LMFDB - Embedded newform 1280.2.n.p.767.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1280,2,Mod(767,1280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1280, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("1280.767");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1280 = 2^{8} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1280.n (of order $4$, degree $2$, 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:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.49787136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 320)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			767.4
Root			$-1.09445 - 0.895644i$ of defining polynomial
Character	$\chi$	$=$	1280.767
Dual form			1280.2.n.p.1023.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.18890 + 2.18890i) q^{3} +(2.18890 + 0.456850i) q^{5} +(-1.79129 + 1.79129i) q^{7} +6.58258i q^{9} +O(q^{10})$	\(q+(2.18890 + 2.18890i) q^{3} +(2.18890 + 0.456850i) q^{5} +(-1.79129 + 1.79129i) q^{7} +6.58258i q^{9} +0.913701i q^{11} +(1.73205 - 1.73205i) q^{13} +(3.79129 + 5.79129i) q^{15} +(3.00000 + 3.00000i) q^{17} -3.46410 q^{19} -7.84190 q^{21} +(-3.79129 - 3.79129i) q^{23} +(4.58258 + 2.00000i) q^{25} +(-7.84190 + 7.84190i) q^{27} -5.29150i q^{29} -7.58258i q^{31} +(-2.00000 + 2.00000i) q^{33} +(-4.73930 + 3.10260i) q^{35} +(5.19615 + 5.19615i) q^{37} +7.58258 q^{39} -1.58258 q^{41} +(-0.361500 - 0.361500i) q^{43} +(-3.00725 + 14.4086i) q^{45} +(-3.79129 + 3.79129i) q^{47} +0.582576i q^{49} +13.1334i q^{51} +(2.64575 - 2.64575i) q^{53} +(-0.417424 + 2.00000i) q^{55} +(-7.58258 - 7.58258i) q^{57} +5.29150 q^{59} -6.20520 q^{61} +(-11.7913 - 11.7913i) q^{63} +(4.58258 - 3.00000i) q^{65} +(0.361500 - 0.361500i) q^{67} -16.5975i q^{69} +4.41742i q^{71} +(8.58258 - 8.58258i) q^{73} +(5.65300 + 14.4086i) q^{75} +(-1.63670 - 1.63670i) q^{77} +12.0000 q^{79} -14.5826 q^{81} +(3.10260 + 3.10260i) q^{83} +(5.19615 + 7.93725i) q^{85} +(11.5826 - 11.5826i) q^{87} -15.1652i q^{89} +6.20520i q^{91} +(16.5975 - 16.5975i) q^{93} +(-7.58258 - 1.58258i) q^{95} +(-8.58258 - 8.58258i) q^{97} -6.01450 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{7}+O(q^{10}) $ 8 * q + 4 * q^7	$ 8 q + 4 q^{7} + 12 q^{15} + 24 q^{17} - 12 q^{23} - 16 q^{33} + 24 q^{39} + 24 q^{41} - 12 q^{47} - 40 q^{55} - 24 q^{57} - 76 q^{63} + 32 q^{73} + 96 q^{79} - 80 q^{81} + 56 q^{87} - 24 q^{95} - 32 q^{97}+O(q^{100}) $ 8 * q + 4 * q^7 + 12 * q^15 + 24 * q^17 - 12 * q^23 - 16 * q^33 + 24 * q^39 + 24 * q^41 - 12 * q^47 - 40 * q^55 - 24 * q^57 - 76 * q^63 + 32 * q^73 + 96 * q^79 - 80 * q^81 + 56 * q^87 - 24 * q^95 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$257$	$261$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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
$3$	2.18890	+	2.18890i	1.26376	+	1.26376i	0.949255	+	0.314508i	$0.101839\pi$
$3$	2.18890	+	2.18890i	1.26376	+	1.26376i	0.314508	+	0.949255i	$0.398161\pi$
$4$		0			0
$5$	2.18890	+	0.456850i	0.978906	+	0.204310i
$5$	2.18890	+	0.456850i	0.978906	+	0.204310i
$6$		0			0
$7$	−1.79129	+	1.79129i	−0.677043	+	0.677043i	−0.959330	−	0.282287i	$-0.908907\pi$
$7$	−1.79129	+	1.79129i	−0.677043	+	0.677043i	0.282287	+	0.959330i	$0.408907\pi$
$8$		0			0
$9$			6.58258i			2.19419i
$10$		0			0
$11$			0.913701i			0.275491i	0.990468	+	0.137746i	$0.0439856\pi$
$11$			0.913701i			0.275491i	−0.990468	+	0.137746i	$0.956014\pi$
$12$		0			0
$13$	1.73205	−	1.73205i	0.480384	−	0.480384i	−0.424870	−	0.905254i	$-0.639680\pi$
$13$	1.73205	−	1.73205i	0.480384	−	0.480384i	0.905254	+	0.424870i	$0.139680\pi$
$14$		0			0
$15$	3.79129	+	5.79129i	0.978906	+	1.49530i
$16$		0			0
$17$	3.00000	+	3.00000i	0.727607	+	0.727607i	0.970143	−	0.242536i	$-0.0779791\pi$
$17$	3.00000	+	3.00000i	0.727607	+	0.727607i	−0.242536	+	0.970143i	$0.577979\pi$
$18$		0			0
$19$	−3.46410			−0.794719			−0.397360	−	0.917663i	$-0.630073\pi$
$19$	−3.46410			−0.794719			−0.397360	+	0.917663i	$0.630073\pi$
$20$		0			0
$21$	−7.84190			−1.71124
$22$		0			0
$23$	−3.79129	−	3.79129i	−0.790538	−	0.790538i	0.191043	−	0.981582i	$-0.438813\pi$
$23$	−3.79129	−	3.79129i	−0.790538	−	0.790538i	−0.981582	+	0.191043i	$0.938813\pi$
$24$		0			0
$25$	4.58258	+	2.00000i	0.916515	+	0.400000i
$26$		0			0
$27$	−7.84190	+	7.84190i	−1.50918	+	1.50918i
$28$		0			0
$29$		−	5.29150i		−	0.982607i	−0.870988	−	0.491304i	$-0.836521\pi$
$29$		−	5.29150i		−	0.982607i	0.870988	−	0.491304i	$-0.163479\pi$
$30$		0			0
$31$		−	7.58258i		−	1.36187i	−0.732343	−	0.680935i	$-0.761573\pi$
$31$		−	7.58258i		−	1.36187i	0.732343	−	0.680935i	$-0.238427\pi$
$32$		0			0
$33$	−2.00000	+	2.00000i	−0.348155	+	0.348155i
$34$		0			0
$35$	−4.73930	+	3.10260i	−0.801088	+	0.524435i
$36$		0			0
$37$	5.19615	+	5.19615i	0.854242	+	0.854242i	0.990652	−	0.136410i	$-0.0435565\pi$
$37$	5.19615	+	5.19615i	0.854242	+	0.854242i	−0.136410	+	0.990652i	$0.543557\pi$
$38$		0			0
$39$	7.58258			1.21418
$40$		0			0
$41$	−1.58258			−0.247157			−0.123578	−	0.992335i	$-0.539437\pi$
$41$	−1.58258			−0.247157			−0.123578	+	0.992335i	$0.539437\pi$
$42$		0			0
$43$	−0.361500	−	0.361500i	−0.0551282	−	0.0551282i	0.679005	−	0.734133i	$-0.262411\pi$
$43$	−0.361500	−	0.361500i	−0.0551282	−	0.0551282i	−0.734133	+	0.679005i	$0.762411\pi$
$44$		0			0
$45$	−3.00725	+	14.4086i	−0.448295	+	2.14791i
$46$		0			0
$47$	−3.79129	+	3.79129i	−0.553016	+	0.553016i	−0.927310	−	0.374294i	$-0.877885\pi$
$47$	−3.79129	+	3.79129i	−0.553016	+	0.553016i	0.374294	+	0.927310i	$0.377885\pi$
$48$		0			0
$49$			0.582576i			0.0832251i
$50$		0			0
$51$			13.1334i			1.83904i
$52$		0			0
$53$	2.64575	−	2.64575i	0.363422	−	0.363422i	−0.501649	−	0.865071i	$-0.667273\pi$
$53$	2.64575	−	2.64575i	0.363422	−	0.363422i	0.865071	+	0.501649i	$0.167273\pi$
$54$		0			0
$55$	−0.417424	+	2.00000i	−0.0562855	+	0.269680i
$56$		0			0
$57$	−7.58258	−	7.58258i	−1.00434	−	1.00434i
$58$		0			0
$59$	5.29150			0.688895			0.344447	−	0.938806i	$-0.388066\pi$
$59$	5.29150			0.688895			0.344447	+	0.938806i	$0.388066\pi$
$60$		0			0
$61$	−6.20520			−0.794495			−0.397247	−	0.917712i	$-0.630035\pi$
$61$	−6.20520			−0.794495			−0.397247	+	0.917712i	$0.630035\pi$
$62$		0			0
$63$	−11.7913	−	11.7913i	−1.48556	−	1.48556i
$64$		0			0
$65$	4.58258	−	3.00000i	0.568399	−	0.372104i
$66$		0			0
$67$	0.361500	−	0.361500i	0.0441643	−	0.0441643i	−0.684680	−	0.728844i	$-0.740058\pi$
$67$	0.361500	−	0.361500i	0.0441643	−	0.0441643i	0.728844	+	0.684680i	$0.240058\pi$
$68$		0			0
$69$		−	16.5975i		−	1.99811i
$70$		0			0
$71$			4.41742i			0.524252i	0.965034	+	0.262126i	$0.0844236\pi$
$71$			4.41742i			0.524252i	−0.965034	+	0.262126i	$0.915576\pi$
$72$		0			0
$73$	8.58258	−	8.58258i	1.00451	−	1.00451i	0.00452474	−	0.999990i	$-0.498560\pi$
$73$	8.58258	−	8.58258i	1.00451	−	1.00451i	0.999990	−	0.00452474i	$-0.00144028\pi$
$74$		0			0
$75$	5.65300	+	14.4086i	0.652753	+	1.66376i
$76$		0			0
$77$	−1.63670	−	1.63670i	−0.186519	−	0.186519i
$78$		0			0
$79$	12.0000			1.35011			0.675053	−	0.737769i	$-0.264121\pi$
$79$	12.0000			1.35011			0.675053	+	0.737769i	$0.264121\pi$
$80$		0			0
$81$	−14.5826			−1.62029
$82$		0			0
$83$	3.10260	+	3.10260i	0.340555	+	0.340555i	0.856576	−	0.516021i	$-0.172587\pi$
$83$	3.10260	+	3.10260i	0.340555	+	0.340555i	−0.516021	+	0.856576i	$0.672587\pi$
$84$		0			0
$85$	5.19615	+	7.93725i	0.563602	+	0.860916i
$86$		0			0
$87$	11.5826	−	11.5826i	1.24178	−	1.24178i
$88$		0			0
$89$		−	15.1652i		−	1.60750i	−0.594965	−	0.803751i	$-0.702834\pi$
$89$		−	15.1652i		−	1.60750i	0.594965	−	0.803751i	$-0.297166\pi$
$90$		0			0
$91$			6.20520i			0.650482i
$92$		0			0
$93$	16.5975	−	16.5975i	1.72108	−	1.72108i
$94$		0			0
$95$	−7.58258	−	1.58258i	−0.777956	−	0.162369i
$96$		0			0
$97$	−8.58258	−	8.58258i	−0.871429	−	0.871429i	0.121200	−	0.992628i	$-0.461326\pi$
$97$	−8.58258	−	8.58258i	−0.871429	−	0.871429i	−0.992628	+	0.121200i	$0.961326\pi$
$98$		0			0
$99$	−6.01450			−0.604480
$100$		0			0
$101$	−17.5112			−1.74243			−0.871215	−	0.490901i	$-0.836668\pi$
$101$	−17.5112			−1.74243			−0.871215	+	0.490901i	$0.836668\pi$
$102$		0			0
$103$	3.37386	+	3.37386i	0.332437	+	0.332437i	0.853511	−	0.521075i	$-0.174469\pi$
$103$	3.37386	+	3.37386i	0.332437	+	0.332437i	−0.521075	+	0.853511i	$0.674469\pi$
$104$		0			0
$105$	−17.1652	−	3.58258i	−1.67515	−	0.349624i
$106$		0			0
$107$	−0.361500	+	0.361500i	−0.0349475	+	0.0349475i	−0.724365	−	0.689417i	$-0.757867\pi$
$107$	−0.361500	+	0.361500i	−0.0349475	+	0.0349475i	0.689417	+	0.724365i	$0.257867\pi$
$108$		0			0
$109$			9.66930i			0.926151i	0.886319	+	0.463076i	$0.153254\pi$
$109$			9.66930i			0.926151i	−0.886319	+	0.463076i	$0.846746\pi$
$110$		0			0
$111$			22.7477i			2.15912i
$112$		0			0
$113$	4.58258	−	4.58258i	0.431092	−	0.431092i	−0.457907	−	0.889000i	$-0.651401\pi$
$113$	4.58258	−	4.58258i	0.431092	−	0.431092i	0.889000	+	0.457907i	$0.151401\pi$
$114$		0			0
$115$	−6.56670	−	10.0308i	−0.612348	−	0.935377i
$116$		0			0
$117$	11.4014	+	11.4014i	1.05406	+	1.05406i
$118$		0			0
$119$	−10.7477			−0.985243
$120$		0			0
$121$	10.1652			0.924105
$122$		0			0
$123$	−3.46410	−	3.46410i	−0.312348	−	0.312348i
$124$		0			0
$125$	9.11710	+	6.47135i	0.815459	+	0.578815i
$126$		0			0
$127$	5.79129	−	5.79129i	0.513894	−	0.513894i	−0.401823	−	0.915717i	$-0.631623\pi$
$127$	5.79129	−	5.79129i	0.513894	−	0.513894i	0.915717	+	0.401823i	$0.131623\pi$
$128$		0			0
$129$		−	1.58258i		−	0.139338i
$130$		0			0
$131$			6.01450i			0.525490i	0.964865	+	0.262745i	$0.0846277\pi$
$131$			6.01450i			0.525490i	−0.964865	+	0.262745i	$0.915372\pi$
$132$		0			0
$133$	6.20520	−	6.20520i	0.538059	−	0.538059i
$134$		0			0
$135$	−20.7477	+	13.5826i	−1.78568	+	1.16900i
$136$		0			0
$137$	6.16515	+	6.16515i	0.526724	+	0.526724i	0.919594	−	0.392870i	$-0.128518\pi$
$137$	6.16515	+	6.16515i	0.526724	+	0.526724i	−0.392870	+	0.919594i	$0.628518\pi$
$138$		0			0
$139$	−22.8027			−1.93410			−0.967050	−	0.254585i	$-0.918061\pi$
$139$	−22.8027			−1.93410			−0.967050	+	0.254585i	$0.918061\pi$
$140$		0			0
$141$	−16.5975			−1.39776
$142$		0			0
$143$	1.58258	+	1.58258i	0.132342	+	0.132342i
$144$		0			0
$145$	2.41742	−	11.5826i	0.200756	−	0.961881i
$146$		0			0
$147$	−1.27520	+	1.27520i	−0.105177	+	0.105177i
$148$		0			0
$149$			0.913701i			0.0748533i	0.999299	+	0.0374266i	$0.0119160\pi$
$149$			0.913701i			0.0748533i	−0.999299	+	0.0374266i	$0.988084\pi$
$150$		0			0
$151$			14.7477i			1.20015i	0.799943	+	0.600077i	$0.204863\pi$
$151$			14.7477i			1.20015i	−0.799943	+	0.600077i	$0.795137\pi$
$152$		0			0
$153$	−19.7477	+	19.7477i	−1.59651	+	1.59651i
$154$		0			0
$155$	3.46410	−	16.5975i	0.278243	−	1.33314i
$156$		0			0
$157$	−4.47315	−	4.47315i	−0.356996	−	0.356996i	0.505708	−	0.862705i	$-0.331231\pi$
$157$	−4.47315	−	4.47315i	−0.356996	−	0.356996i	−0.862705	+	0.505708i	$0.831231\pi$
$158$		0			0
$159$	11.5826			0.918558
$160$		0			0
$161$	13.5826			1.07046
$162$		0			0
$163$	0.361500	+	0.361500i	0.0283149	+	0.0283149i	0.721122	−	0.692808i	$-0.243626\pi$
$163$	0.361500	+	0.361500i	0.0283149	+	0.0283149i	−0.692808	+	0.721122i	$0.743626\pi$
$164$		0			0
$165$	−5.29150	+	3.46410i	−0.411943	+	0.269680i
$166$		0			0
$167$	15.7913	−	15.7913i	1.22197	−	1.22197i	0.255035	−	0.966932i	$-0.417913\pi$
$167$	15.7913	−	15.7913i	1.22197	−	1.22197i	0.966932	−	0.255035i	$-0.0820869\pi$
$168$		0			0
$169$			7.00000i			0.538462i
$170$		0			0
$171$		−	22.8027i		−	1.74377i
$172$		0			0
$173$	−8.66025	+	8.66025i	−0.658427	+	0.658427i	−0.955008	−	0.296581i	$-0.904154\pi$
$173$	−8.66025	+	8.66025i	−0.658427	+	0.658427i	0.296581	+	0.955008i	$0.404154\pi$
$174$		0			0
$175$	−11.7913	+	4.62614i	−0.891338	+	0.349703i
$176$		0			0
$177$	11.5826	+	11.5826i	0.870600	+	0.870600i
$178$		0			0
$179$	19.1479			1.43118			0.715591	−	0.698520i	$-0.246157\pi$
$179$	19.1479			1.43118			0.715591	+	0.698520i	$0.246157\pi$
$180$		0			0
$181$	−6.92820			−0.514969			−0.257485	−	0.966282i	$-0.582894\pi$
$181$	−6.92820			−0.514969			−0.257485	+	0.966282i	$0.582894\pi$
$182$		0			0
$183$	−13.5826	−	13.5826i	−1.00405	−	1.00405i
$184$		0			0
$185$	9.00000	+	13.7477i	0.661693	+	1.01075i
$186$		0			0
$187$	−2.74110	+	2.74110i	−0.200449	+	0.200449i
$188$		0			0
$189$		−	28.0942i		−	2.04355i
$190$		0			0
$191$			4.41742i			0.319634i	0.987147	+	0.159817i	$0.0510903\pi$
$191$			4.41742i			0.319634i	−0.987147	+	0.159817i	$0.948910\pi$
$192$		0			0
$193$	−4.16515	+	4.16515i	−0.299814	+	0.299814i	−0.840941	−	0.541127i	$-0.817998\pi$
$193$	−4.16515	+	4.16515i	−0.299814	+	0.299814i	0.541127	+	0.840941i	$0.317998\pi$
$194$		0			0
$195$	16.5975	+	3.46410i	1.18857	+	0.248069i
$196$		0			0
$197$	−2.64575	−	2.64575i	−0.188502	−	0.188502i	0.606546	−	0.795048i	$-0.292554\pi$
$197$	−2.64575	−	2.64575i	−0.188502	−	0.188502i	−0.795048	+	0.606546i	$0.792554\pi$
$198$		0			0
$199$	4.00000			0.283552			0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000			0.283552			0.141776	+	0.989899i	$0.454719\pi$
$200$		0			0
$201$	1.58258			0.111626
$202$		0			0
$203$	9.47860	+	9.47860i	0.665268	+	0.665268i
$204$		0			0
$205$	−3.46410	−	0.723000i	−0.241943	−	0.0504965i
$206$		0			0
$207$	24.9564	−	24.9564i	1.73459	−	1.73459i
$208$		0			0
$209$		−	3.16515i		−	0.218938i
$210$		0			0
$211$		−	23.5257i		−	1.61958i	−0.586722	−	0.809788i	$-0.699582\pi$
$211$		−	23.5257i		−	1.61958i	0.586722	−	0.809788i	$-0.300418\pi$
$212$		0			0
$213$	−9.66930	+	9.66930i	−0.662530	+	0.662530i
$214$		0			0
$215$	−0.626136	−	0.956439i	−0.0427022	−	0.0652286i
$216$		0			0
$217$	13.5826	+	13.5826i	0.922045	+	0.922045i
$218$		0			0
$219$	37.5728			2.53894
$220$		0			0
$221$	10.3923			0.699062
$222$		0			0
$223$	1.37386	+	1.37386i	0.0920007	+	0.0920007i	0.751609	−	0.659609i	$-0.229278\pi$
$223$	1.37386	+	1.37386i	0.0920007	+	0.0920007i	−0.659609	+	0.751609i	$0.729278\pi$
$224$		0			0
$225$	−13.1652	+	30.1652i	−0.877677	+	2.01101i
$226$		0			0
$227$	11.8582	−	11.8582i	0.787057	−	0.787057i	−0.193954	−	0.981011i	$-0.562131\pi$
$227$	11.8582	−	11.8582i	0.787057	−	0.787057i	0.981011	+	0.193954i	$0.0621312\pi$
$228$		0			0
$229$			3.46410i			0.228914i	0.993428	+	0.114457i	$0.0365129\pi$
$229$			3.46410i			0.228914i	−0.993428	+	0.114457i	$0.963487\pi$
$230$		0			0
$231$		−	7.16515i		−	0.471432i
$232$		0			0
$233$	12.1652	−	12.1652i	0.796966	−	0.796966i	−0.185650	−	0.982616i	$-0.559439\pi$
$233$	12.1652	−	12.1652i	0.796966	−	0.796966i	0.982616	+	0.185650i	$0.0594392\pi$
$234$		0			0
$235$	−10.0308	+	6.56670i	−0.654338	+	0.428364i
$236$		0			0
$237$	26.2668	+	26.2668i	1.70621	+	1.70621i
$238$		0			0
$239$	−15.1652			−0.980952			−0.490476	−	0.871455i	$-0.663177\pi$
$239$	−15.1652			−0.980952			−0.490476	+	0.871455i	$0.663177\pi$
$240$		0			0
$241$	16.7477			1.07882			0.539408	−	0.842045i	$-0.318648\pi$
$241$	16.7477			1.07882			0.539408	+	0.842045i	$0.318648\pi$
$242$		0			0
$243$	−8.39410	−	8.39410i	−0.538482	−	0.538482i
$244$		0			0
$245$	−0.266150	+	1.27520i	−0.0170037	+	0.0814696i
$246$		0			0
$247$	−6.00000	+	6.00000i	−0.381771	+	0.381771i
$248$		0			0
$249$			13.5826i			0.860761i
$250$		0			0
$251$			12.9427i			0.816936i	0.912773	+	0.408468i	$0.133937\pi$
$251$			12.9427i			0.816936i	−0.912773	+	0.408468i	$0.866063\pi$
$252$		0			0
$253$	3.46410	−	3.46410i	0.217786	−	0.217786i
$254$		0			0
$255$	−6.00000	+	28.7477i	−0.375735	+	1.80025i
$256$		0			0
$257$	7.74773	+	7.74773i	0.483290	+	0.483290i	0.906181	−	0.422891i	$-0.138985\pi$
$257$	7.74773	+	7.74773i	0.483290	+	0.483290i	−0.422891	+	0.906181i	$0.638985\pi$
$258$		0			0
$259$	−18.6156			−1.15672
$260$		0			0
$261$	34.8317			2.15603
$262$		0			0
$263$	−14.2087	−	14.2087i	−0.876147	−	0.876147i	0.116987	−	0.993133i	$-0.462676\pi$
$263$	−14.2087	−	14.2087i	−0.876147	−	0.876147i	−0.993133	+	0.116987i	$0.962676\pi$
$264$		0			0
$265$	7.00000	−	4.58258i	0.430007	−	0.281505i
$266$		0			0
$267$	33.1950	−	33.1950i	2.03150	−	2.03150i
$268$		0			0
$269$			13.3241i			0.812385i	0.913788	+	0.406193i	$0.133144\pi$
$269$			13.3241i			0.812385i	−0.913788	+	0.406193i	$0.866856\pi$
$270$		0			0
$271$		−	18.7477i		−	1.13884i	−0.822046	−	0.569422i	$-0.807167\pi$
$271$		−	18.7477i		−	1.13884i	0.822046	−	0.569422i	$-0.192833\pi$
$272$		0			0
$273$	−13.5826	+	13.5826i	−0.822055	+	0.822055i
$274$		0			0
$275$	−1.82740	+	4.18710i	−0.110196	+	0.252492i
$276$		0			0
$277$	−21.7937	−	21.7937i	−1.30945	−	1.30945i	−0.921808	−	0.387646i	$-0.873288\pi$
$277$	−21.7937	−	21.7937i	−1.30945	−	1.30945i	−0.387646	−	0.921808i	$-0.626712\pi$
$278$		0			0
$279$	49.9129			2.98821
$280$		0			0
$281$	−16.7477			−0.999086			−0.499543	−	0.866289i	$-0.666499\pi$
$281$	−16.7477			−0.999086			−0.499543	+	0.866289i	$0.666499\pi$
$282$		0			0
$283$	−22.4412	−	22.4412i	−1.33399	−	1.33399i	−0.901765	−	0.432226i	$-0.857728\pi$
$283$	−22.4412	−	22.4412i	−1.33399	−	1.33399i	−0.432226	−	0.901765i	$-0.642272\pi$
$284$		0			0
$285$	−13.1334	−	20.0616i	−0.777956	−	1.18835i
$286$		0			0
$287$	2.83485	−	2.83485i	0.167336	−	0.167336i
$288$		0			0
$289$			1.00000i			0.0588235i
$290$		0			0
$291$		−	37.5728i		−	2.20256i
$292$		0			0
$293$	18.1389	−	18.1389i	1.05968	−	1.05968i	0.0615814	−	0.998102i	$-0.480386\pi$
$293$	18.1389	−	18.1389i	1.05968	−	1.05968i	0.998102	−	0.0615814i	$-0.0196144\pi$
$294$		0			0
$295$	11.5826	+	2.41742i	0.674364	+	0.140748i
$296$		0			0
$297$	−7.16515	−	7.16515i	−0.415764	−	0.415764i
$298$		0			0
$299$	−13.1334			−0.759525
$300$		0			0
$301$	1.29510			0.0746484
$302$		0			0
$303$	−38.3303	−	38.3303i	−2.20202	−	2.20202i
$304$		0			0
$305$	−13.5826	−	2.83485i	−0.777736	−	0.162323i
$306$		0			0
$307$	−6.56670	+	6.56670i	−0.374782	+	0.374782i	−0.869215	−	0.494434i	$-0.835375\pi$
$307$	−6.56670	+	6.56670i	−0.374782	+	0.374782i	0.494434	+	0.869215i	$0.335375\pi$
$308$		0			0
$309$			14.7701i			0.840242i
$310$		0			0
$311$			19.5826i			1.11043i	0.831708	+	0.555213i	$0.187363\pi$
$311$			19.5826i			1.11043i	−0.831708	+	0.555213i	$0.812637\pi$
$312$		0			0
$313$	6.58258	−	6.58258i	0.372069	−	0.372069i	−0.496161	−	0.868230i	$-0.665258\pi$
$313$	6.58258	−	6.58258i	0.372069	−	0.372069i	0.868230	+	0.496161i	$0.165258\pi$
$314$		0			0
$315$	−20.4231	−	31.1968i	−1.15071	−	1.75774i
$316$		0			0
$317$	−14.1425	−	14.1425i	−0.794320	−	0.794320i	0.187874	−	0.982193i	$-0.439840\pi$
$317$	−14.1425	−	14.1425i	−0.794320	−	0.794320i	−0.982193	+	0.187874i	$0.939840\pi$
$318$		0			0
$319$	4.83485			0.270700
$320$		0			0
$321$	−1.58258			−0.0883308
$322$		0			0
$323$	−10.3923	−	10.3923i	−0.578243	−	0.578243i
$324$		0			0
$325$	11.4014	−	4.47315i	0.632433	−	0.248126i
$326$		0			0
$327$	−21.1652	+	21.1652i	−1.17044	+	1.17044i
$328$		0			0
$329$		−	13.5826i		−	0.748832i
$330$		0			0
$331$		−	9.66930i		−	0.531473i	−0.964046	−	0.265737i	$-0.914385\pi$
$331$		−	9.66930i		−	0.531473i	0.964046	−	0.265737i	$-0.0856151\pi$
$332$		0			0
$333$	−34.2041	+	34.2041i	−1.87437	+	1.87437i
$334$		0			0
$335$	0.956439	−	0.626136i	0.0522559	−	0.0342095i
$336$		0			0
$337$	1.00000	+	1.00000i	0.0544735	+	0.0544735i	0.733819	−	0.679345i	$-0.237736\pi$
$337$	1.00000	+	1.00000i	0.0544735	+	0.0544735i	−0.679345	+	0.733819i	$0.737736\pi$
$338$		0			0
$339$	20.0616			1.08960
$340$		0			0
$341$	6.92820			0.375183
$342$		0			0
$343$	−13.5826	−	13.5826i	−0.733390	−	0.733390i
$344$		0			0
$345$	7.58258	−	36.3303i	0.408232	−	1.95596i
$346$		0			0
$347$	−1.27520	+	1.27520i	−0.0684564	+	0.0684564i	−0.740506	−	0.672050i	$-0.765414\pi$
$347$	−1.27520	+	1.27520i	−0.0684564	+	0.0684564i	0.672050	+	0.740506i	$0.265414\pi$
$348$		0			0
$349$			10.3923i			0.556287i	0.960539	+	0.278144i	$0.0897191\pi$
$349$			10.3923i			0.556287i	−0.960539	+	0.278144i	$0.910281\pi$
$350$		0			0
$351$			27.1652i			1.44997i
$352$		0			0
$353$	24.1652	−	24.1652i	1.28618	−	1.28618i	0.349093	−	0.937088i	$-0.386490\pi$
$353$	24.1652	−	24.1652i	1.28618	−	1.28618i	0.937088	−	0.349093i	$-0.113510\pi$
$354$		0			0
$355$	−2.01810	+	9.66930i	−0.107110	+	0.513193i
$356$		0			0
$357$	−23.5257	−	23.5257i	−1.24511	−	1.24511i
$358$		0			0
$359$	27.1652			1.43372			0.716861	−	0.697216i	$-0.245578\pi$
$359$	27.1652			1.43372			0.716861	+	0.697216i	$0.245578\pi$
$360$		0			0
$361$	−7.00000			−0.368421
$362$		0			0
$363$	22.2505	+	22.2505i	1.16785	+	1.16785i
$364$		0			0
$365$	22.7074	−	14.8655i	1.18856	−	0.778094i
$366$		0			0
$367$	−16.5390	+	16.5390i	−0.863330	+	0.863330i	−0.991723	−	0.128394i	$-0.959018\pi$
$367$	−16.5390	+	16.5390i	−0.863330	+	0.863330i	0.128394	+	0.991723i	$0.459018\pi$
$368$		0			0
$369$		−	10.4174i		−	0.542309i
$370$		0			0
$371$			9.47860i			0.492105i
$372$		0			0
$373$	−5.19615	+	5.19615i	−0.269047	+	0.269047i	−0.828716	−	0.559669i	$-0.810928\pi$
$373$	−5.19615	+	5.19615i	−0.269047	+	0.269047i	0.559669	+	0.828716i	$0.310928\pi$
$374$		0			0
$375$	5.79129	+	34.1216i	0.299061	+	1.76203i
$376$		0			0
$377$	−9.16515	−	9.16515i	−0.472029	−	0.472029i
$378$		0			0
$379$	10.3923			0.533817			0.266908	−	0.963722i	$-0.413998\pi$
$379$	10.3923			0.533817			0.266908	+	0.963722i	$0.413998\pi$
$380$		0			0
$381$	25.3531			1.29888
$382$		0			0
$383$	17.3739	+	17.3739i	0.887763	+	0.887763i	0.994308	−	0.106545i	$-0.0339788\pi$
$383$	17.3739	+	17.3739i	0.887763	+	0.887763i	−0.106545	+	0.994308i	$0.533979\pi$
$384$		0			0
$385$	−2.83485	−	4.33030i	−0.144477	−	0.220693i
$386$		0			0
$387$	2.37960	−	2.37960i	0.120962	−	0.120962i
$388$		0			0
$389$			35.5547i			1.80270i	0.433096	+	0.901348i	$0.357421\pi$
$389$			35.5547i			1.80270i	−0.433096	+	0.901348i	$0.642579\pi$
$390$		0			0
$391$		−	22.7477i		−	1.15040i
$392$		0			0
$393$	−13.1652	+	13.1652i	−0.664094	+	0.664094i
$394$		0			0
$395$	26.2668	+	5.48220i	1.32163	+	0.275840i
$396$		0			0
$397$	−7.93725	−	7.93725i	−0.398359	−	0.398359i	0.479295	−	0.877654i	$-0.340893\pi$
$397$	−7.93725	−	7.93725i	−0.398359	−	0.398359i	−0.877654	+	0.479295i	$0.840893\pi$
$398$		0			0
$399$	27.1652			1.35996
$400$		0			0
$401$	−24.3303			−1.21500			−0.607499	−	0.794321i	$-0.707827\pi$
$401$	−24.3303			−1.21500			−0.607499	+	0.794321i	$0.707827\pi$
$402$		0			0
$403$	−13.1334	−	13.1334i	−0.654222	−	0.654222i
$404$		0			0
$405$	−31.9198	−	6.66205i	−1.58611	−	0.331040i
$406$		0			0
$407$	−4.74773	+	4.74773i	−0.235336	+	0.235336i
$408$		0			0
$409$		−	16.4174i		−	0.811789i	−0.913920	−	0.405895i	$-0.866960\pi$
$409$		−	16.4174i		−	0.811789i	0.913920	−	0.405895i	$-0.133040\pi$
$410$		0			0
$411$			26.9898i			1.33131i
$412$		0			0
$413$	−9.47860	+	9.47860i	−0.466412	+	0.466412i
$414$		0			0
$415$	5.37386	+	8.20871i	0.263793	+	0.402950i
$416$		0			0
$417$	−49.9129	−	49.9129i	−2.44424	−	2.44424i
$418$		0			0
$419$	20.9753			1.02471			0.512355	−	0.858773i	$-0.328773\pi$
$419$	20.9753			1.02471			0.512355	+	0.858773i	$0.328773\pi$
$420$		0			0
$421$	13.1334			0.640083			0.320042	−	0.947404i	$-0.396303\pi$
$421$	13.1334			0.640083			0.320042	+	0.947404i	$0.396303\pi$
$422$		0			0
$423$	−24.9564	−	24.9564i	−1.21342	−	1.21342i
$424$		0			0
$425$	7.74773	+	19.7477i	0.375820	+	0.957905i
$426$		0			0
$427$	11.1153	−	11.1153i	0.537907	−	0.537907i
$428$		0			0
$429$			6.92820i			0.334497i
$430$		0			0
$431$		−	10.7477i		−	0.517700i	−0.965918	−	0.258850i	$-0.916656\pi$
$431$		−	10.7477i		−	0.517700i	0.965918	−	0.258850i	$-0.0833435\pi$
$432$		0			0
$433$	−5.41742	+	5.41742i	−0.260345	+	0.260345i	−0.825194	−	0.564849i	$-0.808934\pi$
$433$	−5.41742	+	5.41742i	−0.260345	+	0.260345i	0.564849	+	0.825194i	$0.308934\pi$
$434$		0			0
$435$	30.6446	−	20.0616i	1.46930	−	0.961881i
$436$		0			0
$437$	13.1334	+	13.1334i	0.628256	+	0.628256i
$438$		0			0
$439$	−25.4955			−1.21683			−0.608416	−	0.793618i	$-0.708195\pi$
$439$	−25.4955			−1.21683			−0.608416	+	0.793618i	$0.708195\pi$
$440$		0			0
$441$	−3.83485			−0.182612
$442$		0			0
$443$	14.4086	+	14.4086i	0.684574	+	0.684574i	0.961027	−	0.276454i	$-0.0891592\pi$
$443$	14.4086	+	14.4086i	0.684574	+	0.684574i	−0.276454	+	0.961027i	$0.589159\pi$
$444$		0			0
$445$	6.92820	−	33.1950i	0.328428	−	1.57359i
$446$		0			0
$447$	−2.00000	+	2.00000i	−0.0945968	+	0.0945968i
$448$		0			0
$449$			19.5826i			0.924159i	0.886839	+	0.462079i	$0.152897\pi$
$449$			19.5826i			0.924159i	−0.886839	+	0.462079i	$0.847103\pi$
$450$		0			0
$451$		−	1.44600i		−	0.0680895i
$452$		0			0
$453$	−32.2813	+	32.2813i	−1.51671	+	1.51671i
$454$		0			0
$455$	−2.83485	+	13.5826i	−0.132900	+	0.636761i
$456$		0			0
$457$	−12.5826	−	12.5826i	−0.588588	−	0.588588i	0.348661	−	0.937249i	$-0.386636\pi$
$457$	−12.5826	−	12.5826i	−0.588588	−	0.588588i	−0.937249	+	0.348661i	$0.886636\pi$
$458$		0			0
$459$	−47.0514			−2.19617
$460$		0			0
$461$	−3.65480			−0.170221			−0.0851106	−	0.996372i	$-0.527124\pi$
$461$	−3.65480			−0.170221			−0.0851106	+	0.996372i	$0.527124\pi$
$462$		0			0
$463$	−12.2087	−	12.2087i	−0.567387	−	0.567387i	0.364009	−	0.931396i	$-0.381408\pi$
$463$	−12.2087	−	12.2087i	−0.567387	−	0.567387i	−0.931396	+	0.364009i	$0.881408\pi$
$464$		0			0
$465$	43.9129	−	28.7477i	2.03641	−	1.33314i
$466$		0			0
$467$	−16.2360	+	16.2360i	−0.751313	+	0.751313i	−0.974724	−	0.223411i	$-0.928281\pi$
$467$	−16.2360	+	16.2360i	−0.751313	+	0.751313i	0.223411	+	0.974724i	$0.428281\pi$
$468$		0			0
$469$			1.29510i			0.0598022i
$470$		0			0
$471$		−	19.5826i		−	0.902317i
$472$		0			0
$473$	0.330303	−	0.330303i	0.0151873	−	0.0151873i
$474$		0			0
$475$	−15.8745	−	6.92820i	−0.728372	−	0.317888i
$476$		0			0
$477$	17.4159	+	17.4159i	0.797417	+	0.797417i
$478$		0			0
$479$	33.4955			1.53045			0.765223	−	0.643765i	$-0.222629\pi$
$479$	33.4955			1.53045			0.765223	+	0.643765i	$0.222629\pi$
$480$		0			0
$481$	18.0000			0.820729
$482$		0			0
$483$	29.7309	+	29.7309i	1.35280	+	1.35280i
$484$		0			0
$485$	−14.8655	−	22.7074i	−0.675006	−	1.03109i
$486$		0			0
$487$	13.3739	−	13.3739i	0.606028	−	0.606028i	−0.335878	−	0.941906i	$-0.609033\pi$
$487$	13.3739	−	13.3739i	0.606028	−	0.606028i	0.941906	+	0.335878i	$0.109033\pi$
$488$		0			0
$489$			1.58258i			0.0715665i
$490$		0			0
$491$		−	27.1805i		−	1.22664i	−0.789835	−	0.613320i	$-0.789834\pi$
$491$		−	27.1805i		−	1.22664i	0.789835	−	0.613320i	$-0.210166\pi$
$492$		0			0
$493$	15.8745	−	15.8745i	0.714952	−	0.714952i
$494$		0			0
$495$	−13.1652	−	2.74773i	−0.591730	−	0.123501i
$496$		0			0
$497$	−7.91288	−	7.91288i	−0.354941	−	0.354941i
$498$		0			0
$499$	−24.2487			−1.08552			−0.542761	−	0.839887i	$-0.682621\pi$
$499$	−24.2487			−1.08552			−0.542761	+	0.839887i	$0.682621\pi$
$500$		0			0
$501$	69.1311			3.08855
$502$		0			0
$503$	14.5390	+	14.5390i	0.648263	+	0.648263i	0.952573	−	0.304310i	$-0.0984260\pi$
$503$	14.5390	+	14.5390i	0.648263	+	0.648263i	−0.304310	+	0.952573i	$0.598426\pi$
$504$		0			0
$505$	−38.3303	−	8.00000i	−1.70568	−	0.355995i
$506$		0			0
$507$	−15.3223	+	15.3223i	−0.680488	+	0.680488i
$508$		0			0
$509$			3.84550i			0.170449i	0.996362	+	0.0852244i	$0.0271607\pi$
$509$			3.84550i			0.170449i	−0.996362	+	0.0852244i	$0.972839\pi$
$510$		0			0
$511$			30.7477i			1.36020i
$512$		0			0
$513$	27.1652	−	27.1652i	1.19937	−	1.19937i
$514$		0			0
$515$	5.84370	+	8.92640i	0.257504	+	0.393344i
$516$		0			0
$517$	−3.46410	−	3.46410i	−0.152351	−	0.152351i
$518$		0			0
$519$	−37.9129			−1.66419
$520$		0			0
$521$	14.8348			0.649927			0.324963	−	0.945727i	$-0.394648\pi$
$521$	14.8348			0.649927			0.324963	+	0.945727i	$0.394648\pi$
$522$		0			0
$523$	−23.8872	−	23.8872i	−1.04451	−	1.04451i	−0.998962	−	0.0455529i	$-0.985495\pi$
$523$	−23.8872	−	23.8872i	−1.04451	−	1.04451i	−0.0455529	−	0.998962i	$-0.514505\pi$
$524$		0			0
$525$	−35.9361	−	15.6838i	−1.56838	−	0.684497i
$526$		0			0
$527$	22.7477	−	22.7477i	0.990907	−	0.990907i
$528$		0			0
$529$			5.74773i			0.249901i
$530$		0			0
$531$			34.8317i			1.51157i
$532$		0			0
$533$	−2.74110	+	2.74110i	−0.118730	+	0.118730i
$534$		0			0
$535$	−0.956439	+	0.626136i	−0.0413505	+	0.0270702i
$536$		0			0
$537$	41.9129	+	41.9129i	1.80867	+	1.80867i
$538$		0			0
$539$	−0.532300			−0.0229278
$540$		0			0
$541$		0			0			−	1.00000i	$-0.5\pi$
$541$		0			0				1.00000i	$0.5\pi$
$542$		0			0
$543$	−15.1652	−	15.1652i	−0.650799	−	0.650799i
$544$		0			0
$545$	−4.41742	+	21.1652i	−0.189222	+	0.906615i
$546$		0			0
$547$	−23.1642	+	23.1642i	−0.990430	+	0.990430i	−0.999955	−	0.00952449i	$-0.996968\pi$
$547$	−23.1642	+	23.1642i	−0.990430	+	0.990430i	0.00952449	+	0.999955i	$0.496968\pi$
$548$		0			0
$549$		−	40.8462i		−	1.74327i
$550$		0			0
$551$			18.3303i			0.780897i
$552$		0			0
$553$	−21.4955	+	21.4955i	−0.914080	+	0.914080i
$554$		0			0
$555$	−10.3923	+	49.7925i	−0.441129	+	2.11357i
$556$		0			0
$557$	−20.8800	−	20.8800i	−0.884712	−	0.884712i	0.109297	−	0.994009i	$-0.465140\pi$
$557$	−20.8800	−	20.8800i	−0.884712	−	0.884712i	−0.994009	+	0.109297i	$0.965140\pi$
$558$		0			0
$559$	−1.25227			−0.0529655
$560$		0			0
$561$	−12.0000			−0.506640
$562$		0			0
$563$	−11.6675	−	11.6675i	−0.491727	−	0.491727i	0.417123	−	0.908850i	$-0.363038\pi$
$563$	−11.6675	−	11.6675i	−0.491727	−	0.491727i	−0.908850	+	0.417123i	$0.863038\pi$
$564$		0			0
$565$	12.1244	−	7.93725i	0.510075	−	0.333923i
$566$		0			0
$567$	26.1216	−	26.1216i	1.09700	−	1.09700i
$568$		0			0
$569$			22.7477i			0.953634i	0.879002	+	0.476817i	$0.158210\pi$
$569$			22.7477i			0.953634i	−0.879002	+	0.476817i	$0.841790\pi$
$570$		0			0
$571$			8.22330i			0.344135i	0.985085	+	0.172067i	$0.0550447\pi$
$571$			8.22330i			0.344135i	−0.985085	+	0.172067i	$0.944955\pi$
$572$		0			0
$573$	−9.66930	+	9.66930i	−0.403941	+	0.403941i
$574$		0			0
$575$	−9.79129	−	24.9564i	−0.408325	−	1.04076i
$576$		0			0
$577$	15.7477	+	15.7477i	0.655586	+	0.655586i	0.954333	−	0.298746i	$-0.0965684\pi$
$577$	15.7477	+	15.7477i	0.655586	+	0.655586i	−0.298746	+	0.954333i	$0.596568\pi$
$578$		0			0
$579$	−18.2342			−0.757788
$580$		0			0
$581$	−11.1153			−0.461141
$582$		0			0
$583$	2.41742	+	2.41742i	0.100119	+	0.100119i
$584$		0			0
$585$	19.7477	+	30.1652i	0.816468	+	1.24718i
$586$		0			0
$587$	−4.54860	+	4.54860i	−0.187741	+	0.187741i	−0.794719	−	0.606978i	$-0.792382\pi$
$587$	−4.54860	+	4.54860i	−0.187741	+	0.187741i	0.606978	+	0.794719i	$0.292382\pi$
$588$		0			0
$589$			26.2668i			1.08231i
$590$		0			0
$591$		−	11.5826i		−	0.476444i
$592$		0			0
$593$	−18.1652	+	18.1652i	−0.745953	+	0.745953i	−0.973717	−	0.227763i	$-0.926859\pi$
$593$	−18.1652	+	18.1652i	−0.745953	+	0.745953i	0.227763	+	0.973717i	$0.426859\pi$
$594$		0			0
$595$	−23.5257	−	4.91010i	−0.964460	−	0.201295i
$596$		0			0
$597$	8.75560	+	8.75560i	0.358343	+	0.358343i
$598$		0			0
$599$	−5.66970			−0.231658			−0.115829	−	0.993269i	$-0.536952\pi$
$599$	−5.66970			−0.231658			−0.115829	+	0.993269i	$0.536952\pi$
$600$		0			0
$601$	−24.7477			−1.00948			−0.504740	−	0.863271i	$-0.668412\pi$
$601$	−24.7477			−1.00948			−0.504740	+	0.863271i	$0.668412\pi$
$602$		0			0
$603$	2.37960	+	2.37960i	0.0969049	+	0.0969049i
$604$		0			0
$605$	22.2505	+	4.64395i	0.904612	+	0.188803i
$606$		0			0
$607$	7.37386	−	7.37386i	0.299296	−	0.299296i	−0.541442	−	0.840738i	$-0.682121\pi$
$607$	7.37386	−	7.37386i	0.299296	−	0.299296i	0.840738	+	0.541442i	$0.182121\pi$
$608$		0			0
$609$			41.4955i			1.68148i
$610$		0			0
$611$			13.1334i			0.531321i
$612$		0			0
$613$	−8.66025	+	8.66025i	−0.349784	+	0.349784i	−0.860029	−	0.510245i	$-0.829555\pi$
$613$	−8.66025	+	8.66025i	−0.349784	+	0.349784i	0.510245	+	0.860029i	$0.329555\pi$
$614$		0			0
$615$	−6.00000	−	9.16515i	−0.241943	−	0.369575i
$616$		0			0
$617$	−3.00000	−	3.00000i	−0.120775	−	0.120775i	0.644136	−	0.764911i	$-0.277217\pi$
$617$	−3.00000	−	3.00000i	−0.120775	−	0.120775i	−0.764911	+	0.644136i	$0.777217\pi$
$618$		0			0
$619$	−2.01810			−0.0811143			−0.0405572	−	0.999177i	$-0.512913\pi$
$619$	−2.01810			−0.0811143			−0.0405572	+	0.999177i	$0.512913\pi$
$620$		0			0
$621$	59.4618			2.38612
$622$		0			0
$623$	27.1652	+	27.1652i	1.08835	+	1.08835i
$624$		0			0
$625$	17.0000	+	18.3303i	0.680000	+	0.733212i
$626$		0			0
$627$	6.92820	−	6.92820i	0.276686	−	0.276686i
$628$		0			0
$629$			31.1769i			1.24310i
$630$		0			0
$631$		−	17.0780i		−	0.679866i	−0.940450	−	0.339933i	$-0.889596\pi$
$631$		−	17.0780i		−	0.679866i	0.940450	−	0.339933i	$-0.110404\pi$
$632$		0			0
$633$	51.4955	−	51.4955i	2.04676	−	2.04676i
$634$		0			0
$635$	15.3223	−	10.0308i	0.608047	−	0.398060i
$636$		0			0
$637$	1.00905	+	1.00905i	0.0399800	+	0.0399800i
$638$		0			0
$639$	−29.0780			−1.15031
$640$		0			0
$641$	−19.9129			−0.786511			−0.393256	−	0.919429i	$-0.628651\pi$
$641$	−19.9129			−0.786511			−0.393256	+	0.919429i	$0.628651\pi$
$642$		0			0
$643$	−10.7538	−	10.7538i	−0.424089	−	0.424089i	0.462520	−	0.886609i	$-0.346945\pi$
$643$	−10.7538	−	10.7538i	−0.424089	−	0.424089i	−0.886609	+	0.462520i	$0.846945\pi$
$644$		0			0
$645$	0.723000	−	3.46410i	0.0284681	−	0.136399i
$646$		0			0
$647$	32.5390	−	32.5390i	1.27924	−	1.27924i	0.338148	−	0.941093i	$-0.390200\pi$
$647$	32.5390	−	32.5390i	1.27924	−	1.27924i	0.941093	−	0.338148i	$-0.109800\pi$
$648$		0			0
$649$			4.83485i			0.189784i
$650$		0			0
$651$			59.4618i			2.33049i
$652$		0			0
$653$	−4.47315	+	4.47315i	−0.175048	+	0.175048i	−0.789193	−	0.614145i	$-0.789501\pi$
$653$	−4.47315	+	4.47315i	−0.175048	+	0.175048i	0.614145	+	0.789193i	$0.289501\pi$
$654$		0			0
$655$	−2.74773	+	13.1652i	−0.107363	+	0.514405i
$656$		0			0
$657$	56.4955	+	56.4955i	2.20410	+	2.20410i
$658$		0			0
$659$	38.4865			1.49922			0.749611	−	0.661879i	$-0.230241\pi$
$659$	38.4865			1.49922			0.749611	+	0.661879i	$0.230241\pi$
$660$		0			0
$661$	−37.9542			−1.47625			−0.738124	−	0.674665i	$-0.764288\pi$
$661$	−37.9542			−1.47625			−0.738124	+	0.674665i	$0.764288\pi$
$662$		0			0
$663$	22.7477	+	22.7477i	0.883449	+	0.883449i
$664$		0			0
$665$	16.4174	−	10.7477i	0.636640	−	0.416779i
$666$		0			0
$667$	−20.0616	+	20.0616i	−0.776789	+	0.776789i
$668$		0			0
$669$			6.01450i			0.232534i
$670$		0			0
$671$		−	5.66970i		−	0.218876i
$672$		0			0
$673$	−9.41742	+	9.41742i	−0.363015	+	0.363015i	−0.864922	−	0.501907i	$-0.832632\pi$
$673$	−9.41742	+	9.41742i	−0.363015	+	0.363015i	0.501907	+	0.864922i	$0.332632\pi$
$674$		0			0
$675$	−51.6199	+	20.2523i	−1.98685	+	0.779512i
$676$		0			0
$677$	2.45505	+	2.45505i	0.0943553	+	0.0943553i	0.752709	−	0.658354i	$-0.228747\pi$
$677$	2.45505	+	2.45505i	0.0943553	+	0.0943553i	−0.658354	+	0.752709i	$0.728747\pi$
$678$		0			0
$679$	30.7477			1.17999
$680$		0			0
$681$	51.9129			1.98931
$682$		0			0
$683$	32.8335	+	32.8335i	1.25634	+	1.25634i	0.952828	+	0.303512i	$0.0981592\pi$
$683$	32.8335	+	32.8335i	1.25634	+	1.25634i	0.303512	+	0.952828i	$0.401841\pi$
$684$		0			0
$685$	10.6784	+	16.3115i	0.407999	+	0.623229i
$686$		0			0
$687$	−7.58258	+	7.58258i	−0.289293	+	0.289293i
$688$		0			0
$689$		−	9.16515i		−	0.349164i
$690$		0			0
$691$			15.1515i			0.576391i	0.957572	+	0.288195i	$0.0930552\pi$
$691$			15.1515i			0.576391i	−0.957572	+	0.288195i	$0.906945\pi$
$692$		0			0
$693$	10.7737	−	10.7737i	0.409259	−	0.409259i
$694$		0			0
$695$	−49.9129	−	10.4174i	−1.89330	−	0.395155i
$696$		0			0
$697$	−4.74773	−	4.74773i	−0.179833	−	0.179833i
$698$		0			0
$699$	53.2566			2.01435
$700$		0			0
$701$	−25.1624			−0.950371			−0.475186	−	0.879886i	$-0.657619\pi$
$701$	−25.1624			−0.950371			−0.475186	+	0.879886i	$0.657619\pi$
$702$		0			0
$703$	−18.0000	−	18.0000i	−0.678883	−	0.678883i
$704$		0			0
$705$	−36.3303	−	7.58258i	−1.36828	−	0.285576i
$706$		0			0
$707$	31.3676	−	31.3676i	1.17970	−	1.17970i
$708$		0			0
$709$			36.6591i			1.37676i	0.725349	+	0.688381i	$0.241678\pi$
$709$			36.6591i			1.37676i	−0.725349	+	0.688381i	$0.758322\pi$
$710$		0			0
$711$			78.9909i			2.96239i
$712$		0			0
$713$	−28.7477	+	28.7477i	−1.07661	+	1.07661i
$714$		0			0
$715$	2.74110	+	4.18710i	0.102511	+	0.156589i
$716$		0			0
$717$	−33.1950	−	33.1950i	−1.23969	−	1.23969i
$718$		0			0
$719$	−51.8258			−1.93277			−0.966387	−	0.257091i	$-0.917236\pi$
$719$	−51.8258			−1.93277			−0.966387	+	0.257091i	$0.917236\pi$
$720$		0			0
$721$	−12.0871			−0.450148
$722$		0			0
$723$	36.6591	+	36.6591i	1.36337	+	1.36337i
$724$		0			0
$725$	10.5830	−	24.2487i	0.393043	−	0.900575i
$726$		0			0
$727$	−16.9564	+	16.9564i	−0.628880	+	0.628880i	−0.947786	−	0.318907i	$-0.896684\pi$
$727$	−16.9564	+	16.9564i	−0.628880	+	0.628880i	0.318907	+	0.947786i	$0.396684\pi$
$728$		0			0
$729$			7.00000i			0.259259i
$730$		0			0
$731$		−	2.16900i		−	0.0802234i
$732$		0			0
$733$	−14.1425	+	14.1425i	−0.522364	+	0.522364i	−0.918285	−	0.395921i	$-0.870425\pi$
$733$	−14.1425	+	14.1425i	−0.522364	+	0.522364i	0.395921	+	0.918285i	$0.370425\pi$
$734$		0			0
$735$	−3.37386	+	2.20871i	−0.124447	+	0.0814696i
$736$		0			0
$737$	0.330303	+	0.330303i	0.0121669	+	0.0121669i
$738$		0			0
$739$	−29.7309			−1.09367			−0.546835	−	0.837241i	$-0.684167\pi$
$739$	−29.7309			−1.09367			−0.546835	+	0.837241i	$0.684167\pi$
$740$		0			0
$741$	−26.2668			−0.964935
$742$		0			0
$743$	21.7913	+	21.7913i	0.799445	+	0.799445i	0.983008	−	0.183563i	$-0.0587632\pi$
$743$	21.7913	+	21.7913i	0.799445	+	0.799445i	−0.183563	+	0.983008i	$0.558763\pi$
$744$		0			0
$745$	−0.417424	+	2.00000i	−0.0152932	+	0.0732743i
$746$		0			0
$747$	−20.4231	+	20.4231i	−0.747243	+	0.747243i
$748$		0			0
$749$		−	1.29510i		−	0.0473220i
$750$		0			0
$751$			41.0780i			1.49896i	0.662028	+	0.749479i	$0.269696\pi$
$751$			41.0780i			1.49896i	−0.662028	+	0.749479i	$0.730304\pi$
$752$		0			0
$753$	−28.3303	+	28.3303i	−1.03241	+	1.03241i
$754$		0			0
$755$	−6.73750	+	32.2813i	−0.245203	+	1.17484i
$756$		0			0
$757$	−27.2759	−	27.2759i	−0.991358	−	0.991358i	0.00860486	−	0.999963i	$-0.497261\pi$
$757$	−27.2759	−	27.2759i	−0.991358	−	0.991358i	−0.999963	+	0.00860486i	$0.997261\pi$
$758$		0			0
$759$	15.1652			0.550460
$760$		0			0
$761$	−6.00000			−0.217500			−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000			−0.217500			−0.108750	+	0.994069i	$0.534685\pi$
$762$		0			0
$763$	−17.3205	−	17.3205i	−0.627044	−	0.627044i
$764$		0			0
$765$	−52.2476	+	34.2041i	−1.88902	+	1.23665i
$766$		0			0
$767$	9.16515	−	9.16515i	0.330934	−	0.330934i
$768$		0			0
$769$		−	17.4955i		−	0.630902i	−0.948942	−	0.315451i	$-0.897844\pi$
$769$		−	17.4955i		−	0.630902i	0.948942	−	0.315451i	$-0.102156\pi$
$770$		0			0
$771$			33.9180i			1.22153i
$772$		0			0
$773$	31.4630	−	31.4630i	1.13164	−	1.13164i	0.141740	−	0.989904i	$-0.454730\pi$
$773$	31.4630	−	31.4630i	1.13164	−	1.13164i	0.989904	−	0.141740i	$-0.0452698\pi$
$774$		0			0
$775$	15.1652	−	34.7477i	0.544748	−	1.24818i
$776$		0			0
$777$	−40.7477	−	40.7477i	−1.46182	−	1.46182i
$778$		0			0
$779$	5.48220			0.196420
$780$		0			0
$781$	−4.03620			−0.144427
$782$		0			0
$783$	41.4955	+	41.4955i	1.48293	+	1.48293i
$784$		0			0
$785$	−7.74773	−	11.8348i	−0.276528	−	0.422404i
$786$		0			0
$787$	−18.9771	+	18.9771i	−0.676461	+	0.676461i	−0.959198	−	0.282737i	$-0.908758\pi$
$787$	−18.9771	+	18.9771i	−0.676461	+	0.676461i	0.282737	+	0.959198i	$0.408758\pi$
$788$		0			0
$789$		−	62.2029i		−	2.21448i
$790$		0			0
$791$			16.4174i			0.583736i
$792$		0			0
$793$	−10.7477	+	10.7477i	−0.381663	+	0.381663i
$794$		0			0
$795$	25.3531	+	5.29150i	0.899182	+	0.187670i
$796$		0			0
$797$	−3.17805	−	3.17805i	−0.112572	−	0.112572i	0.648577	−	0.761149i	$-0.275365\pi$
$797$	−3.17805	−	3.17805i	−0.112572	−	0.112572i	−0.761149	+	0.648577i	$0.775365\pi$
$798$		0			0
$799$	−22.7477			−0.804757
$800$		0			0
$801$	99.8258			3.52717
$802$		0			0
$803$	7.84190	+	7.84190i	0.276735	+	0.276735i
$804$		0			0
$805$	29.7309	+	6.20520i	1.04788	+	0.218705i
$806$		0			0
$807$	−29.1652	+	29.1652i	−1.02666	+	1.02666i
$808$		0			0
$809$		−	6.33030i		−	0.222562i	−0.993789	−	0.111281i	$-0.964505\pi$
$809$		−	6.33030i		−	0.222562i	0.993789	−	0.111281i	$-0.0354953\pi$
$810$		0			0
$811$		−	49.7925i		−	1.74845i	−0.485519	−	0.874226i	$-0.661369\pi$
$811$		−	49.7925i		−	1.74845i	0.485519	−	0.874226i	$-0.338631\pi$
$812$		0			0
$813$	41.0369	−	41.0369i	1.43923	−	1.43923i
$814$		0			0
$815$	0.626136	+	0.956439i	0.0219326	+	0.0335026i
$816$		0			0
$817$	1.25227	+	1.25227i	0.0438115	+	0.0438115i
$818$		0			0
$819$	−40.8462			−1.42728
$820$		0			0
$821$	−17.8528			−0.623067			−0.311534	−	0.950235i	$-0.600843\pi$
$821$	−17.8528			−0.623067			−0.311534	+	0.950235i	$0.600843\pi$
$822$		0			0
$823$	−7.79129	−	7.79129i	−0.271587	−	0.271587i	0.558152	−	0.829739i	$-0.311511\pi$
$823$	−7.79129	−	7.79129i	−0.271587	−	0.271587i	−0.829739	+	0.558152i	$0.811511\pi$
$824$		0			0
$825$	−13.1652	+	5.16515i	−0.458352	+	0.179827i
$826$		0			0
$827$	−32.6428	+	32.6428i	−1.13510	+	1.13510i	−0.145786	+	0.989316i	$0.546571\pi$
$827$	−32.6428	+	32.6428i	−1.13510	+	1.13510i	−0.989316	+	0.145786i	$0.953429\pi$
$828$		0			0
$829$			23.5257i			0.817082i	0.912740	+	0.408541i	$0.133962\pi$
$829$			23.5257i			0.817082i	−0.912740	+	0.408541i	$0.866038\pi$
$830$		0			0
$831$		−	95.4083i		−	3.30968i
$832$		0			0
$833$	−1.74773	+	1.74773i	−0.0605552	+	0.0605552i
$834$		0			0
$835$	41.7798	−	27.3513i	1.44585	−	0.946531i
$836$		0			0
$837$	59.4618	+	59.4618i	2.05530	+	2.05530i
$838$		0			0
$839$	−6.33030			−0.218546			−0.109273	−	0.994012i	$-0.534852\pi$
$839$	−6.33030			−0.218546			−0.109273	+	0.994012i	$0.534852\pi$
$840$		0			0
$841$	1.00000			0.0344828
$842$		0			0
$843$	−36.6591	−	36.6591i	−1.26261	−	1.26261i
$844$		0			0
$845$	−3.19795	+	15.3223i	−0.110013	+	0.527103i
$846$		0			0
$847$	−18.2087	+	18.2087i	−0.625659	+	0.625659i
$848$		0			0
$849$		−	98.2432i		−	3.37170i
$850$		0			0
$851$		−	39.4002i		−	1.35062i
$852$		0			0
$853$	−26.5529	+	26.5529i	−0.909153	+	0.909153i	−0.996204	−	0.0870511i	$-0.972256\pi$
$853$	−26.5529	+	26.5529i	−0.909153	+	0.909153i	0.0870511	+	0.996204i	$0.472256\pi$
$854$		0			0
$855$	10.4174	−	49.9129i	0.356268	−	1.70698i
$856$		0			0
$857$	−2.66970	−	2.66970i	−0.0911951	−	0.0911951i	0.660038	−	0.751233i	$-0.270540\pi$
$857$	−2.66970	−	2.66970i	−0.0911951	−	0.0911951i	−0.751233	+	0.660038i	$0.770540\pi$
$858$		0			0
$859$	−29.7309			−1.01441			−0.507203	−	0.861827i	$-0.669321\pi$
$859$	−29.7309			−1.01441			−0.507203	+	0.861827i	$0.669321\pi$
$860$		0			0
$861$	12.4104			0.422946
$862$		0			0
$863$	−17.7042	−	17.7042i	−0.602657	−	0.602657i	0.338360	−	0.941017i	$-0.390128\pi$
$863$	−17.7042	−	17.7042i	−0.602657	−	0.602657i	−0.941017	+	0.338360i	$0.890128\pi$
$864$		0			0
$865$	−22.9129	+	15.0000i	−0.779061	+	0.510015i
$866$		0			0
$867$	−2.18890	+	2.18890i	−0.0743390	+	0.0743390i
$868$		0			0
$869$			10.9644i			0.371942i
$870$		0			0
$871$		−	1.25227i		−	0.0424316i
$872$		0			0
$873$	56.4955	−	56.4955i	1.91208	−	1.91208i
$874$		0			0
$875$	−27.9234	+	4.73930i	−0.943984	+	0.160218i
$876$		0			0
$877$	35.6501	+	35.6501i	1.20382	+	1.20382i	0.972996	+	0.230821i	$0.0741412\pi$
$877$	35.6501	+	35.6501i	1.20382	+	1.20382i	0.230821	+	0.972996i	$0.425859\pi$
$878$		0			0
$879$	79.4083			2.67838
$880$		0			0
$881$	−46.4174			−1.56384			−0.781921	−	0.623377i	$-0.785760\pi$
$881$	−46.4174			−1.56384			−0.781921	+	0.623377i	$0.785760\pi$
$882$		0			0
$883$	14.2179	+	14.2179i	0.478471	+	0.478471i	0.904642	−	0.426172i	$-0.140138\pi$
$883$	14.2179	+	14.2179i	0.478471	+	0.478471i	−0.426172	+	0.904642i	$0.640138\pi$
$884$		0			0
$885$	20.0616	+	30.6446i	0.674364	+	1.03011i
$886$		0			0
$887$	−0.956439	+	0.956439i	−0.0321141	+	0.0321141i	−0.722981	−	0.690867i	$-0.757229\pi$
$887$	−0.956439	+	0.956439i	−0.0321141	+	0.0321141i	0.690867	+	0.722981i	$0.257229\pi$
$888$		0			0
$889$			20.7477i			0.695856i
$890$		0			0
$891$		−	13.3241i		−	0.446374i
$892$		0			0
$893$	13.1334	−	13.1334i	0.439493	−	0.439493i
$894$		0			0
$895$	41.9129	+	8.74773i	1.40099	+	0.292404i
$896$		0			0
$897$	−28.7477	−	28.7477i	−0.959859	−	0.959859i
$898$		0			0
$899$	−40.1232			−1.33818
$900$		0			0
$901$	15.8745			0.528857
$902$		0			0
$903$	2.83485	+	2.83485i	0.0943379	+	0.0943379i
$904$		0			0
$905$	−15.1652	−	3.16515i	−0.504107	−	0.105213i
$906$		0			0
$907$	−12.7719	+	12.7719i	−0.424084	+	0.424084i	−0.886607	−	0.462523i	$-0.846944\pi$
$907$	−12.7719	+	12.7719i	−0.424084	+	0.424084i	0.462523	+	0.886607i	$0.346944\pi$
$908$		0			0
$909$		−	115.269i		−	3.82323i
$910$		0			0
$911$			40.4174i			1.33909i	0.742772	+	0.669545i	$0.233511\pi$
$911$			40.4174i			1.33909i	−0.742772	+	0.669545i	$0.766489\pi$
$912$		0			0
$913$	−2.83485	+	2.83485i	−0.0938198	+	0.0938198i
$914$		0			0
$915$	−23.5257	−	35.9361i	−0.777736	−	1.18801i
$916$		0			0
$917$	−10.7737	−	10.7737i	−0.355779	−	0.355779i
$918$		0			0
$919$	−5.66970			−0.187026			−0.0935130	−	0.995618i	$-0.529810\pi$
$919$	−5.66970			−0.187026			−0.0935130	+	0.995618i	$0.529810\pi$
$920$		0			0
$921$	−28.7477			−0.947270
$922$		0			0
$923$	7.65120	+	7.65120i	0.251842	+	0.251842i
$924$		0			0
$925$	13.4195	+	34.2041i	0.441229	+	1.12462i
$926$		0			0
$927$	−22.2087	+	22.2087i	−0.729430	+	0.729430i
$928$		0			0
$929$		−	25.9129i		−	0.850174i	−0.905153	−	0.425087i	$-0.860244\pi$
$929$		−	25.9129i		−	0.850174i	0.905153	−	0.425087i	$-0.139756\pi$
$930$		0			0
$931$		−	2.01810i		−	0.0661406i
$932$		0			0
$933$	−42.8643	+	42.8643i	−1.40331	+	1.40331i
$934$		0			0
$935$	−7.25227	+	4.74773i	−0.237175	+	0.155267i
$936$		0			0
$937$	−15.8348	−	15.8348i	−0.517302	−	0.517302i	0.399452	−	0.916754i	$-0.369200\pi$
$937$	−15.8348	−	15.8348i	−0.517302	−	0.517302i	−0.916754	+	0.399452i	$0.869200\pi$
$938$		0			0
$939$	28.8172			0.940414
$940$		0			0
$941$	3.27340			0.106710			0.0533549	−	0.998576i	$-0.483009\pi$
$941$	3.27340			0.106710			0.0533549	+	0.998576i	$0.483009\pi$
$942$		0			0
$943$	6.00000	+	6.00000i	0.195387	+	0.195387i
$944$		0			0
$945$	12.8348	−	61.4955i	0.417518	−	2.00045i
$946$		0			0
$947$	30.2831	−	30.2831i	0.984069	−	0.984069i	−0.0158061	−	0.999875i	$-0.505031\pi$
$947$	30.2831	−	30.2831i	0.984069	−	0.984069i	0.999875	+	0.0158061i	$0.00503144\pi$
$948$		0			0
$949$		−	29.7309i		−	0.965106i
$950$		0			0
$951$		−	61.9129i		−	2.00766i
$952$		0			0
$953$	−34.9129	+	34.9129i	−1.13094	+	1.13094i	−0.140918	+	0.990021i	$0.545005\pi$
$953$	−34.9129	+	34.9129i	−1.13094	+	1.13094i	−0.990021	+	0.140918i	$0.954995\pi$
$954$		0			0
$955$	−2.01810	+	9.66930i	−0.0653042	+	0.312891i
$956$		0			0
$957$	10.5830	+	10.5830i	0.342100	+	0.342100i
$958$		0			0
$959$	−22.0871			−0.713230
$960$		0			0
$961$	−26.4955			−0.854692
$962$		0			0
$963$	−2.37960	−	2.37960i	−0.0766816	−	0.0766816i
$964$		0			0
$965$	−11.0200	+	7.21425i	−0.354745	+	0.232235i
$966$		0			0
$967$	−4.20871	+	4.20871i	−0.135343	+	0.135343i	−0.771533	−	0.636190i	$-0.780510\pi$
$967$	−4.20871	+	4.20871i	−0.135343	+	0.135343i	0.636190	+	0.771533i	$0.280510\pi$
$968$		0			0
$969$		−	45.4955i		−	1.46152i
$970$		0			0
$971$		−	0.532300i		−	0.0170823i	−0.999964	−	0.00854116i	$-0.997281\pi$
$971$		−	0.532300i		−	0.0170823i	0.999964	−	0.00854116i	$-0.00271877\pi$
$972$		0			0
$973$	40.8462	−	40.8462i	1.30947	−	1.30947i
$974$		0			0
$975$	34.7477	+	15.1652i	1.11282	+	0.485674i
$976$		0			0
$977$	19.4174	+	19.4174i	0.621218	+	0.621218i	0.945843	−	0.324625i	$-0.105238\pi$
$977$	19.4174	+	19.4174i	0.621218	+	0.621218i	−0.324625	+	0.945843i	$0.605238\pi$
$978$		0			0
$979$	13.8564			0.442853
$980$		0			0
$981$	−63.6489			−2.03215
$982$		0			0
$983$	−23.7042	−	23.7042i	−0.756045	−	0.756045i	0.219555	−	0.975600i	$-0.429540\pi$
$983$	−23.7042	−	23.7042i	−0.756045	−	0.756045i	−0.975600	+	0.219555i	$0.929540\pi$
$984$		0			0
$985$	−4.58258	−	7.00000i	−0.146013	−	0.223039i
$986$		0			0
$987$	29.7309	−	29.7309i	0.946345	−	0.946345i
$988$		0			0
$989$			2.74110i			0.0871620i
$990$		0			0
$991$		−	30.7477i		−	0.976734i	−0.872638	−	0.488367i	$-0.837593\pi$
$991$		−	30.7477i		−	0.976734i	0.872638	−	0.488367i	$-0.162407\pi$
$992$		0			0
$993$	21.1652	−	21.1652i	0.671656	−	0.671656i
$994$		0			0
$995$	8.75560	+	1.82740i	0.277571	+	0.0579325i
$996$		0			0
$997$	14.1425	+	14.1425i	0.447896	+	0.447896i	0.894655	−	0.446758i	$-0.147422\pi$
$997$	14.1425	+	14.1425i	0.447896	+	0.447896i	−0.446758	+	0.894655i	$0.647422\pi$
$998$		0			0
$999$	−81.4955			−2.57840

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.n.p.767.4		8
4.3	odd	2		1280.2.n.n.767.1		8
5.3	odd	4		1280.2.n.n.1023.1		8
8.3	odd	2		1280.2.n.n.767.4		8
8.5	even	2	inner	1280.2.n.p.767.1		8
16.3	odd	4		320.2.o.f.287.4	yes	8
16.5	even	4		320.2.o.e.287.4	yes	8
16.11	odd	4		320.2.o.f.287.1	yes	8
16.13	even	4		320.2.o.e.287.1	yes	8
20.3	even	4	inner	1280.2.n.p.1023.4		8
40.3	even	4	inner	1280.2.n.p.1023.1		8
40.13	odd	4		1280.2.n.n.1023.4		8
80.3	even	4		320.2.o.e.223.4	yes	8
80.13	odd	4		320.2.o.f.223.1	yes	8
80.19	odd	4		1600.2.o.e.607.1		8
80.27	even	4		1600.2.o.l.543.4		8
80.29	even	4		1600.2.o.l.607.4		8
80.37	odd	4		1600.2.o.e.543.1		8
80.43	even	4		320.2.o.e.223.1	✓	8
80.53	odd	4		320.2.o.f.223.4	yes	8
80.59	odd	4		1600.2.o.e.607.4		8
80.67	even	4		1600.2.o.l.543.1		8
80.69	even	4		1600.2.o.l.607.1		8
80.77	odd	4		1600.2.o.e.543.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
320.2.o.e.223.1	✓	8	80.43	even	4
320.2.o.e.223.4	yes	8	80.3	even	4
320.2.o.e.287.1	yes	8	16.13	even	4
320.2.o.e.287.4	yes	8	16.5	even	4
320.2.o.f.223.1	yes	8	80.13	odd	4
320.2.o.f.223.4	yes	8	80.53	odd	4
320.2.o.f.287.1	yes	8	16.11	odd	4
320.2.o.f.287.4	yes	8	16.3	odd	4
1280.2.n.n.767.1		8	4.3	odd	2
1280.2.n.n.767.4		8	8.3	odd	2
1280.2.n.n.1023.1		8	5.3	odd	4
1280.2.n.n.1023.4		8	40.13	odd	4
1280.2.n.p.767.1		8	8.5	even	2	inner
1280.2.n.p.767.4		8	1.1	even	1	trivial
1280.2.n.p.1023.1		8	40.3	even	4	inner
1280.2.n.p.1023.4		8	20.3	even	4	inner
1600.2.o.e.543.1		8	80.37	odd	4
1600.2.o.e.543.4		8	80.77	odd	4
1600.2.o.e.607.1		8	80.19	odd	4
1600.2.o.e.607.4		8	80.59	odd	4
1600.2.o.l.543.1		8	80.67	even	4
1600.2.o.l.543.4		8	80.27	even	4
1600.2.o.l.607.1		8	80.69	even	4
1600.2.o.l.607.4		8	80.29	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.n (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.18890 + 2.18890i) q^{3} +(2.18890 + 0.456850i) q^{5} +(-1.79129 + 1.79129i) q^{7} +6.58258i q^{9} +O(q^{10})\)	\(q+(2.18890 + 2.18890i) q^{3} +(2.18890 + 0.456850i) q^{5} +(-1.79129 + 1.79129i) q^{7} +6.58258i q^{9} +0.913701i q^{11} +(1.73205 - 1.73205i) q^{13} +(3.79129 + 5.79129i) q^{15} +(3.00000 + 3.00000i) q^{17} -3.46410 q^{19} -7.84190 q^{21} +(-3.79129 - 3.79129i) q^{23} +(4.58258 + 2.00000i) q^{25} +(-7.84190 + 7.84190i) q^{27} -5.29150i q^{29} -7.58258i q^{31} +(-2.00000 + 2.00000i) q^{33} +(-4.73930 + 3.10260i) q^{35} +(5.19615 + 5.19615i) q^{37} +7.58258 q^{39} -1.58258 q^{41} +(-0.361500 - 0.361500i) q^{43} +(-3.00725 + 14.4086i) q^{45} +(-3.79129 + 3.79129i) q^{47} +0.582576i q^{49} +13.1334i q^{51} +(2.64575 - 2.64575i) q^{53} +(-0.417424 + 2.00000i) q^{55} +(-7.58258 - 7.58258i) q^{57} +5.29150 q^{59} -6.20520 q^{61} +(-11.7913 - 11.7913i) q^{63} +(4.58258 - 3.00000i) q^{65} +(0.361500 - 0.361500i) q^{67} -16.5975i q^{69} +4.41742i q^{71} +(8.58258 - 8.58258i) q^{73} +(5.65300 + 14.4086i) q^{75} +(-1.63670 - 1.63670i) q^{77} +12.0000 q^{79} -14.5826 q^{81} +(3.10260 + 3.10260i) q^{83} +(5.19615 + 7.93725i) q^{85} +(11.5826 - 11.5826i) q^{87} -15.1652i q^{89} +6.20520i q^{91} +(16.5975 - 16.5975i) q^{93} +(-7.58258 - 1.58258i) q^{95} +(-8.58258 - 8.58258i) q^{97} -6.01450 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{7}+O(q^{10}) \) 8 * q + 4 * q^7	\( 8 q + 4 q^{7} + 12 q^{15} + 24 q^{17} - 12 q^{23} - 16 q^{33} + 24 q^{39} + 24 q^{41} - 12 q^{47} - 40 q^{55} - 24 q^{57} - 76 q^{63} + 32 q^{73} + 96 q^{79} - 80 q^{81} + 56 q^{87} - 24 q^{95} - 32 q^{97}+O(q^{100}) \) 8 * q + 4 * q^7 + 12 * q^15 + 24 * q^17 - 12 * q^23 - 16 * q^33 + 24 * q^39 + 24 * q^41 - 12 * q^47 - 40 * q^55 - 24 * q^57 - 76 * q^63 + 32 * q^73 + 96 * q^79 - 80 * q^81 + 56 * q^87 - 24 * q^95 - 32 * q^97

Introduction

L-functions

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