Properties

Label 6047.2.a.a.1.16
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 1.16
Character \(\chi\) = 6047.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.47362 q^{2}\) \(-1.15677 q^{3}\) \(+4.11880 q^{4}\) \(-1.98795 q^{5}\) \(+2.86140 q^{6}\) \(+3.96077 q^{7}\) \(-5.24112 q^{8}\) \(-1.66189 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.47362 q^{2}\) \(-1.15677 q^{3}\) \(+4.11880 q^{4}\) \(-1.98795 q^{5}\) \(+2.86140 q^{6}\) \(+3.96077 q^{7}\) \(-5.24112 q^{8}\) \(-1.66189 q^{9}\) \(+4.91743 q^{10}\) \(+5.11047 q^{11}\) \(-4.76450 q^{12}\) \(-4.76182 q^{13}\) \(-9.79746 q^{14}\) \(+2.29959 q^{15}\) \(+4.72694 q^{16}\) \(+3.22229 q^{17}\) \(+4.11089 q^{18}\) \(+4.92788 q^{19}\) \(-8.18797 q^{20}\) \(-4.58169 q^{21}\) \(-12.6414 q^{22}\) \(+5.40140 q^{23}\) \(+6.06275 q^{24}\) \(-1.04807 q^{25}\) \(+11.7789 q^{26}\) \(+5.39272 q^{27}\) \(+16.3137 q^{28}\) \(-5.48142 q^{29}\) \(-5.68832 q^{30}\) \(-2.66643 q^{31}\) \(-1.21042 q^{32}\) \(-5.91163 q^{33}\) \(-7.97073 q^{34}\) \(-7.87381 q^{35}\) \(-6.84500 q^{36}\) \(-8.02900 q^{37}\) \(-12.1897 q^{38}\) \(+5.50831 q^{39}\) \(+10.4191 q^{40}\) \(-6.98765 q^{41}\) \(+11.3334 q^{42}\) \(-5.36631 q^{43}\) \(+21.0490 q^{44}\) \(+3.30375 q^{45}\) \(-13.3610 q^{46}\) \(+4.93552 q^{47}\) \(-5.46797 q^{48}\) \(+8.68773 q^{49}\) \(+2.59252 q^{50}\) \(-3.72744 q^{51}\) \(-19.6130 q^{52}\) \(+11.6038 q^{53}\) \(-13.3396 q^{54}\) \(-10.1593 q^{55}\) \(-20.7589 q^{56}\) \(-5.70041 q^{57}\) \(+13.5589 q^{58}\) \(-2.29690 q^{59}\) \(+9.47157 q^{60}\) \(+7.14940 q^{61}\) \(+6.59574 q^{62}\) \(-6.58237 q^{63}\) \(-6.45976 q^{64}\) \(+9.46624 q^{65}\) \(+14.6231 q^{66}\) \(-9.02586 q^{67}\) \(+13.2720 q^{68}\) \(-6.24817 q^{69}\) \(+19.4768 q^{70}\) \(-3.54275 q^{71}\) \(+8.71016 q^{72}\) \(-9.97676 q^{73}\) \(+19.8607 q^{74}\) \(+1.21237 q^{75}\) \(+20.2970 q^{76}\) \(+20.2414 q^{77}\) \(-13.6255 q^{78}\) \(+9.54296 q^{79}\) \(-9.39690 q^{80}\) \(-1.25246 q^{81}\) \(+17.2848 q^{82}\) \(-10.7984 q^{83}\) \(-18.8711 q^{84}\) \(-6.40575 q^{85}\) \(+13.2742 q^{86}\) \(+6.34072 q^{87}\) \(-26.7846 q^{88}\) \(-11.4905 q^{89}\) \(-8.17222 q^{90}\) \(-18.8605 q^{91}\) \(+22.2473 q^{92}\) \(+3.08444 q^{93}\) \(-12.2086 q^{94}\) \(-9.79637 q^{95}\) \(+1.40017 q^{96}\) \(-4.30261 q^{97}\) \(-21.4902 q^{98}\) \(-8.49304 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(217q \) \(\mathstrut -\mathstrut 20q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 184q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 152q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(217q \) \(\mathstrut -\mathstrut 20q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 184q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 152q^{9} \) \(\mathstrut -\mathstrut 46q^{10} \) \(\mathstrut -\mathstrut 32q^{11} \) \(\mathstrut -\mathstrut 72q^{12} \) \(\mathstrut -\mathstrut 80q^{13} \) \(\mathstrut -\mathstrut 22q^{14} \) \(\mathstrut -\mathstrut 43q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut -\mathstrut 61q^{17} \) \(\mathstrut -\mathstrut 88q^{18} \) \(\mathstrut -\mathstrut 43q^{19} \) \(\mathstrut -\mathstrut 41q^{20} \) \(\mathstrut -\mathstrut 61q^{21} \) \(\mathstrut -\mathstrut 93q^{22} \) \(\mathstrut -\mathstrut 60q^{23} \) \(\mathstrut -\mathstrut 41q^{24} \) \(\mathstrut +\mathstrut 26q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 93q^{27} \) \(\mathstrut -\mathstrut 126q^{28} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut -\mathstrut 36q^{30} \) \(\mathstrut -\mathstrut 100q^{31} \) \(\mathstrut -\mathstrut 114q^{32} \) \(\mathstrut -\mathstrut 133q^{33} \) \(\mathstrut -\mathstrut 75q^{34} \) \(\mathstrut -\mathstrut 37q^{35} \) \(\mathstrut +\mathstrut 75q^{36} \) \(\mathstrut -\mathstrut 264q^{37} \) \(\mathstrut -\mathstrut 35q^{38} \) \(\mathstrut -\mathstrut 47q^{39} \) \(\mathstrut -\mathstrut 118q^{40} \) \(\mathstrut -\mathstrut 72q^{41} \) \(\mathstrut -\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 107q^{43} \) \(\mathstrut -\mathstrut 59q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 111q^{46} \) \(\mathstrut -\mathstrut 54q^{47} \) \(\mathstrut -\mathstrut 135q^{48} \) \(\mathstrut +\mathstrut 33q^{49} \) \(\mathstrut -\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 26q^{51} \) \(\mathstrut -\mathstrut 173q^{52} \) \(\mathstrut -\mathstrut 103q^{53} \) \(\mathstrut -\mathstrut 28q^{54} \) \(\mathstrut -\mathstrut 78q^{55} \) \(\mathstrut -\mathstrut 44q^{56} \) \(\mathstrut -\mathstrut 205q^{57} \) \(\mathstrut -\mathstrut 189q^{58} \) \(\mathstrut -\mathstrut 38q^{59} \) \(\mathstrut -\mathstrut 105q^{60} \) \(\mathstrut -\mathstrut 108q^{61} \) \(\mathstrut -\mathstrut 14q^{62} \) \(\mathstrut -\mathstrut 116q^{63} \) \(\mathstrut +\mathstrut 39q^{64} \) \(\mathstrut -\mathstrut 146q^{65} \) \(\mathstrut +\mathstrut 5q^{66} \) \(\mathstrut -\mathstrut 206q^{67} \) \(\mathstrut -\mathstrut 62q^{68} \) \(\mathstrut -\mathstrut 55q^{69} \) \(\mathstrut -\mathstrut 125q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 225q^{72} \) \(\mathstrut -\mathstrut 326q^{73} \) \(\mathstrut +\mathstrut 3q^{74} \) \(\mathstrut -\mathstrut 95q^{75} \) \(\mathstrut -\mathstrut 84q^{76} \) \(\mathstrut -\mathstrut 79q^{77} \) \(\mathstrut -\mathstrut 86q^{78} \) \(\mathstrut -\mathstrut 117q^{79} \) \(\mathstrut -\mathstrut 39q^{80} \) \(\mathstrut +\mathstrut q^{81} \) \(\mathstrut -\mathstrut 96q^{82} \) \(\mathstrut -\mathstrut 23q^{83} \) \(\mathstrut -\mathstrut 57q^{84} \) \(\mathstrut -\mathstrut 224q^{85} \) \(\mathstrut -\mathstrut 7q^{86} \) \(\mathstrut -\mathstrut 45q^{87} \) \(\mathstrut -\mathstrut 250q^{88} \) \(\mathstrut -\mathstrut 104q^{89} \) \(\mathstrut -\mathstrut 36q^{90} \) \(\mathstrut -\mathstrut 96q^{91} \) \(\mathstrut -\mathstrut 137q^{92} \) \(\mathstrut -\mathstrut 155q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 447q^{97} \) \(\mathstrut -\mathstrut 46q^{98} \) \(\mathstrut -\mathstrut 94q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.47362 −1.74911 −0.874557 0.484922i \(-0.838848\pi\)
−0.874557 + 0.484922i \(0.838848\pi\)
\(3\) −1.15677 −0.667860 −0.333930 0.942598i \(-0.608375\pi\)
−0.333930 + 0.942598i \(0.608375\pi\)
\(4\) 4.11880 2.05940
\(5\) −1.98795 −0.889037 −0.444519 0.895770i \(-0.646625\pi\)
−0.444519 + 0.895770i \(0.646625\pi\)
\(6\) 2.86140 1.16816
\(7\) 3.96077 1.49703 0.748516 0.663117i \(-0.230767\pi\)
0.748516 + 0.663117i \(0.230767\pi\)
\(8\) −5.24112 −1.85302
\(9\) −1.66189 −0.553963
\(10\) 4.91743 1.55503
\(11\) 5.11047 1.54087 0.770433 0.637522i \(-0.220040\pi\)
0.770433 + 0.637522i \(0.220040\pi\)
\(12\) −4.76450 −1.37539
\(13\) −4.76182 −1.32069 −0.660345 0.750962i \(-0.729590\pi\)
−0.660345 + 0.750962i \(0.729590\pi\)
\(14\) −9.79746 −2.61848
\(15\) 2.29959 0.593752
\(16\) 4.72694 1.18173
\(17\) 3.22229 0.781520 0.390760 0.920493i \(-0.372212\pi\)
0.390760 + 0.920493i \(0.372212\pi\)
\(18\) 4.11089 0.968945
\(19\) 4.92788 1.13053 0.565267 0.824908i \(-0.308773\pi\)
0.565267 + 0.824908i \(0.308773\pi\)
\(20\) −8.18797 −1.83088
\(21\) −4.58169 −0.999808
\(22\) −12.6414 −2.69515
\(23\) 5.40140 1.12627 0.563135 0.826365i \(-0.309595\pi\)
0.563135 + 0.826365i \(0.309595\pi\)
\(24\) 6.06275 1.23755
\(25\) −1.04807 −0.209613
\(26\) 11.7789 2.31004
\(27\) 5.39272 1.03783
\(28\) 16.3137 3.08299
\(29\) −5.48142 −1.01787 −0.508937 0.860804i \(-0.669961\pi\)
−0.508937 + 0.860804i \(0.669961\pi\)
\(30\) −5.68832 −1.03854
\(31\) −2.66643 −0.478905 −0.239453 0.970908i \(-0.576968\pi\)
−0.239453 + 0.970908i \(0.576968\pi\)
\(32\) −1.21042 −0.213973
\(33\) −5.91163 −1.02908
\(34\) −7.97073 −1.36697
\(35\) −7.87381 −1.33092
\(36\) −6.84500 −1.14083
\(37\) −8.02900 −1.31996 −0.659980 0.751283i \(-0.729435\pi\)
−0.659980 + 0.751283i \(0.729435\pi\)
\(38\) −12.1897 −1.97743
\(39\) 5.50831 0.882036
\(40\) 10.4191 1.64740
\(41\) −6.98765 −1.09129 −0.545644 0.838017i \(-0.683715\pi\)
−0.545644 + 0.838017i \(0.683715\pi\)
\(42\) 11.3334 1.74878
\(43\) −5.36631 −0.818355 −0.409178 0.912455i \(-0.634184\pi\)
−0.409178 + 0.912455i \(0.634184\pi\)
\(44\) 21.0490 3.17326
\(45\) 3.30375 0.492494
\(46\) −13.3610 −1.96998
\(47\) 4.93552 0.719920 0.359960 0.932968i \(-0.382790\pi\)
0.359960 + 0.932968i \(0.382790\pi\)
\(48\) −5.46797 −0.789233
\(49\) 8.68773 1.24110
\(50\) 2.59252 0.366637
\(51\) −3.72744 −0.521946
\(52\) −19.6130 −2.71983
\(53\) 11.6038 1.59390 0.796949 0.604046i \(-0.206446\pi\)
0.796949 + 0.604046i \(0.206446\pi\)
\(54\) −13.3396 −1.81528
\(55\) −10.1593 −1.36989
\(56\) −20.7589 −2.77402
\(57\) −5.70041 −0.755038
\(58\) 13.5589 1.78038
\(59\) −2.29690 −0.299032 −0.149516 0.988759i \(-0.547771\pi\)
−0.149516 + 0.988759i \(0.547771\pi\)
\(60\) 9.47157 1.22277
\(61\) 7.14940 0.915386 0.457693 0.889110i \(-0.348676\pi\)
0.457693 + 0.889110i \(0.348676\pi\)
\(62\) 6.59574 0.837660
\(63\) −6.58237 −0.829301
\(64\) −6.45976 −0.807470
\(65\) 9.46624 1.17414
\(66\) 14.6231 1.79998
\(67\) −9.02586 −1.10268 −0.551342 0.834279i \(-0.685884\pi\)
−0.551342 + 0.834279i \(0.685884\pi\)
\(68\) 13.2720 1.60946
\(69\) −6.24817 −0.752191
\(70\) 19.4768 2.32793
\(71\) −3.54275 −0.420447 −0.210224 0.977653i \(-0.567419\pi\)
−0.210224 + 0.977653i \(0.567419\pi\)
\(72\) 8.71016 1.02650
\(73\) −9.97676 −1.16769 −0.583846 0.811864i \(-0.698453\pi\)
−0.583846 + 0.811864i \(0.698453\pi\)
\(74\) 19.8607 2.30876
\(75\) 1.21237 0.139992
\(76\) 20.2970 2.32822
\(77\) 20.2414 2.30672
\(78\) −13.6255 −1.54278
\(79\) 9.54296 1.07367 0.536834 0.843688i \(-0.319620\pi\)
0.536834 + 0.843688i \(0.319620\pi\)
\(80\) −9.39690 −1.05061
\(81\) −1.25246 −0.139162
\(82\) 17.2848 1.90879
\(83\) −10.7984 −1.18528 −0.592638 0.805469i \(-0.701914\pi\)
−0.592638 + 0.805469i \(0.701914\pi\)
\(84\) −18.8711 −2.05901
\(85\) −6.40575 −0.694801
\(86\) 13.2742 1.43140
\(87\) 6.34072 0.679797
\(88\) −26.7846 −2.85525
\(89\) −11.4905 −1.21799 −0.608997 0.793172i \(-0.708428\pi\)
−0.608997 + 0.793172i \(0.708428\pi\)
\(90\) −8.17222 −0.861428
\(91\) −18.8605 −1.97712
\(92\) 22.2473 2.31944
\(93\) 3.08444 0.319842
\(94\) −12.2086 −1.25922
\(95\) −9.79637 −1.00509
\(96\) 1.40017 0.142904
\(97\) −4.30261 −0.436864 −0.218432 0.975852i \(-0.570094\pi\)
−0.218432 + 0.975852i \(0.570094\pi\)
\(98\) −21.4902 −2.17083
\(99\) −8.49304 −0.853582
\(100\) −4.31678 −0.431678
\(101\) 2.68605 0.267272 0.133636 0.991030i \(-0.457335\pi\)
0.133636 + 0.991030i \(0.457335\pi\)
\(102\) 9.22028 0.912944
\(103\) −11.7528 −1.15804 −0.579021 0.815313i \(-0.696565\pi\)
−0.579021 + 0.815313i \(0.696565\pi\)
\(104\) 24.9572 2.44726
\(105\) 9.10817 0.888866
\(106\) −28.7033 −2.78791
\(107\) −1.59645 −0.154334 −0.0771672 0.997018i \(-0.524588\pi\)
−0.0771672 + 0.997018i \(0.524588\pi\)
\(108\) 22.2116 2.13731
\(109\) −9.81328 −0.939942 −0.469971 0.882682i \(-0.655736\pi\)
−0.469971 + 0.882682i \(0.655736\pi\)
\(110\) 25.1304 2.39609
\(111\) 9.28769 0.881548
\(112\) 18.7223 1.76909
\(113\) 0.277458 0.0261011 0.0130505 0.999915i \(-0.495846\pi\)
0.0130505 + 0.999915i \(0.495846\pi\)
\(114\) 14.1007 1.32065
\(115\) −10.7377 −1.00130
\(116\) −22.5769 −2.09621
\(117\) 7.91361 0.731614
\(118\) 5.68167 0.523040
\(119\) 12.7628 1.16996
\(120\) −12.0524 −1.10023
\(121\) 15.1169 1.37427
\(122\) −17.6849 −1.60112
\(123\) 8.08308 0.728827
\(124\) −10.9825 −0.986258
\(125\) 12.0232 1.07539
\(126\) 16.2823 1.45054
\(127\) −18.4767 −1.63955 −0.819773 0.572688i \(-0.805901\pi\)
−0.819773 + 0.572688i \(0.805901\pi\)
\(128\) 18.3998 1.62633
\(129\) 6.20758 0.546547
\(130\) −23.4159 −2.05371
\(131\) 5.83726 0.510004 0.255002 0.966941i \(-0.417924\pi\)
0.255002 + 0.966941i \(0.417924\pi\)
\(132\) −24.3488 −2.11929
\(133\) 19.5182 1.69244
\(134\) 22.3266 1.92872
\(135\) −10.7204 −0.922669
\(136\) −16.8884 −1.44817
\(137\) −7.26903 −0.621035 −0.310517 0.950568i \(-0.600502\pi\)
−0.310517 + 0.950568i \(0.600502\pi\)
\(138\) 15.4556 1.31567
\(139\) 7.12864 0.604643 0.302322 0.953206i \(-0.402238\pi\)
0.302322 + 0.953206i \(0.402238\pi\)
\(140\) −32.4307 −2.74089
\(141\) −5.70925 −0.480806
\(142\) 8.76343 0.735410
\(143\) −24.3351 −2.03501
\(144\) −7.85565 −0.654637
\(145\) 10.8968 0.904927
\(146\) 24.6787 2.04243
\(147\) −10.0497 −0.828884
\(148\) −33.0699 −2.71833
\(149\) −1.57696 −0.129190 −0.0645950 0.997912i \(-0.520576\pi\)
−0.0645950 + 0.997912i \(0.520576\pi\)
\(150\) −2.99894 −0.244862
\(151\) −11.6876 −0.951126 −0.475563 0.879682i \(-0.657756\pi\)
−0.475563 + 0.879682i \(0.657756\pi\)
\(152\) −25.8276 −2.09490
\(153\) −5.35509 −0.432934
\(154\) −50.0696 −4.03473
\(155\) 5.30072 0.425764
\(156\) 22.6877 1.81647
\(157\) −10.6097 −0.846749 −0.423375 0.905955i \(-0.639155\pi\)
−0.423375 + 0.905955i \(0.639155\pi\)
\(158\) −23.6057 −1.87797
\(159\) −13.4228 −1.06450
\(160\) 2.40624 0.190230
\(161\) 21.3937 1.68606
\(162\) 3.09810 0.243410
\(163\) −0.248571 −0.0194696 −0.00973479 0.999953i \(-0.503099\pi\)
−0.00973479 + 0.999953i \(0.503099\pi\)
\(164\) −28.7808 −2.24740
\(165\) 11.7520 0.914892
\(166\) 26.7111 2.07318
\(167\) 12.6222 0.976736 0.488368 0.872638i \(-0.337592\pi\)
0.488368 + 0.872638i \(0.337592\pi\)
\(168\) 24.0132 1.85266
\(169\) 9.67490 0.744223
\(170\) 15.8454 1.21529
\(171\) −8.18959 −0.626274
\(172\) −22.1028 −1.68532
\(173\) −5.22401 −0.397174 −0.198587 0.980083i \(-0.563635\pi\)
−0.198587 + 0.980083i \(0.563635\pi\)
\(174\) −15.6845 −1.18904
\(175\) −4.15115 −0.313797
\(176\) 24.1569 1.82089
\(177\) 2.65698 0.199711
\(178\) 28.4232 2.13041
\(179\) 14.7585 1.10310 0.551552 0.834140i \(-0.314036\pi\)
0.551552 + 0.834140i \(0.314036\pi\)
\(180\) 13.6075 1.01424
\(181\) −4.26428 −0.316961 −0.158481 0.987362i \(-0.550660\pi\)
−0.158481 + 0.987362i \(0.550660\pi\)
\(182\) 46.6537 3.45820
\(183\) −8.27019 −0.611350
\(184\) −28.3094 −2.08700
\(185\) 15.9612 1.17349
\(186\) −7.62974 −0.559440
\(187\) 16.4674 1.20422
\(188\) 20.3285 1.48261
\(189\) 21.3594 1.55366
\(190\) 24.2325 1.75801
\(191\) −15.8224 −1.14487 −0.572436 0.819949i \(-0.694002\pi\)
−0.572436 + 0.819949i \(0.694002\pi\)
\(192\) 7.47244 0.539277
\(193\) 17.1175 1.23214 0.616071 0.787690i \(-0.288723\pi\)
0.616071 + 0.787690i \(0.288723\pi\)
\(194\) 10.6430 0.764126
\(195\) −10.9502 −0.784163
\(196\) 35.7831 2.55593
\(197\) 0.357470 0.0254687 0.0127343 0.999919i \(-0.495946\pi\)
0.0127343 + 0.999919i \(0.495946\pi\)
\(198\) 21.0086 1.49301
\(199\) 3.01864 0.213986 0.106993 0.994260i \(-0.465878\pi\)
0.106993 + 0.994260i \(0.465878\pi\)
\(200\) 5.49304 0.388416
\(201\) 10.4408 0.736439
\(202\) −6.64428 −0.467490
\(203\) −21.7106 −1.52379
\(204\) −15.3526 −1.07490
\(205\) 13.8911 0.970195
\(206\) 29.0721 2.02555
\(207\) −8.97654 −0.623912
\(208\) −22.5088 −1.56071
\(209\) 25.1838 1.74200
\(210\) −22.5302 −1.55473
\(211\) 28.6777 1.97426 0.987128 0.159931i \(-0.0511270\pi\)
0.987128 + 0.159931i \(0.0511270\pi\)
\(212\) 47.7936 3.28248
\(213\) 4.09814 0.280800
\(214\) 3.94901 0.269948
\(215\) 10.6679 0.727548
\(216\) −28.2639 −1.92311
\(217\) −10.5611 −0.716936
\(218\) 24.2743 1.64407
\(219\) 11.5408 0.779855
\(220\) −41.8444 −2.82115
\(221\) −15.3440 −1.03215
\(222\) −22.9742 −1.54193
\(223\) −3.57398 −0.239331 −0.119666 0.992814i \(-0.538182\pi\)
−0.119666 + 0.992814i \(0.538182\pi\)
\(224\) −4.79419 −0.320325
\(225\) 1.74177 0.116118
\(226\) −0.686327 −0.0456538
\(227\) 0.972324 0.0645354 0.0322677 0.999479i \(-0.489727\pi\)
0.0322677 + 0.999479i \(0.489727\pi\)
\(228\) −23.4789 −1.55493
\(229\) 17.0130 1.12425 0.562125 0.827052i \(-0.309984\pi\)
0.562125 + 0.827052i \(0.309984\pi\)
\(230\) 26.5610 1.75138
\(231\) −23.4146 −1.54057
\(232\) 28.7287 1.88613
\(233\) 28.0964 1.84066 0.920330 0.391143i \(-0.127920\pi\)
0.920330 + 0.391143i \(0.127920\pi\)
\(234\) −19.5753 −1.27968
\(235\) −9.81156 −0.640036
\(236\) −9.46050 −0.615826
\(237\) −11.0390 −0.717059
\(238\) −31.5703 −2.04640
\(239\) 18.0406 1.16695 0.583475 0.812131i \(-0.301693\pi\)
0.583475 + 0.812131i \(0.301693\pi\)
\(240\) 10.8700 0.701657
\(241\) −19.2249 −1.23839 −0.619193 0.785239i \(-0.712540\pi\)
−0.619193 + 0.785239i \(0.712540\pi\)
\(242\) −37.3935 −2.40375
\(243\) −14.7294 −0.944889
\(244\) 29.4470 1.88515
\(245\) −17.2708 −1.10339
\(246\) −19.9945 −1.27480
\(247\) −23.4657 −1.49308
\(248\) 13.9751 0.887419
\(249\) 12.4912 0.791599
\(250\) −29.7409 −1.88098
\(251\) 19.9196 1.25731 0.628656 0.777684i \(-0.283605\pi\)
0.628656 + 0.777684i \(0.283605\pi\)
\(252\) −27.1115 −1.70786
\(253\) 27.6037 1.73543
\(254\) 45.7045 2.86775
\(255\) 7.40996 0.464029
\(256\) −32.5947 −2.03717
\(257\) −10.3923 −0.648255 −0.324127 0.946013i \(-0.605071\pi\)
−0.324127 + 0.946013i \(0.605071\pi\)
\(258\) −15.3552 −0.955973
\(259\) −31.8011 −1.97602
\(260\) 38.9896 2.41803
\(261\) 9.10951 0.563864
\(262\) −14.4392 −0.892055
\(263\) −23.3307 −1.43863 −0.719315 0.694684i \(-0.755544\pi\)
−0.719315 + 0.694684i \(0.755544\pi\)
\(264\) 30.9835 1.90690
\(265\) −23.0677 −1.41703
\(266\) −48.2807 −2.96028
\(267\) 13.2919 0.813450
\(268\) −37.1757 −2.27087
\(269\) 23.6402 1.44137 0.720686 0.693262i \(-0.243827\pi\)
0.720686 + 0.693262i \(0.243827\pi\)
\(270\) 26.5183 1.61385
\(271\) 20.7607 1.26113 0.630563 0.776138i \(-0.282824\pi\)
0.630563 + 0.776138i \(0.282824\pi\)
\(272\) 15.2316 0.923550
\(273\) 21.8172 1.32044
\(274\) 17.9808 1.08626
\(275\) −5.35611 −0.322985
\(276\) −25.7350 −1.54906
\(277\) 6.03974 0.362893 0.181446 0.983401i \(-0.441922\pi\)
0.181446 + 0.983401i \(0.441922\pi\)
\(278\) −17.6336 −1.05759
\(279\) 4.43131 0.265296
\(280\) 41.2676 2.46621
\(281\) −29.1943 −1.74158 −0.870792 0.491652i \(-0.836393\pi\)
−0.870792 + 0.491652i \(0.836393\pi\)
\(282\) 14.1225 0.840985
\(283\) −5.39130 −0.320479 −0.160240 0.987078i \(-0.551227\pi\)
−0.160240 + 0.987078i \(0.551227\pi\)
\(284\) −14.5919 −0.865870
\(285\) 11.3321 0.671257
\(286\) 60.1959 3.55946
\(287\) −27.6765 −1.63369
\(288\) 2.01158 0.118533
\(289\) −6.61684 −0.389226
\(290\) −26.9545 −1.58282
\(291\) 4.97712 0.291764
\(292\) −41.0923 −2.40475
\(293\) 8.51179 0.497264 0.248632 0.968598i \(-0.420019\pi\)
0.248632 + 0.968598i \(0.420019\pi\)
\(294\) 24.8591 1.44981
\(295\) 4.56613 0.265850
\(296\) 42.0809 2.44591
\(297\) 27.5593 1.59916
\(298\) 3.90081 0.225968
\(299\) −25.7205 −1.48745
\(300\) 4.99350 0.288300
\(301\) −21.2548 −1.22510
\(302\) 28.9108 1.66363
\(303\) −3.10714 −0.178501
\(304\) 23.2938 1.33599
\(305\) −14.2126 −0.813812
\(306\) 13.2465 0.757250
\(307\) −1.74243 −0.0994456 −0.0497228 0.998763i \(-0.515834\pi\)
−0.0497228 + 0.998763i \(0.515834\pi\)
\(308\) 83.3705 4.75047
\(309\) 13.5953 0.773410
\(310\) −13.1120 −0.744711
\(311\) −4.16702 −0.236290 −0.118145 0.992996i \(-0.537695\pi\)
−0.118145 + 0.992996i \(0.537695\pi\)
\(312\) −28.8697 −1.63443
\(313\) −0.511143 −0.0288915 −0.0144457 0.999896i \(-0.504598\pi\)
−0.0144457 + 0.999896i \(0.504598\pi\)
\(314\) 26.2445 1.48106
\(315\) 13.0854 0.737279
\(316\) 39.3056 2.21111
\(317\) −15.0285 −0.844083 −0.422041 0.906577i \(-0.638686\pi\)
−0.422041 + 0.906577i \(0.638686\pi\)
\(318\) 33.2030 1.86193
\(319\) −28.0126 −1.56841
\(320\) 12.8417 0.717871
\(321\) 1.84672 0.103074
\(322\) −52.9200 −2.94912
\(323\) 15.8791 0.883535
\(324\) −5.15862 −0.286590
\(325\) 4.99070 0.276834
\(326\) 0.614870 0.0340545
\(327\) 11.3517 0.627750
\(328\) 36.6231 2.02217
\(329\) 19.5485 1.07774
\(330\) −29.0700 −1.60025
\(331\) −1.74647 −0.0959945 −0.0479973 0.998847i \(-0.515284\pi\)
−0.0479973 + 0.998847i \(0.515284\pi\)
\(332\) −44.4764 −2.44096
\(333\) 13.3433 0.731209
\(334\) −31.2226 −1.70842
\(335\) 17.9429 0.980327
\(336\) −21.6574 −1.18151
\(337\) −0.479629 −0.0261270 −0.0130635 0.999915i \(-0.504158\pi\)
−0.0130635 + 0.999915i \(0.504158\pi\)
\(338\) −23.9320 −1.30173
\(339\) −0.320955 −0.0174319
\(340\) −26.3840 −1.43087
\(341\) −13.6267 −0.737928
\(342\) 20.2580 1.09542
\(343\) 6.68473 0.360942
\(344\) 28.1255 1.51642
\(345\) 12.4210 0.668726
\(346\) 12.9222 0.694703
\(347\) −22.9963 −1.23450 −0.617252 0.786765i \(-0.711754\pi\)
−0.617252 + 0.786765i \(0.711754\pi\)
\(348\) 26.1162 1.39997
\(349\) 2.11195 0.113050 0.0565251 0.998401i \(-0.481998\pi\)
0.0565251 + 0.998401i \(0.481998\pi\)
\(350\) 10.2684 0.548868
\(351\) −25.6791 −1.37065
\(352\) −6.18580 −0.329704
\(353\) 14.5534 0.774597 0.387298 0.921954i \(-0.373408\pi\)
0.387298 + 0.921954i \(0.373408\pi\)
\(354\) −6.57237 −0.349318
\(355\) 7.04280 0.373793
\(356\) −47.3273 −2.50834
\(357\) −14.7636 −0.781370
\(358\) −36.5070 −1.92946
\(359\) −9.26449 −0.488961 −0.244481 0.969654i \(-0.578617\pi\)
−0.244481 + 0.969654i \(0.578617\pi\)
\(360\) −17.3153 −0.912599
\(361\) 5.28401 0.278106
\(362\) 10.5482 0.554401
\(363\) −17.4868 −0.917817
\(364\) −77.6826 −4.07168
\(365\) 19.8333 1.03812
\(366\) 20.4573 1.06932
\(367\) −30.4579 −1.58989 −0.794943 0.606683i \(-0.792500\pi\)
−0.794943 + 0.606683i \(0.792500\pi\)
\(368\) 25.5321 1.33095
\(369\) 11.6127 0.604533
\(370\) −39.4820 −2.05257
\(371\) 45.9599 2.38612
\(372\) 12.7042 0.658682
\(373\) 30.0149 1.55411 0.777057 0.629430i \(-0.216711\pi\)
0.777057 + 0.629430i \(0.216711\pi\)
\(374\) −40.7342 −2.10631
\(375\) −13.9081 −0.718210
\(376\) −25.8677 −1.33402
\(377\) 26.1015 1.34430
\(378\) −52.8350 −2.71754
\(379\) 35.9517 1.84671 0.923356 0.383944i \(-0.125434\pi\)
0.923356 + 0.383944i \(0.125434\pi\)
\(380\) −40.3493 −2.06988
\(381\) 21.3733 1.09499
\(382\) 39.1388 2.00251
\(383\) −18.3720 −0.938763 −0.469382 0.882995i \(-0.655523\pi\)
−0.469382 + 0.882995i \(0.655523\pi\)
\(384\) −21.2843 −1.08616
\(385\) −40.2389 −2.05076
\(386\) −42.3422 −2.15516
\(387\) 8.91822 0.453339
\(388\) −17.7216 −0.899679
\(389\) 18.4284 0.934359 0.467179 0.884163i \(-0.345270\pi\)
0.467179 + 0.884163i \(0.345270\pi\)
\(390\) 27.0867 1.37159
\(391\) 17.4049 0.880203
\(392\) −45.5334 −2.29979
\(393\) −6.75235 −0.340611
\(394\) −0.884245 −0.0445476
\(395\) −18.9709 −0.954530
\(396\) −34.9812 −1.75787
\(397\) −30.4121 −1.52634 −0.763170 0.646197i \(-0.776358\pi\)
−0.763170 + 0.646197i \(0.776358\pi\)
\(398\) −7.46698 −0.374286
\(399\) −22.5780 −1.13032
\(400\) −4.95414 −0.247707
\(401\) −0.850211 −0.0424575 −0.0212288 0.999775i \(-0.506758\pi\)
−0.0212288 + 0.999775i \(0.506758\pi\)
\(402\) −25.8266 −1.28812
\(403\) 12.6971 0.632485
\(404\) 11.0633 0.550421
\(405\) 2.48981 0.123720
\(406\) 53.7039 2.66528
\(407\) −41.0320 −2.03388
\(408\) 19.5360 0.967174
\(409\) 13.6394 0.674426 0.337213 0.941428i \(-0.390516\pi\)
0.337213 + 0.941428i \(0.390516\pi\)
\(410\) −34.3613 −1.69698
\(411\) 8.40857 0.414764
\(412\) −48.4076 −2.38487
\(413\) −9.09752 −0.447660
\(414\) 22.2046 1.09129
\(415\) 21.4666 1.05375
\(416\) 5.76378 0.282593
\(417\) −8.24618 −0.403817
\(418\) −62.2952 −3.04696
\(419\) 23.7321 1.15939 0.579694 0.814834i \(-0.303172\pi\)
0.579694 + 0.814834i \(0.303172\pi\)
\(420\) 37.5148 1.83053
\(421\) −16.1972 −0.789403 −0.394702 0.918809i \(-0.629152\pi\)
−0.394702 + 0.918809i \(0.629152\pi\)
\(422\) −70.9379 −3.45320
\(423\) −8.20230 −0.398809
\(424\) −60.8167 −2.95352
\(425\) −3.37717 −0.163817
\(426\) −10.1372 −0.491151
\(427\) 28.3171 1.37036
\(428\) −6.57545 −0.317836
\(429\) 28.1501 1.35910
\(430\) −26.3885 −1.27256
\(431\) 1.80172 0.0867857 0.0433928 0.999058i \(-0.486183\pi\)
0.0433928 + 0.999058i \(0.486183\pi\)
\(432\) 25.4911 1.22644
\(433\) −4.90168 −0.235560 −0.117780 0.993040i \(-0.537578\pi\)
−0.117780 + 0.993040i \(0.537578\pi\)
\(434\) 26.1242 1.25400
\(435\) −12.6050 −0.604365
\(436\) −40.4190 −1.93572
\(437\) 26.6175 1.27329
\(438\) −28.5476 −1.36406
\(439\) −39.5364 −1.88697 −0.943484 0.331417i \(-0.892473\pi\)
−0.943484 + 0.331417i \(0.892473\pi\)
\(440\) 53.2463 2.53842
\(441\) −14.4381 −0.687526
\(442\) 37.9552 1.80534
\(443\) −39.1295 −1.85910 −0.929550 0.368696i \(-0.879804\pi\)
−0.929550 + 0.368696i \(0.879804\pi\)
\(444\) 38.2542 1.81546
\(445\) 22.8426 1.08284
\(446\) 8.84067 0.418618
\(447\) 1.82418 0.0862808
\(448\) −25.5857 −1.20881
\(449\) −9.16876 −0.432701 −0.216350 0.976316i \(-0.569415\pi\)
−0.216350 + 0.976316i \(0.569415\pi\)
\(450\) −4.30848 −0.203104
\(451\) −35.7102 −1.68153
\(452\) 1.14280 0.0537526
\(453\) 13.5199 0.635219
\(454\) −2.40516 −0.112880
\(455\) 37.4936 1.75773
\(456\) 29.8765 1.39910
\(457\) 0.884269 0.0413644 0.0206822 0.999786i \(-0.493416\pi\)
0.0206822 + 0.999786i \(0.493416\pi\)
\(458\) −42.0837 −1.96644
\(459\) 17.3769 0.811085
\(460\) −44.2265 −2.06207
\(461\) −36.1534 −1.68383 −0.841915 0.539610i \(-0.818572\pi\)
−0.841915 + 0.539610i \(0.818572\pi\)
\(462\) 57.9189 2.69463
\(463\) −30.7944 −1.43114 −0.715569 0.698542i \(-0.753832\pi\)
−0.715569 + 0.698542i \(0.753832\pi\)
\(464\) −25.9103 −1.20286
\(465\) −6.13170 −0.284351
\(466\) −69.5000 −3.21952
\(467\) 36.0502 1.66821 0.834103 0.551609i \(-0.185986\pi\)
0.834103 + 0.551609i \(0.185986\pi\)
\(468\) 32.5946 1.50669
\(469\) −35.7494 −1.65075
\(470\) 24.2701 1.11950
\(471\) 12.2730 0.565510
\(472\) 12.0384 0.554110
\(473\) −27.4244 −1.26097
\(474\) 27.3063 1.25422
\(475\) −5.16474 −0.236975
\(476\) 52.5673 2.40942
\(477\) −19.2842 −0.882961
\(478\) −44.6256 −2.04113
\(479\) 24.4073 1.11520 0.557599 0.830110i \(-0.311723\pi\)
0.557599 + 0.830110i \(0.311723\pi\)
\(480\) −2.78346 −0.127047
\(481\) 38.2326 1.74326
\(482\) 47.5552 2.16608
\(483\) −24.7476 −1.12605
\(484\) 62.2636 2.83016
\(485\) 8.55337 0.388389
\(486\) 36.4349 1.65272
\(487\) −0.951975 −0.0431381 −0.0215690 0.999767i \(-0.506866\pi\)
−0.0215690 + 0.999767i \(0.506866\pi\)
\(488\) −37.4708 −1.69622
\(489\) 0.287539 0.0130029
\(490\) 42.7213 1.92995
\(491\) −24.2740 −1.09547 −0.547734 0.836652i \(-0.684510\pi\)
−0.547734 + 0.836652i \(0.684510\pi\)
\(492\) 33.2926 1.50095
\(493\) −17.6627 −0.795489
\(494\) 58.0452 2.61158
\(495\) 16.8837 0.758866
\(496\) −12.6041 −0.565939
\(497\) −14.0320 −0.629423
\(498\) −30.8985 −1.38460
\(499\) 34.7282 1.55465 0.777323 0.629101i \(-0.216577\pi\)
0.777323 + 0.629101i \(0.216577\pi\)
\(500\) 49.5213 2.21466
\(501\) −14.6010 −0.652323
\(502\) −49.2735 −2.19918
\(503\) 3.32544 0.148274 0.0741371 0.997248i \(-0.476380\pi\)
0.0741371 + 0.997248i \(0.476380\pi\)
\(504\) 34.4990 1.53671
\(505\) −5.33974 −0.237615
\(506\) −68.2811 −3.03547
\(507\) −11.1916 −0.497037
\(508\) −76.1021 −3.37648
\(509\) 23.4919 1.04126 0.520630 0.853782i \(-0.325697\pi\)
0.520630 + 0.853782i \(0.325697\pi\)
\(510\) −18.3294 −0.811641
\(511\) −39.5157 −1.74807
\(512\) 43.8273 1.93691
\(513\) 26.5747 1.17330
\(514\) 25.7067 1.13387
\(515\) 23.3640 1.02954
\(516\) 25.5678 1.12556
\(517\) 25.2229 1.10930
\(518\) 78.6638 3.45629
\(519\) 6.04296 0.265257
\(520\) −49.6137 −2.17570
\(521\) 12.4943 0.547387 0.273693 0.961817i \(-0.411755\pi\)
0.273693 + 0.961817i \(0.411755\pi\)
\(522\) −22.5335 −0.986263
\(523\) −23.5277 −1.02879 −0.514396 0.857552i \(-0.671984\pi\)
−0.514396 + 0.857552i \(0.671984\pi\)
\(524\) 24.0425 1.05030
\(525\) 4.80192 0.209573
\(526\) 57.7112 2.51633
\(527\) −8.59202 −0.374274
\(528\) −27.9439 −1.21610
\(529\) 6.17516 0.268485
\(530\) 57.0607 2.47856
\(531\) 3.81720 0.165652
\(532\) 80.3917 3.48542
\(533\) 33.2739 1.44125
\(534\) −32.8791 −1.42282
\(535\) 3.17365 0.137209
\(536\) 47.3056 2.04329
\(537\) −17.0722 −0.736719
\(538\) −58.4770 −2.52112
\(539\) 44.3984 1.91238
\(540\) −44.1554 −1.90015
\(541\) −5.46465 −0.234944 −0.117472 0.993076i \(-0.537479\pi\)
−0.117472 + 0.993076i \(0.537479\pi\)
\(542\) −51.3542 −2.20585
\(543\) 4.93277 0.211686
\(544\) −3.90031 −0.167225
\(545\) 19.5083 0.835643
\(546\) −53.9675 −2.30959
\(547\) −36.5765 −1.56390 −0.781949 0.623343i \(-0.785774\pi\)
−0.781949 + 0.623343i \(0.785774\pi\)
\(548\) −29.9397 −1.27896
\(549\) −11.8815 −0.507090
\(550\) 13.2490 0.564939
\(551\) −27.0118 −1.15074
\(552\) 32.7474 1.39382
\(553\) 37.7975 1.60731
\(554\) −14.9400 −0.634741
\(555\) −18.4634 −0.783729
\(556\) 29.3615 1.24520
\(557\) 17.1346 0.726017 0.363009 0.931786i \(-0.381750\pi\)
0.363009 + 0.931786i \(0.381750\pi\)
\(558\) −10.9614 −0.464033
\(559\) 25.5534 1.08079
\(560\) −37.2190 −1.57279
\(561\) −19.0490 −0.804249
\(562\) 72.2156 3.04623
\(563\) −9.36361 −0.394629 −0.197315 0.980340i \(-0.563222\pi\)
−0.197315 + 0.980340i \(0.563222\pi\)
\(564\) −23.5153 −0.990173
\(565\) −0.551572 −0.0232048
\(566\) 13.3360 0.560555
\(567\) −4.96069 −0.208329
\(568\) 18.5680 0.779095
\(569\) −12.7583 −0.534856 −0.267428 0.963578i \(-0.586174\pi\)
−0.267428 + 0.963578i \(0.586174\pi\)
\(570\) −28.0314 −1.17411
\(571\) 0.642131 0.0268723 0.0134362 0.999910i \(-0.495723\pi\)
0.0134362 + 0.999910i \(0.495723\pi\)
\(572\) −100.232 −4.19089
\(573\) 18.3029 0.764614
\(574\) 68.4612 2.85751
\(575\) −5.66102 −0.236081
\(576\) 10.7354 0.447309
\(577\) 8.71278 0.362718 0.181359 0.983417i \(-0.441950\pi\)
0.181359 + 0.983417i \(0.441950\pi\)
\(578\) 16.3676 0.680801
\(579\) −19.8009 −0.822899
\(580\) 44.8816 1.86361
\(581\) −42.7700 −1.77440
\(582\) −12.3115 −0.510329
\(583\) 59.3007 2.45598
\(584\) 52.2894 2.16375
\(585\) −15.7318 −0.650432
\(586\) −21.0550 −0.869772
\(587\) −42.6579 −1.76068 −0.880341 0.474342i \(-0.842686\pi\)
−0.880341 + 0.474342i \(0.842686\pi\)
\(588\) −41.3927 −1.70701
\(589\) −13.1399 −0.541418
\(590\) −11.2949 −0.465002
\(591\) −0.413509 −0.0170095
\(592\) −37.9526 −1.55984
\(593\) 27.0832 1.11217 0.556087 0.831124i \(-0.312302\pi\)
0.556087 + 0.831124i \(0.312302\pi\)
\(594\) −68.1714 −2.79711
\(595\) −25.3717 −1.04014
\(596\) −6.49520 −0.266054
\(597\) −3.49187 −0.142913
\(598\) 63.6228 2.60173
\(599\) 23.5621 0.962720 0.481360 0.876523i \(-0.340143\pi\)
0.481360 + 0.876523i \(0.340143\pi\)
\(600\) −6.35416 −0.259408
\(601\) −28.4361 −1.15993 −0.579966 0.814641i \(-0.696934\pi\)
−0.579966 + 0.814641i \(0.696934\pi\)
\(602\) 52.5762 2.14285
\(603\) 15.0000 0.610846
\(604\) −48.1390 −1.95875
\(605\) −30.0516 −1.22177
\(606\) 7.68589 0.312218
\(607\) −7.54000 −0.306039 −0.153020 0.988223i \(-0.548900\pi\)
−0.153020 + 0.988223i \(0.548900\pi\)
\(608\) −5.96479 −0.241904
\(609\) 25.1142 1.01768
\(610\) 35.1566 1.42345
\(611\) −23.5021 −0.950792
\(612\) −22.0566 −0.891584
\(613\) −48.8950 −1.97485 −0.987425 0.158090i \(-0.949466\pi\)
−0.987425 + 0.158090i \(0.949466\pi\)
\(614\) 4.31011 0.173942
\(615\) −16.0687 −0.647954
\(616\) −106.088 −4.27440
\(617\) −33.6863 −1.35616 −0.678080 0.734988i \(-0.737188\pi\)
−0.678080 + 0.734988i \(0.737188\pi\)
\(618\) −33.6296 −1.35278
\(619\) 19.7767 0.794891 0.397446 0.917626i \(-0.369897\pi\)
0.397446 + 0.917626i \(0.369897\pi\)
\(620\) 21.8326 0.876820
\(621\) 29.1283 1.16888
\(622\) 10.3076 0.413298
\(623\) −45.5114 −1.82338
\(624\) 26.0375 1.04233
\(625\) −18.6612 −0.746449
\(626\) 1.26437 0.0505345
\(627\) −29.1318 −1.16341
\(628\) −43.6994 −1.74380
\(629\) −25.8718 −1.03158
\(630\) −32.3683 −1.28959
\(631\) −23.5576 −0.937812 −0.468906 0.883248i \(-0.655352\pi\)
−0.468906 + 0.883248i \(0.655352\pi\)
\(632\) −50.0158 −1.98952
\(633\) −33.1735 −1.31853
\(634\) 37.1747 1.47640
\(635\) 36.7308 1.45762
\(636\) −55.2861 −2.19224
\(637\) −41.3694 −1.63912
\(638\) 69.2926 2.74332
\(639\) 5.88766 0.232912
\(640\) −36.5779 −1.44587
\(641\) 18.5968 0.734528 0.367264 0.930117i \(-0.380295\pi\)
0.367264 + 0.930117i \(0.380295\pi\)
\(642\) −4.56808 −0.180288
\(643\) −47.1695 −1.86018 −0.930092 0.367326i \(-0.880273\pi\)
−0.930092 + 0.367326i \(0.880273\pi\)
\(644\) 88.1166 3.47228
\(645\) −12.3403 −0.485900
\(646\) −39.2788 −1.54540
\(647\) 14.6194 0.574746 0.287373 0.957819i \(-0.407218\pi\)
0.287373 + 0.957819i \(0.407218\pi\)
\(648\) 6.56427 0.257869
\(649\) −11.7383 −0.460767
\(650\) −12.3451 −0.484214
\(651\) 12.2168 0.478813
\(652\) −1.02381 −0.0400957
\(653\) −38.7475 −1.51631 −0.758153 0.652076i \(-0.773898\pi\)
−0.758153 + 0.652076i \(0.773898\pi\)
\(654\) −28.0798 −1.09801
\(655\) −11.6042 −0.453412
\(656\) −33.0302 −1.28961
\(657\) 16.5803 0.646858
\(658\) −48.3556 −1.88510
\(659\) −43.4033 −1.69075 −0.845377 0.534171i \(-0.820624\pi\)
−0.845377 + 0.534171i \(0.820624\pi\)
\(660\) 48.4042 1.88413
\(661\) 23.2920 0.905954 0.452977 0.891522i \(-0.350362\pi\)
0.452977 + 0.891522i \(0.350362\pi\)
\(662\) 4.32010 0.167905
\(663\) 17.7494 0.689329
\(664\) 56.5956 2.19634
\(665\) −38.8012 −1.50465
\(666\) −33.0063 −1.27897
\(667\) −29.6073 −1.14640
\(668\) 51.9884 2.01149
\(669\) 4.13426 0.159840
\(670\) −44.3840 −1.71470
\(671\) 36.5368 1.41049
\(672\) 5.54576 0.213932
\(673\) −10.5468 −0.406550 −0.203275 0.979122i \(-0.565159\pi\)
−0.203275 + 0.979122i \(0.565159\pi\)
\(674\) 1.18642 0.0456992
\(675\) −5.65192 −0.217543
\(676\) 39.8490 1.53265
\(677\) 18.2109 0.699901 0.349950 0.936768i \(-0.386198\pi\)
0.349950 + 0.936768i \(0.386198\pi\)
\(678\) 0.793920 0.0304903
\(679\) −17.0417 −0.654000
\(680\) 33.5733 1.28748
\(681\) −1.12475 −0.0431006
\(682\) 33.7073 1.29072
\(683\) 27.2275 1.04183 0.520916 0.853608i \(-0.325591\pi\)
0.520916 + 0.853608i \(0.325591\pi\)
\(684\) −33.7313 −1.28975
\(685\) 14.4504 0.552123
\(686\) −16.5355 −0.631328
\(687\) −19.6801 −0.750842
\(688\) −25.3662 −0.967078
\(689\) −55.2550 −2.10505
\(690\) −30.7249 −1.16968
\(691\) −22.2115 −0.844965 −0.422482 0.906371i \(-0.638841\pi\)
−0.422482 + 0.906371i \(0.638841\pi\)
\(692\) −21.5167 −0.817941
\(693\) −33.6390 −1.27784
\(694\) 56.8841 2.15929
\(695\) −14.1714 −0.537550
\(696\) −33.2325 −1.25967
\(697\) −22.5162 −0.852863
\(698\) −5.22417 −0.197738
\(699\) −32.5011 −1.22930
\(700\) −17.0978 −0.646235
\(701\) −10.7216 −0.404950 −0.202475 0.979287i \(-0.564898\pi\)
−0.202475 + 0.979287i \(0.564898\pi\)
\(702\) 63.5205 2.39743
\(703\) −39.5660 −1.49226
\(704\) −33.0124 −1.24420
\(705\) 11.3497 0.427454
\(706\) −35.9995 −1.35486
\(707\) 10.6389 0.400115
\(708\) 10.9436 0.411286
\(709\) −31.0661 −1.16671 −0.583356 0.812217i \(-0.698261\pi\)
−0.583356 + 0.812217i \(0.698261\pi\)
\(710\) −17.4212 −0.653807
\(711\) −15.8593 −0.594772
\(712\) 60.2233 2.25696
\(713\) −14.4025 −0.539377
\(714\) 36.5194 1.36671
\(715\) 48.3769 1.80920
\(716\) 60.7875 2.27174
\(717\) −20.8688 −0.779359
\(718\) 22.9168 0.855249
\(719\) −13.0252 −0.485759 −0.242879 0.970057i \(-0.578092\pi\)
−0.242879 + 0.970057i \(0.578092\pi\)
\(720\) 15.6166 0.581997
\(721\) −46.5504 −1.73363
\(722\) −13.0707 −0.486439
\(723\) 22.2388 0.827068
\(724\) −17.5637 −0.652750
\(725\) 5.74488 0.213360
\(726\) 43.2556 1.60537
\(727\) 27.9746 1.03752 0.518761 0.854920i \(-0.326394\pi\)
0.518761 + 0.854920i \(0.326394\pi\)
\(728\) 98.8500 3.66363
\(729\) 20.7958 0.770215
\(730\) −49.0600 −1.81579
\(731\) −17.2918 −0.639561
\(732\) −34.0633 −1.25901
\(733\) 32.5559 1.20248 0.601241 0.799068i \(-0.294673\pi\)
0.601241 + 0.799068i \(0.294673\pi\)
\(734\) 75.3412 2.78089
\(735\) 19.9782 0.736909
\(736\) −6.53795 −0.240992
\(737\) −46.1264 −1.69909
\(738\) −28.7254 −1.05740
\(739\) −34.3878 −1.26497 −0.632487 0.774571i \(-0.717966\pi\)
−0.632487 + 0.774571i \(0.717966\pi\)
\(740\) 65.7412 2.41669
\(741\) 27.1443 0.997171
\(742\) −113.687 −4.17359
\(743\) −45.8745 −1.68297 −0.841486 0.540280i \(-0.818318\pi\)
−0.841486 + 0.540280i \(0.818318\pi\)
\(744\) −16.1659 −0.592671
\(745\) 3.13492 0.114855
\(746\) −74.2456 −2.71832
\(747\) 17.9457 0.656600
\(748\) 67.8261 2.47997
\(749\) −6.32317 −0.231043
\(750\) 34.4033 1.25623
\(751\) −21.0332 −0.767511 −0.383755 0.923435i \(-0.625369\pi\)
−0.383755 + 0.923435i \(0.625369\pi\)
\(752\) 23.3299 0.850755
\(753\) −23.0423 −0.839708
\(754\) −64.5652 −2.35133
\(755\) 23.2344 0.845586
\(756\) 87.9750 3.19962
\(757\) −12.6169 −0.458570 −0.229285 0.973359i \(-0.573639\pi\)
−0.229285 + 0.973359i \(0.573639\pi\)
\(758\) −88.9308 −3.23011
\(759\) −31.9311 −1.15902
\(760\) 51.3439 1.86244
\(761\) −40.0184 −1.45067 −0.725333 0.688398i \(-0.758314\pi\)
−0.725333 + 0.688398i \(0.758314\pi\)
\(762\) −52.8695 −1.91526
\(763\) −38.8682 −1.40712
\(764\) −65.1696 −2.35775
\(765\) 10.6456 0.384894
\(766\) 45.4453 1.64200
\(767\) 10.9374 0.394928
\(768\) 37.7045 1.36054
\(769\) −18.3969 −0.663410 −0.331705 0.943383i \(-0.607624\pi\)
−0.331705 + 0.943383i \(0.607624\pi\)
\(770\) 99.5358 3.58702
\(771\) 12.0215 0.432943
\(772\) 70.5035 2.53748
\(773\) −17.8218 −0.641005 −0.320502 0.947248i \(-0.603852\pi\)
−0.320502 + 0.947248i \(0.603852\pi\)
\(774\) −22.0603 −0.792941
\(775\) 2.79459 0.100385
\(776\) 22.5505 0.809516
\(777\) 36.7864 1.31971
\(778\) −45.5850 −1.63430
\(779\) −34.4343 −1.23374
\(780\) −45.1019 −1.61491
\(781\) −18.1051 −0.647852
\(782\) −43.0531 −1.53958
\(783\) −29.5597 −1.05638
\(784\) 41.0664 1.46666
\(785\) 21.0916 0.752791
\(786\) 16.7028 0.595768
\(787\) 19.8815 0.708699 0.354350 0.935113i \(-0.384702\pi\)
0.354350 + 0.935113i \(0.384702\pi\)
\(788\) 1.47235 0.0524502
\(789\) 26.9882 0.960804
\(790\) 46.9268 1.66958
\(791\) 1.09895 0.0390741
\(792\) 44.5130 1.58170
\(793\) −34.0441 −1.20894
\(794\) 75.2281 2.66975
\(795\) 26.6839 0.946381
\(796\) 12.4332 0.440683
\(797\) 16.1138 0.570780 0.285390 0.958412i \(-0.407877\pi\)
0.285390 + 0.958412i \(0.407877\pi\)
\(798\) 55.8495 1.97705
\(799\) 15.9037 0.562632
\(800\) 1.26860 0.0448516
\(801\) 19.0960 0.674724
\(802\) 2.10310 0.0742630
\(803\) −50.9860 −1.79926
\(804\) 43.0037 1.51662
\(805\) −42.5296 −1.49897
\(806\) −31.4077 −1.10629
\(807\) −27.3463 −0.962634
\(808\) −14.0779 −0.495260
\(809\) −49.6717 −1.74636 −0.873182 0.487394i \(-0.837948\pi\)
−0.873182 + 0.487394i \(0.837948\pi\)
\(810\) −6.15886 −0.216400
\(811\) 23.4580 0.823721 0.411861 0.911247i \(-0.364879\pi\)
0.411861 + 0.911247i \(0.364879\pi\)
\(812\) −89.4219 −3.13809
\(813\) −24.0153 −0.842255
\(814\) 101.498 3.55749
\(815\) 0.494146 0.0173092
\(816\) −17.6194 −0.616802
\(817\) −26.4446 −0.925178
\(818\) −33.7388 −1.17965
\(819\) 31.3440 1.09525
\(820\) 57.2146 1.99802
\(821\) −6.82351 −0.238142 −0.119071 0.992886i \(-0.537992\pi\)
−0.119071 + 0.992886i \(0.537992\pi\)
\(822\) −20.7996 −0.725470
\(823\) 50.7653 1.76957 0.884783 0.466003i \(-0.154306\pi\)
0.884783 + 0.466003i \(0.154306\pi\)
\(824\) 61.5980 2.14587
\(825\) 6.19577 0.215709
\(826\) 22.5038 0.783008
\(827\) 29.1029 1.01201 0.506004 0.862531i \(-0.331122\pi\)
0.506004 + 0.862531i \(0.331122\pi\)
\(828\) −36.9726 −1.28489
\(829\) 5.01550 0.174196 0.0870978 0.996200i \(-0.472241\pi\)
0.0870978 + 0.996200i \(0.472241\pi\)
\(830\) −53.1003 −1.84314
\(831\) −6.98657 −0.242361
\(832\) 30.7602 1.06642
\(833\) 27.9944 0.969949
\(834\) 20.3979 0.706322
\(835\) −25.0923 −0.868355
\(836\) 103.727 3.58748
\(837\) −14.3793 −0.497022
\(838\) −58.7042 −2.02790
\(839\) 39.0970 1.34978 0.674889 0.737919i \(-0.264191\pi\)
0.674889 + 0.737919i \(0.264191\pi\)
\(840\) −47.7370 −1.64708
\(841\) 1.04591 0.0360660
\(842\) 40.0657 1.38076
\(843\) 33.7710 1.16313
\(844\) 118.118 4.06579
\(845\) −19.2332 −0.661642
\(846\) 20.2894 0.697563
\(847\) 59.8747 2.05732
\(848\) 54.8502 1.88356
\(849\) 6.23648 0.214035
\(850\) 8.35385 0.286535
\(851\) −43.3679 −1.48663
\(852\) 16.8794 0.578280
\(853\) 11.5722 0.396226 0.198113 0.980179i \(-0.436519\pi\)
0.198113 + 0.980179i \(0.436519\pi\)
\(854\) −70.0459 −2.39692
\(855\) 16.2805 0.556781
\(856\) 8.36717 0.285984
\(857\) −21.7197 −0.741931 −0.370965 0.928647i \(-0.620973\pi\)
−0.370965 + 0.928647i \(0.620973\pi\)
\(858\) −69.6326 −2.37722
\(859\) 25.3500 0.864929 0.432465 0.901651i \(-0.357644\pi\)
0.432465 + 0.901651i \(0.357644\pi\)
\(860\) 43.9392 1.49831
\(861\) 32.0153 1.09108
\(862\) −4.45677 −0.151798
\(863\) −35.2773 −1.20085 −0.600427 0.799680i \(-0.705003\pi\)
−0.600427 + 0.799680i \(0.705003\pi\)
\(864\) −6.52744 −0.222068
\(865\) 10.3851 0.353102
\(866\) 12.1249 0.412021
\(867\) 7.65414 0.259948
\(868\) −43.4992 −1.47646
\(869\) 48.7690 1.65438
\(870\) 31.1801 1.05710
\(871\) 42.9795 1.45630
\(872\) 51.4326 1.74173
\(873\) 7.15047 0.242007
\(874\) −65.8416 −2.22712
\(875\) 47.6213 1.60989
\(876\) 47.5343 1.60603
\(877\) −36.8648 −1.24484 −0.622418 0.782685i \(-0.713849\pi\)
−0.622418 + 0.782685i \(0.713849\pi\)
\(878\) 97.7981 3.30052
\(879\) −9.84617 −0.332103
\(880\) −48.0226 −1.61884
\(881\) −42.2675 −1.42403 −0.712013 0.702166i \(-0.752217\pi\)
−0.712013 + 0.702166i \(0.752217\pi\)
\(882\) 35.7143 1.20256
\(883\) −2.92169 −0.0983228 −0.0491614 0.998791i \(-0.515655\pi\)
−0.0491614 + 0.998791i \(0.515655\pi\)
\(884\) −63.1988 −2.12560
\(885\) −5.28195 −0.177551
\(886\) 96.7916 3.25178
\(887\) −28.1458 −0.945045 −0.472522 0.881319i \(-0.656656\pi\)
−0.472522 + 0.881319i \(0.656656\pi\)
\(888\) −48.6779 −1.63352
\(889\) −73.1822 −2.45445
\(890\) −56.5039 −1.89402
\(891\) −6.40064 −0.214429
\(892\) −14.7205 −0.492879
\(893\) 24.3217 0.813894
\(894\) −4.51233 −0.150915
\(895\) −29.3392 −0.980701
\(896\) 72.8776 2.43467
\(897\) 29.7526 0.993411
\(898\) 22.6800 0.756843
\(899\) 14.6158 0.487465
\(900\) 7.17400 0.239133
\(901\) 37.3907 1.24566
\(902\) 88.3335 2.94118
\(903\) 24.5868 0.818198
\(904\) −1.45419 −0.0483657
\(905\) 8.47716 0.281790
\(906\) −33.4430 −1.11107
\(907\) 15.0677 0.500314 0.250157 0.968205i \(-0.419518\pi\)
0.250157 + 0.968205i \(0.419518\pi\)
\(908\) 4.00481 0.132904
\(909\) −4.46393 −0.148059
\(910\) −92.7451 −3.07447
\(911\) 22.6204 0.749446 0.374723 0.927137i \(-0.377738\pi\)
0.374723 + 0.927137i \(0.377738\pi\)
\(912\) −26.9455 −0.892254
\(913\) −55.1848 −1.82635
\(914\) −2.18735 −0.0723510
\(915\) 16.4407 0.543513
\(916\) 70.0732 2.31528
\(917\) 23.1201 0.763492
\(918\) −42.9839 −1.41868
\(919\) 53.5550 1.76661 0.883307 0.468794i \(-0.155311\pi\)
0.883307 + 0.468794i \(0.155311\pi\)
\(920\) 56.2776 1.85542
\(921\) 2.01558 0.0664158
\(922\) 89.4298 2.94521
\(923\) 16.8699 0.555281
\(924\) −96.4402 −3.17265
\(925\) 8.41492 0.276681
\(926\) 76.1737 2.50322
\(927\) 19.5319 0.641513
\(928\) 6.63480 0.217798
\(929\) 9.46835 0.310647 0.155323 0.987864i \(-0.450358\pi\)
0.155323 + 0.987864i \(0.450358\pi\)
\(930\) 15.1675 0.497362
\(931\) 42.8121 1.40311
\(932\) 115.724 3.79066
\(933\) 4.82027 0.157808
\(934\) −89.1746 −2.91788
\(935\) −32.7364 −1.07059
\(936\) −41.4762 −1.35569
\(937\) −12.1646 −0.397399 −0.198699 0.980060i \(-0.563672\pi\)
−0.198699 + 0.980060i \(0.563672\pi\)
\(938\) 88.4305 2.88736
\(939\) 0.591273 0.0192955
\(940\) −40.4119 −1.31809
\(941\) −35.5745 −1.15970 −0.579848 0.814725i \(-0.696888\pi\)
−0.579848 + 0.814725i \(0.696888\pi\)
\(942\) −30.3587 −0.989141
\(943\) −37.7431 −1.22908
\(944\) −10.8573 −0.353376
\(945\) −42.4613 −1.38127
\(946\) 67.8376 2.20559
\(947\) −13.5175 −0.439261 −0.219631 0.975583i \(-0.570485\pi\)
−0.219631 + 0.975583i \(0.570485\pi\)
\(948\) −45.4674 −1.47671
\(949\) 47.5075 1.54216
\(950\) 12.7756 0.414496
\(951\) 17.3844 0.563729
\(952\) −66.8912 −2.16796
\(953\) −59.8971 −1.94026 −0.970128 0.242592i \(-0.922002\pi\)
−0.970128 + 0.242592i \(0.922002\pi\)
\(954\) 47.7017 1.54440
\(955\) 31.4542 1.01783
\(956\) 74.3057 2.40322
\(957\) 32.4041 1.04748
\(958\) −60.3745 −1.95061
\(959\) −28.7910 −0.929709
\(960\) −14.8548 −0.479437
\(961\) −23.8901 −0.770650
\(962\) −94.5731 −3.04916
\(963\) 2.65312 0.0854955
\(964\) −79.1837 −2.55033
\(965\) −34.0286 −1.09542
\(966\) 61.2161 1.96960
\(967\) 23.2796 0.748622 0.374311 0.927303i \(-0.377879\pi\)
0.374311 + 0.927303i \(0.377879\pi\)
\(968\) −79.2296 −2.54653
\(969\) −18.3684 −0.590078
\(970\) −21.1578 −0.679336
\(971\) 21.2215 0.681030 0.340515 0.940239i \(-0.389399\pi\)
0.340515 + 0.940239i \(0.389399\pi\)
\(972\) −60.6674 −1.94591
\(973\) 28.2349 0.905171
\(974\) 2.35483 0.0754535
\(975\) −5.77307 −0.184886
\(976\) 33.7947 1.08174
\(977\) 4.00120 0.128010 0.0640049 0.997950i \(-0.479613\pi\)
0.0640049 + 0.997950i \(0.479613\pi\)
\(978\) −0.711262 −0.0227436
\(979\) −58.7221 −1.87677
\(980\) −71.1349 −2.27232
\(981\) 16.3086 0.520693
\(982\) 60.0446 1.91610
\(983\) −35.0210 −1.11699 −0.558497 0.829506i \(-0.688622\pi\)
−0.558497 + 0.829506i \(0.688622\pi\)
\(984\) −42.3644 −1.35053
\(985\) −0.710631 −0.0226426
\(986\) 43.6909 1.39140
\(987\) −22.6131 −0.719782
\(988\) −96.6505 −3.07486
\(989\) −28.9856 −0.921689
\(990\) −41.7639 −1.32734
\(991\) −32.1070 −1.01991 −0.509957 0.860200i \(-0.670339\pi\)
−0.509957 + 0.860200i \(0.670339\pi\)
\(992\) 3.22749 0.102473
\(993\) 2.02026 0.0641109
\(994\) 34.7100 1.10093
\(995\) −6.00090 −0.190241
\(996\) 51.4489 1.63022
\(997\) 36.3063 1.14983 0.574916 0.818212i \(-0.305035\pi\)
0.574916 + 0.818212i \(0.305035\pi\)
\(998\) −85.9044 −2.71925
\(999\) −43.2982 −1.36989
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 \(a_p\))