LMFDB - Embedded newform 520.2.w.f.57.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [520,2,Mod(57,520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(520, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 1, 3]))

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

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

chi := DirichletCharacter("520.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 520 = 2^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	520.w (of order $4$, degree $2$, 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:	$4.15222090511$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 41 x^{18} + 640 x^{16} + 4888 x^{14} + 19956 x^{12} + 45364 x^{10} + 57952 x^{8} + 41120 x^{6} + \cdots + 256 $ x^20 + 41x^18 + 640x^16 + 4888x^14 + 19956x^12 + 45364x^10 + 57952x^8 + 41120x^6 + 16016x^4 + 3200*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			57.9
Root			$1.79929i$ of defining polynomial
Character	$\chi$	$=$	520.57
Dual form			520.2.w.f.73.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.75903 - 1.75903i) q^{3} +(-2.07584 - 0.831197i) q^{5} -4.71535i q^{7} -3.18840i q^{9} +O(q^{10})$	\(q+(1.75903 - 1.75903i) q^{3} +(-2.07584 - 0.831197i) q^{5} -4.71535i q^{7} -3.18840i q^{9} +(-0.281047 - 0.281047i) q^{11} +(1.52961 + 3.26501i) q^{13} +(-5.11358 + 2.18937i) q^{15} +(-4.84321 + 4.84321i) q^{17} +(-0.782284 - 0.782284i) q^{19} +(-8.29446 - 8.29446i) q^{21} +(-2.30324 - 2.30324i) q^{23} +(3.61822 + 3.45086i) q^{25} +(-0.331406 - 0.331406i) q^{27} -6.24720i q^{29} +(6.66847 - 6.66847i) q^{31} -0.988743 q^{33} +(-3.91938 + 9.78831i) q^{35} -3.15078i q^{37} +(8.43390 + 3.05264i) q^{39} +(8.37025 - 8.37025i) q^{41} +(3.55538 + 3.55538i) q^{43} +(-2.65019 + 6.61861i) q^{45} +3.57021i q^{47} -15.2345 q^{49} +17.0388i q^{51} +(1.47921 - 1.47921i) q^{53} +(0.349803 + 0.817015i) q^{55} -2.75213 q^{57} +(4.52346 - 4.52346i) q^{59} +4.05191 q^{61} -15.0344 q^{63} +(-0.461351 - 8.04905i) q^{65} +7.84255 q^{67} -8.10296 q^{69} +(-5.41956 + 5.41956i) q^{71} +9.61771 q^{73} +(12.4348 - 0.294387i) q^{75} +(-1.32524 + 1.32524i) q^{77} -1.86018i q^{79} +8.39930 q^{81} +6.71033i q^{83} +(14.0794 - 6.02807i) q^{85} +(-10.9890 - 10.9890i) q^{87} +(-10.0574 + 10.0574i) q^{89} +(15.3957 - 7.21263i) q^{91} -23.4601i q^{93} +(0.973664 + 2.27413i) q^{95} -13.5640 q^{97} +(-0.896092 + 0.896092i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{5}+O(q^{10}) $ 20 * q - 2 * q^5	$ 20 q - 2 q^{5} + 2 q^{11} + 4 q^{13} - 16 q^{15} - 6 q^{17} - 2 q^{19} + 6 q^{21} + 14 q^{23} + 14 q^{25} + 6 q^{27} + 10 q^{31} - 12 q^{33} - 16 q^{35} + 32 q^{39} + 28 q^{41} + 14 q^{45} - 16 q^{49} + 20 q^{53} - 48 q^{55} + 32 q^{57} - 14 q^{59} + 12 q^{61} + 8 q^{63} - 40 q^{65} + 36 q^{67} + 24 q^{69} - 48 q^{71} - 8 q^{73} - 22 q^{75} - 12 q^{77} - 4 q^{81} - 6 q^{85} - 28 q^{89} - 8 q^{91} - 2 q^{95} + 4 q^{97} - 42 q^{99}+O(q^{100}) $ 20 * q - 2 * q^5 + 2 * q^11 + 4 * q^13 - 16 * q^15 - 6 * q^17 - 2 * q^19 + 6 * q^21 + 14 * q^23 + 14 * q^25 + 6 * q^27 + 10 * q^31 - 12 * q^33 - 16 * q^35 + 32 * q^39 + 28 * q^41 + 14 * q^45 - 16 * q^49 + 20 * q^53 - 48 * q^55 + 32 * q^57 - 14 * q^59 + 12 * q^61 + 8 * q^63 - 40 * q^65 + 36 * q^67 + 24 * q^69 - 48 * q^71 - 8 * q^73 - 22 * q^75 - 12 * q^77 - 4 * q^81 - 6 * q^85 - 28 * q^89 - 8 * q^91 - 2 * q^95 + 4 * q^97 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	1.75903	−	1.75903i	1.01558	−	1.01558i	0.0157021	−	0.999877i	$-0.495002\pi$
$3$	1.75903	−	1.75903i	1.01558	−	1.01558i	0.999877	−	0.0157021i	$-0.00499835\pi$
$4$		0			0
$5$	−2.07584	−	0.831197i	−0.928344	−	0.371723i
$5$	−2.07584	−	0.831197i	−0.928344	−	0.371723i
$6$		0			0
$7$		−	4.71535i		−	1.78223i	−0.453774	−	0.891117i	$-0.649922\pi$
$7$		−	4.71535i		−	1.78223i	0.453774	−	0.891117i	$-0.350078\pi$
$8$		0			0
$9$		−	3.18840i		−	1.06280i
$10$		0			0
$11$	−0.281047	−	0.281047i	−0.0847389	−	0.0847389i	0.663467	−	0.748206i	$-0.269084\pi$
$11$	−0.281047	−	0.281047i	−0.0847389	−	0.0847389i	−0.748206	+	0.663467i	$0.769084\pi$
$12$		0			0
$13$	1.52961	+	3.26501i	0.424237	+	0.905551i
$13$	1.52961	+	3.26501i	0.424237	+	0.905551i
$14$		0			0
$15$	−5.11358	+	2.18937i	−1.32032	+	0.565293i
$16$		0			0
$17$	−4.84321	+	4.84321i	−1.17465	+	1.17465i	−0.193564	+	0.981088i	$0.562005\pi$
$17$	−4.84321	+	4.84321i	−1.17465	+	1.17465i	−0.981088	+	0.193564i	$0.937995\pi$
$18$		0			0
$19$	−0.782284	−	0.782284i	−0.179468	−	0.179468i	0.611656	−	0.791124i	$-0.290504\pi$
$19$	−0.782284	−	0.782284i	−0.179468	−	0.179468i	−0.791124	+	0.611656i	$0.790504\pi$
$20$		0			0
$21$	−8.29446	−	8.29446i	−1.81000	−	1.81000i
$22$		0			0
$23$	−2.30324	−	2.30324i	−0.480259	−	0.480259i	0.424955	−	0.905214i	$-0.360290\pi$
$23$	−2.30324	−	2.30324i	−0.480259	−	0.480259i	−0.905214	+	0.424955i	$0.860290\pi$
$24$		0			0
$25$	3.61822	+	3.45086i	0.723644	+	0.690173i
$26$		0			0
$27$	−0.331406	−	0.331406i	−0.0637792	−	0.0637792i
$28$		0			0
$29$		−	6.24720i		−	1.16008i	−0.814590	−	0.580038i	$-0.803038\pi$
$29$		−	6.24720i		−	1.16008i	0.814590	−	0.580038i	$-0.196962\pi$
$30$		0			0
$31$	6.66847	−	6.66847i	1.19769	−	1.19769i	0.222837	−	0.974856i	$-0.428468\pi$
$31$	6.66847	−	6.66847i	1.19769	−	1.19769i	0.974856	−	0.222837i	$-0.0715316\pi$
$32$		0			0
$33$	−0.988743			−0.172118
$34$		0			0
$35$	−3.91938	+	9.78831i	−0.662497	+	1.65453i
$36$		0			0
$37$		−	3.15078i		−	0.517985i	−0.965879	−	0.258993i	$-0.916609\pi$
$37$		−	3.15078i		−	0.517985i	0.965879	−	0.258993i	$-0.0833905\pi$
$38$		0			0
$39$	8.43390	+	3.05264i	1.35050	+	0.488813i
$40$		0			0
$41$	8.37025	−	8.37025i	1.30721	−	1.30721i	0.383795	−	0.923418i	$-0.374617\pi$
$41$	8.37025	−	8.37025i	1.30721	−	1.30721i	0.923418	−	0.383795i	$-0.125383\pi$
$42$		0			0
$43$	3.55538	+	3.55538i	0.542190	+	0.542190i	0.924170	−	0.381980i	$-0.124758\pi$
$43$	3.55538	+	3.55538i	0.542190	+	0.542190i	−0.381980	+	0.924170i	$0.624758\pi$
$44$		0			0
$45$	−2.65019	+	6.61861i	−0.395067	+	0.986645i
$46$		0			0
$47$			3.57021i			0.520769i	0.965505	+	0.260384i	$0.0838493\pi$
$47$			3.57021i			0.520769i	−0.965505	+	0.260384i	$0.916151\pi$
$48$		0			0
$49$	−15.2345			−2.17636
$50$		0			0
$51$			17.0388i			2.38590i
$52$		0			0
$53$	1.47921	−	1.47921i	0.203185	−	0.203185i	−0.598178	−	0.801363i	$-0.704108\pi$
$53$	1.47921	−	1.47921i	0.203185	−	0.203185i	0.801363	+	0.598178i	$0.204108\pi$
$54$		0			0
$55$	0.349803	+	0.817015i	0.0471675	+	0.110166i
$56$		0			0
$57$	−2.75213			−0.364528
$58$		0			0
$59$	4.52346	−	4.52346i	0.588904	−	0.588904i	−0.348431	−	0.937335i	$-0.613285\pi$
$59$	4.52346	−	4.52346i	0.588904	−	0.588904i	0.937335	+	0.348431i	$0.113285\pi$
$60$		0			0
$61$	4.05191			0.518794			0.259397	−	0.965771i	$-0.416476\pi$
$61$	4.05191			0.518794			0.259397	+	0.965771i	$0.416476\pi$
$62$		0			0
$63$	−15.0344			−1.89416
$64$		0			0
$65$	−0.461351	−	8.04905i	−0.0572235	−	0.998361i
$66$		0			0
$67$	7.84255			0.958120			0.479060	−	0.877782i	$-0.340978\pi$
$67$	7.84255			0.958120			0.479060	+	0.877782i	$0.340978\pi$
$68$		0			0
$69$	−8.10296			−0.975482
$70$		0			0
$71$	−5.41956	+	5.41956i	−0.643184	+	0.643184i	−0.951337	−	0.308153i	$-0.900289\pi$
$71$	−5.41956	+	5.41956i	−0.643184	+	0.643184i	0.308153	+	0.951337i	$0.400289\pi$
$72$		0			0
$73$	9.61771			1.12567			0.562834	−	0.826570i	$-0.309711\pi$
$73$	9.61771			1.12567			0.562834	+	0.826570i	$0.309711\pi$
$74$		0			0
$75$	12.4348	−	0.294387i	1.43584	−	0.0339929i
$76$		0			0
$77$	−1.32524	+	1.32524i	−0.151025	+	0.151025i
$78$		0			0
$79$		−	1.86018i		−	0.209287i	−0.994510	−	0.104643i	$-0.966630\pi$
$79$		−	1.86018i		−	0.209287i	0.994510	−	0.104643i	$-0.0333701\pi$
$80$		0			0
$81$	8.39930			0.933255
$82$		0			0
$83$			6.71033i			0.736554i	0.929716	+	0.368277i	$0.120052\pi$
$83$			6.71033i			0.736554i	−0.929716	+	0.368277i	$0.879948\pi$
$84$		0			0
$85$	14.0794	−	6.02807i	1.52713	−	0.653836i
$86$		0			0
$87$	−10.9890	−	10.9890i	−1.17815	−	1.17815i
$88$		0			0
$89$	−10.0574	+	10.0574i	−1.06608	+	1.06608i	−0.0684279	+	0.997656i	$0.521798\pi$
$89$	−10.0574	+	10.0574i	−1.06608	+	1.06608i	−0.997656	+	0.0684279i	$0.978202\pi$
$90$		0			0
$91$	15.3957	−	7.21263i	1.61390	−	0.756089i
$92$		0			0
$93$		−	23.4601i		−	2.43270i
$94$		0			0
$95$	0.973664	+	2.27413i	0.0998958	+	0.233321i
$96$		0			0
$97$	−13.5640			−1.37722			−0.688608	−	0.725134i	$-0.741778\pi$
$97$	−13.5640			−1.37722			−0.688608	+	0.725134i	$0.741778\pi$
$98$		0			0
$99$	−0.896092	+	0.896092i	−0.0900606	+	0.0900606i
$100$		0			0
$101$			0.932039i			0.0927413i	0.998924	+	0.0463707i	$0.0147655\pi$
$101$			0.932039i			0.0927413i	−0.998924	+	0.0463707i	$0.985234\pi$
$102$		0			0
$103$	−4.49429	−	4.49429i	−0.442836	−	0.442836i	0.450128	−	0.892964i	$-0.351378\pi$
$103$	−4.49429	−	4.49429i	−0.442836	−	0.442836i	−0.892964	+	0.450128i	$0.851378\pi$
$104$		0			0
$105$	10.3236	+	24.1123i	1.00748	+	2.35312i
$106$		0			0
$107$	4.80764	+	4.80764i	0.464772	+	0.464772i	0.900216	−	0.435444i	$-0.143409\pi$
$107$	4.80764	+	4.80764i	0.464772	+	0.464772i	−0.435444	+	0.900216i	$0.643409\pi$
$108$		0			0
$109$	2.13756	+	2.13756i	0.204741	+	0.204741i	0.802028	−	0.597287i	$-0.203755\pi$
$109$	2.13756	+	2.13756i	0.204741	+	0.204741i	−0.597287	+	0.802028i	$0.703755\pi$
$110$		0			0
$111$	−5.54233	−	5.54233i	−0.526055	−	0.526055i
$112$		0			0
$113$	−6.15291	+	6.15291i	−0.578817	+	0.578817i	−0.934577	−	0.355760i	$-0.884222\pi$
$113$	−6.15291	+	6.15291i	−0.578817	+	0.578817i	0.355760	+	0.934577i	$0.384222\pi$
$114$		0			0
$115$	2.86671	+	6.69561i	0.267322	+	0.624369i
$116$		0			0
$117$	10.4102	−	4.87700i	0.962421	−	0.450879i
$118$		0			0
$119$	22.8374	+	22.8374i	2.09350	+	2.09350i
$120$		0			0
$121$		−	10.8420i		−	0.985639i
$122$		0			0
$123$		−	29.4471i		−	2.65516i
$124$		0			0
$125$	−4.64250	−	10.1709i	−0.415238	−	0.909713i
$126$		0			0
$127$	−7.83780	+	7.83780i	−0.695492	+	0.695492i	−0.963435	−	0.267943i	$-0.913656\pi$
$127$	−7.83780	+	7.83780i	−0.695492	+	0.695492i	0.267943	+	0.963435i	$0.413656\pi$
$128$		0			0
$129$	12.5081			1.10127
$130$		0			0
$131$	0.640461			0.0559574			0.0279787	−	0.999609i	$-0.491093\pi$
$131$	0.640461			0.0559574			0.0279787	+	0.999609i	$0.491093\pi$
$132$		0			0
$133$	−3.68874	+	3.68874i	−0.319854	+	0.319854i
$134$		0			0
$135$	0.412483	+	0.963411i	0.0355008	+	0.0829172i
$136$		0			0
$137$			2.64527i			0.226001i	0.993595	+	0.113000i	$0.0360461\pi$
$137$			2.64527i			0.226001i	−0.993595	+	0.113000i	$0.963954\pi$
$138$		0			0
$139$			5.69897i			0.483381i	0.970353	+	0.241690i	$0.0777018\pi$
$139$			5.69897i			0.483381i	−0.970353	+	0.241690i	$0.922298\pi$
$140$		0			0
$141$	6.28012	+	6.28012i	0.528882	+	0.528882i
$142$		0			0
$143$	0.487731	−	1.34751i	0.0407861	−	0.112685i
$144$		0			0
$145$	−5.19265	+	12.9682i	−0.431227	+	1.07695i
$146$		0			0
$147$	−26.7980	+	26.7980i	−2.21026	+	2.21026i
$148$		0			0
$149$	13.1616	+	13.1616i	1.07824	+	1.07824i	0.996667	+	0.0815732i	$0.0259944\pi$
$149$	13.1616	+	13.1616i	1.07824	+	1.07824i	0.0815732	+	0.996667i	$0.474006\pi$
$150$		0			0
$151$	−7.99575	−	7.99575i	−0.650685	−	0.650685i	0.302473	−	0.953158i	$-0.402188\pi$
$151$	−7.99575	−	7.99575i	−0.650685	−	0.650685i	−0.953158	+	0.302473i	$0.902188\pi$
$152$		0			0
$153$	15.4421	+	15.4421i	1.24842	+	1.24842i
$154$		0			0
$155$	−19.3855	+	8.29986i	−1.55708	+	0.666661i
$156$		0			0
$157$	14.4321	+	14.4321i	1.15181	+	1.15181i	0.986190	+	0.165616i	$0.0529613\pi$
$157$	14.4321	+	14.4321i	1.15181	+	1.15181i	0.165616	+	0.986190i	$0.447039\pi$
$158$		0			0
$159$		−	5.20397i		−	0.412702i
$160$		0			0
$161$	−10.8606	+	10.8606i	−0.855934	+	0.855934i
$162$		0			0
$163$	5.33972			0.418239			0.209120	−	0.977890i	$-0.432940\pi$
$163$	5.33972			0.418239			0.209120	+	0.977890i	$0.432940\pi$
$164$		0			0
$165$	2.05247	+	0.821841i	0.159785	+	0.0639802i
$166$		0			0
$167$		−	5.51667i		−	0.426893i	−0.976955	−	0.213446i	$-0.931531\pi$
$167$		−	5.51667i		−	0.426893i	0.976955	−	0.213446i	$-0.0684688\pi$
$168$		0			0
$169$	−8.32060	+	9.98837i	−0.640046	+	0.768336i
$170$		0			0
$171$	−2.49424	+	2.49424i	−0.190739	+	0.190739i
$172$		0			0
$173$	1.95916	+	1.95916i	0.148952	+	0.148952i	0.777650	−	0.628698i	$-0.216412\pi$
$173$	1.95916	+	1.95916i	0.148952	+	0.148952i	−0.628698	+	0.777650i	$0.716412\pi$
$174$		0			0
$175$	16.2720	−	17.0612i	1.23005	−	1.28970i
$176$		0			0
$177$		−	15.9138i		−	1.19616i
$178$		0			0
$179$	19.2189			1.43649			0.718245	−	0.695790i	$-0.244946\pi$
$179$	19.2189			1.43649			0.718245	+	0.695790i	$0.244946\pi$
$180$		0			0
$181$			2.95172i			0.219399i	0.993965	+	0.109700i	$0.0349889\pi$
$181$			2.95172i			0.219399i	−0.993965	+	0.109700i	$0.965011\pi$
$182$		0			0
$183$	7.12745	−	7.12745i	0.526876	−	0.526876i
$184$		0			0
$185$	−2.61892	+	6.54052i	−0.192547	+	0.480868i
$186$		0			0
$187$	2.72234			0.199077
$188$		0			0
$189$	−1.56270	+	1.56270i	−0.113669	+	0.113669i
$190$		0			0
$191$	2.18940			0.158420			0.0792099	−	0.996858i	$-0.474760\pi$
$191$	2.18940			0.158420			0.0792099	+	0.996858i	$0.474760\pi$
$192$		0			0
$193$	1.11351			0.0801521			0.0400761	−	0.999197i	$-0.487240\pi$
$193$	1.11351			0.0801521			0.0400761	+	0.999197i	$0.487240\pi$
$194$		0			0
$195$	−14.9701	−	13.3470i	−1.07203	−	0.955800i
$196$		0			0
$197$	−5.59534			−0.398651			−0.199326	−	0.979933i	$-0.563875\pi$
$197$	−5.59534			−0.398651			−0.199326	+	0.979933i	$0.563875\pi$
$198$		0			0
$199$	7.48117			0.530326			0.265163	−	0.964204i	$-0.414574\pi$
$199$	7.48117			0.530326			0.265163	+	0.964204i	$0.414574\pi$
$200$		0			0
$201$	13.7953	−	13.7953i	0.973046	−	0.973046i
$202$		0			0
$203$	−29.4577			−2.06753
$204$		0			0
$205$	−24.3326	+	10.4180i	−1.69946	+	0.727623i
$206$		0			0
$207$	−7.34366	+	7.34366i	−0.510420	+	0.510420i
$208$		0			0
$209$			0.439717i			0.0304159i
$210$		0			0
$211$	14.9472			1.02901			0.514504	−	0.857488i	$-0.327976\pi$
$211$	14.9472			1.02901			0.514504	+	0.857488i	$0.327976\pi$
$212$		0			0
$213$			19.0664i			1.30641i
$214$		0			0
$215$	−4.42517	−	10.3356i	−0.301794	−	0.704883i
$216$		0			0
$217$	−31.4442	−	31.4442i	−2.13457	−	2.13457i
$218$		0			0
$219$	16.9179	−	16.9179i	1.14320	−	1.14320i
$220$		0			0
$221$	−23.2214	−	8.40493i	−1.56204	−	0.565377i
$222$		0			0
$223$		−	19.7086i		−	1.31978i	−0.751360	−	0.659892i	$-0.770602\pi$
$223$		−	19.7086i		−	1.31978i	0.751360	−	0.659892i	$-0.229398\pi$
$224$		0			0
$225$	11.0027	−	11.5363i	0.733516	−	0.769090i
$226$		0			0
$227$	−14.2779			−0.947660			−0.473830	−	0.880616i	$-0.657129\pi$
$227$	−14.2779			−0.947660			−0.473830	+	0.880616i	$0.657129\pi$
$228$		0			0
$229$	0.113080	−	0.113080i	0.00747252	−	0.00747252i	−0.703361	−	0.710833i	$-0.748318\pi$
$229$	0.113080	−	0.113080i	0.00747252	−	0.00747252i	0.710833	+	0.703361i	$0.248318\pi$
$230$		0			0
$231$			4.66227i			0.306755i
$232$		0			0
$233$	1.15635	+	1.15635i	0.0757551	+	0.0757551i	0.743969	−	0.668214i	$-0.232941\pi$
$233$	1.15635	+	1.15635i	0.0757551	+	0.0757551i	−0.668214	+	0.743969i	$0.732941\pi$
$234$		0			0
$235$	2.96755	−	7.41118i	0.193582	−	0.483452i
$236$		0			0
$237$	−3.27212	−	3.27212i	−0.212547	−	0.212547i
$238$		0			0
$239$	−9.16538	−	9.16538i	−0.592859	−	0.592859i	0.345543	−	0.938403i	$-0.387695\pi$
$239$	−9.16538	−	9.16538i	−0.592859	−	0.592859i	−0.938403	+	0.345543i	$0.887695\pi$
$240$		0			0
$241$	−0.539502	−	0.539502i	−0.0347524	−	0.0347524i	0.689517	−	0.724269i	$-0.257823\pi$
$241$	−0.539502	−	0.539502i	−0.0347524	−	0.0347524i	−0.724269	+	0.689517i	$0.757823\pi$
$242$		0			0
$243$	15.7689	−	15.7689i	1.01157	−	1.01157i
$244$		0			0
$245$	31.6244	+	12.6629i	2.02041	+	0.809002i
$246$		0			0
$247$	1.35758	−	3.75075i	0.0863807	−	0.238655i
$248$		0			0
$249$	11.8037	+	11.8037i	0.748029	+	0.748029i
$250$		0			0
$251$		−	15.2991i		−	0.965674i	−0.875710	−	0.482837i	$-0.839606\pi$
$251$		−	15.2991i		−	0.965674i	0.875710	−	0.482837i	$-0.160394\pi$
$252$		0			0
$253$			1.29464i			0.0813933i
$254$		0			0
$255$	14.1626	−	35.3697i	0.886894	−	2.21494i
$256$		0			0
$257$	7.25113	−	7.25113i	0.452313	−	0.452313i	−0.443809	−	0.896122i	$-0.646373\pi$
$257$	7.25113	−	7.25113i	0.452313	−	0.452313i	0.896122	+	0.443809i	$0.146373\pi$
$258$		0			0
$259$	−14.8570			−0.923171
$260$		0			0
$261$	−19.9186			−1.23293
$262$		0			0
$263$	−11.0473	+	11.0473i	−0.681208	+	0.681208i	−0.960273	−	0.279064i	$-0.909976\pi$
$263$	−11.0473	+	11.0473i	−0.681208	+	0.681208i	0.279064	+	0.960273i	$0.409976\pi$
$264$		0			0
$265$	−4.30013	+	1.84109i	−0.264155	+	0.113097i
$266$		0			0
$267$			35.3827i			2.16538i
$268$		0			0
$269$			7.22615i			0.440586i	0.975434	+	0.220293i	$0.0707013\pi$
$269$			7.22615i			0.440586i	−0.975434	+	0.220293i	$0.929299\pi$
$270$		0			0
$271$	−1.58439	−	1.58439i	−0.0962449	−	0.0962449i	0.657345	−	0.753590i	$-0.271679\pi$
$271$	−1.58439	−	1.58439i	−0.0962449	−	0.0962449i	−0.753590	+	0.657345i	$0.771679\pi$
$272$		0			0
$273$	14.3942	−	39.7688i	0.871179	−	2.40692i
$274$		0			0
$275$	−0.0470352	−	1.98675i	−0.00283633	−	0.119805i
$276$		0			0
$277$	−11.0009	+	11.0009i	−0.660978	+	0.660978i	−0.955611	−	0.294633i	$-0.904803\pi$
$277$	−11.0009	+	11.0009i	−0.660978	+	0.660978i	0.294633	+	0.955611i	$0.404803\pi$
$278$		0			0
$279$	−21.2618	−	21.2618i	−1.27291	−	1.27291i
$280$		0			0
$281$	5.01859	+	5.01859i	0.299384	+	0.299384i	0.840772	−	0.541389i	$-0.182101\pi$
$281$	5.01859	+	5.01859i	0.299384	+	0.299384i	−0.541389	+	0.840772i	$0.682101\pi$
$282$		0			0
$283$	15.5151	+	15.5151i	0.922274	+	0.922274i	0.997190	−	0.0749155i	$-0.0238687\pi$
$283$	15.5151	+	15.5151i	0.922274	+	0.922274i	−0.0749155	+	0.997190i	$0.523869\pi$
$284$		0			0
$285$	5.71298	+	2.28756i	0.338407	+	0.135503i
$286$		0			0
$287$	−39.4686	−	39.4686i	−2.32976	−	2.32976i
$288$		0			0
$289$		−	29.9134i		−	1.75961i
$290$		0			0
$291$	−23.8595	+	23.8595i	−1.39867	+	1.39867i
$292$		0			0
$293$	−0.864418			−0.0504999			−0.0252499	−	0.999681i	$-0.508038\pi$
$293$	−0.864418			−0.0504999			−0.0252499	+	0.999681i	$0.508038\pi$
$294$		0			0
$295$	−13.1499	+	5.63009i	−0.765614	+	0.327796i
$296$		0			0
$297$			0.186282i			0.0108092i
$298$		0			0
$299$	3.99706	−	11.0432i	0.231156	−	0.638643i
$300$		0			0
$301$	16.7648	−	16.7648i	0.966310	−	0.966310i
$302$		0			0
$303$	1.63949	+	1.63949i	0.0941861	+	0.0941861i
$304$		0			0
$305$	−8.41112	−	3.36794i	−0.481619	−	0.192848i
$306$		0			0
$307$		−	16.2003i		−	0.924601i	−0.886723	−	0.462300i	$-0.847024\pi$
$307$		−	16.2003i		−	0.924601i	0.886723	−	0.462300i	$-0.152976\pi$
$308$		0			0
$309$	−15.8112			−0.899469
$310$		0			0
$311$			28.2345i			1.60103i	0.599312	+	0.800516i	$0.295441\pi$
$311$			28.2345i			1.60103i	−0.599312	+	0.800516i	$0.704559\pi$
$312$		0			0
$313$	−11.9671	+	11.9671i	−0.676423	+	0.676423i	−0.959189	−	0.282766i	$-0.908748\pi$
$313$	−11.9671	+	11.9671i	−0.676423	+	0.676423i	0.282766	+	0.959189i	$0.408748\pi$
$314$		0			0
$315$	31.2091	+	12.4966i	1.75843	+	0.704102i
$316$		0			0
$317$	−1.66668			−0.0936100			−0.0468050	−	0.998904i	$-0.514904\pi$
$317$	−1.66668			−0.0936100			−0.0468050	+	0.998904i	$0.514904\pi$
$318$		0			0
$319$	−1.75576	+	1.75576i	−0.0983036	+	0.0983036i
$320$		0			0
$321$	16.9136			0.944025
$322$		0			0
$323$	7.57753			0.421625
$324$		0			0
$325$	−5.73266	+	17.0920i	−0.317991	+	0.948094i
$326$		0			0
$327$	7.52008			0.415861
$328$		0			0
$329$	16.8348			0.928132
$330$		0			0
$331$	−18.0216	+	18.0216i	−0.990556	+	0.990556i	−0.999956	−	0.00939989i	$-0.997008\pi$
$331$	−18.0216	+	18.0216i	−0.990556	+	0.990556i	0.00939989	+	0.999956i	$0.497008\pi$
$332$		0			0
$333$	−10.0460			−0.550515
$334$		0			0
$335$	−16.2799	−	6.51871i	−0.889465	−	0.356155i
$336$		0			0
$337$	11.7241	−	11.7241i	0.638653	−	0.638653i	−0.311570	−	0.950223i	$-0.600855\pi$
$337$	11.7241	−	11.7241i	0.638653	−	0.638653i	0.950223	+	0.311570i	$0.100855\pi$
$338$		0			0
$339$			21.6464i			1.17567i
$340$		0			0
$341$	−3.74831			−0.202982
$342$		0			0
$343$			38.8286i			2.09655i
$344$		0			0
$345$	16.8205	+	6.73516i	0.905583	+	0.362609i
$346$		0			0
$347$	3.40632	+	3.40632i	0.182861	+	0.182861i	0.792601	−	0.609740i	$-0.208726\pi$
$347$	3.40632	+	3.40632i	0.182861	+	0.182861i	−0.609740	+	0.792601i	$0.708726\pi$
$348$		0			0
$349$	12.7962	−	12.7962i	0.684963	−	0.684963i	−0.276151	−	0.961114i	$-0.589059\pi$
$349$	12.7962	−	12.7962i	0.684963	−	0.684963i	0.961114	+	0.276151i	$0.0890589\pi$
$350$		0			0
$351$	0.575124	−	1.58897i	0.0306979	−	0.0848128i
$352$		0			0
$353$		−	5.38245i		−	0.286479i	−0.989688	−	0.143239i	$-0.954248\pi$
$353$		−	5.38245i		−	0.286479i	0.989688	−	0.143239i	$-0.0457519\pi$
$354$		0			0
$355$	15.7549	−	6.74542i	0.836182	−	0.358010i
$356$		0			0
$357$	80.3437			4.25224
$358$		0			0
$359$	−23.2099	+	23.2099i	−1.22497	+	1.22497i	−0.259131	+	0.965842i	$0.583436\pi$
$359$	−23.2099	+	23.2099i	−1.22497	+	1.22497i	−0.965842	+	0.259131i	$0.916564\pi$
$360$		0			0
$361$		−	17.7761i		−	0.935582i
$362$		0			0
$363$	−19.0715	−	19.0715i	−1.00099	−	1.00099i
$364$		0			0
$365$	−19.9648	−	7.99422i	−1.04501	−	0.418437i
$366$		0			0
$367$	23.7526	+	23.7526i	1.23987	+	1.23987i	0.960052	+	0.279822i	$0.0902756\pi$
$367$	23.7526	+	23.7526i	1.23987	+	1.23987i	0.279822	+	0.960052i	$0.409724\pi$
$368$		0			0
$369$	−26.6877	−	26.6877i	−1.38931	−	1.38931i
$370$		0			0
$371$	−6.97500	−	6.97500i	−0.362124	−	0.362124i
$372$		0			0
$373$	−17.3318	+	17.3318i	−0.897406	+	0.897406i	−0.995206	−	0.0978000i	$-0.968819\pi$
$373$	−17.3318	+	17.3318i	−0.897406	+	0.897406i	0.0978000	+	0.995206i	$0.468819\pi$
$374$		0			0
$375$	−26.0573	−	9.72464i	−1.34559	−	0.502178i
$376$		0			0
$377$	20.3972	−	9.55576i	1.05051	−	0.492147i
$378$		0			0
$379$	−16.1822	−	16.1822i	−0.831224	−	0.831224i	0.156460	−	0.987684i	$-0.449992\pi$
$379$	−16.1822	−	16.1822i	−0.831224	−	0.831224i	−0.987684	+	0.156460i	$0.949992\pi$
$380$		0			0
$381$			27.5739i			1.41265i
$382$		0			0
$383$			23.5091i			1.20126i	0.799528	+	0.600628i	$0.205083\pi$
$383$			23.5091i			1.20126i	−0.799528	+	0.600628i	$0.794917\pi$
$384$		0			0
$385$	3.85251	−	1.64944i	0.196342	−	0.0840635i
$386$		0			0
$387$	11.3360	−	11.3360i	0.576240	−	0.576240i
$388$		0			0
$389$	−33.7108			−1.70921			−0.854604	−	0.519280i	$-0.826200\pi$
$389$	−33.7108			−1.70921			−0.854604	+	0.519280i	$0.826200\pi$
$390$		0			0
$391$	22.3102			1.12827
$392$		0			0
$393$	1.12659	−	1.12659i	0.0568291	−	0.0568291i
$394$		0			0
$395$	−1.54618	+	3.86143i	−0.0777966	+	0.194290i
$396$		0			0
$397$			29.2446i			1.46774i	0.679288	+	0.733872i	$0.262289\pi$
$397$			29.2446i			1.46774i	−0.679288	+	0.733872i	$0.737711\pi$
$398$		0			0
$399$			12.9772i			0.649675i
$400$		0			0
$401$	−15.8234	−	15.8234i	−0.790184	−	0.790184i	0.191340	−	0.981524i	$-0.438717\pi$
$401$	−15.8234	−	15.8234i	−0.790184	−	0.790184i	−0.981524	+	0.191340i	$0.938717\pi$
$402$		0			0
$403$	31.9728	+	11.5725i	1.59268	+	0.576467i
$404$		0			0
$405$	−17.4356	−	6.98147i	−0.866382	−	0.346912i
$406$		0			0
$407$	−0.885518	+	0.885518i	−0.0438935	+	0.0438935i
$408$		0			0
$409$	22.0977	+	22.0977i	1.09266	+	1.09266i	0.995244	+	0.0974166i	$0.0310579\pi$
$409$	22.0977	+	22.0977i	1.09266	+	1.09266i	0.0974166	+	0.995244i	$0.468942\pi$
$410$		0			0
$411$	4.65312	+	4.65312i	0.229522	+	0.229522i
$412$		0			0
$413$	−21.3297	−	21.3297i	−1.04956	−	1.04956i
$414$		0			0
$415$	5.57761	−	13.9296i	0.273794	−	0.683776i
$416$		0			0
$417$	10.0247	+	10.0247i	0.490911	+	0.490911i
$418$		0			0
$419$			14.4832i			0.707549i	0.935331	+	0.353775i	$0.115102\pi$
$419$			14.4832i			0.707549i	−0.935331	+	0.353775i	$0.884898\pi$
$420$		0			0
$421$	−22.1266	+	22.1266i	−1.07839	+	1.07839i	−0.0817310	+	0.996654i	$0.526045\pi$
$421$	−22.1266	+	22.1266i	−1.07839	+	1.07839i	−0.996654	+	0.0817310i	$0.973955\pi$
$422$		0			0
$423$	11.3833			0.553473
$424$		0			0
$425$	−34.2371	+	0.810546i	−1.66074	+	0.0393173i
$426$		0			0
$427$		−	19.1062i		−	0.924613i
$428$		0			0
$429$	−1.51239	−	3.22826i	−0.0730188	−	0.155862i
$430$		0			0
$431$	18.2677	−	18.2677i	0.879924	−	0.879924i	−0.113603	−	0.993526i	$-0.536239\pi$
$431$	18.2677	−	18.2677i	0.879924	−	0.879924i	0.993526	+	0.113603i	$0.0362391\pi$
$432$		0			0
$433$	−9.20010	−	9.20010i	−0.442129	−	0.442129i	0.450598	−	0.892727i	$-0.351211\pi$
$433$	−9.20010	−	9.20010i	−0.442129	−	0.442129i	−0.892727	+	0.450598i	$0.851211\pi$
$434$		0			0
$435$	13.6774	+	31.9455i	0.655782	+	1.53167i
$436$		0			0
$437$			3.60358i			0.172382i
$438$		0			0
$439$	14.5148			0.692752			0.346376	−	0.938096i	$-0.387412\pi$
$439$	14.5148			0.692752			0.346376	+	0.938096i	$0.387412\pi$
$440$		0			0
$441$			48.5737i			2.31304i
$442$		0			0
$443$	16.0331	−	16.0331i	0.761757	−	0.761757i	−0.214883	−	0.976640i	$-0.568937\pi$
$443$	16.0331	−	16.0331i	0.761757	−	0.761757i	0.976640	+	0.214883i	$0.0689371\pi$
$444$		0			0
$445$	29.2373	−	12.5179i	1.38598	−	0.593405i
$446$		0			0
$447$	46.3034			2.19008
$448$		0			0
$449$	−26.3022	+	26.3022i	−1.24128	+	1.24128i	−0.281810	+	0.959470i	$0.590935\pi$
$449$	−26.3022	+	26.3022i	−1.24128	+	1.24128i	−0.959470	+	0.281810i	$0.909065\pi$
$450$		0			0
$451$	−4.70487			−0.221544
$452$		0			0
$453$	−28.1296			−1.32164
$454$		0			0
$455$	−37.9541	+	2.17543i	−1.77931	+	0.101986i
$456$		0			0
$457$	−27.9739			−1.30856			−0.654282	−	0.756251i	$-0.727029\pi$
$457$	−27.9739			−1.30856			−0.654282	+	0.756251i	$0.727029\pi$
$458$		0			0
$459$	3.21014			0.149837
$460$		0			0
$461$	19.2175	−	19.2175i	0.895046	−	0.895046i	−0.0999465	−	0.994993i	$-0.531867\pi$
$461$	19.2175	−	19.2175i	0.895046	−	0.895046i	0.994993	+	0.0999465i	$0.0318672\pi$
$462$		0			0
$463$	−28.8100			−1.33892			−0.669458	−	0.742850i	$-0.733474\pi$
$463$	−28.8100			−1.33892			−0.669458	+	0.742850i	$0.733474\pi$
$464$		0			0
$465$	−19.5000	+	48.6995i	−0.904291	+	2.25838i
$466$		0			0
$467$	24.2034	−	24.2034i	1.12000	−	1.12000i	0.128259	−	0.991741i	$-0.459061\pi$
$467$	24.2034	−	24.2034i	1.12000	−	1.12000i	0.991741	−	0.128259i	$-0.0409390\pi$
$468$		0			0
$469$		−	36.9804i		−	1.70759i
$470$		0			0
$471$	50.7731			2.33950
$472$		0			0
$473$		−	1.99846i		−	0.0918892i
$474$		0			0
$475$	−0.130921	−	5.53003i	−0.00600705	−	0.253735i
$476$		0			0
$477$	−4.71632	−	4.71632i	−0.215946	−	0.215946i
$478$		0			0
$479$	11.9541	−	11.9541i	0.546197	−	0.546197i	−0.379142	−	0.925339i	$-0.623781\pi$
$479$	11.9541	−	11.9541i	0.546197	−	0.546197i	0.925339	+	0.379142i	$0.123781\pi$
$480$		0			0
$481$	10.2873	−	4.81946i	0.469062	−	0.219748i
$482$		0			0
$483$			38.2083i			1.73854i
$484$		0			0
$485$	28.1567	+	11.2744i	1.27853	+	0.511942i
$486$		0			0
$487$	−12.7489			−0.577709			−0.288854	−	0.957373i	$-0.593274\pi$
$487$	−12.7489			−0.577709			−0.288854	+	0.957373i	$0.593274\pi$
$488$		0			0
$489$	9.39275	−	9.39275i	0.424755	−	0.424755i
$490$		0			0
$491$			9.59961i			0.433224i	0.976258	+	0.216612i	$0.0695007\pi$
$491$			9.59961i			0.433224i	−0.976258	+	0.216612i	$0.930499\pi$
$492$		0			0
$493$	30.2565	+	30.2565i	1.36269	+	1.36269i
$494$		0			0
$495$	2.60497	−	1.11531i	0.117085	−	0.0501296i
$496$		0			0
$497$	25.5551	+	25.5551i	1.14630	+	1.14630i
$498$		0			0
$499$	−24.5467	−	24.5467i	−1.09886	−	1.09886i	−0.994544	−	0.104319i	$-0.966734\pi$
$499$	−24.5467	−	24.5467i	−1.09886	−	1.09886i	−0.104319	−	0.994544i	$-0.533266\pi$
$500$		0			0
$501$	−9.70401	−	9.70401i	−0.433543	−	0.433543i
$502$		0			0
$503$	−3.95718	+	3.95718i	−0.176442	+	0.176442i	−0.789803	−	0.613361i	$-0.789817\pi$
$503$	−3.95718	+	3.95718i	−0.176442	+	0.176442i	0.613361	+	0.789803i	$0.289817\pi$
$504$		0			0
$505$	0.774708	−	1.93476i	0.0344741	−	0.0860958i
$506$		0			0
$507$	2.93366	+	32.2061i	0.130289	+	1.43032i
$508$		0			0
$509$	−3.11209	−	3.11209i	−0.137941	−	0.137941i	0.634765	−	0.772706i	$-0.281097\pi$
$509$	−3.11209	−	3.11209i	−0.137941	−	0.137941i	−0.772706	+	0.634765i	$0.781097\pi$
$510$		0			0
$511$		−	45.3509i		−	2.00620i
$512$		0			0
$513$			0.518508i			0.0228927i
$514$		0			0
$515$	5.59378	+	13.0651i	0.246492	+	0.575716i
$516$		0			0
$517$	1.00340	−	1.00340i	0.0441294	−	0.0441294i
$518$		0			0
$519$	6.89245			0.302545
$520$		0			0
$521$	−15.7076			−0.688163			−0.344081	−	0.938940i	$-0.611810\pi$
$521$	−15.7076			−0.688163			−0.344081	+	0.938940i	$0.611810\pi$
$522$		0			0
$523$	5.02118	−	5.02118i	0.219561	−	0.219561i	−0.588752	−	0.808313i	$-0.700381\pi$
$523$	5.02118	−	5.02118i	0.219561	−	0.219561i	0.808313	+	0.588752i	$0.200381\pi$
$524$		0			0
$525$	−1.38814	−	58.6343i	−0.0605832	−	2.55901i
$526$		0			0
$527$			64.5936i			2.81374i
$528$		0			0
$529$		−	12.3902i		−	0.538702i
$530$		0			0
$531$	−14.4226	−	14.4226i	−0.625888	−	0.625888i
$532$		0			0
$533$	40.1322	+	14.5258i	1.73832	+	0.629181i
$534$		0			0
$535$	−5.98379	−	13.9760i	−0.258702	−	0.604235i
$536$		0			0
$537$	33.8067	−	33.8067i	1.45887	−	1.45887i
$538$		0			0
$539$	4.28162	+	4.28162i	0.184422	+	0.184422i
$540$		0			0
$541$	−18.7010	−	18.7010i	−0.804018	−	0.804018i	0.179703	−	0.983721i	$-0.442486\pi$
$541$	−18.7010	−	18.7010i	−0.804018	−	0.804018i	−0.983721	+	0.179703i	$0.942486\pi$
$542$		0			0
$543$	5.19217	+	5.19217i	0.222817	+	0.222817i
$544$		0			0
$545$	−2.66050	−	6.21396i	−0.113963	−	0.266177i
$546$		0			0
$547$	27.8583	+	27.8583i	1.19114	+	1.19114i	0.976749	+	0.214386i	$0.0687751\pi$
$547$	27.8583	+	27.8583i	1.19114	+	1.19114i	0.214386	+	0.976749i	$0.431225\pi$
$548$		0			0
$549$		−	12.9191i		−	0.551375i
$550$		0			0
$551$	−4.88708	+	4.88708i	−0.208197	+	0.208197i
$552$		0			0
$553$	−8.77139			−0.372998
$554$		0			0
$555$	6.89822	+	16.1118i	0.292813	+	0.683906i
$556$		0			0
$557$			18.9228i			0.801783i	0.916126	+	0.400892i	$0.131300\pi$
$557$			18.9228i			0.801783i	−0.916126	+	0.400892i	$0.868700\pi$
$558$		0			0
$559$	−6.17002	+	17.0467i	−0.260964	+	0.720998i
$560$		0			0
$561$	4.78870	−	4.78870i	0.202179	−	0.202179i
$562$		0			0
$563$	18.3970	+	18.3970i	0.775341	+	0.775341i	0.979035	−	0.203694i	$-0.0652947\pi$
$563$	18.3970	+	18.3970i	0.775341	+	0.775341i	−0.203694	+	0.979035i	$0.565295\pi$
$564$		0			0
$565$	17.8867	−	7.65818i	0.752501	−	0.322182i
$566$		0			0
$567$		−	39.6056i		−	1.66328i
$568$		0			0
$569$	20.8685			0.874854			0.437427	−	0.899254i	$-0.355890\pi$
$569$	20.8685			0.874854			0.437427	+	0.899254i	$0.355890\pi$
$570$		0			0
$571$			3.59879i			0.150605i	0.997161	+	0.0753023i	$0.0239922\pi$
$571$			3.59879i			0.150605i	−0.997161	+	0.0753023i	$0.976008\pi$
$572$		0			0
$573$	3.85124	−	3.85124i	0.160888	−	0.160888i
$574$		0			0
$575$	−0.385464	−	16.2818i	−0.0160750	−	0.678999i
$576$		0			0
$577$	−20.9808			−0.873442			−0.436721	−	0.899597i	$-0.643860\pi$
$577$	−20.9808			−0.873442			−0.436721	+	0.899597i	$0.643860\pi$
$578$		0			0
$579$	1.95870	−	1.95870i	0.0814008	−	0.0814008i
$580$		0			0
$581$	31.6415			1.31271
$582$		0			0
$583$	−0.831457			−0.0344354
$584$		0			0
$585$	−25.6636	+	1.47097i	−1.06106	+	0.0608172i
$586$		0			0
$587$	6.80302			0.280791			0.140395	−	0.990096i	$-0.455163\pi$
$587$	6.80302			0.280791			0.140395	+	0.990096i	$0.455163\pi$
$588$		0			0
$589$	−10.4333			−0.429895
$590$		0			0
$591$	−9.84239	+	9.84239i	−0.404862	+	0.404862i
$592$		0			0
$593$	−10.9868			−0.451174			−0.225587	−	0.974223i	$-0.572430\pi$
$593$	−10.9868			−0.451174			−0.225587	+	0.974223i	$0.572430\pi$
$594$		0			0
$595$	−28.4244	−	66.3893i	−1.16529	−	2.72170i
$596$		0			0
$597$	13.1596	−	13.1596i	0.538588	−	0.538588i
$598$		0			0
$599$		−	46.6176i		−	1.90474i	−0.304941	−	0.952371i	$-0.598637\pi$
$599$		−	46.6176i		−	1.90474i	0.304941	−	0.952371i	$-0.401363\pi$
$600$		0			0
$601$	−0.301935			−0.0123162			−0.00615809	−	0.999981i	$-0.501960\pi$
$601$	−0.301935			−0.0123162			−0.00615809	+	0.999981i	$0.501960\pi$
$602$		0			0
$603$		−	25.0052i		−	1.01829i
$604$		0			0
$605$	−9.01186	+	22.5063i	−0.366384	+	0.915012i
$606$		0			0
$607$	−9.09452	−	9.09452i	−0.369135	−	0.369135i	0.498026	−	0.867162i	$-0.334058\pi$
$607$	−9.09452	−	9.09452i	−0.369135	−	0.369135i	−0.867162	+	0.498026i	$0.834058\pi$
$608$		0			0
$609$	−51.8171	+	51.8171i	−2.09974	+	2.09974i
$610$		0			0
$611$	−11.6568	+	5.46102i	−0.471583	+	0.220929i
$612$		0			0
$613$			36.3083i			1.46648i	0.679970	+	0.733240i	$0.261993\pi$
$613$			36.3083i			1.46648i	−0.679970	+	0.733240i	$0.738007\pi$
$614$		0			0
$615$	−24.4764	+	61.1275i	−0.986982	+	2.46490i
$616$		0			0
$617$	11.4457			0.460787			0.230394	−	0.973098i	$-0.425999\pi$
$617$	11.4457			0.460787			0.230394	+	0.973098i	$0.425999\pi$
$618$		0			0
$619$	9.93208	−	9.93208i	0.399204	−	0.399204i	−0.478748	−	0.877952i	$-0.658909\pi$
$619$	9.93208	−	9.93208i	0.399204	−	0.399204i	0.877952	+	0.478748i	$0.158909\pi$
$620$		0			0
$621$			1.52662i			0.0612611i
$622$		0			0
$623$	47.4242	+	47.4242i	1.90001	+	1.90001i
$624$		0			0
$625$	1.18306	+	24.9720i	0.0473225	+	0.998880i
$626$		0			0
$627$	0.773478	+	0.773478i	0.0308897	+	0.0308897i
$628$		0			0
$629$	15.2599	+	15.2599i	0.608452	+	0.608452i
$630$		0			0
$631$	14.8060	+	14.8060i	0.589419	+	0.589419i	0.937474	−	0.348055i	$-0.113158\pi$
$631$	14.8060	+	14.8060i	0.589419	+	0.589419i	−0.348055	+	0.937474i	$0.613158\pi$
$632$		0			0
$633$	26.2926	−	26.2926i	1.04504	−	1.04504i
$634$		0			0
$635$	22.7848	−	9.75526i	0.904186	−	0.387126i
$636$		0			0
$637$	−23.3028	−	49.7408i	−0.923291	−	1.97080i
$638$		0			0
$639$	17.2798	+	17.2798i	0.683576	+	0.683576i
$640$		0			0
$641$		−	14.1792i		−	0.560046i	−0.959993	−	0.280023i	$-0.909658\pi$
$641$		−	14.1792i		−	0.560046i	0.959993	−	0.280023i	$-0.0903422\pi$
$642$		0			0
$643$			0.488940i			0.0192819i	0.999954	+	0.00964096i	$0.00306886\pi$
$643$			0.488940i			0.0192819i	−0.999954	+	0.00964096i	$0.996931\pi$
$644$		0			0
$645$	−25.9647	−	10.3967i	−1.02236	−	0.409368i
$646$		0			0
$647$	22.4849	−	22.4849i	0.883972	−	0.883972i	−0.109964	−	0.993936i	$-0.535074\pi$
$647$	22.4849	−	22.4849i	0.883972	−	0.883972i	0.993936	+	0.109964i	$0.0350735\pi$
$648$		0			0
$649$	−2.54261			−0.0998062
$650$		0			0
$651$	−110.623			−4.33564
$652$		0			0
$653$	−4.78979	+	4.78979i	−0.187439	+	0.187439i	−0.794588	−	0.607149i	$-0.792313\pi$
$653$	−4.78979	+	4.78979i	−0.187439	+	0.187439i	0.607149	+	0.794588i	$0.292313\pi$
$654$		0			0
$655$	−1.32950	−	0.532350i	−0.0519477	−	0.0208006i
$656$		0			0
$657$		−	30.6651i		−	1.19636i
$658$		0			0
$659$			9.69986i			0.377853i	0.981991	+	0.188926i	$0.0605008\pi$
$659$			9.69986i			0.377853i	−0.981991	+	0.188926i	$0.939499\pi$
$660$		0			0
$661$	27.5418	+	27.5418i	1.07125	+	1.07125i	0.997259	+	0.0739913i	$0.0235737\pi$
$661$	27.5418	+	27.5418i	1.07125	+	1.07125i	0.0739913	+	0.997259i	$0.476426\pi$
$662$		0			0
$663$	−55.6317	+	26.0626i	−2.16056	+	1.01219i
$664$		0			0
$665$	10.7233	−	4.59116i	0.415832	−	0.178038i
$666$		0			0
$667$	−14.3888	+	14.3888i	−0.557137	+	0.557137i
$668$		0			0
$669$	−34.6681	−	34.6681i	−1.34034	−	1.34034i
$670$		0			0
$671$	−1.13878	−	1.13878i	−0.0439621	−	0.0439621i
$672$		0			0
$673$	17.6307	+	17.6307i	0.679615	+	0.679615i	0.959913	−	0.280298i	$-0.0904332\pi$
$673$	17.6307	+	17.6307i	0.679615	+	0.679615i	−0.280298	+	0.959913i	$0.590433\pi$
$674$		0			0
$675$	−0.0554632	−	2.34274i	−0.00213478	−	0.0901721i
$676$		0			0
$677$	−11.5028	−	11.5028i	−0.442089	−	0.442089i	0.450625	−	0.892714i	$-0.351201\pi$
$677$	−11.5028	−	11.5028i	−0.442089	−	0.442089i	−0.892714	+	0.450625i	$0.851201\pi$
$678$		0			0
$679$			63.9590i			2.45452i
$680$		0			0
$681$	−25.1154	+	25.1154i	−0.962424	+	0.962424i
$682$		0			0
$683$	−48.3576			−1.85035			−0.925175	−	0.379540i	$-0.876082\pi$
$683$	−48.3576			−1.85035			−0.925175	+	0.379540i	$0.876082\pi$
$684$		0			0
$685$	2.19874	−	5.49116i	0.0840097	−	0.209807i
$686$		0			0
$687$		−	0.397822i		−	0.0151779i
$688$		0			0
$689$	7.09226	+	2.56703i	0.270194	+	0.0977961i
$690$		0			0
$691$	19.4135	−	19.4135i	0.738525	−	0.738525i	−0.233768	−	0.972292i	$-0.575106\pi$
$691$	19.4135	−	19.4135i	0.738525	−	0.738525i	0.972292	+	0.233768i	$0.0751056\pi$
$692$		0			0
$693$	4.22538	+	4.22538i	0.160509	+	0.160509i
$694$		0			0
$695$	4.73697	−	11.8302i	0.179684	−	0.448743i
$696$		0			0
$697$			81.0778i			3.07104i
$698$		0			0
$699$	4.06812			0.153871
$700$		0			0
$701$			7.83662i			0.295985i	0.988988	+	0.147992i	$0.0472811\pi$
$701$			7.83662i			0.295985i	−0.988988	+	0.147992i	$0.952719\pi$
$702$		0			0
$703$	−2.46480	+	2.46480i	−0.0929619	+	0.0929619i
$704$		0			0
$705$	−7.81651	−	18.2565i	−0.294387	−	0.687581i
$706$		0			0
$707$	4.39489			0.165287
$708$		0			0
$709$	8.86339	−	8.86339i	0.332872	−	0.332872i	−0.520804	−	0.853676i	$-0.674368\pi$
$709$	8.86339	−	8.86339i	0.332872	−	0.332872i	0.853676	+	0.520804i	$0.174368\pi$
$710$		0			0
$711$	−5.93100			−0.222430
$712$		0			0
$713$	−30.7182			−1.15041
$714$		0			0
$715$	−2.13250	+	2.39182i	−0.0797510	+	0.0894491i
$716$		0			0
$717$	−32.2444			−1.20419
$718$		0			0
$719$	8.10825			0.302387			0.151193	−	0.988504i	$-0.451688\pi$
$719$	8.10825			0.302387			0.151193	+	0.988504i	$0.451688\pi$
$720$		0			0
$721$	−21.1921	+	21.1921i	−0.789237	+	0.789237i
$722$		0			0
$723$	−1.89800			−0.0705875
$724$		0			0
$725$	21.5582	−	22.6038i	0.800653	−	0.839482i
$726$		0			0
$727$	−7.70651	+	7.70651i	−0.285819	+	0.285819i	−0.835424	−	0.549606i	$-0.814778\pi$
$727$	−7.70651	+	7.70651i	−0.285819	+	0.285819i	0.549606	+	0.835424i	$0.314778\pi$
$728$		0			0
$729$		−	30.2781i		−	1.12141i
$730$		0			0
$731$	−34.4389			−1.27377
$732$		0			0
$733$		−	12.7323i		−	0.470277i	−0.971962	−	0.235139i	$-0.924446\pi$
$733$		−	12.7323i		−	0.470277i	0.971962	−	0.235139i	$-0.0755544\pi$
$734$		0			0
$735$	77.9028	−	33.3540i	2.87349	−	1.23028i
$736$		0			0
$737$	−2.20413	−	2.20413i	−0.0811901	−	0.0811901i
$738$		0			0
$739$	10.7053	−	10.7053i	0.393801	−	0.393801i	−0.482239	−	0.876040i	$-0.660176\pi$
$739$	10.7053	−	10.7053i	0.393801	−	0.393801i	0.876040	+	0.482239i	$0.160176\pi$
$740$		0			0
$741$	−4.20967	−	8.98573i	−0.154646	−	0.330099i
$742$		0			0
$743$		−	43.4613i		−	1.59444i	−0.603689	−	0.797220i	$-0.706303\pi$
$743$		−	43.4613i		−	1.59444i	0.603689	−	0.797220i	$-0.293697\pi$
$744$		0			0
$745$	−16.3815	−	38.2613i	−0.600171	−	1.40178i
$746$		0			0
$747$	21.3952			0.782810
$748$		0			0
$749$	22.6697	−	22.6697i	0.828333	−	0.828333i
$750$		0			0
$751$			40.6226i			1.48234i	0.671317	+	0.741171i	$0.265729\pi$
$751$			40.6226i			1.48234i	−0.671317	+	0.741171i	$0.734271\pi$
$752$		0			0
$753$	−26.9117	−	26.9117i	−0.980718	−	0.980718i
$754$		0			0
$755$	9.95186	+	23.2440i	0.362185	+	0.845934i
$756$		0			0
$757$	−12.9354	−	12.9354i	−0.470145	−	0.470145i	0.431816	−	0.901962i	$-0.357873\pi$
$757$	−12.9354	−	12.9354i	−0.470145	−	0.470145i	−0.901962	+	0.431816i	$0.857873\pi$
$758$		0			0
$759$	2.27732	+	2.27732i	0.0826613	+	0.0826613i
$760$		0			0
$761$	31.6508	+	31.6508i	1.14734	+	1.14734i	0.987074	+	0.160267i	$0.0512356\pi$
$761$	31.6508	+	31.6508i	1.14734	+	1.14734i	0.160267	+	0.987074i	$0.448764\pi$
$762$		0			0
$763$	10.0793	−	10.0793i	0.364896	−	0.364896i
$764$		0			0
$765$	−19.2199	−	44.8908i	−0.694897	−	1.62303i
$766$		0			0
$767$	21.6883	+	7.85003i	0.783117	+	0.283448i
$768$		0			0
$769$	10.1433	+	10.1433i	0.365776	+	0.365776i	0.865934	−	0.500158i	$-0.166725\pi$
$769$	10.1433	+	10.1433i	0.365776	+	0.365776i	−0.500158	+	0.865934i	$0.666725\pi$
$770$		0			0
$771$		−	25.5100i		−	0.918719i
$772$		0			0
$773$		−	20.8119i		−	0.748551i	−0.927317	−	0.374276i	$-0.877891\pi$
$773$		−	20.8119i		−	0.748551i	0.927317	−	0.374276i	$-0.122109\pi$
$774$		0			0
$775$	47.1400	−	1.11602i	1.69332	−	0.0400885i
$776$		0			0
$777$	−26.1340	+	26.1340i	−0.937553	+	0.937553i
$778$		0			0
$779$	−13.0958			−0.469206
$780$		0			0
$781$	3.04631			0.109005
$782$		0			0
$783$	−2.07036	+	2.07036i	−0.0739887	+	0.0739887i
$784$		0			0
$785$	−17.9628	−	41.9546i	−0.641120	−	1.49743i
$786$		0			0
$787$		−	40.0291i		−	1.42688i	−0.700714	−	0.713442i	$-0.747135\pi$
$787$		−	40.0291i		−	1.42688i	0.700714	−	0.713442i	$-0.252865\pi$
$788$		0			0
$789$			38.8653i			1.38364i
$790$		0			0
$791$	29.0131	+	29.0131i	1.03159	+	1.03159i
$792$		0			0
$793$	6.19783	+	13.2295i	0.220092	+	0.469795i
$794$		0			0
$795$	−4.32553	+	10.8026i	−0.153411	+	0.383129i
$796$		0			0
$797$	5.76153	−	5.76153i	0.204084	−	0.204084i	−0.597663	−	0.801747i	$-0.703904\pi$
$797$	5.76153	−	5.76153i	0.204084	−	0.204084i	0.801747	+	0.597663i	$0.203904\pi$
$798$		0			0
$799$	−17.2913	−	17.2913i	−0.611722	−	0.611722i
$800$		0			0
$801$	32.0671	+	32.0671i	1.13303	+	1.13303i
$802$		0			0
$803$	−2.70303	−	2.70303i	−0.0953879	−	0.0953879i
$804$		0			0
$805$	31.5721	−	13.5176i	1.11277	−	0.476431i
$806$		0			0
$807$	12.7110	+	12.7110i	0.447450	+	0.447450i
$808$		0			0
$809$		−	11.4657i		−	0.403112i	−0.979477	−	0.201556i	$-0.935400\pi$
$809$		−	11.4657i		−	0.403112i	0.979477	−	0.201556i	$-0.0645998\pi$
$810$		0			0
$811$	5.25440	−	5.25440i	0.184507	−	0.184507i	−0.608810	−	0.793316i	$-0.708353\pi$
$811$	5.25440	−	5.25440i	0.184507	−	0.184507i	0.793316	+	0.608810i	$0.208353\pi$
$812$		0			0
$813$	−5.57399			−0.195489
$814$		0			0
$815$	−11.0844	−	4.43836i	−0.388270	−	0.155469i
$816$		0			0
$817$		−	5.56263i		−	0.194612i
$818$		0			0
$819$	−22.9968	−	49.0876i	−0.803572	−	1.71526i
$820$		0			0
$821$	25.7094	−	25.7094i	0.897263	−	0.897263i	−0.0979307	−	0.995193i	$-0.531222\pi$
$821$	25.7094	−	25.7094i	0.897263	−	0.897263i	0.995193	+	0.0979307i	$0.0312223\pi$
$822$		0			0
$823$	−13.3073	−	13.3073i	−0.463865	−	0.463865i	0.436055	−	0.899920i	$-0.356375\pi$
$823$	−13.3073	−	13.3073i	−0.463865	−	0.463865i	−0.899920	+	0.436055i	$0.856375\pi$
$824$		0			0
$825$	−3.57749	−	3.41202i	−0.124552	−	0.118791i
$826$		0			0
$827$		−	40.4261i		−	1.40575i	−0.711311	−	0.702877i	$-0.751898\pi$
$827$		−	40.4261i		−	1.40575i	0.711311	−	0.702877i	$-0.248102\pi$
$828$		0			0
$829$	−9.00868			−0.312884			−0.156442	−	0.987687i	$-0.550002\pi$
$829$	−9.00868			−0.312884			−0.156442	+	0.987687i	$0.550002\pi$
$830$		0			0
$831$			38.7018i			1.34255i
$832$		0			0
$833$	73.7840	−	73.7840i	2.55646	−	2.55646i
$834$		0			0
$835$	−4.58544	+	11.4517i	−0.158686	+	0.396303i
$836$		0			0
$837$	−4.41995			−0.152776
$838$		0			0
$839$	15.2917	−	15.2917i	0.527929	−	0.527929i	−0.392025	−	0.919954i	$-0.628225\pi$
$839$	15.2917	−	15.2917i	0.527929	−	0.527929i	0.919954	+	0.392025i	$0.128225\pi$
$840$		0			0
$841$	−10.0275			−0.345776
$842$		0			0
$843$	17.6557			0.608096
$844$		0			0
$845$	25.5745	−	13.8182i	0.879791	−	0.475360i
$846$		0			0
$847$	−51.1239			−1.75664
$848$		0			0
$849$	54.5830			1.87328
$850$		0			0
$851$	−7.25701	+	7.25701i	−0.248767	+	0.248767i
$852$		0			0
$853$	−26.8763			−0.920226			−0.460113	−	0.887860i	$-0.652191\pi$
$853$	−26.8763			−0.920226			−0.460113	+	0.887860i	$0.652191\pi$
$854$		0			0
$855$	7.25083	−	3.10443i	0.247973	−	0.106169i
$856$		0			0
$857$	6.53408	−	6.53408i	0.223200	−	0.223200i	−0.586645	−	0.809844i	$-0.699551\pi$
$857$	6.53408	−	6.53408i	0.223200	−	0.223200i	0.809844	+	0.586645i	$0.199551\pi$
$858$		0			0
$859$			10.4798i			0.357565i	0.983889	+	0.178783i	$0.0572159\pi$
$859$			10.4798i			0.357565i	−0.983889	+	0.178783i	$0.942784\pi$
$860$		0			0
$861$	−138.853			−4.73211
$862$		0			0
$863$		−	6.95053i		−	0.236599i	−0.992978	−	0.118299i	$-0.962256\pi$
$863$		−	6.95053i		−	0.236599i	0.992978	−	0.118299i	$-0.0377443\pi$
$864$		0			0
$865$	−2.43845	−	5.69535i	−0.0829099	−	0.193648i
$866$		0			0
$867$	−52.6188	−	52.6188i	−1.78703	−	1.78703i
$868$		0			0
$869$	−0.522798	+	0.522798i	−0.0177347	+	0.0177347i
$870$		0			0
$871$	11.9960	+	25.6060i	0.406470	+	0.867627i
$872$		0			0
$873$			43.2475i			1.46371i
$874$		0			0
$875$	−47.9593	+	21.8910i	−1.62132	+	0.740051i
$876$		0			0
$877$	−17.4225			−0.588318			−0.294159	−	0.955757i	$-0.595039\pi$
$877$	−17.4225			−0.588318			−0.294159	+	0.955757i	$0.595039\pi$
$878$		0			0
$879$	−1.52054	+	1.52054i	−0.0512866	+	0.0512866i
$880$		0			0
$881$			22.8509i			0.769866i	0.922944	+	0.384933i	$0.125775\pi$
$881$			22.8509i			0.769866i	−0.922944	+	0.384933i	$0.874225\pi$
$882$		0			0
$883$	−24.3552	−	24.3552i	−0.819618	−	0.819618i	0.166434	−	0.986053i	$-0.446775\pi$
$883$	−24.3552	−	24.3552i	−0.819618	−	0.819618i	−0.986053	+	0.166434i	$0.946775\pi$
$884$		0			0
$885$	−13.2275	+	33.0346i	−0.444639	+	1.11044i
$886$		0			0
$887$	−9.83517	−	9.83517i	−0.330233	−	0.330233i	0.522442	−	0.852675i	$-0.325021\pi$
$887$	−9.83517	−	9.83517i	−0.330233	−	0.330233i	−0.852675	+	0.522442i	$0.825021\pi$
$888$		0			0
$889$	36.9580	+	36.9580i	1.23953	+	1.23953i
$890$		0			0
$891$	−2.36060	−	2.36060i	−0.0790831	−	0.0790831i
$892$		0			0
$893$	2.79292	−	2.79292i	0.0934614	−	0.0934614i
$894$		0			0
$895$	−39.8954	−	15.9747i	−1.33356	−	0.533976i
$896$		0			0
$897$	−12.3944	−	26.4563i	−0.413835	−	0.883349i
$898$		0			0
$899$	−41.6593	−	41.6593i	−1.38941	−	1.38941i
$900$		0			0
$901$			14.3283i			0.477344i
$902$		0			0
$903$		−	58.9799i		−	1.96273i
$904$		0			0
$905$	2.45346	−	6.12729i	0.0815557	−	0.203678i
$906$		0			0
$907$	10.1522	−	10.1522i	0.337098	−	0.337098i	−0.518176	−	0.855274i	$-0.673389\pi$
$907$	10.1522	−	10.1522i	0.337098	−	0.337098i	0.855274	+	0.518176i	$0.173389\pi$
$908$		0			0
$909$	2.97171			0.0985656
$910$		0			0
$911$	19.9290			0.660277			0.330139	−	0.943932i	$-0.392904\pi$
$911$	19.9290			0.660277			0.330139	+	0.943932i	$0.392904\pi$
$912$		0			0
$913$	1.88592	−	1.88592i	0.0624148	−	0.0624148i
$914$		0			0
$915$	−20.7198	+	8.87113i	−0.684974	+	0.293270i
$916$		0			0
$917$		−	3.02000i		−	0.0997292i
$918$		0			0
$919$			14.8038i			0.488332i	0.969733	+	0.244166i	$0.0785141\pi$
$919$			14.8038i			0.488332i	−0.969733	+	0.244166i	$0.921486\pi$
$920$		0			0
$921$	−28.4969	−	28.4969i	−0.939005	−	0.939005i
$922$		0			0
$923$	−25.9847	−	9.40514i	−0.855298	−	0.309574i
$924$		0			0
$925$	10.8729	−	11.4002i	0.357499	−	0.374837i
$926$		0			0
$927$	−14.3296	+	14.3296i	−0.470646	+	0.470646i
$928$		0			0
$929$	−7.78926	−	7.78926i	−0.255557	−	0.255557i	0.567687	−	0.823244i	$-0.307838\pi$
$929$	−7.78926	−	7.78926i	−0.255557	−	0.255557i	−0.823244	+	0.567687i	$0.807838\pi$
$930$		0			0
$931$	11.9177	+	11.9177i	0.390587	+	0.390587i
$932$		0			0
$933$	49.6654	+	49.6654i	1.62597	+	1.62597i
$934$		0			0
$935$	−5.65115	−	2.26280i	−0.184812	−	0.0740016i
$936$		0			0
$937$	37.2503	+	37.2503i	1.21692	+	1.21692i	0.968707	+	0.248209i	$0.0798419\pi$
$937$	37.2503	+	37.2503i	1.21692	+	1.21692i	0.248209	+	0.968707i	$0.420158\pi$
$938$		0			0
$939$			42.1012i			1.37392i
$940$		0			0
$941$	2.77514	−	2.77514i	0.0904671	−	0.0904671i	−0.660425	−	0.750892i	$-0.729624\pi$
$941$	2.77514	−	2.77514i	0.0904671	−	0.0904671i	0.750892	+	0.660425i	$0.229624\pi$
$942$		0			0
$943$	−38.5574			−1.25560
$944$		0			0
$945$	4.54282	−	1.94500i	0.147778	−	0.0632708i
$946$		0			0
$947$			40.5927i			1.31909i	0.751667	+	0.659543i	$0.229250\pi$
$947$			40.5927i			1.31909i	−0.751667	+	0.659543i	$0.770750\pi$
$948$		0			0
$949$	14.7113	+	31.4019i	0.477550	+	1.01935i
$950$		0			0
$951$	−2.93175	+	2.93175i	−0.0950684	+	0.0950684i
$952$		0			0
$953$	−12.4282	−	12.4282i	−0.402590	−	0.402590i	0.476555	−	0.879145i	$-0.341885\pi$
$953$	−12.4282	−	12.4282i	−0.402590	−	0.402590i	−0.879145	+	0.476555i	$0.841885\pi$
$954$		0			0
$955$	−4.54485	−	1.81983i	−0.147068	−	0.0588882i
$956$		0			0
$957$			6.17688i			0.199670i
$958$		0			0
$959$	12.4734			0.402786
$960$		0			0
$961$		−	57.9370i		−	1.86893i
$962$		0			0
$963$	15.3287	−	15.3287i	0.493960	−	0.493960i
$964$		0			0
$965$	−2.31147	−	0.925546i	−0.0744087	−	0.0297944i
$966$		0			0
$967$	13.2989			0.427663			0.213832	−	0.976871i	$-0.431406\pi$
$967$	13.2989			0.427663			0.213832	+	0.976871i	$0.431406\pi$
$968$		0			0
$969$	13.3291	−	13.3291i	0.428194	−	0.428194i
$970$		0			0
$971$	6.37939			0.204724			0.102362	−	0.994747i	$-0.467360\pi$
$971$	6.37939			0.204724			0.102362	+	0.994747i	$0.467360\pi$
$972$		0			0
$973$	26.8726			0.861498
$974$		0			0
$975$	19.9815	+	40.1494i	0.639920	+	1.28581i
$976$		0			0
$977$	−1.33256			−0.0426324			−0.0213162	−	0.999773i	$-0.506786\pi$
$977$	−1.33256			−0.0426324			−0.0213162	+	0.999773i	$0.506786\pi$
$978$		0			0
$979$	5.65322			0.180678
$980$		0			0
$981$	6.81540	−	6.81540i	0.217599	−	0.217599i
$982$		0			0
$983$	50.5175			1.61126			0.805630	−	0.592420i	$-0.201827\pi$
$983$	50.5175			1.61126			0.805630	+	0.592420i	$0.201827\pi$
$984$		0			0
$985$	11.6150	+	4.65083i	0.370086	+	0.148188i
$986$		0			0
$987$	29.6130	−	29.6130i	0.942591	−	0.942591i
$988$		0			0
$989$		−	16.3778i		−	0.520783i
$990$		0			0
$991$	−33.3018			−1.05787			−0.528933	−	0.848664i	$-0.677408\pi$
$991$	−33.3018			−1.05787			−0.528933	+	0.848664i	$0.677408\pi$
$992$		0			0
$993$			63.4012i			2.01198i
$994$		0			0
$995$	−15.5297	−	6.21833i	−0.492325	−	0.197134i
$996$		0			0
$997$	14.1643	+	14.1643i	0.448587	+	0.448587i	0.894885	−	0.446297i	$-0.147258\pi$
$997$	14.1643	+	14.1643i	0.448587	+	0.448587i	−0.446297	+	0.894885i	$0.647258\pi$
$998$		0			0
$999$	−1.04419	+	1.04419i	−0.0330367	+	0.0330367i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	520.2.w.f.57.9	✓	20
4.3	odd	2		1040.2.bg.p.577.2		20
5.3	odd	4		520.2.bh.f.473.9	yes	20
13.8	odd	4		520.2.bh.f.177.9	yes	20
20.3	even	4		1040.2.cd.p.993.2		20
52.47	even	4		1040.2.cd.p.177.2		20
65.8	even	4	inner	520.2.w.f.73.9	yes	20
260.203	odd	4		1040.2.bg.p.593.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.w.f.57.9	✓	20	1.1	even	1	trivial
520.2.w.f.73.9	yes	20	65.8	even	4	inner
520.2.bh.f.177.9	yes	20	13.8	odd	4
520.2.bh.f.473.9	yes	20	5.3	odd	4
1040.2.bg.p.577.2		20	4.3	odd	2
1040.2.bg.p.593.2		20	260.203	odd	4
1040.2.cd.p.177.2		20	52.47	even	4
1040.2.cd.p.993.2		20	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.75903 - 1.75903i) q^{3} +(-2.07584 - 0.831197i) q^{5} -4.71535i q^{7} -3.18840i q^{9} +O(q^{10})\)	\(q+(1.75903 - 1.75903i) q^{3} +(-2.07584 - 0.831197i) q^{5} -4.71535i q^{7} -3.18840i q^{9} +(-0.281047 - 0.281047i) q^{11} +(1.52961 + 3.26501i) q^{13} +(-5.11358 + 2.18937i) q^{15} +(-4.84321 + 4.84321i) q^{17} +(-0.782284 - 0.782284i) q^{19} +(-8.29446 - 8.29446i) q^{21} +(-2.30324 - 2.30324i) q^{23} +(3.61822 + 3.45086i) q^{25} +(-0.331406 - 0.331406i) q^{27} -6.24720i q^{29} +(6.66847 - 6.66847i) q^{31} -0.988743 q^{33} +(-3.91938 + 9.78831i) q^{35} -3.15078i q^{37} +(8.43390 + 3.05264i) q^{39} +(8.37025 - 8.37025i) q^{41} +(3.55538 + 3.55538i) q^{43} +(-2.65019 + 6.61861i) q^{45} +3.57021i q^{47} -15.2345 q^{49} +17.0388i q^{51} +(1.47921 - 1.47921i) q^{53} +(0.349803 + 0.817015i) q^{55} -2.75213 q^{57} +(4.52346 - 4.52346i) q^{59} +4.05191 q^{61} -15.0344 q^{63} +(-0.461351 - 8.04905i) q^{65} +7.84255 q^{67} -8.10296 q^{69} +(-5.41956 + 5.41956i) q^{71} +9.61771 q^{73} +(12.4348 - 0.294387i) q^{75} +(-1.32524 + 1.32524i) q^{77} -1.86018i q^{79} +8.39930 q^{81} +6.71033i q^{83} +(14.0794 - 6.02807i) q^{85} +(-10.9890 - 10.9890i) q^{87} +(-10.0574 + 10.0574i) q^{89} +(15.3957 - 7.21263i) q^{91} -23.4601i q^{93} +(0.973664 + 2.27413i) q^{95} -13.5640 q^{97} +(-0.896092 + 0.896092i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{5}+O(q^{10}) \) 20 * q - 2 * q^5	\( 20 q - 2 q^{5} + 2 q^{11} + 4 q^{13} - 16 q^{15} - 6 q^{17} - 2 q^{19} + 6 q^{21} + 14 q^{23} + 14 q^{25} + 6 q^{27} + 10 q^{31} - 12 q^{33} - 16 q^{35} + 32 q^{39} + 28 q^{41} + 14 q^{45} - 16 q^{49} + 20 q^{53} - 48 q^{55} + 32 q^{57} - 14 q^{59} + 12 q^{61} + 8 q^{63} - 40 q^{65} + 36 q^{67} + 24 q^{69} - 48 q^{71} - 8 q^{73} - 22 q^{75} - 12 q^{77} - 4 q^{81} - 6 q^{85} - 28 q^{89} - 8 q^{91} - 2 q^{95} + 4 q^{97} - 42 q^{99}+O(q^{100}) \) 20 * q - 2 * q^5 + 2 * q^11 + 4 * q^13 - 16 * q^15 - 6 * q^17 - 2 * q^19 + 6 * q^21 + 14 * q^23 + 14 * q^25 + 6 * q^27 + 10 * q^31 - 12 * q^33 - 16 * q^35 + 32 * q^39 + 28 * q^41 + 14 * q^45 - 16 * q^49 + 20 * q^53 - 48 * q^55 + 32 * q^57 - 14 * q^59 + 12 * q^61 + 8 * q^63 - 40 * q^65 + 36 * q^67 + 24 * q^69 - 48 * q^71 - 8 * q^73 - 22 * q^75 - 12 * q^77 - 4 * q^81 - 6 * q^85 - 28 * q^89 - 8 * q^91 - 2 * q^95 + 4 * q^97 - 42 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more