LMFDB - Embedded newform 570.6.a.h.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:	$0$
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} - 12189x^{2} - 95210x + 4841400 $ x^4 - 12189x^2 - 95210x + 4841400
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			$112.485$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} -10.5154 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} -10.5154 q^{7} -64.0000 q^{8} +81.0000 q^{9} +100.000 q^{10} +66.1919 q^{11} -144.000 q^{12} -874.716 q^{13} +42.0617 q^{14} +225.000 q^{15} +256.000 q^{16} +1227.37 q^{17} -324.000 q^{18} +361.000 q^{19} -400.000 q^{20} +94.6388 q^{21} -264.768 q^{22} -3272.08 q^{23} +576.000 q^{24} +625.000 q^{25} +3498.87 q^{26} -729.000 q^{27} -168.247 q^{28} -5080.10 q^{29} -900.000 q^{30} +4228.51 q^{31} -1024.00 q^{32} -595.728 q^{33} -4909.47 q^{34} +262.885 q^{35} +1296.00 q^{36} -1935.06 q^{37} -1444.00 q^{38} +7872.45 q^{39} +1600.00 q^{40} +12797.0 q^{41} -378.555 q^{42} +2473.55 q^{43} +1059.07 q^{44} -2025.00 q^{45} +13088.3 q^{46} -17382.0 q^{47} -2304.00 q^{48} -16696.4 q^{49} -2500.00 q^{50} -11046.3 q^{51} -13995.5 q^{52} -2024.34 q^{53} +2916.00 q^{54} -1654.80 q^{55} +672.987 q^{56} -3249.00 q^{57} +20320.4 q^{58} -35917.4 q^{59} +3600.00 q^{60} +1192.25 q^{61} -16914.0 q^{62} -851.749 q^{63} +4096.00 q^{64} +21867.9 q^{65} +2382.91 q^{66} -12384.0 q^{67} +19637.9 q^{68} +29448.7 q^{69} -1051.54 q^{70} +1344.72 q^{71} -5184.00 q^{72} -85915.6 q^{73} +7740.24 q^{74} -5625.00 q^{75} +5776.00 q^{76} -696.036 q^{77} -31489.8 q^{78} -29890.4 q^{79} -6400.00 q^{80} +6561.00 q^{81} -51187.8 q^{82} +103323. q^{83} +1514.22 q^{84} -30684.2 q^{85} -9894.20 q^{86} +45720.9 q^{87} -4236.28 q^{88} +69639.0 q^{89} +8100.00 q^{90} +9198.01 q^{91} -52353.3 q^{92} -38056.6 q^{93} +69527.9 q^{94} -9025.00 q^{95} +9216.00 q^{96} +7983.55 q^{97} +66785.7 q^{98} +5361.55 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} + 144 q^{6} - 88 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 - 88 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} + 144 q^{6} - 88 q^{7} - 256 q^{8} + 324 q^{9} + 400 q^{10} + 940 q^{11} - 576 q^{12} - 34 q^{13} + 352 q^{14} + 900 q^{15} + 1024 q^{16} - 138 q^{17} - 1296 q^{18} + 1444 q^{19} - 1600 q^{20} + 792 q^{21} - 3760 q^{22} + 486 q^{23} + 2304 q^{24} + 2500 q^{25} + 136 q^{26} - 2916 q^{27} - 1408 q^{28} + 3296 q^{29} - 3600 q^{30} - 6686 q^{31} - 4096 q^{32} - 8460 q^{33} + 552 q^{34} + 2200 q^{35} + 5184 q^{36} - 14218 q^{37} - 5776 q^{38} + 306 q^{39} + 6400 q^{40} + 1342 q^{41} - 3168 q^{42} - 26330 q^{43} + 15040 q^{44} - 8100 q^{45} - 1944 q^{46} - 7010 q^{47} - 9216 q^{48} + 192 q^{49} - 10000 q^{50} + 1242 q^{51} - 544 q^{52} - 22782 q^{53} + 11664 q^{54} - 23500 q^{55} + 5632 q^{56} - 12996 q^{57} - 13184 q^{58} - 13358 q^{59} + 14400 q^{60} + 16008 q^{61} + 26744 q^{62} - 7128 q^{63} + 16384 q^{64} + 850 q^{65} + 33840 q^{66} - 22696 q^{67} - 2208 q^{68} - 4374 q^{69} - 8800 q^{70} + 52584 q^{71} - 20736 q^{72} - 101048 q^{73} + 56872 q^{74} - 22500 q^{75} + 23104 q^{76} - 103772 q^{77} - 1224 q^{78} - 113090 q^{79} - 25600 q^{80} + 26244 q^{81} - 5368 q^{82} - 65384 q^{83} + 12672 q^{84} + 3450 q^{85} + 105320 q^{86} - 29664 q^{87} - 60160 q^{88} + 97354 q^{89} + 32400 q^{90} - 125600 q^{91} + 7776 q^{92} + 60174 q^{93} + 28040 q^{94} - 36100 q^{95} + 36864 q^{96} - 198934 q^{97} - 768 q^{98} + 76140 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 - 36 * q^3 + 64 * q^4 - 100 * q^5 + 144 * q^6 - 88 * q^7 - 256 * q^8 + 324 * q^9 + 400 * q^10 + 940 * q^11 - 576 * q^12 - 34 * q^13 + 352 * q^14 + 900 * q^15 + 1024 * q^16 - 138 * q^17 - 1296 * q^18 + 1444 * q^19 - 1600 * q^20 + 792 * q^21 - 3760 * q^22 + 486 * q^23 + 2304 * q^24 + 2500 * q^25 + 136 * q^26 - 2916 * q^27 - 1408 * q^28 + 3296 * q^29 - 3600 * q^30 - 6686 * q^31 - 4096 * q^32 - 8460 * q^33 + 552 * q^34 + 2200 * q^35 + 5184 * q^36 - 14218 * q^37 - 5776 * q^38 + 306 * q^39 + 6400 * q^40 + 1342 * q^41 - 3168 * q^42 - 26330 * q^43 + 15040 * q^44 - 8100 * q^45 - 1944 * q^46 - 7010 * q^47 - 9216 * q^48 + 192 * q^49 - 10000 * q^50 + 1242 * q^51 - 544 * q^52 - 22782 * q^53 + 11664 * q^54 - 23500 * q^55 + 5632 * q^56 - 12996 * q^57 - 13184 * q^58 - 13358 * q^59 + 14400 * q^60 + 16008 * q^61 + 26744 * q^62 - 7128 * q^63 + 16384 * q^64 + 850 * q^65 + 33840 * q^66 - 22696 * q^67 - 2208 * q^68 - 4374 * q^69 - 8800 * q^70 + 52584 * q^71 - 20736 * q^72 - 101048 * q^73 + 56872 * q^74 - 22500 * q^75 + 23104 * q^76 - 103772 * q^77 - 1224 * q^78 - 113090 * q^79 - 25600 * q^80 + 26244 * q^81 - 5368 * q^82 - 65384 * q^83 + 12672 * q^84 + 3450 * q^85 + 105320 * q^86 - 29664 * q^87 - 60160 * q^88 + 97354 * q^89 + 32400 * q^90 - 125600 * q^91 + 7776 * q^92 + 60174 * q^93 + 28040 * q^94 - 36100 * q^95 + 36864 * q^96 - 198934 * q^97 - 768 * q^98 + 76140 * 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
$7$	−10.5154	−0.0811113	−0.0405557	−	0.999177i	$-0.512913\pi$
$7$	−10.5154	−0.0811113	−0.0405557	+	0.999177i	$0.512913\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	100.000	0.316228
$11$	66.1919	0.164939	0.0824695	−	0.996594i	$-0.473719\pi$
$11$	66.1919	0.164939	0.0824695	+	0.996594i	$0.473719\pi$
$12$	−144.000	−0.288675
$13$	−874.716	−1.43552	−0.717759	−	0.696291i	$-0.754832\pi$
$13$	−874.716	−1.43552	−0.717759	+	0.696291i	$0.754832\pi$
$14$	42.0617	0.0573544
$15$	225.000	0.258199
$16$	256.000	0.250000
$17$	1227.37	1.03004	0.515018	−	0.857179i	$-0.327785\pi$
$17$	1227.37	1.03004	0.515018	+	0.857179i	$0.327785\pi$
$18$	−324.000	−0.235702
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	−400.000	−0.223607
$21$	94.6388	0.0468296
$22$	−264.768	−0.116630
$23$	−3272.08	−1.28975	−0.644873	−	0.764290i	$-0.723090\pi$
$23$	−3272.08	−1.28975	−0.644873	+	0.764290i	$0.723090\pi$
$24$	576.000	0.204124
$25$	625.000	0.200000
$26$	3498.87	1.01507
$27$	−729.000	−0.192450
$28$	−168.247	−0.0405557
$29$	−5080.10	−1.12170	−0.560851	−	0.827917i	$-0.689526\pi$
$29$	−5080.10	−1.12170	−0.560851	+	0.827917i	$0.689526\pi$
$30$	−900.000	−0.182574
$31$	4228.51	0.790283	0.395142	−	0.918620i	$-0.370696\pi$
$31$	4228.51	0.790283	0.395142	+	0.918620i	$0.370696\pi$
$32$	−1024.00	−0.176777
$33$	−595.728	−0.0952276
$34$	−4909.47	−0.728346
$35$	262.885	0.0362741
$36$	1296.00	0.166667
$37$	−1935.06	−0.232375	−0.116188	−	0.993227i	$-0.537067\pi$
$37$	−1935.06	−0.232375	−0.116188	+	0.993227i	$0.537067\pi$
$38$	−1444.00	−0.162221
$39$	7872.45	0.828797
$40$	1600.00	0.158114
$41$	12797.0	1.18890	0.594452	−	0.804131i	$-0.297369\pi$
$41$	12797.0	1.18890	0.594452	+	0.804131i	$0.297369\pi$
$42$	−378.555	−0.0331136
$43$	2473.55	0.204009	0.102005	−	0.994784i	$-0.467474\pi$
$43$	2473.55	0.204009	0.102005	+	0.994784i	$0.467474\pi$
$44$	1059.07	0.0824695
$45$	−2025.00	−0.149071
$46$	13088.3	0.911988
$47$	−17382.0	−1.14777	−0.573884	−	0.818936i	$-0.694564\pi$
$47$	−17382.0	−1.14777	−0.573884	+	0.818936i	$0.694564\pi$
$48$	−2304.00	−0.144338
$49$	−16696.4	−0.993421
$50$	−2500.00	−0.141421
$51$	−11046.3	−0.594692
$52$	−13995.5	−0.717759
$53$	−2024.34	−0.0989908	−0.0494954	−	0.998774i	$-0.515761\pi$
$53$	−2024.34	−0.0989908	−0.0494954	+	0.998774i	$0.515761\pi$
$54$	2916.00	0.136083
$55$	−1654.80	−0.0737630
$56$	672.987	0.0286772
$57$	−3249.00	−0.132453
$58$	20320.4	0.793163
$59$	−35917.4	−1.34330	−0.671652	−	0.740867i	$-0.734415\pi$
$59$	−35917.4	−1.34330	−0.671652	+	0.740867i	$0.734415\pi$
$60$	3600.00	0.129099
$61$	1192.25	0.0410243	0.0205121	−	0.999790i	$-0.493470\pi$
$61$	1192.25	0.0410243	0.0205121	+	0.999790i	$0.493470\pi$
$62$	−16914.0	−0.558815
$63$	−851.749	−0.0270371
$64$	4096.00	0.125000
$65$	21867.9	0.641983
$66$	2382.91	0.0673361
$67$	−12384.0	−0.337035	−0.168518	−	0.985699i	$-0.553898\pi$
$67$	−12384.0	−0.337035	−0.168518	+	0.985699i	$0.553898\pi$
$68$	19637.9	0.515018
$69$	29448.7	0.744635
$70$	−1051.54	−0.0256497
$71$	1344.72	0.0316582	0.0158291	−	0.999875i	$-0.494961\pi$
$71$	1344.72	0.0316582	0.0158291	+	0.999875i	$0.494961\pi$
$72$	−5184.00	−0.117851
$73$	−85915.6	−1.88697	−0.943484	−	0.331417i	$-0.892473\pi$
$73$	−85915.6	−1.88697	−0.943484	+	0.331417i	$0.892473\pi$
$74$	7740.24	0.164314
$75$	−5625.00	−0.115470
$76$	5776.00	0.114708
$77$	−696.036	−0.0133784
$78$	−31489.8	−0.586048
$79$	−29890.4	−0.538846	−0.269423	−	0.963022i	$-0.586833\pi$
$79$	−29890.4	−0.538846	−0.269423	+	0.963022i	$0.586833\pi$
$80$	−6400.00	−0.111803
$81$	6561.00	0.111111
$82$	−51187.8	−0.840682
$83$	103323.	1.64628	0.823139	−	0.567840i	$-0.192221\pi$
$83$	103323.	1.64628	0.823139	+	0.567840i	$0.192221\pi$
$84$	1514.22	0.0234148
$85$	−30684.2	−0.460646
$86$	−9894.20	−0.144256
$87$	45720.9	0.647615
$88$	−4236.28	−0.0583148
$89$	69639.0	0.931918	0.465959	−	0.884806i	$-0.345709\pi$
$89$	69639.0	0.931918	0.465959	+	0.884806i	$0.345709\pi$
$90$	8100.00	0.105409
$91$	9198.01	0.116437
$92$	−52353.3	−0.644873
$93$	−38056.6	−0.456270
$94$	69527.9	0.811595
$95$	−9025.00	−0.102598
$96$	9216.00	0.102062
$97$	7983.55	0.0861523	0.0430762	−	0.999072i	$-0.486284\pi$
$97$	7983.55	0.0861523	0.0430762	+	0.999072i	$0.486284\pi$
$98$	66785.7	0.702455
$99$	5361.55	0.0549797
$100$	10000.0	0.100000
$101$	173434.	1.69173	0.845866	−	0.533396i	$-0.179084\pi$
$101$	173434.	1.69173	0.845866	+	0.533396i	$0.179084\pi$
$102$	44185.3	0.420511
$103$	−109651.	−1.01840	−0.509199	−	0.860649i	$-0.670058\pi$
$103$	−109651.	−1.01840	−0.509199	+	0.860649i	$0.670058\pi$
$104$	55981.8	0.507533
$105$	−2365.97	−0.0209429
$106$	8097.38	0.0699971
$107$	−29319.7	−0.247571	−0.123786	−	0.992309i	$-0.539504\pi$
$107$	−29319.7	−0.247571	−0.123786	+	0.992309i	$0.539504\pi$
$108$	−11664.0	−0.0962250
$109$	−130344.	−1.05081	−0.525405	−	0.850852i	$-0.676086\pi$
$109$	−130344.	−1.05081	−0.525405	+	0.850852i	$0.676086\pi$
$110$	6619.19	0.0521583
$111$	17415.5	0.134162
$112$	−2691.95	−0.0202778
$113$	−97239.6	−0.716386	−0.358193	−	0.933648i	$-0.616607\pi$
$113$	−97239.6	−0.716386	−0.358193	+	0.933648i	$0.616607\pi$
$114$	12996.0	0.0936586
$115$	81802.0	0.576792
$116$	−81281.6	−0.560851
$117$	−70852.0	−0.478506
$118$	143669.	0.949859
$119$	−12906.3	−0.0835476
$120$	−14400.0	−0.0912871
$121$	−156670.	−0.972795
$122$	−4768.98	−0.0290086
$123$	−115173.	−0.686414
$124$	67656.1	0.395142
$125$	−15625.0	−0.0894427
$126$	3407.00	0.0191181
$127$	−8838.07	−0.0486237	−0.0243119	−	0.999704i	$-0.507739\pi$
$127$	−8838.07	−0.0486237	−0.0243119	+	0.999704i	$0.507739\pi$
$128$	−16384.0	−0.0883883
$129$	−22261.9	−0.117785
$130$	−87471.6	−0.453951
$131$	27351.3	0.139252	0.0696258	−	0.997573i	$-0.477819\pi$
$131$	27351.3	0.139252	0.0696258	+	0.997573i	$0.477819\pi$
$132$	−9531.64	−0.0476138
$133$	−3796.07	−0.0186082
$134$	49536.1	0.238320
$135$	18225.0	0.0860663
$136$	−78551.6	−0.364173
$137$	319324.	1.45355	0.726776	−	0.686875i	$-0.241018\pi$
$137$	319324.	1.45355	0.726776	+	0.686875i	$0.241018\pi$
$138$	−117795.	−0.526537
$139$	95968.5	0.421300	0.210650	−	0.977562i	$-0.432442\pi$
$139$	95968.5	0.421300	0.210650	+	0.977562i	$0.432442\pi$
$140$	4206.17	0.0181370
$141$	156438.	0.662665
$142$	−5378.88	−0.0223857
$143$	−57899.2	−0.236773
$144$	20736.0	0.0833333
$145$	127003.	0.501640
$146$	343662.	1.33429
$147$	150268.	0.573552
$148$	−30961.0	−0.116188
$149$	310092.	1.14426	0.572131	−	0.820162i	$-0.306117\pi$
$149$	310092.	1.14426	0.572131	+	0.820162i	$0.306117\pi$
$150$	22500.0	0.0816497
$151$	168888.	0.602777	0.301388	−	0.953502i	$-0.402550\pi$
$151$	168888.	0.602777	0.301388	+	0.953502i	$0.402550\pi$
$152$	−23104.0	−0.0811107
$153$	99416.8	0.343345
$154$	2784.14	0.00945997
$155$	−105713.	−0.353425
$156$	125959.	0.414399
$157$	358056.	1.15931	0.579657	−	0.814860i	$-0.303186\pi$
$157$	358056.	1.15931	0.579657	+	0.814860i	$0.303186\pi$
$158$	119562.	0.381022
$159$	18219.1	0.0571524
$160$	25600.0	0.0790569
$161$	34407.3	0.104613
$162$	−26244.0	−0.0785674
$163$	534539.	1.57583	0.787916	−	0.615782i	$-0.211160\pi$
$163$	534539.	1.57583	0.787916	+	0.615782i	$0.211160\pi$
$164$	204751.	0.594452
$165$	14893.2	0.0425871
$166$	−413293.	−1.16409
$167$	−540897.	−1.50080	−0.750402	−	0.660982i	$-0.770140\pi$
$167$	−540897.	−1.50080	−0.750402	+	0.660982i	$0.770140\pi$
$168$	−6056.88	−0.0165568
$169$	393836.	1.06071
$170$	122737.	0.325726
$171$	29241.0	0.0764719
$172$	39576.8	0.102005
$173$	437917.	1.11244	0.556220	−	0.831035i	$-0.312251\pi$
$173$	437917.	1.11244	0.556220	+	0.831035i	$0.312251\pi$
$174$	−182884.	−0.457933
$175$	−6572.14	−0.0162223
$176$	16945.1	0.0412348
$177$	323256.	0.775557
$178$	−278556.	−0.658966
$179$	694936.	1.62111	0.810555	−	0.585662i	$-0.199166\pi$
$179$	694936.	1.62111	0.810555	+	0.585662i	$0.199166\pi$
$180$	−32400.0	−0.0745356
$181$	455065.	1.03247	0.516235	−	0.856447i	$-0.327333\pi$
$181$	455065.	1.03247	0.516235	+	0.856447i	$0.327333\pi$
$182$	−36792.0	−0.0823333
$183$	−10730.2	−0.0236854
$184$	209413.	0.455994
$185$	48376.5	0.103921
$186$	152226.	0.322632
$187$	81241.9	0.169893
$188$	−278112.	−0.573884
$189$	7665.74	0.0156099
$190$	36100.0	0.0725476
$191$	826894.	1.64009	0.820043	−	0.572302i	$-0.193949\pi$
$191$	826894.	1.64009	0.820043	+	0.572302i	$0.193949\pi$
$192$	−36864.0	−0.0721688
$193$	158735.	0.306746	0.153373	−	0.988168i	$-0.450986\pi$
$193$	158735.	0.306746	0.153373	+	0.988168i	$0.450986\pi$
$194$	−31934.2	−0.0609189
$195$	−196811.	−0.370649
$196$	−267143.	−0.496710
$197$	−30891.0	−0.0567109	−0.0283554	−	0.999598i	$-0.509027\pi$
$197$	−30891.0	−0.0567109	−0.0283554	+	0.999598i	$0.509027\pi$
$198$	−21446.2	−0.0388765
$199$	−685548.	−1.22717	−0.613586	−	0.789628i	$-0.710273\pi$
$199$	−685548.	−1.22717	−0.613586	+	0.789628i	$0.710273\pi$
$200$	−40000.0	−0.0707107
$201$	111456.	0.194587
$202$	−693737.	−1.19623
$203$	53419.4	0.0909827
$204$	−176741.	−0.297346
$205$	−319924.	−0.531694
$206$	438602.	0.720117
$207$	−265038.	−0.429915
$208$	−223927.	−0.358880
$209$	23895.3	0.0378396
$210$	9463.88	0.0148088
$211$	575965.	0.890615	0.445308	−	0.895378i	$-0.353094\pi$
$211$	575965.	0.890615	0.445308	+	0.895378i	$0.353094\pi$
$212$	−32389.5	−0.0494954
$213$	−12102.5	−0.0182779
$214$	117279.	0.175059
$215$	−61838.7	−0.0912356
$216$	46656.0	0.0680414
$217$	−44464.5	−0.0641009
$218$	521375.	0.743035
$219$	773240.	1.08944
$220$	−26476.8	−0.0368815
$221$	−1.07360e6	−1.47864
$222$	−69662.1	−0.0948668
$223$	484279.	0.652129	0.326065	−	0.945347i	$-0.394277\pi$
$223$	484279.	0.652129	0.326065	+	0.945347i	$0.394277\pi$
$224$	10767.8	0.0143386
$225$	50625.0	0.0666667
$226$	388959.	0.506562
$227$	685095.	0.882441	0.441221	−	0.897399i	$-0.354546\pi$
$227$	685095.	0.882441	0.441221	+	0.897399i	$0.354546\pi$
$228$	−51984.0	−0.0662266
$229$	333924.	0.420784	0.210392	−	0.977617i	$-0.432526\pi$
$229$	333924.	0.420784	0.210392	+	0.977617i	$0.432526\pi$
$230$	−327208.	−0.407853
$231$	6264.32	0.00772404
$232$	325126.	0.396581
$233$	1.18664e6	1.43195	0.715975	−	0.698126i	$-0.245982\pi$
$233$	1.18664e6	1.43195	0.715975	+	0.698126i	$0.245982\pi$
$234$	283408.	0.338355
$235$	434549.	0.513298
$236$	−574678.	−0.671652
$237$	269014.	0.311103
$238$	51625.2	0.0590771
$239$	235450.	0.266627	0.133313	−	0.991074i	$-0.457438\pi$
$239$	235450.	0.266627	0.133313	+	0.991074i	$0.457438\pi$
$240$	57600.0	0.0645497
$241$	−1.66380e6	−1.84526	−0.922629	−	0.385688i	$-0.873964\pi$
$241$	−1.66380e6	−1.84526	−0.922629	+	0.385688i	$0.873964\pi$
$242$	626679.	0.687870
$243$	−59049.0	−0.0641500
$244$	19075.9	0.0205121
$245$	417411.	0.444271
$246$	460690.	0.485368
$247$	−315773.	−0.329331
$248$	−270624.	−0.279407
$249$	−929910.	−0.950479
$250$	62500.0	0.0632456
$251$	1.73127e6	1.73453	0.867264	−	0.497848i	$-0.165876\pi$
$251$	1.73127e6	1.73453	0.867264	+	0.497848i	$0.165876\pi$
$252$	−13628.0	−0.0135186
$253$	−216585.	−0.212729
$254$	35352.3	0.0343822
$255$	276158.	0.265954
$256$	65536.0	0.0625000
$257$	1.78790e6	1.68854	0.844269	−	0.535919i	$-0.180035\pi$
$257$	1.78790e6	1.68854	0.844269	+	0.535919i	$0.180035\pi$
$258$	89047.8	0.0832863
$259$	20348.0	0.0188483
$260$	349887.	0.320992
$261$	−411488.	−0.373900
$262$	−109405.	−0.0984657
$263$	−1.77137e6	−1.57914	−0.789570	−	0.613661i	$-0.789696\pi$
$263$	−1.77137e6	−1.57914	−0.789570	+	0.613661i	$0.789696\pi$
$264$	38126.6	0.0336680
$265$	50608.6	0.0442700
$266$	15184.3	0.0131580
$267$	−626751.	−0.538043
$268$	−198145.	−0.168518
$269$	399884.	0.336941	0.168470	−	0.985707i	$-0.446117\pi$
$269$	399884.	0.336941	0.168470	+	0.985707i	$0.446117\pi$
$270$	−72900.0	−0.0608581
$271$	1.06163e6	0.878113	0.439057	−	0.898459i	$-0.355313\pi$
$271$	1.06163e6	0.878113	0.439057	+	0.898459i	$0.355313\pi$
$272$	314206.	0.257509
$273$	−82782.1	−0.0672248
$274$	−1.27730e6	−1.02782
$275$	41370.0	0.0329878
$276$	471179.	0.372318
$277$	−982207.	−0.769137	−0.384569	−	0.923096i	$-0.625650\pi$
$277$	−982207.	−0.769137	−0.384569	+	0.923096i	$0.625650\pi$
$278$	−383874.	−0.297904
$279$	342509.	0.263428
$280$	−16824.7	−0.0128248
$281$	1.86767e6	1.41102	0.705511	−	0.708699i	$-0.250717\pi$
$281$	1.86767e6	1.41102	0.705511	+	0.708699i	$0.250717\pi$
$282$	−625751.	−0.468575
$283$	812578.	0.603114	0.301557	−	0.953448i	$-0.402494\pi$
$283$	812578.	0.603114	0.301557	+	0.953448i	$0.402494\pi$
$284$	21515.5	0.0158291
$285$	81225.0	0.0592349
$286$	231597.	0.167424
$287$	−134565.	−0.0964336
$288$	−82944.0	−0.0589256
$289$	86575.7	0.0609749
$290$	−508010.	−0.354713
$291$	−71852.0	−0.0497401
$292$	−1.37465e6	−0.943484
$293$	−1.14928e6	−0.782091	−0.391046	−	0.920371i	$-0.627887\pi$
$293$	−1.14928e6	−0.782091	−0.391046	+	0.920371i	$0.627887\pi$
$294$	−601071.	−0.405562
$295$	897934.	0.600744
$296$	123844.	0.0821571
$297$	−48253.9	−0.0317425
$298$	−1.24037e6	−0.809115
$299$	2.86214e6	1.85145
$300$	−90000.0	−0.0577350
$301$	−26010.4	−0.0165474
$302$	−675552.	−0.426227
$303$	−1.56091e6	−0.976722
$304$	92416.0	0.0573539
$305$	−29806.1	−0.0183466
$306$	−397667.	−0.242782
$307$	297507.	0.180157	0.0900784	−	0.995935i	$-0.471288\pi$
$307$	297507.	0.180157	0.0900784	+	0.995935i	$0.471288\pi$
$308$	−11136.6	−0.00668921
$309$	986855.	0.587973
$310$	422851.	0.249909
$311$	483996.	0.283753	0.141877	−	0.989884i	$-0.454686\pi$
$311$	483996.	0.283753	0.141877	+	0.989884i	$0.454686\pi$
$312$	−503837.	−0.293024
$313$	−1.00708e6	−0.581036	−0.290518	−	0.956870i	$-0.593828\pi$
$313$	−1.00708e6	−0.581036	−0.290518	+	0.956870i	$0.593828\pi$
$314$	−1.43222e6	−0.819759
$315$	21293.7	0.0120914
$316$	−478247.	−0.269423
$317$	−3.31056e6	−1.85035	−0.925174	−	0.379543i	$-0.876081\pi$
$317$	−3.31056e6	−1.85035	−0.925174	+	0.379543i	$0.876081\pi$
$318$	−72876.4	−0.0404128
$319$	−336262.	−0.185012
$320$	−102400.	−0.0559017
$321$	263877.	0.142935
$322$	−137629.	−0.0739726
$323$	443080.	0.236307
$324$	104976.	0.0555556
$325$	−546698.	−0.287104
$326$	−2.13815e6	−1.11428
$327$	1.17309e6	0.606686
$328$	−819005.	−0.420341
$329$	182779.	0.0930970
$330$	−59572.8	−0.0301136
$331$	−631259.	−0.316692	−0.158346	−	0.987384i	$-0.550616\pi$
$331$	−631259.	−0.316692	−0.158346	+	0.987384i	$0.550616\pi$
$332$	1.65317e6	0.823139
$333$	−156740.	−0.0774584
$334$	2.16359e6	1.06123
$335$	309601.	0.150727
$336$	24227.5	0.0117074
$337$	−2.41418e6	−1.15796	−0.578981	−	0.815341i	$-0.696549\pi$
$337$	−2.41418e6	−1.15796	−0.578981	+	0.815341i	$0.696549\pi$
$338$	−1.57534e6	−0.750038
$339$	875157.	0.413606
$340$	−490947.	−0.230323
$341$	279893.	0.130349
$342$	−116964.	−0.0540738
$343$	352303.	0.161689
$344$	−158307.	−0.0721281
$345$	−736218.	−0.333011
$346$	−1.75167e6	−0.786614
$347$	−3.27280e6	−1.45913	−0.729567	−	0.683909i	$-0.760278\pi$
$347$	−3.27280e6	−1.45913	−0.729567	+	0.683909i	$0.760278\pi$
$348$	731534.	0.323807
$349$	−931844.	−0.409524	−0.204762	−	0.978812i	$-0.565642\pi$
$349$	−931844.	−0.409524	−0.204762	+	0.978812i	$0.565642\pi$
$350$	26288.5	0.0114709
$351$	637668.	0.276266
$352$	−67780.6	−0.0291574
$353$	−2.27634e6	−0.972300	−0.486150	−	0.873875i	$-0.661599\pi$
$353$	−2.27634e6	−0.972300	−0.486150	+	0.873875i	$0.661599\pi$
$354$	−1.29302e6	−0.548402
$355$	−33618.0	−0.0141580
$356$	1.11422e6	0.465959
$357$	116157.	0.0482362
$358$	−2.77975e6	−1.14630
$359$	−2.60281e6	−1.06588	−0.532938	−	0.846154i	$-0.678912\pi$
$359$	−2.60281e6	−1.06588	−0.532938	+	0.846154i	$0.678912\pi$
$360$	129600.	0.0527046
$361$	130321.	0.0526316
$362$	−1.82026e6	−0.730067
$363$	1.41003e6	0.561644
$364$	147168.	0.0582184
$365$	2.14789e6	0.843878
$366$	42920.8	0.0167481
$367$	−326323.	−0.126469	−0.0632343	−	0.997999i	$-0.520142\pi$
$367$	−326323.	−0.126469	−0.0632343	+	0.997999i	$0.520142\pi$
$368$	−837652.	−0.322436
$369$	1.03655e6	0.396301
$370$	−193506.	−0.0734835
$371$	21286.8	0.00802927
$372$	−608905.	−0.228135
$373$	−36470.4	−0.0135728	−0.00678639	−	0.999977i	$-0.502160\pi$
$373$	−36470.4	−0.0135728	−0.00678639	+	0.999977i	$0.502160\pi$
$374$	−324968.	−0.120133
$375$	140625.	0.0516398
$376$	1.11245e6	0.405797
$377$	4.44365e6	1.61022
$378$	−30663.0	−0.0110379
$379$	2.65210e6	0.948401	0.474201	−	0.880417i	$-0.342737\pi$
$379$	2.65210e6	0.948401	0.474201	+	0.880417i	$0.342737\pi$
$380$	−144400.	−0.0512989
$381$	79542.6	0.0280729
$382$	−3.30758e6	−1.15972
$383$	2.15645e6	0.751177	0.375588	−	0.926787i	$-0.377441\pi$
$383$	2.15645e6	0.751177	0.375588	+	0.926787i	$0.377441\pi$
$384$	147456.	0.0510310
$385$	17400.9	0.00598301
$386$	−634940.	−0.216902
$387$	200357.	0.0680030
$388$	127737.	0.0430762
$389$	1.53622e6	0.514729	0.257365	−	0.966314i	$-0.417146\pi$
$389$	1.53622e6	0.514729	0.257365	+	0.966314i	$0.417146\pi$
$390$	787245.	0.262089
$391$	−4.01605e6	−1.32849
$392$	1.06857e6	0.351227
$393$	−246162.	−0.0803969
$394$	123564.	0.0401007
$395$	747261.	0.240979
$396$	85784.8	0.0274898
$397$	1.81121e6	0.576755	0.288378	−	0.957517i	$-0.406884\pi$
$397$	1.81121e6	0.576755	0.288378	+	0.957517i	$0.406884\pi$
$398$	2.74219e6	0.867741
$399$	34164.6	0.0107435
$400$	160000.	0.0500000
$401$	4.91605e6	1.52670	0.763352	−	0.645983i	$-0.223552\pi$
$401$	4.91605e6	1.52670	0.763352	+	0.645983i	$0.223552\pi$
$402$	−445825.	−0.137594
$403$	−3.69874e6	−1.13447
$404$	2.77495e6	0.845866
$405$	−164025.	−0.0496904
$406$	−213678.	−0.0643345
$407$	−128085.	−0.0383278
$408$	706964.	0.210255
$409$	−4.08251e6	−1.20675	−0.603377	−	0.797456i	$-0.706179\pi$
$409$	−4.08251e6	−1.20675	−0.603377	+	0.797456i	$0.706179\pi$
$410$	1.27970e6	0.375965
$411$	−2.87392e6	−0.839209
$412$	−1.75441e6	−0.509199
$413$	377686.	0.108957
$414$	1.06015e6	0.303996
$415$	−2.58308e6	−0.736238
$416$	895710.	0.253766
$417$	−863716.	−0.243238
$418$	−95581.2	−0.0267566
$419$	−2.50230e6	−0.696314	−0.348157	−	0.937436i	$-0.613192\pi$
$419$	−2.50230e6	−0.696314	−0.348157	+	0.937436i	$0.613192\pi$
$420$	−37855.5	−0.0104714
$421$	3.82730e6	1.05242	0.526208	−	0.850356i	$-0.323613\pi$
$421$	3.82730e6	1.05242	0.526208	+	0.850356i	$0.323613\pi$
$422$	−2.30386e6	−0.629760
$423$	−1.40794e6	−0.382590
$424$	129558.	0.0349985
$425$	767105.	0.206007
$426$	48410.0	0.0129244
$427$	−12537.0	−0.00332753
$428$	−469115.	−0.123786
$429$	521093.	0.136701
$430$	247355.	0.0645133
$431$	−5.31675e6	−1.37865	−0.689324	−	0.724453i	$-0.742092\pi$
$431$	−5.31675e6	−1.37865	−0.689324	+	0.724453i	$0.742092\pi$
$432$	−186624.	−0.0481125
$433$	−4.00409e6	−1.02632	−0.513162	−	0.858292i	$-0.671526\pi$
$433$	−4.00409e6	−1.02632	−0.513162	+	0.858292i	$0.671526\pi$
$434$	177858.	0.0453262
$435$	−1.14302e6	−0.289622
$436$	−2.08550e6	−0.525405
$437$	−1.18122e6	−0.295888
$438$	−3.09296e6	−0.770352
$439$	6.13019e6	1.51814	0.759071	−	0.651008i	$-0.225653\pi$
$439$	6.13019e6	1.51814	0.759071	+	0.651008i	$0.225653\pi$
$440$	105907.	0.0260792
$441$	−1.35241e6	−0.331140
$442$	4.29440e6	1.04555
$443$	2.80375e6	0.678783	0.339391	−	0.940645i	$-0.389779\pi$
$443$	2.80375e6	0.678783	0.339391	+	0.940645i	$0.389779\pi$
$444$	278649.	0.0670810
$445$	−1.74098e6	−0.416766
$446$	−1.93712e6	−0.461125
$447$	−2.79083e6	−0.660640
$448$	−43071.2	−0.0101389
$449$	−4.77657e6	−1.11815	−0.559076	−	0.829117i	$-0.688844\pi$
$449$	−4.77657e6	−1.11815	−0.559076	+	0.829117i	$0.688844\pi$
$450$	−202500.	−0.0471405
$451$	847055.	0.196097
$452$	−1.55583e6	−0.358193
$453$	−1.51999e6	−0.348013
$454$	−2.74038e6	−0.623980
$455$	−229950.	−0.0520721
$456$	207936.	0.0468293
$457$	7.30147e6	1.63538	0.817692	−	0.575656i	$-0.195253\pi$
$457$	7.30147e6	1.63538	0.817692	+	0.575656i	$0.195253\pi$
$458$	−1.33570e6	−0.297539
$459$	−894751.	−0.198231
$460$	1.30883e6	0.288396
$461$	−813153.	−0.178205	−0.0891026	−	0.996022i	$-0.528400\pi$
$461$	−813153.	−0.178205	−0.0891026	+	0.996022i	$0.528400\pi$
$462$	−25057.3	−0.00546172
$463$	−6.50694e6	−1.41067	−0.705333	−	0.708876i	$-0.749202\pi$
$463$	−6.50694e6	−1.41067	−0.705333	+	0.708876i	$0.749202\pi$
$464$	−1.30051e6	−0.280425
$465$	951414.	0.204050
$466$	−4.74655e6	−1.01254
$467$	8.09261e6	1.71710	0.858552	−	0.512727i	$-0.171365\pi$
$467$	8.09261e6	1.71710	0.858552	+	0.512727i	$0.171365\pi$
$468$	−1.13363e6	−0.239253
$469$	130223.	0.0273374
$470$	−1.73820e6	−0.362956
$471$	−3.22250e6	−0.669331
$472$	2.29871e6	0.474930
$473$	163729.	0.0336491
$474$	−1.07606e6	−0.219983
$475$	225625.	0.0458831
$476$	−206501.	−0.0417738
$477$	−163972.	−0.0329969
$478$	−941799.	−0.188533
$479$	6.41880e6	1.27825	0.639124	−	0.769104i	$-0.279297\pi$
$479$	6.41880e6	1.27825	0.639124	+	0.769104i	$0.279297\pi$
$480$	−230400.	−0.0456435
$481$	1.69263e6	0.333579
$482$	6.65518e6	1.30479
$483$	−309666.	−0.0603983
$484$	−2.50671e6	−0.486398
$485$	−199589.	−0.0385285
$486$	236196.	0.0453609
$487$	3.36343e6	0.642628	0.321314	−	0.946973i	$-0.395875\pi$
$487$	3.36343e6	0.642628	0.321314	+	0.946973i	$0.395875\pi$
$488$	−76303.7	−0.0145043
$489$	−4.81085e6	−0.909807
$490$	−1.66964e6	−0.314147
$491$	6.64506e6	1.24393	0.621964	−	0.783046i	$-0.286335\pi$
$491$	6.64506e6	1.24393	0.621964	+	0.783046i	$0.286335\pi$
$492$	−1.84276e6	−0.343207
$493$	−6.23515e6	−1.15539
$494$	1.26309e6	0.232872
$495$	−134039.	−0.0245877
$496$	1.08250e6	0.197571
$497$	−14140.3	−0.00256784
$498$	3.71964e6	0.672090
$499$	2.60161e6	0.467726	0.233863	−	0.972270i	$-0.424863\pi$
$499$	2.60161e6	0.467726	0.233863	+	0.972270i	$0.424863\pi$
$500$	−250000.	−0.0447214
$501$	4.86808e6	0.866489
$502$	−6.92509e6	−1.22650
$503$	−2.28476e6	−0.402643	−0.201322	−	0.979525i	$-0.564524\pi$
$503$	−2.28476e6	−0.402643	−0.201322	+	0.979525i	$0.564524\pi$
$504$	54511.9	0.00955906
$505$	−4.33586e6	−0.756565
$506$	866341.	0.150422
$507$	−3.54452e6	−0.612404
$508$	−141409.	−0.0243119
$509$	3.09638e6	0.529736	0.264868	−	0.964285i	$-0.414672\pi$
$509$	3.09638e6	0.529736	0.264868	+	0.964285i	$0.414672\pi$
$510$	−1.10463e6	−0.188058
$511$	903438.	0.153055
$512$	−262144.	−0.0441942
$513$	−263169.	−0.0441511
$514$	−7.15161e6	−1.19398
$515$	2.74126e6	0.455442
$516$	−356191.	−0.0588923
$517$	−1.15055e6	−0.189312
$518$	−81391.9	−0.0133277
$519$	−3.94125e6	−0.642268
$520$	−1.39955e6	−0.226975
$521$	253549.	0.0409231	0.0204615	−	0.999791i	$-0.493486\pi$
$521$	253549.	0.0409231	0.0204615	+	0.999791i	$0.493486\pi$
$522$	1.64595e6	0.264388
$523$	−7.72045e6	−1.23421	−0.617104	−	0.786882i	$-0.711694\pi$
$523$	−7.72045e6	−1.23421	−0.617104	+	0.786882i	$0.711694\pi$
$524$	437621.	0.0696258
$525$	59149.2	0.00936593
$526$	7.08549e6	1.11662
$527$	5.18993e6	0.814020
$528$	−152506.	−0.0238069
$529$	4.27016e6	0.663444
$530$	−202434.	−0.0313036
$531$	−2.90931e6	−0.447768
$532$	−60737.1	−0.00930411
$533$	−1.11937e7	−1.70669
$534$	2.50701e6	0.380454
$535$	732993.	0.110717
$536$	792578.	0.119160
$537$	−6.25443e6	−0.935948
$538$	−1.59954e6	−0.238253
$539$	−1.10517e6	−0.163854
$540$	291600.	0.0430331
$541$	−5.90078e6	−0.866795	−0.433397	−	0.901203i	$-0.642685\pi$
$541$	−5.90078e6	−0.866795	−0.433397	+	0.901203i	$0.642685\pi$
$542$	−4.24653e6	−0.620920
$543$	−4.09559e6	−0.596097
$544$	−1.25683e6	−0.182086
$545$	3.25860e6	0.469937
$546$	331128.	0.0475351
$547$	−4.08905e6	−0.584325	−0.292162	−	0.956369i	$-0.594375\pi$
$547$	−4.08905e6	−0.584325	−0.292162	+	0.956369i	$0.594375\pi$
$548$	5.10919e6	0.726776
$549$	96571.9	0.0136748
$550$	−165480.	−0.0233259
$551$	−1.83392e6	−0.257336
$552$	−1.88472e6	−0.263268
$553$	314310.	0.0437065
$554$	3.92883e6	0.543862
$555$	−435388.	−0.0599991
$556$	1.53550e6	0.210650
$557$	−3.45071e6	−0.471271	−0.235636	−	0.971841i	$-0.575717\pi$
$557$	−3.45071e6	−0.471271	−0.235636	+	0.971841i	$0.575717\pi$
$558$	−1.37004e6	−0.186272
$559$	−2.16365e6	−0.292859
$560$	67298.7	0.00906852
$561$	−731177.	−0.0980879
$562$	−7.47067e6	−0.997743
$563$	1.23336e7	1.63991	0.819954	−	0.572429i	$-0.193999\pi$
$563$	1.23336e7	1.63991	0.819954	+	0.572429i	$0.193999\pi$
$564$	2.50300e6	0.331332
$565$	2.43099e6	0.320378
$566$	−3.25031e6	−0.426466
$567$	−68991.7	−0.00901237
$568$	−86062.1	−0.0111929
$569$	−2.08834e6	−0.270408	−0.135204	−	0.990818i	$-0.543169\pi$
$569$	−2.08834e6	−0.270408	−0.135204	+	0.990818i	$0.543169\pi$
$570$	−324900.	−0.0418854
$571$	7.14230e6	0.916744	0.458372	−	0.888760i	$-0.348433\pi$
$571$	7.14230e6	0.916744	0.458372	+	0.888760i	$0.348433\pi$
$572$	−926387.	−0.118387
$573$	−7.44205e6	−0.946904
$574$	538261.	0.0681889
$575$	−2.04505e6	−0.257949
$576$	331776.	0.0416667
$577$	4.68494e6	0.585820	0.292910	−	0.956140i	$-0.405376\pi$
$577$	4.68494e6	0.585820	0.292910	+	0.956140i	$0.405376\pi$
$578$	−346303.	−0.0431158
$579$	−1.42861e6	−0.177100
$580$	2.03204e6	0.250820
$581$	−1.08649e6	−0.133532
$582$	287408.	0.0351715
$583$	−133995.	−0.0163274
$584$	5.49860e6	0.667144
$585$	1.77130e6	0.213994
$586$	4.59713e6	0.553022
$587$	8.15202e6	0.976496	0.488248	−	0.872705i	$-0.337636\pi$
$587$	8.15202e6	0.976496	0.488248	+	0.872705i	$0.337636\pi$
$588$	2.40429e6	0.286776
$589$	1.52649e6	0.181303
$590$	−3.59174e6	−0.424790
$591$	278019.	0.0327420
$592$	−495375.	−0.0580938
$593$	−9.03224e6	−1.05477	−0.527386	−	0.849626i	$-0.676828\pi$
$593$	−9.03224e6	−1.05477	−0.527386	+	0.849626i	$0.676828\pi$
$594$	193016.	0.0224454
$595$	322657.	0.0373636
$596$	4.96148e6	0.572131
$597$	6.16993e6	0.708508
$598$	−1.14486e7	−1.30918
$599$	3.13283e6	0.356755	0.178377	−	0.983962i	$-0.442915\pi$
$599$	3.13283e6	0.356755	0.178377	+	0.983962i	$0.442915\pi$
$600$	360000.	0.0408248
$601$	−9.28095e6	−1.04811	−0.524054	−	0.851685i	$-0.675581\pi$
$601$	−9.28095e6	−1.04811	−0.524054	+	0.851685i	$0.675581\pi$
$602$	104042.	0.0117008
$603$	−1.00311e6	−0.112345
$604$	2.70221e6	0.301388
$605$	3.91674e6	0.435047
$606$	6.24363e6	0.690647
$607$	7.63319e6	0.840881	0.420441	−	0.907320i	$-0.361876\pi$
$607$	7.63319e6	0.840881	0.420441	+	0.907320i	$0.361876\pi$
$608$	−369664.	−0.0405554
$609$	−480774.	−0.0525289
$610$	119225.	0.0129730
$611$	1.52043e7	1.64764
$612$	1.59067e6	0.171673
$613$	−6.06515e6	−0.651914	−0.325957	−	0.945385i	$-0.605686\pi$
$613$	−6.06515e6	−0.651914	−0.325957	+	0.945385i	$0.605686\pi$
$614$	−1.19003e6	−0.127390
$615$	2.87931e6	0.306974
$616$	44546.3	0.00472999
$617$	8.16997e6	0.863988	0.431994	−	0.901876i	$-0.357810\pi$
$617$	8.16997e6	0.863988	0.431994	+	0.901876i	$0.357810\pi$
$618$	−3.94742e6	−0.415760
$619$	5.82724e6	0.611275	0.305637	−	0.952148i	$-0.401130\pi$
$619$	5.82724e6	0.611275	0.305637	+	0.952148i	$0.401130\pi$
$620$	−1.69140e6	−0.176713
$621$	2.38535e6	0.248212
$622$	−1.93598e6	−0.200644
$623$	−732284.	−0.0755891
$624$	2.01535e6	0.207199
$625$	390625.	0.0400000
$626$	4.02832e6	0.410854
$627$	−215058.	−0.0218467
$628$	5.72889e6	0.579657
$629$	−2.37503e6	−0.239355
$630$	−85174.9	−0.00854988
$631$	−6.02034e6	−0.601933	−0.300966	−	0.953635i	$-0.597309\pi$
$631$	−6.02034e6	−0.601933	−0.300966	+	0.953635i	$0.597309\pi$
$632$	1.91299e6	0.190511
$633$	−5.18369e6	−0.514197
$634$	1.32422e7	1.30839
$635$	220952.	0.0217452
$636$	291506.	0.0285762
$637$	1.46046e7	1.42607
$638$	1.34505e6	0.130823
$639$	108922.	0.0105527
$640$	409600.	0.0395285
$641$	−2.14234e6	−0.205942	−0.102971	−	0.994684i	$-0.532835\pi$
$641$	−2.14234e6	−0.205942	−0.102971	+	0.994684i	$0.532835\pi$
$642$	−1.05551e6	−0.101071
$643$	−1.40168e6	−0.133697	−0.0668485	−	0.997763i	$-0.521294\pi$
$643$	−1.40168e6	−0.133697	−0.0668485	+	0.997763i	$0.521294\pi$
$644$	550516.	0.0523065
$645$	556549.	0.0526749
$646$	−1.77232e6	−0.167094
$647$	−3.65566e6	−0.343324	−0.171662	−	0.985156i	$-0.554914\pi$
$647$	−3.65566e6	−0.343324	−0.171662	+	0.985156i	$0.554914\pi$
$648$	−419904.	−0.0392837
$649$	−2.37744e6	−0.221563
$650$	2.18679e6	0.203013
$651$	400181.	0.0370087
$652$	8.55262e6	0.787916
$653$	−1.86886e7	−1.71512	−0.857559	−	0.514386i	$-0.828020\pi$
$653$	−1.86886e7	−1.71512	−0.857559	+	0.514386i	$0.828020\pi$
$654$	−4.69238e6	−0.428992
$655$	−683783.	−0.0622752
$656$	3.27602e6	0.297226
$657$	−6.95916e6	−0.628990
$658$	−731115.	−0.0658295
$659$	9.00992e6	0.808178	0.404089	−	0.914720i	$-0.367589\pi$
$659$	9.00992e6	0.808178	0.404089	+	0.914720i	$0.367589\pi$
$660$	238291.	0.0212935
$661$	1.06803e7	0.950782	0.475391	−	0.879775i	$-0.342307\pi$
$661$	1.06803e7	0.950782	0.475391	+	0.879775i	$0.342307\pi$
$662$	2.52503e6	0.223935
$663$	9.66239e6	0.853691
$664$	−6.61269e6	−0.582047
$665$	94901.7	0.00832185
$666$	626959.	0.0547714
$667$	1.66225e7	1.44671
$668$	−8.65436e6	−0.750402
$669$	−4.35851e6	−0.376507
$670$	−1.23840e6	−0.106580
$671$	78917.0	0.00676651
$672$	−96910.1	−0.00827839
$673$	9.91478e6	0.843811	0.421906	−	0.906640i	$-0.361361\pi$
$673$	9.91478e6	0.843811	0.421906	+	0.906640i	$0.361361\pi$
$674$	9.65671e6	0.818803
$675$	−455625.	−0.0384900
$676$	6.30137e6	0.530357
$677$	8.93681e6	0.749395	0.374698	−	0.927147i	$-0.377747\pi$
$677$	8.93681e6	0.749395	0.374698	+	0.927147i	$0.377747\pi$
$678$	−3.50063e6	−0.292463
$679$	−83950.4	−0.00698793
$680$	1.96379e6	0.162863
$681$	−6.16585e6	−0.509478
$682$	−1.11957e6	−0.0921703
$683$	−1.30553e6	−0.107086	−0.0535431	−	0.998566i	$-0.517051\pi$
$683$	−1.30553e6	−0.107086	−0.0535431	+	0.998566i	$0.517051\pi$
$684$	467856.	0.0382360
$685$	−7.98311e6	−0.650048
$686$	−1.40921e6	−0.114331
$687$	−3.00532e6	−0.242940
$688$	633229.	0.0510023
$689$	1.77073e6	0.142103
$690$	2.94487e6	0.235474
$691$	6.36719e6	0.507286	0.253643	−	0.967298i	$-0.418371\pi$
$691$	6.36719e6	0.507286	0.253643	+	0.967298i	$0.418371\pi$
$692$	7.00668e6	0.556220
$693$	−56378.9	−0.00445947
$694$	1.30912e7	1.03176
$695$	−2.39921e6	−0.188411
$696$	−2.92614e6	−0.228966
$697$	1.57066e7	1.22461
$698$	3.72738e6	0.289577
$699$	−1.06797e7	−0.826737
$700$	−105154.	−0.00811113
$701$	2.08393e7	1.60173	0.800864	−	0.598847i	$-0.204374\pi$
$701$	2.08393e7	1.60173	0.800864	+	0.598847i	$0.204374\pi$
$702$	−2.55067e6	−0.195349
$703$	−698557.	−0.0533106
$704$	271122.	0.0206174
$705$	−3.91094e6	−0.296353
$706$	9.10536e6	0.687520
$707$	−1.82373e6	−0.137219
$708$	5.17210e6	0.387778
$709$	1.06242e7	0.793747	0.396874	−	0.917873i	$-0.370095\pi$
$709$	1.06242e7	0.793747	0.396874	+	0.917873i	$0.370095\pi$
$710$	134472.	0.0100112
$711$	−2.42113e6	−0.179615
$712$	−4.45690e6	−0.329483
$713$	−1.38360e7	−1.01926
$714$	−464626.	−0.0341082
$715$	1.44748e6	0.105888
$716$	1.11190e7	0.810555
$717$	−2.11905e6	−0.153937
$718$	1.04113e7	0.753688
$719$	1.39687e7	1.00771	0.503854	−	0.863789i	$-0.331915\pi$
$719$	1.39687e7	1.00771	0.503854	+	0.863789i	$0.331915\pi$
$720$	−518400.	−0.0372678
$721$	1.15302e6	0.0826037
$722$	−521284.	−0.0372161
$723$	1.49742e7	1.06536
$724$	7.28105e6	0.516235
$725$	−3.17506e6	−0.224340
$726$	−5.64011e6	−0.397142
$727$	2.45689e7	1.72405	0.862024	−	0.506867i	$-0.169196\pi$
$727$	2.45689e7	1.72405	0.862024	+	0.506867i	$0.169196\pi$
$728$	−588673.	−0.0411666
$729$	531441.	0.0370370
$730$	−8.59156e6	−0.596712
$731$	3.03596e6	0.210137
$732$	−171683.	−0.0118427
$733$	4.84507e6	0.333073	0.166537	−	0.986035i	$-0.446742\pi$
$733$	4.84507e6	0.333073	0.166537	+	0.986035i	$0.446742\pi$
$734$	1.30529e6	0.0894268
$735$	−3.75670e6	−0.256500
$736$	3.35061e6	0.227997
$737$	−819723.	−0.0555903
$738$	−4.14621e6	−0.280227
$739$	−1.20395e6	−0.0810958	−0.0405479	−	0.999178i	$-0.512910\pi$
$739$	−1.20395e6	−0.0810958	−0.0405479	+	0.999178i	$0.512910\pi$
$740$	774024.	0.0519607
$741$	2.84195e6	0.190139
$742$	−85147.3	−0.00567755
$743$	9.10124e6	0.604824	0.302412	−	0.953177i	$-0.402208\pi$
$743$	9.10124e6	0.604824	0.302412	+	0.953177i	$0.402208\pi$
$744$	2.43562e6	0.161316
$745$	−7.75231e6	−0.511729
$746$	145882.	0.00959740
$747$	8.36919e6	0.548759
$748$	1.29987e6	0.0849466
$749$	308309.	0.0200808
$750$	−562500.	−0.0365148
$751$	−3.60925e6	−0.233516	−0.116758	−	0.993160i	$-0.537250\pi$
$751$	−3.60925e6	−0.233516	−0.116758	+	0.993160i	$0.537250\pi$
$752$	−4.44978e6	−0.286942
$753$	−1.55815e7	−1.00143
$754$	−1.77746e7	−1.13860
$755$	−4.22220e6	−0.269570
$756$	122652.	0.00780494
$757$	−7.04425e6	−0.446781	−0.223391	−	0.974729i	$-0.571713\pi$
$757$	−7.04425e6	−0.446781	−0.223391	+	0.974729i	$0.571713\pi$
$758$	−1.06084e7	−0.670621
$759$	1.94927e6	0.122819
$760$	577600.	0.0362738
$761$	−2.29176e7	−1.43452	−0.717261	−	0.696805i	$-0.754604\pi$
$761$	−2.29176e7	−1.43452	−0.717261	+	0.696805i	$0.754604\pi$
$762$	−318171.	−0.0198505
$763$	1.37062e6	0.0852326
$764$	1.32303e7	0.820043
$765$	−2.48542e6	−0.153549
$766$	−8.62579e6	−0.531162
$767$	3.14175e7	1.92834
$768$	−589824.	−0.0360844
$769$	1.10398e7	0.673200	0.336600	−	0.941648i	$-0.390723\pi$
$769$	1.10398e7	0.673200	0.336600	+	0.941648i	$0.390723\pi$
$770$	−69603.6	−0.00423063
$771$	−1.60911e7	−0.974878
$772$	2.53976e6	0.153373
$773$	−1.32121e7	−0.795284	−0.397642	−	0.917541i	$-0.630171\pi$
$773$	−1.32121e7	−0.795284	−0.397642	+	0.917541i	$0.630171\pi$
$774$	−801430.	−0.0480854
$775$	2.64282e6	0.158057
$776$	−510947.	−0.0304594
$777$	−183132.	−0.0108821
$778$	−6.14487e6	−0.363968
$779$	4.61970e6	0.272753
$780$	−3.14898e6	−0.185325
$781$	89009.7	0.00522167
$782$	1.60642e7	0.939381
$783$	3.70339e6	0.215872
$784$	−4.27429e6	−0.248355
$785$	−8.95139e6	−0.518461
$786$	984648.	0.0568492
$787$	−1.39201e7	−0.801137	−0.400569	−	0.916267i	$-0.631187\pi$
$787$	−1.39201e7	−0.801137	−0.400569	+	0.916267i	$0.631187\pi$
$788$	−494256.	−0.0283554
$789$	1.59424e7	0.911717
$790$	−2.98904e6	−0.170398
$791$	1.02252e6	0.0581070
$792$	−343139.	−0.0194383
$793$	−1.04288e6	−0.0588911
$794$	−7.24482e6	−0.407828
$795$	−455478.	−0.0255593
$796$	−1.09688e7	−0.613586
$797$	−2.08340e6	−0.116179	−0.0580895	−	0.998311i	$-0.518501\pi$
$797$	−2.08340e6	−0.116179	−0.0580895	+	0.998311i	$0.518501\pi$
$798$	−136658.	−0.00759677
$799$	−2.13341e7	−1.18224
$800$	−640000.	−0.0353553
$801$	5.64076e6	0.310639
$802$	−1.96642e7	−1.07954
$803$	−5.68692e6	−0.311235
$804$	1.78330e6	0.0972937
$805$	−860182.	−0.0467844
$806$	1.47950e7	0.802189
$807$	−3.59896e6	−0.194533
$808$	−1.10998e7	−0.598117
$809$	−1.56168e7	−0.838920	−0.419460	−	0.907774i	$-0.637781\pi$
$809$	−1.56168e7	−0.838920	−0.419460	+	0.907774i	$0.637781\pi$
$810$	656100.	0.0351364
$811$	−1.30878e7	−0.698738	−0.349369	−	0.936985i	$-0.613604\pi$
$811$	−1.30878e7	−0.698738	−0.349369	+	0.936985i	$0.613604\pi$
$812$	854710.	0.0454913
$813$	−9.55468e6	−0.506979
$814$	512341.	0.0271018
$815$	−1.33635e7	−0.704734
$816$	−2.82786e6	−0.148673
$817$	892951.	0.0468029
$818$	1.63300e7	0.853305
$819$	745039.	0.0388123
$820$	−5.11878e6	−0.265847
$821$	1.66790e7	0.863601	0.431801	−	0.901969i	$-0.357878\pi$
$821$	1.66790e7	0.863601	0.431801	+	0.901969i	$0.357878\pi$
$822$	1.14957e7	0.593410
$823$	2.35861e7	1.21383	0.606913	−	0.794768i	$-0.292408\pi$
$823$	2.35861e7	1.21383	0.606913	+	0.794768i	$0.292408\pi$
$824$	7.01764e6	0.360058
$825$	−372330.	−0.0190455
$826$	−1.51074e6	−0.0770444
$827$	1.31992e7	0.671097	0.335548	−	0.942023i	$-0.391078\pi$
$827$	1.31992e7	0.671097	0.335548	+	0.942023i	$0.391078\pi$
$828$	−4.24061e6	−0.214958
$829$	−3.82796e7	−1.93456	−0.967278	−	0.253720i	$-0.918346\pi$
$829$	−3.82796e7	−1.93456	−0.967278	+	0.253720i	$0.918346\pi$
$830$	1.03323e7	0.520599
$831$	8.83987e6	0.444062
$832$	−3.58284e6	−0.179440
$833$	−2.04927e7	−1.02326
$834$	3.45487e6	0.171995
$835$	1.35224e7	0.671180
$836$	382325.	0.0189198
$837$	−3.08258e6	−0.152090
$838$	1.00092e7	0.492368
$839$	3.43196e6	0.168321	0.0841604	−	0.996452i	$-0.473179\pi$
$839$	3.43196e6	0.168321	0.0841604	+	0.996452i	$0.473179\pi$
$840$	151422.	0.00740442
$841$	5.29627e6	0.258214
$842$	−1.53092e7	−0.744170
$843$	−1.68090e7	−0.814654
$844$	9.21544e6	0.445308
$845$	−9.84589e6	−0.474366
$846$	5.63176e6	0.270532
$847$	1.64745e6	0.0789047
$848$	−518232.	−0.0247477
$849$	−7.31321e6	−0.348208
$850$	−3.06842e6	−0.145669
$851$	6.33167e6	0.299705
$852$	−193640.	−0.00913894
$853$	2.08978e7	0.983396	0.491698	−	0.870766i	$-0.336376\pi$
$853$	2.08978e7	0.983396	0.491698	+	0.870766i	$0.336376\pi$
$854$	50147.8	0.00235292
$855$	−731025.	−0.0341993
$856$	1.87646e6	0.0875296
$857$	2.94317e7	1.36887	0.684437	−	0.729072i	$-0.260048\pi$
$857$	2.94317e7	1.36887	0.684437	+	0.729072i	$0.260048\pi$
$858$	−2.08437e6	−0.0966622
$859$	6.94733e6	0.321244	0.160622	−	0.987016i	$-0.448650\pi$
$859$	6.94733e6	0.321244	0.160622	+	0.987016i	$0.448650\pi$
$860$	−989420.	−0.0456178
$861$	1.21109e6	0.0556760
$862$	2.12670e7	0.974851
$863$	−3.55495e7	−1.62483	−0.812413	−	0.583083i	$-0.801846\pi$
$863$	−3.55495e7	−1.62483	−0.812413	+	0.583083i	$0.801846\pi$
$864$	746496.	0.0340207
$865$	−1.09479e7	−0.497498
$866$	1.60164e7	0.725721
$867$	−779181.	−0.0352039
$868$	−711432.	−0.0320505
$869$	−1.97851e6	−0.0888767
$870$	4.57209e6	0.204794
$871$	1.08325e7	0.483820
$872$	8.34201e6	0.371518
$873$	646668.	0.0287174
$874$	4.72488e6	0.209224
$875$	164303.	0.00725482
$876$	1.23718e7	0.544721
$877$	−2.98092e7	−1.30874	−0.654368	−	0.756177i	$-0.727065\pi$
$877$	−2.98092e7	−1.30874	−0.654368	+	0.756177i	$0.727065\pi$
$878$	−2.45208e7	−1.07349
$879$	1.03435e7	0.451541
$880$	−423628.	−0.0184407
$881$	1.02355e7	0.444294	0.222147	−	0.975013i	$-0.428693\pi$
$881$	1.02355e7	0.444294	0.222147	+	0.975013i	$0.428693\pi$
$882$	5.40964e6	0.234152
$883$	2.30916e7	0.996670	0.498335	−	0.866984i	$-0.333945\pi$
$883$	2.30916e7	0.996670	0.498335	+	0.866984i	$0.333945\pi$
$884$	−1.71776e7	−0.739318
$885$	−8.08140e6	−0.346840
$886$	−1.12150e7	−0.479972
$887$	−3.34284e7	−1.42661	−0.713307	−	0.700851i	$-0.752804\pi$
$887$	−3.34284e7	−1.42661	−0.713307	+	0.700851i	$0.752804\pi$
$888$	−1.11459e6	−0.0474334
$889$	92936.0	0.00394393
$890$	6.96390e6	0.294698
$891$	434285.	0.0183266
$892$	7.74847e6	0.326065
$893$	−6.27489e6	−0.263316
$894$	1.11633e7	0.467143
$895$	−1.73734e7	−0.724982
$896$	172285.	0.00716930
$897$	−2.57593e7	−1.06894
$898$	1.91063e7	0.790652
$899$	−2.14812e7	−0.886462
$900$	810000.	0.0333333
$901$	−2.48462e6	−0.101964
$902$	−3.38822e6	−0.138661
$903$	234094.	0.00955367
$904$	6.22334e6	0.253281
$905$	−1.13766e7	−0.461735
$906$	6.07997e6	0.246082
$907$	−1.70296e7	−0.687365	−0.343682	−	0.939086i	$-0.611674\pi$
$907$	−1.70296e7	−0.687365	−0.343682	+	0.939086i	$0.611674\pi$
$908$	1.09615e7	0.441221
$909$	1.40482e7	0.563911
$910$	919801.	0.0368206
$911$	−2.35019e7	−0.938225	−0.469113	−	0.883138i	$-0.655426\pi$
$911$	−2.35019e7	−0.938225	−0.469113	+	0.883138i	$0.655426\pi$
$912$	−831744.	−0.0331133
$913$	6.83917e6	0.271535
$914$	−2.92059e7	−1.15639
$915$	268255.	0.0105924
$916$	5.34278e6	0.210392
$917$	−287611.	−0.0112949
$918$	3.57901e6	0.140170
$919$	4.73811e7	1.85062	0.925309	−	0.379214i	$-0.123806\pi$
$919$	4.73811e7	1.85062	0.925309	+	0.379214i	$0.123806\pi$
$920$	−5.23533e6	−0.203927
$921$	−2.67756e6	−0.104014
$922$	3.25261e6	0.126010
$923$	−1.17625e6	−0.0454459
$924$	100229.	0.00386202
$925$	−1.20941e6	−0.0464751
$926$	2.60277e7	0.997491
$927$	−8.88170e6	−0.339466
$928$	5.20202e6	0.198291
$929$	−2.83937e7	−1.07940	−0.539701	−	0.841857i	$-0.681463\pi$
$929$	−2.83937e7	−1.07940	−0.539701	+	0.841857i	$0.681463\pi$
$930$	−3.80566e6	−0.144285
$931$	−6.02741e6	−0.227906
$932$	1.89862e7	0.715975
$933$	−4.35596e6	−0.163825
$934$	−3.23705e7	−1.21418
$935$	−2.03105e6	−0.0759786
$936$	4.53453e6	0.169178
$937$	1.79655e6	0.0668483	0.0334241	−	0.999441i	$-0.489359\pi$
$937$	1.79655e6	0.0668483	0.0334241	+	0.999441i	$0.489359\pi$
$938$	−520893.	−0.0193304
$939$	9.06371e6	0.335461
$940$	6.95279e6	0.256649
$941$	7.86302e6	0.289478	0.144739	−	0.989470i	$-0.453766\pi$
$941$	7.86302e6	0.289478	0.144739	+	0.989470i	$0.453766\pi$
$942$	1.28900e7	0.473288
$943$	−4.18726e7	−1.53338
$944$	−9.19484e6	−0.335826
$945$	−191644.	−0.00698095
$946$	−654916.	−0.0237935
$947$	3.70426e7	1.34223	0.671114	−	0.741354i	$-0.265816\pi$
$947$	3.70426e7	1.34223	0.671114	+	0.741354i	$0.265816\pi$
$948$	4.30422e6	0.155551
$949$	7.51518e7	2.70878
$950$	−902500.	−0.0324443
$951$	2.97950e7	1.06830
$952$	826003.	0.0295385
$953$	3.15822e7	1.12645	0.563223	−	0.826305i	$-0.309561\pi$
$953$	3.15822e7	1.12645	0.563223	+	0.826305i	$0.309561\pi$
$954$	655888.	0.0233324
$955$	−2.06724e7	−0.733469
$956$	3.76720e6	0.133313
$957$	3.02636e6	0.106817
$958$	−2.56752e7	−0.903858
$959$	−3.35783e6	−0.117900
$960$	921600.	0.0322749
$961$	−1.07489e7	−0.375453
$962$	−6.77051e6	−0.235876
$963$	−2.37490e6	−0.0825237
$964$	−2.66207e7	−0.922629
$965$	−3.96837e6	−0.137181
$966$	1.23866e6	0.0427081
$967$	−4.02100e6	−0.138283	−0.0691414	−	0.997607i	$-0.522026\pi$
$967$	−4.02100e6	−0.138283	−0.0691414	+	0.997607i	$0.522026\pi$
$968$	1.00269e7	0.343935
$969$	−3.98772e6	−0.136432
$970$	798355.	0.0272438
$971$	−3.42810e7	−1.16683	−0.583413	−	0.812176i	$-0.698283\pi$
$971$	−3.42810e7	−1.16683	−0.583413	+	0.812176i	$0.698283\pi$
$972$	−944784.	−0.0320750
$973$	−1.00915e6	−0.0341722
$974$	−1.34537e7	−0.454407
$975$	4.92028e6	0.165759
$976$	305215.	0.0102561
$977$	−2.03856e7	−0.683262	−0.341631	−	0.939834i	$-0.610979\pi$
$977$	−2.03856e7	−0.683262	−0.341631	+	0.939834i	$0.610979\pi$
$978$	1.92434e7	0.643331
$979$	4.60954e6	0.153710
$980$	6.67857e6	0.222136
$981$	−1.05579e7	−0.350270
$982$	−2.65802e7	−0.879590
$983$	5.34481e6	0.176420	0.0882101	−	0.996102i	$-0.471885\pi$
$983$	5.34481e6	0.176420	0.0882101	+	0.996102i	$0.471885\pi$
$984$	7.37104e6	0.242684
$985$	772275.	0.0253619
$986$	2.49406e7	0.816986
$987$	−1.64501e6	−0.0537496
$988$	−5.05236e6	−0.164665
$989$	−8.09365e6	−0.263120
$990$	536155.	0.0173861
$991$	4.03349e7	1.30466	0.652329	−	0.757936i	$-0.273792\pi$
$991$	4.03349e7	1.30466	0.652329	+	0.757936i	$0.273792\pi$
$992$	−4.32999e6	−0.139704
$993$	5.68133e6	0.182842
$994$	56561.2	0.00181574
$995$	1.71387e7	0.548808
$996$	−1.48786e7	−0.475239
$997$	−3.05968e7	−0.974852	−0.487426	−	0.873164i	$-0.662064\pi$
$997$	−3.05968e7	−0.974852	−0.487426	+	0.873164i	$0.662064\pi$
$998$	−1.04065e7	−0.330732
$999$	1.41066e6	0.0447207

Twists

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

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

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} -10.5154 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} -10.5154 q^{7} -64.0000 q^{8} +81.0000 q^{9} +100.000 q^{10} +66.1919 q^{11} -144.000 q^{12} -874.716 q^{13} +42.0617 q^{14} +225.000 q^{15} +256.000 q^{16} +1227.37 q^{17} -324.000 q^{18} +361.000 q^{19} -400.000 q^{20} +94.6388 q^{21} -264.768 q^{22} -3272.08 q^{23} +576.000 q^{24} +625.000 q^{25} +3498.87 q^{26} -729.000 q^{27} -168.247 q^{28} -5080.10 q^{29} -900.000 q^{30} +4228.51 q^{31} -1024.00 q^{32} -595.728 q^{33} -4909.47 q^{34} +262.885 q^{35} +1296.00 q^{36} -1935.06 q^{37} -1444.00 q^{38} +7872.45 q^{39} +1600.00 q^{40} +12797.0 q^{41} -378.555 q^{42} +2473.55 q^{43} +1059.07 q^{44} -2025.00 q^{45} +13088.3 q^{46} -17382.0 q^{47} -2304.00 q^{48} -16696.4 q^{49} -2500.00 q^{50} -11046.3 q^{51} -13995.5 q^{52} -2024.34 q^{53} +2916.00 q^{54} -1654.80 q^{55} +672.987 q^{56} -3249.00 q^{57} +20320.4 q^{58} -35917.4 q^{59} +3600.00 q^{60} +1192.25 q^{61} -16914.0 q^{62} -851.749 q^{63} +4096.00 q^{64} +21867.9 q^{65} +2382.91 q^{66} -12384.0 q^{67} +19637.9 q^{68} +29448.7 q^{69} -1051.54 q^{70} +1344.72 q^{71} -5184.00 q^{72} -85915.6 q^{73} +7740.24 q^{74} -5625.00 q^{75} +5776.00 q^{76} -696.036 q^{77} -31489.8 q^{78} -29890.4 q^{79} -6400.00 q^{80} +6561.00 q^{81} -51187.8 q^{82} +103323. q^{83} +1514.22 q^{84} -30684.2 q^{85} -9894.20 q^{86} +45720.9 q^{87} -4236.28 q^{88} +69639.0 q^{89} +8100.00 q^{90} +9198.01 q^{91} -52353.3 q^{92} -38056.6 q^{93} +69527.9 q^{94} -9025.00 q^{95} +9216.00 q^{96} +7983.55 q^{97} +66785.7 q^{98} +5361.55 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} + 144 q^{6} - 88 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) \) 4 * q - 16 * q^2 - 36 * q^3 + 64 * q^4 - 100 * q^5 + 144 * q^6 - 88 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} + 144 q^{6} - 88 q^{7} - 256 q^{8} + 324 q^{9} + 400 q^{10} + 940 q^{11} - 576 q^{12} - 34 q^{13} + 352 q^{14} + 900 q^{15} + 1024 q^{16} - 138 q^{17} - 1296 q^{18} + 1444 q^{19} - 1600 q^{20} + 792 q^{21} - 3760 q^{22} + 486 q^{23} + 2304 q^{24} + 2500 q^{25} + 136 q^{26} - 2916 q^{27} - 1408 q^{28} + 3296 q^{29} - 3600 q^{30} - 6686 q^{31} - 4096 q^{32} - 8460 q^{33} + 552 q^{34} + 2200 q^{35} + 5184 q^{36} - 14218 q^{37} - 5776 q^{38} + 306 q^{39} + 6400 q^{40} + 1342 q^{41} - 3168 q^{42} - 26330 q^{43} + 15040 q^{44} - 8100 q^{45} - 1944 q^{46} - 7010 q^{47} - 9216 q^{48} + 192 q^{49} - 10000 q^{50} + 1242 q^{51} - 544 q^{52} - 22782 q^{53} + 11664 q^{54} - 23500 q^{55} + 5632 q^{56} - 12996 q^{57} - 13184 q^{58} - 13358 q^{59} + 14400 q^{60} + 16008 q^{61} + 26744 q^{62} - 7128 q^{63} + 16384 q^{64} + 850 q^{65} + 33840 q^{66} - 22696 q^{67} - 2208 q^{68} - 4374 q^{69} - 8800 q^{70} + 52584 q^{71} - 20736 q^{72} - 101048 q^{73} + 56872 q^{74} - 22500 q^{75} + 23104 q^{76} - 103772 q^{77} - 1224 q^{78} - 113090 q^{79} - 25600 q^{80} + 26244 q^{81} - 5368 q^{82} - 65384 q^{83} + 12672 q^{84} + 3450 q^{85} + 105320 q^{86} - 29664 q^{87} - 60160 q^{88} + 97354 q^{89} + 32400 q^{90} - 125600 q^{91} + 7776 q^{92} + 60174 q^{93} + 28040 q^{94} - 36100 q^{95} + 36864 q^{96} - 198934 q^{97} - 768 q^{98} + 76140 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 - 36 * q^3 + 64 * q^4 - 100 * q^5 + 144 * q^6 - 88 * q^7 - 256 * q^8 + 324 * q^9 + 400 * q^10 + 940 * q^11 - 576 * q^12 - 34 * q^13 + 352 * q^14 + 900 * q^15 + 1024 * q^16 - 138 * q^17 - 1296 * q^18 + 1444 * q^19 - 1600 * q^20 + 792 * q^21 - 3760 * q^22 + 486 * q^23 + 2304 * q^24 + 2500 * q^25 + 136 * q^26 - 2916 * q^27 - 1408 * q^28 + 3296 * q^29 - 3600 * q^30 - 6686 * q^31 - 4096 * q^32 - 8460 * q^33 + 552 * q^34 + 2200 * q^35 + 5184 * q^36 - 14218 * q^37 - 5776 * q^38 + 306 * q^39 + 6400 * q^40 + 1342 * q^41 - 3168 * q^42 - 26330 * q^43 + 15040 * q^44 - 8100 * q^45 - 1944 * q^46 - 7010 * q^47 - 9216 * q^48 + 192 * q^49 - 10000 * q^50 + 1242 * q^51 - 544 * q^52 - 22782 * q^53 + 11664 * q^54 - 23500 * q^55 + 5632 * q^56 - 12996 * q^57 - 13184 * q^58 - 13358 * q^59 + 14400 * q^60 + 16008 * q^61 + 26744 * q^62 - 7128 * q^63 + 16384 * q^64 + 850 * q^65 + 33840 * q^66 - 22696 * q^67 - 2208 * q^68 - 4374 * q^69 - 8800 * q^70 + 52584 * q^71 - 20736 * q^72 - 101048 * q^73 + 56872 * q^74 - 22500 * q^75 + 23104 * q^76 - 103772 * q^77 - 1224 * q^78 - 113090 * q^79 - 25600 * q^80 + 26244 * q^81 - 5368 * q^82 - 65384 * q^83 + 12672 * q^84 + 3450 * q^85 + 105320 * q^86 - 29664 * q^87 - 60160 * q^88 + 97354 * q^89 + 32400 * q^90 - 125600 * q^91 + 7776 * q^92 + 60174 * q^93 + 28040 * q^94 - 36100 * q^95 + 36864 * q^96 - 198934 * q^97 - 768 * q^98 + 76140 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more