LMFDB - Embedded newform 570.6.a.i.1.1

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} - x^{3} - 2696x^{2} + 13833x + 894635 $ x^4 - x^3 - 2696x^2 + 13833x + 894635
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-50.6958$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} -198.741 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} -198.741 q^{7} -64.0000 q^{8} +81.0000 q^{9} +100.000 q^{10} -301.688 q^{11} -144.000 q^{12} -414.182 q^{13} +794.966 q^{14} +225.000 q^{15} +256.000 q^{16} +1804.45 q^{17} -324.000 q^{18} -361.000 q^{19} -400.000 q^{20} +1788.67 q^{21} +1206.75 q^{22} +2577.82 q^{23} +576.000 q^{24} +625.000 q^{25} +1656.73 q^{26} -729.000 q^{27} -3179.86 q^{28} +2841.62 q^{29} -900.000 q^{30} -510.669 q^{31} -1024.00 q^{32} +2715.19 q^{33} -7217.80 q^{34} +4968.53 q^{35} +1296.00 q^{36} +6458.05 q^{37} +1444.00 q^{38} +3727.64 q^{39} +1600.00 q^{40} -15588.5 q^{41} -7154.69 q^{42} +1117.24 q^{43} -4827.01 q^{44} -2025.00 q^{45} -10311.3 q^{46} +11966.1 q^{47} -2304.00 q^{48} +22691.1 q^{49} -2500.00 q^{50} -16240.0 q^{51} -6626.91 q^{52} +10801.4 q^{53} +2916.00 q^{54} +7542.20 q^{55} +12719.4 q^{56} +3249.00 q^{57} -11366.5 q^{58} -24206.6 q^{59} +3600.00 q^{60} +24297.8 q^{61} +2042.68 q^{62} -16098.1 q^{63} +4096.00 q^{64} +10354.6 q^{65} -10860.8 q^{66} +44459.2 q^{67} +28871.2 q^{68} -23200.4 q^{69} -19874.1 q^{70} -17048.7 q^{71} -5184.00 q^{72} +4995.94 q^{73} -25832.2 q^{74} -5625.00 q^{75} -5776.00 q^{76} +59957.9 q^{77} -14910.6 q^{78} -32826.8 q^{79} -6400.00 q^{80} +6561.00 q^{81} +62353.9 q^{82} -4543.51 q^{83} +28618.8 q^{84} -45111.2 q^{85} -4468.95 q^{86} -25574.6 q^{87} +19308.0 q^{88} -20581.8 q^{89} +8100.00 q^{90} +82315.1 q^{91} +41245.1 q^{92} +4596.02 q^{93} -47864.4 q^{94} +9025.00 q^{95} +9216.00 q^{96} +115889. q^{97} -90764.5 q^{98} -24436.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} + 144 q^{6} + 108 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 + 108 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} + 144 q^{6} + 108 q^{7} - 256 q^{8} + 324 q^{9} + 400 q^{10} - 460 q^{11} - 576 q^{12} + 296 q^{13} - 432 q^{14} + 900 q^{15} + 1024 q^{16} - 412 q^{17} - 1296 q^{18} - 1444 q^{19} - 1600 q^{20} - 972 q^{21} + 1840 q^{22} - 768 q^{23} + 2304 q^{24} + 2500 q^{25} - 1184 q^{26} - 2916 q^{27} + 1728 q^{28} - 1828 q^{29} - 3600 q^{30} + 3856 q^{31} - 4096 q^{32} + 4140 q^{33} + 1648 q^{34} - 2700 q^{35} + 5184 q^{36} + 11456 q^{37} + 5776 q^{38} - 2664 q^{39} + 6400 q^{40} - 12904 q^{41} + 3888 q^{42} + 15096 q^{43} - 7360 q^{44} - 8100 q^{45} + 3072 q^{46} + 17040 q^{47} - 9216 q^{48} + 33708 q^{49} - 10000 q^{50} + 3708 q^{51} + 4736 q^{52} + 16728 q^{53} + 11664 q^{54} + 11500 q^{55} - 6912 q^{56} + 12996 q^{57} + 7312 q^{58} - 19760 q^{59} + 14400 q^{60} + 47168 q^{61} - 15424 q^{62} + 8748 q^{63} + 16384 q^{64} - 7400 q^{65} - 16560 q^{66} + 104580 q^{67} - 6592 q^{68} + 6912 q^{69} + 10800 q^{70} - 36764 q^{71} - 20736 q^{72} + 74356 q^{73} - 45824 q^{74} - 22500 q^{75} - 23104 q^{76} + 75356 q^{77} + 10656 q^{78} + 80920 q^{79} - 25600 q^{80} + 26244 q^{81} + 51616 q^{82} + 19416 q^{83} - 15552 q^{84} + 10300 q^{85} - 60384 q^{86} + 16452 q^{87} + 29440 q^{88} - 4760 q^{89} + 32400 q^{90} + 32288 q^{91} - 12288 q^{92} - 34704 q^{93} - 68160 q^{94} + 36100 q^{95} + 36864 q^{96} + 139572 q^{97} - 134832 q^{98} - 37260 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 - 36 * q^3 + 64 * q^4 - 100 * q^5 + 144 * q^6 + 108 * q^7 - 256 * q^8 + 324 * q^9 + 400 * q^10 - 460 * q^11 - 576 * q^12 + 296 * q^13 - 432 * q^14 + 900 * q^15 + 1024 * q^16 - 412 * q^17 - 1296 * q^18 - 1444 * q^19 - 1600 * q^20 - 972 * q^21 + 1840 * q^22 - 768 * q^23 + 2304 * q^24 + 2500 * q^25 - 1184 * q^26 - 2916 * q^27 + 1728 * q^28 - 1828 * q^29 - 3600 * q^30 + 3856 * q^31 - 4096 * q^32 + 4140 * q^33 + 1648 * q^34 - 2700 * q^35 + 5184 * q^36 + 11456 * q^37 + 5776 * q^38 - 2664 * q^39 + 6400 * q^40 - 12904 * q^41 + 3888 * q^42 + 15096 * q^43 - 7360 * q^44 - 8100 * q^45 + 3072 * q^46 + 17040 * q^47 - 9216 * q^48 + 33708 * q^49 - 10000 * q^50 + 3708 * q^51 + 4736 * q^52 + 16728 * q^53 + 11664 * q^54 + 11500 * q^55 - 6912 * q^56 + 12996 * q^57 + 7312 * q^58 - 19760 * q^59 + 14400 * q^60 + 47168 * q^61 - 15424 * q^62 + 8748 * q^63 + 16384 * q^64 - 7400 * q^65 - 16560 * q^66 + 104580 * q^67 - 6592 * q^68 + 6912 * q^69 + 10800 * q^70 - 36764 * q^71 - 20736 * q^72 + 74356 * q^73 - 45824 * q^74 - 22500 * q^75 - 23104 * q^76 + 75356 * q^77 + 10656 * q^78 + 80920 * q^79 - 25600 * q^80 + 26244 * q^81 + 51616 * q^82 + 19416 * q^83 - 15552 * q^84 + 10300 * q^85 - 60384 * q^86 + 16452 * q^87 + 29440 * q^88 - 4760 * q^89 + 32400 * q^90 + 32288 * q^91 - 12288 * q^92 - 34704 * q^93 - 68160 * q^94 + 36100 * q^95 + 36864 * q^96 + 139572 * q^97 - 134832 * q^98 - 37260 * 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
$7$	−198.741	−1.53300	−0.766502	−	0.642242i	$-0.778004\pi$
$7$	−198.741	−1.53300	−0.766502	+	0.642242i	$0.778004\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	100.000	0.316228
$11$	−301.688	−0.751755	−0.375877	−	0.926669i	$-0.622659\pi$
$11$	−301.688	−0.751755	−0.375877	+	0.926669i	$0.622659\pi$
$12$	−144.000	−0.288675
$13$	−414.182	−0.679725	−0.339862	−	0.940475i	$-0.610380\pi$
$13$	−414.182	−0.679725	−0.339862	+	0.940475i	$0.610380\pi$
$14$	794.966	1.08400
$15$	225.000	0.258199
$16$	256.000	0.250000
$17$	1804.45	1.51434	0.757168	−	0.653220i	$-0.226582\pi$
$17$	1804.45	1.51434	0.757168	+	0.653220i	$0.226582\pi$
$18$	−324.000	−0.235702
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	−400.000	−0.223607
$21$	1788.67	0.885080
$22$	1206.75	0.531571
$23$	2577.82	1.01609	0.508046	−	0.861330i	$-0.330368\pi$
$23$	2577.82	1.01609	0.508046	+	0.861330i	$0.330368\pi$
$24$	576.000	0.204124
$25$	625.000	0.200000
$26$	1656.73	0.480638
$27$	−729.000	−0.192450
$28$	−3179.86	−0.766502
$29$	2841.62	0.627439	0.313719	−	0.949516i	$-0.398425\pi$
$29$	2841.62	0.627439	0.313719	+	0.949516i	$0.398425\pi$
$30$	−900.000	−0.182574
$31$	−510.669	−0.0954411	−0.0477206	−	0.998861i	$-0.515196\pi$
$31$	−510.669	−0.0954411	−0.0477206	+	0.998861i	$0.515196\pi$
$32$	−1024.00	−0.176777
$33$	2715.19	0.434026
$34$	−7217.80	−1.07080
$35$	4968.53	0.685580
$36$	1296.00	0.166667
$37$	6458.05	0.775527	0.387764	−	0.921759i	$-0.373248\pi$
$37$	6458.05	0.775527	0.387764	+	0.921759i	$0.373248\pi$
$38$	1444.00	0.162221
$39$	3727.64	0.392439
$40$	1600.00	0.158114
$41$	−15588.5	−1.44825	−0.724125	−	0.689668i	$-0.757756\pi$
$41$	−15588.5	−1.44825	−0.724125	+	0.689668i	$0.757756\pi$
$42$	−7154.69	−0.625846
$43$	1117.24	0.0921455	0.0460727	−	0.998938i	$-0.485329\pi$
$43$	1117.24	0.0921455	0.0460727	+	0.998938i	$0.485329\pi$
$44$	−4827.01	−0.375877
$45$	−2025.00	−0.149071
$46$	−10311.3	−0.718485
$47$	11966.1	0.790147	0.395074	−	0.918649i	$-0.370719\pi$
$47$	11966.1	0.790147	0.395074	+	0.918649i	$0.370719\pi$
$48$	−2304.00	−0.144338
$49$	22691.1	1.35010
$50$	−2500.00	−0.141421
$51$	−16240.0	−0.874303
$52$	−6626.91	−0.339862
$53$	10801.4	0.528190	0.264095	−	0.964497i	$-0.414927\pi$
$53$	10801.4	0.528190	0.264095	+	0.964497i	$0.414927\pi$
$54$	2916.00	0.136083
$55$	7542.20	0.336195
$56$	12719.4	0.541999
$57$	3249.00	0.132453
$58$	−11366.5	−0.443666
$59$	−24206.6	−0.905323	−0.452662	−	0.891682i	$-0.649525\pi$
$59$	−24206.6	−0.905323	−0.452662	+	0.891682i	$0.649525\pi$
$60$	3600.00	0.129099
$61$	24297.8	0.836068	0.418034	−	0.908431i	$-0.362719\pi$
$61$	24297.8	0.836068	0.418034	+	0.908431i	$0.362719\pi$
$62$	2042.68	0.0674871
$63$	−16098.1	−0.511001
$64$	4096.00	0.125000
$65$	10354.6	0.303982
$66$	−10860.8	−0.306903
$67$	44459.2	1.20997	0.604985	−	0.796237i	$-0.293179\pi$
$67$	44459.2	1.20997	0.604985	+	0.796237i	$0.293179\pi$
$68$	28871.2	0.757168
$69$	−23200.4	−0.586641
$70$	−19874.1	−0.484778
$71$	−17048.7	−0.401371	−0.200685	−	0.979656i	$-0.564317\pi$
$71$	−17048.7	−0.401371	−0.200685	+	0.979656i	$0.564317\pi$
$72$	−5184.00	−0.117851
$73$	4995.94	0.109726	0.0548631	−	0.998494i	$-0.482528\pi$
$73$	4995.94	0.109726	0.0548631	+	0.998494i	$0.482528\pi$
$74$	−25832.2	−0.548380
$75$	−5625.00	−0.115470
$76$	−5776.00	−0.114708
$77$	59957.9	1.15244
$78$	−14910.6	−0.277496
$79$	−32826.8	−0.591780	−0.295890	−	0.955222i	$-0.595616\pi$
$79$	−32826.8	−0.591780	−0.295890	+	0.955222i	$0.595616\pi$
$80$	−6400.00	−0.111803
$81$	6561.00	0.111111
$82$	62353.9	1.02407
$83$	−4543.51	−0.0723930	−0.0361965	−	0.999345i	$-0.511524\pi$
$83$	−4543.51	−0.0723930	−0.0361965	+	0.999345i	$0.511524\pi$
$84$	28618.8	0.442540
$85$	−45111.2	−0.677232
$86$	−4468.95	−0.0651567
$87$	−25574.6	−0.362252
$88$	19308.0	0.265785
$89$	−20581.8	−0.275428	−0.137714	−	0.990472i	$-0.543975\pi$
$89$	−20581.8	−0.275428	−0.137714	+	0.990472i	$0.543975\pi$
$90$	8100.00	0.105409
$91$	82315.1	1.04202
$92$	41245.1	0.508046
$93$	4596.02	0.0551030
$94$	−47864.4	−0.558718
$95$	9025.00	0.102598
$96$	9216.00	0.102062
$97$	115889.	1.25058	0.625290	−	0.780393i	$-0.284981\pi$
$97$	115889.	1.25058	0.625290	+	0.780393i	$0.284981\pi$
$98$	−90764.5	−0.954665
$99$	−24436.7	−0.250585
$100$	10000.0	0.100000
$101$	69844.0	0.681280	0.340640	−	0.940194i	$-0.389356\pi$
$101$	69844.0	0.681280	0.340640	+	0.940194i	$0.389356\pi$
$102$	64960.2	0.618225
$103$	−6073.57	−0.0564093	−0.0282047	−	0.999602i	$-0.508979\pi$
$103$	−6073.57	−0.0564093	−0.0282047	+	0.999602i	$0.508979\pi$
$104$	26507.7	0.240319
$105$	−44716.8	−0.395820
$106$	−43205.6	−0.373487
$107$	−176308.	−1.48872	−0.744359	−	0.667780i	$-0.767245\pi$
$107$	−176308.	−1.48872	−0.744359	+	0.667780i	$0.767245\pi$
$108$	−11664.0	−0.0962250
$109$	11317.0	0.0912360	0.0456180	−	0.998959i	$-0.485474\pi$
$109$	11317.0	0.0912360	0.0456180	+	0.998959i	$0.485474\pi$
$110$	−30168.8	−0.237726
$111$	−58122.4	−0.447751
$112$	−50877.8	−0.383251
$113$	220212.	1.62235	0.811177	−	0.584801i	$-0.198827\pi$
$113$	220212.	1.62235	0.811177	+	0.584801i	$0.198827\pi$
$114$	−12996.0	−0.0936586
$115$	−64445.5	−0.454410
$116$	45466.0	0.313719
$117$	−33548.8	−0.226575
$118$	96826.4	0.640160
$119$	−358619.	−2.32148
$120$	−14400.0	−0.0912871
$121$	−70035.4	−0.434865
$122$	−97191.0	−0.591189
$123$	140296.	0.836148
$124$	−8170.71	−0.0477206
$125$	−15625.0	−0.0894427
$126$	64392.2	0.361332
$127$	194607.	1.07066	0.535328	−	0.844645i	$-0.320188\pi$
$127$	194607.	1.07066	0.535328	+	0.844645i	$0.320188\pi$
$128$	−16384.0	−0.0883883
$129$	−10055.1	−0.0532002
$130$	−41418.2	−0.214948
$131$	81446.7	0.414663	0.207331	−	0.978271i	$-0.433522\pi$
$131$	81446.7	0.414663	0.207331	+	0.978271i	$0.433522\pi$
$132$	43443.0	0.217013
$133$	71745.6	0.351695
$134$	−177837.	−0.855577
$135$	18225.0	0.0860663
$136$	−115485.	−0.535399
$137$	150418.	0.684697	0.342348	−	0.939573i	$-0.388778\pi$
$137$	150418.	0.684697	0.342348	+	0.939573i	$0.388778\pi$
$138$	92801.4	0.414817
$139$	91266.1	0.400657	0.200328	−	0.979729i	$-0.435799\pi$
$139$	91266.1	0.400657	0.200328	+	0.979729i	$0.435799\pi$
$140$	79496.6	0.342790
$141$	−107695.	−0.456192
$142$	68194.8	0.283812
$143$	124954.	0.510986
$144$	20736.0	0.0833333
$145$	−71040.6	−0.280599
$146$	−19983.8	−0.0775881
$147$	−204220.	−0.779481
$148$	103329.	0.387764
$149$	−428133.	−1.57984	−0.789920	−	0.613210i	$-0.789878\pi$
$149$	−428133.	−1.57984	−0.789920	+	0.613210i	$0.789878\pi$
$150$	22500.0	0.0816497
$151$	−317579.	−1.13347	−0.566734	−	0.823901i	$-0.691793\pi$
$151$	−317579.	−1.13347	−0.566734	+	0.823901i	$0.691793\pi$
$152$	23104.0	0.0811107
$153$	146160.	0.504779
$154$	−239831.	−0.814900
$155$	12766.7	0.0426826
$156$	59642.2	0.196220
$157$	−532116.	−1.72289	−0.861444	−	0.507853i	$-0.830439\pi$
$157$	−532116.	−1.72289	−0.861444	+	0.507853i	$0.830439\pi$
$158$	131307.	0.418452
$159$	−97212.6	−0.304951
$160$	25600.0	0.0790569
$161$	−512319.	−1.55767
$162$	−26244.0	−0.0785674
$163$	−459461.	−1.35450	−0.677251	−	0.735752i	$-0.736829\pi$
$163$	−459461.	−1.35450	−0.677251	+	0.735752i	$0.736829\pi$
$164$	−249415.	−0.724125
$165$	−67879.8	−0.194102
$166$	18174.1	0.0511896
$167$	−159215.	−0.441767	−0.220883	−	0.975300i	$-0.570894\pi$
$167$	−159215.	−0.441767	−0.220883	+	0.975300i	$0.570894\pi$
$168$	−114475.	−0.312923
$169$	−199746.	−0.537975
$170$	180445.	0.478875
$171$	−29241.0	−0.0764719
$172$	17875.8	0.0460727
$173$	−713321.	−1.81205	−0.906025	−	0.423225i	$-0.860898\pi$
$173$	−713321.	−1.81205	−0.906025	+	0.423225i	$0.860898\pi$
$174$	102298.	0.256151
$175$	−124213.	−0.306601
$176$	−77232.1	−0.187939
$177$	217859.	0.522689
$178$	82327.1	0.194757
$179$	−388360.	−0.905944	−0.452972	−	0.891525i	$-0.649636\pi$
$179$	−388360.	−0.905944	−0.452972	+	0.891525i	$0.649636\pi$
$180$	−32400.0	−0.0745356
$181$	467365.	1.06038	0.530188	−	0.847880i	$-0.322121\pi$
$181$	467365.	1.06038	0.530188	+	0.847880i	$0.322121\pi$
$182$	−329260.	−0.736820
$183$	−218680.	−0.482704
$184$	−164980.	−0.359242
$185$	−161451.	−0.346826
$186$	−18384.1	−0.0389637
$187$	−544380.	−1.13841
$188$	191458.	0.395074
$189$	144882.	0.295027
$190$	−36100.0	−0.0725476
$191$	−911864.	−1.80862	−0.904308	−	0.426880i	$-0.859613\pi$
$191$	−911864.	−1.80862	−0.904308	+	0.426880i	$0.859613\pi$
$192$	−36864.0	−0.0721688
$193$	451916.	0.873303	0.436651	−	0.899631i	$-0.356164\pi$
$193$	451916.	0.873303	0.436651	+	0.899631i	$0.356164\pi$
$194$	−463554.	−0.884293
$195$	−93191.0	−0.175504
$196$	363058.	0.675050
$197$	−203508.	−0.373608	−0.186804	−	0.982397i	$-0.559813\pi$
$197$	−203508.	−0.373608	−0.186804	+	0.982397i	$0.559813\pi$
$198$	97746.9	0.177190
$199$	633693.	1.13435	0.567174	−	0.823598i	$-0.308037\pi$
$199$	633693.	1.13435	0.567174	+	0.823598i	$0.308037\pi$
$200$	−40000.0	−0.0707107
$201$	−400132.	−0.698576
$202$	−279376.	−0.481738
$203$	−564748.	−0.961866
$204$	−259841.	−0.437151
$205$	389712.	0.647677
$206$	24294.3	0.0398874
$207$	208803.	0.338697
$208$	−106031.	−0.169931
$209$	108909.	0.172464
$210$	178867.	0.279887
$211$	238810.	0.369271	0.184636	−	0.982807i	$-0.440889\pi$
$211$	238810.	0.369271	0.184636	+	0.982807i	$0.440889\pi$
$212$	172822.	0.264095
$213$	153438.	0.231731
$214$	705232.	1.05268
$215$	−27930.9	−0.0412087
$216$	46656.0	0.0680414
$217$	101491.	0.146312
$218$	−45268.1	−0.0645136
$219$	−44963.5	−0.0633504
$220$	120675.	0.168097
$221$	−747371.	−1.02933
$222$	232490.	0.316608
$223$	112222.	0.151117	0.0755587	−	0.997141i	$-0.475926\pi$
$223$	112222.	0.151117	0.0755587	+	0.997141i	$0.475926\pi$
$224$	203511.	0.270999
$225$	50625.0	0.0666667
$226$	−880849.	−1.14718
$227$	4499.63	0.00579578	0.00289789	−	0.999996i	$-0.499078\pi$
$227$	4499.63	0.00579578	0.00289789	+	0.999996i	$0.499078\pi$
$228$	51984.0	0.0662266
$229$	1.36542e6	1.72059	0.860297	−	0.509793i	$-0.170278\pi$
$229$	1.36542e6	1.72059	0.860297	+	0.509793i	$0.170278\pi$
$230$	257782.	0.321316
$231$	−539621.	−0.665363
$232$	−181864.	−0.221833
$233$	493115.	0.595057	0.297528	−	0.954713i	$-0.403838\pi$
$233$	493115.	0.595057	0.297528	+	0.954713i	$0.403838\pi$
$234$	134195.	0.160213
$235$	−299153.	−0.353365
$236$	−387306.	−0.452662
$237$	295441.	0.341664
$238$	1.43447e6	1.64154
$239$	−1.08076e6	−1.22386	−0.611932	−	0.790910i	$-0.709607\pi$
$239$	−1.08076e6	−1.22386	−0.611932	+	0.790910i	$0.709607\pi$
$240$	57600.0	0.0645497
$241$	−301534.	−0.334421	−0.167210	−	0.985921i	$-0.553476\pi$
$241$	−301534.	−0.334421	−0.167210	+	0.985921i	$0.553476\pi$
$242$	280142.	0.307496
$243$	−59049.0	−0.0641500
$244$	388764.	0.418034
$245$	−567278.	−0.603783
$246$	−561185.	−0.591246
$247$	149520.	0.155940
$248$	32682.8	0.0337435
$249$	40891.6	0.0417961
$250$	62500.0	0.0632456
$251$	1.53187e6	1.53475	0.767377	−	0.641196i	$-0.221561\pi$
$251$	1.53187e6	1.53475	0.767377	+	0.641196i	$0.221561\pi$
$252$	−257569.	−0.255501
$253$	−777696.	−0.763851
$254$	−778429.	−0.757067
$255$	406001.	0.391000
$256$	65536.0	0.0625000
$257$	116577.	0.110098	0.0550490	−	0.998484i	$-0.482468\pi$
$257$	116577.	0.110098	0.0550490	+	0.998484i	$0.482468\pi$
$258$	40220.5	0.0376182
$259$	−1.28348e6	−1.18889
$260$	165673.	0.151991
$261$	230171.	0.209146
$262$	−325787.	−0.293211
$263$	−1.82569e6	−1.62756	−0.813780	−	0.581174i	$-0.802594\pi$
$263$	−1.82569e6	−1.62756	−0.813780	+	0.581174i	$0.802594\pi$
$264$	−173772.	−0.153451
$265$	−270035.	−0.236214
$266$	−286983.	−0.248686
$267$	185236.	0.159018
$268$	711347.	0.604985
$269$	−1.08156e6	−0.911319	−0.455659	−	0.890154i	$-0.650597\pi$
$269$	−1.08156e6	−0.911319	−0.455659	+	0.890154i	$0.650597\pi$
$270$	−72900.0	−0.0608581
$271$	−321112.	−0.265603	−0.132801	−	0.991143i	$-0.542397\pi$
$271$	−321112.	−0.265603	−0.132801	+	0.991143i	$0.542397\pi$
$272$	461939.	0.378584
$273$	−740836.	−0.601611
$274$	−601672.	−0.484154
$275$	−188555.	−0.150351
$276$	−371206.	−0.293320
$277$	546630.	0.428049	0.214025	−	0.976828i	$-0.431343\pi$
$277$	546630.	0.428049	0.214025	+	0.976828i	$0.431343\pi$
$278$	−365064.	−0.283307
$279$	−41364.2	−0.0318137
$280$	−317986.	−0.242389
$281$	−423500.	−0.319954	−0.159977	−	0.987121i	$-0.551142\pi$
$281$	−423500.	−0.319954	−0.159977	+	0.987121i	$0.551142\pi$
$282$	430780.	0.322576
$283$	−2.14279e6	−1.59043	−0.795214	−	0.606329i	$-0.792641\pi$
$283$	−2.14279e6	−1.59043	−0.795214	+	0.606329i	$0.792641\pi$
$284$	−272779.	−0.200685
$285$	−81225.0	−0.0592349
$286$	−499815.	−0.361322
$287$	3.09807e6	2.22017
$288$	−82944.0	−0.0589256
$289$	1.83618e6	1.29321
$290$	284162.	0.198414
$291$	−1.04300e6	−0.722022
$292$	79935.1	0.0548631
$293$	263928.	0.179604	0.0898020	−	0.995960i	$-0.471377\pi$
$293$	263928.	0.179604	0.0898020	+	0.995960i	$0.471377\pi$
$294$	816881.	0.551176
$295$	605165.	0.404873
$296$	−413315.	−0.274190
$297$	219930.	0.144675
$298$	1.71253e6	1.11712
$299$	−1.06769e6	−0.690662
$300$	−90000.0	−0.0577350
$301$	−222041.	−0.141259
$302$	1.27032e6	0.801484
$303$	−628596.	−0.393337
$304$	−92416.0	−0.0573539
$305$	−607444.	−0.373901
$306$	−584642.	−0.356933
$307$	798387.	0.483468	0.241734	−	0.970343i	$-0.422284\pi$
$307$	798387.	0.483468	0.241734	+	0.970343i	$0.422284\pi$
$308$	959326.	0.576221
$309$	54662.1	0.0325680
$310$	−51066.9	−0.0301811
$311$	2.02222e6	1.18557	0.592786	−	0.805360i	$-0.298028\pi$
$311$	2.02222e6	1.18557	0.592786	+	0.805360i	$0.298028\pi$
$312$	−238569.	−0.138748
$313$	−362645.	−0.209229	−0.104614	−	0.994513i	$-0.533361\pi$
$313$	−362645.	−0.209229	−0.104614	+	0.994513i	$0.533361\pi$
$314$	2.12846e6	1.21827
$315$	402451.	0.228527
$316$	−525228.	−0.295890
$317$	−2.11373e6	−1.18141	−0.590705	−	0.806888i	$-0.701150\pi$
$317$	−2.11373e6	−1.18141	−0.590705	+	0.806888i	$0.701150\pi$
$318$	388850.	0.215633
$319$	−857283.	−0.471680
$320$	−102400.	−0.0559017
$321$	1.58677e6	0.859512
$322$	2.04928e6	1.10144
$323$	−651406.	−0.347413
$324$	104976.	0.0555556
$325$	−258864.	−0.135945
$326$	1.83784e6	0.957778
$327$	−101853.	−0.0526751
$328$	997662.	0.512034
$329$	−2.37816e6	−1.21130
$330$	271519.	0.137251
$331$	−1.32876e6	−0.666619	−0.333310	−	0.942817i	$-0.608165\pi$
$331$	−1.32876e6	−0.666619	−0.333310	+	0.942817i	$0.608165\pi$
$332$	−72696.2	−0.0361965
$333$	523102.	0.258509
$334$	636860.	0.312376
$335$	−1.11148e6	−0.541115
$336$	457900.	0.221270
$337$	−3.74811e6	−1.79779	−0.898893	−	0.438168i	$-0.855628\pi$
$337$	−3.74811e6	−1.79779	−0.898893	+	0.438168i	$0.855628\pi$
$338$	798985.	0.380405
$339$	−1.98191e6	−0.936666
$340$	−721780.	−0.338616
$341$	154063.	0.0717483
$342$	116964.	0.0540738
$343$	−1.16942e6	−0.536705
$344$	−71503.2	−0.0325784
$345$	580009.	0.262354
$346$	2.85329e6	1.28131
$347$	1.31314e6	0.585448	0.292724	−	0.956197i	$-0.405438\pi$
$347$	1.31314e6	0.585448	0.292724	+	0.956197i	$0.405438\pi$
$348$	−409194.	−0.181126
$349$	210346.	0.0924421	0.0462211	−	0.998931i	$-0.485282\pi$
$349$	210346.	0.0924421	0.0462211	+	0.998931i	$0.485282\pi$
$350$	496853.	0.216799
$351$	301939.	0.130813
$352$	308928.	0.132893
$353$	3.92766e6	1.67763	0.838816	−	0.544415i	$-0.183248\pi$
$353$	3.92766e6	1.67763	0.838816	+	0.544415i	$0.183248\pi$
$354$	−871437.	−0.369597
$355$	426218.	0.179498
$356$	−329309.	−0.137714
$357$	3.22757e6	1.34031
$358$	1.55344e6	0.640599
$359$	4.41991e6	1.80999	0.904997	−	0.425418i	$-0.139873\pi$
$359$	4.41991e6	1.80999	0.904997	+	0.425418i	$0.139873\pi$
$360$	129600.	0.0527046
$361$	130321.	0.0526316
$362$	−1.86946e6	−0.749799
$363$	630319.	0.251069
$364$	1.31704e6	0.521010
$365$	−124899.	−0.0490710
$366$	874719.	0.341323
$367$	1.56154e6	0.605184	0.302592	−	0.953120i	$-0.402148\pi$
$367$	1.56154e6	0.605184	0.302592	+	0.953120i	$0.402148\pi$
$368$	659921.	0.254023
$369$	−1.26267e6	−0.482750
$370$	645805.	0.245243
$371$	−2.14669e6	−0.809718
$372$	73536.4	0.0275515
$373$	2.44097e6	0.908429	0.454214	−	0.890892i	$-0.349920\pi$
$373$	2.44097e6	0.908429	0.454214	+	0.890892i	$0.349920\pi$
$374$	2.17752e6	0.804977
$375$	140625.	0.0516398
$376$	−765830.	−0.279359
$377$	−1.17695e6	−0.426486
$378$	−579530.	−0.208615
$379$	807979.	0.288936	0.144468	−	0.989509i	$-0.453853\pi$
$379$	807979.	0.288936	0.144468	+	0.989509i	$0.453853\pi$
$380$	144400.	0.0512989
$381$	−1.75146e6	−0.618143
$382$	3.64745e6	1.27888
$383$	−684813.	−0.238548	−0.119274	−	0.992861i	$-0.538057\pi$
$383$	−684813.	−0.238548	−0.119274	+	0.992861i	$0.538057\pi$
$384$	147456.	0.0510310
$385$	−1.49895e6	−0.515388
$386$	−1.80767e6	−0.617518
$387$	90496.2	0.0307152
$388$	1.85422e6	0.625290
$389$	1.16065e6	0.388890	0.194445	−	0.980913i	$-0.437709\pi$
$389$	1.16065e6	0.388890	0.194445	+	0.980913i	$0.437709\pi$
$390$	372764.	0.124100
$391$	4.65154e6	1.53870
$392$	−1.45223e6	−0.477333
$393$	−733020.	−0.239406
$394$	814033.	0.264181
$395$	820669.	0.264652
$396$	−390987.	−0.125292
$397$	−3.70712e6	−1.18049	−0.590243	−	0.807226i	$-0.700968\pi$
$397$	−3.70712e6	−1.18049	−0.590243	+	0.807226i	$0.700968\pi$
$398$	−2.53477e6	−0.802105
$399$	−645711.	−0.203051
$400$	160000.	0.0500000
$401$	4.29269e6	1.33312	0.666559	−	0.745452i	$-0.267767\pi$
$401$	4.29269e6	1.33312	0.666559	+	0.745452i	$0.267767\pi$
$402$	1.60053e6	0.493968
$403$	211510.	0.0648737
$404$	1.11750e6	0.340640
$405$	−164025.	−0.0496904
$406$	2.25899e6	0.680142
$407$	−1.94831e6	−0.583006
$408$	1.03936e6	0.309113
$409$	3.44742e6	1.01903	0.509514	−	0.860462i	$-0.329825\pi$
$409$	3.44742e6	1.01903	0.509514	+	0.860462i	$0.329825\pi$
$410$	−1.55885e6	−0.457977
$411$	−1.35376e6	−0.395310
$412$	−97177.1	−0.0282047
$413$	4.81085e6	1.38786
$414$	−835213.	−0.239495
$415$	113588.	0.0323751
$416$	424122.	0.120159
$417$	−821395.	−0.231319
$418$	−435637.	−0.121951
$419$	−4.12052e6	−1.14661	−0.573307	−	0.819341i	$-0.694340\pi$
$419$	−4.12052e6	−1.14661	−0.573307	+	0.819341i	$0.694340\pi$
$420$	−715469.	−0.197910
$421$	954304.	0.262411	0.131205	−	0.991355i	$-0.458115\pi$
$421$	954304.	0.262411	0.131205	+	0.991355i	$0.458115\pi$
$422$	−955238.	−0.261114
$423$	969254.	0.263382
$424$	−691290.	−0.186743
$425$	1.12778e6	0.302867
$426$	−613754.	−0.163859
$427$	−4.82897e6	−1.28170
$428$	−2.82093e6	−0.744359
$429$	−1.12458e6	−0.295018
$430$	111724.	0.0291390
$431$	−7.40001e6	−1.91884	−0.959421	−	0.281979i	$-0.909009\pi$
$431$	−7.40001e6	−1.91884	−0.959421	+	0.281979i	$0.909009\pi$
$432$	−186624.	−0.0481125
$433$	7.14705e6	1.83192	0.915962	−	0.401265i	$-0.131429\pi$
$433$	7.14705e6	1.83192	0.915962	+	0.401265i	$0.131429\pi$
$434$	−405964.	−0.103458
$435$	639365.	0.162004
$436$	181072.	0.0456180
$437$	−930592.	−0.233107
$438$	179854.	0.0447955
$439$	4.71861e6	1.16857	0.584283	−	0.811550i	$-0.301376\pi$
$439$	4.71861e6	1.16857	0.584283	+	0.811550i	$0.301376\pi$
$440$	−482701.	−0.118863
$441$	1.83798e6	0.450033
$442$	2.98948e6	0.727847
$443$	−1.37982e6	−0.334052	−0.167026	−	0.985952i	$-0.553416\pi$
$443$	−1.37982e6	−0.334052	−0.167026	+	0.985952i	$0.553416\pi$
$444$	−929959.	−0.223875
$445$	514545.	0.123175
$446$	−448886.	−0.106856
$447$	3.85320e6	0.912121
$448$	−814045.	−0.191625
$449$	−1.41603e6	−0.331480	−0.165740	−	0.986170i	$-0.553001\pi$
$449$	−1.41603e6	−0.331480	−0.165740	+	0.986170i	$0.553001\pi$
$450$	−202500.	−0.0471405
$451$	4.70285e6	1.08873
$452$	3.52340e6	0.811177
$453$	2.85821e6	0.654409
$454$	−17998.5	−0.00409823
$455$	−2.05788e6	−0.466006
$456$	−207936.	−0.0468293
$457$	−3.37617e6	−0.756196	−0.378098	−	0.925766i	$-0.623422\pi$
$457$	−3.37617e6	−0.756196	−0.378098	+	0.925766i	$0.623422\pi$
$458$	−5.46169e6	−1.21664
$459$	−1.31544e6	−0.291434
$460$	−1.03113e6	−0.227205
$461$	−8.33350e6	−1.82631	−0.913156	−	0.407609i	$-0.866362\pi$
$461$	−8.33350e6	−1.82631	−0.913156	+	0.407609i	$0.866362\pi$
$462$	2.15848e6	0.470483
$463$	3.91094e6	0.847869	0.423935	−	0.905693i	$-0.360649\pi$
$463$	3.91094e6	0.847869	0.423935	+	0.905693i	$0.360649\pi$
$464$	727455.	0.156860
$465$	−114901.	−0.0246428
$466$	−1.97246e6	−0.420769
$467$	−1.24245e6	−0.263625	−0.131813	−	0.991275i	$-0.542080\pi$
$467$	−1.24245e6	−0.263625	−0.131813	+	0.991275i	$0.542080\pi$
$468$	−536780.	−0.113287
$469$	−8.83588e6	−1.85489
$470$	1.19661e6	0.249866
$471$	4.78904e6	0.994710
$472$	1.54922e6	0.320080
$473$	−337057.	−0.0692708
$474$	−1.18176e6	−0.241593
$475$	−225625.	−0.0458831
$476$	−5.73790e6	−1.16074
$477$	874913.	0.176063
$478$	4.32303e6	0.865403
$479$	−124888.	−0.0248703	−0.0124352	−	0.999923i	$-0.503958\pi$
$479$	−124888.	−0.0248703	−0.0124352	+	0.999923i	$0.503958\pi$
$480$	−230400.	−0.0456435
$481$	−2.67481e6	−0.527145
$482$	1.20614e6	0.236471
$483$	4.61087e6	0.899322
$484$	−1.12057e6	−0.217433
$485$	−2.89721e6	−0.559276
$486$	236196.	0.0453609
$487$	3.21672e6	0.614599	0.307299	−	0.951613i	$-0.400575\pi$
$487$	3.21672e6	0.614599	0.307299	+	0.951613i	$0.400575\pi$
$488$	−1.55506e6	−0.295595
$489$	4.13515e6	0.782022
$490$	2.26911e6	0.426939
$491$	−28485.2	−0.00533231	−0.00266616	−	0.999996i	$-0.500849\pi$
$491$	−28485.2	−0.00533231	−0.00266616	+	0.999996i	$0.500849\pi$
$492$	2.24474e6	0.418074
$493$	5.12756e6	0.950154
$494$	−598079.	−0.110266
$495$	610918.	0.112065
$496$	−130731.	−0.0238603
$497$	3.38828e6	0.615303
$498$	−163566.	−0.0295543
$499$	3.58835e6	0.645124	0.322562	−	0.946548i	$-0.395456\pi$
$499$	3.58835e6	0.645124	0.322562	+	0.946548i	$0.395456\pi$
$500$	−250000.	−0.0447214
$501$	1.43294e6	0.255054
$502$	−6.12750e6	−1.08524
$503$	7.41843e6	1.30735	0.653676	−	0.756775i	$-0.273226\pi$
$503$	7.41843e6	1.30735	0.653676	+	0.756775i	$0.273226\pi$
$504$	1.03028e6	0.180666
$505$	−1.74610e6	−0.304678
$506$	3.11079e6	0.540124
$507$	1.79772e6	0.310600
$508$	3.11372e6	0.535328
$509$	−6.14946e6	−1.05207	−0.526033	−	0.850464i	$-0.676321\pi$
$509$	−6.14946e6	−1.05207	−0.526033	+	0.850464i	$0.676321\pi$
$510$	−1.62400e6	−0.276479
$511$	−992900.	−0.168211
$512$	−262144.	−0.0441942
$513$	263169.	0.0441511
$514$	−466308.	−0.0778511
$515$	151839.	0.0252270
$516$	−160882.	−0.0266001
$517$	−3.61003e6	−0.593997
$518$	5.13393e6	0.840669
$519$	6.41989e6	1.04619
$520$	−662691.	−0.107474
$521$	−1.23809e7	−1.99829	−0.999144	−	0.0413730i	$-0.986827\pi$
$521$	−1.23809e7	−1.99829	−0.999144	+	0.0413730i	$0.986827\pi$
$522$	−920686.	−0.147889
$523$	5.11228e6	0.817261	0.408630	−	0.912700i	$-0.366007\pi$
$523$	5.11228e6	0.817261	0.408630	+	0.912700i	$0.366007\pi$
$524$	1.30315e6	0.207331
$525$	1.11792e6	0.177016
$526$	7.30275e6	1.15086
$527$	−921477.	−0.144530
$528$	695089.	0.108506
$529$	208803.	0.0324412
$530$	1.08014e6	0.167028
$531$	−1.96073e6	−0.301774
$532$	1.14793e6	0.175848
$533$	6.45646e6	0.984412
$534$	−740944.	−0.112443
$535$	4.40770e6	0.665775
$536$	−2.84539e6	−0.427789
$537$	3.49524e6	0.523047
$538$	4.32624e6	0.644400
$539$	−6.84564e6	−1.01494
$540$	291600.	0.0430331
$541$	8.48019e6	1.24570	0.622848	−	0.782343i	$-0.285975\pi$
$541$	8.48019e6	1.24570	0.622848	+	0.782343i	$0.285975\pi$
$542$	1.28445e6	0.187810
$543$	−4.20629e6	−0.612209
$544$	−1.84776e6	−0.267699
$545$	−282926.	−0.0408020
$546$	2.96334e6	0.425403
$547$	−7.70141e6	−1.10053	−0.550265	−	0.834990i	$-0.685473\pi$
$547$	−7.70141e6	−1.10053	−0.550265	+	0.834990i	$0.685473\pi$
$548$	2.40669e6	0.342348
$549$	1.96812e6	0.278689
$550$	754220.	0.106314
$551$	−1.02583e6	−0.143944
$552$	1.48482e6	0.207409
$553$	6.52403e6	0.907201
$554$	−2.18652e6	−0.302677
$555$	1.45306e6	0.200240
$556$	1.46026e6	0.200328
$557$	1.24208e6	0.169634	0.0848168	−	0.996397i	$-0.472969\pi$
$557$	1.24208e6	0.169634	0.0848168	+	0.996397i	$0.472969\pi$
$558$	165457.	0.0224957
$559$	−462739.	−0.0626336
$560$	1.27194e6	0.171395
$561$	4.89942e6	0.657261
$562$	1.69400e6	0.226242
$563$	3.60364e6	0.479149	0.239574	−	0.970878i	$-0.422992\pi$
$563$	3.60364e6	0.479149	0.239574	+	0.970878i	$0.422992\pi$
$564$	−1.72312e6	−0.228096
$565$	−5.50531e6	−0.725539
$566$	8.57117e6	1.12460
$567$	−1.30394e6	−0.170334
$568$	1.09112e6	0.141906
$569$	−9.60760e6	−1.24404	−0.622020	−	0.783001i	$-0.713688\pi$
$569$	−9.60760e6	−1.24404	−0.622020	+	0.783001i	$0.713688\pi$
$570$	324900.	0.0418854
$571$	1.86747e6	0.239698	0.119849	−	0.992792i	$-0.461759\pi$
$571$	1.86747e6	0.239698	0.119849	+	0.992792i	$0.461759\pi$
$572$	1.99926e6	0.255493
$573$	8.20677e6	1.04421
$574$	−1.23923e7	−1.56990
$575$	1.61114e6	0.203218
$576$	331776.	0.0416667
$577$	−2.55886e6	−0.319968	−0.159984	−	0.987120i	$-0.551144\pi$
$577$	−2.55886e6	−0.319968	−0.159984	+	0.987120i	$0.551144\pi$
$578$	−7.34472e6	−0.914441
$579$	−4.06725e6	−0.504201
$580$	−1.13665e6	−0.140300
$581$	902984.	0.110979
$582$	4.17199e6	0.510547
$583$	−3.25865e6	−0.397069
$584$	−319740.	−0.0387941
$585$	838719.	0.101327
$586$	−1.05571e6	−0.126999
$587$	−1.35801e7	−1.62671	−0.813353	−	0.581771i	$-0.802360\pi$
$587$	−1.35801e7	−1.62671	−0.813353	+	0.581771i	$0.802360\pi$
$588$	−3.26752e6	−0.389740
$589$	184352.	0.0218957
$590$	−2.42066e6	−0.286288
$591$	1.83157e6	0.215703
$592$	1.65326e6	0.193882
$593$	6.22471e6	0.726913	0.363456	−	0.931611i	$-0.381597\pi$
$593$	6.22471e6	0.726913	0.363456	+	0.931611i	$0.381597\pi$
$594$	−879722.	−0.102301
$595$	8.96547e6	1.03820
$596$	−6.85013e6	−0.789920
$597$	−5.70324e6	−0.654916
$598$	4.27074e6	0.488372
$599$	−4.47755e6	−0.509887	−0.254943	−	0.966956i	$-0.582057\pi$
$599$	−4.47755e6	−0.509887	−0.254943	+	0.966956i	$0.582057\pi$
$600$	360000.	0.0408248
$601$	−1.16870e7	−1.31983	−0.659913	−	0.751342i	$-0.729407\pi$
$601$	−1.16870e7	−1.31983	−0.659913	+	0.751342i	$0.729407\pi$
$602$	888165.	0.0998855
$603$	3.60119e6	0.403323
$604$	−5.08127e6	−0.566734
$605$	1.75089e6	0.194478
$606$	2.51438e6	0.278131
$607$	4.20389e6	0.463105	0.231552	−	0.972822i	$-0.425620\pi$
$607$	4.20389e6	0.463105	0.231552	+	0.972822i	$0.425620\pi$
$608$	369664.	0.0405554
$609$	5.08273e6	0.555334
$610$	2.42978e6	0.264388
$611$	−4.95614e6	−0.537082
$612$	2.33857e6	0.252389
$613$	1.57832e7	1.69646	0.848232	−	0.529625i	$-0.177667\pi$
$613$	1.57832e7	1.69646	0.848232	+	0.529625i	$0.177667\pi$
$614$	−3.19355e6	−0.341863
$615$	−3.50740e6	−0.373937
$616$	−3.83730e6	−0.407450
$617$	−8.30305e6	−0.878061	−0.439031	−	0.898472i	$-0.644678\pi$
$617$	−8.30305e6	−0.878061	−0.439031	+	0.898472i	$0.644678\pi$
$618$	−218649.	−0.0230290
$619$	−8.94606e6	−0.938437	−0.469219	−	0.883082i	$-0.655464\pi$
$619$	−8.94606e6	−0.938437	−0.469219	+	0.883082i	$0.655464\pi$
$620$	204268.	0.0213413
$621$	−1.87923e6	−0.195547
$622$	−8.08889e6	−0.838326
$623$	4.09045e6	0.422232
$624$	954276.	0.0981098
$625$	390625.	0.0400000
$626$	1.45058e6	0.147947
$627$	−980184.	−0.0995723
$628$	−8.51385e6	−0.861444
$629$	1.16532e7	1.17441
$630$	−1.60981e6	−0.161593
$631$	−1.40262e7	−1.40238	−0.701189	−	0.712975i	$-0.747347\pi$
$631$	−1.40262e7	−1.40238	−0.701189	+	0.712975i	$0.747347\pi$
$632$	2.10091e6	0.209226
$633$	−2.14929e6	−0.213199
$634$	8.45490e6	0.835383
$635$	−4.86518e6	−0.478812
$636$	−1.55540e6	−0.152475
$637$	−9.39826e6	−0.917696
$638$	3.42913e6	0.333528
$639$	−1.38095e6	−0.133790
$640$	409600.	0.0395285
$641$	1.24158e7	1.19352	0.596762	−	0.802419i	$-0.296454\pi$
$641$	1.24158e7	1.19352	0.596762	+	0.802419i	$0.296454\pi$
$642$	−6.34709e6	−0.607767
$643$	−6.94150e6	−0.662104	−0.331052	−	0.943613i	$-0.607404\pi$
$643$	−6.94150e6	−0.662104	−0.331052	+	0.943613i	$0.607404\pi$
$644$	−8.19711e6	−0.778836
$645$	251378.	0.0237919
$646$	2.60562e6	0.245658
$647$	−1.17234e7	−1.10101	−0.550507	−	0.834831i	$-0.685566\pi$
$647$	−1.17234e7	−1.10101	−0.550507	+	0.834831i	$0.685566\pi$
$648$	−419904.	−0.0392837
$649$	7.30284e6	0.680581
$650$	1.03546e6	0.0961276
$651$	−913420.	−0.0844730
$652$	−7.35138e6	−0.677251
$653$	1.47343e7	1.35222	0.676108	−	0.736802i	$-0.263665\pi$
$653$	1.47343e7	1.35222	0.676108	+	0.736802i	$0.263665\pi$
$654$	407413.	0.0372469
$655$	−2.03617e6	−0.185443
$656$	−3.99065e6	−0.362063
$657$	404671.	0.0365754
$658$	9.51264e6	0.856517
$659$	−8.13783e6	−0.729953	−0.364977	−	0.931017i	$-0.618923\pi$
$659$	−8.13783e6	−0.729953	−0.364977	+	0.931017i	$0.618923\pi$
$660$	−1.08608e6	−0.0970511
$661$	−6.10515e6	−0.543491	−0.271746	−	0.962369i	$-0.587601\pi$
$661$	−6.10515e6	−0.543491	−0.271746	+	0.962369i	$0.587601\pi$
$662$	5.31505e6	0.471371
$663$	6.72634e6	0.594285
$664$	290785.	0.0255948
$665$	−1.79364e6	−0.157283
$666$	−2.09241e6	−0.182793
$667$	7.32519e6	0.637535
$668$	−2.54744e6	−0.220883
$669$	−1.00999e6	−0.0872476
$670$	4.44592e6	0.382626
$671$	−7.33034e6	−0.628518
$672$	−1.83160e6	−0.156462
$673$	−1.51100e7	−1.28596	−0.642978	−	0.765885i	$-0.722301\pi$
$673$	−1.51100e7	−1.28596	−0.642978	+	0.765885i	$0.722301\pi$
$674$	1.49925e7	1.27123
$675$	−455625.	−0.0384900
$676$	−3.19594e6	−0.268987
$677$	1.53998e6	0.129135	0.0645673	−	0.997913i	$-0.479433\pi$
$677$	1.53998e6	0.129135	0.0645673	+	0.997913i	$0.479433\pi$
$678$	7.92764e6	0.662323
$679$	−2.30319e7	−1.91714
$680$	2.88712e6	0.239438
$681$	−40496.6	−0.00334619
$682$	−616251.	−0.0507337
$683$	−3.95959e6	−0.324787	−0.162394	−	0.986726i	$-0.551921\pi$
$683$	−3.95959e6	−0.324787	−0.162394	+	0.986726i	$0.551921\pi$
$684$	−467856.	−0.0382360
$685$	−3.76045e6	−0.306206
$686$	4.67768e6	0.379508
$687$	−1.22888e7	−0.993386
$688$	286013.	0.0230364
$689$	−4.47375e6	−0.359024
$690$	−2.32004e6	−0.185512
$691$	−4.52472e6	−0.360493	−0.180247	−	0.983621i	$-0.557690\pi$
$691$	−4.52472e6	−0.360493	−0.180247	+	0.983621i	$0.557690\pi$
$692$	−1.14131e7	−0.906025
$693$	4.85659e6	0.384148
$694$	−5.25257e6	−0.413974
$695$	−2.28165e6	−0.179179
$696$	1.63677e6	0.128075
$697$	−2.81286e7	−2.19314
$698$	−841383.	−0.0653665
$699$	−4.43803e6	−0.343556
$700$	−1.98741e6	−0.153300
$701$	1.15106e7	0.884716	0.442358	−	0.896839i	$-0.354142\pi$
$701$	1.15106e7	0.884716	0.442358	+	0.896839i	$0.354142\pi$
$702$	−1.20776e6	−0.0924988
$703$	−2.33136e6	−0.177918
$704$	−1.23571e6	−0.0939693
$705$	2.69237e6	0.204015
$706$	−1.57106e7	−1.18626
$707$	−1.38809e7	−1.04440
$708$	3.48575e6	0.261344
$709$	−1.51111e6	−0.112896	−0.0564482	−	0.998406i	$-0.517978\pi$
$709$	−1.51111e6	−0.112896	−0.0564482	+	0.998406i	$0.517978\pi$
$710$	−1.70487e6	−0.126925
$711$	−2.65897e6	−0.197260
$712$	1.31723e6	0.0973785
$713$	−1.31641e6	−0.0969769
$714$	−1.29103e7	−0.947742
$715$	−3.12384e6	−0.228520
$716$	−6.21376e6	−0.452972
$717$	9.72681e6	0.706598
$718$	−1.76796e7	−1.27986
$719$	−2.12663e7	−1.53415	−0.767077	−	0.641555i	$-0.778289\pi$
$719$	−2.12663e7	−1.53415	−0.767077	+	0.641555i	$0.778289\pi$
$720$	−518400.	−0.0372678
$721$	1.20707e6	0.0864757
$722$	−521284.	−0.0372161
$723$	2.71381e6	0.193078
$724$	7.47785e6	0.530188
$725$	1.77601e6	0.125488
$726$	−2.52128e6	−0.177533
$727$	1.16437e7	0.817064	0.408532	−	0.912744i	$-0.366041\pi$
$727$	1.16437e7	0.817064	0.408532	+	0.912744i	$0.366041\pi$
$728$	−5.26817e6	−0.368410
$729$	531441.	0.0370370
$730$	499594.	0.0346985
$731$	2.01600e6	0.139539
$732$	−3.49888e6	−0.241352
$733$	1.12994e7	0.776777	0.388389	−	0.921496i	$-0.373032\pi$
$733$	1.12994e7	0.776777	0.388389	+	0.921496i	$0.373032\pi$
$734$	−6.24616e6	−0.427930
$735$	5.10551e6	0.348594
$736$	−2.63969e6	−0.179621
$737$	−1.34128e7	−0.909600
$738$	5.05066e6	0.341356
$739$	−2.81064e6	−0.189319	−0.0946595	−	0.995510i	$-0.530176\pi$
$739$	−2.81064e6	−0.189319	−0.0946595	+	0.995510i	$0.530176\pi$
$740$	−2.58322e6	−0.173413
$741$	−1.34568e6	−0.0900317
$742$	8.58674e6	0.572557
$743$	−1.42712e7	−0.948395	−0.474197	−	0.880419i	$-0.657262\pi$
$743$	−1.42712e7	−0.948395	−0.474197	+	0.880419i	$0.657262\pi$
$744$	−294146.	−0.0194818
$745$	1.07033e7	0.706526
$746$	−9.76389e6	−0.642356
$747$	−368025.	−0.0241310
$748$	−8.71009e6	−0.569205
$749$	3.50397e7	2.28221
$750$	−562500.	−0.0365148
$751$	−2.96243e6	−0.191667	−0.0958336	−	0.995397i	$-0.530552\pi$
$751$	−2.96243e6	−0.191667	−0.0958336	+	0.995397i	$0.530552\pi$
$752$	3.06332e6	0.197537
$753$	−1.37869e7	−0.886091
$754$	4.70780e6	0.301571
$755$	7.93948e6	0.506903
$756$	2.31812e6	0.147513
$757$	7.80798e6	0.495221	0.247610	−	0.968860i	$-0.420355\pi$
$757$	7.80798e6	0.495221	0.247610	+	0.968860i	$0.420355\pi$
$758$	−3.23191e6	−0.204309
$759$	6.99927e6	0.441010
$760$	−577600.	−0.0362738
$761$	−5.51776e6	−0.345383	−0.172691	−	0.984976i	$-0.555246\pi$
$761$	−5.51776e6	−0.345383	−0.172691	+	0.984976i	$0.555246\pi$
$762$	7.00586e6	0.437093
$763$	−2.24916e6	−0.139865
$764$	−1.45898e7	−0.904308
$765$	−3.65401e6	−0.225744
$766$	2.73925e6	0.168679
$767$	1.00259e7	0.615370
$768$	−589824.	−0.0360844
$769$	2.70117e6	0.164716	0.0823581	−	0.996603i	$-0.473755\pi$
$769$	2.70117e6	0.164716	0.0823581	+	0.996603i	$0.473755\pi$
$770$	5.99579e6	0.364434
$771$	−1.04919e6	−0.0635652
$772$	7.23066e6	0.436651
$773$	5.50350e6	0.331276	0.165638	−	0.986187i	$-0.447032\pi$
$773$	5.50350e6	0.331276	0.165638	+	0.986187i	$0.447032\pi$
$774$	−361985.	−0.0217189
$775$	−319168.	−0.0190882
$776$	−7.41687e6	−0.442147
$777$	1.15513e7	0.686404
$778$	−4.64259e6	−0.274987
$779$	5.62744e6	0.332252
$780$	−1.49106e6	−0.0877521
$781$	5.14339e6	0.301732
$782$	−1.86062e7	−1.08803
$783$	−2.07154e6	−0.120751
$784$	5.80893e6	0.337525
$785$	1.33029e7	0.770499
$786$	2.93208e6	0.169285
$787$	−2.45039e7	−1.41026	−0.705129	−	0.709079i	$-0.749111\pi$
$787$	−2.45039e7	−1.41026	−0.705129	+	0.709079i	$0.749111\pi$
$788$	−3.25613e6	−0.186804
$789$	1.64312e7	0.939672
$790$	−3.28268e6	−0.187137
$791$	−4.37653e7	−2.48707
$792$	1.56395e6	0.0885951
$793$	−1.00637e7	−0.568296
$794$	1.48285e7	0.834730
$795$	2.43032e6	0.136378
$796$	1.01391e7	0.567174
$797$	−631419.	−0.0352105	−0.0176052	−	0.999845i	$-0.505604\pi$
$797$	−631419.	−0.0352105	−0.0176052	+	0.999845i	$0.505604\pi$
$798$	2.58284e6	0.143579
$799$	2.15922e7	1.19655
$800$	−640000.	−0.0353553
$801$	−1.66712e6	−0.0918093
$802$	−1.71708e7	−0.942656
$803$	−1.50722e6	−0.0824872
$804$	−6.40212e6	−0.349288
$805$	1.28080e7	0.696612
$806$	−846040.	−0.0458726
$807$	9.73405e6	0.526150
$808$	−4.47002e6	−0.240869
$809$	1.99246e7	1.07033	0.535165	−	0.844747i	$-0.320249\pi$
$809$	1.99246e7	1.07033	0.535165	+	0.844747i	$0.320249\pi$
$810$	656100.	0.0351364
$811$	2.16776e7	1.15734	0.578668	−	0.815563i	$-0.303573\pi$
$811$	2.16776e7	1.15734	0.578668	+	0.815563i	$0.303573\pi$
$812$	−9.03597e6	−0.480933
$813$	2.89000e6	0.153346
$814$	7.79326e6	0.412248
$815$	1.14865e7	0.605752
$816$	−4.15745e6	−0.218576
$817$	−403322.	−0.0211396
$818$	−1.37897e7	−0.720562
$819$	6.66752e6	0.347340
$820$	6.23539e6	0.323839
$821$	2.80653e7	1.45315	0.726577	−	0.687085i	$-0.241110\pi$
$821$	2.80653e7	1.45315	0.726577	+	0.687085i	$0.241110\pi$
$822$	5.41504e6	0.279526
$823$	2.38700e7	1.22844	0.614218	−	0.789137i	$-0.289472\pi$
$823$	2.38700e7	1.22844	0.614218	+	0.789137i	$0.289472\pi$
$824$	388709.	0.0199437
$825$	1.69699e6	0.0868051
$826$	−1.92434e7	−0.981368
$827$	7.07804e6	0.359873	0.179937	−	0.983678i	$-0.442411\pi$
$827$	7.07804e6	0.359873	0.179937	+	0.983678i	$0.442411\pi$
$828$	3.34085e6	0.169349
$829$	7.00193e6	0.353860	0.176930	−	0.984223i	$-0.443383\pi$
$829$	7.00193e6	0.353860	0.176930	+	0.984223i	$0.443383\pi$
$830$	−454351.	−0.0228927
$831$	−4.91967e6	−0.247134
$832$	−1.69649e6	−0.0849656
$833$	4.09450e7	2.04451
$834$	3.28558e6	0.163567
$835$	3.98038e6	0.197564
$836$	1.74255e6	0.0862322
$837$	372278.	0.0183677
$838$	1.64821e7	0.810779
$839$	8.56136e6	0.419892	0.209946	−	0.977713i	$-0.432671\pi$
$839$	8.56136e6	0.419892	0.209946	+	0.977713i	$0.432671\pi$
$840$	2.86188e6	0.139943
$841$	−1.24363e7	−0.606320
$842$	−3.81722e6	−0.185552
$843$	3.81150e6	0.184726
$844$	3.82095e6	0.184636
$845$	4.99365e6	0.240590
$846$	−3.87702e6	−0.186239
$847$	1.39189e7	0.666650
$848$	2.76516e6	0.132048
$849$	1.92851e7	0.918234
$850$	−4.51112e6	−0.214160
$851$	1.66477e7	0.788006
$852$	2.45501e6	0.115866
$853$	−3.54395e7	−1.66769	−0.833844	−	0.552001i	$-0.813865\pi$
$853$	−3.54395e7	−1.66769	−0.833844	+	0.552001i	$0.813865\pi$
$854$	1.93159e7	0.906295
$855$	731025.	0.0341993
$856$	1.12837e7	0.526341
$857$	−3.44320e7	−1.60144	−0.800719	−	0.599040i	$-0.795549\pi$
$857$	−3.44320e7	−1.60144	−0.800719	+	0.599040i	$0.795549\pi$
$858$	4.49833e6	0.208609
$859$	−2.86492e7	−1.32474	−0.662368	−	0.749178i	$-0.730449\pi$
$859$	−2.86492e7	−1.32474	−0.662368	+	0.749178i	$0.730449\pi$
$860$	−446895.	−0.0206044
$861$	−2.78827e7	−1.28182
$862$	2.96000e7	1.35683
$863$	9.18363e6	0.419747	0.209873	−	0.977729i	$-0.432695\pi$
$863$	9.18363e6	0.419747	0.209873	+	0.977729i	$0.432695\pi$
$864$	746496.	0.0340207
$865$	1.78330e7	0.810373
$866$	−2.85882e7	−1.29537
$867$	−1.65256e7	−0.746638
$868$	1.62386e6	0.0731558
$869$	9.90343e6	0.444873
$870$	−2.55746e6	−0.114554
$871$	−1.84142e7	−0.822446
$872$	−724290.	−0.0322568
$873$	9.38698e6	0.416860
$874$	3.72237e6	0.164832
$875$	3.10533e6	0.137116
$876$	−719416.	−0.0316752
$877$	−1.66240e7	−0.729855	−0.364927	−	0.931036i	$-0.618906\pi$
$877$	−1.66240e7	−0.729855	−0.364927	+	0.931036i	$0.618906\pi$
$878$	−1.88745e7	−0.826301
$879$	−2.37535e6	−0.103694
$880$	1.93080e6	0.0840487
$881$	4.29594e7	1.86474	0.932371	−	0.361503i	$-0.117736\pi$
$881$	4.29594e7	1.86474	0.932371	+	0.361503i	$0.117736\pi$
$882$	−7.35193e6	−0.318222
$883$	−783434.	−0.0338143	−0.0169072	−	0.999857i	$-0.505382\pi$
$883$	−783434.	−0.0338143	−0.0169072	+	0.999857i	$0.505382\pi$
$884$	−1.19579e7	−0.514666
$885$	−5.44648e6	−0.233753
$886$	5.51930e6	0.236211
$887$	−3.06447e7	−1.30781	−0.653907	−	0.756575i	$-0.726871\pi$
$887$	−3.06447e7	−1.30781	−0.653907	+	0.756575i	$0.726871\pi$
$888$	3.71984e6	0.158304
$889$	−3.86765e7	−1.64132
$890$	−2.05818e6	−0.0870980
$891$	−1.97937e6	−0.0835283
$892$	1.79555e6	0.0755587
$893$	−4.31976e6	−0.181272
$894$	−1.54128e7	−0.644967
$895$	9.70899e6	0.405151
$896$	3.25618e6	0.135500
$897$	9.60917e6	0.398754
$898$	5.66413e6	0.234392
$899$	−1.45113e6	−0.0598835
$900$	810000.	0.0333333
$901$	1.94906e7	0.799858
$902$	−1.88114e7	−0.769848
$903$	1.99837e6	0.0815561
$904$	−1.40936e7	−0.573589
$905$	−1.16841e7	−0.474215
$906$	−1.14328e7	−0.462737
$907$	1.13750e6	0.0459129	0.0229564	−	0.999736i	$-0.492692\pi$
$907$	1.13750e6	0.0459129	0.0229564	+	0.999736i	$0.492692\pi$
$908$	71994.0	0.00289789
$909$	5.65736e6	0.227093
$910$	8.23151e6	0.329516
$911$	299756.	0.0119666	0.00598331	−	0.999982i	$-0.498095\pi$
$911$	299756.	0.0119666	0.00598331	+	0.999982i	$0.498095\pi$
$912$	831744.	0.0331133
$913$	1.37072e6	0.0544218
$914$	1.35047e7	0.534711
$915$	5.46700e6	0.215872
$916$	2.18468e7	0.860297
$917$	−1.61868e7	−0.635680
$918$	5.26177e6	0.206075
$919$	2.91570e7	1.13882	0.569409	−	0.822055i	$-0.307172\pi$
$919$	2.91570e7	1.13882	0.569409	+	0.822055i	$0.307172\pi$
$920$	4.12451e6	0.160658
$921$	−7.18549e6	−0.279130
$922$	3.33340e7	1.29140
$923$	7.06127e6	0.272822
$924$	−8.63393e6	−0.332682
$925$	4.03628e6	0.155105
$926$	−1.56438e7	−0.599534
$927$	−491959.	−0.0188031
$928$	−2.90982e6	−0.110917
$929$	−1.17436e7	−0.446439	−0.223219	−	0.974768i	$-0.571657\pi$
$929$	−1.17436e7	−0.446439	−0.223219	+	0.974768i	$0.571657\pi$
$930$	459602.	0.0174251
$931$	−8.19150e6	−0.309734
$932$	7.88984e6	0.297528
$933$	−1.82000e7	−0.684490
$934$	4.96980e6	0.186411
$935$	1.36095e7	0.509112
$936$	2.14712e6	0.0801063
$937$	1.29902e7	0.483355	0.241677	−	0.970357i	$-0.422302\pi$
$937$	1.29902e7	0.483355	0.241677	+	0.970357i	$0.422302\pi$
$938$	3.53435e7	1.31160
$939$	3.26381e6	0.120798
$940$	−4.78644e6	−0.176682
$941$	−9.92638e6	−0.365441	−0.182720	−	0.983165i	$-0.558490\pi$
$941$	−9.92638e6	−0.365441	−0.182720	+	0.983165i	$0.558490\pi$
$942$	−1.91562e7	−0.703366
$943$	−4.01842e7	−1.47155
$944$	−6.19689e6	−0.226331
$945$	−3.62206e6	−0.131940
$946$	1.34823e6	0.0489819
$947$	9.18578e6	0.332844	0.166422	−	0.986055i	$-0.446779\pi$
$947$	9.18578e6	0.332844	0.166422	+	0.986055i	$0.446779\pi$
$948$	4.72705e6	0.170832
$949$	−2.06923e6	−0.0745836
$950$	902500.	0.0324443
$951$	1.90235e7	0.682087
$952$	2.29516e7	0.820768
$953$	2.14198e7	0.763981	0.381991	−	0.924166i	$-0.375239\pi$
$953$	2.14198e7	0.763981	0.381991	+	0.924166i	$0.375239\pi$
$954$	−3.49965e6	−0.124496
$955$	2.27966e7	0.808838
$956$	−1.72921e7	−0.611932
$957$	7.71555e6	0.272325
$958$	499551.	0.0175860
$959$	−2.98943e7	−1.04964
$960$	921600.	0.0322749
$961$	−2.83684e7	−0.990891
$962$	1.06992e7	0.372748
$963$	−1.42809e7	−0.496239
$964$	−4.82454e6	−0.167210
$965$	−1.12979e7	−0.390553
$966$	−1.84435e7	−0.635917
$967$	−7.43130e6	−0.255563	−0.127782	−	0.991802i	$-0.540786\pi$
$967$	−7.43130e6	−0.255563	−0.127782	+	0.991802i	$0.540786\pi$
$968$	4.48227e6	0.153748
$969$	5.86266e6	0.200579
$970$	1.15889e7	0.395468
$971$	−1.82581e7	−0.621451	−0.310725	−	0.950500i	$-0.600572\pi$
$971$	−1.82581e7	−0.621451	−0.310725	+	0.950500i	$0.600572\pi$
$972$	−944784.	−0.0320750
$973$	−1.81384e7	−0.614208
$974$	−1.28669e7	−0.434587
$975$	2.32977e6	0.0784878
$976$	6.22023e6	0.209017
$977$	1.40074e7	0.469483	0.234742	−	0.972058i	$-0.424576\pi$
$977$	1.40074e7	0.469483	0.234742	+	0.972058i	$0.424576\pi$
$978$	−1.65406e7	−0.552973
$979$	6.20927e6	0.207054
$980$	−9.07645e6	−0.301892
$981$	916679.	0.0304120
$982$	113941.	0.00377051
$983$	3.36595e7	1.11102	0.555512	−	0.831508i	$-0.312522\pi$
$983$	3.36595e7	1.11102	0.555512	+	0.831508i	$0.312522\pi$
$984$	−8.97896e6	−0.295623
$985$	5.08771e6	0.167083
$986$	−2.05103e7	−0.671860
$987$	2.14034e7	0.699344
$988$	2.39232e6	0.0779698
$989$	2.88003e6	0.0936282
$990$	−2.44367e6	−0.0792419
$991$	4.03291e6	0.130447	0.0652235	−	0.997871i	$-0.479224\pi$
$991$	4.03291e6	0.130447	0.0652235	+	0.997871i	$0.479224\pi$
$992$	522925.	0.0168718
$993$	1.19589e7	0.384873
$994$	−1.35531e7	−0.435085
$995$	−1.58423e7	−0.507296
$996$	654266.	0.0208981
$997$	1.78782e7	0.569622	0.284811	−	0.958584i	$-0.408069\pi$
$997$	1.78782e7	0.569622	0.284811	+	0.958584i	$0.408069\pi$
$998$	−1.43534e7	−0.456171
$999$	−4.70792e6	−0.149250

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.6.a.i.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} -198.741 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} -198.741 q^{7} -64.0000 q^{8} +81.0000 q^{9} +100.000 q^{10} -301.688 q^{11} -144.000 q^{12} -414.182 q^{13} +794.966 q^{14} +225.000 q^{15} +256.000 q^{16} +1804.45 q^{17} -324.000 q^{18} -361.000 q^{19} -400.000 q^{20} +1788.67 q^{21} +1206.75 q^{22} +2577.82 q^{23} +576.000 q^{24} +625.000 q^{25} +1656.73 q^{26} -729.000 q^{27} -3179.86 q^{28} +2841.62 q^{29} -900.000 q^{30} -510.669 q^{31} -1024.00 q^{32} +2715.19 q^{33} -7217.80 q^{34} +4968.53 q^{35} +1296.00 q^{36} +6458.05 q^{37} +1444.00 q^{38} +3727.64 q^{39} +1600.00 q^{40} -15588.5 q^{41} -7154.69 q^{42} +1117.24 q^{43} -4827.01 q^{44} -2025.00 q^{45} -10311.3 q^{46} +11966.1 q^{47} -2304.00 q^{48} +22691.1 q^{49} -2500.00 q^{50} -16240.0 q^{51} -6626.91 q^{52} +10801.4 q^{53} +2916.00 q^{54} +7542.20 q^{55} +12719.4 q^{56} +3249.00 q^{57} -11366.5 q^{58} -24206.6 q^{59} +3600.00 q^{60} +24297.8 q^{61} +2042.68 q^{62} -16098.1 q^{63} +4096.00 q^{64} +10354.6 q^{65} -10860.8 q^{66} +44459.2 q^{67} +28871.2 q^{68} -23200.4 q^{69} -19874.1 q^{70} -17048.7 q^{71} -5184.00 q^{72} +4995.94 q^{73} -25832.2 q^{74} -5625.00 q^{75} -5776.00 q^{76} +59957.9 q^{77} -14910.6 q^{78} -32826.8 q^{79} -6400.00 q^{80} +6561.00 q^{81} +62353.9 q^{82} -4543.51 q^{83} +28618.8 q^{84} -45111.2 q^{85} -4468.95 q^{86} -25574.6 q^{87} +19308.0 q^{88} -20581.8 q^{89} +8100.00 q^{90} +82315.1 q^{91} +41245.1 q^{92} +4596.02 q^{93} -47864.4 q^{94} +9025.00 q^{95} +9216.00 q^{96} +115889. q^{97} -90764.5 q^{98} -24436.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} + 144 q^{6} + 108 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) \) 4 * q - 16 * q^2 - 36 * q^3 + 64 * q^4 - 100 * q^5 + 144 * q^6 + 108 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} + 144 q^{6} + 108 q^{7} - 256 q^{8} + 324 q^{9} + 400 q^{10} - 460 q^{11} - 576 q^{12} + 296 q^{13} - 432 q^{14} + 900 q^{15} + 1024 q^{16} - 412 q^{17} - 1296 q^{18} - 1444 q^{19} - 1600 q^{20} - 972 q^{21} + 1840 q^{22} - 768 q^{23} + 2304 q^{24} + 2500 q^{25} - 1184 q^{26} - 2916 q^{27} + 1728 q^{28} - 1828 q^{29} - 3600 q^{30} + 3856 q^{31} - 4096 q^{32} + 4140 q^{33} + 1648 q^{34} - 2700 q^{35} + 5184 q^{36} + 11456 q^{37} + 5776 q^{38} - 2664 q^{39} + 6400 q^{40} - 12904 q^{41} + 3888 q^{42} + 15096 q^{43} - 7360 q^{44} - 8100 q^{45} + 3072 q^{46} + 17040 q^{47} - 9216 q^{48} + 33708 q^{49} - 10000 q^{50} + 3708 q^{51} + 4736 q^{52} + 16728 q^{53} + 11664 q^{54} + 11500 q^{55} - 6912 q^{56} + 12996 q^{57} + 7312 q^{58} - 19760 q^{59} + 14400 q^{60} + 47168 q^{61} - 15424 q^{62} + 8748 q^{63} + 16384 q^{64} - 7400 q^{65} - 16560 q^{66} + 104580 q^{67} - 6592 q^{68} + 6912 q^{69} + 10800 q^{70} - 36764 q^{71} - 20736 q^{72} + 74356 q^{73} - 45824 q^{74} - 22500 q^{75} - 23104 q^{76} + 75356 q^{77} + 10656 q^{78} + 80920 q^{79} - 25600 q^{80} + 26244 q^{81} + 51616 q^{82} + 19416 q^{83} - 15552 q^{84} + 10300 q^{85} - 60384 q^{86} + 16452 q^{87} + 29440 q^{88} - 4760 q^{89} + 32400 q^{90} + 32288 q^{91} - 12288 q^{92} - 34704 q^{93} - 68160 q^{94} + 36100 q^{95} + 36864 q^{96} + 139572 q^{97} - 134832 q^{98} - 37260 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 - 36 * q^3 + 64 * q^4 - 100 * q^5 + 144 * q^6 + 108 * q^7 - 256 * q^8 + 324 * q^9 + 400 * q^10 - 460 * q^11 - 576 * q^12 + 296 * q^13 - 432 * q^14 + 900 * q^15 + 1024 * q^16 - 412 * q^17 - 1296 * q^18 - 1444 * q^19 - 1600 * q^20 - 972 * q^21 + 1840 * q^22 - 768 * q^23 + 2304 * q^24 + 2500 * q^25 - 1184 * q^26 - 2916 * q^27 + 1728 * q^28 - 1828 * q^29 - 3600 * q^30 + 3856 * q^31 - 4096 * q^32 + 4140 * q^33 + 1648 * q^34 - 2700 * q^35 + 5184 * q^36 + 11456 * q^37 + 5776 * q^38 - 2664 * q^39 + 6400 * q^40 - 12904 * q^41 + 3888 * q^42 + 15096 * q^43 - 7360 * q^44 - 8100 * q^45 + 3072 * q^46 + 17040 * q^47 - 9216 * q^48 + 33708 * q^49 - 10000 * q^50 + 3708 * q^51 + 4736 * q^52 + 16728 * q^53 + 11664 * q^54 + 11500 * q^55 - 6912 * q^56 + 12996 * q^57 + 7312 * q^58 - 19760 * q^59 + 14400 * q^60 + 47168 * q^61 - 15424 * q^62 + 8748 * q^63 + 16384 * q^64 - 7400 * q^65 - 16560 * q^66 + 104580 * q^67 - 6592 * q^68 + 6912 * q^69 + 10800 * q^70 - 36764 * q^71 - 20736 * q^72 + 74356 * q^73 - 45824 * q^74 - 22500 * q^75 - 23104 * q^76 + 75356 * q^77 + 10656 * q^78 + 80920 * q^79 - 25600 * q^80 + 26244 * q^81 + 51616 * q^82 + 19416 * q^83 - 15552 * q^84 + 10300 * q^85 - 60384 * q^86 + 16452 * q^87 + 29440 * q^88 - 4760 * q^89 + 32400 * q^90 + 32288 * q^91 - 12288 * q^92 - 34704 * q^93 - 68160 * q^94 + 36100 * q^95 + 36864 * q^96 + 139572 * q^97 - 134832 * q^98 - 37260 * q^99

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