LMFDB - Embedded newform 570.6.a.m.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("570.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$91.4187772934$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 39154x^{2} - 3172892x - 35506440 $ x^4 - x^3 - 39154x^2 - 3172892x - 35506440
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-128.214$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} -70.9208 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} -70.9208 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -424.457 q^{11} +144.000 q^{12} +434.708 q^{13} +283.683 q^{14} +225.000 q^{15} +256.000 q^{16} -1586.72 q^{17} -324.000 q^{18} +361.000 q^{19} +400.000 q^{20} -638.287 q^{21} +1697.83 q^{22} -59.0837 q^{23} -576.000 q^{24} +625.000 q^{25} -1738.83 q^{26} +729.000 q^{27} -1134.73 q^{28} -3146.64 q^{29} -900.000 q^{30} +1192.82 q^{31} -1024.00 q^{32} -3820.11 q^{33} +6346.87 q^{34} -1773.02 q^{35} +1296.00 q^{36} +6112.20 q^{37} -1444.00 q^{38} +3912.37 q^{39} -1600.00 q^{40} +17325.3 q^{41} +2553.15 q^{42} +3183.12 q^{43} -6791.32 q^{44} +2025.00 q^{45} +236.335 q^{46} +13572.7 q^{47} +2304.00 q^{48} -11777.2 q^{49} -2500.00 q^{50} -14280.5 q^{51} +6955.33 q^{52} +16309.1 q^{53} -2916.00 q^{54} -10611.4 q^{55} +4538.93 q^{56} +3249.00 q^{57} +12586.6 q^{58} -3875.52 q^{59} +3600.00 q^{60} +37196.6 q^{61} -4771.27 q^{62} -5744.58 q^{63} +4096.00 q^{64} +10867.7 q^{65} +15280.5 q^{66} +10788.2 q^{67} -25387.5 q^{68} -531.753 q^{69} +7092.08 q^{70} +45527.6 q^{71} -5184.00 q^{72} -23326.8 q^{73} -24448.8 q^{74} +5625.00 q^{75} +5776.00 q^{76} +30102.8 q^{77} -15649.5 q^{78} +30489.0 q^{79} +6400.00 q^{80} +6561.00 q^{81} -69301.0 q^{82} -51553.1 q^{83} -10212.6 q^{84} -39667.9 q^{85} -12732.5 q^{86} -28319.7 q^{87} +27165.3 q^{88} -61870.8 q^{89} -8100.00 q^{90} -30829.9 q^{91} -945.339 q^{92} +10735.4 q^{93} -54291.0 q^{94} +9025.00 q^{95} -9216.00 q^{96} +33681.5 q^{97} +47109.0 q^{98} -34381.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} + 268 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 + 268 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} + 268 q^{7} - 256 q^{8} + 324 q^{9} - 400 q^{10} + 338 q^{11} + 576 q^{12} + 1302 q^{13} - 1072 q^{14} + 900 q^{15} + 1024 q^{16} + 542 q^{17} - 1296 q^{18} + 1444 q^{19} + 1600 q^{20} + 2412 q^{21} - 1352 q^{22} - 88 q^{23} - 2304 q^{24} + 2500 q^{25} - 5208 q^{26} + 2916 q^{27} + 4288 q^{28} + 5014 q^{29} - 3600 q^{30} + 4962 q^{31} - 4096 q^{32} + 3042 q^{33} - 2168 q^{34} + 6700 q^{35} + 5184 q^{36} + 8022 q^{37} - 5776 q^{38} + 11718 q^{39} - 6400 q^{40} + 2764 q^{41} - 9648 q^{42} + 25346 q^{43} + 5408 q^{44} + 8100 q^{45} + 352 q^{46} + 10008 q^{47} + 9216 q^{48} + 37248 q^{49} - 10000 q^{50} + 4878 q^{51} + 20832 q^{52} - 224 q^{53} - 11664 q^{54} + 8450 q^{55} - 17152 q^{56} + 12996 q^{57} - 20056 q^{58} + 29654 q^{59} + 14400 q^{60} + 27276 q^{61} - 19848 q^{62} + 21708 q^{63} + 16384 q^{64} + 32550 q^{65} - 12168 q^{66} + 26024 q^{67} + 8672 q^{68} - 792 q^{69} - 26800 q^{70} - 26940 q^{71} - 20736 q^{72} - 60916 q^{73} - 32088 q^{74} + 22500 q^{75} + 23104 q^{76} - 21228 q^{77} - 46872 q^{78} + 34902 q^{79} + 25600 q^{80} + 26244 q^{81} - 11056 q^{82} - 48430 q^{83} + 38592 q^{84} + 13550 q^{85} - 101384 q^{86} + 45126 q^{87} - 21632 q^{88} - 38348 q^{89} - 32400 q^{90} + 69280 q^{91} - 1408 q^{92} + 44658 q^{93} - 40032 q^{94} + 36100 q^{95} - 36864 q^{96} + 45942 q^{97} - 148992 q^{98} + 27378 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 + 100 * q^5 - 144 * q^6 + 268 * q^7 - 256 * q^8 + 324 * q^9 - 400 * q^10 + 338 * q^11 + 576 * q^12 + 1302 * q^13 - 1072 * q^14 + 900 * q^15 + 1024 * q^16 + 542 * q^17 - 1296 * q^18 + 1444 * q^19 + 1600 * q^20 + 2412 * q^21 - 1352 * q^22 - 88 * q^23 - 2304 * q^24 + 2500 * q^25 - 5208 * q^26 + 2916 * q^27 + 4288 * q^28 + 5014 * q^29 - 3600 * q^30 + 4962 * q^31 - 4096 * q^32 + 3042 * q^33 - 2168 * q^34 + 6700 * q^35 + 5184 * q^36 + 8022 * q^37 - 5776 * q^38 + 11718 * q^39 - 6400 * q^40 + 2764 * q^41 - 9648 * q^42 + 25346 * q^43 + 5408 * q^44 + 8100 * q^45 + 352 * q^46 + 10008 * q^47 + 9216 * q^48 + 37248 * q^49 - 10000 * q^50 + 4878 * q^51 + 20832 * q^52 - 224 * q^53 - 11664 * q^54 + 8450 * q^55 - 17152 * q^56 + 12996 * q^57 - 20056 * q^58 + 29654 * q^59 + 14400 * q^60 + 27276 * q^61 - 19848 * q^62 + 21708 * q^63 + 16384 * q^64 + 32550 * q^65 - 12168 * q^66 + 26024 * q^67 + 8672 * q^68 - 792 * q^69 - 26800 * q^70 - 26940 * q^71 - 20736 * q^72 - 60916 * q^73 - 32088 * q^74 + 22500 * q^75 + 23104 * q^76 - 21228 * q^77 - 46872 * q^78 + 34902 * q^79 + 25600 * q^80 + 26244 * q^81 - 11056 * q^82 - 48430 * q^83 + 38592 * q^84 + 13550 * q^85 - 101384 * q^86 + 45126 * q^87 - 21632 * q^88 - 38348 * q^89 - 32400 * q^90 + 69280 * q^91 - 1408 * q^92 + 44658 * q^93 - 40032 * q^94 + 36100 * q^95 - 36864 * q^96 + 45942 * q^97 - 148992 * q^98 + 27378 * 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
$7$	−70.9208	−0.547052	−0.273526	−	0.961865i	$-0.588190\pi$
$7$	−70.9208	−0.547052	−0.273526	+	0.961865i	$0.588190\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	−100.000	−0.316228
$11$	−424.457	−1.05767	−0.528837	−	0.848723i	$-0.677372\pi$
$11$	−424.457	−1.05767	−0.528837	+	0.848723i	$0.677372\pi$
$12$	144.000	0.288675
$13$	434.708	0.713410	0.356705	−	0.934217i	$-0.383900\pi$
$13$	434.708	0.713410	0.356705	+	0.934217i	$0.383900\pi$
$14$	283.683	0.386824
$15$	225.000	0.258199
$16$	256.000	0.250000
$17$	−1586.72	−1.33161	−0.665805	−	0.746125i	$-0.731912\pi$
$17$	−1586.72	−1.33161	−0.665805	+	0.746125i	$0.731912\pi$
$18$	−324.000	−0.235702
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	400.000	0.223607
$21$	−638.287	−0.315841
$22$	1697.83	0.747889
$23$	−59.0837	−0.0232888	−0.0116444	−	0.999932i	$-0.503707\pi$
$23$	−59.0837	−0.0232888	−0.0116444	+	0.999932i	$0.503707\pi$
$24$	−576.000	−0.204124
$25$	625.000	0.200000
$26$	−1738.83	−0.504457
$27$	729.000	0.192450
$28$	−1134.73	−0.273526
$29$	−3146.64	−0.694787	−0.347394	−	0.937719i	$-0.612933\pi$
$29$	−3146.64	−0.694787	−0.347394	+	0.937719i	$0.612933\pi$
$30$	−900.000	−0.182574
$31$	1192.82	0.222931	0.111465	−	0.993768i	$-0.464446\pi$
$31$	1192.82	0.222931	0.111465	+	0.993768i	$0.464446\pi$
$32$	−1024.00	−0.176777
$33$	−3820.11	−0.610649
$34$	6346.87	0.941591
$35$	−1773.02	−0.244649
$36$	1296.00	0.166667
$37$	6112.20	0.733995	0.366998	−	0.930222i	$-0.380386\pi$
$37$	6112.20	0.733995	0.366998	+	0.930222i	$0.380386\pi$
$38$	−1444.00	−0.162221
$39$	3912.37	0.411888
$40$	−1600.00	−0.158114
$41$	17325.3	1.60961	0.804804	−	0.593541i	$-0.202271\pi$
$41$	17325.3	1.60961	0.804804	+	0.593541i	$0.202271\pi$
$42$	2553.15	0.223333
$43$	3183.12	0.262532	0.131266	−	0.991347i	$-0.458096\pi$
$43$	3183.12	0.262532	0.131266	+	0.991347i	$0.458096\pi$
$44$	−6791.32	−0.528837
$45$	2025.00	0.149071
$46$	236.335	0.0164677
$47$	13572.7	0.896238	0.448119	−	0.893974i	$-0.352094\pi$
$47$	13572.7	0.896238	0.448119	+	0.893974i	$0.352094\pi$
$48$	2304.00	0.144338
$49$	−11777.2	−0.700734
$50$	−2500.00	−0.141421
$51$	−14280.5	−0.768806
$52$	6955.33	0.356705
$53$	16309.1	0.797517	0.398758	−	0.917056i	$-0.369441\pi$
$53$	16309.1	0.797517	0.398758	+	0.917056i	$0.369441\pi$
$54$	−2916.00	−0.136083
$55$	−10611.4	−0.473007
$56$	4538.93	0.193412
$57$	3249.00	0.132453
$58$	12586.6	0.491289
$59$	−3875.52	−0.144944	−0.0724720	−	0.997370i	$-0.523089\pi$
$59$	−3875.52	−0.144944	−0.0724720	+	0.997370i	$0.523089\pi$
$60$	3600.00	0.129099
$61$	37196.6	1.27991	0.639955	−	0.768413i	$-0.278953\pi$
$61$	37196.6	1.27991	0.639955	+	0.768413i	$0.278953\pi$
$62$	−4771.27	−0.157636
$63$	−5744.58	−0.182351
$64$	4096.00	0.125000
$65$	10867.7	0.319047
$66$	15280.5	0.431794
$67$	10788.2	0.293604	0.146802	−	0.989166i	$-0.453102\pi$
$67$	10788.2	0.293604	0.146802	+	0.989166i	$0.453102\pi$
$68$	−25387.5	−0.665805
$69$	−531.753	−0.0134458
$70$	7092.08	0.172993
$71$	45527.6	1.07184	0.535919	−	0.844269i	$-0.319965\pi$
$71$	45527.6	1.07184	0.535919	+	0.844269i	$0.319965\pi$
$72$	−5184.00	−0.117851
$73$	−23326.8	−0.512329	−0.256164	−	0.966633i	$-0.582459\pi$
$73$	−23326.8	−0.512329	−0.256164	+	0.966633i	$0.582459\pi$
$74$	−24448.8	−0.519013
$75$	5625.00	0.115470
$76$	5776.00	0.114708
$77$	30102.8	0.578603
$78$	−15649.5	−0.291249
$79$	30489.0	0.549636	0.274818	−	0.961496i	$-0.411382\pi$
$79$	30489.0	0.549636	0.274818	+	0.961496i	$0.411382\pi$
$80$	6400.00	0.111803
$81$	6561.00	0.111111
$82$	−69301.0	−1.13816
$83$	−51553.1	−0.821410	−0.410705	−	0.911768i	$-0.634717\pi$
$83$	−51553.1	−0.821410	−0.410705	+	0.911768i	$0.634717\pi$
$84$	−10212.6	−0.157920
$85$	−39667.9	−0.595515
$86$	−12732.5	−0.185638
$87$	−28319.7	−0.401136
$88$	27165.3	0.373945
$89$	−61870.8	−0.827962	−0.413981	−	0.910285i	$-0.635862\pi$
$89$	−61870.8	−0.827962	−0.413981	+	0.910285i	$0.635862\pi$
$90$	−8100.00	−0.105409
$91$	−30829.9	−0.390272
$92$	−945.339	−0.0116444
$93$	10735.4	0.128709
$94$	−54291.0	−0.633736
$95$	9025.00	0.102598
$96$	−9216.00	−0.102062
$97$	33681.5	0.363465	0.181732	−	0.983348i	$-0.441830\pi$
$97$	33681.5	0.363465	0.181732	+	0.983348i	$0.441830\pi$
$98$	47109.0	0.495494
$99$	−34381.0	−0.352558
$100$	10000.0	0.100000
$101$	−8942.61	−0.0872290	−0.0436145	−	0.999048i	$-0.513887\pi$
$101$	−8942.61	−0.0872290	−0.0436145	+	0.999048i	$0.513887\pi$
$102$	57121.8	0.543628
$103$	−49830.9	−0.462813	−0.231407	−	0.972857i	$-0.574333\pi$
$103$	−49830.9	−0.462813	−0.231407	+	0.972857i	$0.574333\pi$
$104$	−27821.3	−0.252229
$105$	−15957.2	−0.141248
$106$	−65236.3	−0.563929
$107$	190999.	1.61277	0.806383	−	0.591394i	$-0.201422\pi$
$107$	190999.	1.61277	0.806383	+	0.591394i	$0.201422\pi$
$108$	11664.0	0.0962250
$109$	−30577.0	−0.246507	−0.123253	−	0.992375i	$-0.539333\pi$
$109$	−30577.0	−0.246507	−0.123253	+	0.992375i	$0.539333\pi$
$110$	42445.7	0.334466
$111$	55009.8	0.423772
$112$	−18155.7	−0.136763
$113$	−117520.	−0.865799	−0.432900	−	0.901442i	$-0.642510\pi$
$113$	−117520.	−0.865799	−0.432900	+	0.901442i	$0.642510\pi$
$114$	−12996.0	−0.0936586
$115$	−1477.09	−0.0104151
$116$	−50346.2	−0.347394
$117$	35211.4	0.237803
$118$	15502.1	0.102491
$119$	112531.	0.728460
$120$	−14400.0	−0.0912871
$121$	19112.9	0.118676
$122$	−148787.	−0.905032
$123$	155927.	0.929307
$124$	19085.1	0.111465
$125$	15625.0	0.0894427
$126$	22978.3	0.128941
$127$	291458.	1.60349	0.801745	−	0.597666i	$-0.203905\pi$
$127$	291458.	1.60349	0.801745	+	0.597666i	$0.203905\pi$
$128$	−16384.0	−0.0883883
$129$	28648.1	0.151573
$130$	−43470.8	−0.225600
$131$	−113849.	−0.579632	−0.289816	−	0.957082i	$-0.593594\pi$
$131$	−113849.	−0.579632	−0.289816	+	0.957082i	$0.593594\pi$
$132$	−61121.8	−0.305324
$133$	−25602.4	−0.125502
$134$	−43152.9	−0.207610
$135$	18225.0	0.0860663
$136$	101550.	0.470796
$137$	30591.3	0.139250	0.0696252	−	0.997573i	$-0.477820\pi$
$137$	30591.3	0.139250	0.0696252	+	0.997573i	$0.477820\pi$
$138$	2127.01	0.00950763
$139$	217838.	0.956304	0.478152	−	0.878277i	$-0.341307\pi$
$139$	217838.	0.956304	0.478152	+	0.878277i	$0.341307\pi$
$140$	−28368.3	−0.122325
$141$	122155.	0.517443
$142$	−182111.	−0.757904
$143$	−184515.	−0.754556
$144$	20736.0	0.0833333
$145$	−78666.0	−0.310718
$146$	93307.3	0.362271
$147$	−105995.	−0.404569
$148$	97795.2	0.366998
$149$	−230640.	−0.851079	−0.425539	−	0.904940i	$-0.639916\pi$
$149$	−230640.	−0.851079	−0.425539	+	0.904940i	$0.639916\pi$
$150$	−22500.0	−0.0816497
$151$	335694.	1.19812	0.599061	−	0.800703i	$-0.295541\pi$
$151$	335694.	1.19812	0.599061	+	0.800703i	$0.295541\pi$
$152$	−23104.0	−0.0811107
$153$	−128524.	−0.443870
$154$	−120411.	−0.409134
$155$	29820.4	0.0996976
$156$	62598.0	0.205944
$157$	103033.	0.333602	0.166801	−	0.985991i	$-0.446656\pi$
$157$	103033.	0.333602	0.166801	+	0.985991i	$0.446656\pi$
$158$	−121956.	−0.388652
$159$	146782.	0.460446
$160$	−25600.0	−0.0790569
$161$	4190.26	0.0127402
$162$	−26244.0	−0.0785674
$163$	130792.	0.385577	0.192789	−	0.981240i	$-0.438247\pi$
$163$	130792.	0.385577	0.192789	+	0.981240i	$0.438247\pi$
$164$	277204.	0.804804
$165$	−95502.9	−0.273090
$166$	206212.	0.580824
$167$	235238.	0.652705	0.326352	−	0.945248i	$-0.394180\pi$
$167$	235238.	0.652705	0.326352	+	0.945248i	$0.394180\pi$
$168$	40850.4	0.111666
$169$	−182322.	−0.491046
$170$	158672.	0.421092
$171$	29241.0	0.0764719
$172$	50929.9	0.131266
$173$	154896.	0.393483	0.196741	−	0.980455i	$-0.436964\pi$
$173$	154896.	0.393483	0.196741	+	0.980455i	$0.436964\pi$
$174$	113279.	0.283646
$175$	−44325.5	−0.109410
$176$	−108661.	−0.264419
$177$	−34879.7	−0.0836835
$178$	247483.	0.585458
$179$	220690.	0.514814	0.257407	−	0.966303i	$-0.417132\pi$
$179$	220690.	0.514814	0.257407	+	0.966303i	$0.417132\pi$
$180$	32400.0	0.0745356
$181$	460477.	1.04475	0.522373	−	0.852717i	$-0.325047\pi$
$181$	460477.	1.04475	0.522373	+	0.852717i	$0.325047\pi$
$182$	123319.	0.275964
$183$	334770.	0.738956
$184$	3781.35	0.00823385
$185$	152805.	0.328253
$186$	−42941.4	−0.0910111
$187$	673494.	1.40841
$188$	217164.	0.448119
$189$	−51701.3	−0.105280
$190$	−36100.0	−0.0725476
$191$	−519113.	−1.02962	−0.514812	−	0.857303i	$-0.672138\pi$
$191$	−519113.	−1.02962	−0.514812	+	0.857303i	$0.672138\pi$
$192$	36864.0	0.0721688
$193$	836538.	1.61656	0.808282	−	0.588796i	$-0.200398\pi$
$193$	836538.	1.61656	0.808282	+	0.588796i	$0.200398\pi$
$194$	−134726.	−0.257008
$195$	97809.3	0.184202
$196$	−188436.	−0.350367
$197$	375924.	0.690136	0.345068	−	0.938578i	$-0.387856\pi$
$197$	375924.	0.690136	0.345068	+	0.938578i	$0.387856\pi$
$198$	137524.	0.249296
$199$	931354.	1.66718	0.833589	−	0.552385i	$-0.186282\pi$
$199$	931354.	1.66718	0.833589	+	0.552385i	$0.186282\pi$
$200$	−40000.0	−0.0707107
$201$	97093.9	0.169513
$202$	35770.4	0.0616802
$203$	223162.	0.380085
$204$	−228487.	−0.384403
$205$	433131.	0.719838
$206$	199324.	0.327258
$207$	−4785.78	−0.00776295
$208$	111285.	0.178353
$209$	−153229.	−0.242647
$210$	63828.7	0.0998776
$211$	801186.	1.23887	0.619437	−	0.785046i	$-0.287361\pi$
$211$	801186.	1.23887	0.619437	+	0.785046i	$0.287361\pi$
$212$	260945.	0.398758
$213$	409749.	0.618826
$214$	−763995.	−1.14040
$215$	79578.0	0.117408
$216$	−46656.0	−0.0680414
$217$	−84595.6	−0.121955
$218$	122308.	0.174307
$219$	−209942.	−0.295793
$220$	−169783.	−0.236503
$221$	−689759.	−0.949985
$222$	−220039.	−0.299652
$223$	721812.	0.971990	0.485995	−	0.873962i	$-0.338457\pi$
$223$	721812.	0.971990	0.485995	+	0.873962i	$0.338457\pi$
$224$	72622.9	0.0967060
$225$	50625.0	0.0666667
$226$	470082.	0.612212
$227$	−98999.5	−0.127517	−0.0637585	−	0.997965i	$-0.520309\pi$
$227$	−98999.5	−0.127517	−0.0637585	+	0.997965i	$0.520309\pi$
$228$	51984.0	0.0662266
$229$	−1.20946e6	−1.52406	−0.762030	−	0.647542i	$-0.775797\pi$
$229$	−1.20946e6	−1.52406	−0.762030	+	0.647542i	$0.775797\pi$
$230$	5908.37	0.00736458
$231$	270926.	0.334057
$232$	201385.	0.245644
$233$	244144.	0.294616	0.147308	−	0.989091i	$-0.452939\pi$
$233$	244144.	0.294616	0.147308	+	0.989091i	$0.452939\pi$
$234$	−140845.	−0.168152
$235$	339319.	0.400810
$236$	−62008.4	−0.0724720
$237$	274401.	0.317333
$238$	−450125.	−0.515099
$239$	−910052.	−1.03056	−0.515278	−	0.857023i	$-0.672311\pi$
$239$	−910052.	−1.03056	−0.515278	+	0.857023i	$0.672311\pi$
$240$	57600.0	0.0645497
$241$	1.13156e6	1.25497	0.627486	−	0.778627i	$-0.284084\pi$
$241$	1.13156e6	1.25497	0.627486	+	0.778627i	$0.284084\pi$
$242$	−76451.7	−0.0839168
$243$	59049.0	0.0641500
$244$	595146.	0.639955
$245$	−294431.	−0.313378
$246$	−623709.	−0.657119
$247$	156930.	0.163668
$248$	−76340.3	−0.0788179
$249$	−463978.	−0.474241
$250$	−62500.0	−0.0632456
$251$	661454.	0.662698	0.331349	−	0.943508i	$-0.392496\pi$
$251$	661454.	0.662698	0.331349	+	0.943508i	$0.392496\pi$
$252$	−91913.4	−0.0911753
$253$	25078.5	0.0246320
$254$	−1.16583e6	−1.13384
$255$	−357011.	−0.343820
$256$	65536.0	0.0625000
$257$	−1.04229e6	−0.984364	−0.492182	−	0.870492i	$-0.663801\pi$
$257$	−1.04229e6	−0.984364	−0.492182	+	0.870492i	$0.663801\pi$
$258$	−114592.	−0.107178
$259$	−433482.	−0.401533
$260$	173883.	0.159523
$261$	−254878.	−0.231596
$262$	455398.	0.409862
$263$	827987.	0.738133	0.369066	−	0.929403i	$-0.379678\pi$
$263$	827987.	0.738133	0.369066	+	0.929403i	$0.379678\pi$
$264$	244487.	0.215897
$265$	407727.	0.356660
$266$	102410.	0.0887435
$267$	−556837.	−0.478024
$268$	172611.	0.146802
$269$	1.20075e6	1.01175	0.505873	−	0.862608i	$-0.331170\pi$
$269$	1.20075e6	1.01175	0.505873	+	0.862608i	$0.331170\pi$
$270$	−72900.0	−0.0608581
$271$	335669.	0.277644	0.138822	−	0.990317i	$-0.455668\pi$
$271$	335669.	0.277644	0.138822	+	0.990317i	$0.455668\pi$
$272$	−406200.	−0.332903
$273$	−277469.	−0.225324
$274$	−122365.	−0.0984649
$275$	−265286.	−0.211535
$276$	−8508.05	−0.00672291
$277$	1.89258e6	1.48202	0.741012	−	0.671492i	$-0.234346\pi$
$277$	1.89258e6	1.48202	0.741012	+	0.671492i	$0.234346\pi$
$278$	−871350.	−0.676209
$279$	96618.2	0.0743102
$280$	113473.	0.0864965
$281$	1.11184e6	0.839991	0.419996	−	0.907526i	$-0.362032\pi$
$281$	1.11184e6	0.839991	0.419996	+	0.907526i	$0.362032\pi$
$282$	−488619.	−0.365887
$283$	−1.05166e6	−0.780567	−0.390284	−	0.920695i	$-0.627623\pi$
$283$	−1.05166e6	−0.780567	−0.390284	+	0.920695i	$0.627623\pi$
$284$	728442.	0.535919
$285$	81225.0	0.0592349
$286$	738060.	0.533552
$287$	−1.22872e6	−0.880539
$288$	−82944.0	−0.0589256
$289$	1.09782e6	0.773188
$290$	314664.	0.219711
$291$	303134.	0.209846
$292$	−373229.	−0.256164
$293$	1.11859e6	0.761202	0.380601	−	0.924739i	$-0.375717\pi$
$293$	1.11859e6	0.761202	0.380601	+	0.924739i	$0.375717\pi$
$294$	423981.	0.286074
$295$	−96888.1	−0.0648209
$296$	−391181.	−0.259506
$297$	−309429.	−0.203550
$298$	922561.	0.601803
$299$	−25684.2	−0.0166145
$300$	90000.0	0.0577350
$301$	−225750.	−0.143619
$302$	−1.34278e6	−0.847201
$303$	−80483.5	−0.0503617
$304$	92416.0	0.0573539
$305$	929916.	0.572393
$306$	514097.	0.313864
$307$	267560.	0.162022	0.0810112	−	0.996713i	$-0.474185\pi$
$307$	267560.	0.162022	0.0810112	+	0.996713i	$0.474185\pi$
$308$	481646.	0.289302
$309$	−448478.	−0.267205
$310$	−119282.	−0.0704969
$311$	564281.	0.330822	0.165411	−	0.986225i	$-0.447105\pi$
$311$	564281.	0.330822	0.165411	+	0.986225i	$0.447105\pi$
$312$	−250392.	−0.145624
$313$	−401197.	−0.231471	−0.115736	−	0.993280i	$-0.536923\pi$
$313$	−401197.	−0.231471	−0.115736	+	0.993280i	$0.536923\pi$
$314$	−412134.	−0.235892
$315$	−143615.	−0.0815497
$316$	487824.	0.274818
$317$	16683.0	0.00932449	0.00466224	−	0.999989i	$-0.498516\pi$
$317$	16683.0	0.00932449	0.00466224	+	0.999989i	$0.498516\pi$
$318$	−587127.	−0.325585
$319$	1.33561e6	0.734859
$320$	102400.	0.0559017
$321$	1.71899e6	0.931130
$322$	−16761.0	−0.00900868
$323$	−572805.	−0.305493
$324$	104976.	0.0555556
$325$	271693.	0.142682
$326$	−523167.	−0.272644
$327$	−275193.	−0.142321
$328$	−1.10882e6	−0.569082
$329$	−962590.	−0.490288
$330$	382011.	0.193104
$331$	−2.37141e6	−1.18970	−0.594849	−	0.803838i	$-0.702788\pi$
$331$	−2.37141e6	−1.18970	−0.594849	+	0.803838i	$0.702788\pi$
$332$	−824850.	−0.410705
$333$	495088.	0.244665
$334$	−940953.	−0.461532
$335$	269705.	0.131304
$336$	−163402.	−0.0789601
$337$	−1.13740e6	−0.545555	−0.272778	−	0.962077i	$-0.587942\pi$
$337$	−1.13740e6	−0.545555	−0.272778	+	0.962077i	$0.587942\pi$
$338$	729287.	0.347222
$339$	−1.05768e6	−0.499869
$340$	−634687.	−0.297757
$341$	−506300.	−0.235788
$342$	−116964.	−0.0540738
$343$	2.02722e6	0.930390
$344$	−203720.	−0.0928190
$345$	−13293.8	−0.00601315
$346$	−619585.	−0.278234
$347$	−1.38681e6	−0.618290	−0.309145	−	0.951015i	$-0.600043\pi$
$347$	−1.38681e6	−0.618290	−0.309145	+	0.951015i	$0.600043\pi$
$348$	−453116.	−0.200568
$349$	−2.02768e6	−0.891121	−0.445560	−	0.895252i	$-0.646996\pi$
$349$	−2.02768e6	−0.891121	−0.445560	+	0.895252i	$0.646996\pi$
$350$	177302.	0.0773648
$351$	316902.	0.137296
$352$	434644.	0.186972
$353$	−3.01402e6	−1.28739	−0.643693	−	0.765283i	$-0.722599\pi$
$353$	−3.01402e6	−1.28739	−0.643693	+	0.765283i	$0.722599\pi$
$354$	139519.	0.0591732
$355$	1.13819e6	0.479341
$356$	−989933.	−0.413981
$357$	1.01278e6	0.420577
$358$	−882761.	−0.364029
$359$	−1.42115e6	−0.581974	−0.290987	−	0.956727i	$-0.593984\pi$
$359$	−1.42115e6	−0.581974	−0.290987	+	0.956727i	$0.593984\pi$
$360$	−129600.	−0.0527046
$361$	130321.	0.0526316
$362$	−1.84191e6	−0.738748
$363$	172016.	0.0685178
$364$	−493278.	−0.195136
$365$	−583171.	−0.229120
$366$	−1.33908e6	−0.522521
$367$	129477.	0.0501794	0.0250897	−	0.999685i	$-0.492013\pi$
$367$	129477.	0.0501794	0.0250897	+	0.999685i	$0.492013\pi$
$368$	−15125.4	−0.00582221
$369$	1.40335e6	0.536536
$370$	−611220.	−0.232110
$371$	−1.15665e6	−0.436283
$372$	171766.	0.0643545
$373$	−1.88154e6	−0.700230	−0.350115	−	0.936707i	$-0.613858\pi$
$373$	−1.88154e6	−0.700230	−0.350115	+	0.936707i	$0.613858\pi$
$374$	−2.69398e6	−0.995897
$375$	140625.	0.0516398
$376$	−868656.	−0.316868
$377$	−1.36787e6	−0.495668
$378$	206805.	0.0744443
$379$	−3.06386e6	−1.09565	−0.547824	−	0.836594i	$-0.684544\pi$
$379$	−3.06386e6	−1.09565	−0.547824	+	0.836594i	$0.684544\pi$
$380$	144400.	0.0512989
$381$	2.62312e6	0.925775
$382$	2.07645e6	0.728054
$383$	−2.30188e6	−0.801837	−0.400919	−	0.916114i	$-0.631309\pi$
$383$	−2.30188e6	−0.801837	−0.400919	+	0.916114i	$0.631309\pi$
$384$	−147456.	−0.0510310
$385$	752571.	0.258759
$386$	−3.34615e6	−1.14308
$387$	257833.	0.0875106
$388$	538904.	0.181732
$389$	4.00419e6	1.34165	0.670826	−	0.741614i	$-0.265940\pi$
$389$	4.00419e6	1.34165	0.670826	+	0.741614i	$0.265940\pi$
$390$	−391237.	−0.130250
$391$	93749.1	0.0310117
$392$	753743.	0.247747
$393$	−1.02464e6	−0.334651
$394$	−1.50370e6	−0.488000
$395$	762225.	0.245805
$396$	−550097.	−0.176279
$397$	−946037.	−0.301253	−0.150627	−	0.988591i	$-0.548129\pi$
$397$	−946037.	−0.301253	−0.150627	+	0.988591i	$0.548129\pi$
$398$	−3.72541e6	−1.17887
$399$	−230422.	−0.0724588
$400$	160000.	0.0500000
$401$	−566175.	−0.175829	−0.0879144	−	0.996128i	$-0.528020\pi$
$401$	−566175.	−0.175829	−0.0879144	+	0.996128i	$0.528020\pi$
$402$	−388376.	−0.119863
$403$	518528.	0.159041
$404$	−143082.	−0.0436145
$405$	164025.	0.0496904
$406$	−892648.	−0.268760
$407$	−2.59437e6	−0.776328
$408$	913949.	0.271814
$409$	−1.77345e6	−0.524216	−0.262108	−	0.965038i	$-0.584418\pi$
$409$	−1.77345e6	−0.524216	−0.262108	+	0.965038i	$0.584418\pi$
$410$	−1.73253e6	−0.509002
$411$	275322.	0.0803962
$412$	−797295.	−0.231407
$413$	274855.	0.0792919
$414$	19143.1	0.00548923
$415$	−1.28883e6	−0.367346
$416$	−445141.	−0.126114
$417$	1.96054e6	0.552122
$418$	612916.	0.171578
$419$	−3.72599e6	−1.03683	−0.518414	−	0.855130i	$-0.673477\pi$
$419$	−3.72599e6	−1.03683	−0.518414	+	0.855130i	$0.673477\pi$
$420$	−255315.	−0.0706241
$421$	−186198.	−0.0511999	−0.0256000	−	0.999672i	$-0.508150\pi$
$421$	−186198.	−0.0511999	−0.0256000	+	0.999672i	$0.508150\pi$
$422$	−3.20475e6	−0.876017
$423$	1.09939e6	0.298746
$424$	−1.04378e6	−0.281965
$425$	−991699.	−0.266322
$426$	−1.63900e6	−0.437576
$427$	−2.63802e6	−0.700177
$428$	3.05598e6	0.806383
$429$	−1.66064e6	−0.435643
$430$	−318312.	−0.0830199
$431$	5.29721e6	1.37358	0.686790	−	0.726856i	$-0.259019\pi$
$431$	5.29721e6	1.37358	0.686790	+	0.726856i	$0.259019\pi$
$432$	186624.	0.0481125
$433$	6.39018e6	1.63792	0.818961	−	0.573849i	$-0.194550\pi$
$433$	6.39018e6	1.63792	0.818961	+	0.573849i	$0.194550\pi$
$434$	338382.	0.0862350
$435$	−707994.	−0.179393
$436$	−489232.	−0.123253
$437$	−21329.2	−0.00534283
$438$	839766.	0.209157
$439$	−1.57271e6	−0.389481	−0.194740	−	0.980855i	$-0.562386\pi$
$439$	−1.57271e6	−0.389481	−0.194740	+	0.980855i	$0.562386\pi$
$440$	679132.	0.167233
$441$	−953956.	−0.233578
$442$	2.75904e6	0.671741
$443$	1.60421e6	0.388375	0.194188	−	0.980964i	$-0.437793\pi$
$443$	1.60421e6	0.388375	0.194188	+	0.980964i	$0.437793\pi$
$444$	880157.	0.211886
$445$	−1.54677e6	−0.370276
$446$	−2.88725e6	−0.687301
$447$	−2.07576e6	−0.491370
$448$	−290492.	−0.0683815
$449$	−6.08434e6	−1.42429	−0.712144	−	0.702033i	$-0.752276\pi$
$449$	−6.08434e6	−1.42429	−0.712144	+	0.702033i	$0.752276\pi$
$450$	−202500.	−0.0471405
$451$	−7.35383e6	−1.70244
$452$	−1.88033e6	−0.432900
$453$	3.02125e6	0.691736
$454$	395998.	0.0901682
$455$	−770746.	−0.174535
$456$	−207936.	−0.0468293
$457$	5.27622e6	1.18177	0.590884	−	0.806757i	$-0.298779\pi$
$457$	5.27622e6	1.18177	0.590884	+	0.806757i	$0.298779\pi$
$458$	4.83783e6	1.07767
$459$	−1.15672e6	−0.256269
$460$	−23633.5	−0.00520754
$461$	−5.02650e6	−1.10157	−0.550787	−	0.834646i	$-0.685672\pi$
$461$	−5.02650e6	−1.10157	−0.550787	+	0.834646i	$0.685672\pi$
$462$	−1.08370e6	−0.236214
$463$	5.23215e6	1.13430	0.567150	−	0.823615i	$-0.308046\pi$
$463$	5.23215e6	1.13430	0.567150	+	0.823615i	$0.308046\pi$
$464$	−805539.	−0.173697
$465$	268384.	0.0575605
$466$	−976576.	−0.208325
$467$	1.53407e6	0.325501	0.162750	−	0.986667i	$-0.447963\pi$
$467$	1.53407e6	0.325501	0.162750	+	0.986667i	$0.447963\pi$
$468$	563382.	0.118902
$469$	−765109.	−0.160617
$470$	−1.35727e6	−0.283415
$471$	927301.	0.192605
$472$	248034.	0.0512455
$473$	−1.35110e6	−0.277673
$474$	−1.09760e6	−0.224388
$475$	225625.	0.0458831
$476$	1.80050e6	0.364230
$477$	1.32104e6	0.265839
$478$	3.64021e6	0.728713
$479$	479006.	0.0953898	0.0476949	−	0.998862i	$-0.484812\pi$
$479$	479006.	0.0953898	0.0476949	+	0.998862i	$0.484812\pi$
$480$	−230400.	−0.0456435
$481$	2.65702e6	0.523640
$482$	−4.52623e6	−0.887400
$483$	37712.3	0.00735556
$484$	305807.	0.0593381
$485$	842038.	0.162546
$486$	−236196.	−0.0453609
$487$	−2.75400e6	−0.526190	−0.263095	−	0.964770i	$-0.584743\pi$
$487$	−2.75400e6	−0.526190	−0.263095	+	0.964770i	$0.584743\pi$
$488$	−2.38058e6	−0.452516
$489$	1.17713e6	0.222613
$490$	1.17772e6	0.221592
$491$	−3.42335e6	−0.640837	−0.320419	−	0.947276i	$-0.603824\pi$
$491$	−3.42335e6	−0.640837	−0.320419	+	0.947276i	$0.603824\pi$
$492$	2.49484e6	0.464654
$493$	4.99283e6	0.925186
$494$	−627719.	−0.115730
$495$	−859526.	−0.157669
$496$	305361.	0.0557327
$497$	−3.22886e6	−0.586351
$498$	1.85591e6	0.335339
$499$	−1.85318e6	−0.333170	−0.166585	−	0.986027i	$-0.553274\pi$
$499$	−1.85318e6	−0.333170	−0.166585	+	0.986027i	$0.553274\pi$
$500$	250000.	0.0447214
$501$	2.11714e6	0.376839
$502$	−2.64582e6	−0.468598
$503$	6.45275e6	1.13717	0.568584	−	0.822625i	$-0.307491\pi$
$503$	6.45275e6	1.13717	0.568584	+	0.822625i	$0.307491\pi$
$504$	367653.	0.0644707
$505$	−223565.	−0.0390100
$506$	−100314.	−0.0174175
$507$	−1.64090e6	−0.283505
$508$	4.66332e6	0.801745
$509$	−1.13203e7	−1.93671	−0.968355	−	0.249576i	$-0.919709\pi$
$509$	−1.13203e7	−1.93671	−0.968355	+	0.249576i	$0.919709\pi$
$510$	1.42805e6	0.243118
$511$	1.65436e6	0.280270
$512$	−262144.	−0.0441942
$513$	263169.	0.0441511
$514$	4.16916e6	0.696051
$515$	−1.24577e6	−0.206976
$516$	458369.	0.0757864
$517$	−5.76105e6	−0.947928
$518$	1.73393e6	0.283927
$519$	1.39407e6	0.227177
$520$	−695533.	−0.112800
$521$	−5.48806e6	−0.885777	−0.442888	−	0.896577i	$-0.646046\pi$
$521$	−5.48806e6	−0.885777	−0.442888	+	0.896577i	$0.646046\pi$
$522$	1.01951e6	0.163763
$523$	6.89470e6	1.10220	0.551101	−	0.834439i	$-0.314208\pi$
$523$	6.89470e6	1.10220	0.551101	+	0.834439i	$0.314208\pi$
$524$	−1.82159e6	−0.289816
$525$	−398929.	−0.0631681
$526$	−3.31195e6	−0.521939
$527$	−1.89266e6	−0.296857
$528$	−977949.	−0.152662
$529$	−6.43285e6	−0.999458
$530$	−1.63091e6	−0.252197
$531$	−313917.	−0.0483147
$532$	−409639.	−0.0627512
$533$	7.53143e6	1.14831
$534$	2.22735e6	0.338014
$535$	4.77497e6	0.721250
$536$	−690446.	−0.103805
$537$	1.98621e6	0.297228
$538$	−4.80300e6	−0.715413
$539$	4.99893e6	0.741149
$540$	291600.	0.0430331
$541$	−2.80191e6	−0.411587	−0.205793	−	0.978595i	$-0.565977\pi$
$541$	−2.80191e6	−0.411587	−0.205793	+	0.978595i	$0.565977\pi$
$542$	−1.34268e6	−0.196324
$543$	4.14429e6	0.603185
$544$	1.62480e6	0.235398
$545$	−764426.	−0.110241
$546$	1.10987e6	0.159328
$547$	6.37022e6	0.910304	0.455152	−	0.890414i	$-0.349585\pi$
$547$	6.37022e6	0.910304	0.455152	+	0.890414i	$0.349585\pi$
$548$	489461.	0.0696252
$549$	3.01293e6	0.426636
$550$	1.06114e6	0.149578
$551$	−1.13594e6	−0.159395
$552$	34032.2	0.00475381
$553$	−2.16230e6	−0.300680
$554$	−7.57033e6	−1.04795
$555$	1.37524e6	0.189517
$556$	3.48540e6	0.478152
$557$	8.20081e6	1.12000	0.560001	−	0.828492i	$-0.310801\pi$
$557$	8.20081e6	1.12000	0.560001	+	0.828492i	$0.310801\pi$
$558$	−386473.	−0.0525453
$559$	1.38373e6	0.187293
$560$	−453893.	−0.0611623
$561$	6.06144e6	0.813147
$562$	−4.44734e6	−0.593964
$563$	9.42484e6	1.25315	0.626575	−	0.779361i	$-0.284456\pi$
$563$	9.42484e6	1.25315	0.626575	+	0.779361i	$0.284456\pi$
$564$	1.95448e6	0.258721
$565$	−2.93801e6	−0.387197
$566$	4.20665e6	0.551945
$567$	−465311.	−0.0607835
$568$	−2.91377e6	−0.378952
$569$	−9.94455e6	−1.28767	−0.643835	−	0.765164i	$-0.722658\pi$
$569$	−9.94455e6	−1.28767	−0.643835	+	0.765164i	$0.722658\pi$
$570$	−324900.	−0.0418854
$571$	−2.04818e6	−0.262892	−0.131446	−	0.991323i	$-0.541962\pi$
$571$	−2.04818e6	−0.262892	−0.131446	+	0.991323i	$0.541962\pi$
$572$	−2.95224e6	−0.377278
$573$	−4.67202e6	−0.594454
$574$	4.91488e6	0.622635
$575$	−36927.3	−0.00465777
$576$	331776.	0.0416667
$577$	−1.18520e6	−0.148202	−0.0741008	−	0.997251i	$-0.523609\pi$
$577$	−1.18520e6	−0.148202	−0.0741008	+	0.997251i	$0.523609\pi$
$578$	−4.39126e6	−0.546726
$579$	7.52885e6	0.933323
$580$	−1.25866e6	−0.155359
$581$	3.65619e6	0.449354
$582$	−1.21253e6	−0.148384
$583$	−6.92251e6	−0.843513
$584$	1.49292e6	0.181136
$585$	880284.	0.106349
$586$	−4.47434e6	−0.538251
$587$	−9.38735e6	−1.12447	−0.562235	−	0.826978i	$-0.690058\pi$
$587$	−9.38735e6	−1.12447	−0.562235	+	0.826978i	$0.690058\pi$
$588$	−1.69592e6	−0.202285
$589$	430607.	0.0511438
$590$	387552.	0.0458353
$591$	3.38332e6	0.398450
$592$	1.56472e6	0.183499
$593$	522811.	0.0610531	0.0305266	−	0.999534i	$-0.490282\pi$
$593$	522811.	0.0610531	0.0305266	+	0.999534i	$0.490282\pi$
$594$	1.23772e6	0.143931
$595$	2.81328e6	0.325777
$596$	−3.69025e6	−0.425539
$597$	8.38218e6	0.962546
$598$	102737.	0.0117482
$599$	2.07339e6	0.236110	0.118055	−	0.993007i	$-0.462334\pi$
$599$	2.07339e6	0.236110	0.118055	+	0.993007i	$0.462334\pi$
$600$	−360000.	−0.0408248
$601$	−1.48680e7	−1.67906	−0.839531	−	0.543311i	$-0.817170\pi$
$601$	−1.48680e7	−1.67906	−0.839531	+	0.543311i	$0.817170\pi$
$602$	902998.	0.101554
$603$	873845.	0.0978681
$604$	5.37111e6	0.599061
$605$	477823.	0.0530736
$606$	321934.	0.0356111
$607$	6.42430e6	0.707707	0.353854	−	0.935301i	$-0.384871\pi$
$607$	6.42430e6	0.707707	0.353854	+	0.935301i	$0.384871\pi$
$608$	−369664.	−0.0405554
$609$	2.00846e6	0.219442
$610$	−3.71966e6	−0.404743
$611$	5.90018e6	0.639385
$612$	−2.05639e6	−0.221935
$613$	1.34202e7	1.44247	0.721235	−	0.692690i	$-0.243575\pi$
$613$	1.34202e7	1.44247	0.721235	+	0.692690i	$0.243575\pi$
$614$	−1.07024e6	−0.114567
$615$	3.89818e6	0.415599
$616$	−1.92658e6	−0.204567
$617$	1.44685e7	1.53007	0.765033	−	0.643991i	$-0.222723\pi$
$617$	1.44685e7	1.53007	0.765033	+	0.643991i	$0.222723\pi$
$618$	1.79391e6	0.188943
$619$	1.51094e7	1.58497	0.792483	−	0.609894i	$-0.208788\pi$
$619$	1.51094e7	1.58497	0.792483	+	0.609894i	$0.208788\pi$
$620$	477127.	0.0498488
$621$	−43072.0	−0.00448194
$622$	−2.25713e6	−0.233927
$623$	4.38793e6	0.452938
$624$	1.00157e6	0.102972
$625$	390625.	0.0400000
$626$	1.60479e6	0.163675
$627$	−1.37906e6	−0.140092
$628$	1.64854e6	0.166801
$629$	−9.69833e6	−0.977396
$630$	574458.	0.0576643
$631$	827007.	0.0826868	0.0413434	−	0.999145i	$-0.486836\pi$
$631$	827007.	0.0826868	0.0413434	+	0.999145i	$0.486836\pi$
$632$	−1.95130e6	−0.194326
$633$	7.21068e6	0.715265
$634$	−66731.8	−0.00659341
$635$	7.28644e6	0.717102
$636$	2.34851e6	0.230223
$637$	−5.11966e6	−0.499911
$638$	−5.34245e6	−0.519624
$639$	3.68774e6	0.357279
$640$	−409600.	−0.0395285
$641$	2.10060e6	0.201929	0.100964	−	0.994890i	$-0.467807\pi$
$641$	2.10060e6	0.201929	0.100964	+	0.994890i	$0.467807\pi$
$642$	−6.87596e6	−0.658409
$643$	2.96705e6	0.283008	0.141504	−	0.989938i	$-0.454806\pi$
$643$	2.96705e6	0.283008	0.141504	+	0.989938i	$0.454806\pi$
$644$	67044.2	0.00637010
$645$	716202.	0.0677854
$646$	2.29122e6	0.216016
$647$	−2.57086e6	−0.241445	−0.120723	−	0.992686i	$-0.538521\pi$
$647$	−2.57086e6	−0.241445	−0.120723	+	0.992686i	$0.538521\pi$
$648$	−419904.	−0.0392837
$649$	1.64499e6	0.153304
$650$	−1.08677e6	−0.100891
$651$	−761360.	−0.0704105
$652$	2.09267e6	0.192789
$653$	−700959.	−0.0643294	−0.0321647	−	0.999483i	$-0.510240\pi$
$653$	−700959.	−0.0643294	−0.0321647	+	0.999483i	$0.510240\pi$
$654$	1.10077e6	0.100636
$655$	−2.84623e6	−0.259219
$656$	4.43526e6	0.402402
$657$	−1.88947e6	−0.170776
$658$	3.85036e6	0.346686
$659$	−1.71014e7	−1.53398	−0.766989	−	0.641660i	$-0.778246\pi$
$659$	−1.71014e7	−1.53398	−0.766989	+	0.641660i	$0.778246\pi$
$660$	−1.52805e6	−0.136545
$661$	1.85258e7	1.64920	0.824601	−	0.565715i	$-0.191400\pi$
$661$	1.85258e7	1.64920	0.824601	+	0.565715i	$0.191400\pi$
$662$	9.48564e6	0.841243
$663$	−6.20783e6	−0.548474
$664$	3.29940e6	0.290412
$665$	−640060.	−0.0561263
$666$	−1.98035e6	−0.173004
$667$	185915.	0.0161808
$668$	3.76381e6	0.326352
$669$	6.49631e6	0.561179
$670$	−1.07882e6	−0.0928458
$671$	−1.57884e7	−1.35373
$672$	653606.	0.0558332
$673$	1.62516e7	1.38311	0.691557	−	0.722322i	$-0.256925\pi$
$673$	1.62516e7	1.38311	0.691557	+	0.722322i	$0.256925\pi$
$674$	4.54960e6	0.385766
$675$	455625.	0.0384900
$676$	−2.91715e6	−0.245523
$677$	8.11531e6	0.680508	0.340254	−	0.940334i	$-0.389487\pi$
$677$	8.11531e6	0.680508	0.340254	+	0.940334i	$0.389487\pi$
$678$	4.23073e6	0.353461
$679$	−2.38872e6	−0.198834
$680$	2.53875e6	0.210546
$681$	−890995.	−0.0736220
$682$	2.02520e6	0.166727
$683$	−1.47875e7	−1.21295	−0.606475	−	0.795103i	$-0.707417\pi$
$683$	−1.47875e7	−1.21295	−0.606475	+	0.795103i	$0.707417\pi$
$684$	467856.	0.0382360
$685$	764782.	0.0622747
$686$	−8.10887e6	−0.657885
$687$	−1.08851e7	−0.879916
$688$	814879.	0.0656330
$689$	7.08969e6	0.568957
$690$	53175.3	0.00425194
$691$	−1.57667e7	−1.25616	−0.628081	−	0.778148i	$-0.716159\pi$
$691$	−1.57667e7	−1.25616	−0.628081	+	0.778148i	$0.716159\pi$
$692$	2.47834e6	0.196741
$693$	2.43833e6	0.192868
$694$	5.54723e6	0.437197
$695$	5.44594e6	0.427672
$696$	1.81246e6	0.141823
$697$	−2.74903e7	−2.14337
$698$	8.11073e6	0.630118
$699$	2.19730e6	0.170097
$700$	−709208.	−0.0547052
$701$	−1.51464e7	−1.16416	−0.582082	−	0.813130i	$-0.697762\pi$
$701$	−1.51464e7	−1.16416	−0.582082	+	0.813130i	$0.697762\pi$
$702$	−1.26761e6	−0.0970829
$703$	2.20650e6	0.168390
$704$	−1.73858e6	−0.132209
$705$	3.05387e6	0.231408
$706$	1.20561e7	0.910320
$707$	634217.	0.0477188
$708$	−558075.	−0.0418417
$709$	8.26009e6	0.617119	0.308560	−	0.951205i	$-0.400153\pi$
$709$	8.26009e6	0.617119	0.308560	+	0.951205i	$0.400153\pi$
$710$	−4.55276e6	−0.338945
$711$	2.46961e6	0.183212
$712$	3.95973e6	0.292729
$713$	−70476.0	−0.00519180
$714$	−4.05113e6	−0.297393
$715$	−4.61288e6	−0.337448
$716$	3.53104e6	0.257407
$717$	−8.19046e6	−0.594991
$718$	5.68460e6	0.411518
$719$	6.81658e6	0.491750	0.245875	−	0.969302i	$-0.420925\pi$
$719$	6.81658e6	0.491750	0.245875	+	0.969302i	$0.420925\pi$
$720$	518400.	0.0372678
$721$	3.53405e6	0.253183
$722$	−521284.	−0.0372161
$723$	1.01840e7	0.724559
$724$	7.36763e6	0.522373
$725$	−1.96665e6	−0.138957
$726$	−688066.	−0.0484494
$727$	5.61211e6	0.393813	0.196907	−	0.980422i	$-0.436910\pi$
$727$	5.61211e6	0.393813	0.196907	+	0.980422i	$0.436910\pi$
$728$	1.97311e6	0.137982
$729$	531441.	0.0370370
$730$	2.33268e6	0.162013
$731$	−5.05072e6	−0.349590
$732$	5.35632e6	0.369478
$733$	−6.12350e6	−0.420959	−0.210479	−	0.977598i	$-0.567503\pi$
$733$	−6.12350e6	−0.420959	−0.210479	+	0.977598i	$0.567503\pi$
$734$	−517906.	−0.0354822
$735$	−2.64988e6	−0.180929
$736$	60501.7	0.00411692
$737$	−4.57913e6	−0.310538
$738$	−5.61338e6	−0.379388
$739$	−1.87069e7	−1.26006	−0.630031	−	0.776570i	$-0.716958\pi$
$739$	−1.87069e7	−1.26006	−0.630031	+	0.776570i	$0.716958\pi$
$740$	2.44488e6	0.164126
$741$	1.41237e6	0.0944935
$742$	4.62661e6	0.308499
$743$	−1.63435e7	−1.08611	−0.543055	−	0.839697i	$-0.682733\pi$
$743$	−1.63435e7	−1.08611	−0.543055	+	0.839697i	$0.682733\pi$
$744$	−687063.	−0.0455055
$745$	−5.76601e6	−0.380614
$746$	7.52615e6	0.495137
$747$	−4.17580e6	−0.273803
$748$	1.07759e7	0.704206
$749$	−1.35458e7	−0.882266
$750$	−562500.	−0.0365148
$751$	−3.02253e7	−1.95556	−0.977779	−	0.209640i	$-0.932771\pi$
$751$	−3.02253e7	−1.95556	−0.977779	+	0.209640i	$0.932771\pi$
$752$	3.47462e6	0.224059
$753$	5.95309e6	0.382609
$754$	5.47148e6	0.350490
$755$	8.39235e6	0.535817
$756$	−827220.	−0.0526401
$757$	6.42262e6	0.407354	0.203677	−	0.979038i	$-0.434711\pi$
$757$	6.42262e6	0.407354	0.203677	+	0.979038i	$0.434711\pi$
$758$	1.22554e7	0.774740
$759$	225706.	0.0142213
$760$	−577600.	−0.0362738
$761$	205823.	0.0128835	0.00644173	−	0.999979i	$-0.497950\pi$
$761$	205823.	0.0128835	0.00644173	+	0.999979i	$0.497950\pi$
$762$	−1.04925e7	−0.654622
$763$	2.16855e6	0.134852
$764$	−8.30581e6	−0.514812
$765$	−3.21310e6	−0.198505
$766$	9.20753e6	0.566984
$767$	−1.68472e6	−0.103405
$768$	589824.	0.0360844
$769$	−2.52857e6	−0.154191	−0.0770955	−	0.997024i	$-0.524565\pi$
$769$	−2.52857e6	−0.154191	−0.0770955	+	0.997024i	$0.524565\pi$
$770$	−3.01028e6	−0.182970
$771$	−9.38061e6	−0.568323
$772$	1.33846e7	0.808282
$773$	−1.30603e7	−0.786148	−0.393074	−	0.919507i	$-0.628588\pi$
$773$	−1.30603e7	−0.786148	−0.393074	+	0.919507i	$0.628588\pi$
$774$	−1.03133e6	−0.0618794
$775$	745511.	0.0445861
$776$	−2.15562e6	−0.128504
$777$	−3.90134e6	−0.231825
$778$	−1.60167e7	−0.948692
$779$	6.25442e6	0.369269
$780$	1.56495e6	0.0921009
$781$	−1.93245e7	−1.13366
$782$	−374996.	−0.0219286
$783$	−2.29390e6	−0.133712
$784$	−3.01497e6	−0.175184
$785$	2.57584e6	0.149192
$786$	4.09858e6	0.236634
$787$	2.45143e7	1.41086	0.705429	−	0.708781i	$-0.250755\pi$
$787$	2.45143e7	1.41086	0.705429	+	0.708781i	$0.250755\pi$
$788$	6.01478e6	0.345068
$789$	7.45189e6	0.426161
$790$	−3.04890e6	−0.173810
$791$	8.33464e6	0.473637
$792$	2.20039e6	0.124648
$793$	1.61697e7	0.913100
$794$	3.78415e6	0.213018
$795$	3.66954e6	0.205918
$796$	1.49017e7	0.833589
$797$	286670.	0.0159859	0.00799294	−	0.999968i	$-0.497456\pi$
$797$	286670.	0.0159859	0.00799294	+	0.999968i	$0.497456\pi$
$798$	921687.	0.0512361
$799$	−2.15361e7	−1.19344
$800$	−640000.	−0.0353553
$801$	−5.01153e6	−0.275987
$802$	2.26470e6	0.124330
$803$	9.90124e6	0.541877
$804$	1.55350e6	0.0847563
$805$	104757.	0.00569759
$806$	−2.07411e6	−0.112459
$807$	1.08067e7	0.584132
$808$	572327.	0.0308401
$809$	1.78669e7	0.959791	0.479896	−	0.877326i	$-0.340675\pi$
$809$	1.78669e7	0.959791	0.479896	+	0.877326i	$0.340675\pi$
$810$	−656100.	−0.0351364
$811$	−1.20577e7	−0.643745	−0.321873	−	0.946783i	$-0.604312\pi$
$811$	−1.20577e7	−0.643745	−0.321873	+	0.946783i	$0.604312\pi$
$812$	3.57059e6	0.190042
$813$	3.02102e6	0.160298
$814$	1.03775e7	0.548947
$815$	3.26979e6	0.172435
$816$	−3.65580e6	−0.192201
$817$	1.14911e6	0.0602289
$818$	7.09380e6	0.370677
$819$	−2.49722e6	−0.130091
$820$	6.93010e6	0.359919
$821$	−1.17493e7	−0.608352	−0.304176	−	0.952616i	$-0.598381\pi$
$821$	−1.17493e7	−0.608352	−0.304176	+	0.952616i	$0.598381\pi$
$822$	−1.10129e6	−0.0568487
$823$	1.10676e7	0.569577	0.284789	−	0.958590i	$-0.408077\pi$
$823$	1.10676e7	0.569577	0.284789	+	0.958590i	$0.408077\pi$
$824$	3.18918e6	0.163629
$825$	−2.38757e6	−0.122130
$826$	−1.09942e6	−0.0560678
$827$	2.51507e7	1.27875	0.639376	−	0.768895i	$-0.279193\pi$
$827$	2.51507e7	1.27875	0.639376	+	0.768895i	$0.279193\pi$
$828$	−76572.4	−0.00388147
$829$	−463735.	−0.0234360	−0.0117180	−	0.999931i	$-0.503730\pi$
$829$	−463735.	−0.0234360	−0.0117180	+	0.999931i	$0.503730\pi$
$830$	5.15531e6	0.259752
$831$	1.70332e7	0.855647
$832$	1.78056e6	0.0891763
$833$	1.86872e7	0.933105
$834$	−7.84215e6	−0.390409
$835$	5.88096e6	0.291898
$836$	−2.45166e6	−0.121324
$837$	869564.	0.0429030
$838$	1.49040e7	0.733148
$839$	3.53079e7	1.73168	0.865840	−	0.500321i	$-0.166785\pi$
$839$	3.53079e7	1.73168	0.865840	+	0.500321i	$0.166785\pi$
$840$	1.02126e6	0.0499388
$841$	−1.06098e7	−0.517271
$842$	744791.	0.0362038
$843$	1.00065e7	0.484969
$844$	1.28190e7	0.619437
$845$	−4.55805e6	−0.219602
$846$	−4.39757e6	−0.211245
$847$	−1.35550e6	−0.0649221
$848$	4.17512e6	0.199379
$849$	−9.46497e6	−0.450661
$850$	3.96679e6	0.188318
$851$	−361131.	−0.0170939
$852$	6.55598e6	0.309413
$853$	−2.30045e6	−0.108253	−0.0541266	−	0.998534i	$-0.517237\pi$
$853$	−2.30045e6	−0.108253	−0.0541266	+	0.998534i	$0.517237\pi$
$854$	1.05521e7	0.495100
$855$	731025.	0.0341993
$856$	−1.22239e7	−0.570199
$857$	−1.10358e7	−0.513275	−0.256637	−	0.966508i	$-0.582615\pi$
$857$	−1.10358e7	−0.513275	−0.256637	+	0.966508i	$0.582615\pi$
$858$	6.64254e6	0.308046
$859$	−1.14946e7	−0.531509	−0.265754	−	0.964041i	$-0.585621\pi$
$859$	−1.14946e7	−0.531509	−0.265754	+	0.964041i	$0.585621\pi$
$860$	1.27325e6	0.0587039
$861$	−1.10585e7	−0.508379
$862$	−2.11888e7	−0.971268
$863$	−2.89632e7	−1.32379	−0.661896	−	0.749596i	$-0.730248\pi$
$863$	−2.89632e7	−1.32379	−0.661896	+	0.749596i	$0.730248\pi$
$864$	−746496.	−0.0340207
$865$	3.87241e6	0.175971
$866$	−2.55607e7	−1.15819
$867$	9.88034e6	0.446400
$868$	−1.35353e6	−0.0609773
$869$	−1.29413e7	−0.581337
$870$	2.83197e6	0.126850
$871$	4.68972e6	0.209460
$872$	1.95693e6	0.0871533
$873$	2.72820e6	0.121155
$874$	85316.8	0.00377795
$875$	−1.10814e6	−0.0489298
$876$	−3.35906e6	−0.147897
$877$	−4.14794e7	−1.82110	−0.910550	−	0.413400i	$-0.864341\pi$
$877$	−4.14794e7	−1.82110	−0.910550	+	0.413400i	$0.864341\pi$
$878$	6.29082e6	0.275405
$879$	1.00673e7	0.439480
$880$	−2.71653e6	−0.118252
$881$	−1.07385e6	−0.0466125	−0.0233063	−	0.999728i	$-0.507419\pi$
$881$	−1.07385e6	−0.0466125	−0.0233063	+	0.999728i	$0.507419\pi$
$882$	3.81583e6	0.165165
$883$	−1.19542e7	−0.515963	−0.257981	−	0.966150i	$-0.583057\pi$
$883$	−1.19542e7	−0.515963	−0.257981	+	0.966150i	$0.583057\pi$
$884$	−1.10361e7	−0.474993
$885$	−871993.	−0.0374244
$886$	−6.41683e6	−0.274623
$887$	−2.95563e7	−1.26137	−0.630683	−	0.776040i	$-0.717225\pi$
$887$	−2.95563e7	−1.26137	−0.630683	+	0.776040i	$0.717225\pi$
$888$	−3.52063e6	−0.149826
$889$	−2.06704e7	−0.877192
$890$	6.18708e6	0.261825
$891$	−2.78486e6	−0.117519
$892$	1.15490e7	0.485995
$893$	4.89976e6	0.205611
$894$	8.30305e6	0.347451
$895$	5.51726e6	0.230232
$896$	1.16197e6	0.0483530
$897$	−231157.	−0.00959239
$898$	2.43374e7	1.00712
$899$	−3.75337e6	−0.154889
$900$	810000.	0.0333333
$901$	−2.58779e7	−1.06198
$902$	2.94153e7	1.20381
$903$	−2.03175e6	−0.0829182
$904$	7.52130e6	0.306106
$905$	1.15119e7	0.467225
$906$	−1.20850e7	−0.489132
$907$	−2.22140e6	−0.0896620	−0.0448310	−	0.998995i	$-0.514275\pi$
$907$	−2.22140e6	−0.0896620	−0.0448310	+	0.998995i	$0.514275\pi$
$908$	−1.58399e6	−0.0637585
$909$	−724351.	−0.0290763
$910$	3.08299e6	0.123415
$911$	1.76872e7	0.706096	0.353048	−	0.935605i	$-0.385145\pi$
$911$	1.76872e7	0.706096	0.353048	+	0.935605i	$0.385145\pi$
$912$	831744.	0.0331133
$913$	2.18821e7	0.868784
$914$	−2.11049e7	−0.835636
$915$	8.36924e6	0.330471
$916$	−1.93513e7	−0.762030
$917$	8.07429e6	0.317089
$918$	4.62687e6	0.181209
$919$	−1.05563e7	−0.412308	−0.206154	−	0.978520i	$-0.566095\pi$
$919$	−1.05563e7	−0.412308	−0.206154	+	0.978520i	$0.566095\pi$
$920$	94533.9	0.00368229
$921$	2.40804e6	0.0935437
$922$	2.01060e7	0.778930
$923$	1.97912e7	0.764661
$924$	4.33481e6	0.167028
$925$	3.82012e6	0.146799
$926$	−2.09286e7	−0.802071
$927$	−4.03630e6	−0.154271
$928$	3.22216e6	0.122822
$929$	1.03562e7	0.393698	0.196849	−	0.980434i	$-0.436929\pi$
$929$	1.03562e7	0.393698	0.196849	+	0.980434i	$0.436929\pi$
$930$	−1.07354e6	−0.0407014
$931$	−4.25158e6	−0.160759
$932$	3.90630e6	0.147308
$933$	5.07853e6	0.191000
$934$	−6.13627e6	−0.230164
$935$	1.68373e7	0.629861
$936$	−2.25353e6	−0.0840762
$937$	−3.78726e7	−1.40921	−0.704606	−	0.709598i	$-0.748876\pi$
$937$	−3.78726e7	−1.40921	−0.704606	+	0.709598i	$0.748876\pi$
$938$	3.06043e6	0.113573
$939$	−3.61077e6	−0.133640
$940$	5.42910e6	0.200405
$941$	−3.06386e7	−1.12796	−0.563981	−	0.825788i	$-0.690731\pi$
$941$	−3.06386e7	−1.12796	−0.563981	+	0.825788i	$0.690731\pi$
$942$	−3.70920e6	−0.136193
$943$	−1.02364e6	−0.0374859
$944$	−992134.	−0.0362360
$945$	−1.29253e6	−0.0470827
$946$	5.40440e6	0.196345
$947$	2.61377e7	0.947093	0.473546	−	0.880769i	$-0.342974\pi$
$947$	2.61377e7	0.947093	0.473546	+	0.880769i	$0.342974\pi$
$948$	4.39042e6	0.158666
$949$	−1.01404e7	−0.365501
$950$	−902500.	−0.0324443
$951$	150147.	0.00538350
$952$	−7.20200e6	−0.257550
$953$	2.26998e7	0.809635	0.404817	−	0.914398i	$-0.367335\pi$
$953$	2.26998e7	0.809635	0.404817	+	0.914398i	$0.367335\pi$
$954$	−5.28414e6	−0.187976
$955$	−1.29778e7	−0.460462
$956$	−1.45608e7	−0.515278
$957$	1.20205e7	0.424271
$958$	−1.91602e6	−0.0674508
$959$	−2.16956e6	−0.0761772
$960$	921600.	0.0322749
$961$	−2.72063e7	−0.950302
$962$	−1.06281e7	−0.370269
$963$	1.54709e7	0.537588
$964$	1.81049e7	0.627486
$965$	2.09135e7	0.722949
$966$	−150849.	−0.00520117
$967$	−7.85571e6	−0.270159	−0.135079	−	0.990835i	$-0.543129\pi$
$967$	−7.85571e6	−0.270159	−0.135079	+	0.990835i	$0.543129\pi$
$968$	−1.22323e6	−0.0419584
$969$	−5.15525e6	−0.176376
$970$	−3.36815e6	−0.114938
$971$	−1.04223e7	−0.354744	−0.177372	−	0.984144i	$-0.556760\pi$
$971$	−1.04223e7	−0.354744	−0.177372	+	0.984144i	$0.556760\pi$
$972$	944784.	0.0320750
$973$	−1.54492e7	−0.523148
$974$	1.10160e7	0.372072
$975$	2.44523e6	0.0823775
$976$	9.52234e6	0.319977
$977$	−1.15180e7	−0.386046	−0.193023	−	0.981194i	$-0.561829\pi$
$977$	−1.15180e7	−0.386046	−0.193023	+	0.981194i	$0.561829\pi$
$978$	−4.70850e6	−0.157411
$979$	2.62615e7	0.875715
$980$	−4.71090e6	−0.156689
$981$	−2.47674e6	−0.0821689
$982$	1.36934e7	0.453140
$983$	−9.96368e6	−0.328879	−0.164439	−	0.986387i	$-0.552582\pi$
$983$	−9.96368e6	−0.328879	−0.164439	+	0.986387i	$0.552582\pi$
$984$	−9.97934e6	−0.328560
$985$	9.39810e6	0.308638
$986$	−1.99713e7	−0.654205
$987$	−8.66331e6	−0.283068
$988$	2.51087e6	0.0818338
$989$	−188070.	−0.00611406
$990$	3.43810e6	0.111489
$991$	5.86825e7	1.89812	0.949061	−	0.315091i	$-0.102035\pi$
$991$	5.86825e7	1.89812	0.949061	+	0.315091i	$0.102035\pi$
$992$	−1.22145e6	−0.0394089
$993$	−2.13427e7	−0.686872
$994$	1.29154e7	0.414613
$995$	2.32838e7	0.745585
$996$	−7.42365e6	−0.237121
$997$	−2.25368e7	−0.718049	−0.359025	−	0.933328i	$-0.616891\pi$
$997$	−2.25368e7	−0.718049	−0.359025	+	0.933328i	$0.616891\pi$
$998$	7.41270e6	0.235586
$999$	4.45579e6	0.141257

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.6.a.m.1.2	✓	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} -70.9208 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} -70.9208 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -424.457 q^{11} +144.000 q^{12} +434.708 q^{13} +283.683 q^{14} +225.000 q^{15} +256.000 q^{16} -1586.72 q^{17} -324.000 q^{18} +361.000 q^{19} +400.000 q^{20} -638.287 q^{21} +1697.83 q^{22} -59.0837 q^{23} -576.000 q^{24} +625.000 q^{25} -1738.83 q^{26} +729.000 q^{27} -1134.73 q^{28} -3146.64 q^{29} -900.000 q^{30} +1192.82 q^{31} -1024.00 q^{32} -3820.11 q^{33} +6346.87 q^{34} -1773.02 q^{35} +1296.00 q^{36} +6112.20 q^{37} -1444.00 q^{38} +3912.37 q^{39} -1600.00 q^{40} +17325.3 q^{41} +2553.15 q^{42} +3183.12 q^{43} -6791.32 q^{44} +2025.00 q^{45} +236.335 q^{46} +13572.7 q^{47} +2304.00 q^{48} -11777.2 q^{49} -2500.00 q^{50} -14280.5 q^{51} +6955.33 q^{52} +16309.1 q^{53} -2916.00 q^{54} -10611.4 q^{55} +4538.93 q^{56} +3249.00 q^{57} +12586.6 q^{58} -3875.52 q^{59} +3600.00 q^{60} +37196.6 q^{61} -4771.27 q^{62} -5744.58 q^{63} +4096.00 q^{64} +10867.7 q^{65} +15280.5 q^{66} +10788.2 q^{67} -25387.5 q^{68} -531.753 q^{69} +7092.08 q^{70} +45527.6 q^{71} -5184.00 q^{72} -23326.8 q^{73} -24448.8 q^{74} +5625.00 q^{75} +5776.00 q^{76} +30102.8 q^{77} -15649.5 q^{78} +30489.0 q^{79} +6400.00 q^{80} +6561.00 q^{81} -69301.0 q^{82} -51553.1 q^{83} -10212.6 q^{84} -39667.9 q^{85} -12732.5 q^{86} -28319.7 q^{87} +27165.3 q^{88} -61870.8 q^{89} -8100.00 q^{90} -30829.9 q^{91} -945.339 q^{92} +10735.4 q^{93} -54291.0 q^{94} +9025.00 q^{95} -9216.00 q^{96} +33681.5 q^{97} +47109.0 q^{98} -34381.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} + 268 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 + 100 * q^5 - 144 * q^6 + 268 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} + 268 q^{7} - 256 q^{8} + 324 q^{9} - 400 q^{10} + 338 q^{11} + 576 q^{12} + 1302 q^{13} - 1072 q^{14} + 900 q^{15} + 1024 q^{16} + 542 q^{17} - 1296 q^{18} + 1444 q^{19} + 1600 q^{20} + 2412 q^{21} - 1352 q^{22} - 88 q^{23} - 2304 q^{24} + 2500 q^{25} - 5208 q^{26} + 2916 q^{27} + 4288 q^{28} + 5014 q^{29} - 3600 q^{30} + 4962 q^{31} - 4096 q^{32} + 3042 q^{33} - 2168 q^{34} + 6700 q^{35} + 5184 q^{36} + 8022 q^{37} - 5776 q^{38} + 11718 q^{39} - 6400 q^{40} + 2764 q^{41} - 9648 q^{42} + 25346 q^{43} + 5408 q^{44} + 8100 q^{45} + 352 q^{46} + 10008 q^{47} + 9216 q^{48} + 37248 q^{49} - 10000 q^{50} + 4878 q^{51} + 20832 q^{52} - 224 q^{53} - 11664 q^{54} + 8450 q^{55} - 17152 q^{56} + 12996 q^{57} - 20056 q^{58} + 29654 q^{59} + 14400 q^{60} + 27276 q^{61} - 19848 q^{62} + 21708 q^{63} + 16384 q^{64} + 32550 q^{65} - 12168 q^{66} + 26024 q^{67} + 8672 q^{68} - 792 q^{69} - 26800 q^{70} - 26940 q^{71} - 20736 q^{72} - 60916 q^{73} - 32088 q^{74} + 22500 q^{75} + 23104 q^{76} - 21228 q^{77} - 46872 q^{78} + 34902 q^{79} + 25600 q^{80} + 26244 q^{81} - 11056 q^{82} - 48430 q^{83} + 38592 q^{84} + 13550 q^{85} - 101384 q^{86} + 45126 q^{87} - 21632 q^{88} - 38348 q^{89} - 32400 q^{90} + 69280 q^{91} - 1408 q^{92} + 44658 q^{93} - 40032 q^{94} + 36100 q^{95} - 36864 q^{96} + 45942 q^{97} - 148992 q^{98} + 27378 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 + 100 * q^5 - 144 * q^6 + 268 * q^7 - 256 * q^8 + 324 * q^9 - 400 * q^10 + 338 * q^11 + 576 * q^12 + 1302 * q^13 - 1072 * q^14 + 900 * q^15 + 1024 * q^16 + 542 * q^17 - 1296 * q^18 + 1444 * q^19 + 1600 * q^20 + 2412 * q^21 - 1352 * q^22 - 88 * q^23 - 2304 * q^24 + 2500 * q^25 - 5208 * q^26 + 2916 * q^27 + 4288 * q^28 + 5014 * q^29 - 3600 * q^30 + 4962 * q^31 - 4096 * q^32 + 3042 * q^33 - 2168 * q^34 + 6700 * q^35 + 5184 * q^36 + 8022 * q^37 - 5776 * q^38 + 11718 * q^39 - 6400 * q^40 + 2764 * q^41 - 9648 * q^42 + 25346 * q^43 + 5408 * q^44 + 8100 * q^45 + 352 * q^46 + 10008 * q^47 + 9216 * q^48 + 37248 * q^49 - 10000 * q^50 + 4878 * q^51 + 20832 * q^52 - 224 * q^53 - 11664 * q^54 + 8450 * q^55 - 17152 * q^56 + 12996 * q^57 - 20056 * q^58 + 29654 * q^59 + 14400 * q^60 + 27276 * q^61 - 19848 * q^62 + 21708 * q^63 + 16384 * q^64 + 32550 * q^65 - 12168 * q^66 + 26024 * q^67 + 8672 * q^68 - 792 * q^69 - 26800 * q^70 - 26940 * q^71 - 20736 * q^72 - 60916 * q^73 - 32088 * q^74 + 22500 * q^75 + 23104 * q^76 - 21228 * q^77 - 46872 * q^78 + 34902 * q^79 + 25600 * q^80 + 26244 * q^81 - 11056 * q^82 - 48430 * q^83 + 38592 * q^84 + 13550 * q^85 - 101384 * q^86 + 45126 * q^87 - 21632 * q^88 - 38348 * q^89 - 32400 * q^90 + 69280 * q^91 - 1408 * q^92 + 44658 * q^93 - 40032 * q^94 + 36100 * q^95 - 36864 * q^96 + 45942 * q^97 - 148992 * q^98 + 27378 * q^99

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