Properties

Label 8035.2.a.e.1.12
Level 8035
Weight 2
Character 8035.1
Self dual Yes
Analytic conductor 64.160
Analytic rank 0
Dimension 153
CM No

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Newspace parameters

Level: \( N \) = \( 8035 = 5 \cdot 1607 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8035.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1597980241\)
Analytic rank: \(0\)
Dimension: \(153\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 8035.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.51924 q^{2} -1.73731 q^{3} +4.34657 q^{4} +1.00000 q^{5} +4.37670 q^{6} -5.14815 q^{7} -5.91158 q^{8} +0.0182398 q^{9} +O(q^{10})\) \(q-2.51924 q^{2} -1.73731 q^{3} +4.34657 q^{4} +1.00000 q^{5} +4.37670 q^{6} -5.14815 q^{7} -5.91158 q^{8} +0.0182398 q^{9} -2.51924 q^{10} +1.49876 q^{11} -7.55134 q^{12} -5.55026 q^{13} +12.9694 q^{14} -1.73731 q^{15} +6.19955 q^{16} -2.59367 q^{17} -0.0459504 q^{18} +4.66946 q^{19} +4.34657 q^{20} +8.94393 q^{21} -3.77574 q^{22} +1.25547 q^{23} +10.2702 q^{24} +1.00000 q^{25} +13.9825 q^{26} +5.18024 q^{27} -22.3768 q^{28} -2.96767 q^{29} +4.37670 q^{30} -6.58366 q^{31} -3.79500 q^{32} -2.60381 q^{33} +6.53409 q^{34} -5.14815 q^{35} +0.0792806 q^{36} +11.5124 q^{37} -11.7635 q^{38} +9.64252 q^{39} -5.91158 q^{40} +1.49195 q^{41} -22.5319 q^{42} +9.01775 q^{43} +6.51448 q^{44} +0.0182398 q^{45} -3.16283 q^{46} -2.14466 q^{47} -10.7705 q^{48} +19.5035 q^{49} -2.51924 q^{50} +4.50601 q^{51} -24.1246 q^{52} -8.39169 q^{53} -13.0503 q^{54} +1.49876 q^{55} +30.4337 q^{56} -8.11228 q^{57} +7.47628 q^{58} -8.30122 q^{59} -7.55134 q^{60} +1.72561 q^{61} +16.5858 q^{62} -0.0939012 q^{63} -2.83859 q^{64} -5.55026 q^{65} +6.55962 q^{66} -14.6099 q^{67} -11.2736 q^{68} -2.18114 q^{69} +12.9694 q^{70} +2.20528 q^{71} -0.107826 q^{72} -11.1249 q^{73} -29.0024 q^{74} -1.73731 q^{75} +20.2961 q^{76} -7.71585 q^{77} -24.2918 q^{78} -0.117660 q^{79} +6.19955 q^{80} -9.05439 q^{81} -3.75858 q^{82} -9.42988 q^{83} +38.8754 q^{84} -2.59367 q^{85} -22.7179 q^{86} +5.15576 q^{87} -8.86005 q^{88} -17.9566 q^{89} -0.0459504 q^{90} +28.5736 q^{91} +5.45699 q^{92} +11.4378 q^{93} +5.40293 q^{94} +4.66946 q^{95} +6.59309 q^{96} -15.3455 q^{97} -49.1340 q^{98} +0.0273371 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153q + 18q^{2} + 7q^{3} + 176q^{4} + 153q^{5} + 19q^{6} + 5q^{7} + 57q^{8} + 206q^{9} + O(q^{10}) \) \( 153q + 18q^{2} + 7q^{3} + 176q^{4} + 153q^{5} + 19q^{6} + 5q^{7} + 57q^{8} + 206q^{9} + 18q^{10} + 38q^{11} + 14q^{12} + 28q^{13} + 53q^{14} + 7q^{15} + 214q^{16} + 50q^{17} + 47q^{18} + 65q^{19} + 176q^{20} + 109q^{21} + 13q^{22} + 52q^{23} + 66q^{24} + 153q^{25} + 36q^{26} + 19q^{27} + 26q^{28} + 172q^{29} + 19q^{30} + 60q^{31} + 107q^{32} + 4q^{33} + 40q^{34} + 5q^{35} + 241q^{36} + 65q^{37} + 29q^{38} + 56q^{39} + 57q^{40} + 152q^{41} - 19q^{42} + 22q^{43} + 97q^{44} + 206q^{45} + 86q^{46} + 37q^{47} - 4q^{48} + 260q^{49} + 18q^{50} + 102q^{51} - 6q^{52} + 169q^{53} + 64q^{54} + 38q^{55} + 146q^{56} + 40q^{57} - 9q^{58} + 64q^{59} + 14q^{60} + 164q^{61} + 12q^{62} + 19q^{63} + 259q^{64} + 28q^{65} + 6q^{66} + 5q^{67} + 112q^{68} + 119q^{69} + 53q^{70} + 100q^{71} + 77q^{72} + 10q^{73} + 98q^{74} + 7q^{75} + 126q^{76} + 80q^{77} - 4q^{78} + 110q^{79} + 214q^{80} + 305q^{81} - 27q^{82} + 36q^{83} + 172q^{84} + 50q^{85} + 44q^{86} + 23q^{87} + 47q^{88} + 143q^{89} + 47q^{90} + 82q^{91} + 130q^{92} + 31q^{93} + 77q^{94} + 65q^{95} + 57q^{96} + 11q^{97} + 29q^{98} + 99q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.51924 −1.78137 −0.890686 0.454619i \(-0.849775\pi\)
−0.890686 + 0.454619i \(0.849775\pi\)
\(3\) −1.73731 −1.00304 −0.501518 0.865147i \(-0.667225\pi\)
−0.501518 + 0.865147i \(0.667225\pi\)
\(4\) 4.34657 2.17329
\(5\) 1.00000 0.447214
\(6\) 4.37670 1.78678
\(7\) −5.14815 −1.94582 −0.972910 0.231186i \(-0.925739\pi\)
−0.972910 + 0.231186i \(0.925739\pi\)
\(8\) −5.91158 −2.09006
\(9\) 0.0182398 0.00607993
\(10\) −2.51924 −0.796654
\(11\) 1.49876 0.451893 0.225947 0.974140i \(-0.427452\pi\)
0.225947 + 0.974140i \(0.427452\pi\)
\(12\) −7.55134 −2.17988
\(13\) −5.55026 −1.53937 −0.769683 0.638426i \(-0.779586\pi\)
−0.769683 + 0.638426i \(0.779586\pi\)
\(14\) 12.9694 3.46623
\(15\) −1.73731 −0.448571
\(16\) 6.19955 1.54989
\(17\) −2.59367 −0.629058 −0.314529 0.949248i \(-0.601847\pi\)
−0.314529 + 0.949248i \(0.601847\pi\)
\(18\) −0.0459504 −0.0108306
\(19\) 4.66946 1.07125 0.535623 0.844457i \(-0.320077\pi\)
0.535623 + 0.844457i \(0.320077\pi\)
\(20\) 4.34657 0.971923
\(21\) 8.94393 1.95173
\(22\) −3.77574 −0.804990
\(23\) 1.25547 0.261783 0.130892 0.991397i \(-0.458216\pi\)
0.130892 + 0.991397i \(0.458216\pi\)
\(24\) 10.2702 2.09640
\(25\) 1.00000 0.200000
\(26\) 13.9825 2.74218
\(27\) 5.18024 0.996937
\(28\) −22.3768 −4.22882
\(29\) −2.96767 −0.551083 −0.275541 0.961289i \(-0.588857\pi\)
−0.275541 + 0.961289i \(0.588857\pi\)
\(30\) 4.37670 0.799072
\(31\) −6.58366 −1.18246 −0.591230 0.806503i \(-0.701357\pi\)
−0.591230 + 0.806503i \(0.701357\pi\)
\(32\) −3.79500 −0.670868
\(33\) −2.60381 −0.453265
\(34\) 6.53409 1.12059
\(35\) −5.14815 −0.870197
\(36\) 0.0792806 0.0132134
\(37\) 11.5124 1.89262 0.946311 0.323258i \(-0.104778\pi\)
0.946311 + 0.323258i \(0.104778\pi\)
\(38\) −11.7635 −1.90829
\(39\) 9.64252 1.54404
\(40\) −5.91158 −0.934703
\(41\) 1.49195 0.233004 0.116502 0.993190i \(-0.462832\pi\)
0.116502 + 0.993190i \(0.462832\pi\)
\(42\) −22.5319 −3.47675
\(43\) 9.01775 1.37519 0.687597 0.726092i \(-0.258665\pi\)
0.687597 + 0.726092i \(0.258665\pi\)
\(44\) 6.51448 0.982094
\(45\) 0.0182398 0.00271903
\(46\) −3.16283 −0.466334
\(47\) −2.14466 −0.312831 −0.156416 0.987691i \(-0.549994\pi\)
−0.156416 + 0.987691i \(0.549994\pi\)
\(48\) −10.7705 −1.55459
\(49\) 19.5035 2.78621
\(50\) −2.51924 −0.356274
\(51\) 4.50601 0.630968
\(52\) −24.1246 −3.34548
\(53\) −8.39169 −1.15269 −0.576343 0.817208i \(-0.695521\pi\)
−0.576343 + 0.817208i \(0.695521\pi\)
\(54\) −13.0503 −1.77592
\(55\) 1.49876 0.202093
\(56\) 30.4337 4.06688
\(57\) −8.11228 −1.07450
\(58\) 7.47628 0.981683
\(59\) −8.30122 −1.08073 −0.540364 0.841432i \(-0.681713\pi\)
−0.540364 + 0.841432i \(0.681713\pi\)
\(60\) −7.55134 −0.974873
\(61\) 1.72561 0.220941 0.110471 0.993879i \(-0.464764\pi\)
0.110471 + 0.993879i \(0.464764\pi\)
\(62\) 16.5858 2.10640
\(63\) −0.0939012 −0.0118304
\(64\) −2.83859 −0.354823
\(65\) −5.55026 −0.688426
\(66\) 6.55962 0.807434
\(67\) −14.6099 −1.78488 −0.892441 0.451165i \(-0.851009\pi\)
−0.892441 + 0.451165i \(0.851009\pi\)
\(68\) −11.2736 −1.36712
\(69\) −2.18114 −0.262578
\(70\) 12.9694 1.55014
\(71\) 2.20528 0.261719 0.130859 0.991401i \(-0.458226\pi\)
0.130859 + 0.991401i \(0.458226\pi\)
\(72\) −0.107826 −0.0127074
\(73\) −11.1249 −1.30207 −0.651037 0.759046i \(-0.725666\pi\)
−0.651037 + 0.759046i \(0.725666\pi\)
\(74\) −29.0024 −3.37146
\(75\) −1.73731 −0.200607
\(76\) 20.2961 2.32813
\(77\) −7.71585 −0.879303
\(78\) −24.2918 −2.75051
\(79\) −0.117660 −0.0132378 −0.00661891 0.999978i \(-0.502107\pi\)
−0.00661891 + 0.999978i \(0.502107\pi\)
\(80\) 6.19955 0.693131
\(81\) −9.05439 −1.00604
\(82\) −3.75858 −0.415066
\(83\) −9.42988 −1.03506 −0.517532 0.855664i \(-0.673149\pi\)
−0.517532 + 0.855664i \(0.673149\pi\)
\(84\) 38.8754 4.24166
\(85\) −2.59367 −0.281323
\(86\) −22.7179 −2.44973
\(87\) 5.15576 0.552755
\(88\) −8.86005 −0.944485
\(89\) −17.9566 −1.90339 −0.951696 0.307043i \(-0.900660\pi\)
−0.951696 + 0.307043i \(0.900660\pi\)
\(90\) −0.0459504 −0.00484360
\(91\) 28.5736 2.99533
\(92\) 5.45699 0.568931
\(93\) 11.4378 1.18605
\(94\) 5.40293 0.557269
\(95\) 4.66946 0.479076
\(96\) 6.59309 0.672904
\(97\) −15.3455 −1.55809 −0.779047 0.626965i \(-0.784297\pi\)
−0.779047 + 0.626965i \(0.784297\pi\)
\(98\) −49.1340 −4.96328
\(99\) 0.0273371 0.00274748
\(100\) 4.34657 0.434657
\(101\) −3.08894 −0.307361 −0.153681 0.988121i \(-0.549113\pi\)
−0.153681 + 0.988121i \(0.549113\pi\)
\(102\) −11.3517 −1.12399
\(103\) −10.0468 −0.989939 −0.494970 0.868910i \(-0.664821\pi\)
−0.494970 + 0.868910i \(0.664821\pi\)
\(104\) 32.8108 3.21737
\(105\) 8.94393 0.872838
\(106\) 21.1407 2.05336
\(107\) 6.65751 0.643606 0.321803 0.946807i \(-0.395711\pi\)
0.321803 + 0.946807i \(0.395711\pi\)
\(108\) 22.5163 2.16663
\(109\) −7.58670 −0.726674 −0.363337 0.931658i \(-0.618363\pi\)
−0.363337 + 0.931658i \(0.618363\pi\)
\(110\) −3.77574 −0.360003
\(111\) −20.0005 −1.89837
\(112\) −31.9163 −3.01580
\(113\) 10.8606 1.02168 0.510842 0.859675i \(-0.329334\pi\)
0.510842 + 0.859675i \(0.329334\pi\)
\(114\) 20.4368 1.91408
\(115\) 1.25547 0.117073
\(116\) −12.8992 −1.19766
\(117\) −0.101236 −0.00935924
\(118\) 20.9128 1.92518
\(119\) 13.3526 1.22403
\(120\) 10.2702 0.937541
\(121\) −8.75371 −0.795792
\(122\) −4.34722 −0.393579
\(123\) −2.59198 −0.233711
\(124\) −28.6164 −2.56983
\(125\) 1.00000 0.0894427
\(126\) 0.236560 0.0210744
\(127\) 14.5290 1.28924 0.644619 0.764504i \(-0.277016\pi\)
0.644619 + 0.764504i \(0.277016\pi\)
\(128\) 14.7411 1.30294
\(129\) −15.6666 −1.37937
\(130\) 13.9825 1.22634
\(131\) −6.76961 −0.591463 −0.295732 0.955271i \(-0.595563\pi\)
−0.295732 + 0.955271i \(0.595563\pi\)
\(132\) −11.3177 −0.985075
\(133\) −24.0391 −2.08445
\(134\) 36.8058 3.17954
\(135\) 5.18024 0.445844
\(136\) 15.3327 1.31477
\(137\) −18.6539 −1.59371 −0.796857 0.604168i \(-0.793506\pi\)
−0.796857 + 0.604168i \(0.793506\pi\)
\(138\) 5.49481 0.467749
\(139\) −17.7056 −1.50177 −0.750884 0.660434i \(-0.770372\pi\)
−0.750884 + 0.660434i \(0.770372\pi\)
\(140\) −22.3768 −1.89119
\(141\) 3.72594 0.313781
\(142\) −5.55563 −0.466218
\(143\) −8.31852 −0.695630
\(144\) 0.113079 0.00942321
\(145\) −2.96767 −0.246452
\(146\) 28.0264 2.31948
\(147\) −33.8836 −2.79467
\(148\) 50.0393 4.11321
\(149\) 5.93816 0.486473 0.243237 0.969967i \(-0.421791\pi\)
0.243237 + 0.969967i \(0.421791\pi\)
\(150\) 4.37670 0.357356
\(151\) −5.81861 −0.473512 −0.236756 0.971569i \(-0.576084\pi\)
−0.236756 + 0.971569i \(0.576084\pi\)
\(152\) −27.6039 −2.23897
\(153\) −0.0473081 −0.00382463
\(154\) 19.4381 1.56637
\(155\) −6.58366 −0.528812
\(156\) 41.9119 3.35564
\(157\) 1.97300 0.157463 0.0787313 0.996896i \(-0.474913\pi\)
0.0787313 + 0.996896i \(0.474913\pi\)
\(158\) 0.296415 0.0235815
\(159\) 14.5789 1.15619
\(160\) −3.79500 −0.300021
\(161\) −6.46335 −0.509383
\(162\) 22.8102 1.79214
\(163\) −15.7510 −1.23371 −0.616855 0.787077i \(-0.711594\pi\)
−0.616855 + 0.787077i \(0.711594\pi\)
\(164\) 6.48488 0.506384
\(165\) −2.60381 −0.202706
\(166\) 23.7561 1.84383
\(167\) −11.4177 −0.883528 −0.441764 0.897131i \(-0.645647\pi\)
−0.441764 + 0.897131i \(0.645647\pi\)
\(168\) −52.8728 −4.07922
\(169\) 17.8054 1.36965
\(170\) 6.53409 0.501142
\(171\) 0.0851699 0.00651310
\(172\) 39.1963 2.98869
\(173\) 12.4032 0.942996 0.471498 0.881867i \(-0.343714\pi\)
0.471498 + 0.881867i \(0.343714\pi\)
\(174\) −12.9886 −0.984663
\(175\) −5.14815 −0.389164
\(176\) 9.29165 0.700384
\(177\) 14.4218 1.08401
\(178\) 45.2369 3.39065
\(179\) 11.0424 0.825348 0.412674 0.910879i \(-0.364595\pi\)
0.412674 + 0.910879i \(0.364595\pi\)
\(180\) 0.0792806 0.00590922
\(181\) −15.3615 −1.14181 −0.570905 0.821016i \(-0.693407\pi\)
−0.570905 + 0.821016i \(0.693407\pi\)
\(182\) −71.9838 −5.33579
\(183\) −2.99791 −0.221612
\(184\) −7.42181 −0.547143
\(185\) 11.5124 0.846406
\(186\) −28.8147 −2.11280
\(187\) −3.88730 −0.284267
\(188\) −9.32194 −0.679872
\(189\) −26.6687 −1.93986
\(190\) −11.7635 −0.853413
\(191\) −7.97570 −0.577101 −0.288551 0.957465i \(-0.593173\pi\)
−0.288551 + 0.957465i \(0.593173\pi\)
\(192\) 4.93150 0.355900
\(193\) 0.286972 0.0206567 0.0103283 0.999947i \(-0.496712\pi\)
0.0103283 + 0.999947i \(0.496712\pi\)
\(194\) 38.6589 2.77555
\(195\) 9.64252 0.690515
\(196\) 84.7733 6.05524
\(197\) 12.5769 0.896069 0.448034 0.894016i \(-0.352124\pi\)
0.448034 + 0.894016i \(0.352124\pi\)
\(198\) −0.0688687 −0.00489428
\(199\) −4.64955 −0.329598 −0.164799 0.986327i \(-0.552698\pi\)
−0.164799 + 0.986327i \(0.552698\pi\)
\(200\) −5.91158 −0.418012
\(201\) 25.3819 1.79030
\(202\) 7.78179 0.547525
\(203\) 15.2780 1.07231
\(204\) 19.5857 1.37127
\(205\) 1.49195 0.104202
\(206\) 25.3103 1.76345
\(207\) 0.0228995 0.00159162
\(208\) −34.4092 −2.38585
\(209\) 6.99840 0.484089
\(210\) −22.5319 −1.55485
\(211\) 26.9726 1.85687 0.928434 0.371497i \(-0.121155\pi\)
0.928434 + 0.371497i \(0.121155\pi\)
\(212\) −36.4751 −2.50512
\(213\) −3.83125 −0.262513
\(214\) −16.7719 −1.14650
\(215\) 9.01775 0.615006
\(216\) −30.6234 −2.08366
\(217\) 33.8937 2.30085
\(218\) 19.1127 1.29448
\(219\) 19.3274 1.30603
\(220\) 6.51448 0.439206
\(221\) 14.3956 0.968351
\(222\) 50.3861 3.38170
\(223\) 25.5584 1.71152 0.855760 0.517373i \(-0.173090\pi\)
0.855760 + 0.517373i \(0.173090\pi\)
\(224\) 19.5372 1.30539
\(225\) 0.0182398 0.00121599
\(226\) −27.3606 −1.82000
\(227\) −23.0291 −1.52849 −0.764247 0.644923i \(-0.776889\pi\)
−0.764247 + 0.644923i \(0.776889\pi\)
\(228\) −35.2606 −2.33519
\(229\) 2.84890 0.188261 0.0941304 0.995560i \(-0.469993\pi\)
0.0941304 + 0.995560i \(0.469993\pi\)
\(230\) −3.16283 −0.208551
\(231\) 13.4048 0.881972
\(232\) 17.5436 1.15180
\(233\) 28.5323 1.86921 0.934605 0.355686i \(-0.115753\pi\)
0.934605 + 0.355686i \(0.115753\pi\)
\(234\) 0.255037 0.0166723
\(235\) −2.14466 −0.139902
\(236\) −36.0819 −2.34873
\(237\) 0.204412 0.0132780
\(238\) −33.6385 −2.18046
\(239\) 3.50969 0.227023 0.113511 0.993537i \(-0.463790\pi\)
0.113511 + 0.993537i \(0.463790\pi\)
\(240\) −10.7705 −0.695235
\(241\) 22.8121 1.46945 0.734727 0.678363i \(-0.237310\pi\)
0.734727 + 0.678363i \(0.237310\pi\)
\(242\) 22.0527 1.41760
\(243\) 0.189551 0.0121597
\(244\) 7.50047 0.480169
\(245\) 19.5035 1.24603
\(246\) 6.52982 0.416326
\(247\) −25.9167 −1.64904
\(248\) 38.9199 2.47141
\(249\) 16.3826 1.03821
\(250\) −2.51924 −0.159331
\(251\) −27.8012 −1.75480 −0.877398 0.479763i \(-0.840723\pi\)
−0.877398 + 0.479763i \(0.840723\pi\)
\(252\) −0.408149 −0.0257109
\(253\) 1.88165 0.118298
\(254\) −36.6020 −2.29661
\(255\) 4.50601 0.282177
\(256\) −31.4592 −1.96620
\(257\) −16.1111 −1.00498 −0.502491 0.864583i \(-0.667583\pi\)
−0.502491 + 0.864583i \(0.667583\pi\)
\(258\) 39.4680 2.45717
\(259\) −59.2674 −3.68270
\(260\) −24.1246 −1.49615
\(261\) −0.0541297 −0.00335054
\(262\) 17.0543 1.05362
\(263\) −7.69079 −0.474234 −0.237117 0.971481i \(-0.576203\pi\)
−0.237117 + 0.971481i \(0.576203\pi\)
\(264\) 15.3926 0.947351
\(265\) −8.39169 −0.515497
\(266\) 60.5602 3.71318
\(267\) 31.1961 1.90917
\(268\) −63.5029 −3.87906
\(269\) 3.64349 0.222147 0.111074 0.993812i \(-0.464571\pi\)
0.111074 + 0.993812i \(0.464571\pi\)
\(270\) −13.0503 −0.794214
\(271\) −20.5532 −1.24852 −0.624259 0.781218i \(-0.714599\pi\)
−0.624259 + 0.781218i \(0.714599\pi\)
\(272\) −16.0796 −0.974970
\(273\) −49.6412 −3.00442
\(274\) 46.9938 2.83900
\(275\) 1.49876 0.0903787
\(276\) −9.48047 −0.570657
\(277\) 16.1849 0.972456 0.486228 0.873832i \(-0.338373\pi\)
0.486228 + 0.873832i \(0.338373\pi\)
\(278\) 44.6047 2.67521
\(279\) −0.120085 −0.00718927
\(280\) 30.4337 1.81876
\(281\) 10.0276 0.598196 0.299098 0.954222i \(-0.403314\pi\)
0.299098 + 0.954222i \(0.403314\pi\)
\(282\) −9.38655 −0.558961
\(283\) 3.50549 0.208380 0.104190 0.994557i \(-0.466775\pi\)
0.104190 + 0.994557i \(0.466775\pi\)
\(284\) 9.58541 0.568789
\(285\) −8.11228 −0.480530
\(286\) 20.9564 1.23918
\(287\) −7.68079 −0.453383
\(288\) −0.0692200 −0.00407883
\(289\) −10.2729 −0.604286
\(290\) 7.47628 0.439022
\(291\) 26.6598 1.56282
\(292\) −48.3553 −2.82978
\(293\) −1.20570 −0.0704380 −0.0352190 0.999380i \(-0.511213\pi\)
−0.0352190 + 0.999380i \(0.511213\pi\)
\(294\) 85.3609 4.97835
\(295\) −8.30122 −0.483316
\(296\) −68.0563 −3.95569
\(297\) 7.76394 0.450509
\(298\) −14.9597 −0.866590
\(299\) −6.96819 −0.402981
\(300\) −7.55134 −0.435977
\(301\) −46.4248 −2.67588
\(302\) 14.6585 0.843500
\(303\) 5.36645 0.308294
\(304\) 28.9485 1.66031
\(305\) 1.72561 0.0988079
\(306\) 0.119180 0.00681309
\(307\) −20.9436 −1.19532 −0.597659 0.801751i \(-0.703902\pi\)
−0.597659 + 0.801751i \(0.703902\pi\)
\(308\) −33.5375 −1.91098
\(309\) 17.4544 0.992944
\(310\) 16.5858 0.942011
\(311\) −30.0309 −1.70290 −0.851449 0.524437i \(-0.824276\pi\)
−0.851449 + 0.524437i \(0.824276\pi\)
\(312\) −57.0026 −3.22713
\(313\) −2.14851 −0.121441 −0.0607204 0.998155i \(-0.519340\pi\)
−0.0607204 + 0.998155i \(0.519340\pi\)
\(314\) −4.97046 −0.280500
\(315\) −0.0939012 −0.00529073
\(316\) −0.511419 −0.0287696
\(317\) −6.34033 −0.356108 −0.178054 0.984021i \(-0.556980\pi\)
−0.178054 + 0.984021i \(0.556980\pi\)
\(318\) −36.7279 −2.05960
\(319\) −4.44783 −0.249031
\(320\) −2.83859 −0.158682
\(321\) −11.5662 −0.645560
\(322\) 16.2827 0.907401
\(323\) −12.1110 −0.673877
\(324\) −39.3556 −2.18642
\(325\) −5.55026 −0.307873
\(326\) 39.6805 2.19770
\(327\) 13.1804 0.728880
\(328\) −8.81979 −0.486992
\(329\) 11.0411 0.608713
\(330\) 6.55962 0.361095
\(331\) −9.37810 −0.515467 −0.257733 0.966216i \(-0.582976\pi\)
−0.257733 + 0.966216i \(0.582976\pi\)
\(332\) −40.9877 −2.24949
\(333\) 0.209983 0.0115070
\(334\) 28.7639 1.57389
\(335\) −14.6099 −0.798223
\(336\) 55.4484 3.02496
\(337\) 7.94442 0.432760 0.216380 0.976309i \(-0.430575\pi\)
0.216380 + 0.976309i \(0.430575\pi\)
\(338\) −44.8562 −2.43985
\(339\) −18.8683 −1.02478
\(340\) −11.2736 −0.611397
\(341\) −9.86733 −0.534346
\(342\) −0.214563 −0.0116023
\(343\) −64.3699 −3.47565
\(344\) −53.3092 −2.87424
\(345\) −2.18114 −0.117428
\(346\) −31.2466 −1.67983
\(347\) −7.27951 −0.390785 −0.195392 0.980725i \(-0.562598\pi\)
−0.195392 + 0.980725i \(0.562598\pi\)
\(348\) 22.4099 1.20130
\(349\) 3.79150 0.202954 0.101477 0.994838i \(-0.467643\pi\)
0.101477 + 0.994838i \(0.467643\pi\)
\(350\) 12.9694 0.693246
\(351\) −28.7517 −1.53465
\(352\) −5.68780 −0.303161
\(353\) 9.49982 0.505624 0.252812 0.967515i \(-0.418645\pi\)
0.252812 + 0.967515i \(0.418645\pi\)
\(354\) −36.3319 −1.93102
\(355\) 2.20528 0.117044
\(356\) −78.0495 −4.13661
\(357\) −23.1976 −1.22775
\(358\) −27.8185 −1.47025
\(359\) 14.4756 0.763993 0.381997 0.924164i \(-0.375237\pi\)
0.381997 + 0.924164i \(0.375237\pi\)
\(360\) −0.107826 −0.00568293
\(361\) 2.80381 0.147569
\(362\) 38.6993 2.03399
\(363\) 15.2079 0.798208
\(364\) 124.197 6.50971
\(365\) −11.1249 −0.582305
\(366\) 7.55246 0.394773
\(367\) −35.8718 −1.87249 −0.936247 0.351344i \(-0.885725\pi\)
−0.936247 + 0.351344i \(0.885725\pi\)
\(368\) 7.78335 0.405735
\(369\) 0.0272129 0.00141665
\(370\) −29.0024 −1.50776
\(371\) 43.2017 2.24292
\(372\) 49.7154 2.57763
\(373\) 12.9922 0.672713 0.336356 0.941735i \(-0.390805\pi\)
0.336356 + 0.941735i \(0.390805\pi\)
\(374\) 9.79304 0.506386
\(375\) −1.73731 −0.0897142
\(376\) 12.6784 0.653837
\(377\) 16.4714 0.848318
\(378\) 67.1848 3.45561
\(379\) 6.22008 0.319504 0.159752 0.987157i \(-0.448931\pi\)
0.159752 + 0.987157i \(0.448931\pi\)
\(380\) 20.2961 1.04117
\(381\) −25.2413 −1.29315
\(382\) 20.0927 1.02803
\(383\) 35.2079 1.79904 0.899520 0.436880i \(-0.143916\pi\)
0.899520 + 0.436880i \(0.143916\pi\)
\(384\) −25.6098 −1.30689
\(385\) −7.71585 −0.393236
\(386\) −0.722951 −0.0367972
\(387\) 0.164482 0.00836109
\(388\) −66.7001 −3.38619
\(389\) 7.63794 0.387259 0.193629 0.981075i \(-0.437974\pi\)
0.193629 + 0.981075i \(0.437974\pi\)
\(390\) −24.2918 −1.23006
\(391\) −3.25628 −0.164677
\(392\) −115.296 −5.82335
\(393\) 11.7609 0.593259
\(394\) −31.6843 −1.59623
\(395\) −0.117660 −0.00592013
\(396\) 0.118823 0.00597106
\(397\) −1.51998 −0.0762854 −0.0381427 0.999272i \(-0.512144\pi\)
−0.0381427 + 0.999272i \(0.512144\pi\)
\(398\) 11.7133 0.587137
\(399\) 41.7633 2.09078
\(400\) 6.19955 0.309978
\(401\) 27.8375 1.39014 0.695070 0.718942i \(-0.255373\pi\)
0.695070 + 0.718942i \(0.255373\pi\)
\(402\) −63.9430 −3.18919
\(403\) 36.5411 1.82024
\(404\) −13.4263 −0.667984
\(405\) −9.05439 −0.449916
\(406\) −38.4890 −1.91018
\(407\) 17.2543 0.855263
\(408\) −26.6377 −1.31876
\(409\) 14.9561 0.739530 0.369765 0.929125i \(-0.379438\pi\)
0.369765 + 0.929125i \(0.379438\pi\)
\(410\) −3.75858 −0.185623
\(411\) 32.4077 1.59855
\(412\) −43.6691 −2.15142
\(413\) 42.7360 2.10290
\(414\) −0.0576893 −0.00283528
\(415\) −9.42988 −0.462894
\(416\) 21.0633 1.03271
\(417\) 30.7601 1.50633
\(418\) −17.6307 −0.862343
\(419\) −39.1182 −1.91105 −0.955524 0.294914i \(-0.904709\pi\)
−0.955524 + 0.294914i \(0.904709\pi\)
\(420\) 38.8754 1.89693
\(421\) 16.5435 0.806279 0.403139 0.915139i \(-0.367919\pi\)
0.403139 + 0.915139i \(0.367919\pi\)
\(422\) −67.9504 −3.30777
\(423\) −0.0391182 −0.00190199
\(424\) 49.6081 2.40918
\(425\) −2.59367 −0.125812
\(426\) 9.65184 0.467633
\(427\) −8.88369 −0.429912
\(428\) 28.9374 1.39874
\(429\) 14.4518 0.697741
\(430\) −22.7179 −1.09555
\(431\) −21.5105 −1.03612 −0.518061 0.855343i \(-0.673346\pi\)
−0.518061 + 0.855343i \(0.673346\pi\)
\(432\) 32.1152 1.54514
\(433\) 0.853375 0.0410106 0.0205053 0.999790i \(-0.493473\pi\)
0.0205053 + 0.999790i \(0.493473\pi\)
\(434\) −85.3864 −4.09868
\(435\) 5.15576 0.247200
\(436\) −32.9761 −1.57927
\(437\) 5.86236 0.280435
\(438\) −48.6905 −2.32652
\(439\) 8.42789 0.402241 0.201121 0.979566i \(-0.435542\pi\)
0.201121 + 0.979566i \(0.435542\pi\)
\(440\) −8.86005 −0.422386
\(441\) 0.355739 0.0169400
\(442\) −36.2659 −1.72499
\(443\) 10.4539 0.496679 0.248340 0.968673i \(-0.420115\pi\)
0.248340 + 0.968673i \(0.420115\pi\)
\(444\) −86.9338 −4.12569
\(445\) −17.9566 −0.851222
\(446\) −64.3879 −3.04885
\(447\) −10.3164 −0.487950
\(448\) 14.6135 0.690422
\(449\) 7.84557 0.370255 0.185128 0.982714i \(-0.440730\pi\)
0.185128 + 0.982714i \(0.440730\pi\)
\(450\) −0.0459504 −0.00216612
\(451\) 2.23608 0.105293
\(452\) 47.2066 2.22041
\(453\) 10.1087 0.474949
\(454\) 58.0158 2.72282
\(455\) 28.5736 1.33955
\(456\) 47.9564 2.24577
\(457\) −32.9157 −1.53973 −0.769866 0.638205i \(-0.779677\pi\)
−0.769866 + 0.638205i \(0.779677\pi\)
\(458\) −7.17708 −0.335363
\(459\) −13.4358 −0.627132
\(460\) 5.45699 0.254433
\(461\) 10.5433 0.491050 0.245525 0.969390i \(-0.421040\pi\)
0.245525 + 0.969390i \(0.421040\pi\)
\(462\) −33.7700 −1.57112
\(463\) −15.1692 −0.704975 −0.352487 0.935817i \(-0.614664\pi\)
−0.352487 + 0.935817i \(0.614664\pi\)
\(464\) −18.3982 −0.854116
\(465\) 11.4378 0.530417
\(466\) −71.8796 −3.32976
\(467\) −7.23586 −0.334836 −0.167418 0.985886i \(-0.553543\pi\)
−0.167418 + 0.985886i \(0.553543\pi\)
\(468\) −0.440028 −0.0203403
\(469\) 75.2139 3.47306
\(470\) 5.40293 0.249218
\(471\) −3.42771 −0.157941
\(472\) 49.0734 2.25879
\(473\) 13.5155 0.621442
\(474\) −0.514964 −0.0236531
\(475\) 4.66946 0.214249
\(476\) 58.0382 2.66018
\(477\) −0.153063 −0.00700825
\(478\) −8.84174 −0.404412
\(479\) −14.8903 −0.680355 −0.340178 0.940361i \(-0.610487\pi\)
−0.340178 + 0.940361i \(0.610487\pi\)
\(480\) 6.59309 0.300932
\(481\) −63.8967 −2.91344
\(482\) −57.4691 −2.61764
\(483\) 11.2288 0.510929
\(484\) −38.0487 −1.72948
\(485\) −15.3455 −0.696801
\(486\) −0.477524 −0.0216609
\(487\) 3.47978 0.157684 0.0788420 0.996887i \(-0.474878\pi\)
0.0788420 + 0.996887i \(0.474878\pi\)
\(488\) −10.2011 −0.461780
\(489\) 27.3643 1.23746
\(490\) −49.1340 −2.21965
\(491\) 7.96411 0.359415 0.179708 0.983720i \(-0.442485\pi\)
0.179708 + 0.983720i \(0.442485\pi\)
\(492\) −11.2662 −0.507921
\(493\) 7.69717 0.346663
\(494\) 65.2904 2.93756
\(495\) 0.0273371 0.00122871
\(496\) −40.8158 −1.83268
\(497\) −11.3531 −0.509257
\(498\) −41.2717 −1.84943
\(499\) −32.5746 −1.45824 −0.729120 0.684386i \(-0.760070\pi\)
−0.729120 + 0.684386i \(0.760070\pi\)
\(500\) 4.34657 0.194385
\(501\) 19.8361 0.886209
\(502\) 70.0379 3.12595
\(503\) 34.9807 1.55971 0.779856 0.625959i \(-0.215292\pi\)
0.779856 + 0.625959i \(0.215292\pi\)
\(504\) 0.555105 0.0247263
\(505\) −3.08894 −0.137456
\(506\) −4.74033 −0.210733
\(507\) −30.9335 −1.37381
\(508\) 63.1512 2.80188
\(509\) −36.7736 −1.62996 −0.814980 0.579490i \(-0.803252\pi\)
−0.814980 + 0.579490i \(0.803252\pi\)
\(510\) −11.3517 −0.502663
\(511\) 57.2728 2.53360
\(512\) 49.7710 2.19959
\(513\) 24.1889 1.06797
\(514\) 40.5877 1.79025
\(515\) −10.0468 −0.442714
\(516\) −68.0961 −2.99776
\(517\) −3.21434 −0.141366
\(518\) 149.309 6.56026
\(519\) −21.5481 −0.945858
\(520\) 32.8108 1.43885
\(521\) 42.0157 1.84074 0.920370 0.391049i \(-0.127888\pi\)
0.920370 + 0.391049i \(0.127888\pi\)
\(522\) 0.136366 0.00596856
\(523\) −18.3141 −0.800818 −0.400409 0.916336i \(-0.631132\pi\)
−0.400409 + 0.916336i \(0.631132\pi\)
\(524\) −29.4246 −1.28542
\(525\) 8.94393 0.390345
\(526\) 19.3749 0.844788
\(527\) 17.0759 0.743837
\(528\) −16.1425 −0.702510
\(529\) −21.4238 −0.931469
\(530\) 21.1407 0.918292
\(531\) −0.151413 −0.00657075
\(532\) −104.488 −4.53011
\(533\) −8.28072 −0.358678
\(534\) −78.5904 −3.40094
\(535\) 6.65751 0.287829
\(536\) 86.3675 3.73051
\(537\) −19.1841 −0.827853
\(538\) −9.17882 −0.395727
\(539\) 29.2311 1.25907
\(540\) 22.5163 0.968946
\(541\) −29.0873 −1.25056 −0.625280 0.780400i \(-0.715015\pi\)
−0.625280 + 0.780400i \(0.715015\pi\)
\(542\) 51.7784 2.22407
\(543\) 26.6876 1.14528
\(544\) 9.84300 0.422015
\(545\) −7.58670 −0.324979
\(546\) 125.058 5.35199
\(547\) −17.6482 −0.754584 −0.377292 0.926094i \(-0.623145\pi\)
−0.377292 + 0.926094i \(0.623145\pi\)
\(548\) −81.0808 −3.46360
\(549\) 0.0314747 0.00134331
\(550\) −3.77574 −0.160998
\(551\) −13.8574 −0.590345
\(552\) 12.8940 0.548804
\(553\) 0.605734 0.0257584
\(554\) −40.7736 −1.73231
\(555\) −20.0005 −0.848975
\(556\) −76.9587 −3.26377
\(557\) 22.6676 0.960458 0.480229 0.877143i \(-0.340554\pi\)
0.480229 + 0.877143i \(0.340554\pi\)
\(558\) 0.302522 0.0128068
\(559\) −50.0509 −2.11693
\(560\) −31.9163 −1.34871
\(561\) 6.75344 0.285130
\(562\) −25.2619 −1.06561
\(563\) 36.9122 1.55566 0.777832 0.628473i \(-0.216320\pi\)
0.777832 + 0.628473i \(0.216320\pi\)
\(564\) 16.1951 0.681936
\(565\) 10.8606 0.456911
\(566\) −8.83116 −0.371202
\(567\) 46.6134 1.95758
\(568\) −13.0367 −0.547007
\(569\) 35.7955 1.50062 0.750312 0.661084i \(-0.229903\pi\)
0.750312 + 0.661084i \(0.229903\pi\)
\(570\) 20.4368 0.856003
\(571\) 5.31789 0.222547 0.111273 0.993790i \(-0.464507\pi\)
0.111273 + 0.993790i \(0.464507\pi\)
\(572\) −36.1571 −1.51180
\(573\) 13.8562 0.578853
\(574\) 19.3498 0.807644
\(575\) 1.25547 0.0523567
\(576\) −0.0517752 −0.00215730
\(577\) 18.0746 0.752457 0.376229 0.926527i \(-0.377221\pi\)
0.376229 + 0.926527i \(0.377221\pi\)
\(578\) 25.8798 1.07646
\(579\) −0.498558 −0.0207194
\(580\) −12.8992 −0.535610
\(581\) 48.5465 2.01405
\(582\) −67.1624 −2.78397
\(583\) −12.5771 −0.520892
\(584\) 65.7659 2.72141
\(585\) −0.101236 −0.00418558
\(586\) 3.03746 0.125476
\(587\) 15.3696 0.634372 0.317186 0.948363i \(-0.397262\pi\)
0.317186 + 0.948363i \(0.397262\pi\)
\(588\) −147.277 −6.07362
\(589\) −30.7421 −1.26671
\(590\) 20.9128 0.860966
\(591\) −21.8500 −0.898789
\(592\) 71.3715 2.93335
\(593\) 27.6247 1.13441 0.567205 0.823576i \(-0.308025\pi\)
0.567205 + 0.823576i \(0.308025\pi\)
\(594\) −19.5592 −0.802525
\(595\) 13.3526 0.547405
\(596\) 25.8107 1.05725
\(597\) 8.07771 0.330599
\(598\) 17.5545 0.717859
\(599\) 3.05798 0.124946 0.0624728 0.998047i \(-0.480101\pi\)
0.0624728 + 0.998047i \(0.480101\pi\)
\(600\) 10.2702 0.419281
\(601\) 9.55225 0.389644 0.194822 0.980839i \(-0.437587\pi\)
0.194822 + 0.980839i \(0.437587\pi\)
\(602\) 116.955 4.76674
\(603\) −0.266481 −0.0108519
\(604\) −25.2910 −1.02908
\(605\) −8.75371 −0.355889
\(606\) −13.5194 −0.549187
\(607\) 19.0675 0.773927 0.386963 0.922095i \(-0.373524\pi\)
0.386963 + 0.922095i \(0.373524\pi\)
\(608\) −17.7206 −0.718665
\(609\) −26.5426 −1.07556
\(610\) −4.34722 −0.176014
\(611\) 11.9035 0.481562
\(612\) −0.205628 −0.00831202
\(613\) −19.6124 −0.792137 −0.396068 0.918221i \(-0.629626\pi\)
−0.396068 + 0.918221i \(0.629626\pi\)
\(614\) 52.7621 2.12930
\(615\) −2.59198 −0.104519
\(616\) 45.6129 1.83780
\(617\) −19.8107 −0.797549 −0.398775 0.917049i \(-0.630564\pi\)
−0.398775 + 0.917049i \(0.630564\pi\)
\(618\) −43.9717 −1.76880
\(619\) 15.2080 0.611260 0.305630 0.952150i \(-0.401133\pi\)
0.305630 + 0.952150i \(0.401133\pi\)
\(620\) −28.6164 −1.14926
\(621\) 6.50363 0.260982
\(622\) 75.6552 3.03350
\(623\) 92.4431 3.70365
\(624\) 59.7793 2.39309
\(625\) 1.00000 0.0400000
\(626\) 5.41260 0.216331
\(627\) −12.1584 −0.485559
\(628\) 8.57579 0.342211
\(629\) −29.8593 −1.19057
\(630\) 0.236560 0.00942477
\(631\) 43.5896 1.73527 0.867637 0.497198i \(-0.165638\pi\)
0.867637 + 0.497198i \(0.165638\pi\)
\(632\) 0.695559 0.0276678
\(633\) −46.8597 −1.86250
\(634\) 15.9728 0.634361
\(635\) 14.5290 0.576564
\(636\) 63.3684 2.51272
\(637\) −108.249 −4.28900
\(638\) 11.2052 0.443616
\(639\) 0.0402238 0.00159123
\(640\) 14.7411 0.582693
\(641\) −6.85324 −0.270687 −0.135343 0.990799i \(-0.543214\pi\)
−0.135343 + 0.990799i \(0.543214\pi\)
\(642\) 29.1379 1.14998
\(643\) −45.2395 −1.78407 −0.892035 0.451966i \(-0.850723\pi\)
−0.892035 + 0.451966i \(0.850723\pi\)
\(644\) −28.0934 −1.10704
\(645\) −15.6666 −0.616873
\(646\) 30.5106 1.20043
\(647\) −5.24149 −0.206064 −0.103032 0.994678i \(-0.532854\pi\)
−0.103032 + 0.994678i \(0.532854\pi\)
\(648\) 53.5258 2.10269
\(649\) −12.4416 −0.488374
\(650\) 13.9825 0.548437
\(651\) −58.8838 −2.30784
\(652\) −68.4627 −2.68121
\(653\) 25.3428 0.991739 0.495869 0.868397i \(-0.334850\pi\)
0.495869 + 0.868397i \(0.334850\pi\)
\(654\) −33.2047 −1.29841
\(655\) −6.76961 −0.264510
\(656\) 9.24943 0.361130
\(657\) −0.202916 −0.00791652
\(658\) −27.8151 −1.08435
\(659\) −7.73809 −0.301433 −0.150717 0.988577i \(-0.548158\pi\)
−0.150717 + 0.988577i \(0.548158\pi\)
\(660\) −11.3177 −0.440539
\(661\) −31.9013 −1.24082 −0.620409 0.784279i \(-0.713033\pi\)
−0.620409 + 0.784279i \(0.713033\pi\)
\(662\) 23.6257 0.918239
\(663\) −25.0096 −0.971291
\(664\) 55.7455 2.16334
\(665\) −24.0391 −0.932195
\(666\) −0.528998 −0.0204983
\(667\) −3.72582 −0.144264
\(668\) −49.6278 −1.92016
\(669\) −44.4029 −1.71672
\(670\) 36.8058 1.42193
\(671\) 2.58627 0.0998419
\(672\) −33.9422 −1.30935
\(673\) −38.1816 −1.47179 −0.735896 0.677094i \(-0.763239\pi\)
−0.735896 + 0.677094i \(0.763239\pi\)
\(674\) −20.0139 −0.770906
\(675\) 5.18024 0.199387
\(676\) 77.3926 2.97664
\(677\) 34.4757 1.32501 0.662505 0.749057i \(-0.269493\pi\)
0.662505 + 0.749057i \(0.269493\pi\)
\(678\) 47.5338 1.82552
\(679\) 79.0008 3.03177
\(680\) 15.3327 0.587983
\(681\) 40.0086 1.53313
\(682\) 24.8582 0.951869
\(683\) 13.7480 0.526053 0.263027 0.964789i \(-0.415279\pi\)
0.263027 + 0.964789i \(0.415279\pi\)
\(684\) 0.370197 0.0141548
\(685\) −18.6539 −0.712731
\(686\) 162.163 6.19142
\(687\) −4.94942 −0.188832
\(688\) 55.9061 2.13140
\(689\) 46.5761 1.77441
\(690\) 5.49481 0.209184
\(691\) −0.759840 −0.0289057 −0.0144528 0.999896i \(-0.504601\pi\)
−0.0144528 + 0.999896i \(0.504601\pi\)
\(692\) 53.9113 2.04940
\(693\) −0.140735 −0.00534610
\(694\) 18.3388 0.696133
\(695\) −17.7056 −0.671611
\(696\) −30.4787 −1.15529
\(697\) −3.86964 −0.146573
\(698\) −9.55170 −0.361537
\(699\) −49.5693 −1.87488
\(700\) −22.3768 −0.845765
\(701\) 9.20642 0.347722 0.173861 0.984770i \(-0.444376\pi\)
0.173861 + 0.984770i \(0.444376\pi\)
\(702\) 72.4324 2.73378
\(703\) 53.7565 2.02746
\(704\) −4.25436 −0.160342
\(705\) 3.72594 0.140327
\(706\) −23.9323 −0.900705
\(707\) 15.9024 0.598070
\(708\) 62.6854 2.35586
\(709\) 7.88236 0.296028 0.148014 0.988985i \(-0.452712\pi\)
0.148014 + 0.988985i \(0.452712\pi\)
\(710\) −5.55563 −0.208499
\(711\) −0.00214610 −8.04850e−5 0
\(712\) 106.152 3.97820
\(713\) −8.26558 −0.309549
\(714\) 58.4404 2.18708
\(715\) −8.31852 −0.311095
\(716\) 47.9966 1.79372
\(717\) −6.09740 −0.227712
\(718\) −36.4675 −1.36096
\(719\) 43.4286 1.61961 0.809807 0.586696i \(-0.199572\pi\)
0.809807 + 0.586696i \(0.199572\pi\)
\(720\) 0.113079 0.00421419
\(721\) 51.7224 1.92624
\(722\) −7.06348 −0.262876
\(723\) −39.6316 −1.47391
\(724\) −66.7698 −2.48148
\(725\) −2.96767 −0.110217
\(726\) −38.3124 −1.42191
\(727\) 10.4078 0.386003 0.193002 0.981198i \(-0.438178\pi\)
0.193002 + 0.981198i \(0.438178\pi\)
\(728\) −168.915 −6.26042
\(729\) 26.8339 0.993846
\(730\) 28.0264 1.03730
\(731\) −23.3891 −0.865078
\(732\) −13.0306 −0.481626
\(733\) −16.8278 −0.621547 −0.310774 0.950484i \(-0.600588\pi\)
−0.310774 + 0.950484i \(0.600588\pi\)
\(734\) 90.3697 3.33561
\(735\) −33.8836 −1.24981
\(736\) −4.76451 −0.175622
\(737\) −21.8967 −0.806576
\(738\) −0.0685558 −0.00252357
\(739\) −22.1330 −0.814177 −0.407088 0.913389i \(-0.633456\pi\)
−0.407088 + 0.913389i \(0.633456\pi\)
\(740\) 50.0393 1.83948
\(741\) 45.0253 1.65405
\(742\) −108.835 −3.99547
\(743\) −6.93513 −0.254425 −0.127213 0.991875i \(-0.540603\pi\)
−0.127213 + 0.991875i \(0.540603\pi\)
\(744\) −67.6158 −2.47891
\(745\) 5.93816 0.217557
\(746\) −32.7306 −1.19835
\(747\) −0.171999 −0.00629311
\(748\) −16.8964 −0.617795
\(749\) −34.2739 −1.25234
\(750\) 4.37670 0.159814
\(751\) −3.76795 −0.137495 −0.0687473 0.997634i \(-0.521900\pi\)
−0.0687473 + 0.997634i \(0.521900\pi\)
\(752\) −13.2960 −0.484854
\(753\) 48.2993 1.76012
\(754\) −41.4953 −1.51117
\(755\) −5.81861 −0.211761
\(756\) −115.917 −4.21587
\(757\) 31.8436 1.15738 0.578688 0.815549i \(-0.303565\pi\)
0.578688 + 0.815549i \(0.303565\pi\)
\(758\) −15.6699 −0.569156
\(759\) −3.26900 −0.118657
\(760\) −27.6039 −1.00130
\(761\) 31.1249 1.12828 0.564139 0.825680i \(-0.309208\pi\)
0.564139 + 0.825680i \(0.309208\pi\)
\(762\) 63.5889 2.30358
\(763\) 39.0575 1.41398
\(764\) −34.6669 −1.25421
\(765\) −0.0473081 −0.00171043
\(766\) −88.6972 −3.20476
\(767\) 46.0740 1.66364
\(768\) 54.6543 1.97217
\(769\) 25.9026 0.934070 0.467035 0.884239i \(-0.345322\pi\)
0.467035 + 0.884239i \(0.345322\pi\)
\(770\) 19.4381 0.700500
\(771\) 27.9899 1.00803
\(772\) 1.24734 0.0448929
\(773\) 18.3208 0.658953 0.329476 0.944164i \(-0.393128\pi\)
0.329476 + 0.944164i \(0.393128\pi\)
\(774\) −0.414370 −0.0148942
\(775\) −6.58366 −0.236492
\(776\) 90.7159 3.25651
\(777\) 102.966 3.69388
\(778\) −19.2418 −0.689852
\(779\) 6.96660 0.249604
\(780\) 41.9119 1.50069
\(781\) 3.30519 0.118269
\(782\) 8.20335 0.293351
\(783\) −15.3732 −0.549395
\(784\) 120.913 4.31832
\(785\) 1.97300 0.0704194
\(786\) −29.6285 −1.05681
\(787\) −1.36139 −0.0485285 −0.0242642 0.999706i \(-0.507724\pi\)
−0.0242642 + 0.999706i \(0.507724\pi\)
\(788\) 54.6665 1.94741
\(789\) 13.3613 0.475674
\(790\) 0.296415 0.0105460
\(791\) −55.9123 −1.98801
\(792\) −0.161605 −0.00574240
\(793\) −9.57757 −0.340109
\(794\) 3.82919 0.135893
\(795\) 14.5789 0.517062
\(796\) −20.2096 −0.716311
\(797\) −0.955825 −0.0338571 −0.0169285 0.999857i \(-0.505389\pi\)
−0.0169285 + 0.999857i \(0.505389\pi\)
\(798\) −105.212 −3.72446
\(799\) 5.56256 0.196789
\(800\) −3.79500 −0.134174
\(801\) −0.327524 −0.0115725
\(802\) −70.1295 −2.47636
\(803\) −16.6736 −0.588399
\(804\) 110.324 3.89083
\(805\) −6.46335 −0.227803
\(806\) −92.0557 −3.24252
\(807\) −6.32986 −0.222822
\(808\) 18.2605 0.642404
\(809\) −15.4375 −0.542752 −0.271376 0.962473i \(-0.587479\pi\)
−0.271376 + 0.962473i \(0.587479\pi\)
\(810\) 22.8102 0.801468
\(811\) −11.7026 −0.410934 −0.205467 0.978664i \(-0.565871\pi\)
−0.205467 + 0.978664i \(0.565871\pi\)
\(812\) 66.4070 2.33043
\(813\) 35.7072 1.25231
\(814\) −43.4677 −1.52354
\(815\) −15.7510 −0.551732
\(816\) 27.9353 0.977930
\(817\) 42.1080 1.47317
\(818\) −37.6779 −1.31738
\(819\) 0.521177 0.0182114
\(820\) 6.48488 0.226462
\(821\) 1.73635 0.0605991 0.0302996 0.999541i \(-0.490354\pi\)
0.0302996 + 0.999541i \(0.490354\pi\)
\(822\) −81.6427 −2.84762
\(823\) −42.1245 −1.46837 −0.734184 0.678950i \(-0.762435\pi\)
−0.734184 + 0.678950i \(0.762435\pi\)
\(824\) 59.3924 2.06903
\(825\) −2.60381 −0.0906530
\(826\) −107.662 −3.74605
\(827\) 21.4627 0.746330 0.373165 0.927765i \(-0.378273\pi\)
0.373165 + 0.927765i \(0.378273\pi\)
\(828\) 0.0995343 0.00345906
\(829\) −21.4225 −0.744034 −0.372017 0.928226i \(-0.621334\pi\)
−0.372017 + 0.928226i \(0.621334\pi\)
\(830\) 23.7561 0.824587
\(831\) −28.1181 −0.975407
\(832\) 15.7549 0.546203
\(833\) −50.5857 −1.75269
\(834\) −77.4920 −2.68333
\(835\) −11.4177 −0.395126
\(836\) 30.4191 1.05206
\(837\) −34.1049 −1.17884
\(838\) 98.5481 3.40429
\(839\) −44.3450 −1.53096 −0.765479 0.643461i \(-0.777498\pi\)
−0.765479 + 0.643461i \(0.777498\pi\)
\(840\) −52.8728 −1.82428
\(841\) −20.1929 −0.696308
\(842\) −41.6769 −1.43628
\(843\) −17.4210 −0.600012
\(844\) 117.238 4.03551
\(845\) 17.8054 0.612526
\(846\) 0.0985482 0.00338816
\(847\) 45.0655 1.54847
\(848\) −52.0247 −1.78654
\(849\) −6.09011 −0.209012
\(850\) 6.53409 0.224117
\(851\) 14.4534 0.495457
\(852\) −16.6528 −0.570516
\(853\) −11.6413 −0.398591 −0.199296 0.979939i \(-0.563865\pi\)
−0.199296 + 0.979939i \(0.563865\pi\)
\(854\) 22.3801 0.765833
\(855\) 0.0851699 0.00291275
\(856\) −39.3564 −1.34518
\(857\) 37.9736 1.29715 0.648576 0.761150i \(-0.275365\pi\)
0.648576 + 0.761150i \(0.275365\pi\)
\(858\) −36.4076 −1.24294
\(859\) −50.5332 −1.72417 −0.862086 0.506762i \(-0.830842\pi\)
−0.862086 + 0.506762i \(0.830842\pi\)
\(860\) 39.1963 1.33658
\(861\) 13.3439 0.454759
\(862\) 54.1900 1.84572
\(863\) 40.6994 1.38542 0.692711 0.721215i \(-0.256416\pi\)
0.692711 + 0.721215i \(0.256416\pi\)
\(864\) −19.6590 −0.668813
\(865\) 12.4032 0.421720
\(866\) −2.14986 −0.0730551
\(867\) 17.8471 0.606120
\(868\) 147.321 5.00041
\(869\) −0.176345 −0.00598209
\(870\) −12.9886 −0.440355
\(871\) 81.0887 2.74759
\(872\) 44.8494 1.51879
\(873\) −0.279898 −0.00947311
\(874\) −14.7687 −0.499558
\(875\) −5.14815 −0.174039
\(876\) 84.0081 2.83837
\(877\) −4.56054 −0.153999 −0.0769993 0.997031i \(-0.524534\pi\)
−0.0769993 + 0.997031i \(0.524534\pi\)
\(878\) −21.2319 −0.716542
\(879\) 2.09468 0.0706518
\(880\) 9.29165 0.313221
\(881\) −14.3939 −0.484942 −0.242471 0.970159i \(-0.577958\pi\)
−0.242471 + 0.970159i \(0.577958\pi\)
\(882\) −0.896193 −0.0301764
\(883\) 56.8544 1.91330 0.956651 0.291238i \(-0.0940671\pi\)
0.956651 + 0.291238i \(0.0940671\pi\)
\(884\) 62.5714 2.10451
\(885\) 14.4218 0.484783
\(886\) −26.3359 −0.884771
\(887\) −49.9388 −1.67678 −0.838391 0.545069i \(-0.816503\pi\)
−0.838391 + 0.545069i \(0.816503\pi\)
\(888\) 118.235 3.96770
\(889\) −74.7974 −2.50862
\(890\) 45.2369 1.51634
\(891\) −13.5704 −0.454624
\(892\) 111.092 3.71962
\(893\) −10.0144 −0.335120
\(894\) 25.9895 0.869220
\(895\) 11.0424 0.369107
\(896\) −75.8894 −2.53529
\(897\) 12.1059 0.404204
\(898\) −19.7649 −0.659563
\(899\) 19.5381 0.651633
\(900\) 0.0792806 0.00264269
\(901\) 21.7653 0.725107
\(902\) −5.63322 −0.187566
\(903\) 80.6542 2.68400
\(904\) −64.2036 −2.13538
\(905\) −15.3615 −0.510633
\(906\) −25.4663 −0.846061
\(907\) −47.9971 −1.59372 −0.796859 0.604165i \(-0.793507\pi\)
−0.796859 + 0.604165i \(0.793507\pi\)
\(908\) −100.098 −3.32186
\(909\) −0.0563417 −0.00186873
\(910\) −71.9838 −2.38624
\(911\) −16.0865 −0.532970 −0.266485 0.963839i \(-0.585862\pi\)
−0.266485 + 0.963839i \(0.585862\pi\)
\(912\) −50.2925 −1.66535
\(913\) −14.1331 −0.467738
\(914\) 82.9226 2.74284
\(915\) −2.99791 −0.0991078
\(916\) 12.3830 0.409145
\(917\) 34.8510 1.15088
\(918\) 33.8481 1.11715
\(919\) −16.7174 −0.551456 −0.275728 0.961236i \(-0.588919\pi\)
−0.275728 + 0.961236i \(0.588919\pi\)
\(920\) −7.42181 −0.244690
\(921\) 36.3856 1.19895
\(922\) −26.5611 −0.874742
\(923\) −12.2399 −0.402881
\(924\) 58.2650 1.91678
\(925\) 11.5124 0.378524
\(926\) 38.2150 1.25582
\(927\) −0.183251 −0.00601876
\(928\) 11.2623 0.369703
\(929\) 13.0869 0.429368 0.214684 0.976684i \(-0.431128\pi\)
0.214684 + 0.976684i \(0.431128\pi\)
\(930\) −28.8147 −0.944871
\(931\) 91.0707 2.98472
\(932\) 124.018 4.06233
\(933\) 52.1730 1.70807
\(934\) 18.2289 0.596467
\(935\) −3.88730 −0.127128
\(936\) 0.598463 0.0195614
\(937\) 23.2606 0.759891 0.379945 0.925009i \(-0.375943\pi\)
0.379945 + 0.925009i \(0.375943\pi\)
\(938\) −189.482 −6.18681
\(939\) 3.73262 0.121809
\(940\) −9.32194 −0.304048
\(941\) −5.97362 −0.194734 −0.0973672 0.995249i \(-0.531042\pi\)
−0.0973672 + 0.995249i \(0.531042\pi\)
\(942\) 8.63523 0.281351
\(943\) 1.87310 0.0609965
\(944\) −51.4639 −1.67501
\(945\) −26.6687 −0.867531
\(946\) −34.0487 −1.10702
\(947\) 12.6464 0.410953 0.205477 0.978662i \(-0.434126\pi\)
0.205477 + 0.978662i \(0.434126\pi\)
\(948\) 0.888493 0.0288569
\(949\) 61.7463 2.00437
\(950\) −11.7635 −0.381658
\(951\) 11.0151 0.357189
\(952\) −78.9352 −2.55830
\(953\) −25.2773 −0.818812 −0.409406 0.912352i \(-0.634264\pi\)
−0.409406 + 0.912352i \(0.634264\pi\)
\(954\) 0.385601 0.0124843
\(955\) −7.97570 −0.258087
\(956\) 15.2551 0.493385
\(957\) 7.72725 0.249787
\(958\) 37.5123 1.21197
\(959\) 96.0334 3.10108
\(960\) 4.93150 0.159163
\(961\) 12.3446 0.398212
\(962\) 160.971 5.18992
\(963\) 0.121432 0.00391308
\(964\) 99.1543 3.19355
\(965\) 0.286972 0.00923794
\(966\) −28.2881 −0.910156
\(967\) 19.2151 0.617915 0.308957 0.951076i \(-0.400020\pi\)
0.308957 + 0.951076i \(0.400020\pi\)
\(968\) 51.7483 1.66325
\(969\) 21.0406 0.675922
\(970\) 38.6589 1.24126
\(971\) 19.0233 0.610485 0.305243 0.952275i \(-0.401262\pi\)
0.305243 + 0.952275i \(0.401262\pi\)
\(972\) 0.823896 0.0264265
\(973\) 91.1511 2.92217
\(974\) −8.76640 −0.280894
\(975\) 9.64252 0.308808
\(976\) 10.6980 0.342434
\(977\) −20.3813 −0.652057 −0.326028 0.945360i \(-0.605711\pi\)
−0.326028 + 0.945360i \(0.605711\pi\)
\(978\) −68.9372 −2.20437
\(979\) −26.9126 −0.860130
\(980\) 84.7733 2.70798
\(981\) −0.138380 −0.00441813
\(982\) −20.0635 −0.640252
\(983\) −1.48484 −0.0473592 −0.0236796 0.999720i \(-0.507538\pi\)
−0.0236796 + 0.999720i \(0.507538\pi\)
\(984\) 15.3227 0.488470
\(985\) 12.5769 0.400734
\(986\) −19.3910 −0.617536
\(987\) −19.1817 −0.610561
\(988\) −112.649 −3.58384
\(989\) 11.3215 0.360003
\(990\) −0.0688687 −0.00218879
\(991\) −29.5152 −0.937582 −0.468791 0.883309i \(-0.655310\pi\)
−0.468791 + 0.883309i \(0.655310\pi\)
\(992\) 24.9850 0.793274
\(993\) 16.2926 0.517032
\(994\) 28.6012 0.907176
\(995\) −4.64955 −0.147401
\(996\) 71.2082 2.25632
\(997\) −33.6203 −1.06476 −0.532382 0.846504i \(-0.678703\pi\)
−0.532382 + 0.846504i \(0.678703\pi\)
\(998\) 82.0633 2.59767
\(999\) 59.6368 1.88682
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 \(a_p\))