Properties

Label 8007.2.a.e.1.15
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 46
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(46\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.42497 q^{2}\) \(+1.00000 q^{3}\) \(+0.0305258 q^{4}\) \(+0.348852 q^{5}\) \(-1.42497 q^{6}\) \(-0.489415 q^{7}\) \(+2.80643 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.42497 q^{2}\) \(+1.00000 q^{3}\) \(+0.0305258 q^{4}\) \(+0.348852 q^{5}\) \(-1.42497 q^{6}\) \(-0.489415 q^{7}\) \(+2.80643 q^{8}\) \(+1.00000 q^{9}\) \(-0.497102 q^{10}\) \(+2.33512 q^{11}\) \(+0.0305258 q^{12}\) \(+5.30367 q^{13}\) \(+0.697399 q^{14}\) \(+0.348852 q^{15}\) \(-4.06012 q^{16}\) \(-1.00000 q^{17}\) \(-1.42497 q^{18}\) \(-4.47923 q^{19}\) \(+0.0106490 q^{20}\) \(-0.489415 q^{21}\) \(-3.32746 q^{22}\) \(+2.78427 q^{23}\) \(+2.80643 q^{24}\) \(-4.87830 q^{25}\) \(-7.55754 q^{26}\) \(+1.00000 q^{27}\) \(-0.0149398 q^{28}\) \(+0.169133 q^{29}\) \(-0.497102 q^{30}\) \(+2.78442 q^{31}\) \(+0.172665 q^{32}\) \(+2.33512 q^{33}\) \(+1.42497 q^{34}\) \(-0.170733 q^{35}\) \(+0.0305258 q^{36}\) \(-11.1454 q^{37}\) \(+6.38275 q^{38}\) \(+5.30367 q^{39}\) \(+0.979029 q^{40}\) \(+0.741898 q^{41}\) \(+0.697399 q^{42}\) \(-3.38376 q^{43}\) \(+0.0712813 q^{44}\) \(+0.348852 q^{45}\) \(-3.96749 q^{46}\) \(-0.461826 q^{47}\) \(-4.06012 q^{48}\) \(-6.76047 q^{49}\) \(+6.95141 q^{50}\) \(-1.00000 q^{51}\) \(+0.161898 q^{52}\) \(-9.58285 q^{53}\) \(-1.42497 q^{54}\) \(+0.814611 q^{55}\) \(-1.37351 q^{56}\) \(-4.47923 q^{57}\) \(-0.241009 q^{58}\) \(-10.0596 q^{59}\) \(+0.0106490 q^{60}\) \(+1.32822 q^{61}\) \(-3.96770 q^{62}\) \(-0.489415 q^{63}\) \(+7.87420 q^{64}\) \(+1.85019 q^{65}\) \(-3.32746 q^{66}\) \(-2.14227 q^{67}\) \(-0.0305258 q^{68}\) \(+2.78427 q^{69}\) \(+0.243289 q^{70}\) \(+8.64535 q^{71}\) \(+2.80643 q^{72}\) \(+1.89207 q^{73}\) \(+15.8818 q^{74}\) \(-4.87830 q^{75}\) \(-0.136732 q^{76}\) \(-1.14284 q^{77}\) \(-7.55754 q^{78}\) \(-5.45077 q^{79}\) \(-1.41638 q^{80}\) \(+1.00000 q^{81}\) \(-1.05718 q^{82}\) \(-14.7039 q^{83}\) \(-0.0149398 q^{84}\) \(-0.348852 q^{85}\) \(+4.82174 q^{86}\) \(+0.169133 q^{87}\) \(+6.55335 q^{88}\) \(-6.89341 q^{89}\) \(-0.497102 q^{90}\) \(-2.59569 q^{91}\) \(+0.0849920 q^{92}\) \(+2.78442 q^{93}\) \(+0.658086 q^{94}\) \(-1.56259 q^{95}\) \(+0.172665 q^{96}\) \(+7.97411 q^{97}\) \(+9.63344 q^{98}\) \(+2.33512 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 43q^{12} \) \(\mathstrut -\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 19q^{15} \) \(\mathstrut +\mathstrut 33q^{16} \) \(\mathstrut -\mathstrut 46q^{17} \) \(\mathstrut -\mathstrut 5q^{18} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 56q^{20} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 64q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 11q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut +\mathstrut 46q^{27} \) \(\mathstrut -\mathstrut 38q^{28} \) \(\mathstrut -\mathstrut 51q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 19q^{31} \) \(\mathstrut -\mathstrut 61q^{32} \) \(\mathstrut -\mathstrut 25q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 39q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut -\mathstrut 48q^{38} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 53q^{41} \) \(\mathstrut -\mathstrut 28q^{42} \) \(\mathstrut -\mathstrut 33q^{43} \) \(\mathstrut -\mathstrut 62q^{44} \) \(\mathstrut -\mathstrut 19q^{45} \) \(\mathstrut +\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 45q^{47} \) \(\mathstrut +\mathstrut 33q^{48} \) \(\mathstrut +\mathstrut 21q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 63q^{52} \) \(\mathstrut -\mathstrut 47q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 82q^{56} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut -\mathstrut 21q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 74q^{64} \) \(\mathstrut -\mathstrut 85q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut -\mathstrut 52q^{67} \) \(\mathstrut -\mathstrut 43q^{68} \) \(\mathstrut -\mathstrut 64q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 48q^{71} \) \(\mathstrut -\mathstrut 18q^{72} \) \(\mathstrut -\mathstrut 39q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 42q^{76} \) \(\mathstrut -\mathstrut 78q^{77} \) \(\mathstrut -\mathstrut 13q^{78} \) \(\mathstrut -\mathstrut 26q^{79} \) \(\mathstrut -\mathstrut 78q^{80} \) \(\mathstrut +\mathstrut 46q^{81} \) \(\mathstrut +\mathstrut 3q^{82} \) \(\mathstrut -\mathstrut 47q^{83} \) \(\mathstrut -\mathstrut 38q^{84} \) \(\mathstrut +\mathstrut 19q^{85} \) \(\mathstrut -\mathstrut 6q^{86} \) \(\mathstrut -\mathstrut 51q^{87} \) \(\mathstrut -\mathstrut 58q^{88} \) \(\mathstrut -\mathstrut 58q^{89} \) \(\mathstrut -\mathstrut 10q^{90} \) \(\mathstrut -\mathstrut 43q^{91} \) \(\mathstrut -\mathstrut 68q^{92} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 78q^{95} \) \(\mathstrut -\mathstrut 61q^{96} \) \(\mathstrut -\mathstrut 44q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut -\mathstrut 25q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.42497 −1.00760 −0.503801 0.863820i \(-0.668066\pi\)
−0.503801 + 0.863820i \(0.668066\pi\)
\(3\) 1.00000 0.577350
\(4\) 0.0305258 0.0152629
\(5\) 0.348852 0.156011 0.0780057 0.996953i \(-0.475145\pi\)
0.0780057 + 0.996953i \(0.475145\pi\)
\(6\) −1.42497 −0.581740
\(7\) −0.489415 −0.184981 −0.0924907 0.995714i \(-0.529483\pi\)
−0.0924907 + 0.995714i \(0.529483\pi\)
\(8\) 2.80643 0.992224
\(9\) 1.00000 0.333333
\(10\) −0.497102 −0.157197
\(11\) 2.33512 0.704065 0.352033 0.935988i \(-0.385491\pi\)
0.352033 + 0.935988i \(0.385491\pi\)
\(12\) 0.0305258 0.00881203
\(13\) 5.30367 1.47097 0.735486 0.677540i \(-0.236954\pi\)
0.735486 + 0.677540i \(0.236954\pi\)
\(14\) 0.697399 0.186388
\(15\) 0.348852 0.0900732
\(16\) −4.06012 −1.01503
\(17\) −1.00000 −0.242536
\(18\) −1.42497 −0.335868
\(19\) −4.47923 −1.02761 −0.513803 0.857908i \(-0.671764\pi\)
−0.513803 + 0.857908i \(0.671764\pi\)
\(20\) 0.0106490 0.00238118
\(21\) −0.489415 −0.106799
\(22\) −3.32746 −0.709418
\(23\) 2.78427 0.580561 0.290280 0.956942i \(-0.406251\pi\)
0.290280 + 0.956942i \(0.406251\pi\)
\(24\) 2.80643 0.572861
\(25\) −4.87830 −0.975660
\(26\) −7.55754 −1.48216
\(27\) 1.00000 0.192450
\(28\) −0.0149398 −0.00282335
\(29\) 0.169133 0.0314073 0.0157036 0.999877i \(-0.495001\pi\)
0.0157036 + 0.999877i \(0.495001\pi\)
\(30\) −0.497102 −0.0907580
\(31\) 2.78442 0.500096 0.250048 0.968233i \(-0.419554\pi\)
0.250048 + 0.968233i \(0.419554\pi\)
\(32\) 0.172665 0.0305231
\(33\) 2.33512 0.406492
\(34\) 1.42497 0.244380
\(35\) −0.170733 −0.0288592
\(36\) 0.0305258 0.00508763
\(37\) −11.1454 −1.83229 −0.916145 0.400848i \(-0.868716\pi\)
−0.916145 + 0.400848i \(0.868716\pi\)
\(38\) 6.38275 1.03542
\(39\) 5.30367 0.849266
\(40\) 0.979029 0.154798
\(41\) 0.741898 0.115865 0.0579325 0.998321i \(-0.481549\pi\)
0.0579325 + 0.998321i \(0.481549\pi\)
\(42\) 0.697399 0.107611
\(43\) −3.38376 −0.516018 −0.258009 0.966142i \(-0.583066\pi\)
−0.258009 + 0.966142i \(0.583066\pi\)
\(44\) 0.0712813 0.0107461
\(45\) 0.348852 0.0520038
\(46\) −3.96749 −0.584974
\(47\) −0.461826 −0.0673643 −0.0336821 0.999433i \(-0.510723\pi\)
−0.0336821 + 0.999433i \(0.510723\pi\)
\(48\) −4.06012 −0.586028
\(49\) −6.76047 −0.965782
\(50\) 6.95141 0.983078
\(51\) −1.00000 −0.140028
\(52\) 0.161898 0.0224513
\(53\) −9.58285 −1.31631 −0.658153 0.752884i \(-0.728662\pi\)
−0.658153 + 0.752884i \(0.728662\pi\)
\(54\) −1.42497 −0.193913
\(55\) 0.814611 0.109842
\(56\) −1.37351 −0.183543
\(57\) −4.47923 −0.593289
\(58\) −0.241009 −0.0316461
\(59\) −10.0596 −1.30965 −0.654825 0.755780i \(-0.727258\pi\)
−0.654825 + 0.755780i \(0.727258\pi\)
\(60\) 0.0106490 0.00137478
\(61\) 1.32822 0.170061 0.0850305 0.996378i \(-0.472901\pi\)
0.0850305 + 0.996378i \(0.472901\pi\)
\(62\) −3.96770 −0.503898
\(63\) −0.489415 −0.0616605
\(64\) 7.87420 0.984275
\(65\) 1.85019 0.229488
\(66\) −3.32746 −0.409583
\(67\) −2.14227 −0.261720 −0.130860 0.991401i \(-0.541774\pi\)
−0.130860 + 0.991401i \(0.541774\pi\)
\(68\) −0.0305258 −0.00370179
\(69\) 2.78427 0.335187
\(70\) 0.243289 0.0290786
\(71\) 8.64535 1.02601 0.513007 0.858384i \(-0.328531\pi\)
0.513007 + 0.858384i \(0.328531\pi\)
\(72\) 2.80643 0.330741
\(73\) 1.89207 0.221450 0.110725 0.993851i \(-0.464683\pi\)
0.110725 + 0.993851i \(0.464683\pi\)
\(74\) 15.8818 1.84622
\(75\) −4.87830 −0.563298
\(76\) −0.136732 −0.0156842
\(77\) −1.14284 −0.130239
\(78\) −7.55754 −0.855723
\(79\) −5.45077 −0.613259 −0.306630 0.951829i \(-0.599201\pi\)
−0.306630 + 0.951829i \(0.599201\pi\)
\(80\) −1.41638 −0.158356
\(81\) 1.00000 0.111111
\(82\) −1.05718 −0.116746
\(83\) −14.7039 −1.61397 −0.806984 0.590574i \(-0.798901\pi\)
−0.806984 + 0.590574i \(0.798901\pi\)
\(84\) −0.0149398 −0.00163006
\(85\) −0.348852 −0.0378383
\(86\) 4.82174 0.519941
\(87\) 0.169133 0.0181330
\(88\) 6.55335 0.698590
\(89\) −6.89341 −0.730700 −0.365350 0.930870i \(-0.619051\pi\)
−0.365350 + 0.930870i \(0.619051\pi\)
\(90\) −0.497102 −0.0523991
\(91\) −2.59569 −0.272103
\(92\) 0.0849920 0.00886103
\(93\) 2.78442 0.288731
\(94\) 0.658086 0.0678764
\(95\) −1.56259 −0.160318
\(96\) 0.172665 0.0176225
\(97\) 7.97411 0.809648 0.404824 0.914395i \(-0.367333\pi\)
0.404824 + 0.914395i \(0.367333\pi\)
\(98\) 9.63344 0.973124
\(99\) 2.33512 0.234688
\(100\) −0.148914 −0.0148914
\(101\) 4.19110 0.417030 0.208515 0.978019i \(-0.433137\pi\)
0.208515 + 0.978019i \(0.433137\pi\)
\(102\) 1.42497 0.141093
\(103\) −8.44324 −0.831937 −0.415969 0.909379i \(-0.636557\pi\)
−0.415969 + 0.909379i \(0.636557\pi\)
\(104\) 14.8844 1.45953
\(105\) −0.170733 −0.0166619
\(106\) 13.6552 1.32631
\(107\) −17.0461 −1.64791 −0.823954 0.566657i \(-0.808236\pi\)
−0.823954 + 0.566657i \(0.808236\pi\)
\(108\) 0.0305258 0.00293734
\(109\) −12.2364 −1.17203 −0.586017 0.810299i \(-0.699305\pi\)
−0.586017 + 0.810299i \(0.699305\pi\)
\(110\) −1.16079 −0.110677
\(111\) −11.1454 −1.05787
\(112\) 1.98708 0.187762
\(113\) −11.3345 −1.06626 −0.533131 0.846033i \(-0.678985\pi\)
−0.533131 + 0.846033i \(0.678985\pi\)
\(114\) 6.38275 0.597799
\(115\) 0.971299 0.0905741
\(116\) 0.00516293 0.000479366 0
\(117\) 5.30367 0.490324
\(118\) 14.3346 1.31961
\(119\) 0.489415 0.0448646
\(120\) 0.979029 0.0893727
\(121\) −5.54722 −0.504292
\(122\) −1.89267 −0.171354
\(123\) 0.741898 0.0668947
\(124\) 0.0849965 0.00763291
\(125\) −3.44607 −0.308225
\(126\) 0.697399 0.0621293
\(127\) −10.7485 −0.953775 −0.476888 0.878964i \(-0.658235\pi\)
−0.476888 + 0.878964i \(0.658235\pi\)
\(128\) −11.5658 −1.02228
\(129\) −3.38376 −0.297923
\(130\) −2.63646 −0.231233
\(131\) 0.693525 0.0605936 0.0302968 0.999541i \(-0.490355\pi\)
0.0302968 + 0.999541i \(0.490355\pi\)
\(132\) 0.0712813 0.00620424
\(133\) 2.19220 0.190088
\(134\) 3.05266 0.263710
\(135\) 0.348852 0.0300244
\(136\) −2.80643 −0.240650
\(137\) 15.8390 1.35322 0.676610 0.736341i \(-0.263448\pi\)
0.676610 + 0.736341i \(0.263448\pi\)
\(138\) −3.96749 −0.337735
\(139\) 9.19610 0.780003 0.390001 0.920814i \(-0.372475\pi\)
0.390001 + 0.920814i \(0.372475\pi\)
\(140\) −0.00521177 −0.000440475 0
\(141\) −0.461826 −0.0388928
\(142\) −12.3193 −1.03381
\(143\) 12.3847 1.03566
\(144\) −4.06012 −0.338343
\(145\) 0.0590025 0.00489989
\(146\) −2.69613 −0.223134
\(147\) −6.76047 −0.557594
\(148\) −0.340221 −0.0279660
\(149\) −9.54121 −0.781646 −0.390823 0.920466i \(-0.627810\pi\)
−0.390823 + 0.920466i \(0.627810\pi\)
\(150\) 6.95141 0.567580
\(151\) 5.67816 0.462082 0.231041 0.972944i \(-0.425787\pi\)
0.231041 + 0.972944i \(0.425787\pi\)
\(152\) −12.5707 −1.01962
\(153\) −1.00000 −0.0808452
\(154\) 1.62851 0.131229
\(155\) 0.971350 0.0780207
\(156\) 0.161898 0.0129623
\(157\) 1.00000 0.0798087
\(158\) 7.76715 0.617921
\(159\) −9.58285 −0.759969
\(160\) 0.0602345 0.00476195
\(161\) −1.36266 −0.107393
\(162\) −1.42497 −0.111956
\(163\) 12.6255 0.988909 0.494455 0.869203i \(-0.335368\pi\)
0.494455 + 0.869203i \(0.335368\pi\)
\(164\) 0.0226470 0.00176843
\(165\) 0.814611 0.0634174
\(166\) 20.9526 1.62624
\(167\) −2.36517 −0.183022 −0.0915112 0.995804i \(-0.529170\pi\)
−0.0915112 + 0.995804i \(0.529170\pi\)
\(168\) −1.37351 −0.105969
\(169\) 15.1289 1.16376
\(170\) 0.497102 0.0381260
\(171\) −4.47923 −0.342535
\(172\) −0.103292 −0.00787593
\(173\) 16.5360 1.25721 0.628603 0.777726i \(-0.283627\pi\)
0.628603 + 0.777726i \(0.283627\pi\)
\(174\) −0.241009 −0.0182709
\(175\) 2.38751 0.180479
\(176\) −9.48086 −0.714647
\(177\) −10.0596 −0.756127
\(178\) 9.82287 0.736255
\(179\) 17.6710 1.32079 0.660395 0.750918i \(-0.270389\pi\)
0.660395 + 0.750918i \(0.270389\pi\)
\(180\) 0.0106490 0.000793728 0
\(181\) 2.10984 0.156824 0.0784118 0.996921i \(-0.475015\pi\)
0.0784118 + 0.996921i \(0.475015\pi\)
\(182\) 3.69877 0.274171
\(183\) 1.32822 0.0981848
\(184\) 7.81387 0.576046
\(185\) −3.88809 −0.285858
\(186\) −3.96770 −0.290926
\(187\) −2.33512 −0.170761
\(188\) −0.0140976 −0.00102817
\(189\) −0.489415 −0.0355997
\(190\) 2.22663 0.161537
\(191\) −8.00882 −0.579498 −0.289749 0.957103i \(-0.593572\pi\)
−0.289749 + 0.957103i \(0.593572\pi\)
\(192\) 7.87420 0.568271
\(193\) 7.43250 0.535003 0.267502 0.963557i \(-0.413802\pi\)
0.267502 + 0.963557i \(0.413802\pi\)
\(194\) −11.3628 −0.815804
\(195\) 1.85019 0.132495
\(196\) −0.206369 −0.0147406
\(197\) 19.8609 1.41503 0.707517 0.706696i \(-0.249815\pi\)
0.707517 + 0.706696i \(0.249815\pi\)
\(198\) −3.32746 −0.236473
\(199\) −2.82278 −0.200102 −0.100051 0.994982i \(-0.531901\pi\)
−0.100051 + 0.994982i \(0.531901\pi\)
\(200\) −13.6906 −0.968073
\(201\) −2.14227 −0.151104
\(202\) −5.97217 −0.420201
\(203\) −0.0827764 −0.00580977
\(204\) −0.0305258 −0.00213723
\(205\) 0.258813 0.0180763
\(206\) 12.0313 0.838262
\(207\) 2.78427 0.193520
\(208\) −21.5335 −1.49308
\(209\) −10.4595 −0.723502
\(210\) 0.243289 0.0167885
\(211\) 25.3175 1.74293 0.871465 0.490457i \(-0.163170\pi\)
0.871465 + 0.490457i \(0.163170\pi\)
\(212\) −0.292524 −0.0200906
\(213\) 8.64535 0.592370
\(214\) 24.2901 1.66044
\(215\) −1.18043 −0.0805047
\(216\) 2.80643 0.190954
\(217\) −1.36274 −0.0925085
\(218\) 17.4364 1.18094
\(219\) 1.89207 0.127854
\(220\) 0.0248666 0.00167651
\(221\) −5.30367 −0.356763
\(222\) 15.8818 1.06592
\(223\) 6.67044 0.446685 0.223343 0.974740i \(-0.428303\pi\)
0.223343 + 0.974740i \(0.428303\pi\)
\(224\) −0.0845047 −0.00564621
\(225\) −4.87830 −0.325220
\(226\) 16.1513 1.07437
\(227\) −16.0647 −1.06625 −0.533125 0.846037i \(-0.678982\pi\)
−0.533125 + 0.846037i \(0.678982\pi\)
\(228\) −0.136732 −0.00905530
\(229\) −26.9121 −1.77840 −0.889200 0.457519i \(-0.848738\pi\)
−0.889200 + 0.457519i \(0.848738\pi\)
\(230\) −1.38407 −0.0912626
\(231\) −1.14284 −0.0751935
\(232\) 0.474662 0.0311631
\(233\) −2.77499 −0.181796 −0.0908978 0.995860i \(-0.528974\pi\)
−0.0908978 + 0.995860i \(0.528974\pi\)
\(234\) −7.55754 −0.494052
\(235\) −0.161109 −0.0105096
\(236\) −0.307077 −0.0199890
\(237\) −5.45077 −0.354065
\(238\) −0.697399 −0.0452057
\(239\) −22.6060 −1.46226 −0.731130 0.682238i \(-0.761007\pi\)
−0.731130 + 0.682238i \(0.761007\pi\)
\(240\) −1.41638 −0.0914270
\(241\) 30.2829 1.95070 0.975348 0.220673i \(-0.0708253\pi\)
0.975348 + 0.220673i \(0.0708253\pi\)
\(242\) 7.90459 0.508126
\(243\) 1.00000 0.0641500
\(244\) 0.0405449 0.00259562
\(245\) −2.35840 −0.150673
\(246\) −1.05718 −0.0674033
\(247\) −23.7563 −1.51158
\(248\) 7.81428 0.496207
\(249\) −14.7039 −0.931824
\(250\) 4.91052 0.310569
\(251\) 29.1827 1.84199 0.920997 0.389570i \(-0.127376\pi\)
0.920997 + 0.389570i \(0.127376\pi\)
\(252\) −0.0149398 −0.000941117 0
\(253\) 6.50161 0.408752
\(254\) 15.3162 0.961026
\(255\) −0.348852 −0.0218460
\(256\) 0.732449 0.0457780
\(257\) 8.11579 0.506249 0.253124 0.967434i \(-0.418542\pi\)
0.253124 + 0.967434i \(0.418542\pi\)
\(258\) 4.82174 0.300188
\(259\) 5.45471 0.338939
\(260\) 0.0564786 0.00350265
\(261\) 0.169133 0.0104691
\(262\) −0.988250 −0.0610543
\(263\) −5.33971 −0.329261 −0.164630 0.986355i \(-0.552643\pi\)
−0.164630 + 0.986355i \(0.552643\pi\)
\(264\) 6.55335 0.403331
\(265\) −3.34300 −0.205359
\(266\) −3.12381 −0.191533
\(267\) −6.89341 −0.421870
\(268\) −0.0653944 −0.00399460
\(269\) −17.1954 −1.04842 −0.524211 0.851588i \(-0.675640\pi\)
−0.524211 + 0.851588i \(0.675640\pi\)
\(270\) −0.497102 −0.0302527
\(271\) −28.5092 −1.73181 −0.865904 0.500210i \(-0.833256\pi\)
−0.865904 + 0.500210i \(0.833256\pi\)
\(272\) 4.06012 0.246181
\(273\) −2.59569 −0.157099
\(274\) −22.5701 −1.36351
\(275\) −11.3914 −0.686928
\(276\) 0.0849920 0.00511592
\(277\) 12.2251 0.734537 0.367268 0.930115i \(-0.380293\pi\)
0.367268 + 0.930115i \(0.380293\pi\)
\(278\) −13.1041 −0.785933
\(279\) 2.78442 0.166699
\(280\) −0.479152 −0.0286348
\(281\) −14.9343 −0.890906 −0.445453 0.895305i \(-0.646957\pi\)
−0.445453 + 0.895305i \(0.646957\pi\)
\(282\) 0.658086 0.0391885
\(283\) 16.2222 0.964308 0.482154 0.876087i \(-0.339855\pi\)
0.482154 + 0.876087i \(0.339855\pi\)
\(284\) 0.263906 0.0156599
\(285\) −1.56259 −0.0925598
\(286\) −17.6478 −1.04353
\(287\) −0.363096 −0.0214329
\(288\) 0.172665 0.0101744
\(289\) 1.00000 0.0588235
\(290\) −0.0840766 −0.00493715
\(291\) 7.97411 0.467451
\(292\) 0.0577569 0.00337997
\(293\) 3.47252 0.202867 0.101433 0.994842i \(-0.467657\pi\)
0.101433 + 0.994842i \(0.467657\pi\)
\(294\) 9.63344 0.561834
\(295\) −3.50932 −0.204320
\(296\) −31.2788 −1.81804
\(297\) 2.33512 0.135497
\(298\) 13.5959 0.787589
\(299\) 14.7668 0.853989
\(300\) −0.148914 −0.00859755
\(301\) 1.65606 0.0954538
\(302\) −8.09117 −0.465595
\(303\) 4.19110 0.240773
\(304\) 18.1862 1.04305
\(305\) 0.463352 0.0265315
\(306\) 1.42497 0.0814598
\(307\) −30.0799 −1.71675 −0.858377 0.513020i \(-0.828527\pi\)
−0.858377 + 0.513020i \(0.828527\pi\)
\(308\) −0.0348861 −0.00198782
\(309\) −8.44324 −0.480319
\(310\) −1.38414 −0.0786139
\(311\) −22.8202 −1.29402 −0.647009 0.762483i \(-0.723980\pi\)
−0.647009 + 0.762483i \(0.723980\pi\)
\(312\) 14.8844 0.842662
\(313\) 12.6425 0.714595 0.357298 0.933991i \(-0.383698\pi\)
0.357298 + 0.933991i \(0.383698\pi\)
\(314\) −1.42497 −0.0804154
\(315\) −0.170733 −0.00961973
\(316\) −0.166389 −0.00936010
\(317\) 15.0795 0.846947 0.423474 0.905908i \(-0.360811\pi\)
0.423474 + 0.905908i \(0.360811\pi\)
\(318\) 13.6552 0.765747
\(319\) 0.394947 0.0221128
\(320\) 2.74693 0.153558
\(321\) −17.0461 −0.951420
\(322\) 1.94175 0.108209
\(323\) 4.47923 0.249231
\(324\) 0.0305258 0.00169588
\(325\) −25.8729 −1.43517
\(326\) −17.9910 −0.996427
\(327\) −12.2364 −0.676674
\(328\) 2.08209 0.114964
\(329\) 0.226025 0.0124611
\(330\) −1.16079 −0.0638995
\(331\) −6.17594 −0.339460 −0.169730 0.985491i \(-0.554290\pi\)
−0.169730 + 0.985491i \(0.554290\pi\)
\(332\) −0.448849 −0.0246338
\(333\) −11.1454 −0.610763
\(334\) 3.37029 0.184414
\(335\) −0.747335 −0.0408313
\(336\) 1.98708 0.108404
\(337\) −9.67193 −0.526863 −0.263432 0.964678i \(-0.584854\pi\)
−0.263432 + 0.964678i \(0.584854\pi\)
\(338\) −21.5581 −1.17261
\(339\) −11.3345 −0.615606
\(340\) −0.0106490 −0.000577522 0
\(341\) 6.50195 0.352100
\(342\) 6.38275 0.345140
\(343\) 6.73458 0.363633
\(344\) −9.49629 −0.512006
\(345\) 0.971299 0.0522930
\(346\) −23.5632 −1.26676
\(347\) −37.1764 −1.99573 −0.997867 0.0652755i \(-0.979207\pi\)
−0.997867 + 0.0652755i \(0.979207\pi\)
\(348\) 0.00516293 0.000276762 0
\(349\) −7.65529 −0.409778 −0.204889 0.978785i \(-0.565683\pi\)
−0.204889 + 0.978785i \(0.565683\pi\)
\(350\) −3.40212 −0.181851
\(351\) 5.30367 0.283089
\(352\) 0.403193 0.0214903
\(353\) −5.89078 −0.313535 −0.156767 0.987636i \(-0.550107\pi\)
−0.156767 + 0.987636i \(0.550107\pi\)
\(354\) 14.3346 0.761875
\(355\) 3.01595 0.160070
\(356\) −0.210427 −0.0111526
\(357\) 0.489415 0.0259026
\(358\) −25.1805 −1.33083
\(359\) −21.6384 −1.14203 −0.571015 0.820939i \(-0.693450\pi\)
−0.571015 + 0.820939i \(0.693450\pi\)
\(360\) 0.979029 0.0515994
\(361\) 1.06351 0.0559744
\(362\) −3.00646 −0.158016
\(363\) −5.54722 −0.291153
\(364\) −0.0792355 −0.00415307
\(365\) 0.660052 0.0345487
\(366\) −1.89267 −0.0989312
\(367\) −22.9579 −1.19839 −0.599196 0.800602i \(-0.704513\pi\)
−0.599196 + 0.800602i \(0.704513\pi\)
\(368\) −11.3045 −0.589286
\(369\) 0.741898 0.0386217
\(370\) 5.54039 0.288031
\(371\) 4.68999 0.243492
\(372\) 0.0849965 0.00440686
\(373\) −7.42511 −0.384458 −0.192229 0.981350i \(-0.561572\pi\)
−0.192229 + 0.981350i \(0.561572\pi\)
\(374\) 3.32746 0.172059
\(375\) −3.44607 −0.177954
\(376\) −1.29608 −0.0668404
\(377\) 0.897027 0.0461993
\(378\) 0.697399 0.0358703
\(379\) 8.31064 0.426889 0.213444 0.976955i \(-0.431532\pi\)
0.213444 + 0.976955i \(0.431532\pi\)
\(380\) −0.0476992 −0.00244692
\(381\) −10.7485 −0.550662
\(382\) 11.4123 0.583904
\(383\) −16.3401 −0.834938 −0.417469 0.908691i \(-0.637083\pi\)
−0.417469 + 0.908691i \(0.637083\pi\)
\(384\) −11.5658 −0.590214
\(385\) −0.398683 −0.0203188
\(386\) −10.5911 −0.539071
\(387\) −3.38376 −0.172006
\(388\) 0.243416 0.0123576
\(389\) −2.10522 −0.106739 −0.0533694 0.998575i \(-0.516996\pi\)
−0.0533694 + 0.998575i \(0.516996\pi\)
\(390\) −2.63646 −0.133502
\(391\) −2.78427 −0.140807
\(392\) −18.9728 −0.958272
\(393\) 0.693525 0.0349837
\(394\) −28.3012 −1.42579
\(395\) −1.90151 −0.0956754
\(396\) 0.0712813 0.00358202
\(397\) 15.6209 0.783993 0.391996 0.919967i \(-0.371785\pi\)
0.391996 + 0.919967i \(0.371785\pi\)
\(398\) 4.02236 0.201623
\(399\) 2.19220 0.109747
\(400\) 19.8065 0.990325
\(401\) 38.8161 1.93838 0.969191 0.246309i \(-0.0792178\pi\)
0.969191 + 0.246309i \(0.0792178\pi\)
\(402\) 3.05266 0.152253
\(403\) 14.7676 0.735628
\(404\) 0.127937 0.00636508
\(405\) 0.348852 0.0173346
\(406\) 0.117954 0.00585394
\(407\) −26.0258 −1.29005
\(408\) −2.80643 −0.138939
\(409\) 20.1758 0.997630 0.498815 0.866708i \(-0.333769\pi\)
0.498815 + 0.866708i \(0.333769\pi\)
\(410\) −0.368799 −0.0182137
\(411\) 15.8390 0.781282
\(412\) −0.257736 −0.0126978
\(413\) 4.92333 0.242261
\(414\) −3.96749 −0.194991
\(415\) −5.12950 −0.251797
\(416\) 0.915756 0.0448987
\(417\) 9.19610 0.450335
\(418\) 14.9045 0.729002
\(419\) 25.0095 1.22179 0.610897 0.791710i \(-0.290809\pi\)
0.610897 + 0.791710i \(0.290809\pi\)
\(420\) −0.00521177 −0.000254308 0
\(421\) 12.4874 0.608598 0.304299 0.952577i \(-0.401578\pi\)
0.304299 + 0.952577i \(0.401578\pi\)
\(422\) −36.0766 −1.75618
\(423\) −0.461826 −0.0224548
\(424\) −26.8936 −1.30607
\(425\) 4.87830 0.236632
\(426\) −12.3193 −0.596873
\(427\) −0.650050 −0.0314581
\(428\) −0.520345 −0.0251518
\(429\) 12.3847 0.597939
\(430\) 1.68207 0.0811168
\(431\) −13.8286 −0.666101 −0.333050 0.942909i \(-0.608078\pi\)
−0.333050 + 0.942909i \(0.608078\pi\)
\(432\) −4.06012 −0.195343
\(433\) 6.15204 0.295648 0.147824 0.989014i \(-0.452773\pi\)
0.147824 + 0.989014i \(0.452773\pi\)
\(434\) 1.94185 0.0932118
\(435\) 0.0590025 0.00282896
\(436\) −0.373525 −0.0178886
\(437\) −12.4714 −0.596588
\(438\) −2.69613 −0.128826
\(439\) −15.1854 −0.724760 −0.362380 0.932030i \(-0.618036\pi\)
−0.362380 + 0.932030i \(0.618036\pi\)
\(440\) 2.28615 0.108988
\(441\) −6.76047 −0.321927
\(442\) 7.55754 0.359476
\(443\) 10.2396 0.486500 0.243250 0.969964i \(-0.421786\pi\)
0.243250 + 0.969964i \(0.421786\pi\)
\(444\) −0.340221 −0.0161462
\(445\) −2.40478 −0.113997
\(446\) −9.50514 −0.450081
\(447\) −9.54121 −0.451284
\(448\) −3.85375 −0.182073
\(449\) −35.5269 −1.67662 −0.838309 0.545195i \(-0.816455\pi\)
−0.838309 + 0.545195i \(0.816455\pi\)
\(450\) 6.95141 0.327693
\(451\) 1.73242 0.0815765
\(452\) −0.345995 −0.0162742
\(453\) 5.67816 0.266783
\(454\) 22.8916 1.07436
\(455\) −0.905513 −0.0424511
\(456\) −12.5707 −0.588675
\(457\) 30.1442 1.41008 0.705042 0.709166i \(-0.250928\pi\)
0.705042 + 0.709166i \(0.250928\pi\)
\(458\) 38.3488 1.79192
\(459\) −1.00000 −0.0466760
\(460\) 0.0296496 0.00138242
\(461\) −13.0371 −0.607198 −0.303599 0.952800i \(-0.598188\pi\)
−0.303599 + 0.952800i \(0.598188\pi\)
\(462\) 1.62851 0.0757652
\(463\) 14.2463 0.662083 0.331041 0.943616i \(-0.392600\pi\)
0.331041 + 0.943616i \(0.392600\pi\)
\(464\) −0.686702 −0.0318793
\(465\) 0.971350 0.0450453
\(466\) 3.95426 0.183178
\(467\) 13.3593 0.618196 0.309098 0.951030i \(-0.399973\pi\)
0.309098 + 0.951030i \(0.399973\pi\)
\(468\) 0.161898 0.00748376
\(469\) 1.04846 0.0484133
\(470\) 0.229575 0.0105895
\(471\) 1.00000 0.0460776
\(472\) −28.2316 −1.29947
\(473\) −7.90148 −0.363310
\(474\) 7.76715 0.356757
\(475\) 21.8510 1.00259
\(476\) 0.0149398 0.000684763 0
\(477\) −9.58285 −0.438769
\(478\) 32.2128 1.47338
\(479\) 6.22110 0.284249 0.142125 0.989849i \(-0.454607\pi\)
0.142125 + 0.989849i \(0.454607\pi\)
\(480\) 0.0602345 0.00274931
\(481\) −59.1114 −2.69525
\(482\) −43.1521 −1.96553
\(483\) −1.36266 −0.0620034
\(484\) −0.169333 −0.00769696
\(485\) 2.78178 0.126314
\(486\) −1.42497 −0.0646377
\(487\) 23.2152 1.05198 0.525991 0.850490i \(-0.323694\pi\)
0.525991 + 0.850490i \(0.323694\pi\)
\(488\) 3.72756 0.168739
\(489\) 12.6255 0.570947
\(490\) 3.36064 0.151818
\(491\) 24.7210 1.11564 0.557821 0.829961i \(-0.311638\pi\)
0.557821 + 0.829961i \(0.311638\pi\)
\(492\) 0.0226470 0.00102101
\(493\) −0.169133 −0.00761739
\(494\) 33.8520 1.52307
\(495\) 0.814611 0.0366140
\(496\) −11.3051 −0.507613
\(497\) −4.23116 −0.189794
\(498\) 20.9526 0.938909
\(499\) 22.1365 0.990967 0.495483 0.868617i \(-0.334991\pi\)
0.495483 + 0.868617i \(0.334991\pi\)
\(500\) −0.105194 −0.00470441
\(501\) −2.36517 −0.105668
\(502\) −41.5843 −1.85600
\(503\) 20.4650 0.912490 0.456245 0.889854i \(-0.349194\pi\)
0.456245 + 0.889854i \(0.349194\pi\)
\(504\) −1.37351 −0.0611810
\(505\) 1.46207 0.0650615
\(506\) −9.26456 −0.411860
\(507\) 15.1289 0.671897
\(508\) −0.328106 −0.0145574
\(509\) −39.2385 −1.73922 −0.869608 0.493743i \(-0.835629\pi\)
−0.869608 + 0.493743i \(0.835629\pi\)
\(510\) 0.497102 0.0220120
\(511\) −0.926007 −0.0409641
\(512\) 22.0879 0.976155
\(513\) −4.47923 −0.197763
\(514\) −11.5647 −0.510098
\(515\) −2.94544 −0.129792
\(516\) −0.103292 −0.00454717
\(517\) −1.07842 −0.0474288
\(518\) −7.77278 −0.341516
\(519\) 16.5360 0.725848
\(520\) 5.19245 0.227704
\(521\) −30.3709 −1.33057 −0.665286 0.746589i \(-0.731690\pi\)
−0.665286 + 0.746589i \(0.731690\pi\)
\(522\) −0.241009 −0.0105487
\(523\) 35.2499 1.54137 0.770686 0.637215i \(-0.219914\pi\)
0.770686 + 0.637215i \(0.219914\pi\)
\(524\) 0.0211704 0.000924833 0
\(525\) 2.38751 0.104200
\(526\) 7.60890 0.331764
\(527\) −2.78442 −0.121291
\(528\) −9.48086 −0.412602
\(529\) −15.2478 −0.662949
\(530\) 4.76365 0.206920
\(531\) −10.0596 −0.436550
\(532\) 0.0669187 0.00290129
\(533\) 3.93478 0.170434
\(534\) 9.82287 0.425077
\(535\) −5.94656 −0.257092
\(536\) −6.01214 −0.259685
\(537\) 17.6710 0.762559
\(538\) 24.5029 1.05639
\(539\) −15.7865 −0.679973
\(540\) 0.0106490 0.000458259 0
\(541\) −41.6138 −1.78912 −0.894559 0.446950i \(-0.852510\pi\)
−0.894559 + 0.446950i \(0.852510\pi\)
\(542\) 40.6246 1.74497
\(543\) 2.10984 0.0905421
\(544\) −0.172665 −0.00740294
\(545\) −4.26869 −0.182851
\(546\) 3.69877 0.158293
\(547\) 19.8902 0.850444 0.425222 0.905089i \(-0.360196\pi\)
0.425222 + 0.905089i \(0.360196\pi\)
\(548\) 0.483499 0.0206540
\(549\) 1.32822 0.0566870
\(550\) 16.2324 0.692151
\(551\) −0.757588 −0.0322743
\(552\) 7.81387 0.332580
\(553\) 2.66769 0.113442
\(554\) −17.4204 −0.740121
\(555\) −3.88809 −0.165040
\(556\) 0.280718 0.0119051
\(557\) −23.5130 −0.996276 −0.498138 0.867098i \(-0.665983\pi\)
−0.498138 + 0.867098i \(0.665983\pi\)
\(558\) −3.96770 −0.167966
\(559\) −17.9463 −0.759049
\(560\) 0.693198 0.0292930
\(561\) −2.33512 −0.0985888
\(562\) 21.2809 0.897679
\(563\) −24.4768 −1.03158 −0.515788 0.856716i \(-0.672501\pi\)
−0.515788 + 0.856716i \(0.672501\pi\)
\(564\) −0.0140976 −0.000593616 0
\(565\) −3.95407 −0.166349
\(566\) −23.1160 −0.971639
\(567\) −0.489415 −0.0205535
\(568\) 24.2626 1.01804
\(569\) −34.2509 −1.43587 −0.717936 0.696109i \(-0.754913\pi\)
−0.717936 + 0.696109i \(0.754913\pi\)
\(570\) 2.22663 0.0932635
\(571\) 14.6683 0.613847 0.306924 0.951734i \(-0.400700\pi\)
0.306924 + 0.951734i \(0.400700\pi\)
\(572\) 0.378052 0.0158072
\(573\) −8.00882 −0.334573
\(574\) 0.517399 0.0215958
\(575\) −13.5825 −0.566430
\(576\) 7.87420 0.328092
\(577\) 0.531756 0.0221373 0.0110686 0.999939i \(-0.496477\pi\)
0.0110686 + 0.999939i \(0.496477\pi\)
\(578\) −1.42497 −0.0592707
\(579\) 7.43250 0.308884
\(580\) 0.00180110 7.47865e−5 0
\(581\) 7.19633 0.298554
\(582\) −11.3628 −0.471005
\(583\) −22.3771 −0.926765
\(584\) 5.30997 0.219728
\(585\) 1.85019 0.0764961
\(586\) −4.94822 −0.204409
\(587\) −35.3636 −1.45961 −0.729806 0.683655i \(-0.760389\pi\)
−0.729806 + 0.683655i \(0.760389\pi\)
\(588\) −0.206369 −0.00851050
\(589\) −12.4721 −0.513902
\(590\) 5.00065 0.205874
\(591\) 19.8609 0.816970
\(592\) 45.2516 1.85983
\(593\) −18.5077 −0.760018 −0.380009 0.924983i \(-0.624079\pi\)
−0.380009 + 0.924983i \(0.624079\pi\)
\(594\) −3.32746 −0.136528
\(595\) 0.170733 0.00699939
\(596\) −0.291253 −0.0119302
\(597\) −2.82278 −0.115529
\(598\) −21.0422 −0.860481
\(599\) 0.315731 0.0129004 0.00645021 0.999979i \(-0.497947\pi\)
0.00645021 + 0.999979i \(0.497947\pi\)
\(600\) −13.6906 −0.558917
\(601\) −39.7301 −1.62063 −0.810313 0.585997i \(-0.800703\pi\)
−0.810313 + 0.585997i \(0.800703\pi\)
\(602\) −2.35983 −0.0961795
\(603\) −2.14227 −0.0872400
\(604\) 0.173330 0.00705270
\(605\) −1.93516 −0.0786753
\(606\) −5.97217 −0.242603
\(607\) 35.1286 1.42583 0.712914 0.701252i \(-0.247375\pi\)
0.712914 + 0.701252i \(0.247375\pi\)
\(608\) −0.773406 −0.0313657
\(609\) −0.0827764 −0.00335427
\(610\) −0.660260 −0.0267332
\(611\) −2.44937 −0.0990910
\(612\) −0.0305258 −0.00123393
\(613\) 38.1985 1.54282 0.771411 0.636337i \(-0.219551\pi\)
0.771411 + 0.636337i \(0.219551\pi\)
\(614\) 42.8629 1.72980
\(615\) 0.258813 0.0104363
\(616\) −3.20731 −0.129226
\(617\) −26.9450 −1.08477 −0.542383 0.840131i \(-0.682478\pi\)
−0.542383 + 0.840131i \(0.682478\pi\)
\(618\) 12.0313 0.483971
\(619\) 25.6530 1.03108 0.515541 0.856865i \(-0.327591\pi\)
0.515541 + 0.856865i \(0.327591\pi\)
\(620\) 0.0296512 0.00119082
\(621\) 2.78427 0.111729
\(622\) 32.5181 1.30386
\(623\) 3.37374 0.135166
\(624\) −21.5335 −0.862031
\(625\) 23.1893 0.927574
\(626\) −18.0151 −0.720028
\(627\) −10.4595 −0.417714
\(628\) 0.0305258 0.00121811
\(629\) 11.1454 0.444395
\(630\) 0.243289 0.00969287
\(631\) −3.37801 −0.134476 −0.0672382 0.997737i \(-0.521419\pi\)
−0.0672382 + 0.997737i \(0.521419\pi\)
\(632\) −15.2972 −0.608490
\(633\) 25.3175 1.00628
\(634\) −21.4877 −0.853386
\(635\) −3.74963 −0.148800
\(636\) −0.292524 −0.0115993
\(637\) −35.8553 −1.42064
\(638\) −0.562786 −0.0222809
\(639\) 8.64535 0.342005
\(640\) −4.03475 −0.159487
\(641\) −0.774988 −0.0306102 −0.0153051 0.999883i \(-0.504872\pi\)
−0.0153051 + 0.999883i \(0.504872\pi\)
\(642\) 24.2901 0.958653
\(643\) −11.1018 −0.437813 −0.218907 0.975746i \(-0.570249\pi\)
−0.218907 + 0.975746i \(0.570249\pi\)
\(644\) −0.0415964 −0.00163913
\(645\) −1.18043 −0.0464794
\(646\) −6.38275 −0.251126
\(647\) −22.1721 −0.871676 −0.435838 0.900025i \(-0.643548\pi\)
−0.435838 + 0.900025i \(0.643548\pi\)
\(648\) 2.80643 0.110247
\(649\) −23.4904 −0.922079
\(650\) 36.8680 1.44608
\(651\) −1.36274 −0.0534098
\(652\) 0.385404 0.0150936
\(653\) −31.2762 −1.22393 −0.611966 0.790884i \(-0.709621\pi\)
−0.611966 + 0.790884i \(0.709621\pi\)
\(654\) 17.4364 0.681819
\(655\) 0.241938 0.00945329
\(656\) −3.01220 −0.117606
\(657\) 1.89207 0.0738167
\(658\) −0.322077 −0.0125559
\(659\) −25.7084 −1.00146 −0.500729 0.865604i \(-0.666935\pi\)
−0.500729 + 0.865604i \(0.666935\pi\)
\(660\) 0.0248666 0.000967932 0
\(661\) 47.5950 1.85123 0.925616 0.378463i \(-0.123547\pi\)
0.925616 + 0.378463i \(0.123547\pi\)
\(662\) 8.80049 0.342041
\(663\) −5.30367 −0.205977
\(664\) −41.2656 −1.60142
\(665\) 0.764754 0.0296559
\(666\) 15.8818 0.615406
\(667\) 0.470913 0.0182338
\(668\) −0.0721987 −0.00279345
\(669\) 6.67044 0.257894
\(670\) 1.06493 0.0411417
\(671\) 3.10155 0.119734
\(672\) −0.0845047 −0.00325984
\(673\) 15.1214 0.582888 0.291444 0.956588i \(-0.405864\pi\)
0.291444 + 0.956588i \(0.405864\pi\)
\(674\) 13.7822 0.530869
\(675\) −4.87830 −0.187766
\(676\) 0.461821 0.0177623
\(677\) 10.4928 0.403269 0.201635 0.979461i \(-0.435375\pi\)
0.201635 + 0.979461i \(0.435375\pi\)
\(678\) 16.1513 0.620287
\(679\) −3.90265 −0.149770
\(680\) −0.979029 −0.0375441
\(681\) −16.0647 −0.615599
\(682\) −9.26505 −0.354777
\(683\) 21.8847 0.837395 0.418698 0.908126i \(-0.362487\pi\)
0.418698 + 0.908126i \(0.362487\pi\)
\(684\) −0.136732 −0.00522808
\(685\) 5.52548 0.211118
\(686\) −9.59654 −0.366398
\(687\) −26.9121 −1.02676
\(688\) 13.7385 0.523774
\(689\) −50.8242 −1.93625
\(690\) −1.38407 −0.0526905
\(691\) −16.2348 −0.617602 −0.308801 0.951127i \(-0.599928\pi\)
−0.308801 + 0.951127i \(0.599928\pi\)
\(692\) 0.504773 0.0191886
\(693\) −1.14284 −0.0434130
\(694\) 52.9751 2.01091
\(695\) 3.20808 0.121689
\(696\) 0.474662 0.0179920
\(697\) −0.741898 −0.0281014
\(698\) 10.9085 0.412893
\(699\) −2.77499 −0.104960
\(700\) 0.0728807 0.00275463
\(701\) 12.7919 0.483145 0.241573 0.970383i \(-0.422337\pi\)
0.241573 + 0.970383i \(0.422337\pi\)
\(702\) −7.55754 −0.285241
\(703\) 49.9227 1.88287
\(704\) 18.3872 0.692993
\(705\) −0.161109 −0.00606772
\(706\) 8.39416 0.315918
\(707\) −2.05119 −0.0771429
\(708\) −0.307077 −0.0115407
\(709\) 10.0571 0.377703 0.188852 0.982006i \(-0.439523\pi\)
0.188852 + 0.982006i \(0.439523\pi\)
\(710\) −4.29762 −0.161287
\(711\) −5.45077 −0.204420
\(712\) −19.3459 −0.725018
\(713\) 7.75258 0.290336
\(714\) −0.697399 −0.0260995
\(715\) 4.32043 0.161575
\(716\) 0.539420 0.0201591
\(717\) −22.6060 −0.844236
\(718\) 30.8340 1.15071
\(719\) 15.1650 0.565558 0.282779 0.959185i \(-0.408744\pi\)
0.282779 + 0.959185i \(0.408744\pi\)
\(720\) −1.41638 −0.0527854
\(721\) 4.13225 0.153893
\(722\) −1.51547 −0.0564000
\(723\) 30.2829 1.12623
\(724\) 0.0644046 0.00239358
\(725\) −0.825084 −0.0306429
\(726\) 7.90459 0.293367
\(727\) −3.04565 −0.112957 −0.0564785 0.998404i \(-0.517987\pi\)
−0.0564785 + 0.998404i \(0.517987\pi\)
\(728\) −7.28464 −0.269987
\(729\) 1.00000 0.0370370
\(730\) −0.940551 −0.0348114
\(731\) 3.38376 0.125153
\(732\) 0.0405449 0.00149858
\(733\) 3.09265 0.114230 0.0571149 0.998368i \(-0.481810\pi\)
0.0571149 + 0.998368i \(0.481810\pi\)
\(734\) 32.7142 1.20750
\(735\) −2.35840 −0.0869911
\(736\) 0.480746 0.0177205
\(737\) −5.00246 −0.184268
\(738\) −1.05718 −0.0389153
\(739\) 50.0797 1.84221 0.921105 0.389314i \(-0.127288\pi\)
0.921105 + 0.389314i \(0.127288\pi\)
\(740\) −0.118687 −0.00436302
\(741\) −23.7563 −0.872711
\(742\) −6.68307 −0.245343
\(743\) −8.37497 −0.307248 −0.153624 0.988129i \(-0.549094\pi\)
−0.153624 + 0.988129i \(0.549094\pi\)
\(744\) 7.81428 0.286485
\(745\) −3.32847 −0.121946
\(746\) 10.5805 0.387381
\(747\) −14.7039 −0.537989
\(748\) −0.0712813 −0.00260630
\(749\) 8.34261 0.304832
\(750\) 4.91052 0.179307
\(751\) 17.9225 0.654002 0.327001 0.945024i \(-0.393962\pi\)
0.327001 + 0.945024i \(0.393962\pi\)
\(752\) 1.87507 0.0683768
\(753\) 29.1827 1.06348
\(754\) −1.27823 −0.0465505
\(755\) 1.98084 0.0720900
\(756\) −0.0149398 −0.000543354 0
\(757\) −27.2271 −0.989585 −0.494793 0.869011i \(-0.664756\pi\)
−0.494793 + 0.869011i \(0.664756\pi\)
\(758\) −11.8424 −0.430134
\(759\) 6.50161 0.235993
\(760\) −4.38530 −0.159072
\(761\) −15.9627 −0.578649 −0.289325 0.957231i \(-0.593431\pi\)
−0.289325 + 0.957231i \(0.593431\pi\)
\(762\) 15.3162 0.554849
\(763\) 5.98868 0.216805
\(764\) −0.244475 −0.00884481
\(765\) −0.348852 −0.0126128
\(766\) 23.2840 0.841286
\(767\) −53.3528 −1.92646
\(768\) 0.732449 0.0264300
\(769\) −30.0755 −1.08455 −0.542276 0.840201i \(-0.682437\pi\)
−0.542276 + 0.840201i \(0.682437\pi\)
\(770\) 0.568109 0.0204732
\(771\) 8.11579 0.292283
\(772\) 0.226883 0.00816569
\(773\) 17.7997 0.640210 0.320105 0.947382i \(-0.396282\pi\)
0.320105 + 0.947382i \(0.396282\pi\)
\(774\) 4.82174 0.173314
\(775\) −13.5832 −0.487924
\(776\) 22.3788 0.803352
\(777\) 5.45471 0.195687
\(778\) 2.99986 0.107550
\(779\) −3.32313 −0.119064
\(780\) 0.0564786 0.00202226
\(781\) 20.1879 0.722381
\(782\) 3.96749 0.141877
\(783\) 0.169133 0.00604434
\(784\) 27.4483 0.980297
\(785\) 0.348852 0.0124511
\(786\) −0.988250 −0.0352497
\(787\) −46.2565 −1.64887 −0.824433 0.565960i \(-0.808506\pi\)
−0.824433 + 0.565960i \(0.808506\pi\)
\(788\) 0.606271 0.0215975
\(789\) −5.33971 −0.190099
\(790\) 2.70959 0.0964028
\(791\) 5.54728 0.197239
\(792\) 6.55335 0.232863
\(793\) 7.04443 0.250155
\(794\) −22.2593 −0.789953
\(795\) −3.34300 −0.118564
\(796\) −0.0861675 −0.00305413
\(797\) 4.46866 0.158288 0.0791440 0.996863i \(-0.474781\pi\)
0.0791440 + 0.996863i \(0.474781\pi\)
\(798\) −3.12381 −0.110582
\(799\) 0.461826 0.0163382
\(800\) −0.842311 −0.0297802
\(801\) −6.89341 −0.243567
\(802\) −55.3116 −1.95312
\(803\) 4.41821 0.155915
\(804\) −0.0653944 −0.00230628
\(805\) −0.475368 −0.0167545
\(806\) −21.0434 −0.741221
\(807\) −17.1954 −0.605307
\(808\) 11.7620 0.413787
\(809\) 29.6131 1.04114 0.520570 0.853819i \(-0.325719\pi\)
0.520570 + 0.853819i \(0.325719\pi\)
\(810\) −0.497102 −0.0174664
\(811\) 37.9980 1.33429 0.667144 0.744928i \(-0.267516\pi\)
0.667144 + 0.744928i \(0.267516\pi\)
\(812\) −0.00252681 −8.86738e−5 0
\(813\) −28.5092 −0.999860
\(814\) 37.0859 1.29986
\(815\) 4.40445 0.154281
\(816\) 4.06012 0.142133
\(817\) 15.1566 0.530264
\(818\) −28.7498 −1.00521
\(819\) −2.59569 −0.0907009
\(820\) 0.00790045 0.000275896 0
\(821\) −10.6176 −0.370556 −0.185278 0.982686i \(-0.559319\pi\)
−0.185278 + 0.982686i \(0.559319\pi\)
\(822\) −22.5701 −0.787222
\(823\) 1.67879 0.0585191 0.0292595 0.999572i \(-0.490685\pi\)
0.0292595 + 0.999572i \(0.490685\pi\)
\(824\) −23.6954 −0.825468
\(825\) −11.3914 −0.396598
\(826\) −7.01557 −0.244103
\(827\) −4.13727 −0.143867 −0.0719336 0.997409i \(-0.522917\pi\)
−0.0719336 + 0.997409i \(0.522917\pi\)
\(828\) 0.0849920 0.00295368
\(829\) −38.3100 −1.33056 −0.665281 0.746593i \(-0.731688\pi\)
−0.665281 + 0.746593i \(0.731688\pi\)
\(830\) 7.30936 0.253711
\(831\) 12.2251 0.424085
\(832\) 41.7621 1.44784
\(833\) 6.76047 0.234237
\(834\) −13.1041 −0.453759
\(835\) −0.825095 −0.0285536
\(836\) −0.319285 −0.0110427
\(837\) 2.78442 0.0962436
\(838\) −35.6377 −1.23108
\(839\) −5.84342 −0.201737 −0.100869 0.994900i \(-0.532162\pi\)
−0.100869 + 0.994900i \(0.532162\pi\)
\(840\) −0.479152 −0.0165323
\(841\) −28.9714 −0.999014
\(842\) −17.7941 −0.613225
\(843\) −14.9343 −0.514365
\(844\) 0.772837 0.0266021
\(845\) 5.27774 0.181560
\(846\) 0.658086 0.0226255
\(847\) 2.71489 0.0932847
\(848\) 38.9075 1.33609
\(849\) 16.2222 0.556743
\(850\) −6.95141 −0.238431
\(851\) −31.0318 −1.06376
\(852\) 0.263906 0.00904127
\(853\) −49.7842 −1.70458 −0.852289 0.523070i \(-0.824786\pi\)
−0.852289 + 0.523070i \(0.824786\pi\)
\(854\) 0.926299 0.0316973
\(855\) −1.56259 −0.0534394
\(856\) −47.8387 −1.63509
\(857\) −18.0709 −0.617292 −0.308646 0.951177i \(-0.599876\pi\)
−0.308646 + 0.951177i \(0.599876\pi\)
\(858\) −17.6478 −0.602485
\(859\) −45.4163 −1.54958 −0.774791 0.632217i \(-0.782145\pi\)
−0.774791 + 0.632217i \(0.782145\pi\)
\(860\) −0.0360336 −0.00122873
\(861\) −0.363096 −0.0123743
\(862\) 19.7053 0.671165
\(863\) 37.7648 1.28553 0.642765 0.766064i \(-0.277787\pi\)
0.642765 + 0.766064i \(0.277787\pi\)
\(864\) 0.172665 0.00587418
\(865\) 5.76860 0.196138
\(866\) −8.76645 −0.297896
\(867\) 1.00000 0.0339618
\(868\) −0.0415986 −0.00141195
\(869\) −12.7282 −0.431774
\(870\) −0.0840766 −0.00285046
\(871\) −11.3619 −0.384983
\(872\) −34.3406 −1.16292
\(873\) 7.97411 0.269883
\(874\) 17.7713 0.601123
\(875\) 1.68656 0.0570160
\(876\) 0.0577569 0.00195142
\(877\) −55.5063 −1.87431 −0.937157 0.348909i \(-0.886552\pi\)
−0.937157 + 0.348909i \(0.886552\pi\)
\(878\) 21.6387 0.730270
\(879\) 3.47252 0.117125
\(880\) −3.30742 −0.111493
\(881\) −37.8148 −1.27401 −0.637007 0.770858i \(-0.719828\pi\)
−0.637007 + 0.770858i \(0.719828\pi\)
\(882\) 9.63344 0.324375
\(883\) −15.4684 −0.520552 −0.260276 0.965534i \(-0.583814\pi\)
−0.260276 + 0.965534i \(0.583814\pi\)
\(884\) −0.161898 −0.00544523
\(885\) −3.50932 −0.117964
\(886\) −14.5911 −0.490199
\(887\) −31.4518 −1.05605 −0.528024 0.849230i \(-0.677067\pi\)
−0.528024 + 0.849230i \(0.677067\pi\)
\(888\) −31.2788 −1.04965
\(889\) 5.26048 0.176431
\(890\) 3.42673 0.114864
\(891\) 2.33512 0.0782294
\(892\) 0.203620 0.00681771
\(893\) 2.06863 0.0692239
\(894\) 13.5959 0.454715
\(895\) 6.16455 0.206058
\(896\) 5.66047 0.189103
\(897\) 14.7668 0.493051
\(898\) 50.6246 1.68936
\(899\) 0.470938 0.0157067
\(900\) −0.148914 −0.00496380
\(901\) 9.58285 0.319251
\(902\) −2.46864 −0.0821967
\(903\) 1.65606 0.0551103
\(904\) −31.8096 −1.05797
\(905\) 0.736023 0.0244662
\(906\) −8.09117 −0.268811
\(907\) −3.71802 −0.123455 −0.0617274 0.998093i \(-0.519661\pi\)
−0.0617274 + 0.998093i \(0.519661\pi\)
\(908\) −0.490386 −0.0162740
\(909\) 4.19110 0.139010
\(910\) 1.29032 0.0427738
\(911\) 46.3971 1.53721 0.768603 0.639726i \(-0.220952\pi\)
0.768603 + 0.639726i \(0.220952\pi\)
\(912\) 18.1862 0.602206
\(913\) −34.3355 −1.13634
\(914\) −42.9544 −1.42080
\(915\) 0.463352 0.0153179
\(916\) −0.821511 −0.0271435
\(917\) −0.339422 −0.0112087
\(918\) 1.42497 0.0470309
\(919\) −4.45244 −0.146872 −0.0734362 0.997300i \(-0.523397\pi\)
−0.0734362 + 0.997300i \(0.523397\pi\)
\(920\) 2.72588 0.0898697
\(921\) −30.0799 −0.991168
\(922\) 18.5774 0.611814
\(923\) 45.8520 1.50924
\(924\) −0.0348861 −0.00114767
\(925\) 54.3705 1.78769
\(926\) −20.3005 −0.667116
\(927\) −8.44324 −0.277312
\(928\) 0.0292034 0.000958648 0
\(929\) 2.68218 0.0879996 0.0439998 0.999032i \(-0.485990\pi\)
0.0439998 + 0.999032i \(0.485990\pi\)
\(930\) −1.38414 −0.0453877
\(931\) 30.2817 0.992443
\(932\) −0.0847087 −0.00277473
\(933\) −22.8202 −0.747101
\(934\) −19.0366 −0.622896
\(935\) −0.814611 −0.0266406
\(936\) 14.8844 0.486511
\(937\) 35.8050 1.16970 0.584849 0.811142i \(-0.301154\pi\)
0.584849 + 0.811142i \(0.301154\pi\)
\(938\) −1.49402 −0.0487814
\(939\) 12.6425 0.412572
\(940\) −0.00491798 −0.000160407 0
\(941\) 28.7903 0.938537 0.469269 0.883056i \(-0.344518\pi\)
0.469269 + 0.883056i \(0.344518\pi\)
\(942\) −1.42497 −0.0464279
\(943\) 2.06565 0.0672667
\(944\) 40.8432 1.32933
\(945\) −0.170733 −0.00555396
\(946\) 11.2593 0.366073
\(947\) 2.70980 0.0880566 0.0440283 0.999030i \(-0.485981\pi\)
0.0440283 + 0.999030i \(0.485981\pi\)
\(948\) −0.166389 −0.00540406
\(949\) 10.0349 0.325747
\(950\) −31.1370 −1.01022
\(951\) 15.0795 0.488985
\(952\) 1.37351 0.0445157
\(953\) 6.09947 0.197581 0.0987905 0.995108i \(-0.468503\pi\)
0.0987905 + 0.995108i \(0.468503\pi\)
\(954\) 13.6552 0.442104
\(955\) −2.79389 −0.0904083
\(956\) −0.690065 −0.0223183
\(957\) 0.394947 0.0127668
\(958\) −8.86486 −0.286410
\(959\) −7.75186 −0.250321
\(960\) 2.74693 0.0886568
\(961\) −23.2470 −0.749904
\(962\) 84.2317 2.71574
\(963\) −17.0461 −0.549302
\(964\) 0.924410 0.0297732
\(965\) 2.59284 0.0834666
\(966\) 1.94175 0.0624747
\(967\) 58.5178 1.88181 0.940903 0.338676i \(-0.109979\pi\)
0.940903 + 0.338676i \(0.109979\pi\)
\(968\) −15.5679 −0.500371
\(969\) 4.47923 0.143894
\(970\) −3.96395 −0.127275
\(971\) 44.3759 1.42409 0.712044 0.702134i \(-0.247769\pi\)
0.712044 + 0.702134i \(0.247769\pi\)
\(972\) 0.0305258 0.000979114 0
\(973\) −4.50071 −0.144286
\(974\) −33.0809 −1.05998
\(975\) −25.8729 −0.828596
\(976\) −5.39273 −0.172617
\(977\) −26.3430 −0.842788 −0.421394 0.906878i \(-0.638459\pi\)
−0.421394 + 0.906878i \(0.638459\pi\)
\(978\) −17.9910 −0.575288
\(979\) −16.0969 −0.514460
\(980\) −0.0719921 −0.00229970
\(981\) −12.2364 −0.390678
\(982\) −35.2265 −1.12412
\(983\) −6.15658 −0.196364 −0.0981821 0.995168i \(-0.531303\pi\)
−0.0981821 + 0.995168i \(0.531303\pi\)
\(984\) 2.08209 0.0663745
\(985\) 6.92853 0.220761
\(986\) 0.241009 0.00767530
\(987\) 0.226025 0.00719444
\(988\) −0.725181 −0.0230711
\(989\) −9.42130 −0.299580
\(990\) −1.16079 −0.0368924
\(991\) 60.2209 1.91298 0.956490 0.291765i \(-0.0942426\pi\)
0.956490 + 0.291765i \(0.0942426\pi\)
\(992\) 0.480771 0.0152645
\(993\) −6.17594 −0.195987
\(994\) 6.02926 0.191236
\(995\) −0.984732 −0.0312181
\(996\) −0.448849 −0.0142223
\(997\) 35.5554 1.12605 0.563025 0.826440i \(-0.309637\pi\)
0.563025 + 0.826440i \(0.309637\pi\)
\(998\) −31.5438 −0.998501
\(999\) −11.1454 −0.352624
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 \(a_p\))