Properties

Label 6038.2.a.a.1.1
Level 6038
Weight 2
Character 6038.1
Self dual Yes
Analytic conductor 48.214
Analytic rank 2
Dimension 2
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6038 = 2 \cdot 3019 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6038.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2136727404\)
Analytic rank: \(2\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(1.61803\)
Character \(\chi\) = 6038.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.61803 q^{3}\) \(+1.00000 q^{4}\) \(-1.38197 q^{5}\) \(-2.61803 q^{6}\) \(-3.00000 q^{7}\) \(+1.00000 q^{8}\) \(+3.85410 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.61803 q^{3}\) \(+1.00000 q^{4}\) \(-1.38197 q^{5}\) \(-2.61803 q^{6}\) \(-3.00000 q^{7}\) \(+1.00000 q^{8}\) \(+3.85410 q^{9}\) \(-1.38197 q^{10}\) \(-2.38197 q^{11}\) \(-2.61803 q^{12}\) \(-3.00000 q^{13}\) \(-3.00000 q^{14}\) \(+3.61803 q^{15}\) \(+1.00000 q^{16}\) \(-7.47214 q^{17}\) \(+3.85410 q^{18}\) \(-3.00000 q^{19}\) \(-1.38197 q^{20}\) \(+7.85410 q^{21}\) \(-2.38197 q^{22}\) \(+1.47214 q^{23}\) \(-2.61803 q^{24}\) \(-3.09017 q^{25}\) \(-3.00000 q^{26}\) \(-2.23607 q^{27}\) \(-3.00000 q^{28}\) \(-9.23607 q^{29}\) \(+3.61803 q^{30}\) \(-6.09017 q^{31}\) \(+1.00000 q^{32}\) \(+6.23607 q^{33}\) \(-7.47214 q^{34}\) \(+4.14590 q^{35}\) \(+3.85410 q^{36}\) \(-1.85410 q^{37}\) \(-3.00000 q^{38}\) \(+7.85410 q^{39}\) \(-1.38197 q^{40}\) \(+11.1803 q^{41}\) \(+7.85410 q^{42}\) \(-9.23607 q^{43}\) \(-2.38197 q^{44}\) \(-5.32624 q^{45}\) \(+1.47214 q^{46}\) \(+11.5623 q^{47}\) \(-2.61803 q^{48}\) \(+2.00000 q^{49}\) \(-3.09017 q^{50}\) \(+19.5623 q^{51}\) \(-3.00000 q^{52}\) \(-9.00000 q^{53}\) \(-2.23607 q^{54}\) \(+3.29180 q^{55}\) \(-3.00000 q^{56}\) \(+7.85410 q^{57}\) \(-9.23607 q^{58}\) \(-9.76393 q^{59}\) \(+3.61803 q^{60}\) \(-2.38197 q^{61}\) \(-6.09017 q^{62}\) \(-11.5623 q^{63}\) \(+1.00000 q^{64}\) \(+4.14590 q^{65}\) \(+6.23607 q^{66}\) \(+1.85410 q^{67}\) \(-7.47214 q^{68}\) \(-3.85410 q^{69}\) \(+4.14590 q^{70}\) \(-11.9443 q^{71}\) \(+3.85410 q^{72}\) \(+0.708204 q^{73}\) \(-1.85410 q^{74}\) \(+8.09017 q^{75}\) \(-3.00000 q^{76}\) \(+7.14590 q^{77}\) \(+7.85410 q^{78}\) \(-1.85410 q^{79}\) \(-1.38197 q^{80}\) \(-5.70820 q^{81}\) \(+11.1803 q^{82}\) \(-1.94427 q^{83}\) \(+7.85410 q^{84}\) \(+10.3262 q^{85}\) \(-9.23607 q^{86}\) \(+24.1803 q^{87}\) \(-2.38197 q^{88}\) \(-16.7984 q^{89}\) \(-5.32624 q^{90}\) \(+9.00000 q^{91}\) \(+1.47214 q^{92}\) \(+15.9443 q^{93}\) \(+11.5623 q^{94}\) \(+4.14590 q^{95}\) \(-2.61803 q^{96}\) \(+13.7639 q^{97}\) \(+2.00000 q^{98}\) \(-9.18034 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut -\mathstrut 5q^{10} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 3q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut -\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 5q^{15} \) \(\mathstrut +\mathstrut 2q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut q^{18} \) \(\mathstrut -\mathstrut 6q^{19} \) \(\mathstrut -\mathstrut 5q^{20} \) \(\mathstrut +\mathstrut 9q^{21} \) \(\mathstrut -\mathstrut 7q^{22} \) \(\mathstrut -\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 3q^{24} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut +\mathstrut 5q^{30} \) \(\mathstrut -\mathstrut q^{31} \) \(\mathstrut +\mathstrut 2q^{32} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 6q^{34} \) \(\mathstrut +\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut q^{36} \) \(\mathstrut +\mathstrut 3q^{37} \) \(\mathstrut -\mathstrut 6q^{38} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 5q^{40} \) \(\mathstrut +\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 14q^{43} \) \(\mathstrut -\mathstrut 7q^{44} \) \(\mathstrut +\mathstrut 5q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut +\mathstrut 3q^{47} \) \(\mathstrut -\mathstrut 3q^{48} \) \(\mathstrut +\mathstrut 4q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 19q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 20q^{55} \) \(\mathstrut -\mathstrut 6q^{56} \) \(\mathstrut +\mathstrut 9q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 5q^{60} \) \(\mathstrut -\mathstrut 7q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut -\mathstrut 3q^{63} \) \(\mathstrut +\mathstrut 2q^{64} \) \(\mathstrut +\mathstrut 15q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut -\mathstrut 3q^{67} \) \(\mathstrut -\mathstrut 6q^{68} \) \(\mathstrut -\mathstrut q^{69} \) \(\mathstrut +\mathstrut 15q^{70} \) \(\mathstrut -\mathstrut 6q^{71} \) \(\mathstrut +\mathstrut q^{72} \) \(\mathstrut -\mathstrut 12q^{73} \) \(\mathstrut +\mathstrut 3q^{74} \) \(\mathstrut +\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 6q^{76} \) \(\mathstrut +\mathstrut 21q^{77} \) \(\mathstrut +\mathstrut 9q^{78} \) \(\mathstrut +\mathstrut 3q^{79} \) \(\mathstrut -\mathstrut 5q^{80} \) \(\mathstrut +\mathstrut 2q^{81} \) \(\mathstrut +\mathstrut 14q^{83} \) \(\mathstrut +\mathstrut 9q^{84} \) \(\mathstrut +\mathstrut 5q^{85} \) \(\mathstrut -\mathstrut 14q^{86} \) \(\mathstrut +\mathstrut 26q^{87} \) \(\mathstrut -\mathstrut 7q^{88} \) \(\mathstrut -\mathstrut 9q^{89} \) \(\mathstrut +\mathstrut 5q^{90} \) \(\mathstrut +\mathstrut 18q^{91} \) \(\mathstrut -\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut +\mathstrut 3q^{94} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut -\mathstrut 3q^{96} \) \(\mathstrut +\mathstrut 32q^{97} \) \(\mathstrut +\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −2.61803 −1.51152 −0.755761 0.654847i \(-0.772733\pi\)
−0.755761 + 0.654847i \(0.772733\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.38197 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(6\) −2.61803 −1.06881
\(7\) −3.00000 −1.13389 −0.566947 0.823754i \(-0.691875\pi\)
−0.566947 + 0.823754i \(0.691875\pi\)
\(8\) 1.00000 0.353553
\(9\) 3.85410 1.28470
\(10\) −1.38197 −0.437016
\(11\) −2.38197 −0.718190 −0.359095 0.933301i \(-0.616915\pi\)
−0.359095 + 0.933301i \(0.616915\pi\)
\(12\) −2.61803 −0.755761
\(13\) −3.00000 −0.832050 −0.416025 0.909353i \(-0.636577\pi\)
−0.416025 + 0.909353i \(0.636577\pi\)
\(14\) −3.00000 −0.801784
\(15\) 3.61803 0.934172
\(16\) 1.00000 0.250000
\(17\) −7.47214 −1.81226 −0.906130 0.423000i \(-0.860977\pi\)
−0.906130 + 0.423000i \(0.860977\pi\)
\(18\) 3.85410 0.908421
\(19\) −3.00000 −0.688247 −0.344124 0.938924i \(-0.611824\pi\)
−0.344124 + 0.938924i \(0.611824\pi\)
\(20\) −1.38197 −0.309017
\(21\) 7.85410 1.71391
\(22\) −2.38197 −0.507837
\(23\) 1.47214 0.306962 0.153481 0.988152i \(-0.450952\pi\)
0.153481 + 0.988152i \(0.450952\pi\)
\(24\) −2.61803 −0.534404
\(25\) −3.09017 −0.618034
\(26\) −3.00000 −0.588348
\(27\) −2.23607 −0.430331
\(28\) −3.00000 −0.566947
\(29\) −9.23607 −1.71509 −0.857547 0.514405i \(-0.828013\pi\)
−0.857547 + 0.514405i \(0.828013\pi\)
\(30\) 3.61803 0.660560
\(31\) −6.09017 −1.09383 −0.546913 0.837189i \(-0.684197\pi\)
−0.546913 + 0.837189i \(0.684197\pi\)
\(32\) 1.00000 0.176777
\(33\) 6.23607 1.08556
\(34\) −7.47214 −1.28146
\(35\) 4.14590 0.700785
\(36\) 3.85410 0.642350
\(37\) −1.85410 −0.304812 −0.152406 0.988318i \(-0.548702\pi\)
−0.152406 + 0.988318i \(0.548702\pi\)
\(38\) −3.00000 −0.486664
\(39\) 7.85410 1.25766
\(40\) −1.38197 −0.218508
\(41\) 11.1803 1.74608 0.873038 0.487652i \(-0.162147\pi\)
0.873038 + 0.487652i \(0.162147\pi\)
\(42\) 7.85410 1.21191
\(43\) −9.23607 −1.40849 −0.704244 0.709958i \(-0.748714\pi\)
−0.704244 + 0.709958i \(0.748714\pi\)
\(44\) −2.38197 −0.359095
\(45\) −5.32624 −0.793989
\(46\) 1.47214 0.217055
\(47\) 11.5623 1.68654 0.843268 0.537494i \(-0.180629\pi\)
0.843268 + 0.537494i \(0.180629\pi\)
\(48\) −2.61803 −0.377881
\(49\) 2.00000 0.285714
\(50\) −3.09017 −0.437016
\(51\) 19.5623 2.73927
\(52\) −3.00000 −0.416025
\(53\) −9.00000 −1.23625 −0.618123 0.786082i \(-0.712106\pi\)
−0.618123 + 0.786082i \(0.712106\pi\)
\(54\) −2.23607 −0.304290
\(55\) 3.29180 0.443866
\(56\) −3.00000 −0.400892
\(57\) 7.85410 1.04030
\(58\) −9.23607 −1.21276
\(59\) −9.76393 −1.27116 −0.635578 0.772037i \(-0.719238\pi\)
−0.635578 + 0.772037i \(0.719238\pi\)
\(60\) 3.61803 0.467086
\(61\) −2.38197 −0.304979 −0.152490 0.988305i \(-0.548729\pi\)
−0.152490 + 0.988305i \(0.548729\pi\)
\(62\) −6.09017 −0.773452
\(63\) −11.5623 −1.45671
\(64\) 1.00000 0.125000
\(65\) 4.14590 0.514235
\(66\) 6.23607 0.767607
\(67\) 1.85410 0.226515 0.113257 0.993566i \(-0.463872\pi\)
0.113257 + 0.993566i \(0.463872\pi\)
\(68\) −7.47214 −0.906130
\(69\) −3.85410 −0.463979
\(70\) 4.14590 0.495530
\(71\) −11.9443 −1.41752 −0.708762 0.705448i \(-0.750746\pi\)
−0.708762 + 0.705448i \(0.750746\pi\)
\(72\) 3.85410 0.454210
\(73\) 0.708204 0.0828890 0.0414445 0.999141i \(-0.486804\pi\)
0.0414445 + 0.999141i \(0.486804\pi\)
\(74\) −1.85410 −0.215535
\(75\) 8.09017 0.934172
\(76\) −3.00000 −0.344124
\(77\) 7.14590 0.814351
\(78\) 7.85410 0.889302
\(79\) −1.85410 −0.208603 −0.104301 0.994546i \(-0.533261\pi\)
−0.104301 + 0.994546i \(0.533261\pi\)
\(80\) −1.38197 −0.154508
\(81\) −5.70820 −0.634245
\(82\) 11.1803 1.23466
\(83\) −1.94427 −0.213412 −0.106706 0.994291i \(-0.534030\pi\)
−0.106706 + 0.994291i \(0.534030\pi\)
\(84\) 7.85410 0.856953
\(85\) 10.3262 1.12004
\(86\) −9.23607 −0.995951
\(87\) 24.1803 2.59240
\(88\) −2.38197 −0.253918
\(89\) −16.7984 −1.78062 −0.890312 0.455351i \(-0.849514\pi\)
−0.890312 + 0.455351i \(0.849514\pi\)
\(90\) −5.32624 −0.561435
\(91\) 9.00000 0.943456
\(92\) 1.47214 0.153481
\(93\) 15.9443 1.65334
\(94\) 11.5623 1.19256
\(95\) 4.14590 0.425360
\(96\) −2.61803 −0.267202
\(97\) 13.7639 1.39752 0.698758 0.715358i \(-0.253737\pi\)
0.698758 + 0.715358i \(0.253737\pi\)
\(98\) 2.00000 0.202031
\(99\) −9.18034 −0.922659
\(100\) −3.09017 −0.309017
\(101\) 5.23607 0.521008 0.260504 0.965473i \(-0.416111\pi\)
0.260504 + 0.965473i \(0.416111\pi\)
\(102\) 19.5623 1.93696
\(103\) 5.14590 0.507040 0.253520 0.967330i \(-0.418412\pi\)
0.253520 + 0.967330i \(0.418412\pi\)
\(104\) −3.00000 −0.294174
\(105\) −10.8541 −1.05925
\(106\) −9.00000 −0.874157
\(107\) −3.76393 −0.363873 −0.181937 0.983310i \(-0.558237\pi\)
−0.181937 + 0.983310i \(0.558237\pi\)
\(108\) −2.23607 −0.215166
\(109\) −9.47214 −0.907266 −0.453633 0.891189i \(-0.649872\pi\)
−0.453633 + 0.891189i \(0.649872\pi\)
\(110\) 3.29180 0.313860
\(111\) 4.85410 0.460731
\(112\) −3.00000 −0.283473
\(113\) −4.38197 −0.412221 −0.206110 0.978529i \(-0.566081\pi\)
−0.206110 + 0.978529i \(0.566081\pi\)
\(114\) 7.85410 0.735604
\(115\) −2.03444 −0.189713
\(116\) −9.23607 −0.857547
\(117\) −11.5623 −1.06894
\(118\) −9.76393 −0.898843
\(119\) 22.4164 2.05491
\(120\) 3.61803 0.330280
\(121\) −5.32624 −0.484203
\(122\) −2.38197 −0.215653
\(123\) −29.2705 −2.63923
\(124\) −6.09017 −0.546913
\(125\) 11.1803 1.00000
\(126\) −11.5623 −1.03005
\(127\) −12.4164 −1.10178 −0.550889 0.834579i \(-0.685711\pi\)
−0.550889 + 0.834579i \(0.685711\pi\)
\(128\) 1.00000 0.0883883
\(129\) 24.1803 2.12896
\(130\) 4.14590 0.363619
\(131\) 21.6180 1.88878 0.944388 0.328833i \(-0.106655\pi\)
0.944388 + 0.328833i \(0.106655\pi\)
\(132\) 6.23607 0.542780
\(133\) 9.00000 0.780399
\(134\) 1.85410 0.160170
\(135\) 3.09017 0.265959
\(136\) −7.47214 −0.640730
\(137\) 8.56231 0.731527 0.365764 0.930708i \(-0.380808\pi\)
0.365764 + 0.930708i \(0.380808\pi\)
\(138\) −3.85410 −0.328083
\(139\) −15.4721 −1.31233 −0.656165 0.754618i \(-0.727822\pi\)
−0.656165 + 0.754618i \(0.727822\pi\)
\(140\) 4.14590 0.350392
\(141\) −30.2705 −2.54924
\(142\) −11.9443 −1.00234
\(143\) 7.14590 0.597570
\(144\) 3.85410 0.321175
\(145\) 12.7639 1.05999
\(146\) 0.708204 0.0586114
\(147\) −5.23607 −0.431864
\(148\) −1.85410 −0.152406
\(149\) −2.23607 −0.183186 −0.0915929 0.995797i \(-0.529196\pi\)
−0.0915929 + 0.995797i \(0.529196\pi\)
\(150\) 8.09017 0.660560
\(151\) −9.79837 −0.797380 −0.398690 0.917086i \(-0.630535\pi\)
−0.398690 + 0.917086i \(0.630535\pi\)
\(152\) −3.00000 −0.243332
\(153\) −28.7984 −2.32821
\(154\) 7.14590 0.575833
\(155\) 8.41641 0.676022
\(156\) 7.85410 0.628831
\(157\) 8.09017 0.645666 0.322833 0.946456i \(-0.395365\pi\)
0.322833 + 0.946456i \(0.395365\pi\)
\(158\) −1.85410 −0.147504
\(159\) 23.5623 1.86861
\(160\) −1.38197 −0.109254
\(161\) −4.41641 −0.348062
\(162\) −5.70820 −0.448479
\(163\) 0.854102 0.0668984 0.0334492 0.999440i \(-0.489351\pi\)
0.0334492 + 0.999440i \(0.489351\pi\)
\(164\) 11.1803 0.873038
\(165\) −8.61803 −0.670913
\(166\) −1.94427 −0.150905
\(167\) −5.23607 −0.405179 −0.202590 0.979264i \(-0.564936\pi\)
−0.202590 + 0.979264i \(0.564936\pi\)
\(168\) 7.85410 0.605957
\(169\) −4.00000 −0.307692
\(170\) 10.3262 0.791986
\(171\) −11.5623 −0.884192
\(172\) −9.23607 −0.704244
\(173\) −7.67376 −0.583425 −0.291713 0.956506i \(-0.594225\pi\)
−0.291713 + 0.956506i \(0.594225\pi\)
\(174\) 24.1803 1.83311
\(175\) 9.27051 0.700785
\(176\) −2.38197 −0.179547
\(177\) 25.5623 1.92138
\(178\) −16.7984 −1.25909
\(179\) −9.00000 −0.672692 −0.336346 0.941739i \(-0.609191\pi\)
−0.336346 + 0.941739i \(0.609191\pi\)
\(180\) −5.32624 −0.396994
\(181\) −18.0000 −1.33793 −0.668965 0.743294i \(-0.733262\pi\)
−0.668965 + 0.743294i \(0.733262\pi\)
\(182\) 9.00000 0.667124
\(183\) 6.23607 0.460983
\(184\) 1.47214 0.108527
\(185\) 2.56231 0.188384
\(186\) 15.9443 1.16909
\(187\) 17.7984 1.30155
\(188\) 11.5623 0.843268
\(189\) 6.70820 0.487950
\(190\) 4.14590 0.300775
\(191\) 22.3607 1.61796 0.808981 0.587835i \(-0.200019\pi\)
0.808981 + 0.587835i \(0.200019\pi\)
\(192\) −2.61803 −0.188940
\(193\) 3.14590 0.226447 0.113223 0.993570i \(-0.463882\pi\)
0.113223 + 0.993570i \(0.463882\pi\)
\(194\) 13.7639 0.988193
\(195\) −10.8541 −0.777278
\(196\) 2.00000 0.142857
\(197\) −2.79837 −0.199376 −0.0996879 0.995019i \(-0.531784\pi\)
−0.0996879 + 0.995019i \(0.531784\pi\)
\(198\) −9.18034 −0.652418
\(199\) 21.2705 1.50783 0.753913 0.656974i \(-0.228164\pi\)
0.753913 + 0.656974i \(0.228164\pi\)
\(200\) −3.09017 −0.218508
\(201\) −4.85410 −0.342382
\(202\) 5.23607 0.368408
\(203\) 27.7082 1.94473
\(204\) 19.5623 1.36964
\(205\) −15.4508 −1.07913
\(206\) 5.14590 0.358532
\(207\) 5.67376 0.394354
\(208\) −3.00000 −0.208013
\(209\) 7.14590 0.494292
\(210\) −10.8541 −0.749004
\(211\) 17.8541 1.22913 0.614564 0.788867i \(-0.289332\pi\)
0.614564 + 0.788867i \(0.289332\pi\)
\(212\) −9.00000 −0.618123
\(213\) 31.2705 2.14262
\(214\) −3.76393 −0.257297
\(215\) 12.7639 0.870493
\(216\) −2.23607 −0.152145
\(217\) 18.2705 1.24028
\(218\) −9.47214 −0.641534
\(219\) −1.85410 −0.125289
\(220\) 3.29180 0.221933
\(221\) 22.4164 1.50789
\(222\) 4.85410 0.325786
\(223\) −1.58359 −0.106045 −0.0530226 0.998593i \(-0.516886\pi\)
−0.0530226 + 0.998593i \(0.516886\pi\)
\(224\) −3.00000 −0.200446
\(225\) −11.9098 −0.793989
\(226\) −4.38197 −0.291484
\(227\) 13.8541 0.919529 0.459765 0.888041i \(-0.347934\pi\)
0.459765 + 0.888041i \(0.347934\pi\)
\(228\) 7.85410 0.520151
\(229\) 26.5967 1.75756 0.878781 0.477225i \(-0.158357\pi\)
0.878781 + 0.477225i \(0.158357\pi\)
\(230\) −2.03444 −0.134147
\(231\) −18.7082 −1.23091
\(232\) −9.23607 −0.606378
\(233\) 4.14590 0.271607 0.135803 0.990736i \(-0.456638\pi\)
0.135803 + 0.990736i \(0.456638\pi\)
\(234\) −11.5623 −0.755852
\(235\) −15.9787 −1.04234
\(236\) −9.76393 −0.635578
\(237\) 4.85410 0.315308
\(238\) 22.4164 1.45304
\(239\) 3.70820 0.239864 0.119932 0.992782i \(-0.461732\pi\)
0.119932 + 0.992782i \(0.461732\pi\)
\(240\) 3.61803 0.233543
\(241\) −10.4164 −0.670980 −0.335490 0.942044i \(-0.608902\pi\)
−0.335490 + 0.942044i \(0.608902\pi\)
\(242\) −5.32624 −0.342384
\(243\) 21.6525 1.38901
\(244\) −2.38197 −0.152490
\(245\) −2.76393 −0.176581
\(246\) −29.2705 −1.86622
\(247\) 9.00000 0.572656
\(248\) −6.09017 −0.386726
\(249\) 5.09017 0.322576
\(250\) 11.1803 0.707107
\(251\) 0.944272 0.0596019 0.0298010 0.999556i \(-0.490513\pi\)
0.0298010 + 0.999556i \(0.490513\pi\)
\(252\) −11.5623 −0.728357
\(253\) −3.50658 −0.220457
\(254\) −12.4164 −0.779075
\(255\) −27.0344 −1.69296
\(256\) 1.00000 0.0625000
\(257\) −1.58359 −0.0987818 −0.0493909 0.998780i \(-0.515728\pi\)
−0.0493909 + 0.998780i \(0.515728\pi\)
\(258\) 24.1803 1.50540
\(259\) 5.56231 0.345625
\(260\) 4.14590 0.257118
\(261\) −35.5967 −2.20338
\(262\) 21.6180 1.33557
\(263\) 18.3607 1.13217 0.566084 0.824348i \(-0.308458\pi\)
0.566084 + 0.824348i \(0.308458\pi\)
\(264\) 6.23607 0.383803
\(265\) 12.4377 0.764041
\(266\) 9.00000 0.551825
\(267\) 43.9787 2.69145
\(268\) 1.85410 0.113257
\(269\) −5.56231 −0.339140 −0.169570 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(270\) 3.09017 0.188062
\(271\) −6.61803 −0.402017 −0.201008 0.979590i \(-0.564422\pi\)
−0.201008 + 0.979590i \(0.564422\pi\)
\(272\) −7.47214 −0.453065
\(273\) −23.5623 −1.42606
\(274\) 8.56231 0.517268
\(275\) 7.36068 0.443866
\(276\) −3.85410 −0.231990
\(277\) −20.5623 −1.23547 −0.617735 0.786387i \(-0.711949\pi\)
−0.617735 + 0.786387i \(0.711949\pi\)
\(278\) −15.4721 −0.927957
\(279\) −23.4721 −1.40524
\(280\) 4.14590 0.247765
\(281\) −25.3607 −1.51289 −0.756446 0.654057i \(-0.773066\pi\)
−0.756446 + 0.654057i \(0.773066\pi\)
\(282\) −30.2705 −1.80258
\(283\) 10.7082 0.636537 0.318268 0.948001i \(-0.396899\pi\)
0.318268 + 0.948001i \(0.396899\pi\)
\(284\) −11.9443 −0.708762
\(285\) −10.8541 −0.642942
\(286\) 7.14590 0.422546
\(287\) −33.5410 −1.97986
\(288\) 3.85410 0.227105
\(289\) 38.8328 2.28428
\(290\) 12.7639 0.749524
\(291\) −36.0344 −2.11238
\(292\) 0.708204 0.0414445
\(293\) −32.0902 −1.87473 −0.937364 0.348352i \(-0.886741\pi\)
−0.937364 + 0.348352i \(0.886741\pi\)
\(294\) −5.23607 −0.305374
\(295\) 13.4934 0.785617
\(296\) −1.85410 −0.107767
\(297\) 5.32624 0.309060
\(298\) −2.23607 −0.129532
\(299\) −4.41641 −0.255407
\(300\) 8.09017 0.467086
\(301\) 27.7082 1.59707
\(302\) −9.79837 −0.563833
\(303\) −13.7082 −0.787516
\(304\) −3.00000 −0.172062
\(305\) 3.29180 0.188488
\(306\) −28.7984 −1.64629
\(307\) 3.90983 0.223146 0.111573 0.993756i \(-0.464411\pi\)
0.111573 + 0.993756i \(0.464411\pi\)
\(308\) 7.14590 0.407175
\(309\) −13.4721 −0.766403
\(310\) 8.41641 0.478020
\(311\) 24.7639 1.40423 0.702117 0.712062i \(-0.252238\pi\)
0.702117 + 0.712062i \(0.252238\pi\)
\(312\) 7.85410 0.444651
\(313\) 32.7426 1.85072 0.925362 0.379085i \(-0.123761\pi\)
0.925362 + 0.379085i \(0.123761\pi\)
\(314\) 8.09017 0.456555
\(315\) 15.9787 0.900299
\(316\) −1.85410 −0.104301
\(317\) −10.6180 −0.596368 −0.298184 0.954508i \(-0.596381\pi\)
−0.298184 + 0.954508i \(0.596381\pi\)
\(318\) 23.5623 1.32131
\(319\) 22.0000 1.23176
\(320\) −1.38197 −0.0772542
\(321\) 9.85410 0.550002
\(322\) −4.41641 −0.246117
\(323\) 22.4164 1.24728
\(324\) −5.70820 −0.317122
\(325\) 9.27051 0.514235
\(326\) 0.854102 0.0473043
\(327\) 24.7984 1.37135
\(328\) 11.1803 0.617331
\(329\) −34.6869 −1.91235
\(330\) −8.61803 −0.474407
\(331\) −5.43769 −0.298883 −0.149441 0.988771i \(-0.547748\pi\)
−0.149441 + 0.988771i \(0.547748\pi\)
\(332\) −1.94427 −0.106706
\(333\) −7.14590 −0.391593
\(334\) −5.23607 −0.286505
\(335\) −2.56231 −0.139994
\(336\) 7.85410 0.428476
\(337\) 4.61803 0.251560 0.125780 0.992058i \(-0.459857\pi\)
0.125780 + 0.992058i \(0.459857\pi\)
\(338\) −4.00000 −0.217571
\(339\) 11.4721 0.623081
\(340\) 10.3262 0.560019
\(341\) 14.5066 0.785575
\(342\) −11.5623 −0.625218
\(343\) 15.0000 0.809924
\(344\) −9.23607 −0.497975
\(345\) 5.32624 0.286755
\(346\) −7.67376 −0.412544
\(347\) −8.67376 −0.465632 −0.232816 0.972521i \(-0.574794\pi\)
−0.232816 + 0.972521i \(0.574794\pi\)
\(348\) 24.1803 1.29620
\(349\) −22.7082 −1.21554 −0.607771 0.794112i \(-0.707936\pi\)
−0.607771 + 0.794112i \(0.707936\pi\)
\(350\) 9.27051 0.495530
\(351\) 6.70820 0.358057
\(352\) −2.38197 −0.126959
\(353\) −6.81966 −0.362974 −0.181487 0.983393i \(-0.558091\pi\)
−0.181487 + 0.983393i \(0.558091\pi\)
\(354\) 25.5623 1.35862
\(355\) 16.5066 0.876078
\(356\) −16.7984 −0.890312
\(357\) −58.6869 −3.10604
\(358\) −9.00000 −0.475665
\(359\) −14.5967 −0.770387 −0.385193 0.922836i \(-0.625865\pi\)
−0.385193 + 0.922836i \(0.625865\pi\)
\(360\) −5.32624 −0.280717
\(361\) −10.0000 −0.526316
\(362\) −18.0000 −0.946059
\(363\) 13.9443 0.731884
\(364\) 9.00000 0.471728
\(365\) −0.978714 −0.0512282
\(366\) 6.23607 0.325964
\(367\) 4.88854 0.255180 0.127590 0.991827i \(-0.459276\pi\)
0.127590 + 0.991827i \(0.459276\pi\)
\(368\) 1.47214 0.0767404
\(369\) 43.0902 2.24318
\(370\) 2.56231 0.133208
\(371\) 27.0000 1.40177
\(372\) 15.9443 0.826672
\(373\) −12.0000 −0.621336 −0.310668 0.950518i \(-0.600553\pi\)
−0.310668 + 0.950518i \(0.600553\pi\)
\(374\) 17.7984 0.920332
\(375\) −29.2705 −1.51152
\(376\) 11.5623 0.596280
\(377\) 27.7082 1.42705
\(378\) 6.70820 0.345033
\(379\) 22.8328 1.17284 0.586421 0.810006i \(-0.300536\pi\)
0.586421 + 0.810006i \(0.300536\pi\)
\(380\) 4.14590 0.212680
\(381\) 32.5066 1.66536
\(382\) 22.3607 1.14407
\(383\) −2.29180 −0.117105 −0.0585527 0.998284i \(-0.518649\pi\)
−0.0585527 + 0.998284i \(0.518649\pi\)
\(384\) −2.61803 −0.133601
\(385\) −9.87539 −0.503296
\(386\) 3.14590 0.160122
\(387\) −35.5967 −1.80948
\(388\) 13.7639 0.698758
\(389\) −27.2361 −1.38092 −0.690462 0.723369i \(-0.742593\pi\)
−0.690462 + 0.723369i \(0.742593\pi\)
\(390\) −10.8541 −0.549619
\(391\) −11.0000 −0.556294
\(392\) 2.00000 0.101015
\(393\) −56.5967 −2.85493
\(394\) −2.79837 −0.140980
\(395\) 2.56231 0.128924
\(396\) −9.18034 −0.461329
\(397\) −8.56231 −0.429730 −0.214865 0.976644i \(-0.568931\pi\)
−0.214865 + 0.976644i \(0.568931\pi\)
\(398\) 21.2705 1.06619
\(399\) −23.5623 −1.17959
\(400\) −3.09017 −0.154508
\(401\) −14.0557 −0.701910 −0.350955 0.936392i \(-0.614143\pi\)
−0.350955 + 0.936392i \(0.614143\pi\)
\(402\) −4.85410 −0.242101
\(403\) 18.2705 0.910119
\(404\) 5.23607 0.260504
\(405\) 7.88854 0.391985
\(406\) 27.7082 1.37514
\(407\) 4.41641 0.218913
\(408\) 19.5623 0.968478
\(409\) −33.4164 −1.65234 −0.826168 0.563425i \(-0.809484\pi\)
−0.826168 + 0.563425i \(0.809484\pi\)
\(410\) −15.4508 −0.763063
\(411\) −22.4164 −1.10572
\(412\) 5.14590 0.253520
\(413\) 29.2918 1.44136
\(414\) 5.67376 0.278850
\(415\) 2.68692 0.131896
\(416\) −3.00000 −0.147087
\(417\) 40.5066 1.98362
\(418\) 7.14590 0.349517
\(419\) 0.673762 0.0329154 0.0164577 0.999865i \(-0.494761\pi\)
0.0164577 + 0.999865i \(0.494761\pi\)
\(420\) −10.8541 −0.529626
\(421\) 33.3951 1.62758 0.813789 0.581160i \(-0.197401\pi\)
0.813789 + 0.581160i \(0.197401\pi\)
\(422\) 17.8541 0.869124
\(423\) 44.5623 2.16669
\(424\) −9.00000 −0.437079
\(425\) 23.0902 1.12004
\(426\) 31.2705 1.51506
\(427\) 7.14590 0.345814
\(428\) −3.76393 −0.181937
\(429\) −18.7082 −0.903241
\(430\) 12.7639 0.615531
\(431\) −24.7639 −1.19284 −0.596418 0.802674i \(-0.703410\pi\)
−0.596418 + 0.802674i \(0.703410\pi\)
\(432\) −2.23607 −0.107583
\(433\) 5.58359 0.268330 0.134165 0.990959i \(-0.457165\pi\)
0.134165 + 0.990959i \(0.457165\pi\)
\(434\) 18.2705 0.877013
\(435\) −33.4164 −1.60219
\(436\) −9.47214 −0.453633
\(437\) −4.41641 −0.211265
\(438\) −1.85410 −0.0885924
\(439\) −13.0000 −0.620456 −0.310228 0.950662i \(-0.600405\pi\)
−0.310228 + 0.950662i \(0.600405\pi\)
\(440\) 3.29180 0.156930
\(441\) 7.70820 0.367057
\(442\) 22.4164 1.06624
\(443\) 4.52786 0.215125 0.107563 0.994198i \(-0.465695\pi\)
0.107563 + 0.994198i \(0.465695\pi\)
\(444\) 4.85410 0.230365
\(445\) 23.2148 1.10049
\(446\) −1.58359 −0.0749853
\(447\) 5.85410 0.276890
\(448\) −3.00000 −0.141737
\(449\) −17.3607 −0.819301 −0.409651 0.912243i \(-0.634349\pi\)
−0.409651 + 0.912243i \(0.634349\pi\)
\(450\) −11.9098 −0.561435
\(451\) −26.6312 −1.25401
\(452\) −4.38197 −0.206110
\(453\) 25.6525 1.20526
\(454\) 13.8541 0.650205
\(455\) −12.4377 −0.583088
\(456\) 7.85410 0.367802
\(457\) −41.0344 −1.91951 −0.959755 0.280838i \(-0.909388\pi\)
−0.959755 + 0.280838i \(0.909388\pi\)
\(458\) 26.5967 1.24278
\(459\) 16.7082 0.779872
\(460\) −2.03444 −0.0948563
\(461\) −2.38197 −0.110939 −0.0554696 0.998460i \(-0.517666\pi\)
−0.0554696 + 0.998460i \(0.517666\pi\)
\(462\) −18.7082 −0.870384
\(463\) 26.3607 1.22508 0.612542 0.790438i \(-0.290147\pi\)
0.612542 + 0.790438i \(0.290147\pi\)
\(464\) −9.23607 −0.428774
\(465\) −22.0344 −1.02182
\(466\) 4.14590 0.192055
\(467\) 31.7984 1.47145 0.735727 0.677279i \(-0.236841\pi\)
0.735727 + 0.677279i \(0.236841\pi\)
\(468\) −11.5623 −0.534468
\(469\) −5.56231 −0.256843
\(470\) −15.9787 −0.737043
\(471\) −21.1803 −0.975939
\(472\) −9.76393 −0.449421
\(473\) 22.0000 1.01156
\(474\) 4.85410 0.222956
\(475\) 9.27051 0.425360
\(476\) 22.4164 1.02745
\(477\) −34.6869 −1.58820
\(478\) 3.70820 0.169609
\(479\) −13.8541 −0.633010 −0.316505 0.948591i \(-0.602509\pi\)
−0.316505 + 0.948591i \(0.602509\pi\)
\(480\) 3.61803 0.165140
\(481\) 5.56231 0.253619
\(482\) −10.4164 −0.474454
\(483\) 11.5623 0.526103
\(484\) −5.32624 −0.242102
\(485\) −19.0213 −0.863712
\(486\) 21.6525 0.982176
\(487\) 15.8885 0.719979 0.359989 0.932956i \(-0.382780\pi\)
0.359989 + 0.932956i \(0.382780\pi\)
\(488\) −2.38197 −0.107827
\(489\) −2.23607 −0.101118
\(490\) −2.76393 −0.124862
\(491\) −6.27051 −0.282984 −0.141492 0.989939i \(-0.545190\pi\)
−0.141492 + 0.989939i \(0.545190\pi\)
\(492\) −29.2705 −1.31962
\(493\) 69.0132 3.10820
\(494\) 9.00000 0.404929
\(495\) 12.6869 0.570235
\(496\) −6.09017 −0.273457
\(497\) 35.8328 1.60732
\(498\) 5.09017 0.228096
\(499\) −5.65248 −0.253040 −0.126520 0.991964i \(-0.540381\pi\)
−0.126520 + 0.991964i \(0.540381\pi\)
\(500\) 11.1803 0.500000
\(501\) 13.7082 0.612437
\(502\) 0.944272 0.0421449
\(503\) 5.29180 0.235950 0.117975 0.993017i \(-0.462360\pi\)
0.117975 + 0.993017i \(0.462360\pi\)
\(504\) −11.5623 −0.515026
\(505\) −7.23607 −0.322001
\(506\) −3.50658 −0.155886
\(507\) 10.4721 0.465084
\(508\) −12.4164 −0.550889
\(509\) −28.4164 −1.25954 −0.629768 0.776784i \(-0.716850\pi\)
−0.629768 + 0.776784i \(0.716850\pi\)
\(510\) −27.0344 −1.19711
\(511\) −2.12461 −0.0939873
\(512\) 1.00000 0.0441942
\(513\) 6.70820 0.296174
\(514\) −1.58359 −0.0698493
\(515\) −7.11146 −0.313368
\(516\) 24.1803 1.06448
\(517\) −27.5410 −1.21125
\(518\) 5.56231 0.244394
\(519\) 20.0902 0.881861
\(520\) 4.14590 0.181810
\(521\) −12.6525 −0.554315 −0.277158 0.960824i \(-0.589392\pi\)
−0.277158 + 0.960824i \(0.589392\pi\)
\(522\) −35.5967 −1.55803
\(523\) −6.03444 −0.263868 −0.131934 0.991259i \(-0.542119\pi\)
−0.131934 + 0.991259i \(0.542119\pi\)
\(524\) 21.6180 0.944388
\(525\) −24.2705 −1.05925
\(526\) 18.3607 0.800564
\(527\) 45.5066 1.98230
\(528\) 6.23607 0.271390
\(529\) −20.8328 −0.905775
\(530\) 12.4377 0.540259
\(531\) −37.6312 −1.63305
\(532\) 9.00000 0.390199
\(533\) −33.5410 −1.45282
\(534\) 43.9787 1.90315
\(535\) 5.20163 0.224886
\(536\) 1.85410 0.0800850
\(537\) 23.5623 1.01679
\(538\) −5.56231 −0.239808
\(539\) −4.76393 −0.205197
\(540\) 3.09017 0.132980
\(541\) −31.7082 −1.36324 −0.681621 0.731705i \(-0.738725\pi\)
−0.681621 + 0.731705i \(0.738725\pi\)
\(542\) −6.61803 −0.284269
\(543\) 47.1246 2.02231
\(544\) −7.47214 −0.320365
\(545\) 13.0902 0.560721
\(546\) −23.5623 −1.00837
\(547\) 9.94427 0.425186 0.212593 0.977141i \(-0.431809\pi\)
0.212593 + 0.977141i \(0.431809\pi\)
\(548\) 8.56231 0.365764
\(549\) −9.18034 −0.391807
\(550\) 7.36068 0.313860
\(551\) 27.7082 1.18041
\(552\) −3.85410 −0.164041
\(553\) 5.56231 0.236533
\(554\) −20.5623 −0.873609
\(555\) −6.70820 −0.284747
\(556\) −15.4721 −0.656165
\(557\) −7.76393 −0.328968 −0.164484 0.986380i \(-0.552596\pi\)
−0.164484 + 0.986380i \(0.552596\pi\)
\(558\) −23.4721 −0.993655
\(559\) 27.7082 1.17193
\(560\) 4.14590 0.175196
\(561\) −46.5967 −1.96732
\(562\) −25.3607 −1.06978
\(563\) −33.2705 −1.40218 −0.701092 0.713070i \(-0.747304\pi\)
−0.701092 + 0.713070i \(0.747304\pi\)
\(564\) −30.2705 −1.27462
\(565\) 6.05573 0.254766
\(566\) 10.7082 0.450099
\(567\) 17.1246 0.719166
\(568\) −11.9443 −0.501171
\(569\) −13.9656 −0.585467 −0.292733 0.956194i \(-0.594565\pi\)
−0.292733 + 0.956194i \(0.594565\pi\)
\(570\) −10.8541 −0.454628
\(571\) −25.0000 −1.04622 −0.523109 0.852266i \(-0.675228\pi\)
−0.523109 + 0.852266i \(0.675228\pi\)
\(572\) 7.14590 0.298785
\(573\) −58.5410 −2.44559
\(574\) −33.5410 −1.39998
\(575\) −4.54915 −0.189713
\(576\) 3.85410 0.160588
\(577\) −4.41641 −0.183857 −0.0919287 0.995766i \(-0.529303\pi\)
−0.0919287 + 0.995766i \(0.529303\pi\)
\(578\) 38.8328 1.61523
\(579\) −8.23607 −0.342279
\(580\) 12.7639 0.529993
\(581\) 5.83282 0.241986
\(582\) −36.0344 −1.49368
\(583\) 21.4377 0.887859
\(584\) 0.708204 0.0293057
\(585\) 15.9787 0.660639
\(586\) −32.0902 −1.32563
\(587\) −40.9443 −1.68995 −0.844975 0.534805i \(-0.820385\pi\)
−0.844975 + 0.534805i \(0.820385\pi\)
\(588\) −5.23607 −0.215932
\(589\) 18.2705 0.752823
\(590\) 13.4934 0.555515
\(591\) 7.32624 0.301361
\(592\) −1.85410 −0.0762031
\(593\) 30.2148 1.24077 0.620386 0.784296i \(-0.286976\pi\)
0.620386 + 0.784296i \(0.286976\pi\)
\(594\) 5.32624 0.218538
\(595\) −30.9787 −1.27000
\(596\) −2.23607 −0.0915929
\(597\) −55.6869 −2.27911
\(598\) −4.41641 −0.180600
\(599\) −16.1459 −0.659704 −0.329852 0.944033i \(-0.606999\pi\)
−0.329852 + 0.944033i \(0.606999\pi\)
\(600\) 8.09017 0.330280
\(601\) −17.2705 −0.704479 −0.352239 0.935910i \(-0.614580\pi\)
−0.352239 + 0.935910i \(0.614580\pi\)
\(602\) 27.7082 1.12930
\(603\) 7.14590 0.291003
\(604\) −9.79837 −0.398690
\(605\) 7.36068 0.299254
\(606\) −13.7082 −0.556858
\(607\) 6.41641 0.260434 0.130217 0.991486i \(-0.458433\pi\)
0.130217 + 0.991486i \(0.458433\pi\)
\(608\) −3.00000 −0.121666
\(609\) −72.5410 −2.93951
\(610\) 3.29180 0.133281
\(611\) −34.6869 −1.40328
\(612\) −28.7984 −1.16411
\(613\) 23.4164 0.945780 0.472890 0.881122i \(-0.343211\pi\)
0.472890 + 0.881122i \(0.343211\pi\)
\(614\) 3.90983 0.157788
\(615\) 40.4508 1.63114
\(616\) 7.14590 0.287916
\(617\) 21.3262 0.858562 0.429281 0.903171i \(-0.358767\pi\)
0.429281 + 0.903171i \(0.358767\pi\)
\(618\) −13.4721 −0.541929
\(619\) 44.8541 1.80284 0.901419 0.432947i \(-0.142526\pi\)
0.901419 + 0.432947i \(0.142526\pi\)
\(620\) 8.41641 0.338011
\(621\) −3.29180 −0.132095
\(622\) 24.7639 0.992943
\(623\) 50.3951 2.01904
\(624\) 7.85410 0.314416
\(625\) 0 0
\(626\) 32.7426 1.30866
\(627\) −18.7082 −0.747134
\(628\) 8.09017 0.322833
\(629\) 13.8541 0.552399
\(630\) 15.9787 0.636607
\(631\) 15.2705 0.607909 0.303955 0.952686i \(-0.401693\pi\)
0.303955 + 0.952686i \(0.401693\pi\)
\(632\) −1.85410 −0.0737522
\(633\) −46.7426 −1.85785
\(634\) −10.6180 −0.421696
\(635\) 17.1591 0.680936
\(636\) 23.5623 0.934306
\(637\) −6.00000 −0.237729
\(638\) 22.0000 0.870988
\(639\) −46.0344 −1.82109
\(640\) −1.38197 −0.0546270
\(641\) 18.8197 0.743332 0.371666 0.928367i \(-0.378787\pi\)
0.371666 + 0.928367i \(0.378787\pi\)
\(642\) 9.85410 0.388910
\(643\) −30.3050 −1.19511 −0.597555 0.801828i \(-0.703861\pi\)
−0.597555 + 0.801828i \(0.703861\pi\)
\(644\) −4.41641 −0.174031
\(645\) −33.4164 −1.31577
\(646\) 22.4164 0.881962
\(647\) 2.67376 0.105116 0.0525582 0.998618i \(-0.483262\pi\)
0.0525582 + 0.998618i \(0.483262\pi\)
\(648\) −5.70820 −0.224239
\(649\) 23.2574 0.912931
\(650\) 9.27051 0.363619
\(651\) −47.8328 −1.87472
\(652\) 0.854102 0.0334492
\(653\) 18.0902 0.707923 0.353962 0.935260i \(-0.384834\pi\)
0.353962 + 0.935260i \(0.384834\pi\)
\(654\) 24.7984 0.969693
\(655\) −29.8754 −1.16733
\(656\) 11.1803 0.436519
\(657\) 2.72949 0.106488
\(658\) −34.6869 −1.35224
\(659\) 2.47214 0.0963007 0.0481504 0.998840i \(-0.484667\pi\)
0.0481504 + 0.998840i \(0.484667\pi\)
\(660\) −8.61803 −0.335457
\(661\) 45.7082 1.77784 0.888922 0.458059i \(-0.151455\pi\)
0.888922 + 0.458059i \(0.151455\pi\)
\(662\) −5.43769 −0.211342
\(663\) −58.6869 −2.27921
\(664\) −1.94427 −0.0754524
\(665\) −12.4377 −0.482313
\(666\) −7.14590 −0.276898
\(667\) −13.5967 −0.526468
\(668\) −5.23607 −0.202590
\(669\) 4.14590 0.160290
\(670\) −2.56231 −0.0989905
\(671\) 5.67376 0.219033
\(672\) 7.85410 0.302979
\(673\) −18.5410 −0.714704 −0.357352 0.933970i \(-0.616320\pi\)
−0.357352 + 0.933970i \(0.616320\pi\)
\(674\) 4.61803 0.177880
\(675\) 6.90983 0.265959
\(676\) −4.00000 −0.153846
\(677\) −22.8885 −0.879678 −0.439839 0.898077i \(-0.644965\pi\)
−0.439839 + 0.898077i \(0.644965\pi\)
\(678\) 11.4721 0.440585
\(679\) −41.2918 −1.58463
\(680\) 10.3262 0.395993
\(681\) −36.2705 −1.38989
\(682\) 14.5066 0.555486
\(683\) 9.38197 0.358991 0.179495 0.983759i \(-0.442553\pi\)
0.179495 + 0.983759i \(0.442553\pi\)
\(684\) −11.5623 −0.442096
\(685\) −11.8328 −0.452109
\(686\) 15.0000 0.572703
\(687\) −69.6312 −2.65660
\(688\) −9.23607 −0.352122
\(689\) 27.0000 1.02862
\(690\) 5.32624 0.202766
\(691\) −15.0902 −0.574057 −0.287029 0.957922i \(-0.592667\pi\)
−0.287029 + 0.957922i \(0.592667\pi\)
\(692\) −7.67376 −0.291713
\(693\) 27.5410 1.04620
\(694\) −8.67376 −0.329252
\(695\) 21.3820 0.811064
\(696\) 24.1803 0.916553
\(697\) −83.5410 −3.16434
\(698\) −22.7082 −0.859518
\(699\) −10.8541 −0.410540
\(700\) 9.27051 0.350392
\(701\) −49.2148 −1.85882 −0.929408 0.369053i \(-0.879682\pi\)
−0.929408 + 0.369053i \(0.879682\pi\)
\(702\) 6.70820 0.253185
\(703\) 5.56231 0.209786
\(704\) −2.38197 −0.0897737
\(705\) 41.8328 1.57551
\(706\) −6.81966 −0.256661
\(707\) −15.7082 −0.590768
\(708\) 25.5623 0.960690
\(709\) −17.0557 −0.640541 −0.320271 0.947326i \(-0.603774\pi\)
−0.320271 + 0.947326i \(0.603774\pi\)
\(710\) 16.5066 0.619481
\(711\) −7.14590 −0.267992
\(712\) −16.7984 −0.629546
\(713\) −8.96556 −0.335763
\(714\) −58.6869 −2.19630
\(715\) −9.87539 −0.369319
\(716\) −9.00000 −0.336346
\(717\) −9.70820 −0.362560
\(718\) −14.5967 −0.544746
\(719\) −15.0557 −0.561484 −0.280742 0.959783i \(-0.590581\pi\)
−0.280742 + 0.959783i \(0.590581\pi\)
\(720\) −5.32624 −0.198497
\(721\) −15.4377 −0.574930
\(722\) −10.0000 −0.372161
\(723\) 27.2705 1.01420
\(724\) −18.0000 −0.668965
\(725\) 28.5410 1.05999
\(726\) 13.9443 0.517520
\(727\) −2.47214 −0.0916864 −0.0458432 0.998949i \(-0.514597\pi\)
−0.0458432 + 0.998949i \(0.514597\pi\)
\(728\) 9.00000 0.333562
\(729\) −39.5623 −1.46527
\(730\) −0.978714 −0.0362238
\(731\) 69.0132 2.55254
\(732\) 6.23607 0.230492
\(733\) −1.11146 −0.0410526 −0.0205263 0.999789i \(-0.506534\pi\)
−0.0205263 + 0.999789i \(0.506534\pi\)
\(734\) 4.88854 0.180439
\(735\) 7.23607 0.266906
\(736\) 1.47214 0.0542637
\(737\) −4.41641 −0.162680
\(738\) 43.0902 1.58617
\(739\) −38.4721 −1.41522 −0.707610 0.706603i \(-0.750227\pi\)
−0.707610 + 0.706603i \(0.750227\pi\)
\(740\) 2.56231 0.0941922
\(741\) −23.5623 −0.865583
\(742\) 27.0000 0.991201
\(743\) −12.7639 −0.468263 −0.234132 0.972205i \(-0.575225\pi\)
−0.234132 + 0.972205i \(0.575225\pi\)
\(744\) 15.9443 0.584545
\(745\) 3.09017 0.113215
\(746\) −12.0000 −0.439351
\(747\) −7.49342 −0.274170
\(748\) 17.7984 0.650773
\(749\) 11.2918 0.412593
\(750\) −29.2705 −1.06881
\(751\) −23.5623 −0.859801 −0.429900 0.902876i \(-0.641451\pi\)
−0.429900 + 0.902876i \(0.641451\pi\)
\(752\) 11.5623 0.421634
\(753\) −2.47214 −0.0900896
\(754\) 27.7082 1.00907
\(755\) 13.5410 0.492808
\(756\) 6.70820 0.243975
\(757\) 11.7082 0.425542 0.212771 0.977102i \(-0.431751\pi\)
0.212771 + 0.977102i \(0.431751\pi\)
\(758\) 22.8328 0.829325
\(759\) 9.18034 0.333225
\(760\) 4.14590 0.150388
\(761\) −3.03444 −0.109998 −0.0549992 0.998486i \(-0.517516\pi\)
−0.0549992 + 0.998486i \(0.517516\pi\)
\(762\) 32.5066 1.17759
\(763\) 28.4164 1.02874
\(764\) 22.3607 0.808981
\(765\) 39.7984 1.43891
\(766\) −2.29180 −0.0828060
\(767\) 29.2918 1.05767
\(768\) −2.61803 −0.0944702
\(769\) −13.4164 −0.483808 −0.241904 0.970300i \(-0.577772\pi\)
−0.241904 + 0.970300i \(0.577772\pi\)
\(770\) −9.87539 −0.355884
\(771\) 4.14590 0.149311
\(772\) 3.14590 0.113223
\(773\) −41.2361 −1.48316 −0.741579 0.670865i \(-0.765923\pi\)
−0.741579 + 0.670865i \(0.765923\pi\)
\(774\) −35.5967 −1.27950
\(775\) 18.8197 0.676022
\(776\) 13.7639 0.494096
\(777\) −14.5623 −0.522420
\(778\) −27.2361 −0.976460
\(779\) −33.5410 −1.20173
\(780\) −10.8541 −0.388639
\(781\) 28.4508 1.01805
\(782\) −11.0000 −0.393359
\(783\) 20.6525 0.738059
\(784\) 2.00000 0.0714286
\(785\) −11.1803 −0.399043
\(786\) −56.5967 −2.01874
\(787\) −7.94427 −0.283183 −0.141591 0.989925i \(-0.545222\pi\)
−0.141591 + 0.989925i \(0.545222\pi\)
\(788\) −2.79837 −0.0996879
\(789\) −48.0689 −1.71130
\(790\) 2.56231 0.0911628
\(791\) 13.1459 0.467414
\(792\) −9.18034 −0.326209
\(793\) 7.14590 0.253758
\(794\) −8.56231 −0.303865
\(795\) −32.5623 −1.15487
\(796\) 21.2705 0.753913
\(797\) −30.9443 −1.09610 −0.548051 0.836445i \(-0.684630\pi\)
−0.548051 + 0.836445i \(0.684630\pi\)
\(798\) −23.5623 −0.834097
\(799\) −86.3951 −3.05644
\(800\) −3.09017 −0.109254
\(801\) −64.7426 −2.28757
\(802\) −14.0557 −0.496325
\(803\) −1.68692 −0.0595300
\(804\) −4.85410 −0.171191
\(805\) 6.10333 0.215114
\(806\) 18.2705 0.643551
\(807\) 14.5623 0.512617
\(808\) 5.23607 0.184204
\(809\) 31.1459 1.09503 0.547516 0.836795i \(-0.315574\pi\)
0.547516 + 0.836795i \(0.315574\pi\)
\(810\) 7.88854 0.277175
\(811\) −22.9443 −0.805682 −0.402841 0.915270i \(-0.631977\pi\)
−0.402841 + 0.915270i \(0.631977\pi\)
\(812\) 27.7082 0.972367
\(813\) 17.3262 0.607658
\(814\) 4.41641 0.154795
\(815\) −1.18034 −0.0413455
\(816\) 19.5623 0.684818
\(817\) 27.7082 0.969387
\(818\) −33.4164 −1.16838
\(819\) 34.6869 1.21206
\(820\) −15.4508 −0.539567
\(821\) −1.49342 −0.0521208 −0.0260604 0.999660i \(-0.508296\pi\)
−0.0260604 + 0.999660i \(0.508296\pi\)
\(822\) −22.4164 −0.781862
\(823\) 19.4164 0.676813 0.338407 0.941000i \(-0.390112\pi\)
0.338407 + 0.941000i \(0.390112\pi\)
\(824\) 5.14590 0.179266
\(825\) −19.2705 −0.670913
\(826\) 29.2918 1.01919
\(827\) 40.9443 1.42377 0.711886 0.702295i \(-0.247841\pi\)
0.711886 + 0.702295i \(0.247841\pi\)
\(828\) 5.67376 0.197177
\(829\) −7.29180 −0.253255 −0.126627 0.991950i \(-0.540415\pi\)
−0.126627 + 0.991950i \(0.540415\pi\)
\(830\) 2.68692 0.0932643
\(831\) 53.8328 1.86744
\(832\) −3.00000 −0.104006
\(833\) −14.9443 −0.517788
\(834\) 40.5066 1.40263
\(835\) 7.23607 0.250414
\(836\) 7.14590 0.247146
\(837\) 13.6180 0.470708
\(838\) 0.673762 0.0232747
\(839\) 15.3475 0.529855 0.264928 0.964268i \(-0.414652\pi\)
0.264928 + 0.964268i \(0.414652\pi\)
\(840\) −10.8541 −0.374502
\(841\) 56.3050 1.94155
\(842\) 33.3951 1.15087
\(843\) 66.3951 2.28677
\(844\) 17.8541 0.614564
\(845\) 5.52786 0.190164
\(846\) 44.5623 1.53208
\(847\) 15.9787 0.549035
\(848\) −9.00000 −0.309061
\(849\) −28.0344 −0.962140
\(850\) 23.0902 0.791986
\(851\) −2.72949 −0.0935657
\(852\) 31.2705 1.07131
\(853\) 13.4377 0.460098 0.230049 0.973179i \(-0.426111\pi\)
0.230049 + 0.973179i \(0.426111\pi\)
\(854\) 7.14590 0.244528
\(855\) 15.9787 0.546460
\(856\) −3.76393 −0.128649
\(857\) −32.0902 −1.09618 −0.548090 0.836420i \(-0.684645\pi\)
−0.548090 + 0.836420i \(0.684645\pi\)
\(858\) −18.7082 −0.638688
\(859\) 16.0557 0.547814 0.273907 0.961756i \(-0.411684\pi\)
0.273907 + 0.961756i \(0.411684\pi\)
\(860\) 12.7639 0.435246
\(861\) 87.8115 2.99261
\(862\) −24.7639 −0.843463
\(863\) −44.0132 −1.49823 −0.749113 0.662443i \(-0.769520\pi\)
−0.749113 + 0.662443i \(0.769520\pi\)
\(864\) −2.23607 −0.0760726
\(865\) 10.6049 0.360577
\(866\) 5.58359 0.189738
\(867\) −101.666 −3.45275
\(868\) 18.2705 0.620142
\(869\) 4.41641 0.149816
\(870\) −33.4164 −1.13292
\(871\) −5.56231 −0.188472
\(872\) −9.47214 −0.320767
\(873\) 53.0476 1.79539
\(874\) −4.41641 −0.149387
\(875\) −33.5410 −1.13389
\(876\) −1.85410 −0.0626443
\(877\) −35.1246 −1.18607 −0.593037 0.805175i \(-0.702071\pi\)
−0.593037 + 0.805175i \(0.702071\pi\)
\(878\) −13.0000 −0.438729
\(879\) 84.0132 2.83369
\(880\) 3.29180 0.110966
\(881\) −57.7214 −1.94468 −0.972341 0.233566i \(-0.924961\pi\)
−0.972341 + 0.233566i \(0.924961\pi\)
\(882\) 7.70820 0.259549
\(883\) −51.0344 −1.71745 −0.858723 0.512440i \(-0.828742\pi\)
−0.858723 + 0.512440i \(0.828742\pi\)
\(884\) 22.4164 0.753945
\(885\) −35.3262 −1.18748
\(886\) 4.52786 0.152117
\(887\) −3.70820 −0.124509 −0.0622547 0.998060i \(-0.519829\pi\)
−0.0622547 + 0.998060i \(0.519829\pi\)
\(888\) 4.85410 0.162893
\(889\) 37.2492 1.24930
\(890\) 23.2148 0.778161
\(891\) 13.5967 0.455508
\(892\) −1.58359 −0.0530226
\(893\) −34.6869 −1.16075
\(894\) 5.85410 0.195790
\(895\) 12.4377 0.415746
\(896\) −3.00000 −0.100223
\(897\) 11.5623 0.386054
\(898\) −17.3607 −0.579333
\(899\) 56.2492 1.87602
\(900\) −11.9098 −0.396994
\(901\) 67.2492 2.24040
\(902\) −26.6312 −0.886722
\(903\) −72.5410 −2.41401
\(904\) −4.38197 −0.145742
\(905\) 24.8754 0.826886
\(906\) 25.6525 0.852246
\(907\) −21.4164 −0.711120 −0.355560 0.934653i \(-0.615710\pi\)
−0.355560 + 0.934653i \(0.615710\pi\)
\(908\) 13.8541 0.459765
\(909\) 20.1803 0.669340
\(910\) −12.4377 −0.412306
\(911\) 8.56231 0.283682 0.141841 0.989889i \(-0.454698\pi\)
0.141841 + 0.989889i \(0.454698\pi\)
\(912\) 7.85410 0.260075
\(913\) 4.63119 0.153270
\(914\) −41.0344 −1.35730
\(915\) −8.61803 −0.284903
\(916\) 26.5967 0.878781
\(917\) −64.8541 −2.14167
\(918\) 16.7082 0.551453
\(919\) 43.7214 1.44223 0.721117 0.692813i \(-0.243629\pi\)
0.721117 + 0.692813i \(0.243629\pi\)
\(920\) −2.03444 −0.0670736
\(921\) −10.2361 −0.337290
\(922\) −2.38197 −0.0784459
\(923\) 35.8328 1.17945
\(924\) −18.7082 −0.615455
\(925\) 5.72949 0.188384
\(926\) 26.3607 0.866266
\(927\) 19.8328 0.651395
\(928\) −9.23607 −0.303189
\(929\) 41.8328 1.37249 0.686245 0.727370i \(-0.259258\pi\)
0.686245 + 0.727370i \(0.259258\pi\)
\(930\) −22.0344 −0.722538
\(931\) −6.00000 −0.196642
\(932\) 4.14590 0.135803
\(933\) −64.8328 −2.12253
\(934\) 31.7984 1.04047
\(935\) −24.5967 −0.804400
\(936\) −11.5623 −0.377926
\(937\) −8.83282 −0.288556 −0.144278 0.989537i \(-0.546086\pi\)
−0.144278 + 0.989537i \(0.546086\pi\)
\(938\) −5.56231 −0.181616
\(939\) −85.7214 −2.79741
\(940\) −15.9787 −0.521168
\(941\) 1.79837 0.0586253 0.0293127 0.999570i \(-0.490668\pi\)
0.0293127 + 0.999570i \(0.490668\pi\)
\(942\) −21.1803 −0.690093
\(943\) 16.4590 0.535978
\(944\) −9.76393 −0.317789
\(945\) −9.27051 −0.301570
\(946\) 22.0000 0.715282
\(947\) −16.2016 −0.526482 −0.263241 0.964730i \(-0.584791\pi\)
−0.263241 + 0.964730i \(0.584791\pi\)
\(948\) 4.85410 0.157654
\(949\) −2.12461 −0.0689678
\(950\) 9.27051 0.300775
\(951\) 27.7984 0.901424
\(952\) 22.4164 0.726520
\(953\) −26.3475 −0.853480 −0.426740 0.904374i \(-0.640338\pi\)
−0.426740 + 0.904374i \(0.640338\pi\)
\(954\) −34.6869 −1.12303
\(955\) −30.9017 −0.999956
\(956\) 3.70820 0.119932
\(957\) −57.5967 −1.86184
\(958\) −13.8541 −0.447606
\(959\) −25.6869 −0.829474
\(960\) 3.61803 0.116772
\(961\) 6.09017 0.196457
\(962\) 5.56231 0.179336
\(963\) −14.5066 −0.467468
\(964\) −10.4164 −0.335490
\(965\) −4.34752 −0.139952
\(966\) 11.5623 0.372011
\(967\) 58.8328 1.89194 0.945968 0.324260i \(-0.105115\pi\)
0.945968 + 0.324260i \(0.105115\pi\)
\(968\) −5.32624 −0.171192
\(969\) −58.6869 −1.88530
\(970\) −19.0213 −0.610737
\(971\) −31.2492 −1.00284 −0.501418 0.865205i \(-0.667188\pi\)
−0.501418 + 0.865205i \(0.667188\pi\)
\(972\) 21.6525 0.694503
\(973\) 46.4164 1.48804
\(974\) 15.8885 0.509102
\(975\) −24.2705 −0.777278
\(976\) −2.38197 −0.0762449
\(977\) −13.7639 −0.440347 −0.220174 0.975461i \(-0.570662\pi\)
−0.220174 + 0.975461i \(0.570662\pi\)
\(978\) −2.23607 −0.0715016
\(979\) 40.0132 1.27883
\(980\) −2.76393 −0.0882906
\(981\) −36.5066 −1.16557
\(982\) −6.27051 −0.200100
\(983\) −10.7426 −0.342637 −0.171319 0.985216i \(-0.554803\pi\)
−0.171319 + 0.985216i \(0.554803\pi\)
\(984\) −29.2705 −0.933110
\(985\) 3.86726 0.123221
\(986\) 69.0132 2.19783
\(987\) 90.8115 2.89056
\(988\) 9.00000 0.286328
\(989\) −13.5967 −0.432351
\(990\) 12.6869 0.403217
\(991\) −9.30495 −0.295582 −0.147791 0.989019i \(-0.547216\pi\)
−0.147791 + 0.989019i \(0.547216\pi\)
\(992\) −6.09017 −0.193363
\(993\) 14.2361 0.451768
\(994\) 35.8328 1.13655
\(995\) −29.3951 −0.931888
\(996\) 5.09017 0.161288
\(997\) 35.0000 1.10846 0.554231 0.832363i \(-0.313013\pi\)
0.554231 + 0.832363i \(0.313013\pi\)
\(998\) −5.65248 −0.178926
\(999\) 4.14590 0.131170
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 \(a_p\))