Properties

Label 40.6.d.a.21.20
Level $40$
Weight $6$
Character 40.21
Analytic conductor $6.415$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [40,6,Mod(21,40)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(40, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("40.21");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 40 = 2^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 40.d (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(6.41535279252\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 2 x^{19} - 17 x^{18} + 78 x^{17} + 253 x^{16} - 884 x^{15} + 2396 x^{14} + 19376 x^{13} - 109104 x^{12} - 96128 x^{11} + 3580672 x^{10} - 1538048 x^{9} + \cdots + 1099511627776 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{42}\cdot 3^{4}\cdot 5^{12} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 21.20
Root \(2.93366 - 2.71913i\) of defining polynomial
Character \(\chi\) \(=\) 40.21
Dual form 40.6.d.a.21.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(5.65278 + 0.214529i) q^{2} +18.7876i q^{3} +(31.9080 + 2.42537i) q^{4} +25.0000i q^{5} +(-4.03048 + 106.202i) q^{6} -107.536 q^{7} +(179.848 + 20.5552i) q^{8} -109.975 q^{9} +O(q^{10})\) \(q+(5.65278 + 0.214529i) q^{2} +18.7876i q^{3} +(31.9080 + 2.42537i) q^{4} +25.0000i q^{5} +(-4.03048 + 106.202i) q^{6} -107.536 q^{7} +(179.848 + 20.5552i) q^{8} -109.975 q^{9} +(-5.36321 + 141.320i) q^{10} +272.206i q^{11} +(-45.5669 + 599.475i) q^{12} -198.402i q^{13} +(-607.879 - 23.0696i) q^{14} -469.691 q^{15} +(1012.24 + 154.777i) q^{16} +2065.79 q^{17} +(-621.667 - 23.5928i) q^{18} -1891.04i q^{19} +(-60.6342 + 797.699i) q^{20} -2020.35i q^{21} +(-58.3959 + 1538.72i) q^{22} -987.677 q^{23} +(-386.184 + 3378.93i) q^{24} -625.000 q^{25} +(42.5629 - 1121.52i) q^{26} +2499.22i q^{27} +(-3431.26 - 260.815i) q^{28} -8015.26i q^{29} +(-2655.06 - 100.762i) q^{30} +827.342 q^{31} +(5688.74 + 1092.07i) q^{32} -5114.10 q^{33} +(11677.5 + 443.170i) q^{34} -2688.40i q^{35} +(-3509.09 - 266.730i) q^{36} -9426.30i q^{37} +(405.681 - 10689.6i) q^{38} +3727.50 q^{39} +(-513.881 + 4496.21i) q^{40} -8221.07 q^{41} +(433.423 - 11420.6i) q^{42} +9301.63i q^{43} +(-660.198 + 8685.52i) q^{44} -2749.38i q^{45} +(-5583.12 - 211.885i) q^{46} +13837.9 q^{47} +(-2907.89 + 19017.5i) q^{48} -5242.97 q^{49} +(-3532.99 - 134.080i) q^{50} +38811.3i q^{51} +(481.198 - 6330.60i) q^{52} +27751.2i q^{53} +(-536.154 + 14127.6i) q^{54} -6805.14 q^{55} +(-19340.2 - 2210.43i) q^{56} +35528.1 q^{57} +(1719.50 - 45308.5i) q^{58} +25106.1i q^{59} +(-14986.9 - 1139.17i) q^{60} -26404.6i q^{61} +(4676.79 + 177.488i) q^{62} +11826.3 q^{63} +(31923.0 + 7393.66i) q^{64} +4960.05 q^{65} +(-28908.9 - 1097.12i) q^{66} +38563.9i q^{67} +(65915.1 + 5010.29i) q^{68} -18556.1i q^{69} +(576.739 - 15197.0i) q^{70} -71073.0 q^{71} +(-19778.9 - 2260.57i) q^{72} +18622.0 q^{73} +(2022.21 - 53284.8i) q^{74} -11742.3i q^{75} +(4586.46 - 60339.1i) q^{76} -29271.9i q^{77} +(21070.8 + 799.656i) q^{78} -75599.4 q^{79} +(-3869.43 + 25305.9i) q^{80} -73678.4 q^{81} +(-46471.9 - 1763.65i) q^{82} -125298. i q^{83} +(4900.09 - 64465.2i) q^{84} +51644.7i q^{85} +(-1995.47 + 52580.1i) q^{86} +150588. q^{87} +(-5595.25 + 48955.8i) q^{88} +30341.5 q^{89} +(589.821 - 15541.7i) q^{90} +21335.4i q^{91} +(-31514.7 - 2395.48i) q^{92} +15543.8i q^{93} +(78222.6 + 2968.62i) q^{94} +47275.9 q^{95} +(-20517.5 + 106878. i) q^{96} +15635.2 q^{97} +(-29637.4 - 1124.77i) q^{98} -29935.9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 2 q^{2} - 32 q^{4} + 204 q^{6} - 196 q^{7} + 248 q^{8} - 1620 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 2 q^{2} - 32 q^{4} + 204 q^{6} - 196 q^{7} + 248 q^{8} - 1620 q^{9} - 50 q^{10} - 1876 q^{12} + 2708 q^{14} + 900 q^{15} + 3080 q^{16} - 5294 q^{18} - 1900 q^{20} + 13836 q^{22} - 4676 q^{23} + 1032 q^{24} - 12500 q^{25} - 8084 q^{26} + 2108 q^{28} + 5800 q^{30} + 7160 q^{31} + 6792 q^{32} + 5672 q^{33} + 21132 q^{34} + 18344 q^{36} - 19580 q^{38} - 44904 q^{39} + 6200 q^{40} + 11608 q^{41} - 17116 q^{42} + 72296 q^{44} - 28516 q^{46} + 44180 q^{47} - 88856 q^{48} + 18756 q^{49} - 1250 q^{50} - 39680 q^{52} - 100584 q^{54} - 24200 q^{55} - 53624 q^{56} + 5032 q^{57} + 59496 q^{58} - 31300 q^{60} + 59824 q^{62} + 240620 q^{63} - 11264 q^{64} - 56688 q^{66} + 11576 q^{68} + 29800 q^{70} - 200312 q^{71} + 235912 q^{72} - 105136 q^{73} + 78876 q^{74} - 153872 q^{76} + 95864 q^{78} + 282080 q^{79} + 16000 q^{80} + 65172 q^{81} - 223032 q^{82} - 297128 q^{84} + 27452 q^{86} - 332592 q^{87} + 86896 q^{88} - 3160 q^{89} + 51750 q^{90} + 107916 q^{92} + 148820 q^{94} + 144400 q^{95} + 395168 q^{96} + 147376 q^{97} + 216942 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/40\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(21\) \(31\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.65278 + 0.214529i 0.999281 + 0.0379236i
\(3\) 18.7876i 1.20523i 0.798033 + 0.602614i \(0.205874\pi\)
−0.798033 + 0.602614i \(0.794126\pi\)
\(4\) 31.9080 + 2.42537i 0.997124 + 0.0757927i
\(5\) 25.0000i 0.447214i
\(6\) −4.03048 + 106.202i −0.0457066 + 1.20436i
\(7\) −107.536 −0.829487 −0.414743 0.909938i \(-0.636129\pi\)
−0.414743 + 0.909938i \(0.636129\pi\)
\(8\) 179.848 + 20.5552i 0.993532 + 0.113553i
\(9\) −109.975 −0.452573
\(10\) −5.36321 + 141.320i −0.0169600 + 0.446892i
\(11\) 272.206i 0.678290i 0.940734 + 0.339145i \(0.110138\pi\)
−0.940734 + 0.339145i \(0.889862\pi\)
\(12\) −45.5669 + 599.475i −0.0913475 + 1.20176i
\(13\) 198.402i 0.325602i −0.986659 0.162801i \(-0.947947\pi\)
0.986659 0.162801i \(-0.0520529\pi\)
\(14\) −607.879 23.0696i −0.828890 0.0314572i
\(15\) −469.691 −0.538994
\(16\) 1012.24 + 154.777i 0.988511 + 0.151149i
\(17\) 2065.79 1.73366 0.866829 0.498606i \(-0.166154\pi\)
0.866829 + 0.498606i \(0.166154\pi\)
\(18\) −621.667 23.5928i −0.452248 0.0171632i
\(19\) 1891.04i 1.20176i −0.799341 0.600878i \(-0.794818\pi\)
0.799341 0.600878i \(-0.205182\pi\)
\(20\) −60.6342 + 797.699i −0.0338955 + 0.445927i
\(21\) 2020.35i 0.999720i
\(22\) −58.3959 + 1538.72i −0.0257232 + 0.677802i
\(23\) −987.677 −0.389310 −0.194655 0.980872i \(-0.562359\pi\)
−0.194655 + 0.980872i \(0.562359\pi\)
\(24\) −386.184 + 3378.93i −0.136857 + 1.19743i
\(25\) −625.000 −0.200000
\(26\) 42.5629 1121.52i 0.0123480 0.325368i
\(27\) 2499.22i 0.659774i
\(28\) −3431.26 260.815i −0.827101 0.0628690i
\(29\) 8015.26i 1.76979i −0.465788 0.884896i \(-0.654229\pi\)
0.465788 0.884896i \(-0.345771\pi\)
\(30\) −2655.06 100.762i −0.538606 0.0204406i
\(31\) 827.342 0.154625 0.0773127 0.997007i \(-0.475366\pi\)
0.0773127 + 0.997007i \(0.475366\pi\)
\(32\) 5688.74 + 1092.07i 0.982068 + 0.188529i
\(33\) −5114.10 −0.817494
\(34\) 11677.5 + 443.170i 1.73241 + 0.0657466i
\(35\) 2688.40i 0.370958i
\(36\) −3509.09 266.730i −0.451271 0.0343018i
\(37\) 9426.30i 1.13198i −0.824414 0.565988i \(-0.808495\pi\)
0.824414 0.565988i \(-0.191505\pi\)
\(38\) 405.681 10689.6i 0.0455749 1.20089i
\(39\) 3727.50 0.392425
\(40\) −513.881 + 4496.21i −0.0507823 + 0.444321i
\(41\) −8221.07 −0.763780 −0.381890 0.924208i \(-0.624727\pi\)
−0.381890 + 0.924208i \(0.624727\pi\)
\(42\) 433.423 11420.6i 0.0379130 0.999001i
\(43\) 9301.63i 0.767164i 0.923507 + 0.383582i \(0.125310\pi\)
−0.923507 + 0.383582i \(0.874690\pi\)
\(44\) −660.198 + 8685.52i −0.0514094 + 0.676339i
\(45\) 2749.38i 0.202397i
\(46\) −5583.12 211.885i −0.389030 0.0147640i
\(47\) 13837.9 0.913745 0.456873 0.889532i \(-0.348969\pi\)
0.456873 + 0.889532i \(0.348969\pi\)
\(48\) −2907.89 + 19017.5i −0.182169 + 1.19138i
\(49\) −5242.97 −0.311952
\(50\) −3532.99 134.080i −0.199856 0.00758473i
\(51\) 38811.3i 2.08945i
\(52\) 481.198 6330.60i 0.0246783 0.324666i
\(53\) 27751.2i 1.35704i 0.734582 + 0.678520i \(0.237378\pi\)
−0.734582 + 0.678520i \(0.762622\pi\)
\(54\) −536.154 + 14127.6i −0.0250210 + 0.659299i
\(55\) −6805.14 −0.303340
\(56\) −19340.2 2210.43i −0.824122 0.0941905i
\(57\) 35528.1 1.44839
\(58\) 1719.50 45308.5i 0.0671170 1.76852i
\(59\) 25106.1i 0.938965i 0.882942 + 0.469482i \(0.155559\pi\)
−0.882942 + 0.469482i \(0.844441\pi\)
\(60\) −14986.9 1139.17i −0.537444 0.0408518i
\(61\) 26404.6i 0.908563i −0.890858 0.454282i \(-0.849896\pi\)
0.890858 0.454282i \(-0.150104\pi\)
\(62\) 4676.79 + 177.488i 0.154514 + 0.00586396i
\(63\) 11826.3 0.375404
\(64\) 31923.0 + 7393.66i 0.974212 + 0.225637i
\(65\) 4960.05 0.145614
\(66\) −28908.9 1097.12i −0.816905 0.0310023i
\(67\) 38563.9i 1.04953i 0.851248 + 0.524764i \(0.175846\pi\)
−0.851248 + 0.524764i \(0.824154\pi\)
\(68\) 65915.1 + 5010.29i 1.72867 + 0.131399i
\(69\) 18556.1i 0.469207i
\(70\) 576.739 15197.0i 0.0140681 0.370691i
\(71\) −71073.0 −1.67324 −0.836621 0.547782i \(-0.815472\pi\)
−0.836621 + 0.547782i \(0.815472\pi\)
\(72\) −19778.9 2260.57i −0.449646 0.0513909i
\(73\) 18622.0 0.408996 0.204498 0.978867i \(-0.434444\pi\)
0.204498 + 0.978867i \(0.434444\pi\)
\(74\) 2022.21 53284.8i 0.0429286 1.13116i
\(75\) 11742.3i 0.241045i
\(76\) 4586.46 60339.1i 0.0910843 1.19830i
\(77\) 29271.9i 0.562632i
\(78\) 21070.8 + 799.656i 0.392143 + 0.0148822i
\(79\) −75599.4 −1.36286 −0.681429 0.731884i \(-0.738641\pi\)
−0.681429 + 0.731884i \(0.738641\pi\)
\(80\) −3869.43 + 25305.9i −0.0675961 + 0.442076i
\(81\) −73678.4 −1.24775
\(82\) −46471.9 1763.65i −0.763231 0.0289653i
\(83\) 125298.i 1.99641i −0.0599304 0.998203i \(-0.519088\pi\)
0.0599304 0.998203i \(-0.480912\pi\)
\(84\) 4900.09 64465.2i 0.0757715 0.996845i
\(85\) 51644.7i 0.775315i
\(86\) −1995.47 + 52580.1i −0.0290936 + 0.766612i
\(87\) 150588. 2.13300
\(88\) −5595.25 + 48955.8i −0.0770217 + 0.673903i
\(89\) 30341.5 0.406034 0.203017 0.979175i \(-0.434925\pi\)
0.203017 + 0.979175i \(0.434925\pi\)
\(90\) 589.821 15541.7i 0.00767563 0.202251i
\(91\) 21335.4i 0.270083i
\(92\) −31514.7 2395.48i −0.388190 0.0295068i
\(93\) 15543.8i 0.186359i
\(94\) 78222.6 + 2968.62i 0.913088 + 0.0346526i
\(95\) 47275.9 0.537441
\(96\) −20517.5 + 106878.i −0.227220 + 1.18361i
\(97\) 15635.2 0.168723 0.0843617 0.996435i \(-0.473115\pi\)
0.0843617 + 0.996435i \(0.473115\pi\)
\(98\) −29637.4 1124.77i −0.311727 0.0118303i
\(99\) 29935.9i 0.306976i
\(100\) −19942.5 1515.85i −0.199425 0.0151585i
\(101\) 102692.i 1.00169i −0.865538 0.500843i \(-0.833024\pi\)
0.865538 0.500843i \(-0.166976\pi\)
\(102\) −8326.12 + 219392.i −0.0792396 + 2.08795i
\(103\) −35981.8 −0.334187 −0.167093 0.985941i \(-0.553438\pi\)
−0.167093 + 0.985941i \(0.553438\pi\)
\(104\) 4078.20 35682.3i 0.0369730 0.323496i
\(105\) 50508.8 0.447088
\(106\) −5953.43 + 156872.i −0.0514639 + 1.35606i
\(107\) 94984.6i 0.802035i −0.916070 0.401018i \(-0.868657\pi\)
0.916070 0.401018i \(-0.131343\pi\)
\(108\) −6061.52 + 79745.0i −0.0500060 + 0.657876i
\(109\) 173158.i 1.39597i 0.716113 + 0.697984i \(0.245919\pi\)
−0.716113 + 0.697984i \(0.754081\pi\)
\(110\) −38468.0 1459.90i −0.303122 0.0115038i
\(111\) 177098. 1.36429
\(112\) −108852. 16644.1i −0.819957 0.125376i
\(113\) −237780. −1.75178 −0.875891 0.482510i \(-0.839725\pi\)
−0.875891 + 0.482510i \(0.839725\pi\)
\(114\) 200833. + 7621.80i 1.44735 + 0.0549282i
\(115\) 24691.9i 0.174105i
\(116\) 19439.9 255750.i 0.134137 1.76470i
\(117\) 21819.3i 0.147359i
\(118\) −5385.97 + 141919.i −0.0356090 + 0.938289i
\(119\) −222147. −1.43805
\(120\) −84473.2 9654.61i −0.535508 0.0612043i
\(121\) 86955.1 0.539923
\(122\) 5664.54 149260.i 0.0344560 0.907910i
\(123\) 154454.i 0.920529i
\(124\) 26398.8 + 2006.61i 0.154181 + 0.0117195i
\(125\) 15625.0i 0.0894427i
\(126\) 66851.7 + 2537.08i 0.375133 + 0.0142367i
\(127\) −63282.9 −0.348158 −0.174079 0.984732i \(-0.555695\pi\)
−0.174079 + 0.984732i \(0.555695\pi\)
\(128\) 178867. + 48643.2i 0.964954 + 0.262420i
\(129\) −174756. −0.924607
\(130\) 28038.1 + 1064.07i 0.145509 + 0.00552221i
\(131\) 180082.i 0.916835i −0.888737 0.458417i \(-0.848416\pi\)
0.888737 0.458417i \(-0.151584\pi\)
\(132\) −163180. 12403.6i −0.815142 0.0619601i
\(133\) 203355.i 0.996840i
\(134\) −8273.05 + 217993.i −0.0398019 + 1.04877i
\(135\) −62480.5 −0.295060
\(136\) 371529. + 42462.8i 1.72244 + 0.196862i
\(137\) 365739. 1.66483 0.832414 0.554155i \(-0.186958\pi\)
0.832414 + 0.554155i \(0.186958\pi\)
\(138\) 3980.81 104894.i 0.0177940 0.468869i
\(139\) 111886.i 0.491180i 0.969374 + 0.245590i \(0.0789817\pi\)
−0.969374 + 0.245590i \(0.921018\pi\)
\(140\) 6520.37 85781.5i 0.0281159 0.369891i
\(141\) 259981.i 1.10127i
\(142\) −401760. 15247.2i −1.67204 0.0634554i
\(143\) 54006.1 0.220853
\(144\) −111321. 17021.6i −0.447374 0.0684062i
\(145\) 200381. 0.791475
\(146\) 105266. + 3994.95i 0.408702 + 0.0155106i
\(147\) 98503.1i 0.375973i
\(148\) 22862.2 300774.i 0.0857955 1.12872i
\(149\) 136480.i 0.503621i −0.967777 0.251811i \(-0.918974\pi\)
0.967777 0.251811i \(-0.0810260\pi\)
\(150\) 2519.05 66376.5i 0.00914132 0.240872i
\(151\) 186354. 0.665115 0.332557 0.943083i \(-0.392088\pi\)
0.332557 + 0.943083i \(0.392088\pi\)
\(152\) 38870.7 340100.i 0.136463 1.19398i
\(153\) −227186. −0.784607
\(154\) 6279.67 165468.i 0.0213371 0.562228i
\(155\) 20683.6i 0.0691506i
\(156\) 118937. + 9040.56i 0.391296 + 0.0297430i
\(157\) 74689.6i 0.241830i 0.992663 + 0.120915i \(0.0385829\pi\)
−0.992663 + 0.120915i \(0.961417\pi\)
\(158\) −427347. 16218.2i −1.36188 0.0516845i
\(159\) −521380. −1.63554
\(160\) −27301.9 + 142219.i −0.0843126 + 0.439194i
\(161\) 106211. 0.322927
\(162\) −416488. 15806.1i −1.24685 0.0473192i
\(163\) 548779.i 1.61781i 0.587937 + 0.808907i \(0.299940\pi\)
−0.587937 + 0.808907i \(0.700060\pi\)
\(164\) −262317. 19939.1i −0.761583 0.0578890i
\(165\) 127852.i 0.365594i
\(166\) 26880.0 708282.i 0.0757109 1.99497i
\(167\) 224312. 0.622387 0.311194 0.950347i \(-0.399271\pi\)
0.311194 + 0.950347i \(0.399271\pi\)
\(168\) 41528.8 363357.i 0.113521 0.993254i
\(169\) 331930. 0.893983
\(170\) −11079.3 + 291936.i −0.0294028 + 0.774758i
\(171\) 207967.i 0.543882i
\(172\) −22559.9 + 296796.i −0.0581454 + 0.764957i
\(173\) 165260.i 0.419809i −0.977722 0.209905i \(-0.932685\pi\)
0.977722 0.209905i \(-0.0673154\pi\)
\(174\) 851240. + 32305.4i 2.13147 + 0.0808912i
\(175\) 67210.1 0.165897
\(176\) −42131.2 + 275536.i −0.102523 + 0.670497i
\(177\) −471684. −1.13167
\(178\) 171514. + 6509.12i 0.405742 + 0.0153983i
\(179\) 431975.i 1.00769i −0.863795 0.503844i \(-0.831919\pi\)
0.863795 0.503844i \(-0.168081\pi\)
\(180\) 6668.26 87727.2i 0.0153402 0.201815i
\(181\) 216944.i 0.492210i 0.969243 + 0.246105i \(0.0791508\pi\)
−0.969243 + 0.246105i \(0.920849\pi\)
\(182\) −4577.05 + 120604.i −0.0102425 + 0.269889i
\(183\) 496080. 1.09503
\(184\) −177632. 20301.9i −0.386792 0.0442072i
\(185\) 235658. 0.506235
\(186\) −3334.59 + 87865.8i −0.00706741 + 0.186225i
\(187\) 562319.i 1.17592i
\(188\) 441539. + 33562.0i 0.911117 + 0.0692552i
\(189\) 268756.i 0.547274i
\(190\) 267241. + 10142.0i 0.537055 + 0.0203817i
\(191\) −34566.0 −0.0685592 −0.0342796 0.999412i \(-0.510914\pi\)
−0.0342796 + 0.999412i \(0.510914\pi\)
\(192\) −138909. + 599757.i −0.271943 + 1.17415i
\(193\) −473601. −0.915208 −0.457604 0.889156i \(-0.651292\pi\)
−0.457604 + 0.889156i \(0.651292\pi\)
\(194\) 88382.7 + 3354.21i 0.168602 + 0.00639861i
\(195\) 93187.6i 0.175498i
\(196\) −167293. 12716.1i −0.311055 0.0236437i
\(197\) 394784.i 0.724760i 0.932030 + 0.362380i \(0.118036\pi\)
−0.932030 + 0.362380i \(0.881964\pi\)
\(198\) 6422.10 169221.i 0.0116416 0.306755i
\(199\) −477089. −0.854017 −0.427009 0.904248i \(-0.640433\pi\)
−0.427009 + 0.904248i \(0.640433\pi\)
\(200\) −112405. 12847.0i −0.198706 0.0227106i
\(201\) −724524. −1.26492
\(202\) 22030.3 580493.i 0.0379875 1.00096i
\(203\) 861930.i 1.46802i
\(204\) −94131.6 + 1.23839e6i −0.158365 + 2.08344i
\(205\) 205527.i 0.341573i
\(206\) −203397. 7719.11i −0.333946 0.0126736i
\(207\) 108620. 0.176191
\(208\) 30708.1 200829.i 0.0492146 0.321862i
\(209\) 514751. 0.815139
\(210\) 285515. + 10835.6i 0.446767 + 0.0169552i
\(211\) 435894.i 0.674023i −0.941500 0.337012i \(-0.890584\pi\)
0.941500 0.337012i \(-0.109416\pi\)
\(212\) −67306.9 + 885485.i −0.102854 + 1.35314i
\(213\) 1.33529e6i 2.01664i
\(214\) 20376.9 536927.i 0.0304161 0.801458i
\(215\) −232541. −0.343086
\(216\) −51372.1 + 449481.i −0.0749191 + 0.655506i
\(217\) −88969.2 −0.128260
\(218\) −37147.3 + 978823.i −0.0529402 + 1.39496i
\(219\) 349863.i 0.492933i
\(220\) −217138. 16505.0i −0.302468 0.0229910i
\(221\) 409856.i 0.564483i
\(222\) 1.00110e6 + 37992.5i 1.36331 + 0.0517388i
\(223\) 1.14075e6 1.53613 0.768067 0.640369i \(-0.221219\pi\)
0.768067 + 0.640369i \(0.221219\pi\)
\(224\) −611746. 117437.i −0.814612 0.156382i
\(225\) 68734.6 0.0905147
\(226\) −1.34412e6 51010.7i −1.75052 0.0664339i
\(227\) 1.08895e6i 1.40262i −0.712854 0.701312i \(-0.752598\pi\)
0.712854 0.701312i \(-0.247402\pi\)
\(228\) 1.13363e6 + 86168.7i 1.44422 + 0.109777i
\(229\) 474386.i 0.597783i −0.954287 0.298891i \(-0.903383\pi\)
0.954287 0.298891i \(-0.0966168\pi\)
\(230\) 5297.12 139578.i 0.00660268 0.173979i
\(231\) 549951. 0.678100
\(232\) 164756. 1.44153e6i 0.200965 1.75835i
\(233\) −271057. −0.327093 −0.163547 0.986536i \(-0.552293\pi\)
−0.163547 + 0.986536i \(0.552293\pi\)
\(234\) −4680.87 + 123340.i −0.00558839 + 0.147253i
\(235\) 345947.i 0.408639i
\(236\) −60891.5 + 801084.i −0.0711667 + 0.936264i
\(237\) 1.42033e6i 1.64255i
\(238\) −1.25575e6 47656.8i −1.43701 0.0545359i
\(239\) −824404. −0.933567 −0.466784 0.884372i \(-0.654587\pi\)
−0.466784 + 0.884372i \(0.654587\pi\)
\(240\) −475438. 72697.4i −0.532802 0.0814686i
\(241\) −86717.2 −0.0961750 −0.0480875 0.998843i \(-0.515313\pi\)
−0.0480875 + 0.998843i \(0.515313\pi\)
\(242\) 491539. + 18654.4i 0.539535 + 0.0204758i
\(243\) 776933.i 0.844050i
\(244\) 64040.9 842517.i 0.0688625 0.905950i
\(245\) 131074.i 0.139509i
\(246\) 33134.9 873097.i 0.0349098 0.919867i
\(247\) −375186. −0.391294
\(248\) 148796. + 17006.2i 0.153625 + 0.0175581i
\(249\) 2.35405e6 2.40612
\(250\) 3352.01 88324.8i 0.00339199 0.0893784i
\(251\) 411977.i 0.412751i −0.978473 0.206376i \(-0.933833\pi\)
0.978473 0.206376i \(-0.0661669\pi\)
\(252\) 377354. + 28683.2i 0.374324 + 0.0284529i
\(253\) 268851.i 0.264065i
\(254\) −357725. 13576.0i −0.347908 0.0132034i
\(255\) −970282. −0.934431
\(256\) 1.00066e6 + 313341.i 0.954308 + 0.298826i
\(257\) −88057.5 −0.0831637 −0.0415818 0.999135i \(-0.513240\pi\)
−0.0415818 + 0.999135i \(0.513240\pi\)
\(258\) −987857. 37490.1i −0.923942 0.0350645i
\(259\) 1.01367e6i 0.938958i
\(260\) 158265. + 12029.9i 0.145195 + 0.0110365i
\(261\) 881480.i 0.800961i
\(262\) 38632.6 1.01796e6i 0.0347697 0.916175i
\(263\) −126284. −0.112579 −0.0562896 0.998414i \(-0.517927\pi\)
−0.0562896 + 0.998414i \(0.517927\pi\)
\(264\) −919763. 105122.i −0.812206 0.0928286i
\(265\) −693781. −0.606886
\(266\) −43625.4 + 1.14952e6i −0.0378038 + 0.996123i
\(267\) 570045.i 0.489363i
\(268\) −93531.6 + 1.23049e6i −0.0795465 + 1.04651i
\(269\) 1.88178e6i 1.58558i 0.609495 + 0.792790i \(0.291372\pi\)
−0.609495 + 0.792790i \(0.708628\pi\)
\(270\) −353189. 13403.8i −0.294848 0.0111897i
\(271\) −1.17095e6 −0.968532 −0.484266 0.874921i \(-0.660913\pi\)
−0.484266 + 0.874921i \(0.660913\pi\)
\(272\) 2.09106e6 + 319736.i 1.71374 + 0.262041i
\(273\) −400841. −0.325511
\(274\) 2.06744e6 + 78461.3i 1.66363 + 0.0631363i
\(275\) 170128.i 0.135658i
\(276\) 45005.4 592088.i 0.0355625 0.467857i
\(277\) 1.11420e6i 0.872496i 0.899827 + 0.436248i \(0.143693\pi\)
−0.899827 + 0.436248i \(0.856307\pi\)
\(278\) −24002.8 + 632470.i −0.0186273 + 0.490826i
\(279\) −90987.2 −0.0699793
\(280\) 55260.8 483505.i 0.0421233 0.368558i
\(281\) −1.87861e6 −1.41929 −0.709646 0.704558i \(-0.751145\pi\)
−0.709646 + 0.704558i \(0.751145\pi\)
\(282\) −55773.4 + 1.46962e6i −0.0417642 + 1.10048i
\(283\) 3072.89i 0.00228077i 0.999999 + 0.00114038i \(0.000362996\pi\)
−0.999999 + 0.00114038i \(0.999637\pi\)
\(284\) −2.26779e6 172378.i −1.66843 0.126820i
\(285\) 888203.i 0.647739i
\(286\) 305285. + 11585.9i 0.220694 + 0.00837554i
\(287\) 884062. 0.633546
\(288\) −625621. 120101.i −0.444458 0.0853230i
\(289\) 2.84762e6 2.00557
\(290\) 1.13271e6 + 42987.5i 0.790906 + 0.0300156i
\(291\) 293749.i 0.203350i
\(292\) 594190. + 45165.2i 0.407820 + 0.0309989i
\(293\) 2.45968e6i 1.67382i 0.547339 + 0.836911i \(0.315641\pi\)
−0.547339 + 0.836911i \(0.684359\pi\)
\(294\) 21131.7 556817.i 0.0142583 0.375702i
\(295\) −627653. −0.419918
\(296\) 193760. 1.69531e6i 0.128539 1.12465i
\(297\) −680301. −0.447518
\(298\) 29278.9 771493.i 0.0190992 0.503259i
\(299\) 195957.i 0.126760i
\(300\) 28479.3 374672.i 0.0182695 0.240352i
\(301\) 1.00026e6i 0.636352i
\(302\) 1.05342e6 + 39978.3i 0.664636 + 0.0252236i
\(303\) 1.92933e6 1.20726
\(304\) 292689. 1.91417e6i 0.181645 1.18795i
\(305\) 660115. 0.406322
\(306\) −1.28423e6 48737.8i −0.784043 0.0297552i
\(307\) 257478.i 0.155917i 0.996957 + 0.0779585i \(0.0248402\pi\)
−0.996957 + 0.0779585i \(0.975160\pi\)
\(308\) 70995.2 934008.i 0.0426434 0.561014i
\(309\) 676012.i 0.402771i
\(310\) −4437.21 + 116920.i −0.00262244 + 0.0691009i
\(311\) 2.43192e6 1.42576 0.712882 0.701284i \(-0.247390\pi\)
0.712882 + 0.701284i \(0.247390\pi\)
\(312\) 670386. + 76619.7i 0.389887 + 0.0445609i
\(313\) −2.62542e6 −1.51474 −0.757369 0.652987i \(-0.773515\pi\)
−0.757369 + 0.652987i \(0.773515\pi\)
\(314\) −16023.0 + 422204.i −0.00917109 + 0.241656i
\(315\) 295658.i 0.167886i
\(316\) −2.41222e6 183356.i −1.35894 0.103295i
\(317\) 2.54754e6i 1.42388i 0.702240 + 0.711940i \(0.252183\pi\)
−0.702240 + 0.711940i \(0.747817\pi\)
\(318\) −2.94725e6 111851.i −1.63436 0.0620257i
\(319\) 2.18180e6 1.20043
\(320\) −184841. + 798074.i −0.100908 + 0.435681i
\(321\) 1.78454e6 0.966635
\(322\) 600388. + 22785.3i 0.322695 + 0.0122466i
\(323\) 3.90648e6i 2.08343i
\(324\) −2.35093e6 178697.i −1.24416 0.0945704i
\(325\) 124001.i 0.0651205i
\(326\) −117729. + 3.10213e6i −0.0613534 + 1.61665i
\(327\) −3.25322e6 −1.68246
\(328\) −1.47855e6 168986.i −0.758840 0.0867294i
\(329\) −1.48807e6 −0.757940
\(330\) 27428.0 722723.i 0.0138647 0.365331i
\(331\) 2.11710e6i 1.06211i 0.847336 + 0.531057i \(0.178205\pi\)
−0.847336 + 0.531057i \(0.821795\pi\)
\(332\) 303893. 3.99800e6i 0.151313 1.99066i
\(333\) 1.03666e6i 0.512302i
\(334\) 1.26799e6 + 48121.2i 0.621940 + 0.0236032i
\(335\) −964097. −0.469363
\(336\) 312704. 2.04507e6i 0.151107 0.988234i
\(337\) −1.56954e6 −0.752832 −0.376416 0.926451i \(-0.622844\pi\)
−0.376416 + 0.926451i \(0.622844\pi\)
\(338\) 1.87633e6 + 71208.4i 0.893340 + 0.0339031i
\(339\) 4.46733e6i 2.11129i
\(340\) −125257. + 1.64788e6i −0.0587633 + 0.773085i
\(341\) 225207.i 0.104881i
\(342\) −44614.9 + 1.17560e6i −0.0206260 + 0.543491i
\(343\) 2.37117e6 1.08825
\(344\) −191197. + 1.67288e6i −0.0871136 + 0.762202i
\(345\) 463903. 0.209836
\(346\) 35452.9 934178.i 0.0159207 0.419507i
\(347\) 428538.i 0.191058i 0.995427 + 0.0955292i \(0.0304543\pi\)
−0.995427 + 0.0955292i \(0.969546\pi\)
\(348\) 4.80495e6 + 365230.i 2.12687 + 0.161666i
\(349\) 522898.i 0.229802i −0.993377 0.114901i \(-0.963345\pi\)
0.993377 0.114901i \(-0.0366551\pi\)
\(350\) 379924. + 14418.5i 0.165778 + 0.00629143i
\(351\) 495850. 0.214824
\(352\) −297269. + 1.54851e6i −0.127877 + 0.666126i
\(353\) 1.89389e6 0.808943 0.404472 0.914550i \(-0.367455\pi\)
0.404472 + 0.914550i \(0.367455\pi\)
\(354\) −2.66633e6 101190.i −1.13085 0.0429169i
\(355\) 1.77682e6i 0.748297i
\(356\) 968136. + 73589.3i 0.404866 + 0.0307744i
\(357\) 4.17361e6i 1.73317i
\(358\) 92671.0 2.44186e6i 0.0382152 1.00696i
\(359\) −2.57094e6 −1.05282 −0.526412 0.850229i \(-0.676463\pi\)
−0.526412 + 0.850229i \(0.676463\pi\)
\(360\) 56514.2 494472.i 0.0229827 0.201088i
\(361\) −1.09992e6 −0.444216
\(362\) −46540.6 + 1.22634e6i −0.0186664 + 0.491856i
\(363\) 1.63368e6i 0.650730i
\(364\) −51746.1 + 680768.i −0.0204703 + 0.269306i
\(365\) 465550.i 0.182909i
\(366\) 2.80424e6 + 106423.i 1.09424 + 0.0415274i
\(367\) −2.47263e6 −0.958282 −0.479141 0.877738i \(-0.659052\pi\)
−0.479141 + 0.877738i \(0.659052\pi\)
\(368\) −999761. 152870.i −0.384837 0.0588439i
\(369\) 904114. 0.345667
\(370\) 1.33212e6 + 50555.3i 0.505871 + 0.0191983i
\(371\) 2.98426e6i 1.12565i
\(372\) −37699.4 + 495971.i −0.0141246 + 0.185823i
\(373\) 2.62533e6i 0.977038i 0.872553 + 0.488519i \(0.162463\pi\)
−0.872553 + 0.488519i \(0.837537\pi\)
\(374\) −120633. + 3.17867e6i −0.0445953 + 1.17508i
\(375\) 293557. 0.107799
\(376\) 2.48872e6 + 284441.i 0.907835 + 0.103758i
\(377\) −1.59024e6 −0.576249
\(378\) 57655.9 1.51922e6i 0.0207546 0.546880i
\(379\) 2.14283e6i 0.766284i 0.923689 + 0.383142i \(0.125158\pi\)
−0.923689 + 0.383142i \(0.874842\pi\)
\(380\) 1.50848e6 + 114661.i 0.535896 + 0.0407341i
\(381\) 1.18894e6i 0.419610i
\(382\) −195394. 7415.39i −0.0685098 0.00260001i
\(383\) −641783. −0.223559 −0.111779 0.993733i \(-0.535655\pi\)
−0.111779 + 0.993733i \(0.535655\pi\)
\(384\) −913890. + 3.36050e6i −0.316276 + 1.16299i
\(385\) 731799. 0.251617
\(386\) −2.67717e6 101601.i −0.914549 0.0347080i
\(387\) 1.02295e6i 0.347198i
\(388\) 498889. + 37921.2i 0.168238 + 0.0127880i
\(389\) 2.36321e6i 0.791823i −0.918289 0.395911i \(-0.870429\pi\)
0.918289 0.395911i \(-0.129571\pi\)
\(390\) −19991.4 + 526769.i −0.00665551 + 0.175372i
\(391\) −2.04033e6 −0.674930
\(392\) −942941. 107771.i −0.309934 0.0354230i
\(393\) 3.38331e6 1.10499
\(394\) −84692.5 + 2.23163e6i −0.0274855 + 0.724239i
\(395\) 1.88998e6i 0.609489i
\(396\) 72605.5 955193.i 0.0232665 0.306093i
\(397\) 403888.i 0.128613i −0.997930 0.0643065i \(-0.979516\pi\)
0.997930 0.0643065i \(-0.0204835\pi\)
\(398\) −2.69688e6 102349.i −0.853403 0.0323874i
\(399\) −3.82056e6 −1.20142
\(400\) −632647. 96735.6i −0.197702 0.0302299i
\(401\) 2.28335e6 0.709108 0.354554 0.935036i \(-0.384633\pi\)
0.354554 + 0.935036i \(0.384633\pi\)
\(402\) −4.09558e6 155431.i −1.26401 0.0479703i
\(403\) 164146.i 0.0503464i
\(404\) 249065. 3.27668e6i 0.0759204 0.998804i
\(405\) 1.84196e6i 0.558011i
\(406\) −184909. + 4.87230e6i −0.0556726 + 1.46696i
\(407\) 2.56589e6 0.767807
\(408\) −797775. + 6.98015e6i −0.237263 + 2.07594i
\(409\) 3.27964e6 0.969435 0.484717 0.874671i \(-0.338922\pi\)
0.484717 + 0.874671i \(0.338922\pi\)
\(410\) 44091.3 1.16180e6i 0.0129537 0.341327i
\(411\) 6.87136e6i 2.00650i
\(412\) −1.14810e6 87269.0i −0.333226 0.0253289i
\(413\) 2.69981e6i 0.778859i
\(414\) 614006. + 23302.1i 0.176064 + 0.00668181i
\(415\) 3.13245e6 0.892820
\(416\) 216670. 1.12866e6i 0.0613854 0.319764i
\(417\) −2.10208e6 −0.591983
\(418\) 2.90978e6 + 110429.i 0.814552 + 0.0309130i
\(419\) 604670.i 0.168261i 0.996455 + 0.0841305i \(0.0268113\pi\)
−0.996455 + 0.0841305i \(0.973189\pi\)
\(420\) 1.61163e6 + 122502.i 0.445802 + 0.0338860i
\(421\) 3.46346e6i 0.952367i −0.879346 0.476184i \(-0.842020\pi\)
0.879346 0.476184i \(-0.157980\pi\)
\(422\) 93511.7 2.46402e6i 0.0255614 0.673538i
\(423\) −1.52183e6 −0.413537
\(424\) −570433. + 4.99102e6i −0.154096 + 1.34826i
\(425\) −1.29112e6 −0.346732
\(426\) 286459. 7.54813e6i 0.0764782 2.01519i
\(427\) 2.83945e6i 0.753641i
\(428\) 230372. 3.03076e6i 0.0607884 0.799728i
\(429\) 1.01465e6i 0.266178i
\(430\) −1.31450e6 49886.6i −0.342839 0.0130111i
\(431\) 5.00345e6 1.29741 0.648704 0.761041i \(-0.275311\pi\)
0.648704 + 0.761041i \(0.275311\pi\)
\(432\) −386822. + 2.52980e6i −0.0997244 + 0.652194i
\(433\) −4.11259e6 −1.05413 −0.527067 0.849824i \(-0.676708\pi\)
−0.527067 + 0.849824i \(0.676708\pi\)
\(434\) −502924. 19086.4i −0.128167 0.00486408i
\(435\) 3.76469e6i 0.953908i
\(436\) −419971. + 5.52511e6i −0.105804 + 1.39195i
\(437\) 1.86773e6i 0.467855i
\(438\) −75055.7 + 1.97770e6i −0.0186938 + 0.492579i
\(439\) 4.20313e6 1.04091 0.520454 0.853890i \(-0.325763\pi\)
0.520454 + 0.853890i \(0.325763\pi\)
\(440\) −1.22389e6 139881.i −0.301378 0.0344451i
\(441\) 576598. 0.141181
\(442\) 87925.9 2.31683e6i 0.0214073 0.564077i
\(443\) 1.32165e6i 0.319969i 0.987120 + 0.159984i \(0.0511443\pi\)
−0.987120 + 0.159984i \(0.948856\pi\)
\(444\) 5.65083e6 + 429527.i 1.36036 + 0.103403i
\(445\) 758538.i 0.181584i
\(446\) 6.44843e6 + 244724.i 1.53503 + 0.0582558i
\(447\) 2.56414e6 0.606978
\(448\) −3.43287e6 795086.i −0.808095 0.187163i
\(449\) −5.52202e6 −1.29265 −0.646327 0.763061i \(-0.723696\pi\)
−0.646327 + 0.763061i \(0.723696\pi\)
\(450\) 388542. + 14745.5i 0.0904495 + 0.00343265i
\(451\) 2.23782e6i 0.518064i
\(452\) −7.58709e6 576705.i −1.74674 0.132772i
\(453\) 3.50115e6i 0.801615i
\(454\) 233610. 6.15557e6i 0.0531926 1.40162i
\(455\) −533385. −0.120785
\(456\) 6.38968e6 + 730289.i 1.43902 + 0.164469i
\(457\) 3.46838e6 0.776849 0.388424 0.921481i \(-0.373019\pi\)
0.388424 + 0.921481i \(0.373019\pi\)
\(458\) 101769. 2.68160e6i 0.0226701 0.597352i
\(459\) 5.16286e6i 1.14382i
\(460\) 59887.0 787869.i 0.0131959 0.173604i
\(461\) 2.42345e6i 0.531107i 0.964096 + 0.265554i \(0.0855547\pi\)
−0.964096 + 0.265554i \(0.914445\pi\)
\(462\) 3.10875e6 + 117980.i 0.677612 + 0.0257160i
\(463\) −6.58501e6 −1.42759 −0.713796 0.700354i \(-0.753026\pi\)
−0.713796 + 0.700354i \(0.753026\pi\)
\(464\) 1.24058e6 8.11332e6i 0.267503 1.74946i
\(465\) −388595. −0.0833422
\(466\) −1.53223e6 58149.5i −0.326858 0.0124046i
\(467\) 1.15697e6i 0.245488i −0.992438 0.122744i \(-0.960831\pi\)
0.992438 0.122744i \(-0.0391694\pi\)
\(468\) −52919.8 + 696210.i −0.0111687 + 0.146935i
\(469\) 4.14701e6i 0.870569i
\(470\) −74215.5 + 1.95557e6i −0.0154971 + 0.408345i
\(471\) −1.40324e6 −0.291461
\(472\) −516062. + 4.51529e6i −0.106622 + 0.932891i
\(473\) −2.53196e6 −0.520359
\(474\) 304702. 8.02884e6i 0.0622916 1.64137i
\(475\) 1.18190e6i 0.240351i
\(476\) −7.08825e6 538788.i −1.43391 0.108993i
\(477\) 3.05195e6i 0.614160i
\(478\) −4.66018e6 176858.i −0.932896 0.0354043i
\(479\) −380517. −0.0757767 −0.0378883 0.999282i \(-0.512063\pi\)
−0.0378883 + 0.999282i \(0.512063\pi\)
\(480\) −2.67195e6 512937.i −0.529329 0.101616i
\(481\) −1.87020e6 −0.368574
\(482\) −490193. 18603.3i −0.0961059 0.00364731i
\(483\) 1.99545e6i 0.389201i
\(484\) 2.77456e6 + 210898.i 0.538370 + 0.0409222i
\(485\) 390881.i 0.0754554i
\(486\) 166674. 4.39184e6i 0.0320094 0.843443i
\(487\) 2.67715e6 0.511505 0.255753 0.966742i \(-0.417677\pi\)
0.255753 + 0.966742i \(0.417677\pi\)
\(488\) 542753. 4.74883e6i 0.103170 0.902687i
\(489\) −1.03103e7 −1.94983
\(490\) 28119.2 740935.i 0.00529069 0.139409i
\(491\) 5.10695e6i 0.956000i −0.878360 0.478000i \(-0.841362\pi\)
0.878360 0.478000i \(-0.158638\pi\)
\(492\) 374609. 4.92832e6i 0.0697694 0.917881i
\(493\) 1.65578e7i 3.06822i
\(494\) −2.12084e6 80488.0i −0.391013 0.0148393i
\(495\) 748397. 0.137284
\(496\) 837465. + 128054.i 0.152849 + 0.0233715i
\(497\) 7.64292e6 1.38793
\(498\) 1.33070e7 + 505011.i 2.40439 + 0.0912489i
\(499\) 259376.i 0.0466313i 0.999728 + 0.0233157i \(0.00742228\pi\)
−0.999728 + 0.0233157i \(0.992578\pi\)
\(500\) 37896.4 498562.i 0.00677911 0.0891854i
\(501\) 4.21429e6i 0.750118i
\(502\) 88380.7 2.32882e6i 0.0156530 0.412454i
\(503\) −324388. −0.0571669 −0.0285835 0.999591i \(-0.509100\pi\)
−0.0285835 + 0.999591i \(0.509100\pi\)
\(504\) 2.12695e6 + 243093.i 0.372975 + 0.0426281i
\(505\) 2.56729e6 0.447967
\(506\) 57676.2 1.51976e6i 0.0100143 0.263875i
\(507\) 6.23617e6i 1.07745i
\(508\) −2.01923e6 153484.i −0.347157 0.0263879i
\(509\) 1.13575e7i 1.94307i 0.236890 + 0.971537i \(0.423872\pi\)
−0.236890 + 0.971537i \(0.576128\pi\)
\(510\) −5.48479e6 208153.i −0.933759 0.0354370i
\(511\) −2.00254e6 −0.339257
\(512\) 5.58932e6 + 1.98592e6i 0.942289 + 0.334802i
\(513\) 4.72612e6 0.792887
\(514\) −497770. 18890.8i −0.0831038 0.00315387i
\(515\) 899544.i 0.149453i
\(516\) −5.57610e6 423847.i −0.921947 0.0700785i
\(517\) 3.76675e6i 0.619784i
\(518\) −217461. + 5.73005e6i −0.0356087 + 0.938283i
\(519\) 3.10484e6 0.505966
\(520\) 892057. + 101955.i 0.144672 + 0.0165348i
\(521\) 9.15918e6 1.47830 0.739149 0.673541i \(-0.235228\pi\)
0.739149 + 0.673541i \(0.235228\pi\)
\(522\) −189103. + 4.98282e6i −0.0303754 + 0.800385i
\(523\) 7.08351e6i 1.13238i 0.824273 + 0.566192i \(0.191584\pi\)
−0.824273 + 0.566192i \(0.808416\pi\)
\(524\) 436764. 5.74604e6i 0.0694894 0.914198i
\(525\) 1.26272e6i 0.199944i
\(526\) −713855. 27091.5i −0.112498 0.00426942i
\(527\) 1.70911e6 0.268068
\(528\) −5.17667e6 791545.i −0.808101 0.123564i
\(529\) −5.46084e6 −0.848438
\(530\) −3.92179e6 148836.i −0.606450 0.0230153i
\(531\) 2.76105e6i 0.424950i
\(532\) −493210. + 6.48864e6i −0.0755532 + 0.993973i
\(533\) 1.63108e6i 0.248689i
\(534\) −122291. + 3.22234e6i −0.0185584 + 0.489011i
\(535\) 2.37461e6 0.358681
\(536\) −792690. + 6.93566e6i −0.119177 + 1.04274i
\(537\) 8.11579e6 1.21449
\(538\) −403696. + 1.06373e7i −0.0601310 + 1.58444i
\(539\) 1.42717e6i 0.211594i
\(540\) −1.99362e6 151538.i −0.294211 0.0223634i
\(541\) 2.53136e6i 0.371843i −0.982565 0.185922i \(-0.940473\pi\)
0.982565 0.185922i \(-0.0595271\pi\)
\(542\) −6.61911e6 251201.i −0.967835 0.0367303i
\(543\) −4.07586e6 −0.593225
\(544\) 1.17517e7 + 2.25599e6i 1.70257 + 0.326844i
\(545\) −4.32894e6 −0.624296
\(546\) −2.26587e6 85991.9i −0.325277 0.0123446i
\(547\) 1.30020e7i 1.85798i −0.370108 0.928989i \(-0.620679\pi\)
0.370108 0.928989i \(-0.379321\pi\)
\(548\) 1.16700e7 + 887050.i 1.66004 + 0.126182i
\(549\) 2.90386e6i 0.411192i
\(550\) 36497.4 961700.i 0.00514464 0.135560i
\(551\) −1.51571e7 −2.12686
\(552\) 381425. 3.33729e6i 0.0532797 0.466172i
\(553\) 8.12967e6 1.13047
\(554\) −239027. + 6.29833e6i −0.0330882 + 0.871868i
\(555\) 4.42745e6i 0.610128i
\(556\) −271366. + 3.57007e6i −0.0372279 + 0.489767i
\(557\) 5.70438e6i 0.779059i 0.921014 + 0.389530i \(0.127362\pi\)
−0.921014 + 0.389530i \(0.872638\pi\)
\(558\) −514331. 19519.4i −0.0699290 0.00265387i
\(559\) 1.84546e6 0.249790
\(560\) 416103. 2.72130e6i 0.0560700 0.366696i
\(561\) −1.05646e7 −1.41725
\(562\) −1.06194e7 403016.i −1.41827 0.0538247i
\(563\) 1.98939e6i 0.264514i −0.991215 0.132257i \(-0.957778\pi\)
0.991215 0.132257i \(-0.0422224\pi\)
\(564\) −630550. + 8.29547e6i −0.0834683 + 1.09810i
\(565\) 5.94451e6i 0.783420i
\(566\) −659.223 + 17370.4i −8.64951e−5 + 0.00227913i
\(567\) 7.92310e6 1.03499
\(568\) −1.27824e7 1.46092e6i −1.66242 0.190001i
\(569\) 1.30277e6 0.168689 0.0843447 0.996437i \(-0.473120\pi\)
0.0843447 + 0.996437i \(0.473120\pi\)
\(570\) −190545. + 5.02082e6i −0.0245646 + 0.647273i
\(571\) 2.90628e6i 0.373033i −0.982452 0.186517i \(-0.940280\pi\)
0.982452 0.186517i \(-0.0597199\pi\)
\(572\) 1.72322e6 + 130985.i 0.220218 + 0.0167390i
\(573\) 649413.i 0.0826294i
\(574\) 4.99741e6 + 189656.i 0.633090 + 0.0240264i
\(575\) 617298. 0.0778619
\(576\) −3.51074e6 813120.i −0.440902 0.102117i
\(577\) 4.01853e6 0.502490 0.251245 0.967923i \(-0.419160\pi\)
0.251245 + 0.967923i \(0.419160\pi\)
\(578\) 1.60970e7 + 610896.i 2.00413 + 0.0760585i
\(579\) 8.89785e6i 1.10303i
\(580\) 6.39376e6 + 485998.i 0.789199 + 0.0599881i
\(581\) 1.34741e7i 1.65599i
\(582\) −63017.6 + 1.66050e6i −0.00771178 + 0.203204i
\(583\) −7.55404e6 −0.920466
\(584\) 3.34914e6 + 382780.i 0.406351 + 0.0464426i
\(585\) −545483. −0.0659009
\(586\) −527671. + 1.39040e7i −0.0634774 + 1.67262i
\(587\) 1.29654e7i 1.55307i −0.630074 0.776535i \(-0.716975\pi\)
0.630074 0.776535i \(-0.283025\pi\)
\(588\) 238906. 3.14303e6i 0.0284960 0.374891i
\(589\) 1.56454e6i 0.185822i
\(590\) −3.54798e6 134649.i −0.419616 0.0159248i
\(591\) −7.41706e6 −0.873501
\(592\) 1.45897e6 9.54163e6i 0.171097 1.11897i
\(593\) −107000. −0.0124953 −0.00624767 0.999980i \(-0.501989\pi\)
−0.00624767 + 0.999980i \(0.501989\pi\)
\(594\) −3.84560e6 145944.i −0.447196 0.0169715i
\(595\) 5.55367e6i 0.643114i
\(596\) 331015. 4.35480e6i 0.0381708 0.502173i
\(597\) 8.96337e6i 1.02928i
\(598\) −42038.4 + 1.10770e6i −0.00480721 + 0.126669i
\(599\) 1.06394e7 1.21157 0.605785 0.795629i \(-0.292859\pi\)
0.605785 + 0.795629i \(0.292859\pi\)
\(600\) 241365. 2.11183e6i 0.0273714 0.239486i
\(601\) −6.42705e6 −0.725814 −0.362907 0.931825i \(-0.618216\pi\)
−0.362907 + 0.931825i \(0.618216\pi\)
\(602\) 214585. 5.65427e6i 0.0241328 0.635894i
\(603\) 4.24108e6i 0.474988i
\(604\) 5.94618e6 + 451977.i 0.663202 + 0.0504109i
\(605\) 2.17388e6i 0.241461i
\(606\) 1.09061e7 + 413897.i 1.20639 + 0.0457836i
\(607\) 1.96807e6 0.216805 0.108403 0.994107i \(-0.465426\pi\)
0.108403 + 0.994107i \(0.465426\pi\)
\(608\) 2.06515e6 1.07576e7i 0.226565 1.18021i
\(609\) −1.61936e7 −1.76930
\(610\) 3.73149e6 + 141614.i 0.406030 + 0.0154092i
\(611\) 2.74546e6i 0.297518i
\(612\) −7.24903e6 551009.i −0.782350 0.0594675i
\(613\) 8.12485e6i 0.873301i 0.899631 + 0.436651i \(0.143835\pi\)
−0.899631 + 0.436651i \(0.856165\pi\)
\(614\) −55236.3 + 1.45547e6i −0.00591294 + 0.155805i
\(615\) 3.86136e6 0.411673
\(616\) 601692. 5.26451e6i 0.0638885 0.558993i
\(617\) 1.40750e6 0.148846 0.0744229 0.997227i \(-0.476289\pi\)
0.0744229 + 0.997227i \(0.476289\pi\)
\(618\) 145024. 3.82135e6i 0.0152745 0.402481i
\(619\) 5.01827e6i 0.526414i −0.964739 0.263207i \(-0.915220\pi\)
0.964739 0.263207i \(-0.0847802\pi\)
\(620\) −50165.2 + 659970.i −0.00524111 + 0.0689517i
\(621\) 2.46842e6i 0.256856i
\(622\) 1.37471e7 + 521715.i 1.42474 + 0.0540702i
\(623\) −3.26281e6 −0.336800
\(624\) 3.77311e6 + 576932.i 0.387916 + 0.0593148i
\(625\) 390625. 0.0400000
\(626\) −1.48409e7 563227.i −1.51365 0.0574444i
\(627\) 9.67095e6i 0.982427i
\(628\) −181150. + 2.38319e6i −0.0183290 + 0.241135i
\(629\) 1.94727e7i 1.96246i
\(630\) −63427.1 + 1.67129e6i −0.00636683 + 0.167765i
\(631\) 5.59458e6 0.559363 0.279682 0.960093i \(-0.409771\pi\)
0.279682 + 0.960093i \(0.409771\pi\)
\(632\) −1.35964e7 1.55396e6i −1.35404 0.154756i
\(633\) 8.18942e6 0.812351
\(634\) −546521. + 1.44007e7i −0.0539987 + 1.42286i
\(635\) 1.58207e6i 0.155701i
\(636\) −1.66362e7 1.26454e6i −1.63084 0.123962i
\(637\) 1.04022e6i 0.101572i
\(638\) 1.23332e7 + 468058.i 1.19957 + 0.0455248i
\(639\) 7.81627e6 0.757265
\(640\) −1.21608e6 + 4.47169e6i −0.117358 + 0.431540i
\(641\) 3.70806e6 0.356453 0.178226 0.983990i \(-0.442964\pi\)
0.178226 + 0.983990i \(0.442964\pi\)
\(642\) 1.00876e7 + 382834.i 0.965940 + 0.0366583i
\(643\) 1.36989e6i 0.130665i −0.997864 0.0653325i \(-0.979189\pi\)
0.997864 0.0653325i \(-0.0208108\pi\)
\(644\) 3.38897e6 + 257601.i 0.321998 + 0.0244755i
\(645\) 4.36889e6i 0.413497i
\(646\) 838052. 2.20825e7i 0.0790114 2.08193i
\(647\) −1.38641e7 −1.30206 −0.651028 0.759053i \(-0.725662\pi\)
−0.651028 + 0.759053i \(0.725662\pi\)
\(648\) −1.32510e7 1.51448e6i −1.23968 0.141686i
\(649\) −6.83402e6 −0.636890
\(650\) −26601.8 + 700952.i −0.00246961 + 0.0650736i
\(651\) 1.67152e6i 0.154582i
\(652\) −1.33099e6 + 1.75104e7i −0.122618 + 1.61316i
\(653\) 1.00652e7i 0.923714i 0.886954 + 0.461857i \(0.152817\pi\)
−0.886954 + 0.461857i \(0.847183\pi\)
\(654\) −1.83898e7 697909.i −1.68125 0.0638050i
\(655\) 4.50204e6 0.410021
\(656\) −8.32165e6 1.27243e6i −0.755005 0.115445i
\(657\) −2.04796e6 −0.185101
\(658\) −8.41176e6 319234.i −0.757394 0.0287438i
\(659\) 2.94962e6i 0.264578i 0.991211 + 0.132289i \(0.0422326\pi\)
−0.991211 + 0.132289i \(0.957767\pi\)
\(660\) 310089. 4.07951e6i 0.0277094 0.364543i
\(661\) 2.46213e6i 0.219184i 0.993977 + 0.109592i \(0.0349544\pi\)
−0.993977 + 0.109592i \(0.965046\pi\)
\(662\) −454178. + 1.19675e7i −0.0402793 + 1.06135i
\(663\) 7.70023e6 0.680331
\(664\) 2.57553e6 2.25346e7i 0.226697 1.98349i
\(665\) −5.08387e6 −0.445801
\(666\) −222393. + 5.86002e6i −0.0194283 + 0.511933i
\(667\) 7.91648e6i 0.688997i
\(668\) 7.15733e6 + 544038.i 0.620597 + 0.0471724i
\(669\) 2.14320e7i 1.85139i
\(670\) −5.44983e6 206826.i −0.469025 0.0178000i
\(671\) 7.18748e6 0.616269
\(672\) 2.20637e6 1.14933e7i 0.188476 0.981793i
\(673\) 8.46100e6 0.720085 0.360043 0.932936i \(-0.382762\pi\)
0.360043 + 0.932936i \(0.382762\pi\)
\(674\) −8.87229e6 336712.i −0.752291 0.0285501i
\(675\) 1.56201e6i 0.131955i
\(676\) 1.05912e7 + 805051.i 0.891412 + 0.0677574i
\(677\) 2.01968e7i 1.69360i 0.531913 + 0.846799i \(0.321473\pi\)
−0.531913 + 0.846799i \(0.678527\pi\)
\(678\) 958370. 2.52529e7i 0.0800680 2.10978i
\(679\) −1.68135e6 −0.139954
\(680\) −1.06157e6 + 9.28822e6i −0.0880392 + 0.770301i
\(681\) 2.04587e7 1.69048
\(682\) −48313.4 + 1.27305e6i −0.00397746 + 0.104805i
\(683\) 5.52541e6i 0.453224i 0.973985 + 0.226612i \(0.0727649\pi\)
−0.973985 + 0.226612i \(0.927235\pi\)
\(684\) −504397. + 6.63582e6i −0.0412223 + 0.542318i
\(685\) 9.14346e6i 0.744534i
\(686\) 1.34037e7 + 508683.i 1.08746 + 0.0412703i
\(687\) 8.91259e6 0.720464
\(688\) −1.43968e6 + 9.41544e6i −0.115956 + 0.758350i
\(689\) 5.50590e6 0.441855
\(690\) 2.62234e6 + 99520.4i 0.209685 + 0.00795773i
\(691\) 1.66737e7i 1.32843i 0.747543 + 0.664214i \(0.231234\pi\)
−0.747543 + 0.664214i \(0.768766\pi\)
\(692\) 400816. 5.27310e6i 0.0318185 0.418602i
\(693\) 3.21919e6i 0.254632i
\(694\) −91933.7 + 2.42244e6i −0.00724563 + 0.190921i
\(695\) −2.79716e6 −0.219662
\(696\) 2.70830e7 + 3.09537e6i 2.11921 + 0.242208i
\(697\) −1.69830e7 −1.32413
\(698\) 112177. 2.95583e6i 0.00871493 0.229637i
\(699\) 5.09253e6i 0.394222i
\(700\) 2.14454e6 + 163009.i 0.165420 + 0.0125738i
\(701\) 1.49989e7i 1.15283i −0.817157 0.576415i \(-0.804451\pi\)
0.817157 0.576415i \(-0.195549\pi\)
\(702\) 2.80293e6 + 106374.i 0.214669 + 0.00814690i
\(703\) −1.78255e7 −1.36036
\(704\) −2.01260e6 + 8.68961e6i −0.153047 + 0.660798i
\(705\) −6.49953e6 −0.492503
\(706\) 1.07058e7 + 406294.i 0.808362 + 0.0306781i
\(707\) 1.10431e7i 0.830884i
\(708\) −1.50505e7 1.14401e6i −1.12841 0.0857720i
\(709\) 1.84405e7i 1.37771i −0.724900 0.688854i \(-0.758114\pi\)
0.724900 0.688854i \(-0.241886\pi\)
\(710\) 381180. 1.00440e7i 0.0283781 0.747758i
\(711\) 8.31407e6 0.616793
\(712\) 5.45688e6 + 623677.i 0.403408 + 0.0461063i
\(713\) −817147. −0.0601972
\(714\) 895359. 2.35925e7i 0.0657282 1.73193i
\(715\) 1.35015e6i 0.0987684i
\(716\) 1.04770e6 1.37834e7i 0.0763754 1.00479i
\(717\) 1.54886e7i 1.12516i
\(718\) −1.45330e7 551540.i −1.05207 0.0399269i
\(719\) −334083. −0.0241009 −0.0120504 0.999927i \(-0.503836\pi\)
−0.0120504 + 0.999927i \(0.503836\pi\)
\(720\) 425541. 2.78302e6i 0.0305922 0.200072i
\(721\) 3.86934e6 0.277204
\(722\) −6.21763e6 235965.i −0.443897 0.0168463i
\(723\) 1.62921e6i 0.115913i
\(724\) −526168. + 6.92223e6i −0.0373059 + 0.490794i
\(725\) 5.00953e6i 0.353959i
\(726\) −350471. + 9.23485e6i −0.0246780 + 0.650262i
\(727\) −2.11438e7 −1.48370 −0.741851 0.670564i \(-0.766052\pi\)
−0.741851 + 0.670564i \(0.766052\pi\)
\(728\) −438554. + 3.83714e6i −0.0306686 + 0.268336i
\(729\) −3.30712e6 −0.230479
\(730\) −99873.7 + 2.63165e6i −0.00693656 + 0.182777i
\(731\) 1.92152e7i 1.33000i
\(732\) 1.58289e7 + 1.20318e6i 1.09188 + 0.0829950i
\(733\) 1.48236e6i 0.101904i −0.998701 0.0509521i \(-0.983774\pi\)
0.998701 0.0509521i \(-0.0162256\pi\)
\(734\) −1.39772e7 530449.i −0.957593 0.0363415i
\(735\) 2.46258e6 0.168140
\(736\) −5.61864e6 1.07862e6i −0.382328 0.0733960i
\(737\) −1.04973e7 −0.711884
\(738\) 5.11076e6 + 193958.i 0.345418 + 0.0131089i
\(739\) 1.69772e7i 1.14355i 0.820411 + 0.571775i \(0.193745\pi\)
−0.820411 + 0.571775i \(0.806255\pi\)
\(740\) 7.51935e6 + 571556.i 0.504779 + 0.0383689i
\(741\) 7.04885e6i 0.471599i
\(742\) 640209. 1.68694e7i 0.0426886 1.12484i
\(743\) −2.01294e7 −1.33770 −0.668849 0.743399i \(-0.733213\pi\)
−0.668849 + 0.743399i \(0.733213\pi\)
\(744\) −319507. + 2.79553e6i −0.0211616 + 0.185153i
\(745\) 3.41201e6 0.225226
\(746\) −563208. + 1.48404e7i −0.0370529 + 0.976336i
\(747\) 1.37797e7i 0.903520i
\(748\) −1.36383e6 + 1.79424e7i −0.0891264 + 1.17254i
\(749\) 1.02143e7i 0.665278i
\(750\) 1.65941e6 + 62976.3i 0.107721 + 0.00408812i
\(751\) −1.16155e7 −0.751514 −0.375757 0.926718i \(-0.622617\pi\)
−0.375757 + 0.926718i \(0.622617\pi\)
\(752\) 1.40072e7 + 2.14179e6i 0.903247 + 0.138112i
\(753\) 7.74007e6 0.497459
\(754\) −8.98930e6 341152.i −0.575834 0.0218534i
\(755\) 4.65885e6i 0.297448i
\(756\) 651833. 8.57547e6i 0.0414793 0.545699i
\(757\) 9.97313e6i 0.632545i −0.948668 0.316273i \(-0.897569\pi\)
0.948668 0.316273i \(-0.102431\pi\)
\(758\) −459698. + 1.21130e7i −0.0290603 + 0.765733i
\(759\) 5.05108e6 0.318258
\(760\) 8.50251e6 + 971768.i 0.533965 + 0.0610280i
\(761\) 2.00566e7 1.25544 0.627719 0.778440i \(-0.283989\pi\)
0.627719 + 0.778440i \(0.283989\pi\)
\(762\) 255061. 6.72080e6i 0.0159131 0.419308i
\(763\) 1.86207e7i 1.15794i
\(764\) −1.10293e6 83835.2i −0.0683620 0.00519628i
\(765\) 5.67964e6i 0.350887i
\(766\) −3.62786e6 137681.i −0.223398 0.00847816i
\(767\) 4.98110e6 0.305729
\(768\) −5.88695e6 + 1.88001e7i −0.360153 + 1.15016i
\(769\) 2.63971e7 1.60968 0.804842 0.593489i \(-0.202250\pi\)
0.804842 + 0.593489i \(0.202250\pi\)
\(770\) 4.13670e6 + 156992.i 0.251436 + 0.00954223i
\(771\) 1.65439e6i 0.100231i
\(772\) −1.51117e7 1.14866e6i −0.912575 0.0693661i
\(773\) 902367.i 0.0543169i −0.999631 0.0271584i \(-0.991354\pi\)
0.999631 0.0271584i \(-0.00864586\pi\)
\(774\) 219452. 5.78252e6i 0.0131670 0.346948i
\(775\) −517089. −0.0309251
\(776\) 2.81198e6 + 321386.i 0.167632 + 0.0191590i
\(777\) −1.90444e7 −1.13166
\(778\) 506976. 1.33587e7i 0.0300288 0.791253i
\(779\) 1.55463e7i 0.917877i
\(780\) −226014. + 2.97343e6i −0.0133015 + 0.174993i
\(781\) 1.93465e7i 1.13494i
\(782\) −1.15335e7 437709.i −0.674444 0.0255958i
\(783\) 2.00319e7 1.16766
\(784\) −5.30712e6 811492.i −0.308368 0.0471513i
\(785\) −1.86724e6 −0.108150
\(786\) 1.91251e7 + 725816.i 1.10420 + 0.0419054i
\(787\) 1.59032e7i 0.915269i −0.889140 0.457635i \(-0.848697\pi\)
0.889140 0.457635i \(-0.151303\pi\)
\(788\) −957497. + 1.25968e7i −0.0549315 + 0.722675i
\(789\) 2.37258e6i 0.135684i
\(790\) 405456. 1.06837e7i 0.0231140 0.609050i
\(791\) 2.55700e7 1.45308
\(792\) 615340. 5.38392e6i 0.0348580 0.304990i
\(793\) −5.23873e6 −0.295830
\(794\) 86645.5 2.28309e6i 0.00487747 0.128520i
\(795\) 1.30345e7i 0.731436i
\(796\) −1.52229e7 1.15712e6i −0.851561 0.0647283i
\(797\) 2.52099e7i 1.40580i −0.711287 0.702902i \(-0.751887\pi\)
0.711287 0.702902i \(-0.248113\pi\)
\(798\) −2.15968e7 819619.i −1.20055 0.0455622i
\(799\) 2.85861e7 1.58412
\(800\) −3.55546e6 682546.i −0.196414 0.0377057i
\(801\) −3.33682e6 −0.183760
\(802\) 1.29073e7 + 489845.i 0.708598 + 0.0268920i
\(803\) 5.06901e6i 0.277418i
\(804\) −2.31181e7 1.75724e6i −1.26128 0.0958717i
\(805\) 2.65527e6i 0.144417i
\(806\) 35214.1 927884.i 0.00190932 0.0503102i
\(807\) −3.53542e7 −1.91099
\(808\) 2.11085e6 1.84689e7i 0.113744 0.995206i
\(809\) −1.43630e7 −0.771570 −0.385785 0.922589i \(-0.626069\pi\)
−0.385785 + 0.922589i \(0.626069\pi\)
\(810\) 395153. 1.04122e7i 0.0211618 0.557610i
\(811\) 1.49512e7i 0.798222i −0.916903 0.399111i \(-0.869319\pi\)
0.916903 0.399111i \(-0.130681\pi\)
\(812\) −2.09050e6 + 2.75024e7i −0.111265 + 1.46380i
\(813\) 2.19993e7i 1.16730i
\(814\) 1.45044e7 + 550457.i 0.767255 + 0.0291180i
\(815\) −1.37195e7 −0.723508
\(816\) −6.00709e6 + 3.92861e7i −0.315819 + 2.06545i
\(817\) 1.75897e7 0.921943
\(818\) 1.85391e7 + 703577.i 0.968737 + 0.0367645i
\(819\) 2.34637e6i 0.122232i
\(820\) 498477. 6.55793e6i 0.0258887 0.340590i
\(821\) 2.49701e7i 1.29289i −0.762960 0.646446i \(-0.776254\pi\)
0.762960 0.646446i \(-0.223746\pi\)
\(822\) −1.47410e6 + 3.88423e7i −0.0760936 + 2.00505i
\(823\) 2.50946e7 1.29146 0.645729 0.763567i \(-0.276554\pi\)
0.645729 + 0.763567i \(0.276554\pi\)
\(824\) −6.47126e6 739614.i −0.332025 0.0379478i
\(825\) 3.19631e6 0.163499
\(826\) 579187. 1.52615e7i 0.0295372 0.778298i
\(827\) 2.47367e7i 1.25770i −0.777526 0.628850i \(-0.783526\pi\)
0.777526 0.628850i \(-0.216474\pi\)
\(828\) 3.46584e6 + 263443.i 0.175684 + 0.0133540i
\(829\) 1.02078e7i 0.515878i 0.966161 + 0.257939i \(0.0830434\pi\)
−0.966161 + 0.257939i \(0.916957\pi\)
\(830\) 1.77071e7 + 671999.i 0.892177 + 0.0338590i
\(831\) −2.09332e7 −1.05156
\(832\) 1.46692e6 6.33358e6i 0.0734678 0.317206i
\(833\) −1.08309e7 −0.540818
\(834\) −1.18826e7 450957.i −0.591558 0.0224502i
\(835\) 5.60779e6i 0.278340i
\(836\) 1.64246e7 + 1.24846e6i 0.812794 + 0.0617816i
\(837\) 2.06771e6i 0.102018i
\(838\) −129719. + 3.41807e6i −0.00638107 + 0.168140i
\(839\) 2.64451e7 1.29700 0.648501 0.761214i \(-0.275396\pi\)
0.648501 + 0.761214i \(0.275396\pi\)
\(840\) 9.08392e6 + 1.03822e6i 0.444197 + 0.0507681i
\(841\) −4.37332e7 −2.13217
\(842\) 743010. 1.95782e7i 0.0361172 0.951682i
\(843\) 3.52947e7i 1.71057i
\(844\) 1.05720e6 1.39085e7i 0.0510860 0.672084i
\(845\) 8.29824e6i 0.399801i
\(846\) −8.60256e6 326475.i −0.413239 0.0156828i
\(847\) −9.35082e6 −0.447859
\(848\) −4.29525e6 + 2.80908e7i −0.205116 + 1.34145i
\(849\) −57732.4 −0.00274885
\(850\) −7.29841e6 276981.i −0.346482 0.0131493i
\(851\) 9.31014e6i 0.440689i
\(852\) 3.23858e6 4.26065e7i 0.152846 2.01084i
\(853\) 2.30070e7i 1.08265i 0.840814 + 0.541324i \(0.182077\pi\)
−0.840814 + 0.541324i \(0.817923\pi\)
\(854\) −609143. + 1.60508e7i −0.0285808 + 0.753099i
\(855\) −5.19919e6 −0.243232
\(856\) 1.95243e6 1.70828e7i 0.0910733 0.796848i
\(857\) −1.81332e7 −0.843379 −0.421689 0.906740i \(-0.638563\pi\)
−0.421689 + 0.906740i \(0.638563\pi\)
\(858\) −217671. + 5.73558e6i −0.0100944 + 0.265986i
\(859\) 1.83891e6i 0.0850310i 0.999096 + 0.0425155i \(0.0135372\pi\)
−0.999096 + 0.0425155i \(0.986463\pi\)
\(860\) −7.41990e6 563997.i −0.342099 0.0260034i
\(861\) 1.66094e7i 0.763567i
\(862\) 2.82834e7 + 1.07338e6i 1.29647 + 0.0492024i
\(863\) 1.14230e7 0.522097 0.261049 0.965326i \(-0.415932\pi\)
0.261049 + 0.965326i \(0.415932\pi\)
\(864\) −2.72933e6 + 1.42174e7i −0.124386 + 0.647942i
\(865\) 4.13150e6 0.187744
\(866\) −2.32476e7 882268.i −1.05338 0.0399766i
\(867\) 5.35001e7i 2.41717i
\(868\) −2.83883e6 215783.i −0.127891 0.00972116i
\(869\) 2.05786e7i 0.924413i
\(870\) −807634. + 2.12810e7i −0.0361757 + 0.953222i
\(871\) 7.65115e6 0.341729
\(872\) −3.55930e6 + 3.11421e7i −0.158516 + 1.38694i
\(873\) −1.71949e6 −0.0763597
\(874\) −400682. + 1.05579e7i −0.0177428 + 0.467519i
\(875\) 1.68025e6i 0.0741915i
\(876\) −848547. + 1.11634e7i −0.0373608 + 0.491515i
\(877\) 2.12365e7i 0.932362i 0.884689 + 0.466181i \(0.154370\pi\)
−0.884689 + 0.466181i \(0.845630\pi\)
\(878\) 2.37594e7 + 901692.i 1.04016 + 0.0394750i
\(879\) −4.62116e7 −2.01734
\(880\) −6.88840e6 1.05328e6i −0.299855 0.0458497i
\(881\) 1.35067e7 0.586287 0.293143 0.956069i \(-0.405299\pi\)
0.293143 + 0.956069i \(0.405299\pi\)
\(882\) 3.25938e6 + 123697.i 0.141080 + 0.00535410i
\(883\) 2.44466e7i 1.05515i 0.849507 + 0.527577i \(0.176900\pi\)
−0.849507 + 0.527577i \(0.823100\pi\)
\(884\) 994052. 1.30777e7i 0.0427837 0.562859i
\(885\) 1.17921e7i 0.506096i
\(886\) −283532. + 7.47100e6i −0.0121344 + 0.319738i
\(887\) 8.02242e6 0.342371 0.171185 0.985239i \(-0.445240\pi\)
0.171185 + 0.985239i \(0.445240\pi\)
\(888\) 3.18508e7 + 3.64029e6i 1.35546 + 0.154919i
\(889\) 6.80520e6 0.288793
\(890\) −162728. + 4.28785e6i −0.00688632 + 0.181453i
\(891\) 2.00557e7i 0.846337i
\(892\) 3.63991e7 + 2.76674e6i 1.53172 + 0.116428i
\(893\) 2.61680e7i 1.09810i
\(894\) 1.44945e7 + 550081.i 0.606542 + 0.0230188i
\(895\) 1.07994e7 0.450652
\(896\) −1.92347e7 5.23090e6i −0.800416 0.217674i
\(897\) −3.68157e6 −0.152775
\(898\) −3.12148e7 1.18463e6i −1.29172 0.0490221i
\(899\) 6.63136e6i 0.273655i
\(900\) 2.19318e6 + 166707.i 0.0902543 + 0.00686035i
\(901\) 5.73281e7i 2.35264i
\(902\) 480076. 1.26499e7i 0.0196469 0.517692i
\(903\) 1.87926e7 0.766949
\(904\) −4.27644e7 4.88763e6i −1.74045 0.198920i
\(905\) −5.42359e6 −0.220123
\(906\) −751097. + 1.97913e7i −0.0304001 + 0.801038i
\(907\) 2.02868e7i 0.818831i −0.912348 0.409416i \(-0.865733\pi\)
0.912348 0.409416i \(-0.134267\pi\)
\(908\) 2.64109e6 3.47460e7i 0.106309 1.39859i
\(909\) 1.12935e7i 0.453336i
\(910\) −3.01511e6 114426.i −0.120698 0.00458060i
\(911\) 1.72893e7 0.690209 0.345104 0.938564i \(-0.387844\pi\)
0.345104 + 0.938564i \(0.387844\pi\)
\(912\) 3.59628e7 + 5.49894e6i 1.43175 + 0.218923i
\(913\) 3.41068e7 1.35414
\(914\) 1.96060e7 + 744067.i 0.776290 + 0.0294609i
\(915\) 1.24020e7i 0.489710i
\(916\) 1.15056e6 1.51367e7i 0.0453076 0.596063i
\(917\) 1.93653e7i 0.760502i
\(918\) −1.10758e6 + 2.91845e7i −0.0433779 + 1.14300i
\(919\) −2.14060e7 −0.836079 −0.418039 0.908429i \(-0.637283\pi\)
−0.418039 + 0.908429i \(0.637283\pi\)
\(920\) 507548. 4.44080e6i 0.0197701 0.172978i
\(921\) −4.83740e6 −0.187916
\(922\) −519900. + 1.36993e7i −0.0201415 + 0.530725i
\(923\) 1.41010e7i 0.544812i
\(924\) 1.75478e7 + 1.33383e6i 0.676149 + 0.0513950i
\(925\) 5.89144e6i 0.226395i
\(926\) −3.72237e7 1.41267e6i −1.42656 0.0541395i
\(927\) 3.95710e6 0.151244
\(928\) 8.75326e6 4.55967e7i 0.333657 1.73806i
\(929\) 4.14158e7 1.57444 0.787221 0.616670i \(-0.211519\pi\)
0.787221 + 0.616670i \(0.211519\pi\)
\(930\) −2.19664e6 83364.7i −0.0832823 0.00316064i
\(931\) 9.91466e6i 0.374890i
\(932\) −8.64889e6 657414.i −0.326152 0.0247913i
\(933\) 4.56900e7i 1.71837i
\(934\) 248203. 6.54010e6i 0.00930979 0.245311i
\(935\) −1.40580e7 −0.525889
\(936\) −448501. + 3.92417e6i −0.0167330 + 0.146406i
\(937\) 1.39335e7 0.518455 0.259228 0.965816i \(-0.416532\pi\)
0.259228 + 0.965816i \(0.416532\pi\)
\(938\) 889652. 2.34422e7i 0.0330151 0.869943i
\(939\) 4.93254e7i 1.82560i
\(940\) −839049. + 1.10385e7i −0.0309719 + 0.407464i
\(941\) 1.51311e7i 0.557051i 0.960429 + 0.278526i \(0.0898457\pi\)
−0.960429 + 0.278526i \(0.910154\pi\)
\(942\) −7.93222e6 301035.i −0.291251 0.0110532i
\(943\) 8.11975e6 0.297347
\(944\) −3.88585e6 + 2.54133e7i −0.141924 + 0.928177i
\(945\) 6.71891e6 0.244748
\(946\) −1.43126e7 543177.i −0.519985 0.0197339i
\(947\) 2.72196e7i 0.986296i −0.869945 0.493148i \(-0.835846\pi\)
0.869945 0.493148i \(-0.164154\pi\)
\(948\) 3.44483e6 4.53200e7i 0.124494 1.63783i
\(949\) 3.69464e6i 0.133170i
\(950\) −253551. + 6.68102e6i −0.00911499 + 0.240178i
\(951\) −4.78623e7 −1.71610
\(952\) −3.99528e7 4.56628e6i −1.42874 0.163294i
\(953\) −2.79494e7 −0.996873 −0.498437 0.866926i \(-0.666092\pi\)
−0.498437 + 0.866926i \(0.666092\pi\)
\(954\) 654730. 1.72520e7i 0.0232912 0.613718i
\(955\) 864150.i 0.0306606i
\(956\) −2.63051e7 1.99948e6i −0.930882 0.0707576i
\(957\) 4.09908e7i 1.44679i
\(958\) −2.15098e6 81631.8i −0.0757221 0.00287373i
\(959\) −3.93301e7 −1.38095
\(960\) −1.49939e7 3.47273e6i −0.525094 0.121617i
\(961\) −2.79447e7 −0.976091
\(962\) −1.05718e7 401210.i −0.368309 0.0139777i
\(963\) 1.04460e7i 0.362980i
\(964\) −2.76697e6 210321.i −0.0958984 0.00728937i
\(965\) 1.18400e7i 0.409293i
\(966\) −428081. + 1.12799e7i −0.0147599 + 0.388921i
\(967\) 3.73167e7 1.28333 0.641663 0.766987i \(-0.278245\pi\)
0.641663 + 0.766987i \(0.278245\pi\)
\(968\) 1.56387e7 + 1.78738e6i 0.536431 + 0.0613097i
\(969\) 7.33936e7 2.51101
\(970\) −83855.2 + 2.20957e6i −0.00286154 + 0.0754011i
\(971\) 1.77774e7i 0.605091i −0.953135 0.302545i \(-0.902164\pi\)
0.953135 0.302545i \(-0.0978364\pi\)
\(972\) 1.88435e6 2.47904e7i 0.0639728 0.841622i
\(973\) 1.20318e7i 0.407427i
\(974\) 1.51333e7 + 574325.i 0.511137 + 0.0193981i
\(975\) −2.32969e6 −0.0784850
\(976\) 4.08683e6 2.67277e7i 0.137329 0.898125i
\(977\) 1.67378e7 0.561000 0.280500 0.959854i \(-0.409500\pi\)
0.280500 + 0.959854i \(0.409500\pi\)
\(978\) −5.82817e7 2.21184e6i −1.94843 0.0739448i
\(979\) 8.25913e6i 0.275409i
\(980\) 317903. 4.18232e6i 0.0105738 0.139108i
\(981\) 1.90431e7i 0.631778i
\(982\) 1.09559e6 2.88685e7i 0.0362550 0.955312i
\(983\) −2.99351e7 −0.988091 −0.494045 0.869436i \(-0.664482\pi\)
−0.494045 + 0.869436i \(0.664482\pi\)
\(984\) 3.17485e6 2.77784e7i 0.104529 0.914575i
\(985\) −9.86961e6 −0.324123
\(986\) 3.55212e6 9.35978e7i 0.116358 3.06601i
\(987\) 2.79574e7i 0.913490i
\(988\) −1.19714e7 909963.i −0.390169 0.0296573i
\(989\) 9.18701e6i 0.298664i
\(990\) 4.23053e6 + 160553.i 0.137185 + 0.00520630i
\(991\) 1.30589e7 0.422398 0.211199 0.977443i \(-0.432263\pi\)
0.211199 + 0.977443i \(0.432263\pi\)
\(992\) 4.70654e6 + 903519.i 0.151853 + 0.0291513i
\(993\) −3.97753e7 −1.28009
\(994\) 4.32038e7 + 1.63962e6i 1.38693 + 0.0526354i
\(995\) 1.19272e7i 0.381928i
\(996\) 7.51130e7 + 5.70944e6i 2.39920 + 0.182367i
\(997\) 7.99417e6i 0.254704i 0.991858 + 0.127352i \(0.0406477\pi\)
−0.991858 + 0.127352i \(0.959352\pi\)
\(998\) −55643.4 + 1.46619e6i −0.00176843 + 0.0465978i
\(999\) 2.35584e7 0.746848
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 40.6.d.a.21.20 yes 20
3.2 odd 2 360.6.k.b.181.1 20
4.3 odd 2 160.6.d.a.81.4 20
5.2 odd 4 200.6.f.b.149.12 20
5.3 odd 4 200.6.f.c.149.9 20
5.4 even 2 200.6.d.b.101.1 20
8.3 odd 2 160.6.d.a.81.17 20
8.5 even 2 inner 40.6.d.a.21.19 20
20.3 even 4 800.6.f.b.49.17 20
20.7 even 4 800.6.f.c.49.4 20
20.19 odd 2 800.6.d.c.401.17 20
24.5 odd 2 360.6.k.b.181.2 20
40.3 even 4 800.6.f.c.49.3 20
40.13 odd 4 200.6.f.b.149.11 20
40.19 odd 2 800.6.d.c.401.4 20
40.27 even 4 800.6.f.b.49.18 20
40.29 even 2 200.6.d.b.101.2 20
40.37 odd 4 200.6.f.c.149.10 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.6.d.a.21.19 20 8.5 even 2 inner
40.6.d.a.21.20 yes 20 1.1 even 1 trivial
160.6.d.a.81.4 20 4.3 odd 2
160.6.d.a.81.17 20 8.3 odd 2
200.6.d.b.101.1 20 5.4 even 2
200.6.d.b.101.2 20 40.29 even 2
200.6.f.b.149.11 20 40.13 odd 4
200.6.f.b.149.12 20 5.2 odd 4
200.6.f.c.149.9 20 5.3 odd 4
200.6.f.c.149.10 20 40.37 odd 4
360.6.k.b.181.1 20 3.2 odd 2
360.6.k.b.181.2 20 24.5 odd 2
800.6.d.c.401.4 20 40.19 odd 2
800.6.d.c.401.17 20 20.19 odd 2
800.6.f.b.49.17 20 20.3 even 4
800.6.f.b.49.18 20 40.27 even 4
800.6.f.c.49.3 20 40.3 even 4
800.6.f.c.49.4 20 20.7 even 4