Properties

Label 8015.2.a.l.1.44
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.44
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.36004 q^{2} +3.37769 q^{3} -0.150287 q^{4} -1.00000 q^{5} +4.59380 q^{6} -1.00000 q^{7} -2.92448 q^{8} +8.40880 q^{9} +O(q^{10})\) \(q+1.36004 q^{2} +3.37769 q^{3} -0.150287 q^{4} -1.00000 q^{5} +4.59380 q^{6} -1.00000 q^{7} -2.92448 q^{8} +8.40880 q^{9} -1.36004 q^{10} +6.45750 q^{11} -0.507624 q^{12} +3.96000 q^{13} -1.36004 q^{14} -3.37769 q^{15} -3.67684 q^{16} -4.58527 q^{17} +11.4363 q^{18} +6.23815 q^{19} +0.150287 q^{20} -3.37769 q^{21} +8.78247 q^{22} +1.03015 q^{23} -9.87799 q^{24} +1.00000 q^{25} +5.38576 q^{26} +18.2692 q^{27} +0.150287 q^{28} -10.2138 q^{29} -4.59380 q^{30} -2.95134 q^{31} +0.848305 q^{32} +21.8114 q^{33} -6.23615 q^{34} +1.00000 q^{35} -1.26373 q^{36} -0.589617 q^{37} +8.48415 q^{38} +13.3757 q^{39} +2.92448 q^{40} +3.44305 q^{41} -4.59380 q^{42} +3.73038 q^{43} -0.970479 q^{44} -8.40880 q^{45} +1.40105 q^{46} -6.19041 q^{47} -12.4192 q^{48} +1.00000 q^{49} +1.36004 q^{50} -15.4876 q^{51} -0.595137 q^{52} +5.95352 q^{53} +24.8469 q^{54} -6.45750 q^{55} +2.92448 q^{56} +21.0706 q^{57} -13.8911 q^{58} +10.5027 q^{59} +0.507624 q^{60} -6.64857 q^{61} -4.01394 q^{62} -8.40880 q^{63} +8.50741 q^{64} -3.96000 q^{65} +29.6645 q^{66} +7.71541 q^{67} +0.689107 q^{68} +3.47953 q^{69} +1.36004 q^{70} -3.30265 q^{71} -24.5914 q^{72} -13.3597 q^{73} -0.801903 q^{74} +3.37769 q^{75} -0.937514 q^{76} -6.45750 q^{77} +18.1914 q^{78} -3.62340 q^{79} +3.67684 q^{80} +36.4815 q^{81} +4.68269 q^{82} -5.79752 q^{83} +0.507624 q^{84} +4.58527 q^{85} +5.07347 q^{86} -34.4989 q^{87} -18.8848 q^{88} +12.8246 q^{89} -11.4363 q^{90} -3.96000 q^{91} -0.154819 q^{92} -9.96870 q^{93} -8.41921 q^{94} -6.23815 q^{95} +2.86531 q^{96} +13.1504 q^{97} +1.36004 q^{98} +54.2998 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36004 0.961695 0.480847 0.876804i \(-0.340329\pi\)
0.480847 + 0.876804i \(0.340329\pi\)
\(3\) 3.37769 1.95011 0.975055 0.221961i \(-0.0712459\pi\)
0.975055 + 0.221961i \(0.0712459\pi\)
\(4\) −0.150287 −0.0751436
\(5\) −1.00000 −0.447214
\(6\) 4.59380 1.87541
\(7\) −1.00000 −0.377964
\(8\) −2.92448 −1.03396
\(9\) 8.40880 2.80293
\(10\) −1.36004 −0.430083
\(11\) 6.45750 1.94701 0.973505 0.228666i \(-0.0734363\pi\)
0.973505 + 0.228666i \(0.0734363\pi\)
\(12\) −0.507624 −0.146538
\(13\) 3.96000 1.09831 0.549153 0.835722i \(-0.314950\pi\)
0.549153 + 0.835722i \(0.314950\pi\)
\(14\) −1.36004 −0.363486
\(15\) −3.37769 −0.872116
\(16\) −3.67684 −0.919210
\(17\) −4.58527 −1.11209 −0.556045 0.831152i \(-0.687682\pi\)
−0.556045 + 0.831152i \(0.687682\pi\)
\(18\) 11.4363 2.69557
\(19\) 6.23815 1.43113 0.715565 0.698546i \(-0.246169\pi\)
0.715565 + 0.698546i \(0.246169\pi\)
\(20\) 0.150287 0.0336052
\(21\) −3.37769 −0.737073
\(22\) 8.78247 1.87243
\(23\) 1.03015 0.214801 0.107401 0.994216i \(-0.465747\pi\)
0.107401 + 0.994216i \(0.465747\pi\)
\(24\) −9.87799 −2.01634
\(25\) 1.00000 0.200000
\(26\) 5.38576 1.05623
\(27\) 18.2692 3.51592
\(28\) 0.150287 0.0284016
\(29\) −10.2138 −1.89665 −0.948323 0.317307i \(-0.897221\pi\)
−0.948323 + 0.317307i \(0.897221\pi\)
\(30\) −4.59380 −0.838709
\(31\) −2.95134 −0.530076 −0.265038 0.964238i \(-0.585384\pi\)
−0.265038 + 0.964238i \(0.585384\pi\)
\(32\) 0.848305 0.149961
\(33\) 21.8114 3.79689
\(34\) −6.23615 −1.06949
\(35\) 1.00000 0.169031
\(36\) −1.26373 −0.210622
\(37\) −0.589617 −0.0969324 −0.0484662 0.998825i \(-0.515433\pi\)
−0.0484662 + 0.998825i \(0.515433\pi\)
\(38\) 8.48415 1.37631
\(39\) 13.3757 2.14182
\(40\) 2.92448 0.462401
\(41\) 3.44305 0.537714 0.268857 0.963180i \(-0.413354\pi\)
0.268857 + 0.963180i \(0.413354\pi\)
\(42\) −4.59380 −0.708839
\(43\) 3.73038 0.568877 0.284439 0.958694i \(-0.408193\pi\)
0.284439 + 0.958694i \(0.408193\pi\)
\(44\) −0.970479 −0.146305
\(45\) −8.40880 −1.25351
\(46\) 1.40105 0.206573
\(47\) −6.19041 −0.902964 −0.451482 0.892280i \(-0.649104\pi\)
−0.451482 + 0.892280i \(0.649104\pi\)
\(48\) −12.4192 −1.79256
\(49\) 1.00000 0.142857
\(50\) 1.36004 0.192339
\(51\) −15.4876 −2.16870
\(52\) −0.595137 −0.0825306
\(53\) 5.95352 0.817778 0.408889 0.912584i \(-0.365916\pi\)
0.408889 + 0.912584i \(0.365916\pi\)
\(54\) 24.8469 3.38124
\(55\) −6.45750 −0.870729
\(56\) 2.92448 0.390800
\(57\) 21.0706 2.79086
\(58\) −13.8911 −1.82399
\(59\) 10.5027 1.36733 0.683666 0.729795i \(-0.260385\pi\)
0.683666 + 0.729795i \(0.260385\pi\)
\(60\) 0.507624 0.0655339
\(61\) −6.64857 −0.851262 −0.425631 0.904897i \(-0.639948\pi\)
−0.425631 + 0.904897i \(0.639948\pi\)
\(62\) −4.01394 −0.509771
\(63\) −8.40880 −1.05941
\(64\) 8.50741 1.06343
\(65\) −3.96000 −0.491177
\(66\) 29.6645 3.65144
\(67\) 7.71541 0.942588 0.471294 0.881976i \(-0.343787\pi\)
0.471294 + 0.881976i \(0.343787\pi\)
\(68\) 0.689107 0.0835665
\(69\) 3.47953 0.418887
\(70\) 1.36004 0.162556
\(71\) −3.30265 −0.391952 −0.195976 0.980609i \(-0.562788\pi\)
−0.195976 + 0.980609i \(0.562788\pi\)
\(72\) −24.5914 −2.89812
\(73\) −13.3597 −1.56363 −0.781815 0.623510i \(-0.785706\pi\)
−0.781815 + 0.623510i \(0.785706\pi\)
\(74\) −0.801903 −0.0932193
\(75\) 3.37769 0.390022
\(76\) −0.937514 −0.107540
\(77\) −6.45750 −0.735901
\(78\) 18.1914 2.05978
\(79\) −3.62340 −0.407665 −0.203832 0.979006i \(-0.565340\pi\)
−0.203832 + 0.979006i \(0.565340\pi\)
\(80\) 3.67684 0.411083
\(81\) 36.4815 4.05350
\(82\) 4.68269 0.517116
\(83\) −5.79752 −0.636361 −0.318180 0.948030i \(-0.603072\pi\)
−0.318180 + 0.948030i \(0.603072\pi\)
\(84\) 0.507624 0.0553863
\(85\) 4.58527 0.497342
\(86\) 5.07347 0.547086
\(87\) −34.4989 −3.69867
\(88\) −18.8848 −2.01313
\(89\) 12.8246 1.35940 0.679702 0.733489i \(-0.262109\pi\)
0.679702 + 0.733489i \(0.262109\pi\)
\(90\) −11.4363 −1.20549
\(91\) −3.96000 −0.415121
\(92\) −0.154819 −0.0161409
\(93\) −9.96870 −1.03371
\(94\) −8.41921 −0.868376
\(95\) −6.23815 −0.640021
\(96\) 2.86531 0.292440
\(97\) 13.1504 1.33522 0.667609 0.744512i \(-0.267318\pi\)
0.667609 + 0.744512i \(0.267318\pi\)
\(98\) 1.36004 0.137385
\(99\) 54.2998 5.45734
\(100\) −0.150287 −0.0150287
\(101\) −3.40236 −0.338548 −0.169274 0.985569i \(-0.554142\pi\)
−0.169274 + 0.985569i \(0.554142\pi\)
\(102\) −21.0638 −2.08563
\(103\) 12.5015 1.23181 0.615906 0.787820i \(-0.288790\pi\)
0.615906 + 0.787820i \(0.288790\pi\)
\(104\) −11.5809 −1.13560
\(105\) 3.37769 0.329629
\(106\) 8.09703 0.786453
\(107\) 3.51408 0.339719 0.169860 0.985468i \(-0.445669\pi\)
0.169860 + 0.985468i \(0.445669\pi\)
\(108\) −2.74563 −0.264199
\(109\) 4.62692 0.443179 0.221589 0.975140i \(-0.428876\pi\)
0.221589 + 0.975140i \(0.428876\pi\)
\(110\) −8.78247 −0.837376
\(111\) −1.99154 −0.189029
\(112\) 3.67684 0.347429
\(113\) −0.924504 −0.0869700 −0.0434850 0.999054i \(-0.513846\pi\)
−0.0434850 + 0.999054i \(0.513846\pi\)
\(114\) 28.6568 2.68396
\(115\) −1.03015 −0.0960621
\(116\) 1.53500 0.142521
\(117\) 33.2988 3.07848
\(118\) 14.2841 1.31496
\(119\) 4.58527 0.420331
\(120\) 9.87799 0.901733
\(121\) 30.6993 2.79085
\(122\) −9.04233 −0.818654
\(123\) 11.6296 1.04860
\(124\) 0.443548 0.0398318
\(125\) −1.00000 −0.0894427
\(126\) −11.4363 −1.01883
\(127\) −16.0087 −1.42054 −0.710272 0.703927i \(-0.751428\pi\)
−0.710272 + 0.703927i \(0.751428\pi\)
\(128\) 9.87382 0.872731
\(129\) 12.6001 1.10937
\(130\) −5.38576 −0.472363
\(131\) −22.2455 −1.94360 −0.971800 0.235805i \(-0.924227\pi\)
−0.971800 + 0.235805i \(0.924227\pi\)
\(132\) −3.27798 −0.285312
\(133\) −6.23815 −0.540916
\(134\) 10.4933 0.906482
\(135\) −18.2692 −1.57237
\(136\) 13.4095 1.14986
\(137\) −2.69337 −0.230110 −0.115055 0.993359i \(-0.536704\pi\)
−0.115055 + 0.993359i \(0.536704\pi\)
\(138\) 4.73231 0.402841
\(139\) −0.256702 −0.0217732 −0.0108866 0.999941i \(-0.503465\pi\)
−0.0108866 + 0.999941i \(0.503465\pi\)
\(140\) −0.150287 −0.0127016
\(141\) −20.9093 −1.76088
\(142\) −4.49174 −0.376938
\(143\) 25.5717 2.13841
\(144\) −30.9178 −2.57648
\(145\) 10.2138 0.848206
\(146\) −18.1697 −1.50374
\(147\) 3.37769 0.278587
\(148\) 0.0886118 0.00728384
\(149\) 2.32524 0.190491 0.0952457 0.995454i \(-0.469636\pi\)
0.0952457 + 0.995454i \(0.469636\pi\)
\(150\) 4.59380 0.375082
\(151\) −10.5195 −0.856065 −0.428032 0.903763i \(-0.640793\pi\)
−0.428032 + 0.903763i \(0.640793\pi\)
\(152\) −18.2433 −1.47973
\(153\) −38.5566 −3.11712
\(154\) −8.78247 −0.707712
\(155\) 2.95134 0.237057
\(156\) −2.01019 −0.160944
\(157\) 7.41148 0.591501 0.295750 0.955265i \(-0.404430\pi\)
0.295750 + 0.955265i \(0.404430\pi\)
\(158\) −4.92798 −0.392049
\(159\) 20.1091 1.59476
\(160\) −0.848305 −0.0670644
\(161\) −1.03015 −0.0811873
\(162\) 49.6163 3.89823
\(163\) 9.24420 0.724061 0.362031 0.932166i \(-0.382084\pi\)
0.362031 + 0.932166i \(0.382084\pi\)
\(164\) −0.517446 −0.0404057
\(165\) −21.8114 −1.69802
\(166\) −7.88487 −0.611985
\(167\) 17.7621 1.37447 0.687236 0.726434i \(-0.258824\pi\)
0.687236 + 0.726434i \(0.258824\pi\)
\(168\) 9.87799 0.762103
\(169\) 2.68159 0.206276
\(170\) 6.23615 0.478291
\(171\) 52.4554 4.01136
\(172\) −0.560628 −0.0427475
\(173\) 13.4338 1.02135 0.510675 0.859774i \(-0.329395\pi\)
0.510675 + 0.859774i \(0.329395\pi\)
\(174\) −46.9199 −3.55699
\(175\) −1.00000 −0.0755929
\(176\) −23.7432 −1.78971
\(177\) 35.4748 2.66645
\(178\) 17.4420 1.30733
\(179\) 14.0462 1.04986 0.524931 0.851145i \(-0.324091\pi\)
0.524931 + 0.851145i \(0.324091\pi\)
\(180\) 1.26373 0.0941932
\(181\) 0.354696 0.0263643 0.0131822 0.999913i \(-0.495804\pi\)
0.0131822 + 0.999913i \(0.495804\pi\)
\(182\) −5.38576 −0.399219
\(183\) −22.4568 −1.66006
\(184\) −3.01266 −0.222096
\(185\) 0.589617 0.0433495
\(186\) −13.5579 −0.994110
\(187\) −29.6094 −2.16525
\(188\) 0.930339 0.0678519
\(189\) −18.2692 −1.32889
\(190\) −8.48415 −0.615505
\(191\) 19.2297 1.39141 0.695706 0.718326i \(-0.255092\pi\)
0.695706 + 0.718326i \(0.255092\pi\)
\(192\) 28.7354 2.07380
\(193\) −19.2757 −1.38749 −0.693746 0.720220i \(-0.744041\pi\)
−0.693746 + 0.720220i \(0.744041\pi\)
\(194\) 17.8851 1.28407
\(195\) −13.3757 −0.957850
\(196\) −0.150287 −0.0107348
\(197\) −24.4848 −1.74447 −0.872235 0.489087i \(-0.837330\pi\)
−0.872235 + 0.489087i \(0.837330\pi\)
\(198\) 73.8500 5.24829
\(199\) 17.9754 1.27424 0.637121 0.770764i \(-0.280125\pi\)
0.637121 + 0.770764i \(0.280125\pi\)
\(200\) −2.92448 −0.206792
\(201\) 26.0603 1.83815
\(202\) −4.62735 −0.325580
\(203\) 10.2138 0.716865
\(204\) 2.32759 0.162964
\(205\) −3.44305 −0.240473
\(206\) 17.0026 1.18463
\(207\) 8.66234 0.602074
\(208\) −14.5603 −1.00957
\(209\) 40.2829 2.78642
\(210\) 4.59380 0.317002
\(211\) 1.58864 0.109366 0.0546831 0.998504i \(-0.482585\pi\)
0.0546831 + 0.998504i \(0.482585\pi\)
\(212\) −0.894737 −0.0614508
\(213\) −11.1553 −0.764351
\(214\) 4.77930 0.326706
\(215\) −3.73038 −0.254410
\(216\) −53.4280 −3.63532
\(217\) 2.95134 0.200350
\(218\) 6.29281 0.426203
\(219\) −45.1248 −3.04925
\(220\) 0.970479 0.0654297
\(221\) −18.1577 −1.22142
\(222\) −2.70858 −0.181788
\(223\) 14.2542 0.954532 0.477266 0.878759i \(-0.341628\pi\)
0.477266 + 0.878759i \(0.341628\pi\)
\(224\) −0.848305 −0.0566798
\(225\) 8.40880 0.560587
\(226\) −1.25736 −0.0836386
\(227\) −12.9564 −0.859945 −0.429972 0.902842i \(-0.641477\pi\)
−0.429972 + 0.902842i \(0.641477\pi\)
\(228\) −3.16663 −0.209715
\(229\) 1.00000 0.0660819
\(230\) −1.40105 −0.0923824
\(231\) −21.8114 −1.43509
\(232\) 29.8699 1.96106
\(233\) 0.404052 0.0264703 0.0132351 0.999912i \(-0.495787\pi\)
0.0132351 + 0.999912i \(0.495787\pi\)
\(234\) 45.2878 2.96056
\(235\) 6.19041 0.403818
\(236\) −1.57842 −0.102746
\(237\) −12.2387 −0.794992
\(238\) 6.23615 0.404230
\(239\) −25.4023 −1.64314 −0.821568 0.570111i \(-0.806900\pi\)
−0.821568 + 0.570111i \(0.806900\pi\)
\(240\) 12.4192 0.801658
\(241\) −20.2053 −1.30154 −0.650768 0.759276i \(-0.725553\pi\)
−0.650768 + 0.759276i \(0.725553\pi\)
\(242\) 41.7524 2.68394
\(243\) 68.4155 4.38885
\(244\) 0.999195 0.0639669
\(245\) −1.00000 −0.0638877
\(246\) 15.8167 1.00843
\(247\) 24.7031 1.57182
\(248\) 8.63112 0.548077
\(249\) −19.5822 −1.24097
\(250\) −1.36004 −0.0860166
\(251\) −30.4644 −1.92290 −0.961448 0.274986i \(-0.911327\pi\)
−0.961448 + 0.274986i \(0.911327\pi\)
\(252\) 1.26373 0.0796078
\(253\) 6.65221 0.418221
\(254\) −21.7725 −1.36613
\(255\) 15.4876 0.969872
\(256\) −3.58601 −0.224126
\(257\) −25.5667 −1.59481 −0.797404 0.603446i \(-0.793794\pi\)
−0.797404 + 0.603446i \(0.793794\pi\)
\(258\) 17.1366 1.06688
\(259\) 0.589617 0.0366370
\(260\) 0.595137 0.0369088
\(261\) −85.8854 −5.31617
\(262\) −30.2548 −1.86915
\(263\) −4.76256 −0.293672 −0.146836 0.989161i \(-0.546909\pi\)
−0.146836 + 0.989161i \(0.546909\pi\)
\(264\) −63.7871 −3.92583
\(265\) −5.95352 −0.365722
\(266\) −8.48415 −0.520196
\(267\) 43.3175 2.65099
\(268\) −1.15953 −0.0708294
\(269\) −19.8697 −1.21148 −0.605738 0.795664i \(-0.707122\pi\)
−0.605738 + 0.795664i \(0.707122\pi\)
\(270\) −24.8469 −1.51214
\(271\) −8.44148 −0.512784 −0.256392 0.966573i \(-0.582534\pi\)
−0.256392 + 0.966573i \(0.582534\pi\)
\(272\) 16.8593 1.02224
\(273\) −13.3757 −0.809531
\(274\) −3.66310 −0.221296
\(275\) 6.45750 0.389402
\(276\) −0.522929 −0.0314766
\(277\) −6.48803 −0.389828 −0.194914 0.980820i \(-0.562443\pi\)
−0.194914 + 0.980820i \(0.562443\pi\)
\(278\) −0.349125 −0.0209391
\(279\) −24.8172 −1.48577
\(280\) −2.92448 −0.174771
\(281\) −24.3084 −1.45012 −0.725059 0.688686i \(-0.758188\pi\)
−0.725059 + 0.688686i \(0.758188\pi\)
\(282\) −28.4375 −1.69343
\(283\) 27.2146 1.61774 0.808869 0.587989i \(-0.200080\pi\)
0.808869 + 0.587989i \(0.200080\pi\)
\(284\) 0.496346 0.0294527
\(285\) −21.0706 −1.24811
\(286\) 34.7786 2.05650
\(287\) −3.44305 −0.203237
\(288\) 7.13323 0.420329
\(289\) 4.02468 0.236746
\(290\) 13.8911 0.815715
\(291\) 44.4179 2.60382
\(292\) 2.00779 0.117497
\(293\) −20.1971 −1.17992 −0.589962 0.807431i \(-0.700857\pi\)
−0.589962 + 0.807431i \(0.700857\pi\)
\(294\) 4.59380 0.267916
\(295\) −10.5027 −0.611489
\(296\) 1.72432 0.100224
\(297\) 117.974 6.84553
\(298\) 3.16243 0.183195
\(299\) 4.07940 0.235918
\(300\) −0.507624 −0.0293077
\(301\) −3.73038 −0.215015
\(302\) −14.3070 −0.823273
\(303\) −11.4921 −0.660206
\(304\) −22.9367 −1.31551
\(305\) 6.64857 0.380696
\(306\) −52.4386 −2.99771
\(307\) 28.6017 1.63238 0.816192 0.577781i \(-0.196081\pi\)
0.816192 + 0.577781i \(0.196081\pi\)
\(308\) 0.970479 0.0552982
\(309\) 42.2263 2.40217
\(310\) 4.01394 0.227976
\(311\) 6.15790 0.349183 0.174591 0.984641i \(-0.444140\pi\)
0.174591 + 0.984641i \(0.444140\pi\)
\(312\) −39.1168 −2.21455
\(313\) 17.1771 0.970906 0.485453 0.874263i \(-0.338655\pi\)
0.485453 + 0.874263i \(0.338655\pi\)
\(314\) 10.0799 0.568843
\(315\) 8.40880 0.473782
\(316\) 0.544551 0.0306334
\(317\) −6.33591 −0.355860 −0.177930 0.984043i \(-0.556940\pi\)
−0.177930 + 0.984043i \(0.556940\pi\)
\(318\) 27.3493 1.53367
\(319\) −65.9553 −3.69279
\(320\) −8.50741 −0.475579
\(321\) 11.8695 0.662490
\(322\) −1.40105 −0.0780774
\(323\) −28.6036 −1.59155
\(324\) −5.48270 −0.304594
\(325\) 3.96000 0.219661
\(326\) 12.5725 0.696326
\(327\) 15.6283 0.864248
\(328\) −10.0691 −0.555974
\(329\) 6.19041 0.341288
\(330\) −29.6645 −1.63298
\(331\) −3.24627 −0.178431 −0.0892157 0.996012i \(-0.528436\pi\)
−0.0892157 + 0.996012i \(0.528436\pi\)
\(332\) 0.871293 0.0478184
\(333\) −4.95797 −0.271695
\(334\) 24.1572 1.32182
\(335\) −7.71541 −0.421538
\(336\) 12.4192 0.677524
\(337\) 21.4690 1.16949 0.584745 0.811217i \(-0.301194\pi\)
0.584745 + 0.811217i \(0.301194\pi\)
\(338\) 3.64707 0.198375
\(339\) −3.12269 −0.169601
\(340\) −0.689107 −0.0373721
\(341\) −19.0583 −1.03206
\(342\) 71.3415 3.85770
\(343\) −1.00000 −0.0539949
\(344\) −10.9094 −0.588196
\(345\) −3.47953 −0.187332
\(346\) 18.2705 0.982227
\(347\) −13.5146 −0.725500 −0.362750 0.931887i \(-0.618162\pi\)
−0.362750 + 0.931887i \(0.618162\pi\)
\(348\) 5.18474 0.277931
\(349\) −7.79214 −0.417104 −0.208552 0.978011i \(-0.566875\pi\)
−0.208552 + 0.978011i \(0.566875\pi\)
\(350\) −1.36004 −0.0726973
\(351\) 72.3462 3.86155
\(352\) 5.47793 0.291975
\(353\) −26.8091 −1.42691 −0.713453 0.700704i \(-0.752870\pi\)
−0.713453 + 0.700704i \(0.752870\pi\)
\(354\) 48.2472 2.56431
\(355\) 3.30265 0.175286
\(356\) −1.92737 −0.102150
\(357\) 15.4876 0.819692
\(358\) 19.1034 1.00965
\(359\) 19.0469 1.00526 0.502630 0.864502i \(-0.332366\pi\)
0.502630 + 0.864502i \(0.332366\pi\)
\(360\) 24.5914 1.29608
\(361\) 19.9145 1.04813
\(362\) 0.482401 0.0253544
\(363\) 103.693 5.44246
\(364\) 0.595137 0.0311936
\(365\) 13.3597 0.699277
\(366\) −30.5422 −1.59647
\(367\) 0.744542 0.0388648 0.0194324 0.999811i \(-0.493814\pi\)
0.0194324 + 0.999811i \(0.493814\pi\)
\(368\) −3.78770 −0.197448
\(369\) 28.9519 1.50718
\(370\) 0.801903 0.0416890
\(371\) −5.95352 −0.309091
\(372\) 1.49817 0.0776764
\(373\) 25.6146 1.32627 0.663137 0.748498i \(-0.269224\pi\)
0.663137 + 0.748498i \(0.269224\pi\)
\(374\) −40.2700 −2.08231
\(375\) −3.37769 −0.174423
\(376\) 18.1037 0.933628
\(377\) −40.4464 −2.08310
\(378\) −24.8469 −1.27799
\(379\) −3.83861 −0.197176 −0.0985882 0.995128i \(-0.531433\pi\)
−0.0985882 + 0.995128i \(0.531433\pi\)
\(380\) 0.937514 0.0480935
\(381\) −54.0725 −2.77022
\(382\) 26.1532 1.33811
\(383\) 8.49369 0.434007 0.217004 0.976171i \(-0.430372\pi\)
0.217004 + 0.976171i \(0.430372\pi\)
\(384\) 33.3507 1.70192
\(385\) 6.45750 0.329105
\(386\) −26.2157 −1.33434
\(387\) 31.3680 1.59452
\(388\) −1.97633 −0.100333
\(389\) −16.6735 −0.845382 −0.422691 0.906274i \(-0.638914\pi\)
−0.422691 + 0.906274i \(0.638914\pi\)
\(390\) −18.1914 −0.921160
\(391\) −4.72352 −0.238879
\(392\) −2.92448 −0.147709
\(393\) −75.1385 −3.79024
\(394\) −33.3003 −1.67765
\(395\) 3.62340 0.182313
\(396\) −8.16056 −0.410084
\(397\) 13.3378 0.669403 0.334701 0.942324i \(-0.391365\pi\)
0.334701 + 0.942324i \(0.391365\pi\)
\(398\) 24.4473 1.22543
\(399\) −21.0706 −1.05485
\(400\) −3.67684 −0.183842
\(401\) −17.2923 −0.863537 −0.431768 0.901985i \(-0.642110\pi\)
−0.431768 + 0.901985i \(0.642110\pi\)
\(402\) 35.4431 1.76774
\(403\) −11.6873 −0.582185
\(404\) 0.511331 0.0254397
\(405\) −36.4815 −1.81278
\(406\) 13.8911 0.689405
\(407\) −3.80745 −0.188728
\(408\) 45.2932 2.24235
\(409\) −25.9115 −1.28124 −0.640621 0.767857i \(-0.721323\pi\)
−0.640621 + 0.767857i \(0.721323\pi\)
\(410\) −4.68269 −0.231261
\(411\) −9.09738 −0.448741
\(412\) −1.87882 −0.0925627
\(413\) −10.5027 −0.516803
\(414\) 11.7811 0.579011
\(415\) 5.79752 0.284589
\(416\) 3.35929 0.164703
\(417\) −0.867059 −0.0424601
\(418\) 54.7864 2.67969
\(419\) −3.40443 −0.166317 −0.0831587 0.996536i \(-0.526501\pi\)
−0.0831587 + 0.996536i \(0.526501\pi\)
\(420\) −0.507624 −0.0247695
\(421\) −7.91794 −0.385897 −0.192948 0.981209i \(-0.561805\pi\)
−0.192948 + 0.981209i \(0.561805\pi\)
\(422\) 2.16061 0.105177
\(423\) −52.0539 −2.53095
\(424\) −17.4109 −0.845550
\(425\) −4.58527 −0.222418
\(426\) −15.1717 −0.735072
\(427\) 6.64857 0.321747
\(428\) −0.528121 −0.0255277
\(429\) 86.3733 4.17014
\(430\) −5.07347 −0.244664
\(431\) 32.0430 1.54346 0.771728 0.635953i \(-0.219393\pi\)
0.771728 + 0.635953i \(0.219393\pi\)
\(432\) −67.1731 −3.23187
\(433\) −17.7521 −0.853111 −0.426556 0.904461i \(-0.640273\pi\)
−0.426556 + 0.904461i \(0.640273\pi\)
\(434\) 4.01394 0.192675
\(435\) 34.4989 1.65410
\(436\) −0.695367 −0.0333020
\(437\) 6.42624 0.307409
\(438\) −61.3716 −2.93245
\(439\) −18.6554 −0.890374 −0.445187 0.895438i \(-0.646863\pi\)
−0.445187 + 0.895438i \(0.646863\pi\)
\(440\) 18.8848 0.900299
\(441\) 8.40880 0.400419
\(442\) −24.6952 −1.17463
\(443\) −10.7790 −0.512128 −0.256064 0.966660i \(-0.582426\pi\)
−0.256064 + 0.966660i \(0.582426\pi\)
\(444\) 0.299303 0.0142043
\(445\) −12.8246 −0.607944
\(446\) 19.3863 0.917968
\(447\) 7.85396 0.371479
\(448\) −8.50741 −0.401937
\(449\) 38.5050 1.81716 0.908582 0.417706i \(-0.137166\pi\)
0.908582 + 0.417706i \(0.137166\pi\)
\(450\) 11.4363 0.539113
\(451\) 22.2335 1.04693
\(452\) 0.138941 0.00653524
\(453\) −35.5316 −1.66942
\(454\) −17.6212 −0.827004
\(455\) 3.96000 0.185648
\(456\) −61.6204 −2.88564
\(457\) −30.6274 −1.43269 −0.716346 0.697746i \(-0.754187\pi\)
−0.716346 + 0.697746i \(0.754187\pi\)
\(458\) 1.36004 0.0635506
\(459\) −83.7694 −3.91002
\(460\) 0.154819 0.00721845
\(461\) 26.2669 1.22337 0.611685 0.791102i \(-0.290492\pi\)
0.611685 + 0.791102i \(0.290492\pi\)
\(462\) −29.6645 −1.38012
\(463\) 4.00857 0.186294 0.0931471 0.995652i \(-0.470307\pi\)
0.0931471 + 0.995652i \(0.470307\pi\)
\(464\) 37.5543 1.74342
\(465\) 9.96870 0.462288
\(466\) 0.549527 0.0254563
\(467\) 25.2478 1.16833 0.584165 0.811635i \(-0.301422\pi\)
0.584165 + 0.811635i \(0.301422\pi\)
\(468\) −5.00439 −0.231328
\(469\) −7.71541 −0.356265
\(470\) 8.41921 0.388349
\(471\) 25.0337 1.15349
\(472\) −30.7149 −1.41377
\(473\) 24.0889 1.10761
\(474\) −16.6452 −0.764539
\(475\) 6.23815 0.286226
\(476\) −0.689107 −0.0315852
\(477\) 50.0619 2.29218
\(478\) −34.5481 −1.58019
\(479\) −13.7155 −0.626678 −0.313339 0.949641i \(-0.601448\pi\)
−0.313339 + 0.949641i \(0.601448\pi\)
\(480\) −2.86531 −0.130783
\(481\) −2.33488 −0.106461
\(482\) −27.4800 −1.25168
\(483\) −3.47953 −0.158324
\(484\) −4.61371 −0.209714
\(485\) −13.1504 −0.597128
\(486\) 93.0479 4.22074
\(487\) −17.5234 −0.794060 −0.397030 0.917806i \(-0.629959\pi\)
−0.397030 + 0.917806i \(0.629959\pi\)
\(488\) 19.4436 0.880171
\(489\) 31.2240 1.41200
\(490\) −1.36004 −0.0614404
\(491\) 26.0639 1.17625 0.588124 0.808771i \(-0.299867\pi\)
0.588124 + 0.808771i \(0.299867\pi\)
\(492\) −1.74777 −0.0787956
\(493\) 46.8328 2.10924
\(494\) 33.5972 1.51161
\(495\) −54.2998 −2.44060
\(496\) 10.8516 0.487251
\(497\) 3.30265 0.148144
\(498\) −26.6327 −1.19344
\(499\) 14.7288 0.659353 0.329676 0.944094i \(-0.393060\pi\)
0.329676 + 0.944094i \(0.393060\pi\)
\(500\) 0.150287 0.00672104
\(501\) 59.9949 2.68037
\(502\) −41.4329 −1.84924
\(503\) 37.4425 1.66948 0.834739 0.550646i \(-0.185619\pi\)
0.834739 + 0.550646i \(0.185619\pi\)
\(504\) 24.5914 1.09539
\(505\) 3.40236 0.151403
\(506\) 9.04728 0.402200
\(507\) 9.05758 0.402261
\(508\) 2.40591 0.106745
\(509\) −11.4069 −0.505600 −0.252800 0.967519i \(-0.581351\pi\)
−0.252800 + 0.967519i \(0.581351\pi\)
\(510\) 21.0638 0.932721
\(511\) 13.3597 0.590997
\(512\) −24.6248 −1.08827
\(513\) 113.966 5.03174
\(514\) −34.7718 −1.53372
\(515\) −12.5015 −0.550883
\(516\) −1.89363 −0.0833623
\(517\) −39.9746 −1.75808
\(518\) 0.801903 0.0352336
\(519\) 45.3751 1.99175
\(520\) 11.5809 0.507858
\(521\) −25.2331 −1.10548 −0.552741 0.833353i \(-0.686418\pi\)
−0.552741 + 0.833353i \(0.686418\pi\)
\(522\) −116.808 −5.11253
\(523\) −34.2126 −1.49601 −0.748006 0.663692i \(-0.768989\pi\)
−0.748006 + 0.663692i \(0.768989\pi\)
\(524\) 3.34322 0.146049
\(525\) −3.37769 −0.147415
\(526\) −6.47727 −0.282423
\(527\) 13.5327 0.589492
\(528\) −80.1972 −3.49013
\(529\) −21.9388 −0.953860
\(530\) −8.09703 −0.351712
\(531\) 88.3149 3.83254
\(532\) 0.937514 0.0406464
\(533\) 13.6345 0.590574
\(534\) 58.9136 2.54944
\(535\) −3.51408 −0.151927
\(536\) −22.5636 −0.974598
\(537\) 47.4437 2.04735
\(538\) −27.0236 −1.16507
\(539\) 6.45750 0.278144
\(540\) 2.74563 0.118153
\(541\) −6.96248 −0.299340 −0.149670 0.988736i \(-0.547821\pi\)
−0.149670 + 0.988736i \(0.547821\pi\)
\(542\) −11.4808 −0.493141
\(543\) 1.19805 0.0514134
\(544\) −3.88971 −0.166770
\(545\) −4.62692 −0.198196
\(546\) −18.1914 −0.778522
\(547\) 30.8734 1.32005 0.660025 0.751244i \(-0.270546\pi\)
0.660025 + 0.751244i \(0.270546\pi\)
\(548\) 0.404779 0.0172913
\(549\) −55.9065 −2.38603
\(550\) 8.78247 0.374486
\(551\) −63.7149 −2.71435
\(552\) −10.1758 −0.433112
\(553\) 3.62340 0.154083
\(554\) −8.82399 −0.374896
\(555\) 1.99154 0.0845363
\(556\) 0.0385790 0.00163611
\(557\) −12.8506 −0.544497 −0.272248 0.962227i \(-0.587767\pi\)
−0.272248 + 0.962227i \(0.587767\pi\)
\(558\) −33.7524 −1.42885
\(559\) 14.7723 0.624801
\(560\) −3.67684 −0.155375
\(561\) −100.011 −4.22248
\(562\) −33.0605 −1.39457
\(563\) −6.95821 −0.293254 −0.146627 0.989192i \(-0.546842\pi\)
−0.146627 + 0.989192i \(0.546842\pi\)
\(564\) 3.14240 0.132319
\(565\) 0.924504 0.0388942
\(566\) 37.0129 1.55577
\(567\) −36.4815 −1.53208
\(568\) 9.65853 0.405263
\(569\) 15.5638 0.652467 0.326233 0.945289i \(-0.394220\pi\)
0.326233 + 0.945289i \(0.394220\pi\)
\(570\) −28.6568 −1.20030
\(571\) −29.9752 −1.25442 −0.627212 0.778849i \(-0.715804\pi\)
−0.627212 + 0.778849i \(0.715804\pi\)
\(572\) −3.84310 −0.160688
\(573\) 64.9520 2.71341
\(574\) −4.68269 −0.195452
\(575\) 1.03015 0.0429603
\(576\) 71.5371 2.98071
\(577\) 23.9159 0.995631 0.497815 0.867283i \(-0.334136\pi\)
0.497815 + 0.867283i \(0.334136\pi\)
\(578\) 5.47373 0.227677
\(579\) −65.1072 −2.70576
\(580\) −1.53500 −0.0637372
\(581\) 5.79752 0.240522
\(582\) 60.4102 2.50408
\(583\) 38.4448 1.59222
\(584\) 39.0701 1.61673
\(585\) −33.2988 −1.37674
\(586\) −27.4688 −1.13473
\(587\) −23.0481 −0.951297 −0.475648 0.879636i \(-0.657787\pi\)
−0.475648 + 0.879636i \(0.657787\pi\)
\(588\) −0.507624 −0.0209340
\(589\) −18.4109 −0.758607
\(590\) −14.2841 −0.588066
\(591\) −82.7021 −3.40191
\(592\) 2.16793 0.0891012
\(593\) −45.3262 −1.86132 −0.930662 0.365879i \(-0.880768\pi\)
−0.930662 + 0.365879i \(0.880768\pi\)
\(594\) 160.449 6.58331
\(595\) −4.58527 −0.187978
\(596\) −0.349454 −0.0143142
\(597\) 60.7153 2.48491
\(598\) 5.54815 0.226881
\(599\) −20.1009 −0.821299 −0.410649 0.911793i \(-0.634698\pi\)
−0.410649 + 0.911793i \(0.634698\pi\)
\(600\) −9.87799 −0.403267
\(601\) −42.2021 −1.72146 −0.860730 0.509062i \(-0.829992\pi\)
−0.860730 + 0.509062i \(0.829992\pi\)
\(602\) −5.07347 −0.206779
\(603\) 64.8774 2.64201
\(604\) 1.58095 0.0643277
\(605\) −30.6993 −1.24811
\(606\) −15.6298 −0.634916
\(607\) −20.9304 −0.849538 −0.424769 0.905302i \(-0.639645\pi\)
−0.424769 + 0.905302i \(0.639645\pi\)
\(608\) 5.29186 0.214613
\(609\) 34.4989 1.39797
\(610\) 9.04233 0.366113
\(611\) −24.5140 −0.991731
\(612\) 5.79456 0.234231
\(613\) −3.62915 −0.146580 −0.0732901 0.997311i \(-0.523350\pi\)
−0.0732901 + 0.997311i \(0.523350\pi\)
\(614\) 38.8995 1.56986
\(615\) −11.6296 −0.468949
\(616\) 18.8848 0.760892
\(617\) −11.9647 −0.481680 −0.240840 0.970565i \(-0.577423\pi\)
−0.240840 + 0.970565i \(0.577423\pi\)
\(618\) 57.4295 2.31015
\(619\) −19.0617 −0.766154 −0.383077 0.923716i \(-0.625136\pi\)
−0.383077 + 0.923716i \(0.625136\pi\)
\(620\) −0.443548 −0.0178133
\(621\) 18.8201 0.755224
\(622\) 8.37500 0.335807
\(623\) −12.8246 −0.513806
\(624\) −49.1801 −1.96878
\(625\) 1.00000 0.0400000
\(626\) 23.3615 0.933715
\(627\) 136.063 5.43384
\(628\) −1.11385 −0.0444475
\(629\) 2.70355 0.107798
\(630\) 11.4363 0.455634
\(631\) 3.16427 0.125967 0.0629837 0.998015i \(-0.479938\pi\)
0.0629837 + 0.998015i \(0.479938\pi\)
\(632\) 10.5966 0.421509
\(633\) 5.36593 0.213276
\(634\) −8.61710 −0.342229
\(635\) 16.0087 0.635287
\(636\) −3.02214 −0.119836
\(637\) 3.96000 0.156901
\(638\) −89.7020 −3.55133
\(639\) −27.7713 −1.09862
\(640\) −9.87382 −0.390297
\(641\) 2.87174 0.113427 0.0567134 0.998390i \(-0.481938\pi\)
0.0567134 + 0.998390i \(0.481938\pi\)
\(642\) 16.1430 0.637113
\(643\) −11.4902 −0.453128 −0.226564 0.973996i \(-0.572749\pi\)
−0.226564 + 0.973996i \(0.572749\pi\)
\(644\) 0.154819 0.00610070
\(645\) −12.6001 −0.496127
\(646\) −38.9021 −1.53058
\(647\) 46.2754 1.81927 0.909636 0.415406i \(-0.136360\pi\)
0.909636 + 0.415406i \(0.136360\pi\)
\(648\) −106.689 −4.19115
\(649\) 67.8210 2.66221
\(650\) 5.38576 0.211247
\(651\) 9.96870 0.390704
\(652\) −1.38928 −0.0544085
\(653\) −25.7640 −1.00822 −0.504112 0.863638i \(-0.668180\pi\)
−0.504112 + 0.863638i \(0.668180\pi\)
\(654\) 21.2552 0.831143
\(655\) 22.2455 0.869205
\(656\) −12.6595 −0.494272
\(657\) −112.339 −4.38275
\(658\) 8.41921 0.328215
\(659\) 9.40930 0.366534 0.183267 0.983063i \(-0.441333\pi\)
0.183267 + 0.983063i \(0.441333\pi\)
\(660\) 3.27798 0.127595
\(661\) −38.6122 −1.50184 −0.750921 0.660392i \(-0.770390\pi\)
−0.750921 + 0.660392i \(0.770390\pi\)
\(662\) −4.41507 −0.171596
\(663\) −61.3309 −2.38190
\(664\) 16.9547 0.657971
\(665\) 6.23815 0.241905
\(666\) −6.74304 −0.261288
\(667\) −10.5217 −0.407402
\(668\) −2.66941 −0.103283
\(669\) 48.1463 1.86144
\(670\) −10.4933 −0.405391
\(671\) −42.9332 −1.65742
\(672\) −2.86531 −0.110532
\(673\) −17.4897 −0.674177 −0.337088 0.941473i \(-0.609442\pi\)
−0.337088 + 0.941473i \(0.609442\pi\)
\(674\) 29.1987 1.12469
\(675\) 18.2692 0.703184
\(676\) −0.403008 −0.0155003
\(677\) 4.16596 0.160111 0.0800555 0.996790i \(-0.474490\pi\)
0.0800555 + 0.996790i \(0.474490\pi\)
\(678\) −4.24699 −0.163105
\(679\) −13.1504 −0.504665
\(680\) −13.4095 −0.514232
\(681\) −43.7626 −1.67699
\(682\) −25.9200 −0.992529
\(683\) 7.58991 0.290420 0.145210 0.989401i \(-0.453614\pi\)
0.145210 + 0.989401i \(0.453614\pi\)
\(684\) −7.88337 −0.301428
\(685\) 2.69337 0.102908
\(686\) −1.36004 −0.0519266
\(687\) 3.37769 0.128867
\(688\) −13.7160 −0.522918
\(689\) 23.5759 0.898171
\(690\) −4.73231 −0.180156
\(691\) 38.3885 1.46037 0.730183 0.683251i \(-0.239435\pi\)
0.730183 + 0.683251i \(0.239435\pi\)
\(692\) −2.01892 −0.0767479
\(693\) −54.2998 −2.06268
\(694\) −18.3804 −0.697709
\(695\) 0.256702 0.00973725
\(696\) 100.891 3.82428
\(697\) −15.7873 −0.597986
\(698\) −10.5976 −0.401126
\(699\) 1.36476 0.0516200
\(700\) 0.150287 0.00568032
\(701\) −3.40419 −0.128575 −0.0642873 0.997931i \(-0.520477\pi\)
−0.0642873 + 0.997931i \(0.520477\pi\)
\(702\) 98.3938 3.71364
\(703\) −3.67812 −0.138723
\(704\) 54.9366 2.07050
\(705\) 20.9093 0.787489
\(706\) −36.4615 −1.37225
\(707\) 3.40236 0.127959
\(708\) −5.33140 −0.200366
\(709\) −42.7334 −1.60488 −0.802442 0.596730i \(-0.796467\pi\)
−0.802442 + 0.596730i \(0.796467\pi\)
\(710\) 4.49174 0.168572
\(711\) −30.4685 −1.14266
\(712\) −37.5052 −1.40557
\(713\) −3.04032 −0.113861
\(714\) 21.0638 0.788293
\(715\) −25.5717 −0.956327
\(716\) −2.11096 −0.0788904
\(717\) −85.8010 −3.20430
\(718\) 25.9046 0.966752
\(719\) 41.7859 1.55835 0.779175 0.626806i \(-0.215638\pi\)
0.779175 + 0.626806i \(0.215638\pi\)
\(720\) 30.9178 1.15224
\(721\) −12.5015 −0.465581
\(722\) 27.0846 1.00798
\(723\) −68.2472 −2.53814
\(724\) −0.0533062 −0.00198111
\(725\) −10.2138 −0.379329
\(726\) 141.027 5.23399
\(727\) −16.7980 −0.623003 −0.311501 0.950246i \(-0.600832\pi\)
−0.311501 + 0.950246i \(0.600832\pi\)
\(728\) 11.5809 0.429218
\(729\) 121.642 4.50525
\(730\) 18.1697 0.672491
\(731\) −17.1048 −0.632643
\(732\) 3.37497 0.124743
\(733\) −0.461723 −0.0170541 −0.00852707 0.999964i \(-0.502714\pi\)
−0.00852707 + 0.999964i \(0.502714\pi\)
\(734\) 1.01261 0.0373760
\(735\) −3.37769 −0.124588
\(736\) 0.873883 0.0322118
\(737\) 49.8223 1.83523
\(738\) 39.3758 1.44944
\(739\) 9.48506 0.348914 0.174457 0.984665i \(-0.444183\pi\)
0.174457 + 0.984665i \(0.444183\pi\)
\(740\) −0.0886118 −0.00325743
\(741\) 83.4394 3.06522
\(742\) −8.09703 −0.297251
\(743\) 10.9388 0.401305 0.200653 0.979662i \(-0.435694\pi\)
0.200653 + 0.979662i \(0.435694\pi\)
\(744\) 29.1533 1.06881
\(745\) −2.32524 −0.0851903
\(746\) 34.8370 1.27547
\(747\) −48.7502 −1.78368
\(748\) 4.44991 0.162705
\(749\) −3.51408 −0.128402
\(750\) −4.59380 −0.167742
\(751\) −49.9282 −1.82190 −0.910952 0.412512i \(-0.864652\pi\)
−0.910952 + 0.412512i \(0.864652\pi\)
\(752\) 22.7611 0.830013
\(753\) −102.899 −3.74986
\(754\) −55.0088 −2.00330
\(755\) 10.5195 0.382844
\(756\) 2.74563 0.0998577
\(757\) 12.5798 0.457221 0.228610 0.973518i \(-0.426582\pi\)
0.228610 + 0.973518i \(0.426582\pi\)
\(758\) −5.22067 −0.189623
\(759\) 22.4691 0.815577
\(760\) 18.2433 0.661756
\(761\) −37.9549 −1.37587 −0.687933 0.725775i \(-0.741482\pi\)
−0.687933 + 0.725775i \(0.741482\pi\)
\(762\) −73.5409 −2.66411
\(763\) −4.62692 −0.167506
\(764\) −2.88998 −0.104556
\(765\) 38.5566 1.39402
\(766\) 11.5518 0.417382
\(767\) 41.5906 1.50175
\(768\) −12.1124 −0.437070
\(769\) 1.76521 0.0636551 0.0318276 0.999493i \(-0.489867\pi\)
0.0318276 + 0.999493i \(0.489867\pi\)
\(770\) 8.78247 0.316498
\(771\) −86.3564 −3.11005
\(772\) 2.89688 0.104261
\(773\) 33.5449 1.20653 0.603263 0.797542i \(-0.293867\pi\)
0.603263 + 0.797542i \(0.293867\pi\)
\(774\) 42.6618 1.53345
\(775\) −2.95134 −0.106015
\(776\) −38.4580 −1.38056
\(777\) 1.99154 0.0714462
\(778\) −22.6767 −0.812999
\(779\) 21.4783 0.769538
\(780\) 2.01019 0.0719763
\(781\) −21.3269 −0.763135
\(782\) −6.42418 −0.229728
\(783\) −186.598 −6.66845
\(784\) −3.67684 −0.131316
\(785\) −7.41148 −0.264527
\(786\) −102.191 −3.64505
\(787\) −8.04269 −0.286691 −0.143345 0.989673i \(-0.545786\pi\)
−0.143345 + 0.989673i \(0.545786\pi\)
\(788\) 3.67975 0.131086
\(789\) −16.0864 −0.572693
\(790\) 4.92798 0.175330
\(791\) 0.924504 0.0328716
\(792\) −158.799 −5.64267
\(793\) −26.3283 −0.934946
\(794\) 18.1399 0.643761
\(795\) −20.1091 −0.713198
\(796\) −2.70147 −0.0957510
\(797\) −23.0283 −0.815704 −0.407852 0.913048i \(-0.633722\pi\)
−0.407852 + 0.913048i \(0.633722\pi\)
\(798\) −28.6568 −1.01444
\(799\) 28.3847 1.00418
\(800\) 0.848305 0.0299921
\(801\) 107.839 3.81032
\(802\) −23.5183 −0.830458
\(803\) −86.2701 −3.04440
\(804\) −3.91653 −0.138125
\(805\) 1.03015 0.0363081
\(806\) −15.8952 −0.559884
\(807\) −67.1137 −2.36251
\(808\) 9.95014 0.350045
\(809\) −10.3051 −0.362308 −0.181154 0.983455i \(-0.557983\pi\)
−0.181154 + 0.983455i \(0.557983\pi\)
\(810\) −49.6163 −1.74334
\(811\) −47.9310 −1.68308 −0.841542 0.540192i \(-0.818352\pi\)
−0.841542 + 0.540192i \(0.818352\pi\)
\(812\) −1.53500 −0.0538678
\(813\) −28.5127 −0.999985
\(814\) −5.17829 −0.181499
\(815\) −9.24420 −0.323810
\(816\) 56.9455 1.99349
\(817\) 23.2707 0.814138
\(818\) −35.2407 −1.23216
\(819\) −33.2988 −1.16356
\(820\) 0.517446 0.0180700
\(821\) −41.1248 −1.43526 −0.717632 0.696422i \(-0.754774\pi\)
−0.717632 + 0.696422i \(0.754774\pi\)
\(822\) −12.3728 −0.431551
\(823\) 13.0688 0.455551 0.227775 0.973714i \(-0.426855\pi\)
0.227775 + 0.973714i \(0.426855\pi\)
\(824\) −36.5604 −1.27364
\(825\) 21.8114 0.759377
\(826\) −14.2841 −0.497006
\(827\) −40.2117 −1.39830 −0.699149 0.714976i \(-0.746438\pi\)
−0.699149 + 0.714976i \(0.746438\pi\)
\(828\) −1.30184 −0.0452420
\(829\) −16.8210 −0.584219 −0.292109 0.956385i \(-0.594357\pi\)
−0.292109 + 0.956385i \(0.594357\pi\)
\(830\) 7.88487 0.273688
\(831\) −21.9146 −0.760208
\(832\) 33.6893 1.16797
\(833\) −4.58527 −0.158870
\(834\) −1.17924 −0.0408336
\(835\) −17.7621 −0.614682
\(836\) −6.05400 −0.209382
\(837\) −53.9187 −1.86370
\(838\) −4.63017 −0.159947
\(839\) 51.6954 1.78472 0.892362 0.451319i \(-0.149047\pi\)
0.892362 + 0.451319i \(0.149047\pi\)
\(840\) −9.87799 −0.340823
\(841\) 75.3207 2.59727
\(842\) −10.7687 −0.371115
\(843\) −82.1063 −2.82789
\(844\) −0.238752 −0.00821817
\(845\) −2.68159 −0.0922495
\(846\) −70.7955 −2.43400
\(847\) −30.6993 −1.05484
\(848\) −21.8901 −0.751710
\(849\) 91.9224 3.15477
\(850\) −6.23615 −0.213898
\(851\) −0.607395 −0.0208212
\(852\) 1.67650 0.0574360
\(853\) 34.8050 1.19170 0.595850 0.803096i \(-0.296815\pi\)
0.595850 + 0.803096i \(0.296815\pi\)
\(854\) 9.04233 0.309422
\(855\) −52.4554 −1.79394
\(856\) −10.2769 −0.351256
\(857\) 20.5379 0.701562 0.350781 0.936458i \(-0.385916\pi\)
0.350781 + 0.936458i \(0.385916\pi\)
\(858\) 117.471 4.01040
\(859\) −0.0193579 −0.000660483 0 −0.000330242 1.00000i \(-0.500105\pi\)
−0.000330242 1.00000i \(0.500105\pi\)
\(860\) 0.560628 0.0191172
\(861\) −11.6296 −0.396334
\(862\) 43.5798 1.48433
\(863\) −17.6114 −0.599498 −0.299749 0.954018i \(-0.596903\pi\)
−0.299749 + 0.954018i \(0.596903\pi\)
\(864\) 15.4979 0.527249
\(865\) −13.4338 −0.456762
\(866\) −24.1436 −0.820433
\(867\) 13.5941 0.461681
\(868\) −0.443548 −0.0150550
\(869\) −23.3981 −0.793727
\(870\) 46.9199 1.59073
\(871\) 30.5530 1.03525
\(872\) −13.5313 −0.458229
\(873\) 110.579 3.74253
\(874\) 8.73996 0.295633
\(875\) 1.00000 0.0338062
\(876\) 6.78168 0.229132
\(877\) −0.199030 −0.00672076 −0.00336038 0.999994i \(-0.501070\pi\)
−0.00336038 + 0.999994i \(0.501070\pi\)
\(878\) −25.3721 −0.856268
\(879\) −68.2194 −2.30098
\(880\) 23.7432 0.800383
\(881\) −26.3858 −0.888962 −0.444481 0.895788i \(-0.646612\pi\)
−0.444481 + 0.895788i \(0.646612\pi\)
\(882\) 11.4363 0.385081
\(883\) 11.5555 0.388874 0.194437 0.980915i \(-0.437712\pi\)
0.194437 + 0.980915i \(0.437712\pi\)
\(884\) 2.72886 0.0917815
\(885\) −35.4748 −1.19247
\(886\) −14.6599 −0.492510
\(887\) −4.46179 −0.149812 −0.0749061 0.997191i \(-0.523866\pi\)
−0.0749061 + 0.997191i \(0.523866\pi\)
\(888\) 5.82423 0.195448
\(889\) 16.0087 0.536915
\(890\) −17.4420 −0.584656
\(891\) 235.579 7.89220
\(892\) −2.14222 −0.0717269
\(893\) −38.6167 −1.29226
\(894\) 10.6817 0.357250
\(895\) −14.0462 −0.469513
\(896\) −9.87382 −0.329861
\(897\) 13.7789 0.460066
\(898\) 52.3684 1.74756
\(899\) 30.1442 1.00537
\(900\) −1.26373 −0.0421245
\(901\) −27.2985 −0.909444
\(902\) 30.2385 1.00683
\(903\) −12.6001 −0.419304
\(904\) 2.70369 0.0899235
\(905\) −0.354696 −0.0117905
\(906\) −48.3245 −1.60547
\(907\) 29.0786 0.965538 0.482769 0.875748i \(-0.339631\pi\)
0.482769 + 0.875748i \(0.339631\pi\)
\(908\) 1.94718 0.0646193
\(909\) −28.6098 −0.948927
\(910\) 5.38576 0.178536
\(911\) −11.5780 −0.383597 −0.191799 0.981434i \(-0.561432\pi\)
−0.191799 + 0.981434i \(0.561432\pi\)
\(912\) −77.4730 −2.56539
\(913\) −37.4375 −1.23900
\(914\) −41.6546 −1.37781
\(915\) 22.4568 0.742400
\(916\) −0.150287 −0.00496563
\(917\) 22.2455 0.734612
\(918\) −113.930 −3.76025
\(919\) −52.3713 −1.72757 −0.863785 0.503860i \(-0.831913\pi\)
−0.863785 + 0.503860i \(0.831913\pi\)
\(920\) 3.01266 0.0993244
\(921\) 96.6076 3.18333
\(922\) 35.7240 1.17651
\(923\) −13.0785 −0.430484
\(924\) 3.27798 0.107838
\(925\) −0.589617 −0.0193865
\(926\) 5.45183 0.179158
\(927\) 105.123 3.45268
\(928\) −8.66438 −0.284422
\(929\) −13.7941 −0.452570 −0.226285 0.974061i \(-0.572658\pi\)
−0.226285 + 0.974061i \(0.572658\pi\)
\(930\) 13.5579 0.444579
\(931\) 6.23815 0.204447
\(932\) −0.0607237 −0.00198907
\(933\) 20.7995 0.680945
\(934\) 34.3381 1.12358
\(935\) 29.6094 0.968330
\(936\) −97.3817 −3.18302
\(937\) 4.12464 0.134746 0.0673730 0.997728i \(-0.478538\pi\)
0.0673730 + 0.997728i \(0.478538\pi\)
\(938\) −10.4933 −0.342618
\(939\) 58.0189 1.89337
\(940\) −0.930339 −0.0303443
\(941\) −33.8580 −1.10374 −0.551870 0.833930i \(-0.686086\pi\)
−0.551870 + 0.833930i \(0.686086\pi\)
\(942\) 34.0469 1.10931
\(943\) 3.54686 0.115502
\(944\) −38.6166 −1.25686
\(945\) 18.2692 0.594299
\(946\) 32.7619 1.06518
\(947\) 17.3206 0.562843 0.281421 0.959584i \(-0.409194\pi\)
0.281421 + 0.959584i \(0.409194\pi\)
\(948\) 1.83933 0.0597385
\(949\) −52.9043 −1.71734
\(950\) 8.48415 0.275262
\(951\) −21.4008 −0.693967
\(952\) −13.4095 −0.434605
\(953\) 0.954709 0.0309261 0.0154630 0.999880i \(-0.495078\pi\)
0.0154630 + 0.999880i \(0.495078\pi\)
\(954\) 68.0863 2.20437
\(955\) −19.2297 −0.622259
\(956\) 3.81763 0.123471
\(957\) −222.777 −7.20135
\(958\) −18.6537 −0.602672
\(959\) 2.69337 0.0869735
\(960\) −28.7354 −0.927431
\(961\) −22.2896 −0.719020
\(962\) −3.17554 −0.102383
\(963\) 29.5492 0.952210
\(964\) 3.03659 0.0978021
\(965\) 19.2757 0.620505
\(966\) −4.73231 −0.152260
\(967\) 4.66747 0.150096 0.0750478 0.997180i \(-0.476089\pi\)
0.0750478 + 0.997180i \(0.476089\pi\)
\(968\) −89.7796 −2.88562
\(969\) −96.6141 −3.10369
\(970\) −17.8851 −0.574254
\(971\) −55.8522 −1.79238 −0.896191 0.443669i \(-0.853677\pi\)
−0.896191 + 0.443669i \(0.853677\pi\)
\(972\) −10.2820 −0.329794
\(973\) 0.256702 0.00822948
\(974\) −23.8325 −0.763643
\(975\) 13.3757 0.428364
\(976\) 24.4457 0.782489
\(977\) −39.7299 −1.27107 −0.635536 0.772071i \(-0.719221\pi\)
−0.635536 + 0.772071i \(0.719221\pi\)
\(978\) 42.4660 1.35791
\(979\) 82.8148 2.64677
\(980\) 0.150287 0.00480075
\(981\) 38.9069 1.24220
\(982\) 35.4480 1.13119
\(983\) 12.8512 0.409888 0.204944 0.978774i \(-0.434299\pi\)
0.204944 + 0.978774i \(0.434299\pi\)
\(984\) −34.0104 −1.08421
\(985\) 24.4848 0.780151
\(986\) 63.6945 2.02845
\(987\) 20.9093 0.665550
\(988\) −3.71255 −0.118112
\(989\) 3.84285 0.122196
\(990\) −73.8500 −2.34711
\(991\) −39.8412 −1.26560 −0.632799 0.774316i \(-0.718094\pi\)
−0.632799 + 0.774316i \(0.718094\pi\)
\(992\) −2.50363 −0.0794905
\(993\) −10.9649 −0.347961
\(994\) 4.49174 0.142469
\(995\) −17.9754 −0.569858
\(996\) 2.94296 0.0932512
\(997\) −20.6146 −0.652871 −0.326435 0.945220i \(-0.605848\pi\)
−0.326435 + 0.945220i \(0.605848\pi\)
\(998\) 20.0318 0.634096
\(999\) −10.7719 −0.340806
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 \(a_p\))