Properties

Label 6047.2.a.a.1.9
Level 6047
Weight 2
Character 6047.1
Self dual Yes
Analytic conductor 48.286
Analytic rank 1
Dimension 217
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6047 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2855381023\)
Analytic rank: \(1\)
Dimension: \(217\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 6047.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.63907 q^{2}\) \(-2.61338 q^{3}\) \(+4.96471 q^{4}\) \(+2.16033 q^{5}\) \(+6.89691 q^{6}\) \(-4.93155 q^{7}\) \(-7.82409 q^{8}\) \(+3.82978 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.63907 q^{2}\) \(-2.61338 q^{3}\) \(+4.96471 q^{4}\) \(+2.16033 q^{5}\) \(+6.89691 q^{6}\) \(-4.93155 q^{7}\) \(-7.82409 q^{8}\) \(+3.82978 q^{9}\) \(-5.70128 q^{10}\) \(+3.19144 q^{11}\) \(-12.9747 q^{12}\) \(-1.07068 q^{13}\) \(+13.0147 q^{14}\) \(-5.64578 q^{15}\) \(+10.7189 q^{16}\) \(+1.60771 q^{17}\) \(-10.1071 q^{18}\) \(+6.87862 q^{19}\) \(+10.7254 q^{20}\) \(+12.8880 q^{21}\) \(-8.42244 q^{22}\) \(-3.73417 q^{23}\) \(+20.4473 q^{24}\) \(-0.332958 q^{25}\) \(+2.82561 q^{26}\) \(-2.16852 q^{27}\) \(-24.4837 q^{28}\) \(-6.89546 q^{29}\) \(+14.8996 q^{30}\) \(-0.842199 q^{31}\) \(-12.6398 q^{32}\) \(-8.34045 q^{33}\) \(-4.24287 q^{34}\) \(-10.6538 q^{35}\) \(+19.0137 q^{36}\) \(-7.20247 q^{37}\) \(-18.1532 q^{38}\) \(+2.79811 q^{39}\) \(-16.9026 q^{40}\) \(-5.79439 q^{41}\) \(-34.0124 q^{42}\) \(+10.9683 q^{43}\) \(+15.8446 q^{44}\) \(+8.27359 q^{45}\) \(+9.85476 q^{46}\) \(+4.10295 q^{47}\) \(-28.0127 q^{48}\) \(+17.3201 q^{49}\) \(+0.878701 q^{50}\) \(-4.20157 q^{51}\) \(-5.31563 q^{52}\) \(+10.2681 q^{53}\) \(+5.72289 q^{54}\) \(+6.89457 q^{55}\) \(+38.5848 q^{56}\) \(-17.9765 q^{57}\) \(+18.1976 q^{58}\) \(-6.74275 q^{59}\) \(-28.0297 q^{60}\) \(+4.80345 q^{61}\) \(+2.22263 q^{62}\) \(-18.8867 q^{63}\) \(+11.9196 q^{64}\) \(-2.31303 q^{65}\) \(+22.0111 q^{66}\) \(-7.02579 q^{67}\) \(+7.98182 q^{68}\) \(+9.75883 q^{69}\) \(+28.1161 q^{70}\) \(-0.767086 q^{71}\) \(-29.9645 q^{72}\) \(-7.31240 q^{73}\) \(+19.0079 q^{74}\) \(+0.870147 q^{75}\) \(+34.1504 q^{76}\) \(-15.7387 q^{77}\) \(-7.38441 q^{78}\) \(-0.462629 q^{79}\) \(+23.1564 q^{80}\) \(-5.82214 q^{81}\) \(+15.2918 q^{82}\) \(+6.92183 q^{83}\) \(+63.9853 q^{84}\) \(+3.47320 q^{85}\) \(-28.9460 q^{86}\) \(+18.0205 q^{87}\) \(-24.9701 q^{88}\) \(-9.42966 q^{89}\) \(-21.8346 q^{90}\) \(+5.28012 q^{91}\) \(-18.5391 q^{92}\) \(+2.20099 q^{93}\) \(-10.8280 q^{94}\) \(+14.8601 q^{95}\) \(+33.0328 q^{96}\) \(-18.3317 q^{97}\) \(-45.7091 q^{98}\) \(+12.2225 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(217q \) \(\mathstrut -\mathstrut 20q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 184q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 152q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(217q \) \(\mathstrut -\mathstrut 20q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 184q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 152q^{9} \) \(\mathstrut -\mathstrut 46q^{10} \) \(\mathstrut -\mathstrut 32q^{11} \) \(\mathstrut -\mathstrut 72q^{12} \) \(\mathstrut -\mathstrut 80q^{13} \) \(\mathstrut -\mathstrut 22q^{14} \) \(\mathstrut -\mathstrut 43q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut -\mathstrut 61q^{17} \) \(\mathstrut -\mathstrut 88q^{18} \) \(\mathstrut -\mathstrut 43q^{19} \) \(\mathstrut -\mathstrut 41q^{20} \) \(\mathstrut -\mathstrut 61q^{21} \) \(\mathstrut -\mathstrut 93q^{22} \) \(\mathstrut -\mathstrut 60q^{23} \) \(\mathstrut -\mathstrut 41q^{24} \) \(\mathstrut +\mathstrut 26q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 93q^{27} \) \(\mathstrut -\mathstrut 126q^{28} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut -\mathstrut 36q^{30} \) \(\mathstrut -\mathstrut 100q^{31} \) \(\mathstrut -\mathstrut 114q^{32} \) \(\mathstrut -\mathstrut 133q^{33} \) \(\mathstrut -\mathstrut 75q^{34} \) \(\mathstrut -\mathstrut 37q^{35} \) \(\mathstrut +\mathstrut 75q^{36} \) \(\mathstrut -\mathstrut 264q^{37} \) \(\mathstrut -\mathstrut 35q^{38} \) \(\mathstrut -\mathstrut 47q^{39} \) \(\mathstrut -\mathstrut 118q^{40} \) \(\mathstrut -\mathstrut 72q^{41} \) \(\mathstrut -\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 107q^{43} \) \(\mathstrut -\mathstrut 59q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 111q^{46} \) \(\mathstrut -\mathstrut 54q^{47} \) \(\mathstrut -\mathstrut 135q^{48} \) \(\mathstrut +\mathstrut 33q^{49} \) \(\mathstrut -\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 26q^{51} \) \(\mathstrut -\mathstrut 173q^{52} \) \(\mathstrut -\mathstrut 103q^{53} \) \(\mathstrut -\mathstrut 28q^{54} \) \(\mathstrut -\mathstrut 78q^{55} \) \(\mathstrut -\mathstrut 44q^{56} \) \(\mathstrut -\mathstrut 205q^{57} \) \(\mathstrut -\mathstrut 189q^{58} \) \(\mathstrut -\mathstrut 38q^{59} \) \(\mathstrut -\mathstrut 105q^{60} \) \(\mathstrut -\mathstrut 108q^{61} \) \(\mathstrut -\mathstrut 14q^{62} \) \(\mathstrut -\mathstrut 116q^{63} \) \(\mathstrut +\mathstrut 39q^{64} \) \(\mathstrut -\mathstrut 146q^{65} \) \(\mathstrut +\mathstrut 5q^{66} \) \(\mathstrut -\mathstrut 206q^{67} \) \(\mathstrut -\mathstrut 62q^{68} \) \(\mathstrut -\mathstrut 55q^{69} \) \(\mathstrut -\mathstrut 125q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 225q^{72} \) \(\mathstrut -\mathstrut 326q^{73} \) \(\mathstrut +\mathstrut 3q^{74} \) \(\mathstrut -\mathstrut 95q^{75} \) \(\mathstrut -\mathstrut 84q^{76} \) \(\mathstrut -\mathstrut 79q^{77} \) \(\mathstrut -\mathstrut 86q^{78} \) \(\mathstrut -\mathstrut 117q^{79} \) \(\mathstrut -\mathstrut 39q^{80} \) \(\mathstrut +\mathstrut q^{81} \) \(\mathstrut -\mathstrut 96q^{82} \) \(\mathstrut -\mathstrut 23q^{83} \) \(\mathstrut -\mathstrut 57q^{84} \) \(\mathstrut -\mathstrut 224q^{85} \) \(\mathstrut -\mathstrut 7q^{86} \) \(\mathstrut -\mathstrut 45q^{87} \) \(\mathstrut -\mathstrut 250q^{88} \) \(\mathstrut -\mathstrut 104q^{89} \) \(\mathstrut -\mathstrut 36q^{90} \) \(\mathstrut -\mathstrut 96q^{91} \) \(\mathstrut -\mathstrut 137q^{92} \) \(\mathstrut -\mathstrut 155q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 447q^{97} \) \(\mathstrut -\mathstrut 46q^{98} \) \(\mathstrut -\mathstrut 94q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.63907 −1.86611 −0.933053 0.359738i \(-0.882866\pi\)
−0.933053 + 0.359738i \(0.882866\pi\)
\(3\) −2.61338 −1.50884 −0.754419 0.656393i \(-0.772081\pi\)
−0.754419 + 0.656393i \(0.772081\pi\)
\(4\) 4.96471 2.48235
\(5\) 2.16033 0.966131 0.483065 0.875584i \(-0.339523\pi\)
0.483065 + 0.875584i \(0.339523\pi\)
\(6\) 6.89691 2.81565
\(7\) −4.93155 −1.86395 −0.931975 0.362524i \(-0.881915\pi\)
−0.931975 + 0.362524i \(0.881915\pi\)
\(8\) −7.82409 −2.76623
\(9\) 3.82978 1.27659
\(10\) −5.70128 −1.80290
\(11\) 3.19144 0.962254 0.481127 0.876651i \(-0.340228\pi\)
0.481127 + 0.876651i \(0.340228\pi\)
\(12\) −12.9747 −3.74547
\(13\) −1.07068 −0.296954 −0.148477 0.988916i \(-0.547437\pi\)
−0.148477 + 0.988916i \(0.547437\pi\)
\(14\) 13.0147 3.47833
\(15\) −5.64578 −1.45773
\(16\) 10.7189 2.67973
\(17\) 1.60771 0.389928 0.194964 0.980810i \(-0.437541\pi\)
0.194964 + 0.980810i \(0.437541\pi\)
\(18\) −10.1071 −2.38226
\(19\) 6.87862 1.57806 0.789032 0.614352i \(-0.210583\pi\)
0.789032 + 0.614352i \(0.210583\pi\)
\(20\) 10.7254 2.39828
\(21\) 12.8880 2.81240
\(22\) −8.42244 −1.79567
\(23\) −3.73417 −0.778629 −0.389314 0.921105i \(-0.627288\pi\)
−0.389314 + 0.921105i \(0.627288\pi\)
\(24\) 20.4473 4.17380
\(25\) −0.332958 −0.0665916
\(26\) 2.82561 0.554148
\(27\) −2.16852 −0.417333
\(28\) −24.4837 −4.62698
\(29\) −6.89546 −1.28045 −0.640227 0.768186i \(-0.721160\pi\)
−0.640227 + 0.768186i \(0.721160\pi\)
\(30\) 14.8996 2.72029
\(31\) −0.842199 −0.151263 −0.0756317 0.997136i \(-0.524097\pi\)
−0.0756317 + 0.997136i \(0.524097\pi\)
\(32\) −12.6398 −2.23443
\(33\) −8.34045 −1.45189
\(34\) −4.24287 −0.727646
\(35\) −10.6538 −1.80082
\(36\) 19.0137 3.16895
\(37\) −7.20247 −1.18408 −0.592040 0.805909i \(-0.701677\pi\)
−0.592040 + 0.805909i \(0.701677\pi\)
\(38\) −18.1532 −2.94484
\(39\) 2.79811 0.448055
\(40\) −16.9026 −2.67254
\(41\) −5.79439 −0.904932 −0.452466 0.891782i \(-0.649456\pi\)
−0.452466 + 0.891782i \(0.649456\pi\)
\(42\) −34.0124 −5.24823
\(43\) 10.9683 1.67264 0.836322 0.548239i \(-0.184702\pi\)
0.836322 + 0.548239i \(0.184702\pi\)
\(44\) 15.8446 2.38866
\(45\) 8.27359 1.23335
\(46\) 9.85476 1.45300
\(47\) 4.10295 0.598477 0.299238 0.954178i \(-0.403267\pi\)
0.299238 + 0.954178i \(0.403267\pi\)
\(48\) −28.0127 −4.04328
\(49\) 17.3201 2.47431
\(50\) 0.878701 0.124267
\(51\) −4.20157 −0.588337
\(52\) −5.31563 −0.737145
\(53\) 10.2681 1.41043 0.705214 0.708994i \(-0.250851\pi\)
0.705214 + 0.708994i \(0.250851\pi\)
\(54\) 5.72289 0.778787
\(55\) 6.89457 0.929663
\(56\) 38.5848 5.15612
\(57\) −17.9765 −2.38104
\(58\) 18.1976 2.38946
\(59\) −6.74275 −0.877832 −0.438916 0.898528i \(-0.644637\pi\)
−0.438916 + 0.898528i \(0.644637\pi\)
\(60\) −28.0297 −3.61861
\(61\) 4.80345 0.615018 0.307509 0.951545i \(-0.400505\pi\)
0.307509 + 0.951545i \(0.400505\pi\)
\(62\) 2.22263 0.282274
\(63\) −18.8867 −2.37950
\(64\) 11.9196 1.48996
\(65\) −2.31303 −0.286896
\(66\) 22.0111 2.70937
\(67\) −7.02579 −0.858337 −0.429168 0.903225i \(-0.641193\pi\)
−0.429168 + 0.903225i \(0.641193\pi\)
\(68\) 7.98182 0.967938
\(69\) 9.75883 1.17482
\(70\) 28.1161 3.36052
\(71\) −0.767086 −0.0910363 −0.0455182 0.998964i \(-0.514494\pi\)
−0.0455182 + 0.998964i \(0.514494\pi\)
\(72\) −29.9645 −3.53135
\(73\) −7.31240 −0.855852 −0.427926 0.903814i \(-0.640756\pi\)
−0.427926 + 0.903814i \(0.640756\pi\)
\(74\) 19.0079 2.20962
\(75\) 0.870147 0.100476
\(76\) 34.1504 3.91731
\(77\) −15.7387 −1.79359
\(78\) −7.38441 −0.836119
\(79\) −0.462629 −0.0520498 −0.0260249 0.999661i \(-0.508285\pi\)
−0.0260249 + 0.999661i \(0.508285\pi\)
\(80\) 23.1564 2.58897
\(81\) −5.82214 −0.646905
\(82\) 15.2918 1.68870
\(83\) 6.92183 0.759770 0.379885 0.925034i \(-0.375964\pi\)
0.379885 + 0.925034i \(0.375964\pi\)
\(84\) 63.9853 6.98137
\(85\) 3.47320 0.376721
\(86\) −28.9460 −3.12133
\(87\) 18.0205 1.93200
\(88\) −24.9701 −2.66182
\(89\) −9.42966 −0.999542 −0.499771 0.866158i \(-0.666582\pi\)
−0.499771 + 0.866158i \(0.666582\pi\)
\(90\) −21.8346 −2.30157
\(91\) 5.28012 0.553507
\(92\) −18.5391 −1.93283
\(93\) 2.20099 0.228232
\(94\) −10.8280 −1.11682
\(95\) 14.8601 1.52462
\(96\) 33.0328 3.37139
\(97\) −18.3317 −1.86131 −0.930653 0.365903i \(-0.880760\pi\)
−0.930653 + 0.365903i \(0.880760\pi\)
\(98\) −45.7091 −4.61732
\(99\) 12.2225 1.22841
\(100\) −1.65304 −0.165304
\(101\) −2.26779 −0.225654 −0.112827 0.993615i \(-0.535991\pi\)
−0.112827 + 0.993615i \(0.535991\pi\)
\(102\) 11.0883 1.09790
\(103\) 12.6151 1.24300 0.621502 0.783412i \(-0.286523\pi\)
0.621502 + 0.783412i \(0.286523\pi\)
\(104\) 8.37711 0.821444
\(105\) 27.8424 2.71714
\(106\) −27.0982 −2.63201
\(107\) −13.0541 −1.26199 −0.630995 0.775787i \(-0.717353\pi\)
−0.630995 + 0.775787i \(0.717353\pi\)
\(108\) −10.7661 −1.03597
\(109\) 4.39101 0.420583 0.210291 0.977639i \(-0.432559\pi\)
0.210291 + 0.977639i \(0.432559\pi\)
\(110\) −18.1953 −1.73485
\(111\) 18.8228 1.78658
\(112\) −52.8608 −4.99488
\(113\) 15.3052 1.43979 0.719895 0.694083i \(-0.244190\pi\)
0.719895 + 0.694083i \(0.244190\pi\)
\(114\) 47.4413 4.44328
\(115\) −8.06706 −0.752257
\(116\) −34.2339 −3.17854
\(117\) −4.10048 −0.379089
\(118\) 17.7946 1.63813
\(119\) −7.92851 −0.726805
\(120\) 44.1731 4.03243
\(121\) −0.814733 −0.0740667
\(122\) −12.6766 −1.14769
\(123\) 15.1430 1.36540
\(124\) −4.18127 −0.375489
\(125\) −11.5210 −1.03047
\(126\) 49.8434 4.44041
\(127\) 15.6534 1.38902 0.694508 0.719485i \(-0.255622\pi\)
0.694508 + 0.719485i \(0.255622\pi\)
\(128\) −6.17713 −0.545986
\(129\) −28.6643 −2.52375
\(130\) 6.10426 0.535379
\(131\) 21.7055 1.89641 0.948207 0.317653i \(-0.102895\pi\)
0.948207 + 0.317653i \(0.102895\pi\)
\(132\) −41.4079 −3.60410
\(133\) −33.9222 −2.94143
\(134\) 18.5416 1.60175
\(135\) −4.68473 −0.403198
\(136\) −12.5789 −1.07863
\(137\) −10.3435 −0.883709 −0.441854 0.897087i \(-0.645679\pi\)
−0.441854 + 0.897087i \(0.645679\pi\)
\(138\) −25.7543 −2.19235
\(139\) −10.2121 −0.866182 −0.433091 0.901350i \(-0.642577\pi\)
−0.433091 + 0.901350i \(0.642577\pi\)
\(140\) −52.8929 −4.47027
\(141\) −10.7226 −0.903005
\(142\) 2.02440 0.169884
\(143\) −3.41702 −0.285745
\(144\) 41.0511 3.42092
\(145\) −14.8965 −1.23709
\(146\) 19.2980 1.59711
\(147\) −45.2642 −3.73333
\(148\) −35.7582 −2.93930
\(149\) −20.0446 −1.64211 −0.821057 0.570846i \(-0.806615\pi\)
−0.821057 + 0.570846i \(0.806615\pi\)
\(150\) −2.29638 −0.187499
\(151\) 19.6680 1.60056 0.800279 0.599627i \(-0.204684\pi\)
0.800279 + 0.599627i \(0.204684\pi\)
\(152\) −53.8189 −4.36529
\(153\) 6.15718 0.497778
\(154\) 41.5356 3.34704
\(155\) −1.81943 −0.146140
\(156\) 13.8918 1.11223
\(157\) 9.20843 0.734913 0.367456 0.930041i \(-0.380229\pi\)
0.367456 + 0.930041i \(0.380229\pi\)
\(158\) 1.22091 0.0971305
\(159\) −26.8344 −2.12811
\(160\) −27.3063 −2.15875
\(161\) 18.4152 1.45132
\(162\) 15.3651 1.20719
\(163\) 12.9973 1.01803 0.509015 0.860758i \(-0.330010\pi\)
0.509015 + 0.860758i \(0.330010\pi\)
\(164\) −28.7675 −2.24636
\(165\) −18.0182 −1.40271
\(166\) −18.2672 −1.41781
\(167\) −8.50955 −0.658488 −0.329244 0.944245i \(-0.606794\pi\)
−0.329244 + 0.944245i \(0.606794\pi\)
\(168\) −100.837 −7.77974
\(169\) −11.8536 −0.911818
\(170\) −9.16602 −0.703002
\(171\) 26.3436 2.01454
\(172\) 54.4542 4.15209
\(173\) 2.58531 0.196558 0.0982789 0.995159i \(-0.468666\pi\)
0.0982789 + 0.995159i \(0.468666\pi\)
\(174\) −47.5574 −3.60531
\(175\) 1.64200 0.124123
\(176\) 34.2088 2.57858
\(177\) 17.6214 1.32451
\(178\) 24.8856 1.86525
\(179\) 7.99001 0.597201 0.298601 0.954378i \(-0.403480\pi\)
0.298601 + 0.954378i \(0.403480\pi\)
\(180\) 41.0760 3.06162
\(181\) −17.6435 −1.31143 −0.655715 0.755009i \(-0.727633\pi\)
−0.655715 + 0.755009i \(0.727633\pi\)
\(182\) −13.9346 −1.03290
\(183\) −12.5533 −0.927963
\(184\) 29.2165 2.15387
\(185\) −15.5597 −1.14398
\(186\) −5.80857 −0.425905
\(187\) 5.13091 0.375209
\(188\) 20.3700 1.48563
\(189\) 10.6942 0.777887
\(190\) −39.2169 −2.84510
\(191\) 26.1081 1.88911 0.944556 0.328349i \(-0.106492\pi\)
0.944556 + 0.328349i \(0.106492\pi\)
\(192\) −31.1506 −2.24810
\(193\) −16.4654 −1.18520 −0.592601 0.805496i \(-0.701899\pi\)
−0.592601 + 0.805496i \(0.701899\pi\)
\(194\) 48.3788 3.47340
\(195\) 6.04484 0.432880
\(196\) 85.9895 6.14211
\(197\) 10.4944 0.747697 0.373849 0.927490i \(-0.378038\pi\)
0.373849 + 0.927490i \(0.378038\pi\)
\(198\) −32.2560 −2.29234
\(199\) 0.713974 0.0506123 0.0253061 0.999680i \(-0.491944\pi\)
0.0253061 + 0.999680i \(0.491944\pi\)
\(200\) 2.60509 0.184208
\(201\) 18.3611 1.29509
\(202\) 5.98487 0.421094
\(203\) 34.0053 2.38670
\(204\) −20.8596 −1.46046
\(205\) −12.5178 −0.874283
\(206\) −33.2922 −2.31958
\(207\) −14.3010 −0.993991
\(208\) −11.4766 −0.795756
\(209\) 21.9527 1.51850
\(210\) −73.4782 −5.07048
\(211\) −19.9346 −1.37235 −0.686177 0.727435i \(-0.740712\pi\)
−0.686177 + 0.727435i \(0.740712\pi\)
\(212\) 50.9780 3.50118
\(213\) 2.00469 0.137359
\(214\) 34.4508 2.35501
\(215\) 23.6951 1.61599
\(216\) 16.9667 1.15444
\(217\) 4.15334 0.281947
\(218\) −11.5882 −0.784853
\(219\) 19.1101 1.29134
\(220\) 34.2295 2.30775
\(221\) −1.72135 −0.115791
\(222\) −49.6748 −3.33396
\(223\) −11.6845 −0.782449 −0.391225 0.920295i \(-0.627948\pi\)
−0.391225 + 0.920295i \(0.627948\pi\)
\(224\) 62.3340 4.16486
\(225\) −1.27515 −0.0850103
\(226\) −40.3915 −2.68680
\(227\) −0.752714 −0.0499594 −0.0249797 0.999688i \(-0.507952\pi\)
−0.0249797 + 0.999688i \(0.507952\pi\)
\(228\) −89.2480 −5.91059
\(229\) 20.9529 1.38461 0.692304 0.721606i \(-0.256596\pi\)
0.692304 + 0.721606i \(0.256596\pi\)
\(230\) 21.2896 1.40379
\(231\) 41.1313 2.70624
\(232\) 53.9507 3.54203
\(233\) 2.07648 0.136034 0.0680172 0.997684i \(-0.478333\pi\)
0.0680172 + 0.997684i \(0.478333\pi\)
\(234\) 10.8215 0.707421
\(235\) 8.86374 0.578207
\(236\) −33.4758 −2.17909
\(237\) 1.20903 0.0785347
\(238\) 20.9239 1.35630
\(239\) 27.5639 1.78296 0.891480 0.453060i \(-0.149668\pi\)
0.891480 + 0.453060i \(0.149668\pi\)
\(240\) −60.5167 −3.90634
\(241\) 23.0386 1.48405 0.742024 0.670373i \(-0.233866\pi\)
0.742024 + 0.670373i \(0.233866\pi\)
\(242\) 2.15014 0.138216
\(243\) 21.7211 1.39341
\(244\) 23.8477 1.52669
\(245\) 37.4173 2.39050
\(246\) −39.9634 −2.54797
\(247\) −7.36482 −0.468612
\(248\) 6.58944 0.418430
\(249\) −18.0894 −1.14637
\(250\) 30.4047 1.92296
\(251\) −1.70872 −0.107853 −0.0539266 0.998545i \(-0.517174\pi\)
−0.0539266 + 0.998545i \(0.517174\pi\)
\(252\) −93.7671 −5.90677
\(253\) −11.9174 −0.749239
\(254\) −41.3105 −2.59205
\(255\) −9.07679 −0.568411
\(256\) −7.53740 −0.471087
\(257\) 24.8962 1.55298 0.776490 0.630129i \(-0.216998\pi\)
0.776490 + 0.630129i \(0.216998\pi\)
\(258\) 75.6471 4.70958
\(259\) 35.5193 2.20706
\(260\) −11.4835 −0.712178
\(261\) −26.4081 −1.63462
\(262\) −57.2823 −3.53891
\(263\) 7.88216 0.486035 0.243017 0.970022i \(-0.421863\pi\)
0.243017 + 0.970022i \(0.421863\pi\)
\(264\) 65.2564 4.01625
\(265\) 22.1825 1.36266
\(266\) 89.5233 5.48902
\(267\) 24.6433 1.50815
\(268\) −34.8810 −2.13070
\(269\) −1.18365 −0.0721682 −0.0360841 0.999349i \(-0.511488\pi\)
−0.0360841 + 0.999349i \(0.511488\pi\)
\(270\) 12.3634 0.752410
\(271\) −12.6181 −0.766497 −0.383249 0.923645i \(-0.625195\pi\)
−0.383249 + 0.923645i \(0.625195\pi\)
\(272\) 17.2329 1.04490
\(273\) −13.7990 −0.835152
\(274\) 27.2974 1.64909
\(275\) −1.06261 −0.0640780
\(276\) 48.4497 2.91633
\(277\) 4.87985 0.293202 0.146601 0.989196i \(-0.453167\pi\)
0.146601 + 0.989196i \(0.453167\pi\)
\(278\) 26.9506 1.61639
\(279\) −3.22543 −0.193102
\(280\) 83.3561 4.98148
\(281\) −7.37182 −0.439766 −0.219883 0.975526i \(-0.570568\pi\)
−0.219883 + 0.975526i \(0.570568\pi\)
\(282\) 28.2977 1.68510
\(283\) −25.2378 −1.50023 −0.750116 0.661306i \(-0.770002\pi\)
−0.750116 + 0.661306i \(0.770002\pi\)
\(284\) −3.80836 −0.225984
\(285\) −38.8352 −2.30040
\(286\) 9.01776 0.533231
\(287\) 28.5753 1.68675
\(288\) −48.4078 −2.85246
\(289\) −14.4153 −0.847957
\(290\) 39.3129 2.30853
\(291\) 47.9079 2.80841
\(292\) −36.3040 −2.12453
\(293\) 1.59810 0.0933620 0.0466810 0.998910i \(-0.485136\pi\)
0.0466810 + 0.998910i \(0.485136\pi\)
\(294\) 119.456 6.96679
\(295\) −14.5666 −0.848100
\(296\) 56.3528 3.27544
\(297\) −6.92071 −0.401580
\(298\) 52.8990 3.06436
\(299\) 3.99811 0.231217
\(300\) 4.32003 0.249417
\(301\) −54.0904 −3.11772
\(302\) −51.9053 −2.98681
\(303\) 5.92661 0.340475
\(304\) 73.7314 4.22879
\(305\) 10.3770 0.594188
\(306\) −16.2492 −0.928908
\(307\) 6.57035 0.374990 0.187495 0.982266i \(-0.439963\pi\)
0.187495 + 0.982266i \(0.439963\pi\)
\(308\) −78.1381 −4.45233
\(309\) −32.9681 −1.87549
\(310\) 4.80161 0.272713
\(311\) 21.5953 1.22456 0.612279 0.790642i \(-0.290253\pi\)
0.612279 + 0.790642i \(0.290253\pi\)
\(312\) −21.8926 −1.23943
\(313\) 2.53635 0.143363 0.0716816 0.997428i \(-0.477163\pi\)
0.0716816 + 0.997428i \(0.477163\pi\)
\(314\) −24.3017 −1.37143
\(315\) −40.8016 −2.29891
\(316\) −2.29682 −0.129206
\(317\) 16.1835 0.908955 0.454477 0.890758i \(-0.349826\pi\)
0.454477 + 0.890758i \(0.349826\pi\)
\(318\) 70.8180 3.97128
\(319\) −22.0064 −1.23212
\(320\) 25.7504 1.43949
\(321\) 34.1154 1.90414
\(322\) −48.5992 −2.70833
\(323\) 11.0588 0.615331
\(324\) −28.9052 −1.60585
\(325\) 0.356492 0.0197746
\(326\) −34.3009 −1.89975
\(327\) −11.4754 −0.634591
\(328\) 45.3358 2.50325
\(329\) −20.2339 −1.11553
\(330\) 47.5512 2.61761
\(331\) −10.3701 −0.569990 −0.284995 0.958529i \(-0.591992\pi\)
−0.284995 + 0.958529i \(0.591992\pi\)
\(332\) 34.3649 1.88602
\(333\) −27.5839 −1.51159
\(334\) 22.4573 1.22881
\(335\) −15.1780 −0.829265
\(336\) 138.146 7.53647
\(337\) 18.2753 0.995518 0.497759 0.867316i \(-0.334156\pi\)
0.497759 + 0.867316i \(0.334156\pi\)
\(338\) 31.2826 1.70155
\(339\) −39.9983 −2.17241
\(340\) 17.2434 0.935155
\(341\) −2.68783 −0.145554
\(342\) −69.5226 −3.75935
\(343\) −50.8943 −2.74803
\(344\) −85.8166 −4.62692
\(345\) 21.0823 1.13503
\(346\) −6.82283 −0.366798
\(347\) 10.1150 0.543004 0.271502 0.962438i \(-0.412480\pi\)
0.271502 + 0.962438i \(0.412480\pi\)
\(348\) 89.4664 4.79590
\(349\) 17.3544 0.928959 0.464480 0.885584i \(-0.346241\pi\)
0.464480 + 0.885584i \(0.346241\pi\)
\(350\) −4.33335 −0.231627
\(351\) 2.32180 0.123929
\(352\) −40.3393 −2.15009
\(353\) −12.4099 −0.660510 −0.330255 0.943892i \(-0.607135\pi\)
−0.330255 + 0.943892i \(0.607135\pi\)
\(354\) −46.5042 −2.47167
\(355\) −1.65716 −0.0879530
\(356\) −46.8155 −2.48122
\(357\) 20.7202 1.09663
\(358\) −21.0862 −1.11444
\(359\) −5.21033 −0.274991 −0.137495 0.990502i \(-0.543905\pi\)
−0.137495 + 0.990502i \(0.543905\pi\)
\(360\) −64.7333 −3.41175
\(361\) 28.3154 1.49029
\(362\) 46.5624 2.44727
\(363\) 2.12921 0.111755
\(364\) 26.2143 1.37400
\(365\) −15.7972 −0.826865
\(366\) 33.1290 1.73168
\(367\) 6.55179 0.342000 0.171000 0.985271i \(-0.445300\pi\)
0.171000 + 0.985271i \(0.445300\pi\)
\(368\) −40.0263 −2.08651
\(369\) −22.1912 −1.15523
\(370\) 41.0633 2.13478
\(371\) −50.6375 −2.62897
\(372\) 10.9273 0.566553
\(373\) 0.791518 0.0409832 0.0204916 0.999790i \(-0.493477\pi\)
0.0204916 + 0.999790i \(0.493477\pi\)
\(374\) −13.5409 −0.700181
\(375\) 30.1087 1.55481
\(376\) −32.1018 −1.65553
\(377\) 7.38285 0.380236
\(378\) −28.2227 −1.45162
\(379\) −23.8054 −1.22280 −0.611401 0.791321i \(-0.709394\pi\)
−0.611401 + 0.791321i \(0.709394\pi\)
\(380\) 73.7762 3.78464
\(381\) −40.9084 −2.09580
\(382\) −68.9011 −3.52529
\(383\) −24.6059 −1.25730 −0.628652 0.777687i \(-0.716393\pi\)
−0.628652 + 0.777687i \(0.716393\pi\)
\(384\) 16.1432 0.823804
\(385\) −34.0009 −1.73285
\(386\) 43.4533 2.21172
\(387\) 42.0060 2.13528
\(388\) −91.0118 −4.62042
\(389\) −21.9215 −1.11146 −0.555731 0.831362i \(-0.687562\pi\)
−0.555731 + 0.831362i \(0.687562\pi\)
\(390\) −15.9528 −0.807800
\(391\) −6.00348 −0.303609
\(392\) −135.514 −6.84451
\(393\) −56.7247 −2.86138
\(394\) −27.6956 −1.39528
\(395\) −0.999433 −0.0502869
\(396\) 60.6811 3.04934
\(397\) −29.0404 −1.45749 −0.728747 0.684783i \(-0.759897\pi\)
−0.728747 + 0.684783i \(0.759897\pi\)
\(398\) −1.88423 −0.0944479
\(399\) 88.6518 4.43814
\(400\) −3.56895 −0.178447
\(401\) 8.51289 0.425114 0.212557 0.977149i \(-0.431821\pi\)
0.212557 + 0.977149i \(0.431821\pi\)
\(402\) −48.4562 −2.41678
\(403\) 0.901728 0.0449183
\(404\) −11.2589 −0.560153
\(405\) −12.5778 −0.624995
\(406\) −89.7424 −4.45384
\(407\) −22.9862 −1.13939
\(408\) 32.8734 1.62748
\(409\) −6.36265 −0.314613 −0.157306 0.987550i \(-0.550281\pi\)
−0.157306 + 0.987550i \(0.550281\pi\)
\(410\) 33.0355 1.63150
\(411\) 27.0317 1.33337
\(412\) 62.6304 3.08558
\(413\) 33.2522 1.63623
\(414\) 37.7415 1.85489
\(415\) 14.9535 0.734037
\(416\) 13.5333 0.663523
\(417\) 26.6882 1.30693
\(418\) −57.9347 −2.83368
\(419\) −2.20293 −0.107620 −0.0538100 0.998551i \(-0.517137\pi\)
−0.0538100 + 0.998551i \(0.517137\pi\)
\(420\) 138.230 6.74491
\(421\) 23.8482 1.16229 0.581144 0.813800i \(-0.302605\pi\)
0.581144 + 0.813800i \(0.302605\pi\)
\(422\) 52.6088 2.56096
\(423\) 15.7134 0.764011
\(424\) −80.3383 −3.90157
\(425\) −0.535301 −0.0259659
\(426\) −5.29052 −0.256327
\(427\) −23.6884 −1.14636
\(428\) −64.8099 −3.13270
\(429\) 8.92997 0.431143
\(430\) −62.5331 −3.01561
\(431\) −3.43706 −0.165557 −0.0827786 0.996568i \(-0.526379\pi\)
−0.0827786 + 0.996568i \(0.526379\pi\)
\(432\) −23.2442 −1.11834
\(433\) 4.48870 0.215713 0.107856 0.994166i \(-0.465601\pi\)
0.107856 + 0.994166i \(0.465601\pi\)
\(434\) −10.9610 −0.526144
\(435\) 38.9302 1.86656
\(436\) 21.8001 1.04404
\(437\) −25.6860 −1.22873
\(438\) −50.4330 −2.40978
\(439\) 3.69410 0.176310 0.0881549 0.996107i \(-0.471903\pi\)
0.0881549 + 0.996107i \(0.471903\pi\)
\(440\) −53.9437 −2.57166
\(441\) 66.3323 3.15868
\(442\) 4.54277 0.216077
\(443\) 29.2116 1.38788 0.693942 0.720031i \(-0.255872\pi\)
0.693942 + 0.720031i \(0.255872\pi\)
\(444\) 93.4499 4.43493
\(445\) −20.3712 −0.965688
\(446\) 30.8362 1.46013
\(447\) 52.3841 2.47768
\(448\) −58.7823 −2.77720
\(449\) −7.75912 −0.366176 −0.183088 0.983097i \(-0.558609\pi\)
−0.183088 + 0.983097i \(0.558609\pi\)
\(450\) 3.36523 0.158638
\(451\) −18.4924 −0.870775
\(452\) 75.9858 3.57407
\(453\) −51.4000 −2.41498
\(454\) 1.98647 0.0932296
\(455\) 11.4068 0.534760
\(456\) 140.650 6.58652
\(457\) 19.3592 0.905587 0.452793 0.891616i \(-0.350428\pi\)
0.452793 + 0.891616i \(0.350428\pi\)
\(458\) −55.2963 −2.58383
\(459\) −3.48636 −0.162729
\(460\) −40.0506 −1.86737
\(461\) 19.5018 0.908288 0.454144 0.890928i \(-0.349945\pi\)
0.454144 + 0.890928i \(0.349945\pi\)
\(462\) −108.549 −5.05014
\(463\) −37.3746 −1.73694 −0.868472 0.495739i \(-0.834897\pi\)
−0.868472 + 0.495739i \(0.834897\pi\)
\(464\) −73.9119 −3.43127
\(465\) 4.75487 0.220502
\(466\) −5.47997 −0.253855
\(467\) −3.07291 −0.142198 −0.0710988 0.997469i \(-0.522651\pi\)
−0.0710988 + 0.997469i \(0.522651\pi\)
\(468\) −20.3577 −0.941033
\(469\) 34.6480 1.59990
\(470\) −23.3921 −1.07900
\(471\) −24.0652 −1.10886
\(472\) 52.7559 2.42829
\(473\) 35.0045 1.60951
\(474\) −3.19071 −0.146554
\(475\) −2.29029 −0.105086
\(476\) −39.3627 −1.80419
\(477\) 39.3244 1.80054
\(478\) −72.7431 −3.32719
\(479\) 25.1273 1.14810 0.574048 0.818822i \(-0.305372\pi\)
0.574048 + 0.818822i \(0.305372\pi\)
\(480\) 71.3618 3.25721
\(481\) 7.71156 0.351617
\(482\) −60.8006 −2.76939
\(483\) −48.1261 −2.18981
\(484\) −4.04491 −0.183860
\(485\) −39.6027 −1.79827
\(486\) −57.3235 −2.60025
\(487\) −21.2383 −0.962400 −0.481200 0.876611i \(-0.659799\pi\)
−0.481200 + 0.876611i \(0.659799\pi\)
\(488\) −37.5826 −1.70128
\(489\) −33.9670 −1.53604
\(490\) −98.7470 −4.46093
\(491\) −15.3456 −0.692537 −0.346268 0.938135i \(-0.612551\pi\)
−0.346268 + 0.938135i \(0.612551\pi\)
\(492\) 75.1805 3.38940
\(493\) −11.0859 −0.499284
\(494\) 19.4363 0.874481
\(495\) 26.4047 1.18680
\(496\) −9.02747 −0.405345
\(497\) 3.78292 0.169687
\(498\) 47.7393 2.13925
\(499\) −12.9205 −0.578400 −0.289200 0.957269i \(-0.593389\pi\)
−0.289200 + 0.957269i \(0.593389\pi\)
\(500\) −57.1983 −2.55798
\(501\) 22.2387 0.993552
\(502\) 4.50943 0.201266
\(503\) 1.57060 0.0700294 0.0350147 0.999387i \(-0.488852\pi\)
0.0350147 + 0.999387i \(0.488852\pi\)
\(504\) 147.771 6.58226
\(505\) −4.89919 −0.218011
\(506\) 31.4508 1.39816
\(507\) 30.9781 1.37579
\(508\) 77.7146 3.44803
\(509\) 21.0386 0.932520 0.466260 0.884648i \(-0.345601\pi\)
0.466260 + 0.884648i \(0.345601\pi\)
\(510\) 23.9543 1.06072
\(511\) 36.0614 1.59526
\(512\) 32.2460 1.42509
\(513\) −14.9165 −0.658577
\(514\) −65.7028 −2.89803
\(515\) 27.2529 1.20090
\(516\) −142.310 −6.26484
\(517\) 13.0943 0.575887
\(518\) −93.7381 −4.11862
\(519\) −6.75642 −0.296574
\(520\) 18.0974 0.793622
\(521\) −39.7729 −1.74248 −0.871242 0.490854i \(-0.836685\pi\)
−0.871242 + 0.490854i \(0.836685\pi\)
\(522\) 69.6928 3.05037
\(523\) −27.1594 −1.18760 −0.593798 0.804614i \(-0.702372\pi\)
−0.593798 + 0.804614i \(0.702372\pi\)
\(524\) 107.761 4.70757
\(525\) −4.29117 −0.187282
\(526\) −20.8016 −0.906992
\(527\) −1.35401 −0.0589818
\(528\) −89.4006 −3.89066
\(529\) −9.05596 −0.393737
\(530\) −58.5412 −2.54287
\(531\) −25.8232 −1.12063
\(532\) −168.414 −7.30167
\(533\) 6.20396 0.268723
\(534\) −65.0355 −2.81436
\(535\) −28.2012 −1.21925
\(536\) 54.9704 2.37436
\(537\) −20.8810 −0.901080
\(538\) 3.12373 0.134673
\(539\) 55.2761 2.38091
\(540\) −23.2583 −1.00088
\(541\) 4.42692 0.190328 0.0951640 0.995462i \(-0.469662\pi\)
0.0951640 + 0.995462i \(0.469662\pi\)
\(542\) 33.3002 1.43037
\(543\) 46.1092 1.97873
\(544\) −20.3212 −0.871266
\(545\) 9.48606 0.406338
\(546\) 36.4165 1.55848
\(547\) −24.9234 −1.06565 −0.532824 0.846226i \(-0.678869\pi\)
−0.532824 + 0.846226i \(0.678869\pi\)
\(548\) −51.3527 −2.19368
\(549\) 18.3961 0.785128
\(550\) 2.80432 0.119576
\(551\) −47.4312 −2.02064
\(552\) −76.3539 −3.24984
\(553\) 2.28148 0.0970182
\(554\) −12.8783 −0.547146
\(555\) 40.6636 1.72607
\(556\) −50.7003 −2.15017
\(557\) 15.2656 0.646825 0.323412 0.946258i \(-0.395170\pi\)
0.323412 + 0.946258i \(0.395170\pi\)
\(558\) 8.51216 0.360348
\(559\) −11.7435 −0.496698
\(560\) −114.197 −4.82571
\(561\) −13.4090 −0.566130
\(562\) 19.4548 0.820650
\(563\) −8.22548 −0.346663 −0.173331 0.984864i \(-0.555453\pi\)
−0.173331 + 0.984864i \(0.555453\pi\)
\(564\) −53.2345 −2.24158
\(565\) 33.0643 1.39103
\(566\) 66.6044 2.79959
\(567\) 28.7122 1.20580
\(568\) 6.00174 0.251828
\(569\) 12.5574 0.526433 0.263217 0.964737i \(-0.415217\pi\)
0.263217 + 0.964737i \(0.415217\pi\)
\(570\) 102.489 4.29279
\(571\) 15.1996 0.636082 0.318041 0.948077i \(-0.396975\pi\)
0.318041 + 0.948077i \(0.396975\pi\)
\(572\) −16.9645 −0.709321
\(573\) −68.2304 −2.85037
\(574\) −75.4124 −3.14765
\(575\) 1.24332 0.0518501
\(576\) 45.6496 1.90207
\(577\) 0.0610618 0.00254204 0.00127102 0.999999i \(-0.499595\pi\)
0.00127102 + 0.999999i \(0.499595\pi\)
\(578\) 38.0429 1.58238
\(579\) 43.0303 1.78828
\(580\) −73.9567 −3.07089
\(581\) −34.1353 −1.41617
\(582\) −126.432 −5.24079
\(583\) 32.7699 1.35719
\(584\) 57.2129 2.36749
\(585\) −8.85839 −0.366250
\(586\) −4.21750 −0.174223
\(587\) −4.68625 −0.193422 −0.0967112 0.995312i \(-0.530832\pi\)
−0.0967112 + 0.995312i \(0.530832\pi\)
\(588\) −224.724 −9.26744
\(589\) −5.79317 −0.238703
\(590\) 38.4423 1.58265
\(591\) −27.4260 −1.12815
\(592\) −77.2027 −3.17301
\(593\) 32.4354 1.33196 0.665982 0.745968i \(-0.268013\pi\)
0.665982 + 0.745968i \(0.268013\pi\)
\(594\) 18.2642 0.749391
\(595\) −17.1282 −0.702189
\(596\) −99.5154 −4.07631
\(597\) −1.86589 −0.0763657
\(598\) −10.5513 −0.431475
\(599\) −14.5396 −0.594074 −0.297037 0.954866i \(-0.595998\pi\)
−0.297037 + 0.954866i \(0.595998\pi\)
\(600\) −6.80811 −0.277940
\(601\) 14.7154 0.600254 0.300127 0.953899i \(-0.402971\pi\)
0.300127 + 0.953899i \(0.402971\pi\)
\(602\) 142.749 5.81800
\(603\) −26.9072 −1.09575
\(604\) 97.6459 3.97315
\(605\) −1.76010 −0.0715581
\(606\) −15.6408 −0.635363
\(607\) −38.2022 −1.55058 −0.775290 0.631606i \(-0.782396\pi\)
−0.775290 + 0.631606i \(0.782396\pi\)
\(608\) −86.9447 −3.52607
\(609\) −88.8688 −3.60115
\(610\) −27.3858 −1.10882
\(611\) −4.39296 −0.177720
\(612\) 30.5686 1.23566
\(613\) 12.1945 0.492529 0.246265 0.969203i \(-0.420797\pi\)
0.246265 + 0.969203i \(0.420797\pi\)
\(614\) −17.3396 −0.699771
\(615\) 32.7139 1.31915
\(616\) 123.141 4.96149
\(617\) 2.26798 0.0913053 0.0456527 0.998957i \(-0.485463\pi\)
0.0456527 + 0.998957i \(0.485463\pi\)
\(618\) 87.0054 3.49987
\(619\) −19.8887 −0.799393 −0.399696 0.916648i \(-0.630884\pi\)
−0.399696 + 0.916648i \(0.630884\pi\)
\(620\) −9.03295 −0.362772
\(621\) 8.09764 0.324947
\(622\) −56.9917 −2.28516
\(623\) 46.5028 1.86309
\(624\) 29.9927 1.20067
\(625\) −23.2243 −0.928974
\(626\) −6.69362 −0.267531
\(627\) −57.3708 −2.29117
\(628\) 45.7172 1.82431
\(629\) −11.5795 −0.461705
\(630\) 107.678 4.29001
\(631\) −15.5054 −0.617259 −0.308630 0.951182i \(-0.599870\pi\)
−0.308630 + 0.951182i \(0.599870\pi\)
\(632\) 3.61965 0.143982
\(633\) 52.0967 2.07066
\(634\) −42.7094 −1.69621
\(635\) 33.8166 1.34197
\(636\) −133.225 −5.28272
\(637\) −18.5444 −0.734755
\(638\) 58.0765 2.29927
\(639\) −2.93777 −0.116216
\(640\) −13.3447 −0.527494
\(641\) 20.4038 0.805903 0.402951 0.915221i \(-0.367984\pi\)
0.402951 + 0.915221i \(0.367984\pi\)
\(642\) −90.0331 −3.55332
\(643\) 8.54820 0.337108 0.168554 0.985692i \(-0.446090\pi\)
0.168554 + 0.985692i \(0.446090\pi\)
\(644\) 91.4263 3.60270
\(645\) −61.9244 −2.43827
\(646\) −29.1851 −1.14827
\(647\) −1.67458 −0.0658343 −0.0329172 0.999458i \(-0.510480\pi\)
−0.0329172 + 0.999458i \(0.510480\pi\)
\(648\) 45.5530 1.78949
\(649\) −21.5191 −0.844697
\(650\) −0.940810 −0.0369016
\(651\) −10.8543 −0.425413
\(652\) 64.5279 2.52711
\(653\) 2.98021 0.116625 0.0583124 0.998298i \(-0.481428\pi\)
0.0583124 + 0.998298i \(0.481428\pi\)
\(654\) 30.2844 1.18422
\(655\) 46.8910 1.83218
\(656\) −62.1096 −2.42497
\(657\) −28.0049 −1.09257
\(658\) 53.3987 2.08170
\(659\) −25.7630 −1.00359 −0.501793 0.864988i \(-0.667326\pi\)
−0.501793 + 0.864988i \(0.667326\pi\)
\(660\) −89.4549 −3.48203
\(661\) −36.6810 −1.42673 −0.713363 0.700795i \(-0.752829\pi\)
−0.713363 + 0.700795i \(0.752829\pi\)
\(662\) 27.3673 1.06366
\(663\) 4.49855 0.174709
\(664\) −54.1570 −2.10170
\(665\) −73.2834 −2.84181
\(666\) 72.7958 2.82078
\(667\) 25.7488 0.996999
\(668\) −42.2474 −1.63460
\(669\) 30.5360 1.18059
\(670\) 40.0560 1.54750
\(671\) 15.3299 0.591804
\(672\) −162.903 −6.28411
\(673\) 20.1544 0.776897 0.388448 0.921470i \(-0.373011\pi\)
0.388448 + 0.921470i \(0.373011\pi\)
\(674\) −48.2298 −1.85774
\(675\) 0.722027 0.0277908
\(676\) −58.8499 −2.26346
\(677\) 19.2465 0.739702 0.369851 0.929091i \(-0.379409\pi\)
0.369851 + 0.929091i \(0.379409\pi\)
\(678\) 105.558 4.05395
\(679\) 90.4038 3.46938
\(680\) −27.1746 −1.04210
\(681\) 1.96713 0.0753807
\(682\) 7.09337 0.271619
\(683\) −38.8796 −1.48769 −0.743844 0.668353i \(-0.767000\pi\)
−0.743844 + 0.668353i \(0.767000\pi\)
\(684\) 130.788 5.00081
\(685\) −22.3455 −0.853778
\(686\) 134.314 5.12812
\(687\) −54.7580 −2.08915
\(688\) 117.568 4.48223
\(689\) −10.9939 −0.418832
\(690\) −55.6378 −2.11809
\(691\) 16.8904 0.642541 0.321271 0.946987i \(-0.395890\pi\)
0.321271 + 0.946987i \(0.395890\pi\)
\(692\) 12.8353 0.487926
\(693\) −60.2758 −2.28969
\(694\) −26.6943 −1.01330
\(695\) −22.0616 −0.836845
\(696\) −140.994 −5.34436
\(697\) −9.31572 −0.352858
\(698\) −45.7995 −1.73354
\(699\) −5.42663 −0.205254
\(700\) 8.15204 0.308118
\(701\) −19.9076 −0.751900 −0.375950 0.926640i \(-0.622684\pi\)
−0.375950 + 0.926640i \(0.622684\pi\)
\(702\) −6.12740 −0.231264
\(703\) −49.5431 −1.86855
\(704\) 38.0408 1.43372
\(705\) −23.1644 −0.872420
\(706\) 32.7505 1.23258
\(707\) 11.1837 0.420607
\(708\) 87.4851 3.28789
\(709\) −24.0591 −0.903560 −0.451780 0.892129i \(-0.649211\pi\)
−0.451780 + 0.892129i \(0.649211\pi\)
\(710\) 4.37337 0.164130
\(711\) −1.77176 −0.0664464
\(712\) 73.7784 2.76496
\(713\) 3.14492 0.117778
\(714\) −54.6822 −2.04643
\(715\) −7.38189 −0.276067
\(716\) 39.6681 1.48247
\(717\) −72.0350 −2.69020
\(718\) 13.7505 0.513162
\(719\) −27.4751 −1.02465 −0.512324 0.858793i \(-0.671215\pi\)
−0.512324 + 0.858793i \(0.671215\pi\)
\(720\) 88.6840 3.30506
\(721\) −62.2120 −2.31690
\(722\) −74.7265 −2.78103
\(723\) −60.2088 −2.23919
\(724\) −87.5947 −3.25543
\(725\) 2.29590 0.0852675
\(726\) −5.61914 −0.208546
\(727\) 19.1027 0.708478 0.354239 0.935155i \(-0.384740\pi\)
0.354239 + 0.935155i \(0.384740\pi\)
\(728\) −41.3121 −1.53113
\(729\) −39.2991 −1.45552
\(730\) 41.6901 1.54302
\(731\) 17.6338 0.652210
\(732\) −62.3232 −2.30353
\(733\) −20.8917 −0.771652 −0.385826 0.922572i \(-0.626084\pi\)
−0.385826 + 0.922572i \(0.626084\pi\)
\(734\) −17.2906 −0.638209
\(735\) −97.7858 −3.60688
\(736\) 47.1994 1.73979
\(737\) −22.4224 −0.825938
\(738\) 58.5643 2.15578
\(739\) −48.3360 −1.77807 −0.889035 0.457839i \(-0.848623\pi\)
−0.889035 + 0.457839i \(0.848623\pi\)
\(740\) −77.2496 −2.83975
\(741\) 19.2471 0.707060
\(742\) 133.636 4.90593
\(743\) 40.0843 1.47055 0.735274 0.677770i \(-0.237053\pi\)
0.735274 + 0.677770i \(0.237053\pi\)
\(744\) −17.2207 −0.631343
\(745\) −43.3029 −1.58650
\(746\) −2.08887 −0.0764791
\(747\) 26.5091 0.969916
\(748\) 25.4735 0.931403
\(749\) 64.3770 2.35228
\(750\) −79.4591 −2.90144
\(751\) −20.4773 −0.747226 −0.373613 0.927585i \(-0.621881\pi\)
−0.373613 + 0.927585i \(0.621881\pi\)
\(752\) 43.9792 1.60376
\(753\) 4.46553 0.162733
\(754\) −19.4839 −0.709561
\(755\) 42.4894 1.54635
\(756\) 53.0935 1.93099
\(757\) −54.5851 −1.98393 −0.991965 0.126509i \(-0.959623\pi\)
−0.991965 + 0.126509i \(0.959623\pi\)
\(758\) 62.8242 2.28188
\(759\) 31.1447 1.13048
\(760\) −116.267 −4.21744
\(761\) −19.0522 −0.690641 −0.345320 0.938485i \(-0.612230\pi\)
−0.345320 + 0.938485i \(0.612230\pi\)
\(762\) 107.960 3.91099
\(763\) −21.6545 −0.783945
\(764\) 129.619 4.68945
\(765\) 13.3016 0.480919
\(766\) 64.9368 2.34626
\(767\) 7.21935 0.260676
\(768\) 19.6981 0.710795
\(769\) −25.2230 −0.909564 −0.454782 0.890603i \(-0.650283\pi\)
−0.454782 + 0.890603i \(0.650283\pi\)
\(770\) 89.7308 3.23367
\(771\) −65.0632 −2.34320
\(772\) −81.7457 −2.94209
\(773\) −37.7604 −1.35815 −0.679073 0.734071i \(-0.737618\pi\)
−0.679073 + 0.734071i \(0.737618\pi\)
\(774\) −110.857 −3.98467
\(775\) 0.280417 0.0100729
\(776\) 143.429 5.14881
\(777\) −92.8256 −3.33010
\(778\) 57.8523 2.07411
\(779\) −39.8574 −1.42804
\(780\) 30.0109 1.07456
\(781\) −2.44811 −0.0876001
\(782\) 15.8436 0.566566
\(783\) 14.9530 0.534375
\(784\) 185.653 6.63047
\(785\) 19.8933 0.710022
\(786\) 149.701 5.33964
\(787\) −42.8825 −1.52860 −0.764298 0.644863i \(-0.776914\pi\)
−0.764298 + 0.644863i \(0.776914\pi\)
\(788\) 52.1018 1.85605
\(789\) −20.5991 −0.733347
\(790\) 2.63758 0.0938408
\(791\) −75.4782 −2.68370
\(792\) −95.6298 −3.39806
\(793\) −5.14297 −0.182632
\(794\) 76.6396 2.71984
\(795\) −57.9713 −2.05603
\(796\) 3.54467 0.125638
\(797\) −22.1168 −0.783417 −0.391708 0.920089i \(-0.628116\pi\)
−0.391708 + 0.920089i \(0.628116\pi\)
\(798\) −233.959 −8.28205
\(799\) 6.59636 0.233363
\(800\) 4.20854 0.148794
\(801\) −36.1135 −1.27601
\(802\) −22.4662 −0.793307
\(803\) −23.3371 −0.823547
\(804\) 91.1574 3.21487
\(805\) 39.7831 1.40217
\(806\) −2.37973 −0.0838223
\(807\) 3.09332 0.108890
\(808\) 17.7434 0.624211
\(809\) −41.6883 −1.46568 −0.732841 0.680400i \(-0.761806\pi\)
−0.732841 + 0.680400i \(0.761806\pi\)
\(810\) 33.1937 1.16631
\(811\) 3.63013 0.127471 0.0637356 0.997967i \(-0.479699\pi\)
0.0637356 + 0.997967i \(0.479699\pi\)
\(812\) 168.826 5.92464
\(813\) 32.9760 1.15652
\(814\) 60.6624 2.12621
\(815\) 28.0786 0.983549
\(816\) −45.0363 −1.57659
\(817\) 75.4465 2.63954
\(818\) 16.7915 0.587101
\(819\) 20.2217 0.706603
\(820\) −62.1473 −2.17028
\(821\) −34.9767 −1.22069 −0.610347 0.792134i \(-0.708970\pi\)
−0.610347 + 0.792134i \(0.708970\pi\)
\(822\) −71.3385 −2.48822
\(823\) 16.0144 0.558227 0.279114 0.960258i \(-0.409959\pi\)
0.279114 + 0.960258i \(0.409959\pi\)
\(824\) −98.7018 −3.43844
\(825\) 2.77702 0.0966834
\(826\) −87.7550 −3.05339
\(827\) −44.4318 −1.54504 −0.772522 0.634988i \(-0.781005\pi\)
−0.772522 + 0.634988i \(0.781005\pi\)
\(828\) −71.0005 −2.46744
\(829\) −19.1757 −0.665999 −0.332999 0.942927i \(-0.608061\pi\)
−0.332999 + 0.942927i \(0.608061\pi\)
\(830\) −39.4633 −1.36979
\(831\) −12.7529 −0.442394
\(832\) −12.7622 −0.442448
\(833\) 27.8458 0.964800
\(834\) −70.4322 −2.43887
\(835\) −18.3835 −0.636186
\(836\) 108.989 3.76945
\(837\) 1.82633 0.0631272
\(838\) 5.81369 0.200830
\(839\) −4.38904 −0.151526 −0.0757632 0.997126i \(-0.524139\pi\)
−0.0757632 + 0.997126i \(0.524139\pi\)
\(840\) −217.842 −7.51625
\(841\) 18.5473 0.639563
\(842\) −62.9371 −2.16895
\(843\) 19.2654 0.663535
\(844\) −98.9694 −3.40667
\(845\) −25.6078 −0.880936
\(846\) −41.4688 −1.42573
\(847\) 4.01789 0.138057
\(848\) 110.063 3.77957
\(849\) 65.9561 2.26361
\(850\) 1.41270 0.0484551
\(851\) 26.8953 0.921958
\(852\) 9.95270 0.340974
\(853\) −9.57344 −0.327788 −0.163894 0.986478i \(-0.552406\pi\)
−0.163894 + 0.986478i \(0.552406\pi\)
\(854\) 62.5155 2.13924
\(855\) 56.9109 1.94631
\(856\) 102.137 3.49095
\(857\) −15.2770 −0.521852 −0.260926 0.965359i \(-0.584028\pi\)
−0.260926 + 0.965359i \(0.584028\pi\)
\(858\) −23.5669 −0.804559
\(859\) −24.2200 −0.826375 −0.413187 0.910646i \(-0.635585\pi\)
−0.413187 + 0.910646i \(0.635585\pi\)
\(860\) 117.639 4.01146
\(861\) −74.6783 −2.54503
\(862\) 9.07065 0.308948
\(863\) 40.7869 1.38840 0.694202 0.719780i \(-0.255757\pi\)
0.694202 + 0.719780i \(0.255757\pi\)
\(864\) 27.4098 0.932500
\(865\) 5.58514 0.189900
\(866\) −11.8460 −0.402543
\(867\) 37.6726 1.27943
\(868\) 20.6201 0.699893
\(869\) −1.47645 −0.0500852
\(870\) −102.740 −3.48321
\(871\) 7.52239 0.254886
\(872\) −34.3557 −1.16343
\(873\) −70.2065 −2.37613
\(874\) 67.7871 2.29293
\(875\) 56.8162 1.92074
\(876\) 94.8762 3.20557
\(877\) −27.8717 −0.941162 −0.470581 0.882357i \(-0.655956\pi\)
−0.470581 + 0.882357i \(0.655956\pi\)
\(878\) −9.74900 −0.329013
\(879\) −4.17645 −0.140868
\(880\) 73.9023 2.49125
\(881\) 52.2726 1.76111 0.880554 0.473946i \(-0.157171\pi\)
0.880554 + 0.473946i \(0.157171\pi\)
\(882\) −175.056 −5.89443
\(883\) −32.4986 −1.09367 −0.546833 0.837242i \(-0.684167\pi\)
−0.546833 + 0.837242i \(0.684167\pi\)
\(884\) −8.54600 −0.287433
\(885\) 38.0681 1.27965
\(886\) −77.0915 −2.58994
\(887\) 44.9956 1.51080 0.755402 0.655262i \(-0.227442\pi\)
0.755402 + 0.655262i \(0.227442\pi\)
\(888\) −147.271 −4.94210
\(889\) −77.1955 −2.58905
\(890\) 53.7611 1.80208
\(891\) −18.5810 −0.622487
\(892\) −58.0100 −1.94232
\(893\) 28.2226 0.944435
\(894\) −138.246 −4.62362
\(895\) 17.2611 0.576974
\(896\) 30.4628 1.01769
\(897\) −10.4486 −0.348869
\(898\) 20.4769 0.683323
\(899\) 5.80735 0.193686
\(900\) −6.33077 −0.211026
\(901\) 16.5081 0.549965
\(902\) 48.8029 1.62496
\(903\) 141.359 4.70414
\(904\) −119.749 −3.98279
\(905\) −38.1158 −1.26701
\(906\) 135.648 4.50662
\(907\) 3.35018 0.111241 0.0556205 0.998452i \(-0.482286\pi\)
0.0556205 + 0.998452i \(0.482286\pi\)
\(908\) −3.73701 −0.124017
\(909\) −8.68514 −0.288068
\(910\) −30.1034 −0.997920
\(911\) 15.6754 0.519349 0.259675 0.965696i \(-0.416385\pi\)
0.259675 + 0.965696i \(0.416385\pi\)
\(912\) −192.688 −6.38055
\(913\) 22.0906 0.731092
\(914\) −51.0904 −1.68992
\(915\) −27.1192 −0.896534
\(916\) 104.025 3.43709
\(917\) −107.041 −3.53482
\(918\) 9.20077 0.303671
\(919\) 57.9810 1.91262 0.956308 0.292361i \(-0.0944410\pi\)
0.956308 + 0.292361i \(0.0944410\pi\)
\(920\) 63.1174 2.08092
\(921\) −17.1708 −0.565799
\(922\) −51.4666 −1.69496
\(923\) 0.821305 0.0270336
\(924\) 204.205 6.71785
\(925\) 2.39812 0.0788497
\(926\) 98.6342 3.24132
\(927\) 48.3131 1.58681
\(928\) 87.1575 2.86109
\(929\) −38.5791 −1.26574 −0.632870 0.774258i \(-0.718123\pi\)
−0.632870 + 0.774258i \(0.718123\pi\)
\(930\) −12.5485 −0.411480
\(931\) 119.139 3.90461
\(932\) 10.3091 0.337686
\(933\) −56.4369 −1.84766
\(934\) 8.10965 0.265356
\(935\) 11.0845 0.362501
\(936\) 32.0825 1.04865
\(937\) −7.42711 −0.242633 −0.121317 0.992614i \(-0.538712\pi\)
−0.121317 + 0.992614i \(0.538712\pi\)
\(938\) −91.4386 −2.98558
\(939\) −6.62847 −0.216312
\(940\) 44.0059 1.43531
\(941\) 53.1892 1.73392 0.866959 0.498380i \(-0.166071\pi\)
0.866959 + 0.498380i \(0.166071\pi\)
\(942\) 63.5098 2.06926
\(943\) 21.6373 0.704606
\(944\) −72.2750 −2.35235
\(945\) 23.1030 0.751540
\(946\) −92.3794 −3.00351
\(947\) −17.1430 −0.557073 −0.278537 0.960426i \(-0.589849\pi\)
−0.278537 + 0.960426i \(0.589849\pi\)
\(948\) 6.00247 0.194951
\(949\) 7.82926 0.254149
\(950\) 6.04425 0.196101
\(951\) −42.2937 −1.37147
\(952\) 62.0333 2.01051
\(953\) −8.63477 −0.279708 −0.139854 0.990172i \(-0.544663\pi\)
−0.139854 + 0.990172i \(0.544663\pi\)
\(954\) −103.780 −3.36000
\(955\) 56.4021 1.82513
\(956\) 136.847 4.42594
\(957\) 57.5112 1.85907
\(958\) −66.3128 −2.14247
\(959\) 51.0097 1.64719
\(960\) −67.2957 −2.17196
\(961\) −30.2907 −0.977119
\(962\) −20.3514 −0.656155
\(963\) −49.9943 −1.61105
\(964\) 114.380 3.68393
\(965\) −35.5707 −1.14506
\(966\) 127.008 4.08643
\(967\) −24.8735 −0.799879 −0.399940 0.916541i \(-0.630969\pi\)
−0.399940 + 0.916541i \(0.630969\pi\)
\(968\) 6.37454 0.204886
\(969\) −28.9010 −0.928434
\(970\) 104.514 3.35575
\(971\) −47.1838 −1.51420 −0.757100 0.653300i \(-0.773384\pi\)
−0.757100 + 0.653300i \(0.773384\pi\)
\(972\) 107.839 3.45893
\(973\) 50.3616 1.61452
\(974\) 56.0495 1.79594
\(975\) −0.931651 −0.0298367
\(976\) 51.4878 1.64808
\(977\) 39.4494 1.26210 0.631049 0.775743i \(-0.282625\pi\)
0.631049 + 0.775743i \(0.282625\pi\)
\(978\) 89.6414 2.86642
\(979\) −30.0941 −0.961813
\(980\) 185.766 5.93408
\(981\) 16.8166 0.536913
\(982\) 40.4981 1.29235
\(983\) 14.2938 0.455901 0.227951 0.973673i \(-0.426798\pi\)
0.227951 + 0.973673i \(0.426798\pi\)
\(984\) −118.480 −3.77700
\(985\) 22.6715 0.722373
\(986\) 29.2565 0.931718
\(987\) 52.8789 1.68315
\(988\) −36.5642 −1.16326
\(989\) −40.9574 −1.30237
\(990\) −69.6838 −2.21470
\(991\) −8.18171 −0.259900 −0.129950 0.991521i \(-0.541482\pi\)
−0.129950 + 0.991521i \(0.541482\pi\)
\(992\) 10.6453 0.337988
\(993\) 27.1009 0.860022
\(994\) −9.98340 −0.316654
\(995\) 1.54242 0.0488981
\(996\) −89.8086 −2.84570
\(997\) −27.6249 −0.874888 −0.437444 0.899246i \(-0.644116\pi\)
−0.437444 + 0.899246i \(0.644116\pi\)
\(998\) 34.0981 1.07936
\(999\) 15.6187 0.494155
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 \(a_p\))