Properties

Label 6047.2.a.a.1.17
Level 6047
Weight 2
Character 6047.1
Self dual Yes
Analytic conductor 48.286
Analytic rank 1
Dimension 217
CM No

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Newspace parameters

Level: \( N \) = \( 6047 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2855381023\)
Analytic rank: \(1\)
Dimension: \(217\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 6047.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.46440 q^{2}\) \(-0.383920 q^{3}\) \(+4.07326 q^{4}\) \(+2.75346 q^{5}\) \(+0.946133 q^{6}\) \(-1.51513 q^{7}\) \(-5.10935 q^{8}\) \(-2.85261 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.46440 q^{2}\) \(-0.383920 q^{3}\) \(+4.07326 q^{4}\) \(+2.75346 q^{5}\) \(+0.946133 q^{6}\) \(-1.51513 q^{7}\) \(-5.10935 q^{8}\) \(-2.85261 q^{9}\) \(-6.78563 q^{10}\) \(-0.490721 q^{11}\) \(-1.56381 q^{12}\) \(+6.57761 q^{13}\) \(+3.73388 q^{14}\) \(-1.05711 q^{15}\) \(+4.44495 q^{16}\) \(+1.76071 q^{17}\) \(+7.02996 q^{18}\) \(+3.09958 q^{19}\) \(+11.2156 q^{20}\) \(+0.581688 q^{21}\) \(+1.20933 q^{22}\) \(+1.97369 q^{23}\) \(+1.96158 q^{24}\) \(+2.58155 q^{25}\) \(-16.2098 q^{26}\) \(+2.24693 q^{27}\) \(-6.17151 q^{28}\) \(-8.69525 q^{29}\) \(+2.60514 q^{30}\) \(-4.84352 q^{31}\) \(-0.735440 q^{32}\) \(+0.188398 q^{33}\) \(-4.33908 q^{34}\) \(-4.17184 q^{35}\) \(-11.6194 q^{36}\) \(-8.55284 q^{37}\) \(-7.63860 q^{38}\) \(-2.52528 q^{39}\) \(-14.0684 q^{40}\) \(-2.34454 q^{41}\) \(-1.43351 q^{42}\) \(-3.75266 q^{43}\) \(-1.99884 q^{44}\) \(-7.85454 q^{45}\) \(-4.86396 q^{46}\) \(+8.55989 q^{47}\) \(-1.70651 q^{48}\) \(-4.70439 q^{49}\) \(-6.36197 q^{50}\) \(-0.675971 q^{51}\) \(+26.7923 q^{52}\) \(-1.97617 q^{53}\) \(-5.53734 q^{54}\) \(-1.35118 q^{55}\) \(+7.74131 q^{56}\) \(-1.18999 q^{57}\) \(+21.4286 q^{58}\) \(-1.53501 q^{59}\) \(-4.30589 q^{60}\) \(+0.845887 q^{61}\) \(+11.9364 q^{62}\) \(+4.32206 q^{63}\) \(-7.07749 q^{64}\) \(+18.1112 q^{65}\) \(-0.464288 q^{66}\) \(+12.3716 q^{67}\) \(+7.17182 q^{68}\) \(-0.757740 q^{69}\) \(+10.2811 q^{70}\) \(-8.60699 q^{71}\) \(+14.5750 q^{72}\) \(-12.3060 q^{73}\) \(+21.0776 q^{74}\) \(-0.991109 q^{75}\) \(+12.6254 q^{76}\) \(+0.743505 q^{77}\) \(+6.22329 q^{78}\) \(-7.25392 q^{79}\) \(+12.2390 q^{80}\) \(+7.69517 q^{81}\) \(+5.77788 q^{82}\) \(-7.67069 q^{83}\) \(+2.36937 q^{84}\) \(+4.84804 q^{85}\) \(+9.24805 q^{86}\) \(+3.33828 q^{87}\) \(+2.50727 q^{88}\) \(+14.8251 q^{89}\) \(+19.3567 q^{90}\) \(-9.96590 q^{91}\) \(+8.03936 q^{92}\) \(+1.85953 q^{93}\) \(-21.0950 q^{94}\) \(+8.53457 q^{95}\) \(+0.282351 q^{96}\) \(+7.97348 q^{97}\) \(+11.5935 q^{98}\) \(+1.39983 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(217q \) \(\mathstrut -\mathstrut 20q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 184q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 152q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(217q \) \(\mathstrut -\mathstrut 20q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 184q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 152q^{9} \) \(\mathstrut -\mathstrut 46q^{10} \) \(\mathstrut -\mathstrut 32q^{11} \) \(\mathstrut -\mathstrut 72q^{12} \) \(\mathstrut -\mathstrut 80q^{13} \) \(\mathstrut -\mathstrut 22q^{14} \) \(\mathstrut -\mathstrut 43q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut -\mathstrut 61q^{17} \) \(\mathstrut -\mathstrut 88q^{18} \) \(\mathstrut -\mathstrut 43q^{19} \) \(\mathstrut -\mathstrut 41q^{20} \) \(\mathstrut -\mathstrut 61q^{21} \) \(\mathstrut -\mathstrut 93q^{22} \) \(\mathstrut -\mathstrut 60q^{23} \) \(\mathstrut -\mathstrut 41q^{24} \) \(\mathstrut +\mathstrut 26q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 93q^{27} \) \(\mathstrut -\mathstrut 126q^{28} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut -\mathstrut 36q^{30} \) \(\mathstrut -\mathstrut 100q^{31} \) \(\mathstrut -\mathstrut 114q^{32} \) \(\mathstrut -\mathstrut 133q^{33} \) \(\mathstrut -\mathstrut 75q^{34} \) \(\mathstrut -\mathstrut 37q^{35} \) \(\mathstrut +\mathstrut 75q^{36} \) \(\mathstrut -\mathstrut 264q^{37} \) \(\mathstrut -\mathstrut 35q^{38} \) \(\mathstrut -\mathstrut 47q^{39} \) \(\mathstrut -\mathstrut 118q^{40} \) \(\mathstrut -\mathstrut 72q^{41} \) \(\mathstrut -\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 107q^{43} \) \(\mathstrut -\mathstrut 59q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 111q^{46} \) \(\mathstrut -\mathstrut 54q^{47} \) \(\mathstrut -\mathstrut 135q^{48} \) \(\mathstrut +\mathstrut 33q^{49} \) \(\mathstrut -\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 26q^{51} \) \(\mathstrut -\mathstrut 173q^{52} \) \(\mathstrut -\mathstrut 103q^{53} \) \(\mathstrut -\mathstrut 28q^{54} \) \(\mathstrut -\mathstrut 78q^{55} \) \(\mathstrut -\mathstrut 44q^{56} \) \(\mathstrut -\mathstrut 205q^{57} \) \(\mathstrut -\mathstrut 189q^{58} \) \(\mathstrut -\mathstrut 38q^{59} \) \(\mathstrut -\mathstrut 105q^{60} \) \(\mathstrut -\mathstrut 108q^{61} \) \(\mathstrut -\mathstrut 14q^{62} \) \(\mathstrut -\mathstrut 116q^{63} \) \(\mathstrut +\mathstrut 39q^{64} \) \(\mathstrut -\mathstrut 146q^{65} \) \(\mathstrut +\mathstrut 5q^{66} \) \(\mathstrut -\mathstrut 206q^{67} \) \(\mathstrut -\mathstrut 62q^{68} \) \(\mathstrut -\mathstrut 55q^{69} \) \(\mathstrut -\mathstrut 125q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 225q^{72} \) \(\mathstrut -\mathstrut 326q^{73} \) \(\mathstrut +\mathstrut 3q^{74} \) \(\mathstrut -\mathstrut 95q^{75} \) \(\mathstrut -\mathstrut 84q^{76} \) \(\mathstrut -\mathstrut 79q^{77} \) \(\mathstrut -\mathstrut 86q^{78} \) \(\mathstrut -\mathstrut 117q^{79} \) \(\mathstrut -\mathstrut 39q^{80} \) \(\mathstrut +\mathstrut q^{81} \) \(\mathstrut -\mathstrut 96q^{82} \) \(\mathstrut -\mathstrut 23q^{83} \) \(\mathstrut -\mathstrut 57q^{84} \) \(\mathstrut -\mathstrut 224q^{85} \) \(\mathstrut -\mathstrut 7q^{86} \) \(\mathstrut -\mathstrut 45q^{87} \) \(\mathstrut -\mathstrut 250q^{88} \) \(\mathstrut -\mathstrut 104q^{89} \) \(\mathstrut -\mathstrut 36q^{90} \) \(\mathstrut -\mathstrut 96q^{91} \) \(\mathstrut -\mathstrut 137q^{92} \) \(\mathstrut -\mathstrut 155q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 447q^{97} \) \(\mathstrut -\mathstrut 46q^{98} \) \(\mathstrut -\mathstrut 94q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.46440 −1.74259 −0.871297 0.490756i \(-0.836720\pi\)
−0.871297 + 0.490756i \(0.836720\pi\)
\(3\) −0.383920 −0.221656 −0.110828 0.993840i \(-0.535350\pi\)
−0.110828 + 0.993840i \(0.535350\pi\)
\(4\) 4.07326 2.03663
\(5\) 2.75346 1.23139 0.615693 0.787986i \(-0.288876\pi\)
0.615693 + 0.787986i \(0.288876\pi\)
\(6\) 0.946133 0.386257
\(7\) −1.51513 −0.572664 −0.286332 0.958130i \(-0.592436\pi\)
−0.286332 + 0.958130i \(0.592436\pi\)
\(8\) −5.10935 −1.80643
\(9\) −2.85261 −0.950868
\(10\) −6.78563 −2.14580
\(11\) −0.490721 −0.147958 −0.0739790 0.997260i \(-0.523570\pi\)
−0.0739790 + 0.997260i \(0.523570\pi\)
\(12\) −1.56381 −0.451433
\(13\) 6.57761 1.82430 0.912150 0.409857i \(-0.134421\pi\)
0.912150 + 0.409857i \(0.134421\pi\)
\(14\) 3.73388 0.997921
\(15\) −1.05711 −0.272945
\(16\) 4.44495 1.11124
\(17\) 1.76071 0.427034 0.213517 0.976939i \(-0.431508\pi\)
0.213517 + 0.976939i \(0.431508\pi\)
\(18\) 7.02996 1.65698
\(19\) 3.09958 0.711092 0.355546 0.934659i \(-0.384295\pi\)
0.355546 + 0.934659i \(0.384295\pi\)
\(20\) 11.2156 2.50788
\(21\) 0.581688 0.126935
\(22\) 1.20933 0.257831
\(23\) 1.97369 0.411543 0.205771 0.978600i \(-0.434030\pi\)
0.205771 + 0.978600i \(0.434030\pi\)
\(24\) 1.96158 0.400407
\(25\) 2.58155 0.516310
\(26\) −16.2098 −3.17901
\(27\) 2.24693 0.432423
\(28\) −6.17151 −1.16631
\(29\) −8.69525 −1.61467 −0.807334 0.590095i \(-0.799090\pi\)
−0.807334 + 0.590095i \(0.799090\pi\)
\(30\) 2.60514 0.475631
\(31\) −4.84352 −0.869922 −0.434961 0.900449i \(-0.643238\pi\)
−0.434961 + 0.900449i \(0.643238\pi\)
\(32\) −0.735440 −0.130009
\(33\) 0.188398 0.0327959
\(34\) −4.33908 −0.744147
\(35\) −4.17184 −0.705170
\(36\) −11.6194 −1.93657
\(37\) −8.55284 −1.40608 −0.703039 0.711151i \(-0.748174\pi\)
−0.703039 + 0.711151i \(0.748174\pi\)
\(38\) −7.63860 −1.23914
\(39\) −2.52528 −0.404368
\(40\) −14.0684 −2.22441
\(41\) −2.34454 −0.366155 −0.183078 0.983098i \(-0.558606\pi\)
−0.183078 + 0.983098i \(0.558606\pi\)
\(42\) −1.43351 −0.221196
\(43\) −3.75266 −0.572275 −0.286137 0.958189i \(-0.592371\pi\)
−0.286137 + 0.958189i \(0.592371\pi\)
\(44\) −1.99884 −0.301336
\(45\) −7.85454 −1.17089
\(46\) −4.86396 −0.717152
\(47\) 8.55989 1.24859 0.624294 0.781189i \(-0.285387\pi\)
0.624294 + 0.781189i \(0.285387\pi\)
\(48\) −1.70651 −0.246313
\(49\) −4.70439 −0.672056
\(50\) −6.36197 −0.899718
\(51\) −0.675971 −0.0946548
\(52\) 26.7923 3.71543
\(53\) −1.97617 −0.271448 −0.135724 0.990747i \(-0.543336\pi\)
−0.135724 + 0.990747i \(0.543336\pi\)
\(54\) −5.53734 −0.753537
\(55\) −1.35118 −0.182193
\(56\) 7.74131 1.03448
\(57\) −1.18999 −0.157618
\(58\) 21.4286 2.81371
\(59\) −1.53501 −0.199841 −0.0999205 0.994995i \(-0.531859\pi\)
−0.0999205 + 0.994995i \(0.531859\pi\)
\(60\) −4.30589 −0.555888
\(61\) 0.845887 0.108305 0.0541524 0.998533i \(-0.482754\pi\)
0.0541524 + 0.998533i \(0.482754\pi\)
\(62\) 11.9364 1.51592
\(63\) 4.32206 0.544528
\(64\) −7.07749 −0.884686
\(65\) 18.1112 2.24642
\(66\) −0.464288 −0.0571498
\(67\) 12.3716 1.51143 0.755714 0.654901i \(-0.227290\pi\)
0.755714 + 0.654901i \(0.227290\pi\)
\(68\) 7.17182 0.869711
\(69\) −0.757740 −0.0912211
\(70\) 10.2811 1.22882
\(71\) −8.60699 −1.02146 −0.510731 0.859741i \(-0.670625\pi\)
−0.510731 + 0.859741i \(0.670625\pi\)
\(72\) 14.5750 1.71768
\(73\) −12.3060 −1.44031 −0.720155 0.693813i \(-0.755930\pi\)
−0.720155 + 0.693813i \(0.755930\pi\)
\(74\) 21.0776 2.45022
\(75\) −0.991109 −0.114443
\(76\) 12.6254 1.44823
\(77\) 0.743505 0.0847302
\(78\) 6.22329 0.704649
\(79\) −7.25392 −0.816130 −0.408065 0.912953i \(-0.633796\pi\)
−0.408065 + 0.912953i \(0.633796\pi\)
\(80\) 12.2390 1.36836
\(81\) 7.69517 0.855019
\(82\) 5.77788 0.638060
\(83\) −7.67069 −0.841967 −0.420984 0.907068i \(-0.638315\pi\)
−0.420984 + 0.907068i \(0.638315\pi\)
\(84\) 2.36937 0.258519
\(85\) 4.84804 0.525843
\(86\) 9.24805 0.997242
\(87\) 3.33828 0.357901
\(88\) 2.50727 0.267276
\(89\) 14.8251 1.57146 0.785729 0.618571i \(-0.212288\pi\)
0.785729 + 0.618571i \(0.212288\pi\)
\(90\) 19.3567 2.04038
\(91\) −9.96590 −1.04471
\(92\) 8.03936 0.838161
\(93\) 1.85953 0.192824
\(94\) −21.0950 −2.17578
\(95\) 8.53457 0.875629
\(96\) 0.282351 0.0288173
\(97\) 7.97348 0.809584 0.404792 0.914409i \(-0.367344\pi\)
0.404792 + 0.914409i \(0.367344\pi\)
\(98\) 11.5935 1.17112
\(99\) 1.39983 0.140689
\(100\) 10.5153 1.05153
\(101\) −3.35992 −0.334325 −0.167162 0.985929i \(-0.553460\pi\)
−0.167162 + 0.985929i \(0.553460\pi\)
\(102\) 1.66586 0.164945
\(103\) −13.8547 −1.36515 −0.682573 0.730818i \(-0.739139\pi\)
−0.682573 + 0.730818i \(0.739139\pi\)
\(104\) −33.6073 −3.29547
\(105\) 1.60165 0.156305
\(106\) 4.87008 0.473024
\(107\) 0.443578 0.0428823 0.0214411 0.999770i \(-0.493175\pi\)
0.0214411 + 0.999770i \(0.493175\pi\)
\(108\) 9.15236 0.880686
\(109\) −6.59935 −0.632103 −0.316051 0.948742i \(-0.602357\pi\)
−0.316051 + 0.948742i \(0.602357\pi\)
\(110\) 3.32985 0.317489
\(111\) 3.28361 0.311666
\(112\) −6.73467 −0.636366
\(113\) −18.5727 −1.74717 −0.873586 0.486670i \(-0.838211\pi\)
−0.873586 + 0.486670i \(0.838211\pi\)
\(114\) 2.93261 0.274664
\(115\) 5.43448 0.506768
\(116\) −35.4181 −3.28848
\(117\) −18.7633 −1.73467
\(118\) 3.78287 0.348242
\(119\) −2.66769 −0.244547
\(120\) 5.40114 0.493055
\(121\) −10.7592 −0.978108
\(122\) −2.08460 −0.188731
\(123\) 0.900116 0.0811607
\(124\) −19.7289 −1.77171
\(125\) −6.65911 −0.595609
\(126\) −10.6513 −0.948891
\(127\) −14.5466 −1.29081 −0.645403 0.763842i \(-0.723311\pi\)
−0.645403 + 0.763842i \(0.723311\pi\)
\(128\) 18.9126 1.67166
\(129\) 1.44072 0.126848
\(130\) −44.6332 −3.91459
\(131\) 16.9749 1.48310 0.741550 0.670898i \(-0.234091\pi\)
0.741550 + 0.670898i \(0.234091\pi\)
\(132\) 0.767394 0.0667931
\(133\) −4.69625 −0.407217
\(134\) −30.4885 −2.63381
\(135\) 6.18684 0.532479
\(136\) −8.99607 −0.771406
\(137\) 0.252997 0.0216150 0.0108075 0.999942i \(-0.496560\pi\)
0.0108075 + 0.999942i \(0.496560\pi\)
\(138\) 1.86737 0.158961
\(139\) 9.10749 0.772487 0.386243 0.922397i \(-0.373772\pi\)
0.386243 + 0.922397i \(0.373772\pi\)
\(140\) −16.9930 −1.43617
\(141\) −3.28632 −0.276758
\(142\) 21.2111 1.77999
\(143\) −3.22777 −0.269920
\(144\) −12.6797 −1.05664
\(145\) −23.9420 −1.98828
\(146\) 30.3270 2.50988
\(147\) 1.80611 0.148966
\(148\) −34.8380 −2.86366
\(149\) 2.23660 0.183229 0.0916146 0.995795i \(-0.470797\pi\)
0.0916146 + 0.995795i \(0.470797\pi\)
\(150\) 2.44249 0.199428
\(151\) 5.42668 0.441617 0.220809 0.975317i \(-0.429130\pi\)
0.220809 + 0.975317i \(0.429130\pi\)
\(152\) −15.8368 −1.28454
\(153\) −5.02260 −0.406053
\(154\) −1.83229 −0.147650
\(155\) −13.3364 −1.07121
\(156\) −10.2861 −0.823549
\(157\) 10.7019 0.854106 0.427053 0.904227i \(-0.359552\pi\)
0.427053 + 0.904227i \(0.359552\pi\)
\(158\) 17.8766 1.42218
\(159\) 0.758693 0.0601683
\(160\) −2.02501 −0.160091
\(161\) −2.99039 −0.235676
\(162\) −18.9640 −1.48995
\(163\) −9.01921 −0.706439 −0.353219 0.935541i \(-0.614913\pi\)
−0.353219 + 0.935541i \(0.614913\pi\)
\(164\) −9.54993 −0.745724
\(165\) 0.518746 0.0403843
\(166\) 18.9036 1.46721
\(167\) −1.69186 −0.130920 −0.0654602 0.997855i \(-0.520852\pi\)
−0.0654602 + 0.997855i \(0.520852\pi\)
\(168\) −2.97205 −0.229298
\(169\) 30.2649 2.32807
\(170\) −11.9475 −0.916331
\(171\) −8.84188 −0.676155
\(172\) −15.2856 −1.16551
\(173\) 8.89462 0.676245 0.338123 0.941102i \(-0.390208\pi\)
0.338123 + 0.941102i \(0.390208\pi\)
\(174\) −8.22686 −0.623677
\(175\) −3.91137 −0.295672
\(176\) −2.18123 −0.164417
\(177\) 0.589321 0.0442960
\(178\) −36.5350 −2.73841
\(179\) −8.87552 −0.663388 −0.331694 0.943387i \(-0.607620\pi\)
−0.331694 + 0.943387i \(0.607620\pi\)
\(180\) −31.9936 −2.38466
\(181\) 9.36321 0.695962 0.347981 0.937502i \(-0.386867\pi\)
0.347981 + 0.937502i \(0.386867\pi\)
\(182\) 24.5600 1.82051
\(183\) −0.324753 −0.0240065
\(184\) −10.0843 −0.743423
\(185\) −23.5499 −1.73142
\(186\) −4.58261 −0.336014
\(187\) −0.864016 −0.0631831
\(188\) 34.8667 2.54292
\(189\) −3.40439 −0.247633
\(190\) −21.0326 −1.52586
\(191\) 1.47014 0.106376 0.0531879 0.998585i \(-0.483062\pi\)
0.0531879 + 0.998585i \(0.483062\pi\)
\(192\) 2.71719 0.196096
\(193\) −11.7784 −0.847825 −0.423913 0.905703i \(-0.639344\pi\)
−0.423913 + 0.905703i \(0.639344\pi\)
\(194\) −19.6498 −1.41078
\(195\) −6.95325 −0.497933
\(196\) −19.1622 −1.36873
\(197\) 7.30749 0.520637 0.260319 0.965523i \(-0.416172\pi\)
0.260319 + 0.965523i \(0.416172\pi\)
\(198\) −3.44975 −0.245163
\(199\) −8.06238 −0.571527 −0.285763 0.958300i \(-0.592247\pi\)
−0.285763 + 0.958300i \(0.592247\pi\)
\(200\) −13.1900 −0.932677
\(201\) −4.74970 −0.335018
\(202\) 8.28019 0.582592
\(203\) 13.1744 0.924662
\(204\) −2.75341 −0.192777
\(205\) −6.45560 −0.450878
\(206\) 34.1435 2.37889
\(207\) −5.63016 −0.391323
\(208\) 29.2372 2.02723
\(209\) −1.52103 −0.105212
\(210\) −3.94712 −0.272377
\(211\) −9.33441 −0.642607 −0.321304 0.946976i \(-0.604121\pi\)
−0.321304 + 0.946976i \(0.604121\pi\)
\(212\) −8.04948 −0.552840
\(213\) 3.30440 0.226414
\(214\) −1.09315 −0.0747264
\(215\) −10.3328 −0.704691
\(216\) −11.4804 −0.781141
\(217\) 7.33855 0.498173
\(218\) 16.2634 1.10150
\(219\) 4.72453 0.319254
\(220\) −5.50372 −0.371061
\(221\) 11.5812 0.779038
\(222\) −8.09212 −0.543108
\(223\) 25.2328 1.68971 0.844857 0.534993i \(-0.179686\pi\)
0.844857 + 0.534993i \(0.179686\pi\)
\(224\) 1.11429 0.0744513
\(225\) −7.36414 −0.490943
\(226\) 45.7705 3.04461
\(227\) −17.7626 −1.17894 −0.589472 0.807789i \(-0.700664\pi\)
−0.589472 + 0.807789i \(0.700664\pi\)
\(228\) −4.84715 −0.321010
\(229\) 21.8863 1.44629 0.723144 0.690698i \(-0.242696\pi\)
0.723144 + 0.690698i \(0.242696\pi\)
\(230\) −13.3927 −0.883090
\(231\) −0.285447 −0.0187810
\(232\) 44.4271 2.91678
\(233\) −23.4777 −1.53808 −0.769038 0.639203i \(-0.779265\pi\)
−0.769038 + 0.639203i \(0.779265\pi\)
\(234\) 46.2403 3.02282
\(235\) 23.5693 1.53749
\(236\) −6.25249 −0.407003
\(237\) 2.78493 0.180900
\(238\) 6.57426 0.426146
\(239\) 12.4407 0.804725 0.402362 0.915480i \(-0.368189\pi\)
0.402362 + 0.915480i \(0.368189\pi\)
\(240\) −4.69880 −0.303307
\(241\) −12.1085 −0.779975 −0.389987 0.920820i \(-0.627521\pi\)
−0.389987 + 0.920820i \(0.627521\pi\)
\(242\) 26.5149 1.70445
\(243\) −9.69513 −0.621943
\(244\) 3.44552 0.220577
\(245\) −12.9534 −0.827560
\(246\) −2.21825 −0.141430
\(247\) 20.3878 1.29725
\(248\) 24.7473 1.57145
\(249\) 2.94493 0.186627
\(250\) 16.4107 1.03790
\(251\) −25.5974 −1.61569 −0.807847 0.589392i \(-0.799367\pi\)
−0.807847 + 0.589392i \(0.799367\pi\)
\(252\) 17.6049 1.10900
\(253\) −0.968532 −0.0608911
\(254\) 35.8488 2.24935
\(255\) −1.86126 −0.116557
\(256\) −32.4533 −2.02833
\(257\) −20.7063 −1.29163 −0.645813 0.763495i \(-0.723482\pi\)
−0.645813 + 0.763495i \(0.723482\pi\)
\(258\) −3.55051 −0.221045
\(259\) 12.9586 0.805210
\(260\) 73.7716 4.57512
\(261\) 24.8041 1.53534
\(262\) −41.8328 −2.58444
\(263\) 0.253673 0.0156422 0.00782108 0.999969i \(-0.497510\pi\)
0.00782108 + 0.999969i \(0.497510\pi\)
\(264\) −0.962591 −0.0592434
\(265\) −5.44132 −0.334257
\(266\) 11.5734 0.709614
\(267\) −5.69166 −0.348324
\(268\) 50.3927 3.07822
\(269\) 9.70811 0.591914 0.295957 0.955201i \(-0.404361\pi\)
0.295957 + 0.955201i \(0.404361\pi\)
\(270\) −15.2469 −0.927894
\(271\) 8.51004 0.516948 0.258474 0.966018i \(-0.416780\pi\)
0.258474 + 0.966018i \(0.416780\pi\)
\(272\) 7.82626 0.474537
\(273\) 3.82611 0.231567
\(274\) −0.623486 −0.0376661
\(275\) −1.26682 −0.0763922
\(276\) −3.08647 −0.185784
\(277\) −18.7286 −1.12529 −0.562647 0.826697i \(-0.690217\pi\)
−0.562647 + 0.826697i \(0.690217\pi\)
\(278\) −22.4445 −1.34613
\(279\) 13.8167 0.827181
\(280\) 21.3154 1.27384
\(281\) 23.4720 1.40022 0.700111 0.714034i \(-0.253134\pi\)
0.700111 + 0.714034i \(0.253134\pi\)
\(282\) 8.09879 0.482276
\(283\) 3.38077 0.200966 0.100483 0.994939i \(-0.467961\pi\)
0.100483 + 0.994939i \(0.467961\pi\)
\(284\) −35.0585 −2.08034
\(285\) −3.27660 −0.194089
\(286\) 7.95452 0.470360
\(287\) 3.55227 0.209684
\(288\) 2.09792 0.123621
\(289\) −13.8999 −0.817642
\(290\) 59.0027 3.46476
\(291\) −3.06118 −0.179450
\(292\) −50.1257 −2.93338
\(293\) 24.0072 1.40251 0.701257 0.712908i \(-0.252622\pi\)
0.701257 + 0.712908i \(0.252622\pi\)
\(294\) −4.45098 −0.259586
\(295\) −4.22658 −0.246081
\(296\) 43.6995 2.53998
\(297\) −1.10262 −0.0639804
\(298\) −5.51187 −0.319294
\(299\) 12.9822 0.750777
\(300\) −4.03705 −0.233079
\(301\) 5.68575 0.327721
\(302\) −13.3735 −0.769559
\(303\) 1.28994 0.0741053
\(304\) 13.7775 0.790193
\(305\) 2.32912 0.133365
\(306\) 12.3777 0.707585
\(307\) −19.3638 −1.10515 −0.552575 0.833463i \(-0.686355\pi\)
−0.552575 + 0.833463i \(0.686355\pi\)
\(308\) 3.02849 0.172564
\(309\) 5.31910 0.302593
\(310\) 32.8663 1.86668
\(311\) 27.0134 1.53179 0.765896 0.642965i \(-0.222296\pi\)
0.765896 + 0.642965i \(0.222296\pi\)
\(312\) 12.9025 0.730462
\(313\) 5.79613 0.327617 0.163808 0.986492i \(-0.447622\pi\)
0.163808 + 0.986492i \(0.447622\pi\)
\(314\) −26.3738 −1.48836
\(315\) 11.9006 0.670524
\(316\) −29.5471 −1.66216
\(317\) −34.8756 −1.95881 −0.979403 0.201913i \(-0.935284\pi\)
−0.979403 + 0.201913i \(0.935284\pi\)
\(318\) −1.86972 −0.104849
\(319\) 4.26694 0.238903
\(320\) −19.4876 −1.08939
\(321\) −0.170298 −0.00950513
\(322\) 7.36951 0.410687
\(323\) 5.45745 0.303661
\(324\) 31.3445 1.74136
\(325\) 16.9804 0.941903
\(326\) 22.2269 1.23104
\(327\) 2.53362 0.140110
\(328\) 11.9791 0.661434
\(329\) −12.9693 −0.715022
\(330\) −1.27840 −0.0703735
\(331\) 24.1011 1.32472 0.662359 0.749187i \(-0.269555\pi\)
0.662359 + 0.749187i \(0.269555\pi\)
\(332\) −31.2447 −1.71478
\(333\) 24.3979 1.33699
\(334\) 4.16943 0.228141
\(335\) 34.0647 1.86115
\(336\) 2.58558 0.141055
\(337\) −28.9879 −1.57907 −0.789537 0.613703i \(-0.789679\pi\)
−0.789537 + 0.613703i \(0.789679\pi\)
\(338\) −74.5848 −4.05688
\(339\) 7.13043 0.387272
\(340\) 19.7473 1.07095
\(341\) 2.37682 0.128712
\(342\) 21.7899 1.17826
\(343\) 17.7336 0.957526
\(344\) 19.1736 1.03377
\(345\) −2.08641 −0.112328
\(346\) −21.9199 −1.17842
\(347\) 19.0577 1.02307 0.511536 0.859262i \(-0.329077\pi\)
0.511536 + 0.859262i \(0.329077\pi\)
\(348\) 13.5977 0.728914
\(349\) −13.2415 −0.708804 −0.354402 0.935093i \(-0.615315\pi\)
−0.354402 + 0.935093i \(0.615315\pi\)
\(350\) 9.63918 0.515236
\(351\) 14.7794 0.788868
\(352\) 0.360896 0.0192358
\(353\) 0.242265 0.0128945 0.00644723 0.999979i \(-0.497948\pi\)
0.00644723 + 0.999979i \(0.497948\pi\)
\(354\) −1.45232 −0.0771900
\(355\) −23.6990 −1.25781
\(356\) 60.3865 3.20048
\(357\) 1.02418 0.0542054
\(358\) 21.8728 1.15601
\(359\) −22.7156 −1.19888 −0.599442 0.800418i \(-0.704611\pi\)
−0.599442 + 0.800418i \(0.704611\pi\)
\(360\) 40.1316 2.11512
\(361\) −9.39261 −0.494348
\(362\) −23.0747 −1.21278
\(363\) 4.13067 0.216804
\(364\) −40.5938 −2.12769
\(365\) −33.8842 −1.77358
\(366\) 0.800322 0.0418335
\(367\) −11.2808 −0.588853 −0.294426 0.955674i \(-0.595129\pi\)
−0.294426 + 0.955674i \(0.595129\pi\)
\(368\) 8.77296 0.457322
\(369\) 6.68804 0.348166
\(370\) 58.0364 3.01717
\(371\) 2.99415 0.155449
\(372\) 7.57434 0.392711
\(373\) 4.52292 0.234188 0.117094 0.993121i \(-0.462642\pi\)
0.117094 + 0.993121i \(0.462642\pi\)
\(374\) 2.12928 0.110102
\(375\) 2.55657 0.132021
\(376\) −43.7355 −2.25549
\(377\) −57.1939 −2.94564
\(378\) 8.38977 0.431523
\(379\) −18.9674 −0.974288 −0.487144 0.873322i \(-0.661961\pi\)
−0.487144 + 0.873322i \(0.661961\pi\)
\(380\) 34.7636 1.78333
\(381\) 5.58475 0.286116
\(382\) −3.62302 −0.185370
\(383\) 3.48139 0.177891 0.0889455 0.996036i \(-0.471650\pi\)
0.0889455 + 0.996036i \(0.471650\pi\)
\(384\) −7.26095 −0.370534
\(385\) 2.04721 0.104336
\(386\) 29.0266 1.47741
\(387\) 10.7048 0.544158
\(388\) 32.4781 1.64883
\(389\) 16.5741 0.840341 0.420171 0.907445i \(-0.361970\pi\)
0.420171 + 0.907445i \(0.361970\pi\)
\(390\) 17.1356 0.867694
\(391\) 3.47509 0.175743
\(392\) 24.0364 1.21402
\(393\) −6.51699 −0.328739
\(394\) −18.0086 −0.907259
\(395\) −19.9734 −1.00497
\(396\) 5.70189 0.286531
\(397\) −32.7913 −1.64575 −0.822874 0.568223i \(-0.807631\pi\)
−0.822874 + 0.568223i \(0.807631\pi\)
\(398\) 19.8689 0.995939
\(399\) 1.80299 0.0902623
\(400\) 11.4749 0.573743
\(401\) 10.8159 0.540118 0.270059 0.962844i \(-0.412957\pi\)
0.270059 + 0.962844i \(0.412957\pi\)
\(402\) 11.7052 0.583800
\(403\) −31.8588 −1.58700
\(404\) −13.6859 −0.680897
\(405\) 21.1884 1.05286
\(406\) −32.4670 −1.61131
\(407\) 4.19706 0.208040
\(408\) 3.45377 0.170987
\(409\) 25.1851 1.24532 0.622661 0.782492i \(-0.286052\pi\)
0.622661 + 0.782492i \(0.286052\pi\)
\(410\) 15.9092 0.785698
\(411\) −0.0971307 −0.00479110
\(412\) −56.4339 −2.78030
\(413\) 2.32573 0.114442
\(414\) 13.8750 0.681917
\(415\) −21.1209 −1.03679
\(416\) −4.83744 −0.237175
\(417\) −3.49655 −0.171227
\(418\) 3.74842 0.183341
\(419\) 19.4311 0.949274 0.474637 0.880182i \(-0.342579\pi\)
0.474637 + 0.880182i \(0.342579\pi\)
\(420\) 6.52396 0.318337
\(421\) −27.4686 −1.33874 −0.669368 0.742931i \(-0.733435\pi\)
−0.669368 + 0.742931i \(0.733435\pi\)
\(422\) 23.0037 1.11980
\(423\) −24.4180 −1.18724
\(424\) 10.0970 0.490352
\(425\) 4.54535 0.220482
\(426\) −8.14336 −0.394547
\(427\) −1.28163 −0.0620222
\(428\) 1.80681 0.0873354
\(429\) 1.23921 0.0598295
\(430\) 25.4641 1.22799
\(431\) 18.3898 0.885804 0.442902 0.896570i \(-0.353949\pi\)
0.442902 + 0.896570i \(0.353949\pi\)
\(432\) 9.98752 0.480525
\(433\) −12.9935 −0.624430 −0.312215 0.950012i \(-0.601071\pi\)
−0.312215 + 0.950012i \(0.601071\pi\)
\(434\) −18.0851 −0.868113
\(435\) 9.19183 0.440715
\(436\) −26.8809 −1.28736
\(437\) 6.11761 0.292645
\(438\) −11.6431 −0.556330
\(439\) −11.2837 −0.538540 −0.269270 0.963065i \(-0.586782\pi\)
−0.269270 + 0.963065i \(0.586782\pi\)
\(440\) 6.90366 0.329119
\(441\) 13.4198 0.639037
\(442\) −28.5408 −1.35755
\(443\) −2.81020 −0.133517 −0.0667584 0.997769i \(-0.521266\pi\)
−0.0667584 + 0.997769i \(0.521266\pi\)
\(444\) 13.3750 0.634749
\(445\) 40.8203 1.93507
\(446\) −62.1837 −2.94448
\(447\) −0.858675 −0.0406139
\(448\) 10.7233 0.506628
\(449\) 34.8829 1.64622 0.823112 0.567879i \(-0.192236\pi\)
0.823112 + 0.567879i \(0.192236\pi\)
\(450\) 18.1482 0.855513
\(451\) 1.15052 0.0541756
\(452\) −75.6515 −3.55835
\(453\) −2.08341 −0.0978873
\(454\) 43.7741 2.05442
\(455\) −27.4407 −1.28644
\(456\) 6.08008 0.284726
\(457\) −14.4690 −0.676834 −0.338417 0.940996i \(-0.609891\pi\)
−0.338417 + 0.940996i \(0.609891\pi\)
\(458\) −53.9366 −2.52029
\(459\) 3.95619 0.184659
\(460\) 22.1361 1.03210
\(461\) 33.1178 1.54245 0.771225 0.636562i \(-0.219644\pi\)
0.771225 + 0.636562i \(0.219644\pi\)
\(462\) 0.703454 0.0327277
\(463\) 11.2461 0.522652 0.261326 0.965251i \(-0.415840\pi\)
0.261326 + 0.965251i \(0.415840\pi\)
\(464\) −38.6500 −1.79428
\(465\) 5.12013 0.237440
\(466\) 57.8585 2.68024
\(467\) 23.4853 1.08677 0.543384 0.839484i \(-0.317143\pi\)
0.543384 + 0.839484i \(0.317143\pi\)
\(468\) −76.4279 −3.53288
\(469\) −18.7445 −0.865541
\(470\) −58.0842 −2.67923
\(471\) −4.10868 −0.189318
\(472\) 7.84289 0.360998
\(473\) 1.84151 0.0846727
\(474\) −6.86317 −0.315236
\(475\) 8.00171 0.367144
\(476\) −10.8662 −0.498052
\(477\) 5.63724 0.258112
\(478\) −30.6590 −1.40231
\(479\) −23.7888 −1.08694 −0.543469 0.839429i \(-0.682889\pi\)
−0.543469 + 0.839429i \(0.682889\pi\)
\(480\) 0.777441 0.0354852
\(481\) −56.2572 −2.56511
\(482\) 29.8401 1.35918
\(483\) 1.14807 0.0522390
\(484\) −43.8250 −1.99205
\(485\) 21.9547 0.996910
\(486\) 23.8927 1.08379
\(487\) 10.7009 0.484906 0.242453 0.970163i \(-0.422048\pi\)
0.242453 + 0.970163i \(0.422048\pi\)
\(488\) −4.32194 −0.195645
\(489\) 3.46266 0.156587
\(490\) 31.9223 1.44210
\(491\) −32.6989 −1.47568 −0.737841 0.674974i \(-0.764155\pi\)
−0.737841 + 0.674974i \(0.764155\pi\)
\(492\) 3.66641 0.165295
\(493\) −15.3098 −0.689518
\(494\) −50.2437 −2.26057
\(495\) 3.85439 0.173242
\(496\) −21.5292 −0.966691
\(497\) 13.0407 0.584954
\(498\) −7.25749 −0.325216
\(499\) −39.4925 −1.76793 −0.883963 0.467557i \(-0.845134\pi\)
−0.883963 + 0.467557i \(0.845134\pi\)
\(500\) −27.1243 −1.21304
\(501\) 0.649541 0.0290193
\(502\) 63.0823 2.81550
\(503\) 34.9015 1.55618 0.778091 0.628151i \(-0.216188\pi\)
0.778091 + 0.628151i \(0.216188\pi\)
\(504\) −22.0829 −0.983651
\(505\) −9.25142 −0.411683
\(506\) 2.38685 0.106108
\(507\) −11.6193 −0.516032
\(508\) −59.2523 −2.62890
\(509\) −31.1087 −1.37887 −0.689434 0.724348i \(-0.742141\pi\)
−0.689434 + 0.724348i \(0.742141\pi\)
\(510\) 4.58689 0.203111
\(511\) 18.6452 0.824814
\(512\) 42.1527 1.86290
\(513\) 6.96455 0.307492
\(514\) 51.0287 2.25078
\(515\) −38.1484 −1.68102
\(516\) 5.86844 0.258344
\(517\) −4.20052 −0.184739
\(518\) −31.9352 −1.40315
\(519\) −3.41482 −0.149894
\(520\) −92.5364 −4.05799
\(521\) −8.85774 −0.388064 −0.194032 0.980995i \(-0.562157\pi\)
−0.194032 + 0.980995i \(0.562157\pi\)
\(522\) −61.1272 −2.67547
\(523\) 36.3920 1.59131 0.795655 0.605750i \(-0.207127\pi\)
0.795655 + 0.605750i \(0.207127\pi\)
\(524\) 69.1431 3.02053
\(525\) 1.50166 0.0655376
\(526\) −0.625152 −0.0272579
\(527\) −8.52802 −0.371486
\(528\) 0.837420 0.0364440
\(529\) −19.1045 −0.830633
\(530\) 13.4096 0.582475
\(531\) 4.37877 0.190022
\(532\) −19.1291 −0.829351
\(533\) −15.4215 −0.667977
\(534\) 14.0265 0.606987
\(535\) 1.22137 0.0528046
\(536\) −63.2107 −2.73029
\(537\) 3.40749 0.147044
\(538\) −23.9247 −1.03147
\(539\) 2.30855 0.0994361
\(540\) 25.2007 1.08446
\(541\) −26.6181 −1.14440 −0.572201 0.820113i \(-0.693910\pi\)
−0.572201 + 0.820113i \(0.693910\pi\)
\(542\) −20.9721 −0.900830
\(543\) −3.59472 −0.154264
\(544\) −1.29489 −0.0555181
\(545\) −18.1711 −0.778362
\(546\) −9.42907 −0.403527
\(547\) −28.7520 −1.22935 −0.614674 0.788781i \(-0.710713\pi\)
−0.614674 + 0.788781i \(0.710713\pi\)
\(548\) 1.03052 0.0440218
\(549\) −2.41298 −0.102984
\(550\) 3.12195 0.133120
\(551\) −26.9516 −1.14818
\(552\) 3.87156 0.164784
\(553\) 10.9906 0.467368
\(554\) 46.1548 1.96093
\(555\) 9.04128 0.383781
\(556\) 37.0972 1.57327
\(557\) −32.1673 −1.36297 −0.681486 0.731831i \(-0.738666\pi\)
−0.681486 + 0.731831i \(0.738666\pi\)
\(558\) −34.0497 −1.44144
\(559\) −24.6835 −1.04400
\(560\) −18.5436 −0.783612
\(561\) 0.331713 0.0140049
\(562\) −57.8444 −2.44002
\(563\) 37.9128 1.59783 0.798916 0.601442i \(-0.205407\pi\)
0.798916 + 0.601442i \(0.205407\pi\)
\(564\) −13.3860 −0.563654
\(565\) −51.1392 −2.15144
\(566\) −8.33157 −0.350202
\(567\) −11.6592 −0.489639
\(568\) 43.9761 1.84520
\(569\) 5.85738 0.245554 0.122777 0.992434i \(-0.460820\pi\)
0.122777 + 0.992434i \(0.460820\pi\)
\(570\) 8.07484 0.338218
\(571\) 37.3153 1.56160 0.780799 0.624782i \(-0.214812\pi\)
0.780799 + 0.624782i \(0.214812\pi\)
\(572\) −13.1476 −0.549727
\(573\) −0.564417 −0.0235789
\(574\) −8.75422 −0.365394
\(575\) 5.09518 0.212484
\(576\) 20.1893 0.841220
\(577\) −34.7013 −1.44463 −0.722317 0.691562i \(-0.756923\pi\)
−0.722317 + 0.691562i \(0.756923\pi\)
\(578\) 34.2549 1.42482
\(579\) 4.52195 0.187926
\(580\) −97.5222 −4.04939
\(581\) 11.6221 0.482164
\(582\) 7.54397 0.312708
\(583\) 0.969750 0.0401630
\(584\) 62.8758 2.60182
\(585\) −51.6641 −2.13605
\(586\) −59.1633 −2.44401
\(587\) 37.5599 1.55026 0.775131 0.631800i \(-0.217684\pi\)
0.775131 + 0.631800i \(0.217684\pi\)
\(588\) 7.35677 0.303388
\(589\) −15.0129 −0.618595
\(590\) 10.4160 0.428820
\(591\) −2.80549 −0.115403
\(592\) −38.0170 −1.56249
\(593\) −14.0043 −0.575087 −0.287544 0.957768i \(-0.592839\pi\)
−0.287544 + 0.957768i \(0.592839\pi\)
\(594\) 2.71729 0.111492
\(595\) −7.34539 −0.301132
\(596\) 9.11026 0.373171
\(597\) 3.09531 0.126683
\(598\) −31.9932 −1.30830
\(599\) 11.3086 0.462058 0.231029 0.972947i \(-0.425791\pi\)
0.231029 + 0.972947i \(0.425791\pi\)
\(600\) 5.06392 0.206734
\(601\) 9.94851 0.405808 0.202904 0.979199i \(-0.434962\pi\)
0.202904 + 0.979199i \(0.434962\pi\)
\(602\) −14.0120 −0.571085
\(603\) −35.2912 −1.43717
\(604\) 22.1043 0.899412
\(605\) −29.6250 −1.20443
\(606\) −3.17893 −0.129135
\(607\) −12.7104 −0.515901 −0.257950 0.966158i \(-0.583047\pi\)
−0.257950 + 0.966158i \(0.583047\pi\)
\(608\) −2.27956 −0.0924482
\(609\) −5.05792 −0.204957
\(610\) −5.73988 −0.232401
\(611\) 56.3036 2.27780
\(612\) −20.4584 −0.826981
\(613\) −13.1924 −0.532837 −0.266418 0.963857i \(-0.585840\pi\)
−0.266418 + 0.963857i \(0.585840\pi\)
\(614\) 47.7201 1.92583
\(615\) 2.47843 0.0999401
\(616\) −3.79883 −0.153059
\(617\) −29.9611 −1.20619 −0.603094 0.797670i \(-0.706065\pi\)
−0.603094 + 0.797670i \(0.706065\pi\)
\(618\) −13.1084 −0.527297
\(619\) −14.7338 −0.592201 −0.296100 0.955157i \(-0.595686\pi\)
−0.296100 + 0.955157i \(0.595686\pi\)
\(620\) −54.3229 −2.18166
\(621\) 4.43475 0.177960
\(622\) −66.5719 −2.66929
\(623\) −22.4619 −0.899917
\(624\) −11.2247 −0.449349
\(625\) −31.2433 −1.24973
\(626\) −14.2840 −0.570903
\(627\) 0.583954 0.0233209
\(628\) 43.5917 1.73950
\(629\) −15.0590 −0.600443
\(630\) −29.3279 −1.16845
\(631\) −2.01127 −0.0800674 −0.0400337 0.999198i \(-0.512747\pi\)
−0.0400337 + 0.999198i \(0.512747\pi\)
\(632\) 37.0628 1.47428
\(633\) 3.58367 0.142438
\(634\) 85.9473 3.41340
\(635\) −40.0536 −1.58948
\(636\) 3.09036 0.122541
\(637\) −30.9436 −1.22603
\(638\) −10.5155 −0.416311
\(639\) 24.5523 0.971276
\(640\) 52.0752 2.05845
\(641\) −12.8645 −0.508116 −0.254058 0.967189i \(-0.581765\pi\)
−0.254058 + 0.967189i \(0.581765\pi\)
\(642\) 0.419683 0.0165636
\(643\) 19.7336 0.778219 0.389109 0.921192i \(-0.372783\pi\)
0.389109 + 0.921192i \(0.372783\pi\)
\(644\) −12.1806 −0.479985
\(645\) 3.96697 0.156199
\(646\) −13.4493 −0.529157
\(647\) 12.0645 0.474303 0.237152 0.971473i \(-0.423786\pi\)
0.237152 + 0.971473i \(0.423786\pi\)
\(648\) −39.3173 −1.54453
\(649\) 0.753261 0.0295681
\(650\) −41.8465 −1.64135
\(651\) −2.81742 −0.110423
\(652\) −36.7376 −1.43876
\(653\) −18.5800 −0.727091 −0.363545 0.931576i \(-0.618434\pi\)
−0.363545 + 0.931576i \(0.618434\pi\)
\(654\) −6.24386 −0.244154
\(655\) 46.7396 1.82627
\(656\) −10.4214 −0.406886
\(657\) 35.1042 1.36955
\(658\) 31.9616 1.24599
\(659\) 32.5260 1.26703 0.633516 0.773730i \(-0.281611\pi\)
0.633516 + 0.773730i \(0.281611\pi\)
\(660\) 2.11299 0.0822480
\(661\) −16.2296 −0.631258 −0.315629 0.948883i \(-0.602216\pi\)
−0.315629 + 0.948883i \(0.602216\pi\)
\(662\) −59.3948 −2.30845
\(663\) −4.44627 −0.172679
\(664\) 39.1922 1.52095
\(665\) −12.9310 −0.501441
\(666\) −60.1261 −2.32984
\(667\) −17.1617 −0.664505
\(668\) −6.89141 −0.266637
\(669\) −9.68738 −0.374536
\(670\) −83.9489 −3.24323
\(671\) −0.415095 −0.0160246
\(672\) −0.427797 −0.0165026
\(673\) 4.23575 0.163276 0.0816381 0.996662i \(-0.473985\pi\)
0.0816381 + 0.996662i \(0.473985\pi\)
\(674\) 71.4379 2.75168
\(675\) 5.80057 0.223264
\(676\) 123.277 4.74142
\(677\) −6.04484 −0.232322 −0.116161 0.993230i \(-0.537059\pi\)
−0.116161 + 0.993230i \(0.537059\pi\)
\(678\) −17.5722 −0.674858
\(679\) −12.0808 −0.463620
\(680\) −24.7703 −0.949898
\(681\) 6.81942 0.261321
\(682\) −5.85743 −0.224293
\(683\) 46.9061 1.79481 0.897406 0.441205i \(-0.145449\pi\)
0.897406 + 0.441205i \(0.145449\pi\)
\(684\) −36.0153 −1.37708
\(685\) 0.696617 0.0266164
\(686\) −43.7028 −1.66858
\(687\) −8.40259 −0.320579
\(688\) −16.6804 −0.635934
\(689\) −12.9985 −0.495203
\(690\) 5.14174 0.195743
\(691\) 3.02295 0.114998 0.0574992 0.998346i \(-0.481687\pi\)
0.0574992 + 0.998346i \(0.481687\pi\)
\(692\) 36.2301 1.37726
\(693\) −2.12093 −0.0805673
\(694\) −46.9659 −1.78280
\(695\) 25.0771 0.951229
\(696\) −17.0565 −0.646523
\(697\) −4.12804 −0.156361
\(698\) 32.6325 1.23516
\(699\) 9.01357 0.340925
\(700\) −15.9321 −0.602175
\(701\) 17.4390 0.658661 0.329331 0.944215i \(-0.393177\pi\)
0.329331 + 0.944215i \(0.393177\pi\)
\(702\) −36.4225 −1.37468
\(703\) −26.5102 −0.999851
\(704\) 3.47308 0.130896
\(705\) −9.04874 −0.340795
\(706\) −0.597038 −0.0224698
\(707\) 5.09071 0.191456
\(708\) 2.40046 0.0902148
\(709\) −41.1828 −1.54665 −0.773325 0.634009i \(-0.781408\pi\)
−0.773325 + 0.634009i \(0.781408\pi\)
\(710\) 58.4038 2.19186
\(711\) 20.6926 0.776032
\(712\) −75.7466 −2.83873
\(713\) −9.55961 −0.358010
\(714\) −2.52399 −0.0944580
\(715\) −8.88754 −0.332375
\(716\) −36.1523 −1.35108
\(717\) −4.77625 −0.178372
\(718\) 55.9804 2.08917
\(719\) −4.28286 −0.159724 −0.0798618 0.996806i \(-0.525448\pi\)
−0.0798618 + 0.996806i \(0.525448\pi\)
\(720\) −34.9131 −1.30113
\(721\) 20.9916 0.781770
\(722\) 23.1471 0.861447
\(723\) 4.64868 0.172886
\(724\) 38.1388 1.41742
\(725\) −22.4472 −0.833668
\(726\) −10.1796 −0.377801
\(727\) −25.3185 −0.939010 −0.469505 0.882930i \(-0.655568\pi\)
−0.469505 + 0.882930i \(0.655568\pi\)
\(728\) 50.9193 1.88720
\(729\) −19.3634 −0.717161
\(730\) 83.5041 3.09062
\(731\) −6.60733 −0.244381
\(732\) −1.32281 −0.0488923
\(733\) −42.6912 −1.57684 −0.788418 0.615139i \(-0.789100\pi\)
−0.788418 + 0.615139i \(0.789100\pi\)
\(734\) 27.8004 1.02613
\(735\) 4.97306 0.183434
\(736\) −1.45153 −0.0535042
\(737\) −6.07100 −0.223628
\(738\) −16.4820 −0.606711
\(739\) 9.90573 0.364388 0.182194 0.983263i \(-0.441680\pi\)
0.182194 + 0.983263i \(0.441680\pi\)
\(740\) −95.9250 −3.52627
\(741\) −7.82729 −0.287543
\(742\) −7.37879 −0.270884
\(743\) 5.06666 0.185878 0.0929388 0.995672i \(-0.470374\pi\)
0.0929388 + 0.995672i \(0.470374\pi\)
\(744\) −9.50097 −0.348322
\(745\) 6.15839 0.225626
\(746\) −11.1463 −0.408094
\(747\) 21.8814 0.800600
\(748\) −3.51937 −0.128681
\(749\) −0.672076 −0.0245571
\(750\) −6.30041 −0.230058
\(751\) −38.1075 −1.39056 −0.695281 0.718738i \(-0.744720\pi\)
−0.695281 + 0.718738i \(0.744720\pi\)
\(752\) 38.0483 1.38748
\(753\) 9.82737 0.358129
\(754\) 140.949 5.13305
\(755\) 14.9422 0.543801
\(756\) −13.8670 −0.504337
\(757\) 5.80484 0.210980 0.105490 0.994420i \(-0.466359\pi\)
0.105490 + 0.994420i \(0.466359\pi\)
\(758\) 46.7432 1.69779
\(759\) 0.371839 0.0134969
\(760\) −43.6061 −1.58176
\(761\) 40.6473 1.47346 0.736731 0.676186i \(-0.236368\pi\)
0.736731 + 0.676186i \(0.236368\pi\)
\(762\) −13.7631 −0.498583
\(763\) 9.99885 0.361983
\(764\) 5.98828 0.216648
\(765\) −13.8295 −0.500008
\(766\) −8.57955 −0.309992
\(767\) −10.0967 −0.364570
\(768\) 12.4595 0.449593
\(769\) 3.68035 0.132717 0.0663584 0.997796i \(-0.478862\pi\)
0.0663584 + 0.997796i \(0.478862\pi\)
\(770\) −5.04515 −0.181814
\(771\) 7.94959 0.286297
\(772\) −47.9764 −1.72671
\(773\) −1.43706 −0.0516874 −0.0258437 0.999666i \(-0.508227\pi\)
−0.0258437 + 0.999666i \(0.508227\pi\)
\(774\) −26.3810 −0.948246
\(775\) −12.5038 −0.449149
\(776\) −40.7393 −1.46246
\(777\) −4.97508 −0.178480
\(778\) −40.8453 −1.46437
\(779\) −7.26708 −0.260370
\(780\) −28.3224 −1.01411
\(781\) 4.22363 0.151133
\(782\) −8.56400 −0.306248
\(783\) −19.5377 −0.698219
\(784\) −20.9108 −0.746815
\(785\) 29.4673 1.05173
\(786\) 16.0605 0.572858
\(787\) −37.7835 −1.34683 −0.673417 0.739262i \(-0.735174\pi\)
−0.673417 + 0.739262i \(0.735174\pi\)
\(788\) 29.7654 1.06035
\(789\) −0.0973903 −0.00346719
\(790\) 49.2224 1.75125
\(791\) 28.1400 1.00054
\(792\) −7.15225 −0.254144
\(793\) 5.56391 0.197580
\(794\) 80.8109 2.86787
\(795\) 2.08903 0.0740903
\(796\) −32.8402 −1.16399
\(797\) −29.5725 −1.04751 −0.523755 0.851869i \(-0.675469\pi\)
−0.523755 + 0.851869i \(0.675469\pi\)
\(798\) −4.44328 −0.157290
\(799\) 15.0715 0.533190
\(800\) −1.89858 −0.0671248
\(801\) −42.2902 −1.49425
\(802\) −26.6546 −0.941207
\(803\) 6.03883 0.213106
\(804\) −19.3468 −0.682308
\(805\) −8.23392 −0.290208
\(806\) 78.5127 2.76549
\(807\) −3.72714 −0.131202
\(808\) 17.1670 0.603934
\(809\) −39.2331 −1.37936 −0.689680 0.724114i \(-0.742249\pi\)
−0.689680 + 0.724114i \(0.742249\pi\)
\(810\) −52.2166 −1.83470
\(811\) −34.8404 −1.22341 −0.611705 0.791086i \(-0.709516\pi\)
−0.611705 + 0.791086i \(0.709516\pi\)
\(812\) 53.6628 1.88320
\(813\) −3.26718 −0.114585
\(814\) −10.3432 −0.362530
\(815\) −24.8340 −0.869898
\(816\) −3.00466 −0.105184
\(817\) −11.6317 −0.406940
\(818\) −62.0661 −2.17009
\(819\) 28.4288 0.993382
\(820\) −26.2953 −0.918273
\(821\) −28.5486 −0.996352 −0.498176 0.867076i \(-0.665997\pi\)
−0.498176 + 0.867076i \(0.665997\pi\)
\(822\) 0.239369 0.00834894
\(823\) 45.5139 1.58652 0.793258 0.608886i \(-0.208383\pi\)
0.793258 + 0.608886i \(0.208383\pi\)
\(824\) 70.7886 2.46604
\(825\) 0.486358 0.0169328
\(826\) −5.73153 −0.199425
\(827\) 29.7716 1.03526 0.517630 0.855605i \(-0.326814\pi\)
0.517630 + 0.855605i \(0.326814\pi\)
\(828\) −22.9331 −0.796981
\(829\) 6.09594 0.211721 0.105860 0.994381i \(-0.466240\pi\)
0.105860 + 0.994381i \(0.466240\pi\)
\(830\) 52.0504 1.80670
\(831\) 7.19030 0.249429
\(832\) −46.5529 −1.61393
\(833\) −8.28305 −0.286991
\(834\) 8.61689 0.298379
\(835\) −4.65848 −0.161213
\(836\) −6.19556 −0.214278
\(837\) −10.8831 −0.376174
\(838\) −47.8861 −1.65420
\(839\) −31.1384 −1.07502 −0.537509 0.843258i \(-0.680634\pi\)
−0.537509 + 0.843258i \(0.680634\pi\)
\(840\) −8.18342 −0.282355
\(841\) 46.6074 1.60715
\(842\) 67.6936 2.33287
\(843\) −9.01138 −0.310368
\(844\) −38.0215 −1.30875
\(845\) 83.3332 2.86675
\(846\) 60.1757 2.06888
\(847\) 16.3015 0.560127
\(848\) −8.78400 −0.301644
\(849\) −1.29795 −0.0445454
\(850\) −11.2016 −0.384210
\(851\) −16.8806 −0.578661
\(852\) 13.4597 0.461121
\(853\) −53.5520 −1.83359 −0.916793 0.399362i \(-0.869232\pi\)
−0.916793 + 0.399362i \(0.869232\pi\)
\(854\) 3.15844 0.108080
\(855\) −24.3458 −0.832608
\(856\) −2.26639 −0.0774638
\(857\) 0.768297 0.0262445 0.0131223 0.999914i \(-0.495823\pi\)
0.0131223 + 0.999914i \(0.495823\pi\)
\(858\) −3.05390 −0.104258
\(859\) −48.3896 −1.65103 −0.825516 0.564379i \(-0.809116\pi\)
−0.825516 + 0.564379i \(0.809116\pi\)
\(860\) −42.0882 −1.43520
\(861\) −1.36379 −0.0464778
\(862\) −45.3197 −1.54360
\(863\) −36.0238 −1.22627 −0.613133 0.789980i \(-0.710091\pi\)
−0.613133 + 0.789980i \(0.710091\pi\)
\(864\) −1.65249 −0.0562187
\(865\) 24.4910 0.832718
\(866\) 32.0213 1.08813
\(867\) 5.33646 0.181236
\(868\) 29.8918 1.01460
\(869\) 3.55965 0.120753
\(870\) −22.6523 −0.767986
\(871\) 81.3754 2.75730
\(872\) 33.7184 1.14185
\(873\) −22.7452 −0.769808
\(874\) −15.0762 −0.509961
\(875\) 10.0894 0.341084
\(876\) 19.2443 0.650203
\(877\) 50.3964 1.70177 0.850883 0.525355i \(-0.176067\pi\)
0.850883 + 0.525355i \(0.176067\pi\)
\(878\) 27.8075 0.938457
\(879\) −9.21685 −0.310876
\(880\) −6.00594 −0.202460
\(881\) −0.288305 −0.00971323 −0.00485661 0.999988i \(-0.501546\pi\)
−0.00485661 + 0.999988i \(0.501546\pi\)
\(882\) −33.0717 −1.11358
\(883\) −11.8874 −0.400042 −0.200021 0.979792i \(-0.564101\pi\)
−0.200021 + 0.979792i \(0.564101\pi\)
\(884\) 47.1734 1.58661
\(885\) 1.62267 0.0545455
\(886\) 6.92546 0.232665
\(887\) −49.8737 −1.67460 −0.837298 0.546747i \(-0.815866\pi\)
−0.837298 + 0.546747i \(0.815866\pi\)
\(888\) −16.7771 −0.563003
\(889\) 22.0400 0.739198
\(890\) −100.598 −3.37204
\(891\) −3.77618 −0.126507
\(892\) 102.780 3.44132
\(893\) 26.5321 0.887862
\(894\) 2.11612 0.0707736
\(895\) −24.4384 −0.816886
\(896\) −28.6550 −0.957298
\(897\) −4.98411 −0.166415
\(898\) −85.9653 −2.86870
\(899\) 42.1156 1.40463
\(900\) −29.9961 −0.999869
\(901\) −3.47946 −0.115918
\(902\) −2.83533 −0.0944061
\(903\) −2.18287 −0.0726415
\(904\) 94.8944 3.15614
\(905\) 25.7812 0.856997
\(906\) 5.13436 0.170578
\(907\) −46.5713 −1.54638 −0.773188 0.634177i \(-0.781339\pi\)
−0.773188 + 0.634177i \(0.781339\pi\)
\(908\) −72.3517 −2.40108
\(909\) 9.58453 0.317899
\(910\) 67.6249 2.24174
\(911\) −29.3891 −0.973704 −0.486852 0.873484i \(-0.661855\pi\)
−0.486852 + 0.873484i \(0.661855\pi\)
\(912\) −5.28946 −0.175151
\(913\) 3.76417 0.124576
\(914\) 35.6575 1.17945
\(915\) −0.894196 −0.0295612
\(916\) 89.1487 2.94555
\(917\) −25.7190 −0.849318
\(918\) −9.74963 −0.321786
\(919\) 37.4374 1.23495 0.617473 0.786592i \(-0.288157\pi\)
0.617473 + 0.786592i \(0.288157\pi\)
\(920\) −27.7667 −0.915440
\(921\) 7.43415 0.244964
\(922\) −81.6156 −2.68787
\(923\) −56.6134 −1.86345
\(924\) −1.16270 −0.0382500
\(925\) −22.0796 −0.725971
\(926\) −27.7149 −0.910769
\(927\) 39.5220 1.29807
\(928\) 6.39484 0.209921
\(929\) 23.2733 0.763572 0.381786 0.924251i \(-0.375309\pi\)
0.381786 + 0.924251i \(0.375309\pi\)
\(930\) −12.6180 −0.413762
\(931\) −14.5816 −0.477894
\(932\) −95.6310 −3.13250
\(933\) −10.3710 −0.339531
\(934\) −57.8771 −1.89380
\(935\) −2.37903 −0.0778027
\(936\) 95.8684 3.13356
\(937\) −13.5879 −0.443896 −0.221948 0.975059i \(-0.571242\pi\)
−0.221948 + 0.975059i \(0.571242\pi\)
\(938\) 46.1939 1.50829
\(939\) −2.22525 −0.0726184
\(940\) 96.0041 3.13131
\(941\) −2.37562 −0.0774431 −0.0387216 0.999250i \(-0.512329\pi\)
−0.0387216 + 0.999250i \(0.512329\pi\)
\(942\) 10.1254 0.329905
\(943\) −4.62739 −0.150689
\(944\) −6.82304 −0.222071
\(945\) −9.37385 −0.304931
\(946\) −4.53821 −0.147550
\(947\) 58.0115 1.88512 0.942561 0.334034i \(-0.108410\pi\)
0.942561 + 0.334034i \(0.108410\pi\)
\(948\) 11.3437 0.368428
\(949\) −80.9442 −2.62756
\(950\) −19.7194 −0.639782
\(951\) 13.3894 0.434182
\(952\) 13.6302 0.441757
\(953\) −19.2010 −0.621983 −0.310991 0.950413i \(-0.600661\pi\)
−0.310991 + 0.950413i \(0.600661\pi\)
\(954\) −13.8924 −0.449784
\(955\) 4.04798 0.130990
\(956\) 50.6744 1.63893
\(957\) −1.63817 −0.0529544
\(958\) 58.6251 1.89409
\(959\) −0.383322 −0.0123781
\(960\) 7.48168 0.241470
\(961\) −7.54031 −0.243236
\(962\) 138.640 4.46994
\(963\) −1.26535 −0.0407754
\(964\) −49.3210 −1.58852
\(965\) −32.4313 −1.04400
\(966\) −2.82931 −0.0910314
\(967\) 55.0032 1.76878 0.884392 0.466745i \(-0.154573\pi\)
0.884392 + 0.466745i \(0.154573\pi\)
\(968\) 54.9725 1.76688
\(969\) −2.09522 −0.0673083
\(970\) −54.1051 −1.73721
\(971\) −15.0193 −0.481991 −0.240995 0.970526i \(-0.577474\pi\)
−0.240995 + 0.970526i \(0.577474\pi\)
\(972\) −39.4908 −1.26667
\(973\) −13.7990 −0.442375
\(974\) −26.3714 −0.844994
\(975\) −6.51912 −0.208779
\(976\) 3.75993 0.120352
\(977\) −38.4411 −1.22984 −0.614920 0.788590i \(-0.710812\pi\)
−0.614920 + 0.788590i \(0.710812\pi\)
\(978\) −8.53337 −0.272867
\(979\) −7.27499 −0.232510
\(980\) −52.7625 −1.68544
\(981\) 18.8253 0.601047
\(982\) 80.5832 2.57151
\(983\) 20.0840 0.640581 0.320291 0.947319i \(-0.396219\pi\)
0.320291 + 0.947319i \(0.396219\pi\)
\(984\) −4.59901 −0.146611
\(985\) 20.1209 0.641105
\(986\) 37.7294 1.20155
\(987\) 4.97918 0.158489
\(988\) 83.0449 2.64201
\(989\) −7.40658 −0.235516
\(990\) −9.49875 −0.301890
\(991\) 13.8875 0.441151 0.220575 0.975370i \(-0.429207\pi\)
0.220575 + 0.975370i \(0.429207\pi\)
\(992\) 3.56212 0.113097
\(993\) −9.25291 −0.293632
\(994\) −32.1374 −1.01934
\(995\) −22.1994 −0.703770
\(996\) 11.9955 0.380091
\(997\) 12.3506 0.391147 0.195573 0.980689i \(-0.437343\pi\)
0.195573 + 0.980689i \(0.437343\pi\)
\(998\) 97.3252 3.08078
\(999\) −19.2177 −0.608020
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 \(a_p\))