Properties

Label 8015.2.a.l.1.5
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.41590 q^{2}\) \(+1.84179 q^{3}\) \(+3.83658 q^{4}\) \(-1.00000 q^{5}\) \(-4.44959 q^{6}\) \(-1.00000 q^{7}\) \(-4.43701 q^{8}\) \(+0.392199 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.41590 q^{2}\) \(+1.84179 q^{3}\) \(+3.83658 q^{4}\) \(-1.00000 q^{5}\) \(-4.44959 q^{6}\) \(-1.00000 q^{7}\) \(-4.43701 q^{8}\) \(+0.392199 q^{9}\) \(+2.41590 q^{10}\) \(+5.68645 q^{11}\) \(+7.06619 q^{12}\) \(-3.60089 q^{13}\) \(+2.41590 q^{14}\) \(-1.84179 q^{15}\) \(+3.04621 q^{16}\) \(+3.68593 q^{17}\) \(-0.947514 q^{18}\) \(-1.18056 q^{19}\) \(-3.83658 q^{20}\) \(-1.84179 q^{21}\) \(-13.7379 q^{22}\) \(-1.47328 q^{23}\) \(-8.17204 q^{24}\) \(+1.00000 q^{25}\) \(+8.69939 q^{26}\) \(-4.80303 q^{27}\) \(-3.83658 q^{28}\) \(+0.109372 q^{29}\) \(+4.44959 q^{30}\) \(-0.502367 q^{31}\) \(+1.51468 q^{32}\) \(+10.4733 q^{33}\) \(-8.90486 q^{34}\) \(+1.00000 q^{35}\) \(+1.50470 q^{36}\) \(-5.90785 q^{37}\) \(+2.85212 q^{38}\) \(-6.63208 q^{39}\) \(+4.43701 q^{40}\) \(-12.3065 q^{41}\) \(+4.44959 q^{42}\) \(+2.28127 q^{43}\) \(+21.8165 q^{44}\) \(-0.392199 q^{45}\) \(+3.55930 q^{46}\) \(+4.46248 q^{47}\) \(+5.61048 q^{48}\) \(+1.00000 q^{49}\) \(-2.41590 q^{50}\) \(+6.78873 q^{51}\) \(-13.8151 q^{52}\) \(+10.4858 q^{53}\) \(+11.6036 q^{54}\) \(-5.68645 q^{55}\) \(+4.43701 q^{56}\) \(-2.17435 q^{57}\) \(-0.264233 q^{58}\) \(-4.74028 q^{59}\) \(-7.06619 q^{60}\) \(-10.9072 q^{61}\) \(+1.21367 q^{62}\) \(-0.392199 q^{63}\) \(-9.75172 q^{64}\) \(+3.60089 q^{65}\) \(-25.3023 q^{66}\) \(+15.8281 q^{67}\) \(+14.1414 q^{68}\) \(-2.71347 q^{69}\) \(-2.41590 q^{70}\) \(+5.08199 q^{71}\) \(-1.74019 q^{72}\) \(+9.19853 q^{73}\) \(+14.2728 q^{74}\) \(+1.84179 q^{75}\) \(-4.52932 q^{76}\) \(-5.68645 q^{77}\) \(+16.0225 q^{78}\) \(-2.03869 q^{79}\) \(-3.04621 q^{80}\) \(-10.0228 q^{81}\) \(+29.7313 q^{82}\) \(+11.0455 q^{83}\) \(-7.06619 q^{84}\) \(-3.68593 q^{85}\) \(-5.51132 q^{86}\) \(+0.201441 q^{87}\) \(-25.2308 q^{88}\) \(+7.76347 q^{89}\) \(+0.947514 q^{90}\) \(+3.60089 q^{91}\) \(-5.65235 q^{92}\) \(-0.925256 q^{93}\) \(-10.7809 q^{94}\) \(+1.18056 q^{95}\) \(+2.78972 q^{96}\) \(+19.1651 q^{97}\) \(-2.41590 q^{98}\) \(+2.23022 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 37q^{12} \) \(\mathstrut +\mathstrut 31q^{13} \) \(\mathstrut -\mathstrut 2q^{14} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut +\mathstrut 64q^{16} \) \(\mathstrut +\mathstrut 30q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 64q^{20} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 7q^{22} \) \(\mathstrut +\mathstrut 29q^{24} \) \(\mathstrut +\mathstrut 62q^{25} \) \(\mathstrut +\mathstrut 59q^{27} \) \(\mathstrut -\mathstrut 64q^{28} \) \(\mathstrut -\mathstrut 29q^{29} \) \(\mathstrut -\mathstrut 3q^{30} \) \(\mathstrut +\mathstrut 20q^{31} \) \(\mathstrut +\mathstrut 22q^{32} \) \(\mathstrut +\mathstrut 72q^{33} \) \(\mathstrut +\mathstrut 13q^{34} \) \(\mathstrut +\mathstrut 62q^{35} \) \(\mathstrut +\mathstrut 53q^{36} \) \(\mathstrut +\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut -\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 13q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 44q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 58q^{47} \) \(\mathstrut +\mathstrut 64q^{48} \) \(\mathstrut +\mathstrut 62q^{49} \) \(\mathstrut +\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut +\mathstrut 82q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 13q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 21q^{57} \) \(\mathstrut +\mathstrut 18q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut -\mathstrut 37q^{60} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut +\mathstrut 48q^{62} \) \(\mathstrut -\mathstrut 69q^{63} \) \(\mathstrut +\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 31q^{65} \) \(\mathstrut +\mathstrut 25q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 65q^{68} \) \(\mathstrut +\mathstrut 27q^{69} \) \(\mathstrut +\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 35q^{71} \) \(\mathstrut +\mathstrut 53q^{72} \) \(\mathstrut +\mathstrut 116q^{73} \) \(\mathstrut -\mathstrut 69q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 65q^{76} \) \(\mathstrut +\mathstrut 13q^{77} \) \(\mathstrut +\mathstrut 102q^{78} \) \(\mathstrut -\mathstrut 83q^{79} \) \(\mathstrut -\mathstrut 64q^{80} \) \(\mathstrut +\mathstrut 126q^{81} \) \(\mathstrut +\mathstrut 71q^{82} \) \(\mathstrut +\mathstrut 84q^{83} \) \(\mathstrut -\mathstrut 37q^{84} \) \(\mathstrut -\mathstrut 30q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut +\mathstrut 20q^{88} \) \(\mathstrut -\mathstrut 16q^{89} \) \(\mathstrut -\mathstrut 18q^{90} \) \(\mathstrut -\mathstrut 31q^{91} \) \(\mathstrut +\mathstrut 19q^{92} \) \(\mathstrut +\mathstrut 65q^{93} \) \(\mathstrut +\mathstrut 54q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 17q^{96} \) \(\mathstrut +\mathstrut 155q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.41590 −1.70830 −0.854150 0.520026i \(-0.825922\pi\)
−0.854150 + 0.520026i \(0.825922\pi\)
\(3\) 1.84179 1.06336 0.531680 0.846946i \(-0.321561\pi\)
0.531680 + 0.846946i \(0.321561\pi\)
\(4\) 3.83658 1.91829
\(5\) −1.00000 −0.447214
\(6\) −4.44959 −1.81654
\(7\) −1.00000 −0.377964
\(8\) −4.43701 −1.56872
\(9\) 0.392199 0.130733
\(10\) 2.41590 0.763975
\(11\) 5.68645 1.71453 0.857264 0.514877i \(-0.172163\pi\)
0.857264 + 0.514877i \(0.172163\pi\)
\(12\) 7.06619 2.03983
\(13\) −3.60089 −0.998706 −0.499353 0.866399i \(-0.666429\pi\)
−0.499353 + 0.866399i \(0.666429\pi\)
\(14\) 2.41590 0.645677
\(15\) −1.84179 −0.475549
\(16\) 3.04621 0.761552
\(17\) 3.68593 0.893971 0.446985 0.894541i \(-0.352498\pi\)
0.446985 + 0.894541i \(0.352498\pi\)
\(18\) −0.947514 −0.223331
\(19\) −1.18056 −0.270839 −0.135420 0.990788i \(-0.543238\pi\)
−0.135420 + 0.990788i \(0.543238\pi\)
\(20\) −3.83658 −0.857886
\(21\) −1.84179 −0.401912
\(22\) −13.7379 −2.92893
\(23\) −1.47328 −0.307200 −0.153600 0.988133i \(-0.549087\pi\)
−0.153600 + 0.988133i \(0.549087\pi\)
\(24\) −8.17204 −1.66811
\(25\) 1.00000 0.200000
\(26\) 8.69939 1.70609
\(27\) −4.80303 −0.924343
\(28\) −3.83658 −0.725046
\(29\) 0.109372 0.0203099 0.0101550 0.999948i \(-0.496768\pi\)
0.0101550 + 0.999948i \(0.496768\pi\)
\(30\) 4.44959 0.812380
\(31\) −0.502367 −0.0902278 −0.0451139 0.998982i \(-0.514365\pi\)
−0.0451139 + 0.998982i \(0.514365\pi\)
\(32\) 1.51468 0.267760
\(33\) 10.4733 1.82316
\(34\) −8.90486 −1.52717
\(35\) 1.00000 0.169031
\(36\) 1.50470 0.250784
\(37\) −5.90785 −0.971245 −0.485622 0.874169i \(-0.661407\pi\)
−0.485622 + 0.874169i \(0.661407\pi\)
\(38\) 2.85212 0.462675
\(39\) −6.63208 −1.06198
\(40\) 4.43701 0.701552
\(41\) −12.3065 −1.92195 −0.960975 0.276634i \(-0.910781\pi\)
−0.960975 + 0.276634i \(0.910781\pi\)
\(42\) 4.44959 0.686587
\(43\) 2.28127 0.347890 0.173945 0.984755i \(-0.444349\pi\)
0.173945 + 0.984755i \(0.444349\pi\)
\(44\) 21.8165 3.28896
\(45\) −0.392199 −0.0584655
\(46\) 3.55930 0.524789
\(47\) 4.46248 0.650920 0.325460 0.945556i \(-0.394481\pi\)
0.325460 + 0.945556i \(0.394481\pi\)
\(48\) 5.61048 0.809803
\(49\) 1.00000 0.142857
\(50\) −2.41590 −0.341660
\(51\) 6.78873 0.950612
\(52\) −13.8151 −1.91581
\(53\) 10.4858 1.44034 0.720168 0.693800i \(-0.244065\pi\)
0.720168 + 0.693800i \(0.244065\pi\)
\(54\) 11.6036 1.57906
\(55\) −5.68645 −0.766760
\(56\) 4.43701 0.592920
\(57\) −2.17435 −0.287999
\(58\) −0.264233 −0.0346955
\(59\) −4.74028 −0.617132 −0.308566 0.951203i \(-0.599849\pi\)
−0.308566 + 0.951203i \(0.599849\pi\)
\(60\) −7.06619 −0.912241
\(61\) −10.9072 −1.39652 −0.698262 0.715843i \(-0.746043\pi\)
−0.698262 + 0.715843i \(0.746043\pi\)
\(62\) 1.21367 0.154136
\(63\) −0.392199 −0.0494124
\(64\) −9.75172 −1.21897
\(65\) 3.60089 0.446635
\(66\) −25.3023 −3.11450
\(67\) 15.8281 1.93371 0.966855 0.255325i \(-0.0821823\pi\)
0.966855 + 0.255325i \(0.0821823\pi\)
\(68\) 14.1414 1.71490
\(69\) −2.71347 −0.326664
\(70\) −2.41590 −0.288756
\(71\) 5.08199 0.603122 0.301561 0.953447i \(-0.402492\pi\)
0.301561 + 0.953447i \(0.402492\pi\)
\(72\) −1.74019 −0.205083
\(73\) 9.19853 1.07661 0.538303 0.842751i \(-0.319066\pi\)
0.538303 + 0.842751i \(0.319066\pi\)
\(74\) 14.2728 1.65918
\(75\) 1.84179 0.212672
\(76\) −4.52932 −0.519549
\(77\) −5.68645 −0.648031
\(78\) 16.0225 1.81419
\(79\) −2.03869 −0.229370 −0.114685 0.993402i \(-0.536586\pi\)
−0.114685 + 0.993402i \(0.536586\pi\)
\(80\) −3.04621 −0.340576
\(81\) −10.0228 −1.11364
\(82\) 29.7313 3.28327
\(83\) 11.0455 1.21240 0.606199 0.795313i \(-0.292694\pi\)
0.606199 + 0.795313i \(0.292694\pi\)
\(84\) −7.06619 −0.770985
\(85\) −3.68593 −0.399796
\(86\) −5.51132 −0.594300
\(87\) 0.201441 0.0215967
\(88\) −25.2308 −2.68961
\(89\) 7.76347 0.822926 0.411463 0.911426i \(-0.365018\pi\)
0.411463 + 0.911426i \(0.365018\pi\)
\(90\) 0.947514 0.0998767
\(91\) 3.60089 0.377475
\(92\) −5.65235 −0.589299
\(93\) −0.925256 −0.0959446
\(94\) −10.7809 −1.11197
\(95\) 1.18056 0.121123
\(96\) 2.78972 0.284725
\(97\) 19.1651 1.94592 0.972959 0.230980i \(-0.0741931\pi\)
0.972959 + 0.230980i \(0.0741931\pi\)
\(98\) −2.41590 −0.244043
\(99\) 2.23022 0.224145
\(100\) 3.83658 0.383658
\(101\) 11.0929 1.10378 0.551892 0.833916i \(-0.313906\pi\)
0.551892 + 0.833916i \(0.313906\pi\)
\(102\) −16.4009 −1.62393
\(103\) 12.9130 1.27236 0.636179 0.771542i \(-0.280514\pi\)
0.636179 + 0.771542i \(0.280514\pi\)
\(104\) 15.9772 1.56669
\(105\) 1.84179 0.179741
\(106\) −25.3327 −2.46053
\(107\) 2.35579 0.227743 0.113871 0.993495i \(-0.463675\pi\)
0.113871 + 0.993495i \(0.463675\pi\)
\(108\) −18.4272 −1.77316
\(109\) −9.01416 −0.863400 −0.431700 0.902017i \(-0.642086\pi\)
−0.431700 + 0.902017i \(0.642086\pi\)
\(110\) 13.7379 1.30986
\(111\) −10.8810 −1.03278
\(112\) −3.04621 −0.287839
\(113\) −11.5859 −1.08991 −0.544954 0.838466i \(-0.683453\pi\)
−0.544954 + 0.838466i \(0.683453\pi\)
\(114\) 5.25301 0.491990
\(115\) 1.47328 0.137384
\(116\) 0.419616 0.0389604
\(117\) −1.41226 −0.130564
\(118\) 11.4521 1.05425
\(119\) −3.68593 −0.337889
\(120\) 8.17204 0.746002
\(121\) 21.3357 1.93961
\(122\) 26.3507 2.38568
\(123\) −22.6660 −2.04372
\(124\) −1.92737 −0.173083
\(125\) −1.00000 −0.0894427
\(126\) 0.947514 0.0844112
\(127\) 7.09207 0.629320 0.314660 0.949204i \(-0.398110\pi\)
0.314660 + 0.949204i \(0.398110\pi\)
\(128\) 20.5299 1.81460
\(129\) 4.20162 0.369932
\(130\) −8.69939 −0.762987
\(131\) 8.23872 0.719820 0.359910 0.932987i \(-0.382807\pi\)
0.359910 + 0.932987i \(0.382807\pi\)
\(132\) 40.1815 3.49735
\(133\) 1.18056 0.102368
\(134\) −38.2392 −3.30336
\(135\) 4.80303 0.413379
\(136\) −16.3545 −1.40239
\(137\) −22.8731 −1.95418 −0.977089 0.212833i \(-0.931731\pi\)
−0.977089 + 0.212833i \(0.931731\pi\)
\(138\) 6.55548 0.558040
\(139\) −20.9188 −1.77431 −0.887155 0.461472i \(-0.847321\pi\)
−0.887155 + 0.461472i \(0.847321\pi\)
\(140\) 3.83658 0.324250
\(141\) 8.21897 0.692162
\(142\) −12.2776 −1.03031
\(143\) −20.4762 −1.71231
\(144\) 1.19472 0.0995598
\(145\) −0.109372 −0.00908287
\(146\) −22.2227 −1.83917
\(147\) 1.84179 0.151908
\(148\) −22.6660 −1.86313
\(149\) −18.5957 −1.52342 −0.761709 0.647920i \(-0.775639\pi\)
−0.761709 + 0.647920i \(0.775639\pi\)
\(150\) −4.44959 −0.363308
\(151\) 14.5397 1.18322 0.591611 0.806223i \(-0.298492\pi\)
0.591611 + 0.806223i \(0.298492\pi\)
\(152\) 5.23816 0.424870
\(153\) 1.44562 0.116871
\(154\) 13.7379 1.10703
\(155\) 0.502367 0.0403511
\(156\) −25.4445 −2.03719
\(157\) 6.38544 0.509614 0.254807 0.966992i \(-0.417988\pi\)
0.254807 + 0.966992i \(0.417988\pi\)
\(158\) 4.92527 0.391834
\(159\) 19.3127 1.53159
\(160\) −1.51468 −0.119746
\(161\) 1.47328 0.116111
\(162\) 24.2140 1.90244
\(163\) 0.772563 0.0605118 0.0302559 0.999542i \(-0.490368\pi\)
0.0302559 + 0.999542i \(0.490368\pi\)
\(164\) −47.2149 −3.68686
\(165\) −10.4733 −0.815341
\(166\) −26.6848 −2.07114
\(167\) −3.11243 −0.240847 −0.120424 0.992723i \(-0.538425\pi\)
−0.120424 + 0.992723i \(0.538425\pi\)
\(168\) 8.17204 0.630487
\(169\) −0.0336215 −0.00258627
\(170\) 8.90486 0.682971
\(171\) −0.463014 −0.0354076
\(172\) 8.75227 0.667354
\(173\) −16.6843 −1.26849 −0.634244 0.773133i \(-0.718688\pi\)
−0.634244 + 0.773133i \(0.718688\pi\)
\(174\) −0.486662 −0.0368937
\(175\) −1.00000 −0.0755929
\(176\) 17.3221 1.30570
\(177\) −8.73062 −0.656233
\(178\) −18.7558 −1.40581
\(179\) 9.82181 0.734117 0.367058 0.930198i \(-0.380365\pi\)
0.367058 + 0.930198i \(0.380365\pi\)
\(180\) −1.50470 −0.112154
\(181\) 10.7755 0.800934 0.400467 0.916311i \(-0.368848\pi\)
0.400467 + 0.916311i \(0.368848\pi\)
\(182\) −8.69939 −0.644842
\(183\) −20.0888 −1.48501
\(184\) 6.53694 0.481910
\(185\) 5.90785 0.434354
\(186\) 2.23533 0.163902
\(187\) 20.9599 1.53274
\(188\) 17.1207 1.24865
\(189\) 4.80303 0.349369
\(190\) −2.85212 −0.206914
\(191\) −16.2308 −1.17442 −0.587211 0.809434i \(-0.699774\pi\)
−0.587211 + 0.809434i \(0.699774\pi\)
\(192\) −17.9606 −1.29620
\(193\) 6.54001 0.470760 0.235380 0.971903i \(-0.424366\pi\)
0.235380 + 0.971903i \(0.424366\pi\)
\(194\) −46.3009 −3.32421
\(195\) 6.63208 0.474933
\(196\) 3.83658 0.274042
\(197\) 2.73432 0.194812 0.0974060 0.995245i \(-0.468945\pi\)
0.0974060 + 0.995245i \(0.468945\pi\)
\(198\) −5.38798 −0.382907
\(199\) 17.6264 1.24950 0.624752 0.780823i \(-0.285200\pi\)
0.624752 + 0.780823i \(0.285200\pi\)
\(200\) −4.43701 −0.313744
\(201\) 29.1521 2.05623
\(202\) −26.7993 −1.88560
\(203\) −0.109372 −0.00767643
\(204\) 26.0455 1.82355
\(205\) 12.3065 0.859522
\(206\) −31.1966 −2.17357
\(207\) −0.577818 −0.0401611
\(208\) −10.9690 −0.760566
\(209\) −6.71319 −0.464361
\(210\) −4.44959 −0.307051
\(211\) 20.9791 1.44426 0.722130 0.691758i \(-0.243163\pi\)
0.722130 + 0.691758i \(0.243163\pi\)
\(212\) 40.2297 2.76298
\(213\) 9.35998 0.641335
\(214\) −5.69136 −0.389053
\(215\) −2.28127 −0.155581
\(216\) 21.3111 1.45003
\(217\) 0.502367 0.0341029
\(218\) 21.7773 1.47495
\(219\) 16.9418 1.14482
\(220\) −21.8165 −1.47087
\(221\) −13.2726 −0.892814
\(222\) 26.2875 1.76430
\(223\) −6.24347 −0.418094 −0.209047 0.977906i \(-0.567036\pi\)
−0.209047 + 0.977906i \(0.567036\pi\)
\(224\) −1.51468 −0.101204
\(225\) 0.392199 0.0261466
\(226\) 27.9904 1.86189
\(227\) −3.14486 −0.208732 −0.104366 0.994539i \(-0.533281\pi\)
−0.104366 + 0.994539i \(0.533281\pi\)
\(228\) −8.34207 −0.552467
\(229\) 1.00000 0.0660819
\(230\) −3.55930 −0.234693
\(231\) −10.4733 −0.689089
\(232\) −0.485285 −0.0318606
\(233\) 15.2893 1.00164 0.500818 0.865553i \(-0.333033\pi\)
0.500818 + 0.865553i \(0.333033\pi\)
\(234\) 3.41189 0.223042
\(235\) −4.46248 −0.291100
\(236\) −18.1865 −1.18384
\(237\) −3.75484 −0.243903
\(238\) 8.90486 0.577216
\(239\) −18.5392 −1.19920 −0.599599 0.800300i \(-0.704673\pi\)
−0.599599 + 0.800300i \(0.704673\pi\)
\(240\) −5.61048 −0.362155
\(241\) 12.1978 0.785729 0.392864 0.919596i \(-0.371484\pi\)
0.392864 + 0.919596i \(0.371484\pi\)
\(242\) −51.5449 −3.31343
\(243\) −4.05079 −0.259858
\(244\) −41.8464 −2.67894
\(245\) −1.00000 −0.0638877
\(246\) 54.7588 3.49130
\(247\) 4.25106 0.270489
\(248\) 2.22901 0.141542
\(249\) 20.3434 1.28921
\(250\) 2.41590 0.152795
\(251\) 6.83753 0.431581 0.215790 0.976440i \(-0.430767\pi\)
0.215790 + 0.976440i \(0.430767\pi\)
\(252\) −1.50470 −0.0947874
\(253\) −8.37771 −0.526702
\(254\) −17.1338 −1.07507
\(255\) −6.78873 −0.425127
\(256\) −30.0947 −1.88092
\(257\) 13.8680 0.865062 0.432531 0.901619i \(-0.357621\pi\)
0.432531 + 0.901619i \(0.357621\pi\)
\(258\) −10.1507 −0.631955
\(259\) 5.90785 0.367096
\(260\) 13.8151 0.856776
\(261\) 0.0428957 0.00265518
\(262\) −19.9039 −1.22967
\(263\) −2.83744 −0.174964 −0.0874821 0.996166i \(-0.527882\pi\)
−0.0874821 + 0.996166i \(0.527882\pi\)
\(264\) −46.4699 −2.86002
\(265\) −10.4858 −0.644138
\(266\) −2.85212 −0.174875
\(267\) 14.2987 0.875066
\(268\) 60.7258 3.70942
\(269\) −4.18748 −0.255315 −0.127658 0.991818i \(-0.540746\pi\)
−0.127658 + 0.991818i \(0.540746\pi\)
\(270\) −11.6036 −0.706175
\(271\) −2.34290 −0.142321 −0.0711605 0.997465i \(-0.522670\pi\)
−0.0711605 + 0.997465i \(0.522670\pi\)
\(272\) 11.2281 0.680805
\(273\) 6.63208 0.401392
\(274\) 55.2591 3.33832
\(275\) 5.68645 0.342906
\(276\) −10.4105 −0.626636
\(277\) 15.6039 0.937548 0.468774 0.883318i \(-0.344696\pi\)
0.468774 + 0.883318i \(0.344696\pi\)
\(278\) 50.5378 3.03105
\(279\) −0.197028 −0.0117957
\(280\) −4.43701 −0.265162
\(281\) 18.2199 1.08691 0.543455 0.839438i \(-0.317116\pi\)
0.543455 + 0.839438i \(0.317116\pi\)
\(282\) −19.8562 −1.18242
\(283\) 21.2708 1.26442 0.632208 0.774799i \(-0.282149\pi\)
0.632208 + 0.774799i \(0.282149\pi\)
\(284\) 19.4975 1.15696
\(285\) 2.17435 0.128797
\(286\) 49.4686 2.92514
\(287\) 12.3065 0.726429
\(288\) 0.594054 0.0350050
\(289\) −3.41388 −0.200817
\(290\) 0.264233 0.0155163
\(291\) 35.2981 2.06921
\(292\) 35.2909 2.06524
\(293\) −12.7199 −0.743102 −0.371551 0.928413i \(-0.621174\pi\)
−0.371551 + 0.928413i \(0.621174\pi\)
\(294\) −4.44959 −0.259505
\(295\) 4.74028 0.275990
\(296\) 26.2132 1.52361
\(297\) −27.3122 −1.58481
\(298\) 44.9253 2.60245
\(299\) 5.30511 0.306802
\(300\) 7.06619 0.407967
\(301\) −2.28127 −0.131490
\(302\) −35.1264 −2.02130
\(303\) 20.4308 1.17372
\(304\) −3.59623 −0.206258
\(305\) 10.9072 0.624544
\(306\) −3.49247 −0.199651
\(307\) 29.6780 1.69381 0.846906 0.531742i \(-0.178463\pi\)
0.846906 + 0.531742i \(0.178463\pi\)
\(308\) −21.8165 −1.24311
\(309\) 23.7831 1.35297
\(310\) −1.21367 −0.0689319
\(311\) 20.9266 1.18664 0.593318 0.804968i \(-0.297818\pi\)
0.593318 + 0.804968i \(0.297818\pi\)
\(312\) 29.4266 1.66595
\(313\) 11.7270 0.662849 0.331424 0.943482i \(-0.392471\pi\)
0.331424 + 0.943482i \(0.392471\pi\)
\(314\) −15.4266 −0.870573
\(315\) 0.392199 0.0220979
\(316\) −7.82160 −0.439999
\(317\) −18.6950 −1.05001 −0.525007 0.851098i \(-0.675937\pi\)
−0.525007 + 0.851098i \(0.675937\pi\)
\(318\) −46.6575 −2.61642
\(319\) 0.621939 0.0348219
\(320\) 9.75172 0.545138
\(321\) 4.33888 0.242173
\(322\) −3.55930 −0.198352
\(323\) −4.35147 −0.242122
\(324\) −38.4532 −2.13629
\(325\) −3.60089 −0.199741
\(326\) −1.86644 −0.103372
\(327\) −16.6022 −0.918104
\(328\) 54.6040 3.01500
\(329\) −4.46248 −0.246025
\(330\) 25.3023 1.39285
\(331\) −25.5643 −1.40514 −0.702570 0.711615i \(-0.747964\pi\)
−0.702570 + 0.711615i \(0.747964\pi\)
\(332\) 42.3768 2.32573
\(333\) −2.31705 −0.126974
\(334\) 7.51933 0.411440
\(335\) −15.8281 −0.864782
\(336\) −5.61048 −0.306077
\(337\) −22.1380 −1.20593 −0.602966 0.797767i \(-0.706015\pi\)
−0.602966 + 0.797767i \(0.706015\pi\)
\(338\) 0.0812262 0.00441812
\(339\) −21.3388 −1.15896
\(340\) −14.1414 −0.766925
\(341\) −2.85668 −0.154698
\(342\) 1.11860 0.0604868
\(343\) −1.00000 −0.0539949
\(344\) −10.1220 −0.545741
\(345\) 2.71347 0.146088
\(346\) 40.3078 2.16696
\(347\) −2.23912 −0.120202 −0.0601011 0.998192i \(-0.519142\pi\)
−0.0601011 + 0.998192i \(0.519142\pi\)
\(348\) 0.772845 0.0414289
\(349\) −7.44072 −0.398293 −0.199146 0.979970i \(-0.563817\pi\)
−0.199146 + 0.979970i \(0.563817\pi\)
\(350\) 2.41590 0.129135
\(351\) 17.2952 0.923147
\(352\) 8.61312 0.459081
\(353\) 24.6583 1.31243 0.656215 0.754574i \(-0.272156\pi\)
0.656215 + 0.754574i \(0.272156\pi\)
\(354\) 21.0923 1.12104
\(355\) −5.08199 −0.269724
\(356\) 29.7852 1.57861
\(357\) −6.78873 −0.359298
\(358\) −23.7285 −1.25409
\(359\) 15.3161 0.808353 0.404177 0.914681i \(-0.367558\pi\)
0.404177 + 0.914681i \(0.367558\pi\)
\(360\) 1.74019 0.0917160
\(361\) −17.6063 −0.926646
\(362\) −26.0325 −1.36824
\(363\) 39.2959 2.06250
\(364\) 13.8151 0.724108
\(365\) −9.19853 −0.481473
\(366\) 48.5326 2.53684
\(367\) −26.3431 −1.37510 −0.687548 0.726139i \(-0.741313\pi\)
−0.687548 + 0.726139i \(0.741313\pi\)
\(368\) −4.48791 −0.233948
\(369\) −4.82659 −0.251262
\(370\) −14.2728 −0.742007
\(371\) −10.4858 −0.544396
\(372\) −3.54982 −0.184050
\(373\) −8.33152 −0.431390 −0.215695 0.976461i \(-0.569202\pi\)
−0.215695 + 0.976461i \(0.569202\pi\)
\(374\) −50.6370 −2.61838
\(375\) −1.84179 −0.0951097
\(376\) −19.8001 −1.02111
\(377\) −0.393837 −0.0202836
\(378\) −11.6036 −0.596827
\(379\) −18.1365 −0.931610 −0.465805 0.884887i \(-0.654235\pi\)
−0.465805 + 0.884887i \(0.654235\pi\)
\(380\) 4.52932 0.232349
\(381\) 13.0621 0.669193
\(382\) 39.2121 2.00627
\(383\) −5.08393 −0.259777 −0.129888 0.991529i \(-0.541462\pi\)
−0.129888 + 0.991529i \(0.541462\pi\)
\(384\) 37.8117 1.92957
\(385\) 5.68645 0.289808
\(386\) −15.8000 −0.804201
\(387\) 0.894710 0.0454806
\(388\) 73.5284 3.73284
\(389\) 13.3041 0.674546 0.337273 0.941407i \(-0.390495\pi\)
0.337273 + 0.941407i \(0.390495\pi\)
\(390\) −16.0225 −0.811329
\(391\) −5.43041 −0.274627
\(392\) −4.43701 −0.224103
\(393\) 15.1740 0.765427
\(394\) −6.60584 −0.332797
\(395\) 2.03869 0.102578
\(396\) 8.55641 0.429976
\(397\) 8.79036 0.441176 0.220588 0.975367i \(-0.429202\pi\)
0.220588 + 0.975367i \(0.429202\pi\)
\(398\) −42.5837 −2.13453
\(399\) 2.17435 0.108854
\(400\) 3.04621 0.152310
\(401\) 24.2459 1.21078 0.605392 0.795928i \(-0.293016\pi\)
0.605392 + 0.795928i \(0.293016\pi\)
\(402\) −70.4286 −3.51266
\(403\) 1.80897 0.0901111
\(404\) 42.5588 2.11738
\(405\) 10.0228 0.498036
\(406\) 0.264233 0.0131137
\(407\) −33.5947 −1.66523
\(408\) −30.1216 −1.49124
\(409\) 16.2720 0.804598 0.402299 0.915508i \(-0.368211\pi\)
0.402299 + 0.915508i \(0.368211\pi\)
\(410\) −29.7313 −1.46832
\(411\) −42.1274 −2.07799
\(412\) 49.5419 2.44075
\(413\) 4.74028 0.233254
\(414\) 1.39595 0.0686073
\(415\) −11.0455 −0.542200
\(416\) −5.45418 −0.267413
\(417\) −38.5281 −1.88673
\(418\) 16.2184 0.793269
\(419\) 20.6920 1.01087 0.505435 0.862865i \(-0.331332\pi\)
0.505435 + 0.862865i \(0.331332\pi\)
\(420\) 7.06619 0.344795
\(421\) 25.8775 1.26119 0.630597 0.776110i \(-0.282810\pi\)
0.630597 + 0.776110i \(0.282810\pi\)
\(422\) −50.6834 −2.46723
\(423\) 1.75018 0.0850967
\(424\) −46.5256 −2.25948
\(425\) 3.68593 0.178794
\(426\) −22.6128 −1.09559
\(427\) 10.9072 0.527836
\(428\) 9.03819 0.436877
\(429\) −37.7130 −1.82080
\(430\) 5.51132 0.265779
\(431\) 25.0934 1.20871 0.604354 0.796716i \(-0.293431\pi\)
0.604354 + 0.796716i \(0.293431\pi\)
\(432\) −14.6310 −0.703935
\(433\) 40.8732 1.96424 0.982120 0.188255i \(-0.0602833\pi\)
0.982120 + 0.188255i \(0.0602833\pi\)
\(434\) −1.21367 −0.0582580
\(435\) −0.201441 −0.00965836
\(436\) −34.5836 −1.65625
\(437\) 1.73929 0.0832017
\(438\) −40.9297 −1.95570
\(439\) 9.81138 0.468272 0.234136 0.972204i \(-0.424774\pi\)
0.234136 + 0.972204i \(0.424774\pi\)
\(440\) 25.2308 1.20283
\(441\) 0.392199 0.0186761
\(442\) 32.0654 1.52519
\(443\) −37.6513 −1.78887 −0.894435 0.447199i \(-0.852422\pi\)
−0.894435 + 0.447199i \(0.852422\pi\)
\(444\) −41.7460 −1.98118
\(445\) −7.76347 −0.368024
\(446\) 15.0836 0.714230
\(447\) −34.2494 −1.61994
\(448\) 9.75172 0.460726
\(449\) 4.50308 0.212514 0.106257 0.994339i \(-0.466113\pi\)
0.106257 + 0.994339i \(0.466113\pi\)
\(450\) −0.947514 −0.0446662
\(451\) −69.9802 −3.29524
\(452\) −44.4502 −2.09076
\(453\) 26.7791 1.25819
\(454\) 7.59768 0.356577
\(455\) −3.60089 −0.168812
\(456\) 9.64759 0.451790
\(457\) −21.9985 −1.02904 −0.514522 0.857477i \(-0.672031\pi\)
−0.514522 + 0.857477i \(0.672031\pi\)
\(458\) −2.41590 −0.112888
\(459\) −17.7036 −0.826336
\(460\) 5.65235 0.263542
\(461\) 11.8084 0.549971 0.274985 0.961448i \(-0.411327\pi\)
0.274985 + 0.961448i \(0.411327\pi\)
\(462\) 25.3023 1.17717
\(463\) 19.6391 0.912708 0.456354 0.889798i \(-0.349155\pi\)
0.456354 + 0.889798i \(0.349155\pi\)
\(464\) 0.333171 0.0154671
\(465\) 0.925256 0.0429077
\(466\) −36.9375 −1.71109
\(467\) 37.4721 1.73400 0.867001 0.498306i \(-0.166044\pi\)
0.867001 + 0.498306i \(0.166044\pi\)
\(468\) −5.41826 −0.250459
\(469\) −15.8281 −0.730874
\(470\) 10.7809 0.497287
\(471\) 11.7607 0.541902
\(472\) 21.0327 0.968107
\(473\) 12.9723 0.596467
\(474\) 9.07133 0.416660
\(475\) −1.18056 −0.0541678
\(476\) −14.1414 −0.648170
\(477\) 4.11252 0.188299
\(478\) 44.7888 2.04859
\(479\) 19.0649 0.871097 0.435549 0.900165i \(-0.356554\pi\)
0.435549 + 0.900165i \(0.356554\pi\)
\(480\) −2.78972 −0.127333
\(481\) 21.2735 0.969988
\(482\) −29.4687 −1.34226
\(483\) 2.71347 0.123467
\(484\) 81.8560 3.72073
\(485\) −19.1651 −0.870241
\(486\) 9.78631 0.443916
\(487\) 43.1263 1.95424 0.977119 0.212692i \(-0.0682231\pi\)
0.977119 + 0.212692i \(0.0682231\pi\)
\(488\) 48.3953 2.19075
\(489\) 1.42290 0.0643458
\(490\) 2.41590 0.109139
\(491\) 16.3884 0.739599 0.369800 0.929112i \(-0.379426\pi\)
0.369800 + 0.929112i \(0.379426\pi\)
\(492\) −86.9600 −3.92046
\(493\) 0.403139 0.0181565
\(494\) −10.2702 −0.462076
\(495\) −2.23022 −0.100241
\(496\) −1.53031 −0.0687132
\(497\) −5.08199 −0.227959
\(498\) −49.1478 −2.20236
\(499\) 9.03204 0.404330 0.202165 0.979351i \(-0.435202\pi\)
0.202165 + 0.979351i \(0.435202\pi\)
\(500\) −3.83658 −0.171577
\(501\) −5.73246 −0.256107
\(502\) −16.5188 −0.737270
\(503\) 35.9740 1.60400 0.802001 0.597323i \(-0.203769\pi\)
0.802001 + 0.597323i \(0.203769\pi\)
\(504\) 1.74019 0.0775141
\(505\) −11.0929 −0.493627
\(506\) 20.2397 0.899766
\(507\) −0.0619238 −0.00275013
\(508\) 27.2093 1.20722
\(509\) −28.0950 −1.24529 −0.622645 0.782505i \(-0.713942\pi\)
−0.622645 + 0.782505i \(0.713942\pi\)
\(510\) 16.4009 0.726244
\(511\) −9.19853 −0.406919
\(512\) 31.6461 1.39857
\(513\) 5.67027 0.250348
\(514\) −33.5037 −1.47779
\(515\) −12.9130 −0.569016
\(516\) 16.1199 0.709637
\(517\) 25.3757 1.11602
\(518\) −14.2728 −0.627110
\(519\) −30.7291 −1.34886
\(520\) −15.9772 −0.700644
\(521\) −31.5502 −1.38224 −0.691119 0.722741i \(-0.742882\pi\)
−0.691119 + 0.722741i \(0.742882\pi\)
\(522\) −0.103632 −0.00453584
\(523\) 5.55677 0.242981 0.121490 0.992593i \(-0.461233\pi\)
0.121490 + 0.992593i \(0.461233\pi\)
\(524\) 31.6085 1.38082
\(525\) −1.84179 −0.0803824
\(526\) 6.85498 0.298891
\(527\) −1.85169 −0.0806610
\(528\) 31.9037 1.38843
\(529\) −20.8295 −0.905628
\(530\) 25.3327 1.10038
\(531\) −1.85913 −0.0806795
\(532\) 4.52932 0.196371
\(533\) 44.3143 1.91946
\(534\) −34.5442 −1.49488
\(535\) −2.35579 −0.101850
\(536\) −70.2294 −3.03345
\(537\) 18.0897 0.780630
\(538\) 10.1165 0.436155
\(539\) 5.68645 0.244933
\(540\) 18.4272 0.792981
\(541\) −1.33575 −0.0574284 −0.0287142 0.999588i \(-0.509141\pi\)
−0.0287142 + 0.999588i \(0.509141\pi\)
\(542\) 5.66022 0.243127
\(543\) 19.8462 0.851681
\(544\) 5.58300 0.239369
\(545\) 9.01416 0.386124
\(546\) −16.0225 −0.685698
\(547\) −15.9150 −0.680475 −0.340238 0.940340i \(-0.610507\pi\)
−0.340238 + 0.940340i \(0.610507\pi\)
\(548\) −87.7544 −3.74868
\(549\) −4.27779 −0.182572
\(550\) −13.7379 −0.585786
\(551\) −0.129121 −0.00550072
\(552\) 12.0397 0.512443
\(553\) 2.03869 0.0866938
\(554\) −37.6975 −1.60161
\(555\) 10.8810 0.461874
\(556\) −80.2567 −3.40364
\(557\) 6.88978 0.291929 0.145965 0.989290i \(-0.453371\pi\)
0.145965 + 0.989290i \(0.453371\pi\)
\(558\) 0.476000 0.0201507
\(559\) −8.21458 −0.347440
\(560\) 3.04621 0.128726
\(561\) 38.6037 1.62985
\(562\) −44.0176 −1.85677
\(563\) −16.4197 −0.692010 −0.346005 0.938233i \(-0.612462\pi\)
−0.346005 + 0.938233i \(0.612462\pi\)
\(564\) 31.5327 1.32777
\(565\) 11.5859 0.487422
\(566\) −51.3881 −2.16000
\(567\) 10.0228 0.420917
\(568\) −22.5488 −0.946128
\(569\) −45.2388 −1.89651 −0.948255 0.317510i \(-0.897153\pi\)
−0.948255 + 0.317510i \(0.897153\pi\)
\(570\) −5.25301 −0.220024
\(571\) −4.97457 −0.208179 −0.104090 0.994568i \(-0.533193\pi\)
−0.104090 + 0.994568i \(0.533193\pi\)
\(572\) −78.5588 −3.28471
\(573\) −29.8938 −1.24883
\(574\) −29.7313 −1.24096
\(575\) −1.47328 −0.0614399
\(576\) −3.82461 −0.159359
\(577\) −11.0207 −0.458798 −0.229399 0.973332i \(-0.573676\pi\)
−0.229399 + 0.973332i \(0.573676\pi\)
\(578\) 8.24761 0.343055
\(579\) 12.0453 0.500588
\(580\) −0.419616 −0.0174236
\(581\) −11.0455 −0.458243
\(582\) −85.2767 −3.53483
\(583\) 59.6269 2.46950
\(584\) −40.8139 −1.68889
\(585\) 1.41226 0.0583899
\(586\) 30.7299 1.26944
\(587\) 20.6143 0.850845 0.425423 0.904995i \(-0.360125\pi\)
0.425423 + 0.904995i \(0.360125\pi\)
\(588\) 7.06619 0.291405
\(589\) 0.593075 0.0244372
\(590\) −11.4521 −0.471474
\(591\) 5.03604 0.207155
\(592\) −17.9965 −0.739653
\(593\) −13.3783 −0.549382 −0.274691 0.961533i \(-0.588576\pi\)
−0.274691 + 0.961533i \(0.588576\pi\)
\(594\) 65.9835 2.70734
\(595\) 3.68593 0.151109
\(596\) −71.3439 −2.92236
\(597\) 32.4642 1.32867
\(598\) −12.8166 −0.524110
\(599\) −43.1644 −1.76365 −0.881825 0.471576i \(-0.843685\pi\)
−0.881825 + 0.471576i \(0.843685\pi\)
\(600\) −8.17204 −0.333622
\(601\) −8.81945 −0.359753 −0.179876 0.983689i \(-0.557570\pi\)
−0.179876 + 0.983689i \(0.557570\pi\)
\(602\) 5.51132 0.224624
\(603\) 6.20776 0.252800
\(604\) 55.7827 2.26977
\(605\) −21.3357 −0.867418
\(606\) −49.3588 −2.00507
\(607\) 2.72131 0.110455 0.0552273 0.998474i \(-0.482412\pi\)
0.0552273 + 0.998474i \(0.482412\pi\)
\(608\) −1.78817 −0.0725198
\(609\) −0.201441 −0.00816280
\(610\) −26.3507 −1.06691
\(611\) −16.0689 −0.650078
\(612\) 5.54624 0.224193
\(613\) −15.7229 −0.635042 −0.317521 0.948251i \(-0.602850\pi\)
−0.317521 + 0.948251i \(0.602850\pi\)
\(614\) −71.6991 −2.89354
\(615\) 22.6660 0.913981
\(616\) 25.2308 1.01658
\(617\) −19.4975 −0.784941 −0.392471 0.919765i \(-0.628380\pi\)
−0.392471 + 0.919765i \(0.628380\pi\)
\(618\) −57.4577 −2.31129
\(619\) 26.6453 1.07096 0.535482 0.844547i \(-0.320130\pi\)
0.535482 + 0.844547i \(0.320130\pi\)
\(620\) 1.92737 0.0774052
\(621\) 7.07620 0.283958
\(622\) −50.5565 −2.02713
\(623\) −7.76347 −0.311037
\(624\) −20.2027 −0.808755
\(625\) 1.00000 0.0400000
\(626\) −28.3313 −1.13235
\(627\) −12.3643 −0.493783
\(628\) 24.4983 0.977588
\(629\) −21.7760 −0.868264
\(630\) −0.947514 −0.0377499
\(631\) −23.7433 −0.945205 −0.472603 0.881276i \(-0.656685\pi\)
−0.472603 + 0.881276i \(0.656685\pi\)
\(632\) 9.04567 0.359818
\(633\) 38.6391 1.53577
\(634\) 45.1652 1.79374
\(635\) −7.09207 −0.281440
\(636\) 74.0947 2.93805
\(637\) −3.60089 −0.142672
\(638\) −1.50254 −0.0594863
\(639\) 1.99315 0.0788479
\(640\) −20.5299 −0.811514
\(641\) 12.2448 0.483642 0.241821 0.970321i \(-0.422255\pi\)
0.241821 + 0.970321i \(0.422255\pi\)
\(642\) −10.4823 −0.413704
\(643\) 46.9824 1.85281 0.926403 0.376535i \(-0.122884\pi\)
0.926403 + 0.376535i \(0.122884\pi\)
\(644\) 5.65235 0.222734
\(645\) −4.20162 −0.165439
\(646\) 10.5127 0.413618
\(647\) 17.5500 0.689963 0.344981 0.938610i \(-0.387885\pi\)
0.344981 + 0.938610i \(0.387885\pi\)
\(648\) 44.4711 1.74699
\(649\) −26.9554 −1.05809
\(650\) 8.69939 0.341218
\(651\) 0.925256 0.0362637
\(652\) 2.96400 0.116079
\(653\) −28.3693 −1.11018 −0.555089 0.831791i \(-0.687316\pi\)
−0.555089 + 0.831791i \(0.687316\pi\)
\(654\) 40.1093 1.56840
\(655\) −8.23872 −0.321913
\(656\) −37.4881 −1.46366
\(657\) 3.60765 0.140748
\(658\) 10.7809 0.420284
\(659\) −18.2749 −0.711887 −0.355944 0.934507i \(-0.615840\pi\)
−0.355944 + 0.934507i \(0.615840\pi\)
\(660\) −40.1815 −1.56406
\(661\) 11.1886 0.435188 0.217594 0.976039i \(-0.430179\pi\)
0.217594 + 0.976039i \(0.430179\pi\)
\(662\) 61.7608 2.40040
\(663\) −24.4454 −0.949382
\(664\) −49.0088 −1.90191
\(665\) −1.18056 −0.0457802
\(666\) 5.59777 0.216909
\(667\) −0.161136 −0.00623920
\(668\) −11.9411 −0.462015
\(669\) −11.4992 −0.444584
\(670\) 38.2392 1.47731
\(671\) −62.0232 −2.39438
\(672\) −2.78972 −0.107616
\(673\) 2.56259 0.0987807 0.0493904 0.998780i \(-0.484272\pi\)
0.0493904 + 0.998780i \(0.484272\pi\)
\(674\) 53.4832 2.06010
\(675\) −4.80303 −0.184869
\(676\) −0.128992 −0.00496121
\(677\) −21.7010 −0.834036 −0.417018 0.908898i \(-0.636925\pi\)
−0.417018 + 0.908898i \(0.636925\pi\)
\(678\) 51.5524 1.97986
\(679\) −19.1651 −0.735488
\(680\) 16.3545 0.627167
\(681\) −5.79218 −0.221957
\(682\) 6.90147 0.264271
\(683\) 20.1403 0.770649 0.385324 0.922781i \(-0.374090\pi\)
0.385324 + 0.922781i \(0.374090\pi\)
\(684\) −1.77639 −0.0679221
\(685\) 22.8731 0.873935
\(686\) 2.41590 0.0922396
\(687\) 1.84179 0.0702688
\(688\) 6.94921 0.264936
\(689\) −37.7582 −1.43847
\(690\) −6.55548 −0.249563
\(691\) 7.24524 0.275622 0.137811 0.990459i \(-0.455993\pi\)
0.137811 + 0.990459i \(0.455993\pi\)
\(692\) −64.0109 −2.43333
\(693\) −2.23022 −0.0847189
\(694\) 5.40950 0.205342
\(695\) 20.9188 0.793495
\(696\) −0.893795 −0.0338792
\(697\) −45.3609 −1.71817
\(698\) 17.9761 0.680404
\(699\) 28.1597 1.06510
\(700\) −3.83658 −0.145009
\(701\) 1.56344 0.0590505 0.0295253 0.999564i \(-0.490600\pi\)
0.0295253 + 0.999564i \(0.490600\pi\)
\(702\) −41.7834 −1.57701
\(703\) 6.97458 0.263051
\(704\) −55.4526 −2.08995
\(705\) −8.21897 −0.309544
\(706\) −59.5721 −2.24203
\(707\) −11.0929 −0.417191
\(708\) −33.4957 −1.25885
\(709\) −1.00811 −0.0378602 −0.0189301 0.999821i \(-0.506026\pi\)
−0.0189301 + 0.999821i \(0.506026\pi\)
\(710\) 12.2776 0.460770
\(711\) −0.799571 −0.0299863
\(712\) −34.4466 −1.29094
\(713\) 0.740127 0.0277180
\(714\) 16.4009 0.613788
\(715\) 20.4762 0.765768
\(716\) 37.6822 1.40825
\(717\) −34.1453 −1.27518
\(718\) −37.0022 −1.38091
\(719\) 7.23617 0.269863 0.134932 0.990855i \(-0.456918\pi\)
0.134932 + 0.990855i \(0.456918\pi\)
\(720\) −1.19472 −0.0445245
\(721\) −12.9130 −0.480906
\(722\) 42.5350 1.58299
\(723\) 22.4658 0.835512
\(724\) 41.3410 1.53643
\(725\) 0.109372 0.00406198
\(726\) −94.9349 −3.52337
\(727\) −15.9774 −0.592567 −0.296284 0.955100i \(-0.595747\pi\)
−0.296284 + 0.955100i \(0.595747\pi\)
\(728\) −15.9772 −0.592153
\(729\) 22.6076 0.837319
\(730\) 22.2227 0.822501
\(731\) 8.40860 0.311003
\(732\) −77.0723 −2.84868
\(733\) −4.46744 −0.165009 −0.0825043 0.996591i \(-0.526292\pi\)
−0.0825043 + 0.996591i \(0.526292\pi\)
\(734\) 63.6422 2.34908
\(735\) −1.84179 −0.0679355
\(736\) −2.23154 −0.0822556
\(737\) 90.0057 3.31540
\(738\) 11.6606 0.429231
\(739\) 25.5916 0.941404 0.470702 0.882292i \(-0.344001\pi\)
0.470702 + 0.882292i \(0.344001\pi\)
\(740\) 22.6660 0.833217
\(741\) 7.82958 0.287627
\(742\) 25.3327 0.929992
\(743\) −2.45997 −0.0902477 −0.0451239 0.998981i \(-0.514368\pi\)
−0.0451239 + 0.998981i \(0.514368\pi\)
\(744\) 4.10537 0.150510
\(745\) 18.5957 0.681293
\(746\) 20.1281 0.736944
\(747\) 4.33202 0.158500
\(748\) 80.4143 2.94024
\(749\) −2.35579 −0.0860787
\(750\) 4.44959 0.162476
\(751\) 50.2396 1.83327 0.916635 0.399725i \(-0.130894\pi\)
0.916635 + 0.399725i \(0.130894\pi\)
\(752\) 13.5936 0.495709
\(753\) 12.5933 0.458926
\(754\) 0.951472 0.0346506
\(755\) −14.5397 −0.529153
\(756\) 18.4272 0.670191
\(757\) −28.9065 −1.05063 −0.525313 0.850909i \(-0.676052\pi\)
−0.525313 + 0.850909i \(0.676052\pi\)
\(758\) 43.8160 1.59147
\(759\) −15.4300 −0.560074
\(760\) −5.23816 −0.190008
\(761\) −5.39044 −0.195403 −0.0977017 0.995216i \(-0.531149\pi\)
−0.0977017 + 0.995216i \(0.531149\pi\)
\(762\) −31.5568 −1.14318
\(763\) 9.01416 0.326335
\(764\) −62.2710 −2.25289
\(765\) −1.44562 −0.0522665
\(766\) 12.2823 0.443777
\(767\) 17.0692 0.616334
\(768\) −55.4281 −2.00009
\(769\) 50.7622 1.83053 0.915266 0.402849i \(-0.131980\pi\)
0.915266 + 0.402849i \(0.131980\pi\)
\(770\) −13.7379 −0.495079
\(771\) 25.5420 0.919872
\(772\) 25.0913 0.903056
\(773\) 47.8152 1.71979 0.859897 0.510468i \(-0.170528\pi\)
0.859897 + 0.510468i \(0.170528\pi\)
\(774\) −2.16153 −0.0776946
\(775\) −0.502367 −0.0180456
\(776\) −85.0355 −3.05260
\(777\) 10.8810 0.390355
\(778\) −32.1415 −1.15233
\(779\) 14.5286 0.520540
\(780\) 25.4445 0.911061
\(781\) 28.8985 1.03407
\(782\) 13.1193 0.469146
\(783\) −0.525318 −0.0187733
\(784\) 3.04621 0.108793
\(785\) −6.38544 −0.227906
\(786\) −36.6589 −1.30758
\(787\) 9.88872 0.352495 0.176247 0.984346i \(-0.443604\pi\)
0.176247 + 0.984346i \(0.443604\pi\)
\(788\) 10.4904 0.373706
\(789\) −5.22598 −0.186050
\(790\) −4.92527 −0.175233
\(791\) 11.5859 0.411947
\(792\) −9.89548 −0.351621
\(793\) 39.2756 1.39472
\(794\) −21.2367 −0.753661
\(795\) −19.3127 −0.684950
\(796\) 67.6253 2.39691
\(797\) −35.0166 −1.24035 −0.620176 0.784463i \(-0.712939\pi\)
−0.620176 + 0.784463i \(0.712939\pi\)
\(798\) −5.25301 −0.185955
\(799\) 16.4484 0.581903
\(800\) 1.51468 0.0535519
\(801\) 3.04482 0.107584
\(802\) −58.5758 −2.06838
\(803\) 52.3069 1.84587
\(804\) 111.844 3.94445
\(805\) −1.47328 −0.0519262
\(806\) −4.37029 −0.153937
\(807\) −7.71247 −0.271492
\(808\) −49.2192 −1.73153
\(809\) 31.1080 1.09370 0.546849 0.837231i \(-0.315827\pi\)
0.546849 + 0.837231i \(0.315827\pi\)
\(810\) −24.2140 −0.850795
\(811\) 35.2043 1.23619 0.618094 0.786104i \(-0.287905\pi\)
0.618094 + 0.786104i \(0.287905\pi\)
\(812\) −0.419616 −0.0147256
\(813\) −4.31513 −0.151338
\(814\) 81.1614 2.84471
\(815\) −0.772563 −0.0270617
\(816\) 20.6799 0.723940
\(817\) −2.69317 −0.0942222
\(818\) −39.3115 −1.37450
\(819\) 1.41226 0.0493485
\(820\) 47.2149 1.64881
\(821\) −19.5393 −0.681926 −0.340963 0.940077i \(-0.610753\pi\)
−0.340963 + 0.940077i \(0.610753\pi\)
\(822\) 101.776 3.54984
\(823\) 21.9467 0.765013 0.382507 0.923953i \(-0.375061\pi\)
0.382507 + 0.923953i \(0.375061\pi\)
\(824\) −57.2952 −1.99597
\(825\) 10.4733 0.364632
\(826\) −11.4521 −0.398468
\(827\) 10.8659 0.377844 0.188922 0.981992i \(-0.439501\pi\)
0.188922 + 0.981992i \(0.439501\pi\)
\(828\) −2.21685 −0.0770407
\(829\) 47.4450 1.64783 0.823916 0.566712i \(-0.191785\pi\)
0.823916 + 0.566712i \(0.191785\pi\)
\(830\) 26.6848 0.926241
\(831\) 28.7392 0.996950
\(832\) 35.1148 1.21739
\(833\) 3.68593 0.127710
\(834\) 93.0801 3.22310
\(835\) 3.11243 0.107710
\(836\) −25.7557 −0.890781
\(837\) 2.41288 0.0834015
\(838\) −49.9899 −1.72687
\(839\) 53.9888 1.86390 0.931950 0.362586i \(-0.118106\pi\)
0.931950 + 0.362586i \(0.118106\pi\)
\(840\) −8.17204 −0.281962
\(841\) −28.9880 −0.999588
\(842\) −62.5176 −2.15450
\(843\) 33.5573 1.15578
\(844\) 80.4880 2.77051
\(845\) 0.0336215 0.00115661
\(846\) −4.22826 −0.145371
\(847\) −21.3357 −0.733102
\(848\) 31.9419 1.09689
\(849\) 39.1763 1.34453
\(850\) −8.90486 −0.305434
\(851\) 8.70391 0.298366
\(852\) 35.9103 1.23027
\(853\) 2.20747 0.0755823 0.0377911 0.999286i \(-0.487968\pi\)
0.0377911 + 0.999286i \(0.487968\pi\)
\(854\) −26.3507 −0.901703
\(855\) 0.463014 0.0158348
\(856\) −10.4527 −0.357265
\(857\) −53.6896 −1.83400 −0.917001 0.398884i \(-0.869398\pi\)
−0.917001 + 0.398884i \(0.869398\pi\)
\(858\) 91.1109 3.11047
\(859\) 12.9934 0.443328 0.221664 0.975123i \(-0.428851\pi\)
0.221664 + 0.975123i \(0.428851\pi\)
\(860\) −8.75227 −0.298450
\(861\) 22.6660 0.772455
\(862\) −60.6233 −2.06484
\(863\) −4.35114 −0.148114 −0.0740572 0.997254i \(-0.523595\pi\)
−0.0740572 + 0.997254i \(0.523595\pi\)
\(864\) −7.27503 −0.247502
\(865\) 16.6843 0.567285
\(866\) −98.7456 −3.35551
\(867\) −6.28766 −0.213540
\(868\) 1.92737 0.0654194
\(869\) −11.5929 −0.393262
\(870\) 0.486662 0.0164994
\(871\) −56.9952 −1.93121
\(872\) 39.9959 1.35443
\(873\) 7.51651 0.254395
\(874\) −4.20196 −0.142134
\(875\) 1.00000 0.0338062
\(876\) 64.9985 2.19610
\(877\) −2.50039 −0.0844321 −0.0422161 0.999109i \(-0.513442\pi\)
−0.0422161 + 0.999109i \(0.513442\pi\)
\(878\) −23.7033 −0.799949
\(879\) −23.4273 −0.790184
\(880\) −17.3221 −0.583927
\(881\) 48.3556 1.62914 0.814570 0.580065i \(-0.196973\pi\)
0.814570 + 0.580065i \(0.196973\pi\)
\(882\) −0.947514 −0.0319044
\(883\) 26.7698 0.900874 0.450437 0.892808i \(-0.351268\pi\)
0.450437 + 0.892808i \(0.351268\pi\)
\(884\) −50.9216 −1.71268
\(885\) 8.73062 0.293476
\(886\) 90.9620 3.05593
\(887\) 42.9236 1.44123 0.720617 0.693333i \(-0.243859\pi\)
0.720617 + 0.693333i \(0.243859\pi\)
\(888\) 48.2792 1.62014
\(889\) −7.09207 −0.237861
\(890\) 18.7558 0.628695
\(891\) −56.9940 −1.90937
\(892\) −23.9536 −0.802026
\(893\) −5.26823 −0.176295
\(894\) 82.7431 2.76734
\(895\) −9.82181 −0.328307
\(896\) −20.5299 −0.685854
\(897\) 9.77090 0.326241
\(898\) −10.8790 −0.363037
\(899\) −0.0549451 −0.00183252
\(900\) 1.50470 0.0501568
\(901\) 38.6500 1.28762
\(902\) 169.065 5.62926
\(903\) −4.20162 −0.139821
\(904\) 51.4067 1.70976
\(905\) −10.7755 −0.358189
\(906\) −64.6956 −2.14937
\(907\) 11.3109 0.375572 0.187786 0.982210i \(-0.439869\pi\)
0.187786 + 0.982210i \(0.439869\pi\)
\(908\) −12.0655 −0.400409
\(909\) 4.35062 0.144301
\(910\) 8.69939 0.288382
\(911\) 46.6223 1.54467 0.772333 0.635218i \(-0.219090\pi\)
0.772333 + 0.635218i \(0.219090\pi\)
\(912\) −6.62351 −0.219326
\(913\) 62.8094 2.07869
\(914\) 53.1461 1.75792
\(915\) 20.0888 0.664115
\(916\) 3.83658 0.126764
\(917\) −8.23872 −0.272066
\(918\) 42.7703 1.41163
\(919\) 1.64331 0.0542077 0.0271038 0.999633i \(-0.491372\pi\)
0.0271038 + 0.999633i \(0.491372\pi\)
\(920\) −6.53694 −0.215517
\(921\) 54.6607 1.80113
\(922\) −28.5279 −0.939515
\(923\) −18.2997 −0.602341
\(924\) −40.1815 −1.32187
\(925\) −5.90785 −0.194249
\(926\) −47.4462 −1.55918
\(927\) 5.06447 0.166339
\(928\) 0.165664 0.00543817
\(929\) −21.3327 −0.699903 −0.349952 0.936768i \(-0.613802\pi\)
−0.349952 + 0.936768i \(0.613802\pi\)
\(930\) −2.23533 −0.0732993
\(931\) −1.18056 −0.0386913
\(932\) 58.6587 1.92143
\(933\) 38.5424 1.26182
\(934\) −90.5290 −2.96220
\(935\) −20.9599 −0.685461
\(936\) 6.26622 0.204818
\(937\) 27.7518 0.906611 0.453306 0.891355i \(-0.350245\pi\)
0.453306 + 0.891355i \(0.350245\pi\)
\(938\) 38.2392 1.24855
\(939\) 21.5987 0.704846
\(940\) −17.1207 −0.558415
\(941\) −10.2245 −0.333308 −0.166654 0.986015i \(-0.553296\pi\)
−0.166654 + 0.986015i \(0.553296\pi\)
\(942\) −28.4126 −0.925732
\(943\) 18.1309 0.590423
\(944\) −14.4399 −0.469978
\(945\) −4.80303 −0.156243
\(946\) −31.3398 −1.01894
\(947\) −3.85369 −0.125228 −0.0626140 0.998038i \(-0.519944\pi\)
−0.0626140 + 0.998038i \(0.519944\pi\)
\(948\) −14.4058 −0.467877
\(949\) −33.1228 −1.07521
\(950\) 2.85212 0.0925350
\(951\) −34.4322 −1.11654
\(952\) 16.3545 0.530053
\(953\) −8.38095 −0.271486 −0.135743 0.990744i \(-0.543342\pi\)
−0.135743 + 0.990744i \(0.543342\pi\)
\(954\) −9.93544 −0.321672
\(955\) 16.2308 0.525218
\(956\) −71.1270 −2.30041
\(957\) 1.14548 0.0370282
\(958\) −46.0589 −1.48810
\(959\) 22.8731 0.738610
\(960\) 17.9606 0.579677
\(961\) −30.7476 −0.991859
\(962\) −51.3947 −1.65703
\(963\) 0.923938 0.0297735
\(964\) 46.7978 1.50726
\(965\) −6.54001 −0.210530
\(966\) −6.55548 −0.210919
\(967\) 2.09521 0.0673776 0.0336888 0.999432i \(-0.489275\pi\)
0.0336888 + 0.999432i \(0.489275\pi\)
\(968\) −94.6664 −3.04269
\(969\) −8.01450 −0.257463
\(970\) 46.3009 1.48663
\(971\) −0.737084 −0.0236542 −0.0118271 0.999930i \(-0.503765\pi\)
−0.0118271 + 0.999930i \(0.503765\pi\)
\(972\) −15.5412 −0.498484
\(973\) 20.9188 0.670626
\(974\) −104.189 −3.33843
\(975\) −6.63208 −0.212397
\(976\) −33.2256 −1.06352
\(977\) −24.4738 −0.782988 −0.391494 0.920181i \(-0.628042\pi\)
−0.391494 + 0.920181i \(0.628042\pi\)
\(978\) −3.43759 −0.109922
\(979\) 44.1465 1.41093
\(980\) −3.83658 −0.122555
\(981\) −3.53534 −0.112875
\(982\) −39.5928 −1.26346
\(983\) 21.2441 0.677582 0.338791 0.940862i \(-0.389982\pi\)
0.338791 + 0.940862i \(0.389982\pi\)
\(984\) 100.569 3.20603
\(985\) −2.73432 −0.0871225
\(986\) −0.973945 −0.0310167
\(987\) −8.21897 −0.261613
\(988\) 16.3096 0.518876
\(989\) −3.36094 −0.106872
\(990\) 5.38798 0.171241
\(991\) 24.7706 0.786865 0.393433 0.919353i \(-0.371287\pi\)
0.393433 + 0.919353i \(0.371287\pi\)
\(992\) −0.760924 −0.0241594
\(993\) −47.0841 −1.49417
\(994\) 12.2776 0.389422
\(995\) −17.6264 −0.558795
\(996\) 78.0493 2.47309
\(997\) −46.3714 −1.46860 −0.734299 0.678827i \(-0.762489\pi\)
−0.734299 + 0.678827i \(0.762489\pi\)
\(998\) −21.8205 −0.690717
\(999\) 28.3756 0.897763
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 \(a_p\))