Properties

Label 4017.2.a.j.1.11
Level 4017
Weight 2
Character 4017.1
Self dual Yes
Analytic conductor 32.076
Analytic rank 0
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0759064919\)
Analytic rank: \(0\)
Dimension: \(25\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.254687 q^{2} -1.00000 q^{3} -1.93513 q^{4} -0.644426 q^{5} +0.254687 q^{6} +3.73934 q^{7} +1.00223 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.254687 q^{2} -1.00000 q^{3} -1.93513 q^{4} -0.644426 q^{5} +0.254687 q^{6} +3.73934 q^{7} +1.00223 q^{8} +1.00000 q^{9} +0.164127 q^{10} -2.16169 q^{11} +1.93513 q^{12} +1.00000 q^{13} -0.952363 q^{14} +0.644426 q^{15} +3.61501 q^{16} +6.60210 q^{17} -0.254687 q^{18} +5.07149 q^{19} +1.24705 q^{20} -3.73934 q^{21} +0.550555 q^{22} -1.31455 q^{23} -1.00223 q^{24} -4.58471 q^{25} -0.254687 q^{26} -1.00000 q^{27} -7.23613 q^{28} +6.79091 q^{29} -0.164127 q^{30} -2.74661 q^{31} -2.92515 q^{32} +2.16169 q^{33} -1.68147 q^{34} -2.40973 q^{35} -1.93513 q^{36} -2.15149 q^{37} -1.29164 q^{38} -1.00000 q^{39} -0.645862 q^{40} +1.71235 q^{41} +0.952363 q^{42} +6.80465 q^{43} +4.18316 q^{44} -0.644426 q^{45} +0.334800 q^{46} +4.86401 q^{47} -3.61501 q^{48} +6.98268 q^{49} +1.16767 q^{50} -6.60210 q^{51} -1.93513 q^{52} +1.28229 q^{53} +0.254687 q^{54} +1.39305 q^{55} +3.74767 q^{56} -5.07149 q^{57} -1.72956 q^{58} +4.33667 q^{59} -1.24705 q^{60} -9.11013 q^{61} +0.699527 q^{62} +3.73934 q^{63} -6.48503 q^{64} -0.644426 q^{65} -0.550555 q^{66} -10.0994 q^{67} -12.7759 q^{68} +1.31455 q^{69} +0.613727 q^{70} +1.97915 q^{71} +1.00223 q^{72} -10.0930 q^{73} +0.547956 q^{74} +4.58471 q^{75} -9.81401 q^{76} -8.08331 q^{77} +0.254687 q^{78} -11.7940 q^{79} -2.32961 q^{80} +1.00000 q^{81} -0.436113 q^{82} +11.9265 q^{83} +7.23613 q^{84} -4.25456 q^{85} -1.73306 q^{86} -6.79091 q^{87} -2.16651 q^{88} -7.92637 q^{89} +0.164127 q^{90} +3.73934 q^{91} +2.54384 q^{92} +2.74661 q^{93} -1.23880 q^{94} -3.26820 q^{95} +2.92515 q^{96} +13.9493 q^{97} -1.77840 q^{98} -2.16169 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.254687 −0.180091 −0.0900455 0.995938i \(-0.528701\pi\)
−0.0900455 + 0.995938i \(0.528701\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.93513 −0.967567
\(5\) −0.644426 −0.288196 −0.144098 0.989563i \(-0.546028\pi\)
−0.144098 + 0.989563i \(0.546028\pi\)
\(6\) 0.254687 0.103976
\(7\) 3.73934 1.41334 0.706669 0.707544i \(-0.250197\pi\)
0.706669 + 0.707544i \(0.250197\pi\)
\(8\) 1.00223 0.354341
\(9\) 1.00000 0.333333
\(10\) 0.164127 0.0519015
\(11\) −2.16169 −0.651775 −0.325887 0.945409i \(-0.605663\pi\)
−0.325887 + 0.945409i \(0.605663\pi\)
\(12\) 1.93513 0.558625
\(13\) 1.00000 0.277350
\(14\) −0.952363 −0.254530
\(15\) 0.644426 0.166390
\(16\) 3.61501 0.903754
\(17\) 6.60210 1.60124 0.800622 0.599170i \(-0.204503\pi\)
0.800622 + 0.599170i \(0.204503\pi\)
\(18\) −0.254687 −0.0600303
\(19\) 5.07149 1.16348 0.581740 0.813375i \(-0.302372\pi\)
0.581740 + 0.813375i \(0.302372\pi\)
\(20\) 1.24705 0.278849
\(21\) −3.73934 −0.815991
\(22\) 0.550555 0.117379
\(23\) −1.31455 −0.274103 −0.137052 0.990564i \(-0.543763\pi\)
−0.137052 + 0.990564i \(0.543763\pi\)
\(24\) −1.00223 −0.204579
\(25\) −4.58471 −0.916943
\(26\) −0.254687 −0.0499483
\(27\) −1.00000 −0.192450
\(28\) −7.23613 −1.36750
\(29\) 6.79091 1.26104 0.630520 0.776173i \(-0.282842\pi\)
0.630520 + 0.776173i \(0.282842\pi\)
\(30\) −0.164127 −0.0299654
\(31\) −2.74661 −0.493306 −0.246653 0.969104i \(-0.579331\pi\)
−0.246653 + 0.969104i \(0.579331\pi\)
\(32\) −2.92515 −0.517099
\(33\) 2.16169 0.376302
\(34\) −1.68147 −0.288370
\(35\) −2.40973 −0.407319
\(36\) −1.93513 −0.322522
\(37\) −2.15149 −0.353702 −0.176851 0.984238i \(-0.556591\pi\)
−0.176851 + 0.984238i \(0.556591\pi\)
\(38\) −1.29164 −0.209532
\(39\) −1.00000 −0.160128
\(40\) −0.645862 −0.102120
\(41\) 1.71235 0.267424 0.133712 0.991020i \(-0.457310\pi\)
0.133712 + 0.991020i \(0.457310\pi\)
\(42\) 0.952363 0.146953
\(43\) 6.80465 1.03770 0.518850 0.854866i \(-0.326360\pi\)
0.518850 + 0.854866i \(0.326360\pi\)
\(44\) 4.18316 0.630636
\(45\) −0.644426 −0.0960654
\(46\) 0.334800 0.0493635
\(47\) 4.86401 0.709488 0.354744 0.934963i \(-0.384568\pi\)
0.354744 + 0.934963i \(0.384568\pi\)
\(48\) −3.61501 −0.521782
\(49\) 6.98268 0.997526
\(50\) 1.16767 0.165133
\(51\) −6.60210 −0.924478
\(52\) −1.93513 −0.268355
\(53\) 1.28229 0.176136 0.0880681 0.996114i \(-0.471931\pi\)
0.0880681 + 0.996114i \(0.471931\pi\)
\(54\) 0.254687 0.0346585
\(55\) 1.39305 0.187839
\(56\) 3.74767 0.500804
\(57\) −5.07149 −0.671735
\(58\) −1.72956 −0.227102
\(59\) 4.33667 0.564587 0.282293 0.959328i \(-0.408905\pi\)
0.282293 + 0.959328i \(0.408905\pi\)
\(60\) −1.24705 −0.160994
\(61\) −9.11013 −1.16643 −0.583217 0.812317i \(-0.698206\pi\)
−0.583217 + 0.812317i \(0.698206\pi\)
\(62\) 0.699527 0.0888400
\(63\) 3.73934 0.471113
\(64\) −6.48503 −0.810629
\(65\) −0.644426 −0.0799312
\(66\) −0.550555 −0.0677687
\(67\) −10.0994 −1.23384 −0.616920 0.787026i \(-0.711620\pi\)
−0.616920 + 0.787026i \(0.711620\pi\)
\(68\) −12.7759 −1.54931
\(69\) 1.31455 0.158254
\(70\) 0.613727 0.0733544
\(71\) 1.97915 0.234882 0.117441 0.993080i \(-0.462531\pi\)
0.117441 + 0.993080i \(0.462531\pi\)
\(72\) 1.00223 0.118114
\(73\) −10.0930 −1.18129 −0.590647 0.806930i \(-0.701127\pi\)
−0.590647 + 0.806930i \(0.701127\pi\)
\(74\) 0.547956 0.0636986
\(75\) 4.58471 0.529397
\(76\) −9.81401 −1.12574
\(77\) −8.08331 −0.921178
\(78\) 0.254687 0.0288376
\(79\) −11.7940 −1.32693 −0.663463 0.748209i \(-0.730914\pi\)
−0.663463 + 0.748209i \(0.730914\pi\)
\(80\) −2.32961 −0.260458
\(81\) 1.00000 0.111111
\(82\) −0.436113 −0.0481606
\(83\) 11.9265 1.30910 0.654552 0.756017i \(-0.272857\pi\)
0.654552 + 0.756017i \(0.272857\pi\)
\(84\) 7.23613 0.789527
\(85\) −4.25456 −0.461472
\(86\) −1.73306 −0.186880
\(87\) −6.79091 −0.728062
\(88\) −2.16651 −0.230951
\(89\) −7.92637 −0.840193 −0.420097 0.907479i \(-0.638004\pi\)
−0.420097 + 0.907479i \(0.638004\pi\)
\(90\) 0.164127 0.0173005
\(91\) 3.73934 0.391990
\(92\) 2.54384 0.265213
\(93\) 2.74661 0.284811
\(94\) −1.23880 −0.127772
\(95\) −3.26820 −0.335310
\(96\) 2.92515 0.298547
\(97\) 13.9493 1.41634 0.708170 0.706042i \(-0.249521\pi\)
0.708170 + 0.706042i \(0.249521\pi\)
\(98\) −1.77840 −0.179645
\(99\) −2.16169 −0.217258
\(100\) 8.87204 0.887204
\(101\) −4.53003 −0.450754 −0.225377 0.974272i \(-0.572361\pi\)
−0.225377 + 0.974272i \(0.572361\pi\)
\(102\) 1.68147 0.166490
\(103\) −1.00000 −0.0985329
\(104\) 1.00223 0.0982766
\(105\) 2.40973 0.235166
\(106\) −0.326583 −0.0317205
\(107\) −9.63958 −0.931893 −0.465946 0.884813i \(-0.654286\pi\)
−0.465946 + 0.884813i \(0.654286\pi\)
\(108\) 1.93513 0.186208
\(109\) 6.50575 0.623138 0.311569 0.950223i \(-0.399145\pi\)
0.311569 + 0.950223i \(0.399145\pi\)
\(110\) −0.354792 −0.0338281
\(111\) 2.15149 0.204210
\(112\) 13.5178 1.27731
\(113\) 14.2418 1.33976 0.669878 0.742472i \(-0.266347\pi\)
0.669878 + 0.742472i \(0.266347\pi\)
\(114\) 1.29164 0.120973
\(115\) 0.847132 0.0789955
\(116\) −13.1413 −1.22014
\(117\) 1.00000 0.0924500
\(118\) −1.10450 −0.101677
\(119\) 24.6875 2.26310
\(120\) 0.645862 0.0589589
\(121\) −6.32709 −0.575190
\(122\) 2.32023 0.210064
\(123\) −1.71235 −0.154397
\(124\) 5.31507 0.477307
\(125\) 6.17664 0.552456
\(126\) −0.952363 −0.0848432
\(127\) −5.59992 −0.496913 −0.248456 0.968643i \(-0.579923\pi\)
−0.248456 + 0.968643i \(0.579923\pi\)
\(128\) 7.50196 0.663086
\(129\) −6.80465 −0.599116
\(130\) 0.164127 0.0143949
\(131\) 10.0378 0.877003 0.438501 0.898731i \(-0.355509\pi\)
0.438501 + 0.898731i \(0.355509\pi\)
\(132\) −4.18316 −0.364098
\(133\) 18.9640 1.64439
\(134\) 2.57219 0.222204
\(135\) 0.644426 0.0554634
\(136\) 6.61681 0.567387
\(137\) 5.55075 0.474233 0.237116 0.971481i \(-0.423798\pi\)
0.237116 + 0.971481i \(0.423798\pi\)
\(138\) −0.334800 −0.0285001
\(139\) 8.74256 0.741534 0.370767 0.928726i \(-0.379095\pi\)
0.370767 + 0.928726i \(0.379095\pi\)
\(140\) 4.66315 0.394108
\(141\) −4.86401 −0.409623
\(142\) −0.504064 −0.0423001
\(143\) −2.16169 −0.180770
\(144\) 3.61501 0.301251
\(145\) −4.37624 −0.363427
\(146\) 2.57055 0.212740
\(147\) −6.98268 −0.575922
\(148\) 4.16342 0.342231
\(149\) 10.0949 0.827003 0.413501 0.910504i \(-0.364306\pi\)
0.413501 + 0.910504i \(0.364306\pi\)
\(150\) −1.16767 −0.0953397
\(151\) 0.629840 0.0512557 0.0256278 0.999672i \(-0.491842\pi\)
0.0256278 + 0.999672i \(0.491842\pi\)
\(152\) 5.08279 0.412269
\(153\) 6.60210 0.533748
\(154\) 2.05871 0.165896
\(155\) 1.76999 0.142169
\(156\) 1.93513 0.154935
\(157\) 2.57454 0.205471 0.102735 0.994709i \(-0.467241\pi\)
0.102735 + 0.994709i \(0.467241\pi\)
\(158\) 3.00377 0.238967
\(159\) −1.28229 −0.101692
\(160\) 1.88505 0.149026
\(161\) −4.91556 −0.387401
\(162\) −0.254687 −0.0200101
\(163\) −8.11253 −0.635422 −0.317711 0.948188i \(-0.602914\pi\)
−0.317711 + 0.948188i \(0.602914\pi\)
\(164\) −3.31362 −0.258751
\(165\) −1.39305 −0.108449
\(166\) −3.03753 −0.235758
\(167\) 14.8223 1.14698 0.573490 0.819212i \(-0.305589\pi\)
0.573490 + 0.819212i \(0.305589\pi\)
\(168\) −3.74767 −0.289139
\(169\) 1.00000 0.0769231
\(170\) 1.08358 0.0831070
\(171\) 5.07149 0.387827
\(172\) −13.1679 −1.00404
\(173\) −5.58518 −0.424634 −0.212317 0.977201i \(-0.568101\pi\)
−0.212317 + 0.977201i \(0.568101\pi\)
\(174\) 1.72956 0.131117
\(175\) −17.1438 −1.29595
\(176\) −7.81455 −0.589044
\(177\) −4.33667 −0.325964
\(178\) 2.01874 0.151311
\(179\) −6.51826 −0.487197 −0.243599 0.969876i \(-0.578328\pi\)
−0.243599 + 0.969876i \(0.578328\pi\)
\(180\) 1.24705 0.0929497
\(181\) 5.43008 0.403615 0.201807 0.979425i \(-0.435319\pi\)
0.201807 + 0.979425i \(0.435319\pi\)
\(182\) −0.952363 −0.0705938
\(183\) 9.11013 0.673440
\(184\) −1.31748 −0.0971261
\(185\) 1.38647 0.101936
\(186\) −0.699527 −0.0512918
\(187\) −14.2717 −1.04365
\(188\) −9.41251 −0.686478
\(189\) −3.73934 −0.271997
\(190\) 0.832369 0.0603864
\(191\) 18.9436 1.37071 0.685354 0.728210i \(-0.259647\pi\)
0.685354 + 0.728210i \(0.259647\pi\)
\(192\) 6.48503 0.468017
\(193\) 3.56540 0.256643 0.128322 0.991733i \(-0.459041\pi\)
0.128322 + 0.991733i \(0.459041\pi\)
\(194\) −3.55271 −0.255070
\(195\) 0.644426 0.0461483
\(196\) −13.5124 −0.965173
\(197\) −10.2323 −0.729024 −0.364512 0.931199i \(-0.618764\pi\)
−0.364512 + 0.931199i \(0.618764\pi\)
\(198\) 0.550555 0.0391263
\(199\) 24.0522 1.70502 0.852509 0.522713i \(-0.175080\pi\)
0.852509 + 0.522713i \(0.175080\pi\)
\(200\) −4.59493 −0.324911
\(201\) 10.0994 0.712358
\(202\) 1.15374 0.0811768
\(203\) 25.3935 1.78228
\(204\) 12.7759 0.894495
\(205\) −1.10348 −0.0770705
\(206\) 0.254687 0.0177449
\(207\) −1.31455 −0.0913678
\(208\) 3.61501 0.250656
\(209\) −10.9630 −0.758326
\(210\) −0.613727 −0.0423512
\(211\) 11.5341 0.794041 0.397020 0.917810i \(-0.370044\pi\)
0.397020 + 0.917810i \(0.370044\pi\)
\(212\) −2.48140 −0.170424
\(213\) −1.97915 −0.135609
\(214\) 2.45508 0.167826
\(215\) −4.38509 −0.299061
\(216\) −1.00223 −0.0681930
\(217\) −10.2705 −0.697209
\(218\) −1.65693 −0.112222
\(219\) 10.0930 0.682020
\(220\) −2.69574 −0.181747
\(221\) 6.60210 0.444105
\(222\) −0.547956 −0.0367764
\(223\) 24.6702 1.65204 0.826018 0.563644i \(-0.190601\pi\)
0.826018 + 0.563644i \(0.190601\pi\)
\(224\) −10.9382 −0.730836
\(225\) −4.58471 −0.305648
\(226\) −3.62720 −0.241278
\(227\) −20.4670 −1.35845 −0.679223 0.733932i \(-0.737683\pi\)
−0.679223 + 0.733932i \(0.737683\pi\)
\(228\) 9.81401 0.649949
\(229\) 2.02798 0.134013 0.0670063 0.997753i \(-0.478655\pi\)
0.0670063 + 0.997753i \(0.478655\pi\)
\(230\) −0.215754 −0.0142264
\(231\) 8.08331 0.531842
\(232\) 6.80604 0.446839
\(233\) −4.31964 −0.282989 −0.141494 0.989939i \(-0.545191\pi\)
−0.141494 + 0.989939i \(0.545191\pi\)
\(234\) −0.254687 −0.0166494
\(235\) −3.13449 −0.204472
\(236\) −8.39205 −0.546276
\(237\) 11.7940 0.766101
\(238\) −6.28759 −0.407564
\(239\) −4.38877 −0.283886 −0.141943 0.989875i \(-0.545335\pi\)
−0.141943 + 0.989875i \(0.545335\pi\)
\(240\) 2.32961 0.150376
\(241\) 18.4681 1.18963 0.594817 0.803861i \(-0.297225\pi\)
0.594817 + 0.803861i \(0.297225\pi\)
\(242\) 1.61143 0.103587
\(243\) −1.00000 −0.0641500
\(244\) 17.6293 1.12860
\(245\) −4.49982 −0.287483
\(246\) 0.436113 0.0278056
\(247\) 5.07149 0.322691
\(248\) −2.75273 −0.174799
\(249\) −11.9265 −0.755811
\(250\) −1.57311 −0.0994923
\(251\) −11.2714 −0.711446 −0.355723 0.934592i \(-0.615765\pi\)
−0.355723 + 0.934592i \(0.615765\pi\)
\(252\) −7.23613 −0.455833
\(253\) 2.84166 0.178654
\(254\) 1.42623 0.0894896
\(255\) 4.25456 0.266431
\(256\) 11.0594 0.691213
\(257\) 14.3567 0.895547 0.447774 0.894147i \(-0.352217\pi\)
0.447774 + 0.894147i \(0.352217\pi\)
\(258\) 1.73306 0.107895
\(259\) −8.04515 −0.499901
\(260\) 1.24705 0.0773388
\(261\) 6.79091 0.420347
\(262\) −2.55649 −0.157940
\(263\) 18.9401 1.16789 0.583947 0.811792i \(-0.301508\pi\)
0.583947 + 0.811792i \(0.301508\pi\)
\(264\) 2.16651 0.133339
\(265\) −0.826342 −0.0507618
\(266\) −4.82990 −0.296140
\(267\) 7.92637 0.485086
\(268\) 19.5437 1.19382
\(269\) 26.4369 1.61189 0.805945 0.591991i \(-0.201658\pi\)
0.805945 + 0.591991i \(0.201658\pi\)
\(270\) −0.164127 −0.00998846
\(271\) −15.6578 −0.951142 −0.475571 0.879677i \(-0.657759\pi\)
−0.475571 + 0.879677i \(0.657759\pi\)
\(272\) 23.8667 1.44713
\(273\) −3.73934 −0.226315
\(274\) −1.41370 −0.0854050
\(275\) 9.91074 0.597640
\(276\) −2.54384 −0.153121
\(277\) 0.0438679 0.00263577 0.00131788 0.999999i \(-0.499581\pi\)
0.00131788 + 0.999999i \(0.499581\pi\)
\(278\) −2.22662 −0.133544
\(279\) −2.74661 −0.164435
\(280\) −2.41510 −0.144330
\(281\) −8.85075 −0.527991 −0.263996 0.964524i \(-0.585040\pi\)
−0.263996 + 0.964524i \(0.585040\pi\)
\(282\) 1.23880 0.0737695
\(283\) −0.731884 −0.0435060 −0.0217530 0.999763i \(-0.506925\pi\)
−0.0217530 + 0.999763i \(0.506925\pi\)
\(284\) −3.82992 −0.227264
\(285\) 3.26820 0.193592
\(286\) 0.550555 0.0325550
\(287\) 6.40306 0.377961
\(288\) −2.92515 −0.172366
\(289\) 26.5877 1.56398
\(290\) 1.11457 0.0654499
\(291\) −13.9493 −0.817724
\(292\) 19.5313 1.14298
\(293\) −17.4078 −1.01698 −0.508488 0.861069i \(-0.669795\pi\)
−0.508488 + 0.861069i \(0.669795\pi\)
\(294\) 1.77840 0.103718
\(295\) −2.79467 −0.162712
\(296\) −2.15628 −0.125331
\(297\) 2.16169 0.125434
\(298\) −2.57103 −0.148936
\(299\) −1.31455 −0.0760226
\(300\) −8.87204 −0.512227
\(301\) 25.4449 1.46662
\(302\) −0.160412 −0.00923069
\(303\) 4.53003 0.260243
\(304\) 18.3335 1.05150
\(305\) 5.87081 0.336161
\(306\) −1.68147 −0.0961232
\(307\) 6.42085 0.366457 0.183229 0.983070i \(-0.441345\pi\)
0.183229 + 0.983070i \(0.441345\pi\)
\(308\) 15.6423 0.891302
\(309\) 1.00000 0.0568880
\(310\) −0.450794 −0.0256034
\(311\) 21.8263 1.23766 0.618828 0.785527i \(-0.287608\pi\)
0.618828 + 0.785527i \(0.287608\pi\)
\(312\) −1.00223 −0.0567400
\(313\) −26.9981 −1.52602 −0.763012 0.646384i \(-0.776280\pi\)
−0.763012 + 0.646384i \(0.776280\pi\)
\(314\) −0.655702 −0.0370034
\(315\) −2.40973 −0.135773
\(316\) 22.8229 1.28389
\(317\) −29.5618 −1.66036 −0.830178 0.557498i \(-0.811761\pi\)
−0.830178 + 0.557498i \(0.811761\pi\)
\(318\) 0.326583 0.0183139
\(319\) −14.6799 −0.821914
\(320\) 4.17912 0.233620
\(321\) 9.63958 0.538029
\(322\) 1.25193 0.0697674
\(323\) 33.4825 1.86301
\(324\) −1.93513 −0.107507
\(325\) −4.58471 −0.254314
\(326\) 2.06616 0.114434
\(327\) −6.50575 −0.359769
\(328\) 1.71616 0.0947593
\(329\) 18.1882 1.00275
\(330\) 0.354792 0.0195307
\(331\) 3.54256 0.194716 0.0973582 0.995249i \(-0.468961\pi\)
0.0973582 + 0.995249i \(0.468961\pi\)
\(332\) −23.0794 −1.26665
\(333\) −2.15149 −0.117901
\(334\) −3.77504 −0.206561
\(335\) 6.50833 0.355588
\(336\) −13.5178 −0.737455
\(337\) −17.6455 −0.961214 −0.480607 0.876936i \(-0.659584\pi\)
−0.480607 + 0.876936i \(0.659584\pi\)
\(338\) −0.254687 −0.0138532
\(339\) −14.2418 −0.773508
\(340\) 8.23315 0.446505
\(341\) 5.93733 0.321525
\(342\) −1.29164 −0.0698441
\(343\) −0.0647594 −0.00349668
\(344\) 6.81981 0.367700
\(345\) −0.847132 −0.0456081
\(346\) 1.42247 0.0764727
\(347\) 21.9422 1.17792 0.588959 0.808163i \(-0.299538\pi\)
0.588959 + 0.808163i \(0.299538\pi\)
\(348\) 13.1413 0.704449
\(349\) 15.6683 0.838703 0.419351 0.907824i \(-0.362258\pi\)
0.419351 + 0.907824i \(0.362258\pi\)
\(350\) 4.36631 0.233389
\(351\) −1.00000 −0.0533761
\(352\) 6.32328 0.337032
\(353\) 23.1715 1.23330 0.616648 0.787239i \(-0.288490\pi\)
0.616648 + 0.787239i \(0.288490\pi\)
\(354\) 1.10450 0.0587033
\(355\) −1.27542 −0.0676920
\(356\) 15.3386 0.812943
\(357\) −24.6875 −1.30660
\(358\) 1.66012 0.0877399
\(359\) 26.0955 1.37727 0.688635 0.725109i \(-0.258210\pi\)
0.688635 + 0.725109i \(0.258210\pi\)
\(360\) −0.645862 −0.0340399
\(361\) 6.72001 0.353685
\(362\) −1.38297 −0.0726874
\(363\) 6.32709 0.332086
\(364\) −7.23613 −0.379276
\(365\) 6.50418 0.340444
\(366\) −2.32023 −0.121281
\(367\) 15.3892 0.803310 0.401655 0.915791i \(-0.368435\pi\)
0.401655 + 0.915791i \(0.368435\pi\)
\(368\) −4.75213 −0.247722
\(369\) 1.71235 0.0891413
\(370\) −0.353117 −0.0183577
\(371\) 4.79492 0.248940
\(372\) −5.31507 −0.275573
\(373\) −15.1942 −0.786724 −0.393362 0.919384i \(-0.628688\pi\)
−0.393362 + 0.919384i \(0.628688\pi\)
\(374\) 3.63482 0.187952
\(375\) −6.17664 −0.318960
\(376\) 4.87485 0.251401
\(377\) 6.79091 0.349750
\(378\) 0.952363 0.0489842
\(379\) −10.8656 −0.558126 −0.279063 0.960273i \(-0.590024\pi\)
−0.279063 + 0.960273i \(0.590024\pi\)
\(380\) 6.32441 0.324435
\(381\) 5.59992 0.286893
\(382\) −4.82468 −0.246852
\(383\) 7.53663 0.385104 0.192552 0.981287i \(-0.438324\pi\)
0.192552 + 0.981287i \(0.438324\pi\)
\(384\) −7.50196 −0.382833
\(385\) 5.20909 0.265480
\(386\) −0.908062 −0.0462192
\(387\) 6.80465 0.345900
\(388\) −26.9938 −1.37040
\(389\) 4.82746 0.244762 0.122381 0.992483i \(-0.460947\pi\)
0.122381 + 0.992483i \(0.460947\pi\)
\(390\) −0.164127 −0.00831090
\(391\) −8.67881 −0.438906
\(392\) 6.99824 0.353465
\(393\) −10.0378 −0.506338
\(394\) 2.60604 0.131291
\(395\) 7.60035 0.382415
\(396\) 4.18316 0.210212
\(397\) −13.3155 −0.668285 −0.334142 0.942523i \(-0.608447\pi\)
−0.334142 + 0.942523i \(0.608447\pi\)
\(398\) −6.12580 −0.307058
\(399\) −18.9640 −0.949389
\(400\) −16.5738 −0.828690
\(401\) −16.9664 −0.847261 −0.423630 0.905835i \(-0.639244\pi\)
−0.423630 + 0.905835i \(0.639244\pi\)
\(402\) −2.57219 −0.128289
\(403\) −2.74661 −0.136819
\(404\) 8.76621 0.436135
\(405\) −0.644426 −0.0320218
\(406\) −6.46741 −0.320972
\(407\) 4.65085 0.230534
\(408\) −6.61681 −0.327581
\(409\) 7.28698 0.360318 0.180159 0.983638i \(-0.442339\pi\)
0.180159 + 0.983638i \(0.442339\pi\)
\(410\) 0.281043 0.0138797
\(411\) −5.55075 −0.273798
\(412\) 1.93513 0.0953372
\(413\) 16.2163 0.797953
\(414\) 0.334800 0.0164545
\(415\) −7.68575 −0.377279
\(416\) −2.92515 −0.143417
\(417\) −8.74256 −0.428125
\(418\) 2.79214 0.136568
\(419\) 31.9297 1.55987 0.779935 0.625861i \(-0.215252\pi\)
0.779935 + 0.625861i \(0.215252\pi\)
\(420\) −4.66315 −0.227538
\(421\) 25.2163 1.22897 0.614484 0.788929i \(-0.289364\pi\)
0.614484 + 0.788929i \(0.289364\pi\)
\(422\) −2.93759 −0.143000
\(423\) 4.86401 0.236496
\(424\) 1.28515 0.0624123
\(425\) −30.2687 −1.46825
\(426\) 0.504064 0.0244220
\(427\) −34.0659 −1.64856
\(428\) 18.6539 0.901669
\(429\) 2.16169 0.104367
\(430\) 1.11683 0.0538582
\(431\) 28.1693 1.35687 0.678434 0.734661i \(-0.262659\pi\)
0.678434 + 0.734661i \(0.262659\pi\)
\(432\) −3.61501 −0.173927
\(433\) 14.6452 0.703805 0.351903 0.936037i \(-0.385535\pi\)
0.351903 + 0.936037i \(0.385535\pi\)
\(434\) 2.61577 0.125561
\(435\) 4.37624 0.209825
\(436\) −12.5895 −0.602928
\(437\) −6.66674 −0.318914
\(438\) −2.57055 −0.122826
\(439\) −27.9316 −1.33310 −0.666550 0.745460i \(-0.732230\pi\)
−0.666550 + 0.745460i \(0.732230\pi\)
\(440\) 1.39615 0.0665591
\(441\) 6.98268 0.332509
\(442\) −1.68147 −0.0799793
\(443\) −8.49135 −0.403436 −0.201718 0.979444i \(-0.564653\pi\)
−0.201718 + 0.979444i \(0.564653\pi\)
\(444\) −4.16342 −0.197587
\(445\) 5.10796 0.242140
\(446\) −6.28317 −0.297517
\(447\) −10.0949 −0.477470
\(448\) −24.2497 −1.14569
\(449\) −7.50853 −0.354350 −0.177175 0.984179i \(-0.556696\pi\)
−0.177175 + 0.984179i \(0.556696\pi\)
\(450\) 1.16767 0.0550444
\(451\) −3.70157 −0.174300
\(452\) −27.5598 −1.29630
\(453\) −0.629840 −0.0295925
\(454\) 5.21269 0.244644
\(455\) −2.40973 −0.112970
\(456\) −5.08279 −0.238023
\(457\) 38.7505 1.81267 0.906335 0.422560i \(-0.138868\pi\)
0.906335 + 0.422560i \(0.138868\pi\)
\(458\) −0.516500 −0.0241345
\(459\) −6.60210 −0.308159
\(460\) −1.63932 −0.0764335
\(461\) 13.1493 0.612425 0.306213 0.951963i \(-0.400938\pi\)
0.306213 + 0.951963i \(0.400938\pi\)
\(462\) −2.05871 −0.0957801
\(463\) 8.91855 0.414480 0.207240 0.978290i \(-0.433552\pi\)
0.207240 + 0.978290i \(0.433552\pi\)
\(464\) 24.5492 1.13967
\(465\) −1.76999 −0.0820813
\(466\) 1.10016 0.0509637
\(467\) −29.5599 −1.36787 −0.683935 0.729543i \(-0.739733\pi\)
−0.683935 + 0.729543i \(0.739733\pi\)
\(468\) −1.93513 −0.0894516
\(469\) −37.7652 −1.74383
\(470\) 0.798315 0.0368235
\(471\) −2.57454 −0.118628
\(472\) 4.34634 0.200056
\(473\) −14.7096 −0.676346
\(474\) −3.00377 −0.137968
\(475\) −23.2513 −1.06684
\(476\) −47.7736 −2.18970
\(477\) 1.28229 0.0587120
\(478\) 1.11776 0.0511254
\(479\) 20.6892 0.945316 0.472658 0.881246i \(-0.343295\pi\)
0.472658 + 0.881246i \(0.343295\pi\)
\(480\) −1.88505 −0.0860402
\(481\) −2.15149 −0.0980994
\(482\) −4.70358 −0.214242
\(483\) 4.91556 0.223666
\(484\) 12.2438 0.556535
\(485\) −8.98931 −0.408184
\(486\) 0.254687 0.0115528
\(487\) −30.5248 −1.38321 −0.691605 0.722276i \(-0.743096\pi\)
−0.691605 + 0.722276i \(0.743096\pi\)
\(488\) −9.13043 −0.413315
\(489\) 8.11253 0.366861
\(490\) 1.14605 0.0517731
\(491\) −40.7131 −1.83735 −0.918677 0.395009i \(-0.870742\pi\)
−0.918677 + 0.395009i \(0.870742\pi\)
\(492\) 3.31362 0.149390
\(493\) 44.8343 2.01923
\(494\) −1.29164 −0.0581138
\(495\) 1.39305 0.0626130
\(496\) −9.92905 −0.445827
\(497\) 7.40072 0.331968
\(498\) 3.03753 0.136115
\(499\) −17.9990 −0.805746 −0.402873 0.915256i \(-0.631988\pi\)
−0.402873 + 0.915256i \(0.631988\pi\)
\(500\) −11.9526 −0.534538
\(501\) −14.8223 −0.662209
\(502\) 2.87069 0.128125
\(503\) −8.49851 −0.378930 −0.189465 0.981887i \(-0.560675\pi\)
−0.189465 + 0.981887i \(0.560675\pi\)
\(504\) 3.74767 0.166935
\(505\) 2.91927 0.129906
\(506\) −0.723734 −0.0321739
\(507\) −1.00000 −0.0444116
\(508\) 10.8366 0.480797
\(509\) −19.6135 −0.869351 −0.434676 0.900587i \(-0.643137\pi\)
−0.434676 + 0.900587i \(0.643137\pi\)
\(510\) −1.08358 −0.0479819
\(511\) −37.7411 −1.66957
\(512\) −17.8206 −0.787567
\(513\) −5.07149 −0.223912
\(514\) −3.65647 −0.161280
\(515\) 0.644426 0.0283968
\(516\) 13.1679 0.579685
\(517\) −10.5145 −0.462427
\(518\) 2.04900 0.0900277
\(519\) 5.58518 0.245162
\(520\) −0.645862 −0.0283229
\(521\) 39.6357 1.73647 0.868237 0.496150i \(-0.165253\pi\)
0.868237 + 0.496150i \(0.165253\pi\)
\(522\) −1.72956 −0.0757007
\(523\) −26.5714 −1.16189 −0.580943 0.813945i \(-0.697316\pi\)
−0.580943 + 0.813945i \(0.697316\pi\)
\(524\) −19.4244 −0.848559
\(525\) 17.1438 0.748218
\(526\) −4.82379 −0.210327
\(527\) −18.1334 −0.789904
\(528\) 7.81455 0.340084
\(529\) −21.2719 −0.924867
\(530\) 0.210459 0.00914174
\(531\) 4.33667 0.188196
\(532\) −36.6980 −1.59106
\(533\) 1.71235 0.0741700
\(534\) −2.01874 −0.0873596
\(535\) 6.21199 0.268568
\(536\) −10.1219 −0.437200
\(537\) 6.51826 0.281284
\(538\) −6.73315 −0.290287
\(539\) −15.0944 −0.650162
\(540\) −1.24705 −0.0536645
\(541\) 0.912594 0.0392355 0.0196177 0.999808i \(-0.493755\pi\)
0.0196177 + 0.999808i \(0.493755\pi\)
\(542\) 3.98783 0.171292
\(543\) −5.43008 −0.233027
\(544\) −19.3122 −0.828002
\(545\) −4.19248 −0.179586
\(546\) 0.952363 0.0407574
\(547\) −12.8909 −0.551173 −0.275586 0.961276i \(-0.588872\pi\)
−0.275586 + 0.961276i \(0.588872\pi\)
\(548\) −10.7414 −0.458852
\(549\) −9.11013 −0.388811
\(550\) −2.52414 −0.107630
\(551\) 34.4400 1.46719
\(552\) 1.31748 0.0560758
\(553\) −44.1017 −1.87540
\(554\) −0.0111726 −0.000474678 0
\(555\) −1.38647 −0.0588526
\(556\) −16.9180 −0.717484
\(557\) −34.7494 −1.47238 −0.736189 0.676776i \(-0.763377\pi\)
−0.736189 + 0.676776i \(0.763377\pi\)
\(558\) 0.699527 0.0296133
\(559\) 6.80465 0.287806
\(560\) −8.71121 −0.368116
\(561\) 14.2717 0.602552
\(562\) 2.25417 0.0950865
\(563\) 1.06371 0.0448300 0.0224150 0.999749i \(-0.492864\pi\)
0.0224150 + 0.999749i \(0.492864\pi\)
\(564\) 9.41251 0.396338
\(565\) −9.17778 −0.386112
\(566\) 0.186402 0.00783504
\(567\) 3.73934 0.157038
\(568\) 1.98356 0.0832283
\(569\) −2.43593 −0.102119 −0.0510597 0.998696i \(-0.516260\pi\)
−0.0510597 + 0.998696i \(0.516260\pi\)
\(570\) −0.832369 −0.0348641
\(571\) −6.01254 −0.251617 −0.125809 0.992055i \(-0.540152\pi\)
−0.125809 + 0.992055i \(0.540152\pi\)
\(572\) 4.18316 0.174907
\(573\) −18.9436 −0.791379
\(574\) −1.63078 −0.0680673
\(575\) 6.02685 0.251337
\(576\) −6.48503 −0.270210
\(577\) −9.32838 −0.388345 −0.194173 0.980967i \(-0.562202\pi\)
−0.194173 + 0.980967i \(0.562202\pi\)
\(578\) −6.77154 −0.281659
\(579\) −3.56540 −0.148173
\(580\) 8.46861 0.351640
\(581\) 44.5973 1.85021
\(582\) 3.55271 0.147265
\(583\) −2.77192 −0.114801
\(584\) −10.1155 −0.418581
\(585\) −0.644426 −0.0266437
\(586\) 4.43355 0.183148
\(587\) 8.00992 0.330605 0.165302 0.986243i \(-0.447140\pi\)
0.165302 + 0.986243i \(0.447140\pi\)
\(588\) 13.5124 0.557243
\(589\) −13.9294 −0.573952
\(590\) 0.711766 0.0293029
\(591\) 10.2323 0.420902
\(592\) −7.77766 −0.319660
\(593\) 30.2498 1.24221 0.621106 0.783727i \(-0.286684\pi\)
0.621106 + 0.783727i \(0.286684\pi\)
\(594\) −0.550555 −0.0225896
\(595\) −15.9093 −0.652217
\(596\) −19.5349 −0.800181
\(597\) −24.0522 −0.984392
\(598\) 0.334800 0.0136910
\(599\) 19.8497 0.811037 0.405519 0.914087i \(-0.367091\pi\)
0.405519 + 0.914087i \(0.367091\pi\)
\(600\) 4.59493 0.187587
\(601\) 41.7106 1.70141 0.850705 0.525643i \(-0.176175\pi\)
0.850705 + 0.525643i \(0.176175\pi\)
\(602\) −6.48049 −0.264125
\(603\) −10.0994 −0.411280
\(604\) −1.21883 −0.0495933
\(605\) 4.07734 0.165767
\(606\) −1.15374 −0.0468675
\(607\) −43.3222 −1.75839 −0.879196 0.476460i \(-0.841920\pi\)
−0.879196 + 0.476460i \(0.841920\pi\)
\(608\) −14.8349 −0.601634
\(609\) −25.3935 −1.02900
\(610\) −1.49522 −0.0605397
\(611\) 4.86401 0.196777
\(612\) −12.7759 −0.516437
\(613\) 0.808238 0.0326444 0.0163222 0.999867i \(-0.494804\pi\)
0.0163222 + 0.999867i \(0.494804\pi\)
\(614\) −1.63531 −0.0659957
\(615\) 1.10348 0.0444967
\(616\) −8.10132 −0.326411
\(617\) −41.6766 −1.67784 −0.838918 0.544257i \(-0.816812\pi\)
−0.838918 + 0.544257i \(0.816812\pi\)
\(618\) −0.254687 −0.0102450
\(619\) 43.6835 1.75579 0.877894 0.478855i \(-0.158948\pi\)
0.877894 + 0.478855i \(0.158948\pi\)
\(620\) −3.42517 −0.137558
\(621\) 1.31455 0.0527512
\(622\) −5.55888 −0.222891
\(623\) −29.6394 −1.18748
\(624\) −3.61501 −0.144716
\(625\) 18.9432 0.757727
\(626\) 6.87607 0.274823
\(627\) 10.9630 0.437820
\(628\) −4.98208 −0.198807
\(629\) −14.2043 −0.566364
\(630\) 0.613727 0.0244515
\(631\) 4.26254 0.169689 0.0848446 0.996394i \(-0.472961\pi\)
0.0848446 + 0.996394i \(0.472961\pi\)
\(632\) −11.8203 −0.470185
\(633\) −11.5341 −0.458440
\(634\) 7.52901 0.299015
\(635\) 3.60874 0.143208
\(636\) 2.48140 0.0983941
\(637\) 6.98268 0.276664
\(638\) 3.73877 0.148019
\(639\) 1.97915 0.0782939
\(640\) −4.83446 −0.191099
\(641\) 30.2657 1.19542 0.597712 0.801711i \(-0.296077\pi\)
0.597712 + 0.801711i \(0.296077\pi\)
\(642\) −2.45508 −0.0968941
\(643\) 19.5187 0.769741 0.384871 0.922970i \(-0.374246\pi\)
0.384871 + 0.922970i \(0.374246\pi\)
\(644\) 9.51228 0.374836
\(645\) 4.38509 0.172663
\(646\) −8.52755 −0.335512
\(647\) 13.9595 0.548803 0.274402 0.961615i \(-0.411520\pi\)
0.274402 + 0.961615i \(0.411520\pi\)
\(648\) 1.00223 0.0393712
\(649\) −9.37455 −0.367983
\(650\) 1.16767 0.0457997
\(651\) 10.2705 0.402534
\(652\) 15.6988 0.614814
\(653\) 28.5723 1.11812 0.559060 0.829127i \(-0.311162\pi\)
0.559060 + 0.829127i \(0.311162\pi\)
\(654\) 1.65693 0.0647912
\(655\) −6.46859 −0.252749
\(656\) 6.19016 0.241685
\(657\) −10.0930 −0.393764
\(658\) −4.63230 −0.180586
\(659\) 37.5112 1.46123 0.730615 0.682790i \(-0.239234\pi\)
0.730615 + 0.682790i \(0.239234\pi\)
\(660\) 2.69574 0.104932
\(661\) −33.2455 −1.29310 −0.646549 0.762872i \(-0.723789\pi\)
−0.646549 + 0.762872i \(0.723789\pi\)
\(662\) −0.902244 −0.0350667
\(663\) −6.60210 −0.256404
\(664\) 11.9531 0.463869
\(665\) −12.2209 −0.473907
\(666\) 0.547956 0.0212329
\(667\) −8.92701 −0.345655
\(668\) −28.6831 −1.10978
\(669\) −24.6702 −0.953803
\(670\) −1.65759 −0.0640382
\(671\) 19.6933 0.760251
\(672\) 10.9382 0.421948
\(673\) 28.0118 1.07978 0.539888 0.841737i \(-0.318467\pi\)
0.539888 + 0.841737i \(0.318467\pi\)
\(674\) 4.49409 0.173106
\(675\) 4.58471 0.176466
\(676\) −1.93513 −0.0744282
\(677\) 35.7561 1.37422 0.687109 0.726555i \(-0.258880\pi\)
0.687109 + 0.726555i \(0.258880\pi\)
\(678\) 3.62720 0.139302
\(679\) 52.1613 2.00177
\(680\) −4.26404 −0.163519
\(681\) 20.4670 0.784299
\(682\) −1.51216 −0.0579037
\(683\) −7.99852 −0.306055 −0.153027 0.988222i \(-0.548902\pi\)
−0.153027 + 0.988222i \(0.548902\pi\)
\(684\) −9.81401 −0.375248
\(685\) −3.57705 −0.136672
\(686\) 0.0164934 0.000629720 0
\(687\) −2.02798 −0.0773722
\(688\) 24.5989 0.937824
\(689\) 1.28229 0.0488514
\(690\) 0.215754 0.00821361
\(691\) −9.17935 −0.349199 −0.174599 0.984640i \(-0.555863\pi\)
−0.174599 + 0.984640i \(0.555863\pi\)
\(692\) 10.8081 0.410862
\(693\) −8.08331 −0.307059
\(694\) −5.58839 −0.212132
\(695\) −5.63393 −0.213707
\(696\) −6.80604 −0.257982
\(697\) 11.3051 0.428211
\(698\) −3.99051 −0.151043
\(699\) 4.31964 0.163384
\(700\) 33.1756 1.25392
\(701\) 6.22959 0.235288 0.117644 0.993056i \(-0.462466\pi\)
0.117644 + 0.993056i \(0.462466\pi\)
\(702\) 0.254687 0.00961255
\(703\) −10.9112 −0.411525
\(704\) 14.0186 0.528347
\(705\) 3.13449 0.118052
\(706\) −5.90149 −0.222105
\(707\) −16.9393 −0.637069
\(708\) 8.39205 0.315392
\(709\) −46.8130 −1.75810 −0.879049 0.476731i \(-0.841822\pi\)
−0.879049 + 0.476731i \(0.841822\pi\)
\(710\) 0.324832 0.0121907
\(711\) −11.7940 −0.442309
\(712\) −7.94403 −0.297715
\(713\) 3.61057 0.135217
\(714\) 6.28759 0.235307
\(715\) 1.39305 0.0520971
\(716\) 12.6137 0.471396
\(717\) 4.38877 0.163902
\(718\) −6.64620 −0.248034
\(719\) −22.9077 −0.854314 −0.427157 0.904177i \(-0.640485\pi\)
−0.427157 + 0.904177i \(0.640485\pi\)
\(720\) −2.32961 −0.0868194
\(721\) −3.73934 −0.139260
\(722\) −1.71150 −0.0636954
\(723\) −18.4681 −0.686835
\(724\) −10.5079 −0.390524
\(725\) −31.1344 −1.15630
\(726\) −1.61143 −0.0598057
\(727\) 32.6195 1.20979 0.604895 0.796305i \(-0.293215\pi\)
0.604895 + 0.796305i \(0.293215\pi\)
\(728\) 3.74767 0.138898
\(729\) 1.00000 0.0370370
\(730\) −1.65653 −0.0613109
\(731\) 44.9249 1.66161
\(732\) −17.6293 −0.651599
\(733\) 3.46368 0.127934 0.0639670 0.997952i \(-0.479625\pi\)
0.0639670 + 0.997952i \(0.479625\pi\)
\(734\) −3.91943 −0.144669
\(735\) 4.49982 0.165978
\(736\) 3.84527 0.141739
\(737\) 21.8318 0.804186
\(738\) −0.436113 −0.0160535
\(739\) −23.0306 −0.847194 −0.423597 0.905851i \(-0.639233\pi\)
−0.423597 + 0.905851i \(0.639233\pi\)
\(740\) −2.68301 −0.0986296
\(741\) −5.07149 −0.186306
\(742\) −1.22121 −0.0448319
\(743\) 41.3720 1.51779 0.758896 0.651211i \(-0.225739\pi\)
0.758896 + 0.651211i \(0.225739\pi\)
\(744\) 2.75273 0.100920
\(745\) −6.50539 −0.238339
\(746\) 3.86976 0.141682
\(747\) 11.9265 0.436368
\(748\) 27.6177 1.00980
\(749\) −36.0457 −1.31708
\(750\) 1.57311 0.0574419
\(751\) −2.76373 −0.100850 −0.0504250 0.998728i \(-0.516058\pi\)
−0.0504250 + 0.998728i \(0.516058\pi\)
\(752\) 17.5835 0.641203
\(753\) 11.2714 0.410753
\(754\) −1.72956 −0.0629868
\(755\) −0.405886 −0.0147717
\(756\) 7.23613 0.263176
\(757\) −25.7833 −0.937111 −0.468556 0.883434i \(-0.655225\pi\)
−0.468556 + 0.883434i \(0.655225\pi\)
\(758\) 2.76732 0.100514
\(759\) −2.84166 −0.103146
\(760\) −3.27548 −0.118814
\(761\) −22.3274 −0.809367 −0.404683 0.914457i \(-0.632618\pi\)
−0.404683 + 0.914457i \(0.632618\pi\)
\(762\) −1.42623 −0.0516668
\(763\) 24.3272 0.880705
\(764\) −36.6584 −1.32625
\(765\) −4.25456 −0.153824
\(766\) −1.91948 −0.0693538
\(767\) 4.33667 0.156588
\(768\) −11.0594 −0.399072
\(769\) −11.3354 −0.408764 −0.204382 0.978891i \(-0.565518\pi\)
−0.204382 + 0.978891i \(0.565518\pi\)
\(770\) −1.32669 −0.0478106
\(771\) −14.3567 −0.517044
\(772\) −6.89953 −0.248320
\(773\) −31.8718 −1.14635 −0.573174 0.819433i \(-0.694288\pi\)
−0.573174 + 0.819433i \(0.694288\pi\)
\(774\) −1.73306 −0.0622934
\(775\) 12.5924 0.452334
\(776\) 13.9804 0.501867
\(777\) 8.04515 0.288618
\(778\) −1.22949 −0.0440794
\(779\) 8.68416 0.311142
\(780\) −1.24705 −0.0446516
\(781\) −4.27831 −0.153090
\(782\) 2.21038 0.0790431
\(783\) −6.79091 −0.242687
\(784\) 25.2425 0.901518
\(785\) −1.65910 −0.0592158
\(786\) 2.55649 0.0911869
\(787\) 18.3423 0.653833 0.326917 0.945053i \(-0.393990\pi\)
0.326917 + 0.945053i \(0.393990\pi\)
\(788\) 19.8009 0.705379
\(789\) −18.9401 −0.674284
\(790\) −1.93571 −0.0688695
\(791\) 53.2549 1.89353
\(792\) −2.16651 −0.0769835
\(793\) −9.11013 −0.323510
\(794\) 3.39128 0.120352
\(795\) 0.826342 0.0293073
\(796\) −46.5443 −1.64972
\(797\) 0.714027 0.0252921 0.0126461 0.999920i \(-0.495975\pi\)
0.0126461 + 0.999920i \(0.495975\pi\)
\(798\) 4.82990 0.170977
\(799\) 32.1126 1.13606
\(800\) 13.4110 0.474150
\(801\) −7.92637 −0.280064
\(802\) 4.32112 0.152584
\(803\) 21.8179 0.769937
\(804\) −19.5437 −0.689254
\(805\) 3.16772 0.111647
\(806\) 0.699527 0.0246398
\(807\) −26.4369 −0.930625
\(808\) −4.54012 −0.159721
\(809\) −11.6088 −0.408145 −0.204072 0.978956i \(-0.565418\pi\)
−0.204072 + 0.978956i \(0.565418\pi\)
\(810\) 0.164127 0.00576684
\(811\) 36.2146 1.27167 0.635834 0.771826i \(-0.280656\pi\)
0.635834 + 0.771826i \(0.280656\pi\)
\(812\) −49.1399 −1.72447
\(813\) 15.6578 0.549142
\(814\) −1.18451 −0.0415171
\(815\) 5.22792 0.183126
\(816\) −23.8667 −0.835501
\(817\) 34.5097 1.20734
\(818\) −1.85590 −0.0648900
\(819\) 3.73934 0.130663
\(820\) 2.13539 0.0745709
\(821\) −12.7163 −0.443802 −0.221901 0.975069i \(-0.571226\pi\)
−0.221901 + 0.975069i \(0.571226\pi\)
\(822\) 1.41370 0.0493086
\(823\) −57.3548 −1.99926 −0.999632 0.0271267i \(-0.991364\pi\)
−0.999632 + 0.0271267i \(0.991364\pi\)
\(824\) −1.00223 −0.0349143
\(825\) −9.91074 −0.345048
\(826\) −4.13009 −0.143704
\(827\) −30.0051 −1.04338 −0.521690 0.853135i \(-0.674698\pi\)
−0.521690 + 0.853135i \(0.674698\pi\)
\(828\) 2.54384 0.0884045
\(829\) −55.1564 −1.91566 −0.957831 0.287332i \(-0.907232\pi\)
−0.957831 + 0.287332i \(0.907232\pi\)
\(830\) 1.95746 0.0679445
\(831\) −0.0438679 −0.00152176
\(832\) −6.48503 −0.224828
\(833\) 46.1003 1.59728
\(834\) 2.22662 0.0771015
\(835\) −9.55185 −0.330555
\(836\) 21.2149 0.733732
\(837\) 2.74661 0.0949368
\(838\) −8.13210 −0.280919
\(839\) −44.0453 −1.52061 −0.760307 0.649564i \(-0.774951\pi\)
−0.760307 + 0.649564i \(0.774951\pi\)
\(840\) 2.41510 0.0833289
\(841\) 17.1165 0.590223
\(842\) −6.42227 −0.221326
\(843\) 8.85075 0.304836
\(844\) −22.3201 −0.768288
\(845\) −0.644426 −0.0221689
\(846\) −1.23880 −0.0425908
\(847\) −23.6591 −0.812938
\(848\) 4.63550 0.159184
\(849\) 0.731884 0.0251182
\(850\) 7.70906 0.264419
\(851\) 2.82824 0.0969510
\(852\) 3.82992 0.131211
\(853\) 9.63675 0.329956 0.164978 0.986297i \(-0.447245\pi\)
0.164978 + 0.986297i \(0.447245\pi\)
\(854\) 8.67615 0.296892
\(855\) −3.26820 −0.111770
\(856\) −9.66106 −0.330208
\(857\) 5.95689 0.203484 0.101742 0.994811i \(-0.467558\pi\)
0.101742 + 0.994811i \(0.467558\pi\)
\(858\) −0.550555 −0.0187956
\(859\) −52.8737 −1.80403 −0.902014 0.431707i \(-0.857911\pi\)
−0.902014 + 0.431707i \(0.857911\pi\)
\(860\) 8.48575 0.289362
\(861\) −6.40306 −0.218216
\(862\) −7.17437 −0.244360
\(863\) −18.4493 −0.628022 −0.314011 0.949419i \(-0.601673\pi\)
−0.314011 + 0.949419i \(0.601673\pi\)
\(864\) 2.92515 0.0995158
\(865\) 3.59924 0.122378
\(866\) −3.72995 −0.126749
\(867\) −26.5877 −0.902965
\(868\) 19.8749 0.674596
\(869\) 25.4949 0.864857
\(870\) −1.11457 −0.0377875
\(871\) −10.0994 −0.342206
\(872\) 6.52025 0.220804
\(873\) 13.9493 0.472113
\(874\) 1.69793 0.0574335
\(875\) 23.0966 0.780807
\(876\) −19.5313 −0.659900
\(877\) 6.40935 0.216428 0.108214 0.994128i \(-0.465487\pi\)
0.108214 + 0.994128i \(0.465487\pi\)
\(878\) 7.11381 0.240080
\(879\) 17.4078 0.587151
\(880\) 5.03590 0.169760
\(881\) 27.7176 0.933828 0.466914 0.884303i \(-0.345366\pi\)
0.466914 + 0.884303i \(0.345366\pi\)
\(882\) −1.77840 −0.0598818
\(883\) −21.2500 −0.715120 −0.357560 0.933890i \(-0.616391\pi\)
−0.357560 + 0.933890i \(0.616391\pi\)
\(884\) −12.7759 −0.429702
\(885\) 2.79467 0.0939417
\(886\) 2.16264 0.0726553
\(887\) 39.7947 1.33617 0.668087 0.744083i \(-0.267113\pi\)
0.668087 + 0.744083i \(0.267113\pi\)
\(888\) 2.15628 0.0723601
\(889\) −20.9400 −0.702306
\(890\) −1.30093 −0.0436073
\(891\) −2.16169 −0.0724194
\(892\) −47.7401 −1.59846
\(893\) 24.6678 0.825475
\(894\) 2.57103 0.0859881
\(895\) 4.20054 0.140408
\(896\) 28.0524 0.937165
\(897\) 1.31455 0.0438917
\(898\) 1.91233 0.0638152
\(899\) −18.6520 −0.622079
\(900\) 8.87204 0.295735
\(901\) 8.46581 0.282037
\(902\) 0.942742 0.0313899
\(903\) −25.4449 −0.846754
\(904\) 14.2735 0.474730
\(905\) −3.49929 −0.116320
\(906\) 0.160412 0.00532934
\(907\) 17.2661 0.573312 0.286656 0.958034i \(-0.407456\pi\)
0.286656 + 0.958034i \(0.407456\pi\)
\(908\) 39.6065 1.31439
\(909\) −4.53003 −0.150251
\(910\) 0.613727 0.0203449
\(911\) −29.8074 −0.987564 −0.493782 0.869586i \(-0.664386\pi\)
−0.493782 + 0.869586i \(0.664386\pi\)
\(912\) −18.3335 −0.607083
\(913\) −25.7814 −0.853240
\(914\) −9.86925 −0.326446
\(915\) −5.87081 −0.194083
\(916\) −3.92441 −0.129666
\(917\) 37.5346 1.23950
\(918\) 1.68147 0.0554968
\(919\) −46.2600 −1.52598 −0.762988 0.646413i \(-0.776268\pi\)
−0.762988 + 0.646413i \(0.776268\pi\)
\(920\) 0.849020 0.0279914
\(921\) −6.42085 −0.211574
\(922\) −3.34897 −0.110292
\(923\) 1.97915 0.0651445
\(924\) −15.6423 −0.514593
\(925\) 9.86396 0.324325
\(926\) −2.27144 −0.0746442
\(927\) −1.00000 −0.0328443
\(928\) −19.8645 −0.652083
\(929\) 1.34876 0.0442512 0.0221256 0.999755i \(-0.492957\pi\)
0.0221256 + 0.999755i \(0.492957\pi\)
\(930\) 0.450794 0.0147821
\(931\) 35.4126 1.16060
\(932\) 8.35908 0.273811
\(933\) −21.8263 −0.714561
\(934\) 7.52854 0.246341
\(935\) 9.19706 0.300776
\(936\) 1.00223 0.0327589
\(937\) −13.3982 −0.437702 −0.218851 0.975758i \(-0.570231\pi\)
−0.218851 + 0.975758i \(0.570231\pi\)
\(938\) 9.61831 0.314049
\(939\) 26.9981 0.881050
\(940\) 6.06567 0.197840
\(941\) 15.0246 0.489788 0.244894 0.969550i \(-0.421247\pi\)
0.244894 + 0.969550i \(0.421247\pi\)
\(942\) 0.655702 0.0213639
\(943\) −2.25097 −0.0733018
\(944\) 15.6771 0.510247
\(945\) 2.40973 0.0783885
\(946\) 3.74633 0.121804
\(947\) 32.1115 1.04348 0.521741 0.853104i \(-0.325283\pi\)
0.521741 + 0.853104i \(0.325283\pi\)
\(948\) −22.8229 −0.741254
\(949\) −10.0930 −0.327632
\(950\) 5.92182 0.192129
\(951\) 29.5618 0.958607
\(952\) 24.7425 0.801909
\(953\) −16.7620 −0.542973 −0.271487 0.962442i \(-0.587515\pi\)
−0.271487 + 0.962442i \(0.587515\pi\)
\(954\) −0.326583 −0.0105735
\(955\) −12.2077 −0.395033
\(956\) 8.49287 0.274679
\(957\) 14.6799 0.474532
\(958\) −5.26929 −0.170243
\(959\) 20.7562 0.670251
\(960\) −4.17912 −0.134881
\(961\) −23.4561 −0.756649
\(962\) 0.547956 0.0176668
\(963\) −9.63958 −0.310631
\(964\) −35.7382 −1.15105
\(965\) −2.29764 −0.0739636
\(966\) −1.25193 −0.0402802
\(967\) 49.6640 1.59709 0.798544 0.601937i \(-0.205604\pi\)
0.798544 + 0.601937i \(0.205604\pi\)
\(968\) −6.34119 −0.203813
\(969\) −33.4825 −1.07561
\(970\) 2.28946 0.0735102
\(971\) −49.0060 −1.57268 −0.786339 0.617795i \(-0.788026\pi\)
−0.786339 + 0.617795i \(0.788026\pi\)
\(972\) 1.93513 0.0620695
\(973\) 32.6914 1.04804
\(974\) 7.77427 0.249104
\(975\) 4.58471 0.146828
\(976\) −32.9333 −1.05417
\(977\) −53.9425 −1.72577 −0.862886 0.505398i \(-0.831346\pi\)
−0.862886 + 0.505398i \(0.831346\pi\)
\(978\) −2.06616 −0.0660684
\(979\) 17.1344 0.547617
\(980\) 8.70776 0.278159
\(981\) 6.50575 0.207713
\(982\) 10.3691 0.330891
\(983\) 21.3824 0.681992 0.340996 0.940065i \(-0.389236\pi\)
0.340996 + 0.940065i \(0.389236\pi\)
\(984\) −1.71616 −0.0547093
\(985\) 6.59398 0.210102
\(986\) −11.4187 −0.363646
\(987\) −18.1882 −0.578936
\(988\) −9.81401 −0.312225
\(989\) −8.94507 −0.284437
\(990\) −0.354792 −0.0112760
\(991\) 50.0625 1.59029 0.795143 0.606421i \(-0.207396\pi\)
0.795143 + 0.606421i \(0.207396\pi\)
\(992\) 8.03427 0.255088
\(993\) −3.54256 −0.112420
\(994\) −1.88487 −0.0597844
\(995\) −15.4999 −0.491380
\(996\) 23.0794 0.731298
\(997\) 36.5990 1.15910 0.579552 0.814935i \(-0.303228\pi\)
0.579552 + 0.814935i \(0.303228\pi\)
\(998\) 4.58411 0.145108
\(999\) 2.15149 0.0680700
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 \(a_p\))