Properties

Label 5.6.b.a.4.2
Level 5
Weight 6
Character 5.4
Analytic conductor 0.802
Analytic rank 0
Dimension 2
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 5.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(0.801919099065\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-11}) \)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{2} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 4.2
Root \(0.500000 - 1.65831i\)
Character \(\chi\) = 5.4
Dual form 5.6.b.a.4.1

$q$-expansion

\(f(q)\)  \(=\)  \(q\)\(+6.63325i q^{2}\) \(-19.8997i q^{3}\) \(-12.0000 q^{4}\) \(+(-45.0000 + 33.1662i) q^{5}\) \(+132.000 q^{6}\) \(-59.6992i q^{7}\) \(+132.665i q^{8}\) \(-153.000 q^{9}\) \(+O(q^{10})\) \(q\)\(+6.63325i q^{2}\) \(-19.8997i q^{3}\) \(-12.0000 q^{4}\) \(+(-45.0000 + 33.1662i) q^{5}\) \(+132.000 q^{6}\) \(-59.6992i q^{7}\) \(+132.665i q^{8}\) \(-153.000 q^{9}\) \(+(-220.000 - 298.496i) q^{10}\) \(+252.000 q^{11}\) \(+238.797i q^{12}\) \(-119.398i q^{13}\) \(+396.000 q^{14}\) \(+(660.000 + 895.489i) q^{15}\) \(-1264.00 q^{16}\) \(-689.858i q^{17}\) \(-1014.89i q^{18}\) \(-220.000 q^{19}\) \(+(540.000 - 397.995i) q^{20}\) \(-1188.00 q^{21}\) \(+1671.58i q^{22}\) \(+2434.40i q^{23}\) \(+2640.00 q^{24}\) \(+(925.000 - 2984.96i) q^{25}\) \(+792.000 q^{26}\) \(-1790.98i q^{27}\) \(+716.391i q^{28}\) \(-6930.00 q^{29}\) \(+(-5940.00 + 4377.94i) q^{30}\) \(+6752.00 q^{31}\) \(-4139.15i q^{32}\) \(-5014.74i q^{33}\) \(+4576.00 q^{34}\) \(+(1980.00 + 2686.47i) q^{35}\) \(+1836.00 q^{36}\) \(+13969.6i q^{37}\) \(-1459.31i q^{38}\) \(-2376.00 q^{39}\) \(+(-4400.00 - 5969.92i) q^{40}\) \(-198.000 q^{41}\) \(-7880.30i q^{42}\) \(-417.895i q^{43}\) \(-3024.00 q^{44}\) \(+(6885.00 - 5074.44i) q^{45}\) \(-16148.0 q^{46}\) \(-10540.2i q^{47}\) \(+25153.3i q^{48}\) \(+13243.0 q^{49}\) \(+(19800.0 + 6135.76i) q^{50}\) \(-13728.0 q^{51}\) \(+1432.78i q^{52}\) \(-5823.99i q^{53}\) \(+11880.0 q^{54}\) \(+(-11340.0 + 8357.89i) q^{55}\) \(+7920.00 q^{56}\) \(+4377.94i q^{57}\) \(-45968.4i q^{58}\) \(-24660.0 q^{59}\) \(+(-7920.00 - 10745.9i) q^{60}\) \(-5698.00 q^{61}\) \(+44787.7i q^{62}\) \(+9133.98i q^{63}\) \(-12992.0 q^{64}\) \(+(3960.00 + 5372.93i) q^{65}\) \(+33264.0 q^{66}\) \(-43640.1i q^{67}\) \(+8278.30i q^{68}\) \(+48444.0 q^{69}\) \(+(-17820.0 + 13133.8i) q^{70}\) \(+53352.0 q^{71}\) \(-20297.7i q^{72}\) \(+70922.7i q^{73}\) \(-92664.0 q^{74}\) \(+(-59400.0 - 18407.3i) q^{75}\) \(+2640.00 q^{76}\) \(-15044.2i q^{77}\) \(-15760.6i q^{78}\) \(+51920.0 q^{79}\) \(+(56880.0 - 41922.1i) q^{80}\) \(-72819.0 q^{81}\) \(-1313.38i q^{82}\) \(-61841.8i q^{83}\) \(+14256.0 q^{84}\) \(+(22880.0 + 31043.6i) q^{85}\) \(+2772.00 q^{86}\) \(+137905. i q^{87}\) \(+33431.6i q^{88}\) \(-9990.00 q^{89}\) \(+(33660.0 + 45669.9i) q^{90}\) \(-7128.00 q^{91}\) \(-29212.8i q^{92}\) \(-134363. i q^{93}\) \(+69916.0 q^{94}\) \(+(9900.00 - 7296.57i) q^{95}\) \(-82368.0 q^{96}\) \(-101250. i q^{97}\) \(+87844.1i q^{98}\) \(-38556.0 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)  \(=\)  \(2q \) \(\mathstrut -\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut 90q^{5} \) \(\mathstrut +\mathstrut 264q^{6} \) \(\mathstrut -\mathstrut 306q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut 90q^{5} \) \(\mathstrut +\mathstrut 264q^{6} \) \(\mathstrut -\mathstrut 306q^{9} \) \(\mathstrut -\mathstrut 440q^{10} \) \(\mathstrut +\mathstrut 504q^{11} \) \(\mathstrut +\mathstrut 792q^{14} \) \(\mathstrut +\mathstrut 1320q^{15} \) \(\mathstrut -\mathstrut 2528q^{16} \) \(\mathstrut -\mathstrut 440q^{19} \) \(\mathstrut +\mathstrut 1080q^{20} \) \(\mathstrut -\mathstrut 2376q^{21} \) \(\mathstrut +\mathstrut 5280q^{24} \) \(\mathstrut +\mathstrut 1850q^{25} \) \(\mathstrut +\mathstrut 1584q^{26} \) \(\mathstrut -\mathstrut 13860q^{29} \) \(\mathstrut -\mathstrut 11880q^{30} \) \(\mathstrut +\mathstrut 13504q^{31} \) \(\mathstrut +\mathstrut 9152q^{34} \) \(\mathstrut +\mathstrut 3960q^{35} \) \(\mathstrut +\mathstrut 3672q^{36} \) \(\mathstrut -\mathstrut 4752q^{39} \) \(\mathstrut -\mathstrut 8800q^{40} \) \(\mathstrut -\mathstrut 396q^{41} \) \(\mathstrut -\mathstrut 6048q^{44} \) \(\mathstrut +\mathstrut 13770q^{45} \) \(\mathstrut -\mathstrut 32296q^{46} \) \(\mathstrut +\mathstrut 26486q^{49} \) \(\mathstrut +\mathstrut 39600q^{50} \) \(\mathstrut -\mathstrut 27456q^{51} \) \(\mathstrut +\mathstrut 23760q^{54} \) \(\mathstrut -\mathstrut 22680q^{55} \) \(\mathstrut +\mathstrut 15840q^{56} \) \(\mathstrut -\mathstrut 49320q^{59} \) \(\mathstrut -\mathstrut 15840q^{60} \) \(\mathstrut -\mathstrut 11396q^{61} \) \(\mathstrut -\mathstrut 25984q^{64} \) \(\mathstrut +\mathstrut 7920q^{65} \) \(\mathstrut +\mathstrut 66528q^{66} \) \(\mathstrut +\mathstrut 96888q^{69} \) \(\mathstrut -\mathstrut 35640q^{70} \) \(\mathstrut +\mathstrut 106704q^{71} \) \(\mathstrut -\mathstrut 185328q^{74} \) \(\mathstrut -\mathstrut 118800q^{75} \) \(\mathstrut +\mathstrut 5280q^{76} \) \(\mathstrut +\mathstrut 103840q^{79} \) \(\mathstrut +\mathstrut 113760q^{80} \) \(\mathstrut -\mathstrut 145638q^{81} \) \(\mathstrut +\mathstrut 28512q^{84} \) \(\mathstrut +\mathstrut 45760q^{85} \) \(\mathstrut +\mathstrut 5544q^{86} \) \(\mathstrut -\mathstrut 19980q^{89} \) \(\mathstrut +\mathstrut 67320q^{90} \) \(\mathstrut -\mathstrut 14256q^{91} \) \(\mathstrut +\mathstrut 139832q^{94} \) \(\mathstrut +\mathstrut 19800q^{95} \) \(\mathstrut -\mathstrut 164736q^{96} \) \(\mathstrut -\mathstrut 77112q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.63325i 1.17260i 0.810093 + 0.586302i \(0.199417\pi\)
−0.810093 + 0.586302i \(0.800583\pi\)
\(3\) 19.8997i 1.27657i −0.769800 0.638285i \(-0.779644\pi\)
0.769800 0.638285i \(-0.220356\pi\)
\(4\) −12.0000 −0.375000
\(5\) −45.0000 + 33.1662i −0.804984 + 0.593296i
\(6\) 132.000 1.49691
\(7\) 59.6992i 0.460494i −0.973132 0.230247i \(-0.926047\pi\)
0.973132 0.230247i \(-0.0739534\pi\)
\(8\) 132.665i 0.732877i
\(9\) −153.000 −0.629630
\(10\) −220.000 298.496i −0.695701 0.943928i
\(11\) 252.000 0.627941 0.313970 0.949433i \(-0.398341\pi\)
0.313970 + 0.949433i \(0.398341\pi\)
\(12\) 238.797i 0.478714i
\(13\) 119.398i 0.195948i −0.995189 0.0979739i \(-0.968764\pi\)
0.995189 0.0979739i \(-0.0312362\pi\)
\(14\) 396.000 0.539977
\(15\) 660.000 + 895.489i 0.757383 + 1.02762i
\(16\) −1264.00 −1.23438
\(17\) 689.858i 0.578945i −0.957186 0.289473i \(-0.906520\pi\)
0.957186 0.289473i \(-0.0934799\pi\)
\(18\) 1014.89i 0.738306i
\(19\) −220.000 −0.139810 −0.0699051 0.997554i \(-0.522270\pi\)
−0.0699051 + 0.997554i \(0.522270\pi\)
\(20\) 540.000 397.995i 0.301869 0.222486i
\(21\) −1188.00 −0.587852
\(22\) 1671.58i 0.736326i
\(23\) 2434.40i 0.959561i 0.877388 + 0.479781i \(0.159284\pi\)
−0.877388 + 0.479781i \(0.840716\pi\)
\(24\) 2640.00 0.935569
\(25\) 925.000 2984.96i 0.296000 0.955188i
\(26\) 792.000 0.229769
\(27\) 1790.98i 0.472804i
\(28\) 716.391i 0.172685i
\(29\) −6930.00 −1.53016 −0.765082 0.643932i \(-0.777302\pi\)
−0.765082 + 0.643932i \(0.777302\pi\)
\(30\) −5940.00 + 4377.94i −1.20499 + 0.888111i
\(31\) 6752.00 1.26191 0.630955 0.775820i \(-0.282663\pi\)
0.630955 + 0.775820i \(0.282663\pi\)
\(32\) 4139.15i 0.714556i
\(33\) 5014.74i 0.801610i
\(34\) 4576.00 0.678873
\(35\) 1980.00 + 2686.47i 0.273209 + 0.370690i
\(36\) 1836.00 0.236111
\(37\) 13969.6i 1.67757i 0.544464 + 0.838785i \(0.316733\pi\)
−0.544464 + 0.838785i \(0.683267\pi\)
\(38\) 1459.31i 0.163942i
\(39\) −2376.00 −0.250141
\(40\) −4400.00 5969.92i −0.434813 0.589955i
\(41\) −198.000 −0.0183952 −0.00919762 0.999958i \(-0.502928\pi\)
−0.00919762 + 0.999958i \(0.502928\pi\)
\(42\) 7880.30i 0.689318i
\(43\) 417.895i 0.0344664i −0.999851 0.0172332i \(-0.994514\pi\)
0.999851 0.0172332i \(-0.00548577\pi\)
\(44\) −3024.00 −0.235478
\(45\) 6885.00 5074.44i 0.506842 0.373557i
\(46\) −16148.0 −1.12519
\(47\) 10540.2i 0.695994i −0.937496 0.347997i \(-0.886862\pi\)
0.937496 0.347997i \(-0.113138\pi\)
\(48\) 25153.3i 1.57577i
\(49\) 13243.0 0.787945
\(50\) 19800.0 + 6135.76i 1.12006 + 0.347091i
\(51\) −13728.0 −0.739064
\(52\) 1432.78i 0.0734804i
\(53\) 5823.99i 0.284794i −0.989810 0.142397i \(-0.954519\pi\)
0.989810 0.142397i \(-0.0454810\pi\)
\(54\) 11880.0 0.554411
\(55\) −11340.0 + 8357.89i −0.505483 + 0.372555i
\(56\) 7920.00 0.337485
\(57\) 4377.94i 0.178477i
\(58\) 45968.4i 1.79428i
\(59\) −24660.0 −0.922281 −0.461140 0.887327i \(-0.652560\pi\)
−0.461140 + 0.887327i \(0.652560\pi\)
\(60\) −7920.00 10745.9i −0.284019 0.385357i
\(61\) −5698.00 −0.196064 −0.0980320 0.995183i \(-0.531255\pi\)
−0.0980320 + 0.995183i \(0.531255\pi\)
\(62\) 44787.7i 1.47972i
\(63\) 9133.98i 0.289941i
\(64\) −12992.0 −0.396484
\(65\) 3960.00 + 5372.93i 0.116255 + 0.157735i
\(66\) 33264.0 0.939971
\(67\) 43640.1i 1.18768i −0.804583 0.593840i \(-0.797611\pi\)
0.804583 0.593840i \(-0.202389\pi\)
\(68\) 8278.30i 0.217104i
\(69\) 48444.0 1.22495
\(70\) −17820.0 + 13133.8i −0.434673 + 0.320366i
\(71\) 53352.0 1.25604 0.628022 0.778196i \(-0.283865\pi\)
0.628022 + 0.778196i \(0.283865\pi\)
\(72\) 20297.7i 0.461441i
\(73\) 70922.7i 1.55768i 0.627223 + 0.778840i \(0.284192\pi\)
−0.627223 + 0.778840i \(0.715808\pi\)
\(74\) −92664.0 −1.96712
\(75\) −59400.0 18407.3i −1.21936 0.377865i
\(76\) 2640.00 0.0524288
\(77\) 15044.2i 0.289163i
\(78\) 15760.6i 0.293316i
\(79\) 51920.0 0.935981 0.467990 0.883734i \(-0.344978\pi\)
0.467990 + 0.883734i \(0.344978\pi\)
\(80\) 56880.0 41922.1i 0.993653 0.732350i
\(81\) −72819.0 −1.23320
\(82\) 1313.38i 0.0215703i
\(83\) 61841.8i 0.985342i −0.870216 0.492671i \(-0.836021\pi\)
0.870216 0.492671i \(-0.163979\pi\)
\(84\) 14256.0 0.220445
\(85\) 22880.0 + 31043.6i 0.343486 + 0.466042i
\(86\) 2772.00 0.0404154
\(87\) 137905.i 1.95336i
\(88\) 33431.6i 0.460204i
\(89\) −9990.00 −0.133687 −0.0668437 0.997763i \(-0.521293\pi\)
−0.0668437 + 0.997763i \(0.521293\pi\)
\(90\) 33660.0 + 45669.9i 0.438034 + 0.594325i
\(91\) −7128.00 −0.0902328
\(92\) 29212.8i 0.359836i
\(93\) 134363.i 1.61092i
\(94\) 69916.0 0.816125
\(95\) 9900.00 7296.57i 0.112545 0.0829488i
\(96\) −82368.0 −0.912180
\(97\) 101250.i 1.09261i −0.837586 0.546305i \(-0.816034\pi\)
0.837586 0.546305i \(-0.183966\pi\)
\(98\) 87844.1i 0.923948i
\(99\) −38556.0 −0.395370
\(100\) −11100.0 + 35819.5i −0.111000 + 0.358195i
\(101\) −109098. −1.06418 −0.532088 0.846689i \(-0.678592\pi\)
−0.532088 + 0.846689i \(0.678592\pi\)
\(102\) 91061.3i 0.866629i
\(103\) 70624.2i 0.655935i 0.944689 + 0.327967i \(0.106364\pi\)
−0.944689 + 0.327967i \(0.893636\pi\)
\(104\) 15840.0 0.143606
\(105\) 53460.0 39401.5i 0.473212 0.348770i
\(106\) 38632.0 0.333951
\(107\) 97117.4i 0.820045i 0.912075 + 0.410022i \(0.134479\pi\)
−0.912075 + 0.410022i \(0.865521\pi\)
\(108\) 21491.7i 0.177301i
\(109\) −21010.0 −0.169379 −0.0846895 0.996407i \(-0.526990\pi\)
−0.0846895 + 0.996407i \(0.526990\pi\)
\(110\) −55440.0 75221.1i −0.436859 0.592731i
\(111\) 277992. 2.14153
\(112\) 75459.8i 0.568422i
\(113\) 105018.i 0.773688i 0.922145 + 0.386844i \(0.126435\pi\)
−0.922145 + 0.386844i \(0.873565\pi\)
\(114\) −29040.0 −0.209283
\(115\) −80740.0 109548.i −0.569304 0.772432i
\(116\) 83160.0 0.573812
\(117\) 18268.0i 0.123375i
\(118\) 163576.i 1.08147i
\(119\) −41184.0 −0.266601
\(120\) −118800. + 87558.9i −0.753119 + 0.555069i
\(121\) −97547.0 −0.605690
\(122\) 37796.3i 0.229905i
\(123\) 3940.15i 0.0234828i
\(124\) −81024.0 −0.473216
\(125\) 57375.0 + 165002.i 0.328434 + 0.944527i
\(126\) −60588.0 −0.339985
\(127\) 87220.6i 0.479855i −0.970791 0.239927i \(-0.922876\pi\)
0.970791 0.239927i \(-0.0771236\pi\)
\(128\) 218632.i 1.17947i
\(129\) −8316.00 −0.0439987
\(130\) −35640.0 + 26267.7i −0.184961 + 0.136321i
\(131\) 192852. 0.981852 0.490926 0.871201i \(-0.336659\pi\)
0.490926 + 0.871201i \(0.336659\pi\)
\(132\) 60176.8i 0.300604i
\(133\) 13133.8i 0.0643817i
\(134\) 289476. 1.39268
\(135\) 59400.0 + 80594.0i 0.280512 + 0.380599i
\(136\) 91520.0 0.424296
\(137\) 143570.i 0.653525i −0.945106 0.326763i \(-0.894042\pi\)
0.945106 0.326763i \(-0.105958\pi\)
\(138\) 321341.i 1.43638i
\(139\) −318340. −1.39751 −0.698754 0.715362i \(-0.746262\pi\)
−0.698754 + 0.715362i \(0.746262\pi\)
\(140\) −23760.0 32237.6i −0.102453 0.139009i
\(141\) −209748. −0.888485
\(142\) 353897.i 1.47284i
\(143\) 30088.4i 0.123044i
\(144\) 193392. 0.777199
\(145\) 311850. 229842.i 1.23176 0.907841i
\(146\) −470448. −1.82654
\(147\) 263532.i 1.00587i
\(148\) 167635.i 0.629088i
\(149\) 84150.0 0.310519 0.155260 0.987874i \(-0.450379\pi\)
0.155260 + 0.987874i \(0.450379\pi\)
\(150\) 122100. 394015.i 0.443085 1.42983i
\(151\) −155848. −0.556236 −0.278118 0.960547i \(-0.589711\pi\)
−0.278118 + 0.960547i \(0.589711\pi\)
\(152\) 29186.3i 0.102464i
\(153\) 105548.i 0.364521i
\(154\) 99792.0 0.339074
\(155\) −303840. + 223939.i −1.01582 + 0.748686i
\(156\) 28512.0 0.0938029
\(157\) 356643.i 1.15474i 0.816482 + 0.577371i \(0.195921\pi\)
−0.816482 + 0.577371i \(0.804079\pi\)
\(158\) 344398.i 1.09753i
\(159\) −115896. −0.363560
\(160\) 137280. + 186262.i 0.423943 + 0.575206i
\(161\) 145332. 0.441872
\(162\) 483027.i 1.44605i
\(163\) 144890.i 0.427139i −0.976928 0.213570i \(-0.931491\pi\)
0.976928 0.213570i \(-0.0685090\pi\)
\(164\) 2376.00 0.00689822
\(165\) 166320. + 225663.i 0.475592 + 0.645284i
\(166\) 410212. 1.15542
\(167\) 18102.1i 0.0502272i −0.999685 0.0251136i \(-0.992005\pi\)
0.999685 0.0251136i \(-0.00799474\pi\)
\(168\) 157606.i 0.430824i
\(169\) 357037. 0.961604
\(170\) −205920. + 151769.i −0.546482 + 0.402773i
\(171\) 33660.0 0.0880286
\(172\) 5014.74i 0.0129249i
\(173\) 492572.i 1.25128i −0.780112 0.625640i \(-0.784838\pi\)
0.780112 0.625640i \(-0.215162\pi\)
\(174\) −914760. −2.29052
\(175\) −178200. 55221.8i −0.439858 0.136306i
\(176\) −318528. −0.775115
\(177\) 490728.i 1.17736i
\(178\) 66266.2i 0.156762i
\(179\) 444420. 1.03672 0.518359 0.855163i \(-0.326543\pi\)
0.518359 + 0.855163i \(0.326543\pi\)
\(180\) −82620.0 + 60893.2i −0.190066 + 0.140084i
\(181\) 156902. 0.355985 0.177993 0.984032i \(-0.443040\pi\)
0.177993 + 0.984032i \(0.443040\pi\)
\(182\) 47281.8i 0.105807i
\(183\) 113389.i 0.250289i
\(184\) −322960. −0.703241
\(185\) −463320. 628633.i −0.995295 1.35042i
\(186\) 891264. 1.88897
\(187\) 173844.i 0.363543i
\(188\) 126483.i 0.260998i
\(189\) −106920. −0.217723
\(190\) 48400.0 + 65669.2i 0.0972661 + 0.131971i
\(191\) 332352. 0.659196 0.329598 0.944121i \(-0.393087\pi\)
0.329598 + 0.944121i \(0.393087\pi\)
\(192\) 258538.i 0.506140i
\(193\) 786120.i 1.51913i 0.650430 + 0.759566i \(0.274589\pi\)
−0.650430 + 0.759566i \(0.725411\pi\)
\(194\) 671616. 1.28120
\(195\) 106920. 78803.0i 0.201360 0.148408i
\(196\) −158916. −0.295480
\(197\) 59606.4i 0.109428i 0.998502 + 0.0547138i \(0.0174247\pi\)
−0.998502 + 0.0547138i \(0.982575\pi\)
\(198\) 255752.i 0.463613i
\(199\) −395800. −0.708505 −0.354253 0.935150i \(-0.615265\pi\)
−0.354253 + 0.935150i \(0.615265\pi\)
\(200\) 396000. + 122715.i 0.700036 + 0.216932i
\(201\) −868428. −1.51616
\(202\) 723674.i 1.24786i
\(203\) 413716.i 0.704631i
\(204\) 164736. 0.277149
\(205\) 8910.00 6566.92i 0.0148079 0.0109138i
\(206\) −468468. −0.769151
\(207\) 372464.i 0.604168i
\(208\) 150920.i 0.241873i
\(209\) −55440.0 −0.0877925
\(210\) 261360. + 354614.i 0.408969 + 0.554890i
\(211\) −251548. −0.388969 −0.194484 0.980906i \(-0.562303\pi\)
−0.194484 + 0.980906i \(0.562303\pi\)
\(212\) 69887.9i 0.106798i
\(213\) 1.06169e6i 1.60343i
\(214\) −644204. −0.961588
\(215\) 13860.0 + 18805.3i 0.0204488 + 0.0277449i
\(216\) 237600. 0.346507
\(217\) 403089.i 0.581101i
\(218\) 139365.i 0.198615i
\(219\) 1.41134e6 1.98849
\(220\) 136080. 100295.i 0.189556 0.139708i
\(221\) −82368.0 −0.113443
\(222\) 1.84399e6i 2.51117i
\(223\) 288765.i 0.388851i −0.980917 0.194425i \(-0.937716\pi\)
0.980917 0.194425i \(-0.0622842\pi\)
\(224\) −247104. −0.329048
\(225\) −141525. + 456699.i −0.186370 + 0.601415i
\(226\) −696608. −0.907230
\(227\) 1.16414e6i 1.49948i 0.661731 + 0.749741i \(0.269822\pi\)
−0.661731 + 0.749741i \(0.730178\pi\)
\(228\) 52535.3i 0.0669290i
\(229\) 547670. 0.690129 0.345064 0.938579i \(-0.387857\pi\)
0.345064 + 0.938579i \(0.387857\pi\)
\(230\) 726660. 535569.i 0.905757 0.667568i
\(231\) −299376. −0.369137
\(232\) 919368.i 1.12142i
\(233\) 48104.3i 0.0580489i 0.999579 + 0.0290245i \(0.00924007\pi\)
−0.999579 + 0.0290245i \(0.990760\pi\)
\(234\) −121176. −0.144669
\(235\) 349580. + 474311.i 0.412930 + 0.560264i
\(236\) 295920. 0.345855
\(237\) 1.03319e6i 1.19484i
\(238\) 273184.i 0.312617i
\(239\) −1.00584e6 −1.13903 −0.569514 0.821982i \(-0.692868\pi\)
−0.569514 + 0.821982i \(0.692868\pi\)
\(240\) −834240. 1.13190e6i −0.934895 1.26847i
\(241\) 895202. 0.992838 0.496419 0.868083i \(-0.334648\pi\)
0.496419 + 0.868083i \(0.334648\pi\)
\(242\) 647054.i 0.710235i
\(243\) 1.01387e6i 1.10146i
\(244\) 68376.0 0.0735240
\(245\) −595935. + 439221.i −0.634284 + 0.467485i
\(246\) −26136.0 −0.0275360
\(247\) 26267.7i 0.0273955i
\(248\) 895754.i 0.924825i
\(249\) −1.23064e6 −1.25786
\(250\) −1.09450e6 + 380583.i −1.10756 + 0.385123i
\(251\) 558252. 0.559301 0.279651 0.960102i \(-0.409781\pi\)
0.279651 + 0.960102i \(0.409781\pi\)
\(252\) 109608.i 0.108728i
\(253\) 613469.i 0.602548i
\(254\) 578556. 0.562680
\(255\) 617760. 455306.i 0.594935 0.438483i
\(256\) 1.03450e6 0.986572
\(257\) 787924.i 0.744135i −0.928206 0.372067i \(-0.878649\pi\)
0.928206 0.372067i \(-0.121351\pi\)
\(258\) 55162.1i 0.0515931i
\(259\) 833976. 0.772510
\(260\) −47520.0 64475.2i −0.0435956 0.0591506i
\(261\) 1.06029e6 0.963437
\(262\) 1.27924e6i 1.15132i
\(263\) 1.63173e6i 1.45465i −0.686291 0.727327i \(-0.740762\pi\)
0.686291 0.727327i \(-0.259238\pi\)
\(264\) 665280. 0.587482
\(265\) 193160. + 262080.i 0.168967 + 0.229255i
\(266\) −87120.0 −0.0754942
\(267\) 198798.i 0.170661i
\(268\) 523682.i 0.445380i
\(269\) −1.73637e6 −1.46306 −0.731529 0.681810i \(-0.761193\pi\)
−0.731529 + 0.681810i \(0.761193\pi\)
\(270\) −534600. + 394015.i −0.446292 + 0.328930i
\(271\) −1.72005e6 −1.42271 −0.711357 0.702831i \(-0.751919\pi\)
−0.711357 + 0.702831i \(0.751919\pi\)
\(272\) 871980.i 0.714635i
\(273\) 141845.i 0.115188i
\(274\) 952336. 0.766326
\(275\) 233100. 752211.i 0.185871 0.599802i
\(276\) −581328. −0.459355
\(277\) 1.27243e6i 0.996402i 0.867062 + 0.498201i \(0.166006\pi\)
−0.867062 + 0.498201i \(0.833994\pi\)
\(278\) 2.11163e6i 1.63872i
\(279\) −1.03306e6 −0.794536
\(280\) −356400. + 262677.i −0.271671 + 0.200229i
\(281\) 1.46500e6 1.10681 0.553404 0.832913i \(-0.313329\pi\)
0.553404 + 0.832913i \(0.313329\pi\)
\(282\) 1.39131e6i 1.04184i
\(283\) 1.65051e6i 1.22504i −0.790455 0.612521i \(-0.790156\pi\)
0.790455 0.612521i \(-0.209844\pi\)
\(284\) −640224. −0.471016
\(285\) −145200. 197008.i −0.105890 0.143672i
\(286\) 199584. 0.144281
\(287\) 11820.5i 0.00847089i
\(288\) 633290.i 0.449905i
\(289\) 943953. 0.664823
\(290\) 1.52460e6 + 2.06858e6i 1.06454 + 1.44437i
\(291\) −2.01485e6 −1.39479
\(292\) 851072.i 0.584130i
\(293\) 2.38772e6i 1.62485i 0.583064 + 0.812426i \(0.301854\pi\)
−0.583064 + 0.812426i \(0.698146\pi\)
\(294\) 1.74808e6 1.17948
\(295\) 1.10970e6 817880.i 0.742422 0.547185i
\(296\) −1.85328e6 −1.22945
\(297\) 451326.i 0.296893i
\(298\) 558188.i 0.364116i
\(299\) 290664. 0.188024
\(300\) 712800. + 220887.i 0.457261 + 0.141699i
\(301\) −24948.0 −0.0158716
\(302\) 1.03378e6i 0.652244i
\(303\) 2.17102e6i 1.35849i
\(304\) 278080. 0.172578
\(305\) 256410. 188981.i 0.157828 0.116324i
\(306\) −700128. −0.427439
\(307\) 928264.i 0.562115i 0.959691 + 0.281058i \(0.0906852\pi\)
−0.959691 + 0.281058i \(0.909315\pi\)
\(308\) 180531.i 0.108436i
\(309\) 1.40540e6 0.837346
\(310\) −1.48544e6 2.01545e6i −0.877912 1.19115i
\(311\) 568152. 0.333092 0.166546 0.986034i \(-0.446739\pi\)
0.166546 + 0.986034i \(0.446739\pi\)
\(312\) 315212.i 0.183323i
\(313\) 1.72244e6i 0.993766i −0.867818 0.496883i \(-0.834478\pi\)
0.867818 0.496883i \(-0.165522\pi\)
\(314\) −2.36570e6 −1.35405
\(315\) −302940. 411029.i −0.172021 0.233398i
\(316\) −623040. −0.350993
\(317\) 131643.i 0.0735785i 0.999323 + 0.0367893i \(0.0117130\pi\)
−0.999323 + 0.0367893i \(0.988287\pi\)
\(318\) 768767.i 0.426311i
\(319\) −1.74636e6 −0.960853
\(320\) 584640. 430896.i 0.319164 0.235233i
\(321\) 1.93261e6 1.04684
\(322\) 964023.i 0.518141i
\(323\) 151769.i 0.0809424i
\(324\) 873828. 0.462449
\(325\) −356400. 110444.i −0.187167 0.0580006i
\(326\) 961092. 0.500865
\(327\) 418094.i 0.216224i
\(328\) 26267.7i 0.0134815i
\(329\) −629244. −0.320501
\(330\) −1.49688e6 + 1.10324e6i −0.756662 + 0.557681i
\(331\) −1.58055e6 −0.792935 −0.396468 0.918049i \(-0.629764\pi\)
−0.396468 + 0.918049i \(0.629764\pi\)
\(332\) 742101.i 0.369503i
\(333\) 2.13735e6i 1.05625i
\(334\) 120076. 0.0588966
\(335\) 1.44738e6 + 1.96381e6i 0.704645 + 0.956063i
\(336\) 1.50163e6 0.725630
\(337\) 1.22885e6i 0.589419i 0.955587 + 0.294709i \(0.0952228\pi\)
−0.955587 + 0.294709i \(0.904777\pi\)
\(338\) 2.36832e6i 1.12758i
\(339\) 2.08982e6 0.987667
\(340\) −274560. 372523.i −0.128807 0.174766i
\(341\) 1.70150e6 0.792405
\(342\) 223275.i 0.103223i
\(343\) 1.79396e6i 0.823338i
\(344\) 55440.0 0.0252596
\(345\) −2.17998e6 + 1.60671e6i −0.986063 + 0.726756i
\(346\) 3.26735e6 1.46726
\(347\) 3.84224e6i 1.71301i −0.516137 0.856506i \(-0.672630\pi\)
0.516137 0.856506i \(-0.327370\pi\)
\(348\) 1.65486e6i 0.732511i
\(349\) −1.59445e6 −0.700725 −0.350362 0.936614i \(-0.613942\pi\)
−0.350362 + 0.936614i \(0.613942\pi\)
\(350\) 366300. 1.18205e6i 0.159833 0.515779i
\(351\) −213840. −0.0926448
\(352\) 1.04307e6i 0.448699i
\(353\) 295365.i 0.126160i −0.998008 0.0630802i \(-0.979908\pi\)
0.998008 0.0630802i \(-0.0200924\pi\)
\(354\) −3.25512e6 −1.38057
\(355\) −2.40084e6 + 1.76949e6i −1.01110 + 0.745206i
\(356\) 119880. 0.0501328
\(357\) 819551.i 0.340334i
\(358\) 2.94795e6i 1.21566i
\(359\) 1.10484e6 0.452442 0.226221 0.974076i \(-0.427363\pi\)
0.226221 + 0.974076i \(0.427363\pi\)
\(360\) 673200. + 913398.i 0.273771 + 0.371453i
\(361\) −2.42770e6 −0.980453
\(362\) 1.04077e6i 0.417430i
\(363\) 1.94116e6i 0.773206i
\(364\) 85536.0 0.0338373
\(365\) −2.35224e6 3.19152e6i −0.924165 1.25391i
\(366\) −752136. −0.293490
\(367\) 1.83760e6i 0.712174i −0.934453 0.356087i \(-0.884111\pi\)
0.934453 0.356087i \(-0.115889\pi\)
\(368\) 3.07708e6i 1.18446i
\(369\) 30294.0 0.0115822
\(370\) 4.16988e6 3.07332e6i 1.58350 1.16709i
\(371\) −347688. −0.131146
\(372\) 1.61236e6i 0.604093i
\(373\) 2.93350e6i 1.09173i 0.837874 + 0.545864i \(0.183798\pi\)
−0.837874 + 0.545864i \(0.816202\pi\)
\(374\) 1.15315e6 0.426292
\(375\) 3.28350e6 1.14175e6i 1.20575 0.419268i
\(376\) 1.39832e6 0.510078
\(377\) 827432.i 0.299832i
\(378\) 709227.i 0.255303i
\(379\) 5.09342e6 1.82143 0.910713 0.413040i \(-0.135533\pi\)
0.910713 + 0.413040i \(0.135533\pi\)
\(380\) −118800. + 87558.9i −0.0422044 + 0.0311058i
\(381\) −1.73567e6 −0.612568
\(382\) 2.20457e6i 0.772976i
\(383\) 3.17485e6i 1.10593i 0.833205 + 0.552964i \(0.186503\pi\)
−0.833205 + 0.552964i \(0.813497\pi\)
\(384\) −4.35072e6 −1.50568
\(385\) 498960. + 676989.i 0.171559 + 0.232772i
\(386\) −5.21453e6 −1.78134
\(387\) 63937.9i 0.0217011i
\(388\) 1.21500e6i 0.409729i
\(389\) 1.79991e6 0.603083 0.301541 0.953453i \(-0.402499\pi\)
0.301541 + 0.953453i \(0.402499\pi\)
\(390\) 522720. + 709227.i 0.174023 + 0.236115i
\(391\) 1.67939e6 0.555533
\(392\) 1.75688e6i 0.577467i
\(393\) 3.83771e6i 1.25340i
\(394\) −395384. −0.128315
\(395\) −2.33640e6 + 1.72199e6i −0.753450 + 0.555314i
\(396\) 462672. 0.148264
\(397\) 4.90405e6i 1.56163i −0.624760 0.780817i \(-0.714803\pi\)
0.624760 0.780817i \(-0.285197\pi\)
\(398\) 2.62544e6i 0.830796i
\(399\) 261360. 0.0821877
\(400\) −1.16920e6 + 3.77299e6i −0.365375 + 1.17906i
\(401\) −642798. −0.199624 −0.0998122 0.995006i \(-0.531824\pi\)
−0.0998122 + 0.995006i \(0.531824\pi\)
\(402\) 5.76050e6i 1.77785i
\(403\) 806179.i 0.247268i
\(404\) 1.30918e6 0.399066
\(405\) 3.27686e6 2.41513e6i 0.992704 0.731650i
\(406\) −2.74428e6 −0.826254
\(407\) 3.52035e6i 1.05341i
\(408\) 1.82123e6i 0.541643i
\(409\) −2.05711e6 −0.608064 −0.304032 0.952662i \(-0.598333\pi\)
−0.304032 + 0.952662i \(0.598333\pi\)
\(410\) 43560.0 + 59102.3i 0.0127976 + 0.0173638i
\(411\) −2.85701e6 −0.834271
\(412\) 847490.i 0.245975i
\(413\) 1.47218e6i 0.424704i
\(414\) 2.47064e6 0.708450
\(415\) 2.05106e6 + 2.78288e6i 0.584599 + 0.793185i
\(416\) −494208. −0.140016
\(417\) 6.33489e6i 1.78402i
\(418\) 367747.i 0.102946i
\(419\) −2.93742e6 −0.817393 −0.408697 0.912670i \(-0.634017\pi\)
−0.408697 + 0.912670i \(0.634017\pi\)
\(420\) −641520. + 472818.i −0.177454 + 0.130789i
\(421\) 2.71770e6 0.747303 0.373651 0.927569i \(-0.378106\pi\)
0.373651 + 0.927569i \(0.378106\pi\)
\(422\) 1.66858e6i 0.456106i
\(423\) 1.61266e6i 0.438219i
\(424\) 772640. 0.208719
\(425\) −2.05920e6 638119.i −0.553001 0.171368i
\(426\) 7.04246e6 1.88019
\(427\) 340166.i 0.0902862i
\(428\) 1.16541e6i 0.307517i
\(429\) −598752. −0.157074
\(430\) −124740. + 91936.8i −0.0325338 + 0.0239783i
\(431\) 4.99435e6 1.29505 0.647524 0.762045i \(-0.275804\pi\)
0.647524 + 0.762045i \(0.275804\pi\)
\(432\) 2.26380e6i 0.583617i
\(433\) 2.08183e6i 0.533612i −0.963750 0.266806i \(-0.914032\pi\)
0.963750 0.266806i \(-0.0859684\pi\)
\(434\) 2.67379e6 0.681402
\(435\) −4.57380e6 6.20574e6i −1.15892 1.57243i
\(436\) 252120. 0.0635172
\(437\) 535569.i 0.134156i
\(438\) 9.36180e6i 2.33171i
\(439\) −4.70404e6 −1.16496 −0.582478 0.812846i \(-0.697917\pi\)
−0.582478 + 0.812846i \(0.697917\pi\)
\(440\) −1.10880e6 1.50442e6i −0.273037 0.370457i
\(441\) −2.02618e6 −0.496114
\(442\) 546368.i 0.133024i
\(443\) 5.70103e6i 1.38021i −0.723711 0.690103i \(-0.757565\pi\)
0.723711 0.690103i \(-0.242435\pi\)
\(444\) −3.33590e6 −0.803075
\(445\) 449550. 331331.i 0.107616 0.0793162i
\(446\) 1.91545e6 0.455968
\(447\) 1.67456e6i 0.396399i
\(448\) 775613.i 0.182579i
\(449\) 6.20325e6 1.45212 0.726062 0.687630i \(-0.241349\pi\)
0.726062 + 0.687630i \(0.241349\pi\)
\(450\) −3.02940e6 938771.i −0.705221 0.218539i
\(451\) −49896.0 −0.0115511
\(452\) 1.26021e6i 0.290133i
\(453\) 3.10134e6i 0.710074i
\(454\) −7.72204e6 −1.75830
\(455\) 320760. 236409.i 0.0726360 0.0535347i
\(456\) −580800. −0.130802
\(457\) 2.15371e6i 0.482388i −0.970477 0.241194i \(-0.922461\pi\)
0.970477 0.241194i \(-0.0775391\pi\)
\(458\) 3.63283e6i 0.809248i
\(459\) −1.23552e6 −0.273727
\(460\) 968880. + 1.31458e6i 0.213489 + 0.289662i
\(461\) −3.85130e6 −0.844024 −0.422012 0.906590i \(-0.638676\pi\)
−0.422012 + 0.906590i \(0.638676\pi\)
\(462\) 1.98584e6i 0.432851i
\(463\) 2.08213e6i 0.451394i −0.974198 0.225697i \(-0.927534\pi\)
0.974198 0.225697i \(-0.0724659\pi\)
\(464\) 8.75952e6 1.88880
\(465\) 4.45632e6 + 6.04634e6i 0.955749 + 1.29676i
\(466\) −319088. −0.0680684
\(467\) 1.30822e6i 0.277579i 0.990322 + 0.138790i \(0.0443212\pi\)
−0.990322 + 0.138790i \(0.955679\pi\)
\(468\) 219216.i 0.0462655i
\(469\) −2.60528e6 −0.546919
\(470\) −3.14622e6 + 2.31885e6i −0.656968 + 0.484204i
\(471\) 7.09711e6 1.47411
\(472\) 3.27152e6i 0.675919i
\(473\) 105309.i 0.0216429i
\(474\) 6.85344e6 1.40108
\(475\) −203500. + 656692.i −0.0413838 + 0.133545i
\(476\) 494208. 0.0999752
\(477\) 891071.i 0.179315i
\(478\) 6.67199e6i 1.33563i
\(479\) −6.76368e6 −1.34693 −0.673464 0.739220i \(-0.735194\pi\)
−0.673464 + 0.739220i \(0.735194\pi\)
\(480\) 3.70656e6 2.73184e6i 0.734291 0.541193i
\(481\) 1.66795e6 0.328716
\(482\) 5.93810e6i 1.16421i
\(483\) 2.89207e6i 0.564080i
\(484\) 1.17056e6 0.227134
\(485\) 3.35808e6 + 4.55625e6i 0.648241 + 0.879534i
\(486\) −6.72527e6 −1.29157
\(487\) 6.67193e6i 1.27476i 0.770549 + 0.637381i \(0.219982\pi\)
−0.770549 + 0.637381i \(0.780018\pi\)
\(488\) 755925.i 0.143691i
\(489\) −2.88328e6 −0.545273
\(490\) −2.91346e6 3.95299e6i −0.548175 0.743764i
\(491\) −6.87575e6 −1.28711 −0.643556 0.765399i \(-0.722542\pi\)
−0.643556 + 0.765399i \(0.722542\pi\)
\(492\) 47281.8i 0.00880605i
\(493\) 4.78072e6i 0.885881i
\(494\) −174240. −0.0321241
\(495\) 1.73502e6 1.27876e6i 0.318267 0.234572i
\(496\) −8.53453e6 −1.55767
\(497\) 3.18507e6i 0.578400i
\(498\) 8.16312e6i 1.47497i
\(499\) 6.94010e6 1.24771 0.623856 0.781539i \(-0.285565\pi\)
0.623856 + 0.781539i \(0.285565\pi\)
\(500\) −688500. 1.98002e6i −0.123163 0.354198i
\(501\) −360228. −0.0641185
\(502\) 3.70302e6i 0.655839i
\(503\) 921007.i 0.162309i 0.996702 + 0.0811546i \(0.0258607\pi\)
−0.996702 + 0.0811546i \(0.974139\pi\)
\(504\) −1.21176e6 −0.212491
\(505\) 4.90941e6 3.61837e6i 0.856645 0.631371i
\(506\) −4.06930e6 −0.706550
\(507\) 7.10495e6i 1.22755i
\(508\) 1.04665e6i 0.179946i
\(509\) 4.97979e6 0.851955 0.425977 0.904734i \(-0.359930\pi\)
0.425977 + 0.904734i \(0.359930\pi\)
\(510\) 3.02016e6 + 4.09776e6i 0.514167 + 0.697623i
\(511\) 4.23403e6 0.717302
\(512\) 134151.i 0.0226161i
\(513\) 394015.i 0.0661027i
\(514\) 5.22650e6 0.872575
\(515\) −2.34234e6 3.17809e6i −0.389163 0.528017i
\(516\) 99792.0 0.0164995
\(517\) 2.65614e6i 0.437043i
\(518\) 5.53197e6i 0.905848i
\(519\) −9.80206e6 −1.59735
\(520\) −712800. + 525353.i −0.115600 + 0.0852007i
\(521\) −147798. −0.0238547 −0.0119274 0.999929i \(-0.503797\pi\)
−0.0119274 + 0.999929i \(0.503797\pi\)
\(522\) 7.03317e6i 1.12973i
\(523\) 1.23884e7i 1.98043i 0.139543 + 0.990216i \(0.455437\pi\)
−0.139543 + 0.990216i \(0.544563\pi\)
\(524\) −2.31422e6 −0.368194
\(525\) −1.09890e6 + 3.54614e6i −0.174004 + 0.561509i
\(526\) 1.08237e7 1.70573
\(527\) 4.65792e6i 0.730576i
\(528\) 6.33863e6i 0.989488i
\(529\) 510027. 0.0792417
\(530\) −1.73844e6 + 1.28128e6i −0.268825 + 0.198132i
\(531\) 3.77298e6 0.580695
\(532\) 157606.i 0.0241431i
\(533\) 23640.9i 0.00360451i
\(534\) −1.31868e6 −0.200118
\(535\) −3.22102e6 4.37028e6i −0.486529 0.660123i
\(536\) 5.78952e6 0.870423
\(537\) 8.84385e6i 1.32344i
\(538\) 1.15178e7i 1.71559i
\(539\) 3.33724e6 0.494783
\(540\) −712800. 967128.i −0.105192 0.142725i
\(541\) −9.99810e6 −1.46867 −0.734335 0.678787i \(-0.762506\pi\)
−0.734335 + 0.678787i \(0.762506\pi\)
\(542\) 1.14095e7i 1.66828i
\(543\) 3.12231e6i 0.454440i
\(544\) −2.85542e6 −0.413688
\(545\) 945450. 696823.i 0.136348 0.100492i
\(546\) −940896. −0.135070
\(547\) 1.18580e7i 1.69451i 0.531189 + 0.847253i \(0.321745\pi\)
−0.531189 + 0.847253i \(0.678255\pi\)
\(548\) 1.72284e6i 0.245072i
\(549\) 871794. 0.123448
\(550\) 4.98960e6 + 1.54621e6i 0.703330 + 0.217953i
\(551\) 1.52460e6 0.213933
\(552\) 6.42682e6i 0.897736i
\(553\) 3.09958e6i 0.431013i
\(554\) −8.44034e6 −1.16838
\(555\) −1.25096e7 + 9.21995e6i −1.72390 + 1.27056i
\(556\) 3.82008e6 0.524065
\(557\) 904550.i 0.123536i 0.998091 + 0.0617681i \(0.0196739\pi\)
−0.998091 + 0.0617681i \(0.980326\pi\)
\(558\) 6.85252e6i 0.931676i
\(559\) −49896.0 −0.00675361
\(560\) −2.50272e6 3.39569e6i −0.337242 0.457571i
\(561\) −3.45946e6 −0.464088
\(562\) 9.71772e6i 1.29785i
\(563\) 8.68719e6i 1.15507i −0.816366 0.577535i \(-0.804015\pi\)
0.816366 0.577535i \(-0.195985\pi\)
\(564\) 2.51698e6 0.333182
\(565\) −3.48304e6 4.72579e6i −0.459026 0.622807i
\(566\) 1.09482e7 1.43649
\(567\) 4.34724e6i 0.567879i
\(568\) 7.07794e6i 0.920526i
\(569\) −2.27007e6 −0.293940 −0.146970 0.989141i \(-0.546952\pi\)
−0.146970 + 0.989141i \(0.546952\pi\)
\(570\) 1.30680e6 963148.i 0.168470 0.124167i
\(571\) 1.43807e7 1.84582 0.922908 0.385021i \(-0.125806\pi\)
0.922908 + 0.385021i \(0.125806\pi\)
\(572\) 361061.i 0.0461414i
\(573\) 6.61372e6i 0.841510i
\(574\) −78408.0 −0.00993300
\(575\) 7.26660e6 + 2.25182e6i 0.916562 + 0.284030i
\(576\) 1.98778e6 0.249638
\(577\) 5.63943e6i 0.705173i 0.935779 + 0.352586i \(0.114698\pi\)
−0.935779 + 0.352586i \(0.885302\pi\)
\(578\) 6.26148e6i 0.779574i
\(579\) 1.56436e7 1.93928
\(580\) −3.74220e6 + 2.75811e6i −0.461910 + 0.340440i
\(581\) −3.69191e6 −0.453744
\(582\) 1.33650e7i 1.63554i
\(583\) 1.46765e6i 0.178834i
\(584\) −9.40896e6 −1.14159
\(585\) −605880. 822059.i −0.0731976 0.0993146i
\(586\) −1.58383e7 −1.90531
\(587\) 1.28473e6i 0.153893i 0.997035 + 0.0769464i \(0.0245170\pi\)
−0.997035 + 0.0769464i \(0.975483\pi\)
\(588\) 3.16239e6i 0.377200i
\(589\) −1.48544e6 −0.176428
\(590\) 5.42520e6 + 7.36092e6i 0.641632 + 0.870566i
\(591\) 1.18615e6 0.139692
\(592\) 1.76576e7i 2.07075i
\(593\) 7.00943e6i 0.818552i 0.912411 + 0.409276i \(0.134219\pi\)
−0.912411 + 0.409276i \(0.865781\pi\)
\(594\) 2.99376e6 0.348138
\(595\) 1.85328e6 1.36592e6i 0.214609 0.158173i
\(596\) −1.00980e6 −0.116445
\(597\) 7.87632e6i 0.904456i
\(598\) 1.92805e6i 0.220478i
\(599\) −8.80020e6 −1.00213 −0.501067 0.865409i \(-0.667059\pi\)
−0.501067 + 0.865409i \(0.667059\pi\)
\(600\) 2.44200e6 7.88030e6i 0.276928 0.893644i
\(601\) −1.07670e7 −1.21593 −0.607965 0.793964i \(-0.708014\pi\)
−0.607965 + 0.793964i \(0.708014\pi\)
\(602\) 165486.i 0.0186110i
\(603\) 6.67694e6i 0.747798i
\(604\) 1.87018e6 0.208588
\(605\) 4.38962e6 3.23527e6i 0.487571 0.359353i
\(606\) −1.44009e7 −1.59298
\(607\) 1.51219e7i 1.66584i −0.553391 0.832921i \(-0.686667\pi\)
0.553391 0.832921i \(-0.313333\pi\)
\(608\) 910613.i 0.0999021i
\(609\) 8.23284e6 0.899511
\(610\) 1.25356e6 + 1.70083e6i 0.136402 + 0.185070i
\(611\) −1.25849e6 −0.136379
\(612\) 1.26658e6i 0.136695i
\(613\) 8.31622e6i 0.893871i −0.894566 0.446936i \(-0.852515\pi\)
0.894566 0.446936i \(-0.147485\pi\)
\(614\) −6.15740e6 −0.659139
\(615\) −130680. 177307.i −0.0139323 0.0189033i
\(616\) 1.99584e6 0.211921
\(617\) 1.21083e7i 1.28047i 0.768178 + 0.640237i \(0.221164\pi\)
−0.768178 + 0.640237i \(0.778836\pi\)
\(618\) 9.32240e6i 0.981875i
\(619\) 9.73238e6 1.02092 0.510461 0.859901i \(-0.329475\pi\)
0.510461 + 0.859901i \(0.329475\pi\)
\(620\) 3.64608e6 2.68726e6i 0.380932 0.280757i
\(621\) 4.35996e6 0.453684
\(622\) 3.76869e6i 0.390584i
\(623\) 596395.i 0.0615622i
\(624\) 3.00326e6 0.308768
\(625\) −8.05437e6 5.52218e6i −0.824768 0.565471i
\(626\) 1.14254e7 1.16529
\(627\) 1.10324e6i 0.112073i
\(628\) 4.27972e6i 0.433028i
\(629\) 9.63706e6 0.971220
\(630\) 2.72646e6 2.00948e6i 0.273683 0.201712i
\(631\) −8.60145e6 −0.859999 −0.430000 0.902829i \(-0.641486\pi\)
−0.430000 + 0.902829i \(0.641486\pi\)
\(632\) 6.88797e6i 0.685959i
\(633\) 5.00574e6i 0.496546i
\(634\) −873224. −0.0862785
\(635\) 2.89278e6 + 3.92493e6i 0.284696 + 0.386276i
\(636\) 1.39075e6 0.136335
\(637\) 1.58119e6i 0.154396i
\(638\) 1.15840e7i 1.12670i
\(639\) −8.16286e6 −0.790842
\(640\) 7.25120e6 + 9.83844e6i 0.699777 + 0.949459i
\(641\) −6.42440e6 −0.617572 −0.308786 0.951132i \(-0.599923\pi\)
−0.308786 + 0.951132i \(0.599923\pi\)
\(642\) 1.28195e7i 1.22753i
\(643\) 3.64721e6i 0.347883i 0.984756 + 0.173941i \(0.0556503\pi\)
−0.984756 + 0.173941i \(0.944350\pi\)
\(644\) −1.74398e6 −0.165702
\(645\) 374220. 275811.i 0.0354183 0.0261043i
\(646\) −1.00672e6 −0.0949134
\(647\) 3.78036e6i 0.355036i 0.984118 + 0.177518i \(0.0568068\pi\)
−0.984118 + 0.177518i \(0.943193\pi\)
\(648\) 9.66053e6i 0.903782i
\(649\) −6.21432e6 −0.579138
\(650\) 732600. 2.36409e6i 0.0680117 0.219473i
\(651\) −8.02138e6 −0.741816
\(652\) 1.73868e6i 0.160177i
\(653\) 1.66957e7i 1.53223i −0.642706 0.766113i \(-0.722188\pi\)
0.642706 0.766113i \(-0.277812\pi\)
\(654\) −2.77332e6 −0.253545
\(655\) −8.67834e6 + 6.39618e6i −0.790375 + 0.582529i
\(656\) 250272. 0.0227066
\(657\) 1.08512e7i 0.980761i
\(658\) 4.17393e6i 0.375821i
\(659\) −1.22166e6 −0.109581 −0.0547907 0.998498i \(-0.517449\pi\)
−0.0547907 + 0.998498i \(0.517449\pi\)
\(660\) −1.99584e6 2.70796e6i −0.178347 0.241981i
\(661\) 1.62789e7 1.44918 0.724589 0.689182i \(-0.242030\pi\)
0.724589 + 0.689182i \(0.242030\pi\)
\(662\) 1.04842e7i 0.929799i
\(663\) 1.63910e6i 0.144818i
\(664\) 8.20424e6 0.722135
\(665\) −435600. 591023.i −0.0381974 0.0518263i
\(666\) 1.41776e7 1.23856
\(667\) 1.68704e7i 1.46829i
\(668\) 217226.i 0.0188352i
\(669\) −5.74636e6 −0.496395
\(670\) −1.30264e7 + 9.60083e6i −1.12108 + 0.826270i
\(671\) −1.43590e6 −0.123117
\(672\) 4.91731e6i 0.420053i
\(673\) 1.43928e7i 1.22492i 0.790503 + 0.612459i \(0.209819\pi\)
−0.790503 + 0.612459i \(0.790181\pi\)
\(674\) −8.15126e6 −0.691155
\(675\) −5.34600e6 1.65665e6i −0.451616 0.139950i
\(676\) −4.28444e6 −0.360602
\(677\) 2.62429e6i 0.220059i 0.993928 + 0.110030i \(0.0350946\pi\)
−0.993928 + 0.110030i \(0.964905\pi\)
\(678\) 1.38623e7i 1.15814i
\(679\) −6.04454e6 −0.503140
\(680\) −4.11840e6 + 3.03538e6i −0.341552 + 0.251733i
\(681\) 2.31661e7 1.91419
\(682\) 1.12865e7i 0.929177i
\(683\) 1.03039e7i 0.845184i 0.906320 + 0.422592i \(0.138880\pi\)
−0.906320 + 0.422592i \(0.861120\pi\)
\(684\) −403920. −0.0330107
\(685\) 4.76168e6 + 6.46065e6i 0.387734 + 0.526078i
\(686\) 1.18998e7 0.965449
\(687\) 1.08985e7i 0.880998i
\(688\) 528219.i 0.0425444i
\(689\) −695376. −0.0558048
\(690\) −1.06577e7 1.44604e7i −0.852197 1.15626i
\(691\) 4.50285e6 0.358751 0.179375 0.983781i \(-0.442592\pi\)
0.179375 + 0.983781i \(0.442592\pi\)
\(692\) 5.91086e6i 0.469230i
\(693\) 2.30176e6i 0.182066i
\(694\) 2.54865e7 2.00868
\(695\) 1.43253e7 1.05581e7i 1.12497 0.829136i
\(696\) −1.82952e7 −1.43157
\(697\) 136592.i 0.0106498i
\(698\) 1.05764e7i 0.821672i
\(699\) 957264. 0.0741035
\(700\) 2.13840e6 + 662662.i 0.164947 + 0.0511148i
\(701\) −4.88090e6 −0.375150 −0.187575 0.982250i \(-0.560063\pi\)
−0.187575 + 0.982250i \(0.560063\pi\)
\(702\) 1.41845e6i 0.108636i
\(703\) 3.07332e6i 0.234541i
\(704\) −3.27398e6 −0.248969
\(705\) 9.43866e6 6.95655e6i 0.715217 0.527134i
\(706\) 1.95923e6 0.147936
\(707\) 6.51307e6i 0.490046i
\(708\) 5.88873e6i 0.441508i
\(709\) −9.96961e6 −0.744839 −0.372420 0.928064i \(-0.621472\pi\)
−0.372420 + 0.928064i \(0.621472\pi\)
\(710\) −1.17374e7 1.59254e7i −0.873831 1.18561i
\(711\) −7.94376e6 −0.589321
\(712\) 1.32532e6i 0.0979765i
\(713\) 1.64371e7i 1.21088i
\(714\) −5.43629e6 −0.399077
\(715\) 997920. + 1.35398e6i 0.0730013 + 0.0990482i
\(716\) −5.33304e6 −0.388770
\(717\) 2.00160e7i 1.45405i
\(718\) 7.32868e6i 0.530536i
\(719\) −1.19167e7 −0.859675 −0.429838 0.902906i \(-0.641429\pi\)
−0.429838 + 0.902906i \(0.641429\pi\)
\(720\) −8.70264e6 + 6.41409e6i −0.625633 + 0.461109i
\(721\) 4.21621e6 0.302054
\(722\) 1.61035e7i 1.14968i
\(723\) 1.78143e7i 1.26743i
\(724\) −1.88282e6 −0.133494
\(725\) −6.41025e6 + 2.06858e7i −0.452929 + 1.46160i
\(726\) −1.28762e7 −0.906664
\(727\) 1.38269e6i 0.0970264i −0.998823 0.0485132i \(-0.984552\pi\)
0.998823 0.0485132i \(-0.0154483\pi\)
\(728\) 945636.i 0.0661296i
\(729\) 2.48079e6 0.172890
\(730\) 2.11702e7 1.56030e7i 1.47034 1.08368i
\(731\) −288288. −0.0199541
\(732\) 1.36067e6i 0.0938585i
\(733\) 6.09661e6i 0.419110i −0.977797 0.209555i \(-0.932798\pi\)
0.977797 0.209555i \(-0.0672016\pi\)
\(734\) 1.21893e7 0.835099
\(735\) 8.74038e6 + 1.18590e7i 0.596777 + 0.809707i
\(736\) 1.00764e7 0.685660
\(737\) 1.09973e7i 0.745793i
\(738\) 200948.i 0.0135813i
\(739\) 6.16946e6 0.415562 0.207781 0.978175i \(-0.433376\pi\)
0.207781 + 0.978175i \(0.433376\pi\)
\(740\) 5.55984e6 + 7.54360e6i 0.373236 + 0.506406i
\(741\) 522720. 0.0349723
\(742\) 2.30630e6i 0.153782i
\(743\) 1.57574e7i 1.04716i −0.851978 0.523578i \(-0.824597\pi\)
0.851978 0.523578i \(-0.175403\pi\)
\(744\) 1.78253e7 1.18060
\(745\) −3.78675e6 + 2.79094e6i −0.249963 + 0.184230i
\(746\) −1.94586e7 −1.28016
\(747\) 9.46179e6i 0.620400i
\(748\) 2.08613e6i 0.136329i
\(749\) 5.79784e6 0.377626
\(750\) 7.57350e6 + 2.17803e7i 0.491636 + 1.41387i
\(751\) −1.51816e7 −0.982243 −0.491122 0.871091i \(-0.663413\pi\)
−0.491122 + 0.871091i \(0.663413\pi\)
\(752\) 1.33229e7i 0.859118i
\(753\) 1.11091e7i 0.713987i
\(754\) −5.48856e6 −0.351585
\(755\) 7.01316e6 5.16889e6i 0.447761 0.330012i
\(756\) 1.28304e6 0.0816461
\(757\) 652274.i 0.0413705i −0.999786 0.0206852i \(-0.993415\pi\)
0.999786 0.0206852i \(-0.00658478\pi\)
\(758\) 3.37859e7i 2.13581i
\(759\) 1.22079e7 0.769194
\(760\) 968000. + 1.31338e6i 0.0607913 + 0.0824817i
\(761\) 4.51420e6 0.282566 0.141283 0.989969i \(-0.454877\pi\)
0.141283 + 0.989969i \(0.454877\pi\)
\(762\) 1.15131e7i 0.718300i
\(763\) 1.25428e6i 0.0779980i
\(764\) −3.98822e6 −0.247199
\(765\) −3.50064e6 4.74967e6i −0.216269 0.293434i
\(766\) −2.10596e7 −1.29681
\(767\) 2.94437e6i 0.180719i
\(768\) 2.05862e7i 1.25943i
\(769\) −1.20799e7 −0.736625 −0.368312 0.929702i \(-0.620064\pi\)
−0.368312 + 0.929702i \(0.620064\pi\)
\(770\) −4.49064e6 + 3.30973e6i −0.272949 + 0.201171i
\(771\) −1.56795e7 −0.949939
\(772\) 9.43344e6i 0.569674i
\(773\) 1.04245e7i 0.627492i −0.949507 0.313746i \(-0.898416\pi\)
0.949507 0.313746i \(-0.101584\pi\)
\(774\) −424116. −0.0254467
\(775\) 6.24560e6 2.01545e7i 0.373525 1.20536i
\(776\) 1.34323e7 0.800750
\(777\) 1.65959e7i 0.986163i
\(778\) 1.19393e7i 0.707177i
\(779\) 43560.0 0.00257184
\(780\) −1.28304e6 + 945636.i −0.0755099 + 0.0556529i
\(781\) 1.34447e7 0.788721
\(782\) 1.11398e7i 0.651421i
\(783\) 1.24115e7i 0.723467i
\(784\) −1.67392e7 −0.972620
\(785\) −1.18285e7 1.60489e7i −0.685104 0.929549i
\(786\) 2.54565e7 1.46974
\(787\) 3.45366e7i 1.98766i 0.110913 + 0.993830i \(0.464622\pi\)
−0.110913 + 0.993830i \(0.535378\pi\)
\(788\) 715277.i 0.0410354i
\(789\) −3.24711e7 −1.85697
\(790\) −1.14224e7 1.54979e7i −0.651163 0.883498i
\(791\) 6.26947e6 0.356279