Properties

Label 6025.2.a.h.1.7
Level 6025
Weight 2
Character 6025.1
Self dual Yes
Analytic conductor 48.110
Analytic rank 0
Dimension 12
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6025.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1098672178\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(0.0822506\)
Character \(\chi\) = 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.0822506 q^{2} -1.81824 q^{3} -1.99323 q^{4} +0.149552 q^{6} -0.690569 q^{7} +0.328446 q^{8} +0.306010 q^{9} +O(q^{10})\) \(q-0.0822506 q^{2} -1.81824 q^{3} -1.99323 q^{4} +0.149552 q^{6} -0.690569 q^{7} +0.328446 q^{8} +0.306010 q^{9} -2.95833 q^{11} +3.62419 q^{12} +1.93470 q^{13} +0.0567997 q^{14} +3.95945 q^{16} +2.07477 q^{17} -0.0251695 q^{18} +3.74689 q^{19} +1.25562 q^{21} +0.243324 q^{22} -4.34832 q^{23} -0.597195 q^{24} -0.159131 q^{26} +4.89833 q^{27} +1.37647 q^{28} -8.10772 q^{29} -2.80197 q^{31} -0.982559 q^{32} +5.37896 q^{33} -0.170651 q^{34} -0.609951 q^{36} +9.72312 q^{37} -0.308183 q^{38} -3.51777 q^{39} -4.09401 q^{41} -0.103276 q^{42} -3.02779 q^{43} +5.89665 q^{44} +0.357652 q^{46} -6.71240 q^{47} -7.19925 q^{48} -6.52312 q^{49} -3.77244 q^{51} -3.85632 q^{52} +0.0484656 q^{53} -0.402890 q^{54} -0.226814 q^{56} -6.81275 q^{57} +0.666864 q^{58} +4.50676 q^{59} -9.62232 q^{61} +0.230464 q^{62} -0.211321 q^{63} -7.83809 q^{64} -0.442423 q^{66} +0.964160 q^{67} -4.13551 q^{68} +7.90631 q^{69} +7.76289 q^{71} +0.100508 q^{72} -16.4250 q^{73} -0.799732 q^{74} -7.46842 q^{76} +2.04293 q^{77} +0.289338 q^{78} -6.83310 q^{79} -9.82439 q^{81} +0.336735 q^{82} +9.15477 q^{83} -2.50275 q^{84} +0.249037 q^{86} +14.7418 q^{87} -0.971651 q^{88} -2.36597 q^{89} -1.33605 q^{91} +8.66723 q^{92} +5.09467 q^{93} +0.552099 q^{94} +1.78653 q^{96} +5.25335 q^{97} +0.536530 q^{98} -0.905280 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 3q^{2} - q^{3} + 13q^{4} - q^{6} - 3q^{7} - 9q^{8} + 15q^{9} + O(q^{10}) \) \( 12q - 3q^{2} - q^{3} + 13q^{4} - q^{6} - 3q^{7} - 9q^{8} + 15q^{9} + 22q^{11} + 7q^{12} + 5q^{13} + 6q^{14} + 15q^{16} + 4q^{17} + q^{18} - 6q^{19} - 14q^{21} + 12q^{22} - 32q^{23} - 15q^{24} + 8q^{26} + 5q^{27} + 11q^{28} + 6q^{29} + 8q^{31} - q^{32} + 24q^{33} - 19q^{34} - 8q^{36} + 8q^{37} + 10q^{38} + 31q^{39} - q^{41} + 49q^{42} + 2q^{43} + 42q^{44} - 25q^{46} - 34q^{47} + 49q^{48} - 9q^{49} - 3q^{51} + 41q^{52} - 5q^{53} - 40q^{54} + q^{56} + 22q^{57} + 33q^{58} + 26q^{59} - 26q^{61} + 17q^{62} + 4q^{63} + 13q^{64} - 2q^{66} - 6q^{67} + 35q^{68} - 2q^{69} + 94q^{71} - 17q^{72} + 22q^{73} + 26q^{74} - 20q^{76} + 7q^{77} - 54q^{78} + 9q^{79} + 4q^{81} - 15q^{82} + 8q^{83} + 2q^{84} + 9q^{86} - 4q^{87} - 6q^{88} - 3q^{89} - 20q^{91} - 36q^{92} - 12q^{93} + 48q^{94} - 23q^{96} + 29q^{97} - 28q^{98} + 36q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0822506 −0.0581599 −0.0290800 0.999577i \(-0.509258\pi\)
−0.0290800 + 0.999577i \(0.509258\pi\)
\(3\) −1.81824 −1.04976 −0.524882 0.851175i \(-0.675890\pi\)
−0.524882 + 0.851175i \(0.675890\pi\)
\(4\) −1.99323 −0.996617
\(5\) 0 0
\(6\) 0.149552 0.0610542
\(7\) −0.690569 −0.261010 −0.130505 0.991448i \(-0.541660\pi\)
−0.130505 + 0.991448i \(0.541660\pi\)
\(8\) 0.328446 0.116123
\(9\) 0.306010 0.102003
\(10\) 0 0
\(11\) −2.95833 −0.891970 −0.445985 0.895040i \(-0.647147\pi\)
−0.445985 + 0.895040i \(0.647147\pi\)
\(12\) 3.62419 1.04621
\(13\) 1.93470 0.536591 0.268295 0.963337i \(-0.413540\pi\)
0.268295 + 0.963337i \(0.413540\pi\)
\(14\) 0.0567997 0.0151803
\(15\) 0 0
\(16\) 3.95945 0.989864
\(17\) 2.07477 0.503206 0.251603 0.967830i \(-0.419042\pi\)
0.251603 + 0.967830i \(0.419042\pi\)
\(18\) −0.0251695 −0.00593251
\(19\) 3.74689 0.859595 0.429797 0.902925i \(-0.358585\pi\)
0.429797 + 0.902925i \(0.358585\pi\)
\(20\) 0 0
\(21\) 1.25562 0.273999
\(22\) 0.243324 0.0518769
\(23\) −4.34832 −0.906688 −0.453344 0.891336i \(-0.649769\pi\)
−0.453344 + 0.891336i \(0.649769\pi\)
\(24\) −0.597195 −0.121902
\(25\) 0 0
\(26\) −0.159131 −0.0312081
\(27\) 4.89833 0.942684
\(28\) 1.37647 0.260127
\(29\) −8.10772 −1.50557 −0.752783 0.658269i \(-0.771289\pi\)
−0.752783 + 0.658269i \(0.771289\pi\)
\(30\) 0 0
\(31\) −2.80197 −0.503249 −0.251624 0.967825i \(-0.580965\pi\)
−0.251624 + 0.967825i \(0.580965\pi\)
\(32\) −0.982559 −0.173694
\(33\) 5.37896 0.936358
\(34\) −0.170651 −0.0292664
\(35\) 0 0
\(36\) −0.609951 −0.101658
\(37\) 9.72312 1.59847 0.799236 0.601018i \(-0.205238\pi\)
0.799236 + 0.601018i \(0.205238\pi\)
\(38\) −0.308183 −0.0499940
\(39\) −3.51777 −0.563293
\(40\) 0 0
\(41\) −4.09401 −0.639378 −0.319689 0.947523i \(-0.603578\pi\)
−0.319689 + 0.947523i \(0.603578\pi\)
\(42\) −0.103276 −0.0159358
\(43\) −3.02779 −0.461733 −0.230867 0.972985i \(-0.574156\pi\)
−0.230867 + 0.972985i \(0.574156\pi\)
\(44\) 5.89665 0.888953
\(45\) 0 0
\(46\) 0.357652 0.0527329
\(47\) −6.71240 −0.979104 −0.489552 0.871974i \(-0.662840\pi\)
−0.489552 + 0.871974i \(0.662840\pi\)
\(48\) −7.19925 −1.03912
\(49\) −6.52312 −0.931874
\(50\) 0 0
\(51\) −3.77244 −0.528248
\(52\) −3.85632 −0.534776
\(53\) 0.0484656 0.00665726 0.00332863 0.999994i \(-0.498940\pi\)
0.00332863 + 0.999994i \(0.498940\pi\)
\(54\) −0.402890 −0.0548264
\(55\) 0 0
\(56\) −0.226814 −0.0303093
\(57\) −6.81275 −0.902371
\(58\) 0.666864 0.0875636
\(59\) 4.50676 0.586730 0.293365 0.956000i \(-0.405225\pi\)
0.293365 + 0.956000i \(0.405225\pi\)
\(60\) 0 0
\(61\) −9.62232 −1.23201 −0.616006 0.787742i \(-0.711250\pi\)
−0.616006 + 0.787742i \(0.711250\pi\)
\(62\) 0.230464 0.0292689
\(63\) −0.211321 −0.0266240
\(64\) −7.83809 −0.979762
\(65\) 0 0
\(66\) −0.442423 −0.0544585
\(67\) 0.964160 0.117791 0.0588954 0.998264i \(-0.481242\pi\)
0.0588954 + 0.998264i \(0.481242\pi\)
\(68\) −4.13551 −0.501504
\(69\) 7.90631 0.951808
\(70\) 0 0
\(71\) 7.76289 0.921286 0.460643 0.887586i \(-0.347619\pi\)
0.460643 + 0.887586i \(0.347619\pi\)
\(72\) 0.100508 0.0118450
\(73\) −16.4250 −1.92241 −0.961203 0.275841i \(-0.911044\pi\)
−0.961203 + 0.275841i \(0.911044\pi\)
\(74\) −0.799732 −0.0929670
\(75\) 0 0
\(76\) −7.46842 −0.856687
\(77\) 2.04293 0.232813
\(78\) 0.289338 0.0327611
\(79\) −6.83310 −0.768783 −0.384392 0.923170i \(-0.625589\pi\)
−0.384392 + 0.923170i \(0.625589\pi\)
\(80\) 0 0
\(81\) −9.82439 −1.09160
\(82\) 0.336735 0.0371862
\(83\) 9.15477 1.00487 0.502433 0.864616i \(-0.332438\pi\)
0.502433 + 0.864616i \(0.332438\pi\)
\(84\) −2.50275 −0.273072
\(85\) 0 0
\(86\) 0.249037 0.0268544
\(87\) 14.7418 1.58049
\(88\) −0.971651 −0.103578
\(89\) −2.36597 −0.250793 −0.125396 0.992107i \(-0.540020\pi\)
−0.125396 + 0.992107i \(0.540020\pi\)
\(90\) 0 0
\(91\) −1.33605 −0.140056
\(92\) 8.66723 0.903621
\(93\) 5.09467 0.528292
\(94\) 0.552099 0.0569447
\(95\) 0 0
\(96\) 1.78653 0.182337
\(97\) 5.25335 0.533396 0.266698 0.963780i \(-0.414067\pi\)
0.266698 + 0.963780i \(0.414067\pi\)
\(98\) 0.536530 0.0541977
\(99\) −0.905280 −0.0909840
\(100\) 0 0
\(101\) 9.93584 0.988653 0.494327 0.869276i \(-0.335415\pi\)
0.494327 + 0.869276i \(0.335415\pi\)
\(102\) 0.310285 0.0307228
\(103\) −19.2644 −1.89818 −0.949090 0.315005i \(-0.897994\pi\)
−0.949090 + 0.315005i \(0.897994\pi\)
\(104\) 0.635446 0.0623106
\(105\) 0 0
\(106\) −0.00398632 −0.000387186 0
\(107\) 7.88030 0.761817 0.380909 0.924613i \(-0.375611\pi\)
0.380909 + 0.924613i \(0.375611\pi\)
\(108\) −9.76352 −0.939495
\(109\) −1.72728 −0.165443 −0.0827215 0.996573i \(-0.526361\pi\)
−0.0827215 + 0.996573i \(0.526361\pi\)
\(110\) 0 0
\(111\) −17.6790 −1.67802
\(112\) −2.73427 −0.258365
\(113\) −14.0431 −1.32107 −0.660533 0.750797i \(-0.729670\pi\)
−0.660533 + 0.750797i \(0.729670\pi\)
\(114\) 0.560353 0.0524818
\(115\) 0 0
\(116\) 16.1606 1.50047
\(117\) 0.592040 0.0547341
\(118\) −0.370684 −0.0341242
\(119\) −1.43277 −0.131342
\(120\) 0 0
\(121\) −2.24829 −0.204390
\(122\) 0.791441 0.0716537
\(123\) 7.44392 0.671195
\(124\) 5.58499 0.501547
\(125\) 0 0
\(126\) 0.0173813 0.00154845
\(127\) 1.65498 0.146856 0.0734278 0.997301i \(-0.476606\pi\)
0.0734278 + 0.997301i \(0.476606\pi\)
\(128\) 2.60981 0.230676
\(129\) 5.50525 0.484711
\(130\) 0 0
\(131\) 17.1541 1.49876 0.749381 0.662139i \(-0.230351\pi\)
0.749381 + 0.662139i \(0.230351\pi\)
\(132\) −10.7215 −0.933190
\(133\) −2.58748 −0.224363
\(134\) −0.0793027 −0.00685071
\(135\) 0 0
\(136\) 0.681450 0.0584339
\(137\) −14.7651 −1.26147 −0.630733 0.776000i \(-0.717245\pi\)
−0.630733 + 0.776000i \(0.717245\pi\)
\(138\) −0.650298 −0.0553571
\(139\) 20.3570 1.72666 0.863329 0.504641i \(-0.168375\pi\)
0.863329 + 0.504641i \(0.168375\pi\)
\(140\) 0 0
\(141\) 12.2048 1.02783
\(142\) −0.638502 −0.0535819
\(143\) −5.72349 −0.478623
\(144\) 1.21163 0.100970
\(145\) 0 0
\(146\) 1.35097 0.111807
\(147\) 11.8606 0.978247
\(148\) −19.3805 −1.59306
\(149\) 8.37820 0.686369 0.343185 0.939268i \(-0.388494\pi\)
0.343185 + 0.939268i \(0.388494\pi\)
\(150\) 0 0
\(151\) −22.0074 −1.79093 −0.895467 0.445128i \(-0.853158\pi\)
−0.895467 + 0.445128i \(0.853158\pi\)
\(152\) 1.23065 0.0998188
\(153\) 0.634902 0.0513288
\(154\) −0.168032 −0.0135404
\(155\) 0 0
\(156\) 7.01173 0.561388
\(157\) 0.208187 0.0166151 0.00830757 0.999965i \(-0.497356\pi\)
0.00830757 + 0.999965i \(0.497356\pi\)
\(158\) 0.562026 0.0447124
\(159\) −0.0881222 −0.00698855
\(160\) 0 0
\(161\) 3.00281 0.236655
\(162\) 0.808062 0.0634873
\(163\) −7.85060 −0.614906 −0.307453 0.951563i \(-0.599477\pi\)
−0.307453 + 0.951563i \(0.599477\pi\)
\(164\) 8.16033 0.637215
\(165\) 0 0
\(166\) −0.752985 −0.0584430
\(167\) 13.8766 1.07380 0.536900 0.843646i \(-0.319595\pi\)
0.536900 + 0.843646i \(0.319595\pi\)
\(168\) 0.412404 0.0318176
\(169\) −9.25692 −0.712071
\(170\) 0 0
\(171\) 1.14659 0.0876816
\(172\) 6.03509 0.460171
\(173\) −19.3500 −1.47115 −0.735577 0.677441i \(-0.763089\pi\)
−0.735577 + 0.677441i \(0.763089\pi\)
\(174\) −1.21252 −0.0919211
\(175\) 0 0
\(176\) −11.7134 −0.882929
\(177\) −8.19439 −0.615928
\(178\) 0.194603 0.0145861
\(179\) −7.02479 −0.525057 −0.262529 0.964924i \(-0.584556\pi\)
−0.262529 + 0.964924i \(0.584556\pi\)
\(180\) 0 0
\(181\) 7.22067 0.536708 0.268354 0.963320i \(-0.413520\pi\)
0.268354 + 0.963320i \(0.413520\pi\)
\(182\) 0.109891 0.00814563
\(183\) 17.4957 1.29332
\(184\) −1.42819 −0.105287
\(185\) 0 0
\(186\) −0.419039 −0.0307254
\(187\) −6.13786 −0.448845
\(188\) 13.3794 0.975793
\(189\) −3.38263 −0.246050
\(190\) 0 0
\(191\) 20.7694 1.50282 0.751412 0.659834i \(-0.229373\pi\)
0.751412 + 0.659834i \(0.229373\pi\)
\(192\) 14.2516 1.02852
\(193\) 19.7206 1.41952 0.709762 0.704442i \(-0.248803\pi\)
0.709762 + 0.704442i \(0.248803\pi\)
\(194\) −0.432091 −0.0310223
\(195\) 0 0
\(196\) 13.0021 0.928721
\(197\) 16.2977 1.16116 0.580582 0.814201i \(-0.302825\pi\)
0.580582 + 0.814201i \(0.302825\pi\)
\(198\) 0.0744598 0.00529162
\(199\) 4.79014 0.339564 0.169782 0.985482i \(-0.445694\pi\)
0.169782 + 0.985482i \(0.445694\pi\)
\(200\) 0 0
\(201\) −1.75308 −0.123653
\(202\) −0.817229 −0.0575000
\(203\) 5.59893 0.392968
\(204\) 7.51936 0.526461
\(205\) 0 0
\(206\) 1.58451 0.110398
\(207\) −1.33063 −0.0924853
\(208\) 7.66038 0.531152
\(209\) −11.0845 −0.766733
\(210\) 0 0
\(211\) −4.30473 −0.296350 −0.148175 0.988961i \(-0.547340\pi\)
−0.148175 + 0.988961i \(0.547340\pi\)
\(212\) −0.0966033 −0.00663474
\(213\) −14.1148 −0.967132
\(214\) −0.648159 −0.0443072
\(215\) 0 0
\(216\) 1.60884 0.109467
\(217\) 1.93495 0.131353
\(218\) 0.142069 0.00962215
\(219\) 29.8647 2.01807
\(220\) 0 0
\(221\) 4.01407 0.270016
\(222\) 1.45411 0.0975933
\(223\) −14.8068 −0.991540 −0.495770 0.868454i \(-0.665114\pi\)
−0.495770 + 0.868454i \(0.665114\pi\)
\(224\) 0.678524 0.0453358
\(225\) 0 0
\(226\) 1.15505 0.0768331
\(227\) 11.9026 0.790000 0.395000 0.918681i \(-0.370745\pi\)
0.395000 + 0.918681i \(0.370745\pi\)
\(228\) 13.5794 0.899319
\(229\) −5.11465 −0.337985 −0.168993 0.985617i \(-0.554051\pi\)
−0.168993 + 0.985617i \(0.554051\pi\)
\(230\) 0 0
\(231\) −3.71454 −0.244399
\(232\) −2.66295 −0.174831
\(233\) 14.9300 0.978097 0.489048 0.872257i \(-0.337344\pi\)
0.489048 + 0.872257i \(0.337344\pi\)
\(234\) −0.0486956 −0.00318333
\(235\) 0 0
\(236\) −8.98303 −0.584746
\(237\) 12.4242 0.807041
\(238\) 0.117846 0.00763884
\(239\) 29.8624 1.93164 0.965820 0.259215i \(-0.0834638\pi\)
0.965820 + 0.259215i \(0.0834638\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) 0.184923 0.0118873
\(243\) 3.16814 0.203237
\(244\) 19.1795 1.22784
\(245\) 0 0
\(246\) −0.612266 −0.0390367
\(247\) 7.24912 0.461250
\(248\) −0.920296 −0.0584388
\(249\) −16.6456 −1.05487
\(250\) 0 0
\(251\) 13.0620 0.824464 0.412232 0.911079i \(-0.364749\pi\)
0.412232 + 0.911079i \(0.364749\pi\)
\(252\) 0.421213 0.0265339
\(253\) 12.8638 0.808738
\(254\) −0.136123 −0.00854111
\(255\) 0 0
\(256\) 15.4615 0.966346
\(257\) −6.35830 −0.396620 −0.198310 0.980139i \(-0.563545\pi\)
−0.198310 + 0.980139i \(0.563545\pi\)
\(258\) −0.452810 −0.0281907
\(259\) −6.71448 −0.417218
\(260\) 0 0
\(261\) −2.48105 −0.153573
\(262\) −1.41094 −0.0871679
\(263\) −4.66189 −0.287465 −0.143732 0.989617i \(-0.545910\pi\)
−0.143732 + 0.989617i \(0.545910\pi\)
\(264\) 1.76670 0.108733
\(265\) 0 0
\(266\) 0.212822 0.0130489
\(267\) 4.30192 0.263273
\(268\) −1.92180 −0.117392
\(269\) −10.5251 −0.641728 −0.320864 0.947125i \(-0.603973\pi\)
−0.320864 + 0.947125i \(0.603973\pi\)
\(270\) 0 0
\(271\) 10.3212 0.626968 0.313484 0.949593i \(-0.398504\pi\)
0.313484 + 0.949593i \(0.398504\pi\)
\(272\) 8.21497 0.498106
\(273\) 2.42926 0.147025
\(274\) 1.21444 0.0733667
\(275\) 0 0
\(276\) −15.7591 −0.948588
\(277\) −22.1023 −1.32800 −0.663999 0.747734i \(-0.731142\pi\)
−0.663999 + 0.747734i \(0.731142\pi\)
\(278\) −1.67437 −0.100422
\(279\) −0.857432 −0.0513331
\(280\) 0 0
\(281\) 4.22803 0.252223 0.126111 0.992016i \(-0.459750\pi\)
0.126111 + 0.992016i \(0.459750\pi\)
\(282\) −1.00385 −0.0597784
\(283\) 3.06769 0.182355 0.0911776 0.995835i \(-0.470937\pi\)
0.0911776 + 0.995835i \(0.470937\pi\)
\(284\) −15.4733 −0.918169
\(285\) 0 0
\(286\) 0.470761 0.0278367
\(287\) 2.82720 0.166884
\(288\) −0.300673 −0.0177173
\(289\) −12.6953 −0.746783
\(290\) 0 0
\(291\) −9.55186 −0.559940
\(292\) 32.7390 1.91590
\(293\) 15.4694 0.903735 0.451867 0.892085i \(-0.350758\pi\)
0.451867 + 0.892085i \(0.350758\pi\)
\(294\) −0.975542 −0.0568948
\(295\) 0 0
\(296\) 3.19352 0.185619
\(297\) −14.4909 −0.840846
\(298\) −0.689112 −0.0399192
\(299\) −8.41272 −0.486520
\(300\) 0 0
\(301\) 2.09089 0.120517
\(302\) 1.81012 0.104161
\(303\) −18.0658 −1.03785
\(304\) 14.8356 0.850881
\(305\) 0 0
\(306\) −0.0522210 −0.00298528
\(307\) 20.2412 1.15523 0.577614 0.816310i \(-0.303984\pi\)
0.577614 + 0.816310i \(0.303984\pi\)
\(308\) −4.07204 −0.232026
\(309\) 35.0274 1.99264
\(310\) 0 0
\(311\) 1.49434 0.0847363 0.0423681 0.999102i \(-0.486510\pi\)
0.0423681 + 0.999102i \(0.486510\pi\)
\(312\) −1.15540 −0.0654114
\(313\) 21.6470 1.22356 0.611780 0.791028i \(-0.290454\pi\)
0.611780 + 0.791028i \(0.290454\pi\)
\(314\) −0.0171235 −0.000966335 0
\(315\) 0 0
\(316\) 13.6200 0.766183
\(317\) −28.9329 −1.62504 −0.812518 0.582936i \(-0.801904\pi\)
−0.812518 + 0.582936i \(0.801904\pi\)
\(318\) 0.00724810 0.000406453 0
\(319\) 23.9853 1.34292
\(320\) 0 0
\(321\) −14.3283 −0.799728
\(322\) −0.246983 −0.0137638
\(323\) 7.77394 0.432553
\(324\) 19.5823 1.08791
\(325\) 0 0
\(326\) 0.645716 0.0357629
\(327\) 3.14061 0.173676
\(328\) −1.34466 −0.0742465
\(329\) 4.63537 0.255556
\(330\) 0 0
\(331\) −27.5701 −1.51539 −0.757695 0.652609i \(-0.773675\pi\)
−0.757695 + 0.652609i \(0.773675\pi\)
\(332\) −18.2476 −1.00147
\(333\) 2.97538 0.163050
\(334\) −1.14135 −0.0624521
\(335\) 0 0
\(336\) 4.97158 0.271222
\(337\) 8.25450 0.449651 0.224826 0.974399i \(-0.427819\pi\)
0.224826 + 0.974399i \(0.427819\pi\)
\(338\) 0.761387 0.0414140
\(339\) 25.5338 1.38681
\(340\) 0 0
\(341\) 8.28915 0.448883
\(342\) −0.0943074 −0.00509956
\(343\) 9.33864 0.504239
\(344\) −0.994464 −0.0536179
\(345\) 0 0
\(346\) 1.59155 0.0855622
\(347\) −21.2018 −1.13817 −0.569085 0.822278i \(-0.692703\pi\)
−0.569085 + 0.822278i \(0.692703\pi\)
\(348\) −29.3839 −1.57514
\(349\) 21.3257 1.14154 0.570770 0.821110i \(-0.306645\pi\)
0.570770 + 0.821110i \(0.306645\pi\)
\(350\) 0 0
\(351\) 9.47682 0.505835
\(352\) 2.90673 0.154929
\(353\) −2.80184 −0.149127 −0.0745635 0.997216i \(-0.523756\pi\)
−0.0745635 + 0.997216i \(0.523756\pi\)
\(354\) 0.673993 0.0358223
\(355\) 0 0
\(356\) 4.71594 0.249944
\(357\) 2.60513 0.137878
\(358\) 0.577793 0.0305373
\(359\) 4.62788 0.244250 0.122125 0.992515i \(-0.461029\pi\)
0.122125 + 0.992515i \(0.461029\pi\)
\(360\) 0 0
\(361\) −4.96085 −0.261097
\(362\) −0.593904 −0.0312149
\(363\) 4.08793 0.214561
\(364\) 2.66305 0.139582
\(365\) 0 0
\(366\) −1.43903 −0.0752194
\(367\) 0.106183 0.00554270 0.00277135 0.999996i \(-0.499118\pi\)
0.00277135 + 0.999996i \(0.499118\pi\)
\(368\) −17.2170 −0.897497
\(369\) −1.25281 −0.0652187
\(370\) 0 0
\(371\) −0.0334688 −0.00173761
\(372\) −10.1549 −0.526505
\(373\) 16.6703 0.863157 0.431579 0.902075i \(-0.357957\pi\)
0.431579 + 0.902075i \(0.357957\pi\)
\(374\) 0.504843 0.0261048
\(375\) 0 0
\(376\) −2.20466 −0.113697
\(377\) −15.6860 −0.807872
\(378\) 0.278223 0.0143103
\(379\) −16.5660 −0.850939 −0.425469 0.904973i \(-0.639891\pi\)
−0.425469 + 0.904973i \(0.639891\pi\)
\(380\) 0 0
\(381\) −3.00915 −0.154164
\(382\) −1.70830 −0.0874041
\(383\) 25.0198 1.27845 0.639226 0.769019i \(-0.279255\pi\)
0.639226 + 0.769019i \(0.279255\pi\)
\(384\) −4.74526 −0.242156
\(385\) 0 0
\(386\) −1.62203 −0.0825594
\(387\) −0.926534 −0.0470984
\(388\) −10.4712 −0.531592
\(389\) −32.6696 −1.65641 −0.828207 0.560423i \(-0.810639\pi\)
−0.828207 + 0.560423i \(0.810639\pi\)
\(390\) 0 0
\(391\) −9.02178 −0.456251
\(392\) −2.14249 −0.108212
\(393\) −31.1904 −1.57335
\(394\) −1.34050 −0.0675333
\(395\) 0 0
\(396\) 1.80443 0.0906763
\(397\) 21.9103 1.09964 0.549822 0.835282i \(-0.314695\pi\)
0.549822 + 0.835282i \(0.314695\pi\)
\(398\) −0.393992 −0.0197490
\(399\) 4.70467 0.235528
\(400\) 0 0
\(401\) 10.2229 0.510508 0.255254 0.966874i \(-0.417841\pi\)
0.255254 + 0.966874i \(0.417841\pi\)
\(402\) 0.144192 0.00719162
\(403\) −5.42099 −0.270039
\(404\) −19.8045 −0.985309
\(405\) 0 0
\(406\) −0.460516 −0.0228550
\(407\) −28.7642 −1.42579
\(408\) −1.23904 −0.0613418
\(409\) −16.7739 −0.829417 −0.414709 0.909954i \(-0.636117\pi\)
−0.414709 + 0.909954i \(0.636117\pi\)
\(410\) 0 0
\(411\) 26.8465 1.32424
\(412\) 38.3985 1.89176
\(413\) −3.11223 −0.153143
\(414\) 0.109445 0.00537894
\(415\) 0 0
\(416\) −1.90096 −0.0932023
\(417\) −37.0140 −1.81258
\(418\) 0.911708 0.0445931
\(419\) 32.5790 1.59159 0.795793 0.605569i \(-0.207054\pi\)
0.795793 + 0.605569i \(0.207054\pi\)
\(420\) 0 0
\(421\) 11.5346 0.562163 0.281082 0.959684i \(-0.409307\pi\)
0.281082 + 0.959684i \(0.409307\pi\)
\(422\) 0.354066 0.0172357
\(423\) −2.05406 −0.0998721
\(424\) 0.0159183 0.000773062 0
\(425\) 0 0
\(426\) 1.16095 0.0562483
\(427\) 6.64487 0.321568
\(428\) −15.7073 −0.759240
\(429\) 10.4067 0.502441
\(430\) 0 0
\(431\) 15.2713 0.735590 0.367795 0.929907i \(-0.380113\pi\)
0.367795 + 0.929907i \(0.380113\pi\)
\(432\) 19.3947 0.933129
\(433\) −8.69941 −0.418067 −0.209034 0.977908i \(-0.567032\pi\)
−0.209034 + 0.977908i \(0.567032\pi\)
\(434\) −0.159151 −0.00763949
\(435\) 0 0
\(436\) 3.44287 0.164883
\(437\) −16.2927 −0.779384
\(438\) −2.45639 −0.117371
\(439\) 29.4040 1.40338 0.701689 0.712484i \(-0.252430\pi\)
0.701689 + 0.712484i \(0.252430\pi\)
\(440\) 0 0
\(441\) −1.99614 −0.0950543
\(442\) −0.330160 −0.0157041
\(443\) 35.7878 1.70033 0.850164 0.526518i \(-0.176503\pi\)
0.850164 + 0.526518i \(0.176503\pi\)
\(444\) 35.2384 1.67234
\(445\) 0 0
\(446\) 1.21787 0.0576679
\(447\) −15.2336 −0.720525
\(448\) 5.41274 0.255728
\(449\) −7.50777 −0.354314 −0.177157 0.984183i \(-0.556690\pi\)
−0.177157 + 0.984183i \(0.556690\pi\)
\(450\) 0 0
\(451\) 12.1114 0.570306
\(452\) 27.9912 1.31660
\(453\) 40.0147 1.88006
\(454\) −0.978992 −0.0459464
\(455\) 0 0
\(456\) −2.23762 −0.104786
\(457\) 31.7902 1.48708 0.743540 0.668691i \(-0.233145\pi\)
0.743540 + 0.668691i \(0.233145\pi\)
\(458\) 0.420683 0.0196572
\(459\) 10.1629 0.474364
\(460\) 0 0
\(461\) −12.8715 −0.599487 −0.299743 0.954020i \(-0.596901\pi\)
−0.299743 + 0.954020i \(0.596901\pi\)
\(462\) 0.305523 0.0142142
\(463\) 11.8687 0.551587 0.275794 0.961217i \(-0.411059\pi\)
0.275794 + 0.961217i \(0.411059\pi\)
\(464\) −32.1021 −1.49030
\(465\) 0 0
\(466\) −1.22800 −0.0568860
\(467\) 18.9191 0.875473 0.437736 0.899103i \(-0.355780\pi\)
0.437736 + 0.899103i \(0.355780\pi\)
\(468\) −1.18007 −0.0545490
\(469\) −0.665818 −0.0307446
\(470\) 0 0
\(471\) −0.378535 −0.0174420
\(472\) 1.48023 0.0681329
\(473\) 8.95719 0.411852
\(474\) −1.02190 −0.0469374
\(475\) 0 0
\(476\) 2.85585 0.130898
\(477\) 0.0148310 0.000679063 0
\(478\) −2.45620 −0.112344
\(479\) 23.7911 1.08704 0.543522 0.839395i \(-0.317091\pi\)
0.543522 + 0.839395i \(0.317091\pi\)
\(480\) 0 0
\(481\) 18.8114 0.857725
\(482\) −0.0822506 −0.00374641
\(483\) −5.45985 −0.248432
\(484\) 4.48136 0.203698
\(485\) 0 0
\(486\) −0.260582 −0.0118202
\(487\) −1.59589 −0.0723165 −0.0361583 0.999346i \(-0.511512\pi\)
−0.0361583 + 0.999346i \(0.511512\pi\)
\(488\) −3.16041 −0.143065
\(489\) 14.2743 0.645506
\(490\) 0 0
\(491\) −31.8604 −1.43784 −0.718920 0.695093i \(-0.755363\pi\)
−0.718920 + 0.695093i \(0.755363\pi\)
\(492\) −14.8375 −0.668925
\(493\) −16.8217 −0.757610
\(494\) −0.596244 −0.0268263
\(495\) 0 0
\(496\) −11.0943 −0.498148
\(497\) −5.36081 −0.240465
\(498\) 1.36911 0.0613513
\(499\) 17.3389 0.776194 0.388097 0.921619i \(-0.373133\pi\)
0.388097 + 0.921619i \(0.373133\pi\)
\(500\) 0 0
\(501\) −25.2310 −1.12724
\(502\) −1.07435 −0.0479508
\(503\) 13.8066 0.615607 0.307803 0.951450i \(-0.400406\pi\)
0.307803 + 0.951450i \(0.400406\pi\)
\(504\) −0.0694076 −0.00309166
\(505\) 0 0
\(506\) −1.05805 −0.0470362
\(507\) 16.8313 0.747506
\(508\) −3.29876 −0.146359
\(509\) 37.2876 1.65274 0.826372 0.563124i \(-0.190401\pi\)
0.826372 + 0.563124i \(0.190401\pi\)
\(510\) 0 0
\(511\) 11.3426 0.501768
\(512\) −6.49133 −0.286879
\(513\) 18.3535 0.810326
\(514\) 0.522974 0.0230674
\(515\) 0 0
\(516\) −10.9733 −0.483071
\(517\) 19.8575 0.873332
\(518\) 0.552270 0.0242653
\(519\) 35.1830 1.54436
\(520\) 0 0
\(521\) 35.4359 1.55248 0.776238 0.630439i \(-0.217125\pi\)
0.776238 + 0.630439i \(0.217125\pi\)
\(522\) 0.204067 0.00893179
\(523\) 22.2983 0.975036 0.487518 0.873113i \(-0.337902\pi\)
0.487518 + 0.873113i \(0.337902\pi\)
\(524\) −34.1922 −1.49369
\(525\) 0 0
\(526\) 0.383443 0.0167189
\(527\) −5.81345 −0.253238
\(528\) 21.2978 0.926866
\(529\) −4.09210 −0.177917
\(530\) 0 0
\(531\) 1.37912 0.0598485
\(532\) 5.15746 0.223604
\(533\) −7.92071 −0.343084
\(534\) −0.353835 −0.0153119
\(535\) 0 0
\(536\) 0.316674 0.0136782
\(537\) 12.7728 0.551186
\(538\) 0.865698 0.0373229
\(539\) 19.2975 0.831203
\(540\) 0 0
\(541\) −28.0367 −1.20539 −0.602697 0.797970i \(-0.705907\pi\)
−0.602697 + 0.797970i \(0.705907\pi\)
\(542\) −0.848925 −0.0364644
\(543\) −13.1289 −0.563416
\(544\) −2.03859 −0.0874037
\(545\) 0 0
\(546\) −0.199808 −0.00855099
\(547\) 13.1556 0.562491 0.281245 0.959636i \(-0.409253\pi\)
0.281245 + 0.959636i \(0.409253\pi\)
\(548\) 29.4303 1.25720
\(549\) −2.94453 −0.125669
\(550\) 0 0
\(551\) −30.3787 −1.29418
\(552\) 2.59679 0.110527
\(553\) 4.71872 0.200660
\(554\) 1.81793 0.0772363
\(555\) 0 0
\(556\) −40.5763 −1.72082
\(557\) 20.1003 0.851678 0.425839 0.904799i \(-0.359979\pi\)
0.425839 + 0.904799i \(0.359979\pi\)
\(558\) 0.0705243 0.00298553
\(559\) −5.85787 −0.247762
\(560\) 0 0
\(561\) 11.1601 0.471181
\(562\) −0.347757 −0.0146693
\(563\) 1.97240 0.0831268 0.0415634 0.999136i \(-0.486766\pi\)
0.0415634 + 0.999136i \(0.486766\pi\)
\(564\) −24.3270 −1.02435
\(565\) 0 0
\(566\) −0.252319 −0.0106058
\(567\) 6.78441 0.284919
\(568\) 2.54969 0.106983
\(569\) 19.0863 0.800139 0.400070 0.916485i \(-0.368986\pi\)
0.400070 + 0.916485i \(0.368986\pi\)
\(570\) 0 0
\(571\) 10.1484 0.424697 0.212348 0.977194i \(-0.431889\pi\)
0.212348 + 0.977194i \(0.431889\pi\)
\(572\) 11.4083 0.477004
\(573\) −37.7639 −1.57761
\(574\) −0.232539 −0.00970597
\(575\) 0 0
\(576\) −2.39854 −0.0999391
\(577\) −11.2993 −0.470395 −0.235198 0.971948i \(-0.575574\pi\)
−0.235198 + 0.971948i \(0.575574\pi\)
\(578\) 1.04420 0.0434329
\(579\) −35.8569 −1.49016
\(580\) 0 0
\(581\) −6.32200 −0.262281
\(582\) 0.785646 0.0325661
\(583\) −0.143377 −0.00593807
\(584\) −5.39474 −0.223236
\(585\) 0 0
\(586\) −1.27237 −0.0525611
\(587\) −36.1850 −1.49352 −0.746758 0.665095i \(-0.768391\pi\)
−0.746758 + 0.665095i \(0.768391\pi\)
\(588\) −23.6410 −0.974938
\(589\) −10.4987 −0.432590
\(590\) 0 0
\(591\) −29.6332 −1.21895
\(592\) 38.4983 1.58227
\(593\) 28.2897 1.16172 0.580858 0.814005i \(-0.302717\pi\)
0.580858 + 0.814005i \(0.302717\pi\)
\(594\) 1.19188 0.0489035
\(595\) 0 0
\(596\) −16.6997 −0.684047
\(597\) −8.70965 −0.356462
\(598\) 0.691951 0.0282960
\(599\) −10.9989 −0.449404 −0.224702 0.974427i \(-0.572141\pi\)
−0.224702 + 0.974427i \(0.572141\pi\)
\(600\) 0 0
\(601\) −10.3224 −0.421058 −0.210529 0.977588i \(-0.567519\pi\)
−0.210529 + 0.977588i \(0.567519\pi\)
\(602\) −0.171977 −0.00700927
\(603\) 0.295043 0.0120151
\(604\) 43.8658 1.78488
\(605\) 0 0
\(606\) 1.48592 0.0603614
\(607\) 26.4559 1.07381 0.536906 0.843642i \(-0.319593\pi\)
0.536906 + 0.843642i \(0.319593\pi\)
\(608\) −3.68154 −0.149306
\(609\) −10.1802 −0.412524
\(610\) 0 0
\(611\) −12.9865 −0.525378
\(612\) −1.26551 −0.0511552
\(613\) −33.8484 −1.36712 −0.683561 0.729893i \(-0.739570\pi\)
−0.683561 + 0.729893i \(0.739570\pi\)
\(614\) −1.66485 −0.0671879
\(615\) 0 0
\(616\) 0.670992 0.0270350
\(617\) 0.659865 0.0265651 0.0132826 0.999912i \(-0.495772\pi\)
0.0132826 + 0.999912i \(0.495772\pi\)
\(618\) −2.88103 −0.115892
\(619\) −34.8866 −1.40221 −0.701106 0.713057i \(-0.747310\pi\)
−0.701106 + 0.713057i \(0.747310\pi\)
\(620\) 0 0
\(621\) −21.2995 −0.854720
\(622\) −0.122910 −0.00492826
\(623\) 1.63387 0.0654595
\(624\) −13.9284 −0.557584
\(625\) 0 0
\(626\) −1.78048 −0.0711622
\(627\) 20.1544 0.804888
\(628\) −0.414966 −0.0165589
\(629\) 20.1733 0.804361
\(630\) 0 0
\(631\) −6.39474 −0.254571 −0.127285 0.991866i \(-0.540626\pi\)
−0.127285 + 0.991866i \(0.540626\pi\)
\(632\) −2.24430 −0.0892735
\(633\) 7.82705 0.311097
\(634\) 2.37975 0.0945120
\(635\) 0 0
\(636\) 0.175648 0.00696491
\(637\) −12.6203 −0.500035
\(638\) −1.97280 −0.0781041
\(639\) 2.37553 0.0939743
\(640\) 0 0
\(641\) 16.9466 0.669352 0.334676 0.942333i \(-0.391373\pi\)
0.334676 + 0.942333i \(0.391373\pi\)
\(642\) 1.17851 0.0465121
\(643\) −14.3993 −0.567852 −0.283926 0.958846i \(-0.591637\pi\)
−0.283926 + 0.958846i \(0.591637\pi\)
\(644\) −5.98531 −0.235854
\(645\) 0 0
\(646\) −0.639411 −0.0251573
\(647\) −4.38744 −0.172488 −0.0862441 0.996274i \(-0.527486\pi\)
−0.0862441 + 0.996274i \(0.527486\pi\)
\(648\) −3.22678 −0.126760
\(649\) −13.3325 −0.523346
\(650\) 0 0
\(651\) −3.51822 −0.137890
\(652\) 15.6481 0.612826
\(653\) 4.56970 0.178826 0.0894132 0.995995i \(-0.471501\pi\)
0.0894132 + 0.995995i \(0.471501\pi\)
\(654\) −0.258317 −0.0101010
\(655\) 0 0
\(656\) −16.2101 −0.632897
\(657\) −5.02624 −0.196092
\(658\) −0.381262 −0.0148631
\(659\) −13.6506 −0.531751 −0.265875 0.964007i \(-0.585661\pi\)
−0.265875 + 0.964007i \(0.585661\pi\)
\(660\) 0 0
\(661\) 32.4151 1.26080 0.630401 0.776270i \(-0.282891\pi\)
0.630401 + 0.776270i \(0.282891\pi\)
\(662\) 2.26766 0.0881350
\(663\) −7.29856 −0.283453
\(664\) 3.00685 0.116688
\(665\) 0 0
\(666\) −0.244726 −0.00948295
\(667\) 35.2550 1.36508
\(668\) −27.6592 −1.07017
\(669\) 26.9225 1.04088
\(670\) 0 0
\(671\) 28.4660 1.09892
\(672\) −1.23372 −0.0475919
\(673\) −0.237992 −0.00917391 −0.00458696 0.999989i \(-0.501460\pi\)
−0.00458696 + 0.999989i \(0.501460\pi\)
\(674\) −0.678938 −0.0261517
\(675\) 0 0
\(676\) 18.4512 0.709662
\(677\) 30.9534 1.18964 0.594818 0.803860i \(-0.297224\pi\)
0.594818 + 0.803860i \(0.297224\pi\)
\(678\) −2.10017 −0.0806566
\(679\) −3.62780 −0.139222
\(680\) 0 0
\(681\) −21.6417 −0.829313
\(682\) −0.681788 −0.0261070
\(683\) 28.5801 1.09359 0.546794 0.837267i \(-0.315848\pi\)
0.546794 + 0.837267i \(0.315848\pi\)
\(684\) −2.28542 −0.0873850
\(685\) 0 0
\(686\) −0.768108 −0.0293265
\(687\) 9.29968 0.354805
\(688\) −11.9884 −0.457053
\(689\) 0.0937666 0.00357222
\(690\) 0 0
\(691\) −6.89241 −0.262200 −0.131100 0.991369i \(-0.541851\pi\)
−0.131100 + 0.991369i \(0.541851\pi\)
\(692\) 38.5691 1.46618
\(693\) 0.625158 0.0237478
\(694\) 1.74386 0.0661959
\(695\) 0 0
\(696\) 4.84189 0.183531
\(697\) −8.49415 −0.321739
\(698\) −1.75405 −0.0663919
\(699\) −27.1464 −1.02677
\(700\) 0 0
\(701\) −29.3972 −1.11032 −0.555158 0.831745i \(-0.687342\pi\)
−0.555158 + 0.831745i \(0.687342\pi\)
\(702\) −0.779474 −0.0294194
\(703\) 36.4314 1.37404
\(704\) 23.1877 0.873918
\(705\) 0 0
\(706\) 0.230453 0.00867321
\(707\) −6.86138 −0.258049
\(708\) 16.3333 0.613845
\(709\) −10.8690 −0.408195 −0.204098 0.978951i \(-0.565426\pi\)
−0.204098 + 0.978951i \(0.565426\pi\)
\(710\) 0 0
\(711\) −2.09100 −0.0784186
\(712\) −0.777094 −0.0291228
\(713\) 12.1839 0.456290
\(714\) −0.214273 −0.00801898
\(715\) 0 0
\(716\) 14.0021 0.523281
\(717\) −54.2972 −2.02776
\(718\) −0.380646 −0.0142056
\(719\) −30.8283 −1.14970 −0.574850 0.818259i \(-0.694940\pi\)
−0.574850 + 0.818259i \(0.694940\pi\)
\(720\) 0 0
\(721\) 13.3034 0.495445
\(722\) 0.408032 0.0151854
\(723\) −1.81824 −0.0676212
\(724\) −14.3925 −0.534892
\(725\) 0 0
\(726\) −0.336235 −0.0124788
\(727\) −28.0322 −1.03966 −0.519828 0.854271i \(-0.674004\pi\)
−0.519828 + 0.854271i \(0.674004\pi\)
\(728\) −0.438819 −0.0162637
\(729\) 23.7127 0.878248
\(730\) 0 0
\(731\) −6.28197 −0.232347
\(732\) −34.8731 −1.28895
\(733\) −25.8442 −0.954578 −0.477289 0.878746i \(-0.658381\pi\)
−0.477289 + 0.878746i \(0.658381\pi\)
\(734\) −0.00873360 −0.000322363 0
\(735\) 0 0
\(736\) 4.27248 0.157486
\(737\) −2.85230 −0.105066
\(738\) 0.103044 0.00379312
\(739\) −43.0752 −1.58455 −0.792273 0.610166i \(-0.791103\pi\)
−0.792273 + 0.610166i \(0.791103\pi\)
\(740\) 0 0
\(741\) −13.1807 −0.484204
\(742\) 0.00275283 0.000101059 0
\(743\) −13.1212 −0.481372 −0.240686 0.970603i \(-0.577372\pi\)
−0.240686 + 0.970603i \(0.577372\pi\)
\(744\) 1.67332 0.0613470
\(745\) 0 0
\(746\) −1.37114 −0.0502012
\(747\) 2.80146 0.102500
\(748\) 12.2342 0.447327
\(749\) −5.44189 −0.198842
\(750\) 0 0
\(751\) 33.6870 1.22926 0.614629 0.788817i \(-0.289306\pi\)
0.614629 + 0.788817i \(0.289306\pi\)
\(752\) −26.5775 −0.969180
\(753\) −23.7498 −0.865492
\(754\) 1.29019 0.0469858
\(755\) 0 0
\(756\) 6.74238 0.245218
\(757\) 46.0911 1.67521 0.837604 0.546278i \(-0.183956\pi\)
0.837604 + 0.546278i \(0.183956\pi\)
\(758\) 1.36256 0.0494905
\(759\) −23.3895 −0.848984
\(760\) 0 0
\(761\) 14.2727 0.517387 0.258693 0.965960i \(-0.416708\pi\)
0.258693 + 0.965960i \(0.416708\pi\)
\(762\) 0.247505 0.00896615
\(763\) 1.19280 0.0431823
\(764\) −41.3983 −1.49774
\(765\) 0 0
\(766\) −2.05789 −0.0743547
\(767\) 8.71925 0.314834
\(768\) −28.1128 −1.01443
\(769\) 13.0154 0.469349 0.234674 0.972074i \(-0.424598\pi\)
0.234674 + 0.972074i \(0.424598\pi\)
\(770\) 0 0
\(771\) 11.5609 0.416357
\(772\) −39.3079 −1.41472
\(773\) 29.9438 1.07700 0.538502 0.842624i \(-0.318990\pi\)
0.538502 + 0.842624i \(0.318990\pi\)
\(774\) 0.0762080 0.00273924
\(775\) 0 0
\(776\) 1.72544 0.0619397
\(777\) 12.2086 0.437980
\(778\) 2.68709 0.0963369
\(779\) −15.3398 −0.549606
\(780\) 0 0
\(781\) −22.9652 −0.821759
\(782\) 0.742046 0.0265355
\(783\) −39.7143 −1.41927
\(784\) −25.8280 −0.922428
\(785\) 0 0
\(786\) 2.56542 0.0915057
\(787\) −13.7932 −0.491676 −0.245838 0.969311i \(-0.579063\pi\)
−0.245838 + 0.969311i \(0.579063\pi\)
\(788\) −32.4852 −1.15724
\(789\) 8.47646 0.301770
\(790\) 0 0
\(791\) 9.69774 0.344812
\(792\) −0.297335 −0.0105654
\(793\) −18.6163 −0.661086
\(794\) −1.80213 −0.0639553
\(795\) 0 0
\(796\) −9.54788 −0.338416
\(797\) −18.4152 −0.652300 −0.326150 0.945318i \(-0.605751\pi\)
−0.326150 + 0.945318i \(0.605751\pi\)
\(798\) −0.386962 −0.0136983
\(799\) −13.9267 −0.492691
\(800\) 0 0
\(801\) −0.724013 −0.0255817
\(802\) −0.840841 −0.0296911
\(803\) 48.5907 1.71473
\(804\) 3.49429 0.123234
\(805\) 0 0
\(806\) 0.445879 0.0157054
\(807\) 19.1372 0.673663
\(808\) 3.26339 0.114806
\(809\) −14.7007 −0.516849 −0.258425 0.966031i \(-0.583203\pi\)
−0.258425 + 0.966031i \(0.583203\pi\)
\(810\) 0 0
\(811\) −46.3555 −1.62776 −0.813882 0.581031i \(-0.802650\pi\)
−0.813882 + 0.581031i \(0.802650\pi\)
\(812\) −11.1600 −0.391639
\(813\) −18.7665 −0.658168
\(814\) 2.36587 0.0829238
\(815\) 0 0
\(816\) −14.9368 −0.522893
\(817\) −11.3448 −0.396903
\(818\) 1.37967 0.0482389
\(819\) −0.408844 −0.0142862
\(820\) 0 0
\(821\) 39.2626 1.37027 0.685137 0.728414i \(-0.259742\pi\)
0.685137 + 0.728414i \(0.259742\pi\)
\(822\) −2.20814 −0.0770177
\(823\) 29.0804 1.01368 0.506839 0.862041i \(-0.330814\pi\)
0.506839 + 0.862041i \(0.330814\pi\)
\(824\) −6.32732 −0.220423
\(825\) 0 0
\(826\) 0.255982 0.00890677
\(827\) −30.7270 −1.06848 −0.534242 0.845332i \(-0.679403\pi\)
−0.534242 + 0.845332i \(0.679403\pi\)
\(828\) 2.65226 0.0921725
\(829\) −16.4599 −0.571675 −0.285837 0.958278i \(-0.592272\pi\)
−0.285837 + 0.958278i \(0.592272\pi\)
\(830\) 0 0
\(831\) 40.1873 1.39408
\(832\) −15.1644 −0.525731
\(833\) −13.5340 −0.468925
\(834\) 3.04442 0.105420
\(835\) 0 0
\(836\) 22.0941 0.764139
\(837\) −13.7250 −0.474405
\(838\) −2.67964 −0.0925665
\(839\) 43.2285 1.49241 0.746206 0.665715i \(-0.231873\pi\)
0.746206 + 0.665715i \(0.231873\pi\)
\(840\) 0 0
\(841\) 36.7351 1.26673
\(842\) −0.948729 −0.0326954
\(843\) −7.68758 −0.264774
\(844\) 8.58034 0.295347
\(845\) 0 0
\(846\) 0.168948 0.00580855
\(847\) 1.55260 0.0533478
\(848\) 0.191897 0.00658978
\(849\) −5.57781 −0.191430
\(850\) 0 0
\(851\) −42.2793 −1.44931
\(852\) 28.1342 0.963861
\(853\) −8.36996 −0.286582 −0.143291 0.989681i \(-0.545768\pi\)
−0.143291 + 0.989681i \(0.545768\pi\)
\(854\) −0.546544 −0.0187024
\(855\) 0 0
\(856\) 2.58825 0.0884646
\(857\) −18.3641 −0.627305 −0.313653 0.949538i \(-0.601553\pi\)
−0.313653 + 0.949538i \(0.601553\pi\)
\(858\) −0.855958 −0.0292219
\(859\) 2.47499 0.0844457 0.0422228 0.999108i \(-0.486556\pi\)
0.0422228 + 0.999108i \(0.486556\pi\)
\(860\) 0 0
\(861\) −5.14053 −0.175189
\(862\) −1.25607 −0.0427819
\(863\) 10.0917 0.343525 0.171762 0.985138i \(-0.445054\pi\)
0.171762 + 0.985138i \(0.445054\pi\)
\(864\) −4.81290 −0.163738
\(865\) 0 0
\(866\) 0.715532 0.0243148
\(867\) 23.0832 0.783946
\(868\) −3.85682 −0.130909
\(869\) 20.2146 0.685732
\(870\) 0 0
\(871\) 1.86536 0.0632055
\(872\) −0.567316 −0.0192118
\(873\) 1.60758 0.0544083
\(874\) 1.34008 0.0453289
\(875\) 0 0
\(876\) −59.5274 −2.01125
\(877\) −53.6453 −1.81147 −0.905736 0.423843i \(-0.860681\pi\)
−0.905736 + 0.423843i \(0.860681\pi\)
\(878\) −2.41850 −0.0816203
\(879\) −28.1272 −0.948708
\(880\) 0 0
\(881\) 30.6985 1.03426 0.517130 0.855907i \(-0.327001\pi\)
0.517130 + 0.855907i \(0.327001\pi\)
\(882\) 0.164184 0.00552835
\(883\) 21.8831 0.736424 0.368212 0.929742i \(-0.379970\pi\)
0.368212 + 0.929742i \(0.379970\pi\)
\(884\) −8.00099 −0.269102
\(885\) 0 0
\(886\) −2.94356 −0.0988910
\(887\) 23.3921 0.785431 0.392715 0.919660i \(-0.371536\pi\)
0.392715 + 0.919660i \(0.371536\pi\)
\(888\) −5.80660 −0.194857
\(889\) −1.14288 −0.0383308
\(890\) 0 0
\(891\) 29.0638 0.973673
\(892\) 29.5135 0.988186
\(893\) −25.1506 −0.841633
\(894\) 1.25297 0.0419057
\(895\) 0 0
\(896\) −1.80225 −0.0602089
\(897\) 15.2964 0.510731
\(898\) 0.617518 0.0206069
\(899\) 22.7176 0.757674
\(900\) 0 0
\(901\) 0.100555 0.00334997
\(902\) −0.996173 −0.0331689
\(903\) −3.80175 −0.126514
\(904\) −4.61240 −0.153406
\(905\) 0 0
\(906\) −3.29124 −0.109344
\(907\) 2.98723 0.0991893 0.0495947 0.998769i \(-0.484207\pi\)
0.0495947 + 0.998769i \(0.484207\pi\)
\(908\) −23.7246 −0.787328
\(909\) 3.04047 0.100846
\(910\) 0 0
\(911\) 42.1883 1.39776 0.698880 0.715239i \(-0.253682\pi\)
0.698880 + 0.715239i \(0.253682\pi\)
\(912\) −26.9748 −0.893224
\(913\) −27.0828 −0.896311
\(914\) −2.61476 −0.0864885
\(915\) 0 0
\(916\) 10.1947 0.336842
\(917\) −11.8461 −0.391192
\(918\) −0.835906 −0.0275890
\(919\) −53.2428 −1.75632 −0.878160 0.478367i \(-0.841229\pi\)
−0.878160 + 0.478367i \(0.841229\pi\)
\(920\) 0 0
\(921\) −36.8035 −1.21272
\(922\) 1.05869 0.0348661
\(923\) 15.0189 0.494353
\(924\) 7.40396 0.243572
\(925\) 0 0
\(926\) −0.976211 −0.0320803
\(927\) −5.89511 −0.193621
\(928\) 7.96631 0.261507
\(929\) −27.2213 −0.893103 −0.446552 0.894758i \(-0.647348\pi\)
−0.446552 + 0.894758i \(0.647348\pi\)
\(930\) 0 0
\(931\) −24.4414 −0.801033
\(932\) −29.7590 −0.974788
\(933\) −2.71708 −0.0889531
\(934\) −1.55611 −0.0509174
\(935\) 0 0
\(936\) 0.194453 0.00635590
\(937\) −7.54293 −0.246417 −0.123208 0.992381i \(-0.539318\pi\)
−0.123208 + 0.992381i \(0.539318\pi\)
\(938\) 0.0547639 0.00178811
\(939\) −39.3595 −1.28445
\(940\) 0 0
\(941\) 35.4553 1.15581 0.577905 0.816104i \(-0.303870\pi\)
0.577905 + 0.816104i \(0.303870\pi\)
\(942\) 0.0311347 0.00101442
\(943\) 17.8021 0.579716
\(944\) 17.8443 0.580783
\(945\) 0 0
\(946\) −0.736734 −0.0239533
\(947\) −33.0630 −1.07440 −0.537202 0.843454i \(-0.680519\pi\)
−0.537202 + 0.843454i \(0.680519\pi\)
\(948\) −24.7644 −0.804311
\(949\) −31.7776 −1.03155
\(950\) 0 0
\(951\) 52.6071 1.70590
\(952\) −0.470588 −0.0152518
\(953\) 5.14501 0.166663 0.0833316 0.996522i \(-0.473444\pi\)
0.0833316 + 0.996522i \(0.473444\pi\)
\(954\) −0.00121986 −3.94943e−5 0
\(955\) 0 0
\(956\) −59.5228 −1.92511
\(957\) −43.6111 −1.40975
\(958\) −1.95683 −0.0632223
\(959\) 10.1963 0.329255
\(960\) 0 0
\(961\) −23.1490 −0.746741
\(962\) −1.54725 −0.0498852
\(963\) 2.41145 0.0777080
\(964\) −1.99323 −0.0641978
\(965\) 0 0
\(966\) 0.449076 0.0144488
\(967\) −2.82789 −0.0909390 −0.0454695 0.998966i \(-0.514478\pi\)
−0.0454695 + 0.998966i \(0.514478\pi\)
\(968\) −0.738440 −0.0237344
\(969\) −14.1349 −0.454079
\(970\) 0 0
\(971\) −43.0152 −1.38042 −0.690211 0.723608i \(-0.742482\pi\)
−0.690211 + 0.723608i \(0.742482\pi\)
\(972\) −6.31486 −0.202549
\(973\) −14.0579 −0.450676
\(974\) 0.131263 0.00420592
\(975\) 0 0
\(976\) −38.0991 −1.21952
\(977\) 5.45876 0.174641 0.0873207 0.996180i \(-0.472170\pi\)
0.0873207 + 0.996180i \(0.472170\pi\)
\(978\) −1.17407 −0.0375426
\(979\) 6.99933 0.223700
\(980\) 0 0
\(981\) −0.528564 −0.0168758
\(982\) 2.62054 0.0836246
\(983\) −16.8518 −0.537489 −0.268745 0.963211i \(-0.586609\pi\)
−0.268745 + 0.963211i \(0.586609\pi\)
\(984\) 2.44492 0.0779413
\(985\) 0 0
\(986\) 1.38359 0.0440625
\(987\) −8.42824 −0.268274
\(988\) −14.4492 −0.459690
\(989\) 13.1658 0.418648
\(990\) 0 0
\(991\) 57.3144 1.82065 0.910326 0.413892i \(-0.135831\pi\)
0.910326 + 0.413892i \(0.135831\pi\)
\(992\) 2.75310 0.0874111
\(993\) 50.1292 1.59080
\(994\) 0.440929 0.0139854
\(995\) 0 0
\(996\) 33.1786 1.05130
\(997\) 39.3642 1.24668 0.623339 0.781952i \(-0.285776\pi\)
0.623339 + 0.781952i \(0.285776\pi\)
\(998\) −1.42613 −0.0451434
\(999\) 47.6271 1.50685
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 \(a_p\))