LMFDB - Embedded newform 1280.3.e.f.639.2

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			639.2
Root			$-1.37720i$ of defining polynomial
Character	$\chi$	$=$	1280.639
Dual form			1280.3.e.f.639.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.75441i q^{3} +(-2.54778 - 4.30219i) q^{5} +3.84997 q^{7} +1.41325 q^{9} +O(q^{10})$	$q-2.75441i q^{3} +(-2.54778 - 4.30219i) q^{5} +3.84997 q^{7} +1.41325 q^{9} -6.19112 q^{11} +16.1132 q^{13} +(-11.8500 + 7.01762i) q^{15} -5.20875i q^{17} +36.2264 q^{19} -10.6044i q^{21} +22.0411 q^{23} +(-12.0176 + 21.9221i) q^{25} -28.6823i q^{27} -20.0352i q^{29} +26.4175i q^{31} +17.0529i q^{33} +(-9.80888 - 16.5633i) q^{35} +69.3219 q^{37} -44.3822i q^{39} -11.6220 q^{41} -25.8542i q^{43} +(-3.60065 - 6.08006i) q^{45} +66.1853 q^{47} -34.1777 q^{49} -14.3470 q^{51} -39.5751 q^{53} +(15.7736 + 26.6354i) q^{55} -99.7821i q^{57} -27.7736 q^{59} -54.1954i q^{61} +5.44096 q^{63} +(-41.0529 - 69.3219i) q^{65} +107.507i q^{67} -60.7101i q^{69} +70.7997i q^{71} -37.4351i q^{73} +(60.3822 + 33.1014i) q^{75} -23.8356 q^{77} +97.6530i q^{79} -66.2835 q^{81} -126.163i q^{83} +(-22.4090 + 13.2707i) q^{85} -55.1852 q^{87} -133.635 q^{89} +62.0352 q^{91} +72.7645 q^{93} +(-92.2969 - 155.853i) q^{95} +6.40900i q^{97} -8.74960 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$		−	2.75441i		−	0.918135i	−0.888401	−	0.459068i	$-0.848184\pi$
$3$		−	2.75441i		−	0.918135i	0.888401	−	0.459068i	$-0.151816\pi$
$4$		0			0
$5$	−2.54778	−	4.30219i	−0.509556	−	0.860437i
$5$	−2.54778	−	4.30219i	−0.509556	−	0.860437i
$6$		0			0
$7$	3.84997			0.549995			0.274998	−	0.961445i	$-0.411323\pi$
$7$	3.84997			0.549995			0.274998	+	0.961445i	$0.411323\pi$
$8$		0			0
$9$	1.41325			0.157028
$10$		0			0
$11$	−6.19112			−0.562829			−0.281415	−	0.959586i	$-0.590804\pi$
$11$	−6.19112			−0.562829			−0.281415	+	0.959586i	$0.590804\pi$
$12$		0			0
$13$	16.1132			1.23948			0.619738	−	0.784809i	$-0.287239\pi$
$13$	16.1132			1.23948			0.619738	+	0.784809i	$0.287239\pi$
$14$		0			0
$15$	−11.8500	+	7.01762i	−0.789998	+	0.467842i
$16$		0			0
$17$		−	5.20875i		−	0.306397i	−0.988195	−	0.153198i	$-0.951043\pi$
$17$		−	5.20875i		−	0.306397i	0.988195	−	0.153198i	$-0.0489574\pi$
$18$		0			0
$19$	36.2264			1.90665			0.953326	−	0.301944i	$-0.0976357\pi$
$19$	36.2264			1.90665			0.953326	+	0.301944i	$0.0976357\pi$
$20$		0			0
$21$		−	10.6044i		−	0.504970i
$22$		0			0
$23$	22.0411			0.958308			0.479154	−	0.877731i	$-0.340943\pi$
$23$	22.0411			0.958308			0.479154	+	0.877731i	$0.340943\pi$
$24$		0			0
$25$	−12.0176	+	21.9221i	−0.480705	+	0.876882i
$26$		0			0
$27$		−	28.6823i		−	1.06231i
$28$		0			0
$29$		−	20.0352i		−	0.690871i	−0.938443	−	0.345435i	$-0.887731\pi$
$29$		−	20.0352i		−	0.690871i	0.938443	−	0.345435i	$-0.112269\pi$
$30$		0			0
$31$			26.4175i			0.852177i	0.904681	+	0.426089i	$0.140109\pi$
$31$			26.4175i			0.852177i	−0.904681	+	0.426089i	$0.859891\pi$
$32$		0			0
$33$			17.0529i			0.516754i
$34$		0			0
$35$	−9.80888	−	16.5633i	−0.280254	−	0.473237i
$36$		0			0
$37$	69.3219			1.87357			0.936783	−	0.349911i	$-0.113788\pi$
$37$	69.3219			1.87357			0.936783	+	0.349911i	$0.113788\pi$
$38$		0			0
$39$		−	44.3822i		−	1.13801i
$40$		0			0
$41$	−11.6220			−0.283463			−0.141732	−	0.989905i	$-0.545267\pi$
$41$	−11.6220			−0.283463			−0.141732	+	0.989905i	$0.545267\pi$
$42$		0			0
$43$		−	25.8542i		−	0.601261i	−0.953741	−	0.300630i	$-0.902803\pi$
$43$		−	25.8542i		−	0.601261i	0.953741	−	0.300630i	$-0.0971971\pi$
$44$		0			0
$45$	−3.60065	−	6.08006i	−0.0800144	−	0.135112i
$46$		0			0
$47$	66.1853			1.40820			0.704099	−	0.710102i	$-0.251351\pi$
$47$	66.1853			1.40820			0.704099	+	0.710102i	$0.251351\pi$
$48$		0			0
$49$	−34.1777			−0.697505
$50$		0			0
$51$	−14.3470			−0.281314
$52$		0			0
$53$	−39.5751			−0.746699			−0.373350	−	0.927691i	$-0.621791\pi$
$53$	−39.5751			−0.746699			−0.373350	+	0.927691i	$0.621791\pi$
$54$		0			0
$55$	15.7736	+	26.6354i	0.286793	+	0.484280i
$56$		0			0
$57$		−	99.7821i		−	1.75056i
$58$		0			0
$59$	−27.7736			−0.470739			−0.235370	−	0.971906i	$-0.575630\pi$
$59$	−27.7736			−0.470739			−0.235370	+	0.971906i	$0.575630\pi$
$60$		0			0
$61$		−	54.1954i		−	0.888449i	−0.895916	−	0.444224i	$-0.853479\pi$
$61$		−	54.1954i		−	0.888449i	0.895916	−	0.444224i	$-0.146521\pi$
$62$		0			0
$63$	5.44096			0.0863645
$64$		0			0
$65$	−41.0529	−	69.3219i	−0.631583	−	1.06649i
$66$		0			0
$67$			107.507i			1.60459i	0.596931	+	0.802293i	$0.296387\pi$
$67$			107.507i			1.60459i	−0.596931	+	0.802293i	$0.703613\pi$
$68$		0			0
$69$		−	60.7101i		−	0.879857i
$70$		0			0
$71$			70.7997i			0.997179i	0.866838	+	0.498590i	$0.166149\pi$
$71$			70.7997i			0.997179i	−0.866838	+	0.498590i	$0.833851\pi$
$72$		0			0
$73$		−	37.4351i		−	0.512810i	−0.966569	−	0.256405i	$-0.917462\pi$
$73$		−	37.4351i		−	0.512810i	0.966569	−	0.256405i	$-0.0825380\pi$
$74$		0			0
$75$	60.3822	+	33.1014i	0.805097	+	0.441352i
$76$		0			0
$77$	−23.8356			−0.309554
$78$		0			0
$79$			97.6530i			1.23611i	0.786133	+	0.618057i	$0.212080\pi$
$79$			97.6530i			1.23611i	−0.786133	+	0.618057i	$0.787920\pi$
$80$		0			0
$81$	−66.2835			−0.818315
$82$		0			0
$83$		−	126.163i		−	1.52003i	−0.649904	−	0.760017i	$-0.725191\pi$
$83$		−	126.163i		−	1.52003i	0.649904	−	0.760017i	$-0.274809\pi$
$84$		0			0
$85$	−22.4090	+	13.2707i	−0.263635	+	0.156126i
$86$		0			0
$87$	−55.1852			−0.634313
$88$		0			0
$89$	−133.635			−1.50151			−0.750757	−	0.660579i	$-0.770311\pi$
$89$	−133.635			−1.50151			−0.750757	+	0.660579i	$0.770311\pi$
$90$		0			0
$91$	62.0352			0.681706
$92$		0			0
$93$	72.7645			0.782414
$94$		0			0
$95$	−92.2969	−	155.853i	−0.971546	−	1.64055i
$96$		0			0
$97$			6.40900i			0.0660722i	0.999454	+	0.0330361i	$0.0105176\pi$
$97$			6.40900i			0.0660722i	−0.999454	+	0.0330361i	$0.989482\pi$
$98$		0			0
$99$	−8.74960			−0.0883798
$100$		0			0
$101$		−	121.564i		−	1.20361i	−0.798644	−	0.601803i	$-0.794449\pi$
$101$		−	121.564i		−	1.20361i	0.798644	−	0.601803i	$-0.205551\pi$
$102$		0			0
$103$	−9.95891			−0.0966884			−0.0483442	−	0.998831i	$-0.515394\pi$
$103$	−9.95891			−0.0966884			−0.0483442	+	0.998831i	$0.515394\pi$
$104$		0			0
$105$	−45.6220	+	27.0176i	−0.434495	+	0.257311i
$106$		0			0
$107$			134.842i			1.26020i	0.776512	+	0.630102i	$0.216987\pi$
$107$			134.842i			1.26020i	−0.776512	+	0.630102i	$0.783013\pi$
$108$		0			0
$109$		−	28.2306i		−	0.258996i	−0.991580	−	0.129498i	$-0.958663\pi$
$109$		−	28.2306i		−	0.258996i	0.991580	−	0.129498i	$-0.0413367\pi$
$110$		0			0
$111$		−	190.941i		−	1.72019i
$112$		0			0
$113$		−	190.052i		−	1.68188i	−0.541130	−	0.840939i	$-0.682003\pi$
$113$		−	190.052i		−	1.68188i	0.541130	−	0.840939i	$-0.317997\pi$
$114$		0			0
$115$	−56.1559	−	94.8249i	−0.488312	−	0.824564i
$116$		0			0
$117$	22.7719			0.194632
$118$		0			0
$119$		−	20.0535i		−	0.168517i
$120$		0			0
$121$	−82.6700			−0.683223
$122$		0			0
$123$			32.0117i			0.260258i
$124$		0			0
$125$	124.931	−	4.15055i	0.999449	−	0.0332044i
$126$		0			0
$127$	60.0646			0.472950			0.236475	−	0.971638i	$-0.424008\pi$
$127$	60.0646			0.472950			0.236475	+	0.971638i	$0.424008\pi$
$128$		0			0
$129$	−71.2130			−0.552039
$130$		0			0
$131$	−111.985			−0.854848			−0.427424	−	0.904051i	$-0.640579\pi$
$131$	−111.985			−0.854848			−0.427424	+	0.904051i	$0.640579\pi$
$132$		0			0
$133$	139.470			1.04865
$134$		0			0
$135$	−123.397	+	73.0763i	−0.914049	+	0.541306i
$136$		0			0
$137$			42.6439i			0.311269i	0.987815	+	0.155635i	$0.0497422\pi$
$137$			42.6439i			0.311269i	−0.987815	+	0.155635i	$0.950258\pi$
$138$		0			0
$139$	−222.332			−1.59951			−0.799756	−	0.600325i	$-0.795038\pi$
$139$	−222.332			−1.59951			−0.799756	+	0.600325i	$0.795038\pi$
$140$		0			0
$141$		−	182.301i		−	1.29292i
$142$		0			0
$143$	−99.7587			−0.697614
$144$		0			0
$145$	−86.1954	+	51.0454i	−0.594451	+	0.352037i
$146$		0			0
$147$			94.1394i			0.640404i
$148$		0			0
$149$		−	20.0981i		−	0.134887i	−0.997723	−	0.0674434i	$-0.978516\pi$
$149$		−	20.0981i		−	0.134887i	0.997723	−	0.0674434i	$-0.0214842\pi$
$150$		0			0
$151$		−	86.0522i		−	0.569882i	−0.958545	−	0.284941i	$-0.908026\pi$
$151$		−	86.0522i		−	0.569882i	0.958545	−	0.284941i	$-0.0919741\pi$
$152$		0			0
$153$		−	7.36126i		−	0.0481128i
$154$		0			0
$155$	113.653	−	67.3060i	0.733245	−	0.434232i
$156$		0			0
$157$	16.0342			0.102129			0.0510643	−	0.998695i	$-0.483739\pi$
$157$	16.0342			0.102129			0.0510643	+	0.998695i	$0.483739\pi$
$158$		0			0
$159$			109.006i			0.685571i
$160$		0			0
$161$	84.8575			0.527065
$162$		0			0
$163$			179.157i			1.09912i	0.835454	+	0.549561i	$0.185205\pi$
$163$			179.157i			1.09912i	−0.835454	+	0.549561i	$0.814795\pi$
$164$		0			0
$165$	73.3646	−	43.4470i	0.444634	−	0.263315i
$166$		0			0
$167$	137.800			0.825149			0.412574	−	0.910924i	$-0.364630\pi$
$167$	137.800			0.825149			0.412574	+	0.910924i	$0.364630\pi$
$168$		0			0
$169$	90.6347			0.536300
$170$		0			0
$171$	51.1969			0.299397
$172$		0			0
$173$	−62.8895			−0.363523			−0.181762	−	0.983343i	$-0.558180\pi$
$173$	−62.8895			−0.363523			−0.181762	+	0.983343i	$0.558180\pi$
$174$		0			0
$175$	−46.2675	+	84.3992i	−0.264385	+	0.482281i
$176$		0			0
$177$			76.4998i			0.432203i
$178$		0			0
$179$	238.020			1.32972			0.664861	−	0.746967i	$-0.268491\pi$
$179$	238.020			1.32972			0.664861	+	0.746967i	$0.268491\pi$
$180$		0			0
$181$		−	186.718i		−	1.03159i	−0.856712	−	0.515795i	$-0.827497\pi$
$181$		−	186.718i		−	1.03159i	0.856712	−	0.515795i	$-0.172503\pi$
$182$		0			0
$183$	−149.276			−0.815716
$184$		0			0
$185$	−176.617	−	298.236i	−0.954687	−	1.61209i
$186$		0			0
$187$			32.2480i			0.172449i
$188$		0			0
$189$		−	110.426i		−	0.584264i
$190$		0			0
$191$			123.447i			0.646319i	0.946344	+	0.323160i	$0.104745\pi$
$191$			123.447i			0.646319i	−0.946344	+	0.323160i	$0.895255\pi$
$192$		0			0
$193$			162.355i			0.841220i	0.907242	+	0.420610i	$0.138184\pi$
$193$			162.355i			0.841220i	−0.907242	+	0.420610i	$0.861816\pi$
$194$		0			0
$195$	−190.941	+	113.076i	−0.979183	+	0.579878i
$196$		0			0
$197$	−113.540			−0.576344			−0.288172	−	0.957579i	$-0.593048\pi$
$197$	−113.540			−0.576344			−0.288172	+	0.957579i	$0.593048\pi$
$198$		0			0
$199$		−	325.928i		−	1.63783i	−0.573915	−	0.818915i	$-0.694576\pi$
$199$		−	325.928i		−	1.63783i	0.573915	−	0.818915i	$-0.305424\pi$
$200$		0			0
$201$	296.118			1.47323
$202$		0			0
$203$		−	77.1351i		−	0.379976i
$204$		0			0
$205$	29.6103	+	50.0000i	0.144441	+	0.243902i
$206$		0			0
$207$	31.1496			0.150481
$208$		0			0
$209$	−224.282			−1.07312
$210$		0			0
$211$	130.731			0.619580			0.309790	−	0.950805i	$-0.399741\pi$
$211$	130.731			0.619580			0.309790	+	0.950805i	$0.399741\pi$
$212$		0			0
$213$	195.011			0.915546
$214$		0			0
$215$	−111.230	+	65.8709i	−0.517347	+	0.306376i
$216$		0			0
$217$			101.707i			0.468694i
$218$		0			0
$219$	−103.112			−0.470829
$220$		0			0
$221$		−	83.9295i		−	0.379772i
$222$		0			0
$223$	93.3889			0.418784			0.209392	−	0.977832i	$-0.432851\pi$
$223$	93.3889			0.418784			0.209392	+	0.977832i	$0.432851\pi$
$224$		0			0
$225$	−16.9839	+	30.9813i	−0.0754840	+	0.137695i
$226$		0			0
$227$		−	14.9957i		−	0.0660602i	−0.999454	−	0.0330301i	$-0.989484\pi$
$227$		−	14.9957i		−	0.0660602i	0.999454	−	0.0330301i	$-0.0105157\pi$
$228$		0			0
$229$			144.106i			0.629283i	0.949211	+	0.314641i	$0.101884\pi$
$229$			144.106i			0.629283i	−0.949211	+	0.314641i	$0.898116\pi$
$230$		0			0
$231$			65.6530i			0.284212i
$232$		0			0
$233$			126.528i			0.543040i	0.962433	+	0.271520i	$0.0875263\pi$
$233$			126.528i			0.543040i	−0.962433	+	0.271520i	$0.912474\pi$
$234$		0			0
$235$	−168.626	−	284.741i	−0.717556	−	1.21167i
$236$		0			0
$237$	268.976			1.13492
$238$		0			0
$239$			1.65300i			0.00691630i	0.999994	+	0.00345815i	$0.00110077\pi$
$239$			1.65300i			0.00691630i	−0.999994	+	0.00345815i	$0.998899\pi$
$240$		0			0
$241$	206.928			0.858622			0.429311	−	0.903157i	$-0.358756\pi$
$241$	206.928			0.858622			0.429311	+	0.903157i	$0.358756\pi$
$242$		0			0
$243$		−	75.5692i		−	0.310984i
$244$		0			0
$245$	87.0774	+	147.039i	0.355418	+	0.600159i
$246$		0			0
$247$	583.722			2.36325
$248$		0			0
$249$	−347.503			−1.39560
$250$		0			0
$251$	−74.1206			−0.295301			−0.147651	−	0.989040i	$-0.547171\pi$
$251$	−74.1206			−0.295301			−0.147651	+	0.989040i	$0.547171\pi$
$252$		0			0
$253$	−136.459			−0.539364
$254$		0			0
$255$	36.5530	+	61.7235i	0.143345	+	0.242053i
$256$		0			0
$257$		−	274.682i		−	1.06880i	−0.845231	−	0.534402i	$-0.820537\pi$
$257$		−	274.682i		−	1.06880i	0.845231	−	0.534402i	$-0.179463\pi$
$258$		0			0
$259$	266.887			1.03045
$260$		0			0
$261$		−	28.3148i		−	0.108486i
$262$		0			0
$263$	75.5382			0.287218			0.143609	−	0.989635i	$-0.454129\pi$
$263$	75.5382			0.287218			0.143609	+	0.989635i	$0.454129\pi$
$264$		0			0
$265$	100.829	+	170.259i	0.380485	+	0.642488i
$266$		0			0
$267$			368.084i			1.37859i
$268$		0			0
$269$			314.087i			1.16761i	0.811895	+	0.583804i	$0.198436\pi$
$269$			314.087i			1.16761i	−0.811895	+	0.583804i	$0.801564\pi$
$270$		0			0
$271$			128.158i			0.472908i	0.971643	+	0.236454i	$0.0759852\pi$
$271$			128.158i			0.472908i	−0.971643	+	0.236454i	$0.924015\pi$
$272$		0			0
$273$		−	170.870i		−	0.625898i
$274$		0			0
$275$	74.4026	−	135.722i	0.270555	−	0.493535i
$276$		0			0
$277$	−242.118			−0.874073			−0.437037	−	0.899444i	$-0.643972\pi$
$277$	−242.118			−0.874073			−0.437037	+	0.899444i	$0.643972\pi$
$278$		0			0
$279$			37.3345i			0.133815i
$280$		0			0
$281$	−28.8562			−0.102691			−0.0513456	−	0.998681i	$-0.516351\pi$
$281$	−28.8562			−0.102691			−0.0513456	+	0.998681i	$0.516351\pi$
$282$		0			0
$283$		−	269.993i		−	0.954039i	−0.878893	−	0.477020i	$-0.841717\pi$
$283$		−	269.993i		−	0.954039i	0.878893	−	0.477020i	$-0.158283\pi$
$284$		0			0
$285$	−429.281	+	254.223i	−1.50625	+	0.892011i
$286$		0			0
$287$	−44.7443			−0.155904
$288$		0			0
$289$	261.869			0.906121
$290$		0			0
$291$	17.6530			0.0606632
$292$		0			0
$293$	−353.448			−1.20631			−0.603154	−	0.797625i	$-0.706089\pi$
$293$	−353.448			−1.20631			−0.603154	+	0.797625i	$0.706089\pi$
$294$		0			0
$295$	70.7611	+	119.487i	0.239868	+	0.405042i
$296$		0			0
$297$			177.576i			0.597898i
$298$		0			0
$299$	355.152			1.18780
$300$		0			0
$301$		−	99.5379i		−	0.330691i
$302$		0			0
$303$	−334.837			−1.10507
$304$		0			0
$305$	−233.159	+	138.078i	−0.764454	+	0.452715i
$306$		0			0
$307$		−	260.946i		−	0.849985i	−0.905197	−	0.424993i	$-0.860277\pi$
$307$		−	260.946i		−	0.849985i	0.905197	−	0.424993i	$-0.139723\pi$
$308$		0			0
$309$			27.4309i			0.0887730i
$310$		0			0
$311$			141.570i			0.455208i	0.973754	+	0.227604i	$0.0730892\pi$
$311$			141.570i			0.455208i	−0.973754	+	0.227604i	$0.926911\pi$
$312$		0			0
$313$		−	365.950i		−	1.16917i	−0.811333	−	0.584584i	$-0.801258\pi$
$313$		−	365.950i		−	1.16917i	0.811333	−	0.584584i	$-0.198742\pi$
$314$		0			0
$315$	−13.8624	−	23.4080i	−0.0440076	−	0.0743113i
$316$		0			0
$317$	−9.22805			−0.0291106			−0.0145553	−	0.999894i	$-0.504633\pi$
$317$	−9.22805			−0.0291106			−0.0145553	+	0.999894i	$0.504633\pi$
$318$		0			0
$319$			124.041i			0.388842i
$320$		0			0
$321$	371.409			1.15704
$322$		0			0
$323$		−	188.694i		−	0.584192i
$324$		0			0
$325$	−193.642	+	353.234i	−0.595822	+	1.08687i
$326$		0			0
$327$	−77.7586			−0.237794
$328$		0			0
$329$	254.811			0.774502
$330$		0			0
$331$	53.3799			0.161268			0.0806342	−	0.996744i	$-0.474305\pi$
$331$	53.3799			0.161268			0.0806342	+	0.996744i	$0.474305\pi$
$332$		0			0
$333$	97.9692			0.294202
$334$		0			0
$335$	462.516	−	273.905i	1.38065	−	0.817626i
$336$		0			0
$337$		−	350.458i		−	1.03994i	−0.854186	−	0.519968i	$-0.825944\pi$
$337$		−	350.458i		−	1.03994i	0.854186	−	0.519968i	$-0.174056\pi$
$338$		0			0
$339$	−523.481			−1.54419
$340$		0			0
$341$		−	163.554i		−	0.479630i
$342$		0			0
$343$	−320.232			−0.933620
$344$		0			0
$345$	−261.186	+	154.676i	−0.757062	+	0.448336i
$346$		0			0
$347$		−	70.8302i		−	0.204122i	−0.994778	−	0.102061i	$-0.967456\pi$
$347$		−	70.8302i		−	0.204122i	0.994778	−	0.102061i	$-0.0325436\pi$
$348$		0			0
$349$			373.045i			1.06890i	0.845201	+	0.534449i	$0.179481\pi$
$349$			373.045i			1.06890i	−0.845201	+	0.534449i	$0.820519\pi$
$350$		0			0
$351$		−	462.163i		−	1.31670i
$352$		0			0
$353$			543.568i			1.53985i	0.638132	+	0.769927i	$0.279707\pi$
$353$			543.568i			1.53985i	−0.638132	+	0.769927i	$0.720293\pi$
$354$		0			0
$355$	304.594	−	180.382i	0.858010	−	0.508119i
$356$		0			0
$357$	−55.2355			−0.154721
$358$		0			0
$359$			500.805i			1.39500i	0.716585	+	0.697500i	$0.245704\pi$
$359$			500.805i			1.39500i	−0.716585	+	0.697500i	$0.754296\pi$
$360$		0			0
$361$	951.350			2.63532
$362$		0			0
$363$			227.707i			0.627291i
$364$		0			0
$365$	−161.053	+	95.3765i	−0.441241	+	0.261305i
$366$		0			0
$367$	142.499			0.388281			0.194140	−	0.980974i	$-0.437808\pi$
$367$	142.499			0.388281			0.194140	+	0.980974i	$0.437808\pi$
$368$		0			0
$369$	−16.4248			−0.0445116
$370$		0			0
$371$	−152.363			−0.410681
$372$		0			0
$373$	−160.000			−0.428954			−0.214477	−	0.976729i	$-0.568805\pi$
$373$	−160.000			−0.428954			−0.214477	+	0.976729i	$0.568805\pi$
$374$		0			0
$375$	−11.4323	−	344.111i	−0.0304862	−	0.917629i
$376$		0			0
$377$		−	322.832i		−	0.856317i
$378$		0			0
$379$	192.796			0.508698			0.254349	−	0.967113i	$-0.418139\pi$
$379$	192.796			0.508698			0.254349	+	0.967113i	$0.418139\pi$
$380$		0			0
$381$		−	165.442i		−	0.434232i
$382$		0			0
$383$	605.286			1.58038			0.790191	−	0.612861i	$-0.209981\pi$
$383$	605.286			1.58038			0.790191	+	0.612861i	$0.209981\pi$
$384$		0			0
$385$	60.7280	+	102.545i	0.157735	+	0.266352i
$386$		0			0
$387$		−	36.5384i		−	0.0944146i
$388$		0			0
$389$			522.159i			1.34231i	0.741317	+	0.671155i	$0.234202\pi$
$389$			522.159i			1.34231i	−0.741317	+	0.671155i	$0.765798\pi$
$390$		0			0
$391$		−	114.806i		−	0.293623i
$392$		0			0
$393$			308.452i			0.784866i
$394$		0			0
$395$	420.121	−	248.798i	1.06360	−	0.629870i
$396$		0			0
$397$	−357.537			−0.900598			−0.450299	−	0.892878i	$-0.648683\pi$
$397$	−357.537			−0.900598			−0.450299	+	0.892878i	$0.648683\pi$
$398$		0			0
$399$		−	384.158i		−	0.962802i
$400$		0			0
$401$	262.506			0.654629			0.327315	−	0.944915i	$-0.393856\pi$
$401$	262.506			0.654629			0.327315	+	0.944915i	$0.393856\pi$
$402$		0			0
$403$			425.670i			1.05625i
$404$		0			0
$405$	168.876	+	285.164i	0.416977	+	0.704108i
$406$		0			0
$407$	−429.181			−1.05450
$408$		0			0
$409$	63.2015			0.154527			0.0772634	−	0.997011i	$-0.475382\pi$
$409$	63.2015			0.154527			0.0772634	+	0.997011i	$0.475382\pi$
$410$		0			0
$411$	117.459			0.285787
$412$		0			0
$413$	−106.928			−0.258905
$414$		0			0
$415$	−542.776	+	321.435i	−1.30789	+	0.774542i
$416$		0			0
$417$			612.393i			1.46857i
$418$		0			0
$419$	−673.390			−1.60714			−0.803568	−	0.595213i	$-0.797068\pi$
$419$	−673.390			−1.60714			−0.803568	+	0.595213i	$0.797068\pi$
$420$		0			0
$421$		−	84.6877i		−	0.201158i	−0.994929	−	0.100579i	$-0.967930\pi$
$421$		−	84.6877i		−	0.201158i	0.994929	−	0.100579i	$-0.0320696\pi$
$422$		0			0
$423$	93.5363			0.221126
$424$		0			0
$425$	114.186	+	62.5968i	0.268674	+	0.147286i
$426$		0			0
$427$		−	208.650i		−	0.488643i
$428$		0			0
$429$			274.776i			0.640504i
$430$		0			0
$431$			672.158i			1.55953i	0.626072	+	0.779766i	$0.284662\pi$
$431$			672.158i			1.55953i	−0.626072	+	0.779766i	$0.715338\pi$
$432$		0			0
$433$			562.185i			1.29835i	0.760640	+	0.649174i	$0.224885\pi$
$433$			562.185i			1.29835i	−0.760640	+	0.649174i	$0.775115\pi$
$434$		0			0
$435$	140.600	+	237.417i	0.323218	+	0.545786i
$436$		0			0
$437$	798.469			1.82716
$438$		0			0
$439$			384.842i			0.876633i	0.898821	+	0.438316i	$0.144425\pi$
$439$			384.842i			0.876633i	−0.898821	+	0.438316i	$0.855575\pi$
$440$		0			0
$441$	−48.3017			−0.109528
$442$		0			0
$443$			461.625i			1.04204i	0.853544	+	0.521021i	$0.174449\pi$
$443$			461.625i			1.04204i	−0.853544	+	0.521021i	$0.825551\pi$
$444$		0			0
$445$	340.472	+	574.922i	0.765106	+	1.29196i
$446$		0			0
$447$	−55.3584			−0.123844
$448$		0			0
$449$	48.7390			0.108550			0.0542750	−	0.998526i	$-0.482715\pi$
$449$	48.7390			0.108550			0.0542750	+	0.998526i	$0.482715\pi$
$450$		0			0
$451$	71.9532			0.159542
$452$		0			0
$453$	−237.023			−0.523229
$454$		0			0
$455$	−158.052	−	266.887i	−0.347368	−	0.586565i
$456$		0			0
$457$			762.588i			1.66868i	0.551248	+	0.834341i	$0.314152\pi$
$457$			762.588i			1.66868i	−0.551248	+	0.834341i	$0.685848\pi$
$458$		0			0
$459$	−149.399			−0.325488
$460$		0			0
$461$		−	406.436i		−	0.881639i	−0.897596	−	0.440820i	$-0.854688\pi$
$461$		−	406.436i		−	0.881639i	0.897596	−	0.440820i	$-0.145312\pi$
$462$		0			0
$463$	−260.743			−0.563159			−0.281580	−	0.959538i	$-0.590858\pi$
$463$	−260.743			−0.563159			−0.281580	+	0.959538i	$0.590858\pi$
$464$		0			0
$465$	−185.388	−	313.046i	−0.398684	−	0.673218i
$466$		0			0
$467$			594.738i			1.27353i	0.771058	+	0.636765i	$0.219728\pi$
$467$			594.738i			1.27353i	−0.771058	+	0.636765i	$0.780272\pi$
$468$		0			0
$469$			413.899i			0.882515i
$470$		0			0
$471$		−	44.1647i		−	0.0937679i
$472$		0			0
$473$			160.067i			0.338407i
$474$		0			0
$475$	−435.355	+	794.157i	−0.916537	+	1.67191i
$476$		0			0
$477$	−55.9294			−0.117252
$478$		0			0
$479$		−	534.894i		−	1.11669i	−0.829609	−	0.558344i	$-0.811437\pi$
$479$		−	534.894i		−	1.11669i	0.829609	−	0.558344i	$-0.188563\pi$
$480$		0			0
$481$	1117.00			2.32224
$482$		0			0
$483$		−	233.732i		−	0.483917i
$484$		0			0
$485$	27.5727	−	16.3287i	0.0568510	−	0.0336675i
$486$		0			0
$487$	−264.298			−0.542706			−0.271353	−	0.962480i	$-0.587471\pi$
$487$	−264.298			−0.542706			−0.271353	+	0.962480i	$0.587471\pi$
$488$		0			0
$489$	493.471			1.00914
$490$		0			0
$491$	−539.150			−1.09807			−0.549033	−	0.835801i	$-0.685004\pi$
$491$	−539.150			−1.09807			−0.549033	+	0.835801i	$0.685004\pi$
$492$		0			0
$493$	−104.359			−0.211681
$494$		0			0
$495$	22.2921	+	37.6424i	0.0450345	+	0.0760453i
$496$		0			0
$497$			272.577i			0.548444i
$498$		0			0
$499$	138.218			0.276991			0.138495	−	0.990363i	$-0.455773\pi$
$499$	138.218			0.276991			0.138495	+	0.990363i	$0.455773\pi$
$500$		0			0
$501$		−	379.557i		−	0.757598i
$502$		0			0
$503$	389.170			0.773697			0.386848	−	0.922143i	$-0.373564\pi$
$503$	389.170			0.773697			0.386848	+	0.922143i	$0.373564\pi$
$504$		0			0
$505$	−522.992	+	309.719i	−1.03563	+	0.613305i
$506$		0			0
$507$		−	249.645i		−	0.492396i
$508$		0			0
$509$		−	468.599i		−	0.920627i	−0.887756	−	0.460314i	$-0.847737\pi$
$509$		−	468.599i		−	0.920627i	0.887756	−	0.460314i	$-0.152263\pi$
$510$		0			0
$511$		−	144.124i		−	0.282043i
$512$		0			0
$513$		−	1039.06i		−	2.02545i
$514$		0			0
$515$	25.3731	+	42.8451i	0.0492682	+	0.0831943i
$516$		0			0
$517$	−409.761			−0.792575
$518$		0			0
$519$			173.223i			0.333764i
$520$		0			0
$521$	931.151			1.78724			0.893619	−	0.448826i	$-0.148158\pi$
$521$	931.151			1.78724			0.893619	+	0.448826i	$0.148158\pi$
$522$		0			0
$523$		−	227.656i		−	0.435289i	−0.976028	−	0.217645i	$-0.930163\pi$
$523$		−	227.656i		−	0.435289i	0.976028	−	0.217645i	$-0.0698374\pi$
$524$		0			0
$525$	232.470	+	127.439i	0.442799	+	0.242742i
$526$		0			0
$527$	137.602			0.261104
$528$		0			0
$529$	−43.1902			−0.0816451
$530$		0			0
$531$	−39.2511			−0.0739191
$532$		0			0
$533$	−187.267			−0.351346
$534$		0			0
$535$	580.115	−	343.548i	1.08433	−	0.642145i
$536$		0			0
$537$		−	655.605i		−	1.22087i
$538$		0			0
$539$	211.599			0.392576
$540$		0			0
$541$			388.174i			0.717511i	0.933431	+	0.358756i	$0.116799\pi$
$541$			388.174i			0.717511i	−0.933431	+	0.358756i	$0.883201\pi$
$542$		0			0
$543$	−514.296			−0.947139
$544$		0			0
$545$	−121.453	+	71.9254i	−0.222850	+	0.131973i
$546$		0			0
$547$		−	473.059i		−	0.864824i	−0.901676	−	0.432412i	$-0.857663\pi$
$547$		−	473.059i		−	0.864824i	0.901676	−	0.432412i	$-0.142337\pi$
$548$		0			0
$549$		−	76.5916i		−	0.139511i
$550$		0			0
$551$		−	725.804i		−	1.31725i
$552$		0			0
$553$			375.961i			0.679857i
$554$		0			0
$555$	−821.463	+	486.475i	−1.48011	+	0.876532i
$556$		0			0
$557$	−419.101			−0.752426			−0.376213	−	0.926533i	$-0.622774\pi$
$557$	−419.101			−0.752426			−0.376213	+	0.926533i	$0.622774\pi$
$558$		0			0
$559$		−	416.594i		−	0.745248i
$560$		0			0
$561$	88.8241			0.158332
$562$		0			0
$563$			145.910i			0.259165i	0.991569	+	0.129582i	$0.0413637\pi$
$563$			145.910i			0.259165i	−0.991569	+	0.129582i	$0.958636\pi$
$564$		0			0
$565$	−817.640	+	484.211i	−1.44715	+	0.857011i
$566$		0			0
$567$	−255.189			−0.450069
$568$		0			0
$569$	−950.513			−1.67050			−0.835249	−	0.549872i	$-0.814677\pi$
$569$	−950.513			−1.67050			−0.835249	+	0.549872i	$0.814677\pi$
$570$		0			0
$571$	−404.107			−0.707717			−0.353859	−	0.935299i	$-0.615131\pi$
$571$	−404.107			−0.707717			−0.353859	+	0.935299i	$0.615131\pi$
$572$		0			0
$573$	340.023			0.593408
$574$		0			0
$575$	−264.882	+	483.186i	−0.460664	+	0.840324i
$576$		0			0
$577$			847.944i			1.46957i	0.678298	+	0.734787i	$0.262718\pi$
$577$			847.944i			1.46957i	−0.678298	+	0.734787i	$0.737282\pi$
$578$		0			0
$579$	447.193			0.772354
$580$		0			0
$581$		−	485.723i		−	0.836011i
$582$		0			0
$583$	245.014			0.420264
$584$		0			0
$585$	−58.0179	−	97.9692i	−0.0991760	−	0.167469i
$586$		0			0
$587$		−	658.243i		−	1.12137i	−0.828030	−	0.560684i	$-0.810538\pi$
$587$		−	658.243i		−	1.12137i	0.828030	−	0.560684i	$-0.189462\pi$
$588$		0			0
$589$			957.010i			1.62480i
$590$		0			0
$591$			312.735i			0.529162i
$592$		0			0
$593$		−	282.430i		−	0.476274i	−0.971232	−	0.238137i	$-0.923463\pi$
$593$		−	282.430i		−	0.476274i	0.971232	−	0.238137i	$-0.0765367\pi$
$594$		0			0
$595$	−86.2739	+	51.0920i	−0.144998	+	0.0858688i
$596$		0			0
$597$	−897.739			−1.50375
$598$		0			0
$599$		−	498.597i		−	0.832382i	−0.909277	−	0.416191i	$-0.863365\pi$
$599$		−	498.597i		−	0.832382i	0.909277	−	0.416191i	$-0.136635\pi$
$600$		0			0
$601$	287.496			0.478363			0.239182	−	0.970975i	$-0.423121\pi$
$601$	287.496			0.478363			0.239182	+	0.970975i	$0.423121\pi$
$602$		0			0
$603$			151.934i			0.251964i
$604$		0			0
$605$	210.625	+	355.662i	0.348141	+	0.587871i
$606$		0			0
$607$	−844.260			−1.39087			−0.695437	−	0.718587i	$-0.744789\pi$
$607$	−844.260			−1.39087			−0.695437	+	0.718587i	$0.744789\pi$
$608$		0			0
$609$	−212.461			−0.348869
$610$		0			0
$611$	1066.46			1.74543
$612$		0			0
$613$	975.340			1.59109			0.795547	−	0.605892i	$-0.207184\pi$
$613$	975.340			1.59109			0.795547	+	0.605892i	$0.207184\pi$
$614$		0			0
$615$	137.720	−	81.5588i	0.223935	−	0.132616i
$616$		0			0
$617$		−	319.229i		−	0.517389i	−0.965959	−	0.258695i	$-0.916708\pi$
$617$		−	319.229i		−	0.517389i	0.965959	−	0.258695i	$-0.0832923\pi$
$618$		0			0
$619$	845.837			1.36646			0.683228	−	0.730205i	$-0.260575\pi$
$619$	845.837			1.36646			0.683228	+	0.730205i	$0.260575\pi$
$620$		0			0
$621$		−	632.190i		−	1.01802i
$622$		0			0
$623$	−514.489			−0.825826
$624$		0			0
$625$	−336.153	−	526.902i	−0.537846	−	0.843043i
$626$		0			0
$627$			617.764i			0.985269i
$628$		0			0
$629$		−	361.080i		−	0.574055i
$630$		0			0
$631$			322.653i			0.511335i	0.966765	+	0.255668i	$0.0822953\pi$
$631$			322.653i			0.511335i	−0.966765	+	0.255668i	$0.917705\pi$
$632$		0			0
$633$		−	360.087i		−	0.568858i
$634$		0			0
$635$	−153.032	−	258.409i	−0.240995	−	0.406944i
$636$		0			0
$637$	−550.712			−0.864541
$638$		0			0
$639$			100.058i			0.156585i
$640$		0			0
$641$	167.659			0.261558			0.130779	−	0.991412i	$-0.458252\pi$
$641$	167.659			0.261558			0.130779	+	0.991412i	$0.458252\pi$
$642$		0			0
$643$		−	118.227i		−	0.183867i	−0.995765	−	0.0919335i	$-0.970695\pi$
$643$		−	118.227i		−	0.183867i	0.995765	−	0.0919335i	$-0.0293047\pi$
$644$		0			0
$645$	181.435	+	306.372i	0.281295	+	0.474995i
$646$		0			0
$647$	−783.464			−1.21092			−0.605459	−	0.795876i	$-0.707011\pi$
$647$	−783.464			−1.21092			−0.605459	+	0.795876i	$0.707011\pi$
$648$		0			0
$649$	171.950			0.264946
$650$		0			0
$651$	280.141			0.430324
$652$		0			0
$653$	28.4352			0.0435455			0.0217727	−	0.999763i	$-0.493069\pi$
$653$	28.4352			0.0435455			0.0217727	+	0.999763i	$0.493069\pi$
$654$		0			0
$655$	285.314	+	481.781i	0.435593	+	0.735543i
$656$		0			0
$657$		−	52.9051i		−	0.0805253i
$658$		0			0
$659$	−594.296			−0.901814			−0.450907	−	0.892571i	$-0.648899\pi$
$659$	−594.296			−0.901814			−0.450907	+	0.892571i	$0.648899\pi$
$660$		0			0
$661$			495.511i			0.749638i	0.927098	+	0.374819i	$0.122295\pi$
$661$			495.511i			0.749638i	−0.927098	+	0.374819i	$0.877705\pi$
$662$		0			0
$663$	−231.176			−0.348682
$664$		0			0
$665$	−355.340	−	600.028i	−0.534346	−	0.902297i
$666$		0			0
$667$		−	441.599i		−	0.662067i
$668$		0			0
$669$		−	257.231i		−	0.384501i
$670$		0			0
$671$			335.530i			0.500045i
$672$		0			0
$673$		−	168.874i		−	0.250927i	−0.992098	−	0.125464i	$-0.959958\pi$
$673$		−	168.874i		−	0.250927i	0.992098	−	0.125464i	$-0.0400418\pi$
$674$		0			0
$675$	628.775	+	344.693i	0.931519	+	0.510657i
$676$		0			0
$677$	895.899			1.32334			0.661668	−	0.749797i	$-0.269849\pi$
$677$	895.899			1.32334			0.661668	+	0.749797i	$0.269849\pi$
$678$		0			0
$679$			24.6745i			0.0363394i
$680$		0			0
$681$	−41.3042			−0.0606522
$682$		0			0
$683$		−	359.410i		−	0.526223i	−0.964765	−	0.263112i	$-0.915251\pi$
$683$		−	359.410i		−	0.526223i	0.964765	−	0.263112i	$-0.0847487\pi$
$684$		0			0
$685$	183.462	−	108.647i	0.267828	−	0.158609i
$686$		0			0
$687$	396.926			0.577767
$688$		0			0
$689$	−637.680			−0.925516
$690$		0			0
$691$	−515.701			−0.746311			−0.373155	−	0.927769i	$-0.621724\pi$
$691$	−515.701			−0.746311			−0.373155	+	0.927769i	$0.621724\pi$
$692$		0			0
$693$	−33.6857			−0.0486085
$694$		0			0
$695$	566.454	+	956.514i	0.815041	+	1.37628i
$696$		0			0
$697$			60.5360i			0.0868523i
$698$		0			0
$699$	348.510			0.498584
$700$		0			0
$701$		−	1370.37i		−	1.95488i	−0.211221	−	0.977438i	$-0.567744\pi$
$701$		−	1370.37i		−	1.95488i	0.211221	−	0.977438i	$-0.432256\pi$
$702$		0			0
$703$	2511.28			3.57224
$704$		0			0
$705$	−784.293	+	464.463i	−1.11247	+	0.658813i
$706$		0			0
$707$		−	468.018i		−	0.661978i
$708$		0			0
$709$			662.128i			0.933890i	0.884286	+	0.466945i	$0.154645\pi$
$709$			662.128i			0.933890i	−0.884286	+	0.466945i	$0.845355\pi$
$710$		0			0
$711$			138.008i			0.194104i
$712$		0			0
$713$			582.270i			0.816649i
$714$		0			0
$715$	254.163	+	429.181i	0.355473	+	0.600253i
$716$		0			0
$717$	4.55302			0.00635010
$718$		0			0
$719$			370.003i			0.514608i	0.966331	+	0.257304i	$0.0828341\pi$
$719$			370.003i			0.514608i	−0.966331	+	0.257304i	$0.917166\pi$
$720$		0			0
$721$	−38.3415			−0.0531782
$722$		0			0
$723$		−	569.964i		−	0.788331i
$724$		0			0
$725$	439.214	+	240.776i	0.605812	+	0.332105i
$726$		0			0
$727$	−607.695			−0.835894			−0.417947	−	0.908471i	$-0.637250\pi$
$727$	−607.695			−0.835894			−0.417947	+	0.908471i	$0.637250\pi$
$728$		0			0
$729$	−804.700			−1.10384
$730$		0			0
$731$	−134.668			−0.184224
$732$		0			0
$733$	−1066.76			−1.45533			−0.727666	−	0.685931i	$-0.759395\pi$
$733$	−1066.76			−1.45533			−0.727666	+	0.685931i	$0.759395\pi$
$734$		0			0
$735$	405.005	−	239.847i	0.551027	−	0.326322i
$736$		0			0
$737$		−	665.591i		−	0.903108i
$738$		0			0
$739$	−558.366			−0.755570			−0.377785	−	0.925893i	$-0.623314\pi$
$739$	−558.366			−0.755570			−0.377785	+	0.925893i	$0.623314\pi$
$740$		0			0
$741$		−	1607.81i		−	2.16978i
$742$		0			0
$743$	1112.00			1.49664			0.748319	−	0.663339i	$-0.230861\pi$
$743$	1112.00			1.49664			0.748319	+	0.663339i	$0.230861\pi$
$744$		0			0
$745$	−86.4659	+	51.2056i	−0.116062	+	0.0687324i
$746$		0			0
$747$		−	178.299i		−	0.238687i
$748$		0			0
$749$			519.137i			0.693107i
$750$		0			0
$751$		−	1207.34i		−	1.60764i	−0.594873	−	0.803820i	$-0.702798\pi$
$751$		−	1207.34i		−	1.60764i	0.594873	−	0.803820i	$-0.297202\pi$
$752$		0			0
$753$			204.158i			0.271127i
$754$		0			0
$755$	−370.213	+	219.242i	−0.490348	+	0.290387i
$756$		0			0
$757$	87.7776			0.115955			0.0579773	−	0.998318i	$-0.481535\pi$
$757$	87.7776			0.115955			0.0579773	+	0.998318i	$0.481535\pi$
$758$		0			0
$759$			375.864i			0.495209i
$760$		0			0
$761$	−67.0202			−0.0880686			−0.0440343	−	0.999030i	$-0.514021\pi$
$761$	−67.0202			−0.0880686			−0.0440343	+	0.999030i	$0.514021\pi$
$762$		0			0
$763$		−	108.687i		−	0.142447i
$764$		0			0
$765$	−31.6695	+	18.7549i	−0.0413980	+	0.0245162i
$766$		0			0
$767$	−447.522			−0.583470
$768$		0			0
$769$	342.869			0.445863			0.222932	−	0.974834i	$-0.428437\pi$
$769$	342.869			0.445863			0.222932	+	0.974834i	$0.428437\pi$
$770$		0			0
$771$	−756.587			−0.981306
$772$		0			0
$773$	−244.756			−0.316631			−0.158316	−	0.987389i	$-0.550606\pi$
$773$	−244.756			−0.316631			−0.158316	+	0.987389i	$0.550606\pi$
$774$		0			0
$775$	−579.126	−	317.475i	−0.747259	−	0.409646i
$776$		0			0
$777$		−	735.116i		−	0.946095i
$778$		0			0
$779$	−421.023			−0.540466
$780$		0			0
$781$		−	438.330i		−	0.561242i
$782$		0			0
$783$	−574.657			−0.733917
$784$		0			0
$785$	−40.8516	−	68.9821i	−0.0520403	−	0.0878753i
$786$		0			0
$787$		−	1120.38i		−	1.42361i	−0.702376	−	0.711806i	$-0.747877\pi$
$787$		−	1120.38i		−	1.42361i	0.702376	−	0.711806i	$-0.252123\pi$
$788$		0			0
$789$		−	208.063i		−	0.263705i
$790$		0			0
$791$		−	731.695i		−	0.925025i
$792$		0			0
$793$		−	873.260i		−	1.10121i
$794$		0			0
$795$	468.963	−	277.723i	0.589891	−	0.349337i
$796$		0			0
$797$	1344.51			1.68696			0.843480	−	0.537161i	$-0.180503\pi$
$797$	1344.51			1.68696			0.843480	+	0.537161i	$0.180503\pi$
$798$		0			0
$799$		−	344.742i		−	0.431467i
$800$		0			0
$801$	−188.859			−0.235779
$802$		0			0
$803$			231.765i			0.288624i
$804$		0			0
$805$	−216.198	−	365.073i	−0.268569	−	0.453507i
$806$		0			0
$807$	865.122			1.07202
$808$		0			0
$809$	−345.363			−0.426901			−0.213451	−	0.976954i	$-0.568470\pi$
$809$	−345.363			−0.426901			−0.213451	+	0.976954i	$0.568470\pi$
$810$		0			0
$811$	1275.44			1.57268			0.786338	−	0.617797i	$-0.211975\pi$
$811$	1275.44			1.57268			0.786338	+	0.617797i	$0.211975\pi$
$812$		0			0
$813$	352.999			0.434193
$814$		0			0
$815$	770.766	−	456.452i	0.945725	−	0.560064i
$816$		0			0
$817$		−	936.604i		−	1.14639i
$818$		0			0
$819$	87.6713			0.107047
$820$		0			0
$821$		−	1257.99i		−	1.53226i	−0.642684	−	0.766131i	$-0.722179\pi$
$821$		−	1257.99i		−	1.53226i	0.642684	−	0.766131i	$-0.277821\pi$
$822$		0			0
$823$	−206.093			−0.250417			−0.125208	−	0.992130i	$-0.539960\pi$
$823$	−206.093			−0.250417			−0.125208	+	0.992130i	$0.539960\pi$
$824$		0			0
$825$	−373.834	−	204.935i	−0.453132	−	0.248406i
$826$		0			0
$827$			615.606i			0.744384i	0.928156	+	0.372192i	$0.121394\pi$
$827$			615.606i			0.744384i	−0.928156	+	0.372192i	$0.878606\pi$
$828$		0			0
$829$		−	1214.12i		−	1.46456i	−0.681002	−	0.732281i	$-0.738456\pi$
$829$		−	1214.12i		−	1.46456i	0.681002	−	0.732281i	$-0.261544\pi$
$830$		0			0
$831$			666.892i			0.802518i
$832$		0			0
$833$			178.023i			0.213713i
$834$		0			0
$835$	−351.084	−	592.841i	−0.420460	−	0.709989i
$836$		0			0
$837$	757.715			0.905275
$838$		0			0
$839$			1338.99i			1.59593i	0.602701	+	0.797967i	$0.294091\pi$
$839$			1338.99i			1.59593i	−0.602701	+	0.797967i	$0.705909\pi$
$840$		0			0
$841$	439.589			0.522698
$842$		0			0
$843$			79.4817i			0.0942844i
$844$		0			0
$845$	−230.917	−	389.928i	−0.273275	−	0.461453i
$846$		0			0
$847$	−318.277			−0.375769
$848$		0			0
$849$	−743.671			−0.875937
$850$		0			0
$851$	1527.93			1.79545
$852$		0			0
$853$	−112.066			−0.131379			−0.0656893	−	0.997840i	$-0.520925\pi$
$853$	−112.066			−0.131379			−0.0656893	+	0.997840i	$0.520925\pi$
$854$		0			0
$855$	−130.438	−	220.259i	−0.152560	−	0.257612i
$856$		0			0
$857$			1089.15i			1.27089i	0.772148	+	0.635443i	$0.219183\pi$
$857$			1089.15i			1.27089i	−0.772148	+	0.635443i	$0.780817\pi$
$858$		0			0
$859$	−719.610			−0.837729			−0.418865	−	0.908049i	$-0.637572\pi$
$859$	−719.610			−0.837729			−0.418865	+	0.908049i	$0.637572\pi$
$860$		0			0
$861$			123.244i			0.143141i
$862$		0			0
$863$	114.135			0.132254			0.0661269	−	0.997811i	$-0.478936\pi$
$863$	114.135			0.132254			0.0661269	+	0.997811i	$0.478936\pi$
$864$		0			0
$865$	160.229	+	270.563i	0.185236	+	0.312789i
$866$		0			0
$867$		−	721.293i		−	0.831942i
$868$		0			0
$869$		−	604.582i		−	0.695721i
$870$		0			0
$871$			1732.28i			1.98884i
$872$		0			0
$873$			9.05752i			0.0103752i
$874$		0			0
$875$	480.981	−	15.9795i	0.549692	−	0.0182623i
$876$		0			0
$877$	1427.99			1.62827			0.814135	−	0.580675i	$-0.197211\pi$
$877$	1427.99			1.62827			0.814135	+	0.580675i	$0.197211\pi$
$878$		0			0
$879$			973.539i			1.10755i
$880$		0			0
$881$	364.165			0.413354			0.206677	−	0.978409i	$-0.433735\pi$
$881$	364.165			0.413354			0.206677	+	0.978409i	$0.433735\pi$
$882$		0			0
$883$			800.458i			0.906521i	0.891378	+	0.453260i	$0.149739\pi$
$883$			800.458i			0.906521i	−0.891378	+	0.453260i	$0.850261\pi$
$884$		0			0
$885$	329.117	−	194.905i	0.371883	−	0.220231i
$886$		0			0
$887$	591.672			0.667049			0.333524	−	0.942741i	$-0.391762\pi$
$887$	591.672			0.667049			0.333524	+	0.942741i	$0.391762\pi$
$888$		0			0
$889$	231.247			0.260120
$890$		0			0
$891$	410.369			0.460572
$892$		0			0
$893$	2397.65			2.68494
$894$		0			0
$895$	−606.424	−	1024.01i	−0.677568	−	1.14414i
$896$		0			0
$897$		−	978.233i		−	1.09056i
$898$		0			0
$899$	529.281			0.588744
$900$		0			0
$901$			206.136i			0.228786i
$902$		0			0
$903$	−274.168			−0.303619
$904$		0			0
$905$	−803.295	+	475.716i	−0.887618	+	0.525653i
$906$		0			0
$907$			545.657i			0.601606i	0.953686	+	0.300803i	$0.0972547\pi$
$907$			545.657i			0.601606i	−0.953686	+	0.300803i	$0.902745\pi$
$908$		0			0
$909$		−	171.801i		−	0.189000i
$910$		0			0
$911$		−	929.286i		−	1.02007i	−0.860153	−	0.510036i	$-0.829632\pi$
$911$		−	929.286i		−	1.02007i	0.860153	−	0.510036i	$-0.170368\pi$
$912$		0			0
$913$			781.089i			0.855520i
$914$		0			0
$915$	380.323	+	642.213i	0.415653	+	0.701873i
$916$		0			0
$917$	−431.139			−0.470163
$918$		0			0
$919$		−	171.353i		−	0.186456i	−0.995645	−	0.0932278i	$-0.970282\pi$
$919$		−	171.353i		−	0.186456i	0.995645	−	0.0932278i	$-0.0297185\pi$
$920$		0			0
$921$	−718.750			−0.780402
$922$		0			0
$923$			1140.81i			1.23598i
$924$		0			0
$925$	−833.085	+	1519.68i	−0.900632	+	1.64290i
$926$		0			0
$927$	−14.0744			−0.0151828
$928$		0			0
$929$	−1178.62			−1.26870			−0.634350	−	0.773046i	$-0.718732\pi$
$929$	−1178.62			−1.26870			−0.634350	+	0.773046i	$0.718732\pi$
$930$		0			0
$931$	−1238.14			−1.32990
$932$		0			0
$933$	389.940			0.417943
$934$		0			0
$935$	138.737	−	82.1609i	0.148382	−	0.0878726i
$936$		0			0
$937$			412.624i			0.440367i	0.975458	+	0.220183i	$0.0706656\pi$
$937$			412.624i			0.440367i	−0.975458	+	0.220183i	$0.929334\pi$
$938$		0			0
$939$	−1007.97			−1.07346
$940$		0			0
$941$		−	1121.33i		−	1.19163i	−0.803120	−	0.595817i	$-0.796828\pi$
$941$		−	1121.33i		−	1.19163i	0.803120	−	0.595817i	$-0.203172\pi$
$942$		0			0
$943$	−256.161			−0.271645
$944$		0			0
$945$	−475.073	+	281.341i	−0.502723	+	0.297716i
$946$		0			0
$947$		−	1395.22i		−	1.47331i	−0.676271	−	0.736653i	$-0.736405\pi$
$947$		−	1395.22i		−	1.47331i	0.676271	−	0.736653i	$-0.263595\pi$
$948$		0			0
$949$		−	603.199i		−	0.635615i
$950$		0			0
$951$			25.4178i			0.0267275i
$952$		0			0
$953$		−	476.331i		−	0.499822i	−0.968269	−	0.249911i	$-0.919599\pi$
$953$		−	476.331i		−	0.499822i	0.968269	−	0.249911i	$-0.0804014\pi$
$954$		0			0
$955$	531.092	−	314.516i	0.556117	−	0.329336i
$956$		0			0
$957$	341.658			0.357010
$958$		0			0
$959$			164.178i			0.171197i
$960$		0			0
$961$	263.116			0.273794
$962$		0			0
$963$			190.565i			0.197887i
$964$		0			0
$965$	698.484	−	413.646i	0.723817	−	0.428649i
$966$		0			0
$967$	−140.846			−0.145653			−0.0728263	−	0.997345i	$-0.523202\pi$
$967$	−140.846			−0.145653			−0.0728263	+	0.997345i	$0.523202\pi$
$968$		0			0
$969$	−519.740			−0.536367
$970$		0			0
$971$	−1144.98			−1.17918			−0.589588	−	0.807704i	$-0.700710\pi$
$971$	−1144.98			−1.17918			−0.589588	+	0.807704i	$0.700710\pi$
$972$		0			0
$973$	−855.971			−0.879724
$974$		0			0
$975$	972.950	+	533.369i	0.997898	+	0.547045i
$976$		0			0
$977$			55.8912i			0.0572070i	0.999591	+	0.0286035i	$0.00910602\pi$
$977$			55.8912i			0.0572070i	−0.999591	+	0.0286035i	$0.990894\pi$
$978$		0			0
$979$	827.349			0.845096
$980$		0			0
$981$		−	39.8969i		−	0.0406696i
$982$		0			0
$983$	−1028.74			−1.04653			−0.523267	−	0.852169i	$-0.675287\pi$
$983$	−1028.74			−1.04653			−0.523267	+	0.852169i	$0.675287\pi$
$984$		0			0
$985$	289.275	+	488.469i	0.293680	+	0.495908i
$986$		0			0
$987$		−	701.853i		−	0.711098i
$988$		0			0
$989$		−	569.855i		−	0.576193i
$990$		0			0
$991$			666.207i			0.672257i	0.941816	+	0.336129i	$0.109118\pi$
$991$			666.207i			0.672257i	−0.941816	+	0.336129i	$0.890882\pi$
$992$		0			0
$993$		−	147.030i		−	0.148066i
$994$		0			0
$995$	−1402.20	+	830.394i	−1.40925	+	0.834567i
$996$		0			0
$997$	−737.006			−0.739224			−0.369612	−	0.929186i	$-0.620509\pi$
$997$	−737.006			−0.739224			−0.369612	+	0.929186i	$0.620509\pi$
$998$		0			0
$999$		−	1988.31i		−	1.99030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.3.e.f.639.2		6
4.3	odd	2		1280.3.e.g.639.5		6
5.4	even	2		1280.3.e.i.639.5		6
8.3	odd	2		1280.3.e.i.639.2		6
8.5	even	2		1280.3.e.h.639.5		6
16.3	odd	4		320.3.h.g.319.2		6
16.5	even	4		160.3.h.b.159.1	yes	6
16.11	odd	4		160.3.h.a.159.5	✓	6
16.13	even	4		320.3.h.f.319.6		6
20.19	odd	2		1280.3.e.h.639.2		6
40.19	odd	2	inner	1280.3.e.f.639.5		6
40.29	even	2		1280.3.e.g.639.2		6
48.5	odd	4		1440.3.j.b.1279.2		6
48.11	even	4		1440.3.j.a.1279.2		6
80.3	even	4		1600.3.b.w.1151.2		6
80.13	odd	4		1600.3.b.w.1151.5		6
80.19	odd	4		320.3.h.f.319.5		6
80.27	even	4		800.3.b.h.351.2		6
80.29	even	4		320.3.h.g.319.1		6
80.37	odd	4		800.3.b.h.351.5		6
80.43	even	4		800.3.b.i.351.5		6
80.53	odd	4		800.3.b.i.351.2		6
80.59	odd	4		160.3.h.b.159.2	yes	6
80.67	even	4		1600.3.b.v.1151.5		6
80.69	even	4		160.3.h.a.159.6	yes	6
80.77	odd	4		1600.3.b.v.1151.2		6
240.59	even	4		1440.3.j.b.1279.1		6
240.149	odd	4		1440.3.j.a.1279.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.3.h.a.159.5	✓	6	16.11	odd	4
160.3.h.a.159.6	yes	6	80.69	even	4
160.3.h.b.159.1	yes	6	16.5	even	4
160.3.h.b.159.2	yes	6	80.59	odd	4
320.3.h.f.319.5		6	80.19	odd	4
320.3.h.f.319.6		6	16.13	even	4
320.3.h.g.319.1		6	80.29	even	4
320.3.h.g.319.2		6	16.3	odd	4
800.3.b.h.351.2		6	80.27	even	4
800.3.b.h.351.5		6	80.37	odd	4
800.3.b.i.351.2		6	80.53	odd	4
800.3.b.i.351.5		6	80.43	even	4
1280.3.e.f.639.2		6	1.1	even	1	trivial
1280.3.e.f.639.5		6	40.19	odd	2	inner
1280.3.e.g.639.2		6	40.29	even	2
1280.3.e.g.639.5		6	4.3	odd	2
1280.3.e.h.639.2		6	20.19	odd	2
1280.3.e.h.639.5		6	8.5	even	2
1280.3.e.i.639.2		6	8.3	odd	2
1280.3.e.i.639.5		6	5.4	even	2
1440.3.j.a.1279.1		6	240.149	odd	4
1440.3.j.a.1279.2		6	48.11	even	4
1440.3.j.b.1279.1		6	240.59	even	4
1440.3.j.b.1279.2		6	48.5	odd	4
1600.3.b.v.1151.2		6	80.77	odd	4
1600.3.b.v.1151.5		6	80.67	even	4
1600.3.b.w.1151.2		6	80.3	even	4
1600.3.b.w.1151.5		6	80.13	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)

\(f(q)\)	\(=\)	\(q-2.75441i q^{3} +(-2.54778 - 4.30219i) q^{5} +3.84997 q^{7} +1.41325 q^{9} +O(q^{10})\)	\(q-2.75441i q^{3} +(-2.54778 - 4.30219i) q^{5} +3.84997 q^{7} +1.41325 q^{9} -6.19112 q^{11} +16.1132 q^{13} +(-11.8500 + 7.01762i) q^{15} -5.20875i q^{17} +36.2264 q^{19} -10.6044i q^{21} +22.0411 q^{23} +(-12.0176 + 21.9221i) q^{25} -28.6823i q^{27} -20.0352i q^{29} +26.4175i q^{31} +17.0529i q^{33} +(-9.80888 - 16.5633i) q^{35} +69.3219 q^{37} -44.3822i q^{39} -11.6220 q^{41} -25.8542i q^{43} +(-3.60065 - 6.08006i) q^{45} +66.1853 q^{47} -34.1777 q^{49} -14.3470 q^{51} -39.5751 q^{53} +(15.7736 + 26.6354i) q^{55} -99.7821i q^{57} -27.7736 q^{59} -54.1954i q^{61} +5.44096 q^{63} +(-41.0529 - 69.3219i) q^{65} +107.507i q^{67} -60.7101i q^{69} +70.7997i q^{71} -37.4351i q^{73} +(60.3822 + 33.1014i) q^{75} -23.8356 q^{77} +97.6530i q^{79} -66.2835 q^{81} -126.163i q^{83} +(-22.4090 + 13.2707i) q^{85} -55.1852 q^{87} -133.635 q^{89} +62.0352 q^{91} +72.7645 q^{93} +(-92.2969 - 155.853i) q^{95} +6.40900i q^{97} -8.74960 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 8 q^{5} - 12 q^{7} - 18 q^{9}+O(q^{10}) \) 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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