LMFDB - Embedded newform 570.6.a.j.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} - 25872x^{2} - 1407374x - 6356280 $ x^4 - 25872x^2 - 1407374x - 6356280
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			$-121.221$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +36.0000 q^{6} -171.600 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +36.0000 q^{6} -171.600 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} +409.367 q^{11} -144.000 q^{12} -730.649 q^{13} +686.401 q^{14} -225.000 q^{15} +256.000 q^{16} +248.437 q^{17} -324.000 q^{18} +361.000 q^{19} +400.000 q^{20} +1544.40 q^{21} -1637.47 q^{22} +1713.53 q^{23} +576.000 q^{24} +625.000 q^{25} +2922.59 q^{26} -729.000 q^{27} -2745.60 q^{28} -935.716 q^{29} +900.000 q^{30} +396.792 q^{31} -1024.00 q^{32} -3684.30 q^{33} -993.748 q^{34} -4290.01 q^{35} +1296.00 q^{36} -495.885 q^{37} -1444.00 q^{38} +6575.84 q^{39} -1600.00 q^{40} +17125.9 q^{41} -6177.61 q^{42} -22082.9 q^{43} +6549.87 q^{44} +2025.00 q^{45} -6854.11 q^{46} +11811.6 q^{47} -2304.00 q^{48} +12639.6 q^{49} -2500.00 q^{50} -2235.93 q^{51} -11690.4 q^{52} +6642.10 q^{53} +2916.00 q^{54} +10234.2 q^{55} +10982.4 q^{56} -3249.00 q^{57} +3742.87 q^{58} +606.503 q^{59} -3600.00 q^{60} -33867.0 q^{61} -1587.17 q^{62} -13899.6 q^{63} +4096.00 q^{64} -18266.2 q^{65} +14737.2 q^{66} +4109.20 q^{67} +3974.99 q^{68} -15421.8 q^{69} +17160.0 q^{70} +39645.6 q^{71} -5184.00 q^{72} +40536.8 q^{73} +1983.54 q^{74} -5625.00 q^{75} +5776.00 q^{76} -70247.4 q^{77} -26303.4 q^{78} +62602.2 q^{79} +6400.00 q^{80} +6561.00 q^{81} -68503.6 q^{82} -31307.4 q^{83} +24710.4 q^{84} +6210.93 q^{85} +88331.5 q^{86} +8421.45 q^{87} -26199.5 q^{88} +84209.3 q^{89} -8100.00 q^{90} +125380. q^{91} +27416.4 q^{92} -3571.13 q^{93} -47246.3 q^{94} +9025.00 q^{95} +9216.00 q^{96} +17525.0 q^{97} -50558.6 q^{98} +33158.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} + 100 q^{5} + 144 q^{6} - 108 q^{7} - 256 q^{8} + 324 q^{9} - 400 q^{10} - 246 q^{11} - 576 q^{12} + 640 q^{13} + 432 q^{14} - 900 q^{15} + 1024 q^{16} - 612 q^{17} - 1296 q^{18} + 1444 q^{19} + 1600 q^{20} + 972 q^{21} + 984 q^{22} - 1242 q^{23} + 2304 q^{24} + 2500 q^{25} - 2560 q^{26} - 2916 q^{27} - 1728 q^{28} - 6230 q^{29} + 3600 q^{30} - 11360 q^{31} - 4096 q^{32} + 2214 q^{33} + 2448 q^{34} - 2700 q^{35} + 5184 q^{36} - 4792 q^{37} - 5776 q^{38} - 5760 q^{39} - 6400 q^{40} + 9170 q^{41} - 3888 q^{42} - 11412 q^{43} - 3936 q^{44} + 8100 q^{45} + 4968 q^{46} - 29858 q^{47} - 9216 q^{48} + 31092 q^{49} - 10000 q^{50} + 5508 q^{51} + 10240 q^{52} + 27498 q^{53} + 11664 q^{54} - 6150 q^{55} + 6912 q^{56} - 12996 q^{57} + 24920 q^{58} + 54984 q^{59} - 14400 q^{60} + 20868 q^{61} + 45440 q^{62} - 8748 q^{63} + 16384 q^{64} + 16000 q^{65} - 8856 q^{66} - 20244 q^{67} - 9792 q^{68} + 11178 q^{69} + 10800 q^{70} + 86864 q^{71} - 20736 q^{72} - 3728 q^{73} + 19168 q^{74} - 22500 q^{75} + 23104 q^{76} + 18796 q^{77} + 23040 q^{78} + 164192 q^{79} + 25600 q^{80} + 26244 q^{81} - 36680 q^{82} - 60506 q^{83} + 15552 q^{84} - 15300 q^{85} + 45648 q^{86} + 56070 q^{87} + 15744 q^{88} + 113798 q^{89} - 32400 q^{90} + 159528 q^{91} - 19872 q^{92} + 102240 q^{93} + 119432 q^{94} + 36100 q^{95} + 36864 q^{96} + 79440 q^{97} - 124368 q^{98} - 19926 q^{99}+O(q^{100}) \) 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 - 246 * q^11 - 576 * q^12 + 640 * q^13 + 432 * q^14 - 900 * q^15 + 1024 * q^16 - 612 * q^17 - 1296 * q^18 + 1444 * q^19 + 1600 * q^20 + 972 * q^21 + 984 * q^22 - 1242 * q^23 + 2304 * q^24 + 2500 * q^25 - 2560 * q^26 - 2916 * q^27 - 1728 * q^28 - 6230 * q^29 + 3600 * q^30 - 11360 * q^31 - 4096 * q^32 + 2214 * q^33 + 2448 * q^34 - 2700 * q^35 + 5184 * q^36 - 4792 * q^37 - 5776 * q^38 - 5760 * q^39 - 6400 * q^40 + 9170 * q^41 - 3888 * q^42 - 11412 * q^43 - 3936 * q^44 + 8100 * q^45 + 4968 * q^46 - 29858 * q^47 - 9216 * q^48 + 31092 * q^49 - 10000 * q^50 + 5508 * q^51 + 10240 * q^52 + 27498 * q^53 + 11664 * q^54 - 6150 * q^55 + 6912 * q^56 - 12996 * q^57 + 24920 * q^58 + 54984 * q^59 - 14400 * q^60 + 20868 * q^61 + 45440 * q^62 - 8748 * q^63 + 16384 * q^64 + 16000 * q^65 - 8856 * q^66 - 20244 * q^67 - 9792 * q^68 + 11178 * q^69 + 10800 * q^70 + 86864 * q^71 - 20736 * q^72 - 3728 * q^73 + 19168 * q^74 - 22500 * q^75 + 23104 * q^76 + 18796 * q^77 + 23040 * q^78 + 164192 * q^79 + 25600 * q^80 + 26244 * q^81 - 36680 * q^82 - 60506 * q^83 + 15552 * q^84 - 15300 * q^85 + 45648 * q^86 + 56070 * q^87 + 15744 * q^88 + 113798 * q^89 - 32400 * q^90 + 159528 * q^91 - 19872 * q^92 + 102240 * q^93 + 119432 * q^94 + 36100 * q^95 + 36864 * q^96 + 79440 * q^97 - 124368 * q^98 - 19926 * 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
$7$	−171.600	−1.32365	−0.661824	−	0.749659i	$-0.730218\pi$
$7$	−171.600	−1.32365	−0.661824	+	0.749659i	$0.730218\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	−100.000	−0.316228
$11$	409.367	1.02007	0.510036	−	0.860153i	$-0.329632\pi$
$11$	409.367	1.02007	0.510036	+	0.860153i	$0.329632\pi$
$12$	−144.000	−0.288675
$13$	−730.649	−1.19909	−0.599543	−	0.800343i	$-0.704651\pi$
$13$	−730.649	−1.19909	−0.599543	+	0.800343i	$0.704651\pi$
$14$	686.401	0.935961
$15$	−225.000	−0.258199
$16$	256.000	0.250000
$17$	248.437	0.208494	0.104247	−	0.994551i	$-0.466757\pi$
$17$	248.437	0.208494	0.104247	+	0.994551i	$0.466757\pi$
$18$	−324.000	−0.235702
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	400.000	0.223607
$21$	1544.40	0.764209
$22$	−1637.47	−0.721300
$23$	1713.53	0.675416	0.337708	−	0.941251i	$-0.390348\pi$
$23$	1713.53	0.675416	0.337708	+	0.941251i	$0.390348\pi$
$24$	576.000	0.204124
$25$	625.000	0.200000
$26$	2922.59	0.847882
$27$	−729.000	−0.192450
$28$	−2745.60	−0.661824
$29$	−935.716	−0.206609	−0.103305	−	0.994650i	$-0.532942\pi$
$29$	−935.716	−0.206609	−0.103305	+	0.994650i	$0.532942\pi$
$30$	900.000	0.182574
$31$	396.792	0.0741582	0.0370791	−	0.999312i	$-0.488195\pi$
$31$	396.792	0.0741582	0.0370791	+	0.999312i	$0.488195\pi$
$32$	−1024.00	−0.176777
$33$	−3684.30	−0.588939
$34$	−993.748	−0.147428
$35$	−4290.01	−0.591954
$36$	1296.00	0.166667
$37$	−495.885	−0.0595494	−0.0297747	−	0.999557i	$-0.509479\pi$
$37$	−495.885	−0.0595494	−0.0297747	+	0.999557i	$0.509479\pi$
$38$	−1444.00	−0.162221
$39$	6575.84	0.692293
$40$	−1600.00	−0.158114
$41$	17125.9	1.59109	0.795543	−	0.605897i	$-0.207186\pi$
$41$	17125.9	1.59109	0.795543	+	0.605897i	$0.207186\pi$
$42$	−6177.61	−0.540377
$43$	−22082.9	−1.82131	−0.910656	−	0.413165i	$-0.864423\pi$
$43$	−22082.9	−1.82131	−0.910656	+	0.413165i	$0.864423\pi$
$44$	6549.87	0.510036
$45$	2025.00	0.149071
$46$	−6854.11	−0.477591
$47$	11811.6	0.779944	0.389972	−	0.920827i	$-0.372485\pi$
$47$	11811.6	0.779944	0.389972	+	0.920827i	$0.372485\pi$
$48$	−2304.00	−0.144338
$49$	12639.6	0.752046
$50$	−2500.00	−0.141421
$51$	−2235.93	−0.120374
$52$	−11690.4	−0.599543
$53$	6642.10	0.324800	0.162400	−	0.986725i	$-0.448077\pi$
$53$	6642.10	0.324800	0.162400	+	0.986725i	$0.448077\pi$
$54$	2916.00	0.136083
$55$	10234.2	0.456190
$56$	10982.4	0.467981
$57$	−3249.00	−0.132453
$58$	3742.87	0.146095
$59$	606.503	0.0226831	0.0113416	−	0.999936i	$-0.496390\pi$
$59$	606.503	0.0226831	0.0113416	+	0.999936i	$0.496390\pi$
$60$	−3600.00	−0.129099
$61$	−33867.0	−1.16534	−0.582669	−	0.812710i	$-0.697992\pi$
$61$	−33867.0	−1.16534	−0.582669	+	0.812710i	$0.697992\pi$
$62$	−1587.17	−0.0524377
$63$	−13899.6	−0.441216
$64$	4096.00	0.125000
$65$	−18266.2	−0.536247
$66$	14737.2	0.416443
$67$	4109.20	0.111833	0.0559165	−	0.998435i	$-0.482192\pi$
$67$	4109.20	0.111833	0.0559165	+	0.998435i	$0.482192\pi$
$68$	3974.99	0.104247
$69$	−15421.8	−0.389952
$70$	17160.0	0.418575
$71$	39645.6	0.933360	0.466680	−	0.884426i	$-0.345450\pi$
$71$	39645.6	0.933360	0.466680	+	0.884426i	$0.345450\pi$
$72$	−5184.00	−0.117851
$73$	40536.8	0.890311	0.445156	−	0.895453i	$-0.353148\pi$
$73$	40536.8	0.890311	0.445156	+	0.895453i	$0.353148\pi$
$74$	1983.54	0.0421078
$75$	−5625.00	−0.115470
$76$	5776.00	0.114708
$77$	−70247.4	−1.35022
$78$	−26303.4	−0.489525
$79$	62602.2	1.12855	0.564276	−	0.825586i	$-0.309155\pi$
$79$	62602.2	1.12855	0.564276	+	0.825586i	$0.309155\pi$
$80$	6400.00	0.111803
$81$	6561.00	0.111111
$82$	−68503.6	−1.12507
$83$	−31307.4	−0.498829	−0.249415	−	0.968397i	$-0.580238\pi$
$83$	−31307.4	−0.498829	−0.249415	+	0.968397i	$0.580238\pi$
$84$	24710.4	0.382105
$85$	6210.93	0.0932415
$86$	88331.5	1.28786
$87$	8421.45	0.119286
$88$	−26199.5	−0.360650
$89$	84209.3	1.12690	0.563449	−	0.826151i	$-0.309474\pi$
$89$	84209.3	1.12690	0.563449	+	0.826151i	$0.309474\pi$
$90$	−8100.00	−0.105409
$91$	125380.	1.58717
$92$	27416.4	0.337708
$93$	−3571.13	−0.0428152
$94$	−47246.3	−0.551504
$95$	9025.00	0.102598
$96$	9216.00	0.102062
$97$	17525.0	0.189117	0.0945583	−	0.995519i	$-0.469856\pi$
$97$	17525.0	0.189117	0.0945583	+	0.995519i	$0.469856\pi$
$98$	−50558.6	−0.531777
$99$	33158.7	0.340024
$100$	10000.0	0.100000
$101$	4156.11	0.0405400	0.0202700	−	0.999795i	$-0.493547\pi$
$101$	4156.11	0.0405400	0.0202700	+	0.999795i	$0.493547\pi$
$102$	8943.73	0.0851174
$103$	12638.4	0.117381	0.0586906	−	0.998276i	$-0.481307\pi$
$103$	12638.4	0.117381	0.0586906	+	0.998276i	$0.481307\pi$
$104$	46761.5	0.423941
$105$	38610.1	0.341765
$106$	−26568.4	−0.229668
$107$	−80915.4	−0.683238	−0.341619	−	0.939839i	$-0.610975\pi$
$107$	−80915.4	−0.683238	−0.341619	+	0.939839i	$0.610975\pi$
$108$	−11664.0	−0.0962250
$109$	31453.7	0.253574	0.126787	−	0.991930i	$-0.459533\pi$
$109$	31453.7	0.253574	0.126787	+	0.991930i	$0.459533\pi$
$110$	−40936.7	−0.322575
$111$	4462.97	0.0343808
$112$	−43929.7	−0.330912
$113$	−73882.1	−0.544306	−0.272153	−	0.962254i	$-0.587736\pi$
$113$	−73882.1	−0.544306	−0.272153	+	0.962254i	$0.587736\pi$
$114$	12996.0	0.0936586
$115$	42838.2	0.302055
$116$	−14971.5	−0.103305
$117$	−59182.5	−0.399695
$118$	−2426.01	−0.0160394
$119$	−42631.9	−0.275973
$120$	14400.0	0.0912871
$121$	6530.00	0.0405462
$122$	135468.	0.824018
$123$	−154133.	−0.918614
$124$	6348.68	0.0370791
$125$	15625.0	0.0894427
$126$	55598.5	0.311987
$127$	197930.	1.08894	0.544469	−	0.838781i	$-0.316731\pi$
$127$	197930.	1.08894	0.544469	+	0.838781i	$0.316731\pi$
$128$	−16384.0	−0.0883883
$129$	198746.	1.05154
$130$	73064.9	0.379184
$131$	−296740.	−1.51077	−0.755383	−	0.655283i	$-0.772549\pi$
$131$	−296740.	−1.51077	−0.755383	+	0.655283i	$0.772549\pi$
$132$	−58948.8	−0.294469
$133$	−61947.7	−0.303666
$134$	−16436.8	−0.0790779
$135$	−18225.0	−0.0860663
$136$	−15900.0	−0.0737138
$137$	−103798.	−0.472486	−0.236243	−	0.971694i	$-0.575916\pi$
$137$	−103798.	−0.472486	−0.236243	+	0.971694i	$0.575916\pi$
$138$	61687.0	0.275738
$139$	−208201.	−0.914001	−0.457000	−	0.889466i	$-0.651076\pi$
$139$	−208201.	−0.914001	−0.457000	+	0.889466i	$0.651076\pi$
$140$	−68640.1	−0.295977
$141$	−106304.	−0.450301
$142$	−158582.	−0.659985
$143$	−299103.	−1.22315
$144$	20736.0	0.0833333
$145$	−23392.9	−0.0923984
$146$	−162147.	−0.629545
$147$	−113757.	−0.434194
$148$	−7934.17	−0.0297747
$149$	−502065.	−1.85265	−0.926327	−	0.376721i	$-0.877051\pi$
$149$	−502065.	−1.85265	−0.926327	+	0.376721i	$0.877051\pi$
$150$	22500.0	0.0816497
$151$	−367258.	−1.31078	−0.655389	−	0.755292i	$-0.727495\pi$
$151$	−367258.	−1.31078	−0.655389	+	0.755292i	$0.727495\pi$
$152$	−23104.0	−0.0811107
$153$	20123.4	0.0694981
$154$	280990.	0.954747
$155$	9919.80	0.0331645
$156$	105213.	0.346146
$157$	154312.	0.499632	0.249816	−	0.968293i	$-0.419630\pi$
$157$	154312.	0.499632	0.249816	+	0.968293i	$0.419630\pi$
$158$	−250409.	−0.798007
$159$	−59778.9	−0.187523
$160$	−25600.0	−0.0790569
$161$	−294042.	−0.894014
$162$	−26244.0	−0.0785674
$163$	−463772.	−1.36721	−0.683606	−	0.729852i	$-0.739589\pi$
$163$	−463772.	−1.36721	−0.683606	+	0.729852i	$0.739589\pi$
$164$	274014.	0.795543
$165$	−92107.5	−0.263381
$166$	125230.	0.352726
$167$	−540213.	−1.49891	−0.749453	−	0.662058i	$-0.769683\pi$
$167$	−540213.	−1.49891	−0.749453	+	0.662058i	$0.769683\pi$
$168$	−98841.7	−0.270189
$169$	162555.	0.437807
$170$	−24843.7	−0.0659317
$171$	29241.0	0.0764719
$172$	−353326.	−0.910656
$173$	−381768.	−0.969804	−0.484902	−	0.874569i	$-0.661145\pi$
$173$	−381768.	−0.969804	−0.484902	+	0.874569i	$0.661145\pi$
$174$	−33685.8	−0.0843478
$175$	−107250.	−0.264730
$176$	104798.	0.255018
$177$	−5458.53	−0.0130961
$178$	−336837.	−0.796838
$179$	197548.	0.460828	0.230414	−	0.973093i	$-0.425992\pi$
$179$	197548.	0.460828	0.230414	+	0.973093i	$0.425992\pi$
$180$	32400.0	0.0745356
$181$	−641241.	−1.45487	−0.727436	−	0.686176i	$-0.759288\pi$
$181$	−641241.	−1.45487	−0.727436	+	0.686176i	$0.759288\pi$
$182$	−501518.	−1.12230
$183$	304803.	0.672808
$184$	−109666.	−0.238796
$185$	−12397.1	−0.0266313
$186$	14284.5	0.0302749
$187$	101702.	0.212679
$188$	188985.	0.389972
$189$	125097.	0.254736
$190$	−36100.0	−0.0725476
$191$	−25116.2	−0.0498162	−0.0249081	−	0.999690i	$-0.507929\pi$
$191$	−25116.2	−0.0498162	−0.0249081	+	0.999690i	$0.507929\pi$
$192$	−36864.0	−0.0721688
$193$	−53912.4	−0.104183	−0.0520913	−	0.998642i	$-0.516589\pi$
$193$	−53912.4	−0.104183	−0.0520913	+	0.998642i	$0.516589\pi$
$194$	−70100.2	−0.133726
$195$	164396.	0.309603
$196$	202234.	0.376023
$197$	483800.	0.888179	0.444090	−	0.895982i	$-0.353527\pi$
$197$	483800.	0.888179	0.444090	+	0.895982i	$0.353527\pi$
$198$	−132635.	−0.240433
$199$	−808124.	−1.44659	−0.723295	−	0.690540i	$-0.757373\pi$
$199$	−808124.	−1.44659	−0.723295	+	0.690540i	$0.757373\pi$
$200$	−40000.0	−0.0707107
$201$	−36982.8	−0.0645668
$202$	−16624.4	−0.0286661
$203$	160569.	0.273478
$204$	−35774.9	−0.0601871
$205$	428147.	0.711555
$206$	−50553.6	−0.0830011
$207$	138796.	0.225139
$208$	−187046.	−0.299771
$209$	147781.	0.234020
$210$	−154440.	−0.241664
$211$	−28301.7	−0.0437629	−0.0218814	−	0.999761i	$-0.506966\pi$
$211$	−28301.7	−0.0437629	−0.0218814	+	0.999761i	$0.506966\pi$
$212$	106274.	0.162400
$213$	−356811.	−0.538876
$214$	323662.	0.483122
$215$	−552072.	−0.814516
$216$	46656.0	0.0680414
$217$	−68089.6	−0.0981594
$218$	−125815.	−0.179304
$219$	−364831.	−0.514022
$220$	163747.	0.228095
$221$	−181520.	−0.250002
$222$	−17851.9	−0.0243109
$223$	1.24055e6	1.67052	0.835260	−	0.549855i	$-0.185317\pi$
$223$	1.24055e6	1.67052	0.835260	+	0.549855i	$0.185317\pi$
$224$	175719.	0.233990
$225$	50625.0	0.0666667
$226$	295528.	0.384882
$227$	−1.09798e6	−1.41427	−0.707134	−	0.707080i	$-0.750012\pi$
$227$	−1.09798e6	−1.41427	−0.707134	+	0.707080i	$0.750012\pi$
$228$	−51984.0	−0.0662266
$229$	971661.	1.22441	0.612204	−	0.790700i	$-0.290283\pi$
$229$	971661.	1.22441	0.612204	+	0.790700i	$0.290283\pi$
$230$	−171353.	−0.213585
$231$	632227.	0.779548
$232$	59885.9	0.0730473
$233$	84185.8	0.101590	0.0507948	−	0.998709i	$-0.483825\pi$
$233$	84185.8	0.101590	0.0507948	+	0.998709i	$0.483825\pi$
$234$	236730.	0.282627
$235$	295290.	0.348802
$236$	9704.05	0.0113416
$237$	−563420.	−0.651570
$238$	170527.	0.195143
$239$	−1.37097e6	−1.55251	−0.776253	−	0.630422i	$-0.782882\pi$
$239$	−1.37097e6	−1.55251	−0.776253	+	0.630422i	$0.782882\pi$
$240$	−57600.0	−0.0645497
$241$	936952.	1.03914	0.519571	−	0.854427i	$-0.326092\pi$
$241$	936952.	1.03914	0.519571	+	0.854427i	$0.326092\pi$
$242$	−26120.0	−0.0286705
$243$	−59049.0	−0.0641500
$244$	−541872.	−0.582669
$245$	315991.	0.336325
$246$	616532.	0.649558
$247$	−263764.	−0.275089
$248$	−25394.7	−0.0262189
$249$	281767.	0.287999
$250$	−62500.0	−0.0632456
$251$	−1.30701e6	−1.30946	−0.654732	−	0.755861i	$-0.727218\pi$
$251$	−1.30701e6	−1.30946	−0.654732	+	0.755861i	$0.727218\pi$
$252$	−222394.	−0.220608
$253$	701461.	0.688973
$254$	−791722.	−0.769996
$255$	−55898.3	−0.0538330
$256$	65536.0	0.0625000
$257$	−996635.	−0.941246	−0.470623	−	0.882334i	$-0.655971\pi$
$257$	−996635.	−0.941246	−0.470623	+	0.882334i	$0.655971\pi$
$258$	−794983.	−0.743548
$259$	85094.1	0.0788224
$260$	−292259.	−0.268124
$261$	−75793.0	−0.0688697
$262$	1.18696e6	1.06827
$263$	−380225.	−0.338962	−0.169481	−	0.985533i	$-0.554209\pi$
$263$	−380225.	−0.338962	−0.169481	+	0.985533i	$0.554209\pi$
$264$	235795.	0.208221
$265$	166053.	0.145255
$266$	247791.	0.214724
$267$	−757884.	−0.650615
$268$	65747.2	0.0559165
$269$	693730.	0.584534	0.292267	−	0.956337i	$-0.405590\pi$
$269$	693730.	0.584534	0.292267	+	0.956337i	$0.405590\pi$
$270$	72900.0	0.0608581
$271$	−2.05362e6	−1.69862	−0.849311	−	0.527892i	$-0.822983\pi$
$271$	−2.05362e6	−1.69862	−0.849311	+	0.527892i	$0.822983\pi$
$272$	63599.9	0.0521236
$273$	−1.12842e6	−0.916352
$274$	415193.	0.334098
$275$	255854.	0.204014
$276$	−246748.	−0.194976
$277$	−191006.	−0.149571	−0.0747855	−	0.997200i	$-0.523827\pi$
$277$	−191006.	−0.149571	−0.0747855	+	0.997200i	$0.523827\pi$
$278$	832806.	0.646296
$279$	32140.2	0.0247194
$280$	274560.	0.209287
$281$	771836.	0.583121	0.291561	−	0.956552i	$-0.405825\pi$
$281$	771836.	0.583121	0.291561	+	0.956552i	$0.405825\pi$
$282$	425217.	0.318411
$283$	−442073.	−0.328117	−0.164058	−	0.986451i	$-0.552459\pi$
$283$	−442073.	−0.328117	−0.164058	+	0.986451i	$0.552459\pi$
$284$	634330.	0.466680
$285$	−81225.0	−0.0592349
$286$	1.19641e6	0.864900
$287$	−2.93881e6	−2.10604
$288$	−82944.0	−0.0589256
$289$	−1.35814e6	−0.956530
$290$	93571.6	0.0653355
$291$	−157725.	−0.109187
$292$	648588.	0.445156
$293$	882501.	0.600546	0.300273	−	0.953853i	$-0.402922\pi$
$293$	882501.	0.600546	0.300273	+	0.953853i	$0.402922\pi$
$294$	455027.	0.307022
$295$	15162.6	0.0101442
$296$	31736.7	0.0210539
$297$	−298428.	−0.196313
$298$	2.00826e6	1.31002
$299$	−1.25199e6	−0.809882
$300$	−90000.0	−0.0577350
$301$	3.78943e6	2.41078
$302$	1.46903e6	0.926860
$303$	−37405.0	−0.0234058
$304$	92416.0	0.0573539
$305$	−846674.	−0.521155
$306$	−80493.6	−0.0491426
$307$	−2.40614e6	−1.45705	−0.728527	−	0.685017i	$-0.759795\pi$
$307$	−2.40614e6	−1.45705	−0.728527	+	0.685017i	$0.759795\pi$
$308$	−1.12396e6	−0.675108
$309$	−113746.	−0.0677701
$310$	−39679.2	−0.0234509
$311$	671897.	0.393914	0.196957	−	0.980412i	$-0.436894\pi$
$311$	671897.	0.393914	0.196957	+	0.980412i	$0.436894\pi$
$312$	−420854.	−0.244762
$313$	−2.60623e6	−1.50367	−0.751833	−	0.659353i	$-0.770830\pi$
$313$	−2.60623e6	−1.50367	−0.751833	+	0.659353i	$0.770830\pi$
$314$	−617248.	−0.353293
$315$	−347491.	−0.197318
$316$	1.00164e6	0.564276
$317$	1.80892e6	1.01104	0.505522	−	0.862814i	$-0.331300\pi$
$317$	1.80892e6	1.01104	0.505522	+	0.862814i	$0.331300\pi$
$318$	239116.	0.132599
$319$	−383051.	−0.210756
$320$	102400.	0.0559017
$321$	728239.	0.394468
$322$	1.17617e6	0.632163
$323$	89685.8	0.0478319
$324$	104976.	0.0555556
$325$	−456655.	−0.239817
$326$	1.85509e6	0.966764
$327$	−283083.	−0.146401
$328$	−1.09606e6	−0.562534
$329$	−2.02687e6	−1.03237
$330$	368430.	0.186239
$331$	−1.77150e6	−0.888735	−0.444367	−	0.895845i	$-0.646571\pi$
$331$	−1.77150e6	−0.888735	−0.444367	+	0.895845i	$0.646571\pi$
$332$	−500919.	−0.249415
$333$	−40166.7	−0.0198498
$334$	2.16085e6	1.05989
$335$	102730.	0.0500132
$336$	395367.	0.191052
$337$	1.77477e6	0.851271	0.425636	−	0.904895i	$-0.360051\pi$
$337$	1.77477e6	0.851271	0.425636	+	0.904895i	$0.360051\pi$
$338$	−650218.	−0.309576
$339$	664939.	0.314255
$340$	99374.8	0.0466207
$341$	162433.	0.0756466
$342$	−116964.	−0.0540738
$343$	715119.	0.328203
$344$	1.41330e6	0.643931
$345$	−385544.	−0.174392
$346$	1.52707e6	0.685755
$347$	−2.21658e6	−0.988235	−0.494117	−	0.869395i	$-0.664509\pi$
$347$	−2.21658e6	−0.988235	−0.494117	+	0.869395i	$0.664509\pi$
$348$	134743.	0.0596429
$349$	2.44678e6	1.07531	0.537653	−	0.843166i	$-0.319311\pi$
$349$	2.44678e6	1.07531	0.537653	+	0.843166i	$0.319311\pi$
$350$	429001.	0.187192
$351$	532643.	0.230764
$352$	−419191.	−0.180325
$353$	637853.	0.272448	0.136224	−	0.990678i	$-0.456503\pi$
$353$	637853.	0.272448	0.136224	+	0.990678i	$0.456503\pi$
$354$	21834.1	0.00926035
$355$	991141.	0.417411
$356$	1.34735e6	0.563449
$357$	383687.	0.159333
$358$	−790191.	−0.325855
$359$	3.99786e6	1.63716	0.818580	−	0.574392i	$-0.194761\pi$
$359$	3.99786e6	1.63716	0.818580	+	0.574392i	$0.194761\pi$
$360$	−129600.	−0.0527046
$361$	130321.	0.0526316
$362$	2.56496e6	1.02875
$363$	−58770.0	−0.0234093
$364$	2.00607e6	0.793584
$365$	1.01342e6	0.398159
$366$	−1.21921e6	−0.475747
$367$	2.49330e6	0.966294	0.483147	−	0.875539i	$-0.339494\pi$
$367$	2.49330e6	0.966294	0.483147	+	0.875539i	$0.339494\pi$
$368$	438663.	0.168854
$369$	1.38720e6	0.530362
$370$	49588.5	0.0188312
$371$	−1.13979e6	−0.429921
$372$	−57138.1	−0.0214076
$373$	−3.44698e6	−1.28282	−0.641411	−	0.767197i	$-0.721651\pi$
$373$	−3.44698e6	−1.28282	−0.641411	+	0.767197i	$0.721651\pi$
$374$	−406807.	−0.150387
$375$	−140625.	−0.0516398
$376$	−755941.	−0.275752
$377$	683680.	0.247742
$378$	−500386.	−0.180126
$379$	1.53562e6	0.549143	0.274572	−	0.961567i	$-0.411464\pi$
$379$	1.53562e6	0.549143	0.274572	+	0.961567i	$0.411464\pi$
$380$	144400.	0.0512989
$381$	−1.78137e6	−0.628699
$382$	100465.	0.0352254
$383$	−3.26271e6	−1.13653	−0.568267	−	0.822844i	$-0.692386\pi$
$383$	−3.26271e6	−1.13653	−0.568267	+	0.822844i	$0.692386\pi$
$384$	147456.	0.0510310
$385$	−1.75619e6	−0.603835
$386$	215650.	0.0736683
$387$	−1.78871e6	−0.607104
$388$	280401.	0.0945583
$389$	−2.17490e6	−0.728728	−0.364364	−	0.931257i	$-0.618714\pi$
$389$	−2.17490e6	−0.728728	−0.364364	+	0.931257i	$0.618714\pi$
$390$	−657584.	−0.218922
$391$	425704.	0.140820
$392$	−808937.	−0.265889
$393$	2.67066e6	0.872242
$394$	−1.93520e6	−0.628038
$395$	1.56506e6	0.504704
$396$	530539.	0.170012
$397$	4.42115e6	1.40786	0.703930	−	0.710270i	$-0.251427\pi$
$397$	4.42115e6	1.40786	0.703930	+	0.710270i	$0.251427\pi$
$398$	3.23250e6	1.02289
$399$	557529.	0.175322
$400$	160000.	0.0500000
$401$	−761947.	−0.236627	−0.118313	−	0.992976i	$-0.537749\pi$
$401$	−761947.	−0.236627	−0.118313	+	0.992976i	$0.537749\pi$
$402$	147931.	0.0456556
$403$	−289916.	−0.0889220
$404$	66497.7	0.0202700
$405$	164025.	0.0496904
$406$	−642277.	−0.193378
$407$	−202999.	−0.0607446
$408$	143100.	0.0425587
$409$	−2.47581e6	−0.731829	−0.365915	−	0.930648i	$-0.619244\pi$
$409$	−2.47581e6	−0.731829	−0.365915	+	0.930648i	$0.619244\pi$
$410$	−1.71259e6	−0.503146
$411$	934185.	0.272790
$412$	202214.	0.0586906
$413$	−104076.	−0.0300245
$414$	−555183.	−0.159197
$415$	−782685.	−0.223083
$416$	748184.	0.211970
$417$	1.87381e6	0.527699
$418$	−591125.	−0.165477
$419$	3.00254e6	0.835514	0.417757	−	0.908559i	$-0.362816\pi$
$419$	3.00254e6	0.835514	0.417757	+	0.908559i	$0.362816\pi$
$420$	617761.	0.170882
$421$	−999018.	−0.274706	−0.137353	−	0.990522i	$-0.543859\pi$
$421$	−999018.	−0.274706	−0.137353	+	0.990522i	$0.543859\pi$
$422$	113207.	0.0309450
$423$	956738.	0.259981
$424$	−425094.	−0.114834
$425$	155273.	0.0416989
$426$	1.42724e6	0.381043
$427$	5.81158e6	1.54250
$428$	−1.29465e6	−0.341619
$429$	2.69193e6	0.706188
$430$	2.20829e6	0.575950
$431$	2.42741e6	0.629433	0.314717	−	0.949186i	$-0.398091\pi$
$431$	2.42741e6	0.629433	0.314717	+	0.949186i	$0.398091\pi$
$432$	−186624.	−0.0481125
$433$	−1.03044e6	−0.264120	−0.132060	−	0.991242i	$-0.542159\pi$
$433$	−1.03044e6	−0.264120	−0.132060	+	0.991242i	$0.542159\pi$
$434$	272359.	0.0694091
$435$	210536.	0.0533462
$436$	503259.	0.126787
$437$	618584.	0.154951
$438$	1.45932e6	0.363468
$439$	−1.35893e6	−0.336540	−0.168270	−	0.985741i	$-0.553818\pi$
$439$	−1.35893e6	−0.336540	−0.168270	+	0.985741i	$0.553818\pi$
$440$	−654987.	−0.161287
$441$	1.02381e6	0.250682
$442$	726081.	0.176778
$443$	1.54725e6	0.374586	0.187293	−	0.982304i	$-0.440029\pi$
$443$	1.54725e6	0.374586	0.187293	+	0.982304i	$0.440029\pi$
$444$	71407.5	0.0171904
$445$	2.10523e6	0.503965
$446$	−4.96220e6	−1.18124
$447$	4.51858e6	1.06963
$448$	−702875.	−0.165456
$449$	−1.84939e6	−0.432924	−0.216462	−	0.976291i	$-0.569452\pi$
$449$	−1.84939e6	−0.432924	−0.216462	+	0.976291i	$0.569452\pi$
$450$	−202500.	−0.0471405
$451$	7.01077e6	1.62302
$452$	−1.18211e6	−0.272153
$453$	3.30532e6	0.756778
$454$	4.39194e6	1.00004
$455$	3.13449e6	0.709803
$456$	207936.	0.0468293
$457$	−2.80271e6	−0.627751	−0.313876	−	0.949464i	$-0.601628\pi$
$457$	−2.80271e6	−0.627751	−0.313876	+	0.949464i	$0.601628\pi$
$458$	−3.88665e6	−0.865787
$459$	−181111.	−0.0401247
$460$	685411.	0.151028
$461$	7.18545e6	1.57471	0.787357	−	0.616497i	$-0.211449\pi$
$461$	7.18545e6	1.57471	0.787357	+	0.616497i	$0.211449\pi$
$462$	−2.52891e6	−0.551224
$463$	−2.63573e6	−0.571411	−0.285706	−	0.958317i	$-0.592228\pi$
$463$	−2.63573e6	−0.571411	−0.285706	+	0.958317i	$0.592228\pi$
$464$	−239543.	−0.0516523
$465$	−89278.2	−0.0191476
$466$	−336743.	−0.0718346
$467$	−8.54094e6	−1.81223	−0.906115	−	0.423031i	$-0.860966\pi$
$467$	−8.54094e6	−1.81223	−0.906115	+	0.423031i	$0.860966\pi$
$468$	−946921.	−0.199848
$469$	−705139.	−0.148028
$470$	−1.18116e6	−0.246640
$471$	−1.38881e6	−0.288463
$472$	−38816.2	−0.00801970
$473$	−9.03999e6	−1.85787
$474$	2.25368e6	0.460730
$475$	225625.	0.0458831
$476$	−682110.	−0.137987
$477$	538010.	0.108267
$478$	5.48388e6	1.09779
$479$	2.83289e6	0.564145	0.282072	−	0.959393i	$-0.408978\pi$
$479$	2.83289e6	0.564145	0.282072	+	0.959393i	$0.408978\pi$
$480$	230400.	0.0456435
$481$	362318.	0.0714048
$482$	−3.74781e6	−0.734784
$483$	2.64638e6	0.516159
$484$	104480.	0.0202731
$485$	438126.	0.0845755
$486$	236196.	0.0453609
$487$	8.31365e6	1.58843	0.794217	−	0.607634i	$-0.207881\pi$
$487$	8.31365e6	1.58843	0.794217	+	0.607634i	$0.207881\pi$
$488$	2.16749e6	0.412009
$489$	4.17395e6	0.789360
$490$	−1.26396e6	−0.237818
$491$	−5.74720e6	−1.07585	−0.537926	−	0.842992i	$-0.680792\pi$
$491$	−5.74720e6	−1.07585	−0.537926	+	0.842992i	$0.680792\pi$
$492$	−2.46613e6	−0.459307
$493$	−232467.	−0.0430768
$494$	1.05506e6	0.194517
$495$	828967.	0.152063
$496$	101579.	0.0185395
$497$	−6.80320e6	−1.23544
$498$	−1.12707e6	−0.203646
$499$	−1.91364e6	−0.344040	−0.172020	−	0.985093i	$-0.555029\pi$
$499$	−1.91364e6	−0.344040	−0.172020	+	0.985093i	$0.555029\pi$
$500$	250000.	0.0447214
$501$	4.86192e6	0.865393
$502$	5.22802e6	0.925930
$503$	−5.35043e6	−0.942906	−0.471453	−	0.881891i	$-0.656270\pi$
$503$	−5.35043e6	−0.942906	−0.471453	+	0.881891i	$0.656270\pi$
$504$	889576.	0.155994
$505$	103903.	0.0181300
$506$	−2.80584e6	−0.487178
$507$	−1.46299e6	−0.252768
$508$	3.16689e6	0.544469
$509$	−1.51272e6	−0.258801	−0.129400	−	0.991592i	$-0.541305\pi$
$509$	−1.51272e6	−0.258801	−0.129400	+	0.991592i	$0.541305\pi$
$510$	223593.	0.0380657
$511$	−6.95612e6	−1.17846
$512$	−262144.	−0.0441942
$513$	−263169.	−0.0441511
$514$	3.98654e6	0.665562
$515$	315960.	0.0524945
$516$	3.17993e6	0.525768
$517$	4.83527e6	0.795599
$518$	−340376.	−0.0557359
$519$	3.43591e6	0.559916
$520$	1.16904e6	0.189592
$521$	3.46529e6	0.559300	0.279650	−	0.960102i	$-0.409782\pi$
$521$	3.46529e6	0.559300	0.279650	+	0.960102i	$0.409782\pi$
$522$	303172.	0.0486982
$523$	−1.12493e7	−1.79833	−0.899165	−	0.437609i	$-0.855825\pi$
$523$	−1.12493e7	−1.79833	−0.899165	+	0.437609i	$0.855825\pi$
$524$	−4.74784e6	−0.755383
$525$	965251.	0.152842
$526$	1.52090e6	0.239683
$527$	98577.9	0.0154615
$528$	−943181.	−0.147235
$529$	−3.50017e6	−0.543813
$530$	−664210.	−0.102711
$531$	49126.8	0.00756105
$532$	−991163.	−0.151833
$533$	−1.25130e7	−1.90785
$534$	3.03153e6	0.460055
$535$	−2.02289e6	−0.305553
$536$	−262989.	−0.0395389
$537$	−1.77793e6	−0.266059
$538$	−2.77492e6	−0.413328
$539$	5.17425e6	0.767141
$540$	−291600.	−0.0430331
$541$	−2.89954e6	−0.425928	−0.212964	−	0.977060i	$-0.568312\pi$
$541$	−2.89954e6	−0.425928	−0.212964	+	0.977060i	$0.568312\pi$
$542$	8.21448e6	1.20111
$543$	5.77116e6	0.839970
$544$	−254400.	−0.0368569
$545$	786342.	0.113402
$546$	4.51366e6	0.647959
$547$	5.58514e6	0.798116	0.399058	−	0.916926i	$-0.369337\pi$
$547$	5.58514e6	0.798116	0.399058	+	0.916926i	$0.369337\pi$
$548$	−1.66077e6	−0.236243
$549$	−2.74322e6	−0.388446
$550$	−1.02342e6	−0.144260
$551$	−337794.	−0.0473994
$552$	986992.	0.137869
$553$	−1.07426e7	−1.49381
$554$	764024.	0.105763
$555$	111574.	0.0153756
$556$	−3.33122e6	−0.457000
$557$	8.64348e6	1.18046	0.590229	−	0.807236i	$-0.299037\pi$
$557$	8.64348e6	1.18046	0.590229	+	0.807236i	$0.299037\pi$
$558$	−128561.	−0.0174792
$559$	1.61348e7	2.18391
$560$	−1.09824e6	−0.147988
$561$	−915317.	−0.122790
$562$	−3.08734e6	−0.412329
$563$	−6.25367e6	−0.831503	−0.415751	−	0.909478i	$-0.636481\pi$
$563$	−6.25367e6	−0.831503	−0.415751	+	0.909478i	$0.636481\pi$
$564$	−1.70087e6	−0.225150
$565$	−1.84705e6	−0.243421
$566$	1.76829e6	0.232014
$567$	−1.12587e6	−0.147072
$568$	−2.53732e6	−0.329993
$569$	4.27118e6	0.553054	0.276527	−	0.961006i	$-0.410816\pi$
$569$	4.27118e6	0.553054	0.276527	+	0.961006i	$0.410816\pi$
$570$	324900.	0.0418854
$571$	5.52096e6	0.708638	0.354319	−	0.935125i	$-0.384713\pi$
$571$	5.52096e6	0.708638	0.354319	+	0.935125i	$0.384713\pi$
$572$	−4.78565e6	−0.611577
$573$	226046.	0.0287614
$574$	1.17552e7	1.48919
$575$	1.07095e6	0.135083
$576$	331776.	0.0416667
$577$	9.36372e6	1.17087	0.585435	−	0.810719i	$-0.300924\pi$
$577$	9.36372e6	1.17087	0.585435	+	0.810719i	$0.300924\pi$
$578$	5.43254e6	0.676369
$579$	485212.	0.0601499
$580$	−374287.	−0.0461992
$581$	5.37236e6	0.660275
$582$	630901.	0.0772065
$583$	2.71905e6	0.331319
$584$	−2.59435e6	−0.314773
$585$	−1.47956e6	−0.178749
$586$	−3.53000e6	−0.424650
$587$	−884221.	−0.105917	−0.0529585	−	0.998597i	$-0.516865\pi$
$587$	−884221.	−0.105917	−0.0529585	+	0.998597i	$0.516865\pi$
$588$	−1.82011e6	−0.217097
$589$	143242.	0.0170130
$590$	−60650.3	−0.00717304
$591$	−4.35420e6	−0.512791
$592$	−126947.	−0.0148873
$593$	511432.	0.0597243	0.0298621	−	0.999554i	$-0.490493\pi$
$593$	511432.	0.0597243	0.0298621	+	0.999554i	$0.490493\pi$
$594$	1.19371e6	0.138814
$595$	−1.06580e6	−0.123419
$596$	−8.03304e6	−0.926327
$597$	7.27311e6	0.835189
$598$	5.00795e6	0.572673
$599$	−703758.	−0.0801412	−0.0400706	−	0.999197i	$-0.512758\pi$
$599$	−703758.	−0.0801412	−0.0400706	+	0.999197i	$0.512758\pi$
$600$	360000.	0.0408248
$601$	709095.	0.0800790	0.0400395	−	0.999198i	$-0.487252\pi$
$601$	709095.	0.0800790	0.0400395	+	0.999198i	$0.487252\pi$
$602$	−1.51577e7	−1.70468
$603$	332845.	0.0372777
$604$	−5.87613e6	−0.655389
$605$	163250.	0.0181328
$606$	149620.	0.0165504
$607$	2.68774e6	0.296084	0.148042	−	0.988981i	$-0.452703\pi$
$607$	2.68774e6	0.296084	0.148042	+	0.988981i	$0.452703\pi$
$608$	−369664.	−0.0405554
$609$	−1.44512e6	−0.157892
$610$	3.38670e6	0.368512
$611$	−8.63012e6	−0.935220
$612$	321974.	0.0347490
$613$	−411753.	−0.0442574	−0.0221287	−	0.999755i	$-0.507044\pi$
$613$	−411753.	−0.0442574	−0.0221287	+	0.999755i	$0.507044\pi$
$614$	9.62458e6	1.03029
$615$	−3.85333e6	−0.410817
$616$	4.49583e6	0.477374
$617$	1.67449e6	0.177080	0.0885402	−	0.996073i	$-0.471780\pi$
$617$	1.67449e6	0.177080	0.0885402	+	0.996073i	$0.471780\pi$
$618$	454982.	0.0479207
$619$	−5.59624e6	−0.587043	−0.293521	−	0.955953i	$-0.594827\pi$
$619$	−5.59624e6	−0.587043	−0.293521	+	0.955953i	$0.594827\pi$
$620$	158717.	0.0165823
$621$	−1.24916e6	−0.129984
$622$	−2.68759e6	−0.278539
$623$	−1.44503e7	−1.49162
$624$	1.68341e6	0.173073
$625$	390625.	0.0400000
$626$	1.04249e7	1.06325
$627$	−1.33003e6	−0.135112
$628$	2.46899e6	0.249816
$629$	−123196.	−0.0124157
$630$	1.38996e6	0.139525
$631$	8.26101e6	0.825961	0.412980	−	0.910740i	$-0.364488\pi$
$631$	8.26101e6	0.825961	0.412980	+	0.910740i	$0.364488\pi$
$632$	−4.00654e6	−0.399004
$633$	254715.	0.0252665
$634$	−7.23566e6	−0.714916
$635$	4.94826e6	0.486988
$636$	−956463.	−0.0937616
$637$	−9.23514e6	−0.901768
$638$	1.53220e6	0.149027
$639$	3.21130e6	0.311120
$640$	−409600.	−0.0395285
$641$	−9.91722e6	−0.953333	−0.476667	−	0.879084i	$-0.658155\pi$
$641$	−9.91722e6	−0.953333	−0.476667	+	0.879084i	$0.658155\pi$
$642$	−2.91296e6	−0.278931
$643$	−1.85918e7	−1.77334	−0.886672	−	0.462398i	$-0.846989\pi$
$643$	−1.85918e7	−1.77334	−0.886672	+	0.462398i	$0.846989\pi$
$644$	−4.70467e6	−0.447007
$645$	4.96865e6	0.470261
$646$	−358743.	−0.0338222
$647$	1.58431e7	1.48792	0.743961	−	0.668223i	$-0.232945\pi$
$647$	1.58431e7	1.48792	0.743961	+	0.668223i	$0.232945\pi$
$648$	−419904.	−0.0392837
$649$	248282.	0.0231384
$650$	1.82662e6	0.169576
$651$	612807.	0.0566723
$652$	−7.42035e6	−0.683606
$653$	−1.30198e7	−1.19487	−0.597435	−	0.801918i	$-0.703813\pi$
$653$	−1.30198e7	−1.19487	−0.597435	+	0.801918i	$0.703813\pi$
$654$	1.13233e6	0.103521
$655$	−7.41849e6	−0.675635
$656$	4.38423e6	0.397771
$657$	3.28348e6	0.296770
$658$	8.10748e6	0.729997
$659$	4.47538e6	0.401436	0.200718	−	0.979649i	$-0.435672\pi$
$659$	4.47538e6	0.401436	0.200718	+	0.979649i	$0.435672\pi$
$660$	−1.47372e6	−0.131691
$661$	406289.	0.0361686	0.0180843	−	0.999836i	$-0.494243\pi$
$661$	406289.	0.0361686	0.0180843	+	0.999836i	$0.494243\pi$
$662$	7.08601e6	0.628430
$663$	1.63368e6	0.144339
$664$	2.00367e6	0.176363
$665$	−1.54869e6	−0.135804
$666$	160667.	0.0140359
$667$	−1.60338e6	−0.139547
$668$	−8.64342e6	−0.749453
$669$	−1.11649e7	−0.964476
$670$	−410920.	−0.0353647
$671$	−1.38640e7	−1.18873
$672$	−1.58147e6	−0.135094
$673$	−1.64638e7	−1.40118	−0.700588	−	0.713566i	$-0.747079\pi$
$673$	−1.64638e7	−1.40118	−0.700588	+	0.713566i	$0.747079\pi$
$674$	−7.09909e6	−0.601940
$675$	−455625.	−0.0384900
$676$	2.60087e6	0.218903
$677$	1.62449e7	1.36222	0.681108	−	0.732183i	$-0.261498\pi$
$677$	1.62449e7	1.36222	0.681108	+	0.732183i	$0.261498\pi$
$678$	−2.65976e6	−0.222212
$679$	−3.00730e6	−0.250324
$680$	−397499.	−0.0329658
$681$	9.88186e6	0.816528
$682$	−649734.	−0.0534902
$683$	−1.69563e7	−1.39084	−0.695422	−	0.718601i	$-0.744783\pi$
$683$	−1.69563e7	−1.39084	−0.695422	+	0.718601i	$0.744783\pi$
$684$	467856.	0.0382360
$685$	−2.59496e6	−0.211302
$686$	−2.86048e6	−0.232075
$687$	−8.74495e6	−0.706912
$688$	−5.65322e6	−0.455328
$689$	−4.85304e6	−0.389463
$690$	1.54218e6	0.123314
$691$	4.86180e6	0.387348	0.193674	−	0.981066i	$-0.437960\pi$
$691$	4.86180e6	0.387348	0.193674	+	0.981066i	$0.437960\pi$
$692$	−6.10828e6	−0.484902
$693$	−5.69004e6	−0.450072
$694$	8.86633e6	0.698787
$695$	−5.20503e6	−0.408754
$696$	−538973.	−0.0421739
$697$	4.25471e6	0.331732
$698$	−9.78714e6	−0.760356
$699$	−757672.	−0.0586527
$700$	−1.71600e6	−0.132365
$701$	3.68475e6	0.283213	0.141606	−	0.989923i	$-0.454773\pi$
$701$	3.68475e6	0.283213	0.141606	+	0.989923i	$0.454773\pi$
$702$	−2.13057e6	−0.163175
$703$	−179015.	−0.0136616
$704$	1.67677e6	0.127509
$705$	−2.65761e6	−0.201381
$706$	−2.55141e6	−0.192650
$707$	−713189.	−0.0536607
$708$	−87336.5	−0.00654806
$709$	−1.23146e7	−0.920036	−0.460018	−	0.887910i	$-0.652157\pi$
$709$	−1.23146e7	−0.920036	−0.460018	+	0.887910i	$0.652157\pi$
$710$	−3.96456e6	−0.295154
$711$	5.07078e6	0.376184
$712$	−5.38939e6	−0.398419
$713$	679914.	0.0500876
$714$	−1.53475e6	−0.112666
$715$	−7.47758e6	−0.547011
$716$	3.16076e6	0.230414
$717$	1.23387e7	0.896340
$718$	−1.59914e7	−1.15765
$719$	−3.56575e6	−0.257234	−0.128617	−	0.991694i	$-0.541054\pi$
$719$	−3.56575e6	−0.257234	−0.128617	+	0.991694i	$0.541054\pi$
$720$	518400.	0.0372678
$721$	−2.16875e6	−0.155372
$722$	−521284.	−0.0372161
$723$	−8.43257e6	−0.599949
$724$	−1.02598e7	−0.727436
$725$	−584823.	−0.0413218
$726$	235080.	0.0165529
$727$	−3.60456e6	−0.252939	−0.126469	−	0.991970i	$-0.540365\pi$
$727$	−3.60456e6	−0.252939	−0.126469	+	0.991970i	$0.540365\pi$
$728$	−8.02429e6	−0.561149
$729$	531441.	0.0370370
$730$	−4.05368e6	−0.281541
$731$	−5.48620e6	−0.379733
$732$	4.87684e6	0.336404
$733$	4.02534e6	0.276721	0.138361	−	0.990382i	$-0.455817\pi$
$733$	4.02534e6	0.276721	0.138361	+	0.990382i	$0.455817\pi$
$734$	−9.97320e6	−0.683273
$735$	−2.84392e6	−0.194178
$736$	−1.75465e6	−0.119398
$737$	1.68217e6	0.114078
$738$	−5.54879e6	−0.375023
$739$	−1.64929e7	−1.11093	−0.555463	−	0.831542i	$-0.687459\pi$
$739$	−1.64929e7	−1.11093	−0.555463	+	0.831542i	$0.687459\pi$
$740$	−198354.	−0.0133156
$741$	2.37388e6	0.158823
$742$	4.55914e6	0.304000
$743$	−1.78193e7	−1.18419	−0.592093	−	0.805870i	$-0.701698\pi$
$743$	−1.78193e7	−1.18419	−0.592093	+	0.805870i	$0.701698\pi$
$744$	228552.	0.0151375
$745$	−1.25516e7	−0.828532
$746$	1.37879e7	0.907092
$747$	−2.53590e6	−0.166276
$748$	1.62723e6	0.106340
$749$	1.38851e7	0.904367
$750$	562500.	0.0365148
$751$	−1.50688e7	−0.974941	−0.487471	−	0.873139i	$-0.662080\pi$
$751$	−1.50688e7	−0.974941	−0.487471	+	0.873139i	$0.662080\pi$
$752$	3.02377e6	0.194986
$753$	1.17631e7	0.756019
$754$	−2.73472e6	−0.175180
$755$	−9.18145e6	−0.586197
$756$	2.00155e6	0.127368
$757$	1.62784e7	1.03246	0.516228	−	0.856451i	$-0.327336\pi$
$757$	1.62784e7	1.03246	0.516228	+	0.856451i	$0.327336\pi$
$758$	−6.14248e6	−0.388303
$759$	−6.31315e6	−0.397779
$760$	−577600.	−0.0362738
$761$	4.51093e6	0.282361	0.141180	−	0.989984i	$-0.454910\pi$
$761$	4.51093e6	0.282361	0.141180	+	0.989984i	$0.454910\pi$
$762$	7.12550e6	0.444557
$763$	−5.39746e6	−0.335644
$764$	−401859.	−0.0249081
$765$	503085.	0.0310805
$766$	1.30509e7	0.803650
$767$	−443141.	−0.0271990
$768$	−589824.	−0.0360844
$769$	9.47467e6	0.577761	0.288881	−	0.957365i	$-0.406717\pi$
$769$	9.47467e6	0.577761	0.288881	+	0.957365i	$0.406717\pi$
$770$	7.02474e6	0.426976
$771$	8.96971e6	0.543429
$772$	−862598.	−0.0520913
$773$	−2.83231e6	−0.170487	−0.0852436	−	0.996360i	$-0.527167\pi$
$773$	−2.83231e6	−0.170487	−0.0852436	+	0.996360i	$0.527167\pi$
$774$	7.15485e6	0.429287
$775$	247995.	0.0148316
$776$	−1.12160e6	−0.0668628
$777$	−765847.	−0.0455082
$778$	8.69961e6	0.515289
$779$	6.18245e6	0.365020
$780$	2.63034e6	0.154801
$781$	1.62296e7	0.952094
$782$	−1.70282e6	−0.0995751
$783$	682137.	0.0397619
$784$	3.23575e6	0.188012
$785$	3.85780e6	0.223442
$786$	−1.06826e7	−0.616768
$787$	7.88470e6	0.453783	0.226892	−	0.973920i	$-0.427144\pi$
$787$	7.88470e6	0.453783	0.226892	+	0.973920i	$0.427144\pi$
$788$	7.74081e6	0.444090
$789$	3.42203e6	0.195700
$790$	−6.26022e6	−0.356880
$791$	1.26782e7	0.720470
$792$	−2.12216e6	−0.120217
$793$	2.47449e7	1.39734
$794$	−1.76846e7	−0.995507
$795$	−1.49447e6	−0.0838630
$796$	−1.29300e7	−0.723295
$797$	2.80785e7	1.56577	0.782884	−	0.622168i	$-0.213748\pi$
$797$	2.80785e7	1.56577	0.782884	+	0.622168i	$0.213748\pi$
$798$	−2.23012e6	−0.123971
$799$	2.93444e6	0.162614
$800$	−640000.	−0.0353553
$801$	6.82095e6	0.375633
$802$	3.04779e6	0.167320
$803$	1.65944e7	0.908181
$804$	−591724.	−0.0322834
$805$	−7.35105e6	−0.399815
$806$	1.15966e6	0.0628773
$807$	−6.24357e6	−0.337481
$808$	−265991.	−0.0143330
$809$	−6.92130e6	−0.371806	−0.185903	−	0.982568i	$-0.559521\pi$
$809$	−6.92130e6	−0.371806	−0.185903	+	0.982568i	$0.559521\pi$
$810$	−656100.	−0.0351364
$811$	1.34048e6	0.0715661	0.0357831	−	0.999360i	$-0.488607\pi$
$811$	1.34048e6	0.0715661	0.0357831	+	0.999360i	$0.488607\pi$
$812$	2.56911e6	0.136739
$813$	1.84826e7	0.980700
$814$	811996.	0.0429529
$815$	−1.15943e7	−0.611435
$816$	−572399.	−0.0300936
$817$	−7.97192e6	−0.417838
$818$	9.90326e6	0.517481
$819$	1.01557e7	0.529056
$820$	6.85036e6	0.355778
$821$	−1.10064e7	−0.569883	−0.284942	−	0.958545i	$-0.591974\pi$
$821$	−1.10064e7	−0.569883	−0.284942	+	0.958545i	$0.591974\pi$
$822$	−3.73674e6	−0.192892
$823$	2.42966e7	1.25039	0.625195	−	0.780468i	$-0.285019\pi$
$823$	2.42966e7	1.25039	0.625195	+	0.780468i	$0.285019\pi$
$824$	−808857.	−0.0415006
$825$	−2.30269e6	−0.117788
$826$	416304.	0.0212305
$827$	2.55224e7	1.29765	0.648826	−	0.760937i	$-0.275260\pi$
$827$	2.55224e7	1.29765	0.648826	+	0.760937i	$0.275260\pi$
$828$	2.22073e6	0.112569
$829$	1.78840e7	0.903814	0.451907	−	0.892065i	$-0.350744\pi$
$829$	1.78840e7	0.903814	0.451907	+	0.892065i	$0.350744\pi$
$830$	3.13074e6	0.157744
$831$	1.71905e6	0.0863549
$832$	−2.99274e6	−0.149886
$833$	3.14016e6	0.156797
$834$	−7.49525e6	−0.373139
$835$	−1.35053e7	−0.670331
$836$	2.36450e6	0.117010
$837$	−289262.	−0.0142717
$838$	−1.20102e7	−0.590798
$839$	−3.35619e7	−1.64605	−0.823023	−	0.568008i	$-0.807714\pi$
$839$	−3.35619e7	−1.64605	−0.823023	+	0.568008i	$0.807714\pi$
$840$	−2.47104e6	−0.120832
$841$	−1.96356e7	−0.957313
$842$	3.99607e6	0.194246
$843$	−6.94652e6	−0.336665
$844$	−452826.	−0.0218814
$845$	4.06386e6	0.195793
$846$	−3.82695e6	−0.183835
$847$	−1.12055e6	−0.0536689
$848$	1.70038e6	0.0812000
$849$	3.97866e6	0.189438
$850$	−621093.	−0.0294855
$851$	−849714.	−0.0402206
$852$	−5.70897e6	−0.269438
$853$	1.75136e7	0.824142	0.412071	−	0.911152i	$-0.364805\pi$
$853$	1.75136e7	0.824142	0.412071	+	0.911152i	$0.364805\pi$
$854$	−2.32463e7	−1.09071
$855$	731025.	0.0341993
$856$	5.17859e6	0.241561
$857$	1.91536e7	0.890840	0.445420	−	0.895322i	$-0.353054\pi$
$857$	1.91536e7	0.890840	0.445420	+	0.895322i	$0.353054\pi$
$858$	−1.07677e7	−0.499350
$859$	3.02413e7	1.39836	0.699178	−	0.714948i	$-0.253549\pi$
$859$	3.02413e7	1.39836	0.699178	+	0.714948i	$0.253549\pi$
$860$	−8.83315e6	−0.407258
$861$	2.64493e7	1.21592
$862$	−9.70963e6	−0.445076
$863$	−1.44389e7	−0.659946	−0.329973	−	0.943990i	$-0.607040\pi$
$863$	−1.44389e7	−0.659946	−0.329973	+	0.943990i	$0.607040\pi$
$864$	746496.	0.0340207
$865$	−9.54419e6	−0.433709
$866$	4.12174e6	0.186761
$867$	1.22232e7	0.552253
$868$	−1.08943e6	−0.0490797
$869$	2.56273e7	1.15120
$870$	−842145.	−0.0377215
$871$	−3.00238e6	−0.134097
$872$	−2.01304e6	−0.0896521
$873$	1.41953e6	0.0630389
$874$	−2.47433e6	−0.109567
$875$	−2.68125e6	−0.118391
$876$	−5.83729e6	−0.257011
$877$	−1.70799e7	−0.749870	−0.374935	−	0.927051i	$-0.622335\pi$
$877$	−1.70799e7	−0.749870	−0.374935	+	0.927051i	$0.622335\pi$
$878$	5.43574e6	0.237970
$879$	−7.94251e6	−0.346725
$880$	2.61995e6	0.114047
$881$	2.02133e7	0.877400	0.438700	−	0.898634i	$-0.355439\pi$
$881$	2.02133e7	0.877400	0.438700	+	0.898634i	$0.355439\pi$
$882$	−4.09525e6	−0.177259
$883$	2.66270e7	1.14926	0.574632	−	0.818412i	$-0.305145\pi$
$883$	2.66270e7	1.14926	0.574632	+	0.818412i	$0.305145\pi$
$884$	−2.90432e6	−0.125001
$885$	−136463.	−0.00585676
$886$	−6.18901e6	−0.264872
$887$	1.77998e7	0.759638	0.379819	−	0.925061i	$-0.375986\pi$
$887$	1.77998e7	0.759638	0.379819	+	0.925061i	$0.375986\pi$
$888$	−285630.	−0.0121555
$889$	−3.39649e7	−1.44137
$890$	−8.42093e6	−0.356357
$891$	2.68585e6	0.113341
$892$	1.98488e7	0.835260
$893$	4.26398e6	0.178931
$894$	−1.80743e7	−0.756343
$895$	4.93869e6	0.206089
$896$	2.81150e6	0.116995
$897$	1.12679e7	0.467586
$898$	7.39754e6	0.306123
$899$	−371285.	−0.0153217
$900$	810000.	0.0333333
$901$	1.65014e6	0.0677189
$902$	−2.80431e7	−1.14765
$903$	−3.41048e7	−1.39186
$904$	4.72845e6	0.192441
$905$	−1.60310e7	−0.650638
$906$	−1.32213e7	−0.535123
$907$	−4.04476e7	−1.63258	−0.816289	−	0.577643i	$-0.803973\pi$
$907$	−4.04476e7	−1.63258	−0.816289	+	0.577643i	$0.803973\pi$
$908$	−1.75678e7	−0.707134
$909$	336645.	0.0135133
$910$	−1.25380e7	−0.501907
$911$	−8.24751e6	−0.329251	−0.164626	−	0.986356i	$-0.552642\pi$
$911$	−8.24751e6	−0.329251	−0.164626	+	0.986356i	$0.552642\pi$
$912$	−831744.	−0.0331133
$913$	−1.28162e7	−0.508842
$914$	1.12108e7	0.443887
$915$	7.62007e6	0.300889
$916$	1.55466e7	0.612204
$917$	5.09206e7	1.99972
$918$	724442.	0.0283725
$919$	−1.96298e7	−0.766704	−0.383352	−	0.923602i	$-0.625230\pi$
$919$	−1.96298e7	−0.766704	−0.383352	+	0.923602i	$0.625230\pi$
$920$	−2.74164e6	−0.106793
$921$	2.16553e7	0.841231
$922$	−2.87418e7	−1.11349
$923$	−2.89670e7	−1.11918
$924$	1.01156e7	0.389774
$925$	−309928.	−0.0119099
$926$	1.05429e7	0.404049
$927$	1.02371e6	0.0391271
$928$	958174.	0.0365237
$929$	−2.47430e6	−0.0940619	−0.0470310	−	0.998893i	$-0.514976\pi$
$929$	−2.47430e6	−0.0940619	−0.0470310	+	0.998893i	$0.514976\pi$
$930$	357113.	0.0135394
$931$	4.56291e6	0.172531
$932$	1.34697e6	0.0507948
$933$	−6.04707e6	−0.227426
$934$	3.41638e7	1.28144
$935$	2.54255e6	0.0951130
$936$	3.78768e6	0.141314
$937$	−1.99378e7	−0.741872	−0.370936	−	0.928658i	$-0.620963\pi$
$937$	−1.99378e7	−0.741872	−0.370936	+	0.928658i	$0.620963\pi$
$938$	2.82056e6	0.104671
$939$	2.34561e7	0.868142
$940$	4.72463e6	0.174401
$941$	−2.44027e6	−0.0898387	−0.0449193	−	0.998991i	$-0.514303\pi$
$941$	−2.44027e6	−0.0898387	−0.0449193	+	0.998991i	$0.514303\pi$
$942$	5.55523e6	0.203974
$943$	2.93457e7	1.07465
$944$	155265.	0.00567078
$945$	3.12741e6	0.113922
$946$	3.61600e7	1.31371
$947$	−2.17049e7	−0.786471	−0.393236	−	0.919438i	$-0.628644\pi$
$947$	−2.17049e7	−0.786471	−0.393236	+	0.919438i	$0.628644\pi$
$948$	−9.01472e6	−0.325785
$949$	−2.96181e7	−1.06756
$950$	−902500.	−0.0324443
$951$	−1.62802e7	−0.583727
$952$	2.72844e6	0.0975713
$953$	−1.92314e7	−0.685928	−0.342964	−	0.939349i	$-0.611431\pi$
$953$	−1.92314e7	−0.685928	−0.342964	+	0.939349i	$0.611431\pi$
$954$	−2.15204e6	−0.0765561
$955$	−627905.	−0.0222785
$956$	−2.19355e7	−0.776253
$957$	3.44746e6	0.121680
$958$	−1.13316e7	−0.398911
$959$	1.78118e7	0.625405
$960$	−921600.	−0.0322749
$961$	−2.84717e7	−0.994501
$962$	−1.44927e6	−0.0504908
$963$	−6.55415e6	−0.227746
$964$	1.49912e7	0.519571
$965$	−1.34781e6	−0.0465919
$966$	−1.05855e7	−0.364980
$967$	−4.40745e7	−1.51573	−0.757865	−	0.652412i	$-0.773757\pi$
$967$	−4.40745e7	−1.51573	−0.757865	+	0.652412i	$0.773757\pi$
$968$	−417920.	−0.0143352
$969$	−807172.	−0.0276157
$970$	−1.75250e6	−0.0598039
$971$	4.69411e7	1.59773	0.798867	−	0.601507i	$-0.205433\pi$
$971$	4.69411e7	1.59773	0.798867	+	0.601507i	$0.205433\pi$
$972$	−944784.	−0.0320750
$973$	3.57274e7	1.20982
$974$	−3.32546e7	−1.12319
$975$	4.10990e6	0.138459
$976$	−8.66995e6	−0.291334
$977$	−2.26994e7	−0.760812	−0.380406	−	0.924820i	$-0.624216\pi$
$977$	−2.26994e7	−0.760812	−0.380406	+	0.924820i	$0.624216\pi$
$978$	−1.66958e7	−0.558162
$979$	3.44725e7	1.14952
$980$	5.05586e6	0.168163
$981$	2.54775e6	0.0845248
$982$	2.29888e7	0.760743
$983$	8.94734e6	0.295332	0.147666	−	0.989037i	$-0.452824\pi$
$983$	8.94734e6	0.295332	0.147666	+	0.989037i	$0.452824\pi$
$984$	9.86452e6	0.324779
$985$	1.20950e7	0.397206
$986$	929867.	0.0304599
$987$	1.82418e7	0.596040
$988$	−4.22023e6	−0.137545
$989$	−3.78396e7	−1.23014
$990$	−3.31587e6	−0.107525
$991$	−4.83394e6	−0.156357	−0.0781785	−	0.996939i	$-0.524910\pi$
$991$	−4.83394e6	−0.156357	−0.0781785	+	0.996939i	$0.524910\pi$
$992$	−406315.	−0.0131094
$993$	1.59435e7	0.513111
$994$	2.72128e7	0.873589
$995$	−2.02031e7	−0.646934
$996$	4.50827e6	0.144000
$997$	7.01989e6	0.223662	0.111831	−	0.993727i	$-0.464328\pi$
$997$	7.01989e6	0.223662	0.111831	+	0.993727i	$0.464328\pi$
$998$	7.65456e6	0.243273
$999$	361501.	0.0114603

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.6.a.j.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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +36.0000 q^{6} -171.600 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +36.0000 q^{6} -171.600 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} +409.367 q^{11} -144.000 q^{12} -730.649 q^{13} +686.401 q^{14} -225.000 q^{15} +256.000 q^{16} +248.437 q^{17} -324.000 q^{18} +361.000 q^{19} +400.000 q^{20} +1544.40 q^{21} -1637.47 q^{22} +1713.53 q^{23} +576.000 q^{24} +625.000 q^{25} +2922.59 q^{26} -729.000 q^{27} -2745.60 q^{28} -935.716 q^{29} +900.000 q^{30} +396.792 q^{31} -1024.00 q^{32} -3684.30 q^{33} -993.748 q^{34} -4290.01 q^{35} +1296.00 q^{36} -495.885 q^{37} -1444.00 q^{38} +6575.84 q^{39} -1600.00 q^{40} +17125.9 q^{41} -6177.61 q^{42} -22082.9 q^{43} +6549.87 q^{44} +2025.00 q^{45} -6854.11 q^{46} +11811.6 q^{47} -2304.00 q^{48} +12639.6 q^{49} -2500.00 q^{50} -2235.93 q^{51} -11690.4 q^{52} +6642.10 q^{53} +2916.00 q^{54} +10234.2 q^{55} +10982.4 q^{56} -3249.00 q^{57} +3742.87 q^{58} +606.503 q^{59} -3600.00 q^{60} -33867.0 q^{61} -1587.17 q^{62} -13899.6 q^{63} +4096.00 q^{64} -18266.2 q^{65} +14737.2 q^{66} +4109.20 q^{67} +3974.99 q^{68} -15421.8 q^{69} +17160.0 q^{70} +39645.6 q^{71} -5184.00 q^{72} +40536.8 q^{73} +1983.54 q^{74} -5625.00 q^{75} +5776.00 q^{76} -70247.4 q^{77} -26303.4 q^{78} +62602.2 q^{79} +6400.00 q^{80} +6561.00 q^{81} -68503.6 q^{82} -31307.4 q^{83} +24710.4 q^{84} +6210.93 q^{85} +88331.5 q^{86} +8421.45 q^{87} -26199.5 q^{88} +84209.3 q^{89} -8100.00 q^{90} +125380. q^{91} +27416.4 q^{92} -3571.13 q^{93} -47246.3 q^{94} +9025.00 q^{95} +9216.00 q^{96} +17525.0 q^{97} -50558.6 q^{98} +33158.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} + 100 q^{5} + 144 q^{6} - 108 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) \) 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	\( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} + 100 q^{5} + 144 q^{6} - 108 q^{7} - 256 q^{8} + 324 q^{9} - 400 q^{10} - 246 q^{11} - 576 q^{12} + 640 q^{13} + 432 q^{14} - 900 q^{15} + 1024 q^{16} - 612 q^{17} - 1296 q^{18} + 1444 q^{19} + 1600 q^{20} + 972 q^{21} + 984 q^{22} - 1242 q^{23} + 2304 q^{24} + 2500 q^{25} - 2560 q^{26} - 2916 q^{27} - 1728 q^{28} - 6230 q^{29} + 3600 q^{30} - 11360 q^{31} - 4096 q^{32} + 2214 q^{33} + 2448 q^{34} - 2700 q^{35} + 5184 q^{36} - 4792 q^{37} - 5776 q^{38} - 5760 q^{39} - 6400 q^{40} + 9170 q^{41} - 3888 q^{42} - 11412 q^{43} - 3936 q^{44} + 8100 q^{45} + 4968 q^{46} - 29858 q^{47} - 9216 q^{48} + 31092 q^{49} - 10000 q^{50} + 5508 q^{51} + 10240 q^{52} + 27498 q^{53} + 11664 q^{54} - 6150 q^{55} + 6912 q^{56} - 12996 q^{57} + 24920 q^{58} + 54984 q^{59} - 14400 q^{60} + 20868 q^{61} + 45440 q^{62} - 8748 q^{63} + 16384 q^{64} + 16000 q^{65} - 8856 q^{66} - 20244 q^{67} - 9792 q^{68} + 11178 q^{69} + 10800 q^{70} + 86864 q^{71} - 20736 q^{72} - 3728 q^{73} + 19168 q^{74} - 22500 q^{75} + 23104 q^{76} + 18796 q^{77} + 23040 q^{78} + 164192 q^{79} + 25600 q^{80} + 26244 q^{81} - 36680 q^{82} - 60506 q^{83} + 15552 q^{84} - 15300 q^{85} + 45648 q^{86} + 56070 q^{87} + 15744 q^{88} + 113798 q^{89} - 32400 q^{90} + 159528 q^{91} - 19872 q^{92} + 102240 q^{93} + 119432 q^{94} + 36100 q^{95} + 36864 q^{96} + 79440 q^{97} - 124368 q^{98} - 19926 q^{99}+O(q^{100}) \) 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 - 246 * q^11 - 576 * q^12 + 640 * q^13 + 432 * q^14 - 900 * q^15 + 1024 * q^16 - 612 * q^17 - 1296 * q^18 + 1444 * q^19 + 1600 * q^20 + 972 * q^21 + 984 * q^22 - 1242 * q^23 + 2304 * q^24 + 2500 * q^25 - 2560 * q^26 - 2916 * q^27 - 1728 * q^28 - 6230 * q^29 + 3600 * q^30 - 11360 * q^31 - 4096 * q^32 + 2214 * q^33 + 2448 * q^34 - 2700 * q^35 + 5184 * q^36 - 4792 * q^37 - 5776 * q^38 - 5760 * q^39 - 6400 * q^40 + 9170 * q^41 - 3888 * q^42 - 11412 * q^43 - 3936 * q^44 + 8100 * q^45 + 4968 * q^46 - 29858 * q^47 - 9216 * q^48 + 31092 * q^49 - 10000 * q^50 + 5508 * q^51 + 10240 * q^52 + 27498 * q^53 + 11664 * q^54 - 6150 * q^55 + 6912 * q^56 - 12996 * q^57 + 24920 * q^58 + 54984 * q^59 - 14400 * q^60 + 20868 * q^61 + 45440 * q^62 - 8748 * q^63 + 16384 * q^64 + 16000 * q^65 - 8856 * q^66 - 20244 * q^67 - 9792 * q^68 + 11178 * q^69 + 10800 * q^70 + 86864 * q^71 - 20736 * q^72 - 3728 * q^73 + 19168 * q^74 - 22500 * q^75 + 23104 * q^76 + 18796 * q^77 + 23040 * q^78 + 164192 * q^79 + 25600 * q^80 + 26244 * q^81 - 36680 * q^82 - 60506 * q^83 + 15552 * q^84 - 15300 * q^85 + 45648 * q^86 + 56070 * q^87 + 15744 * q^88 + 113798 * q^89 - 32400 * q^90 + 159528 * q^91 - 19872 * q^92 + 102240 * q^93 + 119432 * q^94 + 36100 * q^95 + 36864 * q^96 + 79440 * q^97 - 124368 * q^98 - 19926 * q^99

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