Properties

Label 8018.2.a.d.1.1
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(30\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-3.23056 q^{3}\) \(+1.00000 q^{4}\) \(-3.65226 q^{5}\) \(-3.23056 q^{6}\) \(+2.39039 q^{7}\) \(+1.00000 q^{8}\) \(+7.43653 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-3.23056 q^{3}\) \(+1.00000 q^{4}\) \(-3.65226 q^{5}\) \(-3.23056 q^{6}\) \(+2.39039 q^{7}\) \(+1.00000 q^{8}\) \(+7.43653 q^{9}\) \(-3.65226 q^{10}\) \(+0.229147 q^{11}\) \(-3.23056 q^{12}\) \(-1.51971 q^{13}\) \(+2.39039 q^{14}\) \(+11.7989 q^{15}\) \(+1.00000 q^{16}\) \(+1.23485 q^{17}\) \(+7.43653 q^{18}\) \(+1.00000 q^{19}\) \(-3.65226 q^{20}\) \(-7.72231 q^{21}\) \(+0.229147 q^{22}\) \(-8.59225 q^{23}\) \(-3.23056 q^{24}\) \(+8.33901 q^{25}\) \(-1.51971 q^{26}\) \(-14.3325 q^{27}\) \(+2.39039 q^{28}\) \(-2.80955 q^{29}\) \(+11.7989 q^{30}\) \(+4.09925 q^{31}\) \(+1.00000 q^{32}\) \(-0.740273 q^{33}\) \(+1.23485 q^{34}\) \(-8.73034 q^{35}\) \(+7.43653 q^{36}\) \(-7.69336 q^{37}\) \(+1.00000 q^{38}\) \(+4.90953 q^{39}\) \(-3.65226 q^{40}\) \(+6.97582 q^{41}\) \(-7.72231 q^{42}\) \(-10.4732 q^{43}\) \(+0.229147 q^{44}\) \(-27.1601 q^{45}\) \(-8.59225 q^{46}\) \(+11.1963 q^{47}\) \(-3.23056 q^{48}\) \(-1.28603 q^{49}\) \(+8.33901 q^{50}\) \(-3.98926 q^{51}\) \(-1.51971 q^{52}\) \(+2.41819 q^{53}\) \(-14.3325 q^{54}\) \(-0.836904 q^{55}\) \(+2.39039 q^{56}\) \(-3.23056 q^{57}\) \(-2.80955 q^{58}\) \(+5.91884 q^{59}\) \(+11.7989 q^{60}\) \(+5.03288 q^{61}\) \(+4.09925 q^{62}\) \(+17.7762 q^{63}\) \(+1.00000 q^{64}\) \(+5.55039 q^{65}\) \(-0.740273 q^{66}\) \(-1.27570 q^{67}\) \(+1.23485 q^{68}\) \(+27.7578 q^{69}\) \(-8.73034 q^{70}\) \(+10.5869 q^{71}\) \(+7.43653 q^{72}\) \(-5.30920 q^{73}\) \(-7.69336 q^{74}\) \(-26.9397 q^{75}\) \(+1.00000 q^{76}\) \(+0.547751 q^{77}\) \(+4.90953 q^{78}\) \(+4.63819 q^{79}\) \(-3.65226 q^{80}\) \(+23.9924 q^{81}\) \(+6.97582 q^{82}\) \(+0.441306 q^{83}\) \(-7.72231 q^{84}\) \(-4.51000 q^{85}\) \(-10.4732 q^{86}\) \(+9.07644 q^{87}\) \(+0.229147 q^{88}\) \(+3.69080 q^{89}\) \(-27.1601 q^{90}\) \(-3.63271 q^{91}\) \(-8.59225 q^{92}\) \(-13.2429 q^{93}\) \(+11.1963 q^{94}\) \(-3.65226 q^{95}\) \(-3.23056 q^{96}\) \(+7.94507 q^{97}\) \(-1.28603 q^{98}\) \(+1.70406 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(30q \) \(\mathstrut +\mathstrut 30q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(30q \) \(\mathstrut +\mathstrut 30q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut -\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 17q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 19q^{13} \) \(\mathstrut -\mathstrut 15q^{14} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 10q^{18} \) \(\mathstrut +\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 14q^{21} \) \(\mathstrut -\mathstrut 17q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 10q^{24} \) \(\mathstrut -\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 19q^{26} \) \(\mathstrut -\mathstrut 37q^{27} \) \(\mathstrut -\mathstrut 15q^{28} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 30q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 18q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 10q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut +\mathstrut 30q^{38} \) \(\mathstrut -\mathstrut 12q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 14q^{42} \) \(\mathstrut -\mathstrut 61q^{43} \) \(\mathstrut -\mathstrut 17q^{44} \) \(\mathstrut -\mathstrut 14q^{45} \) \(\mathstrut -\mathstrut 15q^{46} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut -\mathstrut q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 19q^{52} \) \(\mathstrut -\mathstrut 19q^{53} \) \(\mathstrut -\mathstrut 37q^{54} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 37q^{58} \) \(\mathstrut -\mathstrut 6q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 32q^{61} \) \(\mathstrut -\mathstrut 11q^{62} \) \(\mathstrut -\mathstrut 24q^{63} \) \(\mathstrut +\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 18q^{68} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 10q^{72} \) \(\mathstrut -\mathstrut 58q^{73} \) \(\mathstrut -\mathstrut 46q^{74} \) \(\mathstrut -\mathstrut 42q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut -\mathstrut 32q^{77} \) \(\mathstrut -\mathstrut 42q^{79} \) \(\mathstrut -\mathstrut 12q^{80} \) \(\mathstrut -\mathstrut 38q^{81} \) \(\mathstrut -\mathstrut 28q^{82} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 48q^{85} \) \(\mathstrut -\mathstrut 61q^{86} \) \(\mathstrut -\mathstrut 15q^{87} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut -\mathstrut 39q^{89} \) \(\mathstrut -\mathstrut 14q^{90} \) \(\mathstrut -\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 15q^{92} \) \(\mathstrut -\mathstrut 45q^{93} \) \(\mathstrut -\mathstrut 4q^{94} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut -\mathstrut 10q^{96} \) \(\mathstrut -\mathstrut 33q^{97} \) \(\mathstrut -\mathstrut q^{98} \) \(\mathstrut -\mathstrut 38q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −3.23056 −1.86517 −0.932583 0.360956i \(-0.882450\pi\)
−0.932583 + 0.360956i \(0.882450\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.65226 −1.63334 −0.816670 0.577104i \(-0.804183\pi\)
−0.816670 + 0.577104i \(0.804183\pi\)
\(6\) −3.23056 −1.31887
\(7\) 2.39039 0.903483 0.451742 0.892149i \(-0.350803\pi\)
0.451742 + 0.892149i \(0.350803\pi\)
\(8\) 1.00000 0.353553
\(9\) 7.43653 2.47884
\(10\) −3.65226 −1.15495
\(11\) 0.229147 0.0690904 0.0345452 0.999403i \(-0.489002\pi\)
0.0345452 + 0.999403i \(0.489002\pi\)
\(12\) −3.23056 −0.932583
\(13\) −1.51971 −0.421493 −0.210746 0.977541i \(-0.567589\pi\)
−0.210746 + 0.977541i \(0.567589\pi\)
\(14\) 2.39039 0.638859
\(15\) 11.7989 3.04645
\(16\) 1.00000 0.250000
\(17\) 1.23485 0.299496 0.149748 0.988724i \(-0.452154\pi\)
0.149748 + 0.988724i \(0.452154\pi\)
\(18\) 7.43653 1.75281
\(19\) 1.00000 0.229416
\(20\) −3.65226 −0.816670
\(21\) −7.72231 −1.68515
\(22\) 0.229147 0.0488543
\(23\) −8.59225 −1.79161 −0.895804 0.444450i \(-0.853399\pi\)
−0.895804 + 0.444450i \(0.853399\pi\)
\(24\) −3.23056 −0.659436
\(25\) 8.33901 1.66780
\(26\) −1.51971 −0.298041
\(27\) −14.3325 −2.75829
\(28\) 2.39039 0.451742
\(29\) −2.80955 −0.521721 −0.260860 0.965377i \(-0.584006\pi\)
−0.260860 + 0.965377i \(0.584006\pi\)
\(30\) 11.7989 2.15417
\(31\) 4.09925 0.736246 0.368123 0.929777i \(-0.380000\pi\)
0.368123 + 0.929777i \(0.380000\pi\)
\(32\) 1.00000 0.176777
\(33\) −0.740273 −0.128865
\(34\) 1.23485 0.211775
\(35\) −8.73034 −1.47570
\(36\) 7.43653 1.23942
\(37\) −7.69336 −1.26478 −0.632391 0.774650i \(-0.717926\pi\)
−0.632391 + 0.774650i \(0.717926\pi\)
\(38\) 1.00000 0.162221
\(39\) 4.90953 0.786154
\(40\) −3.65226 −0.577473
\(41\) 6.97582 1.08944 0.544720 0.838618i \(-0.316636\pi\)
0.544720 + 0.838618i \(0.316636\pi\)
\(42\) −7.72231 −1.19158
\(43\) −10.4732 −1.59715 −0.798573 0.601898i \(-0.794411\pi\)
−0.798573 + 0.601898i \(0.794411\pi\)
\(44\) 0.229147 0.0345452
\(45\) −27.1601 −4.04880
\(46\) −8.59225 −1.26686
\(47\) 11.1963 1.63315 0.816574 0.577241i \(-0.195871\pi\)
0.816574 + 0.577241i \(0.195871\pi\)
\(48\) −3.23056 −0.466291
\(49\) −1.28603 −0.183718
\(50\) 8.33901 1.17931
\(51\) −3.98926 −0.558609
\(52\) −1.51971 −0.210746
\(53\) 2.41819 0.332164 0.166082 0.986112i \(-0.446888\pi\)
0.166082 + 0.986112i \(0.446888\pi\)
\(54\) −14.3325 −1.95040
\(55\) −0.836904 −0.112848
\(56\) 2.39039 0.319430
\(57\) −3.23056 −0.427898
\(58\) −2.80955 −0.368912
\(59\) 5.91884 0.770567 0.385284 0.922798i \(-0.374104\pi\)
0.385284 + 0.922798i \(0.374104\pi\)
\(60\) 11.7989 1.52323
\(61\) 5.03288 0.644394 0.322197 0.946673i \(-0.395579\pi\)
0.322197 + 0.946673i \(0.395579\pi\)
\(62\) 4.09925 0.520605
\(63\) 17.7762 2.23959
\(64\) 1.00000 0.125000
\(65\) 5.55039 0.688442
\(66\) −0.740273 −0.0911214
\(67\) −1.27570 −0.155851 −0.0779257 0.996959i \(-0.524830\pi\)
−0.0779257 + 0.996959i \(0.524830\pi\)
\(68\) 1.23485 0.149748
\(69\) 27.7578 3.34164
\(70\) −8.73034 −1.04347
\(71\) 10.5869 1.25643 0.628214 0.778041i \(-0.283786\pi\)
0.628214 + 0.778041i \(0.283786\pi\)
\(72\) 7.43653 0.876403
\(73\) −5.30920 −0.621395 −0.310697 0.950509i \(-0.600563\pi\)
−0.310697 + 0.950509i \(0.600563\pi\)
\(74\) −7.69336 −0.894335
\(75\) −26.9397 −3.11073
\(76\) 1.00000 0.114708
\(77\) 0.547751 0.0624220
\(78\) 4.90953 0.555895
\(79\) 4.63819 0.521838 0.260919 0.965361i \(-0.415974\pi\)
0.260919 + 0.965361i \(0.415974\pi\)
\(80\) −3.65226 −0.408335
\(81\) 23.9924 2.66582
\(82\) 6.97582 0.770350
\(83\) 0.441306 0.0484396 0.0242198 0.999707i \(-0.492290\pi\)
0.0242198 + 0.999707i \(0.492290\pi\)
\(84\) −7.72231 −0.842573
\(85\) −4.51000 −0.489178
\(86\) −10.4732 −1.12935
\(87\) 9.07644 0.973096
\(88\) 0.229147 0.0244271
\(89\) 3.69080 0.391224 0.195612 0.980681i \(-0.437331\pi\)
0.195612 + 0.980681i \(0.437331\pi\)
\(90\) −27.1601 −2.86293
\(91\) −3.63271 −0.380812
\(92\) −8.59225 −0.895804
\(93\) −13.2429 −1.37322
\(94\) 11.1963 1.15481
\(95\) −3.65226 −0.374714
\(96\) −3.23056 −0.329718
\(97\) 7.94507 0.806699 0.403350 0.915046i \(-0.367846\pi\)
0.403350 + 0.915046i \(0.367846\pi\)
\(98\) −1.28603 −0.129908
\(99\) 1.70406 0.171264
\(100\) 8.33901 0.833901
\(101\) 15.3822 1.53059 0.765295 0.643679i \(-0.222593\pi\)
0.765295 + 0.643679i \(0.222593\pi\)
\(102\) −3.98926 −0.394996
\(103\) 11.3311 1.11649 0.558243 0.829677i \(-0.311476\pi\)
0.558243 + 0.829677i \(0.311476\pi\)
\(104\) −1.51971 −0.149020
\(105\) 28.2039 2.75242
\(106\) 2.41819 0.234875
\(107\) −7.66030 −0.740549 −0.370275 0.928922i \(-0.620736\pi\)
−0.370275 + 0.928922i \(0.620736\pi\)
\(108\) −14.3325 −1.37914
\(109\) −3.71384 −0.355721 −0.177860 0.984056i \(-0.556918\pi\)
−0.177860 + 0.984056i \(0.556918\pi\)
\(110\) −0.836904 −0.0797957
\(111\) 24.8539 2.35903
\(112\) 2.39039 0.225871
\(113\) −11.5383 −1.08543 −0.542716 0.839916i \(-0.682604\pi\)
−0.542716 + 0.839916i \(0.682604\pi\)
\(114\) −3.23056 −0.302570
\(115\) 31.3811 2.92631
\(116\) −2.80955 −0.260860
\(117\) −11.3014 −1.04481
\(118\) 5.91884 0.544873
\(119\) 2.95178 0.270589
\(120\) 11.7989 1.07708
\(121\) −10.9475 −0.995227
\(122\) 5.03288 0.455656
\(123\) −22.5358 −2.03199
\(124\) 4.09925 0.368123
\(125\) −12.1949 −1.09075
\(126\) 17.7762 1.58363
\(127\) 3.97747 0.352943 0.176471 0.984306i \(-0.443532\pi\)
0.176471 + 0.984306i \(0.443532\pi\)
\(128\) 1.00000 0.0883883
\(129\) 33.8343 2.97894
\(130\) 5.55039 0.486802
\(131\) 12.8956 1.12669 0.563346 0.826221i \(-0.309514\pi\)
0.563346 + 0.826221i \(0.309514\pi\)
\(132\) −0.740273 −0.0644325
\(133\) 2.39039 0.207273
\(134\) −1.27570 −0.110204
\(135\) 52.3460 4.50522
\(136\) 1.23485 0.105888
\(137\) 8.89558 0.760001 0.380000 0.924986i \(-0.375924\pi\)
0.380000 + 0.924986i \(0.375924\pi\)
\(138\) 27.7578 2.36290
\(139\) −18.2310 −1.54634 −0.773168 0.634202i \(-0.781329\pi\)
−0.773168 + 0.634202i \(0.781329\pi\)
\(140\) −8.73034 −0.737848
\(141\) −36.1703 −3.04609
\(142\) 10.5869 0.888429
\(143\) −0.348238 −0.0291211
\(144\) 7.43653 0.619711
\(145\) 10.2612 0.852148
\(146\) −5.30920 −0.439392
\(147\) 4.15458 0.342664
\(148\) −7.69336 −0.632391
\(149\) 5.63027 0.461249 0.230625 0.973043i \(-0.425923\pi\)
0.230625 + 0.973043i \(0.425923\pi\)
\(150\) −26.9397 −2.19962
\(151\) −22.9354 −1.86646 −0.933228 0.359284i \(-0.883021\pi\)
−0.933228 + 0.359284i \(0.883021\pi\)
\(152\) 1.00000 0.0811107
\(153\) 9.18301 0.742402
\(154\) 0.547751 0.0441390
\(155\) −14.9715 −1.20254
\(156\) 4.90953 0.393077
\(157\) −14.9345 −1.19191 −0.595953 0.803020i \(-0.703225\pi\)
−0.595953 + 0.803020i \(0.703225\pi\)
\(158\) 4.63819 0.368995
\(159\) −7.81211 −0.619541
\(160\) −3.65226 −0.288737
\(161\) −20.5388 −1.61869
\(162\) 23.9924 1.88502
\(163\) 9.70135 0.759868 0.379934 0.925014i \(-0.375947\pi\)
0.379934 + 0.925014i \(0.375947\pi\)
\(164\) 6.97582 0.544720
\(165\) 2.70367 0.210481
\(166\) 0.441306 0.0342520
\(167\) −15.6073 −1.20773 −0.603863 0.797088i \(-0.706373\pi\)
−0.603863 + 0.797088i \(0.706373\pi\)
\(168\) −7.72231 −0.595789
\(169\) −10.6905 −0.822344
\(170\) −4.51000 −0.345901
\(171\) 7.43653 0.568686
\(172\) −10.4732 −0.798573
\(173\) −6.52314 −0.495945 −0.247972 0.968767i \(-0.579764\pi\)
−0.247972 + 0.968767i \(0.579764\pi\)
\(174\) 9.07644 0.688083
\(175\) 19.9335 1.50683
\(176\) 0.229147 0.0172726
\(177\) −19.1212 −1.43724
\(178\) 3.69080 0.276637
\(179\) −6.02767 −0.450529 −0.225265 0.974298i \(-0.572325\pi\)
−0.225265 + 0.974298i \(0.572325\pi\)
\(180\) −27.1601 −2.02440
\(181\) 2.88974 0.214793 0.107396 0.994216i \(-0.465749\pi\)
0.107396 + 0.994216i \(0.465749\pi\)
\(182\) −3.63271 −0.269275
\(183\) −16.2590 −1.20190
\(184\) −8.59225 −0.633429
\(185\) 28.0982 2.06582
\(186\) −13.2429 −0.971014
\(187\) 0.282963 0.0206923
\(188\) 11.1963 0.816574
\(189\) −34.2603 −2.49207
\(190\) −3.65226 −0.264963
\(191\) 6.86116 0.496456 0.248228 0.968702i \(-0.420152\pi\)
0.248228 + 0.968702i \(0.420152\pi\)
\(192\) −3.23056 −0.233146
\(193\) −1.24997 −0.0899747 −0.0449874 0.998988i \(-0.514325\pi\)
−0.0449874 + 0.998988i \(0.514325\pi\)
\(194\) 7.94507 0.570423
\(195\) −17.9309 −1.28406
\(196\) −1.28603 −0.0918590
\(197\) −0.390431 −0.0278171 −0.0139085 0.999903i \(-0.504427\pi\)
−0.0139085 + 0.999903i \(0.504427\pi\)
\(198\) 1.70406 0.121102
\(199\) −3.56651 −0.252823 −0.126411 0.991978i \(-0.540346\pi\)
−0.126411 + 0.991978i \(0.540346\pi\)
\(200\) 8.33901 0.589657
\(201\) 4.12122 0.290689
\(202\) 15.3822 1.08229
\(203\) −6.71593 −0.471366
\(204\) −3.98926 −0.279304
\(205\) −25.4775 −1.77943
\(206\) 11.3311 0.789475
\(207\) −63.8965 −4.44111
\(208\) −1.51971 −0.105373
\(209\) 0.229147 0.0158504
\(210\) 28.2039 1.94625
\(211\) −1.00000 −0.0688428
\(212\) 2.41819 0.166082
\(213\) −34.2015 −2.34345
\(214\) −7.66030 −0.523647
\(215\) 38.2508 2.60868
\(216\) −14.3325 −0.975202
\(217\) 9.79881 0.665186
\(218\) −3.71384 −0.251533
\(219\) 17.1517 1.15900
\(220\) −0.836904 −0.0564241
\(221\) −1.87662 −0.126235
\(222\) 24.8539 1.66808
\(223\) −9.58727 −0.642011 −0.321006 0.947077i \(-0.604021\pi\)
−0.321006 + 0.947077i \(0.604021\pi\)
\(224\) 2.39039 0.159715
\(225\) 62.0133 4.13422
\(226\) −11.5383 −0.767516
\(227\) −18.3617 −1.21871 −0.609354 0.792898i \(-0.708571\pi\)
−0.609354 + 0.792898i \(0.708571\pi\)
\(228\) −3.23056 −0.213949
\(229\) 5.24337 0.346492 0.173246 0.984879i \(-0.444574\pi\)
0.173246 + 0.984879i \(0.444574\pi\)
\(230\) 31.3811 2.06921
\(231\) −1.76954 −0.116427
\(232\) −2.80955 −0.184456
\(233\) 2.53591 0.166133 0.0830666 0.996544i \(-0.473529\pi\)
0.0830666 + 0.996544i \(0.473529\pi\)
\(234\) −11.3014 −0.738796
\(235\) −40.8918 −2.66749
\(236\) 5.91884 0.385284
\(237\) −14.9840 −0.973314
\(238\) 2.95178 0.191335
\(239\) −20.2316 −1.30868 −0.654338 0.756202i \(-0.727052\pi\)
−0.654338 + 0.756202i \(0.727052\pi\)
\(240\) 11.7989 0.761613
\(241\) 1.33108 0.0857424 0.0428712 0.999081i \(-0.486349\pi\)
0.0428712 + 0.999081i \(0.486349\pi\)
\(242\) −10.9475 −0.703731
\(243\) −34.5114 −2.21391
\(244\) 5.03288 0.322197
\(245\) 4.69690 0.300074
\(246\) −22.5358 −1.43683
\(247\) −1.51971 −0.0966971
\(248\) 4.09925 0.260302
\(249\) −1.42567 −0.0903479
\(250\) −12.1949 −0.771276
\(251\) 30.4215 1.92019 0.960093 0.279681i \(-0.0902286\pi\)
0.960093 + 0.279681i \(0.0902286\pi\)
\(252\) 17.7762 1.11980
\(253\) −1.96889 −0.123783
\(254\) 3.97747 0.249568
\(255\) 14.5698 0.912399
\(256\) 1.00000 0.0625000
\(257\) 16.4111 1.02369 0.511847 0.859077i \(-0.328962\pi\)
0.511847 + 0.859077i \(0.328962\pi\)
\(258\) 33.8343 2.10643
\(259\) −18.3902 −1.14271
\(260\) 5.55039 0.344221
\(261\) −20.8933 −1.29326
\(262\) 12.8956 0.796691
\(263\) −5.15303 −0.317749 −0.158875 0.987299i \(-0.550787\pi\)
−0.158875 + 0.987299i \(0.550787\pi\)
\(264\) −0.740273 −0.0455607
\(265\) −8.83186 −0.542537
\(266\) 2.39039 0.146564
\(267\) −11.9234 −0.729698
\(268\) −1.27570 −0.0779257
\(269\) 4.03782 0.246190 0.123095 0.992395i \(-0.460718\pi\)
0.123095 + 0.992395i \(0.460718\pi\)
\(270\) 52.3460 3.18567
\(271\) −13.4426 −0.816579 −0.408289 0.912853i \(-0.633875\pi\)
−0.408289 + 0.912853i \(0.633875\pi\)
\(272\) 1.23485 0.0748739
\(273\) 11.7357 0.710277
\(274\) 8.89558 0.537402
\(275\) 1.91086 0.115229
\(276\) 27.7578 1.67082
\(277\) 11.7483 0.705889 0.352944 0.935644i \(-0.385180\pi\)
0.352944 + 0.935644i \(0.385180\pi\)
\(278\) −18.2310 −1.09342
\(279\) 30.4842 1.82504
\(280\) −8.73034 −0.521737
\(281\) 14.9416 0.891340 0.445670 0.895197i \(-0.352965\pi\)
0.445670 + 0.895197i \(0.352965\pi\)
\(282\) −36.1703 −2.15391
\(283\) 1.92528 0.114446 0.0572229 0.998361i \(-0.481775\pi\)
0.0572229 + 0.998361i \(0.481775\pi\)
\(284\) 10.5869 0.628214
\(285\) 11.7989 0.698904
\(286\) −0.348238 −0.0205917
\(287\) 16.6749 0.984291
\(288\) 7.43653 0.438202
\(289\) −15.4751 −0.910302
\(290\) 10.2612 0.602560
\(291\) −25.6670 −1.50463
\(292\) −5.30920 −0.310697
\(293\) −31.4958 −1.84000 −0.920002 0.391914i \(-0.871813\pi\)
−0.920002 + 0.391914i \(0.871813\pi\)
\(294\) 4.15458 0.242300
\(295\) −21.6171 −1.25860
\(296\) −7.69336 −0.447168
\(297\) −3.28424 −0.190571
\(298\) 5.63027 0.326153
\(299\) 13.0578 0.755150
\(300\) −26.9397 −1.55536
\(301\) −25.0350 −1.44300
\(302\) −22.9354 −1.31978
\(303\) −49.6933 −2.85481
\(304\) 1.00000 0.0573539
\(305\) −18.3814 −1.05252
\(306\) 9.18301 0.524958
\(307\) 12.8647 0.734228 0.367114 0.930176i \(-0.380346\pi\)
0.367114 + 0.930176i \(0.380346\pi\)
\(308\) 0.547751 0.0312110
\(309\) −36.6058 −2.08243
\(310\) −14.9715 −0.850325
\(311\) −25.7290 −1.45896 −0.729478 0.684004i \(-0.760237\pi\)
−0.729478 + 0.684004i \(0.760237\pi\)
\(312\) 4.90953 0.277947
\(313\) −24.5398 −1.38707 −0.693537 0.720421i \(-0.743948\pi\)
−0.693537 + 0.720421i \(0.743948\pi\)
\(314\) −14.9345 −0.842804
\(315\) −64.9234 −3.65802
\(316\) 4.63819 0.260919
\(317\) 19.5030 1.09540 0.547698 0.836676i \(-0.315504\pi\)
0.547698 + 0.836676i \(0.315504\pi\)
\(318\) −7.81211 −0.438082
\(319\) −0.643801 −0.0360459
\(320\) −3.65226 −0.204168
\(321\) 24.7471 1.38125
\(322\) −20.5388 −1.14458
\(323\) 1.23485 0.0687090
\(324\) 23.9924 1.33291
\(325\) −12.6729 −0.702967
\(326\) 9.70135 0.537308
\(327\) 11.9978 0.663478
\(328\) 6.97582 0.385175
\(329\) 26.7635 1.47552
\(330\) 2.70367 0.148832
\(331\) 8.66544 0.476296 0.238148 0.971229i \(-0.423460\pi\)
0.238148 + 0.971229i \(0.423460\pi\)
\(332\) 0.441306 0.0242198
\(333\) −57.2119 −3.13519
\(334\) −15.6073 −0.853991
\(335\) 4.65919 0.254558
\(336\) −7.72231 −0.421287
\(337\) −14.4531 −0.787309 −0.393654 0.919259i \(-0.628789\pi\)
−0.393654 + 0.919259i \(0.628789\pi\)
\(338\) −10.6905 −0.581485
\(339\) 37.2752 2.02451
\(340\) −4.51000 −0.244589
\(341\) 0.939330 0.0508676
\(342\) 7.43653 0.402121
\(343\) −19.8069 −1.06947
\(344\) −10.4732 −0.564677
\(345\) −101.379 −5.45804
\(346\) −6.52314 −0.350686
\(347\) −0.431535 −0.0231660 −0.0115830 0.999933i \(-0.503687\pi\)
−0.0115830 + 0.999933i \(0.503687\pi\)
\(348\) 9.07644 0.486548
\(349\) −5.76879 −0.308796 −0.154398 0.988009i \(-0.549344\pi\)
−0.154398 + 0.988009i \(0.549344\pi\)
\(350\) 19.9335 1.06549
\(351\) 21.7813 1.16260
\(352\) 0.229147 0.0122136
\(353\) −16.3363 −0.869494 −0.434747 0.900553i \(-0.643162\pi\)
−0.434747 + 0.900553i \(0.643162\pi\)
\(354\) −19.1212 −1.01628
\(355\) −38.6659 −2.05218
\(356\) 3.69080 0.195612
\(357\) −9.53591 −0.504694
\(358\) −6.02767 −0.318572
\(359\) 10.6597 0.562600 0.281300 0.959620i \(-0.409234\pi\)
0.281300 + 0.959620i \(0.409234\pi\)
\(360\) −27.1601 −1.43147
\(361\) 1.00000 0.0526316
\(362\) 2.88974 0.151881
\(363\) 35.3665 1.85626
\(364\) −3.63271 −0.190406
\(365\) 19.3906 1.01495
\(366\) −16.2590 −0.849873
\(367\) −23.8708 −1.24605 −0.623023 0.782204i \(-0.714096\pi\)
−0.623023 + 0.782204i \(0.714096\pi\)
\(368\) −8.59225 −0.447902
\(369\) 51.8759 2.70055
\(370\) 28.0982 1.46075
\(371\) 5.78042 0.300105
\(372\) −13.2429 −0.686611
\(373\) −27.5695 −1.42749 −0.713747 0.700404i \(-0.753003\pi\)
−0.713747 + 0.700404i \(0.753003\pi\)
\(374\) 0.282963 0.0146316
\(375\) 39.3965 2.03443
\(376\) 11.1963 0.577405
\(377\) 4.26972 0.219902
\(378\) −34.2603 −1.76216
\(379\) 4.83139 0.248172 0.124086 0.992271i \(-0.460400\pi\)
0.124086 + 0.992271i \(0.460400\pi\)
\(380\) −3.65226 −0.187357
\(381\) −12.8494 −0.658297
\(382\) 6.86116 0.351047
\(383\) 28.5696 1.45984 0.729919 0.683534i \(-0.239558\pi\)
0.729919 + 0.683534i \(0.239558\pi\)
\(384\) −3.23056 −0.164859
\(385\) −2.00053 −0.101956
\(386\) −1.24997 −0.0636217
\(387\) −77.8842 −3.95908
\(388\) 7.94507 0.403350
\(389\) 17.6906 0.896947 0.448474 0.893796i \(-0.351968\pi\)
0.448474 + 0.893796i \(0.351968\pi\)
\(390\) −17.9309 −0.907966
\(391\) −10.6102 −0.536578
\(392\) −1.28603 −0.0649541
\(393\) −41.6600 −2.10147
\(394\) −0.390431 −0.0196696
\(395\) −16.9399 −0.852339
\(396\) 1.70406 0.0856321
\(397\) −26.1741 −1.31364 −0.656821 0.754047i \(-0.728099\pi\)
−0.656821 + 0.754047i \(0.728099\pi\)
\(398\) −3.56651 −0.178773
\(399\) −7.72231 −0.386599
\(400\) 8.33901 0.416951
\(401\) −39.1083 −1.95298 −0.976489 0.215569i \(-0.930839\pi\)
−0.976489 + 0.215569i \(0.930839\pi\)
\(402\) 4.12122 0.205548
\(403\) −6.22968 −0.310323
\(404\) 15.3822 0.765295
\(405\) −87.6264 −4.35419
\(406\) −6.71593 −0.333306
\(407\) −1.76291 −0.0873842
\(408\) −3.98926 −0.197498
\(409\) −30.0877 −1.48774 −0.743870 0.668324i \(-0.767012\pi\)
−0.743870 + 0.668324i \(0.767012\pi\)
\(410\) −25.4775 −1.25824
\(411\) −28.7377 −1.41753
\(412\) 11.3311 0.558243
\(413\) 14.1483 0.696195
\(414\) −63.8965 −3.14034
\(415\) −1.61176 −0.0791184
\(416\) −1.51971 −0.0745101
\(417\) 58.8964 2.88417
\(418\) 0.229147 0.0112079
\(419\) −1.17310 −0.0573098 −0.0286549 0.999589i \(-0.509122\pi\)
−0.0286549 + 0.999589i \(0.509122\pi\)
\(420\) 28.2039 1.37621
\(421\) 16.7829 0.817950 0.408975 0.912546i \(-0.365886\pi\)
0.408975 + 0.912546i \(0.365886\pi\)
\(422\) −1.00000 −0.0486792
\(423\) 83.2616 4.04832
\(424\) 2.41819 0.117438
\(425\) 10.2974 0.499499
\(426\) −34.2015 −1.65707
\(427\) 12.0306 0.582200
\(428\) −7.66030 −0.370275
\(429\) 1.12500 0.0543157
\(430\) 38.2508 1.84462
\(431\) −7.56515 −0.364401 −0.182200 0.983261i \(-0.558322\pi\)
−0.182200 + 0.983261i \(0.558322\pi\)
\(432\) −14.3325 −0.689572
\(433\) 7.92605 0.380902 0.190451 0.981697i \(-0.439005\pi\)
0.190451 + 0.981697i \(0.439005\pi\)
\(434\) 9.79881 0.470358
\(435\) −33.1495 −1.58940
\(436\) −3.71384 −0.177860
\(437\) −8.59225 −0.411023
\(438\) 17.1517 0.819539
\(439\) 8.97895 0.428542 0.214271 0.976774i \(-0.431262\pi\)
0.214271 + 0.976774i \(0.431262\pi\)
\(440\) −0.836904 −0.0398979
\(441\) −9.56357 −0.455408
\(442\) −1.87662 −0.0892618
\(443\) 31.4899 1.49613 0.748065 0.663625i \(-0.230983\pi\)
0.748065 + 0.663625i \(0.230983\pi\)
\(444\) 24.8539 1.17951
\(445\) −13.4798 −0.639002
\(446\) −9.58727 −0.453970
\(447\) −18.1889 −0.860306
\(448\) 2.39039 0.112935
\(449\) 15.3450 0.724176 0.362088 0.932144i \(-0.382064\pi\)
0.362088 + 0.932144i \(0.382064\pi\)
\(450\) 62.0133 2.92333
\(451\) 1.59849 0.0752698
\(452\) −11.5383 −0.542716
\(453\) 74.0942 3.48125
\(454\) −18.3617 −0.861756
\(455\) 13.2676 0.621995
\(456\) −3.23056 −0.151285
\(457\) −19.5714 −0.915510 −0.457755 0.889078i \(-0.651346\pi\)
−0.457755 + 0.889078i \(0.651346\pi\)
\(458\) 5.24337 0.245007
\(459\) −17.6985 −0.826095
\(460\) 31.3811 1.46315
\(461\) −6.56806 −0.305905 −0.152953 0.988234i \(-0.548878\pi\)
−0.152953 + 0.988234i \(0.548878\pi\)
\(462\) −1.76954 −0.0823266
\(463\) −30.7081 −1.42713 −0.713563 0.700591i \(-0.752920\pi\)
−0.713563 + 0.700591i \(0.752920\pi\)
\(464\) −2.80955 −0.130430
\(465\) 48.3664 2.24294
\(466\) 2.53591 0.117474
\(467\) 13.3222 0.616480 0.308240 0.951309i \(-0.400260\pi\)
0.308240 + 0.951309i \(0.400260\pi\)
\(468\) −11.3014 −0.522407
\(469\) −3.04942 −0.140809
\(470\) −40.8918 −1.88620
\(471\) 48.2469 2.22310
\(472\) 5.91884 0.272437
\(473\) −2.39990 −0.110347
\(474\) −14.9840 −0.688237
\(475\) 8.33901 0.382620
\(476\) 2.95178 0.135295
\(477\) 17.9829 0.823383
\(478\) −20.2316 −0.925373
\(479\) 32.9788 1.50684 0.753420 0.657540i \(-0.228403\pi\)
0.753420 + 0.657540i \(0.228403\pi\)
\(480\) 11.7989 0.538542
\(481\) 11.6917 0.533096
\(482\) 1.33108 0.0606290
\(483\) 66.3520 3.01912
\(484\) −10.9475 −0.497613
\(485\) −29.0175 −1.31762
\(486\) −34.5114 −1.56547
\(487\) 30.1843 1.36778 0.683891 0.729584i \(-0.260286\pi\)
0.683891 + 0.729584i \(0.260286\pi\)
\(488\) 5.03288 0.227828
\(489\) −31.3408 −1.41728
\(490\) 4.69690 0.212184
\(491\) −5.62352 −0.253786 −0.126893 0.991916i \(-0.540500\pi\)
−0.126893 + 0.991916i \(0.540500\pi\)
\(492\) −22.5358 −1.01599
\(493\) −3.46938 −0.156253
\(494\) −1.51971 −0.0683752
\(495\) −6.22366 −0.279733
\(496\) 4.09925 0.184062
\(497\) 25.3067 1.13516
\(498\) −1.42567 −0.0638856
\(499\) −7.32951 −0.328114 −0.164057 0.986451i \(-0.552458\pi\)
−0.164057 + 0.986451i \(0.552458\pi\)
\(500\) −12.1949 −0.545374
\(501\) 50.4202 2.25261
\(502\) 30.4215 1.35778
\(503\) −43.4235 −1.93616 −0.968078 0.250649i \(-0.919356\pi\)
−0.968078 + 0.250649i \(0.919356\pi\)
\(504\) 17.7762 0.791816
\(505\) −56.1800 −2.49998
\(506\) −1.96889 −0.0875277
\(507\) 34.5362 1.53381
\(508\) 3.97747 0.176471
\(509\) −3.39862 −0.150641 −0.0753206 0.997159i \(-0.523998\pi\)
−0.0753206 + 0.997159i \(0.523998\pi\)
\(510\) 14.5698 0.645163
\(511\) −12.6911 −0.561420
\(512\) 1.00000 0.0441942
\(513\) −14.3325 −0.632795
\(514\) 16.4111 0.723860
\(515\) −41.3841 −1.82360
\(516\) 33.8343 1.48947
\(517\) 2.56560 0.112835
\(518\) −18.3902 −0.808017
\(519\) 21.0734 0.925020
\(520\) 5.55039 0.243401
\(521\) −13.3063 −0.582960 −0.291480 0.956577i \(-0.594148\pi\)
−0.291480 + 0.956577i \(0.594148\pi\)
\(522\) −20.8933 −0.914476
\(523\) 7.85981 0.343686 0.171843 0.985124i \(-0.445028\pi\)
0.171843 + 0.985124i \(0.445028\pi\)
\(524\) 12.8956 0.563346
\(525\) −64.3964 −2.81049
\(526\) −5.15303 −0.224683
\(527\) 5.06196 0.220503
\(528\) −0.740273 −0.0322163
\(529\) 50.8267 2.20986
\(530\) −8.83186 −0.383632
\(531\) 44.0156 1.91012
\(532\) 2.39039 0.103637
\(533\) −10.6013 −0.459191
\(534\) −11.9234 −0.515974
\(535\) 27.9774 1.20957
\(536\) −1.27570 −0.0551018
\(537\) 19.4728 0.840311
\(538\) 4.03782 0.174083
\(539\) −0.294689 −0.0126931
\(540\) 52.3460 2.25261
\(541\) −27.9735 −1.20268 −0.601338 0.798995i \(-0.705366\pi\)
−0.601338 + 0.798995i \(0.705366\pi\)
\(542\) −13.4426 −0.577409
\(543\) −9.33549 −0.400624
\(544\) 1.23485 0.0529438
\(545\) 13.5639 0.581013
\(546\) 11.7357 0.502242
\(547\) 37.5390 1.60505 0.802525 0.596618i \(-0.203489\pi\)
0.802525 + 0.596618i \(0.203489\pi\)
\(548\) 8.89558 0.380000
\(549\) 37.4272 1.59735
\(550\) 1.91086 0.0814793
\(551\) −2.80955 −0.119691
\(552\) 27.7578 1.18145
\(553\) 11.0871 0.471472
\(554\) 11.7483 0.499139
\(555\) −90.7729 −3.85309
\(556\) −18.2310 −0.773168
\(557\) 17.5000 0.741498 0.370749 0.928733i \(-0.379101\pi\)
0.370749 + 0.928733i \(0.379101\pi\)
\(558\) 30.4842 1.29050
\(559\) 15.9163 0.673186
\(560\) −8.73034 −0.368924
\(561\) −0.914128 −0.0385945
\(562\) 14.9416 0.630273
\(563\) −41.3629 −1.74324 −0.871619 0.490183i \(-0.836930\pi\)
−0.871619 + 0.490183i \(0.836930\pi\)
\(564\) −36.1703 −1.52304
\(565\) 42.1409 1.77288
\(566\) 1.92528 0.0809253
\(567\) 57.3512 2.40852
\(568\) 10.5869 0.444214
\(569\) 1.60985 0.0674882 0.0337441 0.999431i \(-0.489257\pi\)
0.0337441 + 0.999431i \(0.489257\pi\)
\(570\) 11.7989 0.494200
\(571\) −24.5836 −1.02879 −0.514396 0.857553i \(-0.671984\pi\)
−0.514396 + 0.857553i \(0.671984\pi\)
\(572\) −0.348238 −0.0145606
\(573\) −22.1654 −0.925972
\(574\) 16.6749 0.695999
\(575\) −71.6508 −2.98805
\(576\) 7.43653 0.309855
\(577\) −9.27040 −0.385932 −0.192966 0.981205i \(-0.561811\pi\)
−0.192966 + 0.981205i \(0.561811\pi\)
\(578\) −15.4751 −0.643681
\(579\) 4.03810 0.167818
\(580\) 10.2612 0.426074
\(581\) 1.05489 0.0437644
\(582\) −25.6670 −1.06393
\(583\) 0.554121 0.0229493
\(584\) −5.30920 −0.219696
\(585\) 41.2757 1.70654
\(586\) −31.4958 −1.30108
\(587\) −18.0076 −0.743252 −0.371626 0.928383i \(-0.621200\pi\)
−0.371626 + 0.928383i \(0.621200\pi\)
\(588\) 4.15458 0.171332
\(589\) 4.09925 0.168907
\(590\) −21.6171 −0.889964
\(591\) 1.26131 0.0518834
\(592\) −7.69336 −0.316195
\(593\) −23.9198 −0.982270 −0.491135 0.871084i \(-0.663418\pi\)
−0.491135 + 0.871084i \(0.663418\pi\)
\(594\) −3.28424 −0.134754
\(595\) −10.7807 −0.441964
\(596\) 5.63027 0.230625
\(597\) 11.5218 0.471557
\(598\) 13.0578 0.533972
\(599\) −11.3110 −0.462156 −0.231078 0.972935i \(-0.574225\pi\)
−0.231078 + 0.972935i \(0.574225\pi\)
\(600\) −26.9397 −1.09981
\(601\) 13.2639 0.541047 0.270524 0.962713i \(-0.412803\pi\)
0.270524 + 0.962713i \(0.412803\pi\)
\(602\) −25.0350 −1.02035
\(603\) −9.48677 −0.386331
\(604\) −22.9354 −0.933228
\(605\) 39.9831 1.62554
\(606\) −49.6933 −2.01865
\(607\) 0.994203 0.0403535 0.0201767 0.999796i \(-0.493577\pi\)
0.0201767 + 0.999796i \(0.493577\pi\)
\(608\) 1.00000 0.0405554
\(609\) 21.6962 0.879176
\(610\) −18.3814 −0.744241
\(611\) −17.0152 −0.688360
\(612\) 9.18301 0.371201
\(613\) −10.7488 −0.434139 −0.217069 0.976156i \(-0.569650\pi\)
−0.217069 + 0.976156i \(0.569650\pi\)
\(614\) 12.8647 0.519178
\(615\) 82.3067 3.31892
\(616\) 0.547751 0.0220695
\(617\) −37.3375 −1.50315 −0.751575 0.659647i \(-0.770706\pi\)
−0.751575 + 0.659647i \(0.770706\pi\)
\(618\) −36.6058 −1.47250
\(619\) −29.9203 −1.20260 −0.601300 0.799023i \(-0.705350\pi\)
−0.601300 + 0.799023i \(0.705350\pi\)
\(620\) −14.9715 −0.601271
\(621\) 123.148 4.94177
\(622\) −25.7290 −1.03164
\(623\) 8.82246 0.353464
\(624\) 4.90953 0.196539
\(625\) 2.84404 0.113762
\(626\) −24.5398 −0.980809
\(627\) −0.740273 −0.0295637
\(628\) −14.9345 −0.595953
\(629\) −9.50016 −0.378796
\(630\) −64.9234 −2.58661
\(631\) 8.60650 0.342619 0.171310 0.985217i \(-0.445200\pi\)
0.171310 + 0.985217i \(0.445200\pi\)
\(632\) 4.63819 0.184497
\(633\) 3.23056 0.128403
\(634\) 19.5030 0.774562
\(635\) −14.5267 −0.576476
\(636\) −7.81211 −0.309770
\(637\) 1.95439 0.0774358
\(638\) −0.643801 −0.0254883
\(639\) 78.7294 3.11449
\(640\) −3.65226 −0.144368
\(641\) −18.2571 −0.721111 −0.360556 0.932738i \(-0.617413\pi\)
−0.360556 + 0.932738i \(0.617413\pi\)
\(642\) 24.7471 0.976689
\(643\) −39.5014 −1.55778 −0.778892 0.627158i \(-0.784218\pi\)
−0.778892 + 0.627158i \(0.784218\pi\)
\(644\) −20.5388 −0.809344
\(645\) −123.572 −4.86563
\(646\) 1.23485 0.0485846
\(647\) −12.9526 −0.509219 −0.254609 0.967044i \(-0.581947\pi\)
−0.254609 + 0.967044i \(0.581947\pi\)
\(648\) 23.9924 0.942510
\(649\) 1.35628 0.0532388
\(650\) −12.6729 −0.497073
\(651\) −31.6557 −1.24068
\(652\) 9.70135 0.379934
\(653\) −30.0711 −1.17677 −0.588387 0.808579i \(-0.700237\pi\)
−0.588387 + 0.808579i \(0.700237\pi\)
\(654\) 11.9978 0.469150
\(655\) −47.0980 −1.84027
\(656\) 6.97582 0.272360
\(657\) −39.4820 −1.54034
\(658\) 26.7635 1.04335
\(659\) 0.699015 0.0272298 0.0136149 0.999907i \(-0.495666\pi\)
0.0136149 + 0.999907i \(0.495666\pi\)
\(660\) 2.70367 0.105240
\(661\) −18.0802 −0.703239 −0.351619 0.936143i \(-0.614369\pi\)
−0.351619 + 0.936143i \(0.614369\pi\)
\(662\) 8.66544 0.336792
\(663\) 6.06254 0.235450
\(664\) 0.441306 0.0171260
\(665\) −8.73034 −0.338548
\(666\) −57.2119 −2.21692
\(667\) 24.1404 0.934719
\(668\) −15.6073 −0.603863
\(669\) 30.9723 1.19746
\(670\) 4.65919 0.180000
\(671\) 1.15327 0.0445215
\(672\) −7.72231 −0.297895
\(673\) −21.9960 −0.847885 −0.423943 0.905689i \(-0.639354\pi\)
−0.423943 + 0.905689i \(0.639354\pi\)
\(674\) −14.4531 −0.556711
\(675\) −119.519 −4.60028
\(676\) −10.6905 −0.411172
\(677\) 39.9127 1.53397 0.766985 0.641665i \(-0.221756\pi\)
0.766985 + 0.641665i \(0.221756\pi\)
\(678\) 37.2752 1.43154
\(679\) 18.9918 0.728839
\(680\) −4.51000 −0.172951
\(681\) 59.3185 2.27309
\(682\) 0.939330 0.0359688
\(683\) 4.85952 0.185945 0.0929723 0.995669i \(-0.470363\pi\)
0.0929723 + 0.995669i \(0.470363\pi\)
\(684\) 7.43653 0.284343
\(685\) −32.4890 −1.24134
\(686\) −19.8069 −0.756229
\(687\) −16.9390 −0.646265
\(688\) −10.4732 −0.399287
\(689\) −3.67496 −0.140005
\(690\) −101.379 −3.85942
\(691\) −17.1704 −0.653194 −0.326597 0.945164i \(-0.605902\pi\)
−0.326597 + 0.945164i \(0.605902\pi\)
\(692\) −6.52314 −0.247972
\(693\) 4.07337 0.154734
\(694\) −0.431535 −0.0163808
\(695\) 66.5845 2.52569
\(696\) 9.07644 0.344041
\(697\) 8.61410 0.326282
\(698\) −5.76879 −0.218352
\(699\) −8.19242 −0.309866
\(700\) 19.9335 0.753416
\(701\) −40.5003 −1.52968 −0.764838 0.644223i \(-0.777181\pi\)
−0.764838 + 0.644223i \(0.777181\pi\)
\(702\) 21.7813 0.822081
\(703\) −7.69336 −0.290161
\(704\) 0.229147 0.00863630
\(705\) 132.103 4.97530
\(706\) −16.3363 −0.614825
\(707\) 36.7696 1.38286
\(708\) −19.1212 −0.718618
\(709\) −6.78729 −0.254902 −0.127451 0.991845i \(-0.540680\pi\)
−0.127451 + 0.991845i \(0.540680\pi\)
\(710\) −38.6659 −1.45111
\(711\) 34.4921 1.29355
\(712\) 3.69080 0.138319
\(713\) −35.2217 −1.31906
\(714\) −9.53591 −0.356872
\(715\) 1.27186 0.0475647
\(716\) −6.02767 −0.225265
\(717\) 65.3595 2.44090
\(718\) 10.6597 0.397818
\(719\) −25.9395 −0.967379 −0.483690 0.875240i \(-0.660704\pi\)
−0.483690 + 0.875240i \(0.660704\pi\)
\(720\) −27.1601 −1.01220
\(721\) 27.0858 1.00873
\(722\) 1.00000 0.0372161
\(723\) −4.30013 −0.159924
\(724\) 2.88974 0.107396
\(725\) −23.4289 −0.870127
\(726\) 35.3665 1.31258
\(727\) 48.0383 1.78164 0.890821 0.454354i \(-0.150130\pi\)
0.890821 + 0.454354i \(0.150130\pi\)
\(728\) −3.63271 −0.134637
\(729\) 39.5141 1.46349
\(730\) 19.3906 0.717677
\(731\) −12.9328 −0.478338
\(732\) −16.2590 −0.600951
\(733\) 38.1311 1.40840 0.704202 0.710000i \(-0.251305\pi\)
0.704202 + 0.710000i \(0.251305\pi\)
\(734\) −23.8708 −0.881087
\(735\) −15.1736 −0.559688
\(736\) −8.59225 −0.316714
\(737\) −0.292322 −0.0107678
\(738\) 51.8759 1.90958
\(739\) 30.5081 1.12226 0.561130 0.827728i \(-0.310367\pi\)
0.561130 + 0.827728i \(0.310367\pi\)
\(740\) 28.0982 1.03291
\(741\) 4.90953 0.180356
\(742\) 5.78042 0.212206
\(743\) 49.0897 1.80093 0.900464 0.434931i \(-0.143227\pi\)
0.900464 + 0.434931i \(0.143227\pi\)
\(744\) −13.2429 −0.485507
\(745\) −20.5632 −0.753377
\(746\) −27.5695 −1.00939
\(747\) 3.28178 0.120074
\(748\) 0.282963 0.0103461
\(749\) −18.3111 −0.669074
\(750\) 39.3965 1.43856
\(751\) −20.4439 −0.746009 −0.373004 0.927830i \(-0.621672\pi\)
−0.373004 + 0.927830i \(0.621672\pi\)
\(752\) 11.1963 0.408287
\(753\) −98.2784 −3.58147
\(754\) 4.26972 0.155494
\(755\) 83.7661 3.04856
\(756\) −34.2603 −1.24603
\(757\) −10.5719 −0.384242 −0.192121 0.981371i \(-0.561537\pi\)
−0.192121 + 0.981371i \(0.561537\pi\)
\(758\) 4.83139 0.175484
\(759\) 6.36061 0.230876
\(760\) −3.65226 −0.132481
\(761\) −32.1882 −1.16682 −0.583410 0.812178i \(-0.698282\pi\)
−0.583410 + 0.812178i \(0.698282\pi\)
\(762\) −12.8494 −0.465486
\(763\) −8.87752 −0.321388
\(764\) 6.86116 0.248228
\(765\) −33.5388 −1.21260
\(766\) 28.5696 1.03226
\(767\) −8.99495 −0.324789
\(768\) −3.23056 −0.116573
\(769\) −51.8063 −1.86818 −0.934092 0.357032i \(-0.883789\pi\)
−0.934092 + 0.357032i \(0.883789\pi\)
\(770\) −2.00053 −0.0720941
\(771\) −53.0169 −1.90936
\(772\) −1.24997 −0.0449874
\(773\) 16.1272 0.580056 0.290028 0.957018i \(-0.406335\pi\)
0.290028 + 0.957018i \(0.406335\pi\)
\(774\) −77.8842 −2.79949
\(775\) 34.1837 1.22791
\(776\) 7.94507 0.285211
\(777\) 59.4105 2.13134
\(778\) 17.6906 0.634238
\(779\) 6.97582 0.249935
\(780\) −17.9309 −0.642029
\(781\) 2.42594 0.0868071
\(782\) −10.6102 −0.379418
\(783\) 40.2679 1.43906
\(784\) −1.28603 −0.0459295
\(785\) 54.5448 1.94679
\(786\) −41.6600 −1.48596
\(787\) 6.45141 0.229968 0.114984 0.993367i \(-0.463318\pi\)
0.114984 + 0.993367i \(0.463318\pi\)
\(788\) −0.390431 −0.0139085
\(789\) 16.6472 0.592655
\(790\) −16.9399 −0.602695
\(791\) −27.5811 −0.980669
\(792\) 1.70406 0.0605511
\(793\) −7.64854 −0.271608
\(794\) −26.1741 −0.928885
\(795\) 28.5319 1.01192
\(796\) −3.56651 −0.126411
\(797\) 12.7652 0.452166 0.226083 0.974108i \(-0.427408\pi\)
0.226083 + 0.974108i \(0.427408\pi\)
\(798\) −7.72231 −0.273367
\(799\) 13.8258 0.489120
\(800\) 8.33901 0.294829
\(801\) 27.4467 0.969783
\(802\) −39.1083 −1.38096
\(803\) −1.21659 −0.0429324
\(804\) 4.12122 0.145344
\(805\) 75.0132 2.64387
\(806\) −6.22968 −0.219431
\(807\) −13.0444 −0.459186
\(808\) 15.3822 0.541146
\(809\) −24.6877 −0.867973 −0.433986 0.900919i \(-0.642893\pi\)
−0.433986 + 0.900919i \(0.642893\pi\)
\(810\) −87.6264 −3.07888
\(811\) −17.4948 −0.614326 −0.307163 0.951657i \(-0.599380\pi\)
−0.307163 + 0.951657i \(0.599380\pi\)
\(812\) −6.71593 −0.235683
\(813\) 43.4271 1.52306
\(814\) −1.76291 −0.0617900
\(815\) −35.4319 −1.24112
\(816\) −3.98926 −0.139652
\(817\) −10.4732 −0.366411
\(818\) −30.0877 −1.05199
\(819\) −27.0148 −0.943973
\(820\) −25.4775 −0.889713
\(821\) −51.4035 −1.79400 −0.896998 0.442035i \(-0.854257\pi\)
−0.896998 + 0.442035i \(0.854257\pi\)
\(822\) −28.7377 −1.00234
\(823\) 23.3674 0.814537 0.407268 0.913308i \(-0.366481\pi\)
0.407268 + 0.913308i \(0.366481\pi\)
\(824\) 11.3311 0.394738
\(825\) −6.17315 −0.214921
\(826\) 14.1483 0.492284
\(827\) 0.778285 0.0270636 0.0135318 0.999908i \(-0.495693\pi\)
0.0135318 + 0.999908i \(0.495693\pi\)
\(828\) −63.8965 −2.22056
\(829\) −40.8249 −1.41791 −0.708954 0.705255i \(-0.750832\pi\)
−0.708954 + 0.705255i \(0.750832\pi\)
\(830\) −1.61176 −0.0559451
\(831\) −37.9537 −1.31660
\(832\) −1.51971 −0.0526866
\(833\) −1.58805 −0.0550227
\(834\) 58.8964 2.03942
\(835\) 57.0018 1.97263
\(836\) 0.229147 0.00792521
\(837\) −58.7524 −2.03078
\(838\) −1.17310 −0.0405242
\(839\) 19.6042 0.676813 0.338407 0.941000i \(-0.390112\pi\)
0.338407 + 0.941000i \(0.390112\pi\)
\(840\) 28.2039 0.973127
\(841\) −21.1064 −0.727807
\(842\) 16.7829 0.578378
\(843\) −48.2697 −1.66250
\(844\) −1.00000 −0.0344214
\(845\) 39.0444 1.34317
\(846\) 83.2616 2.86259
\(847\) −26.1688 −0.899171
\(848\) 2.41819 0.0830410
\(849\) −6.21972 −0.213460
\(850\) 10.2974 0.353199
\(851\) 66.1033 2.26599
\(852\) −34.2015 −1.17172
\(853\) 36.3411 1.24429 0.622147 0.782900i \(-0.286261\pi\)
0.622147 + 0.782900i \(0.286261\pi\)
\(854\) 12.0306 0.411677
\(855\) −27.1601 −0.928857
\(856\) −7.66030 −0.261824
\(857\) −30.1884 −1.03122 −0.515609 0.856824i \(-0.672434\pi\)
−0.515609 + 0.856824i \(0.672434\pi\)
\(858\) 1.12500 0.0384070
\(859\) 47.8902 1.63399 0.816996 0.576643i \(-0.195638\pi\)
0.816996 + 0.576643i \(0.195638\pi\)
\(860\) 38.2508 1.30434
\(861\) −53.8694 −1.83587
\(862\) −7.56515 −0.257670
\(863\) −35.5990 −1.21180 −0.605901 0.795540i \(-0.707187\pi\)
−0.605901 + 0.795540i \(0.707187\pi\)
\(864\) −14.3325 −0.487601
\(865\) 23.8242 0.810047
\(866\) 7.92605 0.269338
\(867\) 49.9934 1.69786
\(868\) 9.79881 0.332593
\(869\) 1.06283 0.0360540
\(870\) −33.1495 −1.12387
\(871\) 1.93870 0.0656903
\(872\) −3.71384 −0.125766
\(873\) 59.0837 1.99968
\(874\) −8.59225 −0.290637
\(875\) −29.1507 −0.985473
\(876\) 17.1517 0.579502
\(877\) −26.1504 −0.883035 −0.441518 0.897253i \(-0.645560\pi\)
−0.441518 + 0.897253i \(0.645560\pi\)
\(878\) 8.97895 0.303025
\(879\) 101.749 3.43191
\(880\) −0.836904 −0.0282120
\(881\) 19.1848 0.646353 0.323176 0.946339i \(-0.395249\pi\)
0.323176 + 0.946339i \(0.395249\pi\)
\(882\) −9.56357 −0.322022
\(883\) −17.2507 −0.580532 −0.290266 0.956946i \(-0.593744\pi\)
−0.290266 + 0.956946i \(0.593744\pi\)
\(884\) −1.87662 −0.0631176
\(885\) 69.8355 2.34750
\(886\) 31.4899 1.05792
\(887\) 18.2485 0.612726 0.306363 0.951915i \(-0.400888\pi\)
0.306363 + 0.951915i \(0.400888\pi\)
\(888\) 24.8539 0.834042
\(889\) 9.50770 0.318878
\(890\) −13.4798 −0.451843
\(891\) 5.49778 0.184183
\(892\) −9.58727 −0.321006
\(893\) 11.1963 0.374670
\(894\) −18.1889 −0.608328
\(895\) 22.0146 0.735867
\(896\) 2.39039 0.0798574
\(897\) −42.1839 −1.40848
\(898\) 15.3450 0.512070
\(899\) −11.5171 −0.384115
\(900\) 62.0133 2.06711
\(901\) 2.98611 0.0994816
\(902\) 1.59849 0.0532238
\(903\) 80.8772 2.69143
\(904\) −11.5383 −0.383758
\(905\) −10.5541 −0.350830
\(906\) 74.0942 2.46162
\(907\) −36.7014 −1.21865 −0.609325 0.792920i \(-0.708560\pi\)
−0.609325 + 0.792920i \(0.708560\pi\)
\(908\) −18.3617 −0.609354
\(909\) 114.391 3.79409
\(910\) 13.2676 0.439817
\(911\) 56.9332 1.88628 0.943141 0.332392i \(-0.107856\pi\)
0.943141 + 0.332392i \(0.107856\pi\)
\(912\) −3.23056 −0.106975
\(913\) 0.101124 0.00334671
\(914\) −19.5714 −0.647363
\(915\) 59.3822 1.96312
\(916\) 5.24337 0.173246
\(917\) 30.8255 1.01795
\(918\) −17.6985 −0.584137
\(919\) −10.3542 −0.341555 −0.170777 0.985310i \(-0.554628\pi\)
−0.170777 + 0.985310i \(0.554628\pi\)
\(920\) 31.3811 1.03461
\(921\) −41.5603 −1.36946
\(922\) −6.56806 −0.216308
\(923\) −16.0890 −0.529576
\(924\) −1.76954 −0.0582137
\(925\) −64.1550 −2.10940
\(926\) −30.7081 −1.00913
\(927\) 84.2640 2.76759
\(928\) −2.80955 −0.0922281
\(929\) 47.3203 1.55253 0.776265 0.630407i \(-0.217112\pi\)
0.776265 + 0.630407i \(0.217112\pi\)
\(930\) 48.3664 1.58600
\(931\) −1.28603 −0.0421478
\(932\) 2.53591 0.0830666
\(933\) 83.1191 2.72120
\(934\) 13.3222 0.435917
\(935\) −1.03345 −0.0337975
\(936\) −11.3014 −0.369398
\(937\) 49.3905 1.61352 0.806759 0.590880i \(-0.201219\pi\)
0.806759 + 0.590880i \(0.201219\pi\)
\(938\) −3.04942 −0.0995671
\(939\) 79.2774 2.58712
\(940\) −40.8918 −1.33374
\(941\) −45.4484 −1.48157 −0.740787 0.671740i \(-0.765547\pi\)
−0.740787 + 0.671740i \(0.765547\pi\)
\(942\) 48.2469 1.57197
\(943\) −59.9379 −1.95185
\(944\) 5.91884 0.192642
\(945\) 125.127 4.07039
\(946\) −2.39990 −0.0780275
\(947\) −20.7896 −0.675572 −0.337786 0.941223i \(-0.609678\pi\)
−0.337786 + 0.941223i \(0.609678\pi\)
\(948\) −14.9840 −0.486657
\(949\) 8.06846 0.261913
\(950\) 8.33901 0.270553
\(951\) −63.0055 −2.04309
\(952\) 2.95178 0.0956677
\(953\) −20.4516 −0.662492 −0.331246 0.943545i \(-0.607469\pi\)
−0.331246 + 0.943545i \(0.607469\pi\)
\(954\) 17.9829 0.582219
\(955\) −25.0587 −0.810882
\(956\) −20.2316 −0.654338
\(957\) 2.07984 0.0672316
\(958\) 32.9788 1.06550
\(959\) 21.2639 0.686648
\(960\) 11.7989 0.380806
\(961\) −14.1962 −0.457941
\(962\) 11.6917 0.376956
\(963\) −56.9661 −1.83571
\(964\) 1.33108 0.0428712
\(965\) 4.56521 0.146959
\(966\) 66.3520 2.13484
\(967\) −14.1009 −0.453453 −0.226727 0.973958i \(-0.572802\pi\)
−0.226727 + 0.973958i \(0.572802\pi\)
\(968\) −10.9475 −0.351866
\(969\) −3.98926 −0.128154
\(970\) −29.0175 −0.931695
\(971\) −47.7636 −1.53281 −0.766404 0.642359i \(-0.777956\pi\)
−0.766404 + 0.642359i \(0.777956\pi\)
\(972\) −34.5114 −1.10695
\(973\) −43.5793 −1.39709
\(974\) 30.1843 0.967168
\(975\) 40.9406 1.31115
\(976\) 5.03288 0.161099
\(977\) −29.6642 −0.949041 −0.474520 0.880245i \(-0.657378\pi\)
−0.474520 + 0.880245i \(0.657378\pi\)
\(978\) −31.3408 −1.00217
\(979\) 0.845736 0.0270298
\(980\) 4.69690 0.150037
\(981\) −27.6180 −0.881776
\(982\) −5.62352 −0.179454
\(983\) 37.5964 1.19914 0.599569 0.800323i \(-0.295339\pi\)
0.599569 + 0.800323i \(0.295339\pi\)
\(984\) −22.5358 −0.718415
\(985\) 1.42596 0.0454348
\(986\) −3.46938 −0.110488
\(987\) −86.4612 −2.75209
\(988\) −1.51971 −0.0483486
\(989\) 89.9882 2.86146
\(990\) −6.22366 −0.197801
\(991\) 55.2980 1.75660 0.878300 0.478110i \(-0.158678\pi\)
0.878300 + 0.478110i \(0.158678\pi\)
\(992\) 4.09925 0.130151
\(993\) −27.9942 −0.888370
\(994\) 25.3067 0.802681
\(995\) 13.0258 0.412946
\(996\) −1.42567 −0.0451739
\(997\) −41.9755 −1.32938 −0.664689 0.747120i \(-0.731436\pi\)
−0.664689 + 0.747120i \(0.731436\pi\)
\(998\) −7.32951 −0.232012
\(999\) 110.265 3.48863
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 \(a_p\))