LMFDB - Embedded newform 124.6.f.a.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,6,Mod(33,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("124.33");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	124.f (of order $5$, degree $4$, 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:	$19.8875936568$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			109.1
Character	$\chi$	$=$	124.109
Dual form			124.6.f.a.33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-21.7500 - 15.8023i) q^{3} -26.6888 q^{5} +(-46.2791 + 142.432i) q^{7} +(148.259 + 456.295i) q^{9} +O(q^{10})$	\(q+(-21.7500 - 15.8023i) q^{3} -26.6888 q^{5} +(-46.2791 + 142.432i) q^{7} +(148.259 + 456.295i) q^{9} +(53.6179 - 165.019i) q^{11} +(684.216 + 497.112i) q^{13} +(580.483 + 421.746i) q^{15} +(-444.272 - 1367.33i) q^{17} +(-2426.00 + 1762.59i) q^{19} +(3257.34 - 2366.59i) q^{21} +(-706.831 - 2175.40i) q^{23} -2412.71 q^{25} +(1967.09 - 6054.09i) q^{27} +(3738.58 - 2716.23i) q^{29} +(3838.05 - 3728.08i) q^{31} +(-3773.87 + 2741.88i) q^{33} +(1235.14 - 3801.36i) q^{35} +4924.45 q^{37} +(-7026.19 - 21624.4i) q^{39} +(9302.94 - 6758.98i) q^{41} +(-1497.30 + 1087.85i) q^{43} +(-3956.87 - 12178.0i) q^{45} +(12861.5 + 9344.46i) q^{47} +(-4548.09 - 3304.38i) q^{49} +(-11944.0 + 36759.9i) q^{51} +(5993.12 + 18444.9i) q^{53} +(-1431.00 + 4404.16i) q^{55} +80618.6 q^{57} +(-29277.0 - 21271.0i) q^{59} +35110.8 q^{61} -71852.6 q^{63} +(-18260.9 - 13267.3i) q^{65} -8530.75 q^{67} +(-19002.8 + 58484.6i) q^{69} +(-14105.9 - 43413.4i) q^{71} +(7533.30 - 23185.1i) q^{73} +(52476.4 + 38126.4i) q^{75} +(21022.6 + 15273.8i) q^{77} +(-14199.4 - 43701.3i) q^{79} +(-44133.0 + 32064.5i) q^{81} +(57767.9 - 41970.8i) q^{83} +(11857.1 + 36492.4i) q^{85} -124237. q^{87} +(10240.9 - 31518.4i) q^{89} +(-102470. + 74448.6i) q^{91} +(-142390. + 20435.8i) q^{93} +(64747.1 - 47041.5i) q^{95} +(33219.9 - 102240. i) q^{97} +83246.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9}+O(q^{10}) $ 56 * q + 2 * q^3 - 58 * q^5 + 104 * q^7 - 1234 * q^9	$ 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9} - 509 q^{11} - 117 q^{13} + 89 q^{15} - 3504 q^{17} + 262 q^{19} + 352 q^{21} - 2448 q^{23} + 49618 q^{25} + 14324 q^{27} - 9888 q^{29} - 12771 q^{31} + 27699 q^{33} + 13840 q^{35} + 76096 q^{37} + 33520 q^{39} - 4843 q^{41} - 40778 q^{43} + 56692 q^{45} + 38922 q^{47} - 17126 q^{49} - 69292 q^{51} - 41728 q^{53} - 172096 q^{55} + 57066 q^{57} - 58198 q^{59} + 176328 q^{61} - 37444 q^{63} + 143863 q^{65} + 9812 q^{67} - 9250 q^{69} - 67356 q^{71} - 63512 q^{73} - 198012 q^{75} - 74257 q^{77} + 137651 q^{79} + 196077 q^{81} + 156427 q^{83} + 238828 q^{85} - 558144 q^{87} - 99292 q^{89} - 243609 q^{91} - 325925 q^{93} - 75077 q^{95} - 476340 q^{97} + 745812 q^{99}+O(q^{100}) $ 56 * q + 2 * q^3 - 58 * q^5 + 104 * q^7 - 1234 * q^9 - 509 * q^11 - 117 * q^13 + 89 * q^15 - 3504 * q^17 + 262 * q^19 + 352 * q^21 - 2448 * q^23 + 49618 * q^25 + 14324 * q^27 - 9888 * q^29 - 12771 * q^31 + 27699 * q^33 + 13840 * q^35 + 76096 * q^37 + 33520 * q^39 - 4843 * q^41 - 40778 * q^43 + 56692 * q^45 + 38922 * q^47 - 17126 * q^49 - 69292 * q^51 - 41728 * q^53 - 172096 * q^55 + 57066 * q^57 - 58198 * q^59 + 176328 * q^61 - 37444 * q^63 + 143863 * q^65 + 9812 * q^67 - 9250 * q^69 - 67356 * q^71 - 63512 * q^73 - 198012 * q^75 - 74257 * q^77 + 137651 * q^79 + 196077 * q^81 + 156427 * q^83 + 238828 * q^85 - 558144 * q^87 - 99292 * q^89 - 243609 * q^91 - 325925 * q^93 - 75077 * q^95 - 476340 * q^97 + 745812 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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
$3$	−21.7500	−	15.8023i	−1.39527	−	1.01372i	−0.995264	−	0.0972047i	$-0.969010\pi$
$3$	−21.7500	−	15.8023i	−1.39527	−	1.01372i	−0.400001	−	0.916515i	$-0.630990\pi$
$4$		0			0
$5$	−26.6888			−0.477424			−0.238712	−	0.971090i	$-0.576725\pi$
$5$	−26.6888			−0.477424			−0.238712	+	0.971090i	$0.576725\pi$
$6$		0			0
$7$	−46.2791	+	142.432i	−0.356977	+	1.09866i	0.597878	+	0.801587i	$0.296011\pi$
$7$	−46.2791	+	142.432i	−0.356977	+	1.09866i	−0.954854	+	0.297074i	$0.903989\pi$
$8$		0			0
$9$	148.259	+	456.295i	0.610121	+	1.87776i
$10$		0			0
$11$	53.6179	−	165.019i	0.133607	−	0.411199i	−0.861764	−	0.507309i	$-0.830640\pi$
$11$	53.6179	−	165.019i	0.133607	−	0.411199i	0.995371	+	0.0961105i	$0.0306402\pi$
$12$		0			0
$13$	684.216	+	497.112i	1.12288	+	0.815822i	0.984644	−	0.174576i	$-0.0558556\pi$
$13$	684.216	+	497.112i	1.12288	+	0.815822i	0.138240	+	0.990399i	$0.455856\pi$
$14$		0			0
$15$	580.483	+	421.746i	0.666134	+	0.483974i
$16$		0			0
$17$	−444.272	−	1367.33i	−0.372843	−	1.14749i	−0.944922	−	0.327295i	$-0.893863\pi$
$17$	−444.272	−	1367.33i	−0.372843	−	1.14749i	0.572079	−	0.820198i	$-0.306137\pi$
$18$		0			0
$19$	−2426.00	+	1762.59i	−1.54172	+	1.12013i	−0.592480	+	0.805585i	$0.701851\pi$
$19$	−2426.00	+	1762.59i	−1.54172	+	1.12013i	−0.949243	+	0.314543i	$0.898149\pi$
$20$		0			0
$21$	3257.34	−	2366.59i	1.61181	−	1.17105i
$22$		0			0
$23$	−706.831	−	2175.40i	−0.278610	−	0.857472i	−0.988242	−	0.152900i	$-0.951139\pi$
$23$	−706.831	−	2175.40i	−0.278610	−	0.857472i	0.709632	−	0.704572i	$-0.248861\pi$
$24$		0			0
$25$	−2412.71			−0.772066
$26$		0			0
$27$	1967.09	−	6054.09i	0.519296	−	1.59823i
$28$		0			0
$29$	3738.58	−	2716.23i	0.825489	−	0.599753i	−0.0927907	−	0.995686i	$-0.529579\pi$
$29$	3738.58	−	2716.23i	0.825489	−	0.599753i	0.918279	+	0.395933i	$0.129579\pi$
$30$		0			0
$31$	3838.05	−	3728.08i	0.717308	−	0.696756i
$31$	3838.05	−	3728.08i	0.717308	−	0.696756i
$32$		0			0
$33$	−3773.87	+	2741.88i	−0.603257	+	0.438292i
$34$		0			0
$35$	1235.14	−	3801.36i	0.170429	−	0.524528i
$36$		0			0
$37$	4924.45			0.591362			0.295681	−	0.955287i	$-0.404453\pi$
$37$	4924.45			0.591362			0.295681	+	0.955287i	$0.404453\pi$
$38$		0			0
$39$	−7026.19	−	21624.4i	−0.739705	−	2.27658i
$40$		0			0
$41$	9302.94	−	6758.98i	0.864292	−	0.627945i	−0.0647572	−	0.997901i	$-0.520627\pi$
$41$	9302.94	−	6758.98i	0.864292	−	0.627945i	0.929049	+	0.369956i	$0.120627\pi$
$42$		0			0
$43$	−1497.30	+	1087.85i	−0.123492	+	0.0897218i	−0.647817	−	0.761796i	$-0.724318\pi$
$43$	−1497.30	+	1087.85i	−0.123492	+	0.0897218i	0.524325	+	0.851518i	$0.324318\pi$
$44$		0			0
$45$	−3956.87	−	12178.0i	−0.291287	−	0.896488i
$46$		0			0
$47$	12861.5	+	9344.46i	0.849275	+	0.617035i	0.924946	−	0.380098i	$-0.124110\pi$
$47$	12861.5	+	9344.46i	0.849275	+	0.617035i	−0.0756709	+	0.997133i	$0.524110\pi$
$48$		0			0
$49$	−4548.09	−	3304.38i	−0.270607	−	0.196608i
$50$		0			0
$51$	−11944.0	+	36759.9i	−0.643021	+	1.97902i
$52$		0			0
$53$	5993.12	+	18444.9i	0.293065	+	0.901960i	0.983865	+	0.178914i	$0.0572585\pi$
$53$	5993.12	+	18444.9i	0.293065	+	0.901960i	−0.690800	+	0.723046i	$0.742741\pi$
$54$		0			0
$55$	−1431.00	+	4404.16i	−0.0637870	+	0.196316i
$56$		0			0
$57$	80618.6			3.28661
$58$		0			0
$59$	−29277.0	−	21271.0i	−1.09496	−	0.795533i	−0.114728	−	0.993397i	$-0.536600\pi$
$59$	−29277.0	−	21271.0i	−1.09496	−	0.795533i	−0.980230	+	0.197864i	$0.936600\pi$
$60$		0			0
$61$	35110.8			1.20814			0.604069	−	0.796932i	$-0.293545\pi$
$61$	35110.8			1.20814			0.604069	+	0.796932i	$0.293545\pi$
$62$		0			0
$63$	−71852.6			−2.28082
$64$		0			0
$65$	−18260.9	−	13267.3i	−0.536092	−	0.389494i
$66$		0			0
$67$	−8530.75			−0.232167			−0.116083	−	0.993239i	$-0.537034\pi$
$67$	−8530.75			−0.232167			−0.116083	+	0.993239i	$0.537034\pi$
$68$		0			0
$69$	−19002.8	+	58484.6i	−0.480502	+	1.47883i
$70$		0			0
$71$	−14105.9	−	43413.4i	−0.332089	−	1.02206i	−0.968138	−	0.250416i	$-0.919433\pi$
$71$	−14105.9	−	43413.4i	−0.332089	−	1.02206i	0.636050	−	0.771648i	$-0.280567\pi$
$72$		0			0
$73$	7533.30	−	23185.1i	0.165454	−	0.509216i	−0.833615	−	0.552346i	$-0.813733\pi$
$73$	7533.30	−	23185.1i	0.165454	−	0.509216i	0.999069	+	0.0431296i	$0.0137328\pi$
$74$		0			0
$75$	52476.4	+	38126.4i	1.07724	+	0.782658i
$76$		0			0
$77$	21022.6	+	15273.8i	0.404074	+	0.293577i
$78$		0			0
$79$	−14199.4	−	43701.3i	−0.255978	−	0.787819i	−0.993635	−	0.112644i	$-0.964068\pi$
$79$	−14199.4	−	43701.3i	−0.255978	−	0.787819i	0.737658	−	0.675175i	$-0.235932\pi$
$80$		0			0
$81$	−44133.0	+	32064.5i	−0.747396	+	0.543015i
$82$		0			0
$83$	57767.9	−	41970.8i	0.920431	−	0.668732i	−0.0232004	−	0.999731i	$-0.507386\pi$
$83$	57767.9	−	41970.8i	0.920431	−	0.668732i	0.943631	+	0.330999i	$0.107386\pi$
$84$		0			0
$85$	11857.1	+	36492.4i	0.178004	+	0.547841i
$86$		0			0
$87$	−124237.			−1.75976
$88$		0			0
$89$	10240.9	−	31518.4i	0.137046	−	0.421783i	−0.858857	−	0.512215i	$-0.828825\pi$
$89$	10240.9	−	31518.4i	0.137046	−	0.421783i	0.995903	+	0.0904326i	$0.0288250\pi$
$90$		0			0
$91$	−102470.	+	74448.6i	−1.29716	+	0.942439i
$92$		0			0
$93$	−142390.	+	20435.8i	−1.70715	+	0.245010i
$94$		0			0
$95$	64747.1	−	47041.5i	0.736057	−	0.534776i
$96$		0			0
$97$	33219.9	−	102240.i	0.358484	−	1.10330i	−0.595478	−	0.803372i	$-0.703037\pi$
$97$	33219.9	−	102240.i	0.358484	−	1.10330i	0.953962	−	0.299928i	$-0.0969627\pi$
$98$		0			0
$99$	83246.7			0.853648
$100$		0			0
$101$	53189.2	+	163699.i	0.518824	+	1.59678i	0.776215	+	0.630468i	$0.217137\pi$
$101$	53189.2	+	163699.i	0.518824	+	1.59678i	−0.257391	+	0.966307i	$0.582863\pi$
$102$		0			0
$103$	52378.7	−	38055.3i	0.486476	−	0.353446i	−0.317351	−	0.948308i	$-0.602793\pi$
$103$	52378.7	−	38055.3i	0.486476	−	0.353446i	0.803828	+	0.594862i	$0.202793\pi$
$104$		0			0
$105$	−86934.5	+	63161.6i	−0.769518	+	0.559088i
$106$		0			0
$107$	58011.3	+	178540.i	0.489839	+	1.50757i	0.824848	+	0.565354i	$0.191260\pi$
$107$	58011.3	+	178540.i	0.489839	+	1.50757i	−0.335010	+	0.942215i	$0.608740\pi$
$108$		0			0
$109$	27059.5	+	19659.9i	0.218149	+	0.158495i	0.691493	−	0.722383i	$-0.256953\pi$
$109$	27059.5	+	19659.9i	0.218149	+	0.158495i	−0.473344	+	0.880878i	$0.656953\pi$
$110$		0			0
$111$	−107107.	−	77817.8i	−0.825107	−	0.599476i
$112$		0			0
$113$	−39256.4	+	120819.i	−0.289211	+	0.890099i	0.695894	+	0.718144i	$0.255008\pi$
$113$	−39256.4	+	120819.i	−0.289211	+	0.890099i	−0.985105	+	0.171955i	$0.944992\pi$
$114$		0			0
$115$	18864.5	+	58059.0i	0.133015	+	0.409378i
$116$		0			0
$117$	−125388.	+	385906.i	−0.846823	+	2.60625i
$118$		0			0
$119$	215312.			1.39380
$120$		0			0
$121$	105937.	+	76967.5i	0.657783	+	0.477908i
$122$		0			0
$123$	−309147.			−1.84248
$124$		0			0
$125$	147795.			0.846028
$126$		0			0
$127$	129424.	+	94031.7i	0.712039	+	0.517327i	0.883831	−	0.467807i	$-0.154956\pi$
$127$	129424.	+	94031.7i	0.712039	+	0.517327i	−0.171792	+	0.985133i	$0.554956\pi$
$128$		0			0
$129$	49756.8			0.263256
$130$		0			0
$131$	96356.9	−	296556.i	0.490574	−	1.50983i	−0.333168	−	0.942868i	$-0.608118\pi$
$131$	96356.9	−	296556.i	0.490574	−	1.50983i	0.823742	−	0.566965i	$-0.191882\pi$
$132$		0			0
$133$	−138777.	−	427112.i	−0.680282	−	2.09369i
$134$		0			0
$135$	−52499.4	+	161577.i	−0.247925	+	0.763034i
$136$		0			0
$137$	−151756.	−	110257.i	−0.690786	−	0.501886i	0.186132	−	0.982525i	$-0.440405\pi$
$137$	−151756.	−	110257.i	−0.690786	−	0.501886i	−0.876919	+	0.480639i	$0.840405\pi$
$138$		0			0
$139$	−122791.	−	89213.2i	−0.539052	−	0.391644i	0.284681	−	0.958622i	$-0.408112\pi$
$139$	−122791.	−	89213.2i	−0.539052	−	0.391644i	−0.823733	+	0.566978i	$0.808112\pi$
$140$		0			0
$141$	−132075.	−	406485.i	−0.559464	−	1.72185i
$142$		0			0
$143$	118719.	−	86254.4i	0.485490	−	0.352729i
$144$		0			0
$145$	−99778.2	+	72493.1i	−0.394109	+	0.286337i
$146$		0			0
$147$	46704.3	+	143741.i	0.178264	+	0.548640i
$148$		0			0
$149$	−117531.			−0.433697			−0.216848	−	0.976205i	$-0.569578\pi$
$149$	−117531.			−0.433697			−0.216848	+	0.976205i	$0.569578\pi$
$150$		0			0
$151$	149025.	−	458651.i	0.531883	−	1.63697i	−0.218408	−	0.975858i	$-0.570086\pi$
$151$	149025.	−	458651.i	0.531883	−	1.63697i	0.750290	−	0.661109i	$-0.229914\pi$
$152$		0			0
$153$	558038.	−	405438.i	1.92724	−	1.40022i
$154$		0			0
$155$	−102433.	+	99498.0i	−0.342461	+	0.332648i
$156$		0			0
$157$	296642.	−	215523.i	0.960469	−	0.697822i	0.00720949	−	0.999974i	$-0.497705\pi$
$157$	296642.	−	215523.i	0.960469	−	0.697822i	0.953260	+	0.302152i	$0.0977051\pi$
$158$		0			0
$159$	161122.	−	495883.i	0.505432	−	1.55556i
$160$		0			0
$161$	342559.			1.04153
$162$		0			0
$163$	198060.	+	609567.i	0.583887	+	1.79702i	0.603697	+	0.797214i	$0.293694\pi$
$163$	198060.	+	609567.i	0.583887	+	1.79702i	−0.0198100	+	0.999804i	$0.506306\pi$
$164$		0			0
$165$	100720.	−	73177.5i	0.288010	−	0.209251i
$166$		0			0
$167$	68541.4	−	49798.2i	0.190179	−	0.138173i	−0.488622	−	0.872496i	$-0.662500\pi$
$167$	68541.4	−	49798.2i	0.190179	−	0.138173i	0.678800	+	0.734323i	$0.262500\pi$
$168$		0			0
$169$	106295.	+	327143.i	0.286283	+	0.881090i
$170$		0			0
$171$	−1.16394e6	−	845651.i	−3.04397	−	2.21157i
$172$		0			0
$173$	−182473.	−	132575.i	−0.463536	−	0.336779i	0.331381	−	0.943497i	$-0.392486\pi$
$173$	−182473.	−	132575.i	−0.463536	−	0.336779i	−0.794917	+	0.606718i	$0.792486\pi$
$174$		0			0
$175$	111658.	−	343648.i	0.275610	−	0.848239i
$176$		0			0
$177$	300645.	+	925291.i	0.721309	+	2.21996i
$178$		0			0
$179$	8146.05	−	25071.0i	0.0190027	−	0.0584842i	−0.941106	−	0.338113i	$-0.890211\pi$
$179$	8146.05	−	25071.0i	0.0190027	−	0.0584842i	0.960108	+	0.279629i	$0.0902114\pi$
$180$		0			0
$181$	−72253.0			−0.163930			−0.0819652	−	0.996635i	$-0.526120\pi$
$181$	−72253.0			−0.163930			−0.0819652	+	0.996635i	$0.526120\pi$
$182$		0			0
$183$	−763661.	−	554832.i	−1.68567	−	1.22471i
$184$		0			0
$185$	−131428.			−0.282331
$186$		0			0
$187$	−249456.			−0.521662
$188$		0			0
$189$	771263.	+	560355.i	1.57054	+	1.14106i
$190$		0			0
$191$	146192.			0.289961			0.144980	−	0.989435i	$-0.453688\pi$
$191$	146192.			0.289961			0.144980	+	0.989435i	$0.453688\pi$
$192$		0			0
$193$	−89454.4	+	275312.i	−0.172866	+	0.532026i	−0.999530	−	0.0306703i	$-0.990236\pi$
$193$	−89454.4	+	275312.i	−0.172866	+	0.532026i	0.826664	+	0.562696i	$0.190236\pi$
$194$		0			0
$195$	187521.	+	577130.i	0.353153	+	1.08689i
$196$		0			0
$197$	119110.	−	366583.i	0.218667	−	0.672987i	−0.780206	−	0.625522i	$-0.784886\pi$
$197$	119110.	−	366583.i	0.218667	−	0.672987i	0.998873	−	0.0474643i	$-0.0151140\pi$
$198$		0			0
$199$	−9347.05	−	6791.03i	−0.0167318	−	0.0121563i	0.579388	−	0.815052i	$-0.303292\pi$
$199$	−9347.05	−	6791.03i	−0.0167318	−	0.0121563i	−0.596120	+	0.802896i	$0.703292\pi$
$200$		0			0
$201$	185544.	+	134806.i	0.323934	+	0.235352i
$202$		0			0
$203$	213862.	+	658199.i	0.364245	+	1.12103i
$204$		0			0
$205$	−248285.	+	180389.i	−0.412634	+	0.299796i
$206$		0			0
$207$	887832.	−	645047.i	1.44014	−	1.04632i
$208$		0			0
$209$	160784.	+	494842.i	0.254611	+	0.783611i
$210$		0			0
$211$	−61040.0			−0.0943861			−0.0471931	−	0.998886i	$-0.515028\pi$
$211$	−61040.0			−0.0943861			−0.0471931	+	0.998886i	$0.515028\pi$
$212$		0			0
$213$	−379230.	+	1.16715e6i	−0.572734	+	1.76269i
$214$		0			0
$215$	39961.1	−	29033.5i	0.0589579	−	0.0428354i
$216$		0			0
$217$	353378.	+	719194.i	0.509436	+	1.03680i
$218$		0			0
$219$	−530228.	+	385233.i	−0.747055	+	0.542767i
$220$		0			0
$221$	375737.	−	1.15640e6i	0.517491	−	1.59267i
$222$		0			0
$223$	−1.07543e6			−1.44817			−0.724083	−	0.689713i	$-0.757737\pi$
$223$	−1.07543e6			−1.44817			−0.724083	+	0.689713i	$0.757737\pi$
$224$		0			0
$225$	−357706.	−	1.10091e6i	−0.471053	−	1.44975i
$226$		0			0
$227$	244158.	−	177391.i	0.314489	−	0.228490i	−0.419331	−	0.907833i	$-0.637735\pi$
$227$	244158.	−	177391.i	0.314489	−	0.228490i	0.733820	+	0.679344i	$0.237735\pi$
$228$		0			0
$229$	82310.7	−	59802.3i	0.103721	−	0.0753579i	−0.534716	−	0.845032i	$-0.679581\pi$
$229$	82310.7	−	59802.3i	0.103721	−	0.0753579i	0.638437	+	0.769674i	$0.279581\pi$
$230$		0			0
$231$	−215881.	−	664413.i	−0.266186	−	0.819235i
$232$		0			0
$233$	682802.	+	496085.i	0.823958	+	0.598640i	0.917843	−	0.396943i	$-0.129929\pi$
$233$	682802.	+	496085.i	0.823958	+	0.598640i	−0.0938856	+	0.995583i	$0.529929\pi$
$234$		0			0
$235$	−343260.	−	249393.i	−0.405465	−	0.294587i
$236$		0			0
$237$	−381744.	+	1.17489e6i	−0.441470	+	1.35871i
$238$		0			0
$239$	482533.	+	1.48508e6i	0.546427	+	1.68173i	0.717572	+	0.696484i	$0.245253\pi$
$239$	482533.	+	1.48508e6i	0.546427	+	1.68173i	−0.171145	+	0.985246i	$0.554747\pi$
$240$		0			0
$241$	341482.	−	1.05097e6i	0.378726	−	1.16560i	−0.562205	−	0.826998i	$-0.690047\pi$
$241$	341482.	−	1.05097e6i	0.378726	−	1.16560i	0.940931	−	0.338600i	$-0.109953\pi$
$242$		0			0
$243$	−80263.7			−0.0871974
$244$		0			0
$245$	121383.	+	88190.2i	0.129194	+	0.0938653i
$246$		0			0
$247$	−2.53611e6			−2.64500
$248$		0			0
$249$	−1.91969e6			−1.96215
$250$		0			0
$251$	−1.05809e6	−	768751.i	−1.06008	−	0.770196i	−0.0859802	−	0.996297i	$-0.527402\pi$
$251$	−1.05809e6	−	768751.i	−1.06008	−	0.770196i	−0.974104	+	0.226101i	$0.927402\pi$
$252$		0			0
$253$	−396881.			−0.389816
$254$		0			0
$255$	318772.	−	981080.i	0.306994	−	0.944831i
$256$		0			0
$257$	−505145.	−	1.55468e6i	−0.477071	−	1.46827i	−0.843144	−	0.537687i	$-0.819298\pi$
$257$	−505145.	−	1.55468e6i	−0.477071	−	1.46827i	0.366073	−	0.930586i	$-0.380702\pi$
$258$		0			0
$259$	−227899.	+	701402.i	−0.211103	+	0.649707i
$260$		0			0
$261$	1.79368e6	+	1.30319e6i	1.62984	+	1.18415i
$262$		0			0
$263$	1.13975e6	+	828078.i	1.01606	+	0.738214i	0.965472	−	0.260506i	$-0.0838893\pi$
$263$	1.13975e6	+	828078.i	1.01606	+	0.738214i	0.0505915	+	0.998719i	$0.483889\pi$
$264$		0			0
$265$	−159949.	−	492274.i	−0.139916	−	0.430618i
$266$		0			0
$267$	−720804.	+	523695.i	−0.618784	+	0.449573i
$268$		0			0
$269$	421106.	−	305951.i	0.354822	−	0.257793i	−0.396067	−	0.918222i	$-0.629625\pi$
$269$	421106.	−	305951.i	0.354822	−	0.257793i	0.750889	+	0.660428i	$0.229625\pi$
$270$		0			0
$271$	154785.	+	476378.i	0.128028	+	0.394030i	0.994441	−	0.105299i	$-0.0335800\pi$
$271$	154785.	+	476378.i	0.128028	+	0.394030i	−0.866413	+	0.499329i	$0.833580\pi$
$272$		0			0
$273$	3.40518e6			2.76524
$274$		0			0
$275$	−129364.	+	398142.i	−0.103153	+	0.317473i
$276$		0			0
$277$	20780.8	−	15098.1i	0.0162728	−	0.0118229i	−0.579619	−	0.814888i	$-0.696799\pi$
$277$	20780.8	−	15098.1i	0.0162728	−	0.0118229i	0.595892	+	0.803065i	$0.296799\pi$
$278$		0			0
$279$	2.27013e6	+	1.19856e6i	1.74598	+	0.921827i
$280$		0			0
$281$	−475825.	+	345707.i	−0.359486	+	0.261182i	−0.752837	−	0.658206i	$-0.771315\pi$
$281$	−475825.	+	345707.i	−0.359486	+	0.261182i	0.393352	+	0.919388i	$0.371315\pi$
$282$		0			0
$283$	−295083.	+	908173.i	−0.219017	+	0.674066i	0.779827	+	0.625996i	$0.215307\pi$
$283$	−295083.	+	908173.i	−0.219017	+	0.674066i	−0.998844	+	0.0480704i	$0.984693\pi$
$284$		0			0
$285$	−2.15162e6			−1.56911
$286$		0			0
$287$	532166.	+	1.63784e6i	0.381367	+	1.17373i
$288$		0			0
$289$	−523518.	+	380358.i	−0.368712	+	0.267885i
$290$		0			0
$291$	−2.33817e6	+	1.69878e6i	−1.61862	+	1.17599i
$292$		0			0
$293$	393034.	+	1.20963e6i	0.267461	+	0.823161i	0.991116	+	0.132999i	$0.0424608\pi$
$293$	393034.	+	1.20963e6i	0.267461	+	0.823161i	−0.723655	+	0.690162i	$0.757539\pi$
$294$		0			0
$295$	781370.	+	567699.i	0.522759	+	0.379807i
$296$		0			0
$297$	−893567.	−	649214.i	−0.587809	−	0.427068i
$298$		0			0
$299$	597793.	−	1.83982e6i	0.386699	−	1.19014i
$300$		0			0
$301$	−85651.6	−	263609.i	−0.0544903	−	0.167704i
$302$		0			0
$303$	1.42997e6	−	4.40098e6i	0.894786	−	2.75387i
$304$		0			0
$305$	−937067.			−0.576794
$306$		0			0
$307$	1.22837e6	+	892465.i	0.743848	+	0.540437i	0.893914	−	0.448239i	$-0.147949\pi$
$307$	1.22837e6	+	892465.i	0.743848	+	0.540437i	−0.150066	+	0.988676i	$0.547949\pi$
$308$		0			0
$309$	−1.74060e6			−1.03706
$310$		0			0
$311$	838425.			0.491545			0.245773	−	0.969328i	$-0.420958\pi$
$311$	838425.			0.491545			0.245773	+	0.969328i	$0.420958\pi$
$312$		0			0
$313$	−2.19212e6	−	1.59267e6i	−1.26474	−	0.918891i	−0.265764	−	0.964038i	$-0.585624\pi$
$313$	−2.19212e6	−	1.59267e6i	−1.26474	−	0.918891i	−0.998980	+	0.0451474i	$0.985624\pi$
$314$		0			0
$315$	1.91766e6			1.08892
$316$		0			0
$317$	−664445.	+	2.04495e6i	−0.371373	+	1.14297i	0.574519	+	0.818491i	$0.305189\pi$
$317$	−664445.	+	2.04495e6i	−0.371373	+	1.14297i	−0.945893	+	0.324479i	$0.894811\pi$
$318$		0			0
$319$	−247775.	−	762574.i	−0.136327	−	0.419571i
$320$		0			0
$321$	1.55961e6	−	4.79997e6i	0.844797	−	2.60002i
$322$		0			0
$323$	3.48784e6	+	2.53406e6i	1.86016	+	1.35149i
$324$		0			0
$325$	−1.65081e6	−	1.19938e6i	−0.866940	−	0.629869i
$326$		0			0
$327$	−277874.	−	855207.i	−0.143707	−	0.442285i
$328$		0			0
$329$	−1.92617e6	+	1.39945e6i	−0.981083	+	0.712799i
$330$		0			0
$331$	−825552.	+	599799.i	−0.414166	+	0.300909i	−0.775286	−	0.631610i	$-0.782394\pi$
$331$	−825552.	+	599799.i	−0.414166	+	0.300909i	0.361120	+	0.932519i	$0.382394\pi$
$332$		0			0
$333$	730096.	+	2.24701e6i	0.360802	+	1.11044i
$334$		0			0
$335$	227676.			0.110842
$336$		0			0
$337$	−1.08433e6	+	3.33724e6i	−0.520102	+	1.60071i	0.253702	+	0.967282i	$0.418352\pi$
$337$	−1.08433e6	+	3.33724e6i	−0.520102	+	1.60071i	−0.773803	+	0.633426i	$0.781648\pi$
$338$		0			0
$339$	2.76305e6	−	2.00747e6i	1.30584	−	0.948746i
$340$		0			0
$341$	−409415.	−	833241.i	−0.190668	−	0.388047i
$342$		0			0
$343$	−1.35521e6	+	984616.i	−0.621971	+	0.451889i
$344$		0			0
$345$	507163.	−	1.56089e6i	0.229403	−	0.706031i
$346$		0			0
$347$	4.38790e6			1.95629			0.978145	−	0.207923i	$-0.0666704\pi$
$347$	4.38790e6			1.95629			0.978145	+	0.207923i	$0.0666704\pi$
$348$		0			0
$349$	−962993.	−	2.96379e6i	−0.423214	−	1.30252i	−0.904694	−	0.426061i	$-0.859901\pi$
$349$	−962993.	−	2.96379e6i	−0.423214	−	1.30252i	0.481481	−	0.876457i	$-0.340099\pi$
$350$		0			0
$351$	4.35547e6	−	3.16444e6i	1.88698	−	1.37097i
$352$		0			0
$353$	1.15223e6	−	837143.i	0.492155	−	0.357571i	−0.313858	−	0.949470i	$-0.601621\pi$
$353$	1.15223e6	−	837143.i	0.492155	−	0.357571i	0.806012	+	0.591899i	$0.201621\pi$
$354$		0			0
$355$	376469.	+	1.15865e6i	0.158547	+	0.487958i
$356$		0			0
$357$	−4.68305e6	−	3.40243e6i	−1.94472	−	1.41292i
$358$		0			0
$359$	−121674.	−	88401.4i	−0.0498267	−	0.0362012i	0.562593	−	0.826734i	$-0.309804\pi$
$359$	−121674.	−	88401.4i	−0.0498267	−	0.0362012i	−0.612420	+	0.790533i	$0.709804\pi$
$360$		0			0
$361$	2.01358e6	−	6.19718e6i	0.813209	−	2.50280i
$362$		0			0
$363$	−1.08786e6	−	3.34809e6i	−0.433318	−	1.33362i
$364$		0			0
$365$	−201055.	+	618784.i	−0.0789919	+	0.243112i
$366$		0			0
$367$	102384.			0.0396794			0.0198397	−	0.999803i	$-0.493684\pi$
$367$	102384.			0.0396794			0.0198397	+	0.999803i	$0.493684\pi$
$368$		0			0
$369$	4.46334e6	+	3.24281e6i	1.70645	+	1.23981i
$370$		0			0
$371$	−2.90451e6			−1.09557
$372$		0			0
$373$	−4.23392e6			−1.57569			−0.787844	−	0.615875i	$-0.788803\pi$
$373$	−4.23392e6			−1.57569			−0.787844	+	0.615875i	$0.788803\pi$
$374$		0			0
$375$	−3.21454e6	−	2.33550e6i	−1.18043	−	0.857635i
$376$		0			0
$377$	3.90826e6			1.41622
$378$		0			0
$379$	757954.	−	2.33274e6i	0.271047	−	0.834197i	−0.719191	−	0.694812i	$-0.755487\pi$
$379$	757954.	−	2.33274e6i	0.271047	−	0.834197i	0.990238	−	0.139385i	$-0.0445125\pi$
$380$		0			0
$381$	−1.32905e6	−	4.09038e6i	−0.469059	−	1.44362i
$382$		0			0
$383$	513463.	−	1.58028e6i	0.178859	−	0.550473i	−0.820929	−	0.571030i	$-0.806544\pi$
$383$	513463.	−	1.58028e6i	0.178859	−	0.550473i	0.999789	+	0.0205572i	$0.00654402\pi$
$384$		0			0
$385$	−561070.	−	407641.i	−0.192915	−	0.140161i
$386$		0			0
$387$	−718370.	−	521926.i	−0.243821	−	0.177146i
$388$		0			0
$389$	436955.	+	1.34481e6i	0.146407	+	0.450595i	0.997189	−	0.0749237i	$-0.0238713\pi$
$389$	436955.	+	1.34481e6i	0.146407	+	0.450595i	−0.850782	+	0.525519i	$0.823871\pi$
$390$		0			0
$391$	−2.66046e6	+	1.93294e6i	−0.880066	+	0.639405i
$392$		0			0
$393$	−6.78204e6	+	4.92744e6i	−2.21503	+	1.60931i
$394$		0			0
$395$	378966.	+	1.16634e6i	0.122210	+	0.376124i
$396$		0			0
$397$	5.73602e6			1.82656			0.913281	−	0.407330i	$-0.133540\pi$
$397$	5.73602e6			1.82656			0.913281	+	0.407330i	$0.133540\pi$
$398$		0			0
$399$	−3.73096e6	+	1.14827e7i	−1.17324	+	3.61087i
$400$		0			0
$401$	4.29975e6	−	3.12395e6i	1.33531	−	0.970159i	0.335707	−	0.941967i	$-0.391025\pi$
$401$	4.29975e6	−	3.12395e6i	1.33531	−	0.970159i	0.999603	−	0.0281924i	$-0.00897512\pi$
$402$		0			0
$403$	4.47932e6	−	642871.i	1.37388	−	0.197179i
$404$		0			0
$405$	1.17786e6	−	855764.i	0.356825	−	0.259249i
$406$		0			0
$407$	264039.	−	812627.i	0.0790099	−	0.243167i
$408$		0			0
$409$	−1.97200e6			−0.582906			−0.291453	−	0.956585i	$-0.594139\pi$
$409$	−1.97200e6			−0.582906			−0.291453	+	0.956585i	$0.594139\pi$
$410$		0			0
$411$	1.55838e6	+	4.79619e6i	0.455059	+	1.40053i
$412$		0			0
$413$	4.38460e6	−	3.18560e6i	1.26490	−	0.919001i
$414$		0			0
$415$	−1.54176e6	+	1.12015e6i	−0.439436	+	0.319269i
$416$		0			0
$417$	1.26094e6	+	3.88078e6i	0.355103	+	1.09290i
$418$		0			0
$419$	−1.98969e6	−	1.44560e6i	−0.553670	−	0.402265i	0.275467	−	0.961311i	$-0.411168\pi$
$419$	−1.98969e6	−	1.44560e6i	−0.553670	−	0.402265i	−0.829137	+	0.559046i	$0.811168\pi$
$420$		0			0
$421$	355801.	+	258504.i	0.0978366	+	0.0710824i	0.635628	−	0.771995i	$-0.280741\pi$
$421$	355801.	+	258504.i	0.0978366	+	0.0710824i	−0.537791	+	0.843078i	$0.680741\pi$
$422$		0			0
$423$	−2.35699e6	+	7.25407e6i	−0.640481	+	1.97120i
$424$		0			0
$425$	1.07190e6	+	3.29896e6i	0.287859	+	0.885940i
$426$		0			0
$427$	−1.62490e6	+	5.00092e6i	−0.431277	+	1.32733i
$428$		0			0
$429$	−3.94516e6			−1.03496
$430$		0			0
$431$	−4.78481e6	−	3.47637e6i	−1.24071	−	0.901430i	−0.243067	−	0.970010i	$-0.578153\pi$
$431$	−4.78481e6	−	3.47637e6i	−1.24071	−	0.901430i	−0.997646	+	0.0685791i	$0.978153\pi$
$432$		0			0
$433$	−3.30384e6			−0.846837			−0.423418	−	0.905934i	$-0.639170\pi$
$433$	−3.30384e6			−0.846837			−0.423418	+	0.905934i	$0.639170\pi$
$434$		0			0
$435$	3.31574e6			0.840151
$436$		0			0
$437$	5.54912e6	+	4.03167e6i	1.39002	+	1.00991i
$438$		0			0
$439$	6.25526e6			1.54912			0.774558	−	0.632503i	$-0.217972\pi$
$439$	6.25526e6			1.54912			0.774558	+	0.632503i	$0.217972\pi$
$440$		0			0
$441$	833478.	−	2.56518e6i	0.204079	−	0.628089i
$442$		0			0
$443$	514049.	+	1.58208e6i	0.124450	+	0.383018i	0.993801	−	0.111178i	$-0.0354624\pi$
$443$	514049.	+	1.58208e6i	0.124450	+	0.383018i	−0.869350	+	0.494196i	$0.835462\pi$
$444$		0			0
$445$	−273319.	+	841189.i	−0.0654289	+	0.201369i
$446$		0			0
$447$	2.55630e6	+	1.85726e6i	0.605122	+	0.439647i
$448$		0			0
$449$	−5.81564e6	−	4.22531e6i	−1.36139	−	0.989106i	−0.998355	−	0.0573292i	$-0.981742\pi$
$449$	−5.81564e6	−	4.22531e6i	−1.36139	−	0.989106i	−0.363032	−	0.931777i	$-0.618258\pi$
$450$		0			0
$451$	−616555.	−	1.89756e6i	−0.142735	−	0.439293i
$452$		0			0
$453$	−1.04890e7	+	7.62073e6i	−2.40154	+	1.74482i
$454$		0			0
$455$	2.73480e6	−	1.98695e6i	0.619294	−	0.449943i
$456$		0			0
$457$	2.15900e6	+	6.64473e6i	0.483574	+	1.48829i	0.834036	+	0.551710i	$0.186024\pi$
$457$	2.15900e6	+	6.64473e6i	0.483574	+	1.48829i	−0.350463	+	0.936577i	$0.613976\pi$
$458$		0			0
$459$	−9.15184e6			−2.02757
$460$		0			0
$461$	1.96508e6	−	6.04790e6i	0.430654	−	1.32542i	−0.466822	−	0.884351i	$-0.654601\pi$
$461$	1.96508e6	−	6.04790e6i	0.430654	−	1.32542i	0.897476	−	0.441064i	$-0.145399\pi$
$462$		0			0
$463$	−615022.	+	446840.i	−0.133333	+	0.0968722i	−0.652453	−	0.757829i	$-0.726260\pi$
$463$	−615022.	+	446840.i	−0.133333	+	0.0968722i	0.519120	+	0.854702i	$0.326260\pi$
$464$		0			0
$465$	3.80022e6	−	545407.i	0.815035	−	0.116974i
$466$		0			0
$467$	1.07875e6	−	783755.i	0.228890	−	0.166298i	−0.467429	−	0.884031i	$-0.654820\pi$
$467$	1.07875e6	−	783755.i	0.228890	−	0.166298i	0.696319	+	0.717732i	$0.254820\pi$
$468$		0			0
$469$	394796.	−	1.21506e6i	0.0828782	−	0.255073i
$470$		0			0
$471$	−9.85774e6			−2.04750
$472$		0			0
$473$	99233.9	+	305411.i	0.0203942	+	0.0627670i
$474$		0			0
$475$	5.85322e6	−	4.25261e6i	1.19031	−	0.864812i
$476$		0			0
$477$	−7.52780e6	+	5.46927e6i	−1.51486	+	1.10061i
$478$		0			0
$479$	2.25445e6	+	6.93847e6i	0.448953	+	1.38174i	0.878090	+	0.478496i	$0.158818\pi$
$479$	2.25445e6	+	6.93847e6i	0.448953	+	1.38174i	−0.429137	+	0.903240i	$0.641182\pi$
$480$		0			0
$481$	3.36939e6	+	2.44800e6i	0.664031	+	0.482447i
$482$		0			0
$483$	−7.45068e6	−	5.41323e6i	−1.45321	−	1.05582i
$484$		0			0
$485$	−886602.	+	2.72868e6i	−0.171149	+	0.526742i
$486$		0			0
$487$	2.02370e6	+	6.22832e6i	0.386656	+	1.19000i	0.935272	+	0.353930i	$0.115155\pi$
$487$	2.02370e6	+	6.22832e6i	0.386656	+	1.19000i	−0.548616	+	0.836074i	$0.684845\pi$
$488$		0			0
$489$	5.32476e6	−	1.63879e7i	1.00700	−	3.09921i
$490$		0			0
$491$	5.94893e6			1.11362			0.556808	−	0.830642i	$-0.312026\pi$
$491$	5.94893e6			1.11362			0.556808	+	0.830642i	$0.312026\pi$
$492$		0			0
$493$	−5.37492e6	−	3.90511e6i	−0.995990	−	0.723629i
$494$		0			0
$495$	−2.22176e6			−0.407552
$496$		0			0
$497$	6.83628e6			1.24145
$498$		0			0
$499$	−6.42970e6	−	4.67145e6i	−1.15595	−	0.839847i	−0.166689	−	0.986009i	$-0.553308\pi$
$499$	−6.42970e6	−	4.67145e6i	−1.15595	−	0.839847i	−0.989261	+	0.146163i	$0.953308\pi$
$500$		0			0
$501$	−2.27770e6			−0.405418
$502$		0			0
$503$	1.71561e6	−	5.28009e6i	0.302341	−	0.930511i	−0.678315	−	0.734771i	$-0.737289\pi$
$503$	1.71561e6	−	5.28009e6i	0.302341	−	0.930511i	0.980656	−	0.195739i	$-0.0627106\pi$
$504$		0			0
$505$	−1.41956e6	−	4.36895e6i	−0.247699	−	0.762340i
$506$		0			0
$507$	2.85769e6	−	8.79507e6i	0.493737	−	1.51957i
$508$		0			0
$509$	−462236.	−	335834.i	−0.0790804	−	0.0574553i	0.547543	−	0.836778i	$-0.315563\pi$
$509$	−462236.	−	335834.i	−0.0790804	−	0.0574553i	−0.626623	+	0.779323i	$0.715563\pi$
$510$		0			0
$511$	2.95368e6	+	2.14597e6i	0.500393	+	0.363557i
$512$		0			0
$513$	5.89872e6	+	1.81544e7i	0.989610	+	3.04571i
$514$		0			0
$515$	−1.39793e6	+	1.01565e6i	−0.232256	+	0.168744i
$516$		0			0
$517$	2.23162e6	−	1.62137e6i	0.367193	−	0.266781i
$518$		0			0
$519$	1.87381e6	+	5.76700e6i	0.305357	+	0.939792i
$520$		0			0
$521$	−2.71739e6			−0.438590			−0.219295	−	0.975659i	$-0.570376\pi$
$521$	−2.71739e6			−0.438590			−0.219295	+	0.975659i	$0.570376\pi$
$522$		0			0
$523$	−1.29608e6	+	3.98892e6i	−0.207194	+	0.637678i	0.792422	+	0.609973i	$0.208820\pi$
$523$	−1.29608e6	+	3.98892e6i	−0.207194	+	0.637678i	−0.999616	+	0.0277047i	$0.991180\pi$
$524$		0			0
$525$	−7.85899e6	+	5.70989e6i	−1.24442	+	0.904127i
$526$		0			0
$527$	−6.80264e6	−	3.59159e6i	−1.06697	−	0.563326i
$528$		0			0
$529$	974346.	−	707904.i	0.151382	−	0.109985i
$530$		0			0
$531$	5.36527e6	−	1.65126e7i	0.825763	−	2.54144i
$532$		0			0
$533$	9.72518e6			1.48279
$534$		0			0
$535$	−1.54825e6	−	4.76504e6i	−0.233861	−	0.719750i
$536$		0			0
$537$	−573357.	+	416568.i	−0.0858003	+	0.0623376i
$538$		0			0
$539$	−789145.	+	573347.i	−0.117000	+	0.0850053i
$540$		0			0
$541$	−3.24332e6	−	9.98190e6i	−0.476427	−	1.46629i	−0.844024	−	0.536306i	$-0.819819\pi$
$541$	−3.24332e6	−	9.98190e6i	−0.476427	−	1.46629i	0.367597	−	0.929985i	$-0.380181\pi$
$542$		0			0
$543$	1.57150e6	+	1.14176e6i	0.228726	+	0.166179i
$544$		0			0
$545$	−722188.	−	524700.i	−0.104150	−	0.0756693i
$546$		0			0
$547$	−1.14384e6	+	3.52039e6i	−0.163455	+	0.503063i	−0.998919	−	0.0464820i	$-0.985199\pi$
$547$	−1.14384e6	+	3.52039e6i	−0.163455	+	0.503063i	0.835464	+	0.549545i	$0.185199\pi$
$548$		0			0
$549$	5.20551e6	+	1.60209e7i	0.737110	+	2.26859i
$550$		0			0
$551$	−4.28217e6	+	1.31792e7i	−0.600876	+	1.84931i
$552$		0			0
$553$	6.88162e6			0.956924
$554$		0			0
$555$	2.85856e6	+	2.07687e6i	0.393926	+	0.286204i
$556$		0			0
$557$	−1.01944e7			−1.39226			−0.696132	−	0.717913i	$-0.745097\pi$
$557$	−1.01944e7			−1.39226			−0.696132	+	0.717913i	$0.745097\pi$
$558$		0			0
$559$	−1.56526e6			−0.211864
$560$		0			0
$561$	5.42567e6	+	3.94198e6i	0.727857	+	0.528819i
$562$		0			0
$563$	3.31607e6			0.440913			0.220457	−	0.975397i	$-0.429245\pi$
$563$	3.31607e6			0.440913			0.220457	+	0.975397i	$0.429245\pi$
$564$		0			0
$565$	1.04771e6	−	3.22451e6i	0.138076	−	0.424955i
$566$		0			0
$567$	−2.52459e6	−	7.76989e6i	−0.329787	−	1.01498i
$568$		0			0
$569$	1.69736e6	−	5.22394e6i	0.219783	−	0.676422i	−0.778997	−	0.627028i	$-0.784271\pi$
$569$	1.69736e6	−	5.22394e6i	0.219783	−	0.676422i	0.998779	−	0.0493936i	$-0.0157289\pi$
$570$		0			0
$571$	161411.	+	117272.i	0.0207178	+	0.0150523i	0.598096	−	0.801424i	$-0.295924\pi$
$571$	161411.	+	117272.i	0.0207178	+	0.0150523i	−0.577378	+	0.816477i	$0.695924\pi$
$572$		0			0
$573$	−3.17968e6	−	2.31017e6i	−0.404572	−	0.293939i
$574$		0			0
$575$	1.70538e6	+	5.24861e6i	0.215105	+	0.662025i
$576$		0			0
$577$	6.93626e6	−	5.03949e6i	0.867333	−	0.630154i	−0.0625371	−	0.998043i	$-0.519919\pi$
$577$	6.93626e6	−	5.03949e6i	0.867333	−	0.630154i	0.929870	+	0.367888i	$0.119919\pi$
$578$		0			0
$579$	6.29621e6	−	4.57447e6i	0.780518	−	0.567080i
$580$		0			0
$581$	3.30456e6	+	1.01704e7i	0.406138	+	1.24996i
$582$		0			0
$583$	3.36510e6			0.410040
$584$		0			0
$585$	3.34647e6	−	1.02994e7i	0.404294	−	1.24429i
$586$		0			0
$587$	−1.99734e6	+	1.45115e6i	−0.239252	+	0.173827i	−0.700950	−	0.713210i	$-0.747240\pi$
$587$	−1.99734e6	+	1.45115e6i	−0.239252	+	0.173827i	0.461698	+	0.887037i	$0.347240\pi$
$588$		0			0
$589$	−2.74002e6	+	1.58092e7i	−0.325436	+	1.87768i
$590$		0			0
$591$	−8.38350e6	+	6.09097e6i	−0.987317	+	0.717328i
$592$		0			0
$593$	1.67007e6	−	5.13993e6i	0.195028	−	0.600234i	−0.804948	−	0.593345i	$-0.797807\pi$
$593$	1.67007e6	−	5.13993e6i	0.195028	−	0.600234i	0.999976	−	0.00688944i	$-0.00219299\pi$
$594$		0			0
$595$	−5.74643e6			−0.665435
$596$		0			0
$597$	95984.6	+	295410.i	0.0110221	+	0.0339227i
$598$		0			0
$599$	1.08924e7	−	7.91381e6i	1.24039	−	0.901195i	0.242764	−	0.970085i	$-0.421946\pi$
$599$	1.08924e7	−	7.91381e6i	1.24039	−	0.901195i	0.997624	+	0.0688909i	$0.0219460\pi$
$600$		0			0
$601$	6.80663e6	−	4.94531e6i	0.768681	−	0.558479i	−0.132880	−	0.991132i	$-0.542422\pi$
$601$	6.80663e6	−	4.94531e6i	0.768681	−	0.558479i	0.901561	+	0.432653i	$0.142422\pi$
$602$		0			0
$603$	−1.26476e6	−	3.89254e6i	−0.141650	−	0.435953i
$604$		0			0
$605$	−2.82733e6	−	2.05417e6i	−0.314042	−	0.228165i
$606$		0			0
$607$	−1.09299e7	−	7.94102e6i	−1.20405	−	0.874792i	−0.209371	−	0.977836i	$-0.567142\pi$
$607$	−1.09299e7	−	7.94102e6i	−1.20405	−	0.874792i	−0.994677	+	0.103045i	$0.967142\pi$
$608$		0			0
$609$	5.74957e6	−	1.76954e7i	0.628192	−	1.93338i
$610$		0			0
$611$	4.15483e6	+	1.27872e7i	0.450246	+	1.38572i
$612$		0			0
$613$	−313982.	+	966338.i	−0.0337484	+	0.103867i	−0.966512	−	0.256622i	$-0.917390\pi$
$613$	−313982.	+	966338.i	−0.0337484	+	0.103867i	0.932763	+	0.360489i	$0.117390\pi$
$614$		0			0
$615$	8.25077e6			0.879643
$616$		0			0
$617$	−1.14704e7	−	8.33372e6i	−1.21301	−	0.881305i	−0.217511	−	0.976058i	$-0.569794\pi$
$617$	−1.14704e7	−	8.33372e6i	−1.21301	−	0.881305i	−0.995501	+	0.0947527i	$0.969794\pi$
$618$		0			0
$619$	5.12797e6			0.537922			0.268961	−	0.963151i	$-0.413320\pi$
$619$	5.12797e6			0.537922			0.268961	+	0.963151i	$0.413320\pi$
$620$		0			0
$621$	−1.45605e7			−1.51512
$622$		0			0
$623$	4.01530e6	+	2.91728e6i	0.414474	+	0.301133i
$624$		0			0
$625$	3.59523e6			0.368152
$626$		0			0
$627$	4.32260e6	−	1.33036e7i	0.439113	−	1.35145i
$628$		0			0
$629$	−2.18779e6	−	6.73334e6i	−0.220485	−	0.678584i
$630$		0			0
$631$	935703.	−	2.87980e6i	0.0935544	−	0.287931i	−0.893320	−	0.449422i	$-0.851630\pi$
$631$	935703.	−	2.87980e6i	0.0935544	−	0.287931i	0.986874	+	0.161491i	$0.0516301\pi$
$632$		0			0
$633$	1.32762e6	+	964574.i	0.131694	+	0.0956811i
$634$		0			0
$635$	−3.45416e6	−	2.50960e6i	−0.339945	−	0.246984i
$636$		0			0
$637$	−1.46923e6	−	4.52182e6i	−0.143463	−	0.441535i
$638$		0			0
$639$	1.77180e7	−	1.28729e7i	1.71657	−	1.24716i
$640$		0			0
$641$	1.79066e6	−	1.30099e6i	0.172134	−	0.125063i	−0.498382	−	0.866957i	$-0.666072\pi$
$641$	1.79066e6	−	1.30099e6i	0.172134	−	0.125063i	0.670517	+	0.741894i	$0.266072\pi$
$642$		0			0
$643$	−2.13532e6	−	6.57183e6i	−0.203674	−	0.626843i	−0.999765	−	0.0216669i	$-0.993103\pi$
$643$	−2.13532e6	−	6.57183e6i	−0.203674	−	0.626843i	0.796092	−	0.605176i	$-0.206897\pi$
$644$		0			0
$645$	−1.32795e6			−0.125685
$646$		0			0
$647$	4.52020e6	−	1.39117e7i	0.424519	−	1.30653i	−0.478936	−	0.877850i	$-0.658977\pi$
$647$	4.52020e6	−	1.39117e7i	0.424519	−	1.30653i	0.903454	−	0.428684i	$-0.141023\pi$
$648$		0			0
$649$	−5.07989e6	+	3.69076e6i	−0.473416	+	0.343957i
$650$		0			0
$651$	3.67896e6	−	2.12267e7i	0.340230	−	1.96304i
$652$		0			0
$653$	−1.47422e7	+	1.07108e7i	−1.35294	+	0.982968i	−0.354080	+	0.935215i	$0.615206\pi$
$653$	−1.47422e7	+	1.07108e7i	−1.35294	+	0.982968i	−0.998859	+	0.0477522i	$0.984794\pi$
$654$		0			0
$655$	−2.57165e6	+	7.91474e6i	−0.234212	+	0.720831i
$656$		0			0
$657$	1.16961e7			1.05713
$658$		0			0
$659$	−2.18466e6	−	6.72370e6i	−0.195962	−	0.603108i	−0.999964	−	0.00848169i	$-0.997300\pi$
$659$	−2.18466e6	−	6.72370e6i	−0.195962	−	0.603108i	0.804002	−	0.594626i	$-0.202700\pi$
$660$		0			0
$661$	−5.58119e6	+	4.05497e6i	−0.496848	+	0.360981i	−0.807812	−	0.589441i	$-0.799348\pi$
$661$	−5.58119e6	+	4.05497e6i	−0.496848	+	0.360981i	0.310964	+	0.950422i	$0.399348\pi$
$662$		0			0
$663$	−2.64461e7	+	1.92142e7i	−2.33656	+	1.69761i
$664$		0			0
$665$	3.70380e6	+	1.13991e7i	0.324783	+	0.999580i
$666$		0			0
$667$	−8.55144e6	−	6.21299e6i	−0.744260	−	0.540737i
$668$		0			0
$669$	2.33906e7	+	1.69942e7i	2.02058	+	1.46803i
$670$		0			0
$671$	1.88257e6	−	5.79394e6i	0.161415	−	0.496784i
$672$		0			0
$673$	−3.56696e6	−	1.09780e7i	−0.303571	−	0.934295i	−0.980207	−	0.197977i	$-0.936563\pi$
$673$	−3.56696e6	−	1.09780e7i	−0.303571	−	0.934295i	0.676636	−	0.736318i	$-0.263437\pi$
$674$		0			0
$675$	−4.74602e6	+	1.46067e7i	−0.400931	+	1.23394i
$676$		0			0
$677$	5.20391e6			0.436373			0.218187	−	0.975907i	$-0.429986\pi$
$677$	5.20391e6			0.436373			0.218187	+	0.975907i	$0.429986\pi$
$678$		0			0
$679$	1.30250e7	+	9.46320e6i	1.08418	+	0.787705i
$680$		0			0
$681$	−8.11362e6			−0.670420
$682$		0			0
$683$	8.17958e6			0.670933			0.335467	−	0.942052i	$-0.391106\pi$
$683$	8.17958e6			0.670933			0.335467	+	0.942052i	$0.391106\pi$
$684$		0			0
$685$	4.05019e6	+	2.94263e6i	0.329798	+	0.239613i
$686$		0			0
$687$	−2.73528e6			−0.221110
$688$		0			0
$689$	−5.06861e6	+	1.55996e7i	−0.406762	+	1.25188i
$690$		0			0
$691$	6.82672e6	+	2.10105e7i	0.543898	+	1.67395i	0.723596	+	0.690223i	$0.242488\pi$
$691$	6.82672e6	+	2.10105e7i	0.543898	+	1.67395i	−0.179699	+	0.983722i	$0.557512\pi$
$692$		0			0
$693$	−3.85258e6	+	1.18570e7i	−0.304732	+	0.937870i
$694$		0			0
$695$	3.27716e6	+	2.38100e6i	0.257357	+	0.186981i
$696$		0			0
$697$	−1.33748e7	−	9.71734e6i	−1.04281	−	0.757644i
$698$		0			0
$699$	−7.01167e6	−	2.15797e7i	−0.542786	−	1.67052i
$700$		0			0
$701$	5.31409e6	−	3.86092e6i	0.408446	−	0.296753i	−0.364527	−	0.931193i	$-0.618769\pi$
$701$	5.31409e6	−	3.86092e6i	0.408446	−	0.296753i	0.772972	+	0.634440i	$0.218769\pi$
$702$		0			0
$703$	−1.19467e7	+	8.67980e6i	−0.911717	+	0.662401i
$704$		0			0
$705$	3.52492e6	+	1.08486e7i	0.267102	+	0.822055i
$706$		0			0
$707$	−2.57777e7			−1.93952
$708$		0			0
$709$	−5.54476e6	+	1.70650e7i	−0.414255	+	1.27494i	0.498661	+	0.866797i	$0.333825\pi$
$709$	−5.54476e6	+	1.70650e7i	−0.414255	+	1.27494i	−0.912916	+	0.408148i	$0.866175\pi$
$710$		0			0
$711$	1.78355e7	−	1.29582e7i	1.32316	−	0.961329i
$712$		0			0
$713$	−1.08229e7	−	5.71417e6i	−0.797298	−	0.420949i
$714$		0			0
$715$	−3.16847e6	+	2.30203e6i	−0.231785	+	0.168401i
$716$		0			0
$717$	1.29727e7	−	3.99258e7i	0.942392	−	2.90038i
$718$		0			0
$719$	−1.86398e7			−1.34468			−0.672342	−	0.740241i	$-0.734711\pi$
$719$	−1.86398e7			−1.34468			−0.672342	+	0.740241i	$0.734711\pi$
$720$		0			0
$721$	2.99628e6	+	9.22159e6i	0.214656	+	0.660644i
$722$		0			0
$723$	−2.40350e7	+	1.74625e7i	−1.71001	+	1.24240i
$724$		0			0
$725$	−9.02008e6	+	6.55347e6i	−0.637332	+	0.463049i
$726$		0			0
$727$	3.72319e6	+	1.14588e7i	0.261264	+	0.804087i	0.992531	+	0.121995i	$0.0389293\pi$
$727$	3.72319e6	+	1.14588e7i	0.261264	+	0.804087i	−0.731267	+	0.682091i	$0.761071\pi$
$728$		0			0
$729$	1.24701e7	+	9.06003e6i	0.869060	+	0.631409i
$730$		0			0
$731$	2.15265e6	+	1.56400e6i	0.148998	+	0.108254i
$732$		0			0
$733$	−561422.	+	1.72788e6i	−0.0385948	+	0.118783i	−0.968498	−	0.249022i	$-0.919891\pi$
$733$	−561422.	+	1.72788e6i	−0.0385948	+	0.118783i	0.929903	+	0.367805i	$0.119891\pi$
$734$		0			0
$735$	−1.24648e6	−	3.83628e6i	−0.0851075	−	0.261934i
$736$		0			0
$737$	−457401.	+	1.40773e6i	−0.0310190	+	0.0954667i
$738$		0			0
$739$	1.51132e7			1.01800			0.508998	−	0.860768i	$-0.330016\pi$
$739$	1.51132e7			1.01800			0.508998	+	0.860768i	$0.330016\pi$
$740$		0			0
$741$	5.51605e7	+	4.00764e7i	3.69048	+	2.68129i
$742$		0			0
$743$	−1.42040e7			−0.943928			−0.471964	−	0.881618i	$-0.656455\pi$
$743$	−1.42040e7			−0.943928			−0.471964	+	0.881618i	$0.656455\pi$
$744$		0			0
$745$	3.13676e6			0.207057
$746$		0			0
$747$	2.77157e7	+	2.01366e7i	1.81729	+	1.32034i
$748$		0			0
$749$	−2.81147e7			−1.83117
$750$		0			0
$751$	6.51260e6	−	2.00437e7i	0.421361	−	1.29682i	−0.485074	−	0.874473i	$-0.661207\pi$
$751$	6.51260e6	−	2.00437e7i	0.421361	−	1.29682i	0.906436	−	0.422344i	$-0.138793\pi$
$752$		0			0
$753$	1.08655e7	+	3.34407e7i	0.698336	+	2.14926i
$754$		0			0
$755$	−3.97729e6	+	1.22409e7i	−0.253934	+	0.781528i
$756$		0			0
$757$	−1.21281e7	−	8.81159e6i	−0.769225	−	0.558875i	0.132501	−	0.991183i	$-0.457699\pi$
$757$	−1.21281e7	−	8.81159e6i	−0.769225	−	0.558875i	−0.901726	+	0.432308i	$0.857699\pi$
$758$		0			0
$759$	8.63218e6	+	6.27164e6i	0.543896	+	0.395164i
$760$		0			0
$761$	−420785.	−	1.29504e6i	−0.0263389	−	0.0810629i	0.937023	−	0.349268i	$-0.113570\pi$
$761$	−420785.	−	1.29504e6i	−0.0263389	−	0.0810629i	−0.963362	+	0.268205i	$0.913570\pi$
$762$		0			0
$763$	−4.05250e6	+	2.94431e6i	−0.252006	+	0.183093i
$764$		0			0
$765$	−1.48934e7	+	1.08207e7i	−0.920110	+	0.668499i
$766$		0			0
$767$	−9.45774e6	−	2.91079e7i	−0.580496	−	1.78658i
$768$		0			0
$769$	1.74032e7			1.06124			0.530621	−	0.847609i	$-0.321959\pi$
$769$	1.74032e7			1.06124			0.530621	+	0.847609i	$0.321959\pi$
$770$		0			0
$771$	−1.35806e7	+	4.17967e7i	−0.822777	+	2.53225i
$772$		0			0
$773$	397342.	−	288686.i	0.0239175	−	0.0173771i	−0.575762	−	0.817617i	$-0.695295\pi$
$773$	397342.	−	288686.i	0.0239175	−	0.0173771i	0.599680	+	0.800240i	$0.295295\pi$
$774$		0			0
$775$	−9.26007e6	+	8.99475e6i	−0.553809	+	0.537941i
$776$		0			0
$777$	1.60406e7	−	1.16542e7i	0.953165	−	0.692515i
$778$		0			0
$779$	−1.06556e7	+	3.27946e7i	−0.629121	+	1.93623i
$780$		0			0
$781$	−7.92036e6			−0.464641
$782$		0			0
$783$	−9.09020e6	−	2.79767e7i	−0.529869	−	1.63077i
$784$		0			0
$785$	−7.91703e6	+	5.75206e6i	−0.458551	+	0.333157i
$786$		0			0
$787$	2.65583e7	−	1.92957e7i	1.52849	−	1.11051i	0.571422	−	0.820656i	$-0.306392\pi$
$787$	2.65583e7	−	1.92957e7i	1.52849	−	1.11051i	0.957070	−	0.289858i	$-0.0936080\pi$
$788$		0			0
$789$	−1.17041e7	−	3.60215e7i	−0.669337	−	2.06001i
$790$		0			0
$791$	−1.53918e7	−	1.11828e7i	−0.874676	−	0.635489i
$792$		0			0
$793$	2.40234e7	+	1.74540e7i	1.35660	+	0.985625i
$794$		0			0
$795$	−4.30017e6	+	1.32345e7i	−0.241306	+	0.742662i
$796$		0			0
$797$	−6.51026e6	−	2.00365e7i	−0.363038	−	1.11732i	−0.951200	−	0.308574i	$-0.900148\pi$
$797$	−6.51026e6	−	2.00365e7i	−0.363038	−	1.11732i	0.588162	−	0.808743i	$-0.299852\pi$
$798$		0			0
$799$	7.06291e6	−	2.17374e7i	0.391397	−	1.20459i
$800$		0			0
$801$	1.59000e7			0.875621
$802$		0			0
$803$	−3.42206e6	−	2.48627e6i	−0.187283	−	0.136069i
$804$		0			0
$805$	−9.14251e6			−0.497251
$806$		0			0
$807$	−1.39938e7			−0.756401
$808$		0			0
$809$	−2.42534e7	−	1.76211e7i	−1.30287	−	0.946592i	−0.302893	−	0.953025i	$-0.597953\pi$
$809$	−2.42534e7	−	1.76211e7i	−1.30287	−	0.946592i	−0.999979	+	0.00643228i	$0.997953\pi$
$810$		0			0
$811$	−1.62144e7			−0.865663			−0.432831	−	0.901475i	$-0.642485\pi$
$811$	−1.62144e7			−0.865663			−0.432831	+	0.901475i	$0.642485\pi$
$812$		0			0
$813$	4.16131e6	−	1.28072e7i	0.220802	−	0.679560i
$814$		0			0
$815$	−5.28600e6	−	1.62686e7i	−0.278762	−	0.857940i
$816$		0			0
$817$	1.71501e6	−	5.27825e6i	0.0898899	−	0.276653i
$818$		0			0
$819$	−4.91626e7	−	3.57188e7i	−2.56109	−	1.86074i
$820$		0			0
$821$	2.01401e7	+	1.46327e7i	1.04281	+	0.757645i	0.970832	−	0.239761i	$-0.0770692\pi$
$821$	2.01401e7	+	1.46327e7i	1.04281	+	0.757645i	0.0719768	+	0.997406i	$0.477069\pi$
$822$		0			0
$823$	7.12482e6	+	2.19280e7i	0.366669	+	1.12849i	0.948929	+	0.315489i	$0.102169\pi$
$823$	7.12482e6	+	2.19280e7i	0.366669	+	1.12849i	−0.582260	+	0.813003i	$0.697831\pi$
$824$		0			0
$825$	9.10524e6	−	6.61534e6i	0.465754	−	0.338390i
$826$		0			0
$827$	1.05678e7	−	7.67794e6i	0.537304	−	0.390374i	−0.285779	−	0.958296i	$-0.592252\pi$
$827$	1.05678e7	−	7.67794e6i	0.537304	−	0.390374i	0.823083	+	0.567922i	$0.192252\pi$
$828$		0			0
$829$	−1.08677e6	−	3.34474e6i	−0.0549227	−	0.169035i	0.919832	−	0.392312i	$-0.128325\pi$
$829$	−1.08677e6	−	3.34474e6i	−0.0549227	−	0.169035i	−0.974755	+	0.223277i	$0.928325\pi$
$830$		0			0
$831$	−690569.			−0.0346900
$832$		0			0
$833$	−2.49759e6	+	7.68678e6i	−0.124712	+	0.383824i
$834$		0			0
$835$	−1.82929e6	+	1.32906e6i	−0.0907959	+	0.0659671i
$836$		0			0
$837$	−1.50203e7	−	3.05693e7i	−0.741081	−	1.50825i
$838$		0			0
$839$	1.07481e6	−	780895.i	0.0527141	−	0.0382990i	−0.561116	−	0.827737i	$-0.689628\pi$
$839$	1.07481e6	−	780895.i	0.0527141	−	0.0382990i	0.613830	+	0.789438i	$0.289628\pi$
$840$		0			0
$841$	260725.	−	802430.i	0.0127114	−	0.0391217i
$842$		0			0
$843$	1.58122e7			0.766342
$844$		0			0
$845$	−2.83689e6	−	8.73105e6i	−0.136679	−	0.420654i
$846$		0			0
$847$	−1.58653e7	+	1.15268e7i	−0.759872	+	0.552079i
$848$		0			0
$849$	2.07693e7	−	1.50898e7i	0.988901	−	0.718479i
$850$		0			0
$851$	−3.48076e6	−	1.07127e7i	−0.164759	−	0.507077i
$852$		0			0
$853$	2.82309e7	+	2.05109e7i	1.32847	+	0.965190i	0.999785	+	0.0207507i	$0.00660563\pi$
$853$	2.82309e7	+	2.05109e7i	1.32847	+	0.965190i	0.328686	+	0.944439i	$0.393394\pi$
$854$		0			0
$855$	3.10642e7	+	2.25694e7i	1.45326	+	1.05586i
$856$		0			0
$857$	−4.83514e6	+	1.48810e7i	−0.224883	+	0.692120i	0.773420	+	0.633894i	$0.218544\pi$
$857$	−4.83514e6	+	1.48810e7i	−0.224883	+	0.692120i	−0.998303	+	0.0582260i	$0.981456\pi$
$858$		0			0
$859$	−1.16235e6	−	3.57736e6i	−0.0537472	−	0.165417i	0.920580	−	0.390555i	$-0.127717\pi$
$859$	−1.16235e6	−	3.57736e6i	−0.0537472	−	0.165417i	−0.974327	+	0.225138i	$0.927717\pi$
$860$		0			0
$861$	1.43070e7	−	4.40325e7i	0.657721	−	2.02426i
$862$		0			0
$863$	2.28727e7			1.04542			0.522710	−	0.852511i	$-0.324921\pi$
$863$	2.28727e7			1.04542			0.522710	+	0.852511i	$0.324921\pi$
$864$		0			0
$865$	4.87000e6	+	3.53826e6i	0.221304	+	0.160786i
$866$		0			0
$867$	1.73971e7			0.786011
$868$		0			0
$869$	−7.97288e6			−0.358151
$870$		0			0
$871$	−5.83687e6	−	4.24074e6i	−0.260696	−	0.189407i
$872$		0			0
$873$	5.15770e7			2.29045
$874$		0			0
$875$	−6.83982e6	+	2.10508e7i	−0.302012	+	0.929498i
$876$		0			0
$877$	4.36264e6	+	1.34268e7i	0.191536	+	0.589487i	1.00000		0.000940911i	$0.000299501\pi$
$877$	4.36264e6	+	1.34268e7i	0.191536	+	0.589487i	−0.808464	+	0.588546i	$0.799700\pi$
$878$		0			0
$879$	1.05665e7	−	3.25204e7i	0.461275	−	1.41966i
$880$		0			0
$881$	177161.	+	128715.i	0.00769002	+	0.00558713i	0.591624	−	0.806214i	$-0.298487\pi$
$881$	177161.	+	128715.i	0.00769002	+	0.00558713i	−0.583934	+	0.811801i	$0.698487\pi$
$882$		0			0
$883$	2.20677e7	+	1.60332e7i	0.952480	+	0.692018i	0.951392	−	0.307982i	$-0.0996536\pi$
$883$	2.20677e7	+	1.60332e7i	0.952480	+	0.692018i	0.00108823	+	0.999999i	$0.499654\pi$
$884$		0			0
$885$	−8.02387e6	−	2.46949e7i	−0.344370	−	1.05986i
$886$		0			0
$887$	2.99501e7	−	2.17600e7i	1.27817	−	0.928645i	0.278675	−	0.960386i	$-0.410105\pi$
$887$	2.99501e7	−	2.17600e7i	1.27817	−	0.928645i	0.999496	+	0.0317401i	$0.0101049\pi$
$888$		0			0
$889$	−1.93828e7	+	1.40824e7i	−0.822548	+	0.597616i
$890$		0			0
$891$	2.92493e6	+	9.00201e6i	0.123430	+	0.379879i
$892$		0			0
$893$	−4.76725e7			−2.00051
$894$		0			0
$895$	−217409.	+	669115.i	−0.00907234	+	0.0279218i
$896$		0			0
$897$	−4.20754e7	+	3.05696e7i	−1.74601	+	1.26855i
$898$		0			0
$899$	4.22249e6	−	2.43627e7i	0.174249	−	1.00537i
$900$		0			0
$901$	2.25577e7	−	1.63891e7i	0.925726	−	0.672580i
$902$		0			0
$903$	−2.30270e6	+	7.08699e6i	−0.0939763	+	0.289229i
$904$		0			0
$905$	1.92835e6			0.0782643
$906$		0			0
$907$	−8.23511e6	−	2.53451e7i	−0.332392	−	1.02300i	−0.967992	−	0.250980i	$-0.919247\pi$
$907$	−8.23511e6	−	2.53451e7i	−0.332392	−	1.02300i	0.635600	−	0.772019i	$-0.280753\pi$
$908$		0			0
$909$	−6.68095e7	+	4.85400e7i	−2.68181	+	1.94845i
$910$		0			0
$911$	−1.22331e7	+	8.88788e6i	−0.488361	+	0.354815i	−0.804554	−	0.593880i	$-0.797595\pi$
$911$	−1.22331e7	+	8.88788e6i	−0.488361	+	0.354815i	0.316192	+	0.948695i	$0.397595\pi$
$912$		0			0
$913$	−3.82858e6	−	1.17832e7i	−0.152006	−	0.467827i
$914$		0			0
$915$	2.03812e7	+	1.48078e7i	0.804781	+	0.584708i
$916$		0			0
$917$	3.77799e7	+	2.74487e7i	1.48367	+	1.07795i
$918$		0			0
$919$	1.22765e6	−	3.77832e6i	0.0479497	−	0.147574i	−0.924215	−	0.381873i	$-0.875279\pi$
$919$	1.22765e6	−	3.77832e6i	0.0479497	−	0.147574i	0.972165	+	0.234298i	$0.0752793\pi$
$920$		0			0
$921$	−1.26141e7	−	3.88223e7i	−0.490013	−	1.50811i
$922$		0			0
$923$	1.19299e7	−	3.67163e7i	0.460926	−	1.41858i
$924$		0			0
$925$	−1.18813e7			−0.456571
$926$		0			0
$927$	2.51301e7	+	1.82581e7i	0.960495	+	0.697840i
$928$		0			0
$929$	−1.45693e7			−0.553858			−0.276929	−	0.960890i	$-0.589317\pi$
$929$	−1.45693e7			−0.553858			−0.276929	+	0.960890i	$0.589317\pi$
$930$		0			0
$931$	1.68579e7			0.637427
$932$		0			0
$933$	−1.82358e7	−	1.32491e7i	−0.685836	−	0.498289i
$934$		0			0
$935$	6.65768e6			0.249054
$936$		0			0
$937$	1.11430e7	−	3.42945e7i	0.414622	−	1.27607i	−0.497967	−	0.867196i	$-0.665920\pi$
$937$	1.11430e7	−	3.42945e7i	0.414622	−	1.27607i	0.912589	−	0.408878i	$-0.134080\pi$
$938$		0			0
$939$	2.25108e7	+	6.92811e7i	0.833157	+	2.56419i
$940$		0			0
$941$	−1.00536e7	+	3.09419e7i	−0.370125	+	1.13913i	0.576584	+	0.817038i	$0.304385\pi$
$941$	−1.00536e7	+	3.09419e7i	−0.370125	+	1.13913i	−0.946709	+	0.322090i	$0.895615\pi$
$942$		0			0
$943$	−2.12791e7	−	1.54602e7i	−0.779245	−	0.566155i
$944$		0			0
$945$	−2.05841e7	−	1.49552e7i	−0.749813	−	0.544771i
$946$		0			0
$947$	1.43962e7	+	4.43069e7i	0.521642	+	1.60545i	0.770862	+	0.637002i	$0.219826\pi$
$947$	1.43962e7	+	4.43069e7i	0.521642	+	1.60545i	−0.249220	+	0.968447i	$0.580174\pi$
$948$		0			0
$949$	1.66800e7	−	1.21187e7i	0.601216	−	0.436809i
$950$		0			0
$951$	4.67667e7	−	3.39780e7i	1.67682	−	1.21828i
$952$		0			0
$953$	194037.	+	597185.i	0.00692074	+	0.0212999i	0.954457	−	0.298348i	$-0.0964355\pi$
$953$	194037.	+	597185.i	0.00692074	+	0.0212999i	−0.947537	+	0.319648i	$0.896435\pi$
$954$		0			0
$955$	−3.90169e6			−0.138434
$956$		0			0
$957$	−6.66132e6	+	2.05014e7i	−0.235115	+	0.723610i
$958$		0			0
$959$	2.27273e7	−	1.65123e7i	0.797997	−	0.579779i
$960$		0			0
$961$	832032.	−	2.86171e7i	0.0290624	−	0.999578i
$962$		0			0
$963$	−7.28664e7	+	5.29406e7i	−2.53199	+	1.83960i
$964$		0			0
$965$	2.38744e6	−	7.34777e6i	0.0825303	−	0.254002i
$966$		0			0
$967$	8.40862e6			0.289174			0.144587	−	0.989492i	$-0.453815\pi$
$967$	8.40862e6			0.289174			0.144587	+	0.989492i	$0.453815\pi$
$968$		0			0
$969$	−3.58165e7	−	1.10232e8i	−1.22539	−	3.77136i
$970$		0			0
$971$	−3.95646e7	+	2.87454e7i	−1.34666	+	0.978407i	−0.347492	+	0.937683i	$0.612966\pi$
$971$	−3.95646e7	+	2.87454e7i	−1.34666	+	0.978407i	−0.999170	+	0.0407242i	$0.987034\pi$
$972$		0			0
$973$	1.83895e7	−	1.33608e7i	0.622714	−	0.452428i
$974$		0			0
$975$	1.69521e7	+	5.21733e7i	0.571101	+	1.75767i
$976$		0			0
$977$	2.29871e7	+	1.67011e7i	0.770457	+	0.559770i	0.902100	−	0.431527i	$-0.142025\pi$
$977$	2.29871e7	+	1.67011e7i	0.770457	+	0.559770i	−0.131643	+	0.991297i	$0.542025\pi$
$978$		0			0
$979$	−4.65203e6	−	3.37990e6i	−0.155126	−	0.112706i
$980$		0			0
$981$	−4.95889e6	+	1.52619e7i	−0.164518	+	0.506333i
$982$		0			0
$983$	−3.46752e6	−	1.06719e7i	−0.114455	−	0.352256i	0.877378	−	0.479800i	$-0.159291\pi$
$983$	−3.46752e6	−	1.06719e7i	−0.114455	−	0.352256i	−0.991833	+	0.127544i	$0.959291\pi$
$984$		0			0
$985$	−3.17891e6	+	9.78367e6i	−0.104397	+	0.321300i
$986$		0			0
$987$	6.40089e7			2.09145
$988$		0			0
$989$	3.42485e6	+	2.48830e6i	0.111340	+	0.0808932i
$990$		0			0
$991$	1.05212e7			0.340316			0.170158	−	0.985417i	$-0.445572\pi$
$991$	1.05212e7			0.340316			0.170158	+	0.985417i	$0.445572\pi$
$992$		0			0
$993$	2.74340e7			0.882909
$994$		0			0
$995$	249462.	+	181245.i	0.00798816	+	0.00580374i
$996$		0			0
$997$	1.66018e7			0.528954			0.264477	−	0.964392i	$-0.414801\pi$
$997$	1.66018e7			0.528954			0.264477	+	0.964392i	$0.414801\pi$
$998$		0			0
$999$	9.68685e6	−	2.98131e7i	0.307092	−	0.945133i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.6.f.a.109.1	yes	56
31.2	even	5	inner	124.6.f.a.33.1	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.6.f.a.33.1	✓	56	31.2	even	5	inner
124.6.f.a.109.1	yes	56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	124.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-21.7500 - 15.8023i) q^{3} -26.6888 q^{5} +(-46.2791 + 142.432i) q^{7} +(148.259 + 456.295i) q^{9} +O(q^{10})\)	\(q+(-21.7500 - 15.8023i) q^{3} -26.6888 q^{5} +(-46.2791 + 142.432i) q^{7} +(148.259 + 456.295i) q^{9} +(53.6179 - 165.019i) q^{11} +(684.216 + 497.112i) q^{13} +(580.483 + 421.746i) q^{15} +(-444.272 - 1367.33i) q^{17} +(-2426.00 + 1762.59i) q^{19} +(3257.34 - 2366.59i) q^{21} +(-706.831 - 2175.40i) q^{23} -2412.71 q^{25} +(1967.09 - 6054.09i) q^{27} +(3738.58 - 2716.23i) q^{29} +(3838.05 - 3728.08i) q^{31} +(-3773.87 + 2741.88i) q^{33} +(1235.14 - 3801.36i) q^{35} +4924.45 q^{37} +(-7026.19 - 21624.4i) q^{39} +(9302.94 - 6758.98i) q^{41} +(-1497.30 + 1087.85i) q^{43} +(-3956.87 - 12178.0i) q^{45} +(12861.5 + 9344.46i) q^{47} +(-4548.09 - 3304.38i) q^{49} +(-11944.0 + 36759.9i) q^{51} +(5993.12 + 18444.9i) q^{53} +(-1431.00 + 4404.16i) q^{55} +80618.6 q^{57} +(-29277.0 - 21271.0i) q^{59} +35110.8 q^{61} -71852.6 q^{63} +(-18260.9 - 13267.3i) q^{65} -8530.75 q^{67} +(-19002.8 + 58484.6i) q^{69} +(-14105.9 - 43413.4i) q^{71} +(7533.30 - 23185.1i) q^{73} +(52476.4 + 38126.4i) q^{75} +(21022.6 + 15273.8i) q^{77} +(-14199.4 - 43701.3i) q^{79} +(-44133.0 + 32064.5i) q^{81} +(57767.9 - 41970.8i) q^{83} +(11857.1 + 36492.4i) q^{85} -124237. q^{87} +(10240.9 - 31518.4i) q^{89} +(-102470. + 74448.6i) q^{91} +(-142390. + 20435.8i) q^{93} +(64747.1 - 47041.5i) q^{95} +(33219.9 - 102240. i) q^{97} +83246.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9}+O(q^{10}) \) 56 * q + 2 * q^3 - 58 * q^5 + 104 * q^7 - 1234 * q^9	\( 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9} - 509 q^{11} - 117 q^{13} + 89 q^{15} - 3504 q^{17} + 262 q^{19} + 352 q^{21} - 2448 q^{23} + 49618 q^{25} + 14324 q^{27} - 9888 q^{29} - 12771 q^{31} + 27699 q^{33} + 13840 q^{35} + 76096 q^{37} + 33520 q^{39} - 4843 q^{41} - 40778 q^{43} + 56692 q^{45} + 38922 q^{47} - 17126 q^{49} - 69292 q^{51} - 41728 q^{53} - 172096 q^{55} + 57066 q^{57} - 58198 q^{59} + 176328 q^{61} - 37444 q^{63} + 143863 q^{65} + 9812 q^{67} - 9250 q^{69} - 67356 q^{71} - 63512 q^{73} - 198012 q^{75} - 74257 q^{77} + 137651 q^{79} + 196077 q^{81} + 156427 q^{83} + 238828 q^{85} - 558144 q^{87} - 99292 q^{89} - 243609 q^{91} - 325925 q^{93} - 75077 q^{95} - 476340 q^{97} + 745812 q^{99}+O(q^{100}) \) 56 * q + 2 * q^3 - 58 * q^5 + 104 * q^7 - 1234 * q^9 - 509 * q^11 - 117 * q^13 + 89 * q^15 - 3504 * q^17 + 262 * q^19 + 352 * q^21 - 2448 * q^23 + 49618 * q^25 + 14324 * q^27 - 9888 * q^29 - 12771 * q^31 + 27699 * q^33 + 13840 * q^35 + 76096 * q^37 + 33520 * q^39 - 4843 * q^41 - 40778 * q^43 + 56692 * q^45 + 38922 * q^47 - 17126 * q^49 - 69292 * q^51 - 41728 * q^53 - 172096 * q^55 + 57066 * q^57 - 58198 * q^59 + 176328 * q^61 - 37444 * q^63 + 143863 * q^65 + 9812 * q^67 - 9250 * q^69 - 67356 * q^71 - 63512 * q^73 - 198012 * q^75 - 74257 * q^77 + 137651 * q^79 + 196077 * q^81 + 156427 * q^83 + 238828 * q^85 - 558144 * q^87 - 99292 * q^89 - 243609 * q^91 - 325925 * q^93 - 75077 * q^95 - 476340 * q^97 + 745812 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more