LMFDB - Embedded newform 1280.3.e.i.639.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1280.639");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			639.1
Root			$-2.65109i$ of defining polynomial
Character	$\chi$	$=$	1280.639
Dual form			1280.3.e.i.639.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.30219i q^{3} +(4.75441 + 1.54778i) q^{5} -0.206625 q^{7} -19.1132 q^{9} +O(q^{10})$	$q-5.30219i q^{3} +(4.75441 + 1.54778i) q^{5} -0.206625 q^{7} -19.1132 q^{9} -15.0176 q^{11} +11.6999 q^{13} +(8.20662 - 25.2087i) q^{15} -18.1911i q^{17} -19.3999 q^{19} +1.09556i q^{21} -27.2242 q^{23} +(20.2087 + 14.7176i) q^{25} +53.6220i q^{27} +44.4175i q^{29} -20.3822i q^{31} +79.6262i q^{33} +(-0.982377 - 0.319810i) q^{35} -18.1089 q^{37} -62.0352i q^{39} +32.3043 q^{41} -4.06244i q^{43} +(-90.8718 - 29.5830i) q^{45} -5.37588 q^{47} -48.9573 q^{49} -96.4527 q^{51} -79.1703 q^{53} +(-71.3999 - 23.2440i) q^{55} +102.862i q^{57} -83.3999 q^{59} -36.7486i q^{61} +3.94925 q^{63} +(55.6262 + 18.1089i) q^{65} +4.51518i q^{67} +144.348i q^{69} +41.6530i q^{71} -41.5910i q^{73} +(78.0352 - 107.151i) q^{75} +3.10301 q^{77} +15.5473i q^{79} +112.295 q^{81} +50.9862i q^{83} +(28.1559 - 86.4880i) q^{85} +235.510 q^{87} -10.8885 q^{89} -2.41749 q^{91} -108.070 q^{93} +(-92.2349 - 30.0268i) q^{95} -12.1559i q^{97} +287.035 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 8 q^{5} + 12 q^{7} - 18 q^{9}+O(q^{10}) $ 6 * q + 8 * q^5 + 12 * q^7 - 18 * q^9	$ 6 q + 8 q^{5} + 12 q^{7} - 18 q^{9} - 8 q^{11} + 36 q^{15} + 24 q^{19} - 68 q^{23} + 10 q^{25} - 88 q^{35} - 208 q^{37} + 68 q^{41} - 232 q^{45} - 268 q^{47} - 62 q^{49} - 192 q^{51} + 64 q^{53} - 288 q^{55} - 360 q^{59} + 172 q^{63} + 304 q^{75} + 400 q^{77} + 238 q^{81} + 304 q^{85} + 584 q^{87} - 76 q^{89} + 208 q^{91} - 320 q^{93} + 32 q^{95} + 856 q^{99}+O(q^{100}) $ 6 * q + 8 * q^5 + 12 * q^7 - 18 * q^9 - 8 * q^11 + 36 * q^15 + 24 * q^19 - 68 * q^23 + 10 * q^25 - 88 * q^35 - 208 * q^37 + 68 * q^41 - 232 * q^45 - 268 * q^47 - 62 * q^49 - 192 * q^51 + 64 * q^53 - 288 * q^55 - 360 * q^59 + 172 * q^63 + 304 * q^75 + 400 * q^77 + 238 * q^81 + 304 * q^85 + 584 * q^87 - 76 * q^89 + 208 * q^91 - 320 * q^93 + 32 * q^95 + 856 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		−	5.30219i		−	1.76740i	−0.468058	−	0.883698i	$-0.655046\pi$
$3$		−	5.30219i		−	1.76740i	0.468058	−	0.883698i	$-0.344954\pi$
$4$		0			0
$5$	4.75441	+	1.54778i	0.950881	+	0.309556i
$5$	4.75441	+	1.54778i	0.950881	+	0.309556i
$6$		0			0
$7$	−0.206625			−0.0295178			−0.0147589	−	0.999891i	$-0.504698\pi$
$7$	−0.206625			−0.0295178			−0.0147589	+	0.999891i	$0.504698\pi$
$8$		0			0
$9$	−19.1132			−2.12369
$10$		0			0
$11$	−15.0176			−1.36524			−0.682619	−	0.730774i	$-0.739159\pi$
$11$	−15.0176			−1.36524			−0.682619	+	0.730774i	$0.739159\pi$
$12$		0			0
$13$	11.6999			0.899995			0.449998	−	0.893030i	$-0.351425\pi$
$13$	11.6999			0.899995			0.449998	+	0.893030i	$0.351425\pi$
$14$		0			0
$15$	8.20662	−	25.2087i	0.547108	−	1.68058i
$16$		0			0
$17$		−	18.1911i		−	1.07007i	−0.844831	−	0.535033i	$-0.820299\pi$
$17$		−	18.1911i		−	1.07007i	0.844831	−	0.535033i	$-0.179701\pi$
$18$		0			0
$19$	−19.3999			−1.02105			−0.510523	−	0.859864i	$-0.670548\pi$
$19$	−19.3999			−1.02105			−0.510523	+	0.859864i	$0.670548\pi$
$20$		0			0
$21$			1.09556i			0.0521696i
$22$		0			0
$23$	−27.2242			−1.18366			−0.591831	−	0.806062i	$-0.701595\pi$
$23$	−27.2242			−1.18366			−0.591831	+	0.806062i	$0.701595\pi$
$24$		0			0
$25$	20.2087	+	14.7176i	0.808350	+	0.588702i
$26$		0			0
$27$			53.6220i			1.98600i
$28$		0			0
$29$			44.4175i			1.53164i	0.643056	+	0.765819i	$0.277666\pi$
$29$			44.4175i			1.53164i	−0.643056	+	0.765819i	$0.722334\pi$
$30$		0			0
$31$		−	20.3822i		−	0.657492i	−0.944418	−	0.328746i	$-0.893374\pi$
$31$		−	20.3822i		−	0.657492i	0.944418	−	0.328746i	$-0.106626\pi$
$32$		0			0
$33$			79.6262i			2.41292i
$34$		0			0
$35$	−0.982377	−	0.319810i	−0.0280679	−	0.00913742i
$36$		0			0
$37$	−18.1089			−0.489431			−0.244715	−	0.969595i	$-0.578695\pi$
$37$	−18.1089			−0.489431			−0.244715	+	0.969595i	$0.578695\pi$
$38$		0			0
$39$		−	62.0352i		−	1.59065i
$40$		0			0
$41$	32.3043			0.787910			0.393955	−	0.919130i	$-0.371107\pi$
$41$	32.3043			0.787910			0.393955	+	0.919130i	$0.371107\pi$
$42$		0			0
$43$		−	4.06244i		−	0.0944753i	−0.998884	−	0.0472377i	$-0.984958\pi$
$43$		−	4.06244i		−	0.0944753i	0.998884	−	0.0472377i	$-0.0150418\pi$
$44$		0			0
$45$	−90.8718	−	29.5830i	−2.01937	−	0.657401i
$46$		0			0
$47$	−5.37588			−0.114380			−0.0571902	−	0.998363i	$-0.518214\pi$
$47$	−5.37588			−0.114380			−0.0571902	+	0.998363i	$0.518214\pi$
$48$		0			0
$49$	−48.9573			−0.999129
$50$		0			0
$51$	−96.4527			−1.89123
$52$		0			0
$53$	−79.1703			−1.49378			−0.746890	−	0.664948i	$-0.768454\pi$
$53$	−79.1703			−1.49378			−0.746890	+	0.664948i	$0.768454\pi$
$54$		0			0
$55$	−71.3999	−	23.2440i	−1.29818	−	0.422618i
$56$		0			0
$57$			102.862i			1.80459i
$58$		0			0
$59$	−83.3999			−1.41356			−0.706779	−	0.707435i	$-0.749852\pi$
$59$	−83.3999			−1.41356			−0.706779	+	0.707435i	$0.749852\pi$
$60$		0			0
$61$		−	36.7486i		−	0.602435i	−0.953555	−	0.301218i	$-0.902607\pi$
$61$		−	36.7486i		−	0.602435i	0.953555	−	0.301218i	$-0.0973931\pi$
$62$		0			0
$63$	3.94925			0.0626866
$64$		0			0
$65$	55.6262	+	18.1089i	0.855788	+	0.278599i
$66$		0			0
$67$			4.51518i			0.0673907i	0.999432	+	0.0336954i	$0.0107276\pi$
$67$			4.51518i			0.0673907i	−0.999432	+	0.0336954i	$0.989272\pi$
$68$		0			0
$69$			144.348i			2.09200i
$70$		0			0
$71$			41.6530i			0.586662i	0.956011	+	0.293331i	$0.0947638\pi$
$71$			41.6530i			0.586662i	−0.956011	+	0.293331i	$0.905236\pi$
$72$		0			0
$73$		−	41.5910i		−	0.569740i	−0.958566	−	0.284870i	$-0.908050\pi$
$73$		−	41.5910i		−	0.569740i	0.958566	−	0.284870i	$-0.0919504\pi$
$74$		0			0
$75$	78.0352	−	107.151i	1.04047	−	1.42867i
$76$		0			0
$77$	3.10301			0.0402988
$78$		0			0
$79$			15.5473i			0.196801i	0.995147	+	0.0984004i	$0.0313726\pi$
$79$			15.5473i			0.196801i	−0.995147	+	0.0984004i	$0.968627\pi$
$80$		0			0
$81$	112.295			1.38636
$82$		0			0
$83$			50.9862i			0.614291i	0.951663	+	0.307146i	$0.0993739\pi$
$83$			50.9862i			0.614291i	−0.951663	+	0.307146i	$0.900626\pi$
$84$		0			0
$85$	28.1559	−	86.4880i	0.331246	−	1.01751i
$86$		0			0
$87$	235.510			2.70701
$88$		0			0
$89$	−10.8885			−0.122343			−0.0611713	−	0.998127i	$-0.519484\pi$
$89$	−10.8885			−0.122343			−0.0611713	+	0.998127i	$0.519484\pi$
$90$		0			0
$91$	−2.41749			−0.0265659
$92$		0			0
$93$	−108.070			−1.16205
$94$		0			0
$95$	−92.2349	−	30.0268i	−0.970893	−	0.316071i
$96$		0			0
$97$		−	12.1559i		−	0.125318i	−0.998035	−	0.0626592i	$-0.980042\pi$
$97$		−	12.1559i		−	0.125318i	0.998035	−	0.0626592i	$-0.0199581\pi$
$98$		0			0
$99$	287.035			2.89934
$100$		0			0
$101$		−	127.723i		−	1.26459i	−0.774728	−	0.632294i	$-0.782113\pi$
$101$		−	127.723i		−	1.26459i	0.774728	−	0.632294i	$-0.217887\pi$
$102$		0			0
$103$	4.77575			0.0463665			0.0231833	−	0.999731i	$-0.492620\pi$
$103$	4.77575			0.0463665			0.0231833	+	0.999731i	$0.492620\pi$
$104$		0			0
$105$	−1.69569	+	5.20875i	−0.0161494	+	0.0496071i
$106$		0			0
$107$			107.213i			1.00199i	0.865449	+	0.500997i	$0.167033\pi$
$107$			107.213i			1.00199i	−0.865449	+	0.500997i	$0.832967\pi$
$108$		0			0
$109$			53.6689i			0.492376i	0.969222	+	0.246188i	$0.0791780\pi$
$109$			53.6689i			0.492376i	−0.969222	+	0.246188i	$0.920822\pi$
$110$		0			0
$111$			96.0170i			0.865018i
$112$		0			0
$113$			20.5063i			0.181471i	0.995875	+	0.0907356i	$0.0289218\pi$
$113$			20.5063i			0.181471i	−0.995875	+	0.0907356i	$0.971078\pi$
$114$		0			0
$115$	−129.435	−	42.1372i	−1.12552	−	0.366410i
$116$		0			0
$117$	−223.623			−1.91131
$118$		0			0
$119$			3.75873i			0.0315860i
$120$		0			0
$121$	104.529			0.863876
$122$		0			0
$123$		−	171.283i		−	1.39255i
$124$		0			0
$125$	73.3010	+	101.252i	0.586408	+	0.810016i
$126$		0			0
$127$	138.477			1.09037			0.545184	−	0.838316i	$-0.316460\pi$
$127$	138.477			1.09037			0.545184	+	0.838316i	$0.316460\pi$
$128$		0			0
$129$	−21.5398			−0.166975
$130$		0			0
$131$	219.105			1.67256			0.836279	−	0.548304i	$-0.184726\pi$
$131$	219.105			1.67256			0.836279	+	0.548304i	$0.184726\pi$
$132$		0			0
$133$	4.00849			0.0301390
$134$		0			0
$135$	−82.9951	+	254.941i	−0.614779	+	1.88845i
$136$		0			0
$137$			59.7821i			0.436366i	0.975908	+	0.218183i	$0.0700129\pi$
$137$			59.7821i			0.436366i	−0.975908	+	0.218183i	$0.929987\pi$
$138$		0			0
$139$	26.6524			0.191744			0.0958718	−	0.995394i	$-0.469436\pi$
$139$	26.6524			0.191744			0.0958718	+	0.995394i	$0.469436\pi$
$140$		0			0
$141$			28.5039i			0.202155i
$142$		0			0
$143$	−175.705			−1.22871
$144$		0			0
$145$	−68.7486	+	211.179i	−0.474128	+	1.45641i
$146$		0			0
$147$			259.581i			1.76586i
$148$		0			0
$149$		−	143.463i		−	0.962838i	−0.876490	−	0.481419i	$-0.840121\pi$
$149$		−	143.463i		−	0.962838i	0.876490	−	0.481419i	$-0.159879\pi$
$150$		0			0
$151$			83.4937i			0.552939i	0.961023	+	0.276469i	$0.0891644\pi$
$151$			83.4937i			0.552939i	−0.961023	+	0.276469i	$0.910836\pi$
$152$		0			0
$153$			347.690i			2.27249i
$154$		0			0
$155$	31.5473	−	96.9055i	0.203531	−	0.625197i
$156$		0			0
$157$	−169.673			−1.08072			−0.540360	−	0.841434i	$-0.681712\pi$
$157$	−169.673			−1.08072			−0.540360	+	0.841434i	$0.681712\pi$
$158$		0			0
$159$			419.776i			2.64010i
$160$		0			0
$161$	5.62520			0.0349391
$162$		0			0
$163$		−	275.478i		−	1.69005i	−0.534726	−	0.845026i	$-0.679585\pi$
$163$		−	275.478i		−	1.69005i	0.534726	−	0.845026i	$-0.320415\pi$
$164$		0			0
$165$	−123.244	+	378.575i	−0.746933	+	2.29440i
$166$		0			0
$167$	132.481			0.793299			0.396650	−	0.917970i	$-0.370173\pi$
$167$	132.481			0.793299			0.396650	+	0.917970i	$0.370173\pi$
$168$		0			0
$169$	−32.1115			−0.190009
$170$		0			0
$171$	370.793			2.16838
$172$		0			0
$173$	−272.614			−1.57580			−0.787901	−	0.615801i	$-0.788832\pi$
$173$	−272.614			−1.57580			−0.787901	+	0.615801i	$0.788832\pi$
$174$		0			0
$175$	−4.17562	−	3.04101i	−0.0238607	−	0.0173772i
$176$		0			0
$177$			442.202i			2.49831i
$178$		0			0
$179$	−157.523			−0.880014			−0.440007	−	0.897994i	$-0.645024\pi$
$179$	−157.523			−0.880014			−0.440007	+	0.897994i	$0.645024\pi$
$180$		0			0
$181$			335.063i			1.85118i	0.378529	+	0.925590i	$0.376430\pi$
$181$			335.063i			1.85118i	−0.378529	+	0.925590i	$0.623570\pi$
$182$		0			0
$183$	−194.848			−1.06474
$184$		0			0
$185$	−86.0972	−	28.0287i	−0.465391	−	0.151506i
$186$		0			0
$187$			273.187i			1.46090i
$188$		0			0
$189$		−	11.0796i		−	0.0586223i
$190$		0			0
$191$		−	298.575i		−	1.56322i	−0.623766	−	0.781611i	$-0.714398\pi$
$191$		−	298.575i		−	1.56322i	0.623766	−	0.781611i	$-0.285602\pi$
$192$		0			0
$193$		−	191.915i		−	0.994376i	−0.867643	−	0.497188i	$-0.834366\pi$
$193$		−	191.915i		−	0.994376i	0.867643	−	0.497188i	$-0.165634\pi$
$194$		0			0
$195$	96.0170	−	294.941i	0.492395	−	1.51252i
$196$		0			0
$197$	59.2472			0.300747			0.150374	−	0.988629i	$-0.451952\pi$
$197$	59.2472			0.300747			0.150374	+	0.988629i	$0.451952\pi$
$198$		0			0
$199$		−	309.100i		−	1.55327i	−0.629953	−	0.776633i	$-0.716926\pi$
$199$		−	309.100i		−	1.55327i	0.629953	−	0.776633i	$-0.283074\pi$
$200$		0			0
$201$	23.9403			0.119106
$202$		0			0
$203$		−	9.17775i		−	0.0452106i
$204$		0			0
$205$	153.588	+	50.0000i	0.749209	+	0.243902i
$206$		0			0
$207$	520.342			2.51373
$208$		0			0
$209$	291.340			1.39397
$210$		0			0
$211$	−205.693			−0.974850			−0.487425	−	0.873165i	$-0.662064\pi$
$211$	−205.693			−0.974850			−0.487425	+	0.873165i	$0.662064\pi$
$212$		0			0
$213$	220.852			1.03686
$214$		0			0
$215$	6.28777	−	19.3145i	0.0292454	−	0.0898348i
$216$		0			0
$217$			4.21147i			0.0194077i
$218$		0			0
$219$	−220.523			−1.00696
$220$		0			0
$221$		−	212.835i		−	0.963054i
$222$		0			0
$223$	228.723			1.02567			0.512833	−	0.858488i	$-0.328596\pi$
$223$	228.723			1.02567			0.512833	+	0.858488i	$0.328596\pi$
$224$		0			0
$225$	−386.254	−	281.299i	−1.71668	−	1.25022i
$226$		0			0
$227$			282.403i			1.24407i	0.782991	+	0.622033i	$0.213693\pi$
$227$			282.403i			1.24407i	−0.782991	+	0.622033i	$0.786307\pi$
$228$		0			0
$229$		−	49.2525i		−	0.215076i	−0.994201	−	0.107538i	$-0.965703\pi$
$229$		−	49.2525i		−	0.215076i	0.994201	−	0.107538i	$-0.0342968\pi$
$230$		0			0
$231$		−	16.4527i		−	0.0712240i
$232$		0			0
$233$		−	124.273i		−	0.533363i	−0.963785	−	0.266681i	$-0.914073\pi$
$233$		−	124.273i		−	0.533363i	0.963785	−	0.266681i	$-0.0859271\pi$
$234$		0			0
$235$	−25.5591	−	8.32069i	−0.108762	−	0.0354072i
$236$		0			0
$237$	82.4345			0.347825
$238$		0			0
$239$		−	80.4527i		−	0.336622i	−0.985734	−	0.168311i	$-0.946169\pi$
$239$		−	80.4527i		−	0.336622i	0.985734	−	0.168311i	$-0.0538313\pi$
$240$		0			0
$241$	−1.20979			−0.00501988			−0.00250994	−	0.999997i	$-0.500799\pi$
$241$	−1.20979			−0.00501988			−0.00250994	+	0.999997i	$0.500799\pi$
$242$		0			0
$243$		−	112.812i		−	0.464247i
$244$		0			0
$245$	−232.763	−	75.7752i	−0.950053	−	0.309287i
$246$		0			0
$247$	−226.977			−0.918936
$248$		0			0
$249$	270.338			1.08570
$250$		0			0
$251$	−211.853			−0.844034			−0.422017	−	0.906588i	$-0.638678\pi$
$251$	−211.853			−0.844034			−0.422017	+	0.906588i	$0.638678\pi$
$252$		0			0
$253$	408.843			1.61598
$254$		0			0
$255$	−458.575	−	149.288i	−1.79834	−	0.585442i
$256$		0			0
$257$		−	182.646i		−	0.710685i	−0.934736	−	0.355342i	$-0.884364\pi$
$257$		−	182.646i		−	0.710685i	0.934736	−	0.355342i	$-0.115636\pi$
$258$		0			0
$259$	3.74175			0.0144469
$260$		0			0
$261$		−	848.960i		−	3.25272i
$262$		0			0
$263$	74.6636			0.283892			0.141946	−	0.989874i	$-0.454664\pi$
$263$	74.6636			0.283892			0.141946	+	0.989874i	$0.454664\pi$
$264$		0			0
$265$	−376.408	−	122.538i	−1.42041	−	0.462409i
$266$		0			0
$267$			57.7329i			0.216228i
$268$		0			0
$269$		−	184.089i		−	0.684344i	−0.939637	−	0.342172i	$-0.888837\pi$
$269$		−	184.089i		−	0.684344i	0.939637	−	0.342172i	$-0.111163\pi$
$270$		0			0
$271$		−	234.746i		−	0.866222i	−0.901341	−	0.433111i	$-0.857416\pi$
$271$		−	234.746i		−	0.866222i	0.901341	−	0.433111i	$-0.142584\pi$
$272$		0			0
$273$			12.8180i			0.0469524i
$274$		0			0
$275$	−303.487	−	221.023i	−1.10359	−	0.803719i
$276$		0			0
$277$	452.208			1.63252			0.816260	−	0.577684i	$-0.196043\pi$
$277$	452.208			1.63252			0.816260	+	0.577684i	$0.196043\pi$
$278$		0			0
$279$			389.570i			1.39631i
$280$		0			0
$281$	196.110			0.697900			0.348950	−	0.937141i	$-0.386538\pi$
$281$	196.110			0.697900			0.348950	+	0.937141i	$0.386538\pi$
$282$		0			0
$283$			418.449i			1.47862i	0.673366	+	0.739309i	$0.264848\pi$
$283$			418.449i			1.47862i	−0.673366	+	0.739309i	$0.735152\pi$
$284$		0			0
$285$	−159.207	+	489.046i	−0.558623	+	1.71595i
$286$		0			0
$287$	−6.67486			−0.0232574
$288$		0			0
$289$	−41.9170			−0.145042
$290$		0			0
$291$	−64.4527			−0.221487
$292$		0			0
$293$	−286.666			−0.978383			−0.489191	−	0.872176i	$-0.662708\pi$
$293$	−286.666			−0.978383			−0.489191	+	0.872176i	$0.662708\pi$
$294$		0			0
$295$	−396.517	−	129.085i	−1.34412	−	0.437575i
$296$		0			0
$297$		−	805.275i		−	2.71136i
$298$		0			0
$299$	−318.522			−1.06529
$300$		0			0
$301$			0.839400i			0.00278870i
$302$		0			0
$303$	−677.214			−2.23503
$304$		0			0
$305$	56.8787	−	174.718i	0.186488	−	0.572844i
$306$		0			0
$307$			261.715i			0.852493i	0.904607	+	0.426247i	$0.140164\pi$
$307$			261.715i			0.852493i	−0.904607	+	0.426247i	$0.859836\pi$
$308$		0			0
$309$		−	25.3219i		−	0.0819480i
$310$		0			0
$311$		−	578.904i		−	1.86143i	−0.365747	−	0.930714i	$-0.619187\pi$
$311$		−	578.904i		−	1.86143i	0.365747	−	0.930714i	$-0.380813\pi$
$312$		0			0
$313$			99.3124i			0.317292i	0.987336	+	0.158646i	$0.0507129\pi$
$313$			99.3124i			0.317292i	−0.987336	+	0.158646i	$0.949287\pi$
$314$		0			0
$315$	18.7764	+	6.11258i	0.0596075	+	0.0194050i
$316$		0			0
$317$	−191.623			−0.604489			−0.302245	−	0.953230i	$-0.597736\pi$
$317$	−191.623			−0.604489			−0.302245	+	0.953230i	$0.597736\pi$
$318$		0			0
$319$		−	667.045i		−	2.09105i
$320$		0			0
$321$	568.466			1.77092
$322$		0			0
$323$			352.905i			1.09259i
$324$		0			0
$325$	236.441	+	172.194i	0.727511	+	0.529829i
$326$		0			0
$327$	284.563			0.870222
$328$		0			0
$329$	1.11079			0.00337626
$330$		0			0
$331$	−530.187			−1.60177			−0.800886	−	0.598816i	$-0.795638\pi$
$331$	−530.187			−1.60177			−0.800886	+	0.598816i	$0.795638\pi$
$332$		0			0
$333$	346.120			1.03940
$334$		0			0
$335$	−6.98851	+	21.4670i	−0.0208612	+	0.0640806i
$336$		0			0
$337$		−	487.427i		−	1.44637i	−0.690653	−	0.723186i	$-0.742677\pi$
$337$		−	487.427i		−	1.44637i	0.690653	−	0.723186i	$-0.257323\pi$
$338$		0			0
$339$	108.728			0.320731
$340$		0			0
$341$			306.093i			0.897633i
$342$		0			0
$343$	20.2404			0.0590099
$344$		0			0
$345$	−223.419	+	686.289i	−0.647592	+	1.98924i
$346$		0			0
$347$		−	310.497i		−	0.894804i	−0.894333	−	0.447402i	$-0.852349\pi$
$347$		−	310.497i		−	0.894804i	0.894333	−	0.447402i	$-0.147651\pi$
$348$		0			0
$349$		−	253.004i		−	0.724941i	−0.931995	−	0.362471i	$-0.881933\pi$
$349$		−	253.004i		−	0.724941i	0.931995	−	0.362471i	$-0.118067\pi$
$350$		0			0
$351$			627.374i			1.78739i
$352$		0			0
$353$			322.639i			0.913992i	0.889469	+	0.456996i	$0.151075\pi$
$353$			322.639i			0.913992i	−0.889469	+	0.456996i	$0.848925\pi$
$354$		0			0
$355$	−64.4697	+	198.035i	−0.181605	+	0.557846i
$356$		0			0
$357$	19.9295			0.0558250
$358$		0			0
$359$		−	254.975i		−	0.710236i	−0.934822	−	0.355118i	$-0.884441\pi$
$359$		−	254.975i		−	0.710236i	0.934822	−	0.355118i	$-0.115559\pi$
$360$		0			0
$361$	15.3550			0.0425347
$362$		0			0
$363$		−	554.232i		−	1.52681i
$364$		0			0
$365$	64.3738	−	197.740i	0.176366	−	0.541755i
$366$		0			0
$367$	207.935			0.566581			0.283291	−	0.959034i	$-0.408574\pi$
$367$	207.935			0.566581			0.283291	+	0.959034i	$0.408574\pi$
$368$		0			0
$369$	−617.438			−1.67327
$370$		0			0
$371$	16.3585			0.0440931
$372$		0			0
$373$	−203.826			−0.546450			−0.273225	−	0.961950i	$-0.588090\pi$
$373$	−203.826			−0.546450			−0.273225	+	0.961950i	$0.588090\pi$
$374$		0			0
$375$	536.857	−	388.656i	1.43162	−	1.03642i
$376$		0			0
$377$			519.682i			1.37847i
$378$		0			0
$379$	454.099			1.19815			0.599076	−	0.800692i	$-0.295535\pi$
$379$	454.099			1.19815			0.599076	+	0.800692i	$0.295535\pi$
$380$		0			0
$381$		−	734.229i		−	1.92711i
$382$		0			0
$383$	541.569			1.41402			0.707009	−	0.707205i	$-0.250044\pi$
$383$	541.569			1.41402			0.707009	+	0.707205i	$0.250044\pi$
$384$		0			0
$385$	14.7530	+	4.80278i	0.0383194	+	0.0124748i
$386$		0			0
$387$			77.6462i			0.200636i
$388$		0			0
$389$			423.431i			1.08851i	0.838919	+	0.544256i	$0.183188\pi$
$389$			423.431i			1.08851i	−0.838919	+	0.544256i	$0.816812\pi$
$390$		0			0
$391$			495.240i			1.26660i
$392$		0			0
$393$		−	1161.74i		−	2.95607i
$394$		0			0
$395$	−24.0638	+	73.9180i	−0.0609209	+	0.187134i
$396$		0			0
$397$	11.7772			0.0296654			0.0148327	−	0.999890i	$-0.495278\pi$
$397$	11.7772			0.0296654			0.0148327	+	0.999890i	$0.495278\pi$
$398$		0			0
$399$		−	21.2538i		−	0.0532676i
$400$		0			0
$401$	127.442			0.317809			0.158905	−	0.987294i	$-0.449204\pi$
$401$	127.442			0.317809			0.158905	+	0.987294i	$0.449204\pi$
$402$		0			0
$403$		−	238.471i		−	0.591739i
$404$		0			0
$405$	533.897	+	173.808i	1.31826	+	0.429156i
$406$		0			0
$407$	271.953			0.668190
$408$		0			0
$409$	−608.012			−1.48658			−0.743290	−	0.668969i	$-0.766736\pi$
$409$	−608.012			−1.48658			−0.743290	+	0.668969i	$0.766736\pi$
$410$		0			0
$411$	316.976			0.771231
$412$		0			0
$413$	17.2325			0.0417251
$414$		0			0
$415$	−78.9155	+	242.409i	−0.190158	+	0.584118i
$416$		0			0
$417$		−	141.316i		−	0.338887i
$418$		0			0
$419$	−565.630			−1.34995			−0.674976	−	0.737840i	$-0.735846\pi$
$419$	−565.630			−1.34995			−0.674976	+	0.737840i	$0.735846\pi$
$420$		0			0
$421$		−	711.356i		−	1.68968i	−0.535018	−	0.844841i	$-0.679695\pi$
$421$		−	711.356i		−	1.68968i	0.535018	−	0.844841i	$-0.320305\pi$
$422$		0			0
$423$	102.750			0.242908
$424$		0			0
$425$	267.729	−	367.620i	0.629950	−	0.864988i
$426$		0			0
$427$			7.59316i			0.0177826i
$428$		0			0
$429$			931.622i			2.17161i
$430$		0			0
$431$			309.254i			0.717526i	0.933429	+	0.358763i	$0.116801\pi$
$431$			309.254i			0.717526i	−0.933429	+	0.358763i	$0.883199\pi$
$432$		0			0
$433$		−	187.374i		−	0.432735i	−0.976312	−	0.216368i	$-0.930579\pi$
$433$		−	187.374i		−	0.432735i	0.976312	−	0.216368i	$-0.0694210\pi$
$434$		0			0
$435$	1119.71	+	364.518i	2.57404	+	0.837972i
$436$		0			0
$437$	528.147			1.20857
$438$		0			0
$439$		−	289.657i		−	0.659811i	−0.944014	−	0.329906i	$-0.892983\pi$
$439$		−	289.657i		−	0.659811i	0.944014	−	0.329906i	$-0.107017\pi$
$440$		0			0
$441$	935.730			2.12184
$442$		0			0
$443$		−	295.516i		−	0.667079i	−0.942736	−	0.333539i	$-0.891757\pi$
$443$		−	295.516i		−	0.667079i	0.942736	−	0.333539i	$-0.108243\pi$
$444$		0			0
$445$	−51.7683	−	16.8530i	−0.116333	−	0.0378719i
$446$		0			0
$447$	−760.667			−1.70172
$448$		0			0
$449$	−604.409			−1.34612			−0.673061	−	0.739587i	$-0.735021\pi$
$449$	−604.409			−1.34612			−0.673061	+	0.739587i	$0.735021\pi$
$450$		0			0
$451$	−485.134			−1.07569
$452$		0			0
$453$	442.699			0.977262
$454$		0			0
$455$	−11.4937	−	3.74175i	−0.0252610	−	0.00822363i
$456$		0			0
$457$		−	392.507i		−	0.858877i	−0.903096	−	0.429438i	$-0.858712\pi$
$457$		−	392.507i		−	0.858877i	0.903096	−	0.429438i	$-0.141288\pi$
$458$		0			0
$459$	975.444			2.12515
$460$		0			0
$461$		−	400.277i		−	0.868279i	−0.900846	−	0.434139i	$-0.857053\pi$
$461$		−	400.277i		−	0.868279i	0.900846	−	0.434139i	$-0.142947\pi$
$462$		0			0
$463$	−732.679			−1.58246			−0.791230	−	0.611518i	$-0.790559\pi$
$463$	−732.679			−1.58246			−0.791230	+	0.611518i	$0.790559\pi$
$464$		0			0
$465$	−513.811	−	167.269i	−1.10497	−	0.359719i
$466$		0			0
$467$		−	592.126i		−	1.26794i	−0.773360	−	0.633968i	$-0.781425\pi$
$467$		−	592.126i		−	1.26794i	0.773360	−	0.633968i	$-0.218575\pi$
$468$		0			0
$469$		−	0.932947i		−	0.00198923i
$470$		0			0
$471$			899.639i			1.91006i
$472$		0			0
$473$			61.0082i			0.128981i
$474$		0			0
$475$	−392.047	−	285.519i	−0.825362	−	0.601092i
$476$		0			0
$477$	1513.20			3.17232
$478$		0			0
$479$			309.151i			0.645409i	0.946500	+	0.322705i	$0.104592\pi$
$479$			309.151i			0.645409i	−0.946500	+	0.322705i	$0.895408\pi$
$480$		0			0
$481$	−211.873			−0.440485
$482$		0			0
$483$		−	29.8259i		−	0.0617513i
$484$		0			0
$485$	18.8146	−	57.7940i	0.0387931	−	0.119163i
$486$		0			0
$487$	−570.769			−1.17201			−0.586005	−	0.810307i	$-0.699300\pi$
$487$	−570.769			−1.17201			−0.586005	+	0.810307i	$0.699300\pi$
$488$		0			0
$489$	−1460.64			−2.98699
$490$		0			0
$491$	−301.659			−0.614378			−0.307189	−	0.951649i	$-0.599388\pi$
$491$	−301.659			−0.614378			−0.307189	+	0.951649i	$0.599388\pi$
$492$		0			0
$493$	808.004			1.63895
$494$		0			0
$495$	1364.68	+	444.267i	2.75693	+	0.897509i
$496$		0			0
$497$		−	8.60653i		−	0.0173170i
$498$		0			0
$499$	517.758			1.03759			0.518795	−	0.854898i	$-0.326381\pi$
$499$	517.758			1.03759			0.518795	+	0.854898i	$0.326381\pi$
$500$		0			0
$501$		−	702.439i		−	1.40207i
$502$		0			0
$503$	−406.671			−0.808491			−0.404246	−	0.914650i	$-0.632466\pi$
$503$	−406.671			−0.808491			−0.404246	+	0.914650i	$0.632466\pi$
$504$		0			0
$505$	197.688	−	607.249i	0.391461	−	1.20247i
$506$		0			0
$507$			170.261i			0.335821i
$508$		0			0
$509$			627.097i			1.23202i	0.787739	+	0.616009i	$0.211252\pi$
$509$			627.097i			1.23202i	−0.787739	+	0.616009i	$0.788748\pi$
$510$		0			0
$511$			8.59372i			0.0168175i
$512$		0			0
$513$		−	1040.26i		−	2.02780i
$514$		0			0
$515$	22.7059	+	7.39182i	0.0440891	+	0.0143530i
$516$		0			0
$517$	80.7330			0.156157
$518$		0			0
$519$			1445.45i			2.78507i
$520$		0			0
$521$	111.743			0.214478			0.107239	−	0.994233i	$-0.465799\pi$
$521$	111.743			0.214478			0.107239	+	0.994233i	$0.465799\pi$
$522$		0			0
$523$			769.813i			1.47192i	0.677027	+	0.735959i	$0.263268\pi$
$523$			769.813i			1.47192i	−0.677027	+	0.735959i	$0.736732\pi$
$524$		0			0
$525$	−16.1240	+	22.1399i	−0.0307124	+	0.0421713i
$526$		0			0
$527$	−370.776			−0.703560
$528$		0			0
$529$	212.160			0.401058
$530$		0			0
$531$	1594.04			3.00195
$532$		0			0
$533$	377.958			0.709115
$534$		0			0
$535$	−165.943	+	509.736i	−0.310174	+	0.952778i
$536$		0			0
$537$			835.214i			1.55533i
$538$		0			0
$539$	735.222			1.36405
$540$		0			0
$541$		−	225.558i		−	0.416927i	−0.978030	−	0.208463i	$-0.933154\pi$
$541$		−	225.558i		−	0.416927i	0.978030	−	0.208463i	$-0.0668462\pi$
$542$		0			0
$543$	1776.57			3.27177
$544$		0			0
$545$	−83.0678	+	255.164i	−0.152418	+	0.468191i
$546$		0			0
$547$		−	882.346i		−	1.61306i	−0.591190	−	0.806532i	$-0.701342\pi$
$547$		−	882.346i		−	1.61306i	0.591190	−	0.806532i	$-0.298658\pi$
$548$		0			0
$549$			702.382i			1.27938i
$550$		0			0
$551$		−	861.694i		−	1.56387i
$552$		0			0
$553$		−	3.21245i		−	0.00580913i
$554$		0			0
$555$	−148.613	+	456.504i	−0.267772	+	0.822529i
$556$		0			0
$557$	−303.119			−0.544199			−0.272100	−	0.962269i	$-0.587718\pi$
$557$	−303.119			−0.544199			−0.272100	+	0.962269i	$0.587718\pi$
$558$		0			0
$559$		−	47.5303i		−	0.0850273i
$560$		0			0
$561$	1448.49			2.58198
$562$		0			0
$563$			344.003i			0.611017i	0.952189	+	0.305508i	$0.0988264\pi$
$563$			344.003i			0.611017i	−0.952189	+	0.305508i	$0.901174\pi$
$564$		0			0
$565$	−31.7392	+	97.4950i	−0.0561756	+	0.172558i
$566$		0			0
$567$	−23.2029			−0.0409223
$568$		0			0
$569$	228.925			0.402329			0.201165	−	0.979557i	$-0.435527\pi$
$569$	228.925			0.402329			0.201165	+	0.979557i	$0.435527\pi$
$570$		0			0
$571$	371.169			0.650033			0.325017	−	0.945708i	$-0.394630\pi$
$571$	371.169			0.650033			0.325017	+	0.945708i	$0.394630\pi$
$572$		0			0
$573$	−1583.10			−2.76283
$574$		0			0
$575$	−550.168	−	400.674i	−0.956814	−	0.696825i
$576$		0			0
$577$		−	580.289i		−	1.00570i	−0.864374	−	0.502850i	$-0.832285\pi$
$577$		−	580.289i		−	1.00570i	0.864374	−	0.502850i	$-0.167715\pi$
$578$		0			0
$579$	−1017.57			−1.75746
$580$		0			0
$581$		−	10.5350i		−	0.0181325i
$582$		0			0
$583$	1188.95			2.03936
$584$		0			0
$585$	−1063.19	−	346.120i	−1.81743	−	0.591657i
$586$		0			0
$587$			65.0801i			0.110869i	0.998462	+	0.0554345i	$0.0176544\pi$
$587$			65.0801i			0.110869i	−0.998462	+	0.0554345i	$0.982346\pi$
$588$		0			0
$589$			395.413i			0.671329i
$590$		0			0
$591$		−	314.140i		−	0.531539i
$592$		0			0
$593$			1002.90i			1.69124i	0.533787	+	0.845619i	$0.320768\pi$
$593$			1002.90i			1.69124i	−0.533787	+	0.845619i	$0.679232\pi$
$594$		0			0
$595$	−5.81770	+	17.8705i	−0.00977764	+	0.0300345i
$596$		0			0
$597$	−1638.91			−2.74524
$598$		0			0
$599$			888.567i			1.48342i	0.670722	+	0.741709i	$0.265984\pi$
$599$			888.567i			1.48342i	−0.670722	+	0.741709i	$0.734016\pi$
$600$		0			0
$601$	−132.065			−0.219742			−0.109871	−	0.993946i	$-0.535044\pi$
$601$	−132.065			−0.219742			−0.109871	+	0.993946i	$0.535044\pi$
$602$		0			0
$603$		−	86.2995i		−	0.143117i
$604$		0			0
$605$	496.973	+	161.788i	0.821443	+	0.267418i
$606$		0			0
$607$	−700.090			−1.15336			−0.576680	−	0.816970i	$-0.695652\pi$
$607$	−700.090			−1.15336			−0.576680	+	0.816970i	$0.695652\pi$
$608$		0			0
$609$	−48.6621			−0.0799050
$610$		0			0
$611$	−62.8975			−0.102942
$612$		0			0
$613$	727.420			1.18666			0.593328	−	0.804961i	$-0.297814\pi$
$613$	727.420			1.18666			0.593328	+	0.804961i	$0.297814\pi$
$614$		0			0
$615$	265.109	−	814.351i	0.431072	−	1.32415i
$616$		0			0
$617$		−	99.7137i		−	0.161611i	−0.996730	−	0.0808053i	$-0.974251\pi$
$617$		−	99.7137i		−	0.161611i	0.996730	−	0.0808053i	$-0.0257492\pi$
$618$		0			0
$619$	−721.349			−1.16535			−0.582673	−	0.812707i	$-0.697993\pi$
$619$	−721.349			−1.16535			−0.582673	+	0.812707i	$0.697993\pi$
$620$		0			0
$621$		−	1459.82i		−	2.35075i
$622$		0			0
$623$	2.24983			0.00361129
$624$		0			0
$625$	191.787	+	594.847i	0.306859	+	0.951755i
$626$		0			0
$627$		−	1544.74i		−	2.46370i
$628$		0			0
$629$			329.422i			0.523723i
$630$		0			0
$631$		−	796.856i		−	1.26285i	−0.775438	−	0.631423i	$-0.782471\pi$
$631$		−	796.856i		−	1.26285i	0.775438	−	0.631423i	$-0.217529\pi$
$632$		0			0
$633$			1090.62i			1.72295i
$634$		0			0
$635$	658.375	+	214.332i	1.03681	+	0.337530i
$636$		0			0
$637$	−572.797			−0.899211
$638$		0			0
$639$		−	796.121i		−	1.24589i
$640$		0			0
$641$	205.013			0.319833			0.159917	−	0.987131i	$-0.448877\pi$
$641$	205.013			0.319833			0.159917	+	0.987131i	$0.448877\pi$
$642$		0			0
$643$			495.044i			0.769897i	0.922938	+	0.384949i	$0.125781\pi$
$643$			495.044i			0.769897i	−0.922938	+	0.384949i	$0.874219\pi$
$644$		0			0
$645$	−102.409	−	33.3389i	−0.158774	−	0.0516882i
$646$		0			0
$647$	−1121.84			−1.73391			−0.866953	−	0.498389i	$-0.833925\pi$
$647$	−1121.84			−1.73391			−0.866953	+	0.498389i	$0.833925\pi$
$648$		0			0
$649$	1252.47			1.92984
$650$		0			0
$651$	22.3300			0.0343011
$652$		0			0
$653$	−622.987			−0.954038			−0.477019	−	0.878893i	$-0.658283\pi$
$653$	−622.987			−0.954038			−0.477019	+	0.878893i	$0.658283\pi$
$654$		0			0
$655$	1041.71	+	339.127i	1.59040	+	0.517751i
$656$		0			0
$657$			794.936i			1.20995i
$658$		0			0
$659$	−264.030			−0.400653			−0.200326	−	0.979729i	$-0.564200\pi$
$659$	−264.030			−0.400653			−0.200326	+	0.979729i	$0.564200\pi$
$660$		0			0
$661$		−	1285.15i		−	1.94425i	−0.234469	−	0.972124i	$-0.575335\pi$
$661$		−	1285.15i		−	1.94425i	0.234469	−	0.972124i	$-0.424665\pi$
$662$		0			0
$663$	−1128.49			−1.70210
$664$		0			0
$665$	19.0580	+	6.20427i	0.0286586	+	0.00932972i
$666$		0			0
$667$		−	1209.23i		−	1.81294i
$668$		0			0
$669$		−	1212.73i		−	1.81276i
$670$		0			0
$671$			551.876i			0.822468i
$672$		0			0
$673$		−	1244.16i		−	1.84868i	−0.381565	−	0.924342i	$-0.624615\pi$
$673$		−	1244.16i		−	1.84868i	0.381565	−	0.924342i	$-0.375385\pi$
$674$		0			0
$675$	−789.185	+	1083.63i	−1.16916	+	1.60538i
$676$		0			0
$677$	−963.335			−1.42295			−0.711473	−	0.702713i	$-0.751972\pi$
$677$	−963.335			−1.42295			−0.711473	+	0.702713i	$0.751972\pi$
$678$		0			0
$679$			2.51170i			0.00369912i
$680$		0			0
$681$	1497.35			2.19876
$682$		0			0
$683$			770.819i			1.12858i	0.825577	+	0.564289i	$0.190850\pi$
$683$			770.819i			1.12858i	−0.825577	+	0.564289i	$0.809150\pi$
$684$		0			0
$685$	−92.5296	+	284.228i	−0.135080	+	0.414932i
$686$		0			0
$687$	−261.146			−0.380125
$688$		0			0
$689$	−926.287			−1.34439
$690$		0			0
$691$	−408.765			−0.591555			−0.295778	−	0.955257i	$-0.595579\pi$
$691$	−408.765			−0.591555			−0.295778	+	0.955257i	$0.595579\pi$
$692$		0			0
$693$	−59.3084			−0.0855821
$694$		0			0
$695$	126.716	+	41.2520i	0.182325	+	0.0593554i
$696$		0			0
$697$		−	587.652i		−	0.843116i
$698$		0			0
$699$	−658.921			−0.942663
$700$		0			0
$701$			1335.62i			1.90530i	0.304068	+	0.952650i	$0.401655\pi$
$701$			1335.62i			1.90530i	−0.304068	+	0.952650i	$0.598345\pi$
$702$		0			0
$703$	351.311			0.499731
$704$		0			0
$705$	−44.1178	+	135.519i	−0.0625785	+	0.192226i
$706$		0			0
$707$			26.3908i			0.0373279i
$708$		0			0
$709$		−	362.956i		−	0.511927i	−0.966686	−	0.255964i	$-0.917607\pi$
$709$		−	362.956i		−	0.511927i	0.966686	−	0.255964i	$-0.0823927\pi$
$710$		0			0
$711$		−	297.158i		−	0.417943i
$712$		0			0
$713$			554.891i			0.778249i
$714$		0			0
$715$	−835.374	−	271.953i	−1.16836	−	0.380354i
$716$		0			0
$717$	−426.575			−0.594945
$718$		0			0
$719$		−	648.098i		−	0.901388i	−0.892679	−	0.450694i	$-0.851177\pi$
$719$		−	648.098i		−	0.901388i	0.892679	−	0.450694i	$-0.148823\pi$
$720$		0			0
$721$	−0.986788			−0.00136864
$722$		0			0
$723$			6.41453i			0.00887211i
$724$		0			0
$725$	−653.717	+	897.622i	−0.901679	+	1.23810i
$726$		0			0
$727$	431.123			0.593017			0.296508	−	0.955030i	$-0.404178\pi$
$727$	431.123			0.593017			0.296508	+	0.955030i	$0.404178\pi$
$728$		0			0
$729$	412.506			0.565852
$730$		0			0
$731$	−73.9003			−0.101095
$732$		0			0
$733$	1464.87			1.99846			0.999231	−	0.0392126i	$-0.0124850\pi$
$733$	1464.87			1.99846			0.999231	+	0.0392126i	$0.0124850\pi$
$734$		0			0
$735$	−401.774	+	1234.15i	−0.546632	+	1.67912i
$736$		0			0
$737$		−	67.8073i		−	0.0920044i
$738$		0			0
$739$	−99.1951			−0.134229			−0.0671144	−	0.997745i	$-0.521379\pi$
$739$	−99.1951			−0.134229			−0.0671144	+	0.997745i	$0.521379\pi$
$740$		0			0
$741$			1203.48i			1.62412i
$742$		0			0
$743$	602.719			0.811196			0.405598	−	0.914052i	$-0.367063\pi$
$743$	602.719			0.811196			0.405598	+	0.914052i	$0.367063\pi$
$744$		0			0
$745$	222.049	−	682.081i	0.298053	−	0.915545i
$746$		0			0
$747$		−	974.508i		−	1.30456i
$748$		0			0
$749$		−	22.1529i		−	0.0295767i
$750$		0			0
$751$		−	541.472i		−	0.721001i	−0.932759	−	0.360501i	$-0.882606\pi$
$751$		−	541.472i		−	0.721001i	0.932759	−	0.360501i	$-0.117394\pi$
$752$		0			0
$753$			1123.28i			1.49174i
$754$		0			0
$755$	−129.230	+	396.963i	−0.171166	+	0.525779i
$756$		0			0
$757$	1092.79			1.44358			0.721789	−	0.692113i	$-0.243320\pi$
$757$	1092.79			1.44358			0.721789	+	0.692113i	$0.243320\pi$
$758$		0			0
$759$		−	2167.76i		−	2.85608i
$760$		0			0
$761$	18.7706			0.0246657			0.0123328	−	0.999924i	$-0.496074\pi$
$761$	18.7706			0.0246657			0.0123328	+	0.999924i	$0.496074\pi$
$762$		0			0
$763$		−	11.0893i		−	0.0145338i
$764$		0			0
$765$	−538.149	+	1653.06i	−0.703462	+	2.16086i
$766$		0			0
$767$	−975.773			−1.27219
$768$		0			0
$769$	39.0830			0.0508231			0.0254116	−	0.999677i	$-0.491910\pi$
$769$	39.0830			0.0508231			0.0254116	+	0.999677i	$0.491910\pi$
$770$		0			0
$771$	−968.423			−1.25606
$772$		0			0
$773$	−31.2171			−0.0403843			−0.0201922	−	0.999796i	$-0.506428\pi$
$773$	−31.2171			−0.0403843			−0.0201922	+	0.999796i	$0.506428\pi$
$774$		0			0
$775$	299.977	−	411.900i	0.387067	−	0.531484i
$776$		0			0
$777$		−	19.8395i		−	0.0255334i
$778$		0			0
$779$	−626.699			−0.804492
$780$		0			0
$781$		−	625.529i		−	0.800933i
$782$		0			0
$783$	−2381.75			−3.04183
$784$		0			0
$785$	−806.695	−	262.617i	−1.02764	−	0.334544i
$786$		0			0
$787$			988.563i			1.25612i	0.778167	+	0.628058i	$0.216150\pi$
$787$			988.563i			1.25612i	−0.778167	+	0.628058i	$0.783850\pi$
$788$		0			0
$789$		−	395.880i		−	0.501750i
$790$		0			0
$791$		−	4.23710i		−	0.00535663i
$792$		0			0
$793$		−	429.956i		−	0.542189i
$794$		0			0
$795$	−649.721	+	1995.78i	−0.817259	+	2.51042i
$796$		0			0
$797$	118.920			0.149210			0.0746048	−	0.997213i	$-0.476230\pi$
$797$	118.920			0.149210			0.0746048	+	0.997213i	$0.476230\pi$
$798$		0			0
$799$			97.7933i			0.122395i
$800$		0			0
$801$	208.114			0.259818
$802$		0			0
$803$			624.598i			0.777831i
$804$		0			0
$805$	26.7445	+	8.70658i	0.0332230	+	0.0108156i
$806$		0			0
$807$	−976.072			−1.20951
$808$		0			0
$809$	−1214.04			−1.50067			−0.750337	−	0.661056i	$-0.770109\pi$
$809$	−1214.04			−1.50067			−0.750337	+	0.661056i	$0.770109\pi$
$810$		0			0
$811$	706.666			0.871351			0.435676	−	0.900104i	$-0.356509\pi$
$811$	706.666			0.871351			0.435676	+	0.900104i	$0.356509\pi$
$812$		0			0
$813$	−1244.67			−1.53096
$814$		0			0
$815$	426.380	−	1309.74i	0.523166	−	1.60704i
$816$		0			0
$817$			78.8108i			0.0964636i
$818$		0			0
$819$	46.2060			0.0564176
$820$		0			0
$821$		−	991.775i		−	1.20801i	−0.796981	−	0.604004i	$-0.793571\pi$
$821$		−	991.775i		−	1.20801i	0.796981	−	0.604004i	$-0.206429\pi$
$822$		0			0
$823$	523.998			0.636693			0.318347	−	0.947974i	$-0.396872\pi$
$823$	523.998			0.636693			0.318347	+	0.947974i	$0.396872\pi$
$824$		0			0
$825$	−1171.90	+	1609.15i	−1.42049	+	1.95048i
$826$		0			0
$827$			318.794i			0.385483i	0.981250	+	0.192741i	$0.0617379\pi$
$827$			318.794i			0.385483i	−0.981250	+	0.192741i	$0.938262\pi$
$828$		0			0
$829$		−	1034.11i		−	1.24742i	−0.781655	−	0.623711i	$-0.785624\pi$
$829$		−	1034.11i		−	1.24742i	0.781655	−	0.623711i	$-0.214376\pi$
$830$		0			0
$831$		−	2397.69i		−	2.88531i
$832$		0			0
$833$			890.588i			1.06913i
$834$		0			0
$835$	629.868	+	205.052i	0.754333	+	0.245571i
$836$		0			0
$837$	1092.94			1.30578
$838$		0			0
$839$			445.284i			0.530732i	0.964148	+	0.265366i	$0.0854928\pi$
$839$			445.284i			0.530732i	−0.964148	+	0.265366i	$0.914507\pi$
$840$		0			0
$841$	−1131.91			−1.34591
$842$		0			0
$843$		−	1039.81i		−	1.23346i
$844$		0			0
$845$	−152.671	−	49.7016i	−0.180676	−	0.0588184i
$846$		0			0
$847$	−21.5983			−0.0254997
$848$		0			0
$849$	2218.69			2.61330
$850$		0			0
$851$	493.002			0.579321
$852$		0			0
$853$	−1200.49			−1.40737			−0.703684	−	0.710513i	$-0.748463\pi$
$853$	−1200.49			−1.40737			−0.703684	+	0.710513i	$0.748463\pi$
$854$		0			0
$855$	1762.90	+	573.907i	2.06187	+	0.671236i
$856$		0			0
$857$			1223.15i			1.42724i	0.700531	+	0.713622i	$0.252946\pi$
$857$			1223.15i			1.42724i	−0.700531	+	0.713622i	$0.747054\pi$
$858$		0			0
$859$	210.033			0.244509			0.122254	−	0.992499i	$-0.460988\pi$
$859$	210.033			0.244509			0.122254	+	0.992499i	$0.460988\pi$
$860$		0			0
$861$			35.3914i			0.0411050i
$862$		0			0
$863$	1560.47			1.80819			0.904095	−	0.427333i	$-0.140547\pi$
$863$	1560.47			1.80819			0.904095	+	0.427333i	$0.140547\pi$
$864$		0			0
$865$	−1296.12	−	421.947i	−1.49840	−	0.487800i
$866$		0			0
$867$			222.252i			0.256346i
$868$		0			0
$869$		−	233.483i		−	0.268680i
$870$		0			0
$871$			52.8273i			0.0606513i
$872$		0			0
$873$			232.338i			0.266137i
$874$		0			0
$875$	−15.1458	−	20.9211i	−0.0173095	−	0.0239099i
$876$		0			0
$877$	1011.66			1.15354			0.576771	−	0.816906i	$-0.304313\pi$
$877$	1011.66			1.15354			0.576771	+	0.816906i	$0.304313\pi$
$878$		0			0
$879$			1519.96i			1.72919i
$880$		0			0
$881$	266.455			0.302446			0.151223	−	0.988500i	$-0.451679\pi$
$881$	266.455			0.302446			0.151223	+	0.988500i	$0.451679\pi$
$882$		0			0
$883$			469.871i			0.532130i	0.963955	+	0.266065i	$0.0857237\pi$
$883$			469.871i			0.532130i	−0.963955	+	0.266065i	$0.914276\pi$
$884$		0			0
$885$	−684.431	+	2102.41i	−0.773369	+	2.37560i
$886$		0			0
$887$	−764.559			−0.861961			−0.430980	−	0.902361i	$-0.641832\pi$
$887$	−764.559			−0.861961			−0.430980	+	0.902361i	$0.641832\pi$
$888$		0			0
$889$	−28.6127			−0.0321853
$890$		0			0
$891$	−1686.41			−1.89271
$892$		0			0
$893$	104.291			0.116788
$894$		0			0
$895$	−748.926	−	243.810i	−0.836789	−	0.272414i
$896$		0			0
$897$			1688.86i			1.88279i
$898$		0			0
$899$	905.328			1.00704
$900$		0			0
$901$			1440.20i			1.59844i
$902$		0			0
$903$	4.45065			0.00492874
$904$		0			0
$905$	−518.605	+	1593.03i	−0.573044	+	1.76025i
$906$		0			0
$907$		−	1333.20i		−	1.46990i	−0.678123	−	0.734948i	$-0.737206\pi$
$907$		−	1333.20i		−	1.46990i	0.678123	−	0.734948i	$-0.262794\pi$
$908$		0			0
$909$			2441.20i			2.68559i
$910$		0			0
$911$			1496.11i			1.64227i	0.570736	+	0.821134i	$0.306658\pi$
$911$			1496.11i			1.64227i	−0.570736	+	0.821134i	$0.693342\pi$
$912$		0			0
$913$		−	765.691i		−	0.838654i
$914$		0			0
$915$	−926.385	−	301.582i	−1.01244	−	0.329597i
$916$		0			0
$917$	−45.2725			−0.0493702
$918$		0			0
$919$		−	564.228i		−	0.613959i	−0.951716	−	0.306980i	$-0.900682\pi$
$919$		−	564.228i		−	0.613959i	0.951716	−	0.306980i	$-0.0993183\pi$
$920$		0			0
$921$	1387.66			1.50669
$922$		0			0
$923$			487.337i			0.527993i
$924$		0			0
$925$	−365.959	−	266.519i	−0.395631	−	0.288129i
$926$		0			0
$927$	−91.2798			−0.0984680
$928$		0			0
$929$	1449.16			1.55991			0.779957	−	0.625833i	$-0.215241\pi$
$929$	1449.16			1.55991			0.779957	+	0.625833i	$0.215241\pi$
$930$		0			0
$931$	949.765			1.02016
$932$		0			0
$933$	−3069.46			−3.28988
$934$		0			0
$935$	−422.834	+	1298.84i	−0.452229	+	1.38914i
$936$		0			0
$937$			258.795i			0.276196i	0.990419	+	0.138098i	$0.0440989\pi$
$937$			258.795i			0.276196i	−0.990419	+	0.138098i	$0.955901\pi$
$938$		0			0
$939$	526.573			0.560781
$940$		0			0
$941$			20.3444i			0.0216200i	0.999942	+	0.0108100i	$0.00344100\pi$
$941$			20.3444i			0.0216200i	−0.999942	+	0.0108100i	$0.996559\pi$
$942$		0			0
$943$	−879.461			−0.932620
$944$		0			0
$945$	17.1488	−	52.6770i	0.0181469	−	0.0557429i
$946$		0			0
$947$		−	613.539i		−	0.647876i	−0.946078	−	0.323938i	$-0.894993\pi$
$947$		−	613.539i		−	0.647876i	0.946078	−	0.323938i	$-0.105007\pi$
$948$		0			0
$949$		−	486.612i		−	0.512763i
$950$		0			0
$951$			1016.02i			1.06837i
$952$		0			0
$953$			81.6126i			0.0856376i	0.999083	+	0.0428188i	$0.0136338\pi$
$953$			81.6126i			0.0856376i	−0.999083	+	0.0428188i	$0.986366\pi$
$954$		0			0
$955$	462.129	−	1419.55i	0.483905	−	1.48644i
$956$		0			0
$957$	−3536.80			−3.69571
$958$		0			0
$959$		−	12.3525i		−	0.0128806i
$960$		0			0
$961$	545.564			0.567704
$962$		0			0
$963$		−	2049.19i		−	2.12792i
$964$		0			0
$965$	297.042	−	912.440i	0.307815	−	0.945534i
$966$		0			0
$967$	−127.482			−0.131833			−0.0659165	−	0.997825i	$-0.520997\pi$
$967$	−127.482			−0.131833			−0.0659165	+	0.997825i	$0.520997\pi$
$968$		0			0
$969$	1871.17			1.93103
$970$		0			0
$971$	−1122.62			−1.15615			−0.578076	−	0.815983i	$-0.696196\pi$
$971$	−1122.62			−1.15615			−0.578076	+	0.815983i	$0.696196\pi$
$972$		0			0
$973$	−5.50703			−0.00565985
$974$		0			0
$975$	913.007	−	1253.65i	0.936418	−	1.28580i
$976$		0			0
$977$			424.837i			0.434838i	0.976078	+	0.217419i	$0.0697639\pi$
$977$			424.837i			0.434838i	−0.976078	+	0.217419i	$0.930236\pi$
$978$		0			0
$979$	163.519			0.167027
$980$		0			0
$981$		−	1025.78i		−	1.04565i
$982$		0			0
$983$	663.324			0.674795			0.337398	−	0.941362i	$-0.390453\pi$
$983$	663.324			0.674795			0.337398	+	0.941362i	$0.390453\pi$
$984$		0			0
$985$	281.685	+	91.7017i	0.285975	+	0.0930982i
$986$		0			0
$987$		−	5.88961i		−	0.00596719i
$988$		0			0
$989$			110.597i			0.111827i
$990$		0			0
$991$			1771.36i			1.78745i	0.448616	+	0.893724i	$0.351917\pi$
$991$			1771.36i			1.78745i	−0.448616	+	0.893724i	$0.648083\pi$
$992$		0			0
$993$			2811.15i			2.83097i
$994$		0			0
$995$	478.419	−	1469.59i	0.480823	−	1.47697i
$996$		0			0
$997$	447.066			0.448411			0.224205	−	0.974542i	$-0.428021\pi$
$997$	447.066			0.448411			0.224205	+	0.974542i	$0.428021\pi$
$998$		0			0
$999$		−	971.038i		−	0.972010i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.3.e.i.639.1		6
4.3	odd	2		1280.3.e.h.639.6		6
5.4	even	2		1280.3.e.f.639.6		6
8.3	odd	2		1280.3.e.f.639.1		6
8.5	even	2		1280.3.e.g.639.6		6
16.3	odd	4		320.3.h.f.319.1		6
16.5	even	4		160.3.h.a.159.2	yes	6
16.11	odd	4		160.3.h.b.159.6	yes	6
16.13	even	4		320.3.h.g.319.5		6
20.19	odd	2		1280.3.e.g.639.1		6
40.19	odd	2	inner	1280.3.e.i.639.6		6
40.29	even	2		1280.3.e.h.639.1		6
48.5	odd	4		1440.3.j.a.1279.3		6
48.11	even	4		1440.3.j.b.1279.3		6
80.3	even	4		1600.3.b.v.1151.1		6
80.13	odd	4		1600.3.b.v.1151.6		6
80.19	odd	4		320.3.h.g.319.6		6
80.27	even	4		800.3.b.i.351.1		6
80.29	even	4		320.3.h.f.319.2		6
80.37	odd	4		800.3.b.i.351.6		6
80.43	even	4		800.3.b.h.351.6		6
80.53	odd	4		800.3.b.h.351.1		6
80.59	odd	4		160.3.h.a.159.1	✓	6
80.67	even	4		1600.3.b.w.1151.6		6
80.69	even	4		160.3.h.b.159.5	yes	6
80.77	odd	4		1600.3.b.w.1151.1		6
240.59	even	4		1440.3.j.a.1279.4		6
240.149	odd	4		1440.3.j.b.1279.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.3.h.a.159.1	✓	6	80.59	odd	4
160.3.h.a.159.2	yes	6	16.5	even	4
160.3.h.b.159.5	yes	6	80.69	even	4
160.3.h.b.159.6	yes	6	16.11	odd	4
320.3.h.f.319.1		6	16.3	odd	4
320.3.h.f.319.2		6	80.29	even	4
320.3.h.g.319.5		6	16.13	even	4
320.3.h.g.319.6		6	80.19	odd	4
800.3.b.h.351.1		6	80.53	odd	4
800.3.b.h.351.6		6	80.43	even	4
800.3.b.i.351.1		6	80.27	even	4
800.3.b.i.351.6		6	80.37	odd	4
1280.3.e.f.639.1		6	8.3	odd	2
1280.3.e.f.639.6		6	5.4	even	2
1280.3.e.g.639.1		6	20.19	odd	2
1280.3.e.g.639.6		6	8.5	even	2
1280.3.e.h.639.1		6	40.29	even	2
1280.3.e.h.639.6		6	4.3	odd	2
1280.3.e.i.639.1		6	1.1	even	1	trivial
1280.3.e.i.639.6		6	40.19	odd	2	inner
1440.3.j.a.1279.3		6	48.5	odd	4
1440.3.j.a.1279.4		6	240.59	even	4
1440.3.j.b.1279.3		6	48.11	even	4
1440.3.j.b.1279.4		6	240.149	odd	4
1600.3.b.v.1151.1		6	80.3	even	4
1600.3.b.v.1151.6		6	80.13	odd	4
1600.3.b.w.1151.1		6	80.77	odd	4
1600.3.b.w.1151.6		6	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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1280.e (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-5.30219i q^{3} +(4.75441 + 1.54778i) q^{5} -0.206625 q^{7} -19.1132 q^{9} +O(q^{10})\)	\(q-5.30219i q^{3} +(4.75441 + 1.54778i) q^{5} -0.206625 q^{7} -19.1132 q^{9} -15.0176 q^{11} +11.6999 q^{13} +(8.20662 - 25.2087i) q^{15} -18.1911i q^{17} -19.3999 q^{19} +1.09556i q^{21} -27.2242 q^{23} +(20.2087 + 14.7176i) q^{25} +53.6220i q^{27} +44.4175i q^{29} -20.3822i q^{31} +79.6262i q^{33} +(-0.982377 - 0.319810i) q^{35} -18.1089 q^{37} -62.0352i q^{39} +32.3043 q^{41} -4.06244i q^{43} +(-90.8718 - 29.5830i) q^{45} -5.37588 q^{47} -48.9573 q^{49} -96.4527 q^{51} -79.1703 q^{53} +(-71.3999 - 23.2440i) q^{55} +102.862i q^{57} -83.3999 q^{59} -36.7486i q^{61} +3.94925 q^{63} +(55.6262 + 18.1089i) q^{65} +4.51518i q^{67} +144.348i q^{69} +41.6530i q^{71} -41.5910i q^{73} +(78.0352 - 107.151i) q^{75} +3.10301 q^{77} +15.5473i q^{79} +112.295 q^{81} +50.9862i q^{83} +(28.1559 - 86.4880i) q^{85} +235.510 q^{87} -10.8885 q^{89} -2.41749 q^{91} -108.070 q^{93} +(-92.2349 - 30.0268i) q^{95} -12.1559i q^{97} +287.035 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 8 q^{5} + 12 q^{7} - 18 q^{9}+O(q^{10}) \) 6 * q + 8 * q^5 + 12 * q^7 - 18 * q^9	\( 6 q + 8 q^{5} + 12 q^{7} - 18 q^{9} - 8 q^{11} + 36 q^{15} + 24 q^{19} - 68 q^{23} + 10 q^{25} - 88 q^{35} - 208 q^{37} + 68 q^{41} - 232 q^{45} - 268 q^{47} - 62 q^{49} - 192 q^{51} + 64 q^{53} - 288 q^{55} - 360 q^{59} + 172 q^{63} + 304 q^{75} + 400 q^{77} + 238 q^{81} + 304 q^{85} + 584 q^{87} - 76 q^{89} + 208 q^{91} - 320 q^{93} + 32 q^{95} + 856 q^{99}+O(q^{100}) \) 6 * q + 8 * q^5 + 12 * q^7 - 18 * q^9 - 8 * q^11 + 36 * q^15 + 24 * q^19 - 68 * q^23 + 10 * q^25 - 88 * q^35 - 208 * q^37 + 68 * q^41 - 232 * q^45 - 268 * q^47 - 62 * q^49 - 192 * q^51 + 64 * q^53 - 288 * q^55 - 360 * q^59 + 172 * q^63 + 304 * q^75 + 400 * q^77 + 238 * q^81 + 304 * q^85 + 584 * q^87 - 76 * q^89 + 208 * q^91 - 320 * q^93 + 32 * q^95 + 856 * q^99

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