LMFDB - Embedded newform 1280.3.e.h.639.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1280,3,Mod(639,1280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1280, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1280.639");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1280 = 2^{8} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1280.e (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$34.8774738381$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.1827904.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 9x^{4} + 14x^{2} + 1 $ x^6 + 9x^4 + 14x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 160)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			639.4
Root			$0.273891i$ of defining polynomial
Character	$\chi$	$=$	1280.639
Dual form			1280.3.e.h.639.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.547781i q^{3} +(-3.30219 - 3.75441i) q^{5} -10.0566 q^{7} +8.69994 q^{9} +O(q^{10})$	$q+0.547781i q^{3} +(-3.30219 - 3.75441i) q^{5} -10.0566 q^{7} +8.69994 q^{9} -17.2087 q^{11} +4.41325 q^{13} +(2.05659 - 1.80888i) q^{15} +27.0176i q^{17} +4.82650 q^{19} -5.50881i q^{21} -15.2653 q^{23} +(-3.19112 + 24.7955i) q^{25} +9.69569i q^{27} +2.38225i q^{29} -38.0352i q^{31} -9.42663i q^{33} +(33.2087 + 37.7565i) q^{35} -16.5691 q^{37} +2.41749i q^{39} +13.3177 q^{41} -59.7918i q^{43} +(-28.7288 - 32.6631i) q^{45} +62.4388 q^{47} +52.1351 q^{49} -14.7997 q^{51} +71.5952 q^{53} +(56.8265 + 64.6086i) q^{55} +2.64386i q^{57} +68.8265 q^{59} -40.9439i q^{61} -87.4917 q^{63} +(-14.5734 - 16.5691i) q^{65} -51.0080i q^{67} -8.36206i q^{69} -40.4527i q^{71} +35.8441i q^{73} +(-13.5825 - 1.74804i) q^{75} +173.061 q^{77} +126.800i q^{79} +72.9883 q^{81} -75.1490i q^{83} +(101.435 - 89.2172i) q^{85} -1.30495 q^{87} +106.523 q^{89} -44.3822 q^{91} +20.8350 q^{93} +(-15.9380 - 18.1206i) q^{95} +85.4351i q^{97} -149.715 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 8 q^{5} - 12 q^{7} - 18 q^{9}+O(q^{10}) $ 6 * q + 8 * q^5 - 12 * q^7 - 18 * q^9	$ 6 q + 8 q^{5} - 12 q^{7} - 18 q^{9} + 8 q^{11} - 36 q^{15} - 24 q^{19} + 68 q^{23} + 10 q^{25} + 88 q^{35} - 208 q^{37} + 68 q^{41} - 232 q^{45} + 268 q^{47} - 62 q^{49} + 192 q^{51} + 64 q^{53} + 288 q^{55} + 360 q^{59} - 172 q^{63} - 304 q^{75} + 400 q^{77} + 238 q^{81} + 304 q^{85} - 584 q^{87} - 76 q^{89} - 208 q^{91} - 320 q^{93} - 32 q^{95} - 856 q^{99}+O(q^{100}) $ 6 * q + 8 * q^5 - 12 * q^7 - 18 * q^9 + 8 * q^11 - 36 * q^15 - 24 * q^19 + 68 * q^23 + 10 * q^25 + 88 * q^35 - 208 * q^37 + 68 * q^41 - 232 * q^45 + 268 * q^47 - 62 * q^49 + 192 * q^51 + 64 * q^53 + 288 * q^55 + 360 * q^59 - 172 * q^63 - 304 * q^75 + 400 * q^77 + 238 * q^81 + 304 * q^85 - 584 * q^87 - 76 * q^89 - 208 * q^91 - 320 * q^93 - 32 * q^95 - 856 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$			0.547781i			0.182594i	0.995824	+	0.0912969i	$0.0291012\pi$
$3$			0.547781i			0.182594i	−0.995824	+	0.0912969i	$0.970899\pi$
$4$		0			0
$5$	−3.30219	−	3.75441i	−0.660437	−	0.750881i
$5$	−3.30219	−	3.75441i	−0.660437	−	0.750881i
$6$		0			0
$7$	−10.0566			−1.43666			−0.718328	−	0.695705i	$-0.755092\pi$
$7$	−10.0566			−1.43666			−0.718328	+	0.695705i	$0.755092\pi$
$8$		0			0
$9$	8.69994			0.966660
$10$		0			0
$11$	−17.2087			−1.56443			−0.782216	−	0.623008i	$-0.785911\pi$
$11$	−17.2087			−1.56443			−0.782216	+	0.623008i	$0.785911\pi$
$12$		0			0
$13$	4.41325			0.339481			0.169740	−	0.985489i	$-0.445707\pi$
$13$	4.41325			0.339481			0.169740	+	0.985489i	$0.445707\pi$
$14$		0			0
$15$	2.05659	−	1.80888i	0.137106	−	0.120592i
$16$		0			0
$17$			27.0176i			1.58927i	0.607086	+	0.794636i	$0.292338\pi$
$17$			27.0176i			1.58927i	−0.607086	+	0.794636i	$0.707662\pi$
$18$		0			0
$19$	4.82650			0.254026			0.127013	−	0.991901i	$-0.459461\pi$
$19$	4.82650			0.254026			0.127013	+	0.991901i	$0.459461\pi$
$20$		0			0
$21$		−	5.50881i		−	0.262324i
$22$		0			0
$23$	−15.2653			−0.663710			−0.331855	−	0.943330i	$-0.607675\pi$
$23$	−15.2653			−0.663710			−0.331855	+	0.943330i	$0.607675\pi$
$24$		0			0
$25$	−3.19112	+	24.7955i	−0.127645	+	0.991820i
$26$		0			0
$27$			9.69569i			0.359100i
$28$		0			0
$29$			2.38225i			0.0821465i	0.999156	+	0.0410733i	$0.0130777\pi$
$29$			2.38225i			0.0821465i	−0.999156	+	0.0410733i	$0.986922\pi$
$30$		0			0
$31$		−	38.0352i		−	1.22694i	−0.789717	−	0.613472i	$-0.789772\pi$
$31$		−	38.0352i		−	1.22694i	0.789717	−	0.613472i	$-0.210228\pi$
$32$		0			0
$33$		−	9.42663i		−	0.285655i
$34$		0			0
$35$	33.2087	+	37.7565i	0.948821	+	1.07876i
$36$		0			0
$37$	−16.5691			−0.447814			−0.223907	−	0.974610i	$-0.571881\pi$
$37$	−16.5691			−0.447814			−0.223907	+	0.974610i	$0.571881\pi$
$38$		0			0
$39$			2.41749i			0.0619870i
$40$		0			0
$41$	13.3177			0.324822			0.162411	−	0.986723i	$-0.448073\pi$
$41$	13.3177			0.324822			0.162411	+	0.986723i	$0.448073\pi$
$42$		0			0
$43$		−	59.7918i		−	1.39051i	−0.718765	−	0.695253i	$-0.755292\pi$
$43$		−	59.7918i		−	1.39051i	0.718765	−	0.695253i	$-0.244708\pi$
$44$		0			0
$45$	−28.7288	−	32.6631i	−0.638418	−	0.725846i
$46$		0			0
$47$	62.4388			1.32849			0.664243	−	0.747517i	$-0.268754\pi$
$47$	62.4388			1.32849			0.664243	+	0.747517i	$0.268754\pi$
$48$		0			0
$49$	52.1351			1.06398
$50$		0			0
$51$	−14.7997			−0.290191
$52$		0			0
$53$	71.5952			1.35085			0.675427	−	0.737427i	$-0.263959\pi$
$53$	71.5952			1.35085			0.675427	+	0.737427i	$0.263959\pi$
$54$		0			0
$55$	56.8265	+	64.6086i	1.03321	+	1.17470i
$56$		0			0
$57$			2.64386i			0.0463836i
$58$		0			0
$59$	68.8265			1.16655			0.583275	−	0.812274i	$-0.301771\pi$
$59$	68.8265			1.16655			0.583275	+	0.812274i	$0.301771\pi$
$60$		0			0
$61$		−	40.9439i		−	0.671212i	−0.942002	−	0.335606i	$-0.891059\pi$
$61$		−	40.9439i		−	0.671212i	0.942002	−	0.335606i	$-0.108941\pi$
$62$		0			0
$63$	−87.4917			−1.38876
$64$		0			0
$65$	−14.5734	−	16.5691i	−0.224206	−	0.254910i
$66$		0			0
$67$		−	51.0080i		−	0.761313i	−0.924717	−	0.380656i	$-0.875698\pi$
$67$		−	51.0080i		−	0.761313i	0.924717	−	0.380656i	$-0.124302\pi$
$68$		0			0
$69$		−	8.36206i		−	0.121189i
$70$		0			0
$71$		−	40.4527i		−	0.569757i	−0.958564	−	0.284878i	$-0.908047\pi$
$71$		−	40.4527i		−	0.569757i	0.958564	−	0.284878i	$-0.0919532\pi$
$72$		0			0
$73$			35.8441i			0.491015i	0.969395	+	0.245508i	$0.0789547\pi$
$73$			35.8441i			0.491015i	−0.969395	+	0.245508i	$0.921045\pi$
$74$		0			0
$75$	−13.5825	−	1.74804i	−0.181100	−	0.0233072i
$76$		0			0
$77$	173.061			2.24755
$78$		0			0
$79$			126.800i			1.60506i	0.596612	+	0.802530i	$0.296513\pi$
$79$			126.800i			1.60506i	−0.596612	+	0.802530i	$0.703487\pi$
$80$		0			0
$81$	72.9883			0.901090
$82$		0			0
$83$		−	75.1490i		−	0.905409i	−0.891661	−	0.452705i	$-0.850459\pi$
$83$		−	75.1490i		−	0.905409i	0.891661	−	0.452705i	$-0.149541\pi$
$84$		0			0
$85$	101.435	−	89.2172i	1.19335	−	1.04961i
$86$		0			0
$87$	−1.30495			−0.0149994
$88$		0			0
$89$	106.523			1.19689			0.598445	−	0.801164i	$-0.295785\pi$
$89$	106.523			1.19689			0.598445	+	0.801164i	$0.295785\pi$
$90$		0			0
$91$	−44.3822			−0.487717
$92$		0			0
$93$	20.8350			0.224032
$94$		0			0
$95$	−15.9380	−	18.1206i	−0.167768	−	0.190744i
$96$		0			0
$97$			85.4351i			0.880774i	0.897808	+	0.440387i	$0.145159\pi$
$97$			85.4351i			0.880774i	−0.897808	+	0.440387i	$0.854841\pi$
$98$		0			0
$99$	−149.715			−1.51227
$100$		0			0
$101$		−	83.2877i		−	0.824631i	−0.911041	−	0.412315i	$-0.864720\pi$
$101$		−	83.2877i		−	0.824631i	0.911041	−	0.412315i	$-0.135280\pi$
$102$		0			0
$103$	−47.2653			−0.458887			−0.229443	−	0.973322i	$-0.573691\pi$
$103$	−47.2653			−0.458887			−0.229443	+	0.973322i	$0.573691\pi$
$104$		0			0
$105$	−20.6823	+	18.1911i	−0.196974	+	0.173249i
$106$		0			0
$107$			189.628i			1.77223i	0.463467	+	0.886114i	$0.346605\pi$
$107$			189.628i			1.77223i	−0.463467	+	0.886114i	$0.653395\pi$
$108$		0			0
$109$		−	84.5617i		−	0.775795i	−0.921702	−	0.387898i	$-0.873201\pi$
$109$		−	84.5617i		−	0.775795i	0.921702	−	0.387898i	$-0.126799\pi$
$110$		0			0
$111$		−	9.07626i		−	0.0817681i
$112$		0			0
$113$			114.558i			1.01379i	0.862007	+	0.506896i	$0.169207\pi$
$113$			114.558i			1.01379i	−0.862007	+	0.506896i	$0.830793\pi$
$114$		0			0
$115$	50.4090	+	57.3123i	0.438339	+	0.498368i
$116$		0			0
$117$	38.3950			0.328162
$118$		0			0
$119$		−	271.705i		−	2.28324i
$120$		0			0
$121$	175.141			1.44745
$122$		0			0
$123$			7.29518i			0.0593104i
$124$		0			0
$125$	103.630	−	69.8986i	0.829040	−	0.559189i
$126$		0			0
$127$	44.4121			0.349701			0.174851	−	0.984595i	$-0.444056\pi$
$127$	44.4121			0.349701			0.174851	+	0.984595i	$0.444056\pi$
$128$		0			0
$129$	32.7528			0.253898
$130$		0			0
$131$	47.1200			0.359695			0.179847	−	0.983695i	$-0.442440\pi$
$131$	47.1200			0.359695			0.179847	+	0.983695i	$0.442440\pi$
$132$		0			0
$133$	−48.5381			−0.364948
$134$		0			0
$135$	36.4016	−	32.0170i	0.269641	−	0.237163i
$136$		0			0
$137$		−	62.8617i		−	0.458845i	−0.973327	−	0.229422i	$-0.926316\pi$
$137$		−	62.8617i		−	0.458845i	0.973327	−	0.229422i	$-0.0736837\pi$
$138$		0			0
$139$	128.320			0.923167			0.461584	−	0.887097i	$-0.347281\pi$
$139$	128.320			0.923167			0.461584	+	0.887097i	$0.347281\pi$
$140$		0			0
$141$			34.2028i			0.242573i
$142$		0			0
$143$	−75.9465			−0.531094
$144$		0			0
$145$	8.94393	−	7.86663i	0.0616823	−	0.0542526i
$146$		0			0
$147$			28.5586i			0.194276i
$148$		0			0
$149$		−	165.561i		−	1.11115i	−0.831467	−	0.555574i	$-0.812499\pi$
$149$		−	165.561i		−	1.11115i	0.831467	−	0.555574i	$-0.187501\pi$
$150$		0			0
$151$			218.558i			1.44741i	0.690111	+	0.723704i	$0.257562\pi$
$151$			218.558i			1.44741i	−0.690111	+	0.723704i	$0.742438\pi$
$152$		0			0
$153$			235.052i			1.53628i
$154$		0			0
$155$	−142.800	+	125.599i	−0.921289	+	0.810319i
$156$		0			0
$157$	−174.293			−1.11014			−0.555072	−	0.831802i	$-0.687309\pi$
$157$	−174.293			−1.11014			−0.555072	+	0.831802i	$0.687309\pi$
$158$		0			0
$159$			39.2185i			0.246657i
$160$		0			0
$161$	153.517			0.953524
$162$		0			0
$163$			52.6353i			0.322916i	0.986880	+	0.161458i	$0.0516196\pi$
$163$			52.6353i			0.322916i	−0.986880	+	0.161458i	$0.948380\pi$
$164$		0			0
$165$	−35.3914	+	31.1285i	−0.214493	+	0.188657i
$166$		0			0
$167$	76.6812			0.459169			0.229584	−	0.973289i	$-0.426263\pi$
$167$	76.6812			0.459169			0.229584	+	0.973289i	$0.426263\pi$
$168$		0			0
$169$	−149.523			−0.884753
$170$		0			0
$171$	41.9902			0.245557
$172$		0			0
$173$	9.72437			0.0562102			0.0281051	−	0.999605i	$-0.491053\pi$
$173$	9.72437			0.0562102			0.0281051	+	0.999605i	$0.491053\pi$
$174$		0			0
$175$	32.0918	−	249.358i	0.183382	−	1.42490i
$176$		0			0
$177$			37.7019i			0.213005i
$178$		0			0
$179$	−155.502			−0.868728			−0.434364	−	0.900738i	$-0.643027\pi$
$179$	−155.502			−0.868728			−0.434364	+	0.900738i	$0.643027\pi$
$180$		0			0
$181$			250.346i			1.38313i	0.722316	+	0.691563i	$0.243077\pi$
$181$			250.346i			1.38313i	−0.722316	+	0.691563i	$0.756923\pi$
$182$		0			0
$183$	22.4283			0.122559
$184$		0			0
$185$	54.7144	+	62.2072i	0.295753	+	0.336255i
$186$		0			0
$187$		−	464.939i		−	2.48631i
$188$		0			0
$189$		−	97.5056i		−	0.515903i
$190$		0			0
$191$			111.128i			0.581825i	0.956750	+	0.290912i	$0.0939588\pi$
$191$			111.128i			0.581825i	−0.956750	+	0.290912i	$0.906041\pi$
$192$		0			0
$193$		−	10.2701i		−	0.0532130i	−0.999646	−	0.0266065i	$-0.991530\pi$
$193$		−	10.2701i		−	0.0532130i	0.999646	−	0.0266065i	$-0.00847011\pi$
$194$		0			0
$195$	9.07626	−	7.98302i	0.0465449	−	0.0409386i
$196$		0			0
$197$	163.213			0.828492			0.414246	−	0.910165i	$-0.364045\pi$
$197$	163.213			0.828492			0.414246	+	0.910165i	$0.364045\pi$
$198$		0			0
$199$			195.028i			0.980041i	0.871711	+	0.490021i	$0.163011\pi$
$199$			195.028i			0.980041i	−0.871711	+	0.490021i	$0.836989\pi$
$200$		0			0
$201$	27.9412			0.139011
$202$		0			0
$203$		−	23.9573i		−	0.118016i
$204$		0			0
$205$	−43.9775	−	50.0000i	−0.214524	−	0.243902i
$206$		0			0
$207$	−132.807			−0.641582
$208$		0			0
$209$	−83.0580			−0.397407
$210$		0			0
$211$	297.038			1.40776			0.703881	−	0.710317i	$-0.251449\pi$
$211$	297.038			1.40776			0.703881	+	0.710317i	$0.251449\pi$
$212$		0			0
$213$	22.1592			0.104034
$214$		0			0
$215$	−224.483	+	197.444i	−1.04411	+	0.918342i
$216$		0			0
$217$			382.505i			1.76270i
$218$		0			0
$219$	−19.6347			−0.0896563
$220$		0			0
$221$			119.236i			0.539527i
$222$		0			0
$223$	405.335			1.81764			0.908822	−	0.417184i	$-0.136983\pi$
$223$	405.335			1.81764			0.908822	+	0.417184i	$0.136983\pi$
$224$		0			0
$225$	−27.7626	+	215.719i	−0.123389	+	0.958752i
$226$		0			0
$227$			36.6013i			0.161239i	0.996745	+	0.0806196i	$0.0256899\pi$
$227$			36.6013i			0.161239i	−0.996745	+	0.0806196i	$0.974310\pi$
$228$		0			0
$229$		−	91.1467i		−	0.398021i	−0.979997	−	0.199010i	$-0.936227\pi$
$229$		−	91.1467i		−	0.398021i	0.979997	−	0.199010i	$-0.0637727\pi$
$230$		0			0
$231$			94.7997i			0.410388i
$232$		0			0
$233$		−	338.802i		−	1.45409i	−0.686592	−	0.727043i	$-0.740894\pi$
$233$		−	338.802i		−	1.45409i	0.686592	−	0.727043i	$-0.259106\pi$
$234$		0			0
$235$	−206.185	−	234.421i	−0.877382	−	0.997535i
$236$		0			0
$237$	−69.4585			−0.293074
$238$		0			0
$239$			30.7997i			0.128869i	0.997922	+	0.0644346i	$0.0205244\pi$
$239$			30.7997i			0.128869i	−0.997922	+	0.0644346i	$0.979476\pi$
$240$		0			0
$241$	240.282			0.997020			0.498510	−	0.866884i	$-0.333881\pi$
$241$	240.282			0.997020			0.498510	+	0.866884i	$0.333881\pi$
$242$		0			0
$243$			127.243i			0.523633i
$244$		0			0
$245$	−172.160	−	195.736i	−0.702693	−	0.798923i
$246$		0			0
$247$	21.3005			0.0862370
$248$		0			0
$249$	41.1652			0.165322
$250$		0			0
$251$	86.0268			0.342736			0.171368	−	0.985207i	$-0.445181\pi$
$251$	86.0268			0.342736			0.171368	+	0.985207i	$0.445181\pi$
$252$		0			0
$253$	262.697			1.03833
$254$		0			0
$255$	48.8715	+	55.5642i	0.191653	+	0.217899i
$256$		0			0
$257$		−	355.963i		−	1.38507i	−0.721383	−	0.692536i	$-0.756493\pi$
$257$		−	355.963i		−	1.38507i	0.721383	−	0.692536i	$-0.243507\pi$
$258$		0			0
$259$	166.629			0.643355
$260$		0			0
$261$			20.7254i			0.0794077i
$262$		0			0
$263$	73.1254			0.278043			0.139022	−	0.990289i	$-0.455604\pi$
$263$	73.1254			0.278043			0.139022	+	0.990289i	$0.455604\pi$
$264$		0			0
$265$	−236.421	−	268.798i	−0.892154	−	1.01433i
$266$		0			0
$267$			58.3514i			0.218545i
$268$		0			0
$269$		−	268.002i		−	0.996290i	−0.867094	−	0.498145i	$-0.834015\pi$
$269$		−	268.002i		−	0.996290i	0.867094	−	0.498145i	$-0.165985\pi$
$270$		0			0
$271$		−	229.412i		−	0.846538i	−0.906004	−	0.423269i	$-0.860883\pi$
$271$		−	229.412i		−	0.846538i	0.906004	−	0.423269i	$-0.139117\pi$
$272$		0			0
$273$		−	24.3118i		−	0.0890541i
$274$		0			0
$275$	54.9153	−	426.699i	0.199692	−	1.55163i
$276$		0			0
$277$	−126.327			−0.456053			−0.228026	−	0.973655i	$-0.573227\pi$
$277$	−126.327			−0.456053			−0.228026	+	0.973655i	$0.573227\pi$
$278$		0			0
$279$		−	330.904i		−	1.18604i
$280$		0			0
$281$	458.746			1.63255			0.816275	−	0.577664i	$-0.196036\pi$
$281$	458.746			1.63255			0.816275	+	0.577664i	$0.196036\pi$
$282$		0			0
$283$			465.558i			1.64508i	0.568706	+	0.822541i	$0.307444\pi$
$283$			465.558i			1.64508i	−0.568706	+	0.822541i	$0.692556\pi$
$284$		0			0
$285$	9.92614	−	8.73053i	0.0348286	−	0.0306335i
$286$		0			0
$287$	−133.931			−0.466657
$288$		0			0
$289$	−440.952			−1.52579
$290$		0			0
$291$	−46.7997			−0.160824
$292$		0			0
$293$	165.218			0.563884			0.281942	−	0.959431i	$-0.409021\pi$
$293$	165.218			0.563884			0.281942	+	0.959431i	$0.409021\pi$
$294$		0			0
$295$	−227.278	−	258.403i	−0.770434	−	0.875941i
$296$		0			0
$297$		−	166.851i		−	0.561787i
$298$		0			0
$299$	−67.3697			−0.225317
$300$		0			0
$301$			601.302i			1.99768i
$302$		0			0
$303$	45.6234			0.150572
$304$		0			0
$305$	−153.720	+	135.205i	−0.504000	+	0.443293i
$306$		0			0
$307$			235.339i			0.766577i	0.923629	+	0.383288i	$0.125208\pi$
$307$			235.339i			0.766577i	−0.923629	+	0.383288i	$0.874792\pi$
$308$		0			0
$309$		−	25.8911i		−	0.0837898i
$310$		0			0
$311$		−	210.665i		−	0.677381i	−0.940898	−	0.338691i	$-0.890016\pi$
$311$		−	210.665i		−	0.677381i	0.940898	−	0.338691i	$-0.109984\pi$
$312$		0			0
$313$		−	318.738i		−	1.01833i	−0.860668	−	0.509166i	$-0.829954\pi$
$313$		−	318.738i		−	1.01833i	0.860668	−	0.509166i	$-0.170046\pi$
$314$		0			0
$315$	288.914	+	328.479i	0.917187	+	1.04279i
$316$		0			0
$317$	70.3950			0.222066			0.111033	−	0.993817i	$-0.464584\pi$
$317$	70.3950			0.222066			0.111033	+	0.993817i	$0.464584\pi$
$318$		0			0
$319$		−	40.9955i		−	0.128513i
$320$		0			0
$321$	−103.875			−0.323598
$322$		0			0
$323$			130.401i			0.403717i
$324$		0			0
$325$	−14.0832	+	109.429i	−0.0433330	+	0.336704i
$326$		0			0
$327$	46.3213			0.141655
$328$		0			0
$329$	−627.922			−1.90858
$330$		0			0
$331$	−280.807			−0.848359			−0.424180	−	0.905578i	$-0.639438\pi$
$331$	−280.807			−0.848359			−0.424180	+	0.905578i	$0.639438\pi$
$332$		0			0
$333$	−144.150			−0.432884
$334$		0			0
$335$	−191.505	+	168.438i	−0.571656	+	0.502800i
$336$		0			0
$337$		−	120.969i		−	0.358959i	−0.983762	−	0.179480i	$-0.942559\pi$
$337$		−	120.969i		−	0.358959i	0.983762	−	0.179480i	$-0.0574414\pi$
$338$		0			0
$339$	−62.7530			−0.185112
$340$		0			0
$341$			654.539i			1.91947i
$342$		0			0
$343$	−31.5280			−0.0919182
$344$		0			0
$345$	−31.3946	+	27.6131i	−0.0909988	+	0.0800380i
$346$		0			0
$347$		−	214.333i		−	0.617675i	−0.951115	−	0.308838i	$-0.900060\pi$
$347$		−	214.333i		−	0.617675i	0.951115	−	0.308838i	$-0.0999399\pi$
$348$		0			0
$349$			418.041i			1.19782i	0.800815	+	0.598912i	$0.204400\pi$
$349$			418.041i			1.19782i	−0.800815	+	0.598912i	$0.795600\pi$
$350$		0			0
$351$			42.7895i			0.121907i
$352$		0			0
$353$		−	364.929i		−	1.03379i	−0.856048	−	0.516897i	$-0.827087\pi$
$353$		−	364.929i		−	1.03379i	0.856048	−	0.516897i	$-0.172913\pi$
$354$		0			0
$355$	−151.876	+	133.583i	−0.427820	+	0.376289i
$356$		0			0
$357$	148.835			0.416905
$358$		0			0
$359$			242.169i			0.674567i	0.941403	+	0.337283i	$0.109508\pi$
$359$			242.169i			0.674567i	−0.941403	+	0.337283i	$0.890492\pi$
$360$		0			0
$361$	−337.705			−0.935471
$362$		0			0
$363$			95.9389i			0.264295i
$364$		0			0
$365$	134.573	−	118.364i	0.368694	−	0.324285i
$366$		0			0
$367$	−224.564			−0.611891			−0.305945	−	0.952049i	$-0.598972\pi$
$367$	−224.564			−0.611891			−0.305945	+	0.952049i	$0.598972\pi$
$368$		0			0
$369$	115.863			0.313992
$370$		0			0
$371$	−720.004			−1.94071
$372$		0			0
$373$	−572.174			−1.53398			−0.766989	−	0.641660i	$-0.778246\pi$
$373$	−572.174			−1.53398			−0.766989	+	0.641660i	$0.778246\pi$
$374$		0			0
$375$	38.2891	+	56.7666i	0.102104	+	0.151378i
$376$		0			0
$377$			10.5135i			0.0278872i
$378$		0			0
$379$	122.896			0.324263			0.162132	−	0.986769i	$-0.448163\pi$
$379$	122.896			0.324263			0.162132	+	0.986769i	$0.448163\pi$
$380$		0			0
$381$			24.3281i			0.0638533i
$382$		0			0
$383$	−289.717			−0.756442			−0.378221	−	0.925715i	$-0.623464\pi$
$383$	−289.717			−0.756442			−0.378221	+	0.925715i	$0.623464\pi$
$384$		0			0
$385$	−571.481	−	649.743i	−1.48437	−	1.68764i
$386$		0			0
$387$		−	520.185i		−	1.34415i
$388$		0			0
$389$			111.590i			0.286863i	0.989660	+	0.143432i	$0.0458137\pi$
$389$			111.590i			0.286863i	−0.989660	+	0.143432i	$0.954186\pi$
$390$		0			0
$391$		−	412.433i		−	1.05482i
$392$		0			0
$393$			25.8114i			0.0656780i
$394$		0			0
$395$	476.058	−	418.716i	1.20521	−	1.06004i
$396$		0			0
$397$	−705.314			−1.77661			−0.888305	−	0.459253i	$-0.848117\pi$
$397$	−705.314			−1.77661			−0.888305	+	0.459253i	$0.848117\pi$
$398$		0			0
$399$		−	26.5883i		−	0.0666373i
$400$		0			0
$401$	432.052			1.07744			0.538718	−	0.842486i	$-0.318909\pi$
$401$	432.052			1.07744			0.538718	+	0.842486i	$0.318909\pi$
$402$		0			0
$403$		−	167.859i		−	0.416524i
$404$		0			0
$405$	−241.021	−	274.028i	−0.595114	−	0.676612i
$406$		0			0
$407$	285.134			0.700575
$408$		0			0
$409$	98.8102			0.241590			0.120795	−	0.992677i	$-0.461456\pi$
$409$	98.8102			0.241590			0.120795	+	0.992677i	$0.461456\pi$
$410$		0			0
$411$	34.4345			0.0837822
$412$		0			0
$413$	−692.160			−1.67593
$414$		0			0
$415$	−282.140	+	248.156i	−0.679855	+	0.597966i
$416$		0			0
$417$			70.2914i			0.168565i
$418$		0			0
$419$	204.980			0.489213			0.244607	−	0.969622i	$-0.421341\pi$
$419$	204.980			0.489213			0.244607	+	0.969622i	$0.421341\pi$
$420$		0			0
$421$			449.956i			1.06878i	0.845238	+	0.534390i	$0.179459\pi$
$421$			449.956i			1.06878i	−0.845238	+	0.534390i	$0.820541\pi$
$422$		0			0
$423$	543.214			1.28419
$424$		0			0
$425$	−669.915	−	86.2166i	−1.57627	−	0.202863i
$426$		0			0
$427$			411.756i			0.964301i
$428$		0			0
$429$		−	41.6021i		−	0.0969745i
$430$		0			0
$431$			314.588i			0.729903i	0.931026	+	0.364952i	$0.118914\pi$
$431$			314.588i			0.729903i	−0.931026	+	0.364952i	$0.881086\pi$
$432$		0			0
$433$			330.441i			0.763143i	0.924339	+	0.381571i	$0.124617\pi$
$433$			330.441i			0.763143i	−0.924339	+	0.381571i	$0.875383\pi$
$434$		0			0
$435$	4.30919	+	4.89932i	0.00990619	+	0.0112628i
$436$		0			0
$437$	−73.6781			−0.168600
$438$		0			0
$439$			664.815i			1.51439i	0.653191	+	0.757193i	$0.273430\pi$
$439$			664.815i			1.51439i	−0.653191	+	0.757193i	$0.726570\pi$
$440$		0			0
$441$	453.572			1.02851
$442$		0			0
$443$		−	312.860i		−	0.706229i	−0.935580	−	0.353115i	$-0.885123\pi$
$443$		−	312.860i		−	0.706229i	0.935580	−	0.353115i	$-0.114877\pi$
$444$		0			0
$445$	−351.760	−	399.931i	−0.790471	−	0.898722i
$446$		0			0
$447$	90.6912			0.202889
$448$		0			0
$449$	−246.330			−0.548620			−0.274310	−	0.961641i	$-0.588449\pi$
$449$	−246.330			−0.548620			−0.274310	+	0.961641i	$0.588449\pi$
$450$		0			0
$451$	−229.181			−0.508161
$452$		0			0
$453$	−119.722			−0.264287
$454$		0			0
$455$	146.558	+	166.629i	0.322107	+	0.366218i
$456$		0			0
$457$		−	707.094i		−	1.54725i	−0.633642	−	0.773626i	$-0.718441\pi$
$457$		−	707.094i		−	1.54725i	0.633642	−	0.773626i	$-0.281559\pi$
$458$		0			0
$459$	−261.955			−0.570707
$460$		0			0
$461$			611.288i			1.32600i	0.748618	+	0.663002i	$0.230718\pi$
$461$			611.288i			1.32600i	−0.748618	+	0.663002i	$0.769282\pi$
$462$		0			0
$463$	334.063			0.721519			0.360760	−	0.932659i	$-0.382518\pi$
$463$	334.063			0.721519			0.360760	+	0.932659i	$0.382518\pi$
$464$		0			0
$465$	−68.8010	−	78.2230i	−0.147959	−	0.168222i
$466$		0			0
$467$			128.864i			0.275939i	0.990436	+	0.137970i	$0.0440577\pi$
$467$			128.864i			0.275939i	−0.990436	+	0.137970i	$0.955942\pi$
$468$		0			0
$469$			512.966i			1.09374i
$470$		0			0
$471$		−	95.4742i		−	0.202705i
$472$		0			0
$473$			1028.94i			2.17535i
$474$		0			0
$475$	−15.4020	+	119.675i	−0.0324252	+	0.251948i
$476$		0			0
$477$	622.874			1.30582
$478$		0			0
$479$		−	510.257i		−	1.06525i	−0.846350	−	0.532627i	$-0.821205\pi$
$479$		−	510.257i		−	1.06525i	0.846350	−	0.532627i	$-0.178795\pi$
$480$		0			0
$481$	−73.1237			−0.152024
$482$		0			0
$483$			84.0939i			0.174107i
$484$		0			0
$485$	320.758	−	282.123i	0.661357	−	0.581696i
$486$		0			0
$487$	−616.472			−1.26586			−0.632928	−	0.774211i	$-0.718147\pi$
$487$	−616.472			−1.26586			−0.632928	+	0.774211i	$0.718147\pi$
$488$		0			0
$489$	−28.8326			−0.0589624
$490$		0			0
$491$	603.190			1.22849			0.614247	−	0.789114i	$-0.289460\pi$
$491$	603.190			1.22849			0.614247	+	0.789114i	$0.289460\pi$
$492$		0			0
$493$	−64.3627			−0.130553
$494$		0			0
$495$	494.387	+	562.091i	0.998761	+	1.13554i
$496$		0			0
$497$			406.817i			0.818545i
$498$		0			0
$499$	867.976			1.73943			0.869716	−	0.493553i	$-0.164302\pi$
$499$	867.976			1.73943			0.869716	+	0.493553i	$0.164302\pi$
$500$		0			0
$501$			42.0045i			0.0838413i
$502$		0			0
$503$	−57.8408			−0.114992			−0.0574958	−	0.998346i	$-0.518312\pi$
$503$	−57.8408			−0.114992			−0.0574958	+	0.998346i	$0.518312\pi$
$504$		0			0
$505$	−312.696	+	275.032i	−0.619200	+	0.544617i
$506$		0			0
$507$		−	81.9060i		−	0.161550i
$508$		0			0
$509$			168.498i			0.331038i	0.986207	+	0.165519i	$0.0529299\pi$
$509$			168.498i			0.331038i	−0.986207	+	0.165519i	$0.947070\pi$
$510$		0			0
$511$		−	360.470i		−	0.705420i
$512$		0			0
$513$			46.7962i			0.0912207i
$514$		0			0
$515$	156.079	+	177.453i	0.303066	+	0.344569i
$516$		0			0
$517$	−1074.49			−2.07833
$518$		0			0
$519$			5.32682i			0.0102636i
$520$		0			0
$521$	87.1060			0.167190			0.0835951	−	0.996500i	$-0.473360\pi$
$521$	87.1060			0.167190			0.0835951	+	0.996500i	$0.473360\pi$
$522$		0			0
$523$		−	243.469i		−	0.465524i	−0.972534	−	0.232762i	$-0.925224\pi$
$523$		−	243.469i		−	0.465524i	0.972534	−	0.232762i	$-0.0747763\pi$
$524$		0			0
$525$	136.594	+	17.5793i	0.260179	+	0.0334844i
$526$		0			0
$527$	1027.62			1.94995
$528$		0			0
$529$	−295.969			−0.559488
$530$		0			0
$531$	598.786			1.12766
$532$		0			0
$533$	58.7743			0.110271
$534$		0			0
$535$	711.942	−	626.189i	1.33073	−	1.17045i
$536$		0			0
$537$		−	85.1812i		−	0.158624i
$538$		0			0
$539$	−897.179			−1.66452
$540$		0			0
$541$			812.616i			1.50206i	0.660266	+	0.751032i	$0.270443\pi$
$541$			812.616i			1.50206i	−0.660266	+	0.751032i	$0.729557\pi$
$542$		0			0
$543$	−137.135			−0.252550
$544$		0			0
$545$	−317.479	+	279.238i	−0.582530	+	0.512364i
$546$		0			0
$547$		−	104.713i		−	0.191431i	−0.995409	−	0.0957155i	$-0.969486\pi$
$547$		−	104.713i		−	0.191431i	0.995409	−	0.0957155i	$-0.0305139\pi$
$548$		0			0
$549$		−	356.210i		−	0.648833i
$550$		0			0
$551$			11.4979i			0.0208674i
$552$		0			0
$553$		−	1275.17i		−	2.30592i
$554$		0			0
$555$	−34.0759	+	29.9715i	−0.0613981	+	0.0540027i
$556$		0			0
$557$	260.018			0.466818			0.233409	−	0.972379i	$-0.425012\pi$
$557$	260.018			0.466818			0.233409	+	0.972379i	$0.425012\pi$
$558$		0			0
$559$		−	263.876i		−	0.472050i
$560$		0			0
$561$	254.685			0.453984
$562$		0			0
$563$			39.9073i			0.0708833i	0.999372	+	0.0354416i	$0.0112838\pi$
$563$			39.9073i			0.0708833i	−0.999372	+	0.0354416i	$0.988716\pi$
$564$		0			0
$565$	430.099	−	378.293i	0.761237	−	0.669546i
$566$		0			0
$567$	−734.014			−1.29456
$568$		0			0
$569$	211.588			0.371860			0.185930	−	0.982563i	$-0.440470\pi$
$569$	211.588			0.371860			0.185930	+	0.982563i	$0.440470\pi$
$570$		0			0
$571$	−556.938			−0.975372			−0.487686	−	0.873019i	$-0.662159\pi$
$571$	−556.938			−0.975372			−0.487686	+	0.873019i	$0.662159\pi$
$572$		0			0
$573$	−60.8741			−0.106237
$574$		0			0
$575$	48.7136	−	378.512i	0.0847193	−	0.658281i
$576$		0			0
$577$		−	516.233i		−	0.894684i	−0.894363	−	0.447342i	$-0.852371\pi$
$577$		−	516.233i		−	0.894684i	0.894363	−	0.447342i	$-0.147629\pi$
$578$		0			0
$579$	5.62577			0.00971636
$580$		0			0
$581$			755.742i			1.30076i
$582$		0			0
$583$	−1232.06			−2.11332
$584$		0			0
$585$	−126.787	−	144.150i	−0.216731	−	0.246411i
$586$		0			0
$587$			934.677i			1.59229i	0.605103	+	0.796147i	$0.293132\pi$
$587$			934.677i			1.59229i	−0.605103	+	0.796147i	$0.706868\pi$
$588$		0			0
$589$		−	183.577i		−	0.311676i
$590$		0			0
$591$			89.4050i			0.151277i
$592$		0			0
$593$		−	634.665i		−	1.07026i	−0.844769	−	0.535131i	$-0.820262\pi$
$593$		−	634.665i		−	1.07026i	0.844769	−	0.535131i	$-0.179738\pi$
$594$		0			0
$595$	−1020.09	+	897.221i	−1.71444	+	1.50794i
$596$		0			0
$597$	−106.833			−0.178949
$598$		0			0
$599$			914.029i			1.52593i	0.646443	+	0.762963i	$0.276256\pi$
$599$			914.029i			1.52593i	−0.646443	+	0.762963i	$0.723744\pi$
$600$		0			0
$601$	598.569			0.995955			0.497977	−	0.867190i	$-0.334076\pi$
$601$	598.569			0.995955			0.497977	+	0.867190i	$0.334076\pi$
$602$		0			0
$603$		−	443.766i		−	0.735930i
$604$		0			0
$605$	−578.348	−	657.550i	−0.955948	−	1.08686i
$606$		0			0
$607$	−201.830			−0.332504			−0.166252	−	0.986083i	$-0.553166\pi$
$607$	−201.830			−0.332504			−0.166252	+	0.986083i	$0.553166\pi$
$608$		0			0
$609$	13.1234			0.0215490
$610$		0			0
$611$	275.558			0.450995
$612$		0			0
$613$	71.9205			0.117325			0.0586627	−	0.998278i	$-0.481316\pi$
$613$	71.9205			0.117325			0.0586627	+	0.998278i	$0.481316\pi$
$614$		0			0
$615$	27.3891	−	24.0900i	0.0445350	−	0.0391708i
$616$		0			0
$617$		−	204.485i		−	0.331418i	−0.986175	−	0.165709i	$-0.947009\pi$
$617$		−	204.485i		−	0.331418i	0.986175	−	0.165709i	$-0.0529912\pi$
$618$		0			0
$619$	−287.512			−0.464479			−0.232239	−	0.972659i	$-0.574605\pi$
$619$	−287.512			−0.464479			−0.232239	+	0.972659i	$0.574605\pi$
$620$		0			0
$621$		−	148.008i		−	0.238338i
$622$		0			0
$623$	−1071.26			−1.71952
$624$		0			0
$625$	−604.633	−	158.251i	−0.967414	−	0.253202i
$626$		0			0
$627$		−	45.4976i		−	0.0725640i
$628$		0			0
$629$		−	447.658i		−	0.711699i
$630$		0			0
$631$			274.203i			0.434554i	0.976110	+	0.217277i	$0.0697175\pi$
$631$			274.203i			0.434554i	−0.976110	+	0.217277i	$0.930283\pi$
$632$		0			0
$633$			162.712i			0.257049i
$634$		0			0
$635$	−146.657	−	166.741i	−0.230956	−	0.262584i
$636$		0			0
$637$	230.085			0.361201
$638$		0			0
$639$		−	351.936i		−	0.550761i
$640$		0			0
$641$	681.328			1.06291			0.531457	−	0.847085i	$-0.321645\pi$
$641$	681.328			1.06291			0.531457	+	0.847085i	$0.321645\pi$
$642$		0			0
$643$		−	527.270i		−	0.820016i	−0.912082	−	0.410008i	$-0.865526\pi$
$643$		−	527.270i		−	0.820016i	0.912082	−	0.410008i	$-0.134474\pi$
$644$		0			0
$645$	−108.156	−	122.967i	−0.167684	−	0.190647i
$646$		0			0
$647$	551.627			0.852592			0.426296	−	0.904584i	$-0.359818\pi$
$647$	551.627			0.852592			0.426296	+	0.904584i	$0.359818\pi$
$648$		0			0
$649$	−1184.42			−1.82499
$650$		0			0
$651$	−209.529			−0.321857
$652$		0			0
$653$	699.422			1.07109			0.535545	−	0.844507i	$-0.320106\pi$
$653$	699.422			1.07109			0.535545	+	0.844507i	$0.320106\pi$
$654$		0			0
$655$	−155.599	−	176.908i	−0.237556	−	0.270088i
$656$		0			0
$657$			311.842i			0.474645i
$658$		0			0
$659$	−38.3257			−0.0581574			−0.0290787	−	0.999577i	$-0.509257\pi$
$659$	−38.3257			−0.0581574			−0.0290787	+	0.999577i	$0.509257\pi$
$660$		0			0
$661$			392.364i			0.593591i	0.954941	+	0.296796i	$0.0959180\pi$
$661$			392.364i			0.593591i	−0.954941	+	0.296796i	$0.904082\pi$
$662$		0			0
$663$	−65.3150			−0.0985143
$664$		0			0
$665$	160.282	+	182.232i	0.241026	+	0.274033i
$666$		0			0
$667$		−	36.3658i		−	0.0545215i
$668$		0			0
$669$			222.035i			0.331890i
$670$		0			0
$671$			704.594i			1.05007i
$672$		0			0
$673$		−	427.290i		−	0.634904i	−0.948274	−	0.317452i	$-0.897173\pi$
$673$		−	427.290i		−	0.634904i	0.948274	−	0.317452i	$-0.102827\pi$
$674$		0			0
$675$	−240.409	−	30.9402i	−0.356162	−	0.0458373i
$676$		0			0
$677$	131.234			0.193847			0.0969233	−	0.995292i	$-0.469100\pi$
$677$	131.234			0.193847			0.0969233	+	0.995292i	$0.469100\pi$
$678$		0			0
$679$		−	859.186i		−	1.26537i
$680$		0			0
$681$	−20.0495			−0.0294413
$682$		0			0
$683$		−	896.229i		−	1.31219i	−0.754676	−	0.656097i	$-0.772206\pi$
$683$		−	896.229i		−	1.31219i	0.754676	−	0.656097i	$-0.227794\pi$
$684$		0			0
$685$	−236.008	+	207.581i	−0.344538	+	0.303038i
$686$		0			0
$687$	49.9285			0.0726761
$688$		0			0
$689$	315.968			0.458589
$690$		0			0
$691$	−520.465			−0.753206			−0.376603	−	0.926375i	$-0.622908\pi$
$691$	−520.465			−0.753206			−0.376603	+	0.926375i	$0.622908\pi$
$692$		0			0
$693$	1505.62			2.17262
$694$		0			0
$695$	−423.737	−	481.766i	−0.609694	−	0.693189i
$696$		0			0
$697$			359.812i			0.516230i
$698$		0			0
$699$	185.589			0.265507
$700$		0			0
$701$		−	80.7527i		−	0.115196i	−0.998340	−	0.0575982i	$-0.981656\pi$
$701$		−	80.7527i		−	0.115196i	0.998340	−	0.0575982i	$-0.0183442\pi$
$702$		0			0
$703$	−79.9709			−0.113757
$704$		0			0
$705$	128.411	−	112.944i	0.182144	−	0.160204i
$706$		0			0
$707$			837.591i			1.18471i
$708$		0			0
$709$		−	174.828i		−	0.246584i	−0.992370	−	0.123292i	$-0.960655\pi$
$709$		−	174.828i		−	0.246584i	0.992370	−	0.123292i	$-0.0393452\pi$
$710$		0			0
$711$			1103.15i			1.55155i
$712$		0			0
$713$			580.621i			0.814335i
$714$		0			0
$715$	250.789	+	285.134i	0.350755	+	0.398789i
$716$		0			0
$717$	−16.8715			−0.0235307
$718$		0			0
$719$		−	889.905i		−	1.23770i	−0.785510	−	0.618849i	$-0.787599\pi$
$719$		−	889.905i		−	1.23770i	0.785510	−	0.618849i	$-0.212401\pi$
$720$		0			0
$721$	475.328			0.659263
$722$		0			0
$723$			131.622i			0.182050i
$724$		0			0
$725$	−59.0690	−	7.60205i	−0.0814745	−	0.0104856i
$726$		0			0
$727$	408.818			0.562335			0.281168	−	0.959659i	$-0.409278\pi$
$727$	408.818			0.562335			0.281168	+	0.959659i	$0.409278\pi$
$728$		0			0
$729$	587.194			0.805478
$730$		0			0
$731$	1615.43			2.20989
$732$		0			0
$733$	388.369			0.529835			0.264917	−	0.964271i	$-0.414655\pi$
$733$	388.369			0.529835			0.264917	+	0.964271i	$0.414655\pi$
$734$		0			0
$735$	107.221	−	94.3058i	0.145878	−	0.128307i
$736$		0			0
$737$			877.783i			1.19102i
$738$		0			0
$739$	−109.561			−0.148256			−0.0741280	−	0.997249i	$-0.523617\pi$
$739$	−109.561			−0.148256			−0.0741280	+	0.997249i	$0.523617\pi$
$740$		0			0
$741$			11.6680i			0.0157463i
$742$		0			0
$743$	732.717			0.986160			0.493080	−	0.869984i	$-0.335871\pi$
$743$	732.717			0.986160			0.493080	+	0.869984i	$0.335871\pi$
$744$		0			0
$745$	−621.583	+	546.713i	−0.834340	+	0.733844i
$746$		0			0
$747$		−	653.791i		−	0.875222i
$748$		0			0
$749$		−	1907.02i		−	2.54608i
$750$		0			0
$751$			420.809i			0.560332i	0.959952	+	0.280166i	$0.0903895\pi$
$751$			420.809i			0.560332i	−0.959952	+	0.280166i	$0.909610\pi$
$752$		0			0
$753$			47.1238i			0.0625814i
$754$		0			0
$755$	820.557	−	721.721i	1.08683	−	0.955922i
$756$		0			0
$757$	1306.99			1.72654			0.863269	−	0.504744i	$-0.168413\pi$
$757$	1306.99			1.72654			0.863269	+	0.504744i	$0.168413\pi$
$758$		0			0
$759$			143.901i			0.189592i
$760$		0			0
$761$	1402.25			1.84264			0.921320	−	0.388804i	$-0.127112\pi$
$761$	1402.25			1.84264			0.921320	+	0.388804i	$0.127112\pi$
$762$		0			0
$763$			850.402i			1.11455i
$764$		0			0
$765$	882.479	−	776.184i	1.15357	−	1.01462i
$766$		0			0
$767$	303.748			0.396021
$768$		0			0
$769$	−359.952			−0.468078			−0.234039	−	0.972227i	$-0.575194\pi$
$769$	−359.952			−0.468078			−0.234039	+	0.972227i	$0.575194\pi$
$770$		0			0
$771$	194.990			0.252905
$772$		0			0
$773$	−437.539			−0.566027			−0.283013	−	0.959116i	$-0.591334\pi$
$773$	−437.539			−0.566027			−0.283013	+	0.959116i	$0.591334\pi$
$774$		0			0
$775$	943.103	+	121.375i	1.21691	+	0.156613i
$776$		0			0
$777$			91.2762i			0.117473i
$778$		0			0
$779$	64.2778			0.0825132
$780$		0			0
$781$			696.141i			0.891346i
$782$		0			0
$783$	−23.0975			−0.0294988
$784$		0			0
$785$	575.547	+	654.365i	0.733181	+	0.833586i
$786$		0			0
$787$		−	438.946i		−	0.557746i	−0.960328	−	0.278873i	$-0.910039\pi$
$787$		−	438.946i		−	0.557746i	0.960328	−	0.278873i	$-0.0899608\pi$
$788$		0			0
$789$			40.0567i			0.0507690i
$790$		0			0
$791$		−	1152.07i		−	1.45647i
$792$		0			0
$793$		−	180.696i		−	0.227864i
$794$		0			0
$795$	147.242	−	129.507i	0.185210	−	0.162902i
$796$		0			0
$797$	−982.414			−1.23264			−0.616320	−	0.787496i	$-0.711377\pi$
$797$	−982.414			−1.23264			−0.616320	+	0.787496i	$0.711377\pi$
$798$		0			0
$799$			1686.95i			2.11133i
$800$		0			0
$801$	926.745			1.15699
$802$		0			0
$803$		−	616.832i		−	0.768160i
$804$		0			0
$805$	−506.943	−	576.366i	−0.629743	−	0.715983i
$806$		0			0
$807$	146.806			0.181916
$808$		0			0
$809$	449.408			0.555510			0.277755	−	0.960652i	$-0.410410\pi$
$809$	449.408			0.555510			0.277755	+	0.960652i	$0.410410\pi$
$810$		0			0
$811$	610.106			0.752288			0.376144	−	0.926561i	$-0.377250\pi$
$811$	610.106			0.752288			0.376144	+	0.926561i	$0.377250\pi$
$812$		0			0
$813$	125.667			0.154572
$814$		0			0
$815$	197.614	−	173.811i	0.242471	−	0.213266i
$816$		0			0
$817$		−	288.585i		−	0.353225i
$818$		0			0
$819$	−386.123			−0.471456
$820$		0			0
$821$		−	1099.76i		−	1.33954i	−0.742568	−	0.669770i	$-0.766393\pi$
$821$		−	1099.76i		−	1.33954i	0.742568	−	0.669770i	$-0.233607\pi$
$822$		0			0
$823$	236.092			0.286867			0.143434	−	0.989660i	$-0.454186\pi$
$823$	236.092			0.286867			0.143434	+	0.989660i	$0.454186\pi$
$824$		0			0
$825$	233.738	+	30.0815i	0.283319	+	0.0364625i
$826$		0			0
$827$			1266.81i			1.53182i	0.642950	+	0.765908i	$0.277710\pi$
$827$			1266.81i			1.53182i	−0.642950	+	0.765908i	$0.722290\pi$
$828$		0			0
$829$			41.7642i			0.0503790i	0.999683	+	0.0251895i	$0.00801891\pi$
$829$			41.7642i			0.0503790i	−0.999683	+	0.0251895i	$0.991981\pi$
$830$		0			0
$831$		−	69.1993i		−	0.0832723i
$832$		0			0
$833$			1408.57i			1.69095i
$834$		0			0
$835$	−253.215	−	287.892i	−0.303252	−	0.344781i
$836$		0			0
$837$	368.778			0.440595
$838$		0			0
$839$		−	816.273i		−	0.972912i	−0.873705	−	0.486456i	$-0.838289\pi$
$839$		−	816.273i		−	0.972912i	0.873705	−	0.486456i	$-0.161711\pi$
$840$		0			0
$841$	835.325			0.993252
$842$		0			0
$843$			251.293i			0.298093i
$844$		0			0
$845$	493.754	+	561.371i	0.584324	+	0.664344i
$846$		0			0
$847$	−1761.32			−2.07948
$848$		0			0
$849$	−255.024			−0.300381
$850$		0			0
$851$	252.933			0.297219
$852$		0			0
$853$	−1215.58			−1.42507			−0.712533	−	0.701639i	$-0.752452\pi$
$853$	−1215.58			−1.42507			−0.712533	+	0.701639i	$0.752452\pi$
$854$		0			0
$855$	−138.660	−	157.648i	−0.162175	−	0.184384i
$856$		0			0
$857$			997.998i			1.16452i	0.813001	+	0.582262i	$0.197832\pi$
$857$			997.998i			1.16452i	−0.813001	+	0.582262i	$0.802168\pi$
$858$		0			0
$859$	1110.42			1.29269			0.646347	−	0.763044i	$-0.276296\pi$
$859$	1110.42			1.29269			0.646347	+	0.763044i	$0.276296\pi$
$860$		0			0
$861$		−	73.3646i		−	0.0852086i
$862$		0			0
$863$	1372.33			1.59019			0.795094	−	0.606486i	$-0.207422\pi$
$863$	1372.33			1.59019			0.795094	+	0.606486i	$0.207422\pi$
$864$		0			0
$865$	−32.1117	−	36.5092i	−0.0371233	−	0.0422072i
$866$		0			0
$867$		−	241.545i		−	0.278599i
$868$		0			0
$869$		−	2182.06i		−	2.51101i
$870$		0			0
$871$		−	225.111i		−	0.258451i
$872$		0			0
$873$			743.280i			0.851409i
$874$		0			0
$875$	−1042.17	+	702.942i	−1.19105	+	0.803362i
$876$		0			0
$877$	776.337			0.885219			0.442609	−	0.896714i	$-0.354053\pi$
$877$	776.337			0.885219			0.442609	+	0.896714i	$0.354053\pi$
$878$		0			0
$879$			90.5034i			0.102962i
$880$		0			0
$881$	1047.38			1.18885			0.594427	−	0.804150i	$-0.297379\pi$
$881$	1047.38			1.18885			0.594427	+	0.804150i	$0.297379\pi$
$882$		0			0
$883$		−	1175.41i		−	1.33116i	−0.746327	−	0.665579i	$-0.768185\pi$
$883$		−	1175.41i		−	1.33116i	0.746327	−	0.665579i	$-0.231815\pi$
$884$		0			0
$885$	141.548	−	124.499i	0.159941	−	0.140676i
$886$		0			0
$887$	109.768			0.123752			0.0618762	−	0.998084i	$-0.480292\pi$
$887$	109.768			0.123752			0.0618762	+	0.998084i	$0.480292\pi$
$888$		0			0
$889$	−446.634			−0.502401
$890$		0			0
$891$	−1256.04			−1.40969
$892$		0			0
$893$	301.361			0.337470
$894$		0			0
$895$	513.497	+	583.818i	0.573740	+	0.652311i
$896$		0			0
$897$		−	36.9039i		−	0.0411414i
$898$		0			0
$899$	90.6094			0.100789
$900$		0			0
$901$			1934.33i			2.14687i
$902$		0			0
$903$	−329.382			−0.364764
$904$		0			0
$905$	939.899	−	826.688i	1.03856	−	0.913468i
$906$		0			0
$907$		−	1639.15i		−	1.80722i	−0.428358	−	0.903609i	$-0.640908\pi$
$907$		−	1639.15i		−	1.80722i	0.428358	−	0.903609i	$-0.359092\pi$
$908$		0			0
$909$		−	724.598i		−	0.797137i
$910$		0			0
$911$		−	6.82023i		−	0.00748654i	−0.999993	−	0.00374327i	$-0.998808\pi$
$911$		−	6.82023i		−	0.00748654i	0.999993	−	0.00374327i	$-0.00119152\pi$
$912$		0			0
$913$			1293.22i			1.41645i
$914$		0			0
$915$	−74.0625	−	84.2050i	−0.0809426	−	0.0920273i
$916$		0			0
$917$	−473.867			−0.516757
$918$		0			0
$919$		−	72.4188i		−	0.0788017i	−0.999223	−	0.0394009i	$-0.987455\pi$
$919$		−	72.4188i		−	0.0788017i	0.999223	−	0.0394009i	$-0.0125449\pi$
$920$		0			0
$921$	−128.914			−0.139972
$922$		0			0
$923$		−	178.528i		−	0.193421i
$924$		0			0
$925$	52.8741	−	410.840i	0.0571612	−	0.444151i
$926$		0			0
$927$	−411.205			−0.443587
$928$		0			0
$929$	−368.537			−0.396703			−0.198352	−	0.980131i	$-0.563559\pi$
$929$	−368.537			−0.396703			−0.198352	+	0.980131i	$0.563559\pi$
$930$		0			0
$931$	251.630			0.270279
$932$		0			0
$933$	115.399			0.123686
$934$		0			0
$935$	−1745.57	+	1535.32i	−1.86692	+	1.64205i
$936$		0			0
$937$			590.172i			0.629852i	0.949116	+	0.314926i	$0.101980\pi$
$937$			590.172i			0.629852i	−0.949116	+	0.314926i	$0.898020\pi$
$938$		0			0
$939$	174.599			0.185941
$940$		0			0
$941$			189.017i			0.200869i	0.994944	+	0.100434i	$0.0320232\pi$
$941$			189.017i			0.200869i	−0.994944	+	0.100434i	$0.967977\pi$
$942$		0			0
$943$	−203.299			−0.215588
$944$		0			0
$945$	−366.076	+	321.982i	−0.387382	+	0.340721i
$946$		0			0
$947$			664.319i			0.701498i	0.936470	+	0.350749i	$0.114073\pi$
$947$			664.319i			0.701498i	−0.936470	+	0.350749i	$0.885927\pi$
$948$		0			0
$949$			158.189i			0.166690i
$950$		0			0
$951$			38.5610i			0.0405479i
$952$		0			0
$953$			173.943i			0.182522i	0.995827	+	0.0912610i	$0.0290898\pi$
$953$			173.943i			0.182522i	−0.995827	+	0.0912610i	$0.970910\pi$
$954$		0			0
$955$	417.221	−	366.967i	0.436881	−	0.384259i
$956$		0			0
$957$	22.4566			0.0234656
$958$		0			0
$959$			632.175i			0.659202i
$960$		0			0
$961$	−485.680			−0.505390
$962$		0			0
$963$			1649.76i			1.71314i
$964$		0			0
$965$	−38.5581	+	33.9138i	−0.0399566	+	0.0351438i
$966$		0			0
$967$	255.364			0.264078			0.132039	−	0.991245i	$-0.457848\pi$
$967$	255.364			0.264078			0.132039	+	0.991245i	$0.457848\pi$
$968$		0			0
$969$	−71.4309			−0.0737161
$970$		0			0
$971$	−1623.60			−1.67209			−0.836046	−	0.548659i	$-0.815139\pi$
$971$	−1623.60			−1.67209			−0.836046	+	0.548659i	$0.815139\pi$
$972$		0			0
$973$	−1290.46			−1.32627
$974$		0			0
$975$	−59.9430	−	7.71453i	−0.0614800	−	0.00791233i
$976$		0			0
$977$			104.946i			0.107416i	0.998557	+	0.0537082i	$0.0171041\pi$
$977$			104.946i			0.107416i	−0.998557	+	0.0537082i	$0.982896\pi$
$978$		0			0
$979$	−1833.13			−1.87245
$980$		0			0
$981$		−	735.681i		−	0.749930i
$982$		0			0
$983$	−889.933			−0.905323			−0.452662	−	0.891682i	$-0.649525\pi$
$983$	−889.933			−0.905323			−0.452662	+	0.891682i	$0.649525\pi$
$984$		0			0
$985$	−538.960	−	612.768i	−0.547167	−	0.622099i
$986$		0			0
$987$		−	343.964i		−	0.348494i
$988$		0			0
$989$			912.742i			0.922894i
$990$		0			0
$991$		−	1509.57i		−	1.52328i	−0.648001	−	0.761639i	$-0.724395\pi$
$991$		−	1509.57i		−	1.52328i	0.648001	−	0.761639i	$-0.275605\pi$
$992$		0			0
$993$		−	153.821i		−	0.154905i
$994$		0			0
$995$	732.215	−	644.020i	0.735894	−	0.647256i
$996$		0			0
$997$	1599.93			1.60474			0.802371	−	0.596825i	$-0.203571\pi$
$997$	1599.93			1.60474			0.802371	+	0.596825i	$0.203571\pi$
$998$		0			0
$999$		−	160.649i		−	0.160810i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.3.e.h.639.4		6
4.3	odd	2		1280.3.e.i.639.3		6
5.4	even	2		1280.3.e.g.639.3		6
8.3	odd	2		1280.3.e.g.639.4		6
8.5	even	2		1280.3.e.f.639.3		6
16.3	odd	4		160.3.h.a.159.4	yes	6
16.5	even	4		320.3.h.f.319.3		6
16.11	odd	4		320.3.h.g.319.3		6
16.13	even	4		160.3.h.b.159.4	yes	6
20.19	odd	2		1280.3.e.f.639.4		6
40.19	odd	2	inner	1280.3.e.h.639.3		6
40.29	even	2		1280.3.e.i.639.4		6
48.29	odd	4		1440.3.j.b.1279.5		6
48.35	even	4		1440.3.j.a.1279.5		6
80.3	even	4		800.3.b.i.351.4		6
80.13	odd	4		800.3.b.i.351.3		6
80.19	odd	4		160.3.h.b.159.3	yes	6
80.27	even	4		1600.3.b.v.1151.4		6
80.29	even	4		160.3.h.a.159.3	✓	6
80.37	odd	4		1600.3.b.v.1151.3		6
80.43	even	4		1600.3.b.w.1151.3		6
80.53	odd	4		1600.3.b.w.1151.4		6
80.59	odd	4		320.3.h.f.319.4		6
80.67	even	4		800.3.b.h.351.3		6
80.69	even	4		320.3.h.g.319.4		6
80.77	odd	4		800.3.b.h.351.4		6
240.29	odd	4		1440.3.j.a.1279.6		6
240.179	even	4		1440.3.j.b.1279.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.3.h.a.159.3	✓	6	80.29	even	4
160.3.h.a.159.4	yes	6	16.3	odd	4
160.3.h.b.159.3	yes	6	80.19	odd	4
160.3.h.b.159.4	yes	6	16.13	even	4
320.3.h.f.319.3		6	16.5	even	4
320.3.h.f.319.4		6	80.59	odd	4
320.3.h.g.319.3		6	16.11	odd	4
320.3.h.g.319.4		6	80.69	even	4
800.3.b.h.351.3		6	80.67	even	4
800.3.b.h.351.4		6	80.77	odd	4
800.3.b.i.351.3		6	80.13	odd	4
800.3.b.i.351.4		6	80.3	even	4
1280.3.e.f.639.3		6	8.5	even	2
1280.3.e.f.639.4		6	20.19	odd	2
1280.3.e.g.639.3		6	5.4	even	2
1280.3.e.g.639.4		6	8.3	odd	2
1280.3.e.h.639.3		6	40.19	odd	2	inner
1280.3.e.h.639.4		6	1.1	even	1	trivial
1280.3.e.i.639.3		6	4.3	odd	2
1280.3.e.i.639.4		6	40.29	even	2
1440.3.j.a.1279.5		6	48.35	even	4
1440.3.j.a.1279.6		6	240.29	odd	4
1440.3.j.b.1279.5		6	48.29	odd	4
1440.3.j.b.1279.6		6	240.179	even	4
1600.3.b.v.1151.3		6	80.37	odd	4
1600.3.b.v.1151.4		6	80.27	even	4
1600.3.b.w.1151.3		6	80.43	even	4
1600.3.b.w.1151.4		6	80.53	odd	4

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:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1280.e (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+0.547781i q^{3} +(-3.30219 - 3.75441i) q^{5} -10.0566 q^{7} +8.69994 q^{9} +O(q^{10})\)	\(q+0.547781i q^{3} +(-3.30219 - 3.75441i) q^{5} -10.0566 q^{7} +8.69994 q^{9} -17.2087 q^{11} +4.41325 q^{13} +(2.05659 - 1.80888i) q^{15} +27.0176i q^{17} +4.82650 q^{19} -5.50881i q^{21} -15.2653 q^{23} +(-3.19112 + 24.7955i) q^{25} +9.69569i q^{27} +2.38225i q^{29} -38.0352i q^{31} -9.42663i q^{33} +(33.2087 + 37.7565i) q^{35} -16.5691 q^{37} +2.41749i q^{39} +13.3177 q^{41} -59.7918i q^{43} +(-28.7288 - 32.6631i) q^{45} +62.4388 q^{47} +52.1351 q^{49} -14.7997 q^{51} +71.5952 q^{53} +(56.8265 + 64.6086i) q^{55} +2.64386i q^{57} +68.8265 q^{59} -40.9439i q^{61} -87.4917 q^{63} +(-14.5734 - 16.5691i) q^{65} -51.0080i q^{67} -8.36206i q^{69} -40.4527i q^{71} +35.8441i q^{73} +(-13.5825 - 1.74804i) q^{75} +173.061 q^{77} +126.800i q^{79} +72.9883 q^{81} -75.1490i q^{83} +(101.435 - 89.2172i) q^{85} -1.30495 q^{87} +106.523 q^{89} -44.3822 q^{91} +20.8350 q^{93} +(-15.9380 - 18.1206i) q^{95} +85.4351i q^{97} -149.715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 8 q^{5} - 12 q^{7} - 18 q^{9}+O(q^{10}) \) 6 * q + 8 * q^5 - 12 * q^7 - 18 * q^9	\( 6 q + 8 q^{5} - 12 q^{7} - 18 q^{9} + 8 q^{11} - 36 q^{15} - 24 q^{19} + 68 q^{23} + 10 q^{25} + 88 q^{35} - 208 q^{37} + 68 q^{41} - 232 q^{45} + 268 q^{47} - 62 q^{49} + 192 q^{51} + 64 q^{53} + 288 q^{55} + 360 q^{59} - 172 q^{63} - 304 q^{75} + 400 q^{77} + 238 q^{81} + 304 q^{85} - 584 q^{87} - 76 q^{89} - 208 q^{91} - 320 q^{93} - 32 q^{95} - 856 q^{99}+O(q^{100}) \) 6 * q + 8 * q^5 - 12 * q^7 - 18 * q^9 + 8 * q^11 - 36 * q^15 - 24 * q^19 + 68 * q^23 + 10 * q^25 + 88 * q^35 - 208 * q^37 + 68 * q^41 - 232 * q^45 + 268 * q^47 - 62 * q^49 + 192 * q^51 + 64 * q^53 + 288 * q^55 + 360 * q^59 - 172 * q^63 - 304 * q^75 + 400 * q^77 + 238 * q^81 + 304 * q^85 - 584 * q^87 - 76 * q^89 - 208 * q^91 - 320 * q^93 - 32 * q^95 - 856 * q^99

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