LMFDB - Embedded newform 48.5.l.a.19.4

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			19.4
Character	$\chi$	$=$	48.19
Dual form			48.5.l.a.43.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.09682 + 2.53174i) q^{2} +(3.67423 - 3.67423i) q^{3} +(3.18056 - 15.6807i) q^{4} +(-7.37831 + 7.37831i) q^{5} +(-2.07622 + 20.6807i) q^{6} -75.1984 q^{7} +(29.8498 + 56.6126i) q^{8} -27.0000i q^{9} +O(q^{10})$	\(q+(-3.09682 + 2.53174i) q^{2} +(3.67423 - 3.67423i) q^{3} +(3.18056 - 15.6807i) q^{4} +(-7.37831 + 7.37831i) q^{5} +(-2.07622 + 20.6807i) q^{6} -75.1984 q^{7} +(29.8498 + 56.6126i) q^{8} -27.0000i q^{9} +(4.16931 - 41.5293i) q^{10} +(-55.7993 - 55.7993i) q^{11} +(-45.9284 - 69.3007i) q^{12} +(-199.825 - 199.825i) q^{13} +(232.876 - 190.383i) q^{14} +54.2193i q^{15} +(-235.768 - 99.7468i) q^{16} +153.639 q^{17} +(68.3570 + 83.6141i) q^{18} +(1.48508 - 1.48508i) q^{19} +(92.2299 + 139.164i) q^{20} +(-276.296 + 276.296i) q^{21} +(314.070 + 31.5308i) q^{22} -693.840 q^{23} +(317.683 + 98.3327i) q^{24} +516.121i q^{25} +(1124.73 + 112.916i) q^{26} +(-99.2043 - 99.2043i) q^{27} +(-239.173 + 1179.16i) q^{28} +(1019.37 + 1019.37i) q^{29} +(-137.269 - 167.907i) q^{30} -1124.80i q^{31} +(982.664 - 288.006i) q^{32} -410.039 q^{33} +(-475.793 + 388.975i) q^{34} +(554.837 - 554.837i) q^{35} +(-423.379 - 85.8752i) q^{36} +(55.0136 - 55.0136i) q^{37} +(-0.839182 + 8.35886i) q^{38} -1468.41 q^{39} +(-637.947 - 197.464i) q^{40} -16.6904i q^{41} +(156.128 - 1555.15i) q^{42} +(-213.904 - 213.904i) q^{43} +(-1052.44 + 697.498i) q^{44} +(199.214 + 199.214i) q^{45} +(2148.70 - 1756.62i) q^{46} -1363.39i q^{47} +(-1232.76 + 499.774i) q^{48} +3253.80 q^{49} +(-1306.69 - 1598.33i) q^{50} +(564.507 - 564.507i) q^{51} +(-3768.95 + 2497.84i) q^{52} +(-1485.98 + 1485.98i) q^{53} +(558.378 + 56.0580i) q^{54} +823.410 q^{55} +(-2244.66 - 4257.18i) q^{56} -10.9131i q^{57} +(-5737.56 - 576.018i) q^{58} +(723.736 + 723.736i) q^{59} +(850.196 + 172.448i) q^{60} +(2594.41 + 2594.41i) q^{61} +(2847.71 + 3483.31i) q^{62} +2030.36i q^{63} +(-2313.97 + 3379.75i) q^{64} +2948.74 q^{65} +(1269.82 - 1038.11i) q^{66} +(4638.03 - 4638.03i) q^{67} +(488.659 - 2409.17i) q^{68} +(-2549.33 + 2549.33i) q^{69} +(-313.525 + 3122.93i) q^{70} -8625.82 q^{71} +(1528.54 - 805.946i) q^{72} -8791.90i q^{73} +(-31.0868 + 309.647i) q^{74} +(1896.35 + 1896.35i) q^{75} +(-18.5637 - 28.0105i) q^{76} +(4196.02 + 4196.02i) q^{77} +(4547.39 - 3717.63i) q^{78} -5388.26i q^{79} +(2475.53 - 1003.61i) q^{80} -729.000 q^{81} +(42.2557 + 51.6870i) q^{82} +(-6986.30 + 6986.30i) q^{83} +(3453.74 + 5211.30i) q^{84} +(-1133.60 + 1133.60i) q^{85} +(1203.97 + 120.872i) q^{86} +7490.77 q^{87} +(1493.34 - 4824.54i) q^{88} -8182.73i q^{89} +(-1121.29 - 112.571i) q^{90} +(15026.5 + 15026.5i) q^{91} +(-2206.80 + 10879.9i) q^{92} +(-4132.79 - 4132.79i) q^{93} +(3451.76 + 4222.19i) q^{94} +21.9148i q^{95} +(2552.34 - 4668.74i) q^{96} -14827.4 q^{97} +(-10076.4 + 8237.77i) q^{98} +(-1506.58 + 1506.58i) 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 $

$2$	−3.09682	+	2.53174i	−0.774204	+	0.632936i
$2$	−3.09682	+	2.53174i	−0.774204	+	0.632936i
$3$	3.67423	−	3.67423i	0.408248	−	0.408248i
$3$	3.67423	−	3.67423i	0.408248	−	0.408248i
$4$	3.18056	−	15.6807i	0.198785	−	0.980043i
$5$	−7.37831	+	7.37831i	−0.295133	+	0.295133i	−0.839104	−	0.543971i	$-0.816920\pi$
$5$	−7.37831	+	7.37831i	−0.295133	+	0.295133i	0.543971	+	0.839104i	$0.316920\pi$
$6$	−2.07622	+	20.6807i	−0.0576728	+	0.574463i
$7$	−75.1984			−1.53466			−0.767330	−	0.641252i	$-0.778415\pi$
$7$	−75.1984			−1.53466			−0.767330	+	0.641252i	$0.778415\pi$
$8$	29.8498	+	56.6126i	0.466404	+	0.884572i
$9$		−	27.0000i		−	0.333333i
$10$	4.16931	−	41.5293i	0.0416931	−	0.415293i
$11$	−55.7993	−	55.7993i	−0.461151	−	0.461151i	0.437881	−	0.899033i	$-0.355729\pi$
$11$	−55.7993	−	55.7993i	−0.461151	−	0.461151i	−0.899033	+	0.437881i	$0.855729\pi$
$12$	−45.9284	−	69.3007i	−0.318947	−	0.481255i
$13$	−199.825	−	199.825i	−1.18240	−	1.18240i	−0.979122	−	0.203275i	$-0.934842\pi$
$13$	−199.825	−	199.825i	−1.18240	−	1.18240i	−0.203275	−	0.979122i	$-0.565158\pi$
$14$	232.876	−	190.383i	1.18814	−	0.971341i
$15$			54.2193i			0.240975i
$16$	−235.768	−	99.7468i	−0.920969	−	0.389636i
$17$	153.639			0.531624			0.265812	−	0.964025i	$-0.414360\pi$
$17$	153.639			0.531624			0.265812	+	0.964025i	$0.414360\pi$
$18$	68.3570	+	83.6141i	0.210979	+	0.258068i
$19$	1.48508	−	1.48508i	0.00411379	−	0.00411379i	−0.705047	−	0.709161i	$-0.749074\pi$
$19$	1.48508	−	1.48508i	0.00411379	−	0.00411379i	0.709161	+	0.705047i	$0.249074\pi$
$20$	92.2299	+	139.164i	0.230575	+	0.347911i
$21$	−276.296	+	276.296i	−0.626523	+	0.626523i
$22$	314.070	+	31.5308i	0.648904	+	0.0651463i
$23$	−693.840			−1.31161			−0.655803	−	0.754932i	$-0.727670\pi$
$23$	−693.840			−1.31161			−0.655803	+	0.754932i	$0.727670\pi$
$24$	317.683	+	98.3327i	0.551534	+	0.170716i
$25$			516.121i			0.825794i
$26$	1124.73	+	112.916i	1.66380	+	0.167036i
$27$	−99.2043	−	99.2043i	−0.136083	−	0.136083i
$28$	−239.173	+	1179.16i	−0.305068	+	1.50403i
$29$	1019.37	+	1019.37i	1.21209	+	1.21209i	0.970339	+	0.241748i	$0.0777208\pi$
$29$	1019.37	+	1019.37i	1.21209	+	1.21209i	0.241748	+	0.970339i	$0.422279\pi$
$30$	−137.269	−	167.907i	−0.152521	−	0.186564i
$31$		−	1124.80i		−	1.17045i	−0.810871	−	0.585225i	$-0.801006\pi$
$31$		−	1124.80i		−	1.17045i	0.810871	−	0.585225i	$-0.198994\pi$
$32$	982.664	−	288.006i	0.959633	−	0.281256i
$33$	−410.039			−0.376528
$34$	−475.793	+	388.975i	−0.411586	+	0.336484i
$35$	554.837	−	554.837i	0.452928	−	0.452928i
$36$	−423.379	−	85.8752i	−0.326681	−	0.0662617i
$37$	55.0136	−	55.0136i	0.0401852	−	0.0401852i	−0.686729	−	0.726914i	$-0.740954\pi$
$37$	55.0136	−	55.0136i	0.0401852	−	0.0401852i	0.726914	+	0.686729i	$0.240954\pi$
$38$	−0.839182	+	8.35886i	−0.000581151	+	0.00578868i
$39$	−1468.41			−0.965423
$40$	−637.947	−	197.464i	−0.398717	−	0.123415i
$41$		−	16.6904i		−	0.00992883i	−0.999988	−	0.00496441i	$-0.998420\pi$
$41$		−	16.6904i		−	0.00992883i	0.999988	−	0.00496441i	$-0.00158023\pi$
$42$	156.128	−	1555.15i	0.0885082	−	0.881605i
$43$	−213.904	−	213.904i	−0.115686	−	0.115686i	0.646894	−	0.762580i	$-0.276068\pi$
$43$	−213.904	−	213.904i	−0.115686	−	0.115686i	−0.762580	+	0.646894i	$0.776068\pi$
$44$	−1052.44	+	697.498i	−0.543618	+	0.360278i
$45$	199.214	+	199.214i	0.0983775	+	0.0983775i
$46$	2148.70	−	1756.62i	1.01545	−	0.830163i
$47$		−	1363.39i		−	0.617200i	−0.951192	−	0.308600i	$-0.900140\pi$
$47$		−	1363.39i		−	0.617200i	0.951192	−	0.308600i	$-0.0998605\pi$
$48$	−1232.76	+	499.774i	−0.535052	+	0.216916i
$49$	3253.80			1.35518
$50$	−1306.69	−	1598.33i	−0.522674	−	0.639333i
$51$	564.507	−	564.507i	0.217035	−	0.217035i
$52$	−3768.95	+	2497.84i	−1.39384	+	0.923757i
$53$	−1485.98	+	1485.98i	−0.529005	+	0.529005i	−0.920276	−	0.391270i	$-0.872036\pi$
$53$	−1485.98	+	1485.98i	−0.529005	+	0.529005i	0.391270	+	0.920276i	$0.372036\pi$
$54$	558.378	+	56.0580i	0.191488	+	0.0192243i
$55$	823.410			0.272202
$56$	−2244.66	−	4257.18i	−0.715772	−	1.35752i
$57$		−	10.9131i		−	0.00335890i
$58$	−5737.56	−	576.018i	−1.70558	−	0.171230i
$59$	723.736	+	723.736i	0.207910	+	0.207910i	0.803379	−	0.595468i	$-0.203034\pi$
$59$	723.736	+	723.736i	0.207910	+	0.207910i	−0.595468	+	0.803379i	$0.703034\pi$
$60$	850.196	+	172.448i	0.236166	+	0.0479022i
$61$	2594.41	+	2594.41i	0.697235	+	0.697235i	0.963813	−	0.266578i	$-0.0858931\pi$
$61$	2594.41	+	2594.41i	0.697235	+	0.697235i	−0.266578	+	0.963813i	$0.585893\pi$
$62$	2847.71	+	3483.31i	0.740819	+	0.906167i
$63$			2030.36i			0.511554i
$64$	−2313.97	+	3379.75i	−0.564935	+	0.825135i
$65$	2948.74			0.697927
$66$	1269.82	−	1038.11i	0.291510	−	0.238318i
$67$	4638.03	−	4638.03i	1.03320	−	1.03320i	0.0337695	−	0.999430i	$-0.489249\pi$
$67$	4638.03	−	4638.03i	1.03320	−	1.03320i	0.999430	−	0.0337695i	$-0.0107512\pi$
$68$	488.659	−	2409.17i	0.105679	−	0.521014i
$69$	−2549.33	+	2549.33i	−0.535461	+	0.535461i
$70$	−313.525	+	3122.93i	−0.0639847	+	0.637334i
$71$	−8625.82			−1.71113			−0.855566	−	0.517694i	$-0.826791\pi$
$71$	−8625.82			−1.71113			−0.855566	+	0.517694i	$0.826791\pi$
$72$	1528.54	−	805.946i	0.294857	−	0.155468i
$73$		−	8791.90i		−	1.64982i	−0.565262	−	0.824911i	$-0.691225\pi$
$73$		−	8791.90i		−	1.64982i	0.565262	−	0.824911i	$-0.308775\pi$
$74$	−31.0868	+	309.647i	−0.00567692	+	0.0565462i
$75$	1896.35	+	1896.35i	0.337129	+	0.337129i
$76$	−18.5637	−	28.0105i	−0.00321393	−	0.00484946i
$77$	4196.02	+	4196.02i	0.707711	+	0.707711i
$78$	4547.39	−	3717.63i	0.747435	−	0.611050i
$79$		−	5388.26i		−	0.863364i	−0.902026	−	0.431682i	$-0.857920\pi$
$79$		−	5388.26i		−	0.863364i	0.902026	−	0.431682i	$-0.142080\pi$
$80$	2475.53	−	1003.61i	0.386802	−	0.156814i
$81$	−729.000			−0.111111
$82$	42.2557	+	51.6870i	0.00628431	+	0.00768694i
$83$	−6986.30	+	6986.30i	−1.01412	+	1.01412i	−0.0142255	+	0.999899i	$0.504528\pi$
$83$	−6986.30	+	6986.30i	−1.01412	+	1.01412i	−0.999899	+	0.0142255i	$0.995472\pi$
$84$	3453.74	+	5211.30i	0.489476	+	0.738563i
$85$	−1133.60	+	1133.60i	−0.156900	+	0.156900i
$86$	1203.97	+	120.872i	0.162787	+	0.0163429i
$87$	7490.77			0.989665
$88$	1493.34	−	4824.54i	0.192839	−	0.623004i
$89$		−	8182.73i		−	1.03304i	−0.856274	−	0.516521i	$-0.827227\pi$
$89$		−	8182.73i		−	1.03304i	0.856274	−	0.516521i	$-0.172773\pi$
$90$	−1121.29	−	112.571i	−0.138431	−	0.0138977i
$91$	15026.5	+	15026.5i	1.81458	+	1.81458i
$92$	−2206.80	+	10879.9i	−0.260728	+	1.28543i
$93$	−4132.79	−	4132.79i	−0.477834	−	0.477834i
$94$	3451.76	+	4222.19i	0.390648	+	0.477839i
$95$			21.9148i			0.00242823i
$96$	2552.34	−	4668.74i	0.276946	−	0.506591i
$97$	−14827.4			−1.57587			−0.787937	−	0.615756i	$-0.788851\pi$
$97$	−14827.4			−1.57587			−0.787937	+	0.615756i	$0.788851\pi$
$98$	−10076.4	+	8237.77i	−1.04919	+	0.857744i
$99$	−1506.58	+	1506.58i	−0.153717	+	0.153717i
$100$	8093.13	+	1641.55i	0.809313	+	0.164155i
$101$	−6283.15	+	6283.15i	−0.615934	+	0.615934i	−0.944486	−	0.328552i	$-0.893440\pi$
$101$	−6283.15	+	6283.15i	−0.615934	+	0.615934i	0.328552	+	0.944486i	$0.393440\pi$
$102$	−318.989	+	3177.36i	−0.0306602	+	0.305398i
$103$	−11891.6			−1.12090			−0.560450	−	0.828188i	$-0.689372\pi$
$103$	−11891.6			−1.12090			−0.560450	+	0.828188i	$0.689372\pi$
$104$	5347.87	−	17277.4i	0.494441	−	1.59739i
$105$		−	4077.20i		−	0.369814i
$106$	839.689	−	8363.90i	0.0747320	−	0.744385i
$107$	−7667.77	−	7667.77i	−0.669733	−	0.669733i	0.287921	−	0.957654i	$-0.407036\pi$
$107$	−7667.77	−	7667.77i	−0.669733	−	0.669733i	−0.957654	+	0.287921i	$0.907036\pi$
$108$	−1871.12	+	1240.07i	−0.160418	+	0.106316i
$109$	−2611.55	−	2611.55i	−0.219809	−	0.219809i	0.588609	−	0.808418i	$-0.299676\pi$
$109$	−2611.55	−	2611.55i	−0.219809	−	0.219809i	−0.808418	+	0.588609i	$0.799676\pi$
$110$	−2549.95	+	2084.66i	−0.210740	+	0.172286i
$111$		−	404.266i		−	0.0328111i
$112$	17729.4	+	7500.80i	1.41337	+	0.597959i
$113$	9026.47			0.706905			0.353452	−	0.935452i	$-0.385008\pi$
$113$	9026.47			0.706905			0.353452	+	0.935452i	$0.385008\pi$
$114$	27.6291	+	33.7958i	0.00212597	+	0.00260047i
$115$	5119.37	−	5119.37i	0.387098	−	0.387098i
$116$	19226.5	−	12742.2i	1.42884	−	0.946953i
$117$	−5395.28	+	5395.28i	−0.394132	+	0.394132i
$118$	−4073.59	−	408.965i	−0.292559	−	0.0293713i
$119$	−11553.4			−0.815862
$120$	−3069.50	+	1618.44i	−0.213159	+	0.112392i
$121$		−	8413.87i		−	0.574679i
$122$	−14602.8	−	1466.04i	−0.981107	−	0.0984976i
$123$	−61.3243	−	61.3243i	−0.00405343	−	0.00405343i
$124$	−17637.7	−	3577.50i	−1.14709	−	0.232668i
$125$	−8419.55	−	8419.55i	−0.538851	−	0.538851i
$126$	−5140.34	−	6287.64i	−0.323780	−	0.396047i
$127$			9307.93i			0.577093i	0.957466	+	0.288546i	$0.0931719\pi$
$127$			9307.93i			0.577093i	−0.957466	+	0.288546i	$0.906828\pi$
$128$	−1390.71	−	16324.9i	−0.0848823	−	0.996391i
$129$	−1571.87			−0.0944575
$130$	−9131.72	+	7465.46i	−0.540339	+	0.441743i
$131$	12733.0	−	12733.0i	0.741974	−	0.741974i	−0.230984	−	0.972958i	$-0.574194\pi$
$131$	12733.0	−	12733.0i	0.741974	−	0.741974i	0.972958	+	0.230984i	$0.0741945\pi$
$132$	−1304.16	+	6429.70i	−0.0748483	+	0.369014i
$133$	−111.676	+	111.676i	−0.00631328	+	0.00631328i
$134$	−2620.84	+	26105.4i	−0.145959	+	1.45386i
$135$	1463.92			0.0803249
$136$	4586.11	+	8697.92i	0.247951	+	0.470260i
$137$			459.808i			0.0244983i	0.999925	+	0.0122491i	$0.00389912\pi$
$137$			459.808i			0.0244983i	−0.999925	+	0.0122491i	$0.996101\pi$
$138$	1440.56	−	14349.1i	0.0756440	−	0.753469i
$139$	11300.2	+	11300.2i	0.584866	+	0.584866i	0.936236	−	0.351371i	$-0.114284\pi$
$139$	11300.2	+	11300.2i	0.584866	+	0.584866i	−0.351371	+	0.936236i	$0.614284\pi$
$140$	−6935.53	−	10464.9i	−0.353854	−	0.533925i
$141$	−5009.43	−	5009.43i	−0.251971	−	0.251971i
$142$	26712.6	−	21838.3i	1.32477	−	1.08304i
$143$			22300.2i			1.09053i
$144$	−2693.16	+	6365.74i	−0.129879	+	0.306990i
$145$	−15042.4			−0.715453
$146$	22258.8	+	27226.9i	1.04423	+	1.27730i
$147$	11955.2	−	11955.2i	0.553251	−	0.553251i
$148$	−687.677	−	1037.62i	−0.0313950	−	0.0473715i
$149$	17921.7	−	17921.7i	0.807249	−	0.807249i	−0.176968	−	0.984217i	$-0.556629\pi$
$149$	17921.7	−	17921.7i	0.807249	−	0.807249i	0.984217	+	0.176968i	$0.0566289\pi$
$150$	−10673.7	−	1071.58i	−0.474387	−	0.0476258i
$151$	15015.0			0.658524			0.329262	−	0.944239i	$-0.393200\pi$
$151$	15015.0			0.658524			0.329262	+	0.944239i	$0.393200\pi$
$152$	128.404	+	39.7448i	0.00555764	+	0.00172026i
$153$		−	4148.26i		−	0.177208i
$154$	−23617.5	−	2371.07i	−0.995848	−	0.0999775i
$155$	8299.14	+	8299.14i	0.345438	+	0.345438i
$156$	−4670.36	+	23025.7i	−0.191912	+	0.946156i
$157$	−6513.36	−	6513.36i	−0.264244	−	0.264244i	0.562532	−	0.826776i	$-0.309827\pi$
$157$	−6513.36	−	6513.36i	−0.264244	−	0.264244i	−0.826776	+	0.562532i	$0.809827\pi$
$158$	13641.7	+	16686.4i	0.546454	+	0.668420i
$159$			10919.6i			0.431931i
$160$	−5125.40	+	9375.40i	−0.200211	+	0.366227i
$161$	52175.6			2.01287
$162$	2257.58	−	1845.64i	0.0860227	−	0.0703262i
$163$	−35216.2	+	35216.2i	−1.32546	+	1.32546i	−0.416180	+	0.909282i	$0.636631\pi$
$163$	−35216.2	+	35216.2i	−1.32546	+	1.32546i	−0.909282	+	0.416180i	$0.863369\pi$
$164$	−261.716	−	53.0847i	−0.00973068	−	0.00197370i
$165$	3025.40	−	3025.40i	0.111126	−	0.111126i
$166$	3947.79	−	39322.8i	0.143264	−	1.42701i
$167$	17020.5			0.610294			0.305147	−	0.952305i	$-0.401294\pi$
$167$	17020.5			0.610294			0.305147	+	0.952305i	$0.401294\pi$
$168$	−23889.3	−	7394.46i	−0.846417	−	0.261992i
$169$			51299.1i			1.79612i
$170$	640.569	−	6380.53i	0.0221650	−	0.220780i
$171$	−40.0971	−	40.0971i	−0.00137126	−	0.00137126i
$172$	−4034.50	+	2673.83i	−0.136374	+	0.0903809i
$173$	37148.9	+	37148.9i	1.24123	+	1.24123i	0.959489	+	0.281745i	$0.0909133\pi$
$173$	37148.9	+	37148.9i	1.24123	+	1.24123i	0.281745	+	0.959489i	$0.409087\pi$
$174$	−23197.6	+	18964.7i	−0.766203	+	0.626394i
$175$		−	38811.5i		−	1.26731i
$176$	7589.89	+	18721.5i	0.245025	+	0.604387i
$177$	5318.35			0.169758
$178$	20716.6	+	25340.4i	0.653849	+	0.799786i
$179$	2443.13	−	2443.13i	0.0762500	−	0.0762500i	−0.667953	−	0.744203i	$-0.732829\pi$
$179$	2443.13	−	2443.13i	0.0762500	−	0.0762500i	0.744203	+	0.667953i	$0.232829\pi$
$180$	3757.43	−	2490.21i	0.115970	−	0.0768582i
$181$	14673.1	−	14673.1i	0.447884	−	0.447884i	−0.446767	−	0.894651i	$-0.647425\pi$
$181$	14673.1	−	14673.1i	0.447884	−	0.447884i	0.894651	+	0.446767i	$0.147425\pi$
$182$	−84577.6	−	8491.12i	−2.55336	−	0.256343i
$183$	19065.0			0.569290
$184$	−20711.0	−	39280.1i	−0.611738	−	1.16021i
$185$			811.815i			0.0237199i
$186$	23261.6	+	2335.34i	0.672379	+	0.0675031i
$187$	−8572.97	−	8572.97i	−0.245159	−	0.245159i
$188$	−21379.0	−	4336.36i	−0.604883	−	0.122690i
$189$	7460.00	+	7460.00i	0.208841	+	0.208841i
$190$	−55.4825	−	67.8660i	−0.00153691	−	0.00187995i
$191$		−	41150.7i		−	1.12800i	−0.825774	−	0.564001i	$-0.809261\pi$
$191$		−	41150.7i		−	1.12800i	0.825774	−	0.564001i	$-0.190739\pi$
$192$	3915.93	+	20920.1i	0.106226	+	0.567494i
$193$	−57638.6			−1.54739			−0.773694	−	0.633560i	$-0.781593\pi$
$193$	−57638.6			−1.54739			−0.773694	+	0.633560i	$0.781593\pi$
$194$	45917.8	−	37539.2i	1.22005	−	0.997427i
$195$	10834.4	−	10834.4i	0.284928	−	0.284928i
$196$	10348.9	−	51021.7i	0.269390	−	1.32814i
$197$	−5213.67	+	5213.67i	−0.134342	+	0.134342i	−0.771080	−	0.636738i	$-0.780283\pi$
$197$	−5213.67	+	5213.67i	−0.134342	+	0.134342i	0.636738	+	0.771080i	$0.280283\pi$
$198$	851.332	−	8479.88i	0.0217154	−	0.216301i
$199$	−18810.1			−0.474990			−0.237495	−	0.971389i	$-0.576326\pi$
$199$	−18810.1			−0.474990			−0.237495	+	0.971389i	$0.576326\pi$
$200$	−29219.0	+	15406.1i	−0.730474	+	0.385153i
$201$		−	34082.4i		−	0.843604i
$202$	3550.45	−	35365.1i	0.0870124	−	0.866706i
$203$	−76654.6	−	76654.6i	−1.86014	−	1.86014i
$204$	−7056.41	−	10647.3i	−0.169560	−	0.255846i
$205$	123.147	+	123.147i	0.00293032	+	0.00293032i
$206$	36826.2	−	30106.5i	0.867806	−	0.709457i
$207$			18733.7i			0.437202i
$208$	27180.4	+	67044.3i	0.628246	+	1.54965i
$209$	−165.733			−0.00379416
$210$	10322.4	+	12626.4i	0.234069	+	0.286312i
$211$	−3788.67	+	3788.67i	−0.0850986	+	0.0850986i	−0.748375	−	0.663276i	$-0.769165\pi$
$211$	−3788.67	+	3788.67i	−0.0850986	+	0.0850986i	0.663276	+	0.748375i	$0.269165\pi$
$212$	18574.9	+	28027.4i	0.413290	+	0.623606i
$213$	−31693.3	+	31693.3i	−0.698567	+	0.698567i
$214$	43158.5	+	4332.87i	0.942408	+	0.0946125i
$215$	3156.50			0.0682856
$216$	2654.98	−	8577.45i	0.0569055	−	0.183845i
$217$			84583.3i			1.79624i
$218$	14699.3	+	1475.73i	0.309302	+	0.0310522i
$219$	−32303.5	−	32303.5i	−0.673537	−	0.673537i
$220$	2618.91	−	12911.6i	0.0541096	−	0.266769i
$221$	−30701.0	−	30701.0i	−0.628590	−	0.628590i
$222$	1023.50	+	1251.94i	0.0207673	+	0.0254025i
$223$		−	47183.5i		−	0.948812i	−0.880306	−	0.474406i	$-0.842663\pi$
$223$		−	47183.5i		−	0.948812i	0.880306	−	0.474406i	$-0.157337\pi$
$224$	−73894.7	+	21657.6i	−1.47271	+	0.431633i
$225$	13935.3			0.275265
$226$	−27953.3	+	22852.7i	−0.547289	+	0.447425i
$227$	−41707.5	+	41707.5i	−0.809399	+	0.809399i	−0.984543	−	0.175144i	$-0.943961\pi$
$227$	−41707.5	+	41707.5i	−0.809399	+	0.809399i	0.175144	+	0.984543i	$0.443961\pi$
$228$	−171.124	−	34.7097i	−0.00329187	−	0.000667699i
$229$	60647.9	−	60647.9i	1.15650	−	1.15650i	0.171275	−	0.985223i	$-0.445211\pi$
$229$	60647.9	−	60647.9i	1.15650	−	1.15650i	0.985223	−	0.171275i	$-0.0547888\pi$
$230$	−2892.83	+	28814.7i	−0.0546849	+	0.544701i
$231$	30834.3			0.577843
$232$	−27281.0	+	88136.8i	−0.506856	+	1.63750i
$233$			43912.5i			0.808866i	0.914568	+	0.404433i	$0.132531\pi$
$233$			43912.5i			0.808866i	−0.914568	+	0.404433i	$0.867469\pi$
$234$	3048.74	−	30367.6i	0.0556786	−	0.554599i
$235$	10059.6	+	10059.6i	0.182156	+	0.182156i
$236$	13650.6	−	9046.79i	0.245091	−	0.162432i
$237$	−19797.7	−	19797.7i	−0.352467	−	0.352467i
$238$	35778.9	−	29250.3i	0.631644	−	0.516388i
$239$			80352.6i			1.40671i	0.710840	+	0.703354i	$0.248315\pi$
$239$			80352.6i			1.40671i	−0.710840	+	0.703354i	$0.751685\pi$
$240$	5408.20	−	12783.2i	0.0938924	−	0.221930i
$241$	4743.44			0.0816694			0.0408347	−	0.999166i	$-0.486998\pi$
$241$	4743.44			0.0816694			0.0408347	+	0.999166i	$0.486998\pi$
$242$	21301.8	+	26056.2i	0.363735	+	0.444919i
$243$	−2678.52	+	2678.52i	−0.0453609	+	0.0453609i
$244$	48933.8	−	32430.5i	0.821920	−	0.544720i
$245$	−24007.5	+	24007.5i	−0.399959	+	0.399959i
$246$	345.167	+	34.6529i	0.00570374	+	0.000572623i
$247$	−593.512			−0.00972827
$248$	63678.0	−	33575.2i	1.03535	−	0.545902i
$249$			51338.6i			0.828029i
$250$	47389.9	+	4757.68i	0.758239	+	0.0761229i
$251$	−44387.3	−	44387.3i	−0.704550	−	0.704550i	0.260834	−	0.965384i	$-0.416002\pi$
$251$	−44387.3	−	44387.3i	−0.704550	−	0.704550i	−0.965384	+	0.260834i	$0.916002\pi$
$252$	31837.4	+	6457.67i	0.501345	+	0.101689i
$253$	38715.8	+	38715.8i	0.604849	+	0.604849i
$254$	−23565.3	−	28825.0i	−0.365263	−	0.446788i
$255$			8330.22i			0.128108i
$256$	45637.1	+	47034.2i	0.696368	+	0.717685i
$257$	−82215.6			−1.24477			−0.622383	−	0.782712i	$-0.713836\pi$
$257$	−82215.6			−1.24477			−0.622383	+	0.782712i	$0.713836\pi$
$258$	4867.79	−	3979.56i	0.0731294	−	0.0597855i
$259$	−4136.93	+	4136.93i	−0.0616707	+	0.0616707i
$260$	9378.66	−	46238.3i	0.138738	−	0.683999i
$261$	27522.9	−	27522.9i	0.404029	−	0.404029i
$262$	−7195.11	+	71668.5i	−0.104818	+	1.04406i
$263$	70454.8			1.01859			0.509294	−	0.860592i	$-0.329906\pi$
$263$	70454.8			1.01859			0.509294	+	0.860592i	$0.329906\pi$
$264$	−12239.6	−	23213.4i	−0.175614	−	0.333067i
$265$		−	21928.0i		−	0.312253i
$266$	63.1051	−	628.573i	0.000891870	−	0.00888367i
$267$	−30065.3	−	30065.3i	−0.421738	−	0.421738i
$268$	−57976.0	−	87479.1i	−0.807195	−	1.21796i
$269$	−35276.4	−	35276.4i	−0.487505	−	0.487505i	0.420013	−	0.907518i	$-0.362026\pi$
$269$	−35276.4	−	35276.4i	−0.487505	−	0.487505i	−0.907518	+	0.420013i	$0.862026\pi$
$270$	−4533.50	+	3706.27i	−0.0621879	+	0.0508405i
$271$			28305.0i			0.385411i	0.981257	+	0.192706i	$0.0617263\pi$
$271$			28305.0i			0.385411i	−0.981257	+	0.192706i	$0.938274\pi$
$272$	−36223.2	−	15325.0i	−0.489609	−	0.207140i
$273$	110422.			1.48160
$274$	−1164.12	−	1423.94i	−0.0155058	−	0.0189667i
$275$	28799.2	−	28799.2i	0.380816	−	0.380816i
$276$	31867.0	+	48083.6i	0.418333	+	0.631217i
$277$	48989.6	−	48989.6i	0.638475	−	0.638475i	−0.311704	−	0.950179i	$-0.600900\pi$
$277$	48989.6	−	48989.6i	0.638475	−	0.638475i	0.950179	+	0.311704i	$0.100900\pi$
$278$	−63603.8	−	6385.46i	−0.822988	−	0.0826233i
$279$	−30369.7			−0.390150
$280$	47972.6	+	14849.0i	0.611895	+	0.189400i
$281$		−	42574.4i		−	0.539183i	−0.962975	−	0.269591i	$-0.913111\pi$
$281$		−	42574.4i		−	0.539183i	0.962975	−	0.269591i	$-0.0868887\pi$
$282$	28195.9	+	2830.71i	0.354558	+	0.0355957i
$283$	37205.8	+	37205.8i	0.464556	+	0.464556i	0.900145	−	0.435589i	$-0.143460\pi$
$283$	37205.8	+	37205.8i	0.464556	+	0.464556i	−0.435589	+	0.900145i	$0.643460\pi$
$284$	−27434.9	+	135259.i	−0.340148	+	1.67698i
$285$	80.5200	+	80.5200i	0.000991320	+	0.000991320i
$286$	−56458.3	−	69059.6i	−0.690234	−	0.844291i
$287$			1255.09i			0.0152374i
$288$	−7776.17	−	26531.9i	−0.0937520	−	0.319878i
$289$	−59916.0			−0.717376
$290$	46583.6	−	38083.5i	0.553907	−	0.452835i
$291$	−54479.4	+	54479.4i	−0.643348	+	0.643348i
$292$	−137863.	−	27963.2i	−1.61690	−	0.327960i
$293$	2135.64	−	2135.64i	0.0248767	−	0.0248767i	−0.694559	−	0.719436i	$-0.744400\pi$
$293$	2135.64	−	2135.64i	0.0248767	−	0.0248767i	0.719436	+	0.694559i	$0.244400\pi$
$294$	−6755.60	+	67290.6i	−0.0781572	+	0.778502i
$295$	−10679.9			−0.122722
$296$	4756.61	+	1472.32i	0.0542893	+	0.0168042i
$297$			11071.1i			0.125509i
$298$	−10127.1	+	100874.i	−0.114039	+	1.13591i
$299$	138647.	+	138647.i	1.55084	+	1.55084i
$300$	35767.5	−	23704.6i	0.397417	−	0.263385i
$301$	16085.2	+	16085.2i	0.177539	+	0.177539i
$302$	−46498.7	+	38014.1i	−0.509832	+	0.416803i
$303$			46171.5i			0.502908i
$304$	−498.266	+	202.002i	−0.00539156	+	0.00218579i
$305$	−38284.8			−0.411553
$306$	10502.3	+	12846.4i	0.112161	+	0.137195i
$307$	26542.3	−	26542.3i	0.281619	−	0.281619i	−0.552136	−	0.833754i	$-0.686187\pi$
$307$	26542.3	−	26542.3i	0.281619	−	0.281619i	0.833754	+	0.552136i	$0.186187\pi$
$308$	79142.1	−	52450.7i	0.834269	−	0.552905i
$309$	−43692.6	+	43692.6i	−0.457605	+	0.457605i
$310$	−46712.2	−	4689.64i	−0.486079	−	0.0487996i
$311$	124017.			1.28222			0.641109	−	0.767450i	$-0.278475\pi$
$311$	124017.			1.28222			0.641109	+	0.767450i	$0.278475\pi$
$312$	−43831.7	−	83130.4i	−0.450277	−	0.853986i
$313$		−	139060.i		−	1.41943i	−0.704489	−	0.709715i	$-0.748824\pi$
$313$		−	139060.i		−	1.41943i	0.704489	−	0.709715i	$-0.251176\pi$
$314$	36660.8	+	3680.54i	0.371829	+	0.0373295i
$315$	−14980.6	−	14980.6i	−0.150976	−	0.150976i
$316$	−84491.6	−	17137.7i	−0.846134	−	0.171624i
$317$	−102920.	−	102920.i	−1.02419	−	1.02419i	−0.999700	−	0.0244920i	$-0.992203\pi$
$317$	−102920.	−	102920.i	−1.02419	−	1.02419i	−0.0244920	−	0.999700i	$-0.507797\pi$
$318$	−27645.7	−	33816.2i	−0.273384	−	0.334403i
$319$		−	113760.i		−	1.11791i
$320$	−7863.66	−	42010.1i	−0.0767936	−	0.410255i
$321$	−56346.4			−0.546835
$322$	−161578.	+	132095.i	−1.55837	+	1.27402i
$323$	228.167	−	228.167i	0.00218699	−	0.00218699i
$324$	−2318.63	+	11431.2i	−0.0220872	+	0.108894i
$325$	103134.	−	103134.i	0.976415	−	0.976415i
$326$	19899.8	−	198217.i	0.187247	−	1.86511i
$327$	−19190.9			−0.179474
$328$	944.885	−	498.204i	0.00878276	−	0.00463084i
$329$			102525.i			0.947193i
$330$	−1709.58	+	17028.6i	−0.0156986	+	0.156370i
$331$	51404.9	+	51404.9i	0.469190	+	0.469190i	0.901652	−	0.432462i	$-0.142355\pi$
$331$	51404.9	+	51404.9i	0.469190	+	0.469190i	−0.432462	+	0.901652i	$0.642355\pi$
$332$	87329.7	+	131770.i	0.792293	+	1.19548i
$333$	−1485.37	−	1485.37i	−0.0133951	−	0.0133951i
$334$	−52709.4	+	43091.5i	−0.472492	+	0.386277i
$335$			68441.7i			0.609861i
$336$	92701.6	−	37582.2i	0.821124	−	0.332892i
$337$	50638.9			0.445886			0.222943	−	0.974831i	$-0.428434\pi$
$337$	50638.9			0.445886			0.222943	+	0.974831i	$0.428434\pi$
$338$	−129876.	−	158864.i	−1.13683	−	1.39057i
$339$	33165.4	−	33165.4i	0.288593	−	0.288593i
$340$	14170.1	+	21381.1i	0.122579	+	0.184958i
$341$	−62763.2	+	62763.2i	−0.539754	+	0.539754i
$342$	225.689	+	22.6579i	0.00192956	+	0.000193717i
$343$	−64128.8			−0.545086
$344$	5724.66	−	18494.7i	0.0483764	−	0.156289i
$345$		−	37619.5i		−	0.316064i
$346$	−209095.	−	20991.9i	−1.74659	−	0.175348i
$347$	−4848.09	−	4848.09i	−0.0402635	−	0.0402635i	0.686688	−	0.726952i	$-0.259064\pi$
$347$	−4848.09	−	4848.09i	−0.0402635	−	0.0402635i	−0.726952	+	0.686688i	$0.759064\pi$
$348$	23824.9	−	117461.i	0.196731	−	0.969914i
$349$	−27215.3	−	27215.3i	−0.223440	−	0.223440i	0.586505	−	0.809945i	$-0.300503\pi$
$349$	−27215.3	−	27215.3i	−0.223440	−	0.223440i	−0.809945	+	0.586505i	$0.800503\pi$
$350$	98260.6	+	120192.i	0.802127	+	0.981159i
$351$			39647.0i			0.321808i
$352$	−70902.5	−	38761.4i	−0.572237	−	0.312834i
$353$	205801.			1.65157			0.825785	−	0.563985i	$-0.190732\pi$
$353$	205801.			1.65157			0.825785	+	0.563985i	$0.190732\pi$
$354$	−16470.0	+	13464.7i	−0.131427	+	0.107446i
$355$	63644.0	−	63644.0i	0.505011	−	0.505011i
$356$	−128311.	−	26025.7i	−1.01243	−	0.205353i
$357$	−42450.0	+	42450.0i	−0.333074	+	0.333074i
$358$	−1380.55	+	13751.3i	−0.0107718	+	0.107294i
$359$	−54565.2			−0.423377			−0.211688	−	0.977337i	$-0.567896\pi$
$359$	−54565.2			−0.423377			−0.211688	+	0.977337i	$0.567896\pi$
$360$	−5331.53	+	17224.6i	−0.0411383	+	0.132906i
$361$			130317.i			0.999966i
$362$	−8291.43	+	82588.6i	−0.0632721	+	0.630236i
$363$	−30914.5	−	30914.5i	−0.234612	−	0.234612i
$364$	283419.	−	187833.i	2.13908	−	1.41765i
$365$	64869.4	+	64869.4i	0.486916	+	0.486916i
$366$	−59040.7	+	48267.5i	−0.440747	+	0.360324i
$367$		−	30555.7i		−	0.226861i	−0.993546	−	0.113431i	$-0.963816\pi$
$367$		−	30555.7i		−	0.226861i	0.993546	−	0.113431i	$-0.0361840\pi$
$368$	163585.	+	69208.3i	1.20795	+	0.511049i
$369$	−450.640			−0.00330961
$370$	−2055.31	−	2514.04i	−0.0150132	−	0.0183641i
$371$	111743.	−	111743.i	0.811844	−	0.811844i
$372$	−77949.5	+	51660.4i	−0.563284	+	0.373312i
$373$	−63808.8	+	63808.8i	−0.458630	+	0.458630i	−0.898206	−	0.439575i	$-0.855129\pi$
$373$	−63808.8	+	63808.8i	−0.458630	+	0.458630i	0.439575	+	0.898206i	$0.355129\pi$
$374$	48253.5	+	4844.38i	0.344973	+	0.0346334i
$375$	−61870.8			−0.439970
$376$	77185.3	−	40697.1i	0.545958	−	0.287864i
$377$		−	407389.i		−	2.86634i
$378$	−41989.1	−	4215.47i	−0.293868	−	0.0295027i
$379$	144344.	+	144344.i	1.00489	+	1.00489i	0.999988	+	0.00490625i	$0.00156171\pi$
$379$	144344.	+	144344.i	1.00489	+	1.00489i	0.00490625	+	0.999988i	$0.498438\pi$
$380$	343.639	+	69.7013i	0.00237977	+	0.000482696i
$381$	34199.5	+	34199.5i	0.235597	+	0.235597i
$382$	104183.	+	127436.i	0.713953	+	0.873304i
$383$			180882.i			1.23310i	0.787316	+	0.616550i	$0.211470\pi$
$383$			180882.i			1.23310i	−0.787316	+	0.616550i	$0.788530\pi$
$384$	−65091.2	−	54871.6i	−0.441428	−	0.372122i
$385$	−61919.1			−0.417737
$386$	178496.	−	145926.i	1.19799	−	0.979397i
$387$	−5775.41	+	5775.41i	−0.0385621	+	0.0385621i
$388$	−47159.5	+	232504.i	−0.313260	+	1.54442i
$389$	−177413.	+	177413.i	−1.17243	+	1.17243i	−0.190798	+	0.981629i	$0.561108\pi$
$389$	−177413.	+	177413.i	−1.17243	+	1.17243i	−0.981629	+	0.190798i	$0.938892\pi$
$390$	−6122.24	+	60981.9i	−0.0402514	+	0.400933i
$391$	−106601.			−0.697282
$392$	97125.3	+	184206.i	0.632063	+	1.19876i
$393$		−	93568.1i		−	0.605819i
$394$	2946.12	−	29345.5i	0.0189783	−	0.189038i
$395$	39756.2	+	39756.2i	0.254807	+	0.254807i
$396$	18832.5	+	28416.0i	0.120093	+	0.181206i
$397$	46053.2	+	46053.2i	0.292199	+	0.292199i	0.837948	−	0.545750i	$-0.183755\pi$
$397$	46053.2	+	46053.2i	0.292199	+	0.292199i	−0.545750	+	0.837948i	$0.683755\pi$
$398$	58251.4	−	47622.3i	0.367740	−	0.300638i
$399$			820.644i			0.00515477i
$400$	51481.4	−	121685.i	0.321759	−	0.760530i
$401$	−201852.			−1.25529			−0.627645	−	0.778499i	$-0.715981\pi$
$401$	−201852.			−1.25529			−0.627645	+	0.778499i	$0.715981\pi$
$402$	86287.9	+	105547.i	0.533947	+	0.653122i
$403$	−224764.	+	224764.i	−1.38394	+	1.38394i
$404$	78540.1	+	118508.i	0.481204	+	0.726081i
$405$	5378.79	−	5378.79i	0.0327925	−	0.0327925i
$406$	431455.	+	43315.7i	2.61748	+	0.262780i
$407$	−6139.44			−0.0370629
$408$	48808.6	+	15107.8i	0.293208	+	0.0907569i
$409$			80543.5i			0.481486i	0.970589	+	0.240743i	$0.0773911\pi$
$409$			80543.5i			0.481486i	−0.970589	+	0.240743i	$0.922609\pi$
$410$	−693.138	−	69.5872i	−0.00412337	−	0.000413963i
$411$	1689.44	+	1689.44i	0.0100014	+	0.0100014i
$412$	−37822.1	+	186469.i	−0.222818	+	1.09853i
$413$	−54423.7	−	54423.7i	−0.319072	−	0.319072i
$414$	−47428.8	−	58014.8i	−0.276721	−	0.338484i
$415$		−	103094.i		−	0.598602i
$416$	−253912.	−	138810.i	−1.46722	−	0.802110i
$417$	83039.1			0.477541
$418$	513.244	−	419.593i	0.00293746	−	0.00240146i
$419$	53127.5	−	53127.5i	0.302615	−	0.302615i	−0.539421	−	0.842036i	$-0.681357\pi$
$419$	53127.5	−	53127.5i	0.302615	−	0.302615i	0.842036	+	0.539421i	$0.181357\pi$
$420$	−63933.4	−	12967.8i	−0.362434	−	0.0735136i
$421$	65518.2	−	65518.2i	0.369656	−	0.369656i	−0.497696	−	0.867352i	$-0.665820\pi$
$421$	65518.2	−	65518.2i	0.369656	−	0.369656i	0.867352	+	0.497696i	$0.165820\pi$
$422$	2140.89	−	21324.8i	0.0120218	−	0.119746i
$423$	−36811.7			−0.205733
$424$	−128481.	−	39768.8i	−0.714673	−	0.221213i
$425$			79296.5i			0.439012i
$426$	17909.1	−	178388.i	0.0986858	−	0.982981i
$427$	−195095.	−	195095.i	−1.07002	−	1.07002i
$428$	−144624.	+	95848.1i	−0.789500	+	0.523234i
$429$	81936.1	+	81936.1i	0.445206	+	0.445206i
$430$	−9775.11	+	7991.45i	−0.0528670	+	0.0432204i
$431$		−	330521.i		−	1.77928i	−0.456662	−	0.889640i	$-0.650955\pi$
$431$		−	330521.i		−	1.77928i	0.456662	−	0.889640i	$-0.349045\pi$
$432$	13493.9	+	33284.5i	0.0723053	+	0.178351i
$433$	116484.			0.621284			0.310642	−	0.950527i	$-0.399456\pi$
$433$	116484.			0.621284			0.310642	+	0.950527i	$0.399456\pi$
$434$	−214143.	−	261939.i	−1.13691	−	1.39066i
$435$	−55269.3	+	55269.3i	−0.292082	+	0.292082i
$436$	−49257.2	+	32644.8i	−0.259117	+	0.171728i
$437$	−1030.41	+	1030.41i	−0.00539568	+	0.00539568i
$438$	181822.	+	18253.9i	0.947761	+	0.0951499i
$439$	−77944.2			−0.404441			−0.202220	−	0.979340i	$-0.564816\pi$
$439$	−77944.2			−0.404441			−0.202220	+	0.979340i	$0.564816\pi$
$440$	24578.6	+	46615.4i	0.126956	+	0.240782i
$441$		−	87852.5i		−	0.451728i
$442$	172802.	+	17348.4i	0.884515	+	0.0888003i
$443$	49346.1	+	49346.1i	0.251447	+	0.251447i	0.821564	−	0.570117i	$-0.193102\pi$
$443$	49346.1	+	49346.1i	0.251447	+	0.251447i	−0.570117	+	0.821564i	$0.693102\pi$
$444$	−6339.16	−	1285.79i	−0.0321563	−	0.00652236i
$445$	60374.7	+	60374.7i	0.304884	+	0.304884i
$446$	119456.	+	146119.i	0.600537	+	0.734574i
$447$		−	131697.i		−	0.659116i
$448$	174007.	−	254152.i	0.866984	−	1.26630i
$449$	−295574.			−1.46613			−0.733067	−	0.680157i	$-0.761912\pi$
$449$	−295574.			−1.46613			−0.733067	+	0.680157i	$0.761912\pi$
$450$	−43155.0	+	35280.5i	−0.213111	+	0.174225i
$451$	−931.310	+	931.310i	−0.00457869	+	0.00457869i
$452$	28709.2	−	141541.i	0.140522	−	0.692797i
$453$	55168.6	−	55168.6i	0.268841	−	0.268841i
$454$	23567.9	−	234753.i	0.114343	−	1.13894i
$455$	−221741.			−1.07108
$456$	617.817	−	325.753i	0.00297119	−	0.00156660i
$457$		−	225110.i		−	1.07786i	−0.842351	−	0.538929i	$-0.818829\pi$
$457$		−	225110.i		−	1.07786i	0.842351	−	0.538929i	$-0.181171\pi$
$458$	−34270.7	+	341361.i	−0.163377	+	1.62736i
$459$	−15241.7	−	15241.7i	−0.0723449	−	0.0723449i
$460$	−63992.8	−	96557.7i	−0.302423	−	0.456322i
$461$	194743.	+	194743.i	0.916345	+	0.916345i	0.996761	−	0.0804164i	$-0.0256250\pi$
$461$	194743.	+	194743.i	0.916345	+	0.916345i	−0.0804164	+	0.996761i	$0.525625\pi$
$462$	−95488.2	+	78064.5i	−0.447369	+	0.365738i
$463$		−	215686.i		−	1.00614i	−0.864245	−	0.503071i	$-0.832203\pi$
$463$		−	215686.i		−	1.00614i	0.864245	−	0.503071i	$-0.167797\pi$
$464$	−138655.	−	342012.i	−0.644022	−	1.58857i
$465$	60986.0			0.282049
$466$	−111175.	−	135989.i	−0.511960	−	0.626227i
$467$	−29966.7	+	29966.7i	−0.137406	+	0.137406i	−0.772464	−	0.635058i	$-0.780976\pi$
$467$	−29966.7	+	29966.7i	−0.137406	+	0.137406i	0.635058	+	0.772464i	$0.280976\pi$
$468$	67441.6	+	101762.i	0.307919	+	0.464614i
$469$	−348772.	+	348772.i	−1.58561	+	1.58561i
$470$	−56620.8	−	5684.41i	−0.256319	−	0.0257330i
$471$	−47863.2			−0.215755
$472$	−19369.2	+	62576.0i	−0.0869415	+	0.280882i
$473$			23871.4i			0.106698i
$474$	111433.	+	11187.2i	0.495970	+	0.0497926i
$475$	766.481	+	766.481i	0.00339714	+	0.00339714i
$476$	−36746.4	+	181166.i	−0.162181	+	0.799580i
$477$	40121.3	+	40121.3i	0.176335	+	0.176335i
$478$	−203432.	−	248837.i	−0.890356	−	1.08908i
$479$			44819.5i			0.195342i	0.995219	+	0.0976710i	$0.0311393\pi$
$479$			44819.5i			0.195342i	−0.995219	+	0.0976710i	$0.968861\pi$
$480$	15615.5	+	53279.4i	0.0677756	+	0.231247i
$481$	−21986.2			−0.0950298
$482$	−14689.6	+	12009.2i	−0.0632288	+	0.0516915i
$483$	191706.	−	191706.i	0.821751	−	0.821751i
$484$	−131935.	−	26760.9i	−0.563210	−	0.114238i
$485$	109401.	−	109401.i	0.465092	−	0.465092i
$486$	1513.56	−	15076.2i	0.00640809	−	0.0638292i
$487$	−96133.2			−0.405336			−0.202668	−	0.979247i	$-0.564961\pi$
$487$	−96133.2			−0.405336			−0.202668	+	0.979247i	$0.564961\pi$
$488$	−69433.6	+	224319.i	−0.291561	+	0.941947i
$489$			258785.i			1.08224i
$490$	13566.1	−	135128.i	0.0565017	−	0.562798i
$491$	−29861.4	−	29861.4i	−0.123865	−	0.123865i	0.642457	−	0.766322i	$-0.277915\pi$
$491$	−29861.4	−	29861.4i	−0.123865	−	0.123865i	−0.766322	+	0.642457i	$0.777915\pi$
$492$	−1156.65	+	766.561i	−0.00477829	+	0.00316677i
$493$	156615.	+	156615.i	0.644375	+	0.644375i
$494$	1838.00	−	1502.62i	0.00753167	−	0.00615737i
$495$		−	22232.1i		−	0.0907338i
$496$	−112195.	+	265192.i	−0.456049	+	1.07795i
$497$	648647.			2.62601
$498$	−129976.	−	158986.i	−0.524089	−	0.641064i
$499$	142289.	−	142289.i	0.571441	−	0.571441i	−0.361090	−	0.932531i	$-0.617595\pi$
$499$	142289.	−	142289.i	0.571441	−	0.571441i	0.932531	+	0.361090i	$0.117595\pi$
$500$	−158803.	+	105245.i	−0.635213	+	0.420982i
$501$	62537.3	−	62537.3i	0.249151	−	0.249151i
$502$	249837.	+	25082.2i	0.991400	+	0.0995310i
$503$	−29608.1			−0.117024			−0.0585119	−	0.998287i	$-0.518636\pi$
$503$	−29608.1			−0.117024			−0.0585119	+	0.998287i	$0.518636\pi$
$504$	−114944.	+	60605.8i	−0.452506	+	0.238591i
$505$		−	92718.1i		−	0.363565i
$506$	−217914.	−	21877.4i	−0.851107	−	0.0854464i
$507$	188485.	+	188485.i	0.733264	+	0.733264i
$508$	145955.	+	29604.4i	0.565576	+	0.114717i
$509$	−42011.9	−	42011.9i	−0.162158	−	0.162158i	0.621364	−	0.783522i	$-0.286579\pi$
$509$	−42011.9	−	42011.9i	−0.162158	−	0.162158i	−0.783522	+	0.621364i	$0.786579\pi$
$510$	−21090.0	−	25797.2i	−0.0810841	−	0.0991817i
$511$			661137.i			2.53192i
$512$	−260408.	−	30114.9i	−0.993379	−	0.114879i
$513$	−294.653			−0.00111963
$514$	254607.	−	208149.i	0.963704	−	0.787857i
$515$	87740.1	−	87740.1i	0.330814	−	0.330814i
$516$	−4999.42	+	24648.0i	−0.0187768	+	0.0925724i
$517$	−76076.5	+	76076.5i	−0.284623	+	0.284623i
$518$	2337.68	−	23285.0i	0.00871215	−	0.0867793i
$519$	272988.			1.01346
$520$	88019.5	+	166936.i	0.325516	+	0.617367i
$521$			171404.i			0.631461i	0.948849	+	0.315730i	$0.102250\pi$
$521$			171404.i			0.631461i	−0.948849	+	0.315730i	$0.897750\pi$
$522$	−15552.5	+	154914.i	−0.0570767	+	0.568525i
$523$	33771.5	+	33771.5i	0.123466	+	0.123466i	0.766140	−	0.642674i	$-0.222175\pi$
$523$	33771.5	+	33771.5i	0.123466	+	0.123466i	−0.642674	+	0.766140i	$0.722175\pi$
$524$	−159164.	−	240161.i	−0.579673	−	0.874660i
$525$	−142602.	−	142602.i	−0.517378	−	0.517378i
$526$	−218186.	+	178373.i	−0.788596	+	0.644701i
$527$		−	172814.i		−	0.622239i
$528$	96674.2	+	40900.1i	0.346771	+	0.146709i
$529$	201573.			0.720312
$530$	55516.0	+	67907.0i	0.197636	+	0.241748i
$531$	19540.9	−	19540.9i	0.0693034	−	0.0693034i
$532$	1395.96	+	2106.34i	0.00493230	+	0.00744227i
$533$	−3335.15	+	3335.15i	−0.0117398	+	0.0117398i
$534$	169224.	+	16989.1i	0.593444	+	0.0595784i
$535$	113150.			0.395320
$536$	401016.	+	124127.i	1.39583	+	0.432051i
$537$		−	17953.2i		−	0.0622579i
$538$	198555.	+	19933.8i	0.685988	+	0.0688693i
$539$	−181560.	−	181560.i	−0.624945	−	0.624945i
$540$	4656.09	−	22955.3i	0.0159674	−	0.0787219i
$541$	−222600.	−	222600.i	−0.760555	−	0.760555i	0.215868	−	0.976423i	$-0.430742\pi$
$541$	−222600.	−	222600.i	−0.760555	−	0.760555i	−0.976423	+	0.215868i	$0.930742\pi$
$542$	−71661.0	−	87655.4i	−0.243941	−	0.298387i
$543$		−	107825.i		−	0.365696i
$544$	150976.	−	44249.1i	0.510164	−	0.149522i
$545$	38537.7			0.129746
$546$	−341956.	+	279560.i	−1.14706	+	0.937755i
$547$	188563.	−	188563.i	0.630207	−	0.630207i	−0.317913	−	0.948120i	$-0.602982\pi$
$547$	188563.	−	188563.i	0.630207	−	0.630207i	0.948120	+	0.317913i	$0.102982\pi$
$548$	7210.11	+	1462.45i	0.0240094	+	0.00486990i
$549$	70049.1	−	70049.1i	0.232412	−	0.232412i
$550$	−16273.7	+	162098.i	−0.0537974	+	0.535861i
$551$	3027.68			0.00997255
$552$	−220421.	−	68227.1i	−0.723395	−	0.223913i
$553$			405188.i			1.32497i
$554$	−27682.8	+	275741.i	−0.0901967	+	0.898424i
$555$	2982.80	+	2982.80i	0.00968362	+	0.00968362i
$556$	213136.	−	141254.i	0.689456	−	0.456931i
$557$	61525.3	+	61525.3i	0.198309	+	0.198309i	0.799275	−	0.600965i	$-0.205217\pi$
$557$	61525.3	+	61525.3i	0.198309	+	0.198309i	−0.600965	+	0.799275i	$0.705217\pi$
$558$	94049.3	−	76888.1i	0.302056	−	0.246940i
$559$			85486.8i			0.273574i
$560$	−186156.	+	75469.6i	−0.593610	+	0.240656i
$561$	−62998.2			−0.200172
$562$	107787.	+	131845.i	0.341268	+	0.417438i
$563$	−268422.	+	268422.i	−0.846839	+	0.846839i	−0.989737	−	0.142899i	$-0.954358\pi$
$563$	−268422.	+	268422.i	−0.846839	+	0.846839i	0.142899	+	0.989737i	$0.454358\pi$
$564$	−94484.2	+	62618.5i	−0.297030	+	0.196854i
$565$	−66600.1	+	66600.1i	−0.208631	+	0.208631i
$566$	−209415.	−	21024.1i	−0.653695	−	0.0656273i
$567$	54819.6			0.170518
$568$	−257479.	−	488330.i	−0.798078	−	1.51362i
$569$			265433.i			0.819841i	0.912121	+	0.409921i	$0.134444\pi$
$569$			265433.i			0.819841i	−0.912121	+	0.409921i	$0.865556\pi$
$570$	−453.212	−	45.4999i	−0.00139493	−	0.000140043i
$571$	−8306.09	−	8306.09i	−0.0254756	−	0.0254756i	0.694254	−	0.719730i	$-0.255734\pi$
$571$	−8306.09	−	8306.09i	−0.0254756	−	0.0254756i	−0.719730	+	0.694254i	$0.755734\pi$
$572$	349682.	+	70927.2i	1.06876	+	0.216781i
$573$	−151197.	−	151197.i	−0.460505	−	0.460505i
$574$	−3177.56	−	3886.78i	−0.00964428	−	0.0117968i
$575$		−	358105.i		−	1.08312i
$576$	91253.4	+	62477.3i	0.275045	+	0.188312i
$577$	−262735.			−0.789163			−0.394581	−	0.918861i	$-0.629110\pi$
$577$	−262735.			−0.789163			−0.394581	+	0.918861i	$0.629110\pi$
$578$	185549.	−	151692.i	0.555396	−	0.454053i
$579$	−211778.	+	211778.i	−0.631718	+	0.631718i
$580$	−47843.3	+	235875.i	−0.142221	+	0.701174i
$581$	525359.	−	525359.i	1.55634	−	1.55634i
$582$	30785.0	−	306640.i	0.0908851	−	0.905281i
$583$	165833.			0.487903
$584$	497733.	−	262437.i	1.45939	−	0.769484i
$585$		−	79616.1i		−	0.232642i
$586$	−1206.80	+	12020.6i	−0.00351430	+	0.0350050i
$587$	129866.	+	129866.i	0.376895	+	0.376895i	0.869981	−	0.493086i	$-0.164131\pi$
$587$	129866.	+	129866.i	0.376895	+	0.376895i	−0.493086	+	0.869981i	$0.664131\pi$
$588$	−149442.	−	225490.i	−0.432232	−	0.652188i
$589$	−1670.42	−	1670.42i	−0.00481499	−	0.00481499i
$590$	33073.7	−	27038.7i	0.0950121	−	0.0776752i
$591$			38312.5i			0.109690i
$592$	−18457.9	+	7483.01i	−0.0526670	+	0.0213517i
$593$	−46524.5			−0.132304			−0.0661519	−	0.997810i	$-0.521072\pi$
$593$	−46524.5			−0.132304			−0.0661519	+	0.997810i	$0.521072\pi$
$594$	−28029.1	−	34285.1i	−0.0794394	−	0.0971700i
$595$	85244.8	−	85244.8i	0.240788	−	0.240788i
$596$	−224024.	−	338026.i	−0.630669	−	0.951607i
$597$	−69112.7	+	69112.7i	−0.193914	+	0.193914i
$598$	−780381.	−	78345.8i	−2.18225	−	0.219085i
$599$	17157.0			0.0478176			0.0239088	−	0.999714i	$-0.492389\pi$
$599$	17157.0			0.0478176			0.0239088	+	0.999714i	$0.492389\pi$
$600$	−50751.6	+	163963.i	−0.140977	+	0.455453i
$601$		−	420721.i		−	1.16478i	−0.812909	−	0.582391i	$-0.802117\pi$
$601$		−	420721.i		−	1.16478i	0.812909	−	0.582391i	$-0.197883\pi$
$602$	−90536.7	−	9089.38i	−0.249823	−	0.0250808i
$603$	−125227.	−	125227.i	−0.344400	−	0.344400i
$604$	47756.2	−	235446.i	0.130905	−	0.645382i
$605$	62080.2	+	62080.2i	0.169606	+	0.169606i
$606$	−116894.	−	142985.i	−0.318309	−	0.389354i
$607$			295552.i			0.802151i	0.916045	+	0.401075i	$0.131363\pi$
$607$			295552.i			0.802151i	−0.916045	+	0.401075i	$0.868637\pi$
$608$	1031.62	−	1887.05i	0.00279070	−	0.00510476i
$609$	−563294.			−1.51880
$610$	118561.	−	96927.1i	0.318627	−	0.260487i
$611$	−272440.	+	272440.i	−0.729775	+	0.729775i
$612$	−65047.6	−	13193.8i	−0.173671	−	0.0352263i
$613$	237548.	−	237548.i	0.632166	−	0.632166i	−0.316445	−	0.948611i	$-0.602489\pi$
$613$	237548.	−	237548.i	0.632166	−	0.632166i	0.948611	+	0.316445i	$0.102489\pi$
$614$	−14998.4	+	149395.i	−0.0397840	+	0.396277i
$615$	904.940			0.00239260
$616$	−112297.	+	362798.i	−0.295942	+	0.956100i
$617$		−	157274.i		−	0.413129i	−0.978433	−	0.206564i	$-0.933772\pi$
$617$		−	157274.i		−	0.413129i	0.978433	−	0.206564i	$-0.0662283\pi$
$618$	24689.6	−	245927.i	0.0646454	−	0.643915i
$619$	−101885.	−	101885.i	−0.265906	−	0.265906i	0.561542	−	0.827448i	$-0.310208\pi$
$619$	−101885.	−	101885.i	−0.265906	−	0.265906i	−0.827448	+	0.561542i	$0.810208\pi$
$620$	156532.	−	103740.i	0.407212	−	0.269876i
$621$	68831.9	+	68831.9i	0.178487	+	0.178487i
$622$	−384059.	+	313980.i	−0.992699	+	0.811562i
$623$			615328.i			1.58537i
$624$	346204.	+	146469.i	0.889124	+	0.376163i
$625$	−198331.			−0.507729
$626$	352064.	+	430644.i	0.898407	+	1.09893i
$627$	−608.941	+	608.941i	−0.00154896	+	0.00154896i
$628$	−122850.	+	81417.8i	−0.311499	+	0.206443i
$629$	8452.25	−	8452.25i	0.0213634	−	0.0213634i
$630$	84319.2	+	8465.17i	0.212445	+	0.0213282i
$631$	176991.			0.444522			0.222261	−	0.974987i	$-0.428656\pi$
$631$	176991.			0.444522			0.222261	+	0.974987i	$0.428656\pi$
$632$	305043.	−	160839.i	0.763708	−	0.402676i
$633$			27841.0i			0.0694827i
$634$	579292.	+	58157.6i	1.44118	+	0.144686i
$635$	−68676.8	−	68676.8i	−0.170319	−	0.170319i
$636$	171228.	+	34730.6i	0.423311	+	0.0858615i
$637$	−650190.	−	650190.i	−1.60236	−	1.60236i
$638$	288010.	+	352293.i	0.707566	+	0.865492i
$639$			232897.i			0.570377i
$640$	130711.	+	110189.i	0.319119	+	0.269016i
$641$	−805640.			−1.96076			−0.980382	−	0.197109i	$-0.936845\pi$
$641$	−805640.			−1.96076			−0.980382	+	0.197109i	$0.936845\pi$
$642$	174495.	−	142655.i	0.423362	−	0.346111i
$643$	−197514.	+	197514.i	−0.477723	+	0.477723i	−0.904403	−	0.426679i	$-0.859683\pi$
$643$	−197514.	+	197514.i	−0.477723	+	0.477723i	0.426679	+	0.904403i	$0.359683\pi$
$644$	165948.	−	818150.i	0.400129	−	1.97270i
$645$	11597.7	−	11597.7i	0.0278775	−	0.0278775i
$646$	−128.931	+	1284.25i	−0.000308954	+	0.00307740i
$647$	269568.			0.643961			0.321980	−	0.946746i	$-0.395652\pi$
$647$	269568.			0.643961			0.321980	+	0.946746i	$0.395652\pi$
$648$	−21760.5	−	41270.6i	−0.0518226	−	0.0982858i
$649$		−	80767.9i		−	0.191756i
$650$	−58278.4	+	580495.i	−0.137937	+	1.37395i
$651$	310779.	+	310779.i	0.733313	+	0.733313i
$652$	440207.	+	664222.i	1.03553	+	1.56249i
$653$	−177758.	−	177758.i	−0.416871	−	0.416871i	0.467253	−	0.884124i	$-0.345244\pi$
$653$	−177758.	−	177758.i	−0.416871	−	0.416871i	−0.884124	+	0.467253i	$0.845244\pi$
$654$	59430.8	−	48586.5i	0.138949	−	0.113595i
$655$			187896.i			0.437961i
$656$	−1664.81	+	3935.05i	−0.00386863	+	0.00914414i
$657$	−237381.			−0.549941
$658$	−259567.	−	317502.i	−0.599512	−	0.733321i
$659$	−270687.	+	270687.i	−0.623300	+	0.623300i	−0.946374	−	0.323074i	$-0.895284\pi$
$659$	−270687.	+	270687.i	−0.623300	+	0.623300i	0.323074	+	0.946374i	$0.395284\pi$
$660$	−37817.9	−	57062.8i	−0.0868179	−	0.130998i
$661$	−226535.	+	226535.i	−0.518480	+	0.518480i	−0.917111	−	0.398631i	$-0.869485\pi$
$661$	−226535.	+	226535.i	−0.518480	+	0.518480i	0.398631	+	0.917111i	$0.369485\pi$
$662$	−289336.	−	29047.7i	−0.660216	−	0.0662820i
$663$	−225605.			−0.513242
$664$	−604053.	−	186973.i	−1.37006	−	0.424074i
$665$		−	1647.95i		−	0.00372651i
$666$	8360.48	+	839.344i	0.0188487	+	0.00189231i
$667$	−707276.	−	707276.i	−1.58978	−	1.58978i
$668$	54134.7	−	266893.i	0.121317	−	0.598114i
$669$	−173363.	−	173363.i	−0.387351	−	0.387351i
$670$	−173277.	−	211951.i	−0.386003	−	0.472157i
$671$		−	289533.i		−	0.643062i
$672$	−191931.	+	351082.i	−0.425018	+	0.777445i
$673$	374105.			0.825968			0.412984	−	0.910738i	$-0.364487\pi$
$673$	374105.			0.825968			0.412984	+	0.910738i	$0.364487\pi$
$674$	−156819.	+	128205.i	−0.345207	+	0.282217i
$675$	51201.4	−	51201.4i	0.112376	−	0.112376i
$676$	804405.	+	163160.i	1.76028	+	0.357043i
$677$	494448.	−	494448.i	1.07881	−	1.07881i	0.0821882	−	0.996617i	$-0.473809\pi$
$677$	494448.	−	494448.i	1.07881	−	1.07881i	0.996617	−	0.0821882i	$-0.0261909\pi$
$678$	−18740.9	+	186673.i	−0.0407692	+	0.406090i
$679$	1.11500e6			2.41843
$680$	−98013.8	−	30338.2i	−0.211967	−	0.0656104i
$681$			306486.i			0.660871i
$682$	35465.9	−	353266.i	0.0762505	−	0.759510i
$683$	−32303.8	−	32303.8i	−0.0692489	−	0.0692489i	0.671634	−	0.740883i	$-0.265593\pi$
$683$	−32303.8	−	32303.8i	−0.0692489	−	0.0692489i	−0.740883	+	0.671634i	$0.765593\pi$
$684$	−756.282	+	501.219i	−0.00161649	+	0.00107131i
$685$	−3392.61	−	3392.61i	−0.00723024	−	0.00723024i
$686$	198595.	−	162358.i	0.422008	−	0.345004i
$687$		−	445670.i		−	0.944277i
$688$	29095.5	+	71768.0i	0.0614680	+	0.151619i
$689$	593870.			1.25099
$690$	95242.9	+	116501.i	0.200048	+	0.244698i
$691$	−211383.	+	211383.i	−0.442704	+	0.442704i	−0.892920	−	0.450216i	$-0.851347\pi$
$691$	−211383.	+	211383.i	−0.442704	+	0.442704i	0.450216	+	0.892920i	$0.351347\pi$
$692$	700675.	−	464366.i	1.46320	−	0.969724i
$693$	113292.	−	113292.i	0.235904	−	0.235904i
$694$	27287.8	+	2739.54i	0.0566564	+	0.00568798i
$695$	−166753.			−0.345226
$696$	223598.	+	424072.i	0.461583	+	0.875430i
$697$		−	2564.30i		−	0.00527840i
$698$	153183.	+	15378.7i	0.314412	+	0.0315652i
$699$	161345.	+	161345.i	0.330218	+	0.330218i
$700$	−608590.	−	123442.i	−1.24202	−	0.251923i
$701$	85966.4	+	85966.4i	0.174941	+	0.174941i	0.789146	−	0.614205i	$-0.210523\pi$
$701$	85966.4	+	85966.4i	0.174941	+	0.174941i	−0.614205	+	0.789146i	$0.710523\pi$
$702$	−100376.	−	122780.i	−0.203683	−	0.249145i
$703$		−	163.399i		−	0.000330627i
$704$	317706.	−	59469.8i	0.641033	−	0.119992i
$705$	73922.3			0.148730
$706$	−637327.	+	521034.i	−1.27865	+	1.04534i
$707$	472482.	−	472482.i	0.945250	−	0.945250i
$708$	16915.3	−	83395.4i	0.0337454	−	0.166370i
$709$	−284280.	+	284280.i	−0.565528	+	0.565528i	−0.930872	−	0.365344i	$-0.880951\pi$
$709$	−284280.	+	284280.i	−0.565528	+	0.565528i	0.365344	+	0.930872i	$0.380951\pi$
$710$	−35963.7	+	358224.i	−0.0713423	+	0.710621i
$711$	−145483.			−0.287788
$712$	463246.	−	244253.i	0.913800	−	0.481815i
$713$			780433.i			1.53517i
$714$	23987.5	−	238932.i	0.0470531	−	0.468682i
$715$	−164538.	−	164538.i	−0.321850	−	0.321850i
$716$	−30539.4	−	46080.4i	−0.0595710	−	0.0898857i
$717$	295234.	+	295234.i	0.574286	+	0.574286i
$718$	168979.	−	138145.i	0.327780	−	0.267970i
$719$			315720.i			0.610723i	0.952237	+	0.305362i	$0.0987773\pi$
$719$			315720.i			0.610723i	−0.952237	+	0.305362i	$0.901223\pi$
$720$	−27097.4	−	66839.4i	−0.0522712	−	0.128934i
$721$	894231.			1.72020
$722$	−329928.	−	403567.i	−0.632914	−	0.774178i
$723$	17428.5	−	17428.5i	0.0333414	−	0.0333414i
$724$	−183416.	−	276754.i	−0.349913	−	0.527978i
$725$	−526116.	+	526116.i	−1.00093	+	1.00093i
$726$	174004.	+	17469.1i	0.330132	+	0.0331433i
$727$	719343.			1.36103			0.680514	−	0.732735i	$-0.261756\pi$
$727$	719343.			1.36103			0.680514	+	0.732735i	$0.261756\pi$
$728$	−402151.	+	1.29923e6i	−0.758799	+	2.45145i
$729$			19683.0i			0.0370370i
$730$	−365121.	−	36656.1i	−0.685159	−	0.0687861i
$731$	−32864.1	−	32864.1i	−0.0615016	−	0.0615016i
$732$	60637.3	−	298952.i	0.113166	−	0.557929i
$733$	−189775.	−	189775.i	−0.353209	−	0.353209i	0.508093	−	0.861302i	$-0.330351\pi$
$733$	−189775.	−	189775.i	−0.353209	−	0.353209i	−0.861302	+	0.508093i	$0.830351\pi$
$734$	77359.2	+	94625.5i	0.143589	+	0.175637i
$735$			176419.i			0.326565i
$736$	−681812.	+	199830.i	−1.25866	+	0.368897i
$737$	−517598.			−0.952922
$738$	1395.55	−	1140.90i	0.00256231	−	0.00209477i
$739$	67770.3	−	67770.3i	0.124094	−	0.124094i	−0.642332	−	0.766426i	$-0.722033\pi$
$739$	67770.3	−	67770.3i	0.124094	−	0.124094i	0.766426	+	0.642332i	$0.222033\pi$
$740$	12729.8	+	2582.03i	0.0232466	+	0.00471517i
$741$	−2180.70	+	2180.70i	−0.00397155	+	0.00397155i
$742$	−63143.2	+	628952.i	−0.114688	+	1.14238i
$743$	−738948.			−1.33856			−0.669278	−	0.743012i	$-0.733396\pi$
$743$	−738948.			−1.33856			−0.669278	+	0.743012i	$0.733396\pi$
$744$	110605.	−	357331.i	0.199815	−	0.645542i
$745$			264464.i			0.476491i
$746$	36056.8	−	359152.i	0.0647902	−	0.645357i
$747$	188630.	+	188630.i	0.338041	+	0.338041i
$748$	−161697.	+	107163.i	−0.289000	+	0.191532i
$749$	576604.	+	576604.i	1.02781	+	1.02781i
$750$	191603.	−	156641.i	0.340627	−	0.278473i
$751$		−	26133.9i		−	0.0463366i	−0.999732	−	0.0231683i	$-0.992625\pi$
$751$		−	26133.9i		−	0.0463366i	0.999732	−	0.0231683i	$-0.00737537\pi$
$752$	−135994.	+	321445.i	−0.240483	+	0.568422i
$753$	−326179.			−0.575262
$754$	1.03140e6	+	1.26161e6i	1.81421	+	2.21913i
$755$	−110785.	+	110785.i	−0.194352	+	0.194352i
$756$	140705.	−	93251.0i	0.246188	−	0.163159i
$757$	531245.	−	531245.i	0.927050	−	0.927050i	−0.0704645	−	0.997514i	$-0.522448\pi$
$757$	531245.	−	531245.i	0.927050	−	0.927050i	0.997514	+	0.0704645i	$0.0224482\pi$
$758$	−812449.	−	81565.3i	−1.41403	−	0.141960i
$759$	284502.			0.493857
$760$	−1240.65	+	654.152i	−0.00214794	+	0.00113254i
$761$			45993.9i			0.0794202i	0.999211	+	0.0397101i	$0.0126434\pi$
$761$			45993.9i			0.0794202i	−0.999211	+	0.0397101i	$0.987357\pi$
$762$	−192494.	−	19325.3i	−0.331518	−	0.0332826i
$763$	196385.	+	196385.i	0.337333	+	0.337333i
$764$	−645271.	−	130882.i	−1.10549	−	0.224230i
$765$	30607.2	+	30607.2i	0.0522998	+	0.0522998i
$766$	−457947.	−	560159.i	−0.780473	−	0.954672i
$767$		−	289241.i		−	0.491665i
$768$	340496.	+	5133.20i	0.577285	+	0.00870294i
$769$	290329.			0.490950			0.245475	−	0.969403i	$-0.421056\pi$
$769$	290329.			0.490950			0.245475	+	0.969403i	$0.421056\pi$
$770$	191752.	−	156763.i	0.323414	−	0.264401i
$771$	−302079.	+	302079.i	−0.508174	+	0.508174i
$772$	−183323.	+	903814.i	−0.307598	+	1.51651i
$773$	238999.	−	238999.i	0.399978	−	0.399978i	−0.478247	−	0.878225i	$-0.658728\pi$
$773$	238999.	−	238999.i	0.399978	−	0.399978i	0.878225	+	0.478247i	$0.158728\pi$
$774$	3263.54	−	32507.2i	0.00544763	−	0.0542623i
$775$	580534.			0.966550
$776$	−442596.	−	839418.i	−0.734994	−	1.39397i
$777$			30400.1i			0.0503539i
$778$	100252.	−	998579.i	0.165628	−	1.64977i
$779$	−24.7865	−	24.7865i	−4.08451e−5	−	4.08451e-5i
$780$	−135431.	−	204350.i	−0.222602	−	0.335881i
$781$	481315.	+	481315.i	0.789091	+	0.789091i
$782$	330124.	−	269887.i	0.539839	−	0.441334i
$783$		−	202251.i		−	0.329888i
$784$	−767141.	−	324556.i	−1.24808	−	0.528028i
$785$	96115.2			0.155974
$786$	236890.	+	289763.i	0.383444	+	0.469028i
$787$	766083.	−	766083.i	1.23688	−	1.23688i	0.275606	−	0.961271i	$-0.411122\pi$
$787$	766083.	−	766083.i	1.23688	−	1.23688i	0.961271	−	0.275606i	$-0.0888784\pi$
$788$	65171.6	+	98336.4i	0.104956	+	0.158366i
$789$	258867.	−	258867.i	0.415837	−	0.415837i
$790$	−223770.	−	22465.3i	−0.358549	−	0.0359963i
$791$	−678776.			−1.08486
$792$	−130263.	−	40320.3i	−0.207668	−	0.0642796i
$793$		−	1.03686e6i		−	1.64882i
$794$	−259213.	−	26023.5i	−0.411165	−	0.0412786i
$795$	−80568.6	−	80568.6i	−0.127477	−	0.127477i
$796$	−59826.7	+	294955.i	−0.0944210	+	0.465511i
$797$	−198491.	−	198491.i	−0.312482	−	0.312482i	0.533389	−	0.845870i	$-0.320918\pi$
$797$	−198491.	−	198491.i	−0.312482	−	0.312482i	−0.845870	+	0.533389i	$0.820918\pi$
$798$	−2077.66	−	2541.39i	−0.00326264	−	0.00399085i
$799$		−	209471.i		−	0.328118i
$800$	148646.	+	507173.i	0.232259	+	0.792459i
$801$	−220934.			−0.344347
$802$	625099.	−	511037.i	0.971852	−	0.794518i
$803$	−490582.	+	490582.i	−0.760818	+	0.760818i
$804$	−534436.	−	108401.i	−0.826768	−	0.167696i
$805$	−384968.	+	384968.i	−0.594064	+	0.594064i
$806$	127008.	−	1.26510e6i	0.195507	−	1.94739i
$807$	−259227.			−0.398046
$808$	−543256.	−	168154.i	−0.832113	−	0.257564i
$809$		−	438190.i		−	0.669523i	−0.942303	−	0.334761i	$-0.891344\pi$
$809$		−	438190.i		−	0.669523i	0.942303	−	0.334761i	$-0.108656\pi$
$810$	−3039.42	+	30274.8i	−0.00463256	+	0.0461436i
$811$	243859.	+	243859.i	0.370763	+	0.370763i	0.867755	−	0.496992i	$-0.165562\pi$
$811$	243859.	+	243859.i	0.370763	+	0.370763i	−0.496992	+	0.867755i	$0.665562\pi$
$812$	−1.44580e6	+	958192.i	−2.19279	+	1.45325i
$813$	103999.	+	103999.i	0.157344	+	0.157344i
$814$	19012.7	−	15543.5i	0.0286943	−	0.0234585i
$815$		−	519672.i		−	0.782374i
$816$	−189400.	+	76784.9i	−0.284447	+	0.115318i
$817$	−635.329			−0.000951820
$818$	−203915.	−	249428.i	−0.304750	−	0.372769i
$819$	405716.	−	405716.i	0.604859	−	0.604859i
$820$	2322.70	−	1539.35i	0.00345434	−	0.00228934i
$821$	139828.	−	139828.i	0.207447	−	0.207447i	−0.595734	−	0.803182i	$-0.703139\pi$
$821$	139828.	−	139828.i	0.207447	−	0.207447i	0.803182	+	0.595734i	$0.203139\pi$
$822$	−9509.14	−	954.664i	−0.0140733	−	0.00141288i
$823$	−1.22203e6			−1.80420			−0.902098	−	0.431531i	$-0.857974\pi$
$823$	−1.22203e6			−1.80420			−0.902098	+	0.431531i	$0.857974\pi$
$824$	−354963.	−	673216.i	−0.522792	−	0.991516i
$825$		−	211630.i		−	0.310935i
$826$	306327.	+	30753.5i	0.448979	+	0.0450749i
$827$	−622087.	−	622087.i	−0.909578	−	0.909578i	0.0866603	−	0.996238i	$-0.472381\pi$
$827$	−622087.	−	622087.i	−0.909578	−	0.909578i	−0.996238	+	0.0866603i	$0.972381\pi$
$828$	293757.	+	59583.6i	0.428477	+	0.0869093i
$829$	−51687.6	−	51687.6i	−0.0752103	−	0.0752103i	0.668501	−	0.743711i	$-0.266936\pi$
$829$	−51687.6	−	51687.6i	−0.0752103	−	0.0752103i	−0.743711	+	0.668501i	$0.766936\pi$
$830$	261008.	+	319264.i	0.378877	+	0.463440i
$831$		−	359998.i		−	0.521313i
$832$	1.13775e6	−	212970.i	1.64361	−	0.307660i
$833$	499911.			0.720448
$834$	−257157.	+	210234.i	−0.369714	+	0.302253i
$835$	−125583.	+	125583.i	−0.180118	+	0.180118i
$836$	−527.124	+	2598.80i	−0.000754223	+	0.00371844i
$837$	−111585.	+	111585.i	−0.159278	+	0.159278i
$838$	−30021.0	+	299031.i	−0.0427502	+	0.425822i
$839$	894798.			1.27116			0.635581	−	0.772034i	$-0.280761\pi$
$839$	894798.			1.27116			0.635581	+	0.772034i	$0.280761\pi$
$840$	230821.	−	121704.i	0.327127	−	0.172483i
$841$			1.37093e6i			1.93831i
$842$	−37022.8	+	368773.i	−0.0522209	+	0.520158i
$843$	−156428.	−	156428.i	−0.220121	−	0.220121i
$844$	47358.9	+	71459.1i	0.0664839	+	0.100317i
$845$	−378501.	−	378501.i	−0.530094	−	0.530094i
$846$	113999.	−	93197.6i	0.159280	−	0.130216i
$847$			632710.i			0.881937i
$848$	498567.	−	202124.i	0.693317	−	0.281078i
$849$	273406.			0.379308
$850$	−200758.	−	245567.i	−0.277866	−	0.339885i
$851$	−38170.6	+	38170.6i	−0.0527072	+	0.0527072i
$852$	396170.	+	597775.i	0.545761	+	0.823490i
$853$	−166203.	+	166203.i	−0.228423	+	0.228423i	−0.812034	−	0.583610i	$-0.801640\pi$
$853$	−166203.	+	166203.i	−0.228423	+	0.228423i	0.583610	+	0.812034i	$0.301640\pi$
$854$	1.09811e6	+	110244.i	1.50567	+	0.151160i
$855$	591.699			0.000809410
$856$	205211.	−	662974.i	0.280061	−	0.904793i
$857$			269725.i			0.367248i	0.982997	+	0.183624i	$0.0587829\pi$
$857$			269725.i			0.367248i	−0.982997	+	0.183624i	$0.941217\pi$
$858$	−461183.	−	46300.1i	−0.626467	−	0.0628938i
$859$	−338403.	−	338403.i	−0.458615	−	0.458615i	0.439586	−	0.898201i	$-0.355125\pi$
$859$	−338403.	−	338403.i	−0.458615	−	0.458615i	−0.898201	+	0.439586i	$0.855125\pi$
$860$	10039.5	−	49496.1i	0.0135742	−	0.0669229i
$861$	4611.49	+	4611.49i	0.00622063	+	0.00622063i
$862$	836794.	+	1.02356e6i	1.12617	+	1.37753i
$863$		−	492311.i		−	0.661025i	−0.943802	−	0.330512i	$-0.892778\pi$
$863$		−	492311.i		−	0.661025i	0.943802	−	0.330512i	$-0.107222\pi$
$864$	−126056.	−	68913.1i	−0.168864	−	0.0923154i
$865$	−548193.			−0.732657
$866$	−360730.	+	294907.i	−0.481001	+	0.393233i
$867$	−220145.	+	220145.i	−0.292868	+	0.292868i
$868$	1.32632e6	+	269022.i	1.76040	+	0.357066i
$869$	−300661.	+	300661.i	−0.398142	+	0.398142i
$870$	31231.3	−	311086.i	0.0412622	−	0.411001i
$871$	−1.85359e6			−2.44330
$872$	69892.4	−	225801.i	0.0919172	−	0.296957i
$873$			400340.i			0.525292i
$874$	582.258	−	5799.71i	0.000762242	−	0.00759248i
$875$	633136.	+	633136.i	0.826954	+	0.826954i
$876$	−609285.	+	403798.i	−0.793985	+	0.526206i
$877$	865543.	+	865543.i	1.12536	+	1.12536i	0.990923	+	0.134432i	$0.0429211\pi$
$877$	865543.	+	865543.i	1.12536	+	1.12536i	0.134432	+	0.990923i	$0.457079\pi$
$878$	241379.	−	197335.i	0.313120	−	0.255985i
$879$		−	15693.7i		−	0.0203117i
$880$	−194134.	−	82132.5i	−0.250689	−	0.106060i
$881$	203211.			0.261816			0.130908	−	0.991395i	$-0.458211\pi$
$881$	203211.			0.261816			0.130908	+	0.991395i	$0.458211\pi$
$882$	222420.	+	272063.i	0.285915	+	0.349730i
$883$	98983.9	−	98983.9i	0.126953	−	0.126953i	−0.640775	−	0.767728i	$-0.721387\pi$
$883$	98983.9	−	98983.9i	0.126953	−	0.126953i	0.767728	+	0.640775i	$0.221387\pi$
$884$	−579059.	+	383766.i	−0.741000	+	0.491091i
$885$	−39240.4	+	39240.4i	−0.0501011	+	0.0501011i
$886$	−277748.	−	27884.3i	−0.353821	−	0.0355216i
$887$	55470.1			0.0705036			0.0352518	−	0.999378i	$-0.488777\pi$
$887$	55470.1			0.0705036			0.0352518	+	0.999378i	$0.488777\pi$
$888$	22886.5	−	12067.3i	0.0290238	−	0.0153032i
$889$		−	699941.i		−	0.885642i
$890$	−339823.	−	34116.3i	−0.429015	−	0.0430707i
$891$	40677.7	+	40677.7i	0.0512390	+	0.0512390i
$892$	−739869.	−	150070.i	−0.929876	−	0.188610i
$893$	−2024.75	−	2024.75i	−0.00253903	−	0.00253903i
$894$	333423.	+	407842.i	0.417178	+	0.510290i
$895$			36052.3i			0.0450077i
$896$	104579.	+	1.22760e6i	0.130266	+	1.52912i
$897$	1.01884e6			1.26626
$898$	915339.	−	748317.i	1.13509	−	0.927968i
$899$	1.14658e6	−	1.14658e6i	1.41869	−	1.41869i
$900$	44322.0	−	218515.i	0.0547185	−	0.269771i
$901$	−228304.	+	228304.i	−0.281232	+	0.281232i
$902$	526.261	−	5241.94i	0.000646827	−	0.00644286i
$903$	118202.			0.144960
$904$	269439.	+	511012.i	0.329703	+	0.625308i
$905$			216526.i			0.264370i
$906$	−31174.5	+	310520.i	−0.0379789	+	0.378297i
$907$	−449923.	−	449923.i	−0.546919	−	0.546919i	0.378629	−	0.925548i	$-0.376396\pi$
$907$	−449923.	−	449923.i	−0.546919	−	0.546919i	−0.925548	+	0.378629i	$0.876396\pi$
$908$	521349.	+	786656.i	0.632349	+	0.954142i
$909$	169645.	+	169645.i	0.205311	+	0.205311i
$910$	686691.	−	561390.i	0.829236	−	0.677926i
$911$			488322.i			0.588396i	0.955744	+	0.294198i	$0.0950526\pi$
$911$			488322.i			0.588396i	−0.955744	+	0.294198i	$0.904947\pi$
$912$	−1088.54	+	2572.95i	−0.00130875	+	0.00309344i
$913$	779662.			0.935329
$914$	569920.	+	697124.i	0.682215	+	0.834483i
$915$	−140667.	+	140667.i	−0.168016	+	0.168016i
$916$	−758107.	−	1.14390e6i	−0.903524	−	1.36331i
$917$	−957502.	+	957502.i	−1.13868	+	1.13868i
$918$	85788.8	+	8612.71i	0.101799	+	0.0102201i
$919$	−1.11696e6			−1.32254			−0.661268	−	0.750150i	$-0.729981\pi$
$919$	−1.11696e6			−1.32254			−0.661268	+	0.750150i	$0.729981\pi$
$920$	442633.	+	137008.i	0.522960	+	0.161872i
$921$		−	195045.i		−	0.229941i
$922$	−1.09612e6	−	110044.i	−1.28943	−	0.129451i
$923$	1.72365e6	+	1.72365e6i	2.02324	+	2.02324i
$924$	98070.4	−	483503.i	0.114867	−	0.566311i
$925$	28393.7	+	28393.7i	0.0331847	+	0.0331847i
$926$	546061.	+	667940.i	0.636824	+	0.778960i
$927$			321074.i			0.373633i
$928$	1.29528e6	+	708110.i	1.50407	+	0.822252i
$929$	−1.58745e6			−1.83937			−0.919685	−	0.392658i	$-0.871556\pi$
$929$	−1.58745e6			−1.83937			−0.919685	+	0.392658i	$0.871556\pi$
$930$	−188863.	+	154401.i	−0.218363	+	0.178519i
$931$	4832.14	−	4832.14i	0.00557494	−	0.00557494i
$932$	688578.	+	139666.i	0.792723	+	0.160790i
$933$	455669.	−	455669.i	0.523463	−	0.523463i
$934$	16933.5	−	168669.i	0.0194112	−	0.193349i
$935$	126508.			0.144709
$936$	−466489.	−	144392.i	−0.532463	−	0.164814i
$937$		−	951087.i		−	1.08328i	−0.840610	−	0.541640i	$-0.817803\pi$
$937$		−	951087.i		−	1.08328i	0.840610	−	0.541640i	$-0.182197\pi$
$938$	197083.	−	1.96309e6i	0.223997	−	2.23118i
$939$	−510939.	−	510939.i	−0.579480	−	0.579480i
$940$	189736.	−	125746.i	0.214730	−	0.142311i
$941$	−342574.	−	342574.i	−0.386879	−	0.386879i	0.486693	−	0.873573i	$-0.338203\pi$
$941$	−342574.	−	342574.i	−0.386879	−	0.386879i	−0.873573	+	0.486693i	$0.838203\pi$
$942$	148224.	−	121177.i	0.167038	−	0.136559i
$943$			11580.4i			0.0130227i
$944$	−98443.4	−	242824.i	−0.110470	−	0.272488i
$945$	−110084.			−0.123271
$946$	−60436.2	−	73925.4i	−0.0675329	−	0.0826059i
$947$	525531.	−	525531.i	0.586001	−	0.586001i	−0.350545	−	0.936546i	$-0.614004\pi$
$947$	525531.	−	525531.i	0.586001	−	0.586001i	0.936546	+	0.350545i	$0.114004\pi$
$948$	−373410.	+	247474.i	−0.415498	+	0.275368i
$949$	−1.75684e6	+	1.75684e6i	−1.95074	+	1.95074i
$950$	−4314.18	−	433.120i	−0.00478026	−	0.000479911i
$951$	−756305.			−0.836249
$952$	−344868.	−	654070.i	−0.380521	−	0.721689i
$953$		−	995589.i		−	1.09621i	−0.836409	−	0.548106i	$-0.815349\pi$
$953$		−	995589.i		−	1.09621i	0.836409	−	0.548106i	$-0.184651\pi$
$954$	−225825.	−	22671.6i	−0.248128	−	0.0249107i
$955$	303622.	+	303622.i	0.332910	+	0.332910i
$956$	1.25998e6	+	255566.i	1.37863	+	0.279633i
$957$	−417980.	−	417980.i	−0.456385	−	0.456385i
$958$	−113471.	−	138798.i	−0.123639	−	0.151235i
$959$		−	34576.8i		−	0.0375966i
$960$	−183248.	−	125462.i	−0.198837	−	0.136135i
$961$	−341659.			−0.369952
$962$	68087.2	−	55663.3i	0.0735725	−	0.0601477i
$963$	−207030.	+	207030.i	−0.223244	+	0.223244i
$964$	15086.8	−	74380.4i	0.0162347	−	0.0800395i
$965$	425276.	−	425276.i	0.456684	−	0.456684i
$966$	−108328.	+	1.07903e6i	−0.116088	+	1.15632i
$967$	−383866.			−0.410513			−0.205256	−	0.978708i	$-0.565803\pi$
$967$	−383866.			−0.410513			−0.205256	+	0.978708i	$0.565803\pi$
$968$	476331.	−	251153.i	0.508345	−	0.268032i
$969$		−	1676.68i		−	0.00178567i
$970$	−61820.0	+	615771.i	−0.0657030	+	0.654449i
$971$	−25911.8	−	25911.8i	−0.0274827	−	0.0274827i	0.693232	−	0.720715i	$-0.256186\pi$
$971$	−25911.8	−	25911.8i	−0.0274827	−	0.0274827i	−0.720715	+	0.693232i	$0.756186\pi$
$972$	33481.8	+	50520.2i	0.0354386	+	0.0534727i
$973$	−849756.	−	849756.i	−0.897570	−	0.897570i
$974$	297707.	−	243384.i	0.313813	−	0.256552i
$975$		−	757876.i		−	0.797240i
$976$	−352895.	−	870464.i	−0.370464	−	0.913800i
$977$	266639.			0.279341			0.139670	−	0.990198i	$-0.455396\pi$
$977$	266639.			0.279341			0.139670	+	0.990198i	$0.455396\pi$
$978$	−655177.	−	801411.i	−0.684985	−	0.837871i
$979$	−456591.	+	456591.i	−0.476389	+	0.476389i
$980$	300097.	+	452812.i	0.312471	+	0.471483i
$981$	−70512.0	+	70512.0i	−0.0732698	+	0.0732698i
$982$	168077.	+	16873.9i	0.174295	+	0.0174982i
$983$	1.26080e6			1.30479			0.652394	−	0.757880i	$-0.273765\pi$
$983$	1.26080e6			1.30479			0.652394	+	0.757880i	$0.273765\pi$
$984$	1641.21	−	5302.25i	0.00169501	−	0.00547608i
$985$		−	76936.3i		−	0.0792973i
$986$	−881515.	−	88499.1i	−0.906725	−	0.0910301i
$987$	376701.	+	376701.i	0.386690	+	0.386690i
$988$	−1887.70	+	9306.68i	−0.00193384	+	0.00953412i
$989$	148415.	+	148415.i	0.151735	+	0.151735i
$990$	56285.8	+	68848.6i	0.0574287	+	0.0702465i
$991$		−	96177.4i		−	0.0979323i	−0.998800	−	0.0489661i	$-0.984407\pi$
$991$		−	96177.4i		−	0.0979323i	0.998800	−	0.0489661i	$-0.0155926\pi$
$992$	−323950.	−	1.10530e6i	−0.329196	−	1.12320i
$993$	377748.			0.383092
$994$	−2.00874e6	+	1.64221e6i	−2.03307	+	1.66209i
$995$	138787.	−	138787.i	0.140185	−	0.140185i
$996$	805025.	+	163286.i	0.811504	+	0.164600i
$997$	1.05984e6	−	1.05984e6i	1.06623	−	1.06623i	0.0685868	−	0.997645i	$-0.478151\pi$
$997$	1.05984e6	−	1.05984e6i	1.06623	−	1.06623i	0.997645	−	0.0685868i	$-0.0218490\pi$
$998$	−80404.3	+	800884.i	−0.0807268	+	0.804098i
$999$	−10915.2			−0.0109370

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.5.l.a.19.4	✓	32
3.2	odd	2		144.5.m.c.19.13		32
4.3	odd	2		192.5.l.a.175.4		32
8.3	odd	2		384.5.l.a.223.13		32
8.5	even	2		384.5.l.b.223.4		32
12.11	even	2		576.5.m.b.559.10		32
16.3	odd	4		384.5.l.b.31.4		32
16.5	even	4		192.5.l.a.79.4		32
16.11	odd	4	inner	48.5.l.a.43.4	yes	32
16.13	even	4		384.5.l.a.31.13		32
48.5	odd	4		576.5.m.b.271.10		32
48.11	even	4		144.5.m.c.91.13		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.5.l.a.19.4	✓	32	1.1	even	1	trivial
48.5.l.a.43.4	yes	32	16.11	odd	4	inner
144.5.m.c.19.13		32	3.2	odd	2
144.5.m.c.91.13		32	48.11	even	4
192.5.l.a.79.4		32	16.5	even	4
192.5.l.a.175.4		32	4.3	odd	2
384.5.l.a.31.13		32	16.13	even	4
384.5.l.a.223.13		32	8.3	odd	2
384.5.l.b.31.4		32	16.3	odd	4
384.5.l.b.223.4		32	8.5	even	2
576.5.m.b.271.10		32	48.5	odd	4
576.5.m.b.559.10		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)

\(f(q)\)	\(=\)	\(q+(-3.09682 + 2.53174i) q^{2} +(3.67423 - 3.67423i) q^{3} +(3.18056 - 15.6807i) q^{4} +(-7.37831 + 7.37831i) q^{5} +(-2.07622 + 20.6807i) q^{6} -75.1984 q^{7} +(29.8498 + 56.6126i) q^{8} -27.0000i q^{9} +O(q^{10})\)	\(q+(-3.09682 + 2.53174i) q^{2} +(3.67423 - 3.67423i) q^{3} +(3.18056 - 15.6807i) q^{4} +(-7.37831 + 7.37831i) q^{5} +(-2.07622 + 20.6807i) q^{6} -75.1984 q^{7} +(29.8498 + 56.6126i) q^{8} -27.0000i q^{9} +(4.16931 - 41.5293i) q^{10} +(-55.7993 - 55.7993i) q^{11} +(-45.9284 - 69.3007i) q^{12} +(-199.825 - 199.825i) q^{13} +(232.876 - 190.383i) q^{14} +54.2193i q^{15} +(-235.768 - 99.7468i) q^{16} +153.639 q^{17} +(68.3570 + 83.6141i) q^{18} +(1.48508 - 1.48508i) q^{19} +(92.2299 + 139.164i) q^{20} +(-276.296 + 276.296i) q^{21} +(314.070 + 31.5308i) q^{22} -693.840 q^{23} +(317.683 + 98.3327i) q^{24} +516.121i q^{25} +(1124.73 + 112.916i) q^{26} +(-99.2043 - 99.2043i) q^{27} +(-239.173 + 1179.16i) q^{28} +(1019.37 + 1019.37i) q^{29} +(-137.269 - 167.907i) q^{30} -1124.80i q^{31} +(982.664 - 288.006i) q^{32} -410.039 q^{33} +(-475.793 + 388.975i) q^{34} +(554.837 - 554.837i) q^{35} +(-423.379 - 85.8752i) q^{36} +(55.0136 - 55.0136i) q^{37} +(-0.839182 + 8.35886i) q^{38} -1468.41 q^{39} +(-637.947 - 197.464i) q^{40} -16.6904i q^{41} +(156.128 - 1555.15i) q^{42} +(-213.904 - 213.904i) q^{43} +(-1052.44 + 697.498i) q^{44} +(199.214 + 199.214i) q^{45} +(2148.70 - 1756.62i) q^{46} -1363.39i q^{47} +(-1232.76 + 499.774i) q^{48} +3253.80 q^{49} +(-1306.69 - 1598.33i) q^{50} +(564.507 - 564.507i) q^{51} +(-3768.95 + 2497.84i) q^{52} +(-1485.98 + 1485.98i) q^{53} +(558.378 + 56.0580i) q^{54} +823.410 q^{55} +(-2244.66 - 4257.18i) q^{56} -10.9131i q^{57} +(-5737.56 - 576.018i) q^{58} +(723.736 + 723.736i) q^{59} +(850.196 + 172.448i) q^{60} +(2594.41 + 2594.41i) q^{61} +(2847.71 + 3483.31i) q^{62} +2030.36i q^{63} +(-2313.97 + 3379.75i) q^{64} +2948.74 q^{65} +(1269.82 - 1038.11i) q^{66} +(4638.03 - 4638.03i) q^{67} +(488.659 - 2409.17i) q^{68} +(-2549.33 + 2549.33i) q^{69} +(-313.525 + 3122.93i) q^{70} -8625.82 q^{71} +(1528.54 - 805.946i) q^{72} -8791.90i q^{73} +(-31.0868 + 309.647i) q^{74} +(1896.35 + 1896.35i) q^{75} +(-18.5637 - 28.0105i) q^{76} +(4196.02 + 4196.02i) q^{77} +(4547.39 - 3717.63i) q^{78} -5388.26i q^{79} +(2475.53 - 1003.61i) q^{80} -729.000 q^{81} +(42.2557 + 51.6870i) q^{82} +(-6986.30 + 6986.30i) q^{83} +(3453.74 + 5211.30i) q^{84} +(-1133.60 + 1133.60i) q^{85} +(1203.97 + 120.872i) q^{86} +7490.77 q^{87} +(1493.34 - 4824.54i) q^{88} -8182.73i q^{89} +(-1121.29 - 112.571i) q^{90} +(15026.5 + 15026.5i) q^{91} +(-2206.80 + 10879.9i) q^{92} +(-4132.79 - 4132.79i) q^{93} +(3451.76 + 4222.19i) q^{94} +21.9148i q^{95} +(2552.34 - 4668.74i) q^{96} -14827.4 q^{97} +(-10076.4 + 8237.77i) q^{98} +(-1506.58 + 1506.58i) 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

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