Properties

Label 17.4.a.b.1.1
Level 17
Weight 4
Character 17.1
Self dual Yes
Analytic conductor 1.003
Analytic rank 0
Dimension 3
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 17 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 17.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.0030324701\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.2636.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-3.58966\)
Character \(\chi\) = 17.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.03251 q^{2} +8.47535 q^{3} +17.3261 q^{4} +0.885690 q^{5} -42.6523 q^{6} +3.81828 q^{7} -46.9339 q^{8} +44.8316 q^{9} +O(q^{10})\) \(q-5.03251 q^{2} +8.47535 q^{3} +17.3261 q^{4} +0.885690 q^{5} -42.6523 q^{6} +3.81828 q^{7} -46.9339 q^{8} +44.8316 q^{9} -4.45724 q^{10} -52.3720 q^{11} +146.845 q^{12} -8.06025 q^{13} -19.2156 q^{14} +7.50653 q^{15} +97.5862 q^{16} -17.0000 q^{17} -225.616 q^{18} -66.5154 q^{19} +15.3456 q^{20} +32.3613 q^{21} +263.563 q^{22} +180.226 q^{23} -397.782 q^{24} -124.216 q^{25} +40.5633 q^{26} +151.129 q^{27} +66.1562 q^{28} -41.2800 q^{29} -37.7767 q^{30} -34.9114 q^{31} -115.632 q^{32} -443.871 q^{33} +85.5527 q^{34} +3.38182 q^{35} +776.759 q^{36} +130.368 q^{37} +334.739 q^{38} -68.3134 q^{39} -41.5689 q^{40} -17.9081 q^{41} -162.859 q^{42} +277.620 q^{43} -907.405 q^{44} +39.7069 q^{45} -906.987 q^{46} +463.789 q^{47} +827.078 q^{48} -328.421 q^{49} +625.116 q^{50} -144.081 q^{51} -139.653 q^{52} -329.944 q^{53} -760.560 q^{54} -46.3853 q^{55} -179.207 q^{56} -563.741 q^{57} +207.742 q^{58} +678.656 q^{59} +130.059 q^{60} +340.280 q^{61} +175.692 q^{62} +171.180 q^{63} -198.770 q^{64} -7.13888 q^{65} +2233.79 q^{66} +15.3925 q^{67} -294.545 q^{68} +1527.48 q^{69} -17.0190 q^{70} -670.203 q^{71} -2104.12 q^{72} +193.480 q^{73} -656.080 q^{74} -1052.77 q^{75} -1152.46 q^{76} -199.971 q^{77} +343.788 q^{78} +1080.15 q^{79} +86.4311 q^{80} +70.4207 q^{81} +90.1229 q^{82} -865.668 q^{83} +560.697 q^{84} -15.0567 q^{85} -1397.13 q^{86} -349.863 q^{87} +2458.02 q^{88} +1129.46 q^{89} -199.825 q^{90} -30.7763 q^{91} +3122.61 q^{92} -295.886 q^{93} -2334.02 q^{94} -58.9120 q^{95} -980.023 q^{96} -379.412 q^{97} +1652.78 q^{98} -2347.92 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + q^{2} + 4q^{3} + 25q^{4} - 8q^{5} - 74q^{6} + 22q^{7} - 39q^{8} + 59q^{9} + O(q^{10}) \) \( 3q + q^{2} + 4q^{3} + 25q^{4} - 8q^{5} - 74q^{6} + 22q^{7} - 39q^{8} + 59q^{9} - 56q^{10} - 28q^{11} + 22q^{12} + 30q^{13} + 92q^{14} + 108q^{15} + 137q^{16} - 51q^{17} - 103q^{18} + 80q^{19} - 168q^{20} - 192q^{21} + 286q^{22} + 142q^{23} - 666q^{24} - 223q^{25} + 26q^{26} - 20q^{27} + 476q^{28} - 456q^{29} + 400q^{30} + 230q^{31} - 71q^{32} - 332q^{33} - 17q^{34} - 332q^{35} + 1313q^{36} + 356q^{37} + 724q^{38} + 268q^{39} - 424q^{40} - 294q^{41} - 1128q^{42} + 556q^{43} - 1122q^{44} - 384q^{45} - 704q^{46} + 640q^{47} + 774q^{48} - 269q^{49} + 547q^{50} - 68q^{51} - 774q^{52} + 302q^{53} - 1100q^{54} + 76q^{55} + 684q^{56} - 720q^{57} - 1304q^{58} + 636q^{59} + 1328q^{60} - 84q^{61} + 508q^{62} + 1122q^{63} - 919q^{64} + 408q^{65} + 2468q^{66} + 1008q^{67} - 425q^{68} + 576q^{69} - 1504q^{70} - 402q^{71} - 927q^{72} + 838q^{73} + 836q^{74} - 1548q^{75} - 908q^{76} - 504q^{77} + 1308q^{78} - 594q^{79} - 40q^{80} - 505q^{81} + 358q^{82} - 2396q^{83} - 2040q^{84} + 136q^{85} - 1264q^{86} + 1428q^{87} + 1838q^{88} - 170q^{89} - 2008q^{90} - 1016q^{91} + 4896q^{92} + 632q^{93} - 2016q^{94} - 472q^{95} + 678q^{96} - 270q^{97} + 2857q^{98} - 2920q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.03251 −1.77926 −0.889630 0.456681i \(-0.849038\pi\)
−0.889630 + 0.456681i \(0.849038\pi\)
\(3\) 8.47535 1.63108 0.815541 0.578699i \(-0.196439\pi\)
0.815541 + 0.578699i \(0.196439\pi\)
\(4\) 17.3261 2.16577
\(5\) 0.885690 0.0792185 0.0396092 0.999215i \(-0.487389\pi\)
0.0396092 + 0.999215i \(0.487389\pi\)
\(6\) −42.6523 −2.90212
\(7\) 3.81828 0.206168 0.103084 0.994673i \(-0.467129\pi\)
0.103084 + 0.994673i \(0.467129\pi\)
\(8\) −46.9339 −2.07421
\(9\) 44.8316 1.66043
\(10\) −4.45724 −0.140950
\(11\) −52.3720 −1.43552 −0.717761 0.696289i \(-0.754833\pi\)
−0.717761 + 0.696289i \(0.754833\pi\)
\(12\) 146.845 3.53255
\(13\) −8.06025 −0.171962 −0.0859811 0.996297i \(-0.527402\pi\)
−0.0859811 + 0.996297i \(0.527402\pi\)
\(14\) −19.2156 −0.366827
\(15\) 7.50653 0.129212
\(16\) 97.5862 1.52478
\(17\) −17.0000 −0.242536
\(18\) −225.616 −2.95434
\(19\) −66.5154 −0.803141 −0.401570 0.915828i \(-0.631535\pi\)
−0.401570 + 0.915828i \(0.631535\pi\)
\(20\) 15.3456 0.171569
\(21\) 32.3613 0.336277
\(22\) 263.563 2.55417
\(23\) 180.226 1.63390 0.816948 0.576711i \(-0.195664\pi\)
0.816948 + 0.576711i \(0.195664\pi\)
\(24\) −397.782 −3.38320
\(25\) −124.216 −0.993724
\(26\) 40.5633 0.305966
\(27\) 151.129 1.07722
\(28\) 66.1562 0.446512
\(29\) −41.2800 −0.264328 −0.132164 0.991228i \(-0.542193\pi\)
−0.132164 + 0.991228i \(0.542193\pi\)
\(30\) −37.7767 −0.229902
\(31\) −34.9114 −0.202267 −0.101133 0.994873i \(-0.532247\pi\)
−0.101133 + 0.994873i \(0.532247\pi\)
\(32\) −115.632 −0.638783
\(33\) −443.871 −2.34146
\(34\) 85.5527 0.431534
\(35\) 3.38182 0.0163323
\(36\) 776.759 3.59611
\(37\) 130.368 0.579255 0.289627 0.957139i \(-0.406469\pi\)
0.289627 + 0.957139i \(0.406469\pi\)
\(38\) 334.739 1.42900
\(39\) −68.3134 −0.280485
\(40\) −41.5689 −0.164315
\(41\) −17.9081 −0.0682142 −0.0341071 0.999418i \(-0.510859\pi\)
−0.0341071 + 0.999418i \(0.510859\pi\)
\(42\) −162.859 −0.598325
\(43\) 277.620 0.984573 0.492287 0.870433i \(-0.336161\pi\)
0.492287 + 0.870433i \(0.336161\pi\)
\(44\) −907.405 −3.10901
\(45\) 39.7069 0.131537
\(46\) −906.987 −2.90713
\(47\) 463.789 1.43937 0.719687 0.694299i \(-0.244285\pi\)
0.719687 + 0.694299i \(0.244285\pi\)
\(48\) 827.078 2.48705
\(49\) −328.421 −0.957495
\(50\) 625.116 1.76809
\(51\) −144.081 −0.395596
\(52\) −139.653 −0.372431
\(53\) −329.944 −0.855118 −0.427559 0.903987i \(-0.640626\pi\)
−0.427559 + 0.903987i \(0.640626\pi\)
\(54\) −760.560 −1.91665
\(55\) −46.3853 −0.113720
\(56\) −179.207 −0.427635
\(57\) −563.741 −1.30999
\(58\) 207.742 0.470308
\(59\) 678.656 1.49752 0.748759 0.662843i \(-0.230650\pi\)
0.748759 + 0.662843i \(0.230650\pi\)
\(60\) 130.059 0.279843
\(61\) 340.280 0.714237 0.357118 0.934059i \(-0.383759\pi\)
0.357118 + 0.934059i \(0.383759\pi\)
\(62\) 175.692 0.359885
\(63\) 171.180 0.342328
\(64\) −198.770 −0.388223
\(65\) −7.13888 −0.0136226
\(66\) 2233.79 4.16606
\(67\) 15.3925 0.0280671 0.0140336 0.999902i \(-0.495533\pi\)
0.0140336 + 0.999902i \(0.495533\pi\)
\(68\) −294.545 −0.525276
\(69\) 1527.48 2.66502
\(70\) −17.0190 −0.0290595
\(71\) −670.203 −1.12026 −0.560130 0.828405i \(-0.689249\pi\)
−0.560130 + 0.828405i \(0.689249\pi\)
\(72\) −2104.12 −3.44408
\(73\) 193.480 0.310207 0.155103 0.987898i \(-0.450429\pi\)
0.155103 + 0.987898i \(0.450429\pi\)
\(74\) −656.080 −1.03065
\(75\) −1052.77 −1.62085
\(76\) −1152.46 −1.73942
\(77\) −199.971 −0.295959
\(78\) 343.788 0.499055
\(79\) 1080.15 1.53831 0.769156 0.639061i \(-0.220677\pi\)
0.769156 + 0.639061i \(0.220677\pi\)
\(80\) 86.4311 0.120791
\(81\) 70.4207 0.0965990
\(82\) 90.1229 0.121371
\(83\) −865.668 −1.14481 −0.572406 0.819970i \(-0.693990\pi\)
−0.572406 + 0.819970i \(0.693990\pi\)
\(84\) 560.697 0.728298
\(85\) −15.0567 −0.0192133
\(86\) −1397.13 −1.75181
\(87\) −349.863 −0.431141
\(88\) 2458.02 2.97757
\(89\) 1129.46 1.34520 0.672599 0.740008i \(-0.265178\pi\)
0.672599 + 0.740008i \(0.265178\pi\)
\(90\) −199.825 −0.234038
\(91\) −30.7763 −0.0354531
\(92\) 3122.61 3.53864
\(93\) −295.886 −0.329914
\(94\) −2334.02 −2.56102
\(95\) −58.9120 −0.0636236
\(96\) −980.023 −1.04191
\(97\) −379.412 −0.397149 −0.198574 0.980086i \(-0.563631\pi\)
−0.198574 + 0.980086i \(0.563631\pi\)
\(98\) 1652.78 1.70363
\(99\) −2347.92 −2.38359
\(100\) −2152.18 −2.15218
\(101\) 131.732 0.129780 0.0648902 0.997892i \(-0.479330\pi\)
0.0648902 + 0.997892i \(0.479330\pi\)
\(102\) 725.089 0.703868
\(103\) 195.988 0.187488 0.0937442 0.995596i \(-0.470116\pi\)
0.0937442 + 0.995596i \(0.470116\pi\)
\(104\) 378.299 0.356685
\(105\) 28.6621 0.0266394
\(106\) 1660.45 1.52148
\(107\) −485.147 −0.438326 −0.219163 0.975688i \(-0.570333\pi\)
−0.219163 + 0.975688i \(0.570333\pi\)
\(108\) 2618.49 2.33300
\(109\) −1255.12 −1.10292 −0.551460 0.834201i \(-0.685929\pi\)
−0.551460 + 0.834201i \(0.685929\pi\)
\(110\) 233.435 0.202337
\(111\) 1104.92 0.944812
\(112\) 372.612 0.314362
\(113\) −1013.35 −0.843612 −0.421806 0.906686i \(-0.638604\pi\)
−0.421806 + 0.906686i \(0.638604\pi\)
\(114\) 2837.03 2.33081
\(115\) 159.624 0.129435
\(116\) −715.224 −0.572473
\(117\) −361.354 −0.285531
\(118\) −3415.34 −2.66447
\(119\) −64.9108 −0.0500031
\(120\) −352.311 −0.268012
\(121\) 1411.83 1.06073
\(122\) −1712.46 −1.27081
\(123\) −151.778 −0.111263
\(124\) −604.880 −0.438063
\(125\) −220.728 −0.157940
\(126\) −861.464 −0.609090
\(127\) 1927.72 1.34691 0.673456 0.739227i \(-0.264809\pi\)
0.673456 + 0.739227i \(0.264809\pi\)
\(128\) 1925.37 1.32953
\(129\) 2352.93 1.60592
\(130\) 35.9265 0.0242381
\(131\) −406.738 −0.271274 −0.135637 0.990759i \(-0.543308\pi\)
−0.135637 + 0.990759i \(0.543308\pi\)
\(132\) −7690.58 −5.07105
\(133\) −253.975 −0.165582
\(134\) −77.4631 −0.0499387
\(135\) 133.854 0.0853355
\(136\) 797.877 0.503069
\(137\) −130.552 −0.0814149 −0.0407074 0.999171i \(-0.512961\pi\)
−0.0407074 + 0.999171i \(0.512961\pi\)
\(138\) −7687.03 −4.74177
\(139\) 2073.54 1.26529 0.632644 0.774443i \(-0.281970\pi\)
0.632644 + 0.774443i \(0.281970\pi\)
\(140\) 58.5938 0.0353720
\(141\) 3930.78 2.34774
\(142\) 3372.80 1.99323
\(143\) 422.131 0.246856
\(144\) 4374.95 2.53180
\(145\) −36.5613 −0.0209397
\(146\) −973.689 −0.551939
\(147\) −2783.48 −1.56175
\(148\) 2258.78 1.25453
\(149\) −1852.73 −1.01867 −0.509334 0.860569i \(-0.670108\pi\)
−0.509334 + 0.860569i \(0.670108\pi\)
\(150\) 5298.08 2.88391
\(151\) 2050.86 1.10527 0.552637 0.833422i \(-0.313622\pi\)
0.552637 + 0.833422i \(0.313622\pi\)
\(152\) 3121.83 1.66588
\(153\) −762.138 −0.402714
\(154\) 1006.36 0.526588
\(155\) −30.9207 −0.0160233
\(156\) −1183.61 −0.607465
\(157\) −262.991 −0.133688 −0.0668438 0.997763i \(-0.521293\pi\)
−0.0668438 + 0.997763i \(0.521293\pi\)
\(158\) −5435.88 −2.73706
\(159\) −2796.39 −1.39477
\(160\) −102.414 −0.0506035
\(161\) 688.152 0.336857
\(162\) −354.393 −0.171875
\(163\) −1444.98 −0.694354 −0.347177 0.937800i \(-0.612860\pi\)
−0.347177 + 0.937800i \(0.612860\pi\)
\(164\) −310.279 −0.147736
\(165\) −393.132 −0.185487
\(166\) 4356.48 2.03692
\(167\) −501.565 −0.232409 −0.116204 0.993225i \(-0.537073\pi\)
−0.116204 + 0.993225i \(0.537073\pi\)
\(168\) −1518.84 −0.697508
\(169\) −2132.03 −0.970429
\(170\) 75.7731 0.0341855
\(171\) −2981.99 −1.33356
\(172\) 4810.08 2.13236
\(173\) −2590.14 −1.13829 −0.569146 0.822237i \(-0.692726\pi\)
−0.569146 + 0.822237i \(0.692726\pi\)
\(174\) 1760.69 0.767112
\(175\) −474.290 −0.204874
\(176\) −5110.79 −2.18886
\(177\) 5751.85 2.44257
\(178\) −5684.02 −2.39346
\(179\) 2165.65 0.904294 0.452147 0.891943i \(-0.350658\pi\)
0.452147 + 0.891943i \(0.350658\pi\)
\(180\) 687.968 0.284878
\(181\) −1925.56 −0.790750 −0.395375 0.918520i \(-0.629385\pi\)
−0.395375 + 0.918520i \(0.629385\pi\)
\(182\) 154.882 0.0630803
\(183\) 2884.00 1.16498
\(184\) −8458.69 −3.38904
\(185\) 115.466 0.0458877
\(186\) 1489.05 0.587003
\(187\) 890.324 0.348165
\(188\) 8035.68 3.11735
\(189\) 577.055 0.222088
\(190\) 296.475 0.113203
\(191\) −2783.52 −1.05449 −0.527247 0.849712i \(-0.676776\pi\)
−0.527247 + 0.849712i \(0.676776\pi\)
\(192\) −1684.65 −0.633223
\(193\) 2258.27 0.842246 0.421123 0.907004i \(-0.361636\pi\)
0.421123 + 0.907004i \(0.361636\pi\)
\(194\) 1909.39 0.706631
\(195\) −60.5045 −0.0222196
\(196\) −5690.27 −2.07371
\(197\) −1270.70 −0.459560 −0.229780 0.973243i \(-0.573801\pi\)
−0.229780 + 0.973243i \(0.573801\pi\)
\(198\) 11815.9 4.24102
\(199\) −4794.36 −1.70786 −0.853928 0.520392i \(-0.825786\pi\)
−0.853928 + 0.520392i \(0.825786\pi\)
\(200\) 5829.92 2.06119
\(201\) 130.457 0.0457798
\(202\) −662.942 −0.230913
\(203\) −157.619 −0.0544960
\(204\) −2496.37 −0.856769
\(205\) −15.8611 −0.00540383
\(206\) −986.313 −0.333591
\(207\) 8079.80 2.71297
\(208\) −786.569 −0.262205
\(209\) 3483.54 1.15293
\(210\) −144.242 −0.0473984
\(211\) −2807.00 −0.915837 −0.457918 0.888994i \(-0.651405\pi\)
−0.457918 + 0.888994i \(0.651405\pi\)
\(212\) −5716.66 −1.85199
\(213\) −5680.21 −1.82724
\(214\) 2441.50 0.779896
\(215\) 245.885 0.0779964
\(216\) −7093.09 −2.23437
\(217\) −133.302 −0.0417009
\(218\) 6316.38 1.96238
\(219\) 1639.81 0.505973
\(220\) −803.679 −0.246291
\(221\) 137.024 0.0417070
\(222\) −5560.51 −1.68107
\(223\) 4684.30 1.40665 0.703327 0.710866i \(-0.251697\pi\)
0.703327 + 0.710866i \(0.251697\pi\)
\(224\) −441.516 −0.131697
\(225\) −5568.79 −1.65001
\(226\) 5099.70 1.50101
\(227\) −1395.72 −0.408095 −0.204047 0.978961i \(-0.565410\pi\)
−0.204047 + 0.978961i \(0.565410\pi\)
\(228\) −9767.47 −2.83713
\(229\) 894.638 0.258163 0.129082 0.991634i \(-0.458797\pi\)
0.129082 + 0.991634i \(0.458797\pi\)
\(230\) −803.309 −0.230298
\(231\) −1694.83 −0.482733
\(232\) 1937.43 0.548270
\(233\) 1196.13 0.336313 0.168156 0.985760i \(-0.446219\pi\)
0.168156 + 0.985760i \(0.446219\pi\)
\(234\) 1818.52 0.508035
\(235\) 410.773 0.114025
\(236\) 11758.5 3.24328
\(237\) 9154.67 2.50911
\(238\) 326.664 0.0889685
\(239\) 4948.82 1.33938 0.669691 0.742639i \(-0.266426\pi\)
0.669691 + 0.742639i \(0.266426\pi\)
\(240\) 732.534 0.197020
\(241\) −6702.73 −1.79154 −0.895770 0.444518i \(-0.853375\pi\)
−0.895770 + 0.444518i \(0.853375\pi\)
\(242\) −7105.03 −1.88731
\(243\) −3483.65 −0.919656
\(244\) 5895.75 1.54687
\(245\) −290.879 −0.0758513
\(246\) 763.824 0.197966
\(247\) 536.130 0.138110
\(248\) 1638.53 0.419543
\(249\) −7336.85 −1.86728
\(250\) 1110.81 0.281016
\(251\) −4756.08 −1.19602 −0.598010 0.801489i \(-0.704042\pi\)
−0.598010 + 0.801489i \(0.704042\pi\)
\(252\) 2965.89 0.741402
\(253\) −9438.77 −2.34550
\(254\) −9701.29 −2.39651
\(255\) −127.611 −0.0313385
\(256\) −8099.28 −1.97736
\(257\) 2892.84 0.702143 0.351071 0.936349i \(-0.385817\pi\)
0.351071 + 0.936349i \(0.385817\pi\)
\(258\) −11841.1 −2.85735
\(259\) 497.784 0.119424
\(260\) −123.689 −0.0295034
\(261\) −1850.65 −0.438898
\(262\) 2046.92 0.482667
\(263\) 5415.48 1.26971 0.634853 0.772633i \(-0.281061\pi\)
0.634853 + 0.772633i \(0.281061\pi\)
\(264\) 20832.6 4.85666
\(265\) −292.228 −0.0677412
\(266\) 1278.13 0.294613
\(267\) 9572.58 2.19413
\(268\) 266.693 0.0607869
\(269\) 5787.00 1.31167 0.655835 0.754904i \(-0.272317\pi\)
0.655835 + 0.754904i \(0.272317\pi\)
\(270\) −673.620 −0.151834
\(271\) 5465.13 1.22503 0.612515 0.790459i \(-0.290158\pi\)
0.612515 + 0.790459i \(0.290158\pi\)
\(272\) −1658.97 −0.369815
\(273\) −260.840 −0.0578270
\(274\) 657.006 0.144858
\(275\) 6505.42 1.42651
\(276\) 26465.3 5.77182
\(277\) −1207.65 −0.261952 −0.130976 0.991386i \(-0.541811\pi\)
−0.130976 + 0.991386i \(0.541811\pi\)
\(278\) −10435.1 −2.25128
\(279\) −1565.13 −0.335850
\(280\) −158.722 −0.0338766
\(281\) −1197.18 −0.254155 −0.127077 0.991893i \(-0.540560\pi\)
−0.127077 + 0.991893i \(0.540560\pi\)
\(282\) −19781.7 −4.17724
\(283\) 3164.73 0.664748 0.332374 0.943148i \(-0.392150\pi\)
0.332374 + 0.943148i \(0.392150\pi\)
\(284\) −11612.0 −2.42622
\(285\) −499.300 −0.103775
\(286\) −2124.38 −0.439221
\(287\) −68.3784 −0.0140636
\(288\) −5183.98 −1.06066
\(289\) 289.000 0.0588235
\(290\) 183.995 0.0372571
\(291\) −3215.65 −0.647782
\(292\) 3352.26 0.671836
\(293\) 7456.21 1.48668 0.743339 0.668915i \(-0.233241\pi\)
0.743339 + 0.668915i \(0.233241\pi\)
\(294\) 14007.9 2.77877
\(295\) 601.079 0.118631
\(296\) −6118.70 −1.20149
\(297\) −7914.94 −1.54637
\(298\) 9323.89 1.81248
\(299\) −1452.66 −0.280969
\(300\) −18240.5 −3.51038
\(301\) 1060.03 0.202988
\(302\) −10321.0 −1.96657
\(303\) 1116.47 0.211683
\(304\) −6490.98 −1.22462
\(305\) 301.383 0.0565808
\(306\) 3835.46 0.716532
\(307\) −6535.48 −1.21498 −0.607491 0.794327i \(-0.707824\pi\)
−0.607491 + 0.794327i \(0.707824\pi\)
\(308\) −3464.73 −0.640978
\(309\) 1661.07 0.305809
\(310\) 155.608 0.0285096
\(311\) −8935.89 −1.62928 −0.814642 0.579963i \(-0.803067\pi\)
−0.814642 + 0.579963i \(0.803067\pi\)
\(312\) 3206.22 0.581783
\(313\) −2628.71 −0.474707 −0.237353 0.971423i \(-0.576280\pi\)
−0.237353 + 0.971423i \(0.576280\pi\)
\(314\) 1323.50 0.237865
\(315\) 151.612 0.0271187
\(316\) 18714.9 3.33163
\(317\) 4268.54 0.756293 0.378147 0.925746i \(-0.376562\pi\)
0.378147 + 0.925746i \(0.376562\pi\)
\(318\) 14072.9 2.48166
\(319\) 2161.92 0.379449
\(320\) −176.048 −0.0307544
\(321\) −4111.79 −0.714946
\(322\) −3463.13 −0.599357
\(323\) 1130.76 0.194790
\(324\) 1220.12 0.209211
\(325\) 1001.21 0.170883
\(326\) 7271.89 1.23544
\(327\) −10637.5 −1.79895
\(328\) 840.500 0.141490
\(329\) 1770.88 0.296753
\(330\) 1978.44 0.330029
\(331\) 992.298 0.164778 0.0823892 0.996600i \(-0.473745\pi\)
0.0823892 + 0.996600i \(0.473745\pi\)
\(332\) −14998.7 −2.47940
\(333\) 5844.63 0.961812
\(334\) 2524.13 0.413516
\(335\) 13.6330 0.00222344
\(336\) 3158.02 0.512750
\(337\) 8042.26 1.29997 0.649985 0.759947i \(-0.274775\pi\)
0.649985 + 0.759947i \(0.274775\pi\)
\(338\) 10729.5 1.72665
\(339\) −8588.52 −1.37600
\(340\) −260.875 −0.0416116
\(341\) 1828.38 0.290359
\(342\) 15006.9 2.37275
\(343\) −2563.68 −0.403573
\(344\) −13029.8 −2.04221
\(345\) 1352.87 0.211119
\(346\) 13034.9 2.02532
\(347\) −7414.16 −1.14701 −0.573506 0.819202i \(-0.694417\pi\)
−0.573506 + 0.819202i \(0.694417\pi\)
\(348\) −6061.78 −0.933751
\(349\) −859.194 −0.131781 −0.0658905 0.997827i \(-0.520989\pi\)
−0.0658905 + 0.997827i \(0.520989\pi\)
\(350\) 2386.87 0.364525
\(351\) −1218.14 −0.185241
\(352\) 6055.89 0.916988
\(353\) 569.084 0.0858053 0.0429027 0.999079i \(-0.486339\pi\)
0.0429027 + 0.999079i \(0.486339\pi\)
\(354\) −28946.3 −4.34598
\(355\) −593.592 −0.0887453
\(356\) 19569.2 2.91339
\(357\) −550.142 −0.0815592
\(358\) −10898.7 −1.60897
\(359\) −5005.21 −0.735835 −0.367918 0.929858i \(-0.619929\pi\)
−0.367918 + 0.929858i \(0.619929\pi\)
\(360\) −1863.60 −0.272834
\(361\) −2434.71 −0.354965
\(362\) 9690.40 1.40695
\(363\) 11965.7 1.73013
\(364\) −533.235 −0.0767833
\(365\) 171.363 0.0245741
\(366\) −14513.7 −2.07280
\(367\) −10975.3 −1.56105 −0.780523 0.625127i \(-0.785047\pi\)
−0.780523 + 0.625127i \(0.785047\pi\)
\(368\) 17587.5 2.49134
\(369\) −802.851 −0.113265
\(370\) −581.083 −0.0816462
\(371\) −1259.82 −0.176298
\(372\) −5126.57 −0.714517
\(373\) −3211.72 −0.445835 −0.222918 0.974837i \(-0.571558\pi\)
−0.222918 + 0.974837i \(0.571558\pi\)
\(374\) −4480.56 −0.619477
\(375\) −1870.74 −0.257613
\(376\) −21767.4 −2.98556
\(377\) 332.727 0.0454544
\(378\) −2904.03 −0.395152
\(379\) 8051.48 1.09123 0.545616 0.838035i \(-0.316296\pi\)
0.545616 + 0.838035i \(0.316296\pi\)
\(380\) −1020.72 −0.137794
\(381\) 16338.1 2.19692
\(382\) 14008.1 1.87622
\(383\) −2584.16 −0.344763 −0.172382 0.985030i \(-0.555146\pi\)
−0.172382 + 0.985030i \(0.555146\pi\)
\(384\) 16318.2 2.16858
\(385\) −177.112 −0.0234454
\(386\) −11364.7 −1.49858
\(387\) 12446.2 1.63482
\(388\) −6573.74 −0.860132
\(389\) −5174.31 −0.674417 −0.337208 0.941430i \(-0.609483\pi\)
−0.337208 + 0.941430i \(0.609483\pi\)
\(390\) 304.489 0.0395344
\(391\) −3063.83 −0.396278
\(392\) 15414.1 1.98604
\(393\) −3447.25 −0.442470
\(394\) 6394.79 0.817677
\(395\) 956.680 0.121863
\(396\) −40680.4 −5.16230
\(397\) −5149.36 −0.650980 −0.325490 0.945545i \(-0.605529\pi\)
−0.325490 + 0.945545i \(0.605529\pi\)
\(398\) 24127.7 3.03872
\(399\) −2152.53 −0.270078
\(400\) −12121.7 −1.51522
\(401\) 8700.49 1.08350 0.541748 0.840541i \(-0.317763\pi\)
0.541748 + 0.840541i \(0.317763\pi\)
\(402\) −656.527 −0.0814542
\(403\) 281.394 0.0347823
\(404\) 2282.41 0.281074
\(405\) 62.3709 0.00765243
\(406\) 793.219 0.0969625
\(407\) −6827.65 −0.831533
\(408\) 6762.29 0.820547
\(409\) 12346.0 1.49260 0.746299 0.665611i \(-0.231829\pi\)
0.746299 + 0.665611i \(0.231829\pi\)
\(410\) 79.8209 0.00961482
\(411\) −1106.48 −0.132794
\(412\) 3395.72 0.406056
\(413\) 2591.30 0.308740
\(414\) −40661.7 −4.82708
\(415\) −766.713 −0.0906903
\(416\) 932.023 0.109847
\(417\) 17574.0 2.06379
\(418\) −17531.0 −2.05136
\(419\) −5763.33 −0.671974 −0.335987 0.941867i \(-0.609070\pi\)
−0.335987 + 0.941867i \(0.609070\pi\)
\(420\) 496.604 0.0576947
\(421\) −1876.12 −0.217188 −0.108594 0.994086i \(-0.534635\pi\)
−0.108594 + 0.994086i \(0.534635\pi\)
\(422\) 14126.2 1.62951
\(423\) 20792.4 2.38998
\(424\) 15485.6 1.77369
\(425\) 2111.66 0.241014
\(426\) 28585.7 3.25113
\(427\) 1299.29 0.147253
\(428\) −8405.72 −0.949313
\(429\) 3577.71 0.402642
\(430\) −1237.42 −0.138776
\(431\) 83.9299 0.00937996 0.00468998 0.999989i \(-0.498507\pi\)
0.00468998 + 0.999989i \(0.498507\pi\)
\(432\) 14748.1 1.64252
\(433\) −15345.0 −1.70308 −0.851539 0.524291i \(-0.824331\pi\)
−0.851539 + 0.524291i \(0.824331\pi\)
\(434\) 670.842 0.0741968
\(435\) −309.870 −0.0341543
\(436\) −21746.3 −2.38867
\(437\) −11987.8 −1.31225
\(438\) −8252.36 −0.900258
\(439\) 3064.74 0.333194 0.166597 0.986025i \(-0.446722\pi\)
0.166597 + 0.986025i \(0.446722\pi\)
\(440\) 2177.05 0.235879
\(441\) −14723.6 −1.58985
\(442\) −689.575 −0.0742076
\(443\) −1792.97 −0.192295 −0.0961474 0.995367i \(-0.530652\pi\)
−0.0961474 + 0.995367i \(0.530652\pi\)
\(444\) 19144.0 2.04624
\(445\) 1000.35 0.106564
\(446\) −23573.8 −2.50281
\(447\) −15702.6 −1.66153
\(448\) −758.960 −0.0800391
\(449\) 2499.19 0.262681 0.131341 0.991337i \(-0.458072\pi\)
0.131341 + 0.991337i \(0.458072\pi\)
\(450\) 28025.0 2.93580
\(451\) 937.885 0.0979231
\(452\) −17557.5 −1.82707
\(453\) 17381.7 1.80279
\(454\) 7024.00 0.726107
\(455\) −27.2583 −0.00280854
\(456\) 26458.6 2.71719
\(457\) 14784.4 1.51331 0.756656 0.653813i \(-0.226832\pi\)
0.756656 + 0.653813i \(0.226832\pi\)
\(458\) −4502.28 −0.459340
\(459\) −2569.20 −0.261263
\(460\) 2765.67 0.280326
\(461\) −17746.9 −1.79297 −0.896483 0.443078i \(-0.853887\pi\)
−0.896483 + 0.443078i \(0.853887\pi\)
\(462\) 8529.23 0.858909
\(463\) 18486.4 1.85559 0.927793 0.373096i \(-0.121704\pi\)
0.927793 + 0.373096i \(0.121704\pi\)
\(464\) −4028.36 −0.403043
\(465\) −262.064 −0.0261353
\(466\) −6019.52 −0.598388
\(467\) 7406.57 0.733908 0.366954 0.930239i \(-0.380401\pi\)
0.366954 + 0.930239i \(0.380401\pi\)
\(468\) −6260.87 −0.618395
\(469\) 58.7731 0.00578655
\(470\) −2067.22 −0.202880
\(471\) −2228.94 −0.218055
\(472\) −31852.0 −3.10616
\(473\) −14539.5 −1.41338
\(474\) −46071.0 −4.46437
\(475\) 8262.24 0.798101
\(476\) −1124.65 −0.108295
\(477\) −14791.9 −1.41986
\(478\) −24905.0 −2.38311
\(479\) −18550.9 −1.76955 −0.884775 0.466019i \(-0.845688\pi\)
−0.884775 + 0.466019i \(0.845688\pi\)
\(480\) −867.997 −0.0825384
\(481\) −1050.80 −0.0996100
\(482\) 33731.6 3.18762
\(483\) 5832.34 0.549442
\(484\) 24461.5 2.29729
\(485\) −336.041 −0.0314615
\(486\) 17531.5 1.63631
\(487\) 10203.4 0.949406 0.474703 0.880146i \(-0.342556\pi\)
0.474703 + 0.880146i \(0.342556\pi\)
\(488\) −15970.7 −1.48147
\(489\) −12246.7 −1.13255
\(490\) 1463.85 0.134959
\(491\) −1247.46 −0.114658 −0.0573290 0.998355i \(-0.518258\pi\)
−0.0573290 + 0.998355i \(0.518258\pi\)
\(492\) −2629.73 −0.240970
\(493\) 701.760 0.0641089
\(494\) −2698.08 −0.245734
\(495\) −2079.53 −0.188824
\(496\) −3406.87 −0.308413
\(497\) −2559.03 −0.230962
\(498\) 36922.7 3.32238
\(499\) 70.0303 0.00628254 0.00314127 0.999995i \(-0.499000\pi\)
0.00314127 + 0.999995i \(0.499000\pi\)
\(500\) −3824.36 −0.342061
\(501\) −4250.94 −0.379078
\(502\) 23935.0 2.12803
\(503\) 1444.29 0.128028 0.0640138 0.997949i \(-0.479610\pi\)
0.0640138 + 0.997949i \(0.479610\pi\)
\(504\) −8034.15 −0.710058
\(505\) 116.674 0.0102810
\(506\) 47500.7 4.17325
\(507\) −18069.7 −1.58285
\(508\) 33400.0 2.91710
\(509\) 14272.8 1.24289 0.621445 0.783458i \(-0.286546\pi\)
0.621445 + 0.783458i \(0.286546\pi\)
\(510\) 642.204 0.0557593
\(511\) 738.761 0.0639547
\(512\) 25356.7 2.18871
\(513\) −10052.4 −0.865157
\(514\) −14558.3 −1.24929
\(515\) 173.585 0.0148525
\(516\) 40767.2 3.47805
\(517\) −24289.6 −2.06625
\(518\) −2505.10 −0.212486
\(519\) −21952.3 −1.85665
\(520\) 335.055 0.0282561
\(521\) 14874.0 1.25075 0.625376 0.780324i \(-0.284946\pi\)
0.625376 + 0.780324i \(0.284946\pi\)
\(522\) 9313.42 0.780914
\(523\) −8142.90 −0.680811 −0.340406 0.940279i \(-0.610564\pi\)
−0.340406 + 0.940279i \(0.610564\pi\)
\(524\) −7047.21 −0.587517
\(525\) −4019.78 −0.334167
\(526\) −27253.4 −2.25914
\(527\) 593.494 0.0490569
\(528\) −43315.7 −3.57022
\(529\) 20314.2 1.66962
\(530\) 1470.64 0.120529
\(531\) 30425.3 2.48652
\(532\) −4400.40 −0.358612
\(533\) 144.344 0.0117303
\(534\) −48174.1 −3.90393
\(535\) −429.689 −0.0347235
\(536\) −722.432 −0.0582170
\(537\) 18354.7 1.47498
\(538\) −29123.1 −2.33380
\(539\) 17200.0 1.37451
\(540\) 2319.17 0.184817
\(541\) 3179.67 0.252689 0.126344 0.991986i \(-0.459676\pi\)
0.126344 + 0.991986i \(0.459676\pi\)
\(542\) −27503.3 −2.17965
\(543\) −16319.8 −1.28978
\(544\) 1965.75 0.154928
\(545\) −1111.64 −0.0873716
\(546\) 1312.68 0.102889
\(547\) 2107.07 0.164702 0.0823509 0.996603i \(-0.473757\pi\)
0.0823509 + 0.996603i \(0.473757\pi\)
\(548\) −2261.97 −0.176326
\(549\) 15255.3 1.18594
\(550\) −32738.6 −2.53814
\(551\) 2745.76 0.212292
\(552\) −71690.4 −5.52780
\(553\) 4124.33 0.317151
\(554\) 6077.51 0.466081
\(555\) 978.614 0.0748466
\(556\) 35926.4 2.74032
\(557\) 467.382 0.0355540 0.0177770 0.999842i \(-0.494341\pi\)
0.0177770 + 0.999842i \(0.494341\pi\)
\(558\) 7876.55 0.597565
\(559\) −2237.69 −0.169309
\(560\) 330.019 0.0249033
\(561\) 7545.81 0.567887
\(562\) 6024.80 0.452208
\(563\) 14612.6 1.09387 0.546935 0.837175i \(-0.315794\pi\)
0.546935 + 0.837175i \(0.315794\pi\)
\(564\) 68105.2 5.08466
\(565\) −897.515 −0.0668297
\(566\) −15926.5 −1.18276
\(567\) 268.886 0.0199156
\(568\) 31455.3 2.32365
\(569\) 11602.3 0.854821 0.427410 0.904058i \(-0.359426\pi\)
0.427410 + 0.904058i \(0.359426\pi\)
\(570\) 2512.73 0.184643
\(571\) −10534.9 −0.772104 −0.386052 0.922477i \(-0.626161\pi\)
−0.386052 + 0.922477i \(0.626161\pi\)
\(572\) 7313.91 0.534633
\(573\) −23591.3 −1.71997
\(574\) 344.115 0.0250228
\(575\) −22386.8 −1.62364
\(576\) −8911.18 −0.644617
\(577\) 14404.7 1.03930 0.519650 0.854379i \(-0.326062\pi\)
0.519650 + 0.854379i \(0.326062\pi\)
\(578\) −1454.40 −0.104662
\(579\) 19139.6 1.37377
\(580\) −633.466 −0.0453504
\(581\) −3305.37 −0.236024
\(582\) 16182.8 1.15257
\(583\) 17279.8 1.22754
\(584\) −9080.77 −0.643433
\(585\) −320.047 −0.0226194
\(586\) −37523.5 −2.64519
\(587\) −11004.9 −0.773799 −0.386900 0.922122i \(-0.626454\pi\)
−0.386900 + 0.922122i \(0.626454\pi\)
\(588\) −48227.0 −3.38240
\(589\) 2322.14 0.162449
\(590\) −3024.94 −0.211076
\(591\) −10769.6 −0.749581
\(592\) 12722.2 0.883239
\(593\) 1853.59 0.128361 0.0641804 0.997938i \(-0.479557\pi\)
0.0641804 + 0.997938i \(0.479557\pi\)
\(594\) 39832.0 2.75139
\(595\) −57.4909 −0.00396117
\(596\) −32100.7 −2.20620
\(597\) −40633.9 −2.78565
\(598\) 7310.53 0.499916
\(599\) 19074.7 1.30112 0.650559 0.759456i \(-0.274535\pi\)
0.650559 + 0.759456i \(0.274535\pi\)
\(600\) 49410.7 3.36197
\(601\) −27776.0 −1.88520 −0.942600 0.333923i \(-0.891627\pi\)
−0.942600 + 0.333923i \(0.891627\pi\)
\(602\) −5334.62 −0.361168
\(603\) 690.073 0.0466035
\(604\) 35533.4 2.39377
\(605\) 1250.44 0.0840291
\(606\) −5618.67 −0.376638
\(607\) 18728.3 1.25232 0.626159 0.779695i \(-0.284626\pi\)
0.626159 + 0.779695i \(0.284626\pi\)
\(608\) 7691.32 0.513033
\(609\) −1335.88 −0.0888874
\(610\) −1516.71 −0.100672
\(611\) −3738.25 −0.247518
\(612\) −13204.9 −0.872184
\(613\) −24405.3 −1.60802 −0.804012 0.594613i \(-0.797305\pi\)
−0.804012 + 0.594613i \(0.797305\pi\)
\(614\) 32889.8 2.16177
\(615\) −134.428 −0.00881409
\(616\) 9385.43 0.613880
\(617\) −22516.4 −1.46917 −0.734584 0.678518i \(-0.762623\pi\)
−0.734584 + 0.678518i \(0.762623\pi\)
\(618\) −8359.35 −0.544114
\(619\) −5146.53 −0.334179 −0.167089 0.985942i \(-0.553437\pi\)
−0.167089 + 0.985942i \(0.553437\pi\)
\(620\) −535.736 −0.0347027
\(621\) 27237.4 1.76006
\(622\) 44969.9 2.89892
\(623\) 4312.60 0.277337
\(624\) −6666.45 −0.427679
\(625\) 15331.4 0.981213
\(626\) 13229.0 0.844627
\(627\) 29524.3 1.88052
\(628\) −4556.62 −0.289536
\(629\) −2216.26 −0.140490
\(630\) −762.990 −0.0482512
\(631\) −3858.77 −0.243447 −0.121724 0.992564i \(-0.538842\pi\)
−0.121724 + 0.992564i \(0.538842\pi\)
\(632\) −50695.8 −3.19078
\(633\) −23790.3 −1.49381
\(634\) −21481.5 −1.34564
\(635\) 1707.36 0.106700
\(636\) −48450.7 −3.02075
\(637\) 2647.15 0.164653
\(638\) −10879.9 −0.675138
\(639\) −30046.3 −1.86011
\(640\) 1705.28 0.105324
\(641\) 18689.3 1.15161 0.575805 0.817587i \(-0.304689\pi\)
0.575805 + 0.817587i \(0.304689\pi\)
\(642\) 20692.6 1.27208
\(643\) 26473.5 1.62366 0.811831 0.583893i \(-0.198471\pi\)
0.811831 + 0.583893i \(0.198471\pi\)
\(644\) 11923.0 0.729555
\(645\) 2083.96 0.127219
\(646\) −5690.57 −0.346583
\(647\) 14397.7 0.874855 0.437427 0.899254i \(-0.355890\pi\)
0.437427 + 0.899254i \(0.355890\pi\)
\(648\) −3305.12 −0.200366
\(649\) −35542.6 −2.14972
\(650\) −5038.59 −0.304046
\(651\) −1129.78 −0.0680177
\(652\) −25036.0 −1.50381
\(653\) 20939.5 1.25486 0.627431 0.778672i \(-0.284107\pi\)
0.627431 + 0.778672i \(0.284107\pi\)
\(654\) 53533.6 3.20081
\(655\) −360.244 −0.0214899
\(656\) −1747.59 −0.104012
\(657\) 8674.02 0.515077
\(658\) −8911.96 −0.528001
\(659\) 4031.76 0.238323 0.119162 0.992875i \(-0.461979\pi\)
0.119162 + 0.992875i \(0.461979\pi\)
\(660\) −6811.47 −0.401721
\(661\) 6691.52 0.393752 0.196876 0.980428i \(-0.436920\pi\)
0.196876 + 0.980428i \(0.436920\pi\)
\(662\) −4993.75 −0.293184
\(663\) 1161.33 0.0680275
\(664\) 40629.2 2.37458
\(665\) −224.943 −0.0131171
\(666\) −29413.1 −1.71131
\(667\) −7439.71 −0.431884
\(668\) −8690.19 −0.503344
\(669\) 39701.1 2.29437
\(670\) −68.6083 −0.00395607
\(671\) −17821.2 −1.02530
\(672\) −3742.01 −0.214808
\(673\) 10319.2 0.591048 0.295524 0.955335i \(-0.404506\pi\)
0.295524 + 0.955335i \(0.404506\pi\)
\(674\) −40472.7 −2.31298
\(675\) −18772.6 −1.07046
\(676\) −36939.9 −2.10172
\(677\) −19813.3 −1.12480 −0.562398 0.826866i \(-0.690121\pi\)
−0.562398 + 0.826866i \(0.690121\pi\)
\(678\) 43221.8 2.44826
\(679\) −1448.70 −0.0818793
\(680\) 706.671 0.0398524
\(681\) −11829.3 −0.665636
\(682\) −9201.33 −0.516624
\(683\) 5924.61 0.331916 0.165958 0.986133i \(-0.446928\pi\)
0.165958 + 0.986133i \(0.446928\pi\)
\(684\) −51666.4 −2.88818
\(685\) −115.629 −0.00644957
\(686\) 12901.7 0.718061
\(687\) 7582.38 0.421085
\(688\) 27091.9 1.50126
\(689\) 2659.43 0.147048
\(690\) −6808.33 −0.375636
\(691\) 1973.16 0.108629 0.0543143 0.998524i \(-0.482703\pi\)
0.0543143 + 0.998524i \(0.482703\pi\)
\(692\) −44877.1 −2.46528
\(693\) −8965.03 −0.491419
\(694\) 37311.8 2.04083
\(695\) 1836.51 0.100234
\(696\) 16420.4 0.894274
\(697\) 304.439 0.0165444
\(698\) 4323.90 0.234473
\(699\) 10137.6 0.548554
\(700\) −8217.63 −0.443710
\(701\) −12840.1 −0.691815 −0.345907 0.938269i \(-0.612429\pi\)
−0.345907 + 0.938269i \(0.612429\pi\)
\(702\) 6130.30 0.329591
\(703\) −8671.50 −0.465223
\(704\) 10410.0 0.557302
\(705\) 3481.45 0.185984
\(706\) −2863.92 −0.152670
\(707\) 502.990 0.0267566
\(708\) 99657.5 5.29005
\(709\) −27749.7 −1.46990 −0.734952 0.678119i \(-0.762796\pi\)
−0.734952 + 0.678119i \(0.762796\pi\)
\(710\) 2987.26 0.157901
\(711\) 48425.0 2.55426
\(712\) −53010.0 −2.79022
\(713\) −6291.92 −0.330483
\(714\) 2768.60 0.145115
\(715\) 373.877 0.0195555
\(716\) 37522.4 1.95849
\(717\) 41943.0 2.18464
\(718\) 25188.8 1.30924
\(719\) 16888.3 0.875979 0.437989 0.898980i \(-0.355691\pi\)
0.437989 + 0.898980i \(0.355691\pi\)
\(720\) 3874.85 0.200565
\(721\) 748.339 0.0386541
\(722\) 12252.7 0.631575
\(723\) −56808.0 −2.92215
\(724\) −33362.6 −1.71258
\(725\) 5127.62 0.262669
\(726\) −60217.6 −3.07835
\(727\) 2135.25 0.108930 0.0544649 0.998516i \(-0.482655\pi\)
0.0544649 + 0.998516i \(0.482655\pi\)
\(728\) 1444.45 0.0735371
\(729\) −31426.5 −1.59663
\(730\) −862.386 −0.0437238
\(731\) −4719.54 −0.238794
\(732\) 49968.6 2.52308
\(733\) 4795.27 0.241633 0.120817 0.992675i \(-0.461449\pi\)
0.120817 + 0.992675i \(0.461449\pi\)
\(734\) 55233.1 2.77751
\(735\) −2465.30 −0.123720
\(736\) −20839.9 −1.04371
\(737\) −806.138 −0.0402910
\(738\) 4040.36 0.201528
\(739\) −32747.6 −1.63010 −0.815048 0.579393i \(-0.803290\pi\)
−0.815048 + 0.579393i \(0.803290\pi\)
\(740\) 2000.58 0.0993821
\(741\) 4543.89 0.225269
\(742\) 6340.05 0.313680
\(743\) 12299.4 0.607298 0.303649 0.952784i \(-0.401795\pi\)
0.303649 + 0.952784i \(0.401795\pi\)
\(744\) 13887.1 0.684309
\(745\) −1640.94 −0.0806974
\(746\) 16163.0 0.793257
\(747\) −38809.3 −1.90088
\(748\) 15425.9 0.754046
\(749\) −1852.43 −0.0903688
\(750\) 9414.54 0.458361
\(751\) 30102.6 1.46266 0.731332 0.682021i \(-0.238899\pi\)
0.731332 + 0.682021i \(0.238899\pi\)
\(752\) 45259.4 2.19474
\(753\) −40309.4 −1.95081
\(754\) −1674.45 −0.0808753
\(755\) 1816.42 0.0875581
\(756\) 9998.14 0.480990
\(757\) 38826.3 1.86416 0.932078 0.362257i \(-0.117994\pi\)
0.932078 + 0.362257i \(0.117994\pi\)
\(758\) −40519.2 −1.94159
\(759\) −79996.9 −3.82570
\(760\) 2764.97 0.131968
\(761\) 19981.6 0.951815 0.475907 0.879495i \(-0.342120\pi\)
0.475907 + 0.879495i \(0.342120\pi\)
\(762\) −82221.8 −3.90890
\(763\) −4792.39 −0.227387
\(764\) −48227.7 −2.28379
\(765\) −675.017 −0.0319024
\(766\) 13004.8 0.613424
\(767\) −5470.14 −0.257517
\(768\) −68644.2 −3.22524
\(769\) −22407.7 −1.05077 −0.525384 0.850865i \(-0.676078\pi\)
−0.525384 + 0.850865i \(0.676078\pi\)
\(770\) 891.320 0.0417155
\(771\) 24517.9 1.14525
\(772\) 39127.0 1.82411
\(773\) −6902.77 −0.321184 −0.160592 0.987021i \(-0.551340\pi\)
−0.160592 + 0.987021i \(0.551340\pi\)
\(774\) −62635.4 −2.90876
\(775\) 4336.54 0.200997
\(776\) 17807.3 0.823768
\(777\) 4218.89 0.194790
\(778\) 26039.8 1.19996
\(779\) 1191.17 0.0547856
\(780\) −1048.31 −0.0481225
\(781\) 35099.9 1.60816
\(782\) 15418.8 0.705082
\(783\) −6238.62 −0.284738
\(784\) −32049.3 −1.45997
\(785\) −232.928 −0.0105905
\(786\) 17348.3 0.787270
\(787\) −22185.9 −1.00488 −0.502442 0.864611i \(-0.667565\pi\)
−0.502442 + 0.864611i \(0.667565\pi\)
\(788\) −22016.3 −0.995301
\(789\) 45898.1 2.07099
\(790\) −4814.50 −0.216826
\(791\) −3869.27 −0.173926
\(792\) 110197. 4.94405
\(793\) −2742.74 −0.122822
\(794\) 25914.2 1.15826
\(795\) −2476.73 −0.110491
\(796\) −83067.8 −3.69882
\(797\) −16291.1 −0.724040 −0.362020 0.932170i \(-0.617913\pi\)
−0.362020 + 0.932170i \(0.617913\pi\)
\(798\) 10832.6 0.480539
\(799\) −7884.41 −0.349100
\(800\) 14363.3 0.634775
\(801\) 50635.5 2.23361
\(802\) −43785.3 −1.92782
\(803\) −10132.9 −0.445309
\(804\) 2260.32 0.0991485
\(805\) 609.489 0.0266853
\(806\) −1416.12 −0.0618867
\(807\) 49046.8 2.13944
\(808\) −6182.70 −0.269191
\(809\) 17696.8 0.769082 0.384541 0.923108i \(-0.374360\pi\)
0.384541 + 0.923108i \(0.374360\pi\)
\(810\) −313.882 −0.0136157
\(811\) −3095.34 −0.134022 −0.0670111 0.997752i \(-0.521346\pi\)
−0.0670111 + 0.997752i \(0.521346\pi\)
\(812\) −2730.93 −0.118026
\(813\) 46318.9 1.99812
\(814\) 34360.2 1.47951
\(815\) −1279.81 −0.0550057
\(816\) −14060.3 −0.603198
\(817\) −18466.0 −0.790751
\(818\) −62131.5 −2.65572
\(819\) −1379.75 −0.0588674
\(820\) −274.811 −0.0117034
\(821\) 12323.5 0.523864 0.261932 0.965086i \(-0.415640\pi\)
0.261932 + 0.965086i \(0.415640\pi\)
\(822\) 5568.36 0.236276
\(823\) −34436.5 −1.45854 −0.729271 0.684225i \(-0.760140\pi\)
−0.729271 + 0.684225i \(0.760140\pi\)
\(824\) −9198.50 −0.388889
\(825\) 55135.7 2.32676
\(826\) −13040.8 −0.549329
\(827\) 18761.6 0.788880 0.394440 0.918922i \(-0.370939\pi\)
0.394440 + 0.918922i \(0.370939\pi\)
\(828\) 139992. 5.87567
\(829\) 22423.8 0.939457 0.469728 0.882811i \(-0.344352\pi\)
0.469728 + 0.882811i \(0.344352\pi\)
\(830\) 3858.49 0.161362
\(831\) −10235.3 −0.427265
\(832\) 1602.13 0.0667596
\(833\) 5583.15 0.232227
\(834\) −88441.1 −3.67202
\(835\) −444.231 −0.0184111
\(836\) 60356.4 2.49697
\(837\) −5276.13 −0.217885
\(838\) 29004.0 1.19562
\(839\) 9128.63 0.375632 0.187816 0.982204i \(-0.439859\pi\)
0.187816 + 0.982204i \(0.439859\pi\)
\(840\) −1345.22 −0.0552555
\(841\) −22685.0 −0.930131
\(842\) 9441.58 0.386435
\(843\) −10146.5 −0.414547
\(844\) −48634.4 −1.98349
\(845\) −1888.32 −0.0768759
\(846\) −104638. −4.25240
\(847\) 5390.75 0.218688
\(848\) −32198.0 −1.30387
\(849\) 26822.2 1.08426
\(850\) −10627.0 −0.428826
\(851\) 23495.7 0.946442
\(852\) −98416.1 −3.95737
\(853\) 27204.8 1.09200 0.545999 0.837786i \(-0.316150\pi\)
0.545999 + 0.837786i \(0.316150\pi\)
\(854\) −6538.68 −0.262001
\(855\) −2641.12 −0.105643
\(856\) 22769.8 0.909179
\(857\) −38060.0 −1.51704 −0.758520 0.651649i \(-0.774077\pi\)
−0.758520 + 0.651649i \(0.774077\pi\)
\(858\) −18004.9 −0.716405
\(859\) −33326.2 −1.32372 −0.661860 0.749627i \(-0.730233\pi\)
−0.661860 + 0.749627i \(0.730233\pi\)
\(860\) 4260.24 0.168922
\(861\) −579.531 −0.0229389
\(862\) −422.378 −0.0166894
\(863\) −41724.2 −1.64578 −0.822890 0.568201i \(-0.807640\pi\)
−0.822890 + 0.568201i \(0.807640\pi\)
\(864\) −17475.4 −0.688108
\(865\) −2294.06 −0.0901737
\(866\) 77223.8 3.03022
\(867\) 2449.38 0.0959460
\(868\) −2309.60 −0.0903146
\(869\) −56569.7 −2.20828
\(870\) 1559.42 0.0607694
\(871\) −124.068 −0.00482649
\(872\) 58907.5 2.28768
\(873\) −17009.6 −0.659438
\(874\) 60328.6 2.33483
\(875\) −842.801 −0.0325621
\(876\) 28411.6 1.09582
\(877\) −49337.3 −1.89966 −0.949830 0.312767i \(-0.898744\pi\)
−0.949830 + 0.312767i \(0.898744\pi\)
\(878\) −15423.3 −0.592838
\(879\) 63194.0 2.42489
\(880\) −4526.57 −0.173398
\(881\) 8845.46 0.338265 0.169132 0.985593i \(-0.445903\pi\)
0.169132 + 0.985593i \(0.445903\pi\)
\(882\) 74096.8 2.82876
\(883\) 14724.2 0.561165 0.280582 0.959830i \(-0.409472\pi\)
0.280582 + 0.959830i \(0.409472\pi\)
\(884\) 2374.10 0.0903277
\(885\) 5094.36 0.193497
\(886\) 9023.14 0.342143
\(887\) 3864.38 0.146283 0.0731415 0.997322i \(-0.476698\pi\)
0.0731415 + 0.997322i \(0.476698\pi\)
\(888\) −51858.1 −1.95974
\(889\) 7360.60 0.277690
\(890\) −5034.28 −0.189606
\(891\) −3688.07 −0.138670
\(892\) 81160.9 3.04649
\(893\) −30849.1 −1.15602
\(894\) 79023.2 2.95630
\(895\) 1918.10 0.0716368
\(896\) 7351.61 0.274107
\(897\) −12311.8 −0.458283
\(898\) −12577.2 −0.467379
\(899\) 1441.14 0.0534648
\(900\) −96485.6 −3.57354
\(901\) 5609.04 0.207397
\(902\) −4719.92 −0.174231
\(903\) 8984.15 0.331089
\(904\) 47560.6 1.74982
\(905\) −1705.45 −0.0626421
\(906\) −87473.7 −3.20764
\(907\) −743.409 −0.0272155 −0.0136078 0.999907i \(-0.504332\pi\)
−0.0136078 + 0.999907i \(0.504332\pi\)
\(908\) −24182.5 −0.883839
\(909\) 5905.76 0.215491
\(910\) 137.177 0.00499713
\(911\) 16291.0 0.592475 0.296238 0.955114i \(-0.404268\pi\)
0.296238 + 0.955114i \(0.404268\pi\)
\(912\) −55013.4 −1.99745
\(913\) 45336.8 1.64340
\(914\) −74402.5 −2.69258
\(915\) 2554.33 0.0922879
\(916\) 15500.6 0.559122
\(917\) −1553.04 −0.0559280
\(918\) 12929.5 0.464856
\(919\) −6188.99 −0.222150 −0.111075 0.993812i \(-0.535429\pi\)
−0.111075 + 0.993812i \(0.535429\pi\)
\(920\) −7491.78 −0.268474
\(921\) −55390.5 −1.98174
\(922\) 89311.6 3.19015
\(923\) 5402.00 0.192643
\(924\) −29364.8 −1.04549
\(925\) −16193.8 −0.575620
\(926\) −93033.0 −3.30157
\(927\) 8786.47 0.311311
\(928\) 4773.30 0.168848
\(929\) −31661.7 −1.11818 −0.559089 0.829108i \(-0.688849\pi\)
−0.559089 + 0.829108i \(0.688849\pi\)
\(930\) 1318.84 0.0465015
\(931\) 21845.0 0.769003
\(932\) 20724.3 0.728376
\(933\) −75734.8 −2.65750
\(934\) −37273.6 −1.30581
\(935\) 788.551 0.0275811
\(936\) 16959.8 0.592251
\(937\) 35010.5 1.22064 0.610322 0.792153i \(-0.291040\pi\)
0.610322 + 0.792153i \(0.291040\pi\)
\(938\) −295.776 −0.0102958
\(939\) −22279.2 −0.774286
\(940\) 7117.12 0.246952
\(941\) −45625.8 −1.58061 −0.790307 0.612711i \(-0.790079\pi\)
−0.790307 + 0.612711i \(0.790079\pi\)
\(942\) 11217.2 0.387977
\(943\) −3227.51 −0.111455
\(944\) 66227.5 2.28339
\(945\) 511.092 0.0175934
\(946\) 73170.2 2.51477
\(947\) −21508.4 −0.738044 −0.369022 0.929421i \(-0.620307\pi\)
−0.369022 + 0.929421i \(0.620307\pi\)
\(948\) 158615. 5.43416
\(949\) −1559.50 −0.0533439
\(950\) −41579.8 −1.42003
\(951\) 36177.4 1.23358
\(952\) 3046.52 0.103717
\(953\) 35686.7 1.21302 0.606509 0.795076i \(-0.292569\pi\)
0.606509 + 0.795076i \(0.292569\pi\)
\(954\) 74440.5 2.52631
\(955\) −2465.34 −0.0835355
\(956\) 85744.0 2.90079
\(957\) 18323.0 0.618912
\(958\) 93357.8 3.14849
\(959\) −498.486 −0.0167851
\(960\) −1492.07 −0.0501630
\(961\) −28572.2 −0.959088
\(962\) 5288.17 0.177232
\(963\) −21749.9 −0.727810
\(964\) −116133. −3.88006
\(965\) 2000.12 0.0667215
\(966\) −29351.3 −0.977600
\(967\) −3731.33 −0.124086 −0.0620432 0.998073i \(-0.519762\pi\)
−0.0620432 + 0.998073i \(0.519762\pi\)
\(968\) −66262.5 −2.20016
\(969\) 9583.60 0.317719
\(970\) 1691.13 0.0559782
\(971\) 17645.1 0.583171 0.291585 0.956545i \(-0.405817\pi\)
0.291585 + 0.956545i \(0.405817\pi\)
\(972\) −60358.3 −1.99176
\(973\) 7917.35 0.260862
\(974\) −51348.7 −1.68924
\(975\) 8485.59 0.278725
\(976\) 33206.7 1.08906
\(977\) 24941.2 0.816723 0.408362 0.912820i \(-0.366100\pi\)
0.408362 + 0.912820i \(0.366100\pi\)
\(978\) 61631.8 2.01510
\(979\) −59152.1 −1.93106
\(980\) −5039.81 −0.164276
\(981\) −56268.9 −1.83132
\(982\) 6277.85 0.204006
\(983\) −22506.2 −0.730252 −0.365126 0.930958i \(-0.618974\pi\)
−0.365126 + 0.930958i \(0.618974\pi\)
\(984\) 7123.53 0.230782
\(985\) −1125.44 −0.0364057
\(986\) −3531.62 −0.114066
\(987\) 15008.8 0.484029
\(988\) 9289.07 0.299114
\(989\) 50034.2 1.60869
\(990\) 10465.3 0.335967
\(991\) 32694.1 1.04799 0.523997 0.851720i \(-0.324440\pi\)
0.523997 + 0.851720i \(0.324440\pi\)
\(992\) 4036.88 0.129205
\(993\) 8410.08 0.268767
\(994\) 12878.3 0.410941
\(995\) −4246.32 −0.135294
\(996\) −127119. −4.04410
\(997\) 18248.8 0.579686 0.289843 0.957074i \(-0.406397\pi\)
0.289843 + 0.957074i \(0.406397\pi\)
\(998\) −352.428 −0.0111783
\(999\) 19702.5 0.623983
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 \(a_p\))