LMFDB - Embedded newform 160.6.n.d.127.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,6,Mod(63,160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("160.63");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	160.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:	$25.6614111701$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 1375 x^{14} + 743087 x^{12} + 198706725 x^{10} + 26872635188 x^{8} + 1612811892960 x^{6} + \cdots + 177426662425600 $ x^16 + 1375x^14 + 743087x^12 + 198706725x^10 + 26872635188x^8 + 1612811892960x^6 + 24971013117824x^4 + 124211190826240*x^2 + 177426662425600
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{41}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.3
Root			$13.0932i$ of defining polynomial
Character	$\chi$	$=$	160.127
Dual form			160.6.n.d.63.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-12.0932 - 12.0932i) q^{3} +(-34.4070 - 44.0586i) q^{5} +(74.8536 - 74.8536i) q^{7} +49.4886i q^{9} +O(q^{10})$	\(q+(-12.0932 - 12.0932i) q^{3} +(-34.4070 - 44.0586i) q^{5} +(74.8536 - 74.8536i) q^{7} +49.4886i q^{9} -432.151i q^{11} +(639.311 - 639.311i) q^{13} +(-116.717 + 948.896i) q^{15} +(-1424.91 - 1424.91i) q^{17} +2374.16 q^{19} -1810.43 q^{21} +(-170.300 - 170.300i) q^{23} +(-757.313 + 3031.85i) q^{25} +(-2340.16 + 2340.16i) q^{27} -5000.18i q^{29} +7161.45i q^{31} +(-5226.06 + 5226.06i) q^{33} +(-5873.43 - 722.451i) q^{35} +(-4647.57 - 4647.57i) q^{37} -15462.6 q^{39} +1578.52 q^{41} +(4528.62 + 4528.62i) q^{43} +(2180.40 - 1702.76i) q^{45} +(-489.826 + 489.826i) q^{47} +5600.89i q^{49} +34463.4i q^{51} +(-1533.89 + 1533.89i) q^{53} +(-19039.9 + 14869.0i) q^{55} +(-28711.1 - 28711.1i) q^{57} -2548.73 q^{59} -31490.8 q^{61} +(3704.40 + 3704.40i) q^{63} +(-50163.9 - 6170.32i) q^{65} +(37974.7 - 37974.7i) q^{67} +4118.92i q^{69} +41449.8i q^{71} +(37660.5 - 37660.5i) q^{73} +(45822.9 - 27506.3i) q^{75} +(-32348.0 - 32348.0i) q^{77} -39767.6 q^{79} +68625.6 q^{81} +(40365.6 + 40365.6i) q^{83} +(-13752.6 + 111807. i) q^{85} +(-60468.0 + 60468.0i) q^{87} -48313.3i q^{89} -95709.4i q^{91} +(86604.6 - 86604.6i) q^{93} +(-81687.9 - 104602. i) q^{95} +(60161.4 + 60161.4i) q^{97} +21386.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 10 q^{3} - 42 q^{5} - 86 q^{7}+O(q^{10}) $ 16 * q + 10 * q^3 - 42 * q^5 - 86 * q^7	$ 16 q + 10 q^{3} - 42 q^{5} - 86 q^{7} + 536 q^{13} - 698 q^{15} - 1828 q^{17} + 2512 q^{19} - 4284 q^{21} - 7642 q^{23} + 9140 q^{25} - 12272 q^{27} + 11876 q^{33} + 10518 q^{35} - 7620 q^{37} + 11244 q^{39} - 21284 q^{41} + 20002 q^{43} + 686 q^{45} + 25298 q^{47} + 12852 q^{53} - 10584 q^{55} + 55848 q^{57} - 142704 q^{59} - 20564 q^{61} - 115282 q^{63} - 38256 q^{65} - 10506 q^{67} + 15432 q^{73} + 256226 q^{75} + 133852 q^{77} - 159344 q^{79} - 236116 q^{81} - 61222 q^{83} + 7056 q^{85} + 162176 q^{87} + 122180 q^{93} + 267512 q^{95} - 17344 q^{97} + 107332 q^{99}+O(q^{100}) $ 16 * q + 10 * q^3 - 42 * q^5 - 86 * q^7 + 536 * q^13 - 698 * q^15 - 1828 * q^17 + 2512 * q^19 - 4284 * q^21 - 7642 * q^23 + 9140 * q^25 - 12272 * q^27 + 11876 * q^33 + 10518 * q^35 - 7620 * q^37 + 11244 * q^39 - 21284 * q^41 + 20002 * q^43 + 686 * q^45 + 25298 * q^47 + 12852 * q^53 - 10584 * q^55 + 55848 * q^57 - 142704 * q^59 - 20564 * q^61 - 115282 * q^63 - 38256 * q^65 - 10506 * q^67 + 15432 * q^73 + 256226 * q^75 + 133852 * q^77 - 159344 * q^79 - 236116 * q^81 - 61222 * q^83 + 7056 * q^85 + 162176 * q^87 + 122180 * q^93 + 267512 * q^95 - 17344 * q^97 + 107332 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	−12.0932	−	12.0932i	−0.775776	−	0.775776i	0.203334	−	0.979110i	$-0.434822\pi$
$3$	−12.0932	−	12.0932i	−0.775776	−	0.775776i	−0.979110	+	0.203334i	$0.934822\pi$
$4$		0			0
$5$	−34.4070	−	44.0586i	−0.615492	−	0.788143i
$5$	−34.4070	−	44.0586i	−0.615492	−	0.788143i
$6$		0			0
$7$	74.8536	−	74.8536i	0.577388	−	0.577388i	−0.356795	−	0.934183i	$-0.616131\pi$
$7$	74.8536	−	74.8536i	0.577388	−	0.577388i	0.934183	+	0.356795i	$0.116131\pi$
$8$		0			0
$9$			49.4886i			0.203657i
$10$		0			0
$11$		−	432.151i		−	1.07685i	−0.842675	−	0.538423i	$-0.819020\pi$
$11$		−	432.151i		−	1.07685i	0.842675	−	0.538423i	$-0.180980\pi$
$12$		0			0
$13$	639.311	−	639.311i	1.04919	−	1.04919i	0.0504631	−	0.998726i	$-0.483930\pi$
$13$	639.311	−	639.311i	1.04919	−	1.04919i	0.998726	−	0.0504631i	$-0.0160697\pi$
$14$		0			0
$15$	−116.717	+	948.896i	−0.133939	+	1.08891i
$16$		0			0
$17$	−1424.91	−	1424.91i	−1.19582	−	1.19582i	−0.975406	−	0.220416i	$-0.929259\pi$
$17$	−1424.91	−	1424.91i	−1.19582	−	1.19582i	−0.220416	−	0.975406i	$-0.570741\pi$
$18$		0			0
$19$	2374.16			1.50878			0.754391	−	0.656426i	$-0.227932\pi$
$19$	2374.16			1.50878			0.754391	+	0.656426i	$0.227932\pi$
$20$		0			0
$21$	−1810.43			−0.895847
$22$		0			0
$23$	−170.300	−	170.300i	−0.0671265	−	0.0671265i	0.672747	−	0.739873i	$-0.265114\pi$
$23$	−170.300	−	170.300i	−0.0671265	−	0.0671265i	−0.739873	+	0.672747i	$0.765114\pi$
$24$		0			0
$25$	−757.313	+	3031.85i	−0.242340	+	0.970191i
$26$		0			0
$27$	−2340.16	+	2340.16i	−0.617784	+	0.617784i
$28$		0			0
$29$		−	5000.18i		−	1.10406i	−0.833826	−	0.552028i	$-0.813854\pi$
$29$		−	5000.18i		−	1.10406i	0.833826	−	0.552028i	$-0.186146\pi$
$30$		0			0
$31$			7161.45i			1.33843i	0.743067	+	0.669217i	$0.233370\pi$
$31$			7161.45i			1.33843i	−0.743067	+	0.669217i	$0.766630\pi$
$32$		0			0
$33$	−5226.06	+	5226.06i	−0.835391	+	0.835391i
$34$		0			0
$35$	−5873.43	−	722.451i	−0.810441	−	0.0996870i
$36$		0			0
$37$	−4647.57	−	4647.57i	−0.558113	−	0.558113i	0.370657	−	0.928770i	$-0.379133\pi$
$37$	−4647.57	−	4647.57i	−0.558113	−	0.558113i	−0.928770	+	0.370657i	$0.879133\pi$
$38$		0			0
$39$	−15462.6			−1.62787
$40$		0			0
$41$	1578.52			0.146653			0.0733264	−	0.997308i	$-0.476639\pi$
$41$	1578.52			0.146653			0.0733264	+	0.997308i	$0.476639\pi$
$42$		0			0
$43$	4528.62	+	4528.62i	0.373504	+	0.373504i	0.868752	−	0.495248i	$-0.164923\pi$
$43$	4528.62	+	4528.62i	0.373504	+	0.373504i	−0.495248	+	0.868752i	$0.664923\pi$
$44$		0			0
$45$	2180.40	−	1702.76i	0.160511	−	0.125349i
$46$		0			0
$47$	−489.826	+	489.826i	−0.0323443	+	0.0323443i	−0.723094	−	0.690750i	$-0.757281\pi$
$47$	−489.826	+	489.826i	−0.0323443	+	0.0323443i	0.690750	+	0.723094i	$0.257281\pi$
$48$		0			0
$49$			5600.89i			0.333247i
$50$		0			0
$51$			34463.4i			1.85538i
$52$		0			0
$53$	−1533.89	+	1533.89i	−0.0750073	+	0.0750073i	−0.743615	−	0.668608i	$-0.766891\pi$
$53$	−1533.89	+	1533.89i	−0.0750073	+	0.0750073i	0.668608	+	0.743615i	$0.266891\pi$
$54$		0			0
$55$	−19039.9	+	14869.0i	−0.848709	+	0.662789i
$56$		0			0
$57$	−28711.1	−	28711.1i	−1.17048	−	1.17048i
$58$		0			0
$59$	−2548.73			−0.0953222			−0.0476611	−	0.998864i	$-0.515177\pi$
$59$	−2548.73			−0.0953222			−0.0476611	+	0.998864i	$0.515177\pi$
$60$		0			0
$61$	−31490.8			−1.08358			−0.541788	−	0.840515i	$-0.682252\pi$
$61$	−31490.8			−1.08358			−0.541788	+	0.840515i	$0.682252\pi$
$62$		0			0
$63$	3704.40	+	3704.40i	0.117589	+	0.117589i
$64$		0			0
$65$	−50163.9	−	6170.32i	−1.47268	−	0.181144i
$66$		0			0
$67$	37974.7	−	37974.7i	1.03349	−	1.03349i	0.0340720	−	0.999419i	$-0.489152\pi$
$67$	37974.7	−	37974.7i	1.03349	−	1.03349i	0.999419	−	0.0340720i	$-0.0108476\pi$
$68$		0			0
$69$			4118.92i			0.104150i
$70$		0			0
$71$			41449.8i			0.975835i	0.872890	+	0.487917i	$0.162243\pi$
$71$			41449.8i			0.975835i	−0.872890	+	0.487917i	$0.837757\pi$
$72$		0			0
$73$	37660.5	−	37660.5i	0.827140	−	0.827140i	−0.159980	−	0.987120i	$-0.551143\pi$
$73$	37660.5	−	37660.5i	0.827140	−	0.827140i	0.987120	+	0.159980i	$0.0511430\pi$
$74$		0			0
$75$	45822.9	−	27506.3i	0.940653	−	0.564650i
$76$		0			0
$77$	−32348.0	−	32348.0i	−0.621757	−	0.621757i
$78$		0			0
$79$	−39767.6			−0.716905			−0.358453	−	0.933548i	$-0.616696\pi$
$79$	−39767.6			−0.716905			−0.358453	+	0.933548i	$0.616696\pi$
$80$		0			0
$81$	68625.6			1.16218
$82$		0			0
$83$	40365.6	+	40365.6i	0.643156	+	0.643156i	0.951330	−	0.308174i	$-0.0997178\pi$
$83$	40365.6	+	40365.6i	0.643156	+	0.643156i	−0.308174	+	0.951330i	$0.599718\pi$
$84$		0			0
$85$	−13752.6	+	111807.i	−0.206461	+	1.67850i
$86$		0			0
$87$	−60468.0	+	60468.0i	−0.856500	+	0.856500i
$88$		0			0
$89$		−	48313.3i		−	0.646535i	−0.946308	−	0.323267i	$-0.895219\pi$
$89$		−	48313.3i		−	0.646535i	0.946308	−	0.323267i	$-0.104781\pi$
$90$		0			0
$91$		−	95709.4i		−	1.21158i
$92$		0			0
$93$	86604.6	−	86604.6i	1.03833	−	1.03833i
$94$		0			0
$95$	−81687.9	−	104602.i	−0.928642	−	1.18914i
$96$		0			0
$97$	60161.4	+	60161.4i	0.649216	+	0.649216i	0.952803	−	0.303588i	$-0.0981846\pi$
$97$	60161.4	+	60161.4i	0.649216	+	0.649216i	−0.303588	+	0.952803i	$0.598185\pi$
$98$		0			0
$99$	21386.5			0.219307
$100$		0			0
$101$	802.130			0.00782422			0.00391211	−	0.999992i	$-0.498755\pi$
$101$	802.130			0.00782422			0.00391211	+	0.999992i	$0.498755\pi$
$102$		0			0
$103$	−12372.7	−	12372.7i	−0.114914	−	0.114914i	0.647312	−	0.762226i	$-0.275893\pi$
$103$	−12372.7	−	12372.7i	−0.114914	−	0.114914i	−0.762226	+	0.647312i	$0.775893\pi$
$104$		0			0
$105$	62291.6	+	79765.0i	0.551386	+	0.706056i
$106$		0			0
$107$	143629.	−	143629.i	1.21278	−	1.21278i	0.242675	−	0.970108i	$-0.421975\pi$
$107$	143629.	−	143629.i	1.21278	−	1.21278i	0.970108	−	0.242675i	$-0.0780248\pi$
$108$		0			0
$109$			226385.i			1.82508i	0.408992	+	0.912538i	$0.365880\pi$
$109$			226385.i			1.82508i	−0.408992	+	0.912538i	$0.634120\pi$
$110$		0			0
$111$			112408.i			0.865941i
$112$		0			0
$113$	−70878.0	+	70878.0i	−0.522174	+	0.522174i	−0.918228	−	0.396053i	$-0.870380\pi$
$113$	−70878.0	+	70878.0i	−0.522174	+	0.522174i	0.396053	+	0.918228i	$0.370380\pi$
$114$		0			0
$115$	−1643.65	+	13362.7i	−0.0115895	+	0.0942211i
$116$		0			0
$117$	31638.6	+	31638.6i	0.213674	+	0.213674i
$118$		0			0
$119$	−213320.			−1.38091
$120$		0			0
$121$	−25703.1			−0.159596
$122$		0			0
$123$	−19089.3	−	19089.3i	−0.113770	−	0.113770i
$124$		0			0
$125$	159636.	−	70950.8i	0.913808	−	0.406146i
$126$		0			0
$127$	234054.	−	234054.i	1.28768	−	1.28768i	0.351484	−	0.936194i	$-0.385677\pi$
$127$	234054.	−	234054.i	1.28768	−	1.28768i	0.936194	−	0.351484i	$-0.114323\pi$
$128$		0			0
$129$		−	109531.i		−	0.579510i
$130$		0			0
$131$			108910.i			0.554483i	0.960800	+	0.277241i	$0.0894202\pi$
$131$			108910.i			0.554483i	−0.960800	+	0.277241i	$0.910580\pi$
$132$		0			0
$133$	177714.	−	177714.i	0.871152	−	0.871152i
$134$		0			0
$135$	183622.	+	22586.1i	0.867143	+	0.106661i
$136$		0			0
$137$	229642.	+	229642.i	1.04532	+	1.04532i	0.998923	+	0.0463976i	$0.0147741\pi$
$137$	229642.	+	229642.i	1.04532	+	1.04532i	0.0463976	+	0.998923i	$0.485226\pi$
$138$		0			0
$139$	304587.			1.33713			0.668565	−	0.743653i	$-0.266909\pi$
$139$	304587.			1.33713			0.668565	+	0.743653i	$0.266909\pi$
$140$		0			0
$141$	11847.1			0.0501838
$142$		0			0
$143$	−276279.	−	276279.i	−1.12981	−	1.12981i
$144$		0			0
$145$	−220301.	+	172042.i	−0.870154	+	0.679537i
$146$		0			0
$147$	67732.4	−	67732.4i	0.258525	−	0.258525i
$148$		0			0
$149$		−	306960.i		−	1.13270i	−0.824164	−	0.566351i	$-0.808355\pi$
$149$		−	306960.i		−	1.13270i	0.824164	−	0.566351i	$-0.191645\pi$
$150$		0			0
$151$			37640.8i			0.134343i	0.997741	+	0.0671717i	$0.0213975\pi$
$151$			37640.8i			0.134343i	−0.997741	+	0.0671717i	$0.978602\pi$
$152$		0			0
$153$	70517.0	−	70517.0i	0.243537	−	0.243537i
$154$		0			0
$155$	315523.	−	246404.i	1.05488	−	0.823795i
$156$		0			0
$157$	−221182.	−	221182.i	−0.716144	−	0.716144i	0.251669	−	0.967813i	$-0.419020\pi$
$157$	−221182.	−	221182.i	−0.716144	−	0.716144i	−0.967813	+	0.251669i	$0.919020\pi$
$158$		0			0
$159$	37099.0			0.116378
$160$		0			0
$161$	−25495.1			−0.0775160
$162$		0			0
$163$	−338684.	−	338684.i	−0.998447	−	0.998447i	0.00155132	−	0.999999i	$-0.499506\pi$
$163$	−338684.	−	338684.i	−0.998447	−	0.998447i	−0.999999	+	0.00155132i	$0.999506\pi$
$164$		0			0
$165$	410066.	+	50439.5i	1.17258	+	0.144232i
$166$		0			0
$167$	−192088.	+	192088.i	−0.532979	+	0.532979i	−0.921458	−	0.388479i	$-0.873001\pi$
$167$	−192088.	+	192088.i	−0.532979	+	0.532979i	0.388479	+	0.921458i	$0.373001\pi$
$168$		0			0
$169$		−	446144.i		−	1.20160i
$170$		0			0
$171$			117494.i			0.307274i
$172$		0			0
$173$	−358281.	+	358281.i	−0.910142	+	0.910142i	−0.996283	−	0.0861412i	$-0.972546\pi$
$173$	−358281.	+	358281.i	−0.910142	+	0.910142i	0.0861412	+	0.996283i	$0.472546\pi$
$174$		0			0
$175$	170257.	+	283632.i	0.420252	+	0.700101i
$176$		0			0
$177$	30822.2	+	30822.2i	0.0739486	+	0.0739486i
$178$		0			0
$179$	−425231.			−0.991956			−0.495978	−	0.868335i	$-0.665190\pi$
$179$	−425231.			−0.991956			−0.495978	+	0.868335i	$0.665190\pi$
$180$		0			0
$181$	−698872.			−1.58563			−0.792813	−	0.609465i	$-0.791384\pi$
$181$	−698872.			−1.58563			−0.792813	+	0.609465i	$0.791384\pi$
$182$		0			0
$183$	380823.	+	380823.i	0.840612	+	0.840612i
$184$		0			0
$185$	−44856.2	+	364675.i	−0.0963591	+	0.783387i
$186$		0			0
$187$	−615778.	+	615778.i	−1.28772	+	1.28772i
$188$		0			0
$189$			350339.i			0.713402i
$190$		0			0
$191$			191378.i			0.379584i	0.981824	+	0.189792i	$0.0607813\pi$
$191$			191378.i			0.379584i	−0.981824	+	0.189792i	$0.939219\pi$
$192$		0			0
$193$	72951.2	−	72951.2i	0.140974	−	0.140974i	−0.633098	−	0.774072i	$-0.718217\pi$
$193$	72951.2	−	72951.2i	0.140974	−	0.140974i	0.774072	+	0.633098i	$0.218217\pi$
$194$		0			0
$195$	532021.	+	681258.i	1.00194	+	1.28300i
$196$		0			0
$197$	328053.	+	328053.i	0.602252	+	0.602252i	0.940910	−	0.338657i	$-0.109973\pi$
$197$	328053.	+	328053.i	0.602252	+	0.602252i	−0.338657	+	0.940910i	$0.609973\pi$
$198$		0			0
$199$	−355637.			−0.636611			−0.318306	−	0.947988i	$-0.603114\pi$
$199$	−355637.			−0.636611			−0.318306	+	0.947988i	$0.603114\pi$
$200$		0			0
$201$	−918467.			−1.60352
$202$		0			0
$203$	−374282.	−	374282.i	−0.637468	−	0.637468i
$204$		0			0
$205$	−54312.2	−	69547.3i	−0.0902636	−	0.115583i
$206$		0			0
$207$	8427.89	−	8427.89i	0.0136708	−	0.0136708i
$208$		0			0
$209$		−	1.02600e6i		−	1.62472i
$210$		0			0
$211$			636070.i			0.983555i	0.870721	+	0.491778i	$0.163653\pi$
$211$			636070.i			0.983555i	−0.870721	+	0.491778i	$0.836347\pi$
$212$		0			0
$213$	501258.	−	501258.i	0.757029	−	0.757029i
$214$		0			0
$215$	43708.1	−	355341.i	0.0644861	−	0.524263i
$216$		0			0
$217$	536060.	+	536060.i	0.772795	+	0.772795i
$218$		0			0
$219$	−910869.			−1.28335
$220$		0			0
$221$	−1.82193e6			−2.50929
$222$		0			0
$223$	−254820.	−	254820.i	−0.343140	−	0.343140i	0.514407	−	0.857546i	$-0.328012\pi$
$223$	−254820.	−	254820.i	−0.343140	−	0.343140i	−0.857546	+	0.514407i	$0.828012\pi$
$224$		0			0
$225$	−150042.	−	37478.3i	−0.197586	−	0.0493542i
$226$		0			0
$227$	−623645.	+	623645.i	−0.803291	+	0.803291i	−0.983608	−	0.180318i	$-0.942287\pi$
$227$	−623645.	+	623645.i	−0.803291	+	0.803291i	0.180318	+	0.983608i	$0.442287\pi$
$228$		0			0
$229$			156295.i			0.196950i	0.995140	+	0.0984749i	$0.0313964\pi$
$229$			156295.i			0.196950i	−0.995140	+	0.0984749i	$0.968604\pi$
$230$		0			0
$231$			782379.i			0.964689i
$232$		0			0
$233$	580116.	−	580116.i	0.700044	−	0.700044i	−0.264376	−	0.964420i	$-0.585166\pi$
$233$	580116.	−	580116.i	0.700044	−	0.700044i	0.964420	+	0.264376i	$0.0851660\pi$
$234$		0			0
$235$	38434.5	+	4727.57i	0.0453996	+	0.00558429i
$236$		0			0
$237$	480916.	+	480916.i	0.556158	+	0.556158i
$238$		0			0
$239$	909455.			1.02988			0.514940	−	0.857226i	$-0.327814\pi$
$239$	909455.			1.02988			0.514940	+	0.857226i	$0.327814\pi$
$240$		0			0
$241$	−955010.			−1.05917			−0.529585	−	0.848257i	$-0.677652\pi$
$241$	−955010.			−1.05917			−0.529585	+	0.848257i	$0.677652\pi$
$242$		0			0
$243$	−261240.	−	261240.i	−0.283808	−	0.283808i
$244$		0			0
$245$	246767.	−	192710.i	0.262647	−	0.205111i
$246$		0			0
$247$	1.51783e6	−	1.51783e6i	1.58300	−	1.58300i
$248$		0			0
$249$		−	976296.i		−	0.997891i
$250$		0			0
$251$			211230.i			0.211627i	0.994386	+	0.105814i	$0.0337447\pi$
$251$			211230.i			0.211627i	−0.994386	+	0.105814i	$0.966255\pi$
$252$		0			0
$253$	−73595.1	+	73595.1i	−0.0722849	+	0.0722849i
$254$		0			0
$255$	1.51841e6	−	1.18578e6i	1.46231	−	1.14197i
$256$		0			0
$257$	−398055.	−	398055.i	−0.375933	−	0.375933i	0.493700	−	0.869632i	$-0.335644\pi$
$257$	−398055.	−	398055.i	−0.375933	−	0.375933i	−0.869632	+	0.493700i	$0.835644\pi$
$258$		0			0
$259$	−695775.			−0.644495
$260$		0			0
$261$	247452.			0.224848
$262$		0			0
$263$	−359761.	−	359761.i	−0.320719	−	0.320719i	0.528324	−	0.849043i	$-0.322821\pi$
$263$	−359761.	−	359761.i	−0.320719	−	0.320719i	−0.849043	+	0.528324i	$0.822821\pi$
$264$		0			0
$265$	120357.	+	14804.3i	0.105283	+	0.0129501i
$266$		0			0
$267$	−584260.	+	584260.i	−0.501566	+	0.501566i
$268$		0			0
$269$		−	1.65759e6i		−	1.39668i	−0.715768	−	0.698338i	$-0.753923\pi$
$269$		−	1.65759e6i		−	1.39668i	0.715768	−	0.698338i	$-0.246077\pi$
$270$		0			0
$271$			2.14221e6i			1.77189i	0.463786	+	0.885947i	$0.346491\pi$
$271$			2.14221e6i			1.77189i	−0.463786	+	0.885947i	$0.653509\pi$
$272$		0			0
$273$	−1.15743e6	+	1.15743e6i	−0.939913	+	0.939913i
$274$		0			0
$275$	1.31021e6	+	327273.i	1.04475	+	0.260963i
$276$		0			0
$277$	−889567.	−	889567.i	−0.696593	−	0.696593i	0.267081	−	0.963674i	$-0.413941\pi$
$277$	−889567.	−	889567.i	−0.696593	−	0.696593i	−0.963674	+	0.267081i	$0.913941\pi$
$278$		0			0
$279$	−354410.			−0.272581
$280$		0			0
$281$	2.06917e6			1.56326			0.781628	−	0.623744i	$-0.214389\pi$
$281$	2.06917e6			1.56326			0.781628	+	0.623744i	$0.214389\pi$
$282$		0			0
$283$	−22257.7	−	22257.7i	−0.0165201	−	0.0165201i	0.698798	−	0.715319i	$-0.253718\pi$
$283$	−22257.7	−	22257.7i	−0.0165201	−	0.0165201i	−0.715319	+	0.698798i	$0.753718\pi$
$284$		0			0
$285$	−277106.	+	2.25283e6i	−0.202085	+	1.64292i
$286$		0			0
$287$	118158.	−	118158.i	0.0846755	−	0.0846755i
$288$		0			0
$289$			2.64090e6i			1.85998i
$290$		0			0
$291$		−	1.45508e6i		−	1.00729i
$292$		0			0
$293$	1.96878e6	−	1.96878e6i	1.33976	−	1.33976i	0.443478	−	0.896285i	$-0.353744\pi$
$293$	1.96878e6	−	1.96878e6i	1.33976	−	1.33976i	0.896285	−	0.443478i	$-0.146256\pi$
$294$		0			0
$295$	87694.2	+	112293.i	0.0586700	+	0.0751275i
$296$		0			0
$297$	1.01130e6	+	1.01130e6i	0.665258	+	0.665258i
$298$		0			0
$299$	−217749.			−0.140857
$300$		0			0
$301$	677967.			0.431313
$302$		0			0
$303$	−9700.28	−	9700.28i	−0.00606984	−	0.00606984i
$304$		0			0
$305$	1.08351e6	+	1.38744e6i	0.666932	+	0.854013i
$306$		0			0
$307$	1.43983e6	−	1.43983e6i	0.871897	−	0.871897i	−0.120782	−	0.992679i	$-0.538540\pi$
$307$	1.43983e6	−	1.43983e6i	0.871897	−	0.871897i	0.992679	+	0.120782i	$0.0385403\pi$
$308$		0			0
$309$			299251.i			0.178295i
$310$		0			0
$311$		−	1.55159e6i		−	0.909652i	−0.890580	−	0.454826i	$-0.849701\pi$
$311$		−	1.55159e6i		−	0.909652i	0.890580	−	0.454826i	$-0.150299\pi$
$312$		0			0
$313$	1.08899e6	−	1.08899e6i	0.628293	−	0.628293i	−0.319346	−	0.947638i	$-0.603463\pi$
$313$	1.08899e6	−	1.08899e6i	0.628293	−	0.628293i	0.947638	+	0.319346i	$0.103463\pi$
$314$		0			0
$315$	35753.1	−	290668.i	0.0203019	−	0.165052i
$316$		0			0
$317$	408691.	+	408691.i	0.228427	+	0.228427i	0.812035	−	0.583609i	$-0.198360\pi$
$317$	408691.	+	408691.i	0.228427	+	0.228427i	−0.583609	+	0.812035i	$0.698360\pi$
$318$		0			0
$319$	−2.16083e6			−1.18890
$320$		0			0
$321$	−3.47386e6			−1.88170
$322$		0			0
$323$	−3.38298e6	−	3.38298e6i	−1.80423	−	1.80423i
$324$		0			0
$325$	1.45414e6	+	2.42245e6i	0.763654	+	1.27217i
$326$		0			0
$327$	2.73771e6	−	2.73771e6i	1.41585	−	1.41585i
$328$		0			0
$329$			73330.5i			0.0373504i
$330$		0			0
$331$			2.36055e6i			1.18425i	0.805846	+	0.592125i	$0.201711\pi$
$331$			2.36055e6i			1.18425i	−0.805846	+	0.592125i	$0.798289\pi$
$332$		0			0
$333$	230002.	−	230002.i	0.113663	−	0.113663i
$334$		0			0
$335$	−2.97970e6	−	366513.i	−1.45064	−	0.178434i
$336$		0			0
$337$	288933.	+	288933.i	0.138587	+	0.138587i	0.772997	−	0.634410i	$-0.218757\pi$
$337$	288933.	+	288933.i	0.138587	+	0.138587i	−0.634410	+	0.772997i	$0.718757\pi$
$338$		0			0
$339$	1.71428e6			0.810181
$340$		0			0
$341$	3.09483e6			1.44129
$342$		0			0
$343$	1.67731e6	+	1.67731e6i	0.769800	+	0.769800i
$344$		0			0
$345$	181474.	−	141720.i	0.0820853	−	0.0641036i
$346$		0			0
$347$	−253490.	+	253490.i	−0.113015	+	0.113015i	−0.761353	−	0.648338i	$-0.775465\pi$
$347$	−253490.	+	253490.i	−0.113015	+	0.113015i	0.648338	+	0.761353i	$0.275465\pi$
$348$		0			0
$349$		−	1.91470e6i		−	0.841467i	−0.907184	−	0.420734i	$-0.861773\pi$
$349$		−	1.91470e6i		−	0.841467i	0.907184	−	0.420734i	$-0.138227\pi$
$350$		0			0
$351$			2.99218e6i			1.29634i
$352$		0			0
$353$	1.91118e6	−	1.91118e6i	0.816327	−	0.816327i	−0.169247	−	0.985574i	$-0.554133\pi$
$353$	1.91118e6	−	1.91118e6i	0.816327	−	0.816327i	0.985574	+	0.169247i	$0.0541335\pi$
$354$		0			0
$355$	1.82622e6	−	1.42616e6i	0.769098	−	0.600618i
$356$		0			0
$357$	2.57971e6	+	2.57971e6i	1.07127	+	1.07127i
$358$		0			0
$359$	−1.08922e6			−0.446046			−0.223023	−	0.974813i	$-0.571592\pi$
$359$	−1.08922e6			−0.446046			−0.223023	+	0.974813i	$0.571592\pi$
$360$		0			0
$361$	3.16055e6			1.27642
$362$		0			0
$363$	310832.	+	310832.i	0.123811	+	0.123811i
$364$		0			0
$365$	−2.95505e6	−	363481.i	−1.16100	−	0.142807i
$366$		0			0
$367$	2.58206e6	−	2.58206e6i	1.00069	−	1.00069i	0.000695182	−	1.00000i	$-0.499779\pi$
$367$	2.58206e6	−	2.58206e6i	1.00069	−	1.00069i	1.00000		0.000695182i	$-0.000221283\pi$
$368$		0			0
$369$			78118.7i			0.0298668i
$370$		0			0
$371$			229634.i			0.0866166i
$372$		0			0
$373$	−2.18094e6	+	2.18094e6i	−0.811656	+	0.811656i	−0.984882	−	0.173226i	$-0.944581\pi$
$373$	−2.18094e6	+	2.18094e6i	−0.811656	+	0.811656i	0.173226	+	0.984882i	$0.444581\pi$
$374$		0			0
$375$	−2.78852e6	−	1.07248e6i	−1.02399	−	0.393832i
$376$		0			0
$377$	−3.19667e6	−	3.19667e6i	−1.15836	−	1.15836i
$378$		0			0
$379$	5.02445e6			1.79676			0.898381	−	0.439218i	$-0.144744\pi$
$379$	5.02445e6			1.79676			0.898381	+	0.439218i	$0.144744\pi$
$380$		0			0
$381$	−5.66091e6			−1.99790
$382$		0			0
$383$	1.02036e6	+	1.02036e6i	0.355433	+	0.355433i	0.862126	−	0.506694i	$-0.169132\pi$
$383$	1.02036e6	+	1.02036e6i	0.355433	+	0.355433i	−0.506694	+	0.862126i	$0.669132\pi$
$384$		0			0
$385$	−312208.	+	2.53821e6i	−0.107347	+	0.872720i
$386$		0			0
$387$	−224115.	+	224115.i	−0.0760666	+	0.0760666i
$388$		0			0
$389$		−	2.41206e6i		−	0.808190i	−0.914717	−	0.404095i	$-0.867586\pi$
$389$		−	2.41206e6i		−	0.808190i	0.914717	−	0.404095i	$-0.132414\pi$
$390$		0			0
$391$			485325.i			0.160543i
$392$		0			0
$393$	1.31706e6	−	1.31706e6i	0.430154	−	0.430154i
$394$		0			0
$395$	1.36829e6	+	1.75210e6i	0.441249	+	0.565024i
$396$		0			0
$397$	−1.12093e6	−	1.12093e6i	−0.356947	−	0.356947i	0.505739	−	0.862686i	$-0.331220\pi$
$397$	−1.12093e6	−	1.12093e6i	−0.356947	−	0.356947i	−0.862686	+	0.505739i	$0.831220\pi$
$398$		0			0
$399$	−4.29826e6			−1.35164
$400$		0			0
$401$	−2.29941e6			−0.714095			−0.357047	−	0.934086i	$-0.616217\pi$
$401$	−2.29941e6			−0.714095			−0.357047	+	0.934086i	$0.616217\pi$
$402$		0			0
$403$	4.57840e6	+	4.57840e6i	1.40427	+	1.40427i
$404$		0			0
$405$	−2.36120e6	−	3.02355e6i	−0.715313	−	0.915965i
$406$		0			0
$407$	−2.00845e6	+	2.00845e6i	−0.601001	+	0.601001i
$408$		0			0
$409$			533417.i			0.157673i	0.996888	+	0.0788367i	$0.0251206\pi$
$409$			533417.i			0.157673i	−0.996888	+	0.0788367i	$0.974879\pi$
$410$		0			0
$411$		−	5.55419e6i		−	1.62187i
$412$		0			0
$413$	−190782.	+	190782.i	−0.0550378	+	0.0550378i
$414$		0			0
$415$	389590.	−	3.16731e6i	0.111042	−	0.902757i
$416$		0			0
$417$	−3.68341e6	−	3.68341e6i	−1.03731	−	1.03731i
$418$		0			0
$419$	−6.05004e6			−1.68354			−0.841769	−	0.539838i	$-0.818486\pi$
$419$	−6.05004e6			−1.68354			−0.841769	+	0.539838i	$0.818486\pi$
$420$		0			0
$421$	3.83846e6			1.05548			0.527742	−	0.849405i	$-0.323039\pi$
$421$	3.83846e6			1.05548			0.527742	+	0.849405i	$0.323039\pi$
$422$		0			0
$423$	−24240.8	−	24240.8i	−0.00658713	−	0.00658713i
$424$		0			0
$425$	5.39923e6	−	3.24102e6i	1.44997	−	0.870381i
$426$		0			0
$427$	−2.35720e6	+	2.35720e6i	−0.625643	+	0.625643i
$428$		0			0
$429$			6.68216e6i			1.75297i
$430$		0			0
$431$			6.93974e6i			1.79949i	0.436415	+	0.899746i	$0.356248\pi$
$431$			6.93974e6i			1.79949i	−0.436415	+	0.899746i	$0.643752\pi$
$432$		0			0
$433$	−1.39202e6	+	1.39202e6i	−0.356800	+	0.356800i	−0.862632	−	0.505832i	$-0.831186\pi$
$433$	−1.39202e6	+	1.39202e6i	−0.356800	+	0.356800i	0.505832	+	0.862632i	$0.331186\pi$
$434$		0			0
$435$	4.74466e6	+	583608.i	1.20221	+	0.147876i
$436$		0			0
$437$	−404319.	−	404319.i	−0.101279	−	0.101279i
$438$		0			0
$439$	−1.54253e6			−0.382008			−0.191004	−	0.981589i	$-0.561174\pi$
$439$	−1.54253e6			−0.382008			−0.191004	+	0.981589i	$0.561174\pi$
$440$		0			0
$441$	−277180.			−0.0678681
$442$		0			0
$443$	−4.00791e6	−	4.00791e6i	−0.970306	−	0.970306i	0.0292655	−	0.999572i	$-0.490683\pi$
$443$	−4.00791e6	−	4.00791e6i	−0.970306	−	0.970306i	−0.999572	+	0.0292655i	$0.990683\pi$
$444$		0			0
$445$	−2.12861e6	+	1.66232e6i	−0.509562	+	0.397937i
$446$		0			0
$447$	−3.71211e6	+	3.71211e6i	−0.878723	+	0.878723i
$448$		0			0
$449$			736658.i			0.172445i	0.996276	+	0.0862224i	$0.0274795\pi$
$449$			736658.i			0.172445i	−0.996276	+	0.0862224i	$0.972520\pi$
$450$		0			0
$451$		−	682158.i		−	0.157922i
$452$		0			0
$453$	455196.	−	455196.i	0.104220	−	0.104220i
$454$		0			0
$455$	−4.21682e6	+	3.29308e6i	−0.954897	+	0.745716i
$456$		0			0
$457$	821326.	+	821326.i	0.183961	+	0.183961i	0.793079	−	0.609119i	$-0.208477\pi$
$457$	821326.	+	821326.i	0.183961	+	0.183961i	−0.609119	+	0.793079i	$0.708477\pi$
$458$		0			0
$459$	6.66906e6			1.47752
$460$		0			0
$461$	1.76885e6			0.387649			0.193825	−	0.981036i	$-0.437911\pi$
$461$	1.76885e6			0.387649			0.193825	+	0.981036i	$0.437911\pi$
$462$		0			0
$463$	−1.41538e6	−	1.41538e6i	−0.306847	−	0.306847i	0.536839	−	0.843685i	$-0.319618\pi$
$463$	−1.41538e6	−	1.41538e6i	−0.306847	−	0.306847i	−0.843685	+	0.536839i	$0.819618\pi$
$464$		0			0
$465$	−6.79548e6	−	835866.i	−1.45743	−	0.179269i
$466$		0			0
$467$	−1.37109e6	+	1.37109e6i	−0.290921	+	0.290921i	−0.837444	−	0.546523i	$-0.815951\pi$
$467$	−1.37109e6	+	1.37109e6i	−0.290921	+	0.290921i	0.546523	+	0.837444i	$0.315951\pi$
$468$		0			0
$469$		−	5.68508e6i		−	1.19345i
$470$		0			0
$471$			5.34957e6i			1.11113i
$472$		0			0
$473$	1.95705e6	−	1.95705e6i	0.402206	−	0.402206i
$474$		0			0
$475$	−1.79798e6	+	7.19810e6i	−0.365638	+	1.46381i
$476$		0			0
$477$	−75909.9	−	75909.9i	−0.0152757	−	0.0152757i
$478$		0			0
$479$	−4.00023e6			−0.796610			−0.398305	−	0.917253i	$-0.630401\pi$
$479$	−4.00023e6			−0.796610			−0.398305	+	0.917253i	$0.630401\pi$
$480$		0			0
$481$	−5.94249e6			−1.17113
$482$		0			0
$483$	308316.	+	308316.i	0.0601351	+	0.0601351i
$484$		0			0
$485$	580650.	−	4.72060e6i	0.112088	−	0.911262i
$486$		0			0
$487$	−3.10730e6	+	3.10730e6i	−0.593691	+	0.593691i	−0.938626	−	0.344935i	$-0.887901\pi$
$487$	−3.10730e6	+	3.10730e6i	−0.593691	+	0.593691i	0.344935	+	0.938626i	$0.387901\pi$
$488$		0			0
$489$			8.19151e6i			1.54914i
$490$		0			0
$491$		−	1.03641e7i		−	1.94012i	−0.242871	−	0.970059i	$-0.578089\pi$
$491$		−	1.03641e7i		−	1.94012i	0.242871	−	0.970059i	$-0.421911\pi$
$492$		0			0
$493$	−7.12483e6	+	7.12483e6i	−1.32025	+	1.32025i
$494$		0			0
$495$	−735847.	−	942259.i	−0.134982	−	0.172845i
$496$		0			0
$497$	3.10266e6	+	3.10266e6i	0.563435	+	0.563435i
$498$		0			0
$499$	6.57165e6			1.18147			0.590735	−	0.806865i	$-0.298838\pi$
$499$	6.57165e6			1.18147			0.590735	+	0.806865i	$0.298838\pi$
$500$		0			0
$501$	4.64591e6			0.826944
$502$		0			0
$503$	2.25431e6	+	2.25431e6i	0.397278	+	0.397278i	0.877272	−	0.479994i	$-0.159361\pi$
$503$	2.25431e6	+	2.25431e6i	0.397278	+	0.397278i	−0.479994	+	0.877272i	$0.659361\pi$
$504$		0			0
$505$	−27598.9	−	35340.7i	−0.00481574	−	0.00616661i
$506$		0			0
$507$	−5.39529e6	+	5.39529e6i	−0.932169	+	0.932169i
$508$		0			0
$509$		−	5.08256e6i		−	0.869538i	−0.900542	−	0.434769i	$-0.856830\pi$
$509$		−	5.08256e6i		−	0.869538i	0.900542	−	0.434769i	$-0.143170\pi$
$510$		0			0
$511$		−	5.63805e6i		−	0.955161i
$512$		0			0
$513$	−5.55592e6	+	5.55592e6i	−0.932101	+	0.932101i
$514$		0			0
$515$	−119416.	+	970835.i	−0.0198401	+	0.161297i
$516$		0			0
$517$	211679.	+	211679.i	0.0348298	+	0.0348298i
$518$		0			0
$519$	8.66550e6			1.41213
$520$		0			0
$521$	−5.06706e6			−0.817827			−0.408914	−	0.912573i	$-0.634092\pi$
$521$	−5.06706e6			−0.817827			−0.408914	+	0.912573i	$0.634092\pi$
$522$		0			0
$523$	1.85174e6	+	1.85174e6i	0.296023	+	0.296023i	0.839454	−	0.543431i	$-0.182875\pi$
$523$	1.85174e6	+	1.85174e6i	0.296023	+	0.296023i	−0.543431	+	0.839454i	$0.682875\pi$
$524$		0			0
$525$	1.37106e6	−	5.48895e6i	0.217100	−	0.869143i
$526$		0			0
$527$	1.02045e7	−	1.02045e7i	1.60053	−	1.60053i
$528$		0			0
$529$		−	6.37834e6i		−	0.990988i
$530$		0			0
$531$		−	126133.i		−	0.0194130i
$532$		0			0
$533$	1.00916e6	−	1.00916e6i	0.153867	−	0.153867i
$534$		0			0
$535$	−1.12699e7	−	1.38624e6i	−1.70230	−	0.209389i
$536$		0			0
$537$	5.14238e6	+	5.14238e6i	0.769536	+	0.769536i
$538$		0			0
$539$	2.42043e6			0.358856
$540$		0			0
$541$	−1.24844e6			−0.183389			−0.0916946	−	0.995787i	$-0.529228\pi$
$541$	−1.24844e6			−0.183389			−0.0916946	+	0.995787i	$0.529228\pi$
$542$		0			0
$543$	8.45156e6	+	8.45156e6i	1.23009	+	1.23009i
$544$		0			0
$545$	9.97419e6	−	7.78923e6i	1.43842	−	1.12332i
$546$		0			0
$547$	−6.66763e6	+	6.66763e6i	−0.952803	+	0.952803i	−0.998935	−	0.0461324i	$-0.985310\pi$
$547$	−6.66763e6	+	6.66763e6i	−0.952803	+	0.952803i	0.0461324	+	0.998935i	$0.485310\pi$
$548$		0			0
$549$		−	1.55844e6i		−	0.220678i
$550$		0			0
$551$		−	1.18712e7i		−	1.66578i
$552$		0			0
$553$	−2.97675e6	+	2.97675e6i	−0.413932	+	0.413932i
$554$		0			0
$555$	4.95252e6	−	3.86761e6i	0.682486	−	0.532979i
$556$		0			0
$557$	−3.39131e6	−	3.39131e6i	−0.463158	−	0.463158i	0.436531	−	0.899689i	$-0.356207\pi$
$557$	−3.39131e6	−	3.39131e6i	−0.463158	−	0.463158i	−0.899689	+	0.436531i	$0.856207\pi$
$558$		0			0
$559$	5.79039e6			0.783752
$560$		0			0
$561$	1.48934e7			1.99796
$562$		0			0
$563$	−9.26687e6	−	9.26687e6i	−1.23215	−	1.23215i	−0.963138	−	0.269008i	$-0.913304\pi$
$563$	−9.26687e6	−	9.26687e6i	−1.23215	−	1.23215i	−0.269008	−	0.963138i	$-0.586696\pi$
$564$		0			0
$565$	5.56149e6	+	684081.i	0.732942	+	0.0901543i
$566$		0			0
$567$	5.13687e6	−	5.13687e6i	0.671029	−	0.671029i
$568$		0			0
$569$		−	5.78965e6i		−	0.749673i	−0.927091	−	0.374836i	$-0.877699\pi$
$569$		−	5.78965e6i		−	0.749673i	0.927091	−	0.374836i	$-0.122301\pi$
$570$		0			0
$571$		−	1.05138e7i		−	1.34948i	−0.738054	−	0.674742i	$-0.764255\pi$
$571$		−	1.05138e7i		−	1.34948i	0.738054	−	0.674742i	$-0.235745\pi$
$572$		0			0
$573$	2.31436e6	−	2.31436e6i	0.294472	−	0.294472i
$574$		0			0
$575$	645293.	−	387353.i	0.0813930	−	0.0488581i
$576$		0			0
$577$	−2.25024e6	−	2.25024e6i	−0.281378	−	0.281378i	0.552281	−	0.833658i	$-0.313758\pi$
$577$	−2.25024e6	−	2.25024e6i	−0.281378	−	0.281378i	−0.833658	+	0.552281i	$0.813758\pi$
$578$		0			0
$579$	−1.76442e6			−0.218729
$580$		0			0
$581$	6.04303e6			0.742701
$582$		0			0
$583$	662870.	+	662870.i	0.0807713	+	0.0807713i
$584$		0			0
$585$	305361.	−	2.48254e6i	0.0368913	−	0.299921i
$586$		0			0
$587$	−1.05778e6	+	1.05778e6i	−0.126707	+	0.126707i	−0.767617	−	0.640909i	$-0.778557\pi$
$587$	−1.05778e6	+	1.05778e6i	−0.126707	+	0.126707i	0.640909	+	0.767617i	$0.278557\pi$
$588$		0			0
$589$			1.70025e7i			2.01940i
$590$		0			0
$591$		−	7.93439e6i		−	0.934426i
$592$		0			0
$593$	−9.40420e6	+	9.40420e6i	−1.09821	+	1.09821i	−0.103590	+	0.994620i	$0.533033\pi$
$593$	−9.40420e6	+	9.40420e6i	−1.09821	+	1.09821i	−0.994620	+	0.103590i	$0.966967\pi$
$594$		0			0
$595$	7.33970e6	+	9.39856e6i	0.849936	+	1.08835i
$596$		0			0
$597$	4.30077e6	+	4.30077e6i	0.493868	+	0.493868i
$598$		0			0
$599$	1.44361e6			0.164393			0.0821963	−	0.996616i	$-0.473807\pi$
$599$	1.44361e6			0.164393			0.0821963	+	0.996616i	$0.473807\pi$
$600$		0			0
$601$	1.18811e7			1.34174			0.670871	−	0.741574i	$-0.265920\pi$
$601$	1.18811e7			1.34174			0.670871	+	0.741574i	$0.265920\pi$
$602$		0			0
$603$	1.87931e6	+	1.87931e6i	0.210478	+	0.210478i
$604$		0			0
$605$	884368.	+	1.13244e6i	0.0982301	+	0.125785i
$606$		0			0
$607$	7.53042e6	−	7.53042e6i	0.829559	−	0.829559i	−0.157897	−	0.987456i	$-0.550471\pi$
$607$	7.53042e6	−	7.53042e6i	0.829559	−	0.829559i	0.987456	+	0.157897i	$0.0504713\pi$
$608$		0			0
$609$			9.05249e6i			0.989065i
$610$		0			0
$611$			626303.i			0.0678705i
$612$		0			0
$613$	558618.	−	558618.i	0.0600432	−	0.0600432i	−0.676448	−	0.736491i	$-0.736481\pi$
$613$	558618.	−	558618.i	0.0600432	−	0.0600432i	0.736491	+	0.676448i	$0.236481\pi$
$614$		0			0
$615$	−184241.	+	1.49785e6i	−0.0196425	+	0.159691i
$616$		0			0
$617$	−1.59743e6	−	1.59743e6i	−0.168930	−	0.168930i	0.617579	−	0.786509i	$-0.288114\pi$
$617$	−1.59743e6	−	1.59743e6i	−0.168930	−	0.168930i	−0.786509	+	0.617579i	$0.788114\pi$
$618$		0			0
$619$	2.29227e6			0.240458			0.120229	−	0.992746i	$-0.461637\pi$
$619$	2.29227e6			0.240458			0.120229	+	0.992746i	$0.461637\pi$
$620$		0			0
$621$	797058.			0.0829394
$622$		0			0
$623$	−3.61642e6	−	3.61642e6i	−0.373301	−	0.373301i
$624$		0			0
$625$	−8.61858e6	−	4.59211e6i	−0.882543	−	0.470232i
$626$		0			0
$627$	−1.24075e7	+	1.24075e7i	−1.26042	+	1.26042i
$628$		0			0
$629$			1.32448e7i			1.33481i
$630$		0			0
$631$		−	565332.i		−	0.0565237i	−0.999601	−	0.0282618i	$-0.991003\pi$
$631$		−	565332.i		−	0.0565237i	0.999601	−	0.0282618i	$-0.00899722\pi$
$632$		0			0
$633$	7.69209e6	−	7.69209e6i	0.763018	−	0.763018i
$634$		0			0
$635$	−1.83652e7	−	2.25898e6i	−1.80743	−	0.222320i
$636$		0			0
$637$	3.58071e6	+	3.58071e6i	0.349639	+	0.349639i
$638$		0			0
$639$	−2.05129e6			−0.198735
$640$		0			0
$641$	1.12714e7			1.08351			0.541757	−	0.840535i	$-0.317759\pi$
$641$	1.12714e7			1.08351			0.541757	+	0.840535i	$0.317759\pi$
$642$		0			0
$643$	−1.13714e7	−	1.13714e7i	−1.08464	−	1.08464i	−0.996070	−	0.0885717i	$-0.971770\pi$
$643$	−1.13714e7	−	1.13714e7i	−1.08464	−	1.08464i	−0.0885717	−	0.996070i	$-0.528230\pi$
$644$		0			0
$645$	−4.82576e6	+	3.76862e6i	−0.456737	+	0.356684i
$646$		0			0
$647$	−4.10311e6	+	4.10311e6i	−0.385347	+	0.385347i	−0.873024	−	0.487677i	$-0.837844\pi$
$647$	−4.10311e6	+	4.10311e6i	−0.385347	+	0.385347i	0.487677	+	0.873024i	$0.337844\pi$
$648$		0			0
$649$			1.10144e6i			0.102647i
$650$		0			0
$651$		−	1.29653e7i		−	1.19903i
$652$		0			0
$653$	−3.43638e6	+	3.43638e6i	−0.315369	+	0.315369i	−0.846985	−	0.531617i	$-0.821585\pi$
$653$	−3.43638e6	+	3.43638e6i	−0.315369	+	0.315369i	0.531617	+	0.846985i	$0.321585\pi$
$654$		0			0
$655$	4.79840e6	−	3.74726e6i	0.437012	−	0.341280i
$656$		0			0
$657$	1.86377e6	+	1.86377e6i	0.168453	+	0.168453i
$658$		0			0
$659$	1.20483e7			1.08072			0.540358	−	0.841435i	$-0.318289\pi$
$659$	1.20483e7			1.08072			0.540358	+	0.841435i	$0.318289\pi$
$660$		0			0
$661$	−5.84415e6			−0.520257			−0.260128	−	0.965574i	$-0.583765\pi$
$661$	−5.84415e6			−0.520257			−0.260128	+	0.965574i	$0.583765\pi$
$662$		0			0
$663$	2.20328e7	+	2.20328e7i	1.94664	+	1.94664i
$664$		0			0
$665$	−1.39445e7	−	1.71522e6i	−1.22278	−	0.150406i
$666$		0			0
$667$	−851529.	+	851529.i	−0.0741114	+	0.0741114i
$668$		0			0
$669$			6.16315e6i			0.532399i
$670$		0			0
$671$			1.36088e7i			1.16684i
$672$		0			0
$673$	−1.62607e6	+	1.62607e6i	−0.138389	+	0.138389i	−0.772907	−	0.634519i	$-0.781198\pi$
$673$	−1.62607e6	+	1.62607e6i	−0.138389	+	0.138389i	0.634519	+	0.772907i	$0.281198\pi$
$674$		0			0
$675$	−5.32278e6	−	8.86725e6i	−0.449655	−	0.749082i
$676$		0			0
$677$	−6.06713e6	−	6.06713e6i	−0.508759	−	0.508759i	0.405387	−	0.914145i	$-0.367137\pi$
$677$	−6.06713e6	−	6.06713e6i	−0.508759	−	0.508759i	−0.914145	+	0.405387i	$0.867137\pi$
$678$		0			0
$679$	9.00660e6			0.749698
$680$		0			0
$681$	1.50837e7			1.24635
$682$		0			0
$683$	1.08238e7	+	1.08238e7i	0.887824	+	0.887824i	0.994314	−	0.106490i	$-0.0339612\pi$
$683$	1.08238e7	+	1.08238e7i	0.887824	+	0.887824i	−0.106490	+	0.994314i	$0.533961\pi$
$684$		0			0
$685$	2.21639e6	−	1.80190e7i	0.180476	−	1.46725i
$686$		0			0
$687$	1.89010e6	−	1.89010e6i	0.152789	−	0.152789i
$688$		0			0
$689$			1.96126e6i			0.157394i
$690$		0			0
$691$			4.66507e6i			0.371675i	0.982581	+	0.185837i	$0.0594997\pi$
$691$			4.66507e6i			0.371675i	−0.982581	+	0.185837i	$0.940500\pi$
$692$		0			0
$693$	1.60086e6	−	1.60086e6i	0.126625	−	0.126625i
$694$		0			0
$695$	−1.04799e7	−	1.34196e7i	−0.822993	−	1.05385i
$696$		0			0
$697$	−2.24926e6	−	2.24926e6i	−0.175371	−	0.175371i
$698$		0			0
$699$	−1.40309e7			−1.08615
$700$		0			0
$701$	1.20262e7			0.924346			0.462173	−	0.886790i	$-0.347070\pi$
$701$	1.20262e7			0.924346			0.462173	+	0.886790i	$0.347070\pi$
$702$		0			0
$703$	−1.10341e7	−	1.10341e7i	−0.842070	−	0.842070i
$704$		0			0
$705$	−407623.	−	521965.i	−0.0308877	−	0.0395521i
$706$		0			0
$707$	60042.3	−	60042.3i	0.00451761	−	0.00451761i
$708$		0			0
$709$			597301.i			0.0446249i	0.999751	+	0.0223125i	$0.00710287\pi$
$709$			597301.i			0.0446249i	−0.999751	+	0.0223125i	$0.992897\pi$
$710$		0			0
$711$		−	1.96804e6i		−	0.146003i
$712$		0			0
$713$	1.21959e6	−	1.21959e6i	0.0898444	−	0.0898444i
$714$		0			0
$715$	−2.66651e6	+	2.16784e7i	−0.195064	+	1.58585i
$716$		0			0
$717$	−1.09982e7	−	1.09982e7i	−0.798956	−	0.798956i
$718$		0			0
$719$	−5.82261e6			−0.420044			−0.210022	−	0.977697i	$-0.567354\pi$
$719$	−5.82261e6			−0.420044			−0.210022	+	0.977697i	$0.567354\pi$
$720$		0			0
$721$	−1.85229e6			−0.132700
$722$		0			0
$723$	1.15491e7	+	1.15491e7i	0.821678	+	0.821678i
$724$		0			0
$725$	1.51598e7	+	3.78670e6i	1.07115	+	0.267557i
$726$		0			0
$727$	1.33403e7	−	1.33403e7i	0.936115	−	0.936115i	−0.0619631	−	0.998078i	$-0.519736\pi$
$727$	1.33403e7	−	1.33403e7i	0.936115	−	0.936115i	0.998078	+	0.0619631i	$0.0197361\pi$
$728$		0			0
$729$		−	1.03576e7i		−	0.721838i
$730$		0			0
$731$		−	1.29058e7i		−	0.893288i
$732$		0			0
$733$	2.57748e6	−	2.57748e6i	0.177188	−	0.177188i	−0.612941	−	0.790129i	$-0.710014\pi$
$733$	2.57748e6	−	2.57748e6i	0.177188	−	0.177188i	0.790129	+	0.612941i	$0.210014\pi$
$734$		0			0
$735$	−5.31466e6	−	653720.i	−0.362875	−	0.0446348i
$736$		0			0
$737$	−1.64108e7	−	1.64108e7i	−1.11291	−	1.11291i
$738$		0			0
$739$	−1.82125e7			−1.22676			−0.613378	−	0.789790i	$-0.710190\pi$
$739$	−1.82125e7			−1.22676			−0.613378	+	0.789790i	$0.710190\pi$
$740$		0			0
$741$	−3.67106e7			−2.45610
$742$		0			0
$743$	1.20611e7	+	1.20611e7i	0.801524	+	0.801524i	0.983334	−	0.181810i	$-0.0581956\pi$
$743$	1.20611e7	+	1.20611e7i	0.801524	+	0.801524i	−0.181810	+	0.983334i	$0.558196\pi$
$744$		0			0
$745$	−1.35242e7	+	1.05616e7i	−0.892731	+	0.697169i
$746$		0			0
$747$	−1.99764e6	+	1.99764e6i	−0.130983	+	0.130983i
$748$		0			0
$749$		−	2.15023e7i		−	1.40049i
$750$		0			0
$751$			4.92692e6i			0.318769i	0.987217	+	0.159384i	$0.0509509\pi$
$751$			4.92692e6i			0.318769i	−0.987217	+	0.159384i	$0.949049\pi$
$752$		0			0
$753$	2.55444e6	−	2.55444e6i	0.164175	−	0.164175i
$754$		0			0
$755$	1.65840e6	−	1.29511e6i	0.105882	−	0.0826872i
$756$		0			0
$757$	−1.41039e7	−	1.41039e7i	−0.894542	−	0.894542i	0.100405	−	0.994947i	$-0.467986\pi$
$757$	−1.41039e7	−	1.41039e7i	−0.894542	−	0.894542i	−0.994947	+	0.100405i	$0.967986\pi$
$758$		0			0
$759$	1.77999e6			0.112154
$760$		0			0
$761$	−2.16920e7			−1.35781			−0.678904	−	0.734227i	$-0.737545\pi$
$761$	−2.16920e7			−1.35781			−0.678904	+	0.734227i	$0.737545\pi$
$762$		0			0
$763$	1.69457e7	+	1.69457e7i	1.05378	+	1.05378i
$764$		0			0
$765$	−5.53316e6	−	680597.i	−0.341837	−	0.0420471i
$766$		0			0
$767$	−1.62943e6	+	1.62943e6i	−0.100011	+	0.100011i
$768$		0			0
$769$		−	4.75723e6i		−	0.290094i	−0.989425	−	0.145047i	$-0.953667\pi$
$769$		−	4.75723e6i		−	0.290094i	0.989425	−	0.145047i	$-0.0463333\pi$
$770$		0			0
$771$			9.62748e6i			0.583279i
$772$		0			0
$773$	−9.08726e6	+	9.08726e6i	−0.546996	+	0.546996i	−0.925571	−	0.378575i	$-0.876414\pi$
$773$	−9.08726e6	+	9.08726e6i	−0.546996	+	0.546996i	0.378575	+	0.925571i	$0.376414\pi$
$774$		0			0
$775$	−2.17124e7	−	5.42346e6i	−1.29854	−	0.324356i
$776$		0			0
$777$	8.41411e6	+	8.41411e6i	0.499984	+	0.499984i
$778$		0			0
$779$	3.74766e6			0.221267
$780$		0			0
$781$	1.79125e7			1.05082
$782$		0			0
$783$	1.17012e7	+	1.17012e7i	0.682068	+	0.682068i
$784$		0			0
$785$	−2.13474e6	+	1.73552e7i	−0.123643	+	1.00520i
$786$		0			0
$787$	1.01144e7	−	1.01144e7i	0.582107	−	0.582107i	−0.353374	−	0.935482i	$-0.614966\pi$
$787$	1.01144e7	−	1.01144e7i	0.582107	−	0.582107i	0.935482	+	0.353374i	$0.114966\pi$
$788$		0			0
$789$			8.70130e6i			0.497613i
$790$		0			0
$791$			1.06109e7i			0.602994i
$792$		0			0
$793$	−2.01324e7	+	2.01324e7i	−1.13688	+	1.13688i
$794$		0			0
$795$	−1.27647e6	−	1.63453e6i	−0.0716295	−	0.0917223i
$796$		0			0
$797$	−1.51655e6	−	1.51655e6i	−0.0845687	−	0.0845687i	0.663557	−	0.748126i	$-0.269046\pi$
$797$	−1.51655e6	−	1.51655e6i	−0.0845687	−	0.0845687i	−0.748126	+	0.663557i	$0.769046\pi$
$798$		0			0
$799$	1.39592e6			0.0773560
$800$		0			0
$801$	2.39096e6			0.131671
$802$		0			0
$803$	−1.62750e7	−	1.62750e7i	−0.890702	−	0.890702i
$804$		0			0
$805$	877210.	+	1.12328e6i	0.0477105	+	0.0610937i
$806$		0			0
$807$	−2.00454e7	+	2.00454e7i	−1.08351	+	1.08351i
$808$		0			0
$809$			9.03499e6i			0.485351i	0.970107	+	0.242676i	$0.0780251\pi$
$809$			9.03499e6i			0.485351i	−0.970107	+	0.242676i	$0.921975\pi$
$810$		0			0
$811$			3.47086e7i			1.85304i	0.376242	+	0.926521i	$0.377216\pi$
$811$			3.47086e7i			1.85304i	−0.376242	+	0.926521i	$0.622784\pi$
$812$		0			0
$813$	2.59060e7	−	2.59060e7i	1.37459	−	1.37459i
$814$		0			0
$815$	−3.26881e6	+	2.65750e7i	−0.172384	+	1.40146i
$816$		0			0
$817$	1.07517e7	+	1.07517e7i	0.563535	+	0.563535i
$818$		0			0
$819$	4.73652e6			0.246746
$820$		0			0
$821$	2.73477e7			1.41600			0.707999	−	0.706213i	$-0.249598\pi$
$821$	2.73477e7			1.41600			0.707999	+	0.706213i	$0.249598\pi$
$822$		0			0
$823$	−2.05348e7	−	2.05348e7i	−1.05680	−	1.05680i	−0.998287	−	0.0585087i	$-0.981365\pi$
$823$	−2.05348e7	−	2.05348e7i	−1.05680	−	1.05680i	−0.0585087	−	0.998287i	$-0.518635\pi$
$824$		0			0
$825$	−1.18869e7	−	1.98024e7i	−0.608040	−	1.01294i
$826$		0			0
$827$	−1.36628e7	+	1.36628e7i	−0.694667	+	0.694667i	−0.963255	−	0.268588i	$-0.913443\pi$
$827$	−1.36628e7	+	1.36628e7i	−0.694667	+	0.694667i	0.268588	+	0.963255i	$0.413443\pi$
$828$		0			0
$829$			1.58116e7i			0.799079i	0.916716	+	0.399539i	$0.130830\pi$
$829$			1.58116e7i			0.799079i	−0.916716	+	0.399539i	$0.869170\pi$
$830$		0			0
$831$			2.15153e7i			1.08080i
$832$		0			0
$833$	7.98078e6	−	7.98078e6i	0.398504	−	0.398504i
$834$		0			0
$835$	1.50723e7	+	1.85394e6i	0.748107	+	0.0920197i
$836$		0			0
$837$	−1.67590e7	−	1.67590e7i	−0.826863	−	0.826863i
$838$		0			0
$839$	−3.86674e6			−0.189644			−0.0948222	−	0.995494i	$-0.530228\pi$
$839$	−3.86674e6			−0.189644			−0.0948222	+	0.995494i	$0.530228\pi$
$840$		0			0
$841$	−4.49070e6			−0.218939
$842$		0			0
$843$	−2.50228e7	−	2.50228e7i	−1.21274	−	1.21274i
$844$		0			0
$845$	−1.96565e7	+	1.53505e7i	−0.947029	+	0.739572i
$846$		0			0
$847$	−1.92397e6	+	1.92397e6i	−0.0921488	+	0.0921488i
$848$		0			0
$849$			538330.i			0.0256318i
$850$		0			0
$851$			1.58296e6i			0.0749283i
$852$		0			0
$853$	−1.08725e7	+	1.08725e7i	−0.511631	+	0.511631i	−0.915026	−	0.403395i	$-0.867830\pi$
$853$	−1.08725e7	+	1.08725e7i	−0.511631	+	0.511631i	0.403395	+	0.915026i	$0.367830\pi$
$854$		0			0
$855$	5.17661e6	−	4.04262e6i	0.242176	−	0.189124i
$856$		0			0
$857$	−8.24573e6	−	8.24573e6i	−0.383510	−	0.383510i	0.488855	−	0.872365i	$-0.337415\pi$
$857$	−8.24573e6	−	8.24573e6i	−0.383510	−	0.383510i	−0.872365	+	0.488855i	$0.837415\pi$
$858$		0			0
$859$	2.36231e7			1.09233			0.546164	−	0.837678i	$-0.316087\pi$
$859$	2.36231e7			1.09233			0.546164	+	0.837678i	$0.316087\pi$
$860$		0			0
$861$	−2.85780e6			−0.131378
$862$		0			0
$863$	−1.50486e7	−	1.50486e7i	−0.687811	−	0.687811i	0.273937	−	0.961748i	$-0.411674\pi$
$863$	−1.50486e7	−	1.50486e7i	−0.687811	−	0.687811i	−0.961748	+	0.273937i	$0.911674\pi$
$864$		0			0
$865$	2.81128e7	+	3.45796e6i	1.27751	+	0.157138i
$866$		0			0
$867$	3.19369e7	−	3.19369e7i	1.44293	−	1.44293i
$868$		0			0
$869$			1.71856e7i			0.771996i
$870$		0			0
$871$		−	4.85552e7i		−	2.16866i
$872$		0			0
$873$	−2.97731e6	+	2.97731e6i	−0.132217	+	0.132217i
$874$		0			0
$875$	6.63838e6	−	1.72602e7i	0.293118	−	0.762125i
$876$		0			0
$877$	2.37339e7	+	2.37339e7i	1.04201	+	1.04201i	0.999078	+	0.0429276i	$0.0136685\pi$
$877$	2.37339e7	+	2.37339e7i	1.04201	+	1.04201i	0.0429276	+	0.999078i	$0.486332\pi$
$878$		0			0
$879$	−4.76175e7			−2.07871
$880$		0			0
$881$	2.33399e7			1.01311			0.506557	−	0.862206i	$-0.330918\pi$
$881$	2.33399e7			1.01311			0.506557	+	0.862206i	$0.330918\pi$
$882$		0			0
$883$	1.05710e6	+	1.05710e6i	0.0456264	+	0.0456264i	0.729552	−	0.683925i	$-0.239729\pi$
$883$	1.05710e6	+	1.05710e6i	0.0456264	+	0.0456264i	−0.683925	+	0.729552i	$0.739729\pi$
$884$		0			0
$885$	297481.	−	2.41848e6i	0.0127674	−	0.103797i
$886$		0			0
$887$	−6.50661e6	+	6.50661e6i	−0.277681	+	0.277681i	−0.832182	−	0.554502i	$-0.812909\pi$
$887$	−6.50661e6	+	6.50661e6i	−0.277681	+	0.277681i	0.554502	+	0.832182i	$0.312909\pi$
$888$		0			0
$889$		−	3.50396e7i		−	1.48698i
$890$		0			0
$891$		−	2.96566e7i		−	1.25149i
$892$		0			0
$893$	−1.16293e6	+	1.16293e6i	−0.0488004	+	0.0488004i
$894$		0			0
$895$	1.46309e7	+	1.87351e7i	0.610541	+	0.781804i
$896$		0			0
$897$	2.63327e6	+	2.63327e6i	0.109273	+	0.109273i
$898$		0			0
$899$	3.58086e7			1.47771
$900$		0			0
$901$	4.37131e6			0.179391
$902$		0			0
$903$	−8.19876e6	−	8.19876e6i	−0.334602	−	0.334602i
$904$		0			0
$905$	2.40461e7	+	3.07913e7i	0.975940	+	1.24970i
$906$		0			0
$907$	7.42036e6	−	7.42036e6i	0.299507	−	0.299507i	−0.541314	−	0.840821i	$-0.682073\pi$
$907$	7.42036e6	−	7.42036e6i	0.299507	−	0.299507i	0.840821	+	0.541314i	$0.182073\pi$
$908$		0			0
$909$			39696.3i			0.00159346i
$910$		0			0
$911$			3.87110e7i			1.54539i	0.634776	+	0.772696i	$0.281092\pi$
$911$			3.87110e7i			1.54539i	−0.634776	+	0.772696i	$0.718908\pi$
$912$		0			0
$913$	1.74440e7	−	1.74440e7i	0.692580	−	0.692580i
$914$		0			0
$915$	3.67552e6	−	2.98815e7i	0.145133	−	1.17991i
$916$		0			0
$917$	8.15228e6	+	8.15228e6i	0.320151	+	0.320151i
$918$		0			0
$919$	−1.58482e7			−0.618999			−0.309500	−	0.950900i	$-0.600162\pi$
$919$	−1.58482e7			−0.618999			−0.309500	+	0.950900i	$0.600162\pi$
$920$		0			0
$921$	−3.48241e7			−1.35279
$922$		0			0
$923$	2.64993e7	+	2.64993e7i	1.02383	+	1.02383i
$924$		0			0
$925$	1.76104e7	−	1.05711e7i	0.676729	−	0.406223i
$926$		0			0
$927$	612310.	−	612310.i	0.0234030	−	0.0234030i
$928$		0			0
$929$		−	3.37736e7i		−	1.28392i	−0.766738	−	0.641960i	$-0.778122\pi$
$929$		−	3.37736e7i		−	1.28392i	0.766738	−	0.641960i	$-0.221878\pi$
$930$		0			0
$931$			1.32974e7i			0.502797i
$932$		0			0
$933$	−1.87636e7	+	1.87636e7i	−0.705686	+	0.705686i
$934$		0			0
$935$	4.83173e7	+	5.94319e6i	1.80748	+	0.222326i
$936$		0			0
$937$	1.44062e7	+	1.44062e7i	0.536045	+	0.536045i	0.922365	−	0.386320i	$-0.126254\pi$
$937$	1.44062e7	+	1.44062e7i	0.536045	+	0.536045i	−0.386320	+	0.922365i	$0.626254\pi$
$938$		0			0
$939$	−2.63386e7			−0.974829
$940$		0			0
$941$	−4.43127e7			−1.63138			−0.815688	−	0.578493i	$-0.803641\pi$
$941$	−4.43127e7			−1.63138			−0.815688	+	0.578493i	$0.803641\pi$
$942$		0			0
$943$	−268821.	−	268821.i	−0.00984429	−	0.00984429i
$944$		0			0
$945$	1.54354e7	−	1.20541e7i	0.562263	−	0.439093i
$946$		0			0
$947$	2.80551e7	−	2.80551e7i	1.01657	−	1.01657i	0.0167087	−	0.999860i	$-0.494681\pi$
$947$	2.80551e7	−	2.80551e7i	1.01657	−	1.01657i	0.999860	−	0.0167087i	$-0.00531878\pi$
$948$		0			0
$949$		−	4.81536e7i		−	1.73565i
$950$		0			0
$951$		−	9.88472e6i		−	0.354416i
$952$		0			0
$953$	1.45210e7	−	1.45210e7i	0.517921	−	0.517921i	−0.399021	−	0.916942i	$-0.630650\pi$
$953$	1.45210e7	−	1.45210e7i	0.517921	−	0.517921i	0.916942	+	0.399021i	$0.130650\pi$
$954$		0			0
$955$	8.43182e6	−	6.58474e6i	0.299167	−	0.233631i
$956$		0			0
$957$	2.61313e7	+	2.61313e7i	0.922318	+	0.922318i
$958$		0			0
$959$	3.43790e7			1.20711
$960$		0			0
$961$	−2.26573e7			−0.791406
$962$		0			0
$963$	7.10800e6	+	7.10800e6i	0.246991	+	0.246991i
$964$		0			0
$965$	−5.72416e6	−	704090.i	−0.197876	−	0.0243394i
$966$		0			0
$967$	−1.66187e6	+	1.66187e6i	−0.0571519	+	0.0571519i	−0.735105	−	0.677953i	$-0.762867\pi$
$967$	−1.66187e6	+	1.66187e6i	−0.0571519	+	0.0571519i	0.677953	+	0.735105i	$0.262867\pi$
$968$		0			0
$969$			8.18217e7i			2.79936i
$970$		0			0
$971$		−	4.51619e6i		−	0.153718i	−0.997042	−	0.0768589i	$-0.975511\pi$
$971$		−	4.51619e6i		−	0.153718i	0.997042	−	0.0768589i	$-0.0244891\pi$
$972$		0			0
$973$	2.27994e7	−	2.27994e7i	0.772043	−	0.772043i
$974$		0			0
$975$	1.17100e7	−	4.68802e7i	0.394498	−	1.57935i
$976$		0			0
$977$	2.43956e7	+	2.43956e7i	0.817663	+	0.817663i	0.985769	−	0.168106i	$-0.0537651\pi$
$977$	2.43956e7	+	2.43956e7i	0.817663	+	0.817663i	−0.168106	+	0.985769i	$0.553765\pi$
$978$		0			0
$979$	−2.08786e7			−0.696218
$980$		0			0
$981$	−1.12035e7			−0.371689
$982$		0			0
$983$	−1.60097e7	−	1.60097e7i	−0.528445	−	0.528445i	0.391664	−	0.920108i	$-0.371900\pi$
$983$	−1.60097e7	−	1.60097e7i	−0.528445	−	0.528445i	−0.920108	+	0.391664i	$0.871900\pi$
$984$		0			0
$985$	3.16621e6	−	2.57409e7i	0.103980	−	0.845343i
$986$		0			0
$987$	886797.	−	886797.i	0.0289755	−	0.0289755i
$988$		0			0
$989$		−	1.54244e6i		−	0.0501440i
$990$		0			0
$991$		−	4.21742e7i		−	1.36415i	−0.731281	−	0.682076i	$-0.761077\pi$
$991$		−	4.21742e7i		−	1.36415i	0.731281	−	0.682076i	$-0.238923\pi$
$992$		0			0
$993$	2.85465e7	−	2.85465e7i	0.918713	−	0.918713i
$994$		0			0
$995$	1.22364e7	+	1.56689e7i	0.391829	+	0.501741i
$996$		0			0
$997$	1.45114e7	+	1.45114e7i	0.462350	+	0.462350i	0.899425	−	0.437075i	$-0.143986\pi$
$997$	1.45114e7	+	1.45114e7i	0.462350	+	0.462350i	−0.437075	+	0.899425i	$0.643986\pi$
$998$		0			0
$999$	2.17522e7			0.689586

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.6.n.d.127.3	yes	16
4.3	odd	2		160.6.n.c.127.6	yes	16
5.3	odd	4		160.6.n.c.63.6	✓	16
20.3	even	4	inner	160.6.n.d.63.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.6.n.c.63.6	✓	16	5.3	odd	4
160.6.n.c.127.6	yes	16	4.3	odd	2
160.6.n.d.63.3	yes	16	20.3	even	4	inner
160.6.n.d.127.3	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	160.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-12.0932 - 12.0932i) q^{3} +(-34.4070 - 44.0586i) q^{5} +(74.8536 - 74.8536i) q^{7} +49.4886i q^{9} +O(q^{10})\)	\(q+(-12.0932 - 12.0932i) q^{3} +(-34.4070 - 44.0586i) q^{5} +(74.8536 - 74.8536i) q^{7} +49.4886i q^{9} -432.151i q^{11} +(639.311 - 639.311i) q^{13} +(-116.717 + 948.896i) q^{15} +(-1424.91 - 1424.91i) q^{17} +2374.16 q^{19} -1810.43 q^{21} +(-170.300 - 170.300i) q^{23} +(-757.313 + 3031.85i) q^{25} +(-2340.16 + 2340.16i) q^{27} -5000.18i q^{29} +7161.45i q^{31} +(-5226.06 + 5226.06i) q^{33} +(-5873.43 - 722.451i) q^{35} +(-4647.57 - 4647.57i) q^{37} -15462.6 q^{39} +1578.52 q^{41} +(4528.62 + 4528.62i) q^{43} +(2180.40 - 1702.76i) q^{45} +(-489.826 + 489.826i) q^{47} +5600.89i q^{49} +34463.4i q^{51} +(-1533.89 + 1533.89i) q^{53} +(-19039.9 + 14869.0i) q^{55} +(-28711.1 - 28711.1i) q^{57} -2548.73 q^{59} -31490.8 q^{61} +(3704.40 + 3704.40i) q^{63} +(-50163.9 - 6170.32i) q^{65} +(37974.7 - 37974.7i) q^{67} +4118.92i q^{69} +41449.8i q^{71} +(37660.5 - 37660.5i) q^{73} +(45822.9 - 27506.3i) q^{75} +(-32348.0 - 32348.0i) q^{77} -39767.6 q^{79} +68625.6 q^{81} +(40365.6 + 40365.6i) q^{83} +(-13752.6 + 111807. i) q^{85} +(-60468.0 + 60468.0i) q^{87} -48313.3i q^{89} -95709.4i q^{91} +(86604.6 - 86604.6i) q^{93} +(-81687.9 - 104602. i) q^{95} +(60161.4 + 60161.4i) q^{97} +21386.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 10 q^{3} - 42 q^{5} - 86 q^{7}+O(q^{10}) \) 16 * q + 10 * q^3 - 42 * q^5 - 86 * q^7	\( 16 q + 10 q^{3} - 42 q^{5} - 86 q^{7} + 536 q^{13} - 698 q^{15} - 1828 q^{17} + 2512 q^{19} - 4284 q^{21} - 7642 q^{23} + 9140 q^{25} - 12272 q^{27} + 11876 q^{33} + 10518 q^{35} - 7620 q^{37} + 11244 q^{39} - 21284 q^{41} + 20002 q^{43} + 686 q^{45} + 25298 q^{47} + 12852 q^{53} - 10584 q^{55} + 55848 q^{57} - 142704 q^{59} - 20564 q^{61} - 115282 q^{63} - 38256 q^{65} - 10506 q^{67} + 15432 q^{73} + 256226 q^{75} + 133852 q^{77} - 159344 q^{79} - 236116 q^{81} - 61222 q^{83} + 7056 q^{85} + 162176 q^{87} + 122180 q^{93} + 267512 q^{95} - 17344 q^{97} + 107332 q^{99}+O(q^{100}) \) 16 * q + 10 * q^3 - 42 * q^5 - 86 * q^7 + 536 * q^13 - 698 * q^15 - 1828 * q^17 + 2512 * q^19 - 4284 * q^21 - 7642 * q^23 + 9140 * q^25 - 12272 * q^27 + 11876 * q^33 + 10518 * q^35 - 7620 * q^37 + 11244 * q^39 - 21284 * q^41 + 20002 * q^43 + 686 * q^45 + 25298 * q^47 + 12852 * q^53 - 10584 * q^55 + 55848 * q^57 - 142704 * q^59 - 20564 * q^61 - 115282 * q^63 - 38256 * q^65 - 10506 * q^67 + 15432 * q^73 + 256226 * q^75 + 133852 * q^77 - 159344 * q^79 - 236116 * q^81 - 61222 * q^83 + 7056 * q^85 + 162176 * q^87 + 122180 * q^93 + 267512 * q^95 - 17344 * q^97 + 107332 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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