LMFDB - Embedded newform 570.6.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("570.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$91.4187772934$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.237212.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 63x + 71 $ x^3 - x^2 - 63*x + 71
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.12961$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +36.0000 q^{6} -83.0591 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +36.0000 q^{6} -83.0591 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} +449.172 q^{11} -144.000 q^{12} +830.466 q^{13} +332.237 q^{14} -225.000 q^{15} +256.000 q^{16} +301.657 q^{17} -324.000 q^{18} -361.000 q^{19} +400.000 q^{20} +747.532 q^{21} -1796.69 q^{22} +1126.94 q^{23} +576.000 q^{24} +625.000 q^{25} -3321.86 q^{26} -729.000 q^{27} -1328.95 q^{28} -1987.67 q^{29} +900.000 q^{30} +5617.86 q^{31} -1024.00 q^{32} -4042.54 q^{33} -1206.63 q^{34} -2076.48 q^{35} +1296.00 q^{36} +5412.36 q^{37} +1444.00 q^{38} -7474.20 q^{39} -1600.00 q^{40} -11948.6 q^{41} -2990.13 q^{42} +12148.2 q^{43} +7186.74 q^{44} +2025.00 q^{45} -4507.76 q^{46} +498.855 q^{47} -2304.00 q^{48} -9908.18 q^{49} -2500.00 q^{50} -2714.91 q^{51} +13287.5 q^{52} +40645.9 q^{53} +2916.00 q^{54} +11229.3 q^{55} +5315.78 q^{56} +3249.00 q^{57} +7950.69 q^{58} -39073.5 q^{59} -3600.00 q^{60} -14964.4 q^{61} -22471.4 q^{62} -6727.79 q^{63} +4096.00 q^{64} +20761.7 q^{65} +16170.2 q^{66} -31785.7 q^{67} +4826.51 q^{68} -10142.5 q^{69} +8305.91 q^{70} +55566.6 q^{71} -5184.00 q^{72} -51102.8 q^{73} -21649.4 q^{74} -5625.00 q^{75} -5776.00 q^{76} -37307.8 q^{77} +29896.8 q^{78} +4334.41 q^{79} +6400.00 q^{80} +6561.00 q^{81} +47794.3 q^{82} -33436.3 q^{83} +11960.5 q^{84} +7541.42 q^{85} -48592.8 q^{86} +17889.0 q^{87} -28747.0 q^{88} -120660. q^{89} -8100.00 q^{90} -68977.8 q^{91} +18031.1 q^{92} -50560.7 q^{93} -1995.42 q^{94} -9025.00 q^{95} +9216.00 q^{96} -131320. q^{97} +39632.7 q^{98} +36382.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 3 q - 12 q^{2} - 27 q^{3} + 48 q^{4} + 75 q^{5} + 108 q^{6} - 10 q^{7} - 192 q^{8} + 243 q^{9} - 300 q^{10} - 194 q^{11} - 432 q^{12} - 44 q^{13} + 40 q^{14} - 675 q^{15} + 768 q^{16} + 270 q^{17} - 972 q^{18} - 1083 q^{19} + 1200 q^{20} + 90 q^{21} + 776 q^{22} + 1736 q^{23} + 1728 q^{24} + 1875 q^{25} + 176 q^{26} - 2187 q^{27} - 160 q^{28} + 3460 q^{29} + 2700 q^{30} + 2624 q^{31} - 3072 q^{32} + 1746 q^{33} - 1080 q^{34} - 250 q^{35} + 3888 q^{36} + 16332 q^{37} + 4332 q^{38} + 396 q^{39} - 4800 q^{40} - 10100 q^{41} - 360 q^{42} + 22710 q^{43} - 3104 q^{44} + 6075 q^{45} - 6944 q^{46} + 12248 q^{47} - 6912 q^{48} - 39909 q^{49} - 7500 q^{50} - 2430 q^{51} - 704 q^{52} + 3034 q^{53} + 8748 q^{54} - 4850 q^{55} + 640 q^{56} + 9747 q^{57} - 13840 q^{58} + 2044 q^{59} - 10800 q^{60} - 94494 q^{61} - 10496 q^{62} - 810 q^{63} + 12288 q^{64} - 1100 q^{65} - 6984 q^{66} + 12132 q^{67} + 4320 q^{68} - 15624 q^{69} + 1000 q^{70} + 40076 q^{71} - 15552 q^{72} - 79938 q^{73} - 65328 q^{74} - 16875 q^{75} - 17328 q^{76} - 68836 q^{77} - 1584 q^{78} - 12588 q^{79} + 19200 q^{80} + 19683 q^{81} + 40400 q^{82} - 57100 q^{83} + 1440 q^{84} + 6750 q^{85} - 90840 q^{86} - 31140 q^{87} + 12416 q^{88} - 66936 q^{89} - 24300 q^{90} - 125092 q^{91} + 27776 q^{92} - 23616 q^{93} - 48992 q^{94} - 27075 q^{95} + 27648 q^{96} - 10576 q^{97} + 159636 q^{98} - 15714 q^{99}+O(q^{100}) \) 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 - 194 * q^11 - 432 * q^12 - 44 * q^13 + 40 * q^14 - 675 * q^15 + 768 * q^16 + 270 * q^17 - 972 * q^18 - 1083 * q^19 + 1200 * q^20 + 90 * q^21 + 776 * q^22 + 1736 * q^23 + 1728 * q^24 + 1875 * q^25 + 176 * q^26 - 2187 * q^27 - 160 * q^28 + 3460 * q^29 + 2700 * q^30 + 2624 * q^31 - 3072 * q^32 + 1746 * q^33 - 1080 * q^34 - 250 * q^35 + 3888 * q^36 + 16332 * q^37 + 4332 * q^38 + 396 * q^39 - 4800 * q^40 - 10100 * q^41 - 360 * q^42 + 22710 * q^43 - 3104 * q^44 + 6075 * q^45 - 6944 * q^46 + 12248 * q^47 - 6912 * q^48 - 39909 * q^49 - 7500 * q^50 - 2430 * q^51 - 704 * q^52 + 3034 * q^53 + 8748 * q^54 - 4850 * q^55 + 640 * q^56 + 9747 * q^57 - 13840 * q^58 + 2044 * q^59 - 10800 * q^60 - 94494 * q^61 - 10496 * q^62 - 810 * q^63 + 12288 * q^64 - 1100 * q^65 - 6984 * q^66 + 12132 * q^67 + 4320 * q^68 - 15624 * q^69 + 1000 * q^70 + 40076 * q^71 - 15552 * q^72 - 79938 * q^73 - 65328 * q^74 - 16875 * q^75 - 17328 * q^76 - 68836 * q^77 - 1584 * q^78 - 12588 * q^79 + 19200 * q^80 + 19683 * q^81 + 40400 * q^82 - 57100 * q^83 + 1440 * q^84 + 6750 * q^85 - 90840 * q^86 - 31140 * q^87 + 12416 * q^88 - 66936 * q^89 - 24300 * q^90 - 125092 * q^91 + 27776 * q^92 - 23616 * q^93 - 48992 * q^94 - 27075 * q^95 + 27648 * q^96 - 10576 * q^97 + 159636 * q^98 - 15714 * 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
$7$	−83.0591	−0.640682	−0.320341	−	0.947302i	$-0.603797\pi$
$7$	−83.0591	−0.640682	−0.320341	+	0.947302i	$0.603797\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	−100.000	−0.316228
$11$	449.172	1.11926	0.559629	−	0.828743i	$-0.310943\pi$
$11$	449.172	1.11926	0.559629	+	0.828743i	$0.310943\pi$
$12$	−144.000	−0.288675
$13$	830.466	1.36290	0.681449	−	0.731865i	$-0.261350\pi$
$13$	830.466	1.36290	0.681449	+	0.731865i	$0.261350\pi$
$14$	332.237	0.453030
$15$	−225.000	−0.258199
$16$	256.000	0.250000
$17$	301.657	0.253158	0.126579	−	0.991957i	$-0.459600\pi$
$17$	301.657	0.253158	0.126579	+	0.991957i	$0.459600\pi$
$18$	−324.000	−0.235702
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	400.000	0.223607
$21$	747.532	0.369898
$22$	−1796.69	−0.791435
$23$	1126.94	0.444203	0.222102	−	0.975024i	$-0.428708\pi$
$23$	1126.94	0.444203	0.222102	+	0.975024i	$0.428708\pi$
$24$	576.000	0.204124
$25$	625.000	0.200000
$26$	−3321.86	−0.963715
$27$	−729.000	−0.192450
$28$	−1328.95	−0.320341
$29$	−1987.67	−0.438884	−0.219442	−	0.975626i	$-0.570424\pi$
$29$	−1987.67	−0.438884	−0.219442	+	0.975626i	$0.570424\pi$
$30$	900.000	0.182574
$31$	5617.86	1.04994	0.524972	−	0.851119i	$-0.324076\pi$
$31$	5617.86	1.04994	0.524972	+	0.851119i	$0.324076\pi$
$32$	−1024.00	−0.176777
$33$	−4042.54	−0.646204
$34$	−1206.63	−0.179009
$35$	−2076.48	−0.286522
$36$	1296.00	0.166667
$37$	5412.36	0.649953	0.324977	−	0.945722i	$-0.394644\pi$
$37$	5412.36	0.649953	0.324977	+	0.945722i	$0.394644\pi$
$38$	1444.00	0.162221
$39$	−7474.20	−0.786870
$40$	−1600.00	−0.158114
$41$	−11948.6	−1.11009	−0.555043	−	0.831822i	$-0.687298\pi$
$41$	−11948.6	−1.11009	−0.555043	+	0.831822i	$0.687298\pi$
$42$	−2990.13	−0.261557
$43$	12148.2	1.00194	0.500969	−	0.865465i	$-0.332977\pi$
$43$	12148.2	1.00194	0.500969	+	0.865465i	$0.332977\pi$
$44$	7186.74	0.559629
$45$	2025.00	0.149071
$46$	−4507.76	−0.314099
$47$	498.855	0.0329405	0.0164702	−	0.999864i	$-0.494757\pi$
$47$	498.855	0.0329405	0.0164702	+	0.999864i	$0.494757\pi$
$48$	−2304.00	−0.144338
$49$	−9908.18	−0.589527
$50$	−2500.00	−0.141421
$51$	−2714.91	−0.146161
$52$	13287.5	0.681449
$53$	40645.9	1.98759	0.993796	−	0.111220i	$-0.0354757\pi$
$53$	40645.9	1.98759	0.993796	+	0.111220i	$0.0354757\pi$
$54$	2916.00	0.136083
$55$	11229.3	0.500548
$56$	5315.78	0.226515
$57$	3249.00	0.132453
$58$	7950.69	0.310338
$59$	−39073.5	−1.46134	−0.730672	−	0.682729i	$-0.760793\pi$
$59$	−39073.5	−1.46134	−0.730672	+	0.682729i	$0.760793\pi$
$60$	−3600.00	−0.129099
$61$	−14964.4	−0.514913	−0.257456	−	0.966290i	$-0.582884\pi$
$61$	−14964.4	−0.514913	−0.257456	+	0.966290i	$0.582884\pi$
$62$	−22471.4	−0.742423
$63$	−6727.79	−0.213561
$64$	4096.00	0.125000
$65$	20761.7	0.609507
$66$	16170.2	0.456935
$67$	−31785.7	−0.865057	−0.432528	−	0.901620i	$-0.642378\pi$
$67$	−31785.7	−0.865057	−0.432528	+	0.901620i	$0.642378\pi$
$68$	4826.51	0.126579
$69$	−10142.5	−0.256461
$70$	8305.91	0.202601
$71$	55566.6	1.30818	0.654091	−	0.756416i	$-0.273051\pi$
$71$	55566.6	1.30818	0.654091	+	0.756416i	$0.273051\pi$
$72$	−5184.00	−0.117851
$73$	−51102.8	−1.12237	−0.561187	−	0.827689i	$-0.689655\pi$
$73$	−51102.8	−1.12237	−0.561187	+	0.827689i	$0.689655\pi$
$74$	−21649.4	−0.459586
$75$	−5625.00	−0.115470
$76$	−5776.00	−0.114708
$77$	−37307.8	−0.717089
$78$	29896.8	0.556401
$79$	4334.41	0.0781379	0.0390690	−	0.999237i	$-0.487561\pi$
$79$	4334.41	0.0781379	0.0390690	+	0.999237i	$0.487561\pi$
$80$	6400.00	0.111803
$81$	6561.00	0.111111
$82$	47794.3	0.784949
$83$	−33436.3	−0.532750	−0.266375	−	0.963870i	$-0.585826\pi$
$83$	−33436.3	−0.532750	−0.266375	+	0.963870i	$0.585826\pi$
$84$	11960.5	0.184949
$85$	7541.42	0.113215
$86$	−48592.8	−0.708477
$87$	17889.0	0.253390
$88$	−28747.0	−0.395718
$89$	−120660.	−1.61469	−0.807344	−	0.590081i	$-0.799096\pi$
$89$	−120660.	−1.61469	−0.807344	+	0.590081i	$0.799096\pi$
$90$	−8100.00	−0.105409
$91$	−68977.8	−0.873184
$92$	18031.1	0.222102
$93$	−50560.7	−0.606186
$94$	−1995.42	−0.0232924
$95$	−9025.00	−0.102598
$96$	9216.00	0.102062
$97$	−131320.	−1.41711	−0.708554	−	0.705656i	$-0.750652\pi$
$97$	−131320.	−1.41711	−0.708554	+	0.705656i	$0.750652\pi$
$98$	39632.7	0.416859
$99$	36382.9	0.373086
$100$	10000.0	0.100000
$101$	−37149.9	−0.362372	−0.181186	−	0.983449i	$-0.557994\pi$
$101$	−37149.9	−0.362372	−0.181186	+	0.983449i	$0.557994\pi$
$102$	10859.6	0.103351
$103$	164477.	1.52761	0.763805	−	0.645447i	$-0.223329\pi$
$103$	164477.	1.52761	0.763805	+	0.645447i	$0.223329\pi$
$104$	−53149.8	−0.481857
$105$	18688.3	0.165423
$106$	−162584.	−1.40544
$107$	117250.	0.990045	0.495022	−	0.868880i	$-0.335160\pi$
$107$	117250.	0.990045	0.495022	+	0.868880i	$0.335160\pi$
$108$	−11664.0	−0.0962250
$109$	43859.0	0.353584	0.176792	−	0.984248i	$-0.443428\pi$
$109$	43859.0	0.353584	0.176792	+	0.984248i	$0.443428\pi$
$110$	−44917.2	−0.353941
$111$	−48711.2	−0.375251
$112$	−21263.1	−0.160170
$113$	30898.5	0.227636	0.113818	−	0.993502i	$-0.463692\pi$
$113$	30898.5	0.227636	0.113818	+	0.993502i	$0.463692\pi$
$114$	−12996.0	−0.0936586
$115$	28173.5	0.198654
$116$	−31802.7	−0.219442
$117$	67267.8	0.454300
$118$	156294.	1.03333
$119$	−25055.4	−0.162193
$120$	14400.0	0.0912871
$121$	40704.1	0.252740
$122$	59857.4	0.364098
$123$	107537.	0.640908
$124$	89885.7	0.524972
$125$	15625.0	0.0894427
$126$	26911.2	0.151010
$127$	222342.	1.22324	0.611621	−	0.791151i	$-0.290518\pi$
$127$	222342.	1.22324	0.611621	+	0.791151i	$0.290518\pi$
$128$	−16384.0	−0.0883883
$129$	−109334.	−0.578469
$130$	−83046.6	−0.430986
$131$	132739.	0.675801	0.337901	−	0.941182i	$-0.390283\pi$
$131$	132739.	0.675801	0.337901	+	0.941182i	$0.390283\pi$
$132$	−64680.7	−0.323102
$133$	29984.3	0.146982
$134$	127143.	0.611687
$135$	−18225.0	−0.0860663
$136$	−19306.0	−0.0895047
$137$	349295.	1.58998	0.794990	−	0.606623i	$-0.207476\pi$
$137$	349295.	1.58998	0.794990	+	0.606623i	$0.207476\pi$
$138$	40569.9	0.181345
$139$	−234423.	−1.02911	−0.514557	−	0.857456i	$-0.672044\pi$
$139$	−234423.	−1.02911	−0.514557	+	0.857456i	$0.672044\pi$
$140$	−33223.7	−0.143261
$141$	−4489.70	−0.0190182
$142$	−222266.	−0.925024
$143$	373022.	1.52544
$144$	20736.0	0.0833333
$145$	−49691.8	−0.196275
$146$	204411.	0.793638
$147$	89173.6	0.340364
$148$	86597.7	0.324977
$149$	514382.	1.89811	0.949053	−	0.315117i	$-0.102044\pi$
$149$	514382.	1.89811	0.949053	+	0.315117i	$0.102044\pi$
$150$	22500.0	0.0816497
$151$	263335.	0.939868	0.469934	−	0.882701i	$-0.344278\pi$
$151$	263335.	0.939868	0.469934	+	0.882701i	$0.344278\pi$
$152$	23104.0	0.0811107
$153$	24434.2	0.0843858
$154$	149231.	0.507058
$155$	140446.	0.469549
$156$	−119587.	−0.393435
$157$	153715.	0.497698	0.248849	−	0.968542i	$-0.419948\pi$
$157$	153715.	0.497698	0.248849	+	0.968542i	$0.419948\pi$
$158$	−17337.6	−0.0552519
$159$	−365813.	−1.14754
$160$	−25600.0	−0.0790569
$161$	−93602.8	−0.284593
$162$	−26244.0	−0.0785674
$163$	−323964.	−0.955053	−0.477527	−	0.878617i	$-0.658467\pi$
$163$	−323964.	−0.955053	−0.477527	+	0.878617i	$0.658467\pi$
$164$	−191177.	−0.555043
$165$	−101064.	−0.288991
$166$	133745.	0.376711
$167$	501564.	1.39167	0.695833	−	0.718204i	$-0.255035\pi$
$167$	501564.	1.39167	0.695833	+	0.718204i	$0.255035\pi$
$168$	−47842.1	−0.130779
$169$	318381.	0.857493
$170$	−30165.7	−0.0800554
$171$	−29241.0	−0.0764719
$172$	194371.	0.500969
$173$	−211765.	−0.537946	−0.268973	−	0.963148i	$-0.586684\pi$
$173$	−211765.	−0.537946	−0.268973	+	0.963148i	$0.586684\pi$
$174$	−71556.2	−0.179174
$175$	−51912.0	−0.128136
$176$	114988.	0.279815
$177$	351662.	0.843707
$178$	482640.	1.14176
$179$	453997.	1.05906	0.529530	−	0.848291i	$-0.322368\pi$
$179$	453997.	1.05906	0.529530	+	0.848291i	$0.322368\pi$
$180$	32400.0	0.0745356
$181$	−296492.	−0.672692	−0.336346	−	0.941739i	$-0.609191\pi$
$181$	−296492.	−0.672692	−0.336346	+	0.941739i	$0.609191\pi$
$182$	275911.	0.617434
$183$	134679.	0.297285
$184$	−72124.2	−0.157050
$185$	135309.	0.290668
$186$	202243.	0.428638
$187$	135496.	0.283349
$188$	7981.69	0.0164702
$189$	60550.1	0.123299
$190$	36100.0	0.0725476
$191$	812385.	1.61131	0.805654	−	0.592387i	$-0.201814\pi$
$191$	812385.	1.61131	0.805654	+	0.592387i	$0.201814\pi$
$192$	−36864.0	−0.0721688
$193$	656566.	1.26878	0.634389	−	0.773014i	$-0.281252\pi$
$193$	656566.	1.26878	0.634389	+	0.773014i	$0.281252\pi$
$194$	525282.	1.00205
$195$	−186855.	−0.351899
$196$	−158531.	−0.294763
$197$	−116090.	−0.213123	−0.106562	−	0.994306i	$-0.533984\pi$
$197$	−116090.	−0.213123	−0.106562	+	0.994306i	$0.533984\pi$
$198$	−145532.	−0.263812
$199$	−1.04006e6	−1.86177	−0.930887	−	0.365308i	$-0.880964\pi$
$199$	−1.04006e6	−1.86177	−0.930887	+	0.365308i	$0.880964\pi$
$200$	−40000.0	−0.0707107
$201$	286071.	0.499441
$202$	148600.	0.256236
$203$	165094.	0.281185
$204$	−43438.6	−0.0730803
$205$	−298714.	−0.496445
$206$	−657908.	−1.08018
$207$	91282.2	0.148068
$208$	212599.	0.340725
$209$	−162151.	−0.256776
$210$	−74753.2	−0.116972
$211$	−467475.	−0.722856	−0.361428	−	0.932400i	$-0.617711\pi$
$211$	−467475.	−0.722856	−0.361428	+	0.932400i	$0.617711\pi$
$212$	650335.	0.993796
$213$	−500100.	−0.755279
$214$	−469002.	−0.700067
$215$	303705.	0.448081
$216$	46656.0	0.0680414
$217$	−466614.	−0.672680
$218$	−175436.	−0.250022
$219$	459925.	0.648002
$220$	179669.	0.250274
$221$	250516.	0.345028
$222$	194845.	0.265342
$223$	1.02573e6	1.38124	0.690620	−	0.723218i	$-0.257338\pi$
$223$	1.02573e6	1.38124	0.690620	+	0.723218i	$0.257338\pi$
$224$	85052.6	0.113258
$225$	50625.0	0.0666667
$226$	−123594.	−0.160963
$227$	2409.27	0.00310328	0.00155164	−	0.999999i	$-0.499506\pi$
$227$	2409.27	0.00310328	0.00155164	+	0.999999i	$0.499506\pi$
$228$	51984.0	0.0662266
$229$	1.53075e6	1.92893	0.964465	−	0.264211i	$-0.0851114\pi$
$229$	1.53075e6	1.92893	0.964465	+	0.264211i	$0.0851114\pi$
$230$	−112694.	−0.140469
$231$	335770.	0.414011
$232$	127211.	0.155169
$233$	−374419.	−0.451822	−0.225911	−	0.974148i	$-0.572536\pi$
$233$	−374419.	−0.451822	−0.225911	+	0.974148i	$0.572536\pi$
$234$	−269071.	−0.321238
$235$	12471.4	0.0147314
$236$	−625176.	−0.730672
$237$	−39009.7	−0.0451129
$238$	100221.	0.114688
$239$	1.39969e6	1.58503	0.792515	−	0.609852i	$-0.208771\pi$
$239$	1.39969e6	1.58503	0.792515	+	0.609852i	$0.208771\pi$
$240$	−57600.0	−0.0645497
$241$	−756760.	−0.839296	−0.419648	−	0.907687i	$-0.637847\pi$
$241$	−756760.	−0.839296	−0.419648	+	0.907687i	$0.637847\pi$
$242$	−162816.	−0.178714
$243$	−59049.0	−0.0641500
$244$	−239430.	−0.257456
$245$	−247704.	−0.263644
$246$	−430149.	−0.453190
$247$	−299798.	−0.312670
$248$	−359543.	−0.371211
$249$	300927.	0.307583
$250$	−62500.0	−0.0632456
$251$	724221.	0.725582	0.362791	−	0.931870i	$-0.381824\pi$
$251$	724221.	0.725582	0.362791	+	0.931870i	$0.381824\pi$
$252$	−107645.	−0.106780
$253$	506190.	0.497178
$254$	−889368.	−0.864962
$255$	−67872.8	−0.0653650
$256$	65536.0	0.0625000
$257$	75986.3	0.0717633	0.0358816	−	0.999356i	$-0.488576\pi$
$257$	75986.3	0.0717633	0.0358816	+	0.999356i	$0.488576\pi$
$258$	437335.	0.409040
$259$	−449546.	−0.416413
$260$	332186.	0.304753
$261$	−161001.	−0.146295
$262$	−530954.	−0.477864
$263$	−1.11367e6	−0.992808	−0.496404	−	0.868092i	$-0.665347\pi$
$263$	−1.11367e6	−0.992808	−0.496404	+	0.868092i	$0.665347\pi$
$264$	258723.	0.228468
$265$	1.01615e6	0.888878
$266$	−119937.	−0.103932
$267$	1.08594e6	0.932240
$268$	−508571.	−0.432528
$269$	−1.21385e6	−1.02279	−0.511394	−	0.859346i	$-0.670871\pi$
$269$	−1.21385e6	−1.02279	−0.511394	+	0.859346i	$0.670871\pi$
$270$	72900.0	0.0608581
$271$	−32882.0	−0.0271979	−0.0135989	−	0.999908i	$-0.504329\pi$
$271$	−32882.0	−0.0271979	−0.0135989	+	0.999908i	$0.504329\pi$
$272$	77224.1	0.0632894
$273$	620800.	0.504133
$274$	−1.39718e6	−1.12429
$275$	280732.	0.223852
$276$	−162280.	−0.128230
$277$	43967.0	0.0344292	0.0172146	−	0.999852i	$-0.494520\pi$
$277$	43967.0	0.0344292	0.0172146	+	0.999852i	$0.494520\pi$
$278$	937692.	0.727693
$279$	455046.	0.349982
$280$	132895.	0.101301
$281$	2.13630e6	1.61397	0.806987	−	0.590569i	$-0.201097\pi$
$281$	2.13630e6	1.61397	0.806987	+	0.590569i	$0.201097\pi$
$282$	17958.8	0.0134479
$283$	410802.	0.304906	0.152453	−	0.988311i	$-0.451283\pi$
$283$	410802.	0.304906	0.152453	+	0.988311i	$0.451283\pi$
$284$	889066.	0.654091
$285$	81225.0	0.0592349
$286$	−1.49209e6	−1.07865
$287$	992438.	0.711211
$288$	−82944.0	−0.0589256
$289$	−1.32886e6	−0.935911
$290$	198767.	0.138787
$291$	1.18188e6	0.818168
$292$	−817644.	−0.561187
$293$	1.60032e6	1.08903	0.544514	−	0.838752i	$-0.316714\pi$
$293$	1.60032e6	1.08903	0.544514	+	0.838752i	$0.316714\pi$
$294$	−356694.	−0.240673
$295$	−976838.	−0.653533
$296$	−346391.	−0.229793
$297$	−327446.	−0.215401
$298$	−2.05753e6	−1.34216
$299$	935886.	0.605404
$300$	−90000.0	−0.0577350
$301$	−1.00902e6	−0.641924
$302$	−1.05334e6	−0.664587
$303$	334349.	0.209216
$304$	−92416.0	−0.0573539
$305$	−374109.	−0.230276
$306$	−97736.8	−0.0596698
$307$	1.20665e6	0.730692	0.365346	−	0.930872i	$-0.380951\pi$
$307$	1.20665e6	0.730692	0.365346	+	0.930872i	$0.380951\pi$
$308$	−596925.	−0.358544
$309$	−1.48029e6	−0.881966
$310$	−561786.	−0.332022
$311$	−10636.5	−0.00623589	−0.00311795	−	0.999995i	$-0.500992\pi$
$311$	−10636.5	−0.00623589	−0.00311795	+	0.999995i	$0.500992\pi$
$312$	478349.	0.278201
$313$	−191686.	−0.110593	−0.0552967	−	0.998470i	$-0.517610\pi$
$313$	−191686.	−0.110593	−0.0552967	+	0.998470i	$0.517610\pi$
$314$	−614858.	−0.351926
$315$	−168195.	−0.0955072
$316$	69350.5	0.0390690
$317$	755908.	0.422494	0.211247	−	0.977433i	$-0.432247\pi$
$317$	755908.	0.422494	0.211247	+	0.977433i	$0.432247\pi$
$318$	1.46325e6	0.811431
$319$	−892805.	−0.491225
$320$	102400.	0.0559017
$321$	−1.05525e6	−0.571603
$322$	374411.	0.201238
$323$	−108898.	−0.0580783
$324$	104976.	0.0555556
$325$	519041.	0.272580
$326$	1.29586e6	0.675325
$327$	−394731.	−0.204142
$328$	764709.	0.392474
$329$	−41434.5	−0.0211044
$330$	404254.	0.204348
$331$	744387.	0.373447	0.186723	−	0.982413i	$-0.440213\pi$
$331$	744387.	0.373447	0.186723	+	0.982413i	$0.440213\pi$
$332$	−534981.	−0.266375
$333$	438401.	0.216651
$334$	−2.00625e6	−0.984056
$335$	−794642.	−0.386865
$336$	191368.	0.0924744
$337$	−1.23581e6	−0.592757	−0.296378	−	0.955071i	$-0.595779\pi$
$337$	−1.23581e6	−0.592757	−0.296378	+	0.955071i	$0.595779\pi$
$338$	−1.27352e6	−0.606339
$339$	−278087.	−0.131426
$340$	120663.	0.0566077
$341$	2.52338e6	1.17516
$342$	116964.	0.0540738
$343$	2.21894e6	1.01838
$344$	−777485.	−0.354239
$345$	−253562.	−0.114693
$346$	847059.	0.380385
$347$	1.22030e6	0.544057	0.272028	−	0.962289i	$-0.412306\pi$
$347$	1.22030e6	0.544057	0.272028	+	0.962289i	$0.412306\pi$
$348$	286225.	0.126695
$349$	1.09923e6	0.483089	0.241544	−	0.970390i	$-0.422346\pi$
$349$	1.09923e6	0.483089	0.241544	+	0.970390i	$0.422346\pi$
$350$	207648.	0.0906061
$351$	−605410.	−0.262290
$352$	−459952.	−0.197859
$353$	−2.62808e6	−1.12254	−0.561271	−	0.827632i	$-0.689687\pi$
$353$	−2.62808e6	−1.12254	−0.561271	+	0.827632i	$0.689687\pi$
$354$	−1.40665e6	−0.596591
$355$	1.38917e6	0.585037
$356$	−1.93056e6	−0.807344
$357$	225498.	0.0936424
$358$	−1.81599e6	−0.748869
$359$	4.32469e6	1.77100	0.885501	−	0.464638i	$-0.153816\pi$
$359$	4.32469e6	1.77100	0.885501	+	0.464638i	$0.153816\pi$
$360$	−129600.	−0.0527046
$361$	130321.	0.0526316
$362$	1.18597e6	0.475665
$363$	−366337.	−0.145920
$364$	−1.10364e6	−0.436592
$365$	−1.27757e6	−0.501941
$366$	−538717.	−0.210212
$367$	−3.48579e6	−1.35094	−0.675469	−	0.737388i	$-0.736059\pi$
$367$	−3.48579e6	−1.35094	−0.675469	+	0.737388i	$0.736059\pi$
$368$	288497.	0.111051
$369$	−967834.	−0.370028
$370$	−541236.	−0.205533
$371$	−3.37601e6	−1.27341
$372$	−808971.	−0.303093
$373$	−1.72222e6	−0.640940	−0.320470	−	0.947259i	$-0.603841\pi$
$373$	−1.72222e6	−0.640940	−0.320470	+	0.947259i	$0.603841\pi$
$374$	−541983.	−0.200358
$375$	−140625.	−0.0516398
$376$	−31926.7	−0.0116462
$377$	−1.65069e6	−0.598154
$378$	−242200.	−0.0871857
$379$	−2.79357e6	−0.998993	−0.499496	−	0.866316i	$-0.666482\pi$
$379$	−2.79357e6	−0.998993	−0.499496	+	0.866316i	$0.666482\pi$
$380$	−144400.	−0.0512989
$381$	−2.00108e6	−0.706239
$382$	−3.24954e6	−1.13937
$383$	5.24128e6	1.82575	0.912873	−	0.408243i	$-0.133859\pi$
$383$	5.24128e6	1.82575	0.912873	+	0.408243i	$0.133859\pi$
$384$	147456.	0.0510310
$385$	−932695.	−0.320692
$386$	−2.62627e6	−0.897161
$387$	984005.	0.333979
$388$	−2.10113e6	−0.708554
$389$	−3.41011e6	−1.14260	−0.571301	−	0.820741i	$-0.693561\pi$
$389$	−3.41011e6	−1.14260	−0.571301	+	0.820741i	$0.693561\pi$
$390$	747420.	0.248830
$391$	339949.	0.112453
$392$	634123.	0.208429
$393$	−1.19465e6	−0.390174
$394$	464361.	0.150701
$395$	108360.	0.0349443
$396$	582126.	0.186543
$397$	−2.62084e6	−0.834572	−0.417286	−	0.908775i	$-0.637019\pi$
$397$	−2.62084e6	−0.834572	−0.417286	+	0.908775i	$0.637019\pi$
$398$	4.16025e6	1.31647
$399$	−269859.	−0.0848604
$400$	160000.	0.0500000
$401$	−5.19370e6	−1.61293	−0.806466	−	0.591281i	$-0.798623\pi$
$401$	−5.19370e6	−1.61293	−0.806466	+	0.591281i	$0.798623\pi$
$402$	−1.14428e6	−0.353158
$403$	4.66544e6	1.43097
$404$	−594399.	−0.181186
$405$	164025.	0.0496904
$406$	−660377.	−0.198828
$407$	2.43108e6	0.727466
$408$	173754.	0.0516756
$409$	6.61244e6	1.95458	0.977291	−	0.211903i	$-0.0679660\pi$
$409$	6.61244e6	1.95458	0.977291	+	0.211903i	$0.0679660\pi$
$410$	1.19486e6	0.351040
$411$	−3.14366e6	−0.917975
$412$	2.63163e6	0.763805
$413$	3.24541e6	0.936256
$414$	−365129.	−0.104700
$415$	−835908.	−0.238253
$416$	−850397.	−0.240929
$417$	2.10981e6	0.594159
$418$	648604.	0.181568
$419$	−2.86131e6	−0.796214	−0.398107	−	0.917339i	$-0.630333\pi$
$419$	−2.86131e6	−0.796214	−0.398107	+	0.917339i	$0.630333\pi$
$420$	299013.	0.0827117
$421$	−3.67114e6	−1.00948	−0.504738	−	0.863273i	$-0.668411\pi$
$421$	−3.67114e6	−1.00948	−0.504738	+	0.863273i	$0.668411\pi$
$422$	1.86990e6	0.511137
$423$	40407.3	0.0109802
$424$	−2.60134e6	−0.702720
$425$	188535.	0.0506315
$426$	2.00040e6	0.534063
$427$	1.24293e6	0.329895
$428$	1.87601e6	0.495022
$429$	−3.35720e6	−0.880711
$430$	−1.21482e6	−0.316841
$431$	−151206.	−0.0392082	−0.0196041	−	0.999808i	$-0.506241\pi$
$431$	−151206.	−0.0392082	−0.0196041	+	0.999808i	$0.506241\pi$
$432$	−186624.	−0.0481125
$433$	3.10568e6	0.796045	0.398022	−	0.917376i	$-0.369697\pi$
$433$	3.10568e6	0.796045	0.398022	+	0.917376i	$0.369697\pi$
$434$	1.86646e6	0.475657
$435$	447226.	0.113319
$436$	701744.	0.176792
$437$	−406826.	−0.101907
$438$	−1.83970e6	−0.458207
$439$	−811296.	−0.200918	−0.100459	−	0.994941i	$-0.532031\pi$
$439$	−811296.	−0.200918	−0.100459	+	0.994941i	$0.532031\pi$
$440$	−718674.	−0.176970
$441$	−802563.	−0.196509
$442$	−1.00206e6	−0.243972
$443$	3.19236e6	0.772864	0.386432	−	0.922318i	$-0.373707\pi$
$443$	3.19236e6	0.772864	0.386432	+	0.922318i	$0.373707\pi$
$444$	−779379.	−0.187625
$445$	−3.01650e6	−0.722110
$446$	−4.10290e6	−0.976684
$447$	−4.62944e6	−1.09587
$448$	−340210.	−0.0800852
$449$	3.83491e6	0.897716	0.448858	−	0.893603i	$-0.351831\pi$
$449$	3.83491e6	0.897716	0.448858	+	0.893603i	$0.351831\pi$
$450$	−202500.	−0.0471405
$451$	−5.36696e6	−1.24247
$452$	494377.	0.113818
$453$	−2.37002e6	−0.542633
$454$	−9637.08	−0.00219435
$455$	−1.72445e6	−0.390500
$456$	−207936.	−0.0468293
$457$	1.49275e6	0.334346	0.167173	−	0.985928i	$-0.446536\pi$
$457$	1.49275e6	0.334346	0.167173	+	0.985928i	$0.446536\pi$
$458$	−6.12301e6	−1.36396
$459$	−219908.	−0.0487202
$460$	450776.	0.0993268
$461$	−1.42529e6	−0.312358	−0.156179	−	0.987729i	$-0.549918\pi$
$461$	−1.42529e6	−0.312358	−0.156179	+	0.987729i	$0.549918\pi$
$462$	−1.34308e6	−0.292750
$463$	−2.95081e6	−0.639718	−0.319859	−	0.947465i	$-0.603636\pi$
$463$	−2.95081e6	−0.639718	−0.319859	+	0.947465i	$0.603636\pi$
$464$	−508844.	−0.109721
$465$	−1.26402e6	−0.271095
$466$	1.49767e6	0.319487
$467$	262836.	0.0557690	0.0278845	−	0.999611i	$-0.491123\pi$
$467$	262836.	0.0557690	0.0278845	+	0.999611i	$0.491123\pi$
$468$	1.07628e6	0.227150
$469$	2.64009e6	0.554226
$470$	−49885.5	−0.0104167
$471$	−1.38343e6	−0.287346
$472$	2.50070e6	0.516663
$473$	5.45663e6	1.12143
$474$	156039.	0.0318997
$475$	−225625.	−0.0458831
$476$	−400886.	−0.0810967
$477$	3.29232e6	0.662531
$478$	−5.59877e6	−1.12079
$479$	−4.52262e6	−0.900641	−0.450320	−	0.892867i	$-0.648690\pi$
$479$	−4.52262e6	−0.900641	−0.450320	+	0.892867i	$0.648690\pi$
$480$	230400.	0.0456435
$481$	4.49478e6	0.885820
$482$	3.02704e6	0.593472
$483$	842425.	0.164310
$484$	651265.	0.126370
$485$	−3.28301e6	−0.633750
$486$	236196.	0.0453609
$487$	−1.90062e6	−0.363139	−0.181569	−	0.983378i	$-0.558118\pi$
$487$	−1.90062e6	−0.363139	−0.181569	+	0.983378i	$0.558118\pi$
$488$	957719.	0.182049
$489$	2.91568e6	0.551400
$490$	990818.	0.186425
$491$	3.92292e6	0.734354	0.367177	−	0.930151i	$-0.380324\pi$
$491$	3.92292e6	0.734354	0.367177	+	0.930151i	$0.380324\pi$
$492$	1.72059e6	0.320454
$493$	−599595.	−0.111107
$494$	1.19919e6	0.221091
$495$	909572.	0.166849
$496$	1.43817e6	0.262486
$497$	−4.61531e6	−0.838128
$498$	−1.20371e6	−0.217494
$499$	−7.38026e6	−1.32685	−0.663423	−	0.748245i	$-0.730897\pi$
$499$	−7.38026e6	−1.32685	−0.663423	+	0.748245i	$0.730897\pi$
$500$	250000.	0.0447214
$501$	−4.51407e6	−0.803479
$502$	−2.89688e6	−0.513064
$503$	9.49805e6	1.67384	0.836921	−	0.547324i	$-0.184353\pi$
$503$	9.49805e6	1.67384	0.836921	+	0.547324i	$0.184353\pi$
$504$	430579.	0.0755051
$505$	−928749.	−0.162058
$506$	−2.02476e6	−0.351558
$507$	−2.86543e6	−0.495074
$508$	3.55747e6	0.611621
$509$	−5.04555e6	−0.863206	−0.431603	−	0.902064i	$-0.642052\pi$
$509$	−5.04555e6	−0.863206	−0.431603	+	0.902064i	$0.642052\pi$
$510$	271491.	0.0462200
$511$	4.24455e6	0.719084
$512$	−262144.	−0.0441942
$513$	263169.	0.0441511
$514$	−303945.	−0.0507443
$515$	4.11193e6	0.683168
$516$	−1.74934e6	−0.289235
$517$	224072.	0.0368689
$518$	1.79818e6	0.294449
$519$	1.90588e6	0.310583
$520$	−1.32875e6	−0.215493
$521$	1.14113e7	1.84180	0.920899	−	0.389800i	$-0.127456\pi$
$521$	1.14113e7	1.84180	0.920899	+	0.389800i	$0.127456\pi$
$522$	644006.	0.103446
$523$	−8.99403e6	−1.43781	−0.718903	−	0.695111i	$-0.755355\pi$
$523$	−8.99403e6	−1.43781	−0.718903	+	0.695111i	$0.755355\pi$
$524$	2.12382e6	0.337901
$525$	467208.	0.0739796
$526$	4.45466e6	0.702022
$527$	1.69466e6	0.265801
$528$	−1.03489e6	−0.161551
$529$	−5.16635e6	−0.802684
$530$	−4.06459e6	−0.628532
$531$	−3.16495e6	−0.487115
$532$	479750.	0.0734912
$533$	−9.92288e6	−1.51293
$534$	−4.34376e6	−0.659193
$535$	2.93126e6	0.442762
$536$	2.03428e6	0.305844
$537$	−4.08598e6	−0.611449
$538$	4.85542e6	0.723221
$539$	−4.45047e6	−0.659833
$540$	−291600.	−0.0430331
$541$	−2.97181e6	−0.436544	−0.218272	−	0.975888i	$-0.570042\pi$
$541$	−2.97181e6	−0.436544	−0.218272	+	0.975888i	$0.570042\pi$
$542$	131528.	0.0192318
$543$	2.66842e6	0.388379
$544$	−308897.	−0.0447523
$545$	1.09647e6	0.158127
$546$	−2.48320e6	−0.356476
$547$	−8.18991e6	−1.17034	−0.585168	−	0.810912i	$-0.698972\pi$
$547$	−8.18991e6	−1.17034	−0.585168	+	0.810912i	$0.698972\pi$
$548$	5.58873e6	0.794990
$549$	−1.21211e6	−0.171638
$550$	−1.12293e6	−0.158287
$551$	717549.	0.100687
$552$	649118.	0.0906726
$553$	−360012.	−0.0500615
$554$	−175868.	−0.0243451
$555$	−1.21778e6	−0.167817
$556$	−3.75077e6	−0.514557
$557$	−5.27360e6	−0.720226	−0.360113	−	0.932909i	$-0.617262\pi$
$557$	−5.27360e6	−0.720226	−0.360113	+	0.932909i	$0.617262\pi$
$558$	−1.82019e6	−0.247474
$559$	1.00887e7	1.36554
$560$	−531578.	−0.0716304
$561$	−1.21946e6	−0.163591
$562$	−8.54520e6	−1.14125
$563$	9.94443e6	1.32224	0.661118	−	0.750282i	$-0.270082\pi$
$563$	9.94443e6	1.32224	0.661118	+	0.750282i	$0.270082\pi$
$564$	−71835.2	−0.00950910
$565$	772463.	0.101802
$566$	−1.64321e6	−0.215601
$567$	−544951.	−0.0711869
$568$	−3.55626e6	−0.462512
$569$	1.00364e6	0.129956	0.0649782	−	0.997887i	$-0.479302\pi$
$569$	1.00364e6	0.129956	0.0649782	+	0.997887i	$0.479302\pi$
$570$	−324900.	−0.0418854
$571$	1.50607e6	0.193310	0.0966549	−	0.995318i	$-0.469186\pi$
$571$	1.50607e6	0.193310	0.0966549	+	0.995318i	$0.469186\pi$
$572$	5.96835e6	0.762718
$573$	−7.31147e6	−0.930289
$574$	−3.96975e6	−0.502902
$575$	704338.	0.0888406
$576$	331776.	0.0416667
$577$	244518.	0.0305754	0.0152877	−	0.999883i	$-0.495134\pi$
$577$	244518.	0.0305754	0.0152877	+	0.999883i	$0.495134\pi$
$578$	5.31544e6	0.661789
$579$	−5.90910e6	−0.732529
$580$	−795069.	−0.0981374
$581$	2.77719e6	0.341323
$582$	−4.72754e6	−0.578532
$583$	1.82570e7	2.22463
$584$	3.27058e6	0.396819
$585$	1.68169e6	0.203169
$586$	−6.40130e6	−0.770059
$587$	−4.12475e6	−0.494085	−0.247043	−	0.969005i	$-0.579459\pi$
$587$	−4.12475e6	−0.494085	−0.247043	+	0.969005i	$0.579459\pi$
$588$	1.42678e6	0.170182
$589$	−2.02805e6	−0.240874
$590$	3.90735e6	0.462118
$591$	1.04481e6	0.123047
$592$	1.38556e6	0.162488
$593$	3.07783e6	0.359425	0.179713	−	0.983719i	$-0.442483\pi$
$593$	3.07783e6	0.359425	0.179713	+	0.983719i	$0.442483\pi$
$594$	1.30978e6	0.152312
$595$	−626384.	−0.0725351
$596$	8.23012e6	0.949053
$597$	9.36057e6	1.07490
$598$	−3.74355e6	−0.428085
$599$	−1.92410e6	−0.219110	−0.109555	−	0.993981i	$-0.534943\pi$
$599$	−1.92410e6	−0.219110	−0.109555	+	0.993981i	$0.534943\pi$
$600$	360000.	0.0408248
$601$	8.68384e6	0.980677	0.490338	−	0.871532i	$-0.336873\pi$
$601$	8.68384e6	0.980677	0.490338	+	0.871532i	$0.336873\pi$
$602$	4.03608e6	0.453909
$603$	−2.57464e6	−0.288352
$604$	4.21337e6	0.469934
$605$	1.01760e6	0.113029
$606$	−1.33740e6	−0.147938
$607$	−2.80597e6	−0.309109	−0.154555	−	0.987984i	$-0.549394\pi$
$607$	−2.80597e6	−0.309109	−0.154555	+	0.987984i	$0.549394\pi$
$608$	369664.	0.0405554
$609$	−1.48585e6	−0.162342
$610$	1.49644e6	0.162830
$611$	414283.	0.0448945
$612$	390947.	0.0421929
$613$	3.22855e6	0.347021	0.173511	−	0.984832i	$-0.444489\pi$
$613$	3.22855e6	0.347021	0.173511	+	0.984832i	$0.444489\pi$
$614$	−4.82659e6	−0.516677
$615$	2.68843e6	0.286623
$616$	2.38770e6	0.253529
$617$	−3.88713e6	−0.411070	−0.205535	−	0.978650i	$-0.565893\pi$
$617$	−3.88713e6	−0.411070	−0.205535	+	0.978650i	$0.565893\pi$
$618$	5.92118e6	0.623644
$619$	−7.99747e6	−0.838931	−0.419465	−	0.907771i	$-0.637782\pi$
$619$	−7.99747e6	−0.838931	−0.419465	+	0.907771i	$0.637782\pi$
$620$	2.24714e6	0.234775
$621$	−821540.	−0.0854869
$622$	42546.1	0.00440944
$623$	1.00219e7	1.03450
$624$	−1.91339e6	−0.196717
$625$	390625.	0.0400000
$626$	766743.	0.0782013
$627$	1.45936e6	0.148249
$628$	2.45943e6	0.248849
$629$	1.63267e6	0.164541
$630$	672779.	0.0675338
$631$	−1.11410e7	−1.11391	−0.556956	−	0.830542i	$-0.688031\pi$
$631$	−1.11410e7	−1.11391	−0.556956	+	0.830542i	$0.688031\pi$
$632$	−277402.	−0.0276259
$633$	4.20727e6	0.417341
$634$	−3.02363e6	−0.298749
$635$	5.55855e6	0.547050
$636$	−5.85301e6	−0.573768
$637$	−8.22841e6	−0.803465
$638$	3.57122e6	0.347348
$639$	4.50090e6	0.436061
$640$	−409600.	−0.0395285
$641$	1.77282e7	1.70419	0.852096	−	0.523386i	$-0.175331\pi$
$641$	1.77282e7	1.70419	0.852096	+	0.523386i	$0.175331\pi$
$642$	4.22101e6	0.404184
$643$	1.72906e7	1.64924	0.824619	−	0.565688i	$-0.191389\pi$
$643$	1.72906e7	1.64924	0.824619	+	0.565688i	$0.191389\pi$
$644$	−1.49764e6	−0.142296
$645$	−2.73335e6	−0.258699
$646$	435592.	0.0410676
$647$	−6.21624e6	−0.583804	−0.291902	−	0.956448i	$-0.594288\pi$
$647$	−6.21624e6	−0.583804	−0.291902	+	0.956448i	$0.594288\pi$
$648$	−419904.	−0.0392837
$649$	−1.75507e7	−1.63562
$650$	−2.07617e6	−0.192743
$651$	4.19953e6	0.388372
$652$	−5.18342e6	−0.477527
$653$	1.44742e7	1.32834	0.664172	−	0.747580i	$-0.268784\pi$
$653$	1.44742e7	1.32834	0.664172	+	0.747580i	$0.268784\pi$
$654$	1.57892e6	0.144350
$655$	3.31847e6	0.302228
$656$	−3.05883e6	−0.277521
$657$	−4.13932e6	−0.374124
$658$	165738.	0.0149230
$659$	−1.38806e7	−1.24507	−0.622534	−	0.782593i	$-0.713897\pi$
$659$	−1.38806e7	−1.24507	−0.622534	+	0.782593i	$0.713897\pi$
$660$	−1.61702e6	−0.144496
$661$	−1.14516e6	−0.101944	−0.0509720	−	0.998700i	$-0.516232\pi$
$661$	−1.14516e6	−0.101944	−0.0509720	+	0.998700i	$0.516232\pi$
$662$	−2.97755e6	−0.264067
$663$	−2.25464e6	−0.199202
$664$	2.13992e6	0.188355
$665$	749609.	0.0657326
$666$	−1.75360e6	−0.153195
$667$	−2.23999e6	−0.194954
$668$	8.02502e6	0.695833
$669$	−9.23153e6	−0.797459
$670$	3.17857e6	0.273555
$671$	−6.72156e6	−0.576320
$672$	−765473.	−0.0653893
$673$	2.10876e7	1.79469	0.897346	−	0.441328i	$-0.145492\pi$
$673$	2.10876e7	1.79469	0.897346	+	0.441328i	$0.145492\pi$
$674$	4.94323e6	0.419142
$675$	−455625.	−0.0384900
$676$	5.09410e6	0.428746
$677$	1.38381e7	1.16039	0.580196	−	0.814477i	$-0.302976\pi$
$677$	1.38381e7	1.16039	0.580196	+	0.814477i	$0.302976\pi$
$678$	1.11235e6	0.0929322
$679$	1.09074e7	0.907916
$680$	−482651.	−0.0400277
$681$	−21683.4	−0.00179168
$682$	−1.00935e7	−0.830963
$683$	1.91777e7	1.57306	0.786531	−	0.617551i	$-0.211875\pi$
$683$	1.91777e7	1.57306	0.786531	+	0.617551i	$0.211875\pi$
$684$	−467856.	−0.0382360
$685$	8.73239e6	0.711060
$686$	−8.87576e6	−0.720104
$687$	−1.37768e7	−1.11367
$688$	3.10994e6	0.250485
$689$	3.37551e7	2.70889
$690$	1.01425e6	0.0811000
$691$	1.32517e7	1.05579	0.527894	−	0.849310i	$-0.322982\pi$
$691$	1.32517e7	1.05579	0.527894	+	0.849310i	$0.322982\pi$
$692$	−3.38824e6	−0.268973
$693$	−3.02193e6	−0.239030
$694$	−4.88122e6	−0.384706
$695$	−5.86058e6	−0.460234
$696$	−1.14490e6	−0.0895868
$697$	−3.60437e6	−0.281026
$698$	−4.39694e6	−0.341595
$699$	3.36977e6	0.260860
$700$	−830591.	−0.0640682
$701$	−2.03765e7	−1.56615	−0.783077	−	0.621924i	$-0.786351\pi$
$701$	−2.03765e7	−1.56615	−0.783077	+	0.621924i	$0.786351\pi$
$702$	2.42164e6	0.185467
$703$	−1.95386e6	−0.149109
$704$	1.83981e6	0.139907
$705$	−112242.	−0.00850520
$706$	1.05123e7	0.793757
$707$	3.08564e6	0.232165
$708$	5.62659e6	0.421854
$709$	2.01400e7	1.50468	0.752338	−	0.658778i	$-0.228926\pi$
$709$	2.01400e7	1.50468	0.752338	+	0.658778i	$0.228926\pi$
$710$	−5.55666e6	−0.413683
$711$	351087.	0.0260460
$712$	7.72224e6	0.570878
$713$	6.33099e6	0.466389
$714$	−901993.	−0.0662152
$715$	9.32554e6	0.682196
$716$	7.26396e6	0.529530
$717$	−1.25972e7	−0.915118
$718$	−1.72988e7	−1.25229
$719$	−9.13858e6	−0.659260	−0.329630	−	0.944110i	$-0.606924\pi$
$719$	−9.13858e6	−0.659260	−0.329630	+	0.944110i	$0.606924\pi$
$720$	518400.	0.0372678
$721$	−1.36613e7	−0.978712
$722$	−521284.	−0.0372161
$723$	6.81084e6	0.484568
$724$	−4.74387e6	−0.336346
$725$	−1.24229e6	−0.0877768
$726$	1.46535e6	0.103181
$727$	1.42863e7	1.00250	0.501248	−	0.865303i	$-0.332874\pi$
$727$	1.42863e7	1.00250	0.501248	+	0.865303i	$0.332874\pi$
$728$	4.41458e6	0.308717
$729$	531441.	0.0370370
$730$	5.11028e6	0.354926
$731$	3.66459e6	0.253648
$732$	2.15487e6	0.148642
$733$	−8.52310e6	−0.585919	−0.292959	−	0.956125i	$-0.594640\pi$
$733$	−8.52310e6	−0.585919	−0.292959	+	0.956125i	$0.594640\pi$
$734$	1.39431e7	0.955258
$735$	2.22934e6	0.152215
$736$	−1.15399e6	−0.0785248
$737$	−1.42772e7	−0.968222
$738$	3.87134e6	0.261650
$739$	8.01483e6	0.539863	0.269931	−	0.962880i	$-0.412999\pi$
$739$	8.01483e6	0.539863	0.269931	+	0.962880i	$0.412999\pi$
$740$	2.16494e6	0.145334
$741$	2.69818e6	0.180520
$742$	1.35041e7	0.900439
$743$	1.08733e7	0.722584	0.361292	−	0.932453i	$-0.382336\pi$
$743$	1.08733e7	0.722584	0.361292	+	0.932453i	$0.382336\pi$
$744$	3.23588e6	0.214319
$745$	1.28596e7	0.848859
$746$	6.88889e6	0.453213
$747$	−2.70834e6	−0.177583
$748$	2.16793e6	0.141674
$749$	−9.73872e6	−0.634304
$750$	562500.	0.0365148
$751$	−524672.	−0.0339460	−0.0169730	−	0.999856i	$-0.505403\pi$
$751$	−524672.	−0.0339460	−0.0169730	+	0.999856i	$0.505403\pi$
$752$	127707.	0.00823512
$753$	−6.51799e6	−0.418915
$754$	6.60278e6	0.422959
$755$	6.58339e6	0.420322
$756$	968802.	0.0616496
$757$	−9.51792e6	−0.603674	−0.301837	−	0.953360i	$-0.597600\pi$
$757$	−9.51792e6	−0.603674	−0.301837	+	0.953360i	$0.597600\pi$
$758$	1.11743e7	0.706394
$759$	−4.55571e6	−0.287046
$760$	577600.	0.0362738
$761$	−1.40805e7	−0.881366	−0.440683	−	0.897663i	$-0.645264\pi$
$761$	−1.40805e7	−0.881366	−0.440683	+	0.897663i	$0.645264\pi$
$762$	8.00431e6	0.499386
$763$	−3.64289e6	−0.226535
$764$	1.29982e7	0.805654
$765$	610855.	0.0377385
$766$	−2.09651e7	−1.29100
$767$	−3.24492e7	−1.99166
$768$	−589824.	−0.0360844
$769$	−3.88877e6	−0.237135	−0.118568	−	0.992946i	$-0.537830\pi$
$769$	−3.88877e6	−0.237135	−0.118568	+	0.992946i	$0.537830\pi$
$770$	3.73078e6	0.226763
$771$	−683876.	−0.0414326
$772$	1.05051e7	0.634389
$773$	8.64844e6	0.520582	0.260291	−	0.965530i	$-0.416181\pi$
$773$	8.64844e6	0.520582	0.260291	+	0.965530i	$0.416181\pi$
$774$	−3.93602e6	−0.236159
$775$	3.51116e6	0.209989
$776$	8.40451e6	0.501024
$777$	4.04591e6	0.240416
$778$	1.36405e7	0.807941
$779$	4.31343e6	0.254671
$780$	−2.98968e6	−0.175949
$781$	2.49589e7	1.46419
$782$	−1.35980e6	−0.0795165
$783$	1.44901e6	0.0844632
$784$	−2.53649e6	−0.147382
$785$	3.84286e6	0.222577
$786$	4.77859e6	0.275895
$787$	6.08605e6	0.350267	0.175133	−	0.984545i	$-0.443964\pi$
$787$	6.08605e6	0.350267	0.175133	+	0.984545i	$0.443964\pi$
$788$	−1.85745e6	−0.106562
$789$	1.00230e7	0.573198
$790$	−433441.	−0.0247094
$791$	−2.56641e6	−0.145843
$792$	−2.32851e6	−0.131906
$793$	−1.24274e7	−0.701774
$794$	1.04833e7	0.590131
$795$	−9.14533e6	−0.513194
$796$	−1.66410e7	−0.930887
$797$	−2.14374e7	−1.19544	−0.597718	−	0.801706i	$-0.703926\pi$
$797$	−2.14374e7	−1.19544	−0.597718	+	0.801706i	$0.703926\pi$
$798$	1.07944e6	0.0600053
$799$	150483.	0.00833913
$800$	−640000.	−0.0353553
$801$	−9.77346e6	−0.538229
$802$	2.07748e7	1.14051
$803$	−2.29539e7	−1.25623
$804$	4.57714e6	0.249720
$805$	−2.34007e6	−0.127274
$806$	−1.86618e7	−1.01185
$807$	1.09247e7	0.590507
$808$	2.37760e6	0.128118
$809$	−9.24257e6	−0.496503	−0.248251	−	0.968696i	$-0.579856\pi$
$809$	−9.24257e6	−0.496503	−0.248251	+	0.968696i	$0.579856\pi$
$810$	−656100.	−0.0351364
$811$	−1.34962e6	−0.0720543	−0.0360272	−	0.999351i	$-0.511470\pi$
$811$	−1.34962e6	−0.0720543	−0.0360272	+	0.999351i	$0.511470\pi$
$812$	2.64151e6	0.140592
$813$	295938.	0.0157027
$814$	−9.72431e6	−0.514396
$815$	−8.09910e6	−0.427113
$816$	−695017.	−0.0365401
$817$	−4.38550e6	−0.229860
$818$	−2.64498e7	−1.38210
$819$	−5.58720e6	−0.291061
$820$	−4.77943e6	−0.248223
$821$	−2.11187e7	−1.09348	−0.546738	−	0.837304i	$-0.684131\pi$
$821$	−2.11187e7	−1.09348	−0.546738	+	0.837304i	$0.684131\pi$
$822$	1.25746e7	0.649106
$823$	1.78046e7	0.916289	0.458145	−	0.888878i	$-0.348514\pi$
$823$	1.78046e7	0.916289	0.458145	+	0.888878i	$0.348514\pi$
$824$	−1.05265e7	−0.540092
$825$	−2.52659e6	−0.129241
$826$	−1.29816e7	−0.662033
$827$	4.48794e6	0.228183	0.114092	−	0.993470i	$-0.463604\pi$
$827$	4.48794e6	0.228183	0.114092	+	0.993470i	$0.463604\pi$
$828$	1.46052e6	0.0740339
$829$	3.36766e7	1.70193	0.850964	−	0.525224i	$-0.176018\pi$
$829$	3.36766e7	1.70193	0.850964	+	0.525224i	$0.176018\pi$
$830$	3.34363e6	0.168470
$831$	−395703.	−0.0198777
$832$	3.40159e6	0.170362
$833$	−2.98887e6	−0.149243
$834$	−8.43923e6	−0.420134
$835$	1.25391e7	0.622372
$836$	−2.59441e6	−0.128388
$837$	−4.09542e6	−0.202062
$838$	1.14452e7	0.563008
$839$	1.40440e7	0.688791	0.344395	−	0.938825i	$-0.388084\pi$
$839$	1.40440e7	0.688791	0.344395	+	0.938825i	$0.388084\pi$
$840$	−1.19605e6	−0.0584860
$841$	−1.65603e7	−0.807381
$842$	1.46846e7	0.713807
$843$	−1.92267e7	−0.931828
$844$	−7.47960e6	−0.361428
$845$	7.95953e6	0.383482
$846$	−161629.	−0.00776415
$847$	−3.38085e6	−0.161926
$848$	1.04054e7	0.496898
$849$	−3.69722e6	−0.176038
$850$	−754142.	−0.0358019
$851$	6.09941e6	0.288711
$852$	−8.00159e6	−0.377640
$853$	−2.73557e7	−1.28729	−0.643644	−	0.765325i	$-0.722578\pi$
$853$	−2.73557e7	−1.28729	−0.643644	+	0.765325i	$0.722578\pi$
$854$	−4.97171e6	−0.233271
$855$	−731025.	−0.0341993
$856$	−7.50403e6	−0.350034
$857$	−2.08033e7	−0.967565	−0.483782	−	0.875188i	$-0.660737\pi$
$857$	−2.08033e7	−0.967565	−0.483782	+	0.875188i	$0.660737\pi$
$858$	1.34288e7	0.622757
$859$	−9.80490e6	−0.453378	−0.226689	−	0.973967i	$-0.572790\pi$
$859$	−9.80490e6	−0.453378	−0.226689	+	0.973967i	$0.572790\pi$
$860$	4.85928e6	0.224040
$861$	−8.93194e6	−0.410618
$862$	604825.	0.0277244
$863$	−1.41455e7	−0.646536	−0.323268	−	0.946307i	$-0.604782\pi$
$863$	−1.41455e7	−0.646536	−0.323268	+	0.946307i	$0.604782\pi$
$864$	746496.	0.0340207
$865$	−5.29412e6	−0.240577
$866$	−1.24227e7	−0.562889
$867$	1.19597e7	0.540349
$868$	−7.46583e6	−0.336340
$869$	1.94689e6	0.0874566
$870$	−1.78890e6	−0.0801289
$871$	−2.63969e7	−1.17898
$872$	−2.80698e6	−0.125011
$873$	−1.06370e7	−0.472370
$874$	1.62730e6	0.0720593
$875$	−1.29780e6	−0.0573043
$876$	7.35880e6	0.324001
$877$	−2.75657e7	−1.21024	−0.605118	−	0.796135i	$-0.706874\pi$
$877$	−2.75657e7	−1.21024	−0.605118	+	0.796135i	$0.706874\pi$
$878$	3.24519e6	0.142070
$879$	−1.44029e7	−0.628751
$880$	2.87470e6	0.125137
$881$	−2.79775e7	−1.21442	−0.607209	−	0.794542i	$-0.707711\pi$
$881$	−2.79775e7	−1.21442	−0.607209	+	0.794542i	$0.707711\pi$
$882$	3.21025e6	0.138953
$883$	4.03944e7	1.74349	0.871745	−	0.489960i	$-0.162988\pi$
$883$	4.03944e7	1.74349	0.871745	+	0.489960i	$0.162988\pi$
$884$	4.00825e6	0.172514
$885$	8.79154e6	0.377317
$886$	−1.27695e7	−0.546497
$887$	1.87663e7	0.800886	0.400443	−	0.916322i	$-0.368856\pi$
$887$	1.87663e7	0.800886	0.400443	+	0.916322i	$0.368856\pi$
$888$	3.11752e6	0.132671
$889$	−1.84675e7	−0.783708
$890$	1.20660e7	0.510609
$891$	2.94701e6	0.124362
$892$	1.64116e7	0.690620
$893$	−180087.	−0.00755707
$894$	1.85178e7	0.774898
$895$	1.13499e7	0.473626
$896$	1.36084e6	0.0566288
$897$	−8.42298e6	−0.349530
$898$	−1.53396e7	−0.634781
$899$	−1.11665e7	−0.460804
$900$	810000.	0.0333333
$901$	1.22611e7	0.503174
$902$	2.14678e7	0.878561
$903$	9.08118e6	0.370615
$904$	−1.97751e6	−0.0804816
$905$	−7.41229e6	−0.300837
$906$	9.48008e6	0.383700
$907$	−6.19616e6	−0.250095	−0.125047	−	0.992151i	$-0.539908\pi$
$907$	−6.19616e6	−0.250095	−0.125047	+	0.992151i	$0.539908\pi$
$908$	38548.3	0.00155164
$909$	−3.00915e6	−0.120791
$910$	6.89778e6	0.276125
$911$	4.34907e7	1.73620	0.868102	−	0.496386i	$-0.165340\pi$
$911$	4.34907e7	1.73620	0.868102	+	0.496386i	$0.165340\pi$
$912$	831744.	0.0331133
$913$	−1.50186e7	−0.596285
$914$	−5.97099e6	−0.236418
$915$	3.36698e6	0.132950
$916$	2.44921e7	0.964465
$917$	−1.10252e7	−0.432974
$918$	879631.	0.0344504
$919$	2.11943e7	0.827810	0.413905	−	0.910320i	$-0.364165\pi$
$919$	2.11943e7	0.827810	0.413905	+	0.910320i	$0.364165\pi$
$920$	−1.80311e6	−0.0702347
$921$	−1.08598e7	−0.421865
$922$	5.70117e6	0.220870
$923$	4.61462e7	1.78292
$924$	5.37232e6	0.207006
$925$	3.38272e6	0.129991
$926$	1.18032e7	0.452349
$927$	1.33226e7	0.509203
$928$	2.03538e6	0.0775844
$929$	3.93421e7	1.49561	0.747805	−	0.663918i	$-0.231108\pi$
$929$	3.93421e7	1.49561	0.747805	+	0.663918i	$0.231108\pi$
$930$	5.05607e6	0.191693
$931$	3.57685e6	0.135247
$932$	−5.99070e6	−0.225911
$933$	95728.7	0.00360029
$934$	−1.05134e6	−0.0394346
$935$	3.38739e6	0.126717
$936$	−4.30514e6	−0.160619
$937$	−1.88060e7	−0.699759	−0.349879	−	0.936795i	$-0.613777\pi$
$937$	−1.88060e7	−0.699759	−0.349879	+	0.936795i	$0.613777\pi$
$938$	−1.05604e7	−0.391897
$939$	1.72517e6	0.0638511
$940$	199542.	0.00736572
$941$	574726.	0.0211586	0.0105793	−	0.999944i	$-0.496632\pi$
$941$	574726.	0.0211586	0.0105793	+	0.999944i	$0.496632\pi$
$942$	5.53373e6	0.203184
$943$	−1.34653e7	−0.493103
$944$	−1.00028e7	−0.365336
$945$	1.51375e6	0.0551411
$946$	−2.18265e7	−0.792970
$947$	2.18236e7	0.790771	0.395386	−	0.918515i	$-0.370611\pi$
$947$	2.18236e7	0.790771	0.395386	+	0.918515i	$0.370611\pi$
$948$	−624154.	−0.0225565
$949$	−4.24391e7	−1.52968
$950$	902500.	0.0324443
$951$	−6.80318e6	−0.243927
$952$	1.60354e6	0.0573440
$953$	−1.82988e6	−0.0652667	−0.0326333	−	0.999467i	$-0.510389\pi$
$953$	−1.82988e6	−0.0652667	−0.0326333	+	0.999467i	$0.510389\pi$
$954$	−1.31693e7	−0.468480
$955$	2.03096e7	0.720599
$956$	2.23951e7	0.792515
$957$	8.03525e6	0.283609
$958$	1.80905e7	0.636849
$959$	−2.90122e7	−1.01867
$960$	−921600.	−0.0322749
$961$	2.93115e6	0.102383
$962$	−1.79791e7	−0.626369
$963$	9.49728e6	0.330015
$964$	−1.21082e7	−0.419648
$965$	1.64142e7	0.567415
$966$	−3.36970e6	−0.116185
$967$	−1.42689e7	−0.490708	−0.245354	−	0.969434i	$-0.578904\pi$
$967$	−1.42689e7	−0.490708	−0.245354	+	0.969434i	$0.578904\pi$
$968$	−2.60506e6	−0.0893572
$969$	980083.	0.0335315
$970$	1.31320e7	0.448129
$971$	−2.68380e6	−0.0913488	−0.0456744	−	0.998956i	$-0.514544\pi$
$971$	−2.68380e6	−0.0913488	−0.0456744	+	0.998956i	$0.514544\pi$
$972$	−944784.	−0.0320750
$973$	1.94710e7	0.659334
$974$	7.60248e6	0.256778
$975$	−4.67137e6	−0.157374
$976$	−3.83088e6	−0.128728
$977$	−3.47575e6	−0.116496	−0.0582482	−	0.998302i	$-0.518551\pi$
$977$	−3.47575e6	−0.116496	−0.0582482	+	0.998302i	$0.518551\pi$
$978$	−1.16627e7	−0.389899
$979$	−5.41971e7	−1.80725
$980$	−3.96327e6	−0.131822
$981$	3.55258e6	0.117861
$982$	−1.56917e7	−0.519267
$983$	5.66938e6	0.187133	0.0935667	−	0.995613i	$-0.470173\pi$
$983$	5.66938e6	0.187133	0.0935667	+	0.995613i	$0.470173\pi$
$984$	−6.88238e6	−0.226595
$985$	−2.90226e6	−0.0953115
$986$	2.39838e6	0.0785643
$987$	372910.	0.0121846
$988$	−4.79677e6	−0.156335
$989$	1.36903e7	0.445064
$990$	−3.63829e6	−0.117980
$991$	573307.	0.0185440	0.00927200	−	0.999957i	$-0.497049\pi$
$991$	573307.	0.0185440	0.00927200	+	0.999957i	$0.497049\pi$
$992$	−5.75268e6	−0.185606
$993$	−6.69948e6	−0.215610
$994$	1.84613e7	0.592646
$995$	−2.60016e7	−0.832610
$996$	4.81483e6	0.153792
$997$	4.13890e7	1.31870	0.659351	−	0.751835i	$-0.270831\pi$
$997$	4.13890e7	1.31870	0.659351	+	0.751835i	$0.270831\pi$
$998$	2.95210e7	0.938222
$999$	−3.94561e6	−0.125084

Twists

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

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

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +36.0000 q^{6} -83.0591 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +36.0000 q^{6} -83.0591 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} +449.172 q^{11} -144.000 q^{12} +830.466 q^{13} +332.237 q^{14} -225.000 q^{15} +256.000 q^{16} +301.657 q^{17} -324.000 q^{18} -361.000 q^{19} +400.000 q^{20} +747.532 q^{21} -1796.69 q^{22} +1126.94 q^{23} +576.000 q^{24} +625.000 q^{25} -3321.86 q^{26} -729.000 q^{27} -1328.95 q^{28} -1987.67 q^{29} +900.000 q^{30} +5617.86 q^{31} -1024.00 q^{32} -4042.54 q^{33} -1206.63 q^{34} -2076.48 q^{35} +1296.00 q^{36} +5412.36 q^{37} +1444.00 q^{38} -7474.20 q^{39} -1600.00 q^{40} -11948.6 q^{41} -2990.13 q^{42} +12148.2 q^{43} +7186.74 q^{44} +2025.00 q^{45} -4507.76 q^{46} +498.855 q^{47} -2304.00 q^{48} -9908.18 q^{49} -2500.00 q^{50} -2714.91 q^{51} +13287.5 q^{52} +40645.9 q^{53} +2916.00 q^{54} +11229.3 q^{55} +5315.78 q^{56} +3249.00 q^{57} +7950.69 q^{58} -39073.5 q^{59} -3600.00 q^{60} -14964.4 q^{61} -22471.4 q^{62} -6727.79 q^{63} +4096.00 q^{64} +20761.7 q^{65} +16170.2 q^{66} -31785.7 q^{67} +4826.51 q^{68} -10142.5 q^{69} +8305.91 q^{70} +55566.6 q^{71} -5184.00 q^{72} -51102.8 q^{73} -21649.4 q^{74} -5625.00 q^{75} -5776.00 q^{76} -37307.8 q^{77} +29896.8 q^{78} +4334.41 q^{79} +6400.00 q^{80} +6561.00 q^{81} +47794.3 q^{82} -33436.3 q^{83} +11960.5 q^{84} +7541.42 q^{85} -48592.8 q^{86} +17889.0 q^{87} -28747.0 q^{88} -120660. q^{89} -8100.00 q^{90} -68977.8 q^{91} +18031.1 q^{92} -50560.7 q^{93} -1995.42 q^{94} -9025.00 q^{95} +9216.00 q^{96} -131320. q^{97} +39632.7 q^{98} +36382.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 12 q^{2} - 27 q^{3} + 48 q^{4} + 75 q^{5} + 108 q^{6} - 10 q^{7} - 192 q^{8} + 243 q^{9}+O(q^{10}) \) 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	\( 3 q - 12 q^{2} - 27 q^{3} + 48 q^{4} + 75 q^{5} + 108 q^{6} - 10 q^{7} - 192 q^{8} + 243 q^{9} - 300 q^{10} - 194 q^{11} - 432 q^{12} - 44 q^{13} + 40 q^{14} - 675 q^{15} + 768 q^{16} + 270 q^{17} - 972 q^{18} - 1083 q^{19} + 1200 q^{20} + 90 q^{21} + 776 q^{22} + 1736 q^{23} + 1728 q^{24} + 1875 q^{25} + 176 q^{26} - 2187 q^{27} - 160 q^{28} + 3460 q^{29} + 2700 q^{30} + 2624 q^{31} - 3072 q^{32} + 1746 q^{33} - 1080 q^{34} - 250 q^{35} + 3888 q^{36} + 16332 q^{37} + 4332 q^{38} + 396 q^{39} - 4800 q^{40} - 10100 q^{41} - 360 q^{42} + 22710 q^{43} - 3104 q^{44} + 6075 q^{45} - 6944 q^{46} + 12248 q^{47} - 6912 q^{48} - 39909 q^{49} - 7500 q^{50} - 2430 q^{51} - 704 q^{52} + 3034 q^{53} + 8748 q^{54} - 4850 q^{55} + 640 q^{56} + 9747 q^{57} - 13840 q^{58} + 2044 q^{59} - 10800 q^{60} - 94494 q^{61} - 10496 q^{62} - 810 q^{63} + 12288 q^{64} - 1100 q^{65} - 6984 q^{66} + 12132 q^{67} + 4320 q^{68} - 15624 q^{69} + 1000 q^{70} + 40076 q^{71} - 15552 q^{72} - 79938 q^{73} - 65328 q^{74} - 16875 q^{75} - 17328 q^{76} - 68836 q^{77} - 1584 q^{78} - 12588 q^{79} + 19200 q^{80} + 19683 q^{81} + 40400 q^{82} - 57100 q^{83} + 1440 q^{84} + 6750 q^{85} - 90840 q^{86} - 31140 q^{87} + 12416 q^{88} - 66936 q^{89} - 24300 q^{90} - 125092 q^{91} + 27776 q^{92} - 23616 q^{93} - 48992 q^{94} - 27075 q^{95} + 27648 q^{96} - 10576 q^{97} + 159636 q^{98} - 15714 q^{99}+O(q^{100}) \) 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 - 194 * q^11 - 432 * q^12 - 44 * q^13 + 40 * q^14 - 675 * q^15 + 768 * q^16 + 270 * q^17 - 972 * q^18 - 1083 * q^19 + 1200 * q^20 + 90 * q^21 + 776 * q^22 + 1736 * q^23 + 1728 * q^24 + 1875 * q^25 + 176 * q^26 - 2187 * q^27 - 160 * q^28 + 3460 * q^29 + 2700 * q^30 + 2624 * q^31 - 3072 * q^32 + 1746 * q^33 - 1080 * q^34 - 250 * q^35 + 3888 * q^36 + 16332 * q^37 + 4332 * q^38 + 396 * q^39 - 4800 * q^40 - 10100 * q^41 - 360 * q^42 + 22710 * q^43 - 3104 * q^44 + 6075 * q^45 - 6944 * q^46 + 12248 * q^47 - 6912 * q^48 - 39909 * q^49 - 7500 * q^50 - 2430 * q^51 - 704 * q^52 + 3034 * q^53 + 8748 * q^54 - 4850 * q^55 + 640 * q^56 + 9747 * q^57 - 13840 * q^58 + 2044 * q^59 - 10800 * q^60 - 94494 * q^61 - 10496 * q^62 - 810 * q^63 + 12288 * q^64 - 1100 * q^65 - 6984 * q^66 + 12132 * q^67 + 4320 * q^68 - 15624 * q^69 + 1000 * q^70 + 40076 * q^71 - 15552 * q^72 - 79938 * q^73 - 65328 * q^74 - 16875 * q^75 - 17328 * q^76 - 68836 * q^77 - 1584 * q^78 - 12588 * q^79 + 19200 * q^80 + 19683 * q^81 + 40400 * q^82 - 57100 * q^83 + 1440 * q^84 + 6750 * q^85 - 90840 * q^86 - 31140 * q^87 + 12416 * q^88 - 66936 * q^89 - 24300 * q^90 - 125092 * q^91 + 27776 * q^92 - 23616 * q^93 - 48992 * q^94 - 27075 * q^95 + 27648 * q^96 - 10576 * q^97 + 159636 * q^98 - 15714 * q^99

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