Properties

Label 8041.2.a.g.1.15
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 1
Dimension 69
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.87945 q^{2} -2.61165 q^{3} +1.53233 q^{4} -1.23543 q^{5} +4.90847 q^{6} -3.71692 q^{7} +0.878969 q^{8} +3.82074 q^{9} +O(q^{10})\) \(q-1.87945 q^{2} -2.61165 q^{3} +1.53233 q^{4} -1.23543 q^{5} +4.90847 q^{6} -3.71692 q^{7} +0.878969 q^{8} +3.82074 q^{9} +2.32194 q^{10} -1.00000 q^{11} -4.00191 q^{12} -4.16760 q^{13} +6.98576 q^{14} +3.22653 q^{15} -4.71663 q^{16} +1.00000 q^{17} -7.18088 q^{18} -5.54379 q^{19} -1.89309 q^{20} +9.70731 q^{21} +1.87945 q^{22} -0.942351 q^{23} -2.29556 q^{24} -3.47370 q^{25} +7.83280 q^{26} -2.14348 q^{27} -5.69553 q^{28} -2.45710 q^{29} -6.06409 q^{30} -3.17078 q^{31} +7.10672 q^{32} +2.61165 q^{33} -1.87945 q^{34} +4.59201 q^{35} +5.85461 q^{36} +9.01121 q^{37} +10.4193 q^{38} +10.8843 q^{39} -1.08591 q^{40} +1.96599 q^{41} -18.2444 q^{42} +1.00000 q^{43} -1.53233 q^{44} -4.72027 q^{45} +1.77110 q^{46} -4.72284 q^{47} +12.3182 q^{48} +6.81550 q^{49} +6.52864 q^{50} -2.61165 q^{51} -6.38613 q^{52} -7.71299 q^{53} +4.02855 q^{54} +1.23543 q^{55} -3.26706 q^{56} +14.4785 q^{57} +4.61799 q^{58} +9.28151 q^{59} +4.94409 q^{60} -14.6966 q^{61} +5.95932 q^{62} -14.2014 q^{63} -3.92346 q^{64} +5.14880 q^{65} -4.90847 q^{66} -10.9358 q^{67} +1.53233 q^{68} +2.46109 q^{69} -8.63045 q^{70} -1.56038 q^{71} +3.35831 q^{72} +0.378831 q^{73} -16.9361 q^{74} +9.07211 q^{75} -8.49490 q^{76} +3.71692 q^{77} -20.4565 q^{78} -4.75181 q^{79} +5.82709 q^{80} -5.86419 q^{81} -3.69497 q^{82} +17.6463 q^{83} +14.8748 q^{84} -1.23543 q^{85} -1.87945 q^{86} +6.41709 q^{87} -0.878969 q^{88} -1.26378 q^{89} +8.87150 q^{90} +15.4907 q^{91} -1.44399 q^{92} +8.28098 q^{93} +8.87633 q^{94} +6.84899 q^{95} -18.5603 q^{96} +4.07807 q^{97} -12.8094 q^{98} -3.82074 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} + O(q^{10}) \) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} - q^{10} - 69q^{11} - 3q^{12} - 28q^{13} - 15q^{14} - 45q^{15} + 53q^{16} + 69q^{17} - 17q^{18} - 32q^{19} - 21q^{20} - 38q^{21} + 11q^{22} - 41q^{23} - 11q^{24} + 67q^{25} - 6q^{26} - 3q^{27} - 21q^{28} - 22q^{29} - 22q^{30} - 27q^{31} - 87q^{32} + 3q^{33} - 11q^{34} - 44q^{35} + 59q^{36} + 24q^{37} - 22q^{38} - 59q^{39} + q^{40} - 43q^{41} - 15q^{42} + 69q^{43} - 65q^{44} - 12q^{45} - 21q^{46} - 99q^{47} + 2q^{48} + 64q^{49} - 78q^{50} - 3q^{51} - 57q^{52} - 50q^{53} + 20q^{54} + 6q^{55} - 59q^{56} - 15q^{57} + 22q^{58} - 82q^{59} - 86q^{60} - 24q^{61} + 15q^{62} - 63q^{63} + 63q^{64} - 23q^{65} + 10q^{66} - 54q^{67} + 65q^{68} + 36q^{69} + 9q^{70} - 128q^{71} - 69q^{72} + 2q^{73} - 58q^{74} - 31q^{75} - 76q^{76} + 11q^{77} - 19q^{78} - 43q^{79} - 19q^{80} + 49q^{81} - 2q^{82} - 62q^{83} - 82q^{84} - 6q^{85} - 11q^{86} - 62q^{87} + 33q^{88} - 49q^{89} - 37q^{90} - 2q^{91} - 96q^{92} - 29q^{93} - 75q^{94} - 133q^{95} - 86q^{96} + 5q^{97} - 72q^{98} - 56q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.87945 −1.32897 −0.664485 0.747301i \(-0.731349\pi\)
−0.664485 + 0.747301i \(0.731349\pi\)
\(3\) −2.61165 −1.50784 −0.753920 0.656967i \(-0.771839\pi\)
−0.753920 + 0.656967i \(0.771839\pi\)
\(4\) 1.53233 0.766163
\(5\) −1.23543 −0.552503 −0.276252 0.961085i \(-0.589092\pi\)
−0.276252 + 0.961085i \(0.589092\pi\)
\(6\) 4.90847 2.00387
\(7\) −3.71692 −1.40486 −0.702432 0.711751i \(-0.747902\pi\)
−0.702432 + 0.711751i \(0.747902\pi\)
\(8\) 0.878969 0.310762
\(9\) 3.82074 1.27358
\(10\) 2.32194 0.734260
\(11\) −1.00000 −0.301511
\(12\) −4.00191 −1.15525
\(13\) −4.16760 −1.15589 −0.577943 0.816077i \(-0.696144\pi\)
−0.577943 + 0.816077i \(0.696144\pi\)
\(14\) 6.98576 1.86702
\(15\) 3.22653 0.833086
\(16\) −4.71663 −1.17916
\(17\) 1.00000 0.242536
\(18\) −7.18088 −1.69255
\(19\) −5.54379 −1.27183 −0.635916 0.771758i \(-0.719378\pi\)
−0.635916 + 0.771758i \(0.719378\pi\)
\(20\) −1.89309 −0.423307
\(21\) 9.70731 2.11831
\(22\) 1.87945 0.400700
\(23\) −0.942351 −0.196494 −0.0982468 0.995162i \(-0.531323\pi\)
−0.0982468 + 0.995162i \(0.531323\pi\)
\(24\) −2.29556 −0.468580
\(25\) −3.47370 −0.694740
\(26\) 7.83280 1.53614
\(27\) −2.14348 −0.412512
\(28\) −5.69553 −1.07635
\(29\) −2.45710 −0.456271 −0.228136 0.973629i \(-0.573263\pi\)
−0.228136 + 0.973629i \(0.573263\pi\)
\(30\) −6.06409 −1.10715
\(31\) −3.17078 −0.569489 −0.284745 0.958603i \(-0.591909\pi\)
−0.284745 + 0.958603i \(0.591909\pi\)
\(32\) 7.10672 1.25630
\(33\) 2.61165 0.454631
\(34\) −1.87945 −0.322323
\(35\) 4.59201 0.776192
\(36\) 5.85461 0.975769
\(37\) 9.01121 1.48143 0.740717 0.671818i \(-0.234486\pi\)
0.740717 + 0.671818i \(0.234486\pi\)
\(38\) 10.4193 1.69023
\(39\) 10.8843 1.74289
\(40\) −1.08591 −0.171697
\(41\) 1.96599 0.307036 0.153518 0.988146i \(-0.450940\pi\)
0.153518 + 0.988146i \(0.450940\pi\)
\(42\) −18.2444 −2.81517
\(43\) 1.00000 0.152499
\(44\) −1.53233 −0.231007
\(45\) −4.72027 −0.703656
\(46\) 1.77110 0.261134
\(47\) −4.72284 −0.688897 −0.344448 0.938805i \(-0.611934\pi\)
−0.344448 + 0.938805i \(0.611934\pi\)
\(48\) 12.3182 1.77798
\(49\) 6.81550 0.973642
\(50\) 6.52864 0.923289
\(51\) −2.61165 −0.365705
\(52\) −6.38613 −0.885597
\(53\) −7.71299 −1.05946 −0.529730 0.848166i \(-0.677707\pi\)
−0.529730 + 0.848166i \(0.677707\pi\)
\(54\) 4.02855 0.548217
\(55\) 1.23543 0.166586
\(56\) −3.26706 −0.436579
\(57\) 14.4785 1.91772
\(58\) 4.61799 0.606371
\(59\) 9.28151 1.20835 0.604175 0.796852i \(-0.293503\pi\)
0.604175 + 0.796852i \(0.293503\pi\)
\(60\) 4.94409 0.638280
\(61\) −14.6966 −1.88171 −0.940855 0.338809i \(-0.889976\pi\)
−0.940855 + 0.338809i \(0.889976\pi\)
\(62\) 5.95932 0.756834
\(63\) −14.2014 −1.78920
\(64\) −3.92346 −0.490432
\(65\) 5.14880 0.638630
\(66\) −4.90847 −0.604191
\(67\) −10.9358 −1.33602 −0.668010 0.744152i \(-0.732854\pi\)
−0.668010 + 0.744152i \(0.732854\pi\)
\(68\) 1.53233 0.185822
\(69\) 2.46109 0.296281
\(70\) −8.63045 −1.03154
\(71\) −1.56038 −0.185184 −0.0925918 0.995704i \(-0.529515\pi\)
−0.0925918 + 0.995704i \(0.529515\pi\)
\(72\) 3.35831 0.395780
\(73\) 0.378831 0.0443388 0.0221694 0.999754i \(-0.492943\pi\)
0.0221694 + 0.999754i \(0.492943\pi\)
\(74\) −16.9361 −1.96878
\(75\) 9.07211 1.04756
\(76\) −8.49490 −0.974431
\(77\) 3.71692 0.423582
\(78\) −20.4565 −2.31625
\(79\) −4.75181 −0.534620 −0.267310 0.963611i \(-0.586135\pi\)
−0.267310 + 0.963611i \(0.586135\pi\)
\(80\) 5.82709 0.651488
\(81\) −5.86419 −0.651576
\(82\) −3.69497 −0.408042
\(83\) 17.6463 1.93693 0.968466 0.249147i \(-0.0801501\pi\)
0.968466 + 0.249147i \(0.0801501\pi\)
\(84\) 14.8748 1.62297
\(85\) −1.23543 −0.134002
\(86\) −1.87945 −0.202666
\(87\) 6.41709 0.687984
\(88\) −0.878969 −0.0936984
\(89\) −1.26378 −0.133960 −0.0669802 0.997754i \(-0.521336\pi\)
−0.0669802 + 0.997754i \(0.521336\pi\)
\(90\) 8.87150 0.935138
\(91\) 15.4907 1.62386
\(92\) −1.44399 −0.150546
\(93\) 8.28098 0.858698
\(94\) 8.87633 0.915524
\(95\) 6.84899 0.702692
\(96\) −18.5603 −1.89430
\(97\) 4.07807 0.414065 0.207033 0.978334i \(-0.433619\pi\)
0.207033 + 0.978334i \(0.433619\pi\)
\(98\) −12.8094 −1.29394
\(99\) −3.82074 −0.383998
\(100\) −5.32284 −0.532284
\(101\) −4.19158 −0.417078 −0.208539 0.978014i \(-0.566871\pi\)
−0.208539 + 0.978014i \(0.566871\pi\)
\(102\) 4.90847 0.486011
\(103\) 6.79926 0.669951 0.334975 0.942227i \(-0.391272\pi\)
0.334975 + 0.942227i \(0.391272\pi\)
\(104\) −3.66319 −0.359206
\(105\) −11.9927 −1.17037
\(106\) 14.4962 1.40799
\(107\) 5.08133 0.491230 0.245615 0.969367i \(-0.421010\pi\)
0.245615 + 0.969367i \(0.421010\pi\)
\(108\) −3.28451 −0.316052
\(109\) −12.7028 −1.21671 −0.608353 0.793666i \(-0.708170\pi\)
−0.608353 + 0.793666i \(0.708170\pi\)
\(110\) −2.32194 −0.221388
\(111\) −23.5342 −2.23376
\(112\) 17.5313 1.65656
\(113\) −1.29250 −0.121588 −0.0607941 0.998150i \(-0.519363\pi\)
−0.0607941 + 0.998150i \(0.519363\pi\)
\(114\) −27.2115 −2.54859
\(115\) 1.16421 0.108563
\(116\) −3.76507 −0.349578
\(117\) −15.9233 −1.47211
\(118\) −17.4441 −1.60586
\(119\) −3.71692 −0.340730
\(120\) 2.83602 0.258892
\(121\) 1.00000 0.0909091
\(122\) 27.6216 2.50074
\(123\) −5.13448 −0.462961
\(124\) −4.85867 −0.436322
\(125\) 10.4687 0.936349
\(126\) 26.6907 2.37780
\(127\) −15.5239 −1.37752 −0.688762 0.724987i \(-0.741846\pi\)
−0.688762 + 0.724987i \(0.741846\pi\)
\(128\) −6.83951 −0.604533
\(129\) −2.61165 −0.229943
\(130\) −9.67691 −0.848721
\(131\) −0.248366 −0.0216999 −0.0108499 0.999941i \(-0.503454\pi\)
−0.0108499 + 0.999941i \(0.503454\pi\)
\(132\) 4.00191 0.348321
\(133\) 20.6058 1.78675
\(134\) 20.5533 1.77553
\(135\) 2.64813 0.227914
\(136\) 0.878969 0.0753710
\(137\) 10.0029 0.854603 0.427302 0.904109i \(-0.359464\pi\)
0.427302 + 0.904109i \(0.359464\pi\)
\(138\) −4.62550 −0.393749
\(139\) −20.1663 −1.71048 −0.855241 0.518231i \(-0.826591\pi\)
−0.855241 + 0.518231i \(0.826591\pi\)
\(140\) 7.03646 0.594689
\(141\) 12.3344 1.03875
\(142\) 2.93266 0.246104
\(143\) 4.16760 0.348513
\(144\) −18.0210 −1.50175
\(145\) 3.03558 0.252091
\(146\) −0.711993 −0.0589249
\(147\) −17.7997 −1.46810
\(148\) 13.8081 1.13502
\(149\) 22.7000 1.85966 0.929830 0.367989i \(-0.119954\pi\)
0.929830 + 0.367989i \(0.119954\pi\)
\(150\) −17.0506 −1.39217
\(151\) 15.4469 1.25705 0.628524 0.777790i \(-0.283659\pi\)
0.628524 + 0.777790i \(0.283659\pi\)
\(152\) −4.87282 −0.395238
\(153\) 3.82074 0.308888
\(154\) −6.98576 −0.562929
\(155\) 3.91729 0.314645
\(156\) 16.6784 1.33534
\(157\) 13.6005 1.08544 0.542719 0.839914i \(-0.317395\pi\)
0.542719 + 0.839914i \(0.317395\pi\)
\(158\) 8.93077 0.710494
\(159\) 20.1437 1.59750
\(160\) −8.77989 −0.694111
\(161\) 3.50264 0.276047
\(162\) 11.0214 0.865926
\(163\) −6.91743 −0.541815 −0.270907 0.962605i \(-0.587324\pi\)
−0.270907 + 0.962605i \(0.587324\pi\)
\(164\) 3.01254 0.235240
\(165\) −3.22653 −0.251185
\(166\) −33.1653 −2.57413
\(167\) 4.95994 0.383811 0.191906 0.981413i \(-0.438533\pi\)
0.191906 + 0.981413i \(0.438533\pi\)
\(168\) 8.53242 0.658291
\(169\) 4.36892 0.336071
\(170\) 2.32194 0.178084
\(171\) −21.1814 −1.61978
\(172\) 1.53233 0.116839
\(173\) 20.9972 1.59639 0.798193 0.602402i \(-0.205789\pi\)
0.798193 + 0.602402i \(0.205789\pi\)
\(174\) −12.0606 −0.914310
\(175\) 12.9115 0.976016
\(176\) 4.71663 0.355529
\(177\) −24.2401 −1.82200
\(178\) 2.37521 0.178030
\(179\) −2.74331 −0.205045 −0.102522 0.994731i \(-0.532691\pi\)
−0.102522 + 0.994731i \(0.532691\pi\)
\(180\) −7.23299 −0.539115
\(181\) 24.6365 1.83122 0.915610 0.402068i \(-0.131708\pi\)
0.915610 + 0.402068i \(0.131708\pi\)
\(182\) −29.1139 −2.15806
\(183\) 38.3825 2.83732
\(184\) −0.828297 −0.0610629
\(185\) −11.1328 −0.818496
\(186\) −15.5637 −1.14118
\(187\) −1.00000 −0.0731272
\(188\) −7.23693 −0.527807
\(189\) 7.96713 0.579524
\(190\) −12.8723 −0.933857
\(191\) 12.6808 0.917549 0.458775 0.888553i \(-0.348289\pi\)
0.458775 + 0.888553i \(0.348289\pi\)
\(192\) 10.2467 0.739493
\(193\) 13.8459 0.996649 0.498325 0.866991i \(-0.333949\pi\)
0.498325 + 0.866991i \(0.333949\pi\)
\(194\) −7.66452 −0.550280
\(195\) −13.4469 −0.962952
\(196\) 10.4436 0.745969
\(197\) 13.8384 0.985942 0.492971 0.870046i \(-0.335911\pi\)
0.492971 + 0.870046i \(0.335911\pi\)
\(198\) 7.18088 0.510323
\(199\) 7.08749 0.502419 0.251210 0.967933i \(-0.419172\pi\)
0.251210 + 0.967933i \(0.419172\pi\)
\(200\) −3.05328 −0.215899
\(201\) 28.5605 2.01450
\(202\) 7.87786 0.554284
\(203\) 9.13283 0.640999
\(204\) −4.00191 −0.280189
\(205\) −2.42885 −0.169638
\(206\) −12.7789 −0.890345
\(207\) −3.60047 −0.250250
\(208\) 19.6570 1.36297
\(209\) 5.54379 0.383472
\(210\) 22.5397 1.55539
\(211\) 23.4891 1.61706 0.808528 0.588458i \(-0.200265\pi\)
0.808528 + 0.588458i \(0.200265\pi\)
\(212\) −11.8188 −0.811719
\(213\) 4.07518 0.279227
\(214\) −9.55009 −0.652831
\(215\) −1.23543 −0.0842559
\(216\) −1.88405 −0.128193
\(217\) 11.7855 0.800055
\(218\) 23.8742 1.61697
\(219\) −0.989374 −0.0668557
\(220\) 1.89309 0.127632
\(221\) −4.16760 −0.280343
\(222\) 44.2312 2.96861
\(223\) 5.71676 0.382823 0.191411 0.981510i \(-0.438694\pi\)
0.191411 + 0.981510i \(0.438694\pi\)
\(224\) −26.4151 −1.76493
\(225\) −13.2721 −0.884806
\(226\) 2.42919 0.161587
\(227\) −9.48892 −0.629802 −0.314901 0.949125i \(-0.601971\pi\)
−0.314901 + 0.949125i \(0.601971\pi\)
\(228\) 22.1857 1.46929
\(229\) −1.20499 −0.0796278 −0.0398139 0.999207i \(-0.512677\pi\)
−0.0398139 + 0.999207i \(0.512677\pi\)
\(230\) −2.18808 −0.144278
\(231\) −9.70731 −0.638694
\(232\) −2.15971 −0.141792
\(233\) 5.85795 0.383767 0.191884 0.981418i \(-0.438540\pi\)
0.191884 + 0.981418i \(0.438540\pi\)
\(234\) 29.9270 1.95639
\(235\) 5.83476 0.380618
\(236\) 14.2223 0.925792
\(237\) 12.4101 0.806121
\(238\) 6.98576 0.452820
\(239\) −13.3843 −0.865756 −0.432878 0.901452i \(-0.642502\pi\)
−0.432878 + 0.901452i \(0.642502\pi\)
\(240\) −15.2183 −0.982339
\(241\) −13.5993 −0.876010 −0.438005 0.898973i \(-0.644315\pi\)
−0.438005 + 0.898973i \(0.644315\pi\)
\(242\) −1.87945 −0.120816
\(243\) 21.7457 1.39498
\(244\) −22.5200 −1.44170
\(245\) −8.42010 −0.537940
\(246\) 9.64999 0.615261
\(247\) 23.1043 1.47009
\(248\) −2.78702 −0.176976
\(249\) −46.0860 −2.92058
\(250\) −19.6754 −1.24438
\(251\) −24.7495 −1.56217 −0.781087 0.624422i \(-0.785335\pi\)
−0.781087 + 0.624422i \(0.785335\pi\)
\(252\) −21.7611 −1.37082
\(253\) 0.942351 0.0592451
\(254\) 29.1764 1.83069
\(255\) 3.22653 0.202053
\(256\) 20.7014 1.29384
\(257\) 19.8535 1.23842 0.619212 0.785224i \(-0.287452\pi\)
0.619212 + 0.785224i \(0.287452\pi\)
\(258\) 4.90847 0.305588
\(259\) −33.4939 −2.08121
\(260\) 7.88964 0.489295
\(261\) −9.38792 −0.581097
\(262\) 0.466792 0.0288385
\(263\) −27.7326 −1.71007 −0.855034 0.518572i \(-0.826464\pi\)
−0.855034 + 0.518572i \(0.826464\pi\)
\(264\) 2.29556 0.141282
\(265\) 9.52889 0.585355
\(266\) −38.7276 −2.37454
\(267\) 3.30056 0.201991
\(268\) −16.7572 −1.02361
\(269\) 7.62916 0.465158 0.232579 0.972577i \(-0.425284\pi\)
0.232579 + 0.972577i \(0.425284\pi\)
\(270\) −4.97702 −0.302892
\(271\) −17.1206 −1.04000 −0.520002 0.854165i \(-0.674069\pi\)
−0.520002 + 0.854165i \(0.674069\pi\)
\(272\) −4.71663 −0.285988
\(273\) −40.4562 −2.44852
\(274\) −18.7999 −1.13574
\(275\) 3.47370 0.209472
\(276\) 3.77120 0.226999
\(277\) 1.54921 0.0930827 0.0465414 0.998916i \(-0.485180\pi\)
0.0465414 + 0.998916i \(0.485180\pi\)
\(278\) 37.9015 2.27318
\(279\) −12.1147 −0.725289
\(280\) 4.03624 0.241211
\(281\) −6.98042 −0.416417 −0.208209 0.978084i \(-0.566763\pi\)
−0.208209 + 0.978084i \(0.566763\pi\)
\(282\) −23.1819 −1.38046
\(283\) 9.21245 0.547623 0.273812 0.961783i \(-0.411715\pi\)
0.273812 + 0.961783i \(0.411715\pi\)
\(284\) −2.39102 −0.141881
\(285\) −17.8872 −1.05955
\(286\) −7.83280 −0.463163
\(287\) −7.30742 −0.431344
\(288\) 27.1529 1.60000
\(289\) 1.00000 0.0588235
\(290\) −5.70522 −0.335022
\(291\) −10.6505 −0.624343
\(292\) 0.580492 0.0339707
\(293\) 29.7459 1.73777 0.868887 0.495011i \(-0.164836\pi\)
0.868887 + 0.495011i \(0.164836\pi\)
\(294\) 33.4537 1.95106
\(295\) −11.4667 −0.667617
\(296\) 7.92057 0.460374
\(297\) 2.14348 0.124377
\(298\) −42.6636 −2.47143
\(299\) 3.92734 0.227124
\(300\) 13.9014 0.802599
\(301\) −3.71692 −0.214240
\(302\) −29.0316 −1.67058
\(303\) 10.9470 0.628886
\(304\) 26.1480 1.49969
\(305\) 18.1567 1.03965
\(306\) −7.18088 −0.410503
\(307\) −5.66235 −0.323167 −0.161584 0.986859i \(-0.551660\pi\)
−0.161584 + 0.986859i \(0.551660\pi\)
\(308\) 5.69553 0.324533
\(309\) −17.7573 −1.01018
\(310\) −7.36235 −0.418153
\(311\) 5.05158 0.286449 0.143224 0.989690i \(-0.454253\pi\)
0.143224 + 0.989690i \(0.454253\pi\)
\(312\) 9.56700 0.541624
\(313\) 20.3204 1.14858 0.574290 0.818652i \(-0.305278\pi\)
0.574290 + 0.818652i \(0.305278\pi\)
\(314\) −25.5614 −1.44252
\(315\) 17.5449 0.988541
\(316\) −7.28132 −0.409606
\(317\) −0.490531 −0.0275510 −0.0137755 0.999905i \(-0.504385\pi\)
−0.0137755 + 0.999905i \(0.504385\pi\)
\(318\) −37.8590 −2.12303
\(319\) 2.45710 0.137571
\(320\) 4.84718 0.270965
\(321\) −13.2707 −0.740696
\(322\) −6.58303 −0.366858
\(323\) −5.54379 −0.308465
\(324\) −8.98585 −0.499214
\(325\) 14.4770 0.803040
\(326\) 13.0009 0.720056
\(327\) 33.1753 1.83460
\(328\) 1.72804 0.0954152
\(329\) 17.5544 0.967806
\(330\) 6.06409 0.333817
\(331\) 14.6330 0.804303 0.402151 0.915573i \(-0.368263\pi\)
0.402151 + 0.915573i \(0.368263\pi\)
\(332\) 27.0399 1.48401
\(333\) 34.4294 1.88672
\(334\) −9.32194 −0.510074
\(335\) 13.5105 0.738155
\(336\) −45.7858 −2.49782
\(337\) −2.49971 −0.136168 −0.0680840 0.997680i \(-0.521689\pi\)
−0.0680840 + 0.997680i \(0.521689\pi\)
\(338\) −8.21116 −0.446628
\(339\) 3.37556 0.183335
\(340\) −1.89309 −0.102667
\(341\) 3.17078 0.171707
\(342\) 39.8093 2.15264
\(343\) 0.685784 0.0370289
\(344\) 0.878969 0.0473908
\(345\) −3.04052 −0.163696
\(346\) −39.4631 −2.12155
\(347\) 12.7918 0.686698 0.343349 0.939208i \(-0.388439\pi\)
0.343349 + 0.939208i \(0.388439\pi\)
\(348\) 9.83307 0.527108
\(349\) 10.2188 0.546999 0.273499 0.961872i \(-0.411819\pi\)
0.273499 + 0.961872i \(0.411819\pi\)
\(350\) −24.2664 −1.29710
\(351\) 8.93316 0.476817
\(352\) −7.10672 −0.378790
\(353\) 18.6457 0.992413 0.496206 0.868205i \(-0.334726\pi\)
0.496206 + 0.868205i \(0.334726\pi\)
\(354\) 45.5580 2.42138
\(355\) 1.92775 0.102314
\(356\) −1.93652 −0.102636
\(357\) 9.70731 0.513765
\(358\) 5.15592 0.272499
\(359\) −12.1451 −0.640996 −0.320498 0.947249i \(-0.603850\pi\)
−0.320498 + 0.947249i \(0.603850\pi\)
\(360\) −4.14897 −0.218670
\(361\) 11.7336 0.617559
\(362\) −46.3031 −2.43364
\(363\) −2.61165 −0.137076
\(364\) 23.7367 1.24414
\(365\) −0.468020 −0.0244973
\(366\) −72.1379 −3.77071
\(367\) −6.71172 −0.350349 −0.175175 0.984537i \(-0.556049\pi\)
−0.175175 + 0.984537i \(0.556049\pi\)
\(368\) 4.44472 0.231697
\(369\) 7.51152 0.391034
\(370\) 20.9234 1.08776
\(371\) 28.6686 1.48840
\(372\) 12.6892 0.657903
\(373\) −19.3351 −1.00113 −0.500566 0.865699i \(-0.666875\pi\)
−0.500566 + 0.865699i \(0.666875\pi\)
\(374\) 1.87945 0.0971840
\(375\) −27.3406 −1.41186
\(376\) −4.15123 −0.214083
\(377\) 10.2402 0.527397
\(378\) −14.9738 −0.770170
\(379\) −5.49769 −0.282397 −0.141199 0.989981i \(-0.545096\pi\)
−0.141199 + 0.989981i \(0.545096\pi\)
\(380\) 10.4949 0.538376
\(381\) 40.5431 2.07709
\(382\) −23.8329 −1.21940
\(383\) −19.2787 −0.985098 −0.492549 0.870285i \(-0.663935\pi\)
−0.492549 + 0.870285i \(0.663935\pi\)
\(384\) 17.8624 0.911538
\(385\) −4.59201 −0.234031
\(386\) −26.0226 −1.32452
\(387\) 3.82074 0.194219
\(388\) 6.24893 0.317241
\(389\) −12.6496 −0.641362 −0.320681 0.947187i \(-0.603912\pi\)
−0.320681 + 0.947187i \(0.603912\pi\)
\(390\) 25.2727 1.27973
\(391\) −0.942351 −0.0476567
\(392\) 5.99061 0.302572
\(393\) 0.648647 0.0327199
\(394\) −26.0085 −1.31029
\(395\) 5.87054 0.295379
\(396\) −5.85461 −0.294205
\(397\) 11.4929 0.576812 0.288406 0.957508i \(-0.406875\pi\)
0.288406 + 0.957508i \(0.406875\pi\)
\(398\) −13.3206 −0.667700
\(399\) −53.8153 −2.69413
\(400\) 16.3842 0.819208
\(401\) 8.82987 0.440943 0.220471 0.975393i \(-0.429240\pi\)
0.220471 + 0.975393i \(0.429240\pi\)
\(402\) −53.6780 −2.67722
\(403\) 13.2146 0.658264
\(404\) −6.42287 −0.319550
\(405\) 7.24482 0.359998
\(406\) −17.1647 −0.851869
\(407\) −9.01121 −0.446669
\(408\) −2.29556 −0.113647
\(409\) −18.5658 −0.918020 −0.459010 0.888431i \(-0.651796\pi\)
−0.459010 + 0.888431i \(0.651796\pi\)
\(410\) 4.56490 0.225444
\(411\) −26.1240 −1.28860
\(412\) 10.4187 0.513291
\(413\) −34.4986 −1.69757
\(414\) 6.76690 0.332575
\(415\) −21.8008 −1.07016
\(416\) −29.6180 −1.45214
\(417\) 52.6673 2.57913
\(418\) −10.4193 −0.509623
\(419\) 39.3049 1.92017 0.960085 0.279708i \(-0.0902376\pi\)
0.960085 + 0.279708i \(0.0902376\pi\)
\(420\) −18.3768 −0.896696
\(421\) 27.7544 1.35267 0.676333 0.736596i \(-0.263568\pi\)
0.676333 + 0.736596i \(0.263568\pi\)
\(422\) −44.1465 −2.14902
\(423\) −18.0447 −0.877364
\(424\) −6.77948 −0.329241
\(425\) −3.47370 −0.168499
\(426\) −7.65910 −0.371084
\(427\) 54.6262 2.64355
\(428\) 7.78625 0.376363
\(429\) −10.8843 −0.525501
\(430\) 2.32194 0.111974
\(431\) −25.4371 −1.22526 −0.612631 0.790369i \(-0.709889\pi\)
−0.612631 + 0.790369i \(0.709889\pi\)
\(432\) 10.1100 0.486417
\(433\) 19.4336 0.933921 0.466961 0.884278i \(-0.345349\pi\)
0.466961 + 0.884278i \(0.345349\pi\)
\(434\) −22.1503 −1.06325
\(435\) −7.92789 −0.380113
\(436\) −19.4648 −0.932195
\(437\) 5.22419 0.249907
\(438\) 1.85948 0.0888493
\(439\) −18.7491 −0.894847 −0.447423 0.894322i \(-0.647658\pi\)
−0.447423 + 0.894322i \(0.647658\pi\)
\(440\) 1.08591 0.0517687
\(441\) 26.0402 1.24001
\(442\) 7.83280 0.372568
\(443\) −23.4840 −1.11576 −0.557880 0.829922i \(-0.688385\pi\)
−0.557880 + 0.829922i \(0.688385\pi\)
\(444\) −36.0620 −1.71143
\(445\) 1.56132 0.0740136
\(446\) −10.7444 −0.508760
\(447\) −59.2847 −2.80407
\(448\) 14.5832 0.688991
\(449\) 23.5069 1.10936 0.554681 0.832063i \(-0.312840\pi\)
0.554681 + 0.832063i \(0.312840\pi\)
\(450\) 24.9442 1.17588
\(451\) −1.96599 −0.0925748
\(452\) −1.98053 −0.0931563
\(453\) −40.3418 −1.89543
\(454\) 17.8339 0.836988
\(455\) −19.1377 −0.897188
\(456\) 12.7261 0.595955
\(457\) 33.3341 1.55930 0.779651 0.626215i \(-0.215397\pi\)
0.779651 + 0.626215i \(0.215397\pi\)
\(458\) 2.26471 0.105823
\(459\) −2.14348 −0.100049
\(460\) 1.78395 0.0831772
\(461\) 13.1322 0.611629 0.305815 0.952091i \(-0.401071\pi\)
0.305815 + 0.952091i \(0.401071\pi\)
\(462\) 18.2444 0.848806
\(463\) −9.55467 −0.444043 −0.222022 0.975042i \(-0.571266\pi\)
−0.222022 + 0.975042i \(0.571266\pi\)
\(464\) 11.5892 0.538016
\(465\) −10.2306 −0.474433
\(466\) −11.0097 −0.510015
\(467\) −31.1091 −1.43956 −0.719780 0.694202i \(-0.755757\pi\)
−0.719780 + 0.694202i \(0.755757\pi\)
\(468\) −24.3997 −1.12788
\(469\) 40.6475 1.87693
\(470\) −10.9661 −0.505830
\(471\) −35.5198 −1.63667
\(472\) 8.15816 0.375510
\(473\) −1.00000 −0.0459800
\(474\) −23.3241 −1.07131
\(475\) 19.2575 0.883594
\(476\) −5.69553 −0.261054
\(477\) −29.4693 −1.34931
\(478\) 25.1550 1.15056
\(479\) −7.96866 −0.364097 −0.182049 0.983290i \(-0.558273\pi\)
−0.182049 + 0.983290i \(0.558273\pi\)
\(480\) 22.9300 1.04661
\(481\) −37.5551 −1.71237
\(482\) 25.5592 1.16419
\(483\) −9.14769 −0.416234
\(484\) 1.53233 0.0696512
\(485\) −5.03819 −0.228772
\(486\) −40.8698 −1.85389
\(487\) −0.595390 −0.0269797 −0.0134898 0.999909i \(-0.504294\pi\)
−0.0134898 + 0.999909i \(0.504294\pi\)
\(488\) −12.9179 −0.584765
\(489\) 18.0659 0.816970
\(490\) 15.8251 0.714907
\(491\) −4.19963 −0.189527 −0.0947634 0.995500i \(-0.530209\pi\)
−0.0947634 + 0.995500i \(0.530209\pi\)
\(492\) −7.86770 −0.354703
\(493\) −2.45710 −0.110662
\(494\) −43.4234 −1.95371
\(495\) 4.72027 0.212160
\(496\) 14.9554 0.671517
\(497\) 5.79982 0.260158
\(498\) 86.6162 3.88137
\(499\) 3.16092 0.141502 0.0707511 0.997494i \(-0.477460\pi\)
0.0707511 + 0.997494i \(0.477460\pi\)
\(500\) 16.0415 0.717396
\(501\) −12.9536 −0.578726
\(502\) 46.5154 2.07608
\(503\) −21.9706 −0.979621 −0.489810 0.871829i \(-0.662934\pi\)
−0.489810 + 0.871829i \(0.662934\pi\)
\(504\) −12.4826 −0.556018
\(505\) 5.17842 0.230437
\(506\) −1.77110 −0.0787350
\(507\) −11.4101 −0.506740
\(508\) −23.7877 −1.05541
\(509\) 10.2971 0.456413 0.228206 0.973613i \(-0.426714\pi\)
0.228206 + 0.973613i \(0.426714\pi\)
\(510\) −6.06409 −0.268522
\(511\) −1.40808 −0.0622899
\(512\) −25.2282 −1.11494
\(513\) 11.8830 0.524647
\(514\) −37.3136 −1.64583
\(515\) −8.40004 −0.370150
\(516\) −4.00191 −0.176174
\(517\) 4.72284 0.207710
\(518\) 62.9501 2.76587
\(519\) −54.8374 −2.40709
\(520\) 4.52564 0.198462
\(521\) 3.34953 0.146746 0.0733729 0.997305i \(-0.476624\pi\)
0.0733729 + 0.997305i \(0.476624\pi\)
\(522\) 17.6441 0.772261
\(523\) 10.0729 0.440458 0.220229 0.975448i \(-0.429320\pi\)
0.220229 + 0.975448i \(0.429320\pi\)
\(524\) −0.380578 −0.0166256
\(525\) −33.7203 −1.47167
\(526\) 52.1221 2.27263
\(527\) −3.17078 −0.138121
\(528\) −12.3182 −0.536081
\(529\) −22.1120 −0.961390
\(530\) −17.9091 −0.777920
\(531\) 35.4622 1.53893
\(532\) 31.5748 1.36894
\(533\) −8.19346 −0.354898
\(534\) −6.20323 −0.268440
\(535\) −6.27765 −0.271406
\(536\) −9.61222 −0.415185
\(537\) 7.16458 0.309175
\(538\) −14.3386 −0.618181
\(539\) −6.81550 −0.293564
\(540\) 4.05779 0.174620
\(541\) −42.1401 −1.81175 −0.905873 0.423549i \(-0.860784\pi\)
−0.905873 + 0.423549i \(0.860784\pi\)
\(542\) 32.1774 1.38214
\(543\) −64.3421 −2.76118
\(544\) 7.10672 0.304698
\(545\) 15.6935 0.672234
\(546\) 76.0354 3.25401
\(547\) 38.6103 1.65086 0.825429 0.564506i \(-0.190933\pi\)
0.825429 + 0.564506i \(0.190933\pi\)
\(548\) 15.3277 0.654765
\(549\) −56.1519 −2.39651
\(550\) −6.52864 −0.278382
\(551\) 13.6216 0.580301
\(552\) 2.16322 0.0920730
\(553\) 17.6621 0.751068
\(554\) −2.91165 −0.123704
\(555\) 29.0749 1.23416
\(556\) −30.9013 −1.31051
\(557\) 22.9269 0.971444 0.485722 0.874113i \(-0.338557\pi\)
0.485722 + 0.874113i \(0.338557\pi\)
\(558\) 22.7690 0.963888
\(559\) −4.16760 −0.176271
\(560\) −21.6588 −0.915252
\(561\) 2.61165 0.110264
\(562\) 13.1193 0.553406
\(563\) −22.0885 −0.930919 −0.465460 0.885069i \(-0.654111\pi\)
−0.465460 + 0.885069i \(0.654111\pi\)
\(564\) 18.9003 0.795848
\(565\) 1.59680 0.0671778
\(566\) −17.3143 −0.727775
\(567\) 21.7967 0.915376
\(568\) −1.37153 −0.0575481
\(569\) −18.1352 −0.760265 −0.380133 0.924932i \(-0.624122\pi\)
−0.380133 + 0.924932i \(0.624122\pi\)
\(570\) 33.6181 1.40811
\(571\) 33.4079 1.39808 0.699039 0.715083i \(-0.253611\pi\)
0.699039 + 0.715083i \(0.253611\pi\)
\(572\) 6.38613 0.267017
\(573\) −33.1178 −1.38352
\(574\) 13.7339 0.573243
\(575\) 3.27344 0.136512
\(576\) −14.9905 −0.624604
\(577\) 35.7416 1.48794 0.743972 0.668211i \(-0.232940\pi\)
0.743972 + 0.668211i \(0.232940\pi\)
\(578\) −1.87945 −0.0781747
\(579\) −36.1607 −1.50279
\(580\) 4.65150 0.193143
\(581\) −65.5898 −2.72113
\(582\) 20.0171 0.829734
\(583\) 7.71299 0.319439
\(584\) 0.332980 0.0137788
\(585\) 19.6722 0.813346
\(586\) −55.9059 −2.30945
\(587\) −46.7204 −1.92836 −0.964180 0.265250i \(-0.914545\pi\)
−0.964180 + 0.265250i \(0.914545\pi\)
\(588\) −27.2750 −1.12480
\(589\) 17.5782 0.724295
\(590\) 21.5511 0.887243
\(591\) −36.1410 −1.48664
\(592\) −42.5025 −1.74684
\(593\) −8.83285 −0.362722 −0.181361 0.983417i \(-0.558050\pi\)
−0.181361 + 0.983417i \(0.558050\pi\)
\(594\) −4.02855 −0.165294
\(595\) 4.59201 0.188254
\(596\) 34.7839 1.42480
\(597\) −18.5101 −0.757567
\(598\) −7.38124 −0.301841
\(599\) 0.447343 0.0182779 0.00913897 0.999958i \(-0.497091\pi\)
0.00913897 + 0.999958i \(0.497091\pi\)
\(600\) 7.97410 0.325541
\(601\) 32.5502 1.32775 0.663874 0.747844i \(-0.268911\pi\)
0.663874 + 0.747844i \(0.268911\pi\)
\(602\) 6.98576 0.284718
\(603\) −41.7828 −1.70153
\(604\) 23.6696 0.963103
\(605\) −1.23543 −0.0502276
\(606\) −20.5742 −0.835771
\(607\) 45.5242 1.84777 0.923886 0.382669i \(-0.124995\pi\)
0.923886 + 0.382669i \(0.124995\pi\)
\(608\) −39.3982 −1.59781
\(609\) −23.8518 −0.966523
\(610\) −34.1246 −1.38167
\(611\) 19.6829 0.796286
\(612\) 5.85461 0.236659
\(613\) −31.9346 −1.28983 −0.644913 0.764256i \(-0.723106\pi\)
−0.644913 + 0.764256i \(0.723106\pi\)
\(614\) 10.6421 0.429480
\(615\) 6.34332 0.255787
\(616\) 3.26706 0.131634
\(617\) −0.866433 −0.0348813 −0.0174406 0.999848i \(-0.505552\pi\)
−0.0174406 + 0.999848i \(0.505552\pi\)
\(618\) 33.3739 1.34250
\(619\) 6.64791 0.267202 0.133601 0.991035i \(-0.457346\pi\)
0.133601 + 0.991035i \(0.457346\pi\)
\(620\) 6.00257 0.241069
\(621\) 2.01991 0.0810561
\(622\) −9.49417 −0.380682
\(623\) 4.69737 0.188196
\(624\) −51.3374 −2.05514
\(625\) 4.43511 0.177404
\(626\) −38.1912 −1.52643
\(627\) −14.4785 −0.578214
\(628\) 20.8404 0.831623
\(629\) 9.01121 0.359300
\(630\) −32.9747 −1.31374
\(631\) 34.9282 1.39047 0.695235 0.718782i \(-0.255300\pi\)
0.695235 + 0.718782i \(0.255300\pi\)
\(632\) −4.17669 −0.166140
\(633\) −61.3454 −2.43826
\(634\) 0.921928 0.0366144
\(635\) 19.1788 0.761087
\(636\) 30.8666 1.22394
\(637\) −28.4043 −1.12542
\(638\) −4.61799 −0.182828
\(639\) −5.96182 −0.235846
\(640\) 8.44976 0.334006
\(641\) −43.0709 −1.70120 −0.850599 0.525815i \(-0.823760\pi\)
−0.850599 + 0.525815i \(0.823760\pi\)
\(642\) 24.9415 0.984364
\(643\) −3.85352 −0.151968 −0.0759840 0.997109i \(-0.524210\pi\)
−0.0759840 + 0.997109i \(0.524210\pi\)
\(644\) 5.36719 0.211497
\(645\) 3.22653 0.127044
\(646\) 10.4193 0.409941
\(647\) −24.1068 −0.947735 −0.473867 0.880596i \(-0.657142\pi\)
−0.473867 + 0.880596i \(0.657142\pi\)
\(648\) −5.15444 −0.202485
\(649\) −9.28151 −0.364331
\(650\) −27.2088 −1.06722
\(651\) −30.7798 −1.20635
\(652\) −10.5998 −0.415118
\(653\) 22.4035 0.876717 0.438359 0.898800i \(-0.355560\pi\)
0.438359 + 0.898800i \(0.355560\pi\)
\(654\) −62.3512 −2.43813
\(655\) 0.306840 0.0119892
\(656\) −9.27284 −0.362044
\(657\) 1.44741 0.0564689
\(658\) −32.9926 −1.28619
\(659\) −30.7181 −1.19661 −0.598303 0.801270i \(-0.704158\pi\)
−0.598303 + 0.801270i \(0.704158\pi\)
\(660\) −4.94409 −0.192449
\(661\) −11.8599 −0.461295 −0.230648 0.973037i \(-0.574084\pi\)
−0.230648 + 0.973037i \(0.574084\pi\)
\(662\) −27.5020 −1.06890
\(663\) 10.8843 0.422713
\(664\) 15.5105 0.601926
\(665\) −25.4572 −0.987186
\(666\) −64.7083 −2.50740
\(667\) 2.31545 0.0896544
\(668\) 7.60024 0.294062
\(669\) −14.9302 −0.577235
\(670\) −25.3922 −0.980987
\(671\) 14.6966 0.567357
\(672\) 68.9872 2.66124
\(673\) 1.93666 0.0746526 0.0373263 0.999303i \(-0.488116\pi\)
0.0373263 + 0.999303i \(0.488116\pi\)
\(674\) 4.69808 0.180963
\(675\) 7.44580 0.286589
\(676\) 6.69461 0.257485
\(677\) 18.5223 0.711871 0.355935 0.934511i \(-0.384162\pi\)
0.355935 + 0.934511i \(0.384162\pi\)
\(678\) −6.34419 −0.243647
\(679\) −15.1579 −0.581705
\(680\) −1.08591 −0.0416427
\(681\) 24.7818 0.949640
\(682\) −5.95932 −0.228194
\(683\) −30.3340 −1.16070 −0.580349 0.814368i \(-0.697084\pi\)
−0.580349 + 0.814368i \(0.697084\pi\)
\(684\) −32.4567 −1.24101
\(685\) −12.3579 −0.472171
\(686\) −1.28890 −0.0492103
\(687\) 3.14701 0.120066
\(688\) −4.71663 −0.179820
\(689\) 32.1447 1.22461
\(690\) 5.71450 0.217547
\(691\) −36.4084 −1.38504 −0.692521 0.721398i \(-0.743500\pi\)
−0.692521 + 0.721398i \(0.743500\pi\)
\(692\) 32.1745 1.22309
\(693\) 14.2014 0.539465
\(694\) −24.0415 −0.912602
\(695\) 24.9141 0.945047
\(696\) 5.64042 0.213800
\(697\) 1.96599 0.0744671
\(698\) −19.2057 −0.726945
\(699\) −15.2989 −0.578659
\(700\) 19.7846 0.747787
\(701\) −32.4436 −1.22538 −0.612690 0.790324i \(-0.709912\pi\)
−0.612690 + 0.790324i \(0.709912\pi\)
\(702\) −16.7894 −0.633676
\(703\) −49.9562 −1.88414
\(704\) 3.92346 0.147871
\(705\) −15.2384 −0.573910
\(706\) −35.0437 −1.31889
\(707\) 15.5798 0.585937
\(708\) −37.1437 −1.39595
\(709\) 4.86710 0.182788 0.0913940 0.995815i \(-0.470868\pi\)
0.0913940 + 0.995815i \(0.470868\pi\)
\(710\) −3.62311 −0.135973
\(711\) −18.1554 −0.680880
\(712\) −1.11082 −0.0416299
\(713\) 2.98799 0.111901
\(714\) −18.2444 −0.682779
\(715\) −5.14880 −0.192554
\(716\) −4.20365 −0.157098
\(717\) 34.9551 1.30542
\(718\) 22.8262 0.851864
\(719\) −29.3259 −1.09367 −0.546837 0.837239i \(-0.684168\pi\)
−0.546837 + 0.837239i \(0.684168\pi\)
\(720\) 22.2638 0.829721
\(721\) −25.2723 −0.941190
\(722\) −22.0527 −0.820718
\(723\) 35.5167 1.32088
\(724\) 37.7512 1.40301
\(725\) 8.53522 0.316990
\(726\) 4.90847 0.182170
\(727\) −22.2199 −0.824090 −0.412045 0.911163i \(-0.635185\pi\)
−0.412045 + 0.911163i \(0.635185\pi\)
\(728\) 13.6158 0.504635
\(729\) −39.1996 −1.45184
\(730\) 0.879620 0.0325562
\(731\) 1.00000 0.0369863
\(732\) 58.8145 2.17385
\(733\) −11.1130 −0.410469 −0.205235 0.978713i \(-0.565796\pi\)
−0.205235 + 0.978713i \(0.565796\pi\)
\(734\) 12.6143 0.465604
\(735\) 21.9904 0.811128
\(736\) −6.69702 −0.246856
\(737\) 10.9358 0.402825
\(738\) −14.1175 −0.519673
\(739\) 17.2563 0.634782 0.317391 0.948295i \(-0.397193\pi\)
0.317391 + 0.948295i \(0.397193\pi\)
\(740\) −17.0590 −0.627102
\(741\) −60.3405 −2.21666
\(742\) −53.8811 −1.97804
\(743\) 38.8946 1.42690 0.713452 0.700704i \(-0.247131\pi\)
0.713452 + 0.700704i \(0.247131\pi\)
\(744\) 7.27873 0.266851
\(745\) −28.0444 −1.02747
\(746\) 36.3392 1.33047
\(747\) 67.4218 2.46683
\(748\) −1.53233 −0.0560274
\(749\) −18.8869 −0.690112
\(750\) 51.3853 1.87633
\(751\) −3.30930 −0.120758 −0.0603790 0.998176i \(-0.519231\pi\)
−0.0603790 + 0.998176i \(0.519231\pi\)
\(752\) 22.2759 0.812318
\(753\) 64.6371 2.35551
\(754\) −19.2459 −0.700896
\(755\) −19.0836 −0.694523
\(756\) 12.2082 0.444010
\(757\) −50.4906 −1.83511 −0.917557 0.397605i \(-0.869841\pi\)
−0.917557 + 0.397605i \(0.869841\pi\)
\(758\) 10.3326 0.375298
\(759\) −2.46109 −0.0893320
\(760\) 6.02005 0.218370
\(761\) −30.6135 −1.10974 −0.554870 0.831937i \(-0.687232\pi\)
−0.554870 + 0.831937i \(0.687232\pi\)
\(762\) −76.1986 −2.76039
\(763\) 47.2153 1.70931
\(764\) 19.4311 0.702992
\(765\) −4.72027 −0.170662
\(766\) 36.2334 1.30917
\(767\) −38.6816 −1.39671
\(768\) −54.0649 −1.95090
\(769\) −3.34187 −0.120511 −0.0602554 0.998183i \(-0.519192\pi\)
−0.0602554 + 0.998183i \(0.519192\pi\)
\(770\) 8.63045 0.311020
\(771\) −51.8504 −1.86735
\(772\) 21.2164 0.763596
\(773\) −44.1888 −1.58936 −0.794681 0.607028i \(-0.792362\pi\)
−0.794681 + 0.607028i \(0.792362\pi\)
\(774\) −7.18088 −0.258111
\(775\) 11.0143 0.395647
\(776\) 3.58449 0.128676
\(777\) 87.4746 3.13813
\(778\) 23.7743 0.852352
\(779\) −10.8990 −0.390498
\(780\) −20.6050 −0.737778
\(781\) 1.56038 0.0558349
\(782\) 1.77110 0.0633344
\(783\) 5.26673 0.188218
\(784\) −32.1462 −1.14808
\(785\) −16.8025 −0.599708
\(786\) −1.21910 −0.0434838
\(787\) 25.6510 0.914360 0.457180 0.889374i \(-0.348860\pi\)
0.457180 + 0.889374i \(0.348860\pi\)
\(788\) 21.2049 0.755392
\(789\) 72.4281 2.57851
\(790\) −11.0334 −0.392550
\(791\) 4.80412 0.170815
\(792\) −3.35831 −0.119332
\(793\) 61.2497 2.17504
\(794\) −21.6003 −0.766567
\(795\) −24.8862 −0.882621
\(796\) 10.8604 0.384935
\(797\) 9.65198 0.341891 0.170945 0.985280i \(-0.445318\pi\)
0.170945 + 0.985280i \(0.445318\pi\)
\(798\) 101.143 3.58043
\(799\) −4.72284 −0.167082
\(800\) −24.6866 −0.872804
\(801\) −4.82857 −0.170609
\(802\) −16.5953 −0.586000
\(803\) −0.378831 −0.0133686
\(804\) 43.7640 1.54344
\(805\) −4.32728 −0.152517
\(806\) −24.8361 −0.874814
\(807\) −19.9247 −0.701384
\(808\) −3.68427 −0.129612
\(809\) 4.72435 0.166099 0.0830496 0.996545i \(-0.473534\pi\)
0.0830496 + 0.996545i \(0.473534\pi\)
\(810\) −13.6163 −0.478427
\(811\) −16.4749 −0.578511 −0.289256 0.957252i \(-0.593408\pi\)
−0.289256 + 0.957252i \(0.593408\pi\)
\(812\) 13.9945 0.491110
\(813\) 44.7132 1.56816
\(814\) 16.9361 0.593610
\(815\) 8.54603 0.299354
\(816\) 12.3182 0.431223
\(817\) −5.54379 −0.193953
\(818\) 34.8935 1.22002
\(819\) 59.1857 2.06811
\(820\) −3.72179 −0.129971
\(821\) −13.7131 −0.478592 −0.239296 0.970947i \(-0.576917\pi\)
−0.239296 + 0.970947i \(0.576917\pi\)
\(822\) 49.0988 1.71252
\(823\) 34.3716 1.19812 0.599060 0.800704i \(-0.295541\pi\)
0.599060 + 0.800704i \(0.295541\pi\)
\(824\) 5.97634 0.208196
\(825\) −9.07211 −0.315850
\(826\) 64.8384 2.25602
\(827\) 32.4075 1.12692 0.563460 0.826144i \(-0.309470\pi\)
0.563460 + 0.826144i \(0.309470\pi\)
\(828\) −5.51710 −0.191732
\(829\) −23.5988 −0.819620 −0.409810 0.912171i \(-0.634405\pi\)
−0.409810 + 0.912171i \(0.634405\pi\)
\(830\) 40.9735 1.42221
\(831\) −4.04599 −0.140354
\(832\) 16.3514 0.566884
\(833\) 6.81550 0.236143
\(834\) −98.9856 −3.42759
\(835\) −6.12768 −0.212057
\(836\) 8.49490 0.293802
\(837\) 6.79650 0.234921
\(838\) −73.8715 −2.55185
\(839\) −42.2398 −1.45828 −0.729141 0.684364i \(-0.760080\pi\)
−0.729141 + 0.684364i \(0.760080\pi\)
\(840\) −10.5413 −0.363708
\(841\) −22.9627 −0.791816
\(842\) −52.1630 −1.79765
\(843\) 18.2305 0.627890
\(844\) 35.9929 1.23893
\(845\) −5.39751 −0.185680
\(846\) 33.9141 1.16599
\(847\) −3.71692 −0.127715
\(848\) 36.3793 1.24927
\(849\) −24.0597 −0.825728
\(850\) 6.52864 0.223931
\(851\) −8.49171 −0.291092
\(852\) 6.24451 0.213933
\(853\) 35.3128 1.20909 0.604544 0.796572i \(-0.293355\pi\)
0.604544 + 0.796572i \(0.293355\pi\)
\(854\) −102.667 −3.51320
\(855\) 26.1682 0.894933
\(856\) 4.46633 0.152656
\(857\) −7.95792 −0.271837 −0.135919 0.990720i \(-0.543399\pi\)
−0.135919 + 0.990720i \(0.543399\pi\)
\(858\) 20.4565 0.698375
\(859\) 7.50464 0.256055 0.128028 0.991771i \(-0.459135\pi\)
0.128028 + 0.991771i \(0.459135\pi\)
\(860\) −1.89309 −0.0645538
\(861\) 19.0845 0.650397
\(862\) 47.8077 1.62834
\(863\) −36.8899 −1.25575 −0.627874 0.778315i \(-0.716075\pi\)
−0.627874 + 0.778315i \(0.716075\pi\)
\(864\) −15.2331 −0.518241
\(865\) −25.9406 −0.882008
\(866\) −36.5245 −1.24115
\(867\) −2.61165 −0.0886964
\(868\) 18.0593 0.612972
\(869\) 4.75181 0.161194
\(870\) 14.9001 0.505159
\(871\) 45.5761 1.54429
\(872\) −11.1654 −0.378107
\(873\) 15.5812 0.527344
\(874\) −9.81860 −0.332119
\(875\) −38.9113 −1.31544
\(876\) −1.51604 −0.0512224
\(877\) −17.2652 −0.583006 −0.291503 0.956570i \(-0.594155\pi\)
−0.291503 + 0.956570i \(0.594155\pi\)
\(878\) 35.2380 1.18922
\(879\) −77.6860 −2.62028
\(880\) −5.82709 −0.196431
\(881\) −15.6675 −0.527852 −0.263926 0.964543i \(-0.585017\pi\)
−0.263926 + 0.964543i \(0.585017\pi\)
\(882\) −48.9412 −1.64794
\(883\) 34.5296 1.16201 0.581006 0.813899i \(-0.302659\pi\)
0.581006 + 0.813899i \(0.302659\pi\)
\(884\) −6.38613 −0.214789
\(885\) 29.9470 1.00666
\(886\) 44.1370 1.48281
\(887\) −18.1439 −0.609213 −0.304607 0.952478i \(-0.598525\pi\)
−0.304607 + 0.952478i \(0.598525\pi\)
\(888\) −20.6858 −0.694170
\(889\) 57.7012 1.93523
\(890\) −2.93442 −0.0983619
\(891\) 5.86419 0.196458
\(892\) 8.75995 0.293305
\(893\) 26.1824 0.876161
\(894\) 111.422 3.72652
\(895\) 3.38918 0.113288
\(896\) 25.4219 0.849286
\(897\) −10.2569 −0.342467
\(898\) −44.1801 −1.47431
\(899\) 7.79092 0.259842
\(900\) −20.3372 −0.677906
\(901\) −7.71299 −0.256957
\(902\) 3.69497 0.123029
\(903\) 9.70731 0.323039
\(904\) −1.13607 −0.0377850
\(905\) −30.4368 −1.01175
\(906\) 75.8204 2.51896
\(907\) 10.5620 0.350704 0.175352 0.984506i \(-0.443894\pi\)
0.175352 + 0.984506i \(0.443894\pi\)
\(908\) −14.5401 −0.482531
\(909\) −16.0149 −0.531181
\(910\) 35.9683 1.19234
\(911\) −14.9802 −0.496317 −0.248159 0.968719i \(-0.579825\pi\)
−0.248159 + 0.968719i \(0.579825\pi\)
\(912\) −68.2895 −2.26129
\(913\) −17.6463 −0.584007
\(914\) −62.6496 −2.07227
\(915\) −47.4191 −1.56763
\(916\) −1.84643 −0.0610078
\(917\) 0.923158 0.0304854
\(918\) 4.02855 0.132962
\(919\) −5.55199 −0.183143 −0.0915717 0.995798i \(-0.529189\pi\)
−0.0915717 + 0.995798i \(0.529189\pi\)
\(920\) 1.02331 0.0337374
\(921\) 14.7881 0.487284
\(922\) −24.6814 −0.812838
\(923\) 6.50306 0.214051
\(924\) −14.8748 −0.489344
\(925\) −31.3022 −1.02921
\(926\) 17.9575 0.590120
\(927\) 25.9782 0.853235
\(928\) −17.4619 −0.573215
\(929\) 3.40408 0.111684 0.0558420 0.998440i \(-0.482216\pi\)
0.0558420 + 0.998440i \(0.482216\pi\)
\(930\) 19.2279 0.630508
\(931\) −37.7837 −1.23831
\(932\) 8.97629 0.294028
\(933\) −13.1930 −0.431918
\(934\) 58.4680 1.91313
\(935\) 1.23543 0.0404030
\(936\) −13.9961 −0.457477
\(937\) 28.8206 0.941527 0.470763 0.882260i \(-0.343979\pi\)
0.470763 + 0.882260i \(0.343979\pi\)
\(938\) −76.3948 −2.49438
\(939\) −53.0700 −1.73187
\(940\) 8.94075 0.291615
\(941\) 9.36860 0.305408 0.152704 0.988272i \(-0.451202\pi\)
0.152704 + 0.988272i \(0.451202\pi\)
\(942\) 66.7576 2.17508
\(943\) −1.85265 −0.0603306
\(944\) −43.7774 −1.42483
\(945\) −9.84287 −0.320189
\(946\) 1.87945 0.0611061
\(947\) −17.8830 −0.581120 −0.290560 0.956857i \(-0.593842\pi\)
−0.290560 + 0.956857i \(0.593842\pi\)
\(948\) 19.0163 0.617620
\(949\) −1.57882 −0.0512505
\(950\) −36.1934 −1.17427
\(951\) 1.28110 0.0415424
\(952\) −3.26706 −0.105886
\(953\) −20.7617 −0.672538 −0.336269 0.941766i \(-0.609165\pi\)
−0.336269 + 0.941766i \(0.609165\pi\)
\(954\) 55.3860 1.79319
\(955\) −15.6663 −0.506949
\(956\) −20.5091 −0.663310
\(957\) −6.41709 −0.207435
\(958\) 14.9767 0.483875
\(959\) −37.1799 −1.20060
\(960\) −12.6591 −0.408572
\(961\) −20.9461 −0.675682
\(962\) 70.5829 2.27569
\(963\) 19.4144 0.625620
\(964\) −20.8386 −0.671166
\(965\) −17.1057 −0.550652
\(966\) 17.1926 0.553163
\(967\) −7.39961 −0.237956 −0.118978 0.992897i \(-0.537962\pi\)
−0.118978 + 0.992897i \(0.537962\pi\)
\(968\) 0.878969 0.0282511
\(969\) 14.4785 0.465115
\(970\) 9.46901 0.304032
\(971\) 60.0242 1.92627 0.963134 0.269021i \(-0.0867000\pi\)
0.963134 + 0.269021i \(0.0867000\pi\)
\(972\) 33.3214 1.06879
\(973\) 74.9565 2.40299
\(974\) 1.11900 0.0358552
\(975\) −37.8089 −1.21086
\(976\) 69.3185 2.21883
\(977\) −18.6170 −0.595610 −0.297805 0.954627i \(-0.596255\pi\)
−0.297805 + 0.954627i \(0.596255\pi\)
\(978\) −33.9540 −1.08573
\(979\) 1.26378 0.0403906
\(980\) −12.9023 −0.412150
\(981\) −48.5340 −1.54957
\(982\) 7.89300 0.251876
\(983\) 51.8626 1.65416 0.827080 0.562084i \(-0.190000\pi\)
0.827080 + 0.562084i \(0.190000\pi\)
\(984\) −4.51305 −0.143871
\(985\) −17.0964 −0.544736
\(986\) 4.61799 0.147067
\(987\) −45.8460 −1.45930
\(988\) 35.4034 1.12633
\(989\) −0.942351 −0.0299650
\(990\) −8.87150 −0.281955
\(991\) −51.4948 −1.63579 −0.817894 0.575370i \(-0.804858\pi\)
−0.817894 + 0.575370i \(0.804858\pi\)
\(992\) −22.5339 −0.715451
\(993\) −38.2164 −1.21276
\(994\) −10.9005 −0.345742
\(995\) −8.75613 −0.277588
\(996\) −70.6188 −2.23764
\(997\) 28.9337 0.916340 0.458170 0.888865i \(-0.348505\pi\)
0.458170 + 0.888865i \(0.348505\pi\)
\(998\) −5.94079 −0.188052
\(999\) −19.3153 −0.611110
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 \(a_p\))