LMFDB - Embedded newform 1280.2.f.j.129.2

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			129.2
Root			$1.45161 + 1.45161i$ of defining polynomial
Character	$\chi$	$=$	1280.129
Dual form			1280.2.f.j.129.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.90321 q^{3} +(-2.21432 + 0.311108i) q^{5} -3.52543i q^{7} +5.42864 q^{9} +3.80642i q^{11} +2.62222 q^{13} +(6.42864 - 0.903212i) q^{15} +5.80642i q^{17} -5.05086i q^{19} +10.2351i q^{21} +0.474572i q^{23} +(4.80642 - 1.37778i) q^{25} -7.05086 q^{27} +2.00000i q^{29} -2.75557 q^{31} -11.0509i q^{33} +(1.09679 + 7.80642i) q^{35} +7.18421 q^{37} -7.61285 q^{39} -5.18421 q^{41} -1.95407 q^{43} +(-12.0207 + 1.68889i) q^{45} -5.33185i q^{47} -5.42864 q^{49} -16.8573i q^{51} -5.37778 q^{53} +(-1.18421 - 8.42864i) q^{55} +14.6637i q^{57} -5.05086i q^{59} -12.2351i q^{61} -19.1383i q^{63} +(-5.80642 + 0.815792i) q^{65} -7.76049 q^{67} -1.37778i q^{69} +4.85728 q^{71} -6.66370i q^{73} +(-13.9541 + 4.00000i) q^{75} +13.4193 q^{77} +5.24443 q^{79} +4.18421 q^{81} -12.1476 q^{83} +(-1.80642 - 12.8573i) q^{85} -5.80642i q^{87} -12.1017 q^{89} -9.24443i q^{91} +8.00000 q^{93} +(1.57136 + 11.1842i) q^{95} +13.8064i q^{97} +20.6637i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots + 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

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
$3$	−2.90321			−1.67617			−0.838085	−	0.545540i	$-0.816325\pi$
$3$	−2.90321			−1.67617			−0.838085	+	0.545540i	$0.816325\pi$
$4$		0			0
$5$	−2.21432	+	0.311108i	−0.990274	+	0.139132i
$5$	−2.21432	+	0.311108i	−0.990274	+	0.139132i
$6$		0			0
$7$		−	3.52543i		−	1.33249i	−0.745735	−	0.666243i	$-0.767901\pi$
$7$		−	3.52543i		−	1.33249i	0.745735	−	0.666243i	$-0.232099\pi$
$8$		0			0
$9$	5.42864			1.80955
$10$		0			0
$11$			3.80642i			1.14768i	0.818967	+	0.573840i	$0.194547\pi$
$11$			3.80642i			1.14768i	−0.818967	+	0.573840i	$0.805453\pi$
$12$		0			0
$13$	2.62222			0.727272			0.363636	−	0.931541i	$-0.381535\pi$
$13$	2.62222			0.727272			0.363636	+	0.931541i	$0.381535\pi$
$14$		0			0
$15$	6.42864	−	0.903212i	1.65987	−	0.233208i
$16$		0			0
$17$			5.80642i			1.40826i	0.710069	+	0.704132i	$0.248664\pi$
$17$			5.80642i			1.40826i	−0.710069	+	0.704132i	$0.751336\pi$
$18$		0			0
$19$		−	5.05086i		−	1.15875i	−0.815063	−	0.579373i	$-0.803298\pi$
$19$		−	5.05086i		−	1.15875i	0.815063	−	0.579373i	$-0.196702\pi$
$20$		0			0
$21$			10.2351i			2.23347i
$22$		0			0
$23$			0.474572i			0.0989552i	0.998775	+	0.0494776i	$0.0157556\pi$
$23$			0.474572i			0.0989552i	−0.998775	+	0.0494776i	$0.984244\pi$
$24$		0			0
$25$	4.80642	−	1.37778i	0.961285	−	0.275557i
$26$		0			0
$27$	−7.05086			−1.35694
$28$		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
$31$	−2.75557			−0.494915			−0.247457	−	0.968899i	$-0.579595\pi$
$31$	−2.75557			−0.494915			−0.247457	+	0.968899i	$0.579595\pi$
$32$		0			0
$33$		−	11.0509i		−	1.92371i
$34$		0			0
$35$	1.09679	+	7.80642i	0.185391	+	1.31953i
$36$		0			0
$37$	7.18421			1.18108			0.590538	−	0.807010i	$-0.298915\pi$
$37$	7.18421			1.18108			0.590538	+	0.807010i	$0.298915\pi$
$38$		0			0
$39$	−7.61285			−1.21903
$40$		0			0
$41$	−5.18421			−0.809637			−0.404819	−	0.914397i	$-0.632665\pi$
$41$	−5.18421			−0.809637			−0.404819	+	0.914397i	$0.632665\pi$
$42$		0			0
$43$	−1.95407			−0.297992			−0.148996	−	0.988838i	$-0.547604\pi$
$43$	−1.95407			−0.297992			−0.148996	+	0.988838i	$0.547604\pi$
$44$		0			0
$45$	−12.0207	+	1.68889i	−1.79195	+	0.251765i
$46$		0			0
$47$		−	5.33185i		−	0.777730i	−0.921295	−	0.388865i	$-0.872867\pi$
$47$		−	5.33185i		−	0.777730i	0.921295	−	0.388865i	$-0.127133\pi$
$48$		0			0
$49$	−5.42864			−0.775520
$50$		0			0
$51$		−	16.8573i		−	2.36049i
$52$		0			0
$53$	−5.37778			−0.738695			−0.369348	−	0.929291i	$-0.620419\pi$
$53$	−5.37778			−0.738695			−0.369348	+	0.929291i	$0.620419\pi$
$54$		0			0
$55$	−1.18421	−	8.42864i	−0.159679	−	1.13652i
$56$		0			0
$57$			14.6637i			1.94225i
$58$		0			0
$59$		−	5.05086i		−	0.657565i	−0.944406	−	0.328783i	$-0.893362\pi$
$59$		−	5.05086i		−	0.657565i	0.944406	−	0.328783i	$-0.106638\pi$
$60$		0			0
$61$		−	12.2351i		−	1.56654i	−0.621682	−	0.783270i	$-0.713550\pi$
$61$		−	12.2351i		−	1.56654i	0.621682	−	0.783270i	$-0.286450\pi$
$62$		0			0
$63$		−	19.1383i		−	2.41120i
$64$		0			0
$65$	−5.80642	+	0.815792i	−0.720198	+	0.101187i
$66$		0			0
$67$	−7.76049			−0.948095			−0.474047	−	0.880499i	$-0.657207\pi$
$67$	−7.76049			−0.948095			−0.474047	+	0.880499i	$0.657207\pi$
$68$		0			0
$69$		−	1.37778i		−	0.165866i
$70$		0			0
$71$	4.85728			0.576453			0.288226	−	0.957562i	$-0.406934\pi$
$71$	4.85728			0.576453			0.288226	+	0.957562i	$0.406934\pi$
$72$		0			0
$73$		−	6.66370i		−	0.779927i	−0.920830	−	0.389964i	$-0.872488\pi$
$73$		−	6.66370i		−	0.779927i	0.920830	−	0.389964i	$-0.127512\pi$
$74$		0			0
$75$	−13.9541	+	4.00000i	−1.61128	+	0.461880i
$76$		0			0
$77$	13.4193			1.52927
$78$		0			0
$79$	5.24443			0.590045			0.295022	−	0.955490i	$-0.404673\pi$
$79$	5.24443			0.590045			0.295022	+	0.955490i	$0.404673\pi$
$80$		0			0
$81$	4.18421			0.464912
$82$		0			0
$83$	−12.1476			−1.33338			−0.666689	−	0.745336i	$-0.732289\pi$
$83$	−12.1476			−1.33338			−0.666689	+	0.745336i	$0.732289\pi$
$84$		0			0
$85$	−1.80642	−	12.8573i	−0.195934	−	1.39457i
$86$		0			0
$87$		−	5.80642i		−	0.622514i
$88$		0			0
$89$	−12.1017			−1.28278			−0.641389	−	0.767216i	$-0.721642\pi$
$89$	−12.1017			−1.28278			−0.641389	+	0.767216i	$0.721642\pi$
$90$		0			0
$91$		−	9.24443i		−	0.969080i
$92$		0			0
$93$	8.00000			0.829561
$94$		0			0
$95$	1.57136	+	11.1842i	0.161218	+	1.14748i
$96$		0			0
$97$			13.8064i			1.40183i	0.713245	+	0.700915i	$0.247225\pi$
$97$			13.8064i			1.40183i	−0.713245	+	0.700915i	$0.752775\pi$
$98$		0			0
$99$			20.6637i			2.07678i
$100$		0			0
$101$		−	19.7146i		−	1.96167i	−0.194836	−	0.980836i	$-0.562417\pi$
$101$		−	19.7146i		−	1.96167i	0.194836	−	0.980836i	$-0.437583\pi$
$102$		0			0
$103$		−	3.13828i		−	0.309223i	−0.987975	−	0.154612i	$-0.950587\pi$
$103$		−	3.13828i		−	0.309223i	0.987975	−	0.154612i	$-0.0494127\pi$
$104$		0			0
$105$	−3.18421	−	22.6637i	−0.310747	−	2.21175i
$106$		0			0
$107$	5.39207			0.521272			0.260636	−	0.965437i	$-0.416068\pi$
$107$	5.39207			0.521272			0.260636	+	0.965437i	$0.416068\pi$
$108$		0			0
$109$		−	8.62222i		−	0.825858i	−0.910763	−	0.412929i	$-0.864506\pi$
$109$		−	8.62222i		−	0.825858i	0.910763	−	0.412929i	$-0.135494\pi$
$110$		0			0
$111$	−20.8573			−1.97969
$112$		0			0
$113$		−	5.51114i		−	0.518444i	−0.965818	−	0.259222i	$-0.916534\pi$
$113$		−	5.51114i		−	0.518444i	0.965818	−	0.259222i	$-0.0834662\pi$
$114$		0			0
$115$	−0.147643	−	1.05086i	−0.0137678	−	0.0979927i
$116$		0			0
$117$	14.2351			1.31603
$118$		0			0
$119$	20.4701			1.87649
$120$		0			0
$121$	−3.48886			−0.317169
$122$		0			0
$123$	15.0509			1.35709
$124$		0			0
$125$	−10.2143	+	4.54617i	−0.913597	+	0.406622i
$126$		0			0
$127$			10.2810i			0.912291i	0.889905	+	0.456145i	$0.150770\pi$
$127$			10.2810i			0.912291i	−0.889905	+	0.456145i	$0.849230\pi$
$128$		0			0
$129$	5.67307			0.499486
$130$		0			0
$131$			4.66370i			0.407470i	0.979026	+	0.203735i	$0.0653080\pi$
$131$			4.66370i			0.407470i	−0.979026	+	0.203735i	$0.934692\pi$
$132$		0			0
$133$	−17.8064			−1.54401
$134$		0			0
$135$	15.6128	−	2.19358i	1.34374	−	0.188793i
$136$		0			0
$137$		−	11.3461i		−	0.969366i	−0.874690	−	0.484683i	$-0.838935\pi$
$137$		−	11.3461i		−	0.969366i	0.874690	−	0.484683i	$-0.161065\pi$
$138$		0			0
$139$			11.8064i			1.00141i	0.865619	+	0.500704i	$0.166925\pi$
$139$			11.8064i			1.00141i	−0.865619	+	0.500704i	$0.833075\pi$
$140$		0			0
$141$			15.4795i			1.30361i
$142$		0			0
$143$			9.98126i			0.834675i
$144$		0			0
$145$	−0.622216	−	4.42864i	−0.0516722	−	0.367778i
$146$		0			0
$147$	15.7605			1.29990
$148$		0			0
$149$		−	5.47949i		−	0.448898i	−0.974486	−	0.224449i	$-0.927942\pi$
$149$		−	5.47949i		−	0.448898i	0.974486	−	0.224449i	$-0.0720582\pi$
$150$		0			0
$151$	−23.6128			−1.92159			−0.960793	−	0.277266i	$-0.910572\pi$
$151$	−23.6128			−1.92159			−0.960793	+	0.277266i	$0.910572\pi$
$152$		0			0
$153$			31.5210i			2.54832i
$154$		0			0
$155$	6.10171	−	0.857279i	0.490101	−	0.0688583i
$156$		0			0
$157$	−0.815792			−0.0651073			−0.0325536	−	0.999470i	$-0.510364\pi$
$157$	−0.815792			−0.0651073			−0.0325536	+	0.999470i	$0.510364\pi$
$158$		0			0
$159$	15.6128			1.23818
$160$		0			0
$161$	1.67307			0.131856
$162$		0			0
$163$	−10.9032			−0.854005			−0.427003	−	0.904250i	$-0.640431\pi$
$163$	−10.9032			−0.854005			−0.427003	+	0.904250i	$0.640431\pi$
$164$		0			0
$165$	3.43801	+	24.4701i	0.267649	+	1.90500i
$166$		0			0
$167$			6.57628i			0.508888i	0.967088	+	0.254444i	$0.0818925\pi$
$167$			6.57628i			0.508888i	−0.967088	+	0.254444i	$0.918108\pi$
$168$		0			0
$169$	−6.12399			−0.471076
$170$		0			0
$171$		−	27.4193i		−	2.09680i
$172$		0			0
$173$	−10.5303			−0.800608			−0.400304	−	0.916382i	$-0.631095\pi$
$173$	−10.5303			−0.800608			−0.400304	+	0.916382i	$0.631095\pi$
$174$		0			0
$175$	−4.85728	−	16.9447i	−0.367176	−	1.28090i
$176$		0			0
$177$			14.6637i			1.10219i
$178$		0			0
$179$			6.29529i			0.470532i	0.971931	+	0.235266i	$0.0755961\pi$
$179$			6.29529i			0.470532i	−0.971931	+	0.235266i	$0.924404\pi$
$180$		0			0
$181$			0.488863i			0.0363369i	0.999835	+	0.0181684i	$0.00578351\pi$
$181$			0.488863i			0.0363369i	−0.999835	+	0.0181684i	$0.994216\pi$
$182$		0			0
$183$			35.5210i			2.62579i
$184$		0			0
$185$	−15.9081	+	2.23506i	−1.16959	+	0.164325i
$186$		0			0
$187$	−22.1017			−1.61624
$188$		0			0
$189$			24.8573i			1.80810i
$190$		0			0
$191$	−10.4889			−0.758947			−0.379474	−	0.925203i	$-0.623895\pi$
$191$	−10.4889			−0.758947			−0.379474	+	0.925203i	$0.623895\pi$
$192$		0			0
$193$		−	13.8064i		−	0.993808i	−0.867805	−	0.496904i	$-0.834470\pi$
$193$		−	13.8064i		−	0.993808i	0.867805	−	0.496904i	$-0.165530\pi$
$194$		0			0
$195$	16.8573	−	2.36842i	1.20717	−	0.169606i
$196$		0			0
$197$	16.7239			1.19153			0.595765	−	0.803159i	$-0.296849\pi$
$197$	16.7239			1.19153			0.595765	+	0.803159i	$0.296849\pi$
$198$		0			0
$199$	20.8573			1.47853			0.739267	−	0.673413i	$-0.235172\pi$
$199$	20.8573			1.47853			0.739267	+	0.673413i	$0.235172\pi$
$200$		0			0
$201$	22.5303			1.58917
$202$		0			0
$203$	7.05086			0.494873
$204$		0			0
$205$	11.4795	−	1.61285i	0.801763	−	0.112646i
$206$		0			0
$207$			2.57628i			0.179064i
$208$		0			0
$209$	19.2257			1.32987
$210$		0			0
$211$			4.66370i			0.321063i	0.987031	+	0.160531i	$0.0513207\pi$
$211$			4.66370i			0.321063i	−0.987031	+	0.160531i	$0.948679\pi$
$212$		0			0
$213$	−14.1017			−0.966233
$214$		0			0
$215$	4.32693	−	0.607926i	0.295094	−	0.0414602i
$216$		0			0
$217$			9.71456i			0.659467i
$218$		0			0
$219$			19.3461i			1.30729i
$220$		0			0
$221$			15.2257i			1.02419i
$222$		0			0
$223$		−	26.4558i		−	1.77161i	−0.464054	−	0.885807i	$-0.653606\pi$
$223$		−	26.4558i		−	1.77161i	0.464054	−	0.885807i	$-0.346394\pi$
$224$		0			0
$225$	26.0923	−	7.47949i	1.73949	−	0.498633i
$226$		0			0
$227$	12.3225			0.817872			0.408936	−	0.912563i	$-0.365900\pi$
$227$	12.3225			0.817872			0.408936	+	0.912563i	$0.365900\pi$
$228$		0			0
$229$			13.2257i			0.873979i	0.899467	+	0.436989i	$0.143955\pi$
$229$			13.2257i			0.873979i	−0.899467	+	0.436989i	$0.856045\pi$
$230$		0			0
$231$	−38.9590			−2.56331
$232$		0			0
$233$		−	6.66370i		−	0.436554i	−0.975887	−	0.218277i	$-0.929956\pi$
$233$		−	6.66370i		−	0.436554i	0.975887	−	0.218277i	$-0.0700436\pi$
$234$		0			0
$235$	1.65878	+	11.8064i	0.108207	+	0.770166i
$236$		0			0
$237$	−15.2257			−0.989015
$238$		0			0
$239$	−22.9590			−1.48509			−0.742547	−	0.669794i	$-0.766382\pi$
$239$	−22.9590			−1.48509			−0.742547	+	0.669794i	$0.766382\pi$
$240$		0			0
$241$	−14.0415			−0.904492			−0.452246	−	0.891893i	$-0.649377\pi$
$241$	−14.0415			−0.904492			−0.452246	+	0.891893i	$0.649377\pi$
$242$		0			0
$243$	9.00492			0.577666
$244$		0			0
$245$	12.0207	−	1.68889i	0.767977	−	0.107899i
$246$		0			0
$247$		−	13.2444i		−	0.842723i
$248$		0			0
$249$	35.2672			2.23497
$250$		0			0
$251$		−	24.9304i		−	1.57359i	−0.617212	−	0.786797i	$-0.711738\pi$
$251$		−	24.9304i		−	1.57359i	0.617212	−	0.786797i	$-0.288262\pi$
$252$		0			0
$253$	−1.80642			−0.113569
$254$		0			0
$255$	5.24443	+	37.3274i	0.328419	+	2.33753i
$256$		0			0
$257$		−	25.7146i		−	1.60403i	−0.597304	−	0.802015i	$-0.703761\pi$
$257$		−	25.7146i		−	1.60403i	0.597304	−	0.802015i	$-0.296239\pi$
$258$		0			0
$259$		−	25.3274i		−	1.57377i
$260$		0			0
$261$			10.8573i			0.672049i
$262$		0			0
$263$			2.57628i			0.158860i	0.996840	+	0.0794302i	$0.0253101\pi$
$263$			2.57628i			0.158860i	−0.996840	+	0.0794302i	$0.974690\pi$
$264$		0			0
$265$	11.9081	−	1.67307i	0.731511	−	0.102776i
$266$		0			0
$267$	35.1338			2.15016
$268$		0			0
$269$		−	25.7462i		−	1.56977i	−0.619639	−	0.784887i	$-0.712721\pi$
$269$		−	25.7462i		−	1.56977i	0.619639	−	0.784887i	$-0.287279\pi$
$270$		0			0
$271$	30.1847			1.83359			0.916795	−	0.399359i	$-0.130767\pi$
$271$	30.1847			1.83359			0.916795	+	0.399359i	$0.130767\pi$
$272$		0			0
$273$			26.8385i			1.62434i
$274$		0			0
$275$	5.24443	+	18.2953i	0.316251	+	1.10325i
$276$		0			0
$277$	−10.5303			−0.632707			−0.316354	−	0.948641i	$-0.602459\pi$
$277$	−10.5303			−0.632707			−0.316354	+	0.948641i	$0.602459\pi$
$278$		0			0
$279$	−14.9590			−0.895571
$280$		0			0
$281$	7.93978			0.473647			0.236824	−	0.971553i	$-0.423894\pi$
$281$	7.93978			0.473647			0.236824	+	0.971553i	$0.423894\pi$
$282$		0			0
$283$	10.9032			0.648129			0.324064	−	0.946035i	$-0.394951\pi$
$283$	10.9032			0.648129			0.324064	+	0.946035i	$0.394951\pi$
$284$		0			0
$285$	−4.56199	−	32.4701i	−0.270229	−	1.92336i
$286$		0			0
$287$			18.2766i			1.07883i
$288$		0			0
$289$	−16.7146			−0.983209
$290$		0			0
$291$		−	40.0830i		−	2.34971i
$292$		0			0
$293$	−4.42864			−0.258724			−0.129362	−	0.991597i	$-0.541293\pi$
$293$	−4.42864			−0.258724			−0.129362	+	0.991597i	$0.541293\pi$
$294$		0			0
$295$	1.57136	+	11.1842i	0.0914881	+	0.651170i
$296$		0			0
$297$		−	26.8385i		−	1.55733i
$298$		0			0
$299$			1.24443i			0.0719673i
$300$		0			0
$301$			6.88892i			0.397071i
$302$		0			0
$303$			57.2355i			3.28810i
$304$		0			0
$305$	3.80642	+	27.0923i	0.217955	+	1.55130i
$306$		0			0
$307$	−5.27163			−0.300868			−0.150434	−	0.988620i	$-0.548067\pi$
$307$	−5.27163			−0.300868			−0.150434	+	0.988620i	$0.548067\pi$
$308$		0			0
$309$			9.11108i			0.518311i
$310$		0			0
$311$	−0.387152			−0.0219534			−0.0109767	−	0.999940i	$-0.503494\pi$
$311$	−0.387152			−0.0219534			−0.0109767	+	0.999940i	$0.503494\pi$
$312$		0			0
$313$			11.3461i			0.641322i	0.947194	+	0.320661i	$0.103905\pi$
$313$			11.3461i			0.641322i	−0.947194	+	0.320661i	$0.896095\pi$
$314$		0			0
$315$	5.95407	+	42.3783i	0.335474	+	2.38774i
$316$		0			0
$317$	16.7239			0.939309			0.469655	−	0.882850i	$-0.344378\pi$
$317$	16.7239			0.939309			0.469655	+	0.882850i	$0.344378\pi$
$318$		0			0
$319$	−7.61285			−0.426238
$320$		0			0
$321$	−15.6543			−0.873740
$322$		0			0
$323$	29.3274			1.63182
$324$		0			0
$325$	12.6035	−	3.61285i	0.699115	−	0.200405i
$326$		0			0
$327$			25.0321i			1.38428i
$328$		0			0
$329$	−18.7971			−1.03632
$330$		0			0
$331$		−	3.33630i		−	0.183379i	−0.995788	−	0.0916897i	$-0.970773\pi$
$331$		−	3.33630i		−	0.183379i	0.995788	−	0.0916897i	$-0.0292268\pi$
$332$		0			0
$333$	39.0005			2.13721
$334$		0			0
$335$	17.1842	−	2.41435i	0.938874	−	0.131910i
$336$		0			0
$337$		−	3.61285i		−	0.196804i	−0.995147	−	0.0984022i	$-0.968627\pi$
$337$		−	3.61285i		−	0.196804i	0.995147	−	0.0984022i	$-0.0313732\pi$
$338$		0			0
$339$			16.0000i			0.869001i
$340$		0			0
$341$		−	10.4889i		−	0.568004i
$342$		0			0
$343$		−	5.53972i		−	0.299117i
$344$		0			0
$345$	0.428639	+	3.05086i	0.0230772	+	0.164253i
$346$		0			0
$347$	15.7605			0.846067			0.423034	−	0.906114i	$-0.360965\pi$
$347$	15.7605			0.846067			0.423034	+	0.906114i	$0.360965\pi$
$348$		0			0
$349$			0.285442i			0.0152794i	0.999971	+	0.00763968i	$0.00243181\pi$
$349$			0.285442i			0.0152794i	−0.999971	+	0.00763968i	$0.997568\pi$
$350$		0			0
$351$	−18.4889			−0.986862
$352$		0			0
$353$			4.38715i			0.233505i	0.993161	+	0.116752i	$0.0372484\pi$
$353$			4.38715i			0.233505i	−0.993161	+	0.116752i	$0.962752\pi$
$354$		0			0
$355$	−10.7556	+	1.51114i	−0.570846	+	0.0802028i
$356$		0			0
$357$	−59.4291			−3.14532
$358$		0			0
$359$	−20.5906			−1.08673			−0.543364	−	0.839497i	$-0.682850\pi$
$359$	−20.5906			−1.08673			−0.543364	+	0.839497i	$0.682850\pi$
$360$		0			0
$361$	−6.51114			−0.342691
$362$		0			0
$363$	10.1289			0.531630
$364$		0			0
$365$	2.07313	+	14.7556i	0.108513	+	0.772342i
$366$		0			0
$367$		−	16.5575i		−	0.864297i	−0.901802	−	0.432148i	$-0.857756\pi$
$367$		−	16.5575i		−	0.864297i	0.901802	−	0.432148i	$-0.142244\pi$
$368$		0			0
$369$	−28.1432			−1.46508
$370$		0			0
$371$			18.9590i			0.984302i
$372$		0			0
$373$	24.8988			1.28921			0.644605	−	0.764516i	$-0.277022\pi$
$373$	24.8988			1.28921			0.644605	+	0.764516i	$0.277022\pi$
$374$		0			0
$375$	29.6543	−	13.1985i	1.53134	−	0.681568i
$376$		0			0
$377$			5.24443i			0.270102i
$378$		0			0
$379$			9.31756i			0.478611i	0.970944	+	0.239305i	$0.0769197\pi$
$379$			9.31756i			0.478611i	−0.970944	+	0.239305i	$0.923080\pi$
$380$		0			0
$381$		−	29.8479i		−	1.52915i
$382$		0			0
$383$		−	32.5575i		−	1.66361i	−0.555066	−	0.831806i	$-0.687307\pi$
$383$		−	32.5575i		−	1.66361i	0.555066	−	0.831806i	$-0.312693\pi$
$384$		0			0
$385$	−29.7146	+	4.17484i	−1.51439	+	0.212770i
$386$		0			0
$387$	−10.6079			−0.539231
$388$		0			0
$389$		−	18.9906i		−	0.962863i	−0.876484	−	0.481432i	$-0.840117\pi$
$389$		−	18.9906i		−	0.962863i	0.876484	−	0.481432i	$-0.159883\pi$
$390$		0			0
$391$	−2.75557			−0.139355
$392$		0			0
$393$		−	13.5397i		−	0.682988i
$394$		0			0
$395$	−11.6128	+	1.63158i	−0.584306	+	0.0820939i
$396$		0			0
$397$	−32.9906			−1.65575			−0.827876	−	0.560911i	$-0.810451\pi$
$397$	−32.9906			−1.65575			−0.827876	+	0.560911i	$0.810451\pi$
$398$		0			0
$399$	51.6958			2.58803
$400$		0			0
$401$	−16.1017			−0.804081			−0.402041	−	0.915622i	$-0.631699\pi$
$401$	−16.1017			−0.804081			−0.402041	+	0.915622i	$0.631699\pi$
$402$		0			0
$403$	−7.22570			−0.359938
$404$		0			0
$405$	−9.26517	+	1.30174i	−0.460390	+	0.0646840i
$406$		0			0
$407$			27.3461i			1.35550i
$408$		0			0
$409$	−33.3876			−1.65091			−0.825456	−	0.564466i	$-0.809082\pi$
$409$	−33.3876			−1.65091			−0.825456	+	0.564466i	$0.809082\pi$
$410$		0			0
$411$			32.9403i			1.62482i
$412$		0			0
$413$	−17.8064			−0.876197
$414$		0			0
$415$	26.8988	−	3.77923i	1.32041	−	0.185515i
$416$		0			0
$417$		−	34.2766i		−	1.67853i
$418$		0			0
$419$		−	27.4193i		−	1.33952i	−0.742578	−	0.669760i	$-0.766397\pi$
$419$		−	27.4193i		−	1.33952i	0.742578	−	0.669760i	$-0.233603\pi$
$420$		0			0
$421$			12.2351i			0.596301i	0.954519	+	0.298150i	$0.0963696\pi$
$421$			12.2351i			0.596301i	−0.954519	+	0.298150i	$0.903630\pi$
$422$		0			0
$423$		−	28.9447i		−	1.40734i
$424$		0			0
$425$	8.00000	+	27.9081i	0.388057	+	1.35374i
$426$		0			0
$427$	−43.1338			−2.08739
$428$		0			0
$429$		−	28.9777i		−	1.39906i
$430$		0			0
$431$	−28.4701			−1.37136			−0.685679	−	0.727904i	$-0.740495\pi$
$431$	−28.4701			−1.37136			−0.685679	+	0.727904i	$0.740495\pi$
$432$		0			0
$433$		−	34.0098i		−	1.63441i	−0.576348	−	0.817204i	$-0.695523\pi$
$433$		−	34.0098i		−	1.63441i	0.576348	−	0.817204i	$-0.304477\pi$
$434$		0			0
$435$	1.80642	+	12.8573i	0.0866114	+	0.616459i
$436$		0			0
$437$	2.39700			0.114664
$438$		0			0
$439$	−14.8385			−0.708205			−0.354103	−	0.935207i	$-0.615214\pi$
$439$	−14.8385			−0.708205			−0.354103	+	0.935207i	$0.615214\pi$
$440$		0			0
$441$	−29.4701			−1.40334
$442$		0			0
$443$	−13.0968			−0.622247			−0.311124	−	0.950369i	$-0.600705\pi$
$443$	−13.0968			−0.622247			−0.311124	+	0.950369i	$0.600705\pi$
$444$		0			0
$445$	26.7971	−	3.76494i	1.27030	−	0.178475i
$446$		0			0
$447$			15.9081i			0.752429i
$448$		0			0
$449$	21.3876			1.00934			0.504672	−	0.863311i	$-0.331613\pi$
$449$	21.3876			1.00934			0.504672	+	0.863311i	$0.331613\pi$
$450$		0			0
$451$		−	19.7333i		−	0.929205i
$452$		0			0
$453$	68.5531			3.22091
$454$		0			0
$455$	2.87601	+	20.4701i	0.134830	+	0.959654i
$456$		0			0
$457$		−	17.9813i		−	0.841128i	−0.907263	−	0.420564i	$-0.861832\pi$
$457$		−	17.9813i		−	0.841128i	0.907263	−	0.420564i	$-0.138168\pi$
$458$		0			0
$459$		−	40.9403i		−	1.91093i
$460$		0			0
$461$		−	10.7368i		−	0.500064i	−0.968238	−	0.250032i	$-0.919559\pi$
$461$		−	10.7368i		−	0.500064i	0.968238	−	0.250032i	$-0.0804412\pi$
$462$		0			0
$463$			9.30327i			0.432360i	0.976354	+	0.216180i	$0.0693598\pi$
$463$			9.30327i			0.432360i	−0.976354	+	0.216180i	$0.930640\pi$
$464$		0			0
$465$	−17.7146	+	2.48886i	−0.821493	+	0.115418i
$466$		0			0
$467$	8.70964			0.403034			0.201517	−	0.979485i	$-0.435413\pi$
$467$	8.70964			0.403034			0.201517	+	0.979485i	$0.435413\pi$
$468$		0			0
$469$			27.3590i			1.26332i
$470$		0			0
$471$	2.36842			0.109131
$472$		0			0
$473$		−	7.43801i		−	0.342000i
$474$		0			0
$475$	−6.95899	−	24.2766i	−0.319300	−	1.11388i
$476$		0			0
$477$	−29.1941			−1.33670
$478$		0			0
$479$	−23.2257			−1.06121			−0.530605	−	0.847619i	$-0.678035\pi$
$479$	−23.2257			−1.06121			−0.530605	+	0.847619i	$0.678035\pi$
$480$		0			0
$481$	18.8385			0.858964
$482$		0			0
$483$	−4.85728			−0.221014
$484$		0			0
$485$	−4.29529	−	30.5718i	−0.195039	−	1.38820i
$486$		0			0
$487$		−	32.8528i		−	1.48870i	−0.667787	−	0.744352i	$-0.732759\pi$
$487$		−	32.8528i		−	1.48870i	0.667787	−	0.744352i	$-0.267241\pi$
$488$		0			0
$489$	31.6543			1.43146
$490$		0			0
$491$			2.94914i			0.133093i	0.997783	+	0.0665465i	$0.0211981\pi$
$491$			2.94914i			0.133093i	−0.997783	+	0.0665465i	$0.978802\pi$
$492$		0			0
$493$	−11.6128			−0.523016
$494$		0			0
$495$	−6.42864	−	45.7560i	−0.288946	−	2.05658i
$496$		0			0
$497$		−	17.1240i		−	0.768116i
$498$		0			0
$499$			35.0321i			1.56825i	0.620601	+	0.784127i	$0.286889\pi$
$499$			35.0321i			1.56825i	−0.620601	+	0.784127i	$0.713111\pi$
$500$		0			0
$501$		−	19.0923i		−	0.852983i
$502$		0			0
$503$			16.2908i			0.726373i	0.931717	+	0.363186i	$0.118311\pi$
$503$			16.2908i			0.726373i	−0.931717	+	0.363186i	$0.881689\pi$
$504$		0			0
$505$	6.13335	+	43.6543i	0.272931	+	1.94259i
$506$		0			0
$507$	17.7792			0.789603
$508$		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
$511$	−23.4924			−1.03924
$512$		0			0
$513$			35.6128i			1.57235i
$514$		0			0
$515$	0.976342	+	6.94914i	0.0430228	+	0.306216i
$516$		0			0
$517$	20.2953			0.892586
$518$		0			0
$519$	30.5718			1.34195
$520$		0			0
$521$	−11.7146			−0.513224			−0.256612	−	0.966514i	$-0.582606\pi$
$521$	−11.7146			−0.513224			−0.256612	+	0.966514i	$0.582606\pi$
$522$		0			0
$523$	−38.0370			−1.66324			−0.831622	−	0.555342i	$-0.812587\pi$
$523$	−38.0370			−1.66324			−0.831622	+	0.555342i	$0.812587\pi$
$524$		0			0
$525$	14.1017	+	49.1941i	0.615449	+	2.14700i
$526$		0			0
$527$		−	16.0000i		−	0.696971i
$528$		0			0
$529$	22.7748			0.990208
$530$		0			0
$531$		−	27.4193i		−	1.18990i
$532$		0			0
$533$	−13.5941			−0.588826
$534$		0			0
$535$	−11.9398	+	1.67752i	−0.516202	+	0.0725254i
$536$		0			0
$537$		−	18.2766i		−	0.788691i
$538$		0			0
$539$		−	20.6637i		−	0.890049i
$540$		0			0
$541$		−	11.5111i		−	0.494902i	−0.968900	−	0.247451i	$-0.920407\pi$
$541$		−	11.5111i		−	0.494902i	0.968900	−	0.247451i	$-0.0795930\pi$
$542$		0			0
$543$		−	1.41927i		−	0.0609068i
$544$		0			0
$545$	2.68244	+	19.0923i	0.114903	+	0.817826i
$546$		0			0
$547$	30.2208			1.29215			0.646073	−	0.763275i	$-0.276410\pi$
$547$	30.2208			1.29215			0.646073	+	0.763275i	$0.276410\pi$
$548$		0			0
$549$		−	66.4197i		−	2.83473i
$550$		0			0
$551$	10.1017			0.430347
$552$		0			0
$553$		−	18.4889i		−	0.786226i
$554$		0			0
$555$	46.1847	−	6.48886i	1.96043	−	0.275437i
$556$		0			0
$557$	−9.75605			−0.413377			−0.206688	−	0.978407i	$-0.566269\pi$
$557$	−9.75605			−0.413377			−0.206688	+	0.978407i	$0.566269\pi$
$558$		0			0
$559$	−5.12399			−0.216721
$560$		0			0
$561$	64.1659			2.70909
$562$		0			0
$563$	4.50622			0.189914			0.0949572	−	0.995481i	$-0.469729\pi$
$563$	4.50622			0.189914			0.0949572	+	0.995481i	$0.469729\pi$
$564$		0			0
$565$	1.71456	+	12.2034i	0.0721320	+	0.513402i
$566$		0			0
$567$		−	14.7511i		−	0.619489i
$568$		0			0
$569$	5.30465			0.222383			0.111191	−	0.993799i	$-0.464533\pi$
$569$	5.30465			0.222383			0.111191	+	0.993799i	$0.464533\pi$
$570$		0			0
$571$		−	16.3970i		−	0.686193i	−0.939300	−	0.343096i	$-0.888524\pi$
$571$		−	16.3970i		−	0.686193i	0.939300	−	0.343096i	$-0.111476\pi$
$572$		0			0
$573$	30.4514			1.27213
$574$		0			0
$575$	0.653858	+	2.28100i	0.0272678	+	0.0951241i
$576$		0			0
$577$			39.8163i			1.65757i	0.559565	+	0.828786i	$0.310968\pi$
$577$			39.8163i			1.65757i	−0.559565	+	0.828786i	$0.689032\pi$
$578$		0			0
$579$			40.0830i			1.66579i
$580$		0			0
$581$			42.8256i			1.77671i
$582$		0			0
$583$		−	20.4701i		−	0.847786i
$584$		0			0
$585$	−31.5210	+	4.42864i	−1.30323	+	0.183102i
$586$		0			0
$587$	15.1699			0.626130			0.313065	−	0.949732i	$-0.398644\pi$
$587$	15.1699			0.626130			0.313065	+	0.949732i	$0.398644\pi$
$588$		0			0
$589$			13.9180i			0.573480i
$590$		0			0
$591$	−48.5531			−1.99721
$592$		0			0
$593$			8.00000i			0.328521i	0.986417	+	0.164260i	$0.0525237\pi$
$593$			8.00000i			0.328521i	−0.986417	+	0.164260i	$0.947476\pi$
$594$		0			0
$595$	−45.3274	+	6.36842i	−1.85824	+	0.261080i
$596$		0			0
$597$	−60.5531			−2.47827
$598$		0			0
$599$	1.83500			0.0749762			0.0374881	−	0.999297i	$-0.488064\pi$
$599$	1.83500			0.0749762			0.0374881	+	0.999297i	$0.488064\pi$
$600$		0			0
$601$	36.1432			1.47431			0.737156	−	0.675723i	$-0.236168\pi$
$601$	36.1432			1.47431			0.737156	+	0.675723i	$0.236168\pi$
$602$		0			0
$603$	−42.1289			−1.71562
$604$		0			0
$605$	7.72546	−	1.08541i	0.314084	−	0.0441283i
$606$		0			0
$607$		−	17.5353i		−	0.711735i	−0.934536	−	0.355867i	$-0.884185\pi$
$607$		−	17.5353i		−	0.711735i	0.934536	−	0.355867i	$-0.115815\pi$
$608$		0			0
$609$	−20.4701			−0.829491
$610$		0			0
$611$		−	13.9813i		−	0.565621i
$612$		0			0
$613$	−33.9309			−1.37046			−0.685228	−	0.728329i	$-0.740297\pi$
$613$	−33.9309			−1.37046			−0.685228	+	0.728329i	$0.740297\pi$
$614$		0			0
$615$	−33.3274	+	4.68244i	−1.34389	+	0.188814i
$616$		0			0
$617$			9.68598i			0.389943i	0.980809	+	0.194971i	$0.0624614\pi$
$617$			9.68598i			0.389943i	−0.980809	+	0.194971i	$0.937539\pi$
$618$		0			0
$619$			41.4005i			1.66403i	0.554755	+	0.832014i	$0.312812\pi$
$619$			41.4005i			1.66403i	−0.554755	+	0.832014i	$0.687188\pi$
$620$		0			0
$621$		−	3.34614i		−	0.134276i
$622$		0			0
$623$			42.6637i			1.70929i
$624$		0			0
$625$	21.2034	−	13.2444i	0.848137	−	0.529777i
$626$		0			0
$627$	−55.8163			−2.22909
$628$		0			0
$629$			41.7146i			1.66327i
$630$		0			0
$631$	27.8163			1.10735			0.553674	−	0.832733i	$-0.313225\pi$
$631$	27.8163			1.10735			0.553674	+	0.832733i	$0.313225\pi$
$632$		0			0
$633$		−	13.5397i		−	0.538155i
$634$		0			0
$635$	−3.19850	−	22.7654i	−0.126929	−	0.903418i
$636$		0			0
$637$	−14.2351			−0.564014
$638$		0			0
$639$	26.3684			1.04312
$640$		0			0
$641$	42.8988			1.69440			0.847200	−	0.531275i	$-0.178287\pi$
$641$	42.8988			1.69440			0.847200	+	0.531275i	$0.178287\pi$
$642$		0			0
$643$	−27.9639			−1.10279			−0.551395	−	0.834245i	$-0.685904\pi$
$643$	−27.9639			−1.10279			−0.551395	+	0.834245i	$0.685904\pi$
$644$		0			0
$645$	−12.5620	+	1.76494i	−0.494628	+	0.0694943i
$646$		0			0
$647$		−	7.13828i		−	0.280635i	−0.990107	−	0.140317i	$-0.955188\pi$
$647$		−	7.13828i		−	0.280635i	0.990107	−	0.140317i	$-0.0448123\pi$
$648$		0			0
$649$	19.2257			0.754675
$650$		0			0
$651$		−	28.2034i		−	1.10538i
$652$		0			0
$653$	−17.7649			−0.695196			−0.347598	−	0.937644i	$-0.613003\pi$
$653$	−17.7649			−0.695196			−0.347598	+	0.937644i	$0.613003\pi$
$654$		0			0
$655$	−1.45091	−	10.3269i	−0.0566919	−	0.403507i
$656$		0			0
$657$		−	36.1748i		−	1.41131i
$658$		0			0
$659$		−	20.1936i		−	0.786630i	−0.919404	−	0.393315i	$-0.871328\pi$
$659$		−	20.1936i		−	0.786630i	0.919404	−	0.393315i	$-0.128672\pi$
$660$		0			0
$661$		−	22.0701i		−	0.858426i	−0.903203	−	0.429213i	$-0.858791\pi$
$661$		−	22.0701i		−	0.858426i	0.903203	−	0.429213i	$-0.141209\pi$
$662$		0			0
$663$		−	44.2034i		−	1.71672i
$664$		0			0
$665$	39.4291	−	5.53972i	1.52900	−	0.214821i
$666$		0			0
$667$	−0.949145			−0.0367510
$668$		0			0
$669$			76.8069i			2.96953i
$670$		0			0
$671$	46.5718			1.79789
$672$		0			0
$673$			26.0098i			1.00261i	0.865272	+	0.501303i	$0.167146\pi$
$673$			26.0098i			1.00261i	−0.865272	+	0.501303i	$0.832854\pi$
$674$		0			0
$675$	−33.8894	+	9.71456i	−1.30440	+	0.373914i
$676$		0			0
$677$	−7.86665			−0.302340			−0.151170	−	0.988508i	$-0.548304\pi$
$677$	−7.86665			−0.302340			−0.151170	+	0.988508i	$0.548304\pi$
$678$		0			0
$679$	48.6735			1.86792
$680$		0			0
$681$	−35.7748			−1.37089
$682$		0			0
$683$	18.2494			0.698292			0.349146	−	0.937068i	$-0.386472\pi$
$683$	18.2494			0.698292			0.349146	+	0.937068i	$0.386472\pi$
$684$		0			0
$685$	3.52987	+	25.1240i	0.134870	+	0.959938i
$686$		0			0
$687$		−	38.3970i		−	1.46494i
$688$		0			0
$689$	−14.1017			−0.537232
$690$		0			0
$691$		−	25.2543i		−	0.960718i	−0.877072	−	0.480359i	$-0.840506\pi$
$691$		−	25.2543i		−	0.960718i	0.877072	−	0.480359i	$-0.159494\pi$
$692$		0			0
$693$	72.8484			2.76728
$694$		0			0
$695$	−3.67307	−	26.1432i	−0.139328	−	0.991668i
$696$		0			0
$697$		−	30.1017i		−	1.14018i
$698$		0			0
$699$			19.3461i			0.731738i
$700$		0			0
$701$			34.8069i			1.31464i	0.753612	+	0.657319i	$0.228310\pi$
$701$			34.8069i			1.31464i	−0.753612	+	0.657319i	$0.771690\pi$
$702$		0			0
$703$		−	36.2864i		−	1.36857i
$704$		0			0
$705$	−4.81579	−	34.2766i	−0.181373	−	1.29093i
$706$		0			0
$707$	−69.5022			−2.61390
$708$		0			0
$709$		−	7.51114i		−	0.282087i	−0.990003	−	0.141043i	$-0.954954\pi$
$709$		−	7.51114i		−	0.282087i	0.990003	−	0.141043i	$-0.0450457\pi$
$710$		0			0
$711$	28.4701			1.06771
$712$		0			0
$713$		−	1.30772i		−	0.0489744i
$714$		0			0
$715$	−3.10525	−	22.1017i	−0.116130	−	0.826557i
$716$		0			0
$717$	66.6548			2.48927
$718$		0			0
$719$	−26.7556			−0.997814			−0.498907	−	0.866655i	$-0.666265\pi$
$719$	−26.7556			−0.997814			−0.498907	+	0.866655i	$0.666265\pi$
$720$		0			0
$721$	−11.0638			−0.412036
$722$		0			0
$723$	40.7654			1.51608
$724$		0			0
$725$	2.75557	+	9.61285i	0.102339	+	0.357012i
$726$		0			0
$727$		−	25.6271i		−	0.950458i	−0.879862	−	0.475229i	$-0.842365\pi$
$727$		−	25.6271i		−	0.950458i	0.879862	−	0.475229i	$-0.157635\pi$
$728$		0			0
$729$	−38.6958			−1.43318
$730$		0			0
$731$		−	11.3461i		−	0.419652i
$732$		0			0
$733$	−19.6543			−0.725949			−0.362975	−	0.931799i	$-0.618239\pi$
$733$	−19.6543			−0.725949			−0.362975	+	0.931799i	$0.618239\pi$
$734$		0			0
$735$	−34.8988	+	4.90321i	−1.28726	+	0.180858i
$736$		0			0
$737$		−	29.5397i		−	1.08811i
$738$		0			0
$739$			32.5433i			1.19712i	0.801077	+	0.598562i	$0.204261\pi$
$739$			32.5433i			1.19712i	−0.801077	+	0.598562i	$0.795739\pi$
$740$		0			0
$741$			38.4514i			1.41255i
$742$		0			0
$743$		−	23.1383i		−	0.848861i	−0.905461	−	0.424430i	$-0.860474\pi$
$743$		−	23.1383i		−	0.848861i	0.905461	−	0.424430i	$-0.139526\pi$
$744$		0			0
$745$	1.70471	+	12.1334i	0.0624559	+	0.444532i
$746$		0			0
$747$	−65.9452			−2.41281
$748$		0			0
$749$		−	19.0094i		−	0.694587i
$750$		0			0
$751$	−2.48886			−0.0908199			−0.0454099	−	0.998968i	$-0.514459\pi$
$751$	−2.48886			−0.0908199			−0.0454099	+	0.998968i	$0.514459\pi$
$752$		0			0
$753$			72.3783i			2.63761i
$754$		0			0
$755$	52.2864	−	7.34614i	1.90290	−	0.267353i
$756$		0			0
$757$	21.2859			0.773650			0.386825	−	0.922153i	$-0.373572\pi$
$757$	21.2859			0.773650			0.386825	+	0.922153i	$0.373572\pi$
$758$		0			0
$759$	5.24443			0.190361
$760$		0			0
$761$	−19.1240			−0.693244			−0.346622	−	0.938005i	$-0.612671\pi$
$761$	−19.1240			−0.693244			−0.346622	+	0.938005i	$0.612671\pi$
$762$		0			0
$763$	−30.3970			−1.10045
$764$		0			0
$765$	−9.80642	−	69.7975i	−0.354552	−	2.52354i
$766$		0			0
$767$		−	13.2444i		−	0.478229i
$768$		0			0
$769$	33.9625			1.22472			0.612360	−	0.790579i	$-0.290220\pi$
$769$	33.9625			1.22472			0.612360	+	0.790579i	$0.290220\pi$
$770$		0			0
$771$			74.6548i			2.68863i
$772$		0			0
$773$	0.133353			0.00479638			0.00239819	−	0.999997i	$-0.499237\pi$
$773$	0.133353			0.00479638			0.00239819	+	0.999997i	$0.499237\pi$
$774$		0			0
$775$	−13.2444	+	3.79658i	−0.475754	+	0.136377i
$776$		0			0
$777$			73.5308i			2.63790i
$778$		0			0
$779$			26.1847i			0.938164i
$780$		0			0
$781$			18.4889i			0.661584i
$782$		0			0
$783$		−	14.1017i		−	0.503954i
$784$		0			0
$785$	1.80642	−	0.253799i	0.0644740	−	0.00905848i
$786$		0			0
$787$	−1.12537			−0.0401150			−0.0200575	−	0.999799i	$-0.506385\pi$
$787$	−1.12537			−0.0401150			−0.0200575	+	0.999799i	$0.506385\pi$
$788$		0			0
$789$		−	7.47949i		−	0.266277i
$790$		0			0
$791$	−19.4291			−0.690820
$792$		0			0
$793$		−	32.0830i		−	1.13930i
$794$		0			0
$795$	−34.5718	+	4.85728i	−1.22614	+	0.172270i
$796$		0			0
$797$	5.11108			0.181044			0.0905218	−	0.995894i	$-0.471147\pi$
$797$	5.11108			0.181044			0.0905218	+	0.995894i	$0.471147\pi$
$798$		0			0
$799$	30.9590			1.09525
$800$		0			0
$801$	−65.6958			−2.32125
$802$		0			0
$803$	25.3649			0.895107
$804$		0			0
$805$	−3.70471	+	0.520505i	−0.130574	+	0.0183454i
$806$		0			0
$807$			74.7467i			2.63121i
$808$		0			0
$809$	18.7368			0.658752			0.329376	−	0.944199i	$-0.393162\pi$
$809$	18.7368			0.658752			0.329376	+	0.944199i	$0.393162\pi$
$810$		0			0
$811$			37.5210i			1.31754i	0.752344	+	0.658770i	$0.228923\pi$
$811$			37.5210i			1.31754i	−0.752344	+	0.658770i	$0.771077\pi$
$812$		0			0
$813$	−87.6325			−3.07341
$814$		0			0
$815$	24.1432	−	3.39207i	0.845699	−	0.118819i
$816$		0			0
$817$			9.86971i			0.345297i
$818$		0			0
$819$		−	50.1847i		−	1.75359i
$820$		0			0
$821$		−	18.4001i		−	0.642166i	−0.947051	−	0.321083i	$-0.895953\pi$
$821$		−	18.4001i		−	0.642166i	0.947051	−	0.321083i	$-0.104047\pi$
$822$		0			0
$823$		−	0.649413i		−	0.0226371i	−0.999936	−	0.0113186i	$-0.996397\pi$
$823$		−	0.649413i		−	0.0226371i	0.999936	−	0.0113186i	$-0.00360288\pi$
$824$		0			0
$825$	−15.2257	−	53.1151i	−0.530091	−	1.84923i
$826$		0			0
$827$	29.8622			1.03841			0.519205	−	0.854650i	$-0.326228\pi$
$827$	29.8622			1.03841			0.519205	+	0.854650i	$0.326228\pi$
$828$		0			0
$829$		−	21.1753i		−	0.735449i	−0.929935	−	0.367725i	$-0.880137\pi$
$829$		−	21.1753i		−	0.735449i	0.929935	−	0.367725i	$-0.119863\pi$
$830$		0			0
$831$	30.5718			1.06053
$832$		0			0
$833$		−	31.5210i		−	1.09214i
$834$		0			0
$835$	−2.04593	−	14.5620i	−0.0708024	−	0.503939i
$836$		0			0
$837$	19.4291			0.671568
$838$		0			0
$839$	−43.8163			−1.51271			−0.756353	−	0.654164i	$-0.773021\pi$
$839$	−43.8163			−1.51271			−0.756353	+	0.654164i	$0.773021\pi$
$840$		0			0
$841$	25.0000			0.862069
$842$		0			0
$843$	−23.0509			−0.793914
$844$		0			0
$845$	13.5605	−	1.90522i	0.466494	−	0.0655415i
$846$		0			0
$847$			12.2997i			0.422624i
$848$		0			0
$849$	−31.6543			−1.08637
$850$		0			0
$851$			3.40943i			0.116874i
$852$		0			0
$853$	−37.7846			−1.29372			−0.646860	−	0.762608i	$-0.723918\pi$
$853$	−37.7846			−1.29372			−0.646860	+	0.762608i	$0.723918\pi$
$854$		0			0
$855$	8.53035	+	60.7150i	0.291732	+	2.07641i
$856$		0			0
$857$			19.5299i			0.667128i	0.942727	+	0.333564i	$0.108251\pi$
$857$			19.5299i			0.667128i	−0.942727	+	0.333564i	$0.891749\pi$
$858$		0			0
$859$		−	33.2543i		−	1.13462i	−0.823504	−	0.567311i	$-0.807984\pi$
$859$		−	33.2543i		−	1.13462i	0.823504	−	0.567311i	$-0.192016\pi$
$860$		0			0
$861$		−	53.0607i		−	1.80830i
$862$		0			0
$863$			44.9733i			1.53091i	0.643490	+	0.765454i	$0.277486\pi$
$863$			44.9733i			1.53091i	−0.643490	+	0.765454i	$0.722514\pi$
$864$		0			0
$865$	23.3176	−	3.27607i	0.792821	−	0.111390i
$866$		0			0
$867$	48.5259			1.64803
$868$		0			0
$869$			19.9625i			0.677182i
$870$		0			0
$871$	−20.3497			−0.689523
$872$		0			0
$873$			74.9501i			2.53668i
$874$		0			0
$875$	16.0272	+	36.0098i	0.541818	+	1.21735i
$876$		0			0
$877$	8.30819			0.280548			0.140274	−	0.990113i	$-0.455202\pi$
$877$	8.30819			0.280548			0.140274	+	0.990113i	$0.455202\pi$
$878$		0			0
$879$	12.8573			0.433665
$880$		0			0
$881$	−39.3689			−1.32637			−0.663186	−	0.748455i	$-0.730796\pi$
$881$	−39.3689			−1.32637			−0.663186	+	0.748455i	$0.730796\pi$
$882$		0			0
$883$	−7.29036			−0.245340			−0.122670	−	0.992447i	$-0.539146\pi$
$883$	−7.29036			−0.245340			−0.122670	+	0.992447i	$0.539146\pi$
$884$		0			0
$885$	−4.56199	−	32.4701i	−0.153350	−	1.09147i
$886$		0			0
$887$			11.1097i			0.373027i	0.982452	+	0.186514i	$0.0597188\pi$
$887$			11.1097i			0.373027i	−0.982452	+	0.186514i	$0.940281\pi$
$888$		0			0
$889$	36.2449			1.21562
$890$		0			0
$891$			15.9269i			0.533570i
$892$		0			0
$893$	−26.9304			−0.901192
$894$		0			0
$895$	−1.95851	−	13.9398i	−0.0654659	−	0.465955i
$896$		0			0
$897$		−	3.61285i		−	0.120629i
$898$		0			0
$899$		−	5.51114i		−	0.183807i
$900$		0			0
$901$		−	31.2257i		−	1.04028i
$902$		0			0
$903$		−	20.0000i		−	0.665558i
$904$		0			0
$905$	−0.152089	−	1.08250i	−0.00505561	−	0.0359835i
$906$		0			0
$907$	17.5383			0.582351			0.291175	−	0.956670i	$-0.405954\pi$
$907$	17.5383			0.582351			0.291175	+	0.956670i	$0.405954\pi$
$908$		0			0
$909$		−	107.023i		−	3.54974i
$910$		0			0
$911$	44.4701			1.47336			0.736681	−	0.676241i	$-0.236392\pi$
$911$	44.4701			1.47336			0.736681	+	0.676241i	$0.236392\pi$
$912$		0			0
$913$		−	46.2391i		−	1.53029i
$914$		0			0
$915$	−11.0509	−	78.6548i	−0.365330	−	2.60025i
$916$		0			0
$917$	16.4415			0.542948
$918$		0			0
$919$	7.87955			0.259922			0.129961	−	0.991519i	$-0.458515\pi$
$919$	7.87955			0.259922			0.129961	+	0.991519i	$0.458515\pi$
$920$		0			0
$921$	15.3047			0.504306
$922$		0			0
$923$	12.7368			0.419238
$924$		0			0
$925$	34.5303	−	9.89829i	1.13535	−	0.325454i
$926$		0			0
$927$		−	17.0366i		−	0.559554i
$928$		0			0
$929$	−15.7560			−0.516939			−0.258470	−	0.966019i	$-0.583218\pi$
$929$	−15.7560			−0.516939			−0.258470	+	0.966019i	$0.583218\pi$
$930$		0			0
$931$			27.4193i			0.898630i
$932$		0			0
$933$	1.12399			0.0367976
$934$		0			0
$935$	48.9403	−	6.87601i	1.60052	−	0.224870i
$936$		0			0
$937$			10.2766i			0.335720i	0.985811	+	0.167860i	$0.0536857\pi$
$937$			10.2766i			0.335720i	−0.985811	+	0.167860i	$0.946314\pi$
$938$		0			0
$939$		−	32.9403i		−	1.07496i
$940$		0			0
$941$			2.53341i			0.0825869i	0.999147	+	0.0412934i	$0.0131478\pi$
$941$			2.53341i			0.0825869i	−0.999147	+	0.0412934i	$0.986852\pi$
$942$		0			0
$943$		−	2.46028i		−	0.0801178i
$944$		0			0
$945$	−7.73329	−	55.0420i	−0.251564	−	1.79052i
$946$		0			0
$947$	−1.06821			−0.0347121			−0.0173560	−	0.999849i	$-0.505525\pi$
$947$	−1.06821			−0.0347121			−0.0173560	+	0.999849i	$0.505525\pi$
$948$		0			0
$949$		−	17.4737i		−	0.567219i
$950$		0			0
$951$	−48.5531			−1.57444
$952$		0			0
$953$		−	51.6958i		−	1.67459i	−0.546750	−	0.837296i	$-0.684135\pi$
$953$		−	51.6958i		−	1.67459i	0.546750	−	0.837296i	$-0.315865\pi$
$954$		0			0
$955$	23.2257	−	3.26317i	0.751566	−	0.105594i
$956$		0			0
$957$	22.1017			0.714447
$958$		0			0
$959$	−40.0000			−1.29167
$960$		0			0
$961$	−23.4068			−0.755059
$962$		0			0
$963$	29.2716			0.943265
$964$		0			0
$965$	4.29529	+	30.5718i	0.138270	+	0.984142i
$966$		0			0
$967$		−	52.2623i		−	1.68064i	−0.542090	−	0.840320i	$-0.682367\pi$
$967$		−	52.2623i		−	1.68064i	0.542090	−	0.840320i	$-0.317633\pi$
$968$		0			0
$969$	−85.1437			−2.73521
$970$		0			0
$971$			59.3560i			1.90482i	0.304813	+	0.952412i	$0.401406\pi$
$971$			59.3560i			1.90482i	−0.304813	+	0.952412i	$0.598594\pi$
$972$		0			0
$973$	41.6227			1.33436
$974$		0			0
$975$	−36.5906	+	10.4889i	−1.17184	+	0.335912i
$976$		0			0
$977$			47.8707i			1.53152i	0.643128	+	0.765759i	$0.277637\pi$
$977$			47.8707i			1.53152i	−0.643128	+	0.765759i	$0.722363\pi$
$978$		0			0
$979$		−	46.0642i		−	1.47222i
$980$		0			0
$981$		−	46.8069i		−	1.49443i
$982$		0			0
$983$		−	6.01429i		−	0.191826i	−0.995390	−	0.0959130i	$-0.969423\pi$
$983$		−	6.01429i		−	0.191826i	0.995390	−	0.0959130i	$-0.0305771\pi$
$984$		0			0
$985$	−37.0321	+	5.20294i	−1.17994	+	0.165780i
$986$		0			0
$987$	54.5718			1.73704
$988$		0			0
$989$		−	0.927346i		−	0.0294879i
$990$		0			0
$991$	−19.4291			−0.617186			−0.308593	−	0.951194i	$-0.599858\pi$
$991$	−19.4291			−0.617186			−0.308593	+	0.951194i	$0.599858\pi$
$992$		0			0
$993$			9.68598i			0.307375i
$994$		0			0
$995$	−46.1847	+	6.48886i	−1.46415	+	0.205711i
$996$		0			0
$997$	32.1334			1.01767			0.508837	−	0.860863i	$-0.330076\pi$
$997$	32.1334			1.01767			0.508837	+	0.860863i	$0.330076\pi$
$998$		0			0
$999$	−50.6548			−1.60265

Twists

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

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

\(f(q)\)	\(=\)	\(q-2.90321 q^{3} +(-2.21432 + 0.311108i) q^{5} -3.52543i q^{7} +5.42864 q^{9} +3.80642i q^{11} +2.62222 q^{13} +(6.42864 - 0.903212i) q^{15} +5.80642i q^{17} -5.05086i q^{19} +10.2351i q^{21} +0.474572i q^{23} +(4.80642 - 1.37778i) q^{25} -7.05086 q^{27} +2.00000i q^{29} -2.75557 q^{31} -11.0509i q^{33} +(1.09679 + 7.80642i) q^{35} +7.18421 q^{37} -7.61285 q^{39} -5.18421 q^{41} -1.95407 q^{43} +(-12.0207 + 1.68889i) q^{45} -5.33185i q^{47} -5.42864 q^{49} -16.8573i q^{51} -5.37778 q^{53} +(-1.18421 - 8.42864i) q^{55} +14.6637i q^{57} -5.05086i q^{59} -12.2351i q^{61} -19.1383i q^{63} +(-5.80642 + 0.815792i) q^{65} -7.76049 q^{67} -1.37778i q^{69} +4.85728 q^{71} -6.66370i q^{73} +(-13.9541 + 4.00000i) q^{75} +13.4193 q^{77} +5.24443 q^{79} +4.18421 q^{81} -12.1476 q^{83} +(-1.80642 - 12.8573i) q^{85} -5.80642i q^{87} -12.1017 q^{89} -9.24443i q^{91} +8.00000 q^{93} +(1.57136 + 11.1842i) q^{95} +13.8064i q^{97} +20.6637i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{3} + 6 q^{9} + 16 q^{13} + 12 q^{15} + 2 q^{25} - 16 q^{27} - 16 q^{31} + 20 q^{35} + 16 q^{37} + 8 q^{39} - 4 q^{41} + 28 q^{43} - 32 q^{45} - 6 q^{49} - 32 q^{53} + 20 q^{55} - 8 q^{65} + 20 q^{67}+ \cdots + 36 q^{95}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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