Properties

Label 8015.2.a.l.1.53
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

Related objects

Downloads

Learn more about

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 1.53
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.11453 q^{2} -2.77399 q^{3} +2.47123 q^{4} -1.00000 q^{5} -5.86568 q^{6} -1.00000 q^{7} +0.996433 q^{8} +4.69501 q^{9} +O(q^{10})\) \(q+2.11453 q^{2} -2.77399 q^{3} +2.47123 q^{4} -1.00000 q^{5} -5.86568 q^{6} -1.00000 q^{7} +0.996433 q^{8} +4.69501 q^{9} -2.11453 q^{10} +4.53639 q^{11} -6.85517 q^{12} +5.00491 q^{13} -2.11453 q^{14} +2.77399 q^{15} -2.83548 q^{16} +6.37048 q^{17} +9.92773 q^{18} +1.52323 q^{19} -2.47123 q^{20} +2.77399 q^{21} +9.59233 q^{22} -2.04398 q^{23} -2.76409 q^{24} +1.00000 q^{25} +10.5830 q^{26} -4.70193 q^{27} -2.47123 q^{28} -9.52762 q^{29} +5.86568 q^{30} -4.49195 q^{31} -7.98856 q^{32} -12.5839 q^{33} +13.4706 q^{34} +1.00000 q^{35} +11.6024 q^{36} +2.04175 q^{37} +3.22091 q^{38} -13.8836 q^{39} -0.996433 q^{40} +6.84673 q^{41} +5.86568 q^{42} -3.38647 q^{43} +11.2105 q^{44} -4.69501 q^{45} -4.32206 q^{46} -5.40079 q^{47} +7.86558 q^{48} +1.00000 q^{49} +2.11453 q^{50} -17.6716 q^{51} +12.3683 q^{52} +11.1941 q^{53} -9.94236 q^{54} -4.53639 q^{55} -0.996433 q^{56} -4.22542 q^{57} -20.1464 q^{58} +7.44363 q^{59} +6.85517 q^{60} +13.0216 q^{61} -9.49836 q^{62} -4.69501 q^{63} -11.2211 q^{64} -5.00491 q^{65} -26.6090 q^{66} -5.56782 q^{67} +15.7429 q^{68} +5.66999 q^{69} +2.11453 q^{70} -4.39289 q^{71} +4.67826 q^{72} +8.71633 q^{73} +4.31735 q^{74} -2.77399 q^{75} +3.76425 q^{76} -4.53639 q^{77} -29.3572 q^{78} -10.9171 q^{79} +2.83548 q^{80} -1.04193 q^{81} +14.4776 q^{82} +2.08396 q^{83} +6.85517 q^{84} -6.37048 q^{85} -7.16079 q^{86} +26.4295 q^{87} +4.52021 q^{88} -1.27717 q^{89} -9.92773 q^{90} -5.00491 q^{91} -5.05116 q^{92} +12.4606 q^{93} -11.4201 q^{94} -1.52323 q^{95} +22.1602 q^{96} -9.32565 q^{97} +2.11453 q^{98} +21.2984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.11453 1.49520 0.747599 0.664151i \(-0.231207\pi\)
0.747599 + 0.664151i \(0.231207\pi\)
\(3\) −2.77399 −1.60156 −0.800781 0.598957i \(-0.795582\pi\)
−0.800781 + 0.598957i \(0.795582\pi\)
\(4\) 2.47123 1.23562
\(5\) −1.00000 −0.447214
\(6\) −5.86568 −2.39465
\(7\) −1.00000 −0.377964
\(8\) 0.996433 0.352292
\(9\) 4.69501 1.56500
\(10\) −2.11453 −0.668673
\(11\) 4.53639 1.36777 0.683887 0.729588i \(-0.260288\pi\)
0.683887 + 0.729588i \(0.260288\pi\)
\(12\) −6.85517 −1.97892
\(13\) 5.00491 1.38811 0.694056 0.719921i \(-0.255822\pi\)
0.694056 + 0.719921i \(0.255822\pi\)
\(14\) −2.11453 −0.565132
\(15\) 2.77399 0.716240
\(16\) −2.83548 −0.708869
\(17\) 6.37048 1.54507 0.772534 0.634974i \(-0.218989\pi\)
0.772534 + 0.634974i \(0.218989\pi\)
\(18\) 9.92773 2.33999
\(19\) 1.52323 0.349453 0.174726 0.984617i \(-0.444096\pi\)
0.174726 + 0.984617i \(0.444096\pi\)
\(20\) −2.47123 −0.552584
\(21\) 2.77399 0.605334
\(22\) 9.59233 2.04509
\(23\) −2.04398 −0.426200 −0.213100 0.977030i \(-0.568356\pi\)
−0.213100 + 0.977030i \(0.568356\pi\)
\(24\) −2.76409 −0.564218
\(25\) 1.00000 0.200000
\(26\) 10.5830 2.07550
\(27\) −4.70193 −0.904886
\(28\) −2.47123 −0.467019
\(29\) −9.52762 −1.76924 −0.884618 0.466317i \(-0.845581\pi\)
−0.884618 + 0.466317i \(0.845581\pi\)
\(30\) 5.86568 1.07092
\(31\) −4.49195 −0.806778 −0.403389 0.915029i \(-0.632168\pi\)
−0.403389 + 0.915029i \(0.632168\pi\)
\(32\) −7.98856 −1.41219
\(33\) −12.5839 −2.19057
\(34\) 13.4706 2.31018
\(35\) 1.00000 0.169031
\(36\) 11.6024 1.93374
\(37\) 2.04175 0.335662 0.167831 0.985816i \(-0.446324\pi\)
0.167831 + 0.985816i \(0.446324\pi\)
\(38\) 3.22091 0.522501
\(39\) −13.8836 −2.22315
\(40\) −0.996433 −0.157550
\(41\) 6.84673 1.06928 0.534640 0.845080i \(-0.320447\pi\)
0.534640 + 0.845080i \(0.320447\pi\)
\(42\) 5.86568 0.905093
\(43\) −3.38647 −0.516432 −0.258216 0.966087i \(-0.583135\pi\)
−0.258216 + 0.966087i \(0.583135\pi\)
\(44\) 11.2105 1.69004
\(45\) −4.69501 −0.699890
\(46\) −4.32206 −0.637253
\(47\) −5.40079 −0.787787 −0.393893 0.919156i \(-0.628872\pi\)
−0.393893 + 0.919156i \(0.628872\pi\)
\(48\) 7.86558 1.13530
\(49\) 1.00000 0.142857
\(50\) 2.11453 0.299040
\(51\) −17.6716 −2.47452
\(52\) 12.3683 1.71517
\(53\) 11.1941 1.53763 0.768815 0.639471i \(-0.220847\pi\)
0.768815 + 0.639471i \(0.220847\pi\)
\(54\) −9.94236 −1.35298
\(55\) −4.53639 −0.611687
\(56\) −0.996433 −0.133154
\(57\) −4.22542 −0.559671
\(58\) −20.1464 −2.64536
\(59\) 7.44363 0.969078 0.484539 0.874770i \(-0.338987\pi\)
0.484539 + 0.874770i \(0.338987\pi\)
\(60\) 6.85517 0.884998
\(61\) 13.0216 1.66724 0.833622 0.552335i \(-0.186263\pi\)
0.833622 + 0.552335i \(0.186263\pi\)
\(62\) −9.49836 −1.20629
\(63\) −4.69501 −0.591515
\(64\) −11.2211 −1.40264
\(65\) −5.00491 −0.620783
\(66\) −26.6090 −3.27534
\(67\) −5.56782 −0.680218 −0.340109 0.940386i \(-0.610464\pi\)
−0.340109 + 0.940386i \(0.610464\pi\)
\(68\) 15.7429 1.90911
\(69\) 5.66999 0.682586
\(70\) 2.11453 0.252735
\(71\) −4.39289 −0.521340 −0.260670 0.965428i \(-0.583943\pi\)
−0.260670 + 0.965428i \(0.583943\pi\)
\(72\) 4.67826 0.551338
\(73\) 8.71633 1.02017 0.510085 0.860124i \(-0.329614\pi\)
0.510085 + 0.860124i \(0.329614\pi\)
\(74\) 4.31735 0.501881
\(75\) −2.77399 −0.320312
\(76\) 3.76425 0.431790
\(77\) −4.53639 −0.516970
\(78\) −29.3572 −3.32405
\(79\) −10.9171 −1.22828 −0.614138 0.789199i \(-0.710496\pi\)
−0.614138 + 0.789199i \(0.710496\pi\)
\(80\) 2.83548 0.317016
\(81\) −1.04193 −0.115771
\(82\) 14.4776 1.59879
\(83\) 2.08396 0.228744 0.114372 0.993438i \(-0.463514\pi\)
0.114372 + 0.993438i \(0.463514\pi\)
\(84\) 6.85517 0.747960
\(85\) −6.37048 −0.690975
\(86\) −7.16079 −0.772168
\(87\) 26.4295 2.83354
\(88\) 4.52021 0.481856
\(89\) −1.27717 −0.135380 −0.0676898 0.997706i \(-0.521563\pi\)
−0.0676898 + 0.997706i \(0.521563\pi\)
\(90\) −9.92773 −1.04647
\(91\) −5.00491 −0.524657
\(92\) −5.05116 −0.526620
\(93\) 12.4606 1.29211
\(94\) −11.4201 −1.17790
\(95\) −1.52323 −0.156280
\(96\) 22.1602 2.26171
\(97\) −9.32565 −0.946876 −0.473438 0.880827i \(-0.656987\pi\)
−0.473438 + 0.880827i \(0.656987\pi\)
\(98\) 2.11453 0.213600
\(99\) 21.2984 2.14057
\(100\) 2.47123 0.247123
\(101\) −4.40127 −0.437943 −0.218972 0.975731i \(-0.570270\pi\)
−0.218972 + 0.975731i \(0.570270\pi\)
\(102\) −37.3671 −3.69990
\(103\) −11.1776 −1.10137 −0.550683 0.834715i \(-0.685633\pi\)
−0.550683 + 0.834715i \(0.685633\pi\)
\(104\) 4.98706 0.489021
\(105\) −2.77399 −0.270713
\(106\) 23.6703 2.29906
\(107\) −10.8833 −1.05213 −0.526065 0.850444i \(-0.676333\pi\)
−0.526065 + 0.850444i \(0.676333\pi\)
\(108\) −11.6195 −1.11809
\(109\) 2.98412 0.285827 0.142914 0.989735i \(-0.454353\pi\)
0.142914 + 0.989735i \(0.454353\pi\)
\(110\) −9.59233 −0.914593
\(111\) −5.66380 −0.537584
\(112\) 2.83548 0.267927
\(113\) 16.7466 1.57539 0.787693 0.616068i \(-0.211275\pi\)
0.787693 + 0.616068i \(0.211275\pi\)
\(114\) −8.93477 −0.836818
\(115\) 2.04398 0.190602
\(116\) −23.5450 −2.18610
\(117\) 23.4981 2.17240
\(118\) 15.7398 1.44896
\(119\) −6.37048 −0.583981
\(120\) 2.76409 0.252326
\(121\) 9.57884 0.870804
\(122\) 27.5345 2.49286
\(123\) −18.9928 −1.71252
\(124\) −11.1006 −0.996868
\(125\) −1.00000 −0.0894427
\(126\) −9.92773 −0.884432
\(127\) 3.94166 0.349766 0.174883 0.984589i \(-0.444045\pi\)
0.174883 + 0.984589i \(0.444045\pi\)
\(128\) −7.75019 −0.685027
\(129\) 9.39403 0.827098
\(130\) −10.5830 −0.928193
\(131\) 19.8568 1.73490 0.867449 0.497526i \(-0.165758\pi\)
0.867449 + 0.497526i \(0.165758\pi\)
\(132\) −31.0977 −2.70671
\(133\) −1.52323 −0.132081
\(134\) −11.7733 −1.01706
\(135\) 4.70193 0.404677
\(136\) 6.34775 0.544315
\(137\) 3.33683 0.285085 0.142542 0.989789i \(-0.454472\pi\)
0.142542 + 0.989789i \(0.454472\pi\)
\(138\) 11.9893 1.02060
\(139\) 16.6919 1.41579 0.707895 0.706318i \(-0.249645\pi\)
0.707895 + 0.706318i \(0.249645\pi\)
\(140\) 2.47123 0.208857
\(141\) 14.9817 1.26169
\(142\) −9.28888 −0.779506
\(143\) 22.7042 1.89862
\(144\) −13.3126 −1.10938
\(145\) 9.52762 0.791226
\(146\) 18.4309 1.52535
\(147\) −2.77399 −0.228795
\(148\) 5.04564 0.414749
\(149\) −1.80328 −0.147731 −0.0738653 0.997268i \(-0.523533\pi\)
−0.0738653 + 0.997268i \(0.523533\pi\)
\(150\) −5.86568 −0.478930
\(151\) −12.2444 −0.996438 −0.498219 0.867051i \(-0.666012\pi\)
−0.498219 + 0.867051i \(0.666012\pi\)
\(152\) 1.51780 0.123110
\(153\) 29.9094 2.41803
\(154\) −9.59233 −0.772972
\(155\) 4.49195 0.360802
\(156\) −34.3095 −2.74696
\(157\) −1.44303 −0.115166 −0.0575832 0.998341i \(-0.518339\pi\)
−0.0575832 + 0.998341i \(0.518339\pi\)
\(158\) −23.0846 −1.83651
\(159\) −31.0523 −2.46261
\(160\) 7.98856 0.631551
\(161\) 2.04398 0.161088
\(162\) −2.20320 −0.173100
\(163\) 17.2617 1.35204 0.676020 0.736884i \(-0.263703\pi\)
0.676020 + 0.736884i \(0.263703\pi\)
\(164\) 16.9199 1.32122
\(165\) 12.5839 0.979655
\(166\) 4.40659 0.342018
\(167\) 2.90141 0.224518 0.112259 0.993679i \(-0.464191\pi\)
0.112259 + 0.993679i \(0.464191\pi\)
\(168\) 2.76409 0.213254
\(169\) 12.0491 0.926856
\(170\) −13.4706 −1.03314
\(171\) 7.15157 0.546895
\(172\) −8.36875 −0.638112
\(173\) 10.0954 0.767539 0.383770 0.923429i \(-0.374626\pi\)
0.383770 + 0.923429i \(0.374626\pi\)
\(174\) 55.8860 4.23670
\(175\) −1.00000 −0.0755929
\(176\) −12.8628 −0.969573
\(177\) −20.6485 −1.55204
\(178\) −2.70061 −0.202419
\(179\) 21.0779 1.57544 0.787719 0.616035i \(-0.211262\pi\)
0.787719 + 0.616035i \(0.211262\pi\)
\(180\) −11.6024 −0.864795
\(181\) −17.1971 −1.27825 −0.639124 0.769104i \(-0.720703\pi\)
−0.639124 + 0.769104i \(0.720703\pi\)
\(182\) −10.5830 −0.784466
\(183\) −36.1217 −2.67020
\(184\) −2.03669 −0.150147
\(185\) −2.04175 −0.150113
\(186\) 26.3483 1.93195
\(187\) 28.8990 2.11330
\(188\) −13.3466 −0.973402
\(189\) 4.70193 0.342015
\(190\) −3.22091 −0.233670
\(191\) −6.36081 −0.460252 −0.230126 0.973161i \(-0.573914\pi\)
−0.230126 + 0.973161i \(0.573914\pi\)
\(192\) 31.1272 2.24641
\(193\) 20.6184 1.48414 0.742071 0.670321i \(-0.233844\pi\)
0.742071 + 0.670321i \(0.233844\pi\)
\(194\) −19.7194 −1.41577
\(195\) 13.8836 0.994222
\(196\) 2.47123 0.176517
\(197\) 1.73117 0.123341 0.0616704 0.998097i \(-0.480357\pi\)
0.0616704 + 0.998097i \(0.480357\pi\)
\(198\) 45.0360 3.20057
\(199\) −5.29923 −0.375653 −0.187826 0.982202i \(-0.560144\pi\)
−0.187826 + 0.982202i \(0.560144\pi\)
\(200\) 0.996433 0.0704584
\(201\) 15.4451 1.08941
\(202\) −9.30662 −0.654812
\(203\) 9.52762 0.668708
\(204\) −43.6707 −3.05756
\(205\) −6.84673 −0.478197
\(206\) −23.6354 −1.64676
\(207\) −9.59652 −0.667004
\(208\) −14.1913 −0.983990
\(209\) 6.90997 0.477972
\(210\) −5.86568 −0.404770
\(211\) 22.1566 1.52532 0.762661 0.646799i \(-0.223893\pi\)
0.762661 + 0.646799i \(0.223893\pi\)
\(212\) 27.6633 1.89992
\(213\) 12.1858 0.834958
\(214\) −23.0131 −1.57314
\(215\) 3.38647 0.230955
\(216\) −4.68515 −0.318784
\(217\) 4.49195 0.304933
\(218\) 6.31002 0.427368
\(219\) −24.1790 −1.63386
\(220\) −11.2105 −0.755810
\(221\) 31.8837 2.14473
\(222\) −11.9763 −0.803794
\(223\) 11.9524 0.800394 0.400197 0.916429i \(-0.368942\pi\)
0.400197 + 0.916429i \(0.368942\pi\)
\(224\) 7.98856 0.533758
\(225\) 4.69501 0.313000
\(226\) 35.4111 2.35551
\(227\) −16.0218 −1.06340 −0.531701 0.846932i \(-0.678447\pi\)
−0.531701 + 0.846932i \(0.678447\pi\)
\(228\) −10.4420 −0.691538
\(229\) 1.00000 0.0660819
\(230\) 4.32206 0.284988
\(231\) 12.5839 0.827959
\(232\) −9.49364 −0.623288
\(233\) −10.7925 −0.707041 −0.353521 0.935427i \(-0.615016\pi\)
−0.353521 + 0.935427i \(0.615016\pi\)
\(234\) 49.6874 3.24817
\(235\) 5.40079 0.352309
\(236\) 18.3949 1.19741
\(237\) 30.2840 1.96716
\(238\) −13.4706 −0.873166
\(239\) −3.07503 −0.198907 −0.0994535 0.995042i \(-0.531709\pi\)
−0.0994535 + 0.995042i \(0.531709\pi\)
\(240\) −7.86558 −0.507721
\(241\) 12.8381 0.826972 0.413486 0.910511i \(-0.364311\pi\)
0.413486 + 0.910511i \(0.364311\pi\)
\(242\) 20.2547 1.30202
\(243\) 16.9961 1.09030
\(244\) 32.1794 2.06007
\(245\) −1.00000 −0.0638877
\(246\) −40.1607 −2.56055
\(247\) 7.62363 0.485080
\(248\) −4.47593 −0.284222
\(249\) −5.78087 −0.366348
\(250\) −2.11453 −0.133735
\(251\) 25.8710 1.63296 0.816482 0.577371i \(-0.195922\pi\)
0.816482 + 0.577371i \(0.195922\pi\)
\(252\) −11.6024 −0.730886
\(253\) −9.27231 −0.582945
\(254\) 8.33476 0.522969
\(255\) 17.6716 1.10664
\(256\) 6.05418 0.378386
\(257\) 17.1194 1.06788 0.533938 0.845523i \(-0.320711\pi\)
0.533938 + 0.845523i \(0.320711\pi\)
\(258\) 19.8639 1.23668
\(259\) −2.04175 −0.126868
\(260\) −12.3683 −0.767049
\(261\) −44.7323 −2.76886
\(262\) 41.9878 2.59401
\(263\) 24.2501 1.49533 0.747663 0.664078i \(-0.231176\pi\)
0.747663 + 0.664078i \(0.231176\pi\)
\(264\) −12.5390 −0.771722
\(265\) −11.1941 −0.687649
\(266\) −3.22091 −0.197487
\(267\) 3.54285 0.216819
\(268\) −13.7594 −0.840488
\(269\) −25.8726 −1.57748 −0.788740 0.614727i \(-0.789266\pi\)
−0.788740 + 0.614727i \(0.789266\pi\)
\(270\) 9.94236 0.605073
\(271\) 24.6376 1.49663 0.748315 0.663344i \(-0.230863\pi\)
0.748315 + 0.663344i \(0.230863\pi\)
\(272\) −18.0633 −1.09525
\(273\) 13.8836 0.840271
\(274\) 7.05583 0.426258
\(275\) 4.53639 0.273555
\(276\) 14.0118 0.843414
\(277\) −1.74062 −0.104584 −0.0522918 0.998632i \(-0.516653\pi\)
−0.0522918 + 0.998632i \(0.516653\pi\)
\(278\) 35.2955 2.11689
\(279\) −21.0897 −1.26261
\(280\) 0.996433 0.0595482
\(281\) 16.5133 0.985103 0.492551 0.870283i \(-0.336064\pi\)
0.492551 + 0.870283i \(0.336064\pi\)
\(282\) 31.6793 1.88648
\(283\) 11.2747 0.670211 0.335106 0.942181i \(-0.391228\pi\)
0.335106 + 0.942181i \(0.391228\pi\)
\(284\) −10.8558 −0.644175
\(285\) 4.22542 0.250292
\(286\) 48.0087 2.83882
\(287\) −6.84673 −0.404150
\(288\) −37.5064 −2.21008
\(289\) 23.5830 1.38723
\(290\) 20.1464 1.18304
\(291\) 25.8692 1.51648
\(292\) 21.5401 1.26054
\(293\) −8.81104 −0.514746 −0.257373 0.966312i \(-0.582857\pi\)
−0.257373 + 0.966312i \(0.582857\pi\)
\(294\) −5.86568 −0.342093
\(295\) −7.44363 −0.433385
\(296\) 2.03447 0.118251
\(297\) −21.3298 −1.23768
\(298\) −3.81309 −0.220886
\(299\) −10.2300 −0.591614
\(300\) −6.85517 −0.395783
\(301\) 3.38647 0.195193
\(302\) −25.8912 −1.48987
\(303\) 12.2091 0.701393
\(304\) −4.31908 −0.247717
\(305\) −13.0216 −0.745614
\(306\) 63.2443 3.61544
\(307\) −2.39240 −0.136541 −0.0682707 0.997667i \(-0.521748\pi\)
−0.0682707 + 0.997667i \(0.521748\pi\)
\(308\) −11.2105 −0.638776
\(309\) 31.0066 1.76390
\(310\) 9.49836 0.539470
\(311\) 18.4588 1.04670 0.523350 0.852118i \(-0.324682\pi\)
0.523350 + 0.852118i \(0.324682\pi\)
\(312\) −13.8340 −0.783198
\(313\) 15.3111 0.865435 0.432717 0.901530i \(-0.357555\pi\)
0.432717 + 0.901530i \(0.357555\pi\)
\(314\) −3.05133 −0.172197
\(315\) 4.69501 0.264534
\(316\) −26.9788 −1.51768
\(317\) −5.64871 −0.317263 −0.158632 0.987338i \(-0.550708\pi\)
−0.158632 + 0.987338i \(0.550708\pi\)
\(318\) −65.6611 −3.68209
\(319\) −43.2210 −2.41991
\(320\) 11.2211 0.627278
\(321\) 30.1902 1.68505
\(322\) 4.32206 0.240859
\(323\) 9.70370 0.539928
\(324\) −2.57486 −0.143048
\(325\) 5.00491 0.277622
\(326\) 36.5003 2.02157
\(327\) −8.27792 −0.457770
\(328\) 6.82231 0.376699
\(329\) 5.40079 0.297755
\(330\) 26.6090 1.46478
\(331\) 22.5115 1.23735 0.618673 0.785649i \(-0.287671\pi\)
0.618673 + 0.785649i \(0.287671\pi\)
\(332\) 5.14994 0.282640
\(333\) 9.58604 0.525312
\(334\) 6.13512 0.335699
\(335\) 5.56782 0.304203
\(336\) −7.86558 −0.429103
\(337\) 0.912983 0.0497333 0.0248667 0.999691i \(-0.492084\pi\)
0.0248667 + 0.999691i \(0.492084\pi\)
\(338\) 25.4782 1.38583
\(339\) −46.4548 −2.52308
\(340\) −15.7429 −0.853780
\(341\) −20.3772 −1.10349
\(342\) 15.1222 0.817715
\(343\) −1.00000 −0.0539949
\(344\) −3.37439 −0.181935
\(345\) −5.66999 −0.305262
\(346\) 21.3470 1.14762
\(347\) −34.0698 −1.82896 −0.914481 0.404630i \(-0.867400\pi\)
−0.914481 + 0.404630i \(0.867400\pi\)
\(348\) 65.3134 3.50117
\(349\) −30.3306 −1.62356 −0.811780 0.583964i \(-0.801501\pi\)
−0.811780 + 0.583964i \(0.801501\pi\)
\(350\) −2.11453 −0.113026
\(351\) −23.5327 −1.25608
\(352\) −36.2393 −1.93156
\(353\) −4.99889 −0.266064 −0.133032 0.991112i \(-0.542471\pi\)
−0.133032 + 0.991112i \(0.542471\pi\)
\(354\) −43.6619 −2.32060
\(355\) 4.39289 0.233150
\(356\) −3.15618 −0.167277
\(357\) 17.6716 0.935281
\(358\) 44.5699 2.35559
\(359\) 1.51174 0.0797864 0.0398932 0.999204i \(-0.487298\pi\)
0.0398932 + 0.999204i \(0.487298\pi\)
\(360\) −4.67826 −0.246566
\(361\) −16.6798 −0.877883
\(362\) −36.3637 −1.91123
\(363\) −26.5716 −1.39465
\(364\) −12.3683 −0.648275
\(365\) −8.71633 −0.456234
\(366\) −76.3804 −3.99247
\(367\) 7.87025 0.410824 0.205412 0.978676i \(-0.434147\pi\)
0.205412 + 0.978676i \(0.434147\pi\)
\(368\) 5.79567 0.302120
\(369\) 32.1455 1.67343
\(370\) −4.31735 −0.224448
\(371\) −11.1941 −0.581170
\(372\) 30.7931 1.59655
\(373\) 28.0248 1.45107 0.725534 0.688186i \(-0.241593\pi\)
0.725534 + 0.688186i \(0.241593\pi\)
\(374\) 61.1077 3.15980
\(375\) 2.77399 0.143248
\(376\) −5.38153 −0.277531
\(377\) −47.6849 −2.45590
\(378\) 9.94236 0.511380
\(379\) −25.0989 −1.28925 −0.644623 0.764501i \(-0.722985\pi\)
−0.644623 + 0.764501i \(0.722985\pi\)
\(380\) −3.76425 −0.193102
\(381\) −10.9341 −0.560172
\(382\) −13.4501 −0.688168
\(383\) 36.2805 1.85384 0.926922 0.375253i \(-0.122444\pi\)
0.926922 + 0.375253i \(0.122444\pi\)
\(384\) 21.4989 1.09711
\(385\) 4.53639 0.231196
\(386\) 43.5981 2.21909
\(387\) −15.8995 −0.808217
\(388\) −23.0458 −1.16998
\(389\) 7.06651 0.358286 0.179143 0.983823i \(-0.442667\pi\)
0.179143 + 0.983823i \(0.442667\pi\)
\(390\) 29.3572 1.48656
\(391\) −13.0211 −0.658508
\(392\) 0.996433 0.0503275
\(393\) −55.0825 −2.77855
\(394\) 3.66061 0.184419
\(395\) 10.9171 0.549301
\(396\) 52.6332 2.64492
\(397\) 28.7212 1.44147 0.720737 0.693208i \(-0.243803\pi\)
0.720737 + 0.693208i \(0.243803\pi\)
\(398\) −11.2054 −0.561675
\(399\) 4.22542 0.211536
\(400\) −2.83548 −0.141774
\(401\) −5.33183 −0.266259 −0.133130 0.991099i \(-0.542503\pi\)
−0.133130 + 0.991099i \(0.542503\pi\)
\(402\) 32.6590 1.62888
\(403\) −22.4818 −1.11990
\(404\) −10.8766 −0.541129
\(405\) 1.04193 0.0517742
\(406\) 20.1464 0.999851
\(407\) 9.26219 0.459110
\(408\) −17.6086 −0.871755
\(409\) −16.6103 −0.821324 −0.410662 0.911788i \(-0.634702\pi\)
−0.410662 + 0.911788i \(0.634702\pi\)
\(410\) −14.4776 −0.714999
\(411\) −9.25633 −0.456581
\(412\) −27.6225 −1.36086
\(413\) −7.44363 −0.366277
\(414\) −20.2921 −0.997303
\(415\) −2.08396 −0.102297
\(416\) −39.9820 −1.96028
\(417\) −46.3032 −2.26748
\(418\) 14.6113 0.714663
\(419\) −19.7911 −0.966859 −0.483430 0.875383i \(-0.660609\pi\)
−0.483430 + 0.875383i \(0.660609\pi\)
\(420\) −6.85517 −0.334498
\(421\) −6.46224 −0.314950 −0.157475 0.987523i \(-0.550335\pi\)
−0.157475 + 0.987523i \(0.550335\pi\)
\(422\) 46.8507 2.28066
\(423\) −25.3568 −1.23289
\(424\) 11.1542 0.541695
\(425\) 6.37048 0.309013
\(426\) 25.7672 1.24843
\(427\) −13.0216 −0.630159
\(428\) −26.8952 −1.30003
\(429\) −62.9813 −3.04076
\(430\) 7.16079 0.345324
\(431\) −17.2503 −0.830917 −0.415459 0.909612i \(-0.636379\pi\)
−0.415459 + 0.909612i \(0.636379\pi\)
\(432\) 13.3322 0.641446
\(433\) 24.4221 1.17365 0.586826 0.809713i \(-0.300377\pi\)
0.586826 + 0.809713i \(0.300377\pi\)
\(434\) 9.49836 0.455936
\(435\) −26.4295 −1.26720
\(436\) 7.37446 0.353173
\(437\) −3.11346 −0.148937
\(438\) −51.1272 −2.44295
\(439\) −14.7613 −0.704521 −0.352260 0.935902i \(-0.614587\pi\)
−0.352260 + 0.935902i \(0.614587\pi\)
\(440\) −4.52021 −0.215492
\(441\) 4.69501 0.223572
\(442\) 67.4189 3.20679
\(443\) 4.98945 0.237056 0.118528 0.992951i \(-0.462182\pi\)
0.118528 + 0.992951i \(0.462182\pi\)
\(444\) −13.9966 −0.664247
\(445\) 1.27717 0.0605436
\(446\) 25.2738 1.19675
\(447\) 5.00228 0.236600
\(448\) 11.2211 0.530147
\(449\) 2.41343 0.113897 0.0569485 0.998377i \(-0.481863\pi\)
0.0569485 + 0.998377i \(0.481863\pi\)
\(450\) 9.92773 0.467997
\(451\) 31.0595 1.46253
\(452\) 41.3847 1.94657
\(453\) 33.9659 1.59586
\(454\) −33.8785 −1.59000
\(455\) 5.00491 0.234634
\(456\) −4.21035 −0.197168
\(457\) 35.0547 1.63979 0.819895 0.572514i \(-0.194032\pi\)
0.819895 + 0.572514i \(0.194032\pi\)
\(458\) 2.11453 0.0988054
\(459\) −29.9535 −1.39811
\(460\) 5.05116 0.235511
\(461\) 1.74901 0.0814593 0.0407296 0.999170i \(-0.487032\pi\)
0.0407296 + 0.999170i \(0.487032\pi\)
\(462\) 26.6090 1.23796
\(463\) −20.6997 −0.961998 −0.480999 0.876721i \(-0.659726\pi\)
−0.480999 + 0.876721i \(0.659726\pi\)
\(464\) 27.0154 1.25416
\(465\) −12.4606 −0.577847
\(466\) −22.8211 −1.05717
\(467\) −0.629312 −0.0291211 −0.0145605 0.999894i \(-0.504635\pi\)
−0.0145605 + 0.999894i \(0.504635\pi\)
\(468\) 58.0692 2.68425
\(469\) 5.56782 0.257098
\(470\) 11.4201 0.526771
\(471\) 4.00295 0.184446
\(472\) 7.41707 0.341399
\(473\) −15.3624 −0.706362
\(474\) 64.0365 2.94129
\(475\) 1.52323 0.0698906
\(476\) −15.7429 −0.721576
\(477\) 52.5565 2.40639
\(478\) −6.50224 −0.297405
\(479\) −21.9714 −1.00390 −0.501949 0.864897i \(-0.667383\pi\)
−0.501949 + 0.864897i \(0.667383\pi\)
\(480\) −22.1602 −1.01147
\(481\) 10.2188 0.465937
\(482\) 27.1464 1.23649
\(483\) −5.66999 −0.257993
\(484\) 23.6715 1.07598
\(485\) 9.32565 0.423456
\(486\) 35.9387 1.63021
\(487\) 29.1812 1.32233 0.661163 0.750242i \(-0.270063\pi\)
0.661163 + 0.750242i \(0.270063\pi\)
\(488\) 12.9751 0.587357
\(489\) −47.8837 −2.16538
\(490\) −2.11453 −0.0955247
\(491\) −24.2620 −1.09493 −0.547465 0.836829i \(-0.684407\pi\)
−0.547465 + 0.836829i \(0.684407\pi\)
\(492\) −46.9355 −2.11602
\(493\) −60.6955 −2.73359
\(494\) 16.1204 0.725290
\(495\) −21.2984 −0.957291
\(496\) 12.7368 0.571900
\(497\) 4.39289 0.197048
\(498\) −12.2238 −0.547763
\(499\) −28.3371 −1.26854 −0.634272 0.773110i \(-0.718700\pi\)
−0.634272 + 0.773110i \(0.718700\pi\)
\(500\) −2.47123 −0.110517
\(501\) −8.04849 −0.359580
\(502\) 54.7050 2.44160
\(503\) −44.6739 −1.99191 −0.995955 0.0898532i \(-0.971360\pi\)
−0.995955 + 0.0898532i \(0.971360\pi\)
\(504\) −4.67826 −0.208386
\(505\) 4.40127 0.195854
\(506\) −19.6066 −0.871618
\(507\) −33.4241 −1.48442
\(508\) 9.74076 0.432177
\(509\) −10.4258 −0.462114 −0.231057 0.972940i \(-0.574218\pi\)
−0.231057 + 0.972940i \(0.574218\pi\)
\(510\) 37.3671 1.65465
\(511\) −8.71633 −0.385588
\(512\) 28.3021 1.25079
\(513\) −7.16212 −0.316215
\(514\) 36.1994 1.59669
\(515\) 11.1776 0.492545
\(516\) 23.2148 1.02198
\(517\) −24.5001 −1.07751
\(518\) −4.31735 −0.189693
\(519\) −28.0045 −1.22926
\(520\) −4.98706 −0.218697
\(521\) −39.0560 −1.71107 −0.855537 0.517742i \(-0.826773\pi\)
−0.855537 + 0.517742i \(0.826773\pi\)
\(522\) −94.5876 −4.13999
\(523\) −7.37453 −0.322466 −0.161233 0.986916i \(-0.551547\pi\)
−0.161233 + 0.986916i \(0.551547\pi\)
\(524\) 49.0708 2.14367
\(525\) 2.77399 0.121067
\(526\) 51.2776 2.23581
\(527\) −28.6159 −1.24653
\(528\) 35.6813 1.55283
\(529\) −18.8221 −0.818354
\(530\) −23.6703 −1.02817
\(531\) 34.9479 1.51661
\(532\) −3.76425 −0.163201
\(533\) 34.2673 1.48428
\(534\) 7.49146 0.324187
\(535\) 10.8833 0.470527
\(536\) −5.54796 −0.239635
\(537\) −58.4699 −2.52316
\(538\) −54.7083 −2.35864
\(539\) 4.53639 0.195396
\(540\) 11.6195 0.500026
\(541\) −21.5199 −0.925212 −0.462606 0.886564i \(-0.653086\pi\)
−0.462606 + 0.886564i \(0.653086\pi\)
\(542\) 52.0970 2.23776
\(543\) 47.7044 2.04719
\(544\) −50.8910 −2.18193
\(545\) −2.98412 −0.127826
\(546\) 29.3572 1.25637
\(547\) −9.33707 −0.399224 −0.199612 0.979875i \(-0.563968\pi\)
−0.199612 + 0.979875i \(0.563968\pi\)
\(548\) 8.24609 0.352255
\(549\) 61.1365 2.60924
\(550\) 9.59233 0.409018
\(551\) −14.5128 −0.618265
\(552\) 5.64976 0.240470
\(553\) 10.9171 0.464244
\(554\) −3.68059 −0.156373
\(555\) 5.66380 0.240415
\(556\) 41.2496 1.74937
\(557\) 42.6513 1.80719 0.903597 0.428383i \(-0.140917\pi\)
0.903597 + 0.428383i \(0.140917\pi\)
\(558\) −44.5948 −1.88785
\(559\) −16.9490 −0.716866
\(560\) −2.83548 −0.119821
\(561\) −80.1654 −3.38459
\(562\) 34.9179 1.47292
\(563\) 29.6589 1.24997 0.624986 0.780636i \(-0.285105\pi\)
0.624986 + 0.780636i \(0.285105\pi\)
\(564\) 37.0233 1.55896
\(565\) −16.7466 −0.704534
\(566\) 23.8407 1.00210
\(567\) 1.04193 0.0437572
\(568\) −4.37721 −0.183664
\(569\) 22.8690 0.958719 0.479359 0.877619i \(-0.340869\pi\)
0.479359 + 0.877619i \(0.340869\pi\)
\(570\) 8.93477 0.374237
\(571\) 2.19067 0.0916765 0.0458382 0.998949i \(-0.485404\pi\)
0.0458382 + 0.998949i \(0.485404\pi\)
\(572\) 56.1074 2.34597
\(573\) 17.6448 0.737122
\(574\) −14.4776 −0.604284
\(575\) −2.04398 −0.0852400
\(576\) −52.6831 −2.19513
\(577\) −29.1413 −1.21317 −0.606585 0.795019i \(-0.707461\pi\)
−0.606585 + 0.795019i \(0.707461\pi\)
\(578\) 49.8669 2.07419
\(579\) −57.1951 −2.37695
\(580\) 23.5450 0.977652
\(581\) −2.08396 −0.0864572
\(582\) 54.7012 2.26744
\(583\) 50.7809 2.10313
\(584\) 8.68524 0.359398
\(585\) −23.4981 −0.971526
\(586\) −18.6312 −0.769648
\(587\) 11.5862 0.478215 0.239107 0.970993i \(-0.423145\pi\)
0.239107 + 0.970993i \(0.423145\pi\)
\(588\) −6.85517 −0.282702
\(589\) −6.84227 −0.281931
\(590\) −15.7398 −0.647996
\(591\) −4.80224 −0.197538
\(592\) −5.78934 −0.237941
\(593\) 21.8371 0.896742 0.448371 0.893848i \(-0.352004\pi\)
0.448371 + 0.893848i \(0.352004\pi\)
\(594\) −45.1024 −1.85057
\(595\) 6.37048 0.261164
\(596\) −4.45633 −0.182538
\(597\) 14.7000 0.601631
\(598\) −21.6315 −0.884579
\(599\) 30.1002 1.22986 0.614930 0.788582i \(-0.289184\pi\)
0.614930 + 0.788582i \(0.289184\pi\)
\(600\) −2.76409 −0.112844
\(601\) −33.5967 −1.37044 −0.685219 0.728337i \(-0.740293\pi\)
−0.685219 + 0.728337i \(0.740293\pi\)
\(602\) 7.16079 0.291852
\(603\) −26.1410 −1.06454
\(604\) −30.2588 −1.23121
\(605\) −9.57884 −0.389435
\(606\) 25.8164 1.04872
\(607\) 7.67036 0.311330 0.155665 0.987810i \(-0.450248\pi\)
0.155665 + 0.987810i \(0.450248\pi\)
\(608\) −12.1684 −0.493495
\(609\) −26.4295 −1.07098
\(610\) −27.5345 −1.11484
\(611\) −27.0305 −1.09354
\(612\) 73.9131 2.98776
\(613\) 15.5992 0.630048 0.315024 0.949084i \(-0.397987\pi\)
0.315024 + 0.949084i \(0.397987\pi\)
\(614\) −5.05879 −0.204156
\(615\) 18.9928 0.765862
\(616\) −4.52021 −0.182124
\(617\) 12.5666 0.505914 0.252957 0.967478i \(-0.418597\pi\)
0.252957 + 0.967478i \(0.418597\pi\)
\(618\) 65.5644 2.63739
\(619\) −17.4444 −0.701148 −0.350574 0.936535i \(-0.614014\pi\)
−0.350574 + 0.936535i \(0.614014\pi\)
\(620\) 11.1006 0.445813
\(621\) 9.61066 0.385663
\(622\) 39.0316 1.56502
\(623\) 1.27717 0.0511687
\(624\) 39.3665 1.57592
\(625\) 1.00000 0.0400000
\(626\) 32.3758 1.29400
\(627\) −19.1682 −0.765503
\(628\) −3.56606 −0.142301
\(629\) 13.0069 0.518621
\(630\) 9.92773 0.395530
\(631\) −24.3491 −0.969321 −0.484660 0.874702i \(-0.661057\pi\)
−0.484660 + 0.874702i \(0.661057\pi\)
\(632\) −10.8782 −0.432712
\(633\) −61.4621 −2.44290
\(634\) −11.9444 −0.474371
\(635\) −3.94166 −0.156420
\(636\) −76.7375 −3.04284
\(637\) 5.00491 0.198302
\(638\) −91.3921 −3.61825
\(639\) −20.6246 −0.815898
\(640\) 7.75019 0.306353
\(641\) −28.6277 −1.13072 −0.565362 0.824843i \(-0.691264\pi\)
−0.565362 + 0.824843i \(0.691264\pi\)
\(642\) 63.8380 2.51948
\(643\) −34.1050 −1.34497 −0.672486 0.740110i \(-0.734773\pi\)
−0.672486 + 0.740110i \(0.734773\pi\)
\(644\) 5.05116 0.199043
\(645\) −9.39403 −0.369889
\(646\) 20.5188 0.807300
\(647\) 40.7560 1.60229 0.801143 0.598473i \(-0.204226\pi\)
0.801143 + 0.598473i \(0.204226\pi\)
\(648\) −1.03822 −0.0407851
\(649\) 33.7672 1.32548
\(650\) 10.5830 0.415100
\(651\) −12.4606 −0.488370
\(652\) 42.6576 1.67060
\(653\) −18.0164 −0.705037 −0.352518 0.935805i \(-0.614675\pi\)
−0.352518 + 0.935805i \(0.614675\pi\)
\(654\) −17.5039 −0.684457
\(655\) −19.8568 −0.775870
\(656\) −19.4138 −0.757980
\(657\) 40.9232 1.59657
\(658\) 11.4201 0.445203
\(659\) −25.4889 −0.992907 −0.496453 0.868063i \(-0.665365\pi\)
−0.496453 + 0.868063i \(0.665365\pi\)
\(660\) 31.0977 1.21048
\(661\) 29.2232 1.13665 0.568325 0.822804i \(-0.307592\pi\)
0.568325 + 0.822804i \(0.307592\pi\)
\(662\) 47.6013 1.85008
\(663\) −88.4449 −3.43491
\(664\) 2.07652 0.0805848
\(665\) 1.52323 0.0590683
\(666\) 20.2700 0.785445
\(667\) 19.4743 0.754048
\(668\) 7.17007 0.277418
\(669\) −33.1559 −1.28188
\(670\) 11.7733 0.454843
\(671\) 59.0710 2.28041
\(672\) −22.1602 −0.854847
\(673\) 44.6022 1.71929 0.859644 0.510893i \(-0.170685\pi\)
0.859644 + 0.510893i \(0.170685\pi\)
\(674\) 1.93053 0.0743612
\(675\) −4.70193 −0.180977
\(676\) 29.7762 1.14524
\(677\) 12.2997 0.472718 0.236359 0.971666i \(-0.424046\pi\)
0.236359 + 0.971666i \(0.424046\pi\)
\(678\) −98.2301 −3.77250
\(679\) 9.32565 0.357886
\(680\) −6.34775 −0.243425
\(681\) 44.4442 1.70310
\(682\) −43.0883 −1.64993
\(683\) 28.9302 1.10698 0.553492 0.832854i \(-0.313295\pi\)
0.553492 + 0.832854i \(0.313295\pi\)
\(684\) 17.6732 0.675752
\(685\) −3.33683 −0.127494
\(686\) −2.11453 −0.0807331
\(687\) −2.77399 −0.105834
\(688\) 9.60226 0.366083
\(689\) 56.0256 2.13440
\(690\) −11.9893 −0.456427
\(691\) −22.8650 −0.869825 −0.434913 0.900473i \(-0.643221\pi\)
−0.434913 + 0.900473i \(0.643221\pi\)
\(692\) 24.9481 0.948384
\(693\) −21.2984 −0.809059
\(694\) −72.0415 −2.73466
\(695\) −16.6919 −0.633160
\(696\) 26.3352 0.998234
\(697\) 43.6170 1.65211
\(698\) −64.1349 −2.42754
\(699\) 29.9383 1.13237
\(700\) −2.47123 −0.0934038
\(701\) −29.1680 −1.10166 −0.550830 0.834617i \(-0.685689\pi\)
−0.550830 + 0.834617i \(0.685689\pi\)
\(702\) −49.7606 −1.87809
\(703\) 3.11006 0.117298
\(704\) −50.9033 −1.91849
\(705\) −14.9817 −0.564245
\(706\) −10.5703 −0.397819
\(707\) 4.40127 0.165527
\(708\) −51.0273 −1.91772
\(709\) −29.7709 −1.11807 −0.559034 0.829144i \(-0.688828\pi\)
−0.559034 + 0.829144i \(0.688828\pi\)
\(710\) 9.28888 0.348606
\(711\) −51.2561 −1.92225
\(712\) −1.27261 −0.0476932
\(713\) 9.18147 0.343849
\(714\) 37.3671 1.39843
\(715\) −22.7042 −0.849090
\(716\) 52.0884 1.94664
\(717\) 8.53009 0.318562
\(718\) 3.19661 0.119296
\(719\) 18.6006 0.693687 0.346844 0.937923i \(-0.387253\pi\)
0.346844 + 0.937923i \(0.387253\pi\)
\(720\) 13.3126 0.496131
\(721\) 11.1776 0.416277
\(722\) −35.2699 −1.31261
\(723\) −35.6126 −1.32445
\(724\) −42.4979 −1.57942
\(725\) −9.52762 −0.353847
\(726\) −56.1864 −2.08527
\(727\) 31.4828 1.16763 0.583816 0.811886i \(-0.301559\pi\)
0.583816 + 0.811886i \(0.301559\pi\)
\(728\) −4.98706 −0.184833
\(729\) −44.0211 −1.63041
\(730\) −18.4309 −0.682159
\(731\) −21.5734 −0.797922
\(732\) −89.2652 −3.29934
\(733\) 27.5305 1.01686 0.508431 0.861103i \(-0.330226\pi\)
0.508431 + 0.861103i \(0.330226\pi\)
\(734\) 16.6419 0.614263
\(735\) 2.77399 0.102320
\(736\) 16.3285 0.601876
\(737\) −25.2578 −0.930383
\(738\) 67.9725 2.50210
\(739\) 33.1578 1.21973 0.609865 0.792505i \(-0.291224\pi\)
0.609865 + 0.792505i \(0.291224\pi\)
\(740\) −5.04564 −0.185482
\(741\) −21.1479 −0.776886
\(742\) −23.6703 −0.868963
\(743\) 29.1849 1.07069 0.535344 0.844634i \(-0.320182\pi\)
0.535344 + 0.844634i \(0.320182\pi\)
\(744\) 12.4162 0.455199
\(745\) 1.80328 0.0660671
\(746\) 59.2592 2.16963
\(747\) 9.78420 0.357985
\(748\) 71.4160 2.61123
\(749\) 10.8833 0.397668
\(750\) 5.86568 0.214184
\(751\) 14.6743 0.535471 0.267736 0.963492i \(-0.413725\pi\)
0.267736 + 0.963492i \(0.413725\pi\)
\(752\) 15.3138 0.558438
\(753\) −71.7658 −2.61529
\(754\) −100.831 −3.67205
\(755\) 12.2444 0.445620
\(756\) 11.6195 0.422599
\(757\) −30.0394 −1.09180 −0.545901 0.837850i \(-0.683813\pi\)
−0.545901 + 0.837850i \(0.683813\pi\)
\(758\) −53.0724 −1.92768
\(759\) 25.7213 0.933623
\(760\) −1.51780 −0.0550563
\(761\) 15.9968 0.579884 0.289942 0.957044i \(-0.406364\pi\)
0.289942 + 0.957044i \(0.406364\pi\)
\(762\) −23.1205 −0.837568
\(763\) −2.98412 −0.108033
\(764\) −15.7190 −0.568695
\(765\) −29.9094 −1.08138
\(766\) 76.7161 2.77186
\(767\) 37.2547 1.34519
\(768\) −16.7942 −0.606009
\(769\) −18.9162 −0.682137 −0.341068 0.940038i \(-0.610789\pi\)
−0.341068 + 0.940038i \(0.610789\pi\)
\(770\) 9.59233 0.345684
\(771\) −47.4889 −1.71027
\(772\) 50.9527 1.83383
\(773\) 5.47300 0.196850 0.0984251 0.995144i \(-0.468620\pi\)
0.0984251 + 0.995144i \(0.468620\pi\)
\(774\) −33.6200 −1.20844
\(775\) −4.49195 −0.161356
\(776\) −9.29238 −0.333577
\(777\) 5.66380 0.203188
\(778\) 14.9423 0.535709
\(779\) 10.4292 0.373663
\(780\) 34.3095 1.22848
\(781\) −19.9278 −0.713074
\(782\) −27.5336 −0.984599
\(783\) 44.7982 1.60096
\(784\) −2.83548 −0.101267
\(785\) 1.44303 0.0515040
\(786\) −116.474 −4.15448
\(787\) 9.03353 0.322010 0.161005 0.986954i \(-0.448526\pi\)
0.161005 + 0.986954i \(0.448526\pi\)
\(788\) 4.27812 0.152402
\(789\) −67.2695 −2.39486
\(790\) 23.0846 0.821314
\(791\) −16.7466 −0.595440
\(792\) 21.2224 0.754105
\(793\) 65.1719 2.31432
\(794\) 60.7318 2.15529
\(795\) 31.0523 1.10131
\(796\) −13.0956 −0.464162
\(797\) −26.7751 −0.948423 −0.474212 0.880411i \(-0.657267\pi\)
−0.474212 + 0.880411i \(0.657267\pi\)
\(798\) 8.93477 0.316288
\(799\) −34.4056 −1.21718
\(800\) −7.98856 −0.282438
\(801\) −5.99631 −0.211869
\(802\) −11.2743 −0.398110
\(803\) 39.5407 1.39536
\(804\) 38.1683 1.34609
\(805\) −2.04398 −0.0720410
\(806\) −47.5384 −1.67447
\(807\) 71.7702 2.52643
\(808\) −4.38557 −0.154284
\(809\) 24.4374 0.859174 0.429587 0.903026i \(-0.358659\pi\)
0.429587 + 0.903026i \(0.358659\pi\)
\(810\) 2.20320 0.0774126
\(811\) 8.67868 0.304750 0.152375 0.988323i \(-0.451308\pi\)
0.152375 + 0.988323i \(0.451308\pi\)
\(812\) 23.5450 0.826266
\(813\) −68.3445 −2.39695
\(814\) 19.5852 0.686460
\(815\) −17.2617 −0.604650
\(816\) 50.1075 1.75411
\(817\) −5.15837 −0.180469
\(818\) −35.1229 −1.22804
\(819\) −23.4981 −0.821090
\(820\) −16.9199 −0.590867
\(821\) −22.8269 −0.796665 −0.398333 0.917241i \(-0.630411\pi\)
−0.398333 + 0.917241i \(0.630411\pi\)
\(822\) −19.5728 −0.682679
\(823\) −24.1544 −0.841969 −0.420984 0.907068i \(-0.638315\pi\)
−0.420984 + 0.907068i \(0.638315\pi\)
\(824\) −11.1378 −0.388002
\(825\) −12.5839 −0.438115
\(826\) −15.7398 −0.547656
\(827\) 33.1616 1.15314 0.576571 0.817047i \(-0.304390\pi\)
0.576571 + 0.817047i \(0.304390\pi\)
\(828\) −23.7152 −0.824161
\(829\) 26.6091 0.924172 0.462086 0.886835i \(-0.347101\pi\)
0.462086 + 0.886835i \(0.347101\pi\)
\(830\) −4.40659 −0.152955
\(831\) 4.82845 0.167497
\(832\) −56.1606 −1.94702
\(833\) 6.37048 0.220724
\(834\) −97.9094 −3.39032
\(835\) −2.90141 −0.100408
\(836\) 17.0761 0.590590
\(837\) 21.1208 0.730042
\(838\) −41.8489 −1.44565
\(839\) −39.8978 −1.37742 −0.688712 0.725035i \(-0.741824\pi\)
−0.688712 + 0.725035i \(0.741824\pi\)
\(840\) −2.76409 −0.0953702
\(841\) 61.7756 2.13019
\(842\) −13.6646 −0.470913
\(843\) −45.8078 −1.57770
\(844\) 54.7540 1.88471
\(845\) −12.0491 −0.414503
\(846\) −53.6176 −1.84341
\(847\) −9.57884 −0.329133
\(848\) −31.7407 −1.08998
\(849\) −31.2759 −1.07338
\(850\) 13.4706 0.462036
\(851\) −4.17331 −0.143059
\(852\) 30.1140 1.03169
\(853\) −22.7539 −0.779078 −0.389539 0.921010i \(-0.627366\pi\)
−0.389539 + 0.921010i \(0.627366\pi\)
\(854\) −27.5345 −0.942212
\(855\) −7.15157 −0.244579
\(856\) −10.8445 −0.370657
\(857\) 51.4636 1.75796 0.878982 0.476855i \(-0.158223\pi\)
0.878982 + 0.476855i \(0.158223\pi\)
\(858\) −133.176 −4.54654
\(859\) 41.3429 1.41060 0.705301 0.708908i \(-0.250812\pi\)
0.705301 + 0.708908i \(0.250812\pi\)
\(860\) 8.36875 0.285372
\(861\) 18.9928 0.647271
\(862\) −36.4762 −1.24239
\(863\) −22.0809 −0.751644 −0.375822 0.926692i \(-0.622640\pi\)
−0.375822 + 0.926692i \(0.622640\pi\)
\(864\) 37.5616 1.27787
\(865\) −10.0954 −0.343254
\(866\) 51.6413 1.75484
\(867\) −65.4188 −2.22174
\(868\) 11.1006 0.376781
\(869\) −49.5245 −1.68000
\(870\) −55.8860 −1.89471
\(871\) −27.8664 −0.944218
\(872\) 2.97348 0.100695
\(873\) −43.7840 −1.48186
\(874\) −6.58350 −0.222690
\(875\) 1.00000 0.0338062
\(876\) −59.7519 −2.01883
\(877\) −41.4408 −1.39936 −0.699679 0.714457i \(-0.746674\pi\)
−0.699679 + 0.714457i \(0.746674\pi\)
\(878\) −31.2133 −1.05340
\(879\) 24.4417 0.824399
\(880\) 12.8628 0.433606
\(881\) −25.4755 −0.858293 −0.429146 0.903235i \(-0.641186\pi\)
−0.429146 + 0.903235i \(0.641186\pi\)
\(882\) 9.92773 0.334284
\(883\) −18.9663 −0.638268 −0.319134 0.947710i \(-0.603392\pi\)
−0.319134 + 0.947710i \(0.603392\pi\)
\(884\) 78.7919 2.65006
\(885\) 20.6485 0.694093
\(886\) 10.5503 0.354446
\(887\) −22.6669 −0.761081 −0.380540 0.924764i \(-0.624262\pi\)
−0.380540 + 0.924764i \(0.624262\pi\)
\(888\) −5.64359 −0.189387
\(889\) −3.94166 −0.132199
\(890\) 2.70061 0.0905246
\(891\) −4.72662 −0.158348
\(892\) 29.5372 0.988980
\(893\) −8.22665 −0.275294
\(894\) 10.5775 0.353763
\(895\) −21.0779 −0.704557
\(896\) 7.75019 0.258916
\(897\) 28.3778 0.947506
\(898\) 5.10327 0.170298
\(899\) 42.7976 1.42738
\(900\) 11.6024 0.386748
\(901\) 71.3119 2.37574
\(902\) 65.6761 2.18678
\(903\) −9.39403 −0.312614
\(904\) 16.6868 0.554996
\(905\) 17.1971 0.571650
\(906\) 71.8219 2.38612
\(907\) −33.5545 −1.11416 −0.557080 0.830459i \(-0.688078\pi\)
−0.557080 + 0.830459i \(0.688078\pi\)
\(908\) −39.5935 −1.31396
\(909\) −20.6640 −0.685382
\(910\) 10.5830 0.350824
\(911\) −21.5556 −0.714168 −0.357084 0.934072i \(-0.616229\pi\)
−0.357084 + 0.934072i \(0.616229\pi\)
\(912\) 11.9811 0.396733
\(913\) 9.45365 0.312870
\(914\) 74.1242 2.45181
\(915\) 36.1217 1.19415
\(916\) 2.47123 0.0816518
\(917\) −19.8568 −0.655730
\(918\) −63.3376 −2.09045
\(919\) −25.9749 −0.856834 −0.428417 0.903581i \(-0.640929\pi\)
−0.428417 + 0.903581i \(0.640929\pi\)
\(920\) 2.03669 0.0671478
\(921\) 6.63648 0.218680
\(922\) 3.69832 0.121798
\(923\) −21.9860 −0.723678
\(924\) 31.0977 1.02304
\(925\) 2.04175 0.0671324
\(926\) −43.7702 −1.43838
\(927\) −52.4791 −1.72364
\(928\) 76.1120 2.49850
\(929\) 19.5937 0.642848 0.321424 0.946935i \(-0.395838\pi\)
0.321424 + 0.946935i \(0.395838\pi\)
\(930\) −26.3483 −0.863995
\(931\) 1.52323 0.0499219
\(932\) −26.6708 −0.873631
\(933\) −51.2044 −1.67636
\(934\) −1.33070 −0.0435418
\(935\) −28.8990 −0.945097
\(936\) 23.4143 0.765319
\(937\) 25.9639 0.848205 0.424103 0.905614i \(-0.360590\pi\)
0.424103 + 0.905614i \(0.360590\pi\)
\(938\) 11.7733 0.384412
\(939\) −42.4728 −1.38605
\(940\) 13.3466 0.435318
\(941\) 0.188381 0.00614106 0.00307053 0.999995i \(-0.499023\pi\)
0.00307053 + 0.999995i \(0.499023\pi\)
\(942\) 8.46435 0.275783
\(943\) −13.9946 −0.455727
\(944\) −21.1062 −0.686950
\(945\) −4.70193 −0.152954
\(946\) −32.4841 −1.05615
\(947\) −35.5644 −1.15569 −0.577844 0.816147i \(-0.696106\pi\)
−0.577844 + 0.816147i \(0.696106\pi\)
\(948\) 74.8389 2.43065
\(949\) 43.6245 1.41611
\(950\) 3.22091 0.104500
\(951\) 15.6695 0.508117
\(952\) −6.34775 −0.205732
\(953\) 40.5427 1.31331 0.656654 0.754192i \(-0.271971\pi\)
0.656654 + 0.754192i \(0.271971\pi\)
\(954\) 111.132 3.59804
\(955\) 6.36081 0.205831
\(956\) −7.59911 −0.245773
\(957\) 119.895 3.87564
\(958\) −46.4591 −1.50103
\(959\) −3.33683 −0.107752
\(960\) −31.1272 −1.00463
\(961\) −10.8224 −0.349109
\(962\) 21.6079 0.696667
\(963\) −51.0972 −1.64659
\(964\) 31.7258 1.02182
\(965\) −20.6184 −0.663728
\(966\) −11.9893 −0.385751
\(967\) −8.41159 −0.270498 −0.135249 0.990812i \(-0.543184\pi\)
−0.135249 + 0.990812i \(0.543184\pi\)
\(968\) 9.54467 0.306777
\(969\) −26.9179 −0.864729
\(970\) 19.7194 0.633150
\(971\) 25.5983 0.821490 0.410745 0.911750i \(-0.365269\pi\)
0.410745 + 0.911750i \(0.365269\pi\)
\(972\) 42.0013 1.34719
\(973\) −16.6919 −0.535118
\(974\) 61.7044 1.97714
\(975\) −13.8836 −0.444630
\(976\) −36.9224 −1.18186
\(977\) 55.4297 1.77335 0.886676 0.462391i \(-0.153008\pi\)
0.886676 + 0.462391i \(0.153008\pi\)
\(978\) −101.251 −3.23766
\(979\) −5.79373 −0.185169
\(980\) −2.47123 −0.0789406
\(981\) 14.0105 0.447320
\(982\) −51.3027 −1.63714
\(983\) 22.5803 0.720199 0.360100 0.932914i \(-0.382743\pi\)
0.360100 + 0.932914i \(0.382743\pi\)
\(984\) −18.9250 −0.603307
\(985\) −1.73117 −0.0551596
\(986\) −128.342 −4.08725
\(987\) −14.9817 −0.476874
\(988\) 18.8398 0.599372
\(989\) 6.92189 0.220103
\(990\) −45.0360 −1.43134
\(991\) −21.2983 −0.676564 −0.338282 0.941045i \(-0.609846\pi\)
−0.338282 + 0.941045i \(0.609846\pi\)
\(992\) 35.8842 1.13933
\(993\) −62.4467 −1.98169
\(994\) 9.28888 0.294625
\(995\) 5.29923 0.167997
\(996\) −14.2859 −0.452665
\(997\) −49.3983 −1.56446 −0.782230 0.622990i \(-0.785918\pi\)
−0.782230 + 0.622990i \(0.785918\pi\)
\(998\) −59.9197 −1.89673
\(999\) −9.60017 −0.303736
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 \(a_p\))