LMFDB - Embedded newform 48.5.l.a.19.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,5,Mod(19,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	48.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.96175822802$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.16
Character	$\chi$	$=$	48.19
Dual form			48.5.l.a.43.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.90016 + 0.888110i) q^{2} +(3.67423 - 3.67423i) q^{3} +(14.4225 + 6.92754i) q^{4} +(-17.3646 + 17.3646i) q^{5} +(17.5932 - 11.0670i) q^{6} +89.8255 q^{7} +(50.0978 + 39.8273i) q^{8} -27.0000i q^{9} +O(q^{10})$	\(q+(3.90016 + 0.888110i) q^{2} +(3.67423 - 3.67423i) q^{3} +(14.4225 + 6.92754i) q^{4} +(-17.3646 + 17.3646i) q^{5} +(17.5932 - 11.0670i) q^{6} +89.8255 q^{7} +(50.0978 + 39.8273i) q^{8} -27.0000i q^{9} +(-83.1466 + 52.3032i) q^{10} +(-94.2659 - 94.2659i) q^{11} +(78.4451 - 27.5383i) q^{12} +(-100.821 - 100.821i) q^{13} +(350.334 + 79.7749i) q^{14} +127.604i q^{15} +(160.018 + 199.825i) q^{16} -66.1361 q^{17} +(23.9790 - 105.304i) q^{18} +(-324.678 + 324.678i) q^{19} +(-370.736 + 130.148i) q^{20} +(330.040 - 330.040i) q^{21} +(-283.934 - 451.371i) q^{22} -467.308 q^{23} +(330.406 - 37.7360i) q^{24} +21.9384i q^{25} +(-303.678 - 482.757i) q^{26} +(-99.2043 - 99.2043i) q^{27} +(1295.51 + 622.270i) q^{28} +(-321.838 - 321.838i) q^{29} +(-113.326 + 497.674i) q^{30} -1587.33i q^{31} +(446.631 + 921.465i) q^{32} -692.710 q^{33} +(-257.942 - 58.7361i) q^{34} +(-1559.79 + 1559.79i) q^{35} +(187.044 - 389.408i) q^{36} +(982.813 - 982.813i) q^{37} +(-1554.64 + 977.946i) q^{38} -740.879 q^{39} +(-1561.52 + 178.343i) q^{40} -1217.57i q^{41} +(1580.32 - 994.098i) q^{42} +(1303.65 + 1303.65i) q^{43} +(-706.521 - 2012.58i) q^{44} +(468.845 + 468.845i) q^{45} +(-1822.58 - 415.021i) q^{46} +3979.92i q^{47} +(1322.15 + 146.260i) q^{48} +5667.62 q^{49} +(-19.4837 + 85.5634i) q^{50} +(-243.000 + 243.000i) q^{51} +(-755.650 - 2152.53i) q^{52} +(672.674 - 672.674i) q^{53} +(-298.809 - 475.017i) q^{54} +3273.79 q^{55} +(4500.06 + 3577.51i) q^{56} +2385.88i q^{57} +(-969.392 - 1541.05i) q^{58} +(-1188.14 - 1188.14i) q^{59} +(-883.979 + 1840.36i) q^{60} +(-979.221 - 979.221i) q^{61} +(1409.73 - 6190.86i) q^{62} -2425.29i q^{63} +(923.570 + 3990.52i) q^{64} +3501.43 q^{65} +(-2701.68 - 615.202i) q^{66} +(-2267.04 + 2267.04i) q^{67} +(-953.850 - 458.161i) q^{68} +(-1717.00 + 1717.00i) q^{69} +(-7468.69 + 4698.16i) q^{70} +5875.26 q^{71} +(1075.34 - 1352.64i) q^{72} +3661.25i q^{73} +(4705.97 - 2960.28i) q^{74} +(80.6069 + 80.6069i) q^{75} +(-6931.89 + 2433.45i) q^{76} +(-8467.48 - 8467.48i) q^{77} +(-2889.55 - 657.981i) q^{78} -539.165i q^{79} +(-6248.56 - 691.233i) q^{80} -729.000 q^{81} +(1081.34 - 4748.73i) q^{82} +(-3607.17 + 3607.17i) q^{83} +(7046.38 - 2473.64i) q^{84} +(1148.43 - 1148.43i) q^{85} +(3926.66 + 6242.22i) q^{86} -2365.02 q^{87} +(-968.153 - 8476.87i) q^{88} +7549.35i q^{89} +(1412.19 + 2244.96i) q^{90} +(-9056.28 - 9056.28i) q^{91} +(-6739.77 - 3237.30i) q^{92} +(-5832.23 - 5832.23i) q^{93} +(-3534.60 + 15522.3i) q^{94} -11275.8i q^{95} +(5026.70 + 1744.65i) q^{96} -9595.79 q^{97} +(22104.6 + 5033.47i) q^{98} +(-2545.18 + 2545.18i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{4} + 180 q^{8}+O(q^{10}) $ 32 * q + 12 * q^4 + 180 * q^8	$ 32 q + 12 q^{4} + 180 q^{8} + 296 q^{10} - 192 q^{11} + 360 q^{12} - 156 q^{14} + 352 q^{16} - 324 q^{18} + 704 q^{19} - 1200 q^{20} - 1568 q^{22} - 2304 q^{23} + 1188 q^{24} + 2700 q^{26} + 4680 q^{28} - 1728 q^{29} + 1512 q^{30} - 3360 q^{32} - 9312 q^{34} - 5184 q^{35} - 756 q^{36} + 3648 q^{37} - 5880 q^{38} + 5232 q^{40} + 4500 q^{42} + 1088 q^{43} + 18840 q^{44} + 680 q^{46} + 2160 q^{48} + 10976 q^{49} - 25884 q^{50} - 4032 q^{51} - 25584 q^{52} + 960 q^{53} + 972 q^{54} + 11776 q^{55} + 15456 q^{56} + 12624 q^{58} + 13056 q^{59} + 7992 q^{60} + 3776 q^{61} + 21852 q^{62} - 8664 q^{64} + 4032 q^{65} - 8856 q^{66} - 896 q^{67} - 17280 q^{68} - 9792 q^{69} - 18240 q^{70} - 39936 q^{71} + 4860 q^{72} + 24204 q^{74} - 1152 q^{75} + 16776 q^{76} + 9408 q^{77} - 3780 q^{78} - 14232 q^{80} - 23328 q^{81} - 33800 q^{82} + 24000 q^{83} - 11448 q^{84} - 11200 q^{85} - 1200 q^{86} - 11424 q^{88} + 4104 q^{90} + 30528 q^{91} - 11664 q^{92} - 8040 q^{94} + 10080 q^{96} + 52968 q^{98} - 5184 q^{99}+O(q^{100}) $ 32 * q + 12 * q^4 + 180 * q^8 + 296 * q^10 - 192 * q^11 + 360 * q^12 - 156 * q^14 + 352 * q^16 - 324 * q^18 + 704 * q^19 - 1200 * q^20 - 1568 * q^22 - 2304 * q^23 + 1188 * q^24 + 2700 * q^26 + 4680 * q^28 - 1728 * q^29 + 1512 * q^30 - 3360 * q^32 - 9312 * q^34 - 5184 * q^35 - 756 * q^36 + 3648 * q^37 - 5880 * q^38 + 5232 * q^40 + 4500 * q^42 + 1088 * q^43 + 18840 * q^44 + 680 * q^46 + 2160 * q^48 + 10976 * q^49 - 25884 * q^50 - 4032 * q^51 - 25584 * q^52 + 960 * q^53 + 972 * q^54 + 11776 * q^55 + 15456 * q^56 + 12624 * q^58 + 13056 * q^59 + 7992 * q^60 + 3776 * q^61 + 21852 * q^62 - 8664 * q^64 + 4032 * q^65 - 8856 * q^66 - 896 * q^67 - 17280 * q^68 - 9792 * q^69 - 18240 * q^70 - 39936 * q^71 + 4860 * q^72 + 24204 * q^74 - 1152 * q^75 + 16776 * q^76 + 9408 * q^77 - 3780 * q^78 - 14232 * q^80 - 23328 * q^81 - 33800 * q^82 + 24000 * q^83 - 11448 * q^84 - 11200 * q^85 - 1200 * q^86 - 11424 * q^88 + 4104 * q^90 + 30528 * q^91 - 11664 * q^92 - 8040 * q^94 + 10080 * q^96 + 52968 * q^98 - 5184 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	3.90016	+	0.888110i	0.975040	+	0.222027i
$2$	3.90016	+	0.888110i	0.975040	+	0.222027i
$3$	3.67423	−	3.67423i	0.408248	−	0.408248i
$3$	3.67423	−	3.67423i	0.408248	−	0.408248i
$4$	14.4225	+	6.92754i	0.901408	+	0.432971i
$5$	−17.3646	+	17.3646i	−0.694586	+	0.694586i	−0.963237	−	0.268652i	$-0.913422\pi$
$5$	−17.3646	+	17.3646i	−0.694586	+	0.694586i	0.268652	+	0.963237i	$0.413422\pi$
$6$	17.5932	−	11.0670i	0.488701	−	0.307416i
$7$	89.8255			1.83317			0.916587	−	0.399836i	$-0.130933\pi$
$7$	89.8255			1.83317			0.916587	+	0.399836i	$0.130933\pi$
$8$	50.0978	+	39.8273i	0.782777	+	0.622302i
$9$		−	27.0000i		−	0.333333i
$10$	−83.1466	+	52.3032i	−0.831466	+	0.523032i
$11$	−94.2659	−	94.2659i	−0.779057	−	0.779057i	0.200613	−	0.979670i	$-0.435706\pi$
$11$	−94.2659	−	94.2659i	−0.779057	−	0.779057i	−0.979670	+	0.200613i	$0.935706\pi$
$12$	78.4451	−	27.5383i	0.544758	−	0.191238i
$13$	−100.821	−	100.821i	−0.596573	−	0.596573i	0.342826	−	0.939399i	$-0.388616\pi$
$13$	−100.821	−	100.821i	−0.596573	−	0.596573i	−0.939399	+	0.342826i	$0.888616\pi$
$14$	350.334	+	79.7749i	1.78742	+	0.407015i
$15$			127.604i			0.567127i
$16$	160.018	+	199.825i	0.625072	+	0.780567i
$17$	−66.1361			−0.228845			−0.114422	−	0.993432i	$-0.536502\pi$
$17$	−66.1361			−0.228845			−0.114422	+	0.993432i	$0.536502\pi$
$18$	23.9790	−	105.304i	0.0740091	−	0.325013i
$19$	−324.678	+	324.678i	−0.899384	+	0.899384i	−0.995382	−	0.0959975i	$-0.969396\pi$
$19$	−324.678	+	324.678i	−0.899384	+	0.899384i	0.0959975	+	0.995382i	$0.469396\pi$
$20$	−370.736	+	130.148i	−0.926841	+	0.325369i
$21$	330.040	−	330.040i	0.748390	−	0.748390i
$22$	−283.934	−	451.371i	−0.586640	−	0.932584i
$23$	−467.308			−0.883381			−0.441690	−	0.897168i	$-0.645621\pi$
$23$	−467.308			−0.883381			−0.441690	+	0.897168i	$0.645621\pi$
$24$	330.406	−	37.7360i	0.573621	−	0.0655139i
$25$			21.9384i			0.0351015i
$26$	−303.678	−	482.757i	−0.449227	−	0.714138i
$27$	−99.2043	−	99.2043i	−0.136083	−	0.136083i
$28$	1295.51	+	622.270i	1.65244	+	0.793712i
$29$	−321.838	−	321.838i	−0.382685	−	0.382685i	0.489384	−	0.872069i	$-0.337222\pi$
$29$	−321.838	−	321.838i	−0.382685	−	0.382685i	−0.872069	+	0.489384i	$0.837222\pi$
$30$	−113.326	+	497.674i	−0.125918	+	0.552972i
$31$		−	1587.33i		−	1.65175i	−0.563852	−	0.825876i	$-0.690681\pi$
$31$		−	1587.33i		−	1.65175i	0.563852	−	0.825876i	$-0.309319\pi$
$32$	446.631	+	921.465i	0.436163	+	0.899868i
$33$	−692.710			−0.636097
$34$	−257.942	−	58.7361i	−0.223133	−	0.0508098i
$35$	−1559.79	+	1559.79i	−1.27330	+	1.27330i
$36$	187.044	−	389.408i	0.144324	−	0.300469i
$37$	982.813	−	982.813i	0.717906	−	0.717906i	−0.250270	−	0.968176i	$-0.580520\pi$
$37$	982.813	−	982.813i	0.717906	−	0.717906i	0.968176	+	0.250270i	$0.0805195\pi$
$38$	−1554.64	+	977.946i	−1.07662	+	0.677248i
$39$	−740.879			−0.487100
$40$	−1561.52	+	178.343i	−0.975948	+	0.111464i
$41$		−	1217.57i		−	0.724314i	−0.932117	−	0.362157i	$-0.882040\pi$
$41$		−	1217.57i		−	0.724314i	0.932117	−	0.362157i	$-0.117960\pi$
$42$	1580.32	−	994.098i	0.895874	−	0.563547i
$43$	1303.65	+	1303.65i	0.705056	+	0.705056i	0.965491	−	0.260435i	$-0.0838661\pi$
$43$	1303.65	+	1303.65i	0.705056	+	0.705056i	−0.260435	+	0.965491i	$0.583866\pi$
$44$	−706.521	−	2012.58i	−0.364939	−	1.03956i
$45$	468.845	+	468.845i	0.231529	+	0.231529i
$46$	−1822.58	−	415.021i	−0.861332	−	0.196135i
$47$			3979.92i			1.80168i	0.434147	+	0.900842i	$0.357050\pi$
$47$			3979.92i			1.80168i	−0.434147	+	0.900842i	$0.642950\pi$
$48$	1322.15	+	146.260i	0.573850	+	0.0634809i
$49$	5667.62			2.36053
$50$	−19.4837	+	85.5634i	−0.00779349	+	0.0342254i
$51$	−243.000	+	243.000i	−0.0934255	+	0.0934255i
$52$	−755.650	−	2152.53i	−0.279456	−	0.796054i
$53$	672.674	−	672.674i	0.239471	−	0.239471i	−0.577160	−	0.816631i	$-0.695839\pi$
$53$	672.674	−	672.674i	0.239471	−	0.239471i	0.816631	+	0.577160i	$0.195839\pi$
$54$	−298.809	−	475.017i	−0.102472	−	0.162900i
$55$	3273.79			1.08224
$56$	4500.06	+	3577.51i	1.43497	+	1.14079i
$57$			2385.88i			0.734344i
$58$	−969.392	−	1541.05i	−0.288167	−	0.458100i
$59$	−1188.14	−	1188.14i	−0.341323	−	0.341323i	0.515542	−	0.856864i	$-0.327591\pi$
$59$	−1188.14	−	1188.14i	−0.341323	−	0.341323i	−0.856864	+	0.515542i	$0.827591\pi$
$60$	−883.979	+	1840.36i	−0.245550	+	0.511212i
$61$	−979.221	−	979.221i	−0.263161	−	0.263161i	0.563176	−	0.826337i	$-0.309579\pi$
$61$	−979.221	−	979.221i	−0.263161	−	0.263161i	−0.826337	+	0.563176i	$0.809579\pi$
$62$	1409.73	−	6190.86i	0.366734	−	1.61052i
$63$		−	2425.29i		−	0.611058i
$64$	923.570	+	3990.52i	0.225481	+	0.974248i
$65$	3501.43			0.828742
$66$	−2701.68	−	615.202i	−0.620221	−	0.141231i
$67$	−2267.04	+	2267.04i	−0.505021	+	0.505021i	−0.912994	−	0.407973i	$-0.866236\pi$
$67$	−2267.04	+	2267.04i	−0.505021	+	0.505021i	0.407973	+	0.912994i	$0.366236\pi$
$68$	−953.850	−	458.161i	−0.206282	−	0.0990832i
$69$	−1717.00	+	1717.00i	−0.360639	+	0.360639i
$70$	−7468.69	+	4698.16i	−1.52422	+	0.958809i
$71$	5875.26			1.16550			0.582748	−	0.812653i	$-0.301978\pi$
$71$	5875.26			1.16550			0.582748	+	0.812653i	$0.301978\pi$
$72$	1075.34	−	1352.64i	0.207434	−	0.260926i
$73$			3661.25i			0.687043i	0.939145	+	0.343521i	$0.111620\pi$
$73$			3661.25i			0.687043i	−0.939145	+	0.343521i	$0.888380\pi$
$74$	4705.97	−	2960.28i	0.859382	−	0.540592i
$75$	80.6069	+	80.6069i	0.0143301	+	0.0143301i
$76$	−6931.89	+	2433.45i	−1.20012	+	0.421304i
$77$	−8467.48	−	8467.48i	−1.42815	−	1.42815i
$78$	−2889.55	−	657.981i	−0.474942	−	0.108149i
$79$		−	539.165i		−	0.0863908i	−0.999067	−	0.0431954i	$-0.986246\pi$
$79$		−	539.165i		−	0.0863908i	0.999067	−	0.0431954i	$-0.0137538\pi$
$80$	−6248.56	−	691.233i	−0.976337	−	0.108005i
$81$	−729.000			−0.111111
$82$	1081.34	−	4748.73i	0.160818	−	0.706235i
$83$	−3607.17	+	3607.17i	−0.523612	+	0.523612i	−0.918660	−	0.395048i	$-0.870728\pi$
$83$	−3607.17	+	3607.17i	−0.523612	+	0.523612i	0.395048	+	0.918660i	$0.370728\pi$
$84$	7046.38	−	2473.64i	0.998636	−	0.350573i
$85$	1148.43	−	1148.43i	0.158952	−	0.158952i
$86$	3926.66	+	6242.22i	0.530916	+	0.844000i
$87$	−2365.02			−0.312461
$88$	−968.153	−	8476.87i	−0.125020	−	1.09464i
$89$			7549.35i			0.953081i	0.879153	+	0.476540i	$0.158109\pi$
$89$			7549.35i			0.953081i	−0.879153	+	0.476540i	$0.841891\pi$
$90$	1412.19	+	2244.96i	0.174344	+	0.277155i
$91$	−9056.28	−	9056.28i	−1.09362	−	1.09362i
$92$	−6739.77	−	3237.30i	−0.796286	−	0.382479i
$93$	−5832.23	−	5832.23i	−0.674325	−	0.674325i
$94$	−3534.60	+	15522.3i	−0.400023	+	1.75671i
$95$		−	11275.8i		−	1.24940i
$96$	5026.70	+	1744.65i	0.545432	+	0.189307i
$97$	−9595.79			−1.01985			−0.509926	−	0.860218i	$-0.670327\pi$
$97$	−9595.79			−1.01985			−0.509926	+	0.860218i	$0.670327\pi$
$98$	22104.6	+	5033.47i	2.30161	+	0.524101i
$99$	−2545.18	+	2545.18i	−0.259686	+	0.259686i
$100$	−151.979	+	316.408i	−0.0151979	+	0.0316408i
$101$	2342.75	−	2342.75i	0.229659	−	0.229659i	−0.582891	−	0.812550i	$-0.698079\pi$
$101$	2342.75	−	2342.75i	0.229659	−	0.229659i	0.812550	+	0.582891i	$0.198079\pi$
$102$	−1163.55	+	731.928i	−0.111837	+	0.0703506i
$103$	13654.1			1.28703			0.643513	−	0.765435i	$-0.277476\pi$
$103$	13654.1			1.28703			0.643513	+	0.765435i	$0.277476\pi$
$104$	−1035.47	−	9066.32i	−0.0957354	−	0.838232i
$105$			11462.1i			1.03964i
$106$	3220.94	−	2026.13i	0.286663	−	0.180325i
$107$	10621.9	+	10621.9i	0.927761	+	0.927761i	0.997561	−	0.0698004i	$-0.0222362\pi$
$107$	10621.9	+	10621.9i	0.927761	+	0.927761i	−0.0698004	+	0.997561i	$0.522236\pi$
$108$	−743.535	−	2118.02i	−0.0637461	−	0.181586i
$109$	6098.45	+	6098.45i	0.513294	+	0.513294i	0.915534	−	0.402240i	$-0.131768\pi$
$109$	6098.45	+	6098.45i	0.513294	+	0.513294i	−0.402240	+	0.915534i	$0.631768\pi$
$110$	12768.3	+	2907.48i	1.05523	+	0.240288i
$111$		−	7222.17i		−	0.586168i
$112$	14373.7	+	17949.4i	1.14586	+	1.43092i
$113$	2094.31			0.164015			0.0820075	−	0.996632i	$-0.473867\pi$
$113$	2094.31			0.164015			0.0820075	+	0.996632i	$0.473867\pi$
$114$	−2118.93	+	9305.33i	−0.163044	+	0.716015i
$115$	8114.64	−	8114.64i	0.613584	−	0.613584i
$116$	−2412.17	−	6871.26i	−0.179263	−	0.510646i
$117$	−2722.16	+	2722.16i	−0.198858	+	0.198858i
$118$	−3578.75	−	5689.16i	−0.257020	−	0.408586i
$119$	−5940.71			−0.419512
$120$	−5082.11	+	6392.65i	−0.352924	+	0.443934i
$121$			3131.12i			0.213860i
$122$	−2949.47	−	4688.78i	−0.198164	−	0.315021i
$123$	−4473.64	−	4473.64i	−0.295700	−	0.295700i
$124$	10996.3	−	22893.4i	0.715161	−	1.48890i
$125$	−11233.9	−	11233.9i	−0.718967	−	0.718967i
$126$	2153.92	−	9459.02i	0.135672	−	0.595806i
$127$		−	14529.4i		−	0.900823i	−0.892821	−	0.450412i	$-0.851277\pi$
$127$		−	14529.4i		−	0.900823i	0.892821	−	0.450412i	$-0.148723\pi$
$128$	58.0571	+	16383.9i	0.00354352	+	0.999994i
$129$	9579.82			0.575676
$130$	13656.2	+	3109.66i	0.808057	+	0.184003i
$131$	−11099.9	+	11099.9i	−0.646812	+	0.646812i	−0.952221	−	0.305409i	$-0.901207\pi$
$131$	−11099.9	+	11099.9i	−0.646812	+	0.646812i	0.305409	+	0.952221i	$0.401207\pi$
$132$	−9990.63	−	4798.78i	−0.573383	−	0.275412i
$133$	−29164.3	+	29164.3i	−1.64873	+	1.64873i
$134$	−10855.2	+	6828.44i	−0.604544	+	0.380287i
$135$	3445.30			0.189042
$136$	−3313.27	−	2634.02i	−0.179135	−	0.142410i
$137$		−	18444.8i		−	0.982728i	−0.870954	−	0.491364i	$-0.836498\pi$
$137$		−	18444.8i		−	0.982728i	0.870954	−	0.491364i	$-0.163502\pi$
$138$	−8221.47	+	5171.70i	−0.431709	+	0.271566i
$139$	−14540.4	−	14540.4i	−0.752570	−	0.752570i	0.222388	−	0.974958i	$-0.428615\pi$
$139$	−14540.4	−	14540.4i	−0.752570	−	0.752570i	−0.974958	+	0.222388i	$0.928615\pi$
$140$	−33301.6	+	11690.6i	−1.69906	+	0.596458i
$141$	14623.2	+	14623.2i	0.735534	+	0.735534i
$142$	22914.5	+	5217.88i	1.13641	+	0.258772i
$143$			19007.9i			0.929528i
$144$	5395.28	−	4320.50i	0.260189	−	0.208357i
$145$	11177.2			0.531615
$146$	−3251.59	+	14279.5i	−0.152542	+	0.669895i
$147$	20824.2	−	20824.2i	0.963681	−	0.963681i
$148$	20983.1	−	7366.16i	0.957958	−	0.336293i
$149$	19098.8	−	19098.8i	0.860266	−	0.860266i	−0.131103	−	0.991369i	$-0.541852\pi$
$149$	19098.8	−	19098.8i	0.860266	−	0.860266i	0.991369	+	0.131103i	$0.0418518\pi$
$150$	242.792	+	385.968i	0.0107908	+	0.0171541i
$151$	19549.9			0.857415			0.428707	−	0.903443i	$-0.358969\pi$
$151$	19549.9			0.857415			0.428707	+	0.903443i	$0.358969\pi$
$152$	−29196.7	+	3334.58i	−1.26371	+	0.144329i
$153$			1785.68i			0.0762816i
$154$	−25504.5	−	40544.6i	−1.07541	−	1.70959i
$155$	27563.5	+	27563.5i	1.14728	+	1.14728i
$156$	−10685.3	−	5132.47i	−0.439075	−	0.210900i
$157$	1667.24	+	1667.24i	0.0676393	+	0.0676393i	0.740117	−	0.672478i	$-0.234770\pi$
$157$	1667.24	+	1667.24i	0.0676393	+	0.0676393i	−0.672478	+	0.740117i	$0.734770\pi$
$158$	478.837	−	2102.83i	0.0191811	−	0.0842345i
$159$		−	4943.12i		−	0.195527i
$160$	−23756.5	−	8245.32i	−0.927988	−	0.322083i
$161$	−41976.2			−1.61939
$162$	−2843.22	−	647.432i	−0.108338	−	0.0246697i
$163$	−25019.4	+	25019.4i	−0.941676	+	0.941676i	−0.998390	−	0.0567142i	$-0.981938\pi$
$163$	−25019.4	+	25019.4i	−0.941676	+	0.941676i	0.0567142	+	0.998390i	$0.481938\pi$
$164$	8434.78	−	17560.5i	0.313607	−	0.652902i
$165$	12028.7	−	12028.7i	0.441824	−	0.441824i
$166$	−17272.1	+	10865.0i	−0.626799	+	0.394287i
$167$	−8048.66			−0.288596			−0.144298	−	0.989534i	$-0.546092\pi$
$167$	−8048.66			−0.288596			−0.144298	+	0.989534i	$0.546092\pi$
$168$	29678.9	−	3389.66i	1.05155	−	0.120098i
$169$		−	8231.33i		−	0.288202i
$170$	5499.00	−	3459.13i	0.190277	−	0.119693i
$171$	8766.30	+	8766.30i	0.299795	+	0.299795i
$172$	9770.82	+	27833.0i	0.330274	+	0.940812i
$173$	14994.1	+	14994.1i	0.500990	+	0.500990i	0.911746	−	0.410755i	$-0.134735\pi$
$173$	14994.1	+	14994.1i	0.500990	+	0.500990i	−0.410755	+	0.911746i	$0.634735\pi$
$174$	−9223.94	−	2100.39i	−0.304662	−	0.0693748i
$175$			1970.63i			0.0643471i
$176$	3752.43	−	33921.0i	0.121140	−	1.09507i
$177$	−8731.04			−0.278689
$178$	−6704.65	+	29443.7i	−0.211610	+	0.929292i
$179$	22215.1	−	22215.1i	0.693333	−	0.693333i	−0.269631	−	0.962964i	$-0.586902\pi$
$179$	22215.1	−	22215.1i	0.693333	−	0.693333i	0.962964	+	0.269631i	$0.0869016\pi$
$180$	3513.99	+	10009.9i	0.108456	+	0.308947i
$181$	−7611.92	+	7611.92i	−0.232347	+	0.232347i	−0.813672	−	0.581325i	$-0.802535\pi$
$181$	−7611.92	+	7611.92i	−0.232347	+	0.232347i	0.581325	+	0.813672i	$0.302535\pi$
$182$	−27278.0	−	43363.9i	−0.823511	−	1.30914i
$183$	−7195.78			−0.214870
$184$	−23411.1	−	18611.6i	−0.691491	−	0.549729i
$185$			34132.4i			0.997294i
$186$	−17567.0	−	27926.3i	−0.507775	−	0.807212i
$187$	6234.38	+	6234.38i	0.178283	+	0.178283i
$188$	−27571.1	+	57400.5i	−0.780078	+	1.62405i
$189$	−8911.08	−	8911.08i	−0.249463	−	0.249463i
$190$	10014.2	−	43977.5i	0.277401	−	1.21821i
$191$			31974.8i			0.876479i	0.898858	+	0.438239i	$0.144398\pi$
$191$			31974.8i			0.876479i	−0.898858	+	0.438239i	$0.855602\pi$
$192$	18055.5	+	11268.7i	0.489787	+	0.305683i
$193$	17517.2			0.470272			0.235136	−	0.971962i	$-0.424446\pi$
$193$	17517.2			0.470272			0.235136	+	0.971962i	$0.424446\pi$
$194$	−37425.1	−	8522.11i	−0.994397	−	0.226435i
$195$	12865.1	−	12865.1i	0.338332	−	0.338332i
$196$	81741.4	+	39262.7i	2.12780	+	1.02204i
$197$	46651.3	−	46651.3i	1.20207	−	1.20207i	0.228540	−	0.973535i	$-0.426605\pi$
$197$	46651.3	−	46651.3i	1.20207	−	1.20207i	0.973535	−	0.228540i	$-0.0733951\pi$
$198$	−12187.0	+	7666.21i	−0.310861	+	0.195547i
$199$	−48575.7			−1.22663			−0.613314	−	0.789839i	$-0.710164\pi$
$199$	−48575.7			−1.22663			−0.613314	+	0.789839i	$0.710164\pi$
$200$	−873.749	+	1099.07i	−0.0218437	+	0.0274767i
$201$			16659.3i			0.412348i
$202$	11217.7	−	7056.48i	0.274917	−	0.172936i
$203$	−28909.2	−	28909.2i	−0.701527	−	0.701527i
$204$	−5188.06	+	1821.28i	−0.124665	+	0.0437639i
$205$	21142.7	+	21142.7i	0.503098	+	0.503098i
$206$	53253.0	+	12126.3i	1.25490	+	0.285755i
$207$			12617.3i			0.294460i
$208$	4013.37	−	36279.7i	0.0927645	−	0.838566i
$209$	61212.1			1.40134
$210$	−10179.6	+	44703.9i	−0.230829	+	1.01369i
$211$	−43450.3	+	43450.3i	−0.975950	+	0.975950i	−0.999718	−	0.0237673i	$-0.992434\pi$
$211$	−43450.3	+	43450.3i	−0.975950	+	0.975950i	0.0237673	+	0.999718i	$0.492434\pi$
$212$	14361.6	−	5041.68i	0.319545	−	0.112177i
$213$	21587.1	−	21587.1i	0.475811	−	0.475811i
$214$	31993.8	+	50860.7i	0.698616	+	1.11059i
$215$	−45274.8			−0.979444
$216$	−1018.87	−	8920.96i	−0.0218380	−	0.191207i
$217$		−	142583.i		−	3.02795i
$218$	18368.8	+	29201.0i	0.386517	+	0.614448i
$219$	13452.3	+	13452.3i	0.280484	+	0.280484i
$220$	47216.3	+	22679.3i	0.975543	+	0.468580i
$221$	6667.90	+	6667.90i	0.136523	+	0.136523i
$222$	6414.08	−	28167.6i	0.130145	−	0.571537i
$223$			76389.5i			1.53612i	0.640380	+	0.768058i	$0.278777\pi$
$223$			76389.5i			1.53612i	−0.640380	+	0.768058i	$0.721223\pi$
$224$	40118.8	+	82771.0i	0.799562	+	1.64961i
$225$	592.338			0.0117005
$226$	8168.14	+	1859.97i	0.159921	+	0.0364158i
$227$	41467.0	−	41467.0i	0.804731	−	0.804731i	−0.179100	−	0.983831i	$-0.557318\pi$
$227$	41467.0	−	41467.0i	0.804731	−	0.804731i	0.983831	+	0.179100i	$0.0573185\pi$
$228$	−16528.3	+	34410.5i	−0.317950	+	0.661943i
$229$	−26777.4	+	26777.4i	−0.510620	+	0.510620i	−0.914716	−	0.404096i	$-0.867586\pi$
$229$	−26777.4	+	26777.4i	−0.510620	+	0.510620i	0.404096	+	0.914716i	$0.367586\pi$
$230$	38855.1	−	24441.7i	0.734501	−	0.462036i
$231$	−62223.0			−1.16608
$232$	−3305.42	−	28941.3i	−0.0614116	−	0.537702i
$233$		−	98378.0i		−	1.81212i	−0.423153	−	0.906058i	$-0.639077\pi$
$233$		−	98378.0i		−	1.81212i	0.423153	−	0.906058i	$-0.360923\pi$
$234$	−13034.4	+	8199.29i	−0.238046	+	0.149742i
$235$	−69109.9	−	69109.9i	−1.25142	−	1.25142i
$236$	−8905.12	−	25367.0i	−0.159888	−	0.455454i
$237$	−1981.02	−	1981.02i	−0.0352689	−	0.0352689i
$238$	−23169.7	−	5276.00i	−0.409041	−	0.0931432i
$239$			27673.0i			0.484463i	0.970218	+	0.242232i	$0.0778794\pi$
$239$			27673.0i			0.484463i	−0.970218	+	0.242232i	$0.922121\pi$
$240$	−25498.4	+	20418.9i	−0.442681	+	0.354495i
$241$	−46490.2			−0.800438			−0.400219	−	0.916419i	$-0.631066\pi$
$241$	−46490.2			−0.800438			−0.400219	+	0.916419i	$0.631066\pi$
$242$	−2780.78	+	12211.9i	−0.0474827	+	0.208522i
$243$	−2678.52	+	2678.52i	−0.0453609	+	0.0453609i
$244$	−7339.25	−	20906.4i	−0.123274	−	0.351156i
$245$	−98416.2	+	98416.2i	−1.63959	+	1.63959i
$246$	−13474.8	−	21421.0i	−0.222666	−	0.353973i
$247$	65468.5			1.07310
$248$	63219.2	−	79521.8i	1.02789	−	1.29295i
$249$			26507.1i			0.427528i
$250$	−33837.0	−	53790.7i	−0.541391	−	0.860652i
$251$	26522.0	+	26522.0i	0.420978	+	0.420978i	0.885540	−	0.464563i	$-0.153788\pi$
$251$	26522.0	+	26522.0i	0.420978	+	0.420978i	−0.464563	+	0.885540i	$0.653788\pi$
$252$	16801.3	−	34978.8i	0.264571	−	0.550812i
$253$	44051.2	+	44051.2i	0.688204	+	0.688204i
$254$	12903.7	−	56666.9i	0.200007	−	0.878339i
$255$		−	8439.20i		−	0.129784i
$256$	−14324.3	+	63951.4i	−0.218571	+	0.975821i
$257$	−31183.5			−0.472127			−0.236064	−	0.971738i	$-0.575857\pi$
$257$	−31183.5			−0.472127			−0.236064	+	0.971738i	$0.575857\pi$
$258$	37362.9	+	8507.93i	0.561307	+	0.127816i
$259$	88281.7	−	88281.7i	1.31605	−	1.31605i
$260$	50499.5	+	24256.3i	0.747034	+	0.358821i
$261$	−8689.62	+	8689.62i	−0.127562	+	0.127562i
$262$	−53149.5	+	33433.6i	−0.774278	+	0.487058i
$263$	−87530.3			−1.26546			−0.632728	−	0.774374i	$-0.718065\pi$
$263$	−87530.3			−1.26546			−0.632728	+	0.774374i	$0.718065\pi$
$264$	−34703.2	−	27588.8i	−0.497923	−	0.395845i
$265$			23361.5i			0.332666i
$266$	−139647.	+	87844.5i	−1.97364	+	1.24151i
$267$	27738.1	+	27738.1i	0.389094	+	0.389094i
$268$	−48401.4	+	16991.4i	−0.673889	+	0.236570i
$269$	−38179.9	−	38179.9i	−0.527631	−	0.527631i	0.392234	−	0.919865i	$-0.371702\pi$
$269$	−38179.9	−	38179.9i	−0.527631	−	0.527631i	−0.919865	+	0.392234i	$0.871702\pi$
$270$	13437.2	+	3059.80i	0.184324	+	0.0419726i
$271$		−	19976.0i		−	0.272001i	−0.990709	−	0.136000i	$-0.956575\pi$
$271$		−	19976.0i		−	0.272001i	0.990709	−	0.136000i	$-0.0434249\pi$
$272$	−10583.0	−	13215.7i	−0.143044	−	0.178629i
$273$	−66549.8			−0.892938
$274$	16381.0	−	71937.8i	0.218193	−	0.958200i
$275$	2068.05	−	2068.05i	0.0273461	−	0.0273461i
$276$	−36658.1	+	12868.9i	−0.481229	+	0.168936i
$277$	8347.44	−	8347.44i	0.108791	−	0.108791i	−0.650616	−	0.759407i	$-0.725489\pi$
$277$	8347.44	−	8347.44i	0.108791	−	0.108791i	0.759407	+	0.650616i	$0.225489\pi$
$278$	−43796.5	−	69623.4i	−0.566695	−	0.900877i
$279$	−42858.0			−0.550584
$280$	−140264.	+	16019.7i	−1.78908	+	0.204333i
$281$			42474.9i			0.537922i	0.963151	+	0.268961i	$0.0866803\pi$
$281$			42474.9i			0.537922i	−0.963151	+	0.268961i	$0.913320\pi$
$282$	44045.7	+	70019.7i	0.553867	+	0.880485i
$283$	35828.8	+	35828.8i	0.447362	+	0.447362i	0.894477	−	0.447115i	$-0.147548\pi$
$283$	35828.8	+	35828.8i	0.447362	+	0.447362i	−0.447115	+	0.894477i	$0.647548\pi$
$284$	84736.1	+	40701.1i	1.05059	+	0.504626i
$285$	−41430.0	−	41430.0i	−0.510065	−	0.510065i
$286$	−16881.1	+	74134.0i	−0.206381	+	0.906328i
$287$		−	109369.i		−	1.32779i
$288$	24879.5	−	12059.0i	0.299956	−	0.145388i
$289$	−79147.0			−0.947630
$290$	43592.9	+	9926.57i	0.518346	+	0.118033i
$291$	−35257.2	+	35257.2i	−0.416353	+	0.416353i
$292$	−25363.5	+	52804.5i	−0.297470	+	0.619306i
$293$	90088.6	−	90088.6i	1.04938	−	1.04938i	0.0506689	−	0.998716i	$-0.483865\pi$
$293$	90088.6	−	90088.6i	1.04938	−	1.04938i	0.998716	−	0.0506689i	$-0.0161353\pi$
$294$	99711.8	−	62723.5i	1.15359	−	0.725664i
$295$	41263.4			0.474156
$296$	88379.5	−	10093.9i	1.00871	−	0.115206i
$297$			18703.2i			0.212032i
$298$	91450.1	−	57526.5i	1.02980	−	0.647791i
$299$	47114.4	+	47114.4i	0.527001	+	0.527001i
$300$	604.148	+	1720.96i	0.00671275	+	0.0191218i
$301$	117101.	+	117101.i	1.29249	+	1.29249i
$302$	76247.8	+	17362.5i	0.836014	+	0.190370i
$303$		−	17215.6i		−	0.187516i
$304$	−116833.	−	12924.4i	−1.26421	−	0.139850i
$305$	34007.7			0.365575
$306$	−1585.88	+	6964.42i	−0.0169366	+	0.0743776i
$307$	8380.03	−	8380.03i	0.0889137	−	0.0889137i	−0.661251	−	0.750165i	$-0.729974\pi$
$307$	8380.03	−	8380.03i	0.0889137	−	0.0889137i	0.750165	+	0.661251i	$0.229974\pi$
$308$	−63463.6	−	180781.i	−0.668996	−	1.90569i
$309$	50168.2	−	50168.2i	0.525426	−	0.525426i
$310$	83022.6	+	131981.i	0.863919	+	1.37338i
$311$	111760.			1.15549			0.577743	−	0.816219i	$-0.303933\pi$
$311$	111760.			1.15549			0.577743	+	0.816219i	$0.303933\pi$
$312$	−37116.4	−	29507.2i	−0.381291	−	0.303123i
$313$		−	84467.1i		−	0.862182i	−0.902308	−	0.431091i	$-0.858129\pi$
$313$		−	84467.1i		−	0.862182i	0.902308	−	0.431091i	$-0.141871\pi$
$314$	5021.81	+	7983.20i	0.0509332	+	0.0809688i
$315$	42114.3	+	42114.3i	0.424432	+	0.424432i
$316$	3735.09	−	7776.12i	0.0374047	−	0.0778733i
$317$	105937.	+	105937.i	1.05422	+	1.05422i	0.998444	+	0.0557723i	$0.0177621\pi$
$317$	105937.	+	105937.i	1.05422	+	1.05422i	0.0557723	+	0.998444i	$0.482238\pi$
$318$	4390.03	−	19279.0i	0.0434124	−	0.190647i
$319$			60676.7i			0.596266i
$320$	−85331.4	−	53256.4i	−0.833314	−	0.520082i
$321$	78054.9			0.757513
$322$	−163714.	−	37279.5i	−1.57897	−	0.359549i
$323$	21472.9	−	21472.9i	0.205819	−	0.205819i
$324$	−10514.0	−	5050.18i	−0.100156	−	0.0481079i
$325$	2211.85	−	2211.85i	0.0209406	−	0.0209406i
$326$	−119800.	+	75359.7i	−1.12725	+	0.709095i
$327$	44814.2			0.419103
$328$	48492.6	−	60997.6i	0.450742	−	0.566977i
$329$			357498.i			3.30280i
$330$	57596.5	−	36231.0i	0.528893	−	0.332699i
$331$	−22373.4	−	22373.4i	−0.204209	−	0.204209i	0.597592	−	0.801801i	$-0.296124\pi$
$331$	−22373.4	−	22373.4i	−0.204209	−	0.204209i	−0.801801	+	0.597592i	$0.796124\pi$
$332$	−77013.2	+	27035.6i	−0.698697	+	0.245279i
$333$	−26535.9	−	26535.9i	−0.239302	−	0.239302i
$334$	−31391.1	−	7148.09i	−0.281393	−	0.0640762i
$335$		−	78732.6i		−	0.701560i
$336$	118763.	+	13137.9i	1.05197	+	0.116371i
$337$	124397.			1.09534			0.547671	−	0.836694i	$-0.315515\pi$
$337$	124397.			1.09534			0.547671	+	0.836694i	$0.315515\pi$
$338$	7310.32	−	32103.5i	0.0639887	−	0.281008i
$339$	7694.98	−	7694.98i	0.0669588	−	0.0669588i
$340$	24519.1	−	8607.46i	0.212103	−	0.0744590i
$341$	−149631.	+	149631.i	−1.28681	+	1.28681i
$342$	26404.5	+	41975.4i	0.225749	+	0.358875i
$343$	293426.			2.49408
$344$	13389.0	+	117231.i	0.113144	+	0.990659i
$345$		−	59630.2i		−	0.500989i
$346$	45163.1	+	71796.0i	0.377252	+	0.599719i
$347$	−163054.	−	163054.i	−1.35417	−	1.35417i	−0.880938	−	0.473232i	$-0.843087\pi$
$347$	−163054.	−	163054.i	−1.35417	−	1.35417i	−0.473232	−	0.880938i	$-0.656913\pi$
$348$	−34109.5	−	16383.7i	−0.281655	−	0.135287i
$349$	−122260.	−	122260.i	−1.00377	−	1.00377i	−0.999993	−	0.00377908i	$-0.998797\pi$
$349$	−122260.	−	122260.i	−1.00377	−	1.00377i	−0.00377908	−	0.999993i	$-0.501203\pi$
$350$	−1750.14	+	7685.78i	−0.0142868	+	0.0627410i
$351$			20003.7i			0.162367i
$352$	44760.6	−	128965.i	0.361253	−	1.04084i
$353$	−216947.			−1.74102			−0.870511	−	0.492150i	$-0.836211\pi$
$353$	−216947.			−1.74102			−0.870511	+	0.492150i	$0.836211\pi$
$354$	−34052.5	−	7754.12i	−0.271733	−	0.0618765i
$355$	−102022.	+	102022.i	−0.809536	+	0.809536i
$356$	−52298.4	+	108881.i	−0.412657	+	0.859114i
$357$	−21827.6	+	21827.6i	−0.171265	+	0.171265i
$358$	106372.	−	66913.0i	0.829967	−	0.522089i
$359$	−63960.0			−0.496271			−0.248136	−	0.968725i	$-0.579818\pi$
$359$	−63960.0			−0.496271			−0.248136	+	0.968725i	$0.579818\pi$
$360$	4815.25	+	42160.9i	0.0371547	+	0.325316i
$361$		−	80510.1i		−	0.617783i
$362$	−36448.0	+	22927.5i	−0.278135	+	0.174960i
$363$	11504.5	+	11504.5i	0.0873078	+	0.0873078i
$364$	−67876.7	−	193352.i	−0.512292	−	1.45931i
$365$	−63576.3	−	63576.3i	−0.477210	−	0.477210i
$366$	−28064.7	−	6390.64i	−0.209507	−	0.0477070i
$367$		−	71673.9i		−	0.532144i	−0.963953	−	0.266072i	$-0.914274\pi$
$367$		−	71673.9i		−	0.532144i	0.963953	−	0.266072i	$-0.0857258\pi$
$368$	−74777.9	−	93380.0i	−0.552176	−	0.689538i
$369$	−32874.4			−0.241438
$370$	−30313.3	+	133122.i	−0.221427	+	0.972402i
$371$	60423.3	−	60423.3i	0.438992	−	0.438992i
$372$	−43712.5	−	124519.i	−0.315878	−	0.899805i
$373$	−62867.7	+	62867.7i	−0.451866	+	0.451866i	−0.895973	−	0.444108i	$-0.853521\pi$
$373$	−62867.7	+	62867.7i	−0.451866	+	0.451866i	0.444108	+	0.895973i	$0.353521\pi$
$374$	18778.3	+	29851.9i	0.134250	+	0.213417i
$375$	−82551.6			−0.587034
$376$	−158510.	+	199385.i	−1.12119	+	1.41032i
$377$			64895.9i			0.456599i
$378$	−26840.6	−	42668.7i	−0.187849	−	0.298625i
$379$	23713.9	+	23713.9i	0.165092	+	0.165092i	0.784818	−	0.619726i	$-0.212756\pi$
$379$	23713.9	+	23713.9i	0.165092	+	0.165092i	−0.619726	+	0.784818i	$0.712756\pi$
$380$	78113.7	−	162626.i	0.540954	−	1.12622i
$381$	−53384.3	−	53384.3i	−0.367759	−	0.367759i
$382$	−28397.1	+	124707.i	−0.194602	+	0.854602i
$383$		−	121708.i		−	0.829701i	−0.909890	−	0.414850i	$-0.863834\pi$
$383$		−	121708.i		−	0.829701i	0.909890	−	0.414850i	$-0.136166\pi$
$384$	60411.6	+	59985.0i	0.409692	+	0.406799i
$385$	294070.			1.98394
$386$	68319.8	+	15557.2i	0.458534	+	0.104413i
$387$	35198.5	−	35198.5i	0.235019	−	0.235019i
$388$	−138396.	−	66475.2i	−0.919303	−	0.441567i
$389$	40074.9	−	40074.9i	0.264834	−	0.264834i	−0.562181	−	0.827014i	$-0.690037\pi$
$389$	40074.9	−	40074.9i	0.264834	−	0.264834i	0.827014	+	0.562181i	$0.190037\pi$
$390$	61601.5	−	38750.3i	0.405007	−	0.254769i
$391$	30906.0			0.202157
$392$	283935.	+	225726.i	1.84777	+	1.46896i
$393$			81567.6i			0.528120i
$394$	223379.	−	140516.i	1.43896	−	0.905178i
$395$	9362.41	+	9362.41i	0.0600058	+	0.0600058i
$396$	−54339.7	+	19076.1i	−0.346519	+	0.121646i
$397$	−118458.	−	118458.i	−0.751595	−	0.751595i	0.223182	−	0.974777i	$-0.428356\pi$
$397$	−118458.	−	118458.i	−0.751595	−	0.751595i	−0.974777	+	0.223182i	$0.928356\pi$
$398$	−189453.	−	43140.5i	−1.19601	−	0.272345i
$399$			214313.i			1.34618i
$400$	−4383.85	+	3510.55i	−0.0273991	+	0.0219409i
$401$	45116.3			0.280572			0.140286	−	0.990111i	$-0.455198\pi$
$401$	45116.3			0.280572			0.140286	+	0.990111i	$0.455198\pi$
$402$	−14795.2	+	64973.8i	−0.0915525	+	0.402056i
$403$	−160036.	+	160036.i	−0.985390	+	0.985390i
$404$	50017.8	−	17558.9i	0.306452	−	0.107580i
$405$	12658.8	−	12658.8i	0.0771762	−	0.0771762i
$406$	−87076.2	−	138425.i	−0.528259	−	0.839776i
$407$	−185291.			−1.11858
$408$	−21851.8	+	2495.71i	−0.131270	+	0.0149925i
$409$		−	93624.9i		−	0.559687i	−0.960046	−	0.279843i	$-0.909718\pi$
$409$		−	93624.9i		−	0.559687i	0.960046	−	0.279843i	$-0.0902825\pi$
$410$	63682.9	+	101237.i	0.378839	+	0.602242i
$411$	−67770.6	−	67770.6i	−0.401197	−	0.401197i
$412$	196926.	+	94589.1i	1.16014	+	0.557245i
$413$	−106726.	−	106726.i	−0.625704	−	0.625704i
$414$	−11205.6	+	49209.6i	−0.0653782	+	0.287111i
$415$		−	125274.i		−	0.727387i
$416$	47873.1	−	137932.i	0.276634	−	0.797040i
$417$	−106850.			−0.614471
$418$	238737.	+	54363.0i	1.36637	+	0.311136i
$419$	−122699.	+	122699.i	−0.698895	+	0.698895i	−0.964172	−	0.265277i	$-0.914537\pi$
$419$	−122699.	+	122699.i	−0.698895	+	0.698895i	0.265277	+	0.964172i	$0.414537\pi$
$420$	−79403.8	+	165312.i	−0.450135	+	0.937141i
$421$	48594.3	−	48594.3i	0.274171	−	0.274171i	−0.556606	−	0.830777i	$-0.687897\pi$
$421$	48594.3	−	48594.3i	0.274171	−	0.274171i	0.830777	+	0.556606i	$0.187897\pi$
$422$	−208052.	+	130875.i	−1.16828	+	0.734903i
$423$	107458.			0.600561
$424$	60490.2	−	6908.66i	0.336476	−	0.0384293i
$425$		−	1450.92i		−	0.00803279i
$426$	103365.	−	65021.4i	0.569579	−	0.358292i
$427$	−87959.1	−	87959.1i	−0.482419	−	0.482419i
$428$	79611.2	+	226779.i	0.434597	+	1.23798i
$429$	69839.6	+	69839.6i	0.379478	+	0.379478i
$430$	−176579.	−	40209.0i	−0.954997	−	0.217463i
$431$		−	32150.5i		−	0.173075i	−0.996249	−	0.0865374i	$-0.972420\pi$
$431$		−	32150.5i		−	0.173075i	0.996249	−	0.0865374i	$-0.0275802\pi$
$432$	3949.02	−	35698.0i	0.0211603	−	0.191283i
$433$	−91093.8			−0.485862			−0.242931	−	0.970044i	$-0.578109\pi$
$433$	−91093.8			−0.485862			−0.242931	+	0.970044i	$0.578109\pi$
$434$	126629.	−	556097.i	0.672287	−	2.95237i
$435$	41067.6	−	41067.6i	0.217031	−	0.217031i
$436$	45707.7	+	130202.i	0.240446	+	0.684929i
$437$	151725.	−	151725.i	0.794499	−	0.794499i
$438$	40519.0	+	64413.2i	0.211208	+	0.335758i
$439$	−267216.			−1.38655			−0.693273	−	0.720675i	$-0.743832\pi$
$439$	−267216.			−1.38655			−0.693273	+	0.720675i	$0.743832\pi$
$440$	164009.	+	130386.i	0.847156	+	0.673482i
$441$		−	153026.i		−	0.786842i
$442$	20084.1	+	31927.7i	0.102803	+	0.163427i
$443$	167381.	+	167381.i	0.852900	+	0.852900i	0.990489	−	0.137589i	$-0.0439353\pi$
$443$	167381.	+	167381.i	0.852900	+	0.852900i	−0.137589	+	0.990489i	$0.543935\pi$
$444$	50031.9	−	104162.i	0.253794	−	0.528376i
$445$	−131092.	−	131092.i	−0.661996	−	0.661996i
$446$	−67842.3	+	297932.i	−0.341060	+	1.49778i
$447$		−	140347.i		−	0.702404i
$448$	82960.2	+	358450.i	0.413346	+	1.78596i
$449$	175788.			0.871960			0.435980	−	0.899956i	$-0.356402\pi$
$449$	175788.			0.871960			0.435980	+	0.899956i	$0.356402\pi$
$450$	2310.21	+	526.061i	0.0114085	+	0.00259783i
$451$	−114775.	+	114775.i	−0.564282	+	0.564282i
$452$	30205.2	+	14508.4i	0.147844	+	0.0710138i
$453$	71831.0	−	71831.0i	0.350038	−	0.350038i
$454$	198555.	−	124901.i	0.963318	−	0.605973i
$455$	314518.			1.51923
$456$	−95023.3	+	119527.i	−0.456984	+	0.574828i
$457$			393478.i			1.88403i	0.335570	+	0.942015i	$0.391071\pi$
$457$			393478.i			1.88403i	−0.335570	+	0.942015i	$0.608929\pi$
$458$	−128218.	+	80655.0i	−0.611247	+	0.384504i
$459$	6560.99	+	6560.99i	0.0311418	+	0.0311418i
$460$	173248.	−	60819.1i	0.818753	−	0.287425i
$461$	85882.9	+	85882.9i	0.404115	+	0.404115i	0.879680	−	0.475565i	$-0.157756\pi$
$461$	85882.9	+	85882.9i	0.404115	+	0.404115i	−0.475565	+	0.879680i	$0.657756\pi$
$462$	−242680.	−	55260.9i	−1.13697	−	0.258901i
$463$			112113.i			0.522992i	0.965205	+	0.261496i	$0.0842159\pi$
$463$			112113.i			0.522992i	−0.965205	+	0.261496i	$0.915784\pi$
$464$	12811.4	−	115811.i	0.0595058	−	0.537917i
$465$	202549.			0.936753
$466$	87370.4	−	383690.i	0.402339	−	1.76689i
$467$	40803.5	−	40803.5i	0.187096	−	0.187096i	−0.607344	−	0.794439i	$-0.707765\pi$
$467$	40803.5	−	40803.5i	0.187096	−	0.187096i	0.794439	+	0.607344i	$0.207765\pi$
$468$	−58118.3	+	20402.6i	−0.265351	+	0.0931521i
$469$	−203638.	+	203638.i	−0.925791	+	0.925791i
$470$	−208163.	−	330917.i	−0.942339	−	1.49804i
$471$	12251.7			0.0552272
$472$	−12202.8	−	106844.i	−0.0547740	−	0.479585i
$473$		−	245779.i		−	1.09856i
$474$	−5966.93	−	9485.65i	−0.0265579	−	0.0422193i
$475$	−7122.92	−	7122.92i	−0.0315697	−	0.0315697i
$476$	−85680.1	−	41154.5i	−0.378152	−	0.181637i
$477$	−18162.2	−	18162.2i	−0.0798236	−	0.0798236i
$478$	−24576.7	+	107929.i	−0.107564	+	0.472371i
$479$			111665.i			0.486683i	0.969941	+	0.243341i	$0.0782435\pi$
$479$			111665.i			0.486683i	−0.969941	+	0.243341i	$0.921757\pi$
$480$	−117582.	+	56991.7i	−0.510339	+	0.247360i
$481$	−198176.			−0.856566
$482$	−181319.	−	41288.4i	−0.780460	−	0.177719i
$483$	−154230.	+	154230.i	−0.661113	+	0.661113i
$484$	−21690.9	+	45158.6i	−0.0925951	+	0.192775i
$485$	166627.	−	166627.i	0.708375	−	0.708375i
$486$	−12825.5	+	8067.83i	−0.0543001	+	0.0341574i
$487$	63810.7			0.269052			0.134526	−	0.990910i	$-0.457049\pi$
$487$	63810.7			0.269052			0.134526	+	0.990910i	$0.457049\pi$
$488$	−10057.0	−	88056.5i	−0.0422309	−	0.369762i
$489$			183854.i			0.768875i
$490$	−471244.	+	296435.i	−1.96270	+	1.23463i
$491$	100954.	+	100954.i	0.418758	+	0.418758i	0.884775	−	0.466018i	$-0.154312\pi$
$491$	100954.	+	100954.i	0.418758	+	0.418758i	−0.466018	+	0.884775i	$0.654312\pi$
$492$	−33529.9	−	95512.6i	−0.138517	−	0.394576i
$493$	21285.1	+	21285.1i	0.0875754	+	0.0875754i
$494$	255338.	+	58143.2i	1.04631	+	0.238257i
$495$		−	88392.2i		−	0.360748i
$496$	317189.	−	254002.i	1.28930	−	1.03246i
$497$	527748.			2.13656
$498$	−23541.2	+	103382.i	−0.0949229	+	0.416857i
$499$	3018.09	−	3018.09i	0.0121208	−	0.0121208i	−0.701020	−	0.713141i	$-0.747272\pi$
$499$	3018.09	−	3018.09i	0.0121208	−	0.0121208i	0.713141	+	0.701020i	$0.247272\pi$
$500$	−84197.5	−	239844.i	−0.336790	−	0.959374i
$501$	−29572.7	+	29572.7i	−0.117819	+	0.117819i
$502$	79885.7	+	126995.i	0.317002	+	0.503939i
$503$	139696.			0.552140			0.276070	−	0.961138i	$-0.410968\pi$
$503$	139696.			0.552140			0.276070	+	0.961138i	$0.410968\pi$
$504$	96592.7	−	121502.i	0.380262	−	0.478322i
$505$			81362.0i			0.319035i
$506$	132685.	+	210929.i	0.518227	+	0.823827i
$507$	−30243.8	−	30243.8i	−0.117658	−	0.117658i
$508$	100653.	−	209550.i	0.390031	−	0.812009i
$509$	−98475.6	−	98475.6i	−0.380096	−	0.380096i	0.491041	−	0.871137i	$-0.336617\pi$
$509$	−98475.6	−	98475.6i	−0.380096	−	0.380096i	−0.871137	+	0.491041i	$0.836617\pi$
$510$	7494.94	−	32914.3i	0.0288156	−	0.126545i
$511$			328874.i			1.25947i
$512$	−112663.	+	236699.i	−0.429774	+	0.902936i
$513$	64418.9			0.244781
$514$	−121621.	−	27694.4i	−0.460343	−	0.104825i
$515$	−237098.	+	237098.i	−0.893950	+	0.893950i
$516$	138165.	+	66364.6i	0.518919	+	0.249251i
$517$	375171.	−	375171.i	1.40361	−	1.40361i
$518$	422717.	−	265909.i	1.57540	−	0.991000i
$519$	110184.			0.409057
$520$	175414.	+	139453.i	0.648720	+	0.515728i
$521$		−	122222.i		−	0.450271i	−0.974327	−	0.225136i	$-0.927718\pi$
$521$		−	122222.i		−	0.450271i	0.974327	−	0.225136i	$-0.0722825\pi$
$522$	−41608.3	+	26173.6i	−0.152700	+	0.0960555i
$523$	50532.0	+	50532.0i	0.184741	+	0.184741i	0.793418	−	0.608677i	$-0.208300\pi$
$523$	50532.0	+	50532.0i	0.184741	+	0.184741i	−0.608677	+	0.793418i	$0.708300\pi$
$524$	−236984.	+	83193.8i	−0.863092	+	0.302990i
$525$	7240.56	+	7240.56i	0.0262696	+	0.0262696i
$526$	−341382.	−	77736.5i	−1.23387	−	0.280966i
$527$			104980.i			0.377995i
$528$	−110846.	−	138421.i	−0.397606	−	0.496517i
$529$	−61463.8			−0.219638
$530$	−20747.6	+	91113.5i	−0.0738610	+	0.324363i
$531$	−32079.9	+	32079.9i	−0.113774	+	0.113774i
$532$	−622660.	+	218586.i	−2.20003	+	0.772324i
$533$	−122757.	+	122757.i	−0.432106	+	0.432106i
$534$	83548.6	+	132817.i	0.292993	+	0.465771i
$535$	−368892.			−1.28882
$536$	−203864.	+	23283.5i	−0.709594	+	0.0810436i
$537$		−	163247.i		−	0.566104i
$538$	−115000.	−	182816.i	−0.397313	−	0.631610i
$539$	−534263.	−	534263.i	−1.83898	−	1.83898i
$540$	49689.9	+	23867.4i	0.170404	+	0.0818499i
$541$	72575.2	+	72575.2i	0.247967	+	0.247967i	0.820136	−	0.572169i	$-0.193898\pi$
$541$	72575.2	+	72575.2i	0.247967	+	0.247967i	−0.572169	+	0.820136i	$0.693898\pi$
$542$	17740.9	−	77909.7i	0.0603916	−	0.265212i
$543$			55936.0i			0.189711i
$544$	−29538.4	−	60942.1i	−0.0998136	−	0.205930i
$545$	−211795.			−0.713053
$546$	−259555.	−	59103.5i	−0.870651	−	0.198257i
$547$	312820.	−	312820.i	1.04549	−	1.04549i	0.0465736	−	0.998915i	$-0.485170\pi$
$547$	312820.	−	312820.i	1.04549	−	1.04549i	0.998915	−	0.0465736i	$-0.0148302\pi$
$548$	127777.	−	266021.i	0.425493	−	0.885839i
$549$	−26439.0	+	26439.0i	−0.0877203	+	0.0877203i
$550$	9902.36	−	6229.06i	0.0327351	−	0.0205919i
$551$	208987.			0.688361
$552$	−154401.	+	17634.4i	−0.506726	+	0.0578737i
$553$		−	48430.8i		−	0.158369i
$554$	39969.8	−	25142.9i	0.130230	−	0.0819212i
$555$	125410.	+	125410.i	0.407144	+	0.407144i
$556$	−108980.	−	310439.i	−0.352531	−	1.00421i
$557$	127859.	+	127859.i	0.412118	+	0.412118i	0.882476	−	0.470358i	$-0.155875\pi$
$557$	127859.	+	127859.i	0.412118	+	0.412118i	−0.470358	+	0.882476i	$0.655875\pi$
$558$	−167153.	−	38062.6i	−0.536842	−	0.122245i
$559$		−	262870.i		−	0.841234i
$560$	−561280.	−	62090.3i	−1.78979	−	0.197992i
$561$	45813.2			0.145568
$562$	−37722.3	+	165659.i	−0.119433	+	0.524496i
$563$	−16640.0	+	16640.0i	−0.0524972	+	0.0524972i	−0.732868	−	0.680371i	$-0.761819\pi$
$563$	−16640.0	+	16640.0i	−0.0524972	+	0.0524972i	0.680371	+	0.732868i	$0.261819\pi$
$564$	109600.	+	312205.i	0.344551	+	0.981482i
$565$	−36366.9	+	36366.9i	−0.113922	+	0.113922i
$566$	107918.	+	171558.i	0.336870	+	0.535523i
$567$	−65482.8			−0.203686
$568$	294337.	+	233996.i	0.912323	+	0.725290i
$569$		−	2582.50i		−	0.00797655i	−0.999992	−	0.00398828i	$-0.998730\pi$
$569$		−	2582.50i		−	0.00797655i	0.999992	−	0.00398828i	$-0.00126951\pi$
$570$	−124789.	−	198378.i	−0.384085	−	0.610582i
$571$	57323.0	+	57323.0i	0.175815	+	0.175815i	0.789529	−	0.613713i	$-0.210325\pi$
$571$	57323.0	+	57323.0i	0.175815	+	0.175815i	−0.613713	+	0.789529i	$0.710325\pi$
$572$	−131678.	+	274142.i	−0.402459	+	0.837884i
$573$	117483.	+	117483.i	0.357821	+	0.357821i
$574$	97131.6	−	426557.i	0.294806	−	1.29465i
$575$		−	10252.0i		−	0.0310080i
$576$	107744.	−	24936.4i	0.324749	−	0.0751604i
$577$	−572563.			−1.71978			−0.859888	−	0.510484i	$-0.829466\pi$
$577$	−572563.			−1.71978			−0.859888	+	0.510484i	$0.829466\pi$
$578$	−308686.	−	70291.2i	−0.923978	−	0.210400i
$579$	64362.2	−	64362.2i	0.191988	−	0.191988i
$580$	161203.	+	77430.5i	0.479201	+	0.230174i
$581$	−324015.	+	324015.i	−0.959872	+	0.959872i
$582$	−168821.	+	106196.i	−0.498403	+	0.313519i
$583$	−126820.			−0.373123
$584$	−145818.	+	183420.i	−0.427548	+	0.537802i
$585$		−	94538.7i		−	0.276247i
$586$	431369.	−	271352.i	1.25618	−	0.790200i
$587$	374560.	+	374560.i	1.08704	+	1.08704i	0.995832	+	0.0912058i	$0.0290721\pi$
$587$	374560.	+	374560.i	1.08704	+	1.08704i	0.0912058	+	0.995832i	$0.470928\pi$
$588$	444597.	−	156077.i	1.28592	−	0.451423i
$589$	515372.	+	515372.i	1.48556	+	1.48556i
$590$	160934.	+	36646.4i	0.462321	+	0.105276i
$591$		−	342816.i		−	0.981490i
$592$	353659.	+	39122.7i	1.00912	+	0.111631i
$593$	−335988.			−0.955464			−0.477732	−	0.878506i	$-0.658541\pi$
$593$	−335988.			−0.955464			−0.477732	+	0.878506i	$0.658541\pi$
$594$	−16610.5	+	72945.4i	−0.0470770	+	0.206740i
$595$	103158.	−	103158.i	0.291387	−	0.291387i
$596$	407760.	−	143145.i	1.14792	−	0.402980i
$597$	−178478.	+	178478.i	−0.500768	+	0.500768i
$598$	141911.	+	225597.i	0.396839	+	0.630856i
$599$	−210952.			−0.587936			−0.293968	−	0.955815i	$-0.594976\pi$
$599$	−210952.			−0.587936			−0.293968	+	0.955815i	$0.594976\pi$
$600$	827.869	+	7248.58i	0.00229964	+	0.0201350i
$601$			237359.i			0.657139i	0.944480	+	0.328569i	$0.106567\pi$
$601$			237359.i			0.657139i	−0.944480	+	0.328569i	$0.893433\pi$
$602$	352714.	+	560711.i	0.973262	+	1.54720i
$603$	61210.0	+	61210.0i	0.168340	+	0.168340i
$604$	281959.	+	135433.i	0.772880	+	0.371236i
$605$	−54370.7	−	54370.7i	−0.148544	−	0.148544i
$606$	15289.3	−	67143.7i	0.0416336	−	0.182835i
$607$		−	354704.i		−	0.962695i	−0.876530	−	0.481348i	$-0.840148\pi$
$607$		−	354704.i		−	0.962695i	0.876530	−	0.481348i	$-0.159852\pi$
$608$	−444190.	−	154168.i	−1.20160	−	0.417049i
$609$	−212439.			−0.572795
$610$	132635.	+	30202.5i	0.356451	+	0.0811678i
$611$	401259.	−	401259.i	1.07484	−	1.07484i
$612$	−12370.3	+	25753.9i	−0.0330277	+	0.0687608i
$613$	194911.	−	194911.i	0.518699	−	0.518699i	−0.398478	−	0.917178i	$-0.630462\pi$
$613$	194911.	−	194911.i	0.518699	−	0.518699i	0.917178	+	0.398478i	$0.130462\pi$
$614$	40125.9	−	25241.1i	0.106436	−	0.0669532i
$615$	155366.			0.410778
$616$	−86964.8	−	761439.i	−0.229183	−	2.00666i
$617$		−	443656.i		−	1.16540i	−0.812687	−	0.582701i	$-0.801996\pi$
$617$		−	443656.i		−	1.16540i	0.812687	−	0.582701i	$-0.198004\pi$
$618$	240219.	−	151109.i	0.628971	−	0.395653i
$619$	304378.	+	304378.i	0.794388	+	0.794388i	0.982204	−	0.187816i	$-0.0601410\pi$
$619$	304378.	+	304378.i	0.794388	+	0.794388i	−0.187816	+	0.982204i	$0.560141\pi$
$620$	206588.	+	588482.i	0.537429	+	1.53091i
$621$	46359.0	+	46359.0i	0.120213	+	0.120213i
$622$	435881.	+	99255.0i	1.12665	+	0.256550i
$623$			678124.i			1.74716i
$624$	−118554.	−	148046.i	−0.304472	−	0.380214i
$625$	376432.			0.963666
$626$	75016.1	−	329435.i	0.191428	−	0.840663i
$627$	224907.	−	224907.i	0.572096	−	0.572096i
$628$	12495.9	+	35595.7i	0.0316847	+	0.0902564i
$629$	−64999.4	+	64999.4i	−0.164289	+	0.164289i
$630$	126850.	+	201655.i	0.319603	+	0.508074i
$631$	−182483.			−0.458315			−0.229157	−	0.973389i	$-0.573597\pi$
$631$	−182483.			−0.458315			−0.229157	+	0.973389i	$0.573597\pi$
$632$	21473.5	−	27011.0i	0.0537611	−	0.0676248i
$633$			319293.i			0.796860i
$634$	319088.	+	507256.i	0.793838	+	1.26197i
$635$	252297.	+	252297.i	0.625699	+	0.625699i
$636$	34243.7	−	71292.3i	0.0846577	−	0.176250i
$637$	−571414.	−	571414.i	−1.40823	−	1.40823i
$638$	−53887.5	+	236649.i	−0.132387	+	0.581384i
$639$		−	158632.i		−	0.388498i
$640$	−285509.	−	283492.i	−0.697043	−	0.692120i
$641$	−469986.			−1.14385			−0.571925	−	0.820306i	$-0.693803\pi$
$641$	−469986.			−1.14385			−0.571925	+	0.820306i	$0.693803\pi$
$642$	304427.	+	69321.3i	0.738606	+	0.168189i
$643$	536836.	−	536836.i	1.29843	−	1.29843i	0.369006	−	0.929427i	$-0.379698\pi$
$643$	536836.	−	536836.i	1.29843	−	1.29843i	0.929427	−	0.369006i	$-0.120302\pi$
$644$	−605403.	−	290792.i	−1.45973	−	0.701150i
$645$	−166350.	+	166350.i	−0.399856	+	0.399856i
$646$	102818.	−	64677.6i	0.246380	−	0.154985i
$647$	−359725.			−0.859333			−0.429667	−	0.902988i	$-0.641369\pi$
$647$	−359725.			−0.859333			−0.429667	+	0.902988i	$0.641369\pi$
$648$	−36521.3	−	29034.1i	−0.0869753	−	0.0691446i
$649$			224003.i			0.531820i
$650$	10590.9	−	6662.21i	0.0250673	−	0.0157685i
$651$	−523883.	−	523883.i	−1.23615	−	1.23615i
$652$	−534166.	+	187520.i	−1.25655	+	0.441115i
$653$	149383.	+	149383.i	0.350328	+	0.350328i	0.860232	−	0.509904i	$-0.170319\pi$
$653$	149383.	+	149383.i	0.350328	+	0.350328i	−0.509904	+	0.860232i	$0.670319\pi$
$654$	174783.	+	39800.0i	0.408642	+	0.0930523i
$655$		−	385493.i		−	0.898533i
$656$	243302.	−	194834.i	0.565376	−	0.452748i
$657$	98853.8			0.229014
$658$	−317498.	+	1.39430e6i	−0.733312	+	3.22036i
$659$	−381578.	+	381578.i	−0.878644	+	0.878644i	−0.993394	−	0.114750i	$-0.963393\pi$
$659$	−381578.	+	381578.i	−0.878644	+	0.878644i	0.114750	+	0.993394i	$0.463393\pi$
$660$	256813.	−	90154.6i	0.589561	−	0.206966i
$661$	−124940.	+	124940.i	−0.285955	+	0.285955i	−0.835479	−	0.549523i	$-0.814809\pi$
$661$	−124940.	+	124940.i	−0.285955	+	0.285955i	0.549523	+	0.835479i	$0.314809\pi$
$662$	−67389.7	−	107130.i	−0.153772	−	0.244452i
$663$	48998.8			0.111470
$664$	−324375.	+	37047.2i	−0.735717	+	0.0840271i
$665$		−	1.01286e6i		−	2.29036i
$666$	−79927.7	−	127061.i	−0.180197	−	0.286461i
$667$	150398.	+	150398.i	0.338056	+	0.338056i
$668$	−116082.	−	55757.4i	−0.260143	−	0.124954i
$669$	280673.	+	280673.i	0.627117	+	0.627117i
$670$	69923.2	−	307070.i	0.155766	−	0.684050i
$671$			184614.i			0.410034i
$672$	451526.	+	156714.i	0.999872	+	0.347032i
$673$	−428903.			−0.946955			−0.473478	−	0.880806i	$-0.657002\pi$
$673$	−428903.			−0.946955			−0.473478	+	0.880806i	$0.657002\pi$
$674$	485168.	+	110478.i	1.06800	+	0.243196i
$675$	2176.39	−	2176.39i	0.00477671	−	0.00477671i
$676$	57022.9	−	118717.i	0.124783	−	0.259787i
$677$	−104764.	+	104764.i	−0.228579	+	0.228579i	−0.812099	−	0.583520i	$-0.801675\pi$
$677$	−104764.	+	104764.i	−0.228579	+	0.228579i	0.583520	+	0.812099i	$0.301675\pi$
$678$	36845.6	−	23177.7i	0.0801543	−	0.0504209i
$679$	−861947.			−1.86957
$680$	103273.	−	11794.9i	0.223341	−	0.0255080i
$681$		−	304719.i		−	0.657060i
$682$	−716476.	+	450698.i	−1.54040	+	0.968984i
$683$	−463952.	−	463952.i	−0.994561	−	0.994561i	0.00542469	−	0.999985i	$-0.498273\pi$
$683$	−463952.	−	463952.i	−0.994561	−	0.994561i	−0.999985	+	0.00542469i	$0.998273\pi$
$684$	65703.2	+	187161.i	0.140435	+	0.400040i
$685$	320288.	+	320288.i	0.682589	+	0.682589i
$686$	1.14441e6	+	260594.i	2.43183	+	0.553754i
$687$			196773.i			0.416920i
$688$	−51894.2	+	469110.i	−0.109633	+	0.991054i
$689$	−135639.			−0.285724
$690$	52958.2	−	232567.i	0.111233	−	0.488484i
$691$	515030.	−	515030.i	1.07864	−	1.07864i	0.0820090	−	0.996632i	$-0.473866\pi$
$691$	515030.	−	515030.i	1.07864	−	1.07864i	0.996632	−	0.0820090i	$-0.0261336\pi$
$692$	112381.	+	320126.i	0.234682	+	0.668511i
$693$	−228622.	+	228622.i	−0.476049	+	0.476049i
$694$	−491128.	−	780748.i	−1.01971	−	1.62103i
$695$	504978.			1.04545
$696$	−118482.	−	94192.2i	−0.244587	−	0.194445i
$697$			80525.5i			0.165755i
$698$	−368255.	−	585416.i	−0.755853	−	1.20158i
$699$	−361464.	−	361464.i	−0.739793	−	0.739793i
$700$	−13651.6	+	28421.5i	−0.0278605	+	0.0580030i
$701$	−468514.	−	468514.i	−0.953424	−	0.953424i	0.0455384	−	0.998963i	$-0.485500\pi$
$701$	−468514.	−	468514.i	−0.953424	−	0.953424i	−0.998963	+	0.0455384i	$0.985500\pi$
$702$	−17765.5	+	78017.8i	−0.0360498	+	0.158314i
$703$			638195.i			1.29135i
$704$	289109.	−	463231.i	0.583332	−	0.934657i
$705$	−507852.			−1.02178
$706$	−846128.	−	192673.i	−1.69757	−	0.386554i
$707$	210439.	−	210439.i	0.421004	−	0.421004i
$708$	−125924.	−	60484.7i	−0.251212	−	0.120664i
$709$	−177649.	+	177649.i	−0.353403	+	0.353403i	−0.861374	−	0.507971i	$-0.830396\pi$
$709$	−177649.	+	177649.i	−0.353403	+	0.353403i	0.507971	+	0.861374i	$0.330396\pi$
$710$	−488508.	+	307295.i	−0.969070	+	0.609591i
$711$	−14557.5			−0.0287969
$712$	−300670.	+	378206.i	−0.593104	+	0.746050i
$713$			741774.i			1.45913i
$714$	−104516.	+	65745.8i	−0.205016	+	0.128965i
$715$	−330066.	−	330066.i	−0.645637	−	0.645637i
$716$	474294.	−	166502.i	0.925169	−	0.324783i
$717$	101677.	+	101677.i	0.197781	+	0.197781i
$718$	−249454.	−	56803.4i	−0.483885	−	0.110186i
$719$			23226.4i			0.0449287i	0.999748	+	0.0224644i	$0.00715123\pi$
$719$			23226.4i			0.0449287i	−0.999748	+	0.0224644i	$0.992849\pi$
$720$	−18663.3	+	168711.i	−0.0360017	+	0.325446i
$721$	1.22648e6			2.35934
$722$	71501.8	−	314003.i	0.137165	−	0.602364i
$723$	−170816.	+	170816.i	−0.326778	+	0.326778i
$724$	−162515.	+	57051.2i	−0.310039	+	0.108840i
$725$	7060.62	−	7060.62i	0.0134328	−	0.0134328i
$726$	34652.0	+	55086.5i	0.0657439	+	0.104513i
$727$	845037.			1.59885			0.799423	−	0.600768i	$-0.205138\pi$
$727$	845037.			1.59885			0.799423	+	0.600768i	$0.205138\pi$
$728$	−93012.0	−	814387.i	−0.175500	−	1.53663i
$729$			19683.0i			0.0370370i
$730$	−191495.	−	304421.i	−0.359345	−	0.571253i
$731$	−86218.3	−	86218.3i	−0.161348	−	0.161348i
$732$	−103781.	−	49849.0i	−0.193685	−	0.0930325i
$733$	−179935.	−	179935.i	−0.334895	−	0.334895i	0.519547	−	0.854442i	$-0.326101\pi$
$733$	−179935.	−	179935.i	−0.334895	−	0.334895i	−0.854442	+	0.519547i	$0.826101\pi$
$734$	63654.3	−	279540.i	0.118150	−	0.518862i
$735$			723209.i			1.33872i
$736$	−208714.	−	430608.i	−0.385298	−	0.794926i
$737$	427409.			0.786880
$738$	−128216.	−	29196.1i	−0.235412	−	0.0536058i
$739$	−151733.	+	151733.i	−0.277837	+	0.277837i	−0.832245	−	0.554408i	$-0.812945\pi$
$739$	−151733.	+	151733.i	−0.277837	+	0.277837i	0.554408	+	0.832245i	$0.312945\pi$
$740$	−236454.	+	492275.i	−0.431800	+	0.898968i
$741$	240547.	−	240547.i	0.438090	−	0.438090i
$742$	289323.	−	181998.i	0.525503	−	0.330567i
$743$	−576375.			−1.04406			−0.522032	−	0.852926i	$-0.674826\pi$
$743$	−576375.			−1.04406			−0.522032	+	0.852926i	$0.674826\pi$
$744$	−59899.6	−	524464.i	−0.108213	−	0.947480i
$745$			663286.i			1.19506i
$746$	−301027.	+	189361.i	−0.540914	+	0.340261i
$747$	97393.5	+	97393.5i	0.174537	+	0.174537i
$748$	46726.6	+	133104.i	0.0835143	+	0.237897i
$749$	954120.	+	954120.i	1.70075	+	1.70075i
$750$	−321965.	−	73314.9i	−0.572382	−	0.130338i
$751$		−	316650.i		−	0.561435i	−0.959790	−	0.280718i	$-0.909428\pi$
$751$		−	316650.i		−	0.561435i	0.959790	−	0.280718i	$-0.0905725\pi$
$752$	−795289.	+	636860.i	−1.40634	+	1.12618i
$753$	194896.			0.343727
$754$	−57634.7	+	253105.i	−0.101377	+	0.445202i
$755$	−339477.	+	339477.i	−0.595548	+	0.595548i
$756$	−66788.4	−	190252.i	−0.116858	−	0.332879i
$757$	370431.	−	370431.i	0.646420	−	0.646420i	−0.305706	−	0.952126i	$-0.598892\pi$
$757$	370431.	−	370431.i	0.646420	−	0.646420i	0.952126	+	0.305706i	$0.0988923\pi$
$758$	71427.6	+	113549.i	0.124316	+	0.197626i
$759$	323709.			0.561916
$760$	449086.	−	564893.i	0.777503	−	0.978001i
$761$		−	1.11708e6i		−	1.92893i	−0.264218	−	0.964463i	$-0.585114\pi$
$761$		−	1.11708e6i		−	1.92893i	0.264218	−	0.964463i	$-0.414886\pi$
$762$	−160796.	−	255619.i	−0.276928	−	0.440233i
$763$	547796.	+	547796.i	0.940957	+	0.940957i
$764$	−221507.	+	461158.i	−0.379490	+	0.790065i
$765$	−31007.6	−	31007.6i	−0.0529841	−	0.0529841i
$766$	108090.	−	474681.i	0.184216	−	0.808992i
$767$			239579.i			0.407248i
$768$	182342.	+	287603.i	0.309146	+	0.487608i
$769$	214105.			0.362055			0.181028	−	0.983478i	$-0.442058\pi$
$769$	214105.			0.362055			0.181028	+	0.983478i	$0.442058\pi$
$770$	1.14692e6	+	261166.i	1.93442	+	0.440489i
$771$	−114576.	+	114576.i	−0.192745	+	0.192745i
$772$	252642.	+	121351.i	0.423907	+	0.203614i
$773$	503106.	−	503106.i	0.841978	−	0.841978i	−0.147138	−	0.989116i	$-0.547006\pi$
$773$	503106.	−	503106.i	0.841978	−	0.841978i	0.989116	+	0.147138i	$0.0470061\pi$
$774$	168540.	−	106020.i	0.281333	−	0.176972i
$775$	34823.6			0.0579789
$776$	−480728.	−	382175.i	−0.798317	−	0.634656i
$777$		−	648735.i		−	1.07455i
$778$	191890.	−	120708.i	0.317024	−	0.199423i
$779$	395318.	+	395318.i	0.651436	+	0.651436i
$780$	274671.	−	96423.6i	0.451464	−	0.158487i
$781$	−553837.	−	553837.i	−0.907987	−	0.907987i
$782$	120538.	+	27447.9i	0.197111	+	0.0448844i
$783$			63855.4i			0.104154i
$784$	906923.	+	1.13253e6i	1.47550	+	1.84255i
$785$	−57902.1			−0.0939625
$786$	−72440.9	+	318127.i	−0.117257	+	0.514938i
$787$	−437192.	+	437192.i	−0.705868	+	0.705868i	−0.965664	−	0.259796i	$-0.916345\pi$
$787$	−437192.	+	437192.i	−0.705868	+	0.705868i	0.259796	+	0.965664i	$0.416345\pi$
$788$	996008.	−	349651.i	1.60402	−	0.563095i
$789$	−321607.	+	321607.i	−0.516620	+	0.516620i
$790$	28200.1	+	44829.7i	0.0451852	+	0.0718310i
$791$	188122.			0.300668
$792$	−228875.	+	26140.1i	−0.364879	+	0.0416732i
$793$			197452.i			0.313989i
$794$	−356802.	−	567210.i	−0.565961	−	0.899710i
$795$	85835.6	+	85835.6i	0.135810	+	0.135810i
$796$	−700584.	−	336510.i	−1.10569	−	0.531094i
$797$	−37761.0	−	37761.0i	−0.0594466	−	0.0594466i	0.676759	−	0.736205i	$-0.263384\pi$
$797$	−37761.0	−	37761.0i	−0.0594466	−	0.0594466i	−0.736205	+	0.676759i	$0.763384\pi$
$798$	−190334.	+	835856.i	−0.298889	+	1.31258i
$799$		−	263217.i		−	0.412306i
$800$	−20215.5	+	9798.38i	−0.0315867	+	0.0153100i
$801$	203832.			0.317694
$802$	175961.	+	40068.2i	0.273569	+	0.0622947i
$803$	345131.	−	345131.i	0.535245	−	0.535245i
$804$	−115408.	+	240269.i	−0.178535	+	0.371693i
$805$	728902.	−	728902.i	1.12481	−	1.12481i
$806$	−766297.	+	482037.i	−1.17958	+	0.742012i
$807$	−280564.			−0.430809
$808$	210672.	−	24061.1i	0.322689	−	0.0368546i
$809$			1.19381e6i			1.82406i	0.410120	+	0.912032i	$0.365487\pi$
$809$			1.19381e6i			1.82406i	−0.410120	+	0.912032i	$0.634513\pi$
$810$	60613.9	−	38129.0i	0.0923851	−	0.0581147i
$811$	660081.	+	660081.i	1.00359	+	1.00359i	0.999994	+	0.00359390i	$0.00114398\pi$
$811$	660081.	+	660081.i	1.00359	+	1.00359i	0.00359390	+	0.999994i	$0.498856\pi$
$812$	−216674.	−	617214.i	−0.328621	−	0.936104i
$813$	−73396.6	−	73396.6i	−0.111044	−	0.111044i
$814$	−722667.	−	164559.i	−1.09066	−	0.248355i
$815$		−	868906.i		−	1.30815i
$816$	−87441.9	−	9673.07i	−0.131323	−	0.0145273i
$817$	−846531.			−1.26823
$818$	83149.2	−	365152.i	0.124266	−	0.545717i
$819$	−244520.	+	244520.i	−0.364541	+	0.364541i
$820$	158464.	+	451398.i	0.235669	+	0.671323i
$821$	344916.	−	344916.i	0.511714	−	0.511714i	−0.403337	−	0.915051i	$-0.632150\pi$
$821$	344916.	−	344916.i	0.511714	−	0.511714i	0.915051	+	0.403337i	$0.132150\pi$
$822$	−204129.	−	324504.i	−0.302107	−	0.480260i
$823$	−1.06287e6			−1.56921			−0.784603	−	0.619999i	$-0.787133\pi$
$823$	−1.06287e6			−1.56921			−0.784603	+	0.619999i	$0.787133\pi$
$824$	684038.	+	543804.i	1.00745	+	0.800919i
$825$		−	15197.0i		−	0.0223280i
$826$	−321463.	−	511031.i	−0.471163	−	0.749010i
$827$	514170.	+	514170.i	0.751789	+	0.751789i	0.974813	−	0.223024i	$-0.0715928\pi$
$827$	514170.	+	514170.i	0.751789	+	0.751789i	−0.223024	+	0.974813i	$0.571593\pi$
$828$	−87407.1	+	181974.i	−0.127493	+	0.265429i
$829$	613712.	+	613712.i	0.893009	+	0.893009i	0.994805	−	0.101796i	$-0.0324589\pi$
$829$	613712.	+	613712.i	0.893009	+	0.893009i	−0.101796	+	0.994805i	$0.532459\pi$
$830$	111257.	−	488590.i	0.161500	−	0.709232i
$831$		−	61340.9i		−	0.0888277i
$832$	309212.	−	495442.i	0.446694	−	0.715726i
$833$	−374835.			−0.540194
$834$	−416731.	−	94894.3i	−0.599134	−	0.136429i
$835$	139762.	−	139762.i	0.200455	−	0.200455i
$836$	882832.	+	424049.i	1.26318	+	0.606741i
$837$	−157470.	+	157470.i	−0.224775	+	0.224775i
$838$	−587515.	+	369575.i	−0.836625	+	0.526277i
$839$	840032.			1.19336			0.596680	−	0.802479i	$-0.296486\pi$
$839$	840032.			1.19336			0.596680	+	0.802479i	$0.296486\pi$
$840$	−456503.	+	574223.i	−0.646971	+	0.813808i
$841$		−	500122.i		−	0.707105i
$842$	232683.	−	146369.i	0.328201	−	0.206454i
$843$	156063.	+	156063.i	0.219606	+	0.219606i
$844$	−927666.	+	325659.i	−1.30229	+	0.457171i
$845$	142934.	+	142934.i	0.200181	+	0.200181i
$846$	419103.	+	95434.3i	0.585572	+	0.133341i
$847$			281254.i			0.392042i
$848$	242057.	+	26777.1i	0.336610	+	0.0372367i
$849$	263287.			0.365270
$850$	1288.58	−	5658.83i	0.00178350	−	0.00783230i
$851$	−459277.	+	459277.i	−0.634184	+	0.634184i
$852$	460886.	−	161795.i	0.634913	−	0.222887i
$853$	−268667.	+	268667.i	−0.369246	+	0.369246i	−0.867202	−	0.497956i	$-0.834084\pi$
$853$	−268667.	+	268667.i	−0.369246	+	0.369246i	0.497956	+	0.867202i	$0.334084\pi$
$854$	−264937.	−	421172.i	−0.363268	−	0.577489i
$855$	−304447.			−0.416466
$856$	109092.	+	955178.i	0.148883	+	1.30358i
$857$			178340.i			0.242821i	0.992602	+	0.121411i	$0.0387418\pi$
$857$			178340.i			0.242821i	−0.992602	+	0.121411i	$0.961258\pi$
$858$	210360.	+	334411.i	0.285752	+	0.454261i
$859$	−449410.	−	449410.i	−0.609055	−	0.609055i	0.333644	−	0.942699i	$-0.391722\pi$
$859$	−449410.	−	449410.i	−0.609055	−	0.609055i	−0.942699	+	0.333644i	$0.891722\pi$
$860$	−652977.	−	313643.i	−0.882878	−	0.424071i
$861$	−401847.	−	401847.i	−0.542069	−	0.542069i
$862$	28553.2	−	125392.i	0.0384273	−	0.168755i
$863$		−	278925.i		−	0.374512i	−0.982311	−	0.187256i	$-0.940041\pi$
$863$		−	278925.i		−	0.374512i	0.982311	−	0.187256i	$-0.0599594\pi$
$864$	47105.6	−	135721.i	0.0631023	−	0.181811i
$865$	−520735.			−0.695961
$866$	−355280.	−	80901.2i	−0.473735	−	0.107875i
$867$	−290805.	+	290805.i	−0.386868	+	0.386868i
$868$	987750.	−	2.05641e6i	1.31101	−	2.72942i
$869$	−50824.9	+	50824.9i	−0.0673033	+	0.0673033i
$870$	196643.	−	123698.i	0.259801	−	0.163427i
$871$	457129.			0.602563
$872$	62633.8	+	548403.i	0.0823712	+	0.721219i
$873$			259086.i			0.339951i
$874$	726498.	−	457002.i	0.951069	−	0.598268i
$875$	−1.00909e6	−	1.00909e6i	−1.31799	−	1.31799i
$876$	100825.	+	287207.i	0.131389	+	0.374272i
$877$	−391918.	−	391918.i	−0.509560	−	0.509560i	0.404831	−	0.914392i	$-0.367330\pi$
$877$	−391918.	−	391918.i	−0.509560	−	0.509560i	−0.914392	+	0.404831i	$0.867330\pi$
$878$	−1.04219e6	−	237317.i	−1.35194	−	0.307851i
$879$		−	662013.i		−	0.856819i
$880$	523866.	+	654185.i	0.676480	+	0.844764i
$881$	971511.			1.25169			0.625844	−	0.779949i	$-0.284755\pi$
$881$	971511.			1.25169			0.625844	+	0.779949i	$0.284755\pi$
$882$	135904.	−	596825.i	0.174700	−	0.767203i
$883$	86997.4	−	86997.4i	0.111580	−	0.111580i	−0.649113	−	0.760692i	$-0.724860\pi$
$883$	86997.4	−	86997.4i	0.111580	−	0.111580i	0.760692	+	0.649113i	$0.224860\pi$
$884$	49975.8	+	142360.i	0.0639521	+	0.182173i
$885$	151611.	−	151611.i	0.193573	−	0.193573i
$886$	504160.	+	801465.i	0.642245	+	1.02098i
$887$	−266811.			−0.339123			−0.169561	−	0.985520i	$-0.554235\pi$
$887$	−266811.			−0.339123			−0.169561	+	0.985520i	$0.554235\pi$
$888$	287640.	−	361815.i	0.364773	−	0.458839i
$889$		−	1.30511e6i		−	1.65137i
$890$	−394855.	−	627703.i	−0.498492	−	0.792454i
$891$	68719.8	+	68719.8i	0.0865619	+	0.0865619i
$892$	−529192.	+	1.10173e6i	−0.665094	+	1.38467i
$893$	−1.29219e6	−	1.29219e6i	−1.62041	−	1.62041i
$894$	124643.	−	547375.i	0.155953	−	0.684872i
$895$			771514.i			0.963159i
$896$	5215.01	+	1.47169e6i	0.00649590	+	1.83316i
$897$	346219.			0.430294
$898$	685602.	+	156119.i	0.850196	+	0.193599i
$899$	−510864.	+	510864.i	−0.632100	+	0.632100i
$900$	8543.00	+	4103.44i	0.0105469	+	0.00506598i
$901$	−44488.0	+	44488.0i	−0.0548017	+	0.0548017i
$902$	−549576.	+	345710.i	−0.675484	+	0.424912i
$903$	860512.			1.05531
$904$	104920.	+	83410.6i	0.128387	+	0.102067i
$905$		−	264357.i		−	0.322770i
$906$	343946.	−	216359.i	0.419019	−	0.263583i
$907$	−544293.	−	544293.i	−0.661634	−	0.661634i	0.294131	−	0.955765i	$-0.404970\pi$
$907$	−544293.	−	544293.i	−0.661634	−	0.661634i	−0.955765	+	0.294131i	$0.904970\pi$
$908$	885323.	−	310794.i	1.07382	−	0.376965i
$909$	−63254.2	−	63254.2i	−0.0765529	−	0.0765529i
$910$	1.22667e6	+	279327.i	1.48131	+	0.337310i
$911$			234819.i			0.282941i	0.989942	+	0.141470i	$0.0451830\pi$
$911$			234819.i			0.282941i	−0.989942	+	0.141470i	$0.954817\pi$
$912$	−476760.	+	381785.i	−0.573205	+	0.459018i
$913$	680065.			0.815848
$914$	−349451.	+	1.53463e6i	−0.418306	+	1.83701i
$915$	124952.	−	124952.i	0.149246	−	0.149246i
$916$	−571700.	+	200696.i	−0.681361	+	0.239193i
$917$	−997058.	+	997058.i	−1.18572	+	1.18572i
$918$	19762.0	+	31415.8i	0.0234502	+	0.0372789i
$919$	−1.14238e6			−1.35263			−0.676317	−	0.736610i	$-0.736425\pi$
$919$	−1.14238e6			−1.35263			−0.676317	+	0.736610i	$0.736425\pi$
$920$	729710.	−	83341.0i	0.862134	−	0.0984653i
$921$		−	61580.4i		−	0.0725978i
$922$	258684.	+	411231.i	0.304304	+	0.483753i
$923$	−592349.	−	592349.i	−0.695303	−	0.695303i
$924$	−897413.	−	431053.i	−1.05111	−	0.504878i
$925$	21561.4	+	21561.4i	0.0251996	+	0.0251996i
$926$	−99568.9	+	437260.i	−0.116119	+	0.509939i
$927$		−	368660.i		−	0.429009i
$928$	152820.	−	440305.i	0.177453	−	0.511278i
$929$	832146.			0.964202			0.482101	−	0.876116i	$-0.339874\pi$
$929$	832146.			0.964202			0.482101	+	0.876116i	$0.339874\pi$
$930$	789975.	+	179886.i	0.913372	+	0.207985i
$931$	−1.84015e6	+	1.84015e6i	−2.12302	+	2.12302i
$932$	681518.	−	1.41886e6i	0.784594	−	1.63346i
$933$	410632.	−	410632.i	0.471725	−	0.471725i
$934$	195378.	−	122902.i	0.223966	−	0.140886i
$935$	−216516.			−0.247666
$936$	−244791.	+	27957.8i	−0.279411	+	0.0319118i
$937$			1.26470e6i			1.44048i	0.693723	+	0.720242i	$0.255969\pi$
$937$			1.26470e6i			1.44048i	−0.693723	+	0.720242i	$0.744031\pi$
$938$	−975073.	+	613368.i	−1.10823	+	0.697133i
$939$	−310352.	−	310352.i	−0.351984	−	0.351984i
$940$	−517977.	−	1.47550e6i	−0.586212	−	1.66987i
$941$	596498.	+	596498.i	0.673643	+	0.673643i	0.958554	−	0.284911i	$-0.0919639\pi$
$941$	596498.	+	596498.i	0.673643	+	0.673643i	−0.284911	+	0.958554i	$0.591964\pi$
$942$	47783.5	+	10880.8i	0.0538488	+	0.0122620i
$943$			568981.i			0.639845i
$944$	47296.4	−	427546.i	0.0530742	−	0.479777i
$945$	309475.			0.346547
$946$	218279.	−	958579.i	0.243910	−	1.07114i
$947$	−428200.	+	428200.i	−0.477471	+	0.477471i	−0.904322	−	0.426851i	$-0.859623\pi$
$947$	−428200.	+	428200.i	−0.477471	+	0.477471i	0.426851	+	0.904322i	$0.359623\pi$
$948$	−14847.7	−	42294.9i	−0.0165212	−	0.0470621i
$949$	369130.	−	369130.i	0.409871	−	0.409871i
$950$	−21454.6	−	34106.5i	−0.0237724	−	0.0377911i
$951$	778475.			0.860764
$952$	−297616.	−	236603.i	−0.328385	−	0.261063i
$953$			273921.i			0.301606i	0.988564	+	0.150803i	$0.0481859\pi$
$953$			273921.i			0.301606i	−0.988564	+	0.150803i	$0.951814\pi$
$954$	−54705.5	−	86965.5i	−0.0601082	−	0.0955543i
$955$	−555231.	−	555231.i	−0.608790	−	0.608790i
$956$	−191706.	+	399115.i	−0.209759	+	0.436699i
$957$	222940.	+	222940.i	0.243425	+	0.243425i
$958$	−99170.7	+	435511.i	−0.108057	+	0.474535i
$959$		−	1.65682e6i		−	1.80151i
$960$	−509204.	+	117851.i	−0.552522	+	0.127876i
$961$	−1.59611e6			−1.72828
$962$	−772918.	−	176002.i	−0.835187	−	0.190181i
$963$	286792.	−	286792.i	0.309254	−	0.309254i
$964$	−670507.	−	322063.i	−0.721521	−	0.346567i
$965$	−304179.	+	304179.i	−0.326644	+	0.326644i
$966$	−738497.	+	464550.i	−0.791397	+	0.497827i
$967$	715792.			0.765480			0.382740	−	0.923856i	$-0.374981\pi$
$967$	715792.			0.765480			0.382740	+	0.923856i	$0.374981\pi$
$968$	−124704.	+	156862.i	−0.133085	+	0.167404i
$969$		−	157793.i		−	0.168051i
$970$	797858.	−	501891.i	0.847973	−	0.533416i
$971$	332443.	+	332443.i	0.352597	+	0.352597i	0.861075	−	0.508478i	$-0.169792\pi$
$971$	332443.	+	332443.i	0.352597	+	0.352597i	−0.508478	+	0.861075i	$0.669792\pi$
$972$	−57186.5	+	20075.4i	−0.0605287	+	0.0212487i
$973$	−1.30610e6	−	1.30610e6i	−1.37959	−	1.37959i
$974$	248872.	+	56670.9i	0.262336	+	0.0597368i
$975$		−	16253.7i		−	0.0170979i
$976$	38979.8	−	352366.i	0.0409204	−	0.369909i
$977$	−174170.			−0.182467			−0.0912333	−	0.995830i	$-0.529081\pi$
$977$	−174170.			−0.182467			−0.0912333	+	0.995830i	$0.529081\pi$
$978$	−163283.	+	717061.i	−0.170711	+	0.749685i
$979$	711646.	−	711646.i	0.742504	−	0.742504i
$980$	−2.10119e6	+	737628.i	−2.18783	+	0.768042i
$981$	164658.	−	164658.i	0.171098	−	0.171098i
$982$	304080.	+	483397.i	0.315330	+	0.501281i
$983$	1.62409e6			1.68075			0.840376	−	0.542004i	$-0.182334\pi$
$983$	1.62409e6			1.68075			0.840376	+	0.542004i	$0.182334\pi$
$984$	−45946.3	−	402293.i	−0.0474526	−	0.415482i
$985$			1.62017e6i			1.66989i
$986$	64111.9	+	101919.i	0.0659454	+	0.104834i
$987$	1.31353e6	+	1.31353e6i	1.34836	+	1.34836i
$988$	944221.	+	453536.i	0.967297	+	0.464620i
$989$	−609206.	−	609206.i	−0.622833	−	0.622833i
$990$	78502.0	−	344744.i	0.0800959	−	0.351744i
$991$		−	931514.i		−	0.948510i	−0.880387	−	0.474255i	$-0.842717\pi$
$991$		−	931514.i		−	0.948510i	0.880387	−	0.474255i	$-0.157283\pi$
$992$	1.46267e6	−	708952.i	1.48636	−	0.720433i
$993$	−164410.			−0.166736
$994$	2.05830e6	+	468698.i	2.08323	+	0.474374i
$995$	843499.	−	843499.i	0.851998	−	0.851998i
$996$	−183629.	+	382300.i	−0.185107	+	0.385377i
$997$	226779.	−	226779.i	0.228145	−	0.228145i	−0.583772	−	0.811918i	$-0.698424\pi$
$997$	226779.	−	226779.i	0.228145	−	0.228145i	0.811918	+	0.583772i	$0.198424\pi$
$998$	14451.4	−	9090.63i	0.0145094	−	0.00912711i
$999$	−194999.			−0.195389

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.5.l.a.19.16	✓	32
3.2	odd	2		144.5.m.c.19.1		32
4.3	odd	2		192.5.l.a.175.2		32
8.3	odd	2		384.5.l.a.223.15		32
8.5	even	2		384.5.l.b.223.2		32
12.11	even	2		576.5.m.b.559.13		32
16.3	odd	4		384.5.l.b.31.2		32
16.5	even	4		192.5.l.a.79.2		32
16.11	odd	4	inner	48.5.l.a.43.16	yes	32
16.13	even	4		384.5.l.a.31.15		32
48.5	odd	4		576.5.m.b.271.13		32
48.11	even	4		144.5.m.c.91.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.5.l.a.19.16	✓	32	1.1	even	1	trivial
48.5.l.a.43.16	yes	32	16.11	odd	4	inner
144.5.m.c.19.1		32	3.2	odd	2
144.5.m.c.91.1		32	48.11	even	4
192.5.l.a.79.2		32	16.5	even	4
192.5.l.a.175.2		32	4.3	odd	2
384.5.l.a.31.15		32	16.13	even	4
384.5.l.a.223.15		32	8.3	odd	2
384.5.l.b.31.2		32	16.3	odd	4
384.5.l.b.223.2		32	8.5	even	2
576.5.m.b.271.13		32	48.5	odd	4
576.5.m.b.559.13		32	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.90016 + 0.888110i) q^{2} +(3.67423 - 3.67423i) q^{3} +(14.4225 + 6.92754i) q^{4} +(-17.3646 + 17.3646i) q^{5} +(17.5932 - 11.0670i) q^{6} +89.8255 q^{7} +(50.0978 + 39.8273i) q^{8} -27.0000i q^{9} +O(q^{10})\)	\(q+(3.90016 + 0.888110i) q^{2} +(3.67423 - 3.67423i) q^{3} +(14.4225 + 6.92754i) q^{4} +(-17.3646 + 17.3646i) q^{5} +(17.5932 - 11.0670i) q^{6} +89.8255 q^{7} +(50.0978 + 39.8273i) q^{8} -27.0000i q^{9} +(-83.1466 + 52.3032i) q^{10} +(-94.2659 - 94.2659i) q^{11} +(78.4451 - 27.5383i) q^{12} +(-100.821 - 100.821i) q^{13} +(350.334 + 79.7749i) q^{14} +127.604i q^{15} +(160.018 + 199.825i) q^{16} -66.1361 q^{17} +(23.9790 - 105.304i) q^{18} +(-324.678 + 324.678i) q^{19} +(-370.736 + 130.148i) q^{20} +(330.040 - 330.040i) q^{21} +(-283.934 - 451.371i) q^{22} -467.308 q^{23} +(330.406 - 37.7360i) q^{24} +21.9384i q^{25} +(-303.678 - 482.757i) q^{26} +(-99.2043 - 99.2043i) q^{27} +(1295.51 + 622.270i) q^{28} +(-321.838 - 321.838i) q^{29} +(-113.326 + 497.674i) q^{30} -1587.33i q^{31} +(446.631 + 921.465i) q^{32} -692.710 q^{33} +(-257.942 - 58.7361i) q^{34} +(-1559.79 + 1559.79i) q^{35} +(187.044 - 389.408i) q^{36} +(982.813 - 982.813i) q^{37} +(-1554.64 + 977.946i) q^{38} -740.879 q^{39} +(-1561.52 + 178.343i) q^{40} -1217.57i q^{41} +(1580.32 - 994.098i) q^{42} +(1303.65 + 1303.65i) q^{43} +(-706.521 - 2012.58i) q^{44} +(468.845 + 468.845i) q^{45} +(-1822.58 - 415.021i) q^{46} +3979.92i q^{47} +(1322.15 + 146.260i) q^{48} +5667.62 q^{49} +(-19.4837 + 85.5634i) q^{50} +(-243.000 + 243.000i) q^{51} +(-755.650 - 2152.53i) q^{52} +(672.674 - 672.674i) q^{53} +(-298.809 - 475.017i) q^{54} +3273.79 q^{55} +(4500.06 + 3577.51i) q^{56} +2385.88i q^{57} +(-969.392 - 1541.05i) q^{58} +(-1188.14 - 1188.14i) q^{59} +(-883.979 + 1840.36i) q^{60} +(-979.221 - 979.221i) q^{61} +(1409.73 - 6190.86i) q^{62} -2425.29i q^{63} +(923.570 + 3990.52i) q^{64} +3501.43 q^{65} +(-2701.68 - 615.202i) q^{66} +(-2267.04 + 2267.04i) q^{67} +(-953.850 - 458.161i) q^{68} +(-1717.00 + 1717.00i) q^{69} +(-7468.69 + 4698.16i) q^{70} +5875.26 q^{71} +(1075.34 - 1352.64i) q^{72} +3661.25i q^{73} +(4705.97 - 2960.28i) q^{74} +(80.6069 + 80.6069i) q^{75} +(-6931.89 + 2433.45i) q^{76} +(-8467.48 - 8467.48i) q^{77} +(-2889.55 - 657.981i) q^{78} -539.165i q^{79} +(-6248.56 - 691.233i) q^{80} -729.000 q^{81} +(1081.34 - 4748.73i) q^{82} +(-3607.17 + 3607.17i) q^{83} +(7046.38 - 2473.64i) q^{84} +(1148.43 - 1148.43i) q^{85} +(3926.66 + 6242.22i) q^{86} -2365.02 q^{87} +(-968.153 - 8476.87i) q^{88} +7549.35i q^{89} +(1412.19 + 2244.96i) q^{90} +(-9056.28 - 9056.28i) q^{91} +(-6739.77 - 3237.30i) q^{92} +(-5832.23 - 5832.23i) q^{93} +(-3534.60 + 15522.3i) q^{94} -11275.8i q^{95} +(5026.70 + 1744.65i) q^{96} -9595.79 q^{97} +(22104.6 + 5033.47i) q^{98} +(-2545.18 + 2545.18i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{4} + 180 q^{8}+O(q^{10}) \) 32 * q + 12 * q^4 + 180 * q^8	\( 32 q + 12 q^{4} + 180 q^{8} + 296 q^{10} - 192 q^{11} + 360 q^{12} - 156 q^{14} + 352 q^{16} - 324 q^{18} + 704 q^{19} - 1200 q^{20} - 1568 q^{22} - 2304 q^{23} + 1188 q^{24} + 2700 q^{26} + 4680 q^{28} - 1728 q^{29} + 1512 q^{30} - 3360 q^{32} - 9312 q^{34} - 5184 q^{35} - 756 q^{36} + 3648 q^{37} - 5880 q^{38} + 5232 q^{40} + 4500 q^{42} + 1088 q^{43} + 18840 q^{44} + 680 q^{46} + 2160 q^{48} + 10976 q^{49} - 25884 q^{50} - 4032 q^{51} - 25584 q^{52} + 960 q^{53} + 972 q^{54} + 11776 q^{55} + 15456 q^{56} + 12624 q^{58} + 13056 q^{59} + 7992 q^{60} + 3776 q^{61} + 21852 q^{62} - 8664 q^{64} + 4032 q^{65} - 8856 q^{66} - 896 q^{67} - 17280 q^{68} - 9792 q^{69} - 18240 q^{70} - 39936 q^{71} + 4860 q^{72} + 24204 q^{74} - 1152 q^{75} + 16776 q^{76} + 9408 q^{77} - 3780 q^{78} - 14232 q^{80} - 23328 q^{81} - 33800 q^{82} + 24000 q^{83} - 11448 q^{84} - 11200 q^{85} - 1200 q^{86} - 11424 q^{88} + 4104 q^{90} + 30528 q^{91} - 11664 q^{92} - 8040 q^{94} + 10080 q^{96} + 52968 q^{98} - 5184 q^{99}+O(q^{100}) \) 32 * q + 12 * q^4 + 180 * q^8 + 296 * q^10 - 192 * q^11 + 360 * q^12 - 156 * q^14 + 352 * q^16 - 324 * q^18 + 704 * q^19 - 1200 * q^20 - 1568 * q^22 - 2304 * q^23 + 1188 * q^24 + 2700 * q^26 + 4680 * q^28 - 1728 * q^29 + 1512 * q^30 - 3360 * q^32 - 9312 * q^34 - 5184 * q^35 - 756 * q^36 + 3648 * q^37 - 5880 * q^38 + 5232 * q^40 + 4500 * q^42 + 1088 * q^43 + 18840 * q^44 + 680 * q^46 + 2160 * q^48 + 10976 * q^49 - 25884 * q^50 - 4032 * q^51 - 25584 * q^52 + 960 * q^53 + 972 * q^54 + 11776 * q^55 + 15456 * q^56 + 12624 * q^58 + 13056 * q^59 + 7992 * q^60 + 3776 * q^61 + 21852 * q^62 - 8664 * q^64 + 4032 * q^65 - 8856 * q^66 - 896 * q^67 - 17280 * q^68 - 9792 * q^69 - 18240 * q^70 - 39936 * q^71 + 4860 * q^72 + 24204 * q^74 - 1152 * q^75 + 16776 * q^76 + 9408 * q^77 - 3780 * q^78 - 14232 * q^80 - 23328 * q^81 - 33800 * q^82 + 24000 * q^83 - 11448 * q^84 - 11200 * q^85 - 1200 * q^86 - 11424 * q^88 + 4104 * q^90 + 30528 * q^91 - 11664 * q^92 - 8040 * q^94 + 10080 * q^96 + 52968 * q^98 - 5184 * q^99

Introduction

L-functions

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