Properties

Label 8002.2.a.e.1.12
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 0
Dimension 77
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(0\)
Dimension: \(77\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.37610 q^{3} +1.00000 q^{4} -3.32970 q^{5} +2.37610 q^{6} +3.18362 q^{7} -1.00000 q^{8} +2.64585 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.37610 q^{3} +1.00000 q^{4} -3.32970 q^{5} +2.37610 q^{6} +3.18362 q^{7} -1.00000 q^{8} +2.64585 q^{9} +3.32970 q^{10} -3.12572 q^{11} -2.37610 q^{12} -4.61345 q^{13} -3.18362 q^{14} +7.91169 q^{15} +1.00000 q^{16} +5.18964 q^{17} -2.64585 q^{18} +3.13483 q^{19} -3.32970 q^{20} -7.56459 q^{21} +3.12572 q^{22} +5.95882 q^{23} +2.37610 q^{24} +6.08687 q^{25} +4.61345 q^{26} +0.841493 q^{27} +3.18362 q^{28} +1.91697 q^{29} -7.91169 q^{30} -1.12111 q^{31} -1.00000 q^{32} +7.42702 q^{33} -5.18964 q^{34} -10.6005 q^{35} +2.64585 q^{36} -3.03323 q^{37} -3.13483 q^{38} +10.9620 q^{39} +3.32970 q^{40} +7.25292 q^{41} +7.56459 q^{42} -11.0303 q^{43} -3.12572 q^{44} -8.80988 q^{45} -5.95882 q^{46} -2.10688 q^{47} -2.37610 q^{48} +3.13541 q^{49} -6.08687 q^{50} -12.3311 q^{51} -4.61345 q^{52} +11.0192 q^{53} -0.841493 q^{54} +10.4077 q^{55} -3.18362 q^{56} -7.44867 q^{57} -1.91697 q^{58} -5.59792 q^{59} +7.91169 q^{60} -1.78705 q^{61} +1.12111 q^{62} +8.42338 q^{63} +1.00000 q^{64} +15.3614 q^{65} -7.42702 q^{66} +10.2713 q^{67} +5.18964 q^{68} -14.1588 q^{69} +10.6005 q^{70} +7.76365 q^{71} -2.64585 q^{72} -13.9399 q^{73} +3.03323 q^{74} -14.4630 q^{75} +3.13483 q^{76} -9.95109 q^{77} -10.9620 q^{78} +2.57202 q^{79} -3.32970 q^{80} -9.93702 q^{81} -7.25292 q^{82} +11.1175 q^{83} -7.56459 q^{84} -17.2799 q^{85} +11.0303 q^{86} -4.55491 q^{87} +3.12572 q^{88} +10.2553 q^{89} +8.80988 q^{90} -14.6875 q^{91} +5.95882 q^{92} +2.66387 q^{93} +2.10688 q^{94} -10.4380 q^{95} +2.37610 q^{96} +5.61516 q^{97} -3.13541 q^{98} -8.27019 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} + O(q^{10}) \) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} - 18q^{10} + 30q^{11} + 10q^{12} - 2q^{13} - 21q^{14} + 21q^{15} + 77q^{16} + 60q^{17} - 71q^{18} - 3q^{19} + 18q^{20} + 10q^{21} - 30q^{22} + 53q^{23} - 10q^{24} + 59q^{25} + 2q^{26} + 43q^{27} + 21q^{28} + 30q^{29} - 21q^{30} + 22q^{31} - 77q^{32} + 31q^{33} - 60q^{34} + 41q^{35} + 71q^{36} - 3q^{37} + 3q^{38} + 44q^{39} - 18q^{40} + 48q^{41} - 10q^{42} + 21q^{43} + 30q^{44} + 33q^{45} - 53q^{46} + 107q^{47} + 10q^{48} + 24q^{49} - 59q^{50} + 18q^{51} - 2q^{52} + 42q^{53} - 43q^{54} + 49q^{55} - 21q^{56} + 32q^{57} - 30q^{58} + 42q^{59} + 21q^{60} - 31q^{61} - 22q^{62} + 109q^{63} + 77q^{64} + 39q^{65} - 31q^{66} - q^{67} + 60q^{68} - 33q^{69} - 41q^{70} + 58q^{71} - 71q^{72} + 35q^{73} + 3q^{74} + 34q^{75} - 3q^{76} + 86q^{77} - 44q^{78} + 25q^{79} + 18q^{80} + 53q^{81} - 48q^{82} + 107q^{83} + 10q^{84} + 21q^{85} - 21q^{86} + 100q^{87} - 30q^{88} + 34q^{89} - 33q^{90} - 51q^{91} + 53q^{92} + 48q^{93} - 107q^{94} + 118q^{95} - 10q^{96} - 13q^{97} - 24q^{98} + 63q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.37610 −1.37184 −0.685921 0.727676i \(-0.740600\pi\)
−0.685921 + 0.727676i \(0.740600\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.32970 −1.48908 −0.744542 0.667575i \(-0.767332\pi\)
−0.744542 + 0.667575i \(0.767332\pi\)
\(6\) 2.37610 0.970039
\(7\) 3.18362 1.20329 0.601647 0.798762i \(-0.294511\pi\)
0.601647 + 0.798762i \(0.294511\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.64585 0.881950
\(10\) 3.32970 1.05294
\(11\) −3.12572 −0.942440 −0.471220 0.882016i \(-0.656186\pi\)
−0.471220 + 0.882016i \(0.656186\pi\)
\(12\) −2.37610 −0.685921
\(13\) −4.61345 −1.27954 −0.639770 0.768566i \(-0.720971\pi\)
−0.639770 + 0.768566i \(0.720971\pi\)
\(14\) −3.18362 −0.850857
\(15\) 7.91169 2.04279
\(16\) 1.00000 0.250000
\(17\) 5.18964 1.25867 0.629336 0.777134i \(-0.283327\pi\)
0.629336 + 0.777134i \(0.283327\pi\)
\(18\) −2.64585 −0.623633
\(19\) 3.13483 0.719179 0.359590 0.933111i \(-0.382917\pi\)
0.359590 + 0.933111i \(0.382917\pi\)
\(20\) −3.32970 −0.744542
\(21\) −7.56459 −1.65073
\(22\) 3.12572 0.666405
\(23\) 5.95882 1.24250 0.621250 0.783612i \(-0.286625\pi\)
0.621250 + 0.783612i \(0.286625\pi\)
\(24\) 2.37610 0.485019
\(25\) 6.08687 1.21737
\(26\) 4.61345 0.904772
\(27\) 0.841493 0.161945
\(28\) 3.18362 0.601647
\(29\) 1.91697 0.355972 0.177986 0.984033i \(-0.443042\pi\)
0.177986 + 0.984033i \(0.443042\pi\)
\(30\) −7.91169 −1.44447
\(31\) −1.12111 −0.201357 −0.100679 0.994919i \(-0.532101\pi\)
−0.100679 + 0.994919i \(0.532101\pi\)
\(32\) −1.00000 −0.176777
\(33\) 7.42702 1.29288
\(34\) −5.18964 −0.890015
\(35\) −10.6005 −1.79181
\(36\) 2.64585 0.440975
\(37\) −3.03323 −0.498661 −0.249330 0.968418i \(-0.580210\pi\)
−0.249330 + 0.968418i \(0.580210\pi\)
\(38\) −3.13483 −0.508537
\(39\) 10.9620 1.75533
\(40\) 3.32970 0.526471
\(41\) 7.25292 1.13272 0.566358 0.824160i \(-0.308352\pi\)
0.566358 + 0.824160i \(0.308352\pi\)
\(42\) 7.56459 1.16724
\(43\) −11.0303 −1.68210 −0.841050 0.540957i \(-0.818062\pi\)
−0.841050 + 0.540957i \(0.818062\pi\)
\(44\) −3.12572 −0.471220
\(45\) −8.80988 −1.31330
\(46\) −5.95882 −0.878580
\(47\) −2.10688 −0.307320 −0.153660 0.988124i \(-0.549106\pi\)
−0.153660 + 0.988124i \(0.549106\pi\)
\(48\) −2.37610 −0.342960
\(49\) 3.13541 0.447916
\(50\) −6.08687 −0.860813
\(51\) −12.3311 −1.72670
\(52\) −4.61345 −0.639770
\(53\) 11.0192 1.51360 0.756802 0.653644i \(-0.226760\pi\)
0.756802 + 0.653644i \(0.226760\pi\)
\(54\) −0.841493 −0.114513
\(55\) 10.4077 1.40337
\(56\) −3.18362 −0.425429
\(57\) −7.44867 −0.986600
\(58\) −1.91697 −0.251710
\(59\) −5.59792 −0.728788 −0.364394 0.931245i \(-0.618724\pi\)
−0.364394 + 0.931245i \(0.618724\pi\)
\(60\) 7.91169 1.02139
\(61\) −1.78705 −0.228808 −0.114404 0.993434i \(-0.536496\pi\)
−0.114404 + 0.993434i \(0.536496\pi\)
\(62\) 1.12111 0.142381
\(63\) 8.42338 1.06125
\(64\) 1.00000 0.125000
\(65\) 15.3614 1.90534
\(66\) −7.42702 −0.914203
\(67\) 10.2713 1.25484 0.627421 0.778680i \(-0.284110\pi\)
0.627421 + 0.778680i \(0.284110\pi\)
\(68\) 5.18964 0.629336
\(69\) −14.1588 −1.70451
\(70\) 10.6005 1.26700
\(71\) 7.76365 0.921375 0.460688 0.887562i \(-0.347603\pi\)
0.460688 + 0.887562i \(0.347603\pi\)
\(72\) −2.64585 −0.311817
\(73\) −13.9399 −1.63155 −0.815773 0.578372i \(-0.803688\pi\)
−0.815773 + 0.578372i \(0.803688\pi\)
\(74\) 3.03323 0.352606
\(75\) −14.4630 −1.67004
\(76\) 3.13483 0.359590
\(77\) −9.95109 −1.13403
\(78\) −10.9620 −1.24120
\(79\) 2.57202 0.289374 0.144687 0.989477i \(-0.453782\pi\)
0.144687 + 0.989477i \(0.453782\pi\)
\(80\) −3.32970 −0.372271
\(81\) −9.93702 −1.10411
\(82\) −7.25292 −0.800951
\(83\) 11.1175 1.22031 0.610154 0.792282i \(-0.291107\pi\)
0.610154 + 0.792282i \(0.291107\pi\)
\(84\) −7.56459 −0.825365
\(85\) −17.2799 −1.87427
\(86\) 11.0303 1.18942
\(87\) −4.55491 −0.488337
\(88\) 3.12572 0.333203
\(89\) 10.2553 1.08706 0.543532 0.839389i \(-0.317087\pi\)
0.543532 + 0.839389i \(0.317087\pi\)
\(90\) 8.80988 0.928643
\(91\) −14.6875 −1.53966
\(92\) 5.95882 0.621250
\(93\) 2.66387 0.276230
\(94\) 2.10688 0.217308
\(95\) −10.4380 −1.07092
\(96\) 2.37610 0.242510
\(97\) 5.61516 0.570133 0.285066 0.958508i \(-0.407984\pi\)
0.285066 + 0.958508i \(0.407984\pi\)
\(98\) −3.13541 −0.316725
\(99\) −8.27019 −0.831185
\(100\) 6.08687 0.608687
\(101\) −3.24073 −0.322465 −0.161233 0.986916i \(-0.551547\pi\)
−0.161233 + 0.986916i \(0.551547\pi\)
\(102\) 12.3311 1.22096
\(103\) −7.04994 −0.694651 −0.347325 0.937745i \(-0.612910\pi\)
−0.347325 + 0.937745i \(0.612910\pi\)
\(104\) 4.61345 0.452386
\(105\) 25.1878 2.45808
\(106\) −11.0192 −1.07028
\(107\) −5.95942 −0.576119 −0.288059 0.957613i \(-0.593010\pi\)
−0.288059 + 0.957613i \(0.593010\pi\)
\(108\) 0.841493 0.0809727
\(109\) 0.338190 0.0323927 0.0161964 0.999869i \(-0.494844\pi\)
0.0161964 + 0.999869i \(0.494844\pi\)
\(110\) −10.4077 −0.992334
\(111\) 7.20727 0.684084
\(112\) 3.18362 0.300823
\(113\) −16.0462 −1.50950 −0.754752 0.656011i \(-0.772243\pi\)
−0.754752 + 0.656011i \(0.772243\pi\)
\(114\) 7.44867 0.697632
\(115\) −19.8411 −1.85019
\(116\) 1.91697 0.177986
\(117\) −12.2065 −1.12849
\(118\) 5.59792 0.515331
\(119\) 16.5218 1.51455
\(120\) −7.91169 −0.722235
\(121\) −1.22989 −0.111808
\(122\) 1.78705 0.161792
\(123\) −17.2337 −1.55391
\(124\) −1.12111 −0.100679
\(125\) −3.61895 −0.323688
\(126\) −8.42338 −0.750414
\(127\) −13.1241 −1.16458 −0.582290 0.812981i \(-0.697843\pi\)
−0.582290 + 0.812981i \(0.697843\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 26.2090 2.30758
\(130\) −15.3614 −1.34728
\(131\) −6.74933 −0.589692 −0.294846 0.955545i \(-0.595268\pi\)
−0.294846 + 0.955545i \(0.595268\pi\)
\(132\) 7.42702 0.646439
\(133\) 9.98009 0.865384
\(134\) −10.2713 −0.887308
\(135\) −2.80191 −0.241150
\(136\) −5.18964 −0.445008
\(137\) 11.4608 0.979166 0.489583 0.871957i \(-0.337149\pi\)
0.489583 + 0.871957i \(0.337149\pi\)
\(138\) 14.1588 1.20527
\(139\) 8.42584 0.714671 0.357335 0.933976i \(-0.383685\pi\)
0.357335 + 0.933976i \(0.383685\pi\)
\(140\) −10.6005 −0.895903
\(141\) 5.00616 0.421595
\(142\) −7.76365 −0.651511
\(143\) 14.4203 1.20589
\(144\) 2.64585 0.220488
\(145\) −6.38292 −0.530073
\(146\) 13.9399 1.15368
\(147\) −7.45006 −0.614470
\(148\) −3.03323 −0.249330
\(149\) −6.27409 −0.513994 −0.256997 0.966412i \(-0.582733\pi\)
−0.256997 + 0.966412i \(0.582733\pi\)
\(150\) 14.4630 1.18090
\(151\) −15.8952 −1.29353 −0.646765 0.762690i \(-0.723878\pi\)
−0.646765 + 0.762690i \(0.723878\pi\)
\(152\) −3.13483 −0.254268
\(153\) 13.7310 1.11009
\(154\) 9.95109 0.801882
\(155\) 3.73296 0.299838
\(156\) 10.9620 0.877664
\(157\) 7.20509 0.575029 0.287515 0.957776i \(-0.407171\pi\)
0.287515 + 0.957776i \(0.407171\pi\)
\(158\) −2.57202 −0.204619
\(159\) −26.1827 −2.07643
\(160\) 3.32970 0.263236
\(161\) 18.9706 1.49509
\(162\) 9.93702 0.780726
\(163\) −18.7543 −1.46895 −0.734473 0.678638i \(-0.762571\pi\)
−0.734473 + 0.678638i \(0.762571\pi\)
\(164\) 7.25292 0.566358
\(165\) −24.7297 −1.92521
\(166\) −11.1175 −0.862889
\(167\) 18.4553 1.42812 0.714059 0.700086i \(-0.246855\pi\)
0.714059 + 0.700086i \(0.246855\pi\)
\(168\) 7.56459 0.583621
\(169\) 8.28391 0.637224
\(170\) 17.2799 1.32531
\(171\) 8.29429 0.634280
\(172\) −11.0303 −0.841050
\(173\) 1.00758 0.0766045 0.0383023 0.999266i \(-0.487805\pi\)
0.0383023 + 0.999266i \(0.487805\pi\)
\(174\) 4.55491 0.345307
\(175\) 19.3783 1.46486
\(176\) −3.12572 −0.235610
\(177\) 13.3012 0.999781
\(178\) −10.2553 −0.768670
\(179\) 7.43191 0.555487 0.277743 0.960655i \(-0.410413\pi\)
0.277743 + 0.960655i \(0.410413\pi\)
\(180\) −8.80988 −0.656650
\(181\) −0.732910 −0.0544768 −0.0272384 0.999629i \(-0.508671\pi\)
−0.0272384 + 0.999629i \(0.508671\pi\)
\(182\) 14.6875 1.08871
\(183\) 4.24620 0.313888
\(184\) −5.95882 −0.439290
\(185\) 10.0997 0.742548
\(186\) −2.66387 −0.195324
\(187\) −16.2213 −1.18622
\(188\) −2.10688 −0.153660
\(189\) 2.67899 0.194868
\(190\) 10.4380 0.757254
\(191\) −1.87680 −0.135801 −0.0679003 0.997692i \(-0.521630\pi\)
−0.0679003 + 0.997692i \(0.521630\pi\)
\(192\) −2.37610 −0.171480
\(193\) 3.42745 0.246713 0.123357 0.992362i \(-0.460634\pi\)
0.123357 + 0.992362i \(0.460634\pi\)
\(194\) −5.61516 −0.403145
\(195\) −36.5002 −2.61383
\(196\) 3.13541 0.223958
\(197\) −11.9950 −0.854608 −0.427304 0.904108i \(-0.640537\pi\)
−0.427304 + 0.904108i \(0.640537\pi\)
\(198\) 8.27019 0.587736
\(199\) −0.888401 −0.0629771 −0.0314885 0.999504i \(-0.510025\pi\)
−0.0314885 + 0.999504i \(0.510025\pi\)
\(200\) −6.08687 −0.430407
\(201\) −24.4057 −1.72145
\(202\) 3.24073 0.228017
\(203\) 6.10289 0.428339
\(204\) −12.3311 −0.863349
\(205\) −24.1500 −1.68671
\(206\) 7.04994 0.491192
\(207\) 15.7662 1.09582
\(208\) −4.61345 −0.319885
\(209\) −9.79859 −0.677783
\(210\) −25.1878 −1.73812
\(211\) −3.50907 −0.241574 −0.120787 0.992678i \(-0.538542\pi\)
−0.120787 + 0.992678i \(0.538542\pi\)
\(212\) 11.0192 0.756802
\(213\) −18.4472 −1.26398
\(214\) 5.95942 0.407377
\(215\) 36.7274 2.50479
\(216\) −0.841493 −0.0572563
\(217\) −3.56919 −0.242292
\(218\) −0.338190 −0.0229051
\(219\) 33.1227 2.23822
\(220\) 10.4077 0.701686
\(221\) −23.9421 −1.61052
\(222\) −7.20727 −0.483720
\(223\) −11.1884 −0.749231 −0.374615 0.927180i \(-0.622225\pi\)
−0.374615 + 0.927180i \(0.622225\pi\)
\(224\) −3.18362 −0.212714
\(225\) 16.1050 1.07366
\(226\) 16.0462 1.06738
\(227\) −24.7115 −1.64016 −0.820079 0.572250i \(-0.806071\pi\)
−0.820079 + 0.572250i \(0.806071\pi\)
\(228\) −7.44867 −0.493300
\(229\) 14.2933 0.944528 0.472264 0.881457i \(-0.343437\pi\)
0.472264 + 0.881457i \(0.343437\pi\)
\(230\) 19.8411 1.30828
\(231\) 23.6448 1.55571
\(232\) −1.91697 −0.125855
\(233\) 24.1996 1.58537 0.792684 0.609633i \(-0.208683\pi\)
0.792684 + 0.609633i \(0.208683\pi\)
\(234\) 12.2065 0.797964
\(235\) 7.01527 0.457626
\(236\) −5.59792 −0.364394
\(237\) −6.11137 −0.396976
\(238\) −16.5218 −1.07095
\(239\) −20.3277 −1.31489 −0.657444 0.753503i \(-0.728363\pi\)
−0.657444 + 0.753503i \(0.728363\pi\)
\(240\) 7.91169 0.510697
\(241\) 19.8055 1.27578 0.637891 0.770126i \(-0.279807\pi\)
0.637891 + 0.770126i \(0.279807\pi\)
\(242\) 1.22989 0.0790600
\(243\) 21.0869 1.35272
\(244\) −1.78705 −0.114404
\(245\) −10.4400 −0.666985
\(246\) 17.2337 1.09878
\(247\) −14.4624 −0.920219
\(248\) 1.12111 0.0711906
\(249\) −26.4164 −1.67407
\(250\) 3.61895 0.228882
\(251\) 0.326101 0.0205833 0.0102917 0.999947i \(-0.496724\pi\)
0.0102917 + 0.999947i \(0.496724\pi\)
\(252\) 8.42338 0.530623
\(253\) −18.6256 −1.17098
\(254\) 13.1241 0.823482
\(255\) 41.0588 2.57120
\(256\) 1.00000 0.0625000
\(257\) −6.63146 −0.413659 −0.206830 0.978377i \(-0.566315\pi\)
−0.206830 + 0.978377i \(0.566315\pi\)
\(258\) −26.2090 −1.63170
\(259\) −9.65665 −0.600035
\(260\) 15.3614 0.952672
\(261\) 5.07201 0.313950
\(262\) 6.74933 0.416975
\(263\) −2.70731 −0.166940 −0.0834700 0.996510i \(-0.526600\pi\)
−0.0834700 + 0.996510i \(0.526600\pi\)
\(264\) −7.42702 −0.457101
\(265\) −36.6906 −2.25389
\(266\) −9.98009 −0.611919
\(267\) −24.3677 −1.49128
\(268\) 10.2713 0.627421
\(269\) −15.3811 −0.937801 −0.468900 0.883251i \(-0.655350\pi\)
−0.468900 + 0.883251i \(0.655350\pi\)
\(270\) 2.80191 0.170519
\(271\) −3.34226 −0.203028 −0.101514 0.994834i \(-0.532369\pi\)
−0.101514 + 0.994834i \(0.532369\pi\)
\(272\) 5.18964 0.314668
\(273\) 34.8989 2.11217
\(274\) −11.4608 −0.692375
\(275\) −19.0258 −1.14730
\(276\) −14.1588 −0.852257
\(277\) −12.6605 −0.760696 −0.380348 0.924844i \(-0.624196\pi\)
−0.380348 + 0.924844i \(0.624196\pi\)
\(278\) −8.42584 −0.505348
\(279\) −2.96629 −0.177587
\(280\) 10.6005 0.633499
\(281\) −33.1853 −1.97967 −0.989835 0.142220i \(-0.954576\pi\)
−0.989835 + 0.142220i \(0.954576\pi\)
\(282\) −5.00616 −0.298112
\(283\) −5.52575 −0.328472 −0.164236 0.986421i \(-0.552516\pi\)
−0.164236 + 0.986421i \(0.552516\pi\)
\(284\) 7.76365 0.460688
\(285\) 24.8018 1.46913
\(286\) −14.4203 −0.852693
\(287\) 23.0905 1.36299
\(288\) −2.64585 −0.155908
\(289\) 9.93232 0.584254
\(290\) 6.38292 0.374818
\(291\) −13.3422 −0.782132
\(292\) −13.9399 −0.815773
\(293\) −8.68084 −0.507140 −0.253570 0.967317i \(-0.581605\pi\)
−0.253570 + 0.967317i \(0.581605\pi\)
\(294\) 7.45006 0.434496
\(295\) 18.6394 1.08523
\(296\) 3.03323 0.176303
\(297\) −2.63027 −0.152624
\(298\) 6.27409 0.363448
\(299\) −27.4907 −1.58983
\(300\) −14.4630 −0.835022
\(301\) −35.1161 −2.02406
\(302\) 15.8952 0.914663
\(303\) 7.70031 0.442371
\(304\) 3.13483 0.179795
\(305\) 5.95032 0.340714
\(306\) −13.7310 −0.784949
\(307\) −14.0197 −0.800148 −0.400074 0.916483i \(-0.631016\pi\)
−0.400074 + 0.916483i \(0.631016\pi\)
\(308\) −9.95109 −0.567016
\(309\) 16.7514 0.952951
\(310\) −3.73296 −0.212018
\(311\) −18.5350 −1.05102 −0.525510 0.850787i \(-0.676126\pi\)
−0.525510 + 0.850787i \(0.676126\pi\)
\(312\) −10.9620 −0.620602
\(313\) −14.8127 −0.837263 −0.418632 0.908156i \(-0.637490\pi\)
−0.418632 + 0.908156i \(0.637490\pi\)
\(314\) −7.20509 −0.406607
\(315\) −28.0473 −1.58028
\(316\) 2.57202 0.144687
\(317\) 24.5542 1.37910 0.689549 0.724239i \(-0.257809\pi\)
0.689549 + 0.724239i \(0.257809\pi\)
\(318\) 26.1827 1.46826
\(319\) −5.99190 −0.335482
\(320\) −3.32970 −0.186136
\(321\) 14.1602 0.790344
\(322\) −18.9706 −1.05719
\(323\) 16.2686 0.905210
\(324\) −9.93702 −0.552057
\(325\) −28.0815 −1.55768
\(326\) 18.7543 1.03870
\(327\) −0.803574 −0.0444377
\(328\) −7.25292 −0.400475
\(329\) −6.70750 −0.369796
\(330\) 24.7297 1.36133
\(331\) 30.3283 1.66700 0.833498 0.552523i \(-0.186335\pi\)
0.833498 + 0.552523i \(0.186335\pi\)
\(332\) 11.1175 0.610154
\(333\) −8.02549 −0.439794
\(334\) −18.4553 −1.00983
\(335\) −34.2004 −1.86857
\(336\) −7.56459 −0.412682
\(337\) 15.8510 0.863460 0.431730 0.902003i \(-0.357903\pi\)
0.431730 + 0.902003i \(0.357903\pi\)
\(338\) −8.28391 −0.450585
\(339\) 38.1275 2.07080
\(340\) −17.2799 −0.937134
\(341\) 3.50427 0.189767
\(342\) −8.29429 −0.448504
\(343\) −12.3034 −0.664319
\(344\) 11.0303 0.594712
\(345\) 47.1443 2.53817
\(346\) −1.00758 −0.0541676
\(347\) 31.4368 1.68762 0.843808 0.536646i \(-0.180309\pi\)
0.843808 + 0.536646i \(0.180309\pi\)
\(348\) −4.55491 −0.244169
\(349\) 34.2486 1.83329 0.916644 0.399705i \(-0.130887\pi\)
0.916644 + 0.399705i \(0.130887\pi\)
\(350\) −19.3783 −1.03581
\(351\) −3.88218 −0.207216
\(352\) 3.12572 0.166601
\(353\) 30.4436 1.62035 0.810174 0.586189i \(-0.199372\pi\)
0.810174 + 0.586189i \(0.199372\pi\)
\(354\) −13.3012 −0.706952
\(355\) −25.8506 −1.37201
\(356\) 10.2553 0.543532
\(357\) −39.2575 −2.07773
\(358\) −7.43191 −0.392789
\(359\) 9.77774 0.516049 0.258025 0.966138i \(-0.416928\pi\)
0.258025 + 0.966138i \(0.416928\pi\)
\(360\) 8.80988 0.464321
\(361\) −9.17284 −0.482781
\(362\) 0.732910 0.0385209
\(363\) 2.92233 0.153383
\(364\) −14.6875 −0.769832
\(365\) 46.4157 2.42951
\(366\) −4.24620 −0.221952
\(367\) 13.5313 0.706330 0.353165 0.935561i \(-0.385105\pi\)
0.353165 + 0.935561i \(0.385105\pi\)
\(368\) 5.95882 0.310625
\(369\) 19.1901 0.998999
\(370\) −10.0997 −0.525061
\(371\) 35.0809 1.82131
\(372\) 2.66387 0.138115
\(373\) 24.4204 1.26444 0.632219 0.774790i \(-0.282144\pi\)
0.632219 + 0.774790i \(0.282144\pi\)
\(374\) 16.2213 0.838785
\(375\) 8.59898 0.444049
\(376\) 2.10688 0.108654
\(377\) −8.84384 −0.455481
\(378\) −2.67899 −0.137792
\(379\) 5.27058 0.270731 0.135366 0.990796i \(-0.456779\pi\)
0.135366 + 0.990796i \(0.456779\pi\)
\(380\) −10.4380 −0.535459
\(381\) 31.1843 1.59762
\(382\) 1.87680 0.0960255
\(383\) −15.0420 −0.768609 −0.384304 0.923206i \(-0.625559\pi\)
−0.384304 + 0.923206i \(0.625559\pi\)
\(384\) 2.37610 0.121255
\(385\) 33.1341 1.68867
\(386\) −3.42745 −0.174453
\(387\) −29.1845 −1.48353
\(388\) 5.61516 0.285066
\(389\) 8.10304 0.410841 0.205420 0.978674i \(-0.434144\pi\)
0.205420 + 0.978674i \(0.434144\pi\)
\(390\) 36.5002 1.84826
\(391\) 30.9241 1.56390
\(392\) −3.13541 −0.158362
\(393\) 16.0371 0.808964
\(394\) 11.9950 0.604299
\(395\) −8.56403 −0.430903
\(396\) −8.27019 −0.415592
\(397\) −3.71395 −0.186398 −0.0931988 0.995648i \(-0.529709\pi\)
−0.0931988 + 0.995648i \(0.529709\pi\)
\(398\) 0.888401 0.0445315
\(399\) −23.7137 −1.18717
\(400\) 6.08687 0.304343
\(401\) −7.25391 −0.362243 −0.181121 0.983461i \(-0.557973\pi\)
−0.181121 + 0.983461i \(0.557973\pi\)
\(402\) 24.4057 1.21725
\(403\) 5.17218 0.257645
\(404\) −3.24073 −0.161233
\(405\) 33.0873 1.64412
\(406\) −6.10289 −0.302881
\(407\) 9.48104 0.469958
\(408\) 12.3311 0.610480
\(409\) −6.89849 −0.341109 −0.170554 0.985348i \(-0.554556\pi\)
−0.170554 + 0.985348i \(0.554556\pi\)
\(410\) 24.1500 1.19268
\(411\) −27.2321 −1.34326
\(412\) −7.04994 −0.347325
\(413\) −17.8216 −0.876946
\(414\) −15.7662 −0.774864
\(415\) −37.0180 −1.81714
\(416\) 4.61345 0.226193
\(417\) −20.0206 −0.980415
\(418\) 9.79859 0.479265
\(419\) −28.7368 −1.40389 −0.701943 0.712233i \(-0.747684\pi\)
−0.701943 + 0.712233i \(0.747684\pi\)
\(420\) 25.1878 1.22904
\(421\) 19.8686 0.968337 0.484169 0.874975i \(-0.339122\pi\)
0.484169 + 0.874975i \(0.339122\pi\)
\(422\) 3.50907 0.170819
\(423\) −5.57449 −0.271041
\(424\) −11.0192 −0.535140
\(425\) 31.5886 1.53227
\(426\) 18.4472 0.893770
\(427\) −5.68927 −0.275323
\(428\) −5.95942 −0.288059
\(429\) −34.2642 −1.65429
\(430\) −36.7274 −1.77115
\(431\) 20.8178 1.00276 0.501378 0.865228i \(-0.332827\pi\)
0.501378 + 0.865228i \(0.332827\pi\)
\(432\) 0.841493 0.0404863
\(433\) 2.54094 0.122110 0.0610550 0.998134i \(-0.480553\pi\)
0.0610550 + 0.998134i \(0.480553\pi\)
\(434\) 3.56919 0.171326
\(435\) 15.1665 0.727176
\(436\) 0.338190 0.0161964
\(437\) 18.6799 0.893580
\(438\) −33.1227 −1.58266
\(439\) −8.94228 −0.426792 −0.213396 0.976966i \(-0.568452\pi\)
−0.213396 + 0.976966i \(0.568452\pi\)
\(440\) −10.4077 −0.496167
\(441\) 8.29584 0.395040
\(442\) 23.9421 1.13881
\(443\) 26.7326 1.27011 0.635053 0.772469i \(-0.280978\pi\)
0.635053 + 0.772469i \(0.280978\pi\)
\(444\) 7.20727 0.342042
\(445\) −34.1471 −1.61873
\(446\) 11.1884 0.529786
\(447\) 14.9079 0.705118
\(448\) 3.18362 0.150412
\(449\) 9.24604 0.436347 0.218174 0.975910i \(-0.429990\pi\)
0.218174 + 0.975910i \(0.429990\pi\)
\(450\) −16.1050 −0.759195
\(451\) −22.6706 −1.06752
\(452\) −16.0462 −0.754752
\(453\) 37.7685 1.77452
\(454\) 24.7115 1.15977
\(455\) 48.9047 2.29269
\(456\) 7.44867 0.348816
\(457\) −3.05356 −0.142840 −0.0714198 0.997446i \(-0.522753\pi\)
−0.0714198 + 0.997446i \(0.522753\pi\)
\(458\) −14.2933 −0.667882
\(459\) 4.36704 0.203836
\(460\) −19.8411 −0.925094
\(461\) −3.45615 −0.160969 −0.0804844 0.996756i \(-0.525647\pi\)
−0.0804844 + 0.996756i \(0.525647\pi\)
\(462\) −23.6448 −1.10005
\(463\) 28.0621 1.30416 0.652079 0.758151i \(-0.273897\pi\)
0.652079 + 0.758151i \(0.273897\pi\)
\(464\) 1.91697 0.0889930
\(465\) −8.86988 −0.411331
\(466\) −24.1996 −1.12102
\(467\) 23.8285 1.10265 0.551325 0.834291i \(-0.314122\pi\)
0.551325 + 0.834291i \(0.314122\pi\)
\(468\) −12.2065 −0.564246
\(469\) 32.7000 1.50994
\(470\) −7.01527 −0.323590
\(471\) −17.1200 −0.788849
\(472\) 5.59792 0.257665
\(473\) 34.4775 1.58528
\(474\) 6.11137 0.280704
\(475\) 19.0813 0.875510
\(476\) 16.5218 0.757276
\(477\) 29.1552 1.33492
\(478\) 20.3277 0.929767
\(479\) 17.5981 0.804077 0.402039 0.915623i \(-0.368302\pi\)
0.402039 + 0.915623i \(0.368302\pi\)
\(480\) −7.91169 −0.361118
\(481\) 13.9937 0.638057
\(482\) −19.8055 −0.902115
\(483\) −45.0760 −2.05103
\(484\) −1.22989 −0.0559039
\(485\) −18.6968 −0.848976
\(486\) −21.0869 −0.956521
\(487\) −39.5420 −1.79182 −0.895909 0.444238i \(-0.853475\pi\)
−0.895909 + 0.444238i \(0.853475\pi\)
\(488\) 1.78705 0.0808958
\(489\) 44.5620 2.01516
\(490\) 10.4400 0.471630
\(491\) −7.52025 −0.339384 −0.169692 0.985497i \(-0.554277\pi\)
−0.169692 + 0.985497i \(0.554277\pi\)
\(492\) −17.2337 −0.776953
\(493\) 9.94837 0.448052
\(494\) 14.4624 0.650693
\(495\) 27.5372 1.23770
\(496\) −1.12111 −0.0503393
\(497\) 24.7165 1.10869
\(498\) 26.4164 1.18375
\(499\) −20.2139 −0.904899 −0.452450 0.891790i \(-0.649450\pi\)
−0.452450 + 0.891790i \(0.649450\pi\)
\(500\) −3.61895 −0.161844
\(501\) −43.8518 −1.95915
\(502\) −0.326101 −0.0145546
\(503\) 43.3623 1.93343 0.966714 0.255858i \(-0.0823581\pi\)
0.966714 + 0.255858i \(0.0823581\pi\)
\(504\) −8.42338 −0.375207
\(505\) 10.7907 0.480178
\(506\) 18.6256 0.828009
\(507\) −19.6834 −0.874171
\(508\) −13.1241 −0.582290
\(509\) −1.64894 −0.0730878 −0.0365439 0.999332i \(-0.511635\pi\)
−0.0365439 + 0.999332i \(0.511635\pi\)
\(510\) −41.0588 −1.81811
\(511\) −44.3794 −1.96323
\(512\) −1.00000 −0.0441942
\(513\) 2.63794 0.116468
\(514\) 6.63146 0.292501
\(515\) 23.4741 1.03439
\(516\) 26.2090 1.15379
\(517\) 6.58551 0.289631
\(518\) 9.65665 0.424289
\(519\) −2.39410 −0.105089
\(520\) −15.3614 −0.673641
\(521\) −11.8964 −0.521192 −0.260596 0.965448i \(-0.583919\pi\)
−0.260596 + 0.965448i \(0.583919\pi\)
\(522\) −5.07201 −0.221996
\(523\) 2.33214 0.101977 0.0509886 0.998699i \(-0.483763\pi\)
0.0509886 + 0.998699i \(0.483763\pi\)
\(524\) −6.74933 −0.294846
\(525\) −46.0447 −2.00955
\(526\) 2.70731 0.118044
\(527\) −5.81815 −0.253443
\(528\) 7.42702 0.323220
\(529\) 12.5075 0.543807
\(530\) 36.6906 1.59374
\(531\) −14.8113 −0.642755
\(532\) 9.98009 0.432692
\(533\) −33.4610 −1.44936
\(534\) 24.3677 1.05449
\(535\) 19.8430 0.857890
\(536\) −10.2713 −0.443654
\(537\) −17.6590 −0.762040
\(538\) 15.3811 0.663125
\(539\) −9.80042 −0.422134
\(540\) −2.80191 −0.120575
\(541\) −25.2930 −1.08743 −0.543714 0.839270i \(-0.682983\pi\)
−0.543714 + 0.839270i \(0.682983\pi\)
\(542\) 3.34226 0.143562
\(543\) 1.74147 0.0747335
\(544\) −5.18964 −0.222504
\(545\) −1.12607 −0.0482355
\(546\) −34.8989 −1.49353
\(547\) 33.9482 1.45152 0.725760 0.687947i \(-0.241488\pi\)
0.725760 + 0.687947i \(0.241488\pi\)
\(548\) 11.4608 0.489583
\(549\) −4.72826 −0.201797
\(550\) 19.0258 0.811265
\(551\) 6.00937 0.256008
\(552\) 14.1588 0.602637
\(553\) 8.18831 0.348202
\(554\) 12.6605 0.537893
\(555\) −23.9980 −1.01866
\(556\) 8.42584 0.357335
\(557\) −38.9956 −1.65230 −0.826149 0.563452i \(-0.809473\pi\)
−0.826149 + 0.563452i \(0.809473\pi\)
\(558\) 2.96629 0.125573
\(559\) 50.8876 2.15232
\(560\) −10.6005 −0.447952
\(561\) 38.5435 1.62731
\(562\) 33.1853 1.39984
\(563\) 34.3956 1.44960 0.724801 0.688958i \(-0.241932\pi\)
0.724801 + 0.688958i \(0.241932\pi\)
\(564\) 5.00616 0.210797
\(565\) 53.4291 2.24778
\(566\) 5.52575 0.232264
\(567\) −31.6357 −1.32857
\(568\) −7.76365 −0.325755
\(569\) 16.7879 0.703786 0.351893 0.936040i \(-0.385538\pi\)
0.351893 + 0.936040i \(0.385538\pi\)
\(570\) −24.8018 −1.03883
\(571\) 17.8951 0.748888 0.374444 0.927250i \(-0.377834\pi\)
0.374444 + 0.927250i \(0.377834\pi\)
\(572\) 14.4203 0.602945
\(573\) 4.45947 0.186297
\(574\) −23.0905 −0.963779
\(575\) 36.2706 1.51259
\(576\) 2.64585 0.110244
\(577\) 30.8130 1.28276 0.641380 0.767223i \(-0.278362\pi\)
0.641380 + 0.767223i \(0.278362\pi\)
\(578\) −9.93232 −0.413130
\(579\) −8.14397 −0.338452
\(580\) −6.38292 −0.265036
\(581\) 35.3940 1.46839
\(582\) 13.3422 0.553051
\(583\) −34.4429 −1.42648
\(584\) 13.9399 0.576838
\(585\) 40.6439 1.68042
\(586\) 8.68084 0.358602
\(587\) −24.7381 −1.02105 −0.510525 0.859863i \(-0.670549\pi\)
−0.510525 + 0.859863i \(0.670549\pi\)
\(588\) −7.45006 −0.307235
\(589\) −3.51449 −0.144812
\(590\) −18.6394 −0.767371
\(591\) 28.5013 1.17239
\(592\) −3.03323 −0.124665
\(593\) 38.1659 1.56728 0.783642 0.621212i \(-0.213360\pi\)
0.783642 + 0.621212i \(0.213360\pi\)
\(594\) 2.63027 0.107921
\(595\) −55.0126 −2.25530
\(596\) −6.27409 −0.256997
\(597\) 2.11093 0.0863946
\(598\) 27.4907 1.12418
\(599\) 14.8644 0.607343 0.303671 0.952777i \(-0.401788\pi\)
0.303671 + 0.952777i \(0.401788\pi\)
\(600\) 14.4630 0.590450
\(601\) −16.4384 −0.670538 −0.335269 0.942122i \(-0.608827\pi\)
−0.335269 + 0.942122i \(0.608827\pi\)
\(602\) 35.1161 1.43123
\(603\) 27.1764 1.10671
\(604\) −15.8952 −0.646765
\(605\) 4.09514 0.166491
\(606\) −7.70031 −0.312804
\(607\) 40.8144 1.65661 0.828303 0.560281i \(-0.189307\pi\)
0.828303 + 0.560281i \(0.189307\pi\)
\(608\) −3.13483 −0.127134
\(609\) −14.5011 −0.587613
\(610\) −5.95032 −0.240921
\(611\) 9.71999 0.393229
\(612\) 13.7310 0.555043
\(613\) 16.4984 0.666366 0.333183 0.942862i \(-0.391877\pi\)
0.333183 + 0.942862i \(0.391877\pi\)
\(614\) 14.0197 0.565790
\(615\) 57.3828 2.31390
\(616\) 9.95109 0.400941
\(617\) −11.7501 −0.473042 −0.236521 0.971626i \(-0.576007\pi\)
−0.236521 + 0.971626i \(0.576007\pi\)
\(618\) −16.7514 −0.673838
\(619\) 23.0958 0.928297 0.464149 0.885757i \(-0.346360\pi\)
0.464149 + 0.885757i \(0.346360\pi\)
\(620\) 3.73296 0.149919
\(621\) 5.01431 0.201217
\(622\) 18.5350 0.743184
\(623\) 32.6491 1.30806
\(624\) 10.9620 0.438832
\(625\) −18.3844 −0.735375
\(626\) 14.8127 0.592035
\(627\) 23.2824 0.929811
\(628\) 7.20509 0.287515
\(629\) −15.7414 −0.627650
\(630\) 28.0473 1.11743
\(631\) 29.9156 1.19092 0.595461 0.803384i \(-0.296969\pi\)
0.595461 + 0.803384i \(0.296969\pi\)
\(632\) −2.57202 −0.102309
\(633\) 8.33791 0.331402
\(634\) −24.5542 −0.975170
\(635\) 43.6994 1.73416
\(636\) −26.1827 −1.03821
\(637\) −14.4651 −0.573127
\(638\) 5.99190 0.237222
\(639\) 20.5415 0.812607
\(640\) 3.32970 0.131618
\(641\) −14.0426 −0.554650 −0.277325 0.960776i \(-0.589448\pi\)
−0.277325 + 0.960776i \(0.589448\pi\)
\(642\) −14.1602 −0.558857
\(643\) 31.4250 1.23928 0.619641 0.784885i \(-0.287278\pi\)
0.619641 + 0.784885i \(0.287278\pi\)
\(644\) 18.9706 0.747546
\(645\) −87.2681 −3.43618
\(646\) −16.2686 −0.640080
\(647\) 43.6708 1.71688 0.858438 0.512918i \(-0.171435\pi\)
0.858438 + 0.512918i \(0.171435\pi\)
\(648\) 9.93702 0.390363
\(649\) 17.4975 0.686838
\(650\) 28.0815 1.10145
\(651\) 8.48074 0.332386
\(652\) −18.7543 −0.734473
\(653\) 2.41506 0.0945087 0.0472543 0.998883i \(-0.484953\pi\)
0.0472543 + 0.998883i \(0.484953\pi\)
\(654\) 0.803574 0.0314222
\(655\) 22.4732 0.878101
\(656\) 7.25292 0.283179
\(657\) −36.8830 −1.43894
\(658\) 6.70750 0.261486
\(659\) −10.5046 −0.409202 −0.204601 0.978845i \(-0.565590\pi\)
−0.204601 + 0.978845i \(0.565590\pi\)
\(660\) −24.7297 −0.962603
\(661\) 0.552451 0.0214879 0.0107439 0.999942i \(-0.496580\pi\)
0.0107439 + 0.999942i \(0.496580\pi\)
\(662\) −30.3283 −1.17874
\(663\) 56.8889 2.20938
\(664\) −11.1175 −0.431444
\(665\) −33.2307 −1.28863
\(666\) 8.02549 0.310981
\(667\) 11.4229 0.442295
\(668\) 18.4553 0.714059
\(669\) 26.5848 1.02783
\(670\) 34.2004 1.32128
\(671\) 5.58580 0.215637
\(672\) 7.56459 0.291810
\(673\) −4.36721 −0.168344 −0.0841718 0.996451i \(-0.526824\pi\)
−0.0841718 + 0.996451i \(0.526824\pi\)
\(674\) −15.8510 −0.610559
\(675\) 5.12206 0.197148
\(676\) 8.28391 0.318612
\(677\) 31.0621 1.19381 0.596907 0.802311i \(-0.296396\pi\)
0.596907 + 0.802311i \(0.296396\pi\)
\(678\) −38.1275 −1.46428
\(679\) 17.8765 0.686037
\(680\) 17.2799 0.662654
\(681\) 58.7169 2.25004
\(682\) −3.50427 −0.134186
\(683\) 13.8271 0.529078 0.264539 0.964375i \(-0.414780\pi\)
0.264539 + 0.964375i \(0.414780\pi\)
\(684\) 8.29429 0.317140
\(685\) −38.1611 −1.45806
\(686\) 12.3034 0.469744
\(687\) −33.9623 −1.29574
\(688\) −11.0303 −0.420525
\(689\) −50.8366 −1.93672
\(690\) −47.1443 −1.79475
\(691\) −30.0337 −1.14254 −0.571269 0.820763i \(-0.693549\pi\)
−0.571269 + 0.820763i \(0.693549\pi\)
\(692\) 1.00758 0.0383023
\(693\) −26.3291 −1.00016
\(694\) −31.4368 −1.19332
\(695\) −28.0555 −1.06421
\(696\) 4.55491 0.172653
\(697\) 37.6400 1.42572
\(698\) −34.2486 −1.29633
\(699\) −57.5006 −2.17487
\(700\) 19.3783 0.732429
\(701\) −26.7792 −1.01144 −0.505718 0.862699i \(-0.668772\pi\)
−0.505718 + 0.862699i \(0.668772\pi\)
\(702\) 3.88218 0.146524
\(703\) −9.50867 −0.358626
\(704\) −3.12572 −0.117805
\(705\) −16.6690 −0.627790
\(706\) −30.4436 −1.14576
\(707\) −10.3173 −0.388020
\(708\) 13.3012 0.499891
\(709\) 24.3031 0.912721 0.456360 0.889795i \(-0.349153\pi\)
0.456360 + 0.889795i \(0.349153\pi\)
\(710\) 25.8506 0.970155
\(711\) 6.80517 0.255214
\(712\) −10.2553 −0.384335
\(713\) −6.68050 −0.250187
\(714\) 39.2575 1.46917
\(715\) −48.0153 −1.79567
\(716\) 7.43191 0.277743
\(717\) 48.3006 1.80382
\(718\) −9.77774 −0.364902
\(719\) 2.74048 0.102203 0.0511014 0.998693i \(-0.483727\pi\)
0.0511014 + 0.998693i \(0.483727\pi\)
\(720\) −8.80988 −0.328325
\(721\) −22.4443 −0.835869
\(722\) 9.17284 0.341378
\(723\) −47.0598 −1.75017
\(724\) −0.732910 −0.0272384
\(725\) 11.6683 0.433351
\(726\) −2.92233 −0.108458
\(727\) 30.0007 1.11267 0.556333 0.830960i \(-0.312208\pi\)
0.556333 + 0.830960i \(0.312208\pi\)
\(728\) 14.6875 0.544353
\(729\) −20.2935 −0.751610
\(730\) −46.4157 −1.71792
\(731\) −57.2431 −2.11721
\(732\) 4.24620 0.156944
\(733\) 5.09470 0.188177 0.0940885 0.995564i \(-0.470006\pi\)
0.0940885 + 0.995564i \(0.470006\pi\)
\(734\) −13.5313 −0.499450
\(735\) 24.8064 0.914998
\(736\) −5.95882 −0.219645
\(737\) −32.1053 −1.18261
\(738\) −19.1901 −0.706399
\(739\) 37.7134 1.38731 0.693655 0.720307i \(-0.255999\pi\)
0.693655 + 0.720307i \(0.255999\pi\)
\(740\) 10.0997 0.371274
\(741\) 34.3641 1.26240
\(742\) −35.0809 −1.28786
\(743\) 8.71086 0.319570 0.159785 0.987152i \(-0.448920\pi\)
0.159785 + 0.987152i \(0.448920\pi\)
\(744\) −2.66387 −0.0976622
\(745\) 20.8908 0.765380
\(746\) −24.4204 −0.894093
\(747\) 29.4154 1.07625
\(748\) −16.2213 −0.593111
\(749\) −18.9725 −0.693240
\(750\) −8.59898 −0.313990
\(751\) −24.4454 −0.892024 −0.446012 0.895027i \(-0.647156\pi\)
−0.446012 + 0.895027i \(0.647156\pi\)
\(752\) −2.10688 −0.0768300
\(753\) −0.774850 −0.0282371
\(754\) 8.84384 0.322073
\(755\) 52.9260 1.92617
\(756\) 2.67899 0.0974339
\(757\) −42.0307 −1.52763 −0.763816 0.645434i \(-0.776677\pi\)
−0.763816 + 0.645434i \(0.776677\pi\)
\(758\) −5.27058 −0.191436
\(759\) 44.2563 1.60640
\(760\) 10.4380 0.378627
\(761\) 14.6367 0.530579 0.265290 0.964169i \(-0.414532\pi\)
0.265290 + 0.964169i \(0.414532\pi\)
\(762\) −31.1843 −1.12969
\(763\) 1.07667 0.0389780
\(764\) −1.87680 −0.0679003
\(765\) −45.7201 −1.65301
\(766\) 15.0420 0.543488
\(767\) 25.8257 0.932513
\(768\) −2.37610 −0.0857401
\(769\) 16.5708 0.597559 0.298779 0.954322i \(-0.403421\pi\)
0.298779 + 0.954322i \(0.403421\pi\)
\(770\) −33.1341 −1.19407
\(771\) 15.7570 0.567475
\(772\) 3.42745 0.123357
\(773\) 13.1010 0.471212 0.235606 0.971849i \(-0.424293\pi\)
0.235606 + 0.971849i \(0.424293\pi\)
\(774\) 29.1845 1.04901
\(775\) −6.82405 −0.245127
\(776\) −5.61516 −0.201572
\(777\) 22.9452 0.823154
\(778\) −8.10304 −0.290508
\(779\) 22.7367 0.814625
\(780\) −36.5002 −1.30692
\(781\) −24.2670 −0.868341
\(782\) −30.9241 −1.10584
\(783\) 1.61312 0.0576480
\(784\) 3.13541 0.111979
\(785\) −23.9908 −0.856267
\(786\) −16.0371 −0.572024
\(787\) −16.1252 −0.574802 −0.287401 0.957810i \(-0.592791\pi\)
−0.287401 + 0.957810i \(0.592791\pi\)
\(788\) −11.9950 −0.427304
\(789\) 6.43284 0.229015
\(790\) 8.56403 0.304694
\(791\) −51.0851 −1.81638
\(792\) 8.27019 0.293868
\(793\) 8.24444 0.292769
\(794\) 3.71395 0.131803
\(795\) 87.1806 3.09198
\(796\) −0.888401 −0.0314885
\(797\) 18.2281 0.645673 0.322837 0.946455i \(-0.395364\pi\)
0.322837 + 0.946455i \(0.395364\pi\)
\(798\) 23.7137 0.839456
\(799\) −10.9339 −0.386815
\(800\) −6.08687 −0.215203
\(801\) 27.1341 0.958736
\(802\) 7.25391 0.256144
\(803\) 43.5723 1.53763
\(804\) −24.4057 −0.860723
\(805\) −63.1663 −2.22632
\(806\) −5.17218 −0.182182
\(807\) 36.5470 1.28651
\(808\) 3.24073 0.114009
\(809\) −24.4286 −0.858864 −0.429432 0.903099i \(-0.641286\pi\)
−0.429432 + 0.903099i \(0.641286\pi\)
\(810\) −33.0873 −1.16257
\(811\) −8.12806 −0.285415 −0.142707 0.989765i \(-0.545581\pi\)
−0.142707 + 0.989765i \(0.545581\pi\)
\(812\) 6.10289 0.214170
\(813\) 7.94155 0.278522
\(814\) −9.48104 −0.332310
\(815\) 62.4459 2.18739
\(816\) −12.3311 −0.431675
\(817\) −34.5780 −1.20973
\(818\) 6.89849 0.241200
\(819\) −38.8608 −1.35791
\(820\) −24.1500 −0.843355
\(821\) −6.43954 −0.224741 −0.112371 0.993666i \(-0.535844\pi\)
−0.112371 + 0.993666i \(0.535844\pi\)
\(822\) 27.2321 0.949829
\(823\) 7.82533 0.272774 0.136387 0.990656i \(-0.456451\pi\)
0.136387 + 0.990656i \(0.456451\pi\)
\(824\) 7.04994 0.245596
\(825\) 45.2073 1.57392
\(826\) 17.8216 0.620094
\(827\) −44.0561 −1.53198 −0.765990 0.642852i \(-0.777751\pi\)
−0.765990 + 0.642852i \(0.777751\pi\)
\(828\) 15.7662 0.547912
\(829\) −14.4498 −0.501863 −0.250932 0.968005i \(-0.580737\pi\)
−0.250932 + 0.968005i \(0.580737\pi\)
\(830\) 37.0180 1.28491
\(831\) 30.0826 1.04355
\(832\) −4.61345 −0.159943
\(833\) 16.2717 0.563779
\(834\) 20.0206 0.693258
\(835\) −61.4507 −2.12659
\(836\) −9.79859 −0.338891
\(837\) −0.943406 −0.0326089
\(838\) 28.7368 0.992698
\(839\) 23.4747 0.810435 0.405217 0.914220i \(-0.367196\pi\)
0.405217 + 0.914220i \(0.367196\pi\)
\(840\) −25.1878 −0.869061
\(841\) −25.3252 −0.873284
\(842\) −19.8686 −0.684718
\(843\) 78.8516 2.71579
\(844\) −3.50907 −0.120787
\(845\) −27.5829 −0.948881
\(846\) 5.57449 0.191655
\(847\) −3.91548 −0.134538
\(848\) 11.0192 0.378401
\(849\) 13.1297 0.450611
\(850\) −31.5886 −1.08348
\(851\) −18.0745 −0.619586
\(852\) −18.4472 −0.631991
\(853\) −0.379924 −0.0130084 −0.00650418 0.999979i \(-0.502070\pi\)
−0.00650418 + 0.999979i \(0.502070\pi\)
\(854\) 5.68927 0.194683
\(855\) −27.6175 −0.944497
\(856\) 5.95942 0.203689
\(857\) −1.05432 −0.0360151 −0.0180075 0.999838i \(-0.505732\pi\)
−0.0180075 + 0.999838i \(0.505732\pi\)
\(858\) 34.2642 1.16976
\(859\) 8.89477 0.303486 0.151743 0.988420i \(-0.451511\pi\)
0.151743 + 0.988420i \(0.451511\pi\)
\(860\) 36.7274 1.25240
\(861\) −54.8654 −1.86981
\(862\) −20.8178 −0.709056
\(863\) 12.6455 0.430459 0.215229 0.976564i \(-0.430950\pi\)
0.215229 + 0.976564i \(0.430950\pi\)
\(864\) −0.841493 −0.0286282
\(865\) −3.35492 −0.114071
\(866\) −2.54094 −0.0863448
\(867\) −23.6002 −0.801504
\(868\) −3.56919 −0.121146
\(869\) −8.03940 −0.272718
\(870\) −15.1665 −0.514191
\(871\) −47.3862 −1.60562
\(872\) −0.338190 −0.0114526
\(873\) 14.8569 0.502829
\(874\) −18.6799 −0.631857
\(875\) −11.5213 −0.389492
\(876\) 33.1227 1.11911
\(877\) −17.1007 −0.577450 −0.288725 0.957412i \(-0.593231\pi\)
−0.288725 + 0.957412i \(0.593231\pi\)
\(878\) 8.94228 0.301787
\(879\) 20.6265 0.695716
\(880\) 10.4077 0.350843
\(881\) −27.6613 −0.931934 −0.465967 0.884802i \(-0.654293\pi\)
−0.465967 + 0.884802i \(0.654293\pi\)
\(882\) −8.29584 −0.279335
\(883\) 44.9933 1.51414 0.757072 0.653331i \(-0.226629\pi\)
0.757072 + 0.653331i \(0.226629\pi\)
\(884\) −23.9421 −0.805261
\(885\) −44.2890 −1.48876
\(886\) −26.7326 −0.898100
\(887\) 14.6070 0.490454 0.245227 0.969466i \(-0.421137\pi\)
0.245227 + 0.969466i \(0.421137\pi\)
\(888\) −7.20727 −0.241860
\(889\) −41.7822 −1.40133
\(890\) 34.1471 1.14461
\(891\) 31.0603 1.04056
\(892\) −11.1884 −0.374615
\(893\) −6.60471 −0.221018
\(894\) −14.9079 −0.498594
\(895\) −24.7460 −0.827167
\(896\) −3.18362 −0.106357
\(897\) 65.3207 2.18099
\(898\) −9.24604 −0.308544
\(899\) −2.14913 −0.0716776
\(900\) 16.1050 0.536832
\(901\) 57.1857 1.90513
\(902\) 22.6706 0.754848
\(903\) 83.4395 2.77669
\(904\) 16.0462 0.533690
\(905\) 2.44037 0.0811205
\(906\) −37.7685 −1.25477
\(907\) 7.30025 0.242401 0.121200 0.992628i \(-0.461326\pi\)
0.121200 + 0.992628i \(0.461326\pi\)
\(908\) −24.7115 −0.820079
\(909\) −8.57450 −0.284398
\(910\) −48.9047 −1.62118
\(911\) 52.3563 1.73464 0.867321 0.497749i \(-0.165840\pi\)
0.867321 + 0.497749i \(0.165840\pi\)
\(912\) −7.44867 −0.246650
\(913\) −34.7503 −1.15007
\(914\) 3.05356 0.101003
\(915\) −14.1385 −0.467406
\(916\) 14.2933 0.472264
\(917\) −21.4873 −0.709572
\(918\) −4.36704 −0.144134
\(919\) 41.8351 1.38001 0.690007 0.723803i \(-0.257608\pi\)
0.690007 + 0.723803i \(0.257608\pi\)
\(920\) 19.8411 0.654140
\(921\) 33.3123 1.09768
\(922\) 3.45615 0.113822
\(923\) −35.8172 −1.17894
\(924\) 23.6448 0.777856
\(925\) −18.4629 −0.607056
\(926\) −28.0621 −0.922179
\(927\) −18.6531 −0.612648
\(928\) −1.91697 −0.0629276
\(929\) −30.2794 −0.993434 −0.496717 0.867912i \(-0.665461\pi\)
−0.496717 + 0.867912i \(0.665461\pi\)
\(930\) 8.86988 0.290855
\(931\) 9.82899 0.322132
\(932\) 24.1996 0.792684
\(933\) 44.0409 1.44183
\(934\) −23.8285 −0.779691
\(935\) 54.0121 1.76638
\(936\) 12.2065 0.398982
\(937\) −14.9054 −0.486939 −0.243469 0.969909i \(-0.578286\pi\)
−0.243469 + 0.969909i \(0.578286\pi\)
\(938\) −32.7000 −1.06769
\(939\) 35.1965 1.14859
\(940\) 7.01527 0.228813
\(941\) 2.61608 0.0852819 0.0426409 0.999090i \(-0.486423\pi\)
0.0426409 + 0.999090i \(0.486423\pi\)
\(942\) 17.1200 0.557801
\(943\) 43.2188 1.40740
\(944\) −5.59792 −0.182197
\(945\) −8.92022 −0.290175
\(946\) −34.4775 −1.12096
\(947\) −6.17747 −0.200741 −0.100370 0.994950i \(-0.532003\pi\)
−0.100370 + 0.994950i \(0.532003\pi\)
\(948\) −6.11137 −0.198488
\(949\) 64.3112 2.08763
\(950\) −19.0813 −0.619079
\(951\) −58.3431 −1.89191
\(952\) −16.5218 −0.535475
\(953\) 12.4695 0.403927 0.201964 0.979393i \(-0.435268\pi\)
0.201964 + 0.979393i \(0.435268\pi\)
\(954\) −29.1552 −0.943934
\(955\) 6.24917 0.202218
\(956\) −20.3277 −0.657444
\(957\) 14.2374 0.460228
\(958\) −17.5981 −0.568569
\(959\) 36.4869 1.17823
\(960\) 7.91169 0.255349
\(961\) −29.7431 −0.959455
\(962\) −13.9937 −0.451174
\(963\) −15.7677 −0.508108
\(964\) 19.8055 0.637891
\(965\) −11.4124 −0.367377
\(966\) 45.0760 1.45030
\(967\) −56.1967 −1.80716 −0.903582 0.428416i \(-0.859072\pi\)
−0.903582 + 0.428416i \(0.859072\pi\)
\(968\) 1.22989 0.0395300
\(969\) −38.6559 −1.24181
\(970\) 18.6968 0.600317
\(971\) 42.2178 1.35483 0.677417 0.735600i \(-0.263100\pi\)
0.677417 + 0.735600i \(0.263100\pi\)
\(972\) 21.0869 0.676362
\(973\) 26.8246 0.859959
\(974\) 39.5420 1.26701
\(975\) 66.7244 2.13689
\(976\) −1.78705 −0.0572019
\(977\) −7.42062 −0.237407 −0.118703 0.992930i \(-0.537874\pi\)
−0.118703 + 0.992930i \(0.537874\pi\)
\(978\) −44.5620 −1.42493
\(979\) −32.0553 −1.02449
\(980\) −10.4400 −0.333493
\(981\) 0.894801 0.0285688
\(982\) 7.52025 0.239981
\(983\) 34.1733 1.08996 0.544980 0.838449i \(-0.316537\pi\)
0.544980 + 0.838449i \(0.316537\pi\)
\(984\) 17.2337 0.549389
\(985\) 39.9397 1.27258
\(986\) −9.94837 −0.316821
\(987\) 15.9377 0.507302
\(988\) −14.4624 −0.460109
\(989\) −65.7274 −2.09001
\(990\) −27.5372 −0.875190
\(991\) −37.5417 −1.19255 −0.596276 0.802779i \(-0.703354\pi\)
−0.596276 + 0.802779i \(0.703354\pi\)
\(992\) 1.12111 0.0355953
\(993\) −72.0631 −2.28685
\(994\) −24.7165 −0.783959
\(995\) 2.95810 0.0937782
\(996\) −26.4164 −0.837036
\(997\) 30.6259 0.969933 0.484966 0.874533i \(-0.338832\pi\)
0.484966 + 0.874533i \(0.338832\pi\)
\(998\) 20.2139 0.639861
\(999\) −2.55244 −0.0807558
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 \(a_p\))