Properties

Label 6013.2.a.e.1.11
Level 6013
Weight 2
Character 6013.1
Self dual Yes
Analytic conductor 48.014
Analytic rank 0
Dimension 109
CM No

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Newspace parameters

Level: \( N \) = \( 6013 = 7 \cdot 859 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0140467354\)
Analytic rank: \(0\)
Dimension: \(109\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 6013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.28251 q^{2}\) \(-0.277049 q^{3}\) \(+3.20984 q^{4}\) \(+0.585497 q^{5}\) \(+0.632366 q^{6}\) \(+1.00000 q^{7}\) \(-2.76147 q^{8}\) \(-2.92324 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.28251 q^{2}\) \(-0.277049 q^{3}\) \(+3.20984 q^{4}\) \(+0.585497 q^{5}\) \(+0.632366 q^{6}\) \(+1.00000 q^{7}\) \(-2.76147 q^{8}\) \(-2.92324 q^{9}\) \(-1.33640 q^{10}\) \(+3.59107 q^{11}\) \(-0.889282 q^{12}\) \(+0.558307 q^{13}\) \(-2.28251 q^{14}\) \(-0.162211 q^{15}\) \(-0.116600 q^{16}\) \(+2.03684 q^{17}\) \(+6.67233 q^{18}\) \(+5.46372 q^{19}\) \(+1.87935 q^{20}\) \(-0.277049 q^{21}\) \(-8.19664 q^{22}\) \(+3.31065 q^{23}\) \(+0.765062 q^{24}\) \(-4.65719 q^{25}\) \(-1.27434 q^{26}\) \(+1.64103 q^{27}\) \(+3.20984 q^{28}\) \(+3.76294 q^{29}\) \(+0.370248 q^{30}\) \(+6.60139 q^{31}\) \(+5.78909 q^{32}\) \(-0.994900 q^{33}\) \(-4.64910 q^{34}\) \(+0.585497 q^{35}\) \(-9.38315 q^{36}\) \(+5.38098 q^{37}\) \(-12.4710 q^{38}\) \(-0.154678 q^{39}\) \(-1.61684 q^{40}\) \(-4.04781 q^{41}\) \(+0.632366 q^{42}\) \(+1.09056 q^{43}\) \(+11.5268 q^{44}\) \(-1.71155 q^{45}\) \(-7.55659 q^{46}\) \(-1.70506 q^{47}\) \(+0.0323038 q^{48}\) \(+1.00000 q^{49}\) \(+10.6301 q^{50}\) \(-0.564303 q^{51}\) \(+1.79208 q^{52}\) \(+5.93502 q^{53}\) \(-3.74566 q^{54}\) \(+2.10256 q^{55}\) \(-2.76147 q^{56}\) \(-1.51372 q^{57}\) \(-8.58895 q^{58}\) \(-6.28870 q^{59}\) \(-0.520672 q^{60}\) \(+6.18002 q^{61}\) \(-15.0677 q^{62}\) \(-2.92324 q^{63}\) \(-12.9804 q^{64}\) \(+0.326887 q^{65}\) \(+2.27087 q^{66}\) \(-6.69246 q^{67}\) \(+6.53793 q^{68}\) \(-0.917212 q^{69}\) \(-1.33640 q^{70}\) \(-3.98312 q^{71}\) \(+8.07246 q^{72}\) \(+0.643838 q^{73}\) \(-12.2821 q^{74}\) \(+1.29027 q^{75}\) \(+17.5377 q^{76}\) \(+3.59107 q^{77}\) \(+0.353054 q^{78}\) \(+4.71689 q^{79}\) \(-0.0682689 q^{80}\) \(+8.31509 q^{81}\) \(+9.23915 q^{82}\) \(+0.483915 q^{83}\) \(-0.889282 q^{84}\) \(+1.19256 q^{85}\) \(-2.48921 q^{86}\) \(-1.04252 q^{87}\) \(-9.91664 q^{88}\) \(+7.45128 q^{89}\) \(+3.90663 q^{90}\) \(+0.558307 q^{91}\) \(+10.6267 q^{92}\) \(-1.82891 q^{93}\) \(+3.89181 q^{94}\) \(+3.19900 q^{95}\) \(-1.60386 q^{96}\) \(+12.0197 q^{97}\) \(-2.28251 q^{98}\) \(-10.4976 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 48q^{11} \) \(\mathstrut +\mathstrut 72q^{12} \) \(\mathstrut +\mathstrut 29q^{13} \) \(\mathstrut +\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 29q^{15} \) \(\mathstrut +\mathstrut 115q^{16} \) \(\mathstrut +\mathstrut 72q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 58q^{19} \) \(\mathstrut +\mathstrut 88q^{20} \) \(\mathstrut +\mathstrut 38q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 65q^{23} \) \(\mathstrut +\mathstrut 46q^{24} \) \(\mathstrut +\mathstrut 124q^{25} \) \(\mathstrut +\mathstrut 49q^{26} \) \(\mathstrut +\mathstrut 131q^{27} \) \(\mathstrut +\mathstrut 111q^{28} \) \(\mathstrut +\mathstrut 25q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 75q^{32} \) \(\mathstrut +\mathstrut 54q^{33} \) \(\mathstrut +\mathstrut 23q^{34} \) \(\mathstrut +\mathstrut 43q^{35} \) \(\mathstrut +\mathstrut 111q^{36} \) \(\mathstrut +\mathstrut 25q^{37} \) \(\mathstrut +\mathstrut 54q^{38} \) \(\mathstrut +\mathstrut 27q^{39} \) \(\mathstrut +\mathstrut 30q^{40} \) \(\mathstrut +\mathstrut 109q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 38q^{43} \) \(\mathstrut +\mathstrut 68q^{44} \) \(\mathstrut +\mathstrut 84q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut +\mathstrut 121q^{47} \) \(\mathstrut +\mathstrut 106q^{48} \) \(\mathstrut +\mathstrut 109q^{49} \) \(\mathstrut +\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 38q^{52} \) \(\mathstrut +\mathstrut 61q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut +\mathstrut 50q^{55} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 20q^{58} \) \(\mathstrut +\mathstrut 181q^{59} \) \(\mathstrut +\mathstrut 25q^{60} \) \(\mathstrut +\mathstrut 34q^{61} \) \(\mathstrut +\mathstrut 75q^{62} \) \(\mathstrut +\mathstrut 119q^{63} \) \(\mathstrut +\mathstrut 96q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 87q^{67} \) \(\mathstrut +\mathstrut 150q^{68} \) \(\mathstrut +\mathstrut 89q^{69} \) \(\mathstrut +\mathstrut 15q^{70} \) \(\mathstrut +\mathstrut 83q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 32q^{73} \) \(\mathstrut -\mathstrut 19q^{74} \) \(\mathstrut +\mathstrut 112q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 48q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 137q^{80} \) \(\mathstrut +\mathstrut 109q^{81} \) \(\mathstrut -\mathstrut 19q^{82} \) \(\mathstrut +\mathstrut 136q^{83} \) \(\mathstrut +\mathstrut 72q^{84} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 28q^{87} \) \(\mathstrut -\mathstrut 24q^{88} \) \(\mathstrut +\mathstrut 142q^{89} \) \(\mathstrut +\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 29q^{91} \) \(\mathstrut +\mathstrut 96q^{92} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut +\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 52q^{95} \) \(\mathstrut +\mathstrut 88q^{96} \) \(\mathstrut +\mathstrut 75q^{97} \) \(\mathstrut +\mathstrut 19q^{98} \) \(\mathstrut +\mathstrut 84q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.28251 −1.61398 −0.806988 0.590567i \(-0.798904\pi\)
−0.806988 + 0.590567i \(0.798904\pi\)
\(3\) −0.277049 −0.159954 −0.0799770 0.996797i \(-0.525485\pi\)
−0.0799770 + 0.996797i \(0.525485\pi\)
\(4\) 3.20984 1.60492
\(5\) 0.585497 0.261842 0.130921 0.991393i \(-0.458207\pi\)
0.130921 + 0.991393i \(0.458207\pi\)
\(6\) 0.632366 0.258162
\(7\) 1.00000 0.377964
\(8\) −2.76147 −0.976328
\(9\) −2.92324 −0.974415
\(10\) −1.33640 −0.422608
\(11\) 3.59107 1.08275 0.541374 0.840782i \(-0.317904\pi\)
0.541374 + 0.840782i \(0.317904\pi\)
\(12\) −0.889282 −0.256714
\(13\) 0.558307 0.154846 0.0774232 0.996998i \(-0.475331\pi\)
0.0774232 + 0.996998i \(0.475331\pi\)
\(14\) −2.28251 −0.610026
\(15\) −0.162211 −0.0418828
\(16\) −0.116600 −0.0291500
\(17\) 2.03684 0.494006 0.247003 0.969015i \(-0.420554\pi\)
0.247003 + 0.969015i \(0.420554\pi\)
\(18\) 6.67233 1.57268
\(19\) 5.46372 1.25346 0.626732 0.779235i \(-0.284392\pi\)
0.626732 + 0.779235i \(0.284392\pi\)
\(20\) 1.87935 0.420236
\(21\) −0.277049 −0.0604570
\(22\) −8.19664 −1.74753
\(23\) 3.31065 0.690319 0.345159 0.938544i \(-0.387825\pi\)
0.345159 + 0.938544i \(0.387825\pi\)
\(24\) 0.765062 0.156168
\(25\) −4.65719 −0.931439
\(26\) −1.27434 −0.249919
\(27\) 1.64103 0.315816
\(28\) 3.20984 0.606603
\(29\) 3.76294 0.698761 0.349380 0.936981i \(-0.386392\pi\)
0.349380 + 0.936981i \(0.386392\pi\)
\(30\) 0.370248 0.0675978
\(31\) 6.60139 1.18564 0.592822 0.805333i \(-0.298014\pi\)
0.592822 + 0.805333i \(0.298014\pi\)
\(32\) 5.78909 1.02338
\(33\) −0.994900 −0.173190
\(34\) −4.64910 −0.797314
\(35\) 0.585497 0.0989671
\(36\) −9.38315 −1.56386
\(37\) 5.38098 0.884628 0.442314 0.896860i \(-0.354158\pi\)
0.442314 + 0.896860i \(0.354158\pi\)
\(38\) −12.4710 −2.02306
\(39\) −0.154678 −0.0247683
\(40\) −1.61684 −0.255644
\(41\) −4.04781 −0.632161 −0.316081 0.948732i \(-0.602367\pi\)
−0.316081 + 0.948732i \(0.602367\pi\)
\(42\) 0.632366 0.0975761
\(43\) 1.09056 0.166308 0.0831542 0.996537i \(-0.473501\pi\)
0.0831542 + 0.996537i \(0.473501\pi\)
\(44\) 11.5268 1.73772
\(45\) −1.71155 −0.255143
\(46\) −7.55659 −1.11416
\(47\) −1.70506 −0.248708 −0.124354 0.992238i \(-0.539686\pi\)
−0.124354 + 0.992238i \(0.539686\pi\)
\(48\) 0.0323038 0.00466266
\(49\) 1.00000 0.142857
\(50\) 10.6301 1.50332
\(51\) −0.564303 −0.0790182
\(52\) 1.79208 0.248516
\(53\) 5.93502 0.815238 0.407619 0.913152i \(-0.366359\pi\)
0.407619 + 0.913152i \(0.366359\pi\)
\(54\) −3.74566 −0.509719
\(55\) 2.10256 0.283509
\(56\) −2.76147 −0.369017
\(57\) −1.51372 −0.200497
\(58\) −8.58895 −1.12778
\(59\) −6.28870 −0.818718 −0.409359 0.912373i \(-0.634248\pi\)
−0.409359 + 0.912373i \(0.634248\pi\)
\(60\) −0.520672 −0.0672185
\(61\) 6.18002 0.791271 0.395635 0.918408i \(-0.370524\pi\)
0.395635 + 0.918408i \(0.370524\pi\)
\(62\) −15.0677 −1.91360
\(63\) −2.92324 −0.368294
\(64\) −12.9804 −1.62255
\(65\) 0.326887 0.0405454
\(66\) 2.27087 0.279524
\(67\) −6.69246 −0.817615 −0.408807 0.912621i \(-0.634055\pi\)
−0.408807 + 0.912621i \(0.634055\pi\)
\(68\) 6.53793 0.792840
\(69\) −0.917212 −0.110419
\(70\) −1.33640 −0.159731
\(71\) −3.98312 −0.472710 −0.236355 0.971667i \(-0.575953\pi\)
−0.236355 + 0.971667i \(0.575953\pi\)
\(72\) 8.07246 0.951348
\(73\) 0.643838 0.0753555 0.0376777 0.999290i \(-0.488004\pi\)
0.0376777 + 0.999290i \(0.488004\pi\)
\(74\) −12.2821 −1.42777
\(75\) 1.29027 0.148987
\(76\) 17.5377 2.01171
\(77\) 3.59107 0.409240
\(78\) 0.353054 0.0399755
\(79\) 4.71689 0.530691 0.265346 0.964153i \(-0.414514\pi\)
0.265346 + 0.964153i \(0.414514\pi\)
\(80\) −0.0682689 −0.00763270
\(81\) 8.31509 0.923899
\(82\) 9.23915 1.02029
\(83\) 0.483915 0.0531166 0.0265583 0.999647i \(-0.491545\pi\)
0.0265583 + 0.999647i \(0.491545\pi\)
\(84\) −0.889282 −0.0970286
\(85\) 1.19256 0.129352
\(86\) −2.48921 −0.268418
\(87\) −1.04252 −0.111770
\(88\) −9.91664 −1.05712
\(89\) 7.45128 0.789834 0.394917 0.918717i \(-0.370773\pi\)
0.394917 + 0.918717i \(0.370773\pi\)
\(90\) 3.90663 0.411795
\(91\) 0.558307 0.0585265
\(92\) 10.6267 1.10791
\(93\) −1.82891 −0.189649
\(94\) 3.89181 0.401410
\(95\) 3.19900 0.328210
\(96\) −1.60386 −0.163693
\(97\) 12.0197 1.22042 0.610209 0.792241i \(-0.291086\pi\)
0.610209 + 0.792241i \(0.291086\pi\)
\(98\) −2.28251 −0.230568
\(99\) −10.4976 −1.05505
\(100\) −14.9489 −1.49489
\(101\) −12.3084 −1.22474 −0.612368 0.790573i \(-0.709783\pi\)
−0.612368 + 0.790573i \(0.709783\pi\)
\(102\) 1.28803 0.127534
\(103\) −9.60351 −0.946262 −0.473131 0.880992i \(-0.656876\pi\)
−0.473131 + 0.880992i \(0.656876\pi\)
\(104\) −1.54175 −0.151181
\(105\) −0.162211 −0.0158302
\(106\) −13.5467 −1.31578
\(107\) 7.82807 0.756768 0.378384 0.925649i \(-0.376480\pi\)
0.378384 + 0.925649i \(0.376480\pi\)
\(108\) 5.26744 0.506859
\(109\) 8.24191 0.789432 0.394716 0.918803i \(-0.370843\pi\)
0.394716 + 0.918803i \(0.370843\pi\)
\(110\) −4.79911 −0.457577
\(111\) −1.49079 −0.141500
\(112\) −0.116600 −0.0110177
\(113\) −13.8053 −1.29869 −0.649345 0.760494i \(-0.724957\pi\)
−0.649345 + 0.760494i \(0.724957\pi\)
\(114\) 3.45507 0.323597
\(115\) 1.93838 0.180755
\(116\) 12.0785 1.12146
\(117\) −1.63207 −0.150885
\(118\) 14.3540 1.32139
\(119\) 2.03684 0.186717
\(120\) 0.447942 0.0408913
\(121\) 1.89577 0.172342
\(122\) −14.1060 −1.27709
\(123\) 1.12144 0.101117
\(124\) 21.1894 1.90287
\(125\) −5.65426 −0.505732
\(126\) 6.67233 0.594418
\(127\) −12.7291 −1.12953 −0.564764 0.825252i \(-0.691033\pi\)
−0.564764 + 0.825252i \(0.691033\pi\)
\(128\) 18.0498 1.59539
\(129\) −0.302138 −0.0266017
\(130\) −0.746123 −0.0654393
\(131\) 9.78851 0.855226 0.427613 0.903962i \(-0.359355\pi\)
0.427613 + 0.903962i \(0.359355\pi\)
\(132\) −3.19347 −0.277956
\(133\) 5.46372 0.473765
\(134\) 15.2756 1.31961
\(135\) 0.960817 0.0826939
\(136\) −5.62467 −0.482312
\(137\) 10.4659 0.894161 0.447081 0.894494i \(-0.352464\pi\)
0.447081 + 0.894494i \(0.352464\pi\)
\(138\) 2.09354 0.178214
\(139\) 3.70442 0.314205 0.157102 0.987582i \(-0.449785\pi\)
0.157102 + 0.987582i \(0.449785\pi\)
\(140\) 1.87935 0.158834
\(141\) 0.472384 0.0397819
\(142\) 9.09151 0.762942
\(143\) 2.00492 0.167660
\(144\) 0.340850 0.0284042
\(145\) 2.20319 0.182965
\(146\) −1.46956 −0.121622
\(147\) −0.277049 −0.0228506
\(148\) 17.2721 1.41976
\(149\) 11.3829 0.932525 0.466262 0.884646i \(-0.345600\pi\)
0.466262 + 0.884646i \(0.345600\pi\)
\(150\) −2.94505 −0.240462
\(151\) −8.15733 −0.663834 −0.331917 0.943309i \(-0.607695\pi\)
−0.331917 + 0.943309i \(0.607695\pi\)
\(152\) −15.0879 −1.22379
\(153\) −5.95417 −0.481366
\(154\) −8.19664 −0.660504
\(155\) 3.86510 0.310452
\(156\) −0.496492 −0.0397512
\(157\) −8.93067 −0.712745 −0.356372 0.934344i \(-0.615987\pi\)
−0.356372 + 0.934344i \(0.615987\pi\)
\(158\) −10.7663 −0.856523
\(159\) −1.64429 −0.130401
\(160\) 3.38949 0.267963
\(161\) 3.31065 0.260916
\(162\) −18.9793 −1.49115
\(163\) −6.95852 −0.545033 −0.272516 0.962151i \(-0.587856\pi\)
−0.272516 + 0.962151i \(0.587856\pi\)
\(164\) −12.9928 −1.01457
\(165\) −0.582512 −0.0453485
\(166\) −1.10454 −0.0857289
\(167\) 20.1003 1.55541 0.777704 0.628631i \(-0.216384\pi\)
0.777704 + 0.628631i \(0.216384\pi\)
\(168\) 0.765062 0.0590258
\(169\) −12.6883 −0.976023
\(170\) −2.72203 −0.208770
\(171\) −15.9718 −1.22139
\(172\) 3.50052 0.266912
\(173\) 18.1769 1.38196 0.690981 0.722873i \(-0.257179\pi\)
0.690981 + 0.722873i \(0.257179\pi\)
\(174\) 2.37956 0.180394
\(175\) −4.65719 −0.352051
\(176\) −0.418718 −0.0315621
\(177\) 1.74227 0.130957
\(178\) −17.0076 −1.27477
\(179\) −11.2057 −0.837556 −0.418778 0.908089i \(-0.637541\pi\)
−0.418778 + 0.908089i \(0.637541\pi\)
\(180\) −5.49381 −0.409484
\(181\) 2.27379 0.169009 0.0845047 0.996423i \(-0.473069\pi\)
0.0845047 + 0.996423i \(0.473069\pi\)
\(182\) −1.27434 −0.0944604
\(183\) −1.71217 −0.126567
\(184\) −9.14228 −0.673978
\(185\) 3.15055 0.231633
\(186\) 4.17449 0.306089
\(187\) 7.31442 0.534883
\(188\) −5.47297 −0.399157
\(189\) 1.64103 0.119367
\(190\) −7.30173 −0.529723
\(191\) 24.8406 1.79740 0.898700 0.438563i \(-0.144512\pi\)
0.898700 + 0.438563i \(0.144512\pi\)
\(192\) 3.59621 0.259534
\(193\) 15.2276 1.09611 0.548055 0.836443i \(-0.315369\pi\)
0.548055 + 0.836443i \(0.315369\pi\)
\(194\) −27.4351 −1.96973
\(195\) −0.0905637 −0.00648540
\(196\) 3.20984 0.229274
\(197\) −6.88856 −0.490790 −0.245395 0.969423i \(-0.578918\pi\)
−0.245395 + 0.969423i \(0.578918\pi\)
\(198\) 23.9608 1.70282
\(199\) −20.6946 −1.46700 −0.733500 0.679689i \(-0.762115\pi\)
−0.733500 + 0.679689i \(0.762115\pi\)
\(200\) 12.8607 0.909390
\(201\) 1.85414 0.130781
\(202\) 28.0941 1.97669
\(203\) 3.76294 0.264107
\(204\) −1.81132 −0.126818
\(205\) −2.36998 −0.165527
\(206\) 21.9201 1.52724
\(207\) −9.67784 −0.672657
\(208\) −0.0650985 −0.00451377
\(209\) 19.6206 1.35719
\(210\) 0.370248 0.0255496
\(211\) 0.540588 0.0372156 0.0186078 0.999827i \(-0.494077\pi\)
0.0186078 + 0.999827i \(0.494077\pi\)
\(212\) 19.0505 1.30839
\(213\) 1.10352 0.0756118
\(214\) −17.8676 −1.22141
\(215\) 0.638519 0.0435466
\(216\) −4.53165 −0.308340
\(217\) 6.60139 0.448132
\(218\) −18.8122 −1.27412
\(219\) −0.178374 −0.0120534
\(220\) 6.74889 0.455010
\(221\) 1.13718 0.0764950
\(222\) 3.40275 0.228377
\(223\) 3.83858 0.257050 0.128525 0.991706i \(-0.458976\pi\)
0.128525 + 0.991706i \(0.458976\pi\)
\(224\) 5.78909 0.386800
\(225\) 13.6141 0.907607
\(226\) 31.5106 2.09606
\(227\) −22.3502 −1.48344 −0.741719 0.670711i \(-0.765989\pi\)
−0.741719 + 0.670711i \(0.765989\pi\)
\(228\) −4.85879 −0.321781
\(229\) −4.90371 −0.324046 −0.162023 0.986787i \(-0.551802\pi\)
−0.162023 + 0.986787i \(0.551802\pi\)
\(230\) −4.42436 −0.291734
\(231\) −0.994900 −0.0654596
\(232\) −10.3913 −0.682220
\(233\) 11.6431 0.762765 0.381383 0.924417i \(-0.375448\pi\)
0.381383 + 0.924417i \(0.375448\pi\)
\(234\) 3.72521 0.243524
\(235\) −0.998307 −0.0651224
\(236\) −20.1857 −1.31398
\(237\) −1.30681 −0.0848862
\(238\) −4.64910 −0.301356
\(239\) 17.3436 1.12187 0.560933 0.827861i \(-0.310443\pi\)
0.560933 + 0.827861i \(0.310443\pi\)
\(240\) 0.0189138 0.00122088
\(241\) −19.5006 −1.25614 −0.628072 0.778155i \(-0.716156\pi\)
−0.628072 + 0.778155i \(0.716156\pi\)
\(242\) −4.32710 −0.278157
\(243\) −7.22676 −0.463597
\(244\) 19.8369 1.26993
\(245\) 0.585497 0.0374061
\(246\) −2.55969 −0.163200
\(247\) 3.05043 0.194095
\(248\) −18.2296 −1.15758
\(249\) −0.134068 −0.00849621
\(250\) 12.9059 0.816240
\(251\) −14.6005 −0.921573 −0.460787 0.887511i \(-0.652433\pi\)
−0.460787 + 0.887511i \(0.652433\pi\)
\(252\) −9.38315 −0.591083
\(253\) 11.8888 0.747441
\(254\) 29.0544 1.82303
\(255\) −0.330398 −0.0206903
\(256\) −15.2379 −0.952367
\(257\) −9.93889 −0.619971 −0.309985 0.950741i \(-0.600324\pi\)
−0.309985 + 0.950741i \(0.600324\pi\)
\(258\) 0.689631 0.0429346
\(259\) 5.38098 0.334358
\(260\) 1.04926 0.0650721
\(261\) −11.0000 −0.680883
\(262\) −22.3423 −1.38031
\(263\) 11.2040 0.690870 0.345435 0.938443i \(-0.387731\pi\)
0.345435 + 0.938443i \(0.387731\pi\)
\(264\) 2.74739 0.169090
\(265\) 3.47494 0.213464
\(266\) −12.4710 −0.764646
\(267\) −2.06437 −0.126337
\(268\) −21.4817 −1.31221
\(269\) −10.6131 −0.647091 −0.323546 0.946213i \(-0.604875\pi\)
−0.323546 + 0.946213i \(0.604875\pi\)
\(270\) −2.19307 −0.133466
\(271\) −28.0823 −1.70588 −0.852938 0.522012i \(-0.825182\pi\)
−0.852938 + 0.522012i \(0.825182\pi\)
\(272\) −0.237495 −0.0144002
\(273\) −0.154678 −0.00936155
\(274\) −23.8885 −1.44316
\(275\) −16.7243 −1.00851
\(276\) −2.94410 −0.177214
\(277\) 1.71708 0.103169 0.0515847 0.998669i \(-0.483573\pi\)
0.0515847 + 0.998669i \(0.483573\pi\)
\(278\) −8.45536 −0.507119
\(279\) −19.2975 −1.15531
\(280\) −1.61684 −0.0966244
\(281\) 17.9840 1.07284 0.536418 0.843953i \(-0.319777\pi\)
0.536418 + 0.843953i \(0.319777\pi\)
\(282\) −1.07822 −0.0642071
\(283\) 2.60980 0.155136 0.0775682 0.996987i \(-0.475284\pi\)
0.0775682 + 0.996987i \(0.475284\pi\)
\(284\) −12.7852 −0.758661
\(285\) −0.886277 −0.0524985
\(286\) −4.57624 −0.270599
\(287\) −4.04781 −0.238935
\(288\) −16.9229 −0.997192
\(289\) −12.8513 −0.755958
\(290\) −5.02881 −0.295302
\(291\) −3.33005 −0.195211
\(292\) 2.06662 0.120940
\(293\) 0.229207 0.0133904 0.00669520 0.999978i \(-0.497869\pi\)
0.00669520 + 0.999978i \(0.497869\pi\)
\(294\) 0.632366 0.0368803
\(295\) −3.68201 −0.214375
\(296\) −14.8594 −0.863687
\(297\) 5.89304 0.341949
\(298\) −25.9816 −1.50507
\(299\) 1.84836 0.106893
\(300\) 4.14156 0.239113
\(301\) 1.09056 0.0628587
\(302\) 18.6192 1.07141
\(303\) 3.41003 0.195901
\(304\) −0.637069 −0.0365384
\(305\) 3.61839 0.207188
\(306\) 13.5904 0.776914
\(307\) −24.9663 −1.42490 −0.712450 0.701722i \(-0.752415\pi\)
−0.712450 + 0.701722i \(0.752415\pi\)
\(308\) 11.5268 0.656798
\(309\) 2.66064 0.151358
\(310\) −8.82211 −0.501062
\(311\) 5.57802 0.316301 0.158150 0.987415i \(-0.449447\pi\)
0.158150 + 0.987415i \(0.449447\pi\)
\(312\) 0.427140 0.0241820
\(313\) 5.94741 0.336168 0.168084 0.985773i \(-0.446242\pi\)
0.168084 + 0.985773i \(0.446242\pi\)
\(314\) 20.3843 1.15035
\(315\) −1.71155 −0.0964350
\(316\) 15.1405 0.851717
\(317\) −4.11641 −0.231200 −0.115600 0.993296i \(-0.536879\pi\)
−0.115600 + 0.993296i \(0.536879\pi\)
\(318\) 3.75310 0.210464
\(319\) 13.5130 0.756582
\(320\) −7.60001 −0.424853
\(321\) −2.16876 −0.121048
\(322\) −7.55659 −0.421112
\(323\) 11.1287 0.619218
\(324\) 26.6901 1.48278
\(325\) −2.60014 −0.144230
\(326\) 15.8829 0.879671
\(327\) −2.28341 −0.126273
\(328\) 11.1779 0.617197
\(329\) −1.70506 −0.0940029
\(330\) 1.32959 0.0731914
\(331\) −23.5068 −1.29205 −0.646025 0.763316i \(-0.723570\pi\)
−0.646025 + 0.763316i \(0.723570\pi\)
\(332\) 1.55329 0.0852479
\(333\) −15.7299 −0.861994
\(334\) −45.8791 −2.51039
\(335\) −3.91842 −0.214086
\(336\) 0.0323038 0.00176232
\(337\) −25.1793 −1.37160 −0.685801 0.727789i \(-0.740548\pi\)
−0.685801 + 0.727789i \(0.740548\pi\)
\(338\) 28.9611 1.57528
\(339\) 3.82473 0.207731
\(340\) 3.82794 0.207599
\(341\) 23.7060 1.28375
\(342\) 36.4558 1.97130
\(343\) 1.00000 0.0539949
\(344\) −3.01155 −0.162372
\(345\) −0.537025 −0.0289125
\(346\) −41.4889 −2.23046
\(347\) 12.6313 0.678084 0.339042 0.940771i \(-0.389897\pi\)
0.339042 + 0.940771i \(0.389897\pi\)
\(348\) −3.34632 −0.179381
\(349\) 12.2189 0.654063 0.327032 0.945013i \(-0.393952\pi\)
0.327032 + 0.945013i \(0.393952\pi\)
\(350\) 10.6301 0.568202
\(351\) 0.916197 0.0489030
\(352\) 20.7890 1.10806
\(353\) 19.4614 1.03583 0.517914 0.855433i \(-0.326709\pi\)
0.517914 + 0.855433i \(0.326709\pi\)
\(354\) −3.97675 −0.211362
\(355\) −2.33211 −0.123775
\(356\) 23.9174 1.26762
\(357\) −0.564303 −0.0298661
\(358\) 25.5772 1.35180
\(359\) 15.8495 0.836507 0.418253 0.908330i \(-0.362642\pi\)
0.418253 + 0.908330i \(0.362642\pi\)
\(360\) 4.72640 0.249103
\(361\) 10.8523 0.571172
\(362\) −5.18994 −0.272777
\(363\) −0.525219 −0.0275669
\(364\) 1.79208 0.0939304
\(365\) 0.376965 0.0197313
\(366\) 3.90803 0.204276
\(367\) 7.25773 0.378850 0.189425 0.981895i \(-0.439338\pi\)
0.189425 + 0.981895i \(0.439338\pi\)
\(368\) −0.386022 −0.0201228
\(369\) 11.8327 0.615987
\(370\) −7.19115 −0.373850
\(371\) 5.93502 0.308131
\(372\) −5.87050 −0.304371
\(373\) −14.9680 −0.775014 −0.387507 0.921867i \(-0.626664\pi\)
−0.387507 + 0.921867i \(0.626664\pi\)
\(374\) −16.6952 −0.863289
\(375\) 1.56651 0.0808940
\(376\) 4.70847 0.242821
\(377\) 2.10088 0.108201
\(378\) −3.74566 −0.192656
\(379\) −34.7623 −1.78562 −0.892810 0.450434i \(-0.851269\pi\)
−0.892810 + 0.450434i \(0.851269\pi\)
\(380\) 10.2683 0.526751
\(381\) 3.52659 0.180673
\(382\) −56.6988 −2.90096
\(383\) −9.00283 −0.460023 −0.230011 0.973188i \(-0.573876\pi\)
−0.230011 + 0.973188i \(0.573876\pi\)
\(384\) −5.00066 −0.255189
\(385\) 2.10256 0.107156
\(386\) −34.7572 −1.76909
\(387\) −3.18797 −0.162053
\(388\) 38.5814 1.95867
\(389\) 25.3095 1.28324 0.641622 0.767021i \(-0.278262\pi\)
0.641622 + 0.767021i \(0.278262\pi\)
\(390\) 0.206712 0.0104673
\(391\) 6.74326 0.341021
\(392\) −2.76147 −0.139475
\(393\) −2.71189 −0.136797
\(394\) 15.7232 0.792123
\(395\) 2.76172 0.138957
\(396\) −33.6955 −1.69326
\(397\) 34.7997 1.74655 0.873273 0.487230i \(-0.161993\pi\)
0.873273 + 0.487230i \(0.161993\pi\)
\(398\) 47.2356 2.36770
\(399\) −1.51372 −0.0757806
\(400\) 0.543028 0.0271514
\(401\) 4.37821 0.218638 0.109319 0.994007i \(-0.465133\pi\)
0.109319 + 0.994007i \(0.465133\pi\)
\(402\) −4.23208 −0.211077
\(403\) 3.68560 0.183593
\(404\) −39.5081 −1.96560
\(405\) 4.86846 0.241916
\(406\) −8.58895 −0.426262
\(407\) 19.3235 0.957829
\(408\) 1.55831 0.0771477
\(409\) 5.24544 0.259370 0.129685 0.991555i \(-0.458603\pi\)
0.129685 + 0.991555i \(0.458603\pi\)
\(410\) 5.40950 0.267156
\(411\) −2.89956 −0.143025
\(412\) −30.8257 −1.51867
\(413\) −6.28870 −0.309446
\(414\) 22.0898 1.08565
\(415\) 0.283331 0.0139082
\(416\) 3.23209 0.158466
\(417\) −1.02630 −0.0502583
\(418\) −44.7842 −2.19047
\(419\) 1.81371 0.0886055 0.0443028 0.999018i \(-0.485893\pi\)
0.0443028 + 0.999018i \(0.485893\pi\)
\(420\) −0.520672 −0.0254062
\(421\) −12.3131 −0.600104 −0.300052 0.953923i \(-0.597004\pi\)
−0.300052 + 0.953923i \(0.597004\pi\)
\(422\) −1.23390 −0.0600651
\(423\) 4.98430 0.242345
\(424\) −16.3894 −0.795940
\(425\) −9.48594 −0.460136
\(426\) −2.51879 −0.122036
\(427\) 6.18002 0.299072
\(428\) 25.1269 1.21455
\(429\) −0.555460 −0.0268179
\(430\) −1.45742 −0.0702832
\(431\) −19.7490 −0.951277 −0.475639 0.879641i \(-0.657783\pi\)
−0.475639 + 0.879641i \(0.657783\pi\)
\(432\) −0.191343 −0.00920602
\(433\) 11.6397 0.559369 0.279684 0.960092i \(-0.409770\pi\)
0.279684 + 0.960092i \(0.409770\pi\)
\(434\) −15.0677 −0.723274
\(435\) −0.610392 −0.0292660
\(436\) 26.4552 1.26698
\(437\) 18.0885 0.865290
\(438\) 0.407141 0.0194539
\(439\) 25.3971 1.21214 0.606069 0.795412i \(-0.292746\pi\)
0.606069 + 0.795412i \(0.292746\pi\)
\(440\) −5.80616 −0.276798
\(441\) −2.92324 −0.139202
\(442\) −2.59562 −0.123461
\(443\) 24.7323 1.17507 0.587534 0.809199i \(-0.300099\pi\)
0.587534 + 0.809199i \(0.300099\pi\)
\(444\) −4.78521 −0.227096
\(445\) 4.36271 0.206812
\(446\) −8.76159 −0.414873
\(447\) −3.15362 −0.149161
\(448\) −12.9804 −0.613268
\(449\) −7.72381 −0.364509 −0.182255 0.983251i \(-0.558340\pi\)
−0.182255 + 0.983251i \(0.558340\pi\)
\(450\) −31.0743 −1.46486
\(451\) −14.5359 −0.684471
\(452\) −44.3127 −2.08430
\(453\) 2.25998 0.106183
\(454\) 51.0146 2.39423
\(455\) 0.326887 0.0153247
\(456\) 4.18009 0.195751
\(457\) 10.5209 0.492147 0.246073 0.969251i \(-0.420860\pi\)
0.246073 + 0.969251i \(0.420860\pi\)
\(458\) 11.1928 0.523003
\(459\) 3.34250 0.156015
\(460\) 6.22189 0.290097
\(461\) −3.21031 −0.149519 −0.0747595 0.997202i \(-0.523819\pi\)
−0.0747595 + 0.997202i \(0.523819\pi\)
\(462\) 2.27087 0.105650
\(463\) −12.2505 −0.569329 −0.284664 0.958627i \(-0.591882\pi\)
−0.284664 + 0.958627i \(0.591882\pi\)
\(464\) −0.438759 −0.0203689
\(465\) −1.07082 −0.0496581
\(466\) −26.5755 −1.23109
\(467\) −9.45148 −0.437362 −0.218681 0.975796i \(-0.570175\pi\)
−0.218681 + 0.975796i \(0.570175\pi\)
\(468\) −5.23868 −0.242158
\(469\) −6.69246 −0.309029
\(470\) 2.27864 0.105106
\(471\) 2.47423 0.114006
\(472\) 17.3661 0.799338
\(473\) 3.91627 0.180070
\(474\) 2.98280 0.137004
\(475\) −25.4456 −1.16752
\(476\) 6.53793 0.299665
\(477\) −17.3495 −0.794380
\(478\) −39.5870 −1.81067
\(479\) −2.32011 −0.106009 −0.0530043 0.998594i \(-0.516880\pi\)
−0.0530043 + 0.998594i \(0.516880\pi\)
\(480\) −0.939055 −0.0428618
\(481\) 3.00424 0.136982
\(482\) 44.5103 2.02739
\(483\) −0.917212 −0.0417346
\(484\) 6.08511 0.276596
\(485\) 7.03752 0.319557
\(486\) 16.4951 0.748235
\(487\) 18.1997 0.824708 0.412354 0.911024i \(-0.364707\pi\)
0.412354 + 0.911024i \(0.364707\pi\)
\(488\) −17.0660 −0.772540
\(489\) 1.92785 0.0871803
\(490\) −1.33640 −0.0603725
\(491\) 20.3167 0.916880 0.458440 0.888725i \(-0.348408\pi\)
0.458440 + 0.888725i \(0.348408\pi\)
\(492\) 3.59964 0.162284
\(493\) 7.66450 0.345192
\(494\) −6.96264 −0.313264
\(495\) −6.14630 −0.276256
\(496\) −0.769721 −0.0345615
\(497\) −3.98312 −0.178667
\(498\) 0.306011 0.0137127
\(499\) −13.6957 −0.613104 −0.306552 0.951854i \(-0.599175\pi\)
−0.306552 + 0.951854i \(0.599175\pi\)
\(500\) −18.1493 −0.811661
\(501\) −5.56876 −0.248794
\(502\) 33.3257 1.48740
\(503\) 30.6505 1.36664 0.683318 0.730120i \(-0.260536\pi\)
0.683318 + 0.730120i \(0.260536\pi\)
\(504\) 8.07246 0.359576
\(505\) −7.20656 −0.320688
\(506\) −27.1362 −1.20635
\(507\) 3.51527 0.156119
\(508\) −40.8585 −1.81280
\(509\) 20.3721 0.902977 0.451488 0.892277i \(-0.350893\pi\)
0.451488 + 0.892277i \(0.350893\pi\)
\(510\) 0.754136 0.0333937
\(511\) 0.643838 0.0284817
\(512\) −1.31898 −0.0582913
\(513\) 8.96612 0.395864
\(514\) 22.6856 1.00062
\(515\) −5.62283 −0.247771
\(516\) −0.969814 −0.0426937
\(517\) −6.12298 −0.269288
\(518\) −12.2821 −0.539646
\(519\) −5.03588 −0.221051
\(520\) −0.902690 −0.0395856
\(521\) 32.3581 1.41763 0.708817 0.705392i \(-0.249229\pi\)
0.708817 + 0.705392i \(0.249229\pi\)
\(522\) 25.1076 1.09893
\(523\) 30.7731 1.34562 0.672808 0.739817i \(-0.265088\pi\)
0.672808 + 0.739817i \(0.265088\pi\)
\(524\) 31.4196 1.37257
\(525\) 1.29027 0.0563119
\(526\) −25.5733 −1.11505
\(527\) 13.4460 0.585715
\(528\) 0.116005 0.00504848
\(529\) −12.0396 −0.523460
\(530\) −7.93158 −0.344526
\(531\) 18.3834 0.797771
\(532\) 17.5377 0.760355
\(533\) −2.25992 −0.0978880
\(534\) 4.71193 0.203905
\(535\) 4.58331 0.198154
\(536\) 18.4811 0.798260
\(537\) 3.10453 0.133970
\(538\) 24.2245 1.04439
\(539\) 3.59107 0.154678
\(540\) 3.08407 0.132717
\(541\) 28.8613 1.24084 0.620422 0.784268i \(-0.286961\pi\)
0.620422 + 0.784268i \(0.286961\pi\)
\(542\) 64.0980 2.75324
\(543\) −0.629950 −0.0270337
\(544\) 11.7914 0.505553
\(545\) 4.82562 0.206707
\(546\) 0.353054 0.0151093
\(547\) 3.61721 0.154661 0.0773303 0.997006i \(-0.475360\pi\)
0.0773303 + 0.997006i \(0.475360\pi\)
\(548\) 33.5938 1.43506
\(549\) −18.0657 −0.771026
\(550\) 38.1733 1.62772
\(551\) 20.5597 0.875872
\(552\) 2.53286 0.107805
\(553\) 4.71689 0.200582
\(554\) −3.91925 −0.166513
\(555\) −0.872856 −0.0370507
\(556\) 11.8906 0.504273
\(557\) −18.0993 −0.766893 −0.383447 0.923563i \(-0.625263\pi\)
−0.383447 + 0.923563i \(0.625263\pi\)
\(558\) 44.0466 1.86464
\(559\) 0.608866 0.0257523
\(560\) −0.0682689 −0.00288489
\(561\) −2.02645 −0.0855568
\(562\) −41.0486 −1.73153
\(563\) −6.55280 −0.276168 −0.138084 0.990421i \(-0.544094\pi\)
−0.138084 + 0.990421i \(0.544094\pi\)
\(564\) 1.51628 0.0638468
\(565\) −8.08295 −0.340052
\(566\) −5.95689 −0.250387
\(567\) 8.31509 0.349201
\(568\) 10.9993 0.461520
\(569\) −14.9359 −0.626145 −0.313072 0.949729i \(-0.601358\pi\)
−0.313072 + 0.949729i \(0.601358\pi\)
\(570\) 2.02294 0.0847314
\(571\) −1.88374 −0.0788320 −0.0394160 0.999223i \(-0.512550\pi\)
−0.0394160 + 0.999223i \(0.512550\pi\)
\(572\) 6.43547 0.269080
\(573\) −6.88205 −0.287502
\(574\) 9.23915 0.385635
\(575\) −15.4183 −0.642989
\(576\) 37.9450 1.58104
\(577\) −33.2528 −1.38433 −0.692166 0.721739i \(-0.743343\pi\)
−0.692166 + 0.721739i \(0.743343\pi\)
\(578\) 29.3332 1.22010
\(579\) −4.21879 −0.175327
\(580\) 7.07190 0.293645
\(581\) 0.483915 0.0200762
\(582\) 7.60086 0.315066
\(583\) 21.3131 0.882697
\(584\) −1.77794 −0.0735717
\(585\) −0.955571 −0.0395080
\(586\) −0.523166 −0.0216118
\(587\) −7.81534 −0.322574 −0.161287 0.986908i \(-0.551564\pi\)
−0.161287 + 0.986908i \(0.551564\pi\)
\(588\) −0.889282 −0.0366734
\(589\) 36.0682 1.48616
\(590\) 8.40423 0.345997
\(591\) 1.90847 0.0785038
\(592\) −0.627422 −0.0257869
\(593\) 21.2241 0.871569 0.435784 0.900051i \(-0.356471\pi\)
0.435784 + 0.900051i \(0.356471\pi\)
\(594\) −13.4509 −0.551897
\(595\) 1.19256 0.0488903
\(596\) 36.5374 1.49663
\(597\) 5.73341 0.234653
\(598\) −4.21890 −0.172524
\(599\) 29.5623 1.20788 0.603942 0.797028i \(-0.293596\pi\)
0.603942 + 0.797028i \(0.293596\pi\)
\(600\) −3.56304 −0.145461
\(601\) 8.62122 0.351667 0.175834 0.984420i \(-0.443738\pi\)
0.175834 + 0.984420i \(0.443738\pi\)
\(602\) −2.48921 −0.101452
\(603\) 19.5637 0.796696
\(604\) −26.1837 −1.06540
\(605\) 1.10997 0.0451265
\(606\) −7.78343 −0.316180
\(607\) 30.1109 1.22216 0.611082 0.791567i \(-0.290735\pi\)
0.611082 + 0.791567i \(0.290735\pi\)
\(608\) 31.6300 1.28276
\(609\) −1.04252 −0.0422450
\(610\) −8.25900 −0.334397
\(611\) −0.951946 −0.0385116
\(612\) −19.1120 −0.772555
\(613\) 41.1352 1.66143 0.830717 0.556696i \(-0.187931\pi\)
0.830717 + 0.556696i \(0.187931\pi\)
\(614\) 56.9857 2.29976
\(615\) 0.656600 0.0264767
\(616\) −9.91664 −0.399553
\(617\) 23.9281 0.963310 0.481655 0.876361i \(-0.340036\pi\)
0.481655 + 0.876361i \(0.340036\pi\)
\(618\) −6.07293 −0.244289
\(619\) −18.8193 −0.756411 −0.378206 0.925722i \(-0.623459\pi\)
−0.378206 + 0.925722i \(0.623459\pi\)
\(620\) 12.4063 0.498251
\(621\) 5.43287 0.218014
\(622\) −12.7319 −0.510502
\(623\) 7.45128 0.298529
\(624\) 0.0180355 0.000721996 0
\(625\) 19.9754 0.799016
\(626\) −13.5750 −0.542567
\(627\) −5.43586 −0.217087
\(628\) −28.6660 −1.14390
\(629\) 10.9602 0.437011
\(630\) 3.90663 0.155644
\(631\) 28.5364 1.13602 0.568008 0.823023i \(-0.307714\pi\)
0.568008 + 0.823023i \(0.307714\pi\)
\(632\) −13.0256 −0.518129
\(633\) −0.149769 −0.00595278
\(634\) 9.39573 0.373152
\(635\) −7.45288 −0.295759
\(636\) −5.27791 −0.209283
\(637\) 0.558307 0.0221209
\(638\) −30.8435 −1.22111
\(639\) 11.6436 0.460615
\(640\) 10.5681 0.417741
\(641\) −19.2987 −0.762254 −0.381127 0.924523i \(-0.624464\pi\)
−0.381127 + 0.924523i \(0.624464\pi\)
\(642\) 4.95020 0.195369
\(643\) 26.2181 1.03394 0.516970 0.856004i \(-0.327060\pi\)
0.516970 + 0.856004i \(0.327060\pi\)
\(644\) 10.6267 0.418749
\(645\) −0.176901 −0.00696546
\(646\) −25.4014 −0.999404
\(647\) −9.26466 −0.364231 −0.182116 0.983277i \(-0.558295\pi\)
−0.182116 + 0.983277i \(0.558295\pi\)
\(648\) −22.9619 −0.902028
\(649\) −22.5831 −0.886465
\(650\) 5.93485 0.232784
\(651\) −1.82891 −0.0716805
\(652\) −22.3357 −0.874735
\(653\) 30.7628 1.20384 0.601922 0.798555i \(-0.294402\pi\)
0.601922 + 0.798555i \(0.294402\pi\)
\(654\) 5.21190 0.203801
\(655\) 5.73115 0.223934
\(656\) 0.471974 0.0184275
\(657\) −1.88209 −0.0734275
\(658\) 3.89181 0.151719
\(659\) 41.8557 1.63047 0.815234 0.579132i \(-0.196609\pi\)
0.815234 + 0.579132i \(0.196609\pi\)
\(660\) −1.86977 −0.0727807
\(661\) −44.7404 −1.74020 −0.870099 0.492877i \(-0.835945\pi\)
−0.870099 + 0.492877i \(0.835945\pi\)
\(662\) 53.6545 2.08534
\(663\) −0.315054 −0.0122357
\(664\) −1.33632 −0.0518592
\(665\) 3.19900 0.124052
\(666\) 35.9037 1.39124
\(667\) 12.4578 0.482368
\(668\) 64.5187 2.49631
\(669\) −1.06347 −0.0411162
\(670\) 8.94382 0.345530
\(671\) 22.1929 0.856747
\(672\) −1.60386 −0.0618702
\(673\) 28.1938 1.08679 0.543395 0.839477i \(-0.317139\pi\)
0.543395 + 0.839477i \(0.317139\pi\)
\(674\) 57.4719 2.21373
\(675\) −7.64258 −0.294163
\(676\) −40.7274 −1.56644
\(677\) −13.2041 −0.507474 −0.253737 0.967273i \(-0.581660\pi\)
−0.253737 + 0.967273i \(0.581660\pi\)
\(678\) −8.72998 −0.335273
\(679\) 12.0197 0.461275
\(680\) −3.29323 −0.126290
\(681\) 6.19210 0.237282
\(682\) −54.1092 −2.07195
\(683\) −13.9598 −0.534157 −0.267079 0.963675i \(-0.586058\pi\)
−0.267079 + 0.963675i \(0.586058\pi\)
\(684\) −51.2669 −1.96024
\(685\) 6.12775 0.234129
\(686\) −2.28251 −0.0871466
\(687\) 1.35857 0.0518325
\(688\) −0.127159 −0.00484789
\(689\) 3.31356 0.126237
\(690\) 1.22576 0.0466640
\(691\) 45.5447 1.73260 0.866301 0.499522i \(-0.166491\pi\)
0.866301 + 0.499522i \(0.166491\pi\)
\(692\) 58.3449 2.21794
\(693\) −10.4976 −0.398770
\(694\) −28.8311 −1.09441
\(695\) 2.16893 0.0822721
\(696\) 2.87889 0.109124
\(697\) −8.24473 −0.312291
\(698\) −27.8898 −1.05564
\(699\) −3.22571 −0.122007
\(700\) −14.9489 −0.565013
\(701\) −33.3591 −1.25996 −0.629979 0.776612i \(-0.716936\pi\)
−0.629979 + 0.776612i \(0.716936\pi\)
\(702\) −2.09123 −0.0789282
\(703\) 29.4002 1.10885
\(704\) −46.6136 −1.75682
\(705\) 0.276580 0.0104166
\(706\) −44.4209 −1.67180
\(707\) −12.3084 −0.462906
\(708\) 5.59243 0.210176
\(709\) −11.0538 −0.415133 −0.207567 0.978221i \(-0.566554\pi\)
−0.207567 + 0.978221i \(0.566554\pi\)
\(710\) 5.32305 0.199771
\(711\) −13.7886 −0.517113
\(712\) −20.5765 −0.771137
\(713\) 21.8549 0.818473
\(714\) 1.28803 0.0482032
\(715\) 1.17387 0.0439004
\(716\) −35.9686 −1.34421
\(717\) −4.80503 −0.179447
\(718\) −36.1767 −1.35010
\(719\) −30.1215 −1.12334 −0.561671 0.827361i \(-0.689841\pi\)
−0.561671 + 0.827361i \(0.689841\pi\)
\(720\) 0.199567 0.00743741
\(721\) −9.60351 −0.357653
\(722\) −24.7704 −0.921859
\(723\) 5.40261 0.200925
\(724\) 7.29850 0.271247
\(725\) −17.5247 −0.650853
\(726\) 1.19882 0.0444923
\(727\) 13.8529 0.513774 0.256887 0.966441i \(-0.417303\pi\)
0.256887 + 0.966441i \(0.417303\pi\)
\(728\) −1.54175 −0.0571410
\(729\) −22.9431 −0.849744
\(730\) −0.860426 −0.0318458
\(731\) 2.22129 0.0821573
\(732\) −5.49578 −0.203130
\(733\) −6.44859 −0.238184 −0.119092 0.992883i \(-0.537998\pi\)
−0.119092 + 0.992883i \(0.537998\pi\)
\(734\) −16.5658 −0.611456
\(735\) −0.162211 −0.00598325
\(736\) 19.1657 0.706455
\(737\) −24.0331 −0.885270
\(738\) −27.0083 −0.994189
\(739\) 6.67572 0.245570 0.122785 0.992433i \(-0.460817\pi\)
0.122785 + 0.992433i \(0.460817\pi\)
\(740\) 10.1128 0.371753
\(741\) −0.845119 −0.0310462
\(742\) −13.5467 −0.497316
\(743\) 32.6741 1.19870 0.599349 0.800488i \(-0.295426\pi\)
0.599349 + 0.800488i \(0.295426\pi\)
\(744\) 5.05047 0.185159
\(745\) 6.66467 0.244174
\(746\) 34.1646 1.25085
\(747\) −1.41460 −0.0517576
\(748\) 23.4781 0.858446
\(749\) 7.82807 0.286031
\(750\) −3.57556 −0.130561
\(751\) 20.1994 0.737088 0.368544 0.929610i \(-0.379856\pi\)
0.368544 + 0.929610i \(0.379856\pi\)
\(752\) 0.198810 0.00724984
\(753\) 4.04504 0.147409
\(754\) −4.79527 −0.174633
\(755\) −4.77610 −0.173820
\(756\) 5.26744 0.191575
\(757\) 17.5831 0.639068 0.319534 0.947575i \(-0.396474\pi\)
0.319534 + 0.947575i \(0.396474\pi\)
\(758\) 79.3452 2.88195
\(759\) −3.29377 −0.119556
\(760\) −8.83394 −0.320441
\(761\) −3.10123 −0.112419 −0.0562097 0.998419i \(-0.517902\pi\)
−0.0562097 + 0.998419i \(0.517902\pi\)
\(762\) −8.04947 −0.291602
\(763\) 8.24191 0.298377
\(764\) 79.7343 2.88469
\(765\) −3.48615 −0.126042
\(766\) 20.5490 0.742466
\(767\) −3.51102 −0.126776
\(768\) 4.22163 0.152335
\(769\) −17.2489 −0.622011 −0.311005 0.950408i \(-0.600666\pi\)
−0.311005 + 0.950408i \(0.600666\pi\)
\(770\) −4.79911 −0.172948
\(771\) 2.75356 0.0991669
\(772\) 48.8783 1.75917
\(773\) 3.26386 0.117393 0.0586964 0.998276i \(-0.481306\pi\)
0.0586964 + 0.998276i \(0.481306\pi\)
\(774\) 7.27656 0.261550
\(775\) −30.7439 −1.10436
\(776\) −33.1921 −1.19153
\(777\) −1.49079 −0.0534819
\(778\) −57.7692 −2.07112
\(779\) −22.1161 −0.792392
\(780\) −0.290695 −0.0104086
\(781\) −14.3037 −0.511825
\(782\) −15.3915 −0.550401
\(783\) 6.17509 0.220680
\(784\) −0.116600 −0.00416428
\(785\) −5.22888 −0.186627
\(786\) 6.18992 0.220787
\(787\) 40.9928 1.46123 0.730617 0.682788i \(-0.239233\pi\)
0.730617 + 0.682788i \(0.239233\pi\)
\(788\) −22.1112 −0.787678
\(789\) −3.10406 −0.110508
\(790\) −6.30366 −0.224274
\(791\) −13.8053 −0.490859
\(792\) 28.9887 1.03007
\(793\) 3.45035 0.122526
\(794\) −79.4306 −2.81889
\(795\) −0.962727 −0.0341444
\(796\) −66.4264 −2.35442
\(797\) 40.3799 1.43033 0.715165 0.698955i \(-0.246351\pi\)
0.715165 + 0.698955i \(0.246351\pi\)
\(798\) 3.45507 0.122308
\(799\) −3.47293 −0.122863
\(800\) −26.9609 −0.953211
\(801\) −21.7819 −0.769626
\(802\) −9.99331 −0.352876
\(803\) 2.31206 0.0815910
\(804\) 5.95149 0.209893
\(805\) 1.93838 0.0683189
\(806\) −8.41242 −0.296315
\(807\) 2.94034 0.103505
\(808\) 33.9894 1.19574
\(809\) 7.01714 0.246710 0.123355 0.992363i \(-0.460635\pi\)
0.123355 + 0.992363i \(0.460635\pi\)
\(810\) −11.1123 −0.390447
\(811\) −28.5862 −1.00380 −0.501899 0.864926i \(-0.667365\pi\)
−0.501899 + 0.864926i \(0.667365\pi\)
\(812\) 12.0785 0.423870
\(813\) 7.78015 0.272862
\(814\) −44.1060 −1.54591
\(815\) −4.07419 −0.142713
\(816\) 0.0657976 0.00230338
\(817\) 5.95851 0.208462
\(818\) −11.9728 −0.418618
\(819\) −1.63207 −0.0570291
\(820\) −7.60726 −0.265657
\(821\) −10.2753 −0.358611 −0.179305 0.983793i \(-0.557385\pi\)
−0.179305 + 0.983793i \(0.557385\pi\)
\(822\) 6.61827 0.230839
\(823\) 50.9387 1.77561 0.887806 0.460219i \(-0.152229\pi\)
0.887806 + 0.460219i \(0.152229\pi\)
\(824\) 26.5198 0.923862
\(825\) 4.63344 0.161316
\(826\) 14.3540 0.499439
\(827\) 7.44497 0.258887 0.129443 0.991587i \(-0.458681\pi\)
0.129443 + 0.991587i \(0.458681\pi\)
\(828\) −31.0643 −1.07956
\(829\) −38.8390 −1.34893 −0.674467 0.738305i \(-0.735627\pi\)
−0.674467 + 0.738305i \(0.735627\pi\)
\(830\) −0.646705 −0.0224475
\(831\) −0.475715 −0.0165024
\(832\) −7.24707 −0.251247
\(833\) 2.03684 0.0705722
\(834\) 2.34255 0.0811157
\(835\) 11.7687 0.407271
\(836\) 62.9790 2.17818
\(837\) 10.8331 0.374445
\(838\) −4.13981 −0.143007
\(839\) 8.88145 0.306622 0.153311 0.988178i \(-0.451006\pi\)
0.153311 + 0.988178i \(0.451006\pi\)
\(840\) 0.447942 0.0154555
\(841\) −14.8403 −0.511733
\(842\) 28.1048 0.968554
\(843\) −4.98244 −0.171604
\(844\) 1.73520 0.0597281
\(845\) −7.42896 −0.255564
\(846\) −11.3767 −0.391139
\(847\) 1.89577 0.0651393
\(848\) −0.692023 −0.0237642
\(849\) −0.723041 −0.0248147
\(850\) 21.6517 0.742649
\(851\) 17.8146 0.610675
\(852\) 3.54212 0.121351
\(853\) −23.7391 −0.812813 −0.406406 0.913692i \(-0.633218\pi\)
−0.406406 + 0.913692i \(0.633218\pi\)
\(854\) −14.1060 −0.482696
\(855\) −9.35145 −0.319813
\(856\) −21.6170 −0.738854
\(857\) 37.9001 1.29464 0.647321 0.762218i \(-0.275889\pi\)
0.647321 + 0.762218i \(0.275889\pi\)
\(858\) 1.26784 0.0432834
\(859\) −1.00000 −0.0341196
\(860\) 2.04954 0.0698889
\(861\) 1.12144 0.0382186
\(862\) 45.0773 1.53534
\(863\) −30.0303 −1.02224 −0.511121 0.859509i \(-0.670770\pi\)
−0.511121 + 0.859509i \(0.670770\pi\)
\(864\) 9.50004 0.323198
\(865\) 10.6425 0.361856
\(866\) −26.5677 −0.902808
\(867\) 3.56043 0.120919
\(868\) 21.1894 0.719216
\(869\) 16.9387 0.574605
\(870\) 1.39322 0.0472347
\(871\) −3.73645 −0.126605
\(872\) −22.7598 −0.770744
\(873\) −35.1366 −1.18919
\(874\) −41.2871 −1.39656
\(875\) −5.65426 −0.191149
\(876\) −0.572553 −0.0193448
\(877\) 42.6373 1.43976 0.719880 0.694099i \(-0.244197\pi\)
0.719880 + 0.694099i \(0.244197\pi\)
\(878\) −57.9691 −1.95636
\(879\) −0.0635014 −0.00214185
\(880\) −0.245158 −0.00826428
\(881\) 5.82844 0.196365 0.0981826 0.995168i \(-0.468697\pi\)
0.0981826 + 0.995168i \(0.468697\pi\)
\(882\) 6.67233 0.224669
\(883\) 30.1977 1.01623 0.508117 0.861288i \(-0.330342\pi\)
0.508117 + 0.861288i \(0.330342\pi\)
\(884\) 3.65017 0.122768
\(885\) 1.02010 0.0342902
\(886\) −56.4517 −1.89653
\(887\) 56.7148 1.90430 0.952148 0.305638i \(-0.0988696\pi\)
0.952148 + 0.305638i \(0.0988696\pi\)
\(888\) 4.11679 0.138150
\(889\) −12.7291 −0.426922
\(890\) −9.95791 −0.333790
\(891\) 29.8600 1.00035
\(892\) 12.3212 0.412545
\(893\) −9.31597 −0.311747
\(894\) 7.19816 0.240743
\(895\) −6.56093 −0.219308
\(896\) 18.0498 0.603000
\(897\) −0.512086 −0.0170980
\(898\) 17.6297 0.588309
\(899\) 24.8407 0.828482
\(900\) 43.6991 1.45664
\(901\) 12.0887 0.402732
\(902\) 33.1784 1.10472
\(903\) −0.302138 −0.0100545
\(904\) 38.1229 1.26795
\(905\) 1.33130 0.0442538
\(906\) −5.15842 −0.171377
\(907\) −11.4679 −0.380786 −0.190393 0.981708i \(-0.560976\pi\)
−0.190393 + 0.981708i \(0.560976\pi\)
\(908\) −71.7407 −2.38080
\(909\) 35.9806 1.19340
\(910\) −0.746123 −0.0247337
\(911\) 22.9295 0.759688 0.379844 0.925051i \(-0.375978\pi\)
0.379844 + 0.925051i \(0.375978\pi\)
\(912\) 0.176499 0.00584447
\(913\) 1.73777 0.0575118
\(914\) −24.0140 −0.794313
\(915\) −1.00247 −0.0331406
\(916\) −15.7401 −0.520068
\(917\) 9.78851 0.323245
\(918\) −7.62929 −0.251804
\(919\) 15.7261 0.518756 0.259378 0.965776i \(-0.416482\pi\)
0.259378 + 0.965776i \(0.416482\pi\)
\(920\) −5.35278 −0.176476
\(921\) 6.91687 0.227919
\(922\) 7.32756 0.241320
\(923\) −2.22380 −0.0731974
\(924\) −3.19347 −0.105058
\(925\) −25.0603 −0.823976
\(926\) 27.9618 0.918883
\(927\) 28.0734 0.922051
\(928\) 21.7840 0.715095
\(929\) −4.00588 −0.131429 −0.0657144 0.997838i \(-0.520933\pi\)
−0.0657144 + 0.997838i \(0.520933\pi\)
\(930\) 2.44415 0.0801470
\(931\) 5.46372 0.179066
\(932\) 37.3725 1.22418
\(933\) −1.54538 −0.0505936
\(934\) 21.5731 0.705893
\(935\) 4.28257 0.140055
\(936\) 4.50691 0.147313
\(937\) 5.37073 0.175454 0.0877271 0.996145i \(-0.472040\pi\)
0.0877271 + 0.996145i \(0.472040\pi\)
\(938\) 15.2756 0.498766
\(939\) −1.64772 −0.0537714
\(940\) −3.20441 −0.104516
\(941\) 8.96604 0.292285 0.146142 0.989264i \(-0.453314\pi\)
0.146142 + 0.989264i \(0.453314\pi\)
\(942\) −5.64745 −0.184004
\(943\) −13.4009 −0.436393
\(944\) 0.733261 0.0238656
\(945\) 0.960817 0.0312554
\(946\) −8.93891 −0.290629
\(947\) −47.6901 −1.54972 −0.774861 0.632132i \(-0.782180\pi\)
−0.774861 + 0.632132i \(0.782180\pi\)
\(948\) −4.19464 −0.136236
\(949\) 0.359459 0.0116685
\(950\) 58.0798 1.88436
\(951\) 1.14044 0.0369814
\(952\) −5.62467 −0.182297
\(953\) −15.9135 −0.515488 −0.257744 0.966213i \(-0.582979\pi\)
−0.257744 + 0.966213i \(0.582979\pi\)
\(954\) 39.6004 1.28211
\(955\) 14.5441 0.470636
\(956\) 55.6703 1.80051
\(957\) −3.74375 −0.121018
\(958\) 5.29567 0.171095
\(959\) 10.4659 0.337961
\(960\) 2.10557 0.0679571
\(961\) 12.5784 0.405753
\(962\) −6.85720 −0.221085
\(963\) −22.8834 −0.737406
\(964\) −62.5938 −2.01601
\(965\) 8.91574 0.287008
\(966\) 2.09354 0.0673586
\(967\) −55.6860 −1.79074 −0.895371 0.445322i \(-0.853089\pi\)
−0.895371 + 0.445322i \(0.853089\pi\)
\(968\) −5.23511 −0.168263
\(969\) −3.08320 −0.0990465
\(970\) −16.0632 −0.515758
\(971\) 50.7158 1.62755 0.813774 0.581181i \(-0.197409\pi\)
0.813774 + 0.581181i \(0.197409\pi\)
\(972\) −23.1968 −0.744037
\(973\) 3.70442 0.118758
\(974\) −41.5410 −1.33106
\(975\) 0.720366 0.0230702
\(976\) −0.720590 −0.0230655
\(977\) −53.1145 −1.69928 −0.849641 0.527362i \(-0.823181\pi\)
−0.849641 + 0.527362i \(0.823181\pi\)
\(978\) −4.40033 −0.140707
\(979\) 26.7581 0.855191
\(980\) 1.87935 0.0600338
\(981\) −24.0931 −0.769234
\(982\) −46.3730 −1.47982
\(983\) 47.7346 1.52250 0.761248 0.648461i \(-0.224587\pi\)
0.761248 + 0.648461i \(0.224587\pi\)
\(984\) −3.09682 −0.0987232
\(985\) −4.03323 −0.128510
\(986\) −17.4943 −0.557132
\(987\) 0.472384 0.0150362
\(988\) 9.79141 0.311506
\(989\) 3.61046 0.114806
\(990\) 14.0290 0.445870
\(991\) −14.7354 −0.468086 −0.234043 0.972226i \(-0.575196\pi\)
−0.234043 + 0.972226i \(0.575196\pi\)
\(992\) 38.2160 1.21336
\(993\) 6.51253 0.206669
\(994\) 9.09151 0.288365
\(995\) −12.1166 −0.384123
\(996\) −0.430337 −0.0136357
\(997\) −16.4851 −0.522088 −0.261044 0.965327i \(-0.584067\pi\)
−0.261044 + 0.965327i \(0.584067\pi\)
\(998\) 31.2606 0.989536
\(999\) 8.83033 0.279379
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 \(a_p\))