Properties

Label 4003.2.a.b.1.20
Level 4003
Weight 2
Character 4003.1
Self dual Yes
Analytic conductor 31.964
Analytic rank 1
Dimension 152
CM No

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Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(1\)
Dimension: \(152\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.36704 q^{2} -1.77609 q^{3} +3.60290 q^{4} -2.33381 q^{5} +4.20407 q^{6} +1.88575 q^{7} -3.79413 q^{8} +0.154480 q^{9} +O(q^{10})\) \(q-2.36704 q^{2} -1.77609 q^{3} +3.60290 q^{4} -2.33381 q^{5} +4.20407 q^{6} +1.88575 q^{7} -3.79413 q^{8} +0.154480 q^{9} +5.52424 q^{10} +1.82210 q^{11} -6.39906 q^{12} +6.76099 q^{13} -4.46364 q^{14} +4.14505 q^{15} +1.77508 q^{16} -2.35326 q^{17} -0.365662 q^{18} +6.07274 q^{19} -8.40849 q^{20} -3.34925 q^{21} -4.31298 q^{22} -8.81676 q^{23} +6.73870 q^{24} +0.446688 q^{25} -16.0036 q^{26} +5.05389 q^{27} +6.79415 q^{28} +1.35545 q^{29} -9.81153 q^{30} -6.70211 q^{31} +3.38657 q^{32} -3.23620 q^{33} +5.57028 q^{34} -4.40098 q^{35} +0.556577 q^{36} +0.763522 q^{37} -14.3744 q^{38} -12.0081 q^{39} +8.85479 q^{40} -9.44857 q^{41} +7.92781 q^{42} +2.53024 q^{43} +6.56483 q^{44} -0.360529 q^{45} +20.8697 q^{46} +1.02407 q^{47} -3.15269 q^{48} -3.44396 q^{49} -1.05733 q^{50} +4.17960 q^{51} +24.3591 q^{52} +5.46342 q^{53} -11.9628 q^{54} -4.25244 q^{55} -7.15476 q^{56} -10.7857 q^{57} -3.20842 q^{58} -11.6592 q^{59} +14.9342 q^{60} -0.202687 q^{61} +15.8642 q^{62} +0.291311 q^{63} -11.5663 q^{64} -15.7789 q^{65} +7.66023 q^{66} -7.14502 q^{67} -8.47857 q^{68} +15.6593 q^{69} +10.4173 q^{70} +15.7134 q^{71} -0.586119 q^{72} -0.871648 q^{73} -1.80729 q^{74} -0.793357 q^{75} +21.8795 q^{76} +3.43601 q^{77} +28.4237 q^{78} +11.6175 q^{79} -4.14270 q^{80} -9.43958 q^{81} +22.3652 q^{82} +2.43977 q^{83} -12.0670 q^{84} +5.49208 q^{85} -5.98918 q^{86} -2.40740 q^{87} -6.91327 q^{88} +5.23044 q^{89} +0.853387 q^{90} +12.7495 q^{91} -31.7659 q^{92} +11.9035 q^{93} -2.42401 q^{94} -14.1726 q^{95} -6.01485 q^{96} -0.445021 q^{97} +8.15201 q^{98} +0.281478 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} + O(q^{10}) \) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} - 15q^{10} - 40q^{11} - 53q^{12} - 59q^{13} - 36q^{14} - 40q^{15} + 118q^{16} - 93q^{17} - 59q^{18} - 16q^{19} - 108q^{20} - 62q^{21} - 37q^{22} - 107q^{23} - 31q^{24} + 101q^{25} - 64q^{26} - 63q^{27} - 53q^{28} - 124q^{29} - 68q^{30} - 15q^{31} - 129q^{32} - 49q^{33} - 76q^{35} + 45q^{36} - 98q^{37} - 125q^{38} - 47q^{39} - 7q^{40} - 56q^{41} - 84q^{42} - 62q^{43} - 114q^{44} - 142q^{45} - 3q^{46} - 111q^{47} - 92q^{48} + 117q^{49} - 64q^{50} - 21q^{51} - 85q^{52} - 347q^{53} + 3q^{54} - 16q^{55} - 73q^{56} - 115q^{57} - 29q^{58} - 50q^{59} - 54q^{60} - 62q^{61} - 55q^{62} - 70q^{63} + 64q^{64} - 147q^{65} + 34q^{66} - 86q^{67} - 174q^{68} - 104q^{69} - 7q^{70} - 86q^{71} - 139q^{72} - 27q^{73} - 52q^{74} - 49q^{75} - 11q^{76} - 346q^{77} - 59q^{78} - 17q^{79} - 149q^{80} - 8q^{81} - 31q^{82} - 106q^{83} - 51q^{84} - 69q^{85} - 85q^{86} - 32q^{87} - 113q^{88} - 59q^{89} + 10q^{90} - 9q^{91} - 314q^{92} - 230q^{93} + 7q^{94} - 74q^{95} - 54q^{96} - 60q^{97} - 77q^{98} - 96q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.36704 −1.67375 −0.836876 0.547392i \(-0.815621\pi\)
−0.836876 + 0.547392i \(0.815621\pi\)
\(3\) −1.77609 −1.02542 −0.512712 0.858561i \(-0.671359\pi\)
−0.512712 + 0.858561i \(0.671359\pi\)
\(4\) 3.60290 1.80145
\(5\) −2.33381 −1.04371 −0.521857 0.853033i \(-0.674760\pi\)
−0.521857 + 0.853033i \(0.674760\pi\)
\(6\) 4.20407 1.71631
\(7\) 1.88575 0.712745 0.356372 0.934344i \(-0.384013\pi\)
0.356372 + 0.934344i \(0.384013\pi\)
\(8\) −3.79413 −1.34143
\(9\) 0.154480 0.0514935
\(10\) 5.52424 1.74692
\(11\) 1.82210 0.549383 0.274691 0.961532i \(-0.411424\pi\)
0.274691 + 0.961532i \(0.411424\pi\)
\(12\) −6.39906 −1.84725
\(13\) 6.76099 1.87516 0.937580 0.347769i \(-0.113061\pi\)
0.937580 + 0.347769i \(0.113061\pi\)
\(14\) −4.46364 −1.19296
\(15\) 4.14505 1.07025
\(16\) 1.77508 0.443769
\(17\) −2.35326 −0.570750 −0.285375 0.958416i \(-0.592118\pi\)
−0.285375 + 0.958416i \(0.592118\pi\)
\(18\) −0.365662 −0.0861874
\(19\) 6.07274 1.39318 0.696591 0.717469i \(-0.254699\pi\)
0.696591 + 0.717469i \(0.254699\pi\)
\(20\) −8.40849 −1.88020
\(21\) −3.34925 −0.730865
\(22\) −4.31298 −0.919531
\(23\) −8.81676 −1.83842 −0.919211 0.393765i \(-0.871172\pi\)
−0.919211 + 0.393765i \(0.871172\pi\)
\(24\) 6.73870 1.37553
\(25\) 0.446688 0.0893376
\(26\) −16.0036 −3.13856
\(27\) 5.05389 0.972621
\(28\) 6.79415 1.28397
\(29\) 1.35545 0.251702 0.125851 0.992049i \(-0.459834\pi\)
0.125851 + 0.992049i \(0.459834\pi\)
\(30\) −9.81153 −1.79133
\(31\) −6.70211 −1.20374 −0.601868 0.798596i \(-0.705577\pi\)
−0.601868 + 0.798596i \(0.705577\pi\)
\(32\) 3.38657 0.598667
\(33\) −3.23620 −0.563350
\(34\) 5.57028 0.955295
\(35\) −4.40098 −0.743901
\(36\) 0.556577 0.0927629
\(37\) 0.763522 0.125522 0.0627611 0.998029i \(-0.480009\pi\)
0.0627611 + 0.998029i \(0.480009\pi\)
\(38\) −14.3744 −2.33184
\(39\) −12.0081 −1.92283
\(40\) 8.85479 1.40007
\(41\) −9.44857 −1.47562 −0.737809 0.675009i \(-0.764140\pi\)
−0.737809 + 0.675009i \(0.764140\pi\)
\(42\) 7.92781 1.22329
\(43\) 2.53024 0.385857 0.192929 0.981213i \(-0.438201\pi\)
0.192929 + 0.981213i \(0.438201\pi\)
\(44\) 6.56483 0.989685
\(45\) −0.360529 −0.0537445
\(46\) 20.8697 3.07706
\(47\) 1.02407 0.149376 0.0746878 0.997207i \(-0.476204\pi\)
0.0746878 + 0.997207i \(0.476204\pi\)
\(48\) −3.15269 −0.455051
\(49\) −3.44396 −0.491995
\(50\) −1.05733 −0.149529
\(51\) 4.17960 0.585261
\(52\) 24.3591 3.37801
\(53\) 5.46342 0.750459 0.375229 0.926932i \(-0.377564\pi\)
0.375229 + 0.926932i \(0.377564\pi\)
\(54\) −11.9628 −1.62793
\(55\) −4.25244 −0.573398
\(56\) −7.15476 −0.956096
\(57\) −10.7857 −1.42860
\(58\) −3.20842 −0.421286
\(59\) −11.6592 −1.51790 −0.758949 0.651150i \(-0.774287\pi\)
−0.758949 + 0.651150i \(0.774287\pi\)
\(60\) 14.9342 1.92800
\(61\) −0.202687 −0.0259515 −0.0129757 0.999916i \(-0.504130\pi\)
−0.0129757 + 0.999916i \(0.504130\pi\)
\(62\) 15.8642 2.01476
\(63\) 0.291311 0.0367017
\(64\) −11.5663 −1.44579
\(65\) −15.7789 −1.95713
\(66\) 7.66023 0.942909
\(67\) −7.14502 −0.872903 −0.436452 0.899728i \(-0.643765\pi\)
−0.436452 + 0.899728i \(0.643765\pi\)
\(68\) −8.47857 −1.02818
\(69\) 15.6593 1.88516
\(70\) 10.4173 1.24511
\(71\) 15.7134 1.86483 0.932417 0.361385i \(-0.117696\pi\)
0.932417 + 0.361385i \(0.117696\pi\)
\(72\) −0.586119 −0.0690748
\(73\) −0.871648 −0.102019 −0.0510093 0.998698i \(-0.516244\pi\)
−0.0510093 + 0.998698i \(0.516244\pi\)
\(74\) −1.80729 −0.210093
\(75\) −0.793357 −0.0916089
\(76\) 21.8795 2.50975
\(77\) 3.43601 0.391570
\(78\) 28.4237 3.21835
\(79\) 11.6175 1.30707 0.653537 0.756895i \(-0.273285\pi\)
0.653537 + 0.756895i \(0.273285\pi\)
\(80\) −4.14270 −0.463168
\(81\) −9.43958 −1.04884
\(82\) 22.3652 2.46982
\(83\) 2.43977 0.267800 0.133900 0.990995i \(-0.457250\pi\)
0.133900 + 0.990995i \(0.457250\pi\)
\(84\) −12.0670 −1.31662
\(85\) 5.49208 0.595700
\(86\) −5.98918 −0.645830
\(87\) −2.40740 −0.258101
\(88\) −6.91327 −0.736957
\(89\) 5.23044 0.554426 0.277213 0.960809i \(-0.410589\pi\)
0.277213 + 0.960809i \(0.410589\pi\)
\(90\) 0.853387 0.0899549
\(91\) 12.7495 1.33651
\(92\) −31.7659 −3.31182
\(93\) 11.9035 1.23434
\(94\) −2.42401 −0.250018
\(95\) −14.1726 −1.45408
\(96\) −6.01485 −0.613888
\(97\) −0.445021 −0.0451850 −0.0225925 0.999745i \(-0.507192\pi\)
−0.0225925 + 0.999745i \(0.507192\pi\)
\(98\) 8.15201 0.823477
\(99\) 0.281478 0.0282897
\(100\) 1.60937 0.160937
\(101\) 14.5874 1.45150 0.725752 0.687956i \(-0.241492\pi\)
0.725752 + 0.687956i \(0.241492\pi\)
\(102\) −9.89329 −0.979582
\(103\) −9.26218 −0.912630 −0.456315 0.889818i \(-0.650831\pi\)
−0.456315 + 0.889818i \(0.650831\pi\)
\(104\) −25.6521 −2.51539
\(105\) 7.81652 0.762814
\(106\) −12.9322 −1.25608
\(107\) −16.9518 −1.63879 −0.819397 0.573227i \(-0.805691\pi\)
−0.819397 + 0.573227i \(0.805691\pi\)
\(108\) 18.2086 1.75213
\(109\) 11.2234 1.07500 0.537502 0.843263i \(-0.319368\pi\)
0.537502 + 0.843263i \(0.319368\pi\)
\(110\) 10.0657 0.959727
\(111\) −1.35608 −0.128713
\(112\) 3.34734 0.316294
\(113\) −18.3513 −1.72634 −0.863172 0.504910i \(-0.831526\pi\)
−0.863172 + 0.504910i \(0.831526\pi\)
\(114\) 25.5302 2.39113
\(115\) 20.5767 1.91879
\(116\) 4.88357 0.453428
\(117\) 1.04444 0.0965586
\(118\) 27.5978 2.54059
\(119\) −4.43766 −0.406799
\(120\) −15.7269 −1.43566
\(121\) −7.67996 −0.698178
\(122\) 0.479770 0.0434363
\(123\) 16.7815 1.51313
\(124\) −24.1470 −2.16847
\(125\) 10.6266 0.950470
\(126\) −0.689546 −0.0614296
\(127\) −7.53570 −0.668685 −0.334343 0.942452i \(-0.608514\pi\)
−0.334343 + 0.942452i \(0.608514\pi\)
\(128\) 20.6049 1.82123
\(129\) −4.49392 −0.395667
\(130\) 37.3493 3.27575
\(131\) 9.76448 0.853127 0.426563 0.904458i \(-0.359724\pi\)
0.426563 + 0.904458i \(0.359724\pi\)
\(132\) −11.6597 −1.01485
\(133\) 11.4516 0.992983
\(134\) 16.9126 1.46102
\(135\) −11.7948 −1.01514
\(136\) 8.92859 0.765620
\(137\) −12.7679 −1.09083 −0.545416 0.838166i \(-0.683628\pi\)
−0.545416 + 0.838166i \(0.683628\pi\)
\(138\) −37.0663 −3.15529
\(139\) 4.06658 0.344922 0.172461 0.985016i \(-0.444828\pi\)
0.172461 + 0.985016i \(0.444828\pi\)
\(140\) −15.8563 −1.34010
\(141\) −1.81883 −0.153173
\(142\) −37.1942 −3.12127
\(143\) 12.3192 1.03018
\(144\) 0.274215 0.0228512
\(145\) −3.16338 −0.262704
\(146\) 2.06323 0.170754
\(147\) 6.11677 0.504503
\(148\) 2.75089 0.226122
\(149\) 13.9322 1.14137 0.570687 0.821168i \(-0.306677\pi\)
0.570687 + 0.821168i \(0.306677\pi\)
\(150\) 1.87791 0.153331
\(151\) −7.71934 −0.628191 −0.314095 0.949391i \(-0.601701\pi\)
−0.314095 + 0.949391i \(0.601701\pi\)
\(152\) −23.0408 −1.86885
\(153\) −0.363533 −0.0293899
\(154\) −8.13319 −0.655391
\(155\) 15.6415 1.25635
\(156\) −43.2639 −3.46389
\(157\) −10.2850 −0.820829 −0.410414 0.911899i \(-0.634616\pi\)
−0.410414 + 0.911899i \(0.634616\pi\)
\(158\) −27.4992 −2.18772
\(159\) −9.70350 −0.769538
\(160\) −7.90363 −0.624837
\(161\) −16.6262 −1.31033
\(162\) 22.3439 1.75550
\(163\) −4.52977 −0.354799 −0.177399 0.984139i \(-0.556768\pi\)
−0.177399 + 0.984139i \(0.556768\pi\)
\(164\) −34.0422 −2.65825
\(165\) 7.55269 0.587976
\(166\) −5.77505 −0.448231
\(167\) −6.44424 −0.498670 −0.249335 0.968417i \(-0.580212\pi\)
−0.249335 + 0.968417i \(0.580212\pi\)
\(168\) 12.7075 0.980403
\(169\) 32.7110 2.51623
\(170\) −13.0000 −0.997054
\(171\) 0.938120 0.0717398
\(172\) 9.11618 0.695102
\(173\) 4.59374 0.349256 0.174628 0.984635i \(-0.444128\pi\)
0.174628 + 0.984635i \(0.444128\pi\)
\(174\) 5.69843 0.431997
\(175\) 0.842340 0.0636750
\(176\) 3.23436 0.243799
\(177\) 20.7077 1.55649
\(178\) −12.3807 −0.927972
\(179\) 13.7871 1.03049 0.515247 0.857042i \(-0.327700\pi\)
0.515247 + 0.857042i \(0.327700\pi\)
\(180\) −1.29895 −0.0968179
\(181\) 19.7364 1.46699 0.733496 0.679693i \(-0.237887\pi\)
0.733496 + 0.679693i \(0.237887\pi\)
\(182\) −30.1786 −2.23699
\(183\) 0.359990 0.0266112
\(184\) 33.4519 2.46611
\(185\) −1.78192 −0.131009
\(186\) −28.1762 −2.06598
\(187\) −4.28787 −0.313560
\(188\) 3.68961 0.269092
\(189\) 9.53035 0.693231
\(190\) 33.5473 2.43377
\(191\) 3.99926 0.289376 0.144688 0.989477i \(-0.453782\pi\)
0.144688 + 0.989477i \(0.453782\pi\)
\(192\) 20.5428 1.48255
\(193\) −9.49052 −0.683143 −0.341571 0.939856i \(-0.610959\pi\)
−0.341571 + 0.939856i \(0.610959\pi\)
\(194\) 1.05338 0.0756285
\(195\) 28.0247 2.00689
\(196\) −12.4082 −0.886303
\(197\) 20.6141 1.46870 0.734348 0.678773i \(-0.237488\pi\)
0.734348 + 0.678773i \(0.237488\pi\)
\(198\) −0.666272 −0.0473499
\(199\) −2.84743 −0.201849 −0.100924 0.994894i \(-0.532180\pi\)
−0.100924 + 0.994894i \(0.532180\pi\)
\(200\) −1.69479 −0.119840
\(201\) 12.6902 0.895095
\(202\) −34.5291 −2.42946
\(203\) 2.55604 0.179399
\(204\) 15.0587 1.05432
\(205\) 22.0512 1.54012
\(206\) 21.9240 1.52752
\(207\) −1.36202 −0.0946668
\(208\) 12.0013 0.832139
\(209\) 11.0651 0.765390
\(210\) −18.5020 −1.27676
\(211\) 9.28725 0.639361 0.319680 0.947525i \(-0.396424\pi\)
0.319680 + 0.947525i \(0.396424\pi\)
\(212\) 19.6841 1.35191
\(213\) −27.9083 −1.91224
\(214\) 40.1257 2.74294
\(215\) −5.90510 −0.402724
\(216\) −19.1751 −1.30470
\(217\) −12.6385 −0.857956
\(218\) −26.5662 −1.79929
\(219\) 1.54812 0.104612
\(220\) −15.3211 −1.03295
\(221\) −15.9104 −1.07025
\(222\) 3.20990 0.215434
\(223\) −1.70928 −0.114462 −0.0572311 0.998361i \(-0.518227\pi\)
−0.0572311 + 0.998361i \(0.518227\pi\)
\(224\) 6.38622 0.426697
\(225\) 0.0690046 0.00460031
\(226\) 43.4383 2.88947
\(227\) −8.38511 −0.556539 −0.278270 0.960503i \(-0.589761\pi\)
−0.278270 + 0.960503i \(0.589761\pi\)
\(228\) −38.8598 −2.57355
\(229\) −18.2747 −1.20763 −0.603814 0.797125i \(-0.706353\pi\)
−0.603814 + 0.797125i \(0.706353\pi\)
\(230\) −48.7059 −3.21157
\(231\) −6.10265 −0.401525
\(232\) −5.14277 −0.337640
\(233\) 10.7212 0.702366 0.351183 0.936307i \(-0.385779\pi\)
0.351183 + 0.936307i \(0.385779\pi\)
\(234\) −2.47224 −0.161615
\(235\) −2.38998 −0.155905
\(236\) −42.0069 −2.73442
\(237\) −20.6337 −1.34030
\(238\) 10.5041 0.680882
\(239\) 9.71962 0.628710 0.314355 0.949306i \(-0.398212\pi\)
0.314355 + 0.949306i \(0.398212\pi\)
\(240\) 7.35779 0.474943
\(241\) 4.27420 0.275325 0.137663 0.990479i \(-0.456041\pi\)
0.137663 + 0.990479i \(0.456041\pi\)
\(242\) 18.1788 1.16858
\(243\) 1.60384 0.102886
\(244\) −0.730262 −0.0467502
\(245\) 8.03757 0.513501
\(246\) −39.7225 −2.53261
\(247\) 41.0577 2.61244
\(248\) 25.4287 1.61472
\(249\) −4.33324 −0.274608
\(250\) −25.1536 −1.59085
\(251\) −12.8823 −0.813123 −0.406561 0.913623i \(-0.633272\pi\)
−0.406561 + 0.913623i \(0.633272\pi\)
\(252\) 1.04956 0.0661163
\(253\) −16.0650 −1.01000
\(254\) 17.8373 1.11921
\(255\) −9.75440 −0.610844
\(256\) −25.6399 −1.60250
\(257\) −4.96948 −0.309988 −0.154994 0.987915i \(-0.549536\pi\)
−0.154994 + 0.987915i \(0.549536\pi\)
\(258\) 10.6373 0.662249
\(259\) 1.43981 0.0894653
\(260\) −56.8497 −3.52567
\(261\) 0.209391 0.0129610
\(262\) −23.1130 −1.42792
\(263\) 15.3339 0.945530 0.472765 0.881189i \(-0.343256\pi\)
0.472765 + 0.881189i \(0.343256\pi\)
\(264\) 12.2786 0.755693
\(265\) −12.7506 −0.783264
\(266\) −27.1065 −1.66201
\(267\) −9.28971 −0.568521
\(268\) −25.7428 −1.57249
\(269\) −13.4276 −0.818697 −0.409348 0.912378i \(-0.634244\pi\)
−0.409348 + 0.912378i \(0.634244\pi\)
\(270\) 27.9189 1.69909
\(271\) −21.6272 −1.31376 −0.656880 0.753995i \(-0.728124\pi\)
−0.656880 + 0.753995i \(0.728124\pi\)
\(272\) −4.17722 −0.253281
\(273\) −22.6442 −1.37049
\(274\) 30.2221 1.82578
\(275\) 0.813909 0.0490806
\(276\) 56.4190 3.39602
\(277\) 10.9913 0.660405 0.330203 0.943910i \(-0.392883\pi\)
0.330203 + 0.943910i \(0.392883\pi\)
\(278\) −9.62577 −0.577315
\(279\) −1.03535 −0.0619845
\(280\) 16.6979 0.997890
\(281\) −23.5788 −1.40659 −0.703296 0.710898i \(-0.748289\pi\)
−0.703296 + 0.710898i \(0.748289\pi\)
\(282\) 4.30525 0.256374
\(283\) 24.7103 1.46887 0.734437 0.678677i \(-0.237446\pi\)
0.734437 + 0.678677i \(0.237446\pi\)
\(284\) 56.6136 3.35940
\(285\) 25.1718 1.49105
\(286\) −29.1600 −1.72427
\(287\) −17.8176 −1.05174
\(288\) 0.523160 0.0308275
\(289\) −11.4622 −0.674244
\(290\) 7.48786 0.439702
\(291\) 0.790395 0.0463338
\(292\) −3.14046 −0.183781
\(293\) −10.6701 −0.623355 −0.311678 0.950188i \(-0.600891\pi\)
−0.311678 + 0.950188i \(0.600891\pi\)
\(294\) −14.4787 −0.844413
\(295\) 27.2104 1.58425
\(296\) −2.89690 −0.168379
\(297\) 9.20867 0.534341
\(298\) −32.9782 −1.91038
\(299\) −59.6100 −3.44734
\(300\) −2.85838 −0.165029
\(301\) 4.77138 0.275018
\(302\) 18.2720 1.05144
\(303\) −25.9085 −1.48841
\(304\) 10.7796 0.618251
\(305\) 0.473035 0.0270859
\(306\) 0.860499 0.0491915
\(307\) −19.6399 −1.12091 −0.560454 0.828185i \(-0.689373\pi\)
−0.560454 + 0.828185i \(0.689373\pi\)
\(308\) 12.3796 0.705393
\(309\) 16.4504 0.935832
\(310\) −37.0241 −2.10283
\(311\) 7.02760 0.398499 0.199249 0.979949i \(-0.436150\pi\)
0.199249 + 0.979949i \(0.436150\pi\)
\(312\) 45.5603 2.57934
\(313\) −0.482368 −0.0272650 −0.0136325 0.999907i \(-0.504340\pi\)
−0.0136325 + 0.999907i \(0.504340\pi\)
\(314\) 24.3449 1.37386
\(315\) −0.679866 −0.0383061
\(316\) 41.8567 2.35463
\(317\) −2.75407 −0.154684 −0.0773419 0.997005i \(-0.524643\pi\)
−0.0773419 + 0.997005i \(0.524643\pi\)
\(318\) 22.9686 1.28802
\(319\) 2.46977 0.138281
\(320\) 26.9937 1.50899
\(321\) 30.1079 1.68046
\(322\) 39.3549 2.19316
\(323\) −14.2908 −0.795159
\(324\) −34.0098 −1.88944
\(325\) 3.02005 0.167522
\(326\) 10.7222 0.593845
\(327\) −19.9337 −1.10233
\(328\) 35.8491 1.97944
\(329\) 1.93113 0.106467
\(330\) −17.8776 −0.984127
\(331\) −16.8804 −0.927831 −0.463916 0.885879i \(-0.653556\pi\)
−0.463916 + 0.885879i \(0.653556\pi\)
\(332\) 8.79025 0.482428
\(333\) 0.117949 0.00646358
\(334\) 15.2538 0.834651
\(335\) 16.6751 0.911061
\(336\) −5.94517 −0.324336
\(337\) −23.3254 −1.27062 −0.635308 0.772259i \(-0.719127\pi\)
−0.635308 + 0.772259i \(0.719127\pi\)
\(338\) −77.4283 −4.21154
\(339\) 32.5935 1.77023
\(340\) 19.7874 1.07312
\(341\) −12.2119 −0.661312
\(342\) −2.22057 −0.120075
\(343\) −19.6947 −1.06341
\(344\) −9.60004 −0.517600
\(345\) −36.5460 −1.96757
\(346\) −10.8736 −0.584568
\(347\) −3.77491 −0.202648 −0.101324 0.994853i \(-0.532308\pi\)
−0.101324 + 0.994853i \(0.532308\pi\)
\(348\) −8.67363 −0.464955
\(349\) 11.4651 0.613711 0.306855 0.951756i \(-0.400723\pi\)
0.306855 + 0.951756i \(0.400723\pi\)
\(350\) −1.99386 −0.106576
\(351\) 34.1693 1.82382
\(352\) 6.17067 0.328898
\(353\) −26.3914 −1.40467 −0.702337 0.711844i \(-0.747860\pi\)
−0.702337 + 0.711844i \(0.747860\pi\)
\(354\) −49.0161 −2.60518
\(355\) −36.6721 −1.94635
\(356\) 18.8447 0.998770
\(357\) 7.88166 0.417142
\(358\) −32.6346 −1.72479
\(359\) 18.2950 0.965573 0.482787 0.875738i \(-0.339625\pi\)
0.482787 + 0.875738i \(0.339625\pi\)
\(360\) 1.36789 0.0720943
\(361\) 17.8781 0.940955
\(362\) −46.7168 −2.45538
\(363\) 13.6403 0.715929
\(364\) 45.9352 2.40766
\(365\) 2.03426 0.106478
\(366\) −0.852113 −0.0445407
\(367\) 8.15659 0.425770 0.212885 0.977077i \(-0.431714\pi\)
0.212885 + 0.977077i \(0.431714\pi\)
\(368\) −15.6504 −0.815835
\(369\) −1.45962 −0.0759848
\(370\) 4.21788 0.219277
\(371\) 10.3026 0.534886
\(372\) 42.8872 2.22360
\(373\) −23.3249 −1.20772 −0.603860 0.797090i \(-0.706371\pi\)
−0.603860 + 0.797090i \(0.706371\pi\)
\(374\) 10.1496 0.524823
\(375\) −18.8737 −0.974635
\(376\) −3.88544 −0.200376
\(377\) 9.16421 0.471981
\(378\) −22.5587 −1.16030
\(379\) −27.9750 −1.43698 −0.718490 0.695537i \(-0.755166\pi\)
−0.718490 + 0.695537i \(0.755166\pi\)
\(380\) −51.0626 −2.61945
\(381\) 13.3840 0.685686
\(382\) −9.46642 −0.484344
\(383\) −6.10441 −0.311921 −0.155960 0.987763i \(-0.549847\pi\)
−0.155960 + 0.987763i \(0.549847\pi\)
\(384\) −36.5960 −1.86753
\(385\) −8.01901 −0.408687
\(386\) 22.4645 1.14341
\(387\) 0.390872 0.0198691
\(388\) −1.60336 −0.0813985
\(389\) 18.8632 0.956405 0.478202 0.878250i \(-0.341289\pi\)
0.478202 + 0.878250i \(0.341289\pi\)
\(390\) −66.3356 −3.35903
\(391\) 20.7482 1.04928
\(392\) 13.0668 0.659975
\(393\) −17.3426 −0.874816
\(394\) −48.7945 −2.45823
\(395\) −27.1131 −1.36421
\(396\) 1.01414 0.0509624
\(397\) −5.74598 −0.288383 −0.144191 0.989550i \(-0.546058\pi\)
−0.144191 + 0.989550i \(0.546058\pi\)
\(398\) 6.73998 0.337845
\(399\) −20.3391 −1.01823
\(400\) 0.792906 0.0396453
\(401\) 23.9307 1.19504 0.597522 0.801853i \(-0.296152\pi\)
0.597522 + 0.801853i \(0.296152\pi\)
\(402\) −30.0382 −1.49817
\(403\) −45.3129 −2.25720
\(404\) 52.5571 2.61481
\(405\) 22.0302 1.09469
\(406\) −6.05027 −0.300270
\(407\) 1.39121 0.0689598
\(408\) −15.8579 −0.785085
\(409\) −24.0356 −1.18848 −0.594242 0.804287i \(-0.702548\pi\)
−0.594242 + 0.804287i \(0.702548\pi\)
\(410\) −52.1962 −2.57778
\(411\) 22.6768 1.11856
\(412\) −33.3707 −1.64406
\(413\) −21.9863 −1.08187
\(414\) 3.22396 0.158449
\(415\) −5.69398 −0.279506
\(416\) 22.8966 1.12260
\(417\) −7.22259 −0.353692
\(418\) −26.1916 −1.28107
\(419\) 20.6187 1.00729 0.503644 0.863912i \(-0.331993\pi\)
0.503644 + 0.863912i \(0.331993\pi\)
\(420\) 28.1621 1.37417
\(421\) −14.5308 −0.708188 −0.354094 0.935210i \(-0.615211\pi\)
−0.354094 + 0.935210i \(0.615211\pi\)
\(422\) −21.9833 −1.07013
\(423\) 0.158198 0.00769187
\(424\) −20.7289 −1.00669
\(425\) −1.05118 −0.0509895
\(426\) 66.0601 3.20062
\(427\) −0.382217 −0.0184968
\(428\) −61.0757 −2.95220
\(429\) −21.8799 −1.05637
\(430\) 13.9776 0.674061
\(431\) −23.4163 −1.12793 −0.563963 0.825800i \(-0.690724\pi\)
−0.563963 + 0.825800i \(0.690724\pi\)
\(432\) 8.97104 0.431619
\(433\) 31.3876 1.50839 0.754196 0.656650i \(-0.228027\pi\)
0.754196 + 0.656650i \(0.228027\pi\)
\(434\) 29.9159 1.43601
\(435\) 5.61843 0.269383
\(436\) 40.4367 1.93656
\(437\) −53.5419 −2.56126
\(438\) −3.66447 −0.175095
\(439\) −18.6832 −0.891702 −0.445851 0.895107i \(-0.647099\pi\)
−0.445851 + 0.895107i \(0.647099\pi\)
\(440\) 16.1343 0.769172
\(441\) −0.532025 −0.0253345
\(442\) 37.6606 1.79133
\(443\) −25.6976 −1.22093 −0.610464 0.792044i \(-0.709017\pi\)
−0.610464 + 0.792044i \(0.709017\pi\)
\(444\) −4.88582 −0.231871
\(445\) −12.2069 −0.578662
\(446\) 4.04595 0.191581
\(447\) −24.7449 −1.17039
\(448\) −21.8111 −1.03048
\(449\) 6.30831 0.297707 0.148854 0.988859i \(-0.452442\pi\)
0.148854 + 0.988859i \(0.452442\pi\)
\(450\) −0.163337 −0.00769978
\(451\) −17.2162 −0.810680
\(452\) −66.1178 −3.10992
\(453\) 13.7102 0.644162
\(454\) 19.8479 0.931510
\(455\) −29.7550 −1.39493
\(456\) 40.9224 1.91636
\(457\) −28.1392 −1.31630 −0.658149 0.752888i \(-0.728660\pi\)
−0.658149 + 0.752888i \(0.728660\pi\)
\(458\) 43.2571 2.02127
\(459\) −11.8931 −0.555124
\(460\) 74.1357 3.45660
\(461\) −2.61423 −0.121757 −0.0608784 0.998145i \(-0.519390\pi\)
−0.0608784 + 0.998145i \(0.519390\pi\)
\(462\) 14.4452 0.672054
\(463\) 0.288021 0.0133855 0.00669273 0.999978i \(-0.497870\pi\)
0.00669273 + 0.999978i \(0.497870\pi\)
\(464\) 2.40604 0.111697
\(465\) −27.7806 −1.28830
\(466\) −25.3774 −1.17559
\(467\) 10.9711 0.507681 0.253841 0.967246i \(-0.418306\pi\)
0.253841 + 0.967246i \(0.418306\pi\)
\(468\) 3.76301 0.173945
\(469\) −13.4737 −0.622157
\(470\) 5.65719 0.260947
\(471\) 18.2670 0.841697
\(472\) 44.2365 2.03615
\(473\) 4.61034 0.211983
\(474\) 48.8409 2.24334
\(475\) 2.71262 0.124464
\(476\) −15.9884 −0.732828
\(477\) 0.843992 0.0386437
\(478\) −23.0068 −1.05230
\(479\) −28.6512 −1.30911 −0.654553 0.756016i \(-0.727143\pi\)
−0.654553 + 0.756016i \(0.727143\pi\)
\(480\) 14.0375 0.640723
\(481\) 5.16216 0.235374
\(482\) −10.1172 −0.460827
\(483\) 29.5295 1.34364
\(484\) −27.6701 −1.25773
\(485\) 1.03860 0.0471602
\(486\) −3.79636 −0.172206
\(487\) 22.6733 1.02743 0.513713 0.857962i \(-0.328270\pi\)
0.513713 + 0.857962i \(0.328270\pi\)
\(488\) 0.769022 0.0348120
\(489\) 8.04525 0.363819
\(490\) −19.0253 −0.859474
\(491\) 14.6547 0.661358 0.330679 0.943743i \(-0.392722\pi\)
0.330679 + 0.943743i \(0.392722\pi\)
\(492\) 60.4619 2.72583
\(493\) −3.18974 −0.143659
\(494\) −97.1854 −4.37258
\(495\) −0.656918 −0.0295263
\(496\) −11.8968 −0.534181
\(497\) 29.6314 1.32915
\(498\) 10.2570 0.459626
\(499\) −23.4124 −1.04808 −0.524042 0.851692i \(-0.675577\pi\)
−0.524042 + 0.851692i \(0.675577\pi\)
\(500\) 38.2865 1.71222
\(501\) 11.4455 0.511348
\(502\) 30.4929 1.36097
\(503\) −0.00782983 −0.000349115 0 −0.000174557 1.00000i \(-0.500056\pi\)
−0.000174557 1.00000i \(0.500056\pi\)
\(504\) −1.10527 −0.0492327
\(505\) −34.0444 −1.51495
\(506\) 38.0266 1.69049
\(507\) −58.0975 −2.58020
\(508\) −27.1504 −1.20460
\(509\) −30.2553 −1.34104 −0.670520 0.741891i \(-0.733929\pi\)
−0.670520 + 0.741891i \(0.733929\pi\)
\(510\) 23.0891 1.02240
\(511\) −1.64371 −0.0727133
\(512\) 19.4812 0.860954
\(513\) 30.6909 1.35504
\(514\) 11.7630 0.518843
\(515\) 21.6162 0.952524
\(516\) −16.1911 −0.712774
\(517\) 1.86595 0.0820644
\(518\) −3.40809 −0.149743
\(519\) −8.15888 −0.358135
\(520\) 59.8672 2.62535
\(521\) −42.2226 −1.84980 −0.924902 0.380206i \(-0.875853\pi\)
−0.924902 + 0.380206i \(0.875853\pi\)
\(522\) −0.495639 −0.0216935
\(523\) 9.00758 0.393874 0.196937 0.980416i \(-0.436901\pi\)
0.196937 + 0.980416i \(0.436901\pi\)
\(524\) 35.1804 1.53686
\(525\) −1.49607 −0.0652938
\(526\) −36.2961 −1.58258
\(527\) 15.7718 0.687032
\(528\) −5.74451 −0.249998
\(529\) 54.7353 2.37980
\(530\) 30.1813 1.31099
\(531\) −1.80112 −0.0781619
\(532\) 41.2591 1.78881
\(533\) −63.8817 −2.76702
\(534\) 21.9892 0.951564
\(535\) 39.5624 1.71043
\(536\) 27.1091 1.17094
\(537\) −24.4870 −1.05669
\(538\) 31.7838 1.37030
\(539\) −6.27523 −0.270293
\(540\) −42.4956 −1.82872
\(541\) −16.7488 −0.720086 −0.360043 0.932936i \(-0.617238\pi\)
−0.360043 + 0.932936i \(0.617238\pi\)
\(542\) 51.1926 2.19891
\(543\) −35.0535 −1.50429
\(544\) −7.96950 −0.341690
\(545\) −26.1933 −1.12200
\(546\) 53.5999 2.29386
\(547\) −11.8064 −0.504806 −0.252403 0.967622i \(-0.581221\pi\)
−0.252403 + 0.967622i \(0.581221\pi\)
\(548\) −46.0013 −1.96508
\(549\) −0.0313113 −0.00133633
\(550\) −1.92656 −0.0821488
\(551\) 8.23132 0.350666
\(552\) −59.4135 −2.52881
\(553\) 21.9077 0.931610
\(554\) −26.0170 −1.10536
\(555\) 3.16484 0.134340
\(556\) 14.6515 0.621360
\(557\) −38.0782 −1.61342 −0.806712 0.590944i \(-0.798755\pi\)
−0.806712 + 0.590944i \(0.798755\pi\)
\(558\) 2.45071 0.103747
\(559\) 17.1069 0.723545
\(560\) −7.81208 −0.330121
\(561\) 7.61563 0.321532
\(562\) 55.8120 2.35429
\(563\) −36.1831 −1.52493 −0.762467 0.647027i \(-0.776012\pi\)
−0.762467 + 0.647027i \(0.776012\pi\)
\(564\) −6.55306 −0.275934
\(565\) 42.8285 1.80181
\(566\) −58.4904 −2.45853
\(567\) −17.8006 −0.747557
\(568\) −59.6185 −2.50154
\(569\) 27.0449 1.13378 0.566891 0.823793i \(-0.308146\pi\)
0.566891 + 0.823793i \(0.308146\pi\)
\(570\) −59.5828 −2.49565
\(571\) 11.1794 0.467842 0.233921 0.972256i \(-0.424844\pi\)
0.233921 + 0.972256i \(0.424844\pi\)
\(572\) 44.3847 1.85582
\(573\) −7.10302 −0.296733
\(574\) 42.1750 1.76035
\(575\) −3.93834 −0.164240
\(576\) −1.78677 −0.0744488
\(577\) 31.8314 1.32516 0.662580 0.748991i \(-0.269462\pi\)
0.662580 + 0.748991i \(0.269462\pi\)
\(578\) 27.1314 1.12852
\(579\) 16.8560 0.700511
\(580\) −11.3973 −0.473249
\(581\) 4.60079 0.190873
\(582\) −1.87090 −0.0775513
\(583\) 9.95488 0.412289
\(584\) 3.30715 0.136851
\(585\) −2.43753 −0.100779
\(586\) 25.2566 1.04334
\(587\) 45.3267 1.87083 0.935416 0.353550i \(-0.115025\pi\)
0.935416 + 0.353550i \(0.115025\pi\)
\(588\) 22.0381 0.908836
\(589\) −40.7002 −1.67702
\(590\) −64.4082 −2.65164
\(591\) −36.6125 −1.50603
\(592\) 1.35531 0.0557029
\(593\) −32.5014 −1.33467 −0.667337 0.744756i \(-0.732566\pi\)
−0.667337 + 0.744756i \(0.732566\pi\)
\(594\) −21.7973 −0.894355
\(595\) 10.3567 0.424582
\(596\) 50.1964 2.05613
\(597\) 5.05727 0.206980
\(598\) 141.100 5.76999
\(599\) −21.1351 −0.863558 −0.431779 0.901979i \(-0.642114\pi\)
−0.431779 + 0.901979i \(0.642114\pi\)
\(600\) 3.01010 0.122887
\(601\) −1.96009 −0.0799536 −0.0399768 0.999201i \(-0.512728\pi\)
−0.0399768 + 0.999201i \(0.512728\pi\)
\(602\) −11.2941 −0.460312
\(603\) −1.10377 −0.0449488
\(604\) −27.8120 −1.13165
\(605\) 17.9236 0.728698
\(606\) 61.3267 2.49123
\(607\) 4.24667 0.172367 0.0861836 0.996279i \(-0.472533\pi\)
0.0861836 + 0.996279i \(0.472533\pi\)
\(608\) 20.5658 0.834052
\(609\) −4.53975 −0.183960
\(610\) −1.11969 −0.0453351
\(611\) 6.92370 0.280103
\(612\) −1.30977 −0.0529444
\(613\) 20.9780 0.847295 0.423647 0.905827i \(-0.360750\pi\)
0.423647 + 0.905827i \(0.360750\pi\)
\(614\) 46.4885 1.87612
\(615\) −39.1648 −1.57928
\(616\) −13.0367 −0.525263
\(617\) 33.2795 1.33978 0.669892 0.742459i \(-0.266340\pi\)
0.669892 + 0.742459i \(0.266340\pi\)
\(618\) −38.9389 −1.56635
\(619\) 10.2733 0.412918 0.206459 0.978455i \(-0.433806\pi\)
0.206459 + 0.978455i \(0.433806\pi\)
\(620\) 56.3547 2.26326
\(621\) −44.5589 −1.78809
\(622\) −16.6346 −0.666988
\(623\) 9.86328 0.395164
\(624\) −21.3153 −0.853295
\(625\) −27.0339 −1.08136
\(626\) 1.14179 0.0456349
\(627\) −19.6526 −0.784849
\(628\) −37.0556 −1.47868
\(629\) −1.79677 −0.0716418
\(630\) 1.60927 0.0641149
\(631\) 32.6261 1.29883 0.649413 0.760436i \(-0.275015\pi\)
0.649413 + 0.760436i \(0.275015\pi\)
\(632\) −44.0784 −1.75334
\(633\) −16.4949 −0.655615
\(634\) 6.51900 0.258902
\(635\) 17.5869 0.697916
\(636\) −34.9607 −1.38628
\(637\) −23.2846 −0.922569
\(638\) −5.84606 −0.231448
\(639\) 2.42741 0.0960268
\(640\) −48.0879 −1.90084
\(641\) 34.8584 1.37682 0.688412 0.725320i \(-0.258308\pi\)
0.688412 + 0.725320i \(0.258308\pi\)
\(642\) −71.2667 −2.81267
\(643\) −21.9714 −0.866467 −0.433234 0.901282i \(-0.642628\pi\)
−0.433234 + 0.901282i \(0.642628\pi\)
\(644\) −59.9024 −2.36049
\(645\) 10.4880 0.412963
\(646\) 33.8268 1.33090
\(647\) −40.2707 −1.58320 −0.791602 0.611037i \(-0.790753\pi\)
−0.791602 + 0.611037i \(0.790753\pi\)
\(648\) 35.8150 1.40695
\(649\) −21.2442 −0.833908
\(650\) −7.14860 −0.280391
\(651\) 22.4470 0.879769
\(652\) −16.3203 −0.639152
\(653\) −21.7136 −0.849719 −0.424859 0.905259i \(-0.639676\pi\)
−0.424859 + 0.905259i \(0.639676\pi\)
\(654\) 47.1839 1.84504
\(655\) −22.7885 −0.890420
\(656\) −16.7719 −0.654834
\(657\) −0.134653 −0.00525330
\(658\) −4.57107 −0.178199
\(659\) 6.43800 0.250789 0.125394 0.992107i \(-0.459980\pi\)
0.125394 + 0.992107i \(0.459980\pi\)
\(660\) 27.2116 1.05921
\(661\) 15.0975 0.587226 0.293613 0.955924i \(-0.405142\pi\)
0.293613 + 0.955924i \(0.405142\pi\)
\(662\) 39.9567 1.55296
\(663\) 28.2582 1.09746
\(664\) −9.25681 −0.359234
\(665\) −26.7260 −1.03639
\(666\) −0.279191 −0.0108184
\(667\) −11.9507 −0.462734
\(668\) −23.2179 −0.898329
\(669\) 3.03583 0.117372
\(670\) −39.4708 −1.52489
\(671\) −0.369316 −0.0142573
\(672\) −11.3425 −0.437545
\(673\) −3.73600 −0.144012 −0.0720062 0.997404i \(-0.522940\pi\)
−0.0720062 + 0.997404i \(0.522940\pi\)
\(674\) 55.2123 2.12670
\(675\) 2.25751 0.0868917
\(676\) 117.854 4.53286
\(677\) −12.7305 −0.489272 −0.244636 0.969615i \(-0.578669\pi\)
−0.244636 + 0.969615i \(0.578669\pi\)
\(678\) −77.1502 −2.96293
\(679\) −0.839196 −0.0322054
\(680\) −20.8377 −0.799088
\(681\) 14.8927 0.570689
\(682\) 28.9061 1.10687
\(683\) −10.9849 −0.420327 −0.210163 0.977666i \(-0.567400\pi\)
−0.210163 + 0.977666i \(0.567400\pi\)
\(684\) 3.37995 0.129236
\(685\) 29.7978 1.13852
\(686\) 46.6181 1.77989
\(687\) 32.4575 1.23833
\(688\) 4.49136 0.171232
\(689\) 36.9381 1.40723
\(690\) 86.5059 3.29322
\(691\) 38.5232 1.46549 0.732745 0.680503i \(-0.238239\pi\)
0.732745 + 0.680503i \(0.238239\pi\)
\(692\) 16.5508 0.629166
\(693\) 0.530797 0.0201633
\(694\) 8.93539 0.339183
\(695\) −9.49063 −0.360000
\(696\) 9.13400 0.346224
\(697\) 22.2350 0.842210
\(698\) −27.1383 −1.02720
\(699\) −19.0417 −0.720223
\(700\) 3.03487 0.114707
\(701\) −43.6578 −1.64893 −0.824467 0.565911i \(-0.808525\pi\)
−0.824467 + 0.565911i \(0.808525\pi\)
\(702\) −80.8802 −3.05262
\(703\) 4.63667 0.174875
\(704\) −21.0750 −0.794293
\(705\) 4.24481 0.159869
\(706\) 62.4697 2.35108
\(707\) 27.5082 1.03455
\(708\) 74.6079 2.80394
\(709\) −4.35999 −0.163743 −0.0818715 0.996643i \(-0.526090\pi\)
−0.0818715 + 0.996643i \(0.526090\pi\)
\(710\) 86.8044 3.25771
\(711\) 1.79468 0.0673058
\(712\) −19.8450 −0.743722
\(713\) 59.0910 2.21297
\(714\) −18.6562 −0.698192
\(715\) −28.7507 −1.07521
\(716\) 49.6734 1.85638
\(717\) −17.2629 −0.644694
\(718\) −43.3051 −1.61613
\(719\) −40.4810 −1.50969 −0.754844 0.655904i \(-0.772287\pi\)
−0.754844 + 0.655904i \(0.772287\pi\)
\(720\) −0.639966 −0.0238501
\(721\) −17.4661 −0.650472
\(722\) −42.3184 −1.57493
\(723\) −7.59134 −0.282325
\(724\) 71.1081 2.64271
\(725\) 0.605466 0.0224864
\(726\) −32.2871 −1.19829
\(727\) −8.20358 −0.304254 −0.152127 0.988361i \(-0.548612\pi\)
−0.152127 + 0.988361i \(0.548612\pi\)
\(728\) −48.3733 −1.79283
\(729\) 25.4702 0.943340
\(730\) −4.81519 −0.178218
\(731\) −5.95431 −0.220228
\(732\) 1.29701 0.0479388
\(733\) −13.1259 −0.484816 −0.242408 0.970174i \(-0.577937\pi\)
−0.242408 + 0.970174i \(0.577937\pi\)
\(734\) −19.3070 −0.712634
\(735\) −14.2754 −0.526556
\(736\) −29.8586 −1.10060
\(737\) −13.0189 −0.479558
\(738\) 3.45498 0.127180
\(739\) −24.1338 −0.887778 −0.443889 0.896082i \(-0.646402\pi\)
−0.443889 + 0.896082i \(0.646402\pi\)
\(740\) −6.42007 −0.236006
\(741\) −72.9220 −2.67886
\(742\) −24.3868 −0.895266
\(743\) −5.62269 −0.206277 −0.103138 0.994667i \(-0.532888\pi\)
−0.103138 + 0.994667i \(0.532888\pi\)
\(744\) −45.1635 −1.65578
\(745\) −32.5153 −1.19127
\(746\) 55.2112 2.02143
\(747\) 0.376897 0.0137899
\(748\) −15.4488 −0.564863
\(749\) −31.9668 −1.16804
\(750\) 44.6749 1.63130
\(751\) 16.0583 0.585976 0.292988 0.956116i \(-0.405350\pi\)
0.292988 + 0.956116i \(0.405350\pi\)
\(752\) 1.81780 0.0662883
\(753\) 22.8801 0.833795
\(754\) −21.6921 −0.789980
\(755\) 18.0155 0.655651
\(756\) 34.3369 1.24882
\(757\) −6.38875 −0.232203 −0.116102 0.993237i \(-0.537040\pi\)
−0.116102 + 0.993237i \(0.537040\pi\)
\(758\) 66.2181 2.40515
\(759\) 28.5328 1.03568
\(760\) 53.7728 1.95055
\(761\) 23.6038 0.855638 0.427819 0.903864i \(-0.359282\pi\)
0.427819 + 0.903864i \(0.359282\pi\)
\(762\) −31.6806 −1.14767
\(763\) 21.1644 0.766204
\(764\) 14.4089 0.521296
\(765\) 0.848419 0.0306747
\(766\) 14.4494 0.522078
\(767\) −78.8277 −2.84630
\(768\) 45.5387 1.64324
\(769\) 10.3507 0.373256 0.186628 0.982431i \(-0.440244\pi\)
0.186628 + 0.982431i \(0.440244\pi\)
\(770\) 18.9814 0.684041
\(771\) 8.82622 0.317869
\(772\) −34.1934 −1.23065
\(773\) 5.76192 0.207242 0.103621 0.994617i \(-0.466957\pi\)
0.103621 + 0.994617i \(0.466957\pi\)
\(774\) −0.925211 −0.0332560
\(775\) −2.99376 −0.107539
\(776\) 1.68847 0.0606124
\(777\) −2.55722 −0.0917398
\(778\) −44.6501 −1.60079
\(779\) −57.3787 −2.05580
\(780\) 100.970 3.61531
\(781\) 28.6313 1.02451
\(782\) −49.1118 −1.75624
\(783\) 6.85032 0.244810
\(784\) −6.11330 −0.218332
\(785\) 24.0032 0.856710
\(786\) 41.0506 1.46423
\(787\) 38.0221 1.35534 0.677671 0.735365i \(-0.262989\pi\)
0.677671 + 0.735365i \(0.262989\pi\)
\(788\) 74.2706 2.64578
\(789\) −27.2344 −0.969569
\(790\) 64.1780 2.28335
\(791\) −34.6059 −1.23044
\(792\) −1.06797 −0.0379485
\(793\) −1.37037 −0.0486632
\(794\) 13.6010 0.482681
\(795\) 22.6462 0.803177
\(796\) −10.2590 −0.363620
\(797\) 25.7883 0.913467 0.456734 0.889604i \(-0.349019\pi\)
0.456734 + 0.889604i \(0.349019\pi\)
\(798\) 48.1435 1.70426
\(799\) −2.40990 −0.0852561
\(800\) 1.51274 0.0534835
\(801\) 0.808001 0.0285493
\(802\) −56.6451 −2.00021
\(803\) −1.58823 −0.0560473
\(804\) 45.7214 1.61247
\(805\) 38.8024 1.36761
\(806\) 107.258 3.77799
\(807\) 23.8486 0.839511
\(808\) −55.3466 −1.94709
\(809\) 17.5470 0.616918 0.308459 0.951238i \(-0.400187\pi\)
0.308459 + 0.951238i \(0.400187\pi\)
\(810\) −52.1465 −1.83224
\(811\) 42.6832 1.49881 0.749406 0.662111i \(-0.230339\pi\)
0.749406 + 0.662111i \(0.230339\pi\)
\(812\) 9.20916 0.323178
\(813\) 38.4118 1.34716
\(814\) −3.29306 −0.115422
\(815\) 10.5716 0.370308
\(816\) 7.41911 0.259721
\(817\) 15.3655 0.537569
\(818\) 56.8933 1.98923
\(819\) 1.96955 0.0688216
\(820\) 79.4482 2.77445
\(821\) −42.3466 −1.47791 −0.738953 0.673757i \(-0.764680\pi\)
−0.738953 + 0.673757i \(0.764680\pi\)
\(822\) −53.6770 −1.87220
\(823\) −42.6096 −1.48528 −0.742638 0.669693i \(-0.766426\pi\)
−0.742638 + 0.669693i \(0.766426\pi\)
\(824\) 35.1419 1.22423
\(825\) −1.44557 −0.0503284
\(826\) 52.0425 1.81079
\(827\) 2.98989 0.103969 0.0519843 0.998648i \(-0.483445\pi\)
0.0519843 + 0.998648i \(0.483445\pi\)
\(828\) −4.90721 −0.170537
\(829\) 15.6466 0.543428 0.271714 0.962378i \(-0.412410\pi\)
0.271714 + 0.962378i \(0.412410\pi\)
\(830\) 13.4779 0.467824
\(831\) −19.5216 −0.677195
\(832\) −78.1998 −2.71109
\(833\) 8.10455 0.280806
\(834\) 17.0962 0.591992
\(835\) 15.0397 0.520469
\(836\) 39.8665 1.37881
\(837\) −33.8717 −1.17078
\(838\) −48.8053 −1.68595
\(839\) 50.3412 1.73797 0.868986 0.494837i \(-0.164772\pi\)
0.868986 + 0.494837i \(0.164772\pi\)
\(840\) −29.6569 −1.02326
\(841\) −27.1627 −0.936646
\(842\) 34.3951 1.18533
\(843\) 41.8779 1.44235
\(844\) 33.4610 1.15178
\(845\) −76.3413 −2.62622
\(846\) −0.374462 −0.0128743
\(847\) −14.4825 −0.497623
\(848\) 9.69799 0.333030
\(849\) −43.8876 −1.50622
\(850\) 2.48818 0.0853438
\(851\) −6.73179 −0.230763
\(852\) −100.551 −3.44481
\(853\) −28.5473 −0.977441 −0.488721 0.872440i \(-0.662536\pi\)
−0.488721 + 0.872440i \(0.662536\pi\)
\(854\) 0.904725 0.0309590
\(855\) −2.18940 −0.0748758
\(856\) 64.3174 2.19832
\(857\) −36.9117 −1.26088 −0.630439 0.776238i \(-0.717125\pi\)
−0.630439 + 0.776238i \(0.717125\pi\)
\(858\) 51.7907 1.76811
\(859\) 5.86068 0.199964 0.0999820 0.994989i \(-0.468121\pi\)
0.0999820 + 0.994989i \(0.468121\pi\)
\(860\) −21.2755 −0.725488
\(861\) 31.6456 1.07848
\(862\) 55.4275 1.88787
\(863\) −7.84646 −0.267096 −0.133548 0.991042i \(-0.542637\pi\)
−0.133548 + 0.991042i \(0.542637\pi\)
\(864\) 17.1154 0.582276
\(865\) −10.7209 −0.364523
\(866\) −74.2958 −2.52467
\(867\) 20.3578 0.691386
\(868\) −45.5352 −1.54556
\(869\) 21.1683 0.718084
\(870\) −13.2991 −0.450881
\(871\) −48.3074 −1.63683
\(872\) −42.5829 −1.44204
\(873\) −0.0687470 −0.00232673
\(874\) 126.736 4.28691
\(875\) 20.0390 0.677443
\(876\) 5.57772 0.188454
\(877\) 33.5801 1.13392 0.566960 0.823745i \(-0.308119\pi\)
0.566960 + 0.823745i \(0.308119\pi\)
\(878\) 44.2240 1.49249
\(879\) 18.9511 0.639203
\(880\) −7.54840 −0.254457
\(881\) −42.4221 −1.42924 −0.714618 0.699515i \(-0.753399\pi\)
−0.714618 + 0.699515i \(0.753399\pi\)
\(882\) 1.25933 0.0424037
\(883\) −15.1982 −0.511460 −0.255730 0.966748i \(-0.582316\pi\)
−0.255730 + 0.966748i \(0.582316\pi\)
\(884\) −57.3235 −1.92800
\(885\) −48.3280 −1.62453
\(886\) 60.8272 2.04353
\(887\) −17.0850 −0.573659 −0.286830 0.957982i \(-0.592601\pi\)
−0.286830 + 0.957982i \(0.592601\pi\)
\(888\) 5.14514 0.172660
\(889\) −14.2104 −0.476602
\(890\) 28.8942 0.968537
\(891\) −17.1998 −0.576216
\(892\) −6.15838 −0.206198
\(893\) 6.21889 0.208107
\(894\) 58.5722 1.95895
\(895\) −32.1765 −1.07554
\(896\) 38.8555 1.29807
\(897\) 105.873 3.53498
\(898\) −14.9320 −0.498289
\(899\) −9.08441 −0.302982
\(900\) 0.248617 0.00828722
\(901\) −12.8569 −0.428324
\(902\) 40.7515 1.35688
\(903\) −8.47438 −0.282010
\(904\) 69.6272 2.31577
\(905\) −46.0610 −1.53112
\(906\) −32.4527 −1.07817
\(907\) −23.7732 −0.789375 −0.394687 0.918815i \(-0.629147\pi\)
−0.394687 + 0.918815i \(0.629147\pi\)
\(908\) −30.2107 −1.00258
\(909\) 2.25347 0.0747430
\(910\) 70.4313 2.33478
\(911\) 30.1966 1.00046 0.500228 0.865893i \(-0.333249\pi\)
0.500228 + 0.865893i \(0.333249\pi\)
\(912\) −19.1455 −0.633969
\(913\) 4.44550 0.147125
\(914\) 66.6068 2.20316
\(915\) −0.840150 −0.0277745
\(916\) −65.8420 −2.17548
\(917\) 18.4133 0.608062
\(918\) 28.1516 0.929140
\(919\) −25.1830 −0.830712 −0.415356 0.909659i \(-0.636343\pi\)
−0.415356 + 0.909659i \(0.636343\pi\)
\(920\) −78.0706 −2.57391
\(921\) 34.8822 1.14941
\(922\) 6.18800 0.203791
\(923\) 106.238 3.49686
\(924\) −21.9872 −0.723327
\(925\) 0.341056 0.0112139
\(926\) −0.681758 −0.0224040
\(927\) −1.43083 −0.0469945
\(928\) 4.59035 0.150686
\(929\) −42.8929 −1.40727 −0.703634 0.710562i \(-0.748441\pi\)
−0.703634 + 0.710562i \(0.748441\pi\)
\(930\) 65.7580 2.15629
\(931\) −20.9143 −0.685438
\(932\) 38.6272 1.26528
\(933\) −12.4816 −0.408630
\(934\) −25.9690 −0.849733
\(935\) 10.0071 0.327267
\(936\) −3.96274 −0.129526
\(937\) −45.5773 −1.48895 −0.744474 0.667652i \(-0.767299\pi\)
−0.744474 + 0.667652i \(0.767299\pi\)
\(938\) 31.8928 1.04134
\(939\) 0.856727 0.0279582
\(940\) −8.61086 −0.280855
\(941\) 21.3552 0.696159 0.348080 0.937465i \(-0.386834\pi\)
0.348080 + 0.937465i \(0.386834\pi\)
\(942\) −43.2387 −1.40879
\(943\) 83.3058 2.71281
\(944\) −20.6960 −0.673597
\(945\) −22.2421 −0.723534
\(946\) −10.9129 −0.354808
\(947\) 14.6219 0.475146 0.237573 0.971370i \(-0.423648\pi\)
0.237573 + 0.971370i \(0.423648\pi\)
\(948\) −74.3412 −2.41449
\(949\) −5.89320 −0.191301
\(950\) −6.42089 −0.208321
\(951\) 4.89146 0.158616
\(952\) 16.8370 0.545692
\(953\) −28.4565 −0.921797 −0.460898 0.887453i \(-0.652473\pi\)
−0.460898 + 0.887453i \(0.652473\pi\)
\(954\) −1.99777 −0.0646801
\(955\) −9.33352 −0.302026
\(956\) 35.0188 1.13259
\(957\) −4.38652 −0.141796
\(958\) 67.8186 2.19112
\(959\) −24.0769 −0.777485
\(960\) −47.9430 −1.54735
\(961\) 13.9183 0.448979
\(962\) −12.2191 −0.393958
\(963\) −2.61872 −0.0843872
\(964\) 15.3995 0.495985
\(965\) 22.1491 0.713005
\(966\) −69.8977 −2.24892
\(967\) −15.7232 −0.505623 −0.252811 0.967516i \(-0.581355\pi\)
−0.252811 + 0.967516i \(0.581355\pi\)
\(968\) 29.1388 0.936556
\(969\) 25.3816 0.815374
\(970\) −2.45840 −0.0789345
\(971\) 46.7586 1.50056 0.750278 0.661122i \(-0.229920\pi\)
0.750278 + 0.661122i \(0.229920\pi\)
\(972\) 5.77847 0.185344
\(973\) 7.66853 0.245842
\(974\) −53.6687 −1.71966
\(975\) −5.36387 −0.171781
\(976\) −0.359786 −0.0115165
\(977\) 10.4790 0.335254 0.167627 0.985851i \(-0.446390\pi\)
0.167627 + 0.985851i \(0.446390\pi\)
\(978\) −19.0435 −0.608943
\(979\) 9.53037 0.304592
\(980\) 28.9585 0.925046
\(981\) 1.73379 0.0553557
\(982\) −34.6884 −1.10695
\(983\) 13.8286 0.441065 0.220533 0.975380i \(-0.429220\pi\)
0.220533 + 0.975380i \(0.429220\pi\)
\(984\) −63.6711 −2.02976
\(985\) −48.1095 −1.53290
\(986\) 7.55026 0.240449
\(987\) −3.42985 −0.109173
\(988\) 147.927 4.70618
\(989\) −22.3085 −0.709369
\(990\) 1.55495 0.0494197
\(991\) 50.8964 1.61678 0.808389 0.588649i \(-0.200340\pi\)
0.808389 + 0.588649i \(0.200340\pi\)
\(992\) −22.6972 −0.720637
\(993\) 29.9811 0.951420
\(994\) −70.1389 −2.22467
\(995\) 6.64536 0.210672
\(996\) −15.6122 −0.494693
\(997\) 48.2046 1.52665 0.763327 0.646012i \(-0.223565\pi\)
0.763327 + 0.646012i \(0.223565\pi\)
\(998\) 55.4183 1.75423
\(999\) 3.85875 0.122086
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 \(a_p\))