Properties

Label 4033.2.a.d.1.19
Level 4033
Weight 2
Character 4033.1
Self dual Yes
Analytic conductor 32.204
Analytic rank 1
Dimension 79
CM No

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Newspace parameters

Level: \( N \) = \( 4033 = 37 \cdot 109 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4033.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.2036671352\)
Analytic rank: \(1\)
Dimension: \(79\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.79445 q^{2}\) \(-3.46032 q^{3}\) \(+1.22004 q^{4}\) \(+0.638539 q^{5}\) \(+6.20936 q^{6}\) \(-3.14453 q^{7}\) \(+1.39960 q^{8}\) \(+8.97380 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.79445 q^{2}\) \(-3.46032 q^{3}\) \(+1.22004 q^{4}\) \(+0.638539 q^{5}\) \(+6.20936 q^{6}\) \(-3.14453 q^{7}\) \(+1.39960 q^{8}\) \(+8.97380 q^{9}\) \(-1.14582 q^{10}\) \(+4.04630 q^{11}\) \(-4.22172 q^{12}\) \(+1.21584 q^{13}\) \(+5.64269 q^{14}\) \(-2.20955 q^{15}\) \(-4.95158 q^{16}\) \(+4.08941 q^{17}\) \(-16.1030 q^{18}\) \(+2.63464 q^{19}\) \(+0.779042 q^{20}\) \(+10.8811 q^{21}\) \(-7.26087 q^{22}\) \(-5.20650 q^{23}\) \(-4.84306 q^{24}\) \(-4.59227 q^{25}\) \(-2.18175 q^{26}\) \(-20.6713 q^{27}\) \(-3.83645 q^{28}\) \(+1.86432 q^{29}\) \(+3.96491 q^{30}\) \(-0.258488 q^{31}\) \(+6.08615 q^{32}\) \(-14.0015 q^{33}\) \(-7.33822 q^{34}\) \(-2.00791 q^{35}\) \(+10.9484 q^{36}\) \(-1.00000 q^{37}\) \(-4.72772 q^{38}\) \(-4.20718 q^{39}\) \(+0.893699 q^{40}\) \(-3.22464 q^{41}\) \(-19.5255 q^{42}\) \(-3.72099 q^{43}\) \(+4.93664 q^{44}\) \(+5.73012 q^{45}\) \(+9.34279 q^{46}\) \(+7.73073 q^{47}\) \(+17.1341 q^{48}\) \(+2.88808 q^{49}\) \(+8.24058 q^{50}\) \(-14.1507 q^{51}\) \(+1.48337 q^{52}\) \(+1.70538 q^{53}\) \(+37.0935 q^{54}\) \(+2.58372 q^{55}\) \(-4.40109 q^{56}\) \(-9.11669 q^{57}\) \(-3.34542 q^{58}\) \(+0.238157 q^{59}\) \(-2.69573 q^{60}\) \(-9.30387 q^{61}\) \(+0.463844 q^{62}\) \(-28.2184 q^{63}\) \(-1.01810 q^{64}\) \(+0.776359 q^{65}\) \(+25.1249 q^{66}\) \(-12.7784 q^{67}\) \(+4.98923 q^{68}\) \(+18.0162 q^{69}\) \(+3.60308 q^{70}\) \(+0.997540 q^{71}\) \(+12.5597 q^{72}\) \(-2.23889 q^{73}\) \(+1.79445 q^{74}\) \(+15.8907 q^{75}\) \(+3.21436 q^{76}\) \(-12.7237 q^{77}\) \(+7.54956 q^{78}\) \(+9.38330 q^{79}\) \(-3.16178 q^{80}\) \(+44.6077 q^{81}\) \(+5.78644 q^{82}\) \(+9.05619 q^{83}\) \(+13.2753 q^{84}\) \(+2.61125 q^{85}\) \(+6.67712 q^{86}\) \(-6.45114 q^{87}\) \(+5.66320 q^{88}\) \(+13.6724 q^{89}\) \(-10.2824 q^{90}\) \(-3.82324 q^{91}\) \(-6.35213 q^{92}\) \(+0.894452 q^{93}\) \(-13.8724 q^{94}\) \(+1.68232 q^{95}\) \(-21.0600 q^{96}\) \(-5.63517 q^{97}\) \(-5.18251 q^{98}\) \(+36.3107 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut -\mathstrut 13q^{10} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 40q^{12} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 42q^{14} \) \(\mathstrut -\mathstrut 49q^{15} \) \(\mathstrut +\mathstrut 83q^{16} \) \(\mathstrut -\mathstrut 62q^{17} \) \(\mathstrut -\mathstrut 33q^{18} \) \(\mathstrut -\mathstrut 25q^{19} \) \(\mathstrut -\mathstrut 39q^{20} \) \(\mathstrut -\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 31q^{22} \) \(\mathstrut -\mathstrut 94q^{23} \) \(\mathstrut -\mathstrut 39q^{24} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut -\mathstrut 35q^{26} \) \(\mathstrut -\mathstrut 47q^{27} \) \(\mathstrut -\mathstrut 13q^{28} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 15q^{30} \) \(\mathstrut -\mathstrut 37q^{31} \) \(\mathstrut -\mathstrut 105q^{32} \) \(\mathstrut -\mathstrut 60q^{33} \) \(\mathstrut +\mathstrut 9q^{34} \) \(\mathstrut -\mathstrut 60q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 79q^{37} \) \(\mathstrut -\mathstrut 80q^{38} \) \(\mathstrut -\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 64q^{40} \) \(\mathstrut -\mathstrut 37q^{41} \) \(\mathstrut -\mathstrut 30q^{42} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 8q^{45} \) \(\mathstrut +\mathstrut 61q^{46} \) \(\mathstrut -\mathstrut 148q^{47} \) \(\mathstrut -\mathstrut 39q^{48} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut 90q^{50} \) \(\mathstrut -\mathstrut 45q^{51} \) \(\mathstrut -\mathstrut 27q^{52} \) \(\mathstrut -\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 41q^{54} \) \(\mathstrut -\mathstrut 105q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut -\mathstrut 96q^{59} \) \(\mathstrut -\mathstrut 74q^{60} \) \(\mathstrut -\mathstrut 21q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut 60q^{63} \) \(\mathstrut +\mathstrut 132q^{64} \) \(\mathstrut -\mathstrut 15q^{65} \) \(\mathstrut +\mathstrut 71q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 166q^{68} \) \(\mathstrut -\mathstrut 72q^{69} \) \(\mathstrut -\mathstrut 9q^{70} \) \(\mathstrut -\mathstrut 55q^{71} \) \(\mathstrut -\mathstrut 126q^{72} \) \(\mathstrut -\mathstrut 27q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 39q^{75} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 104q^{77} \) \(\mathstrut -\mathstrut 47q^{78} \) \(\mathstrut -\mathstrut 49q^{79} \) \(\mathstrut -\mathstrut 82q^{80} \) \(\mathstrut +\mathstrut 55q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 29q^{84} \) \(\mathstrut +\mathstrut 3q^{85} \) \(\mathstrut -\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 113q^{87} \) \(\mathstrut +\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 68q^{89} \) \(\mathstrut -\mathstrut 39q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 179q^{92} \) \(\mathstrut -\mathstrut 53q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 86q^{95} \) \(\mathstrut +\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 116q^{98} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.79445 −1.26887 −0.634433 0.772978i \(-0.718766\pi\)
−0.634433 + 0.772978i \(0.718766\pi\)
\(3\) −3.46032 −1.99782 −0.998908 0.0467243i \(-0.985122\pi\)
−0.998908 + 0.0467243i \(0.985122\pi\)
\(4\) 1.22004 0.610019
\(5\) 0.638539 0.285563 0.142782 0.989754i \(-0.454395\pi\)
0.142782 + 0.989754i \(0.454395\pi\)
\(6\) 6.20936 2.53496
\(7\) −3.14453 −1.18852 −0.594261 0.804272i \(-0.702555\pi\)
−0.594261 + 0.804272i \(0.702555\pi\)
\(8\) 1.39960 0.494833
\(9\) 8.97380 2.99127
\(10\) −1.14582 −0.362341
\(11\) 4.04630 1.22001 0.610003 0.792399i \(-0.291168\pi\)
0.610003 + 0.792399i \(0.291168\pi\)
\(12\) −4.22172 −1.21871
\(13\) 1.21584 0.337213 0.168606 0.985683i \(-0.446073\pi\)
0.168606 + 0.985683i \(0.446073\pi\)
\(14\) 5.64269 1.50807
\(15\) −2.20955 −0.570503
\(16\) −4.95158 −1.23790
\(17\) 4.08941 0.991827 0.495913 0.868372i \(-0.334833\pi\)
0.495913 + 0.868372i \(0.334833\pi\)
\(18\) −16.1030 −3.79552
\(19\) 2.63464 0.604428 0.302214 0.953240i \(-0.402274\pi\)
0.302214 + 0.953240i \(0.402274\pi\)
\(20\) 0.779042 0.174199
\(21\) 10.8811 2.37445
\(22\) −7.26087 −1.54802
\(23\) −5.20650 −1.08563 −0.542815 0.839852i \(-0.682642\pi\)
−0.542815 + 0.839852i \(0.682642\pi\)
\(24\) −4.84306 −0.988586
\(25\) −4.59227 −0.918454
\(26\) −2.18175 −0.427877
\(27\) −20.6713 −3.97819
\(28\) −3.83645 −0.725021
\(29\) 1.86432 0.346195 0.173098 0.984905i \(-0.444622\pi\)
0.173098 + 0.984905i \(0.444622\pi\)
\(30\) 3.96491 0.723891
\(31\) −0.258488 −0.0464259 −0.0232130 0.999731i \(-0.507390\pi\)
−0.0232130 + 0.999731i \(0.507390\pi\)
\(32\) 6.08615 1.07589
\(33\) −14.0015 −2.43735
\(34\) −7.33822 −1.25849
\(35\) −2.00791 −0.339398
\(36\) 10.9484 1.82473
\(37\) −1.00000 −0.164399
\(38\) −4.72772 −0.766938
\(39\) −4.20718 −0.673688
\(40\) 0.893699 0.141306
\(41\) −3.22464 −0.503604 −0.251802 0.967779i \(-0.581023\pi\)
−0.251802 + 0.967779i \(0.581023\pi\)
\(42\) −19.5255 −3.01285
\(43\) −3.72099 −0.567446 −0.283723 0.958906i \(-0.591570\pi\)
−0.283723 + 0.958906i \(0.591570\pi\)
\(44\) 4.93664 0.744226
\(45\) 5.73012 0.854196
\(46\) 9.34279 1.37752
\(47\) 7.73073 1.12764 0.563821 0.825897i \(-0.309331\pi\)
0.563821 + 0.825897i \(0.309331\pi\)
\(48\) 17.1341 2.47309
\(49\) 2.88808 0.412583
\(50\) 8.24058 1.16539
\(51\) −14.1507 −1.98149
\(52\) 1.48337 0.205706
\(53\) 1.70538 0.234252 0.117126 0.993117i \(-0.462632\pi\)
0.117126 + 0.993117i \(0.462632\pi\)
\(54\) 37.0935 5.04778
\(55\) 2.58372 0.348389
\(56\) −4.40109 −0.588120
\(57\) −9.11669 −1.20754
\(58\) −3.34542 −0.439275
\(59\) 0.238157 0.0310054 0.0155027 0.999880i \(-0.495065\pi\)
0.0155027 + 0.999880i \(0.495065\pi\)
\(60\) −2.69573 −0.348017
\(61\) −9.30387 −1.19124 −0.595619 0.803267i \(-0.703093\pi\)
−0.595619 + 0.803267i \(0.703093\pi\)
\(62\) 0.463844 0.0589082
\(63\) −28.2184 −3.55519
\(64\) −1.01810 −0.127263
\(65\) 0.776359 0.0962955
\(66\) 25.1249 3.09266
\(67\) −12.7784 −1.56113 −0.780567 0.625072i \(-0.785069\pi\)
−0.780567 + 0.625072i \(0.785069\pi\)
\(68\) 4.98923 0.605033
\(69\) 18.0162 2.16889
\(70\) 3.60308 0.430650
\(71\) 0.997540 0.118386 0.0591931 0.998247i \(-0.481147\pi\)
0.0591931 + 0.998247i \(0.481147\pi\)
\(72\) 12.5597 1.48018
\(73\) −2.23889 −0.262042 −0.131021 0.991380i \(-0.541826\pi\)
−0.131021 + 0.991380i \(0.541826\pi\)
\(74\) 1.79445 0.208600
\(75\) 15.8907 1.83490
\(76\) 3.21436 0.368712
\(77\) −12.7237 −1.45000
\(78\) 7.54956 0.854820
\(79\) 9.38330 1.05570 0.527852 0.849336i \(-0.322998\pi\)
0.527852 + 0.849336i \(0.322998\pi\)
\(80\) −3.16178 −0.353498
\(81\) 44.6077 4.95641
\(82\) 5.78644 0.639006
\(83\) 9.05619 0.994046 0.497023 0.867737i \(-0.334426\pi\)
0.497023 + 0.867737i \(0.334426\pi\)
\(84\) 13.2753 1.44846
\(85\) 2.61125 0.283229
\(86\) 6.67712 0.720013
\(87\) −6.45114 −0.691635
\(88\) 5.66320 0.603699
\(89\) 13.6724 1.44927 0.724634 0.689134i \(-0.242009\pi\)
0.724634 + 0.689134i \(0.242009\pi\)
\(90\) −10.2824 −1.08386
\(91\) −3.82324 −0.400784
\(92\) −6.35213 −0.662255
\(93\) 0.894452 0.0927504
\(94\) −13.8724 −1.43083
\(95\) 1.68232 0.172602
\(96\) −21.0600 −2.14943
\(97\) −5.63517 −0.572165 −0.286082 0.958205i \(-0.592353\pi\)
−0.286082 + 0.958205i \(0.592353\pi\)
\(98\) −5.18251 −0.523513
\(99\) 36.3107 3.64936
\(100\) −5.60274 −0.560274
\(101\) −4.16134 −0.414069 −0.207034 0.978334i \(-0.566381\pi\)
−0.207034 + 0.978334i \(0.566381\pi\)
\(102\) 25.3926 2.51424
\(103\) −16.9244 −1.66761 −0.833804 0.552061i \(-0.813842\pi\)
−0.833804 + 0.552061i \(0.813842\pi\)
\(104\) 1.70169 0.166864
\(105\) 6.94799 0.678055
\(106\) −3.06021 −0.297234
\(107\) −9.96975 −0.963812 −0.481906 0.876223i \(-0.660055\pi\)
−0.481906 + 0.876223i \(0.660055\pi\)
\(108\) −25.2197 −2.42677
\(109\) −1.00000 −0.0957826
\(110\) −4.63635 −0.442058
\(111\) 3.46032 0.328439
\(112\) 15.5704 1.47127
\(113\) 10.4500 0.983056 0.491528 0.870862i \(-0.336438\pi\)
0.491528 + 0.870862i \(0.336438\pi\)
\(114\) 16.3594 1.53220
\(115\) −3.32455 −0.310016
\(116\) 2.27454 0.211186
\(117\) 10.9107 1.00869
\(118\) −0.427360 −0.0393417
\(119\) −12.8593 −1.17881
\(120\) −3.09248 −0.282304
\(121\) 5.37254 0.488413
\(122\) 16.6953 1.51152
\(123\) 11.1583 1.00611
\(124\) −0.315366 −0.0283207
\(125\) −6.12504 −0.547840
\(126\) 50.6364 4.51105
\(127\) −14.6429 −1.29935 −0.649674 0.760213i \(-0.725095\pi\)
−0.649674 + 0.760213i \(0.725095\pi\)
\(128\) −10.3454 −0.914410
\(129\) 12.8758 1.13365
\(130\) −1.39313 −0.122186
\(131\) 10.1270 0.884800 0.442400 0.896818i \(-0.354127\pi\)
0.442400 + 0.896818i \(0.354127\pi\)
\(132\) −17.0823 −1.48683
\(133\) −8.28471 −0.718376
\(134\) 22.9302 1.98087
\(135\) −13.1994 −1.13602
\(136\) 5.72354 0.490789
\(137\) 17.3717 1.48416 0.742080 0.670311i \(-0.233839\pi\)
0.742080 + 0.670311i \(0.233839\pi\)
\(138\) −32.3290 −2.75203
\(139\) 2.53559 0.215066 0.107533 0.994202i \(-0.465705\pi\)
0.107533 + 0.994202i \(0.465705\pi\)
\(140\) −2.44972 −0.207039
\(141\) −26.7508 −2.25282
\(142\) −1.79003 −0.150216
\(143\) 4.91964 0.411401
\(144\) −44.4345 −3.70288
\(145\) 1.19044 0.0988607
\(146\) 4.01757 0.332497
\(147\) −9.99369 −0.824265
\(148\) −1.22004 −0.100286
\(149\) −5.95065 −0.487496 −0.243748 0.969839i \(-0.578377\pi\)
−0.243748 + 0.969839i \(0.578377\pi\)
\(150\) −28.5150 −2.32824
\(151\) −20.4659 −1.66549 −0.832744 0.553658i \(-0.813232\pi\)
−0.832744 + 0.553658i \(0.813232\pi\)
\(152\) 3.68744 0.299091
\(153\) 36.6975 2.96682
\(154\) 22.8320 1.83986
\(155\) −0.165055 −0.0132575
\(156\) −5.13292 −0.410963
\(157\) 20.8483 1.66388 0.831939 0.554866i \(-0.187231\pi\)
0.831939 + 0.554866i \(0.187231\pi\)
\(158\) −16.8378 −1.33955
\(159\) −5.90115 −0.467991
\(160\) 3.88624 0.307235
\(161\) 16.3720 1.29030
\(162\) −80.0462 −6.28902
\(163\) 8.39302 0.657392 0.328696 0.944436i \(-0.393391\pi\)
0.328696 + 0.944436i \(0.393391\pi\)
\(164\) −3.93418 −0.307208
\(165\) −8.94049 −0.696016
\(166\) −16.2508 −1.26131
\(167\) −4.79742 −0.371235 −0.185618 0.982622i \(-0.559429\pi\)
−0.185618 + 0.982622i \(0.559429\pi\)
\(168\) 15.2292 1.17496
\(169\) −11.5217 −0.886288
\(170\) −4.68574 −0.359380
\(171\) 23.6427 1.80801
\(172\) −4.53975 −0.346153
\(173\) −5.38797 −0.409640 −0.204820 0.978800i \(-0.565661\pi\)
−0.204820 + 0.978800i \(0.565661\pi\)
\(174\) 11.5762 0.877591
\(175\) 14.4405 1.09160
\(176\) −20.0356 −1.51024
\(177\) −0.824100 −0.0619431
\(178\) −24.5343 −1.83893
\(179\) −6.13478 −0.458535 −0.229268 0.973363i \(-0.573633\pi\)
−0.229268 + 0.973363i \(0.573633\pi\)
\(180\) 6.99097 0.521076
\(181\) 16.0702 1.19449 0.597245 0.802059i \(-0.296262\pi\)
0.597245 + 0.802059i \(0.296262\pi\)
\(182\) 6.86060 0.508541
\(183\) 32.1943 2.37987
\(184\) −7.28702 −0.537206
\(185\) −0.638539 −0.0469463
\(186\) −1.60505 −0.117688
\(187\) 16.5470 1.21003
\(188\) 9.43178 0.687884
\(189\) 65.0014 4.72816
\(190\) −3.01883 −0.219009
\(191\) 11.3267 0.819568 0.409784 0.912183i \(-0.365604\pi\)
0.409784 + 0.912183i \(0.365604\pi\)
\(192\) 3.52296 0.254248
\(193\) 20.6211 1.48434 0.742171 0.670210i \(-0.233796\pi\)
0.742171 + 0.670210i \(0.233796\pi\)
\(194\) 10.1120 0.726000
\(195\) −2.68645 −0.192381
\(196\) 3.52357 0.251684
\(197\) 1.06227 0.0756837 0.0378418 0.999284i \(-0.487952\pi\)
0.0378418 + 0.999284i \(0.487952\pi\)
\(198\) −65.1576 −4.63055
\(199\) −4.74288 −0.336214 −0.168107 0.985769i \(-0.553765\pi\)
−0.168107 + 0.985769i \(0.553765\pi\)
\(200\) −6.42734 −0.454482
\(201\) 44.2174 3.11886
\(202\) 7.46730 0.525397
\(203\) −5.86241 −0.411461
\(204\) −17.2643 −1.20874
\(205\) −2.05906 −0.143811
\(206\) 30.3699 2.11597
\(207\) −46.7221 −3.24741
\(208\) −6.02032 −0.417434
\(209\) 10.6605 0.737405
\(210\) −12.4678 −0.860360
\(211\) 7.61495 0.524235 0.262117 0.965036i \(-0.415579\pi\)
0.262117 + 0.965036i \(0.415579\pi\)
\(212\) 2.08062 0.142898
\(213\) −3.45181 −0.236514
\(214\) 17.8902 1.22295
\(215\) −2.37600 −0.162042
\(216\) −28.9315 −1.96854
\(217\) 0.812825 0.0551782
\(218\) 1.79445 0.121535
\(219\) 7.74728 0.523513
\(220\) 3.15224 0.212524
\(221\) 4.97205 0.334456
\(222\) −6.20936 −0.416745
\(223\) −24.7998 −1.66072 −0.830358 0.557230i \(-0.811864\pi\)
−0.830358 + 0.557230i \(0.811864\pi\)
\(224\) −19.1381 −1.27872
\(225\) −41.2101 −2.74734
\(226\) −18.7520 −1.24737
\(227\) −4.61132 −0.306064 −0.153032 0.988221i \(-0.548904\pi\)
−0.153032 + 0.988221i \(0.548904\pi\)
\(228\) −11.1227 −0.736619
\(229\) −1.26362 −0.0835025 −0.0417512 0.999128i \(-0.513294\pi\)
−0.0417512 + 0.999128i \(0.513294\pi\)
\(230\) 5.96573 0.393369
\(231\) 44.0281 2.89684
\(232\) 2.60930 0.171309
\(233\) 8.15044 0.533953 0.266976 0.963703i \(-0.413975\pi\)
0.266976 + 0.963703i \(0.413975\pi\)
\(234\) −19.5786 −1.27990
\(235\) 4.93637 0.322013
\(236\) 0.290561 0.0189139
\(237\) −32.4692 −2.10910
\(238\) 23.0753 1.49575
\(239\) −9.97624 −0.645309 −0.322655 0.946517i \(-0.604575\pi\)
−0.322655 + 0.946517i \(0.604575\pi\)
\(240\) 10.9408 0.706223
\(241\) 0.698791 0.0450131 0.0225065 0.999747i \(-0.492835\pi\)
0.0225065 + 0.999747i \(0.492835\pi\)
\(242\) −9.64074 −0.619730
\(243\) −92.3431 −5.92381
\(244\) −11.3511 −0.726678
\(245\) 1.84415 0.117819
\(246\) −20.0229 −1.27662
\(247\) 3.20329 0.203821
\(248\) −0.361781 −0.0229731
\(249\) −31.3373 −1.98592
\(250\) 10.9910 0.695135
\(251\) −31.2240 −1.97084 −0.985419 0.170143i \(-0.945577\pi\)
−0.985419 + 0.170143i \(0.945577\pi\)
\(252\) −34.4275 −2.16873
\(253\) −21.0671 −1.32448
\(254\) 26.2759 1.64870
\(255\) −9.03574 −0.565840
\(256\) 20.6004 1.28753
\(257\) −10.3381 −0.644871 −0.322436 0.946591i \(-0.604502\pi\)
−0.322436 + 0.946591i \(0.604502\pi\)
\(258\) −23.1050 −1.43845
\(259\) 3.14453 0.195392
\(260\) 0.947188 0.0587421
\(261\) 16.7300 1.03556
\(262\) −18.1724 −1.12269
\(263\) −16.1000 −0.992769 −0.496385 0.868103i \(-0.665339\pi\)
−0.496385 + 0.868103i \(0.665339\pi\)
\(264\) −19.5965 −1.20608
\(265\) 1.08895 0.0668936
\(266\) 14.8665 0.911522
\(267\) −47.3107 −2.89537
\(268\) −15.5902 −0.952321
\(269\) −3.64020 −0.221947 −0.110973 0.993823i \(-0.535397\pi\)
−0.110973 + 0.993823i \(0.535397\pi\)
\(270\) 23.6856 1.44146
\(271\) 21.9557 1.33371 0.666857 0.745186i \(-0.267639\pi\)
0.666857 + 0.745186i \(0.267639\pi\)
\(272\) −20.2490 −1.22778
\(273\) 13.2296 0.800693
\(274\) −31.1725 −1.88320
\(275\) −18.5817 −1.12052
\(276\) 21.9804 1.32306
\(277\) 29.5407 1.77493 0.887465 0.460875i \(-0.152464\pi\)
0.887465 + 0.460875i \(0.152464\pi\)
\(278\) −4.54997 −0.272889
\(279\) −2.31962 −0.138872
\(280\) −2.81027 −0.167946
\(281\) 5.14782 0.307093 0.153546 0.988141i \(-0.450931\pi\)
0.153546 + 0.988141i \(0.450931\pi\)
\(282\) 48.0029 2.85853
\(283\) 10.7408 0.638474 0.319237 0.947675i \(-0.396573\pi\)
0.319237 + 0.947675i \(0.396573\pi\)
\(284\) 1.21704 0.0722179
\(285\) −5.82136 −0.344828
\(286\) −8.82803 −0.522012
\(287\) 10.1400 0.598544
\(288\) 54.6159 3.21827
\(289\) −0.276746 −0.0162792
\(290\) −2.13618 −0.125441
\(291\) 19.4995 1.14308
\(292\) −2.73153 −0.159851
\(293\) −22.9768 −1.34232 −0.671161 0.741312i \(-0.734204\pi\)
−0.671161 + 0.741312i \(0.734204\pi\)
\(294\) 17.9331 1.04588
\(295\) 0.152073 0.00885401
\(296\) −1.39960 −0.0813501
\(297\) −83.6421 −4.85341
\(298\) 10.6781 0.618567
\(299\) −6.33026 −0.366088
\(300\) 19.3873 1.11932
\(301\) 11.7008 0.674422
\(302\) 36.7249 2.11328
\(303\) 14.3996 0.827233
\(304\) −13.0456 −0.748219
\(305\) −5.94088 −0.340174
\(306\) −65.8518 −3.76449
\(307\) −13.1918 −0.752894 −0.376447 0.926438i \(-0.622854\pi\)
−0.376447 + 0.926438i \(0.622854\pi\)
\(308\) −15.5234 −0.884529
\(309\) 58.5637 3.33157
\(310\) 0.296182 0.0168220
\(311\) −2.56839 −0.145640 −0.0728201 0.997345i \(-0.523200\pi\)
−0.0728201 + 0.997345i \(0.523200\pi\)
\(312\) −5.88837 −0.333364
\(313\) 2.98639 0.168801 0.0844004 0.996432i \(-0.473103\pi\)
0.0844004 + 0.996432i \(0.473103\pi\)
\(314\) −37.4112 −2.11124
\(315\) −18.0186 −1.01523
\(316\) 11.4480 0.643999
\(317\) 18.4006 1.03348 0.516742 0.856141i \(-0.327145\pi\)
0.516742 + 0.856141i \(0.327145\pi\)
\(318\) 10.5893 0.593818
\(319\) 7.54360 0.422360
\(320\) −0.650099 −0.0363416
\(321\) 34.4985 1.92552
\(322\) −29.3787 −1.63721
\(323\) 10.7741 0.599488
\(324\) 54.4231 3.02351
\(325\) −5.58345 −0.309714
\(326\) −15.0608 −0.834142
\(327\) 3.46032 0.191356
\(328\) −4.51321 −0.249200
\(329\) −24.3095 −1.34023
\(330\) 16.0432 0.883151
\(331\) 24.3773 1.33990 0.669948 0.742408i \(-0.266317\pi\)
0.669948 + 0.742408i \(0.266317\pi\)
\(332\) 11.0489 0.606387
\(333\) −8.97380 −0.491761
\(334\) 8.60871 0.471048
\(335\) −8.15952 −0.445802
\(336\) −53.8786 −2.93932
\(337\) 27.1638 1.47970 0.739852 0.672769i \(-0.234895\pi\)
0.739852 + 0.672769i \(0.234895\pi\)
\(338\) 20.6751 1.12458
\(339\) −36.1604 −1.96397
\(340\) 3.18582 0.172775
\(341\) −1.04592 −0.0566399
\(342\) −42.4256 −2.29412
\(343\) 12.9301 0.698157
\(344\) −5.20790 −0.280791
\(345\) 11.5040 0.619355
\(346\) 9.66843 0.519778
\(347\) −11.4545 −0.614911 −0.307455 0.951563i \(-0.599477\pi\)
−0.307455 + 0.951563i \(0.599477\pi\)
\(348\) −7.87063 −0.421910
\(349\) −5.85508 −0.313416 −0.156708 0.987645i \(-0.550088\pi\)
−0.156708 + 0.987645i \(0.550088\pi\)
\(350\) −25.9128 −1.38510
\(351\) −25.1329 −1.34149
\(352\) 24.6264 1.31259
\(353\) −22.2710 −1.18537 −0.592684 0.805435i \(-0.701932\pi\)
−0.592684 + 0.805435i \(0.701932\pi\)
\(354\) 1.47880 0.0785975
\(355\) 0.636968 0.0338068
\(356\) 16.6808 0.884081
\(357\) 44.4972 2.35504
\(358\) 11.0085 0.581819
\(359\) 8.46028 0.446517 0.223258 0.974759i \(-0.428331\pi\)
0.223258 + 0.974759i \(0.428331\pi\)
\(360\) 8.01988 0.422685
\(361\) −12.0587 −0.634667
\(362\) −28.8371 −1.51565
\(363\) −18.5907 −0.975759
\(364\) −4.66450 −0.244486
\(365\) −1.42962 −0.0748297
\(366\) −57.7710 −3.01974
\(367\) −18.1325 −0.946507 −0.473253 0.880926i \(-0.656920\pi\)
−0.473253 + 0.880926i \(0.656920\pi\)
\(368\) 25.7804 1.34390
\(369\) −28.9373 −1.50641
\(370\) 1.14582 0.0595685
\(371\) −5.36261 −0.278413
\(372\) 1.09127 0.0565795
\(373\) −1.31804 −0.0682455 −0.0341227 0.999418i \(-0.510864\pi\)
−0.0341227 + 0.999418i \(0.510864\pi\)
\(374\) −29.6926 −1.53537
\(375\) 21.1946 1.09448
\(376\) 10.8199 0.557995
\(377\) 2.26671 0.116741
\(378\) −116.642 −5.99940
\(379\) −5.70463 −0.293027 −0.146514 0.989209i \(-0.546805\pi\)
−0.146514 + 0.989209i \(0.546805\pi\)
\(380\) 2.05249 0.105291
\(381\) 50.6691 2.59586
\(382\) −20.3251 −1.03992
\(383\) 0.473295 0.0241842 0.0120921 0.999927i \(-0.496151\pi\)
0.0120921 + 0.999927i \(0.496151\pi\)
\(384\) 35.7983 1.82682
\(385\) −8.12459 −0.414067
\(386\) −37.0035 −1.88343
\(387\) −33.3915 −1.69738
\(388\) −6.87512 −0.349031
\(389\) −7.37125 −0.373737 −0.186869 0.982385i \(-0.559834\pi\)
−0.186869 + 0.982385i \(0.559834\pi\)
\(390\) 4.82069 0.244105
\(391\) −21.2915 −1.07676
\(392\) 4.04216 0.204160
\(393\) −35.0427 −1.76767
\(394\) −1.90619 −0.0960324
\(395\) 5.99160 0.301470
\(396\) 44.3004 2.22618
\(397\) −12.2213 −0.613369 −0.306685 0.951811i \(-0.599220\pi\)
−0.306685 + 0.951811i \(0.599220\pi\)
\(398\) 8.51085 0.426610
\(399\) 28.6677 1.43518
\(400\) 22.7390 1.13695
\(401\) −18.5159 −0.924641 −0.462321 0.886713i \(-0.652983\pi\)
−0.462321 + 0.886713i \(0.652983\pi\)
\(402\) −79.3458 −3.95741
\(403\) −0.314280 −0.0156554
\(404\) −5.07699 −0.252590
\(405\) 28.4838 1.41537
\(406\) 10.5198 0.522088
\(407\) −4.04630 −0.200568
\(408\) −19.8053 −0.980506
\(409\) 9.97198 0.493083 0.246541 0.969132i \(-0.420706\pi\)
0.246541 + 0.969132i \(0.420706\pi\)
\(410\) 3.69487 0.182477
\(411\) −60.1114 −2.96508
\(412\) −20.6484 −1.01727
\(413\) −0.748893 −0.0368506
\(414\) 83.8403 4.12053
\(415\) 5.78273 0.283863
\(416\) 7.39977 0.362803
\(417\) −8.77393 −0.429661
\(418\) −19.1298 −0.935668
\(419\) −31.9986 −1.56323 −0.781617 0.623759i \(-0.785605\pi\)
−0.781617 + 0.623759i \(0.785605\pi\)
\(420\) 8.47682 0.413626
\(421\) −21.2305 −1.03471 −0.517356 0.855770i \(-0.673084\pi\)
−0.517356 + 0.855770i \(0.673084\pi\)
\(422\) −13.6646 −0.665183
\(423\) 69.3740 3.37308
\(424\) 2.38685 0.115915
\(425\) −18.7797 −0.910947
\(426\) 6.19408 0.300104
\(427\) 29.2563 1.41581
\(428\) −12.1635 −0.587944
\(429\) −17.0235 −0.821903
\(430\) 4.26360 0.205609
\(431\) 4.76264 0.229408 0.114704 0.993400i \(-0.463408\pi\)
0.114704 + 0.993400i \(0.463408\pi\)
\(432\) 102.355 4.92458
\(433\) 9.61784 0.462204 0.231102 0.972930i \(-0.425767\pi\)
0.231102 + 0.972930i \(0.425767\pi\)
\(434\) −1.45857 −0.0700137
\(435\) −4.11930 −0.197505
\(436\) −1.22004 −0.0584292
\(437\) −13.7173 −0.656185
\(438\) −13.9021 −0.664267
\(439\) −19.9729 −0.953253 −0.476627 0.879106i \(-0.658141\pi\)
−0.476627 + 0.879106i \(0.658141\pi\)
\(440\) 3.61618 0.172394
\(441\) 25.9171 1.23415
\(442\) −8.92208 −0.424380
\(443\) −19.6285 −0.932578 −0.466289 0.884632i \(-0.654409\pi\)
−0.466289 + 0.884632i \(0.654409\pi\)
\(444\) 4.22172 0.200354
\(445\) 8.73034 0.413858
\(446\) 44.5019 2.10723
\(447\) 20.5912 0.973928
\(448\) 3.20146 0.151255
\(449\) 27.6325 1.30406 0.652030 0.758193i \(-0.273918\pi\)
0.652030 + 0.758193i \(0.273918\pi\)
\(450\) 73.9493 3.48600
\(451\) −13.0479 −0.614400
\(452\) 12.7494 0.599683
\(453\) 70.8184 3.32734
\(454\) 8.27476 0.388354
\(455\) −2.44129 −0.114449
\(456\) −12.7597 −0.597529
\(457\) −24.3961 −1.14120 −0.570601 0.821227i \(-0.693290\pi\)
−0.570601 + 0.821227i \(0.693290\pi\)
\(458\) 2.26750 0.105953
\(459\) −84.5332 −3.94567
\(460\) −4.05608 −0.189116
\(461\) −16.4237 −0.764926 −0.382463 0.923971i \(-0.624924\pi\)
−0.382463 + 0.923971i \(0.624924\pi\)
\(462\) −79.0061 −3.67570
\(463\) 0.372151 0.0172953 0.00864767 0.999963i \(-0.497247\pi\)
0.00864767 + 0.999963i \(0.497247\pi\)
\(464\) −9.23133 −0.428554
\(465\) 0.571143 0.0264861
\(466\) −14.6255 −0.677514
\(467\) 5.77830 0.267388 0.133694 0.991023i \(-0.457316\pi\)
0.133694 + 0.991023i \(0.457316\pi\)
\(468\) 13.3114 0.615322
\(469\) 40.1822 1.85544
\(470\) −8.85805 −0.408592
\(471\) −72.1419 −3.32412
\(472\) 0.333325 0.0153425
\(473\) −15.0563 −0.692287
\(474\) 58.2642 2.67617
\(475\) −12.0990 −0.555139
\(476\) −15.6888 −0.719095
\(477\) 15.3037 0.700709
\(478\) 17.9018 0.818811
\(479\) 38.6767 1.76719 0.883593 0.468256i \(-0.155118\pi\)
0.883593 + 0.468256i \(0.155118\pi\)
\(480\) −13.4476 −0.613798
\(481\) −1.21584 −0.0554374
\(482\) −1.25394 −0.0571156
\(483\) −56.6524 −2.57777
\(484\) 6.55471 0.297941
\(485\) −3.59827 −0.163389
\(486\) 165.705 7.51652
\(487\) −15.4186 −0.698686 −0.349343 0.936995i \(-0.613595\pi\)
−0.349343 + 0.936995i \(0.613595\pi\)
\(488\) −13.0217 −0.589464
\(489\) −29.0425 −1.31335
\(490\) −3.30923 −0.149496
\(491\) −18.0859 −0.816206 −0.408103 0.912936i \(-0.633810\pi\)
−0.408103 + 0.912936i \(0.633810\pi\)
\(492\) 13.6135 0.613745
\(493\) 7.62396 0.343366
\(494\) −5.74814 −0.258621
\(495\) 23.1858 1.04212
\(496\) 1.27993 0.0574704
\(497\) −3.13680 −0.140705
\(498\) 56.2331 2.51987
\(499\) −7.97978 −0.357224 −0.178612 0.983920i \(-0.557161\pi\)
−0.178612 + 0.983920i \(0.557161\pi\)
\(500\) −7.47278 −0.334193
\(501\) 16.6006 0.741660
\(502\) 56.0297 2.50073
\(503\) −32.6930 −1.45771 −0.728854 0.684669i \(-0.759947\pi\)
−0.728854 + 0.684669i \(0.759947\pi\)
\(504\) −39.4945 −1.75922
\(505\) −2.65718 −0.118243
\(506\) 37.8037 1.68058
\(507\) 39.8689 1.77064
\(508\) −17.8649 −0.792627
\(509\) −12.6978 −0.562819 −0.281409 0.959588i \(-0.590802\pi\)
−0.281409 + 0.959588i \(0.590802\pi\)
\(510\) 16.2142 0.717975
\(511\) 7.04027 0.311443
\(512\) −16.2756 −0.719287
\(513\) −54.4613 −2.40453
\(514\) 18.5511 0.818255
\(515\) −10.8069 −0.476208
\(516\) 15.7090 0.691550
\(517\) 31.2809 1.37573
\(518\) −5.64269 −0.247926
\(519\) 18.6441 0.818385
\(520\) 1.08659 0.0476502
\(521\) 18.8413 0.825451 0.412725 0.910855i \(-0.364577\pi\)
0.412725 + 0.910855i \(0.364577\pi\)
\(522\) −30.0211 −1.31399
\(523\) 22.8883 1.00084 0.500418 0.865784i \(-0.333180\pi\)
0.500418 + 0.865784i \(0.333180\pi\)
\(524\) 12.3553 0.539745
\(525\) −49.9688 −2.18082
\(526\) 28.8906 1.25969
\(527\) −1.05706 −0.0460465
\(528\) 69.3295 3.01718
\(529\) 4.10766 0.178594
\(530\) −1.95406 −0.0848790
\(531\) 2.13718 0.0927455
\(532\) −10.1077 −0.438223
\(533\) −3.92064 −0.169822
\(534\) 84.8966 3.67383
\(535\) −6.36607 −0.275229
\(536\) −17.8847 −0.772501
\(537\) 21.2283 0.916068
\(538\) 6.53214 0.281620
\(539\) 11.6861 0.503354
\(540\) −16.1038 −0.692996
\(541\) −12.9222 −0.555567 −0.277783 0.960644i \(-0.589600\pi\)
−0.277783 + 0.960644i \(0.589600\pi\)
\(542\) −39.3983 −1.69230
\(543\) −55.6080 −2.38637
\(544\) 24.8887 1.06710
\(545\) −0.638539 −0.0273520
\(546\) −23.7398 −1.01597
\(547\) 29.9884 1.28221 0.641106 0.767452i \(-0.278476\pi\)
0.641106 + 0.767452i \(0.278476\pi\)
\(548\) 21.1941 0.905366
\(549\) −83.4910 −3.56331
\(550\) 33.3439 1.42179
\(551\) 4.91181 0.209250
\(552\) 25.2154 1.07324
\(553\) −29.5061 −1.25473
\(554\) −53.0093 −2.25215
\(555\) 2.20955 0.0937901
\(556\) 3.09351 0.131194
\(557\) −23.4347 −0.992958 −0.496479 0.868049i \(-0.665374\pi\)
−0.496479 + 0.868049i \(0.665374\pi\)
\(558\) 4.16244 0.176210
\(559\) −4.52412 −0.191350
\(560\) 9.94231 0.420139
\(561\) −57.2578 −2.41743
\(562\) −9.23748 −0.389660
\(563\) 37.8916 1.59694 0.798470 0.602035i \(-0.205643\pi\)
0.798470 + 0.602035i \(0.205643\pi\)
\(564\) −32.6370 −1.37426
\(565\) 6.67275 0.280725
\(566\) −19.2738 −0.810137
\(567\) −140.270 −5.89080
\(568\) 1.39616 0.0585815
\(569\) 40.6091 1.70242 0.851211 0.524824i \(-0.175869\pi\)
0.851211 + 0.524824i \(0.175869\pi\)
\(570\) 10.4461 0.437540
\(571\) 35.2834 1.47657 0.738283 0.674491i \(-0.235637\pi\)
0.738283 + 0.674491i \(0.235637\pi\)
\(572\) 6.00215 0.250962
\(573\) −39.1938 −1.63735
\(574\) −18.1957 −0.759472
\(575\) 23.9096 0.997101
\(576\) −9.13626 −0.380678
\(577\) −18.1892 −0.757226 −0.378613 0.925555i \(-0.623599\pi\)
−0.378613 + 0.925555i \(0.623599\pi\)
\(578\) 0.496607 0.0206561
\(579\) −71.3557 −2.96544
\(580\) 1.45238 0.0603069
\(581\) −28.4775 −1.18144
\(582\) −34.9908 −1.45041
\(583\) 6.90047 0.285788
\(584\) −3.13355 −0.129667
\(585\) 6.96689 0.288046
\(586\) 41.2307 1.70323
\(587\) −34.7253 −1.43326 −0.716632 0.697451i \(-0.754317\pi\)
−0.716632 + 0.697451i \(0.754317\pi\)
\(588\) −12.1927 −0.502817
\(589\) −0.681024 −0.0280611
\(590\) −0.272886 −0.0112345
\(591\) −3.67580 −0.151202
\(592\) 4.95158 0.203509
\(593\) −6.41866 −0.263583 −0.131791 0.991277i \(-0.542073\pi\)
−0.131791 + 0.991277i \(0.542073\pi\)
\(594\) 150.091 6.15832
\(595\) −8.21115 −0.336624
\(596\) −7.26002 −0.297382
\(597\) 16.4119 0.671694
\(598\) 11.3593 0.464517
\(599\) 14.9263 0.609871 0.304936 0.952373i \(-0.401365\pi\)
0.304936 + 0.952373i \(0.401365\pi\)
\(600\) 22.2406 0.907970
\(601\) −17.6623 −0.720460 −0.360230 0.932864i \(-0.617302\pi\)
−0.360230 + 0.932864i \(0.617302\pi\)
\(602\) −20.9964 −0.855750
\(603\) −114.671 −4.66977
\(604\) −24.9691 −1.01598
\(605\) 3.43058 0.139473
\(606\) −25.8392 −1.04965
\(607\) −21.7644 −0.883390 −0.441695 0.897165i \(-0.645623\pi\)
−0.441695 + 0.897165i \(0.645623\pi\)
\(608\) 16.0348 0.650298
\(609\) 20.2858 0.822023
\(610\) 10.6606 0.431635
\(611\) 9.39931 0.380255
\(612\) 44.7724 1.80982
\(613\) 25.3984 1.02583 0.512916 0.858439i \(-0.328565\pi\)
0.512916 + 0.858439i \(0.328565\pi\)
\(614\) 23.6719 0.955321
\(615\) 7.12500 0.287308
\(616\) −17.8081 −0.717510
\(617\) −17.5000 −0.704522 −0.352261 0.935902i \(-0.614587\pi\)
−0.352261 + 0.935902i \(0.614587\pi\)
\(618\) −105.089 −4.22732
\(619\) 10.5974 0.425944 0.212972 0.977058i \(-0.431686\pi\)
0.212972 + 0.977058i \(0.431686\pi\)
\(620\) −0.201373 −0.00808735
\(621\) 107.625 4.31884
\(622\) 4.60884 0.184798
\(623\) −42.9932 −1.72249
\(624\) 20.8322 0.833956
\(625\) 19.0503 0.762011
\(626\) −5.35892 −0.214186
\(627\) −36.8889 −1.47320
\(628\) 25.4358 1.01500
\(629\) −4.08941 −0.163055
\(630\) 32.3333 1.28819
\(631\) 44.0126 1.75211 0.876057 0.482207i \(-0.160165\pi\)
0.876057 + 0.482207i \(0.160165\pi\)
\(632\) 13.1329 0.522397
\(633\) −26.3502 −1.04732
\(634\) −33.0190 −1.31135
\(635\) −9.35007 −0.371046
\(636\) −7.19962 −0.285484
\(637\) 3.51144 0.139128
\(638\) −13.5366 −0.535918
\(639\) 8.95173 0.354125
\(640\) −6.60592 −0.261122
\(641\) 20.4319 0.807010 0.403505 0.914977i \(-0.367792\pi\)
0.403505 + 0.914977i \(0.367792\pi\)
\(642\) −61.9057 −2.44322
\(643\) 44.2650 1.74564 0.872821 0.488040i \(-0.162288\pi\)
0.872821 + 0.488040i \(0.162288\pi\)
\(644\) 19.9745 0.787105
\(645\) 8.22171 0.323730
\(646\) −19.3336 −0.760669
\(647\) 44.3296 1.74278 0.871388 0.490595i \(-0.163221\pi\)
0.871388 + 0.490595i \(0.163221\pi\)
\(648\) 62.4330 2.45260
\(649\) 0.963655 0.0378268
\(650\) 10.0192 0.392985
\(651\) −2.81263 −0.110236
\(652\) 10.2398 0.401022
\(653\) 29.5455 1.15620 0.578102 0.815964i \(-0.303794\pi\)
0.578102 + 0.815964i \(0.303794\pi\)
\(654\) −6.20936 −0.242805
\(655\) 6.46649 0.252666
\(656\) 15.9671 0.623409
\(657\) −20.0914 −0.783839
\(658\) 43.6222 1.70057
\(659\) −12.3747 −0.482049 −0.241024 0.970519i \(-0.577483\pi\)
−0.241024 + 0.970519i \(0.577483\pi\)
\(660\) −10.9077 −0.424583
\(661\) −5.78116 −0.224861 −0.112431 0.993660i \(-0.535864\pi\)
−0.112431 + 0.993660i \(0.535864\pi\)
\(662\) −43.7437 −1.70015
\(663\) −17.2049 −0.668182
\(664\) 12.6750 0.491887
\(665\) −5.29011 −0.205142
\(666\) 16.1030 0.623979
\(667\) −9.70658 −0.375840
\(668\) −5.85303 −0.226461
\(669\) 85.8152 3.31781
\(670\) 14.6418 0.565663
\(671\) −37.6462 −1.45332
\(672\) 66.2239 2.55464
\(673\) −37.4386 −1.44315 −0.721575 0.692336i \(-0.756582\pi\)
−0.721575 + 0.692336i \(0.756582\pi\)
\(674\) −48.7439 −1.87755
\(675\) 94.9280 3.65378
\(676\) −14.0570 −0.540652
\(677\) −37.8014 −1.45283 −0.726413 0.687258i \(-0.758814\pi\)
−0.726413 + 0.687258i \(0.758814\pi\)
\(678\) 64.8880 2.49201
\(679\) 17.7200 0.680030
\(680\) 3.65470 0.140151
\(681\) 15.9566 0.611459
\(682\) 1.87685 0.0718683
\(683\) 34.7982 1.33152 0.665758 0.746167i \(-0.268108\pi\)
0.665758 + 0.746167i \(0.268108\pi\)
\(684\) 28.8450 1.10292
\(685\) 11.0925 0.423822
\(686\) −23.2023 −0.885868
\(687\) 4.37253 0.166823
\(688\) 18.4248 0.702439
\(689\) 2.07346 0.0789925
\(690\) −20.6433 −0.785878
\(691\) 29.5475 1.12404 0.562021 0.827123i \(-0.310024\pi\)
0.562021 + 0.827123i \(0.310024\pi\)
\(692\) −6.57353 −0.249888
\(693\) −114.180 −4.33735
\(694\) 20.5545 0.780239
\(695\) 1.61907 0.0614148
\(696\) −9.02901 −0.342244
\(697\) −13.1869 −0.499488
\(698\) 10.5066 0.397682
\(699\) −28.2031 −1.06674
\(700\) 17.6180 0.665898
\(701\) −7.77757 −0.293755 −0.146877 0.989155i \(-0.546922\pi\)
−0.146877 + 0.989155i \(0.546922\pi\)
\(702\) 45.0996 1.70217
\(703\) −2.63464 −0.0993673
\(704\) −4.11955 −0.155262
\(705\) −17.0814 −0.643323
\(706\) 39.9642 1.50407
\(707\) 13.0855 0.492130
\(708\) −1.00543 −0.0377865
\(709\) −38.1007 −1.43090 −0.715451 0.698663i \(-0.753779\pi\)
−0.715451 + 0.698663i \(0.753779\pi\)
\(710\) −1.14301 −0.0428962
\(711\) 84.2039 3.15789
\(712\) 19.1358 0.717146
\(713\) 1.34582 0.0504014
\(714\) −79.8478 −2.98823
\(715\) 3.14138 0.117481
\(716\) −7.48466 −0.279715
\(717\) 34.5210 1.28921
\(718\) −15.1815 −0.566569
\(719\) 7.52410 0.280602 0.140301 0.990109i \(-0.455193\pi\)
0.140301 + 0.990109i \(0.455193\pi\)
\(720\) −28.3732 −1.05741
\(721\) 53.2192 1.98199
\(722\) 21.6386 0.805307
\(723\) −2.41804 −0.0899279
\(724\) 19.6063 0.728661
\(725\) −8.56145 −0.317964
\(726\) 33.3600 1.23811
\(727\) −13.5189 −0.501387 −0.250693 0.968067i \(-0.580659\pi\)
−0.250693 + 0.968067i \(0.580659\pi\)
\(728\) −5.35101 −0.198321
\(729\) 185.713 6.87828
\(730\) 2.56538 0.0949488
\(731\) −15.2167 −0.562808
\(732\) 39.2783 1.45177
\(733\) −49.5274 −1.82933 −0.914667 0.404208i \(-0.867547\pi\)
−0.914667 + 0.404208i \(0.867547\pi\)
\(734\) 32.5377 1.20099
\(735\) −6.38136 −0.235380
\(736\) −31.6875 −1.16802
\(737\) −51.7054 −1.90459
\(738\) 51.9264 1.91144
\(739\) −2.41508 −0.0888402 −0.0444201 0.999013i \(-0.514144\pi\)
−0.0444201 + 0.999013i \(0.514144\pi\)
\(740\) −0.779042 −0.0286381
\(741\) −11.0844 −0.407196
\(742\) 9.62292 0.353269
\(743\) −31.0505 −1.13913 −0.569565 0.821946i \(-0.692888\pi\)
−0.569565 + 0.821946i \(0.692888\pi\)
\(744\) 1.25188 0.0458960
\(745\) −3.79972 −0.139211
\(746\) 2.36515 0.0865943
\(747\) 81.2685 2.97346
\(748\) 20.1879 0.738144
\(749\) 31.3502 1.14551
\(750\) −38.0325 −1.38875
\(751\) 13.4610 0.491198 0.245599 0.969371i \(-0.421015\pi\)
0.245599 + 0.969371i \(0.421015\pi\)
\(752\) −38.2794 −1.39590
\(753\) 108.045 3.93737
\(754\) −4.06749 −0.148129
\(755\) −13.0683 −0.475602
\(756\) 79.3042 2.88427
\(757\) 49.0633 1.78324 0.891618 0.452787i \(-0.149570\pi\)
0.891618 + 0.452787i \(0.149570\pi\)
\(758\) 10.2367 0.371812
\(759\) 72.8988 2.64606
\(760\) 2.35458 0.0854094
\(761\) −28.6130 −1.03722 −0.518610 0.855011i \(-0.673550\pi\)
−0.518610 + 0.855011i \(0.673550\pi\)
\(762\) −90.9230 −3.29379
\(763\) 3.14453 0.113840
\(764\) 13.8189 0.499952
\(765\) 23.4328 0.847215
\(766\) −0.849302 −0.0306865
\(767\) 0.289560 0.0104554
\(768\) −71.2840 −2.57224
\(769\) −39.8840 −1.43825 −0.719127 0.694878i \(-0.755458\pi\)
−0.719127 + 0.694878i \(0.755458\pi\)
\(770\) 14.5791 0.525396
\(771\) 35.7730 1.28833
\(772\) 25.1586 0.905477
\(773\) 25.1545 0.904744 0.452372 0.891829i \(-0.350578\pi\)
0.452372 + 0.891829i \(0.350578\pi\)
\(774\) 59.9192 2.15375
\(775\) 1.18705 0.0426400
\(776\) −7.88698 −0.283126
\(777\) −10.8811 −0.390357
\(778\) 13.2273 0.474222
\(779\) −8.49577 −0.304392
\(780\) −3.27757 −0.117356
\(781\) 4.03635 0.144432
\(782\) 38.2065 1.36626
\(783\) −38.5378 −1.37723
\(784\) −14.3006 −0.510735
\(785\) 13.3125 0.475143
\(786\) 62.8822 2.24293
\(787\) −11.4491 −0.408116 −0.204058 0.978959i \(-0.565413\pi\)
−0.204058 + 0.978959i \(0.565413\pi\)
\(788\) 1.29601 0.0461685
\(789\) 55.7112 1.98337
\(790\) −10.7516 −0.382525
\(791\) −32.8605 −1.16838
\(792\) 50.8205 1.80583
\(793\) −11.3120 −0.401700
\(794\) 21.9305 0.778283
\(795\) −3.76811 −0.133641
\(796\) −5.78650 −0.205097
\(797\) 18.9437 0.671019 0.335509 0.942037i \(-0.391092\pi\)
0.335509 + 0.942037i \(0.391092\pi\)
\(798\) −51.4427 −1.82105
\(799\) 31.6141 1.11843
\(800\) −27.9492 −0.988155
\(801\) 122.693 4.33515
\(802\) 33.2258 1.17325
\(803\) −9.05923 −0.319693
\(804\) 53.9469 1.90256
\(805\) 10.4542 0.368461
\(806\) 0.563958 0.0198646
\(807\) 12.5962 0.443408
\(808\) −5.82421 −0.204895
\(809\) −27.7381 −0.975220 −0.487610 0.873062i \(-0.662131\pi\)
−0.487610 + 0.873062i \(0.662131\pi\)
\(810\) −51.1126 −1.79591
\(811\) −28.0963 −0.986595 −0.493297 0.869861i \(-0.664209\pi\)
−0.493297 + 0.869861i \(0.664209\pi\)
\(812\) −7.15236 −0.250999
\(813\) −75.9737 −2.66451
\(814\) 7.26087 0.254493
\(815\) 5.35927 0.187727
\(816\) 70.0681 2.45288
\(817\) −9.80348 −0.342980
\(818\) −17.8942 −0.625655
\(819\) −34.3090 −1.19885
\(820\) −2.51213 −0.0877273
\(821\) −15.6437 −0.545968 −0.272984 0.962019i \(-0.588011\pi\)
−0.272984 + 0.962019i \(0.588011\pi\)
\(822\) 107.867 3.76229
\(823\) 1.17763 0.0410496 0.0205248 0.999789i \(-0.493466\pi\)
0.0205248 + 0.999789i \(0.493466\pi\)
\(824\) −23.6874 −0.825188
\(825\) 64.2986 2.23859
\(826\) 1.34385 0.0467585
\(827\) 47.8161 1.66273 0.831365 0.555727i \(-0.187560\pi\)
0.831365 + 0.555727i \(0.187560\pi\)
\(828\) −57.0027 −1.98098
\(829\) −14.5616 −0.505747 −0.252873 0.967499i \(-0.581376\pi\)
−0.252873 + 0.967499i \(0.581376\pi\)
\(830\) −10.3768 −0.360184
\(831\) −102.220 −3.54598
\(832\) −1.23785 −0.0429147
\(833\) 11.8105 0.409211
\(834\) 15.7444 0.545182
\(835\) −3.06334 −0.106011
\(836\) 13.0063 0.449831
\(837\) 5.34328 0.184691
\(838\) 57.4198 1.98353
\(839\) 12.1008 0.417768 0.208884 0.977940i \(-0.433017\pi\)
0.208884 + 0.977940i \(0.433017\pi\)
\(840\) 9.72441 0.335524
\(841\) −25.5243 −0.880149
\(842\) 38.0970 1.31291
\(843\) −17.8131 −0.613515
\(844\) 9.29053 0.319793
\(845\) −7.35708 −0.253091
\(846\) −124.488 −4.27999
\(847\) −16.8941 −0.580489
\(848\) −8.44432 −0.289979
\(849\) −37.1665 −1.27555
\(850\) 33.6991 1.15587
\(851\) 5.20650 0.178477
\(852\) −4.21134 −0.144278
\(853\) −24.1041 −0.825307 −0.412654 0.910888i \(-0.635398\pi\)
−0.412654 + 0.910888i \(0.635398\pi\)
\(854\) −52.4989 −1.79647
\(855\) 15.0968 0.516300
\(856\) −13.9537 −0.476926
\(857\) −21.2418 −0.725605 −0.362803 0.931866i \(-0.618180\pi\)
−0.362803 + 0.931866i \(0.618180\pi\)
\(858\) 30.5478 1.04288
\(859\) −51.5073 −1.75741 −0.878703 0.477370i \(-0.841590\pi\)
−0.878703 + 0.477370i \(0.841590\pi\)
\(860\) −2.89881 −0.0988485
\(861\) −35.0876 −1.19578
\(862\) −8.54630 −0.291088
\(863\) −56.3974 −1.91979 −0.959896 0.280358i \(-0.909547\pi\)
−0.959896 + 0.280358i \(0.909547\pi\)
\(864\) −125.808 −4.28009
\(865\) −3.44043 −0.116978
\(866\) −17.2587 −0.586474
\(867\) 0.957631 0.0325228
\(868\) 0.991678 0.0336597
\(869\) 37.9676 1.28796
\(870\) 7.39187 0.250608
\(871\) −15.5365 −0.526434
\(872\) −1.39960 −0.0473964
\(873\) −50.5689 −1.71150
\(874\) 24.6149 0.832611
\(875\) 19.2604 0.651119
\(876\) 9.45197 0.319353
\(877\) −58.5883 −1.97839 −0.989193 0.146618i \(-0.953161\pi\)
−0.989193 + 0.146618i \(0.953161\pi\)
\(878\) 35.8403 1.20955
\(879\) 79.5072 2.68171
\(880\) −12.7935 −0.431269
\(881\) −18.7277 −0.630951 −0.315475 0.948934i \(-0.602164\pi\)
−0.315475 + 0.948934i \(0.602164\pi\)
\(882\) −46.5068 −1.56597
\(883\) 41.8871 1.40961 0.704806 0.709400i \(-0.251034\pi\)
0.704806 + 0.709400i \(0.251034\pi\)
\(884\) 6.06609 0.204025
\(885\) −0.526220 −0.0176887
\(886\) 35.2223 1.18332
\(887\) 47.4909 1.59459 0.797294 0.603591i \(-0.206264\pi\)
0.797294 + 0.603591i \(0.206264\pi\)
\(888\) 4.84306 0.162523
\(889\) 46.0451 1.54430
\(890\) −15.6661 −0.525130
\(891\) 180.496 6.04685
\(892\) −30.2567 −1.01307
\(893\) 20.3677 0.681579
\(894\) −36.9497 −1.23578
\(895\) −3.91730 −0.130941
\(896\) 32.5313 1.08680
\(897\) 21.9047 0.731377
\(898\) −49.5851 −1.65468
\(899\) −0.481905 −0.0160724
\(900\) −50.2779 −1.67593
\(901\) 6.97398 0.232337
\(902\) 23.4137 0.779590
\(903\) −40.4884 −1.34737
\(904\) 14.6259 0.486449
\(905\) 10.2615 0.341102
\(906\) −127.080 −4.22194
\(907\) 15.9132 0.528390 0.264195 0.964469i \(-0.414894\pi\)
0.264195 + 0.964469i \(0.414894\pi\)
\(908\) −5.62598 −0.186705
\(909\) −37.3430 −1.23859
\(910\) 4.38076 0.145221
\(911\) −34.0106 −1.12682 −0.563410 0.826177i \(-0.690511\pi\)
−0.563410 + 0.826177i \(0.690511\pi\)
\(912\) 45.1421 1.49480
\(913\) 36.6441 1.21274
\(914\) 43.7775 1.44803
\(915\) 20.5573 0.679605
\(916\) −1.54167 −0.0509381
\(917\) −31.8447 −1.05160
\(918\) 151.690 5.00653
\(919\) 30.1639 0.995016 0.497508 0.867459i \(-0.334248\pi\)
0.497508 + 0.867459i \(0.334248\pi\)
\(920\) −4.65305 −0.153406
\(921\) 45.6477 1.50414
\(922\) 29.4714 0.970588
\(923\) 1.21285 0.0399213
\(924\) 53.7160 1.76713
\(925\) 4.59227 0.150993
\(926\) −0.667805 −0.0219454
\(927\) −151.876 −4.98826
\(928\) 11.3465 0.372468
\(929\) 42.8317 1.40526 0.702631 0.711555i \(-0.252009\pi\)
0.702631 + 0.711555i \(0.252009\pi\)
\(930\) −1.02488 −0.0336073
\(931\) 7.60906 0.249377
\(932\) 9.94384 0.325721
\(933\) 8.88746 0.290962
\(934\) −10.3689 −0.339279
\(935\) 10.5659 0.345541
\(936\) 15.2706 0.499135
\(937\) 35.1057 1.14685 0.573427 0.819256i \(-0.305614\pi\)
0.573427 + 0.819256i \(0.305614\pi\)
\(938\) −72.1048 −2.35430
\(939\) −10.3339 −0.337233
\(940\) 6.02256 0.196434
\(941\) −30.9999 −1.01057 −0.505285 0.862953i \(-0.668613\pi\)
−0.505285 + 0.862953i \(0.668613\pi\)
\(942\) 129.455 4.21786
\(943\) 16.7891 0.546728
\(944\) −1.17926 −0.0383815
\(945\) 41.5059 1.35019
\(946\) 27.0176 0.878419
\(947\) 16.8063 0.546131 0.273065 0.961995i \(-0.411962\pi\)
0.273065 + 0.961995i \(0.411962\pi\)
\(948\) −39.6137 −1.28659
\(949\) −2.72213 −0.0883640
\(950\) 21.7110 0.704397
\(951\) −63.6721 −2.06471
\(952\) −17.9978 −0.583313
\(953\) −47.6716 −1.54423 −0.772117 0.635481i \(-0.780802\pi\)
−0.772117 + 0.635481i \(0.780802\pi\)
\(954\) −27.4617 −0.889105
\(955\) 7.23251 0.234038
\(956\) −12.1714 −0.393651
\(957\) −26.1032 −0.843798
\(958\) −69.4033 −2.24232
\(959\) −54.6257 −1.76396
\(960\) 2.24955 0.0726039
\(961\) −30.9332 −0.997845
\(962\) 2.18175 0.0703426
\(963\) −89.4666 −2.88302
\(964\) 0.852552 0.0274588
\(965\) 13.1674 0.423874
\(966\) 101.660 3.27085
\(967\) −4.55347 −0.146430 −0.0732149 0.997316i \(-0.523326\pi\)
−0.0732149 + 0.997316i \(0.523326\pi\)
\(968\) 7.51941 0.241683
\(969\) −37.2819 −1.19767
\(970\) 6.45691 0.207319
\(971\) 48.8389 1.56732 0.783658 0.621193i \(-0.213352\pi\)
0.783658 + 0.621193i \(0.213352\pi\)
\(972\) −112.662 −3.61364
\(973\) −7.97323 −0.255610
\(974\) 27.6679 0.886538
\(975\) 19.3205 0.618752
\(976\) 46.0689 1.47463
\(977\) 17.1969 0.550179 0.275090 0.961419i \(-0.411292\pi\)
0.275090 + 0.961419i \(0.411292\pi\)
\(978\) 52.1153 1.66646
\(979\) 55.3225 1.76811
\(980\) 2.24994 0.0718716
\(981\) −8.97380 −0.286511
\(982\) 32.4542 1.03566
\(983\) 45.9245 1.46476 0.732382 0.680894i \(-0.238409\pi\)
0.732382 + 0.680894i \(0.238409\pi\)
\(984\) 15.6171 0.497856
\(985\) 0.678301 0.0216125
\(986\) −13.6808 −0.435685
\(987\) 84.1187 2.67753
\(988\) 3.90814 0.124334
\(989\) 19.3734 0.616037
\(990\) −41.6057 −1.32231
\(991\) 38.3542 1.21836 0.609180 0.793032i \(-0.291499\pi\)
0.609180 + 0.793032i \(0.291499\pi\)
\(992\) −1.57320 −0.0499491
\(993\) −84.3531 −2.67686
\(994\) 5.62882 0.178535
\(995\) −3.02852 −0.0960104
\(996\) −38.2327 −1.21145
\(997\) 53.5169 1.69490 0.847449 0.530878i \(-0.178138\pi\)
0.847449 + 0.530878i \(0.178138\pi\)
\(998\) 14.3193 0.453269
\(999\) 20.6713 0.654010
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 \(a_p\))