999604i	$0.508964\pi$
$827$	−2.02142e7	+	2.02142e7i	−1.02776	+	1.02776i	−0.999604	+	0.0281570i	$0.991036\pi$
$828$		0			0
$829$			4.54977e6i			0.229934i	0.993369	+	0.114967i	$0.0366762\pi$
$829$			4.54977e6i			0.229934i	−0.993369	+	0.114967i	$0.963324\pi$
$830$		0			0
$831$		−	1.39710e6i		−	0.0701818i
$832$		0			0
$833$	1.90566e6	−	1.90566e6i	0.0951551	−	0.0951551i
$834$		0			0
$835$	−9.65290e6	−	8.44696e6i	−0.479117	−	0.419261i
$836$		0			0
$837$	−798135.	−	798135.i	−0.0393788	−	0.0393788i
$838$		0			0
$839$	1.98332e7			0.972719			0.486360	−	0.873759i	$-0.338325\pi$
$839$	1.98332e7			0.972719			0.486360	+	0.873759i	$0.338325\pi$
$840$		0			0
$841$	−4.04300e6			−0.197112
$842$		0			0
$843$	2.04198e6	+	2.04198e6i	0.0989651	+	0.0989651i
$844$		0			0
$845$	2.50389e7	−	1.66827e6i	1.20635	−	0.0803759i
$846$		0			0
$847$	2.44138e7	−	2.44138e7i	1.16930	−	1.16930i
$848$		0			0
$849$		−	237170.i		−	0.0112925i
$850$		0			0
$851$			1.06342e7i			0.503363i
$852$		0			0
$853$	−693392.	+	693392.i	−0.0326292	+	0.0326292i	−0.723233	−	0.690604i	$-0.757345\pi$
$853$	−693392.	+	693392.i	−0.0326292	+	0.0326292i	0.690604	+	0.723233i	$0.257345\pi$
$854$		0			0
$855$	−3.37710e7	+	2.25007e6i	−1.57989	+	0.105264i
$856$		0			0
$857$	2.01743e7	+	2.01743e7i	0.938308	+	0.938308i	0.998205	−	0.0598966i	$-0.0190771\pi$
$857$	2.01743e7	+	2.01743e7i	0.938308	+	0.938308i	−0.0598966	+	0.998205i	$0.519077\pi$
$858$		0			0
$859$	2.16047e7			0.999001			0.499501	−	0.866314i	$-0.333517\pi$
$859$	2.16047e7			0.999001			0.499501	+	0.866314i	$0.333517\pi$
$860$		0			0
$861$	972774.			0.0447202
$862$		0			0
$863$	−7.05264e6	−	7.05264e6i	−0.322348	−	0.322348i	0.527319	−	0.849667i	$-0.323197\pi$
$863$	−7.05264e6	−	7.05264e6i	−0.322348	−	0.322348i	−0.849667	+	0.527319i	$0.823197\pi$
$864$		0			0
$865$	−9.43367e6	−	8.25511e6i	−0.428687	−	0.375131i
$866$		0			0
$867$	485480.	−	485480.i	0.0219343	−	0.0219343i
$868$		0			0
$869$			4.10287e7i			1.84305i
$870$		0			0
$871$		−	5.32041e6i		−	0.237629i
$872$		0			0
$873$	−2.16623e7	+	2.16623e7i	−0.961988	+	0.961988i
$874$		0			0
$875$	2.04541e7	+	1.35714e7i	0.903149	+	0.599244i
$876$		0			0
$877$	−1.77065e7	−	1.77065e7i	−0.777381	−	0.777381i	0.202004	−	0.979385i	$-0.435255\pi$
$877$	−1.77065e7	−	1.77065e7i	−0.777381	−	0.777381i	−0.979385	+	0.202004i	$0.935255\pi$
$878$		0			0
$879$	907969.			0.0396368
$880$		0			0
$881$	−2.88929e7			−1.25416			−0.627078	−	0.778957i	$-0.715749\pi$
$881$	−2.88929e7			−1.25416			−0.627078	+	0.778957i	$0.715749\pi$
$882$		0			0
$883$	−4.58238e6	−	4.58238e6i	−0.197783	−	0.197783i	0.601266	−	0.799049i	$-0.294663\pi$
$883$	−4.58238e6	−	4.58238e6i	−0.197783	−	0.197783i	−0.799049	+	0.601266i	$0.794663\pi$
$884$		0			0
$885$	−731842.	+	836325.i	−0.0314094	+	0.0358936i
$886$		0			0
$887$	9.54412e6	−	9.54412e6i	0.407312	−	0.407312i	−0.473488	−	0.880800i	$-0.657005\pi$
$887$	9.54412e6	−	9.54412e6i	0.407312	−	0.407312i	0.880800	+	0.473488i	$0.157005\pi$
$888$		0			0
$889$		−	9.19643e6i		−	0.390270i
$890$		0			0
$891$			3.70057e7i			1.56162i
$892$		0			0
$893$	2.08247e7	−	2.08247e7i	0.873875	−	0.873875i
$894$		0			0
$895$	−1.89385e6	−	2.84246e7i	−0.0790294	−	1.18614i
$896$		0			0
$897$	3.01345e6	+	3.01345e6i	0.125050	+	0.125050i
$898$		0			0
$899$	9.71808e6			0.401034
$900$		0			0
$901$	9.64987e6			0.396013
$902$		0			0
$903$	−1.78437e6	−	1.78437e6i	−0.0728224	−	0.0728224i
$904$		0			0
$905$	−1.32663e6	−	1.99111e7i	−0.0538427	−	0.808118i
$906$		0			0
$907$	1.57152e7	−	1.57152e7i	0.634312	−	0.634312i	−0.314835	−	0.949147i	$-0.601949\pi$
$907$	1.57152e7	−	1.57152e7i	0.634312	−	0.634312i	0.949147	+	0.314835i	$0.101949\pi$
$908$		0			0
$909$		−	7.61877e6i		−	0.305826i
$910$		0			0
$911$			3.37011e7i			1.34539i	0.739920	+	0.672694i	$0.234863\pi$
$911$			3.37011e7i			1.34539i	−0.739920	+	0.672694i	$0.765137\pi$
$912$		0			0
$913$	4.00889e7	−	4.00889e7i	1.59165	−	1.59165i
$914$		0			0
$915$	−1.03808e6	+	1.18628e6i	−0.0409899	+	0.0468418i
$916$		0			0
$917$	8.32021e6	+	8.32021e6i	0.326747	+	0.326747i
$918$		0			0
$919$	1.69860e7			0.663440			0.331720	−	0.943378i	$-0.392371\pi$
$919$	1.69860e7			0.663440			0.331720	+	0.943378i	$0.392371\pi$
$920$		0			0
$921$	1.30872e6			0.0508391
$922$		0			0
$923$	−7.86139e6	−	7.86139e6i	−0.303735	−	0.303735i
$924$		0			0
$925$	6.66528e6	+	5.09163e6i	0.256132	+	0.195660i
$926$		0			0
$927$	−1.05918e6	+	1.05918e6i	−0.0404827	+	0.0404827i
$928$		0			0
$929$		−	2.74089e7i		−	1.04196i	−0.853568	−	0.520982i	$-0.825566\pi$
$929$		−	2.74089e7i		−	1.04196i	0.853568	−	0.520982i	$-0.174434\pi$
$930$		0			0
$931$			7.36144e6i			0.278348i
$932$		0			0
$933$	−1.31423e6	+	1.31423e6i	−0.0494275	+	0.0494275i
$934$		0			0
$935$	2.46168e7	+	2.15414e7i	0.920878	+	0.805832i
$936$		0			0
$937$	−3.46447e7	−	3.46447e7i	−1.28910	−	1.28910i	−0.935333	−	0.353769i	$-0.884900\pi$
$937$	−3.46447e7	−	3.46447e7i	−1.28910	−	1.28910i	−0.353769	−	0.935333i	$-0.615100\pi$
$938$		0			0
$939$	1.15026e6			0.0425728
$940$		0			0
$941$	1.97677e7			0.727750			0.363875	−	0.931448i	$-0.381454\pi$
$941$	1.97677e7			0.727750			0.363875	+	0.931448i	$0.381454\pi$
$942$		0			0
$943$	1.63304e7	+	1.63304e7i	0.598022	+	0.598022i
$944$		0			0
$945$	−4.51085e6	+	300546.i	−0.164316	+	0.0109479i
$946$		0			0
$947$	−1.45673e7	+	1.45673e7i	−0.527842	+	0.527842i	−0.919928	−	0.392086i	$-0.871753\pi$
$947$	−1.45673e7	+	1.45673e7i	−0.527842	+	0.527842i	0.392086	+	0.919928i	$0.371753\pi$
$948$		0			0
$949$			4.62269e7i			1.66621i
$950$		0			0
$951$			3.20738e6i			0.115000i
$952$		0			0
$953$	−2.23751e7	+	2.23751e7i	−0.798055	+	0.798055i	−0.982789	−	0.184734i	$-0.940858\pi$
$953$	−2.23751e7	+	2.23751e7i	−0.798055	+	0.798055i	0.184734	+	0.982789i	$0.440858\pi$
$954$		0			0
$955$	1.65140e7	−	1.10028e6i	0.585928	−	0.0390388i
$956$		0			0
$957$	2.65411e6	+	2.65411e6i	0.0936782	+	0.0936782i
$958$		0			0
$959$	−5.81757e6			−0.204266
$960$		0			0
$961$	2.47829e7			0.865653
$962$		0			0
$963$	3.64053e7	+	3.64053e7i	1.26502	+	1.26502i
$964$		0			0
$965$	651690.	+	570273.i	0.0225280	+	0.0197136i
$966$		0			0
$967$	−2.87842e7	+	2.87842e7i	−0.989894	+	0.989894i	−0.999949	−	0.0100555i	$-0.996799\pi$
$967$	−2.87842e7	+	2.87842e7i	−0.989894	+	0.989894i	0.0100555	+	0.999949i	$0.496799\pi$
$968$		0			0
$969$		−	2.73087e6i		−	0.0934311i
$970$		0			0
$971$		−	5.09828e7i		−	1.73530i	−0.497173	−	0.867651i	$-0.665629\pi$
$971$		−	5.09828e7i		−	1.73530i	0.497173	−	0.867651i	$-0.334371\pi$
$972$		0			0
$973$	−5.63180e6	+	5.63180e6i	−0.190706	+	0.190706i
$974$		0			0
$975$	3.33160e6	−	445930.i	0.112238	−	0.0150230i
$976$		0			0
$977$	3.93752e7	+	3.93752e7i	1.31973	+	1.31973i	0.913984	+	0.405749i	$0.132989\pi$
$977$	3.93752e7	+	3.93752e7i	1.31973	+	1.31973i	0.405749	+	0.913984i	$0.367011\pi$
$978$		0			0
$979$	1.55768e7			0.519424
$980$		0			0
$981$	4.86093e7			1.61267
$982$		0			0
$983$	2.47236e7	+	2.47236e7i	0.816070	+	0.816070i	0.985536	−	0.169466i	$-0.0542042\pi$
$983$	2.47236e7	+	2.47236e7i	0.816070	+	0.816070i	−0.169466	+	0.985536i	$0.554204\pi$
$984$		0			0
$985$	8.00888e6	−	9.15228e6i	0.263015	−	0.300565i
$986$		0			0
$987$	1.38675e6	−	1.38675e6i	0.0453111	−	0.0453111i
$988$		0			0
$989$		−	5.99100e7i		−	1.94764i
$990$		0			0
$991$		−	2.85549e7i		−	0.923627i	−0.886977	−	0.461814i	$-0.847199\pi$
$991$		−	2.85549e7i		−	0.923627i	0.886977	−	0.461814i	$-0.152801\pi$
$992$		0			0
$993$	621822.	−	621822.i	0.0200121	−	0.0200121i
$994$		0			0
$995$	1.54306e6	+	2.31596e7i	0.0494113	+	0.741608i
$996$		0			0
$997$	−1.29416e7	−	1.29416e7i	−0.412335	−	0.412335i	0.470216	−	0.882551i	$-0.344176\pi$
$997$	−1.29416e7	−	1.29416e7i	−0.412335	−	0.412335i	−0.882551	+	0.470216i	$0.844176\pi$
$998$		0			0
$999$	−1.54475e6			−0.0489716

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.n.d.47.6	yes	20
4.3	odd	2	inner	80.6.n.d.47.5	✓	20
5.2	odd	4		400.6.n.g.143.6		20
5.3	odd	4	inner	80.6.n.d.63.5	yes	20
5.4	even	2		400.6.n.g.207.5		20
20.3	even	4	inner	80.6.n.d.63.6	yes	20
20.7	even	4		400.6.n.g.143.5		20
20.19	odd	2		400.6.n.g.207.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.n.d.47.5	✓	20	4.3	odd	2	inner
80.6.n.d.47.6	yes	20	1.1	even	1	trivial
80.6.n.d.63.5	yes	20	5.3	odd	4	inner
80.6.n.d.63.6	yes	20	20.3	even	4	inner
400.6.n.g.143.5		20	20.7	even	4
400.6.n.g.143.6		20	5.2	odd	4
400.6.n.g.207.5		20	5.4	even	2
400.6.n.g.207.6		20	20.19	odd	2

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	80.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.839817 + 0.839817i) q^{3} +(3.71634 + 55.7780i) q^{5} +(-99.3589 + 99.3589i) q^{7} -241.589i q^{9} +O(q^{10})\)	\(q+(0.839817 + 0.839817i) q^{3} +(3.71634 + 55.7780i) q^{5} +(-99.3589 + 99.3589i) q^{7} -241.589i q^{9} -637.781i q^{11} +(-640.389 + 640.389i) q^{13} +(-43.7223 + 49.9644i) q^{15} +(648.760 + 648.760i) q^{17} -2506.12 q^{19} -166.887 q^{21} +(-2801.60 - 2801.60i) q^{23} +(-3097.38 + 414.580i) q^{25} +(406.966 - 406.966i) q^{27} +4955.21i q^{29} -1961.18i q^{31} +(535.619 - 535.619i) q^{33} +(-5911.30 - 5172.79i) q^{35} +(-1897.88 - 1897.88i) q^{37} -1075.62 q^{39} -5828.95 q^{41} +(10692.1 + 10692.1i) q^{43} +(13475.4 - 897.828i) q^{45} +(-8309.52 + 8309.52i) q^{47} -2937.38i q^{49} +1089.68i q^{51} +(7437.17 - 7437.17i) q^{53} +(35574.2 - 2370.21i) q^{55} +(-2104.68 - 2104.68i) q^{57} +16738.4 q^{59} +23742.5 q^{61} +(24004.1 + 24004.1i) q^{63} +(-38099.5 - 33339.7i) q^{65} +(-4154.05 + 4154.05i) q^{67} -4705.66i q^{69} +12276.0i q^{71} +(36092.8 - 36092.8i) q^{73} +(-2949.40 - 2253.06i) q^{75} +(63369.2 + 63369.2i) q^{77} -64330.4 q^{79} -58022.7 q^{81} +(62856.9 + 62856.9i) q^{83} +(-33775.5 + 38597.6i) q^{85} +(-4161.47 + 4161.47i) q^{87} +24423.5i q^{89} -127257. i q^{91} +(1647.03 - 1647.03i) q^{93} +(-9313.60 - 139787. i) q^{95} +(-89666.0 - 89666.0i) q^{97} -154081. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 44 q^{5}+O(q^{10}) \) 20 * q - 44 * q^5	\( 20 q - 44 q^{5} + 804 q^{13} - 2236 q^{17} - 4520 q^{21} + 948 q^{25} - 11096 q^{33} + 44260 q^{37} - 6760 q^{41} - 92816 q^{45} + 182452 q^{53} - 34288 q^{57} - 41080 q^{61} - 155772 q^{65} + 264372 q^{73} + 399304 q^{77} - 520220 q^{81} - 344796 q^{85} + 713496 q^{93} + 374772 q^{97}+O(q^{100}) \) 20 * q - 44 * q^5 + 804 * q^13 - 2236 * q^17 - 4520 * q^21 + 948 * q^25 - 11096 * q^33 + 44260 * q^37 - 6760 * q^41 - 92816 * q^45 + 182452 * q^53 - 34288 * q^57 - 41080 * q^61 - 155772 * q^65 + 264372 * q^73 + 399304 * q^77 - 520220 * q^81 - 344796 * q^85 + 713496 * q^93 + 374772 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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