LMFDB - Embedded newform 124.6.f.a.33.1

Newspace parameters

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

Newform invariants

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			33.1
Character	$\chi$	$=$	124.33
Dual form			124.6.f.a.109.1

$q$-expansion

$f(q)$	$=$	$q+(-21.7500 + 15.8023i) q^{3} -26.6888 q^{5} +(-46.2791 - 142.432i) q^{7} +(148.259 - 456.295i) q^{9} +O(q^{10})$	\(q+(-21.7500 + 15.8023i) q^{3} -26.6888 q^{5} +(-46.2791 - 142.432i) q^{7} +(148.259 - 456.295i) q^{9} +(53.6179 + 165.019i) q^{11} +(684.216 - 497.112i) q^{13} +(580.483 - 421.746i) q^{15} +(-444.272 + 1367.33i) q^{17} +(-2426.00 - 1762.59i) q^{19} +(3257.34 + 2366.59i) q^{21} +(-706.831 + 2175.40i) q^{23} -2412.71 q^{25} +(1967.09 + 6054.09i) q^{27} +(3738.58 + 2716.23i) q^{29} +(3838.05 + 3728.08i) q^{31} +(-3773.87 - 2741.88i) q^{33} +(1235.14 + 3801.36i) q^{35} +4924.45 q^{37} +(-7026.19 + 21624.4i) q^{39} +(9302.94 + 6758.98i) q^{41} +(-1497.30 - 1087.85i) q^{43} +(-3956.87 + 12178.0i) q^{45} +(12861.5 - 9344.46i) q^{47} +(-4548.09 + 3304.38i) q^{49} +(-11944.0 - 36759.9i) q^{51} +(5993.12 - 18444.9i) q^{53} +(-1431.00 - 4404.16i) q^{55} +80618.6 q^{57} +(-29277.0 + 21271.0i) q^{59} +35110.8 q^{61} -71852.6 q^{63} +(-18260.9 + 13267.3i) q^{65} -8530.75 q^{67} +(-19002.8 - 58484.6i) q^{69} +(-14105.9 + 43413.4i) q^{71} +(7533.30 + 23185.1i) q^{73} +(52476.4 - 38126.4i) q^{75} +(21022.6 - 15273.8i) q^{77} +(-14199.4 + 43701.3i) q^{79} +(-44133.0 - 32064.5i) q^{81} +(57767.9 + 41970.8i) q^{83} +(11857.1 - 36492.4i) q^{85} -124237. q^{87} +(10240.9 + 31518.4i) q^{89} +(-102470. - 74448.6i) q^{91} +(-142390. - 20435.8i) q^{93} +(64747.1 + 47041.5i) q^{95} +(33219.9 + 102240. i) q^{97} +83246.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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	−0.400001	+	0.916515i	$0.630990\pi$
$3$	−21.7500	+	15.8023i	−1.39527	+	1.01372i	−0.995264	+	0.0972047i	$0.969010\pi$
$4$		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	−0.954854	−	0.297074i	$-0.903989\pi$
$7$	−46.2791	−	142.432i	−0.356977	−	1.09866i	0.597878	−	0.801587i	$-0.296011\pi$
$8$		0			0
$9$	148.259	−	456.295i	0.610121	−	1.87776i
$10$		0			0
$11$	53.6179	+	165.019i	0.133607	+	0.411199i	0.995371	−	0.0961105i	$-0.0306402\pi$
$11$	53.6179	+	165.019i	0.133607	+	0.411199i	−0.861764	+	0.507309i	$0.830640\pi$
$12$		0			0
$13$	684.216	−	497.112i	1.12288	−	0.815822i	0.138240	−	0.990399i	$-0.455856\pi$
$13$	684.216	−	497.112i	1.12288	−	0.815822i	0.984644	+	0.174576i	$0.0558556\pi$
$14$		0			0
$15$	580.483	−	421.746i	0.666134	−	0.483974i
$16$		0			0
$17$	−444.272	+	1367.33i	−0.372843	+	1.14749i	0.572079	+	0.820198i	$0.306137\pi$
$17$	−444.272	+	1367.33i	−0.372843	+	1.14749i	−0.944922	+	0.327295i	$0.893863\pi$
$18$		0			0
$19$	−2426.00	−	1762.59i	−1.54172	−	1.12013i	−0.949243	−	0.314543i	$-0.898149\pi$
$19$	−2426.00	−	1762.59i	−1.54172	−	1.12013i	−0.592480	−	0.805585i	$-0.701851\pi$
$20$		0			0
$21$	3257.34	+	2366.59i	1.61181	+	1.17105i
$22$		0			0
$23$	−706.831	+	2175.40i	−0.278610	+	0.857472i	0.709632	+	0.704572i	$0.248861\pi$
$23$	−706.831	+	2175.40i	−0.278610	+	0.857472i	−0.988242	+	0.152900i	$0.951139\pi$
$24$		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	0.918279	−	0.395933i	$-0.129579\pi$
$29$	3738.58	+	2716.23i	0.825489	+	0.599753i	−0.0927907	+	0.995686i	$0.529579\pi$
$30$		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	0.929049	−	0.369956i	$-0.120627\pi$
$41$	9302.94	+	6758.98i	0.864292	+	0.627945i	−0.0647572	+	0.997901i	$0.520627\pi$
$42$		0			0
$43$	−1497.30	−	1087.85i	−0.123492	−	0.0897218i	0.524325	−	0.851518i	$-0.324318\pi$
$43$	−1497.30	−	1087.85i	−0.123492	−	0.0897218i	−0.647817	+	0.761796i	$0.724318\pi$
$44$		0			0
$45$	−3956.87	+	12178.0i	−0.291287	+	0.896488i
$46$		0			0
$47$	12861.5	−	9344.46i	0.849275	−	0.617035i	−0.0756709	−	0.997133i	$-0.524110\pi$
$47$	12861.5	−	9344.46i	0.849275	−	0.617035i	0.924946	+	0.380098i	$0.124110\pi$
$48$		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	−0.690800	−	0.723046i	$-0.742741\pi$
$53$	5993.12	−	18444.9i	0.293065	−	0.901960i	0.983865	−	0.178914i	$-0.0572585\pi$
$54$		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	−0.980230	−	0.197864i	$-0.936600\pi$
$59$	−29277.0	+	21271.0i	−1.09496	+	0.795533i	−0.114728	+	0.993397i	$0.536600\pi$
$60$		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	0.636050	+	0.771648i	$0.280567\pi$
$71$	−14105.9	+	43413.4i	−0.332089	+	1.02206i	−0.968138	+	0.250416i	$0.919433\pi$
$72$		0			0
$73$	7533.30	+	23185.1i	0.165454	+	0.509216i	0.999069	−	0.0431296i	$-0.0137328\pi$
$73$	7533.30	+	23185.1i	0.165454	+	0.509216i	−0.833615	+	0.552346i	$0.813733\pi$
$74$		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	0.737658	+	0.675175i	$0.235932\pi$
$79$	−14199.4	+	43701.3i	−0.255978	+	0.787819i	−0.993635	+	0.112644i	$0.964068\pi$
$80$		0			0
$81$	−44133.0	−	32064.5i	−0.747396	−	0.543015i
$82$		0			0
$83$	57767.9	+	41970.8i	0.920431	+	0.668732i	0.943631	−	0.330999i	$-0.107386\pi$
$83$	57767.9	+	41970.8i	0.920431	+	0.668732i	−0.0232004	+	0.999731i	$0.507386\pi$
$84$		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	0.995903	−	0.0904326i	$-0.0288250\pi$
$89$	10240.9	+	31518.4i	0.137046	+	0.421783i	−0.858857	+	0.512215i	$0.828825\pi$
$90$		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	0.953962	+	0.299928i	$0.0969627\pi$
$97$	33219.9	+	102240.i	0.358484	+	1.10330i	−0.595478	+	0.803372i	$0.703037\pi$
$98$		0			0
$99$	83246.7			0.853648
$100$		0			0
$101$	53189.2	−	163699.i	0.518824	−	1.59678i	−0.257391	−	0.966307i	$-0.582863\pi$
$101$	53189.2	−	163699.i	0.518824	−	1.59678i	0.776215	−	0.630468i	$-0.217137\pi$
$102$		0			0
$103$	52378.7	+	38055.3i	0.486476	+	0.353446i	0.803828	−	0.594862i	$-0.202793\pi$
$103$	52378.7	+	38055.3i	0.486476	+	0.353446i	−0.317351	+	0.948308i	$0.602793\pi$
$104$		0			0
$105$	−86934.5	−	63161.6i	−0.769518	−	0.559088i
$106$		0			0
$107$	58011.3	−	178540.i	0.489839	−	1.50757i	−0.335010	−	0.942215i	$-0.608740\pi$
$107$	58011.3	−	178540.i	0.489839	−	1.50757i	0.824848	−	0.565354i	$-0.191260\pi$
$108$		0			0
$109$	27059.5	−	19659.9i	0.218149	−	0.158495i	−0.473344	−	0.880878i	$-0.656953\pi$
$109$	27059.5	−	19659.9i	0.218149	−	0.158495i	0.691493	+	0.722383i	$0.256953\pi$
$110$		0			0
$111$	−107107.	+	77817.8i	−0.825107	+	0.599476i
$112$		0			0
$113$	−39256.4	−	120819.i	−0.289211	−	0.890099i	−0.985105	−	0.171955i	$-0.944992\pi$
$113$	−39256.4	−	120819.i	−0.289211	−	0.890099i	0.695894	−	0.718144i	$-0.255008\pi$
$114$		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	−0.171792	−	0.985133i	$-0.554956\pi$
$127$	129424.	−	94031.7i	0.712039	−	0.517327i	0.883831	+	0.467807i	$0.154956\pi$
$128$		0			0
$129$	49756.8			0.263256
$130$		0			0
$131$	96356.9	+	296556.i	0.490574	+	1.50983i	0.823742	+	0.566965i	$0.191882\pi$
$131$	96356.9	+	296556.i	0.490574	+	1.50983i	−0.333168	+	0.942868i	$0.608118\pi$
$132$		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	−0.876919	−	0.480639i	$-0.840405\pi$
$137$	−151756.	+	110257.i	−0.690786	+	0.501886i	0.186132	+	0.982525i	$0.440405\pi$
$138$		0			0
$139$	−122791.	+	89213.2i	−0.539052	+	0.391644i	−0.823733	−	0.566978i	$-0.808112\pi$
$139$	−122791.	+	89213.2i	−0.539052	+	0.391644i	0.284681	+	0.958622i	$0.408112\pi$
$140$		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	0.750290	+	0.661109i	$0.229914\pi$
$151$	149025.	+	458651.i	0.531883	+	1.63697i	−0.218408	+	0.975858i	$0.570086\pi$
$152$		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	0.953260	−	0.302152i	$-0.0977051\pi$
$157$	296642.	+	215523.i	0.960469	+	0.697822i	0.00720949	+	0.999974i	$0.497705\pi$
$158$		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	−0.0198100	−	0.999804i	$-0.506306\pi$
$163$	198060.	−	609567.i	0.583887	−	1.79702i	0.603697	−	0.797214i	$-0.293694\pi$
$164$		0			0
$165$	100720.	+	73177.5i	0.288010	+	0.209251i
$166$		0			0
$167$	68541.4	+	49798.2i	0.190179	+	0.138173i	0.678800	−	0.734323i	$-0.262500\pi$
$167$	68541.4	+	49798.2i	0.190179	+	0.138173i	−0.488622	+	0.872496i	$0.662500\pi$
$168$		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	−0.794917	−	0.606718i	$-0.792486\pi$
$173$	−182473.	+	132575.i	−0.463536	+	0.336779i	0.331381	+	0.943497i	$0.392486\pi$
$174$		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	0.960108	−	0.279629i	$-0.0902114\pi$
$179$	8146.05	+	25071.0i	0.0190027	+	0.0584842i	−0.941106	+	0.338113i	$0.890211\pi$
$180$		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	0.826664	−	0.562696i	$-0.190236\pi$
$193$	−89454.4	−	275312.i	−0.172866	−	0.532026i	−0.999530	+	0.0306703i	$0.990236\pi$
$194$		0			0
$195$	187521.	−	577130.i	0.353153	−	1.08689i
$196$		0			0
$197$	119110.	+	366583.i	0.218667	+	0.672987i	0.998873	+	0.0474643i	$0.0151140\pi$
$197$	119110.	+	366583.i	0.218667	+	0.672987i	−0.780206	+	0.625522i	$0.784886\pi$
$198$		0			0
$199$	−9347.05	+	6791.03i	−0.0167318	+	0.0121563i	−0.596120	−	0.802896i	$-0.703292\pi$
$199$	−9347.05	+	6791.03i	−0.0167318	+	0.0121563i	0.579388	+	0.815052i	$0.303292\pi$
$200$		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	0.733820	−	0.679344i	$-0.237735\pi$
$227$	244158.	+	177391.i	0.314489	+	0.228490i	−0.419331	+	0.907833i	$0.637735\pi$
$228$		0			0
$229$	82310.7	+	59802.3i	0.103721	+	0.0753579i	0.638437	−	0.769674i	$-0.279581\pi$
$229$	82310.7	+	59802.3i	0.103721	+	0.0753579i	−0.534716	+	0.845032i	$0.679581\pi$
$230$		0			0
$231$	−215881.	+	664413.i	−0.266186	+	0.819235i
$232$		0			0
$233$	682802.	−	496085.i	0.823958	−	0.598640i	−0.0938856	−	0.995583i	$-0.529929\pi$
$233$	682802.	−	496085.i	0.823958	−	0.598640i	0.917843	+	0.396943i	$0.129929\pi$
$234$		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	−0.171145	−	0.985246i	$-0.554747\pi$
$239$	482533.	−	1.48508e6i	0.546427	−	1.68173i	0.717572	−	0.696484i	$-0.245253\pi$
$240$		0			0
$241$	341482.	+	1.05097e6i	0.378726	+	1.16560i	0.940931	+	0.338600i	$0.109953\pi$
$241$	341482.	+	1.05097e6i	0.378726	+	1.16560i	−0.562205	+	0.826998i	$0.690047\pi$
$242$		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	−0.974104	−	0.226101i	$-0.927402\pi$
$251$	−1.05809e6	+	768751.i	−1.06008	+	0.770196i	−0.0859802	+	0.996297i	$0.527402\pi$
$252$		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	0.366073	+	0.930586i	$0.380702\pi$
$257$	−505145.	+	1.55468e6i	−0.477071	+	1.46827i	−0.843144	+	0.537687i	$0.819298\pi$
$258$		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	0.0505915	−	0.998719i	$-0.483889\pi$
$263$	1.13975e6	−	828078.i	1.01606	−	0.738214i	0.965472	+	0.260506i	$0.0838893\pi$
$264$		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	0.750889	−	0.660428i	$-0.229625\pi$
$269$	421106.	+	305951.i	0.354822	+	0.257793i	−0.396067	+	0.918222i	$0.629625\pi$
$270$		0			0
$271$	154785.	−	476378.i	0.128028	−	0.394030i	−0.866413	−	0.499329i	$-0.833580\pi$
$271$	154785.	−	476378.i	0.128028	−	0.394030i	0.994441	+	0.105299i	$0.0335800\pi$
$272$		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	0.595892	−	0.803065i	$-0.296799\pi$
$277$	20780.8	+	15098.1i	0.0162728	+	0.0118229i	−0.579619	+	0.814888i	$0.696799\pi$
$278$		0			0
$279$	2.27013e6	−	1.19856e6i	1.74598	−	0.921827i
$280$		0			0
$281$	−475825.	−	345707.i	−0.359486	−	0.261182i	0.393352	−	0.919388i	$-0.371315\pi$
$281$	−475825.	−	345707.i	−0.359486	−	0.261182i	−0.752837	+	0.658206i	$0.771315\pi$
$282$		0			0
$283$	−295083.	−	908173.i	−0.219017	−	0.674066i	−0.998844	−	0.0480704i	$-0.984693\pi$
$283$	−295083.	−	908173.i	−0.219017	−	0.674066i	0.779827	−	0.625996i	$-0.215307\pi$
$284$		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	−0.723655	−	0.690162i	$-0.757539\pi$
$293$	393034.	−	1.20963e6i	0.267461	−	0.823161i	0.991116	−	0.132999i	$-0.0424608\pi$
$294$		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	−0.150066	−	0.988676i	$-0.547949\pi$
$307$	1.22837e6	−	892465.i	0.743848	−	0.540437i	0.893914	+	0.448239i	$0.147949\pi$
$308$		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	−0.998980	−	0.0451474i	$-0.985624\pi$
$313$	−2.19212e6	+	1.59267e6i	−1.26474	+	0.918891i	−0.265764	+	0.964038i	$0.585624\pi$
$314$		0			0
$315$	1.91766e6			1.08892
$316$		0			0
$317$	−664445.	−	2.04495e6i	−0.371373	−	1.14297i	−0.945893	−	0.324479i	$-0.894811\pi$
$317$	−664445.	−	2.04495e6i	−0.371373	−	1.14297i	0.574519	−	0.818491i	$-0.305189\pi$
$318$		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	0.361120	−	0.932519i	$-0.382394\pi$
$331$	−825552.	−	599799.i	−0.414166	−	0.300909i	−0.775286	+	0.631610i	$0.782394\pi$
$332$		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	−0.773803	−	0.633426i	$-0.781648\pi$
$337$	−1.08433e6	−	3.33724e6i	−0.520102	−	1.60071i	0.253702	−	0.967282i	$-0.418352\pi$
$338$		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	0.481481	+	0.876457i	$0.340099\pi$
$349$	−962993.	+	2.96379e6i	−0.423214	+	1.30252i	−0.904694	+	0.426061i	$0.859901\pi$
$350$		0			0
$351$	4.35547e6	+	3.16444e6i	1.88698	+	1.37097i
$352$		0			0
$353$	1.15223e6	+	837143.i	0.492155	+	0.357571i	0.806012	−	0.591899i	$-0.201621\pi$
$353$	1.15223e6	+	837143.i	0.492155	+	0.357571i	−0.313858	+	0.949470i	$0.601621\pi$
$354$		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	−0.612420	−	0.790533i	$-0.709804\pi$
$359$	−121674.	+	88401.4i	−0.0498267	+	0.0362012i	0.562593	+	0.826734i	$0.309804\pi$
$360$		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	0.990238	+	0.139385i	$0.0445125\pi$
$379$	757954.	+	2.33274e6i	0.271047	+	0.834197i	−0.719191	+	0.694812i	$0.755487\pi$
$380$		0			0
$381$	−1.32905e6	+	4.09038e6i	−0.469059	+	1.44362i
$382$		0			0
$383$	513463.	+	1.58028e6i	0.178859	+	0.550473i	0.999789	−	0.0205572i	$-0.00654402\pi$
$383$	513463.	+	1.58028e6i	0.178859	+	0.550473i	−0.820929	+	0.571030i	$0.806544\pi$
$384$		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	−0.850782	−	0.525519i	$-0.823871\pi$
$389$	436955.	−	1.34481e6i	0.146407	−	0.450595i	0.997189	+	0.0749237i	$0.0238713\pi$
$390$		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	0.999603	+	0.0281924i	$0.00897512\pi$
$401$	4.29975e6	+	3.12395e6i	1.33531	+	0.970159i	0.335707	+	0.941967i	$0.391025\pi$
$402$		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	−0.829137	−	0.559046i	$-0.811168\pi$
$419$	−1.98969e6	+	1.44560e6i	−0.553670	+	0.402265i	0.275467	+	0.961311i	$0.411168\pi$
$420$		0			0
$421$	355801.	−	258504.i	0.0978366	−	0.0710824i	−0.537791	−	0.843078i	$-0.680741\pi$
$421$	355801.	−	258504.i	0.0978366	−	0.0710824i	0.635628	+	0.771995i	$0.280741\pi$
$422$		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	−0.997646	−	0.0685791i	$-0.978153\pi$
$431$	−4.78481e6	+	3.47637e6i	−1.24071	+	0.901430i	−0.243067	+	0.970010i	$0.578153\pi$
$432$		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	−0.869350	−	0.494196i	$-0.835462\pi$
$443$	514049.	−	1.58208e6i	0.124450	−	0.383018i	0.993801	+	0.111178i	$0.0354624\pi$
$444$		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	−0.363032	+	0.931777i	$0.618258\pi$
$449$	−5.81564e6	+	4.22531e6i	−1.36139	+	0.989106i	−0.998355	+	0.0573292i	$0.981742\pi$
$450$		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	−0.350463	−	0.936577i	$-0.613976\pi$
$457$	2.15900e6	−	6.64473e6i	0.483574	−	1.48829i	0.834036	−	0.551710i	$-0.186024\pi$
$458$		0			0
$459$	−9.15184e6			−2.02757
$460$		0			0
$461$	1.96508e6	+	6.04790e6i	0.430654	+	1.32542i	0.897476	+	0.441064i	$0.145399\pi$
$461$	1.96508e6	+	6.04790e6i	0.430654	+	1.32542i	−0.466822	+	0.884351i	$0.654601\pi$
$462$		0			0
$463$	−615022.	−	446840.i	−0.133333	−	0.0968722i	0.519120	−	0.854702i	$-0.326260\pi$
$463$	−615022.	−	446840.i	−0.133333	−	0.0968722i	−0.652453	+	0.757829i	$0.726260\pi$
$464$		0			0
$465$	3.80022e6	+	545407.i	0.815035	+	0.116974i
$466$		0			0
$467$	1.07875e6	+	783755.i	0.228890	+	0.166298i	0.696319	−	0.717732i	$-0.254820\pi$
$467$	1.07875e6	+	783755.i	0.228890	+	0.166298i	−0.467429	+	0.884031i	$0.654820\pi$
$468$		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	−0.429137	−	0.903240i	$-0.641182\pi$
$479$	2.25445e6	−	6.93847e6i	0.448953	−	1.38174i	0.878090	−	0.478496i	$-0.158818\pi$
$480$		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	−0.548616	−	0.836074i	$-0.684845\pi$
$487$	2.02370e6	−	6.22832e6i	0.386656	−	1.19000i	0.935272	−	0.353930i	$-0.115155\pi$
$488$		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	−0.989261	−	0.146163i	$-0.953308\pi$
$499$	−6.42970e6	+	4.67145e6i	−1.15595	+	0.839847i	−0.166689	+	0.986009i	$0.553308\pi$
$500$		0			0
$501$	−2.27770e6			−0.405418
$502$		0			0
$503$	1.71561e6	+	5.28009e6i	0.302341	+	0.930511i	0.980656	+	0.195739i	$0.0627106\pi$
$503$	1.71561e6	+	5.28009e6i	0.302341	+	0.930511i	−0.678315	+	0.734771i	$0.737289\pi$
$504$		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	−0.626623	−	0.779323i	$-0.715563\pi$
$509$	−462236.	+	335834.i	−0.0790804	+	0.0574553i	0.547543	+	0.836778i	$0.315563\pi$
$510$		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	−0.999616	−	0.0277047i	$-0.991180\pi$
$523$	−1.29608e6	−	3.98892e6i	−0.207194	−	0.637678i	0.792422	−	0.609973i	$-0.208820\pi$
$524$		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	0.367597	+	0.929985i	$0.380181\pi$
$541$	−3.24332e6	+	9.98190e6i	−0.476427	+	1.46629i	−0.844024	+	0.536306i	$0.819819\pi$
$542$		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	0.835464	−	0.549545i	$-0.185199\pi$
$547$	−1.14384e6	−	3.52039e6i	−0.163455	−	0.503063i	−0.998919	+	0.0464820i	$0.985199\pi$
$548$		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	0.998779	+	0.0493936i	$0.0157289\pi$
$569$	1.69736e6	+	5.22394e6i	0.219783	+	0.676422i	−0.778997	+	0.627028i	$0.784271\pi$
$570$		0			0
$571$	161411.	−	117272.i	0.0207178	−	0.0150523i	−0.577378	−	0.816477i	$-0.695924\pi$
$571$	161411.	−	117272.i	0.0207178	−	0.0150523i	0.598096	+	0.801424i	$0.295924\pi$
$572$		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	0.929870	−	0.367888i	$-0.119919\pi$
$577$	6.93626e6	+	5.03949e6i	0.867333	+	0.630154i	−0.0625371	+	0.998043i	$0.519919\pi$
$578$		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	0.461698	−	0.887037i	$-0.347240\pi$
$587$	−1.99734e6	−	1.45115e6i	−0.239252	−	0.173827i	−0.700950	+	0.713210i	$0.747240\pi$
$588$		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	0.999976	+	0.00688944i	$0.00219299\pi$
$593$	1.67007e6	+	5.13993e6i	0.195028	+	0.600234i	−0.804948	+	0.593345i	$0.797807\pi$
$594$		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	0.997624	−	0.0688909i	$-0.0219460\pi$
$599$	1.08924e7	+	7.91381e6i	1.24039	+	0.901195i	0.242764	+	0.970085i	$0.421946\pi$
$600$		0			0
$601$	6.80663e6	+	4.94531e6i	0.768681	+	0.558479i	0.901561	−	0.432653i	$-0.142422\pi$
$601$	6.80663e6	+	4.94531e6i	0.768681	+	0.558479i	−0.132880	+	0.991132i	$0.542422\pi$
$602$		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	−0.994677	−	0.103045i	$-0.967142\pi$
$607$	−1.09299e7	+	7.94102e6i	−1.20405	+	0.874792i	−0.209371	+	0.977836i	$0.567142\pi$
$608$		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	0.932763	−	0.360489i	$-0.117390\pi$
$613$	−313982.	−	966338.i	−0.0337484	−	0.103867i	−0.966512	+	0.256622i	$0.917390\pi$
$614$		0			0
$615$	8.25077e6			0.879643
$616$		0			0
$617$	−1.14704e7	+	8.33372e6i	−1.21301	+	0.881305i	−0.995501	−	0.0947527i	$-0.969794\pi$
$617$	−1.14704e7	+	8.33372e6i	−1.21301	+	0.881305i	−0.217511	+	0.976058i	$0.569794\pi$
$618$		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	0.986874	−	0.161491i	$-0.0516301\pi$
$631$	935703.	+	2.87980e6i	0.0935544	+	0.287931i	−0.893320	+	0.449422i	$0.851630\pi$
$632$		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	0.670517	−	0.741894i	$-0.266072\pi$
$641$	1.79066e6	+	1.30099e6i	0.172134	+	0.125063i	−0.498382	+	0.866957i	$0.666072\pi$
$642$		0			0
$643$	−2.13532e6	+	6.57183e6i	−0.203674	+	0.626843i	0.796092	+	0.605176i	$0.206897\pi$
$643$	−2.13532e6	+	6.57183e6i	−0.203674	+	0.626843i	−0.999765	+	0.0216669i	$0.993103\pi$
$644$		0			0
$645$	−1.32795e6			−0.125685
$646$		0			0
$647$	4.52020e6	+	1.39117e7i	0.424519	+	1.30653i	0.903454	+	0.428684i	$0.141023\pi$
$647$	4.52020e6	+	1.39117e7i	0.424519	+	1.30653i	−0.478936	+	0.877850i	$0.658977\pi$
$648$		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	−0.998859	−	0.0477522i	$-0.984794\pi$
$653$	−1.47422e7	−	1.07108e7i	−1.35294	−	0.982968i	−0.354080	−	0.935215i	$-0.615206\pi$
$654$		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	0.804002	+	0.594626i	$0.202700\pi$
$659$	−2.18466e6	+	6.72370e6i	−0.195962	+	0.603108i	−0.999964	+	0.00848169i	$0.997300\pi$
$660$		0			0
$661$	−5.58119e6	−	4.05497e6i	−0.496848	−	0.360981i	0.310964	−	0.950422i	$-0.399348\pi$
$661$	−5.58119e6	−	4.05497e6i	−0.496848	−	0.360981i	−0.807812	+	0.589441i	$0.799348\pi$
$662$		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	0.676636	+	0.736318i	$0.263437\pi$
$673$	−3.56696e6	+	1.09780e7i	−0.303571	+	0.934295i	−0.980207	+	0.197977i	$0.936563\pi$
$674$		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	−0.179699	−	0.983722i	$-0.557512\pi$
$691$	6.82672e6	−	2.10105e7i	0.543898	−	1.67395i	0.723596	−	0.690223i	$-0.242488\pi$
$692$		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	0.772972	−	0.634440i	$-0.218769\pi$
$701$	5.31409e6	+	3.86092e6i	0.408446	+	0.296753i	−0.364527	+	0.931193i	$0.618769\pi$
$702$		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	−0.912916	−	0.408148i	$-0.866175\pi$
$709$	−5.54476e6	−	1.70650e7i	−0.414255	−	1.27494i	0.498661	−	0.866797i	$-0.333825\pi$
$710$		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	−0.731267	−	0.682091i	$-0.761071\pi$
$727$	3.72319e6	−	1.14588e7i	0.261264	−	0.804087i	0.992531	−	0.121995i	$-0.0389293\pi$
$728$		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	0.929903	−	0.367805i	$-0.119891\pi$
$733$	−561422.	−	1.72788e6i	−0.0385948	−	0.118783i	−0.968498	+	0.249022i	$0.919891\pi$
$734$		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	0.906436	+	0.422344i	$0.138793\pi$
$751$	6.51260e6	+	2.00437e7i	0.421361	+	1.29682i	−0.485074	+	0.874473i	$0.661207\pi$
$752$		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	−0.901726	−	0.432308i	$-0.857699\pi$
$757$	−1.21281e7	+	8.81159e6i	−0.769225	+	0.558875i	0.132501	+	0.991183i	$0.457699\pi$
$758$		0			0
$759$	8.63218e6	−	6.27164e6i	0.543896	−	0.395164i
$760$		0			0
$761$	−420785.	+	1.29504e6i	−0.0263389	+	0.0810629i	−0.963362	−	0.268205i	$-0.913570\pi$
$761$	−420785.	+	1.29504e6i	−0.0263389	+	0.0810629i	0.937023	+	0.349268i	$0.113570\pi$
$762$		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	0.599680	−	0.800240i	$-0.295295\pi$
$773$	397342.	+	288686.i	0.0239175	+	0.0173771i	−0.575762	+	0.817617i	$0.695295\pi$
$774$		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	0.957070	+	0.289858i	$0.0936080\pi$
$787$	2.65583e7	+	1.92957e7i	1.52849	+	1.11051i	0.571422	+	0.820656i	$0.306392\pi$
$788$		0			0
$789$	−1.17041e7	+	3.60215e7i

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

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