Properties

Label 8021.2.a.a.1.13
Level 8021
Weight 2
Character 8021.1
Self dual Yes
Analytic conductor 64.048
Analytic rank 1
Dimension 134
CM No

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Newspace parameters

Level: \( N \) = \( 8021 = 13 \cdot 617 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8021.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0480074613\)
Analytic rank: \(1\)
Dimension: \(134\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 8021.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.36088 q^{2}\) \(+0.842254 q^{3}\) \(+3.57377 q^{4}\) \(-1.49212 q^{5}\) \(-1.98846 q^{6}\) \(-1.11078 q^{7}\) \(-3.71549 q^{8}\) \(-2.29061 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.36088 q^{2}\) \(+0.842254 q^{3}\) \(+3.57377 q^{4}\) \(-1.49212 q^{5}\) \(-1.98846 q^{6}\) \(-1.11078 q^{7}\) \(-3.71549 q^{8}\) \(-2.29061 q^{9}\) \(+3.52272 q^{10}\) \(-4.02952 q^{11}\) \(+3.01003 q^{12}\) \(+1.00000 q^{13}\) \(+2.62242 q^{14}\) \(-1.25674 q^{15}\) \(+1.62430 q^{16}\) \(-0.552282 q^{17}\) \(+5.40786 q^{18}\) \(+3.31880 q^{19}\) \(-5.33250 q^{20}\) \(-0.935560 q^{21}\) \(+9.51322 q^{22}\) \(+6.65139 q^{23}\) \(-3.12939 q^{24}\) \(-2.77358 q^{25}\) \(-2.36088 q^{26}\) \(-4.45604 q^{27}\) \(-3.96968 q^{28}\) \(-4.21363 q^{29}\) \(+2.96703 q^{30}\) \(+8.36402 q^{31}\) \(+3.59619 q^{32}\) \(-3.39388 q^{33}\) \(+1.30387 q^{34}\) \(+1.65742 q^{35}\) \(-8.18611 q^{36}\) \(-7.94263 q^{37}\) \(-7.83530 q^{38}\) \(+0.842254 q^{39}\) \(+5.54396 q^{40}\) \(+10.6180 q^{41}\) \(+2.20875 q^{42}\) \(-1.90766 q^{43}\) \(-14.4006 q^{44}\) \(+3.41786 q^{45}\) \(-15.7032 q^{46}\) \(+6.14413 q^{47}\) \(+1.36808 q^{48}\) \(-5.76617 q^{49}\) \(+6.54809 q^{50}\) \(-0.465162 q^{51}\) \(+3.57377 q^{52}\) \(+6.22973 q^{53}\) \(+10.5202 q^{54}\) \(+6.01252 q^{55}\) \(+4.12710 q^{56}\) \(+2.79528 q^{57}\) \(+9.94789 q^{58}\) \(-1.22581 q^{59}\) \(-4.49132 q^{60}\) \(-5.39620 q^{61}\) \(-19.7465 q^{62}\) \(+2.54436 q^{63}\) \(-11.7388 q^{64}\) \(-1.49212 q^{65}\) \(+8.01255 q^{66}\) \(+2.00241 q^{67}\) \(-1.97373 q^{68}\) \(+5.60216 q^{69}\) \(-3.91297 q^{70}\) \(+0.614736 q^{71}\) \(+8.51074 q^{72}\) \(-10.5550 q^{73}\) \(+18.7516 q^{74}\) \(-2.33606 q^{75}\) \(+11.8606 q^{76}\) \(+4.47591 q^{77}\) \(-1.98846 q^{78}\) \(-0.421182 q^{79}\) \(-2.42366 q^{80}\) \(+3.11871 q^{81}\) \(-25.0679 q^{82}\) \(+4.75340 q^{83}\) \(-3.34348 q^{84}\) \(+0.824071 q^{85}\) \(+4.50375 q^{86}\) \(-3.54895 q^{87}\) \(+14.9716 q^{88}\) \(+10.9624 q^{89}\) \(-8.06918 q^{90}\) \(-1.11078 q^{91}\) \(+23.7706 q^{92}\) \(+7.04463 q^{93}\) \(-14.5056 q^{94}\) \(-4.95205 q^{95}\) \(+3.02891 q^{96}\) \(+5.73345 q^{97}\) \(+13.6133 q^{98}\) \(+9.23004 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 47q^{11} \) \(\mathstrut -\mathstrut 53q^{12} \) \(\mathstrut +\mathstrut 134q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 87q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 52q^{22} \) \(\mathstrut -\mathstrut 44q^{23} \) \(\mathstrut -\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 58q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 117q^{27} \) \(\mathstrut -\mathstrut 71q^{28} \) \(\mathstrut -\mathstrut 42q^{29} \) \(\mathstrut -\mathstrut 21q^{30} \) \(\mathstrut -\mathstrut 82q^{31} \) \(\mathstrut -\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 30q^{34} \) \(\mathstrut -\mathstrut 54q^{35} \) \(\mathstrut +\mathstrut 32q^{36} \) \(\mathstrut -\mathstrut 55q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut 33q^{39} \) \(\mathstrut -\mathstrut 86q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut +\mathstrut 6q^{42} \) \(\mathstrut -\mathstrut 148q^{43} \) \(\mathstrut -\mathstrut 54q^{44} \) \(\mathstrut -\mathstrut 24q^{45} \) \(\mathstrut -\mathstrut 57q^{46} \) \(\mathstrut -\mathstrut 21q^{47} \) \(\mathstrut -\mathstrut 82q^{48} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 17q^{50} \) \(\mathstrut -\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 98q^{52} \) \(\mathstrut -\mathstrut 17q^{53} \) \(\mathstrut -\mathstrut 10q^{54} \) \(\mathstrut -\mathstrut 148q^{55} \) \(\mathstrut -\mathstrut 47q^{56} \) \(\mathstrut -\mathstrut q^{57} \) \(\mathstrut -\mathstrut 58q^{58} \) \(\mathstrut -\mathstrut 64q^{59} \) \(\mathstrut -\mathstrut 16q^{60} \) \(\mathstrut -\mathstrut 112q^{61} \) \(\mathstrut -\mathstrut 15q^{62} \) \(\mathstrut -\mathstrut 58q^{63} \) \(\mathstrut -\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 20q^{66} \) \(\mathstrut -\mathstrut 110q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 40q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 28q^{72} \) \(\mathstrut -\mathstrut 43q^{73} \) \(\mathstrut -\mathstrut 52q^{74} \) \(\mathstrut -\mathstrut 150q^{75} \) \(\mathstrut -\mathstrut 96q^{76} \) \(\mathstrut -\mathstrut 24q^{77} \) \(\mathstrut -\mathstrut 16q^{78} \) \(\mathstrut -\mathstrut 228q^{79} \) \(\mathstrut +\mathstrut 20q^{80} \) \(\mathstrut +\mathstrut 54q^{81} \) \(\mathstrut -\mathstrut 89q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 77q^{87} \) \(\mathstrut -\mathstrut 95q^{88} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 46q^{90} \) \(\mathstrut -\mathstrut 32q^{91} \) \(\mathstrut -\mathstrut 62q^{92} \) \(\mathstrut -\mathstrut 9q^{93} \) \(\mathstrut -\mathstrut 87q^{94} \) \(\mathstrut -\mathstrut 61q^{95} \) \(\mathstrut -\mathstrut 54q^{96} \) \(\mathstrut -\mathstrut 38q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut -\mathstrut 193q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.36088 −1.66940 −0.834698 0.550707i \(-0.814358\pi\)
−0.834698 + 0.550707i \(0.814358\pi\)
\(3\) 0.842254 0.486276 0.243138 0.969992i \(-0.421823\pi\)
0.243138 + 0.969992i \(0.421823\pi\)
\(4\) 3.57377 1.78689
\(5\) −1.49212 −0.667297 −0.333648 0.942698i \(-0.608280\pi\)
−0.333648 + 0.942698i \(0.608280\pi\)
\(6\) −1.98846 −0.811787
\(7\) −1.11078 −0.419835 −0.209918 0.977719i \(-0.567320\pi\)
−0.209918 + 0.977719i \(0.567320\pi\)
\(8\) −3.71549 −1.31363
\(9\) −2.29061 −0.763536
\(10\) 3.52272 1.11398
\(11\) −4.02952 −1.21495 −0.607473 0.794341i \(-0.707817\pi\)
−0.607473 + 0.794341i \(0.707817\pi\)
\(12\) 3.01003 0.868919
\(13\) 1.00000 0.277350
\(14\) 2.62242 0.700872
\(15\) −1.25674 −0.324490
\(16\) 1.62430 0.406076
\(17\) −0.552282 −0.133948 −0.0669740 0.997755i \(-0.521334\pi\)
−0.0669740 + 0.997755i \(0.521334\pi\)
\(18\) 5.40786 1.27464
\(19\) 3.31880 0.761385 0.380693 0.924702i \(-0.375686\pi\)
0.380693 + 0.924702i \(0.375686\pi\)
\(20\) −5.33250 −1.19238
\(21\) −0.935560 −0.204156
\(22\) 9.51322 2.02823
\(23\) 6.65139 1.38691 0.693455 0.720500i \(-0.256088\pi\)
0.693455 + 0.720500i \(0.256088\pi\)
\(24\) −3.12939 −0.638784
\(25\) −2.77358 −0.554715
\(26\) −2.36088 −0.463007
\(27\) −4.45604 −0.857565
\(28\) −3.96968 −0.750198
\(29\) −4.21363 −0.782451 −0.391226 0.920295i \(-0.627949\pi\)
−0.391226 + 0.920295i \(0.627949\pi\)
\(30\) 2.96703 0.541703
\(31\) 8.36402 1.50222 0.751111 0.660175i \(-0.229518\pi\)
0.751111 + 0.660175i \(0.229518\pi\)
\(32\) 3.59619 0.635723
\(33\) −3.39388 −0.590798
\(34\) 1.30387 0.223612
\(35\) 1.65742 0.280155
\(36\) −8.18611 −1.36435
\(37\) −7.94263 −1.30576 −0.652880 0.757461i \(-0.726440\pi\)
−0.652880 + 0.757461i \(0.726440\pi\)
\(38\) −7.83530 −1.27105
\(39\) 0.842254 0.134869
\(40\) 5.54396 0.876578
\(41\) 10.6180 1.65826 0.829129 0.559058i \(-0.188837\pi\)
0.829129 + 0.559058i \(0.188837\pi\)
\(42\) 2.20875 0.340817
\(43\) −1.90766 −0.290915 −0.145457 0.989365i \(-0.546465\pi\)
−0.145457 + 0.989365i \(0.546465\pi\)
\(44\) −14.4006 −2.17097
\(45\) 3.41786 0.509505
\(46\) −15.7032 −2.31530
\(47\) 6.14413 0.896213 0.448107 0.893980i \(-0.352098\pi\)
0.448107 + 0.893980i \(0.352098\pi\)
\(48\) 1.36808 0.197465
\(49\) −5.76617 −0.823738
\(50\) 6.54809 0.926040
\(51\) −0.465162 −0.0651357
\(52\) 3.57377 0.495593
\(53\) 6.22973 0.855720 0.427860 0.903845i \(-0.359268\pi\)
0.427860 + 0.903845i \(0.359268\pi\)
\(54\) 10.5202 1.43162
\(55\) 6.01252 0.810729
\(56\) 4.12710 0.551507
\(57\) 2.79528 0.370243
\(58\) 9.94789 1.30622
\(59\) −1.22581 −0.159587 −0.0797935 0.996811i \(-0.525426\pi\)
−0.0797935 + 0.996811i \(0.525426\pi\)
\(60\) −4.49132 −0.579827
\(61\) −5.39620 −0.690912 −0.345456 0.938435i \(-0.612276\pi\)
−0.345456 + 0.938435i \(0.612276\pi\)
\(62\) −19.7465 −2.50781
\(63\) 2.54436 0.320559
\(64\) −11.7388 −1.46735
\(65\) −1.49212 −0.185075
\(66\) 8.01255 0.986277
\(67\) 2.00241 0.244633 0.122317 0.992491i \(-0.460968\pi\)
0.122317 + 0.992491i \(0.460968\pi\)
\(68\) −1.97373 −0.239350
\(69\) 5.60216 0.674421
\(70\) −3.91297 −0.467689
\(71\) 0.614736 0.0729557 0.0364779 0.999334i \(-0.488386\pi\)
0.0364779 + 0.999334i \(0.488386\pi\)
\(72\) 8.51074 1.00300
\(73\) −10.5550 −1.23537 −0.617686 0.786425i \(-0.711930\pi\)
−0.617686 + 0.786425i \(0.711930\pi\)
\(74\) 18.7516 2.17983
\(75\) −2.33606 −0.269745
\(76\) 11.8606 1.36051
\(77\) 4.47591 0.510077
\(78\) −1.98846 −0.225149
\(79\) −0.421182 −0.0473866 −0.0236933 0.999719i \(-0.507543\pi\)
−0.0236933 + 0.999719i \(0.507543\pi\)
\(80\) −2.42366 −0.270973
\(81\) 3.11871 0.346523
\(82\) −25.0679 −2.76829
\(83\) 4.75340 0.521753 0.260877 0.965372i \(-0.415988\pi\)
0.260877 + 0.965372i \(0.415988\pi\)
\(84\) −3.34348 −0.364803
\(85\) 0.824071 0.0893831
\(86\) 4.50375 0.485652
\(87\) −3.54895 −0.380487
\(88\) 14.9716 1.59598
\(89\) 10.9624 1.16201 0.581007 0.813899i \(-0.302659\pi\)
0.581007 + 0.813899i \(0.302659\pi\)
\(90\) −8.06918 −0.850566
\(91\) −1.11078 −0.116441
\(92\) 23.7706 2.47825
\(93\) 7.04463 0.730495
\(94\) −14.5056 −1.49614
\(95\) −4.95205 −0.508070
\(96\) 3.02891 0.309137
\(97\) 5.73345 0.582144 0.291072 0.956701i \(-0.405988\pi\)
0.291072 + 0.956701i \(0.405988\pi\)
\(98\) 13.6133 1.37515
\(99\) 9.23004 0.927654
\(100\) −9.91213 −0.991213
\(101\) 9.25237 0.920645 0.460323 0.887752i \(-0.347734\pi\)
0.460323 + 0.887752i \(0.347734\pi\)
\(102\) 1.09819 0.108737
\(103\) 0.522737 0.0515068 0.0257534 0.999668i \(-0.491802\pi\)
0.0257534 + 0.999668i \(0.491802\pi\)
\(104\) −3.71549 −0.364334
\(105\) 1.39597 0.136232
\(106\) −14.7077 −1.42854
\(107\) 13.3705 1.29257 0.646287 0.763095i \(-0.276321\pi\)
0.646287 + 0.763095i \(0.276321\pi\)
\(108\) −15.9249 −1.53237
\(109\) −4.35596 −0.417226 −0.208613 0.977998i \(-0.566895\pi\)
−0.208613 + 0.977998i \(0.566895\pi\)
\(110\) −14.1949 −1.35343
\(111\) −6.68972 −0.634960
\(112\) −1.80424 −0.170485
\(113\) −6.53192 −0.614471 −0.307236 0.951633i \(-0.599404\pi\)
−0.307236 + 0.951633i \(0.599404\pi\)
\(114\) −6.59932 −0.618083
\(115\) −9.92467 −0.925481
\(116\) −15.0586 −1.39815
\(117\) −2.29061 −0.211767
\(118\) 2.89400 0.266414
\(119\) 0.613464 0.0562361
\(120\) 4.66943 0.426258
\(121\) 5.23701 0.476092
\(122\) 12.7398 1.15341
\(123\) 8.94308 0.806371
\(124\) 29.8911 2.68430
\(125\) 11.5991 1.03746
\(126\) −6.00694 −0.535141
\(127\) 6.42505 0.570131 0.285066 0.958508i \(-0.407985\pi\)
0.285066 + 0.958508i \(0.407985\pi\)
\(128\) 20.5216 1.81387
\(129\) −1.60673 −0.141465
\(130\) 3.52272 0.308963
\(131\) 11.5028 1.00500 0.502501 0.864576i \(-0.332413\pi\)
0.502501 + 0.864576i \(0.332413\pi\)
\(132\) −12.1289 −1.05569
\(133\) −3.68646 −0.319657
\(134\) −4.72746 −0.408390
\(135\) 6.64894 0.572250
\(136\) 2.05200 0.175958
\(137\) 4.21690 0.360274 0.180137 0.983642i \(-0.442346\pi\)
0.180137 + 0.983642i \(0.442346\pi\)
\(138\) −13.2261 −1.12588
\(139\) −1.06118 −0.0900079 −0.0450039 0.998987i \(-0.514330\pi\)
−0.0450039 + 0.998987i \(0.514330\pi\)
\(140\) 5.92323 0.500605
\(141\) 5.17492 0.435807
\(142\) −1.45132 −0.121792
\(143\) −4.02952 −0.336965
\(144\) −3.72064 −0.310054
\(145\) 6.28724 0.522127
\(146\) 24.9192 2.06233
\(147\) −4.85658 −0.400564
\(148\) −28.3852 −2.33325
\(149\) 15.4857 1.26864 0.634320 0.773070i \(-0.281280\pi\)
0.634320 + 0.773070i \(0.281280\pi\)
\(150\) 5.51516 0.450311
\(151\) −5.34591 −0.435044 −0.217522 0.976055i \(-0.569797\pi\)
−0.217522 + 0.976055i \(0.569797\pi\)
\(152\) −12.3310 −1.00018
\(153\) 1.26506 0.102274
\(154\) −10.5671 −0.851521
\(155\) −12.4801 −1.00243
\(156\) 3.01003 0.240995
\(157\) −23.8554 −1.90387 −0.951936 0.306298i \(-0.900910\pi\)
−0.951936 + 0.306298i \(0.900910\pi\)
\(158\) 0.994361 0.0791071
\(159\) 5.24702 0.416116
\(160\) −5.36595 −0.424216
\(161\) −7.38823 −0.582274
\(162\) −7.36290 −0.578484
\(163\) 3.26411 0.255665 0.127832 0.991796i \(-0.459198\pi\)
0.127832 + 0.991796i \(0.459198\pi\)
\(164\) 37.9464 2.96312
\(165\) 5.06407 0.394238
\(166\) −11.2222 −0.871013
\(167\) −9.45268 −0.731470 −0.365735 0.930719i \(-0.619182\pi\)
−0.365735 + 0.930719i \(0.619182\pi\)
\(168\) 3.47607 0.268184
\(169\) 1.00000 0.0769231
\(170\) −1.94554 −0.149216
\(171\) −7.60207 −0.581345
\(172\) −6.81752 −0.519831
\(173\) −25.7126 −1.95489 −0.977447 0.211183i \(-0.932268\pi\)
−0.977447 + 0.211183i \(0.932268\pi\)
\(174\) 8.37865 0.635184
\(175\) 3.08083 0.232889
\(176\) −6.54516 −0.493360
\(177\) −1.03244 −0.0776033
\(178\) −25.8810 −1.93986
\(179\) 4.60035 0.343846 0.171923 0.985110i \(-0.445002\pi\)
0.171923 + 0.985110i \(0.445002\pi\)
\(180\) 12.2147 0.910427
\(181\) −24.1233 −1.79307 −0.896536 0.442971i \(-0.853925\pi\)
−0.896536 + 0.442971i \(0.853925\pi\)
\(182\) 2.62242 0.194387
\(183\) −4.54497 −0.335974
\(184\) −24.7132 −1.82188
\(185\) 11.8514 0.871330
\(186\) −16.6316 −1.21949
\(187\) 2.22543 0.162740
\(188\) 21.9577 1.60143
\(189\) 4.94968 0.360036
\(190\) 11.6912 0.848170
\(191\) 11.3389 0.820456 0.410228 0.911983i \(-0.365449\pi\)
0.410228 + 0.911983i \(0.365449\pi\)
\(192\) −9.88706 −0.713537
\(193\) −9.79782 −0.705263 −0.352631 0.935762i \(-0.614713\pi\)
−0.352631 + 0.935762i \(0.614713\pi\)
\(194\) −13.5360 −0.971829
\(195\) −1.25674 −0.0899974
\(196\) −20.6070 −1.47193
\(197\) −7.46261 −0.531689 −0.265844 0.964016i \(-0.585651\pi\)
−0.265844 + 0.964016i \(0.585651\pi\)
\(198\) −21.7911 −1.54862
\(199\) 8.02015 0.568533 0.284267 0.958745i \(-0.408250\pi\)
0.284267 + 0.958745i \(0.408250\pi\)
\(200\) 10.3052 0.728688
\(201\) 1.68654 0.118959
\(202\) −21.8438 −1.53692
\(203\) 4.68042 0.328501
\(204\) −1.66238 −0.116390
\(205\) −15.8434 −1.10655
\(206\) −1.23412 −0.0859853
\(207\) −15.2357 −1.05896
\(208\) 1.62430 0.112625
\(209\) −13.3732 −0.925041
\(210\) −3.29572 −0.227426
\(211\) 19.6889 1.35544 0.677719 0.735321i \(-0.262969\pi\)
0.677719 + 0.735321i \(0.262969\pi\)
\(212\) 22.2637 1.52907
\(213\) 0.517764 0.0354766
\(214\) −31.5662 −2.15782
\(215\) 2.84645 0.194126
\(216\) 16.5564 1.12652
\(217\) −9.29059 −0.630686
\(218\) 10.2839 0.696515
\(219\) −8.89002 −0.600732
\(220\) 21.4874 1.44868
\(221\) −0.552282 −0.0371505
\(222\) 15.7936 1.06000
\(223\) 17.1920 1.15126 0.575630 0.817710i \(-0.304757\pi\)
0.575630 + 0.817710i \(0.304757\pi\)
\(224\) −3.99458 −0.266899
\(225\) 6.35318 0.423545
\(226\) 15.4211 1.02580
\(227\) −7.58483 −0.503423 −0.251711 0.967802i \(-0.580993\pi\)
−0.251711 + 0.967802i \(0.580993\pi\)
\(228\) 9.98968 0.661583
\(229\) 5.18139 0.342396 0.171198 0.985237i \(-0.445236\pi\)
0.171198 + 0.985237i \(0.445236\pi\)
\(230\) 23.4310 1.54499
\(231\) 3.76985 0.248038
\(232\) 15.6557 1.02785
\(233\) −23.9444 −1.56865 −0.784325 0.620350i \(-0.786991\pi\)
−0.784325 + 0.620350i \(0.786991\pi\)
\(234\) 5.40786 0.353523
\(235\) −9.16778 −0.598040
\(236\) −4.38077 −0.285164
\(237\) −0.354742 −0.0230430
\(238\) −1.44832 −0.0938805
\(239\) −3.80470 −0.246105 −0.123053 0.992400i \(-0.539268\pi\)
−0.123053 + 0.992400i \(0.539268\pi\)
\(240\) −2.04134 −0.131768
\(241\) 19.5047 1.25641 0.628204 0.778048i \(-0.283790\pi\)
0.628204 + 0.778048i \(0.283790\pi\)
\(242\) −12.3640 −0.794786
\(243\) 15.9949 1.02607
\(244\) −19.2848 −1.23458
\(245\) 8.60382 0.549678
\(246\) −21.1136 −1.34615
\(247\) 3.31880 0.211170
\(248\) −31.0765 −1.97336
\(249\) 4.00357 0.253716
\(250\) −27.3842 −1.73193
\(251\) −27.7486 −1.75148 −0.875738 0.482786i \(-0.839625\pi\)
−0.875738 + 0.482786i \(0.839625\pi\)
\(252\) 9.09297 0.572803
\(253\) −26.8019 −1.68502
\(254\) −15.1688 −0.951775
\(255\) 0.694078 0.0434648
\(256\) −24.9714 −1.56071
\(257\) 4.37896 0.273152 0.136576 0.990630i \(-0.456390\pi\)
0.136576 + 0.990630i \(0.456390\pi\)
\(258\) 3.79330 0.236161
\(259\) 8.82252 0.548205
\(260\) −5.33250 −0.330708
\(261\) 9.65177 0.597430
\(262\) −27.1567 −1.67775
\(263\) 5.94176 0.366384 0.183192 0.983077i \(-0.441357\pi\)
0.183192 + 0.983077i \(0.441357\pi\)
\(264\) 12.6099 0.776088
\(265\) −9.29551 −0.571019
\(266\) 8.70330 0.533634
\(267\) 9.23315 0.565059
\(268\) 7.15616 0.437132
\(269\) 1.03525 0.0631200 0.0315600 0.999502i \(-0.489952\pi\)
0.0315600 + 0.999502i \(0.489952\pi\)
\(270\) −15.6974 −0.955312
\(271\) −1.49617 −0.0908862 −0.0454431 0.998967i \(-0.514470\pi\)
−0.0454431 + 0.998967i \(0.514470\pi\)
\(272\) −0.897074 −0.0543931
\(273\) −0.935560 −0.0566226
\(274\) −9.95561 −0.601441
\(275\) 11.1762 0.673949
\(276\) 20.0209 1.20511
\(277\) −21.0065 −1.26216 −0.631081 0.775717i \(-0.717388\pi\)
−0.631081 + 0.775717i \(0.717388\pi\)
\(278\) 2.50532 0.150259
\(279\) −19.1587 −1.14700
\(280\) −6.15813 −0.368018
\(281\) −19.9178 −1.18819 −0.594097 0.804393i \(-0.702491\pi\)
−0.594097 + 0.804393i \(0.702491\pi\)
\(282\) −12.2174 −0.727535
\(283\) 4.44783 0.264396 0.132198 0.991223i \(-0.457797\pi\)
0.132198 + 0.991223i \(0.457797\pi\)
\(284\) 2.19693 0.130364
\(285\) −4.17089 −0.247062
\(286\) 9.51322 0.562529
\(287\) −11.7943 −0.696195
\(288\) −8.23747 −0.485398
\(289\) −16.6950 −0.982058
\(290\) −14.8434 −0.871637
\(291\) 4.82902 0.283082
\(292\) −37.7213 −2.20747
\(293\) −18.3831 −1.07395 −0.536975 0.843598i \(-0.680433\pi\)
−0.536975 + 0.843598i \(0.680433\pi\)
\(294\) 11.4658 0.668700
\(295\) 1.82906 0.106492
\(296\) 29.5108 1.71528
\(297\) 17.9557 1.04189
\(298\) −36.5600 −2.11787
\(299\) 6.65139 0.384660
\(300\) −8.34854 −0.482003
\(301\) 2.11899 0.122136
\(302\) 12.6211 0.726262
\(303\) 7.79285 0.447687
\(304\) 5.39074 0.309180
\(305\) 8.05177 0.461043
\(306\) −2.98666 −0.170736
\(307\) 29.2624 1.67009 0.835047 0.550179i \(-0.185441\pi\)
0.835047 + 0.550179i \(0.185441\pi\)
\(308\) 15.9959 0.911450
\(309\) 0.440278 0.0250465
\(310\) 29.4641 1.67345
\(311\) −2.48545 −0.140937 −0.0704684 0.997514i \(-0.522449\pi\)
−0.0704684 + 0.997514i \(0.522449\pi\)
\(312\) −3.12939 −0.177167
\(313\) −10.6710 −0.603161 −0.301580 0.953441i \(-0.597514\pi\)
−0.301580 + 0.953441i \(0.597514\pi\)
\(314\) 56.3199 3.17832
\(315\) −3.79649 −0.213908
\(316\) −1.50521 −0.0846745
\(317\) −2.28107 −0.128118 −0.0640589 0.997946i \(-0.520405\pi\)
−0.0640589 + 0.997946i \(0.520405\pi\)
\(318\) −12.3876 −0.694662
\(319\) 16.9789 0.950635
\(320\) 17.5157 0.979158
\(321\) 11.2614 0.628547
\(322\) 17.4428 0.972047
\(323\) −1.83291 −0.101986
\(324\) 11.1455 0.619197
\(325\) −2.77358 −0.153850
\(326\) −7.70617 −0.426806
\(327\) −3.66883 −0.202887
\(328\) −39.4512 −2.17833
\(329\) −6.82478 −0.376262
\(330\) −11.9557 −0.658139
\(331\) −6.30428 −0.346514 −0.173257 0.984877i \(-0.555429\pi\)
−0.173257 + 0.984877i \(0.555429\pi\)
\(332\) 16.9876 0.932314
\(333\) 18.1935 0.996995
\(334\) 22.3167 1.22111
\(335\) −2.98784 −0.163243
\(336\) −1.51963 −0.0829028
\(337\) 7.27617 0.396358 0.198179 0.980166i \(-0.436497\pi\)
0.198179 + 0.980166i \(0.436497\pi\)
\(338\) −2.36088 −0.128415
\(339\) −5.50154 −0.298802
\(340\) 2.94504 0.159717
\(341\) −33.7030 −1.82512
\(342\) 17.9476 0.970496
\(343\) 14.1804 0.765670
\(344\) 7.08788 0.382153
\(345\) −8.35910 −0.450039
\(346\) 60.7045 3.26349
\(347\) −31.9767 −1.71660 −0.858299 0.513150i \(-0.828478\pi\)
−0.858299 + 0.513150i \(0.828478\pi\)
\(348\) −12.6831 −0.679887
\(349\) −12.8206 −0.686273 −0.343137 0.939285i \(-0.611489\pi\)
−0.343137 + 0.939285i \(0.611489\pi\)
\(350\) −7.27349 −0.388784
\(351\) −4.45604 −0.237846
\(352\) −14.4909 −0.772369
\(353\) 25.9102 1.37906 0.689530 0.724257i \(-0.257817\pi\)
0.689530 + 0.724257i \(0.257817\pi\)
\(354\) 2.43748 0.129551
\(355\) −0.917260 −0.0486831
\(356\) 39.1772 2.07639
\(357\) 0.516693 0.0273463
\(358\) −10.8609 −0.574016
\(359\) −31.6273 −1.66922 −0.834612 0.550839i \(-0.814308\pi\)
−0.834612 + 0.550839i \(0.814308\pi\)
\(360\) −12.6990 −0.669298
\(361\) −7.98556 −0.420292
\(362\) 56.9524 2.99335
\(363\) 4.41089 0.231512
\(364\) −3.96968 −0.208068
\(365\) 15.7494 0.824360
\(366\) 10.7301 0.560874
\(367\) −3.51495 −0.183479 −0.0917393 0.995783i \(-0.529243\pi\)
−0.0917393 + 0.995783i \(0.529243\pi\)
\(368\) 10.8039 0.563191
\(369\) −24.3217 −1.26614
\(370\) −27.9797 −1.45459
\(371\) −6.91987 −0.359261
\(372\) 25.1759 1.30531
\(373\) 10.2744 0.531987 0.265993 0.963975i \(-0.414300\pi\)
0.265993 + 0.963975i \(0.414300\pi\)
\(374\) −5.25398 −0.271677
\(375\) 9.76940 0.504490
\(376\) −22.8285 −1.17729
\(377\) −4.21363 −0.217013
\(378\) −11.6856 −0.601043
\(379\) −25.4144 −1.30545 −0.652725 0.757595i \(-0.726374\pi\)
−0.652725 + 0.757595i \(0.726374\pi\)
\(380\) −17.6975 −0.907863
\(381\) 5.41153 0.277241
\(382\) −26.7699 −1.36967
\(383\) 23.8061 1.21643 0.608217 0.793771i \(-0.291885\pi\)
0.608217 + 0.793771i \(0.291885\pi\)
\(384\) 17.2844 0.882040
\(385\) −6.67859 −0.340373
\(386\) 23.1315 1.17736
\(387\) 4.36969 0.222124
\(388\) 20.4901 1.04022
\(389\) 8.82168 0.447277 0.223639 0.974672i \(-0.428206\pi\)
0.223639 + 0.974672i \(0.428206\pi\)
\(390\) 2.96703 0.150241
\(391\) −3.67344 −0.185774
\(392\) 21.4242 1.08208
\(393\) 9.68827 0.488708
\(394\) 17.6183 0.887599
\(395\) 0.628454 0.0316209
\(396\) 32.9861 1.65761
\(397\) −38.5941 −1.93698 −0.968491 0.249047i \(-0.919883\pi\)
−0.968491 + 0.249047i \(0.919883\pi\)
\(398\) −18.9346 −0.949108
\(399\) −3.10494 −0.155441
\(400\) −4.50513 −0.225257
\(401\) −7.47951 −0.373509 −0.186755 0.982407i \(-0.559797\pi\)
−0.186755 + 0.982407i \(0.559797\pi\)
\(402\) −3.98172 −0.198590
\(403\) 8.36402 0.416642
\(404\) 33.0659 1.64509
\(405\) −4.65348 −0.231233
\(406\) −11.0499 −0.548398
\(407\) 32.0050 1.58643
\(408\) 1.72831 0.0855639
\(409\) 18.6152 0.920461 0.460231 0.887799i \(-0.347767\pi\)
0.460231 + 0.887799i \(0.347767\pi\)
\(410\) 37.4044 1.84727
\(411\) 3.55170 0.175193
\(412\) 1.86814 0.0920368
\(413\) 1.36161 0.0670003
\(414\) 35.9698 1.76782
\(415\) −7.09264 −0.348164
\(416\) 3.59619 0.176318
\(417\) −0.893781 −0.0437686
\(418\) 31.5725 1.54426
\(419\) −29.4583 −1.43913 −0.719565 0.694425i \(-0.755659\pi\)
−0.719565 + 0.694425i \(0.755659\pi\)
\(420\) 4.98887 0.243432
\(421\) −14.8376 −0.723141 −0.361571 0.932345i \(-0.617759\pi\)
−0.361571 + 0.932345i \(0.617759\pi\)
\(422\) −46.4831 −2.26276
\(423\) −14.0738 −0.684291
\(424\) −23.1465 −1.12410
\(425\) 1.53180 0.0743031
\(426\) −1.22238 −0.0592245
\(427\) 5.99399 0.290069
\(428\) 47.7831 2.30968
\(429\) −3.39388 −0.163858
\(430\) −6.72014 −0.324074
\(431\) −7.67219 −0.369556 −0.184778 0.982780i \(-0.559157\pi\)
−0.184778 + 0.982780i \(0.559157\pi\)
\(432\) −7.23796 −0.348237
\(433\) 5.51644 0.265103 0.132552 0.991176i \(-0.457683\pi\)
0.132552 + 0.991176i \(0.457683\pi\)
\(434\) 21.9340 1.05287
\(435\) 5.29546 0.253898
\(436\) −15.5672 −0.745535
\(437\) 22.0746 1.05597
\(438\) 20.9883 1.00286
\(439\) −24.2182 −1.15587 −0.577937 0.816081i \(-0.696142\pi\)
−0.577937 + 0.816081i \(0.696142\pi\)
\(440\) −22.3395 −1.06499
\(441\) 13.2080 0.628954
\(442\) 1.30387 0.0620189
\(443\) −31.1350 −1.47927 −0.739634 0.673009i \(-0.765002\pi\)
−0.739634 + 0.673009i \(0.765002\pi\)
\(444\) −23.9075 −1.13460
\(445\) −16.3572 −0.775408
\(446\) −40.5883 −1.92191
\(447\) 13.0429 0.616909
\(448\) 13.0392 0.616046
\(449\) −23.6827 −1.11765 −0.558827 0.829284i \(-0.688749\pi\)
−0.558827 + 0.829284i \(0.688749\pi\)
\(450\) −14.9991 −0.707065
\(451\) −42.7855 −2.01469
\(452\) −23.3436 −1.09799
\(453\) −4.50262 −0.211551
\(454\) 17.9069 0.840412
\(455\) 1.65742 0.0777009
\(456\) −10.3858 −0.486361
\(457\) −23.2451 −1.08736 −0.543680 0.839292i \(-0.682970\pi\)
−0.543680 + 0.839292i \(0.682970\pi\)
\(458\) −12.2327 −0.571595
\(459\) 2.46099 0.114869
\(460\) −35.4685 −1.65373
\(461\) 39.8332 1.85522 0.927608 0.373554i \(-0.121861\pi\)
0.927608 + 0.373554i \(0.121861\pi\)
\(462\) −8.90018 −0.414074
\(463\) 40.0564 1.86158 0.930790 0.365553i \(-0.119120\pi\)
0.930790 + 0.365553i \(0.119120\pi\)
\(464\) −6.84422 −0.317735
\(465\) −10.5114 −0.487456
\(466\) 56.5300 2.61870
\(467\) 29.4700 1.36371 0.681854 0.731489i \(-0.261174\pi\)
0.681854 + 0.731489i \(0.261174\pi\)
\(468\) −8.18611 −0.378403
\(469\) −2.22424 −0.102706
\(470\) 21.6441 0.998366
\(471\) −20.0924 −0.925807
\(472\) 4.55449 0.209637
\(473\) 7.68693 0.353445
\(474\) 0.837505 0.0384679
\(475\) −9.20495 −0.422352
\(476\) 2.19238 0.100488
\(477\) −14.2699 −0.653373
\(478\) 8.98245 0.410848
\(479\) −38.7881 −1.77228 −0.886138 0.463422i \(-0.846621\pi\)
−0.886138 + 0.463422i \(0.846621\pi\)
\(480\) −4.51950 −0.206286
\(481\) −7.94263 −0.362153
\(482\) −46.0483 −2.09744
\(483\) −6.22277 −0.283146
\(484\) 18.7159 0.850721
\(485\) −8.55500 −0.388463
\(486\) −37.7620 −1.71292
\(487\) 25.3558 1.14898 0.574490 0.818512i \(-0.305201\pi\)
0.574490 + 0.818512i \(0.305201\pi\)
\(488\) 20.0495 0.907600
\(489\) 2.74921 0.124323
\(490\) −20.3126 −0.917630
\(491\) 13.1626 0.594021 0.297010 0.954874i \(-0.404010\pi\)
0.297010 + 0.954874i \(0.404010\pi\)
\(492\) 31.9605 1.44089
\(493\) 2.32711 0.104808
\(494\) −7.83530 −0.352527
\(495\) −13.7723 −0.619020
\(496\) 13.5857 0.610017
\(497\) −0.682836 −0.0306294
\(498\) −9.45196 −0.423553
\(499\) 5.54956 0.248432 0.124216 0.992255i \(-0.460358\pi\)
0.124216 + 0.992255i \(0.460358\pi\)
\(500\) 41.4526 1.85382
\(501\) −7.96156 −0.355696
\(502\) 65.5112 2.92391
\(503\) 10.3359 0.460854 0.230427 0.973090i \(-0.425988\pi\)
0.230427 + 0.973090i \(0.425988\pi\)
\(504\) −9.45356 −0.421095
\(505\) −13.8057 −0.614343
\(506\) 63.2761 2.81297
\(507\) 0.842254 0.0374058
\(508\) 22.9617 1.01876
\(509\) 16.9481 0.751213 0.375606 0.926779i \(-0.377434\pi\)
0.375606 + 0.926779i \(0.377434\pi\)
\(510\) −1.63864 −0.0725600
\(511\) 11.7243 0.518653
\(512\) 17.9115 0.791584
\(513\) −14.7887 −0.652937
\(514\) −10.3382 −0.455999
\(515\) −0.779987 −0.0343703
\(516\) −5.74209 −0.252781
\(517\) −24.7579 −1.08885
\(518\) −20.8289 −0.915171
\(519\) −21.6566 −0.950617
\(520\) 5.54396 0.243119
\(521\) 1.07030 0.0468908 0.0234454 0.999725i \(-0.492536\pi\)
0.0234454 + 0.999725i \(0.492536\pi\)
\(522\) −22.7867 −0.997347
\(523\) 24.0357 1.05101 0.525504 0.850791i \(-0.323877\pi\)
0.525504 + 0.850791i \(0.323877\pi\)
\(524\) 41.1083 1.79583
\(525\) 2.59485 0.113248
\(526\) −14.0278 −0.611641
\(527\) −4.61930 −0.201220
\(528\) −5.51269 −0.239909
\(529\) 21.2410 0.923521
\(530\) 21.9456 0.953257
\(531\) 2.80785 0.121850
\(532\) −13.1746 −0.571190
\(533\) 10.6180 0.459918
\(534\) −21.7984 −0.943308
\(535\) −19.9504 −0.862530
\(536\) −7.43995 −0.321357
\(537\) 3.87466 0.167204
\(538\) −2.44409 −0.105372
\(539\) 23.2349 1.00080
\(540\) 23.7618 1.02255
\(541\) −10.4810 −0.450614 −0.225307 0.974288i \(-0.572338\pi\)
−0.225307 + 0.974288i \(0.572338\pi\)
\(542\) 3.53230 0.151725
\(543\) −20.3180 −0.871928
\(544\) −1.98611 −0.0851539
\(545\) 6.49962 0.278413
\(546\) 2.20875 0.0945257
\(547\) −29.8181 −1.27493 −0.637465 0.770479i \(-0.720017\pi\)
−0.637465 + 0.770479i \(0.720017\pi\)
\(548\) 15.0702 0.643769
\(549\) 12.3606 0.527536
\(550\) −26.3857 −1.12509
\(551\) −13.9842 −0.595747
\(552\) −20.8148 −0.885937
\(553\) 0.467840 0.0198946
\(554\) 49.5940 2.10705
\(555\) 9.98186 0.423706
\(556\) −3.79241 −0.160834
\(557\) −1.00405 −0.0425431 −0.0212716 0.999774i \(-0.506771\pi\)
−0.0212716 + 0.999774i \(0.506771\pi\)
\(558\) 45.2314 1.91480
\(559\) −1.90766 −0.0806852
\(560\) 2.69215 0.113764
\(561\) 1.87438 0.0791363
\(562\) 47.0235 1.98357
\(563\) 30.6111 1.29010 0.645052 0.764139i \(-0.276836\pi\)
0.645052 + 0.764139i \(0.276836\pi\)
\(564\) 18.4940 0.778737
\(565\) 9.74641 0.410035
\(566\) −10.5008 −0.441382
\(567\) −3.46420 −0.145483
\(568\) −2.28405 −0.0958365
\(569\) 17.1696 0.719788 0.359894 0.932993i \(-0.382813\pi\)
0.359894 + 0.932993i \(0.382813\pi\)
\(570\) 9.84698 0.412445
\(571\) −32.6019 −1.36435 −0.682174 0.731190i \(-0.738966\pi\)
−0.682174 + 0.731190i \(0.738966\pi\)
\(572\) −14.4006 −0.602118
\(573\) 9.55026 0.398968
\(574\) 27.8450 1.16223
\(575\) −18.4481 −0.769341
\(576\) 26.8890 1.12037
\(577\) 42.5497 1.77137 0.885683 0.464291i \(-0.153691\pi\)
0.885683 + 0.464291i \(0.153691\pi\)
\(578\) 39.4149 1.63944
\(579\) −8.25226 −0.342952
\(580\) 22.4692 0.932982
\(581\) −5.27998 −0.219050
\(582\) −11.4008 −0.472577
\(583\) −25.1028 −1.03965
\(584\) 39.2171 1.62282
\(585\) 3.41786 0.141311
\(586\) 43.4003 1.79285
\(587\) 18.4839 0.762912 0.381456 0.924387i \(-0.375423\pi\)
0.381456 + 0.924387i \(0.375423\pi\)
\(588\) −17.3563 −0.715762
\(589\) 27.7585 1.14377
\(590\) −4.31819 −0.177777
\(591\) −6.28541 −0.258547
\(592\) −12.9013 −0.530238
\(593\) −1.55593 −0.0638945 −0.0319473 0.999490i \(-0.510171\pi\)
−0.0319473 + 0.999490i \(0.510171\pi\)
\(594\) −42.3913 −1.73933
\(595\) −0.915362 −0.0375262
\(596\) 55.3425 2.26692
\(597\) 6.75501 0.276464
\(598\) −15.7032 −0.642150
\(599\) −21.7797 −0.889895 −0.444947 0.895557i \(-0.646778\pi\)
−0.444947 + 0.895557i \(0.646778\pi\)
\(600\) 8.67961 0.354343
\(601\) −9.74175 −0.397374 −0.198687 0.980063i \(-0.563668\pi\)
−0.198687 + 0.980063i \(0.563668\pi\)
\(602\) −5.00268 −0.203894
\(603\) −4.58674 −0.186786
\(604\) −19.1051 −0.777375
\(605\) −7.81424 −0.317694
\(606\) −18.3980 −0.747368
\(607\) 21.5635 0.875236 0.437618 0.899161i \(-0.355822\pi\)
0.437618 + 0.899161i \(0.355822\pi\)
\(608\) 11.9351 0.484030
\(609\) 3.94210 0.159742
\(610\) −19.0093 −0.769664
\(611\) 6.14413 0.248565
\(612\) 4.52104 0.182752
\(613\) 30.3385 1.22536 0.612681 0.790331i \(-0.290091\pi\)
0.612681 + 0.790331i \(0.290091\pi\)
\(614\) −69.0851 −2.78805
\(615\) −13.3442 −0.538088
\(616\) −16.6302 −0.670050
\(617\) 1.00000 0.0402585
\(618\) −1.03944 −0.0418126
\(619\) 19.7686 0.794567 0.397284 0.917696i \(-0.369953\pi\)
0.397284 + 0.917696i \(0.369953\pi\)
\(620\) −44.6011 −1.79122
\(621\) −29.6388 −1.18937
\(622\) 5.86785 0.235279
\(623\) −12.1768 −0.487855
\(624\) 1.36808 0.0547669
\(625\) −3.43939 −0.137575
\(626\) 25.1930 1.00691
\(627\) −11.2636 −0.449825
\(628\) −85.2539 −3.40200
\(629\) 4.38657 0.174904
\(630\) 8.96308 0.357098
\(631\) 7.69381 0.306286 0.153143 0.988204i \(-0.451061\pi\)
0.153143 + 0.988204i \(0.451061\pi\)
\(632\) 1.56490 0.0622483
\(633\) 16.5830 0.659116
\(634\) 5.38535 0.213880
\(635\) −9.58695 −0.380447
\(636\) 18.7517 0.743552
\(637\) −5.76617 −0.228464
\(638\) −40.0852 −1.58699
\(639\) −1.40812 −0.0557043
\(640\) −30.6206 −1.21039
\(641\) −34.7073 −1.37086 −0.685428 0.728140i \(-0.740385\pi\)
−0.685428 + 0.728140i \(0.740385\pi\)
\(642\) −26.5867 −1.04929
\(643\) −4.10986 −0.162077 −0.0810385 0.996711i \(-0.525824\pi\)
−0.0810385 + 0.996711i \(0.525824\pi\)
\(644\) −26.4039 −1.04046
\(645\) 2.39744 0.0943989
\(646\) 4.32730 0.170255
\(647\) −50.6102 −1.98969 −0.994846 0.101401i \(-0.967668\pi\)
−0.994846 + 0.101401i \(0.967668\pi\)
\(648\) −11.5875 −0.455201
\(649\) 4.93943 0.193889
\(650\) 6.54809 0.256837
\(651\) −7.82504 −0.306688
\(652\) 11.6652 0.456843
\(653\) −9.56040 −0.374127 −0.187064 0.982348i \(-0.559897\pi\)
−0.187064 + 0.982348i \(0.559897\pi\)
\(654\) 8.66168 0.338699
\(655\) −17.1635 −0.670635
\(656\) 17.2469 0.673379
\(657\) 24.1774 0.943251
\(658\) 16.1125 0.628131
\(659\) 46.4542 1.80960 0.904799 0.425838i \(-0.140021\pi\)
0.904799 + 0.425838i \(0.140021\pi\)
\(660\) 18.0979 0.704458
\(661\) −21.4062 −0.832605 −0.416303 0.909226i \(-0.636674\pi\)
−0.416303 + 0.909226i \(0.636674\pi\)
\(662\) 14.8837 0.578470
\(663\) −0.465162 −0.0180654
\(664\) −17.6612 −0.685388
\(665\) 5.50064 0.213306
\(666\) −42.9526 −1.66438
\(667\) −28.0265 −1.08519
\(668\) −33.7817 −1.30705
\(669\) 14.4800 0.559830
\(670\) 7.05394 0.272517
\(671\) 21.7441 0.839420
\(672\) −3.36445 −0.129787
\(673\) 51.0194 1.96665 0.983326 0.181849i \(-0.0582082\pi\)
0.983326 + 0.181849i \(0.0582082\pi\)
\(674\) −17.1782 −0.661680
\(675\) 12.3592 0.475704
\(676\) 3.57377 0.137453
\(677\) −39.8547 −1.53174 −0.765870 0.642996i \(-0.777691\pi\)
−0.765870 + 0.642996i \(0.777691\pi\)
\(678\) 12.9885 0.498820
\(679\) −6.36860 −0.244405
\(680\) −3.06183 −0.117416
\(681\) −6.38835 −0.244802
\(682\) 79.5688 3.04685
\(683\) −19.5118 −0.746598 −0.373299 0.927711i \(-0.621773\pi\)
−0.373299 + 0.927711i \(0.621773\pi\)
\(684\) −27.1681 −1.03880
\(685\) −6.29212 −0.240410
\(686\) −33.4783 −1.27821
\(687\) 4.36405 0.166499
\(688\) −3.09861 −0.118133
\(689\) 6.22973 0.237334
\(690\) 19.7349 0.751293
\(691\) −20.5940 −0.783433 −0.391717 0.920086i \(-0.628119\pi\)
−0.391717 + 0.920086i \(0.628119\pi\)
\(692\) −91.8910 −3.49317
\(693\) −10.2525 −0.389462
\(694\) 75.4932 2.86568
\(695\) 1.58340 0.0600619
\(696\) 13.1861 0.499818
\(697\) −5.86415 −0.222120
\(698\) 30.2680 1.14566
\(699\) −20.1673 −0.762797
\(700\) 11.0102 0.416146
\(701\) −29.9768 −1.13221 −0.566104 0.824334i \(-0.691550\pi\)
−0.566104 + 0.824334i \(0.691550\pi\)
\(702\) 10.5202 0.397059
\(703\) −26.3600 −0.994187
\(704\) 47.3017 1.78275
\(705\) −7.72160 −0.290812
\(706\) −61.1709 −2.30220
\(707\) −10.2773 −0.386520
\(708\) −3.68972 −0.138668
\(709\) 5.18527 0.194737 0.0973685 0.995248i \(-0.468957\pi\)
0.0973685 + 0.995248i \(0.468957\pi\)
\(710\) 2.16554 0.0812714
\(711\) 0.964762 0.0361814
\(712\) −40.7308 −1.52645
\(713\) 55.6324 2.08345
\(714\) −1.21985 −0.0456518
\(715\) 6.01252 0.224856
\(716\) 16.4406 0.614414
\(717\) −3.20452 −0.119675
\(718\) 74.6683 2.78660
\(719\) 20.7096 0.772338 0.386169 0.922428i \(-0.373798\pi\)
0.386169 + 0.922428i \(0.373798\pi\)
\(720\) 5.55165 0.206898
\(721\) −0.580646 −0.0216244
\(722\) 18.8530 0.701635
\(723\) 16.4279 0.610961
\(724\) −86.2112 −3.20402
\(725\) 11.6868 0.434038
\(726\) −10.4136 −0.386485
\(727\) 13.6661 0.506849 0.253425 0.967355i \(-0.418443\pi\)
0.253425 + 0.967355i \(0.418443\pi\)
\(728\) 4.12710 0.152960
\(729\) 4.11562 0.152430
\(730\) −37.1824 −1.37618
\(731\) 1.05356 0.0389675
\(732\) −16.2427 −0.600347
\(733\) −35.2869 −1.30335 −0.651676 0.758497i \(-0.725934\pi\)
−0.651676 + 0.758497i \(0.725934\pi\)
\(734\) 8.29838 0.306299
\(735\) 7.24660 0.267295
\(736\) 23.9197 0.881691
\(737\) −8.06875 −0.297216
\(738\) 57.4208 2.11369
\(739\) −24.4833 −0.900633 −0.450316 0.892869i \(-0.648689\pi\)
−0.450316 + 0.892869i \(0.648689\pi\)
\(740\) 42.3541 1.55697
\(741\) 2.79528 0.102687
\(742\) 16.3370 0.599750
\(743\) −33.1324 −1.21551 −0.607756 0.794124i \(-0.707930\pi\)
−0.607756 + 0.794124i \(0.707930\pi\)
\(744\) −26.1743 −0.959596
\(745\) −23.1066 −0.846560
\(746\) −24.2566 −0.888097
\(747\) −10.8882 −0.398377
\(748\) 7.95318 0.290797
\(749\) −14.8517 −0.542668
\(750\) −23.0644 −0.842194
\(751\) 35.6218 1.29986 0.649930 0.759994i \(-0.274798\pi\)
0.649930 + 0.759994i \(0.274798\pi\)
\(752\) 9.97994 0.363931
\(753\) −23.3714 −0.851700
\(754\) 9.94789 0.362281
\(755\) 7.97675 0.290303
\(756\) 17.6890 0.643344
\(757\) 7.19443 0.261486 0.130743 0.991416i \(-0.458264\pi\)
0.130743 + 0.991416i \(0.458264\pi\)
\(758\) 60.0004 2.17931
\(759\) −22.5740 −0.819384
\(760\) 18.3993 0.667413
\(761\) 38.7127 1.40333 0.701667 0.712505i \(-0.252439\pi\)
0.701667 + 0.712505i \(0.252439\pi\)
\(762\) −12.7760 −0.462825
\(763\) 4.83852 0.175166
\(764\) 40.5228 1.46606
\(765\) −1.88762 −0.0682472
\(766\) −56.2034 −2.03071
\(767\) −1.22581 −0.0442615
\(768\) −21.0323 −0.758937
\(769\) 16.6572 0.600674 0.300337 0.953833i \(-0.402901\pi\)
0.300337 + 0.953833i \(0.402901\pi\)
\(770\) 15.7674 0.568217
\(771\) 3.68820 0.132827
\(772\) −35.0152 −1.26022
\(773\) −45.2249 −1.62663 −0.813313 0.581826i \(-0.802338\pi\)
−0.813313 + 0.581826i \(0.802338\pi\)
\(774\) −10.3163 −0.370813
\(775\) −23.1983 −0.833306
\(776\) −21.3026 −0.764719
\(777\) 7.43080 0.266579
\(778\) −20.8270 −0.746683
\(779\) 35.2391 1.26257
\(780\) −4.49132 −0.160815
\(781\) −2.47709 −0.0886372
\(782\) 8.67257 0.310131
\(783\) 18.7761 0.671003
\(784\) −9.36601 −0.334500
\(785\) 35.5952 1.27045
\(786\) −22.8729 −0.815848
\(787\) −45.4763 −1.62105 −0.810527 0.585701i \(-0.800819\pi\)
−0.810527 + 0.585701i \(0.800819\pi\)
\(788\) −26.6697 −0.950067
\(789\) 5.00447 0.178164
\(790\) −1.48371 −0.0527879
\(791\) 7.25553 0.257977
\(792\) −34.2942 −1.21859
\(793\) −5.39620 −0.191625
\(794\) 91.1162 3.23359
\(795\) −7.82919 −0.277673
\(796\) 28.6622 1.01590
\(797\) −40.4312 −1.43215 −0.716073 0.698026i \(-0.754062\pi\)
−0.716073 + 0.698026i \(0.754062\pi\)
\(798\) 7.33039 0.259493
\(799\) −3.39329 −0.120046
\(800\) −9.97432 −0.352645
\(801\) −25.1106 −0.887239
\(802\) 17.6583 0.623535
\(803\) 42.5317 1.50091
\(804\) 6.02731 0.212567
\(805\) 11.0241 0.388550
\(806\) −19.7465 −0.695540
\(807\) 0.871940 0.0306937
\(808\) −34.3771 −1.20938
\(809\) 13.6723 0.480693 0.240346 0.970687i \(-0.422739\pi\)
0.240346 + 0.970687i \(0.422739\pi\)
\(810\) 10.9863 0.386020
\(811\) −51.7356 −1.81668 −0.908342 0.418228i \(-0.862651\pi\)
−0.908342 + 0.418228i \(0.862651\pi\)
\(812\) 16.7267 0.586994
\(813\) −1.26016 −0.0441957
\(814\) −75.5600 −2.64838
\(815\) −4.87044 −0.170604
\(816\) −0.755565 −0.0264500
\(817\) −6.33113 −0.221498
\(818\) −43.9483 −1.53661
\(819\) 2.54436 0.0889072
\(820\) −56.6206 −1.97728
\(821\) 36.9186 1.28847 0.644234 0.764828i \(-0.277176\pi\)
0.644234 + 0.764828i \(0.277176\pi\)
\(822\) −8.38516 −0.292466
\(823\) −11.5662 −0.403171 −0.201586 0.979471i \(-0.564609\pi\)
−0.201586 + 0.979471i \(0.564609\pi\)
\(824\) −1.94223 −0.0676607
\(825\) 9.41318 0.327725
\(826\) −3.21459 −0.111850
\(827\) 25.0866 0.872345 0.436173 0.899863i \(-0.356334\pi\)
0.436173 + 0.899863i \(0.356334\pi\)
\(828\) −54.4490 −1.89223
\(829\) −38.7695 −1.34652 −0.673261 0.739405i \(-0.735107\pi\)
−0.673261 + 0.739405i \(0.735107\pi\)
\(830\) 16.7449 0.581224
\(831\) −17.6929 −0.613758
\(832\) −11.7388 −0.406970
\(833\) 3.18455 0.110338
\(834\) 2.11011 0.0730672
\(835\) 14.1045 0.488108
\(836\) −47.7927 −1.65294
\(837\) −37.2704 −1.28825
\(838\) 69.5475 2.40248
\(839\) −42.1311 −1.45453 −0.727263 0.686359i \(-0.759208\pi\)
−0.727263 + 0.686359i \(0.759208\pi\)
\(840\) −5.18671 −0.178958
\(841\) −11.2453 −0.387770
\(842\) 35.0299 1.20721
\(843\) −16.7758 −0.577790
\(844\) 70.3635 2.42201
\(845\) −1.49212 −0.0513305
\(846\) 33.2266 1.14235
\(847\) −5.81716 −0.199880
\(848\) 10.1190 0.347487
\(849\) 3.74621 0.128569
\(850\) −3.61639 −0.124041
\(851\) −52.8295 −1.81097
\(852\) 1.85037 0.0633926
\(853\) −5.68866 −0.194776 −0.0973881 0.995246i \(-0.531049\pi\)
−0.0973881 + 0.995246i \(0.531049\pi\)
\(854\) −14.1511 −0.484241
\(855\) 11.3432 0.387929
\(856\) −49.6780 −1.69796
\(857\) −46.4025 −1.58508 −0.792540 0.609820i \(-0.791242\pi\)
−0.792540 + 0.609820i \(0.791242\pi\)
\(858\) 8.01255 0.273544
\(859\) −38.4765 −1.31280 −0.656400 0.754413i \(-0.727922\pi\)
−0.656400 + 0.754413i \(0.727922\pi\)
\(860\) 10.1726 0.346882
\(861\) −9.93380 −0.338543
\(862\) 18.1131 0.616936
\(863\) −9.08228 −0.309165 −0.154582 0.987980i \(-0.549403\pi\)
−0.154582 + 0.987980i \(0.549403\pi\)
\(864\) −16.0248 −0.545174
\(865\) 38.3663 1.30449
\(866\) −13.0237 −0.442563
\(867\) −14.0614 −0.477551
\(868\) −33.2025 −1.12696
\(869\) 1.69716 0.0575722
\(870\) −12.5020 −0.423856
\(871\) 2.00241 0.0678491
\(872\) 16.1846 0.548078
\(873\) −13.1331 −0.444488
\(874\) −52.1157 −1.76284
\(875\) −12.8841 −0.435561
\(876\) −31.7709 −1.07344
\(877\) −48.8374 −1.64912 −0.824561 0.565774i \(-0.808578\pi\)
−0.824561 + 0.565774i \(0.808578\pi\)
\(878\) 57.1765 1.92961
\(879\) −15.4832 −0.522236
\(880\) 9.76617 0.329217
\(881\) 7.14183 0.240614 0.120307 0.992737i \(-0.461612\pi\)
0.120307 + 0.992737i \(0.461612\pi\)
\(882\) −31.1826 −1.04997
\(883\) 27.8030 0.935645 0.467823 0.883822i \(-0.345039\pi\)
0.467823 + 0.883822i \(0.345039\pi\)
\(884\) −1.97373 −0.0663837
\(885\) 1.54053 0.0517844
\(886\) 73.5061 2.46949
\(887\) −8.89410 −0.298635 −0.149317 0.988789i \(-0.547708\pi\)
−0.149317 + 0.988789i \(0.547708\pi\)
\(888\) 24.8556 0.834099
\(889\) −7.13682 −0.239361
\(890\) 38.6176 1.29446
\(891\) −12.5669 −0.421006
\(892\) 61.4402 2.05717
\(893\) 20.3911 0.682364
\(894\) −30.7928 −1.02987
\(895\) −6.86428 −0.229447
\(896\) −22.7949 −0.761526
\(897\) 5.60216 0.187051
\(898\) 55.9120 1.86581
\(899\) −35.2429 −1.17542
\(900\) 22.7048 0.756827
\(901\) −3.44057 −0.114622
\(902\) 101.012 3.36332
\(903\) 1.78472 0.0593919
\(904\) 24.2693 0.807185
\(905\) 35.9949 1.19651
\(906\) 10.6302 0.353163
\(907\) 2.26215 0.0751136 0.0375568 0.999294i \(-0.488042\pi\)
0.0375568 + 0.999294i \(0.488042\pi\)
\(908\) −27.1064 −0.899559
\(909\) −21.1935 −0.702946
\(910\) −3.91297 −0.129714
\(911\) 53.1420 1.76067 0.880336 0.474351i \(-0.157317\pi\)
0.880336 + 0.474351i \(0.157317\pi\)
\(912\) 4.54038 0.150347
\(913\) −19.1539 −0.633901
\(914\) 54.8790 1.81524
\(915\) 6.78164 0.224194
\(916\) 18.5171 0.611823
\(917\) −12.7771 −0.421936
\(918\) −5.81011 −0.191762
\(919\) −35.7339 −1.17875 −0.589376 0.807859i \(-0.700626\pi\)
−0.589376 + 0.807859i \(0.700626\pi\)
\(920\) 36.8751 1.21573
\(921\) 24.6464 0.812126
\(922\) −94.0415 −3.09709
\(923\) 0.614736 0.0202343
\(924\) 13.4726 0.443216
\(925\) 22.0295 0.724325
\(926\) −94.5686 −3.10772
\(927\) −1.19739 −0.0393273
\(928\) −15.1530 −0.497423
\(929\) 0.271820 0.00891812 0.00445906 0.999990i \(-0.498581\pi\)
0.00445906 + 0.999990i \(0.498581\pi\)
\(930\) 24.8163 0.813758
\(931\) −19.1368 −0.627182
\(932\) −85.5719 −2.80300
\(933\) −2.09338 −0.0685342
\(934\) −69.5752 −2.27657
\(935\) −3.32061 −0.108596
\(936\) 8.51074 0.278182
\(937\) −47.7399 −1.55959 −0.779797 0.626033i \(-0.784678\pi\)
−0.779797 + 0.626033i \(0.784678\pi\)
\(938\) 5.25117 0.171457
\(939\) −8.98770 −0.293302
\(940\) −32.7636 −1.06863
\(941\) −58.8941 −1.91989 −0.959946 0.280186i \(-0.909604\pi\)
−0.959946 + 0.280186i \(0.909604\pi\)
\(942\) 47.4357 1.54554
\(943\) 70.6246 2.29985
\(944\) −1.99109 −0.0648044
\(945\) −7.38552 −0.240251
\(946\) −18.1479 −0.590041
\(947\) −31.7238 −1.03088 −0.515442 0.856924i \(-0.672372\pi\)
−0.515442 + 0.856924i \(0.672372\pi\)
\(948\) −1.26777 −0.0411752
\(949\) −10.5550 −0.342631
\(950\) 21.7318 0.705073
\(951\) −1.92124 −0.0623006
\(952\) −2.27932 −0.0738732
\(953\) −12.1670 −0.394127 −0.197063 0.980391i \(-0.563140\pi\)
−0.197063 + 0.980391i \(0.563140\pi\)
\(954\) 33.6895 1.09074
\(955\) −16.9190 −0.547488
\(956\) −13.5971 −0.439762
\(957\) 14.3005 0.462271
\(958\) 91.5743 2.95863
\(959\) −4.68405 −0.151256
\(960\) 14.7527 0.476141
\(961\) 38.9569 1.25667
\(962\) 18.7516 0.604577
\(963\) −30.6265 −0.986926
\(964\) 69.7054 2.24506
\(965\) 14.6195 0.470619
\(966\) 14.6912 0.472683
\(967\) 2.43370 0.0782624 0.0391312 0.999234i \(-0.487541\pi\)
0.0391312 + 0.999234i \(0.487541\pi\)
\(968\) −19.4581 −0.625406
\(969\) −1.54378 −0.0495934
\(970\) 20.1974 0.648498
\(971\) 19.2160 0.616670 0.308335 0.951278i \(-0.400228\pi\)
0.308335 + 0.951278i \(0.400228\pi\)
\(972\) 57.1620 1.83347
\(973\) 1.17873 0.0377885
\(974\) −59.8620 −1.91810
\(975\) −2.33606 −0.0748137
\(976\) −8.76506 −0.280563
\(977\) 14.0784 0.450408 0.225204 0.974312i \(-0.427695\pi\)
0.225204 + 0.974312i \(0.427695\pi\)
\(978\) −6.49056 −0.207545
\(979\) −44.1733 −1.41178
\(980\) 30.7481 0.982211
\(981\) 9.97781 0.318567
\(982\) −31.0754 −0.991656
\(983\) 14.2794 0.455443 0.227722 0.973726i \(-0.426872\pi\)
0.227722 + 0.973726i \(0.426872\pi\)
\(984\) −33.2280 −1.05927
\(985\) 11.1351 0.354794
\(986\) −5.49404 −0.174966
\(987\) −5.74820 −0.182967
\(988\) 11.8606 0.377337
\(989\) −12.6886 −0.403473
\(990\) 32.5149 1.03339
\(991\) −14.6386 −0.465010 −0.232505 0.972595i \(-0.574692\pi\)
−0.232505 + 0.972595i \(0.574692\pi\)
\(992\) 30.0786 0.954998
\(993\) −5.30981 −0.168502
\(994\) 1.61210 0.0511326
\(995\) −11.9670 −0.379380
\(996\) 14.3078 0.453362
\(997\) 13.2009 0.418076 0.209038 0.977907i \(-0.432967\pi\)
0.209038 + 0.977907i \(0.432967\pi\)
\(998\) −13.1019 −0.414732
\(999\) 35.3927 1.11977
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 \(a_p\))