LMFDB - Embedded newform 165.6.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,6,Mod(1,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, 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("165.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	165.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:	$26.4633302691$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.3368.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 15x + 11 $ x^3 - x^2 - 15*x + 11
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.723686$ of defining polynomial
Character	$\chi$	$=$	165.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.44737 q^{2} +9.00000 q^{3} -29.9051 q^{4} -25.0000 q^{5} -13.0263 q^{6} +41.5023 q^{7} +89.5997 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-1.44737 q^{2} +9.00000 q^{3} -29.9051 q^{4} -25.0000 q^{5} -13.0263 q^{6} +41.5023 q^{7} +89.5997 q^{8} +81.0000 q^{9} +36.1843 q^{10} +121.000 q^{11} -269.146 q^{12} +434.580 q^{13} -60.0692 q^{14} -225.000 q^{15} +827.280 q^{16} +474.359 q^{17} -117.237 q^{18} -2586.54 q^{19} +747.628 q^{20} +373.520 q^{21} -175.132 q^{22} -3671.69 q^{23} +806.397 q^{24} +625.000 q^{25} -628.999 q^{26} +729.000 q^{27} -1241.13 q^{28} -4269.64 q^{29} +325.659 q^{30} -8415.46 q^{31} -4064.57 q^{32} +1089.00 q^{33} -686.573 q^{34} -1037.56 q^{35} -2422.31 q^{36} +13940.3 q^{37} +3743.68 q^{38} +3911.22 q^{39} -2239.99 q^{40} +1771.24 q^{41} -540.623 q^{42} -11481.3 q^{43} -3618.52 q^{44} -2025.00 q^{45} +5314.30 q^{46} -11048.5 q^{47} +7445.52 q^{48} -15084.6 q^{49} -904.607 q^{50} +4269.23 q^{51} -12996.2 q^{52} +20924.0 q^{53} -1055.13 q^{54} -3025.00 q^{55} +3718.59 q^{56} -23278.8 q^{57} +6179.75 q^{58} -33001.2 q^{59} +6728.65 q^{60} -32348.2 q^{61} +12180.3 q^{62} +3361.68 q^{63} -20590.0 q^{64} -10864.5 q^{65} -1576.19 q^{66} +28892.8 q^{67} -14185.7 q^{68} -33045.2 q^{69} +1501.73 q^{70} -20476.5 q^{71} +7257.58 q^{72} -43333.2 q^{73} -20176.8 q^{74} +5625.00 q^{75} +77350.7 q^{76} +5021.77 q^{77} -5660.99 q^{78} -95301.8 q^{79} -20682.0 q^{80} +6561.00 q^{81} -2563.64 q^{82} -16682.8 q^{83} -11170.2 q^{84} -11859.0 q^{85} +16617.7 q^{86} -38426.7 q^{87} +10841.6 q^{88} +143269. q^{89} +2930.93 q^{90} +18036.1 q^{91} +109802. q^{92} -75739.1 q^{93} +15991.3 q^{94} +64663.4 q^{95} -36581.1 q^{96} -128960. q^{97} +21833.0 q^{98} +9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 2 q^{2} + 27 q^{3} + 28 q^{4} - 75 q^{5} - 18 q^{6} - 232 q^{7} + 24 q^{8} + 243 q^{9}+O(q^{10}) $ 3 * q - 2 * q^2 + 27 * q^3 + 28 * q^4 - 75 * q^5 - 18 * q^6 - 232 * q^7 + 24 * q^8 + 243 * q^9	\( 3 q - 2 q^{2} + 27 q^{3} + 28 q^{4} - 75 q^{5} - 18 q^{6} - 232 q^{7} + 24 q^{8} + 243 q^{9} + 50 q^{10} + 363 q^{11} + 252 q^{12} + 450 q^{13} - 1504 q^{14} - 675 q^{15} - 1360 q^{16} - 334 q^{17} - 162 q^{18} - 4036 q^{19} - 700 q^{20} - 2088 q^{21} - 242 q^{22} - 7060 q^{23} + 216 q^{24} + 1875 q^{25} + 2932 q^{26} + 2187 q^{27} - 8320 q^{28} + 4042 q^{29} + 450 q^{30} - 608 q^{31} - 3104 q^{32} + 3267 q^{33} - 3644 q^{34} + 5800 q^{35} + 2268 q^{36} + 2250 q^{37} - 12632 q^{38} + 4050 q^{39} - 600 q^{40} + 10654 q^{41} - 13536 q^{42} - 35528 q^{43} + 3388 q^{44} - 6075 q^{45} - 41800 q^{46} - 2100 q^{47} - 12240 q^{48} + 7667 q^{49} - 1250 q^{50} - 3006 q^{51} - 14520 q^{52} - 12826 q^{53} - 1458 q^{54} - 9075 q^{55} + 17088 q^{56} - 36324 q^{57} - 17196 q^{58} - 81876 q^{59} - 6300 q^{60} - 62298 q^{61} + 109184 q^{62} - 18792 q^{63} - 72256 q^{64} - 11250 q^{65} - 2178 q^{66} - 46148 q^{67} - 35832 q^{68} - 63540 q^{69} + 37600 q^{70} - 64724 q^{71} + 1944 q^{72} + 810 q^{73} - 44796 q^{74} + 16875 q^{75} + 44656 q^{76} - 28072 q^{77} + 26388 q^{78} + 43876 q^{79} + 34000 q^{80} + 19683 q^{81} + 56060 q^{82} - 101024 q^{83} - 74880 q^{84} + 8350 q^{85} + 24128 q^{86} + 36378 q^{87} + 2904 q^{88} + 60022 q^{89} + 4050 q^{90} - 28568 q^{91} + 38256 q^{92} - 5472 q^{93} + 74552 q^{94} + 100900 q^{95} - 27936 q^{96} - 319746 q^{97} + 431134 q^{98} + 29403 q^{99}+O(q^{100}) \) 3 * q - 2 * q^2 + 27 * q^3 + 28 * q^4 - 75 * q^5 - 18 * q^6 - 232 * q^7 + 24 * q^8 + 243 * q^9 + 50 * q^10 + 363 * q^11 + 252 * q^12 + 450 * q^13 - 1504 * q^14 - 675 * q^15 - 1360 * q^16 - 334 * q^17 - 162 * q^18 - 4036 * q^19 - 700 * q^20 - 2088 * q^21 - 242 * q^22 - 7060 * q^23 + 216 * q^24 + 1875 * q^25 + 2932 * q^26 + 2187 * q^27 - 8320 * q^28 + 4042 * q^29 + 450 * q^30 - 608 * q^31 - 3104 * q^32 + 3267 * q^33 - 3644 * q^34 + 5800 * q^35 + 2268 * q^36 + 2250 * q^37 - 12632 * q^38 + 4050 * q^39 - 600 * q^40 + 10654 * q^41 - 13536 * q^42 - 35528 * q^43 + 3388 * q^44 - 6075 * q^45 - 41800 * q^46 - 2100 * q^47 - 12240 * q^48 + 7667 * q^49 - 1250 * q^50 - 3006 * q^51 - 14520 * q^52 - 12826 * q^53 - 1458 * q^54 - 9075 * q^55 + 17088 * q^56 - 36324 * q^57 - 17196 * q^58 - 81876 * q^59 - 6300 * q^60 - 62298 * q^61 + 109184 * q^62 - 18792 * q^63 - 72256 * q^64 - 11250 * q^65 - 2178 * q^66 - 46148 * q^67 - 35832 * q^68 - 63540 * q^69 + 37600 * q^70 - 64724 * q^71 + 1944 * q^72 + 810 * q^73 - 44796 * q^74 + 16875 * q^75 + 44656 * q^76 - 28072 * q^77 + 26388 * q^78 + 43876 * q^79 + 34000 * q^80 + 19683 * q^81 + 56060 * q^82 - 101024 * q^83 - 74880 * q^84 + 8350 * q^85 + 24128 * q^86 + 36378 * q^87 + 2904 * q^88 + 60022 * q^89 + 4050 * q^90 - 28568 * q^91 + 38256 * q^92 - 5472 * q^93 + 74552 * q^94 + 100900 * q^95 - 27936 * q^96 - 319746 * q^97 + 431134 * q^98 + 29403 * 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 $

$2$	−1.44737	−0.255862	−0.127931	−	0.991783i	$-0.540834\pi$
$2$	−1.44737	−0.255862	−0.127931	+	0.991783i	$0.540834\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	−29.9051	−0.934535
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−13.0263	−0.147722
$7$	41.5023	0.320130	0.160065	−	0.987106i	$-0.448830\pi$
$7$	41.5023	0.320130	0.160065	+	0.987106i	$0.448830\pi$
$8$	89.5997	0.494973
$9$	81.0000	0.333333
$10$	36.1843	0.114425
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−269.146	−0.539554
$13$	434.580	0.713201	0.356600	−	0.934257i	$-0.383936\pi$
$13$	434.580	0.713201	0.356600	+	0.934257i	$0.383936\pi$
$14$	−60.0692	−0.0819090
$15$	−225.000	−0.258199
$16$	827.280	0.807890
$17$	474.359	0.398093	0.199046	−	0.979990i	$-0.436216\pi$
$17$	474.359	0.398093	0.199046	+	0.979990i	$0.436216\pi$
$18$	−117.237	−0.0852872
$19$	−2586.54	−1.64375	−0.821873	−	0.569671i	$-0.807071\pi$
$19$	−2586.54	−1.64375	−0.821873	+	0.569671i	$0.807071\pi$
$20$	747.628	0.417937
$21$	373.520	0.184827
$22$	−175.132	−0.0771452
$23$	−3671.69	−1.44726	−0.723629	−	0.690189i	$-0.757527\pi$
$23$	−3671.69	−1.44726	−0.723629	+	0.690189i	$0.757527\pi$
$24$	806.397	0.285773
$25$	625.000	0.200000
$26$	−628.999	−0.182481
$27$	729.000	0.192450
$28$	−1241.13	−0.299173
$29$	−4269.64	−0.942749	−0.471374	−	0.881933i	$-0.656242\pi$
$29$	−4269.64	−0.942749	−0.471374	+	0.881933i	$0.656242\pi$
$30$	325.659	0.0660632
$31$	−8415.46	−1.57280	−0.786400	−	0.617717i	$-0.788058\pi$
$31$	−8415.46	−1.57280	−0.786400	+	0.617717i	$0.788058\pi$
$32$	−4064.57	−0.701681
$33$	1089.00	0.174078
$34$	−686.573	−0.101857
$35$	−1037.56	−0.143167
$36$	−2422.31	−0.311512
$37$	13940.3	1.67405	0.837024	−	0.547166i	$-0.184294\pi$
$37$	13940.3	1.67405	0.837024	+	0.547166i	$0.184294\pi$
$38$	3743.68	0.420571
$39$	3911.22	0.411767
$40$	−2239.99	−0.221359
$41$	1771.24	0.164558	0.0822788	−	0.996609i	$-0.473780\pi$
$41$	1771.24	0.164558	0.0822788	+	0.996609i	$0.473780\pi$
$42$	−540.623	−0.0472902
$43$	−11481.3	−0.946932	−0.473466	−	0.880812i	$-0.656997\pi$
$43$	−11481.3	−0.946932	−0.473466	+	0.880812i	$0.656997\pi$
$44$	−3618.52	−0.281773
$45$	−2025.00	−0.149071
$46$	5314.30	0.370298
$47$	−11048.5	−0.729556	−0.364778	−	0.931094i	$-0.618855\pi$
$47$	−11048.5	−0.729556	−0.364778	+	0.931094i	$0.618855\pi$
$48$	7445.52	0.466436
$49$	−15084.6	−0.897517
$50$	−904.607	−0.0511723
$51$	4269.23	0.229839
$52$	−12996.2	−0.666511
$53$	20924.0	1.02319	0.511594	−	0.859227i	$-0.329055\pi$
$53$	20924.0	1.02319	0.511594	+	0.859227i	$0.329055\pi$
$54$	−1055.13	−0.0492406
$55$	−3025.00	−0.134840
$56$	3718.59	0.158456
$57$	−23278.8	−0.949017
$58$	6179.75	0.241213
$59$	−33001.2	−1.23424	−0.617121	−	0.786868i	$-0.711701\pi$
$59$	−33001.2	−1.23424	−0.617121	+	0.786868i	$0.711701\pi$
$60$	6728.65	0.241296
$61$	−32348.2	−1.11308	−0.556539	−	0.830821i	$-0.687871\pi$
$61$	−32348.2	−1.11308	−0.556539	+	0.830821i	$0.687871\pi$
$62$	12180.3	0.402419
$63$	3361.68	0.106710
$64$	−20590.0	−0.628357
$65$	−10864.5	−0.318953
$66$	−1576.19	−0.0445398
$67$	28892.8	0.786325	0.393163	−	0.919469i	$-0.371381\pi$
$67$	28892.8	0.786325	0.393163	+	0.919469i	$0.371381\pi$
$68$	−14185.7	−0.372032
$69$	−33045.2	−0.835575
$70$	1501.73	0.0366308
$71$	−20476.5	−0.482069	−0.241034	−	0.970517i	$-0.577487\pi$
$71$	−20476.5	−0.482069	−0.241034	+	0.970517i	$0.577487\pi$
$72$	7257.58	0.164991
$73$	−43333.2	−0.951729	−0.475864	−	0.879519i	$-0.657865\pi$
$73$	−43333.2	−0.951729	−0.475864	+	0.879519i	$0.657865\pi$
$74$	−20176.8	−0.428325
$75$	5625.00	0.115470
$76$	77350.7	1.53614
$77$	5021.77	0.0965229
$78$	−5660.99	−0.105355
$79$	−95301.8	−1.71804	−0.859020	−	0.511942i	$-0.828926\pi$
$79$	−95301.8	−1.71804	−0.859020	+	0.511942i	$0.828926\pi$
$80$	−20682.0	−0.361299
$81$	6561.00	0.111111
$82$	−2563.64	−0.0421040
$83$	−16682.8	−0.265811	−0.132905	−	0.991129i	$-0.542431\pi$
$83$	−16682.8	−0.265811	−0.132905	+	0.991129i	$0.542431\pi$
$84$	−11170.2	−0.172728
$85$	−11859.0	−0.178033
$86$	16617.7	0.242284
$87$	−38426.7	−0.544296
$88$	10841.6	0.149240
$89$	143269.	1.91724	0.958622	−	0.284681i	$-0.0918877\pi$
$89$	143269.	1.91724	0.958622	+	0.284681i	$0.0918877\pi$
$90$	2930.93	0.0381416
$91$	18036.1	0.228317
$92$	109802.	1.35251
$93$	−75739.1	−0.908057
$94$	15991.3	0.186665
$95$	64663.4	0.735105
$96$	−36581.1	−0.405116
$97$	−128960.	−1.39163	−0.695816	−	0.718220i	$-0.744957\pi$
$97$	−128960.	−1.39163	−0.695816	+	0.718220i	$0.744957\pi$
$98$	21833.0	0.229640
$99$	9801.00	0.100504
$100$	−18690.7	−0.186907
$101$	147088.	1.43475	0.717373	−	0.696689i	$-0.245344\pi$
$101$	147088.	1.43475	0.717373	+	0.696689i	$0.245344\pi$
$102$	−6179.16	−0.0588070
$103$	88889.0	0.825572	0.412786	−	0.910828i	$-0.364556\pi$
$103$	88889.0	0.825572	0.412786	+	0.910828i	$0.364556\pi$
$104$	38938.3	0.353015
$105$	−9338.01	−0.0826573
$106$	−30284.8	−0.261794
$107$	146352.	1.23577	0.617886	−	0.786268i	$-0.287989\pi$
$107$	146352.	1.23577	0.617886	+	0.786268i	$0.287989\pi$
$108$	−21800.8	−0.179851
$109$	−111535.	−0.899174	−0.449587	−	0.893236i	$-0.648429\pi$
$109$	−111535.	−0.899174	−0.449587	+	0.893236i	$0.648429\pi$
$110$	4378.30	0.0345004
$111$	125463.	0.966512
$112$	34334.0	0.258630
$113$	−56633.9	−0.417234	−0.208617	−	0.977997i	$-0.566896\pi$
$113$	−56633.9	−0.417234	−0.208617	+	0.977997i	$0.566896\pi$
$114$	33693.1	0.242817
$115$	91792.2	0.647234
$116$	127684.	0.881031
$117$	35201.0	0.237734
$118$	47765.1	0.315795
$119$	19687.0	0.127442
$120$	−20159.9	−0.127802
$121$	14641.0	0.0909091
$122$	46819.9	0.284794
$123$	15941.2	0.0950074
$124$	251665.	1.46984
$125$	−15625.0	−0.0894427
$126$	−4865.61	−0.0273030
$127$	79565.3	0.437738	0.218869	−	0.975754i	$-0.429763\pi$
$127$	79565.3	0.437738	0.218869	+	0.975754i	$0.429763\pi$
$128$	159868.	0.862454
$129$	−103331.	−0.546712
$130$	15725.0	0.0816078
$131$	73365.2	0.373518	0.186759	−	0.982406i	$-0.440202\pi$
$131$	73365.2	0.373518	0.186759	+	0.982406i	$0.440202\pi$
$132$	−32566.7	−0.162682
$133$	−107347.	−0.526213
$134$	−41818.6	−0.201190
$135$	−18225.0	−0.0860663
$136$	42502.4	0.197045
$137$	−130737.	−0.595112	−0.297556	−	0.954704i	$-0.596171\pi$
$137$	−130737.	−0.595112	−0.297556	+	0.954704i	$0.596171\pi$
$138$	47828.7	0.213792
$139$	−366480.	−1.60884	−0.804420	−	0.594060i	$-0.797524\pi$
$139$	−366480.	−1.60884	−0.804420	+	0.594060i	$0.797524\pi$
$140$	31028.3	0.133794
$141$	−99436.5	−0.421209
$142$	29637.0	0.123343
$143$	52584.2	0.215038
$144$	67009.6	0.269297
$145$	106741.	0.421610
$146$	62719.2	0.243511
$147$	−135761.	−0.518181
$148$	−416886.	−1.56446
$149$	476119.	1.75691	0.878455	−	0.477825i	$-0.158575\pi$
$149$	476119.	1.75691	0.878455	+	0.477825i	$0.158575\pi$
$150$	−8141.47	−0.0295444
$151$	231635.	0.826725	0.413362	−	0.910567i	$-0.364354\pi$
$151$	231635.	0.826725	0.413362	+	0.910567i	$0.364354\pi$
$152$	−231753.	−0.813610
$153$	38423.0	0.132698
$154$	−7268.38	−0.0246965
$155$	210386.	0.703378
$156$	−116966.	−0.384810
$157$	−79283.9	−0.256706	−0.128353	−	0.991729i	$-0.540969\pi$
$157$	−79283.9	−0.256706	−0.128353	+	0.991729i	$0.540969\pi$
$158$	137937.	0.439581
$159$	188316.	0.590738
$160$	101614.	0.313801
$161$	−152383.	−0.463311
$162$	−9496.21	−0.0284291
$163$	−303550.	−0.894872	−0.447436	−	0.894316i	$-0.647663\pi$
$163$	−303550.	−0.894872	−0.447436	+	0.894316i	$0.647663\pi$
$164$	−52969.1	−0.153785
$165$	−27225.0	−0.0778499
$166$	24146.2	0.0680108
$167$	−547748.	−1.51981	−0.759906	−	0.650033i	$-0.774755\pi$
$167$	−547748.	−1.51981	−0.759906	+	0.650033i	$0.774755\pi$
$168$	33467.3	0.0914846
$169$	−182433.	−0.491345
$170$	17164.3	0.0455517
$171$	−209509.	−0.547915
$172$	343349.	0.884941
$173$	−350354.	−0.890003	−0.445001	−	0.895530i	$-0.646797\pi$
$173$	−350354.	−0.890003	−0.445001	+	0.895530i	$0.646797\pi$
$174$	55617.8	0.139264
$175$	25938.9	0.0640261
$176$	100101.	0.243588
$177$	−297011.	−0.712590
$178$	−207364.	−0.490549
$179$	185899.	0.433656	0.216828	−	0.976210i	$-0.430429\pi$
$179$	185899.	0.433656	0.216828	+	0.976210i	$0.430429\pi$
$180$	60557.9	0.139312
$181$	247930.	0.562513	0.281257	−	0.959633i	$-0.409249\pi$
$181$	247930.	0.562513	0.281257	+	0.959633i	$0.409249\pi$
$182$	−26104.9	−0.0584176
$183$	−291134.	−0.642636
$184$	−328982.	−0.716354
$185$	−348508.	−0.748657
$186$	109623.	0.232337
$187$	57397.4	0.120030
$188$	330407.	0.681796
$189$	30255.2	0.0616091
$190$	−93592.0	−0.188085
$191$	715625.	1.41939	0.709695	−	0.704509i	$-0.248833\pi$
$191$	715625.	1.41939	0.709695	+	0.704509i	$0.248833\pi$
$192$	−185310.	−0.362782
$193$	315860.	0.610381	0.305191	−	0.952291i	$-0.401280\pi$
$193$	315860.	0.610381	0.305191	+	0.952291i	$0.401280\pi$
$194$	186653.	0.356065
$195$	−97780.6	−0.184148
$196$	451106.	0.838761
$197$	139508.	0.256115	0.128058	−	0.991767i	$-0.459126\pi$
$197$	139508.	0.256115	0.128058	+	0.991767i	$0.459126\pi$
$198$	−14185.7	−0.0257151
$199$	183434.	0.328358	0.164179	−	0.986431i	$-0.447503\pi$
$199$	183434.	0.328358	0.164179	+	0.986431i	$0.447503\pi$
$200$	55999.8	0.0989946
$201$	260035.	0.453985
$202$	−212892.	−0.367096
$203$	−177200.	−0.301802
$204$	−127672.	−0.214793
$205$	−44281.0	−0.0735924
$206$	−128655.	−0.211232
$207$	−297407.	−0.482420
$208$	359519.	0.576188
$209$	−312971.	−0.495608
$210$	13515.6	0.0211488
$211$	−341928.	−0.528723	−0.264361	−	0.964424i	$-0.585161\pi$
$211$	−341928.	−0.528723	−0.264361	+	0.964424i	$0.585161\pi$
$212$	−625735.	−0.956204
$213$	−184288.	−0.278322
$214$	−211825.	−0.316186
$215$	287032.	0.423481
$216$	65318.2	0.0952576
$217$	−349261.	−0.503501
$218$	161432.	0.230064
$219$	−389998.	−0.549481
$220$	90463.0	0.126013
$221$	206147.	0.283920
$222$	−181591.	−0.247293
$223$	−1.01837e6	−1.37133	−0.685665	−	0.727917i	$-0.740489\pi$
$223$	−1.01837e6	−1.37133	−0.685665	+	0.727917i	$0.740489\pi$
$224$	−168689.	−0.224629
$225$	50625.0	0.0666667
$226$	81970.3	0.106754
$227$	−362408.	−0.466802	−0.233401	−	0.972381i	$-0.574985\pi$
$227$	−362408.	−0.466802	−0.233401	+	0.972381i	$0.574985\pi$
$228$	696156.	0.886889
$229$	−1.38333e6	−1.74315	−0.871577	−	0.490258i	$-0.836902\pi$
$229$	−1.38333e6	−1.74315	−0.871577	+	0.490258i	$0.836902\pi$
$230$	−132857.	−0.165602
$231$	45196.0	0.0557275
$232$	−382558.	−0.466635
$233$	1.19085e6	1.43704	0.718519	−	0.695507i	$-0.244820\pi$
$233$	1.19085e6	1.43704	0.718519	+	0.695507i	$0.244820\pi$
$234$	−50948.9	−0.0608269
$235$	276213.	0.326267
$236$	986906.	1.15344
$237$	−857716.	−0.991911
$238$	−28494.3	−0.0326074
$239$	638385.	0.722916	0.361458	−	0.932388i	$-0.382279\pi$
$239$	638385.	0.722916	0.361458	+	0.932388i	$0.382279\pi$
$240$	−186138.	−0.208596
$241$	301289.	0.334150	0.167075	−	0.985944i	$-0.446568\pi$
$241$	301289.	0.334150	0.167075	+	0.985944i	$0.446568\pi$
$242$	−21191.0	−0.0232601
$243$	59049.0	0.0641500
$244$	967378.	1.04021
$245$	377114.	0.401382
$246$	−23072.8	−0.0243087
$247$	−1.12406e6	−1.17232
$248$	−754023.	−0.778494
$249$	−150145.	−0.153466
$250$	22615.2	0.0228850
$251$	−285054.	−0.285590	−0.142795	−	0.989752i	$-0.545609\pi$
$251$	−285054.	−0.285590	−0.142795	+	0.989752i	$0.545609\pi$
$252$	−100532.	−0.0997243
$253$	−444274.	−0.436365
$254$	−115161.	−0.112000
$255$	−106731.	−0.102787
$256$	427492.	0.407688
$257$	−1.72616e6	−1.63022	−0.815112	−	0.579303i	$-0.803325\pi$
$257$	−1.72616e6	−1.63022	−0.815112	+	0.579303i	$0.803325\pi$
$258$	149559.	0.139882
$259$	578554.	0.535913
$260$	324904.	0.298073
$261$	−345841.	−0.314250
$262$	−106187.	−0.0955690
$263$	−1.29514e6	−1.15459	−0.577296	−	0.816535i	$-0.695892\pi$
$263$	−1.29514e6	−1.15459	−0.577296	+	0.816535i	$0.695892\pi$
$264$	97574.1	0.0861638
$265$	−523100.	−0.457583
$266$	155371.	0.134638
$267$	1.28942e6	1.10692
$268$	−864042.	−0.734848
$269$	−1.96289e6	−1.65392	−0.826960	−	0.562261i	$-0.809932\pi$
$269$	−1.96289e6	−1.65392	−0.826960	+	0.562261i	$0.809932\pi$
$270$	26378.4	0.0220211
$271$	436034.	0.360659	0.180330	−	0.983606i	$-0.442284\pi$
$271$	436034.	0.360659	0.180330	+	0.983606i	$0.442284\pi$
$272$	392427.	0.321615
$273$	162325.	0.131819
$274$	189226.	0.152266
$275$	75625.0	0.0603023
$276$	988220.	0.780874
$277$	−1.10131e6	−0.862401	−0.431201	−	0.902256i	$-0.641910\pi$
$277$	−1.10131e6	−0.862401	−0.431201	+	0.902256i	$0.641910\pi$
$278$	530433.	0.411641
$279$	−681652.	−0.524267
$280$	−92964.8	−0.0708636
$281$	1.21262e6	0.916135	0.458067	−	0.888917i	$-0.348542\pi$
$281$	1.21262e6	0.916135	0.458067	+	0.888917i	$0.348542\pi$
$282$	143922.	0.107771
$283$	2.07749e6	1.54196	0.770979	−	0.636860i	$-0.219767\pi$
$283$	2.07749e6	1.54196	0.770979	+	0.636860i	$0.219767\pi$
$284$	612351.	0.450510
$285$	581971.	0.424413
$286$	−76108.9	−0.0550200
$287$	73510.5	0.0526799
$288$	−329230.	−0.233894
$289$	−1.19484e6	−0.841522
$290$	−154494.	−0.107874
$291$	−1.16064e6	−0.803460
$292$	1.29588e6	0.889424
$293$	1.75150e6	1.19190	0.595950	−	0.803021i	$-0.296775\pi$
$293$	1.75150e6	1.19190	0.595950	+	0.803021i	$0.296775\pi$
$294$	196497.	0.132583
$295$	825031.	0.551970
$296$	1.24905e6	0.828609
$297$	88209.0	0.0580259
$298$	−689121.	−0.449526
$299$	−1.59564e6	−1.03219
$300$	−168216.	−0.107911
$301$	−476499.	−0.303142
$302$	−335261.	−0.211527
$303$	1.32380e6	0.828351
$304$	−2.13979e6	−1.32797
$305$	808706.	0.497784
$306$	−55612.4	−0.0339522
$307$	2.76532e6	1.67456	0.837278	−	0.546777i	$-0.184146\pi$
$307$	2.76532e6	1.67456	0.837278	+	0.546777i	$0.184146\pi$
$308$	−150177.	−0.0902040
$309$	800001.	0.476644
$310$	−304507.	−0.179967
$311$	138490.	0.0811925	0.0405962	−	0.999176i	$-0.487074\pi$
$311$	138490.	0.0811925	0.0405962	+	0.999176i	$0.487074\pi$
$312$	350444.	0.203813
$313$	2.25033e6	1.29833	0.649165	−	0.760647i	$-0.275118\pi$
$313$	2.25033e6	1.29833	0.649165	+	0.760647i	$0.275118\pi$
$314$	114753.	0.0656812
$315$	−84042.1	−0.0477222
$316$	2.85001e6	1.60557
$317$	−300036.	−0.167697	−0.0838486	−	0.996479i	$-0.526721\pi$
$317$	−300036.	−0.167697	−0.0838486	+	0.996479i	$0.526721\pi$
$318$	−272563.	−0.151147
$319$	−516626.	−0.284249
$320$	514750.	0.281010
$321$	1.31716e6	0.713473
$322$	220555.	0.118544
$323$	−1.22695e6	−0.654363
$324$	−196207.	−0.103837
$325$	271613.	0.142640
$326$	439350.	0.228963
$327$	−1.00381e6	−0.519139
$328$	158703.	0.0814516
$329$	−458538.	−0.233553
$330$	39404.7	0.0199188
$331$	637880.	0.320014	0.160007	−	0.987116i	$-0.448848\pi$
$331$	637880.	0.320014	0.160007	+	0.987116i	$0.448848\pi$
$332$	498900.	0.248410
$333$	1.12916e6	0.558016
$334$	792796.	0.388862
$335$	−722319.	−0.351655
$336$	309006.	0.149320
$337$	119077.	0.0571153	0.0285576	−	0.999592i	$-0.490909\pi$
$337$	119077.	0.0571153	0.0285576	+	0.999592i	$0.490909\pi$
$338$	264048.	0.125716
$339$	−509705.	−0.240890
$340$	354644.	0.166378
$341$	−1.01827e6	−0.474217
$342$	303238.	0.140190
$343$	−1.32357e6	−0.607453
$344$	−1.02872e6	−0.468706
$345$	826130.	0.373681
$346$	507092.	0.227718
$347$	−2.35817e6	−1.05136	−0.525681	−	0.850682i	$-0.676189\pi$
$347$	−2.35817e6	−1.05136	−0.525681	+	0.850682i	$0.676189\pi$
$348$	1.14916e6	0.508664
$349$	2.71913e6	1.19500	0.597499	−	0.801870i	$-0.296161\pi$
$349$	2.71913e6	1.19500	0.597499	+	0.801870i	$0.296161\pi$
$350$	−37543.3	−0.0163818
$351$	316809.	0.137256
$352$	−491813.	−0.211565
$353$	−787647.	−0.336430	−0.168215	−	0.985750i	$-0.553800\pi$
$353$	−787647.	−0.336430	−0.168215	+	0.985750i	$0.553800\pi$
$354$	429885.	0.182324
$355$	511911.	0.215588
$356$	−4.28448e6	−1.79173
$357$	177183.	0.0735784
$358$	−269065.	−0.110956
$359$	3.28528e6	1.34535	0.672676	−	0.739937i	$-0.265145\pi$
$359$	3.28528e6	1.34535	0.672676	+	0.739937i	$0.265145\pi$
$360$	−181439.	−0.0737862
$361$	4.21407e6	1.70190
$362$	−358847.	−0.143926
$363$	131769.	0.0524864
$364$	−539371.	−0.213370
$365$	1.08333e6	0.425626
$366$	421379.	0.164426
$367$	−700644.	−0.271539	−0.135770	−	0.990740i	$-0.543351\pi$
$367$	−700644.	−0.271539	−0.135770	+	0.990740i	$0.543351\pi$
$368$	−3.03751e6	−1.16923
$369$	143470.	0.0548525
$370$	504420.	0.191553
$371$	868394.	0.327553
$372$	2.26499e6	0.848611
$373$	−2.59078e6	−0.964180	−0.482090	−	0.876122i	$-0.660122\pi$
$373$	−2.59078e6	−0.964180	−0.482090	+	0.876122i	$0.660122\pi$
$374$	−83075.4	−0.0307109
$375$	−140625.	−0.0516398
$376$	−989943.	−0.361111
$377$	−1.85550e6	−0.672369
$378$	−43790.5	−0.0157634
$379$	−672260.	−0.240402	−0.120201	−	0.992750i	$-0.538354\pi$
$379$	−672260.	−0.240402	−0.120201	+	0.992750i	$0.538354\pi$
$380$	−1.93377e6	−0.686982
$381$	716088.	0.252728
$382$	−1.03577e6	−0.363168
$383$	2.41377e6	0.840813	0.420407	−	0.907336i	$-0.361887\pi$
$383$	2.41377e6	0.840813	0.420407	+	0.907336i	$0.361887\pi$
$384$	1.43881e6	0.497938
$385$	−125544.	−0.0431664
$386$	−457167.	−0.156173
$387$	−929983.	−0.315644
$388$	3.85655e6	1.30053
$389$	3.01046e6	1.00869	0.504347	−	0.863501i	$-0.331733\pi$
$389$	3.01046e6	1.00869	0.504347	+	0.863501i	$0.331733\pi$
$390$	141525.	0.0471163
$391$	−1.74170e6	−0.576143
$392$	−1.35157e6	−0.444247
$393$	660287.	0.215651
$394$	−201921.	−0.0655300
$395$	2.38255e6	0.768331
$396$	−293100.	−0.0939243
$397$	871291.	0.277452	0.138726	−	0.990331i	$-0.455699\pi$
$397$	871291.	0.277452	0.138726	+	0.990331i	$0.455699\pi$
$398$	−265498.	−0.0840142
$399$	−966124.	−0.303809
$400$	517050.	0.161578
$401$	−2.01901e6	−0.627014	−0.313507	−	0.949586i	$-0.601504\pi$
$401$	−2.01901e6	−0.627014	−0.313507	+	0.949586i	$0.601504\pi$
$402$	−376367.	−0.116157
$403$	−3.65719e6	−1.12172
$404$	−4.39869e6	−1.34082
$405$	−164025.	−0.0496904
$406$	256474.	0.0772196
$407$	1.68678e6	0.504744
$408$	382522.	0.113764
$409$	−346377.	−0.102386	−0.0511930	−	0.998689i	$-0.516302\pi$
$409$	−346377.	−0.102386	−0.0511930	+	0.998689i	$0.516302\pi$
$410$	64091.1	0.0188295
$411$	−1.17664e6	−0.343588
$412$	−2.65824e6	−0.771526
$413$	−1.36963e6	−0.395118
$414$	430458.	0.123433
$415$	417069.	0.118874
$416$	−1.76638e6	−0.500440
$417$	−3.29832e6	−0.928865
$418$	452985.	0.126807
$419$	−938584.	−0.261179	−0.130589	−	0.991437i	$-0.541687\pi$
$419$	−938584.	−0.261179	−0.130589	+	0.991437i	$0.541687\pi$
$420$	279254.	0.0772461
$421$	4.88046e6	1.34201	0.671004	−	0.741454i	$-0.265863\pi$
$421$	4.88046e6	1.34201	0.671004	+	0.741454i	$0.265863\pi$
$422$	494897.	0.135280
$423$	−894929.	−0.243185
$424$	1.87479e6	0.506450
$425$	296474.	0.0796186
$426$	266733.	0.0712120
$427$	−1.34253e6	−0.356330
$428$	−4.37666e6	−1.15487
$429$	473258.	0.124152
$430$	−415442.	−0.108353
$431$	−5.27493e6	−1.36780	−0.683902	−	0.729574i	$-0.739718\pi$
$431$	−5.27493e6	−1.36780	−0.683902	+	0.729574i	$0.739718\pi$
$432$	603087.	0.155479
$433$	−3.30374e6	−0.846811	−0.423405	−	0.905940i	$-0.639165\pi$
$433$	−3.30374e6	−0.846811	−0.423405	+	0.905940i	$0.639165\pi$
$434$	505510.	0.128827
$435$	960668.	0.243417
$436$	3.33546e6	0.840310
$437$	9.49695e6	2.37892
$438$	564473.	0.140591
$439$	5.92591e6	1.46755	0.733777	−	0.679391i	$-0.237756\pi$
$439$	5.92591e6	1.46755	0.733777	+	0.679391i	$0.237756\pi$
$440$	−271039.	−0.0667422
$441$	−1.22185e6	−0.299172
$442$	−298371.	−0.0726442
$443$	2.36693e6	0.573029	0.286515	−	0.958076i	$-0.407503\pi$
$443$	2.36693e6	0.573029	0.286515	+	0.958076i	$0.407503\pi$
$444$	−3.75198e6	−0.903239
$445$	−3.58173e6	−0.857418
$446$	1.47396e6	0.350871
$447$	4.28507e6	1.01435
$448$	−854532.	−0.201156
$449$	−3.35144e6	−0.784540	−0.392270	−	0.919850i	$-0.628310\pi$
$449$	−3.35144e6	−0.784540	−0.392270	+	0.919850i	$0.628310\pi$
$450$	−73273.2	−0.0170574
$451$	214320.	0.0496160
$452$	1.69364e6	0.389920
$453$	2.08471e6	0.477310
$454$	524539.	0.119437
$455$	−450902.	−0.102107
$456$	−2.08578e6	−0.469738
$457$	4.04376e6	0.905721	0.452861	−	0.891581i	$-0.350404\pi$
$457$	4.04376e6	0.905721	0.452861	+	0.891581i	$0.350404\pi$
$458$	2.00219e6	0.446006
$459$	345807.	0.0766130
$460$	−2.74506e6	−0.604862
$461$	−8.31607e6	−1.82249	−0.911247	−	0.411861i	$-0.864879\pi$
$461$	−8.31607e6	−1.82249	−0.911247	+	0.411861i	$0.864879\pi$
$462$	−65415.4	−0.0142585
$463$	−5.54406e6	−1.20192	−0.600960	−	0.799279i	$-0.705215\pi$
$463$	−5.54406e6	−1.20192	−0.600960	+	0.799279i	$0.705215\pi$
$464$	−3.53218e6	−0.761637
$465$	1.89348e6	0.406095
$466$	−1.72361e6	−0.367683
$467$	−5.54472e6	−1.17649	−0.588244	−	0.808684i	$-0.700180\pi$
$467$	−5.54472e6	−1.17649	−0.588244	+	0.808684i	$0.700180\pi$
$468$	−1.05269e6	−0.222170
$469$	1.19912e6	0.251726
$470$	−399782.	−0.0834793
$471$	−713555.	−0.148209
$472$	−2.95690e6	−0.610916
$473$	−1.38923e6	−0.285511
$474$	1.24143e6	0.253792
$475$	−1.61659e6	−0.328749
$476$	−588741.	−0.119099
$477$	1.69484e6	0.341063
$478$	−923980.	−0.184966
$479$	2.93070e6	0.583624	0.291812	−	0.956476i	$-0.405742\pi$
$479$	2.93070e6	0.583624	0.291812	+	0.956476i	$0.405742\pi$
$480$	914529.	0.181173
$481$	6.05818e6	1.19393
$482$	−436078.	−0.0854961
$483$	−1.37145e6	−0.267493
$484$	−437841.	−0.0849577
$485$	3.22399e6	0.622357
$486$	−85465.9	−0.0164135
$487$	−370838.	−0.0708536	−0.0354268	−	0.999372i	$-0.511279\pi$
$487$	−370838.	−0.0708536	−0.0354268	+	0.999372i	$0.511279\pi$
$488$	−2.89839e6	−0.550944
$489$	−2.73195e6	−0.516655
$490$	−545824.	−0.102698
$491$	592085.	0.110836	0.0554179	−	0.998463i	$-0.482351\pi$
$491$	592085.	0.110836	0.0554179	+	0.998463i	$0.482351\pi$
$492$	−476722.	−0.0887877
$493$	−2.02534e6	−0.375301
$494$	1.62693e6	0.299952
$495$	−245025.	−0.0449467
$496$	−6.96194e6	−1.27065
$497$	−849819.	−0.154325
$498$	217315.	0.0392661
$499$	−6.23154e6	−1.12032	−0.560162	−	0.828383i	$-0.689261\pi$
$499$	−6.23154e6	−1.12032	−0.560162	+	0.828383i	$0.689261\pi$
$500$	467267.	0.0835873
$501$	−4.92974e6	−0.877464
$502$	412579.	0.0730714
$503$	6.58812e6	1.16102	0.580512	−	0.814251i	$-0.302852\pi$
$503$	6.58812e6	1.16102	0.580512	+	0.814251i	$0.302852\pi$
$504$	301206.	0.0528186
$505$	−3.67721e6	−0.641638
$506$	643030.	0.111649
$507$	−1.64190e6	−0.283678
$508$	−2.37941e6	−0.409082
$509$	8.26967e6	1.41479	0.707397	−	0.706816i	$-0.249869\pi$
$509$	8.26967e6	1.41479	0.707397	+	0.706816i	$0.249869\pi$
$510$	154479.	0.0262993
$511$	−1.79842e6	−0.304677
$512$	−5.73451e6	−0.966765
$513$	−1.88559e6	−0.316339
$514$	2.49839e6	0.417112
$515$	−2.22222e6	−0.369207
$516$	3.09014e6	0.510921
$517$	−1.33687e6	−0.219969
$518$	−837383.	−0.137120
$519$	−3.15318e6	−0.513843
$520$	−973457.	−0.157873
$521$	1.99187e6	0.321490	0.160745	−	0.986996i	$-0.448610\pi$
$521$	1.99187e6	0.321490	0.160745	+	0.986996i	$0.448610\pi$
$522$	500560.	0.0804044
$523$	7.99327e6	1.27782	0.638911	−	0.769281i	$-0.279385\pi$
$523$	7.99327e6	1.27782	0.638911	+	0.769281i	$0.279385\pi$
$524$	−2.19399e6	−0.349066
$525$	233450.	0.0369655
$526$	1.87455e6	0.295416
$527$	−3.99194e6	−0.626121
$528$	900907.	0.140636
$529$	7.04495e6	1.09456
$530$	757121.	0.117078
$531$	−2.67310e6	−0.411414
$532$	3.21023e6	0.491764
$533$	769746.	0.117363
$534$	−1.86627e6	−0.283219
$535$	−3.65879e6	−0.552654
$536$	2.58878e6	0.389210
$537$	1.67309e6	0.250371
$538$	2.84103e6	0.423175
$539$	−1.82523e6	−0.270611
$540$	545021.	0.0804320
$541$	−8.83361e6	−1.29761	−0.648806	−	0.760954i	$-0.724731\pi$
$541$	−8.83361e6	−1.29761	−0.648806	+	0.760954i	$0.724731\pi$
$542$	−631103.	−0.0922789
$543$	2.23137e6	0.324767
$544$	−1.92806e6	−0.279334
$545$	2.78837e6	0.402123
$546$	−234944.	−0.0337274
$547$	2.98240e6	0.426184	0.213092	−	0.977032i	$-0.431647\pi$
$547$	2.98240e6	0.426184	0.213092	+	0.977032i	$0.431647\pi$
$548$	3.90972e6	0.556153
$549$	−2.62021e6	−0.371026
$550$	−109457.	−0.0154290
$551$	1.10436e7	1.54964
$552$	−2.96084e6	−0.413587
$553$	−3.95524e6	−0.549997
$554$	1.59400e6	0.220655
$555$	−3.13657e6	−0.432237
$556$	1.09596e7	1.50352
$557$	1.20831e7	1.65021	0.825105	−	0.564979i	$-0.191116\pi$
$557$	1.20831e7	1.65021	0.825105	+	0.564979i	$0.191116\pi$
$558$	986604.	0.134140
$559$	−4.98954e6	−0.675353
$560$	−858350.	−0.115663
$561$	516576.	0.0692991
$562$	−1.75511e6	−0.234404
$563$	−1.18255e7	−1.57235	−0.786176	−	0.618003i	$-0.787942\pi$
$563$	−1.18255e7	−1.57235	−0.786176	+	0.618003i	$0.787942\pi$
$564$	2.97366e6	0.393635
$565$	1.41585e6	0.186593
$566$	−3.00690e6	−0.394528
$567$	272296.	0.0355700
$568$	−1.83468e6	−0.238611
$569$	−1.13220e6	−0.146603	−0.0733014	−	0.997310i	$-0.523353\pi$
$569$	−1.13220e6	−0.146603	−0.0733014	+	0.997310i	$0.523353\pi$
$570$	−842328.	−0.108591
$571$	−2.92831e6	−0.375860	−0.187930	−	0.982182i	$-0.560178\pi$
$571$	−2.92831e6	−0.375860	−0.187930	+	0.982182i	$0.560178\pi$
$572$	−1.57254e6	−0.200961
$573$	6.44062e6	0.819485
$574$	−106397.	−0.0134788
$575$	−2.29480e6	−0.289452
$576$	−1.66779e6	−0.209452
$577$	3.70459e6	0.463235	0.231617	−	0.972807i	$-0.425598\pi$
$577$	3.70459e6	0.463235	0.231617	+	0.972807i	$0.425598\pi$
$578$	1.72938e6	0.215313
$579$	2.84274e6	0.352404
$580$	−3.19210e6	−0.394009
$581$	−692373.	−0.0850941
$582$	1.67987e6	0.205574
$583$	2.53181e6	0.308503
$584$	−3.88264e6	−0.471080
$585$	−880025.	−0.106318
$586$	−2.53507e6	−0.304962
$587$	6.77491e6	0.811537	0.405769	−	0.913976i	$-0.367004\pi$
$587$	6.77491e6	0.811537	0.405769	+	0.913976i	$0.367004\pi$
$588$	4.05995e6	0.484259
$589$	2.17669e7	2.58528
$590$	−1.19413e6	−0.141228
$591$	1.25558e6	0.147868
$592$	1.15325e7	1.35245
$593$	1.58897e7	1.85557	0.927787	−	0.373111i	$-0.121709\pi$
$593$	1.58897e7	1.85557	0.927787	+	0.373111i	$0.121709\pi$
$594$	−127671.	−0.0148466
$595$	−492174.	−0.0569936
$596$	−1.42384e7	−1.64189
$597$	1.65091e6	0.189578
$598$	2.30949e6	0.264097
$599$	4.74611e6	0.540469	0.270234	−	0.962795i	$-0.412899\pi$
$599$	4.74611e6	0.540469	0.270234	+	0.962795i	$0.412899\pi$
$600$	503998.	0.0571546
$601$	−2.55803e6	−0.288882	−0.144441	−	0.989513i	$-0.546138\pi$
$601$	−2.55803e6	−0.288882	−0.144441	+	0.989513i	$0.546138\pi$
$602$	689671.	0.0775623
$603$	2.34031e6	0.262108
$604$	−6.92706e6	−0.772603
$605$	−366025.	−0.0406558
$606$	−1.91602e6	−0.211943
$607$	1.28362e6	0.141405	0.0707025	−	0.997497i	$-0.477476\pi$
$607$	1.28362e6	0.141405	0.0707025	+	0.997497i	$0.477476\pi$
$608$	1.05132e7	1.15339
$609$	−1.59480e6	−0.174246
$610$	−1.17050e6	−0.127364
$611$	−4.80146e6	−0.520320
$612$	−1.14905e6	−0.124011
$613$	1.01402e7	1.08992	0.544960	−	0.838462i	$-0.316545\pi$
$613$	1.01402e7	1.08992	0.544960	+	0.838462i	$0.316545\pi$
$614$	−4.00245e6	−0.428455
$615$	−398529.	−0.0424886
$616$	449950.	0.0477763
$617$	1.44801e7	1.53130	0.765649	−	0.643259i	$-0.222418\pi$
$617$	1.44801e7	1.53130	0.765649	+	0.643259i	$0.222418\pi$
$618$	−1.15790e6	−0.121955
$619$	1.03997e6	0.109092	0.0545462	−	0.998511i	$-0.482629\pi$
$619$	1.03997e6	0.109092	0.0545462	+	0.998511i	$0.482629\pi$
$620$	−6.29163e6	−0.657331
$621$	−2.67666e6	−0.278525
$622$	−200446.	−0.0207740
$623$	5.94599e6	0.613768
$624$	3.23567e6	0.332662
$625$	390625.	0.0400000
$626$	−3.25706e6	−0.332193
$627$	−2.81674e6	−0.286139
$628$	2.37099e6	0.239901
$629$	6.61270e6	0.666426
$630$	121640.	0.0122103
$631$	1.25757e7	1.25736	0.628681	−	0.777664i	$-0.283595\pi$
$631$	1.25757e7	1.25736	0.628681	+	0.777664i	$0.283595\pi$
$632$	−8.53902e6	−0.850384
$633$	−3.07735e6	−0.305258
$634$	434264.	0.0429073
$635$	−1.98913e6	−0.195763
$636$	−5.63161e6	−0.552065
$637$	−6.55545e6	−0.640109
$638$	747750.	0.0727285
$639$	−1.65859e6	−0.160690
$640$	−3.99669e6	−0.385701
$641$	5.13372e6	0.493500	0.246750	−	0.969079i	$-0.420637\pi$
$641$	5.13372e6	0.493500	0.246750	+	0.969079i	$0.420637\pi$
$642$	−1.90643e6	−0.182550
$643$	−1.80636e7	−1.72296	−0.861482	−	0.507788i	$-0.830463\pi$
$643$	−1.80636e7	−1.72296	−0.861482	+	0.507788i	$0.830463\pi$
$644$	4.55704e6	0.432981
$645$	2.58329e6	0.244497
$646$	1.77585e6	0.167426
$647$	−298642.	−0.0280472	−0.0140236	−	0.999902i	$-0.504464\pi$
$647$	−298642.	−0.0280472	−0.0140236	+	0.999902i	$0.504464\pi$
$648$	587864.	0.0549970
$649$	−3.99315e6	−0.372138
$650$	−393125.	−0.0364961
$651$	−3.14335e6	−0.290696
$652$	9.07770e6	0.836289
$653$	1.52761e6	0.140194	0.0700971	−	0.997540i	$-0.477669\pi$
$653$	1.52761e6	0.140194	0.0700971	+	0.997540i	$0.477669\pi$
$654$	1.45289e6	0.132828
$655$	−1.83413e6	−0.167042
$656$	1.46531e6	0.132944
$657$	−3.50999e6	−0.317243
$658$	663675.	0.0597573
$659$	1.69648e7	1.52172	0.760862	−	0.648913i	$-0.224776\pi$
$659$	1.69648e7	1.52172	0.760862	+	0.648913i	$0.224776\pi$
$660$	814167.	0.0727534
$661$	−7.24635e6	−0.645083	−0.322542	−	0.946555i	$-0.604537\pi$
$661$	−7.24635e6	−0.645083	−0.322542	+	0.946555i	$0.604537\pi$
$662$	−923249.	−0.0818793
$663$	1.85532e6	0.163921
$664$	−1.49477e6	−0.131569
$665$	2.68368e6	0.235330
$666$	−1.63432e6	−0.142775
$667$	1.56768e7	1.36440
$668$	1.63805e7	1.42032
$669$	−9.16530e6	−0.791738
$670$	1.04546e6	0.0899751
$671$	−3.91414e6	−0.335606
$672$	−1.51820e6	−0.129690
$673$	−2.29001e7	−1.94895	−0.974473	−	0.224505i	$-0.927923\pi$
$673$	−2.29001e7	−1.94895	−0.974473	+	0.224505i	$0.927923\pi$
$674$	−172348.	−0.0146136
$675$	455625.	0.0384900
$676$	5.45568e6	0.459179
$677$	1.31898e7	1.10603	0.553015	−	0.833171i	$-0.313477\pi$
$677$	1.31898e7	1.10603	0.553015	+	0.833171i	$0.313477\pi$
$678$	737732.	0.0616346
$679$	−5.35212e6	−0.445504
$680$	−1.06256e6	−0.0881213
$681$	−3.26167e6	−0.269508
$682$	1.47382e6	0.121334
$683$	−2.11554e7	−1.73528	−0.867638	−	0.497196i	$-0.834363\pi$
$683$	−2.11554e7	−1.73528	−0.867638	+	0.497196i	$0.834363\pi$
$684$	6.26540e6	0.512046
$685$	3.26844e6	0.266142
$686$	1.91570e6	0.155424
$687$	−1.24499e7	−1.00641
$688$	−9.49822e6	−0.765017
$689$	9.09316e6	0.729738
$690$	−1.19572e6	−0.0956105
$691$	−1.40736e7	−1.12127	−0.560636	−	0.828063i	$-0.689443\pi$
$691$	−1.40736e7	−1.12127	−0.560636	+	0.828063i	$0.689443\pi$
$692$	1.04774e7	0.831739
$693$	406764.	0.0321743
$694$	3.41315e6	0.269003
$695$	9.16200e6	0.719495
$696$	−3.44302e6	−0.269412
$697$	840203.	0.0655092
$698$	−3.93560e6	−0.305754
$699$	1.07177e7	0.829674
$700$	−775706.	−0.0598346
$701$	−5.70759e6	−0.438690	−0.219345	−	0.975647i	$-0.570392\pi$
$701$	−5.70759e6	−0.438690	−0.219345	+	0.975647i	$0.570392\pi$
$702$	−458541.	−0.0351184
$703$	−3.60571e7	−2.75171
$704$	−2.49139e6	−0.189457
$705$	2.48591e6	0.188371
$706$	1.14002e6	0.0860796
$707$	6.10450e6	0.459306
$708$	8.88215e6	0.665940
$709$	−6.05501e6	−0.452375	−0.226188	−	0.974084i	$-0.572626\pi$
$709$	−6.05501e6	−0.452375	−0.226188	+	0.974084i	$0.572626\pi$
$710$	−740926.	−0.0551606
$711$	−7.71945e6	−0.572680
$712$	1.28369e7	0.948985
$713$	3.08989e7	2.27625
$714$	−256449.	−0.0188259
$715$	−1.31461e6	−0.0961679
$716$	−5.55934e6	−0.405266
$717$	5.74546e6	0.417376
$718$	−4.75502e6	−0.344224
$719$	−1.99372e6	−0.143828	−0.0719139	−	0.997411i	$-0.522911\pi$
$719$	−1.99372e6	−0.143828	−0.0719139	+	0.997411i	$0.522911\pi$
$720$	−1.67524e6	−0.120433
$721$	3.68909e6	0.264291
$722$	−6.09933e6	−0.435451
$723$	2.71160e6	0.192921
$724$	−7.41438e6	−0.525688
$725$	−2.66852e6	−0.188550
$726$	−190719.	−0.0134293
$727$	1.66770e7	1.17026	0.585129	−	0.810940i	$-0.301044\pi$
$727$	1.66770e7	1.17026	0.585129	+	0.810940i	$0.301044\pi$
$728$	1.61603e6	0.113011
$729$	531441.	0.0370370
$730$	−1.56798e6	−0.108901
$731$	−5.44624e6	−0.376967
$732$	8.70640e6	0.600566
$733$	−6.22120e6	−0.427676	−0.213838	−	0.976869i	$-0.568596\pi$
$733$	−6.22120e6	−0.427676	−0.213838	+	0.976869i	$0.568596\pi$
$734$	1.01409e6	0.0694764
$735$	3.39403e6	0.231738
$736$	1.49238e7	1.01551
$737$	3.49602e6	0.237086
$738$	−207655.	−0.0140347
$739$	193628.	0.0130424	0.00652118	−	0.999979i	$-0.497924\pi$
$739$	193628.	0.0130424	0.00652118	+	0.999979i	$0.497924\pi$
$740$	1.04222e7	0.699646
$741$	−1.01165e7	−0.676840
$742$	−1.25689e6	−0.0838083
$743$	1.49469e7	0.993295	0.496648	−	0.867952i	$-0.334564\pi$
$743$	1.49469e7	0.993295	0.496648	+	0.867952i	$0.334564\pi$
$744$	−6.78620e6	−0.449464
$745$	−1.19030e7	−0.785714
$746$	3.74982e6	0.246697
$747$	−1.35130e6	−0.0886036
$748$	−1.71648e6	−0.112172
$749$	6.07393e6	0.395608
$750$	203537.	0.0132126
$751$	−3.06276e6	−0.198159	−0.0990793	−	0.995080i	$-0.531590\pi$
$751$	−3.06276e6	−0.198159	−0.0990793	+	0.995080i	$0.531590\pi$
$752$	−9.14020e6	−0.589401
$753$	−2.56548e6	−0.164885
$754$	2.68560e6	0.172033
$755$	−5.79086e6	−0.369723
$756$	−904784.	−0.0575759
$757$	−2.87783e7	−1.82527	−0.912633	−	0.408780i	$-0.865954\pi$
$757$	−2.87783e7	−1.82527	−0.912633	+	0.408780i	$0.865954\pi$
$758$	973009.	0.0615098
$759$	−3.99847e6	−0.251935
$760$	5.79382e6	0.363857
$761$	1.92089e6	0.120238	0.0601189	−	0.998191i	$-0.480852\pi$
$761$	1.92089e6	0.120238	0.0601189	+	0.998191i	$0.480852\pi$
$762$	−1.03645e6	−0.0646635
$763$	−4.62895e6	−0.287853
$764$	−2.14008e7	−1.32647
$765$	−960576.	−0.0593442
$766$	−3.49363e6	−0.215132
$767$	−1.43417e7	−0.880262
$768$	3.84743e6	0.235379
$769$	1.51697e7	0.925043	0.462521	−	0.886608i	$-0.346945\pi$
$769$	1.51697e7	0.925043	0.462521	+	0.886608i	$0.346945\pi$
$770$	181709.	0.0110446
$771$	−1.55354e7	−0.941211
$772$	−9.44583e6	−0.570423
$773$	−1.17588e7	−0.707809	−0.353904	−	0.935282i	$-0.615146\pi$
$773$	−1.17588e7	−0.707809	−0.353904	+	0.935282i	$0.615146\pi$
$774$	1.34603e6	0.0807612
$775$	−5.25966e6	−0.314560
$776$	−1.15548e7	−0.688821
$777$	5.20699e6	0.309410
$778$	−4.35726e6	−0.258086
$779$	−4.58138e6	−0.270491
$780$	2.92414e6	0.172092
$781$	−2.47765e6	−0.145349
$782$	2.52088e6	0.147413
$783$	−3.11256e6	−0.181432
$784$	−1.24791e7	−0.725095
$785$	1.98210e6	0.114802
$786$	−955680.	−0.0551768
$787$	−1.07859e6	−0.0620756	−0.0310378	−	0.999518i	$-0.509881\pi$
$787$	−1.07859e6	−0.0620756	−0.0310378	+	0.999518i	$0.509881\pi$
$788$	−4.17202e6	−0.239348
$789$	−1.16563e7	−0.666604
$790$	−3.44843e6	−0.196586
$791$	−2.35043e6	−0.133569
$792$	878167.	0.0497467
$793$	−1.40579e7	−0.793849
$794$	−1.26108e6	−0.0709892
$795$	−4.70790e6	−0.264186
$796$	−5.48562e6	−0.306862
$797$	7.73047e6	0.431082	0.215541	−	0.976495i	$-0.430848\pi$
$797$	7.73047e6	0.431082	0.215541	+	0.976495i	$0.430848\pi$
$798$	1.39834e6	0.0777331
$799$	−5.24095e6	−0.290431
$800$	−2.54036e6	−0.140336
$801$	1.16048e7	0.639082
$802$	2.92225e6	0.160429
$803$	−5.24331e6	−0.286957
$804$	−7.77637e6	−0.424265
$805$	3.80958e6	0.207199
$806$	5.29332e6	0.287006
$807$	−1.76660e7	−0.954891
$808$	1.31791e7	0.710161
$809$	−1.49228e6	−0.0801639	−0.0400819	−	0.999196i	$-0.512762\pi$
$809$	−1.49228e6	−0.0801639	−0.0400819	+	0.999196i	$0.512762\pi$
$810$	237405.	0.0127139
$811$	−7.38116e6	−0.394069	−0.197035	−	0.980397i	$-0.563131\pi$
$811$	−7.38116e6	−0.394069	−0.197035	+	0.980397i	$0.563131\pi$
$812$	5.29917e6	0.282045
$813$	3.92431e6	0.208227
$814$	−2.44139e6	−0.129145
$815$	7.58875e6	0.400199
$816$	3.53184e6	0.185685
$817$	2.96967e7	1.55652
$818$	501336.	0.0261967
$819$	1.46092e6	0.0761057
$820$	1.32423e6	0.0687746
$821$	−1.42454e7	−0.737594	−0.368797	−	0.929510i	$-0.620230\pi$
$821$	−1.42454e7	−0.737594	−0.368797	+	0.929510i	$0.620230\pi$
$822$	1.70303e6	0.0879109
$823$	−1.91145e7	−0.983702	−0.491851	−	0.870679i	$-0.663680\pi$
$823$	−1.91145e7	−0.983702	−0.491851	+	0.870679i	$0.663680\pi$
$824$	7.96443e6	0.408636
$825$	680625.	0.0348155
$826$	1.98236e6	0.101096
$827$	−2.68783e7	−1.36659	−0.683294	−	0.730143i	$-0.739453\pi$
$827$	−2.68783e7	−1.36659	−0.683294	+	0.730143i	$0.739453\pi$
$828$	8.89398e6	0.450838
$829$	2.27066e7	1.14754	0.573768	−	0.819018i	$-0.305481\pi$
$829$	2.27066e7	1.14754	0.573768	+	0.819018i	$0.305481\pi$
$830$	−603654.	−0.0304154
$831$	−9.91177e6	−0.497908
$832$	−8.94801e6	−0.448145
$833$	−7.15549e6	−0.357295
$834$	4.77389e6	0.237661
$835$	1.36937e7	0.679681
$836$	9.35943e6	0.463163
$837$	−6.13487e6	−0.302686
$838$	1.35848e6	0.0668257
$839$	−1.54859e7	−0.759505	−0.379753	−	0.925088i	$-0.623991\pi$
$839$	−1.54859e7	−0.759505	−0.379753	+	0.925088i	$0.623991\pi$
$840$	−836683.	−0.0409131
$841$	−2.28136e6	−0.111225
$842$	−7.06383e6	−0.343368
$843$	1.09136e7	0.528931
$844$	1.02254e7	0.494110
$845$	4.56082e6	0.219736
$846$	1.29529e6	0.0622218
$847$	607635.	0.0291028
$848$	1.73100e7	0.826623
$849$	1.86974e7	0.890250
$850$	−429108.	−0.0203713
$851$	−5.11844e7	−2.42278
$852$	5.51116e6	0.260102
$853$	−3.77200e6	−0.177500	−0.0887502	−	0.996054i	$-0.528287\pi$
$853$	−3.77200e6	−0.177500	−0.0887502	+	0.996054i	$0.528287\pi$
$854$	1.94313e6	0.0911712
$855$	5.23774e6	0.245035
$856$	1.31131e7	0.611674
$857$	−6.50207e6	−0.302412	−0.151206	−	0.988502i	$-0.548316\pi$
$857$	−6.50207e6	−0.302412	−0.151206	+	0.988502i	$0.548316\pi$
$858$	−684980.	−0.0317658
$859$	−1.10411e7	−0.510538	−0.255269	−	0.966870i	$-0.582164\pi$
$859$	−1.10411e7	−0.510538	−0.255269	+	0.966870i	$0.582164\pi$
$860$	−8.58372e6	−0.395758
$861$	661594.	0.0304147
$862$	7.63479e6	0.349968
$863$	−1.55955e6	−0.0712808	−0.0356404	−	0.999365i	$-0.511347\pi$
$863$	−1.55955e6	−0.0712808	−0.0356404	+	0.999365i	$0.511347\pi$
$864$	−2.96307e6	−0.135039
$865$	8.75884e6	0.398021
$866$	4.78174e6	0.216666
$867$	−1.07536e7	−0.485853
$868$	1.04447e7	0.470539
$869$	−1.15315e7	−0.518009
$870$	−1.39044e6	−0.0622810
$871$	1.25562e7	0.560808
$872$	−9.99348e6	−0.445067
$873$	−1.04457e7	−0.463878
$874$	−1.37456e7	−0.608676
$875$	−648473.	−0.0286333
$876$	1.16629e7	0.513509
$877$	2.78476e7	1.22261	0.611307	−	0.791393i	$-0.290644\pi$
$877$	2.78476e7	1.22261	0.611307	+	0.791393i	$0.290644\pi$
$878$	−8.57700e6	−0.375491
$879$	1.57635e7	0.688144
$880$	−2.50252e6	−0.108936
$881$	−1.52851e7	−0.663481	−0.331740	−	0.943371i	$-0.607636\pi$
$881$	−1.52851e7	−0.663481	−0.331740	+	0.943371i	$0.607636\pi$
$882$	1.76847e6	0.0765467
$883$	−7.82254e6	−0.337634	−0.168817	−	0.985647i	$-0.553995\pi$
$883$	−7.82254e6	−0.337634	−0.168817	+	0.985647i	$0.553995\pi$
$884$	−6.16485e6	−0.265333
$885$	7.42528e6	0.318680
$886$	−3.42583e6	−0.146616
$887$	2.39652e7	1.02276	0.511379	−	0.859355i	$-0.329135\pi$
$887$	2.39652e7	1.02276	0.511379	+	0.859355i	$0.329135\pi$
$888$	1.12414e7	0.478397
$889$	3.30214e6	0.140133
$890$	5.18409e6	0.219380
$891$	793881.	0.0335013
$892$	3.04544e7	1.28156
$893$	2.85774e7	1.19920
$894$	−6.20209e6	−0.259534
$895$	−4.64748e6	−0.193937
$896$	6.63487e6	0.276098
$897$	−1.43608e7	−0.595933
$898$	4.85078e6	0.200734
$899$	3.59309e7	1.48276
$900$	−1.51395e6	−0.0623023
$901$	9.92548e6	0.407324
$902$	−310201.	−0.0126948
$903$	−4.28849e6	−0.175019
$904$	−5.07438e6	−0.206520
$905$	−6.19825e6	−0.251564
$906$	−3.01735e6	−0.122125
$907$	−5.48830e6	−0.221523	−0.110762	−	0.993847i	$-0.535329\pi$
$907$	−5.48830e6	−0.221523	−0.110762	+	0.993847i	$0.535329\pi$
$908$	1.08378e7	0.436243
$909$	1.19142e7	0.478249
$910$	652623.	0.0261251
$911$	−918823.	−0.0366806	−0.0183403	−	0.999832i	$-0.505838\pi$
$911$	−918823.	−0.0366806	−0.0183403	+	0.999832i	$0.505838\pi$
$912$	−1.92581e7	−0.766702
$913$	−2.01861e6	−0.0801450
$914$	−5.85282e6	−0.231739
$915$	7.27835e6	0.287396
$916$	4.13685e7	1.62904
$917$	3.04482e6	0.119574
$918$	−500512.	−0.0196023
$919$	−6.92636e6	−0.270530	−0.135265	−	0.990809i	$-0.543189\pi$
$919$	−6.92636e6	−0.270530	−0.135265	+	0.990809i	$0.543189\pi$
$920$	8.22455e6	0.320363
$921$	2.48879e7	0.966805
$922$	1.20365e7	0.466306
$923$	−8.89866e6	−0.343812
$924$	−1.35159e6	−0.0520793
$925$	8.71269e6	0.334810
$926$	8.02432e6	0.307525
$927$	7.20001e6	0.275191
$928$	1.73542e7	0.661509
$929$	−2.62196e7	−0.996752	−0.498376	−	0.866961i	$-0.666070\pi$
$929$	−2.62196e7	−0.996752	−0.498376	+	0.866961i	$0.666070\pi$
$930$	−2.74057e6	−0.103904
$931$	3.90168e7	1.47529
$932$	−3.56126e7	−1.34296
$933$	1.24641e6	0.0468765
$934$	8.02527e6	0.301018
$935$	−1.43493e6	−0.0536788
$936$	3.15400e6	0.117672
$937$	−216082.	−0.00804027	−0.00402013	−	0.999992i	$-0.501280\pi$
$937$	−216082.	−0.00804027	−0.00402013	+	0.999992i	$0.501280\pi$
$938$	−1.73557e6	−0.0644071
$939$	2.02530e7	0.749592
$940$	−8.26017e6	−0.304908
$941$	2.94074e7	1.08264	0.541318	−	0.840818i	$-0.317926\pi$
$941$	2.94074e7	1.08264	0.541318	+	0.840818i	$0.317926\pi$
$942$	1.03278e6	0.0379211
$943$	−6.50344e6	−0.238157
$944$	−2.73012e7	−0.997132
$945$	−756379.	−0.0275524
$946$	2.01074e6	0.0730513
$947$	−4.18343e7	−1.51585	−0.757927	−	0.652339i	$-0.773788\pi$
$947$	−4.18343e7	−1.51585	−0.757927	+	0.652339i	$0.773788\pi$
$948$	2.56501e7	0.926976
$949$	−1.88317e7	−0.678774
$950$	2.33980e6	0.0841143
$951$	−2.70033e6	−0.0968200
$952$	1.76395e6	0.0630802
$953$	−1.37691e7	−0.491104	−0.245552	−	0.969383i	$-0.578969\pi$
$953$	−1.37691e7	−0.491104	−0.245552	+	0.969383i	$0.578969\pi$
$954$	−2.45307e6	−0.0872648
$955$	−1.78906e7	−0.634771
$956$	−1.90910e7	−0.675590
$957$	−4.64963e6	−0.164111
$958$	−4.24182e6	−0.149327
$959$	−5.42590e6	−0.190513
$960$	4.63275e6	0.162241
$961$	4.21908e7	1.47370
$962$	−8.76844e6	−0.305481
$963$	1.18545e7	0.411924
$964$	−9.01009e6	−0.312275
$965$	−7.89650e6	−0.272971
$966$	1.98500e6	0.0684412
$967$	−4.56284e7	−1.56917	−0.784584	−	0.620022i	$-0.787123\pi$
$967$	−4.56284e7	−1.56917	−0.784584	+	0.620022i	$0.787123\pi$
$968$	1.31183e6	0.0449976
$969$	−1.10425e7	−0.377797
$970$	−4.66632e6	−0.159237
$971$	9.15569e6	0.311633	0.155816	−	0.987786i	$-0.450199\pi$
$971$	9.15569e6	0.311633	0.155816	+	0.987786i	$0.450199\pi$
$972$	−1.76587e6	−0.0599504
$973$	−1.52097e7	−0.515039
$974$	536741.	0.0181287
$975$	2.44451e6	0.0823533
$976$	−2.67610e7	−0.899246
$977$	−1.12269e7	−0.376289	−0.188145	−	0.982141i	$-0.560247\pi$
$977$	−1.12269e7	−0.376289	−0.188145	+	0.982141i	$0.560247\pi$
$978$	3.95415e6	0.132192
$979$	1.73356e7	0.578071
$980$	−1.12776e7	−0.375105
$981$	−9.03431e6	−0.299725
$982$	−856967.	−0.0283586
$983$	−1.92294e7	−0.634718	−0.317359	−	0.948305i	$-0.602796\pi$
$983$	−1.92294e7	−0.634718	−0.317359	+	0.948305i	$0.602796\pi$
$984$	1.42832e6	0.0470261
$985$	−3.48771e6	−0.114538
$986$	2.93142e6	0.0960252
$987$	−4.12684e6	−0.134842
$988$	3.36151e7	1.09557
$989$	4.21556e7	1.37046
$990$	354642.	0.0115001
$991$	4.87732e7	1.57760	0.788801	−	0.614649i	$-0.210702\pi$
$991$	4.87732e7	1.57760	0.788801	+	0.614649i	$0.210702\pi$
$992$	3.42052e7	1.10360
$993$	5.74092e6	0.184760
$994$	1.23000e6	0.0394858
$995$	−4.58586e6	−0.146846
$996$	4.49010e6	0.143419
$997$	2.88621e7	0.919583	0.459791	−	0.888027i	$-0.347924\pi$
$997$	2.88621e7	0.919583	0.459791	+	0.888027i	$0.347924\pi$
$998$	9.01935e6	0.286648
$999$	1.01625e7	0.322171

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.a.b.1.2	✓	3
3.2	odd	2		495.6.a.d.1.2		3
5.4	even	2		825.6.a.i.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.a.b.1.2	✓	3	1.1	even	1	trivial
495.6.a.d.1.2		3	3.2	odd	2
825.6.a.i.1.2		3	5.4	even	2

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	165.a (trivial)

\(f(q)\)	\(=\)	\(q-1.44737 q^{2} +9.00000 q^{3} -29.9051 q^{4} -25.0000 q^{5} -13.0263 q^{6} +41.5023 q^{7} +89.5997 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-1.44737 q^{2} +9.00000 q^{3} -29.9051 q^{4} -25.0000 q^{5} -13.0263 q^{6} +41.5023 q^{7} +89.5997 q^{8} +81.0000 q^{9} +36.1843 q^{10} +121.000 q^{11} -269.146 q^{12} +434.580 q^{13} -60.0692 q^{14} -225.000 q^{15} +827.280 q^{16} +474.359 q^{17} -117.237 q^{18} -2586.54 q^{19} +747.628 q^{20} +373.520 q^{21} -175.132 q^{22} -3671.69 q^{23} +806.397 q^{24} +625.000 q^{25} -628.999 q^{26} +729.000 q^{27} -1241.13 q^{28} -4269.64 q^{29} +325.659 q^{30} -8415.46 q^{31} -4064.57 q^{32} +1089.00 q^{33} -686.573 q^{34} -1037.56 q^{35} -2422.31 q^{36} +13940.3 q^{37} +3743.68 q^{38} +3911.22 q^{39} -2239.99 q^{40} +1771.24 q^{41} -540.623 q^{42} -11481.3 q^{43} -3618.52 q^{44} -2025.00 q^{45} +5314.30 q^{46} -11048.5 q^{47} +7445.52 q^{48} -15084.6 q^{49} -904.607 q^{50} +4269.23 q^{51} -12996.2 q^{52} +20924.0 q^{53} -1055.13 q^{54} -3025.00 q^{55} +3718.59 q^{56} -23278.8 q^{57} +6179.75 q^{58} -33001.2 q^{59} +6728.65 q^{60} -32348.2 q^{61} +12180.3 q^{62} +3361.68 q^{63} -20590.0 q^{64} -10864.5 q^{65} -1576.19 q^{66} +28892.8 q^{67} -14185.7 q^{68} -33045.2 q^{69} +1501.73 q^{70} -20476.5 q^{71} +7257.58 q^{72} -43333.2 q^{73} -20176.8 q^{74} +5625.00 q^{75} +77350.7 q^{76} +5021.77 q^{77} -5660.99 q^{78} -95301.8 q^{79} -20682.0 q^{80} +6561.00 q^{81} -2563.64 q^{82} -16682.8 q^{83} -11170.2 q^{84} -11859.0 q^{85} +16617.7 q^{86} -38426.7 q^{87} +10841.6 q^{88} +143269. q^{89} +2930.93 q^{90} +18036.1 q^{91} +109802. q^{92} -75739.1 q^{93} +15991.3 q^{94} +64663.4 q^{95} -36581.1 q^{96} -128960. q^{97} +21833.0 q^{98} +9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2 q^{2} + 27 q^{3} + 28 q^{4} - 75 q^{5} - 18 q^{6} - 232 q^{7} + 24 q^{8} + 243 q^{9}+O(q^{10}) \) 3 * q - 2 * q^2 + 27 * q^3 + 28 * q^4 - 75 * q^5 - 18 * q^6 - 232 * q^7 + 24 * q^8 + 243 * q^9	\( 3 q - 2 q^{2} + 27 q^{3} + 28 q^{4} - 75 q^{5} - 18 q^{6} - 232 q^{7} + 24 q^{8} + 243 q^{9} + 50 q^{10} + 363 q^{11} + 252 q^{12} + 450 q^{13} - 1504 q^{14} - 675 q^{15} - 1360 q^{16} - 334 q^{17} - 162 q^{18} - 4036 q^{19} - 700 q^{20} - 2088 q^{21} - 242 q^{22} - 7060 q^{23} + 216 q^{24} + 1875 q^{25} + 2932 q^{26} + 2187 q^{27} - 8320 q^{28} + 4042 q^{29} + 450 q^{30} - 608 q^{31} - 3104 q^{32} + 3267 q^{33} - 3644 q^{34} + 5800 q^{35} + 2268 q^{36} + 2250 q^{37} - 12632 q^{38} + 4050 q^{39} - 600 q^{40} + 10654 q^{41} - 13536 q^{42} - 35528 q^{43} + 3388 q^{44} - 6075 q^{45} - 41800 q^{46} - 2100 q^{47} - 12240 q^{48} + 7667 q^{49} - 1250 q^{50} - 3006 q^{51} - 14520 q^{52} - 12826 q^{53} - 1458 q^{54} - 9075 q^{55} + 17088 q^{56} - 36324 q^{57} - 17196 q^{58} - 81876 q^{59} - 6300 q^{60} - 62298 q^{61} + 109184 q^{62} - 18792 q^{63} - 72256 q^{64} - 11250 q^{65} - 2178 q^{66} - 46148 q^{67} - 35832 q^{68} - 63540 q^{69} + 37600 q^{70} - 64724 q^{71} + 1944 q^{72} + 810 q^{73} - 44796 q^{74} + 16875 q^{75} + 44656 q^{76} - 28072 q^{77} + 26388 q^{78} + 43876 q^{79} + 34000 q^{80} + 19683 q^{81} + 56060 q^{82} - 101024 q^{83} - 74880 q^{84} + 8350 q^{85} + 24128 q^{86} + 36378 q^{87} + 2904 q^{88} + 60022 q^{89} + 4050 q^{90} - 28568 q^{91} + 38256 q^{92} - 5472 q^{93} + 74552 q^{94} + 100900 q^{95} - 27936 q^{96} - 319746 q^{97} + 431134 q^{98} + 29403 q^{99}+O(q^{100}) \) 3 * q - 2 * q^2 + 27 * q^3 + 28 * q^4 - 75 * q^5 - 18 * q^6 - 232 * q^7 + 24 * q^8 + 243 * q^9 + 50 * q^10 + 363 * q^11 + 252 * q^12 + 450 * q^13 - 1504 * q^14 - 675 * q^15 - 1360 * q^16 - 334 * q^17 - 162 * q^18 - 4036 * q^19 - 700 * q^20 - 2088 * q^21 - 242 * q^22 - 7060 * q^23 + 216 * q^24 + 1875 * q^25 + 2932 * q^26 + 2187 * q^27 - 8320 * q^28 + 4042 * q^29 + 450 * q^30 - 608 * q^31 - 3104 * q^32 + 3267 * q^33 - 3644 * q^34 + 5800 * q^35 + 2268 * q^36 + 2250 * q^37 - 12632 * q^38 + 4050 * q^39 - 600 * q^40 + 10654 * q^41 - 13536 * q^42 - 35528 * q^43 + 3388 * q^44 - 6075 * q^45 - 41800 * q^46 - 2100 * q^47 - 12240 * q^48 + 7667 * q^49 - 1250 * q^50 - 3006 * q^51 - 14520 * q^52 - 12826 * q^53 - 1458 * q^54 - 9075 * q^55 + 17088 * q^56 - 36324 * q^57 - 17196 * q^58 - 81876 * q^59 - 6300 * q^60 - 62298 * q^61 + 109184 * q^62 - 18792 * q^63 - 72256 * q^64 - 11250 * q^65 - 2178 * q^66 - 46148 * q^67 - 35832 * q^68 - 63540 * q^69 + 37600 * q^70 - 64724 * q^71 + 1944 * q^72 + 810 * q^73 - 44796 * q^74 + 16875 * q^75 + 44656 * q^76 - 28072 * q^77 + 26388 * q^78 + 43876 * q^79 + 34000 * q^80 + 19683 * q^81 + 56060 * q^82 - 101024 * q^83 - 74880 * q^84 + 8350 * q^85 + 24128 * q^86 + 36378 * q^87 + 2904 * q^88 + 60022 * q^89 + 4050 * q^90 - 28568 * q^91 + 38256 * q^92 - 5472 * q^93 + 74552 * q^94 + 100900 * q^95 - 27936 * q^96 - 319746 * q^97 + 431134 * q^98 + 29403 * q^99

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