Properties

Label 8042.2.a.a.1.3
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 1
Dimension 67
CM No

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Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(1\)
Dimension: \(67\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-3.06256 q^{3}\) \(+1.00000 q^{4}\) \(+2.88453 q^{5}\) \(-3.06256 q^{6}\) \(-1.43370 q^{7}\) \(+1.00000 q^{8}\) \(+6.37925 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-3.06256 q^{3}\) \(+1.00000 q^{4}\) \(+2.88453 q^{5}\) \(-3.06256 q^{6}\) \(-1.43370 q^{7}\) \(+1.00000 q^{8}\) \(+6.37925 q^{9}\) \(+2.88453 q^{10}\) \(-0.483144 q^{11}\) \(-3.06256 q^{12}\) \(-6.48480 q^{13}\) \(-1.43370 q^{14}\) \(-8.83403 q^{15}\) \(+1.00000 q^{16}\) \(-3.52260 q^{17}\) \(+6.37925 q^{18}\) \(+3.24983 q^{19}\) \(+2.88453 q^{20}\) \(+4.39077 q^{21}\) \(-0.483144 q^{22}\) \(+0.152574 q^{23}\) \(-3.06256 q^{24}\) \(+3.32051 q^{25}\) \(-6.48480 q^{26}\) \(-10.3491 q^{27}\) \(-1.43370 q^{28}\) \(+5.55838 q^{29}\) \(-8.83403 q^{30}\) \(+10.3693 q^{31}\) \(+1.00000 q^{32}\) \(+1.47966 q^{33}\) \(-3.52260 q^{34}\) \(-4.13554 q^{35}\) \(+6.37925 q^{36}\) \(-0.602528 q^{37}\) \(+3.24983 q^{38}\) \(+19.8601 q^{39}\) \(+2.88453 q^{40}\) \(-6.21391 q^{41}\) \(+4.39077 q^{42}\) \(-1.11490 q^{43}\) \(-0.483144 q^{44}\) \(+18.4011 q^{45}\) \(+0.152574 q^{46}\) \(+2.34195 q^{47}\) \(-3.06256 q^{48}\) \(-4.94452 q^{49}\) \(+3.32051 q^{50}\) \(+10.7882 q^{51}\) \(-6.48480 q^{52}\) \(+0.759256 q^{53}\) \(-10.3491 q^{54}\) \(-1.39364 q^{55}\) \(-1.43370 q^{56}\) \(-9.95278 q^{57}\) \(+5.55838 q^{58}\) \(+3.35854 q^{59}\) \(-8.83403 q^{60}\) \(-10.5197 q^{61}\) \(+10.3693 q^{62}\) \(-9.14590 q^{63}\) \(+1.00000 q^{64}\) \(-18.7056 q^{65}\) \(+1.47966 q^{66}\) \(-10.3686 q^{67}\) \(-3.52260 q^{68}\) \(-0.467266 q^{69}\) \(-4.13554 q^{70}\) \(-6.77033 q^{71}\) \(+6.37925 q^{72}\) \(+4.88971 q^{73}\) \(-0.602528 q^{74}\) \(-10.1693 q^{75}\) \(+3.24983 q^{76}\) \(+0.692681 q^{77}\) \(+19.8601 q^{78}\) \(+1.79926 q^{79}\) \(+2.88453 q^{80}\) \(+12.5571 q^{81}\) \(-6.21391 q^{82}\) \(+9.67161 q^{83}\) \(+4.39077 q^{84}\) \(-10.1610 q^{85}\) \(-1.11490 q^{86}\) \(-17.0228 q^{87}\) \(-0.483144 q^{88}\) \(+9.43835 q^{89}\) \(+18.4011 q^{90}\) \(+9.29723 q^{91}\) \(+0.152574 q^{92}\) \(-31.7567 q^{93}\) \(+2.34195 q^{94}\) \(+9.37423 q^{95}\) \(-3.06256 q^{96}\) \(-11.2789 q^{97}\) \(-4.94452 q^{98}\) \(-3.08210 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut -\mathstrut 11q^{12} \) \(\mathstrut -\mathstrut 51q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 31q^{15} \) \(\mathstrut +\mathstrut 67q^{16} \) \(\mathstrut -\mathstrut 34q^{17} \) \(\mathstrut +\mathstrut 24q^{18} \) \(\mathstrut -\mathstrut 33q^{19} \) \(\mathstrut -\mathstrut 20q^{20} \) \(\mathstrut -\mathstrut 39q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 43q^{23} \) \(\mathstrut -\mathstrut 11q^{24} \) \(\mathstrut -\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut 51q^{26} \) \(\mathstrut -\mathstrut 29q^{27} \) \(\mathstrut -\mathstrut 40q^{28} \) \(\mathstrut -\mathstrut 63q^{29} \) \(\mathstrut -\mathstrut 31q^{30} \) \(\mathstrut -\mathstrut 43q^{31} \) \(\mathstrut +\mathstrut 67q^{32} \) \(\mathstrut -\mathstrut 49q^{33} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut -\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 77q^{37} \) \(\mathstrut -\mathstrut 33q^{38} \) \(\mathstrut -\mathstrut 40q^{39} \) \(\mathstrut -\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 50q^{41} \) \(\mathstrut -\mathstrut 39q^{42} \) \(\mathstrut -\mathstrut 56q^{43} \) \(\mathstrut -\mathstrut 13q^{44} \) \(\mathstrut -\mathstrut 48q^{45} \) \(\mathstrut -\mathstrut 43q^{46} \) \(\mathstrut -\mathstrut 48q^{47} \) \(\mathstrut -\mathstrut 11q^{48} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut -\mathstrut 9q^{50} \) \(\mathstrut -\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut 51q^{52} \) \(\mathstrut -\mathstrut 91q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut -\mathstrut 58q^{55} \) \(\mathstrut -\mathstrut 40q^{56} \) \(\mathstrut -\mathstrut 65q^{57} \) \(\mathstrut -\mathstrut 63q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 31q^{60} \) \(\mathstrut -\mathstrut 45q^{61} \) \(\mathstrut -\mathstrut 43q^{62} \) \(\mathstrut -\mathstrut 67q^{63} \) \(\mathstrut +\mathstrut 67q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 49q^{66} \) \(\mathstrut -\mathstrut 112q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 75q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut -\mathstrut 79q^{73} \) \(\mathstrut -\mathstrut 77q^{74} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 33q^{76} \) \(\mathstrut -\mathstrut 85q^{77} \) \(\mathstrut -\mathstrut 40q^{78} \) \(\mathstrut -\mathstrut 80q^{79} \) \(\mathstrut -\mathstrut 20q^{80} \) \(\mathstrut -\mathstrut 77q^{81} \) \(\mathstrut -\mathstrut 50q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 39q^{84} \) \(\mathstrut -\mathstrut 134q^{85} \) \(\mathstrut -\mathstrut 56q^{86} \) \(\mathstrut -\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 77q^{89} \) \(\mathstrut -\mathstrut 48q^{90} \) \(\mathstrut -\mathstrut 17q^{91} \) \(\mathstrut -\mathstrut 43q^{92} \) \(\mathstrut -\mathstrut 97q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 11q^{96} \) \(\mathstrut -\mathstrut 87q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut -\mathstrut 44q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −3.06256 −1.76817 −0.884084 0.467328i \(-0.845217\pi\)
−0.884084 + 0.467328i \(0.845217\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.88453 1.29000 0.645000 0.764182i \(-0.276857\pi\)
0.645000 + 0.764182i \(0.276857\pi\)
\(6\) −3.06256 −1.25028
\(7\) −1.43370 −0.541886 −0.270943 0.962595i \(-0.587335\pi\)
−0.270943 + 0.962595i \(0.587335\pi\)
\(8\) 1.00000 0.353553
\(9\) 6.37925 2.12642
\(10\) 2.88453 0.912168
\(11\) −0.483144 −0.145673 −0.0728367 0.997344i \(-0.523205\pi\)
−0.0728367 + 0.997344i \(0.523205\pi\)
\(12\) −3.06256 −0.884084
\(13\) −6.48480 −1.79856 −0.899280 0.437373i \(-0.855909\pi\)
−0.899280 + 0.437373i \(0.855909\pi\)
\(14\) −1.43370 −0.383171
\(15\) −8.83403 −2.28094
\(16\) 1.00000 0.250000
\(17\) −3.52260 −0.854355 −0.427178 0.904168i \(-0.640492\pi\)
−0.427178 + 0.904168i \(0.640492\pi\)
\(18\) 6.37925 1.50360
\(19\) 3.24983 0.745562 0.372781 0.927919i \(-0.378404\pi\)
0.372781 + 0.927919i \(0.378404\pi\)
\(20\) 2.88453 0.645000
\(21\) 4.39077 0.958145
\(22\) −0.483144 −0.103007
\(23\) 0.152574 0.0318138 0.0159069 0.999873i \(-0.494936\pi\)
0.0159069 + 0.999873i \(0.494936\pi\)
\(24\) −3.06256 −0.625142
\(25\) 3.32051 0.664102
\(26\) −6.48480 −1.27177
\(27\) −10.3491 −1.99169
\(28\) −1.43370 −0.270943
\(29\) 5.55838 1.03216 0.516082 0.856539i \(-0.327390\pi\)
0.516082 + 0.856539i \(0.327390\pi\)
\(30\) −8.83403 −1.61287
\(31\) 10.3693 1.86239 0.931193 0.364526i \(-0.118769\pi\)
0.931193 + 0.364526i \(0.118769\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.47966 0.257575
\(34\) −3.52260 −0.604120
\(35\) −4.13554 −0.699033
\(36\) 6.37925 1.06321
\(37\) −0.602528 −0.0990550 −0.0495275 0.998773i \(-0.515772\pi\)
−0.0495275 + 0.998773i \(0.515772\pi\)
\(38\) 3.24983 0.527192
\(39\) 19.8601 3.18016
\(40\) 2.88453 0.456084
\(41\) −6.21391 −0.970449 −0.485225 0.874389i \(-0.661262\pi\)
−0.485225 + 0.874389i \(0.661262\pi\)
\(42\) 4.39077 0.677511
\(43\) −1.11490 −0.170021 −0.0850107 0.996380i \(-0.527092\pi\)
−0.0850107 + 0.996380i \(0.527092\pi\)
\(44\) −0.483144 −0.0728367
\(45\) 18.4011 2.74308
\(46\) 0.152574 0.0224958
\(47\) 2.34195 0.341609 0.170804 0.985305i \(-0.445363\pi\)
0.170804 + 0.985305i \(0.445363\pi\)
\(48\) −3.06256 −0.442042
\(49\) −4.94452 −0.706360
\(50\) 3.32051 0.469591
\(51\) 10.7882 1.51064
\(52\) −6.48480 −0.899280
\(53\) 0.759256 0.104292 0.0521459 0.998639i \(-0.483394\pi\)
0.0521459 + 0.998639i \(0.483394\pi\)
\(54\) −10.3491 −1.40834
\(55\) −1.39364 −0.187919
\(56\) −1.43370 −0.191586
\(57\) −9.95278 −1.31828
\(58\) 5.55838 0.729850
\(59\) 3.35854 0.437245 0.218622 0.975810i \(-0.429844\pi\)
0.218622 + 0.975810i \(0.429844\pi\)
\(60\) −8.83403 −1.14047
\(61\) −10.5197 −1.34691 −0.673456 0.739228i \(-0.735191\pi\)
−0.673456 + 0.739228i \(0.735191\pi\)
\(62\) 10.3693 1.31691
\(63\) −9.14590 −1.15228
\(64\) 1.00000 0.125000
\(65\) −18.7056 −2.32014
\(66\) 1.47966 0.182133
\(67\) −10.3686 −1.26673 −0.633365 0.773853i \(-0.718327\pi\)
−0.633365 + 0.773853i \(0.718327\pi\)
\(68\) −3.52260 −0.427178
\(69\) −0.467266 −0.0562522
\(70\) −4.13554 −0.494291
\(71\) −6.77033 −0.803491 −0.401745 0.915751i \(-0.631596\pi\)
−0.401745 + 0.915751i \(0.631596\pi\)
\(72\) 6.37925 0.751802
\(73\) 4.88971 0.572297 0.286149 0.958185i \(-0.407625\pi\)
0.286149 + 0.958185i \(0.407625\pi\)
\(74\) −0.602528 −0.0700425
\(75\) −10.1693 −1.17424
\(76\) 3.24983 0.372781
\(77\) 0.692681 0.0789384
\(78\) 19.8601 2.24871
\(79\) 1.79926 0.202432 0.101216 0.994864i \(-0.467727\pi\)
0.101216 + 0.994864i \(0.467727\pi\)
\(80\) 2.88453 0.322500
\(81\) 12.5571 1.39523
\(82\) −6.21391 −0.686211
\(83\) 9.67161 1.06160 0.530798 0.847498i \(-0.321892\pi\)
0.530798 + 0.847498i \(0.321892\pi\)
\(84\) 4.39077 0.479073
\(85\) −10.1610 −1.10212
\(86\) −1.11490 −0.120223
\(87\) −17.0228 −1.82504
\(88\) −0.483144 −0.0515033
\(89\) 9.43835 1.00046 0.500232 0.865892i \(-0.333248\pi\)
0.500232 + 0.865892i \(0.333248\pi\)
\(90\) 18.4011 1.93965
\(91\) 9.29723 0.974615
\(92\) 0.152574 0.0159069
\(93\) −31.7567 −3.29301
\(94\) 2.34195 0.241554
\(95\) 9.37423 0.961775
\(96\) −3.06256 −0.312571
\(97\) −11.2789 −1.14520 −0.572599 0.819835i \(-0.694065\pi\)
−0.572599 + 0.819835i \(0.694065\pi\)
\(98\) −4.94452 −0.499472
\(99\) −3.08210 −0.309762
\(100\) 3.32051 0.332051
\(101\) −1.98171 −0.197188 −0.0985939 0.995128i \(-0.531434\pi\)
−0.0985939 + 0.995128i \(0.531434\pi\)
\(102\) 10.7882 1.06819
\(103\) −0.0581064 −0.00572539 −0.00286270 0.999996i \(-0.500911\pi\)
−0.00286270 + 0.999996i \(0.500911\pi\)
\(104\) −6.48480 −0.635887
\(105\) 12.6653 1.23601
\(106\) 0.759256 0.0737454
\(107\) −0.246536 −0.0238335 −0.0119167 0.999929i \(-0.503793\pi\)
−0.0119167 + 0.999929i \(0.503793\pi\)
\(108\) −10.3491 −0.995847
\(109\) 7.78701 0.745860 0.372930 0.927859i \(-0.378353\pi\)
0.372930 + 0.927859i \(0.378353\pi\)
\(110\) −1.39364 −0.132879
\(111\) 1.84528 0.175146
\(112\) −1.43370 −0.135471
\(113\) −19.7818 −1.86092 −0.930458 0.366398i \(-0.880591\pi\)
−0.930458 + 0.366398i \(0.880591\pi\)
\(114\) −9.95278 −0.932164
\(115\) 0.440104 0.0410399
\(116\) 5.55838 0.516082
\(117\) −41.3682 −3.82449
\(118\) 3.35854 0.309179
\(119\) 5.05033 0.462963
\(120\) −8.83403 −0.806433
\(121\) −10.7666 −0.978779
\(122\) −10.5197 −0.952410
\(123\) 19.0304 1.71592
\(124\) 10.3693 0.931193
\(125\) −4.84454 −0.433309
\(126\) −9.14590 −0.814782
\(127\) 10.5949 0.940146 0.470073 0.882627i \(-0.344228\pi\)
0.470073 + 0.882627i \(0.344228\pi\)
\(128\) 1.00000 0.0883883
\(129\) 3.41446 0.300626
\(130\) −18.7056 −1.64059
\(131\) −3.12529 −0.273058 −0.136529 0.990636i \(-0.543595\pi\)
−0.136529 + 0.990636i \(0.543595\pi\)
\(132\) 1.47966 0.128788
\(133\) −4.65926 −0.404009
\(134\) −10.3686 −0.895714
\(135\) −29.8524 −2.56929
\(136\) −3.52260 −0.302060
\(137\) −13.1205 −1.12096 −0.560480 0.828168i \(-0.689383\pi\)
−0.560480 + 0.828168i \(0.689383\pi\)
\(138\) −0.467266 −0.0397763
\(139\) 3.96161 0.336019 0.168010 0.985785i \(-0.446266\pi\)
0.168010 + 0.985785i \(0.446266\pi\)
\(140\) −4.13554 −0.349517
\(141\) −7.17236 −0.604022
\(142\) −6.77033 −0.568154
\(143\) 3.13309 0.262003
\(144\) 6.37925 0.531604
\(145\) 16.0333 1.33149
\(146\) 4.88971 0.404675
\(147\) 15.1429 1.24896
\(148\) −0.602528 −0.0495275
\(149\) −20.3529 −1.66738 −0.833688 0.552236i \(-0.813775\pi\)
−0.833688 + 0.552236i \(0.813775\pi\)
\(150\) −10.1693 −0.830316
\(151\) −9.06602 −0.737782 −0.368891 0.929473i \(-0.620262\pi\)
−0.368891 + 0.929473i \(0.620262\pi\)
\(152\) 3.24983 0.263596
\(153\) −22.4715 −1.81672
\(154\) 0.692681 0.0558179
\(155\) 29.9106 2.40248
\(156\) 19.8601 1.59008
\(157\) −0.527734 −0.0421178 −0.0210589 0.999778i \(-0.506704\pi\)
−0.0210589 + 0.999778i \(0.506704\pi\)
\(158\) 1.79926 0.143141
\(159\) −2.32526 −0.184405
\(160\) 2.88453 0.228042
\(161\) −0.218744 −0.0172395
\(162\) 12.5571 0.986579
\(163\) 0.634234 0.0496770 0.0248385 0.999691i \(-0.492093\pi\)
0.0248385 + 0.999691i \(0.492093\pi\)
\(164\) −6.21391 −0.485225
\(165\) 4.26811 0.332272
\(166\) 9.67161 0.750662
\(167\) 8.12754 0.628928 0.314464 0.949269i \(-0.398175\pi\)
0.314464 + 0.949269i \(0.398175\pi\)
\(168\) 4.39077 0.338755
\(169\) 29.0527 2.23482
\(170\) −10.1610 −0.779316
\(171\) 20.7315 1.58538
\(172\) −1.11490 −0.0850107
\(173\) 13.2779 1.00950 0.504752 0.863265i \(-0.331584\pi\)
0.504752 + 0.863265i \(0.331584\pi\)
\(174\) −17.0228 −1.29050
\(175\) −4.76060 −0.359868
\(176\) −0.483144 −0.0364184
\(177\) −10.2857 −0.773122
\(178\) 9.43835 0.707434
\(179\) −17.6305 −1.31776 −0.658881 0.752247i \(-0.728970\pi\)
−0.658881 + 0.752247i \(0.728970\pi\)
\(180\) 18.4011 1.37154
\(181\) −8.45797 −0.628676 −0.314338 0.949311i \(-0.601782\pi\)
−0.314338 + 0.949311i \(0.601782\pi\)
\(182\) 9.29723 0.689157
\(183\) 32.2172 2.38157
\(184\) 0.152574 0.0112479
\(185\) −1.73801 −0.127781
\(186\) −31.7567 −2.32851
\(187\) 1.70192 0.124457
\(188\) 2.34195 0.170804
\(189\) 14.8375 1.07927
\(190\) 9.37423 0.680078
\(191\) 0.369311 0.0267224 0.0133612 0.999911i \(-0.495747\pi\)
0.0133612 + 0.999911i \(0.495747\pi\)
\(192\) −3.06256 −0.221021
\(193\) −21.6489 −1.55832 −0.779162 0.626822i \(-0.784355\pi\)
−0.779162 + 0.626822i \(0.784355\pi\)
\(194\) −11.2789 −0.809778
\(195\) 57.2870 4.10241
\(196\) −4.94452 −0.353180
\(197\) 17.4477 1.24310 0.621548 0.783376i \(-0.286504\pi\)
0.621548 + 0.783376i \(0.286504\pi\)
\(198\) −3.08210 −0.219035
\(199\) 13.9536 0.989143 0.494571 0.869137i \(-0.335325\pi\)
0.494571 + 0.869137i \(0.335325\pi\)
\(200\) 3.32051 0.234796
\(201\) 31.7545 2.23979
\(202\) −1.98171 −0.139433
\(203\) −7.96902 −0.559315
\(204\) 10.7882 0.755322
\(205\) −17.9242 −1.25188
\(206\) −0.0581064 −0.00404846
\(207\) 0.973306 0.0676495
\(208\) −6.48480 −0.449640
\(209\) −1.57014 −0.108609
\(210\) 12.6653 0.873990
\(211\) −17.3079 −1.19152 −0.595762 0.803161i \(-0.703150\pi\)
−0.595762 + 0.803161i \(0.703150\pi\)
\(212\) 0.759256 0.0521459
\(213\) 20.7345 1.42071
\(214\) −0.246536 −0.0168528
\(215\) −3.21598 −0.219328
\(216\) −10.3491 −0.704170
\(217\) −14.8665 −1.00920
\(218\) 7.78701 0.527403
\(219\) −14.9750 −1.01192
\(220\) −1.39364 −0.0939594
\(221\) 22.8433 1.53661
\(222\) 1.84528 0.123847
\(223\) 23.5553 1.57738 0.788691 0.614790i \(-0.210759\pi\)
0.788691 + 0.614790i \(0.210759\pi\)
\(224\) −1.43370 −0.0957928
\(225\) 21.1824 1.41216
\(226\) −19.7818 −1.31587
\(227\) −4.67424 −0.310240 −0.155120 0.987896i \(-0.549576\pi\)
−0.155120 + 0.987896i \(0.549576\pi\)
\(228\) −9.95278 −0.659139
\(229\) 2.18118 0.144136 0.0720682 0.997400i \(-0.477040\pi\)
0.0720682 + 0.997400i \(0.477040\pi\)
\(230\) 0.440104 0.0290196
\(231\) −2.12138 −0.139576
\(232\) 5.55838 0.364925
\(233\) −9.00586 −0.589993 −0.294997 0.955498i \(-0.595319\pi\)
−0.294997 + 0.955498i \(0.595319\pi\)
\(234\) −41.3682 −2.70432
\(235\) 6.75543 0.440676
\(236\) 3.35854 0.218622
\(237\) −5.51033 −0.357935
\(238\) 5.05033 0.327364
\(239\) 1.47634 0.0954966 0.0477483 0.998859i \(-0.484795\pi\)
0.0477483 + 0.998859i \(0.484795\pi\)
\(240\) −8.83403 −0.570234
\(241\) 3.48977 0.224796 0.112398 0.993663i \(-0.464147\pi\)
0.112398 + 0.993663i \(0.464147\pi\)
\(242\) −10.7666 −0.692101
\(243\) −7.40937 −0.475312
\(244\) −10.5197 −0.673456
\(245\) −14.2626 −0.911205
\(246\) 19.0304 1.21334
\(247\) −21.0745 −1.34094
\(248\) 10.3693 0.658453
\(249\) −29.6198 −1.87708
\(250\) −4.84454 −0.306395
\(251\) 21.4745 1.35546 0.677728 0.735313i \(-0.262965\pi\)
0.677728 + 0.735313i \(0.262965\pi\)
\(252\) −9.14590 −0.576138
\(253\) −0.0737151 −0.00463443
\(254\) 10.5949 0.664784
\(255\) 31.1187 1.94873
\(256\) 1.00000 0.0625000
\(257\) −15.5803 −0.971872 −0.485936 0.873994i \(-0.661521\pi\)
−0.485936 + 0.873994i \(0.661521\pi\)
\(258\) 3.41446 0.212575
\(259\) 0.863842 0.0536765
\(260\) −18.7056 −1.16007
\(261\) 35.4583 2.19481
\(262\) −3.12529 −0.193081
\(263\) −26.5632 −1.63796 −0.818980 0.573822i \(-0.805460\pi\)
−0.818980 + 0.573822i \(0.805460\pi\)
\(264\) 1.47966 0.0910665
\(265\) 2.19010 0.134536
\(266\) −4.65926 −0.285678
\(267\) −28.9055 −1.76899
\(268\) −10.3686 −0.633365
\(269\) 10.3748 0.632560 0.316280 0.948666i \(-0.397566\pi\)
0.316280 + 0.948666i \(0.397566\pi\)
\(270\) −29.8524 −1.81676
\(271\) −20.4562 −1.24262 −0.621312 0.783563i \(-0.713400\pi\)
−0.621312 + 0.783563i \(0.713400\pi\)
\(272\) −3.52260 −0.213589
\(273\) −28.4733 −1.72328
\(274\) −13.1205 −0.792639
\(275\) −1.60428 −0.0967420
\(276\) −0.467266 −0.0281261
\(277\) −16.4567 −0.988784 −0.494392 0.869239i \(-0.664609\pi\)
−0.494392 + 0.869239i \(0.664609\pi\)
\(278\) 3.96161 0.237601
\(279\) 66.1486 3.96021
\(280\) −4.13554 −0.247146
\(281\) 16.9764 1.01273 0.506365 0.862319i \(-0.330989\pi\)
0.506365 + 0.862319i \(0.330989\pi\)
\(282\) −7.17236 −0.427108
\(283\) −32.9676 −1.95972 −0.979862 0.199678i \(-0.936010\pi\)
−0.979862 + 0.199678i \(0.936010\pi\)
\(284\) −6.77033 −0.401745
\(285\) −28.7091 −1.70058
\(286\) 3.13309 0.185264
\(287\) 8.90885 0.525873
\(288\) 6.37925 0.375901
\(289\) −4.59131 −0.270077
\(290\) 16.0333 0.941508
\(291\) 34.5423 2.02490
\(292\) 4.88971 0.286149
\(293\) 0.947949 0.0553798 0.0276899 0.999617i \(-0.491185\pi\)
0.0276899 + 0.999617i \(0.491185\pi\)
\(294\) 15.1429 0.883150
\(295\) 9.68781 0.564046
\(296\) −0.602528 −0.0350212
\(297\) 5.00013 0.290137
\(298\) −20.3529 −1.17901
\(299\) −0.989411 −0.0572191
\(300\) −10.1693 −0.587122
\(301\) 1.59843 0.0921322
\(302\) −9.06602 −0.521691
\(303\) 6.06911 0.348661
\(304\) 3.24983 0.186390
\(305\) −30.3444 −1.73752
\(306\) −22.4715 −1.28461
\(307\) −24.2336 −1.38309 −0.691543 0.722335i \(-0.743069\pi\)
−0.691543 + 0.722335i \(0.743069\pi\)
\(308\) 0.692681 0.0394692
\(309\) 0.177954 0.0101235
\(310\) 29.9106 1.69881
\(311\) −19.3580 −1.09769 −0.548846 0.835923i \(-0.684933\pi\)
−0.548846 + 0.835923i \(0.684933\pi\)
\(312\) 19.8601 1.12436
\(313\) 6.42902 0.363390 0.181695 0.983355i \(-0.441842\pi\)
0.181695 + 0.983355i \(0.441842\pi\)
\(314\) −0.527734 −0.0297817
\(315\) −26.3816 −1.48644
\(316\) 1.79926 0.101216
\(317\) −2.70862 −0.152131 −0.0760657 0.997103i \(-0.524236\pi\)
−0.0760657 + 0.997103i \(0.524236\pi\)
\(318\) −2.32526 −0.130394
\(319\) −2.68550 −0.150359
\(320\) 2.88453 0.161250
\(321\) 0.755029 0.0421416
\(322\) −0.218744 −0.0121901
\(323\) −11.4478 −0.636975
\(324\) 12.5571 0.697617
\(325\) −21.5329 −1.19443
\(326\) 0.634234 0.0351270
\(327\) −23.8482 −1.31881
\(328\) −6.21391 −0.343106
\(329\) −3.35765 −0.185113
\(330\) 4.26811 0.234952
\(331\) −3.96763 −0.218081 −0.109040 0.994037i \(-0.534778\pi\)
−0.109040 + 0.994037i \(0.534778\pi\)
\(332\) 9.67161 0.530798
\(333\) −3.84368 −0.210632
\(334\) 8.12754 0.444719
\(335\) −29.9086 −1.63408
\(336\) 4.39077 0.239536
\(337\) −23.9750 −1.30600 −0.653002 0.757356i \(-0.726491\pi\)
−0.653002 + 0.757356i \(0.726491\pi\)
\(338\) 29.0527 1.58026
\(339\) 60.5829 3.29041
\(340\) −10.1610 −0.551059
\(341\) −5.00988 −0.271300
\(342\) 20.7315 1.12103
\(343\) 17.1248 0.924652
\(344\) −1.11490 −0.0601116
\(345\) −1.34784 −0.0725654
\(346\) 13.2779 0.713827
\(347\) −8.51663 −0.457197 −0.228598 0.973521i \(-0.573414\pi\)
−0.228598 + 0.973521i \(0.573414\pi\)
\(348\) −17.0228 −0.912520
\(349\) 31.2865 1.67473 0.837363 0.546648i \(-0.184096\pi\)
0.837363 + 0.546648i \(0.184096\pi\)
\(350\) −4.76060 −0.254465
\(351\) 67.1122 3.58218
\(352\) −0.483144 −0.0257517
\(353\) 5.18757 0.276106 0.138053 0.990425i \(-0.455916\pi\)
0.138053 + 0.990425i \(0.455916\pi\)
\(354\) −10.2857 −0.546680
\(355\) −19.5292 −1.03650
\(356\) 9.43835 0.500232
\(357\) −15.4669 −0.818596
\(358\) −17.6305 −0.931799
\(359\) 9.25641 0.488534 0.244267 0.969708i \(-0.421453\pi\)
0.244267 + 0.969708i \(0.421453\pi\)
\(360\) 18.4011 0.969825
\(361\) −8.43861 −0.444138
\(362\) −8.45797 −0.444541
\(363\) 32.9732 1.73065
\(364\) 9.29723 0.487307
\(365\) 14.1045 0.738264
\(366\) 32.2172 1.68402
\(367\) 21.8879 1.14254 0.571269 0.820763i \(-0.306451\pi\)
0.571269 + 0.820763i \(0.306451\pi\)
\(368\) 0.152574 0.00795346
\(369\) −39.6401 −2.06358
\(370\) −1.73801 −0.0903548
\(371\) −1.08854 −0.0565142
\(372\) −31.7567 −1.64651
\(373\) −11.6751 −0.604513 −0.302256 0.953227i \(-0.597740\pi\)
−0.302256 + 0.953227i \(0.597740\pi\)
\(374\) 1.70192 0.0880043
\(375\) 14.8367 0.766162
\(376\) 2.34195 0.120777
\(377\) −36.0450 −1.85641
\(378\) 14.8375 0.763160
\(379\) 11.9545 0.614062 0.307031 0.951699i \(-0.400664\pi\)
0.307031 + 0.951699i \(0.400664\pi\)
\(380\) 9.37423 0.480888
\(381\) −32.4475 −1.66234
\(382\) 0.369311 0.0188956
\(383\) −28.9705 −1.48032 −0.740162 0.672428i \(-0.765251\pi\)
−0.740162 + 0.672428i \(0.765251\pi\)
\(384\) −3.06256 −0.156285
\(385\) 1.99806 0.101831
\(386\) −21.6489 −1.10190
\(387\) −7.11226 −0.361536
\(388\) −11.2789 −0.572599
\(389\) 2.14809 0.108913 0.0544563 0.998516i \(-0.482657\pi\)
0.0544563 + 0.998516i \(0.482657\pi\)
\(390\) 57.2870 2.90084
\(391\) −0.537456 −0.0271803
\(392\) −4.94452 −0.249736
\(393\) 9.57138 0.482812
\(394\) 17.4477 0.879001
\(395\) 5.19002 0.261138
\(396\) −3.08210 −0.154881
\(397\) 23.4400 1.17642 0.588209 0.808709i \(-0.299833\pi\)
0.588209 + 0.808709i \(0.299833\pi\)
\(398\) 13.9536 0.699429
\(399\) 14.2693 0.714356
\(400\) 3.32051 0.166026
\(401\) −13.8339 −0.690833 −0.345416 0.938450i \(-0.612262\pi\)
−0.345416 + 0.938450i \(0.612262\pi\)
\(402\) 31.7545 1.58377
\(403\) −67.2431 −3.34962
\(404\) −1.98171 −0.0985939
\(405\) 36.2213 1.79985
\(406\) −7.96902 −0.395496
\(407\) 0.291108 0.0144297
\(408\) 10.7882 0.534093
\(409\) −17.9269 −0.886427 −0.443214 0.896416i \(-0.646162\pi\)
−0.443214 + 0.896416i \(0.646162\pi\)
\(410\) −17.9242 −0.885213
\(411\) 40.1823 1.98205
\(412\) −0.0581064 −0.00286270
\(413\) −4.81512 −0.236937
\(414\) 0.973306 0.0478354
\(415\) 27.8980 1.36946
\(416\) −6.48480 −0.317944
\(417\) −12.1326 −0.594138
\(418\) −1.57014 −0.0767978
\(419\) −25.0523 −1.22388 −0.611942 0.790902i \(-0.709612\pi\)
−0.611942 + 0.790902i \(0.709612\pi\)
\(420\) 12.6653 0.618004
\(421\) 2.47187 0.120472 0.0602358 0.998184i \(-0.480815\pi\)
0.0602358 + 0.998184i \(0.480815\pi\)
\(422\) −17.3079 −0.842534
\(423\) 14.9399 0.726403
\(424\) 0.759256 0.0368727
\(425\) −11.6968 −0.567379
\(426\) 20.7345 1.00459
\(427\) 15.0821 0.729872
\(428\) −0.246536 −0.0119167
\(429\) −9.59528 −0.463264
\(430\) −3.21598 −0.155088
\(431\) −32.4551 −1.56331 −0.781653 0.623714i \(-0.785623\pi\)
−0.781653 + 0.623714i \(0.785623\pi\)
\(432\) −10.3491 −0.497924
\(433\) 6.27422 0.301520 0.150760 0.988570i \(-0.451828\pi\)
0.150760 + 0.988570i \(0.451828\pi\)
\(434\) −14.8665 −0.713613
\(435\) −49.1029 −2.35430
\(436\) 7.78701 0.372930
\(437\) 0.495839 0.0237192
\(438\) −14.9750 −0.715534
\(439\) 17.2177 0.821757 0.410878 0.911690i \(-0.365222\pi\)
0.410878 + 0.911690i \(0.365222\pi\)
\(440\) −1.39364 −0.0664393
\(441\) −31.5423 −1.50202
\(442\) 22.8433 1.08655
\(443\) 24.2847 1.15380 0.576901 0.816814i \(-0.304262\pi\)
0.576901 + 0.816814i \(0.304262\pi\)
\(444\) 1.84528 0.0875729
\(445\) 27.2252 1.29060
\(446\) 23.5553 1.11538
\(447\) 62.3320 2.94820
\(448\) −1.43370 −0.0677357
\(449\) −33.1697 −1.56538 −0.782688 0.622414i \(-0.786152\pi\)
−0.782688 + 0.622414i \(0.786152\pi\)
\(450\) 21.1824 0.998547
\(451\) 3.00221 0.141369
\(452\) −19.7818 −0.930458
\(453\) 27.7652 1.30452
\(454\) −4.67424 −0.219373
\(455\) 26.8181 1.25725
\(456\) −9.95278 −0.466082
\(457\) −28.0312 −1.31124 −0.655622 0.755090i \(-0.727593\pi\)
−0.655622 + 0.755090i \(0.727593\pi\)
\(458\) 2.18118 0.101920
\(459\) 36.4559 1.70161
\(460\) 0.440104 0.0205199
\(461\) 0.802123 0.0373586 0.0186793 0.999826i \(-0.494054\pi\)
0.0186793 + 0.999826i \(0.494054\pi\)
\(462\) −2.12138 −0.0986953
\(463\) 12.1613 0.565182 0.282591 0.959240i \(-0.408806\pi\)
0.282591 + 0.959240i \(0.408806\pi\)
\(464\) 5.55838 0.258041
\(465\) −91.6030 −4.24799
\(466\) −9.00586 −0.417188
\(467\) −26.4050 −1.22188 −0.610938 0.791678i \(-0.709208\pi\)
−0.610938 + 0.791678i \(0.709208\pi\)
\(468\) −41.3682 −1.91225
\(469\) 14.8655 0.686424
\(470\) 6.75543 0.311605
\(471\) 1.61621 0.0744713
\(472\) 3.35854 0.154589
\(473\) 0.538660 0.0247676
\(474\) −5.51033 −0.253098
\(475\) 10.7911 0.495129
\(476\) 5.05033 0.231482
\(477\) 4.84348 0.221768
\(478\) 1.47634 0.0675263
\(479\) −4.98181 −0.227625 −0.113812 0.993502i \(-0.536306\pi\)
−0.113812 + 0.993502i \(0.536306\pi\)
\(480\) −8.83403 −0.403217
\(481\) 3.90728 0.178156
\(482\) 3.48977 0.158955
\(483\) 0.669917 0.0304823
\(484\) −10.7666 −0.489390
\(485\) −32.5343 −1.47731
\(486\) −7.40937 −0.336096
\(487\) −9.95116 −0.450930 −0.225465 0.974251i \(-0.572390\pi\)
−0.225465 + 0.974251i \(0.572390\pi\)
\(488\) −10.5197 −0.476205
\(489\) −1.94238 −0.0878374
\(490\) −14.2626 −0.644319
\(491\) −2.81316 −0.126956 −0.0634781 0.997983i \(-0.520219\pi\)
−0.0634781 + 0.997983i \(0.520219\pi\)
\(492\) 19.0304 0.857959
\(493\) −19.5799 −0.881835
\(494\) −21.0745 −0.948187
\(495\) −8.89040 −0.399594
\(496\) 10.3693 0.465597
\(497\) 9.70660 0.435400
\(498\) −29.6198 −1.32730
\(499\) −8.28153 −0.370732 −0.185366 0.982670i \(-0.559347\pi\)
−0.185366 + 0.982670i \(0.559347\pi\)
\(500\) −4.84454 −0.216654
\(501\) −24.8910 −1.11205
\(502\) 21.4745 0.958452
\(503\) −13.0867 −0.583508 −0.291754 0.956493i \(-0.594239\pi\)
−0.291754 + 0.956493i \(0.594239\pi\)
\(504\) −9.14590 −0.407391
\(505\) −5.71631 −0.254372
\(506\) −0.0737151 −0.00327704
\(507\) −88.9755 −3.95154
\(508\) 10.5949 0.470073
\(509\) −11.0722 −0.490769 −0.245384 0.969426i \(-0.578914\pi\)
−0.245384 + 0.969426i \(0.578914\pi\)
\(510\) 31.1187 1.37796
\(511\) −7.01035 −0.310120
\(512\) 1.00000 0.0441942
\(513\) −33.6330 −1.48493
\(514\) −15.5803 −0.687217
\(515\) −0.167610 −0.00738576
\(516\) 3.41446 0.150313
\(517\) −1.13150 −0.0497633
\(518\) 0.863842 0.0379550
\(519\) −40.6644 −1.78497
\(520\) −18.7056 −0.820295
\(521\) −15.7848 −0.691544 −0.345772 0.938319i \(-0.612383\pi\)
−0.345772 + 0.938319i \(0.612383\pi\)
\(522\) 35.4583 1.55197
\(523\) −33.2536 −1.45408 −0.727039 0.686596i \(-0.759104\pi\)
−0.727039 + 0.686596i \(0.759104\pi\)
\(524\) −3.12529 −0.136529
\(525\) 14.5796 0.636306
\(526\) −26.5632 −1.15821
\(527\) −36.5270 −1.59114
\(528\) 1.47966 0.0643938
\(529\) −22.9767 −0.998988
\(530\) 2.19010 0.0951317
\(531\) 21.4250 0.929765
\(532\) −4.65926 −0.202005
\(533\) 40.2960 1.74541
\(534\) −28.9055 −1.25086
\(535\) −0.711139 −0.0307452
\(536\) −10.3686 −0.447857
\(537\) 53.9943 2.33003
\(538\) 10.3748 0.447287
\(539\) 2.38891 0.102898
\(540\) −29.8524 −1.28464
\(541\) −32.5481 −1.39935 −0.699676 0.714461i \(-0.746672\pi\)
−0.699676 + 0.714461i \(0.746672\pi\)
\(542\) −20.4562 −0.878668
\(543\) 25.9030 1.11160
\(544\) −3.52260 −0.151030
\(545\) 22.4619 0.962161
\(546\) −28.4733 −1.21854
\(547\) 8.45240 0.361398 0.180699 0.983538i \(-0.442164\pi\)
0.180699 + 0.983538i \(0.442164\pi\)
\(548\) −13.1205 −0.560480
\(549\) −67.1079 −2.86410
\(550\) −1.60428 −0.0684069
\(551\) 18.0638 0.769542
\(552\) −0.467266 −0.0198882
\(553\) −2.57959 −0.109695
\(554\) −16.4567 −0.699176
\(555\) 5.32275 0.225938
\(556\) 3.96161 0.168010
\(557\) −36.9322 −1.56487 −0.782434 0.622733i \(-0.786022\pi\)
−0.782434 + 0.622733i \(0.786022\pi\)
\(558\) 66.1486 2.80029
\(559\) 7.22994 0.305794
\(560\) −4.13554 −0.174758
\(561\) −5.21223 −0.220061
\(562\) 16.9764 0.716108
\(563\) −1.88240 −0.0793338 −0.0396669 0.999213i \(-0.512630\pi\)
−0.0396669 + 0.999213i \(0.512630\pi\)
\(564\) −7.17236 −0.302011
\(565\) −57.0612 −2.40058
\(566\) −32.9676 −1.38573
\(567\) −18.0031 −0.756057
\(568\) −6.77033 −0.284077
\(569\) 4.40271 0.184571 0.0922857 0.995733i \(-0.470583\pi\)
0.0922857 + 0.995733i \(0.470583\pi\)
\(570\) −28.7091 −1.20249
\(571\) −1.87631 −0.0785213 −0.0392606 0.999229i \(-0.512500\pi\)
−0.0392606 + 0.999229i \(0.512500\pi\)
\(572\) 3.13309 0.131001
\(573\) −1.13104 −0.0472497
\(574\) 8.90885 0.371848
\(575\) 0.506623 0.0211276
\(576\) 6.37925 0.265802
\(577\) 17.7273 0.737999 0.369000 0.929430i \(-0.379700\pi\)
0.369000 + 0.929430i \(0.379700\pi\)
\(578\) −4.59131 −0.190973
\(579\) 66.3011 2.75538
\(580\) 16.0333 0.665746
\(581\) −13.8661 −0.575264
\(582\) 34.5423 1.43182
\(583\) −0.366830 −0.0151925
\(584\) 4.88971 0.202338
\(585\) −119.328 −4.93360
\(586\) 0.947949 0.0391594
\(587\) −10.5360 −0.434869 −0.217435 0.976075i \(-0.569769\pi\)
−0.217435 + 0.976075i \(0.569769\pi\)
\(588\) 15.1429 0.624481
\(589\) 33.6985 1.38852
\(590\) 9.68781 0.398841
\(591\) −53.4345 −2.19800
\(592\) −0.602528 −0.0247638
\(593\) 13.9591 0.573233 0.286616 0.958045i \(-0.407469\pi\)
0.286616 + 0.958045i \(0.407469\pi\)
\(594\) 5.00013 0.205158
\(595\) 14.5678 0.597223
\(596\) −20.3529 −0.833688
\(597\) −42.7336 −1.74897
\(598\) −0.989411 −0.0404600
\(599\) 5.68372 0.232230 0.116115 0.993236i \(-0.462956\pi\)
0.116115 + 0.993236i \(0.462956\pi\)
\(600\) −10.1693 −0.415158
\(601\) 35.5850 1.45154 0.725771 0.687936i \(-0.241483\pi\)
0.725771 + 0.687936i \(0.241483\pi\)
\(602\) 1.59843 0.0651473
\(603\) −66.1442 −2.69360
\(604\) −9.06602 −0.368891
\(605\) −31.0565 −1.26263
\(606\) 6.06911 0.246541
\(607\) −23.7847 −0.965392 −0.482696 0.875788i \(-0.660342\pi\)
−0.482696 + 0.875788i \(0.660342\pi\)
\(608\) 3.24983 0.131798
\(609\) 24.4056 0.988963
\(610\) −30.3444 −1.22861
\(611\) −15.1871 −0.614404
\(612\) −22.4715 −0.908358
\(613\) 43.5242 1.75793 0.878963 0.476891i \(-0.158236\pi\)
0.878963 + 0.476891i \(0.158236\pi\)
\(614\) −24.2336 −0.977990
\(615\) 54.8939 2.21353
\(616\) 0.692681 0.0279089
\(617\) 2.17130 0.0874131 0.0437066 0.999044i \(-0.486083\pi\)
0.0437066 + 0.999044i \(0.486083\pi\)
\(618\) 0.177954 0.00715836
\(619\) 36.8726 1.48204 0.741018 0.671485i \(-0.234343\pi\)
0.741018 + 0.671485i \(0.234343\pi\)
\(620\) 29.9106 1.20124
\(621\) −1.57901 −0.0633634
\(622\) −19.3580 −0.776186
\(623\) −13.5317 −0.542137
\(624\) 19.8601 0.795039
\(625\) −30.5768 −1.22307
\(626\) 6.42902 0.256955
\(627\) 4.80863 0.192038
\(628\) −0.527734 −0.0210589
\(629\) 2.12246 0.0846282
\(630\) −26.3816 −1.05107
\(631\) 32.6365 1.29924 0.649619 0.760260i \(-0.274928\pi\)
0.649619 + 0.760260i \(0.274928\pi\)
\(632\) 1.79926 0.0715707
\(633\) 53.0063 2.10681
\(634\) −2.70862 −0.107573
\(635\) 30.5613 1.21279
\(636\) −2.32526 −0.0922027
\(637\) 32.0642 1.27043
\(638\) −2.68550 −0.106320
\(639\) −43.1897 −1.70856
\(640\) 2.88453 0.114021
\(641\) −0.435366 −0.0171959 −0.00859796 0.999963i \(-0.502737\pi\)
−0.00859796 + 0.999963i \(0.502737\pi\)
\(642\) 0.755029 0.0297986
\(643\) −13.3956 −0.528272 −0.264136 0.964485i \(-0.585087\pi\)
−0.264136 + 0.964485i \(0.585087\pi\)
\(644\) −0.218744 −0.00861973
\(645\) 9.84911 0.387808
\(646\) −11.4478 −0.450409
\(647\) −27.7325 −1.09028 −0.545139 0.838346i \(-0.683523\pi\)
−0.545139 + 0.838346i \(0.683523\pi\)
\(648\) 12.5571 0.493289
\(649\) −1.62266 −0.0636949
\(650\) −21.5329 −0.844588
\(651\) 45.5294 1.78444
\(652\) 0.634234 0.0248385
\(653\) 3.10386 0.121463 0.0607317 0.998154i \(-0.480657\pi\)
0.0607317 + 0.998154i \(0.480657\pi\)
\(654\) −23.8482 −0.932537
\(655\) −9.01500 −0.352245
\(656\) −6.21391 −0.242612
\(657\) 31.1927 1.21694
\(658\) −3.35765 −0.130895
\(659\) −8.19558 −0.319254 −0.159627 0.987177i \(-0.551029\pi\)
−0.159627 + 0.987177i \(0.551029\pi\)
\(660\) 4.26811 0.166136
\(661\) 17.5660 0.683238 0.341619 0.939838i \(-0.389025\pi\)
0.341619 + 0.939838i \(0.389025\pi\)
\(662\) −3.96763 −0.154206
\(663\) −69.9590 −2.71698
\(664\) 9.67161 0.375331
\(665\) −13.4398 −0.521172
\(666\) −3.84368 −0.148940
\(667\) 0.848062 0.0328371
\(668\) 8.12754 0.314464
\(669\) −72.1395 −2.78908
\(670\) −29.9086 −1.15547
\(671\) 5.08254 0.196209
\(672\) 4.39077 0.169378
\(673\) −7.60681 −0.293221 −0.146610 0.989194i \(-0.546836\pi\)
−0.146610 + 0.989194i \(0.546836\pi\)
\(674\) −23.9750 −0.923484
\(675\) −34.3645 −1.32269
\(676\) 29.0527 1.11741
\(677\) 11.4832 0.441334 0.220667 0.975349i \(-0.429177\pi\)
0.220667 + 0.975349i \(0.429177\pi\)
\(678\) 60.5829 2.32667
\(679\) 16.1705 0.620567
\(680\) −10.1610 −0.389658
\(681\) 14.3151 0.548556
\(682\) −5.00988 −0.191838
\(683\) −6.98761 −0.267374 −0.133687 0.991024i \(-0.542682\pi\)
−0.133687 + 0.991024i \(0.542682\pi\)
\(684\) 20.7315 0.792688
\(685\) −37.8465 −1.44604
\(686\) 17.1248 0.653828
\(687\) −6.67998 −0.254857
\(688\) −1.11490 −0.0425053
\(689\) −4.92362 −0.187575
\(690\) −1.34784 −0.0513115
\(691\) 3.36301 0.127935 0.0639674 0.997952i \(-0.479625\pi\)
0.0639674 + 0.997952i \(0.479625\pi\)
\(692\) 13.2779 0.504752
\(693\) 4.41879 0.167856
\(694\) −8.51663 −0.323287
\(695\) 11.4274 0.433465
\(696\) −17.0228 −0.645249
\(697\) 21.8891 0.829109
\(698\) 31.2865 1.18421
\(699\) 27.5809 1.04321
\(700\) −4.76060 −0.179934
\(701\) 10.5048 0.396760 0.198380 0.980125i \(-0.436432\pi\)
0.198380 + 0.980125i \(0.436432\pi\)
\(702\) 67.1122 2.53299
\(703\) −1.95811 −0.0738516
\(704\) −0.483144 −0.0182092
\(705\) −20.6889 −0.779188
\(706\) 5.18757 0.195237
\(707\) 2.84117 0.106853
\(708\) −10.2857 −0.386561
\(709\) −17.2849 −0.649148 −0.324574 0.945860i \(-0.605221\pi\)
−0.324574 + 0.945860i \(0.605221\pi\)
\(710\) −19.5292 −0.732919
\(711\) 11.4779 0.430456
\(712\) 9.43835 0.353717
\(713\) 1.58209 0.0592497
\(714\) −15.4669 −0.578835
\(715\) 9.03750 0.337983
\(716\) −17.6305 −0.658881
\(717\) −4.52138 −0.168854
\(718\) 9.25641 0.345446
\(719\) −36.3531 −1.35574 −0.677871 0.735181i \(-0.737097\pi\)
−0.677871 + 0.735181i \(0.737097\pi\)
\(720\) 18.4011 0.685770
\(721\) 0.0833069 0.00310251
\(722\) −8.43861 −0.314053
\(723\) −10.6876 −0.397477
\(724\) −8.45797 −0.314338
\(725\) 18.4566 0.685462
\(726\) 32.9732 1.22375
\(727\) −9.08532 −0.336956 −0.168478 0.985705i \(-0.553885\pi\)
−0.168478 + 0.985705i \(0.553885\pi\)
\(728\) 9.29723 0.344578
\(729\) −14.9797 −0.554803
\(730\) 14.1045 0.522031
\(731\) 3.92736 0.145259
\(732\) 32.2172 1.19078
\(733\) −0.0796254 −0.00294103 −0.00147052 0.999999i \(-0.500468\pi\)
−0.00147052 + 0.999999i \(0.500468\pi\)
\(734\) 21.8879 0.807896
\(735\) 43.6800 1.61116
\(736\) 0.152574 0.00562394
\(737\) 5.00955 0.184529
\(738\) −39.6401 −1.45917
\(739\) −12.0777 −0.444286 −0.222143 0.975014i \(-0.571305\pi\)
−0.222143 + 0.975014i \(0.571305\pi\)
\(740\) −1.73801 −0.0638905
\(741\) 64.5418 2.37100
\(742\) −1.08854 −0.0399616
\(743\) −3.18574 −0.116873 −0.0584367 0.998291i \(-0.518612\pi\)
−0.0584367 + 0.998291i \(0.518612\pi\)
\(744\) −31.7567 −1.16426
\(745\) −58.7086 −2.15092
\(746\) −11.6751 −0.427455
\(747\) 61.6976 2.25740
\(748\) 1.70192 0.0622284
\(749\) 0.353457 0.0129150
\(750\) 14.8367 0.541759
\(751\) 33.9820 1.24002 0.620010 0.784594i \(-0.287129\pi\)
0.620010 + 0.784594i \(0.287129\pi\)
\(752\) 2.34195 0.0854022
\(753\) −65.7667 −2.39667
\(754\) −36.0450 −1.31268
\(755\) −26.1512 −0.951739
\(756\) 14.8375 0.539636
\(757\) 1.88213 0.0684070 0.0342035 0.999415i \(-0.489111\pi\)
0.0342035 + 0.999415i \(0.489111\pi\)
\(758\) 11.9545 0.434208
\(759\) 0.225757 0.00819445
\(760\) 9.37423 0.340039
\(761\) 20.4575 0.741585 0.370793 0.928716i \(-0.379086\pi\)
0.370793 + 0.928716i \(0.379086\pi\)
\(762\) −32.4475 −1.17545
\(763\) −11.1642 −0.404171
\(764\) 0.369311 0.0133612
\(765\) −64.8198 −2.34356
\(766\) −28.9705 −1.04675
\(767\) −21.7795 −0.786411
\(768\) −3.06256 −0.110510
\(769\) 41.9889 1.51416 0.757078 0.653324i \(-0.226626\pi\)
0.757078 + 0.653324i \(0.226626\pi\)
\(770\) 1.99806 0.0720051
\(771\) 47.7155 1.71843
\(772\) −21.6489 −0.779162
\(773\) −31.9065 −1.14760 −0.573798 0.818997i \(-0.694530\pi\)
−0.573798 + 0.818997i \(0.694530\pi\)
\(774\) −7.11226 −0.255645
\(775\) 34.4315 1.23681
\(776\) −11.2789 −0.404889
\(777\) −2.64556 −0.0949091
\(778\) 2.14809 0.0770129
\(779\) −20.1941 −0.723530
\(780\) 57.2870 2.05120
\(781\) 3.27105 0.117047
\(782\) −0.537456 −0.0192194
\(783\) −57.5245 −2.05576
\(784\) −4.94452 −0.176590
\(785\) −1.52226 −0.0543319
\(786\) 9.57138 0.341400
\(787\) −9.58981 −0.341840 −0.170920 0.985285i \(-0.554674\pi\)
−0.170920 + 0.985285i \(0.554674\pi\)
\(788\) 17.4477 0.621548
\(789\) 81.3515 2.89619
\(790\) 5.19002 0.184652
\(791\) 28.3611 1.00840
\(792\) −3.08210 −0.109518
\(793\) 68.2183 2.42250
\(794\) 23.4400 0.831854
\(795\) −6.70729 −0.237883
\(796\) 13.9536 0.494571
\(797\) 36.9116 1.30748 0.653738 0.756721i \(-0.273200\pi\)
0.653738 + 0.756721i \(0.273200\pi\)
\(798\) 14.2693 0.505126
\(799\) −8.24975 −0.291855
\(800\) 3.32051 0.117398
\(801\) 60.2096 2.12740
\(802\) −13.8339 −0.488493
\(803\) −2.36243 −0.0833685
\(804\) 31.7545 1.11990
\(805\) −0.630974 −0.0222389
\(806\) −67.2431 −2.36854
\(807\) −31.7733 −1.11847
\(808\) −1.98171 −0.0697164
\(809\) 21.3535 0.750748 0.375374 0.926873i \(-0.377514\pi\)
0.375374 + 0.926873i \(0.377514\pi\)
\(810\) 36.2213 1.27269
\(811\) 20.3483 0.714525 0.357262 0.934004i \(-0.383710\pi\)
0.357262 + 0.934004i \(0.383710\pi\)
\(812\) −7.96902 −0.279658
\(813\) 62.6482 2.19717
\(814\) 0.291108 0.0102033
\(815\) 1.82947 0.0640834
\(816\) 10.7882 0.377661
\(817\) −3.62325 −0.126761
\(818\) −17.9269 −0.626799
\(819\) 59.3094 2.07244
\(820\) −17.9242 −0.625940
\(821\) 14.8510 0.518303 0.259152 0.965837i \(-0.416557\pi\)
0.259152 + 0.965837i \(0.416557\pi\)
\(822\) 40.1823 1.40152
\(823\) 52.4416 1.82800 0.913999 0.405716i \(-0.132978\pi\)
0.913999 + 0.405716i \(0.132978\pi\)
\(824\) −0.0581064 −0.00202423
\(825\) 4.91321 0.171056
\(826\) −4.81512 −0.167540
\(827\) −13.4120 −0.466382 −0.233191 0.972431i \(-0.574917\pi\)
−0.233191 + 0.972431i \(0.574917\pi\)
\(828\) 0.973306 0.0338247
\(829\) 19.7377 0.685519 0.342759 0.939423i \(-0.388638\pi\)
0.342759 + 0.939423i \(0.388638\pi\)
\(830\) 27.8980 0.968355
\(831\) 50.3994 1.74834
\(832\) −6.48480 −0.224820
\(833\) 17.4175 0.603482
\(834\) −12.1326 −0.420119
\(835\) 23.4441 0.811317
\(836\) −1.57014 −0.0543043
\(837\) −107.314 −3.70931
\(838\) −25.0523 −0.865417
\(839\) 26.7881 0.924829 0.462415 0.886664i \(-0.346983\pi\)
0.462415 + 0.886664i \(0.346983\pi\)
\(840\) 12.6653 0.436995
\(841\) 1.89553 0.0653632
\(842\) 2.47187 0.0851863
\(843\) −51.9913 −1.79068
\(844\) −17.3079 −0.595762
\(845\) 83.8033 2.88292
\(846\) 14.9399 0.513644
\(847\) 15.4360 0.530387
\(848\) 0.759256 0.0260729
\(849\) 100.965 3.46512
\(850\) −11.6968 −0.401198
\(851\) −0.0919300 −0.00315132
\(852\) 20.7345 0.710353
\(853\) −1.78361 −0.0610697 −0.0305349 0.999534i \(-0.509721\pi\)
−0.0305349 + 0.999534i \(0.509721\pi\)
\(854\) 15.0821 0.516098
\(855\) 59.8005 2.04514
\(856\) −0.246536 −0.00842641
\(857\) −24.3764 −0.832683 −0.416342 0.909208i \(-0.636688\pi\)
−0.416342 + 0.909208i \(0.636688\pi\)
\(858\) −9.59528 −0.327577
\(859\) −23.0734 −0.787256 −0.393628 0.919270i \(-0.628780\pi\)
−0.393628 + 0.919270i \(0.628780\pi\)
\(860\) −3.21598 −0.109664
\(861\) −27.2839 −0.929831
\(862\) −32.4551 −1.10542
\(863\) −24.5020 −0.834057 −0.417028 0.908893i \(-0.636928\pi\)
−0.417028 + 0.908893i \(0.636928\pi\)
\(864\) −10.3491 −0.352085
\(865\) 38.3006 1.30226
\(866\) 6.27422 0.213207
\(867\) 14.0612 0.477542
\(868\) −14.8665 −0.504601
\(869\) −0.869301 −0.0294890
\(870\) −49.1029 −1.66474
\(871\) 67.2386 2.27829
\(872\) 7.78701 0.263701
\(873\) −71.9509 −2.43517
\(874\) 0.495839 0.0167720
\(875\) 6.94559 0.234804
\(876\) −14.9750 −0.505959
\(877\) 19.0444 0.643083 0.321542 0.946895i \(-0.395799\pi\)
0.321542 + 0.946895i \(0.395799\pi\)
\(878\) 17.2177 0.581070
\(879\) −2.90315 −0.0979207
\(880\) −1.39364 −0.0469797
\(881\) −6.20431 −0.209028 −0.104514 0.994523i \(-0.533329\pi\)
−0.104514 + 0.994523i \(0.533329\pi\)
\(882\) −31.5423 −1.06209
\(883\) 38.9149 1.30959 0.654796 0.755806i \(-0.272755\pi\)
0.654796 + 0.755806i \(0.272755\pi\)
\(884\) 22.8433 0.768305
\(885\) −29.6695 −0.997328
\(886\) 24.2847 0.815861
\(887\) −7.63124 −0.256232 −0.128116 0.991759i \(-0.540893\pi\)
−0.128116 + 0.991759i \(0.540893\pi\)
\(888\) 1.84528 0.0619234
\(889\) −15.1899 −0.509452
\(890\) 27.2252 0.912591
\(891\) −6.06689 −0.203248
\(892\) 23.5553 0.788691
\(893\) 7.61094 0.254690
\(894\) 62.3320 2.08469
\(895\) −50.8556 −1.69992
\(896\) −1.43370 −0.0478964
\(897\) 3.03013 0.101173
\(898\) −33.1697 −1.10689
\(899\) 57.6366 1.92229
\(900\) 21.1824 0.706079
\(901\) −2.67455 −0.0891022
\(902\) 3.00221 0.0999628
\(903\) −4.89529 −0.162905
\(904\) −19.7818 −0.657933
\(905\) −24.3973 −0.810992
\(906\) 27.7652 0.922437
\(907\) 28.3606 0.941699 0.470849 0.882214i \(-0.343948\pi\)
0.470849 + 0.882214i \(0.343948\pi\)
\(908\) −4.67424 −0.155120
\(909\) −12.6418 −0.419303
\(910\) 26.8181 0.889013
\(911\) −24.9994 −0.828269 −0.414134 0.910216i \(-0.635916\pi\)
−0.414134 + 0.910216i \(0.635916\pi\)
\(912\) −9.95278 −0.329570
\(913\) −4.67278 −0.154646
\(914\) −28.0312 −0.927189
\(915\) 92.9315 3.07222
\(916\) 2.18118 0.0720682
\(917\) 4.48072 0.147966
\(918\) 36.4559 1.20322
\(919\) 3.90387 0.128777 0.0643883 0.997925i \(-0.479490\pi\)
0.0643883 + 0.997925i \(0.479490\pi\)
\(920\) 0.440104 0.0145098
\(921\) 74.2169 2.44553
\(922\) 0.802123 0.0264165
\(923\) 43.9043 1.44513
\(924\) −2.12138 −0.0697881
\(925\) −2.00070 −0.0657826
\(926\) 12.1613 0.399644
\(927\) −0.370675 −0.0121746
\(928\) 5.55838 0.182463
\(929\) −31.1093 −1.02066 −0.510331 0.859978i \(-0.670477\pi\)
−0.510331 + 0.859978i \(0.670477\pi\)
\(930\) −91.6030 −3.00378
\(931\) −16.0688 −0.526635
\(932\) −9.00586 −0.294997
\(933\) 59.2850 1.94090
\(934\) −26.4050 −0.863997
\(935\) 4.90924 0.160549
\(936\) −41.3682 −1.35216
\(937\) −58.7300 −1.91862 −0.959312 0.282347i \(-0.908887\pi\)
−0.959312 + 0.282347i \(0.908887\pi\)
\(938\) 14.8655 0.485375
\(939\) −19.6892 −0.642534
\(940\) 6.75543 0.220338
\(941\) 22.6950 0.739837 0.369918 0.929064i \(-0.379386\pi\)
0.369918 + 0.929064i \(0.379386\pi\)
\(942\) 1.61621 0.0526591
\(943\) −0.948079 −0.0308737
\(944\) 3.35854 0.109311
\(945\) 42.7993 1.39226
\(946\) 0.538660 0.0175133
\(947\) 35.7710 1.16240 0.581201 0.813760i \(-0.302583\pi\)
0.581201 + 0.813760i \(0.302583\pi\)
\(948\) −5.51033 −0.178967
\(949\) −31.7088 −1.02931
\(950\) 10.7911 0.350109
\(951\) 8.29531 0.268994
\(952\) 5.05033 0.163682
\(953\) 44.3891 1.43790 0.718952 0.695060i \(-0.244622\pi\)
0.718952 + 0.695060i \(0.244622\pi\)
\(954\) 4.84348 0.156814
\(955\) 1.06529 0.0344719
\(956\) 1.47634 0.0477483
\(957\) 8.22448 0.265860
\(958\) −4.98181 −0.160955
\(959\) 18.8108 0.607433
\(960\) −8.83403 −0.285117
\(961\) 76.5230 2.46848
\(962\) 3.90728 0.125976
\(963\) −1.57271 −0.0506800
\(964\) 3.48977 0.112398
\(965\) −62.4470 −2.01024
\(966\) 0.669917 0.0215542
\(967\) 28.6046 0.919863 0.459931 0.887954i \(-0.347874\pi\)
0.459931 + 0.887954i \(0.347874\pi\)
\(968\) −10.7666 −0.346051
\(969\) 35.0596 1.12628
\(970\) −32.5343 −1.04461
\(971\) −1.82156 −0.0584565 −0.0292283 0.999573i \(-0.509305\pi\)
−0.0292283 + 0.999573i \(0.509305\pi\)
\(972\) −7.40937 −0.237656
\(973\) −5.67974 −0.182084
\(974\) −9.95116 −0.318856
\(975\) 65.9456 2.11195
\(976\) −10.5197 −0.336728
\(977\) 45.1289 1.44380 0.721901 0.691996i \(-0.243269\pi\)
0.721901 + 0.691996i \(0.243269\pi\)
\(978\) −1.94238 −0.0621104
\(979\) −4.56008 −0.145741
\(980\) −14.2626 −0.455602
\(981\) 49.6753 1.58601
\(982\) −2.81316 −0.0897716
\(983\) 27.5403 0.878399 0.439200 0.898389i \(-0.355262\pi\)
0.439200 + 0.898389i \(0.355262\pi\)
\(984\) 19.0304 0.606668
\(985\) 50.3283 1.60359
\(986\) −19.5799 −0.623552
\(987\) 10.2830 0.327311
\(988\) −21.0745 −0.670469
\(989\) −0.170105 −0.00540903
\(990\) −8.89040 −0.282556
\(991\) 59.2415 1.88187 0.940934 0.338591i \(-0.109950\pi\)
0.940934 + 0.338591i \(0.109950\pi\)
\(992\) 10.3693 0.329227
\(993\) 12.1511 0.385604
\(994\) 9.70660 0.307875
\(995\) 40.2495 1.27599
\(996\) −29.6198 −0.938541
\(997\) 48.3638 1.53170 0.765849 0.643021i \(-0.222319\pi\)
0.765849 + 0.643021i \(0.222319\pi\)
\(998\) −8.28153 −0.262147
\(999\) 6.23565 0.197287
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 \(a_p\))