LMFDB - Embedded newform 69.6.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,6,Mod(1,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("69.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	69.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:	$11.0664835671$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.5333.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 11x + 8 $ x^3 - x^2 - 11*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.714018$ of defining polynomial
Character	$\chi$	$=$	69.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.2042 q^{2} +9.00000 q^{3} +72.1256 q^{4} -55.5168 q^{5} -91.8378 q^{6} +2.50462 q^{7} -409.450 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-10.2042 q^{2} +9.00000 q^{3} +72.1256 q^{4} -55.5168 q^{5} -91.8378 q^{6} +2.50462 q^{7} -409.450 q^{8} +81.0000 q^{9} +566.504 q^{10} +228.550 q^{11} +649.131 q^{12} +658.703 q^{13} -25.5577 q^{14} -499.651 q^{15} +1870.09 q^{16} -1443.81 q^{17} -826.540 q^{18} -982.167 q^{19} -4004.18 q^{20} +22.5416 q^{21} -2332.17 q^{22} +529.000 q^{23} -3685.05 q^{24} -42.8875 q^{25} -6721.54 q^{26} +729.000 q^{27} +180.648 q^{28} -7157.56 q^{29} +5098.54 q^{30} -9259.98 q^{31} -5980.33 q^{32} +2056.95 q^{33} +14732.9 q^{34} -139.049 q^{35} +5842.18 q^{36} +2422.50 q^{37} +10022.2 q^{38} +5928.33 q^{39} +22731.3 q^{40} -4075.27 q^{41} -230.019 q^{42} -10417.3 q^{43} +16484.3 q^{44} -4496.86 q^{45} -5398.02 q^{46} +9358.08 q^{47} +16830.8 q^{48} -16800.7 q^{49} +437.632 q^{50} -12994.3 q^{51} +47509.4 q^{52} -34280.3 q^{53} -7438.86 q^{54} -12688.4 q^{55} -1025.52 q^{56} -8839.51 q^{57} +73037.2 q^{58} -7268.79 q^{59} -36037.6 q^{60} +26611.7 q^{61} +94490.6 q^{62} +202.874 q^{63} +1181.70 q^{64} -36569.1 q^{65} -20989.5 q^{66} +53450.8 q^{67} -104136. q^{68} +4761.00 q^{69} +1418.88 q^{70} +21673.7 q^{71} -33165.4 q^{72} -82856.3 q^{73} -24719.7 q^{74} -385.987 q^{75} -70839.4 q^{76} +572.432 q^{77} -60493.9 q^{78} -23960.0 q^{79} -103821. q^{80} +6561.00 q^{81} +41584.9 q^{82} +81187.7 q^{83} +1625.83 q^{84} +80155.6 q^{85} +106300. q^{86} -64418.0 q^{87} -93579.7 q^{88} +100115. q^{89} +45886.8 q^{90} +1649.80 q^{91} +38154.5 q^{92} -83339.8 q^{93} -95491.7 q^{94} +54526.8 q^{95} -53822.9 q^{96} +36122.1 q^{97} +171438. q^{98} +18512.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 8 q^{2} + 27 q^{3} + 22 q^{4} - 56 q^{5} - 72 q^{6} - 114 q^{7} - 510 q^{8} + 243 q^{9}+O(q^{10}) $ 3 * q - 8 * q^2 + 27 * q^3 + 22 * q^4 - 56 * q^5 - 72 * q^6 - 114 * q^7 - 510 * q^8 + 243 * q^9	\( 3 q - 8 q^{2} + 27 q^{3} + 22 q^{4} - 56 q^{5} - 72 q^{6} - 114 q^{7} - 510 q^{8} + 243 q^{9} + 282 q^{10} - 376 q^{11} + 198 q^{12} - 858 q^{13} + 588 q^{14} - 504 q^{15} + 2738 q^{16} - 2548 q^{17} - 648 q^{18} - 2846 q^{19} - 4618 q^{20} - 1026 q^{21} - 5050 q^{22} + 1587 q^{23} - 4590 q^{24} + 753 q^{25} - 7788 q^{26} + 2187 q^{27} + 4736 q^{28} - 16370 q^{29} + 2538 q^{30} - 14756 q^{31} - 3878 q^{32} - 3384 q^{33} + 16520 q^{34} - 18520 q^{35} + 1782 q^{36} + 15874 q^{37} + 12438 q^{38} - 7722 q^{39} + 38270 q^{40} + 12606 q^{41} + 5292 q^{42} + 3154 q^{43} + 27114 q^{44} - 4536 q^{45} - 4232 q^{46} + 29928 q^{47} + 24642 q^{48} + 4471 q^{49} + 1452 q^{50} - 22932 q^{51} + 86856 q^{52} - 44084 q^{53} - 5832 q^{54} + 38360 q^{55} - 35704 q^{56} - 25614 q^{57} + 73316 q^{58} - 29300 q^{59} - 41562 q^{60} + 54010 q^{61} + 99908 q^{62} - 9234 q^{63} - 1582 q^{64} - 51216 q^{65} - 45450 q^{66} + 43390 q^{67} - 69840 q^{68} + 14283 q^{69} - 2476 q^{70} + 23424 q^{71} - 41310 q^{72} - 91402 q^{73} - 2294 q^{74} + 6777 q^{75} - 14274 q^{76} - 97208 q^{77} - 70092 q^{78} - 49398 q^{79} - 52626 q^{80} + 19683 q^{81} + 40152 q^{82} - 103936 q^{83} + 42624 q^{84} + 5888 q^{85} + 133634 q^{86} - 147330 q^{87} + 48898 q^{88} + 96112 q^{89} + 22842 q^{90} + 129228 q^{91} + 11638 q^{92} - 132804 q^{93} - 133688 q^{94} - 55928 q^{95} - 34902 q^{96} - 135318 q^{97} + 108440 q^{98} - 30456 q^{99}+O(q^{100}) \) 3 * q - 8 * q^2 + 27 * q^3 + 22 * q^4 - 56 * q^5 - 72 * q^6 - 114 * q^7 - 510 * q^8 + 243 * q^9 + 282 * q^10 - 376 * q^11 + 198 * q^12 - 858 * q^13 + 588 * q^14 - 504 * q^15 + 2738 * q^16 - 2548 * q^17 - 648 * q^18 - 2846 * q^19 - 4618 * q^20 - 1026 * q^21 - 5050 * q^22 + 1587 * q^23 - 4590 * q^24 + 753 * q^25 - 7788 * q^26 + 2187 * q^27 + 4736 * q^28 - 16370 * q^29 + 2538 * q^30 - 14756 * q^31 - 3878 * q^32 - 3384 * q^33 + 16520 * q^34 - 18520 * q^35 + 1782 * q^36 + 15874 * q^37 + 12438 * q^38 - 7722 * q^39 + 38270 * q^40 + 12606 * q^41 + 5292 * q^42 + 3154 * q^43 + 27114 * q^44 - 4536 * q^45 - 4232 * q^46 + 29928 * q^47 + 24642 * q^48 + 4471 * q^49 + 1452 * q^50 - 22932 * q^51 + 86856 * q^52 - 44084 * q^53 - 5832 * q^54 + 38360 * q^55 - 35704 * q^56 - 25614 * q^57 + 73316 * q^58 - 29300 * q^59 - 41562 * q^60 + 54010 * q^61 + 99908 * q^62 - 9234 * q^63 - 1582 * q^64 - 51216 * q^65 - 45450 * q^66 + 43390 * q^67 - 69840 * q^68 + 14283 * q^69 - 2476 * q^70 + 23424 * q^71 - 41310 * q^72 - 91402 * q^73 - 2294 * q^74 + 6777 * q^75 - 14274 * q^76 - 97208 * q^77 - 70092 * q^78 - 49398 * q^79 - 52626 * q^80 + 19683 * q^81 + 40152 * q^82 - 103936 * q^83 + 42624 * q^84 + 5888 * q^85 + 133634 * q^86 - 147330 * q^87 + 48898 * q^88 + 96112 * q^89 + 22842 * q^90 + 129228 * q^91 + 11638 * q^92 - 132804 * q^93 - 133688 * q^94 - 55928 * q^95 - 34902 * q^96 - 135318 * q^97 + 108440 * q^98 - 30456 * 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 $

$2$	−10.2042	−1.80386	−0.901932	−	0.431878i	$-0.857851\pi$
$2$	−10.2042	−1.80386	−0.901932	+	0.431878i	$0.857851\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	72.1256	2.25393
$5$	−55.5168	−0.993114	−0.496557	−	0.868004i	$-0.665403\pi$
$5$	−55.5168	−0.993114	−0.496557	+	0.868004i	$0.665403\pi$
$6$	−91.8378	−1.04146
$7$	2.50462	0.0193196	0.00965978	−	0.999953i	$-0.496925\pi$
$7$	2.50462	0.0193196	0.00965978	+	0.999953i	$0.496925\pi$
$8$	−409.450	−2.26191
$9$	81.0000	0.333333
$10$	566.504	1.79144
$11$	228.550	0.569508	0.284754	−	0.958601i	$-0.408088\pi$
$11$	228.550	0.569508	0.284754	+	0.958601i	$0.408088\pi$
$12$	649.131	1.30130
$13$	658.703	1.08101	0.540507	−	0.841339i	$-0.318232\pi$
$13$	658.703	1.08101	0.540507	+	0.841339i	$0.318232\pi$
$14$	−25.5577	−0.0348499
$15$	−499.651	−0.573375
$16$	1870.09	1.82626
$17$	−1443.81	−1.21168	−0.605839	−	0.795587i	$-0.707162\pi$
$17$	−1443.81	−1.21168	−0.605839	+	0.795587i	$0.707162\pi$
$18$	−826.540	−0.601288
$19$	−982.167	−0.624168	−0.312084	−	0.950055i	$-0.601027\pi$
$19$	−982.167	−0.624168	−0.312084	+	0.950055i	$0.601027\pi$
$20$	−4004.18	−2.23841
$21$	22.5416	0.0111542
$22$	−2332.17	−1.02731
$23$	529.000	0.208514
$23$	529.000	0.208514
$24$	−3685.05	−1.30592
$25$	−42.8875	−0.0137240
$26$	−6721.54	−1.95000
$27$	729.000	0.192450
$28$	180.648	0.0435449
$29$	−7157.56	−1.58041	−0.790205	−	0.612842i	$-0.790026\pi$
$29$	−7157.56	−1.58041	−0.790205	+	0.612842i	$0.790026\pi$
$30$	5098.54	1.03429
$31$	−9259.98	−1.73064	−0.865318	−	0.501223i	$-0.832884\pi$
$31$	−9259.98	−1.73064	−0.865318	+	0.501223i	$0.832884\pi$
$32$	−5980.33	−1.03240
$33$	2056.95	0.328805
$34$	14732.9	2.18570
$35$	−139.049	−0.0191865
$36$	5842.18	0.751309
$37$	2422.50	0.290911	0.145455	−	0.989365i	$-0.453535\pi$
$37$	2422.50	0.290911	0.145455	+	0.989365i	$0.453535\pi$
$38$	10022.2	1.12591
$39$	5928.33	0.624124
$40$	22731.3	2.24634
$41$	−4075.27	−0.378614	−0.189307	−	0.981918i	$-0.560624\pi$
$41$	−4075.27	−0.378614	−0.189307	+	0.981918i	$0.560624\pi$
$42$	−230.019	−0.0201206
$43$	−10417.3	−0.859178	−0.429589	−	0.903024i	$-0.641342\pi$
$43$	−10417.3	−0.859178	−0.429589	+	0.903024i	$0.641342\pi$
$44$	16484.3	1.28363
$45$	−4496.86	−0.331038
$46$	−5398.02	−0.376132
$47$	9358.08	0.617934	0.308967	−	0.951073i	$-0.400017\pi$
$47$	9358.08	0.617934	0.308967	+	0.951073i	$0.400017\pi$
$48$	16830.8	1.05439
$49$	−16800.7	−0.999627
$50$	437.632	0.0247562
$51$	−12994.3	−0.699563
$52$	47509.4	2.43653
$53$	−34280.3	−1.67631	−0.838157	−	0.545428i	$-0.816367\pi$
$53$	−34280.3	−1.67631	−0.838157	+	0.545428i	$0.816367\pi$
$54$	−7438.86	−0.347154
$55$	−12688.4	−0.565586
$56$	−1025.52	−0.0436991
$57$	−8839.51	−0.360364
$58$	73037.2	2.85085
$59$	−7268.79	−0.271852	−0.135926	−	0.990719i	$-0.543401\pi$
$59$	−7268.79	−0.271852	−0.135926	+	0.990719i	$0.543401\pi$
$60$	−36037.6	−1.29234
$61$	26611.7	0.915687	0.457844	−	0.889033i	$-0.348622\pi$
$61$	26611.7	0.915687	0.457844	+	0.889033i	$0.348622\pi$
$62$	94490.6	3.12183
$63$	202.874	0.00643985
$64$	1181.70	0.0360625
$65$	−36569.1	−1.07357
$66$	−20989.5	−0.593120
$67$	53450.8	1.45468	0.727339	−	0.686278i	$-0.240757\pi$
$67$	53450.8	1.45468	0.727339	+	0.686278i	$0.240757\pi$
$68$	−104136.	−2.73103
$69$	4761.00	0.120386
$70$	1418.88	0.0346099
$71$	21673.7	0.510255	0.255128	−	0.966907i	$-0.417882\pi$
$71$	21673.7	0.510255	0.255128	+	0.966907i	$0.417882\pi$
$72$	−33165.4	−0.753970
$73$	−82856.3	−1.81978	−0.909889	−	0.414851i	$-0.863834\pi$
$73$	−82856.3	−1.81978	−0.909889	+	0.414851i	$0.863834\pi$
$74$	−24719.7	−0.524764
$75$	−385.987	−0.00792355
$76$	−70839.4	−1.40683
$77$	572.432	0.0110026
$78$	−60493.9	−1.12584
$79$	−23960.0	−0.431936	−0.215968	−	0.976400i	$-0.569291\pi$
$79$	−23960.0	−0.431936	−0.215968	+	0.976400i	$0.569291\pi$
$80$	−103821.	−1.81368
$81$	6561.00	0.111111
$82$	41584.9	0.682968
$83$	81187.7	1.29359	0.646793	−	0.762666i	$-0.276110\pi$
$83$	81187.7	1.29359	0.646793	+	0.762666i	$0.276110\pi$
$84$	1625.83	0.0251406
$85$	80155.6	1.20334
$86$	106300.	1.54984
$87$	−64418.0	−0.912451
$88$	−93579.7	−1.28818
$89$	100115.	1.33975	0.669876	−	0.742473i	$-0.266347\pi$
$89$	100115.	1.33975	0.669876	+	0.742473i	$0.266347\pi$
$90$	45886.8	0.597148
$91$	1649.80	0.0208847
$92$	38154.5	0.469976
$93$	−83339.8	−0.999183
$94$	−95491.7	−1.11467
$95$	54526.8	0.619870
$96$	−53822.9	−0.596059
$97$	36122.1	0.389802	0.194901	−	0.980823i	$-0.437562\pi$
$97$	36122.1	0.389802	0.194901	+	0.980823i	$0.437562\pi$
$98$	171438.	1.80319
$99$	18512.6	0.189836
$100$	−3093.29	−0.0309329
$101$	−41151.8	−0.401408	−0.200704	−	0.979652i	$-0.564323\pi$
$101$	−41151.8	−0.401408	−0.200704	+	0.979652i	$0.564323\pi$
$102$	132596.	1.26192
$103$	−172534.	−1.60244	−0.801221	−	0.598369i	$-0.795816\pi$
$103$	−172534.	−1.60244	−0.801221	+	0.598369i	$0.795816\pi$
$104$	−269706.	−2.44516
$105$	−1251.44	−0.0110774
$106$	349803.	3.02384
$107$	178228.	1.50493	0.752464	−	0.658633i	$-0.228865\pi$
$107$	178228.	1.50493	0.752464	+	0.658633i	$0.228865\pi$
$108$	52579.6	0.433768
$109$	−138352.	−1.11537	−0.557686	−	0.830052i	$-0.688311\pi$
$109$	−138352.	−1.11537	−0.557686	+	0.830052i	$0.688311\pi$
$110$	129475.	1.02024
$111$	21802.5	0.167958
$112$	4683.86	0.0352825
$113$	−13523.5	−0.0996307	−0.0498153	−	0.998758i	$-0.515863\pi$
$113$	−13523.5	−0.0996307	−0.0498153	+	0.998758i	$0.515863\pi$
$114$	90200.0	0.650047
$115$	−29368.4	−0.207079
$116$	−516243.	−3.56213
$117$	53355.0	0.360338
$118$	74172.1	0.490383
$119$	−3616.20	−0.0234091
$120$	204582.	1.29692
$121$	−108816.	−0.675661
$122$	−271551.	−1.65178
$123$	−36677.4	−0.218593
$124$	−667882.	−3.90073
$125$	175871.	1.00674
$126$	−2070.17	−0.0116166
$127$	158567.	0.872376	0.436188	−	0.899856i	$-0.356328\pi$
$127$	158567.	0.872376	0.436188	+	0.899856i	$0.356328\pi$
$128$	179312.	0.967353
$129$	−93755.6	−0.496047
$130$	373158.	1.93658
$131$	−383514.	−1.95255	−0.976277	−	0.216526i	$-0.930527\pi$
$131$	−383514.	−1.95255	−0.976277	+	0.216526i	$0.930527\pi$
$132$	148359.	0.741103
$133$	−2459.96	−0.0120587
$134$	−545422.	−2.62404
$135$	−40471.7	−0.191125
$136$	591167.	2.74071
$137$	−33171.1	−0.150994	−0.0754968	−	0.997146i	$-0.524054\pi$
$137$	−33171.1	−0.150994	−0.0754968	+	0.997146i	$0.524054\pi$
$138$	−48582.2	−0.217160
$139$	−128488.	−0.564060	−0.282030	−	0.959406i	$-0.591008\pi$
$139$	−128488.	−0.564060	−0.282030	+	0.959406i	$0.591008\pi$
$140$	−10029.0	−0.0432450
$141$	84222.7	0.356764
$142$	−221163.	−0.920431
$143$	150547.	0.615646
$144$	151477.	0.608752
$145$	397365.	1.56953
$146$	845482.	3.28263
$147$	−151207.	−0.577135
$148$	174725.	0.655692
$149$	−184228.	−0.679814	−0.339907	−	0.940459i	$-0.610396\pi$
$149$	−184228.	−0.679814	−0.339907	+	0.940459i	$0.610396\pi$
$150$	3938.69	0.0142930
$151$	−19798.1	−0.0706610	−0.0353305	−	0.999376i	$-0.511248\pi$
$151$	−19798.1	−0.0706610	−0.0353305	+	0.999376i	$0.511248\pi$
$152$	402148.	1.41181
$153$	−116948.	−0.403893
$154$	−5841.21	−0.0198473
$155$	514084.	1.71872
$156$	427585.	1.40673
$157$	193317.	0.625923	0.312962	−	0.949766i	$-0.398679\pi$
$157$	193317.	0.625923	0.312962	+	0.949766i	$0.398679\pi$
$158$	244493.	0.779154
$159$	−308523.	−0.967821
$160$	332008.	1.02530
$161$	1324.95	0.00402841
$162$	−66949.7	−0.200429
$163$	106286.	0.313334	0.156667	−	0.987651i	$-0.449925\pi$
$163$	106286.	0.313334	0.156667	+	0.987651i	$0.449925\pi$
$164$	−293931.	−0.853368
$165$	−114195.	−0.326541
$166$	−828456.	−2.33345
$167$	−77715.5	−0.215634	−0.107817	−	0.994171i	$-0.534386\pi$
$167$	−77715.5	−0.215634	−0.107817	+	0.994171i	$0.534386\pi$
$168$	−9229.66	−0.0252297
$169$	62597.3	0.168593
$170$	−817923.	−2.17065
$171$	−79555.5	−0.208056
$172$	−751353.	−1.93652
$173$	218524.	0.555115	0.277558	−	0.960709i	$-0.410475\pi$
$173$	218524.	0.555115	0.277558	+	0.960709i	$0.410475\pi$
$174$	657334.	1.64594
$175$	−107.417	−0.000265142 0
$176$	427408.	1.04007
$177$	−65419.1	−0.156954
$178$	−1.02159e6	−2.41673
$179$	−545493.	−1.27250	−0.636248	−	0.771485i	$-0.719514\pi$
$179$	−545493.	−1.27250	−0.636248	+	0.771485i	$0.719514\pi$
$180$	−324339.	−0.746135
$181$	510878.	1.15910	0.579549	−	0.814937i	$-0.303229\pi$
$181$	510878.	1.15910	0.579549	+	0.814937i	$0.303229\pi$
$182$	−16834.9	−0.0376732
$183$	239505.	0.528672
$184$	−216599.	−0.471641
$185$	−134490.	−0.288908
$186$	850416.	1.80239
$187$	−329982.	−0.690060
$188$	674957.	1.39278
$189$	1825.87	0.00371805
$190$	−556402.	−1.11816
$191$	−57685.2	−0.114415	−0.0572073	−	0.998362i	$-0.518220\pi$
$191$	−57685.2	−0.114415	−0.0572073	+	0.998362i	$0.518220\pi$
$192$	10635.3	0.0208207
$193$	−822091.	−1.58864	−0.794322	−	0.607497i	$-0.792174\pi$
$193$	−822091.	−1.58864	−0.794322	+	0.607497i	$0.792174\pi$
$194$	−368597.	−0.703149
$195$	−329122.	−0.619827
$196$	−1.21176e6	−2.25308
$197$	971571.	1.78365	0.891824	−	0.452383i	$-0.149426\pi$
$197$	971571.	1.78365	0.891824	+	0.452383i	$0.149426\pi$
$198$	−188906.	−0.342438
$199$	806110.	1.44298	0.721492	−	0.692423i	$-0.243457\pi$
$199$	806110.	1.44298	0.721492	+	0.692423i	$0.243457\pi$
$200$	17560.3	0.0310425
$201$	481057.	0.839859
$202$	419921.	0.724085
$203$	−17927.0	−0.0305329
$204$	−937220.	−1.57676
$205$	226246.	0.376007
$206$	1.76057e6	2.89059
$207$	42849.0	0.0695048
$208$	1.23183e6	1.97421
$209$	−224474.	−0.355468
$210$	12769.9	0.0199820
$211$	−821913.	−1.27092	−0.635462	−	0.772132i	$-0.719190\pi$
$211$	−821913.	−1.27092	−0.635462	+	0.772132i	$0.719190\pi$
$212$	−2.47249e6	−3.77829
$213$	195063.	0.294596
$214$	−1.81867e6	−2.71469
$215$	578334.	0.853262
$216$	−298489.	−0.435305
$217$	−23192.8	−0.0334351
$218$	1.41177e6	2.01198
$219$	−745707.	−1.05065
$220$	−915156.	−1.27479
$221$	−951042.	−1.30984
$222$	−222477.	−0.302973
$223$	511948.	0.689388	0.344694	−	0.938715i	$-0.387983\pi$
$223$	511948.	0.689388	0.344694	+	0.938715i	$0.387983\pi$
$224$	−14978.5	−0.0199456
$225$	−3473.89	−0.00457467
$226$	137996.	0.179720
$227$	−1.45074e6	−1.86864	−0.934321	−	0.356433i	$-0.883993\pi$
$227$	−1.45074e6	−1.86864	−0.934321	+	0.356433i	$0.883993\pi$
$228$	−637555.	−0.812233
$229$	621169.	0.782747	0.391373	−	0.920232i	$-0.372000\pi$
$229$	621169.	0.782747	0.391373	+	0.920232i	$0.372000\pi$
$230$	299681.	0.373542
$231$	5151.89	0.00635238
$232$	2.93066e6	3.57475
$233$	490334.	0.591701	0.295851	−	0.955234i	$-0.404397\pi$
$233$	490334.	0.591701	0.295851	+	0.955234i	$0.404397\pi$
$234$	−544445.	−0.650001
$235$	−519530.	−0.613679
$236$	−524266.	−0.612733
$237$	−215640.	−0.249378
$238$	36900.4	0.0422268
$239$	109503.	0.124003	0.0620014	−	0.998076i	$-0.480252\pi$
$239$	109503.	0.124003	0.0620014	+	0.998076i	$0.480252\pi$
$240$	−934390.	−1.04713
$241$	1.36171e6	1.51022	0.755111	−	0.655597i	$-0.227583\pi$
$241$	1.36171e6	1.51022	0.755111	+	0.655597i	$0.227583\pi$
$242$	1.11038e6	1.21880
$243$	59049.0	0.0641500
$244$	1.91938e6	2.06389
$245$	932722.	0.992744
$246$	374264.	0.394312
$247$	−646957.	−0.674735
$248$	3.79150e6	3.91455
$249$	730690.	0.746852
$250$	−1.79462e6	−1.81603
$251$	8042.27	0.00805739	0.00402869	−	0.999992i	$-0.498718\pi$
$251$	8042.27	0.00805739	0.00402869	+	0.999992i	$0.498718\pi$
$252$	14632.4	0.0145150
$253$	120903.	0.118751
$254$	−1.61805e6	−1.57365
$255$	721400.	0.694746
$256$	−1.86755e6	−1.78104
$257$	1.16730e6	1.10243	0.551214	−	0.834364i	$-0.314165\pi$
$257$	1.16730e6	1.10243	0.551214	+	0.834364i	$0.314165\pi$
$258$	956700.	0.894801
$259$	6067.46	0.00562027
$260$	−2.63757e6	−2.41975
$261$	−579762.	−0.526804
$262$	3.91345e6	3.52214
$263$	−558051.	−0.497490	−0.248745	−	0.968569i	$-0.580018\pi$
$263$	−558051.	−0.497490	−0.248745	+	0.968569i	$0.580018\pi$
$264$	−842218.	−0.743729
$265$	1.90313e6	1.66477
$266$	25101.9	0.0217522
$267$	901036.	0.773506
$268$	3.85517e6	3.27874
$269$	−1.21947e6	−1.02752	−0.513759	−	0.857935i	$-0.671747\pi$
$269$	−1.21947e6	−1.02752	−0.513759	+	0.857935i	$0.671747\pi$
$270$	412981.	0.344763
$271$	1.40581e6	1.16280	0.581399	−	0.813618i	$-0.302505\pi$
$271$	1.40581e6	1.16280	0.581399	+	0.813618i	$0.302505\pi$
$272$	−2.70005e6	−2.21283
$273$	14848.2	0.0120578
$274$	338484.	0.272372
$275$	−9801.94	−0.00781592
$276$	343390.	0.271341
$277$	1.87799e6	1.47060	0.735300	−	0.677742i	$-0.237041\pi$
$277$	1.87799e6	1.47060	0.735300	+	0.677742i	$0.237041\pi$
$278$	1.31112e6	1.01749
$279$	−750058.	−0.576879
$280$	56933.4	0.0433982
$281$	−2.11759e6	−1.59984	−0.799920	−	0.600106i	$-0.795125\pi$
$281$	−2.11759e6	−1.59984	−0.799920	+	0.600106i	$0.795125\pi$
$282$	−859425.	−0.643555
$283$	1.16042e6	0.861288	0.430644	−	0.902522i	$-0.358286\pi$
$283$	1.16042e6	0.861288	0.430644	+	0.902522i	$0.358286\pi$
$284$	1.56323e6	1.15008
$285$	490741.	0.357882
$286$	−1.53621e6	−1.11054
$287$	−10207.0	−0.00731466
$288$	−484406.	−0.344135
$289$	664726.	0.468164
$290$	−4.05479e6	−2.83122
$291$	325099.	0.225052
$292$	−5.97606e6	−4.10165
$293$	−1.27325e6	−0.866449	−0.433225	−	0.901286i	$-0.642624\pi$
$293$	−1.27325e6	−0.866449	−0.433225	+	0.901286i	$0.642624\pi$
$294$	1.54294e6	1.04107
$295$	403540.	0.269980
$296$	−991893.	−0.658015
$297$	166613.	0.109602
$298$	1.87990e6	1.22629
$299$	348454.	0.225407
$300$	−27839.6	−0.0178591
$301$	−26091.4	−0.0165990
$302$	202023.	0.127463
$303$	−370367.	−0.231753
$304$	−1.83674e6	−1.13989
$305$	−1.47739e6	−0.909382
$306$	1.19337e6	0.728568
$307$	−2.26175e6	−1.36961	−0.684807	−	0.728724i	$-0.740114\pi$
$307$	−2.26175e6	−1.36961	−0.684807	+	0.728724i	$0.740114\pi$
$308$	41287.0	0.0247991
$309$	−1.55281e6	−0.925170
$310$	−5.24582e6	−3.10034
$311$	1.20263e6	0.705066	0.352533	−	0.935799i	$-0.385320\pi$
$311$	1.20263e6	0.705066	0.352533	+	0.935799i	$0.385320\pi$
$312$	−2.42735e6	−1.41171
$313$	−484311.	−0.279424	−0.139712	−	0.990192i	$-0.544618\pi$
$313$	−484311.	−0.279424	−0.139712	+	0.990192i	$0.544618\pi$
$314$	−1.97265e6	−1.12908
$315$	−11262.9	−0.00639551
$316$	−1.72813e6	−0.973551
$317$	796624.	0.445251	0.222626	−	0.974904i	$-0.428537\pi$
$317$	796624.	0.445251	0.222626	+	0.974904i	$0.428537\pi$
$318$	3.14823e6	1.74582
$319$	−1.63586e6	−0.900056
$320$	−65603.9	−0.0358142
$321$	1.60405e6	0.868871
$322$	−13520.0	−0.00726670
$323$	1.41806e6	0.756291
$324$	473216.	0.250436
$325$	−28250.1	−0.0148358
$326$	−1.08456e6	−0.565212
$327$	−1.24517e6	−0.643961
$328$	1.66862e6	0.856391
$329$	23438.5	0.0119382
$330$	1.16527e6	0.589036
$331$	−262856.	−0.131871	−0.0659353	−	0.997824i	$-0.521003\pi$
$331$	−262856.	−0.131871	−0.0659353	+	0.997824i	$0.521003\pi$
$332$	5.85572e6	2.91565
$333$	196223.	0.0969703
$334$	793024.	0.388974
$335$	−2.96741e6	−1.44466
$336$	42154.7	0.0203703
$337$	1.23123e6	0.590558	0.295279	−	0.955411i	$-0.404587\pi$
$337$	1.23123e6	0.590558	0.295279	+	0.955411i	$0.404587\pi$
$338$	−638755.	−0.304118
$339$	−121712.	−0.0575218
$340$	5.78127e6	2.71223
$341$	−2.11637e6	−0.985611
$342$	811800.	0.375305
$343$	−84174.7	−0.0386319
$344$	4.26535e6	1.94339
$345$	−264315.	−0.119557
$346$	−2.22986e6	−1.00135
$347$	−3.70344e6	−1.65113	−0.825567	−	0.564305i	$-0.809144\pi$
$347$	−3.70344e6	−1.65113	−0.825567	+	0.564305i	$0.809144\pi$
$348$	−4.64619e6	−2.05660
$349$	1.62884e6	0.715837	0.357918	−	0.933753i	$-0.383487\pi$
$349$	1.62884e6	0.715837	0.357918	+	0.933753i	$0.383487\pi$
$350$	1096.10	0.000478279 0
$351$	480195.	0.208041
$352$	−1.36680e6	−0.587962
$353$	2.56589e6	1.09598	0.547989	−	0.836486i	$-0.315394\pi$
$353$	2.56589e6	1.09598	0.547989	+	0.836486i	$0.315394\pi$
$354$	667549.	0.283123
$355$	−1.20326e6	−0.506742
$356$	7.22086e6	3.01970
$357$	−32545.8	−0.0135152
$358$	5.56631e6	2.29541
$359$	−3.46895e6	−1.42057	−0.710284	−	0.703916i	$-0.751433\pi$
$359$	−3.46895e6	−1.42057	−0.710284	+	0.703916i	$0.751433\pi$
$360$	1.84124e6	0.748779
$361$	−1.51145e6	−0.610414
$362$	−5.21310e6	−2.09086
$363$	−979343.	−0.390093
$364$	118993.	0.0470726
$365$	4.59992e6	1.80725
$366$	−2.44395e6	−0.953653
$367$	1.64135e6	0.636115	0.318058	−	0.948071i	$-0.396969\pi$
$367$	1.64135e6	0.636115	0.318058	+	0.948071i	$0.396969\pi$
$368$	989275.	0.380801
$369$	−330097.	−0.126205
$370$	1.37236e6	0.521151
$371$	−85859.4	−0.0323857
$372$	−6.01094e6	−2.25208
$373$	1.58607e6	0.590268	0.295134	−	0.955456i	$-0.404636\pi$
$373$	1.58607e6	0.590268	0.295134	+	0.955456i	$0.404636\pi$
$374$	3.36721e6	1.24477
$375$	1.58284e6	0.581244
$376$	−3.83166e6	−1.39771
$377$	−4.71471e6	−1.70845
$378$	−18631.5	−0.00670686
$379$	−966030.	−0.345456	−0.172728	−	0.984970i	$-0.555258\pi$
$379$	−966030.	−0.345456	−0.172728	+	0.984970i	$0.555258\pi$
$380$	3.93278e6	1.39714
$381$	1.42710e6	0.503667
$382$	588631.	0.206388
$383$	−3.10322e6	−1.08097	−0.540487	−	0.841352i	$-0.681760\pi$
$383$	−3.10322e6	−1.08097	−0.540487	+	0.841352i	$0.681760\pi$
$384$	1.61381e6	0.558501
$385$	−31779.6	−0.0109269
$386$	8.38878e6	2.86570
$387$	−843800.	−0.286393
$388$	2.60533e6	0.878584
$389$	624568.	0.209269	0.104635	−	0.994511i	$-0.466633\pi$
$389$	624568.	0.209269	0.104635	+	0.994511i	$0.466633\pi$
$390$	3.35842e6	1.11808
$391$	−763775.	−0.252652
$392$	6.87905e6	2.26107
$393$	−3.45163e6	−1.12731
$394$	−9.91410e6	−3.21746
$395$	1.33018e6	0.428962
$396$	1.33523e6	0.427876
$397$	2.80814e6	0.894216	0.447108	−	0.894480i	$-0.352454\pi$
$397$	2.80814e6	0.894216	0.447108	+	0.894480i	$0.352454\pi$
$398$	−8.22570e6	−2.60295
$399$	−22139.6	−0.00696207
$400$	−80203.3	−0.0250635
$401$	3.81287e6	1.18411	0.592053	−	0.805899i	$-0.298318\pi$
$401$	3.81287e6	1.18411	0.592053	+	0.805899i	$0.298318\pi$
$402$	−4.90880e6	−1.51499
$403$	−6.09958e6	−1.87084
$404$	−2.96810e6	−0.904743
$405$	−364246.	−0.110346
$406$	182931.	0.0550771
$407$	553663.	0.165676
$408$	5.32050e6	1.58235
$409$	−3.86268e6	−1.14178	−0.570888	−	0.821028i	$-0.693401\pi$
$409$	−3.86268e6	−1.14178	−0.570888	+	0.821028i	$0.693401\pi$
$410$	−2.30866e6	−0.678266
$411$	−298540.	−0.0871762
$412$	−1.24441e7	−3.61178
$413$	−18205.6	−0.00525206
$414$	−437240.	−0.125377
$415$	−4.50728e6	−1.28468
$416$	−3.93926e6	−1.11604
$417$	−1.15639e6	−0.325660
$418$	2.29058e6	0.641217
$419$	−4.00521e6	−1.11453	−0.557263	−	0.830336i	$-0.688149\pi$
$419$	−4.00521e6	−1.11453	−0.557263	+	0.830336i	$0.688149\pi$
$420$	−90260.7	−0.0249675
$421$	4.89697e6	1.34655	0.673275	−	0.739392i	$-0.264887\pi$
$421$	4.89697e6	1.34655	0.673275	+	0.739392i	$0.264887\pi$
$422$	8.38696e6	2.29257
$423$	758005.	0.205978
$424$	1.40361e7	3.79168
$425$	61921.3	0.0166291
$426$	−1.99047e6	−0.531411
$427$	66652.2	0.0176907
$428$	1.28548e7	3.39200
$429$	1.35492e6	0.355443
$430$	−5.90143e6	−1.53917
$431$	1.81874e6	0.471605	0.235803	−	0.971801i	$-0.424228\pi$
$431$	1.81874e6	0.471605	0.235803	+	0.971801i	$0.424228\pi$
$432$	1.36329e6	0.351463
$433$	545672.	0.139866	0.0699330	−	0.997552i	$-0.477721\pi$
$433$	545672.	0.139866	0.0699330	+	0.997552i	$0.477721\pi$
$434$	236663.	0.0603124
$435$	3.57628e6	0.906168
$436$	−9.97874e6	−2.51397
$437$	−519566.	−0.130148
$438$	7.60934e6	1.89523
$439$	2.81114e6	0.696179	0.348090	−	0.937461i	$-0.386830\pi$
$439$	2.81114e6	0.696179	0.348090	+	0.937461i	$0.386830\pi$
$440$	5.19525e6	1.27931
$441$	−1.36086e6	−0.333209
$442$	9.70462e6	2.36278
$443$	−2.81428e6	−0.681332	−0.340666	−	0.940184i	$-0.610652\pi$
$443$	−2.81428e6	−0.681332	−0.340666	+	0.940184i	$0.610652\pi$
$444$	1.57252e6	0.378564
$445$	−5.55807e6	−1.33053
$446$	−5.22402e6	−1.24356
$447$	−1.65805e6	−0.392491
$448$	2959.70	0.000696712 0
$449$	4.00644e6	0.937871	0.468936	−	0.883232i	$-0.344638\pi$
$449$	4.00644e6	0.937871	0.468936	+	0.883232i	$0.344638\pi$
$450$	35448.2	0.00825207
$451$	−931403.	−0.215624
$452$	−975391.	−0.224560
$453$	−178182.	−0.0407962
$454$	1.48037e7	3.37078
$455$	−91591.8	−0.0207409
$456$	3.61933e6	0.815110
$457$	−5.43801e6	−1.21801	−0.609003	−	0.793168i	$-0.708430\pi$
$457$	−5.43801e6	−1.21801	−0.609003	+	0.793168i	$0.708430\pi$
$458$	−6.33853e6	−1.41197
$459$	−1.05254e6	−0.233188
$460$	−2.11821e6	−0.466740
$461$	2.50966e6	0.550001	0.275000	−	0.961444i	$-0.411322\pi$
$461$	2.50966e6	0.550001	0.275000	+	0.961444i	$0.411322\pi$
$462$	−52570.9	−0.0114588
$463$	108662.	0.0235573	0.0117787	−	0.999931i	$-0.496251\pi$
$463$	108662.	0.0235573	0.0117787	+	0.999931i	$0.496251\pi$
$464$	−1.33852e7	−2.88623
$465$	4.62676e6	0.992303
$466$	−5.00347e6	−1.06735
$467$	3.09125e6	0.655906	0.327953	−	0.944694i	$-0.393641\pi$
$467$	3.09125e6	0.655906	0.327953	+	0.944694i	$0.393641\pi$
$468$	3.84826e6	0.812176
$469$	133874.	0.0281037
$470$	5.30139e6	1.10699
$471$	1.73985e6	0.361377
$472$	2.97620e6	0.614904
$473$	−2.38087e6	−0.489309
$474$	2.20043e6	0.449845
$475$	42122.7	0.00856608
$476$	−260820.	−0.0527624
$477$	−2.77671e6	−0.558772
$478$	−1.11739e6	−0.223684
$479$	−7.74743e6	−1.54283	−0.771417	−	0.636330i	$-0.780452\pi$
$479$	−7.74743e6	−1.54283	−0.771417	+	0.636330i	$0.780452\pi$
$480$	2.98808e6	0.591955
$481$	1.59571e6	0.314479
$482$	−1.38951e7	−2.72424
$483$	11924.5	0.00232580
$484$	−7.84841e6	−1.52289
$485$	−2.00538e6	−0.387118
$486$	−602548.	−0.115718
$487$	6.60929e6	1.26279	0.631397	−	0.775460i	$-0.282482\pi$
$487$	6.60929e6	1.26279	0.631397	+	0.775460i	$0.282482\pi$
$488$	−1.08961e7	−2.07120
$489$	956575.	0.180903
$490$	−9.51768e6	−1.79077
$491$	1.68453e6	0.315337	0.157669	−	0.987492i	$-0.449602\pi$
$491$	1.68453e6	0.315337	0.157669	+	0.987492i	$0.449602\pi$
$492$	−2.64538e6	−0.492692
$493$	1.03341e7	1.91495
$494$	6.60168e6	1.21713
$495$	−1.02776e6	−0.188529
$496$	−1.73170e7	−3.16058
$497$	54284.5	0.00985791
$498$	−7.45610e6	−1.34722
$499$	6.29003e6	1.13084	0.565420	−	0.824803i	$-0.308714\pi$
$499$	6.29003e6	1.13084	0.565420	+	0.824803i	$0.308714\pi$
$500$	1.26848e7	2.26913
$501$	−699440.	−0.124496
$502$	−82064.9	−0.0145344
$503$	3.68350e6	0.649143	0.324572	−	0.945861i	$-0.394780\pi$
$503$	3.68350e6	0.649143	0.324572	+	0.945861i	$0.394780\pi$
$504$	−83066.9	−0.0145664
$505$	2.28462e6	0.398644
$506$	−1.23372e6	−0.214210
$507$	563376.	0.0973371
$508$	1.14367e7	1.96627
$509$	3.33612e6	0.570752	0.285376	−	0.958416i	$-0.407882\pi$
$509$	3.33612e6	0.570752	0.285376	+	0.958416i	$0.407882\pi$
$510$	−7.36131e6	−1.25323
$511$	−207524.	−0.0351573
$512$	1.33189e7	2.24539
$513$	−716000.	−0.120121
$514$	−1.19114e7	−1.98863
$515$	9.57854e6	1.59141
$516$	−6.76218e6	−1.11805
$517$	2.13879e6	0.351918
$518$	−61913.5	−0.0101382
$519$	1.96671e6	0.320496
$520$	1.49732e7	2.42832
$521$	−987399.	−0.159367	−0.0796835	−	0.996820i	$-0.525391\pi$
$521$	−987399.	−0.159367	−0.0796835	+	0.996820i	$0.525391\pi$
$522$	5.91601e6	0.950282
$523$	6.57834e6	1.05163	0.525814	−	0.850600i	$-0.323761\pi$
$523$	6.57834e6	1.05163	0.525814	+	0.850600i	$0.323761\pi$
$524$	−2.76612e7	−4.40091
$525$	−966.753	−0.000153080 0
$526$	5.69446e6	0.897404
$527$	1.33696e7	2.09697
$528$	3.84667e6	0.600483
$529$	279841.	0.0434783
$530$	−1.94200e7	−3.00302
$531$	−588772.	−0.0906172
$532$	−177426.	−0.0271793
$533$	−2.68439e6	−0.409287
$534$	−9.19435e6	−1.39530
$535$	−9.89463e6	−1.49457
$536$	−2.18854e7	−3.29035
$537$	−4.90943e6	−0.734676
$538$	1.24437e7	1.85350
$539$	−3.83981e6	−0.569295
$540$	−2.91905e6	−0.430781
$541$	−6.47470e6	−0.951101	−0.475551	−	0.879688i	$-0.657751\pi$
$541$	−6.47470e6	−0.951101	−0.475551	+	0.879688i	$0.657751\pi$
$542$	−1.43452e7	−2.09753
$543$	4.59790e6	0.669206
$544$	8.63445e6	1.25094
$545$	7.68087e6	1.10769
$546$	−151514.	−0.0217506
$547$	−495799.	−0.0708496	−0.0354248	−	0.999372i	$-0.511278\pi$
$547$	−495799.	−0.0708496	−0.0354248	+	0.999372i	$0.511278\pi$
$548$	−2.39249e6	−0.340328
$549$	2.15554e6	0.305229
$550$	100021.	0.0140989
$551$	7.02992e6	0.986442
$552$	−1.94939e6	−0.272302
$553$	−60010.8	−0.00834481
$554$	−1.91634e7	−2.65276
$555$	−1.21041e6	−0.166801
$556$	−9.26727e6	−1.27135
$557$	3.94887e6	0.539306	0.269653	−	0.962958i	$-0.413091\pi$
$557$	3.94887e6	0.539306	0.269653	+	0.962958i	$0.413091\pi$
$558$	7.65374e6	1.04061
$559$	−6.86190e6	−0.928784
$560$	−260033.	−0.0350395
$561$	−2.96984e6	−0.398406
$562$	2.16083e7	2.88590
$563$	−2.70237e6	−0.359314	−0.179657	−	0.983729i	$-0.557499\pi$
$563$	−2.70237e6	−0.359314	−0.179657	+	0.983729i	$0.557499\pi$
$564$	6.07462e6	0.804120
$565$	750781.	0.0989447
$566$	−1.18411e7	−1.55365
$567$	16432.8	0.00214662
$568$	−8.87430e6	−1.15415
$569$	1.33108e7	1.72355	0.861773	−	0.507294i	$-0.169354\pi$
$569$	1.33108e7	1.72355	0.861773	+	0.507294i	$0.169354\pi$
$570$	−5.00762e6	−0.645571
$571$	−1.10053e7	−1.41257	−0.706286	−	0.707926i	$-0.749631\pi$
$571$	−1.10053e7	−1.41257	−0.706286	+	0.707926i	$0.749631\pi$
$572$	1.08583e7	1.38762
$573$	−519167.	−0.0660572
$574$	104154.	0.0131947
$575$	−22687.5	−0.00286165
$576$	95717.3	0.0120208
$577$	−480544.	−0.0600888	−0.0300444	−	0.999549i	$-0.509565\pi$
$577$	−480544.	−0.0600888	−0.0300444	+	0.999549i	$0.509565\pi$
$578$	−6.78300e6	−0.844505
$579$	−7.39882e6	−0.917204
$580$	2.86602e7	3.53760
$581$	203345.	0.0249915
$582$	−3.31737e6	−0.405963
$583$	−7.83477e6	−0.954674
$584$	3.39255e7	4.11618
$585$	−2.96210e6	−0.357857
$586$	1.29924e7	1.56296
$587$	9.12805e6	1.09341	0.546705	−	0.837325i	$-0.315882\pi$
$587$	9.12805e6	1.09341	0.546705	+	0.837325i	$0.315882\pi$
$588$	−1.09059e7	−1.30082
$589$	9.09485e6	1.08021
$590$	−4.11780e6	−0.487007
$591$	8.74414e6	1.02979
$592$	4.53029e6	0.531278
$593$	−2.66114e6	−0.310765	−0.155382	−	0.987854i	$-0.549661\pi$
$593$	−2.66114e6	−0.310765	−0.155382	+	0.987854i	$0.549661\pi$
$594$	−1.70015e6	−0.197707
$595$	200760.	0.0232479
$596$	−1.32876e7	−1.53225
$597$	7.25499e6	0.833107
$598$	−3.55569e6	−0.406604
$599$	6.44915e6	0.734405	0.367202	−	0.930141i	$-0.380316\pi$
$599$	6.44915e6	0.734405	0.367202	+	0.930141i	$0.380316\pi$
$600$	158042.	0.0179224
$601$	−1.48491e6	−0.167693	−0.0838463	−	0.996479i	$-0.526720\pi$
$601$	−1.48491e6	−0.167693	−0.0838463	+	0.996479i	$0.526720\pi$
$602$	266241.	0.0299423
$603$	4.32951e6	0.484893
$604$	−1.42795e6	−0.159265
$605$	6.04111e6	0.671009
$606$	3.77929e6	0.418051
$607$	−6.56656e6	−0.723379	−0.361690	−	0.932299i	$-0.617800\pi$
$607$	−6.56656e6	−0.723379	−0.361690	+	0.932299i	$0.617800\pi$
$608$	5.87368e6	0.644394
$609$	−161343.	−0.0176281
$610$	1.50756e7	1.64040
$611$	6.16420e6	0.667996
$612$	−8.43498e6	−0.910344
$613$	−9.33817e6	−1.00372	−0.501858	−	0.864950i	$-0.667350\pi$
$613$	−9.33817e6	−1.00372	−0.501858	+	0.864950i	$0.667350\pi$
$614$	2.30793e7	2.47060
$615$	2.03621e6	0.217088
$616$	−234382.	−0.0248870
$617$	7.56128e6	0.799617	0.399809	−	0.916599i	$-0.369077\pi$
$617$	7.56128e6	0.799617	0.399809	+	0.916599i	$0.369077\pi$
$618$	1.58452e7	1.66888
$619$	1.16180e7	1.21872	0.609359	−	0.792895i	$-0.291427\pi$
$619$	1.16180e7	1.21872	0.609359	+	0.792895i	$0.291427\pi$
$620$	3.70786e7	3.87387
$621$	385641.	0.0401286
$622$	−1.22718e7	−1.27184
$623$	250751.	0.0258834
$624$	1.10865e7	1.13981
$625$	−9.62976e6	−0.986088
$626$	4.94201e6	0.504043
$627$	−2.02027e6	−0.205230
$628$	1.39431e7	1.41078
$629$	−3.49763e6	−0.352491
$630$	114929.	0.0115366
$631$	−8.43872e6	−0.843730	−0.421865	−	0.906659i	$-0.638624\pi$
$631$	−8.43872e6	−0.843730	−0.421865	+	0.906659i	$0.638624\pi$
$632$	9.81042e6	0.977001
$633$	−7.39722e6	−0.733768
$634$	−8.12891e6	−0.803173
$635$	−8.80313e6	−0.866369
$636$	−2.22524e7	−2.18140
$637$	−1.10667e7	−1.08061
$638$	1.66926e7	1.62358
$639$	1.75557e6	0.170085
$640$	−9.95483e6	−0.960692
$641$	1.32010e7	1.26900	0.634500	−	0.772923i	$-0.281206\pi$
$641$	1.32010e7	1.26900	0.634500	+	0.772923i	$0.281206\pi$
$642$	−1.63680e7	−1.56733
$643$	−1.57321e7	−1.50058	−0.750290	−	0.661109i	$-0.770086\pi$
$643$	−1.57321e7	−1.50058	−0.750290	+	0.661109i	$0.770086\pi$
$644$	95562.5	0.00907973
$645$	5.20501e6	0.492631
$646$	−1.44702e7	−1.36425
$647$	−6.22066e6	−0.584219	−0.292109	−	0.956385i	$-0.594357\pi$
$647$	−6.22066e6	−0.584219	−0.292109	+	0.956385i	$0.594357\pi$
$648$	−2.68640e6	−0.251323
$649$	−1.66128e6	−0.154822
$650$	288270.	0.0267618
$651$	−208735.	−0.0193038
$652$	7.66595e6	0.706231
$653$	−1.57628e7	−1.44660	−0.723302	−	0.690532i	$-0.757376\pi$
$653$	−1.57628e7	−1.44660	−0.723302	+	0.690532i	$0.757376\pi$
$654$	1.27060e7	1.16162
$655$	2.12915e7	1.93911
$656$	−7.62110e6	−0.691446
$657$	−6.71136e6	−0.606593
$658$	−239171.	−0.0215349
$659$	−5.77008e6	−0.517569	−0.258784	−	0.965935i	$-0.583322\pi$
$659$	−5.77008e6	−0.517569	−0.258784	+	0.965935i	$0.583322\pi$
$660$	−8.23640e6	−0.736000
$661$	−1.48192e7	−1.31924	−0.659618	−	0.751601i	$-0.729282\pi$
$661$	−1.48192e7	−1.31924	−0.659618	+	0.751601i	$0.729282\pi$
$662$	2.68223e6	0.237877
$663$	−8.55938e6	−0.756238
$664$	−3.32423e7	−2.92598
$665$	136569.	0.0119756
$666$	−2.00230e6	−0.174921
$667$	−3.78635e6	−0.329538
$668$	−5.60528e6	−0.486022
$669$	4.60753e6	0.398018
$670$	3.02801e7	2.60597
$671$	6.08209e6	0.521491
$672$	−134806.	−0.0115156
$673$	−1.74615e7	−1.48609	−0.743045	−	0.669242i	$-0.766619\pi$
$673$	−1.74615e7	−1.48609	−0.743045	+	0.669242i	$0.766619\pi$
$674$	−1.25637e7	−1.06529
$675$	−31265.0	−0.00264118
$676$	4.51487e6	0.379995
$677$	−2.10975e7	−1.76913	−0.884564	−	0.466418i	$-0.845544\pi$
$677$	−2.10975e7	−1.76913	−0.884564	+	0.466418i	$0.845544\pi$
$678$	1.24197e6	0.103762
$679$	90472.2	0.00753080
$680$	−3.28197e7	−2.72184
$681$	−1.30567e7	−1.07886
$682$	2.15958e7	1.77791
$683$	−1.43654e7	−1.17833	−0.589163	−	0.808014i	$-0.700542\pi$
$683$	−1.43654e7	−1.17833	−0.589163	+	0.808014i	$0.700542\pi$
$684$	−5.73799e6	−0.468943
$685$	1.84155e6	0.149954
$686$	858935.	0.0696867
$687$	5.59052e6	0.451919
$688$	−1.94812e7	−1.56908
$689$	−2.25806e7	−1.81212
$690$	2.69713e6	0.215664
$691$	1.64154e7	1.30785	0.653923	−	0.756561i	$-0.273122\pi$
$691$	1.64154e7	1.30785	0.653923	+	0.756561i	$0.273122\pi$
$692$	1.57612e7	1.25119
$693$	46367.0	0.00366755
$694$	3.77907e7	2.97842
$695$	7.13324e6	0.560176
$696$	2.63759e7	2.06388
$697$	5.88391e6	0.458758
$698$	−1.66210e7	−1.29127
$699$	4.41301e6	0.341619
$700$	−7747.52	−0.000597609 0
$701$	−1.07940e7	−0.829635	−0.414818	−	0.909905i	$-0.636155\pi$
$701$	−1.07940e7	−0.829635	−0.414818	+	0.909905i	$0.636155\pi$
$702$	−4.90000e6	−0.375278
$703$	−2.37930e6	−0.181577
$704$	270077.	0.0205379
$705$	−4.67577e6	−0.354308
$706$	−2.61829e7	−1.97700
$707$	−103070.	−0.00775502
$708$	−4.71839e6	−0.353762
$709$	2.44390e7	1.82586	0.912930	−	0.408115i	$-0.133814\pi$
$709$	2.44390e7	1.82586	0.912930	+	0.408115i	$0.133814\pi$
$710$	1.22783e7	0.914093
$711$	−1.94076e6	−0.143979
$712$	−4.09921e7	−3.03040
$713$	−4.89853e6	−0.360863
$714$	332103.	0.0243797
$715$	−8.35787e6	−0.611407
$716$	−3.93440e7	−2.86811
$717$	985527.	0.0715930
$718$	3.53978e7	2.56251
$719$	−6.41280e6	−0.462621	−0.231310	−	0.972880i	$-0.574301\pi$
$719$	−6.41280e6	−0.462621	−0.231310	+	0.972880i	$0.574301\pi$
$720$	−8.40951e6	−0.604560
$721$	−432133.	−0.0309585
$722$	1.54231e7	1.10110
$723$	1.22554e7	0.871928
$724$	3.68474e7	2.61252
$725$	306970.	0.0216896
$726$	9.99341e6	0.703675
$727$	−1.58788e7	−1.11424	−0.557122	−	0.830431i	$-0.688095\pi$
$727$	−1.58788e7	−1.11424	−0.557122	+	0.830431i	$0.688095\pi$
$728$	−675512.	−0.0472394
$729$	531441.	0.0370370
$730$	−4.69385e7	−3.26003
$731$	1.50406e7	1.04105
$732$	1.72744e7	1.19159
$733$	2.52517e7	1.73592	0.867962	−	0.496631i	$-0.165430\pi$
$733$	2.52517e7	1.73592	0.867962	+	0.496631i	$0.165430\pi$
$734$	−1.67487e7	−1.14747
$735$	8.39450e6	0.573161
$736$	−3.16359e6	−0.215271
$737$	1.22162e7	0.828450
$738$	3.36837e6	0.227656
$739$	−1.56260e7	−1.05253	−0.526267	−	0.850319i	$-0.676409\pi$
$739$	−1.56260e7	−1.05253	−0.526267	+	0.850319i	$0.676409\pi$
$740$	−9.70015e6	−0.651177
$741$	−5.82261e6	−0.389558
$742$	876126.	0.0584193
$743$	1.42696e7	0.948284	0.474142	−	0.880448i	$-0.342758\pi$
$743$	1.42696e7	0.948284	0.474142	+	0.880448i	$0.342758\pi$
$744$	3.41235e7	2.26006
$745$	1.02278e7	0.675133
$746$	−1.61845e7	−1.06476
$747$	6.57621e6	0.431195
$748$	−2.38002e7	−1.55534
$749$	446393.	0.0290746
$750$	−1.61516e7	−1.04848
$751$	2.22359e7	1.43865	0.719323	−	0.694676i	$-0.244452\pi$
$751$	2.22359e7	1.43865	0.719323	+	0.694676i	$0.244452\pi$
$752$	1.75004e7	1.12851
$753$	72380.4	0.00465193
$754$	4.81098e7	3.08181
$755$	1.09912e6	0.0701745
$756$	131692.	0.00838021
$757$	−1.09113e7	−0.692048	−0.346024	−	0.938226i	$-0.612468\pi$
$757$	−1.09113e7	−0.692048	−0.346024	+	0.938226i	$0.612468\pi$
$758$	9.85756e6	0.623155
$759$	1.08813e6	0.0685607
$760$	−2.23260e7	−1.40209
$761$	2.42444e6	0.151758	0.0758788	−	0.997117i	$-0.475824\pi$
$761$	2.42444e6	0.151758	0.0758788	+	0.997117i	$0.475824\pi$
$762$	−1.45624e7	−0.908546
$763$	−346520.	−0.0215485
$764$	−4.16058e6	−0.257882
$765$	6.49260e6	0.401112
$766$	3.16659e7	1.94993
$767$	−4.78798e6	−0.293876
$768$	−1.68080e7	−1.02828
$769$	2.00363e6	0.122181	0.0610903	−	0.998132i	$-0.480542\pi$
$769$	2.00363e6	0.122181	0.0610903	+	0.998132i	$0.480542\pi$
$770$	324285.	0.0197106
$771$	1.05057e7	0.636487
$772$	−5.92938e7	−3.58069
$773$	3.91181e6	0.235466	0.117733	−	0.993045i	$-0.462437\pi$
$773$	3.91181e6	0.235466	0.117733	+	0.993045i	$0.462437\pi$
$774$	8.61030e6	0.516614
$775$	397137.	0.0237512
$776$	−1.47902e7	−0.881697
$777$	54607.1	0.00324487
$778$	−6.37322e6	−0.377494
$779$	4.00260e6	0.236319
$780$	−2.37381e7	−1.39704
$781$	4.95353e6	0.290594
$782$	7.79371e6	0.455751
$783$	−5.21786e6	−0.304150
$784$	−3.14188e7	−1.82557
$785$	−1.07323e7	−0.621614
$786$	3.52211e7	2.03351
$787$	−2.37516e7	−1.36696	−0.683479	−	0.729970i	$-0.739534\pi$
$787$	−2.37516e7	−1.36696	−0.683479	+	0.729970i	$0.739534\pi$
$788$	7.00752e7	4.02021
$789$	−5.02246e6	−0.287226
$790$	−1.35734e7	−0.773789
$791$	−33871.3	−0.00192482
$792$	−7.57996e6	−0.429392
$793$	1.75292e7	0.989872
$794$	−2.86548e7	−1.61304
$795$	1.71282e7	0.961157
$796$	5.81412e7	3.25238
$797$	−2.50486e7	−1.39681	−0.698405	−	0.715703i	$-0.746106\pi$
$797$	−2.50486e7	−1.39681	−0.698405	+	0.715703i	$0.746106\pi$
$798$	225917.	0.0125586
$799$	−1.35113e7	−0.748737
$800$	256481.	0.0141687
$801$	8.10932e6	0.446584
$802$	−3.89072e7	−2.13597
$803$	−1.89368e7	−1.03638
$804$	3.46965e7	1.89298
$805$	−73556.7	−0.00400067
$806$	6.22413e7	3.37475
$807$	−1.09752e7	−0.593237
$808$	1.68496e7	0.907949
$809$	−2.26709e7	−1.21786	−0.608931	−	0.793223i	$-0.708402\pi$
$809$	−2.26709e7	−1.21786	−0.608931	+	0.793223i	$0.708402\pi$
$810$	3.71683e6	0.199049
$811$	−1.66885e7	−0.890974	−0.445487	−	0.895288i	$-0.646969\pi$
$811$	−1.66885e7	−0.890974	−0.445487	+	0.895288i	$0.646969\pi$
$812$	−1.29300e6	−0.0688188
$813$	1.26523e7	0.671342
$814$	−5.64969e6	−0.298857
$815$	−5.90066e6	−0.311176
$816$	−2.43004e7	−1.27758
$817$	1.02315e7	0.536272
$818$	3.94156e7	2.05961
$819$	133634.	0.00696158
$820$	1.63181e7	0.847492
$821$	−2.41094e7	−1.24833	−0.624164	−	0.781293i	$-0.714560\pi$
$821$	−2.41094e7	−1.24833	−0.624164	+	0.781293i	$0.714560\pi$
$822$	3.04636e6	0.157254
$823$	−9.03070e6	−0.464753	−0.232376	−	0.972626i	$-0.574650\pi$
$823$	−9.03070e6	−0.464753	−0.232376	+	0.972626i	$0.574650\pi$
$824$	7.06441e7	3.62458
$825$	−88217.4	−0.00451252
$826$	185773.	0.00947399
$827$	1.22307e7	0.621852	0.310926	−	0.950434i	$-0.399361\pi$
$827$	1.22307e7	0.621852	0.310926	+	0.950434i	$0.399361\pi$
$828$	3.09051e6	0.156659
$829$	2.01683e7	1.01925	0.509627	−	0.860395i	$-0.329783\pi$
$829$	2.01683e7	1.01925	0.509627	+	0.860395i	$0.329783\pi$
$830$	4.59932e7	2.31739
$831$	1.69019e7	0.849051
$832$	778387.	0.0389841
$833$	2.42570e7	1.21123
$834$	1.18000e7	0.587447
$835$	4.31452e6	0.214149
$836$	−1.61904e7	−0.801199
$837$	−6.75053e6	−0.333061
$838$	4.08700e7	2.01045
$839$	1.80995e7	0.887690	0.443845	−	0.896103i	$-0.353614\pi$
$839$	1.80995e7	0.887690	0.443845	+	0.896103i	$0.353614\pi$
$840$	512401.	0.0250560
$841$	3.07195e7	1.49770
$842$	−4.99697e7	−2.42899
$843$	−1.90583e7	−0.923668
$844$	−5.92810e7	−2.86457
$845$	−3.47520e6	−0.167432
$846$	−7.73483e6	−0.371556
$847$	−272543.	−0.0130535
$848$	−6.41072e7	−3.06138
$849$	1.04438e7	0.497265
$850$	−631857.	−0.0299966
$851$	1.28150e6	0.0606591
$852$	1.40691e7	0.663998
$853$	−1.82781e7	−0.860121	−0.430060	−	0.902800i	$-0.641508\pi$
$853$	−1.82781e7	−0.860121	−0.430060	+	0.902800i	$0.641508\pi$
$854$	−680132.	−0.0319116
$855$	4.41667e6	0.206623
$856$	−7.29753e7	−3.40402
$857$	−1.47267e7	−0.684940	−0.342470	−	0.939529i	$-0.611264\pi$
$857$	−1.47267e7	−0.684940	−0.342470	+	0.939529i	$0.611264\pi$
$858$	−1.38259e7	−0.641172
$859$	−1.82990e7	−0.846142	−0.423071	−	0.906096i	$-0.639048\pi$
$859$	−1.82990e7	−0.846142	−0.423071	+	0.906096i	$0.639048\pi$
$860$	4.17127e7	1.92319
$861$	−91863.1	−0.00422312
$862$	−1.85588e7	−0.850712
$863$	−3.92569e6	−0.179427	−0.0897137	−	0.995968i	$-0.528595\pi$
$863$	−3.92569e6	−0.179427	−0.0897137	+	0.995968i	$0.528595\pi$
$864$	−4.35966e6	−0.198686
$865$	−1.21317e7	−0.551293
$866$	−5.56814e6	−0.252299
$867$	5.98254e6	0.270295
$868$	−1.67279e6	−0.0753603
$869$	−5.47606e6	−0.245991
$870$	−3.64931e7	−1.63460
$871$	3.52082e7	1.57253
$872$	5.66483e7	2.52287
$873$	2.92589e6	0.129934
$874$	5.30176e6	0.234769
$875$	440490.	0.0194499
$876$	−5.37846e7	−2.36809
$877$	−3.49463e7	−1.53427	−0.767135	−	0.641486i	$-0.778318\pi$
$877$	−3.49463e7	−1.53427	−0.767135	+	0.641486i	$0.778318\pi$
$878$	−2.86854e7	−1.25581
$879$	−1.14592e7	−0.500245
$880$	−2.37283e7	−1.03290
$881$	−3.45541e7	−1.49989	−0.749945	−	0.661501i	$-0.769920\pi$
$881$	−3.45541e7	−1.49989	−0.749945	+	0.661501i	$0.769920\pi$
$882$	1.38865e7	0.601064
$883$	2.29538e6	0.0990722	0.0495361	−	0.998772i	$-0.484226\pi$
$883$	2.29538e6	0.0990722	0.0495361	+	0.998772i	$0.484226\pi$
$884$	−6.85945e7	−2.95229
$885$	3.63186e6	0.155873
$886$	2.87175e7	1.22903
$887$	2.48902e7	1.06223	0.531116	−	0.847299i	$-0.321773\pi$
$887$	2.48902e7	1.06223	0.531116	+	0.847299i	$0.321773\pi$
$888$	−8.92704e6	−0.379905
$889$	397151.	0.0168539
$890$	5.67156e7	2.40009
$891$	1.49952e6	0.0632786
$892$	3.69246e7	1.55383
$893$	−9.19120e6	−0.385695
$894$	1.69191e7	0.708000
$895$	3.02840e7	1.26373
$896$	449109.	0.0186888
$897$	3.13609e6	0.130139
$898$	−4.08826e7	−1.69179
$899$	6.62789e7	2.73512
$900$	−250556.	−0.0103110
$901$	4.94943e7	2.03115
$902$	9.50422e6	0.388956
$903$	−234822.	−0.00958341
$904$	5.53719e6	0.225356
$905$	−2.83623e7	−1.15112
$906$	1.81821e6	0.0735908
$907$	−1.12581e7	−0.454411	−0.227205	−	0.973847i	$-0.572959\pi$
$907$	−1.12581e7	−0.454411	−0.227205	+	0.973847i	$0.572959\pi$
$908$	−1.04636e8	−4.21178
$909$	−3.33330e6	−0.133803
$910$	934621.	0.0374138
$911$	−2.07869e7	−0.829837	−0.414919	−	0.909859i	$-0.636190\pi$
$911$	−2.07869e7	−0.829837	−0.414919	+	0.909859i	$0.636190\pi$
$912$	−1.65306e7	−0.658116
$913$	1.85555e7	0.736707
$914$	5.54905e7	2.19712
$915$	−1.32965e7	−0.525032
$916$	4.48022e7	1.76425
$917$	−960558.	−0.0377225
$918$	1.07403e7	0.420639
$919$	−1.17836e7	−0.460244	−0.230122	−	0.973162i	$-0.573913\pi$
$919$	−1.17836e7	−0.460244	−0.230122	+	0.973162i	$0.573913\pi$
$920$	1.20249e7	0.468394
$921$	−2.03557e7	−0.790747
$922$	−2.56091e7	−0.992126
$923$	1.42766e7	0.551594
$924$	371583.	0.0143178
$925$	−103895.	−0.00399246
$926$	−1.10881e6	−0.0424942
$927$	−1.39753e7	−0.534147
$928$	4.28045e7	1.63162
$929$	−2.82219e7	−1.07287	−0.536435	−	0.843942i	$-0.680229\pi$
$929$	−2.82219e7	−1.07287	−0.536435	+	0.843942i	$0.680229\pi$
$930$	−4.72123e7	−1.78998
$931$	1.65011e7	0.623935
$932$	3.53657e7	1.33365
$933$	1.08236e7	0.407070
$934$	−3.15437e7	−1.18316
$935$	1.83196e7	0.685308
$936$	−2.18462e7	−0.815053
$937$	1.34325e7	0.499814	0.249907	−	0.968270i	$-0.419600\pi$
$937$	1.34325e7	0.499814	0.249907	+	0.968270i	$0.419600\pi$
$938$	−1.36608e6	−0.0506953
$939$	−4.35880e6	−0.161325
$940$	−3.74715e7	−1.38319
$941$	4.06264e7	1.49566	0.747832	−	0.663888i	$-0.231095\pi$
$941$	4.06264e7	1.49566	0.747832	+	0.663888i	$0.231095\pi$
$942$	−1.77538e7	−0.651875
$943$	−2.15582e6	−0.0789465
$944$	−1.35933e7	−0.496470
$945$	−101366.	−0.00369245
$946$	2.42949e7	0.882646
$947$	−3.34341e7	−1.21148	−0.605738	−	0.795664i	$-0.707122\pi$
$947$	−3.34341e7	−1.21148	−0.605738	+	0.795664i	$0.707122\pi$
$948$	−1.55532e7	−0.562080
$949$	−5.45778e7	−1.96721
$950$	−429828.	−0.0154520
$951$	7.16962e6	0.257066
$952$	1.48065e6	0.0529493
$953$	−8.95158e6	−0.319277	−0.159638	−	0.987176i	$-0.551033\pi$
$953$	−8.95158e6	−0.319277	−0.159638	+	0.987176i	$0.551033\pi$
$954$	2.83341e7	1.00795
$955$	3.20250e6	0.113627
$956$	7.89797e6	0.279493
$957$	−1.47227e7	−0.519648
$958$	7.90563e7	2.78306
$959$	−83081.1	−0.00291713
$960$	−590435.	−0.0206773
$961$	5.71181e7	1.99510
$962$	−1.62830e7	−0.567277
$963$	1.44365e7	0.501643
$964$	9.82140e7	3.40393
$965$	4.56399e7	1.57771
$966$	−121680.	−0.00419543
$967$	−2.94663e7	−1.01335	−0.506675	−	0.862137i	$-0.669126\pi$
$967$	−2.94663e7	−1.01335	−0.506675	+	0.862137i	$0.669126\pi$
$968$	4.45546e7	1.52829
$969$	1.27626e7	0.436645
$970$	2.04633e7	0.698307
$971$	−3.03617e7	−1.03342	−0.516712	−	0.856159i	$-0.672844\pi$
$971$	−3.03617e7	−1.03342	−0.516712	+	0.856159i	$0.672844\pi$
$972$	4.25895e6	0.144589
$973$	−321814.	−0.0108974
$974$	−6.74425e7	−2.27791
$975$	−254251.	−0.00856548
$976$	4.97661e7	1.67228
$977$	3.77587e6	0.126555	0.0632777	−	0.997996i	$-0.479845\pi$
$977$	3.77587e6	0.126555	0.0632777	+	0.997996i	$0.479845\pi$
$978$	−9.76107e6	−0.326325
$979$	2.28813e7	0.762999
$980$	6.72732e7	2.23757
$981$	−1.12065e7	−0.371791
$982$	−1.71893e7	−0.568826
$983$	1.74788e7	0.576938	0.288469	−	0.957489i	$-0.406854\pi$
$983$	1.74788e7	0.576938	0.288469	+	0.957489i	$0.406854\pi$
$984$	1.50176e7	0.494438
$985$	−5.39385e7	−1.77137
$986$	−1.05452e8	−3.45431
$987$	210946.	0.00689253
$988$	−4.66622e7	−1.52080
$989$	−5.51074e6	−0.179151
$990$	1.04874e7	0.340080
$991$	4.83380e7	1.56352	0.781762	−	0.623576i	$-0.214321\pi$
$991$	4.83380e7	1.56352	0.781762	+	0.623576i	$0.214321\pi$
$992$	5.53777e7	1.78672
$993$	−2.36570e6	−0.0761355
$994$	−553930.	−0.0177823
$995$	−4.47526e7	−1.43305
$996$	5.27014e7	1.68335
$997$	−1.74335e7	−0.555452	−0.277726	−	0.960660i	$-0.589581\pi$
$997$	−1.74335e7	−0.555452	−0.277726	+	0.960660i	$0.589581\pi$
$998$	−6.41847e7	−2.03988
$999$	1.76601e6	0.0559858

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.6.a.b.1.1	✓	3
3.2	odd	2		207.6.a.c.1.3		3
4.3	odd	2		1104.6.a.i.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.6.a.b.1.1	✓	3	1.1	even	1	trivial
207.6.a.c.1.3		3	3.2	odd	2
1104.6.a.i.1.2		3	4.3	odd	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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	69.a (trivial)

\(f(q)\)	\(=\)	\(q-10.2042 q^{2} +9.00000 q^{3} +72.1256 q^{4} -55.5168 q^{5} -91.8378 q^{6} +2.50462 q^{7} -409.450 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-10.2042 q^{2} +9.00000 q^{3} +72.1256 q^{4} -55.5168 q^{5} -91.8378 q^{6} +2.50462 q^{7} -409.450 q^{8} +81.0000 q^{9} +566.504 q^{10} +228.550 q^{11} +649.131 q^{12} +658.703 q^{13} -25.5577 q^{14} -499.651 q^{15} +1870.09 q^{16} -1443.81 q^{17} -826.540 q^{18} -982.167 q^{19} -4004.18 q^{20} +22.5416 q^{21} -2332.17 q^{22} +529.000 q^{23} -3685.05 q^{24} -42.8875 q^{25} -6721.54 q^{26} +729.000 q^{27} +180.648 q^{28} -7157.56 q^{29} +5098.54 q^{30} -9259.98 q^{31} -5980.33 q^{32} +2056.95 q^{33} +14732.9 q^{34} -139.049 q^{35} +5842.18 q^{36} +2422.50 q^{37} +10022.2 q^{38} +5928.33 q^{39} +22731.3 q^{40} -4075.27 q^{41} -230.019 q^{42} -10417.3 q^{43} +16484.3 q^{44} -4496.86 q^{45} -5398.02 q^{46} +9358.08 q^{47} +16830.8 q^{48} -16800.7 q^{49} +437.632 q^{50} -12994.3 q^{51} +47509.4 q^{52} -34280.3 q^{53} -7438.86 q^{54} -12688.4 q^{55} -1025.52 q^{56} -8839.51 q^{57} +73037.2 q^{58} -7268.79 q^{59} -36037.6 q^{60} +26611.7 q^{61} +94490.6 q^{62} +202.874 q^{63} +1181.70 q^{64} -36569.1 q^{65} -20989.5 q^{66} +53450.8 q^{67} -104136. q^{68} +4761.00 q^{69} +1418.88 q^{70} +21673.7 q^{71} -33165.4 q^{72} -82856.3 q^{73} -24719.7 q^{74} -385.987 q^{75} -70839.4 q^{76} +572.432 q^{77} -60493.9 q^{78} -23960.0 q^{79} -103821. q^{80} +6561.00 q^{81} +41584.9 q^{82} +81187.7 q^{83} +1625.83 q^{84} +80155.6 q^{85} +106300. q^{86} -64418.0 q^{87} -93579.7 q^{88} +100115. q^{89} +45886.8 q^{90} +1649.80 q^{91} +38154.5 q^{92} -83339.8 q^{93} -95491.7 q^{94} +54526.8 q^{95} -53822.9 q^{96} +36122.1 q^{97} +171438. q^{98} +18512.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 8 q^{2} + 27 q^{3} + 22 q^{4} - 56 q^{5} - 72 q^{6} - 114 q^{7} - 510 q^{8} + 243 q^{9}+O(q^{10}) \) 3 * q - 8 * q^2 + 27 * q^3 + 22 * q^4 - 56 * q^5 - 72 * q^6 - 114 * q^7 - 510 * q^8 + 243 * q^9	\( 3 q - 8 q^{2} + 27 q^{3} + 22 q^{4} - 56 q^{5} - 72 q^{6} - 114 q^{7} - 510 q^{8} + 243 q^{9} + 282 q^{10} - 376 q^{11} + 198 q^{12} - 858 q^{13} + 588 q^{14} - 504 q^{15} + 2738 q^{16} - 2548 q^{17} - 648 q^{18} - 2846 q^{19} - 4618 q^{20} - 1026 q^{21} - 5050 q^{22} + 1587 q^{23} - 4590 q^{24} + 753 q^{25} - 7788 q^{26} + 2187 q^{27} + 4736 q^{28} - 16370 q^{29} + 2538 q^{30} - 14756 q^{31} - 3878 q^{32} - 3384 q^{33} + 16520 q^{34} - 18520 q^{35} + 1782 q^{36} + 15874 q^{37} + 12438 q^{38} - 7722 q^{39} + 38270 q^{40} + 12606 q^{41} + 5292 q^{42} + 3154 q^{43} + 27114 q^{44} - 4536 q^{45} - 4232 q^{46} + 29928 q^{47} + 24642 q^{48} + 4471 q^{49} + 1452 q^{50} - 22932 q^{51} + 86856 q^{52} - 44084 q^{53} - 5832 q^{54} + 38360 q^{55} - 35704 q^{56} - 25614 q^{57} + 73316 q^{58} - 29300 q^{59} - 41562 q^{60} + 54010 q^{61} + 99908 q^{62} - 9234 q^{63} - 1582 q^{64} - 51216 q^{65} - 45450 q^{66} + 43390 q^{67} - 69840 q^{68} + 14283 q^{69} - 2476 q^{70} + 23424 q^{71} - 41310 q^{72} - 91402 q^{73} - 2294 q^{74} + 6777 q^{75} - 14274 q^{76} - 97208 q^{77} - 70092 q^{78} - 49398 q^{79} - 52626 q^{80} + 19683 q^{81} + 40152 q^{82} - 103936 q^{83} + 42624 q^{84} + 5888 q^{85} + 133634 q^{86} - 147330 q^{87} + 48898 q^{88} + 96112 q^{89} + 22842 q^{90} + 129228 q^{91} + 11638 q^{92} - 132804 q^{93} - 133688 q^{94} - 55928 q^{95} - 34902 q^{96} - 135318 q^{97} + 108440 q^{98} - 30456 q^{99}+O(q^{100}) \) 3 * q - 8 * q^2 + 27 * q^3 + 22 * q^4 - 56 * q^5 - 72 * q^6 - 114 * q^7 - 510 * q^8 + 243 * q^9 + 282 * q^10 - 376 * q^11 + 198 * q^12 - 858 * q^13 + 588 * q^14 - 504 * q^15 + 2738 * q^16 - 2548 * q^17 - 648 * q^18 - 2846 * q^19 - 4618 * q^20 - 1026 * q^21 - 5050 * q^22 + 1587 * q^23 - 4590 * q^24 + 753 * q^25 - 7788 * q^26 + 2187 * q^27 + 4736 * q^28 - 16370 * q^29 + 2538 * q^30 - 14756 * q^31 - 3878 * q^32 - 3384 * q^33 + 16520 * q^34 - 18520 * q^35 + 1782 * q^36 + 15874 * q^37 + 12438 * q^38 - 7722 * q^39 + 38270 * q^40 + 12606 * q^41 + 5292 * q^42 + 3154 * q^43 + 27114 * q^44 - 4536 * q^45 - 4232 * q^46 + 29928 * q^47 + 24642 * q^48 + 4471 * q^49 + 1452 * q^50 - 22932 * q^51 + 86856 * q^52 - 44084 * q^53 - 5832 * q^54 + 38360 * q^55 - 35704 * q^56 - 25614 * q^57 + 73316 * q^58 - 29300 * q^59 - 41562 * q^60 + 54010 * q^61 + 99908 * q^62 - 9234 * q^63 - 1582 * q^64 - 51216 * q^65 - 45450 * q^66 + 43390 * q^67 - 69840 * q^68 + 14283 * q^69 - 2476 * q^70 + 23424 * q^71 - 41310 * q^72 - 91402 * q^73 - 2294 * q^74 + 6777 * q^75 - 14274 * q^76 - 97208 * q^77 - 70092 * q^78 - 49398 * q^79 - 52626 * q^80 + 19683 * q^81 + 40152 * q^82 - 103936 * q^83 + 42624 * q^84 + 5888 * q^85 + 133634 * q^86 - 147330 * q^87 + 48898 * q^88 + 96112 * q^89 + 22842 * q^90 + 129228 * q^91 + 11638 * q^92 - 132804 * q^93 - 133688 * q^94 - 55928 * q^95 - 34902 * q^96 - 135318 * q^97 + 108440 * q^98 - 30456 * q^99

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