LMFDB - Embedded newform 570.6.a.j.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("570.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$91.4187772934$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 25872x^{2} - 1407374x - 6356280 $ x^4 - 25872x^2 - 1407374x - 6356280
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$183.641$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +36.0000 q^{6} +55.7215 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +36.0000 q^{6} +55.7215 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -323.562 q^{11} -144.000 q^{12} +197.723 q^{13} -222.886 q^{14} -225.000 q^{15} +256.000 q^{16} +1232.08 q^{17} -324.000 q^{18} +361.000 q^{19} +400.000 q^{20} -501.494 q^{21} +1294.25 q^{22} -3776.19 q^{23} +576.000 q^{24} +625.000 q^{25} -790.890 q^{26} -729.000 q^{27} +891.544 q^{28} -4736.64 q^{29} +900.000 q^{30} +4826.60 q^{31} -1024.00 q^{32} +2912.06 q^{33} -4928.34 q^{34} +1393.04 q^{35} +1296.00 q^{36} -11273.5 q^{37} -1444.00 q^{38} -1779.50 q^{39} -1600.00 q^{40} -2353.15 q^{41} +2005.97 q^{42} -1920.53 q^{43} -5176.99 q^{44} +2025.00 q^{45} +15104.8 q^{46} -3445.61 q^{47} -2304.00 q^{48} -13702.1 q^{49} -2500.00 q^{50} -11088.8 q^{51} +3163.56 q^{52} +28779.8 q^{53} +2916.00 q^{54} -8089.05 q^{55} -3566.18 q^{56} -3249.00 q^{57} +18946.6 q^{58} +23431.7 q^{59} -3600.00 q^{60} +22487.3 q^{61} -19306.4 q^{62} +4513.44 q^{63} +4096.00 q^{64} +4943.06 q^{65} -11648.2 q^{66} +33101.9 q^{67} +19713.4 q^{68} +33985.7 q^{69} -5572.15 q^{70} +9436.16 q^{71} -5184.00 q^{72} +76218.4 q^{73} +45093.8 q^{74} -5625.00 q^{75} +5776.00 q^{76} -18029.4 q^{77} +7118.01 q^{78} -58507.4 q^{79} +6400.00 q^{80} +6561.00 q^{81} +9412.61 q^{82} -99966.1 q^{83} -8023.90 q^{84} +30802.1 q^{85} +7682.11 q^{86} +42629.8 q^{87} +20708.0 q^{88} -35586.1 q^{89} -8100.00 q^{90} +11017.4 q^{91} -60419.1 q^{92} -43439.4 q^{93} +13782.4 q^{94} +9025.00 q^{95} +9216.00 q^{96} +76052.9 q^{97} +54808.5 q^{98} -26208.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} + 100 q^{5} + 144 q^{6} - 108 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) $ 4 * q - 16 * q^2 - 36 * q^3 + 64 * q^4 + 100 * q^5 + 144 * q^6 - 108 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} + 100 q^{5} + 144 q^{6} - 108 q^{7} - 256 q^{8} + 324 q^{9} - 400 q^{10} - 246 q^{11} - 576 q^{12} + 640 q^{13} + 432 q^{14} - 900 q^{15} + 1024 q^{16} - 612 q^{17} - 1296 q^{18} + 1444 q^{19} + 1600 q^{20} + 972 q^{21} + 984 q^{22} - 1242 q^{23} + 2304 q^{24} + 2500 q^{25} - 2560 q^{26} - 2916 q^{27} - 1728 q^{28} - 6230 q^{29} + 3600 q^{30} - 11360 q^{31} - 4096 q^{32} + 2214 q^{33} + 2448 q^{34} - 2700 q^{35} + 5184 q^{36} - 4792 q^{37} - 5776 q^{38} - 5760 q^{39} - 6400 q^{40} + 9170 q^{41} - 3888 q^{42} - 11412 q^{43} - 3936 q^{44} + 8100 q^{45} + 4968 q^{46} - 29858 q^{47} - 9216 q^{48} + 31092 q^{49} - 10000 q^{50} + 5508 q^{51} + 10240 q^{52} + 27498 q^{53} + 11664 q^{54} - 6150 q^{55} + 6912 q^{56} - 12996 q^{57} + 24920 q^{58} + 54984 q^{59} - 14400 q^{60} + 20868 q^{61} + 45440 q^{62} - 8748 q^{63} + 16384 q^{64} + 16000 q^{65} - 8856 q^{66} - 20244 q^{67} - 9792 q^{68} + 11178 q^{69} + 10800 q^{70} + 86864 q^{71} - 20736 q^{72} - 3728 q^{73} + 19168 q^{74} - 22500 q^{75} + 23104 q^{76} + 18796 q^{77} + 23040 q^{78} + 164192 q^{79} + 25600 q^{80} + 26244 q^{81} - 36680 q^{82} - 60506 q^{83} + 15552 q^{84} - 15300 q^{85} + 45648 q^{86} + 56070 q^{87} + 15744 q^{88} + 113798 q^{89} - 32400 q^{90} + 159528 q^{91} - 19872 q^{92} + 102240 q^{93} + 119432 q^{94} + 36100 q^{95} + 36864 q^{96} + 79440 q^{97} - 124368 q^{98} - 19926 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 - 36 * q^3 + 64 * q^4 + 100 * q^5 + 144 * q^6 - 108 * q^7 - 256 * q^8 + 324 * q^9 - 400 * q^10 - 246 * q^11 - 576 * q^12 + 640 * q^13 + 432 * q^14 - 900 * q^15 + 1024 * q^16 - 612 * q^17 - 1296 * q^18 + 1444 * q^19 + 1600 * q^20 + 972 * q^21 + 984 * q^22 - 1242 * q^23 + 2304 * q^24 + 2500 * q^25 - 2560 * q^26 - 2916 * q^27 - 1728 * q^28 - 6230 * q^29 + 3600 * q^30 - 11360 * q^31 - 4096 * q^32 + 2214 * q^33 + 2448 * q^34 - 2700 * q^35 + 5184 * q^36 - 4792 * q^37 - 5776 * q^38 - 5760 * q^39 - 6400 * q^40 + 9170 * q^41 - 3888 * q^42 - 11412 * q^43 - 3936 * q^44 + 8100 * q^45 + 4968 * q^46 - 29858 * q^47 - 9216 * q^48 + 31092 * q^49 - 10000 * q^50 + 5508 * q^51 + 10240 * q^52 + 27498 * q^53 + 11664 * q^54 - 6150 * q^55 + 6912 * q^56 - 12996 * q^57 + 24920 * q^58 + 54984 * q^59 - 14400 * q^60 + 20868 * q^61 + 45440 * q^62 - 8748 * q^63 + 16384 * q^64 + 16000 * q^65 - 8856 * q^66 - 20244 * q^67 - 9792 * q^68 + 11178 * q^69 + 10800 * q^70 + 86864 * q^71 - 20736 * q^72 - 3728 * q^73 + 19168 * q^74 - 22500 * q^75 + 23104 * q^76 + 18796 * q^77 + 23040 * q^78 + 164192 * q^79 + 25600 * q^80 + 26244 * q^81 - 36680 * q^82 - 60506 * q^83 + 15552 * q^84 - 15300 * q^85 + 45648 * q^86 + 56070 * q^87 + 15744 * q^88 + 113798 * q^89 - 32400 * q^90 + 159528 * q^91 - 19872 * q^92 + 102240 * q^93 + 119432 * q^94 + 36100 * q^95 + 36864 * q^96 + 79440 * q^97 - 124368 * q^98 - 19926 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	16.0000	0.500000
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	36.0000	0.408248
$7$	55.7215	0.429811	0.214906	−	0.976635i	$-0.431056\pi$
$7$	55.7215	0.429811	0.214906	+	0.976635i	$0.431056\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	−100.000	−0.316228
$11$	−323.562	−0.806261	−0.403131	−	0.915142i	$-0.632078\pi$
$11$	−323.562	−0.806261	−0.403131	+	0.915142i	$0.632078\pi$
$12$	−144.000	−0.288675
$13$	197.723	0.324487	0.162244	−	0.986751i	$-0.448127\pi$
$13$	197.723	0.324487	0.162244	+	0.986751i	$0.448127\pi$
$14$	−222.886	−0.303922
$15$	−225.000	−0.258199
$16$	256.000	0.250000
$17$	1232.08	1.03399	0.516997	−	0.855987i	$-0.327050\pi$
$17$	1232.08	1.03399	0.516997	+	0.855987i	$0.327050\pi$
$18$	−324.000	−0.235702
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	400.000	0.223607
$21$	−501.494	−0.248152
$22$	1294.25	0.570113
$23$	−3776.19	−1.48845	−0.744226	−	0.667928i	$-0.767181\pi$
$23$	−3776.19	−1.48845	−0.744226	+	0.667928i	$0.767181\pi$
$24$	576.000	0.204124
$25$	625.000	0.200000
$26$	−790.890	−0.229447
$27$	−729.000	−0.192450
$28$	891.544	0.214906
$29$	−4736.64	−1.04587	−0.522933	−	0.852374i	$-0.675162\pi$
$29$	−4736.64	−1.04587	−0.522933	+	0.852374i	$0.675162\pi$
$30$	900.000	0.182574
$31$	4826.60	0.902064	0.451032	−	0.892508i	$-0.351056\pi$
$31$	4826.60	0.902064	0.451032	+	0.892508i	$0.351056\pi$
$32$	−1024.00	−0.176777
$33$	2912.06	0.465495
$34$	−4928.34	−0.731144
$35$	1393.04	0.192217
$36$	1296.00	0.166667
$37$	−11273.5	−1.35379	−0.676897	−	0.736078i	$-0.736676\pi$
$37$	−11273.5	−1.35379	−0.676897	+	0.736078i	$0.736676\pi$
$38$	−1444.00	−0.162221
$39$	−1779.50	−0.187343
$40$	−1600.00	−0.158114
$41$	−2353.15	−0.218620	−0.109310	−	0.994008i	$-0.534864\pi$
$41$	−2353.15	−0.218620	−0.109310	+	0.994008i	$0.534864\pi$
$42$	2005.97	0.175470
$43$	−1920.53	−0.158398	−0.0791990	−	0.996859i	$-0.525236\pi$
$43$	−1920.53	−0.158398	−0.0791990	+	0.996859i	$0.525236\pi$
$44$	−5176.99	−0.403131
$45$	2025.00	0.149071
$46$	15104.8	1.05249
$47$	−3445.61	−0.227521	−0.113760	−	0.993508i	$-0.536290\pi$
$47$	−3445.61	−0.227521	−0.113760	+	0.993508i	$0.536290\pi$
$48$	−2304.00	−0.144338
$49$	−13702.1	−0.815262
$50$	−2500.00	−0.141421
$51$	−11088.8	−0.596977
$52$	3163.56	0.162244
$53$	28779.8	1.40733	0.703667	−	0.710530i	$-0.251545\pi$
$53$	28779.8	1.40733	0.703667	+	0.710530i	$0.251545\pi$
$54$	2916.00	0.136083
$55$	−8089.05	−0.360571
$56$	−3566.18	−0.151961
$57$	−3249.00	−0.132453
$58$	18946.6	0.739538
$59$	23431.7	0.876342	0.438171	−	0.898892i	$-0.355626\pi$
$59$	23431.7	0.876342	0.438171	+	0.898892i	$0.355626\pi$
$60$	−3600.00	−0.129099
$61$	22487.3	0.773771	0.386886	−	0.922128i	$-0.373551\pi$
$61$	22487.3	0.773771	0.386886	+	0.922128i	$0.373551\pi$
$62$	−19306.4	−0.637855
$63$	4513.44	0.143270
$64$	4096.00	0.125000
$65$	4943.06	0.145115
$66$	−11648.2	−0.329155
$67$	33101.9	0.900879	0.450440	−	0.892807i	$-0.351267\pi$
$67$	33101.9	0.900879	0.450440	+	0.892807i	$0.351267\pi$
$68$	19713.4	0.516997
$69$	33985.7	0.859358
$70$	−5572.15	−0.135918
$71$	9436.16	0.222152	0.111076	−	0.993812i	$-0.464570\pi$
$71$	9436.16	0.222152	0.111076	+	0.993812i	$0.464570\pi$
$72$	−5184.00	−0.117851
$73$	76218.4	1.67399	0.836995	−	0.547211i	$-0.184310\pi$
$73$	76218.4	1.67399	0.836995	+	0.547211i	$0.184310\pi$
$74$	45093.8	0.957277
$75$	−5625.00	−0.115470
$76$	5776.00	0.114708
$77$	−18029.4	−0.346540
$78$	7118.01	0.132471
$79$	−58507.4	−1.05473	−0.527367	−	0.849637i	$-0.676821\pi$
$79$	−58507.4	−1.05473	−0.527367	+	0.849637i	$0.676821\pi$
$80$	6400.00	0.111803
$81$	6561.00	0.111111
$82$	9412.61	0.154588
$83$	−99966.1	−1.59279	−0.796393	−	0.604780i	$-0.793261\pi$
$83$	−99966.1	−1.59279	−0.796393	+	0.604780i	$0.793261\pi$
$84$	−8023.90	−0.124076
$85$	30802.1	0.462416
$86$	7682.11	0.112004
$87$	42629.8	0.603831
$88$	20708.0	0.285056
$89$	−35586.1	−0.476218	−0.238109	−	0.971238i	$-0.576528\pi$
$89$	−35586.1	−0.476218	−0.238109	+	0.971238i	$0.576528\pi$
$90$	−8100.00	−0.105409
$91$	11017.4	0.139468
$92$	−60419.1	−0.744226
$93$	−43439.4	−0.520807
$94$	13782.4	0.160881
$95$	9025.00	0.102598
$96$	9216.00	0.102062
$97$	76052.9	0.820704	0.410352	−	0.911927i	$-0.365406\pi$
$97$	76052.9	0.820704	0.410352	+	0.911927i	$0.365406\pi$
$98$	54808.5	0.576478
$99$	−26208.5	−0.268754
$100$	10000.0	0.100000
$101$	−28533.7	−0.278326	−0.139163	−	0.990269i	$-0.544441\pi$
$101$	−28533.7	−0.278326	−0.139163	+	0.990269i	$0.544441\pi$
$102$	44355.0	0.422126
$103$	−164583.	−1.52859	−0.764295	−	0.644867i	$-0.776913\pi$
$103$	−164583.	−1.52859	−0.764295	+	0.644867i	$0.776913\pi$
$104$	−12654.2	−0.114724
$105$	−12537.3	−0.110977
$106$	−115119.	−0.995136
$107$	−99871.8	−0.843303	−0.421651	−	0.906758i	$-0.638549\pi$
$107$	−99871.8	−0.843303	−0.421651	+	0.906758i	$0.638549\pi$
$108$	−11664.0	−0.0962250
$109$	187471.	1.51136	0.755682	−	0.654939i	$-0.227306\pi$
$109$	187471.	1.51136	0.755682	+	0.654939i	$0.227306\pi$
$110$	32356.2	0.254962
$111$	101461.	0.781613
$112$	14264.7	0.107453
$113$	68254.9	0.502849	0.251425	−	0.967877i	$-0.419101\pi$
$113$	68254.9	0.502849	0.251425	+	0.967877i	$0.419101\pi$
$114$	12996.0	0.0936586
$115$	−94404.8	−0.665656
$116$	−75786.3	−0.522933
$117$	16015.5	0.108162
$118$	−93726.8	−0.619667
$119$	68653.6	0.444422
$120$	14400.0	0.0912871
$121$	−56358.7	−0.349943
$122$	−89949.2	−0.547139
$123$	21178.4	0.126221
$124$	77225.6	0.451032
$125$	15625.0	0.0894427
$126$	−18053.8	−0.101307
$127$	−172249.	−0.947649	−0.473825	−	0.880619i	$-0.657127\pi$
$127$	−172249.	−0.947649	−0.473825	+	0.880619i	$0.657127\pi$
$128$	−16384.0	−0.0883883
$129$	17284.8	0.0914511
$130$	−19772.3	−0.102612
$131$	140517.	0.715404	0.357702	−	0.933836i	$-0.383560\pi$
$131$	140517.	0.715404	0.357702	+	0.933836i	$0.383560\pi$
$132$	46592.9	0.232748
$133$	20115.5	0.0986055
$134$	−132408.	−0.637018
$135$	−18225.0	−0.0860663
$136$	−78853.4	−0.365572
$137$	−222742.	−1.01391	−0.506955	−	0.861972i	$-0.669229\pi$
$137$	−222742.	−1.01391	−0.506955	+	0.861972i	$0.669229\pi$
$138$	−135943.	−0.607658
$139$	−397260.	−1.74397	−0.871983	−	0.489536i	$-0.837166\pi$
$139$	−397260.	−1.74397	−0.871983	+	0.489536i	$0.837166\pi$
$140$	22288.6	0.0961087
$141$	31010.4	0.131359
$142$	−37744.6	−0.157085
$143$	−63975.5	−0.261621
$144$	20736.0	0.0833333
$145$	−118416.	−0.467725
$146$	−304874.	−1.18369
$147$	123319.	0.470692
$148$	−180375.	−0.676897
$149$	64763.5	0.238982	0.119491	−	0.992835i	$-0.461874\pi$
$149$	64763.5	0.238982	0.119491	+	0.992835i	$0.461874\pi$
$150$	22500.0	0.0816497
$151$	496084.	1.77057	0.885285	−	0.465049i	$-0.153963\pi$
$151$	496084.	1.77057	0.885285	+	0.465049i	$0.153963\pi$
$152$	−23104.0	−0.0811107
$153$	99798.8	0.344665
$154$	72117.4	0.245041
$155$	120665.	0.403415
$156$	−28472.0	−0.0936714
$157$	−306681.	−0.992974	−0.496487	−	0.868044i	$-0.665377\pi$
$157$	−306681.	−0.992974	−0.496487	+	0.868044i	$0.665377\pi$
$158$	234030.	0.745810
$159$	−259018.	−0.812525
$160$	−25600.0	−0.0790569
$161$	−210415.	−0.639753
$162$	−26244.0	−0.0785674
$163$	−304398.	−0.897373	−0.448687	−	0.893689i	$-0.648108\pi$
$163$	−304398.	−0.897373	−0.448687	+	0.893689i	$0.648108\pi$
$164$	−37650.5	−0.109310
$165$	72801.4	0.208176
$166$	399864.	1.12627
$167$	−508435.	−1.41073	−0.705366	−	0.708844i	$-0.749217\pi$
$167$	−508435.	−1.41073	−0.705366	+	0.708844i	$0.749217\pi$
$168$	32095.6	0.0877348
$169$	−332199.	−0.894708
$170$	−123208.	−0.326978
$171$	29241.0	0.0764719
$172$	−30728.4	−0.0791990
$173$	−605576.	−1.53834	−0.769172	−	0.639042i	$-0.779331\pi$
$173$	−605576.	−1.53834	−0.769172	+	0.639042i	$0.779331\pi$
$174$	−170519.	−0.426973
$175$	34825.9	0.0859622
$176$	−82831.8	−0.201565
$177$	−210885.	−0.505956
$178$	142344.	0.336737
$179$	−302750.	−0.706240	−0.353120	−	0.935578i	$-0.614879\pi$
$179$	−302750.	−0.706240	−0.353120	+	0.935578i	$0.614879\pi$
$180$	32400.0	0.0745356
$181$	228082.	0.517481	0.258740	−	0.965947i	$-0.416693\pi$
$181$	228082.	0.517481	0.258740	+	0.965947i	$0.416693\pi$
$182$	−44069.6	−0.0986190
$183$	−202386.	−0.446737
$184$	241676.	0.526247
$185$	−281836.	−0.605435
$186$	173758.	0.368266
$187$	−398656.	−0.833669
$188$	−55129.7	−0.113760
$189$	−40621.0	−0.0827172
$190$	−36100.0	−0.0725476
$191$	−4471.26	−0.00886843	−0.00443421	−	0.999990i	$-0.501411\pi$
$191$	−4471.26	−0.00886843	−0.00443421	+	0.999990i	$0.501411\pi$
$192$	−36864.0	−0.0721688
$193$	424454.	0.820233	0.410117	−	0.912033i	$-0.365488\pi$
$193$	424454.	0.820233	0.410117	+	0.912033i	$0.365488\pi$
$194$	−304212.	−0.580325
$195$	−44487.6	−0.0837823
$196$	−219234.	−0.407631
$197$	−866220.	−1.59024	−0.795120	−	0.606453i	$-0.792592\pi$
$197$	−866220.	−1.59024	−0.795120	+	0.606453i	$0.792592\pi$
$198$	104834.	0.190038
$199$	887988.	1.58955	0.794776	−	0.606903i	$-0.207588\pi$
$199$	887988.	1.58955	0.794776	+	0.606903i	$0.207588\pi$
$200$	−40000.0	−0.0707107
$201$	−297917.	−0.520123
$202$	114135.	0.196806
$203$	−263933.	−0.449525
$204$	−177420.	−0.298488
$205$	−58828.8	−0.0977700
$206$	658331.	1.08088
$207$	−305872.	−0.496151
$208$	50617.0	0.0811218
$209$	−116806.	−0.184969
$210$	50149.4	0.0784724
$211$	−233988.	−0.361816	−0.180908	−	0.983500i	$-0.557904\pi$
$211$	−233988.	−0.361816	−0.180908	+	0.983500i	$0.557904\pi$
$212$	460476.	0.703667
$213$	−84925.4	−0.128259
$214$	399487.	0.596305
$215$	−48013.2	−0.0708377
$216$	46656.0	0.0680414
$217$	268946.	0.387717
$218$	−749886.	−1.06870
$219$	−685966.	−0.966478
$220$	−129425.	−0.180285
$221$	243611.	0.335518
$222$	−405844.	−0.552684
$223$	−429226.	−0.577994	−0.288997	−	0.957330i	$-0.593322\pi$
$223$	−429226.	−0.577994	−0.288997	+	0.957330i	$0.593322\pi$
$224$	−57058.8	−0.0759806
$225$	50625.0	0.0666667
$226$	−273020.	−0.355568
$227$	−269561.	−0.347210	−0.173605	−	0.984815i	$-0.555542\pi$
$227$	−269561.	−0.347210	−0.173605	+	0.984815i	$0.555542\pi$
$228$	−51984.0	−0.0662266
$229$	−1.08241e6	−1.36396	−0.681981	−	0.731370i	$-0.738881\pi$
$229$	−1.08241e6	−1.36396	−0.681981	+	0.731370i	$0.738881\pi$
$230$	377619.	0.470690
$231$	162264.	0.200075
$232$	303145.	0.369769
$233$	−1.05017e6	−1.26727	−0.633636	−	0.773632i	$-0.718438\pi$
$233$	−1.05017e6	−1.26727	−0.633636	+	0.773632i	$0.718438\pi$
$234$	−64062.1	−0.0764824
$235$	−86140.1	−0.101750
$236$	374907.	0.438171
$237$	526567.	0.608951
$238$	−274614.	−0.314254
$239$	1.45536e6	1.64806	0.824032	−	0.566543i	$-0.191719\pi$
$239$	1.45536e6	1.64806	0.824032	+	0.566543i	$0.191719\pi$
$240$	−57600.0	−0.0645497
$241$	−436561.	−0.484175	−0.242087	−	0.970254i	$-0.577832\pi$
$241$	−436561.	−0.484175	−0.242087	+	0.970254i	$0.577832\pi$
$242$	225435.	0.247447
$243$	−59049.0	−0.0641500
$244$	359797.	0.386886
$245$	−342553.	−0.364596
$246$	−84713.5	−0.0892514
$247$	71377.8	0.0744425
$248$	−308903.	−0.318928
$249$	899695.	0.919595
$250$	−62500.0	−0.0632456
$251$	−1.58899e6	−1.59197	−0.795987	−	0.605313i	$-0.793048\pi$
$251$	−1.58899e6	−1.59197	−0.795987	+	0.605313i	$0.793048\pi$
$252$	72215.1	0.0716352
$253$	1.22183e6	1.20008
$254$	688996.	0.670089
$255$	−277219.	−0.266976
$256$	65536.0	0.0625000
$257$	259559.	0.245134	0.122567	−	0.992460i	$-0.460887\pi$
$257$	259559.	0.245134	0.122567	+	0.992460i	$0.460887\pi$
$258$	−69139.0	−0.0646657
$259$	−628174.	−0.581876
$260$	79089.0	0.0725576
$261$	−383668.	−0.348622
$262$	−562069.	−0.505867
$263$	−1.65796e6	−1.47804	−0.739018	−	0.673686i	$-0.764710\pi$
$263$	−1.65796e6	−1.47804	−0.739018	+	0.673686i	$0.764710\pi$
$264$	−186372.	−0.164577
$265$	719494.	0.629379
$266$	−80461.9	−0.0697246
$267$	320275.	0.274944
$268$	529631.	0.450440
$269$	−953680.	−0.803567	−0.401783	−	0.915735i	$-0.631610\pi$
$269$	−953680.	−0.803567	−0.401783	+	0.915735i	$0.631610\pi$
$270$	72900.0	0.0608581
$271$	1.51102e6	1.24982	0.624908	−	0.780698i	$-0.285136\pi$
$271$	1.51102e6	1.24982	0.624908	+	0.780698i	$0.285136\pi$
$272$	315414.	0.258499
$273$	−99156.6	−0.0805221
$274$	890966.	0.716943
$275$	−202226.	−0.161252
$276$	543772.	0.429679
$277$	1.60914e6	1.26007	0.630036	−	0.776566i	$-0.283040\pi$
$277$	1.60914e6	1.26007	0.630036	+	0.776566i	$0.283040\pi$
$278$	1.58904e6	1.23317
$279$	390955.	0.300688
$280$	−89154.4	−0.0679591
$281$	−1.10334e6	−0.833572	−0.416786	−	0.909005i	$-0.636844\pi$
$281$	−1.10334e6	−0.833572	−0.416786	+	0.909005i	$0.636844\pi$
$282$	−124042.	−0.0928849
$283$	−1.73551e6	−1.28813	−0.644067	−	0.764969i	$-0.722754\pi$
$283$	−1.73551e6	−1.28813	−0.644067	+	0.764969i	$0.722754\pi$
$284$	150979.	0.111076
$285$	−81225.0	−0.0592349
$286$	255902.	0.184994
$287$	−131121.	−0.0939655
$288$	−82944.0	−0.0589256
$289$	98175.2	0.0691444
$290$	473664.	0.330732
$291$	−684476.	−0.473834
$292$	1.21949e6	0.836995
$293$	−811028.	−0.551908	−0.275954	−	0.961171i	$-0.588994\pi$
$293$	−811028.	−0.551908	−0.275954	+	0.961171i	$0.588994\pi$
$294$	−493276.	−0.332829
$295$	585792.	0.391912
$296$	721501.	0.478639
$297$	235877.	0.155165
$298$	−259054.	−0.168985
$299$	−746639.	−0.482984
$300$	−90000.0	−0.0577350
$301$	−107015.	−0.0680812
$302$	−1.98434e6	−1.25198
$303$	256803.	0.160692
$304$	92416.0	0.0573539
$305$	562182.	0.346041
$306$	−399195.	−0.243715
$307$	−1.77216e6	−1.07314	−0.536572	−	0.843855i	$-0.680281\pi$
$307$	−1.77216e6	−1.07314	−0.536572	+	0.843855i	$0.680281\pi$
$308$	−288470.	−0.173270
$309$	1.48124e6	0.882532
$310$	−482660.	−0.285258
$311$	−772132.	−0.452679	−0.226339	−	0.974048i	$-0.572676\pi$
$311$	−772132.	−0.452679	−0.226339	+	0.974048i	$0.572676\pi$
$312$	113888.	0.0662357
$313$	−306148.	−0.176632	−0.0883162	−	0.996092i	$-0.528149\pi$
$313$	−306148.	−0.176632	−0.0883162	+	0.996092i	$0.528149\pi$
$314$	1.22672e6	0.702139
$315$	112836.	0.0640725
$316$	−936119.	−0.527367
$317$	120173.	0.0671675	0.0335838	−	0.999436i	$-0.489308\pi$
$317$	120173.	0.0671675	0.0335838	+	0.999436i	$0.489308\pi$
$318$	1.03607e6	0.574542
$319$	1.53260e6	0.843240
$320$	102400.	0.0559017
$321$	898846.	0.486881
$322$	841661.	0.452374
$323$	444783.	0.237215
$324$	104976.	0.0555556
$325$	123577.	0.0648975
$326$	1.21759e6	0.634539
$327$	−1.68724e6	−0.872586
$328$	150602.	0.0772940
$329$	−191994.	−0.0977909
$330$	−291206.	−0.147202
$331$	2.29067e6	1.14919	0.574597	−	0.818437i	$-0.305159\pi$
$331$	2.29067e6	1.14919	0.574597	+	0.818437i	$0.305159\pi$
$332$	−1.59946e6	−0.796393
$333$	−913150.	−0.451265
$334$	2.03374e6	0.997538
$335$	827549.	0.402885
$336$	−128382.	−0.0620379
$337$	−2.00112e6	−0.959840	−0.479920	−	0.877312i	$-0.659334\pi$
$337$	−2.00112e6	−0.959840	−0.479920	+	0.877312i	$0.659334\pi$
$338$	1.32880e6	0.632654
$339$	−614294.	−0.290320
$340$	492834.	0.231208
$341$	−1.56170e6	−0.727299
$342$	−116964.	−0.0540738
$343$	−1.70001e6	−0.780220
$344$	122914.	0.0560021
$345$	849644.	0.384317
$346$	2.42230e6	1.08777
$347$	422685.	0.188449	0.0942243	−	0.995551i	$-0.469963\pi$
$347$	422685.	0.188449	0.0942243	+	0.995551i	$0.469963\pi$
$348$	682077.	0.301915
$349$	−99505.8	−0.0437305	−0.0218653	−	0.999761i	$-0.506960\pi$
$349$	−99505.8	−0.0437305	−0.0218653	+	0.999761i	$0.506960\pi$
$350$	−139304.	−0.0607845
$351$	−144140.	−0.0624476
$352$	331327.	0.142528
$353$	−1.81758e6	−0.776350	−0.388175	−	0.921586i	$-0.626894\pi$
$353$	−1.81758e6	−0.776350	−0.388175	+	0.921586i	$0.626894\pi$
$354$	843541.	0.357765
$355$	235904.	0.0993492
$356$	−569378.	−0.238109
$357$	−617882.	−0.256587
$358$	1.21100e6	0.499387
$359$	1.34275e6	0.549871	0.274935	−	0.961463i	$-0.411344\pi$
$359$	1.34275e6	0.549871	0.274935	+	0.961463i	$0.411344\pi$
$360$	−129600.	−0.0527046
$361$	130321.	0.0526316
$362$	−912327.	−0.365914
$363$	507228.	0.202040
$364$	176278.	0.0697341
$365$	1.90546e6	0.748631
$366$	809543.	0.315891
$367$	904456.	0.350528	0.175264	−	0.984522i	$-0.443922\pi$
$367$	904456.	0.350528	0.175264	+	0.984522i	$0.443922\pi$
$368$	−966706.	−0.372113
$369$	−190605.	−0.0728735
$370$	1.12735e6	0.428107
$371$	1.60365e6	0.604888
$372$	−695031.	−0.260403
$373$	4.63728e6	1.72580	0.862901	−	0.505373i	$-0.168645\pi$
$373$	4.63728e6	1.72580	0.862901	+	0.505373i	$0.168645\pi$
$374$	1.59462e6	0.589493
$375$	−140625.	−0.0516398
$376$	220519.	0.0804407
$377$	−936541.	−0.339370
$378$	162484.	0.0584899
$379$	3.96309e6	1.41722	0.708608	−	0.705602i	$-0.249323\pi$
$379$	3.96309e6	1.41722	0.708608	+	0.705602i	$0.249323\pi$
$380$	144400.	0.0512989
$381$	1.55024e6	0.547126
$382$	17885.0	0.00627092
$383$	−2.03540e6	−0.709010	−0.354505	−	0.935054i	$-0.615351\pi$
$383$	−2.03540e6	−0.709010	−0.354505	+	0.935054i	$0.615351\pi$
$384$	147456.	0.0510310
$385$	−450734.	−0.154977
$386$	−1.69782e6	−0.579993
$387$	−155563.	−0.0527993
$388$	1.21685e6	0.410352
$389$	−2.59927e6	−0.870917	−0.435459	−	0.900209i	$-0.643414\pi$
$389$	−2.59927e6	−0.870917	−0.435459	+	0.900209i	$0.643414\pi$
$390$	177950.	0.0592430
$391$	−4.65259e6	−1.53905
$392$	876935.	0.288239
$393$	−1.26465e6	−0.413038
$394$	3.46488e6	1.12447
$395$	−1.46269e6	−0.471692
$396$	−419336.	−0.134377
$397$	−98354.5	−0.0313197	−0.0156599	−	0.999877i	$-0.504985\pi$
$397$	−98354.5	−0.0313197	−0.0156599	+	0.999877i	$0.504985\pi$
$398$	−3.55195e6	−1.12398
$399$	−181039.	−0.0569299
$400$	160000.	0.0500000
$401$	247336.	0.0768116	0.0384058	−	0.999262i	$-0.487772\pi$
$401$	247336.	0.0768116	0.0384058	+	0.999262i	$0.487772\pi$
$402$	1.19167e6	0.367782
$403$	954328.	0.292708
$404$	−456539.	−0.139163
$405$	164025.	0.0496904
$406$	1.05573e6	0.317862
$407$	3.64766e6	1.09151
$408$	709681.	0.211063
$409$	4.43935e6	1.31223	0.656117	−	0.754659i	$-0.272198\pi$
$409$	4.43935e6	1.31223	0.656117	+	0.754659i	$0.272198\pi$
$410$	235315.	0.0691338
$411$	2.00467e6	0.585382
$412$	−2.63332e6	−0.764295
$413$	1.30565e6	0.376662
$414$	1.22349e6	0.350831
$415$	−2.49915e6	−0.712315
$416$	−202468.	−0.0573618
$417$	3.57534e6	1.00688
$418$	467223.	0.130793
$419$	−2.66341e6	−0.741146	−0.370573	−	0.928803i	$-0.620839\pi$
$419$	−2.66341e6	−0.741146	−0.370573	+	0.928803i	$0.620839\pi$
$420$	−200597.	−0.0554884
$421$	1.50786e6	0.414626	0.207313	−	0.978275i	$-0.433528\pi$
$421$	1.50786e6	0.414626	0.207313	+	0.978275i	$0.433528\pi$
$422$	935952.	0.255842
$423$	−279094.	−0.0758402
$424$	−1.84190e6	−0.497568
$425$	770053.	0.206799
$426$	339702.	0.0906930
$427$	1.25303e6	0.332576
$428$	−1.59795e6	−0.421651
$429$	575779.	0.151047
$430$	192053.	0.0500898
$431$	2.72245e6	0.705937	0.352969	−	0.935635i	$-0.385172\pi$
$431$	2.72245e6	0.705937	0.352969	+	0.935635i	$0.385172\pi$
$432$	−186624.	−0.0481125
$433$	527935.	0.135320	0.0676598	−	0.997708i	$-0.478447\pi$
$433$	527935.	0.135320	0.0676598	+	0.997708i	$0.478447\pi$
$434$	−1.07578e6	−0.274157
$435$	1.06574e6	0.270041
$436$	2.99954e6	0.755682
$437$	−1.36321e6	−0.341474
$438$	2.74386e6	0.683403
$439$	−5.25839e6	−1.30224	−0.651121	−	0.758974i	$-0.725701\pi$
$439$	−5.25839e6	−1.30224	−0.651121	+	0.758974i	$0.725701\pi$
$440$	517699.	0.127481
$441$	−1.10987e6	−0.271754
$442$	−974443.	−0.237247
$443$	−4.05256e6	−0.981116	−0.490558	−	0.871408i	$-0.663207\pi$
$443$	−4.05256e6	−0.981116	−0.490558	+	0.871408i	$0.663207\pi$
$444$	1.62338e6	0.390807
$445$	−889653.	−0.212971
$446$	1.71690e6	0.408704
$447$	−582871.	−0.137976
$448$	228235.	0.0537264
$449$	2.18810e6	0.512214	0.256107	−	0.966648i	$-0.417560\pi$
$449$	2.18810e6	0.512214	0.256107	+	0.966648i	$0.417560\pi$
$450$	−202500.	−0.0471405
$451$	761391.	0.176265
$452$	1.09208e6	0.251425
$453$	−4.46476e6	−1.02224
$454$	1.07824e6	0.245514
$455$	275435.	0.0623721
$456$	207936.	0.0468293
$457$	5.70254e6	1.27726	0.638628	−	0.769516i	$-0.279502\pi$
$457$	5.70254e6	1.27726	0.638628	+	0.769516i	$0.279502\pi$
$458$	4.32963e6	0.964467
$459$	−898190.	−0.198992
$460$	−1.51048e6	−0.332828
$461$	5.34460e6	1.17129	0.585643	−	0.810569i	$-0.300842\pi$
$461$	5.34460e6	1.17129	0.585643	+	0.810569i	$0.300842\pi$
$462$	−649057.	−0.141474
$463$	−7.83396e6	−1.69836	−0.849179	−	0.528106i	$-0.822902\pi$
$463$	−7.83396e6	−1.69836	−0.849179	+	0.528106i	$0.822902\pi$
$464$	−1.21258e6	−0.261466
$465$	−1.08599e6	−0.232912
$466$	4.20068e6	0.896096
$467$	1.90391e6	0.403974	0.201987	−	0.979388i	$-0.435260\pi$
$467$	1.90391e6	0.403974	0.201987	+	0.979388i	$0.435260\pi$
$468$	256248.	0.0540812
$469$	1.84449e6	0.387208
$470$	344561.	0.0719484
$471$	2.76013e6	0.573294
$472$	−1.49963e6	−0.309834
$473$	621410.	0.127710
$474$	−2.10627e6	−0.430594
$475$	225625.	0.0458831
$476$	1.09846e6	0.222211
$477$	2.33116e6	0.469112
$478$	−5.82142e6	−1.16536
$479$	−4.60771e6	−0.917585	−0.458792	−	0.888544i	$-0.651718\pi$
$479$	−4.60771e6	−0.917585	−0.458792	+	0.888544i	$0.651718\pi$
$480$	230400.	0.0456435
$481$	−2.22902e6	−0.439289
$482$	1.74624e6	0.342363
$483$	1.89374e6	0.369362
$484$	−901739.	−0.174972
$485$	1.90132e6	0.367030
$486$	236196.	0.0453609
$487$	−6.14863e6	−1.17478	−0.587389	−	0.809305i	$-0.699844\pi$
$487$	−6.14863e6	−1.17478	−0.587389	+	0.809305i	$0.699844\pi$
$488$	−1.43919e6	−0.273569
$489$	2.73958e6	0.518099
$490$	1.37021e6	0.257809
$491$	−4.44651e6	−0.832369	−0.416184	−	0.909280i	$-0.636633\pi$
$491$	−4.44651e6	−0.832369	−0.416184	+	0.909280i	$0.636633\pi$
$492$	338854.	0.0631103
$493$	−5.83595e6	−1.08142
$494$	−285511.	−0.0526388
$495$	−655213.	−0.120190
$496$	1.23561e6	0.225516
$497$	525797.	0.0954832
$498$	−3.59878e6	−0.650252
$499$	7.39955e6	1.33031	0.665156	−	0.746704i	$-0.268365\pi$
$499$	7.39955e6	1.33031	0.665156	+	0.746704i	$0.268365\pi$
$500$	250000.	0.0447214
$501$	4.57592e6	0.814486
$502$	6.35595e6	1.12570
$503$	2.46864e6	0.435048	0.217524	−	0.976055i	$-0.430202\pi$
$503$	2.46864e6	0.435048	0.217524	+	0.976055i	$0.430202\pi$
$504$	−288860.	−0.0506537
$505$	−713342.	−0.124471
$506$	−4.88733e6	−0.848585
$507$	2.98979e6	0.516560
$508$	−2.75599e6	−0.473825
$509$	−2.12404e6	−0.363386	−0.181693	−	0.983355i	$-0.558158\pi$
$509$	−2.12404e6	−0.363386	−0.181693	+	0.983355i	$0.558158\pi$
$510$	1.10888e6	0.188781
$511$	4.24701e6	0.719500
$512$	−262144.	−0.0441942
$513$	−263169.	−0.0441511
$514$	−1.03824e6	−0.173336
$515$	−4.11457e6	−0.683606
$516$	276556.	0.0457255
$517$	1.11487e6	0.183441
$518$	2.51270e6	0.411448
$519$	5.45019e6	0.888163
$520$	−316356.	−0.0513060
$521$	2.05370e6	0.331469	0.165735	−	0.986170i	$-0.447000\pi$
$521$	2.05370e6	0.331469	0.165735	+	0.986170i	$0.447000\pi$
$522$	1.53467e6	0.246513
$523$	1.21833e7	1.94765	0.973827	−	0.227289i	$-0.0729863\pi$
$523$	1.21833e7	1.94765	0.973827	+	0.227289i	$0.0729863\pi$
$524$	2.24827e6	0.357702
$525$	−313433.	−0.0496303
$526$	6.63184e6	1.04513
$527$	5.94678e6	0.932729
$528$	745487.	0.116374
$529$	7.82330e6	1.21549
$530$	−2.87798e6	−0.445038
$531$	1.89797e6	0.292114
$532$	321847.	0.0493027
$533$	−465271.	−0.0709395
$534$	−1.28110e6	−0.194415
$535$	−2.49680e6	−0.377136
$536$	−2.11852e6	−0.318509
$537$	2.72475e6	0.407748
$538$	3.81472e6	0.568208
$539$	4.43348e6	0.657314
$540$	−291600.	−0.0430331
$541$	−2.20773e6	−0.324304	−0.162152	−	0.986766i	$-0.551843\pi$
$541$	−2.20773e6	−0.324304	−0.162152	+	0.986766i	$0.551843\pi$
$542$	−6.04407e6	−0.883753
$543$	−2.05274e6	−0.298768
$544$	−1.26165e6	−0.182786
$545$	4.68679e6	0.675902
$546$	396626.	0.0569377
$547$	387887.	0.0554290	0.0277145	−	0.999616i	$-0.491177\pi$
$547$	387887.	0.0554290	0.0277145	+	0.999616i	$0.491177\pi$
$548$	−3.56386e6	−0.506955
$549$	1.82147e6	0.257924
$550$	808905.	0.114023
$551$	−1.70993e6	−0.239938
$552$	−2.17509e6	−0.303829
$553$	−3.26012e6	−0.453337
$554$	−6.43657e6	−0.891005
$555$	2.53653e6	0.349548
$556$	−6.35616e6	−0.871983
$557$	5.31812e6	0.726307	0.363154	−	0.931729i	$-0.381700\pi$
$557$	5.31812e6	0.726307	0.363154	+	0.931729i	$0.381700\pi$
$558$	−1.56382e6	−0.212618
$559$	−379732.	−0.0513981
$560$	356618.	0.0480544
$561$	3.58790e6	0.481319
$562$	4.41336e6	0.589424
$563$	−1.31055e7	−1.74254	−0.871271	−	0.490802i	$-0.836704\pi$
$563$	−1.31055e7	−1.74254	−0.871271	+	0.490802i	$0.836704\pi$
$564$	496167.	0.0656796
$565$	1.70637e6	0.224881
$566$	6.94204e6	0.910848
$567$	365589.	0.0477568
$568$	−603914.	−0.0785424
$569$	7.43591e6	0.962839	0.481419	−	0.876490i	$-0.340121\pi$
$569$	7.43591e6	0.962839	0.481419	+	0.876490i	$0.340121\pi$
$570$	324900.	0.0418854
$571$	−1.06829e7	−1.37119	−0.685595	−	0.727983i	$-0.740458\pi$
$571$	−1.06829e7	−1.37119	−0.685595	+	0.727983i	$0.740458\pi$
$572$	−1.02361e6	−0.130811
$573$	40241.3	0.00512019
$574$	524485.	0.0664436
$575$	−2.36012e6	−0.297690
$576$	331776.	0.0416667
$577$	1.56085e7	1.95174	0.975868	−	0.218361i	$-0.0700709\pi$
$577$	1.56085e7	1.95174	0.975868	+	0.218361i	$0.0700709\pi$
$578$	−392701.	−0.0488925
$579$	−3.82009e6	−0.473562
$580$	−1.89466e6	−0.233863
$581$	−5.57026e6	−0.684597
$582$	2.73790e6	0.335051
$583$	−9.31203e6	−1.13468
$584$	−4.87798e6	−0.591845
$585$	400388.	0.0483717
$586$	3.24411e6	0.390258
$587$	−1.29739e7	−1.55408	−0.777041	−	0.629450i	$-0.783280\pi$
$587$	−1.29739e7	−1.55408	−0.777041	+	0.629450i	$0.783280\pi$
$588$	1.97310e6	0.235346
$589$	1.74240e6	0.206948
$590$	−2.34317e6	−0.277124
$591$	7.79598e6	0.918125
$592$	−2.88600e6	−0.338449
$593$	−1.28984e7	−1.50626	−0.753130	−	0.657871i	$-0.771457\pi$
$593$	−1.28984e7	−1.50626	−0.753130	+	0.657871i	$0.771457\pi$
$594$	−943507.	−0.109718
$595$	1.71634e6	0.198752
$596$	1.03622e6	0.119491
$597$	−7.99190e6	−0.917728
$598$	2.98655e6	0.341521
$599$	−1.65848e7	−1.88862	−0.944308	−	0.329063i	$-0.893267\pi$
$599$	−1.65848e7	−1.88862	−0.944308	+	0.329063i	$0.893267\pi$
$600$	360000.	0.0408248
$601$	−103666.	−0.0117071	−0.00585357	−	0.999983i	$-0.501863\pi$
$601$	−103666.	−0.0117071	−0.00585357	+	0.999983i	$0.501863\pi$
$602$	428059.	0.0481407
$603$	2.68126e6	0.300293
$604$	7.93735e6	0.885285
$605$	−1.40897e6	−0.156499
$606$	−1.02721e6	−0.113626
$607$	−6.89646e6	−0.759721	−0.379861	−	0.925044i	$-0.624028\pi$
$607$	−6.89646e6	−0.759721	−0.379861	+	0.925044i	$0.624028\pi$
$608$	−369664.	−0.0405554
$609$	2.37540e6	0.259533
$610$	−2.24873e6	−0.244688
$611$	−681274.	−0.0738276
$612$	1.59678e6	0.172332
$613$	−1.09253e7	−1.17431	−0.587154	−	0.809475i	$-0.699752\pi$
$613$	−1.09253e7	−1.17431	−0.587154	+	0.809475i	$0.699752\pi$
$614$	7.08866e6	0.758827
$615$	529460.	0.0564475
$616$	1.15388e6	0.122520
$617$	1.55281e6	0.164212	0.0821060	−	0.996624i	$-0.473835\pi$
$617$	1.55281e6	0.164212	0.0821060	+	0.996624i	$0.473835\pi$
$618$	−5.92498e6	−0.624044
$619$	−1.08260e7	−1.13565	−0.567823	−	0.823150i	$-0.692214\pi$
$619$	−1.08260e7	−1.13565	−0.567823	+	0.823150i	$0.692214\pi$
$620$	1.93064e6	0.201708
$621$	2.75285e6	0.286453
$622$	3.08853e6	0.320092
$623$	−1.98291e6	−0.204684
$624$	−455553.	−0.0468357
$625$	390625.	0.0400000
$626$	1.22459e6	0.124898
$627$	1.05125e6	0.106792
$628$	−4.90690e6	−0.496487
$629$	−1.38898e7	−1.39982
$630$	−451344.	−0.0453061
$631$	9.72446e6	0.972282	0.486141	−	0.873880i	$-0.338404\pi$
$631$	9.72446e6	0.972282	0.486141	+	0.873880i	$0.338404\pi$
$632$	3.74448e6	0.372905
$633$	2.10589e6	0.208894
$634$	−480693.	−0.0474946
$635$	−4.30623e6	−0.423802
$636$	−4.14428e6	−0.406263
$637$	−2.70922e6	−0.264542
$638$	−6.13039e6	−0.596261
$639$	764329.	0.0740505
$640$	−409600.	−0.0395285
$641$	−1.50759e6	−0.144923	−0.0724615	−	0.997371i	$-0.523085\pi$
$641$	−1.50759e6	−0.144923	−0.0724615	+	0.997371i	$0.523085\pi$
$642$	−3.59538e6	−0.344277
$643$	−1.91979e7	−1.83116	−0.915582	−	0.402132i	$-0.868269\pi$
$643$	−1.91979e7	−1.83116	−0.915582	+	0.402132i	$0.868269\pi$
$644$	−3.36664e6	−0.319877
$645$	432119.	0.0408982
$646$	−1.77913e6	−0.167736
$647$	6.64303e6	0.623886	0.311943	−	0.950101i	$-0.399020\pi$
$647$	6.64303e6	0.623886	0.311943	+	0.950101i	$0.399020\pi$
$648$	−419904.	−0.0392837
$649$	−7.58160e6	−0.706560
$650$	−494306.	−0.0458894
$651$	−2.42051e6	−0.223849
$652$	−4.87037e6	−0.448687
$653$	−1.85251e7	−1.70011	−0.850055	−	0.526694i	$-0.823431\pi$
$653$	−1.85251e7	−1.70011	−0.850055	+	0.526694i	$0.823431\pi$
$654$	6.74897e6	0.617012
$655$	3.51293e6	0.319938
$656$	−602407.	−0.0546551
$657$	6.17369e6	0.557997
$658$	767977.	0.0691486
$659$	1.15464e6	0.103570	0.0517848	−	0.998658i	$-0.483509\pi$
$659$	1.15464e6	0.103570	0.0517848	+	0.998658i	$0.483509\pi$
$660$	1.16482e6	0.104088
$661$	−7.84013e6	−0.697943	−0.348971	−	0.937133i	$-0.613469\pi$
$661$	−7.84013e6	−0.697943	−0.348971	+	0.937133i	$0.613469\pi$
$662$	−9.16270e6	−0.812603
$663$	−2.19250e6	−0.193711
$664$	6.39783e6	0.563135
$665$	502887.	0.0440977
$666$	3.65260e6	0.319092
$667$	1.78865e7	1.55672
$668$	−8.13496e6	−0.705366
$669$	3.86303e6	0.333705
$670$	−3.31019e6	−0.284883
$671$	−7.27603e6	−0.623862
$672$	513529.	0.0438674
$673$	1.33341e7	1.13482	0.567410	−	0.823435i	$-0.307945\pi$
$673$	1.33341e7	1.13482	0.567410	+	0.823435i	$0.307945\pi$
$674$	8.00449e6	0.678709
$675$	−455625.	−0.0384900
$676$	−5.31518e6	−0.447354
$677$	1.75174e7	1.46892	0.734458	−	0.678654i	$-0.237437\pi$
$677$	1.75174e7	1.46892	0.734458	+	0.678654i	$0.237437\pi$
$678$	2.45718e6	0.205287
$679$	4.23778e6	0.352748
$680$	−1.97134e6	−0.163489
$681$	2.42605e6	0.200462
$682$	6.24682e6	0.514278
$683$	1.67243e7	1.37182	0.685910	−	0.727687i	$-0.259404\pi$
$683$	1.67243e7	1.37182	0.685910	+	0.727687i	$0.259404\pi$
$684$	467856.	0.0382360
$685$	−5.56854e6	−0.453435
$686$	6.80006e6	0.551699
$687$	9.74167e6	0.787484
$688$	−491655.	−0.0395995
$689$	5.69041e6	0.456662
$690$	−3.39857e6	−0.271753
$691$	−2.04176e7	−1.62671	−0.813354	−	0.581769i	$-0.802361\pi$
$691$	−2.04176e7	−1.62671	−0.813354	+	0.581769i	$0.802361\pi$
$692$	−9.68922e6	−0.769172
$693$	−1.46038e6	−0.115513
$694$	−1.69074e6	−0.133253
$695$	−9.93151e6	−0.779925
$696$	−2.72831e6	−0.213486
$697$	−2.89928e6	−0.226052
$698$	398023.	0.0309222
$699$	9.45152e6	0.731659
$700$	557215.	0.0429811
$701$	5.75032e6	0.441975	0.220987	−	0.975277i	$-0.429072\pi$
$701$	5.75032e6	0.441975	0.220987	+	0.975277i	$0.429072\pi$
$702$	576559.	0.0441571
$703$	−4.06972e6	−0.310582
$704$	−1.32531e6	−0.100783
$705$	775261.	0.0587456
$706$	7.27033e6	0.548962
$707$	−1.58994e6	−0.119628
$708$	−3.37416e6	−0.252978
$709$	−2.56404e6	−0.191562	−0.0957811	−	0.995402i	$-0.530535\pi$
$709$	−2.56404e6	−0.191562	−0.0957811	+	0.995402i	$0.530535\pi$
$710$	−943616.	−0.0702505
$711$	−4.73910e6	−0.351578
$712$	2.27751e6	0.168368
$713$	−1.82262e7	−1.34268
$714$	2.47153e6	0.181435
$715$	−1.59939e6	−0.117001
$716$	−4.84401e6	−0.353120
$717$	−1.30982e7	−0.951511
$718$	−5.37102e6	−0.388817
$719$	5.85540e6	0.422410	0.211205	−	0.977442i	$-0.432261\pi$
$719$	5.85540e6	0.422410	0.211205	+	0.977442i	$0.432261\pi$
$720$	518400.	0.0372678
$721$	−9.17079e6	−0.657005
$722$	−521284.	−0.0372161
$723$	3.92905e6	0.279538
$724$	3.64931e6	0.258740
$725$	−2.96040e6	−0.209173
$726$	−2.02891e6	−0.142864
$727$	1.97861e7	1.38843	0.694214	−	0.719768i	$-0.255752\pi$
$727$	1.97861e7	1.38843	0.694214	+	0.719768i	$0.255752\pi$
$728$	−705113.	−0.0493095
$729$	531441.	0.0370370
$730$	−7.62184e6	−0.529362
$731$	−2.36625e6	−0.163783
$732$	−3.23817e6	−0.223369
$733$	−1.19040e6	−0.0818337	−0.0409168	−	0.999163i	$-0.513028\pi$
$733$	−1.19040e6	−0.0818337	−0.0409168	+	0.999163i	$0.513028\pi$
$734$	−3.61782e6	−0.247860
$735$	3.08298e6	0.210500
$736$	3.86682e6	0.263124
$737$	−1.07105e7	−0.726344
$738$	762422.	0.0515293
$739$	−2.38479e7	−1.60634	−0.803172	−	0.595747i	$-0.796856\pi$
$739$	−2.38479e7	−1.60634	−0.803172	+	0.595747i	$0.796856\pi$
$740$	−4.50938e6	−0.302718
$741$	−642400.	−0.0429794
$742$	−6.41461e6	−0.427721
$743$	7.43500e6	0.494093	0.247047	−	0.969004i	$-0.420540\pi$
$743$	7.43500e6	0.494093	0.247047	+	0.969004i	$0.420540\pi$
$744$	2.78012e6	0.184133
$745$	1.61909e6	0.106876
$746$	−1.85491e7	−1.22033
$747$	−8.09725e6	−0.530929
$748$	−6.37849e6	−0.416835
$749$	−5.56501e6	−0.362461
$750$	562500.	0.0365148
$751$	−3.11090e6	−0.201273	−0.100637	−	0.994923i	$-0.532088\pi$
$751$	−3.11090e6	−0.201273	−0.100637	+	0.994923i	$0.532088\pi$
$752$	−882075.	−0.0568802
$753$	1.43009e7	0.919127
$754$	3.74616e6	0.239971
$755$	1.24021e7	0.791823
$756$	−649936.	−0.0413586
$757$	−5.43869e6	−0.344948	−0.172474	−	0.985014i	$-0.555176\pi$
$757$	−5.43869e6	−0.344948	−0.172474	+	0.985014i	$0.555176\pi$
$758$	−1.58524e7	−1.00212
$759$	−1.09965e7	−0.692867
$760$	−577600.	−0.0362738
$761$	1.55660e7	0.974354	0.487177	−	0.873303i	$-0.338027\pi$
$761$	1.55660e7	0.974354	0.487177	+	0.873303i	$0.338027\pi$
$762$	−6.20097e6	−0.386876
$763$	1.04462e7	0.649601
$764$	−71540.2	−0.00443421
$765$	2.49497e6	0.154139
$766$	8.14160e6	0.501346
$767$	4.63297e6	0.284362
$768$	−589824.	−0.0360844
$769$	7.42681e6	0.452884	0.226442	−	0.974025i	$-0.427291\pi$
$769$	7.42681e6	0.452884	0.226442	+	0.974025i	$0.427291\pi$
$770$	1.80294e6	0.109586
$771$	−2.33604e6	−0.141528
$772$	6.79126e6	0.410117
$773$	1.01626e7	0.611724	0.305862	−	0.952076i	$-0.401055\pi$
$773$	1.01626e7	0.611724	0.305862	+	0.952076i	$0.401055\pi$
$774$	622251.	0.0373347
$775$	3.01663e6	0.180413
$776$	−4.86739e6	−0.290163
$777$	5.65356e6	0.335946
$778$	1.03971e7	0.615831
$779$	−849488.	−0.0501549
$780$	−711801.	−0.0418911
$781$	−3.05318e6	−0.179112
$782$	1.86104e7	1.08827
$783$	3.45301e6	0.201277
$784$	−3.50774e6	−0.203816
$785$	−7.66703e6	−0.444072
$786$	5.05862e6	0.292062
$787$	−1.03062e6	−0.0593148	−0.0296574	−	0.999560i	$-0.509442\pi$
$787$	−1.03062e6	−0.0593148	−0.0296574	+	0.999560i	$0.509442\pi$
$788$	−1.38595e7	−0.795120
$789$	1.49216e7	0.853344
$790$	5.85074e6	0.333536
$791$	3.80327e6	0.216130
$792$	1.67734e6	0.0950188
$793$	4.44624e6	0.251079
$794$	393418.	0.0221464
$795$	−6.47544e6	−0.363372
$796$	1.42078e7	0.794776
$797$	−1.61275e7	−0.899332	−0.449666	−	0.893197i	$-0.648457\pi$
$797$	−1.61275e7	−0.899332	−0.449666	+	0.893197i	$0.648457\pi$
$798$	724157.	0.0402555
$799$	−4.24528e6	−0.235255
$800$	−640000.	−0.0353553
$801$	−2.88248e6	−0.158739
$802$	−989345.	−0.0543140
$803$	−2.46614e7	−1.34967
$804$	−4.76668e6	−0.260061
$805$	−5.26038e6	−0.286106
$806$	−3.81731e6	−0.206976
$807$	8.58312e6	0.463940
$808$	1.82615e6	0.0984032
$809$	6.31826e6	0.339411	0.169706	−	0.985495i	$-0.445718\pi$
$809$	6.31826e6	0.339411	0.169706	+	0.985495i	$0.445718\pi$
$810$	−656100.	−0.0351364
$811$	−2.13453e6	−0.113959	−0.0569796	−	0.998375i	$-0.518147\pi$
$811$	−2.13453e6	−0.113959	−0.0569796	+	0.998375i	$0.518147\pi$
$812$	−4.22293e6	−0.224762
$813$	−1.35992e7	−0.721582
$814$	−1.45906e7	−0.771815
$815$	−7.60995e6	−0.401317
$816$	−2.83872e6	−0.149244
$817$	−693311.	−0.0363390
$818$	−1.77574e7	−0.927890
$819$	892409.	0.0464894
$820$	−941261.	−0.0488850
$821$	3.60470e7	1.86643	0.933214	−	0.359322i	$-0.116992\pi$
$821$	3.60470e7	1.86643	0.933214	+	0.359322i	$0.116992\pi$
$822$	−8.01869e6	−0.413927
$823$	−3.39430e7	−1.74683	−0.873416	−	0.486975i	$-0.838100\pi$
$823$	−3.39430e7	−1.74683	−0.873416	+	0.486975i	$0.838100\pi$
$824$	1.05333e7	0.540438
$825$	1.82004e6	0.0930990
$826$	−5.22260e6	−0.266340
$827$	2.54773e7	1.29536	0.647680	−	0.761913i	$-0.275740\pi$
$827$	2.54773e7	1.29536	0.647680	+	0.761913i	$0.275740\pi$
$828$	−4.89395e6	−0.248075
$829$	1.13108e7	0.571622	0.285811	−	0.958286i	$-0.407737\pi$
$829$	1.13108e7	0.571622	0.285811	+	0.958286i	$0.407737\pi$
$830$	9.99661e6	0.503683
$831$	−1.44823e7	−0.727503
$832$	809871.	0.0405609
$833$	−1.68822e7	−0.842977
$834$	−1.43014e7	−0.711971
$835$	−1.27109e7	−0.630898
$836$	−1.86889e6	−0.0924845
$837$	−3.51859e6	−0.173602
$838$	1.06537e7	0.524069
$839$	3.41934e6	0.167702	0.0838509	−	0.996478i	$-0.473278\pi$
$839$	3.41934e6	0.167702	0.0838509	+	0.996478i	$0.473278\pi$
$840$	802390.	0.0392362
$841$	1.92465e6	0.0938342
$842$	−6.03146e6	−0.293185
$843$	9.93005e6	0.481263
$844$	−3.74381e6	−0.180908
$845$	−8.30497e6	−0.400126
$846$	1.11638e6	0.0536271
$847$	−3.14039e6	−0.150409
$848$	7.36762e6	0.351834
$849$	1.56196e7	0.743704
$850$	−3.08021e6	−0.146229
$851$	4.25707e7	2.01506
$852$	−1.35881e6	−0.0641296
$853$	3.52352e6	0.165807	0.0829037	−	0.996558i	$-0.473581\pi$
$853$	3.52352e6	0.165807	0.0829037	+	0.996558i	$0.473581\pi$
$854$	−5.01210e6	−0.235166
$855$	731025.	0.0341993
$856$	6.39180e6	0.298152
$857$	1.07382e7	0.499434	0.249717	−	0.968319i	$-0.419662\pi$
$857$	1.07382e7	0.499434	0.249717	+	0.968319i	$0.419662\pi$
$858$	−2.30312e6	−0.106807
$859$	3.74704e7	1.73263	0.866313	−	0.499501i	$-0.166483\pi$
$859$	3.74704e7	1.73263	0.866313	+	0.499501i	$0.166483\pi$
$860$	−768211.	−0.0354189
$861$	1.18009e6	0.0542510
$862$	−1.08898e7	−0.499173
$863$	7.80040e6	0.356525	0.178262	−	0.983983i	$-0.442952\pi$
$863$	7.80040e6	0.356525	0.178262	+	0.983983i	$0.442952\pi$
$864$	746496.	0.0340207
$865$	−1.51394e7	−0.687968
$866$	−2.11174e6	−0.0956854
$867$	−883577.	−0.0399206
$868$	4.30313e6	0.193859
$869$	1.89308e7	0.850392
$870$	−4.26298e6	−0.190948
$871$	6.54500e6	0.292324
$872$	−1.19982e7	−0.534348
$873$	6.16029e6	0.273568
$874$	5.45282e6	0.241459
$875$	870649.	0.0384435
$876$	−1.09755e7	−0.483239
$877$	−3.39330e7	−1.48978	−0.744891	−	0.667186i	$-0.767499\pi$
$877$	−3.39330e7	−1.48978	−0.744891	+	0.667186i	$0.767499\pi$
$878$	2.10336e7	0.920824
$879$	7.29925e6	0.318644
$880$	−2.07080e6	−0.0901427
$881$	3.75147e6	0.162840	0.0814202	−	0.996680i	$-0.474054\pi$
$881$	3.75147e6	0.162840	0.0814202	+	0.996680i	$0.474054\pi$
$882$	4.43948e6	0.192159
$883$	−3.16434e7	−1.36578	−0.682891	−	0.730520i	$-0.739278\pi$
$883$	−3.16434e7	−1.36578	−0.682891	+	0.730520i	$0.739278\pi$
$884$	3.89777e6	0.167759
$885$	−5.27213e6	−0.226271
$886$	1.62103e7	0.693754
$887$	2.22713e7	0.950468	0.475234	−	0.879860i	$-0.342363\pi$
$887$	2.22713e7	0.950468	0.475234	+	0.879860i	$0.342363\pi$
$888$	−6.49351e6	−0.276342
$889$	−9.59798e6	−0.407310
$890$	3.55861e6	0.150593
$891$	−2.12289e6	−0.0895846
$892$	−6.86761e6	−0.288997
$893$	−1.24386e6	−0.0521968
$894$	2.33148e6	0.0975638
$895$	−7.56876e6	−0.315840
$896$	−912941.	−0.0379903
$897$	6.71975e6	0.278851
$898$	−8.75239e6	−0.362190
$899$	−2.28619e7	−0.943437
$900$	810000.	0.0333333
$901$	3.54591e7	1.45518
$902$	−3.04556e6	−0.124638
$903$	963132.	0.0393067
$904$	−4.36832e6	−0.177784
$905$	5.70204e6	0.231424
$906$	1.78590e7	0.722832
$907$	1.96192e7	0.791886	0.395943	−	0.918275i	$-0.370418\pi$
$907$	1.96192e7	0.791886	0.395943	+	0.918275i	$0.370418\pi$
$908$	−4.31297e6	−0.173605
$909$	−2.31123e6	−0.0927754
$910$	−1.10174e6	−0.0441037
$911$	1.51503e7	0.604818	0.302409	−	0.953178i	$-0.402209\pi$
$911$	1.51503e7	0.604818	0.302409	+	0.953178i	$0.402209\pi$
$912$	−831744.	−0.0331133
$913$	3.23452e7	1.28420
$914$	−2.28102e7	−0.903156
$915$	−5.05964e6	−0.199787
$916$	−1.73185e7	−0.681981
$917$	7.82983e6	0.307488
$918$	3.59276e6	0.140709
$919$	−4.82506e7	−1.88458	−0.942289	−	0.334800i	$-0.891331\pi$
$919$	−4.82506e7	−1.88458	−0.942289	+	0.334800i	$0.891331\pi$
$920$	6.04191e6	0.235345
$921$	1.59495e7	0.619580
$922$	−2.13784e7	−0.828224
$923$	1.86574e6	0.0720854
$924$	2.59623e6	0.100037
$925$	−7.04591e6	−0.270759
$926$	3.13359e7	1.20092
$927$	−1.33312e7	−0.509530
$928$	4.85032e6	0.184885
$929$	−1.93067e7	−0.733956	−0.366978	−	0.930230i	$-0.619608\pi$
$929$	−1.93067e7	−0.733956	−0.366978	+	0.930230i	$0.619608\pi$
$930$	4.34394e6	0.164694
$931$	−4.94646e6	−0.187034
$932$	−1.68027e7	−0.633636
$933$	6.94918e6	0.261354
$934$	−7.61562e6	−0.285653
$935$	−9.96639e6	−0.372828
$936$	−1.02499e6	−0.0382412
$937$	4.97419e7	1.85086	0.925430	−	0.378919i	$-0.123704\pi$
$937$	4.97419e7	1.85086	0.925430	+	0.378919i	$0.123704\pi$
$938$	−7.37796e6	−0.273797
$939$	2.75533e6	0.101979
$940$	−1.37824e6	−0.0508752
$941$	2.66909e6	0.0982630	0.0491315	−	0.998792i	$-0.484355\pi$
$941$	2.66909e6	0.0982630	0.0491315	+	0.998792i	$0.484355\pi$
$942$	−1.10405e7	−0.405380
$943$	8.88596e6	0.325406
$944$	5.99851e6	0.219086
$945$	−1.01552e6	−0.0369923
$946$	−2.48564e6	−0.0903047
$947$	2.16503e7	0.784493	0.392247	−	0.919860i	$-0.371698\pi$
$947$	2.16503e7	0.784493	0.392247	+	0.919860i	$0.371698\pi$
$948$	8.42507e6	0.304476
$949$	1.50701e7	0.543188
$950$	−902500.	−0.0324443
$951$	−1.08156e6	−0.0387792
$952$	−4.39383e6	−0.157127
$953$	−2.37305e6	−0.0846398	−0.0423199	−	0.999104i	$-0.513475\pi$
$953$	−2.37305e6	−0.0846398	−0.0423199	+	0.999104i	$0.513475\pi$
$954$	−9.32464e6	−0.331712
$955$	−111782.	−0.00396608
$956$	2.32857e7	0.824032
$957$	−1.37934e7	−0.486845
$958$	1.84308e7	0.648830
$959$	−1.24115e7	−0.435790
$960$	−921600.	−0.0322749
$961$	−5.33306e6	−0.186281
$962$	8.91606e6	0.310624
$963$	−8.08962e6	−0.281101
$964$	−6.98497e6	−0.242087
$965$	1.06114e7	0.366819
$966$	−7.57495e6	−0.261178
$967$	1.12757e7	0.387774	0.193887	−	0.981024i	$-0.437890\pi$
$967$	1.12757e7	0.387774	0.193887	+	0.981024i	$0.437890\pi$
$968$	3.60696e6	0.123724
$969$	−4.00304e6	−0.136956
$970$	−7.60529e6	−0.259529
$971$	−4.25830e7	−1.44940	−0.724699	−	0.689065i	$-0.758021\pi$
$971$	−4.25830e7	−1.44940	−0.724699	+	0.689065i	$0.758021\pi$
$972$	−944784.	−0.0320750
$973$	−2.21359e7	−0.749576
$974$	2.45945e7	0.830693
$975$	−1.11219e6	−0.0374686
$976$	5.75675e6	0.193443
$977$	2.96822e7	0.994855	0.497427	−	0.867506i	$-0.334278\pi$
$977$	2.96822e7	0.994855	0.497427	+	0.867506i	$0.334278\pi$
$978$	−1.09583e7	−0.366351
$979$	1.15143e7	0.383956
$980$	−5.48085e6	−0.182298
$981$	1.51852e7	0.503788
$982$	1.77861e7	0.588574
$983$	−2.44497e7	−0.807029	−0.403515	−	0.914973i	$-0.632212\pi$
$983$	−2.44497e7	−0.807029	−0.403515	+	0.914973i	$0.632212\pi$
$984$	−1.35542e6	−0.0446257
$985$	−2.16555e7	−0.711177
$986$	2.33438e7	0.764679
$987$	1.72795e6	0.0564596
$988$	1.14205e6	0.0372212
$989$	7.25229e6	0.235768
$990$	2.62085e6	0.0849874
$991$	2.05824e7	0.665752	0.332876	−	0.942971i	$-0.391981\pi$
$991$	2.05824e7	0.665752	0.332876	+	0.942971i	$0.391981\pi$
$992$	−4.94244e6	−0.159464
$993$	−2.06161e7	−0.663487
$994$	−2.10319e6	−0.0675168
$995$	2.21997e7	0.710869
$996$	1.43951e7	0.459798
$997$	−1.80814e7	−0.576094	−0.288047	−	0.957616i	$-0.593006\pi$
$997$	−1.80814e7	−0.576094	−0.288047	+	0.957616i	$0.593006\pi$
$998$	−2.95982e7	−0.940673
$999$	8.21835e6	0.260538

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.6.a.j.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.6.a.j.1.3	✓	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +36.0000 q^{6} +55.7215 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +36.0000 q^{6} +55.7215 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -323.562 q^{11} -144.000 q^{12} +197.723 q^{13} -222.886 q^{14} -225.000 q^{15} +256.000 q^{16} +1232.08 q^{17} -324.000 q^{18} +361.000 q^{19} +400.000 q^{20} -501.494 q^{21} +1294.25 q^{22} -3776.19 q^{23} +576.000 q^{24} +625.000 q^{25} -790.890 q^{26} -729.000 q^{27} +891.544 q^{28} -4736.64 q^{29} +900.000 q^{30} +4826.60 q^{31} -1024.00 q^{32} +2912.06 q^{33} -4928.34 q^{34} +1393.04 q^{35} +1296.00 q^{36} -11273.5 q^{37} -1444.00 q^{38} -1779.50 q^{39} -1600.00 q^{40} -2353.15 q^{41} +2005.97 q^{42} -1920.53 q^{43} -5176.99 q^{44} +2025.00 q^{45} +15104.8 q^{46} -3445.61 q^{47} -2304.00 q^{48} -13702.1 q^{49} -2500.00 q^{50} -11088.8 q^{51} +3163.56 q^{52} +28779.8 q^{53} +2916.00 q^{54} -8089.05 q^{55} -3566.18 q^{56} -3249.00 q^{57} +18946.6 q^{58} +23431.7 q^{59} -3600.00 q^{60} +22487.3 q^{61} -19306.4 q^{62} +4513.44 q^{63} +4096.00 q^{64} +4943.06 q^{65} -11648.2 q^{66} +33101.9 q^{67} +19713.4 q^{68} +33985.7 q^{69} -5572.15 q^{70} +9436.16 q^{71} -5184.00 q^{72} +76218.4 q^{73} +45093.8 q^{74} -5625.00 q^{75} +5776.00 q^{76} -18029.4 q^{77} +7118.01 q^{78} -58507.4 q^{79} +6400.00 q^{80} +6561.00 q^{81} +9412.61 q^{82} -99966.1 q^{83} -8023.90 q^{84} +30802.1 q^{85} +7682.11 q^{86} +42629.8 q^{87} +20708.0 q^{88} -35586.1 q^{89} -8100.00 q^{90} +11017.4 q^{91} -60419.1 q^{92} -43439.4 q^{93} +13782.4 q^{94} +9025.00 q^{95} +9216.00 q^{96} +76052.9 q^{97} +54808.5 q^{98} -26208.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} + 100 q^{5} + 144 q^{6} - 108 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) \) 4 * q - 16 * q^2 - 36 * q^3 + 64 * q^4 + 100 * q^5 + 144 * q^6 - 108 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} + 100 q^{5} + 144 q^{6} - 108 q^{7} - 256 q^{8} + 324 q^{9} - 400 q^{10} - 246 q^{11} - 576 q^{12} + 640 q^{13} + 432 q^{14} - 900 q^{15} + 1024 q^{16} - 612 q^{17} - 1296 q^{18} + 1444 q^{19} + 1600 q^{20} + 972 q^{21} + 984 q^{22} - 1242 q^{23} + 2304 q^{24} + 2500 q^{25} - 2560 q^{26} - 2916 q^{27} - 1728 q^{28} - 6230 q^{29} + 3600 q^{30} - 11360 q^{31} - 4096 q^{32} + 2214 q^{33} + 2448 q^{34} - 2700 q^{35} + 5184 q^{36} - 4792 q^{37} - 5776 q^{38} - 5760 q^{39} - 6400 q^{40} + 9170 q^{41} - 3888 q^{42} - 11412 q^{43} - 3936 q^{44} + 8100 q^{45} + 4968 q^{46} - 29858 q^{47} - 9216 q^{48} + 31092 q^{49} - 10000 q^{50} + 5508 q^{51} + 10240 q^{52} + 27498 q^{53} + 11664 q^{54} - 6150 q^{55} + 6912 q^{56} - 12996 q^{57} + 24920 q^{58} + 54984 q^{59} - 14400 q^{60} + 20868 q^{61} + 45440 q^{62} - 8748 q^{63} + 16384 q^{64} + 16000 q^{65} - 8856 q^{66} - 20244 q^{67} - 9792 q^{68} + 11178 q^{69} + 10800 q^{70} + 86864 q^{71} - 20736 q^{72} - 3728 q^{73} + 19168 q^{74} - 22500 q^{75} + 23104 q^{76} + 18796 q^{77} + 23040 q^{78} + 164192 q^{79} + 25600 q^{80} + 26244 q^{81} - 36680 q^{82} - 60506 q^{83} + 15552 q^{84} - 15300 q^{85} + 45648 q^{86} + 56070 q^{87} + 15744 q^{88} + 113798 q^{89} - 32400 q^{90} + 159528 q^{91} - 19872 q^{92} + 102240 q^{93} + 119432 q^{94} + 36100 q^{95} + 36864 q^{96} + 79440 q^{97} - 124368 q^{98} - 19926 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 - 36 * q^3 + 64 * q^4 + 100 * q^5 + 144 * q^6 - 108 * q^7 - 256 * q^8 + 324 * q^9 - 400 * q^10 - 246 * q^11 - 576 * q^12 + 640 * q^13 + 432 * q^14 - 900 * q^15 + 1024 * q^16 - 612 * q^17 - 1296 * q^18 + 1444 * q^19 + 1600 * q^20 + 972 * q^21 + 984 * q^22 - 1242 * q^23 + 2304 * q^24 + 2500 * q^25 - 2560 * q^26 - 2916 * q^27 - 1728 * q^28 - 6230 * q^29 + 3600 * q^30 - 11360 * q^31 - 4096 * q^32 + 2214 * q^33 + 2448 * q^34 - 2700 * q^35 + 5184 * q^36 - 4792 * q^37 - 5776 * q^38 - 5760 * q^39 - 6400 * q^40 + 9170 * q^41 - 3888 * q^42 - 11412 * q^43 - 3936 * q^44 + 8100 * q^45 + 4968 * q^46 - 29858 * q^47 - 9216 * q^48 + 31092 * q^49 - 10000 * q^50 + 5508 * q^51 + 10240 * q^52 + 27498 * q^53 + 11664 * q^54 - 6150 * q^55 + 6912 * q^56 - 12996 * q^57 + 24920 * q^58 + 54984 * q^59 - 14400 * q^60 + 20868 * q^61 + 45440 * q^62 - 8748 * q^63 + 16384 * q^64 + 16000 * q^65 - 8856 * q^66 - 20244 * q^67 - 9792 * q^68 + 11178 * q^69 + 10800 * q^70 + 86864 * q^71 - 20736 * q^72 - 3728 * q^73 + 19168 * q^74 - 22500 * q^75 + 23104 * q^76 + 18796 * q^77 + 23040 * q^78 + 164192 * q^79 + 25600 * q^80 + 26244 * q^81 - 36680 * q^82 - 60506 * q^83 + 15552 * q^84 - 15300 * q^85 + 45648 * q^86 + 56070 * q^87 + 15744 * q^88 + 113798 * q^89 - 32400 * q^90 + 159528 * q^91 - 19872 * q^92 + 102240 * q^93 + 119432 * q^94 + 36100 * q^95 + 36864 * q^96 + 79440 * q^97 - 124368 * q^98 - 19926 * q^99

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