LMFDB - Embedded newform 1280.2.f.i.129.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1280,2,Mod(129,1280)]

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([0, 1, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1280.129");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1280 = 2^{8} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1280.f (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:	$10.2208514587$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 640)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			129.6
Root			$-0.854638 - 0.854638i$ of defining polynomial
Character	$\chi$	$=$	1280.129
Dual form			1280.2.f.i.129.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.70928 q^{3} +(-0.539189 + 2.17009i) q^{5} -2.63090i q^{7} -0.0783777 q^{9} +O(q^{10})$	$q+1.70928 q^{3} +(-0.539189 + 2.17009i) q^{5} -2.63090i q^{7} -0.0783777 q^{9} +5.41855i q^{11} -6.34017 q^{13} +(-0.921622 + 3.70928i) q^{15} +3.41855i q^{17} +3.26180i q^{19} -4.49693i q^{21} +1.36910i q^{23} +(-4.41855 - 2.34017i) q^{25} -5.26180 q^{27} +2.00000i q^{29} -4.68035 q^{31} +9.26180i q^{33} +(5.70928 + 1.41855i) q^{35} +5.75872 q^{37} -10.8371 q^{39} +7.75872 q^{41} +4.44748 q^{43} +(0.0422604 - 0.170086i) q^{45} +4.78765i q^{47} +0.0783777 q^{49} +5.84324i q^{51} +1.65983 q^{53} +(-11.7587 - 2.92162i) q^{55} +5.57531i q^{57} +3.26180i q^{59} +2.49693i q^{61} +0.206204i q^{63} +(3.41855 - 13.7587i) q^{65} +7.86603 q^{67} +2.34017i q^{69} +6.15676 q^{71} -13.5753i q^{73} +(-7.55252 - 4.00000i) q^{75} +14.2557 q^{77} -12.6803 q^{79} -8.75872 q^{81} -14.9711 q^{83} +(-7.41855 - 1.84324i) q^{85} +3.41855i q^{87} -8.52359 q^{89} +16.6803i q^{91} -8.00000 q^{93} +(-7.07838 - 1.75872i) q^{95} -4.58145i q^{97} -0.424694i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4 q^{3} + 6 q^{9}+O(q^{10}) $ 6 * q - 4 * q^3 + 6 * q^9	$ 6 q - 4 q^{3} + 6 q^{9} - 16 q^{13} - 12 q^{15} + 2 q^{25} - 16 q^{27} + 16 q^{31} + 20 q^{35} - 16 q^{37} - 8 q^{39} - 4 q^{41} + 28 q^{43} + 32 q^{45} - 6 q^{49} + 32 q^{53} - 20 q^{55} - 8 q^{65} + 20 q^{67} + 24 q^{71} - 44 q^{75} - 32 q^{79} - 2 q^{81} - 60 q^{83} - 16 q^{85} - 20 q^{89} - 48 q^{93} - 36 q^{95}+O(q^{100}) $ 6 * q - 4 * q^3 + 6 * q^9 - 16 * q^13 - 12 * q^15 + 2 * q^25 - 16 * q^27 + 16 * q^31 + 20 * q^35 - 16 * q^37 - 8 * q^39 - 4 * q^41 + 28 * q^43 + 32 * q^45 - 6 * q^49 + 32 * q^53 - 20 * q^55 - 8 * q^65 + 20 * q^67 + 24 * q^71 - 44 * q^75 - 32 * q^79 - 2 * q^81 - 60 * q^83 - 16 * q^85 - 20 * q^89 - 48 * q^93 - 36 * q^95

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
$3$	1.70928			0.986851			0.493425	−	0.869788i	$-0.335745\pi$
$3$	1.70928			0.986851			0.493425	+	0.869788i	$0.335745\pi$
$4$		0			0
$5$	−0.539189	+	2.17009i	−0.241133	+	0.970492i
$5$	−0.539189	+	2.17009i	−0.241133	+	0.970492i
$6$		0			0
$7$		−	2.63090i		−	0.994386i	−0.867640	−	0.497193i	$-0.834364\pi$
$7$		−	2.63090i		−	0.994386i	0.867640	−	0.497193i	$-0.165636\pi$
$8$		0			0
$9$	−0.0783777			−0.0261259
$10$		0			0
$11$			5.41855i			1.63375i	0.576812	+	0.816877i	$0.304297\pi$
$11$			5.41855i			1.63375i	−0.576812	+	0.816877i	$0.695703\pi$
$12$		0			0
$13$	−6.34017			−1.75845			−0.879224	−	0.476409i	$-0.841938\pi$
$13$	−6.34017			−1.75845			−0.879224	+	0.476409i	$0.841938\pi$
$14$		0			0
$15$	−0.921622	+	3.70928i	−0.237962	+	0.957731i
$16$		0			0
$17$			3.41855i			0.829120i	0.910022	+	0.414560i	$0.136065\pi$
$17$			3.41855i			0.829120i	−0.910022	+	0.414560i	$0.863935\pi$
$18$		0			0
$19$			3.26180i			0.748307i	0.927367	+	0.374154i	$0.122067\pi$
$19$			3.26180i			0.748307i	−0.927367	+	0.374154i	$0.877933\pi$
$20$		0			0
$21$		−	4.49693i		−	0.981310i
$22$		0			0
$23$			1.36910i			0.285478i	0.989760	+	0.142739i	$0.0455909\pi$
$23$			1.36910i			0.285478i	−0.989760	+	0.142739i	$0.954409\pi$
$24$		0			0
$25$	−4.41855	−	2.34017i	−0.883710	−	0.468035i
$26$		0			0
$27$	−5.26180			−1.01263
$28$		0			0
$29$			2.00000i			0.371391i	0.982607	+	0.185695i	$0.0594537\pi$
$29$			2.00000i			0.371391i	−0.982607	+	0.185695i	$0.940546\pi$
$30$		0			0
$31$	−4.68035			−0.840615			−0.420307	−	0.907382i	$-0.638078\pi$
$31$	−4.68035			−0.840615			−0.420307	+	0.907382i	$0.638078\pi$
$32$		0			0
$33$			9.26180i			1.61227i
$34$		0			0
$35$	5.70928	+	1.41855i	0.965044	+	0.239779i
$36$		0			0
$37$	5.75872			0.946728			0.473364	−	0.880867i	$-0.343039\pi$
$37$	5.75872			0.946728			0.473364	+	0.880867i	$0.343039\pi$
$38$		0			0
$39$	−10.8371			−1.73533
$40$		0			0
$41$	7.75872			1.21171			0.605855	−	0.795575i	$-0.292831\pi$
$41$	7.75872			1.21171			0.605855	+	0.795575i	$0.292831\pi$
$42$		0			0
$43$	4.44748			0.678234			0.339117	−	0.940744i	$-0.389872\pi$
$43$	4.44748			0.678234			0.339117	+	0.940744i	$0.389872\pi$
$44$		0			0
$45$	0.0422604	−	0.170086i	0.00629981	−	0.0253550i
$46$		0			0
$47$			4.78765i			0.698351i	0.937057	+	0.349175i	$0.113538\pi$
$47$			4.78765i			0.698351i	−0.937057	+	0.349175i	$0.886462\pi$
$48$		0			0
$49$	0.0783777			0.0111968
$50$		0			0
$51$			5.84324i			0.818218i
$52$		0			0
$53$	1.65983			0.227995			0.113997	−	0.993481i	$-0.463634\pi$
$53$	1.65983			0.227995			0.113997	+	0.993481i	$0.463634\pi$
$54$		0			0
$55$	−11.7587	−	2.92162i	−1.58555	−	0.393951i
$56$		0			0
$57$			5.57531i			0.738467i
$58$		0			0
$59$			3.26180i			0.424650i	0.977199	+	0.212325i	$0.0681035\pi$
$59$			3.26180i			0.424650i	−0.977199	+	0.212325i	$0.931897\pi$
$60$		0			0
$61$			2.49693i			0.319699i	0.987141	+	0.159849i	$0.0511009\pi$
$61$			2.49693i			0.319699i	−0.987141	+	0.159849i	$0.948899\pi$
$62$		0			0
$63$			0.206204i			0.0259792i
$64$		0			0
$65$	3.41855	−	13.7587i	0.424019	−	1.70656i
$66$		0			0
$67$	7.86603			0.960989			0.480494	−	0.876998i	$-0.340457\pi$
$67$	7.86603			0.960989			0.480494	+	0.876998i	$0.340457\pi$
$68$		0			0
$69$			2.34017i			0.281724i
$70$		0			0
$71$	6.15676			0.730672			0.365336	−	0.930876i	$-0.380954\pi$
$71$	6.15676			0.730672			0.365336	+	0.930876i	$0.380954\pi$
$72$		0			0
$73$		−	13.5753i		−	1.58887i	−0.607350	−	0.794435i	$-0.707767\pi$
$73$		−	13.5753i		−	1.58887i	0.607350	−	0.794435i	$-0.292233\pi$
$74$		0			0
$75$	−7.55252	−	4.00000i	−0.872090	−	0.461880i
$76$		0			0
$77$	14.2557			1.62458
$78$		0			0
$79$	−12.6803			−1.42665			−0.713325	−	0.700833i	$-0.752812\pi$
$79$	−12.6803			−1.42665			−0.713325	+	0.700833i	$0.752812\pi$
$80$		0			0
$81$	−8.75872			−0.973192
$82$		0			0
$83$	−14.9711			−1.64329			−0.821644	−	0.570001i	$-0.806943\pi$
$83$	−14.9711			−1.64329			−0.821644	+	0.570001i	$0.806943\pi$
$84$		0			0
$85$	−7.41855	−	1.84324i	−0.804655	−	0.199928i
$86$		0			0
$87$			3.41855i			0.366507i
$88$		0			0
$89$	−8.52359			−0.903499			−0.451749	−	0.892145i	$-0.649200\pi$
$89$	−8.52359			−0.903499			−0.451749	+	0.892145i	$0.649200\pi$
$90$		0			0
$91$			16.6803i			1.74858i
$92$		0			0
$93$	−8.00000			−0.829561
$94$		0			0
$95$	−7.07838	−	1.75872i	−0.726226	−	0.180441i
$96$		0			0
$97$		−	4.58145i		−	0.465176i	−0.972575	−	0.232588i	$-0.925281\pi$
$97$		−	4.58145i		−	0.465176i	0.972575	−	0.232588i	$-0.0747193\pi$
$98$		0			0
$99$		−	0.424694i		−	0.0426833i
$100$		0			0
$101$			2.31351i			0.230203i	0.993354	+	0.115101i	$0.0367193\pi$
$101$			2.31351i			0.230203i	−0.993354	+	0.115101i	$0.963281\pi$
$102$		0			0
$103$			16.2062i			1.59684i	0.602098	+	0.798422i	$0.294332\pi$
$103$			16.2062i			1.59684i	−0.602098	+	0.798422i	$0.705668\pi$
$104$		0			0
$105$	9.75872	+	2.42469i	0.952354	+	0.236626i
$106$		0			0
$107$	15.6514			1.51308			0.756540	−	0.653948i	$-0.226888\pi$
$107$	15.6514			1.51308			0.756540	+	0.653948i	$0.226888\pi$
$108$		0			0
$109$		−	12.3402i		−	1.18197i	−0.806681	−	0.590987i	$-0.798738\pi$
$109$		−	12.3402i		−	1.18197i	0.806681	−	0.590987i	$-0.201262\pi$
$110$		0			0
$111$	9.84324			0.934279
$112$		0			0
$113$		−	9.36069i		−	0.880580i	−0.897856	−	0.440290i	$-0.854876\pi$
$113$		−	9.36069i		−	0.880580i	0.897856	−	0.440290i	$-0.145124\pi$
$114$		0			0
$115$	−2.97107	−	0.738205i	−0.277054	−	0.0688379i
$116$		0			0
$117$	0.496928			0.0459411
$118$		0			0
$119$	8.99386			0.824466
$120$		0			0
$121$	−18.3607			−1.66915
$122$		0			0
$123$	13.2618			1.19578
$124$		0			0
$125$	7.46081	−	8.32684i	0.667315	−	0.744775i
$126$		0			0
$127$			1.95055i			0.173083i	0.996248	+	0.0865417i	$0.0275816\pi$
$127$			1.95055i			0.173083i	−0.996248	+	0.0865417i	$0.972418\pi$
$128$		0			0
$129$	7.60197			0.669316
$130$		0			0
$131$			15.5753i			1.36082i	0.732831	+	0.680410i	$0.238198\pi$
$131$			15.5753i			1.36082i	−0.732831	+	0.680410i	$0.761802\pi$
$132$		0			0
$133$	8.58145			0.744106
$134$		0			0
$135$	2.83710	−	11.4186i	0.244179	−	0.982752i
$136$		0			0
$137$			15.2039i			1.29896i	0.760379	+	0.649480i	$0.225013\pi$
$137$			15.2039i			1.29896i	−0.760379	+	0.649480i	$0.774987\pi$
$138$		0			0
$139$		−	2.58145i		−	0.218956i	−0.993989	−	0.109478i	$-0.965082\pi$
$139$		−	2.58145i		−	0.218956i	0.993989	−	0.109478i	$-0.0349179\pi$
$140$		0			0
$141$			8.18342i			0.689168i
$142$		0			0
$143$		−	34.3545i		−	2.87287i
$144$		0			0
$145$	−4.34017	−	1.07838i	−0.360432	−	0.0895544i
$146$		0			0
$147$	0.133969			0.0110496
$148$		0			0
$149$			1.81658i			0.148820i	0.997228	+	0.0744101i	$0.0237074\pi$
$149$			1.81658i			0.148820i	−0.997228	+	0.0744101i	$0.976293\pi$
$150$		0			0
$151$	5.16290			0.420151			0.210075	−	0.977685i	$-0.432629\pi$
$151$	5.16290			0.420151			0.210075	+	0.977685i	$0.432629\pi$
$152$		0			0
$153$		−	0.267938i		−	0.0216615i
$154$		0			0
$155$	2.52359	−	10.1568i	0.202700	−	0.815810i
$156$		0			0
$157$	13.7587			1.09807			0.549033	−	0.835801i	$-0.314996\pi$
$157$	13.7587			1.09807			0.549033	+	0.835801i	$0.314996\pi$
$158$		0			0
$159$	2.83710			0.224997
$160$		0			0
$161$	3.60197			0.283875
$162$		0			0
$163$	−6.29072			−0.492728			−0.246364	−	0.969177i	$-0.579236\pi$
$163$	−6.29072			−0.492728			−0.246364	+	0.969177i	$0.579236\pi$
$164$		0			0
$165$	−20.0989	−	4.99386i	−1.56470	−	0.388771i
$166$		0			0
$167$			3.89269i			0.301226i	0.988593	+	0.150613i	$0.0481247\pi$
$167$			3.89269i			0.301226i	−0.988593	+	0.150613i	$0.951875\pi$
$168$		0			0
$169$	27.1978			2.09214
$170$		0			0
$171$		−	0.255652i		−	0.0195502i
$172$		0			0
$173$	1.44521			0.109877			0.0549387	−	0.998490i	$-0.482504\pi$
$173$	1.44521			0.109877			0.0549387	+	0.998490i	$0.482504\pi$
$174$		0			0
$175$	−6.15676	+	11.6248i	−0.465407	+	0.878749i
$176$		0			0
$177$			5.57531i			0.419066i
$178$		0			0
$179$		−	11.9421i		−	0.892598i	−0.894884	−	0.446299i	$-0.852742\pi$
$179$		−	11.9421i		−	0.892598i	0.894884	−	0.446299i	$-0.147258\pi$
$180$		0			0
$181$			15.3607i			1.14175i	0.821037	+	0.570876i	$0.193396\pi$
$181$			15.3607i			1.14175i	−0.821037	+	0.570876i	$0.806604\pi$
$182$		0			0
$183$			4.26794i			0.315495i
$184$		0			0
$185$	−3.10504	+	12.4969i	−0.228287	+	0.918792i
$186$		0			0
$187$	−18.5236			−1.35458
$188$		0			0
$189$			13.8432i			1.00695i
$190$		0			0
$191$	25.3607			1.83504			0.917518	−	0.397695i	$-0.130190\pi$
$191$	25.3607			1.83504			0.917518	+	0.397695i	$0.130190\pi$
$192$		0			0
$193$			4.58145i			0.329780i	0.986312	+	0.164890i	$0.0527269\pi$
$193$			4.58145i			0.329780i	−0.986312	+	0.164890i	$0.947273\pi$
$194$		0			0
$195$	5.84324	−	23.5174i	0.418443	−	1.68412i
$196$		0			0
$197$	−16.8638			−1.20149			−0.600747	−	0.799439i	$-0.705130\pi$
$197$	−16.8638			−1.20149			−0.600747	+	0.799439i	$0.705130\pi$
$198$		0			0
$199$	−9.84324			−0.697769			−0.348885	−	0.937166i	$-0.613439\pi$
$199$	−9.84324			−0.697769			−0.348885	+	0.937166i	$0.613439\pi$
$200$		0			0
$201$	13.4452			0.948352
$202$		0			0
$203$	5.26180			0.369306
$204$		0			0
$205$	−4.18342	+	16.8371i	−0.292183	+	1.17595i
$206$		0			0
$207$		−	0.107307i		−	0.00745836i
$208$		0			0
$209$	−17.6742			−1.22255
$210$		0			0
$211$			15.5753i			1.07225i	0.844139	+	0.536124i	$0.180112\pi$
$211$			15.5753i			1.07225i	−0.844139	+	0.536124i	$0.819888\pi$
$212$		0			0
$213$	10.5236			0.721065
$214$		0			0
$215$	−2.39803	+	9.65142i	−0.163544	+	0.658221i
$216$		0			0
$217$			12.3135i			0.835896i
$218$		0			0
$219$		−	23.2039i		−	1.56798i
$220$		0			0
$221$		−	21.6742i		−	1.45796i
$222$		0			0
$223$			16.9854i			1.13743i	0.822535	+	0.568715i	$0.192559\pi$
$223$			16.9854i			1.13743i	−0.822535	+	0.568715i	$0.807441\pi$
$224$		0			0
$225$	0.346316	+	0.183417i	0.0230877	+	0.0122278i
$226$		0			0
$227$	−19.9649			−1.32512			−0.662559	−	0.749009i	$-0.730530\pi$
$227$	−19.9649			−1.32512			−0.662559	+	0.749009i	$0.730530\pi$
$228$		0			0
$229$		−	23.6742i		−	1.56444i	−0.623005	−	0.782218i	$-0.714088\pi$
$229$		−	23.6742i		−	1.56444i	0.623005	−	0.782218i	$-0.285912\pi$
$230$		0			0
$231$	24.3668			1.60322
$232$		0			0
$233$		−	13.5753i		−	0.889348i	−0.895693	−	0.444674i	$-0.853320\pi$
$233$		−	13.5753i		−	0.889348i	0.895693	−	0.444674i	$-0.146680\pi$
$234$		0			0
$235$	−10.3896	−	2.58145i	−0.677744	−	0.168395i
$236$		0			0
$237$	−21.6742			−1.40789
$238$		0			0
$239$	8.36683			0.541206			0.270603	−	0.962691i	$-0.412777\pi$
$239$	8.36683			0.541206			0.270603	+	0.962691i	$0.412777\pi$
$240$		0			0
$241$	9.91548			0.638712			0.319356	−	0.947635i	$-0.396533\pi$
$241$	9.91548			0.638712			0.319356	+	0.947635i	$0.396533\pi$
$242$		0			0
$243$	0.814315			0.0522383
$244$		0			0
$245$	−0.0422604	+	0.170086i	−0.00269992	+	0.0108664i
$246$		0			0
$247$		−	20.6803i		−	1.31586i
$248$		0			0
$249$	−25.5897			−1.62168
$250$		0			0
$251$		−	17.6163i		−	1.11193i	−0.831204	−	0.555967i	$-0.812348\pi$
$251$		−	17.6163i		−	1.11193i	0.831204	−	0.555967i	$-0.187652\pi$
$252$		0			0
$253$	−7.41855			−0.466400
$254$		0			0
$255$	−12.6803	−	3.15061i	−0.794074	−	0.197299i
$256$		0			0
$257$			3.68649i			0.229957i	0.993368	+	0.114978i	$0.0366799\pi$
$257$			3.68649i			0.229957i	−0.993368	+	0.114978i	$0.963320\pi$
$258$		0			0
$259$		−	15.1506i		−	0.941413i
$260$		0			0
$261$		−	0.156755i		−	0.00970292i
$262$		0			0
$263$		−	0.107307i		−	0.00661684i	−0.999995	−	0.00330842i	$-0.998947\pi$
$263$		−	0.107307i		−	0.00661684i	0.999995	−	0.00330842i	$-0.00105311\pi$
$264$		0			0
$265$	−0.894960	+	3.60197i	−0.0549770	+	0.221267i
$266$		0			0
$267$	−14.5692			−0.891618
$268$		0			0
$269$			3.85762i			0.235203i	0.993061	+	0.117602i	$0.0375206\pi$
$269$			3.85762i			0.235203i	−0.993061	+	0.117602i	$0.962479\pi$
$270$		0			0
$271$	21.3074			1.29433			0.647165	−	0.762350i	$-0.275954\pi$
$271$	21.3074			1.29433			0.647165	+	0.762350i	$0.275954\pi$
$272$		0			0
$273$			28.5113i			1.72558i
$274$		0			0
$275$	12.6803	−	23.9421i	0.764654	−	1.44377i
$276$		0			0
$277$	1.44521			0.0868344			0.0434172	−	0.999057i	$-0.486176\pi$
$277$	1.44521			0.0868344			0.0434172	+	0.999057i	$0.486176\pi$
$278$		0			0
$279$	0.366835			0.0219618
$280$		0			0
$281$	−12.4391			−0.742053			−0.371026	−	0.928622i	$-0.620994\pi$
$281$	−12.4391			−0.742053			−0.371026	+	0.928622i	$0.620994\pi$
$282$		0			0
$283$	6.29072			0.373945			0.186972	−	0.982365i	$-0.440133\pi$
$283$	6.29072			0.373945			0.186972	+	0.982365i	$0.440133\pi$
$284$		0			0
$285$	−12.0989	−	3.00614i	−0.716677	−	0.178069i
$286$		0			0
$287$		−	20.4124i		−	1.20491i
$288$		0			0
$289$	5.31351			0.312559
$290$		0			0
$291$		−	7.83096i		−	0.459059i
$292$		0			0
$293$	−1.07838			−0.0629995			−0.0314998	−	0.999504i	$-0.510028\pi$
$293$	−1.07838			−0.0629995			−0.0314998	+	0.999504i	$0.510028\pi$
$294$		0			0
$295$	−7.07838	−	1.75872i	−0.412119	−	0.102397i
$296$		0			0
$297$		−	28.5113i		−	1.65439i
$298$		0			0
$299$		−	8.68035i		−	0.501997i
$300$		0			0
$301$		−	11.7009i		−	0.674427i
$302$		0			0
$303$			3.95443i			0.227176i
$304$		0			0
$305$	−5.41855	−	1.34632i	−0.310265	−	0.0770898i
$306$		0			0
$307$	25.2267			1.43977			0.719883	−	0.694096i	$-0.244196\pi$
$307$	25.2267			1.43977			0.719883	+	0.694096i	$0.244196\pi$
$308$		0			0
$309$			27.7009i			1.57585i
$310$		0			0
$311$	18.8371			1.06815			0.534077	−	0.845436i	$-0.320659\pi$
$311$	18.8371			1.06815			0.534077	+	0.845436i	$0.320659\pi$
$312$		0			0
$313$		−	15.2039i		−	0.859377i	−0.902977	−	0.429689i	$-0.858623\pi$
$313$		−	15.2039i		−	0.859377i	0.902977	−	0.429689i	$-0.141377\pi$
$314$		0			0
$315$	−0.447480	−	0.111183i	−0.0252126	−	0.00626444i
$316$		0			0
$317$	−16.8638			−0.947163			−0.473582	−	0.880750i	$-0.657039\pi$
$317$	−16.8638			−0.947163			−0.473582	+	0.880750i	$0.657039\pi$
$318$		0			0
$319$	−10.8371			−0.606761
$320$		0			0
$321$	26.7526			1.49318
$322$		0			0
$323$	−11.1506			−0.620437
$324$		0			0
$325$	28.0144	+	14.8371i	1.55396	+	0.823014i
$326$		0			0
$327$		−	21.0928i		−	1.16643i
$328$		0			0
$329$	12.5958			0.694430
$330$		0			0
$331$			23.5753i			1.29582i	0.761719	+	0.647908i	$0.224356\pi$
$331$			23.5753i			1.29582i	−0.761719	+	0.647908i	$0.775644\pi$
$332$		0			0
$333$	−0.451356			−0.0247341
$334$		0			0
$335$	−4.24128	+	17.0700i	−0.231726	+	0.932632i
$336$		0			0
$337$		−	14.8371i		−	0.808228i	−0.914709	−	0.404114i	$-0.867580\pi$
$337$		−	14.8371i		−	0.808228i	0.914709	−	0.404114i	$-0.132420\pi$
$338$		0			0
$339$		−	16.0000i		−	0.869001i
$340$		0			0
$341$		−	25.3607i		−	1.37336i
$342$		0			0
$343$		−	18.6225i		−	1.00552i
$344$		0			0
$345$	−5.07838	−	1.26180i	−0.273411	−	0.0679328i
$346$		0			0
$347$	0.133969			0.00719184			0.00359592	−	0.999994i	$-0.498855\pi$
$347$	0.133969			0.00719184			0.00359592	+	0.999994i	$0.498855\pi$
$348$		0			0
$349$			22.3135i			1.19441i	0.802087	+	0.597207i	$0.203723\pi$
$349$			22.3135i			1.19441i	−0.802087	+	0.597207i	$0.796277\pi$
$350$		0			0
$351$	33.3607			1.78066
$352$		0			0
$353$		−	22.8371i		−	1.21550i	−0.794130	−	0.607748i	$-0.792073\pi$
$353$		−	22.8371i		−	1.21550i	0.794130	−	0.607748i	$-0.207927\pi$
$354$		0			0
$355$	−3.31965	+	13.3607i	−0.176189	+	0.709112i
$356$		0			0
$357$	15.3730			0.813624
$358$		0			0
$359$	31.8843			1.68279			0.841394	−	0.540422i	$-0.181735\pi$
$359$	31.8843			1.68279			0.841394	+	0.540422i	$0.181735\pi$
$360$		0			0
$361$	8.36069			0.440036
$362$		0			0
$363$	−31.3835			−1.64721
$364$		0			0
$365$	29.4596	+	7.31965i	1.54199	+	0.383128i
$366$		0			0
$367$			30.4619i			1.59010i	0.606547	+	0.795048i	$0.292554\pi$
$367$			30.4619i			1.59010i	−0.606547	+	0.795048i	$0.707446\pi$
$368$		0			0
$369$	−0.608111			−0.0316570
$370$		0			0
$371$		−	4.36683i		−	0.226715i
$372$		0			0
$373$	10.0722			0.521521			0.260760	−	0.965404i	$-0.416027\pi$
$373$	10.0722			0.521521			0.260760	+	0.965404i	$0.416027\pi$
$374$		0			0
$375$	12.7526	−	14.2329i	0.658540	−	0.734982i
$376$		0			0
$377$		−	12.6803i		−	0.653071i
$378$		0			0
$379$			14.7792i			0.759159i	0.925159	+	0.379579i	$0.123931\pi$
$379$			14.7792i			0.759159i	−0.925159	+	0.379579i	$0.876069\pi$
$380$		0			0
$381$			3.33403i			0.170808i
$382$		0			0
$383$			14.4619i			0.738966i	0.929237	+	0.369483i	$0.120465\pi$
$383$			14.4619i			0.738966i	−0.929237	+	0.369483i	$0.879535\pi$
$384$		0			0
$385$	−7.68649	+	30.9360i	−0.391740	+	1.57664i
$386$		0			0
$387$	−0.348583			−0.0177195
$388$		0			0
$389$			3.17727i			0.161094i	0.996751	+	0.0805471i	$0.0256667\pi$
$389$			3.17727i			0.161094i	−0.996751	+	0.0805471i	$0.974333\pi$
$390$		0			0
$391$	−4.68035			−0.236695
$392$		0			0
$393$			26.6225i			1.34293i
$394$		0			0
$395$	6.83710	−	27.5174i	0.344012	−	1.38455i
$396$		0			0
$397$	10.8227			0.543177			0.271589	−	0.962413i	$-0.412451\pi$
$397$	10.8227			0.543177			0.271589	+	0.962413i	$0.412451\pi$
$398$		0			0
$399$	14.6681			0.734321
$400$		0			0
$401$	−12.5236			−0.625398			−0.312699	−	0.949852i	$-0.601233\pi$
$401$	−12.5236			−0.625398			−0.312699	+	0.949852i	$0.601233\pi$
$402$		0			0
$403$	29.6742			1.47818
$404$		0			0
$405$	4.72261	−	19.0072i	0.234668	−	0.944475i
$406$		0			0
$407$			31.2039i			1.54672i
$408$		0			0
$409$	−13.2885			−0.657072			−0.328536	−	0.944491i	$-0.606555\pi$
$409$	−13.2885			−0.657072			−0.328536	+	0.944491i	$0.606555\pi$
$410$		0			0
$411$			25.9877i			1.28188i
$412$		0			0
$413$	8.58145			0.422266
$414$		0			0
$415$	8.07223	−	32.4885i	0.396250	−	1.59480i
$416$		0			0
$417$		−	4.41241i		−	0.216077i
$418$		0			0
$419$		−	0.255652i		−	0.0124894i	−0.999981	−	0.00624471i	$-0.998012\pi$
$419$		−	0.255652i		−	0.0124894i	0.999981	−	0.00624471i	$-0.00198777\pi$
$420$		0			0
$421$		−	2.49693i		−	0.121693i	−0.998147	−	0.0608464i	$-0.980620\pi$
$421$		−	2.49693i		−	0.121693i	0.998147	−	0.0608464i	$-0.0193800\pi$
$422$		0			0
$423$		−	0.375245i		−	0.0182451i
$424$		0			0
$425$	8.00000	−	15.1050i	0.388057	−	0.732702i
$426$		0			0
$427$	6.56916			0.317904
$428$		0			0
$429$		−	58.7214i		−	2.83510i
$430$		0			0
$431$	−0.993857			−0.0478724			−0.0239362	−	0.999713i	$-0.507620\pi$
$431$	−0.993857			−0.0478724			−0.0239362	+	0.999713i	$0.507620\pi$
$432$		0			0
$433$			17.6286i			0.847178i	0.905855	+	0.423589i	$0.139230\pi$
$433$			17.6286i			0.847178i	−0.905855	+	0.423589i	$0.860770\pi$
$434$		0			0
$435$	−7.41855	−	1.84324i	−0.355692	−	0.0883768i
$436$		0			0
$437$	−4.46573			−0.213625
$438$		0			0
$439$	−40.5113			−1.93350			−0.966750	−	0.255725i	$-0.917686\pi$
$439$	−40.5113			−1.93350			−0.966750	+	0.255725i	$0.917686\pi$
$440$		0			0
$441$	−0.00614307			−0.000292527
$442$		0			0
$443$	−17.7093			−0.841393			−0.420697	−	0.907201i	$-0.638214\pi$
$443$	−17.7093			−0.841393			−0.420697	+	0.907201i	$0.638214\pi$
$444$		0			0
$445$	4.59583	−	18.4969i	0.217863	−	0.876839i
$446$		0			0
$447$			3.10504i			0.146863i
$448$		0			0
$449$	1.28846			0.0608061			0.0304030	−	0.999538i	$-0.490321\pi$
$449$	1.28846			0.0608061			0.0304030	+	0.999538i	$0.490321\pi$
$450$		0			0
$451$			42.0410i			1.97964i
$452$		0			0
$453$	8.82482			0.414626
$454$		0			0
$455$	−36.1978	−	8.99386i	−1.69698	−	0.421639i
$456$		0			0
$457$		−	26.3545i		−	1.23281i	−0.787428	−	0.616407i	$-0.788588\pi$
$457$		−	26.3545i		−	1.23281i	0.787428	−	0.616407i	$-0.211412\pi$
$458$		0			0
$459$		−	17.9877i		−	0.839595i
$460$		0			0
$461$			41.0349i			1.91119i	0.294690	+	0.955593i	$0.404783\pi$
$461$			41.0349i			1.91119i	−0.294690	+	0.955593i	$0.595217\pi$
$462$		0			0
$463$		−	28.7708i		−	1.33709i	−0.743670	−	0.668547i	$-0.766917\pi$
$463$		−	28.7708i		−	1.33709i	0.743670	−	0.668547i	$-0.233083\pi$
$464$		0			0
$465$	4.31351	−	17.3607i	0.200034	−	0.805083i
$466$		0			0
$467$	−5.12783			−0.237287			−0.118644	−	0.992937i	$-0.537855\pi$
$467$	−5.12783			−0.237287			−0.118644	+	0.992937i	$0.537855\pi$
$468$		0			0
$469$		−	20.6947i		−	0.955593i
$470$		0			0
$471$	23.5174			1.08363
$472$		0			0
$473$			24.0989i			1.10807i
$474$		0			0
$475$	7.63317	−	14.4124i	0.350234	−	0.661287i
$476$		0			0
$477$	−0.130094			−0.00595657
$478$		0			0
$479$	−13.6742			−0.624790			−0.312395	−	0.949952i	$-0.601131\pi$
$479$	−13.6742			−0.624790			−0.312395	+	0.949952i	$0.601131\pi$
$480$		0			0
$481$	−36.5113			−1.66477
$482$		0			0
$483$	6.15676			0.280142
$484$		0			0
$485$	9.94214	+	2.47027i	0.451449	+	0.112169i
$486$		0			0
$487$			8.51971i			0.386065i	0.981192	+	0.193033i	$0.0618323\pi$
$487$			8.51971i			0.386065i	−0.981192	+	0.193033i	$0.938168\pi$
$488$		0			0
$489$	−10.7526			−0.486249
$490$		0			0
$491$		−	4.73820i		−	0.213832i	−0.994268	−	0.106916i	$-0.965902\pi$
$491$		−	4.73820i		−	0.213832i	0.994268	−	0.106916i	$-0.0340976\pi$
$492$		0			0
$493$	−6.83710			−0.307928
$494$		0			0
$495$	0.921622	+	0.228990i	0.0414238	+	0.0102923i
$496$		0			0
$497$		−	16.1978i		−	0.726570i
$498$		0			0
$499$			11.0928i			0.496580i	0.968686	+	0.248290i	$0.0798686\pi$
$499$			11.0928i			0.496580i	−0.968686	+	0.248290i	$0.920131\pi$
$500$		0			0
$501$			6.65368i			0.297265i
$502$		0			0
$503$		−	8.42082i		−	0.375466i	−0.982220	−	0.187733i	$-0.939886\pi$
$503$		−	8.42082i		−	0.375466i	0.982220	−	0.187733i	$-0.0601139\pi$
$504$		0			0
$505$	−5.02052	−	1.24742i	−0.223410	−	0.0555094i
$506$		0			0
$507$	46.4885			2.06463
$508$		0			0
$509$			26.0000i			1.15243i	0.817298	+	0.576215i	$0.195471\pi$
$509$			26.0000i			1.15243i	−0.817298	+	0.576215i	$0.804529\pi$
$510$		0			0
$511$	−35.7152			−1.57995
$512$		0			0
$513$		−	17.1629i		−	0.757760i
$514$		0			0
$515$	−35.1689	−	8.73820i	−1.54973	−	0.385051i
$516$		0			0
$517$	−25.9421			−1.14093
$518$		0			0
$519$	2.47027			0.108433
$520$		0			0
$521$	10.3135			0.451843			0.225922	−	0.974145i	$-0.427461\pi$
$521$	10.3135			0.451843			0.225922	+	0.974145i	$0.427461\pi$
$522$		0			0
$523$	16.2784			0.711806			0.355903	−	0.934523i	$-0.384173\pi$
$523$	16.2784			0.711806			0.355903	+	0.934523i	$0.384173\pi$
$524$		0			0
$525$	−10.5236	+	19.8699i	−0.459287	+	0.867194i
$526$		0			0
$527$		−	16.0000i		−	0.696971i
$528$		0			0
$529$	21.1256			0.918503
$530$		0			0
$531$		−	0.255652i		−	0.0110944i
$532$		0			0
$533$	−49.1917			−2.13073
$534$		0			0
$535$	−8.43907	+	33.9649i	−0.364853	+	1.46843i
$536$		0			0
$537$		−	20.4124i		−	0.880860i
$538$		0			0
$539$			0.424694i			0.0182929i
$540$		0			0
$541$			3.36069i			0.144487i	0.997387	+	0.0722437i	$0.0230159\pi$
$541$			3.36069i			0.144487i	−0.997387	+	0.0722437i	$0.976984\pi$
$542$		0			0
$543$			26.2557i			1.12674i
$544$		0			0
$545$	26.7792	+	6.65368i	1.14710	+	0.285013i
$546$		0			0
$547$	1.51148			0.0646263			0.0323132	−	0.999478i	$-0.489713\pi$
$547$	1.51148			0.0646263			0.0323132	+	0.999478i	$0.489713\pi$
$548$		0			0
$549$		−	0.195704i		−	0.00835243i
$550$		0			0
$551$	−6.52359			−0.277914
$552$		0			0
$553$			33.3607i			1.41864i
$554$		0			0
$555$	−5.30737	+	21.3607i	−0.225285	+	0.906711i
$556$		0			0
$557$	−36.2290			−1.53507			−0.767536	−	0.641006i	$-0.778517\pi$
$557$	−36.2290			−1.53507			−0.767536	+	0.641006i	$0.778517\pi$
$558$		0			0
$559$	−28.1978			−1.19264
$560$		0			0
$561$	−31.6619			−1.33677
$562$		0			0
$563$	−2.17501			−0.0916656			−0.0458328	−	0.998949i	$-0.514594\pi$
$563$	−2.17501			−0.0916656			−0.0458328	+	0.998949i	$0.514594\pi$
$564$		0			0
$565$	20.3135	+	5.04718i	0.854596	+	0.212336i
$566$		0			0
$567$			23.0433i			0.967728i
$568$		0			0
$569$	33.1194			1.38844			0.694219	−	0.719764i	$-0.255750\pi$
$569$	33.1194			1.38844			0.694219	+	0.719764i	$0.255750\pi$
$570$		0			0
$571$			18.4657i			0.772767i	0.922338	+	0.386383i	$0.126276\pi$
$571$			18.4657i			0.772767i	−0.922338	+	0.386383i	$0.873724\pi$
$572$		0			0
$573$	43.3484			1.81091
$574$		0			0
$575$	3.20394	−	6.04945i	0.133613	−	0.252279i
$576$		0			0
$577$		−	14.2101i		−	0.591573i	−0.955254	−	0.295787i	$-0.904418\pi$
$577$		−	14.2101i		−	0.591573i	0.955254	−	0.295787i	$-0.0955818\pi$
$578$		0			0
$579$			7.83096i			0.325444i
$580$		0			0
$581$			39.3874i			1.63406i
$582$		0			0
$583$			8.99386i			0.372487i
$584$		0			0
$585$	−0.267938	+	1.07838i	−0.0110779	+	0.0445854i
$586$		0			0
$587$	−11.7503			−0.484987			−0.242494	−	0.970153i	$-0.577965\pi$
$587$	−11.7503			−0.484987			−0.242494	+	0.970153i	$0.577965\pi$
$588$		0			0
$589$		−	15.2663i		−	0.629038i
$590$		0			0
$591$	−28.8248			−1.18569
$592$		0			0
$593$		−	8.00000i		−	0.328521i	−0.986417	−	0.164260i	$-0.947476\pi$
$593$		−	8.00000i		−	0.328521i	0.986417	−	0.164260i	$-0.0525237\pi$
$594$		0			0
$595$	−4.84939	+	19.5174i	−0.198806	+	0.800137i
$596$		0			0
$597$	−16.8248			−0.688594
$598$		0			0
$599$	−20.5646			−0.840248			−0.420124	−	0.907467i	$-0.638013\pi$
$599$	−20.5646			−0.840248			−0.420124	+	0.907467i	$0.638013\pi$
$600$		0			0
$601$	8.60811			0.351132			0.175566	−	0.984468i	$-0.443824\pi$
$601$	8.60811			0.351132			0.175566	+	0.984468i	$0.443824\pi$
$602$		0			0
$603$	−0.616522			−0.0251067
$604$		0			0
$605$	9.89988	−	39.8443i	0.402487	−	1.61990i
$606$		0			0
$607$		−	0.259528i		−	0.0105339i	−0.999986	−	0.00526695i	$-0.998323\pi$
$607$		−	0.259528i		−	0.0105339i	0.999986	−	0.00526695i	$-0.00167653\pi$
$608$		0			0
$609$	8.99386			0.364449
$610$		0			0
$611$		−	30.3545i		−	1.22801i
$612$		0			0
$613$	−47.1650			−1.90498			−0.952488	−	0.304576i	$-0.901485\pi$
$613$	−47.1650			−1.90498			−0.952488	+	0.304576i	$0.901485\pi$
$614$		0			0
$615$	−7.15061	+	28.7792i	−0.288341	+	1.16049i
$616$		0			0
$617$			40.2967i			1.62228i	0.584849	+	0.811142i	$0.301154\pi$
$617$			40.2967i			1.62228i	−0.584849	+	0.811142i	$0.698846\pi$
$618$		0			0
$619$			30.6102i			1.23033i	0.788399	+	0.615164i	$0.210910\pi$
$619$			30.6102i			1.23033i	−0.788399	+	0.615164i	$0.789090\pi$
$620$		0			0
$621$		−	7.20394i		−	0.289084i
$622$		0			0
$623$			22.4247i			0.898426i
$624$		0			0
$625$	14.0472	+	20.6803i	0.561887	+	0.827214i
$626$		0			0
$627$	−30.2101			−1.20647
$628$		0			0
$629$			19.6865i			0.784952i
$630$		0			0
$631$	−2.21008			−0.0879819			−0.0439909	−	0.999032i	$-0.514007\pi$
$631$	−2.21008			−0.0879819			−0.0439909	+	0.999032i	$0.514007\pi$
$632$		0			0
$633$			26.6225i			1.05815i
$634$		0			0
$635$	−4.23287	−	1.05172i	−0.167976	−	0.0417361i
$636$		0			0
$637$	−0.496928			−0.0196890
$638$		0			0
$639$	−0.482553			−0.0190895
$640$		0			0
$641$	7.92777			0.313128			0.156564	−	0.987668i	$-0.449958\pi$
$641$	7.92777			0.313128			0.156564	+	0.987668i	$0.449958\pi$
$642$		0			0
$643$	−5.18115			−0.204325			−0.102162	−	0.994768i	$-0.532576\pi$
$643$	−5.18115			−0.204325			−0.102162	+	0.994768i	$0.532576\pi$
$644$		0			0
$645$	−4.09890	+	16.4969i	−0.161394	+	0.649566i
$646$		0			0
$647$			12.2062i			0.479875i	0.970788	+	0.239938i	$0.0771270\pi$
$647$			12.2062i			0.479875i	−0.970788	+	0.239938i	$0.922873\pi$
$648$		0			0
$649$	−17.6742			−0.693773
$650$		0			0
$651$			21.0472i			0.824904i
$652$		0			0
$653$	32.4969			1.27170			0.635852	−	0.771811i	$-0.280649\pi$
$653$	32.4969			1.27170			0.635852	+	0.771811i	$0.280649\pi$
$654$		0			0
$655$	−33.7998	−	8.39803i	−1.32067	−	0.328138i
$656$		0			0
$657$			1.06400i			0.0415107i
$658$		0			0
$659$			29.4186i			1.14598i	0.819561	+	0.572992i	$0.194217\pi$
$659$			29.4186i			1.14598i	−0.819561	+	0.572992i	$0.805783\pi$
$660$		0			0
$661$		−	26.0677i		−	1.01392i	−0.861971	−	0.506958i	$-0.830770\pi$
$661$		−	26.0677i		−	1.01392i	0.861971	−	0.506958i	$-0.169230\pi$
$662$		0			0
$663$		−	37.0472i		−	1.43879i
$664$		0			0
$665$	−4.62702	+	18.6225i	−0.179428	+	0.722149i
$666$		0			0
$667$	−2.73820			−0.106024
$668$		0			0
$669$			29.0328i			1.12247i
$670$		0			0
$671$	−13.5297			−0.522310
$672$		0			0
$673$		−	9.62863i		−	0.371156i	−0.982629	−	0.185578i	$-0.940584\pi$
$673$		−	9.62863i		−	0.371156i	0.982629	−	0.185578i	$-0.0594158\pi$
$674$		0			0
$675$	23.2495	+	12.3135i	0.894874	+	0.473947i
$676$		0			0
$677$	19.0205			0.731018			0.365509	−	0.930808i	$-0.380895\pi$
$677$	19.0205			0.731018			0.365509	+	0.930808i	$0.380895\pi$
$678$		0			0
$679$	−12.0533			−0.462564
$680$		0			0
$681$	−34.1256			−1.30769
$682$		0			0
$683$	17.4947			0.669415			0.334707	−	0.942322i	$-0.391363\pi$
$683$	17.4947			0.669415			0.334707	+	0.942322i	$0.391363\pi$
$684$		0			0
$685$	−32.9939	−	8.19779i	−1.26063	−	0.313222i
$686$		0			0
$687$		−	40.4657i		−	1.54386i
$688$		0			0
$689$	−10.5236			−0.400917
$690$		0			0
$691$			16.3090i			0.620423i	0.950668	+	0.310211i	$0.100400\pi$
$691$			16.3090i			0.620423i	−0.950668	+	0.310211i	$0.899600\pi$
$692$		0			0
$693$	−1.11733			−0.0424437
$694$		0			0
$695$	5.60197	+	1.39189i	0.212495	+	0.0527973i
$696$		0			0
$697$			26.5236i			1.00465i
$698$		0			0
$699$		−	23.2039i		−	0.877653i
$700$		0			0
$701$		−	12.9672i		−	0.489764i	−0.969553	−	0.244882i	$-0.921251\pi$
$701$		−	12.9672i		−	0.489764i	0.969553	−	0.244882i	$-0.0787493\pi$
$702$		0			0
$703$			18.7838i			0.708444i
$704$		0			0
$705$	−17.7587	−	4.41241i	−0.668832	−	0.166181i
$706$		0			0
$707$	6.08661			0.228911
$708$		0			0
$709$			7.36069i			0.276437i	0.990402	+	0.138218i	$0.0441376\pi$
$709$			7.36069i			0.276437i	−0.990402	+	0.138218i	$0.955862\pi$
$710$		0			0
$711$	0.993857			0.0372725
$712$		0			0
$713$		−	6.40787i		−	0.239977i
$714$		0			0
$715$	74.5523	+	18.5236i	2.78810	+	0.692743i
$716$		0			0
$717$	14.3012			0.534089
$718$		0			0
$719$	19.3197			0.720502			0.360251	−	0.932856i	$-0.382691\pi$
$719$	19.3197			0.720502			0.360251	+	0.932856i	$0.382691\pi$
$720$		0			0
$721$	42.6369			1.58788
$722$		0			0
$723$	16.9483			0.630313
$724$		0			0
$725$	4.68035	−	8.83710i	0.173824	−	0.328202i
$726$		0			0
$727$		−	21.1545i		−	0.784577i	−0.919842	−	0.392288i	$-0.871684\pi$
$727$		−	21.1545i		−	0.784577i	0.919842	−	0.392288i	$-0.128316\pi$
$728$		0			0
$729$	27.6681			1.02474
$730$		0			0
$731$			15.2039i			0.562338i
$732$		0			0
$733$	−22.7526			−0.840386			−0.420193	−	0.907435i	$-0.638038\pi$
$733$	−22.7526			−0.840386			−0.420193	+	0.907435i	$0.638038\pi$
$734$		0			0
$735$	−0.0722347	+	0.290725i	−0.00266442	+	0.0107235i
$736$		0			0
$737$			42.6225i			1.57002i
$738$		0			0
$739$			28.4534i			1.04668i	0.852125	+	0.523338i	$0.175314\pi$
$739$			28.4534i			1.04668i	−0.852125	+	0.523338i	$0.824686\pi$
$740$		0			0
$741$		−	35.3484i		−	1.29856i
$742$		0			0
$743$		−	3.79380i		−	0.139181i	−0.997576	−	0.0695904i	$-0.977831\pi$
$743$		−	3.79380i		−	0.139181i	0.997576	−	0.0695904i	$-0.0221692\pi$
$744$		0			0
$745$	−3.94214	−	0.979481i	−0.144429	−	0.0358854i
$746$		0			0
$747$	1.17340			0.0429324
$748$		0			0
$749$		−	41.1773i		−	1.50458i
$750$		0			0
$751$	17.3607			0.633501			0.316750	−	0.948509i	$-0.397408\pi$
$751$	17.3607			0.633501			0.316750	+	0.948509i	$0.397408\pi$
$752$		0			0
$753$		−	30.1112i		−	1.09731i
$754$		0			0
$755$	−2.78378	+	11.2039i	−0.101312	+	0.407753i
$756$		0			0
$757$	−4.76487			−0.173182			−0.0865910	−	0.996244i	$-0.527597\pi$
$757$	−4.76487			−0.173182			−0.0865910	+	0.996244i	$0.527597\pi$
$758$		0			0
$759$	−12.6803			−0.460267
$760$		0			0
$761$	14.1978			0.514670			0.257335	−	0.966322i	$-0.417156\pi$
$761$	14.1978			0.514670			0.257335	+	0.966322i	$0.417156\pi$
$762$		0			0
$763$	−32.4657			−1.17534
$764$		0			0
$765$	0.581449	+	0.144469i	0.0210223	+	0.00522330i
$766$		0			0
$767$		−	20.6803i		−	0.746724i
$768$		0			0
$769$	−54.7091			−1.97286			−0.986430	−	0.164181i	$-0.947502\pi$
$769$	−54.7091			−1.97286			−0.986430	+	0.164181i	$0.947502\pi$
$770$		0			0
$771$			6.30122i			0.226933i
$772$		0			0
$773$	11.0205			0.396381			0.198190	−	0.980164i	$-0.436494\pi$
$773$	11.0205			0.396381			0.198190	+	0.980164i	$0.436494\pi$
$774$		0			0
$775$	20.6803	+	10.9528i	0.742860	+	0.393437i
$776$		0			0
$777$		−	25.8966i		−	0.929034i
$778$		0			0
$779$			25.3074i			0.906731i
$780$		0			0
$781$			33.3607i			1.19374i
$782$		0			0
$783$		−	10.5236i		−	0.376082i
$784$		0			0
$785$	−7.41855	+	29.8576i	−0.264779	+	1.06566i
$786$		0			0
$787$	−33.6925			−1.20101			−0.600503	−	0.799622i	$-0.705033\pi$
$787$	−33.6925			−1.20101			−0.600503	+	0.799622i	$0.705033\pi$
$788$		0			0
$789$		−	0.183417i		−	0.00652984i
$790$		0			0
$791$	−24.6270			−0.875636
$792$		0			0
$793$		−	15.8310i		−	0.562174i
$794$		0			0
$795$	−1.52973	+	6.15676i	−0.0542541	+	0.218358i
$796$		0			0
$797$	−23.7009			−0.839528			−0.419764	−	0.907633i	$-0.637887\pi$
$797$	−23.7009			−0.839528			−0.419764	+	0.907633i	$0.637887\pi$
$798$		0			0
$799$	−16.3668			−0.579017
$800$		0			0
$801$	0.668060			0.0236047
$802$		0			0
$803$	73.5585			2.59582
$804$		0			0
$805$	−1.94214	+	7.81658i	−0.0684515	+	0.275498i
$806$		0			0
$807$			6.59374i			0.232110i
$808$		0			0
$809$	−33.0349			−1.16145			−0.580723	−	0.814102i	$-0.697230\pi$
$809$	−33.0349			−1.16145			−0.580723	+	0.814102i	$0.697230\pi$
$810$		0			0
$811$		−	6.26794i		−	0.220097i	−0.993926	−	0.110049i	$-0.964899\pi$
$811$		−	6.26794i		−	0.220097i	0.993926	−	0.110049i	$-0.0351006\pi$
$812$		0			0
$813$	36.4202			1.27731
$814$		0			0
$815$	3.39189	−	13.6514i	0.118813	−	0.478188i
$816$		0			0
$817$			14.5068i			0.507528i
$818$		0			0
$819$		−	1.30737i		−	0.0456831i
$820$		0			0
$821$			15.0616i			0.525652i	0.964843	+	0.262826i	$0.0846545\pi$
$821$			15.0616i			0.525652i	−0.964843	+	0.262826i	$0.915345\pi$
$822$		0			0
$823$			33.5669i			1.17007i	0.811009	+	0.585034i	$0.198919\pi$
$823$			33.5669i			1.17007i	−0.811009	+	0.585034i	$0.801081\pi$
$824$		0			0
$825$	21.6742	−	40.9237i	0.754599	−	1.42478i
$826$		0			0
$827$	10.6576			0.370600			0.185300	−	0.982682i	$-0.440674\pi$
$827$	10.6576			0.370600			0.185300	+	0.982682i	$0.440674\pi$
$828$		0			0
$829$			52.4846i			1.82287i	0.411447	+	0.911433i	$0.365023\pi$
$829$			52.4846i			1.82287i	−0.411447	+	0.911433i	$0.634977\pi$
$830$		0			0
$831$	2.47027			0.0856926
$832$		0			0
$833$			0.267938i			0.00928351i
$834$		0			0
$835$	−8.44748	−	2.09890i	−0.292337	−	0.0726353i
$836$		0			0
$837$	24.6270			0.851234
$838$		0			0
$839$	18.2101			0.628682			0.314341	−	0.949310i	$-0.398217\pi$
$839$	18.2101			0.628682			0.314341	+	0.949310i	$0.398217\pi$
$840$		0			0
$841$	25.0000			0.862069
$842$		0			0
$843$	−21.2618			−0.732295
$844$		0			0
$845$	−14.6647	+	59.0216i	−0.504483	+	2.03040i
$846$		0			0
$847$			48.3051i			1.65978i
$848$		0			0
$849$	10.7526			0.369028
$850$		0			0
$851$			7.88428i			0.270270i
$852$		0			0
$853$	19.7542			0.676371			0.338185	−	0.941080i	$-0.390187\pi$
$853$	19.7542			0.676371			0.338185	+	0.941080i	$0.390187\pi$
$854$		0			0
$855$	0.554787	+	0.137845i	0.0189733	+	0.00471419i
$856$		0			0
$857$		−	48.9939i		−	1.67360i	−0.547510	−	0.836799i	$-0.684424\pi$
$857$		−	48.9939i		−	1.67360i	0.547510	−	0.836799i	$-0.315576\pi$
$858$		0			0
$859$			24.3090i			0.829412i	0.909956	+	0.414706i	$0.136115\pi$
$859$			24.3090i			0.829412i	−0.909956	+	0.414706i	$0.863885\pi$
$860$		0			0
$861$		−	34.8904i		−	1.18906i
$862$		0			0
$863$			44.3584i			1.50998i	0.655737	+	0.754989i	$0.272358\pi$
$863$			44.3584i			1.50998i	−0.655737	+	0.754989i	$0.727642\pi$
$864$		0			0
$865$	−0.779243	+	3.13624i	−0.0264950	+	0.106635i
$866$		0			0
$867$	9.08225			0.308449
$868$		0			0
$869$		−	68.7091i		−	2.33080i
$870$		0			0
$871$	−49.8720			−1.68985
$872$		0			0
$873$			0.359084i			0.0121531i
$874$		0			0
$875$	−21.9071	−	19.6286i	−0.740594	−	0.663569i
$876$		0			0
$877$	37.9565			1.28170			0.640850	−	0.767666i	$-0.278582\pi$
$877$	37.9565			1.28170			0.640850	+	0.767666i	$0.278582\pi$
$878$		0			0
$879$	−1.84324			−0.0621711
$880$		0			0
$881$	25.0661			0.844498			0.422249	−	0.906480i	$-0.361241\pi$
$881$	25.0661			0.844498			0.422249	+	0.906480i	$0.361241\pi$
$882$		0			0
$883$	−21.1278			−0.711008			−0.355504	−	0.934675i	$-0.615691\pi$
$883$	−21.1278			−0.711008			−0.355504	+	0.934675i	$0.615691\pi$
$884$		0			0
$885$	−12.0989	−	3.00614i	−0.406700	−	0.101050i
$886$		0			0
$887$		−	36.1894i		−	1.21512i	−0.794274	−	0.607560i	$-0.792148\pi$
$887$		−	36.1894i		−	1.21512i	0.794274	−	0.607560i	$-0.207852\pi$
$888$		0			0
$889$	5.13170			0.172112
$890$		0			0
$891$		−	47.4596i		−	1.58996i
$892$		0			0
$893$	−15.6163			−0.522581
$894$		0			0
$895$	25.9155	+	6.43907i	0.866259	+	0.215234i
$896$		0			0
$897$		−	14.8371i		−	0.495396i
$898$		0			0
$899$		−	9.36069i		−	0.312197i
$900$		0			0
$901$			5.67420i			0.189035i
$902$		0			0
$903$		−	20.0000i		−	0.665558i
$904$		0			0
$905$	−33.3340	−	8.28231i	−1.10806	−	0.275313i
$906$		0			0
$907$	−35.2678			−1.17105			−0.585523	−	0.810656i	$-0.699111\pi$
$907$	−35.2678			−1.17105			−0.585523	+	0.810656i	$0.699111\pi$
$908$		0			0
$909$		−	0.181328i		−	0.00601426i
$910$		0			0
$911$	−15.0061			−0.497176			−0.248588	−	0.968609i	$-0.579966\pi$
$911$	−15.0061			−0.497176			−0.248588	+	0.968609i	$0.579966\pi$
$912$		0			0
$913$		−	81.1215i		−	2.68473i
$914$		0			0
$915$	−9.26180	−	2.30122i	−0.306186	−	0.0760761i
$916$		0			0
$917$	40.9770			1.35318
$918$		0			0
$919$	32.8781			1.08455			0.542275	−	0.840201i	$-0.317563\pi$
$919$	32.8781			1.08455			0.542275	+	0.840201i	$0.317563\pi$
$920$		0			0
$921$	43.1194			1.42083
$922$		0			0
$923$	−39.0349			−1.28485
$924$		0			0
$925$	−25.4452	−	13.4764i	−0.836633	−	0.443102i
$926$		0			0
$927$		−	1.27021i		−	0.0417190i
$928$		0			0
$929$	30.2290			0.991781			0.495890	−	0.868385i	$-0.334842\pi$
$929$	30.2290			0.991781			0.495890	+	0.868385i	$0.334842\pi$
$930$		0			0
$931$			0.255652i			0.00837866i
$932$		0			0
$933$	32.1978			1.05411
$934$		0			0
$935$	9.98771	−	40.1978i	0.326633	−	1.31461i
$936$		0			0
$937$			28.4124i			0.928193i	0.885785	+	0.464096i	$0.153621\pi$
$937$			28.4124i			0.928193i	−0.885785	+	0.464096i	$0.846379\pi$
$938$		0			0
$939$		−	25.9877i		−	0.848077i
$940$		0			0
$941$		−	42.0821i		−	1.37184i	−0.727679	−	0.685918i	$-0.759401\pi$
$941$		−	42.0821i		−	1.37184i	0.727679	−	0.685918i	$-0.240599\pi$
$942$		0			0
$943$			10.6225i			0.345916i
$944$		0			0
$945$	−30.0410	−	7.46412i	−0.977235	−	0.242808i
$946$		0			0
$947$	22.2739			0.723805			0.361902	−	0.932216i	$-0.382127\pi$
$947$	22.2739			0.723805			0.361902	+	0.932216i	$0.382127\pi$
$948$		0			0
$949$			86.0698i			2.79394i
$950$		0			0
$951$	−28.8248			−0.934709
$952$		0			0
$953$		−	14.6681i		−	0.475145i	−0.971370	−	0.237573i	$-0.923648\pi$
$953$		−	14.6681i		−	0.475145i	0.971370	−	0.237573i	$-0.0763517\pi$
$954$		0			0
$955$	−13.6742	+	55.0349i	−0.442487	+	1.78089i
$956$		0			0
$957$	−18.5236			−0.598783
$958$		0			0
$959$	40.0000			1.29167
$960$		0			0
$961$	−9.09436			−0.293367
$962$		0			0
$963$	−1.22672			−0.0395306
$964$		0			0
$965$	−9.94214	−	2.47027i	−0.320049	−	0.0795207i
$966$		0			0
$967$			0.403997i			0.0129917i	0.999979	+	0.00649584i	$0.00206770\pi$
$967$			0.403997i			0.0129917i	−0.999979	+	0.00649584i	$0.997932\pi$
$968$		0			0
$969$	−19.0595			−0.612278
$970$		0			0
$971$		−	46.8326i		−	1.50293i	−0.659774	−	0.751464i	$-0.729348\pi$
$971$		−	46.8326i		−	1.50293i	0.659774	−	0.751464i	$-0.270652\pi$
$972$		0			0
$973$	−6.79153			−0.217726
$974$		0			0
$975$	47.8843	+	25.3607i	1.53352	+	0.812192i
$976$		0			0
$977$			53.6041i			1.71495i	0.514529	+	0.857473i	$0.327967\pi$
$977$			53.6041i			1.71495i	−0.514529	+	0.857473i	$0.672033\pi$
$978$		0			0
$979$		−	46.1855i		−	1.47610i
$980$		0			0
$981$			0.967195i			0.0308802i
$982$		0			0
$983$		−	19.9916i		−	0.637633i	−0.947817	−	0.318816i	$-0.896715\pi$
$983$		−	19.9916i		−	0.637633i	0.947817	−	0.318816i	$-0.103285\pi$
$984$		0			0
$985$	9.09275	−	36.5958i	0.289719	−	1.16604i
$986$		0			0
$987$	21.5297			0.685299
$988$		0			0
$989$			6.08906i			0.193621i
$990$		0			0
$991$	−24.6270			−0.782303			−0.391152	−	0.920326i	$-0.627923\pi$
$991$	−24.6270			−0.782303			−0.391152	+	0.920326i	$0.627923\pi$
$992$		0			0
$993$			40.2967i			1.27878i
$994$		0			0
$995$	5.30737	−	21.3607i	0.168255	−	0.677179i
$996$		0			0
$997$	−20.9795			−0.664427			−0.332213	−	0.943204i	$-0.607795\pi$
$997$	−20.9795			−0.664427			−0.332213	+	0.943204i	$0.607795\pi$
$998$		0			0
$999$	−30.3012			−0.958688

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.f.i.129.6		6
4.3	odd	2		1280.2.f.k.129.2		6
5.4	even	2		1280.2.f.l.129.2		6
8.3	odd	2		1280.2.f.j.129.5		6
8.5	even	2		1280.2.f.l.129.1		6
16.3	odd	4		640.2.c.c.129.2	yes	6
16.5	even	4		640.2.c.a.129.2	✓	6
16.11	odd	4		640.2.c.b.129.5	yes	6
16.13	even	4		640.2.c.d.129.5	yes	6
20.19	odd	2		1280.2.f.j.129.6		6
40.19	odd	2		1280.2.f.k.129.1		6
40.29	even	2	inner	1280.2.f.i.129.5		6
80.3	even	4		3200.2.a.bo.1.3		3
80.13	odd	4		3200.2.a.bv.1.1		3
80.19	odd	4		640.2.c.c.129.5	yes	6
80.27	even	4		3200.2.a.br.1.3		3
80.29	even	4		640.2.c.d.129.2	yes	6
80.37	odd	4		3200.2.a.bs.1.1		3
80.43	even	4		3200.2.a.bt.1.1		3
80.53	odd	4		3200.2.a.bq.1.3		3
80.59	odd	4		640.2.c.b.129.2	yes	6
80.67	even	4		3200.2.a.bu.1.1		3
80.69	even	4		640.2.c.a.129.5	yes	6
80.77	odd	4		3200.2.a.bp.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.c.a.129.2	✓	6	16.5	even	4
640.2.c.a.129.5	yes	6	80.69	even	4
640.2.c.b.129.2	yes	6	80.59	odd	4
640.2.c.b.129.5	yes	6	16.11	odd	4
640.2.c.c.129.2	yes	6	16.3	odd	4
640.2.c.c.129.5	yes	6	80.19	odd	4
640.2.c.d.129.2	yes	6	80.29	even	4
640.2.c.d.129.5	yes	6	16.13	even	4
1280.2.f.i.129.5		6	40.29	even	2	inner
1280.2.f.i.129.6		6	1.1	even	1	trivial
1280.2.f.j.129.5		6	8.3	odd	2
1280.2.f.j.129.6		6	20.19	odd	2
1280.2.f.k.129.1		6	40.19	odd	2
1280.2.f.k.129.2		6	4.3	odd	2
1280.2.f.l.129.1		6	8.5	even	2
1280.2.f.l.129.2		6	5.4	even	2
3200.2.a.bo.1.3		3	80.3	even	4
3200.2.a.bp.1.3		3	80.77	odd	4
3200.2.a.bq.1.3		3	80.53	odd	4
3200.2.a.br.1.3		3	80.27	even	4
3200.2.a.bs.1.1		3	80.37	odd	4
3200.2.a.bt.1.1		3	80.43	even	4
3200.2.a.bu.1.1		3	80.67	even	4
3200.2.a.bv.1.1		3	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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1280.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.70928 q^{3} +(-0.539189 + 2.17009i) q^{5} -2.63090i q^{7} -0.0783777 q^{9} +O(q^{10})\)	\(q+1.70928 q^{3} +(-0.539189 + 2.17009i) q^{5} -2.63090i q^{7} -0.0783777 q^{9} +5.41855i q^{11} -6.34017 q^{13} +(-0.921622 + 3.70928i) q^{15} +3.41855i q^{17} +3.26180i q^{19} -4.49693i q^{21} +1.36910i q^{23} +(-4.41855 - 2.34017i) q^{25} -5.26180 q^{27} +2.00000i q^{29} -4.68035 q^{31} +9.26180i q^{33} +(5.70928 + 1.41855i) q^{35} +5.75872 q^{37} -10.8371 q^{39} +7.75872 q^{41} +4.44748 q^{43} +(0.0422604 - 0.170086i) q^{45} +4.78765i q^{47} +0.0783777 q^{49} +5.84324i q^{51} +1.65983 q^{53} +(-11.7587 - 2.92162i) q^{55} +5.57531i q^{57} +3.26180i q^{59} +2.49693i q^{61} +0.206204i q^{63} +(3.41855 - 13.7587i) q^{65} +7.86603 q^{67} +2.34017i q^{69} +6.15676 q^{71} -13.5753i q^{73} +(-7.55252 - 4.00000i) q^{75} +14.2557 q^{77} -12.6803 q^{79} -8.75872 q^{81} -14.9711 q^{83} +(-7.41855 - 1.84324i) q^{85} +3.41855i q^{87} -8.52359 q^{89} +16.6803i q^{91} -8.00000 q^{93} +(-7.07838 - 1.75872i) q^{95} -4.58145i q^{97} -0.424694i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{3} + 6 q^{9}+O(q^{10}) \) 6 * q - 4 * q^3 + 6 * q^9	\( 6 q - 4 q^{3} + 6 q^{9} - 16 q^{13} - 12 q^{15} + 2 q^{25} - 16 q^{27} + 16 q^{31} + 20 q^{35} - 16 q^{37} - 8 q^{39} - 4 q^{41} + 28 q^{43} + 32 q^{45} - 6 q^{49} + 32 q^{53} - 20 q^{55} - 8 q^{65} + 20 q^{67} + 24 q^{71} - 44 q^{75} - 32 q^{79} - 2 q^{81} - 60 q^{83} - 16 q^{85} - 20 q^{89} - 48 q^{93} - 36 q^{95}+O(q^{100}) \) 6 * q - 4 * q^3 + 6 * q^9 - 16 * q^13 - 12 * q^15 + 2 * q^25 - 16 * q^27 + 16 * q^31 + 20 * q^35 - 16 * q^37 - 8 * q^39 - 4 * q^41 + 28 * q^43 + 32 * q^45 - 6 * q^49 + 32 * q^53 - 20 * q^55 - 8 * q^65 + 20 * q^67 + 24 * q^71 - 44 * q^75 - 32 * q^79 - 2 * q^81 - 60 * q^83 - 16 * q^85 - 20 * q^89 - 48 * q^93 - 36 * q^95

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