Properties

Label 6047.2.a.a.1.10
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 1.10
Character \(\chi\) = 6047.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.62503 q^{2}\) \(+1.59617 q^{3}\) \(+4.89080 q^{4}\) \(+2.83370 q^{5}\) \(-4.19001 q^{6}\) \(-4.08027 q^{7}\) \(-7.58846 q^{8}\) \(-0.452230 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.62503 q^{2}\) \(+1.59617 q^{3}\) \(+4.89080 q^{4}\) \(+2.83370 q^{5}\) \(-4.19001 q^{6}\) \(-4.08027 q^{7}\) \(-7.58846 q^{8}\) \(-0.452230 q^{9}\) \(-7.43856 q^{10}\) \(-4.35517 q^{11}\) \(+7.80657 q^{12}\) \(+1.46745 q^{13}\) \(+10.7108 q^{14}\) \(+4.52308 q^{15}\) \(+10.1384 q^{16}\) \(+0.159171 q^{17}\) \(+1.18712 q^{18}\) \(+6.75436 q^{19}\) \(+13.8591 q^{20}\) \(-6.51281 q^{21}\) \(+11.4325 q^{22}\) \(+2.68913 q^{23}\) \(-12.1125 q^{24}\) \(+3.02987 q^{25}\) \(-3.85211 q^{26}\) \(-5.51036 q^{27}\) \(-19.9558 q^{28}\) \(+4.32781 q^{29}\) \(-11.8732 q^{30}\) \(+3.01180 q^{31}\) \(-11.4366 q^{32}\) \(-6.95161 q^{33}\) \(-0.417829 q^{34}\) \(-11.5623 q^{35}\) \(-2.21177 q^{36}\) \(-6.79443 q^{37}\) \(-17.7304 q^{38}\) \(+2.34231 q^{39}\) \(-21.5034 q^{40}\) \(+10.9065 q^{41}\) \(+17.0964 q^{42}\) \(-5.59742 q^{43}\) \(-21.3003 q^{44}\) \(-1.28149 q^{45}\) \(-7.05905 q^{46}\) \(-3.88077 q^{47}\) \(+16.1826 q^{48}\) \(+9.64856 q^{49}\) \(-7.95350 q^{50}\) \(+0.254064 q^{51}\) \(+7.17702 q^{52}\) \(-10.8337 q^{53}\) \(+14.4649 q^{54}\) \(-12.3413 q^{55}\) \(+30.9629 q^{56}\) \(+10.7811 q^{57}\) \(-11.3606 q^{58}\) \(-2.01215 q^{59}\) \(+22.1215 q^{60}\) \(-11.7386 q^{61}\) \(-7.90607 q^{62}\) \(+1.84522 q^{63}\) \(+9.74479 q^{64}\) \(+4.15832 q^{65}\) \(+18.2482 q^{66}\) \(-9.50300 q^{67}\) \(+0.778473 q^{68}\) \(+4.29231 q^{69}\) \(+30.3513 q^{70}\) \(-2.45794 q^{71}\) \(+3.43173 q^{72}\) \(-5.70698 q^{73}\) \(+17.8356 q^{74}\) \(+4.83619 q^{75}\) \(+33.0342 q^{76}\) \(+17.7703 q^{77}\) \(-6.14864 q^{78}\) \(+11.2325 q^{79}\) \(+28.7291 q^{80}\) \(-7.43880 q^{81}\) \(-28.6301 q^{82}\) \(+11.6365 q^{83}\) \(-31.8529 q^{84}\) \(+0.451042 q^{85}\) \(+14.6934 q^{86}\) \(+6.90794 q^{87}\) \(+33.0491 q^{88}\) \(-4.27952 q^{89}\) \(+3.36394 q^{90}\) \(-5.98759 q^{91}\) \(+13.1520 q^{92}\) \(+4.80735 q^{93}\) \(+10.1871 q^{94}\) \(+19.1398 q^{95}\) \(-18.2548 q^{96}\) \(-3.38747 q^{97}\) \(-25.3278 q^{98}\) \(+1.96954 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(217q \) \(\mathstrut -\mathstrut 20q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 184q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 152q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(217q \) \(\mathstrut -\mathstrut 20q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 184q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 152q^{9} \) \(\mathstrut -\mathstrut 46q^{10} \) \(\mathstrut -\mathstrut 32q^{11} \) \(\mathstrut -\mathstrut 72q^{12} \) \(\mathstrut -\mathstrut 80q^{13} \) \(\mathstrut -\mathstrut 22q^{14} \) \(\mathstrut -\mathstrut 43q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut -\mathstrut 61q^{17} \) \(\mathstrut -\mathstrut 88q^{18} \) \(\mathstrut -\mathstrut 43q^{19} \) \(\mathstrut -\mathstrut 41q^{20} \) \(\mathstrut -\mathstrut 61q^{21} \) \(\mathstrut -\mathstrut 93q^{22} \) \(\mathstrut -\mathstrut 60q^{23} \) \(\mathstrut -\mathstrut 41q^{24} \) \(\mathstrut +\mathstrut 26q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 93q^{27} \) \(\mathstrut -\mathstrut 126q^{28} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut -\mathstrut 36q^{30} \) \(\mathstrut -\mathstrut 100q^{31} \) \(\mathstrut -\mathstrut 114q^{32} \) \(\mathstrut -\mathstrut 133q^{33} \) \(\mathstrut -\mathstrut 75q^{34} \) \(\mathstrut -\mathstrut 37q^{35} \) \(\mathstrut +\mathstrut 75q^{36} \) \(\mathstrut -\mathstrut 264q^{37} \) \(\mathstrut -\mathstrut 35q^{38} \) \(\mathstrut -\mathstrut 47q^{39} \) \(\mathstrut -\mathstrut 118q^{40} \) \(\mathstrut -\mathstrut 72q^{41} \) \(\mathstrut -\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 107q^{43} \) \(\mathstrut -\mathstrut 59q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 111q^{46} \) \(\mathstrut -\mathstrut 54q^{47} \) \(\mathstrut -\mathstrut 135q^{48} \) \(\mathstrut +\mathstrut 33q^{49} \) \(\mathstrut -\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 26q^{51} \) \(\mathstrut -\mathstrut 173q^{52} \) \(\mathstrut -\mathstrut 103q^{53} \) \(\mathstrut -\mathstrut 28q^{54} \) \(\mathstrut -\mathstrut 78q^{55} \) \(\mathstrut -\mathstrut 44q^{56} \) \(\mathstrut -\mathstrut 205q^{57} \) \(\mathstrut -\mathstrut 189q^{58} \) \(\mathstrut -\mathstrut 38q^{59} \) \(\mathstrut -\mathstrut 105q^{60} \) \(\mathstrut -\mathstrut 108q^{61} \) \(\mathstrut -\mathstrut 14q^{62} \) \(\mathstrut -\mathstrut 116q^{63} \) \(\mathstrut +\mathstrut 39q^{64} \) \(\mathstrut -\mathstrut 146q^{65} \) \(\mathstrut +\mathstrut 5q^{66} \) \(\mathstrut -\mathstrut 206q^{67} \) \(\mathstrut -\mathstrut 62q^{68} \) \(\mathstrut -\mathstrut 55q^{69} \) \(\mathstrut -\mathstrut 125q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 225q^{72} \) \(\mathstrut -\mathstrut 326q^{73} \) \(\mathstrut +\mathstrut 3q^{74} \) \(\mathstrut -\mathstrut 95q^{75} \) \(\mathstrut -\mathstrut 84q^{76} \) \(\mathstrut -\mathstrut 79q^{77} \) \(\mathstrut -\mathstrut 86q^{78} \) \(\mathstrut -\mathstrut 117q^{79} \) \(\mathstrut -\mathstrut 39q^{80} \) \(\mathstrut +\mathstrut q^{81} \) \(\mathstrut -\mathstrut 96q^{82} \) \(\mathstrut -\mathstrut 23q^{83} \) \(\mathstrut -\mathstrut 57q^{84} \) \(\mathstrut -\mathstrut 224q^{85} \) \(\mathstrut -\mathstrut 7q^{86} \) \(\mathstrut -\mathstrut 45q^{87} \) \(\mathstrut -\mathstrut 250q^{88} \) \(\mathstrut -\mathstrut 104q^{89} \) \(\mathstrut -\mathstrut 36q^{90} \) \(\mathstrut -\mathstrut 96q^{91} \) \(\mathstrut -\mathstrut 137q^{92} \) \(\mathstrut -\mathstrut 155q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 447q^{97} \) \(\mathstrut -\mathstrut 46q^{98} \) \(\mathstrut -\mathstrut 94q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.62503 −1.85618 −0.928090 0.372357i \(-0.878550\pi\)
−0.928090 + 0.372357i \(0.878550\pi\)
\(3\) 1.59617 0.921551 0.460776 0.887517i \(-0.347571\pi\)
0.460776 + 0.887517i \(0.347571\pi\)
\(4\) 4.89080 2.44540
\(5\) 2.83370 1.26727 0.633635 0.773632i \(-0.281562\pi\)
0.633635 + 0.773632i \(0.281562\pi\)
\(6\) −4.19001 −1.71056
\(7\) −4.08027 −1.54220 −0.771098 0.636717i \(-0.780292\pi\)
−0.771098 + 0.636717i \(0.780292\pi\)
\(8\) −7.58846 −2.68293
\(9\) −0.452230 −0.150743
\(10\) −7.43856 −2.35228
\(11\) −4.35517 −1.31313 −0.656567 0.754268i \(-0.727992\pi\)
−0.656567 + 0.754268i \(0.727992\pi\)
\(12\) 7.80657 2.25356
\(13\) 1.46745 0.406998 0.203499 0.979075i \(-0.434769\pi\)
0.203499 + 0.979075i \(0.434769\pi\)
\(14\) 10.7108 2.86259
\(15\) 4.52308 1.16785
\(16\) 10.1384 2.53459
\(17\) 0.159171 0.0386046 0.0193023 0.999814i \(-0.493856\pi\)
0.0193023 + 0.999814i \(0.493856\pi\)
\(18\) 1.18712 0.279807
\(19\) 6.75436 1.54956 0.774778 0.632233i \(-0.217862\pi\)
0.774778 + 0.632233i \(0.217862\pi\)
\(20\) 13.8591 3.09898
\(21\) −6.51281 −1.42121
\(22\) 11.4325 2.43741
\(23\) 2.68913 0.560721 0.280361 0.959895i \(-0.409546\pi\)
0.280361 + 0.959895i \(0.409546\pi\)
\(24\) −12.1125 −2.47245
\(25\) 3.02987 0.605973
\(26\) −3.85211 −0.755461
\(27\) −5.51036 −1.06047
\(28\) −19.9558 −3.77129
\(29\) 4.32781 0.803654 0.401827 0.915716i \(-0.368375\pi\)
0.401827 + 0.915716i \(0.368375\pi\)
\(30\) −11.8732 −2.16775
\(31\) 3.01180 0.540934 0.270467 0.962729i \(-0.412822\pi\)
0.270467 + 0.962729i \(0.412822\pi\)
\(32\) −11.4366 −2.02173
\(33\) −6.95161 −1.21012
\(34\) −0.417829 −0.0716570
\(35\) −11.5623 −1.95438
\(36\) −2.21177 −0.368628
\(37\) −6.79443 −1.11700 −0.558499 0.829505i \(-0.688622\pi\)
−0.558499 + 0.829505i \(0.688622\pi\)
\(38\) −17.7304 −2.87625
\(39\) 2.34231 0.375069
\(40\) −21.5034 −3.39999
\(41\) 10.9065 1.70332 0.851658 0.524098i \(-0.175597\pi\)
0.851658 + 0.524098i \(0.175597\pi\)
\(42\) 17.0964 2.63802
\(43\) −5.59742 −0.853599 −0.426799 0.904346i \(-0.640359\pi\)
−0.426799 + 0.904346i \(0.640359\pi\)
\(44\) −21.3003 −3.21114
\(45\) −1.28149 −0.191033
\(46\) −7.05905 −1.04080
\(47\) −3.88077 −0.566068 −0.283034 0.959110i \(-0.591341\pi\)
−0.283034 + 0.959110i \(0.591341\pi\)
\(48\) 16.1826 2.33575
\(49\) 9.64856 1.37837
\(50\) −7.95350 −1.12480
\(51\) 0.254064 0.0355761
\(52\) 7.17702 0.995273
\(53\) −10.8337 −1.48812 −0.744061 0.668111i \(-0.767103\pi\)
−0.744061 + 0.668111i \(0.767103\pi\)
\(54\) 14.4649 1.96842
\(55\) −12.3413 −1.66410
\(56\) 30.9629 4.13760
\(57\) 10.7811 1.42800
\(58\) −11.3606 −1.49173
\(59\) −2.01215 −0.261960 −0.130980 0.991385i \(-0.541812\pi\)
−0.130980 + 0.991385i \(0.541812\pi\)
\(60\) 22.1215 2.85587
\(61\) −11.7386 −1.50298 −0.751489 0.659745i \(-0.770664\pi\)
−0.751489 + 0.659745i \(0.770664\pi\)
\(62\) −7.90607 −1.00407
\(63\) 1.84522 0.232476
\(64\) 9.74479 1.21810
\(65\) 4.15832 0.515776
\(66\) 18.2482 2.24620
\(67\) −9.50300 −1.16098 −0.580488 0.814269i \(-0.697138\pi\)
−0.580488 + 0.814269i \(0.697138\pi\)
\(68\) 0.778473 0.0944037
\(69\) 4.29231 0.516733
\(70\) 30.3513 3.62768
\(71\) −2.45794 −0.291703 −0.145852 0.989306i \(-0.546592\pi\)
−0.145852 + 0.989306i \(0.546592\pi\)
\(72\) 3.43173 0.404433
\(73\) −5.70698 −0.667952 −0.333976 0.942582i \(-0.608390\pi\)
−0.333976 + 0.942582i \(0.608390\pi\)
\(74\) 17.8356 2.07335
\(75\) 4.83619 0.558435
\(76\) 33.0342 3.78929
\(77\) 17.7703 2.02511
\(78\) −6.14864 −0.696196
\(79\) 11.2325 1.26376 0.631879 0.775067i \(-0.282284\pi\)
0.631879 + 0.775067i \(0.282284\pi\)
\(80\) 28.7291 3.21201
\(81\) −7.43880 −0.826533
\(82\) −28.6301 −3.16166
\(83\) 11.6365 1.27727 0.638636 0.769509i \(-0.279499\pi\)
0.638636 + 0.769509i \(0.279499\pi\)
\(84\) −31.8529 −3.47543
\(85\) 0.451042 0.0489224
\(86\) 14.6934 1.58443
\(87\) 6.90794 0.740608
\(88\) 33.0491 3.52304
\(89\) −4.27952 −0.453629 −0.226814 0.973938i \(-0.572831\pi\)
−0.226814 + 0.973938i \(0.572831\pi\)
\(90\) 3.36394 0.354591
\(91\) −5.98759 −0.627670
\(92\) 13.1520 1.37119
\(93\) 4.80735 0.498499
\(94\) 10.1871 1.05072
\(95\) 19.1398 1.96371
\(96\) −18.2548 −1.86312
\(97\) −3.38747 −0.343946 −0.171973 0.985102i \(-0.555014\pi\)
−0.171973 + 0.985102i \(0.555014\pi\)
\(98\) −25.3278 −2.55850
\(99\) 1.96954 0.197946
\(100\) 14.8185 1.48185
\(101\) −8.26141 −0.822041 −0.411020 0.911626i \(-0.634827\pi\)
−0.411020 + 0.911626i \(0.634827\pi\)
\(102\) −0.666927 −0.0660356
\(103\) 8.96269 0.883120 0.441560 0.897232i \(-0.354425\pi\)
0.441560 + 0.897232i \(0.354425\pi\)
\(104\) −11.1357 −1.09194
\(105\) −18.4554 −1.80106
\(106\) 28.4388 2.76222
\(107\) 3.83017 0.370276 0.185138 0.982713i \(-0.440727\pi\)
0.185138 + 0.982713i \(0.440727\pi\)
\(108\) −26.9501 −2.59327
\(109\) 6.24446 0.598111 0.299055 0.954236i \(-0.403328\pi\)
0.299055 + 0.954236i \(0.403328\pi\)
\(110\) 32.3962 3.08886
\(111\) −10.8451 −1.02937
\(112\) −41.3672 −3.90883
\(113\) 4.52680 0.425845 0.212923 0.977069i \(-0.431702\pi\)
0.212923 + 0.977069i \(0.431702\pi\)
\(114\) −28.3008 −2.65062
\(115\) 7.62018 0.710585
\(116\) 21.1665 1.96526
\(117\) −0.663626 −0.0613522
\(118\) 5.28196 0.486244
\(119\) −0.649459 −0.0595358
\(120\) −34.3232 −3.13327
\(121\) 7.96753 0.724321
\(122\) 30.8143 2.78980
\(123\) 17.4087 1.56969
\(124\) 14.7301 1.32280
\(125\) −5.58277 −0.499338
\(126\) −4.84376 −0.431517
\(127\) 5.55519 0.492943 0.246472 0.969150i \(-0.420729\pi\)
0.246472 + 0.969150i \(0.420729\pi\)
\(128\) −2.70717 −0.239282
\(129\) −8.93446 −0.786635
\(130\) −10.9157 −0.957373
\(131\) −13.5798 −1.18647 −0.593236 0.805029i \(-0.702150\pi\)
−0.593236 + 0.805029i \(0.702150\pi\)
\(132\) −33.9990 −2.95923
\(133\) −27.5596 −2.38972
\(134\) 24.9457 2.15498
\(135\) −15.6147 −1.34390
\(136\) −1.20786 −0.103573
\(137\) −13.6882 −1.16946 −0.584731 0.811227i \(-0.698800\pi\)
−0.584731 + 0.811227i \(0.698800\pi\)
\(138\) −11.2675 −0.959150
\(139\) 0.845489 0.0717134 0.0358567 0.999357i \(-0.488584\pi\)
0.0358567 + 0.999357i \(0.488584\pi\)
\(140\) −56.5487 −4.77924
\(141\) −6.19438 −0.521661
\(142\) 6.45217 0.541454
\(143\) −6.39101 −0.534443
\(144\) −4.58487 −0.382073
\(145\) 12.2637 1.01845
\(146\) 14.9810 1.23984
\(147\) 15.4008 1.27024
\(148\) −33.2302 −2.73151
\(149\) −13.6187 −1.11569 −0.557845 0.829945i \(-0.688372\pi\)
−0.557845 + 0.829945i \(0.688372\pi\)
\(150\) −12.6952 −1.03656
\(151\) −3.32677 −0.270729 −0.135364 0.990796i \(-0.543221\pi\)
−0.135364 + 0.990796i \(0.543221\pi\)
\(152\) −51.2552 −4.15734
\(153\) −0.0719818 −0.00581938
\(154\) −46.6475 −3.75897
\(155\) 8.53453 0.685510
\(156\) 11.4558 0.917195
\(157\) −13.7185 −1.09486 −0.547429 0.836852i \(-0.684393\pi\)
−0.547429 + 0.836852i \(0.684393\pi\)
\(158\) −29.4858 −2.34576
\(159\) −17.2925 −1.37138
\(160\) −32.4080 −2.56207
\(161\) −10.9723 −0.864742
\(162\) 19.5271 1.53419
\(163\) −12.9331 −1.01300 −0.506500 0.862240i \(-0.669061\pi\)
−0.506500 + 0.862240i \(0.669061\pi\)
\(164\) 53.3418 4.16529
\(165\) −19.6988 −1.53355
\(166\) −30.5462 −2.37085
\(167\) 20.5685 1.59164 0.795819 0.605535i \(-0.207041\pi\)
0.795819 + 0.605535i \(0.207041\pi\)
\(168\) 49.4222 3.81301
\(169\) −10.8466 −0.834353
\(170\) −1.18400 −0.0908088
\(171\) −3.05452 −0.233585
\(172\) −27.3759 −2.08739
\(173\) −17.4901 −1.32975 −0.664875 0.746955i \(-0.731515\pi\)
−0.664875 + 0.746955i \(0.731515\pi\)
\(174\) −18.1336 −1.37470
\(175\) −12.3627 −0.934529
\(176\) −44.1543 −3.32826
\(177\) −3.21174 −0.241409
\(178\) 11.2339 0.842016
\(179\) 3.53375 0.264125 0.132062 0.991241i \(-0.457840\pi\)
0.132062 + 0.991241i \(0.457840\pi\)
\(180\) −6.26749 −0.467151
\(181\) 16.8008 1.24879 0.624395 0.781109i \(-0.285345\pi\)
0.624395 + 0.781109i \(0.285345\pi\)
\(182\) 15.7176 1.16507
\(183\) −18.7369 −1.38507
\(184\) −20.4063 −1.50437
\(185\) −19.2534 −1.41554
\(186\) −12.6195 −0.925303
\(187\) −0.693216 −0.0506930
\(188\) −18.9801 −1.38426
\(189\) 22.4837 1.63545
\(190\) −50.2427 −3.64499
\(191\) 16.7452 1.21164 0.605820 0.795602i \(-0.292845\pi\)
0.605820 + 0.795602i \(0.292845\pi\)
\(192\) 15.5544 1.12254
\(193\) −14.4285 −1.03859 −0.519294 0.854596i \(-0.673805\pi\)
−0.519294 + 0.854596i \(0.673805\pi\)
\(194\) 8.89223 0.638425
\(195\) 6.63740 0.475314
\(196\) 47.1892 3.37066
\(197\) 12.4474 0.886842 0.443421 0.896313i \(-0.353765\pi\)
0.443421 + 0.896313i \(0.353765\pi\)
\(198\) −5.17011 −0.367424
\(199\) 12.8130 0.908287 0.454144 0.890928i \(-0.349945\pi\)
0.454144 + 0.890928i \(0.349945\pi\)
\(200\) −22.9920 −1.62578
\(201\) −15.1684 −1.06990
\(202\) 21.6865 1.52585
\(203\) −17.6586 −1.23939
\(204\) 1.24258 0.0869979
\(205\) 30.9059 2.15856
\(206\) −23.5274 −1.63923
\(207\) −1.21610 −0.0845250
\(208\) 14.8775 1.03157
\(209\) −29.4164 −2.03477
\(210\) 48.4460 3.34309
\(211\) −1.14362 −0.0787300 −0.0393650 0.999225i \(-0.512534\pi\)
−0.0393650 + 0.999225i \(0.512534\pi\)
\(212\) −52.9855 −3.63906
\(213\) −3.92329 −0.268820
\(214\) −10.0543 −0.687299
\(215\) −15.8614 −1.08174
\(216\) 41.8151 2.84516
\(217\) −12.2889 −0.834226
\(218\) −16.3919 −1.11020
\(219\) −9.10933 −0.615552
\(220\) −60.3587 −4.06938
\(221\) 0.233575 0.0157120
\(222\) 28.4687 1.91070
\(223\) −28.6960 −1.92163 −0.960815 0.277192i \(-0.910596\pi\)
−0.960815 + 0.277192i \(0.910596\pi\)
\(224\) 46.6644 3.11790
\(225\) −1.37020 −0.0913465
\(226\) −11.8830 −0.790445
\(227\) 24.5098 1.62677 0.813386 0.581725i \(-0.197622\pi\)
0.813386 + 0.581725i \(0.197622\pi\)
\(228\) 52.7284 3.49202
\(229\) −27.2245 −1.79904 −0.899522 0.436875i \(-0.856085\pi\)
−0.899522 + 0.436875i \(0.856085\pi\)
\(230\) −20.0032 −1.31897
\(231\) 28.3644 1.86624
\(232\) −32.8414 −2.15614
\(233\) −18.4644 −1.20964 −0.604821 0.796362i \(-0.706755\pi\)
−0.604821 + 0.796362i \(0.706755\pi\)
\(234\) 1.74204 0.113881
\(235\) −10.9969 −0.717361
\(236\) −9.84103 −0.640597
\(237\) 17.9291 1.16462
\(238\) 1.70485 0.110509
\(239\) −16.0912 −1.04085 −0.520427 0.853906i \(-0.674227\pi\)
−0.520427 + 0.853906i \(0.674227\pi\)
\(240\) 45.8566 2.96003
\(241\) 26.4312 1.70258 0.851290 0.524695i \(-0.175821\pi\)
0.851290 + 0.524695i \(0.175821\pi\)
\(242\) −20.9150 −1.34447
\(243\) 4.65746 0.298776
\(244\) −57.4114 −3.67539
\(245\) 27.3412 1.74676
\(246\) −45.6985 −2.91363
\(247\) 9.91169 0.630666
\(248\) −22.8549 −1.45129
\(249\) 18.5739 1.17707
\(250\) 14.6550 0.926861
\(251\) −8.36179 −0.527791 −0.263896 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(252\) 9.02460 0.568497
\(253\) −11.7116 −0.736302
\(254\) −14.5826 −0.914991
\(255\) 0.719942 0.0450845
\(256\) −12.3832 −0.773947
\(257\) 11.1136 0.693245 0.346622 0.938005i \(-0.387328\pi\)
0.346622 + 0.938005i \(0.387328\pi\)
\(258\) 23.4533 1.46014
\(259\) 27.7231 1.72263
\(260\) 20.3375 1.26128
\(261\) −1.95717 −0.121146
\(262\) 35.6474 2.20230
\(263\) 12.8396 0.791722 0.395861 0.918310i \(-0.370446\pi\)
0.395861 + 0.918310i \(0.370446\pi\)
\(264\) 52.7520 3.24666
\(265\) −30.6995 −1.88585
\(266\) 72.3448 4.43574
\(267\) −6.83086 −0.418042
\(268\) −46.4773 −2.83905
\(269\) 9.21004 0.561546 0.280773 0.959774i \(-0.409409\pi\)
0.280773 + 0.959774i \(0.409409\pi\)
\(270\) 40.9892 2.49452
\(271\) 2.06421 0.125392 0.0626959 0.998033i \(-0.480030\pi\)
0.0626959 + 0.998033i \(0.480030\pi\)
\(272\) 1.61373 0.0978467
\(273\) −9.55723 −0.578430
\(274\) 35.9320 2.17073
\(275\) −13.1956 −0.795724
\(276\) 20.9928 1.26362
\(277\) −14.1120 −0.847910 −0.423955 0.905683i \(-0.639359\pi\)
−0.423955 + 0.905683i \(0.639359\pi\)
\(278\) −2.21944 −0.133113
\(279\) −1.36202 −0.0815423
\(280\) 87.7397 5.24345
\(281\) −7.56810 −0.451475 −0.225737 0.974188i \(-0.572479\pi\)
−0.225737 + 0.974188i \(0.572479\pi\)
\(282\) 16.2605 0.968296
\(283\) 25.3302 1.50573 0.752863 0.658178i \(-0.228672\pi\)
0.752863 + 0.658178i \(0.228672\pi\)
\(284\) −12.0213 −0.713332
\(285\) 30.5505 1.80966
\(286\) 16.7766 0.992022
\(287\) −44.5016 −2.62685
\(288\) 5.17198 0.304762
\(289\) −16.9747 −0.998510
\(290\) −32.1927 −1.89042
\(291\) −5.40699 −0.316963
\(292\) −27.9117 −1.63341
\(293\) −4.60976 −0.269305 −0.134653 0.990893i \(-0.542992\pi\)
−0.134653 + 0.990893i \(0.542992\pi\)
\(294\) −40.4276 −2.35778
\(295\) −5.70183 −0.331974
\(296\) 51.5593 2.99682
\(297\) 23.9986 1.39254
\(298\) 35.7496 2.07092
\(299\) 3.94616 0.228212
\(300\) 23.6529 1.36560
\(301\) 22.8390 1.31642
\(302\) 8.73289 0.502521
\(303\) −13.1866 −0.757552
\(304\) 68.4781 3.92749
\(305\) −33.2638 −1.90468
\(306\) 0.188955 0.0108018
\(307\) 4.39386 0.250771 0.125385 0.992108i \(-0.459983\pi\)
0.125385 + 0.992108i \(0.459983\pi\)
\(308\) 86.9109 4.95221
\(309\) 14.3060 0.813841
\(310\) −22.4034 −1.27243
\(311\) 1.98084 0.112323 0.0561614 0.998422i \(-0.482114\pi\)
0.0561614 + 0.998422i \(0.482114\pi\)
\(312\) −17.7745 −1.00628
\(313\) −2.68152 −0.151569 −0.0757843 0.997124i \(-0.524146\pi\)
−0.0757843 + 0.997124i \(0.524146\pi\)
\(314\) 36.0116 2.03225
\(315\) 5.22880 0.294610
\(316\) 54.9361 3.09040
\(317\) 9.72262 0.546077 0.273038 0.962003i \(-0.411971\pi\)
0.273038 + 0.962003i \(0.411971\pi\)
\(318\) 45.3933 2.54553
\(319\) −18.8484 −1.05531
\(320\) 27.6138 1.54366
\(321\) 6.11361 0.341229
\(322\) 28.8028 1.60512
\(323\) 1.07510 0.0598200
\(324\) −36.3817 −2.02121
\(325\) 4.44618 0.246630
\(326\) 33.9499 1.88031
\(327\) 9.96724 0.551190
\(328\) −82.7639 −4.56987
\(329\) 15.8346 0.872988
\(330\) 51.7100 2.84654
\(331\) −13.1429 −0.722399 −0.361199 0.932489i \(-0.617633\pi\)
−0.361199 + 0.932489i \(0.617633\pi\)
\(332\) 56.9119 3.12344
\(333\) 3.07265 0.168380
\(334\) −53.9930 −2.95436
\(335\) −26.9287 −1.47127
\(336\) −66.0292 −3.60219
\(337\) −30.6858 −1.67156 −0.835781 0.549063i \(-0.814985\pi\)
−0.835781 + 0.549063i \(0.814985\pi\)
\(338\) 28.4727 1.54871
\(339\) 7.22556 0.392438
\(340\) 2.20596 0.119635
\(341\) −13.1169 −0.710319
\(342\) 8.01823 0.433576
\(343\) −10.8068 −0.583515
\(344\) 42.4758 2.29014
\(345\) 12.1631 0.654841
\(346\) 45.9122 2.46825
\(347\) −5.98399 −0.321237 −0.160619 0.987017i \(-0.551349\pi\)
−0.160619 + 0.987017i \(0.551349\pi\)
\(348\) 33.7854 1.81109
\(349\) −22.2652 −1.19183 −0.595914 0.803048i \(-0.703210\pi\)
−0.595914 + 0.803048i \(0.703210\pi\)
\(350\) 32.4524 1.73465
\(351\) −8.08618 −0.431609
\(352\) 49.8084 2.65480
\(353\) 1.40596 0.0748315 0.0374157 0.999300i \(-0.488087\pi\)
0.0374157 + 0.999300i \(0.488087\pi\)
\(354\) 8.43093 0.448099
\(355\) −6.96506 −0.369667
\(356\) −20.9303 −1.10930
\(357\) −1.03665 −0.0548653
\(358\) −9.27621 −0.490263
\(359\) −17.7435 −0.936464 −0.468232 0.883606i \(-0.655109\pi\)
−0.468232 + 0.883606i \(0.655109\pi\)
\(360\) 9.72450 0.512526
\(361\) 26.6213 1.40112
\(362\) −44.1026 −2.31798
\(363\) 12.7176 0.667499
\(364\) −29.2841 −1.53491
\(365\) −16.1719 −0.846475
\(366\) 49.1850 2.57094
\(367\) −12.9260 −0.674731 −0.337366 0.941374i \(-0.609536\pi\)
−0.337366 + 0.941374i \(0.609536\pi\)
\(368\) 27.2633 1.42120
\(369\) −4.93227 −0.256764
\(370\) 50.5408 2.62749
\(371\) 44.2044 2.29498
\(372\) 23.5118 1.21903
\(373\) −15.3574 −0.795177 −0.397588 0.917564i \(-0.630153\pi\)
−0.397588 + 0.917564i \(0.630153\pi\)
\(374\) 1.81972 0.0940953
\(375\) −8.91107 −0.460166
\(376\) 29.4491 1.51872
\(377\) 6.35085 0.327086
\(378\) −59.0205 −3.03569
\(379\) −32.6068 −1.67490 −0.837449 0.546516i \(-0.815954\pi\)
−0.837449 + 0.546516i \(0.815954\pi\)
\(380\) 93.6092 4.80205
\(381\) 8.86705 0.454273
\(382\) −43.9567 −2.24902
\(383\) −20.0159 −1.02277 −0.511384 0.859353i \(-0.670867\pi\)
−0.511384 + 0.859353i \(0.670867\pi\)
\(384\) −4.32112 −0.220511
\(385\) 50.3556 2.56636
\(386\) 37.8754 1.92781
\(387\) 2.53132 0.128674
\(388\) −16.5675 −0.841085
\(389\) 27.0756 1.37279 0.686393 0.727230i \(-0.259193\pi\)
0.686393 + 0.727230i \(0.259193\pi\)
\(390\) −17.4234 −0.882268
\(391\) 0.428030 0.0216464
\(392\) −73.2177 −3.69805
\(393\) −21.6757 −1.09339
\(394\) −32.6749 −1.64614
\(395\) 31.8296 1.60152
\(396\) 9.63264 0.484058
\(397\) 17.6271 0.884679 0.442340 0.896848i \(-0.354149\pi\)
0.442340 + 0.896848i \(0.354149\pi\)
\(398\) −33.6345 −1.68594
\(399\) −43.9899 −2.20225
\(400\) 30.7179 1.53589
\(401\) −34.3268 −1.71420 −0.857098 0.515153i \(-0.827735\pi\)
−0.857098 + 0.515153i \(0.827735\pi\)
\(402\) 39.8177 1.98592
\(403\) 4.41966 0.220159
\(404\) −40.4049 −2.01022
\(405\) −21.0793 −1.04744
\(406\) 46.3545 2.30053
\(407\) 29.5909 1.46677
\(408\) −1.92796 −0.0954480
\(409\) −31.5756 −1.56131 −0.780656 0.624961i \(-0.785115\pi\)
−0.780656 + 0.624961i \(0.785115\pi\)
\(410\) −81.1290 −4.00668
\(411\) −21.8487 −1.07772
\(412\) 43.8348 2.15958
\(413\) 8.21011 0.403993
\(414\) 3.19231 0.156894
\(415\) 32.9744 1.61865
\(416\) −16.7827 −0.822838
\(417\) 1.34955 0.0660876
\(418\) 77.2190 3.77691
\(419\) 29.4354 1.43801 0.719006 0.695003i \(-0.244597\pi\)
0.719006 + 0.695003i \(0.244597\pi\)
\(420\) −90.2616 −4.40431
\(421\) −24.2341 −1.18110 −0.590549 0.807002i \(-0.701089\pi\)
−0.590549 + 0.807002i \(0.701089\pi\)
\(422\) 3.00204 0.146137
\(423\) 1.75500 0.0853310
\(424\) 82.2111 3.99252
\(425\) 0.482266 0.0233933
\(426\) 10.2988 0.498977
\(427\) 47.8968 2.31789
\(428\) 18.7326 0.905474
\(429\) −10.2012 −0.492516
\(430\) 41.6368 2.00790
\(431\) −17.2810 −0.832396 −0.416198 0.909274i \(-0.636638\pi\)
−0.416198 + 0.909274i \(0.636638\pi\)
\(432\) −55.8660 −2.68785
\(433\) −10.1189 −0.486281 −0.243140 0.969991i \(-0.578178\pi\)
−0.243140 + 0.969991i \(0.578178\pi\)
\(434\) 32.2588 1.54847
\(435\) 19.5750 0.938551
\(436\) 30.5404 1.46262
\(437\) 18.1633 0.868869
\(438\) 23.9123 1.14257
\(439\) −31.6553 −1.51082 −0.755411 0.655251i \(-0.772563\pi\)
−0.755411 + 0.655251i \(0.772563\pi\)
\(440\) 93.6512 4.46464
\(441\) −4.36337 −0.207780
\(442\) −0.613143 −0.0291643
\(443\) −30.0671 −1.42853 −0.714265 0.699876i \(-0.753239\pi\)
−0.714265 + 0.699876i \(0.753239\pi\)
\(444\) −53.0412 −2.51722
\(445\) −12.1269 −0.574870
\(446\) 75.3281 3.56689
\(447\) −21.7379 −1.02817
\(448\) −39.7613 −1.87855
\(449\) 4.89363 0.230945 0.115472 0.993311i \(-0.463162\pi\)
0.115472 + 0.993311i \(0.463162\pi\)
\(450\) 3.59681 0.169555
\(451\) −47.4999 −2.23668
\(452\) 22.1397 1.04136
\(453\) −5.31010 −0.249490
\(454\) −64.3390 −3.01958
\(455\) −16.9670 −0.795428
\(456\) −81.8121 −3.83120
\(457\) −34.7775 −1.62682 −0.813412 0.581688i \(-0.802393\pi\)
−0.813412 + 0.581688i \(0.802393\pi\)
\(458\) 71.4652 3.33935
\(459\) −0.877088 −0.0409390
\(460\) 37.2688 1.73767
\(461\) 25.0822 1.16819 0.584097 0.811684i \(-0.301449\pi\)
0.584097 + 0.811684i \(0.301449\pi\)
\(462\) −74.4576 −3.46408
\(463\) −20.6225 −0.958407 −0.479203 0.877704i \(-0.659074\pi\)
−0.479203 + 0.877704i \(0.659074\pi\)
\(464\) 43.8769 2.03693
\(465\) 13.6226 0.631732
\(466\) 48.4696 2.24531
\(467\) −7.12670 −0.329784 −0.164892 0.986312i \(-0.552728\pi\)
−0.164892 + 0.986312i \(0.552728\pi\)
\(468\) −3.24566 −0.150031
\(469\) 38.7748 1.79045
\(470\) 28.8673 1.33155
\(471\) −21.8971 −1.00897
\(472\) 15.2691 0.702818
\(473\) 24.3777 1.12089
\(474\) −47.0644 −2.16174
\(475\) 20.4648 0.938989
\(476\) −3.17638 −0.145589
\(477\) 4.89932 0.224325
\(478\) 42.2400 1.93201
\(479\) −6.29914 −0.287815 −0.143907 0.989591i \(-0.545967\pi\)
−0.143907 + 0.989591i \(0.545967\pi\)
\(480\) −51.7287 −2.36108
\(481\) −9.97050 −0.454616
\(482\) −69.3827 −3.16029
\(483\) −17.5138 −0.796904
\(484\) 38.9676 1.77126
\(485\) −9.59908 −0.435872
\(486\) −12.2260 −0.554583
\(487\) −19.0471 −0.863108 −0.431554 0.902087i \(-0.642035\pi\)
−0.431554 + 0.902087i \(0.642035\pi\)
\(488\) 89.0782 4.03238
\(489\) −20.6435 −0.933531
\(490\) −71.7715 −3.24230
\(491\) −32.8632 −1.48310 −0.741548 0.670900i \(-0.765908\pi\)
−0.741548 + 0.670900i \(0.765908\pi\)
\(492\) 85.1427 3.83853
\(493\) 0.688861 0.0310247
\(494\) −26.0185 −1.17063
\(495\) 5.58109 0.250851
\(496\) 30.5347 1.37105
\(497\) 10.0290 0.449864
\(498\) −48.7571 −2.18486
\(499\) 22.2917 0.997911 0.498956 0.866627i \(-0.333717\pi\)
0.498956 + 0.866627i \(0.333717\pi\)
\(500\) −27.3042 −1.22108
\(501\) 32.8309 1.46678
\(502\) 21.9500 0.979675
\(503\) 20.1406 0.898024 0.449012 0.893526i \(-0.351776\pi\)
0.449012 + 0.893526i \(0.351776\pi\)
\(504\) −14.0024 −0.623715
\(505\) −23.4104 −1.04175
\(506\) 30.7434 1.36671
\(507\) −17.3130 −0.768899
\(508\) 27.1693 1.20544
\(509\) −38.4784 −1.70553 −0.852763 0.522298i \(-0.825075\pi\)
−0.852763 + 0.522298i \(0.825075\pi\)
\(510\) −1.88987 −0.0836850
\(511\) 23.2860 1.03011
\(512\) 37.9206 1.67587
\(513\) −37.2189 −1.64326
\(514\) −29.1735 −1.28679
\(515\) 25.3976 1.11915
\(516\) −43.6967 −1.92364
\(517\) 16.9014 0.743323
\(518\) −72.7740 −3.19751
\(519\) −27.9173 −1.22543
\(520\) −31.5552 −1.38379
\(521\) 29.3759 1.28698 0.643491 0.765454i \(-0.277485\pi\)
0.643491 + 0.765454i \(0.277485\pi\)
\(522\) 5.13763 0.224868
\(523\) −2.88943 −0.126346 −0.0631730 0.998003i \(-0.520122\pi\)
−0.0631730 + 0.998003i \(0.520122\pi\)
\(524\) −66.4161 −2.90140
\(525\) −19.7329 −0.861216
\(526\) −33.7043 −1.46958
\(527\) 0.479390 0.0208825
\(528\) −70.4779 −3.06716
\(529\) −15.7686 −0.685592
\(530\) 80.5871 3.50048
\(531\) 0.909955 0.0394887
\(532\) −134.788 −5.84382
\(533\) 16.0048 0.693246
\(534\) 17.9312 0.775961
\(535\) 10.8536 0.469240
\(536\) 72.1131 3.11481
\(537\) 5.64048 0.243405
\(538\) −24.1767 −1.04233
\(539\) −42.0212 −1.80998
\(540\) −76.3685 −3.28638
\(541\) 6.22221 0.267514 0.133757 0.991014i \(-0.457296\pi\)
0.133757 + 0.991014i \(0.457296\pi\)
\(542\) −5.41862 −0.232750
\(543\) 26.8169 1.15082
\(544\) −1.82037 −0.0780479
\(545\) 17.6949 0.757968
\(546\) 25.0881 1.07367
\(547\) 35.3320 1.51069 0.755344 0.655329i \(-0.227470\pi\)
0.755344 + 0.655329i \(0.227470\pi\)
\(548\) −66.9463 −2.85980
\(549\) 5.30857 0.226564
\(550\) 34.6389 1.47701
\(551\) 29.2316 1.24531
\(552\) −32.5720 −1.38636
\(553\) −45.8317 −1.94896
\(554\) 37.0446 1.57387
\(555\) −30.7318 −1.30449
\(556\) 4.13512 0.175368
\(557\) −45.8297 −1.94187 −0.970934 0.239346i \(-0.923067\pi\)
−0.970934 + 0.239346i \(0.923067\pi\)
\(558\) 3.57536 0.151357
\(559\) −8.21395 −0.347413
\(560\) −117.222 −4.95354
\(561\) −1.10649 −0.0467162
\(562\) 19.8665 0.838018
\(563\) −15.3774 −0.648079 −0.324039 0.946044i \(-0.605041\pi\)
−0.324039 + 0.946044i \(0.605041\pi\)
\(564\) −30.2955 −1.27567
\(565\) 12.8276 0.539661
\(566\) −66.4927 −2.79490
\(567\) 30.3523 1.27468
\(568\) 18.6519 0.782618
\(569\) 38.4097 1.61022 0.805110 0.593125i \(-0.202106\pi\)
0.805110 + 0.593125i \(0.202106\pi\)
\(570\) −80.1961 −3.35905
\(571\) −23.2921 −0.974743 −0.487371 0.873195i \(-0.662044\pi\)
−0.487371 + 0.873195i \(0.662044\pi\)
\(572\) −31.2572 −1.30693
\(573\) 26.7283 1.11659
\(574\) 116.818 4.87590
\(575\) 8.14769 0.339782
\(576\) −4.40689 −0.183620
\(577\) −9.37557 −0.390310 −0.195155 0.980772i \(-0.562521\pi\)
−0.195155 + 0.980772i \(0.562521\pi\)
\(578\) 44.5591 1.85341
\(579\) −23.0304 −0.957112
\(580\) 59.9795 2.49051
\(581\) −47.4800 −1.96980
\(582\) 14.1935 0.588341
\(583\) 47.1826 1.95410
\(584\) 43.3072 1.79206
\(585\) −1.88052 −0.0777498
\(586\) 12.1008 0.499879
\(587\) 27.9399 1.15320 0.576602 0.817025i \(-0.304378\pi\)
0.576602 + 0.817025i \(0.304378\pi\)
\(588\) 75.3222 3.10624
\(589\) 20.3427 0.838208
\(590\) 14.9675 0.616203
\(591\) 19.8683 0.817271
\(592\) −68.8844 −2.83113
\(593\) −5.27502 −0.216619 −0.108310 0.994117i \(-0.534544\pi\)
−0.108310 + 0.994117i \(0.534544\pi\)
\(594\) −62.9970 −2.58480
\(595\) −1.84037 −0.0754479
\(596\) −66.6065 −2.72831
\(597\) 20.4517 0.837033
\(598\) −10.3588 −0.423603
\(599\) 30.8260 1.25952 0.629759 0.776791i \(-0.283154\pi\)
0.629759 + 0.776791i \(0.283154\pi\)
\(600\) −36.6993 −1.49824
\(601\) 4.66282 0.190200 0.0951001 0.995468i \(-0.469683\pi\)
0.0951001 + 0.995468i \(0.469683\pi\)
\(602\) −59.9531 −2.44350
\(603\) 4.29754 0.175009
\(604\) −16.2706 −0.662041
\(605\) 22.5776 0.917910
\(606\) 34.6154 1.40615
\(607\) 10.8487 0.440333 0.220167 0.975462i \(-0.429340\pi\)
0.220167 + 0.975462i \(0.429340\pi\)
\(608\) −77.2470 −3.13278
\(609\) −28.1862 −1.14216
\(610\) 87.3186 3.53543
\(611\) −5.69484 −0.230389
\(612\) −0.352049 −0.0142307
\(613\) −29.7304 −1.20080 −0.600401 0.799699i \(-0.704992\pi\)
−0.600401 + 0.799699i \(0.704992\pi\)
\(614\) −11.5340 −0.465475
\(615\) 49.3312 1.98922
\(616\) −134.849 −5.43322
\(617\) 35.3186 1.42187 0.710937 0.703256i \(-0.248271\pi\)
0.710937 + 0.703256i \(0.248271\pi\)
\(618\) −37.5538 −1.51063
\(619\) −40.6951 −1.63568 −0.817838 0.575449i \(-0.804827\pi\)
−0.817838 + 0.575449i \(0.804827\pi\)
\(620\) 41.7407 1.67635
\(621\) −14.8180 −0.594628
\(622\) −5.19976 −0.208491
\(623\) 17.4616 0.699584
\(624\) 23.7471 0.950647
\(625\) −30.9692 −1.23877
\(626\) 7.03909 0.281339
\(627\) −46.9537 −1.87515
\(628\) −67.0946 −2.67737
\(629\) −1.08147 −0.0431212
\(630\) −13.7258 −0.546848
\(631\) −11.9926 −0.477416 −0.238708 0.971091i \(-0.576724\pi\)
−0.238708 + 0.971091i \(0.576724\pi\)
\(632\) −85.2376 −3.39057
\(633\) −1.82541 −0.0725537
\(634\) −25.5222 −1.01362
\(635\) 15.7418 0.624692
\(636\) −84.5740 −3.35358
\(637\) 14.1588 0.560992
\(638\) 49.4776 1.95884
\(639\) 1.11155 0.0439724
\(640\) −7.67132 −0.303235
\(641\) −27.7186 −1.09482 −0.547410 0.836865i \(-0.684386\pi\)
−0.547410 + 0.836865i \(0.684386\pi\)
\(642\) −16.0484 −0.633381
\(643\) −31.8431 −1.25577 −0.627886 0.778306i \(-0.716079\pi\)
−0.627886 + 0.778306i \(0.716079\pi\)
\(644\) −53.6636 −2.11464
\(645\) −25.3176 −0.996879
\(646\) −2.82216 −0.111037
\(647\) 18.3307 0.720655 0.360327 0.932826i \(-0.382665\pi\)
0.360327 + 0.932826i \(0.382665\pi\)
\(648\) 56.4490 2.21753
\(649\) 8.76326 0.343988
\(650\) −11.6714 −0.457789
\(651\) −19.6153 −0.768782
\(652\) −63.2534 −2.47719
\(653\) −8.48165 −0.331912 −0.165956 0.986133i \(-0.553071\pi\)
−0.165956 + 0.986133i \(0.553071\pi\)
\(654\) −26.1643 −1.02311
\(655\) −38.4811 −1.50358
\(656\) 110.574 4.31721
\(657\) 2.58087 0.100689
\(658\) −41.5663 −1.62042
\(659\) 32.4044 1.26230 0.631149 0.775662i \(-0.282584\pi\)
0.631149 + 0.775662i \(0.282584\pi\)
\(660\) −96.3429 −3.75014
\(661\) 29.9556 1.16514 0.582569 0.812781i \(-0.302048\pi\)
0.582569 + 0.812781i \(0.302048\pi\)
\(662\) 34.5005 1.34090
\(663\) 0.372827 0.0144794
\(664\) −88.3031 −3.42683
\(665\) −78.0956 −3.02842
\(666\) −8.06580 −0.312544
\(667\) 11.6380 0.450626
\(668\) 100.596 3.89219
\(669\) −45.8039 −1.77088
\(670\) 70.6887 2.73094
\(671\) 51.1238 1.97361
\(672\) 74.4845 2.87330
\(673\) 45.7702 1.76431 0.882155 0.470959i \(-0.156092\pi\)
0.882155 + 0.470959i \(0.156092\pi\)
\(674\) 80.5513 3.10272
\(675\) −16.6956 −0.642616
\(676\) −53.0485 −2.04033
\(677\) 16.0580 0.617158 0.308579 0.951199i \(-0.400147\pi\)
0.308579 + 0.951199i \(0.400147\pi\)
\(678\) −18.9673 −0.728436
\(679\) 13.8218 0.530431
\(680\) −3.42272 −0.131255
\(681\) 39.1219 1.49915
\(682\) 34.4323 1.31848
\(683\) 13.4133 0.513245 0.256623 0.966512i \(-0.417390\pi\)
0.256623 + 0.966512i \(0.417390\pi\)
\(684\) −14.9391 −0.571210
\(685\) −38.7883 −1.48202
\(686\) 28.3683 1.08311
\(687\) −43.4550 −1.65791
\(688\) −56.7487 −2.16352
\(689\) −15.8979 −0.605663
\(690\) −31.9286 −1.21550
\(691\) 13.1438 0.500015 0.250007 0.968244i \(-0.419567\pi\)
0.250007 + 0.968244i \(0.419567\pi\)
\(692\) −85.5408 −3.25177
\(693\) −8.03625 −0.305272
\(694\) 15.7082 0.596274
\(695\) 2.39586 0.0908803
\(696\) −52.4206 −1.98700
\(697\) 1.73600 0.0657558
\(698\) 58.4469 2.21225
\(699\) −29.4724 −1.11475
\(700\) −60.4633 −2.28530
\(701\) −11.3745 −0.429609 −0.214805 0.976657i \(-0.568911\pi\)
−0.214805 + 0.976657i \(0.568911\pi\)
\(702\) 21.2265 0.801143
\(703\) −45.8920 −1.73085
\(704\) −42.4402 −1.59953
\(705\) −17.5530 −0.661085
\(706\) −3.69068 −0.138901
\(707\) 33.7087 1.26775
\(708\) −15.7080 −0.590343
\(709\) 19.3343 0.726116 0.363058 0.931767i \(-0.381733\pi\)
0.363058 + 0.931767i \(0.381733\pi\)
\(710\) 18.2835 0.686168
\(711\) −5.07969 −0.190503
\(712\) 32.4750 1.21705
\(713\) 8.09909 0.303313
\(714\) 2.72124 0.101840
\(715\) −18.1102 −0.677283
\(716\) 17.2829 0.645891
\(717\) −25.6844 −0.959200
\(718\) 46.5772 1.73824
\(719\) −9.36113 −0.349111 −0.174556 0.984647i \(-0.555849\pi\)
−0.174556 + 0.984647i \(0.555849\pi\)
\(720\) −12.9922 −0.484189
\(721\) −36.5702 −1.36194
\(722\) −69.8819 −2.60074
\(723\) 42.1887 1.56901
\(724\) 82.1692 3.05380
\(725\) 13.1127 0.486993
\(726\) −33.3840 −1.23900
\(727\) −16.7137 −0.619876 −0.309938 0.950757i \(-0.600308\pi\)
−0.309938 + 0.950757i \(0.600308\pi\)
\(728\) 45.4366 1.68399
\(729\) 29.7505 1.10187
\(730\) 42.4518 1.57121
\(731\) −0.890946 −0.0329528
\(732\) −91.6385 −3.38706
\(733\) −18.0210 −0.665621 −0.332810 0.942994i \(-0.607997\pi\)
−0.332810 + 0.942994i \(0.607997\pi\)
\(734\) 33.9312 1.25242
\(735\) 43.6412 1.60973
\(736\) −30.7545 −1.13363
\(737\) 41.3872 1.52452
\(738\) 12.9474 0.476599
\(739\) −22.0901 −0.812596 −0.406298 0.913741i \(-0.633181\pi\)
−0.406298 + 0.913741i \(0.633181\pi\)
\(740\) −94.1646 −3.46156
\(741\) 15.8208 0.581191
\(742\) −116.038 −4.25989
\(743\) 16.7001 0.612669 0.306334 0.951924i \(-0.400897\pi\)
0.306334 + 0.951924i \(0.400897\pi\)
\(744\) −36.4804 −1.33744
\(745\) −38.5914 −1.41388
\(746\) 40.3137 1.47599
\(747\) −5.26238 −0.192540
\(748\) −3.39038 −0.123965
\(749\) −15.6281 −0.571038
\(750\) 23.3919 0.854150
\(751\) 35.9062 1.31024 0.655118 0.755526i \(-0.272619\pi\)
0.655118 + 0.755526i \(0.272619\pi\)
\(752\) −39.3446 −1.43475
\(753\) −13.3469 −0.486387
\(754\) −16.6712 −0.607129
\(755\) −9.42708 −0.343086
\(756\) 109.963 3.99933
\(757\) 0.282655 0.0102733 0.00513663 0.999987i \(-0.498365\pi\)
0.00513663 + 0.999987i \(0.498365\pi\)
\(758\) 85.5939 3.10891
\(759\) −18.6938 −0.678540
\(760\) −145.242 −5.26848
\(761\) −25.6854 −0.931096 −0.465548 0.885023i \(-0.654143\pi\)
−0.465548 + 0.885023i \(0.654143\pi\)
\(762\) −23.2763 −0.843211
\(763\) −25.4791 −0.922404
\(764\) 81.8975 2.96295
\(765\) −0.203975 −0.00737473
\(766\) 52.5425 1.89844
\(767\) −2.95273 −0.106617
\(768\) −19.7657 −0.713232
\(769\) 3.89942 0.140617 0.0703083 0.997525i \(-0.477602\pi\)
0.0703083 + 0.997525i \(0.477602\pi\)
\(770\) −132.185 −4.76362
\(771\) 17.7392 0.638861
\(772\) −70.5671 −2.53977
\(773\) −22.5597 −0.811416 −0.405708 0.914003i \(-0.632975\pi\)
−0.405708 + 0.914003i \(0.632975\pi\)
\(774\) −6.64481 −0.238843
\(775\) 9.12534 0.327792
\(776\) 25.7057 0.922780
\(777\) 44.2509 1.58749
\(778\) −71.0743 −2.54814
\(779\) 73.6667 2.63938
\(780\) 32.4622 1.16233
\(781\) 10.7047 0.383046
\(782\) −1.12359 −0.0401796
\(783\) −23.8478 −0.852250
\(784\) 97.8206 3.49359
\(785\) −38.8742 −1.38748
\(786\) 56.8995 2.02954
\(787\) 6.16961 0.219923 0.109961 0.993936i \(-0.464927\pi\)
0.109961 + 0.993936i \(0.464927\pi\)
\(788\) 60.8779 2.16869
\(789\) 20.4942 0.729613
\(790\) −83.5539 −2.97271
\(791\) −18.4705 −0.656737
\(792\) −14.9458 −0.531075
\(793\) −17.2259 −0.611709
\(794\) −46.2718 −1.64212
\(795\) −49.0017 −1.73791
\(796\) 62.6657 2.22113
\(797\) −48.1768 −1.70651 −0.853254 0.521495i \(-0.825375\pi\)
−0.853254 + 0.521495i \(0.825375\pi\)
\(798\) 115.475 4.08777
\(799\) −0.617705 −0.0218528
\(800\) −34.6514 −1.22511
\(801\) 1.93533 0.0683815
\(802\) 90.1089 3.18186
\(803\) 24.8549 0.877110
\(804\) −74.1858 −2.61633
\(805\) −31.0924 −1.09586
\(806\) −11.6018 −0.408655
\(807\) 14.7008 0.517494
\(808\) 62.6913 2.20547
\(809\) −13.9473 −0.490360 −0.245180 0.969478i \(-0.578847\pi\)
−0.245180 + 0.969478i \(0.578847\pi\)
\(810\) 55.3340 1.94424
\(811\) 8.73705 0.306799 0.153400 0.988164i \(-0.450978\pi\)
0.153400 + 0.988164i \(0.450978\pi\)
\(812\) −86.3648 −3.03081
\(813\) 3.29484 0.115555
\(814\) −77.6772 −2.72258
\(815\) −36.6486 −1.28374
\(816\) 2.57579 0.0901708
\(817\) −37.8070 −1.32270
\(818\) 82.8870 2.89807
\(819\) 2.70777 0.0946171
\(820\) 151.155 5.27855
\(821\) 49.0432 1.71162 0.855810 0.517291i \(-0.173059\pi\)
0.855810 + 0.517291i \(0.173059\pi\)
\(822\) 57.3537 2.00044
\(823\) −34.1875 −1.19170 −0.595851 0.803095i \(-0.703185\pi\)
−0.595851 + 0.803095i \(0.703185\pi\)
\(824\) −68.0130 −2.36935
\(825\) −21.0625 −0.733301
\(826\) −21.5518 −0.749884
\(827\) 23.7110 0.824512 0.412256 0.911068i \(-0.364741\pi\)
0.412256 + 0.911068i \(0.364741\pi\)
\(828\) −5.94772 −0.206698
\(829\) 18.4764 0.641711 0.320856 0.947128i \(-0.396030\pi\)
0.320856 + 0.947128i \(0.396030\pi\)
\(830\) −86.5589 −3.00450
\(831\) −22.5253 −0.781393
\(832\) 14.3000 0.495763
\(833\) 1.53577 0.0532113
\(834\) −3.54261 −0.122670
\(835\) 58.2850 2.01703
\(836\) −143.870 −4.97584
\(837\) −16.5961 −0.573644
\(838\) −77.2689 −2.66921
\(839\) 16.9350 0.584662 0.292331 0.956317i \(-0.405569\pi\)
0.292331 + 0.956317i \(0.405569\pi\)
\(840\) 140.048 4.83211
\(841\) −10.2701 −0.354140
\(842\) 63.6153 2.19233
\(843\) −12.0800 −0.416057
\(844\) −5.59322 −0.192526
\(845\) −30.7360 −1.05735
\(846\) −4.60694 −0.158390
\(847\) −32.5096 −1.11704
\(848\) −109.836 −3.77178
\(849\) 40.4314 1.38760
\(850\) −1.26597 −0.0434222
\(851\) −18.2711 −0.626324
\(852\) −19.1881 −0.657372
\(853\) −28.5643 −0.978022 −0.489011 0.872278i \(-0.662642\pi\)
−0.489011 + 0.872278i \(0.662642\pi\)
\(854\) −125.731 −4.30241
\(855\) −8.65561 −0.296016
\(856\) −29.0651 −0.993424
\(857\) −5.17766 −0.176865 −0.0884327 0.996082i \(-0.528186\pi\)
−0.0884327 + 0.996082i \(0.528186\pi\)
\(858\) 26.7784 0.914199
\(859\) 35.1695 1.19997 0.599984 0.800012i \(-0.295174\pi\)
0.599984 + 0.800012i \(0.295174\pi\)
\(860\) −77.5751 −2.64529
\(861\) −71.0323 −2.42077
\(862\) 45.3632 1.54508
\(863\) −40.5264 −1.37953 −0.689767 0.724031i \(-0.742287\pi\)
−0.689767 + 0.724031i \(0.742287\pi\)
\(864\) 63.0198 2.14398
\(865\) −49.5618 −1.68515
\(866\) 26.5623 0.902625
\(867\) −27.0945 −0.920178
\(868\) −60.1027 −2.04002
\(869\) −48.9196 −1.65948
\(870\) −51.3851 −1.74212
\(871\) −13.9452 −0.472515
\(872\) −47.3858 −1.60469
\(873\) 1.53192 0.0518475
\(874\) −47.6793 −1.61278
\(875\) 22.7792 0.770077
\(876\) −44.5520 −1.50527
\(877\) −4.37086 −0.147594 −0.0737968 0.997273i \(-0.523512\pi\)
−0.0737968 + 0.997273i \(0.523512\pi\)
\(878\) 83.0961 2.80436
\(879\) −7.35798 −0.248179
\(880\) −125.120 −4.21780
\(881\) 45.5309 1.53398 0.766988 0.641662i \(-0.221755\pi\)
0.766988 + 0.641662i \(0.221755\pi\)
\(882\) 11.4540 0.385676
\(883\) 2.53469 0.0852991 0.0426496 0.999090i \(-0.486420\pi\)
0.0426496 + 0.999090i \(0.486420\pi\)
\(884\) 1.14237 0.0384221
\(885\) −9.10112 −0.305931
\(886\) 78.9271 2.65161
\(887\) −10.7805 −0.361972 −0.180986 0.983486i \(-0.557929\pi\)
−0.180986 + 0.983486i \(0.557929\pi\)
\(888\) 82.2975 2.76172
\(889\) −22.6666 −0.760215
\(890\) 31.8335 1.06706
\(891\) 32.3972 1.08535
\(892\) −140.347 −4.69916
\(893\) −26.2121 −0.877154
\(894\) 57.0626 1.90846
\(895\) 10.0136 0.334717
\(896\) 11.0460 0.369020
\(897\) 6.29876 0.210309
\(898\) −12.8459 −0.428675
\(899\) 13.0345 0.434724
\(900\) −6.70136 −0.223379
\(901\) −1.72441 −0.0574483
\(902\) 124.689 4.15168
\(903\) 36.4550 1.21314
\(904\) −34.3514 −1.14251
\(905\) 47.6083 1.58255
\(906\) 13.9392 0.463099
\(907\) 16.1217 0.535312 0.267656 0.963515i \(-0.413751\pi\)
0.267656 + 0.963515i \(0.413751\pi\)
\(908\) 119.873 3.97811
\(909\) 3.73606 0.123917
\(910\) 44.5391 1.47646
\(911\) 25.7819 0.854192 0.427096 0.904206i \(-0.359537\pi\)
0.427096 + 0.904206i \(0.359537\pi\)
\(912\) 109.303 3.61938
\(913\) −50.6790 −1.67723
\(914\) 91.2922 3.01968
\(915\) −53.0948 −1.75526
\(916\) −133.150 −4.39939
\(917\) 55.4092 1.82977
\(918\) 2.30239 0.0759901
\(919\) −13.8780 −0.457793 −0.228897 0.973451i \(-0.573512\pi\)
−0.228897 + 0.973451i \(0.573512\pi\)
\(920\) −57.8254 −1.90645
\(921\) 7.01336 0.231098
\(922\) −65.8416 −2.16838
\(923\) −3.60690 −0.118723
\(924\) 138.725 4.56371
\(925\) −20.5862 −0.676871
\(926\) 54.1347 1.77898
\(927\) −4.05320 −0.133125
\(928\) −49.4955 −1.62477
\(929\) −52.9687 −1.73785 −0.868923 0.494947i \(-0.835187\pi\)
−0.868923 + 0.494947i \(0.835187\pi\)
\(930\) −35.7598 −1.17261
\(931\) 65.1699 2.13586
\(932\) −90.3057 −2.95806
\(933\) 3.16176 0.103511
\(934\) 18.7078 0.612139
\(935\) −1.96437 −0.0642417
\(936\) 5.03590 0.164603
\(937\) −26.2562 −0.857753 −0.428877 0.903363i \(-0.641090\pi\)
−0.428877 + 0.903363i \(0.641090\pi\)
\(938\) −101.785 −3.32340
\(939\) −4.28018 −0.139678
\(940\) −53.7839 −1.75424
\(941\) 49.8404 1.62475 0.812375 0.583136i \(-0.198174\pi\)
0.812375 + 0.583136i \(0.198174\pi\)
\(942\) 57.4807 1.87282
\(943\) 29.3291 0.955086
\(944\) −20.3999 −0.663960
\(945\) 63.7122 2.07256
\(946\) −63.9924 −2.08057
\(947\) 52.4900 1.70570 0.852849 0.522158i \(-0.174873\pi\)
0.852849 + 0.522158i \(0.174873\pi\)
\(948\) 87.6875 2.84796
\(949\) −8.37472 −0.271855
\(950\) −53.7208 −1.74293
\(951\) 15.5190 0.503238
\(952\) 4.92839 0.159730
\(953\) 4.48607 0.145318 0.0726591 0.997357i \(-0.476852\pi\)
0.0726591 + 0.997357i \(0.476852\pi\)
\(954\) −12.8609 −0.416387
\(955\) 47.4509 1.53548
\(956\) −78.6990 −2.54531
\(957\) −30.0853 −0.972518
\(958\) 16.5354 0.534236
\(959\) 55.8515 1.80354
\(960\) 44.0765 1.42256
\(961\) −21.9291 −0.707390
\(962\) 26.1729 0.843848
\(963\) −1.73212 −0.0558167
\(964\) 129.270 4.16349
\(965\) −40.8861 −1.31617
\(966\) 45.9742 1.47920
\(967\) −46.6336 −1.49964 −0.749818 0.661644i \(-0.769859\pi\)
−0.749818 + 0.661644i \(0.769859\pi\)
\(968\) −60.4613 −1.94330
\(969\) 1.71604 0.0551271
\(970\) 25.1979 0.809057
\(971\) 55.6584 1.78616 0.893082 0.449894i \(-0.148538\pi\)
0.893082 + 0.449894i \(0.148538\pi\)
\(972\) 22.7787 0.730629
\(973\) −3.44982 −0.110596
\(974\) 49.9994 1.60208
\(975\) 7.09688 0.227282
\(976\) −119.011 −3.80943
\(977\) 1.60392 0.0513139 0.0256569 0.999671i \(-0.491832\pi\)
0.0256569 + 0.999671i \(0.491832\pi\)
\(978\) 54.1899 1.73280
\(979\) 18.6381 0.595675
\(980\) 133.720 4.27154
\(981\) −2.82393 −0.0901612
\(982\) 86.2670 2.75289
\(983\) 10.6627 0.340087 0.170044 0.985437i \(-0.445609\pi\)
0.170044 + 0.985437i \(0.445609\pi\)
\(984\) −132.106 −4.21137
\(985\) 35.2723 1.12387
\(986\) −1.80828 −0.0575875
\(987\) 25.2747 0.804503
\(988\) 48.4761 1.54223
\(989\) −15.0522 −0.478631
\(990\) −14.6506 −0.465625
\(991\) 12.4872 0.396669 0.198335 0.980134i \(-0.436447\pi\)
0.198335 + 0.980134i \(0.436447\pi\)
\(992\) −34.4447 −1.09362
\(993\) −20.9783 −0.665728
\(994\) −26.3266 −0.835027
\(995\) 36.3081 1.15105
\(996\) 90.8412 2.87841
\(997\) 35.5503 1.12589 0.562945 0.826494i \(-0.309668\pi\)
0.562945 + 0.826494i \(0.309668\pi\)
\(998\) −58.5163 −1.85230
\(999\) 37.4398 1.18454
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 \(a_p\))