Properties

Label 60.7.c.a.31.14
Level $60$
Weight $7$
Character 60.31
Analytic conductor $13.803$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 60.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.8032450172\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 31.14
Character \(\chi\) \(=\) 60.31
Dual form 60.7.c.a.31.13

$q$-expansion

\(f(q)\) \(=\) \(q+(2.59351 + 7.56794i) q^{2} +15.5885i q^{3} +(-50.5474 + 39.2551i) q^{4} -55.9017 q^{5} +(-117.972 + 40.4289i) q^{6} -671.100i q^{7} +(-428.176 - 280.731i) q^{8} -243.000 q^{9} +O(q^{10})\) \(q+(2.59351 + 7.56794i) q^{2} +15.5885i q^{3} +(-50.5474 + 39.2551i) q^{4} -55.9017 q^{5} +(-117.972 + 40.4289i) q^{6} -671.100i q^{7} +(-428.176 - 280.731i) q^{8} -243.000 q^{9} +(-144.982 - 423.061i) q^{10} +199.628i q^{11} +(-611.927 - 787.955i) q^{12} +2041.73 q^{13} +(5078.84 - 1740.51i) q^{14} -871.421i q^{15} +(1014.07 - 3968.49i) q^{16} -8219.18 q^{17} +(-630.224 - 1839.01i) q^{18} +5147.13i q^{19} +(2825.68 - 2194.43i) q^{20} +10461.4 q^{21} +(-1510.77 + 517.738i) q^{22} -14631.4i q^{23} +(4376.16 - 6674.60i) q^{24} +3125.00 q^{25} +(5295.27 + 15451.7i) q^{26} -3788.00i q^{27} +(26344.1 + 33922.3i) q^{28} -12573.4 q^{29} +(6594.86 - 2260.04i) q^{30} -54422.8i q^{31} +(32663.3 - 2617.90i) q^{32} -3111.89 q^{33} +(-21316.6 - 62202.2i) q^{34} +37515.6i q^{35} +(12283.0 - 9538.99i) q^{36} -11.6361 q^{37} +(-38953.1 + 13349.2i) q^{38} +31827.5i q^{39} +(23935.7 + 15693.3i) q^{40} -67862.4 q^{41} +(27131.8 + 79171.3i) q^{42} -105037. i q^{43} +(-7836.42 - 10090.7i) q^{44} +13584.1 q^{45} +(110729. - 37946.7i) q^{46} +89660.8i q^{47} +(61862.6 + 15807.8i) q^{48} -332726. q^{49} +(8104.73 + 23649.8i) q^{50} -128124. i q^{51} +(-103204. + 80148.5i) q^{52} -1369.17 q^{53} +(28667.3 - 9824.22i) q^{54} -11159.5i q^{55} +(-188398. + 287349. i) q^{56} -80235.8 q^{57} +(-32609.2 - 95154.5i) q^{58} -5601.86i q^{59} +(34207.7 + 44048.0i) q^{60} -132681. q^{61} +(411868. - 141146. i) q^{62} +163077. i q^{63} +(104525. + 240404. i) q^{64} -114136. q^{65} +(-8070.74 - 23550.6i) q^{66} +325492. i q^{67} +(415458. - 322645. i) q^{68} +228081. q^{69} +(-283916. + 97297.4i) q^{70} +303340. i q^{71} +(104047. + 68217.5i) q^{72} -247561. q^{73} +(-30.1783 - 88.0611i) q^{74} +48713.9i q^{75} +(-202051. - 260174. i) q^{76} +133970. q^{77} +(-240868. + 82545.0i) q^{78} -389964. i q^{79} +(-56688.3 + 221845. i) q^{80} +59049.0 q^{81} +(-176002. - 513578. i) q^{82} -215366. i q^{83} +(-528797. + 410664. i) q^{84} +459466. q^{85} +(794916. - 272416. i) q^{86} -195999. i q^{87} +(56041.7 - 85475.8i) q^{88} +46200.5 q^{89} +(35230.6 + 102804. i) q^{90} -1.37021e6i q^{91} +(574357. + 739578. i) q^{92} +848367. q^{93} +(-678547. + 232537. i) q^{94} -287733. i q^{95} +(40809.0 + 509170. i) q^{96} +800223. q^{97} +(-862931. - 2.51805e6i) q^{98} -48509.6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 20q^{2} - 246q^{4} + 162q^{6} - 340q^{8} - 5832q^{9} + O(q^{10}) \) \( 24q + 20q^{2} - 246q^{4} + 162q^{6} - 340q^{8} - 5832q^{9} - 750q^{10} + 5040q^{13} - 2596q^{14} + 4194q^{16} - 4860q^{18} + 7000q^{20} + 19440q^{21} + 45780q^{22} + 24786q^{24} + 75000q^{25} + 75852q^{26} + 54300q^{28} + 132800q^{29} - 10700q^{32} - 173484q^{34} + 59778q^{36} - 69840q^{37} + 215800q^{38} - 14250q^{40} - 70448q^{41} - 189540q^{42} - 395668q^{44} - 158760q^{46} + 252720q^{48} - 642984q^{49} + 62500q^{50} - 210240q^{52} - 644320q^{53} - 39366q^{54} - 917708q^{56} + 408240q^{57} - 1345020q^{58} + 222750q^{60} - 222864q^{61} + 1948520q^{62} + 935922q^{64} + 266000q^{65} - 640548q^{66} + 572680q^{68} - 541728q^{69} + 220500q^{70} + 82620q^{72} + 771120q^{73} - 589164q^{74} - 191544q^{76} + 1383840q^{77} - 693360q^{78} - 946000q^{80} + 1417176q^{81} + 2672520q^{82} + 1256796q^{84} - 372000q^{85} + 1781528q^{86} + 956940q^{88} - 1566224q^{89} + 182250q^{90} - 3040560q^{92} + 1496880q^{93} - 3788352q^{94} - 413262q^{96} - 1666800q^{97} - 2709660q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.59351 + 7.56794i 0.324189 + 0.945992i
\(3\) 15.5885i 0.577350i
\(4\) −50.5474 + 39.2551i −0.789803 + 0.613361i
\(5\) −55.9017 −0.447214
\(6\) −117.972 + 40.4289i −0.546169 + 0.187171i
\(7\) 671.100i 1.95656i −0.207288 0.978280i \(-0.566464\pi\)
0.207288 0.978280i \(-0.433536\pi\)
\(8\) −428.176 280.731i −0.836281 0.548302i
\(9\) −243.000 −0.333333
\(10\) −144.982 423.061i −0.144982 0.423061i
\(11\) 199.628i 0.149983i 0.997184 + 0.0749917i \(0.0238930\pi\)
−0.997184 + 0.0749917i \(0.976107\pi\)
\(12\) −611.927 787.955i −0.354124 0.455993i
\(13\) 2041.73 0.929328 0.464664 0.885487i \(-0.346175\pi\)
0.464664 + 0.885487i \(0.346175\pi\)
\(14\) 5078.84 1740.51i 1.85089 0.634296i
\(15\) 871.421i 0.258199i
\(16\) 1014.07 3968.49i 0.247576 0.968868i
\(17\) −8219.18 −1.67294 −0.836472 0.548009i \(-0.815386\pi\)
−0.836472 + 0.548009i \(0.815386\pi\)
\(18\) −630.224 1839.01i −0.108063 0.315331i
\(19\) 5147.13i 0.750420i 0.926940 + 0.375210i \(0.122429\pi\)
−0.926940 + 0.375210i \(0.877571\pi\)
\(20\) 2825.68 2194.43i 0.353210 0.274303i
\(21\) 10461.4 1.12962
\(22\) −1510.77 + 517.738i −0.141883 + 0.0486230i
\(23\) 14631.4i 1.20255i −0.799044 0.601273i \(-0.794660\pi\)
0.799044 0.601273i \(-0.205340\pi\)
\(24\) 4376.16 6674.60i 0.316562 0.482827i
\(25\) 3125.00 0.200000
\(26\) 5295.27 + 15451.7i 0.301278 + 0.879137i
\(27\) 3788.00i 0.192450i
\(28\) 26344.1 + 33922.3i 1.20008 + 1.54530i
\(29\) −12573.4 −0.515534 −0.257767 0.966207i \(-0.582987\pi\)
−0.257767 + 0.966207i \(0.582987\pi\)
\(30\) 6594.86 2260.04i 0.244254 0.0837053i
\(31\) 54422.8i 1.82682i −0.407041 0.913410i \(-0.633439\pi\)
0.407041 0.913410i \(-0.366561\pi\)
\(32\) 32663.3 2617.90i 0.996804 0.0798919i
\(33\) −3111.89 −0.0865930
\(34\) −21316.6 62202.2i −0.542351 1.58259i
\(35\) 37515.6i 0.875000i
\(36\) 12283.0 9538.99i 0.263268 0.204454i
\(37\) −11.6361 −0.000229721 −0.000114861 1.00000i \(-0.500037\pi\)
−0.000114861 1.00000i \(0.500037\pi\)
\(38\) −38953.1 + 13349.2i −0.709891 + 0.243278i
\(39\) 31827.5i 0.536548i
\(40\) 23935.7 + 15693.3i 0.373996 + 0.245208i
\(41\) −67862.4 −0.984640 −0.492320 0.870414i \(-0.663851\pi\)
−0.492320 + 0.870414i \(0.663851\pi\)
\(42\) 27131.8 + 79171.3i 0.366211 + 1.06861i
\(43\) 105037.i 1.32111i −0.750778 0.660554i \(-0.770321\pi\)
0.750778 0.660554i \(-0.229679\pi\)
\(44\) −7836.42 10090.7i −0.0919940 0.118457i
\(45\) 13584.1 0.149071
\(46\) 110729. 37946.7i 1.13760 0.389853i
\(47\) 89660.8i 0.863592i 0.901971 + 0.431796i \(0.142120\pi\)
−0.901971 + 0.431796i \(0.857880\pi\)
\(48\) 61862.6 + 15807.8i 0.559376 + 0.142938i
\(49\) −332726. −2.82813
\(50\) 8104.73 + 23649.8i 0.0648379 + 0.189198i
\(51\) 128124.i 0.965875i
\(52\) −103204. + 80148.5i −0.733985 + 0.570014i
\(53\) −1369.17 −0.00919668 −0.00459834 0.999989i \(-0.501464\pi\)
−0.00459834 + 0.999989i \(0.501464\pi\)
\(54\) 28667.3 9824.22i 0.182056 0.0623903i
\(55\) 11159.5i 0.0670746i
\(56\) −188398. + 287349.i −1.07279 + 1.63623i
\(57\) −80235.8 −0.433255
\(58\) −32609.2 95154.5i −0.167131 0.487691i
\(59\) 5601.86i 0.0272757i −0.999907 0.0136379i \(-0.995659\pi\)
0.999907 0.0136379i \(-0.00434120\pi\)
\(60\) 34207.7 + 44048.0i 0.158369 + 0.203926i
\(61\) −132681. −0.584548 −0.292274 0.956335i \(-0.594412\pi\)
−0.292274 + 0.956335i \(0.594412\pi\)
\(62\) 411868. 141146.i 1.72816 0.592235i
\(63\) 163077.i 0.652187i
\(64\) 104525. + 240404.i 0.398730 + 0.917068i
\(65\) −114136. −0.415608
\(66\) −8070.74 23550.6i −0.0280725 0.0819163i
\(67\) 325492.i 1.08222i 0.840951 + 0.541111i \(0.181996\pi\)
−0.840951 + 0.541111i \(0.818004\pi\)
\(68\) 415458. 322645.i 1.32130 1.02612i
\(69\) 228081. 0.694290
\(70\) −283916. + 97297.4i −0.827743 + 0.283666i
\(71\) 303340.i 0.847529i 0.905772 + 0.423764i \(0.139292\pi\)
−0.905772 + 0.423764i \(0.860708\pi\)
\(72\) 104047. + 68217.5i 0.278760 + 0.182767i
\(73\) −247561. −0.636376 −0.318188 0.948028i \(-0.603074\pi\)
−0.318188 + 0.948028i \(0.603074\pi\)
\(74\) −30.1783 88.0611i −7.44732e−5 0.000217315i
\(75\) 48713.9i 0.115470i
\(76\) −202051. 260174.i −0.460278 0.592683i
\(77\) 133970. 0.293452
\(78\) −240868. + 82545.0i −0.507570 + 0.173943i
\(79\) 389964.i 0.790939i −0.918479 0.395470i \(-0.870582\pi\)
0.918479 0.395470i \(-0.129418\pi\)
\(80\) −56688.3 + 221845.i −0.110719 + 0.433291i
\(81\) 59049.0 0.111111
\(82\) −176002. 513578.i −0.319210 0.931462i
\(83\) 215366.i 0.376654i −0.982106 0.188327i \(-0.939694\pi\)
0.982106 0.188327i \(-0.0603065\pi\)
\(84\) −528797. + 410664.i −0.892177 + 0.692865i
\(85\) 459466. 0.748164
\(86\) 794916. 272416.i 1.24976 0.428289i
\(87\) 195999.i 0.297644i
\(88\) 56041.7 85475.8i 0.0822362 0.125428i
\(89\) 46200.5 0.0655355 0.0327677 0.999463i \(-0.489568\pi\)
0.0327677 + 0.999463i \(0.489568\pi\)
\(90\) 35230.6 + 102804.i 0.0483273 + 0.141020i
\(91\) 1.37021e6i 1.81829i
\(92\) 574357. + 739578.i 0.737595 + 0.949774i
\(93\) 848367. 1.05471
\(94\) −678547. + 232537.i −0.816952 + 0.279968i
\(95\) 287733.i 0.335598i
\(96\) 40809.0 + 509170.i 0.0461256 + 0.575505i
\(97\) 800223. 0.876791 0.438396 0.898782i \(-0.355547\pi\)
0.438396 + 0.898782i \(0.355547\pi\)
\(98\) −862931. 2.51805e6i −0.916849 2.67539i
\(99\) 48509.6i 0.0499945i
\(100\) −157961. + 122672.i −0.157961 + 0.122672i
\(101\) 850500. 0.825487 0.412743 0.910847i \(-0.364571\pi\)
0.412743 + 0.910847i \(0.364571\pi\)
\(102\) 969637. 332292.i 0.913710 0.313126i
\(103\) 591093.i 0.540934i −0.962729 0.270467i \(-0.912822\pi\)
0.962729 0.270467i \(-0.0871781\pi\)
\(104\) −874220. 573177.i −0.777179 0.509552i
\(105\) −584811. −0.505182
\(106\) −3550.97 10361.8i −0.00298147 0.00869999i
\(107\) 1.02379e6i 0.835718i 0.908512 + 0.417859i \(0.137219\pi\)
−0.908512 + 0.417859i \(0.862781\pi\)
\(108\) 148698. + 191473.i 0.118041 + 0.151998i
\(109\) −1.78875e6 −1.38125 −0.690623 0.723215i \(-0.742663\pi\)
−0.690623 + 0.723215i \(0.742663\pi\)
\(110\) 84454.7 28942.4i 0.0634521 0.0217449i
\(111\) 181.389i 0.000132630i
\(112\) −2.66325e6 680543.i −1.89565 0.484397i
\(113\) 2.22824e6 1.54428 0.772142 0.635450i \(-0.219186\pi\)
0.772142 + 0.635450i \(0.219186\pi\)
\(114\) −208093. 607219.i −0.140457 0.409856i
\(115\) 817919.i 0.537795i
\(116\) 635551. 493569.i 0.407170 0.316209i
\(117\) −496141. −0.309776
\(118\) 42394.5 14528.5i 0.0258026 0.00884250i
\(119\) 5.51589e6i 3.27322i
\(120\) −244635. + 373121.i −0.141571 + 0.215927i
\(121\) 1.73171e6 0.977505
\(122\) −344111. 1.00412e6i −0.189504 0.552978i
\(123\) 1.05787e6i 0.568482i
\(124\) 2.13637e6 + 2.75093e6i 1.12050 + 1.44283i
\(125\) −174693. −0.0894427
\(126\) −1.23416e6 + 422943.i −0.616964 + 0.211432i
\(127\) 1.20836e6i 0.589908i −0.955511 0.294954i \(-0.904696\pi\)
0.955511 0.294954i \(-0.0953043\pi\)
\(128\) −1.54828e6 + 1.41453e6i −0.738275 + 0.674499i
\(129\) 1.63737e6 0.762742
\(130\) −296014. 863777.i −0.134736 0.393162i
\(131\) 283537.i 0.126123i 0.998010 + 0.0630616i \(0.0200865\pi\)
−0.998010 + 0.0630616i \(0.979914\pi\)
\(132\) 157298. 122158.i 0.0683914 0.0531128i
\(133\) 3.45424e6 1.46824
\(134\) −2.46331e6 + 844169.i −1.02377 + 0.350845i
\(135\) 211755.i 0.0860663i
\(136\) 3.51925e6 + 2.30737e6i 1.39905 + 0.917279i
\(137\) −4.15204e6 −1.61473 −0.807364 0.590053i \(-0.799107\pi\)
−0.807364 + 0.590053i \(0.799107\pi\)
\(138\) 591531. + 1.72610e6i 0.225082 + 0.656793i
\(139\) 3.85092e6i 1.43391i 0.697122 + 0.716953i \(0.254464\pi\)
−0.697122 + 0.716953i \(0.745536\pi\)
\(140\) −1.47268e6 1.89632e6i −0.536691 0.691077i
\(141\) −1.39767e6 −0.498595
\(142\) −2.29566e6 + 786716.i −0.801756 + 0.274760i
\(143\) 407587.i 0.139384i
\(144\) −246419. + 964342.i −0.0825253 + 0.322956i
\(145\) 702873. 0.230554
\(146\) −642054. 1.87353e6i −0.206306 0.602007i
\(147\) 5.18669e6i 1.63282i
\(148\) 588.173 456.776i 0.000181435 0.000140902i
\(149\) −3.30508e6 −0.999132 −0.499566 0.866276i \(-0.666507\pi\)
−0.499566 + 0.866276i \(0.666507\pi\)
\(150\) −368664. + 126340.i −0.109234 + 0.0374342i
\(151\) 2.96350e6i 0.860743i −0.902652 0.430371i \(-0.858383\pi\)
0.902652 0.430371i \(-0.141617\pi\)
\(152\) 1.44496e6 2.20387e6i 0.411456 0.627561i
\(153\) 1.99726e6 0.557648
\(154\) 347454. + 1.01388e6i 0.0951339 + 0.277603i
\(155\) 3.04233e6i 0.816979i
\(156\) −1.24939e6 1.60879e6i −0.329098 0.423767i
\(157\) 3010.29 0.000777874 0.000388937 1.00000i \(-0.499876\pi\)
0.000388937 1.00000i \(0.499876\pi\)
\(158\) 2.95122e6 1.01138e6i 0.748222 0.256414i
\(159\) 21343.3i 0.00530971i
\(160\) −1.82593e6 + 146345.i −0.445784 + 0.0357287i
\(161\) −9.81912e6 −2.35285
\(162\) 153144. + 446879.i 0.0360210 + 0.105110i
\(163\) 1.03461e6i 0.238899i 0.992840 + 0.119449i \(0.0381129\pi\)
−0.992840 + 0.119449i \(0.961887\pi\)
\(164\) 3.43026e6 2.66395e6i 0.777671 0.603940i
\(165\) 173960. 0.0387256
\(166\) 1.62988e6 558555.i 0.356312 0.122107i
\(167\) 593738.i 0.127481i −0.997967 0.0637405i \(-0.979697\pi\)
0.997967 0.0637405i \(-0.0203030\pi\)
\(168\) −4.47932e6 2.93684e6i −0.944680 0.619373i
\(169\) −658135. −0.136350
\(170\) 1.19163e6 + 3.47721e6i 0.242547 + 0.707757i
\(171\) 1.25075e6i 0.250140i
\(172\) 4.12325e6 + 5.30936e6i 0.810317 + 1.04341i
\(173\) 1.01324e6 0.195692 0.0978458 0.995202i \(-0.468805\pi\)
0.0978458 + 0.995202i \(0.468805\pi\)
\(174\) 1.48331e6 508327.i 0.281569 0.0964930i
\(175\) 2.09719e6i 0.391312i
\(176\) 792221. + 202437.i 0.145314 + 0.0371323i
\(177\) 87324.3 0.0157476
\(178\) 119822. + 349642.i 0.0212459 + 0.0619960i
\(179\) 1.05856e7i 1.84569i −0.385176 0.922843i \(-0.625859\pi\)
0.385176 0.922843i \(-0.374141\pi\)
\(180\) −686641. + 533246.i −0.117737 + 0.0914345i
\(181\) −2.44921e6 −0.413038 −0.206519 0.978443i \(-0.566214\pi\)
−0.206519 + 0.978443i \(0.566214\pi\)
\(182\) 1.03696e7 3.55365e6i 1.72008 0.589469i
\(183\) 2.06830e6i 0.337489i
\(184\) −4.10748e6 + 6.26480e6i −0.659358 + 1.00567i
\(185\) 650.477 0.000102735
\(186\) 2.20025e6 + 6.42039e6i 0.341927 + 0.997752i
\(187\) 1.64078e6i 0.250914i
\(188\) −3.51964e6 4.53212e6i −0.529694 0.682068i
\(189\) −2.54212e6 −0.376540
\(190\) 2.17755e6 746240.i 0.317473 0.108797i
\(191\) 5.41860e6i 0.777655i 0.921311 + 0.388827i \(0.127120\pi\)
−0.921311 + 0.388827i \(0.872880\pi\)
\(192\) −3.74753e6 + 1.62938e6i −0.529470 + 0.230207i
\(193\) 9.97092e6 1.38696 0.693479 0.720477i \(-0.256077\pi\)
0.693479 + 0.720477i \(0.256077\pi\)
\(194\) 2.07539e6 + 6.05604e6i 0.284246 + 0.829437i
\(195\) 1.77921e6i 0.239951i
\(196\) 1.68184e7 1.30612e7i 2.23366 1.73466i
\(197\) 1.33406e7 1.74492 0.872459 0.488687i \(-0.162524\pi\)
0.872459 + 0.488687i \(0.162524\pi\)
\(198\) 367118. 125810.i 0.0472944 0.0162077i
\(199\) 6.57996e6i 0.834957i −0.908687 0.417479i \(-0.862914\pi\)
0.908687 0.417479i \(-0.137086\pi\)
\(200\) −1.33805e6 877283.i −0.167256 0.109660i
\(201\) −5.07392e6 −0.624821
\(202\) 2.20578e6 + 6.43653e6i 0.267614 + 0.780904i
\(203\) 8.43799e6i 1.00867i
\(204\) 5.02953e6 + 6.47634e6i 0.592430 + 0.762851i
\(205\) 3.79362e6 0.440344
\(206\) 4.47336e6 1.53301e6i 0.511719 0.175365i
\(207\) 3.55543e6i 0.400849i
\(208\) 2.07046e6 8.10259e6i 0.230079 0.900396i
\(209\) −1.02751e6 −0.112551
\(210\) −1.51672e6 4.42581e6i −0.163775 0.477898i
\(211\) 870512.i 0.0926675i 0.998926 + 0.0463337i \(0.0147538\pi\)
−0.998926 + 0.0463337i \(0.985246\pi\)
\(212\) 69208.1 53747.1i 0.00726356 0.00564089i
\(213\) −4.72860e6 −0.489321
\(214\) −7.74798e6 + 2.65521e6i −0.790582 + 0.270931i
\(215\) 5.87177e6i 0.590818i
\(216\) −1.06341e6 + 1.62193e6i −0.105521 + 0.160942i
\(217\) −3.65231e7 −3.57428
\(218\) −4.63916e6 1.35372e7i −0.447785 1.30665i
\(219\) 3.85910e6i 0.367412i
\(220\) 438069. + 564086.i 0.0411410 + 0.0529757i
\(221\) −1.67814e7 −1.55471
\(222\) 1372.74 470.434i 0.000125467 4.29971e-5i
\(223\) 5.16242e6i 0.465521i 0.972534 + 0.232760i \(0.0747758\pi\)
−0.972534 + 0.232760i \(0.925224\pi\)
\(224\) −1.75687e6 2.19203e7i −0.156313 1.95031i
\(225\) −759375. −0.0666667
\(226\) 5.77898e6 + 1.68632e7i 0.500640 + 1.46088i
\(227\) 3.88936e6i 0.332506i −0.986083 0.166253i \(-0.946833\pi\)
0.986083 0.166253i \(-0.0531669\pi\)
\(228\) 4.05571e6 3.14967e6i 0.342186 0.265742i
\(229\) 1.00633e7 0.837978 0.418989 0.907991i \(-0.362385\pi\)
0.418989 + 0.907991i \(0.362385\pi\)
\(230\) −6.18996e6 + 2.12129e6i −0.508750 + 0.174347i
\(231\) 2.08839e6i 0.169424i
\(232\) 5.38361e6 + 3.52973e6i 0.431131 + 0.282668i
\(233\) 6.03617e6 0.477192 0.238596 0.971119i \(-0.423313\pi\)
0.238596 + 0.971119i \(0.423313\pi\)
\(234\) −1.28675e6 3.75477e6i −0.100426 0.293046i
\(235\) 5.01219e6i 0.386210i
\(236\) 219902. + 283159.i 0.0167299 + 0.0215424i
\(237\) 6.07894e6 0.456649
\(238\) −4.17439e7 + 1.43055e7i −3.09644 + 1.06114i
\(239\) 1.34966e6i 0.0988621i −0.998778 0.0494311i \(-0.984259\pi\)
0.998778 0.0494311i \(-0.0157408\pi\)
\(240\) −3.45822e6 883683.i −0.250161 0.0639239i
\(241\) 7.74261e6 0.553141 0.276571 0.960994i \(-0.410802\pi\)
0.276571 + 0.960994i \(0.410802\pi\)
\(242\) 4.49121e6 + 1.31055e7i 0.316897 + 0.924712i
\(243\) 920483.i 0.0641500i
\(244\) 6.70669e6 5.20842e6i 0.461677 0.358539i
\(245\) 1.86000e7 1.26478
\(246\) 8.00589e6 2.74360e6i 0.537780 0.184296i
\(247\) 1.05091e7i 0.697386i
\(248\) −1.52781e7 + 2.33025e7i −1.00165 + 1.52773i
\(249\) 3.35722e6 0.217461
\(250\) −453068. 1.32206e6i −0.0289964 0.0846121i
\(251\) 1.64750e7i 1.04185i −0.853603 0.520924i \(-0.825587\pi\)
0.853603 0.520924i \(-0.174413\pi\)
\(252\) −6.40162e6 8.24313e6i −0.400026 0.515099i
\(253\) 2.92083e6 0.180362
\(254\) 9.14477e6 3.13389e6i 0.558048 0.191242i
\(255\) 7.16237e6i 0.431952i
\(256\) −1.47205e7 8.04865e6i −0.877412 0.479737i
\(257\) 1.38542e7 0.816175 0.408088 0.912943i \(-0.366196\pi\)
0.408088 + 0.912943i \(0.366196\pi\)
\(258\) 4.24655e6 + 1.23915e7i 0.247273 + 0.721548i
\(259\) 7808.97i 0.000449464i
\(260\) 5.76929e6 4.48044e6i 0.328248 0.254918i
\(261\) 3.05533e6 0.171845
\(262\) −2.14579e6 + 735356.i −0.119312 + 0.0408878i
\(263\) 7.65702e6i 0.420913i 0.977603 + 0.210457i \(0.0674950\pi\)
−0.977603 + 0.210457i \(0.932505\pi\)
\(264\) 1.33244e6 + 873603.i 0.0724160 + 0.0474791i
\(265\) 76539.2 0.00411288
\(266\) 8.95862e6 + 2.61415e7i 0.475988 + 1.38894i
\(267\) 720194.i 0.0378369i
\(268\) −1.27772e7 1.64528e7i −0.663793 0.854742i
\(269\) −3.63062e7 −1.86520 −0.932598 0.360917i \(-0.882464\pi\)
−0.932598 + 0.360917i \(0.882464\pi\)
\(270\) −1.60255e6 + 549191.i −0.0814180 + 0.0279018i
\(271\) 144294.i 0.00725002i −0.999993 0.00362501i \(-0.998846\pi\)
0.999993 0.00362501i \(-0.00115388\pi\)
\(272\) −8.33483e6 + 3.26177e7i −0.414181 + 1.62086i
\(273\) 2.13594e7 1.04979
\(274\) −1.07684e7 3.14224e7i −0.523478 1.52752i
\(275\) 623838.i 0.0299967i
\(276\) −1.15289e7 + 8.95333e6i −0.548352 + 0.425851i
\(277\) 4.74727e6 0.223360 0.111680 0.993744i \(-0.464377\pi\)
0.111680 + 0.993744i \(0.464377\pi\)
\(278\) −2.91436e7 + 9.98743e6i −1.35646 + 0.464857i
\(279\) 1.32247e7i 0.608940i
\(280\) 1.05318e7 1.60633e7i 0.479764 0.731746i
\(281\) 4.52651e6 0.204007 0.102003 0.994784i \(-0.467475\pi\)
0.102003 + 0.994784i \(0.467475\pi\)
\(282\) −3.62489e6 1.05775e7i −0.161639 0.471667i
\(283\) 1.07319e7i 0.473497i 0.971571 + 0.236749i \(0.0760818\pi\)
−0.971571 + 0.236749i \(0.923918\pi\)
\(284\) −1.19076e7 1.53330e7i −0.519841 0.669380i
\(285\) 4.48532e6 0.193758
\(286\) −3.08459e6 + 1.05708e6i −0.131856 + 0.0451867i
\(287\) 4.55424e7i 1.92651i
\(288\) −7.93717e6 + 636149.i −0.332268 + 0.0266306i
\(289\) 4.34173e7 1.79874
\(290\) 1.82291e6 + 5.31930e6i 0.0747431 + 0.218102i
\(291\) 1.24742e7i 0.506216i
\(292\) 1.25136e7 9.71804e6i 0.502612 0.390328i
\(293\) 2.88844e7 1.14831 0.574157 0.818745i \(-0.305330\pi\)
0.574157 + 0.818745i \(0.305330\pi\)
\(294\) 3.92525e7 1.34518e7i 1.54463 0.529343i
\(295\) 313153.i 0.0121981i
\(296\) 4982.29 + 3266.60i 0.000192112 + 0.000125957i
\(297\) 756190. 0.0288643
\(298\) −8.57177e6 2.50126e7i −0.323908 0.945171i
\(299\) 2.98734e7i 1.11756i
\(300\) −1.91227e6 2.46236e6i −0.0708249 0.0911985i
\(301\) −7.04906e7 −2.58483
\(302\) 2.24275e7 7.68587e6i 0.814256 0.279044i
\(303\) 1.32580e7i 0.476595i
\(304\) 2.04263e7 + 5.21956e6i 0.727058 + 0.185786i
\(305\) 7.41711e6 0.261418
\(306\) 5.17992e6 + 1.51151e7i 0.180784 + 0.527531i
\(307\) 4.55936e7i 1.57575i −0.615833 0.787877i \(-0.711180\pi\)
0.615833 0.787877i \(-0.288820\pi\)
\(308\) −6.77185e6 + 5.25902e6i −0.231769 + 0.179992i
\(309\) 9.21423e6 0.312308
\(310\) −2.30241e7 + 7.89032e6i −0.772855 + 0.264856i
\(311\) 2.33624e7i 0.776670i −0.921518 0.388335i \(-0.873050\pi\)
0.921518 0.388335i \(-0.126950\pi\)
\(312\) 8.93494e6 1.36277e7i 0.294190 0.448704i
\(313\) 2.77900e7 0.906266 0.453133 0.891443i \(-0.350306\pi\)
0.453133 + 0.891443i \(0.350306\pi\)
\(314\) 7807.23 + 22781.7i 0.000252179 + 0.000735863i
\(315\) 9.11630e6i 0.291667i
\(316\) 1.53081e7 + 1.97116e7i 0.485131 + 0.624686i
\(317\) 7.68469e6 0.241239 0.120620 0.992699i \(-0.461512\pi\)
0.120620 + 0.992699i \(0.461512\pi\)
\(318\) 161525. 55354.2i 0.00502294 0.00172135i
\(319\) 2.51000e6i 0.0773216i
\(320\) −5.84311e6 1.34390e7i −0.178318 0.410125i
\(321\) −1.59593e7 −0.482502
\(322\) −2.54660e7 7.43105e7i −0.762770 2.22578i
\(323\) 4.23052e7i 1.25541i
\(324\) −2.98477e6 + 2.31798e6i −0.0877558 + 0.0681512i
\(325\) 6.38042e6 0.185866
\(326\) −7.82987e6 + 2.68328e6i −0.225996 + 0.0774484i
\(327\) 2.78839e7i 0.797462i
\(328\) 2.90570e7 + 1.90510e7i 0.823435 + 0.539880i
\(329\) 6.01713e7 1.68967
\(330\) 451168. + 1.31652e6i 0.0125544 + 0.0366341i
\(331\) 2.26621e7i 0.624907i −0.949933 0.312453i \(-0.898849\pi\)
0.949933 0.312453i \(-0.101151\pi\)
\(332\) 8.45421e6 + 1.08862e7i 0.231025 + 0.297482i
\(333\) 2827.57 7.65738e−5
\(334\) 4.49338e6 1.53987e6i 0.120596 0.0413280i
\(335\) 1.81956e7i 0.483984i
\(336\) 1.06086e7 4.15160e7i 0.279667 1.09445i
\(337\) −5.15429e7 −1.34673 −0.673363 0.739312i \(-0.735151\pi\)
−0.673363 + 0.739312i \(0.735151\pi\)
\(338\) −1.70688e6 4.98073e6i −0.0442032 0.128986i
\(339\) 3.47349e7i 0.891593i
\(340\) −2.32248e7 + 1.80364e7i −0.590901 + 0.458895i
\(341\) 1.08643e7 0.273993
\(342\) 9.46561e6 3.24384e6i 0.236630 0.0810927i
\(343\) 1.44338e8i 3.57684i
\(344\) −2.94872e7 + 4.49744e7i −0.724366 + 1.10482i
\(345\) −1.27501e7 −0.310496
\(346\) 2.62784e6 + 7.66811e6i 0.0634411 + 0.185123i
\(347\) 2.69989e7i 0.646186i −0.946367 0.323093i \(-0.895277\pi\)
0.946367 0.323093i \(-0.104723\pi\)
\(348\) 7.69398e6 + 9.90725e6i 0.182563 + 0.235080i
\(349\) −3.98391e7 −0.937201 −0.468601 0.883410i \(-0.655242\pi\)
−0.468601 + 0.883410i \(0.655242\pi\)
\(350\) 1.58714e7 5.43909e6i 0.370178 0.126859i
\(351\) 7.73407e6i 0.178849i
\(352\) 522605. + 6.52050e6i 0.0119825 + 0.149504i
\(353\) −3.70984e7 −0.843395 −0.421697 0.906737i \(-0.638566\pi\)
−0.421697 + 0.906737i \(0.638566\pi\)
\(354\) 226477. + 660865.i 0.00510522 + 0.0148971i
\(355\) 1.69572e7i 0.379026i
\(356\) −2.33531e6 + 1.81360e6i −0.0517601 + 0.0401969i
\(357\) −8.59842e7 −1.88979
\(358\) 8.01114e7 2.74540e7i 1.74600 0.598352i
\(359\) 3.23502e7i 0.699186i −0.936902 0.349593i \(-0.886320\pi\)
0.936902 0.349593i \(-0.113680\pi\)
\(360\) −5.81639e6 3.81348e6i −0.124665 0.0817360i
\(361\) 2.05530e7 0.436870
\(362\) −6.35206e6 1.85355e7i −0.133903 0.390731i
\(363\) 2.69947e7i 0.564363i
\(364\) 5.37876e7 + 6.92604e7i 1.11527 + 1.43609i
\(365\) 1.38391e7 0.284596
\(366\) 1.56527e7 5.36416e6i 0.319262 0.109410i
\(367\) 5.83482e6i 0.118040i 0.998257 + 0.0590200i \(0.0187976\pi\)
−0.998257 + 0.0590200i \(0.981202\pi\)
\(368\) −5.80644e7 1.48373e7i −1.16511 0.297722i
\(369\) 1.64906e7 0.328213
\(370\) 1687.02 + 4922.77i 3.33054e−5 + 9.71861e-5i
\(371\) 918853.i 0.0179939i
\(372\) −4.28827e7 + 3.33028e7i −0.833016 + 0.646921i
\(373\) −1.63274e7 −0.314623 −0.157311 0.987549i \(-0.550283\pi\)
−0.157311 + 0.987549i \(0.550283\pi\)
\(374\) 1.24173e7 4.25538e6i 0.237363 0.0813437i
\(375\) 2.72319e6i 0.0516398i
\(376\) 2.51705e7 3.83906e7i 0.473509 0.722206i
\(377\) −2.56715e7 −0.479100
\(378\) −6.59304e6 1.92386e7i −0.122070 0.356204i
\(379\) 6.49860e7i 1.19372i −0.802346 0.596859i \(-0.796415\pi\)
0.802346 0.596859i \(-0.203585\pi\)
\(380\) 1.12950e7 + 1.45442e7i 0.205843 + 0.265056i
\(381\) 1.88364e7 0.340583
\(382\) −4.10076e7 + 1.40532e7i −0.735656 + 0.252107i
\(383\) 5.64474e7i 1.00473i −0.864657 0.502363i \(-0.832464\pi\)
0.864657 0.502363i \(-0.167536\pi\)
\(384\) −2.20503e7 2.41352e7i −0.389422 0.426243i
\(385\) −7.48917e6 −0.131236
\(386\) 2.58597e7 + 7.54593e7i 0.449637 + 1.31205i
\(387\) 2.55241e7i 0.440370i
\(388\) −4.04492e7 + 3.14129e7i −0.692492 + 0.537790i
\(389\) −8.66539e7 −1.47211 −0.736053 0.676924i \(-0.763313\pi\)
−0.736053 + 0.676924i \(0.763313\pi\)
\(390\) 1.34649e7 4.61441e6i 0.226992 0.0777897i
\(391\) 1.20258e8i 2.01179i
\(392\) 1.42465e8 + 9.34064e7i 2.36511 + 1.55067i
\(393\) −4.41990e6 −0.0728173
\(394\) 3.45989e7 + 1.00960e8i 0.565684 + 1.65068i
\(395\) 2.17996e7i 0.353719i
\(396\) 1.90425e6 + 2.45203e6i 0.0306647 + 0.0394858i
\(397\) 1.11044e8 1.77469 0.887346 0.461105i \(-0.152547\pi\)
0.887346 + 0.461105i \(0.152547\pi\)
\(398\) 4.97968e7 1.70652e7i 0.789863 0.270684i
\(399\) 5.38462e7i 0.847689i
\(400\) 3.16897e6 1.24015e7i 0.0495152 0.193774i
\(401\) −5.61325e7 −0.870525 −0.435262 0.900304i \(-0.643344\pi\)
−0.435262 + 0.900304i \(0.643344\pi\)
\(402\) −1.31593e7 3.83991e7i −0.202560 0.591076i
\(403\) 1.11117e8i 1.69771i
\(404\) −4.29905e7 + 3.33865e7i −0.651971 + 0.506321i
\(405\) −3.30094e6 −0.0496904
\(406\) −6.38582e7 + 2.18840e7i −0.954198 + 0.327001i
\(407\) 2322.89i 3.44544e-5i
\(408\) −3.59684e7 + 5.48597e7i −0.529591 + 0.807742i
\(409\) −5.17276e7 −0.756053 −0.378026 0.925795i \(-0.623397\pi\)
−0.378026 + 0.925795i \(0.623397\pi\)
\(410\) 9.83881e6 + 2.87099e7i 0.142755 + 0.416562i
\(411\) 6.47238e7i 0.932264i
\(412\) 2.32034e7 + 2.98782e7i 0.331788 + 0.427231i
\(413\) −3.75941e6 −0.0533666
\(414\) −2.69072e7 + 9.22105e6i −0.379200 + 0.129951i
\(415\) 1.20393e7i 0.168445i
\(416\) 6.66897e7 5.34505e6i 0.926357 0.0742457i
\(417\) −6.00300e7 −0.827866
\(418\) −2.66486e6 7.77614e6i −0.0364877 0.106472i
\(419\) 2.85658e7i 0.388333i 0.980969 + 0.194167i \(0.0622002\pi\)
−0.980969 + 0.194167i \(0.937800\pi\)
\(420\) 2.95606e7 2.29568e7i 0.398994 0.309859i
\(421\) −1.03346e7 −0.138499 −0.0692496 0.997599i \(-0.522060\pi\)
−0.0692496 + 0.997599i \(0.522060\pi\)
\(422\) −6.58798e6 + 2.25769e6i −0.0876627 + 0.0300418i
\(423\) 2.17876e7i 0.287864i
\(424\) 586247. + 384369.i 0.00769101 + 0.00504256i
\(425\) −2.56849e7 −0.334589
\(426\) −1.22637e7 3.57858e7i −0.158633 0.462894i
\(427\) 8.90424e7i 1.14370i
\(428\) −4.01890e7 5.17499e7i −0.512597 0.660052i
\(429\) −6.35365e6 −0.0804733
\(430\) −4.44372e7 + 1.52285e7i −0.558909 + 0.191537i
\(431\) 3.74717e7i 0.468027i −0.972233 0.234014i \(-0.924814\pi\)
0.972233 0.234014i \(-0.0751860\pi\)
\(432\) −1.50326e7 3.84130e6i −0.186459 0.0476460i
\(433\) −7.74967e7 −0.954595 −0.477298 0.878742i \(-0.658384\pi\)
−0.477298 + 0.878742i \(0.658384\pi\)
\(434\) −9.47233e7 2.76405e8i −1.15874 3.38124i
\(435\) 1.09567e7i 0.133110i
\(436\) 9.04167e7 7.02177e7i 1.09091 0.847202i
\(437\) 7.53096e7 0.902414
\(438\) 2.92054e7 1.00086e7i 0.347569 0.119111i
\(439\) 1.06961e8i 1.26425i 0.774868 + 0.632124i \(0.217817\pi\)
−0.774868 + 0.632124i \(0.782183\pi\)
\(440\) −3.13283e6 + 4.77824e6i −0.0367772 + 0.0560932i
\(441\) 8.08525e7 0.942709
\(442\) −4.35227e7 1.27000e8i −0.504022 1.47075i
\(443\) 6.93528e7i 0.797724i −0.917011 0.398862i \(-0.869405\pi\)
0.917011 0.398862i \(-0.130595\pi\)
\(444\) 7120.43 + 9168.71i 8.13499e−5 + 0.000104751i
\(445\) −2.58268e6 −0.0293083
\(446\) −3.90689e7 + 1.33888e7i −0.440379 + 0.150917i
\(447\) 5.15211e7i 0.576849i
\(448\) 1.61335e8 7.01466e7i 1.79430 0.780140i
\(449\) −1.10854e8 −1.22465 −0.612327 0.790605i \(-0.709766\pi\)
−0.612327 + 0.790605i \(0.709766\pi\)
\(450\) −1.96945e6 5.74690e6i −0.0216126 0.0630661i
\(451\) 1.35472e7i 0.147680i
\(452\) −1.12632e8 + 8.74699e7i −1.21968 + 0.947204i
\(453\) 4.61963e7 0.496950
\(454\) 2.94344e7 1.00871e7i 0.314548 0.107795i
\(455\) 7.65969e7i 0.813162i
\(456\) 3.43550e7 + 2.25246e7i 0.362323 + 0.237554i
\(457\) 1.12207e8 1.17564 0.587818 0.808993i \(-0.299987\pi\)
0.587818 + 0.808993i \(0.299987\pi\)
\(458\) 2.60992e7 + 7.61582e7i 0.271664 + 0.792721i
\(459\) 3.11342e7i 0.321958i
\(460\) −3.21075e7 4.13436e7i −0.329863 0.424752i
\(461\) 1.44607e8 1.47600 0.737998 0.674803i \(-0.235771\pi\)
0.737998 + 0.674803i \(0.235771\pi\)
\(462\) −1.58048e7 + 5.41627e6i −0.160274 + 0.0549256i
\(463\) 9.36261e7i 0.943309i −0.881783 0.471655i \(-0.843657\pi\)
0.881783 0.471655i \(-0.156343\pi\)
\(464\) −1.27503e7 + 4.98972e7i −0.127634 + 0.499485i
\(465\) −4.74252e7 −0.471683
\(466\) 1.56549e7 + 4.56813e7i 0.154701 + 0.451420i
\(467\) 5.11897e7i 0.502611i −0.967908 0.251305i \(-0.919140\pi\)
0.967908 0.251305i \(-0.0808598\pi\)
\(468\) 2.50786e7 1.94761e7i 0.244662 0.190005i
\(469\) 2.18438e8 2.11743
\(470\) 3.79319e7 1.29992e7i 0.365352 0.125205i
\(471\) 46925.8i 0.000449106i
\(472\) −1.57261e6 + 2.39858e6i −0.0149553 + 0.0228101i
\(473\) 2.09684e7 0.198144
\(474\) 1.57658e7 + 4.60050e7i 0.148041 + 0.431986i
\(475\) 1.60848e7i 0.150084i
\(476\) −2.16527e8 2.78814e8i −2.00766 2.58519i
\(477\) 332709. 0.00306556
\(478\) 1.02141e7 3.50036e6i 0.0935228 0.0320500i
\(479\) 1.88871e8i 1.71854i 0.511525 + 0.859269i \(0.329081\pi\)
−0.511525 + 0.859269i \(0.670919\pi\)
\(480\) −2.28129e6 2.84635e7i −0.0206280 0.257374i
\(481\) −23757.8 −0.000213487
\(482\) 2.00806e7 + 5.85956e7i 0.179323 + 0.523267i
\(483\) 1.53065e8i 1.35842i
\(484\) −8.75334e7 + 6.79785e7i −0.772036 + 0.599564i
\(485\) −4.47339e7 −0.392113
\(486\) −6.96616e6 + 2.38729e6i −0.0606854 + 0.0207968i
\(487\) 1.41791e8i 1.22761i −0.789456 0.613807i \(-0.789637\pi\)
0.789456 0.613807i \(-0.210363\pi\)
\(488\) 5.68109e7 + 3.72477e7i 0.488846 + 0.320509i
\(489\) −1.61280e7 −0.137928
\(490\) 4.82393e7 + 1.40763e8i 0.410027 + 1.19647i
\(491\) 1.73081e7i 0.146219i 0.997324 + 0.0731095i \(0.0232923\pi\)
−0.997324 + 0.0731095i \(0.976708\pi\)
\(492\) 4.15268e7 + 5.34725e7i 0.348685 + 0.448989i
\(493\) 1.03343e8 0.862460
\(494\) −7.95319e7 + 2.72554e7i −0.659721 + 0.226085i
\(495\) 2.71177e6i 0.0223582i
\(496\) −2.15976e8 5.51886e7i −1.76995 0.452277i
\(497\) 2.03571e8 1.65824
\(498\) 8.70701e6 + 2.54073e7i 0.0704987 + 0.205717i
\(499\) 2.37084e8i 1.90810i −0.299655 0.954048i \(-0.596872\pi\)
0.299655 0.954048i \(-0.403128\pi\)
\(500\) 8.83026e6 6.85759e6i 0.0706421 0.0548607i
\(501\) 9.25547e6 0.0736012
\(502\) 1.24682e8 4.27282e7i 0.985580 0.337756i
\(503\) 2.25165e7i 0.176928i −0.996079 0.0884640i \(-0.971804\pi\)
0.996079 0.0884640i \(-0.0281958\pi\)
\(504\) 4.57808e7 6.98257e7i 0.357595 0.545411i
\(505\) −4.75444e7 −0.369169
\(506\) 7.57522e6 + 2.21047e7i 0.0584715 + 0.170621i
\(507\) 1.02593e7i 0.0787217i
\(508\) 4.74342e7 + 6.10793e7i 0.361827 + 0.465911i
\(509\) −9.38014e7 −0.711305 −0.355653 0.934618i \(-0.615741\pi\)
−0.355653 + 0.934618i \(0.615741\pi\)
\(510\) −5.42043e7 + 1.85757e7i −0.408624 + 0.140034i
\(511\) 1.66138e8i 1.24511i
\(512\) 2.27338e7 1.32278e8i 0.169380 0.985551i
\(513\) 1.94973e7 0.144418
\(514\) 3.59312e7 + 1.04848e8i 0.264595 + 0.772095i
\(515\) 3.30431e7i 0.241913i
\(516\) −8.27648e7 + 6.42752e7i −0.602416 + 0.467837i
\(517\) −1.78988e7 −0.129525
\(518\) −59097.8 + 20252.7i −0.000425189 + 0.000145711i
\(519\) 1.57948e7i 0.112983i
\(520\) 4.88704e7 + 3.20416e7i 0.347565 + 0.227879i
\(521\) 1.78407e8 1.26153 0.630765 0.775974i \(-0.282741\pi\)
0.630765 + 0.775974i \(0.282741\pi\)
\(522\) 7.92404e6 + 2.31225e7i 0.0557102 + 0.162564i
\(523\) 2.26348e8i 1.58224i 0.611662 + 0.791119i \(0.290501\pi\)
−0.611662 + 0.791119i \(0.709499\pi\)
\(524\) −1.11303e7 1.43320e7i −0.0773591 0.0996125i
\(525\) 3.26919e7 0.225924
\(526\) −5.79478e7 + 1.98586e7i −0.398180 + 0.136456i
\(527\) 4.47310e8i 3.05617i
\(528\) −3.15568e6 + 1.23495e7i −0.0214384 + 0.0838972i
\(529\) −6.60414e7 −0.446118
\(530\) 198505. + 579244.i 0.00133335 + 0.00389075i
\(531\) 1.36125e6i 0.00909190i
\(532\) −1.74603e8 + 1.35597e8i −1.15962 + 0.900562i
\(533\) −1.38557e8 −0.915053
\(534\) −5.45038e6 + 1.86783e6i −0.0357934 + 0.0122663i
\(535\) 5.72316e7i 0.373744i
\(536\) 9.13757e7 1.39368e8i 0.593384 0.905041i
\(537\) 1.65014e8 1.06561
\(538\) −9.41608e7 2.74763e8i −0.604677 1.76446i
\(539\) 6.64215e7i 0.424172i
\(540\) −8.31248e6 1.07037e7i −0.0527897 0.0679754i
\(541\) 5.52591e7 0.348990 0.174495 0.984658i \(-0.444171\pi\)
0.174495 + 0.984658i \(0.444171\pi\)
\(542\) 1.09201e6 374228.i 0.00685847 0.00235038i
\(543\) 3.81794e7i 0.238468i
\(544\) −2.68465e8 + 2.15170e7i −1.66760 + 0.133655i
\(545\) 9.99943e7 0.617712
\(546\) 5.53960e7 + 1.61647e8i 0.340330 + 0.993091i
\(547\) 5.20328e7i 0.317918i −0.987285 0.158959i \(-0.949186\pi\)
0.987285 0.158959i \(-0.0508137\pi\)
\(548\) 2.09875e8 1.62989e8i 1.27532 0.990412i
\(549\) 3.22416e7 0.194849
\(550\) −4.72116e6 + 1.61793e6i −0.0283766 + 0.00972461i
\(551\) 6.47167e7i 0.386867i
\(552\) −9.76586e7 6.40292e7i −0.580622 0.380681i
\(553\) −2.61705e8 −1.54752
\(554\) 1.23121e7 + 3.59271e7i 0.0724109 + 0.211297i
\(555\) 10139.9i 5.93138e-5i
\(556\) −1.51168e8 1.94654e8i −0.879502 1.13250i
\(557\) −2.24751e8 −1.30058 −0.650289 0.759687i \(-0.725352\pi\)
−0.650289 + 0.759687i \(0.725352\pi\)
\(558\) −1.00084e8 + 3.42986e7i −0.576052 + 0.197412i
\(559\) 2.14458e8i 1.22774i
\(560\) 1.48880e8 + 3.80435e7i 0.847760 + 0.216629i
\(561\) 2.55772e7 0.144865
\(562\) 1.17396e7 + 3.42563e7i 0.0661367 + 0.192989i
\(563\) 1.16024e8i 0.650165i 0.945686 + 0.325083i \(0.105392\pi\)
−0.945686 + 0.325083i \(0.894608\pi\)
\(564\) 7.06487e7 5.48658e7i 0.393792 0.305819i
\(565\) −1.24563e8 −0.690625
\(566\) −8.12184e7 + 2.78334e7i −0.447925 + 0.153503i
\(567\) 3.96278e7i 0.217396i
\(568\) 8.51568e7 1.29883e8i 0.464702 0.708772i
\(569\) 6.45365e7 0.350323 0.175161 0.984540i \(-0.443955\pi\)
0.175161 + 0.984540i \(0.443955\pi\)
\(570\) 1.16327e7 + 3.39446e7i 0.0628141 + 0.183293i
\(571\) 5.29903e7i 0.284635i −0.989821 0.142317i \(-0.954545\pi\)
0.989821 0.142317i \(-0.0454553\pi\)
\(572\) −1.59999e7 2.06025e7i −0.0854926 0.110086i
\(573\) −8.44676e7 −0.448979
\(574\) −3.44662e8 + 1.18115e8i −1.82246 + 0.624553i
\(575\) 4.57231e7i 0.240509i
\(576\) −2.53995e7 5.84182e7i −0.132910 0.305689i
\(577\) −1.97923e8 −1.03031 −0.515155 0.857097i \(-0.672266\pi\)
−0.515155 + 0.857097i \(0.672266\pi\)
\(578\) 1.12603e8 + 3.28579e8i 0.583134 + 1.70160i
\(579\) 1.55431e8i 0.800760i
\(580\) −3.55284e7 + 2.75913e7i −0.182092 + 0.141413i
\(581\) −1.44532e8 −0.736946
\(582\) −9.44043e7 + 3.23522e7i −0.478876 + 0.164110i
\(583\) 273326.i 0.00137935i
\(584\) 1.06000e8 + 6.94980e7i 0.532189 + 0.348926i
\(585\) 2.77351e7 0.138536
\(586\) 7.49122e7 + 2.18596e8i 0.372271 + 1.08630i
\(587\) 6.20004e7i 0.306535i −0.988185 0.153268i \(-0.951020\pi\)
0.988185 0.153268i \(-0.0489796\pi\)
\(588\) 2.03604e8 + 2.62174e8i 1.00151 + 1.28961i
\(589\) 2.80121e8 1.37088
\(590\) −2.36993e6 + 812168.i −0.0115393 + 0.00395448i
\(591\) 2.07959e8i 1.00743i
\(592\) −11799.8 + 46177.6i −5.68735e−5 + 0.000222570i
\(593\) −3.48324e8 −1.67039 −0.835197 0.549950i \(-0.814647\pi\)
−0.835197 + 0.549950i \(0.814647\pi\)
\(594\) 1.96119e6 + 5.72280e6i 0.00935751 + 0.0273054i
\(595\) 3.08348e8i 1.46383i
\(596\) 1.67063e8 1.29741e8i 0.789117 0.612829i
\(597\) 1.02571e8 0.482063
\(598\) 2.26080e8 7.74770e7i 1.05720 0.362301i
\(599\) 2.16010e8i 1.00506i 0.864559 + 0.502531i \(0.167598\pi\)
−0.864559 + 0.502531i \(0.832402\pi\)
\(600\) 1.36755e7 2.08581e7i 0.0633124 0.0965654i
\(601\) 2.07109e8 0.954058 0.477029 0.878888i \(-0.341714\pi\)
0.477029 + 0.878888i \(0.341714\pi\)
\(602\) −1.82818e8 5.33468e8i −0.837974 2.44523i
\(603\) 7.90946e7i 0.360741i
\(604\) 1.16332e8 + 1.49797e8i 0.527946 + 0.679817i
\(605\) −9.68055e7 −0.437154
\(606\) −1.00336e8 + 3.43848e7i −0.450855 + 0.154507i
\(607\) 7.87805e7i 0.352251i −0.984368 0.176126i \(-0.943644\pi\)
0.984368 0.176126i \(-0.0563565\pi\)
\(608\) 1.34746e7 + 1.68122e8i 0.0599524 + 0.748021i
\(609\) −1.31535e8 −0.582358
\(610\) 1.92364e7 + 5.61322e7i 0.0847489 + 0.247299i
\(611\) 1.83063e8i 0.802560i
\(612\) −1.00956e8 + 7.84027e7i −0.440432 + 0.342040i
\(613\) −2.49628e8 −1.08371 −0.541853 0.840473i \(-0.682277\pi\)
−0.541853 + 0.840473i \(0.682277\pi\)
\(614\) 3.45049e8 1.18248e8i 1.49065 0.510843i
\(615\) 5.91367e7i 0.254233i
\(616\) −5.73628e7 3.76096e7i −0.245408 0.160900i
\(617\) 2.37350e8 1.01049 0.505247 0.862975i \(-0.331401\pi\)
0.505247 + 0.862975i \(0.331401\pi\)
\(618\) 2.38972e7 + 6.97327e7i 0.101247 + 0.295441i
\(619\) 5.81494e7i 0.245173i 0.992458 + 0.122587i \(0.0391190\pi\)
−0.992458 + 0.122587i \(0.960881\pi\)
\(620\) −1.19427e8 1.53782e8i −0.501103 0.645252i
\(621\) −5.54236e7 −0.231430
\(622\) 1.76805e8 6.05908e7i 0.734724 0.251788i
\(623\) 3.10051e7i 0.128224i
\(624\) 1.26307e8 + 3.22753e7i 0.519844 + 0.132836i
\(625\) 9.76562e6 0.0400000
\(626\) 7.20738e7 + 2.10313e8i 0.293802 + 0.857320i
\(627\) 1.60173e7i 0.0649811i
\(628\) −152162. + 118169.i −0.000614367 + 0.000477118i
\(629\) 95639.0 0.000384311
\(630\) 6.89916e7 2.36433e7i 0.275914 0.0945553i
\(631\) 1.07588e8i 0.428227i −0.976809 0.214114i \(-0.931314\pi\)
0.976809 0.214114i \(-0.0686863\pi\)
\(632\) −1.09475e8 + 1.66973e8i −0.433673 + 0.661447i
\(633\) −1.35699e7 −0.0535016
\(634\) 1.99304e7 + 5.81572e7i 0.0782073 + 0.228211i
\(635\) 6.75492e7i 0.263815i
\(636\) 837834. + 1.07885e6i 0.00325677 + 0.00419362i
\(637\) −6.79338e8 −2.62826
\(638\) 1.89955e7 6.50971e6i 0.0731457 0.0250668i
\(639\) 7.37116e7i 0.282510i
\(640\) 8.65512e7 7.90745e7i 0.330167 0.301645i
\(641\) 2.45332e8 0.931492 0.465746 0.884918i \(-0.345786\pi\)
0.465746 + 0.884918i \(0.345786\pi\)
\(642\) −4.13907e7 1.20779e8i −0.156422 0.456443i
\(643\) 3.42151e8i 1.28702i 0.765439 + 0.643509i \(0.222522\pi\)
−0.765439 + 0.643509i \(0.777478\pi\)
\(644\) 4.96331e8 3.85451e8i 1.85829 1.44315i
\(645\) −9.15318e7 −0.341109
\(646\) 3.20163e8 1.09719e8i 1.18761 0.406991i
\(647\) 2.08510e8i 0.769862i −0.922945 0.384931i \(-0.874225\pi\)
0.922945 0.384931i \(-0.125775\pi\)
\(648\) −2.52833e7 1.65769e7i −0.0929201 0.0609224i
\(649\) 1.11829e6 0.00409091
\(650\) 1.65477e7 + 4.82866e7i 0.0602556 + 0.175827i
\(651\) 5.69339e8i 2.06361i
\(652\) −4.06137e7 5.22968e7i −0.146531 0.188683i
\(653\) 4.76031e8 1.70960 0.854802 0.518954i \(-0.173678\pi\)
0.854802 + 0.518954i \(0.173678\pi\)
\(654\) 2.11024e8 7.23173e7i 0.754393 0.258529i
\(655\) 1.58502e7i 0.0564040i
\(656\) −6.88173e7 + 2.69311e8i −0.243773 + 0.953987i
\(657\) 6.01574e7 0.212125
\(658\) 1.56055e8 + 4.55373e8i 0.547773 + 1.59842i
\(659\) 1.75876e8i 0.614540i 0.951622 + 0.307270i \(0.0994155\pi\)
−0.951622 + 0.307270i \(0.900584\pi\)
\(660\) −8.79322e6 + 6.82882e6i −0.0305855 + 0.0237528i
\(661\) 3.80396e8 1.31714 0.658570 0.752520i \(-0.271162\pi\)
0.658570 + 0.752520i \(0.271162\pi\)
\(662\) 1.71505e8 5.87744e7i 0.591157 0.202588i
\(663\) 2.61596e8i 0.897614i
\(664\) −6.04598e7 + 9.22144e7i −0.206520 + 0.314988i
\(665\) −1.93098e8 −0.656617
\(666\) 7333.34 + 21398.9i 2.48244e−5 + 7.24382e-5i
\(667\) 1.83966e8i 0.619954i
\(668\) 2.33073e7 + 3.00119e7i 0.0781920 + 0.100685i
\(669\) −8.04742e7 −0.268769
\(670\) 1.37703e8 4.71905e7i 0.457846 0.156903i
\(671\) 2.64869e7i 0.0876725i
\(672\) 3.41704e8 2.73869e7i 1.12601 0.0902475i
\(673\) −3.67932e8 −1.20704 −0.603521 0.797347i \(-0.706236\pi\)
−0.603521 + 0.797347i \(0.706236\pi\)
\(674\) −1.33677e8 3.90074e8i −0.436594 1.27399i
\(675\) 1.18375e7i 0.0384900i
\(676\) 3.32670e7 2.58352e7i 0.107690 0.0836318i
\(677\) 4.64821e7 0.149803 0.0749014 0.997191i \(-0.476136\pi\)
0.0749014 + 0.997191i \(0.476136\pi\)
\(678\) −2.62871e8 + 9.00854e7i −0.843440 + 0.289045i
\(679\) 5.37030e8i 1.71549i
\(680\) −1.96732e8 1.28986e8i −0.625675 0.410219i
\(681\) 6.06290e7 0.191973
\(682\) 2.81768e7 + 8.22204e7i 0.0888255 + 0.259195i
\(683\) 6.18385e8i 1.94087i −0.241361 0.970435i \(-0.577594\pi\)
0.241361 0.970435i \(-0.422406\pi\)
\(684\) 4.90984e7 + 6.32222e7i 0.153426 + 0.197561i
\(685\) 2.32106e8 0.722129
\(686\) −1.09234e9 + 3.74344e8i −3.38366 + 1.15957i
\(687\) 1.56871e8i 0.483807i
\(688\) −4.16839e8 1.06515e8i −1.27998 0.327075i
\(689\) −2.79549e6 −0.00854673
\(690\) −3.30676e7 9.64919e7i −0.100660 0.293727i
\(691\) 5.57874e7i 0.169084i 0.996420 + 0.0845419i \(0.0269427\pi\)
−0.996420 + 0.0845419i \(0.973057\pi\)
\(692\) −5.12164e7 + 3.97747e7i −0.154558 + 0.120030i
\(693\) −3.25548e7 −0.0978172
\(694\) 2.04326e8 7.00221e7i 0.611287 0.209487i
\(695\) 2.15273e8i 0.641262i
\(696\) −5.50230e7 + 8.39222e7i −0.163199 + 0.248914i
\(697\) 5.57773e8 1.64725
\(698\) −1.03323e8 3.01500e8i −0.303831 0.886585i
\(699\) 9.40946e7i 0.275507i
\(700\) 8.23254e7 + 1.06007e8i 0.240016 + 0.309059i
\(701\) −5.45837e8 −1.58456 −0.792280 0.610158i \(-0.791106\pi\)
−0.792280 + 0.610158i \(0.791106\pi\)
\(702\) 5.85310e7 2.00584e7i 0.169190 0.0579810i
\(703\) 59892.4i 0.000172387i
\(704\) −4.79914e7 + 2.08661e7i −0.137545 + 0.0598029i
\(705\) 7.81323e7 0.222979
\(706\) −9.62152e7 2.80758e8i −0.273420 0.797845i
\(707\) 5.70770e8i 1.61511i
\(708\) −4.41401e6 + 3.42793e6i −0.0124375 + 0.00965899i
\(709\) 2.11110e8 0.592339 0.296170 0.955135i \(-0.404291\pi\)
0.296170 + 0.955135i \(0.404291\pi\)
\(710\) 1.28331e8 4.39788e7i 0.358556 0.122876i
\(711\) 9.47612e7i 0.263646i
\(712\) −1.97819e7 1.29699e7i −0.0548060 0.0359332i
\(713\) −7.96280e8 −2.19684
\(714\) −2.23001e8 6.50723e8i −0.612651 1.78773i
\(715\) 2.27848e7i 0.0623343i
\(716\) 4.15540e8 + 5.35076e8i 1.13207 + 1.45773i
\(717\) 2.10391e7 0.0570781
\(718\) 2.44824e8 8.39006e7i 0.661425 0.226669i
\(719\) 2.73670e8i 0.736276i 0.929771 + 0.368138i \(0.120005\pi\)
−0.929771 + 0.368138i \(0.879995\pi\)
\(720\) 1.37753e7 5.39084e7i 0.0369065 0.144430i
\(721\) −3.96683e8 −1.05837
\(722\) 5.33044e7 + 1.55543e8i 0.141629 + 0.413276i
\(723\) 1.20695e8i 0.319356i
\(724\) 1.23801e8 9.61440e7i 0.326219 0.253342i
\(725\) −3.92918e7 −0.103107
\(726\) −2.04294e8 + 7.00111e7i −0.533883 + 0.182960i
\(727\) 6.77998e8i 1.76451i 0.470768 + 0.882257i \(0.343977\pi\)
−0.470768 + 0.882257i \(0.656023\pi\)
\(728\) −3.84659e8 + 5.86689e8i −0.996969 + 1.52060i
\(729\) −1.43489e7 −0.0370370
\(730\) 3.58919e7 + 1.04733e8i 0.0922630 + 0.269226i
\(731\) 8.63321e8i 2.21014i
\(732\) 8.11912e7 + 1.04547e8i 0.207003 + 0.266550i
\(733\) 4.75863e8 1.20829 0.604143 0.796876i \(-0.293516\pi\)
0.604143 + 0.796876i \(0.293516\pi\)
\(734\) −4.41575e7 + 1.51327e7i −0.111665 + 0.0382673i
\(735\) 2.89945e8i 0.730219i
\(736\) −3.83034e7 4.77909e8i −0.0960737 1.19870i
\(737\) −6.49774e7 −0.162315
\(738\) 4.27685e7 + 1.24800e8i 0.106403 + 0.310487i
\(739\) 4.04862e8i 1.00317i −0.865109 0.501584i \(-0.832751\pi\)
0.865109 0.501584i \(-0.167249\pi\)
\(740\) −32879.9 + 25534.5i −8.11400e−5 + 6.30134e-5i
\(741\) −1.63820e8 −0.402636
\(742\) −6.95382e6 + 2.38306e6i −0.0170221 + 0.00583342i
\(743\) 3.57127e8i 0.870676i 0.900267 + 0.435338i \(0.143371\pi\)
−0.900267 + 0.435338i \(0.856629\pi\)
\(744\) −3.63250e8 2.38163e8i −0.882037 0.578302i
\(745\) 1.84759e8 0.446825
\(746\) −4.23453e7 1.23565e8i −0.101997 0.297631i
\(747\) 5.23339e7i 0.125551i
\(748\) 6.44089e7 + 8.29370e7i 0.153901 + 0.198173i
\(749\) 6.87066e8 1.63513
\(750\) 2.06089e7 7.06264e6i 0.0488508 0.0167411i
\(751\) 1.02196e8i 0.241275i 0.992697 + 0.120637i \(0.0384938\pi\)
−0.992697 + 0.120637i \(0.961506\pi\)
\(752\) 3.55817e8 + 9.09224e7i 0.836708 + 0.213805i
\(753\) 2.56820e8 0.601511
\(754\) −6.65793e7 1.94280e8i −0.155319 0.453225i
\(755\) 1.65664e8i 0.384936i
\(756\) 1.28498e8 9.97914e7i 0.297392 0.230955i
\(757\) 4.38046e8 1.00979 0.504896 0.863180i \(-0.331531\pi\)
0.504896 + 0.863180i \(0.331531\pi\)
\(758\) 4.91810e8 1.68542e8i 1.12925 0.386991i
\(759\) 4.55313e7i 0.104132i
\(760\) −8.07755e7 + 1.23200e8i −0.184009 + 0.280654i
\(761\) 1.40458e8 0.318708 0.159354 0.987222i \(-0.449059\pi\)
0.159354 + 0.987222i \(0.449059\pi\)
\(762\) 4.88525e7 + 1.42553e8i 0.110414 + 0.322189i
\(763\) 1.20043e9i 2.70249i
\(764\) −2.12708e8 2.73896e8i −0.476983 0.614194i
\(765\) −1.11650e8 −0.249388
\(766\) 4.27191e8 1.46397e8i 0.950464 0.325722i
\(767\) 1.14375e7i 0.0253481i
\(768\) 1.25466e8 2.29470e8i 0.276976 0.506574i
\(769\) 2.32792e7 0.0511905 0.0255952 0.999672i \(-0.491852\pi\)
0.0255952 + 0.999672i \(0.491852\pi\)
\(770\) −1.94233e7 5.66776e7i −0.0425452 0.124148i
\(771\) 2.15966e8i 0.471219i
\(772\) −5.04004e8 + 3.91410e8i −1.09542 + 0.850706i
\(773\) 1.98042e8 0.428763 0.214382