LMFDB - Embedded newform 520.2.bh.f.473.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [520,2,Mod(177,520)]

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, 1]))

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

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

chi := DirichletCharacter("520.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 520 = 2^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	520.bh (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			473.9
Root			$-1.79929i$ of defining polynomial
Character	$\chi$	$=$	520.473
Dual form			520.2.bh.f.177.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.75903 + 1.75903i) q^{3} +(0.831197 + 2.07584i) q^{5} -4.71535 q^{7} +3.18840i q^{9} +O(q^{10})$	\(q+(1.75903 + 1.75903i) q^{3} +(0.831197 + 2.07584i) q^{5} -4.71535 q^{7} +3.18840i q^{9} +(-0.281047 - 0.281047i) q^{11} +(-3.26501 + 1.52961i) q^{13} +(-2.18937 + 5.11358i) q^{15} +(4.84321 + 4.84321i) q^{17} +(0.782284 + 0.782284i) q^{19} +(-8.29446 - 8.29446i) q^{21} +(2.30324 - 2.30324i) q^{23} +(-3.61822 + 3.45086i) q^{25} +(-0.331406 + 0.331406i) q^{27} +6.24720i q^{29} +(6.66847 - 6.66847i) q^{31} -0.988743i q^{33} +(-3.91938 - 9.78831i) q^{35} -3.15078 q^{37} +(-8.43390 - 3.05264i) q^{39} +(8.37025 - 8.37025i) q^{41} +(-3.55538 + 3.55538i) q^{43} +(-6.61861 + 2.65019i) q^{45} +3.57021 q^{47} +15.2345 q^{49} +17.0388i q^{51} +(1.47921 + 1.47921i) q^{53} +(0.349803 - 0.817015i) q^{55} +2.75213i q^{57} +(-4.52346 + 4.52346i) q^{59} +4.05191 q^{61} -15.0344i q^{63} +(-5.88909 - 5.50624i) q^{65} -7.84255i q^{67} +8.10296 q^{69} +(-5.41956 + 5.41956i) q^{71} +9.61771i q^{73} +(-12.4348 - 0.294387i) q^{75} +(1.32524 + 1.32524i) q^{77} +1.86018i q^{79} +8.39930 q^{81} -6.71033 q^{83} +(-6.02807 + 14.0794i) q^{85} +(-10.9890 + 10.9890i) q^{87} +(10.0574 - 10.0574i) q^{89} +(15.3957 - 7.21263i) q^{91} +23.4601 q^{93} +(-0.973664 + 2.27413i) q^{95} +13.5640i q^{97} +(0.896092 - 0.896092i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q+O(q^{10}) $ 20 * q	$ 20 q + 2 q^{11} + 4 q^{13} + 10 q^{15} + 6 q^{17} + 2 q^{19} + 6 q^{21} - 14 q^{23} - 14 q^{25} + 6 q^{27} + 10 q^{31} - 16 q^{35} + 4 q^{37} - 32 q^{39} + 28 q^{41} + 2 q^{45} - 20 q^{47} + 16 q^{49} + 20 q^{53} - 48 q^{55} + 14 q^{59} + 12 q^{61} + 12 q^{65} - 24 q^{69} - 48 q^{71} + 22 q^{75} + 12 q^{77} - 4 q^{81} + 16 q^{83} + 28 q^{89} - 8 q^{91} - 28 q^{93} + 2 q^{95} + 42 q^{99}+O(q^{100}) $ 20 * q + 2 * q^11 + 4 * q^13 + 10 * q^15 + 6 * q^17 + 2 * q^19 + 6 * q^21 - 14 * q^23 - 14 * q^25 + 6 * q^27 + 10 * q^31 - 16 * q^35 + 4 * q^37 - 32 * q^39 + 28 * q^41 + 2 * q^45 - 20 * q^47 + 16 * q^49 + 20 * q^53 - 48 * q^55 + 14 * q^59 + 12 * q^61 + 12 * q^65 - 24 * q^69 - 48 * q^71 + 22 * q^75 + 12 * q^77 - 4 * q^81 + 16 * q^83 + 28 * q^89 - 8 * q^91 - 28 * q^93 + 2 * q^95 + 42 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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	0.999877	+	0.0157021i	$0.00499835\pi$
$3$	1.75903	+	1.75903i	1.01558	+	1.01558i	0.0157021	+	0.999877i	$0.495002\pi$
$4$		0			0
$5$	0.831197	+	2.07584i	0.371723	+	0.928344i
$5$	0.831197	+	2.07584i	0.371723	+	0.928344i
$6$		0			0
$7$	−4.71535			−1.78223			−0.891117	−	0.453774i	$-0.850078\pi$
$7$	−4.71535			−1.78223			−0.891117	+	0.453774i	$0.850078\pi$
$8$		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
$13$	−3.26501	+	1.52961i	−0.905551	+	0.424237i
$13$	−3.26501	+	1.52961i	−0.905551	+	0.424237i
$14$		0			0
$15$	−2.18937	+	5.11358i	−0.565293	+	1.32032i
$16$		0			0
$17$	4.84321	+	4.84321i	1.17465	+	1.17465i	0.981088	+	0.193564i	$0.0620048\pi$
$17$	4.84321	+	4.84321i	1.17465	+	1.17465i	0.193564	+	0.981088i	$0.437995\pi$
$18$		0			0
$19$	0.782284	+	0.782284i	0.179468	+	0.179468i	0.791124	−	0.611656i	$-0.209496\pi$
$19$	0.782284	+	0.782284i	0.179468	+	0.179468i	−0.611656	+	0.791124i	$0.709496\pi$
$20$		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	$-0.639710\pi$
$23$	2.30324	−	2.30324i	0.480259	−	0.480259i	0.905214	+	0.424955i	$0.139710\pi$
$24$		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	$0.196962\pi$
$29$			6.24720i			1.16008i	−0.814590	+	0.580038i	$0.803038\pi$
$30$		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
$33$		−	0.988743i		−	0.172118i
$34$		0			0
$35$	−3.91938	−	9.78831i	−0.662497	−	1.65453i
$36$		0			0
$37$	−3.15078			−0.517985			−0.258993	−	0.965879i	$-0.583391\pi$
$37$	−3.15078			−0.517985			−0.258993	+	0.965879i	$0.583391\pi$
$38$		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	$-0.875242\pi$
$43$	−3.55538	+	3.55538i	−0.542190	+	0.542190i	0.381980	+	0.924170i	$0.375242\pi$
$44$		0			0
$45$	−6.61861	+	2.65019i	−0.986645	+	0.395067i
$46$		0			0
$47$	3.57021			0.520769			0.260384	−	0.965505i	$-0.416151\pi$
$47$	3.57021			0.520769			0.260384	+	0.965505i	$0.416151\pi$
$48$		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	0.801363	−	0.598178i	$-0.204108\pi$
$53$	1.47921	+	1.47921i	0.203185	+	0.203185i	−0.598178	+	0.801363i	$0.704108\pi$
$54$		0			0
$55$	0.349803	−	0.817015i	0.0471675	−	0.110166i
$56$		0			0
$57$			2.75213i			0.364528i
$58$		0			0
$59$	−4.52346	+	4.52346i	−0.588904	+	0.588904i	−0.937335	−	0.348431i	$-0.886715\pi$
$59$	−4.52346	+	4.52346i	−0.588904	+	0.588904i	0.348431	+	0.937335i	$0.386715\pi$
$60$		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
$63$		−	15.0344i		−	1.89416i
$64$		0			0
$65$	−5.88909	−	5.50624i	−0.730452	−	0.682964i
$66$		0			0
$67$		−	7.84255i		−	0.958120i	−0.877782	−	0.479060i	$-0.840978\pi$
$67$		−	7.84255i		−	0.958120i	0.877782	−	0.479060i	$-0.159022\pi$
$68$		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
$73$			9.61771i			1.12567i	0.826570	+	0.562834i	$0.190289\pi$
$73$			9.61771i			1.12567i	−0.826570	+	0.562834i	$0.809711\pi$
$74$		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	$0.0333701\pi$
$79$			1.86018i			0.209287i	−0.994510	+	0.104643i	$0.966630\pi$
$80$		0			0
$81$	8.39930			0.933255
$82$		0			0
$83$	−6.71033			−0.736554			−0.368277	−	0.929716i	$-0.620052\pi$
$83$	−6.71033			−0.736554			−0.368277	+	0.929716i	$0.620052\pi$
$84$		0			0
$85$	−6.02807	+	14.0794i	−0.653836	+	1.52713i
$86$		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	$-0.478202\pi$
$89$	10.0574	−	10.0574i	1.06608	−	1.06608i	0.997656	−	0.0684279i	$-0.0217983\pi$
$90$		0			0
$91$	15.3957	−	7.21263i	1.61390	−	0.756089i
$92$		0			0
$93$	23.4601			2.43270
$94$		0			0
$95$	−0.973664	+	2.27413i	−0.0998958	+	0.233321i
$96$		0			0
$97$			13.5640i			1.37722i	0.725134	+	0.688608i	$0.241778\pi$
$97$			13.5640i			1.37722i	−0.725134	+	0.688608i	$0.758222\pi$
$98$		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	$-0.648622\pi$
$103$	4.49429	−	4.49429i	0.442836	−	0.442836i	0.892964	+	0.450128i	$0.148622\pi$
$104$		0			0
$105$	10.3236	−	24.1123i	1.00748	−	2.35312i
$106$		0			0
$107$	4.80764	−	4.80764i	0.464772	−	0.464772i	−0.435444	−	0.900216i	$-0.643409\pi$
$107$	4.80764	−	4.80764i	0.464772	−	0.464772i	0.900216	+	0.435444i	$0.143409\pi$
$108$		0			0
$109$	−2.13756	−	2.13756i	−0.204741	−	0.204741i	0.597287	−	0.802028i	$-0.296245\pi$
$109$	−2.13756	−	2.13756i	−0.204741	−	0.204741i	−0.802028	+	0.597287i	$0.796245\pi$
$110$		0			0
$111$	−5.54233	−	5.54233i	−0.526055	−	0.526055i
$112$		0			0
$113$	−6.15291	−	6.15291i	−0.578817	−	0.578817i	0.355760	−	0.934577i	$-0.384222\pi$
$113$	−6.15291	−	6.15291i	−0.578817	−	0.578817i	−0.934577	+	0.355760i	$0.884222\pi$
$114$		0			0
$115$	6.69561	+	2.86671i	0.624369	+	0.267322i
$116$		0			0
$117$	−4.87700	−	10.4102i	−0.450879	−	0.962421i
$118$		0			0
$119$	−22.8374	−	22.8374i	−2.09350	−	2.09350i
$120$		0			0
$121$		−	10.8420i		−	0.985639i
$122$		0			0
$123$	29.4471			2.65516
$124$		0			0
$125$	−10.1709	−	4.64250i	−0.909713	−	0.415238i
$126$		0			0
$127$	7.83780	+	7.83780i	0.695492	+	0.695492i	0.963435	−	0.267943i	$-0.0863438\pi$
$127$	7.83780	+	7.83780i	0.695492	+	0.695492i	−0.267943	+	0.963435i	$0.586344\pi$
$128$		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
$135$	−0.963411	−	0.412483i	−0.0829172	−	0.0355008i
$136$		0			0
$137$	2.64527			0.226001			0.113000	−	0.993595i	$-0.463954\pi$
$137$	2.64527			0.226001			0.113000	+	0.993595i	$0.463954\pi$
$138$		0			0
$139$		−	5.69897i		−	0.483381i	−0.970353	−	0.241690i	$-0.922298\pi$
$139$		−	5.69897i		−	0.483381i	0.970353	−	0.241690i	$-0.0777018\pi$
$140$		0			0
$141$	6.28012	+	6.28012i	0.528882	+	0.528882i
$142$		0			0
$143$	1.34751	+	0.487731i	0.112685	+	0.0407861i
$144$		0			0
$145$	−12.9682	+	5.19265i	−1.07695	+	0.431227i
$146$		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	$-0.974006\pi$
$149$	−13.1616	−	13.1616i	−1.07824	−	1.07824i	−0.0815732	−	0.996667i	$-0.525994\pi$
$150$		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	0.165616	−	0.986190i	$-0.447039\pi$
$157$	14.4321	−	14.4321i	1.15181	−	1.15181i	0.986190	−	0.165616i	$-0.0529613\pi$
$158$		0			0
$159$			5.20397i			0.412702i
$160$		0			0
$161$	−10.8606	+	10.8606i	−0.855934	+	0.855934i
$162$		0			0
$163$			5.33972i			0.418239i	0.977890	+	0.209120i	$0.0670598\pi$
$163$			5.33972i			0.418239i	−0.977890	+	0.209120i	$0.932940\pi$
$164$		0			0
$165$	2.05247	−	0.821841i	0.159785	−	0.0639802i
$166$		0			0
$167$	−5.51667			−0.426893			−0.213446	−	0.976955i	$-0.568469\pi$
$167$	−5.51667			−0.426893			−0.213446	+	0.976955i	$0.568469\pi$
$168$		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	$-0.783588\pi$
$173$	−1.95916	+	1.95916i	−0.148952	+	0.148952i	0.628698	+	0.777650i	$0.283588\pi$
$174$		0			0
$175$	17.0612	−	16.2720i	1.28970	−	1.23005i
$176$		0			0
$177$	−15.9138			−1.19616
$178$		0			0
$179$	−19.2189			−1.43649			−0.718245	−	0.695790i	$-0.755054\pi$
$179$	−19.2189			−1.43649			−0.718245	+	0.695790i	$0.755054\pi$
$180$		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
$187$		−	2.72234i		−	0.199077i
$188$		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
$193$			1.11351i			0.0801521i	0.999197	+	0.0400761i	$0.0127600\pi$
$193$			1.11351i			0.0801521i	−0.999197	+	0.0400761i	$0.987240\pi$
$194$		0			0
$195$	−0.673452	−	20.0448i	−0.0482269	−	1.43544i
$196$		0			0
$197$			5.59534i			0.398651i	0.979933	+	0.199326i	$0.0638752\pi$
$197$			5.59534i			0.398651i	−0.979933	+	0.199326i	$0.936125\pi$
$198$		0			0
$199$	−7.48117			−0.530326			−0.265163	−	0.964204i	$-0.585426\pi$
$199$	−7.48117			−0.530326			−0.265163	+	0.964204i	$0.585426\pi$
$200$		0			0
$201$	13.7953	−	13.7953i	0.973046	−	0.973046i
$202$		0			0
$203$		−	29.4577i		−	2.06753i
$204$		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
$213$	−19.0664			−1.30641
$214$		0			0
$215$	−10.3356	−	4.42517i	−0.704883	−	0.301794i
$216$		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
$223$	19.7086			1.31978			0.659892	−	0.751360i	$-0.270602\pi$
$223$	19.7086			1.31978			0.659892	+	0.751360i	$0.270602\pi$
$224$		0			0
$225$	−11.0027	−	11.5363i	−0.733516	−	0.769090i
$226$		0			0
$227$			14.2779i			0.947660i	0.880616	+	0.473830i	$0.157129\pi$
$227$			14.2779i			0.947660i	−0.880616	+	0.473830i	$0.842871\pi$
$228$		0			0
$229$	−0.113080	+	0.113080i	−0.00747252	+	0.00747252i	−0.710833	−	0.703361i	$-0.751682\pi$
$229$	−0.113080	+	0.113080i	−0.00747252	+	0.00747252i	0.703361	+	0.710833i	$0.251682\pi$
$230$		0			0
$231$			4.66227i			0.306755i
$232$		0			0
$233$	−1.15635	+	1.15635i	−0.0757551	+	0.0757551i	−0.743969	−	0.668214i	$-0.767059\pi$
$233$	−1.15635	+	1.15635i	−0.0757551	+	0.0757551i	0.668214	+	0.743969i	$0.267059\pi$
$234$		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	0.938403	−	0.345543i	$-0.112305\pi$
$239$	9.16538	+	9.16538i	0.592859	+	0.592859i	−0.345543	+	0.938403i	$0.612305\pi$
$240$		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
$245$	12.6629	+	31.6244i	0.809002	+	2.02041i
$246$		0			0
$247$	−3.75075	−	1.35758i	−0.238655	−	0.0863807i
$248$		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
$253$	−1.29464			−0.0813933
$254$		0			0
$255$	−35.3697	+	14.1626i	−2.21494	+	0.886894i
$256$		0			0
$257$	−7.25113	−	7.25113i	−0.452313	−	0.452313i	0.443809	−	0.896122i	$-0.353627\pi$
$257$	−7.25113	−	7.25113i	−0.452313	−	0.452313i	−0.896122	+	0.443809i	$0.853627\pi$
$258$		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	0.279064	−	0.960273i	$-0.409976\pi$
$263$	−11.0473	−	11.0473i	−0.681208	−	0.681208i	−0.960273	+	0.279064i	$0.909976\pi$
$264$		0			0
$265$	−1.84109	+	4.30013i	−0.113097	+	0.264155i
$266$		0			0
$267$	35.3827			2.16538
$268$		0			0
$269$		−	7.22615i		−	0.440586i	−0.975434	−	0.220293i	$-0.929299\pi$
$269$		−	7.22615i		−	0.440586i	0.975434	−	0.220293i	$-0.0707013\pi$
$270$		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
$273$	39.7688	+	14.3942i	2.40692	+	0.871179i
$274$		0			0
$275$	1.98675	+	0.0470352i	0.119805	+	0.00283633i
$276$		0			0
$277$	11.0009	+	11.0009i	0.660978	+	0.660978i	0.955611	−	0.294633i	$-0.0951973\pi$
$277$	11.0009	+	11.0009i	0.660978	+	0.660978i	−0.294633	+	0.955611i	$0.595197\pi$
$278$		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	$-0.976131\pi$
$283$	−15.5151	+	15.5151i	−0.922274	+	0.922274i	0.0749155	+	0.997190i	$0.476131\pi$
$284$		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
$293$		−	0.864418i		−	0.0504999i	−0.999681	−	0.0252499i	$-0.991962\pi$
$293$		−	0.864418i		−	0.0504999i	0.999681	−	0.0252499i	$-0.00803816\pi$
$294$		0			0
$295$	−13.1499	−	5.63009i	−0.765614	−	0.327796i
$296$		0			0
$297$	0.186282			0.0108092
$298$		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
$305$	3.36794	+	8.41112i	0.192848	+	0.481619i
$306$		0			0
$307$	−16.2003			−0.924601			−0.462300	−	0.886723i	$-0.652976\pi$
$307$	−16.2003			−0.924601			−0.462300	+	0.886723i	$0.652976\pi$
$308$		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	0.282766	−	0.959189i	$-0.408748\pi$
$313$	−11.9671	−	11.9671i	−0.676423	−	0.676423i	−0.959189	+	0.282766i	$0.908748\pi$
$314$		0			0
$315$	31.2091	−	12.4966i	1.75843	−	0.704102i
$316$		0			0
$317$			1.66668i			0.0936100i	0.998904	+	0.0468050i	$0.0149039\pi$
$317$			1.66668i			0.0936100i	−0.998904	+	0.0468050i	$0.985096\pi$
$318$		0			0
$319$	1.75576	−	1.75576i	0.0983036	−	0.0983036i
$320$		0			0
$321$	16.9136			0.944025
$322$		0			0
$323$			7.57753i			0.421625i
$324$		0			0
$325$	6.53507	−	16.8016i	0.362500	−	0.931984i
$326$		0			0
$327$		−	7.52008i		−	0.415861i
$328$		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
$333$		−	10.0460i		−	0.550515i
$334$		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	$-0.399145\pi$
$337$	−11.7241	−	11.7241i	−0.638653	−	0.638653i	−0.950223	+	0.311570i	$0.899145\pi$
$338$		0			0
$339$		−	21.6464i		−	1.17567i
$340$		0			0
$341$	−3.74831			−0.202982
$342$		0			0
$343$	−38.8286			−2.09655
$344$		0			0
$345$	6.73516	+	16.8205i	0.362609	+	0.905583i
$346$		0			0
$347$	3.40632	−	3.40632i	0.182861	−	0.182861i	−0.609740	−	0.792601i	$-0.708726\pi$
$347$	3.40632	−	3.40632i	0.182861	−	0.182861i	0.792601	+	0.609740i	$0.208726\pi$
$348$		0			0
$349$	−12.7962	+	12.7962i	−0.684963	+	0.684963i	−0.961114	−	0.276151i	$-0.910941\pi$
$349$	−12.7962	+	12.7962i	−0.684963	+	0.684963i	0.276151	+	0.961114i	$0.410941\pi$
$350$		0			0
$351$	0.575124	−	1.58897i	0.0306979	−	0.0848128i
$352$		0			0
$353$	5.38245			0.286479			0.143239	−	0.989688i	$-0.454248\pi$
$353$	5.38245			0.286479			0.143239	+	0.989688i	$0.454248\pi$
$354$		0			0
$355$	−15.7549	−	6.74542i	−0.836182	−	0.358010i
$356$		0			0
$357$		−	80.3437i		−	4.25224i
$358$		0			0
$359$	23.2099	−	23.2099i	1.22497	−	1.22497i	0.259131	−	0.965842i	$-0.416564\pi$
$359$	23.2099	−	23.2099i	1.22497	−	1.22497i	0.965842	−	0.259131i	$-0.0834362\pi$
$360$		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	0.279822	−	0.960052i	$-0.409724\pi$
$367$	23.7526	−	23.7526i	1.23987	−	1.23987i	0.960052	−	0.279822i	$-0.0902756\pi$
$368$		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	0.0978000	−	0.995206i	$-0.468819\pi$
$373$	−17.3318	−	17.3318i	−0.897406	−	0.897406i	−0.995206	+	0.0978000i	$0.968819\pi$
$374$		0			0
$375$	−9.72464	−	26.0573i	−0.502178	−	1.34559i
$376$		0			0
$377$	−9.55576	−	20.3972i	−0.492147	−	1.05051i
$378$		0			0
$379$	16.1822	+	16.1822i	0.831224	+	0.831224i	0.987684	−	0.156460i	$-0.0500082\pi$
$379$	16.1822	+	16.1822i	0.831224	+	0.831224i	−0.156460	+	0.987684i	$0.550008\pi$
$380$		0			0
$381$			27.5739i			1.41265i
$382$		0			0
$383$	−23.5091			−1.20126			−0.600628	−	0.799528i	$-0.705083\pi$
$383$	−23.5091			−1.20126			−0.600628	+	0.799528i	$0.705083\pi$
$384$		0			0
$385$	−1.64944	+	3.85251i	−0.0840635	+	0.196342i
$386$		0			0
$387$	−11.3360	−	11.3360i	−0.576240	−	0.576240i
$388$		0			0
$389$	33.7108			1.70921			0.854604	−	0.519280i	$-0.173800\pi$
$389$	33.7108			1.70921			0.854604	+	0.519280i	$0.173800\pi$
$390$		0			0
$391$	22.3102			1.12827
$392$		0			0
$393$	1.12659	+	1.12659i	0.0568291	+	0.0568291i
$394$		0			0
$395$	−3.86143	+	1.54618i	−0.194290	+	0.0777966i
$396$		0			0
$397$	29.2446			1.46774			0.733872	−	0.679288i	$-0.237711\pi$
$397$	29.2446			1.46774			0.733872	+	0.679288i	$0.237711\pi$
$398$		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
$403$	−11.5725	+	31.9728i	−0.576467	+	1.59268i
$404$		0			0
$405$	6.98147	+	17.4356i	0.346912	+	0.866382i
$406$		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	$-0.968942\pi$
$409$	−22.0977	−	22.0977i	−1.09266	−	1.09266i	−0.0974166	−	0.995244i	$-0.531058\pi$
$410$		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	$-0.884898\pi$
$419$		−	14.4832i		−	0.707549i	0.935331	−	0.353775i	$-0.115102\pi$
$420$		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
$423$			11.3833i			0.553473i
$424$		0			0
$425$	−34.2371	−	0.810546i	−1.66074	−	0.0393173i
$426$		0			0
$427$	−19.1062			−0.924613
$428$		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	$-0.648789\pi$
$433$	9.20010	−	9.20010i	0.442129	−	0.442129i	0.892727	+	0.450598i	$0.148789\pi$
$434$		0			0
$435$	−31.9455	−	13.6774i	−1.53167	−	0.655782i
$436$		0			0
$437$	3.60358			0.172382
$438$		0			0
$439$	−14.5148			−0.692752			−0.346376	−	0.938096i	$-0.612588\pi$
$439$	−14.5148			−0.692752			−0.346376	+	0.938096i	$0.612588\pi$
$440$		0			0
$441$			48.5737i			2.31304i
$442$		0			0
$443$	16.0331	+	16.0331i	0.761757	+	0.761757i	0.976640	−	0.214883i	$-0.0689371\pi$
$443$	16.0331	+	16.0331i	0.761757	+	0.761757i	−0.214883	+	0.976640i	$0.568937\pi$
$444$		0			0
$445$	29.2373	+	12.5179i	1.38598	+	0.593405i
$446$		0			0
$447$		−	46.3034i		−	2.19008i
$448$		0			0
$449$	26.3022	−	26.3022i	1.24128	−	1.24128i	0.281810	−	0.959470i	$-0.409065\pi$
$449$	26.3022	−	26.3022i	1.24128	−	1.24128i	0.959470	−	0.281810i	$-0.0909346\pi$
$450$		0			0
$451$	−4.70487			−0.221544
$452$		0			0
$453$		−	28.1296i		−	1.32164i
$454$		0			0
$455$	27.7691	+	25.9638i	1.30184	+	1.21720i
$456$		0			0
$457$			27.9739i			1.30856i	0.756251	+	0.654282i	$0.227029\pi$
$457$			27.9739i			1.30856i	−0.756251	+	0.654282i	$0.772971\pi$
$458$		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
$463$		−	28.8100i		−	1.33892i	−0.742850	−	0.669458i	$-0.766526\pi$
$463$		−	28.8100i		−	1.33892i	0.742850	−	0.669458i	$-0.233474\pi$
$464$		0			0
$465$	19.5000	+	48.6995i	0.904291	+	2.25838i
$466$		0			0
$467$	−24.2034	−	24.2034i	−1.12000	−	1.12000i	−0.991741	−	0.128259i	$-0.959061\pi$
$467$	−24.2034	−	24.2034i	−1.12000	−	1.12000i	−0.128259	−	0.991741i	$-0.540939\pi$
$468$		0			0
$469$			36.9804i			1.70759i
$470$		0			0
$471$	50.7731			2.33950
$472$		0			0
$473$	1.99846			0.0918892
$474$		0			0
$475$	−5.53003	−	0.130921i	−0.253735	−	0.00600705i
$476$		0			0
$477$	−4.71632	+	4.71632i	−0.215946	+	0.215946i
$478$		0			0
$479$	−11.9541	+	11.9541i	−0.546197	+	0.546197i	−0.925339	−	0.379142i	$-0.876219\pi$
$479$	−11.9541	+	11.9541i	−0.546197	+	0.546197i	0.379142	+	0.925339i	$0.376219\pi$
$480$		0			0
$481$	10.2873	−	4.81946i	0.469062	−	0.219748i
$482$		0			0
$483$	−38.2083			−1.73854
$484$		0			0
$485$	−28.1567	+	11.2744i	−1.27853	+	0.511942i
$486$		0			0
$487$			12.7489i			0.577709i	0.957373	+	0.288854i	$0.0932743\pi$
$487$			12.7489i			0.577709i	−0.957373	+	0.288854i	$0.906726\pi$
$488$		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	$0.0332663\pi$
$499$	24.5467	+	24.5467i	1.09886	+	1.09886i	0.104319	+	0.994544i	$0.466734\pi$
$500$		0			0
$501$	−9.70401	−	9.70401i	−0.433543	−	0.433543i
$502$		0			0
$503$	−3.95718	−	3.95718i	−0.176442	−	0.176442i	0.613361	−	0.789803i	$-0.289817\pi$
$503$	−3.95718	−	3.95718i	−0.176442	−	0.176442i	−0.789803	+	0.613361i	$0.789817\pi$
$504$		0			0
$505$	−1.93476	+	0.774708i	−0.0860958	+	0.0344741i
$506$		0			0
$507$	32.2061	−	2.93366i	1.43032	−	0.130289i
$508$		0			0
$509$	3.11209	+	3.11209i	0.137941	+	0.137941i	0.772706	−	0.634765i	$-0.218903\pi$
$509$	3.11209	+	3.11209i	0.137941	+	0.137941i	−0.634765	+	0.772706i	$0.718903\pi$
$510$		0			0
$511$		−	45.3509i		−	2.00620i
$512$		0			0
$513$	−0.518508			−0.0228927
$514$		0			0
$515$	13.0651	+	5.59378i	0.575716	+	0.246492i
$516$		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	0.808313	−	0.588752i	$-0.200381\pi$
$523$	5.02118	+	5.02118i	0.219561	+	0.219561i	−0.588752	+	0.808313i	$0.700381\pi$
$524$		0			0
$525$	58.6343	+	1.38814i	2.55901	+	0.0605832i
$526$		0			0
$527$	64.5936			2.81374
$528$		0			0
$529$			12.3902i			0.538702i
$530$		0			0
$531$	−14.4226	−	14.4226i	−0.625888	−	0.625888i
$532$		0			0
$533$	−14.5258	+	40.1322i	−0.629181	+	1.73832i
$534$		0			0
$535$	13.9760	+	5.98379i	0.604235	+	0.258702i
$536$		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	0.214386	−	0.976749i	$-0.431225\pi$
$547$	27.8583	−	27.8583i	1.19114	−	1.19114i	0.976749	−	0.214386i	$-0.0687751\pi$
$548$		0			0
$549$			12.9191i			0.551375i
$550$		0			0
$551$	−4.88708	+	4.88708i	−0.208197	+	0.208197i
$552$		0			0
$553$		−	8.77139i		−	0.372998i
$554$		0			0
$555$	6.89822	−	16.1118i	0.292813	−	0.683906i
$556$		0			0
$557$	18.9228			0.801783			0.400892	−	0.916126i	$-0.368700\pi$
$557$	18.9228			0.801783			0.400892	+	0.916126i	$0.368700\pi$
$558$		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	$-0.934705\pi$
$563$	−18.3970	+	18.3970i	−0.775341	+	0.775341i	0.203694	+	0.979035i	$0.434705\pi$
$564$		0			0
$565$	7.65818	−	17.8867i	0.322182	−	0.752501i
$566$		0			0
$567$	−39.6056			−1.66328
$568$		0			0
$569$	−20.8685			−0.874854			−0.437427	−	0.899254i	$-0.644110\pi$
$569$	−20.8685			−0.874854			−0.437427	+	0.899254i	$0.644110\pi$
$570$		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
$577$			20.9808i			0.873442i	0.899597	+	0.436721i	$0.143860\pi$
$577$			20.9808i			0.873442i	−0.899597	+	0.436721i	$0.856140\pi$
$578$		0			0
$579$	−1.95870	+	1.95870i	−0.0814008	+	0.0814008i
$580$		0			0
$581$	31.6415			1.31271
$582$		0			0
$583$		−	0.831457i		−	0.0344354i
$584$		0			0
$585$	17.5561	−	18.7768i	0.725855	−	0.776325i
$586$		0			0
$587$		−	6.80302i		−	0.280791i	−0.990096	−	0.140395i	$-0.955163\pi$
$587$		−	6.80302i		−	0.280791i	0.990096	−	0.140395i	$-0.0448374\pi$
$588$		0			0
$589$	10.4333			0.429895
$590$		0			0
$591$	−9.84239	+	9.84239i	−0.404862	+	0.404862i
$592$		0			0
$593$		−	10.9868i		−	0.451174i	−0.974223	−	0.225587i	$-0.927570\pi$
$593$		−	10.9868i		−	0.451174i	0.974223	−	0.225587i	$-0.0724299\pi$
$594$		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	$0.401363\pi$
$599$			46.6176i			1.90474i	−0.304941	+	0.952371i	$0.598637\pi$
$600$		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
$603$	25.0052			1.01829
$604$		0			0
$605$	22.5063	−	9.01186i	0.915012	−	0.366384i
$606$		0			0
$607$	−9.09452	+	9.09452i	−0.369135	+	0.369135i	−0.867162	−	0.498026i	$-0.834058\pi$
$607$	−9.09452	+	9.09452i	−0.369135	+	0.369135i	0.498026	+	0.867162i	$0.334058\pi$
$608$		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
$613$	−36.3083			−1.46648			−0.733240	−	0.679970i	$-0.761993\pi$
$613$	−36.3083			−1.46648			−0.733240	+	0.679970i	$0.761993\pi$
$614$		0			0
$615$	24.4764	+	61.1275i	0.986982	+	2.46490i
$616$		0			0
$617$		−	11.4457i		−	0.460787i	−0.973098	−	0.230394i	$-0.925999\pi$
$617$		−	11.4457i		−	0.460787i	0.973098	−	0.230394i	$-0.0740014\pi$
$618$		0			0
$619$	−9.93208	+	9.93208i	−0.399204	+	0.399204i	−0.877952	−	0.478748i	$-0.841091\pi$
$619$	−9.93208	+	9.93208i	−0.399204	+	0.399204i	0.478748	+	0.877952i	$0.341091\pi$
$620$		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
$635$	−9.75526	+	22.7848i	−0.387126	+	0.904186i
$636$		0			0
$637$	−49.7408	+	23.3028i	−1.97080	+	0.923291i
$638$		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
$643$	−0.488940			−0.0192819			−0.00964096	−	0.999954i	$-0.503069\pi$
$643$	−0.488940			−0.0192819			−0.00964096	+	0.999954i	$0.503069\pi$
$644$		0			0
$645$	−10.3967	−	25.9647i	−0.409368	−	1.02236i
$646$		0			0
$647$	−22.4849	−	22.4849i	−0.883972	−	0.883972i	0.109964	−	0.993936i	$-0.464926\pi$
$647$	−22.4849	−	22.4849i	−0.883972	−	0.883972i	−0.993936	+	0.109964i	$0.964926\pi$
$648$		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	0.607149	−	0.794588i	$-0.292313\pi$
$653$	−4.78979	−	4.78979i	−0.187439	−	0.187439i	−0.794588	+	0.607149i	$0.792313\pi$
$654$		0			0
$655$	0.532350	+	1.32950i	0.0208006	+	0.0519477i
$656$		0			0
$657$	−30.6651			−1.19636
$658$		0			0
$659$		−	9.69986i		−	0.377853i	−0.981991	−	0.188926i	$-0.939499\pi$
$659$		−	9.69986i		−	0.377853i	0.981991	−	0.188926i	$-0.0605008\pi$
$660$		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
$663$	−26.0626	−	55.6317i	−1.01219	−	2.16056i
$664$		0			0
$665$	4.59116	−	10.7233i	0.178038	−	0.415832i
$666$		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	$-0.909567\pi$
$673$	−17.6307	+	17.6307i	−0.679615	+	0.679615i	0.280298	+	0.959913i	$0.409567\pi$
$674$		0			0
$675$	0.0554632	−	2.34274i	0.00213478	−	0.0901721i
$676$		0			0
$677$	−11.5028	+	11.5028i	−0.442089	+	0.442089i	−0.892714	−	0.450625i	$-0.851201\pi$
$677$	−11.5028	+	11.5028i	−0.442089	+	0.442089i	0.450625	+	0.892714i	$0.351201\pi$
$678$		0			0
$679$		−	63.9590i		−	2.45452i
$680$		0			0
$681$	−25.1154	+	25.1154i	−0.962424	+	0.962424i
$682$		0			0
$683$		−	48.3576i		−	1.85035i	−0.379540	−	0.925175i	$-0.623918\pi$
$683$		−	48.3576i		−	1.85035i	0.379540	−	0.925175i	$-0.376082\pi$
$684$		0			0
$685$	2.19874	+	5.49116i	0.0840097	+	0.209807i
$686$		0			0
$687$	−0.397822			−0.0151779
$688$		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
$695$	11.8302	−	4.73697i	0.448743	−	0.179684i
$696$		0			0
$697$	81.0778			3.07104
$698$		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
$707$		−	4.39489i		−	0.165287i
$708$		0			0
$709$	−8.86339	+	8.86339i	−0.332872	+	0.332872i	−0.853676	−	0.520804i	$-0.825632\pi$
$709$	−8.86339	+	8.86339i	−0.332872	+	0.332872i	0.520804	+	0.853676i	$0.325632\pi$
$710$		0			0
$711$	−5.93100			−0.222430
$712$		0			0
$713$		−	30.7182i		−	1.15041i
$714$		0			0
$715$	0.107600	+	3.20262i	0.00402400	+	0.119771i
$716$		0			0
$717$			32.2444i			1.20419i
$718$		0			0
$719$	−8.10825			−0.302387			−0.151193	−	0.988504i	$-0.548312\pi$
$719$	−8.10825			−0.302387			−0.151193	+	0.988504i	$0.548312\pi$
$720$		0			0
$721$	−21.1921	+	21.1921i	−0.789237	+	0.789237i
$722$		0			0
$723$		−	1.89800i		−	0.0705875i
$724$		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	$-0.185222\pi$
$727$	7.70651	+	7.70651i	0.285819	+	0.285819i	−0.549606	+	0.835424i	$0.685222\pi$
$728$		0			0
$729$			30.2781i			1.12141i
$730$		0			0
$731$	−34.4389			−1.27377
$732$		0			0
$733$	12.7323			0.470277			0.235139	−	0.971962i	$-0.424446\pi$
$733$	12.7323			0.470277			0.235139	+	0.971962i	$0.424446\pi$
$734$		0			0
$735$	−33.3540	+	77.9028i	−1.23028	+	2.87349i
$736$		0			0
$737$	−2.20413	+	2.20413i	−0.0811901	+	0.0811901i
$738$		0			0
$739$	−10.7053	+	10.7053i	−0.393801	+	0.393801i	−0.876040	−	0.482239i	$-0.839824\pi$
$739$	−10.7053	+	10.7053i	−0.393801	+	0.393801i	0.482239	+	0.876040i	$0.339824\pi$
$740$		0			0
$741$	−4.20967	−	8.98573i	−0.154646	−	0.330099i
$742$		0			0
$743$	43.4613			1.59444			0.797220	−	0.603689i	$-0.206303\pi$
$743$	43.4613			1.59444			0.797220	+	0.603689i	$0.206303\pi$
$744$		0			0
$745$	16.3815	−	38.2613i	0.600171	−	1.40178i
$746$		0			0
$747$		−	21.3952i		−	0.782810i
$748$		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	−0.901962	−	0.431816i	$-0.857873\pi$
$757$	−12.9354	+	12.9354i	−0.470145	+	0.470145i	0.431816	+	0.901962i	$0.357873\pi$
$758$		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
$765$	−44.8908	−	19.2199i	−1.62303	−	0.694897i
$766$		0			0
$767$	7.85003	−	21.6883i	0.283448	−	0.783117i
$768$		0			0
$769$	−10.1433	−	10.1433i	−0.365776	−	0.365776i	0.500158	−	0.865934i	$-0.333275\pi$
$769$	−10.1433	−	10.1433i	−0.365776	−	0.365776i	−0.865934	+	0.500158i	$0.833275\pi$
$770$		0			0
$771$		−	25.5100i		−	0.918719i
$772$		0			0
$773$	20.8119			0.748551			0.374276	−	0.927317i	$-0.377891\pi$
$773$	20.8119			0.748551			0.374276	+	0.927317i	$0.377891\pi$
$774$		0			0
$775$	−1.11602	+	47.1400i	−0.0400885	+	1.69332i
$776$		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
$785$	41.9546	+	17.9628i	1.49743	+	0.641120i
$786$		0			0
$787$	−40.0291			−1.42688			−0.713442	−	0.700714i	$-0.752865\pi$
$787$	−40.0291			−1.42688			−0.713442	+	0.700714i	$0.752865\pi$
$788$		0			0
$789$		−	38.8653i		−	1.38364i
$790$		0			0
$791$	29.0131	+	29.0131i	1.03159	+	1.03159i
$792$		0			0
$793$	−13.2295	+	6.19783i	−0.469795	+	0.220092i
$794$		0			0
$795$	−10.8026	+	4.32553i	−0.383129	+	0.153411i
$796$		0			0
$797$	−5.76153	−	5.76153i	−0.204084	−	0.204084i	0.597663	−	0.801747i	$-0.296096\pi$
$797$	−5.76153	−	5.76153i	−0.204084	−	0.204084i	−0.801747	+	0.597663i	$0.796096\pi$
$798$		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	$0.0645998\pi$
$809$			11.4657i			0.403112i	−0.979477	+	0.201556i	$0.935400\pi$
$810$		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
$813$		−	5.57399i		−	0.195489i
$814$		0			0
$815$	−11.0844	+	4.43836i	−0.388270	+	0.155469i
$816$		0			0
$817$	−5.56263			−0.194612
$818$		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	$-0.643625\pi$
$823$	13.3073	−	13.3073i	0.463865	−	0.463865i	0.899920	+	0.436055i	$0.143625\pi$
$824$		0			0
$825$	3.41202	+	3.57749i	0.118791	+	0.124552i
$826$		0			0
$827$	−40.4261			−1.40575			−0.702877	−	0.711311i	$-0.748102\pi$
$827$	−40.4261			−1.40575			−0.702877	+	0.711311i	$0.748102\pi$
$828$		0			0
$829$	9.00868			0.312884			0.156442	−	0.987687i	$-0.449998\pi$
$829$	9.00868			0.312884			0.156442	+	0.987687i	$0.449998\pi$
$830$		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
$837$			4.41995i			0.152776i
$838$		0			0
$839$	−15.2917	+	15.2917i	−0.527929	+	0.527929i	−0.919954	−	0.392025i	$-0.871775\pi$
$839$	−15.2917	+	15.2917i	−0.527929	+	0.527929i	0.392025	+	0.919954i	$0.371775\pi$
$840$		0			0
$841$	−10.0275			−0.345776
$842$		0			0
$843$			17.6557i			0.608096i
$844$		0			0
$845$	27.6503	+	8.96993i	0.951200	+	0.308575i
$846$		0			0
$847$			51.1239i			1.75664i
$848$		0			0
$849$	−54.5830			−1.87328
$850$		0			0
$851$	−7.25701	+	7.25701i	−0.248767	+	0.248767i
$852$		0			0
$853$		−	26.8763i		−	0.920226i	−0.887860	−	0.460113i	$-0.847809\pi$
$853$		−	26.8763i		−	0.920226i	0.887860	−	0.460113i	$-0.152191\pi$
$854$		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	$-0.300449\pi$
$857$	−6.53408	−	6.53408i	−0.223200	−	0.223200i	−0.809844	+	0.586645i	$0.800449\pi$
$858$		0			0
$859$		−	10.4798i		−	0.357565i	−0.983889	−	0.178783i	$-0.942784\pi$
$859$		−	10.4798i		−	0.357565i	0.983889	−	0.178783i	$-0.0572159\pi$
$860$		0			0
$861$	−138.853			−4.73211
$862$		0			0
$863$	6.95053			0.236599			0.118299	−	0.992978i	$-0.462256\pi$
$863$	6.95053			0.236599			0.118299	+	0.992978i	$0.462256\pi$
$864$		0			0
$865$	−5.69535	−	2.43845i	−0.193648	−	0.0829099i
$866$		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
$873$	−43.2475			−1.46371
$874$		0			0
$875$	47.9593	+	21.8910i	1.62132	+	0.740051i
$876$		0			0
$877$			17.4225i			0.588318i	0.955757	+	0.294159i	$0.0950395\pi$
$877$			17.4225i			0.588318i	−0.955757	+	0.294159i	$0.904961\pi$
$878$		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	$-0.553225\pi$
$883$	24.3552	−	24.3552i	0.819618	−	0.819618i	0.986053	+	0.166434i	$0.0532254\pi$
$884$		0			0
$885$	−13.2275	−	33.0346i	−0.444639	−	1.11044i
$886$		0			0
$887$	−9.83517	+	9.83517i	−0.330233	+	0.330233i	−0.852675	−	0.522442i	$-0.825021\pi$
$887$	−9.83517	+	9.83517i	−0.330233	+	0.330233i	0.522442	+	0.852675i	$0.325021\pi$
$888$		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
$895$	−15.9747	−	39.8954i	−0.533976	−	1.33356i
$896$		0			0
$897$	−26.4563	+	12.3944i	−0.883349	+	0.413835i
$898$		0			0
$899$	41.6593	+	41.6593i	1.38941	+	1.38941i
$900$		0			0
$901$			14.3283i			0.477344i
$902$		0			0
$903$	58.9799			1.96273
$904$		0			0
$905$	−6.12729	+	2.45346i	−0.203678	+	0.0815557i
$906$		0			0
$907$	−10.1522	−	10.1522i	−0.337098	−	0.337098i	0.518176	−	0.855274i	$-0.326611\pi$
$907$	−10.1522	−	10.1522i	−0.337098	−	0.337098i	−0.855274	+	0.518176i	$0.826611\pi$
$908$		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
$915$	−8.87113	+	20.7198i	−0.293270	+	0.684974i
$916$		0			0
$917$	−3.02000			−0.0997292
$918$		0			0
$919$		−	14.8038i		−	0.488332i	−0.969733	−	0.244166i	$-0.921486\pi$
$919$		−	14.8038i		−	0.488332i	0.969733	−	0.244166i	$-0.0785141\pi$
$920$		0			0
$921$	−28.4969	−	28.4969i	−0.939005	−	0.939005i
$922$		0			0
$923$	9.40514	−	25.9847i	0.309574	−	0.855298i
$924$		0			0
$925$	11.4002	−	10.8729i	0.374837	−	0.357499i
$926$		0			0
$927$	14.3296	+	14.3296i	0.470646	+	0.470646i
$928$		0			0
$929$	7.78926	+	7.78926i	0.255557	+	0.255557i	0.823244	−	0.567687i	$-0.192162\pi$
$929$	7.78926	+	7.78926i	0.255557	+	0.255557i	−0.567687	+	0.823244i	$0.692162\pi$
$930$		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	0.248209	−	0.968707i	$-0.420158\pi$
$937$	37.2503	−	37.2503i	1.21692	−	1.21692i	0.968707	−	0.248209i	$-0.0798419\pi$
$938$		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
$943$		−	38.5574i		−	1.25560i
$944$		0			0
$945$	4.54282	+	1.94500i	0.147778	+	0.0632708i
$946$		0			0
$947$	40.5927			1.31909			0.659543	−	0.751667i	$-0.270750\pi$
$947$	40.5927			1.31909			0.659543	+	0.751667i	$0.270750\pi$
$948$		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	$-0.658115\pi$
$953$	12.4282	−	12.4282i	0.402590	−	0.402590i	0.879145	+	0.476555i	$0.158115\pi$
$954$		0			0
$955$	1.81983	+	4.54485i	0.0588882	+	0.147068i
$956$		0			0
$957$	6.17688			0.199670
$958$		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
$967$		−	13.2989i		−	0.427663i	−0.976871	−	0.213832i	$-0.931406\pi$
$967$		−	13.2989i		−	0.427663i	0.976871	−	0.213832i	$-0.0685944\pi$
$968$		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
$973$			26.8726i			0.861498i
$974$		0			0
$975$	41.0500	−	18.0591i	1.31465	−	0.578355i
$976$		0			0
$977$			1.33256i			0.0426324i	0.999773	+	0.0213162i	$0.00678566\pi$
$977$			1.33256i			0.0426324i	−0.999773	+	0.0213162i	$0.993214\pi$
$978$		0			0
$979$	−5.65322			−0.180678
$980$		0			0
$981$	6.81540	−	6.81540i	0.217599	−	0.217599i
$982$		0			0
$983$			50.5175i			1.61126i	0.592420	+	0.805630i	$0.298173\pi$
$983$			50.5175i			1.61126i	−0.592420	+	0.805630i	$0.701827\pi$
$984$		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
$993$	−63.4012			−2.01198
$994$		0			0
$995$	−6.21833	−	15.5297i	−0.197134	−	0.492325i
$996$		0			0
$997$	14.1643	−	14.1643i	0.448587	−	0.448587i	−0.446297	−	0.894885i	$-0.647258\pi$
$997$	14.1643	−	14.1643i	0.448587	−	0.448587i	0.894885	+	0.446297i	$0.147258\pi$
$998$		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.bh.f.473.9	yes	20
4.3	odd	2		1040.2.cd.p.993.2		20
5.2	odd	4		520.2.w.f.57.9	✓	20
13.8	odd	4		520.2.w.f.73.9	yes	20
20.7	even	4		1040.2.bg.p.577.2		20
52.47	even	4		1040.2.bg.p.593.2		20
65.47	even	4	inner	520.2.bh.f.177.9	yes	20
260.47	odd	4		1040.2.cd.p.177.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.w.f.57.9	✓	20	5.2	odd	4
520.2.w.f.73.9	yes	20	13.8	odd	4
520.2.bh.f.177.9	yes	20	65.47	even	4	inner
520.2.bh.f.473.9	yes	20	1.1	even	1	trivial
1040.2.bg.p.577.2		20	20.7	even	4
1040.2.bg.p.593.2		20	52.47	even	4
1040.2.cd.p.177.2		20	260.47	odd	4
1040.2.cd.p.993.2		20	4.3	odd	2

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.bh (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.75903 + 1.75903i) q^{3} +(0.831197 + 2.07584i) q^{5} -4.71535 q^{7} +3.18840i q^{9} +O(q^{10})\)	\(q+(1.75903 + 1.75903i) q^{3} +(0.831197 + 2.07584i) q^{5} -4.71535 q^{7} +3.18840i q^{9} +(-0.281047 - 0.281047i) q^{11} +(-3.26501 + 1.52961i) q^{13} +(-2.18937 + 5.11358i) q^{15} +(4.84321 + 4.84321i) q^{17} +(0.782284 + 0.782284i) q^{19} +(-8.29446 - 8.29446i) q^{21} +(2.30324 - 2.30324i) q^{23} +(-3.61822 + 3.45086i) q^{25} +(-0.331406 + 0.331406i) q^{27} +6.24720i q^{29} +(6.66847 - 6.66847i) q^{31} -0.988743i q^{33} +(-3.91938 - 9.78831i) q^{35} -3.15078 q^{37} +(-8.43390 - 3.05264i) q^{39} +(8.37025 - 8.37025i) q^{41} +(-3.55538 + 3.55538i) q^{43} +(-6.61861 + 2.65019i) q^{45} +3.57021 q^{47} +15.2345 q^{49} +17.0388i q^{51} +(1.47921 + 1.47921i) q^{53} +(0.349803 - 0.817015i) q^{55} +2.75213i q^{57} +(-4.52346 + 4.52346i) q^{59} +4.05191 q^{61} -15.0344i q^{63} +(-5.88909 - 5.50624i) q^{65} -7.84255i q^{67} +8.10296 q^{69} +(-5.41956 + 5.41956i) q^{71} +9.61771i q^{73} +(-12.4348 - 0.294387i) q^{75} +(1.32524 + 1.32524i) q^{77} +1.86018i q^{79} +8.39930 q^{81} -6.71033 q^{83} +(-6.02807 + 14.0794i) q^{85} +(-10.9890 + 10.9890i) q^{87} +(10.0574 - 10.0574i) q^{89} +(15.3957 - 7.21263i) q^{91} +23.4601 q^{93} +(-0.973664 + 2.27413i) q^{95} +13.5640i q^{97} +(0.896092 - 0.896092i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q+O(q^{10}) \) 20 * q	\( 20 q + 2 q^{11} + 4 q^{13} + 10 q^{15} + 6 q^{17} + 2 q^{19} + 6 q^{21} - 14 q^{23} - 14 q^{25} + 6 q^{27} + 10 q^{31} - 16 q^{35} + 4 q^{37} - 32 q^{39} + 28 q^{41} + 2 q^{45} - 20 q^{47} + 16 q^{49} + 20 q^{53} - 48 q^{55} + 14 q^{59} + 12 q^{61} + 12 q^{65} - 24 q^{69} - 48 q^{71} + 22 q^{75} + 12 q^{77} - 4 q^{81} + 16 q^{83} + 28 q^{89} - 8 q^{91} - 28 q^{93} + 2 q^{95} + 42 q^{99}+O(q^{100}) \) 20 * q + 2 * q^11 + 4 * q^13 + 10 * q^15 + 6 * q^17 + 2 * q^19 + 6 * q^21 - 14 * q^23 - 14 * q^25 + 6 * q^27 + 10 * q^31 - 16 * q^35 + 4 * q^37 - 32 * q^39 + 28 * q^41 + 2 * q^45 - 20 * q^47 + 16 * q^49 + 20 * q^53 - 48 * q^55 + 14 * q^59 + 12 * q^61 + 12 * q^65 - 24 * q^69 - 48 * q^71 + 22 * q^75 + 12 * q^77 - 4 * q^81 + 16 * q^83 + 28 * q^89 - 8 * q^91 - 28 * q^93 + 2 * q^95 + 42 * q^99

Introduction

L-functions

Modular forms

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