LMFDB - Embedded newform 570.6.a.e.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:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 787x - 4530 $ x^3 - 787*x - 4530
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-24.5446$ 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)

$f(q)$	$=$	$q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -36.0000 q^{6} +26.8435 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -36.0000 q^{6} +26.8435 q^{7} +64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -461.692 q^{11} -144.000 q^{12} +695.032 q^{13} +107.374 q^{14} +225.000 q^{15} +256.000 q^{16} +66.6538 q^{17} +324.000 q^{18} +361.000 q^{19} -400.000 q^{20} -241.592 q^{21} -1846.77 q^{22} -3223.72 q^{23} -576.000 q^{24} +625.000 q^{25} +2780.13 q^{26} -729.000 q^{27} +429.497 q^{28} +876.175 q^{29} +900.000 q^{30} +5098.85 q^{31} +1024.00 q^{32} +4155.23 q^{33} +266.615 q^{34} -671.089 q^{35} +1296.00 q^{36} +2669.21 q^{37} +1444.00 q^{38} -6255.28 q^{39} -1600.00 q^{40} -8445.55 q^{41} -966.368 q^{42} +13332.4 q^{43} -7387.07 q^{44} -2025.00 q^{45} -12894.9 q^{46} -1121.47 q^{47} -2304.00 q^{48} -16086.4 q^{49} +2500.00 q^{50} -599.884 q^{51} +11120.5 q^{52} -34796.2 q^{53} -2916.00 q^{54} +11542.3 q^{55} +1717.99 q^{56} -3249.00 q^{57} +3504.70 q^{58} -18084.4 q^{59} +3600.00 q^{60} +7109.95 q^{61} +20395.4 q^{62} +2174.33 q^{63} +4096.00 q^{64} -17375.8 q^{65} +16620.9 q^{66} -19978.9 q^{67} +1066.46 q^{68} +29013.5 q^{69} -2684.35 q^{70} +66452.6 q^{71} +5184.00 q^{72} -51701.2 q^{73} +10676.9 q^{74} -5625.00 q^{75} +5776.00 q^{76} -12393.4 q^{77} -25021.1 q^{78} +38142.5 q^{79} -6400.00 q^{80} +6561.00 q^{81} -33782.2 q^{82} -78470.9 q^{83} -3865.47 q^{84} -1666.34 q^{85} +53329.5 q^{86} -7885.57 q^{87} -29548.3 q^{88} -141292. q^{89} -8100.00 q^{90} +18657.1 q^{91} -51579.5 q^{92} -45889.6 q^{93} -4485.89 q^{94} -9025.00 q^{95} -9216.00 q^{96} -48386.1 q^{97} -64345.7 q^{98} -37397.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 12 q^{2} - 27 q^{3} + 48 q^{4} - 75 q^{5} - 108 q^{6} + 10 q^{7} + 192 q^{8} + 243 q^{9}+O(q^{10}) $ 3 * q + 12 * q^2 - 27 * q^3 + 48 * q^4 - 75 * q^5 - 108 * q^6 + 10 * q^7 + 192 * q^8 + 243 * q^9	\( 3 q + 12 q^{2} - 27 q^{3} + 48 q^{4} - 75 q^{5} - 108 q^{6} + 10 q^{7} + 192 q^{8} + 243 q^{9} - 300 q^{10} - 572 q^{11} - 432 q^{12} + 376 q^{13} + 40 q^{14} + 675 q^{15} + 768 q^{16} + 758 q^{17} + 972 q^{18} + 1083 q^{19} - 1200 q^{20} - 90 q^{21} - 2288 q^{22} + 1098 q^{23} - 1728 q^{24} + 1875 q^{25} + 1504 q^{26} - 2187 q^{27} + 160 q^{28} - 5610 q^{29} + 2700 q^{30} + 7620 q^{31} + 3072 q^{32} + 5148 q^{33} + 3032 q^{34} - 250 q^{35} + 3888 q^{36} - 3824 q^{37} + 4332 q^{38} - 3384 q^{39} - 4800 q^{40} - 8806 q^{41} - 360 q^{42} - 18274 q^{43} - 9152 q^{44} - 6075 q^{45} + 4392 q^{46} - 15358 q^{47} - 6912 q^{48} - 7869 q^{49} + 7500 q^{50} - 6822 q^{51} + 6016 q^{52} - 1572 q^{53} - 8748 q^{54} + 14300 q^{55} + 640 q^{56} - 9747 q^{57} - 22440 q^{58} - 33340 q^{59} + 10800 q^{60} + 26974 q^{61} + 30480 q^{62} + 810 q^{63} + 12288 q^{64} - 9400 q^{65} + 20592 q^{66} + 8180 q^{67} + 12128 q^{68} - 9882 q^{69} - 1000 q^{70} - 20360 q^{71} + 15552 q^{72} - 106318 q^{73} - 15296 q^{74} - 16875 q^{75} + 17328 q^{76} - 33212 q^{77} - 13536 q^{78} - 60680 q^{79} - 19200 q^{80} + 19683 q^{81} - 35224 q^{82} - 183246 q^{83} - 1440 q^{84} - 18950 q^{85} - 73096 q^{86} + 50490 q^{87} - 36608 q^{88} - 196766 q^{89} - 24300 q^{90} - 39084 q^{91} + 17568 q^{92} - 68580 q^{93} - 61432 q^{94} - 27075 q^{95} - 27648 q^{96} - 193852 q^{97} - 31476 q^{98} - 46332 q^{99}+O(q^{100}) \) 3 * q + 12 * q^2 - 27 * q^3 + 48 * q^4 - 75 * q^5 - 108 * q^6 + 10 * q^7 + 192 * q^8 + 243 * q^9 - 300 * q^10 - 572 * q^11 - 432 * q^12 + 376 * q^13 + 40 * q^14 + 675 * q^15 + 768 * q^16 + 758 * q^17 + 972 * q^18 + 1083 * q^19 - 1200 * q^20 - 90 * q^21 - 2288 * q^22 + 1098 * q^23 - 1728 * q^24 + 1875 * q^25 + 1504 * q^26 - 2187 * q^27 + 160 * q^28 - 5610 * q^29 + 2700 * q^30 + 7620 * q^31 + 3072 * q^32 + 5148 * q^33 + 3032 * q^34 - 250 * q^35 + 3888 * q^36 - 3824 * q^37 + 4332 * q^38 - 3384 * q^39 - 4800 * q^40 - 8806 * q^41 - 360 * q^42 - 18274 * q^43 - 9152 * q^44 - 6075 * q^45 + 4392 * q^46 - 15358 * q^47 - 6912 * q^48 - 7869 * q^49 + 7500 * q^50 - 6822 * q^51 + 6016 * q^52 - 1572 * q^53 - 8748 * q^54 + 14300 * q^55 + 640 * q^56 - 9747 * q^57 - 22440 * q^58 - 33340 * q^59 + 10800 * q^60 + 26974 * q^61 + 30480 * q^62 + 810 * q^63 + 12288 * q^64 - 9400 * q^65 + 20592 * q^66 + 8180 * q^67 + 12128 * q^68 - 9882 * q^69 - 1000 * q^70 - 20360 * q^71 + 15552 * q^72 - 106318 * q^73 - 15296 * q^74 - 16875 * q^75 + 17328 * q^76 - 33212 * q^77 - 13536 * q^78 - 60680 * q^79 - 19200 * q^80 + 19683 * q^81 - 35224 * q^82 - 183246 * q^83 - 1440 * q^84 - 18950 * q^85 - 73096 * q^86 + 50490 * q^87 - 36608 * q^88 - 196766 * q^89 - 24300 * q^90 - 39084 * q^91 + 17568 * q^92 - 68580 * q^93 - 61432 * q^94 - 27075 * q^95 - 27648 * q^96 - 193852 * q^97 - 31476 * q^98 - 46332 * 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
$7$	26.8435	0.207059	0.103530	−	0.994626i	$-0.466986\pi$
$7$	26.8435	0.207059	0.103530	+	0.994626i	$0.466986\pi$
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	−100.000	−0.316228
$11$	−461.692	−1.15046	−0.575229	−	0.817993i	$-0.695087\pi$
$11$	−461.692	−1.15046	−0.575229	+	0.817993i	$0.695087\pi$
$12$	−144.000	−0.288675
$13$	695.032	1.14063	0.570317	−	0.821425i	$-0.306820\pi$
$13$	695.032	1.14063	0.570317	+	0.821425i	$0.306820\pi$
$14$	107.374	0.146413
$15$	225.000	0.258199
$16$	256.000	0.250000
$17$	66.6538	0.0559374	0.0279687	−	0.999609i	$-0.491096\pi$
$17$	66.6538	0.0559374	0.0279687	+	0.999609i	$0.491096\pi$
$18$	324.000	0.235702
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	−400.000	−0.223607
$21$	−241.592	−0.119546
$22$	−1846.77	−0.813496
$23$	−3223.72	−1.27068	−0.635342	−	0.772231i	$-0.719141\pi$
$23$	−3223.72	−1.27068	−0.635342	+	0.772231i	$0.719141\pi$
$24$	−576.000	−0.204124
$25$	625.000	0.200000
$26$	2780.13	0.806550
$27$	−729.000	−0.192450
$28$	429.497	0.103530
$29$	876.175	0.193462	0.0967310	−	0.995311i	$-0.469161\pi$
$29$	876.175	0.193462	0.0967310	+	0.995311i	$0.469161\pi$
$30$	900.000	0.182574
$31$	5098.85	0.952945	0.476472	−	0.879189i	$-0.341915\pi$
$31$	5098.85	0.952945	0.476472	+	0.879189i	$0.341915\pi$
$32$	1024.00	0.176777
$33$	4155.23	0.664217
$34$	266.615	0.0395537
$35$	−671.089	−0.0925997
$36$	1296.00	0.166667
$37$	2669.21	0.320538	0.160269	−	0.987073i	$-0.448764\pi$
$37$	2669.21	0.320538	0.160269	+	0.987073i	$0.448764\pi$
$38$	1444.00	0.162221
$39$	−6255.28	−0.658545
$40$	−1600.00	−0.158114
$41$	−8445.55	−0.784636	−0.392318	−	0.919830i	$-0.628327\pi$
$41$	−8445.55	−0.784636	−0.392318	+	0.919830i	$0.628327\pi$
$42$	−966.368	−0.0845316
$43$	13332.4	1.09960	0.549802	−	0.835295i	$-0.314703\pi$
$43$	13332.4	1.09960	0.549802	+	0.835295i	$0.314703\pi$
$44$	−7387.07	−0.575229
$45$	−2025.00	−0.149071
$46$	−12894.9	−0.898510
$47$	−1121.47	−0.0740533	−0.0370266	−	0.999314i	$-0.511789\pi$
$47$	−1121.47	−0.0740533	−0.0370266	+	0.999314i	$0.511789\pi$
$48$	−2304.00	−0.144338
$49$	−16086.4	−0.957126
$50$	2500.00	0.141421
$51$	−599.884	−0.0322955
$52$	11120.5	0.570317
$53$	−34796.2	−1.70154	−0.850769	−	0.525539i	$-0.823864\pi$
$53$	−34796.2	−1.70154	−0.850769	+	0.525539i	$0.823864\pi$
$54$	−2916.00	−0.136083
$55$	11542.3	0.514500
$56$	1717.99	0.0732065
$57$	−3249.00	−0.132453
$58$	3504.70	0.136798
$59$	−18084.4	−0.676354	−0.338177	−	0.941083i	$-0.609810\pi$
$59$	−18084.4	−0.676354	−0.338177	+	0.941083i	$0.609810\pi$
$60$	3600.00	0.129099
$61$	7109.95	0.244648	0.122324	−	0.992490i	$-0.460965\pi$
$61$	7109.95	0.244648	0.122324	+	0.992490i	$0.460965\pi$
$62$	20395.4	0.673834
$63$	2174.33	0.0690198
$64$	4096.00	0.125000
$65$	−17375.8	−0.510107
$66$	16620.9	0.469672
$67$	−19978.9	−0.543731	−0.271865	−	0.962335i	$-0.587641\pi$
$67$	−19978.9	−0.543731	−0.271865	+	0.962335i	$0.587641\pi$
$68$	1066.46	0.0279687
$69$	29013.5	0.733630
$70$	−2684.35	−0.0654779
$71$	66452.6	1.56446	0.782232	−	0.622987i	$-0.214081\pi$
$71$	66452.6	1.56446	0.782232	+	0.622987i	$0.214081\pi$
$72$	5184.00	0.117851
$73$	−51701.2	−1.13552	−0.567758	−	0.823195i	$-0.692189\pi$
$73$	−51701.2	−1.13552	−0.567758	+	0.823195i	$0.692189\pi$
$74$	10676.9	0.226654
$75$	−5625.00	−0.115470
$76$	5776.00	0.114708
$77$	−12393.4	−0.238213
$78$	−25021.1	−0.465662
$79$	38142.5	0.687608	0.343804	−	0.939041i	$-0.388284\pi$
$79$	38142.5	0.687608	0.343804	+	0.939041i	$0.388284\pi$
$80$	−6400.00	−0.111803
$81$	6561.00	0.111111
$82$	−33782.2	−0.554821
$83$	−78470.9	−1.25030	−0.625149	−	0.780506i	$-0.714962\pi$
$83$	−78470.9	−1.25030	−0.625149	+	0.780506i	$0.714962\pi$
$84$	−3865.47	−0.0597729
$85$	−1666.34	−0.0250160
$86$	53329.5	0.777538
$87$	−7885.57	−0.111695
$88$	−29548.3	−0.406748
$89$	−141292.	−1.89079	−0.945396	−	0.325925i	$-0.894324\pi$
$89$	−141292.	−1.89079	−0.945396	+	0.325925i	$0.894324\pi$
$90$	−8100.00	−0.105409
$91$	18657.1	0.236179
$92$	−51579.5	−0.635342
$93$	−45889.6	−0.550183
$94$	−4485.89	−0.0523636
$95$	−9025.00	−0.102598
$96$	−9216.00	−0.102062
$97$	−48386.1	−0.522145	−0.261073	−	0.965319i	$-0.584076\pi$
$97$	−48386.1	−0.522145	−0.261073	+	0.965319i	$0.584076\pi$
$98$	−64345.7	−0.676791
$99$	−37397.0	−0.383486
$100$	10000.0	0.100000
$101$	23630.2	0.230496	0.115248	−	0.993337i	$-0.463234\pi$
$101$	23630.2	0.230496	0.115248	+	0.993337i	$0.463234\pi$
$102$	−2399.54	−0.0228364
$103$	−47198.0	−0.438359	−0.219180	−	0.975684i	$-0.570338\pi$
$103$	−47198.0	−0.438359	−0.219180	+	0.975684i	$0.570338\pi$
$104$	44482.0	0.403275
$105$	6039.80	0.0534625
$106$	−139185.	−1.20317
$107$	−33248.2	−0.280743	−0.140372	−	0.990099i	$-0.544830\pi$
$107$	−33248.2	−0.280743	−0.140372	+	0.990099i	$0.544830\pi$
$108$	−11664.0	−0.0962250
$109$	−155781.	−1.25588	−0.627942	−	0.778260i	$-0.716102\pi$
$109$	−155781.	−1.25588	−0.627942	+	0.778260i	$0.716102\pi$
$110$	46169.2	0.363807
$111$	−24022.9	−0.185062
$112$	6871.95	0.0517648
$113$	−48036.6	−0.353896	−0.176948	−	0.984220i	$-0.556622\pi$
$113$	−48036.6	−0.353896	−0.176948	+	0.984220i	$0.556622\pi$
$114$	−12996.0	−0.0936586
$115$	80593.0	0.568267
$116$	14018.8	0.0967310
$117$	56297.6	0.380211
$118$	−72337.5	−0.478254
$119$	1789.22	0.0115824
$120$	14400.0	0.0912871
$121$	52108.4	0.323552
$122$	28439.8	0.172992
$123$	76009.9	0.453010
$124$	81581.5	0.476472
$125$	−15625.0	−0.0894427
$126$	8697.31	0.0488043
$127$	−165632.	−0.911245	−0.455622	−	0.890173i	$-0.650583\pi$
$127$	−165632.	−0.911245	−0.455622	+	0.890173i	$0.650583\pi$
$128$	16384.0	0.0883883
$129$	−119991.	−0.634857
$130$	−69503.2	−0.360700
$131$	−299677.	−1.52572	−0.762860	−	0.646563i	$-0.776206\pi$
$131$	−299677.	−1.52572	−0.762860	+	0.646563i	$0.776206\pi$
$132$	66483.6	0.332108
$133$	9690.52	0.0475027
$134$	−79915.5	−0.384476
$135$	18225.0	0.0860663
$136$	4265.84	0.0197769
$137$	82967.3	0.377664	0.188832	−	0.982009i	$-0.439530\pi$
$137$	82967.3	0.377664	0.188832	+	0.982009i	$0.439530\pi$
$138$	116054.	0.518755
$139$	189858.	0.833473	0.416736	−	0.909027i	$-0.363174\pi$
$139$	189858.	0.833473	0.416736	+	0.909027i	$0.363174\pi$
$140$	−10737.4	−0.0462999
$141$	10093.3	0.0427547
$142$	265810.	1.10624
$143$	−320890.	−1.31225
$144$	20736.0	0.0833333
$145$	−21904.4	−0.0865189
$146$	−206805.	−0.802932
$147$	144778.	0.552597
$148$	42707.4	0.160269
$149$	38572.9	0.142336	0.0711682	−	0.997464i	$-0.477327\pi$
$149$	38572.9	0.142336	0.0711682	+	0.997464i	$0.477327\pi$
$150$	−22500.0	−0.0816497
$151$	−194819.	−0.695328	−0.347664	−	0.937619i	$-0.613025\pi$
$151$	−194819.	−0.695328	−0.347664	+	0.937619i	$0.613025\pi$
$152$	23104.0	0.0811107
$153$	5398.96	0.0186458
$154$	−49573.8	−0.168442
$155$	−127471.	−0.426170
$156$	−100085.	−0.329273
$157$	−495398.	−1.60400	−0.802001	−	0.597323i	$-0.796231\pi$
$157$	−495398.	−1.60400	−0.802001	+	0.597323i	$0.796231\pi$
$158$	152570.	0.486213
$159$	313166.	0.982384
$160$	−25600.0	−0.0790569
$161$	−86536.1	−0.263107
$162$	26244.0	0.0785674
$163$	222084.	0.654709	0.327354	−	0.944902i	$-0.393843\pi$
$163$	222084.	0.654709	0.327354	+	0.944902i	$0.393843\pi$
$164$	−135129.	−0.392318
$165$	−103881.	−0.297047
$166$	−313884.	−0.884094
$167$	290101.	0.804931	0.402465	−	0.915435i	$-0.368153\pi$
$167$	290101.	0.804931	0.402465	+	0.915435i	$0.368153\pi$
$168$	−15461.9	−0.0422658
$169$	111776.	0.301045
$170$	−6665.38	−0.0176890
$171$	29241.0	0.0764719
$172$	213318.	0.549802
$173$	−292063.	−0.741928	−0.370964	−	0.928647i	$-0.620973\pi$
$173$	−292063.	−0.741928	−0.370964	+	0.928647i	$0.620973\pi$
$174$	−31542.3	−0.0789805
$175$	16777.2	0.0414119
$176$	−118193.	−0.287614
$177$	162759.	0.390493
$178$	−565169.	−1.33699
$179$	−432036.	−1.00783	−0.503915	−	0.863753i	$-0.668108\pi$
$179$	−432036.	−1.00783	−0.503915	+	0.863753i	$0.668108\pi$
$180$	−32400.0	−0.0745356
$181$	−176178.	−0.399718	−0.199859	−	0.979825i	$-0.564048\pi$
$181$	−176178.	−0.399718	−0.199859	+	0.979825i	$0.564048\pi$
$182$	74628.4	0.167004
$183$	−63989.6	−0.141248
$184$	−206318.	−0.449255
$185$	−66730.3	−0.143349
$186$	−183558.	−0.389038
$187$	−30773.5	−0.0643536
$188$	−17943.6	−0.0370266
$189$	−19568.9	−0.0398486
$190$	−36100.0	−0.0725476
$191$	60847.5	0.120687	0.0603433	−	0.998178i	$-0.480780\pi$
$191$	60847.5	0.120687	0.0603433	+	0.998178i	$0.480780\pi$
$192$	−36864.0	−0.0721688
$193$	73984.7	0.142971	0.0714856	−	0.997442i	$-0.477226\pi$
$193$	73984.7	0.142971	0.0714856	+	0.997442i	$0.477226\pi$
$194$	−193544.	−0.369213
$195$	156382.	0.294510
$196$	−257383.	−0.478563
$197$	−313051.	−0.574711	−0.287355	−	0.957824i	$-0.592776\pi$
$197$	−313051.	−0.574711	−0.287355	+	0.957824i	$0.592776\pi$
$198$	−149588.	−0.271165
$199$	107616.	0.192639	0.0963197	−	0.995350i	$-0.469293\pi$
$199$	107616.	0.192639	0.0963197	+	0.995350i	$0.469293\pi$
$200$	40000.0	0.0707107
$201$	179810.	0.313923
$202$	94520.9	0.162986
$203$	23519.6	0.0400581
$204$	−9598.15	−0.0161477
$205$	211139.	0.350900
$206$	−188792.	−0.309967
$207$	−261121.	−0.423562
$208$	177928.	0.285158
$209$	−166671.	−0.263933
$210$	24159.2	0.0378037
$211$	−380144.	−0.587817	−0.293909	−	0.955833i	$-0.594956\pi$
$211$	−380144.	−0.587817	−0.293909	+	0.955833i	$0.594956\pi$
$212$	−556739.	−0.850769
$213$	−598073.	−0.903244
$214$	−132993.	−0.198515
$215$	−333310.	−0.491758
$216$	−46656.0	−0.0680414
$217$	136871.	0.197316
$218$	−623126.	−0.888044
$219$	465311.	0.655591
$220$	184677.	0.257250
$221$	46326.5	0.0638041
$222$	−96091.7	−0.130859
$223$	−161403.	−0.217345	−0.108673	−	0.994078i	$-0.534660\pi$
$223$	−161403.	−0.217345	−0.108673	+	0.994078i	$0.534660\pi$
$224$	27487.8	0.0366033
$225$	50625.0	0.0666667
$226$	−192146.	−0.250242
$227$	108574.	0.139850	0.0699249	−	0.997552i	$-0.477724\pi$
$227$	108574.	0.139850	0.0699249	+	0.997552i	$0.477724\pi$
$228$	−51984.0	−0.0662266
$229$	−246623.	−0.310774	−0.155387	−	0.987854i	$-0.549662\pi$
$229$	−246623.	−0.310774	−0.155387	+	0.987854i	$0.549662\pi$
$230$	322372.	0.401826
$231$	111541.	0.137532
$232$	56075.2	0.0683992
$233$	1.43093e6	1.72675	0.863374	−	0.504565i	$-0.168347\pi$
$233$	1.43093e6	1.72675	0.863374	+	0.504565i	$0.168347\pi$
$234$	225190.	0.268850
$235$	28036.8	0.0331176
$236$	−289350.	−0.338177
$237$	−343282.	−0.396991
$238$	7156.90	0.00818997
$239$	510984.	0.578646	0.289323	−	0.957232i	$-0.406570\pi$
$239$	510984.	0.578646	0.289323	+	0.957232i	$0.406570\pi$
$240$	57600.0	0.0645497
$241$	−1.24741e6	−1.38346	−0.691730	−	0.722156i	$-0.743151\pi$
$241$	−1.24741e6	−1.38346	−0.691730	+	0.722156i	$0.743151\pi$
$242$	208433.	0.228786
$243$	−59049.0	−0.0641500
$244$	113759.	0.122324
$245$	402161.	0.428040
$246$	304040.	0.320326
$247$	250906.	0.261679
$248$	326326.	0.336917
$249$	706238.	0.721859
$250$	−62500.0	−0.0632456
$251$	958538.	0.960340	0.480170	−	0.877175i	$-0.340575\pi$
$251$	958538.	0.960340	0.480170	+	0.877175i	$0.340575\pi$
$252$	34789.2	0.0345099
$253$	1.48837e6	1.46187
$254$	−662528.	−0.644347
$255$	14997.1	0.0144430
$256$	65536.0	0.0625000
$257$	1.57164e6	1.48429	0.742147	−	0.670237i	$-0.233808\pi$
$257$	1.57164e6	1.48429	0.742147	+	0.670237i	$0.233808\pi$
$258$	−479966.	−0.448912
$259$	71651.1	0.0663703
$260$	−278013.	−0.255053
$261$	70970.2	0.0644873
$262$	−1.19871e6	−1.07885
$263$	183552.	0.163633	0.0818164	−	0.996647i	$-0.473928\pi$
$263$	183552.	0.163633	0.0818164	+	0.996647i	$0.473928\pi$
$264$	265934.	0.234836
$265$	869904.	0.760951
$266$	38762.1	0.0335895
$267$	1.27163e6	1.09165
$268$	−319662.	−0.271865
$269$	1.26712e6	1.06767	0.533833	−	0.845590i	$-0.320751\pi$
$269$	1.26712e6	1.06767	0.533833	+	0.845590i	$0.320751\pi$
$270$	72900.0	0.0608581
$271$	30355.1	0.0251078	0.0125539	−	0.999921i	$-0.496004\pi$
$271$	30355.1	0.0251078	0.0125539	+	0.999921i	$0.496004\pi$
$272$	17063.4	0.0139844
$273$	−167914.	−0.136358
$274$	331869.	0.267049
$275$	−288557.	−0.230091
$276$	464216.	0.366815
$277$	1.97731e6	1.54837	0.774187	−	0.632957i	$-0.218159\pi$
$277$	1.97731e6	1.54837	0.774187	+	0.632957i	$0.218159\pi$
$278$	759431.	0.589354
$279$	413007.	0.317648
$280$	−42949.7	−0.0327389
$281$	−1.92326e6	−1.45302	−0.726512	−	0.687154i	$-0.758860\pi$
$281$	−1.92326e6	−1.45302	−0.726512	+	0.687154i	$0.758860\pi$
$282$	40373.0	0.0302321
$283$	−2.30913e6	−1.71388	−0.856942	−	0.515413i	$-0.827639\pi$
$283$	−2.30913e6	−1.71388	−0.856942	+	0.515413i	$0.827639\pi$
$284$	1.06324e6	0.782232
$285$	81225.0	0.0592349
$286$	−1.28356e6	−0.927901
$287$	−226708.	−0.162466
$288$	82944.0	0.0589256
$289$	−1.41541e6	−0.996871
$290$	−87617.5	−0.0611781
$291$	435475.	0.301461
$292$	−827219.	−0.567758
$293$	1.86313e6	1.26787	0.633933	−	0.773388i	$-0.281440\pi$
$293$	1.86313e6	1.26787	0.633933	+	0.773388i	$0.281440\pi$
$294$	579111.	0.390745
$295$	452110.	0.302474
$296$	170830.	0.113327
$297$	336573.	0.221406
$298$	154291.	0.100647
$299$	−2.24059e6	−1.44939
$300$	−90000.0	−0.0577350
$301$	357888.	0.227683
$302$	−779278.	−0.491671
$303$	−212672.	−0.133077
$304$	92416.0	0.0573539
$305$	−177749.	−0.109410
$306$	21595.8	0.0131846
$307$	−1.03938e6	−0.629401	−0.314701	−	0.949191i	$-0.601904\pi$
$307$	−1.03938e6	−0.629401	−0.314701	+	0.949191i	$0.601904\pi$
$308$	−198295.	−0.119106
$309$	424782.	0.253087
$310$	−509885.	−0.301348
$311$	−215327.	−0.126240	−0.0631202	−	0.998006i	$-0.520105\pi$
$311$	−215327.	−0.126240	−0.0631202	+	0.998006i	$0.520105\pi$
$312$	−400338.	−0.232831
$313$	−1.75254e6	−1.01113	−0.505565	−	0.862789i	$-0.668716\pi$
$313$	−1.75254e6	−1.01113	−0.505565	+	0.862789i	$0.668716\pi$
$314$	−1.98159e6	−1.13420
$315$	−54358.2	−0.0308666
$316$	610280.	0.343804
$317$	−1.04400e6	−0.583516	−0.291758	−	0.956492i	$-0.594240\pi$
$317$	−1.04400e6	−0.583516	−0.291758	+	0.956492i	$0.594240\pi$
$318$	1.25266e6	0.694650
$319$	−404523.	−0.222570
$320$	−102400.	−0.0559017
$321$	299234.	0.162087
$322$	−346144.	−0.186045
$323$	24062.0	0.0128329
$324$	104976.	0.0555556
$325$	434395.	0.228127
$326$	888336.	0.462949
$327$	1.40203e6	0.725085
$328$	−540515.	−0.277411
$329$	−30104.3	−0.0153334
$330$	−415523.	−0.210044
$331$	1.18820e6	0.596098	0.298049	−	0.954551i	$-0.403664\pi$
$331$	1.18820e6	0.596098	0.298049	+	0.954551i	$0.403664\pi$
$332$	−1.25553e6	−0.625149
$333$	216206.	0.106846
$334$	1.16041e6	0.569172
$335$	499472.	0.243164
$336$	−61847.5	−0.0298864
$337$	134565.	0.0645441	0.0322721	−	0.999479i	$-0.489726\pi$
$337$	134565.	0.0645441	0.0322721	+	0.999479i	$0.489726\pi$
$338$	447103.	0.212871
$339$	432329.	0.204322
$340$	−26661.5	−0.0125080
$341$	−2.35410e6	−1.09632
$342$	116964.	0.0540738
$343$	−882976.	−0.405241
$344$	853273.	0.388769
$345$	−725337.	−0.328089
$346$	−1.16825e6	−0.524622
$347$	3.03721e6	1.35410	0.677051	−	0.735936i	$-0.263258\pi$
$347$	3.03721e6	1.35410	0.677051	+	0.735936i	$0.263258\pi$
$348$	−126169.	−0.0558477
$349$	2.21887e6	0.975143	0.487572	−	0.873083i	$-0.337883\pi$
$349$	2.21887e6	0.975143	0.487572	+	0.873083i	$0.337883\pi$
$350$	67108.9	0.0292826
$351$	−506678.	−0.219515
$352$	−472772.	−0.203374
$353$	1.33785e6	0.571440	0.285720	−	0.958313i	$-0.407767\pi$
$353$	1.33785e6	0.571440	0.285720	+	0.958313i	$0.407767\pi$
$354$	651038.	0.276120
$355$	−1.66131e6	−0.699650
$356$	−2.26068e6	−0.945396
$357$	−16103.0	−0.00668708
$358$	−1.72814e6	−0.712644
$359$	2.15975e6	0.884437	0.442219	−	0.896907i	$-0.354192\pi$
$359$	2.15975e6	0.884437	0.442219	+	0.896907i	$0.354192\pi$
$360$	−129600.	−0.0527046
$361$	130321.	0.0526316
$362$	−704710.	−0.282644
$363$	−468975.	−0.186803
$364$	298514.	0.118089
$365$	1.29253e6	0.507818
$366$	−255958.	−0.0998773
$367$	3.87322e6	1.50109	0.750545	−	0.660820i	$-0.229791\pi$
$367$	3.87322e6	1.50109	0.750545	+	0.660820i	$0.229791\pi$
$368$	−825272.	−0.317671
$369$	−684089.	−0.261545
$370$	−266921.	−0.101363
$371$	−934053.	−0.352319
$372$	−734234.	−0.275091
$373$	1.52601e6	0.567917	0.283958	−	0.958837i	$-0.408352\pi$
$373$	1.52601e6	0.567917	0.283958	+	0.958837i	$0.408352\pi$
$374$	−123094.	−0.0455049
$375$	140625.	0.0516398
$376$	−71774.3	−0.0261818
$377$	608969.	0.220669
$378$	−78275.8	−0.0281772
$379$	1.44276e6	0.515936	0.257968	−	0.966153i	$-0.416947\pi$
$379$	1.44276e6	0.515936	0.257968	+	0.966153i	$0.416947\pi$
$380$	−144400.	−0.0512989
$381$	1.49069e6	0.526107
$382$	243390.	0.0853384
$383$	−4.10118e6	−1.42861	−0.714303	−	0.699837i	$-0.753256\pi$
$383$	−4.10118e6	−1.42861	−0.714303	+	0.699837i	$0.753256\pi$
$384$	−147456.	−0.0510310
$385$	309836.	0.106532
$386$	295939.	0.101096
$387$	1.07992e6	0.366535
$388$	−774178.	−0.261073
$389$	−2.62206e6	−0.878553	−0.439277	−	0.898352i	$-0.644765\pi$
$389$	−2.62206e6	−0.878553	−0.439277	+	0.898352i	$0.644765\pi$
$390$	625528.	0.208250
$391$	−214873.	−0.0710788
$392$	−1.02953e6	−0.338395
$393$	2.69709e6	0.880875
$394$	−1.25220e6	−0.406382
$395$	−953562.	−0.307508
$396$	−598353.	−0.191743
$397$	3.10753e6	0.989554	0.494777	−	0.869020i	$-0.335250\pi$
$397$	3.10753e6	0.989554	0.494777	+	0.869020i	$0.335250\pi$
$398$	430465.	0.136217
$399$	−87214.7	−0.0274257
$400$	160000.	0.0500000
$401$	−5.78749e6	−1.79733	−0.898667	−	0.438631i	$-0.855464\pi$
$401$	−5.78749e6	−1.79733	−0.898667	+	0.438631i	$0.855464\pi$
$402$	719239.	0.221977
$403$	3.54386e6	1.08696
$404$	378084.	0.115248
$405$	−164025.	−0.0496904
$406$	94078.5	0.0283254
$407$	−1.23235e6	−0.368765
$408$	−38392.6	−0.0114182
$409$	3.17362e6	0.938096	0.469048	−	0.883173i	$-0.344597\pi$
$409$	3.17362e6	0.938096	0.469048	+	0.883173i	$0.344597\pi$
$410$	844555.	0.248124
$411$	−746706.	−0.218044
$412$	−755168.	−0.219180
$413$	−485449.	−0.140045
$414$	−1.04449e6	−0.299503
$415$	1.96177e6	0.559150
$416$	711712.	0.201637
$417$	−1.70872e6	−0.481206
$418$	−666683.	−0.186629
$419$	−1.16518e6	−0.324232	−0.162116	−	0.986772i	$-0.551832\pi$
$419$	−1.16518e6	−0.324232	−0.162116	+	0.986772i	$0.551832\pi$
$420$	96636.8	0.0267312
$421$	−2.13245e6	−0.586372	−0.293186	−	0.956055i	$-0.594716\pi$
$421$	−2.13245e6	−0.586372	−0.293186	+	0.956055i	$0.594716\pi$
$422$	−1.52058e6	−0.415650
$423$	−90839.3	−0.0246844
$424$	−2.22696e6	−0.601585
$425$	41658.6	0.0111875
$426$	−2.39229e6	−0.638690
$427$	190856.	0.0506567
$428$	−531972.	−0.140372
$429$	2.88801e6	0.757628
$430$	−1.33324e6	−0.347726
$431$	−546699.	−0.141761	−0.0708803	−	0.997485i	$-0.522581\pi$
$431$	−546699.	−0.141761	−0.0708803	+	0.997485i	$0.522581\pi$
$432$	−186624.	−0.0481125
$433$	2.27440e6	0.582970	0.291485	−	0.956575i	$-0.405851\pi$
$433$	2.27440e6	0.582970	0.291485	+	0.956575i	$0.405851\pi$
$434$	547484.	0.139524
$435$	197139.	0.0499517
$436$	−2.49250e6	−0.627942
$437$	−1.16376e6	−0.291515
$438$	1.86124e6	0.463573
$439$	5.55557e6	1.37584	0.687919	−	0.725787i	$-0.258524\pi$
$439$	5.55557e6	1.37584	0.687919	+	0.725787i	$0.258524\pi$
$440$	738707.	0.181903
$441$	−1.30300e6	−0.319042
$442$	185306.	0.0451163
$443$	−1.77372e6	−0.429413	−0.214706	−	0.976679i	$-0.568879\pi$
$443$	−1.77372e6	−0.429413	−0.214706	+	0.976679i	$0.568879\pi$
$444$	−384367.	−0.0925312
$445$	3.53231e6	0.845587
$446$	−645614.	−0.153686
$447$	−347156.	−0.0821780
$448$	109951.	0.0258824
$449$	6.23783e6	1.46022	0.730109	−	0.683331i	$-0.239469\pi$
$449$	6.23783e6	1.46022	0.730109	+	0.683331i	$0.239469\pi$
$450$	202500.	0.0471405
$451$	3.89924e6	0.902690
$452$	−768585.	−0.176948
$453$	1.75338e6	0.401448
$454$	434297.	0.0988888
$455$	−466428.	−0.105622
$456$	−207936.	−0.0468293
$457$	−5.09553e6	−1.14130	−0.570649	−	0.821194i	$-0.693308\pi$
$457$	−5.09553e6	−1.14130	−0.570649	+	0.821194i	$0.693308\pi$
$458$	−986492.	−0.219751
$459$	−48590.6	−0.0107652
$460$	1.28949e6	0.284134
$461$	−1.95675e6	−0.428829	−0.214414	−	0.976743i	$-0.568784\pi$
$461$	−1.95675e6	−0.428829	−0.214414	+	0.976743i	$0.568784\pi$
$462$	446164.	0.0972500
$463$	2.98394e6	0.646902	0.323451	−	0.946245i	$-0.395157\pi$
$463$	2.98394e6	0.646902	0.323451	+	0.946245i	$0.395157\pi$
$464$	224301.	0.0483655
$465$	1.14724e6	0.246049
$466$	5.72372e6	1.22100
$467$	6.35587e6	1.34860	0.674299	−	0.738458i	$-0.264446\pi$
$467$	6.35587e6	1.34860	0.674299	+	0.738458i	$0.264446\pi$
$468$	900761.	0.190106
$469$	−536304.	−0.112585
$470$	112147.	0.0234177
$471$	4.45858e6	0.926071
$472$	−1.15740e6	−0.239127
$473$	−6.15545e6	−1.26505
$474$	−1.37313e6	−0.280715
$475$	225625.	0.0458831
$476$	28627.6	0.00579118
$477$	−2.81849e6	−0.567180
$478$	2.04394e6	0.409164
$479$	603090.	0.120100	0.0600500	−	0.998195i	$-0.480874\pi$
$479$	603090.	0.120100	0.0600500	+	0.998195i	$0.480874\pi$
$480$	230400.	0.0456435
$481$	1.85519e6	0.365616
$482$	−4.98964e6	−0.978255
$483$	778825.	0.151905
$484$	833734.	0.161776
$485$	1.20965e6	0.233511
$486$	−236196.	−0.0453609
$487$	−4.00184e6	−0.764605	−0.382302	−	0.924037i	$-0.624869\pi$
$487$	−4.00184e6	−0.764605	−0.382302	+	0.924037i	$0.624869\pi$
$488$	455037.	0.0864962
$489$	−1.99876e6	−0.377996
$490$	1.60864e6	0.302670
$491$	−2.29025e6	−0.428724	−0.214362	−	0.976754i	$-0.568767\pi$
$491$	−2.29025e6	−0.428724	−0.214362	+	0.976754i	$0.568767\pi$
$492$	1.21616e6	0.226505
$493$	58400.4	0.0108218
$494$	1.00363e6	0.185035
$495$	934926.	0.171500
$496$	1.30530e6	0.238236
$497$	1.78382e6	0.323937
$498$	2.82495e6	0.510432
$499$	−2.21763e6	−0.398693	−0.199346	−	0.979929i	$-0.563882\pi$
$499$	−2.21763e6	−0.398693	−0.199346	+	0.979929i	$0.563882\pi$
$500$	−250000.	−0.0447214
$501$	−2.61091e6	−0.464727
$502$	3.83415e6	0.679063
$503$	8.84417e6	1.55861	0.779304	−	0.626646i	$-0.215573\pi$
$503$	8.84417e6	1.55861	0.779304	+	0.626646i	$0.215573\pi$
$504$	139157.	0.0244022
$505$	−590755.	−0.103081
$506$	5.95346e6	1.03370
$507$	−1.00598e6	−0.173808
$508$	−2.65011e6	−0.455622
$509$	6.67634e6	1.14220	0.571102	−	0.820879i	$-0.306516\pi$
$509$	6.67634e6	1.14220	0.571102	+	0.820879i	$0.306516\pi$
$510$	59988.4	0.0102127
$511$	−1.38784e6	−0.235119
$512$	262144.	0.0441942
$513$	−263169.	−0.0441511
$514$	6.28655e6	1.04955
$515$	1.17995e6	0.196040
$516$	−1.91986e6	−0.317429
$517$	517775.	0.0851951
$518$	286605.	0.0469309
$519$	2.62857e6	0.428352
$520$	−1.11205e6	−0.180350
$521$	−1.07000e7	−1.72698	−0.863492	−	0.504362i	$-0.831728\pi$
$521$	−1.07000e7	−1.72698	−0.863492	+	0.504362i	$0.831728\pi$
$522$	283881.	0.0455994
$523$	1.21402e7	1.94075	0.970376	−	0.241598i	$-0.0776715\pi$
$523$	1.21402e7	1.94075	0.970376	+	0.241598i	$0.0776715\pi$
$524$	−4.79483e6	−0.762860
$525$	−150995.	−0.0239091
$526$	734209.	0.115706
$527$	339857.	0.0533053
$528$	1.06374e6	0.166054
$529$	3.95603e6	0.614639
$530$	3.47962e6	0.538074
$531$	−1.46484e6	−0.225451
$532$	155048.	0.0237513
$533$	−5.86992e6	−0.894982
$534$	5.08652e6	0.771912
$535$	831206.	0.125552
$536$	−1.27865e6	−0.192238
$537$	3.88833e6	0.581871
$538$	5.06846e6	0.754954
$539$	7.42697e6	1.10113
$540$	291600.	0.0430331
$541$	839191.	0.123273	0.0616364	−	0.998099i	$-0.480368\pi$
$541$	839191.	0.123273	0.0616364	+	0.998099i	$0.480368\pi$
$542$	121420.	0.0177539
$543$	1.58560e6	0.230778
$544$	68253.5	0.00988844
$545$	3.89454e6	0.561648
$546$	−671656.	−0.0964196
$547$	1.21231e7	1.73239	0.866195	−	0.499706i	$-0.166558\pi$
$547$	1.21231e7	1.73239	0.866195	+	0.499706i	$0.166558\pi$
$548$	1.32748e6	0.188832
$549$	575906.	0.0815494
$550$	−1.15423e6	−0.162699
$551$	316299.	0.0443832
$552$	1.85686e6	0.259377
$553$	1.02388e6	0.142376
$554$	7.90925e6	1.09487
$555$	600573.	0.0827625
$556$	3.03773e6	0.416736
$557$	−8.58070e6	−1.17188	−0.585942	−	0.810353i	$-0.699275\pi$
$557$	−8.58070e6	−1.17188	−0.585942	+	0.810353i	$0.699275\pi$
$558$	1.65203e6	0.224611
$559$	9.26643e6	1.25425
$560$	−171799.	−0.0231499
$561$	276962.	0.0371546
$562$	−7.69305e6	−1.02744
$563$	9.84671e6	1.30924	0.654621	−	0.755957i	$-0.272828\pi$
$563$	9.84671e6	1.30924	0.654621	+	0.755957i	$0.272828\pi$
$564$	161492.	0.0213773
$565$	1.20091e6	0.158267
$566$	−9.23650e6	−1.21190
$567$	176120.	0.0230066
$568$	4.25296e6	0.553122
$569$	−5.89834e6	−0.763746	−0.381873	−	0.924215i	$-0.624721\pi$
$569$	−5.89834e6	−0.763746	−0.381873	+	0.924215i	$0.624721\pi$
$570$	324900.	0.0418854
$571$	−855763.	−0.109841	−0.0549203	−	0.998491i	$-0.517490\pi$
$571$	−855763.	−0.109841	−0.0549203	+	0.998491i	$0.517490\pi$
$572$	−5.13425e6	−0.656125
$573$	−547628.	−0.0696785
$574$	−906834.	−0.114881
$575$	−2.01483e6	−0.254137
$576$	331776.	0.0416667
$577$	−4.67708e6	−0.584837	−0.292419	−	0.956290i	$-0.594460\pi$
$577$	−4.67708e6	−0.584837	−0.292419	+	0.956290i	$0.594460\pi$
$578$	−5.66166e6	−0.704894
$579$	−665862.	−0.0825445
$580$	−350470.	−0.0432594
$581$	−2.10644e6	−0.258886
$582$	1.74190e6	0.213165
$583$	1.60651e7	1.95755
$584$	−3.30888e6	−0.401466
$585$	−1.40744e6	−0.170036
$586$	7.45250e6	0.896516
$587$	−6.75702e6	−0.809394	−0.404697	−	0.914451i	$-0.632623\pi$
$587$	−6.75702e6	−0.809394	−0.404697	+	0.914451i	$0.632623\pi$
$588$	2.31645e6	0.276299
$589$	1.84068e6	0.218621
$590$	1.80844e6	0.213882
$591$	2.81746e6	0.331809
$592$	683319.	0.0801344
$593$	−9.62780e6	−1.12432	−0.562161	−	0.827028i	$-0.690030\pi$
$593$	−9.62780e6	−1.12432	−0.562161	+	0.827028i	$0.690030\pi$
$594$	1.34629e6	0.156557
$595$	−44730.6	−0.00517979
$596$	617166.	0.0711682
$597$	−968547.	−0.111220
$598$	−8.96235e6	−1.02487
$599$	−3.69988e6	−0.421328	−0.210664	−	0.977558i	$-0.567563\pi$
$599$	−3.69988e6	−0.421328	−0.210664	+	0.977558i	$0.567563\pi$
$600$	−360000.	−0.0408248
$601$	−5.45250e6	−0.615757	−0.307879	−	0.951426i	$-0.599619\pi$
$601$	−5.45250e6	−0.615757	−0.307879	+	0.951426i	$0.599619\pi$
$602$	1.43155e6	0.160997
$603$	−1.61829e6	−0.181244
$604$	−3.11711e6	−0.347664
$605$	−1.30271e6	−0.144697
$606$	−850688.	−0.0940998
$607$	−8.73780e6	−0.962565	−0.481283	−	0.876565i	$-0.659829\pi$
$607$	−8.73780e6	−0.962565	−0.481283	+	0.876565i	$0.659829\pi$
$608$	369664.	0.0405554
$609$	−211677.	−0.0231276
$610$	−710995.	−0.0773646
$611$	−779459.	−0.0844676
$612$	86383.3	0.00932291
$613$	−3.90939e6	−0.420202	−0.210101	−	0.977680i	$-0.567379\pi$
$613$	−3.90939e6	−0.420202	−0.210101	+	0.977680i	$0.567379\pi$
$614$	−4.15751e6	−0.445054
$615$	−1.90025e6	−0.202592
$616$	−793180.	−0.0842210
$617$	−1.38699e6	−0.146677	−0.0733383	−	0.997307i	$-0.523365\pi$
$617$	−1.38699e6	−0.146677	−0.0733383	+	0.997307i	$0.523365\pi$
$618$	1.69913e6	0.178960
$619$	−9.35563e6	−0.981401	−0.490700	−	0.871328i	$-0.663259\pi$
$619$	−9.35563e6	−0.981401	−0.490700	+	0.871328i	$0.663259\pi$
$620$	−2.03954e6	−0.213085
$621$	2.35009e6	0.244543
$622$	−861310.	−0.0892654
$623$	−3.79279e6	−0.391506
$624$	−1.60135e6	−0.164636
$625$	390625.	0.0400000
$626$	−7.01016e6	−0.714977
$627$	1.50004e6	0.152382
$628$	−7.92636e6	−0.802001
$629$	177913.	0.0179301
$630$	−217433.	−0.0218260
$631$	6.98892e6	0.698774	0.349387	−	0.936978i	$-0.386390\pi$
$631$	6.98892e6	0.698774	0.349387	+	0.936978i	$0.386390\pi$
$632$	2.44112e6	0.243106
$633$	3.42130e6	0.339377
$634$	−4.17601e6	−0.412608
$635$	4.14080e6	0.407521
$636$	5.01065e6	0.491192
$637$	−1.11806e7	−1.09173
$638$	−1.61809e6	−0.157381
$639$	5.38266e6	0.521488
$640$	−409600.	−0.0395285
$641$	−4.17273e6	−0.401121	−0.200560	−	0.979681i	$-0.564276\pi$
$641$	−4.17273e6	−0.401121	−0.200560	+	0.979681i	$0.564276\pi$
$642$	1.19694e6	0.114613
$643$	−5.02102e6	−0.478922	−0.239461	−	0.970906i	$-0.576971\pi$
$643$	−5.02102e6	−0.478922	−0.239461	+	0.970906i	$0.576971\pi$
$644$	−1.38458e6	−0.131554
$645$	2.99979e6	0.283917
$646$	96248.1	0.00907425
$647$	−3.10050e6	−0.291186	−0.145593	−	0.989345i	$-0.546509\pi$
$647$	−3.10050e6	−0.291186	−0.145593	+	0.989345i	$0.546509\pi$
$648$	419904.	0.0392837
$649$	8.34941e6	0.778116
$650$	1.73758e6	0.161310
$651$	−1.23184e6	−0.113920
$652$	3.55334e6	0.327354
$653$	1.78515e7	1.63830	0.819149	−	0.573581i	$-0.194446\pi$
$653$	1.78515e7	1.63830	0.819149	+	0.573581i	$0.194446\pi$
$654$	5.60813e6	0.512712
$655$	7.49192e6	0.682323
$656$	−2.16206e6	−0.196159
$657$	−4.18780e6	−0.378506
$658$	−120417.	−0.0108424
$659$	−1.27328e7	−1.14212	−0.571060	−	0.820908i	$-0.693468\pi$
$659$	−1.27328e7	−1.14212	−0.571060	+	0.820908i	$0.693468\pi$
$660$	−1.66209e6	−0.148523
$661$	1.39414e7	1.24109	0.620545	−	0.784171i	$-0.286912\pi$
$661$	1.39414e7	1.24109	0.620545	+	0.784171i	$0.286912\pi$
$662$	4.75278e6	0.421505
$663$	−416938.	−0.0368373
$664$	−5.02214e6	−0.442047
$665$	−242263.	−0.0212438
$666$	864825.	0.0755514
$667$	−2.82454e6	−0.245829
$668$	4.64162e6	0.402465
$669$	1.45263e6	0.125484
$670$	1.99789e6	0.171943
$671$	−3.28261e6	−0.281457
$672$	−247390.	−0.0211329
$673$	−1.44264e7	−1.22778	−0.613888	−	0.789393i	$-0.710395\pi$
$673$	−1.44264e7	−1.22778	−0.613888	+	0.789393i	$0.710395\pi$
$674$	538259.	0.0456396
$675$	−455625.	−0.0384900
$676$	1.78841e6	0.150522
$677$	−1.59717e7	−1.33931	−0.669653	−	0.742674i	$-0.733557\pi$
$677$	−1.59717e7	−1.33931	−0.669653	+	0.742674i	$0.733557\pi$
$678$	1.72932e6	0.144477
$679$	−1.29886e6	−0.108115
$680$	−106646.	−0.00884449
$681$	−977168.	−0.0807424
$682$	−9.41638e6	−0.775217
$683$	−1.85331e7	−1.52019	−0.760094	−	0.649813i	$-0.774847\pi$
$683$	−1.85331e7	−1.52019	−0.760094	+	0.649813i	$0.774847\pi$
$684$	467856.	0.0382360
$685$	−2.07418e6	−0.168896
$686$	−3.53190e6	−0.286549
$687$	2.21961e6	0.179426
$688$	3.41309e6	0.274901
$689$	−2.41844e7	−1.94083
$690$	−2.90135e6	−0.231994
$691$	−901457.	−0.0718208	−0.0359104	−	0.999355i	$-0.511433\pi$
$691$	−901457.	−0.0718208	−0.0359104	+	0.999355i	$0.511433\pi$
$692$	−4.67301e6	−0.370964
$693$	−1.00387e6	−0.0794043
$694$	1.21488e7	0.957495
$695$	−4.74645e6	−0.372740
$696$	−504677.	−0.0394903
$697$	−562928.	−0.0438905
$698$	8.87548e6	0.689530
$699$	−1.28784e7	−0.996938
$700$	268435.	0.0207059
$701$	−5.29711e6	−0.407140	−0.203570	−	0.979060i	$-0.565254\pi$
$701$	−5.29711e6	−0.407140	−0.203570	+	0.979060i	$0.565254\pi$
$702$	−2.02671e6	−0.155221
$703$	963586.	0.0735364
$704$	−1.89109e6	−0.143807
$705$	−252331.	−0.0191205
$706$	5.35140e6	0.404069
$707$	634319.	0.0477264
$708$	2.60415e6	0.195246
$709$	1.49738e7	1.11871	0.559355	−	0.828928i	$-0.311049\pi$
$709$	1.49738e7	1.11871	0.559355	+	0.828928i	$0.311049\pi$
$710$	−6.64526e6	−0.494727
$711$	3.08954e6	0.229203
$712$	−9.04271e6	−0.668496
$713$	−1.64373e7	−1.21089
$714$	−64412.1	−0.00472848
$715$	8.02226e6	0.586856
$716$	−6.91258e6	−0.503915
$717$	−4.59886e6	−0.334081
$718$	8.63899e6	0.625391
$719$	−2.16702e7	−1.56329	−0.781647	−	0.623721i	$-0.785620\pi$
$719$	−2.16702e7	−1.56329	−0.781647	+	0.623721i	$0.785620\pi$
$720$	−518400.	−0.0372678
$721$	−1.26696e6	−0.0907664
$722$	521284.	0.0372161
$723$	1.12267e7	0.798741
$724$	−2.81884e6	−0.199859
$725$	547609.	0.0386924
$726$	−1.87590e6	−0.132090
$727$	−2.35691e6	−0.165389	−0.0826945	−	0.996575i	$-0.526353\pi$
$727$	−2.35691e6	−0.165389	−0.0826945	+	0.996575i	$0.526353\pi$
$728$	1.19405e6	0.0835018
$729$	531441.	0.0370370
$730$	5.17012e6	0.359082
$731$	888654.	0.0615091
$732$	−1.02383e6	−0.0706239
$733$	1.72670e7	1.18701	0.593507	−	0.804829i	$-0.297743\pi$
$733$	1.72670e7	1.18701	0.593507	+	0.804829i	$0.297743\pi$
$734$	1.54929e7	1.06143
$735$	−3.61945e6	−0.247129
$736$	−3.30109e6	−0.224627
$737$	9.22408e6	0.625539
$738$	−2.73636e6	−0.184940
$739$	−3.55854e6	−0.239696	−0.119848	−	0.992792i	$-0.538241\pi$
$739$	−3.55854e6	−0.239696	−0.119848	+	0.992792i	$0.538241\pi$
$740$	−1.06769e6	−0.0716744
$741$	−2.25816e6	−0.151081
$742$	−3.73621e6	−0.249127
$743$	−1.65918e7	−1.10261	−0.551304	−	0.834304i	$-0.685870\pi$
$743$	−1.65918e7	−1.10261	−0.551304	+	0.834304i	$0.685870\pi$
$744$	−2.93694e6	−0.194519
$745$	−964322.	−0.0636548
$746$	6.10403e6	0.401578
$747$	−6.35614e6	−0.416766
$748$	−492376.	−0.0321768
$749$	−892500.	−0.0581305
$750$	562500.	0.0365148
$751$	−7.86399e6	−0.508795	−0.254398	−	0.967100i	$-0.581877\pi$
$751$	−7.86399e6	−0.508795	−0.254398	+	0.967100i	$0.581877\pi$
$752$	−287097.	−0.0185133
$753$	−8.62684e6	−0.554453
$754$	2.43588e6	0.156037
$755$	4.87049e6	0.310960
$756$	−313103.	−0.0199243
$757$	−5.17968e6	−0.328521	−0.164261	−	0.986417i	$-0.552524\pi$
$757$	−5.17968e6	−0.328521	−0.164261	+	0.986417i	$0.552524\pi$
$758$	5.77104e6	0.364822
$759$	−1.33953e7	−0.844010
$760$	−577600.	−0.0362738
$761$	−2.84735e7	−1.78229	−0.891147	−	0.453715i	$-0.850098\pi$
$761$	−2.84735e7	−1.78229	−0.891147	+	0.453715i	$0.850098\pi$
$762$	5.96275e6	0.372014
$763$	−4.18173e6	−0.260042
$764$	973560.	0.0603433
$765$	−134974.	−0.00833866
$766$	−1.64047e7	−1.01018
$767$	−1.25692e7	−0.771471
$768$	−589824.	−0.0360844
$769$	−1.93458e7	−1.17970	−0.589850	−	0.807513i	$-0.700813\pi$
$769$	−1.93458e7	−1.17970	−0.589850	+	0.807513i	$0.700813\pi$
$770$	1.23934e6	0.0753295
$771$	−1.41447e7	−0.856957
$772$	1.18376e6	0.0714856
$773$	−5.15334e6	−0.310199	−0.155100	−	0.987899i	$-0.549570\pi$
$773$	−5.15334e6	−0.310199	−0.155100	+	0.987899i	$0.549570\pi$
$774$	4.31969e6	0.259179
$775$	3.18678e6	0.190589
$776$	−3.09671e6	−0.184606
$777$	−644860.	−0.0383189
$778$	−1.04882e7	−0.621231
$779$	−3.04884e6	−0.180008
$780$	2.50211e6	0.147255
$781$	−3.06806e7	−1.79985
$782$	−859493.	−0.0502603
$783$	−638731.	−0.0372318
$784$	−4.11812e6	−0.239282
$785$	1.23849e7	0.717331
$786$	1.07884e7	0.622873
$787$	3.37520e7	1.94251	0.971255	−	0.238041i	$-0.0765054\pi$
$787$	3.37520e7	1.94251	0.971255	+	0.238041i	$0.0765054\pi$
$788$	−5.00881e6	−0.287355
$789$	−1.65197e6	−0.0944735
$790$	−3.81425e6	−0.217441
$791$	−1.28947e6	−0.0732775
$792$	−2.39341e6	−0.135583
$793$	4.94164e6	0.279054
$794$	1.24301e7	0.699720
$795$	−7.82914e6	−0.439335
$796$	1.72186e6	0.0963197
$797$	9.08852e6	0.506812	0.253406	−	0.967360i	$-0.418449\pi$
$797$	9.08852e6	0.506812	0.253406	+	0.967360i	$0.418449\pi$
$798$	−348859.	−0.0193929
$799$	−74750.4	−0.00414235
$800$	640000.	0.0353553
$801$	−1.14447e7	−0.630264
$802$	−2.31499e7	−1.27091
$803$	2.38700e7	1.30636
$804$	2.87696e6	0.156962
$805$	2.16340e6	0.117665
$806$	1.41754e7	0.768597
$807$	−1.14040e7	−0.616418
$808$	1.51233e6	0.0814928
$809$	−2.87327e7	−1.54349	−0.771747	−	0.635930i	$-0.780617\pi$
$809$	−2.87327e7	−1.54349	−0.771747	+	0.635930i	$0.780617\pi$
$810$	−656100.	−0.0351364
$811$	5.58168e6	0.297998	0.148999	−	0.988837i	$-0.452395\pi$
$811$	5.58168e6	0.297998	0.148999	+	0.988837i	$0.452395\pi$
$812$	376314.	0.0200291
$813$	−273196.	−0.0144960
$814$	−4.92942e6	−0.260756
$815$	−5.55210e6	−0.292795
$816$	−153570.	−0.00807387
$817$	4.81299e6	0.252267
$818$	1.26945e7	0.663334
$819$	1.51123e6	0.0787263
$820$	3.37822e6	0.175450
$821$	2.58826e7	1.34014	0.670069	−	0.742299i	$-0.266265\pi$
$821$	2.58826e7	1.34014	0.670069	+	0.742299i	$0.266265\pi$
$822$	−2.98682e6	−0.154181
$823$	1.60447e6	0.0825717	0.0412858	−	0.999147i	$-0.486855\pi$
$823$	1.60447e6	0.0825717	0.0412858	+	0.999147i	$0.486855\pi$
$824$	−3.02067e6	−0.154983
$825$	2.59702e6	0.132843
$826$	−1.94180e6	−0.0990270
$827$	−2.34973e7	−1.19469	−0.597344	−	0.801985i	$-0.703777\pi$
$827$	−2.34973e7	−1.19469	−0.597344	+	0.801985i	$0.703777\pi$
$828$	−4.17794e6	−0.211781
$829$	−916597.	−0.0463225	−0.0231612	−	0.999732i	$-0.507373\pi$
$829$	−916597.	−0.0463225	−0.0231612	+	0.999732i	$0.507373\pi$
$830$	7.84709e6	0.395379
$831$	−1.77958e7	−0.893954
$832$	2.84685e6	0.142579
$833$	−1.07222e6	−0.0535392
$834$	−6.83488e6	−0.340264
$835$	−7.25253e6	−0.359976
$836$	−2.66673e6	−0.131966
$837$	−3.71706e6	−0.183394
$838$	−4.66070e6	−0.229267
$839$	1.68932e7	0.828526	0.414263	−	0.910157i	$-0.364039\pi$
$839$	1.68932e7	0.828526	0.414263	+	0.910157i	$0.364039\pi$
$840$	386547.	0.0189018
$841$	−1.97435e7	−0.962572
$842$	−8.52979e6	−0.414628
$843$	1.73094e7	0.838904
$844$	−6.08231e6	−0.293909
$845$	−2.79439e6	−0.134631
$846$	−363357.	−0.0174545
$847$	1.39877e6	0.0669944
$848$	−8.90782e6	−0.425385
$849$	2.07821e7	0.989511
$850$	166634.	0.00791075
$851$	−8.60480e6	−0.407302
$852$	−9.56917e6	−0.451622
$853$	3.75367e7	1.76638	0.883190	−	0.469016i	$-0.155391\pi$
$853$	3.75367e7	1.76638	0.883190	+	0.469016i	$0.155391\pi$
$854$	763425.	0.0358197
$855$	−731025.	−0.0341993
$856$	−2.12789e6	−0.0992576
$857$	3.13841e6	0.145968	0.0729839	−	0.997333i	$-0.476748\pi$
$857$	3.13841e6	0.145968	0.0729839	+	0.997333i	$0.476748\pi$
$858$	1.15521e7	0.535724
$859$	1.03013e7	0.476331	0.238165	−	0.971225i	$-0.423454\pi$
$859$	1.03013e7	0.476331	0.238165	+	0.971225i	$0.423454\pi$
$860$	−5.33295e6	−0.245879
$861$	2.04038e6	0.0937999
$862$	−2.18680e6	−0.100240
$863$	−1.76095e6	−0.0804859	−0.0402429	−	0.999190i	$-0.512813\pi$
$863$	−1.76095e6	−0.0804859	−0.0402429	+	0.999190i	$0.512813\pi$
$864$	−746496.	−0.0340207
$865$	7.30159e6	0.331800
$866$	9.09759e6	0.412222
$867$	1.27387e7	0.575544
$868$	2.18994e6	0.0986580
$869$	−1.76101e7	−0.791064
$870$	788557.	0.0353212
$871$	−1.38859e7	−0.620197
$872$	−9.97001e6	−0.444022
$873$	−3.91928e6	−0.174048
$874$	−4.65505e6	−0.206132
$875$	−419430.	−0.0185199
$876$	7.44497e6	0.327795
$877$	−1.20219e7	−0.527804	−0.263902	−	0.964550i	$-0.585009\pi$
$877$	−1.20219e7	−0.527804	−0.263902	+	0.964550i	$0.585009\pi$
$878$	2.22223e7	0.972865
$879$	−1.67681e7	−0.732002
$880$	2.95483e6	0.128625
$881$	−1.50921e7	−0.655103	−0.327552	−	0.944833i	$-0.606224\pi$
$881$	−1.50921e7	−0.655103	−0.327552	+	0.944833i	$0.606224\pi$
$882$	−5.21200e6	−0.225597
$883$	−3.10505e6	−0.134019	−0.0670096	−	0.997752i	$-0.521346\pi$
$883$	−3.10505e6	−0.134019	−0.0670096	+	0.997752i	$0.521346\pi$
$884$	741224.	0.0319021
$885$	−4.06899e6	−0.174634
$886$	−7.09487e6	−0.303641
$887$	4.12563e7	1.76068	0.880341	−	0.474341i	$-0.157314\pi$
$887$	4.12563e7	1.76068	0.880341	+	0.474341i	$0.157314\pi$
$888$	−1.53747e6	−0.0654295
$889$	−4.44615e6	−0.188682
$890$	1.41292e7	0.597921
$891$	−3.02916e6	−0.127829
$892$	−2.58245e6	−0.108673
$893$	−404852.	−0.0169890
$894$	−1.38862e6	−0.0581086
$895$	1.08009e7	0.450716
$896$	439805.	0.0183016
$897$	2.01653e7	0.836803
$898$	2.49513e7	1.03253
$899$	4.46748e6	0.184359
$900$	810000.	0.0333333
$901$	−2.31930e6	−0.0951797
$902$	1.55970e7	0.638298
$903$	−3.22100e6	−0.131453
$904$	−3.07434e6	−0.125121
$905$	4.40444e6	0.178760
$906$	7.01350e6	0.283867
$907$	−1.85559e7	−0.748967	−0.374484	−	0.927234i	$-0.622180\pi$
$907$	−1.85559e7	−0.748967	−0.374484	+	0.927234i	$0.622180\pi$
$908$	1.73719e6	0.0699249
$909$	1.91405e6	0.0768322
$910$	−1.86571e6	−0.0746863
$911$	−4.16030e7	−1.66084	−0.830421	−	0.557136i	$-0.811900\pi$
$911$	−4.16030e7	−1.66084	−0.830421	+	0.557136i	$0.811900\pi$
$912$	−831744.	−0.0331133
$913$	3.62294e7	1.43841
$914$	−2.03821e7	−0.807020
$915$	1.59974e6	0.0631679
$916$	−3.94597e6	−0.155387
$917$	−8.04439e6	−0.315915
$918$	−194362.	−0.00761212
$919$	−2.05951e7	−0.804407	−0.402203	−	0.915550i	$-0.631755\pi$
$919$	−2.05951e7	−0.804407	−0.402203	+	0.915550i	$0.631755\pi$
$920$	5.15795e6	0.200913
$921$	9.35440e6	0.363385
$922$	−7.82701e6	−0.303228
$923$	4.61866e7	1.78448
$924$	1.78466e6	0.0687661
$925$	1.66826e6	0.0641075
$926$	1.19358e7	0.457429
$927$	−3.82304e6	−0.146120
$928$	897203.	0.0341996
$929$	−2.32592e7	−0.884210	−0.442105	−	0.896963i	$-0.645768\pi$
$929$	−2.32592e7	−0.884210	−0.442105	+	0.896963i	$0.645768\pi$
$930$	4.58896e6	0.173983
$931$	−5.80720e6	−0.219580
$932$	2.28949e7	0.863374
$933$	1.93795e6	0.0728849
$934$	2.54235e7	0.953603
$935$	769338.	0.0287798
$936$	3.60304e6	0.134425
$937$	−3.59934e7	−1.33929	−0.669643	−	0.742683i	$-0.733553\pi$
$937$	−3.59934e7	−1.33929	−0.669643	+	0.742683i	$0.733553\pi$
$938$	−2.14521e6	−0.0796093
$939$	1.57728e7	0.583776
$940$	448589.	0.0165588
$941$	−21612.6	−0.000795668 0	−0.000397834	−	1.00000i	$-0.500127\pi$
$941$	−21612.6	−0.000795668 0	−0.000397834		1.00000i	$0.500127\pi$
$942$	1.78343e7	0.654831
$943$	2.72261e7	0.997025
$944$	−4.62960e6	−0.169088
$945$	489224.	0.0178208
$946$	−2.46218e7	−0.894524
$947$	4.52467e7	1.63950	0.819751	−	0.572721i	$-0.194112\pi$
$947$	4.52467e7	1.63950	0.819751	+	0.572721i	$0.194112\pi$
$948$	−5.49252e6	−0.198495
$949$	−3.59340e7	−1.29521
$950$	902500.	0.0324443
$951$	9.39602e6	0.336893
$952$	114510.	0.00409499
$953$	2.41145e7	0.860093	0.430047	−	0.902807i	$-0.358497\pi$
$953$	2.41145e7	0.860093	0.430047	+	0.902807i	$0.358497\pi$
$954$	−1.12740e7	−0.401057
$955$	−1.52119e6	−0.0539727
$956$	8.17575e6	0.289323
$957$	3.64070e6	0.128501
$958$	2.41236e6	0.0849235
$959$	2.22714e6	0.0781988
$960$	921600.	0.0322749
$961$	−2.63092e6	−0.0918964
$962$	7.42075e6	0.258529
$963$	−2.69311e6	−0.0935810
$964$	−1.99586e7	−0.691730
$965$	−1.84962e6	−0.0639387
$966$	3.11530e6	0.107413
$967$	1.58593e7	0.545404	0.272702	−	0.962099i	$-0.412083\pi$
$967$	1.58593e7	0.545404	0.272702	+	0.962099i	$0.412083\pi$
$968$	3.33493e6	0.114393
$969$	−216558.	−0.00740910
$970$	4.83861e6	0.165117
$971$	−1.42740e7	−0.485845	−0.242923	−	0.970046i	$-0.578106\pi$
$971$	−1.42740e7	−0.485845	−0.242923	+	0.970046i	$0.578106\pi$
$972$	−944784.	−0.0320750
$973$	5.09646e6	0.172578
$974$	−1.60074e7	−0.540657
$975$	−3.90955e6	−0.131709
$976$	1.82015e6	0.0611621
$977$	4.44705e6	0.149051	0.0745256	−	0.997219i	$-0.476256\pi$
$977$	4.44705e6	0.149051	0.0745256	+	0.997219i	$0.476256\pi$
$978$	−7.99502e6	−0.267284
$979$	6.52335e7	2.17527
$980$	6.43457e6	0.214020
$981$	−1.26183e7	−0.418628
$982$	−9.16098e6	−0.303154
$983$	3.21883e7	1.06246	0.531232	−	0.847226i	$-0.321729\pi$
$983$	3.21883e7	1.06246	0.531232	+	0.847226i	$0.321729\pi$
$984$	4.86464e6	0.160163
$985$	7.82627e6	0.257018
$986$	233602.	0.00765215
$987$	270939.	0.00885275
$988$	4.01450e6	0.130840
$989$	−4.29799e7	−1.39725
$990$	3.73970e6	0.121269
$991$	−2.65815e7	−0.859797	−0.429899	−	0.902877i	$-0.641451\pi$
$991$	−2.65815e7	−0.859797	−0.429899	+	0.902877i	$0.641451\pi$
$992$	5.22122e6	0.168458
$993$	−1.06938e7	−0.344158
$994$	7.13529e6	0.229058
$995$	−2.69041e6	−0.0861510
$996$	1.12998e7	0.360930
$997$	−5.19417e7	−1.65492	−0.827462	−	0.561522i	$-0.810216\pi$
$997$	−5.19417e7	−1.65492	−0.827462	+	0.561522i	$0.810216\pi$
$998$	−8.87053e6	−0.281918
$999$	−1.94586e6	−0.0616875

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.6.a.e.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.6.a.e.1.2	✓	3	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)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -36.0000 q^{6} +26.8435 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -36.0000 q^{6} +26.8435 q^{7} +64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -461.692 q^{11} -144.000 q^{12} +695.032 q^{13} +107.374 q^{14} +225.000 q^{15} +256.000 q^{16} +66.6538 q^{17} +324.000 q^{18} +361.000 q^{19} -400.000 q^{20} -241.592 q^{21} -1846.77 q^{22} -3223.72 q^{23} -576.000 q^{24} +625.000 q^{25} +2780.13 q^{26} -729.000 q^{27} +429.497 q^{28} +876.175 q^{29} +900.000 q^{30} +5098.85 q^{31} +1024.00 q^{32} +4155.23 q^{33} +266.615 q^{34} -671.089 q^{35} +1296.00 q^{36} +2669.21 q^{37} +1444.00 q^{38} -6255.28 q^{39} -1600.00 q^{40} -8445.55 q^{41} -966.368 q^{42} +13332.4 q^{43} -7387.07 q^{44} -2025.00 q^{45} -12894.9 q^{46} -1121.47 q^{47} -2304.00 q^{48} -16086.4 q^{49} +2500.00 q^{50} -599.884 q^{51} +11120.5 q^{52} -34796.2 q^{53} -2916.00 q^{54} +11542.3 q^{55} +1717.99 q^{56} -3249.00 q^{57} +3504.70 q^{58} -18084.4 q^{59} +3600.00 q^{60} +7109.95 q^{61} +20395.4 q^{62} +2174.33 q^{63} +4096.00 q^{64} -17375.8 q^{65} +16620.9 q^{66} -19978.9 q^{67} +1066.46 q^{68} +29013.5 q^{69} -2684.35 q^{70} +66452.6 q^{71} +5184.00 q^{72} -51701.2 q^{73} +10676.9 q^{74} -5625.00 q^{75} +5776.00 q^{76} -12393.4 q^{77} -25021.1 q^{78} +38142.5 q^{79} -6400.00 q^{80} +6561.00 q^{81} -33782.2 q^{82} -78470.9 q^{83} -3865.47 q^{84} -1666.34 q^{85} +53329.5 q^{86} -7885.57 q^{87} -29548.3 q^{88} -141292. q^{89} -8100.00 q^{90} +18657.1 q^{91} -51579.5 q^{92} -45889.6 q^{93} -4485.89 q^{94} -9025.00 q^{95} -9216.00 q^{96} -48386.1 q^{97} -64345.7 q^{98} -37397.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 12 q^{2} - 27 q^{3} + 48 q^{4} - 75 q^{5} - 108 q^{6} + 10 q^{7} + 192 q^{8} + 243 q^{9}+O(q^{10}) \) 3 * q + 12 * q^2 - 27 * q^3 + 48 * q^4 - 75 * q^5 - 108 * q^6 + 10 * q^7 + 192 * q^8 + 243 * q^9	\( 3 q + 12 q^{2} - 27 q^{3} + 48 q^{4} - 75 q^{5} - 108 q^{6} + 10 q^{7} + 192 q^{8} + 243 q^{9} - 300 q^{10} - 572 q^{11} - 432 q^{12} + 376 q^{13} + 40 q^{14} + 675 q^{15} + 768 q^{16} + 758 q^{17} + 972 q^{18} + 1083 q^{19} - 1200 q^{20} - 90 q^{21} - 2288 q^{22} + 1098 q^{23} - 1728 q^{24} + 1875 q^{25} + 1504 q^{26} - 2187 q^{27} + 160 q^{28} - 5610 q^{29} + 2700 q^{30} + 7620 q^{31} + 3072 q^{32} + 5148 q^{33} + 3032 q^{34} - 250 q^{35} + 3888 q^{36} - 3824 q^{37} + 4332 q^{38} - 3384 q^{39} - 4800 q^{40} - 8806 q^{41} - 360 q^{42} - 18274 q^{43} - 9152 q^{44} - 6075 q^{45} + 4392 q^{46} - 15358 q^{47} - 6912 q^{48} - 7869 q^{49} + 7500 q^{50} - 6822 q^{51} + 6016 q^{52} - 1572 q^{53} - 8748 q^{54} + 14300 q^{55} + 640 q^{56} - 9747 q^{57} - 22440 q^{58} - 33340 q^{59} + 10800 q^{60} + 26974 q^{61} + 30480 q^{62} + 810 q^{63} + 12288 q^{64} - 9400 q^{65} + 20592 q^{66} + 8180 q^{67} + 12128 q^{68} - 9882 q^{69} - 1000 q^{70} - 20360 q^{71} + 15552 q^{72} - 106318 q^{73} - 15296 q^{74} - 16875 q^{75} + 17328 q^{76} - 33212 q^{77} - 13536 q^{78} - 60680 q^{79} - 19200 q^{80} + 19683 q^{81} - 35224 q^{82} - 183246 q^{83} - 1440 q^{84} - 18950 q^{85} - 73096 q^{86} + 50490 q^{87} - 36608 q^{88} - 196766 q^{89} - 24300 q^{90} - 39084 q^{91} + 17568 q^{92} - 68580 q^{93} - 61432 q^{94} - 27075 q^{95} - 27648 q^{96} - 193852 q^{97} - 31476 q^{98} - 46332 q^{99}+O(q^{100}) \) 3 * q + 12 * q^2 - 27 * q^3 + 48 * q^4 - 75 * q^5 - 108 * q^6 + 10 * q^7 + 192 * q^8 + 243 * q^9 - 300 * q^10 - 572 * q^11 - 432 * q^12 + 376 * q^13 + 40 * q^14 + 675 * q^15 + 768 * q^16 + 758 * q^17 + 972 * q^18 + 1083 * q^19 - 1200 * q^20 - 90 * q^21 - 2288 * q^22 + 1098 * q^23 - 1728 * q^24 + 1875 * q^25 + 1504 * q^26 - 2187 * q^27 + 160 * q^28 - 5610 * q^29 + 2700 * q^30 + 7620 * q^31 + 3072 * q^32 + 5148 * q^33 + 3032 * q^34 - 250 * q^35 + 3888 * q^36 - 3824 * q^37 + 4332 * q^38 - 3384 * q^39 - 4800 * q^40 - 8806 * q^41 - 360 * q^42 - 18274 * q^43 - 9152 * q^44 - 6075 * q^45 + 4392 * q^46 - 15358 * q^47 - 6912 * q^48 - 7869 * q^49 + 7500 * q^50 - 6822 * q^51 + 6016 * q^52 - 1572 * q^53 - 8748 * q^54 + 14300 * q^55 + 640 * q^56 - 9747 * q^57 - 22440 * q^58 - 33340 * q^59 + 10800 * q^60 + 26974 * q^61 + 30480 * q^62 + 810 * q^63 + 12288 * q^64 - 9400 * q^65 + 20592 * q^66 + 8180 * q^67 + 12128 * q^68 - 9882 * q^69 - 1000 * q^70 - 20360 * q^71 + 15552 * q^72 - 106318 * q^73 - 15296 * q^74 - 16875 * q^75 + 17328 * q^76 - 33212 * q^77 - 13536 * q^78 - 60680 * q^79 - 19200 * q^80 + 19683 * q^81 - 35224 * q^82 - 183246 * q^83 - 1440 * q^84 - 18950 * q^85 - 73096 * q^86 + 50490 * q^87 - 36608 * q^88 - 196766 * q^89 - 24300 * q^90 - 39084 * q^91 + 17568 * q^92 - 68580 * q^93 - 61432 * q^94 - 27075 * q^95 - 27648 * q^96 - 193852 * q^97 - 31476 * q^98 - 46332 * q^99

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