Properties

Label 4015.2.a.h.1.4
Level 4015
Weight 2
Character 4015.1
Self dual Yes
Analytic conductor 32.060
Analytic rank 0
Dimension 37
CM No

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Newspace parameters

Level: \( N \) = \( 4015 = 5 \cdot 11 \cdot 73 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0599364115\)
Analytic rank: \(0\)
Dimension: \(37\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 4015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.41139 q^{2}\) \(-3.18109 q^{3}\) \(+3.81483 q^{4}\) \(+1.00000 q^{5}\) \(+7.67086 q^{6}\) \(-3.73754 q^{7}\) \(-4.37626 q^{8}\) \(+7.11932 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.41139 q^{2}\) \(-3.18109 q^{3}\) \(+3.81483 q^{4}\) \(+1.00000 q^{5}\) \(+7.67086 q^{6}\) \(-3.73754 q^{7}\) \(-4.37626 q^{8}\) \(+7.11932 q^{9}\) \(-2.41139 q^{10}\) \(+1.00000 q^{11}\) \(-12.1353 q^{12}\) \(+1.00745 q^{13}\) \(+9.01269 q^{14}\) \(-3.18109 q^{15}\) \(+2.92324 q^{16}\) \(+3.53876 q^{17}\) \(-17.1675 q^{18}\) \(+5.00704 q^{19}\) \(+3.81483 q^{20}\) \(+11.8895 q^{21}\) \(-2.41139 q^{22}\) \(-0.391364 q^{23}\) \(+13.9213 q^{24}\) \(+1.00000 q^{25}\) \(-2.42936 q^{26}\) \(-13.1039 q^{27}\) \(-14.2581 q^{28}\) \(+5.23389 q^{29}\) \(+7.67086 q^{30}\) \(+0.906270 q^{31}\) \(+1.70343 q^{32}\) \(-3.18109 q^{33}\) \(-8.53336 q^{34}\) \(-3.73754 q^{35}\) \(+27.1590 q^{36}\) \(+9.23637 q^{37}\) \(-12.0739 q^{38}\) \(-3.20479 q^{39}\) \(-4.37626 q^{40}\) \(-3.85837 q^{41}\) \(-28.6702 q^{42}\) \(+10.8492 q^{43}\) \(+3.81483 q^{44}\) \(+7.11932 q^{45}\) \(+0.943734 q^{46}\) \(-5.91517 q^{47}\) \(-9.29910 q^{48}\) \(+6.96922 q^{49}\) \(-2.41139 q^{50}\) \(-11.2571 q^{51}\) \(+3.84325 q^{52}\) \(+9.74202 q^{53}\) \(+31.5988 q^{54}\) \(+1.00000 q^{55}\) \(+16.3565 q^{56}\) \(-15.9278 q^{57}\) \(-12.6210 q^{58}\) \(+8.90242 q^{59}\) \(-12.1353 q^{60}\) \(+10.3735 q^{61}\) \(-2.18537 q^{62}\) \(-26.6088 q^{63}\) \(-9.95412 q^{64}\) \(+1.00745 q^{65}\) \(+7.67086 q^{66}\) \(+5.52814 q^{67}\) \(+13.4998 q^{68}\) \(+1.24496 q^{69}\) \(+9.01269 q^{70}\) \(-8.76327 q^{71}\) \(-31.1560 q^{72}\) \(+1.00000 q^{73}\) \(-22.2725 q^{74}\) \(-3.18109 q^{75}\) \(+19.1010 q^{76}\) \(-3.73754 q^{77}\) \(+7.72801 q^{78}\) \(-5.30661 q^{79}\) \(+2.92324 q^{80}\) \(+20.3268 q^{81}\) \(+9.30405 q^{82}\) \(+5.31245 q^{83}\) \(+45.3562 q^{84}\) \(+3.53876 q^{85}\) \(-26.1618 q^{86}\) \(-16.6495 q^{87}\) \(-4.37626 q^{88}\) \(+7.61286 q^{89}\) \(-17.1675 q^{90}\) \(-3.76539 q^{91}\) \(-1.49299 q^{92}\) \(-2.88293 q^{93}\) \(+14.2638 q^{94}\) \(+5.00704 q^{95}\) \(-5.41875 q^{96}\) \(+14.7533 q^{97}\) \(-16.8055 q^{98}\) \(+7.11932 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 37q^{11} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 11q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 43q^{16} \) \(\mathstrut +\mathstrut 38q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 43q^{20} \) \(\mathstrut +\mathstrut 39q^{21} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 9q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 14q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 20q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 15q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 62q^{41} \) \(\mathstrut -\mathstrut 13q^{42} \) \(\mathstrut +\mathstrut 30q^{43} \) \(\mathstrut +\mathstrut 43q^{44} \) \(\mathstrut +\mathstrut 50q^{45} \) \(\mathstrut +\mathstrut 31q^{46} \) \(\mathstrut +\mathstrut 5q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 59q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut +\mathstrut 37q^{55} \) \(\mathstrut +\mathstrut 22q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 40q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 57q^{61} \) \(\mathstrut +\mathstrut 20q^{62} \) \(\mathstrut -\mathstrut 29q^{63} \) \(\mathstrut +\mathstrut 10q^{64} \) \(\mathstrut +\mathstrut 11q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 53q^{68} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 11q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut +\mathstrut 59q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 42q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 61q^{81} \) \(\mathstrut -\mathstrut 22q^{82} \) \(\mathstrut +\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 66q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut -\mathstrut q^{86} \) \(\mathstrut -\mathstrut 26q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 69q^{89} \) \(\mathstrut +\mathstrut 11q^{90} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 21q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut +\mathstrut 34q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 15q^{98} \) \(\mathstrut +\mathstrut 50q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.41139 −1.70511 −0.852557 0.522634i \(-0.824949\pi\)
−0.852557 + 0.522634i \(0.824949\pi\)
\(3\) −3.18109 −1.83660 −0.918301 0.395883i \(-0.870439\pi\)
−0.918301 + 0.395883i \(0.870439\pi\)
\(4\) 3.81483 1.90741
\(5\) 1.00000 0.447214
\(6\) 7.67086 3.13162
\(7\) −3.73754 −1.41266 −0.706329 0.707884i \(-0.749650\pi\)
−0.706329 + 0.707884i \(0.749650\pi\)
\(8\) −4.37626 −1.54724
\(9\) 7.11932 2.37311
\(10\) −2.41139 −0.762550
\(11\) 1.00000 0.301511
\(12\) −12.1353 −3.50316
\(13\) 1.00745 0.279416 0.139708 0.990193i \(-0.455384\pi\)
0.139708 + 0.990193i \(0.455384\pi\)
\(14\) 9.01269 2.40874
\(15\) −3.18109 −0.821354
\(16\) 2.92324 0.730811
\(17\) 3.53876 0.858276 0.429138 0.903239i \(-0.358817\pi\)
0.429138 + 0.903239i \(0.358817\pi\)
\(18\) −17.1675 −4.04642
\(19\) 5.00704 1.14869 0.574347 0.818612i \(-0.305256\pi\)
0.574347 + 0.818612i \(0.305256\pi\)
\(20\) 3.81483 0.853021
\(21\) 11.8895 2.59449
\(22\) −2.41139 −0.514111
\(23\) −0.391364 −0.0816051 −0.0408025 0.999167i \(-0.512991\pi\)
−0.0408025 + 0.999167i \(0.512991\pi\)
\(24\) 13.9213 2.84167
\(25\) 1.00000 0.200000
\(26\) −2.42936 −0.476437
\(27\) −13.1039 −2.52185
\(28\) −14.2581 −2.69452
\(29\) 5.23389 0.971909 0.485954 0.873984i \(-0.338472\pi\)
0.485954 + 0.873984i \(0.338472\pi\)
\(30\) 7.67086 1.40050
\(31\) 0.906270 0.162771 0.0813854 0.996683i \(-0.474066\pi\)
0.0813854 + 0.996683i \(0.474066\pi\)
\(32\) 1.70343 0.301126
\(33\) −3.18109 −0.553756
\(34\) −8.53336 −1.46346
\(35\) −3.73754 −0.631760
\(36\) 27.1590 4.52650
\(37\) 9.23637 1.51845 0.759225 0.650828i \(-0.225578\pi\)
0.759225 + 0.650828i \(0.225578\pi\)
\(38\) −12.0739 −1.95865
\(39\) −3.20479 −0.513177
\(40\) −4.37626 −0.691948
\(41\) −3.85837 −0.602576 −0.301288 0.953533i \(-0.597417\pi\)
−0.301288 + 0.953533i \(0.597417\pi\)
\(42\) −28.6702 −4.42390
\(43\) 10.8492 1.65449 0.827246 0.561839i \(-0.189906\pi\)
0.827246 + 0.561839i \(0.189906\pi\)
\(44\) 3.81483 0.575107
\(45\) 7.11932 1.06129
\(46\) 0.943734 0.139146
\(47\) −5.91517 −0.862817 −0.431408 0.902157i \(-0.641983\pi\)
−0.431408 + 0.902157i \(0.641983\pi\)
\(48\) −9.29910 −1.34221
\(49\) 6.96922 0.995602
\(50\) −2.41139 −0.341023
\(51\) −11.2571 −1.57631
\(52\) 3.84325 0.532962
\(53\) 9.74202 1.33817 0.669084 0.743186i \(-0.266686\pi\)
0.669084 + 0.743186i \(0.266686\pi\)
\(54\) 31.5988 4.30005
\(55\) 1.00000 0.134840
\(56\) 16.3565 2.18572
\(57\) −15.9278 −2.10969
\(58\) −12.6210 −1.65721
\(59\) 8.90242 1.15900 0.579498 0.814974i \(-0.303249\pi\)
0.579498 + 0.814974i \(0.303249\pi\)
\(60\) −12.1353 −1.56666
\(61\) 10.3735 1.32819 0.664093 0.747650i \(-0.268818\pi\)
0.664093 + 0.747650i \(0.268818\pi\)
\(62\) −2.18537 −0.277543
\(63\) −26.6088 −3.35239
\(64\) −9.95412 −1.24427
\(65\) 1.00745 0.124959
\(66\) 7.67086 0.944218
\(67\) 5.52814 0.675370 0.337685 0.941259i \(-0.390356\pi\)
0.337685 + 0.941259i \(0.390356\pi\)
\(68\) 13.4998 1.63709
\(69\) 1.24496 0.149876
\(70\) 9.01269 1.07722
\(71\) −8.76327 −1.04001 −0.520004 0.854164i \(-0.674070\pi\)
−0.520004 + 0.854164i \(0.674070\pi\)
\(72\) −31.1560 −3.67177
\(73\) 1.00000 0.117041
\(74\) −22.2725 −2.58913
\(75\) −3.18109 −0.367320
\(76\) 19.1010 2.19103
\(77\) −3.73754 −0.425932
\(78\) 7.72801 0.875024
\(79\) −5.30661 −0.597041 −0.298520 0.954403i \(-0.596493\pi\)
−0.298520 + 0.954403i \(0.596493\pi\)
\(80\) 2.92324 0.326829
\(81\) 20.3268 2.25853
\(82\) 9.30405 1.02746
\(83\) 5.31245 0.583118 0.291559 0.956553i \(-0.405826\pi\)
0.291559 + 0.956553i \(0.405826\pi\)
\(84\) 45.3562 4.94877
\(85\) 3.53876 0.383833
\(86\) −26.1618 −2.82110
\(87\) −16.6495 −1.78501
\(88\) −4.37626 −0.466511
\(89\) 7.61286 0.806961 0.403481 0.914988i \(-0.367800\pi\)
0.403481 + 0.914988i \(0.367800\pi\)
\(90\) −17.1675 −1.80961
\(91\) −3.76539 −0.394720
\(92\) −1.49299 −0.155655
\(93\) −2.88293 −0.298945
\(94\) 14.2638 1.47120
\(95\) 5.00704 0.513711
\(96\) −5.41875 −0.553049
\(97\) 14.7533 1.49797 0.748987 0.662585i \(-0.230541\pi\)
0.748987 + 0.662585i \(0.230541\pi\)
\(98\) −16.8055 −1.69762
\(99\) 7.11932 0.715519
\(100\) 3.81483 0.381483
\(101\) −4.83677 −0.481276 −0.240638 0.970615i \(-0.577357\pi\)
−0.240638 + 0.970615i \(0.577357\pi\)
\(102\) 27.1454 2.68779
\(103\) −5.61388 −0.553152 −0.276576 0.960992i \(-0.589200\pi\)
−0.276576 + 0.960992i \(0.589200\pi\)
\(104\) −4.40886 −0.432325
\(105\) 11.8895 1.16029
\(106\) −23.4919 −2.28173
\(107\) 14.8416 1.43479 0.717396 0.696666i \(-0.245334\pi\)
0.717396 + 0.696666i \(0.245334\pi\)
\(108\) −49.9892 −4.81022
\(109\) −11.1637 −1.06929 −0.534646 0.845076i \(-0.679555\pi\)
−0.534646 + 0.845076i \(0.679555\pi\)
\(110\) −2.41139 −0.229917
\(111\) −29.3817 −2.78879
\(112\) −10.9257 −1.03239
\(113\) −0.838480 −0.0788775 −0.0394388 0.999222i \(-0.512557\pi\)
−0.0394388 + 0.999222i \(0.512557\pi\)
\(114\) 38.4083 3.59727
\(115\) −0.391364 −0.0364949
\(116\) 19.9664 1.85383
\(117\) 7.17236 0.663085
\(118\) −21.4672 −1.97622
\(119\) −13.2263 −1.21245
\(120\) 13.9213 1.27083
\(121\) 1.00000 0.0909091
\(122\) −25.0145 −2.26471
\(123\) 12.2738 1.10669
\(124\) 3.45726 0.310471
\(125\) 1.00000 0.0894427
\(126\) 64.1643 5.71621
\(127\) −17.4581 −1.54915 −0.774576 0.632480i \(-0.782037\pi\)
−0.774576 + 0.632480i \(0.782037\pi\)
\(128\) 20.5965 1.82049
\(129\) −34.5124 −3.03865
\(130\) −2.42936 −0.213069
\(131\) 9.97137 0.871203 0.435601 0.900140i \(-0.356536\pi\)
0.435601 + 0.900140i \(0.356536\pi\)
\(132\) −12.1353 −1.05624
\(133\) −18.7140 −1.62271
\(134\) −13.3305 −1.15158
\(135\) −13.1039 −1.12781
\(136\) −15.4866 −1.32796
\(137\) 5.70726 0.487604 0.243802 0.969825i \(-0.421605\pi\)
0.243802 + 0.969825i \(0.421605\pi\)
\(138\) −3.00210 −0.255556
\(139\) 4.01965 0.340942 0.170471 0.985363i \(-0.445471\pi\)
0.170471 + 0.985363i \(0.445471\pi\)
\(140\) −14.2581 −1.20503
\(141\) 18.8167 1.58465
\(142\) 21.1317 1.77333
\(143\) 1.00745 0.0842472
\(144\) 20.8115 1.73429
\(145\) 5.23389 0.434651
\(146\) −2.41139 −0.199568
\(147\) −22.1697 −1.82853
\(148\) 35.2352 2.89631
\(149\) 4.11039 0.336737 0.168368 0.985724i \(-0.446150\pi\)
0.168368 + 0.985724i \(0.446150\pi\)
\(150\) 7.67086 0.626323
\(151\) −20.7200 −1.68617 −0.843085 0.537781i \(-0.819263\pi\)
−0.843085 + 0.537781i \(0.819263\pi\)
\(152\) −21.9121 −1.77731
\(153\) 25.1936 2.03678
\(154\) 9.01269 0.726263
\(155\) 0.906270 0.0727934
\(156\) −12.2257 −0.978840
\(157\) −14.8987 −1.18905 −0.594525 0.804077i \(-0.702660\pi\)
−0.594525 + 0.804077i \(0.702660\pi\)
\(158\) 12.7963 1.01802
\(159\) −30.9902 −2.45768
\(160\) 1.70343 0.134668
\(161\) 1.46274 0.115280
\(162\) −49.0160 −3.85106
\(163\) −20.1088 −1.57505 −0.787523 0.616285i \(-0.788637\pi\)
−0.787523 + 0.616285i \(0.788637\pi\)
\(164\) −14.7190 −1.14936
\(165\) −3.18109 −0.247647
\(166\) −12.8104 −0.994282
\(167\) 5.97801 0.462592 0.231296 0.972883i \(-0.425703\pi\)
0.231296 + 0.972883i \(0.425703\pi\)
\(168\) −52.0313 −4.01431
\(169\) −11.9850 −0.921927
\(170\) −8.53336 −0.654479
\(171\) 35.6467 2.72597
\(172\) 41.3879 3.15580
\(173\) −17.0353 −1.29517 −0.647585 0.761993i \(-0.724221\pi\)
−0.647585 + 0.761993i \(0.724221\pi\)
\(174\) 40.1484 3.04364
\(175\) −3.73754 −0.282532
\(176\) 2.92324 0.220348
\(177\) −28.3194 −2.12861
\(178\) −18.3576 −1.37596
\(179\) 2.61486 0.195443 0.0977217 0.995214i \(-0.468844\pi\)
0.0977217 + 0.995214i \(0.468844\pi\)
\(180\) 27.1590 2.02431
\(181\) −19.0515 −1.41609 −0.708045 0.706167i \(-0.750423\pi\)
−0.708045 + 0.706167i \(0.750423\pi\)
\(182\) 9.07983 0.673042
\(183\) −32.9989 −2.43935
\(184\) 1.71271 0.126263
\(185\) 9.23637 0.679072
\(186\) 6.95187 0.509736
\(187\) 3.53876 0.258780
\(188\) −22.5654 −1.64575
\(189\) 48.9765 3.56252
\(190\) −12.0739 −0.875936
\(191\) −20.6531 −1.49440 −0.747202 0.664597i \(-0.768603\pi\)
−0.747202 + 0.664597i \(0.768603\pi\)
\(192\) 31.6649 2.28522
\(193\) −15.4506 −1.11216 −0.556079 0.831129i \(-0.687695\pi\)
−0.556079 + 0.831129i \(0.687695\pi\)
\(194\) −35.5761 −2.55422
\(195\) −3.20479 −0.229500
\(196\) 26.5863 1.89902
\(197\) −17.7491 −1.26457 −0.632287 0.774734i \(-0.717884\pi\)
−0.632287 + 0.774734i \(0.717884\pi\)
\(198\) −17.1675 −1.22004
\(199\) 3.54686 0.251430 0.125715 0.992066i \(-0.459878\pi\)
0.125715 + 0.992066i \(0.459878\pi\)
\(200\) −4.37626 −0.309448
\(201\) −17.5855 −1.24039
\(202\) 11.6634 0.820631
\(203\) −19.5619 −1.37297
\(204\) −42.9440 −3.00668
\(205\) −3.85837 −0.269480
\(206\) 13.5373 0.943186
\(207\) −2.78625 −0.193658
\(208\) 2.94502 0.204201
\(209\) 5.00704 0.346344
\(210\) −28.6702 −1.97843
\(211\) 21.5730 1.48515 0.742573 0.669765i \(-0.233605\pi\)
0.742573 + 0.669765i \(0.233605\pi\)
\(212\) 37.1641 2.55244
\(213\) 27.8767 1.91008
\(214\) −35.7890 −2.44648
\(215\) 10.8492 0.739912
\(216\) 57.3462 3.90192
\(217\) −3.38722 −0.229940
\(218\) 26.9202 1.82326
\(219\) −3.18109 −0.214958
\(220\) 3.81483 0.257196
\(221\) 3.56513 0.239816
\(222\) 70.8509 4.75520
\(223\) −11.2708 −0.754751 −0.377375 0.926060i \(-0.623173\pi\)
−0.377375 + 0.926060i \(0.623173\pi\)
\(224\) −6.36663 −0.425388
\(225\) 7.11932 0.474622
\(226\) 2.02191 0.134495
\(227\) 26.1049 1.73265 0.866323 0.499484i \(-0.166477\pi\)
0.866323 + 0.499484i \(0.166477\pi\)
\(228\) −60.7619 −4.02406
\(229\) −3.59417 −0.237509 −0.118755 0.992924i \(-0.537890\pi\)
−0.118755 + 0.992924i \(0.537890\pi\)
\(230\) 0.943734 0.0622280
\(231\) 11.8895 0.782268
\(232\) −22.9049 −1.50378
\(233\) 30.2333 1.98065 0.990324 0.138774i \(-0.0443162\pi\)
0.990324 + 0.138774i \(0.0443162\pi\)
\(234\) −17.2954 −1.13064
\(235\) −5.91517 −0.385863
\(236\) 33.9612 2.21068
\(237\) 16.8808 1.09653
\(238\) 31.8938 2.06737
\(239\) −6.77695 −0.438364 −0.219182 0.975684i \(-0.570339\pi\)
−0.219182 + 0.975684i \(0.570339\pi\)
\(240\) −9.29910 −0.600254
\(241\) 15.3658 0.989797 0.494899 0.868951i \(-0.335205\pi\)
0.494899 + 0.868951i \(0.335205\pi\)
\(242\) −2.41139 −0.155010
\(243\) −25.3496 −1.62617
\(244\) 39.5730 2.53340
\(245\) 6.96922 0.445247
\(246\) −29.5970 −1.88704
\(247\) 5.04434 0.320964
\(248\) −3.96607 −0.251846
\(249\) −16.8994 −1.07096
\(250\) −2.41139 −0.152510
\(251\) 10.9549 0.691466 0.345733 0.938333i \(-0.387630\pi\)
0.345733 + 0.938333i \(0.387630\pi\)
\(252\) −101.508 −6.39439
\(253\) −0.391364 −0.0246049
\(254\) 42.0983 2.64148
\(255\) −11.2571 −0.704948
\(256\) −29.7580 −1.85987
\(257\) −20.8440 −1.30021 −0.650107 0.759842i \(-0.725276\pi\)
−0.650107 + 0.759842i \(0.725276\pi\)
\(258\) 83.2230 5.18124
\(259\) −34.5213 −2.14505
\(260\) 3.84325 0.238348
\(261\) 37.2618 2.30644
\(262\) −24.0449 −1.48550
\(263\) 10.3355 0.637316 0.318658 0.947870i \(-0.396768\pi\)
0.318658 + 0.947870i \(0.396768\pi\)
\(264\) 13.9213 0.856795
\(265\) 9.74202 0.598447
\(266\) 45.1269 2.76691
\(267\) −24.2172 −1.48207
\(268\) 21.0889 1.28821
\(269\) 5.53726 0.337613 0.168806 0.985649i \(-0.446009\pi\)
0.168806 + 0.985649i \(0.446009\pi\)
\(270\) 31.5988 1.92304
\(271\) 16.4191 0.997392 0.498696 0.866777i \(-0.333812\pi\)
0.498696 + 0.866777i \(0.333812\pi\)
\(272\) 10.3447 0.627238
\(273\) 11.9780 0.724943
\(274\) −13.7624 −0.831420
\(275\) 1.00000 0.0603023
\(276\) 4.74932 0.285876
\(277\) −9.72236 −0.584160 −0.292080 0.956394i \(-0.594347\pi\)
−0.292080 + 0.956394i \(0.594347\pi\)
\(278\) −9.69297 −0.581346
\(279\) 6.45203 0.386273
\(280\) 16.3565 0.977485
\(281\) 29.3091 1.74843 0.874217 0.485535i \(-0.161375\pi\)
0.874217 + 0.485535i \(0.161375\pi\)
\(282\) −45.3745 −2.70201
\(283\) 3.31945 0.197321 0.0986604 0.995121i \(-0.468544\pi\)
0.0986604 + 0.995121i \(0.468544\pi\)
\(284\) −33.4303 −1.98373
\(285\) −15.9278 −0.943483
\(286\) −2.42936 −0.143651
\(287\) 14.4208 0.851233
\(288\) 12.1272 0.714605
\(289\) −4.47715 −0.263362
\(290\) −12.6210 −0.741129
\(291\) −46.9317 −2.75118
\(292\) 3.81483 0.223246
\(293\) 18.2054 1.06357 0.531787 0.846878i \(-0.321521\pi\)
0.531787 + 0.846878i \(0.321521\pi\)
\(294\) 53.4599 3.11784
\(295\) 8.90242 0.518319
\(296\) −40.4208 −2.34941
\(297\) −13.1039 −0.760367
\(298\) −9.91178 −0.574174
\(299\) −0.394280 −0.0228018
\(300\) −12.1353 −0.700632
\(301\) −40.5495 −2.33723
\(302\) 49.9641 2.87511
\(303\) 15.3862 0.883913
\(304\) 14.6368 0.839478
\(305\) 10.3735 0.593983
\(306\) −60.7517 −3.47295
\(307\) 10.1773 0.580849 0.290425 0.956898i \(-0.406203\pi\)
0.290425 + 0.956898i \(0.406203\pi\)
\(308\) −14.2581 −0.812429
\(309\) 17.8582 1.01592
\(310\) −2.18537 −0.124121
\(311\) 29.4742 1.67133 0.835665 0.549240i \(-0.185083\pi\)
0.835665 + 0.549240i \(0.185083\pi\)
\(312\) 14.0250 0.794009
\(313\) −6.00846 −0.339618 −0.169809 0.985477i \(-0.554315\pi\)
−0.169809 + 0.985477i \(0.554315\pi\)
\(314\) 35.9268 2.02746
\(315\) −26.6088 −1.49923
\(316\) −20.2438 −1.13880
\(317\) 2.45441 0.137854 0.0689268 0.997622i \(-0.478043\pi\)
0.0689268 + 0.997622i \(0.478043\pi\)
\(318\) 74.7297 4.19063
\(319\) 5.23389 0.293042
\(320\) −9.95412 −0.556452
\(321\) −47.2125 −2.63514
\(322\) −3.52724 −0.196566
\(323\) 17.7187 0.985896
\(324\) 77.5432 4.30796
\(325\) 1.00745 0.0558833
\(326\) 48.4903 2.68563
\(327\) 35.5128 1.96386
\(328\) 16.8852 0.932331
\(329\) 22.1082 1.21886
\(330\) 7.67086 0.422267
\(331\) −21.8185 −1.19925 −0.599627 0.800279i \(-0.704685\pi\)
−0.599627 + 0.800279i \(0.704685\pi\)
\(332\) 20.2661 1.11225
\(333\) 65.7567 3.60345
\(334\) −14.4153 −0.788773
\(335\) 5.52814 0.302035
\(336\) 34.7558 1.89608
\(337\) 1.44864 0.0789125 0.0394562 0.999221i \(-0.487437\pi\)
0.0394562 + 0.999221i \(0.487437\pi\)
\(338\) 28.9007 1.57199
\(339\) 2.66728 0.144867
\(340\) 13.4998 0.732128
\(341\) 0.906270 0.0490773
\(342\) −85.9583 −4.64809
\(343\) 0.115053 0.00621230
\(344\) −47.4791 −2.55990
\(345\) 1.24496 0.0670266
\(346\) 41.0788 2.20841
\(347\) 6.32104 0.339331 0.169666 0.985502i \(-0.445731\pi\)
0.169666 + 0.985502i \(0.445731\pi\)
\(348\) −63.5148 −3.40475
\(349\) 10.3609 0.554606 0.277303 0.960782i \(-0.410559\pi\)
0.277303 + 0.960782i \(0.410559\pi\)
\(350\) 9.01269 0.481748
\(351\) −13.2016 −0.704647
\(352\) 1.70343 0.0907930
\(353\) 12.1889 0.648747 0.324374 0.945929i \(-0.394846\pi\)
0.324374 + 0.945929i \(0.394846\pi\)
\(354\) 68.2892 3.62953
\(355\) −8.76327 −0.465106
\(356\) 29.0417 1.53921
\(357\) 42.0740 2.22679
\(358\) −6.30545 −0.333253
\(359\) −23.1284 −1.22067 −0.610336 0.792143i \(-0.708966\pi\)
−0.610336 + 0.792143i \(0.708966\pi\)
\(360\) −31.1560 −1.64207
\(361\) 6.07043 0.319496
\(362\) 45.9408 2.41459
\(363\) −3.18109 −0.166964
\(364\) −14.3643 −0.752893
\(365\) 1.00000 0.0523424
\(366\) 79.5735 4.15937
\(367\) −21.8153 −1.13875 −0.569374 0.822079i \(-0.692814\pi\)
−0.569374 + 0.822079i \(0.692814\pi\)
\(368\) −1.14405 −0.0596379
\(369\) −27.4690 −1.42998
\(370\) −22.2725 −1.15789
\(371\) −36.4112 −1.89038
\(372\) −10.9979 −0.570212
\(373\) 14.6544 0.758775 0.379387 0.925238i \(-0.376135\pi\)
0.379387 + 0.925238i \(0.376135\pi\)
\(374\) −8.53336 −0.441249
\(375\) −3.18109 −0.164271
\(376\) 25.8863 1.33499
\(377\) 5.27288 0.271567
\(378\) −118.102 −6.07450
\(379\) 22.8573 1.17410 0.587051 0.809550i \(-0.300289\pi\)
0.587051 + 0.809550i \(0.300289\pi\)
\(380\) 19.1010 0.979860
\(381\) 55.5356 2.84518
\(382\) 49.8027 2.54813
\(383\) 3.99951 0.204365 0.102183 0.994766i \(-0.467417\pi\)
0.102183 + 0.994766i \(0.467417\pi\)
\(384\) −65.5192 −3.34351
\(385\) −3.73754 −0.190483
\(386\) 37.2575 1.89636
\(387\) 77.2392 3.92629
\(388\) 56.2814 2.85726
\(389\) −13.5828 −0.688677 −0.344339 0.938846i \(-0.611897\pi\)
−0.344339 + 0.938846i \(0.611897\pi\)
\(390\) 7.72801 0.391323
\(391\) −1.38495 −0.0700397
\(392\) −30.4991 −1.54044
\(393\) −31.7198 −1.60005
\(394\) 42.8002 2.15624
\(395\) −5.30661 −0.267005
\(396\) 27.1590 1.36479
\(397\) −18.6172 −0.934368 −0.467184 0.884160i \(-0.654732\pi\)
−0.467184 + 0.884160i \(0.654732\pi\)
\(398\) −8.55287 −0.428717
\(399\) 59.5309 2.98027
\(400\) 2.92324 0.146162
\(401\) 21.4575 1.07154 0.535768 0.844365i \(-0.320022\pi\)
0.535768 + 0.844365i \(0.320022\pi\)
\(402\) 42.4056 2.11500
\(403\) 0.913021 0.0454808
\(404\) −18.4514 −0.917993
\(405\) 20.3268 1.01005
\(406\) 47.1714 2.34108
\(407\) 9.23637 0.457830
\(408\) 49.2641 2.43894
\(409\) 6.93930 0.343127 0.171563 0.985173i \(-0.445118\pi\)
0.171563 + 0.985173i \(0.445118\pi\)
\(410\) 9.30405 0.459494
\(411\) −18.1553 −0.895534
\(412\) −21.4160 −1.05509
\(413\) −33.2732 −1.63726
\(414\) 6.71875 0.330208
\(415\) 5.31245 0.260778
\(416\) 1.71612 0.0841396
\(417\) −12.7869 −0.626176
\(418\) −12.0739 −0.590556
\(419\) −4.60237 −0.224840 −0.112420 0.993661i \(-0.535860\pi\)
−0.112420 + 0.993661i \(0.535860\pi\)
\(420\) 45.3562 2.21316
\(421\) −8.05668 −0.392659 −0.196329 0.980538i \(-0.562902\pi\)
−0.196329 + 0.980538i \(0.562902\pi\)
\(422\) −52.0210 −2.53234
\(423\) −42.1120 −2.04756
\(424\) −42.6336 −2.07047
\(425\) 3.53876 0.171655
\(426\) −67.2218 −3.25691
\(427\) −38.7713 −1.87627
\(428\) 56.6181 2.73674
\(429\) −3.20479 −0.154729
\(430\) −26.1618 −1.26163
\(431\) 5.62186 0.270796 0.135398 0.990791i \(-0.456769\pi\)
0.135398 + 0.990791i \(0.456769\pi\)
\(432\) −38.3060 −1.84300
\(433\) −2.91109 −0.139898 −0.0699491 0.997551i \(-0.522284\pi\)
−0.0699491 + 0.997551i \(0.522284\pi\)
\(434\) 8.16793 0.392073
\(435\) −16.6495 −0.798281
\(436\) −42.5877 −2.03958
\(437\) −1.95958 −0.0937392
\(438\) 7.67086 0.366528
\(439\) −3.83236 −0.182909 −0.0914543 0.995809i \(-0.529152\pi\)
−0.0914543 + 0.995809i \(0.529152\pi\)
\(440\) −4.37626 −0.208630
\(441\) 49.6161 2.36267
\(442\) −8.59693 −0.408914
\(443\) −41.4547 −1.96957 −0.984786 0.173771i \(-0.944405\pi\)
−0.984786 + 0.173771i \(0.944405\pi\)
\(444\) −112.086 −5.31937
\(445\) 7.61286 0.360884
\(446\) 27.1784 1.28694
\(447\) −13.0755 −0.618451
\(448\) 37.2040 1.75772
\(449\) 21.4808 1.01374 0.506872 0.862021i \(-0.330802\pi\)
0.506872 + 0.862021i \(0.330802\pi\)
\(450\) −17.1675 −0.809284
\(451\) −3.85837 −0.181683
\(452\) −3.19865 −0.150452
\(453\) 65.9122 3.09682
\(454\) −62.9493 −2.95436
\(455\) −3.76539 −0.176524
\(456\) 69.7044 3.26421
\(457\) 31.2183 1.46033 0.730164 0.683271i \(-0.239443\pi\)
0.730164 + 0.683271i \(0.239443\pi\)
\(458\) 8.66695 0.404980
\(459\) −46.3717 −2.16445
\(460\) −1.49299 −0.0696108
\(461\) 11.7578 0.547616 0.273808 0.961784i \(-0.411717\pi\)
0.273808 + 0.961784i \(0.411717\pi\)
\(462\) −28.6702 −1.33386
\(463\) 17.1003 0.794720 0.397360 0.917663i \(-0.369926\pi\)
0.397360 + 0.917663i \(0.369926\pi\)
\(464\) 15.2999 0.710282
\(465\) −2.88293 −0.133692
\(466\) −72.9044 −3.37723
\(467\) −12.1055 −0.560177 −0.280089 0.959974i \(-0.590364\pi\)
−0.280089 + 0.959974i \(0.590364\pi\)
\(468\) 27.3613 1.26478
\(469\) −20.6617 −0.954067
\(470\) 14.2638 0.657941
\(471\) 47.3942 2.18381
\(472\) −38.9593 −1.79325
\(473\) 10.8492 0.498848
\(474\) −40.7063 −1.86970
\(475\) 5.00704 0.229739
\(476\) −50.4560 −2.31264
\(477\) 69.3566 3.17562
\(478\) 16.3419 0.747461
\(479\) 39.0017 1.78203 0.891017 0.453971i \(-0.149993\pi\)
0.891017 + 0.453971i \(0.149993\pi\)
\(480\) −5.41875 −0.247331
\(481\) 9.30518 0.424280
\(482\) −37.0530 −1.68772
\(483\) −4.65311 −0.211724
\(484\) 3.81483 0.173401
\(485\) 14.7533 0.669914
\(486\) 61.1278 2.77281
\(487\) 27.7762 1.25866 0.629331 0.777138i \(-0.283329\pi\)
0.629331 + 0.777138i \(0.283329\pi\)
\(488\) −45.3970 −2.05503
\(489\) 63.9680 2.89273
\(490\) −16.8055 −0.759197
\(491\) −12.0816 −0.545236 −0.272618 0.962122i \(-0.587890\pi\)
−0.272618 + 0.962122i \(0.587890\pi\)
\(492\) 46.8224 2.11092
\(493\) 18.5215 0.834166
\(494\) −12.1639 −0.547279
\(495\) 7.11932 0.319990
\(496\) 2.64925 0.118955
\(497\) 32.7531 1.46918
\(498\) 40.7511 1.82610
\(499\) 21.4509 0.960276 0.480138 0.877193i \(-0.340587\pi\)
0.480138 + 0.877193i \(0.340587\pi\)
\(500\) 3.81483 0.170604
\(501\) −19.0166 −0.849598
\(502\) −26.4166 −1.17903
\(503\) −8.21145 −0.366131 −0.183065 0.983101i \(-0.558602\pi\)
−0.183065 + 0.983101i \(0.558602\pi\)
\(504\) 116.447 5.18696
\(505\) −4.83677 −0.215233
\(506\) 0.943734 0.0419541
\(507\) 38.1255 1.69321
\(508\) −66.5995 −2.95487
\(509\) −33.8208 −1.49908 −0.749541 0.661958i \(-0.769726\pi\)
−0.749541 + 0.661958i \(0.769726\pi\)
\(510\) 27.1454 1.20202
\(511\) −3.73754 −0.165339
\(512\) 30.5653 1.35081
\(513\) −65.6119 −2.89684
\(514\) 50.2632 2.21701
\(515\) −5.61388 −0.247377
\(516\) −131.659 −5.79595
\(517\) −5.91517 −0.260149
\(518\) 83.2446 3.65756
\(519\) 54.1908 2.37871
\(520\) −4.40886 −0.193341
\(521\) 29.3099 1.28409 0.642045 0.766667i \(-0.278086\pi\)
0.642045 + 0.766667i \(0.278086\pi\)
\(522\) −89.8528 −3.93275
\(523\) −44.5521 −1.94813 −0.974064 0.226274i \(-0.927346\pi\)
−0.974064 + 0.226274i \(0.927346\pi\)
\(524\) 38.0390 1.66174
\(525\) 11.8895 0.518898
\(526\) −24.9230 −1.08670
\(527\) 3.20708 0.139702
\(528\) −9.29910 −0.404691
\(529\) −22.8468 −0.993341
\(530\) −23.4919 −1.02042
\(531\) 63.3792 2.75042
\(532\) −71.3907 −3.09518
\(533\) −3.88711 −0.168369
\(534\) 58.3972 2.52709
\(535\) 14.8416 0.641658
\(536\) −24.1926 −1.04496
\(537\) −8.31809 −0.358952
\(538\) −13.3525 −0.575668
\(539\) 6.96922 0.300185
\(540\) −49.9892 −2.15119
\(541\) 19.3367 0.831352 0.415676 0.909513i \(-0.363545\pi\)
0.415676 + 0.909513i \(0.363545\pi\)
\(542\) −39.5930 −1.70067
\(543\) 60.6046 2.60079
\(544\) 6.02803 0.258450
\(545\) −11.1637 −0.478202
\(546\) −28.8837 −1.23611
\(547\) 1.41250 0.0603940 0.0301970 0.999544i \(-0.490387\pi\)
0.0301970 + 0.999544i \(0.490387\pi\)
\(548\) 21.7722 0.930062
\(549\) 73.8521 3.15193
\(550\) −2.41139 −0.102822
\(551\) 26.2063 1.11643
\(552\) −5.44829 −0.231895
\(553\) 19.8337 0.843414
\(554\) 23.4445 0.996059
\(555\) −29.3817 −1.24718
\(556\) 15.3343 0.650318
\(557\) −36.0610 −1.52795 −0.763977 0.645244i \(-0.776756\pi\)
−0.763977 + 0.645244i \(0.776756\pi\)
\(558\) −15.5584 −0.658639
\(559\) 10.9301 0.462292
\(560\) −10.9257 −0.461697
\(561\) −11.2571 −0.475276
\(562\) −70.6758 −2.98128
\(563\) 10.6282 0.447927 0.223963 0.974598i \(-0.428100\pi\)
0.223963 + 0.974598i \(0.428100\pi\)
\(564\) 71.7824 3.02258
\(565\) −0.838480 −0.0352751
\(566\) −8.00450 −0.336454
\(567\) −75.9723 −3.19054
\(568\) 38.3504 1.60915
\(569\) −29.2742 −1.22724 −0.613619 0.789603i \(-0.710287\pi\)
−0.613619 + 0.789603i \(0.710287\pi\)
\(570\) 38.4083 1.60875
\(571\) 27.3944 1.14642 0.573209 0.819409i \(-0.305698\pi\)
0.573209 + 0.819409i \(0.305698\pi\)
\(572\) 3.84325 0.160694
\(573\) 65.6993 2.74463
\(574\) −34.7743 −1.45145
\(575\) −0.391364 −0.0163210
\(576\) −70.8666 −2.95278
\(577\) 23.7670 0.989431 0.494716 0.869055i \(-0.335272\pi\)
0.494716 + 0.869055i \(0.335272\pi\)
\(578\) 10.7962 0.449061
\(579\) 49.1497 2.04259
\(580\) 19.9664 0.829059
\(581\) −19.8555 −0.823746
\(582\) 113.171 4.69108
\(583\) 9.74202 0.403473
\(584\) −4.37626 −0.181091
\(585\) 7.17236 0.296541
\(586\) −43.9005 −1.81351
\(587\) 9.63677 0.397752 0.198876 0.980025i \(-0.436271\pi\)
0.198876 + 0.980025i \(0.436271\pi\)
\(588\) −84.5735 −3.48775
\(589\) 4.53773 0.186974
\(590\) −21.4672 −0.883792
\(591\) 56.4616 2.32252
\(592\) 27.0002 1.10970
\(593\) −31.8303 −1.30711 −0.653557 0.756878i \(-0.726724\pi\)
−0.653557 + 0.756878i \(0.726724\pi\)
\(594\) 31.5988 1.29651
\(595\) −13.2263 −0.542225
\(596\) 15.6804 0.642296
\(597\) −11.2829 −0.461777
\(598\) 0.950764 0.0388796
\(599\) −1.04975 −0.0428915 −0.0214457 0.999770i \(-0.506827\pi\)
−0.0214457 + 0.999770i \(0.506827\pi\)
\(600\) 13.9213 0.568334
\(601\) 33.2189 1.35503 0.677513 0.735511i \(-0.263058\pi\)
0.677513 + 0.735511i \(0.263058\pi\)
\(602\) 97.7808 3.98525
\(603\) 39.3566 1.60273
\(604\) −79.0432 −3.21622
\(605\) 1.00000 0.0406558
\(606\) −37.1022 −1.50717
\(607\) −6.82799 −0.277140 −0.138570 0.990353i \(-0.544251\pi\)
−0.138570 + 0.990353i \(0.544251\pi\)
\(608\) 8.52912 0.345902
\(609\) 62.2281 2.52161
\(610\) −25.0145 −1.01281
\(611\) −5.95924 −0.241085
\(612\) 96.1092 3.88499
\(613\) −36.1779 −1.46121 −0.730606 0.682800i \(-0.760762\pi\)
−0.730606 + 0.682800i \(0.760762\pi\)
\(614\) −24.5415 −0.990414
\(615\) 12.2738 0.494928
\(616\) 16.3565 0.659021
\(617\) −8.30213 −0.334231 −0.167116 0.985937i \(-0.553445\pi\)
−0.167116 + 0.985937i \(0.553445\pi\)
\(618\) −43.0633 −1.73226
\(619\) −33.2151 −1.33503 −0.667514 0.744598i \(-0.732641\pi\)
−0.667514 + 0.744598i \(0.732641\pi\)
\(620\) 3.45726 0.138847
\(621\) 5.12841 0.205796
\(622\) −71.0740 −2.84981
\(623\) −28.4534 −1.13996
\(624\) −9.36838 −0.375035
\(625\) 1.00000 0.0400000
\(626\) 14.4888 0.579088
\(627\) −15.9278 −0.636096
\(628\) −56.8361 −2.26801
\(629\) 32.6853 1.30325
\(630\) 64.1643 2.55637
\(631\) −29.6197 −1.17914 −0.589572 0.807716i \(-0.700703\pi\)
−0.589572 + 0.807716i \(0.700703\pi\)
\(632\) 23.2231 0.923767
\(633\) −68.6256 −2.72762
\(634\) −5.91856 −0.235056
\(635\) −17.4581 −0.692802
\(636\) −118.222 −4.68782
\(637\) 7.02114 0.278188
\(638\) −12.6210 −0.499669
\(639\) −62.3885 −2.46805
\(640\) 20.5965 0.814147
\(641\) 5.15751 0.203710 0.101855 0.994799i \(-0.467522\pi\)
0.101855 + 0.994799i \(0.467522\pi\)
\(642\) 113.848 4.49322
\(643\) 5.44285 0.214645 0.107323 0.994224i \(-0.465772\pi\)
0.107323 + 0.994224i \(0.465772\pi\)
\(644\) 5.58010 0.219887
\(645\) −34.5124 −1.35892
\(646\) −42.7269 −1.68107
\(647\) −27.8285 −1.09405 −0.547026 0.837116i \(-0.684240\pi\)
−0.547026 + 0.837116i \(0.684240\pi\)
\(648\) −88.9554 −3.49450
\(649\) 8.90242 0.349450
\(650\) −2.42936 −0.0952873
\(651\) 10.7751 0.422308
\(652\) −76.7117 −3.00426
\(653\) 36.1732 1.41557 0.707784 0.706429i \(-0.249695\pi\)
0.707784 + 0.706429i \(0.249695\pi\)
\(654\) −85.6355 −3.34861
\(655\) 9.97137 0.389614
\(656\) −11.2789 −0.440369
\(657\) 7.11932 0.277751
\(658\) −53.3116 −2.07830
\(659\) −42.9499 −1.67309 −0.836546 0.547897i \(-0.815429\pi\)
−0.836546 + 0.547897i \(0.815429\pi\)
\(660\) −12.1353 −0.472366
\(661\) 10.6102 0.412687 0.206344 0.978480i \(-0.433843\pi\)
0.206344 + 0.978480i \(0.433843\pi\)
\(662\) 52.6131 2.04487
\(663\) −11.3410 −0.440447
\(664\) −23.2487 −0.902224
\(665\) −18.7140 −0.725698
\(666\) −158.565 −6.14429
\(667\) −2.04836 −0.0793127
\(668\) 22.8051 0.882355
\(669\) 35.8535 1.38618
\(670\) −13.3305 −0.515004
\(671\) 10.3735 0.400463
\(672\) 20.2528 0.781269
\(673\) −19.2915 −0.743633 −0.371817 0.928306i \(-0.621265\pi\)
−0.371817 + 0.928306i \(0.621265\pi\)
\(674\) −3.49325 −0.134555
\(675\) −13.1039 −0.504371
\(676\) −45.7209 −1.75849
\(677\) 29.1030 1.11852 0.559259 0.828993i \(-0.311086\pi\)
0.559259 + 0.828993i \(0.311086\pi\)
\(678\) −6.43186 −0.247014
\(679\) −55.1412 −2.11612
\(680\) −15.4866 −0.593882
\(681\) −83.0422 −3.18218
\(682\) −2.18537 −0.0836823
\(683\) 36.1708 1.38404 0.692019 0.721879i \(-0.256721\pi\)
0.692019 + 0.721879i \(0.256721\pi\)
\(684\) 135.986 5.19956
\(685\) 5.70726 0.218063
\(686\) −0.277439 −0.0105927
\(687\) 11.4334 0.436210
\(688\) 31.7150 1.20912
\(689\) 9.81459 0.373906
\(690\) −3.00210 −0.114288
\(691\) −12.2018 −0.464178 −0.232089 0.972695i \(-0.574556\pi\)
−0.232089 + 0.972695i \(0.574556\pi\)
\(692\) −64.9867 −2.47042
\(693\) −26.6088 −1.01078
\(694\) −15.2425 −0.578599
\(695\) 4.01965 0.152474
\(696\) 72.8624 2.76184
\(697\) −13.6539 −0.517177
\(698\) −24.9842 −0.945667
\(699\) −96.1747 −3.63766
\(700\) −14.2581 −0.538904
\(701\) 15.7866 0.596251 0.298125 0.954527i \(-0.403639\pi\)
0.298125 + 0.954527i \(0.403639\pi\)
\(702\) 31.8342 1.20150
\(703\) 46.2469 1.74423
\(704\) −9.95412 −0.375160
\(705\) 18.8167 0.708677
\(706\) −29.3921 −1.10619
\(707\) 18.0776 0.679879
\(708\) −108.033 −4.06015
\(709\) −41.8273 −1.57086 −0.785428 0.618953i \(-0.787557\pi\)
−0.785428 + 0.618953i \(0.787557\pi\)
\(710\) 21.1317 0.793059
\(711\) −37.7795 −1.41684
\(712\) −33.3159 −1.24856
\(713\) −0.354682 −0.0132829
\(714\) −101.457 −3.79693
\(715\) 1.00745 0.0376765
\(716\) 9.97522 0.372791
\(717\) 21.5581 0.805101
\(718\) 55.7718 2.08138
\(719\) −0.866060 −0.0322986 −0.0161493 0.999870i \(-0.505141\pi\)
−0.0161493 + 0.999870i \(0.505141\pi\)
\(720\) 20.8115 0.775600
\(721\) 20.9821 0.781414
\(722\) −14.6382 −0.544778
\(723\) −48.8799 −1.81786
\(724\) −72.6783 −2.70107
\(725\) 5.23389 0.194382
\(726\) 7.67086 0.284692
\(727\) 7.80317 0.289404 0.144702 0.989475i \(-0.453778\pi\)
0.144702 + 0.989475i \(0.453778\pi\)
\(728\) 16.4783 0.610727
\(729\) 19.6588 0.728103
\(730\) −2.41139 −0.0892497
\(731\) 38.3929 1.42001
\(732\) −125.885 −4.65285
\(733\) 6.07759 0.224481 0.112240 0.993681i \(-0.464197\pi\)
0.112240 + 0.993681i \(0.464197\pi\)
\(734\) 52.6052 1.94169
\(735\) −22.1697 −0.817742
\(736\) −0.666660 −0.0245734
\(737\) 5.52814 0.203632
\(738\) 66.2385 2.43827
\(739\) −19.8288 −0.729414 −0.364707 0.931122i \(-0.618831\pi\)
−0.364707 + 0.931122i \(0.618831\pi\)
\(740\) 35.2352 1.29527
\(741\) −16.0465 −0.589483
\(742\) 87.8018 3.22330
\(743\) 21.2868 0.780936 0.390468 0.920617i \(-0.372313\pi\)
0.390468 + 0.920617i \(0.372313\pi\)
\(744\) 12.6164 0.462541
\(745\) 4.11039 0.150593
\(746\) −35.3375 −1.29380
\(747\) 37.8211 1.38380
\(748\) 13.4998 0.493600
\(749\) −55.4711 −2.02687
\(750\) 7.67086 0.280100
\(751\) 50.8748 1.85645 0.928223 0.372024i \(-0.121336\pi\)
0.928223 + 0.372024i \(0.121336\pi\)
\(752\) −17.2915 −0.630556
\(753\) −34.8485 −1.26995
\(754\) −12.7150 −0.463053
\(755\) −20.7200 −0.754078
\(756\) 186.837 6.79519
\(757\) 28.2930 1.02833 0.514163 0.857693i \(-0.328103\pi\)
0.514163 + 0.857693i \(0.328103\pi\)
\(758\) −55.1181 −2.00198
\(759\) 1.24496 0.0451893
\(760\) −21.9121 −0.794836
\(761\) 18.3474 0.665094 0.332547 0.943087i \(-0.392092\pi\)
0.332547 + 0.943087i \(0.392092\pi\)
\(762\) −133.918 −4.85135
\(763\) 41.7249 1.51054
\(764\) −78.7879 −2.85045
\(765\) 25.1936 0.910877
\(766\) −9.64439 −0.348466
\(767\) 8.96874 0.323842
\(768\) 94.6628 3.41585
\(769\) −41.5561 −1.49855 −0.749275 0.662259i \(-0.769598\pi\)
−0.749275 + 0.662259i \(0.769598\pi\)
\(770\) 9.01269 0.324795
\(771\) 66.3067 2.38798
\(772\) −58.9414 −2.12135
\(773\) 9.25444 0.332859 0.166430 0.986053i \(-0.446776\pi\)
0.166430 + 0.986053i \(0.446776\pi\)
\(774\) −186.254 −6.69477
\(775\) 0.906270 0.0325542
\(776\) −64.5645 −2.31773
\(777\) 109.815 3.93961
\(778\) 32.7536 1.17427
\(779\) −19.3190 −0.692175
\(780\) −12.2257 −0.437750
\(781\) −8.76327 −0.313574
\(782\) 3.33965 0.119426
\(783\) −68.5845 −2.45101
\(784\) 20.3727 0.727597
\(785\) −14.8987 −0.531759
\(786\) 76.4890 2.72827
\(787\) 29.6165 1.05572 0.527858 0.849333i \(-0.322996\pi\)
0.527858 + 0.849333i \(0.322996\pi\)
\(788\) −67.7099 −2.41207
\(789\) −32.8782 −1.17050
\(790\) 12.7963 0.455273
\(791\) 3.13385 0.111427
\(792\) −31.1560 −1.10708
\(793\) 10.4508 0.371117
\(794\) 44.8933 1.59320
\(795\) −30.9902 −1.09911
\(796\) 13.5306 0.479581
\(797\) 15.2819 0.541313 0.270656 0.962676i \(-0.412759\pi\)
0.270656 + 0.962676i \(0.412759\pi\)
\(798\) −143.553 −5.08171
\(799\) −20.9324 −0.740535
\(800\) 1.70343 0.0602252
\(801\) 54.1984 1.91501
\(802\) −51.7425 −1.82709
\(803\) 1.00000 0.0352892
\(804\) −67.0857 −2.36593
\(805\) 1.46274 0.0515548
\(806\) −2.20166 −0.0775500
\(807\) −17.6145 −0.620060
\(808\) 21.1670 0.744651
\(809\) −17.1012 −0.601246 −0.300623 0.953743i \(-0.597195\pi\)
−0.300623 + 0.953743i \(0.597195\pi\)
\(810\) −49.0160 −1.72224
\(811\) 15.3172 0.537860 0.268930 0.963160i \(-0.413330\pi\)
0.268930 + 0.963160i \(0.413330\pi\)
\(812\) −74.6252 −2.61883
\(813\) −52.2307 −1.83181
\(814\) −22.2725 −0.780652
\(815\) −20.1088 −0.704382
\(816\) −32.9073 −1.15199
\(817\) 54.3225 1.90050
\(818\) −16.7334 −0.585070
\(819\) −26.8070 −0.936712
\(820\) −14.7190 −0.514010
\(821\) −1.62592 −0.0567449 −0.0283725 0.999597i \(-0.509032\pi\)
−0.0283725 + 0.999597i \(0.509032\pi\)
\(822\) 43.7796 1.52699
\(823\) −53.2751 −1.85705 −0.928526 0.371268i \(-0.878923\pi\)
−0.928526 + 0.371268i \(0.878923\pi\)
\(824\) 24.5678 0.855860
\(825\) −3.18109 −0.110751
\(826\) 80.2347 2.79172
\(827\) 25.4849 0.886195 0.443098 0.896473i \(-0.353879\pi\)
0.443098 + 0.896473i \(0.353879\pi\)
\(828\) −10.6291 −0.369385
\(829\) −23.2328 −0.806908 −0.403454 0.915000i \(-0.632190\pi\)
−0.403454 + 0.915000i \(0.632190\pi\)
\(830\) −12.8104 −0.444656
\(831\) 30.9277 1.07287
\(832\) −10.0283 −0.347668
\(833\) 24.6624 0.854502
\(834\) 30.8342 1.06770
\(835\) 5.97801 0.206878
\(836\) 19.1010 0.660621
\(837\) −11.8757 −0.410484
\(838\) 11.0981 0.383379
\(839\) −13.3284 −0.460147 −0.230073 0.973173i \(-0.573897\pi\)
−0.230073 + 0.973173i \(0.573897\pi\)
\(840\) −52.0313 −1.79525
\(841\) −1.60641 −0.0553934
\(842\) 19.4278 0.669528
\(843\) −93.2348 −3.21118
\(844\) 82.2972 2.83279
\(845\) −11.9850 −0.412298
\(846\) 101.549 3.49132
\(847\) −3.73754 −0.128423
\(848\) 28.4783 0.977949
\(849\) −10.5595 −0.362400
\(850\) −8.53336 −0.292692
\(851\) −3.61479 −0.123913
\(852\) 106.345 3.64332
\(853\) 42.5793 1.45789 0.728944 0.684573i \(-0.240011\pi\)
0.728944 + 0.684573i \(0.240011\pi\)
\(854\) 93.4929 3.19926
\(855\) 35.6467 1.21909
\(856\) −64.9507 −2.21997
\(857\) −7.05880 −0.241124 −0.120562 0.992706i \(-0.538470\pi\)
−0.120562 + 0.992706i \(0.538470\pi\)
\(858\) 7.72801 0.263830
\(859\) 40.3688 1.37737 0.688683 0.725063i \(-0.258189\pi\)
0.688683 + 0.725063i \(0.258189\pi\)
\(860\) 41.3879 1.41132
\(861\) −45.8739 −1.56338
\(862\) −13.5565 −0.461737
\(863\) −54.9782 −1.87148 −0.935741 0.352689i \(-0.885267\pi\)
−0.935741 + 0.352689i \(0.885267\pi\)
\(864\) −22.3216 −0.759396
\(865\) −17.0353 −0.579218
\(866\) 7.01980 0.238542
\(867\) 14.2422 0.483690
\(868\) −12.9217 −0.438590
\(869\) −5.30661 −0.180015
\(870\) 40.1484 1.36116
\(871\) 5.56933 0.188709
\(872\) 48.8554 1.65445
\(873\) 105.034 3.55485
\(874\) 4.72531 0.159836
\(875\) −3.73754 −0.126352
\(876\) −12.1353 −0.410014
\(877\) −13.3797 −0.451799 −0.225900 0.974151i \(-0.572532\pi\)
−0.225900 + 0.974151i \(0.572532\pi\)
\(878\) 9.24134 0.311880
\(879\) −57.9131 −1.95336
\(880\) 2.92324 0.0985425
\(881\) −22.2446 −0.749438 −0.374719 0.927138i \(-0.622261\pi\)
−0.374719 + 0.927138i \(0.622261\pi\)
\(882\) −119.644 −4.02862
\(883\) −29.0128 −0.976359 −0.488180 0.872743i \(-0.662339\pi\)
−0.488180 + 0.872743i \(0.662339\pi\)
\(884\) 13.6003 0.457429
\(885\) −28.3194 −0.951945
\(886\) 99.9636 3.35834
\(887\) 54.2574 1.82178 0.910892 0.412644i \(-0.135395\pi\)
0.910892 + 0.412644i \(0.135395\pi\)
\(888\) 128.582 4.31493
\(889\) 65.2502 2.18842
\(890\) −18.3576 −0.615348
\(891\) 20.3268 0.680974
\(892\) −42.9963 −1.43962
\(893\) −29.6175 −0.991112
\(894\) 31.5303 1.05453
\(895\) 2.61486 0.0874050
\(896\) −76.9802 −2.57173
\(897\) 1.25424 0.0418778
\(898\) −51.7988 −1.72855
\(899\) 4.74332 0.158198
\(900\) 27.1590 0.905299
\(901\) 34.4747 1.14852
\(902\) 9.30405 0.309791
\(903\) 128.991 4.29257
\(904\) 3.66941 0.122043
\(905\) −19.0515 −0.633295
\(906\) −158.940 −5.28044
\(907\) −6.44343 −0.213951 −0.106975 0.994262i \(-0.534117\pi\)
−0.106975 + 0.994262i \(0.534117\pi\)
\(908\) 99.5858 3.30487
\(909\) −34.4345 −1.14212
\(910\) 9.07983 0.300993
\(911\) 17.1200 0.567213 0.283606 0.958941i \(-0.408469\pi\)
0.283606 + 0.958941i \(0.408469\pi\)
\(912\) −46.5609 −1.54179
\(913\) 5.31245 0.175817
\(914\) −75.2796 −2.49003
\(915\) −32.9989 −1.09091
\(916\) −13.7111 −0.453028
\(917\) −37.2684 −1.23071
\(918\) 111.821 3.69063
\(919\) 40.2048 1.32623 0.663117 0.748516i \(-0.269233\pi\)
0.663117 + 0.748516i \(0.269233\pi\)
\(920\) 1.71271 0.0564665
\(921\) −32.3749 −1.06679
\(922\) −28.3527 −0.933747
\(923\) −8.82855 −0.290595
\(924\) 45.3562 1.49211
\(925\) 9.23637 0.303690
\(926\) −41.2357 −1.35509
\(927\) −39.9670 −1.31269
\(928\) 8.91555 0.292667
\(929\) −11.7905 −0.386835 −0.193418 0.981117i \(-0.561957\pi\)
−0.193418 + 0.981117i \(0.561957\pi\)
\(930\) 6.95187 0.227961
\(931\) 34.8951 1.14364
\(932\) 115.335 3.77791
\(933\) −93.7601 −3.06957
\(934\) 29.1912 0.955166
\(935\) 3.53876 0.115730
\(936\) −31.3881 −1.02595
\(937\) 9.31105 0.304179 0.152089 0.988367i \(-0.451400\pi\)
0.152089 + 0.988367i \(0.451400\pi\)
\(938\) 49.8234 1.62679
\(939\) 19.1134 0.623744
\(940\) −22.5654 −0.736001
\(941\) 5.53201 0.180338 0.0901692 0.995926i \(-0.471259\pi\)
0.0901692 + 0.995926i \(0.471259\pi\)
\(942\) −114.286 −3.72365
\(943\) 1.51003 0.0491732
\(944\) 26.0239 0.847007
\(945\) 48.9765 1.59321
\(946\) −26.1618 −0.850593
\(947\) 14.4653 0.470058 0.235029 0.971988i \(-0.424482\pi\)
0.235029 + 0.971988i \(0.424482\pi\)
\(948\) 64.3973 2.09153
\(949\) 1.00745 0.0327032
\(950\) −12.0739 −0.391731
\(951\) −7.80770 −0.253182
\(952\) 57.8817 1.87596
\(953\) −23.6932 −0.767497 −0.383749 0.923438i \(-0.625367\pi\)
−0.383749 + 0.923438i \(0.625367\pi\)
\(954\) −167.246 −5.41479
\(955\) −20.6531 −0.668318
\(956\) −25.8529 −0.836142
\(957\) −16.6495 −0.538201
\(958\) −94.0485 −3.03857
\(959\) −21.3311 −0.688817
\(960\) 31.6649 1.02198
\(961\) −30.1787 −0.973506
\(962\) −22.4385 −0.723445
\(963\) 105.662 3.40492
\(964\) 58.6178 1.88795
\(965\) −15.4506 −0.497372
\(966\) 11.2205 0.361013
\(967\) −22.9106 −0.736754 −0.368377 0.929677i \(-0.620086\pi\)
−0.368377 + 0.929677i \(0.620086\pi\)
\(968\) −4.37626 −0.140658
\(969\) −56.3648 −1.81070
\(970\) −35.5761 −1.14228
\(971\) −26.5866 −0.853205 −0.426603 0.904439i \(-0.640290\pi\)
−0.426603 + 0.904439i \(0.640290\pi\)
\(972\) −96.7041 −3.10179
\(973\) −15.0236 −0.481635
\(974\) −66.9795 −2.14616
\(975\) −3.20479 −0.102635
\(976\) 30.3242 0.970654
\(977\) 45.8303 1.46624 0.733120 0.680099i \(-0.238063\pi\)
0.733120 + 0.680099i \(0.238063\pi\)
\(978\) −154.252 −4.93244
\(979\) 7.61286 0.243308
\(980\) 26.5863 0.849270
\(981\) −79.4783 −2.53755
\(982\) 29.1336 0.929690
\(983\) −36.5768 −1.16662 −0.583310 0.812250i \(-0.698243\pi\)
−0.583310 + 0.812250i \(0.698243\pi\)
\(984\) −53.7134 −1.71232
\(985\) −17.7491 −0.565535
\(986\) −44.6627 −1.42235
\(987\) −70.3282 −2.23857
\(988\) 19.2433 0.612210
\(989\) −4.24600 −0.135015
\(990\) −17.1675 −0.545619
\(991\) 18.2871 0.580907 0.290454 0.956889i \(-0.406194\pi\)
0.290454 + 0.956889i \(0.406194\pi\)
\(992\) 1.54376 0.0490146
\(993\) 69.4067 2.20255
\(994\) −78.9806 −2.50511
\(995\) 3.54686 0.112443
\(996\) −64.4682 −2.04275
\(997\) 11.9290 0.377795 0.188898 0.981997i \(-0.439509\pi\)
0.188898 + 0.981997i \(0.439509\pi\)
\(998\) −51.7267 −1.63738
\(999\) −121.033 −3.82931
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 \(a_p\))