LMFDB - Embedded newform 570.6.a.l.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,6,Mod(1,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("570.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	570.a (trivial)

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:	yes
Analytic conductor:	$91.4187772934$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 1748x^{2} - 8028x + 111960 $ x^4 - 1748x^2 - 8028x + 111960
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-11.1347$ of defining polynomial
Character	$\chi$	$=$	570.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} -34.7979 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} -34.7979 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -728.273 q^{11} +144.000 q^{12} -66.1242 q^{13} +139.191 q^{14} +225.000 q^{15} +256.000 q^{16} +2034.62 q^{17} -324.000 q^{18} -361.000 q^{19} +400.000 q^{20} -313.181 q^{21} +2913.09 q^{22} +3349.00 q^{23} -576.000 q^{24} +625.000 q^{25} +264.497 q^{26} +729.000 q^{27} -556.766 q^{28} -6955.75 q^{29} -900.000 q^{30} +3309.68 q^{31} -1024.00 q^{32} -6554.46 q^{33} -8138.47 q^{34} -869.946 q^{35} +1296.00 q^{36} -4990.81 q^{37} +1444.00 q^{38} -595.118 q^{39} -1600.00 q^{40} -6333.87 q^{41} +1252.72 q^{42} +9591.52 q^{43} -11652.4 q^{44} +2025.00 q^{45} -13396.0 q^{46} -15378.7 q^{47} +2304.00 q^{48} -15596.1 q^{49} -2500.00 q^{50} +18311.6 q^{51} -1057.99 q^{52} +31151.4 q^{53} -2916.00 q^{54} -18206.8 q^{55} +2227.06 q^{56} -3249.00 q^{57} +27823.0 q^{58} +7041.16 q^{59} +3600.00 q^{60} -36044.0 q^{61} -13238.7 q^{62} -2818.63 q^{63} +4096.00 q^{64} -1653.11 q^{65} +26217.8 q^{66} -38431.8 q^{67} +32553.9 q^{68} +30141.0 q^{69} +3479.79 q^{70} -52209.1 q^{71} -5184.00 q^{72} -32098.4 q^{73} +19963.3 q^{74} +5625.00 q^{75} -5776.00 q^{76} +25342.3 q^{77} +2380.47 q^{78} -1375.87 q^{79} +6400.00 q^{80} +6561.00 q^{81} +25335.5 q^{82} +33906.2 q^{83} -5010.89 q^{84} +50865.4 q^{85} -38366.1 q^{86} -62601.7 q^{87} +46609.5 q^{88} -3216.02 q^{89} -8100.00 q^{90} +2300.98 q^{91} +53584.0 q^{92} +29787.1 q^{93} +61514.6 q^{94} -9025.00 q^{95} -9216.00 q^{96} -57418.0 q^{97} +62384.4 q^{98} -58990.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} - 26 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) $ 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 + 100 * q^5 - 144 * q^6 - 26 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} - 26 q^{7} - 256 q^{8} + 324 q^{9} - 400 q^{10} - 336 q^{11} + 576 q^{12} - 734 q^{13} + 104 q^{14} + 900 q^{15} + 1024 q^{16} + 480 q^{17} - 1296 q^{18} - 1444 q^{19} + 1600 q^{20} - 234 q^{21} + 1344 q^{22} - 1962 q^{23} - 2304 q^{24} + 2500 q^{25} + 2936 q^{26} + 2916 q^{27} - 416 q^{28} - 8720 q^{29} - 3600 q^{30} - 240 q^{31} - 4096 q^{32} - 3024 q^{33} - 1920 q^{34} - 650 q^{35} + 5184 q^{36} - 14626 q^{37} + 5776 q^{38} - 6606 q^{39} - 6400 q^{40} - 11092 q^{41} + 936 q^{42} - 16778 q^{43} - 5376 q^{44} + 8100 q^{45} + 7848 q^{46} - 34810 q^{47} + 9216 q^{48} - 34032 q^{49} - 10000 q^{50} + 4320 q^{51} - 11744 q^{52} - 18186 q^{53} - 11664 q^{54} - 8400 q^{55} + 1664 q^{56} - 12996 q^{57} + 34880 q^{58} - 38700 q^{59} + 14400 q^{60} - 12080 q^{61} + 960 q^{62} - 2106 q^{63} + 16384 q^{64} - 18350 q^{65} + 12096 q^{66} - 84216 q^{67} + 7680 q^{68} - 17658 q^{69} + 2600 q^{70} + 3592 q^{71} - 20736 q^{72} - 41180 q^{73} + 58504 q^{74} + 22500 q^{75} - 23104 q^{76} - 6696 q^{77} + 26424 q^{78} + 15272 q^{79} + 25600 q^{80} + 26244 q^{81} + 44368 q^{82} + 133106 q^{83} - 3744 q^{84} + 12000 q^{85} + 67112 q^{86} - 78480 q^{87} + 21504 q^{88} + 133704 q^{89} - 32400 q^{90} - 86656 q^{91} - 31392 q^{92} - 2160 q^{93} + 139240 q^{94} - 36100 q^{95} - 36864 q^{96} - 161594 q^{97} + 136128 q^{98} - 27216 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 + 100 * q^5 - 144 * q^6 - 26 * q^7 - 256 * q^8 + 324 * q^9 - 400 * q^10 - 336 * q^11 + 576 * q^12 - 734 * q^13 + 104 * q^14 + 900 * q^15 + 1024 * q^16 + 480 * q^17 - 1296 * q^18 - 1444 * q^19 + 1600 * q^20 - 234 * q^21 + 1344 * q^22 - 1962 * q^23 - 2304 * q^24 + 2500 * q^25 + 2936 * q^26 + 2916 * q^27 - 416 * q^28 - 8720 * q^29 - 3600 * q^30 - 240 * q^31 - 4096 * q^32 - 3024 * q^33 - 1920 * q^34 - 650 * q^35 + 5184 * q^36 - 14626 * q^37 + 5776 * q^38 - 6606 * q^39 - 6400 * q^40 - 11092 * q^41 + 936 * q^42 - 16778 * q^43 - 5376 * q^44 + 8100 * q^45 + 7848 * q^46 - 34810 * q^47 + 9216 * q^48 - 34032 * q^49 - 10000 * q^50 + 4320 * q^51 - 11744 * q^52 - 18186 * q^53 - 11664 * q^54 - 8400 * q^55 + 1664 * q^56 - 12996 * q^57 + 34880 * q^58 - 38700 * q^59 + 14400 * q^60 - 12080 * q^61 + 960 * q^62 - 2106 * q^63 + 16384 * q^64 - 18350 * q^65 + 12096 * q^66 - 84216 * q^67 + 7680 * q^68 - 17658 * q^69 + 2600 * q^70 + 3592 * q^71 - 20736 * q^72 - 41180 * q^73 + 58504 * q^74 + 22500 * q^75 - 23104 * q^76 - 6696 * q^77 + 26424 * q^78 + 15272 * q^79 + 25600 * q^80 + 26244 * q^81 + 44368 * q^82 + 133106 * q^83 - 3744 * q^84 + 12000 * q^85 + 67112 * q^86 - 78480 * q^87 + 21504 * q^88 + 133704 * q^89 - 32400 * q^90 - 86656 * q^91 - 31392 * q^92 - 2160 * q^93 + 139240 * q^94 - 36100 * q^95 - 36864 * q^96 - 161594 * q^97 + 136128 * q^98 - 27216 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	16.0000	0.500000
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−36.0000	−0.408248
$7$	−34.7979	−0.268415	−0.134208	−	0.990953i	$-0.542849\pi$
$7$	−34.7979	−0.268415	−0.134208	+	0.990953i	$0.542849\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	−100.000	−0.316228
$11$	−728.273	−1.81473	−0.907366	−	0.420342i	$-0.861910\pi$
$11$	−728.273	−1.81473	−0.907366	+	0.420342i	$0.861910\pi$
$12$	144.000	0.288675
$13$	−66.1242	−0.108518	−0.0542590	−	0.998527i	$-0.517280\pi$
$13$	−66.1242	−0.108518	−0.0542590	+	0.998527i	$0.517280\pi$
$14$	139.191	0.189798
$15$	225.000	0.258199
$16$	256.000	0.250000
$17$	2034.62	1.70750	0.853749	−	0.520684i	$-0.174323\pi$
$17$	2034.62	1.70750	0.853749	+	0.520684i	$0.174323\pi$
$18$	−324.000	−0.235702
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	400.000	0.223607
$21$	−313.181	−0.154970
$22$	2913.09	1.28321
$23$	3349.00	1.32007	0.660033	−	0.751237i	$-0.270542\pi$
$23$	3349.00	1.32007	0.660033	+	0.751237i	$0.270542\pi$
$24$	−576.000	−0.204124
$25$	625.000	0.200000
$26$	264.497	0.0767339
$27$	729.000	0.192450
$28$	−556.766	−0.134208
$29$	−6955.75	−1.53585	−0.767925	−	0.640540i	$-0.778711\pi$
$29$	−6955.75	−1.53585	−0.767925	+	0.640540i	$0.778711\pi$
$30$	−900.000	−0.182574
$31$	3309.68	0.618559	0.309280	−	0.950971i	$-0.399912\pi$
$31$	3309.68	0.618559	0.309280	+	0.950971i	$0.399912\pi$
$32$	−1024.00	−0.176777
$33$	−6554.46	−1.04774
$34$	−8138.47	−1.20738
$35$	−869.946	−0.120039
$36$	1296.00	0.166667
$37$	−4990.81	−0.599331	−0.299666	−	0.954044i	$-0.596875\pi$
$37$	−4990.81	−0.599331	−0.299666	+	0.954044i	$0.596875\pi$
$38$	1444.00	0.162221
$39$	−595.118	−0.0626529
$40$	−1600.00	−0.158114
$41$	−6333.87	−0.588450	−0.294225	−	0.955736i	$-0.595062\pi$
$41$	−6333.87	−0.588450	−0.294225	+	0.955736i	$0.595062\pi$
$42$	1252.72	0.109580
$43$	9591.52	0.791072	0.395536	−	0.918450i	$-0.370559\pi$
$43$	9591.52	0.791072	0.395536	+	0.918450i	$0.370559\pi$
$44$	−11652.4	−0.907366
$45$	2025.00	0.149071
$46$	−13396.0	−0.933427
$47$	−15378.7	−1.01549	−0.507743	−	0.861509i	$-0.669520\pi$
$47$	−15378.7	−1.01549	−0.507743	+	0.861509i	$0.669520\pi$
$48$	2304.00	0.144338
$49$	−15596.1	−0.927953
$50$	−2500.00	−0.141421
$51$	18311.6	0.985825
$52$	−1057.99	−0.0542590
$53$	31151.4	1.52331	0.761655	−	0.647983i	$-0.224387\pi$
$53$	31151.4	1.52331	0.761655	+	0.647983i	$0.224387\pi$
$54$	−2916.00	−0.136083
$55$	−18206.8	−0.811573
$56$	2227.06	0.0948992
$57$	−3249.00	−0.132453
$58$	27823.0	1.08601
$59$	7041.16	0.263338	0.131669	−	0.991294i	$-0.457966\pi$
$59$	7041.16	0.263338	0.131669	+	0.991294i	$0.457966\pi$
$60$	3600.00	0.129099
$61$	−36044.0	−1.24025	−0.620125	−	0.784503i	$-0.712918\pi$
$61$	−36044.0	−1.24025	−0.620125	+	0.784503i	$0.712918\pi$
$62$	−13238.7	−0.437388
$63$	−2818.63	−0.0894718
$64$	4096.00	0.125000
$65$	−1653.11	−0.0485308
$66$	26217.8	0.740861
$67$	−38431.8	−1.04593	−0.522966	−	0.852353i	$-0.675175\pi$
$67$	−38431.8	−1.04593	−0.522966	+	0.852353i	$0.675175\pi$
$68$	32553.9	0.853749
$69$	30141.0	0.762140
$70$	3479.79	0.0848804
$71$	−52209.1	−1.22914	−0.614568	−	0.788864i	$-0.710670\pi$
$71$	−52209.1	−1.22914	−0.614568	+	0.788864i	$0.710670\pi$
$72$	−5184.00	−0.117851
$73$	−32098.4	−0.704979	−0.352489	−	0.935816i	$-0.614665\pi$
$73$	−32098.4	−0.704979	−0.352489	+	0.935816i	$0.614665\pi$
$74$	19963.3	0.423791
$75$	5625.00	0.115470
$76$	−5776.00	−0.114708
$77$	25342.3	0.487102
$78$	2380.47	0.0443023
$79$	−1375.87	−0.0248032	−0.0124016	−	0.999923i	$-0.503948\pi$
$79$	−1375.87	−0.0248032	−0.0124016	+	0.999923i	$0.503948\pi$
$80$	6400.00	0.111803
$81$	6561.00	0.111111
$82$	25335.5	0.416097
$83$	33906.2	0.540236	0.270118	−	0.962827i	$-0.412937\pi$
$83$	33906.2	0.540236	0.270118	+	0.962827i	$0.412937\pi$
$84$	−5010.89	−0.0774848
$85$	50865.4	0.763617
$86$	−38366.1	−0.559373
$87$	−62601.7	−0.886723
$88$	46609.5	0.641604
$89$	−3216.02	−0.0430372	−0.0215186	−	0.999768i	$-0.506850\pi$
$89$	−3216.02	−0.0430372	−0.0215186	+	0.999768i	$0.506850\pi$
$90$	−8100.00	−0.105409
$91$	2300.98	0.0291279
$92$	53584.0	0.660033
$93$	29787.1	0.357125
$94$	61514.6	0.718057
$95$	−9025.00	−0.102598
$96$	−9216.00	−0.102062
$97$	−57418.0	−0.619610	−0.309805	−	0.950800i	$-0.600264\pi$
$97$	−57418.0	−0.619610	−0.309805	+	0.950800i	$0.600264\pi$
$98$	62384.4	0.656162
$99$	−58990.1	−0.604911
$100$	10000.0	0.100000
$101$	112480.	1.09716	0.548582	−	0.836097i	$-0.315168\pi$
$101$	112480.	1.09716	0.548582	+	0.836097i	$0.315168\pi$
$102$	−73246.2	−0.697083
$103$	−125037.	−1.16131	−0.580653	−	0.814151i	$-0.697203\pi$
$103$	−125037.	−1.16131	−0.580653	+	0.814151i	$0.697203\pi$
$104$	4231.95	0.0383669
$105$	−7829.52	−0.0693046
$106$	−124606.	−1.07714
$107$	−227768.	−1.92324	−0.961619	−	0.274390i	$-0.911524\pi$
$107$	−227768.	−1.92324	−0.961619	+	0.274390i	$0.911524\pi$
$108$	11664.0	0.0962250
$109$	116653.	0.940433	0.470217	−	0.882551i	$-0.344176\pi$
$109$	116653.	0.940433	0.470217	+	0.882551i	$0.344176\pi$
$110$	72827.3	0.573868
$111$	−44917.3	−0.346024
$112$	−8908.25	−0.0671038
$113$	−48462.8	−0.357036	−0.178518	−	0.983937i	$-0.557130\pi$
$113$	−48462.8	−0.357036	−0.178518	+	0.983937i	$0.557130\pi$
$114$	12996.0	0.0936586
$115$	83725.0	0.590351
$116$	−111292.	−0.767925
$117$	−5356.06	−0.0361727
$118$	−28164.6	−0.186208
$119$	−70800.3	−0.458319
$120$	−14400.0	−0.0912871
$121$	369330.	2.29325
$122$	144176.	0.876989
$123$	−57004.9	−0.339742
$124$	52954.8	0.309280
$125$	15625.0	0.0894427
$126$	11274.5	0.0632661
$127$	−70581.1	−0.388310	−0.194155	−	0.980971i	$-0.562197\pi$
$127$	−70581.1	−0.388310	−0.194155	+	0.980971i	$0.562197\pi$
$128$	−16384.0	−0.0883883
$129$	86323.6	0.456726
$130$	6612.42	0.0343164
$131$	−191345.	−0.974180	−0.487090	−	0.873352i	$-0.661942\pi$
$131$	−191345.	−0.974180	−0.487090	+	0.873352i	$0.661942\pi$
$132$	−104871.	−0.523868
$133$	12562.0	0.0615787
$134$	153727.	0.739586
$135$	18225.0	0.0860663
$136$	−130215.	−0.603692
$137$	228382.	1.03958	0.519792	−	0.854293i	$-0.326009\pi$
$137$	228382.	1.03958	0.519792	+	0.854293i	$0.326009\pi$
$138$	−120564.	−0.538915
$139$	346450.	1.52091	0.760455	−	0.649391i	$-0.224976\pi$
$139$	346450.	1.52091	0.760455	+	0.649391i	$0.224976\pi$
$140$	−13919.1	−0.0600195
$141$	−138408.	−0.586291
$142$	208836.	0.869130
$143$	48156.5	0.196931
$144$	20736.0	0.0833333
$145$	−173894.	−0.686853
$146$	128394.	0.498495
$147$	−140365.	−0.535754
$148$	−79853.0	−0.299666
$149$	−399987.	−1.47598	−0.737989	−	0.674812i	$-0.764225\pi$
$149$	−399987.	−1.47598	−0.737989	+	0.674812i	$0.764225\pi$
$150$	−22500.0	−0.0816497
$151$	−236741.	−0.844949	−0.422475	−	0.906375i	$-0.638838\pi$
$151$	−236741.	−0.844949	−0.422475	+	0.906375i	$0.638838\pi$
$152$	23104.0	0.0811107
$153$	164804.	0.569166
$154$	−101369.	−0.344433
$155$	82741.9	0.276628
$156$	−9521.89	−0.0313265
$157$	12755.7	0.0413005	0.0206502	−	0.999787i	$-0.493426\pi$
$157$	12755.7	0.0413005	0.0206502	+	0.999787i	$0.493426\pi$
$158$	5503.46	0.0175385
$159$	280363.	0.879484
$160$	−25600.0	−0.0790569
$161$	−116538.	−0.354326
$162$	−26244.0	−0.0785674
$163$	−616557.	−1.81763	−0.908813	−	0.417204i	$-0.863010\pi$
$163$	−616557.	−1.81763	−0.908813	+	0.417204i	$0.863010\pi$
$164$	−101342.	−0.294225
$165$	−163861.	−0.468562
$166$	−135625.	−0.382005
$167$	84931.6	0.235656	0.117828	−	0.993034i	$-0.462407\pi$
$167$	84931.6	0.235656	0.117828	+	0.993034i	$0.462407\pi$
$168$	20043.6	0.0547901
$169$	−366921.	−0.988224
$170$	−203462.	−0.539958
$171$	−29241.0	−0.0764719
$172$	153464.	0.395536
$173$	317130.	0.805604	0.402802	−	0.915287i	$-0.368036\pi$
$173$	317130.	0.805604	0.402802	+	0.915287i	$0.368036\pi$
$174$	250407.	0.627008
$175$	−21748.7	−0.0536831
$176$	−186438.	−0.453683
$177$	63370.4	0.152038
$178$	12864.1	0.0304319
$179$	−579143.	−1.35099	−0.675497	−	0.737363i	$-0.736071\pi$
$179$	−579143.	−1.35099	−0.675497	+	0.737363i	$0.736071\pi$
$180$	32400.0	0.0745356
$181$	−695720.	−1.57848	−0.789239	−	0.614087i	$-0.789525\pi$
$181$	−695720.	−1.57848	−0.789239	+	0.614087i	$0.789525\pi$
$182$	−9203.92	−0.0205966
$183$	−324396.	−0.716058
$184$	−214336.	−0.466714
$185$	−124770.	−0.268029
$186$	−119148.	−0.252526
$187$	−1.48176e6	−3.09865
$188$	−246058.	−0.507743
$189$	−25367.6	−0.0516566
$190$	36100.0	0.0725476
$191$	527303.	1.04587	0.522934	−	0.852373i	$-0.324837\pi$
$191$	527303.	1.04587	0.522934	+	0.852373i	$0.324837\pi$
$192$	36864.0	0.0721688
$193$	−656407.	−1.26847	−0.634235	−	0.773140i	$-0.718685\pi$
$193$	−656407.	−1.26847	−0.634235	+	0.773140i	$0.718685\pi$
$194$	229672.	0.438131
$195$	−14877.9	−0.0280192
$196$	−249538.	−0.463977
$197$	−279550.	−0.513209	−0.256605	−	0.966516i	$-0.582604\pi$
$197$	−279550.	−0.513209	−0.256605	+	0.966516i	$0.582604\pi$
$198$	235960.	0.427736
$199$	−218593.	−0.391294	−0.195647	−	0.980674i	$-0.562681\pi$
$199$	−218593.	−0.391294	−0.195647	+	0.980674i	$0.562681\pi$
$200$	−40000.0	−0.0707107
$201$	−345886.	−0.603869
$202$	−449919.	−0.775812
$203$	242045.	0.412246
$204$	292985.	0.492912
$205$	−158347.	−0.263163
$206$	500149.	0.821167
$207$	271269.	0.440022
$208$	−16927.8	−0.0271295
$209$	262906.	0.416328
$210$	31318.1	0.0490057
$211$	−294504.	−0.455392	−0.227696	−	0.973732i	$-0.573119\pi$
$211$	−294504.	−0.455392	−0.227696	+	0.973732i	$0.573119\pi$
$212$	498423.	0.761655
$213$	−469881.	−0.709642
$214$	911071.	1.35993
$215$	239788.	0.353778
$216$	−46656.0	−0.0680414
$217$	−115170.	−0.166031
$218$	−466610.	−0.664987
$219$	−288885.	−0.407020
$220$	−291309.	−0.405786
$221$	−134537.	−0.185294
$222$	179669.	0.244676
$223$	285572.	0.384550	0.192275	−	0.981341i	$-0.438413\pi$
$223$	285572.	0.384550	0.192275	+	0.981341i	$0.438413\pi$
$224$	35633.0	0.0474496
$225$	50625.0	0.0666667
$226$	193851.	0.252463
$227$	67546.3	0.0870036	0.0435018	−	0.999053i	$-0.486149\pi$
$227$	67546.3	0.0870036	0.0435018	+	0.999053i	$0.486149\pi$
$228$	−51984.0	−0.0662266
$229$	−709765.	−0.894388	−0.447194	−	0.894437i	$-0.647577\pi$
$229$	−709765.	−0.894388	−0.447194	+	0.894437i	$0.647577\pi$
$230$	−334900.	−0.417441
$231$	228081.	0.281228
$232$	445168.	0.543005
$233$	−402287.	−0.485452	−0.242726	−	0.970095i	$-0.578042\pi$
$233$	−402287.	−0.485452	−0.242726	+	0.970095i	$0.578042\pi$
$234$	21424.2	0.0255780
$235$	−384466.	−0.454139
$236$	112658.	0.131669
$237$	−12382.8	−0.0143202
$238$	283201.	0.324080
$239$	−685564.	−0.776342	−0.388171	−	0.921587i	$-0.626893\pi$
$239$	−685564.	−0.776342	−0.388171	+	0.921587i	$0.626893\pi$
$240$	57600.0	0.0645497
$241$	381683.	0.423311	0.211656	−	0.977344i	$-0.432114\pi$
$241$	381683.	0.423311	0.211656	+	0.977344i	$0.432114\pi$
$242$	−1.47732e6	−1.62157
$243$	59049.0	0.0641500
$244$	−576705.	−0.620125
$245$	−389903.	−0.414993
$246$	228019.	0.240234
$247$	23870.8	0.0248958
$248$	−211819.	−0.218694
$249$	305156.	0.311906
$250$	−62500.0	−0.0632456
$251$	636600.	0.637797	0.318899	−	0.947789i	$-0.396687\pi$
$251$	636600.	0.637797	0.318899	+	0.947789i	$0.396687\pi$
$252$	−45098.0	−0.0447359
$253$	−2.43899e6	−2.39556
$254$	282324.	0.274577
$255$	457789.	0.440874
$256$	65536.0	0.0625000
$257$	1.77849e6	1.67965	0.839823	−	0.542861i	$-0.182659\pi$
$257$	1.77849e6	1.67965	0.839823	+	0.542861i	$0.182659\pi$
$258$	−345295.	−0.322954
$259$	173670.	0.160870
$260$	−26449.7	−0.0242654
$261$	−563415.	−0.511950
$262$	765381.	0.688849
$263$	586447.	0.522805	0.261402	−	0.965230i	$-0.415815\pi$
$263$	586447.	0.522805	0.261402	+	0.965230i	$0.415815\pi$
$264$	419485.	0.370431
$265$	778786.	0.681245
$266$	−50248.1	−0.0435427
$267$	−28944.2	−0.0248475
$268$	−614909.	−0.522966
$269$	634362.	0.534510	0.267255	−	0.963626i	$-0.413883\pi$
$269$	634362.	0.534510	0.267255	+	0.963626i	$0.413883\pi$
$270$	−72900.0	−0.0608581
$271$	−2.24644e6	−1.85811	−0.929057	−	0.369936i	$-0.879380\pi$
$271$	−2.24644e6	−1.85811	−0.929057	+	0.369936i	$0.879380\pi$
$272$	520862.	0.426875
$273$	20708.8	0.0168170
$274$	−913527.	−0.735097
$275$	−455171.	−0.362946
$276$	482256.	0.381070
$277$	−2.06921e6	−1.62034	−0.810168	−	0.586198i	$-0.800624\pi$
$277$	−2.06921e6	−1.62034	−0.810168	+	0.586198i	$0.800624\pi$
$278$	−1.38580e6	−1.07545
$279$	268084.	0.206186
$280$	55676.6	0.0424402
$281$	1.50020e6	1.13340	0.566700	−	0.823924i	$-0.308220\pi$
$281$	1.50020e6	1.13340	0.566700	+	0.823924i	$0.308220\pi$
$282$	553631.	0.414570
$283$	1.12284e6	0.833397	0.416698	−	0.909045i	$-0.363187\pi$
$283$	1.12284e6	0.833397	0.416698	+	0.909045i	$0.363187\pi$
$284$	−835345.	−0.614568
$285$	−81225.0	−0.0592349
$286$	−192626.	−0.139251
$287$	220405.	0.157949
$288$	−82944.0	−0.0589256
$289$	2.71981e6	1.91555
$290$	695575.	0.485678
$291$	−516762.	−0.357732
$292$	−513574.	−0.352489
$293$	796367.	0.541931	0.270966	−	0.962589i	$-0.412657\pi$
$293$	796367.	0.541931	0.270966	+	0.962589i	$0.412657\pi$
$294$	561460.	0.378835
$295$	176029.	0.117768
$296$	319412.	0.211896
$297$	−530911.	−0.349245
$298$	1.59995e6	1.04367
$299$	−221450.	−0.143251
$300$	90000.0	0.0577350
$301$	−333764.	−0.212336
$302$	946963.	0.597470
$303$	1.01232e6	0.633448
$304$	−92416.0	−0.0573539
$305$	−901101.	−0.554656
$306$	−659216.	−0.402461
$307$	−1.16779e6	−0.707161	−0.353581	−	0.935404i	$-0.615036\pi$
$307$	−1.16779e6	−0.707161	−0.353581	+	0.935404i	$0.615036\pi$
$308$	405477.	0.243551
$309$	−1.12534e6	−0.670480
$310$	−330968.	−0.195606
$311$	−2.59581e6	−1.52185	−0.760926	−	0.648839i	$-0.775255\pi$
$311$	−2.59581e6	−1.52185	−0.760926	+	0.648839i	$0.775255\pi$
$312$	38087.5	0.0221512
$313$	−2.31060e6	−1.33310	−0.666551	−	0.745459i	$-0.732230\pi$
$313$	−2.31060e6	−1.33310	−0.666551	+	0.745459i	$0.732230\pi$
$314$	−51022.8	−0.0292039
$315$	−70465.7	−0.0400130
$316$	−22013.9	−0.0124016
$317$	1.73689e6	0.970785	0.485392	−	0.874296i	$-0.338677\pi$
$317$	1.73689e6	0.970785	0.485392	+	0.874296i	$0.338677\pi$
$318$	−1.12145e6	−0.621889
$319$	5.06568e6	2.78716
$320$	102400.	0.0559017
$321$	−2.04991e6	−1.11038
$322$	466152.	0.250546
$323$	−734497.	−0.391727
$324$	104976.	0.0555556
$325$	−41327.6	−0.0217036
$326$	2.46623e6	1.28526
$327$	1.04987e6	0.542959
$328$	405368.	0.208049
$329$	535144.	0.272572
$330$	655446.	0.331323
$331$	−2.28584e6	−1.14677	−0.573385	−	0.819286i	$-0.694370\pi$
$331$	−2.28584e6	−1.14677	−0.573385	+	0.819286i	$0.694370\pi$
$332$	542499.	0.270118
$333$	−404256.	−0.199777
$334$	−339727.	−0.166634
$335$	−960795.	−0.467755
$336$	−80174.3	−0.0387424
$337$	321815.	0.154359	0.0771795	−	0.997017i	$-0.475409\pi$
$337$	321815.	0.154359	0.0771795	+	0.997017i	$0.475409\pi$
$338$	1.46768e6	0.698780
$339$	−436165.	−0.206135
$340$	813847.	0.381808
$341$	−2.41035e6	−1.12252
$342$	116964.	0.0540738
$343$	1.12756e6	0.517492
$344$	−613857.	−0.279686
$345$	753525.	0.340839
$346$	−1.26852e6	−0.569648
$347$	−3.74891e6	−1.67140	−0.835702	−	0.549183i	$-0.814939\pi$
$347$	−3.74891e6	−1.67140	−0.835702	+	0.549183i	$0.814939\pi$
$348$	−1.00163e6	−0.443362
$349$	2.02756e6	0.891066	0.445533	−	0.895265i	$-0.353014\pi$
$349$	2.02756e6	0.891066	0.445533	+	0.895265i	$0.353014\pi$
$350$	86994.6	0.0379597
$351$	−48204.5	−0.0208843
$352$	745751.	0.320802
$353$	3.47368e6	1.48372	0.741861	−	0.670553i	$-0.233943\pi$
$353$	3.47368e6	1.48372	0.741861	+	0.670553i	$0.233943\pi$
$354$	−253482.	−0.107507
$355$	−1.30523e6	−0.549686
$356$	−51456.4	−0.0215186
$357$	−637203.	−0.264611
$358$	2.31657e6	0.955297
$359$	745241.	0.305183	0.152592	−	0.988289i	$-0.451238\pi$
$359$	745241.	0.305183	0.152592	+	0.988289i	$0.451238\pi$
$360$	−129600.	−0.0527046
$361$	130321.	0.0526316
$362$	2.78288e6	1.11615
$363$	3.32397e6	1.32401
$364$	36815.7	0.0145640
$365$	−802460.	−0.315276
$366$	1.29759e6	0.506330
$367$	1.39900e6	0.542193	0.271097	−	0.962552i	$-0.412614\pi$
$367$	1.39900e6	0.542193	0.271097	+	0.962552i	$0.412614\pi$
$368$	857344.	0.330016
$369$	−513044.	−0.196150
$370$	499081.	0.189525
$371$	−1.08400e6	−0.408880
$372$	476594.	0.178563
$373$	−3.92390e6	−1.46031	−0.730156	−	0.683280i	$-0.760553\pi$
$373$	−3.92390e6	−1.46031	−0.730156	+	0.683280i	$0.760553\pi$
$374$	5.92702e6	2.19108
$375$	140625.	0.0516398
$376$	984234.	0.359028
$377$	459943.	0.166667
$378$	101471.	0.0365267
$379$	−306870.	−0.109738	−0.0548689	−	0.998494i	$-0.517474\pi$
$379$	−306870.	−0.109738	−0.0548689	+	0.998494i	$0.517474\pi$
$380$	−144400.	−0.0512989
$381$	−635230.	−0.224191
$382$	−2.10921e6	−0.739540
$383$	430305.	0.149892	0.0749461	−	0.997188i	$-0.476122\pi$
$383$	430305.	0.149892	0.0749461	+	0.997188i	$0.476122\pi$
$384$	−147456.	−0.0510310
$385$	633558.	0.217839
$386$	2.62563e6	0.896943
$387$	776913.	0.263691
$388$	−918688.	−0.309805
$389$	4.87593e6	1.63374	0.816870	−	0.576821i	$-0.195707\pi$
$389$	4.87593e6	1.63374	0.816870	+	0.576821i	$0.195707\pi$
$390$	59511.8	0.0198126
$391$	6.81393e6	2.25401
$392$	998151.	0.328081
$393$	−1.72211e6	−0.562443
$394$	1.11820e6	0.362894
$395$	−34396.6	−0.0110923
$396$	−943842.	−0.302455
$397$	2.84259e6	0.905187	0.452593	−	0.891717i	$-0.350499\pi$
$397$	2.84259e6	0.905187	0.452593	+	0.891717i	$0.350499\pi$
$398$	874371.	0.276687
$399$	113058.	0.0355525
$400$	160000.	0.0500000
$401$	5.62278e6	1.74618	0.873092	−	0.487555i	$-0.162111\pi$
$401$	5.62278e6	1.74618	0.873092	+	0.487555i	$0.162111\pi$
$402$	1.38354e6	0.427000
$403$	−218850.	−0.0671249
$404$	1.79968e6	0.548582
$405$	164025.	0.0496904
$406$	−968180.	−0.291502
$407$	3.63467e6	1.08763
$408$	−1.17194e6	−0.348542
$409$	−4.92272e6	−1.45511	−0.727557	−	0.686047i	$-0.759344\pi$
$409$	−4.92272e6	−1.45511	−0.727557	+	0.686047i	$0.759344\pi$
$410$	633387.	0.186084
$411$	2.05544e6	0.600204
$412$	−2.00060e6	−0.580653
$413$	−245017.	−0.0706840
$414$	−1.08508e6	−0.311142
$415$	847655.	0.241601
$416$	67711.2	0.0191835
$417$	3.11805e6	0.878098
$418$	−1.05163e6	−0.294388
$419$	5.01676e6	1.39601	0.698005	−	0.716093i	$-0.254071\pi$
$419$	5.01676e6	1.39601	0.698005	+	0.716093i	$0.254071\pi$
$420$	−125272.	−0.0346523
$421$	−375340.	−0.103210	−0.0516048	−	0.998668i	$-0.516434\pi$
$421$	−375340.	−0.103210	−0.0516048	+	0.998668i	$0.516434\pi$
$422$	1.17802e6	0.322011
$423$	−1.24567e6	−0.338495
$424$	−1.99369e6	−0.538572
$425$	1.27164e6	0.341500
$426$	1.87953e6	0.501793
$427$	1.25426e6	0.332902
$428$	−3.64428e6	−0.961619
$429$	433408.	0.113698
$430$	−959152.	−0.250159
$431$	−1.12122e6	−0.290736	−0.145368	−	0.989378i	$-0.546437\pi$
$431$	−1.12122e6	−0.290736	−0.145368	+	0.989378i	$0.546437\pi$
$432$	186624.	0.0481125
$433$	−2.27030e6	−0.581920	−0.290960	−	0.956735i	$-0.593975\pi$
$433$	−2.27030e6	−0.581920	−0.290960	+	0.956735i	$0.593975\pi$
$434$	460679.	0.117402
$435$	−1.56504e6	−0.396555
$436$	1.86644e6	0.470217
$437$	−1.20899e6	−0.302844
$438$	1.15554e6	0.287806
$439$	−5.79256e6	−1.43453	−0.717264	−	0.696801i	$-0.754606\pi$
$439$	−5.79256e6	−1.43453	−0.717264	+	0.696801i	$0.754606\pi$
$440$	1.16524e6	0.286934
$441$	−1.26328e6	−0.309318
$442$	538150.	0.131023
$443$	−2.66889e6	−0.646133	−0.323067	−	0.946376i	$-0.604714\pi$
$443$	−2.66889e6	−0.646133	−0.323067	+	0.946376i	$0.604714\pi$
$444$	−718677.	−0.173012
$445$	−80400.6	−0.0192468
$446$	−1.14229e6	−0.271918
$447$	−3.59988e6	−0.852157
$448$	−142532.	−0.0335519
$449$	5.67991e6	1.32961	0.664807	−	0.747015i	$-0.268514\pi$
$449$	5.67991e6	1.32961	0.664807	+	0.747015i	$0.268514\pi$
$450$	−202500.	−0.0471405
$451$	4.61279e6	1.06788
$452$	−775405.	−0.178518
$453$	−2.13067e6	−0.487832
$454$	−270185.	−0.0615208
$455$	57524.5	0.0130264
$456$	207936.	0.0468293
$457$	1.82407e6	0.408555	0.204278	−	0.978913i	$-0.434515\pi$
$457$	1.82407e6	0.408555	0.204278	+	0.978913i	$0.434515\pi$
$458$	2.83906e6	0.632428
$459$	1.48324e6	0.328608
$460$	1.33960e6	0.295176
$461$	−35156.0	−0.00770455	−0.00385228	−	0.999993i	$-0.501226\pi$
$461$	−35156.0	−0.00770455	−0.00385228	+	0.999993i	$0.501226\pi$
$462$	−912324.	−0.198859
$463$	−417675.	−0.0905494	−0.0452747	−	0.998975i	$-0.514416\pi$
$463$	−417675.	−0.0905494	−0.0452747	+	0.998975i	$0.514416\pi$
$464$	−1.78067e6	−0.383962
$465$	744677.	0.159711
$466$	1.60915e6	0.343266
$467$	−244133.	−0.0518005	−0.0259003	−	0.999665i	$-0.508245\pi$
$467$	−244133.	−0.0518005	−0.0259003	+	0.999665i	$0.508245\pi$
$468$	−85697.0	−0.0180863
$469$	1.33734e6	0.280744
$470$	1.53787e6	0.321125
$471$	114801.	0.0238448
$472$	−450634.	−0.0931041
$473$	−6.98524e6	−1.43558
$474$	49531.2	0.0101259
$475$	−225625.	−0.0458831
$476$	−1.13280e6	−0.229159
$477$	2.52327e6	0.507770
$478$	2.74225e6	0.548957
$479$	−1.31036e6	−0.260947	−0.130474	−	0.991452i	$-0.541650\pi$
$479$	−1.31036e6	−0.260947	−0.130474	+	0.991452i	$0.541650\pi$
$480$	−230400.	−0.0456435
$481$	330014.	0.0650383
$482$	−1.52673e6	−0.299326
$483$	−1.04884e6	−0.204570
$484$	5.90928e6	1.14663
$485$	−1.43545e6	−0.277098
$486$	−236196.	−0.0453609
$487$	964931.	0.184363	0.0921815	−	0.995742i	$-0.470616\pi$
$487$	964931.	0.184363	0.0921815	+	0.995742i	$0.470616\pi$
$488$	2.30682e6	0.438494
$489$	−5.54902e6	−1.04941
$490$	1.55961e6	0.293445
$491$	−1.48831e6	−0.278605	−0.139302	−	0.990250i	$-0.544486\pi$
$491$	−1.48831e6	−0.278605	−0.139302	+	0.990250i	$0.544486\pi$
$492$	−912078.	−0.169871
$493$	−1.41523e7	−2.62246
$494$	−95483.4	−0.0176040
$495$	−1.47475e6	−0.270524
$496$	847277.	0.154640
$497$	1.81676e6	0.329919
$498$	−1.22062e6	−0.220551
$499$	2.60544e6	0.468414	0.234207	−	0.972187i	$-0.424751\pi$
$499$	2.60544e6	0.468414	0.234207	+	0.972187i	$0.424751\pi$
$500$	250000.	0.0447214
$501$	764385.	0.136056
$502$	−2.54640e6	−0.450991
$503$	−211417.	−0.0372581	−0.0186291	−	0.999826i	$-0.505930\pi$
$503$	−211417.	−0.0372581	−0.0186291	+	0.999826i	$0.505930\pi$
$504$	180392.	0.0316331
$505$	2.81200e6	0.490666
$506$	9.75594e6	1.69392
$507$	−3.30229e6	−0.570551
$508$	−1.12930e6	−0.194155
$509$	2.18051e6	0.373047	0.186523	−	0.982451i	$-0.440278\pi$
$509$	2.18051e6	0.373047	0.186523	+	0.982451i	$0.440278\pi$
$510$	−1.83116e6	−0.311745
$511$	1.11696e6	0.189227
$512$	−262144.	−0.0441942
$513$	−263169.	−0.0441511
$514$	−7.11394e6	−1.18769
$515$	−3.12593e6	−0.519352
$516$	1.38118e6	0.228363
$517$	1.11999e7	1.84283
$518$	−694679.	−0.113752
$519$	2.85417e6	0.465116
$520$	105799.	0.0171582
$521$	2.61413e6	0.421922	0.210961	−	0.977494i	$-0.432341\pi$
$521$	2.61413e6	0.421922	0.210961	+	0.977494i	$0.432341\pi$
$522$	2.25366e6	0.362003
$523$	2.82035e6	0.450868	0.225434	−	0.974258i	$-0.427620\pi$
$523$	2.82035e6	0.450868	0.225434	+	0.974258i	$0.427620\pi$
$524$	−3.06152e6	−0.487090
$525$	−195738.	−0.0309939
$526$	−2.34579e6	−0.369679
$527$	6.73393e6	1.05619
$528$	−1.67794e6	−0.261934
$529$	4.77946e6	0.742573
$530$	−3.11514e6	−0.481713
$531$	570334.	0.0877794
$532$	200992.	0.0307894
$533$	418822.	0.0638575
$534$	115777.	0.0175699
$535$	−5.69419e6	−0.860098
$536$	2.45963e6	0.369793
$537$	−5.21229e6	−0.779997
$538$	−2.53745e6	−0.377956
$539$	1.13582e7	1.68399
$540$	291600.	0.0430331
$541$	4.83470e6	0.710193	0.355097	−	0.934830i	$-0.384448\pi$
$541$	4.83470e6	0.710193	0.355097	+	0.934830i	$0.384448\pi$
$542$	8.98578e6	1.31389
$543$	−6.26148e6	−0.911334
$544$	−2.08345e6	−0.301846
$545$	2.91631e6	0.420575
$546$	−82835.3	−0.0118914
$547$	1.13682e7	1.62451	0.812256	−	0.583302i	$-0.198239\pi$
$547$	1.13682e7	1.62451	0.812256	+	0.583302i	$0.198239\pi$
$548$	3.65411e6	0.519792
$549$	−2.91957e6	−0.413416
$550$	1.82068e6	0.256642
$551$	2.51102e6	0.352348
$552$	−1.92902e6	−0.269457
$553$	47877.2	0.00665757
$554$	8.27684e6	1.14575
$555$	−1.12293e6	−0.154747
$556$	5.54320e6	0.760455
$557$	−8.36380e6	−1.14226	−0.571131	−	0.820859i	$-0.693495\pi$
$557$	−8.36380e6	−1.14226	−0.571131	+	0.820859i	$0.693495\pi$
$558$	−1.07234e6	−0.145796
$559$	−634231.	−0.0858456
$560$	−222706.	−0.0300098
$561$	−1.33358e7	−1.78901
$562$	−6.00079e6	−0.801434
$563$	−1.98864e6	−0.264415	−0.132207	−	0.991222i	$-0.542206\pi$
$563$	−1.98864e6	−0.264415	−0.132207	+	0.991222i	$0.542206\pi$
$564$	−2.21453e6	−0.293145
$565$	−1.21157e6	−0.159671
$566$	−4.49136e6	−0.589301
$567$	−228309.	−0.0298239
$568$	3.34138e6	0.434565
$569$	6.74689e6	0.873621	0.436811	−	0.899553i	$-0.356108\pi$
$569$	6.74689e6	0.873621	0.436811	+	0.899553i	$0.356108\pi$
$570$	324900.	0.0418854
$571$	1.17682e6	0.151050	0.0755250	−	0.997144i	$-0.475937\pi$
$571$	1.17682e6	0.151050	0.0755250	+	0.997144i	$0.475937\pi$
$572$	770503.	0.0984656
$573$	4.74573e6	0.603832
$574$	−881621.	−0.111687
$575$	2.09312e6	0.264013
$576$	331776.	0.0416667
$577$	−1.42077e7	−1.77658	−0.888290	−	0.459284i	$-0.848106\pi$
$577$	−1.42077e7	−1.77658	−0.888290	+	0.459284i	$0.848106\pi$
$578$	−1.08792e7	−1.35450
$579$	−5.90767e6	−0.732351
$580$	−2.78230e6	−0.343426
$581$	−1.17986e6	−0.145008
$582$	2.06705e6	0.252955
$583$	−2.26867e7	−2.76440
$584$	2.05430e6	0.249248
$585$	−133902.	−0.0161769
$586$	−3.18547e6	−0.383203
$587$	−1.04780e7	−1.25511	−0.627554	−	0.778573i	$-0.715944\pi$
$587$	−1.04780e7	−1.25511	−0.627554	+	0.778573i	$0.715944\pi$
$588$	−2.24584e6	−0.267877
$589$	−1.19479e6	−0.141907
$590$	−704116.	−0.0832749
$591$	−2.51595e6	−0.296301
$592$	−1.27765e6	−0.149833
$593$	−1.55462e7	−1.81546	−0.907732	−	0.419550i	$-0.862188\pi$
$593$	−1.55462e7	−1.81546	−0.907732	+	0.419550i	$0.862188\pi$
$594$	2.12364e6	0.246954
$595$	−1.77001e6	−0.204966
$596$	−6.39979e6	−0.737989
$597$	−1.96734e6	−0.225914
$598$	885800.	0.101294
$599$	1.51170e6	0.172147	0.0860735	−	0.996289i	$-0.472568\pi$
$599$	1.51170e6	0.172147	0.0860735	+	0.996289i	$0.472568\pi$
$600$	−360000.	−0.0408248
$601$	9.17455e6	1.03609	0.518046	−	0.855353i	$-0.326660\pi$
$601$	9.17455e6	1.03609	0.518046	+	0.855353i	$0.326660\pi$
$602$	1.33506e6	0.150144
$603$	−3.11298e6	−0.348644
$604$	−3.78785e6	−0.422475
$605$	9.23326e6	1.02557
$606$	−4.04927e6	−0.447915
$607$	−5.33467e6	−0.587673	−0.293837	−	0.955856i	$-0.594932\pi$
$607$	−5.33467e6	−0.587673	−0.293837	+	0.955856i	$0.594932\pi$
$608$	369664.	0.0405554
$609$	2.17841e6	0.238010
$610$	3.60440e6	0.392201
$611$	1.01690e6	0.110199
$612$	2.63686e6	0.284583
$613$	−9.93455e6	−1.06782	−0.533909	−	0.845542i	$-0.679277\pi$
$613$	−9.93455e6	−1.06782	−0.533909	+	0.845542i	$0.679277\pi$
$614$	4.67116e6	0.500039
$615$	−1.42512e6	−0.151937
$616$	−1.62191e6	−0.172217
$617$	1.37832e7	1.45759	0.728797	−	0.684730i	$-0.240080\pi$
$617$	1.37832e7	1.45759	0.728797	+	0.684730i	$0.240080\pi$
$618$	4.50134e6	0.474101
$619$	811231.	0.0850977	0.0425488	−	0.999094i	$-0.486452\pi$
$619$	811231.	0.0850977	0.0425488	+	0.999094i	$0.486452\pi$
$620$	1.32387e6	0.138314
$621$	2.44142e6	0.254047
$622$	1.03832e7	1.07611
$623$	111911.	0.0115519
$624$	−152350.	−0.0156632
$625$	390625.	0.0400000
$626$	9.24239e6	0.942646
$627$	2.36616e6	0.240367
$628$	204091.	0.0206502
$629$	−1.01544e7	−1.02336
$630$	281863.	0.0282935
$631$	−1.42384e7	−1.42360	−0.711798	−	0.702384i	$-0.752119\pi$
$631$	−1.42384e7	−1.42360	−0.711798	+	0.702384i	$0.752119\pi$
$632$	88055.4	0.00876927
$633$	−2.65054e6	−0.262921
$634$	−6.94754e6	−0.686449
$635$	−1.76453e6	−0.173658
$636$	4.48581e6	0.439742
$637$	1.03128e6	0.100700
$638$	−2.02627e7	−1.97082
$639$	−4.22893e6	−0.409712
$640$	−409600.	−0.0395285
$641$	−5.80851e6	−0.558367	−0.279184	−	0.960238i	$-0.590064\pi$
$641$	−5.80851e6	−0.558367	−0.279184	+	0.960238i	$0.590064\pi$
$642$	8.19964e6	0.785158
$643$	1.29958e7	1.23958	0.619792	−	0.784766i	$-0.287217\pi$
$643$	1.29958e7	1.23958	0.619792	+	0.784766i	$0.287217\pi$
$644$	−1.86461e6	−0.177163
$645$	2.15809e6	0.204254
$646$	2.93799e6	0.276993
$647$	3.59518e6	0.337645	0.168823	−	0.985646i	$-0.446004\pi$
$647$	3.59518e6	0.337645	0.168823	+	0.985646i	$0.446004\pi$
$648$	−419904.	−0.0392837
$649$	−5.12788e6	−0.477888
$650$	165311.	0.0153468
$651$	−1.03653e6	−0.0958580
$652$	−9.86492e6	−0.908813
$653$	1.25098e7	1.14807	0.574036	−	0.818830i	$-0.305377\pi$
$653$	1.25098e7	1.14807	0.574036	+	0.818830i	$0.305377\pi$
$654$	−4.19949e6	−0.383930
$655$	−4.78363e6	−0.435667
$656$	−1.62147e6	−0.147113
$657$	−2.59997e6	−0.234993
$658$	−2.14058e6	−0.192737
$659$	−8.32307e6	−0.746569	−0.373285	−	0.927717i	$-0.621769\pi$
$659$	−8.32307e6	−0.746569	−0.373285	+	0.927717i	$0.621769\pi$
$660$	−2.62178e6	−0.234281
$661$	1.13585e7	1.01115	0.505576	−	0.862782i	$-0.331280\pi$
$661$	1.13585e7	1.01115	0.505576	+	0.862782i	$0.331280\pi$
$662$	9.14337e6	0.810889
$663$	−1.21084e6	−0.106980
$664$	−2.17000e6	−0.191002
$665$	314051.	0.0275388
$666$	1.61702e6	0.141264
$667$	−2.32948e7	−2.02742
$668$	1.35891e6	0.117828
$669$	2.57014e6	0.222020
$670$	3.84318e6	0.330753
$671$	2.62499e7	2.25072
$672$	320697.	0.0273950
$673$	2.02974e7	1.72744	0.863721	−	0.503970i	$-0.168128\pi$
$673$	2.02974e7	1.72744	0.863721	+	0.503970i	$0.168128\pi$
$674$	−1.28726e6	−0.109148
$675$	455625.	0.0384900
$676$	−5.87073e6	−0.494112
$677$	−1.29785e7	−1.08831	−0.544154	−	0.838985i	$-0.683149\pi$
$677$	−1.29785e7	−1.08831	−0.544154	+	0.838985i	$0.683149\pi$
$678$	1.74466e6	0.145759
$679$	1.99802e6	0.166313
$680$	−3.25539e6	−0.269979
$681$	607917.	0.0502315
$682$	9.64139e6	0.793741
$683$	−6.90471e6	−0.566361	−0.283181	−	0.959067i	$-0.591390\pi$
$683$	−6.90471e6	−0.566361	−0.283181	+	0.959067i	$0.591390\pi$
$684$	−467856.	−0.0382360
$685$	5.70954e6	0.464916
$686$	−4.51024e6	−0.365922
$687$	−6.38788e6	−0.516375
$688$	2.45543e6	0.197768
$689$	−2.05986e6	−0.165307
$690$	−3.01410e6	−0.241010
$691$	−6.30159e6	−0.502059	−0.251030	−	0.967979i	$-0.580769\pi$
$691$	−6.30159e6	−0.502059	−0.251030	+	0.967979i	$0.580769\pi$
$692$	5.07408e6	0.402802
$693$	2.05273e6	0.162367
$694$	1.49956e7	1.18186
$695$	8.66125e6	0.680171
$696$	4.00651e6	0.313504
$697$	−1.28870e7	−1.00478
$698$	−8.11024e6	−0.630079
$699$	−3.62058e6	−0.280276
$700$	−347979.	−0.0268415
$701$	−1.76783e7	−1.35877	−0.679383	−	0.733784i	$-0.737752\pi$
$701$	−1.76783e7	−1.35877	−0.679383	+	0.733784i	$0.737752\pi$
$702$	192818.	0.0147674
$703$	1.80168e6	0.137496
$704$	−2.98301e6	−0.226841
$705$	−3.46020e6	−0.262197
$706$	−1.38947e7	−1.04915
$707$	−3.91406e6	−0.294496
$708$	1.01393e6	0.0760192
$709$	1.46096e7	1.09150	0.545750	−	0.837948i	$-0.316245\pi$
$709$	1.46096e7	1.09150	0.545750	+	0.837948i	$0.316245\pi$
$710$	5.22091e6	0.388687
$711$	−111445.	−0.00826775
$712$	205825.	0.0152160
$713$	1.10841e7	0.816539
$714$	2.54881e6	0.187108
$715$	1.20391e6	0.0880703
$716$	−9.26629e6	−0.675497
$717$	−6.17007e6	−0.448221
$718$	−2.98097e6	−0.215797
$719$	−8.48459e6	−0.612081	−0.306040	−	0.952019i	$-0.599004\pi$
$719$	−8.48459e6	−0.612081	−0.306040	+	0.952019i	$0.599004\pi$
$720$	518400.	0.0372678
$721$	4.35103e6	0.311712
$722$	−521284.	−0.0372161
$723$	3.43515e6	0.244399
$724$	−1.11315e7	−0.789239
$725$	−4.34734e6	−0.307170
$726$	−1.32959e7	−0.936216
$727$	2.01554e7	1.41434	0.707172	−	0.707041i	$-0.249971\pi$
$727$	2.01554e7	1.41434	0.707172	+	0.707041i	$0.249971\pi$
$728$	−147263.	−0.0102983
$729$	531441.	0.0370370
$730$	3.20984e6	0.222934
$731$	1.95151e7	1.35075
$732$	−5.19034e6	−0.358029
$733$	−1.16159e7	−0.798536	−0.399268	−	0.916834i	$-0.630736\pi$
$733$	−1.16159e7	−0.798536	−0.399268	+	0.916834i	$0.630736\pi$
$734$	−5.59602e6	−0.383388
$735$	−3.50912e6	−0.239596
$736$	−3.42938e6	−0.233357
$737$	2.79888e7	1.89809
$738$	2.05218e6	0.138699
$739$	1.21925e7	0.821260	0.410630	−	0.911802i	$-0.365309\pi$
$739$	1.21925e7	0.821260	0.410630	+	0.911802i	$0.365309\pi$
$740$	−1.99633e6	−0.134015
$741$	214838.	0.0143736
$742$	4.33601e6	0.289122
$743$	9.89245e6	0.657403	0.328702	−	0.944434i	$-0.393389\pi$
$743$	9.89245e6	0.657403	0.328702	+	0.944434i	$0.393389\pi$
$744$	−1.90637e6	−0.126263
$745$	−9.99967e6	−0.660078
$746$	1.56956e7	1.03260
$747$	2.74640e6	0.180079
$748$	−2.37081e7	−1.54933
$749$	7.92583e6	0.516226
$750$	−562500.	−0.0365148
$751$	2.04640e7	1.32401	0.662005	−	0.749499i	$-0.269706\pi$
$751$	2.04640e7	1.32401	0.662005	+	0.749499i	$0.269706\pi$
$752$	−3.93694e6	−0.253871
$753$	5.72940e6	0.368232
$754$	−1.83977e6	−0.117852
$755$	−5.91852e6	−0.377873
$756$	−405882.	−0.0258283
$757$	7.49992e6	0.475682	0.237841	−	0.971304i	$-0.423560\pi$
$757$	7.49992e6	0.475682	0.237841	+	0.971304i	$0.423560\pi$
$758$	1.22748e6	0.0775964
$759$	−2.19509e7	−1.38308
$760$	577600.	0.0362738
$761$	9.87791e6	0.618306	0.309153	−	0.951012i	$-0.399955\pi$
$761$	9.87791e6	0.618306	0.309153	+	0.951012i	$0.399955\pi$
$762$	2.54092e6	0.158527
$763$	−4.05926e6	−0.252427
$764$	8.43685e6	0.522934
$765$	4.12010e6	0.254539
$766$	−1.72122e6	−0.105990
$767$	−465591.	−0.0285770
$768$	589824.	0.0360844
$769$	1.26960e7	0.774194	0.387097	−	0.922039i	$-0.373478\pi$
$769$	1.26960e7	0.774194	0.387097	+	0.922039i	$0.373478\pi$
$770$	−2.53423e6	−0.154035
$771$	1.60064e7	0.969744
$772$	−1.05025e7	−0.634235
$773$	−2.53194e7	−1.52407	−0.762034	−	0.647537i	$-0.775799\pi$
$773$	−2.53194e7	−1.52407	−0.762034	+	0.647537i	$0.775799\pi$
$774$	−3.10765e6	−0.186458
$775$	2.06855e6	0.123712
$776$	3.67475e6	0.219065
$777$	1.56303e6	0.0928782
$778$	−1.95037e7	−1.15523
$779$	2.28653e6	0.135000
$780$	−238047.	−0.0140096
$781$	3.80224e7	2.23055
$782$	−2.72557e7	−1.59383
$783$	−5.07074e6	−0.295574
$784$	−3.99260e6	−0.231988
$785$	318892.	0.0184701
$786$	6.88843e6	0.397707
$787$	7.24904e6	0.417200	0.208600	−	0.978001i	$-0.433109\pi$
$787$	7.24904e6	0.417200	0.208600	+	0.978001i	$0.433109\pi$
$788$	−4.47281e6	−0.256605
$789$	5.27802e6	0.301841
$790$	137587.	0.00784347
$791$	1.68640e6	0.0958340
$792$	3.77537e6	0.213868
$793$	2.38338e6	0.134589
$794$	−1.13704e7	−0.640064
$795$	7.00907e6	0.393317
$796$	−3.49748e6	−0.195647
$797$	3.70828e6	0.206788	0.103394	−	0.994640i	$-0.467030\pi$
$797$	3.70828e6	0.206788	0.103394	+	0.994640i	$0.467030\pi$
$798$	−452233.	−0.0251394
$799$	−3.12897e7	−1.73394
$800$	−640000.	−0.0353553
$801$	−260498.	−0.0143457
$802$	−2.24911e7	−1.23474
$803$	2.33764e7	1.27935
$804$	−5.53418e6	−0.301935
$805$	−2.91345e6	−0.158459
$806$	875399.	0.0474645
$807$	5.70925e6	0.308600
$808$	−7.19871e6	−0.387906
$809$	3.12858e7	1.68064	0.840322	−	0.542087i	$-0.182366\pi$
$809$	3.12858e7	1.68064	0.840322	+	0.542087i	$0.182366\pi$
$810$	−656100.	−0.0351364
$811$	−2.91468e7	−1.55611	−0.778053	−	0.628198i	$-0.783793\pi$
$811$	−2.91468e7	−1.55611	−0.778053	+	0.628198i	$0.783793\pi$
$812$	3.87272e6	0.206123
$813$	−2.02180e7	−1.07278
$814$	−1.45387e7	−0.769068
$815$	−1.54139e7	−0.812867
$816$	4.68776e6	0.246456
$817$	−3.46254e6	−0.181484
$818$	1.96909e7	1.02892
$819$	186379.	0.00970931
$820$	−2.53355e6	−0.131581
$821$	−1.69702e7	−0.878676	−0.439338	−	0.898322i	$-0.644787\pi$
$821$	−1.69702e7	−0.878676	−0.439338	+	0.898322i	$0.644787\pi$
$822$	−8.22174e6	−0.424409
$823$	3.24176e7	1.66833	0.834163	−	0.551518i	$-0.185951\pi$
$823$	3.24176e7	1.66833	0.834163	+	0.551518i	$0.185951\pi$
$824$	8.00239e6	0.410584
$825$	−4.09653e6	−0.209547
$826$	980069.	0.0499812
$827$	−1.99614e7	−1.01491	−0.507454	−	0.861679i	$-0.669413\pi$
$827$	−1.99614e7	−1.01491	−0.507454	+	0.861679i	$0.669413\pi$
$828$	4.34030e6	0.220011
$829$	−2.56147e7	−1.29450	−0.647252	−	0.762276i	$-0.724082\pi$
$829$	−2.56147e7	−1.29450	−0.647252	+	0.762276i	$0.724082\pi$
$830$	−3.39062e6	−0.170838
$831$	−1.86229e7	−0.935501
$832$	−270845.	−0.0135648
$833$	−3.17321e7	−1.58448
$834$	−1.24722e7	−0.620909
$835$	2.12329e6	0.105389
$836$	4.20650e6	0.208164
$837$	2.41275e6	0.119042
$838$	−2.00670e7	−0.987128
$839$	−1.50288e7	−0.737086	−0.368543	−	0.929611i	$-0.620143\pi$
$839$	−1.50288e7	−0.737086	−0.368543	+	0.929611i	$0.620143\pi$
$840$	501089.	0.0245029
$841$	2.78713e7	1.35883
$842$	1.50136e6	0.0729802
$843$	1.35018e7	0.654368
$844$	−4.71206e6	−0.227696
$845$	−9.17301e6	−0.441947
$846$	4.98268e6	0.239352
$847$	−1.28519e7	−0.615544
$848$	7.97477e6	0.380828
$849$	1.01056e7	0.481162
$850$	−5.08654e6	−0.241477
$851$	−1.67142e7	−0.791157
$852$	−7.51810e6	−0.354821
$853$	1.88378e6	0.0886457	0.0443228	−	0.999017i	$-0.485887\pi$
$853$	1.88378e6	0.0886457	0.0443228	+	0.999017i	$0.485887\pi$
$854$	−5.01702e6	−0.235397
$855$	−731025.	−0.0341993
$856$	1.45771e7	0.679967
$857$	−3.11435e7	−1.44849	−0.724245	−	0.689543i	$-0.757812\pi$
$857$	−3.11435e7	−1.44849	−0.724245	+	0.689543i	$0.757812\pi$
$858$	−1.73363e6	−0.0803968
$859$	3.46396e7	1.60173	0.800867	−	0.598842i	$-0.204372\pi$
$859$	3.46396e7	1.60173	0.800867	+	0.598842i	$0.204372\pi$
$860$	3.83661e6	0.176889
$861$	1.98365e6	0.0911920
$862$	4.48489e6	0.205582
$863$	−1.69513e7	−0.774775	−0.387387	−	0.921917i	$-0.626622\pi$
$863$	−1.69513e7	−0.774775	−0.387387	+	0.921917i	$0.626622\pi$
$864$	−746496.	−0.0340207
$865$	7.92824e6	0.360277
$866$	9.08119e6	0.411479
$867$	2.44783e7	1.10594
$868$	−1.84271e6	−0.0830154
$869$	1.00201e6	0.0450112
$870$	6.26017e6	0.280407
$871$	2.54127e6	0.113503
$872$	−7.46576e6	−0.332493
$873$	−4.65086e6	−0.206537
$874$	4.83596e6	0.214143
$875$	−543717.	−0.0240078
$876$	−4.62217e6	−0.203510
$877$	2.24105e7	0.983904	0.491952	−	0.870622i	$-0.336283\pi$
$877$	2.24105e7	0.983904	0.491952	+	0.870622i	$0.336283\pi$
$878$	2.31702e7	1.01436
$879$	7.16731e6	0.312884
$880$	−4.66095e6	−0.202893
$881$	1.58324e6	0.0687239	0.0343619	−	0.999409i	$-0.489060\pi$
$881$	1.58324e6	0.0687239	0.0343619	+	0.999409i	$0.489060\pi$
$882$	5.05314e6	0.218721
$883$	−3.06933e7	−1.32477	−0.662387	−	0.749162i	$-0.730456\pi$
$883$	−3.06933e7	−1.32477	−0.662387	+	0.749162i	$0.730456\pi$
$884$	−2.15260e6	−0.0926472
$885$	1.58426e6	0.0679936
$886$	1.06756e7	0.456885
$887$	3.64346e7	1.55491	0.777455	−	0.628939i	$-0.216511\pi$
$887$	3.64346e7	1.55491	0.777455	+	0.628939i	$0.216511\pi$
$888$	2.87471e6	0.122338
$889$	2.45607e6	0.104228
$890$	321602.	0.0136096
$891$	−4.77820e6	−0.201637
$892$	4.56914e6	0.192275
$893$	5.55169e6	0.232968
$894$	1.43995e7	0.602566
$895$	−1.44786e7	−0.604183
$896$	570128.	0.0237248
$897$	−1.99305e6	−0.0827060
$898$	−2.27197e7	−0.940180
$899$	−2.30213e7	−0.950014
$900$	810000.	0.0333333
$901$	6.33812e7	2.60105
$902$	−1.84512e7	−0.755105
$903$	−3.00388e6	−0.122592
$904$	3.10162e6	0.126231
$905$	−1.73930e7	−0.705916
$906$	8.52267e6	0.344949
$907$	1.39114e7	0.561502	0.280751	−	0.959781i	$-0.409416\pi$
$907$	1.39114e7	0.561502	0.280751	+	0.959781i	$0.409416\pi$
$908$	1.08074e6	0.0435018
$909$	9.11087e6	0.365721
$910$	−230098.	−0.00921106
$911$	2.84180e7	1.13448	0.567241	−	0.823552i	$-0.308011\pi$
$911$	2.84180e7	1.13448	0.567241	+	0.823552i	$0.308011\pi$
$912$	−831744.	−0.0331133
$913$	−2.46930e7	−0.980384
$914$	−7.29627e6	−0.288892
$915$	−8.10991e6	−0.320231
$916$	−1.13562e7	−0.447194
$917$	6.65840e6	0.261485
$918$	−5.93294e6	−0.232361
$919$	1.56502e7	0.611266	0.305633	−	0.952149i	$-0.401132\pi$
$919$	1.56502e7	0.611266	0.305633	+	0.952149i	$0.401132\pi$
$920$	−5.35840e6	−0.208721
$921$	−1.05101e7	−0.408280
$922$	140624.	0.00544794
$923$	3.45228e6	0.133383
$924$	3.64930e6	0.140614
$925$	−3.11926e6	−0.119866
$926$	1.67070e6	0.0640281
$927$	−1.01280e7	−0.387102
$928$	7.12268e6	0.271502
$929$	7.31654e6	0.278142	0.139071	−	0.990282i	$-0.455588\pi$
$929$	7.31654e6	0.278142	0.139071	+	0.990282i	$0.455588\pi$
$930$	−2.97871e6	−0.112933
$931$	5.63020e6	0.212887
$932$	−6.43659e6	−0.242726
$933$	−2.33623e7	−0.878641
$934$	976531.	0.0366285
$935$	−3.70439e7	−1.38576
$936$	342788.	0.0127890
$937$	−7.57651e6	−0.281916	−0.140958	−	0.990016i	$-0.545018\pi$
$937$	−7.57651e6	−0.281916	−0.140958	+	0.990016i	$0.545018\pi$
$938$	−5.34938e6	−0.198516
$939$	−2.07954e7	−0.769667
$940$	−6.15146e6	−0.227069
$941$	5.63592e6	0.207487	0.103743	−	0.994604i	$-0.466918\pi$
$941$	5.63592e6	0.207487	0.103743	+	0.994604i	$0.466918\pi$
$942$	−459205.	−0.0168609
$943$	−2.12121e7	−0.776793
$944$	1.80254e6	0.0658346
$945$	−634191.	−0.0231015
$946$	2.79410e7	1.01511
$947$	−4.60264e6	−0.166776	−0.0833878	−	0.996517i	$-0.526574\pi$
$947$	−4.60264e6	−0.166776	−0.0833878	+	0.996517i	$0.526574\pi$
$948$	−198125.	−0.00716008
$949$	2.12248e6	0.0765029
$950$	902500.	0.0324443
$951$	1.56320e7	0.560483
$952$	4.53122e6	0.162040
$953$	3.23582e7	1.15412	0.577061	−	0.816701i	$-0.304199\pi$
$953$	3.23582e7	1.15412	0.577061	+	0.816701i	$0.304199\pi$
$954$	−1.00931e7	−0.359048
$955$	1.31826e7	0.467726
$956$	−1.09690e7	−0.388171
$957$	4.55911e7	1.60916
$958$	5.24145e6	0.184518
$959$	−7.94719e6	−0.279041
$960$	921600.	0.0322749
$961$	−1.76752e7	−0.617384
$962$	−1.32005e6	−0.0459890
$963$	−1.84492e7	−0.641079
$964$	6.10693e6	0.211656
$965$	−1.64102e7	−0.567277
$966$	4.19537e6	0.144653
$967$	2.64075e7	0.908158	0.454079	−	0.890961i	$-0.349968\pi$
$967$	2.64075e7	0.908158	0.454079	+	0.890961i	$0.349968\pi$
$968$	−2.36371e7	−0.810786
$969$	−6.61047e6	−0.226164
$970$	5.74180e6	0.195938
$971$	−1.44630e7	−0.492278	−0.246139	−	0.969235i	$-0.579162\pi$
$971$	−1.44630e7	−0.492278	−0.246139	+	0.969235i	$0.579162\pi$
$972$	944784.	0.0320750
$973$	−1.20557e7	−0.408236
$974$	−3.85972e6	−0.130364
$975$	−371949.	−0.0125306
$976$	−9.22728e6	−0.310062
$977$	1.90097e7	0.637146	0.318573	−	0.947898i	$-0.396796\pi$
$977$	1.90097e7	0.637146	0.318573	+	0.947898i	$0.396796\pi$
$978$	2.21961e7	0.742043
$979$	2.34214e6	0.0781010
$980$	−6.23844e6	−0.207497
$981$	9.44886e6	0.313478
$982$	5.95323e6	0.197003
$983$	−3.92625e7	−1.29597	−0.647983	−	0.761654i	$-0.724387\pi$
$983$	−3.92625e7	−1.29597	−0.647983	+	0.761654i	$0.724387\pi$
$984$	3.64831e6	0.120117
$985$	−6.98876e6	−0.229514
$986$	5.66091e7	1.85436
$987$	4.81630e6	0.157369
$988$	381933.	0.0124479
$989$	3.21220e7	1.04427
$990$	5.89901e6	0.191289
$991$	1.42529e7	0.461021	0.230510	−	0.973070i	$-0.425960\pi$
$991$	1.42529e7	0.461021	0.230510	+	0.973070i	$0.425960\pi$
$992$	−3.38911e6	−0.109347
$993$	−2.05726e7	−0.662088
$994$	−7.26705e6	−0.233288
$995$	−5.46482e6	−0.174992
$996$	4.88249e6	0.155953
$997$	3.50736e7	1.11749	0.558743	−	0.829341i	$-0.311284\pi$
$997$	3.50736e7	1.11749	0.558743	+	0.829341i	$0.311284\pi$
$998$	−1.04218e7	−0.331219
$999$	−3.63830e6	−0.115341

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.6.a.l.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.6.a.l.1.2	✓	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	570.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} -34.7979 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} -34.7979 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -728.273 q^{11} +144.000 q^{12} -66.1242 q^{13} +139.191 q^{14} +225.000 q^{15} +256.000 q^{16} +2034.62 q^{17} -324.000 q^{18} -361.000 q^{19} +400.000 q^{20} -313.181 q^{21} +2913.09 q^{22} +3349.00 q^{23} -576.000 q^{24} +625.000 q^{25} +264.497 q^{26} +729.000 q^{27} -556.766 q^{28} -6955.75 q^{29} -900.000 q^{30} +3309.68 q^{31} -1024.00 q^{32} -6554.46 q^{33} -8138.47 q^{34} -869.946 q^{35} +1296.00 q^{36} -4990.81 q^{37} +1444.00 q^{38} -595.118 q^{39} -1600.00 q^{40} -6333.87 q^{41} +1252.72 q^{42} +9591.52 q^{43} -11652.4 q^{44} +2025.00 q^{45} -13396.0 q^{46} -15378.7 q^{47} +2304.00 q^{48} -15596.1 q^{49} -2500.00 q^{50} +18311.6 q^{51} -1057.99 q^{52} +31151.4 q^{53} -2916.00 q^{54} -18206.8 q^{55} +2227.06 q^{56} -3249.00 q^{57} +27823.0 q^{58} +7041.16 q^{59} +3600.00 q^{60} -36044.0 q^{61} -13238.7 q^{62} -2818.63 q^{63} +4096.00 q^{64} -1653.11 q^{65} +26217.8 q^{66} -38431.8 q^{67} +32553.9 q^{68} +30141.0 q^{69} +3479.79 q^{70} -52209.1 q^{71} -5184.00 q^{72} -32098.4 q^{73} +19963.3 q^{74} +5625.00 q^{75} -5776.00 q^{76} +25342.3 q^{77} +2380.47 q^{78} -1375.87 q^{79} +6400.00 q^{80} +6561.00 q^{81} +25335.5 q^{82} +33906.2 q^{83} -5010.89 q^{84} +50865.4 q^{85} -38366.1 q^{86} -62601.7 q^{87} +46609.5 q^{88} -3216.02 q^{89} -8100.00 q^{90} +2300.98 q^{91} +53584.0 q^{92} +29787.1 q^{93} +61514.6 q^{94} -9025.00 q^{95} -9216.00 q^{96} -57418.0 q^{97} +62384.4 q^{98} -58990.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} - 26 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 + 100 * q^5 - 144 * q^6 - 26 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} - 26 q^{7} - 256 q^{8} + 324 q^{9} - 400 q^{10} - 336 q^{11} + 576 q^{12} - 734 q^{13} + 104 q^{14} + 900 q^{15} + 1024 q^{16} + 480 q^{17} - 1296 q^{18} - 1444 q^{19} + 1600 q^{20} - 234 q^{21} + 1344 q^{22} - 1962 q^{23} - 2304 q^{24} + 2500 q^{25} + 2936 q^{26} + 2916 q^{27} - 416 q^{28} - 8720 q^{29} - 3600 q^{30} - 240 q^{31} - 4096 q^{32} - 3024 q^{33} - 1920 q^{34} - 650 q^{35} + 5184 q^{36} - 14626 q^{37} + 5776 q^{38} - 6606 q^{39} - 6400 q^{40} - 11092 q^{41} + 936 q^{42} - 16778 q^{43} - 5376 q^{44} + 8100 q^{45} + 7848 q^{46} - 34810 q^{47} + 9216 q^{48} - 34032 q^{49} - 10000 q^{50} + 4320 q^{51} - 11744 q^{52} - 18186 q^{53} - 11664 q^{54} - 8400 q^{55} + 1664 q^{56} - 12996 q^{57} + 34880 q^{58} - 38700 q^{59} + 14400 q^{60} - 12080 q^{61} + 960 q^{62} - 2106 q^{63} + 16384 q^{64} - 18350 q^{65} + 12096 q^{66} - 84216 q^{67} + 7680 q^{68} - 17658 q^{69} + 2600 q^{70} + 3592 q^{71} - 20736 q^{72} - 41180 q^{73} + 58504 q^{74} + 22500 q^{75} - 23104 q^{76} - 6696 q^{77} + 26424 q^{78} + 15272 q^{79} + 25600 q^{80} + 26244 q^{81} + 44368 q^{82} + 133106 q^{83} - 3744 q^{84} + 12000 q^{85} + 67112 q^{86} - 78480 q^{87} + 21504 q^{88} + 133704 q^{89} - 32400 q^{90} - 86656 q^{91} - 31392 q^{92} - 2160 q^{93} + 139240 q^{94} - 36100 q^{95} - 36864 q^{96} - 161594 q^{97} + 136128 q^{98} - 27216 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 + 100 * q^5 - 144 * q^6 - 26 * q^7 - 256 * q^8 + 324 * q^9 - 400 * q^10 - 336 * q^11 + 576 * q^12 - 734 * q^13 + 104 * q^14 + 900 * q^15 + 1024 * q^16 + 480 * q^17 - 1296 * q^18 - 1444 * q^19 + 1600 * q^20 - 234 * q^21 + 1344 * q^22 - 1962 * q^23 - 2304 * q^24 + 2500 * q^25 + 2936 * q^26 + 2916 * q^27 - 416 * q^28 - 8720 * q^29 - 3600 * q^30 - 240 * q^31 - 4096 * q^32 - 3024 * q^33 - 1920 * q^34 - 650 * q^35 + 5184 * q^36 - 14626 * q^37 + 5776 * q^38 - 6606 * q^39 - 6400 * q^40 - 11092 * q^41 + 936 * q^42 - 16778 * q^43 - 5376 * q^44 + 8100 * q^45 + 7848 * q^46 - 34810 * q^47 + 9216 * q^48 - 34032 * q^49 - 10000 * q^50 + 4320 * q^51 - 11744 * q^52 - 18186 * q^53 - 11664 * q^54 - 8400 * q^55 + 1664 * q^56 - 12996 * q^57 + 34880 * q^58 - 38700 * q^59 + 14400 * q^60 - 12080 * q^61 + 960 * q^62 - 2106 * q^63 + 16384 * q^64 - 18350 * q^65 + 12096 * q^66 - 84216 * q^67 + 7680 * q^68 - 17658 * q^69 + 2600 * q^70 + 3592 * q^71 - 20736 * q^72 - 41180 * q^73 + 58504 * q^74 + 22500 * q^75 - 23104 * q^76 - 6696 * q^77 + 26424 * q^78 + 15272 * q^79 + 25600 * q^80 + 26244 * q^81 + 44368 * q^82 + 133106 * q^83 - 3744 * q^84 + 12000 * q^85 + 67112 * q^86 - 78480 * q^87 + 21504 * q^88 + 133704 * q^89 - 32400 * q^90 - 86656 * q^91 - 31392 * q^92 - 2160 * q^93 + 139240 * q^94 - 36100 * q^95 - 36864 * q^96 - 161594 * q^97 + 136128 * q^98 - 27216 * q^99

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