LMFDB - Embedded newform 2548.2.i.i.165.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2548,2,Mod(165,2548)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2548, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 4]))

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

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

chi := DirichletCharacter("2548.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2548.i (of order $3$, 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:	$20.3458824350$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - x^{2} - 2x + 4 $ x^4 - x^3 - x^2 - 2*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 364)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.1
Root			$1.39564 + 0.228425i$ of defining polynomial
Character	$\chi$	$=$	2548.165
Dual form			2548.2.i.i.1745.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39564 - 2.41733i) q^{3} +(0.395644 + 0.685275i) q^{5} +(-2.39564 + 4.14938i) q^{9} +(-0.395644 - 0.685275i) q^{11} +(-2.50000 + 2.59808i) q^{13} +(1.10436 - 1.91280i) q^{15} -3.00000 q^{17} +(-3.18693 + 5.51993i) q^{19} +6.00000 q^{23} +(2.18693 - 3.78788i) q^{25} +5.00000 q^{27} +(3.39564 - 5.88143i) q^{29} +(-0.500000 + 0.866025i) q^{31} +(-1.10436 + 1.91280i) q^{33} -4.00000 q^{37} +(9.76951 + 2.41733i) q^{39} +(3.79129 - 6.56670i) q^{41} +(4.68693 + 8.11800i) q^{43} -3.79129 q^{45} +(3.08258 + 5.33918i) q^{47} +(4.18693 + 7.25198i) q^{51} +(0.708712 - 1.22753i) q^{53} +(0.313068 - 0.542250i) q^{55} +17.7913 q^{57} +9.00000 q^{59} +(1.00000 - 1.73205i) q^{61} +(-2.76951 - 0.685275i) q^{65} +(3.50000 + 6.06218i) q^{67} +(-8.37386 - 14.5040i) q^{69} +(0.791288 + 1.37055i) q^{71} +(7.00000 - 12.1244i) q^{73} -12.2087 q^{75} +(2.00000 + 3.46410i) q^{79} +(0.208712 + 0.361500i) q^{81} +9.00000 q^{83} +(-1.18693 - 2.05583i) q^{85} -18.9564 q^{87} -8.37386 q^{89} +2.79129 q^{93} -5.04356 q^{95} +(-2.31307 - 4.00635i) q^{97} +3.79129 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} - 3 q^{5} - 5 q^{9} + 3 q^{11} - 10 q^{13} + 9 q^{15} - 12 q^{17} + q^{19} + 24 q^{23} - 5 q^{25} + 20 q^{27} + 9 q^{29} - 2 q^{31} - 9 q^{33} - 16 q^{37} + 7 q^{39} + 6 q^{41} + 5 q^{43}+ \cdots + 6 q^{99}+O(q^{100}) $ 4 * q - q^3 - 3 * q^5 - 5 * q^9 + 3 * q^11 - 10 * q^13 + 9 * q^15 - 12 * q^17 + q^19 + 24 * q^23 - 5 * q^25 + 20 * q^27 + 9 * q^29 - 2 * q^31 - 9 * q^33 - 16 * q^37 + 7 * q^39 + 6 * q^41 + 5 * q^43 - 6 * q^45 - 6 * q^47 + 3 * q^51 + 12 * q^53 + 15 * q^55 + 62 * q^57 + 36 * q^59 + 4 * q^61 + 21 * q^65 + 14 * q^67 - 6 * q^69 - 6 * q^71 + 28 * q^73 - 58 * q^75 + 8 * q^79 + 10 * q^81 + 36 * q^83 + 9 * q^85 - 30 * q^87 - 6 * q^89 + 2 * q^93 - 66 * q^95 - 23 * q^97 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

$n$	$197$	$885$	$1275$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.39564	−	2.41733i	−0.805775	−	1.39564i	−0.915766	−	0.401711i	$-0.868416\pi$
$3$	−1.39564	−	2.41733i	−0.805775	−	1.39564i	0.109991	−	0.993933i	$-0.464918\pi$
$4$		0			0
$5$	0.395644	+	0.685275i	0.176937	+	0.306464i	0.940830	−	0.338879i	$-0.110048\pi$
$5$	0.395644	+	0.685275i	0.176937	+	0.306464i	−0.763893	+	0.645343i	$0.776714\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−2.39564	+	4.14938i	−0.798548	+	1.38313i
$10$		0			0
$11$	−0.395644	−	0.685275i	−0.119291	−	0.206618i	0.800196	−	0.599739i	$-0.204729\pi$
$11$	−0.395644	−	0.685275i	−0.119291	−	0.206618i	−0.919487	+	0.393121i	$0.871396\pi$
$12$		0			0
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$14$		0			0
$15$	1.10436	−	1.91280i	0.285144	−	0.493883i
$16$		0			0
$17$	−3.00000			−0.727607			−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000			−0.727607			−0.363803	+	0.931476i	$0.618522\pi$
$18$		0			0
$19$	−3.18693	+	5.51993i	−0.731132	+	1.26636i	0.225267	+	0.974297i	$0.427674\pi$
$19$	−3.18693	+	5.51993i	−0.731132	+	1.26636i	−0.956400	+	0.292061i	$0.905659\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	6.00000			1.25109			0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000			1.25109			0.625543	+	0.780189i	$0.284877\pi$
$24$		0			0
$25$	2.18693	−	3.78788i	0.437386	−	0.757575i
$26$		0			0
$27$	5.00000			0.962250
$28$		0			0
$29$	3.39564	−	5.88143i	0.630555	−	1.09215i	−0.356883	−	0.934149i	$-0.616161\pi$
$29$	3.39564	−	5.88143i	0.630555	−	1.09215i	0.987438	−	0.158005i	$-0.0505061\pi$
$30$		0			0
$31$	−0.500000	+	0.866025i	−0.0898027	+	0.155543i	−0.907428	−	0.420208i	$-0.861957\pi$
$31$	−0.500000	+	0.866025i	−0.0898027	+	0.155543i	0.817625	+	0.575751i	$0.195290\pi$
$32$		0			0
$33$	−1.10436	+	1.91280i	−0.192244	+	0.332976i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.00000			−0.657596			−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000			−0.657596			−0.328798	+	0.944400i	$0.606644\pi$
$38$		0			0
$39$	9.76951	+	2.41733i	1.56437	+	0.387082i
$40$		0			0
$41$	3.79129	−	6.56670i	0.592100	−	1.02555i	−0.401849	−	0.915706i	$-0.631632\pi$
$41$	3.79129	−	6.56670i	0.592100	−	1.02555i	0.993949	−	0.109841i	$-0.0350342\pi$
$42$		0			0
$43$	4.68693	+	8.11800i	0.714750	+	1.23798i	0.963056	+	0.269302i	$0.0867930\pi$
$43$	4.68693	+	8.11800i	0.714750	+	1.23798i	−0.248305	+	0.968682i	$0.579874\pi$
$44$		0			0
$45$	−3.79129			−0.565172
$46$		0			0
$47$	3.08258	+	5.33918i	0.449640	+	0.778799i	0.998362	−	0.0572054i	$-0.0182190\pi$
$47$	3.08258	+	5.33918i	0.449640	+	0.778799i	−0.548723	+	0.836005i	$0.684886\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	4.18693	+	7.25198i	0.586288	+	1.01548i
$52$		0			0
$53$	0.708712	−	1.22753i	0.0973491	−	0.168614i	−0.813237	−	0.581932i	$-0.802297\pi$
$53$	0.708712	−	1.22753i	0.0973491	−	0.168614i	0.910587	+	0.413318i	$0.135630\pi$
$54$		0			0
$55$	0.313068	−	0.542250i	0.0422141	−	0.0731170i
$56$		0			0
$57$	17.7913			2.35651
$58$		0			0
$59$	9.00000			1.17170			0.585850	−	0.810419i	$-0.300761\pi$
$59$	9.00000			1.17170			0.585850	+	0.810419i	$0.300761\pi$
$60$		0			0
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.76951	−	0.685275i	−0.343515	−	0.0849979i
$66$		0			0
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	0.996659	−	0.0816792i	$-0.0260283\pi$
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	−0.569066	+	0.822292i	$0.692695\pi$
$68$		0			0
$69$	−8.37386	−	14.5040i	−1.00809	−	1.74607i
$70$		0			0
$71$	0.791288	+	1.37055i	0.0939086	+	0.162654i	0.909153	−	0.416463i	$-0.136731\pi$
$71$	0.791288	+	1.37055i	0.0939086	+	0.162654i	−0.815244	+	0.579118i	$0.803397\pi$
$72$		0			0
$73$	7.00000	−	12.1244i	0.819288	−	1.41905i	−0.0869195	−	0.996215i	$-0.527702\pi$
$73$	7.00000	−	12.1244i	0.819288	−	1.41905i	0.906208	−	0.422833i	$-0.138964\pi$
$74$		0			0
$75$	−12.2087			−1.40974
$76$		0			0
$77$		0			0
$78$		0			0
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	−0.731307	+	0.682048i	$0.761089\pi$
$80$		0			0
$81$	0.208712	+	0.361500i	0.0231902	+	0.0401667i
$82$		0			0
$83$	9.00000			0.987878			0.493939	−	0.869496i	$-0.335557\pi$
$83$	9.00000			0.987878			0.493939	+	0.869496i	$0.335557\pi$
$84$		0			0
$85$	−1.18693	−	2.05583i	−0.128741	−	0.222986i
$86$		0			0
$87$	−18.9564			−2.03234
$88$		0			0
$89$	−8.37386			−0.887628			−0.443814	−	0.896119i	$-0.646375\pi$
$89$	−8.37386			−0.887628			−0.443814	+	0.896119i	$0.646375\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	2.79129			0.289443
$94$		0			0
$95$	−5.04356			−0.517458
$96$		0			0
$97$	−2.31307	−	4.00635i	−0.234856	−	0.406783i	0.724374	−	0.689407i	$-0.242129\pi$
$97$	−2.31307	−	4.00635i	−0.234856	−	0.406783i	−0.959231	+	0.282623i	$0.908795\pi$
$98$		0			0
$99$	3.79129			0.381039
$100$		0			0
$101$	8.76951	+	15.1892i	0.872599	+	1.51139i	0.859299	+	0.511474i	$0.170900\pi$
$101$	8.76951	+	15.1892i	0.872599	+	1.51139i	0.0132996	+	0.999912i	$0.495766\pi$
$102$		0			0
$103$	−0.500000	−	0.866025i	−0.0492665	−	0.0853320i	0.840341	−	0.542059i	$-0.182355\pi$
$103$	−0.500000	−	0.866025i	−0.0492665	−	0.0853320i	−0.889607	+	0.456727i	$0.849022\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	14.3739			1.38957			0.694787	−	0.719216i	$-0.255499\pi$
$107$	14.3739			1.38957			0.694787	+	0.719216i	$0.255499\pi$
$108$		0			0
$109$	−4.87386	+	8.44178i	−0.466831	+	0.808576i	−0.999282	−	0.0378852i	$-0.987938\pi$
$109$	−4.87386	+	8.44178i	−0.466831	+	0.808576i	0.532451	+	0.846461i	$0.321271\pi$
$110$		0			0
$111$	5.58258	+	9.66930i	0.529875	+	0.917770i
$112$		0			0
$113$	−3.08258	−	5.33918i	−0.289984	−	0.502268i	0.683821	−	0.729649i	$-0.260317\pi$
$113$	−3.08258	−	5.33918i	−0.289984	−	0.502268i	−0.973806	+	0.227382i	$0.926983\pi$
$114$		0			0
$115$	2.37386	+	4.11165i	0.221364	+	0.383414i
$116$		0			0
$117$	−4.79129	−	16.5975i	−0.442955	−	1.53444i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.18693	−	8.98403i	0.471539	−	0.816730i
$122$		0			0
$123$	−21.1652			−1.90840
$124$		0			0
$125$	7.41742			0.663435
$126$		0			0
$127$	7.68693	−	13.3142i	0.682105	−	1.18144i	−0.292232	−	0.956347i	$-0.594398\pi$
$127$	7.68693	−	13.3142i	0.682105	−	1.18144i	0.974337	−	0.225093i	$-0.0722686\pi$
$128$		0			0
$129$	13.0826	−	22.6597i	1.15186	−	1.99507i
$130$		0			0
$131$	−9.47822	−	16.4168i	−0.828116	−	1.43434i	−0.899514	−	0.436891i	$-0.856080\pi$
$131$	−9.47822	−	16.4168i	−0.828116	−	1.43434i	0.0713986	−	0.997448i	$-0.477254\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	1.97822	+	3.42638i	0.170258	+	0.294896i
$136$		0			0
$137$	−2.37386			−0.202813			−0.101406	−	0.994845i	$-0.532334\pi$
$137$	−2.37386			−0.202813			−0.101406	+	0.994845i	$0.532334\pi$
$138$		0			0
$139$	6.68693	+	11.5821i	0.567178	+	0.982381i	0.996843	+	0.0793931i	$0.0252982\pi$
$139$	6.68693	+	11.5821i	0.567178	+	0.982381i	−0.429665	+	0.902988i	$0.641368\pi$
$140$		0			0
$141$	8.60436	−	14.9032i	0.724617	−	1.25507i
$142$		0			0
$143$	2.76951	+	0.685275i	0.231598	+	0.0573056i
$144$		0			0
$145$	5.37386			0.446275
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−10.9782	+	19.0148i	−0.899371	+	1.55776i	−0.0710706	+	0.997471i	$0.522642\pi$
$149$	−10.9782	+	19.0148i	−0.899371	+	1.55776i	−0.828300	+	0.560285i	$0.810692\pi$
$150$		0			0
$151$	3.50000	−	6.06218i	0.284826	−	0.493333i	−0.687741	−	0.725956i	$-0.741398\pi$
$151$	3.50000	−	6.06218i	0.284826	−	0.493333i	0.972567	+	0.232623i	$0.0747309\pi$
$152$		0			0
$153$	7.18693	−	12.4481i	0.581029	−	1.00637i
$154$		0			0
$155$	−0.791288			−0.0635578
$156$		0			0
$157$	−2.31307	+	4.00635i	−0.184603	+	0.319742i	−0.943443	−	0.331536i	$-0.892433\pi$
$157$	−2.31307	+	4.00635i	−0.184603	+	0.319742i	0.758840	+	0.651277i	$0.225767\pi$
$158$		0			0
$159$	−3.95644			−0.313766
$160$		0			0
$161$		0			0
$162$		0			0
$163$	10.3739	−	17.9681i	0.812544	−	1.40737i	−0.0985346	−	0.995134i	$-0.531416\pi$
$163$	10.3739	−	17.9681i	0.812544	−	1.40737i	0.911078	−	0.412233i	$-0.135251\pi$
$164$		0			0
$165$	−1.74773			−0.136060
$166$		0			0
$167$	−9.08258	+	15.7315i	−0.702831	+	1.21734i	0.264638	+	0.964348i	$0.414748\pi$
$167$	−9.08258	+	15.7315i	−0.702831	+	1.21734i	−0.967469	+	0.252991i	$0.918586\pi$
$168$		0			0
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$		0			0
$171$	−15.2695	−	26.4476i	−1.16769	−	2.02250i
$172$		0			0
$173$	7.66515	−	13.2764i	0.582771	−	1.00939i	−0.412379	−	0.911013i	$-0.635302\pi$
$173$	7.66515	−	13.2764i	0.582771	−	1.00939i	0.995149	−	0.0983759i	$-0.0313647\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−12.5608	−	21.7559i	−0.944127	−	1.63528i
$178$		0			0
$179$	2.29129	+	3.96863i	0.171259	+	0.296629i	0.938860	−	0.344298i	$-0.111883\pi$
$179$	2.29129	+	3.96863i	0.171259	+	0.296629i	−0.767601	+	0.640928i	$0.778550\pi$
$180$		0			0
$181$	2.74773			0.204237			0.102118	−	0.994772i	$-0.467438\pi$
$181$	2.74773			0.204237			0.102118	+	0.994772i	$0.467438\pi$
$182$		0			0
$183$	−5.58258			−0.412676
$184$		0			0
$185$	−1.58258	−	2.74110i	−0.116353	−	0.201530i
$186$		0			0
$187$	1.18693	+	2.05583i	0.0867970	+	0.150337i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	5.76951	−	9.99308i	0.417467	−	0.723074i	−0.578217	−	0.815883i	$-0.696251\pi$
$191$	5.76951	−	9.99308i	0.417467	−	0.723074i	0.995684	+	0.0928091i	$0.0295846\pi$
$192$		0			0
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	0.987945	−	0.154805i	$-0.0494748\pi$
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	−0.628037	+	0.778183i	$0.716141\pi$
$194$		0			0
$195$	2.20871	+	7.65120i	0.158169	+	0.547914i
$196$		0			0
$197$	0.395644	−	0.685275i	0.0281885	−	0.0488238i	−0.851587	−	0.524213i	$-0.824359\pi$
$197$	0.395644	−	0.685275i	0.0281885	−	0.0488238i	0.879775	+	0.475389i	$0.157693\pi$
$198$		0			0
$199$	−15.7477			−1.11633			−0.558163	−	0.829731i	$-0.688494\pi$
$199$	−15.7477			−1.11633			−0.558163	+	0.829731i	$0.688494\pi$
$200$		0			0
$201$	9.76951	−	16.9213i	0.689088	−	1.19354i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	6.00000			0.419058
$206$		0			0
$207$	−14.3739	+	24.8963i	−0.999053	+	1.73041i
$208$		0			0
$209$	5.04356			0.348870
$210$		0			0
$211$	6.50000	−	11.2583i	0.447478	−	0.775055i	−0.550743	−	0.834675i	$-0.685655\pi$
$211$	6.50000	−	11.2583i	0.447478	−	0.775055i	0.998221	+	0.0596196i	$0.0189888\pi$
$212$		0			0
$213$	2.20871	−	3.82560i	0.151338	−	0.262126i
$214$		0			0
$215$	−3.70871	+	6.42368i	−0.252932	+	0.438091i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−39.0780			−2.64065
$220$		0			0
$221$	7.50000	−	7.79423i	0.504505	−	0.524297i
$222$		0			0
$223$	4.31307	−	7.47045i	0.288824	−	0.500259i	−0.684705	−	0.728820i	$-0.740069\pi$
$223$	4.31307	−	7.47045i	0.288824	−	0.500259i	0.973529	+	0.228562i	$0.0734023\pi$
$224$		0			0
$225$	10.4782	+	18.1488i	0.698548	+	1.20992i
$226$		0			0
$227$	13.7477			0.912469			0.456234	−	0.889860i	$-0.349198\pi$
$227$	13.7477			0.912469			0.456234	+	0.889860i	$0.349198\pi$
$228$		0			0
$229$	−13.3739	−	23.1642i	−0.883770	−	1.53073i	−0.847117	−	0.531406i	$-0.821664\pi$
$229$	−13.3739	−	23.1642i	−0.883770	−	1.53073i	−0.0366526	−	0.999328i	$-0.511669\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	13.9782	+	24.2110i	0.915744	+	1.58611i	0.805809	+	0.592176i	$0.201731\pi$
$233$	13.9782	+	24.2110i	0.915744	+	1.58611i	0.109935	+	0.993939i	$0.464936\pi$
$234$		0			0
$235$	−2.43920	+	4.22483i	−0.159116	+	0.275597i
$236$		0			0
$237$	5.58258	−	9.66930i	0.362627	−	0.628089i
$238$		0			0
$239$	−24.4955			−1.58448			−0.792240	−	0.610210i	$-0.791085\pi$
$239$	−24.4955			−1.58448			−0.792240	+	0.610210i	$0.791085\pi$
$240$		0			0
$241$	3.37386			0.217330			0.108665	−	0.994078i	$-0.465342\pi$
$241$	3.37386			0.217330			0.108665	+	0.994078i	$0.465342\pi$
$242$		0			0
$243$	8.08258	−	13.9994i	0.518497	−	0.898064i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−6.37386	−	22.0797i	−0.405559	−	1.40490i
$248$		0			0
$249$	−12.5608	−	21.7559i	−0.796008	−	1.37873i
$250$		0			0
$251$	2.20871	+	3.82560i	0.139413	+	0.241470i	0.927274	−	0.374382i	$-0.122145\pi$
$251$	2.20871	+	3.82560i	0.139413	+	0.241470i	−0.787862	+	0.615852i	$0.788812\pi$
$252$		0			0
$253$	−2.37386	−	4.11165i	−0.149244	−	0.258497i
$254$		0			0
$255$	−3.31307	+	5.73840i	−0.207472	+	0.359353i
$256$		0			0
$257$	0.626136			0.0390573			0.0195287	−	0.999809i	$-0.493783\pi$
$257$	0.626136			0.0390573			0.0195287	+	0.999809i	$0.493783\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	16.2695	+	28.1796i	1.00706	+	1.74427i
$262$		0			0
$263$	5.29129	+	9.16478i	0.326275	+	0.565125i	0.981770	−	0.190075i	$-0.0608732\pi$
$263$	5.29129	+	9.16478i	0.326275	+	0.565125i	−0.655495	+	0.755200i	$0.727540\pi$
$264$		0			0
$265$	1.12159			0.0688988
$266$		0			0
$267$	11.6869	+	20.2424i	0.715229	+	1.23881i
$268$		0			0
$269$	23.3739			1.42513			0.712565	−	0.701606i	$-0.247533\pi$
$269$	23.3739			1.42513			0.712565	+	0.701606i	$0.247533\pi$
$270$		0			0
$271$	−3.74773			−0.227658			−0.113829	−	0.993500i	$-0.536312\pi$
$271$	−3.74773			−0.227658			−0.113829	+	0.993500i	$0.536312\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.46099			−0.208705
$276$		0			0
$277$	32.4955			1.95246			0.976231	−	0.216731i	$-0.0695395\pi$
$277$	32.4955			1.95246			0.976231	+	0.216731i	$0.0695395\pi$
$278$		0			0
$279$	−2.39564	−	4.14938i	−0.143423	−	0.248417i
$280$		0			0
$281$	−22.7477			−1.35702			−0.678508	−	0.734593i	$-0.737373\pi$
$281$	−22.7477			−1.35702			−0.678508	+	0.734593i	$0.737373\pi$
$282$		0			0
$283$	13.0000	+	22.5167i	0.772770	+	1.33848i	0.936039	+	0.351895i	$0.114463\pi$
$283$	13.0000	+	22.5167i	0.772770	+	1.33848i	−0.163270	+	0.986581i	$0.552204\pi$
$284$		0			0
$285$	7.03901	+	12.1919i	0.416955	+	0.722188i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−8.00000			−0.470588
$290$		0			0
$291$	−6.45644	+	11.1829i	−0.378483	+	0.655552i
$292$		0			0
$293$	−6.79129	−	11.7629i	−0.396751	−	0.687193i	0.596572	−	0.802560i	$-0.296529\pi$
$293$	−6.79129	−	11.7629i	−0.396751	−	0.687193i	−0.993323	+	0.115366i	$0.963196\pi$
$294$		0			0
$295$	3.56080	+	6.16748i	0.207318	+	0.359084i
$296$		0			0
$297$	−1.97822	−	3.42638i	−0.114788	−	0.198819i
$298$		0			0
$299$	−15.0000	+	15.5885i	−0.867472	+	0.901504i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	24.4782	−	42.3975i	1.40624	−	2.43567i
$304$		0			0
$305$	1.58258			0.0906180
$306$		0			0
$307$	14.1216			0.805962			0.402981	−	0.915208i	$-0.367974\pi$
$307$	14.1216			0.805962			0.402981	+	0.915208i	$0.367974\pi$
$308$		0			0
$309$	−1.39564	+	2.41733i	−0.0793954	+	0.137517i
$310$		0			0
$311$	9.47822	−	16.4168i	0.537461	−	0.930909i	−0.461579	−	0.887099i	$-0.652717\pi$
$311$	9.47822	−	16.4168i	0.537461	−	0.930909i	0.999040	−	0.0438100i	$-0.0139496\pi$
$312$		0			0
$313$	3.37386	+	5.84370i	0.190702	+	0.330306i	0.945483	−	0.325671i	$-0.105590\pi$
$313$	3.37386	+	5.84370i	0.190702	+	0.330306i	−0.754781	+	0.655977i	$0.772257\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	8.29129	+	14.3609i	0.465685	+	0.806590i	0.999232	−	0.0391801i	$-0.0124746\pi$
$317$	8.29129	+	14.3609i	0.465685	+	0.806590i	−0.533547	+	0.845770i	$0.679141\pi$
$318$		0			0
$319$	−5.37386			−0.300879
$320$		0			0
$321$	−20.0608	−	34.7463i	−1.11968	−	1.93935i
$322$		0			0
$323$	9.56080	−	16.5598i	0.531977	−	0.921411i
$324$		0			0
$325$	4.37386	+	15.1515i	0.242618	+	0.840454i
$326$		0			0
$327$	27.2087			1.50465
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−13.5608	+	23.4880i	−0.745369	+	1.29102i	0.204654	+	0.978834i	$0.434393\pi$
$331$	−13.5608	+	23.4880i	−0.745369	+	1.29102i	−0.950022	+	0.312182i	$0.898940\pi$
$332$		0			0
$333$	9.58258	−	16.5975i	0.525122	−	0.909538i
$334$		0			0
$335$	−2.76951	+	4.79693i	−0.151314	+	0.262084i
$336$		0			0
$337$	−6.37386			−0.347206			−0.173603	−	0.984816i	$-0.555541\pi$
$337$	−6.37386			−0.347206			−0.173603	+	0.984816i	$0.555541\pi$
$338$		0			0
$339$	−8.60436	+	14.9032i	−0.467324	+	0.809430i
$340$		0			0
$341$	0.791288			0.0428506
$342$		0			0
$343$		0			0
$344$		0			0
$345$	6.62614	−	11.4768i	0.356739	−	0.617890i
$346$		0			0
$347$	4.74773			0.254871			0.127436	−	0.991847i	$-0.459325\pi$
$347$	4.74773			0.254871			0.127436	+	0.991847i	$0.459325\pi$
$348$		0			0
$349$	−14.8739	+	25.7623i	−0.796180	+	1.37902i	0.125908	+	0.992042i	$0.459816\pi$
$349$	−14.8739	+	25.7623i	−0.796180	+	1.37902i	−0.922087	+	0.386982i	$0.873518\pi$
$350$		0			0
$351$	−12.5000	+	12.9904i	−0.667201	+	0.693375i
$352$		0			0
$353$	−7.35208	−	12.7342i	−0.391312	−	0.677772i	0.601311	−	0.799015i	$-0.294645\pi$
$353$	−7.35208	−	12.7342i	−0.391312	−	0.677772i	−0.992623	+	0.121243i	$0.961312\pi$
$354$		0			0
$355$	−0.626136	+	1.08450i	−0.0332319	+	0.0575593i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	12.4782	+	21.6129i	0.658575	+	1.14069i	0.980985	+	0.194085i	$0.0621739\pi$
$359$	12.4782	+	21.6129i	0.658575	+	1.14069i	−0.322409	+	0.946600i	$0.604493\pi$
$360$		0			0
$361$	−10.8131	−	18.7288i	−0.569109	−	0.985725i
$362$		0			0
$363$	−28.9564			−1.51982
$364$		0			0
$365$	11.0780			0.579851
$366$		0			0
$367$	1.00000	+	1.73205i	0.0521996	+	0.0904123i	0.890945	−	0.454112i	$-0.150043\pi$
$367$	1.00000	+	1.73205i	0.0521996	+	0.0904123i	−0.838745	+	0.544524i	$0.816710\pi$
$368$		0			0
$369$	18.1652	+	31.4630i	0.945640	+	1.63790i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	7.68693	−	13.3142i	0.398014	−	0.689381i	−0.595467	−	0.803380i	$-0.703033\pi$
$373$	7.68693	−	13.3142i	0.398014	−	0.689381i	0.993481	+	0.113999i	$0.0363661\pi$
$374$		0			0
$375$	−10.3521	−	17.9303i	−0.534579	−	0.925918i
$376$		0			0
$377$	6.79129	+	23.5257i	0.349769	+	1.21164i
$378$		0			0
$379$	−2.81307	+	4.87238i	−0.144498	+	0.250277i	−0.929185	−	0.369614i	$-0.879490\pi$
$379$	−2.81307	+	4.87238i	−0.144498	+	0.250277i	0.784688	+	0.619891i	$0.212823\pi$
$380$		0			0
$381$	−42.9129			−2.19849
$382$		0			0
$383$	−19.2695	+	33.3758i	−0.984626	+	1.70542i	−0.341038	+	0.940049i	$0.610779\pi$
$383$	−19.2695	+	33.3758i	−0.984626	+	1.70542i	−0.643587	+	0.765373i	$0.722555\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−44.9129			−2.28305
$388$		0			0
$389$	−12.1652	+	21.0707i	−0.616798	+	1.06832i	0.373269	+	0.927723i	$0.378237\pi$
$389$	−12.1652	+	21.0707i	−0.616798	+	1.06832i	−0.990066	+	0.140602i	$0.955096\pi$
$390$		0			0
$391$	−18.0000			−0.910299
$392$		0			0
$393$	−26.4564	+	45.8239i	−1.33455	+	2.31151i
$394$		0			0
$395$	−1.58258	+	2.74110i	−0.0796280	+	0.137920i
$396$		0			0
$397$	−15.7477	+	27.2759i	−0.790356	+	1.36894i	0.135391	+	0.990792i	$0.456771\pi$
$397$	−15.7477	+	27.2759i	−0.790356	+	1.36894i	−0.925747	+	0.378144i	$0.876562\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−25.1216			−1.25451			−0.627256	−	0.778813i	$-0.715822\pi$
$401$	−25.1216			−1.25451			−0.627256	+	0.778813i	$0.715822\pi$
$402$		0			0
$403$	−1.00000	−	3.46410i	−0.0498135	−	0.172559i
$404$		0			0
$405$	−0.165151	+	0.286051i	−0.00820644	+	0.0142140i
$406$		0			0
$407$	1.58258	+	2.74110i	0.0784454	+	0.135871i
$408$		0			0
$409$	29.1216			1.43997			0.719985	−	0.693990i	$-0.244149\pi$
$409$	29.1216			1.43997			0.719985	+	0.693990i	$0.244149\pi$
$410$		0			0
$411$	3.31307	+	5.73840i	0.163422	+	0.283055i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	3.56080	+	6.16748i	0.174793	+	0.302750i
$416$		0			0
$417$	18.6652	−	32.3290i	0.914036	−	1.58316i
$418$		0			0
$419$	−0.708712	+	1.22753i	−0.0346229	+	0.0599685i	−0.882818	−	0.469716i	$-0.844356\pi$
$419$	−0.708712	+	1.22753i	−0.0346229	+	0.0599685i	0.848195	+	0.529684i	$0.177690\pi$
$420$		0			0
$421$	23.4955			1.14510			0.572549	−	0.819870i	$-0.305955\pi$
$421$	23.4955			1.14510			0.572549	+	0.819870i	$0.305955\pi$
$422$		0			0
$423$	−29.5390			−1.43624
$424$		0			0
$425$	−6.56080	+	11.3636i	−0.318245	+	0.551217i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−2.20871	−	7.65120i	−0.106638	−	0.369404i
$430$		0			0
$431$	−4.26951	−	7.39500i	−0.205655	−	0.356205i	0.744686	−	0.667415i	$-0.232599\pi$
$431$	−4.26951	−	7.39500i	−0.205655	−	0.356205i	−0.950341	+	0.311210i	$0.899266\pi$
$432$		0			0
$433$	−11.2477	−	19.4816i	−0.540531	−	0.936228i	−0.998874	−	0.0474518i	$-0.984890\pi$
$433$	−11.2477	−	19.4816i	−0.540531	−	0.936228i	0.458342	−	0.888776i	$-0.348443\pi$
$434$		0			0
$435$	−7.50000	−	12.9904i	−0.359597	−	0.622841i
$436$		0			0
$437$	−19.1216	+	33.1196i	−0.914710	+	1.58432i
$438$		0			0
$439$	9.37386			0.447390			0.223695	−	0.974659i	$-0.428188\pi$
$439$	9.37386			0.447390			0.223695	+	0.974659i	$0.428188\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	6.79129	+	11.7629i	0.322664	+	0.558870i	0.981037	−	0.193822i	$-0.0620883\pi$
$443$	6.79129	+	11.7629i	0.322664	+	0.558870i	−0.658373	+	0.752692i	$0.728755\pi$
$444$		0			0
$445$	−3.31307	−	5.73840i	−0.157054	−	0.272026i
$446$		0			0
$447$	61.2867			2.89876
$448$		0			0
$449$	1.41742	+	2.45505i	0.0668924	+	0.115861i	0.897532	−	0.440950i	$-0.145358\pi$
$449$	1.41742	+	2.45505i	0.0668924	+	0.115861i	−0.830639	+	0.556811i	$0.812025\pi$
$450$		0			0
$451$	−6.00000			−0.282529
$452$		0			0
$453$	−19.5390			−0.918023
$454$		0			0
$455$		0			0
$456$		0			0
$457$	17.4955			0.818403			0.409201	−	0.912444i	$-0.365807\pi$
$457$	17.4955			0.818403			0.409201	+	0.912444i	$0.365807\pi$
$458$		0			0
$459$	−15.0000			−0.700140
$460$		0			0
$461$	12.3956	+	21.4699i	0.577323	+	0.999952i	0.995785	+	0.0917181i	$0.0292359\pi$
$461$	12.3956	+	21.4699i	0.577323	+	0.999952i	−0.418462	+	0.908234i	$0.637431\pi$
$462$		0			0
$463$	5.00000			0.232370			0.116185	−	0.993228i	$-0.462933\pi$
$463$	5.00000			0.232370			0.116185	+	0.993228i	$0.462933\pi$
$464$		0			0
$465$	1.10436	+	1.91280i	0.0512133	+	0.0887040i
$466$		0			0
$467$	21.0826	+	36.5161i	0.975585	+	1.68976i	0.677990	+	0.735071i	$0.262851\pi$
$467$	21.0826	+	36.5161i	0.975585	+	1.68976i	0.297595	+	0.954692i	$0.403815\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	12.9129			0.594994
$472$		0			0
$473$	3.70871	−	6.42368i	0.170527	−	0.295361i
$474$		0			0
$475$	13.9392	+	24.1434i	0.639575	+	1.10778i
$476$		0			0
$477$	3.39564	+	5.88143i	0.155476	+	0.269292i
$478$		0			0
$479$	11.1434	+	19.3009i	0.509154	+	0.881880i	0.999944	+	0.0106021i	$0.00337483\pi$
$479$	11.1434	+	19.3009i	0.509154	+	0.881880i	−0.490790	+	0.871278i	$0.663292\pi$
$480$		0			0
$481$	10.0000	−	10.3923i	0.455961	−	0.473848i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.83030	−	3.17018i	0.0831098	−	0.143950i
$486$		0			0
$487$	18.1216			0.821168			0.410584	−	0.911823i	$-0.365325\pi$
$487$	18.1216			0.821168			0.410584	+	0.911823i	$0.365325\pi$
$488$		0			0
$489$	−57.9129			−2.61891
$490$		0			0
$491$	4.89564	−	8.47950i	0.220937	−	0.382675i	−0.734156	−	0.678981i	$-0.762422\pi$
$491$	4.89564	−	8.47950i	0.220937	−	0.382675i	0.955093	+	0.296307i	$0.0957550\pi$
$492$		0			0
$493$	−10.1869	+	17.6443i	−0.458796	+	0.794659i
$494$		0			0
$495$	1.50000	+	2.59808i	0.0674200	+	0.116775i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	10.0608	+	17.4258i	0.450383	+	0.780086i	0.998410	−	0.0563745i	$-0.0179541\pi$
$499$	10.0608	+	17.4258i	0.450383	+	0.780086i	−0.548027	+	0.836461i	$0.684621\pi$
$500$		0			0
$501$	50.7042			2.26530
$502$		0			0
$503$	−8.60436	−	14.9032i	−0.383649	−	0.664500i	0.607932	−	0.793989i	$-0.292000\pi$
$503$	−8.60436	−	14.9032i	−0.383649	−	0.664500i	−0.991581	+	0.129489i	$0.958666\pi$
$504$		0			0
$505$	−6.93920	+	12.0191i	−0.308791	+	0.534841i
$506$		0			0
$507$	−30.7042	+	19.3386i	−1.36362	+	0.858858i
$508$		0			0
$509$	−1.74773			−0.0774666			−0.0387333	−	0.999250i	$-0.512332\pi$
$509$	−1.74773			−0.0774666			−0.0387333	+	0.999250i	$0.512332\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−15.9347	+	27.5996i	−0.703532	+	1.21855i
$514$		0			0
$515$	0.395644	−	0.685275i	0.0174342	−	0.0301968i
$516$		0			0
$517$	2.43920	−	4.22483i	0.107276	−	0.185808i
$518$		0			0
$519$	−42.7913			−1.87833
$520$		0			0
$521$	15.7913	−	27.3513i	0.691829	−	1.19828i	−0.279409	−	0.960172i	$-0.590139\pi$
$521$	15.7913	−	27.3513i	0.691829	−	1.19828i	0.971238	−	0.238111i	$-0.0765281\pi$
$522$		0			0
$523$	26.7477			1.16960			0.584798	−	0.811179i	$-0.301174\pi$
$523$	26.7477			1.16960			0.584798	+	0.811179i	$0.301174\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.50000	−	2.59808i	0.0653410	−	0.113174i
$528$		0			0
$529$	13.0000			0.565217
$530$		0			0
$531$	−21.5608	+	37.3444i	−0.935659	+	1.62061i
$532$		0			0
$533$	7.58258	+	26.2668i	0.328438	+	1.13774i
$534$		0			0
$535$	5.68693	+	9.85005i	0.245868	+	0.425855i
$536$		0			0
$537$	6.39564	−	11.0776i	0.275992	−	0.478033i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−19.5608	−	33.8803i	−0.840984	−	1.45663i	−0.889063	−	0.457784i	$-0.848643\pi$
$541$	−19.5608	−	33.8803i	−0.840984	−	1.45663i	0.0480792	−	0.998844i	$-0.484690\pi$
$542$		0			0
$543$	−3.83485	−	6.64215i	−0.164569	−	0.285042i
$544$		0			0
$545$	−7.71326			−0.330400
$546$		0			0
$547$	−41.7477			−1.78500			−0.892502	−	0.451044i	$-0.851052\pi$
$547$	−41.7477			−1.78500			−0.892502	+	0.451044i	$0.851052\pi$
$548$		0			0
$549$	4.79129	+	8.29875i	0.204487	+	0.354182i
$550$		0			0
$551$	21.6434	+	37.4874i	0.922039	+	1.59702i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−4.41742	+	7.65120i	−0.187509	+	0.324775i
$556$		0			0
$557$	10.1044	+	17.5013i	0.428135	+	0.741552i	0.996707	−	0.0810813i	$-0.0258373\pi$
$557$	10.1044	+	17.5013i	0.428135	+	0.741552i	−0.568572	+	0.822633i	$0.692504\pi$
$558$		0			0
$559$	−32.8085	−	8.11800i	−1.38765	−	0.343355i
$560$		0			0
$561$	3.31307	−	5.73840i	0.139878	−	0.242276i
$562$		0			0
$563$	39.4955			1.66453			0.832267	−	0.554374i	$-0.187042\pi$
$563$	39.4955			1.66453			0.832267	+	0.554374i	$0.187042\pi$
$564$		0			0
$565$	2.43920	−	4.22483i	0.102618	−	0.177740i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−42.0000			−1.76073			−0.880366	−	0.474295i	$-0.842703\pi$
$569$	−42.0000			−1.76073			−0.880366	+	0.474295i	$0.842703\pi$
$570$		0			0
$571$	−7.56080	+	13.0957i	−0.316409	+	0.548037i	−0.979736	−	0.200293i	$-0.935811\pi$
$571$	−7.56080	+	13.0957i	−0.316409	+	0.548037i	0.663327	+	0.748330i	$0.269144\pi$
$572$		0			0
$573$	−32.2087			−1.34554
$574$		0			0
$575$	13.1216	−	22.7273i	0.547208	−	0.947792i
$576$		0			0
$577$	13.2477	−	22.9457i	0.551510	−	0.955244i	−0.446656	−	0.894706i	$-0.647385\pi$
$577$	13.2477	−	22.9457i	0.551510	−	0.955244i	0.998166	−	0.0605376i	$-0.0192815\pi$
$578$		0			0
$579$	13.9564	−	24.1733i	0.580010	−	1.00461i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−1.12159			−0.0464515
$584$		0			0
$585$	9.47822	−	9.85005i	0.391876	−	0.407250i
$586$		0			0
$587$	8.85208	−	15.3323i	0.365365	−	0.632830i	−0.623470	−	0.781847i	$-0.714278\pi$
$587$	8.85208	−	15.3323i	0.365365	−	0.632830i	0.988835	+	0.149017i	$0.0476110\pi$
$588$		0			0
$589$	−3.18693	−	5.51993i	−0.131315	−	0.227445i
$590$		0			0
$591$	−2.20871			−0.0908543
$592$		0			0
$593$	−3.47822	−	6.02445i	−0.142833	−	0.247395i	0.785729	−	0.618571i	$-0.212288\pi$
$593$	−3.47822	−	6.02445i	−0.142833	−	0.247395i	−0.928563	+	0.371176i	$0.878955\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	21.9782	+	38.0674i	0.899509	+	1.55799i
$598$		0			0
$599$	−18.4782	+	32.0052i	−0.755000	+	1.30770i	0.190375	+	0.981711i	$0.439030\pi$
$599$	−18.4782	+	32.0052i	−0.755000	+	1.30770i	−0.945375	+	0.325986i	$0.894304\pi$
$600$		0			0
$601$	−6.18693	+	10.7161i	−0.252370	+	0.437118i	−0.964178	−	0.265256i	$-0.914543\pi$
$601$	−6.18693	+	10.7161i	−0.252370	+	0.437118i	0.711808	+	0.702374i	$0.247877\pi$
$602$		0			0
$603$	−33.5390			−1.36581
$604$		0			0
$605$	8.20871			0.333732
$606$		0			0
$607$	10.8739	−	18.8341i	0.441357	−	0.764452i	−0.556434	−	0.830892i	$-0.687831\pi$
$607$	10.8739	−	18.8341i	0.441357	−	0.764452i	0.997790	+	0.0664400i	$0.0211641\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−21.5780	−	5.33918i	−0.872954	−	0.216000i
$612$		0			0
$613$	10.0608	+	17.4258i	0.406352	+	0.703822i	0.994478	−	0.104947i	$-0.0334674\pi$
$613$	10.0608	+	17.4258i	0.406352	+	0.703822i	−0.588126	+	0.808769i	$0.700134\pi$
$614$		0			0
$615$	−8.37386	−	14.5040i	−0.337667	−	0.584856i
$616$		0			0
$617$	−1.33485	−	2.31203i	−0.0537390	−	0.0930786i	0.837905	−	0.545817i	$-0.183781\pi$
$617$	−1.33485	−	2.31203i	−0.0537390	−	0.0930786i	−0.891644	+	0.452738i	$0.850447\pi$
$618$		0			0
$619$	−17.0000	+	29.4449i	−0.683288	+	1.18349i	0.290684	+	0.956819i	$0.406117\pi$
$619$	−17.0000	+	29.4449i	−0.683288	+	1.18349i	−0.973972	+	0.226670i	$0.927216\pi$
$620$		0			0
$621$	30.0000			1.20386
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−8.00000	−	13.8564i	−0.320000	−	0.554256i
$626$		0			0
$627$	−7.03901	−	12.1919i	−0.281111	−	0.486899i
$628$		0			0
$629$	12.0000			0.478471
$630$		0			0
$631$	14.5608	+	25.2200i	0.579656	+	1.00399i	0.995519	+	0.0945663i	$0.0301464\pi$
$631$	14.5608	+	25.2200i	0.579656	+	1.00399i	−0.415862	+	0.909428i	$0.636520\pi$
$632$		0			0
$633$	−36.2867			−1.44227
$634$		0			0
$635$	12.1652			0.482759
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−7.58258			−0.299962
$640$		0			0
$641$	40.1216			1.58471			0.792354	−	0.610062i	$-0.208855\pi$
$641$	40.1216			1.58471			0.792354	+	0.610062i	$0.208855\pi$
$642$		0			0
$643$	−11.8739	−	20.5661i	−0.468259	−	0.811049i	0.531083	−	0.847320i	$-0.321785\pi$
$643$	−11.8739	−	20.5661i	−0.468259	−	0.811049i	−0.999342	+	0.0362709i	$0.988452\pi$
$644$		0			0
$645$	20.7042			0.815226
$646$		0			0
$647$	−9.79129	−	16.9590i	−0.384935	−	0.666727i	0.606825	−	0.794835i	$-0.292443\pi$
$647$	−9.79129	−	16.9590i	−0.384935	−	0.666727i	−0.991760	+	0.128108i	$0.959110\pi$
$648$		0			0
$649$	−3.56080	−	6.16748i	−0.139773	−	0.242095i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−0.626136			−0.0245026			−0.0122513	−	0.999925i	$-0.503900\pi$
$653$	−0.626136			−0.0245026			−0.0122513	+	0.999925i	$0.503900\pi$
$654$		0			0
$655$	7.50000	−	12.9904i	0.293049	−	0.507576i
$656$		0			0
$657$	33.5390	+	58.0913i	1.30848	+	2.26636i
$658$		0			0
$659$	−10.5826	−	18.3296i	−0.412239	−	0.714018i	0.582896	−	0.812547i	$-0.301920\pi$
$659$	−10.5826	−	18.3296i	−0.412239	−	0.714018i	−0.995134	+	0.0985288i	$0.968586\pi$
$660$		0			0
$661$	9.37386	+	16.2360i	0.364601	+	0.631508i	0.988712	−	0.149828i	$-0.0478720\pi$
$661$	9.37386	+	16.2360i	0.364601	+	0.631508i	−0.624111	+	0.781336i	$0.714539\pi$
$662$		0			0
$663$	−29.3085	−	7.25198i	−1.13825	−	0.281644i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	20.3739	−	35.2886i	0.788879	−	1.36638i
$668$		0			0
$669$	−24.0780			−0.930910
$670$		0			0
$671$	−1.58258			−0.0610947
$672$		0			0
$673$	−10.2477	+	17.7496i	−0.395021	+	0.684196i	−0.993104	−	0.117238i	$-0.962596\pi$
$673$	−10.2477	+	17.7496i	−0.395021	+	0.684196i	0.598083	+	0.801434i	$0.295929\pi$
$674$		0			0
$675$	10.9347	−	18.9394i	0.420875	−	0.728977i
$676$		0			0
$677$	7.02178	+	12.1621i	0.269869	+	0.467427i	0.968828	−	0.247735i	$-0.0796863\pi$
$677$	7.02178	+	12.1621i	0.269869	+	0.467427i	−0.698959	+	0.715162i	$0.746353\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−19.1869	−	33.2327i	−0.735245	−	1.27348i
$682$		0			0
$683$	−31.7477			−1.21479			−0.607397	−	0.794399i	$-0.707786\pi$
$683$	−31.7477			−1.21479			−0.607397	+	0.794399i	$0.707786\pi$
$684$		0			0
$685$	−0.939205	−	1.62675i	−0.0358852	−	0.0621549i
$686$		0			0
$687$	−37.3303	+	64.6580i	−1.42424	+	2.46686i
$688$		0			0
$689$	1.41742	+	4.91010i	0.0539996	+	0.187060i
$690$		0			0
$691$	−5.62614			−0.214028			−0.107014	−	0.994257i	$-0.534129\pi$
$691$	−5.62614			−0.214028			−0.107014	+	0.994257i	$0.534129\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−5.29129	+	9.16478i	−0.200710	+	0.347640i
$696$		0			0
$697$	−11.3739	+	19.7001i	−0.430816	+	0.746195i
$698$		0			0
$699$	39.0172	−	67.5798i	1.47577	−	2.55610i
$700$		0			0
$701$	−34.7477			−1.31240			−0.656202	−	0.754585i	$-0.727838\pi$
$701$	−34.7477			−1.31240			−0.656202	+	0.754585i	$0.727838\pi$
$702$		0			0
$703$	12.7477	−	22.0797i	0.480790	−	0.832752i
$704$		0			0
$705$	13.6170			0.512848
$706$		0			0
$707$		0			0
$708$		0			0
$709$	12.8131	−	22.1929i	0.481205	−	0.833471i	−0.518562	−	0.855040i	$-0.673533\pi$
$709$	12.8131	−	22.1929i	0.481205	−	0.833471i	0.999767	+	0.0215684i	$0.00686598\pi$
$710$		0			0
$711$	−19.1652			−0.718749
$712$		0			0
$713$	−3.00000	+	5.19615i	−0.112351	+	0.194597i
$714$		0			0
$715$	0.626136	+	2.16900i	0.0234162	+	0.0811160i
$716$		0			0
$717$	34.1869	+	59.2135i	1.27673	+	2.21137i
$718$		0			0
$719$	24.4129	−	42.2843i	0.910447	−	1.57694i	0.0970125	−	0.995283i	$-0.469071\pi$
$719$	24.4129	−	42.2843i	0.910447	−	1.57694i	0.813434	−	0.581657i	$-0.197595\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−4.70871	−	8.15573i	−0.175119	−	0.303315i
$724$		0			0
$725$	−14.8521	−	25.7246i	−0.551593	−	0.955386i
$726$		0			0
$727$	28.4955			1.05684			0.528419	−	0.848984i	$-0.322785\pi$
$727$	28.4955			1.05684			0.528419	+	0.848984i	$0.322785\pi$
$728$		0			0
$729$	−43.8693			−1.62479
$730$		0			0
$731$	−14.0608	−	24.3540i	−0.520057	−	0.900766i
$732$		0			0
$733$	−15.4347	−	26.7336i	−0.570092	−	0.987429i	−0.996556	−	0.0829239i	$-0.973574\pi$
$733$	−15.4347	−	26.7336i	−0.570092	−	0.987429i	0.426464	−	0.904505i	$-0.359759\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.76951	−	4.79693i	0.102016	−	0.176697i
$738$		0			0
$739$	−21.3739	−	37.0206i	−0.786250	−	1.36183i	−0.928249	−	0.371959i	$-0.878686\pi$
$739$	−21.3739	−	37.0206i	−0.786250	−	1.36183i	0.141999	−	0.989867i	$-0.454647\pi$
$740$		0			0
$741$	−44.4782	+	46.2231i	−1.63395	+	1.69805i
$742$		0			0
$743$	13.8956	−	24.0680i	0.509782	−	0.882968i	−0.490154	−	0.871636i	$-0.663059\pi$
$743$	13.8956	−	24.0680i	0.509782	−	0.882968i	0.999936	−	0.0113320i	$-0.00360718\pi$
$744$		0			0
$745$	−17.3739			−0.636529
$746$		0			0
$747$	−21.5608	+	37.3444i	−0.788868	+	1.36636i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	5.00000			0.182453			0.0912263	−	0.995830i	$-0.470921\pi$
$751$	5.00000			0.182453			0.0912263	+	0.995830i	$0.470921\pi$
$752$		0			0
$753$	6.16515	−	10.6784i	0.224671	−	0.389141i
$754$		0			0
$755$	5.53901			0.201585
$756$		0			0
$757$	2.00000	−	3.46410i	0.0726912	−	0.125905i	−0.827389	−	0.561630i	$-0.810175\pi$
$757$	2.00000	−	3.46410i	0.0726912	−	0.125905i	0.900080	+	0.435725i	$0.143508\pi$
$758$		0			0
$759$	−6.62614	+	11.4768i	−0.240514	+	0.416582i
$760$		0			0
$761$	−10.2695	+	17.7873i	−0.372269	+	0.644789i	−0.989914	−	0.141668i	$-0.954754\pi$
$761$	−10.2695	+	17.7873i	−0.372269	+	0.644789i	0.617645	+	0.786457i	$0.288087\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	11.3739			0.411223
$766$		0			0
$767$	−22.5000	+	23.3827i	−0.812428	+	0.844300i
$768$		0			0
$769$	17.5000	−	30.3109i	0.631066	−	1.09304i	−0.356268	−	0.934384i	$-0.615951\pi$
$769$	17.5000	−	30.3109i	0.631066	−	1.09304i	0.987334	−	0.158655i	$-0.0507157\pi$
$770$		0			0
$771$	−0.873864	−	1.51358i	−0.0314714	−	0.0545101i
$772$		0			0
$773$	42.4955			1.52846			0.764228	−	0.644947i	$-0.223120\pi$
$773$	42.4955			1.52846			0.764228	+	0.644947i	$0.223120\pi$
$774$		0			0
$775$	2.18693	+	3.78788i	0.0785569	+	0.136065i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	24.1652	+	41.8553i	0.865806	+	1.49962i
$780$		0			0
$781$	0.626136	−	1.08450i	0.0224049	−	0.0388065i
$782$		0			0
$783$	16.9782	−	29.4071i	0.606752	−	1.05093i
$784$		0			0
$785$	−3.66061			−0.130653
$786$		0			0
$787$	−14.0000			−0.499046			−0.249523	−	0.968369i	$-0.580274\pi$
$787$	−14.0000			−0.499046			−0.249523	+	0.968369i	$0.580274\pi$
$788$		0			0
$789$	14.7695	−	25.5815i	0.525808	−	0.910727i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	2.00000	+	6.92820i	0.0710221	+	0.246028i
$794$		0			0
$795$	−1.56534	−	2.71125i	−0.0555169	−	0.0961581i
$796$		0			0
$797$	24.9564	+	43.2258i	0.884002	+	1.53114i	0.846853	+	0.531827i	$0.178494\pi$
$797$	24.9564	+	43.2258i	0.884002	+	1.53114i	0.0371497	+	0.999310i	$0.488172\pi$
$798$		0			0
$799$	−9.24773	−	16.0175i	−0.327161	−	0.566660i
$800$		0			0
$801$	20.0608	−	34.7463i	0.708813	−	1.22770i
$802$		0			0
$803$	−11.0780			−0.390935
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−32.6216	−	56.5023i	−1.14833	−	1.98897i
$808$		0			0
$809$	−3.08258	−	5.33918i	−0.108378	−	0.187715i	0.806736	−	0.590913i	$-0.201232\pi$
$809$	−3.08258	−	5.33918i	−0.108378	−	0.187715i	−0.915113	+	0.403197i	$0.867899\pi$
$810$		0			0
$811$	−25.8693			−0.908395			−0.454197	−	0.890901i	$-0.650074\pi$
$811$	−25.8693			−0.908395			−0.454197	+	0.890901i	$0.650074\pi$
$812$		0			0
$813$	5.23049	+	9.05948i	0.183441	+	0.317730i
$814$		0			0
$815$	16.4174			0.575077
$816$		0			0
$817$	−59.7477			−2.09031
$818$		0			0
$819$		0			0
$820$		0			0
$821$	33.0000			1.15171			0.575854	−	0.817553i	$-0.304670\pi$
$821$	33.0000			1.15171			0.575854	+	0.817553i	$0.304670\pi$
$822$		0			0
$823$	18.2523			0.636234			0.318117	−	0.948051i	$-0.396949\pi$
$823$	18.2523			0.636234			0.318117	+	0.948051i	$0.396949\pi$
$824$		0			0
$825$	4.83030	+	8.36633i	0.168170	+	0.291278i
$826$		0			0
$827$	4.12159			0.143322			0.0716609	−	0.997429i	$-0.477170\pi$
$827$	4.12159			0.143322			0.0716609	+	0.997429i	$0.477170\pi$
$828$		0			0
$829$	−21.1869	−	36.6968i	−0.735853	−	1.27453i	−0.954348	−	0.298696i	$-0.903448\pi$
$829$	−21.1869	−	36.6968i	−0.735853	−	1.27453i	0.218496	−	0.975838i	$-0.429885\pi$
$830$		0			0
$831$	−45.3521	−	78.5521i	−1.57325	−	2.72494i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−14.3739			−0.497428
$836$		0			0
$837$	−2.50000	+	4.33013i	−0.0864126	+	0.149671i
$838$		0			0
$839$	13.0218	+	22.5544i	0.449562	+	0.778664i	0.998357	−	0.0572927i	$-0.0182468\pi$
$839$	13.0218	+	22.5544i	0.449562	+	0.778664i	−0.548796	+	0.835957i	$0.684913\pi$
$840$		0			0
$841$	−8.56080	−	14.8277i	−0.295200	−	0.511301i
$842$		0			0
$843$	31.7477	+	54.9887i	1.09345	+	1.89391i
$844$		0			0
$845$	8.70417	−	5.48220i	0.299432	−	0.188594i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	36.2867	−	62.8505i	1.24536	−	2.15702i
$850$		0			0
$851$	−24.0000			−0.822709
$852$		0			0
$853$	−9.74773			−0.333756			−0.166878	−	0.985978i	$-0.553369\pi$
$853$	−9.74773			−0.333756			−0.166878	+	0.985978i	$0.553369\pi$
$854$		0			0
$855$	12.0826	−	20.9276i	0.413215	−	0.715710i
$856$		0			0
$857$	10.1044	−	17.5013i	0.345158	−	0.597832i	−0.640224	−	0.768188i	$-0.721159\pi$
$857$	10.1044	−	17.5013i	0.345158	−	0.597832i	0.985383	+	0.170356i	$0.0544919\pi$
$858$		0			0
$859$	7.00000	+	12.1244i	0.238837	+	0.413678i	0.960381	−	0.278691i	$-0.0899005\pi$
$859$	7.00000	+	12.1244i	0.238837	+	0.413678i	−0.721544	+	0.692369i	$0.756567\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1.41742	+	2.45505i	0.0482497	+	0.0835709i	0.889142	−	0.457632i	$-0.151302\pi$
$863$	1.41742	+	2.45505i	0.0482497	+	0.0835709i	−0.840892	+	0.541203i	$0.817969\pi$
$864$		0			0
$865$	12.1307			0.412456
$866$		0			0
$867$	11.1652	+	19.3386i	0.379188	+	0.656774i
$868$		0			0
$869$	1.58258	−	2.74110i	0.0536852	−	0.0929855i
$870$		0			0
$871$	−24.5000	−	6.06218i	−0.830151	−	0.205409i
$872$		0			0
$873$	22.1652			0.750177
$874$		0			0
$875$		0			0
$876$		0			0
$877$	11.8739	−	20.5661i	0.400952	−	0.694469i	−0.592889	−	0.805284i	$-0.702013\pi$
$877$	11.8739	−	20.5661i	0.400952	−	0.694469i	0.993841	+	0.110815i	$0.0353461\pi$
$878$		0			0
$879$	−18.9564	+	32.8335i	−0.639385	+	1.10745i
$880$		0			0
$881$	−3.70871	+	6.42368i	−0.124950	+	0.216419i	−0.921713	−	0.387872i	$-0.873210\pi$
$881$	−3.70871	+	6.42368i	−0.124950	+	0.216419i	0.796764	+	0.604291i	$0.206544\pi$
$882$		0			0
$883$	−29.7477			−1.00109			−0.500545	−	0.865710i	$-0.666867\pi$
$883$	−29.7477			−1.00109			−0.500545	+	0.865710i	$0.666867\pi$
$884$		0			0
$885$	9.93920	−	17.2152i	0.334103	−	0.578683i
$886$		0			0
$887$	25.2523			0.847888			0.423944	−	0.905688i	$-0.360645\pi$
$887$	25.2523			0.847888			0.423944	+	0.905688i	$0.360645\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.165151	−	0.286051i	0.00553278	−	0.00958306i
$892$		0			0
$893$	−39.2958			−1.31498
$894$		0			0
$895$	−1.81307	+	3.14033i	−0.0606042	+	0.104970i
$896$		0			0
$897$	58.6170	+	14.5040i	1.95717	+	0.484273i
$898$		0			0
$899$	3.39564	+	5.88143i	0.113251	+	0.196157i
$900$		0			0
$901$	−2.12614	+	3.68258i	−0.0708319	+	0.122684i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.08712	+	1.88295i	0.0361371	+	0.0625914i
$906$		0			0
$907$	−25.4955	−	44.1594i	−0.846563	−	1.46629i	−0.884257	−	0.467000i	$-0.845335\pi$
$907$	−25.4955	−	44.1594i	−0.846563	−	1.46629i	0.0376945	−	0.999289i	$-0.487999\pi$
$908$		0			0
$909$	−84.0345			−2.78725
$910$		0			0
$911$	32.3739			1.07259			0.536297	−	0.844029i	$-0.319823\pi$
$911$	32.3739			1.07259			0.536297	+	0.844029i	$0.319823\pi$
$912$		0			0
$913$	−3.56080	−	6.16748i	−0.117845	−	0.204114i
$914$		0			0
$915$	−2.20871	−	3.82560i	−0.0730178	−	0.126470i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−5.74773	+	9.95536i	−0.189600	+	0.328397i	−0.945117	−	0.326732i	$-0.894052\pi$
$919$	−5.74773	+	9.95536i	−0.189600	+	0.328397i	0.755517	+	0.655129i	$0.227386\pi$
$920$		0			0
$921$	−19.7087	−	34.1365i	−0.649424	−	1.12484i
$922$		0			0
$923$	−5.53901	−	1.37055i	−0.182319	−	0.0451122i
$924$		0			0
$925$	−8.74773	+	15.1515i	−0.287623	+	0.498179i
$926$		0			0
$927$	4.79129			0.157367
$928$		0			0
$929$	23.2913	−	40.3417i	0.764162	−	1.32357i	−0.176526	−	0.984296i	$-0.556486\pi$
$929$	23.2913	−	40.3417i	0.764162	−	1.32357i	0.940688	−	0.339272i	$-0.110181\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−52.9129			−1.73229
$934$		0			0
$935$	−0.939205	+	1.62675i	−0.0307153	+	0.0532004i
$936$		0			0
$937$	17.7477			0.579793			0.289896	−	0.957058i	$-0.406379\pi$
$937$	17.7477			0.579793			0.289896	+	0.957058i	$0.406379\pi$
$938$		0			0
$939$	9.41742	−	16.3115i	0.307326	−	0.532304i
$940$		0			0
$941$	19.0390	−	32.9765i	0.620654	−	1.07500i	−0.368710	−	0.929544i	$-0.620200\pi$
$941$	19.0390	−	32.9765i	0.620654	−	1.07500i	0.989364	−	0.145460i	$-0.0464662\pi$
$942$		0			0
$943$	22.7477	−	39.4002i	0.740768	−	1.28305i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−32.3739			−1.05201			−0.526005	−	0.850482i	$-0.676311\pi$
$947$	−32.3739			−1.05201			−0.526005	+	0.850482i	$0.676311\pi$
$948$		0			0
$949$	14.0000	+	48.4974i	0.454459	+	1.57429i
$950$		0			0
$951$	23.1434	−	40.0855i	0.750475	−	1.29986i
$952$		0			0
$953$	−4.33485	−	7.50818i	−0.140420	−	0.243214i	0.787235	−	0.616653i	$-0.211512\pi$
$953$	−4.33485	−	7.50818i	−0.140420	−	0.243214i	−0.927655	+	0.373439i	$0.878178\pi$
$954$		0			0
$955$	9.13068			0.295462
$956$		0			0
$957$	7.50000	+	12.9904i	0.242441	+	0.419919i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	15.0000	+	25.9808i	0.483871	+	0.838089i
$962$		0			0
$963$	−34.4347	+	59.6426i	−1.10964	+	1.92196i
$964$		0			0
$965$	−3.95644	+	6.85275i	−0.127362	+	0.220598i
$966$		0			0
$967$	3.74773			0.120519			0.0602594	−	0.998183i	$-0.480807\pi$
$967$	3.74773			0.120519			0.0602594	+	0.998183i	$0.480807\pi$
$968$		0			0
$969$	−53.3739			−1.71462
$970$		0			0
$971$	−15.7087	+	27.2083i	−0.504117	+	0.873156i	0.495872	+	0.868396i	$0.334848\pi$
$971$	−15.7087	+	27.2083i	−0.504117	+	0.873156i	−0.999989	+	0.00475994i	$0.998485\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	30.5218	−	31.7192i	0.977479	−	1.01583i
$976$		0			0
$977$	24.4129	+	42.2843i	0.781037	+	1.35280i	0.931338	+	0.364156i	$0.118642\pi$
$977$	24.4129	+	42.2843i	0.781037	+	1.35280i	−0.150301	+	0.988640i	$0.548024\pi$
$978$		0			0
$979$	3.31307	+	5.73840i	0.105886	+	0.183400i
$980$		0			0
$981$	−23.3521	−	40.4470i	−0.745575	−	1.29137i
$982$		0			0
$983$	−7.26951	+	12.5912i	−0.231861	+	0.401596i	−0.958356	−	0.285577i	$-0.907815\pi$
$983$	−7.26951	+	12.5912i	−0.231861	+	0.401596i	0.726495	+	0.687172i	$0.241148\pi$
$984$		0			0
$985$	0.626136			0.0199504
$986$		0			0
$987$		0			0
$988$		0			0
$989$	28.1216	+	48.7080i	0.894215	+	1.54883i
$990$		0			0
$991$	−11.8131	−	20.4608i	−0.375254	−	0.649960i	0.615111	−	0.788441i	$-0.289111\pi$
$991$	−11.8131	−	20.4608i	−0.375254	−	0.649960i	−0.990365	+	0.138481i	$0.955778\pi$
$992$		0			0
$993$	75.7042			2.40240
$994$		0			0
$995$	−6.23049	−	10.7915i	−0.197520	−	0.342114i
$996$		0			0
$997$	−35.0000			−1.10846			−0.554231	−	0.832363i	$-0.686987\pi$
$997$	−35.0000			−1.10846			−0.554231	+	0.832363i	$0.686987\pi$
$998$		0			0
$999$	−20.0000			−0.632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.i.i.165.1		4
7.2	even	3		2548.2.l.l.373.2		4
7.3	odd	6		364.2.k.d.113.2	yes	4
7.4	even	3		2548.2.k.e.1569.1		4
7.5	odd	6		2548.2.l.j.373.1		4
7.6	odd	2		2548.2.i.k.165.2		4
13.3	even	3		2548.2.l.l.1537.2		4
21.17	even	6		3276.2.z.e.3025.1		4
28.3	even	6		1456.2.s.k.113.1		4
91.3	odd	6		364.2.k.d.29.2	✓	4
91.16	even	3	inner	2548.2.i.i.1745.1		4
91.17	odd	6		4732.2.a.h.1.1		2
91.45	even	12		4732.2.g.e.337.1		4
91.55	odd	6		2548.2.l.j.1537.1		4
91.59	even	12		4732.2.g.e.337.2		4
91.68	odd	6		2548.2.i.k.1745.2		4
91.81	even	3		2548.2.k.e.393.1		4
91.87	odd	6		4732.2.a.g.1.1		2
273.185	even	6		3276.2.z.e.757.1		4
364.3	even	6		1456.2.s.k.1121.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.k.d.29.2	✓	4	91.3	odd	6
364.2.k.d.113.2	yes	4	7.3	odd	6
1456.2.s.k.113.1		4	28.3	even	6
1456.2.s.k.1121.1		4	364.3	even	6
2548.2.i.i.165.1		4	1.1	even	1	trivial
2548.2.i.i.1745.1		4	91.16	even	3	inner
2548.2.i.k.165.2		4	7.6	odd	2
2548.2.i.k.1745.2		4	91.68	odd	6
2548.2.k.e.393.1		4	91.81	even	3
2548.2.k.e.1569.1		4	7.4	even	3
2548.2.l.j.373.1		4	7.5	odd	6
2548.2.l.j.1537.1		4	91.55	odd	6
2548.2.l.l.373.2		4	7.2	even	3
2548.2.l.l.1537.2		4	13.3	even	3
3276.2.z.e.757.1		4	273.185	even	6
3276.2.z.e.3025.1		4	21.17	even	6
4732.2.a.g.1.1		2	91.87	odd	6
4732.2.a.h.1.1		2	91.17	odd	6
4732.2.g.e.337.1		4	91.45	even	12
4732.2.g.e.337.2		4	91.59	even	12

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:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2548.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.39564 - 2.41733i) q^{3} +(0.395644 + 0.685275i) q^{5} +(-2.39564 + 4.14938i) q^{9} +(-0.395644 - 0.685275i) q^{11} +(-2.50000 + 2.59808i) q^{13} +(1.10436 - 1.91280i) q^{15} -3.00000 q^{17} +(-3.18693 + 5.51993i) q^{19} +6.00000 q^{23} +(2.18693 - 3.78788i) q^{25} +5.00000 q^{27} +(3.39564 - 5.88143i) q^{29} +(-0.500000 + 0.866025i) q^{31} +(-1.10436 + 1.91280i) q^{33} -4.00000 q^{37} +(9.76951 + 2.41733i) q^{39} +(3.79129 - 6.56670i) q^{41} +(4.68693 + 8.11800i) q^{43} -3.79129 q^{45} +(3.08258 + 5.33918i) q^{47} +(4.18693 + 7.25198i) q^{51} +(0.708712 - 1.22753i) q^{53} +(0.313068 - 0.542250i) q^{55} +17.7913 q^{57} +9.00000 q^{59} +(1.00000 - 1.73205i) q^{61} +(-2.76951 - 0.685275i) q^{65} +(3.50000 + 6.06218i) q^{67} +(-8.37386 - 14.5040i) q^{69} +(0.791288 + 1.37055i) q^{71} +(7.00000 - 12.1244i) q^{73} -12.2087 q^{75} +(2.00000 + 3.46410i) q^{79} +(0.208712 + 0.361500i) q^{81} +9.00000 q^{83} +(-1.18693 - 2.05583i) q^{85} -18.9564 q^{87} -8.37386 q^{89} +2.79129 q^{93} -5.04356 q^{95} +(-2.31307 - 4.00635i) q^{97} +3.79129 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} - 3 q^{5} - 5 q^{9} + 3 q^{11} - 10 q^{13} + 9 q^{15} - 12 q^{17} + q^{19} + 24 q^{23} - 5 q^{25} + 20 q^{27} + 9 q^{29} - 2 q^{31} - 9 q^{33} - 16 q^{37} + 7 q^{39} + 6 q^{41} + 5 q^{43}+ \cdots + 6 q^{99}+O(q^{100}) \) 4 * q - q^3 - 3 * q^5 - 5 * q^9 + 3 * q^11 - 10 * q^13 + 9 * q^15 - 12 * q^17 + q^19 + 24 * q^23 - 5 * q^25 + 20 * q^27 + 9 * q^29 - 2 * q^31 - 9 * q^33 - 16 * q^37 + 7 * q^39 + 6 * q^41 + 5 * q^43 - 6 * q^45 - 6 * q^47 + 3 * q^51 + 12 * q^53 + 15 * q^55 + 62 * q^57 + 36 * q^59 + 4 * q^61 + 21 * q^65 + 14 * q^67 - 6 * q^69 - 6 * q^71 + 28 * q^73 - 58 * q^75 + 8 * q^79 + 10 * q^81 + 36 * q^83 + 9 * q^85 - 30 * q^87 - 6 * q^89 + 2 * q^93 - 66 * q^95 - 23 * q^97 + 6 * q^99

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