Properties

Label 6023.2.a.b.1.8
Level 6023
Weight 2
Character 6023.1
Self dual Yes
Analytic conductor 48.094
Analytic rank 1
Dimension 99
CM No

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Newspace parameters

Level: \( N \) = \( 6023 = 19 \cdot 317 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0938971374\)
Analytic rank: \(1\)
Dimension: \(99\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 6023.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.33180 q^{2} -3.18012 q^{3} +3.43727 q^{4} +0.827568 q^{5} +7.41539 q^{6} -0.00201560 q^{7} -3.35142 q^{8} +7.11317 q^{9} +O(q^{10})\) \(q-2.33180 q^{2} -3.18012 q^{3} +3.43727 q^{4} +0.827568 q^{5} +7.41539 q^{6} -0.00201560 q^{7} -3.35142 q^{8} +7.11317 q^{9} -1.92972 q^{10} -4.05689 q^{11} -10.9309 q^{12} -2.74850 q^{13} +0.00469996 q^{14} -2.63176 q^{15} +0.940277 q^{16} -4.33812 q^{17} -16.5865 q^{18} -1.00000 q^{19} +2.84457 q^{20} +0.00640985 q^{21} +9.45985 q^{22} +1.63671 q^{23} +10.6579 q^{24} -4.31513 q^{25} +6.40895 q^{26} -13.0804 q^{27} -0.00692815 q^{28} +8.93765 q^{29} +6.13674 q^{30} +8.03527 q^{31} +4.51030 q^{32} +12.9014 q^{33} +10.1156 q^{34} -0.00166804 q^{35} +24.4499 q^{36} -2.00336 q^{37} +2.33180 q^{38} +8.74057 q^{39} -2.77352 q^{40} +2.15390 q^{41} -0.0149464 q^{42} +4.53692 q^{43} -13.9446 q^{44} +5.88663 q^{45} -3.81647 q^{46} -1.81610 q^{47} -2.99019 q^{48} -7.00000 q^{49} +10.0620 q^{50} +13.7957 q^{51} -9.44734 q^{52} -9.98836 q^{53} +30.5008 q^{54} -3.35735 q^{55} +0.00675511 q^{56} +3.18012 q^{57} -20.8408 q^{58} +1.65878 q^{59} -9.04608 q^{60} -5.47696 q^{61} -18.7366 q^{62} -0.0143373 q^{63} -12.3976 q^{64} -2.27457 q^{65} -30.0835 q^{66} +10.1927 q^{67} -14.9113 q^{68} -5.20493 q^{69} +0.00388954 q^{70} +10.4802 q^{71} -23.8392 q^{72} -0.992383 q^{73} +4.67142 q^{74} +13.7226 q^{75} -3.43727 q^{76} +0.00817707 q^{77} -20.3812 q^{78} -0.206703 q^{79} +0.778143 q^{80} +20.2577 q^{81} -5.02245 q^{82} -5.35096 q^{83} +0.0220324 q^{84} -3.59008 q^{85} -10.5792 q^{86} -28.4228 q^{87} +13.5963 q^{88} +8.77864 q^{89} -13.7264 q^{90} +0.00553988 q^{91} +5.62580 q^{92} -25.5531 q^{93} +4.23478 q^{94} -0.827568 q^{95} -14.3433 q^{96} -7.70688 q^{97} +16.3226 q^{98} -28.8574 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 99q - 4q^{2} - 3q^{3} + 80q^{4} - 15q^{5} - 12q^{6} - 19q^{7} - 12q^{8} + 58q^{9} + O(q^{10}) \) \( 99q - 4q^{2} - 3q^{3} + 80q^{4} - 15q^{5} - 12q^{6} - 19q^{7} - 12q^{8} + 58q^{9} - 6q^{10} - 9q^{11} - 27q^{12} - 28q^{13} - 13q^{14} - 10q^{15} + 38q^{16} - 36q^{17} - 14q^{18} - 99q^{19} - 34q^{20} - 20q^{21} - 53q^{22} - 38q^{23} - 25q^{24} - 8q^{25} - 3q^{26} - 3q^{27} - 63q^{28} - 34q^{29} - 30q^{30} - 16q^{31} - 43q^{32} - 41q^{33} - 14q^{34} - 25q^{35} - 16q^{36} - 80q^{37} + 4q^{38} - 48q^{39} - 10q^{40} - 32q^{41} - 37q^{42} - 76q^{43} - 21q^{44} - 53q^{45} - 23q^{46} - 31q^{47} - 74q^{48} - 32q^{49} - 29q^{50} - 30q^{51} - 71q^{52} - 35q^{53} - 80q^{54} - 45q^{55} - 33q^{56} + 3q^{57} - 91q^{58} + 12q^{59} - 56q^{60} - 61q^{61} - 46q^{62} - 43q^{63} - 30q^{64} - 46q^{65} - 75q^{66} - 26q^{67} - 55q^{68} - 45q^{69} - 76q^{70} - 41q^{71} - 77q^{72} - 143q^{73} - 64q^{74} - 8q^{75} - 80q^{76} - 58q^{77} - 34q^{78} - 22q^{79} - 36q^{80} - 81q^{81} - 109q^{82} - 7q^{83} - 6q^{84} - 80q^{85} + 32q^{86} - 57q^{87} - 120q^{88} - 28q^{89} - 12q^{90} - 30q^{91} - 107q^{92} - 121q^{93} + 8q^{94} + 15q^{95} + 4q^{96} - 128q^{97} + 54q^{98} - 34q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.33180 −1.64883 −0.824414 0.565987i \(-0.808495\pi\)
−0.824414 + 0.565987i \(0.808495\pi\)
\(3\) −3.18012 −1.83604 −0.918022 0.396530i \(-0.870214\pi\)
−0.918022 + 0.396530i \(0.870214\pi\)
\(4\) 3.43727 1.71863
\(5\) 0.827568 0.370099 0.185050 0.982729i \(-0.440755\pi\)
0.185050 + 0.982729i \(0.440755\pi\)
\(6\) 7.41539 3.02732
\(7\) −0.00201560 −0.000761824 0 −0.000380912 1.00000i \(-0.500121\pi\)
−0.000380912 1.00000i \(0.500121\pi\)
\(8\) −3.35142 −1.18490
\(9\) 7.11317 2.37106
\(10\) −1.92972 −0.610230
\(11\) −4.05689 −1.22320 −0.611600 0.791167i \(-0.709474\pi\)
−0.611600 + 0.791167i \(0.709474\pi\)
\(12\) −10.9309 −3.15549
\(13\) −2.74850 −0.762298 −0.381149 0.924514i \(-0.624471\pi\)
−0.381149 + 0.924514i \(0.624471\pi\)
\(14\) 0.00469996 0.00125612
\(15\) −2.63176 −0.679519
\(16\) 0.940277 0.235069
\(17\) −4.33812 −1.05215 −0.526074 0.850439i \(-0.676336\pi\)
−0.526074 + 0.850439i \(0.676336\pi\)
\(18\) −16.5865 −3.90946
\(19\) −1.00000 −0.229416
\(20\) 2.84457 0.636066
\(21\) 0.00640985 0.00139874
\(22\) 9.45985 2.01685
\(23\) 1.63671 0.341277 0.170639 0.985334i \(-0.445417\pi\)
0.170639 + 0.985334i \(0.445417\pi\)
\(24\) 10.6579 2.17554
\(25\) −4.31513 −0.863026
\(26\) 6.40895 1.25690
\(27\) −13.0804 −2.51732
\(28\) −0.00692815 −0.00130930
\(29\) 8.93765 1.65968 0.829840 0.558001i \(-0.188432\pi\)
0.829840 + 0.558001i \(0.188432\pi\)
\(30\) 6.13674 1.12041
\(31\) 8.03527 1.44318 0.721588 0.692322i \(-0.243412\pi\)
0.721588 + 0.692322i \(0.243412\pi\)
\(32\) 4.51030 0.797315
\(33\) 12.9014 2.24585
\(34\) 10.1156 1.73481
\(35\) −0.00166804 −0.000281951 0
\(36\) 24.4499 4.07498
\(37\) −2.00336 −0.329350 −0.164675 0.986348i \(-0.552657\pi\)
−0.164675 + 0.986348i \(0.552657\pi\)
\(38\) 2.33180 0.378267
\(39\) 8.74057 1.39961
\(40\) −2.77352 −0.438532
\(41\) 2.15390 0.336383 0.168191 0.985754i \(-0.446207\pi\)
0.168191 + 0.985754i \(0.446207\pi\)
\(42\) −0.0149464 −0.00230629
\(43\) 4.53692 0.691875 0.345937 0.938258i \(-0.387561\pi\)
0.345937 + 0.938258i \(0.387561\pi\)
\(44\) −13.9446 −2.10223
\(45\) 5.88663 0.877527
\(46\) −3.81647 −0.562707
\(47\) −1.81610 −0.264906 −0.132453 0.991189i \(-0.542285\pi\)
−0.132453 + 0.991189i \(0.542285\pi\)
\(48\) −2.99019 −0.431597
\(49\) −7.00000 −0.999999
\(50\) 10.0620 1.42298
\(51\) 13.7957 1.93179
\(52\) −9.44734 −1.31011
\(53\) −9.98836 −1.37201 −0.686003 0.727599i \(-0.740636\pi\)
−0.686003 + 0.727599i \(0.740636\pi\)
\(54\) 30.5008 4.15063
\(55\) −3.35735 −0.452706
\(56\) 0.00675511 0.000902689 0
\(57\) 3.18012 0.421217
\(58\) −20.8408 −2.73653
\(59\) 1.65878 0.215955 0.107978 0.994153i \(-0.465563\pi\)
0.107978 + 0.994153i \(0.465563\pi\)
\(60\) −9.04608 −1.16784
\(61\) −5.47696 −0.701253 −0.350627 0.936515i \(-0.614031\pi\)
−0.350627 + 0.936515i \(0.614031\pi\)
\(62\) −18.7366 −2.37955
\(63\) −0.0143373 −0.00180633
\(64\) −12.3976 −1.54971
\(65\) −2.27457 −0.282126
\(66\) −30.0835 −3.70302
\(67\) 10.1927 1.24524 0.622618 0.782526i \(-0.286069\pi\)
0.622618 + 0.782526i \(0.286069\pi\)
\(68\) −14.9113 −1.80826
\(69\) −5.20493 −0.626600
\(70\) 0.00388954 0.000464888 0
\(71\) 10.4802 1.24377 0.621885 0.783108i \(-0.286367\pi\)
0.621885 + 0.783108i \(0.286367\pi\)
\(72\) −23.8392 −2.80947
\(73\) −0.992383 −0.116150 −0.0580748 0.998312i \(-0.518496\pi\)
−0.0580748 + 0.998312i \(0.518496\pi\)
\(74\) 4.67142 0.543041
\(75\) 13.7226 1.58455
\(76\) −3.43727 −0.394282
\(77\) 0.00817707 0.000931863 0
\(78\) −20.3812 −2.30772
\(79\) −0.206703 −0.0232559 −0.0116280 0.999932i \(-0.503701\pi\)
−0.0116280 + 0.999932i \(0.503701\pi\)
\(80\) 0.778143 0.0869990
\(81\) 20.2577 2.25085
\(82\) −5.02245 −0.554637
\(83\) −5.35096 −0.587344 −0.293672 0.955906i \(-0.594877\pi\)
−0.293672 + 0.955906i \(0.594877\pi\)
\(84\) 0.0220324 0.00240393
\(85\) −3.59008 −0.389399
\(86\) −10.5792 −1.14078
\(87\) −28.4228 −3.04725
\(88\) 13.5963 1.44937
\(89\) 8.77864 0.930534 0.465267 0.885170i \(-0.345958\pi\)
0.465267 + 0.885170i \(0.345958\pi\)
\(90\) −13.7264 −1.44689
\(91\) 0.00553988 0.000580737 0
\(92\) 5.62580 0.586530
\(93\) −25.5531 −2.64974
\(94\) 4.23478 0.436784
\(95\) −0.827568 −0.0849066
\(96\) −14.3433 −1.46391
\(97\) −7.70688 −0.782515 −0.391258 0.920281i \(-0.627960\pi\)
−0.391258 + 0.920281i \(0.627960\pi\)
\(98\) 16.3226 1.64883
\(99\) −28.8574 −2.90028
\(100\) −14.8323 −1.48323
\(101\) 0.582809 0.0579917 0.0289958 0.999580i \(-0.490769\pi\)
0.0289958 + 0.999580i \(0.490769\pi\)
\(102\) −32.1688 −3.18519
\(103\) −1.54942 −0.152669 −0.0763344 0.997082i \(-0.524322\pi\)
−0.0763344 + 0.997082i \(0.524322\pi\)
\(104\) 9.21137 0.903250
\(105\) 0.00530458 0.000517674 0
\(106\) 23.2908 2.26220
\(107\) 4.47606 0.432717 0.216358 0.976314i \(-0.430582\pi\)
0.216358 + 0.976314i \(0.430582\pi\)
\(108\) −44.9608 −4.32635
\(109\) −1.62513 −0.155660 −0.0778298 0.996967i \(-0.524799\pi\)
−0.0778298 + 0.996967i \(0.524799\pi\)
\(110\) 7.82866 0.746434
\(111\) 6.37092 0.604701
\(112\) −0.00189522 −0.000179081 0
\(113\) −2.81778 −0.265075 −0.132537 0.991178i \(-0.542312\pi\)
−0.132537 + 0.991178i \(0.542312\pi\)
\(114\) −7.41539 −0.694515
\(115\) 1.35449 0.126306
\(116\) 30.7211 2.85238
\(117\) −19.5506 −1.80745
\(118\) −3.86794 −0.356073
\(119\) 0.00874390 0.000801552 0
\(120\) 8.82014 0.805165
\(121\) 5.45839 0.496217
\(122\) 12.7712 1.15625
\(123\) −6.84966 −0.617613
\(124\) 27.6194 2.48029
\(125\) −7.70890 −0.689505
\(126\) 0.0334316 0.00297833
\(127\) 0.470587 0.0417578 0.0208789 0.999782i \(-0.493354\pi\)
0.0208789 + 0.999782i \(0.493354\pi\)
\(128\) 19.8882 1.75788
\(129\) −14.4280 −1.27031
\(130\) 5.30384 0.465177
\(131\) 9.27777 0.810602 0.405301 0.914183i \(-0.367167\pi\)
0.405301 + 0.914183i \(0.367167\pi\)
\(132\) 44.3456 3.85979
\(133\) 0.00201560 0.000174775 0
\(134\) −23.7673 −2.05318
\(135\) −10.8249 −0.931659
\(136\) 14.5388 1.24669
\(137\) −2.33737 −0.199695 −0.0998474 0.995003i \(-0.531835\pi\)
−0.0998474 + 0.995003i \(0.531835\pi\)
\(138\) 12.1368 1.03315
\(139\) 10.6382 0.902317 0.451158 0.892444i \(-0.351011\pi\)
0.451158 + 0.892444i \(0.351011\pi\)
\(140\) −0.00573351 −0.000484570 0
\(141\) 5.77542 0.486378
\(142\) −24.4377 −2.05076
\(143\) 11.1504 0.932442
\(144\) 6.68835 0.557362
\(145\) 7.39651 0.614247
\(146\) 2.31403 0.191511
\(147\) 22.2608 1.83604
\(148\) −6.88607 −0.566032
\(149\) 18.5949 1.52335 0.761675 0.647959i \(-0.224377\pi\)
0.761675 + 0.647959i \(0.224377\pi\)
\(150\) −31.9984 −2.61266
\(151\) −8.14825 −0.663095 −0.331548 0.943438i \(-0.607571\pi\)
−0.331548 + 0.943438i \(0.607571\pi\)
\(152\) 3.35142 0.271836
\(153\) −30.8577 −2.49470
\(154\) −0.0190672 −0.00153648
\(155\) 6.64973 0.534119
\(156\) 30.0437 2.40542
\(157\) 17.9009 1.42865 0.714324 0.699815i \(-0.246734\pi\)
0.714324 + 0.699815i \(0.246734\pi\)
\(158\) 0.481989 0.0383450
\(159\) 31.7642 2.51906
\(160\) 3.73258 0.295086
\(161\) −0.00329894 −0.000259993 0
\(162\) −47.2367 −3.71127
\(163\) 4.52406 0.354352 0.177176 0.984179i \(-0.443304\pi\)
0.177176 + 0.984179i \(0.443304\pi\)
\(164\) 7.40353 0.578119
\(165\) 10.6768 0.831187
\(166\) 12.4773 0.968430
\(167\) 9.81727 0.759683 0.379842 0.925052i \(-0.375979\pi\)
0.379842 + 0.925052i \(0.375979\pi\)
\(168\) −0.0214821 −0.00165738
\(169\) −5.44573 −0.418902
\(170\) 8.37134 0.642052
\(171\) −7.11317 −0.543958
\(172\) 15.5946 1.18908
\(173\) 23.5554 1.79089 0.895443 0.445175i \(-0.146859\pi\)
0.895443 + 0.445175i \(0.146859\pi\)
\(174\) 66.2762 5.02438
\(175\) 0.00869757 0.000657475 0
\(176\) −3.81460 −0.287537
\(177\) −5.27513 −0.396503
\(178\) −20.4700 −1.53429
\(179\) 12.4215 0.928425 0.464213 0.885724i \(-0.346337\pi\)
0.464213 + 0.885724i \(0.346337\pi\)
\(180\) 20.2339 1.50815
\(181\) 1.65180 0.122777 0.0613885 0.998114i \(-0.480447\pi\)
0.0613885 + 0.998114i \(0.480447\pi\)
\(182\) −0.0129179 −0.000957535 0
\(183\) 17.4174 1.28753
\(184\) −5.48529 −0.404381
\(185\) −1.65791 −0.121892
\(186\) 59.5846 4.36896
\(187\) 17.5993 1.28699
\(188\) −6.24243 −0.455276
\(189\) 0.0263648 0.00191776
\(190\) 1.92972 0.139996
\(191\) −18.9683 −1.37250 −0.686248 0.727368i \(-0.740743\pi\)
−0.686248 + 0.727368i \(0.740743\pi\)
\(192\) 39.4260 2.84533
\(193\) −0.794447 −0.0571855 −0.0285928 0.999591i \(-0.509103\pi\)
−0.0285928 + 0.999591i \(0.509103\pi\)
\(194\) 17.9709 1.29023
\(195\) 7.23341 0.517995
\(196\) −24.0609 −1.71863
\(197\) −8.99506 −0.640871 −0.320436 0.947270i \(-0.603829\pi\)
−0.320436 + 0.947270i \(0.603829\pi\)
\(198\) 67.2895 4.78206
\(199\) −24.2584 −1.71964 −0.859818 0.510601i \(-0.829423\pi\)
−0.859818 + 0.510601i \(0.829423\pi\)
\(200\) 14.4618 1.02260
\(201\) −32.4140 −2.28631
\(202\) −1.35899 −0.0956183
\(203\) −0.0180147 −0.00126439
\(204\) 47.4196 3.32004
\(205\) 1.78250 0.124495
\(206\) 3.61293 0.251725
\(207\) 11.6422 0.809187
\(208\) −2.58435 −0.179193
\(209\) 4.05689 0.280621
\(210\) −0.0123692 −0.000853556 0
\(211\) −7.02109 −0.483352 −0.241676 0.970357i \(-0.577697\pi\)
−0.241676 + 0.970357i \(0.577697\pi\)
\(212\) −34.3327 −2.35798
\(213\) −33.3283 −2.28362
\(214\) −10.4372 −0.713476
\(215\) 3.75461 0.256062
\(216\) 43.8378 2.98278
\(217\) −0.0161959 −0.00109945
\(218\) 3.78948 0.256656
\(219\) 3.15590 0.213256
\(220\) −11.5401 −0.778035
\(221\) 11.9233 0.802049
\(222\) −14.8557 −0.997047
\(223\) −5.77160 −0.386495 −0.193247 0.981150i \(-0.561902\pi\)
−0.193247 + 0.981150i \(0.561902\pi\)
\(224\) −0.00909095 −0.000607414 0
\(225\) −30.6943 −2.04628
\(226\) 6.57049 0.437062
\(227\) 5.43681 0.360854 0.180427 0.983588i \(-0.442252\pi\)
0.180427 + 0.983588i \(0.442252\pi\)
\(228\) 10.9309 0.723918
\(229\) 21.7057 1.43435 0.717176 0.696892i \(-0.245435\pi\)
0.717176 + 0.696892i \(0.245435\pi\)
\(230\) −3.15838 −0.208258
\(231\) −0.0260041 −0.00171094
\(232\) −29.9538 −1.96656
\(233\) −10.3642 −0.678984 −0.339492 0.940609i \(-0.610255\pi\)
−0.339492 + 0.940609i \(0.610255\pi\)
\(234\) 45.5879 2.98017
\(235\) −1.50295 −0.0980415
\(236\) 5.70168 0.371148
\(237\) 0.657341 0.0426989
\(238\) −0.0203890 −0.00132162
\(239\) 4.02776 0.260534 0.130267 0.991479i \(-0.458417\pi\)
0.130267 + 0.991479i \(0.458417\pi\)
\(240\) −2.47459 −0.159734
\(241\) −30.3531 −1.95522 −0.977608 0.210433i \(-0.932513\pi\)
−0.977608 + 0.210433i \(0.932513\pi\)
\(242\) −12.7279 −0.818177
\(243\) −25.1807 −1.61534
\(244\) −18.8258 −1.20520
\(245\) −5.79297 −0.370099
\(246\) 15.9720 1.01834
\(247\) 2.74850 0.174883
\(248\) −26.9295 −1.71003
\(249\) 17.0167 1.07839
\(250\) 17.9756 1.13688
\(251\) 17.6655 1.11504 0.557520 0.830164i \(-0.311753\pi\)
0.557520 + 0.830164i \(0.311753\pi\)
\(252\) −0.0492811 −0.00310442
\(253\) −6.63995 −0.417450
\(254\) −1.09731 −0.0688515
\(255\) 11.4169 0.714954
\(256\) −21.5798 −1.34874
\(257\) −5.52698 −0.344764 −0.172382 0.985030i \(-0.555146\pi\)
−0.172382 + 0.985030i \(0.555146\pi\)
\(258\) 33.6431 2.09453
\(259\) 0.00403796 0.000250907 0
\(260\) −7.81831 −0.484871
\(261\) 63.5750 3.93520
\(262\) −21.6339 −1.33654
\(263\) −11.4711 −0.707341 −0.353670 0.935370i \(-0.615067\pi\)
−0.353670 + 0.935370i \(0.615067\pi\)
\(264\) −43.2380 −2.66111
\(265\) −8.26604 −0.507779
\(266\) −0.00469996 −0.000288173 0
\(267\) −27.9171 −1.70850
\(268\) 35.0350 2.14011
\(269\) 24.6020 1.50001 0.750006 0.661431i \(-0.230051\pi\)
0.750006 + 0.661431i \(0.230051\pi\)
\(270\) 25.2414 1.53614
\(271\) 8.29400 0.503825 0.251912 0.967750i \(-0.418941\pi\)
0.251912 + 0.967750i \(0.418941\pi\)
\(272\) −4.07903 −0.247327
\(273\) −0.0176175 −0.00106626
\(274\) 5.45026 0.329262
\(275\) 17.5060 1.05565
\(276\) −17.8907 −1.07690
\(277\) −18.4444 −1.10821 −0.554107 0.832445i \(-0.686940\pi\)
−0.554107 + 0.832445i \(0.686940\pi\)
\(278\) −24.8060 −1.48777
\(279\) 57.1562 3.42185
\(280\) 0.00559031 0.000334085 0
\(281\) −31.9354 −1.90511 −0.952553 0.304373i \(-0.901553\pi\)
−0.952553 + 0.304373i \(0.901553\pi\)
\(282\) −13.4671 −0.801954
\(283\) 14.6555 0.871181 0.435591 0.900145i \(-0.356540\pi\)
0.435591 + 0.900145i \(0.356540\pi\)
\(284\) 36.0232 2.13759
\(285\) 2.63176 0.155892
\(286\) −26.0004 −1.53744
\(287\) −0.00434140 −0.000256264 0
\(288\) 32.0825 1.89048
\(289\) 1.81925 0.107014
\(290\) −17.2471 −1.01279
\(291\) 24.5088 1.43673
\(292\) −3.41109 −0.199619
\(293\) 2.12337 0.124049 0.0620243 0.998075i \(-0.480244\pi\)
0.0620243 + 0.998075i \(0.480244\pi\)
\(294\) −51.9077 −3.02732
\(295\) 1.37275 0.0799249
\(296\) 6.71408 0.390248
\(297\) 53.0657 3.07918
\(298\) −43.3594 −2.51174
\(299\) −4.49849 −0.260155
\(300\) 47.1684 2.72327
\(301\) −0.00914462 −0.000527087 0
\(302\) 19.0001 1.09333
\(303\) −1.85340 −0.106475
\(304\) −0.940277 −0.0539286
\(305\) −4.53256 −0.259533
\(306\) 71.9539 4.11333
\(307\) 5.93479 0.338716 0.169358 0.985555i \(-0.445831\pi\)
0.169358 + 0.985555i \(0.445831\pi\)
\(308\) 0.0281068 0.00160153
\(309\) 4.92734 0.280306
\(310\) −15.5058 −0.880670
\(311\) 32.0456 1.81714 0.908568 0.417736i \(-0.137176\pi\)
0.908568 + 0.417736i \(0.137176\pi\)
\(312\) −29.2933 −1.65841
\(313\) −2.18698 −0.123616 −0.0618078 0.998088i \(-0.519687\pi\)
−0.0618078 + 0.998088i \(0.519687\pi\)
\(314\) −41.7412 −2.35559
\(315\) −0.0118651 −0.000668521 0
\(316\) −0.710494 −0.0399684
\(317\) −1.00000 −0.0561656
\(318\) −74.0676 −4.15350
\(319\) −36.2591 −2.03012
\(320\) −10.2599 −0.573545
\(321\) −14.2344 −0.794487
\(322\) 0.00769246 0.000428684 0
\(323\) 4.33812 0.241379
\(324\) 69.6310 3.86839
\(325\) 11.8602 0.657883
\(326\) −10.5492 −0.584265
\(327\) 5.16812 0.285798
\(328\) −7.21861 −0.398581
\(329\) 0.00366053 0.000201812 0
\(330\) −24.8961 −1.37048
\(331\) −1.40645 −0.0773057 −0.0386528 0.999253i \(-0.512307\pi\)
−0.0386528 + 0.999253i \(0.512307\pi\)
\(332\) −18.3927 −1.00943
\(333\) −14.2502 −0.780907
\(334\) −22.8919 −1.25259
\(335\) 8.43514 0.460861
\(336\) 0.00602703 0.000328801 0
\(337\) −5.17619 −0.281965 −0.140982 0.990012i \(-0.545026\pi\)
−0.140982 + 0.990012i \(0.545026\pi\)
\(338\) 12.6983 0.690698
\(339\) 8.96088 0.486688
\(340\) −12.3401 −0.669235
\(341\) −32.5982 −1.76529
\(342\) 16.5865 0.896893
\(343\) 0.0282184 0.00152365
\(344\) −15.2051 −0.819805
\(345\) −4.30743 −0.231904
\(346\) −54.9265 −2.95286
\(347\) −2.52961 −0.135796 −0.0678982 0.997692i \(-0.521629\pi\)
−0.0678982 + 0.997692i \(0.521629\pi\)
\(348\) −97.6968 −5.23710
\(349\) −1.63079 −0.0872939 −0.0436470 0.999047i \(-0.513898\pi\)
−0.0436470 + 0.999047i \(0.513898\pi\)
\(350\) −0.0202810 −0.00108406
\(351\) 35.9514 1.91895
\(352\) −18.2978 −0.975276
\(353\) 5.37407 0.286033 0.143016 0.989720i \(-0.454320\pi\)
0.143016 + 0.989720i \(0.454320\pi\)
\(354\) 12.3005 0.653765
\(355\) 8.67307 0.460319
\(356\) 30.1745 1.59925
\(357\) −0.0278067 −0.00147168
\(358\) −28.9644 −1.53081
\(359\) 33.1690 1.75059 0.875297 0.483586i \(-0.160666\pi\)
0.875297 + 0.483586i \(0.160666\pi\)
\(360\) −19.7285 −1.03979
\(361\) 1.00000 0.0526316
\(362\) −3.85165 −0.202438
\(363\) −17.3583 −0.911077
\(364\) 0.0190420 0.000998074 0
\(365\) −0.821264 −0.0429869
\(366\) −40.6138 −2.12292
\(367\) 7.16564 0.374043 0.187022 0.982356i \(-0.440117\pi\)
0.187022 + 0.982356i \(0.440117\pi\)
\(368\) 1.53896 0.0802237
\(369\) 15.3211 0.797582
\(370\) 3.86591 0.200979
\(371\) 0.0201325 0.00104523
\(372\) −87.8329 −4.55393
\(373\) 6.19041 0.320527 0.160264 0.987074i \(-0.448766\pi\)
0.160264 + 0.987074i \(0.448766\pi\)
\(374\) −41.0379 −2.12202
\(375\) 24.5152 1.26596
\(376\) 6.08651 0.313888
\(377\) −24.5652 −1.26517
\(378\) −0.0614773 −0.00316205
\(379\) 2.72449 0.139948 0.0699738 0.997549i \(-0.477708\pi\)
0.0699738 + 0.997549i \(0.477708\pi\)
\(380\) −2.84457 −0.145923
\(381\) −1.49652 −0.0766692
\(382\) 44.2301 2.26301
\(383\) −11.8848 −0.607283 −0.303642 0.952786i \(-0.598203\pi\)
−0.303642 + 0.952786i \(0.598203\pi\)
\(384\) −63.2468 −3.22755
\(385\) 0.00676708 0.000344882 0
\(386\) 1.85249 0.0942891
\(387\) 32.2719 1.64047
\(388\) −26.4906 −1.34486
\(389\) −0.457178 −0.0231798 −0.0115899 0.999933i \(-0.503689\pi\)
−0.0115899 + 0.999933i \(0.503689\pi\)
\(390\) −16.8668 −0.854086
\(391\) −7.10022 −0.359074
\(392\) 23.4599 1.18490
\(393\) −29.5044 −1.48830
\(394\) 20.9746 1.05669
\(395\) −0.171061 −0.00860700
\(396\) −99.1905 −4.98451
\(397\) 8.49801 0.426503 0.213251 0.976997i \(-0.431595\pi\)
0.213251 + 0.976997i \(0.431595\pi\)
\(398\) 56.5657 2.83538
\(399\) −0.00640985 −0.000320894 0
\(400\) −4.05742 −0.202871
\(401\) 19.1177 0.954693 0.477347 0.878715i \(-0.341599\pi\)
0.477347 + 0.878715i \(0.341599\pi\)
\(402\) 75.5828 3.76973
\(403\) −22.0850 −1.10013
\(404\) 2.00327 0.0996665
\(405\) 16.7646 0.833039
\(406\) 0.0420066 0.00208475
\(407\) 8.12741 0.402861
\(408\) −46.2352 −2.28898
\(409\) −5.95756 −0.294582 −0.147291 0.989093i \(-0.547055\pi\)
−0.147291 + 0.989093i \(0.547055\pi\)
\(410\) −4.15642 −0.205271
\(411\) 7.43311 0.366648
\(412\) −5.32577 −0.262382
\(413\) −0.00334344 −0.000164520 0
\(414\) −27.1472 −1.33421
\(415\) −4.42828 −0.217376
\(416\) −12.3966 −0.607792
\(417\) −33.8306 −1.65669
\(418\) −9.45985 −0.462696
\(419\) 17.8748 0.873243 0.436621 0.899645i \(-0.356175\pi\)
0.436621 + 0.899645i \(0.356175\pi\)
\(420\) 0.0182333 0.000889692 0
\(421\) 21.6663 1.05595 0.527976 0.849259i \(-0.322951\pi\)
0.527976 + 0.849259i \(0.322951\pi\)
\(422\) 16.3717 0.796964
\(423\) −12.9182 −0.628106
\(424\) 33.4751 1.62570
\(425\) 18.7195 0.908031
\(426\) 77.7148 3.76529
\(427\) 0.0110394 0.000534232 0
\(428\) 15.3854 0.743682
\(429\) −35.4596 −1.71200
\(430\) −8.75499 −0.422203
\(431\) −25.6505 −1.23554 −0.617770 0.786359i \(-0.711964\pi\)
−0.617770 + 0.786359i \(0.711964\pi\)
\(432\) −12.2992 −0.591744
\(433\) 5.37919 0.258508 0.129254 0.991612i \(-0.458742\pi\)
0.129254 + 0.991612i \(0.458742\pi\)
\(434\) 0.0377654 0.00181280
\(435\) −23.5218 −1.12778
\(436\) −5.58602 −0.267522
\(437\) −1.63671 −0.0782943
\(438\) −7.35891 −0.351622
\(439\) 26.6127 1.27015 0.635077 0.772449i \(-0.280968\pi\)
0.635077 + 0.772449i \(0.280968\pi\)
\(440\) 11.2519 0.536413
\(441\) −49.7922 −2.37105
\(442\) −27.8027 −1.32244
\(443\) 7.78093 0.369683 0.184842 0.982768i \(-0.440823\pi\)
0.184842 + 0.982768i \(0.440823\pi\)
\(444\) 21.8985 1.03926
\(445\) 7.26492 0.344390
\(446\) 13.4582 0.637264
\(447\) −59.1339 −2.79694
\(448\) 0.0249887 0.00118060
\(449\) −6.85465 −0.323491 −0.161746 0.986832i \(-0.551712\pi\)
−0.161746 + 0.986832i \(0.551712\pi\)
\(450\) 71.5727 3.37397
\(451\) −8.73814 −0.411463
\(452\) −9.68547 −0.455566
\(453\) 25.9124 1.21747
\(454\) −12.6775 −0.594986
\(455\) 0.00458462 0.000214930 0
\(456\) −10.6579 −0.499102
\(457\) −37.7910 −1.76779 −0.883893 0.467689i \(-0.845087\pi\)
−0.883893 + 0.467689i \(0.845087\pi\)
\(458\) −50.6132 −2.36500
\(459\) 56.7442 2.64859
\(460\) 4.65573 0.217075
\(461\) −41.0479 −1.91179 −0.955896 0.293706i \(-0.905111\pi\)
−0.955896 + 0.293706i \(0.905111\pi\)
\(462\) 0.0606362 0.00282105
\(463\) 23.5339 1.09371 0.546857 0.837226i \(-0.315824\pi\)
0.546857 + 0.837226i \(0.315824\pi\)
\(464\) 8.40387 0.390140
\(465\) −21.1469 −0.980666
\(466\) 24.1673 1.11953
\(467\) 3.20274 0.148205 0.0741027 0.997251i \(-0.476391\pi\)
0.0741027 + 0.997251i \(0.476391\pi\)
\(468\) −67.2005 −3.10635
\(469\) −0.0205444 −0.000948651 0
\(470\) 3.50456 0.161654
\(471\) −56.9270 −2.62306
\(472\) −5.55927 −0.255886
\(473\) −18.4058 −0.846301
\(474\) −1.53278 −0.0704031
\(475\) 4.31513 0.197992
\(476\) 0.0300551 0.00137757
\(477\) −71.0489 −3.25310
\(478\) −9.39190 −0.429576
\(479\) 21.0787 0.963112 0.481556 0.876415i \(-0.340072\pi\)
0.481556 + 0.876415i \(0.340072\pi\)
\(480\) −11.8700 −0.541791
\(481\) 5.50623 0.251063
\(482\) 70.7773 3.22382
\(483\) 0.0104910 0.000477359 0
\(484\) 18.7620 0.852816
\(485\) −6.37797 −0.289609
\(486\) 58.7162 2.66342
\(487\) −27.8917 −1.26389 −0.631947 0.775011i \(-0.717744\pi\)
−0.631947 + 0.775011i \(0.717744\pi\)
\(488\) 18.3556 0.830918
\(489\) −14.3871 −0.650605
\(490\) 13.5080 0.610230
\(491\) 1.94346 0.0877072 0.0438536 0.999038i \(-0.486036\pi\)
0.0438536 + 0.999038i \(0.486036\pi\)
\(492\) −23.5441 −1.06145
\(493\) −38.7726 −1.74623
\(494\) −6.40895 −0.288352
\(495\) −23.8814 −1.07339
\(496\) 7.55538 0.339246
\(497\) −0.0211239 −0.000947535 0
\(498\) −39.6795 −1.77808
\(499\) −20.6892 −0.926178 −0.463089 0.886312i \(-0.653259\pi\)
−0.463089 + 0.886312i \(0.653259\pi\)
\(500\) −26.4976 −1.18501
\(501\) −31.2201 −1.39481
\(502\) −41.1924 −1.83851
\(503\) 34.6230 1.54376 0.771882 0.635765i \(-0.219315\pi\)
0.771882 + 0.635765i \(0.219315\pi\)
\(504\) 0.0480502 0.00214033
\(505\) 0.482314 0.0214627
\(506\) 15.4830 0.688303
\(507\) 17.3181 0.769123
\(508\) 1.61753 0.0717664
\(509\) 36.8624 1.63390 0.816949 0.576709i \(-0.195663\pi\)
0.816949 + 0.576709i \(0.195663\pi\)
\(510\) −26.6219 −1.17884
\(511\) 0.00200025 8.84856e−5 0
\(512\) 10.5434 0.465959
\(513\) 13.0804 0.577513
\(514\) 12.8878 0.568456
\(515\) −1.28225 −0.0565026
\(516\) −49.5928 −2.18320
\(517\) 7.36773 0.324033
\(518\) −0.00941570 −0.000413702 0
\(519\) −74.9091 −3.28815
\(520\) 7.62303 0.334292
\(521\) 15.6930 0.687521 0.343760 0.939057i \(-0.388299\pi\)
0.343760 + 0.939057i \(0.388299\pi\)
\(522\) −148.244 −6.48846
\(523\) 27.1603 1.18764 0.593819 0.804599i \(-0.297620\pi\)
0.593819 + 0.804599i \(0.297620\pi\)
\(524\) 31.8902 1.39313
\(525\) −0.0276593 −0.00120715
\(526\) 26.7483 1.16628
\(527\) −34.8579 −1.51843
\(528\) 12.1309 0.527930
\(529\) −20.3212 −0.883530
\(530\) 19.2747 0.837240
\(531\) 11.7992 0.512042
\(532\) 0.00692815 0.000300373 0
\(533\) −5.92000 −0.256424
\(534\) 65.0971 2.81703
\(535\) 3.70424 0.160148
\(536\) −34.1600 −1.47549
\(537\) −39.5018 −1.70463
\(538\) −57.3669 −2.47326
\(539\) 28.3982 1.22320
\(540\) −37.2081 −1.60118
\(541\) 9.23382 0.396993 0.198496 0.980102i \(-0.436394\pi\)
0.198496 + 0.980102i \(0.436394\pi\)
\(542\) −19.3399 −0.830721
\(543\) −5.25291 −0.225424
\(544\) −19.5662 −0.838894
\(545\) −1.34491 −0.0576095
\(546\) 0.0410804 0.00175808
\(547\) −14.9271 −0.638238 −0.319119 0.947715i \(-0.603387\pi\)
−0.319119 + 0.947715i \(0.603387\pi\)
\(548\) −8.03416 −0.343202
\(549\) −38.9586 −1.66271
\(550\) −40.8205 −1.74059
\(551\) −8.93765 −0.380757
\(552\) 17.4439 0.742460
\(553\) 0.000416631 0 1.77169e−5 0
\(554\) 43.0085 1.82726
\(555\) 5.27236 0.223799
\(556\) 36.5662 1.55075
\(557\) −30.6559 −1.29893 −0.649466 0.760391i \(-0.725007\pi\)
−0.649466 + 0.760391i \(0.725007\pi\)
\(558\) −133.277 −5.64205
\(559\) −12.4698 −0.527414
\(560\) −0.00156842 −6.62780e−5 0
\(561\) −55.9678 −2.36296
\(562\) 74.4668 3.14119
\(563\) 0.0412890 0.00174012 0.000870061 1.00000i \(-0.499723\pi\)
0.000870061 1.00000i \(0.499723\pi\)
\(564\) 19.8517 0.835907
\(565\) −2.33190 −0.0981039
\(566\) −34.1737 −1.43643
\(567\) −0.0408313 −0.00171475
\(568\) −35.1235 −1.47375
\(569\) −17.0592 −0.715157 −0.357579 0.933883i \(-0.616398\pi\)
−0.357579 + 0.933883i \(0.616398\pi\)
\(570\) −6.13674 −0.257040
\(571\) 3.11814 0.130490 0.0652452 0.997869i \(-0.479217\pi\)
0.0652452 + 0.997869i \(0.479217\pi\)
\(572\) 38.3269 1.60253
\(573\) 60.3214 2.51996
\(574\) 0.0101232 0.000422536 0
\(575\) −7.06261 −0.294531
\(576\) −88.1865 −3.67444
\(577\) −26.2736 −1.09378 −0.546891 0.837204i \(-0.684189\pi\)
−0.546891 + 0.837204i \(0.684189\pi\)
\(578\) −4.24211 −0.176448
\(579\) 2.52644 0.104995
\(580\) 25.4238 1.05567
\(581\) 0.0107854 0.000447453 0
\(582\) −57.1495 −2.36892
\(583\) 40.5217 1.67824
\(584\) 3.32589 0.137626
\(585\) −16.1794 −0.668936
\(586\) −4.95127 −0.204535
\(587\) 34.4625 1.42242 0.711211 0.702979i \(-0.248147\pi\)
0.711211 + 0.702979i \(0.248147\pi\)
\(588\) 76.5165 3.15549
\(589\) −8.03527 −0.331087
\(590\) −3.20098 −0.131782
\(591\) 28.6054 1.17667
\(592\) −1.88371 −0.0774200
\(593\) −17.0831 −0.701518 −0.350759 0.936466i \(-0.614076\pi\)
−0.350759 + 0.936466i \(0.614076\pi\)
\(594\) −123.738 −5.07705
\(595\) 0.00723617 0.000296654 0
\(596\) 63.9155 2.61808
\(597\) 77.1448 3.15733
\(598\) 10.4896 0.428950
\(599\) −1.59196 −0.0650456 −0.0325228 0.999471i \(-0.510354\pi\)
−0.0325228 + 0.999471i \(0.510354\pi\)
\(600\) −45.9903 −1.87754
\(601\) 16.6771 0.680274 0.340137 0.940376i \(-0.389527\pi\)
0.340137 + 0.940376i \(0.389527\pi\)
\(602\) 0.0213234 0.000869076 0
\(603\) 72.5024 2.95252
\(604\) −28.0077 −1.13962
\(605\) 4.51719 0.183650
\(606\) 4.32176 0.175559
\(607\) 3.69644 0.150034 0.0750170 0.997182i \(-0.476099\pi\)
0.0750170 + 0.997182i \(0.476099\pi\)
\(608\) −4.51030 −0.182917
\(609\) 0.0572890 0.00232147
\(610\) 10.5690 0.427926
\(611\) 4.99156 0.201937
\(612\) −106.066 −4.28748
\(613\) −13.8680 −0.560123 −0.280062 0.959982i \(-0.590355\pi\)
−0.280062 + 0.959982i \(0.590355\pi\)
\(614\) −13.8387 −0.558485
\(615\) −5.66856 −0.228578
\(616\) −0.0274048 −0.00110417
\(617\) −36.0640 −1.45188 −0.725941 0.687757i \(-0.758596\pi\)
−0.725941 + 0.687757i \(0.758596\pi\)
\(618\) −11.4895 −0.462177
\(619\) −21.5245 −0.865142 −0.432571 0.901600i \(-0.642394\pi\)
−0.432571 + 0.901600i \(0.642394\pi\)
\(620\) 22.8569 0.917955
\(621\) −21.4087 −0.859103
\(622\) −74.7237 −2.99615
\(623\) −0.0176942 −0.000708904 0
\(624\) 8.21856 0.329006
\(625\) 15.1960 0.607841
\(626\) 5.09959 0.203821
\(627\) −12.9014 −0.515233
\(628\) 61.5302 2.45532
\(629\) 8.69079 0.346525
\(630\) 0.0276669 0.00110228
\(631\) −21.9135 −0.872365 −0.436182 0.899858i \(-0.643670\pi\)
−0.436182 + 0.899858i \(0.643670\pi\)
\(632\) 0.692748 0.0275560
\(633\) 22.3279 0.887455
\(634\) 2.33180 0.0926074
\(635\) 0.389443 0.0154546
\(636\) 109.182 4.32935
\(637\) 19.2395 0.762297
\(638\) 84.5488 3.34732
\(639\) 74.5474 2.94905
\(640\) 16.4588 0.650591
\(641\) −2.31263 −0.0913434 −0.0456717 0.998957i \(-0.514543\pi\)
−0.0456717 + 0.998957i \(0.514543\pi\)
\(642\) 33.1917 1.30997
\(643\) −43.2236 −1.70457 −0.852287 0.523075i \(-0.824785\pi\)
−0.852287 + 0.523075i \(0.824785\pi\)
\(644\) −0.0113394 −0.000446833 0
\(645\) −11.9401 −0.470142
\(646\) −10.1156 −0.397993
\(647\) −16.5179 −0.649385 −0.324693 0.945820i \(-0.605261\pi\)
−0.324693 + 0.945820i \(0.605261\pi\)
\(648\) −67.8918 −2.66704
\(649\) −6.72951 −0.264156
\(650\) −27.6554 −1.08474
\(651\) 0.0515048 0.00201863
\(652\) 15.5504 0.609001
\(653\) 26.9470 1.05452 0.527258 0.849705i \(-0.323220\pi\)
0.527258 + 0.849705i \(0.323220\pi\)
\(654\) −12.0510 −0.471231
\(655\) 7.67798 0.300004
\(656\) 2.02526 0.0790732
\(657\) −7.05899 −0.275397
\(658\) −0.00853561 −0.000332753 0
\(659\) −14.1584 −0.551532 −0.275766 0.961225i \(-0.588932\pi\)
−0.275766 + 0.961225i \(0.588932\pi\)
\(660\) 36.6990 1.42851
\(661\) −46.0427 −1.79085 −0.895426 0.445210i \(-0.853129\pi\)
−0.895426 + 0.445210i \(0.853129\pi\)
\(662\) 3.27956 0.127464
\(663\) −37.9176 −1.47260
\(664\) 17.9333 0.695947
\(665\) 0.00166804 6.46840e−5 0
\(666\) 33.2286 1.28758
\(667\) 14.6283 0.566411
\(668\) 33.7446 1.30562
\(669\) 18.3544 0.709622
\(670\) −19.6690 −0.759881
\(671\) 22.2195 0.857773
\(672\) 0.0289103 0.00111524
\(673\) 28.3368 1.09230 0.546151 0.837687i \(-0.316092\pi\)
0.546151 + 0.837687i \(0.316092\pi\)
\(674\) 12.0698 0.464912
\(675\) 56.4435 2.17251
\(676\) −18.7184 −0.719940
\(677\) −11.3945 −0.437924 −0.218962 0.975733i \(-0.570267\pi\)
−0.218962 + 0.975733i \(0.570267\pi\)
\(678\) −20.8949 −0.802465
\(679\) 0.0155340 0.000596139 0
\(680\) 12.0319 0.461401
\(681\) −17.2897 −0.662544
\(682\) 76.0124 2.91066
\(683\) −24.1339 −0.923460 −0.461730 0.887021i \(-0.652771\pi\)
−0.461730 + 0.887021i \(0.652771\pi\)
\(684\) −24.4499 −0.934864
\(685\) −1.93433 −0.0739069
\(686\) −0.0657994 −0.00251223
\(687\) −69.0267 −2.63353
\(688\) 4.26597 0.162638
\(689\) 27.4530 1.04588
\(690\) 10.0440 0.382370
\(691\) −22.7535 −0.865585 −0.432793 0.901494i \(-0.642472\pi\)
−0.432793 + 0.901494i \(0.642472\pi\)
\(692\) 80.9664 3.07788
\(693\) 0.0581649 0.00220950
\(694\) 5.89853 0.223905
\(695\) 8.80379 0.333947
\(696\) 95.2566 3.61069
\(697\) −9.34386 −0.353924
\(698\) 3.80266 0.143933
\(699\) 32.9595 1.24664
\(700\) 0.0298959 0.00112996
\(701\) 24.6133 0.929630 0.464815 0.885408i \(-0.346121\pi\)
0.464815 + 0.885408i \(0.346121\pi\)
\(702\) −83.8314 −3.16401
\(703\) 2.00336 0.0755580
\(704\) 50.2959 1.89560
\(705\) 4.77955 0.180008
\(706\) −12.5312 −0.471619
\(707\) −0.00117471 −4.41795e−5 0
\(708\) −18.1320 −0.681444
\(709\) 21.2668 0.798692 0.399346 0.916800i \(-0.369237\pi\)
0.399346 + 0.916800i \(0.369237\pi\)
\(710\) −20.2238 −0.758987
\(711\) −1.47031 −0.0551411
\(712\) −29.4209 −1.10259
\(713\) 13.1514 0.492523
\(714\) 0.0648394 0.00242655
\(715\) 9.22770 0.345096
\(716\) 42.6960 1.59562
\(717\) −12.8088 −0.478352
\(718\) −77.3434 −2.88643
\(719\) 0.878476 0.0327616 0.0163808 0.999866i \(-0.494786\pi\)
0.0163808 + 0.999866i \(0.494786\pi\)
\(720\) 5.53506 0.206280
\(721\) 0.00312301 0.000116307 0
\(722\) −2.33180 −0.0867804
\(723\) 96.5266 3.58986
\(724\) 5.67766 0.211009
\(725\) −38.5671 −1.43235
\(726\) 40.4761 1.50221
\(727\) −8.41128 −0.311957 −0.155979 0.987760i \(-0.549853\pi\)
−0.155979 + 0.987760i \(0.549853\pi\)
\(728\) −0.0185664 −0.000688118 0
\(729\) 19.3047 0.714988
\(730\) 1.91502 0.0708780
\(731\) −19.6817 −0.727954
\(732\) 59.8683 2.21280
\(733\) −10.4213 −0.384918 −0.192459 0.981305i \(-0.561646\pi\)
−0.192459 + 0.981305i \(0.561646\pi\)
\(734\) −16.7088 −0.616733
\(735\) 18.4223 0.679518
\(736\) 7.38204 0.272105
\(737\) −41.3507 −1.52317
\(738\) −35.7256 −1.31508
\(739\) −34.8685 −1.28266 −0.641329 0.767266i \(-0.721617\pi\)
−0.641329 + 0.767266i \(0.721617\pi\)
\(740\) −5.69869 −0.209488
\(741\) −8.74057 −0.321093
\(742\) −0.0469449 −0.00172340
\(743\) −28.4787 −1.04478 −0.522392 0.852706i \(-0.674960\pi\)
−0.522392 + 0.852706i \(0.674960\pi\)
\(744\) 85.6391 3.13968
\(745\) 15.3885 0.563791
\(746\) −14.4348 −0.528494
\(747\) −38.0623 −1.39263
\(748\) 60.4934 2.21186
\(749\) −0.00902193 −0.000329654 0
\(750\) −57.1645 −2.08735
\(751\) 17.2874 0.630828 0.315414 0.948954i \(-0.397857\pi\)
0.315414 + 0.948954i \(0.397857\pi\)
\(752\) −1.70764 −0.0622712
\(753\) −56.1786 −2.04726
\(754\) 57.2809 2.08605
\(755\) −6.74323 −0.245411
\(756\) 0.0906228 0.00329592
\(757\) −25.4403 −0.924643 −0.462322 0.886712i \(-0.652983\pi\)
−0.462322 + 0.886712i \(0.652983\pi\)
\(758\) −6.35295 −0.230749
\(759\) 21.1158 0.766456
\(760\) 2.77352 0.100606
\(761\) −15.0480 −0.545490 −0.272745 0.962086i \(-0.587932\pi\)
−0.272745 + 0.962086i \(0.587932\pi\)
\(762\) 3.48959 0.126414
\(763\) 0.00327562 0.000118585 0
\(764\) −65.1990 −2.35882
\(765\) −25.5369 −0.923288
\(766\) 27.7128 1.00131
\(767\) −4.55917 −0.164622
\(768\) 68.6265 2.47635
\(769\) 21.5857 0.778401 0.389201 0.921153i \(-0.372751\pi\)
0.389201 + 0.921153i \(0.372751\pi\)
\(770\) −0.0157794 −0.000568651 0
\(771\) 17.5765 0.633001
\(772\) −2.73073 −0.0982810
\(773\) −41.4298 −1.49013 −0.745063 0.666994i \(-0.767581\pi\)
−0.745063 + 0.666994i \(0.767581\pi\)
\(774\) −75.2515 −2.70486
\(775\) −34.6732 −1.24550
\(776\) 25.8290 0.927206
\(777\) −0.0128412 −0.000460676 0
\(778\) 1.06605 0.0382196
\(779\) −2.15390 −0.0771715
\(780\) 24.8632 0.890245
\(781\) −42.5171 −1.52138
\(782\) 16.5563 0.592051
\(783\) −116.908 −4.17795
\(784\) −6.58193 −0.235069
\(785\) 14.8142 0.528742
\(786\) 68.7983 2.45395
\(787\) −6.40974 −0.228482 −0.114241 0.993453i \(-0.536444\pi\)
−0.114241 + 0.993453i \(0.536444\pi\)
\(788\) −30.9184 −1.10142
\(789\) 36.4796 1.29871
\(790\) 0.398879 0.0141915
\(791\) 0.00567951 0.000201940 0
\(792\) 96.7130 3.43655
\(793\) 15.0534 0.534564
\(794\) −19.8156 −0.703230
\(795\) 26.2870 0.932304
\(796\) −83.3828 −2.95542
\(797\) −23.0604 −0.816841 −0.408421 0.912794i \(-0.633920\pi\)
−0.408421 + 0.912794i \(0.633920\pi\)
\(798\) 0.0149464 0.000529098 0
\(799\) 7.87846 0.278720
\(800\) −19.4625 −0.688104
\(801\) 62.4440 2.20635
\(802\) −44.5786 −1.57412
\(803\) 4.02599 0.142074
\(804\) −111.416 −3.92933
\(805\) −0.00273010 −9.62233e−5 0
\(806\) 51.4976 1.81393
\(807\) −78.2374 −2.75409
\(808\) −1.95324 −0.0687146
\(809\) 26.7526 0.940572 0.470286 0.882514i \(-0.344151\pi\)
0.470286 + 0.882514i \(0.344151\pi\)
\(810\) −39.0916 −1.37354
\(811\) −50.8350 −1.78506 −0.892530 0.450989i \(-0.851071\pi\)
−0.892530 + 0.450989i \(0.851071\pi\)
\(812\) −0.0619214 −0.00217302
\(813\) −26.3759 −0.925044
\(814\) −18.9514 −0.664248
\(815\) 3.74397 0.131145
\(816\) 12.9718 0.454104
\(817\) −4.53692 −0.158727
\(818\) 13.8918 0.485715
\(819\) 0.0394061 0.00137696
\(820\) 6.12692 0.213961
\(821\) −12.0830 −0.421699 −0.210850 0.977519i \(-0.567623\pi\)
−0.210850 + 0.977519i \(0.567623\pi\)
\(822\) −17.3325 −0.604540
\(823\) −6.46816 −0.225466 −0.112733 0.993625i \(-0.535960\pi\)
−0.112733 + 0.993625i \(0.535960\pi\)
\(824\) 5.19274 0.180898
\(825\) −55.6713 −1.93823
\(826\) 0.00779622 0.000271265 0
\(827\) 38.1714 1.32735 0.663675 0.748021i \(-0.268996\pi\)
0.663675 + 0.748021i \(0.268996\pi\)
\(828\) 40.0173 1.39070
\(829\) 20.4881 0.711581 0.355790 0.934566i \(-0.384212\pi\)
0.355790 + 0.934566i \(0.384212\pi\)
\(830\) 10.3258 0.358415
\(831\) 58.6553 2.03473
\(832\) 34.0750 1.18134
\(833\) 30.3668 1.05215
\(834\) 78.8861 2.73160
\(835\) 8.12445 0.281158
\(836\) 13.9446 0.482285
\(837\) −105.104 −3.63294
\(838\) −41.6804 −1.43983
\(839\) −47.0709 −1.62507 −0.812534 0.582914i \(-0.801912\pi\)
−0.812534 + 0.582914i \(0.801912\pi\)
\(840\) −0.0177779 −0.000613394 0
\(841\) 50.8816 1.75454
\(842\) −50.5214 −1.74108
\(843\) 101.558 3.49786
\(844\) −24.1334 −0.830704
\(845\) −4.50671 −0.155036
\(846\) 30.1227 1.03564
\(847\) −0.0110019 −0.000378031 0
\(848\) −9.39182 −0.322516
\(849\) −46.6064 −1.59953
\(850\) −43.6501 −1.49719
\(851\) −3.27891 −0.112400
\(852\) −114.558 −3.92470
\(853\) −11.8014 −0.404073 −0.202036 0.979378i \(-0.564756\pi\)
−0.202036 + 0.979378i \(0.564756\pi\)
\(854\) −0.0257415 −0.000880857 0
\(855\) −5.88663 −0.201318
\(856\) −15.0011 −0.512728
\(857\) −28.6238 −0.977769 −0.488885 0.872348i \(-0.662596\pi\)
−0.488885 + 0.872348i \(0.662596\pi\)
\(858\) 82.6845 2.82280
\(859\) −37.6687 −1.28524 −0.642619 0.766186i \(-0.722152\pi\)
−0.642619 + 0.766186i \(0.722152\pi\)
\(860\) 12.9056 0.440078
\(861\) 0.0138062 0.000470513 0
\(862\) 59.8117 2.03719
\(863\) −27.8120 −0.946732 −0.473366 0.880866i \(-0.656961\pi\)
−0.473366 + 0.880866i \(0.656961\pi\)
\(864\) −58.9964 −2.00710
\(865\) 19.4937 0.662806
\(866\) −12.5432 −0.426234
\(867\) −5.78542 −0.196483
\(868\) −0.0556695 −0.00188955
\(869\) 0.838573 0.0284466
\(870\) 54.8480 1.85952
\(871\) −28.0147 −0.949240
\(872\) 5.44650 0.184442
\(873\) −54.8204 −1.85539
\(874\) 3.81647 0.129094
\(875\) 0.0155380 0.000525282 0
\(876\) 10.8477 0.366509
\(877\) −19.5619 −0.660557 −0.330278 0.943884i \(-0.607143\pi\)
−0.330278 + 0.943884i \(0.607143\pi\)
\(878\) −62.0553 −2.09427
\(879\) −6.75258 −0.227759
\(880\) −3.15684 −0.106417
\(881\) 38.5665 1.29934 0.649669 0.760217i \(-0.274907\pi\)
0.649669 + 0.760217i \(0.274907\pi\)
\(882\) 116.105 3.90946
\(883\) −47.2299 −1.58941 −0.794706 0.606995i \(-0.792375\pi\)
−0.794706 + 0.606995i \(0.792375\pi\)
\(884\) 40.9837 1.37843
\(885\) −4.36553 −0.146746
\(886\) −18.1435 −0.609544
\(887\) −35.5561 −1.19386 −0.596928 0.802295i \(-0.703612\pi\)
−0.596928 + 0.802295i \(0.703612\pi\)
\(888\) −21.3516 −0.716512
\(889\) −0.000948514 0 −3.18121e−5 0
\(890\) −16.9403 −0.567840
\(891\) −82.1832 −2.75324
\(892\) −19.8385 −0.664243
\(893\) 1.81610 0.0607735
\(894\) 137.888 4.61167
\(895\) 10.2796 0.343610
\(896\) −0.0400866 −0.00133920
\(897\) 14.3058 0.477655
\(898\) 15.9836 0.533381
\(899\) 71.8164 2.39521
\(900\) −105.504 −3.51681
\(901\) 43.3306 1.44355
\(902\) 20.3756 0.678432
\(903\) 0.0290810 0.000967755 0
\(904\) 9.44355 0.314088
\(905\) 1.36697 0.0454397
\(906\) −60.4225 −2.00740
\(907\) −7.90809 −0.262584 −0.131292 0.991344i \(-0.541913\pi\)
−0.131292 + 0.991344i \(0.541913\pi\)
\(908\) 18.6878 0.620176
\(909\) 4.14562 0.137502
\(910\) −0.0106904 −0.000354383 0
\(911\) −18.5754 −0.615430 −0.307715 0.951479i \(-0.599564\pi\)
−0.307715 + 0.951479i \(0.599564\pi\)
\(912\) 2.99019 0.0990152
\(913\) 21.7083 0.718439
\(914\) 88.1208 2.91478
\(915\) 14.4141 0.476515
\(916\) 74.6082 2.46513
\(917\) −0.0187003 −0.000617537 0
\(918\) −132.316 −4.36707
\(919\) −56.8714 −1.87601 −0.938007 0.346616i \(-0.887331\pi\)
−0.938007 + 0.346616i \(0.887331\pi\)
\(920\) −4.53944 −0.149661
\(921\) −18.8733 −0.621898
\(922\) 95.7153 3.15222
\(923\) −28.8049 −0.948123
\(924\) −0.0893830 −0.00294048
\(925\) 8.64475 0.284238
\(926\) −54.8763 −1.80335
\(927\) −11.0213 −0.361986
\(928\) 40.3115 1.32329
\(929\) 37.4640 1.22915 0.614576 0.788857i \(-0.289327\pi\)
0.614576 + 0.788857i \(0.289327\pi\)
\(930\) 49.3103 1.61695
\(931\) 7.00000 0.229416
\(932\) −35.6247 −1.16692
\(933\) −101.909 −3.33634
\(934\) −7.46814 −0.244365
\(935\) 14.5646 0.476313
\(936\) 65.5221 2.14166
\(937\) 30.3303 0.990849 0.495424 0.868651i \(-0.335013\pi\)
0.495424 + 0.868651i \(0.335013\pi\)
\(938\) 0.0479053 0.00156416
\(939\) 6.95487 0.226964
\(940\) −5.16603 −0.168497
\(941\) 14.5932 0.475723 0.237862 0.971299i \(-0.423553\pi\)
0.237862 + 0.971299i \(0.423553\pi\)
\(942\) 132.742 4.32497
\(943\) 3.52530 0.114800
\(944\) 1.55972 0.0507644
\(945\) 0.0218186 0.000709760 0
\(946\) 42.9186 1.39540
\(947\) 54.6702 1.77654 0.888271 0.459320i \(-0.151907\pi\)
0.888271 + 0.459320i \(0.151907\pi\)
\(948\) 2.25946 0.0733838
\(949\) 2.72757 0.0885406
\(950\) −10.0620 −0.326454
\(951\) 3.18012 0.103122
\(952\) −0.0293044 −0.000949762 0
\(953\) −1.81395 −0.0587597 −0.0293799 0.999568i \(-0.509353\pi\)
−0.0293799 + 0.999568i \(0.509353\pi\)
\(954\) 165.671 5.36381
\(955\) −15.6975 −0.507960
\(956\) 13.8445 0.447762
\(957\) 115.308 3.72739
\(958\) −49.1513 −1.58801
\(959\) 0.00471119 0.000152132 0
\(960\) 32.6277 1.05305
\(961\) 33.5655 1.08276
\(962\) −12.8394 −0.413959
\(963\) 31.8390 1.02600
\(964\) −104.332 −3.36030
\(965\) −0.657458 −0.0211643
\(966\) −0.0244630 −0.000787083 0
\(967\) −45.3912 −1.45968 −0.729841 0.683617i \(-0.760406\pi\)
−0.729841 + 0.683617i \(0.760406\pi\)
\(968\) −18.2933 −0.587970
\(969\) −13.7957 −0.443183
\(970\) 14.8721 0.477515
\(971\) 34.0361 1.09227 0.546135 0.837697i \(-0.316098\pi\)
0.546135 + 0.837697i \(0.316098\pi\)
\(972\) −86.5528 −2.77618
\(973\) −0.0214422 −0.000687407 0
\(974\) 65.0378 2.08394
\(975\) −37.7167 −1.20790
\(976\) −5.14986 −0.164843
\(977\) 17.2891 0.553126 0.276563 0.960996i \(-0.410804\pi\)
0.276563 + 0.960996i \(0.410804\pi\)
\(978\) 33.5477 1.07274
\(979\) −35.6140 −1.13823
\(980\) −19.9120 −0.636065
\(981\) −11.5598 −0.369078
\(982\) −4.53175 −0.144614
\(983\) −28.9745 −0.924142 −0.462071 0.886843i \(-0.652893\pi\)
−0.462071 + 0.886843i \(0.652893\pi\)
\(984\) 22.9561 0.731812
\(985\) −7.44402 −0.237186
\(986\) 90.4097 2.87923
\(987\) −0.0116409 −0.000370535 0
\(988\) 9.44734 0.300560
\(989\) 7.42562 0.236121
\(990\) 55.6866 1.76984
\(991\) 37.3319 1.18589 0.592943 0.805244i \(-0.297966\pi\)
0.592943 + 0.805244i \(0.297966\pi\)
\(992\) 36.2414 1.15067
\(993\) 4.47269 0.141937
\(994\) 0.0492565 0.00156232
\(995\) −20.0755 −0.636436
\(996\) 58.4910 1.85336
\(997\) 10.7772 0.341316 0.170658 0.985330i \(-0.445411\pi\)
0.170658 + 0.985330i \(0.445411\pi\)
\(998\) 48.2431 1.52711
\(999\) 26.2047 0.829079
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 \(a_p\))