LMFDB - Embedded newform 570.6.a.l.1.4

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} - 1748x^{2} - 8028x + 111960 $ x^4 - 1748x^2 - 8028x + 111960
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			1.4
Root			$43.2864$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +143.725 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +143.725 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} +22.0191 q^{11} +144.000 q^{12} -680.016 q^{13} -574.901 q^{14} +225.000 q^{15} +256.000 q^{16} +580.995 q^{17} -324.000 q^{18} -361.000 q^{19} +400.000 q^{20} +1293.53 q^{21} -88.0764 q^{22} -3253.75 q^{23} -576.000 q^{24} +625.000 q^{25} +2720.07 q^{26} +729.000 q^{27} +2299.61 q^{28} -7456.13 q^{29} -900.000 q^{30} -7764.65 q^{31} -1024.00 q^{32} +198.172 q^{33} -2323.98 q^{34} +3593.13 q^{35} +1296.00 q^{36} -9565.03 q^{37} +1444.00 q^{38} -6120.15 q^{39} -1600.00 q^{40} +249.874 q^{41} -5174.11 q^{42} -9487.44 q^{43} +352.306 q^{44} +2025.00 q^{45} +13015.0 q^{46} +22230.2 q^{47} +2304.00 q^{48} +3849.97 q^{49} -2500.00 q^{50} +5228.96 q^{51} -10880.3 q^{52} -27587.8 q^{53} -2916.00 q^{54} +550.478 q^{55} -9198.42 q^{56} -3249.00 q^{57} +29824.5 q^{58} -37601.3 q^{59} +3600.00 q^{60} +57307.5 q^{61} +31058.6 q^{62} +11641.8 q^{63} +4096.00 q^{64} -17000.4 q^{65} -792.688 q^{66} -60301.0 q^{67} +9295.92 q^{68} -29283.7 q^{69} -14372.5 q^{70} +35616.0 q^{71} -5184.00 q^{72} -15447.8 q^{73} +38260.1 q^{74} +5625.00 q^{75} -5776.00 q^{76} +3164.70 q^{77} +24480.6 q^{78} -64839.9 q^{79} +6400.00 q^{80} +6561.00 q^{81} -999.496 q^{82} +74606.2 q^{83} +20696.4 q^{84} +14524.9 q^{85} +37949.8 q^{86} -67105.2 q^{87} -1409.22 q^{88} +66917.7 q^{89} -8100.00 q^{90} -97735.6 q^{91} -52060.0 q^{92} -69881.8 q^{93} -88920.8 q^{94} -9025.00 q^{95} -9216.00 q^{96} -29257.5 q^{97} -15399.9 q^{98} +1783.55 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} - 26 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 - 26 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} - 26 q^{7} - 256 q^{8} + 324 q^{9} - 400 q^{10} - 336 q^{11} + 576 q^{12} - 734 q^{13} + 104 q^{14} + 900 q^{15} + 1024 q^{16} + 480 q^{17} - 1296 q^{18} - 1444 q^{19} + 1600 q^{20} - 234 q^{21} + 1344 q^{22} - 1962 q^{23} - 2304 q^{24} + 2500 q^{25} + 2936 q^{26} + 2916 q^{27} - 416 q^{28} - 8720 q^{29} - 3600 q^{30} - 240 q^{31} - 4096 q^{32} - 3024 q^{33} - 1920 q^{34} - 650 q^{35} + 5184 q^{36} - 14626 q^{37} + 5776 q^{38} - 6606 q^{39} - 6400 q^{40} - 11092 q^{41} + 936 q^{42} - 16778 q^{43} - 5376 q^{44} + 8100 q^{45} + 7848 q^{46} - 34810 q^{47} + 9216 q^{48} - 34032 q^{49} - 10000 q^{50} + 4320 q^{51} - 11744 q^{52} - 18186 q^{53} - 11664 q^{54} - 8400 q^{55} + 1664 q^{56} - 12996 q^{57} + 34880 q^{58} - 38700 q^{59} + 14400 q^{60} - 12080 q^{61} + 960 q^{62} - 2106 q^{63} + 16384 q^{64} - 18350 q^{65} + 12096 q^{66} - 84216 q^{67} + 7680 q^{68} - 17658 q^{69} + 2600 q^{70} + 3592 q^{71} - 20736 q^{72} - 41180 q^{73} + 58504 q^{74} + 22500 q^{75} - 23104 q^{76} - 6696 q^{77} + 26424 q^{78} + 15272 q^{79} + 25600 q^{80} + 26244 q^{81} + 44368 q^{82} + 133106 q^{83} - 3744 q^{84} + 12000 q^{85} + 67112 q^{86} - 78480 q^{87} + 21504 q^{88} + 133704 q^{89} - 32400 q^{90} - 86656 q^{91} - 31392 q^{92} - 2160 q^{93} + 139240 q^{94} - 36100 q^{95} - 36864 q^{96} - 161594 q^{97} + 136128 q^{98} - 27216 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 + 100 * q^5 - 144 * q^6 - 26 * q^7 - 256 * q^8 + 324 * q^9 - 400 * q^10 - 336 * q^11 + 576 * q^12 - 734 * q^13 + 104 * q^14 + 900 * q^15 + 1024 * q^16 + 480 * q^17 - 1296 * q^18 - 1444 * q^19 + 1600 * q^20 - 234 * q^21 + 1344 * q^22 - 1962 * q^23 - 2304 * q^24 + 2500 * q^25 + 2936 * q^26 + 2916 * q^27 - 416 * q^28 - 8720 * q^29 - 3600 * q^30 - 240 * q^31 - 4096 * q^32 - 3024 * q^33 - 1920 * q^34 - 650 * q^35 + 5184 * q^36 - 14626 * q^37 + 5776 * q^38 - 6606 * q^39 - 6400 * q^40 - 11092 * q^41 + 936 * q^42 - 16778 * q^43 - 5376 * q^44 + 8100 * q^45 + 7848 * q^46 - 34810 * q^47 + 9216 * q^48 - 34032 * q^49 - 10000 * q^50 + 4320 * q^51 - 11744 * q^52 - 18186 * q^53 - 11664 * q^54 - 8400 * q^55 + 1664 * q^56 - 12996 * q^57 + 34880 * q^58 - 38700 * q^59 + 14400 * q^60 - 12080 * q^61 + 960 * q^62 - 2106 * q^63 + 16384 * q^64 - 18350 * q^65 + 12096 * q^66 - 84216 * q^67 + 7680 * q^68 - 17658 * q^69 + 2600 * q^70 + 3592 * q^71 - 20736 * q^72 - 41180 * q^73 + 58504 * q^74 + 22500 * q^75 - 23104 * q^76 - 6696 * q^77 + 26424 * q^78 + 15272 * q^79 + 25600 * q^80 + 26244 * q^81 + 44368 * q^82 + 133106 * q^83 - 3744 * q^84 + 12000 * q^85 + 67112 * q^86 - 78480 * q^87 + 21504 * q^88 + 133704 * q^89 - 32400 * q^90 - 86656 * q^91 - 31392 * q^92 - 2160 * q^93 + 139240 * q^94 - 36100 * q^95 - 36864 * q^96 - 161594 * q^97 + 136128 * q^98 - 27216 * 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
$7$	143.725	1.10863	0.554317	−	0.832306i	$-0.312980\pi$
$7$	143.725	1.10863	0.554317	+	0.832306i	$0.312980\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	−100.000	−0.316228
$11$	22.0191	0.0548679	0.0274339	−	0.999624i	$-0.491266\pi$
$11$	22.0191	0.0548679	0.0274339	+	0.999624i	$0.491266\pi$
$12$	144.000	0.288675
$13$	−680.016	−1.11599	−0.557996	−	0.829844i	$-0.688429\pi$
$13$	−680.016	−1.11599	−0.557996	+	0.829844i	$0.688429\pi$
$14$	−574.901	−0.783923
$15$	225.000	0.258199
$16$	256.000	0.250000
$17$	580.995	0.487585	0.243792	−	0.969827i	$-0.421608\pi$
$17$	580.995	0.487585	0.243792	+	0.969827i	$0.421608\pi$
$18$	−324.000	−0.235702
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	400.000	0.223607
$21$	1293.53	0.640070
$22$	−88.0764	−0.0387974
$23$	−3253.75	−1.28252	−0.641260	−	0.767323i	$-0.721588\pi$
$23$	−3253.75	−1.28252	−0.641260	+	0.767323i	$0.721588\pi$
$24$	−576.000	−0.204124
$25$	625.000	0.200000
$26$	2720.07	0.789125
$27$	729.000	0.192450
$28$	2299.61	0.554317
$29$	−7456.13	−1.64634	−0.823168	−	0.567798i	$-0.807796\pi$
$29$	−7456.13	−1.64634	−0.823168	+	0.567798i	$0.807796\pi$
$30$	−900.000	−0.182574
$31$	−7764.65	−1.45117	−0.725584	−	0.688134i	$-0.758430\pi$
$31$	−7764.65	−1.45117	−0.725584	+	0.688134i	$0.758430\pi$
$32$	−1024.00	−0.176777
$33$	198.172	0.0316780
$34$	−2323.98	−0.344775
$35$	3593.13	0.495796
$36$	1296.00	0.166667
$37$	−9565.03	−1.14863	−0.574317	−	0.818633i	$-0.694733\pi$
$37$	−9565.03	−1.14863	−0.574317	+	0.818633i	$0.694733\pi$
$38$	1444.00	0.162221
$39$	−6120.15	−0.644318
$40$	−1600.00	−0.158114
$41$	249.874	0.0232146	0.0116073	−	0.999933i	$-0.496305\pi$
$41$	249.874	0.0232146	0.0116073	+	0.999933i	$0.496305\pi$
$42$	−5174.11	−0.452598
$43$	−9487.44	−0.782489	−0.391244	−	0.920287i	$-0.627955\pi$
$43$	−9487.44	−0.782489	−0.391244	+	0.920287i	$0.627955\pi$
$44$	352.306	0.0274339
$45$	2025.00	0.149071
$46$	13015.0	0.906879
$47$	22230.2	1.46791	0.733954	−	0.679199i	$-0.237673\pi$
$47$	22230.2	1.46791	0.733954	+	0.679199i	$0.237673\pi$
$48$	2304.00	0.144338
$49$	3849.97	0.229070
$50$	−2500.00	−0.141421
$51$	5228.96	0.281507
$52$	−10880.3	−0.557996
$53$	−27587.8	−1.34905	−0.674523	−	0.738254i	$-0.735651\pi$
$53$	−27587.8	−1.34905	−0.674523	+	0.738254i	$0.735651\pi$
$54$	−2916.00	−0.136083
$55$	550.478	0.0245377
$56$	−9198.42	−0.391961
$57$	−3249.00	−0.132453
$58$	29824.5	1.16414
$59$	−37601.3	−1.40628	−0.703142	−	0.711049i	$-0.748220\pi$
$59$	−37601.3	−1.40628	−0.703142	+	0.711049i	$0.748220\pi$
$60$	3600.00	0.129099
$61$	57307.5	1.97191	0.985954	−	0.167016i	$-0.0534131\pi$
$61$	57307.5	1.97191	0.985954	+	0.167016i	$0.0534131\pi$
$62$	31058.6	1.02613
$63$	11641.8	0.369545
$64$	4096.00	0.125000
$65$	−17000.4	−0.499087
$66$	−792.688	−0.0223997
$67$	−60301.0	−1.64111	−0.820555	−	0.571568i	$-0.806335\pi$
$67$	−60301.0	−1.64111	−0.820555	+	0.571568i	$0.806335\pi$
$68$	9295.92	0.243792
$69$	−29283.7	−0.740464
$70$	−14372.5	−0.350581
$71$	35616.0	0.838492	0.419246	−	0.907873i	$-0.362294\pi$
$71$	35616.0	0.838492	0.419246	+	0.907873i	$0.362294\pi$
$72$	−5184.00	−0.117851
$73$	−15447.8	−0.339280	−0.169640	−	0.985506i	$-0.554261\pi$
$73$	−15447.8	−0.339280	−0.169640	+	0.985506i	$0.554261\pi$
$74$	38260.1	0.812208
$75$	5625.00	0.115470
$76$	−5776.00	−0.114708
$77$	3164.70	0.0608284
$78$	24480.6	0.455602
$79$	−64839.9	−1.16889	−0.584446	−	0.811432i	$-0.698688\pi$
$79$	−64839.9	−1.16889	−0.584446	+	0.811432i	$0.698688\pi$
$80$	6400.00	0.111803
$81$	6561.00	0.111111
$82$	−999.496	−0.0164152
$83$	74606.2	1.18872	0.594360	−	0.804199i	$-0.297405\pi$
$83$	74606.2	1.18872	0.594360	+	0.804199i	$0.297405\pi$
$84$	20696.4	0.320035
$85$	14524.9	0.218055
$86$	37949.8	0.553303
$87$	−67105.2	−0.950513
$88$	−1409.22	−0.0193987
$89$	66917.7	0.895501	0.447750	−	0.894159i	$-0.352225\pi$
$89$	66917.7	0.895501	0.447750	+	0.894159i	$0.352225\pi$
$90$	−8100.00	−0.105409
$91$	−97735.6	−1.23723
$92$	−52060.0	−0.641260
$93$	−69881.8	−0.837832
$94$	−88920.8	−1.03797
$95$	−9025.00	−0.102598
$96$	−9216.00	−0.102062
$97$	−29257.5	−0.315724	−0.157862	−	0.987461i	$-0.550460\pi$
$97$	−29257.5	−0.315724	−0.157862	+	0.987461i	$0.550460\pi$
$98$	−15399.9	−0.161977
$99$	1783.55	0.0182893
$100$	10000.0	0.100000
$101$	−32131.6	−0.313422	−0.156711	−	0.987645i	$-0.550089\pi$
$101$	−32131.6	−0.313422	−0.156711	+	0.987645i	$0.550089\pi$
$102$	−20915.8	−0.199056
$103$	126203.	1.17214	0.586068	−	0.810262i	$-0.300675\pi$
$103$	126203.	1.17214	0.586068	+	0.810262i	$0.300675\pi$
$104$	43521.0	0.394563
$105$	32338.2	0.286248
$106$	110351.	0.953920
$107$	183052.	1.54566	0.772831	−	0.634612i	$-0.218840\pi$
$107$	183052.	1.54566	0.772831	+	0.634612i	$0.218840\pi$
$108$	11664.0	0.0962250
$109$	17314.7	0.139588	0.0697940	−	0.997561i	$-0.477766\pi$
$109$	17314.7	0.139588	0.0697940	+	0.997561i	$0.477766\pi$
$110$	−2201.91	−0.0173507
$111$	−86085.3	−0.663165
$112$	36793.7	0.277159
$113$	26301.9	0.193772	0.0968858	−	0.995296i	$-0.469112\pi$
$113$	26301.9	0.193772	0.0968858	+	0.995296i	$0.469112\pi$
$114$	12996.0	0.0936586
$115$	−81343.7	−0.573561
$116$	−119298.	−0.823168
$117$	−55081.3	−0.371997
$118$	150405.	0.994393
$119$	83503.7	0.540553
$120$	−14400.0	−0.0912871
$121$	−160566.	−0.996990
$122$	−229230.	−1.39435
$123$	2248.87	0.0134030
$124$	−124234.	−0.725584
$125$	15625.0	0.0894427
$126$	−46567.0	−0.261308
$127$	315074.	1.73342	0.866710	−	0.498813i	$-0.166231\pi$
$127$	315074.	1.73342	0.866710	+	0.498813i	$0.166231\pi$
$128$	−16384.0	−0.0883883
$129$	−85387.0	−0.451770
$130$	68001.6	0.352908
$131$	−26220.3	−0.133493	−0.0667466	−	0.997770i	$-0.521262\pi$
$131$	−26220.3	−0.133493	−0.0667466	+	0.997770i	$0.521262\pi$
$132$	3170.75	0.0158390
$133$	−51884.8	−0.254338
$134$	241204.	1.16044
$135$	18225.0	0.0860663
$136$	−37183.7	−0.172387
$137$	90073.9	0.410013	0.205006	−	0.978761i	$-0.434278\pi$
$137$	90073.9	0.410013	0.205006	+	0.978761i	$0.434278\pi$
$138$	117135.	0.523587
$139$	−117387.	−0.515327	−0.257663	−	0.966235i	$-0.582953\pi$
$139$	−117387.	−0.515327	−0.257663	+	0.966235i	$0.582953\pi$
$140$	57490.1	0.247898
$141$	200072.	0.847497
$142$	−142464.	−0.592904
$143$	−14973.4	−0.0612321
$144$	20736.0	0.0833333
$145$	−186403.	−0.736264
$146$	61791.1	0.239907
$147$	34649.7	0.132253
$148$	−153040.	−0.574317
$149$	−267272.	−0.986252	−0.493126	−	0.869958i	$-0.664146\pi$
$149$	−267272.	−0.986252	−0.493126	+	0.869958i	$0.664146\pi$
$150$	−22500.0	−0.0816497
$151$	278134.	0.992686	0.496343	−	0.868127i	$-0.334676\pi$
$151$	278134.	0.992686	0.496343	+	0.868127i	$0.334676\pi$
$152$	23104.0	0.0811107
$153$	47060.6	0.162528
$154$	−12658.8	−0.0430122
$155$	−194116.	−0.648982
$156$	−97922.3	−0.322159
$157$	−439161.	−1.42192	−0.710959	−	0.703234i	$-0.751739\pi$
$157$	−439161.	−1.42192	−0.710959	+	0.703234i	$0.751739\pi$
$158$	259360.	0.826532
$159$	−248290.	−0.778872
$160$	−25600.0	−0.0790569
$161$	−467646.	−1.42185
$162$	−26244.0	−0.0785674
$163$	−160018.	−0.471738	−0.235869	−	0.971785i	$-0.575794\pi$
$163$	−160018.	−0.471738	−0.235869	+	0.971785i	$0.575794\pi$
$164$	3997.98	0.0116073
$165$	4954.30	0.0141668
$166$	−298425.	−0.840552
$167$	−557333.	−1.54641	−0.773203	−	0.634159i	$-0.781346\pi$
$167$	−557333.	−1.54641	−0.773203	+	0.634159i	$0.781346\pi$
$168$	−82785.8	−0.226299
$169$	91129.1	0.245437
$170$	−58099.5	−0.154188
$171$	−29241.0	−0.0764719
$172$	−151799.	−0.391244
$173$	−301346.	−0.765508	−0.382754	−	0.923850i	$-0.625024\pi$
$173$	−301346.	−0.765508	−0.382754	+	0.923850i	$0.625024\pi$
$174$	268421.	0.672114
$175$	89828.3	0.221727
$176$	5636.89	0.0137170
$177$	−338412.	−0.811918
$178$	−267671.	−0.633215
$179$	−233939.	−0.545720	−0.272860	−	0.962054i	$-0.587970\pi$
$179$	−233939.	−0.545720	−0.272860	+	0.962054i	$0.587970\pi$
$180$	32400.0	0.0745356
$181$	−105653.	−0.239708	−0.119854	−	0.992792i	$-0.538243\pi$
$181$	−105653.	−0.239708	−0.119854	+	0.992792i	$0.538243\pi$
$182$	390942.	0.874851
$183$	515767.	1.13848
$184$	208240.	0.453440
$185$	−239126.	−0.513685
$186$	279527.	0.592437
$187$	12793.0	0.0267527
$188$	355683.	0.733954
$189$	104776.	0.213357
$190$	36100.0	0.0725476
$191$	708593.	1.40544	0.702722	−	0.711464i	$-0.251968\pi$
$191$	708593.	1.40544	0.702722	+	0.711464i	$0.251968\pi$
$192$	36864.0	0.0721688
$193$	−561204.	−1.08450	−0.542248	−	0.840219i	$-0.682427\pi$
$193$	−561204.	−1.08450	−0.542248	+	0.840219i	$0.682427\pi$
$194$	117030.	0.223251
$195$	−153004.	−0.288148
$196$	61599.5	0.114535
$197$	323222.	0.593383	0.296691	−	0.954973i	$-0.404117\pi$
$197$	323222.	0.593383	0.296691	+	0.954973i	$0.404117\pi$
$198$	−7134.19	−0.0129325
$199$	142757.	0.255543	0.127771	−	0.991804i	$-0.459218\pi$
$199$	142757.	0.255543	0.127771	+	0.991804i	$0.459218\pi$
$200$	−40000.0	−0.0707107
$201$	−542709.	−0.947495
$202$	128526.	0.221623
$203$	−1.07163e6	−1.82518
$204$	83663.3	0.140754
$205$	6246.85	0.0103819
$206$	−504814.	−0.828825
$207$	−263554.	−0.427507
$208$	−174084.	−0.278998
$209$	−7948.90	−0.0125876
$210$	−129353.	−0.202408
$211$	−871578.	−1.34772	−0.673861	−	0.738858i	$-0.735365\pi$
$211$	−871578.	−1.34772	−0.673861	+	0.738858i	$0.735365\pi$
$212$	−441404.	−0.674523
$213$	320544.	0.484104
$214$	−732207.	−1.09295
$215$	−237186.	−0.349940
$216$	−46656.0	−0.0680414
$217$	−1.11598e6	−1.60881
$218$	−69258.7	−0.0987037
$219$	−139030.	−0.195884
$220$	8807.64	0.0122688
$221$	−395086.	−0.544141
$222$	344341.	0.468928
$223$	−1.44092e6	−1.94033	−0.970167	−	0.242437i	$-0.922053\pi$
$223$	−1.44092e6	−1.94033	−0.970167	+	0.242437i	$0.922053\pi$
$224$	−147175.	−0.195981
$225$	50625.0	0.0666667
$226$	−105207.	−0.137017
$227$	325368.	0.419092	0.209546	−	0.977799i	$-0.432801\pi$
$227$	325368.	0.419092	0.209546	+	0.977799i	$0.432801\pi$
$228$	−51984.0	−0.0662266
$229$	843237.	1.06258	0.531289	−	0.847190i	$-0.321708\pi$
$229$	843237.	1.06258	0.531289	+	0.847190i	$0.321708\pi$
$230$	325375.	0.405569
$231$	28482.3	0.0351193
$232$	477192.	0.582068
$233$	476125.	0.574554	0.287277	−	0.957848i	$-0.407250\pi$
$233$	476125.	0.574554	0.287277	+	0.957848i	$0.407250\pi$
$234$	220325.	0.263042
$235$	555755.	0.656469
$236$	−601621.	−0.703142
$237$	−583559.	−0.674861
$238$	−334015.	−0.382229
$239$	−446149.	−0.505225	−0.252613	−	0.967568i	$-0.581290\pi$
$239$	−446149.	−0.505225	−0.252613	+	0.967568i	$0.581290\pi$
$240$	57600.0	0.0645497
$241$	−1.75121e6	−1.94221	−0.971105	−	0.238651i	$-0.923295\pi$
$241$	−1.75121e6	−1.94221	−0.971105	+	0.238651i	$0.923295\pi$
$242$	642265.	0.704978
$243$	59049.0	0.0641500
$244$	916920.	0.985954
$245$	96249.3	0.102443
$246$	−8995.46	−0.00947732
$247$	245486.	0.256026
$248$	496937.	0.513065
$249$	671456.	0.686308
$250$	−62500.0	−0.0632456
$251$	−1.55907e6	−1.56200	−0.781002	−	0.624528i	$-0.785291\pi$
$251$	−1.55907e6	−1.56200	−0.781002	+	0.624528i	$0.785291\pi$
$252$	186268.	0.184772
$253$	−71644.6	−0.0703692
$254$	−1.26030e6	−1.22571
$255$	130724.	0.125894
$256$	65536.0	0.0625000
$257$	−661468.	−0.624706	−0.312353	−	0.949966i	$-0.601117\pi$
$257$	−661468.	−0.624706	−0.312353	+	0.949966i	$0.601117\pi$
$258$	341548.	0.319450
$259$	−1.37474e6	−1.27342
$260$	−272007.	−0.249543
$261$	−603947.	−0.548779
$262$	104881.	0.0943939
$263$	732158.	0.652703	0.326351	−	0.945249i	$-0.394181\pi$
$263$	732158.	0.652703	0.326351	+	0.945249i	$0.394181\pi$
$264$	−12683.0	−0.0111999
$265$	−689694.	−0.603312
$266$	207539.	0.179844
$267$	602259.	0.517018
$268$	−964816.	−0.820555
$269$	2.17804e6	1.83520	0.917602	−	0.397501i	$-0.130123\pi$
$269$	2.17804e6	1.83520	0.917602	+	0.397501i	$0.130123\pi$
$270$	−72900.0	−0.0608581
$271$	2.09785e6	1.73521	0.867604	−	0.497256i	$-0.165659\pi$
$271$	2.09785e6	1.73521	0.867604	+	0.497256i	$0.165659\pi$
$272$	148735.	0.121896
$273$	−879620.	−0.714313
$274$	−360295.	−0.289923
$275$	13761.9	0.0109736
$276$	−468540.	−0.370232
$277$	1.33707e6	1.04702	0.523510	−	0.852019i	$-0.324622\pi$
$277$	1.33707e6	1.04702	0.523510	+	0.852019i	$0.324622\pi$
$278$	469548.	0.364391
$279$	−628936.	−0.483722
$280$	−229961.	−0.175290
$281$	1.54073e6	1.16402	0.582010	−	0.813182i	$-0.302267\pi$
$281$	1.54073e6	1.16402	0.582010	+	0.813182i	$0.302267\pi$
$282$	−800288.	−0.599271
$283$	−2.00791e6	−1.49032	−0.745158	−	0.666888i	$-0.767626\pi$
$283$	−2.00791e6	−1.49032	−0.745158	+	0.666888i	$0.767626\pi$
$284$	569856.	0.419246
$285$	−81225.0	−0.0592349
$286$	59893.4	0.0432976
$287$	35913.2	0.0257365
$288$	−82944.0	−0.0589256
$289$	−1.08230e6	−0.762261
$290$	745613.	0.520617
$291$	−263318.	−0.182284
$292$	−247164.	−0.169640
$293$	583924.	0.397363	0.198681	−	0.980064i	$-0.436334\pi$
$293$	583924.	0.397363	0.198681	+	0.980064i	$0.436334\pi$
$294$	−138599.	−0.0935172
$295$	−940033.	−0.628909
$296$	612162.	0.406104
$297$	16051.9	0.0105593
$298$	1.06909e6	0.697385
$299$	2.21260e6	1.43128
$300$	90000.0	0.0577350
$301$	−1.36359e6	−0.867494
$302$	−1.11254e6	−0.701935
$303$	−289185.	−0.180954
$304$	−92416.0	−0.0573539
$305$	1.43269e6	0.881864
$306$	−188242.	−0.114925
$307$	−359186.	−0.217507	−0.108754	−	0.994069i	$-0.534686\pi$
$307$	−359186.	−0.217507	−0.108754	+	0.994069i	$0.534686\pi$
$308$	50635.3	0.0304142
$309$	1.13583e6	0.676733
$310$	776465.	0.458899
$311$	881950.	0.517062	0.258531	−	0.966003i	$-0.416762\pi$
$311$	881950.	0.517062	0.258531	+	0.966003i	$0.416762\pi$
$312$	391689.	0.227801
$313$	−2.93883e6	−1.69556	−0.847782	−	0.530344i	$-0.822063\pi$
$313$	−2.93883e6	−1.69556	−0.847782	+	0.530344i	$0.822063\pi$
$314$	1.75664e6	1.00545
$315$	291044.	0.165265
$316$	−1.03744e6	−0.584446
$317$	587223.	0.328212	0.164106	−	0.986443i	$-0.447526\pi$
$317$	587223.	0.328212	0.164106	+	0.986443i	$0.447526\pi$
$318$	993160.	0.550746
$319$	−164177.	−0.0903309
$320$	102400.	0.0559017
$321$	1.64747e6	0.892388
$322$	1.87058e6	1.00540
$323$	−209739.	−0.111860
$324$	104976.	0.0555556
$325$	−425010.	−0.223198
$326$	640074.	0.333569
$327$	155832.	0.0805912
$328$	−15991.9	−0.00820760
$329$	3.19504e6	1.62737
$330$	−19817.2	−0.0100175
$331$	2.45794e6	1.23311	0.616553	−	0.787313i	$-0.288529\pi$
$331$	2.45794e6	1.23311	0.616553	+	0.787313i	$0.288529\pi$
$332$	1.19370e6	0.594360
$333$	−774767.	−0.382878
$334$	2.22933e6	1.09347
$335$	−1.50753e6	−0.733927
$336$	331143.	0.160018
$337$	2.59338e6	1.24392	0.621959	−	0.783050i	$-0.286337\pi$
$337$	2.59338e6	1.24392	0.621959	+	0.783050i	$0.286337\pi$
$338$	−364516.	−0.173550
$339$	236717.	0.111874
$340$	232398.	0.109027
$341$	−170971.	−0.0796225
$342$	116964.	0.0540738
$343$	−1.86225e6	−0.854680
$344$	607196.	0.276652
$345$	−732093.	−0.331145
$346$	1.20538e6	0.541296
$347$	−1.69323e6	−0.754904	−0.377452	−	0.926029i	$-0.623200\pi$
$347$	−1.69323e6	−0.754904	−0.377452	+	0.926029i	$0.623200\pi$
$348$	−1.07368e6	−0.475256
$349$	−2.21693e6	−0.974290	−0.487145	−	0.873321i	$-0.661962\pi$
$349$	−2.21693e6	−0.974290	−0.487145	+	0.873321i	$0.661962\pi$
$350$	−359313.	−0.156785
$351$	−495732.	−0.214773
$352$	−22547.6	−0.00969936
$353$	−1.91471e6	−0.817835	−0.408918	−	0.912571i	$-0.634094\pi$
$353$	−1.91471e6	−0.817835	−0.408918	+	0.912571i	$0.634094\pi$
$354$	1.35365e6	0.574113
$355$	890400.	0.374985
$356$	1.07068e6	0.447750
$357$	751534.	0.312089
$358$	935755.	0.385882
$359$	4.65545e6	1.90645	0.953226	−	0.302260i	$-0.0977410\pi$
$359$	4.65545e6	1.90645	0.953226	+	0.302260i	$0.0977410\pi$
$360$	−129600.	−0.0527046
$361$	130321.	0.0526316
$362$	422610.	0.169499
$363$	−1.44510e6	−0.575612
$364$	−1.56377e6	−0.618613
$365$	−386194.	−0.151731
$366$	−2.06307e6	−0.805028
$367$	−2.93853e6	−1.13884	−0.569422	−	0.822045i	$-0.692833\pi$
$367$	−2.93853e6	−1.13884	−0.569422	+	0.822045i	$0.692833\pi$
$368$	−832960.	−0.320630
$369$	20239.8	0.00773820
$370$	956503.	0.363230
$371$	−3.96506e6	−1.49560
$372$	−1.11811e6	−0.418916
$373$	−829669.	−0.308768	−0.154384	−	0.988011i	$-0.549339\pi$
$373$	−829669.	−0.308768	−0.154384	+	0.988011i	$0.549339\pi$
$374$	−51172.0	−0.0189170
$375$	140625.	0.0516398
$376$	−1.42273e6	−0.518984
$377$	5.07029e6	1.83730
$378$	−419103.	−0.150866
$379$	3.12003e6	1.11574	0.557868	−	0.829930i	$-0.311620\pi$
$379$	3.12003e6	1.11574	0.557868	+	0.829930i	$0.311620\pi$
$380$	−144400.	−0.0512989
$381$	2.83567e6	1.00079
$382$	−2.83437e6	−0.993799
$383$	1.83927e6	0.640692	0.320346	−	0.947301i	$-0.396201\pi$
$383$	1.83927e6	0.640692	0.320346	+	0.947301i	$0.396201\pi$
$384$	−147456.	−0.0510310
$385$	79117.6	0.0272033
$386$	2.24482e6	0.766854
$387$	−768483.	−0.260830
$388$	−468120.	−0.157862
$389$	462203.	0.154867	0.0774334	−	0.996998i	$-0.475327\pi$
$389$	462203.	0.154867	0.0774334	+	0.996998i	$0.475327\pi$
$390$	612015.	0.203751
$391$	−1.89041e6	−0.625338
$392$	−246398.	−0.0809883
$393$	−235982.	−0.0770723
$394$	−1.29289e6	−0.419585
$395$	−1.62100e6	−0.522745
$396$	28536.8	0.00914464
$397$	−5.23910e6	−1.66832	−0.834162	−	0.551520i	$-0.814048\pi$
$397$	−5.23910e6	−1.66832	−0.834162	+	0.551520i	$0.814048\pi$
$398$	−571026.	−0.180696
$399$	−466964.	−0.146842
$400$	160000.	0.0500000
$401$	1.32786e6	0.412375	0.206188	−	0.978512i	$-0.433894\pi$
$401$	1.32786e6	0.412375	0.206188	+	0.978512i	$0.433894\pi$
$402$	2.17084e6	0.669980
$403$	5.28009e6	1.61949
$404$	−514106.	−0.156711
$405$	164025.	0.0496904
$406$	4.28654e6	1.29060
$407$	−210613.	−0.0630232
$408$	−334653.	−0.0995279
$409$	3.96075e6	1.17076	0.585382	−	0.810758i	$-0.300945\pi$
$409$	3.96075e6	1.17076	0.585382	+	0.810758i	$0.300945\pi$
$410$	−24987.4	−0.00734110
$411$	810665.	0.236721
$412$	2.01925e6	0.586068
$413$	−5.40426e6	−1.55905
$414$	1.05421e6	0.302293
$415$	1.86515e6	0.531612
$416$	696337.	0.197281
$417$	−1.05648e6	−0.297524
$418$	31795.6	0.00890074
$419$	6.98380e6	1.94338	0.971688	−	0.236270i	$-0.0759248\pi$
$419$	6.98380e6	1.94338	0.971688	+	0.236270i	$0.0759248\pi$
$420$	517411.	0.143124
$421$	−4.56694e6	−1.25580	−0.627899	−	0.778294i	$-0.716085\pi$
$421$	−4.56694e6	−1.25580	−0.627899	+	0.778294i	$0.716085\pi$
$422$	3.48631e6	0.952983
$423$	1.80065e6	0.489303
$424$	1.76562e6	0.476960
$425$	363122.	0.0975170
$426$	−1.28218e6	−0.342313
$427$	8.23654e6	2.18612
$428$	2.92883e6	0.772831
$429$	−134760.	−0.0353524
$430$	948744.	0.247445
$431$	3.80789e6	0.987394	0.493697	−	0.869634i	$-0.335645\pi$
$431$	3.80789e6	0.987394	0.493697	+	0.869634i	$0.335645\pi$
$432$	186624.	0.0481125
$433$	1.51812e6	0.389122	0.194561	−	0.980890i	$-0.437672\pi$
$433$	1.51812e6	0.389122	0.194561	+	0.980890i	$0.437672\pi$
$434$	4.46391e6	1.13760
$435$	−1.67763e6	−0.425082
$436$	277035.	0.0697940
$437$	1.17460e6	0.294230
$438$	556120.	0.138511
$439$	1.62938e6	0.403515	0.201758	−	0.979435i	$-0.435335\pi$
$439$	1.62938e6	0.403515	0.201758	+	0.979435i	$0.435335\pi$
$440$	−35230.6	−0.00867537
$441$	311848.	0.0763565
$442$	1.58034e6	0.384766
$443$	1.04279e6	0.252458	0.126229	−	0.992001i	$-0.459713\pi$
$443$	1.04279e6	0.252458	0.126229	+	0.992001i	$0.459713\pi$
$444$	−1.37736e6	−0.331582
$445$	1.67294e6	0.400480
$446$	5.76366e6	1.37202
$447$	−2.40545e6	−0.569413
$448$	588699.	0.138579
$449$	295463.	0.0691653	0.0345826	−	0.999402i	$-0.488990\pi$
$449$	295463.	0.0691653	0.0345826	+	0.999402i	$0.488990\pi$
$450$	−202500.	−0.0471405
$451$	5502.00	0.00127374
$452$	420830.	0.0968858
$453$	2.50321e6	0.573128
$454$	−1.30147e6	−0.296343
$455$	−2.44339e6	−0.553304
$456$	207936.	0.0468293
$457$	2.30944e6	0.517269	0.258634	−	0.965975i	$-0.416727\pi$
$457$	2.30944e6	0.517269	0.258634	+	0.965975i	$0.416727\pi$
$458$	−3.37295e6	−0.751357
$459$	423546.	0.0938358
$460$	−1.30150e6	−0.286780
$461$	−5.54578e6	−1.21537	−0.607687	−	0.794176i	$-0.707903\pi$
$461$	−5.54578e6	−1.21537	−0.607687	+	0.794176i	$0.707903\pi$
$462$	−113929.	−0.0248331
$463$	2.98971e6	0.648152	0.324076	−	0.946031i	$-0.394947\pi$
$463$	2.98971e6	0.648152	0.324076	+	0.946031i	$0.394947\pi$
$464$	−1.90877e6	−0.411584
$465$	−1.74705e6	−0.374690
$466$	−1.90450e6	−0.406271
$467$	−4.75166e6	−1.00821	−0.504107	−	0.863641i	$-0.668178\pi$
$467$	−4.75166e6	−1.00821	−0.504107	+	0.863641i	$0.668178\pi$
$468$	−881301.	−0.185999
$469$	−8.66678e6	−1.81939
$470$	−2.22302e6	−0.464193
$471$	−3.95245e6	−0.820944
$472$	2.40648e6	0.497197
$473$	−208905.	−0.0429335
$474$	2.33424e6	0.477198
$475$	−225625.	−0.0458831
$476$	1.33606e6	0.270277
$477$	−2.23461e6	−0.449682
$478$	1.78460e6	0.357248
$479$	1.09533e6	0.218125	0.109063	−	0.994035i	$-0.465215\pi$
$479$	1.09533e6	0.218125	0.109063	+	0.994035i	$0.465215\pi$
$480$	−230400.	−0.0456435
$481$	6.50438e6	1.28187
$482$	7.00485e6	1.37335
$483$	−4.20881e6	−0.820903
$484$	−2.56906e6	−0.498495
$485$	−731438.	−0.141196
$486$	−236196.	−0.0453609
$487$	8.39100e6	1.60321	0.801607	−	0.597852i	$-0.203979\pi$
$487$	8.39100e6	1.60321	0.801607	+	0.597852i	$0.203979\pi$
$488$	−3.66768e6	−0.697175
$489$	−1.44017e6	−0.272358
$490$	−384997.	−0.0724381
$491$	5.04825e6	0.945012	0.472506	−	0.881328i	$-0.343350\pi$
$491$	5.04825e6	0.945012	0.472506	+	0.881328i	$0.343350\pi$
$492$	35981.9	0.00670148
$493$	−4.33198e6	−0.802729
$494$	−981943.	−0.181038
$495$	44588.7	0.00817922
$496$	−1.98775e6	−0.362792
$497$	5.11892e6	0.929581
$498$	−2.68582e6	−0.485293
$499$	−7.74716e6	−1.39281	−0.696404	−	0.717650i	$-0.745218\pi$
$499$	−7.74716e6	−1.39281	−0.696404	+	0.717650i	$0.745218\pi$
$500$	250000.	0.0447214
$501$	−5.01599e6	−0.892818
$502$	6.23629e6	1.10450
$503$	−2.25073e6	−0.396646	−0.198323	−	0.980137i	$-0.563550\pi$
$503$	−2.25073e6	−0.396646	−0.198323	+	0.980137i	$0.563550\pi$
$504$	−745072.	−0.130654
$505$	−803291.	−0.140166
$506$	286579.	0.0497585
$507$	820162.	0.141703
$508$	5.04119e6	0.866710
$509$	4.23673e6	0.724830	0.362415	−	0.932017i	$-0.381952\pi$
$509$	4.23673e6	0.724830	0.362415	+	0.932017i	$0.381952\pi$
$510$	−522896.	−0.0890204
$511$	−2.22024e6	−0.376138
$512$	−262144.	−0.0441942
$513$	−263169.	−0.0441511
$514$	2.64587e6	0.441734
$515$	3.15508e6	0.524195
$516$	−1.36619e6	−0.225885
$517$	489489.	0.0805410
$518$	5.49895e6	0.900441
$519$	−2.71211e6	−0.441966
$520$	1.08803e6	0.176454
$521$	7.23853e6	1.16831	0.584153	−	0.811644i	$-0.301427\pi$
$521$	7.23853e6	1.16831	0.584153	+	0.811644i	$0.301427\pi$
$522$	2.41579e6	0.388045
$523$	−9.10216e6	−1.45509	−0.727546	−	0.686059i	$-0.759339\pi$
$523$	−9.10216e6	−1.45509	−0.727546	+	0.686059i	$0.759339\pi$
$524$	−419524.	−0.0667466
$525$	808455.	0.128014
$526$	−2.92863e6	−0.461531
$527$	−4.51122e6	−0.707567
$528$	50732.0	0.00791949
$529$	4.15054e6	0.644859
$530$	2.75878e6	0.426606
$531$	−3.04571e6	−0.468761
$532$	−830158.	−0.127169
$533$	−169918.	−0.0259073
$534$	−2.40904e6	−0.365587
$535$	4.57629e6	0.691241
$536$	3.85927e6	0.580220
$537$	−2.10545e6	−0.315071
$538$	−8.71214e6	−1.29768
$539$	84772.9	0.0125686
$540$	291600.	0.0430331
$541$	1.00483e7	1.47604	0.738021	−	0.674777i	$-0.235760\pi$
$541$	1.00483e7	1.47604	0.738021	+	0.674777i	$0.235760\pi$
$542$	−8.39141e6	−1.22698
$543$	−950873.	−0.138396
$544$	−594939.	−0.0861936
$545$	432867.	0.0624257
$546$	3.51848e6	0.505096
$547$	−8.03154e6	−1.14771	−0.573853	−	0.818959i	$-0.694552\pi$
$547$	−8.03154e6	−1.14771	−0.573853	+	0.818959i	$0.694552\pi$
$548$	1.44118e6	0.205006
$549$	4.64191e6	0.657303
$550$	−55047.8	−0.00775949
$551$	2.69166e6	0.377695
$552$	1.87416e6	0.261793
$553$	−9.31914e6	−1.29587
$554$	−5.34828e6	−0.740355
$555$	−2.15213e6	−0.296576
$556$	−1.87819e6	−0.257663
$557$	−4.09033e6	−0.558625	−0.279312	−	0.960200i	$-0.590106\pi$
$557$	−4.09033e6	−0.558625	−0.279312	+	0.960200i	$0.590106\pi$
$558$	2.51575e6	0.342043
$559$	6.45162e6	0.873251
$560$	919842.	0.123949
$561$	115137.	0.0154457
$562$	−6.16291e6	−0.823086
$563$	−9.08566e6	−1.20805	−0.604026	−	0.796965i	$-0.706438\pi$
$563$	−9.08566e6	−1.20805	−0.604026	+	0.796965i	$0.706438\pi$
$564$	3.20115e6	0.423749
$565$	657546.	0.0866573
$566$	8.03164e6	1.05381
$567$	942982.	0.123182
$568$	−2.27942e6	−0.296452
$569$	−2.12560e6	−0.275233	−0.137617	−	0.990486i	$-0.543944\pi$
$569$	−2.12560e6	−0.275233	−0.137617	+	0.990486i	$0.543944\pi$
$570$	324900.	0.0418854
$571$	−1.03919e7	−1.33384	−0.666919	−	0.745130i	$-0.732387\pi$
$571$	−1.03919e7	−1.33384	−0.666919	+	0.745130i	$0.732387\pi$
$572$	−239574.	−0.0306160
$573$	6.37734e6	0.811434
$574$	−143653.	−0.0181985
$575$	−2.03359e6	−0.256504
$576$	331776.	0.0416667
$577$	−6.81165e6	−0.851751	−0.425876	−	0.904782i	$-0.640034\pi$
$577$	−6.81165e6	−0.851751	−0.425876	+	0.904782i	$0.640034\pi$
$578$	4.32921e6	0.539000
$579$	−5.05084e6	−0.626134
$580$	−2.98245e6	−0.368132
$581$	1.07228e7	1.31786
$582$	1.05327e6	0.128894
$583$	−607458.	−0.0740193
$584$	988658.	0.119954
$585$	−1.37703e6	−0.166362
$586$	−2.33570e6	−0.280978
$587$	1.09929e7	1.31679	0.658396	−	0.752672i	$-0.271235\pi$
$587$	1.09929e7	1.31679	0.658396	+	0.752672i	$0.271235\pi$
$588$	554396.	0.0661267
$589$	2.80304e6	0.332921
$590$	3.76013e6	0.444706
$591$	2.90899e6	0.342590
$592$	−2.44865e6	−0.287159
$593$	−7.68633e6	−0.897599	−0.448799	−	0.893632i	$-0.648148\pi$
$593$	−7.68633e6	−0.897599	−0.448799	+	0.893632i	$0.648148\pi$
$594$	−64207.7	−0.00746657
$595$	2.08759e6	0.241743
$596$	−4.27635e6	−0.493126
$597$	1.28481e6	0.147538
$598$	−8.85041e6	−1.01207
$599$	−1.36685e7	−1.55652	−0.778260	−	0.627942i	$-0.783898\pi$
$599$	−1.36685e7	−1.55652	−0.778260	+	0.627942i	$0.783898\pi$
$600$	−360000.	−0.0408248
$601$	1.34784e7	1.52213	0.761065	−	0.648676i	$-0.224677\pi$
$601$	1.34784e7	1.52213	0.761065	+	0.648676i	$0.224677\pi$
$602$	5.45434e6	0.613411
$603$	−4.88438e6	−0.547037
$604$	4.45015e6	0.496343
$605$	−4.01415e6	−0.445867
$606$	1.15674e6	0.127954
$607$	−9.50207e6	−1.04676	−0.523379	−	0.852100i	$-0.675329\pi$
$607$	−9.50207e6	−1.04676	−0.523379	+	0.852100i	$0.675329\pi$
$608$	369664.	0.0405554
$609$	−9.64471e6	−1.05377
$610$	−5.73075e6	−0.623572
$611$	−1.51169e7	−1.63817
$612$	752970.	0.0812642
$613$	−1.01982e7	−1.09616	−0.548079	−	0.836426i	$-0.684641\pi$
$613$	−1.01982e7	−1.09616	−0.548079	+	0.836426i	$0.684641\pi$
$614$	1.43674e6	0.153801
$615$	56221.6	0.00599399
$616$	−202541.	−0.0215061
$617$	−1.50295e6	−0.158939	−0.0794695	−	0.996837i	$-0.525323\pi$
$617$	−1.50295e6	−0.158939	−0.0794695	+	0.996837i	$0.525323\pi$
$618$	−4.54332e6	−0.478522
$619$	−1.13727e7	−1.19299	−0.596494	−	0.802618i	$-0.703440\pi$
$619$	−1.13727e7	−1.19299	−0.596494	+	0.802618i	$0.703440\pi$
$620$	−3.10586e6	−0.324491
$621$	−2.37198e6	−0.246821
$622$	−3.52780e6	−0.365618
$623$	9.61777e6	0.992782
$624$	−1.56676e6	−0.161080
$625$	390625.	0.0400000
$626$	1.17553e7	1.19895
$627$	−71540.1	−0.00726743
$628$	−7.02657e6	−0.710959
$629$	−5.55724e6	−0.560057
$630$	−1.16418e6	−0.116860
$631$	7.08095e6	0.707976	0.353988	−	0.935250i	$-0.384825\pi$
$631$	7.08095e6	0.707976	0.353988	+	0.935250i	$0.384825\pi$
$632$	4.14975e6	0.413266
$633$	−7.84420e6	−0.778107
$634$	−2.34889e6	−0.232081
$635$	7.87686e6	0.775209
$636$	−3.97264e6	−0.389436
$637$	−2.61804e6	−0.255640
$638$	656709.	0.0638736
$639$	2.88490e6	0.279497
$640$	−409600.	−0.0395285
$641$	3.61749e6	0.347746	0.173873	−	0.984768i	$-0.444372\pi$
$641$	3.61749e6	0.347746	0.173873	+	0.984768i	$0.444372\pi$
$642$	−6.58986e6	−0.631014
$643$	1.76233e7	1.68097	0.840486	−	0.541834i	$-0.182270\pi$
$643$	1.76233e7	1.68097	0.840486	+	0.541834i	$0.182270\pi$
$644$	−7.48234e6	−0.710923
$645$	−2.13468e6	−0.202038
$646$	838957.	0.0790967
$647$	6.00238e6	0.563719	0.281860	−	0.959456i	$-0.409049\pi$
$647$	6.00238e6	0.563719	0.281860	+	0.959456i	$0.409049\pi$
$648$	−419904.	−0.0392837
$649$	−827948.	−0.0771598
$650$	1.70004e6	0.157825
$651$	−1.00438e7	−0.928849
$652$	−2.56030e6	−0.235869
$653$	3.11144e6	0.285548	0.142774	−	0.989755i	$-0.454398\pi$
$653$	3.11144e6	0.285548	0.142774	+	0.989755i	$0.454398\pi$
$654$	−623328.	−0.0569866
$655$	−655507.	−0.0597000
$656$	63967.7	0.00580365
$657$	−1.25127e6	−0.113093
$658$	−1.27802e7	−1.15073
$659$	1.99394e7	1.78854	0.894271	−	0.447525i	$-0.147694\pi$
$659$	1.99394e7	1.78854	0.894271	+	0.447525i	$0.147694\pi$
$660$	79268.8	0.00708341
$661$	7.46117e6	0.664207	0.332103	−	0.943243i	$-0.392242\pi$
$661$	7.46117e6	0.664207	0.332103	+	0.943243i	$0.392242\pi$
$662$	−9.83174e6	−0.871938
$663$	−3.55578e6	−0.314160
$664$	−4.77480e6	−0.420276
$665$	−1.29712e6	−0.113743
$666$	3.09907e6	0.270736
$667$	2.42604e7	2.11146
$668$	−8.91732e6	−0.773203
$669$	−1.29682e7	−1.12025
$670$	6.03010e6	0.518964
$671$	1.26186e6	0.108194
$672$	−1.32457e6	−0.113149
$673$	8.44956e6	0.719112	0.359556	−	0.933124i	$-0.382928\pi$
$673$	8.44956e6	0.719112	0.359556	+	0.933124i	$0.382928\pi$
$674$	−1.03735e7	−0.879583
$675$	455625.	0.0384900
$676$	1.45807e6	0.122719
$677$	−1.62729e6	−0.136456	−0.0682281	−	0.997670i	$-0.521735\pi$
$677$	−1.62729e6	−0.136456	−0.0682281	+	0.997670i	$0.521735\pi$
$678$	−946867.	−0.0791070
$679$	−4.20505e6	−0.350023
$680$	−929592.	−0.0770939
$681$	2.92831e6	0.241963
$682$	683882.	0.0563016
$683$	−2.67908e6	−0.219752	−0.109876	−	0.993945i	$-0.535045\pi$
$683$	−2.67908e6	−0.219752	−0.109876	+	0.993945i	$0.535045\pi$
$684$	−467856.	−0.0382360
$685$	2.25185e6	0.183363
$686$	7.44901e6	0.604350
$687$	7.58914e6	0.613480
$688$	−2.42879e6	−0.195622
$689$	1.87601e7	1.50552
$690$	2.92837e6	0.234155
$691$	−2.05719e7	−1.63900	−0.819501	−	0.573078i	$-0.805749\pi$
$691$	−2.05719e7	−1.63900	−0.819501	+	0.573078i	$0.805749\pi$
$692$	−4.82153e6	−0.382754
$693$	256341.	0.0202761
$694$	6.77291e6	0.533798
$695$	−2.93467e6	−0.230461
$696$	4.29473e6	0.336057
$697$	145176.	0.0113191
$698$	8.86771e6	0.688927
$699$	4.28512e6	0.331719
$700$	1.43725e6	0.110863
$701$	−9.79995e6	−0.753232	−0.376616	−	0.926369i	$-0.622912\pi$
$701$	−9.79995e6	−0.753232	−0.376616	+	0.926369i	$0.622912\pi$
$702$	1.98293e6	0.151867
$703$	3.45298e6	0.263515
$704$	90190.3	0.00685848
$705$	5.00180e6	0.379012
$706$	7.65883e6	0.578297
$707$	−4.61813e6	−0.347470
$708$	−5.41459e6	−0.405959
$709$	7.31084e6	0.546200	0.273100	−	0.961986i	$-0.411951\pi$
$709$	7.31084e6	0.546200	0.273100	+	0.961986i	$0.411951\pi$
$710$	−3.56160e6	−0.265155
$711$	−5.25203e6	−0.389631
$712$	−4.28273e6	−0.316607
$713$	2.52642e7	1.86115
$714$	−3.00613e6	−0.220680
$715$	−374334.	−0.0273838
$716$	−3.74302e6	−0.272860
$717$	−4.01534e6	−0.291692
$718$	−1.86218e7	−1.34806
$719$	−1.52312e7	−1.09878	−0.549391	−	0.835565i	$-0.685140\pi$
$719$	−1.52312e7	−1.09878	−0.549391	+	0.835565i	$0.685140\pi$
$720$	518400.	0.0372678
$721$	1.81386e7	1.29947
$722$	−521284.	−0.0372161
$723$	−1.57609e7	−1.12134
$724$	−1.69044e6	−0.119854
$725$	−4.66008e6	−0.329267
$726$	5.78038e6	0.407019
$727$	−1.06432e7	−0.746853	−0.373426	−	0.927660i	$-0.621817\pi$
$727$	−1.06432e7	−0.746853	−0.373426	+	0.927660i	$0.621817\pi$
$728$	6.25508e6	0.437426
$729$	531441.	0.0370370
$730$	1.54478e6	0.107290
$731$	−5.51216e6	−0.381530
$732$	8.25228e6	0.569241
$733$	−2.67212e6	−0.183694	−0.0918472	−	0.995773i	$-0.529277\pi$
$733$	−2.67212e6	−0.183694	−0.0918472	+	0.995773i	$0.529277\pi$
$734$	1.17541e7	0.805284
$735$	866244.	0.0591455
$736$	3.33184e6	0.226720
$737$	−1.32777e6	−0.0900442
$738$	−80959.2	−0.00547174
$739$	1.44393e7	0.972602	0.486301	−	0.873791i	$-0.338346\pi$
$739$	1.44393e7	0.972602	0.486301	+	0.873791i	$0.338346\pi$
$740$	−3.82601e6	−0.256843
$741$	2.20937e6	0.147817
$742$	1.58602e7	1.05755
$743$	−2.73689e7	−1.81880	−0.909401	−	0.415921i	$-0.863459\pi$
$743$	−2.73689e7	−1.81880	−0.909401	+	0.415921i	$0.863459\pi$
$744$	4.47244e6	0.296218
$745$	−6.68180e6	−0.441065
$746$	3.31868e6	0.218332
$747$	6.04310e6	0.396240
$748$	204688.	0.0133764
$749$	2.63092e7	1.71357
$750$	−562500.	−0.0365148
$751$	7.55274e6	0.488658	0.244329	−	0.969692i	$-0.421432\pi$
$751$	7.55274e6	0.488658	0.244329	+	0.969692i	$0.421432\pi$
$752$	5.69093e6	0.366977
$753$	−1.40317e7	−0.901824
$754$	−2.02812e7	−1.29917
$755$	6.95335e6	0.443943
$756$	1.67641e6	0.106678
$757$	2.67285e6	0.169525	0.0847626	−	0.996401i	$-0.472987\pi$
$757$	2.67285e6	0.169525	0.0847626	+	0.996401i	$0.472987\pi$
$758$	−1.24801e7	−0.788944
$759$	−644802.	−0.0406277
$760$	577600.	0.0362738
$761$	56635.2	0.00354507	0.00177254	−	0.999998i	$-0.499436\pi$
$761$	56635.2	0.00354507	0.00177254	+	0.999998i	$0.499436\pi$
$762$	−1.13427e7	−0.707665
$763$	2.48856e6	0.154752
$764$	1.13375e7	0.702722
$765$	1.17652e6	0.0726849
$766$	−7.35710e6	−0.453038
$767$	2.55695e7	1.56940
$768$	589824.	0.0360844
$769$	3.64031e6	0.221984	0.110992	−	0.993821i	$-0.464597\pi$
$769$	3.64031e6	0.221984	0.110992	+	0.993821i	$0.464597\pi$
$770$	−316470.	−0.0192356
$771$	−5.95321e6	−0.360674
$772$	−8.97927e6	−0.542248
$773$	3.30328e6	0.198837	0.0994184	−	0.995046i	$-0.468302\pi$
$773$	3.30328e6	0.198837	0.0994184	+	0.995046i	$0.468302\pi$
$774$	3.07393e6	0.184434
$775$	−4.85290e6	−0.290233
$776$	1.87248e6	0.111625
$777$	−1.23726e7	−0.735207
$778$	−1.84881e6	−0.109507
$779$	−90204.5	−0.00532580
$780$	−2.44806e6	−0.144074
$781$	784232.	0.0460063
$782$	7.56165e6	0.442181
$783$	−5.43552e6	−0.316838
$784$	985593.	0.0572674
$785$	−1.09790e7	−0.635901
$786$	943930.	0.0544984
$787$	−9.58387e6	−0.551575	−0.275787	−	0.961219i	$-0.588939\pi$
$787$	−9.58387e6	−0.551575	−0.275787	+	0.961219i	$0.588939\pi$
$788$	5.17155e6	0.296691
$789$	6.58942e6	0.376838
$790$	6.48399e6	0.369636
$791$	3.78024e6	0.214822
$792$	−114147.	−0.00646624
$793$	−3.89700e7	−2.20063
$794$	2.09564e7	1.17968
$795$	−6.20725e6	−0.348322
$796$	2.28410e6	0.127771
$797$	2.39581e7	1.33600	0.667999	−	0.744162i	$-0.267151\pi$
$797$	2.39581e7	1.33600	0.667999	+	0.744162i	$0.267151\pi$
$798$	1.86785e6	0.103833
$799$	1.29156e7	0.715730
$800$	−640000.	−0.0353553
$801$	5.42033e6	0.298500
$802$	−5.31146e6	−0.291593
$803$	−340146.	−0.0186156
$804$	−8.68335e6	−0.473748
$805$	−1.16912e7	−0.635869
$806$	−2.11203e7	−1.14515
$807$	1.96023e7	1.05956
$808$	2.05642e6	0.110811
$809$	−1.56648e7	−0.841497	−0.420748	−	0.907177i	$-0.638232\pi$
$809$	−1.56648e7	−0.841497	−0.420748	+	0.907177i	$0.638232\pi$
$810$	−656100.	−0.0351364
$811$	1.02452e7	0.546978	0.273489	−	0.961875i	$-0.411822\pi$
$811$	1.02452e7	0.546978	0.273489	+	0.961875i	$0.411822\pi$
$812$	−1.71462e7	−0.912592
$813$	1.88807e7	1.00182
$814$	842454.	0.0445641
$815$	−4.00046e6	−0.210968
$816$	1.33861e6	0.0703768
$817$	3.42497e6	0.179515
$818$	−1.58430e7	−0.827855
$819$	−7.91658e6	−0.412409
$820$	99949.6	0.00519094
$821$	−3.15417e7	−1.63316	−0.816578	−	0.577235i	$-0.804132\pi$
$821$	−3.15417e7	−1.63316	−0.816578	+	0.577235i	$0.804132\pi$
$822$	−3.24266e6	−0.167387
$823$	1.51207e7	0.778165	0.389082	−	0.921203i	$-0.372792\pi$
$823$	1.51207e7	0.778165	0.389082	+	0.921203i	$0.372792\pi$
$824$	−8.07702e6	−0.414413
$825$	123857.	0.00633560
$826$	2.16170e7	1.10242
$827$	−1.05641e7	−0.537117	−0.268559	−	0.963263i	$-0.586547\pi$
$827$	−1.05641e7	−0.537117	−0.268559	+	0.963263i	$0.586547\pi$
$828$	−4.21686e6	−0.213753
$829$	1.33956e7	0.676982	0.338491	−	0.940970i	$-0.390083\pi$
$829$	1.33956e7	0.676982	0.338491	+	0.940970i	$0.390083\pi$
$830$	−7.46062e6	−0.375906
$831$	1.20336e7	0.604497
$832$	−2.78535e6	−0.139499
$833$	2.23681e6	0.111691
$834$	4.22593e6	0.210381
$835$	−1.39333e7	−0.691574
$836$	−127182.	−0.00629378
$837$	−5.66043e6	−0.279277
$838$	−2.79352e7	−1.37417
$839$	−796951.	−0.0390865	−0.0195432	−	0.999809i	$-0.506221\pi$
$839$	−796951.	−0.0390865	−0.0195432	+	0.999809i	$0.506221\pi$
$840$	−2.06964e6	−0.101204
$841$	3.50827e7	1.71042
$842$	1.82678e7	0.887984
$843$	1.38666e7	0.672047
$844$	−1.39452e7	−0.673861
$845$	2.27823e6	0.109763
$846$	−7.20259e6	−0.345989
$847$	−2.30774e7	−1.10530
$848$	−7.06247e6	−0.337262
$849$	−1.80712e7	−0.860434
$850$	−1.45249e6	−0.0689549
$851$	3.11222e7	1.47315
$852$	5.12870e6	0.242052
$853$	−1.36872e7	−0.644082	−0.322041	−	0.946726i	$-0.604369\pi$
$853$	−1.36872e7	−0.644082	−0.322041	+	0.946726i	$0.604369\pi$
$854$	−3.29461e7	−1.54582
$855$	−731025.	−0.0341993
$856$	−1.17153e7	−0.546474
$857$	−3.33046e7	−1.54900	−0.774502	−	0.632572i	$-0.781999\pi$
$857$	−3.33046e7	−1.54900	−0.774502	+	0.632572i	$0.781999\pi$
$858$	539041.	0.0249979
$859$	−2.34430e7	−1.08400	−0.542000	−	0.840378i	$-0.682333\pi$
$859$	−2.34430e7	−1.08400	−0.542000	+	0.840378i	$0.682333\pi$
$860$	−3.79498e6	−0.174970
$861$	323219.	0.0148590
$862$	−1.52315e7	−0.698193
$863$	−2.89647e7	−1.32386	−0.661931	−	0.749565i	$-0.730263\pi$
$863$	−2.89647e7	−1.32386	−0.661931	+	0.749565i	$0.730263\pi$
$864$	−746496.	−0.0340207
$865$	−7.53364e6	−0.342345
$866$	−6.07246e6	−0.275150
$867$	−9.74071e6	−0.440092
$868$	−1.78556e7	−0.804407
$869$	−1.42772e6	−0.0641347
$870$	6.71052e6	0.300578
$871$	4.10057e7	1.83146
$872$	−1.10814e6	−0.0493518
$873$	−2.36986e6	−0.105241
$874$	−4.69841e6	−0.208052
$875$	2.24571e6	0.0991592
$876$	−2.22448e6	−0.0979418
$877$	6.78348e6	0.297820	0.148910	−	0.988851i	$-0.452424\pi$
$877$	6.78348e6	0.297820	0.148910	+	0.988851i	$0.452424\pi$
$878$	−6.51750e6	−0.285328
$879$	5.25532e6	0.229418
$880$	140922.	0.00613441
$881$	3.15359e7	1.36888	0.684440	−	0.729069i	$-0.260047\pi$
$881$	3.15359e7	1.36888	0.684440	+	0.729069i	$0.260047\pi$
$882$	−1.24739e6	−0.0539922
$883$	1.24848e7	0.538867	0.269433	−	0.963019i	$-0.413164\pi$
$883$	1.24848e7	0.538867	0.269433	+	0.963019i	$0.413164\pi$
$884$	−6.32138e6	−0.272070
$885$	−8.46030e6	−0.363101
$886$	−4.17118e6	−0.178515
$887$	−3.59436e7	−1.53396	−0.766978	−	0.641673i	$-0.778241\pi$
$887$	−3.59436e7	−1.53396	−0.766978	+	0.641673i	$0.778241\pi$
$888$	5.50946e6	0.234464
$889$	4.52841e7	1.92173
$890$	−6.69177e6	−0.283182
$891$	144467.	0.00609643
$892$	−2.30547e7	−0.970167
$893$	−8.02511e6	−0.336761
$894$	9.62179e6	0.402636
$895$	−5.84847e6	−0.244053
$896$	−2.35480e6	−0.0979903
$897$	1.99134e7	0.826351
$898$	−1.18185e6	−0.0489072
$899$	5.78942e7	2.38911
$900$	810000.	0.0333333
$901$	−1.60284e7	−0.657775
$902$	−22008.0	−0.000900667 0
$903$	−1.22723e7	−0.500848
$904$	−1.68332e6	−0.0685086
$905$	−2.64131e6	−0.107201
$906$	−1.00128e7	−0.405262
$907$	4.08079e7	1.64712	0.823561	−	0.567228i	$-0.191984\pi$
$907$	4.08079e7	1.64712	0.823561	+	0.567228i	$0.191984\pi$
$908$	5.20588e6	0.209546
$909$	−2.60266e6	−0.104474
$910$	9.77356e6	0.391245
$911$	−3.58807e7	−1.43240	−0.716200	−	0.697895i	$-0.754120\pi$
$911$	−3.58807e7	−1.43240	−0.716200	+	0.697895i	$0.754120\pi$
$912$	−831744.	−0.0331133
$913$	1.64276e6	0.0652225
$914$	−9.23776e6	−0.365764
$915$	1.28942e7	0.509145
$916$	1.34918e7	0.531289
$917$	−3.76852e6	−0.147995
$918$	−1.69418e6	−0.0663519
$919$	8.74659e6	0.341625	0.170813	−	0.985304i	$-0.445361\pi$
$919$	8.74659e6	0.341625	0.170813	+	0.985304i	$0.445361\pi$
$920$	5.20600e6	0.202784
$921$	−3.23267e6	−0.125578
$922$	2.21831e7	0.859400
$923$	−2.42195e7	−0.935751
$924$	455717.	0.0175596
$925$	−5.97814e6	−0.229727
$926$	−1.19588e7	−0.458313
$927$	1.02225e7	0.390712
$928$	7.63508e6	0.291034
$929$	7.51249e6	0.285591	0.142796	−	0.989752i	$-0.454391\pi$
$929$	7.51249e6	0.285591	0.142796	+	0.989752i	$0.454391\pi$
$930$	6.98818e6	0.264946
$931$	−1.38984e6	−0.0525521
$932$	7.61800e6	0.287277
$933$	7.93755e6	0.298526
$934$	1.90066e7	0.712916
$935$	319825.	0.0119642
$936$	3.52520e6	0.131521
$937$	−2.96117e7	−1.10183	−0.550915	−	0.834561i	$-0.685721\pi$
$937$	−2.96117e7	−1.10183	−0.550915	+	0.834561i	$0.685721\pi$
$938$	3.46671e7	1.28650
$939$	−2.64495e7	−0.978935
$940$	8.89208e6	0.328234
$941$	2.69305e7	0.991451	0.495725	−	0.868479i	$-0.334902\pi$
$941$	2.69305e7	0.991451	0.495725	+	0.868479i	$0.334902\pi$
$942$	1.58098e7	0.580495
$943$	−813027.	−0.0297732
$944$	−9.62594e6	−0.351571
$945$	2.61939e6	0.0954160
$946$	835620.	0.0303586
$947$	−4.37665e7	−1.58587	−0.792934	−	0.609307i	$-0.791448\pi$
$947$	−4.37665e7	−1.58587	−0.792934	+	0.609307i	$0.791448\pi$
$948$	−9.33695e6	−0.337430
$949$	1.05047e7	0.378634
$950$	902500.	0.0324443
$951$	5.28501e6	0.189494
$952$	−5.34424e6	−0.191114
$953$	−2.79465e7	−0.996770	−0.498385	−	0.866956i	$-0.666073\pi$
$953$	−2.79465e7	−0.996770	−0.498385	+	0.866956i	$0.666073\pi$
$954$	8.93844e6	0.317973
$955$	1.77148e7	0.628534
$956$	−7.13838e6	−0.252613
$957$	−1.47760e6	−0.0521526
$958$	−4.38132e6	−0.154238
$959$	1.29459e7	0.454554
$960$	921600.	0.0322749
$961$	3.16606e7	1.10589
$962$	−2.60175e7	−0.906417
$963$	1.48272e7	0.515221
$964$	−2.80194e7	−0.971105
$965$	−1.40301e7	−0.485001
$966$	1.68353e7	0.580466
$967$	3.58420e7	1.23261	0.616305	−	0.787507i	$-0.288629\pi$
$967$	3.58420e7	1.23261	0.616305	+	0.787507i	$0.288629\pi$
$968$	1.02762e7	0.352489
$969$	−1.88765e6	−0.0645822
$970$	2.92575e6	0.0998408
$971$	1.06495e7	0.362478	0.181239	−	0.983439i	$-0.441989\pi$
$971$	1.06495e7	0.362478	0.181239	+	0.983439i	$0.441989\pi$
$972$	944784.	0.0320750
$973$	−1.68715e7	−0.571309
$974$	−3.35640e7	−1.13364
$975$	−3.82509e6	−0.128864
$976$	1.46707e7	0.492977
$977$	3.97785e7	1.33325	0.666626	−	0.745392i	$-0.267738\pi$
$977$	3.97785e7	1.33325	0.666626	+	0.745392i	$0.267738\pi$
$978$	5.76067e6	0.192586
$979$	1.47347e6	0.0491342
$980$	1.53999e6	0.0512215
$981$	1.40249e6	0.0465293
$982$	−2.01930e7	−0.668224
$983$	1.77849e6	0.0587039	0.0293519	−	0.999569i	$-0.490656\pi$
$983$	1.77849e6	0.0587039	0.0293519	+	0.999569i	$0.490656\pi$
$984$	−143927.	−0.00473866
$985$	8.08054e6	0.265369
$986$	1.73279e7	0.567615
$987$	2.87554e7	0.939564
$988$	3.92777e6	0.128013
$989$	3.08698e7	1.00356
$990$	−178355.	−0.00578358
$991$	4.04276e7	1.30766	0.653829	−	0.756642i	$-0.273162\pi$
$991$	4.04276e7	1.30766	0.653829	+	0.756642i	$0.273162\pi$
$992$	7.95100e6	0.256533
$993$	2.21214e7	0.711934
$994$	−2.04757e7	−0.657313
$995$	3.56891e6	0.114282
$996$	1.07433e7	0.343154
$997$	−1.68285e7	−0.536175	−0.268088	−	0.963395i	$-0.586392\pi$
$997$	−1.68285e7	−0.536175	−0.268088	+	0.963395i	$0.586392\pi$
$998$	3.09886e7	0.984864
$999$	−6.97291e6	−0.221055

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.6.a.l.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.6.a.l.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +143.725 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +143.725 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} +22.0191 q^{11} +144.000 q^{12} -680.016 q^{13} -574.901 q^{14} +225.000 q^{15} +256.000 q^{16} +580.995 q^{17} -324.000 q^{18} -361.000 q^{19} +400.000 q^{20} +1293.53 q^{21} -88.0764 q^{22} -3253.75 q^{23} -576.000 q^{24} +625.000 q^{25} +2720.07 q^{26} +729.000 q^{27} +2299.61 q^{28} -7456.13 q^{29} -900.000 q^{30} -7764.65 q^{31} -1024.00 q^{32} +198.172 q^{33} -2323.98 q^{34} +3593.13 q^{35} +1296.00 q^{36} -9565.03 q^{37} +1444.00 q^{38} -6120.15 q^{39} -1600.00 q^{40} +249.874 q^{41} -5174.11 q^{42} -9487.44 q^{43} +352.306 q^{44} +2025.00 q^{45} +13015.0 q^{46} +22230.2 q^{47} +2304.00 q^{48} +3849.97 q^{49} -2500.00 q^{50} +5228.96 q^{51} -10880.3 q^{52} -27587.8 q^{53} -2916.00 q^{54} +550.478 q^{55} -9198.42 q^{56} -3249.00 q^{57} +29824.5 q^{58} -37601.3 q^{59} +3600.00 q^{60} +57307.5 q^{61} +31058.6 q^{62} +11641.8 q^{63} +4096.00 q^{64} -17000.4 q^{65} -792.688 q^{66} -60301.0 q^{67} +9295.92 q^{68} -29283.7 q^{69} -14372.5 q^{70} +35616.0 q^{71} -5184.00 q^{72} -15447.8 q^{73} +38260.1 q^{74} +5625.00 q^{75} -5776.00 q^{76} +3164.70 q^{77} +24480.6 q^{78} -64839.9 q^{79} +6400.00 q^{80} +6561.00 q^{81} -999.496 q^{82} +74606.2 q^{83} +20696.4 q^{84} +14524.9 q^{85} +37949.8 q^{86} -67105.2 q^{87} -1409.22 q^{88} +66917.7 q^{89} -8100.00 q^{90} -97735.6 q^{91} -52060.0 q^{92} -69881.8 q^{93} -88920.8 q^{94} -9025.00 q^{95} -9216.00 q^{96} -29257.5 q^{97} -15399.9 q^{98} +1783.55 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} - 26 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 + 100 * q^5 - 144 * q^6 - 26 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} - 26 q^{7} - 256 q^{8} + 324 q^{9} - 400 q^{10} - 336 q^{11} + 576 q^{12} - 734 q^{13} + 104 q^{14} + 900 q^{15} + 1024 q^{16} + 480 q^{17} - 1296 q^{18} - 1444 q^{19} + 1600 q^{20} - 234 q^{21} + 1344 q^{22} - 1962 q^{23} - 2304 q^{24} + 2500 q^{25} + 2936 q^{26} + 2916 q^{27} - 416 q^{28} - 8720 q^{29} - 3600 q^{30} - 240 q^{31} - 4096 q^{32} - 3024 q^{33} - 1920 q^{34} - 650 q^{35} + 5184 q^{36} - 14626 q^{37} + 5776 q^{38} - 6606 q^{39} - 6400 q^{40} - 11092 q^{41} + 936 q^{42} - 16778 q^{43} - 5376 q^{44} + 8100 q^{45} + 7848 q^{46} - 34810 q^{47} + 9216 q^{48} - 34032 q^{49} - 10000 q^{50} + 4320 q^{51} - 11744 q^{52} - 18186 q^{53} - 11664 q^{54} - 8400 q^{55} + 1664 q^{56} - 12996 q^{57} + 34880 q^{58} - 38700 q^{59} + 14400 q^{60} - 12080 q^{61} + 960 q^{62} - 2106 q^{63} + 16384 q^{64} - 18350 q^{65} + 12096 q^{66} - 84216 q^{67} + 7680 q^{68} - 17658 q^{69} + 2600 q^{70} + 3592 q^{71} - 20736 q^{72} - 41180 q^{73} + 58504 q^{74} + 22500 q^{75} - 23104 q^{76} - 6696 q^{77} + 26424 q^{78} + 15272 q^{79} + 25600 q^{80} + 26244 q^{81} + 44368 q^{82} + 133106 q^{83} - 3744 q^{84} + 12000 q^{85} + 67112 q^{86} - 78480 q^{87} + 21504 q^{88} + 133704 q^{89} - 32400 q^{90} - 86656 q^{91} - 31392 q^{92} - 2160 q^{93} + 139240 q^{94} - 36100 q^{95} - 36864 q^{96} - 161594 q^{97} + 136128 q^{98} - 27216 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 + 100 * q^5 - 144 * q^6 - 26 * q^7 - 256 * q^8 + 324 * q^9 - 400 * q^10 - 336 * q^11 + 576 * q^12 - 734 * q^13 + 104 * q^14 + 900 * q^15 + 1024 * q^16 + 480 * q^17 - 1296 * q^18 - 1444 * q^19 + 1600 * q^20 - 234 * q^21 + 1344 * q^22 - 1962 * q^23 - 2304 * q^24 + 2500 * q^25 + 2936 * q^26 + 2916 * q^27 - 416 * q^28 - 8720 * q^29 - 3600 * q^30 - 240 * q^31 - 4096 * q^32 - 3024 * q^33 - 1920 * q^34 - 650 * q^35 + 5184 * q^36 - 14626 * q^37 + 5776 * q^38 - 6606 * q^39 - 6400 * q^40 - 11092 * q^41 + 936 * q^42 - 16778 * q^43 - 5376 * q^44 + 8100 * q^45 + 7848 * q^46 - 34810 * q^47 + 9216 * q^48 - 34032 * q^49 - 10000 * q^50 + 4320 * q^51 - 11744 * q^52 - 18186 * q^53 - 11664 * q^54 - 8400 * q^55 + 1664 * q^56 - 12996 * q^57 + 34880 * q^58 - 38700 * q^59 + 14400 * q^60 - 12080 * q^61 + 960 * q^62 - 2106 * q^63 + 16384 * q^64 - 18350 * q^65 + 12096 * q^66 - 84216 * q^67 + 7680 * q^68 - 17658 * q^69 + 2600 * q^70 + 3592 * q^71 - 20736 * q^72 - 41180 * q^73 + 58504 * q^74 + 22500 * q^75 - 23104 * q^76 - 6696 * q^77 + 26424 * q^78 + 15272 * q^79 + 25600 * q^80 + 26244 * q^81 + 44368 * q^82 + 133106 * q^83 - 3744 * q^84 + 12000 * q^85 + 67112 * q^86 - 78480 * q^87 + 21504 * q^88 + 133704 * q^89 - 32400 * q^90 - 86656 * q^91 - 31392 * q^92 - 2160 * q^93 + 139240 * q^94 - 36100 * q^95 - 36864 * q^96 - 161594 * q^97 + 136128 * q^98 - 27216 * q^99

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