LMFDB - Embedded newform 160.6.n.d.63.3

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			63.3
Root			$-13.0932i$ of defining polynomial
Character	$\chi$	$=$	160.63
Dual form			160.6.n.d.127.3

$q$-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 $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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	−0.979110	−	0.203334i	$-0.934822\pi$
$3$	−12.0932	+	12.0932i	−0.775776	+	0.775776i	0.203334	+	0.979110i	$0.434822\pi$
$4$		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	0.934183	−	0.356795i	$-0.116131\pi$
$7$	74.8536	+	74.8536i	0.577388	+	0.577388i	−0.356795	+	0.934183i	$0.616131\pi$
$8$		0			0
$9$		−	49.4886i		−	0.203657i
$10$		0			0
$11$			432.151i			1.07685i	0.842675	+	0.538423i	$0.180980\pi$
$11$			432.151i			1.07685i	−0.842675	+	0.538423i	$0.819020\pi$
$12$		0			0
$13$	639.311	+	639.311i	1.04919	+	1.04919i	0.998726	+	0.0504631i	$0.0160697\pi$
$13$	639.311	+	639.311i	1.04919	+	1.04919i	0.0504631	+	0.998726i	$0.483930\pi$
$14$		0			0
$15$	−116.717	−	948.896i	−0.133939	−	1.08891i
$16$		0			0
$17$	−1424.91	+	1424.91i	−1.19582	+	1.19582i	−0.220416	+	0.975406i	$0.570741\pi$
$17$	−1424.91	+	1424.91i	−1.19582	+	1.19582i	−0.975406	+	0.220416i	$0.929259\pi$
$18$		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	−0.739873	−	0.672747i	$-0.765114\pi$
$23$	−170.300	+	170.300i	−0.0671265	+	0.0671265i	0.672747	+	0.739873i	$0.265114\pi$
$24$		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	$0.186146\pi$
$29$			5000.18i			1.10406i	−0.833826	+	0.552028i	$0.813854\pi$
$30$		0			0
$31$		−	7161.45i		−	1.33843i	−0.743067	−	0.669217i	$-0.766630\pi$
$31$		−	7161.45i		−	1.33843i	0.743067	−	0.669217i	$-0.233370\pi$
$32$		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	−0.928770	−	0.370657i	$-0.879133\pi$
$37$	−4647.57	+	4647.57i	−0.558113	+	0.558113i	0.370657	+	0.928770i	$0.379133\pi$
$38$		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	−0.495248	−	0.868752i	$-0.664923\pi$
$43$	4528.62	−	4528.62i	0.373504	−	0.373504i	0.868752	+	0.495248i	$0.164923\pi$
$44$		0			0
$45$	2180.40	+	1702.76i	0.160511	+	0.125349i
$46$		0			0
$47$	−489.826	−	489.826i	−0.0323443	−	0.0323443i	0.690750	−	0.723094i	$-0.257281\pi$
$47$	−489.826	−	489.826i	−0.0323443	−	0.0323443i	−0.723094	+	0.690750i	$0.757281\pi$
$48$		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	0.668608	−	0.743615i	$-0.266891\pi$
$53$	−1533.89	−	1533.89i	−0.0750073	−	0.0750073i	−0.743615	+	0.668608i	$0.766891\pi$
$54$		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	0.999419	+	0.0340720i	$0.0108476\pi$
$67$	37974.7	+	37974.7i	1.03349	+	1.03349i	0.0340720	+	0.999419i	$0.489152\pi$
$68$		0			0
$69$		−	4118.92i		−	0.104150i
$70$		0			0
$71$		−	41449.8i		−	0.975835i	−0.872890	−	0.487917i	$-0.837757\pi$
$71$		−	41449.8i		−	0.975835i	0.872890	−	0.487917i	$-0.162243\pi$
$72$		0			0
$73$	37660.5	+	37660.5i	0.827140	+	0.827140i	0.987120	−	0.159980i	$-0.0511430\pi$
$73$	37660.5	+	37660.5i	0.827140	+	0.827140i	−0.159980	+	0.987120i	$0.551143\pi$
$74$		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	−0.308174	−	0.951330i	$-0.599718\pi$
$83$	40365.6	−	40365.6i	0.643156	−	0.643156i	0.951330	+	0.308174i	$0.0997178\pi$
$84$		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	$0.104781\pi$
$89$			48313.3i			0.646535i	−0.946308	+	0.323267i	$0.895219\pi$
$90$		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	−0.303588	−	0.952803i	$-0.598185\pi$
$97$	60161.4	−	60161.4i	0.649216	−	0.649216i	0.952803	+	0.303588i	$0.0981846\pi$
$98$		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	−0.762226	−	0.647312i	$-0.775893\pi$
$103$	−12372.7	+	12372.7i	−0.114914	+	0.114914i	0.647312	+	0.762226i	$0.275893\pi$
$104$		0			0
$105$	62291.6	−	79765.0i	0.551386	−	0.706056i
$106$		0			0
$107$	143629.	+	143629.i	1.21278	+	1.21278i	0.970108	+	0.242675i	$0.0780248\pi$
$107$	143629.	+	143629.i	1.21278	+	1.21278i	0.242675	+	0.970108i	$0.421975\pi$
$108$		0			0
$109$		−	226385.i		−	1.82508i	−0.408992	−	0.912538i	$-0.634120\pi$
$109$		−	226385.i		−	1.82508i	0.408992	−	0.912538i	$-0.365880\pi$
$110$		0			0
$111$		−	112408.i		−	0.865941i
$112$		0			0
$113$	−70878.0	−	70878.0i	−0.522174	−	0.522174i	0.396053	−	0.918228i	$-0.370380\pi$
$113$	−70878.0	−	70878.0i	−0.522174	−	0.522174i	−0.918228	+	0.396053i	$0.870380\pi$
$114$		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	0.936194	+	0.351484i	$0.114323\pi$
$127$	234054.	+	234054.i	1.28768	+	1.28768i	0.351484	+	0.936194i	$0.385677\pi$
$128$		0			0
$129$			109531.i			0.579510i
$130$		0			0
$131$		−	108910.i		−	0.554483i	−0.960800	−	0.277241i	$-0.910580\pi$
$131$		−	108910.i		−	0.554483i	0.960800	−	0.277241i	$-0.0894202\pi$
$132$		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	0.0463976	−	0.998923i	$-0.485226\pi$
$137$	229642.	−	229642.i	1.04532	−	1.04532i	0.998923	−	0.0463976i	$-0.0147741\pi$
$138$		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	$0.191645\pi$
$149$			306960.i			1.13270i	−0.824164	+	0.566351i	$0.808355\pi$
$150$		0			0
$151$		−	37640.8i		−	0.134343i	−0.997741	−	0.0671717i	$-0.978602\pi$
$151$		−	37640.8i		−	0.134343i	0.997741	−	0.0671717i	$-0.0213975\pi$
$152$		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	−0.967813	−	0.251669i	$-0.919020\pi$
$157$	−221182.	+	221182.i	−0.716144	+	0.716144i	0.251669	+	0.967813i	$0.419020\pi$
$158$		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	−0.999999	−	0.00155132i	$-0.999506\pi$
$163$	−338684.	+	338684.i	−0.998447	+	0.998447i	0.00155132	+	0.999999i	$0.499506\pi$
$164$		0			0
$165$	410066.	−	50439.5i	1.17258	−	0.144232i
$166$		0			0
$167$	−192088.	−	192088.i	−0.532979	−	0.532979i	0.388479	−	0.921458i	$-0.373001\pi$
$167$	−192088.	−	192088.i	−0.532979	−	0.532979i	−0.921458	+	0.388479i	$0.873001\pi$
$168$		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	0.0861412	−	0.996283i	$-0.472546\pi$
$173$	−358281.	−	358281.i	−0.910142	−	0.910142i	−0.996283	+	0.0861412i	$0.972546\pi$
$174$		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	$-0.939219\pi$
$191$		−	191378.i		−	0.379584i	0.981824	−	0.189792i	$-0.0607813\pi$
$192$		0			0
$193$	72951.2	+	72951.2i	0.140974	+	0.140974i	0.774072	−	0.633098i	$-0.218217\pi$
$193$	72951.2	+	72951.2i	0.140974	+	0.140974i	−0.633098	+	0.774072i	$0.718217\pi$
$194$		0			0
$195$	532021.	−	681258.i	1.00194	−	1.28300i
$196$		0			0
$197$	328053.	−	328053.i	0.602252	−	0.602252i	−0.338657	−	0.940910i	$-0.609973\pi$
$197$	328053.	−	328053.i	0.602252	−	0.602252i	0.940910	+	0.338657i	$0.109973\pi$
$198$		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	$-0.836347\pi$
$211$		−	636070.i		−	0.983555i	0.870721	−	0.491778i	$-0.163653\pi$
$212$		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	−0.857546	−	0.514407i	$-0.828012\pi$
$223$	−254820.	+	254820.i	−0.343140	+	0.343140i	0.514407	+	0.857546i	$0.328012\pi$
$224$		0			0
$225$	−150042.	+	37478.3i	−0.197586	+	0.0493542i
$226$		0			0
$227$	−623645.	−	623645.i	−0.803291	−	0.803291i	0.180318	−	0.983608i	$-0.442287\pi$
$227$	−623645.	−	623645.i	−0.803291	−	0.803291i	−0.983608	+	0.180318i	$0.942287\pi$
$228$		0			0
$229$		−	156295.i		−	0.196950i	−0.995140	−	0.0984749i	$-0.968604\pi$
$229$		−	156295.i		−	0.196950i	0.995140	−	0.0984749i	$-0.0313964\pi$
$230$		0			0
$231$		−	782379.i		−	0.964689i
$232$		0			0
$233$	580116.	+	580116.i	0.700044	+	0.700044i	0.964420	−	0.264376i	$-0.0851660\pi$
$233$	580116.	+	580116.i	0.700044	+	0.700044i	−0.264376	+	0.964420i	$0.585166\pi$
$234$		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	$-0.966255\pi$
$251$		−	211230.i		−	0.211627i	0.994386	−	0.105814i	$-0.0337447\pi$
$252$		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	−0.869632	−	0.493700i	$-0.835644\pi$
$257$	−398055.	+	398055.i	−0.375933	+	0.375933i	0.493700	+	0.869632i	$0.335644\pi$
$258$		0			0
$259$	−695775.			−0.644495
$260$		0			0
$261$	247452.			0.224848
$262$		0			0
$263$	−359761.	+	359761.i	−0.320719	+	0.320719i	−0.849043	−	0.528324i	$-0.822821\pi$
$263$	−359761.	+	359761.i	−0.320719	+	0.320719i	0.528324	+	0.849043i	$0.322821\pi$
$264$		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	$0.246077\pi$
$269$			1.65759e6i			1.39668i	−0.715768	+	0.698338i	$0.753923\pi$
$270$		0			0
$271$		−	2.14221e6i		−	1.77189i	−0.463786	−	0.885947i	$-0.653509\pi$
$271$		−	2.14221e6i		−	1.77189i	0.463786	−	0.885947i	$-0.346491\pi$
$272$		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	−0.963674	−	0.267081i	$-0.913941\pi$
$277$	−889567.	+	889567.i	−0.696593	+	0.696593i	0.267081	+	0.963674i	$0.413941\pi$
$278$		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	−0.715319	−	0.698798i	$-0.753718\pi$
$283$	−22257.7	+	22257.7i	−0.0165201	+	0.0165201i	0.698798	+	0.715319i	$0.253718\pi$
$284$		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	0.896285	+	0.443478i	$0.146256\pi$
$293$	1.96878e6	+	1.96878e6i	1.33976	+	1.33976i	0.443478	+	0.896285i	$0.353744\pi$
$294$		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	0.992679	−	0.120782i	$-0.0385403\pi$
$307$	1.43983e6	+	1.43983e6i	0.871897	+	0.871897i	−0.120782	+	0.992679i	$0.538540\pi$
$308$		0			0
$309$		−	299251.i		−	0.178295i
$310$		0			0
$311$			1.55159e6i			0.909652i	0.890580	+	0.454826i	$0.150299\pi$
$311$			1.55159e6i			0.909652i	−0.890580	+	0.454826i	$0.849701\pi$
$312$		0			0
$313$	1.08899e6	+	1.08899e6i	0.628293	+	0.628293i	0.947638	−	0.319346i	$-0.103463\pi$
$313$	1.08899e6	+	1.08899e6i	0.628293	+	0.628293i	−0.319346	+	0.947638i	$0.603463\pi$
$314$		0			0
$315$	35753.1	+	290668.i	0.0203019	+	0.165052i
$316$		0			0
$317$	408691.	−	408691.i	0.228427	−	0.228427i	−0.583609	−	0.812035i	$-0.698360\pi$
$317$	408691.	−	408691.i	0.228427	−	0.228427i	0.812035	+	0.583609i	$0.198360\pi$
$318$		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	$-0.798289\pi$
$331$		−	2.36055e6i		−	1.18425i	0.805846	−	0.592125i	$-0.201711\pi$
$332$		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	−0.634410	−	0.772997i	$-0.718757\pi$
$337$	288933.	−	288933.i	0.138587	−	0.138587i	0.772997	+	0.634410i	$0.218757\pi$
$338$		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	0.648338	−	0.761353i	$-0.275465\pi$
$347$	−253490.	−	253490.i	−0.113015	−	0.113015i	−0.761353	+	0.648338i	$0.775465\pi$
$348$		0			0
$349$			1.91470e6i			0.841467i	0.907184	+	0.420734i	$0.138227\pi$
$349$			1.91470e6i			0.841467i	−0.907184	+	0.420734i	$0.861773\pi$
$350$		0			0
$351$		−	2.99218e6i		−	1.29634i
$352$		0			0
$353$	1.91118e6	+	1.91118e6i	0.816327	+	0.816327i	0.985574	−	0.169247i	$-0.0541335\pi$
$353$	1.91118e6	+	1.91118e6i	0.816327	+	0.816327i	−0.169247	+	0.985574i	$0.554133\pi$
$354$		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	1.00000		0.000695182i	$0.000221283\pi$
$367$	2.58206e6	+	2.58206e6i	1.00069	+	1.00069i	0.000695182		1.00000i	$0.499779\pi$
$368$		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	0.173226	−	0.984882i	$-0.444581\pi$
$373$	−2.18094e6	−	2.18094e6i	−0.811656	−	0.811656i	−0.984882	+	0.173226i	$0.944581\pi$
$374$		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	−0.506694	−	0.862126i	$-0.669132\pi$
$383$	1.02036e6	−	1.02036e6i	0.355433	−	0.355433i	0.862126	+	0.506694i	$0.169132\pi$
$384$		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	$0.132414\pi$
$389$			2.41206e6i			0.808190i	−0.914717	+	0.404095i	$0.867586\pi$
$390$		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	−0.862686	−	0.505739i	$-0.831220\pi$
$397$	−1.12093e6	+	1.12093e6i	−0.356947	+	0.356947i	0.505739	+	0.862686i	$0.331220\pi$
$398$		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	$-0.974879\pi$
$409$		−	533417.i		−	0.157673i	0.996888	−	0.0788367i	$-0.0251206\pi$
$410$		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	$-0.643752\pi$
$431$		−	6.93974e6i		−	1.79949i	0.436415	−	0.899746i	$-0.356248\pi$
$432$		0			0
$433$	−1.39202e6	−	1.39202e6i	−0.356800	−	0.356800i	0.505832	−	0.862632i	$-0.331186\pi$
$433$	−1.39202e6	−	1.39202e6i	−0.356800	−	0.356800i	−0.862632	+	0.505832i	$0.831186\pi$
$434$		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	−0.999572	−	0.0292655i	$-0.990683\pi$
$443$	−4.00791e6	+	4.00791e6i	−0.970306	+	0.970306i	0.0292655	+	0.999572i	$0.490683\pi$
$444$		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	$-0.972520\pi$
$449$		−	736658.i		−	0.172445i	0.996276	−	0.0862224i	$-0.0274795\pi$
$450$		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	−0.609119	−	0.793079i	$-0.708477\pi$
$457$	821326.	−	821326.i	0.183961	−	0.183961i	0.793079	+	0.609119i	$0.208477\pi$
$458$		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	−0.843685	−	0.536839i	$-0.819618\pi$
$463$	−1.41538e6	+	1.41538e6i	−0.306847	+	0.306847i	0.536839	+	0.843685i	$0.319618\pi$
$464$		0			0
$465$	−6.79548e6	+	835866.i	−1.45743	+	0.179269i
$466$		0			0
$467$	−1.37109e6	−	1.37109e6i	−0.290921	−	0.290921i	0.546523	−	0.837444i	$-0.315951\pi$
$467$	−1.37109e6	−	1.37109e6i	−0.290921	−	0.290921i	−0.837444	+	0.546523i	$0.815951\pi$
$468$		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	0.344935	−	0.938626i	$-0.387901\pi$
$487$	−3.10730e6	−	3.10730e6i	−0.593691	−	0.593691i	−0.938626	+	0.344935i	$0.887901\pi$
$488$		0			0
$489$		−	8.19151e6i		−	1.54914i
$490$		0			0
$491$			1.03641e7i			1.94012i	0.242871	+	0.970059i	$0.421911\pi$
$491$			1.03641e7i			1.94012i	−0.242871	+	0.970059i	$0.578089\pi$
$492$		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	−0.479994	−	0.877272i	$-0.659361\pi$
$503$	2.25431e6	−	2.25431e6i	0.397278	−	0.397278i	0.877272	+	0.479994i	$0.159361\pi$
$504$		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	$0.143170\pi$
$509$			5.08256e6i			0.869538i	−0.900542	+	0.434769i	$0.856830\pi$
$510$		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	−0.543431	−	0.839454i	$-0.682875\pi$
$523$	1.85174e6	−	1.85174e6i	0.296023	−	0.296023i	0.839454	+	0.543431i	$0.182875\pi$
$524$		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	0.0461324	−	0.998935i	$-0.485310\pi$
$547$	−6.66763e6	−	6.66763e6i	−0.952803	−	0.952803i	−0.998935	+	0.0461324i	$0.985310\pi$
$548$		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	−0.899689	−	0.436531i	$-0.856207\pi$
$557$	−3.39131e6	+	3.39131e6i	−0.463158	+	0.463158i	0.436531	+	0.899689i	$0.356207\pi$
$558$		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	−0.269008	+	0.963138i	$0.586696\pi$
$563$	−9.26687e6	+	9.26687e6i	−1.23215	+	1.23215i	−0.963138	+	0.269008i	$0.913304\pi$
$564$		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	$0.122301\pi$
$569$			5.78965e6i			0.749673i	−0.927091	+	0.374836i	$0.877699\pi$
$570$		0			0
$571$			1.05138e7i			1.34948i	0.738054	+	0.674742i	$0.235745\pi$
$571$			1.05138e7i			1.34948i	−0.738054	+	0.674742i	$0.764255\pi$
$572$		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	−0.833658	−	0.552281i	$-0.813758\pi$
$577$	−2.25024e6	+	2.25024e6i	−0.281378	+	0.281378i	0.552281	+	0.833658i	$0.313758\pi$
$578$		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	0.640909	−	0.767617i	$-0.278557\pi$
$587$	−1.05778e6	−	1.05778e6i	−0.126707	−	0.126707i	−0.767617	+	0.640909i	$0.778557\pi$
$588$		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	−0.994620	−	0.103590i	$-0.966967\pi$
$593$	−9.40420e6	−	9.40420e6i	−1.09821	−	1.09821i	−0.103590	−	0.994620i	$-0.533033\pi$
$594$		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	0.987456	−	0.157897i	$-0.0504713\pi$
$607$	7.53042e6	+	7.53042e6i	0.829559	+	0.829559i	−0.157897	+	0.987456i	$0.550471\pi$
$608$		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	0.736491	−	0.676448i	$-0.236481\pi$
$613$	558618.	+	558618.i	0.0600432	+	0.0600432i	−0.676448	+	0.736491i	$0.736481\pi$
$614$		0			0
$615$	−184241.	−	1.49785e6i	−0.0196425	−	0.159691i
$616$		0			0
$617$	−1.59743e6	+	1.59743e6i	−0.168930	+	0.168930i	−0.786509	−	0.617579i	$-0.788114\pi$
$617$	−1.59743e6	+	1.59743e6i	−0.168930	+	0.168930i	0.617579	+	0.786509i	$0.288114\pi$
$618$		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	$0.00899722\pi$
$631$			565332.i			0.0565237i	−0.999601	+	0.0282618i	$0.991003\pi$
$632$		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	−0.0885717	+	0.996070i	$0.528230\pi$
$643$	−1.13714e7	+	1.13714e7i	−1.08464	+	1.08464i	−0.996070	+	0.0885717i	$0.971770\pi$
$644$		0			0
$645$	−4.82576e6	−	3.76862e6i	−0.456737	−	0.356684i
$646$		0			0
$647$	−4.10311e6	−	4.10311e6i	−0.385347	−	0.385347i	0.487677	−	0.873024i	$-0.337844\pi$
$647$	−4.10311e6	−	4.10311e6i	−0.385347	−	0.385347i	−0.873024	+	0.487677i	$0.837844\pi$
$648$		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	0.531617	−	0.846985i	$-0.321585\pi$
$653$	−3.43638e6	−	3.43638e6i	−0.315369	−	0.315369i	−0.846985	+	0.531617i	$0.821585\pi$
$654$		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	0.634519	−	0.772907i	$-0.281198\pi$
$673$	−1.62607e6	−	1.62607e6i	−0.138389	−	0.138389i	−0.772907	+	0.634519i	$0.781198\pi$
$674$		0			0
$675$	−5.32278e6	+	8.86725e6i	−0.449655	+	0.749082i
$676$		0			0
$677$	−6.06713e6	+	6.06713e6i	−0.508759	+	0.508759i	−0.914145	−	0.405387i	$-0.867137\pi$
$677$	−6.06713e6	+	6.06713e6i	−0.508759	+	0.508759i	0.405387	+	0.914145i	$0.367137\pi$
$678$		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	−0.106490	−	0.994314i	$-0.533961\pi$
$683$	1.08238e7	−	1.08238e7i	0.887824	−	0.887824i	0.994314	+	0.106490i	$0.0339612\pi$
$684$		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	$-0.940500\pi$
$691$		−	4.66507e6i		−	0.371675i	0.982581	−	0.185837i	$-0.0594997\pi$
$692$		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	$-0.992897\pi$
$709$		−	597301.i		−	0.0446249i	0.999751	−	0.0223125i	$-0.00710287\pi$
$710$		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	0.998078	−	0.0619631i	$-0.0197361\pi$
$727$	1.33403e7	+	1.33403e7i	0.936115	+	0.936115i	−0.0619631	+	0.998078i	$0.519736\pi$
$728$		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	0.790129	−	0.612941i	$-0.210014\pi$
$733$	2.57748e6	+	2.57748e6i	0.177188	+	0.177188i	−0.612941	+	0.790129i	$0.710014\pi$
$734$		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	−0.181810	−	0.983334i	$-0.558196\pi$
$743$	1.20611e7	−	1.20611e7i	0.801524	−	0.801524i	0.983334	+	0.181810i	$0.0581956\pi$
$744$		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	$-0.949049\pi$
$751$		−	4.92692e6i		−	0.318769i	0.987217	−	0.159384i	$-0.0509509\pi$
$752$		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	−0.994947	−	0.100405i	$-0.967986\pi$
$757$	−1.41039e7	+	1.41039e7i	−0.894542	+	0.894542i	0.100405	+	0.994947i	$0.467986\pi$
$758$		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	$0.0463333\pi$
$769$			4.75723e6i			0.290094i	−0.989425	+	0.145047i	$0.953667\pi$
$770$		0			0
$771$		−	9.62748e6i		−	0.583279i
$772$		0			0
$773$	−9.08726e6	−	9.08726e6i	−0.546996	−	0.546996i	0.378575	−	0.925571i	$-0.376414\pi$
$773$	−9.08726e6	−	9.08726e6i	−0.546996	−	0.546996i	−0.925571	+	0.378575i	$0.876414\pi$
$774$		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	0.935482	−	0.353374i	$-0.114966\pi$
$787$	1.01144e7	+	1.01144e7i	0.582107	+	0.582107i	−0.353374	+	0.935482i	$0.614966\pi$
$788$		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	−0.748126	−	0.663557i	$-0.769046\pi$
$797$	−1.51655e6	+	1.51655e6i	−0.0845687	+	0.0845687i	0.663557	+	0.748126i	$0.269046\pi$
$798$		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	$-0.921975\pi$
$809$		−	9.03499e6i		−	0.485351i	0.970107	−	0.242676i	$-0.0780251\pi$
$810$		0			0
$811$		−	3.47086e7i		−	1.85304i	−0.376242	−	0.926521i	$-0.622784\pi$
$811$		−	3.47086e7i		−	1.85304i	0.376242	−	0.926521i	$-0.377216\pi$
$812$		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	−0.0585087	+	0.998287i	$0.518635\pi$
$823$	−2.05348e7	+	2.05348e7i	−1.05680	+	1.05680i	−0.998287	+	0.0585087i	$0.981365\pi$
$824$		0			0
$825$	−1.18869e7	+	1.98024e7i	−0.608040	+	1.01294i
$826$		0			0
$827$	−1.36628e7	−	1.36628e7i	−0.694667	−	0.694667i	0.268588	−	0.963255i	$-0.413443\pi$
$827$	−1.36628e7	−	1.36628e7i	−0.694667	−	0.694667i	−0.963255	+	0.268588i	$0.913443\pi$
$828$		0			0
$829$		−	1.58116e7i		−	0.799079i	−0.916716	−	0.399539i	$-0.869170\pi$
$829$		−	1.58116e7i		−	0.799079i	0.916716	−	0.399539i	$-0.130830\pi$
$830$		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	0.403395	−	0.915026i	$-0.367830\pi$
$853$	−1.08725e7	−	1.08725e7i	−0.511631	−	0.511631i	−0.915026	+	0.403395i	$0.867830\pi$
$854$		0			0
$855$	5.17661e6	+	4.04262e6i	0.242176	+	0.189124i
$856$		0			0
$857$	−8.24573e6	+	8.24573e6i	−0.383510	+	0.383510i	−0.872365	−	0.488855i	$-0.837415\pi$
$857$	−8.24573e6	+	8.24573e6i	−0.383510	+	0.383510i	0.488855	+	0.872365i	$0.337415\pi$
$858$		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	−0.961748	−	0.273937i	$-0.911674\pi$
$863$	−1.50486e7	+	1.50486e7i	−0.687811	+	0.687811i	0.273937	+	0.961748i	$0.411674\pi$
$864$		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	0.0429276	−	0.999078i	$-0.486332\pi$
$877$	2.37339e7	−	2.37339e7i	1.04201	−	1.04201i	0.999078	−	0.0429276i	$-0.0136685\pi$
$878$		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	−0.683925	−	0.729552i	$-0.739729\pi$
$883$	1.05710e6	−	1.05710e6i	0.0456264	−	0.0456264i	0.729552	+	0.683925i	$0.239729\pi$
$884$		0			0
$885$	297481.	+	2.41848e6i	0.0127674	+	0.103797i
$886$		0			0
$887$	−6.50661e6	−	6.50661e6i	−0.277681	−	0.277681i	0.554502	−	0.832182i	$-0.312909\pi$
$887$	−6.50661e6	−	6.50661e6i	−0.277681	−	0.277681i	−0.832182	+	0.554502i	$0.812909\pi$
$888$		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	0.840821	−	0.541314i	$-0.182073\pi$
$907$	7.42036e6	+	7.42036e6i	0.299507	+	0.299507i	−0.541314	+	0.840821i	$0.682073\pi$
$908$		0			0
$909$		−	39696.3i		−	0.00159346i
$910$		0			0
$911$		−	3.87110e7i		−	1.54539i	−0.634776	−	0.772696i	$-0.718908\pi$
$911$		−	3.87110e7i		−	1.54539i	0.634776	−	0.772696i	$-0.281092\pi$
$912$		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	$0.221878\pi$
$929$			3.37736e7i			1.28392i	−0.766738	+	0.641960i	$0.778122\pi$
$930$		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	−0.386320	−	0.922365i	$-0.626254\pi$
$937$	1.44062e7	−	1.44062e7i	0.536045	−	0.536045i	0.922365	+	0.386320i	$0.126254\pi$
$938$		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	0.999860	+	0.0167087i	$0.00531878\pi$
$947$	2.80551e7	+	2.80551e7i	1.01657	+	1.01657i	0.0167087	+	0.999860i	$0.494681\pi$
$948$		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	0.916942	−	0.399021i	$-0.130650\pi$
$953$	1.45210e7	+	1.45210e7i	0.517921	+	0.517921i	−0.399021	+	0.916942i	$0.630650\pi$
$954$		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	0.677953	−	0.735105i	$-0.262867\pi$
$967$	−1.66187e6	−	1.66187e6i	−0.0571519	−	0.0571519i	−0.735105	+	0.677953i	$0.762867\pi$
$968$		0			0
$969$		−	8.18217e7i		−	2.79936i
$970$		0			0
$971$			4.51619e6i			0.153718i	0.997042	+	0.0768589i	$0.0244891\pi$
$971$			4.51619e6i			0.153718i	−0.997042	+	0.0768589i	$0.975511\pi$
$972$		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	−0.168106	−	0.985769i	$-0.553765\pi$
$977$	2.43956e7	−	2.43956e7i	0.817663	−	0.817663i	0.985769	+	0.168106i	$0.0537651\pi$
$978$		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	−0.920108	−	0.391664i	$-0.871900\pi$
$983$	−1.60097e7	+	1.60097e7i	−0.528445	+	0.528445i	0.391664	+	0.920108i	$0.371900\pi$
$984$		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	$0.238923\pi$
$991$			4.21742e7i			1.36415i	−0.731281	+	0.682076i	$0.761077\pi$
$992$		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	−0.437075	−	0.899425i	$-0.643986\pi$
$997$	1.45114e7	−	1.45114e7i	0.462350	−	0.462350i	0.899425	+	0.437075i	$0.143986\pi$
$998$		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.63.3	yes	16
4.3	odd	2		160.6.n.c.63.6	✓	16
5.2	odd	4		160.6.n.c.127.6	yes	16
20.7	even	4	inner	160.6.n.d.127.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.6.n.c.63.6	✓	16	4.3	odd	2
160.6.n.c.127.6	yes	16	5.2	odd	4
160.6.n.d.63.3	yes	16	1.1	even	1	trivial
160.6.n.d.127.3	yes	16	20.7	even	4	inner

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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