Properties

Label 8035.2.a.e.1.18
Level 8035
Weight 2
Character 8035.1
Self dual Yes
Analytic conductor 64.160
Analytic rank 0
Dimension 153
CM No

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Newspace parameters

Level: \( N \) = \( 8035 = 5 \cdot 1607 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8035.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1597980241\)
Analytic rank: \(0\)
Dimension: \(153\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 8035.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.29854 q^{2}\) \(+0.376180 q^{3}\) \(+3.28327 q^{4}\) \(+1.00000 q^{5}\) \(-0.864664 q^{6}\) \(-1.95111 q^{7}\) \(-2.94965 q^{8}\) \(-2.85849 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.29854 q^{2}\) \(+0.376180 q^{3}\) \(+3.28327 q^{4}\) \(+1.00000 q^{5}\) \(-0.864664 q^{6}\) \(-1.95111 q^{7}\) \(-2.94965 q^{8}\) \(-2.85849 q^{9}\) \(-2.29854 q^{10}\) \(+2.60450 q^{11}\) \(+1.23510 q^{12}\) \(-2.36574 q^{13}\) \(+4.48469 q^{14}\) \(+0.376180 q^{15}\) \(+0.213337 q^{16}\) \(-1.73671 q^{17}\) \(+6.57034 q^{18}\) \(+1.91328 q^{19}\) \(+3.28327 q^{20}\) \(-0.733968 q^{21}\) \(-5.98655 q^{22}\) \(-4.02247 q^{23}\) \(-1.10960 q^{24}\) \(+1.00000 q^{25}\) \(+5.43775 q^{26}\) \(-2.20385 q^{27}\) \(-6.40602 q^{28}\) \(-2.38367 q^{29}\) \(-0.864664 q^{30}\) \(+4.76604 q^{31}\) \(+5.40894 q^{32}\) \(+0.979762 q^{33}\) \(+3.99189 q^{34}\) \(-1.95111 q^{35}\) \(-9.38520 q^{36}\) \(-9.22691 q^{37}\) \(-4.39774 q^{38}\) \(-0.889945 q^{39}\) \(-2.94965 q^{40}\) \(-5.94952 q^{41}\) \(+1.68705 q^{42}\) \(+10.4144 q^{43}\) \(+8.55130 q^{44}\) \(-2.85849 q^{45}\) \(+9.24579 q^{46}\) \(+0.872904 q^{47}\) \(+0.0802530 q^{48}\) \(-3.19318 q^{49}\) \(-2.29854 q^{50}\) \(-0.653316 q^{51}\) \(-7.76738 q^{52}\) \(-2.14307 q^{53}\) \(+5.06562 q^{54}\) \(+2.60450 q^{55}\) \(+5.75509 q^{56}\) \(+0.719737 q^{57}\) \(+5.47896 q^{58}\) \(+9.38810 q^{59}\) \(+1.23510 q^{60}\) \(+0.990473 q^{61}\) \(-10.9549 q^{62}\) \(+5.57722 q^{63}\) \(-12.8593 q^{64}\) \(-2.36574 q^{65}\) \(-2.25202 q^{66}\) \(-3.56243 q^{67}\) \(-5.70209 q^{68}\) \(-1.51317 q^{69}\) \(+4.48469 q^{70}\) \(+9.58765 q^{71}\) \(+8.43154 q^{72}\) \(+0.651431 q^{73}\) \(+21.2084 q^{74}\) \(+0.376180 q^{75}\) \(+6.28182 q^{76}\) \(-5.08167 q^{77}\) \(+2.04557 q^{78}\) \(-6.54717 q^{79}\) \(+0.213337 q^{80}\) \(+7.74642 q^{81}\) \(+13.6752 q^{82}\) \(-12.9789 q^{83}\) \(-2.40982 q^{84}\) \(-1.73671 q^{85}\) \(-23.9378 q^{86}\) \(-0.896691 q^{87}\) \(-7.68238 q^{88}\) \(-10.2616 q^{89}\) \(+6.57034 q^{90}\) \(+4.61582 q^{91}\) \(-13.2069 q^{92}\) \(+1.79289 q^{93}\) \(-2.00640 q^{94}\) \(+1.91328 q^{95}\) \(+2.03474 q^{96}\) \(+2.88823 q^{97}\) \(+7.33964 q^{98}\) \(-7.44494 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut 18q^{10} \) \(\mathstrut +\mathstrut 38q^{11} \) \(\mathstrut +\mathstrut 14q^{12} \) \(\mathstrut +\mathstrut 28q^{13} \) \(\mathstrut +\mathstrut 53q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 214q^{16} \) \(\mathstrut +\mathstrut 50q^{17} \) \(\mathstrut +\mathstrut 47q^{18} \) \(\mathstrut +\mathstrut 65q^{19} \) \(\mathstrut +\mathstrut 176q^{20} \) \(\mathstrut +\mathstrut 109q^{21} \) \(\mathstrut +\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 52q^{23} \) \(\mathstrut +\mathstrut 66q^{24} \) \(\mathstrut +\mathstrut 153q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 19q^{27} \) \(\mathstrut +\mathstrut 26q^{28} \) \(\mathstrut +\mathstrut 172q^{29} \) \(\mathstrut +\mathstrut 19q^{30} \) \(\mathstrut +\mathstrut 60q^{31} \) \(\mathstrut +\mathstrut 107q^{32} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 40q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 241q^{36} \) \(\mathstrut +\mathstrut 65q^{37} \) \(\mathstrut +\mathstrut 29q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 57q^{40} \) \(\mathstrut +\mathstrut 152q^{41} \) \(\mathstrut -\mathstrut 19q^{42} \) \(\mathstrut +\mathstrut 22q^{43} \) \(\mathstrut +\mathstrut 97q^{44} \) \(\mathstrut +\mathstrut 206q^{45} \) \(\mathstrut +\mathstrut 86q^{46} \) \(\mathstrut +\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 260q^{49} \) \(\mathstrut +\mathstrut 18q^{50} \) \(\mathstrut +\mathstrut 102q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 169q^{53} \) \(\mathstrut +\mathstrut 64q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 146q^{56} \) \(\mathstrut +\mathstrut 40q^{57} \) \(\mathstrut -\mathstrut 9q^{58} \) \(\mathstrut +\mathstrut 64q^{59} \) \(\mathstrut +\mathstrut 14q^{60} \) \(\mathstrut +\mathstrut 164q^{61} \) \(\mathstrut +\mathstrut 12q^{62} \) \(\mathstrut +\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 259q^{64} \) \(\mathstrut +\mathstrut 28q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 112q^{68} \) \(\mathstrut +\mathstrut 119q^{69} \) \(\mathstrut +\mathstrut 53q^{70} \) \(\mathstrut +\mathstrut 100q^{71} \) \(\mathstrut +\mathstrut 77q^{72} \) \(\mathstrut +\mathstrut 10q^{73} \) \(\mathstrut +\mathstrut 98q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 126q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 110q^{79} \) \(\mathstrut +\mathstrut 214q^{80} \) \(\mathstrut +\mathstrut 305q^{81} \) \(\mathstrut -\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 36q^{83} \) \(\mathstrut +\mathstrut 172q^{84} \) \(\mathstrut +\mathstrut 50q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 47q^{88} \) \(\mathstrut +\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 47q^{90} \) \(\mathstrut +\mathstrut 82q^{91} \) \(\mathstrut +\mathstrut 130q^{92} \) \(\mathstrut +\mathstrut 31q^{93} \) \(\mathstrut +\mathstrut 77q^{94} \) \(\mathstrut +\mathstrut 65q^{95} \) \(\mathstrut +\mathstrut 57q^{96} \) \(\mathstrut +\mathstrut 11q^{97} \) \(\mathstrut +\mathstrut 29q^{98} \) \(\mathstrut +\mathstrut 99q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.29854 −1.62531 −0.812656 0.582744i \(-0.801979\pi\)
−0.812656 + 0.582744i \(0.801979\pi\)
\(3\) 0.376180 0.217188 0.108594 0.994086i \(-0.465365\pi\)
0.108594 + 0.994086i \(0.465365\pi\)
\(4\) 3.28327 1.64164
\(5\) 1.00000 0.447214
\(6\) −0.864664 −0.352998
\(7\) −1.95111 −0.737449 −0.368725 0.929539i \(-0.620205\pi\)
−0.368725 + 0.929539i \(0.620205\pi\)
\(8\) −2.94965 −1.04286
\(9\) −2.85849 −0.952830
\(10\) −2.29854 −0.726861
\(11\) 2.60450 0.785287 0.392644 0.919691i \(-0.371561\pi\)
0.392644 + 0.919691i \(0.371561\pi\)
\(12\) 1.23510 0.356543
\(13\) −2.36574 −0.656139 −0.328069 0.944654i \(-0.606398\pi\)
−0.328069 + 0.944654i \(0.606398\pi\)
\(14\) 4.48469 1.19858
\(15\) 0.376180 0.0971293
\(16\) 0.213337 0.0533342
\(17\) −1.73671 −0.421214 −0.210607 0.977571i \(-0.567544\pi\)
−0.210607 + 0.977571i \(0.567544\pi\)
\(18\) 6.57034 1.54864
\(19\) 1.91328 0.438936 0.219468 0.975620i \(-0.429568\pi\)
0.219468 + 0.975620i \(0.429568\pi\)
\(20\) 3.28327 0.734162
\(21\) −0.733968 −0.160165
\(22\) −5.98655 −1.27634
\(23\) −4.02247 −0.838742 −0.419371 0.907815i \(-0.637749\pi\)
−0.419371 + 0.907815i \(0.637749\pi\)
\(24\) −1.10960 −0.226496
\(25\) 1.00000 0.200000
\(26\) 5.43775 1.06643
\(27\) −2.20385 −0.424130
\(28\) −6.40602 −1.21062
\(29\) −2.38367 −0.442637 −0.221319 0.975202i \(-0.571036\pi\)
−0.221319 + 0.975202i \(0.571036\pi\)
\(30\) −0.864664 −0.157865
\(31\) 4.76604 0.856006 0.428003 0.903777i \(-0.359217\pi\)
0.428003 + 0.903777i \(0.359217\pi\)
\(32\) 5.40894 0.956175
\(33\) 0.979762 0.170555
\(34\) 3.99189 0.684604
\(35\) −1.95111 −0.329797
\(36\) −9.38520 −1.56420
\(37\) −9.22691 −1.51689 −0.758447 0.651735i \(-0.774042\pi\)
−0.758447 + 0.651735i \(0.774042\pi\)
\(38\) −4.39774 −0.713408
\(39\) −0.889945 −0.142505
\(40\) −2.94965 −0.466381
\(41\) −5.94952 −0.929159 −0.464580 0.885531i \(-0.653795\pi\)
−0.464580 + 0.885531i \(0.653795\pi\)
\(42\) 1.68705 0.260318
\(43\) 10.4144 1.58818 0.794088 0.607803i \(-0.207949\pi\)
0.794088 + 0.607803i \(0.207949\pi\)
\(44\) 8.55130 1.28916
\(45\) −2.85849 −0.426118
\(46\) 9.24579 1.36322
\(47\) 0.872904 0.127326 0.0636631 0.997971i \(-0.479722\pi\)
0.0636631 + 0.997971i \(0.479722\pi\)
\(48\) 0.0802530 0.0115835
\(49\) −3.19318 −0.456168
\(50\) −2.29854 −0.325062
\(51\) −0.653316 −0.0914825
\(52\) −7.76738 −1.07714
\(53\) −2.14307 −0.294373 −0.147186 0.989109i \(-0.547022\pi\)
−0.147186 + 0.989109i \(0.547022\pi\)
\(54\) 5.06562 0.689344
\(55\) 2.60450 0.351191
\(56\) 5.75509 0.769056
\(57\) 0.719737 0.0953315
\(58\) 5.47896 0.719423
\(59\) 9.38810 1.22223 0.611113 0.791543i \(-0.290722\pi\)
0.611113 + 0.791543i \(0.290722\pi\)
\(60\) 1.23510 0.159451
\(61\) 0.990473 0.126817 0.0634085 0.997988i \(-0.479803\pi\)
0.0634085 + 0.997988i \(0.479803\pi\)
\(62\) −10.9549 −1.39128
\(63\) 5.57722 0.702664
\(64\) −12.8593 −1.60742
\(65\) −2.36574 −0.293434
\(66\) −2.25202 −0.277205
\(67\) −3.56243 −0.435220 −0.217610 0.976036i \(-0.569826\pi\)
−0.217610 + 0.976036i \(0.569826\pi\)
\(68\) −5.70209 −0.691480
\(69\) −1.51317 −0.182164
\(70\) 4.48469 0.536023
\(71\) 9.58765 1.13784 0.568922 0.822391i \(-0.307360\pi\)
0.568922 + 0.822391i \(0.307360\pi\)
\(72\) 8.43154 0.993667
\(73\) 0.651431 0.0762442 0.0381221 0.999273i \(-0.487862\pi\)
0.0381221 + 0.999273i \(0.487862\pi\)
\(74\) 21.2084 2.46543
\(75\) 0.376180 0.0434375
\(76\) 6.28182 0.720574
\(77\) −5.08167 −0.579110
\(78\) 2.04557 0.231615
\(79\) −6.54717 −0.736614 −0.368307 0.929704i \(-0.620063\pi\)
−0.368307 + 0.929704i \(0.620063\pi\)
\(80\) 0.213337 0.0238518
\(81\) 7.74642 0.860714
\(82\) 13.6752 1.51017
\(83\) −12.9789 −1.42462 −0.712308 0.701867i \(-0.752350\pi\)
−0.712308 + 0.701867i \(0.752350\pi\)
\(84\) −2.40982 −0.262933
\(85\) −1.73671 −0.188373
\(86\) −23.9378 −2.58128
\(87\) −0.896691 −0.0961353
\(88\) −7.68238 −0.818944
\(89\) −10.2616 −1.08773 −0.543865 0.839173i \(-0.683040\pi\)
−0.543865 + 0.839173i \(0.683040\pi\)
\(90\) 6.57034 0.692575
\(91\) 4.61582 0.483869
\(92\) −13.2069 −1.37691
\(93\) 1.79289 0.185914
\(94\) −2.00640 −0.206945
\(95\) 1.91328 0.196298
\(96\) 2.03474 0.207669
\(97\) 2.88823 0.293255 0.146628 0.989192i \(-0.453158\pi\)
0.146628 + 0.989192i \(0.453158\pi\)
\(98\) 7.33964 0.741416
\(99\) −7.44494 −0.748245
\(100\) 3.28327 0.328327
\(101\) 8.78531 0.874171 0.437085 0.899420i \(-0.356011\pi\)
0.437085 + 0.899420i \(0.356011\pi\)
\(102\) 1.50167 0.148687
\(103\) 6.97491 0.687258 0.343629 0.939105i \(-0.388344\pi\)
0.343629 + 0.939105i \(0.388344\pi\)
\(104\) 6.97811 0.684260
\(105\) −0.733968 −0.0716279
\(106\) 4.92592 0.478448
\(107\) −19.2765 −1.86353 −0.931765 0.363062i \(-0.881731\pi\)
−0.931765 + 0.363062i \(0.881731\pi\)
\(108\) −7.23583 −0.696268
\(109\) 6.38519 0.611590 0.305795 0.952097i \(-0.401078\pi\)
0.305795 + 0.952097i \(0.401078\pi\)
\(110\) −5.98655 −0.570795
\(111\) −3.47098 −0.329451
\(112\) −0.416243 −0.0393313
\(113\) −4.68261 −0.440503 −0.220252 0.975443i \(-0.570688\pi\)
−0.220252 + 0.975443i \(0.570688\pi\)
\(114\) −1.65434 −0.154943
\(115\) −4.02247 −0.375097
\(116\) −7.82625 −0.726649
\(117\) 6.76245 0.625188
\(118\) −21.5789 −1.98650
\(119\) 3.38851 0.310624
\(120\) −1.10960 −0.101292
\(121\) −4.21656 −0.383324
\(122\) −2.27664 −0.206117
\(123\) −2.23809 −0.201802
\(124\) 15.6482 1.40525
\(125\) 1.00000 0.0894427
\(126\) −12.8194 −1.14205
\(127\) −4.92805 −0.437294 −0.218647 0.975804i \(-0.570164\pi\)
−0.218647 + 0.975804i \(0.570164\pi\)
\(128\) 18.7398 1.65638
\(129\) 3.91768 0.344932
\(130\) 5.43775 0.476922
\(131\) 7.78352 0.680050 0.340025 0.940416i \(-0.389565\pi\)
0.340025 + 0.940416i \(0.389565\pi\)
\(132\) 3.21683 0.279989
\(133\) −3.73301 −0.323693
\(134\) 8.18838 0.707369
\(135\) −2.20385 −0.189677
\(136\) 5.12269 0.439267
\(137\) 10.9217 0.933104 0.466552 0.884494i \(-0.345496\pi\)
0.466552 + 0.884494i \(0.345496\pi\)
\(138\) 3.47808 0.296074
\(139\) 0.978402 0.0829870 0.0414935 0.999139i \(-0.486788\pi\)
0.0414935 + 0.999139i \(0.486788\pi\)
\(140\) −6.40602 −0.541407
\(141\) 0.328369 0.0276537
\(142\) −22.0376 −1.84935
\(143\) −6.16159 −0.515258
\(144\) −0.609821 −0.0508184
\(145\) −2.38367 −0.197953
\(146\) −1.49734 −0.123921
\(147\) −1.20121 −0.0990742
\(148\) −30.2945 −2.49019
\(149\) −10.5078 −0.860833 −0.430416 0.902630i \(-0.641633\pi\)
−0.430416 + 0.902630i \(0.641633\pi\)
\(150\) −0.864664 −0.0705995
\(151\) 15.1205 1.23049 0.615243 0.788337i \(-0.289058\pi\)
0.615243 + 0.788337i \(0.289058\pi\)
\(152\) −5.64351 −0.457749
\(153\) 4.96436 0.401345
\(154\) 11.6804 0.941234
\(155\) 4.76604 0.382818
\(156\) −2.92193 −0.233942
\(157\) −3.11282 −0.248430 −0.124215 0.992255i \(-0.539641\pi\)
−0.124215 + 0.992255i \(0.539641\pi\)
\(158\) 15.0489 1.19723
\(159\) −0.806179 −0.0639342
\(160\) 5.40894 0.427614
\(161\) 7.84827 0.618530
\(162\) −17.8054 −1.39893
\(163\) 23.8189 1.86564 0.932818 0.360347i \(-0.117342\pi\)
0.932818 + 0.360347i \(0.117342\pi\)
\(164\) −19.5339 −1.52534
\(165\) 0.979762 0.0762744
\(166\) 29.8324 2.31545
\(167\) 9.31260 0.720631 0.360315 0.932831i \(-0.382669\pi\)
0.360315 + 0.932831i \(0.382669\pi\)
\(168\) 2.16495 0.167029
\(169\) −7.40326 −0.569482
\(170\) 3.99189 0.306164
\(171\) −5.46909 −0.418231
\(172\) 34.1932 2.60721
\(173\) −12.9195 −0.982250 −0.491125 0.871089i \(-0.663414\pi\)
−0.491125 + 0.871089i \(0.663414\pi\)
\(174\) 2.06108 0.156250
\(175\) −1.95111 −0.147490
\(176\) 0.555637 0.0418827
\(177\) 3.53162 0.265452
\(178\) 23.5867 1.76790
\(179\) 19.9484 1.49102 0.745508 0.666496i \(-0.232207\pi\)
0.745508 + 0.666496i \(0.232207\pi\)
\(180\) −9.38520 −0.699531
\(181\) 2.89998 0.215554 0.107777 0.994175i \(-0.465627\pi\)
0.107777 + 0.994175i \(0.465627\pi\)
\(182\) −10.6096 −0.786438
\(183\) 0.372596 0.0275431
\(184\) 11.8649 0.874690
\(185\) −9.22691 −0.678376
\(186\) −4.12102 −0.302168
\(187\) −4.52327 −0.330774
\(188\) 2.86598 0.209023
\(189\) 4.29994 0.312775
\(190\) −4.39774 −0.319046
\(191\) 7.42378 0.537166 0.268583 0.963257i \(-0.413445\pi\)
0.268583 + 0.963257i \(0.413445\pi\)
\(192\) −4.83742 −0.349111
\(193\) −14.5476 −1.04716 −0.523578 0.851978i \(-0.675403\pi\)
−0.523578 + 0.851978i \(0.675403\pi\)
\(194\) −6.63870 −0.476631
\(195\) −0.889945 −0.0637303
\(196\) −10.4841 −0.748863
\(197\) 12.4089 0.884100 0.442050 0.896990i \(-0.354251\pi\)
0.442050 + 0.896990i \(0.354251\pi\)
\(198\) 17.1125 1.21613
\(199\) −15.8896 −1.12638 −0.563190 0.826327i \(-0.690426\pi\)
−0.563190 + 0.826327i \(0.690426\pi\)
\(200\) −2.94965 −0.208572
\(201\) −1.34012 −0.0945245
\(202\) −20.1934 −1.42080
\(203\) 4.65081 0.326423
\(204\) −2.14501 −0.150181
\(205\) −5.94952 −0.415533
\(206\) −16.0321 −1.11701
\(207\) 11.4982 0.799178
\(208\) −0.504700 −0.0349946
\(209\) 4.98314 0.344691
\(210\) 1.68705 0.116418
\(211\) 20.4900 1.41059 0.705295 0.708914i \(-0.250815\pi\)
0.705295 + 0.708914i \(0.250815\pi\)
\(212\) −7.03627 −0.483253
\(213\) 3.60668 0.247126
\(214\) 44.3078 3.02882
\(215\) 10.4144 0.710254
\(216\) 6.50058 0.442308
\(217\) −9.29906 −0.631261
\(218\) −14.6766 −0.994025
\(219\) 0.245055 0.0165593
\(220\) 8.55130 0.576528
\(221\) 4.10861 0.276375
\(222\) 7.97817 0.535460
\(223\) −1.03739 −0.0694686 −0.0347343 0.999397i \(-0.511059\pi\)
−0.0347343 + 0.999397i \(0.511059\pi\)
\(224\) −10.5534 −0.705130
\(225\) −2.85849 −0.190566
\(226\) 10.7632 0.715954
\(227\) 18.2544 1.21158 0.605792 0.795623i \(-0.292856\pi\)
0.605792 + 0.795623i \(0.292856\pi\)
\(228\) 2.36309 0.156500
\(229\) 4.56970 0.301974 0.150987 0.988536i \(-0.451755\pi\)
0.150987 + 0.988536i \(0.451755\pi\)
\(230\) 9.24579 0.609649
\(231\) −1.91162 −0.125775
\(232\) 7.03101 0.461608
\(233\) −18.1220 −1.18721 −0.593605 0.804757i \(-0.702296\pi\)
−0.593605 + 0.804757i \(0.702296\pi\)
\(234\) −15.5437 −1.01613
\(235\) 0.872904 0.0569420
\(236\) 30.8237 2.00645
\(237\) −2.46291 −0.159984
\(238\) −7.78861 −0.504861
\(239\) 21.3923 1.38375 0.691875 0.722017i \(-0.256785\pi\)
0.691875 + 0.722017i \(0.256785\pi\)
\(240\) 0.0802530 0.00518031
\(241\) 18.8211 1.21237 0.606186 0.795323i \(-0.292699\pi\)
0.606186 + 0.795323i \(0.292699\pi\)
\(242\) 9.69192 0.623020
\(243\) 9.52559 0.611067
\(244\) 3.25199 0.208188
\(245\) −3.19318 −0.204005
\(246\) 5.14434 0.327991
\(247\) −4.52632 −0.288003
\(248\) −14.0582 −0.892694
\(249\) −4.88239 −0.309409
\(250\) −2.29854 −0.145372
\(251\) −17.9267 −1.13152 −0.565762 0.824569i \(-0.691418\pi\)
−0.565762 + 0.824569i \(0.691418\pi\)
\(252\) 18.3115 1.15352
\(253\) −10.4765 −0.658654
\(254\) 11.3273 0.710739
\(255\) −0.653316 −0.0409122
\(256\) −17.3554 −1.08471
\(257\) −4.84913 −0.302481 −0.151240 0.988497i \(-0.548327\pi\)
−0.151240 + 0.988497i \(0.548327\pi\)
\(258\) −9.00493 −0.560622
\(259\) 18.0027 1.11863
\(260\) −7.76738 −0.481712
\(261\) 6.81371 0.421758
\(262\) −17.8907 −1.10529
\(263\) 17.8484 1.10058 0.550290 0.834974i \(-0.314517\pi\)
0.550290 + 0.834974i \(0.314517\pi\)
\(264\) −2.88996 −0.177865
\(265\) −2.14307 −0.131648
\(266\) 8.58047 0.526102
\(267\) −3.86022 −0.236241
\(268\) −11.6964 −0.714474
\(269\) 14.1203 0.860929 0.430464 0.902608i \(-0.358350\pi\)
0.430464 + 0.902608i \(0.358350\pi\)
\(270\) 5.06562 0.308284
\(271\) −20.9217 −1.27090 −0.635450 0.772142i \(-0.719185\pi\)
−0.635450 + 0.772142i \(0.719185\pi\)
\(272\) −0.370504 −0.0224651
\(273\) 1.73638 0.105090
\(274\) −25.1039 −1.51658
\(275\) 2.60450 0.157057
\(276\) −4.96816 −0.299048
\(277\) 2.54785 0.153086 0.0765428 0.997066i \(-0.475612\pi\)
0.0765428 + 0.997066i \(0.475612\pi\)
\(278\) −2.24889 −0.134880
\(279\) −13.6237 −0.815628
\(280\) 5.75509 0.343932
\(281\) 14.9393 0.891203 0.445601 0.895232i \(-0.352990\pi\)
0.445601 + 0.895232i \(0.352990\pi\)
\(282\) −0.754769 −0.0449458
\(283\) 11.3429 0.674265 0.337133 0.941457i \(-0.390543\pi\)
0.337133 + 0.941457i \(0.390543\pi\)
\(284\) 31.4789 1.86793
\(285\) 0.719737 0.0426336
\(286\) 14.1626 0.837454
\(287\) 11.6082 0.685208
\(288\) −15.4614 −0.911071
\(289\) −13.9838 −0.822579
\(290\) 5.47896 0.321736
\(291\) 1.08649 0.0636914
\(292\) 2.13882 0.125165
\(293\) 2.48272 0.145042 0.0725210 0.997367i \(-0.476896\pi\)
0.0725210 + 0.997367i \(0.476896\pi\)
\(294\) 2.76103 0.161026
\(295\) 9.38810 0.546596
\(296\) 27.2162 1.58191
\(297\) −5.73993 −0.333064
\(298\) 24.1526 1.39912
\(299\) 9.51612 0.550331
\(300\) 1.23510 0.0713086
\(301\) −20.3195 −1.17120
\(302\) −34.7550 −1.99992
\(303\) 3.30486 0.189859
\(304\) 0.408173 0.0234103
\(305\) 0.990473 0.0567143
\(306\) −11.4108 −0.652311
\(307\) −4.73084 −0.270003 −0.135002 0.990845i \(-0.543104\pi\)
−0.135002 + 0.990845i \(0.543104\pi\)
\(308\) −16.6845 −0.950688
\(309\) 2.62382 0.149264
\(310\) −10.9549 −0.622198
\(311\) 12.2261 0.693281 0.346641 0.937998i \(-0.387322\pi\)
0.346641 + 0.937998i \(0.387322\pi\)
\(312\) 2.62503 0.148613
\(313\) −2.86569 −0.161978 −0.0809892 0.996715i \(-0.525808\pi\)
−0.0809892 + 0.996715i \(0.525808\pi\)
\(314\) 7.15492 0.403776
\(315\) 5.57722 0.314241
\(316\) −21.4962 −1.20925
\(317\) 5.70421 0.320381 0.160190 0.987086i \(-0.448789\pi\)
0.160190 + 0.987086i \(0.448789\pi\)
\(318\) 1.85303 0.103913
\(319\) −6.20829 −0.347597
\(320\) −12.8593 −0.718858
\(321\) −7.25144 −0.404736
\(322\) −18.0395 −1.00530
\(323\) −3.32281 −0.184886
\(324\) 25.4336 1.41298
\(325\) −2.36574 −0.131228
\(326\) −54.7485 −3.03224
\(327\) 2.40198 0.132830
\(328\) 17.5490 0.968982
\(329\) −1.70313 −0.0938966
\(330\) −2.25202 −0.123970
\(331\) 24.5839 1.35126 0.675628 0.737243i \(-0.263873\pi\)
0.675628 + 0.737243i \(0.263873\pi\)
\(332\) −42.6132 −2.33870
\(333\) 26.3750 1.44534
\(334\) −21.4054 −1.17125
\(335\) −3.56243 −0.194636
\(336\) −0.156582 −0.00854227
\(337\) 25.4913 1.38860 0.694299 0.719686i \(-0.255714\pi\)
0.694299 + 0.719686i \(0.255714\pi\)
\(338\) 17.0167 0.925585
\(339\) −1.76150 −0.0956718
\(340\) −5.70209 −0.309239
\(341\) 12.4132 0.672211
\(342\) 12.5709 0.679756
\(343\) 19.8880 1.07385
\(344\) −30.7188 −1.65624
\(345\) −1.51317 −0.0814664
\(346\) 29.6959 1.59646
\(347\) −9.16249 −0.491868 −0.245934 0.969287i \(-0.579095\pi\)
−0.245934 + 0.969287i \(0.579095\pi\)
\(348\) −2.94408 −0.157819
\(349\) −5.70889 −0.305590 −0.152795 0.988258i \(-0.548827\pi\)
−0.152795 + 0.988258i \(0.548827\pi\)
\(350\) 4.48469 0.239717
\(351\) 5.21373 0.278288
\(352\) 14.0876 0.750872
\(353\) 27.0334 1.43885 0.719423 0.694573i \(-0.244407\pi\)
0.719423 + 0.694573i \(0.244407\pi\)
\(354\) −8.11755 −0.431443
\(355\) 9.58765 0.508860
\(356\) −33.6917 −1.78566
\(357\) 1.27469 0.0674637
\(358\) −45.8522 −2.42337
\(359\) 27.7654 1.46540 0.732700 0.680552i \(-0.238260\pi\)
0.732700 + 0.680552i \(0.238260\pi\)
\(360\) 8.43154 0.444381
\(361\) −15.3394 −0.807335
\(362\) −6.66571 −0.350342
\(363\) −1.58619 −0.0832531
\(364\) 15.1550 0.794337
\(365\) 0.651431 0.0340974
\(366\) −0.856426 −0.0447661
\(367\) −30.8849 −1.61218 −0.806090 0.591793i \(-0.798420\pi\)
−0.806090 + 0.591793i \(0.798420\pi\)
\(368\) −0.858140 −0.0447336
\(369\) 17.0066 0.885330
\(370\) 21.2084 1.10257
\(371\) 4.18135 0.217085
\(372\) 5.88655 0.305203
\(373\) −16.2769 −0.842787 −0.421394 0.906878i \(-0.638459\pi\)
−0.421394 + 0.906878i \(0.638459\pi\)
\(374\) 10.3969 0.537611
\(375\) 0.376180 0.0194259
\(376\) −2.57476 −0.132783
\(377\) 5.63916 0.290431
\(378\) −9.88358 −0.508356
\(379\) −2.25071 −0.115611 −0.0578056 0.998328i \(-0.518410\pi\)
−0.0578056 + 0.998328i \(0.518410\pi\)
\(380\) 6.28182 0.322250
\(381\) −1.85384 −0.0949749
\(382\) −17.0638 −0.873062
\(383\) −12.8723 −0.657744 −0.328872 0.944375i \(-0.606668\pi\)
−0.328872 + 0.944375i \(0.606668\pi\)
\(384\) 7.04952 0.359744
\(385\) −5.08167 −0.258986
\(386\) 33.4381 1.70195
\(387\) −29.7693 −1.51326
\(388\) 9.48284 0.481418
\(389\) −26.7313 −1.35533 −0.677666 0.735369i \(-0.737009\pi\)
−0.677666 + 0.735369i \(0.737009\pi\)
\(390\) 2.04557 0.103582
\(391\) 6.98586 0.353290
\(392\) 9.41877 0.475719
\(393\) 2.92801 0.147698
\(394\) −28.5224 −1.43694
\(395\) −6.54717 −0.329424
\(396\) −24.4438 −1.22835
\(397\) −22.6527 −1.13691 −0.568453 0.822716i \(-0.692458\pi\)
−0.568453 + 0.822716i \(0.692458\pi\)
\(398\) 36.5227 1.83072
\(399\) −1.40428 −0.0703022
\(400\) 0.213337 0.0106668
\(401\) −26.0469 −1.30072 −0.650359 0.759627i \(-0.725382\pi\)
−0.650359 + 0.759627i \(0.725382\pi\)
\(402\) 3.08031 0.153632
\(403\) −11.2752 −0.561659
\(404\) 28.8446 1.43507
\(405\) 7.74642 0.384923
\(406\) −10.6900 −0.530538
\(407\) −24.0315 −1.19120
\(408\) 1.92705 0.0954033
\(409\) 14.7319 0.728444 0.364222 0.931312i \(-0.381335\pi\)
0.364222 + 0.931312i \(0.381335\pi\)
\(410\) 13.6752 0.675370
\(411\) 4.10853 0.202659
\(412\) 22.9005 1.12823
\(413\) −18.3172 −0.901330
\(414\) −26.4290 −1.29891
\(415\) −12.9789 −0.637108
\(416\) −12.7962 −0.627383
\(417\) 0.368055 0.0180237
\(418\) −11.4539 −0.560230
\(419\) 28.8541 1.40961 0.704807 0.709399i \(-0.251034\pi\)
0.704807 + 0.709399i \(0.251034\pi\)
\(420\) −2.40982 −0.117587
\(421\) −9.21410 −0.449068 −0.224534 0.974466i \(-0.572086\pi\)
−0.224534 + 0.974466i \(0.572086\pi\)
\(422\) −47.0970 −2.29265
\(423\) −2.49519 −0.121320
\(424\) 6.32130 0.306989
\(425\) −1.73671 −0.0842428
\(426\) −8.29009 −0.401656
\(427\) −1.93252 −0.0935212
\(428\) −63.2900 −3.05924
\(429\) −2.31787 −0.111908
\(430\) −23.9378 −1.15438
\(431\) −10.5288 −0.507154 −0.253577 0.967315i \(-0.581607\pi\)
−0.253577 + 0.967315i \(0.581607\pi\)
\(432\) −0.470162 −0.0226207
\(433\) 28.1946 1.35495 0.677473 0.735548i \(-0.263075\pi\)
0.677473 + 0.735548i \(0.263075\pi\)
\(434\) 21.3742 1.02600
\(435\) −0.896691 −0.0429930
\(436\) 20.9643 1.00401
\(437\) −7.69610 −0.368154
\(438\) −0.563269 −0.0269140
\(439\) −13.2147 −0.630702 −0.315351 0.948975i \(-0.602122\pi\)
−0.315351 + 0.948975i \(0.602122\pi\)
\(440\) −7.68238 −0.366243
\(441\) 9.12767 0.434651
\(442\) −9.44379 −0.449195
\(443\) −13.5025 −0.641521 −0.320761 0.947160i \(-0.603939\pi\)
−0.320761 + 0.947160i \(0.603939\pi\)
\(444\) −11.3962 −0.540838
\(445\) −10.2616 −0.486447
\(446\) 2.38448 0.112908
\(447\) −3.95283 −0.186962
\(448\) 25.0899 1.18539
\(449\) −16.9881 −0.801720 −0.400860 0.916139i \(-0.631289\pi\)
−0.400860 + 0.916139i \(0.631289\pi\)
\(450\) 6.57034 0.309729
\(451\) −15.4956 −0.729657
\(452\) −15.3743 −0.723146
\(453\) 5.68802 0.267246
\(454\) −41.9583 −1.96920
\(455\) 4.61582 0.216393
\(456\) −2.12297 −0.0994174
\(457\) −24.7197 −1.15634 −0.578169 0.815917i \(-0.696233\pi\)
−0.578169 + 0.815917i \(0.696233\pi\)
\(458\) −10.5036 −0.490802
\(459\) 3.82744 0.178650
\(460\) −13.2069 −0.615773
\(461\) 19.1287 0.890911 0.445456 0.895304i \(-0.353042\pi\)
0.445456 + 0.895304i \(0.353042\pi\)
\(462\) 4.39393 0.204424
\(463\) 27.8284 1.29330 0.646649 0.762788i \(-0.276170\pi\)
0.646649 + 0.762788i \(0.276170\pi\)
\(464\) −0.508525 −0.0236077
\(465\) 1.79289 0.0831433
\(466\) 41.6540 1.92959
\(467\) 19.9731 0.924245 0.462122 0.886816i \(-0.347088\pi\)
0.462122 + 0.886816i \(0.347088\pi\)
\(468\) 22.2030 1.02633
\(469\) 6.95069 0.320953
\(470\) −2.00640 −0.0925485
\(471\) −1.17098 −0.0539559
\(472\) −27.6916 −1.27461
\(473\) 27.1243 1.24717
\(474\) 5.66110 0.260023
\(475\) 1.91328 0.0877873
\(476\) 11.1254 0.509932
\(477\) 6.12593 0.280487
\(478\) −49.1709 −2.24903
\(479\) 15.3382 0.700822 0.350411 0.936596i \(-0.386042\pi\)
0.350411 + 0.936596i \(0.386042\pi\)
\(480\) 2.03474 0.0928725
\(481\) 21.8285 0.995293
\(482\) −43.2610 −1.97048
\(483\) 2.95236 0.134337
\(484\) −13.8441 −0.629278
\(485\) 2.88823 0.131148
\(486\) −21.8949 −0.993174
\(487\) 18.8145 0.852565 0.426282 0.904590i \(-0.359823\pi\)
0.426282 + 0.904590i \(0.359823\pi\)
\(488\) −2.92155 −0.132252
\(489\) 8.96018 0.405193
\(490\) 7.33964 0.331571
\(491\) 43.7329 1.97364 0.986819 0.161827i \(-0.0517387\pi\)
0.986819 + 0.161827i \(0.0517387\pi\)
\(492\) −7.34827 −0.331285
\(493\) 4.13975 0.186445
\(494\) 10.4039 0.468095
\(495\) −7.44494 −0.334625
\(496\) 1.01677 0.0456544
\(497\) −18.7065 −0.839103
\(498\) 11.2224 0.502886
\(499\) −33.6518 −1.50646 −0.753230 0.657757i \(-0.771505\pi\)
−0.753230 + 0.657757i \(0.771505\pi\)
\(500\) 3.28327 0.146832
\(501\) 3.50322 0.156512
\(502\) 41.2052 1.83908
\(503\) 12.8581 0.573314 0.286657 0.958033i \(-0.407456\pi\)
0.286657 + 0.958033i \(0.407456\pi\)
\(504\) −16.4509 −0.732779
\(505\) 8.78531 0.390941
\(506\) 24.0807 1.07052
\(507\) −2.78496 −0.123684
\(508\) −16.1801 −0.717878
\(509\) 33.2470 1.47365 0.736824 0.676084i \(-0.236325\pi\)
0.736824 + 0.676084i \(0.236325\pi\)
\(510\) 1.50167 0.0664951
\(511\) −1.27101 −0.0562262
\(512\) 2.41246 0.106617
\(513\) −4.21657 −0.186166
\(514\) 11.1459 0.491625
\(515\) 6.97491 0.307351
\(516\) 12.8628 0.566253
\(517\) 2.27348 0.0999877
\(518\) −41.3798 −1.81813
\(519\) −4.86005 −0.213333
\(520\) 6.97811 0.306011
\(521\) 17.2371 0.755170 0.377585 0.925975i \(-0.376755\pi\)
0.377585 + 0.925975i \(0.376755\pi\)
\(522\) −15.6616 −0.685488
\(523\) −38.4753 −1.68241 −0.841204 0.540718i \(-0.818153\pi\)
−0.841204 + 0.540718i \(0.818153\pi\)
\(524\) 25.5554 1.11639
\(525\) −0.733968 −0.0320330
\(526\) −41.0252 −1.78878
\(527\) −8.27723 −0.360562
\(528\) 0.209019 0.00909640
\(529\) −6.81976 −0.296511
\(530\) 4.92592 0.213968
\(531\) −26.8358 −1.16457
\(532\) −12.2565 −0.531387
\(533\) 14.0750 0.609657
\(534\) 8.87285 0.383966
\(535\) −19.2765 −0.833396
\(536\) 10.5079 0.453874
\(537\) 7.50421 0.323830
\(538\) −32.4560 −1.39928
\(539\) −8.31665 −0.358223
\(540\) −7.23583 −0.311381
\(541\) 3.80320 0.163512 0.0817561 0.996652i \(-0.473947\pi\)
0.0817561 + 0.996652i \(0.473947\pi\)
\(542\) 48.0892 2.06561
\(543\) 1.09091 0.0468156
\(544\) −9.39376 −0.402754
\(545\) 6.38519 0.273512
\(546\) −3.99113 −0.170805
\(547\) −5.70834 −0.244071 −0.122035 0.992526i \(-0.538942\pi\)
−0.122035 + 0.992526i \(0.538942\pi\)
\(548\) 35.8589 1.53182
\(549\) −2.83126 −0.120835
\(550\) −5.98655 −0.255267
\(551\) −4.56063 −0.194290
\(552\) 4.46333 0.189972
\(553\) 12.7742 0.543216
\(554\) −5.85633 −0.248812
\(555\) −3.47098 −0.147335
\(556\) 3.21236 0.136234
\(557\) −13.9051 −0.589179 −0.294589 0.955624i \(-0.595183\pi\)
−0.294589 + 0.955624i \(0.595183\pi\)
\(558\) 31.3145 1.32565
\(559\) −24.6377 −1.04206
\(560\) −0.416243 −0.0175895
\(561\) −1.70156 −0.0718400
\(562\) −34.3385 −1.44848
\(563\) −31.4288 −1.32457 −0.662283 0.749254i \(-0.730412\pi\)
−0.662283 + 0.749254i \(0.730412\pi\)
\(564\) 1.07813 0.0453973
\(565\) −4.68261 −0.196999
\(566\) −26.0721 −1.09589
\(567\) −15.1141 −0.634733
\(568\) −28.2802 −1.18661
\(569\) −33.5490 −1.40645 −0.703223 0.710969i \(-0.748257\pi\)
−0.703223 + 0.710969i \(0.748257\pi\)
\(570\) −1.65434 −0.0692928
\(571\) 15.4601 0.646984 0.323492 0.946231i \(-0.395143\pi\)
0.323492 + 0.946231i \(0.395143\pi\)
\(572\) −20.2302 −0.845866
\(573\) 2.79268 0.116666
\(574\) −26.6818 −1.11368
\(575\) −4.02247 −0.167748
\(576\) 36.7582 1.53159
\(577\) −11.2214 −0.467153 −0.233576 0.972338i \(-0.575043\pi\)
−0.233576 + 0.972338i \(0.575043\pi\)
\(578\) 32.1424 1.33695
\(579\) −5.47250 −0.227429
\(580\) −7.82625 −0.324968
\(581\) 25.3232 1.05058
\(582\) −2.49735 −0.103518
\(583\) −5.58163 −0.231167
\(584\) −1.92149 −0.0795120
\(585\) 6.76245 0.279593
\(586\) −5.70662 −0.235738
\(587\) −8.10118 −0.334372 −0.167186 0.985925i \(-0.553468\pi\)
−0.167186 + 0.985925i \(0.553468\pi\)
\(588\) −3.94390 −0.162644
\(589\) 9.11876 0.375732
\(590\) −21.5789 −0.888389
\(591\) 4.66799 0.192016
\(592\) −1.96844 −0.0809023
\(593\) 31.2125 1.28174 0.640871 0.767649i \(-0.278573\pi\)
0.640871 + 0.767649i \(0.278573\pi\)
\(594\) 13.1934 0.541333
\(595\) 3.38851 0.138915
\(596\) −34.5000 −1.41317
\(597\) −5.97733 −0.244636
\(598\) −21.8732 −0.894460
\(599\) 28.3034 1.15645 0.578223 0.815879i \(-0.303746\pi\)
0.578223 + 0.815879i \(0.303746\pi\)
\(600\) −1.10960 −0.0452992
\(601\) −27.7590 −1.13231 −0.566157 0.824298i \(-0.691570\pi\)
−0.566157 + 0.824298i \(0.691570\pi\)
\(602\) 46.7052 1.90356
\(603\) 10.1832 0.414691
\(604\) 49.6446 2.02001
\(605\) −4.21656 −0.171428
\(606\) −7.59634 −0.308580
\(607\) −33.7033 −1.36798 −0.683988 0.729493i \(-0.739756\pi\)
−0.683988 + 0.729493i \(0.739756\pi\)
\(608\) 10.3488 0.419700
\(609\) 1.74954 0.0708949
\(610\) −2.27664 −0.0921784
\(611\) −2.06507 −0.0835437
\(612\) 16.2994 0.658863
\(613\) 29.7111 1.20002 0.600010 0.799992i \(-0.295163\pi\)
0.600010 + 0.799992i \(0.295163\pi\)
\(614\) 10.8740 0.438840
\(615\) −2.23809 −0.0902486
\(616\) 14.9891 0.603930
\(617\) −20.4746 −0.824275 −0.412138 0.911122i \(-0.635218\pi\)
−0.412138 + 0.911122i \(0.635218\pi\)
\(618\) −6.03095 −0.242600
\(619\) −11.8611 −0.476740 −0.238370 0.971174i \(-0.576613\pi\)
−0.238370 + 0.971174i \(0.576613\pi\)
\(620\) 15.6482 0.628447
\(621\) 8.86490 0.355736
\(622\) −28.1022 −1.12680
\(623\) 20.0215 0.802145
\(624\) −0.189858 −0.00760040
\(625\) 1.00000 0.0400000
\(626\) 6.58690 0.263265
\(627\) 1.87456 0.0748627
\(628\) −10.2202 −0.407831
\(629\) 16.0245 0.638937
\(630\) −12.8194 −0.510739
\(631\) −0.920878 −0.0366596 −0.0183298 0.999832i \(-0.505835\pi\)
−0.0183298 + 0.999832i \(0.505835\pi\)
\(632\) 19.3119 0.768185
\(633\) 7.70793 0.306363
\(634\) −13.1113 −0.520718
\(635\) −4.92805 −0.195564
\(636\) −2.64691 −0.104957
\(637\) 7.55424 0.299310
\(638\) 14.2700 0.564954
\(639\) −27.4062 −1.08417
\(640\) 18.7398 0.740754
\(641\) 1.90133 0.0750982 0.0375491 0.999295i \(-0.488045\pi\)
0.0375491 + 0.999295i \(0.488045\pi\)
\(642\) 16.6677 0.657821
\(643\) −27.1665 −1.07134 −0.535672 0.844426i \(-0.679942\pi\)
−0.535672 + 0.844426i \(0.679942\pi\)
\(644\) 25.7680 1.01540
\(645\) 3.91768 0.154258
\(646\) 7.63760 0.300497
\(647\) 11.7455 0.461762 0.230881 0.972982i \(-0.425839\pi\)
0.230881 + 0.972982i \(0.425839\pi\)
\(648\) −22.8492 −0.897603
\(649\) 24.4513 0.959799
\(650\) 5.43775 0.213286
\(651\) −3.49812 −0.137102
\(652\) 78.2038 3.06270
\(653\) 16.3182 0.638581 0.319291 0.947657i \(-0.396555\pi\)
0.319291 + 0.947657i \(0.396555\pi\)
\(654\) −5.52104 −0.215890
\(655\) 7.78352 0.304127
\(656\) −1.26925 −0.0495560
\(657\) −1.86211 −0.0726477
\(658\) 3.91471 0.152611
\(659\) 27.2824 1.06277 0.531386 0.847130i \(-0.321672\pi\)
0.531386 + 0.847130i \(0.321672\pi\)
\(660\) 3.21683 0.125215
\(661\) 16.4119 0.638351 0.319175 0.947696i \(-0.396594\pi\)
0.319175 + 0.947696i \(0.396594\pi\)
\(662\) −56.5071 −2.19621
\(663\) 1.54558 0.0600252
\(664\) 38.2832 1.48567
\(665\) −3.73301 −0.144760
\(666\) −60.6239 −2.34913
\(667\) 9.58825 0.371259
\(668\) 30.5758 1.18301
\(669\) −0.390245 −0.0150877
\(670\) 8.18838 0.316345
\(671\) 2.57969 0.0995879
\(672\) −3.96999 −0.153146
\(673\) 24.1836 0.932210 0.466105 0.884729i \(-0.345657\pi\)
0.466105 + 0.884729i \(0.345657\pi\)
\(674\) −58.5927 −2.25691
\(675\) −2.20385 −0.0848261
\(676\) −24.3069 −0.934882
\(677\) 17.8432 0.685769 0.342885 0.939377i \(-0.388596\pi\)
0.342885 + 0.939377i \(0.388596\pi\)
\(678\) 4.04888 0.155496
\(679\) −5.63524 −0.216261
\(680\) 5.12269 0.196446
\(681\) 6.86693 0.263141
\(682\) −28.5321 −1.09255
\(683\) −14.4024 −0.551092 −0.275546 0.961288i \(-0.588859\pi\)
−0.275546 + 0.961288i \(0.588859\pi\)
\(684\) −17.9565 −0.686584
\(685\) 10.9217 0.417297
\(686\) −45.7133 −1.74534
\(687\) 1.71903 0.0655850
\(688\) 2.22177 0.0847041
\(689\) 5.06994 0.193149
\(690\) 3.47808 0.132408
\(691\) 24.6527 0.937834 0.468917 0.883242i \(-0.344644\pi\)
0.468917 + 0.883242i \(0.344644\pi\)
\(692\) −42.4182 −1.61250
\(693\) 14.5259 0.551793
\(694\) 21.0603 0.799439
\(695\) 0.978402 0.0371129
\(696\) 2.64493 0.100256
\(697\) 10.3326 0.391375
\(698\) 13.1221 0.496679
\(699\) −6.81712 −0.257847
\(700\) −6.40602 −0.242125
\(701\) 16.0053 0.604512 0.302256 0.953227i \(-0.402260\pi\)
0.302256 + 0.953227i \(0.402260\pi\)
\(702\) −11.9840 −0.452305
\(703\) −17.6536 −0.665820
\(704\) −33.4922 −1.26228
\(705\) 0.328369 0.0123671
\(706\) −62.1374 −2.33857
\(707\) −17.1411 −0.644657
\(708\) 11.5953 0.435776
\(709\) 30.3372 1.13934 0.569668 0.821875i \(-0.307072\pi\)
0.569668 + 0.821875i \(0.307072\pi\)
\(710\) −22.0376 −0.827055
\(711\) 18.7150 0.701868
\(712\) 30.2682 1.13435
\(713\) −19.1712 −0.717969
\(714\) −2.92992 −0.109649
\(715\) −6.16159 −0.230430
\(716\) 65.4962 2.44771
\(717\) 8.04734 0.300534
\(718\) −63.8197 −2.38173
\(719\) 12.1768 0.454117 0.227059 0.973881i \(-0.427089\pi\)
0.227059 + 0.973881i \(0.427089\pi\)
\(720\) −0.609821 −0.0227267
\(721\) −13.6088 −0.506818
\(722\) 35.2581 1.31217
\(723\) 7.08012 0.263312
\(724\) 9.52143 0.353861
\(725\) −2.38367 −0.0885274
\(726\) 3.64591 0.135312
\(727\) −26.0568 −0.966393 −0.483197 0.875512i \(-0.660524\pi\)
−0.483197 + 0.875512i \(0.660524\pi\)
\(728\) −13.6151 −0.504607
\(729\) −19.6559 −0.727997
\(730\) −1.49734 −0.0554189
\(731\) −18.0867 −0.668962
\(732\) 1.22334 0.0452158
\(733\) 43.0593 1.59043 0.795217 0.606325i \(-0.207357\pi\)
0.795217 + 0.606325i \(0.207357\pi\)
\(734\) 70.9902 2.62029
\(735\) −1.20121 −0.0443073
\(736\) −21.7573 −0.801984
\(737\) −9.27837 −0.341773
\(738\) −39.0904 −1.43894
\(739\) 42.0281 1.54603 0.773015 0.634388i \(-0.218748\pi\)
0.773015 + 0.634388i \(0.218748\pi\)
\(740\) −30.2945 −1.11365
\(741\) −1.70271 −0.0625507
\(742\) −9.61100 −0.352831
\(743\) 20.3625 0.747026 0.373513 0.927625i \(-0.378153\pi\)
0.373513 + 0.927625i \(0.378153\pi\)
\(744\) −5.28840 −0.193882
\(745\) −10.5078 −0.384976
\(746\) 37.4131 1.36979
\(747\) 37.1000 1.35742
\(748\) −14.8511 −0.543011
\(749\) 37.6105 1.37426
\(750\) −0.864664 −0.0315731
\(751\) 28.5759 1.04275 0.521375 0.853327i \(-0.325419\pi\)
0.521375 + 0.853327i \(0.325419\pi\)
\(752\) 0.186223 0.00679084
\(753\) −6.74367 −0.245753
\(754\) −12.9618 −0.472042
\(755\) 15.1205 0.550290
\(756\) 14.1179 0.513462
\(757\) 3.89635 0.141615 0.0708077 0.997490i \(-0.477442\pi\)
0.0708077 + 0.997490i \(0.477442\pi\)
\(758\) 5.17334 0.187904
\(759\) −3.94106 −0.143051
\(760\) −5.64351 −0.204711
\(761\) 25.7963 0.935114 0.467557 0.883963i \(-0.345134\pi\)
0.467557 + 0.883963i \(0.345134\pi\)
\(762\) 4.26111 0.154364
\(763\) −12.4582 −0.451017
\(764\) 24.3743 0.881832
\(765\) 4.96436 0.179487
\(766\) 29.5875 1.06904
\(767\) −22.2098 −0.801950
\(768\) −6.52875 −0.235586
\(769\) −21.4791 −0.774557 −0.387279 0.921963i \(-0.626585\pi\)
−0.387279 + 0.921963i \(0.626585\pi\)
\(770\) 11.6804 0.420932
\(771\) −1.82415 −0.0656951
\(772\) −47.7636 −1.71905
\(773\) 30.0115 1.07944 0.539719 0.841846i \(-0.318531\pi\)
0.539719 + 0.841846i \(0.318531\pi\)
\(774\) 68.4260 2.45952
\(775\) 4.76604 0.171201
\(776\) −8.51927 −0.305824
\(777\) 6.77225 0.242953
\(778\) 61.4430 2.20284
\(779\) −11.3831 −0.407842
\(780\) −2.92193 −0.104622
\(781\) 24.9711 0.893535
\(782\) −16.0573 −0.574206
\(783\) 5.25325 0.187736
\(784\) −0.681223 −0.0243294
\(785\) −3.11282 −0.111101
\(786\) −6.73013 −0.240056
\(787\) 37.3021 1.32968 0.664839 0.746987i \(-0.268500\pi\)
0.664839 + 0.746987i \(0.268500\pi\)
\(788\) 40.7419 1.45137
\(789\) 6.71421 0.239032
\(790\) 15.0489 0.535416
\(791\) 9.13628 0.324849
\(792\) 21.9600 0.780314
\(793\) −2.34320 −0.0832096
\(794\) 52.0680 1.84783
\(795\) −0.806179 −0.0285922
\(796\) −52.1697 −1.84911
\(797\) 27.6704 0.980136 0.490068 0.871684i \(-0.336972\pi\)
0.490068 + 0.871684i \(0.336972\pi\)
\(798\) 3.22780 0.114263
\(799\) −1.51598 −0.0536316
\(800\) 5.40894 0.191235
\(801\) 29.3327 1.03642
\(802\) 59.8697 2.11407
\(803\) 1.69665 0.0598736
\(804\) −4.39997 −0.155175
\(805\) 7.84827 0.276615
\(806\) 25.9165 0.912871
\(807\) 5.31177 0.186983
\(808\) −25.9136 −0.911637
\(809\) 3.26796 0.114895 0.0574476 0.998349i \(-0.481704\pi\)
0.0574476 + 0.998349i \(0.481704\pi\)
\(810\) −17.8054 −0.625619
\(811\) 6.83258 0.239924 0.119962 0.992778i \(-0.461723\pi\)
0.119962 + 0.992778i \(0.461723\pi\)
\(812\) 15.2699 0.535867
\(813\) −7.87031 −0.276024
\(814\) 55.2373 1.93607
\(815\) 23.8189 0.834338
\(816\) −0.139376 −0.00487914
\(817\) 19.9256 0.697108
\(818\) −33.8618 −1.18395
\(819\) −13.1943 −0.461045
\(820\) −19.5339 −0.682154
\(821\) 2.52040 0.0879625 0.0439812 0.999032i \(-0.485996\pi\)
0.0439812 + 0.999032i \(0.485996\pi\)
\(822\) −9.44360 −0.329383
\(823\) 2.49335 0.0869128 0.0434564 0.999055i \(-0.486163\pi\)
0.0434564 + 0.999055i \(0.486163\pi\)
\(824\) −20.5735 −0.716713
\(825\) 0.979762 0.0341109
\(826\) 42.1027 1.46494
\(827\) −6.46025 −0.224645 −0.112322 0.993672i \(-0.535829\pi\)
−0.112322 + 0.993672i \(0.535829\pi\)
\(828\) 37.7517 1.31196
\(829\) 38.0882 1.32286 0.661429 0.750007i \(-0.269950\pi\)
0.661429 + 0.750007i \(0.269950\pi\)
\(830\) 29.8324 1.03550
\(831\) 0.958451 0.0332483
\(832\) 30.4218 1.05469
\(833\) 5.54563 0.192145
\(834\) −0.845989 −0.0292942
\(835\) 9.31260 0.322276
\(836\) 16.3610 0.565858
\(837\) −10.5036 −0.363058
\(838\) −66.3221 −2.29106
\(839\) 34.3699 1.18658 0.593291 0.804988i \(-0.297829\pi\)
0.593291 + 0.804988i \(0.297829\pi\)
\(840\) 2.16495 0.0746978
\(841\) −23.3181 −0.804072
\(842\) 21.1790 0.729875
\(843\) 5.61986 0.193558
\(844\) 67.2743 2.31568
\(845\) −7.40326 −0.254680
\(846\) 5.73528 0.197183
\(847\) 8.22696 0.282682
\(848\) −0.457195 −0.0157001
\(849\) 4.26697 0.146442
\(850\) 3.99189 0.136921
\(851\) 37.1149 1.27228
\(852\) 11.8417 0.405691
\(853\) 8.62729 0.295393 0.147696 0.989033i \(-0.452814\pi\)
0.147696 + 0.989033i \(0.452814\pi\)
\(854\) 4.44197 0.152001
\(855\) −5.46909 −0.187039
\(856\) 56.8590 1.94340
\(857\) 6.94918 0.237380 0.118690 0.992931i \(-0.462131\pi\)
0.118690 + 0.992931i \(0.462131\pi\)
\(858\) 5.32770 0.181885
\(859\) 6.32976 0.215969 0.107984 0.994153i \(-0.465560\pi\)
0.107984 + 0.994153i \(0.465560\pi\)
\(860\) 34.1932 1.16598
\(861\) 4.36676 0.148819
\(862\) 24.2008 0.824284
\(863\) 41.7850 1.42238 0.711189 0.703001i \(-0.248157\pi\)
0.711189 + 0.703001i \(0.248157\pi\)
\(864\) −11.9205 −0.405543
\(865\) −12.9195 −0.439276
\(866\) −64.8063 −2.20221
\(867\) −5.26044 −0.178654
\(868\) −30.5313 −1.03630
\(869\) −17.0521 −0.578454
\(870\) 2.06108 0.0698771
\(871\) 8.42780 0.285565
\(872\) −18.8341 −0.637803
\(873\) −8.25597 −0.279422
\(874\) 17.6898 0.598365
\(875\) −1.95111 −0.0659595
\(876\) 0.804583 0.0271843
\(877\) −8.53029 −0.288047 −0.144024 0.989574i \(-0.546004\pi\)
−0.144024 + 0.989574i \(0.546004\pi\)
\(878\) 30.3744 1.02509
\(879\) 0.933949 0.0315013
\(880\) 0.555637 0.0187305
\(881\) 27.2786 0.919040 0.459520 0.888167i \(-0.348021\pi\)
0.459520 + 0.888167i \(0.348021\pi\)
\(882\) −20.9803 −0.706443
\(883\) −25.7131 −0.865314 −0.432657 0.901559i \(-0.642424\pi\)
−0.432657 + 0.901559i \(0.642424\pi\)
\(884\) 13.4897 0.453707
\(885\) 3.53162 0.118714
\(886\) 31.0359 1.04267
\(887\) 8.70465 0.292273 0.146137 0.989264i \(-0.453316\pi\)
0.146137 + 0.989264i \(0.453316\pi\)
\(888\) 10.2382 0.343571
\(889\) 9.61516 0.322482
\(890\) 23.5867 0.790628
\(891\) 20.1756 0.675908
\(892\) −3.40603 −0.114042
\(893\) 1.67011 0.0558881
\(894\) 9.08572 0.303872
\(895\) 19.9484 0.666803
\(896\) −36.5633 −1.22149
\(897\) 3.57977 0.119525
\(898\) 39.0479 1.30304
\(899\) −11.3607 −0.378900
\(900\) −9.38520 −0.312840
\(901\) 3.72188 0.123994
\(902\) 35.6171 1.18592
\(903\) −7.64381 −0.254370
\(904\) 13.8121 0.459383
\(905\) 2.89998 0.0963986
\(906\) −13.0741 −0.434359
\(907\) −32.2856 −1.07203 −0.536013 0.844210i \(-0.680070\pi\)
−0.536013 + 0.844210i \(0.680070\pi\)
\(908\) 59.9341 1.98898
\(909\) −25.1127 −0.832936
\(910\) −10.6096 −0.351706
\(911\) 60.2092 1.99482 0.997410 0.0719291i \(-0.0229155\pi\)
0.997410 + 0.0719291i \(0.0229155\pi\)
\(912\) 0.153546 0.00508443
\(913\) −33.8035 −1.11873
\(914\) 56.8192 1.87941
\(915\) 0.372596 0.0123177
\(916\) 15.0036 0.495732
\(917\) −15.1865 −0.501502
\(918\) −8.79752 −0.290361
\(919\) 52.9782 1.74759 0.873795 0.486294i \(-0.161652\pi\)
0.873795 + 0.486294i \(0.161652\pi\)
\(920\) 11.8649 0.391173
\(921\) −1.77965 −0.0586414
\(922\) −43.9680 −1.44801
\(923\) −22.6819 −0.746584
\(924\) −6.27638 −0.206478
\(925\) −9.22691 −0.303379
\(926\) −63.9647 −2.10201
\(927\) −19.9377 −0.654840
\(928\) −12.8932 −0.423238
\(929\) 23.2960 0.764315 0.382158 0.924097i \(-0.375181\pi\)
0.382158 + 0.924097i \(0.375181\pi\)
\(930\) −4.12102 −0.135134
\(931\) −6.10944 −0.200229
\(932\) −59.4994 −1.94897
\(933\) 4.59923 0.150572
\(934\) −45.9089 −1.50219
\(935\) −4.52327 −0.147927
\(936\) −19.9469 −0.651984
\(937\) −4.65031 −0.151919 −0.0759595 0.997111i \(-0.524202\pi\)
−0.0759595 + 0.997111i \(0.524202\pi\)
\(938\) −15.9764 −0.521649
\(939\) −1.07802 −0.0351797
\(940\) 2.86598 0.0934781
\(941\) 8.53668 0.278288 0.139144 0.990272i \(-0.455565\pi\)
0.139144 + 0.990272i \(0.455565\pi\)
\(942\) 2.69154 0.0876951
\(943\) 23.9318 0.779325
\(944\) 2.00283 0.0651865
\(945\) 4.29994 0.139877
\(946\) −62.3461 −2.02705
\(947\) −44.2799 −1.43890 −0.719452 0.694542i \(-0.755607\pi\)
−0.719452 + 0.694542i \(0.755607\pi\)
\(948\) −8.08642 −0.262635
\(949\) −1.54112 −0.0500268
\(950\) −4.39774 −0.142682
\(951\) 2.14581 0.0695827
\(952\) −9.99492 −0.323937
\(953\) 54.6411 1.77000 0.885000 0.465591i \(-0.154158\pi\)
0.885000 + 0.465591i \(0.154158\pi\)
\(954\) −14.0807 −0.455879
\(955\) 7.42378 0.240228
\(956\) 70.2367 2.27162
\(957\) −2.33543 −0.0754939
\(958\) −35.2555 −1.13905
\(959\) −21.3094 −0.688117
\(960\) −4.83742 −0.156127
\(961\) −8.28486 −0.267253
\(962\) −50.1736 −1.61766
\(963\) 55.1017 1.77563
\(964\) 61.7948 1.99028
\(965\) −14.5476 −0.468302
\(966\) −6.78611 −0.218340
\(967\) −42.7889 −1.37600 −0.687998 0.725712i \(-0.741510\pi\)
−0.687998 + 0.725712i \(0.741510\pi\)
\(968\) 12.4374 0.399753
\(969\) −1.24997 −0.0401550
\(970\) −6.63870 −0.213156
\(971\) −41.8328 −1.34248 −0.671239 0.741241i \(-0.734238\pi\)
−0.671239 + 0.741241i \(0.734238\pi\)
\(972\) 31.2751 1.00315
\(973\) −1.90897 −0.0611987
\(974\) −43.2457 −1.38568
\(975\) −0.889945 −0.0285011
\(976\) 0.211304 0.00676369
\(977\) −1.50352 −0.0481020 −0.0240510 0.999711i \(-0.507656\pi\)
−0.0240510 + 0.999711i \(0.507656\pi\)
\(978\) −20.5953 −0.658565
\(979\) −26.7264 −0.854180
\(980\) −10.4841 −0.334902
\(981\) −18.2520 −0.582741
\(982\) −100.522 −3.20778
\(983\) 10.7313 0.342275 0.171138 0.985247i \(-0.445256\pi\)
0.171138 + 0.985247i \(0.445256\pi\)
\(984\) 6.60159 0.210451
\(985\) 12.4089 0.395381
\(986\) −9.51537 −0.303031
\(987\) −0.640684 −0.0203932
\(988\) −14.8612 −0.472796
\(989\) −41.8914 −1.33207
\(990\) 17.1125 0.543870
\(991\) 18.3111 0.581670 0.290835 0.956773i \(-0.406067\pi\)
0.290835 + 0.956773i \(0.406067\pi\)
\(992\) 25.7792 0.818491
\(993\) 9.24799 0.293476
\(994\) 42.9977 1.36380
\(995\) −15.8896 −0.503733
\(996\) −16.0302 −0.507937
\(997\) −8.65852 −0.274218 −0.137109 0.990556i \(-0.543781\pi\)
−0.137109 + 0.990556i \(0.543781\pi\)
\(998\) 77.3499 2.44847
\(999\) 20.3347 0.643361
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 \(a_p\))