LMFDB - Embedded newform 496.2.i.h.129.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [496,2,Mod(129,496)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(496, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("496.129"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 496 = 2^{4} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	496.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-2,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$3.96057994026$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			129.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	496.129
Dual form			496.2.i.h.273.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.20711 + 2.09077i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(1.20711 - 2.09077i) q^{7} +(-1.41421 - 2.44949i) q^{9} +(-2.62132 - 4.54026i) q^{11} +(-0.914214 - 1.58346i) q^{13} +2.41421 q^{15} +(0.0857864 - 0.148586i) q^{17} +(0.792893 - 1.37333i) q^{19} +(2.91421 + 5.04757i) q^{21} +4.00000 q^{23} +(2.00000 - 3.46410i) q^{25} -0.414214 q^{27} -1.17157 q^{29} +(5.00000 + 2.44949i) q^{31} +12.6569 q^{33} -2.41421 q^{35} +(-0.500000 + 0.866025i) q^{37} +4.41421 q^{39} +(-4.74264 - 8.21449i) q^{41} +(4.44975 - 7.70719i) q^{43} +(-1.41421 + 2.44949i) q^{45} +1.65685 q^{47} +(0.585786 + 1.01461i) q^{49} +(0.207107 + 0.358719i) q^{51} +(-0.0857864 - 0.148586i) q^{53} +(-2.62132 + 4.54026i) q^{55} +(1.91421 + 3.31552i) q^{57} +(-5.03553 + 8.72180i) q^{59} +2.82843 q^{61} -6.82843 q^{63} +(-0.914214 + 1.58346i) q^{65} +(-2.62132 - 4.54026i) q^{67} +(-4.82843 + 8.36308i) q^{69} +(-7.03553 - 12.1859i) q^{71} +(-1.91421 - 3.31552i) q^{73} +(4.82843 + 8.36308i) q^{75} -12.6569 q^{77} +(-7.62132 + 13.2005i) q^{79} +(4.74264 - 8.21449i) q^{81} +(2.03553 + 3.52565i) q^{83} -0.171573 q^{85} +(1.41421 - 2.44949i) q^{87} -12.4853 q^{89} -4.41421 q^{91} +(-11.1569 + 7.49706i) q^{93} -1.58579 q^{95} +10.8284 q^{97} +(-7.41421 + 12.8418i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 2 q^{5} + 2 q^{7} - 2 q^{11} + 2 q^{13} + 4 q^{15} + 6 q^{17} + 6 q^{19} + 6 q^{21} + 16 q^{23} + 8 q^{25} + 4 q^{27} - 16 q^{29} + 20 q^{31} + 28 q^{33} - 4 q^{35} - 2 q^{37} + 12 q^{39}+ \cdots - 24 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 2 * q^5 + 2 * q^7 - 2 * q^11 + 2 * q^13 + 4 * q^15 + 6 * q^17 + 6 * q^19 + 6 * q^21 + 16 * q^23 + 8 * q^25 + 4 * q^27 - 16 * q^29 + 20 * q^31 + 28 * q^33 - 4 * q^35 - 2 * q^37 + 12 * q^39 - 2 * q^41 - 2 * q^43 - 16 * q^47 + 8 * q^49 - 2 * q^51 - 6 * q^53 - 2 * q^55 + 2 * q^57 - 6 * q^59 - 16 * q^63 + 2 * q^65 - 2 * q^67 - 8 * q^69 - 14 * q^71 - 2 * q^73 + 8 * q^75 - 28 * q^77 - 22 * q^79 + 2 * q^81 - 6 * q^83 - 12 * q^85 - 16 * q^89 - 12 * q^91 - 22 * q^93 - 12 * q^95 + 32 * q^97 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/496\mathbb{Z}\right)^\times$.

$n$	$63$	$65$	$373$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−1.20711	+	2.09077i	−0.696923	+	1.20711i	0.272605	+	0.962126i	$0.412115\pi$
$3$	−1.20711	+	2.09077i	−0.696923	+	1.20711i	−0.969528	+	0.244981i	$0.921218\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$		0			0
$7$	1.20711	−	2.09077i	0.456243	−	0.790237i	−0.542515	−	0.840046i	$-0.682528\pi$
$7$	1.20711	−	2.09077i	0.456243	−	0.790237i	0.998759	+	0.0498090i	$0.0158613\pi$
$8$		0			0
$9$	−1.41421	−	2.44949i	−0.471405	−	0.816497i
$10$		0			0
$11$	−2.62132	−	4.54026i	−0.790358	−	1.36894i	−0.925745	−	0.378147i	$-0.876561\pi$
$11$	−2.62132	−	4.54026i	−0.790358	−	1.36894i	0.135388	−	0.990793i	$-0.456772\pi$
$12$		0			0
$13$	−0.914214	−	1.58346i	−0.253557	−	0.439174i	0.710945	−	0.703247i	$-0.248267\pi$
$13$	−0.914214	−	1.58346i	−0.253557	−	0.439174i	−0.964503	+	0.264073i	$0.914934\pi$
$14$		0			0
$15$	2.41421			0.623347
$16$		0			0
$17$	0.0857864	−	0.148586i	0.0208063	−	0.0360375i	−0.855435	−	0.517911i	$-0.826710\pi$
$17$	0.0857864	−	0.148586i	0.0208063	−	0.0360375i	0.876241	+	0.481873i	$0.160043\pi$
$18$		0			0
$19$	0.792893	−	1.37333i	0.181902	−	0.315064i	−0.760626	−	0.649190i	$-0.775108\pi$
$19$	0.792893	−	1.37333i	0.181902	−	0.315064i	0.942528	+	0.334126i	$0.108441\pi$
$20$		0			0
$21$	2.91421	+	5.04757i	0.635934	+	1.10147i
$22$		0			0
$23$	4.00000			0.834058			0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000			0.834058			0.417029	+	0.908893i	$0.363071\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$		0			0
$27$	−0.414214			−0.0797154
$28$		0			0
$29$	−1.17157			−0.217556			−0.108778	−	0.994066i	$-0.534694\pi$
$29$	−1.17157			−0.217556			−0.108778	+	0.994066i	$0.534694\pi$
$30$		0			0
$31$	5.00000	+	2.44949i	0.898027	+	0.439941i
$31$	5.00000	+	2.44949i	0.898027	+	0.439941i
$32$		0			0
$33$	12.6569			2.20328
$34$		0			0
$35$	−2.41421			−0.408077
$36$		0			0
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	0.821995	+	0.569495i	$0.192861\pi$
$38$		0			0
$39$	4.41421			0.706840
$40$		0			0
$41$	−4.74264	−	8.21449i	−0.740676	−	1.28289i	−0.952188	−	0.305513i	$-0.901172\pi$
$41$	−4.74264	−	8.21449i	−0.740676	−	1.28289i	0.211512	−	0.977375i	$-0.432161\pi$
$42$		0			0
$43$	4.44975	−	7.70719i	0.678580	−	1.17534i	−0.296828	−	0.954931i	$-0.595929\pi$
$43$	4.44975	−	7.70719i	0.678580	−	1.17534i	0.975409	−	0.220404i	$-0.0707377\pi$
$44$		0			0
$45$	−1.41421	+	2.44949i	−0.210819	+	0.365148i
$46$		0			0
$47$	1.65685			0.241677			0.120839	−	0.992672i	$-0.461442\pi$
$47$	1.65685			0.241677			0.120839	+	0.992672i	$0.461442\pi$
$48$		0			0
$49$	0.585786	+	1.01461i	0.0836838	+	0.144945i
$50$		0			0
$51$	0.207107	+	0.358719i	0.0290008	+	0.0502308i
$52$		0			0
$53$	−0.0857864	−	0.148586i	−0.0117837	−	0.0204099i	0.860073	−	0.510170i	$-0.170418\pi$
$53$	−0.0857864	−	0.148586i	−0.0117837	−	0.0204099i	−0.871857	+	0.489760i	$0.837084\pi$
$54$		0			0
$55$	−2.62132	+	4.54026i	−0.353459	+	0.612209i
$56$		0			0
$57$	1.91421	+	3.31552i	0.253544	+	0.439151i
$58$		0			0
$59$	−5.03553	+	8.72180i	−0.655571	+	1.13548i	0.326180	+	0.945308i	$0.394239\pi$
$59$	−5.03553	+	8.72180i	−0.655571	+	1.13548i	−0.981750	+	0.190174i	$0.939095\pi$
$60$		0			0
$61$	2.82843			0.362143			0.181071	−	0.983470i	$-0.442043\pi$
$61$	2.82843			0.362143			0.181071	+	0.983470i	$0.442043\pi$
$62$		0			0
$63$	−6.82843			−0.860301
$64$		0			0
$65$	−0.914214	+	1.58346i	−0.113394	+	0.196405i
$66$		0			0
$67$	−2.62132	−	4.54026i	−0.320245	−	0.554681i	0.660293	−	0.751008i	$-0.270432\pi$
$67$	−2.62132	−	4.54026i	−0.320245	−	0.554681i	−0.980539	+	0.196327i	$0.937099\pi$
$68$		0			0
$69$	−4.82843	+	8.36308i	−0.581274	+	1.00680i
$70$		0			0
$71$	−7.03553	−	12.1859i	−0.834964	−	1.44620i	−0.894060	−	0.447948i	$-0.852155\pi$
$71$	−7.03553	−	12.1859i	−0.834964	−	1.44620i	0.0590953	−	0.998252i	$-0.481178\pi$
$72$		0			0
$73$	−1.91421	−	3.31552i	−0.224042	−	0.388052i	0.731990	−	0.681316i	$-0.238592\pi$
$73$	−1.91421	−	3.31552i	−0.224042	−	0.388052i	−0.956032	+	0.293264i	$0.905259\pi$
$74$		0			0
$75$	4.82843	+	8.36308i	0.557539	+	0.965685i
$76$		0			0
$77$	−12.6569			−1.44238
$78$		0			0
$79$	−7.62132	+	13.2005i	−0.857466	+	1.48517i	0.0168732	+	0.999858i	$0.494629\pi$
$79$	−7.62132	+	13.2005i	−0.857466	+	1.48517i	−0.874339	+	0.485316i	$0.838704\pi$
$80$		0			0
$81$	4.74264	−	8.21449i	0.526960	−	0.912722i
$82$		0			0
$83$	2.03553	+	3.52565i	0.223429	+	0.386990i	0.955847	−	0.293865i	$-0.0949416\pi$
$83$	2.03553	+	3.52565i	0.223429	+	0.386990i	−0.732418	+	0.680855i	$0.761608\pi$
$84$		0			0
$85$	−0.171573			−0.0186097
$86$		0			0
$87$	1.41421	−	2.44949i	0.151620	−	0.262613i
$88$		0			0
$89$	−12.4853			−1.32344			−0.661719	−	0.749752i	$-0.730173\pi$
$89$	−12.4853			−1.32344			−0.661719	+	0.749752i	$0.730173\pi$
$90$		0			0
$91$	−4.41421			−0.462735
$92$		0			0
$93$	−11.1569	+	7.49706i	−1.15691	+	0.777408i
$94$		0			0
$95$	−1.58579			−0.162698
$96$		0			0
$97$	10.8284			1.09946			0.549730	−	0.835342i	$-0.314731\pi$
$97$	10.8284			1.09946			0.549730	+	0.835342i	$0.314731\pi$
$98$		0			0
$99$	−7.41421	+	12.8418i	−0.745157	+	1.29065i
$100$		0			0
$101$	8.48528			0.844317			0.422159	−	0.906522i	$-0.361273\pi$
$101$	8.48528			0.844317			0.422159	+	0.906522i	$0.361273\pi$
$102$		0			0
$103$	−6.03553	−	10.4539i	−0.594699	−	1.03005i	−0.993589	−	0.113050i	$-0.963938\pi$
$103$	−6.03553	−	10.4539i	−0.594699	−	1.03005i	0.398890	−	0.916999i	$-0.369395\pi$
$104$		0			0
$105$	2.91421	−	5.04757i	0.284398	−	0.492592i
$106$		0			0
$107$	4.79289	−	8.30153i	0.463346	−	0.802540i	−0.535779	−	0.844358i	$-0.679982\pi$
$107$	4.79289	−	8.30153i	0.463346	−	0.802540i	0.999125	+	0.0418188i	$0.0133152\pi$
$108$		0			0
$109$	−5.17157			−0.495347			−0.247673	−	0.968844i	$-0.579666\pi$
$109$	−5.17157			−0.495347			−0.247673	+	0.968844i	$0.579666\pi$
$110$		0			0
$111$	−1.20711	−	2.09077i	−0.114574	−	0.198447i
$112$		0			0
$113$	−2.67157	−	4.62730i	−0.251320	−	0.435300i	0.712569	−	0.701602i	$-0.247531\pi$
$113$	−2.67157	−	4.62730i	−0.251320	−	0.435300i	−0.963890	+	0.266302i	$0.914198\pi$
$114$		0			0
$115$	−2.00000	−	3.46410i	−0.186501	−	0.323029i
$116$		0			0
$117$	−2.58579	+	4.47871i	−0.239056	+	0.414057i
$118$		0			0
$119$	−0.207107	−	0.358719i	−0.0189854	−	0.0328838i
$120$		0			0
$121$	−8.24264	+	14.2767i	−0.749331	+	1.29788i
$122$		0			0
$123$	22.8995			2.06478
$124$		0			0
$125$	−9.00000			−0.804984
$126$		0			0
$127$	−5.44975	+	9.43924i	−0.483587	+	0.837597i	−0.999822	−	0.0188496i	$-0.994000\pi$
$127$	−5.44975	+	9.43924i	−0.483587	+	0.837597i	0.516235	+	0.856447i	$0.327333\pi$
$128$		0			0
$129$	10.7426	+	18.6068i	0.945837	+	1.63824i
$130$		0			0
$131$	−2.37868	+	4.11999i	−0.207826	+	0.359966i	−0.951030	−	0.309100i	$-0.899972\pi$
$131$	−2.37868	+	4.11999i	−0.207826	+	0.359966i	0.743203	+	0.669066i	$0.233306\pi$
$132$		0			0
$133$	−1.91421	−	3.31552i	−0.165983	−	0.287492i
$134$		0			0
$135$	0.207107	+	0.358719i	0.0178249	+	0.0308737i
$136$		0			0
$137$	3.74264	+	6.48244i	0.319755	+	0.553833i	0.980437	−	0.196834i	$-0.0630659\pi$
$137$	3.74264	+	6.48244i	0.319755	+	0.553833i	−0.660681	+	0.750666i	$0.729733\pi$
$138$		0			0
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$		0			0
$141$	−2.00000	+	3.46410i	−0.168430	+	0.291730i
$142$		0			0
$143$	−4.79289	+	8.30153i	−0.400802	+	0.694209i
$144$		0			0
$145$	0.585786	+	1.01461i	0.0486469	+	0.0842589i
$146$		0			0
$147$	−2.82843			−0.233285
$148$		0			0
$149$	−0.500000	+	0.866025i	−0.0409616	+	0.0709476i	−0.885779	−	0.464107i	$-0.846375\pi$
$149$	−0.500000	+	0.866025i	−0.0409616	+	0.0709476i	0.844818	+	0.535054i	$0.179709\pi$
$150$		0			0
$151$	17.3137			1.40897			0.704485	−	0.709719i	$-0.251178\pi$
$151$	17.3137			1.40897			0.704485	+	0.709719i	$0.251178\pi$
$152$		0			0
$153$	−0.485281			−0.0392327
$154$		0			0
$155$	−0.378680	−	5.55487i	−0.0304163	−	0.446178i
$156$		0			0
$157$	14.8284			1.18344			0.591719	−	0.806145i	$-0.298450\pi$
$157$	14.8284			1.18344			0.591719	+	0.806145i	$0.298450\pi$
$158$		0			0
$159$	0.414214			0.0328493
$160$		0			0
$161$	4.82843	−	8.36308i	0.380533	−	0.659103i
$162$		0			0
$163$	12.9706			1.01593			0.507966	−	0.861377i	$-0.330397\pi$
$163$	12.9706			1.01593			0.507966	+	0.861377i	$0.330397\pi$
$164$		0			0
$165$	−6.32843	−	10.9612i	−0.492667	−	0.853325i
$166$		0			0
$167$	−4.27817	+	7.41002i	−0.331055	+	0.573404i	−0.982719	−	0.185104i	$-0.940738\pi$
$167$	−4.27817	+	7.41002i	−0.331055	+	0.573404i	0.651664	+	0.758508i	$0.274071\pi$
$168$		0			0
$169$	4.82843	−	8.36308i	0.371417	−	0.643314i
$170$		0			0
$171$	−4.48528			−0.342998
$172$		0			0
$173$	7.15685	+	12.3960i	0.544126	+	0.942453i	0.998661	+	0.0517246i	$0.0164718\pi$
$173$	7.15685	+	12.3960i	0.544126	+	0.942453i	−0.454536	+	0.890728i	$0.650195\pi$
$174$		0			0
$175$	−4.82843	−	8.36308i	−0.364995	−	0.632190i
$176$		0			0
$177$	−12.1569	−	21.0563i	−0.913765	−	1.58269i
$178$		0			0
$179$	−3.37868	+	5.85204i	−0.252534	+	0.437402i	−0.964223	−	0.265093i	$-0.914597\pi$
$179$	−3.37868	+	5.85204i	−0.252534	+	0.437402i	0.711689	+	0.702495i	$0.247931\pi$
$180$		0			0
$181$	5.15685	+	8.93193i	0.383306	+	0.663905i	0.991533	−	0.129858i	$-0.0414522\pi$
$181$	5.15685	+	8.93193i	0.383306	+	0.663905i	−0.608227	+	0.793763i	$0.708119\pi$
$182$		0			0
$183$	−3.41421	+	5.91359i	−0.252386	+	0.437145i
$184$		0			0
$185$	1.00000			0.0735215
$186$		0			0
$187$	−0.899495			−0.0657776
$188$		0			0
$189$	−0.500000	+	0.866025i	−0.0363696	+	0.0629941i
$190$		0			0
$191$	−0.550253	−	0.953065i	−0.0398149	−	0.0689614i	0.845431	−	0.534084i	$-0.179343\pi$
$191$	−0.550253	−	0.953065i	−0.0398149	−	0.0689614i	−0.885246	+	0.465123i	$0.846010\pi$
$192$		0			0
$193$	10.5711	−	18.3096i	0.760922	−	1.31796i	−0.181454	−	0.983399i	$-0.558080\pi$
$193$	10.5711	−	18.3096i	0.760922	−	1.31796i	0.942376	−	0.334556i	$-0.108586\pi$
$194$		0			0
$195$	−2.20711	−	3.82282i	−0.158054	−	0.273758i
$196$		0			0
$197$	−1.74264	−	3.01834i	−0.124158	−	0.215048i	0.797245	−	0.603655i	$-0.206290\pi$
$197$	−1.74264	−	3.01834i	−0.124158	−	0.215048i	−0.921404	+	0.388607i	$0.872956\pi$
$198$		0			0
$199$	7.79289	+	13.4977i	0.552424	+	0.956826i	0.998099	+	0.0616310i	$0.0196302\pi$
$199$	7.79289	+	13.4977i	0.552424	+	0.956826i	−0.445675	+	0.895195i	$0.647036\pi$
$200$		0			0
$201$	12.6569			0.892746
$202$		0			0
$203$	−1.41421	+	2.44949i	−0.0992583	+	0.171920i
$204$		0			0
$205$	−4.74264	+	8.21449i	−0.331240	+	0.573725i
$206$		0			0
$207$	−5.65685	−	9.79796i	−0.393179	−	0.681005i
$208$		0			0
$209$	−8.31371			−0.575071
$210$		0			0
$211$	3.79289	−	6.56948i	0.261114	−	0.452262i	−0.705425	−	0.708785i	$-0.749244\pi$
$211$	3.79289	−	6.56948i	0.261114	−	0.452262i	0.966538	+	0.256523i	$0.0825770\pi$
$212$		0			0
$213$	33.9706			2.32762
$214$		0			0
$215$	−8.89949			−0.606941
$216$		0			0
$217$	11.1569	−	7.49706i	0.757377	−	0.508933i
$218$		0			0
$219$	9.24264			0.624560
$220$		0			0
$221$	−0.313708			−0.0211023
$222$		0			0
$223$	0.863961	−	1.49642i	0.0578551	−	0.100208i	−0.835647	−	0.549266i	$-0.814907\pi$
$223$	0.863961	−	1.49642i	0.0578551	−	0.100208i	0.893502	+	0.449059i	$0.148241\pi$
$224$		0			0
$225$	−11.3137			−0.754247
$226$		0			0
$227$	−7.79289	−	13.4977i	−0.517232	−	0.895873i	−0.999800	−	0.0200140i	$-0.993629\pi$
$227$	−7.79289	−	13.4977i	−0.517232	−	0.895873i	0.482567	−	0.875859i	$-0.339704\pi$
$228$		0			0
$229$	−5.74264	+	9.94655i	−0.379484	+	0.657286i	−0.990987	−	0.133956i	$-0.957232\pi$
$229$	−5.74264	+	9.94655i	−0.379484	+	0.657286i	0.611503	+	0.791242i	$0.290565\pi$
$230$		0			0
$231$	15.2782	−	26.4626i	1.00523	−	1.74111i
$232$		0			0
$233$	−14.8284			−0.971443			−0.485721	−	0.874114i	$-0.661443\pi$
$233$	−14.8284			−0.971443			−0.485721	+	0.874114i	$0.661443\pi$
$234$		0			0
$235$	−0.828427	−	1.43488i	−0.0540406	−	0.0936011i
$236$		0			0
$237$	−18.3995	−	31.8689i	−1.19518	−	2.07010i
$238$		0			0
$239$	−6.37868	−	11.0482i	−0.412602	−	0.714648i	0.582571	−	0.812780i	$-0.302047\pi$
$239$	−6.37868	−	11.0482i	−0.412602	−	0.714648i	−0.995173	+	0.0981314i	$0.968713\pi$
$240$		0			0
$241$	−12.3284	+	21.3535i	−0.794144	+	1.37550i	0.129238	+	0.991614i	$0.458747\pi$
$241$	−12.3284	+	21.3535i	−0.794144	+	1.37550i	−0.923381	+	0.383884i	$0.874586\pi$
$242$		0			0
$243$	10.8284	+	18.7554i	0.694644	+	1.20316i
$244$		0			0
$245$	0.585786	−	1.01461i	0.0374245	−	0.0648212i
$246$		0			0
$247$	−2.89949			−0.184490
$248$		0			0
$249$	−9.82843			−0.622851
$250$		0			0
$251$	1.79289	−	3.10538i	0.113166	−	0.196010i	−0.803879	−	0.594793i	$-0.797234\pi$
$251$	1.79289	−	3.10538i	0.113166	−	0.196010i	0.917045	+	0.398783i	$0.130567\pi$
$252$		0			0
$253$	−10.4853	−	18.1610i	−0.659204	−	1.14177i
$254$		0			0
$255$	0.207107	−	0.358719i	0.0129695	−	0.0224639i
$256$		0			0
$257$	0.156854	+	0.271680i	0.00978430	+	0.0169469i	0.870876	−	0.491503i	$-0.163552\pi$
$257$	0.156854	+	0.271680i	0.00978430	+	0.0169469i	−0.861092	+	0.508450i	$0.830219\pi$
$258$		0			0
$259$	1.20711	+	2.09077i	0.0750060	+	0.129914i
$260$		0			0
$261$	1.65685	+	2.86976i	0.102557	+	0.177633i
$262$		0			0
$263$	0.686292			0.0423185			0.0211593	−	0.999776i	$-0.493264\pi$
$263$	0.686292			0.0423185			0.0211593	+	0.999776i	$0.493264\pi$
$264$		0			0
$265$	−0.0857864	+	0.148586i	−0.00526982	+	0.00912759i
$266$		0			0
$267$	15.0711	−	26.1039i	0.922334	−	1.59753i
$268$		0			0
$269$	15.9142	+	27.5642i	0.970307	+	1.68062i	0.694626	+	0.719371i	$0.255570\pi$
$269$	15.9142	+	27.5642i	0.970307	+	1.68062i	0.275681	+	0.961249i	$0.411097\pi$
$270$		0			0
$271$	23.3137			1.41621			0.708103	−	0.706109i	$-0.249551\pi$
$271$	23.3137			1.41621			0.708103	+	0.706109i	$0.249551\pi$
$272$		0			0
$273$	5.32843	−	9.22911i	0.322491	−	0.558571i
$274$		0			0
$275$	−20.9706			−1.26457
$276$		0			0
$277$	−14.1421			−0.849719			−0.424859	−	0.905259i	$-0.639676\pi$
$277$	−14.1421			−0.849719			−0.424859	+	0.905259i	$0.639676\pi$
$278$		0			0
$279$	−1.07107	−	15.7116i	−0.0641232	−	0.940626i
$280$		0			0
$281$	2.00000			0.119310			0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000			0.119310			0.0596550	+	0.998219i	$0.481000\pi$
$282$		0			0
$283$	2.34315			0.139286			0.0696428	−	0.997572i	$-0.477814\pi$
$283$	2.34315			0.139286			0.0696428	+	0.997572i	$0.477814\pi$
$284$		0			0
$285$	1.91421	−	3.31552i	0.113388	−	0.196394i
$286$		0			0
$287$	−22.8995			−1.35171
$288$		0			0
$289$	8.48528	+	14.6969i	0.499134	+	0.864526i
$290$		0			0
$291$	−13.0711	+	22.6398i	−0.766240	+	1.32717i
$292$		0			0
$293$	12.3995	−	21.4766i	0.724386	−	1.25467i	−0.234840	−	0.972034i	$-0.575457\pi$
$293$	12.3995	−	21.4766i	0.724386	−	1.25467i	0.959226	−	0.282640i	$-0.0912101\pi$
$294$		0			0
$295$	10.0711			0.586360
$296$		0			0
$297$	1.08579	+	1.88064i	0.0630037	+	0.109126i
$298$		0			0
$299$	−3.65685	−	6.33386i	−0.211481	−	0.366296i
$300$		0			0
$301$	−10.7426	−	18.6068i	−0.619196	−	1.07248i
$302$		0			0
$303$	−10.2426	+	17.7408i	−0.588424	+	1.01918i
$304$		0			0
$305$	−1.41421	−	2.44949i	−0.0809776	−	0.140257i
$306$		0			0
$307$	−1.37868	+	2.38794i	−0.0786854	+	0.136287i	−0.902683	−	0.430306i	$-0.858406\pi$
$307$	−1.37868	+	2.38794i	−0.0786854	+	0.136287i	0.823998	+	0.566593i	$0.191739\pi$
$308$		0			0
$309$	29.1421			1.65784
$310$		0			0
$311$	11.3137			0.641542			0.320771	−	0.947157i	$-0.396058\pi$
$311$	11.3137			0.641542			0.320771	+	0.947157i	$0.396058\pi$
$312$		0			0
$313$	−1.91421	+	3.31552i	−0.108198	+	0.187404i	−0.915040	−	0.403363i	$-0.867841\pi$
$313$	−1.91421	+	3.31552i	−0.108198	+	0.187404i	0.806842	+	0.590767i	$0.201175\pi$
$314$		0			0
$315$	3.41421	+	5.91359i	0.192369	+	0.333193i
$316$		0			0
$317$	1.08579	−	1.88064i	0.0609838	−	0.105627i	−0.833922	−	0.551883i	$-0.813910\pi$
$317$	1.08579	−	1.88064i	0.0609838	−	0.105627i	0.894905	+	0.446256i	$0.147243\pi$
$318$		0			0
$319$	3.07107	+	5.31925i	0.171947	+	0.297821i
$320$		0			0
$321$	11.5711	+	20.0417i	0.645834	+	1.11862i
$322$		0			0
$323$	−0.136039	−	0.235626i	−0.00756941	−	0.0131106i
$324$		0			0
$325$	−7.31371			−0.405692
$326$		0			0
$327$	6.24264	−	10.8126i	0.345219	−	0.597937i
$328$		0			0
$329$	2.00000	−	3.46410i	0.110264	−	0.190982i
$330$		0			0
$331$	0.378680	+	0.655892i	0.0208141	+	0.0360511i	0.876245	−	0.481866i	$-0.160041\pi$
$331$	0.378680	+	0.655892i	0.0208141	+	0.0360511i	−0.855431	+	0.517917i	$0.826708\pi$
$332$		0			0
$333$	2.82843			0.154997
$334$		0			0
$335$	−2.62132	+	4.54026i	−0.143218	+	0.248061i
$336$		0			0
$337$	−13.3137			−0.725244			−0.362622	−	0.931936i	$-0.618118\pi$
$337$	−13.3137			−0.725244			−0.362622	+	0.931936i	$0.618118\pi$
$338$		0			0
$339$	12.8995			0.700604
$340$		0			0
$341$	−1.98528	−	29.1222i	−0.107509	−	1.57706i
$342$		0			0
$343$	19.7279			1.06521
$344$		0			0
$345$	9.65685			0.519908
$346$		0			0
$347$	11.2782	−	19.5344i	0.605444	−	1.04866i	−0.386537	−	0.922274i	$-0.626329\pi$
$347$	11.2782	−	19.5344i	0.605444	−	1.04866i	0.991981	−	0.126386i	$-0.0403378\pi$
$348$		0			0
$349$	35.1127			1.87954			0.939770	−	0.341808i	$-0.111039\pi$
$349$	35.1127			1.87954			0.939770	+	0.341808i	$0.111039\pi$
$350$		0			0
$351$	0.378680	+	0.655892i	0.0202124	+	0.0350089i
$352$		0			0
$353$	−1.50000	+	2.59808i	−0.0798369	+	0.138282i	−0.903179	−	0.429263i	$-0.858773\pi$
$353$	−1.50000	+	2.59808i	−0.0798369	+	0.138282i	0.823343	+	0.567545i	$0.192107\pi$
$354$		0			0
$355$	−7.03553	+	12.1859i	−0.373407	+	0.646761i
$356$		0			0
$357$	1.00000			0.0529256
$358$		0			0
$359$	13.4497	+	23.2956i	0.709851	+	1.22950i	0.964912	+	0.262572i	$0.0845709\pi$
$359$	13.4497	+	23.2956i	0.709851	+	1.22950i	−0.255062	+	0.966925i	$0.582096\pi$
$360$		0			0
$361$	8.24264	+	14.2767i	0.433823	+	0.751404i
$362$		0			0
$363$	−19.8995	−	34.4669i	−1.04445	−	1.80904i
$364$		0			0
$365$	−1.91421	+	3.31552i	−0.100195	+	0.173542i
$366$		0			0
$367$	9.10660	+	15.7731i	0.475361	+	0.823349i	0.999602	−	0.0282210i	$-0.00898422\pi$
$367$	9.10660	+	15.7731i	0.475361	+	0.823349i	−0.524241	+	0.851570i	$0.675651\pi$
$368$		0			0
$369$	−13.4142	+	23.2341i	−0.698316	+	1.20952i
$370$		0			0
$371$	−0.414214			−0.0215049
$372$		0			0
$373$	10.0000			0.517780			0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000			0.517780			0.258890	+	0.965907i	$0.416643\pi$
$374$		0			0
$375$	10.8640	−	18.8169i	0.561013	−	0.971702i
$376$		0			0
$377$	1.07107	+	1.85514i	0.0551628	+	0.0955448i
$378$		0			0
$379$	−14.6924	+	25.4480i	−0.754697	+	1.30717i	0.190827	+	0.981624i	$0.438883\pi$
$379$	−14.6924	+	25.4480i	−0.754697	+	1.30717i	−0.945525	+	0.325550i	$0.894450\pi$
$380$		0			0
$381$	−13.1569	−	22.7883i	−0.674046	−	1.16748i
$382$		0			0
$383$	12.4497	+	21.5636i	0.636152	+	1.10185i	0.986270	+	0.165142i	$0.0528084\pi$
$383$	12.4497	+	21.5636i	0.636152	+	1.10185i	−0.350117	+	0.936706i	$0.613858\pi$
$384$		0			0
$385$	6.32843	+	10.9612i	0.322527	+	0.558632i
$386$		0			0
$387$	−25.1716			−1.27954
$388$		0			0
$389$	−8.57107	+	14.8455i	−0.434570	+	0.752698i	−0.997260	−	0.0739699i	$-0.976433\pi$
$389$	−8.57107	+	14.8455i	−0.434570	+	0.752698i	0.562690	+	0.826668i	$0.309766\pi$
$390$		0			0
$391$	0.343146	−	0.594346i	0.0173536	−	0.0300574i
$392$		0			0
$393$	−5.74264	−	9.94655i	−0.289678	−	0.501737i
$394$		0			0
$395$	15.2426			0.766940
$396$		0			0
$397$	8.25736	−	14.3022i	0.414425	−	0.717805i	−0.580943	−	0.813944i	$-0.697316\pi$
$397$	8.25736	−	14.3022i	0.414425	−	0.717805i	0.995368	+	0.0961392i	$0.0306494\pi$
$398$		0			0
$399$	9.24264			0.462711
$400$		0			0
$401$	−21.1716			−1.05726			−0.528629	−	0.848853i	$-0.677294\pi$
$401$	−21.1716			−1.05726			−0.528629	+	0.848853i	$0.677294\pi$
$402$		0			0
$403$	−0.692388	−	10.1567i	−0.0344903	−	0.505940i
$404$		0			0
$405$	−9.48528			−0.471327
$406$		0			0
$407$	5.24264			0.259868
$408$		0			0
$409$	−4.67157	+	8.09140i	−0.230994	+	0.400094i	−0.958101	−	0.286431i	$-0.907531\pi$
$409$	−4.67157	+	8.09140i	−0.230994	+	0.400094i	0.727107	+	0.686525i	$0.240865\pi$
$410$		0			0
$411$	−18.0711			−0.891380
$412$		0			0
$413$	12.1569	+	21.0563i	0.598200	+	1.03611i
$414$		0			0
$415$	2.03553	−	3.52565i	0.0999204	−	0.173067i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−28.0000			−1.36789			−0.683945	−	0.729534i	$-0.739737\pi$
$419$	−28.0000			−1.36789			−0.683945	+	0.729534i	$0.739737\pi$
$420$		0			0
$421$	1.42893	+	2.47498i	0.0696419	+	0.120623i	0.898744	−	0.438474i	$-0.144481\pi$
$421$	1.42893	+	2.47498i	0.0696419	+	0.120623i	−0.829102	+	0.559098i	$0.811148\pi$
$422$		0			0
$423$	−2.34315	−	4.05845i	−0.113928	−	0.197328i
$424$		0			0
$425$	−0.343146	−	0.594346i	−0.0166450	−	0.0288300i
$426$		0			0
$427$	3.41421	−	5.91359i	0.165225	−	0.286179i
$428$		0			0
$429$	−11.5711	−	20.0417i	−0.558656	−	0.967621i
$430$		0			0
$431$	−12.6213	+	21.8608i	−0.607948	+	1.05300i	0.383631	+	0.923487i	$0.374674\pi$
$431$	−12.6213	+	21.8608i	−0.607948	+	1.05300i	−0.991578	+	0.129510i	$0.958660\pi$
$432$		0			0
$433$	−35.1127			−1.68741			−0.843704	−	0.536808i	$-0.819630\pi$
$433$	−35.1127			−1.68741			−0.843704	+	0.536808i	$0.819630\pi$
$434$		0			0
$435$	−2.82843			−0.135613
$436$		0			0
$437$	3.17157	−	5.49333i	0.151717	−	0.262781i
$438$		0			0
$439$	−6.03553	−	10.4539i	−0.288060	−	0.498935i	0.685286	−	0.728274i	$-0.259677\pi$
$439$	−6.03553	−	10.4539i	−0.288060	−	0.498935i	−0.973347	+	0.229339i	$0.926344\pi$
$440$		0			0
$441$	1.65685	−	2.86976i	0.0788978	−	0.136655i
$442$		0			0
$443$	−6.62132	−	11.4685i	−0.314588	−	0.544883i	0.664761	−	0.747056i	$-0.268533\pi$
$443$	−6.62132	−	11.4685i	−0.314588	−	0.544883i	−0.979350	+	0.202173i	$0.935200\pi$
$444$		0			0
$445$	6.24264	+	10.8126i	0.295930	+	0.512565i
$446$		0			0
$447$	−1.20711	−	2.09077i	−0.0570942	−	0.0988900i
$448$		0			0
$449$	4.62742			0.218381			0.109191	−	0.994021i	$-0.465174\pi$
$449$	4.62742			0.218381			0.109191	+	0.994021i	$0.465174\pi$
$450$		0			0
$451$	−24.8640	+	43.0656i	−1.17080	+	2.02788i
$452$		0			0
$453$	−20.8995	+	36.1990i	−0.981944	+	1.70078i
$454$		0			0
$455$	2.20711	+	3.82282i	0.103471	+	0.179217i
$456$		0			0
$457$	31.1127			1.45539			0.727695	−	0.685901i	$-0.240591\pi$
$457$	31.1127			1.45539			0.727695	+	0.685901i	$0.240591\pi$
$458$		0			0
$459$	−0.0355339	+	0.0615465i	−0.00165858	+	0.00287275i
$460$		0			0
$461$	26.1421			1.21756			0.608780	−	0.793339i	$-0.291659\pi$
$461$	26.1421			1.21756			0.608780	+	0.793339i	$0.291659\pi$
$462$		0			0
$463$	−24.9706			−1.16048			−0.580240	−	0.814445i	$-0.697041\pi$
$463$	−24.9706			−1.16048			−0.580240	+	0.814445i	$0.697041\pi$
$464$		0			0
$465$	12.0711	+	5.91359i	0.559782	+	0.274236i
$466$		0			0
$467$	8.00000			0.370196			0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000			0.370196			0.185098	+	0.982720i	$0.440740\pi$
$468$		0			0
$469$	−12.6569			−0.584439
$470$		0			0
$471$	−17.8995	+	31.0028i	−0.824765	+	1.42854i
$472$		0			0
$473$	−46.6569			−2.14528
$474$		0			0
$475$	−3.17157	−	5.49333i	−0.145522	−	0.252051i
$476$		0			0
$477$	−0.242641	+	0.420266i	−0.0111098	+	0.0192427i
$478$		0			0
$479$	4.86396	−	8.42463i	0.222240	−	0.384931i	−0.733248	−	0.679962i	$-0.761996\pi$
$479$	4.86396	−	8.42463i	0.222240	−	0.384931i	0.955488	+	0.295030i	$0.0953298\pi$
$480$		0			0
$481$	1.82843			0.0833691
$482$		0			0
$483$	11.6569	+	20.1903i	0.530405	+	0.918689i
$484$		0			0
$485$	−5.41421	−	9.37769i	−0.245847	−	0.425819i
$486$		0			0
$487$	−8.69239	−	15.0557i	−0.393890	−	0.682237i	0.599069	−	0.800697i	$-0.295537\pi$
$487$	−8.69239	−	15.0557i	−0.393890	−	0.682237i	−0.992959	+	0.118460i	$0.962204\pi$
$488$		0			0
$489$	−15.6569	+	27.1185i	−0.708027	+	1.22634i
$490$		0			0
$491$	2.20711	+	3.82282i	0.0996053	+	0.172522i	0.911521	−	0.411253i	$-0.134909\pi$
$491$	2.20711	+	3.82282i	0.0996053	+	0.172522i	−0.811916	+	0.583774i	$0.801575\pi$
$492$		0			0
$493$	−0.100505	+	0.174080i	−0.00452652	+	0.00784016i
$494$		0			0
$495$	14.8284			0.666488
$496$		0			0
$497$	−33.9706			−1.52379
$498$		0			0
$499$	20.1066	−	34.8257i	0.900095	−	1.55901i	0.0727259	−	0.997352i	$-0.476830\pi$
$499$	20.1066	−	34.8257i	0.900095	−	1.55901i	0.827369	−	0.561659i	$-0.189837\pi$
$500$		0			0
$501$	−10.3284	−	17.8894i	−0.461440	−	0.799238i
$502$		0			0
$503$	11.6924	−	20.2518i	0.521338	−	0.902984i	−0.478354	−	0.878167i	$-0.658766\pi$
$503$	11.6924	−	20.2518i	0.521338	−	0.902984i	0.999692	−	0.0248166i	$-0.00790018\pi$
$504$		0			0
$505$	−4.24264	−	7.34847i	−0.188795	−	0.327003i
$506$		0			0
$507$	11.6569	+	20.1903i	0.517699	+	0.896681i
$508$		0			0
$509$	−3.39949	−	5.88810i	−0.150680	−	0.260985i	0.780798	−	0.624784i	$-0.214813\pi$
$509$	−3.39949	−	5.88810i	−0.150680	−	0.260985i	−0.931478	+	0.363799i	$0.881480\pi$
$510$		0			0
$511$	−9.24264			−0.408870
$512$		0			0
$513$	−0.328427	+	0.568852i	−0.0145004	+	0.0251154i
$514$		0			0
$515$	−6.03553	+	10.4539i	−0.265957	+	0.460652i
$516$		0			0
$517$	−4.34315	−	7.52255i	−0.191011	−	0.330841i
$518$		0			0
$519$	−34.5563			−1.51686
$520$		0			0
$521$	−15.2279	+	26.3755i	−0.667147	+	1.15553i	0.311551	+	0.950229i	$0.399152\pi$
$521$	−15.2279	+	26.3755i	−0.667147	+	1.15553i	−0.978698	+	0.205304i	$0.934182\pi$
$522$		0			0
$523$	8.00000			0.349816			0.174908	−	0.984585i	$-0.444037\pi$
$523$	8.00000			0.349816			0.174908	+	0.984585i	$0.444037\pi$
$524$		0			0
$525$	23.3137			1.01749
$526$		0			0
$527$	0.792893	−	0.532799i	0.0345390	−	0.0232091i
$528$		0			0
$529$	−7.00000			−0.304348
$530$		0			0
$531$	28.4853			1.23616
$532$		0			0
$533$	−8.67157	+	15.0196i	−0.375608	+	0.650571i
$534$		0			0
$535$	−9.58579			−0.414430
$536$		0			0
$537$	−8.15685	−	14.1281i	−0.351994	−	0.609672i
$538$		0			0
$539$	3.07107	−	5.31925i	0.132280	−	0.229116i
$540$		0			0
$541$	−12.6421	+	21.8968i	−0.543528	+	0.941418i	0.455170	+	0.890405i	$0.349578\pi$
$541$	−12.6421	+	21.8968i	−0.543528	+	0.941418i	−0.998698	+	0.0510134i	$0.983755\pi$
$542$		0			0
$543$	−24.8995			−1.06854
$544$		0			0
$545$	2.58579	+	4.47871i	0.110763	+	0.191847i
$546$		0			0
$547$	2.86396	+	4.96053i	0.122454	+	0.212097i	0.920735	−	0.390189i	$-0.127590\pi$
$547$	2.86396	+	4.96053i	0.122454	+	0.212097i	−0.798281	+	0.602285i	$0.794257\pi$
$548$		0			0
$549$	−4.00000	−	6.92820i	−0.170716	−	0.295689i
$550$		0			0
$551$	−0.928932	+	1.60896i	−0.0395738	+	0.0685439i
$552$		0			0
$553$	18.3995	+	31.8689i	0.782426	+	1.35520i
$554$		0			0
$555$	−1.20711	+	2.09077i	−0.0512388	+	0.0887483i
$556$		0			0
$557$	44.4853			1.88490			0.942451	−	0.334344i	$-0.108515\pi$
$557$	44.4853			1.88490			0.942451	+	0.334344i	$0.108515\pi$
$558$		0			0
$559$	−16.2721			−0.688236
$560$		0			0
$561$	1.08579	−	1.88064i	0.0458419	−	0.0794006i
$562$		0			0
$563$	2.37868	+	4.11999i	0.100249	+	0.173637i	0.911787	−	0.410663i	$-0.134703\pi$
$563$	2.37868	+	4.11999i	0.100249	+	0.173637i	−0.811538	+	0.584300i	$0.801369\pi$
$564$		0			0
$565$	−2.67157	+	4.62730i	−0.112394	+	0.194672i
$566$		0			0
$567$	−11.4497	−	19.8315i	−0.480844	−	0.832847i
$568$		0			0
$569$	−7.57107	−	13.1135i	−0.317396	−	0.549745i	0.662548	−	0.749019i	$-0.269475\pi$
$569$	−7.57107	−	13.1135i	−0.317396	−	0.549745i	−0.979944	+	0.199274i	$0.936142\pi$
$570$		0			0
$571$	−20.4497	−	35.4200i	−0.855795	−	1.48228i	−0.875905	−	0.482483i	$-0.839735\pi$
$571$	−20.4497	−	35.4200i	−0.855795	−	1.48228i	0.0201099	−	0.999798i	$-0.493598\pi$
$572$		0			0
$573$	2.65685			0.110992
$574$		0			0
$575$	8.00000	−	13.8564i	0.333623	−	0.577852i
$576$		0			0
$577$	16.9853	−	29.4194i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$577$	16.9853	−	29.4194i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833332\pi$
$578$		0			0
$579$	25.5208	+	44.2033i	1.06061	+	1.83703i
$580$		0			0
$581$	9.82843			0.407752
$582$		0			0
$583$	−0.449747	+	0.778985i	−0.0186266	+	0.0322623i
$584$		0			0
$585$	5.17157			0.213818
$586$		0			0
$587$	20.3431			0.839651			0.419826	−	0.907605i	$-0.362091\pi$
$587$	20.3431			0.839651			0.419826	+	0.907605i	$0.362091\pi$
$588$		0			0
$589$	7.32843	−	4.92447i	0.301963	−	0.202909i
$590$		0			0
$591$	8.41421			0.346114
$592$		0			0
$593$	21.3137			0.875249			0.437625	−	0.899158i	$-0.355820\pi$
$593$	21.3137			0.875249			0.437625	+	0.899158i	$0.355820\pi$
$594$		0			0
$595$	−0.207107	+	0.358719i	−0.00849055	+	0.0147061i
$596$		0			0
$597$	−37.6274			−1.53999
$598$		0			0
$599$	17.4497	+	30.2238i	0.712977	+	1.23491i	0.963734	+	0.266863i	$0.0859871\pi$
$599$	17.4497	+	30.2238i	0.712977	+	1.23491i	−0.250757	+	0.968050i	$0.580680\pi$
$600$		0			0
$601$	11.7426	−	20.3389i	0.478992	−	0.829639i	−0.520717	−	0.853729i	$-0.674336\pi$
$601$	11.7426	−	20.3389i	0.478992	−	0.829639i	0.999710	+	0.0240900i	$0.00766884\pi$
$602$		0			0
$603$	−7.41421	+	12.8418i	−0.301930	+	0.522958i
$604$		0			0
$605$	16.4853			0.670222
$606$		0			0
$607$	−2.20711	−	3.82282i	−0.0895837	−	0.155164i	0.817752	−	0.575571i	$-0.195220\pi$
$607$	−2.20711	−	3.82282i	−0.0895837	−	0.155164i	−0.907335	+	0.420408i	$0.861887\pi$
$608$		0			0
$609$	−3.41421	−	5.91359i	−0.138351	−	0.239631i
$610$		0			0
$611$	−1.51472	−	2.62357i	−0.0612790	−	0.106138i
$612$		0			0
$613$	5.15685	−	8.93193i	0.208283	−	0.360757i	−0.742890	−	0.669413i	$-0.766546\pi$
$613$	5.15685	−	8.93193i	0.208283	−	0.360757i	0.951174	+	0.308656i	$0.0998790\pi$
$614$		0			0
$615$	−11.4497	−	19.8315i	−0.461698	−	0.799685i
$616$		0			0
$617$	−11.6421	+	20.1648i	−0.468695	+	0.811803i	−0.999360	−	0.0357786i	$-0.988609\pi$
$617$	−11.6421	+	20.1648i	−0.468695	+	0.811803i	0.530665	+	0.847582i	$0.321942\pi$
$618$		0			0
$619$	31.6569			1.27240			0.636198	−	0.771526i	$-0.280506\pi$
$619$	31.6569			1.27240			0.636198	+	0.771526i	$0.280506\pi$
$620$		0			0
$621$	−1.65685			−0.0664873
$622$		0			0
$623$	−15.0711	+	26.1039i	−0.603810	+	1.04583i
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$		0			0
$627$	10.0355	−	17.3821i	0.400781	−	0.694172i
$628$		0			0
$629$	0.0857864	+	0.148586i	0.00342053	+	0.00592453i
$630$		0			0
$631$	−16.0061	−	27.7234i	−0.637193	−	1.10365i	−0.986046	−	0.166473i	$-0.946762\pi$
$631$	−16.0061	−	27.7234i	−0.637193	−	1.10365i	0.348853	−	0.937177i	$-0.386571\pi$
$632$		0			0
$633$	9.15685	+	15.8601i	0.363952	+	0.630384i
$634$		0			0
$635$	10.8995			0.432533
$636$		0			0
$637$	1.07107	−	1.85514i	0.0424373	−	0.0735035i
$638$		0			0
$639$	−19.8995	+	34.4669i	−0.787212	+	1.36349i
$640$		0			0
$641$	−9.98528	−	17.2950i	−0.394395	−	0.683112i	0.598629	−	0.801027i	$-0.295712\pi$
$641$	−9.98528	−	17.2950i	−0.394395	−	0.683112i	−0.993024	+	0.117915i	$0.962379\pi$
$642$		0			0
$643$	−12.6863			−0.500298			−0.250149	−	0.968207i	$-0.580480\pi$
$643$	−12.6863			−0.500298			−0.250149	+	0.968207i	$0.580480\pi$
$644$		0			0
$645$	10.7426	−	18.6068i	0.422991	−	0.732642i
$646$		0			0
$647$	22.6863			0.891890			0.445945	−	0.895060i	$-0.352868\pi$
$647$	22.6863			0.891890			0.445945	+	0.895060i	$0.352868\pi$
$648$		0			0
$649$	52.7990			2.07254
$650$		0			0
$651$	2.20711	+	32.3762i	0.0865033	+	1.26892i
$652$		0			0
$653$	22.1421			0.866489			0.433244	−	0.901276i	$-0.357369\pi$
$653$	22.1421			0.866489			0.433244	+	0.901276i	$0.357369\pi$
$654$		0			0
$655$	4.75736			0.185885
$656$		0			0
$657$	−5.41421	+	9.37769i	−0.211229	+	0.365859i
$658$		0			0
$659$	−9.65685			−0.376178			−0.188089	−	0.982152i	$-0.560229\pi$
$659$	−9.65685			−0.376178			−0.188089	+	0.982152i	$0.560229\pi$
$660$		0			0
$661$	−16.5711	−	28.7019i	−0.644540	−	1.11638i	−0.984408	−	0.175903i	$-0.943716\pi$
$661$	−16.5711	−	28.7019i	−0.644540	−	1.11638i	0.339868	−	0.940473i	$-0.389618\pi$
$662$		0			0
$663$	0.378680	−	0.655892i	0.0147067	−	0.0254728i
$664$		0			0
$665$	−1.91421	+	3.31552i	−0.0742300	+	0.128570i
$666$		0			0
$667$	−4.68629			−0.181454
$668$		0			0
$669$	2.08579	+	3.61269i	0.0806412	+	0.139675i
$670$		0			0
$671$	−7.41421	−	12.8418i	−0.286223	−	0.495752i
$672$		0			0
$673$	−10.3284	−	17.8894i	−0.398132	−	0.689584i	0.595364	−	0.803456i	$-0.297008\pi$
$673$	−10.3284	−	17.8894i	−0.398132	−	0.689584i	−0.993495	+	0.113872i	$0.963675\pi$
$674$		0			0
$675$	−0.828427	+	1.43488i	−0.0318862	+	0.0552285i
$676$		0			0
$677$	−20.2990	−	35.1589i	−0.780154	−	1.35127i	−0.931852	−	0.362839i	$-0.881808\pi$
$677$	−20.2990	−	35.1589i	−0.780154	−	1.35127i	0.151698	−	0.988427i	$-0.451526\pi$
$678$		0			0
$679$	13.0711	−	22.6398i	0.501622	−	0.868834i
$680$		0			0
$681$	37.6274			1.44189
$682$		0			0
$683$	46.6274			1.78415			0.892074	−	0.451889i	$-0.149250\pi$
$683$	46.6274			1.78415			0.892074	+	0.451889i	$0.149250\pi$
$684$		0			0
$685$	3.74264	−	6.48244i	0.142999	−	0.247681i
$686$		0			0
$687$	−13.8640	−	24.0131i	−0.528943	−	0.916156i
$688$		0			0
$689$	−0.156854	+	0.271680i	−0.00597567	+	0.0103502i
$690$		0			0
$691$	7.03553	+	12.1859i	0.267644	+	0.463574i	0.968253	−	0.249972i	$-0.0804215\pi$
$691$	7.03553	+	12.1859i	0.267644	+	0.463574i	−0.700609	+	0.713546i	$0.747088\pi$
$692$		0			0
$693$	17.8995	+	31.0028i	0.679946	+	1.17770i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−1.62742			−0.0616428
$698$		0			0
$699$	17.8995	−	31.0028i	0.677021	−	1.17263i
$700$		0			0
$701$	−1.74264	+	3.01834i	−0.0658186	+	0.114001i	−0.897057	−	0.441915i	$-0.854299\pi$
$701$	−1.74264	+	3.01834i	−0.0658186	+	0.114001i	0.831238	+	0.555916i	$0.187633\pi$
$702$		0			0
$703$	0.792893	+	1.37333i	0.0299045	+	0.0517962i
$704$		0			0
$705$	4.00000			0.150649
$706$		0			0
$707$	10.2426	−	17.7408i	0.385214	−	0.667210i
$708$		0			0
$709$	−5.31371			−0.199561			−0.0997803	−	0.995009i	$-0.531814\pi$
$709$	−5.31371			−0.199561			−0.0997803	+	0.995009i	$0.531814\pi$
$710$		0			0
$711$	43.1127			1.61685
$712$		0			0
$713$	20.0000	+	9.79796i	0.749006	+	0.366936i
$714$		0			0
$715$	9.58579			0.358488
$716$		0			0
$717$	30.7990			1.15021
$718$		0			0
$719$	3.03553	−	5.25770i	0.113206	−	0.196079i	−0.803855	−	0.594825i	$-0.797221\pi$
$719$	3.03553	−	5.25770i	0.113206	−	0.196079i	0.917061	+	0.398746i	$0.130555\pi$
$720$		0			0
$721$	−29.1421			−1.08531
$722$		0			0
$723$	−29.7635	−	51.5518i	−1.10691	−	1.91723i
$724$		0			0
$725$	−2.34315	+	4.05845i	−0.0870222	+	0.150727i
$726$		0			0
$727$	−23.4203	+	40.5652i	−0.868611	+	1.50448i	−0.00519502	+	0.999987i	$0.501654\pi$
$727$	−23.4203	+	40.5652i	−0.868611	+	1.50448i	−0.863416	+	0.504492i	$0.831680\pi$
$728$		0			0
$729$	−23.8284			−0.882534
$730$		0			0
$731$	−0.763456	−	1.32234i	−0.0282374	−	0.0489087i
$732$		0			0
$733$	14.8137	+	25.6581i	0.547157	+	0.947703i	0.998468	+	0.0553366i	$0.0176232\pi$
$733$	14.8137	+	25.6581i	0.547157	+	0.947703i	−0.451311	+	0.892367i	$0.649043\pi$
$734$		0			0
$735$	1.41421	+	2.44949i	0.0521641	+	0.0903508i
$736$		0			0
$737$	−13.7426	+	23.8030i	−0.506217	+	0.876793i
$738$		0			0
$739$	−3.93503	−	6.81567i	−0.144752	−	0.250718i	0.784528	−	0.620093i	$-0.212905\pi$
$739$	−3.93503	−	6.81567i	−0.144752	−	0.250718i	−0.929281	+	0.369375i	$0.879572\pi$
$740$		0			0
$741$	3.50000	−	6.06218i	0.128576	−	0.222700i
$742$		0			0
$743$	5.65685			0.207530			0.103765	−	0.994602i	$-0.466911\pi$
$743$	5.65685			0.207530			0.103765	+	0.994602i	$0.466911\pi$
$744$		0			0
$745$	1.00000			0.0366372
$746$		0			0
$747$	5.75736	−	9.97204i	0.210651	−	0.364858i
$748$		0			0
$749$	−11.5711	−	20.0417i	−0.422798	−	0.732307i
$750$		0			0
$751$	−0.621320	+	1.07616i	−0.0226723	+	0.0392696i	−0.877139	−	0.480237i	$-0.840551\pi$
$751$	−0.621320	+	1.07616i	−0.0226723	+	0.0392696i	0.854467	+	0.519506i	$0.173884\pi$
$752$		0			0
$753$	4.32843	+	7.49706i	0.157737	+	0.273208i
$754$		0			0
$755$	−8.65685	−	14.9941i	−0.315055	−	0.545692i
$756$		0			0
$757$	−17.3284	−	30.0137i	−0.629812	−	1.09087i	−0.987589	−	0.157060i	$-0.949798\pi$
$757$	−17.3284	−	30.0137i	−0.629812	−	1.09087i	0.357777	−	0.933807i	$-0.383535\pi$
$758$		0			0
$759$	50.6274			1.83766
$760$		0			0
$761$	10.2279	−	17.7153i	0.370762	−	0.642178i	−0.618921	−	0.785453i	$-0.712430\pi$
$761$	10.2279	−	17.7153i	0.370762	−	0.642178i	0.989683	+	0.143275i	$0.0457633\pi$
$762$		0			0
$763$	−6.24264	+	10.8126i	−0.225999	+	0.391441i
$764$		0			0
$765$	0.242641	+	0.420266i	0.00877269	+	0.0151947i
$766$		0			0
$767$	18.4142			0.664899
$768$		0			0
$769$	13.0563	−	22.6143i	0.470824	−	0.815491i	−0.528619	−	0.848859i	$-0.677290\pi$
$769$	13.0563	−	22.6143i	0.470824	−	0.815491i	0.999443	+	0.0333680i	$0.0106233\pi$
$770$		0			0
$771$	−0.757359			−0.0272756
$772$		0			0
$773$	18.0000			0.647415			0.323708	−	0.946157i	$-0.395071\pi$
$773$	18.0000			0.647415			0.323708	+	0.946157i	$0.395071\pi$
$774$		0			0
$775$	18.4853	−	12.4215i	0.664011	−	0.446194i
$776$		0			0
$777$	−5.82843			−0.209094
$778$		0			0
$779$	−15.0416			−0.538922
$780$		0			0
$781$	−36.8848	+	63.8863i	−1.31984	+	2.28603i
$782$		0			0
$783$	0.485281			0.0173425
$784$		0			0
$785$	−7.41421	−	12.8418i	−0.264625	−	0.458343i
$786$		0			0
$787$	19.7929	−	34.2823i	0.705540	−	1.22203i	−0.260956	−	0.965351i	$-0.584038\pi$
$787$	19.7929	−	34.2823i	0.705540	−	1.22203i	0.966496	−	0.256681i	$-0.0826290\pi$
$788$		0			0
$789$	−0.828427	+	1.43488i	−0.0294928	+	0.0510830i
$790$		0			0
$791$	−12.8995			−0.458653
$792$		0			0
$793$	−2.58579	−	4.47871i	−0.0918240	−	0.159044i
$794$		0			0
$795$	−0.207107	−	0.358719i	−0.00734532	−	0.0127225i
$796$		0			0
$797$	11.2279	+	19.4473i	0.397713	+	0.688860i	0.993443	−	0.114325i	$-0.0364705\pi$
$797$	11.2279	+	19.4473i	0.397713	+	0.688860i	−0.595730	+	0.803185i	$0.703137\pi$
$798$		0			0
$799$	0.142136	−	0.246186i	0.00502840	−	0.00870944i
$800$		0			0
$801$	17.6569	+	30.5826i	0.623874	+	1.08058i
$802$		0			0
$803$	−10.0355	+	17.3821i	−0.354146	+	0.613399i
$804$		0			0
$805$	−9.65685			−0.340359
$806$		0			0
$807$	−76.8406			−2.70492
$808$		0			0
$809$	22.9853	−	39.8117i	0.808119	−	1.39970i	−0.106045	−	0.994361i	$-0.533819\pi$
$809$	22.9853	−	39.8117i	0.808119	−	1.39970i	0.914165	−	0.405343i	$-0.132848\pi$
$810$		0			0
$811$	5.86396	+	10.1567i	0.205912	+	0.356649i	0.950423	−	0.310961i	$-0.100651\pi$
$811$	5.86396	+	10.1567i	0.205912	+	0.356649i	−0.744511	+	0.667610i	$0.767317\pi$
$812$		0			0
$813$	−28.1421	+	48.7436i	−0.986988	+	1.70951i
$814$		0			0
$815$	−6.48528	−	11.2328i	−0.227169	−	0.393469i
$816$		0			0
$817$	−7.05635	−	12.2220i	−0.246870	−	0.427592i
$818$		0			0
$819$	6.24264	+	10.8126i	0.218136	+	0.377822i
$820$		0			0
$821$	−8.48528			−0.296138			−0.148069	−	0.988977i	$-0.547306\pi$
$821$	−8.48528			−0.296138			−0.148069	+	0.988977i	$0.547306\pi$
$822$		0			0
$823$	−3.10660	+	5.38079i	−0.108289	+	0.187563i	−0.915077	−	0.403278i	$-0.867871\pi$
$823$	−3.10660	+	5.38079i	−0.108289	+	0.187563i	0.806788	+	0.590841i	$0.201204\pi$
$824$		0			0
$825$	25.3137	−	43.8446i	0.881310	−	1.52647i
$826$		0			0
$827$	8.55025	+	14.8095i	0.297321	+	0.514976i	0.975522	−	0.219901i	$-0.0705734\pi$
$827$	8.55025	+	14.8095i	0.297321	+	0.514976i	−0.678201	+	0.734877i	$0.737240\pi$
$828$		0			0
$829$	−46.4264			−1.61246			−0.806228	−	0.591605i	$-0.798494\pi$
$829$	−46.4264			−1.61246			−0.806228	+	0.591605i	$0.798494\pi$
$830$		0			0
$831$	17.0711	−	29.5680i	0.592189	−	1.02570i
$832$		0			0
$833$	0.201010			0.00696459
$834$		0			0
$835$	8.55635			0.296105
$836$		0			0
$837$	−2.07107	−	1.01461i	−0.0715866	−	0.0350701i
$838$		0			0
$839$	−30.6274			−1.05738			−0.528688	−	0.848816i	$-0.677316\pi$
$839$	−30.6274			−1.05738			−0.528688	+	0.848816i	$0.677316\pi$
$840$		0			0
$841$	−27.6274			−0.952670
$842$		0			0
$843$	−2.41421	+	4.18154i	−0.0831499	+	0.144020i
$844$		0			0
$845$	−9.65685			−0.332206
$846$		0			0
$847$	19.8995	+	34.4669i	0.683755	+	1.18430i
$848$		0			0
$849$	−2.82843	+	4.89898i	−0.0970714	+	0.168133i
$850$		0			0
$851$	−2.00000	+	3.46410i	−0.0685591	+	0.118748i
$852$		0			0
$853$	−32.4853			−1.11227			−0.556137	−	0.831090i	$-0.687717\pi$
$853$	−32.4853			−1.11227			−0.556137	+	0.831090i	$0.687717\pi$
$854$		0			0
$855$	2.24264	+	3.88437i	0.0766967	+	0.132843i
$856$		0			0
$857$	1.25736	+	2.17781i	0.0429506	+	0.0743926i	0.886702	−	0.462342i	$-0.152991\pi$
$857$	1.25736	+	2.17781i	0.0429506	+	0.0743926i	−0.843751	+	0.536735i	$0.819658\pi$
$858$		0			0
$859$	−6.30761	−	10.9251i	−0.215213	−	0.372760i	0.738125	−	0.674663i	$-0.235711\pi$
$859$	−6.30761	−	10.9251i	−0.215213	−	0.372760i	−0.953338	+	0.301904i	$0.902378\pi$
$860$		0			0
$861$	27.6421	−	47.8776i	0.942041	−	1.63166i
$862$		0			0
$863$	−19.6924	−	34.1082i	−0.670337	−	1.16106i	−0.977809	−	0.209500i	$-0.932816\pi$
$863$	−19.6924	−	34.1082i	−0.670337	−	1.16106i	0.307472	−	0.951557i	$-0.400517\pi$
$864$		0			0
$865$	7.15685	−	12.3960i	0.243340	−	0.421478i
$866$		0			0
$867$	−40.9706			−1.39143
$868$		0			0
$869$	79.9117			2.71082
$870$		0			0
$871$	−4.79289	+	8.30153i	−0.162401	+	0.281287i
$872$		0			0
$873$	−15.3137	−	26.5241i	−0.518291	−	0.897705i
$874$		0			0
$875$	−10.8640	+	18.8169i	−0.367269	+	0.636128i
$876$		0			0
$877$	−24.0858	−	41.7178i	−0.813319	−	1.40871i	−0.910529	−	0.413446i	$-0.864325\pi$
$877$	−24.0858	−	41.7178i	−0.813319	−	1.40871i	0.0972093	−	0.995264i	$-0.469008\pi$
$878$		0			0
$879$	29.9350	+	51.8490i	1.00968	+	1.74882i
$880$		0			0
$881$	−17.1569	−	29.7165i	−0.578029	−	1.00118i	−0.995705	−	0.0925798i	$-0.970489\pi$
$881$	−17.1569	−	29.7165i	−0.578029	−	1.00118i	0.417676	−	0.908596i	$-0.362845\pi$
$882$		0			0
$883$	−26.2843			−0.884536			−0.442268	−	0.896883i	$-0.645826\pi$
$883$	−26.2843			−0.884536			−0.442268	+	0.896883i	$0.645826\pi$
$884$		0			0
$885$	−12.1569	+	21.0563i	−0.408648	+	0.707799i
$886$		0			0
$887$	26.6630	−	46.1816i	0.895254	−	1.55063i	0.0617647	−	0.998091i	$-0.480327\pi$
$887$	26.6630	−	46.1816i	0.895254	−	1.55063i	0.833490	−	0.552535i	$-0.186339\pi$
$888$		0			0
$889$	13.1569	+	22.7883i	0.441267	+	0.764296i
$890$		0			0
$891$	−49.7279			−1.66595
$892$		0			0
$893$	1.31371	−	2.27541i	0.0439616	−	0.0761437i
$894$		0			0
$895$	6.75736			0.225874
$896$		0			0
$897$	17.6569			0.589545
$898$		0			0
$899$	−5.85786	−	2.86976i	−0.195371	−	0.0957117i
$900$		0			0
$901$	−0.0294373			−0.000980697
$902$		0			0
$903$	51.8701			1.72613
$904$		0			0
$905$	5.15685	−	8.93193i	0.171420	−	0.296908i
$906$		0			0
$907$	−55.3137			−1.83666			−0.918331	−	0.395814i	$-0.870463\pi$
$907$	−55.3137			−1.83666			−0.918331	+	0.395814i	$0.870463\pi$
$908$		0			0
$909$	−12.0000	−	20.7846i	−0.398015	−	0.689382i
$910$		0			0
$911$	24.5208	−	42.4713i	0.812411	−	1.40714i	−0.0987614	−	0.995111i	$-0.531488\pi$
$911$	24.5208	−	42.4713i	0.812411	−	1.40714i	0.911172	−	0.412026i	$-0.135179\pi$
$912$		0			0
$913$	10.6716	−	18.4837i	0.353178	−	0.611721i
$914$		0			0
$915$	6.82843			0.225741
$916$		0			0
$917$	5.74264	+	9.94655i	0.189639	+	0.328464i
$918$		0			0
$919$	−7.55025	−	13.0774i	−0.249060	−	0.431384i	0.714205	−	0.699936i	$-0.246788\pi$
$919$	−7.55025	−	13.0774i	−0.249060	−	0.431384i	−0.963265	+	0.268552i	$0.913455\pi$
$920$		0			0
$921$	−3.32843	−	5.76500i	−0.109675	−	0.189963i
$922$		0			0
$923$	−12.8640	+	22.2810i	−0.423422	+	0.733389i
$924$		0			0
$925$	2.00000	+	3.46410i	0.0657596	+	0.113899i
$926$		0			0
$927$	−17.0711	+	29.5680i	−0.560687	+	0.971139i
$928$		0			0
$929$	24.4853			0.803336			0.401668	−	0.915785i	$-0.368431\pi$
$929$	24.4853			0.803336			0.401668	+	0.915785i	$0.368431\pi$
$930$		0			0
$931$	1.85786			0.0608890
$932$		0			0
$933$	−13.6569	+	23.6544i	−0.447105	+	0.774409i
$934$		0			0
$935$	0.449747	+	0.778985i	0.0147083	+	0.0254755i
$936$		0			0
$937$	−19.1569	+	33.1806i	−0.625827	+	1.08396i	0.362553	+	0.931963i	$0.381905\pi$
$937$	−19.1569	+	33.1806i	−0.625827	+	1.08396i	−0.988380	+	0.152001i	$0.951428\pi$
$938$		0			0
$939$	−4.62132	−	8.00436i	−0.150811	−	0.261212i
$940$		0			0
$941$	17.5000	+	30.3109i	0.570484	+	0.988107i	0.996516	+	0.0833989i	$0.0265776\pi$
$941$	17.5000	+	30.3109i	0.570484	+	0.988107i	−0.426033	+	0.904708i	$0.640089\pi$
$942$		0			0
$943$	−18.9706	−	32.8580i	−0.617767	−	1.07000i
$944$		0			0
$945$	1.00000			0.0325300
$946$		0			0
$947$	19.4497	−	33.6880i	0.632032	−	1.09471i	−0.355104	−	0.934827i	$-0.615555\pi$
$947$	19.4497	−	33.6880i	0.632032	−	1.09471i	0.987136	−	0.159884i	$-0.0511122\pi$
$948$		0			0
$949$	−3.50000	+	6.06218i	−0.113615	+	0.196787i
$950$		0			0
$951$	2.62132	+	4.54026i	0.0850021	+	0.147228i
$952$		0			0
$953$	20.4853			0.663583			0.331792	−	0.943353i	$-0.392347\pi$
$953$	20.4853			0.663583			0.331792	+	0.943353i	$0.392347\pi$
$954$		0			0
$955$	−0.550253	+	0.953065i	−0.0178058	+	0.0308405i
$956$		0			0
$957$	−14.8284			−0.479335
$958$		0			0
$959$	18.0711			0.583545
$960$		0			0
$961$	19.0000	+	24.4949i	0.612903	+	0.790158i
$962$		0			0
$963$	−27.1127			−0.873694
$964$		0			0
$965$	−21.1421			−0.680589
$966$		0			0
$967$	−23.2782	+	40.3190i	−0.748576	+	1.29657i	0.199930	+	0.979810i	$0.435929\pi$
$967$	−23.2782	+	40.3190i	−0.748576	+	1.29657i	−0.948505	+	0.316761i	$0.897405\pi$
$968$		0			0
$969$	0.656854			0.0211012
$970$		0			0
$971$	29.3492	+	50.8344i	0.941862	+	1.63135i	0.761915	+	0.647676i	$0.224259\pi$
$971$	29.3492	+	50.8344i	0.941862	+	1.63135i	0.179947	+	0.983676i	$0.442408\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	8.82843	−	15.2913i	0.282736	−	0.489713i
$976$		0			0
$977$	16.4853			0.527411			0.263705	−	0.964603i	$-0.415055\pi$
$977$	16.4853			0.527411			0.263705	+	0.964603i	$0.415055\pi$
$978$		0			0
$979$	32.7279	+	56.6864i	1.04599	+	1.81171i
$980$		0			0
$981$	7.31371	+	12.6677i	0.233509	+	0.404449i
$982$		0			0
$983$	24.4203	+	42.2972i	0.778887	+	1.34907i	0.932584	+	0.360954i	$0.117549\pi$
$983$	24.4203	+	42.2972i	0.778887	+	1.34907i	−0.153697	+	0.988118i	$0.549118\pi$
$984$		0			0
$985$	−1.74264	+	3.01834i	−0.0555251	+	0.0961724i
$986$		0			0
$987$	4.82843	+	8.36308i	0.153691	+	0.266200i
$988$		0			0
$989$	17.7990	−	30.8288i	0.565975	−	0.980297i
$990$		0			0
$991$	19.9411			0.633451			0.316725	−	0.948517i	$-0.397417\pi$
$991$	19.9411			0.633451			0.316725	+	0.948517i	$0.397417\pi$
$992$		0			0
$993$	−1.82843			−0.0580234
$994$		0			0
$995$	7.79289	−	13.4977i	0.247051	−	0.427905i
$996$		0			0
$997$	23.2990	+	40.3550i	0.737886	+	1.27806i	0.953445	+	0.301566i	$0.0975093\pi$
$997$	23.2990	+	40.3550i	0.737886	+	1.27806i	−0.215559	+	0.976491i	$0.569157\pi$
$998$		0			0
$999$	0.207107	−	0.358719i	0.00655257	−	0.0113494i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	496.2.i.h.129.1		4
4.3	odd	2		31.2.c.a.5.1	✓	4
12.11	even	2		279.2.h.c.253.2		4
20.3	even	4		775.2.o.d.749.4		8
20.7	even	4		775.2.o.d.749.1		8
20.19	odd	2		775.2.e.e.501.2		4
31.25	even	3	inner	496.2.i.h.273.1		4
124.3	even	30		961.2.g.r.448.1		16
124.7	odd	30		961.2.g.o.338.2		16
124.11	even	30		961.2.d.i.388.2		8
124.15	even	10		961.2.g.r.846.1		16
124.19	odd	30		961.2.g.o.844.1		16
124.23	even	10		961.2.g.r.816.2		16
124.27	even	10		961.2.g.r.235.2		16
124.35	odd	10		961.2.g.o.235.2		16
124.39	odd	10		961.2.g.o.816.2		16
124.43	even	30		961.2.g.r.844.1		16
124.47	odd	10		961.2.g.o.846.1		16
124.51	odd	30		961.2.d.l.388.2		8
124.55	even	30		961.2.g.r.338.2		16
124.59	odd	30		961.2.g.o.448.1		16
124.67	odd	6		961.2.a.a.1.1		2
124.71	odd	30		961.2.d.l.374.2		8
124.75	even	30		961.2.d.i.628.1		8
124.79	even	30		961.2.g.r.732.2		16
124.83	even	30		961.2.d.i.531.1		8
124.87	odd	6		31.2.c.a.25.1	yes	4
124.91	even	10		961.2.g.r.547.1		16
124.95	odd	10		961.2.g.o.547.1		16
124.99	even	6		961.2.c.a.521.1		4
124.103	odd	30		961.2.d.l.531.1		8
124.107	odd	30		961.2.g.o.732.2		16
124.111	odd	30		961.2.d.l.628.1		8
124.115	even	30		961.2.d.i.374.2		8
124.119	even	6		961.2.a.c.1.1		2
124.123	even	2		961.2.c.a.439.1		4
372.119	odd	6		8649.2.a.k.1.2		2
372.191	even	6		8649.2.a.l.1.2		2
372.335	even	6		279.2.h.c.118.2		4
620.87	even	12		775.2.o.d.149.1		8
620.459	odd	6		775.2.e.e.676.2		4
620.583	even	12		775.2.o.d.149.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.c.a.5.1	✓	4	4.3	odd	2
31.2.c.a.25.1	yes	4	124.87	odd	6
279.2.h.c.118.2		4	372.335	even	6
279.2.h.c.253.2		4	12.11	even	2
496.2.i.h.129.1		4	1.1	even	1	trivial
496.2.i.h.273.1		4	31.25	even	3	inner
775.2.e.e.501.2		4	20.19	odd	2
775.2.e.e.676.2		4	620.459	odd	6
775.2.o.d.149.1		8	620.87	even	12
775.2.o.d.149.4		8	620.583	even	12
775.2.o.d.749.1		8	20.7	even	4
775.2.o.d.749.4		8	20.3	even	4
961.2.a.a.1.1		2	124.67	odd	6
961.2.a.c.1.1		2	124.119	even	6
961.2.c.a.439.1		4	124.123	even	2
961.2.c.a.521.1		4	124.99	even	6
961.2.d.i.374.2		8	124.115	even	30
961.2.d.i.388.2		8	124.11	even	30
961.2.d.i.531.1		8	124.83	even	30
961.2.d.i.628.1		8	124.75	even	30
961.2.d.l.374.2		8	124.71	odd	30
961.2.d.l.388.2		8	124.51	odd	30
961.2.d.l.531.1		8	124.103	odd	30
961.2.d.l.628.1		8	124.111	odd	30
961.2.g.o.235.2		16	124.35	odd	10
961.2.g.o.338.2		16	124.7	odd	30
961.2.g.o.448.1		16	124.59	odd	30
961.2.g.o.547.1		16	124.95	odd	10
961.2.g.o.732.2		16	124.107	odd	30
961.2.g.o.816.2		16	124.39	odd	10
961.2.g.o.844.1		16	124.19	odd	30
961.2.g.o.846.1		16	124.47	odd	10
961.2.g.r.235.2		16	124.27	even	10
961.2.g.r.338.2		16	124.55	even	30
961.2.g.r.448.1		16	124.3	even	30
961.2.g.r.547.1		16	124.91	even	10
961.2.g.r.732.2		16	124.79	even	30
961.2.g.r.816.2		16	124.23	even	10
961.2.g.r.844.1		16	124.43	even	30
961.2.g.r.846.1		16	124.15	even	10
8649.2.a.k.1.2		2	372.119	odd	6
8649.2.a.l.1.2		2	372.191	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 496 = 2^{4} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	496.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.20711 + 2.09077i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(1.20711 - 2.09077i) q^{7} +(-1.41421 - 2.44949i) q^{9} +(-2.62132 - 4.54026i) q^{11} +(-0.914214 - 1.58346i) q^{13} +2.41421 q^{15} +(0.0857864 - 0.148586i) q^{17} +(0.792893 - 1.37333i) q^{19} +(2.91421 + 5.04757i) q^{21} +4.00000 q^{23} +(2.00000 - 3.46410i) q^{25} -0.414214 q^{27} -1.17157 q^{29} +(5.00000 + 2.44949i) q^{31} +12.6569 q^{33} -2.41421 q^{35} +(-0.500000 + 0.866025i) q^{37} +4.41421 q^{39} +(-4.74264 - 8.21449i) q^{41} +(4.44975 - 7.70719i) q^{43} +(-1.41421 + 2.44949i) q^{45} +1.65685 q^{47} +(0.585786 + 1.01461i) q^{49} +(0.207107 + 0.358719i) q^{51} +(-0.0857864 - 0.148586i) q^{53} +(-2.62132 + 4.54026i) q^{55} +(1.91421 + 3.31552i) q^{57} +(-5.03553 + 8.72180i) q^{59} +2.82843 q^{61} -6.82843 q^{63} +(-0.914214 + 1.58346i) q^{65} +(-2.62132 - 4.54026i) q^{67} +(-4.82843 + 8.36308i) q^{69} +(-7.03553 - 12.1859i) q^{71} +(-1.91421 - 3.31552i) q^{73} +(4.82843 + 8.36308i) q^{75} -12.6569 q^{77} +(-7.62132 + 13.2005i) q^{79} +(4.74264 - 8.21449i) q^{81} +(2.03553 + 3.52565i) q^{83} -0.171573 q^{85} +(1.41421 - 2.44949i) q^{87} -12.4853 q^{89} -4.41421 q^{91} +(-11.1569 + 7.49706i) q^{93} -1.58579 q^{95} +10.8284 q^{97} +(-7.41421 + 12.8418i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 2 q^{5} + 2 q^{7} - 2 q^{11} + 2 q^{13} + 4 q^{15} + 6 q^{17} + 6 q^{19} + 6 q^{21} + 16 q^{23} + 8 q^{25} + 4 q^{27} - 16 q^{29} + 20 q^{31} + 28 q^{33} - 4 q^{35} - 2 q^{37} + 12 q^{39}+ \cdots - 24 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 2 * q^5 + 2 * q^7 - 2 * q^11 + 2 * q^13 + 4 * q^15 + 6 * q^17 + 6 * q^19 + 6 * q^21 + 16 * q^23 + 8 * q^25 + 4 * q^27 - 16 * q^29 + 20 * q^31 + 28 * q^33 - 4 * q^35 - 2 * q^37 + 12 * q^39 - 2 * q^41 - 2 * q^43 - 16 * q^47 + 8 * q^49 - 2 * q^51 - 6 * q^53 - 2 * q^55 + 2 * q^57 - 6 * q^59 - 16 * q^63 + 2 * q^65 - 2 * q^67 - 8 * q^69 - 14 * q^71 - 2 * q^73 + 8 * q^75 - 28 * q^77 - 22 * q^79 + 2 * q^81 - 6 * q^83 - 12 * q^85 - 16 * q^89 - 12 * q^91 - 22 * q^93 - 12 * q^95 + 32 * q^97 - 24 * q^99

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