Properties

Label 4033.2.a.d.1.3
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 1.3
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.76342 q^{2}\) \(-1.75117 q^{3}\) \(+5.63647 q^{4}\) \(-3.34867 q^{5}\) \(+4.83922 q^{6}\) \(-0.176382 q^{7}\) \(-10.0491 q^{8}\) \(+0.0666133 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.76342 q^{2}\) \(-1.75117 q^{3}\) \(+5.63647 q^{4}\) \(-3.34867 q^{5}\) \(+4.83922 q^{6}\) \(-0.176382 q^{7}\) \(-10.0491 q^{8}\) \(+0.0666133 q^{9}\) \(+9.25378 q^{10}\) \(-3.59328 q^{11}\) \(-9.87044 q^{12}\) \(-2.30488 q^{13}\) \(+0.487418 q^{14}\) \(+5.86411 q^{15}\) \(+16.4968 q^{16}\) \(-6.59292 q^{17}\) \(-0.184080 q^{18}\) \(-1.28173 q^{19}\) \(-18.8747 q^{20}\) \(+0.308876 q^{21}\) \(+9.92974 q^{22}\) \(-0.795686 q^{23}\) \(+17.5977 q^{24}\) \(+6.21361 q^{25}\) \(+6.36934 q^{26}\) \(+5.13687 q^{27}\) \(-0.994174 q^{28}\) \(-1.57744 q^{29}\) \(-16.2050 q^{30}\) \(+5.46108 q^{31}\) \(-25.4894 q^{32}\) \(+6.29247 q^{33}\) \(+18.2190 q^{34}\) \(+0.590647 q^{35}\) \(+0.375463 q^{36}\) \(-1.00000 q^{37}\) \(+3.54196 q^{38}\) \(+4.03625 q^{39}\) \(+33.6510 q^{40}\) \(+2.22182 q^{41}\) \(-0.853554 q^{42}\) \(+4.85478 q^{43}\) \(-20.2534 q^{44}\) \(-0.223066 q^{45}\) \(+2.19881 q^{46}\) \(+2.23578 q^{47}\) \(-28.8888 q^{48}\) \(-6.96889 q^{49}\) \(-17.1708 q^{50}\) \(+11.5454 q^{51}\) \(-12.9914 q^{52}\) \(+1.00587 q^{53}\) \(-14.1953 q^{54}\) \(+12.0327 q^{55}\) \(+1.77248 q^{56}\) \(+2.24454 q^{57}\) \(+4.35914 q^{58}\) \(+5.13677 q^{59}\) \(+33.0529 q^{60}\) \(-0.373404 q^{61}\) \(-15.0912 q^{62}\) \(-0.0117494 q^{63}\) \(+37.4443 q^{64}\) \(+7.71829 q^{65}\) \(-17.3887 q^{66}\) \(+5.08426 q^{67}\) \(-37.1608 q^{68}\) \(+1.39339 q^{69}\) \(-1.63220 q^{70}\) \(+12.6439 q^{71}\) \(-0.669401 q^{72}\) \(-10.2930 q^{73}\) \(+2.76342 q^{74}\) \(-10.8811 q^{75}\) \(-7.22445 q^{76}\) \(+0.633792 q^{77}\) \(-11.1538 q^{78}\) \(-0.467857 q^{79}\) \(-55.2425 q^{80}\) \(-9.19540 q^{81}\) \(-6.13981 q^{82}\) \(-2.93875 q^{83}\) \(+1.74097 q^{84}\) \(+22.0775 q^{85}\) \(-13.4158 q^{86}\) \(+2.76238 q^{87}\) \(+36.1091 q^{88}\) \(+6.61557 q^{89}\) \(+0.616424 q^{90}\) \(+0.406540 q^{91}\) \(-4.48486 q^{92}\) \(-9.56331 q^{93}\) \(-6.17838 q^{94}\) \(+4.29211 q^{95}\) \(+44.6365 q^{96}\) \(-3.26485 q^{97}\) \(+19.2579 q^{98}\) \(-0.239360 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut -\mathstrut 13q^{10} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 40q^{12} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 42q^{14} \) \(\mathstrut -\mathstrut 49q^{15} \) \(\mathstrut +\mathstrut 83q^{16} \) \(\mathstrut -\mathstrut 62q^{17} \) \(\mathstrut -\mathstrut 33q^{18} \) \(\mathstrut -\mathstrut 25q^{19} \) \(\mathstrut -\mathstrut 39q^{20} \) \(\mathstrut -\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 31q^{22} \) \(\mathstrut -\mathstrut 94q^{23} \) \(\mathstrut -\mathstrut 39q^{24} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut -\mathstrut 35q^{26} \) \(\mathstrut -\mathstrut 47q^{27} \) \(\mathstrut -\mathstrut 13q^{28} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 15q^{30} \) \(\mathstrut -\mathstrut 37q^{31} \) \(\mathstrut -\mathstrut 105q^{32} \) \(\mathstrut -\mathstrut 60q^{33} \) \(\mathstrut +\mathstrut 9q^{34} \) \(\mathstrut -\mathstrut 60q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 79q^{37} \) \(\mathstrut -\mathstrut 80q^{38} \) \(\mathstrut -\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 64q^{40} \) \(\mathstrut -\mathstrut 37q^{41} \) \(\mathstrut -\mathstrut 30q^{42} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 8q^{45} \) \(\mathstrut +\mathstrut 61q^{46} \) \(\mathstrut -\mathstrut 148q^{47} \) \(\mathstrut -\mathstrut 39q^{48} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut 90q^{50} \) \(\mathstrut -\mathstrut 45q^{51} \) \(\mathstrut -\mathstrut 27q^{52} \) \(\mathstrut -\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 41q^{54} \) \(\mathstrut -\mathstrut 105q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut -\mathstrut 96q^{59} \) \(\mathstrut -\mathstrut 74q^{60} \) \(\mathstrut -\mathstrut 21q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut 60q^{63} \) \(\mathstrut +\mathstrut 132q^{64} \) \(\mathstrut -\mathstrut 15q^{65} \) \(\mathstrut +\mathstrut 71q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 166q^{68} \) \(\mathstrut -\mathstrut 72q^{69} \) \(\mathstrut -\mathstrut 9q^{70} \) \(\mathstrut -\mathstrut 55q^{71} \) \(\mathstrut -\mathstrut 126q^{72} \) \(\mathstrut -\mathstrut 27q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 39q^{75} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 104q^{77} \) \(\mathstrut -\mathstrut 47q^{78} \) \(\mathstrut -\mathstrut 49q^{79} \) \(\mathstrut -\mathstrut 82q^{80} \) \(\mathstrut +\mathstrut 55q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 29q^{84} \) \(\mathstrut +\mathstrut 3q^{85} \) \(\mathstrut -\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 113q^{87} \) \(\mathstrut +\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 68q^{89} \) \(\mathstrut -\mathstrut 39q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 179q^{92} \) \(\mathstrut -\mathstrut 53q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 86q^{95} \) \(\mathstrut +\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 116q^{98} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.76342 −1.95403 −0.977015 0.213171i \(-0.931621\pi\)
−0.977015 + 0.213171i \(0.931621\pi\)
\(3\) −1.75117 −1.01104 −0.505521 0.862815i \(-0.668700\pi\)
−0.505521 + 0.862815i \(0.668700\pi\)
\(4\) 5.63647 2.81823
\(5\) −3.34867 −1.49757 −0.748786 0.662812i \(-0.769363\pi\)
−0.748786 + 0.662812i \(0.769363\pi\)
\(6\) 4.83922 1.97560
\(7\) −0.176382 −0.0666663 −0.0333331 0.999444i \(-0.510612\pi\)
−0.0333331 + 0.999444i \(0.510612\pi\)
\(8\) −10.0491 −3.55288
\(9\) 0.0666133 0.0222044
\(10\) 9.25378 2.92630
\(11\) −3.59328 −1.08342 −0.541708 0.840567i \(-0.682222\pi\)
−0.541708 + 0.840567i \(0.682222\pi\)
\(12\) −9.87044 −2.84935
\(13\) −2.30488 −0.639258 −0.319629 0.947543i \(-0.603558\pi\)
−0.319629 + 0.947543i \(0.603558\pi\)
\(14\) 0.487418 0.130268
\(15\) 5.86411 1.51411
\(16\) 16.4968 4.12421
\(17\) −6.59292 −1.59902 −0.799509 0.600654i \(-0.794907\pi\)
−0.799509 + 0.600654i \(0.794907\pi\)
\(18\) −0.184080 −0.0433881
\(19\) −1.28173 −0.294050 −0.147025 0.989133i \(-0.546970\pi\)
−0.147025 + 0.989133i \(0.546970\pi\)
\(20\) −18.8747 −4.22051
\(21\) 0.308876 0.0674024
\(22\) 9.92974 2.11703
\(23\) −0.795686 −0.165912 −0.0829560 0.996553i \(-0.526436\pi\)
−0.0829560 + 0.996553i \(0.526436\pi\)
\(24\) 17.5977 3.59211
\(25\) 6.21361 1.24272
\(26\) 6.36934 1.24913
\(27\) 5.13687 0.988592
\(28\) −0.994174 −0.187881
\(29\) −1.57744 −0.292924 −0.146462 0.989216i \(-0.546789\pi\)
−0.146462 + 0.989216i \(0.546789\pi\)
\(30\) −16.2050 −2.95861
\(31\) 5.46108 0.980840 0.490420 0.871486i \(-0.336843\pi\)
0.490420 + 0.871486i \(0.336843\pi\)
\(32\) −25.4894 −4.50594
\(33\) 6.29247 1.09538
\(34\) 18.2190 3.12453
\(35\) 0.590647 0.0998376
\(36\) 0.375463 0.0625772
\(37\) −1.00000 −0.164399
\(38\) 3.54196 0.574582
\(39\) 4.03625 0.646317
\(40\) 33.6510 5.32070
\(41\) 2.22182 0.346990 0.173495 0.984835i \(-0.444494\pi\)
0.173495 + 0.984835i \(0.444494\pi\)
\(42\) −0.853554 −0.131706
\(43\) 4.85478 0.740348 0.370174 0.928963i \(-0.379298\pi\)
0.370174 + 0.928963i \(0.379298\pi\)
\(44\) −20.2534 −3.05332
\(45\) −0.223066 −0.0332527
\(46\) 2.19881 0.324197
\(47\) 2.23578 0.326121 0.163061 0.986616i \(-0.447863\pi\)
0.163061 + 0.986616i \(0.447863\pi\)
\(48\) −28.8888 −4.16974
\(49\) −6.96889 −0.995556
\(50\) −17.1708 −2.42832
\(51\) 11.5454 1.61667
\(52\) −12.9914 −1.80158
\(53\) 1.00587 0.138167 0.0690837 0.997611i \(-0.477992\pi\)
0.0690837 + 0.997611i \(0.477992\pi\)
\(54\) −14.1953 −1.93174
\(55\) 12.0327 1.62249
\(56\) 1.77248 0.236857
\(57\) 2.24454 0.297297
\(58\) 4.35914 0.572382
\(59\) 5.13677 0.668750 0.334375 0.942440i \(-0.391475\pi\)
0.334375 + 0.942440i \(0.391475\pi\)
\(60\) 33.0529 4.26711
\(61\) −0.373404 −0.0478095 −0.0239047 0.999714i \(-0.507610\pi\)
−0.0239047 + 0.999714i \(0.507610\pi\)
\(62\) −15.0912 −1.91659
\(63\) −0.0117494 −0.00148029
\(64\) 37.4443 4.68053
\(65\) 7.71829 0.957336
\(66\) −17.3887 −2.14040
\(67\) 5.08426 0.621141 0.310570 0.950550i \(-0.399480\pi\)
0.310570 + 0.950550i \(0.399480\pi\)
\(68\) −37.1608 −4.50641
\(69\) 1.39339 0.167744
\(70\) −1.63220 −0.195086
\(71\) 12.6439 1.50055 0.750275 0.661126i \(-0.229921\pi\)
0.750275 + 0.661126i \(0.229921\pi\)
\(72\) −0.669401 −0.0788897
\(73\) −10.2930 −1.20470 −0.602352 0.798231i \(-0.705770\pi\)
−0.602352 + 0.798231i \(0.705770\pi\)
\(74\) 2.76342 0.321241
\(75\) −10.8811 −1.25644
\(76\) −7.22445 −0.828701
\(77\) 0.633792 0.0722273
\(78\) −11.1538 −1.26292
\(79\) −0.467857 −0.0526380 −0.0263190 0.999654i \(-0.508379\pi\)
−0.0263190 + 0.999654i \(0.508379\pi\)
\(80\) −55.2425 −6.17630
\(81\) −9.19540 −1.02171
\(82\) −6.13981 −0.678029
\(83\) −2.93875 −0.322570 −0.161285 0.986908i \(-0.551564\pi\)
−0.161285 + 0.986908i \(0.551564\pi\)
\(84\) 1.74097 0.189956
\(85\) 22.0775 2.39464
\(86\) −13.4158 −1.44666
\(87\) 2.76238 0.296158
\(88\) 36.1091 3.84925
\(89\) 6.61557 0.701249 0.350624 0.936516i \(-0.385969\pi\)
0.350624 + 0.936516i \(0.385969\pi\)
\(90\) 0.616424 0.0649768
\(91\) 0.406540 0.0426170
\(92\) −4.48486 −0.467579
\(93\) −9.56331 −0.991669
\(94\) −6.17838 −0.637251
\(95\) 4.29211 0.440361
\(96\) 44.6365 4.55569
\(97\) −3.26485 −0.331495 −0.165748 0.986168i \(-0.553004\pi\)
−0.165748 + 0.986168i \(0.553004\pi\)
\(98\) 19.2579 1.94535
\(99\) −0.239360 −0.0240566
\(100\) 35.0228 3.50228
\(101\) 3.26979 0.325356 0.162678 0.986679i \(-0.447987\pi\)
0.162678 + 0.986679i \(0.447987\pi\)
\(102\) −31.9046 −3.15903
\(103\) −19.3110 −1.90277 −0.951383 0.308009i \(-0.900337\pi\)
−0.951383 + 0.308009i \(0.900337\pi\)
\(104\) 23.1619 2.27121
\(105\) −1.03433 −0.100940
\(106\) −2.77965 −0.269983
\(107\) 18.3716 1.77605 0.888027 0.459791i \(-0.152076\pi\)
0.888027 + 0.459791i \(0.152076\pi\)
\(108\) 28.9538 2.78608
\(109\) −1.00000 −0.0957826
\(110\) −33.2514 −3.17040
\(111\) 1.75117 0.166214
\(112\) −2.90975 −0.274945
\(113\) −0.400266 −0.0376539 −0.0188269 0.999823i \(-0.505993\pi\)
−0.0188269 + 0.999823i \(0.505993\pi\)
\(114\) −6.20260 −0.580927
\(115\) 2.66449 0.248465
\(116\) −8.89121 −0.825528
\(117\) −0.153535 −0.0141944
\(118\) −14.1950 −1.30676
\(119\) 1.16288 0.106601
\(120\) −58.9289 −5.37944
\(121\) 1.91168 0.173789
\(122\) 1.03187 0.0934212
\(123\) −3.89079 −0.350821
\(124\) 30.7812 2.76423
\(125\) −4.06399 −0.363494
\(126\) 0.0324685 0.00289252
\(127\) −15.5224 −1.37739 −0.688694 0.725052i \(-0.741816\pi\)
−0.688694 + 0.725052i \(0.741816\pi\)
\(128\) −52.4952 −4.63997
\(129\) −8.50157 −0.748522
\(130\) −21.3288 −1.87066
\(131\) 6.37464 0.556955 0.278477 0.960443i \(-0.410170\pi\)
0.278477 + 0.960443i \(0.410170\pi\)
\(132\) 35.4673 3.08703
\(133\) 0.226075 0.0196032
\(134\) −14.0499 −1.21373
\(135\) −17.2017 −1.48049
\(136\) 66.2527 5.68112
\(137\) −11.4555 −0.978711 −0.489355 0.872084i \(-0.662768\pi\)
−0.489355 + 0.872084i \(0.662768\pi\)
\(138\) −3.85050 −0.327777
\(139\) 22.6745 1.92323 0.961613 0.274409i \(-0.0884821\pi\)
0.961613 + 0.274409i \(0.0884821\pi\)
\(140\) 3.32916 0.281366
\(141\) −3.91523 −0.329722
\(142\) −34.9402 −2.93212
\(143\) 8.28208 0.692583
\(144\) 1.09891 0.0915756
\(145\) 5.28235 0.438675
\(146\) 28.4438 2.35403
\(147\) 12.2037 1.00655
\(148\) −5.63647 −0.463315
\(149\) 19.5772 1.60383 0.801915 0.597438i \(-0.203815\pi\)
0.801915 + 0.597438i \(0.203815\pi\)
\(150\) 30.0691 2.45513
\(151\) 10.3864 0.845236 0.422618 0.906308i \(-0.361111\pi\)
0.422618 + 0.906308i \(0.361111\pi\)
\(152\) 12.8802 1.04472
\(153\) −0.439176 −0.0355053
\(154\) −1.75143 −0.141134
\(155\) −18.2874 −1.46888
\(156\) 22.7502 1.82147
\(157\) 7.22796 0.576854 0.288427 0.957502i \(-0.406868\pi\)
0.288427 + 0.957502i \(0.406868\pi\)
\(158\) 1.29288 0.102856
\(159\) −1.76146 −0.139693
\(160\) 85.3558 6.74797
\(161\) 0.140345 0.0110607
\(162\) 25.4107 1.99645
\(163\) −12.5252 −0.981050 −0.490525 0.871427i \(-0.663195\pi\)
−0.490525 + 0.871427i \(0.663195\pi\)
\(164\) 12.5232 0.977898
\(165\) −21.0714 −1.64041
\(166\) 8.12099 0.630311
\(167\) 6.57648 0.508903 0.254452 0.967086i \(-0.418105\pi\)
0.254452 + 0.967086i \(0.418105\pi\)
\(168\) −3.10392 −0.239473
\(169\) −7.68753 −0.591349
\(170\) −61.0094 −4.67921
\(171\) −0.0853805 −0.00652921
\(172\) 27.3638 2.08647
\(173\) 12.2550 0.931731 0.465865 0.884856i \(-0.345743\pi\)
0.465865 + 0.884856i \(0.345743\pi\)
\(174\) −7.63361 −0.578702
\(175\) −1.09597 −0.0828477
\(176\) −59.2778 −4.46823
\(177\) −8.99537 −0.676134
\(178\) −18.2816 −1.37026
\(179\) −21.1699 −1.58231 −0.791157 0.611613i \(-0.790521\pi\)
−0.791157 + 0.611613i \(0.790521\pi\)
\(180\) −1.25730 −0.0937139
\(181\) 14.0860 1.04701 0.523504 0.852023i \(-0.324625\pi\)
0.523504 + 0.852023i \(0.324625\pi\)
\(182\) −1.12344 −0.0832749
\(183\) 0.653896 0.0483374
\(184\) 7.99591 0.589466
\(185\) 3.34867 0.246199
\(186\) 26.4274 1.93775
\(187\) 23.6902 1.73240
\(188\) 12.6019 0.919086
\(189\) −0.906054 −0.0659057
\(190\) −11.8609 −0.860479
\(191\) 18.2532 1.32075 0.660376 0.750935i \(-0.270397\pi\)
0.660376 + 0.750935i \(0.270397\pi\)
\(192\) −65.5715 −4.73221
\(193\) 16.3074 1.17383 0.586917 0.809647i \(-0.300342\pi\)
0.586917 + 0.809647i \(0.300342\pi\)
\(194\) 9.02214 0.647752
\(195\) −13.5161 −0.967906
\(196\) −39.2799 −2.80571
\(197\) −8.53385 −0.608011 −0.304006 0.952670i \(-0.598324\pi\)
−0.304006 + 0.952670i \(0.598324\pi\)
\(198\) 0.661452 0.0470073
\(199\) −14.2721 −1.01172 −0.505861 0.862615i \(-0.668825\pi\)
−0.505861 + 0.862615i \(0.668825\pi\)
\(200\) −62.4410 −4.41525
\(201\) −8.90342 −0.627999
\(202\) −9.03579 −0.635756
\(203\) 0.278233 0.0195282
\(204\) 65.0750 4.55616
\(205\) −7.44015 −0.519642
\(206\) 53.3643 3.71806
\(207\) −0.0530032 −0.00368398
\(208\) −38.0232 −2.63643
\(209\) 4.60563 0.318578
\(210\) 2.85827 0.197240
\(211\) −16.9061 −1.16386 −0.581932 0.813237i \(-0.697703\pi\)
−0.581932 + 0.813237i \(0.697703\pi\)
\(212\) 5.66958 0.389388
\(213\) −22.1416 −1.51712
\(214\) −50.7685 −3.47046
\(215\) −16.2571 −1.10872
\(216\) −51.6208 −3.51235
\(217\) −0.963239 −0.0653889
\(218\) 2.76342 0.187162
\(219\) 18.0248 1.21801
\(220\) 67.8221 4.57256
\(221\) 15.1959 1.02219
\(222\) −4.83922 −0.324787
\(223\) 17.9583 1.20258 0.601290 0.799031i \(-0.294654\pi\)
0.601290 + 0.799031i \(0.294654\pi\)
\(224\) 4.49589 0.300394
\(225\) 0.413909 0.0275939
\(226\) 1.10610 0.0735768
\(227\) 13.9871 0.928359 0.464179 0.885741i \(-0.346349\pi\)
0.464179 + 0.885741i \(0.346349\pi\)
\(228\) 12.6513 0.837851
\(229\) −2.38396 −0.157537 −0.0787684 0.996893i \(-0.525099\pi\)
−0.0787684 + 0.996893i \(0.525099\pi\)
\(230\) −7.36310 −0.485509
\(231\) −1.10988 −0.0730248
\(232\) 15.8518 1.04072
\(233\) 8.60107 0.563475 0.281738 0.959492i \(-0.409089\pi\)
0.281738 + 0.959492i \(0.409089\pi\)
\(234\) 0.424282 0.0277362
\(235\) −7.48688 −0.488390
\(236\) 28.9532 1.88469
\(237\) 0.819299 0.0532192
\(238\) −3.21351 −0.208301
\(239\) 27.0519 1.74984 0.874921 0.484265i \(-0.160913\pi\)
0.874921 + 0.484265i \(0.160913\pi\)
\(240\) 96.7392 6.24449
\(241\) 10.9254 0.703770 0.351885 0.936043i \(-0.385541\pi\)
0.351885 + 0.936043i \(0.385541\pi\)
\(242\) −5.28278 −0.339590
\(243\) 0.692138 0.0444007
\(244\) −2.10468 −0.134738
\(245\) 23.3365 1.49092
\(246\) 10.7519 0.685515
\(247\) 2.95424 0.187974
\(248\) −54.8788 −3.48481
\(249\) 5.14626 0.326131
\(250\) 11.2305 0.710278
\(251\) −2.07463 −0.130949 −0.0654747 0.997854i \(-0.520856\pi\)
−0.0654747 + 0.997854i \(0.520856\pi\)
\(252\) −0.0662251 −0.00417179
\(253\) 2.85913 0.179752
\(254\) 42.8948 2.69146
\(255\) −38.6616 −2.42108
\(256\) 70.1776 4.38610
\(257\) 10.1507 0.633183 0.316591 0.948562i \(-0.397462\pi\)
0.316591 + 0.948562i \(0.397462\pi\)
\(258\) 23.4934 1.46263
\(259\) 0.176382 0.0109599
\(260\) 43.5039 2.69799
\(261\) −0.105079 −0.00650421
\(262\) −17.6158 −1.08831
\(263\) 7.22333 0.445410 0.222705 0.974886i \(-0.428511\pi\)
0.222705 + 0.974886i \(0.428511\pi\)
\(264\) −63.2334 −3.89175
\(265\) −3.36834 −0.206916
\(266\) −0.624740 −0.0383053
\(267\) −11.5850 −0.708991
\(268\) 28.6572 1.75052
\(269\) −21.5920 −1.31649 −0.658243 0.752806i \(-0.728700\pi\)
−0.658243 + 0.752806i \(0.728700\pi\)
\(270\) 47.5355 2.89292
\(271\) 9.96214 0.605157 0.302579 0.953124i \(-0.402153\pi\)
0.302579 + 0.953124i \(0.402153\pi\)
\(272\) −108.762 −6.59468
\(273\) −0.711923 −0.0430875
\(274\) 31.6564 1.91243
\(275\) −22.3273 −1.34638
\(276\) 7.85377 0.472741
\(277\) −15.7599 −0.946921 −0.473460 0.880815i \(-0.656995\pi\)
−0.473460 + 0.880815i \(0.656995\pi\)
\(278\) −62.6591 −3.75804
\(279\) 0.363781 0.0217790
\(280\) −5.93545 −0.354711
\(281\) 21.8592 1.30401 0.652004 0.758216i \(-0.273929\pi\)
0.652004 + 0.758216i \(0.273929\pi\)
\(282\) 10.8194 0.644287
\(283\) −12.3680 −0.735199 −0.367599 0.929984i \(-0.619820\pi\)
−0.367599 + 0.929984i \(0.619820\pi\)
\(284\) 71.2667 4.22890
\(285\) −7.51623 −0.445223
\(286\) −22.8868 −1.35333
\(287\) −0.391890 −0.0231325
\(288\) −1.69793 −0.100052
\(289\) 26.4666 1.55686
\(290\) −14.5973 −0.857184
\(291\) 5.71733 0.335156
\(292\) −58.0161 −3.39514
\(293\) −15.2469 −0.890731 −0.445365 0.895349i \(-0.646926\pi\)
−0.445365 + 0.895349i \(0.646926\pi\)
\(294\) −33.7240 −1.96682
\(295\) −17.2013 −1.00150
\(296\) 10.0491 0.584090
\(297\) −18.4582 −1.07106
\(298\) −54.1001 −3.13393
\(299\) 1.83396 0.106061
\(300\) −61.3311 −3.54095
\(301\) −0.856298 −0.0493562
\(302\) −28.7020 −1.65162
\(303\) −5.72598 −0.328949
\(304\) −21.1445 −1.21272
\(305\) 1.25041 0.0715981
\(306\) 1.21363 0.0693783
\(307\) 33.4938 1.91159 0.955796 0.294030i \(-0.0949967\pi\)
0.955796 + 0.294030i \(0.0949967\pi\)
\(308\) 3.57235 0.203553
\(309\) 33.8169 1.92378
\(310\) 50.5356 2.87023
\(311\) −27.8830 −1.58110 −0.790549 0.612399i \(-0.790205\pi\)
−0.790549 + 0.612399i \(0.790205\pi\)
\(312\) −40.5605 −2.29629
\(313\) −20.0481 −1.13318 −0.566592 0.823999i \(-0.691738\pi\)
−0.566592 + 0.823999i \(0.691738\pi\)
\(314\) −19.9739 −1.12719
\(315\) 0.0393449 0.00221684
\(316\) −2.63706 −0.148346
\(317\) 6.73344 0.378188 0.189094 0.981959i \(-0.439445\pi\)
0.189094 + 0.981959i \(0.439445\pi\)
\(318\) 4.86765 0.272964
\(319\) 5.66820 0.317359
\(320\) −125.389 −7.00944
\(321\) −32.1720 −1.79566
\(322\) −0.387832 −0.0216130
\(323\) 8.45037 0.470191
\(324\) −51.8296 −2.87942
\(325\) −14.3216 −0.794421
\(326\) 34.6123 1.91700
\(327\) 1.75117 0.0968402
\(328\) −22.3272 −1.23281
\(329\) −0.394351 −0.0217413
\(330\) 58.2291 3.20541
\(331\) −1.69861 −0.0933638 −0.0466819 0.998910i \(-0.514865\pi\)
−0.0466819 + 0.998910i \(0.514865\pi\)
\(332\) −16.5642 −0.909077
\(333\) −0.0666133 −0.00365038
\(334\) −18.1735 −0.994412
\(335\) −17.0255 −0.930203
\(336\) 5.09548 0.277981
\(337\) −8.53308 −0.464827 −0.232413 0.972617i \(-0.574662\pi\)
−0.232413 + 0.972617i \(0.574662\pi\)
\(338\) 21.2438 1.15551
\(339\) 0.700936 0.0380696
\(340\) 124.439 6.74867
\(341\) −19.6232 −1.06266
\(342\) 0.235942 0.0127583
\(343\) 2.46387 0.133036
\(344\) −48.7861 −2.63037
\(345\) −4.66599 −0.251209
\(346\) −33.8657 −1.82063
\(347\) −16.2306 −0.871303 −0.435652 0.900115i \(-0.643482\pi\)
−0.435652 + 0.900115i \(0.643482\pi\)
\(348\) 15.5701 0.834643
\(349\) −5.72432 −0.306416 −0.153208 0.988194i \(-0.548960\pi\)
−0.153208 + 0.988194i \(0.548960\pi\)
\(350\) 3.02863 0.161887
\(351\) −11.8399 −0.631966
\(352\) 91.5908 4.88180
\(353\) −7.74302 −0.412119 −0.206060 0.978539i \(-0.566064\pi\)
−0.206060 + 0.978539i \(0.566064\pi\)
\(354\) 24.8580 1.32119
\(355\) −42.3402 −2.24718
\(356\) 37.2884 1.97628
\(357\) −2.03640 −0.107778
\(358\) 58.5013 3.09189
\(359\) −0.640157 −0.0337862 −0.0168931 0.999857i \(-0.505377\pi\)
−0.0168931 + 0.999857i \(0.505377\pi\)
\(360\) 2.24161 0.118143
\(361\) −17.3572 −0.913535
\(362\) −38.9256 −2.04588
\(363\) −3.34769 −0.175708
\(364\) 2.29145 0.120105
\(365\) 34.4679 1.80413
\(366\) −1.80699 −0.0944526
\(367\) −10.9837 −0.573343 −0.286672 0.958029i \(-0.592549\pi\)
−0.286672 + 0.958029i \(0.592549\pi\)
\(368\) −13.1263 −0.684255
\(369\) 0.148003 0.00770471
\(370\) −9.25378 −0.481081
\(371\) −0.177419 −0.00921111
\(372\) −53.9033 −2.79476
\(373\) 34.7953 1.80163 0.900816 0.434202i \(-0.142970\pi\)
0.900816 + 0.434202i \(0.142970\pi\)
\(374\) −65.4659 −3.38516
\(375\) 7.11675 0.367508
\(376\) −22.4675 −1.15867
\(377\) 3.63582 0.187254
\(378\) 2.50380 0.128782
\(379\) 5.39583 0.277165 0.138583 0.990351i \(-0.455745\pi\)
0.138583 + 0.990351i \(0.455745\pi\)
\(380\) 24.1923 1.24104
\(381\) 27.1824 1.39260
\(382\) −50.4411 −2.58079
\(383\) −18.4089 −0.940650 −0.470325 0.882493i \(-0.655863\pi\)
−0.470325 + 0.882493i \(0.655863\pi\)
\(384\) 91.9283 4.69120
\(385\) −2.12236 −0.108166
\(386\) −45.0642 −2.29371
\(387\) 0.323393 0.0164390
\(388\) −18.4022 −0.934231
\(389\) −19.2042 −0.973689 −0.486845 0.873489i \(-0.661852\pi\)
−0.486845 + 0.873489i \(0.661852\pi\)
\(390\) 37.3505 1.89132
\(391\) 5.24589 0.265296
\(392\) 70.0308 3.53709
\(393\) −11.1631 −0.563104
\(394\) 23.5826 1.18807
\(395\) 1.56670 0.0788292
\(396\) −1.34915 −0.0677971
\(397\) 10.3905 0.521482 0.260741 0.965409i \(-0.416033\pi\)
0.260741 + 0.965409i \(0.416033\pi\)
\(398\) 39.4398 1.97694
\(399\) −0.395897 −0.0198197
\(400\) 102.505 5.12524
\(401\) −25.8860 −1.29269 −0.646343 0.763047i \(-0.723702\pi\)
−0.646343 + 0.763047i \(0.723702\pi\)
\(402\) 24.6039 1.22713
\(403\) −12.5871 −0.627010
\(404\) 18.4301 0.916930
\(405\) 30.7924 1.53009
\(406\) −0.768875 −0.0381586
\(407\) 3.59328 0.178112
\(408\) −116.020 −5.74385
\(409\) −10.5003 −0.519208 −0.259604 0.965715i \(-0.583592\pi\)
−0.259604 + 0.965715i \(0.583592\pi\)
\(410\) 20.5602 1.01540
\(411\) 20.0606 0.989517
\(412\) −108.846 −5.36244
\(413\) −0.906035 −0.0445831
\(414\) 0.146470 0.00719861
\(415\) 9.84091 0.483071
\(416\) 58.7501 2.88046
\(417\) −39.7070 −1.94446
\(418\) −12.7273 −0.622512
\(419\) −22.4047 −1.09454 −0.547270 0.836956i \(-0.684333\pi\)
−0.547270 + 0.836956i \(0.684333\pi\)
\(420\) −5.82995 −0.284472
\(421\) 11.4152 0.556340 0.278170 0.960532i \(-0.410272\pi\)
0.278170 + 0.960532i \(0.410272\pi\)
\(422\) 46.7186 2.27423
\(423\) 0.148932 0.00724133
\(424\) −10.1081 −0.490893
\(425\) −40.9658 −1.98714
\(426\) 61.1865 2.96449
\(427\) 0.0658619 0.00318728
\(428\) 103.551 5.00534
\(429\) −14.5034 −0.700230
\(430\) 44.9251 2.16648
\(431\) −28.9744 −1.39565 −0.697824 0.716269i \(-0.745848\pi\)
−0.697824 + 0.716269i \(0.745848\pi\)
\(432\) 84.7421 4.07716
\(433\) −9.18671 −0.441485 −0.220742 0.975332i \(-0.570848\pi\)
−0.220742 + 0.975332i \(0.570848\pi\)
\(434\) 2.66183 0.127772
\(435\) −9.25031 −0.443518
\(436\) −5.63647 −0.269938
\(437\) 1.01986 0.0487864
\(438\) −49.8101 −2.38002
\(439\) 17.3245 0.826853 0.413427 0.910537i \(-0.364332\pi\)
0.413427 + 0.910537i \(0.364332\pi\)
\(440\) −120.918 −5.76453
\(441\) −0.464220 −0.0221057
\(442\) −41.9925 −1.99738
\(443\) −28.0561 −1.33298 −0.666492 0.745512i \(-0.732205\pi\)
−0.666492 + 0.745512i \(0.732205\pi\)
\(444\) 9.87044 0.468430
\(445\) −22.1534 −1.05017
\(446\) −49.6264 −2.34988
\(447\) −34.2832 −1.62154
\(448\) −6.60451 −0.312034
\(449\) 7.67474 0.362193 0.181097 0.983465i \(-0.442035\pi\)
0.181097 + 0.983465i \(0.442035\pi\)
\(450\) −1.14380 −0.0539194
\(451\) −7.98363 −0.375934
\(452\) −2.25609 −0.106117
\(453\) −18.1885 −0.854569
\(454\) −38.6523 −1.81404
\(455\) −1.36137 −0.0638220
\(456\) −22.5555 −1.05626
\(457\) −22.7074 −1.06221 −0.531104 0.847307i \(-0.678223\pi\)
−0.531104 + 0.847307i \(0.678223\pi\)
\(458\) 6.58788 0.307832
\(459\) −33.8670 −1.58078
\(460\) 15.0183 0.700233
\(461\) −1.98213 −0.0923169 −0.0461584 0.998934i \(-0.514698\pi\)
−0.0461584 + 0.998934i \(0.514698\pi\)
\(462\) 3.06706 0.142693
\(463\) −13.8669 −0.644451 −0.322225 0.946663i \(-0.604431\pi\)
−0.322225 + 0.946663i \(0.604431\pi\)
\(464\) −26.0228 −1.20808
\(465\) 32.0244 1.48510
\(466\) −23.7683 −1.10105
\(467\) −20.6415 −0.955174 −0.477587 0.878585i \(-0.658488\pi\)
−0.477587 + 0.878585i \(0.658488\pi\)
\(468\) −0.865398 −0.0400030
\(469\) −0.896773 −0.0414091
\(470\) 20.6894 0.954329
\(471\) −12.6574 −0.583223
\(472\) −51.6197 −2.37599
\(473\) −17.4446 −0.802104
\(474\) −2.26406 −0.103992
\(475\) −7.96420 −0.365422
\(476\) 6.55451 0.300425
\(477\) 0.0670045 0.00306793
\(478\) −74.7557 −3.41924
\(479\) −30.0471 −1.37289 −0.686443 0.727184i \(-0.740829\pi\)
−0.686443 + 0.727184i \(0.740829\pi\)
\(480\) −149.473 −6.82247
\(481\) 2.30488 0.105093
\(482\) −30.1916 −1.37519
\(483\) −0.245769 −0.0111829
\(484\) 10.7751 0.489779
\(485\) 10.9329 0.496438
\(486\) −1.91267 −0.0867603
\(487\) −0.485600 −0.0220046 −0.0110023 0.999939i \(-0.503502\pi\)
−0.0110023 + 0.999939i \(0.503502\pi\)
\(488\) 3.75236 0.169861
\(489\) 21.9338 0.991882
\(490\) −64.4885 −2.91330
\(491\) 42.3091 1.90938 0.954692 0.297596i \(-0.0961848\pi\)
0.954692 + 0.297596i \(0.0961848\pi\)
\(492\) −21.9303 −0.988696
\(493\) 10.4000 0.468391
\(494\) −8.16380 −0.367307
\(495\) 0.801539 0.0360265
\(496\) 90.0905 4.04518
\(497\) −2.23016 −0.100036
\(498\) −14.2213 −0.637270
\(499\) 23.9997 1.07437 0.537186 0.843464i \(-0.319487\pi\)
0.537186 + 0.843464i \(0.319487\pi\)
\(500\) −22.9065 −1.02441
\(501\) −11.5166 −0.514522
\(502\) 5.73306 0.255879
\(503\) 1.63735 0.0730057 0.0365029 0.999334i \(-0.488378\pi\)
0.0365029 + 0.999334i \(0.488378\pi\)
\(504\) 0.118071 0.00525928
\(505\) −10.9495 −0.487245
\(506\) −7.90095 −0.351240
\(507\) 13.4622 0.597878
\(508\) −87.4913 −3.88180
\(509\) −9.84015 −0.436157 −0.218078 0.975931i \(-0.569979\pi\)
−0.218078 + 0.975931i \(0.569979\pi\)
\(510\) 106.838 4.73087
\(511\) 1.81550 0.0803131
\(512\) −88.9393 −3.93060
\(513\) −6.58410 −0.290695
\(514\) −28.0506 −1.23726
\(515\) 64.6661 2.84953
\(516\) −47.9188 −2.10951
\(517\) −8.03377 −0.353325
\(518\) −0.487418 −0.0214159
\(519\) −21.4607 −0.942018
\(520\) −77.5616 −3.40130
\(521\) −41.3914 −1.81339 −0.906694 0.421788i \(-0.861403\pi\)
−0.906694 + 0.421788i \(0.861403\pi\)
\(522\) 0.290376 0.0127094
\(523\) 3.91017 0.170980 0.0854899 0.996339i \(-0.472754\pi\)
0.0854899 + 0.996339i \(0.472754\pi\)
\(524\) 35.9304 1.56963
\(525\) 1.91924 0.0837624
\(526\) −19.9611 −0.870344
\(527\) −36.0045 −1.56838
\(528\) 103.806 4.51756
\(529\) −22.3669 −0.972473
\(530\) 9.30813 0.404320
\(531\) 0.342177 0.0148492
\(532\) 1.27427 0.0552464
\(533\) −5.12102 −0.221816
\(534\) 32.0142 1.38539
\(535\) −61.5206 −2.65977
\(536\) −51.0920 −2.20684
\(537\) 37.0722 1.59979
\(538\) 59.6676 2.57245
\(539\) 25.0412 1.07860
\(540\) −96.9569 −4.17236
\(541\) 17.1081 0.735535 0.367767 0.929918i \(-0.380122\pi\)
0.367767 + 0.929918i \(0.380122\pi\)
\(542\) −27.5295 −1.18249
\(543\) −24.6671 −1.05857
\(544\) 168.050 7.20508
\(545\) 3.34867 0.143441
\(546\) 1.96734 0.0841943
\(547\) 34.8810 1.49140 0.745701 0.666281i \(-0.232115\pi\)
0.745701 + 0.666281i \(0.232115\pi\)
\(548\) −64.5686 −2.75824
\(549\) −0.0248737 −0.00106158
\(550\) 61.6995 2.63088
\(551\) 2.02186 0.0861343
\(552\) −14.0022 −0.595974
\(553\) 0.0825217 0.00350918
\(554\) 43.5512 1.85031
\(555\) −5.86411 −0.248918
\(556\) 127.804 5.42010
\(557\) 11.8897 0.503783 0.251891 0.967756i \(-0.418947\pi\)
0.251891 + 0.967756i \(0.418947\pi\)
\(558\) −1.00528 −0.0425568
\(559\) −11.1897 −0.473273
\(560\) 9.74380 0.411751
\(561\) −41.4857 −1.75153
\(562\) −60.4059 −2.54807
\(563\) −19.7699 −0.833201 −0.416600 0.909090i \(-0.636779\pi\)
−0.416600 + 0.909090i \(0.636779\pi\)
\(564\) −22.0681 −0.929234
\(565\) 1.34036 0.0563894
\(566\) 34.1778 1.43660
\(567\) 1.62191 0.0681137
\(568\) −127.059 −5.33128
\(569\) −8.95719 −0.375505 −0.187752 0.982216i \(-0.560120\pi\)
−0.187752 + 0.982216i \(0.560120\pi\)
\(570\) 20.7705 0.869979
\(571\) 32.0748 1.34229 0.671145 0.741327i \(-0.265803\pi\)
0.671145 + 0.741327i \(0.265803\pi\)
\(572\) 46.6817 1.95186
\(573\) −31.9645 −1.33534
\(574\) 1.08295 0.0452017
\(575\) −4.94408 −0.206183
\(576\) 2.49428 0.103929
\(577\) 27.7462 1.15509 0.577544 0.816360i \(-0.304011\pi\)
0.577544 + 0.816360i \(0.304011\pi\)
\(578\) −73.1382 −3.04215
\(579\) −28.5571 −1.18679
\(580\) 29.7738 1.23629
\(581\) 0.518344 0.0215045
\(582\) −15.7993 −0.654904
\(583\) −3.61439 −0.149693
\(584\) 103.435 4.28017
\(585\) 0.514140 0.0212571
\(586\) 42.1334 1.74051
\(587\) −12.5540 −0.518160 −0.259080 0.965856i \(-0.583419\pi\)
−0.259080 + 0.965856i \(0.583419\pi\)
\(588\) 68.7860 2.83669
\(589\) −6.99966 −0.288416
\(590\) 47.5345 1.95696
\(591\) 14.9443 0.614725
\(592\) −16.4968 −0.678015
\(593\) 19.6325 0.806209 0.403105 0.915154i \(-0.367931\pi\)
0.403105 + 0.915154i \(0.367931\pi\)
\(594\) 51.0078 2.09287
\(595\) −3.89409 −0.159642
\(596\) 110.346 4.51997
\(597\) 24.9930 1.02289
\(598\) −5.06799 −0.207246
\(599\) 30.0019 1.22584 0.612922 0.790143i \(-0.289994\pi\)
0.612922 + 0.790143i \(0.289994\pi\)
\(600\) 109.345 4.46400
\(601\) −34.7296 −1.41665 −0.708324 0.705887i \(-0.750549\pi\)
−0.708324 + 0.705887i \(0.750549\pi\)
\(602\) 2.36631 0.0964435
\(603\) 0.338679 0.0137921
\(604\) 58.5428 2.38207
\(605\) −6.40160 −0.260262
\(606\) 15.8233 0.642776
\(607\) −9.33742 −0.378994 −0.189497 0.981881i \(-0.560686\pi\)
−0.189497 + 0.981881i \(0.560686\pi\)
\(608\) 32.6707 1.32497
\(609\) −0.487235 −0.0197438
\(610\) −3.45540 −0.139905
\(611\) −5.15319 −0.208476
\(612\) −2.47540 −0.100062
\(613\) −0.353579 −0.0142809 −0.00714046 0.999975i \(-0.502273\pi\)
−0.00714046 + 0.999975i \(0.502273\pi\)
\(614\) −92.5573 −3.73531
\(615\) 13.0290 0.525380
\(616\) −6.36902 −0.256615
\(617\) −38.8012 −1.56208 −0.781040 0.624481i \(-0.785310\pi\)
−0.781040 + 0.624481i \(0.785310\pi\)
\(618\) −93.4501 −3.75912
\(619\) 28.1691 1.13221 0.566107 0.824332i \(-0.308449\pi\)
0.566107 + 0.824332i \(0.308449\pi\)
\(620\) −103.076 −4.13964
\(621\) −4.08734 −0.164019
\(622\) 77.0522 3.08951
\(623\) −1.16687 −0.0467496
\(624\) 66.5852 2.66554
\(625\) −17.4591 −0.698364
\(626\) 55.4011 2.21427
\(627\) −8.06527 −0.322096
\(628\) 40.7402 1.62571
\(629\) 6.59292 0.262877
\(630\) −0.108726 −0.00433176
\(631\) 25.3595 1.00954 0.504772 0.863253i \(-0.331577\pi\)
0.504772 + 0.863253i \(0.331577\pi\)
\(632\) 4.70153 0.187017
\(633\) 29.6056 1.17672
\(634\) −18.6073 −0.738990
\(635\) 51.9794 2.06274
\(636\) −9.92842 −0.393687
\(637\) 16.0624 0.636417
\(638\) −15.6636 −0.620128
\(639\) 0.842249 0.0333188
\(640\) 175.789 6.94868
\(641\) 28.8401 1.13912 0.569558 0.821951i \(-0.307114\pi\)
0.569558 + 0.821951i \(0.307114\pi\)
\(642\) 88.9045 3.50878
\(643\) −21.6175 −0.852509 −0.426255 0.904603i \(-0.640167\pi\)
−0.426255 + 0.904603i \(0.640167\pi\)
\(644\) 0.791050 0.0311717
\(645\) 28.4690 1.12097
\(646\) −23.3519 −0.918768
\(647\) −8.17114 −0.321241 −0.160620 0.987016i \(-0.551349\pi\)
−0.160620 + 0.987016i \(0.551349\pi\)
\(648\) 92.4052 3.63002
\(649\) −18.4579 −0.724534
\(650\) 39.5766 1.55232
\(651\) 1.68680 0.0661109
\(652\) −70.5979 −2.76483
\(653\) 40.3451 1.57882 0.789412 0.613863i \(-0.210385\pi\)
0.789412 + 0.613863i \(0.210385\pi\)
\(654\) −4.83922 −0.189229
\(655\) −21.3466 −0.834080
\(656\) 36.6530 1.43106
\(657\) −0.685650 −0.0267497
\(658\) 1.08976 0.0424831
\(659\) 47.8631 1.86448 0.932240 0.361841i \(-0.117852\pi\)
0.932240 + 0.361841i \(0.117852\pi\)
\(660\) −118.768 −4.62305
\(661\) 3.88147 0.150972 0.0754859 0.997147i \(-0.475949\pi\)
0.0754859 + 0.997147i \(0.475949\pi\)
\(662\) 4.69395 0.182436
\(663\) −26.6106 −1.03347
\(664\) 29.5317 1.14605
\(665\) −0.757052 −0.0293572
\(666\) 0.184080 0.00713296
\(667\) 1.25515 0.0485996
\(668\) 37.0681 1.43421
\(669\) −31.4482 −1.21586
\(670\) 47.0486 1.81764
\(671\) 1.34175 0.0517975
\(672\) −7.87309 −0.303711
\(673\) 39.8082 1.53449 0.767246 0.641353i \(-0.221626\pi\)
0.767246 + 0.641353i \(0.221626\pi\)
\(674\) 23.5805 0.908285
\(675\) 31.9185 1.22854
\(676\) −43.3305 −1.66656
\(677\) −38.6297 −1.48466 −0.742331 0.670034i \(-0.766280\pi\)
−0.742331 + 0.670034i \(0.766280\pi\)
\(678\) −1.93698 −0.0743891
\(679\) 0.575862 0.0220996
\(680\) −221.859 −8.50789
\(681\) −24.4939 −0.938609
\(682\) 54.2271 2.07646
\(683\) 21.3719 0.817772 0.408886 0.912586i \(-0.365917\pi\)
0.408886 + 0.912586i \(0.365917\pi\)
\(684\) −0.481244 −0.0184008
\(685\) 38.3608 1.46569
\(686\) −6.80869 −0.259957
\(687\) 4.17474 0.159276
\(688\) 80.0885 3.05335
\(689\) −2.31842 −0.0883247
\(690\) 12.8941 0.490869
\(691\) −38.0668 −1.44813 −0.724066 0.689731i \(-0.757729\pi\)
−0.724066 + 0.689731i \(0.757729\pi\)
\(692\) 69.0749 2.62583
\(693\) 0.0422189 0.00160377
\(694\) 44.8518 1.70255
\(695\) −75.9295 −2.88017
\(696\) −27.7594 −1.05222
\(697\) −14.6483 −0.554843
\(698\) 15.8187 0.598745
\(699\) −15.0620 −0.569697
\(700\) −6.17741 −0.233484
\(701\) −7.84038 −0.296127 −0.148064 0.988978i \(-0.547304\pi\)
−0.148064 + 0.988978i \(0.547304\pi\)
\(702\) 32.7185 1.23488
\(703\) 1.28173 0.0483415
\(704\) −134.548 −5.07096
\(705\) 13.1108 0.493783
\(706\) 21.3972 0.805293
\(707\) −0.576734 −0.0216903
\(708\) −50.7021 −1.90550
\(709\) −16.7361 −0.628536 −0.314268 0.949334i \(-0.601759\pi\)
−0.314268 + 0.949334i \(0.601759\pi\)
\(710\) 117.003 4.39106
\(711\) −0.0311655 −0.00116880
\(712\) −66.4803 −2.49145
\(713\) −4.34531 −0.162733
\(714\) 5.62741 0.210601
\(715\) −27.7340 −1.03719
\(716\) −119.324 −4.45933
\(717\) −47.3726 −1.76916
\(718\) 1.76902 0.0660192
\(719\) −36.4046 −1.35766 −0.678831 0.734295i \(-0.737513\pi\)
−0.678831 + 0.734295i \(0.737513\pi\)
\(720\) −3.67988 −0.137141
\(721\) 3.40612 0.126850
\(722\) 47.9650 1.78507
\(723\) −19.1324 −0.711540
\(724\) 79.3955 2.95071
\(725\) −9.80163 −0.364023
\(726\) 9.25106 0.343339
\(727\) 10.9879 0.407518 0.203759 0.979021i \(-0.434684\pi\)
0.203759 + 0.979021i \(0.434684\pi\)
\(728\) −4.08535 −0.151413
\(729\) 26.3742 0.976820
\(730\) −95.2491 −3.52533
\(731\) −32.0072 −1.18383
\(732\) 3.68566 0.136226
\(733\) 1.41767 0.0523629 0.0261814 0.999657i \(-0.491665\pi\)
0.0261814 + 0.999657i \(0.491665\pi\)
\(734\) 30.3525 1.12033
\(735\) −40.8663 −1.50738
\(736\) 20.2816 0.747589
\(737\) −18.2692 −0.672954
\(738\) −0.408993 −0.0150552
\(739\) 52.0980 1.91646 0.958228 0.286006i \(-0.0923277\pi\)
0.958228 + 0.286006i \(0.0923277\pi\)
\(740\) 18.8747 0.693847
\(741\) −5.17339 −0.190049
\(742\) 0.490281 0.0179988
\(743\) 38.1653 1.40015 0.700074 0.714070i \(-0.253150\pi\)
0.700074 + 0.714070i \(0.253150\pi\)
\(744\) 96.1024 3.52328
\(745\) −65.5578 −2.40185
\(746\) −96.1538 −3.52044
\(747\) −0.195760 −0.00716247
\(748\) 133.529 4.88231
\(749\) −3.24044 −0.118403
\(750\) −19.6665 −0.718121
\(751\) −21.8905 −0.798796 −0.399398 0.916778i \(-0.630781\pi\)
−0.399398 + 0.916778i \(0.630781\pi\)
\(752\) 36.8832 1.34499
\(753\) 3.63304 0.132395
\(754\) −10.0473 −0.365900
\(755\) −34.7808 −1.26580
\(756\) −5.10694 −0.185738
\(757\) 42.9653 1.56160 0.780799 0.624782i \(-0.214812\pi\)
0.780799 + 0.624782i \(0.214812\pi\)
\(758\) −14.9109 −0.541589
\(759\) −5.00683 −0.181736
\(760\) −43.1317 −1.56455
\(761\) 18.0950 0.655944 0.327972 0.944687i \(-0.393635\pi\)
0.327972 + 0.944687i \(0.393635\pi\)
\(762\) −75.1162 −2.72117
\(763\) 0.176382 0.00638547
\(764\) 102.883 3.72219
\(765\) 1.47066 0.0531717
\(766\) 50.8714 1.83806
\(767\) −11.8396 −0.427504
\(768\) −122.893 −4.43453
\(769\) −45.4054 −1.63736 −0.818680 0.574250i \(-0.805294\pi\)
−0.818680 + 0.574250i \(0.805294\pi\)
\(770\) 5.86497 0.211359
\(771\) −17.7756 −0.640174
\(772\) 91.9162 3.30814
\(773\) −34.9339 −1.25649 −0.628243 0.778017i \(-0.716226\pi\)
−0.628243 + 0.778017i \(0.716226\pi\)
\(774\) −0.893669 −0.0321223
\(775\) 33.9331 1.21891
\(776\) 32.8087 1.17776
\(777\) −0.308876 −0.0110809
\(778\) 53.0691 1.90262
\(779\) −2.84778 −0.102032
\(780\) −76.1829 −2.72778
\(781\) −45.4330 −1.62572
\(782\) −14.4966 −0.518397
\(783\) −8.10313 −0.289582
\(784\) −114.965 −4.10588
\(785\) −24.2041 −0.863881
\(786\) 30.8483 1.10032
\(787\) −6.56740 −0.234102 −0.117051 0.993126i \(-0.537344\pi\)
−0.117051 + 0.993126i \(0.537344\pi\)
\(788\) −48.1007 −1.71352
\(789\) −12.6493 −0.450328
\(790\) −4.32944 −0.154035
\(791\) 0.0705999 0.00251024
\(792\) 2.40535 0.0854703
\(793\) 0.860651 0.0305626
\(794\) −28.7132 −1.01899
\(795\) 5.89856 0.209200
\(796\) −80.4443 −2.85127
\(797\) 14.1558 0.501424 0.250712 0.968062i \(-0.419335\pi\)
0.250712 + 0.968062i \(0.419335\pi\)
\(798\) 1.09403 0.0387282
\(799\) −14.7403 −0.521474
\(800\) −158.381 −5.59963
\(801\) 0.440684 0.0155708
\(802\) 71.5338 2.52595
\(803\) 36.9856 1.30519
\(804\) −50.1838 −1.76985
\(805\) −0.469970 −0.0165643
\(806\) 34.7835 1.22520
\(807\) 37.8113 1.33102
\(808\) −32.8584 −1.15595
\(809\) 24.4879 0.860950 0.430475 0.902603i \(-0.358346\pi\)
0.430475 + 0.902603i \(0.358346\pi\)
\(810\) −85.0922 −2.98983
\(811\) −51.0011 −1.79089 −0.895446 0.445170i \(-0.853143\pi\)
−0.895446 + 0.445170i \(0.853143\pi\)
\(812\) 1.56825 0.0550349
\(813\) −17.4455 −0.611839
\(814\) −9.92974 −0.348037
\(815\) 41.9428 1.46919
\(816\) 190.462 6.66749
\(817\) −6.22254 −0.217699
\(818\) 29.0168 1.01455
\(819\) 0.0270810 0.000946285 0
\(820\) −41.9361 −1.46447
\(821\) 7.63150 0.266341 0.133171 0.991093i \(-0.457484\pi\)
0.133171 + 0.991093i \(0.457484\pi\)
\(822\) −55.4358 −1.93355
\(823\) −43.7553 −1.52522 −0.762608 0.646861i \(-0.776081\pi\)
−0.762608 + 0.646861i \(0.776081\pi\)
\(824\) 194.057 6.76031
\(825\) 39.0989 1.36125
\(826\) 2.50375 0.0871167
\(827\) 19.5733 0.680632 0.340316 0.940311i \(-0.389466\pi\)
0.340316 + 0.940311i \(0.389466\pi\)
\(828\) −0.298751 −0.0103823
\(829\) 48.5775 1.68717 0.843584 0.536998i \(-0.180442\pi\)
0.843584 + 0.536998i \(0.180442\pi\)
\(830\) −27.1945 −0.943936
\(831\) 27.5983 0.957376
\(832\) −86.3045 −2.99207
\(833\) 45.9453 1.59191
\(834\) 109.727 3.79954
\(835\) −22.0225 −0.762119
\(836\) 25.9595 0.897828
\(837\) 28.0529 0.969650
\(838\) 61.9135 2.13877
\(839\) −51.4208 −1.77524 −0.887622 0.460572i \(-0.847644\pi\)
−0.887622 + 0.460572i \(0.847644\pi\)
\(840\) 10.3940 0.358628
\(841\) −26.5117 −0.914195
\(842\) −31.5448 −1.08711
\(843\) −38.2792 −1.31841
\(844\) −95.2907 −3.28004
\(845\) 25.7430 0.885587
\(846\) −0.411562 −0.0141498
\(847\) −0.337187 −0.0115859
\(848\) 16.5937 0.569831
\(849\) 21.6585 0.743316
\(850\) 113.206 3.88292
\(851\) 0.795686 0.0272758
\(852\) −124.800 −4.27559
\(853\) 27.3523 0.936524 0.468262 0.883590i \(-0.344880\pi\)
0.468262 + 0.883590i \(0.344880\pi\)
\(854\) −0.182004 −0.00622804
\(855\) 0.285911 0.00977796
\(856\) −184.618 −6.31011
\(857\) 14.0844 0.481113 0.240556 0.970635i \(-0.422670\pi\)
0.240556 + 0.970635i \(0.422670\pi\)
\(858\) 40.0789 1.36827
\(859\) −6.32851 −0.215926 −0.107963 0.994155i \(-0.534433\pi\)
−0.107963 + 0.994155i \(0.534433\pi\)
\(860\) −91.6325 −3.12464
\(861\) 0.686268 0.0233879
\(862\) 80.0683 2.72714
\(863\) 19.1930 0.653337 0.326669 0.945139i \(-0.394074\pi\)
0.326669 + 0.945139i \(0.394074\pi\)
\(864\) −130.936 −4.45453
\(865\) −41.0380 −1.39533
\(866\) 25.3867 0.862675
\(867\) −46.3476 −1.57405
\(868\) −5.42927 −0.184281
\(869\) 1.68114 0.0570289
\(870\) 25.5625 0.866648
\(871\) −11.7186 −0.397069
\(872\) 10.0491 0.340304
\(873\) −0.217482 −0.00736066
\(874\) −2.81829 −0.0953301
\(875\) 0.716816 0.0242328
\(876\) 101.596 3.43262
\(877\) −29.0388 −0.980570 −0.490285 0.871562i \(-0.663107\pi\)
−0.490285 + 0.871562i \(0.663107\pi\)
\(878\) −47.8748 −1.61570
\(879\) 26.6999 0.900566
\(880\) 198.502 6.69149
\(881\) 56.3133 1.89724 0.948622 0.316412i \(-0.102478\pi\)
0.948622 + 0.316412i \(0.102478\pi\)
\(882\) 1.28283 0.0431953
\(883\) 50.8746 1.71207 0.856034 0.516920i \(-0.172921\pi\)
0.856034 + 0.516920i \(0.172921\pi\)
\(884\) 85.6511 2.88076
\(885\) 30.1226 1.01256
\(886\) 77.5306 2.60469
\(887\) −1.99453 −0.0669698 −0.0334849 0.999439i \(-0.510661\pi\)
−0.0334849 + 0.999439i \(0.510661\pi\)
\(888\) −17.5977 −0.590539
\(889\) 2.73787 0.0918253
\(890\) 61.2190 2.05206
\(891\) 33.0417 1.10694
\(892\) 101.222 3.38915
\(893\) −2.86567 −0.0958960
\(894\) 94.7387 3.16853
\(895\) 70.8912 2.36963
\(896\) 9.25923 0.309329
\(897\) −3.21159 −0.107232
\(898\) −21.2085 −0.707737
\(899\) −8.61456 −0.287312
\(900\) 2.33298 0.0777661
\(901\) −6.63165 −0.220932
\(902\) 22.0621 0.734587
\(903\) 1.49953 0.0499012
\(904\) 4.02230 0.133780
\(905\) −47.1696 −1.56797
\(906\) 50.2623 1.66985
\(907\) 10.2607 0.340701 0.170351 0.985383i \(-0.445510\pi\)
0.170351 + 0.985383i \(0.445510\pi\)
\(908\) 78.8380 2.61633
\(909\) 0.217811 0.00722435
\(910\) 3.76203 0.124710
\(911\) 17.1599 0.568533 0.284266 0.958745i \(-0.408250\pi\)
0.284266 + 0.958745i \(0.408250\pi\)
\(912\) 37.0278 1.22611
\(913\) 10.5598 0.349477
\(914\) 62.7500 2.07559
\(915\) −2.18968 −0.0723887
\(916\) −13.4371 −0.443975
\(917\) −1.12437 −0.0371301
\(918\) 93.5886 3.08888
\(919\) −38.8770 −1.28244 −0.641218 0.767359i \(-0.721570\pi\)
−0.641218 + 0.767359i \(0.721570\pi\)
\(920\) −26.7757 −0.882768
\(921\) −58.6535 −1.93270
\(922\) 5.47744 0.180390
\(923\) −29.1426 −0.959239
\(924\) −6.25580 −0.205801
\(925\) −6.21361 −0.204302
\(926\) 38.3201 1.25928
\(927\) −1.28637 −0.0422498
\(928\) 40.2082 1.31990
\(929\) 41.7187 1.36875 0.684373 0.729132i \(-0.260076\pi\)
0.684373 + 0.729132i \(0.260076\pi\)
\(930\) −88.4967 −2.90192
\(931\) 8.93226 0.292743
\(932\) 48.4797 1.58800
\(933\) 48.8279 1.59855
\(934\) 57.0410 1.86644
\(935\) −79.3308 −2.59440
\(936\) 1.54289 0.0504309
\(937\) −58.8071 −1.92114 −0.960571 0.278034i \(-0.910317\pi\)
−0.960571 + 0.278034i \(0.910317\pi\)
\(938\) 2.47816 0.0809147
\(939\) 35.1076 1.14569
\(940\) −42.1995 −1.37640
\(941\) 3.86886 0.126121 0.0630607 0.998010i \(-0.479914\pi\)
0.0630607 + 0.998010i \(0.479914\pi\)
\(942\) 34.9777 1.13964
\(943\) −1.76787 −0.0575698
\(944\) 84.7403 2.75806
\(945\) 3.03408 0.0986986
\(946\) 48.2067 1.56734
\(947\) −31.6269 −1.02774 −0.513868 0.857870i \(-0.671788\pi\)
−0.513868 + 0.857870i \(0.671788\pi\)
\(948\) 4.61795 0.149984
\(949\) 23.7241 0.770117
\(950\) 22.0084 0.714046
\(951\) −11.7914 −0.382363
\(952\) −11.6858 −0.378739
\(953\) 10.8278 0.350746 0.175373 0.984502i \(-0.443887\pi\)
0.175373 + 0.984502i \(0.443887\pi\)
\(954\) −0.185161 −0.00599482
\(955\) −61.1239 −1.97792
\(956\) 152.477 4.93146
\(957\) −9.92602 −0.320863
\(958\) 83.0326 2.68266
\(959\) 2.02055 0.0652470
\(960\) 219.577 7.08683
\(961\) −1.17657 −0.0379538
\(962\) −6.36934 −0.205356
\(963\) 1.22380 0.0394363
\(964\) 61.5809 1.98339
\(965\) −54.6082 −1.75790
\(966\) 0.679161 0.0218517
\(967\) −20.5370 −0.660427 −0.330213 0.943906i \(-0.607121\pi\)
−0.330213 + 0.943906i \(0.607121\pi\)
\(968\) −19.2106 −0.617453
\(969\) −14.7981 −0.475383
\(970\) −30.2122 −0.970055
\(971\) −31.4658 −1.00979 −0.504893 0.863182i \(-0.668468\pi\)
−0.504893 + 0.863182i \(0.668468\pi\)
\(972\) 3.90121 0.125131
\(973\) −3.99938 −0.128214
\(974\) 1.34191 0.0429977
\(975\) 25.0797 0.803192
\(976\) −6.15998 −0.197176
\(977\) −57.3742 −1.83556 −0.917782 0.397084i \(-0.870022\pi\)
−0.917782 + 0.397084i \(0.870022\pi\)
\(978\) −60.6123 −1.93817
\(979\) −23.7716 −0.759744
\(980\) 131.536 4.20175
\(981\) −0.0666133 −0.00212680
\(982\) −116.918 −3.73099
\(983\) 53.3569 1.70182 0.850910 0.525312i \(-0.176051\pi\)
0.850910 + 0.525312i \(0.176051\pi\)
\(984\) 39.0989 1.24643
\(985\) 28.5771 0.910541
\(986\) −28.7394 −0.915250
\(987\) 0.690578 0.0219813
\(988\) 16.6515 0.529754
\(989\) −3.86288 −0.122833
\(990\) −2.21499 −0.0703969
\(991\) −44.4308 −1.41139 −0.705695 0.708516i \(-0.749365\pi\)
−0.705695 + 0.708516i \(0.749365\pi\)
\(992\) −139.200 −4.41960
\(993\) 2.97456 0.0943947
\(994\) 6.16285 0.195474
\(995\) 47.7926 1.51513
\(996\) 29.0067 0.919114
\(997\) 52.0182 1.64743 0.823717 0.567002i \(-0.191897\pi\)
0.823717 + 0.567002i \(0.191897\pi\)
\(998\) −66.3210 −2.09936
\(999\) −5.13687 −0.162523
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 \(a_p\))