Properties

Label 6041.2.a.f.1.10
Level 6041
Weight 2
Character 6041.1
Self dual Yes
Analytic conductor 48.238
Analytic rank 0
Dimension 132
CM No

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Newspace parameters

Level: \( N \) = \( 6041 = 7 \cdot 863 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2376278611\)
Analytic rank: \(0\)
Dimension: \(132\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 6041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.58389 q^{2}\) \(+1.40748 q^{3}\) \(+4.67649 q^{4}\) \(-2.16822 q^{5}\) \(-3.63678 q^{6}\) \(+1.00000 q^{7}\) \(-6.91577 q^{8}\) \(-1.01899 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.58389 q^{2}\) \(+1.40748 q^{3}\) \(+4.67649 q^{4}\) \(-2.16822 q^{5}\) \(-3.63678 q^{6}\) \(+1.00000 q^{7}\) \(-6.91577 q^{8}\) \(-1.01899 q^{9}\) \(+5.60245 q^{10}\) \(-3.16802 q^{11}\) \(+6.58209 q^{12}\) \(+1.21704 q^{13}\) \(-2.58389 q^{14}\) \(-3.05174 q^{15}\) \(+8.51660 q^{16}\) \(+4.73910 q^{17}\) \(+2.63296 q^{18}\) \(-4.76821 q^{19}\) \(-10.1397 q^{20}\) \(+1.40748 q^{21}\) \(+8.18583 q^{22}\) \(-5.72257 q^{23}\) \(-9.73383 q^{24}\) \(-0.298806 q^{25}\) \(-3.14471 q^{26}\) \(-5.65666 q^{27}\) \(+4.67649 q^{28}\) \(-8.90251 q^{29}\) \(+7.88536 q^{30}\) \(-3.13011 q^{31}\) \(-8.17444 q^{32}\) \(-4.45894 q^{33}\) \(-12.2453 q^{34}\) \(-2.16822 q^{35}\) \(-4.76530 q^{36}\) \(-1.91415 q^{37}\) \(+12.3205 q^{38}\) \(+1.71297 q^{39}\) \(+14.9949 q^{40}\) \(+5.76268 q^{41}\) \(-3.63678 q^{42}\) \(+4.63071 q^{43}\) \(-14.8152 q^{44}\) \(+2.20940 q^{45}\) \(+14.7865 q^{46}\) \(+2.89486 q^{47}\) \(+11.9870 q^{48}\) \(+1.00000 q^{49}\) \(+0.772083 q^{50}\) \(+6.67021 q^{51}\) \(+5.69149 q^{52}\) \(-0.623615 q^{53}\) \(+14.6162 q^{54}\) \(+6.86898 q^{55}\) \(-6.91577 q^{56}\) \(-6.71117 q^{57}\) \(+23.0031 q^{58}\) \(-12.4131 q^{59}\) \(-14.2714 q^{60}\) \(+13.0829 q^{61}\) \(+8.08786 q^{62}\) \(-1.01899 q^{63}\) \(+4.08866 q^{64}\) \(-2.63882 q^{65}\) \(+11.5214 q^{66}\) \(+11.9649 q^{67}\) \(+22.1624 q^{68}\) \(-8.05442 q^{69}\) \(+5.60245 q^{70}\) \(-7.16977 q^{71}\) \(+7.04710 q^{72}\) \(+6.07721 q^{73}\) \(+4.94595 q^{74}\) \(-0.420565 q^{75}\) \(-22.2985 q^{76}\) \(-3.16802 q^{77}\) \(-4.42612 q^{78}\) \(-11.1885 q^{79}\) \(-18.4659 q^{80}\) \(-4.90469 q^{81}\) \(-14.8901 q^{82}\) \(+2.54325 q^{83}\) \(+6.58209 q^{84}\) \(-10.2754 q^{85}\) \(-11.9653 q^{86}\) \(-12.5301 q^{87}\) \(+21.9093 q^{88}\) \(-8.94330 q^{89}\) \(-5.70885 q^{90}\) \(+1.21704 q^{91}\) \(-26.7616 q^{92}\) \(-4.40558 q^{93}\) \(-7.47999 q^{94}\) \(+10.3385 q^{95}\) \(-11.5054 q^{96}\) \(+9.11453 q^{97}\) \(-2.58389 q^{98}\) \(+3.22819 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut 22q^{10} \) \(\mathstrut +\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 30q^{12} \) \(\mathstrut +\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 59q^{15} \) \(\mathstrut +\mathstrut 254q^{16} \) \(\mathstrut +\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 40q^{19} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 66q^{22} \) \(\mathstrut +\mathstrut 62q^{23} \) \(\mathstrut +\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 235q^{25} \) \(\mathstrut +\mathstrut 25q^{26} \) \(\mathstrut +\mathstrut 37q^{27} \) \(\mathstrut +\mathstrut 174q^{28} \) \(\mathstrut +\mathstrut 28q^{29} \) \(\mathstrut +\mathstrut 45q^{30} \) \(\mathstrut +\mathstrut 121q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 13q^{33} \) \(\mathstrut +\mathstrut 44q^{34} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 274q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 28q^{38} \) \(\mathstrut +\mathstrut 114q^{39} \) \(\mathstrut +\mathstrut 32q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut +\mathstrut 105q^{43} \) \(\mathstrut +\mathstrut 54q^{44} \) \(\mathstrut +\mathstrut 29q^{45} \) \(\mathstrut +\mathstrut 104q^{46} \) \(\mathstrut +\mathstrut 33q^{47} \) \(\mathstrut +\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 132q^{49} \) \(\mathstrut -\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 53q^{51} \) \(\mathstrut -\mathstrut 11q^{52} \) \(\mathstrut +\mathstrut 48q^{53} \) \(\mathstrut +\mathstrut 11q^{54} \) \(\mathstrut +\mathstrut 118q^{55} \) \(\mathstrut +\mathstrut 30q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 87q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 41q^{60} \) \(\mathstrut +\mathstrut 54q^{61} \) \(\mathstrut -\mathstrut 28q^{62} \) \(\mathstrut +\mathstrut 178q^{63} \) \(\mathstrut +\mathstrut 376q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 123q^{67} \) \(\mathstrut -\mathstrut 47q^{68} \) \(\mathstrut +\mathstrut 58q^{69} \) \(\mathstrut +\mathstrut 22q^{70} \) \(\mathstrut +\mathstrut 108q^{71} \) \(\mathstrut +\mathstrut 97q^{72} \) \(\mathstrut +\mathstrut q^{73} \) \(\mathstrut -\mathstrut 10q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 71q^{76} \) \(\mathstrut +\mathstrut 32q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 204q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 296q^{81} \) \(\mathstrut +\mathstrut 80q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut +\mathstrut 30q^{84} \) \(\mathstrut +\mathstrut 94q^{85} \) \(\mathstrut +\mathstrut 48q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut +\mathstrut 155q^{88} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 90q^{93} \) \(\mathstrut +\mathstrut 79q^{94} \) \(\mathstrut +\mathstrut 100q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut +\mathstrut 18q^{97} \) \(\mathstrut +\mathstrut 8q^{98} \) \(\mathstrut +\mathstrut 96q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.58389 −1.82709 −0.913543 0.406741i \(-0.866665\pi\)
−0.913543 + 0.406741i \(0.866665\pi\)
\(3\) 1.40748 0.812611 0.406305 0.913737i \(-0.366817\pi\)
0.406305 + 0.913737i \(0.366817\pi\)
\(4\) 4.67649 2.33825
\(5\) −2.16822 −0.969659 −0.484830 0.874609i \(-0.661118\pi\)
−0.484830 + 0.874609i \(0.661118\pi\)
\(6\) −3.63678 −1.48471
\(7\) 1.00000 0.377964
\(8\) −6.91577 −2.44509
\(9\) −1.01899 −0.339663
\(10\) 5.60245 1.77165
\(11\) −3.16802 −0.955195 −0.477597 0.878579i \(-0.658492\pi\)
−0.477597 + 0.878579i \(0.658492\pi\)
\(12\) 6.58209 1.90008
\(13\) 1.21704 0.337547 0.168773 0.985655i \(-0.446019\pi\)
0.168773 + 0.985655i \(0.446019\pi\)
\(14\) −2.58389 −0.690574
\(15\) −3.05174 −0.787956
\(16\) 8.51660 2.12915
\(17\) 4.73910 1.14940 0.574701 0.818364i \(-0.305118\pi\)
0.574701 + 0.818364i \(0.305118\pi\)
\(18\) 2.63296 0.620595
\(19\) −4.76821 −1.09390 −0.546951 0.837165i \(-0.684212\pi\)
−0.546951 + 0.837165i \(0.684212\pi\)
\(20\) −10.1397 −2.26730
\(21\) 1.40748 0.307138
\(22\) 8.18583 1.74522
\(23\) −5.72257 −1.19324 −0.596619 0.802525i \(-0.703490\pi\)
−0.596619 + 0.802525i \(0.703490\pi\)
\(24\) −9.73383 −1.98691
\(25\) −0.298806 −0.0597612
\(26\) −3.14471 −0.616727
\(27\) −5.65666 −1.08863
\(28\) 4.67649 0.883774
\(29\) −8.90251 −1.65315 −0.826577 0.562824i \(-0.809715\pi\)
−0.826577 + 0.562824i \(0.809715\pi\)
\(30\) 7.88536 1.43966
\(31\) −3.13011 −0.562184 −0.281092 0.959681i \(-0.590697\pi\)
−0.281092 + 0.959681i \(0.590697\pi\)
\(32\) −8.17444 −1.44505
\(33\) −4.45894 −0.776202
\(34\) −12.2453 −2.10006
\(35\) −2.16822 −0.366497
\(36\) −4.76530 −0.794217
\(37\) −1.91415 −0.314684 −0.157342 0.987544i \(-0.550292\pi\)
−0.157342 + 0.987544i \(0.550292\pi\)
\(38\) 12.3205 1.99865
\(39\) 1.71297 0.274294
\(40\) 14.9949 2.37091
\(41\) 5.76268 0.899979 0.449990 0.893034i \(-0.351428\pi\)
0.449990 + 0.893034i \(0.351428\pi\)
\(42\) −3.63678 −0.561168
\(43\) 4.63071 0.706177 0.353089 0.935590i \(-0.385131\pi\)
0.353089 + 0.935590i \(0.385131\pi\)
\(44\) −14.8152 −2.23348
\(45\) 2.20940 0.329358
\(46\) 14.7865 2.18015
\(47\) 2.89486 0.422258 0.211129 0.977458i \(-0.432286\pi\)
0.211129 + 0.977458i \(0.432286\pi\)
\(48\) 11.9870 1.73017
\(49\) 1.00000 0.142857
\(50\) 0.772083 0.109189
\(51\) 6.67021 0.934016
\(52\) 5.69149 0.789268
\(53\) −0.623615 −0.0856601 −0.0428301 0.999082i \(-0.513637\pi\)
−0.0428301 + 0.999082i \(0.513637\pi\)
\(54\) 14.6162 1.98901
\(55\) 6.86898 0.926213
\(56\) −6.91577 −0.924158
\(57\) −6.71117 −0.888917
\(58\) 23.0031 3.02046
\(59\) −12.4131 −1.61605 −0.808027 0.589145i \(-0.799465\pi\)
−0.808027 + 0.589145i \(0.799465\pi\)
\(60\) −14.2714 −1.84243
\(61\) 13.0829 1.67509 0.837544 0.546369i \(-0.183991\pi\)
0.837544 + 0.546369i \(0.183991\pi\)
\(62\) 8.08786 1.02716
\(63\) −1.01899 −0.128381
\(64\) 4.08866 0.511083
\(65\) −2.63882 −0.327305
\(66\) 11.5214 1.41819
\(67\) 11.9649 1.46174 0.730870 0.682517i \(-0.239115\pi\)
0.730870 + 0.682517i \(0.239115\pi\)
\(68\) 22.1624 2.68758
\(69\) −8.05442 −0.969638
\(70\) 5.60245 0.669621
\(71\) −7.16977 −0.850896 −0.425448 0.904983i \(-0.639883\pi\)
−0.425448 + 0.904983i \(0.639883\pi\)
\(72\) 7.04710 0.830509
\(73\) 6.07721 0.711283 0.355642 0.934622i \(-0.384262\pi\)
0.355642 + 0.934622i \(0.384262\pi\)
\(74\) 4.94595 0.574955
\(75\) −0.420565 −0.0485626
\(76\) −22.2985 −2.55781
\(77\) −3.16802 −0.361030
\(78\) −4.42612 −0.501159
\(79\) −11.1885 −1.25880 −0.629400 0.777081i \(-0.716699\pi\)
−0.629400 + 0.777081i \(0.716699\pi\)
\(80\) −18.4659 −2.06455
\(81\) −4.90469 −0.544965
\(82\) −14.8901 −1.64434
\(83\) 2.54325 0.279158 0.139579 0.990211i \(-0.455425\pi\)
0.139579 + 0.990211i \(0.455425\pi\)
\(84\) 6.58209 0.718165
\(85\) −10.2754 −1.11453
\(86\) −11.9653 −1.29025
\(87\) −12.5301 −1.34337
\(88\) 21.9093 2.33554
\(89\) −8.94330 −0.947988 −0.473994 0.880528i \(-0.657188\pi\)
−0.473994 + 0.880528i \(0.657188\pi\)
\(90\) −5.70885 −0.601765
\(91\) 1.21704 0.127581
\(92\) −26.7616 −2.79008
\(93\) −4.40558 −0.456837
\(94\) −7.47999 −0.771502
\(95\) 10.3385 1.06071
\(96\) −11.5054 −1.17426
\(97\) 9.11453 0.925441 0.462720 0.886504i \(-0.346873\pi\)
0.462720 + 0.886504i \(0.346873\pi\)
\(98\) −2.58389 −0.261012
\(99\) 3.22819 0.324445
\(100\) −1.39737 −0.139737
\(101\) 15.3894 1.53130 0.765650 0.643258i \(-0.222418\pi\)
0.765650 + 0.643258i \(0.222418\pi\)
\(102\) −17.2351 −1.70653
\(103\) 9.62828 0.948703 0.474351 0.880336i \(-0.342683\pi\)
0.474351 + 0.880336i \(0.342683\pi\)
\(104\) −8.41678 −0.825333
\(105\) −3.05174 −0.297819
\(106\) 1.61135 0.156509
\(107\) 4.81884 0.465855 0.232927 0.972494i \(-0.425170\pi\)
0.232927 + 0.972494i \(0.425170\pi\)
\(108\) −26.4533 −2.54547
\(109\) −4.66377 −0.446708 −0.223354 0.974737i \(-0.571701\pi\)
−0.223354 + 0.974737i \(0.571701\pi\)
\(110\) −17.7487 −1.69227
\(111\) −2.69413 −0.255716
\(112\) 8.51660 0.804743
\(113\) −9.47571 −0.891400 −0.445700 0.895182i \(-0.647045\pi\)
−0.445700 + 0.895182i \(0.647045\pi\)
\(114\) 17.3409 1.62413
\(115\) 12.4078 1.15703
\(116\) −41.6325 −3.86548
\(117\) −1.24015 −0.114652
\(118\) 32.0742 2.95267
\(119\) 4.73910 0.434433
\(120\) 21.1051 1.92662
\(121\) −0.963631 −0.0876028
\(122\) −33.8047 −3.06053
\(123\) 8.11088 0.731333
\(124\) −14.6379 −1.31453
\(125\) 11.4890 1.02761
\(126\) 2.63296 0.234563
\(127\) 8.40274 0.745622 0.372811 0.927907i \(-0.378394\pi\)
0.372811 + 0.927907i \(0.378394\pi\)
\(128\) 5.78423 0.511258
\(129\) 6.51765 0.573847
\(130\) 6.81842 0.598015
\(131\) 16.9422 1.48025 0.740123 0.672472i \(-0.234767\pi\)
0.740123 + 0.672472i \(0.234767\pi\)
\(132\) −20.8522 −1.81495
\(133\) −4.76821 −0.413456
\(134\) −30.9159 −2.67073
\(135\) 12.2649 1.05560
\(136\) −32.7745 −2.81039
\(137\) −3.15859 −0.269857 −0.134928 0.990855i \(-0.543080\pi\)
−0.134928 + 0.990855i \(0.543080\pi\)
\(138\) 20.8117 1.77161
\(139\) −22.6268 −1.91918 −0.959591 0.281398i \(-0.909202\pi\)
−0.959591 + 0.281398i \(0.909202\pi\)
\(140\) −10.1397 −0.856960
\(141\) 4.07446 0.343132
\(142\) 18.5259 1.55466
\(143\) −3.85562 −0.322423
\(144\) −8.67834 −0.723195
\(145\) 19.3026 1.60300
\(146\) −15.7028 −1.29958
\(147\) 1.40748 0.116087
\(148\) −8.95150 −0.735809
\(149\) −6.38916 −0.523420 −0.261710 0.965147i \(-0.584286\pi\)
−0.261710 + 0.965147i \(0.584286\pi\)
\(150\) 1.08669 0.0887282
\(151\) 20.3502 1.65607 0.828036 0.560675i \(-0.189458\pi\)
0.828036 + 0.560675i \(0.189458\pi\)
\(152\) 32.9758 2.67469
\(153\) −4.82910 −0.390410
\(154\) 8.18583 0.659633
\(155\) 6.78678 0.545127
\(156\) 8.01068 0.641368
\(157\) 6.88006 0.549089 0.274544 0.961574i \(-0.411473\pi\)
0.274544 + 0.961574i \(0.411473\pi\)
\(158\) 28.9098 2.29994
\(159\) −0.877728 −0.0696084
\(160\) 17.7240 1.40121
\(161\) −5.72257 −0.451002
\(162\) 12.6732 0.995699
\(163\) 15.5669 1.21929 0.609647 0.792673i \(-0.291311\pi\)
0.609647 + 0.792673i \(0.291311\pi\)
\(164\) 26.9491 2.10437
\(165\) 9.66798 0.752651
\(166\) −6.57149 −0.510046
\(167\) −6.65907 −0.515294 −0.257647 0.966239i \(-0.582947\pi\)
−0.257647 + 0.966239i \(0.582947\pi\)
\(168\) −9.73383 −0.750981
\(169\) −11.5188 −0.886062
\(170\) 26.5506 2.03634
\(171\) 4.85876 0.371558
\(172\) 21.6555 1.65122
\(173\) 10.6468 0.809461 0.404731 0.914436i \(-0.367365\pi\)
0.404731 + 0.914436i \(0.367365\pi\)
\(174\) 32.3765 2.45446
\(175\) −0.298806 −0.0225876
\(176\) −26.9808 −2.03375
\(177\) −17.4713 −1.31322
\(178\) 23.1085 1.73206
\(179\) −14.5977 −1.09108 −0.545542 0.838083i \(-0.683676\pi\)
−0.545542 + 0.838083i \(0.683676\pi\)
\(180\) 10.3322 0.770120
\(181\) −24.7977 −1.84320 −0.921599 0.388142i \(-0.873117\pi\)
−0.921599 + 0.388142i \(0.873117\pi\)
\(182\) −3.14471 −0.233101
\(183\) 18.4139 1.36120
\(184\) 39.5760 2.91758
\(185\) 4.15030 0.305136
\(186\) 11.3835 0.834681
\(187\) −15.0136 −1.09790
\(188\) 13.5378 0.987344
\(189\) −5.65666 −0.411462
\(190\) −26.7137 −1.93801
\(191\) 16.5849 1.20004 0.600022 0.799984i \(-0.295159\pi\)
0.600022 + 0.799984i \(0.295159\pi\)
\(192\) 5.75472 0.415311
\(193\) −9.06703 −0.652659 −0.326329 0.945256i \(-0.605812\pi\)
−0.326329 + 0.945256i \(0.605812\pi\)
\(194\) −23.5510 −1.69086
\(195\) −3.71410 −0.265972
\(196\) 4.67649 0.334035
\(197\) −2.64107 −0.188169 −0.0940843 0.995564i \(-0.529992\pi\)
−0.0940843 + 0.995564i \(0.529992\pi\)
\(198\) −8.34128 −0.592789
\(199\) 18.4052 1.30471 0.652355 0.757913i \(-0.273781\pi\)
0.652355 + 0.757913i \(0.273781\pi\)
\(200\) 2.06647 0.146122
\(201\) 16.8403 1.18783
\(202\) −39.7645 −2.79782
\(203\) −8.90251 −0.624834
\(204\) 31.1932 2.18396
\(205\) −12.4948 −0.872673
\(206\) −24.8784 −1.73336
\(207\) 5.83124 0.405299
\(208\) 10.3651 0.718688
\(209\) 15.1058 1.04489
\(210\) 7.88536 0.544142
\(211\) 18.9919 1.30745 0.653727 0.756731i \(-0.273205\pi\)
0.653727 + 0.756731i \(0.273205\pi\)
\(212\) −2.91633 −0.200295
\(213\) −10.0913 −0.691447
\(214\) −12.4514 −0.851157
\(215\) −10.0404 −0.684751
\(216\) 39.1202 2.66179
\(217\) −3.13011 −0.212486
\(218\) 12.0507 0.816175
\(219\) 8.55357 0.577996
\(220\) 32.1228 2.16572
\(221\) 5.76769 0.387977
\(222\) 6.96134 0.467215
\(223\) −22.9562 −1.53726 −0.768629 0.639694i \(-0.779061\pi\)
−0.768629 + 0.639694i \(0.779061\pi\)
\(224\) −8.17444 −0.546178
\(225\) 0.304481 0.0202987
\(226\) 24.4842 1.62866
\(227\) 10.5094 0.697532 0.348766 0.937210i \(-0.386601\pi\)
0.348766 + 0.937210i \(0.386601\pi\)
\(228\) −31.3848 −2.07851
\(229\) 21.1762 1.39936 0.699680 0.714456i \(-0.253326\pi\)
0.699680 + 0.714456i \(0.253326\pi\)
\(230\) −32.0604 −2.11400
\(231\) −4.45894 −0.293377
\(232\) 61.5677 4.04212
\(233\) −20.1853 −1.32238 −0.661191 0.750217i \(-0.729949\pi\)
−0.661191 + 0.750217i \(0.729949\pi\)
\(234\) 3.20442 0.209480
\(235\) −6.27670 −0.409446
\(236\) −58.0500 −3.77873
\(237\) −15.7476 −1.02291
\(238\) −12.2453 −0.793747
\(239\) 7.99700 0.517283 0.258642 0.965973i \(-0.416725\pi\)
0.258642 + 0.965973i \(0.416725\pi\)
\(240\) −25.9905 −1.67768
\(241\) 0.668492 0.0430614 0.0215307 0.999768i \(-0.493146\pi\)
0.0215307 + 0.999768i \(0.493146\pi\)
\(242\) 2.48992 0.160058
\(243\) 10.0667 0.645781
\(244\) 61.1819 3.91677
\(245\) −2.16822 −0.138523
\(246\) −20.9576 −1.33621
\(247\) −5.80311 −0.369243
\(248\) 21.6471 1.37459
\(249\) 3.57959 0.226847
\(250\) −29.6863 −1.87753
\(251\) 17.7432 1.11994 0.559969 0.828513i \(-0.310813\pi\)
0.559969 + 0.828513i \(0.310813\pi\)
\(252\) −4.76530 −0.300186
\(253\) 18.1292 1.13977
\(254\) −21.7118 −1.36232
\(255\) −14.4625 −0.905677
\(256\) −23.1231 −1.44520
\(257\) 7.89004 0.492167 0.246083 0.969249i \(-0.420856\pi\)
0.246083 + 0.969249i \(0.420856\pi\)
\(258\) −16.8409 −1.04847
\(259\) −1.91415 −0.118939
\(260\) −12.3404 −0.765321
\(261\) 9.07157 0.561516
\(262\) −43.7768 −2.70454
\(263\) −11.5866 −0.714461 −0.357230 0.934016i \(-0.616279\pi\)
−0.357230 + 0.934016i \(0.616279\pi\)
\(264\) 30.8370 1.89789
\(265\) 1.35214 0.0830611
\(266\) 12.3205 0.755420
\(267\) −12.5875 −0.770345
\(268\) 55.9536 3.41791
\(269\) 11.8549 0.722808 0.361404 0.932409i \(-0.382298\pi\)
0.361404 + 0.932409i \(0.382298\pi\)
\(270\) −31.6912 −1.92866
\(271\) 30.5579 1.85626 0.928130 0.372256i \(-0.121416\pi\)
0.928130 + 0.372256i \(0.121416\pi\)
\(272\) 40.3611 2.44725
\(273\) 1.71297 0.103673
\(274\) 8.16146 0.493052
\(275\) 0.946625 0.0570836
\(276\) −37.6664 −2.26725
\(277\) 19.8591 1.19322 0.596609 0.802532i \(-0.296514\pi\)
0.596609 + 0.802532i \(0.296514\pi\)
\(278\) 58.4652 3.50651
\(279\) 3.18955 0.190953
\(280\) 14.9949 0.896119
\(281\) −11.1487 −0.665075 −0.332538 0.943090i \(-0.607905\pi\)
−0.332538 + 0.943090i \(0.607905\pi\)
\(282\) −10.5280 −0.626931
\(283\) 2.27771 0.135396 0.0676980 0.997706i \(-0.478435\pi\)
0.0676980 + 0.997706i \(0.478435\pi\)
\(284\) −33.5294 −1.98960
\(285\) 14.5513 0.861946
\(286\) 9.96250 0.589095
\(287\) 5.76268 0.340160
\(288\) 8.32968 0.490831
\(289\) 5.45911 0.321124
\(290\) −49.8759 −2.92881
\(291\) 12.8286 0.752023
\(292\) 28.4200 1.66316
\(293\) −12.3883 −0.723735 −0.361867 0.932230i \(-0.617861\pi\)
−0.361867 + 0.932230i \(0.617861\pi\)
\(294\) −3.63678 −0.212102
\(295\) 26.9145 1.56702
\(296\) 13.2378 0.769431
\(297\) 17.9204 1.03985
\(298\) 16.5089 0.956334
\(299\) −6.96461 −0.402774
\(300\) −1.96677 −0.113551
\(301\) 4.63071 0.266910
\(302\) −52.5826 −3.02579
\(303\) 21.6603 1.24435
\(304\) −40.6089 −2.32908
\(305\) −28.3666 −1.62426
\(306\) 12.4779 0.713313
\(307\) 12.2605 0.699744 0.349872 0.936797i \(-0.386225\pi\)
0.349872 + 0.936797i \(0.386225\pi\)
\(308\) −14.8152 −0.844177
\(309\) 13.5516 0.770926
\(310\) −17.5363 −0.995995
\(311\) 10.3731 0.588204 0.294102 0.955774i \(-0.404979\pi\)
0.294102 + 0.955774i \(0.404979\pi\)
\(312\) −11.8465 −0.670675
\(313\) 10.3129 0.582918 0.291459 0.956583i \(-0.405859\pi\)
0.291459 + 0.956583i \(0.405859\pi\)
\(314\) −17.7773 −1.00323
\(315\) 2.20940 0.124486
\(316\) −52.3228 −2.94339
\(317\) −29.3545 −1.64871 −0.824355 0.566073i \(-0.808462\pi\)
−0.824355 + 0.566073i \(0.808462\pi\)
\(318\) 2.26795 0.127181
\(319\) 28.2033 1.57908
\(320\) −8.86514 −0.495576
\(321\) 6.78244 0.378559
\(322\) 14.7865 0.824019
\(323\) −22.5970 −1.25733
\(324\) −22.9367 −1.27426
\(325\) −0.363660 −0.0201722
\(326\) −40.2232 −2.22775
\(327\) −6.56418 −0.363000
\(328\) −39.8534 −2.20053
\(329\) 2.89486 0.159599
\(330\) −24.9810 −1.37516
\(331\) −24.2184 −1.33117 −0.665583 0.746324i \(-0.731817\pi\)
−0.665583 + 0.746324i \(0.731817\pi\)
\(332\) 11.8935 0.652741
\(333\) 1.95050 0.106887
\(334\) 17.2063 0.941487
\(335\) −25.9425 −1.41739
\(336\) 11.9870 0.653943
\(337\) 17.6280 0.960256 0.480128 0.877198i \(-0.340590\pi\)
0.480128 + 0.877198i \(0.340590\pi\)
\(338\) 29.7633 1.61891
\(339\) −13.3369 −0.724361
\(340\) −48.0530 −2.60604
\(341\) 9.91626 0.536996
\(342\) −12.5545 −0.678870
\(343\) 1.00000 0.0539949
\(344\) −32.0249 −1.72667
\(345\) 17.4638 0.940218
\(346\) −27.5102 −1.47896
\(347\) −14.4860 −0.777650 −0.388825 0.921312i \(-0.627119\pi\)
−0.388825 + 0.921312i \(0.627119\pi\)
\(348\) −58.5971 −3.14113
\(349\) −29.0156 −1.55317 −0.776584 0.630013i \(-0.783049\pi\)
−0.776584 + 0.630013i \(0.783049\pi\)
\(350\) 0.772083 0.0412696
\(351\) −6.88440 −0.367462
\(352\) 25.8968 1.38031
\(353\) −19.6237 −1.04447 −0.522233 0.852803i \(-0.674901\pi\)
−0.522233 + 0.852803i \(0.674901\pi\)
\(354\) 45.1439 2.39937
\(355\) 15.5457 0.825079
\(356\) −41.8233 −2.21663
\(357\) 6.67021 0.353025
\(358\) 37.7189 1.99351
\(359\) 35.2330 1.85953 0.929763 0.368160i \(-0.120012\pi\)
0.929763 + 0.368160i \(0.120012\pi\)
\(360\) −15.2797 −0.805311
\(361\) 3.73580 0.196621
\(362\) 64.0746 3.36768
\(363\) −1.35629 −0.0711870
\(364\) 5.69149 0.298315
\(365\) −13.1767 −0.689702
\(366\) −47.5795 −2.48702
\(367\) 32.1168 1.67648 0.838241 0.545300i \(-0.183584\pi\)
0.838241 + 0.545300i \(0.183584\pi\)
\(368\) −48.7368 −2.54058
\(369\) −5.87212 −0.305690
\(370\) −10.7239 −0.557510
\(371\) −0.623615 −0.0323765
\(372\) −20.6027 −1.06820
\(373\) 14.6269 0.757352 0.378676 0.925529i \(-0.376380\pi\)
0.378676 + 0.925529i \(0.376380\pi\)
\(374\) 38.7935 2.00596
\(375\) 16.1706 0.835045
\(376\) −20.0202 −1.03246
\(377\) −10.8347 −0.558017
\(378\) 14.6162 0.751776
\(379\) −30.3842 −1.56073 −0.780366 0.625323i \(-0.784967\pi\)
−0.780366 + 0.625323i \(0.784967\pi\)
\(380\) 48.3481 2.48021
\(381\) 11.8267 0.605901
\(382\) −42.8537 −2.19258
\(383\) −31.9295 −1.63152 −0.815760 0.578390i \(-0.803681\pi\)
−0.815760 + 0.578390i \(0.803681\pi\)
\(384\) 8.14120 0.415454
\(385\) 6.86898 0.350076
\(386\) 23.4282 1.19246
\(387\) −4.71865 −0.239863
\(388\) 42.6241 2.16391
\(389\) 9.15773 0.464315 0.232158 0.972678i \(-0.425421\pi\)
0.232158 + 0.972678i \(0.425421\pi\)
\(390\) 9.59682 0.485954
\(391\) −27.1198 −1.37151
\(392\) −6.91577 −0.349299
\(393\) 23.8458 1.20286
\(394\) 6.82424 0.343800
\(395\) 24.2591 1.22061
\(396\) 15.0966 0.758632
\(397\) 30.1762 1.51450 0.757249 0.653126i \(-0.226543\pi\)
0.757249 + 0.653126i \(0.226543\pi\)
\(398\) −47.5571 −2.38382
\(399\) −6.71117 −0.335979
\(400\) −2.54481 −0.127241
\(401\) −17.5757 −0.877689 −0.438845 0.898563i \(-0.644612\pi\)
−0.438845 + 0.898563i \(0.644612\pi\)
\(402\) −43.5136 −2.17026
\(403\) −3.80948 −0.189764
\(404\) 71.9683 3.58056
\(405\) 10.6345 0.528430
\(406\) 23.0031 1.14163
\(407\) 6.06406 0.300584
\(408\) −46.1296 −2.28376
\(409\) 9.08657 0.449302 0.224651 0.974439i \(-0.427876\pi\)
0.224651 + 0.974439i \(0.427876\pi\)
\(410\) 32.2851 1.59445
\(411\) −4.44567 −0.219289
\(412\) 45.0266 2.21830
\(413\) −12.4131 −0.610811
\(414\) −15.0673 −0.740517
\(415\) −5.51434 −0.270688
\(416\) −9.94864 −0.487772
\(417\) −31.8469 −1.55955
\(418\) −39.0317 −1.90910
\(419\) 28.0626 1.37095 0.685474 0.728097i \(-0.259595\pi\)
0.685474 + 0.728097i \(0.259595\pi\)
\(420\) −14.2714 −0.696375
\(421\) −30.2588 −1.47473 −0.737363 0.675497i \(-0.763929\pi\)
−0.737363 + 0.675497i \(0.763929\pi\)
\(422\) −49.0729 −2.38883
\(423\) −2.94983 −0.143426
\(424\) 4.31278 0.209447
\(425\) −1.41607 −0.0686897
\(426\) 26.0749 1.26333
\(427\) 13.0829 0.633124
\(428\) 22.5353 1.08928
\(429\) −5.42672 −0.262004
\(430\) 25.9434 1.25110
\(431\) −29.1887 −1.40597 −0.702986 0.711204i \(-0.748150\pi\)
−0.702986 + 0.711204i \(0.748150\pi\)
\(432\) −48.1756 −2.31785
\(433\) 20.7721 0.998244 0.499122 0.866532i \(-0.333656\pi\)
0.499122 + 0.866532i \(0.333656\pi\)
\(434\) 8.08786 0.388230
\(435\) 27.1681 1.30261
\(436\) −21.8101 −1.04451
\(437\) 27.2864 1.30529
\(438\) −22.1015 −1.05605
\(439\) 0.684286 0.0326592 0.0163296 0.999867i \(-0.494802\pi\)
0.0163296 + 0.999867i \(0.494802\pi\)
\(440\) −47.5043 −2.26468
\(441\) −1.01899 −0.0485234
\(442\) −14.9031 −0.708867
\(443\) 4.10502 0.195035 0.0975176 0.995234i \(-0.468910\pi\)
0.0975176 + 0.995234i \(0.468910\pi\)
\(444\) −12.5991 −0.597926
\(445\) 19.3911 0.919225
\(446\) 59.3162 2.80871
\(447\) −8.99263 −0.425337
\(448\) 4.08866 0.193171
\(449\) −28.5382 −1.34680 −0.673401 0.739277i \(-0.735167\pi\)
−0.673401 + 0.739277i \(0.735167\pi\)
\(450\) −0.786745 −0.0370875
\(451\) −18.2563 −0.859656
\(452\) −44.3131 −2.08431
\(453\) 28.6425 1.34574
\(454\) −27.1551 −1.27445
\(455\) −2.63882 −0.123710
\(456\) 46.4129 2.17348
\(457\) −38.9381 −1.82145 −0.910724 0.413016i \(-0.864475\pi\)
−0.910724 + 0.413016i \(0.864475\pi\)
\(458\) −54.7169 −2.55675
\(459\) −26.8075 −1.25127
\(460\) 58.0250 2.70543
\(461\) −26.6744 −1.24235 −0.621175 0.783672i \(-0.713345\pi\)
−0.621175 + 0.783672i \(0.713345\pi\)
\(462\) 11.5214 0.536025
\(463\) −1.71039 −0.0794884 −0.0397442 0.999210i \(-0.512654\pi\)
−0.0397442 + 0.999210i \(0.512654\pi\)
\(464\) −75.8191 −3.51982
\(465\) 9.55228 0.442976
\(466\) 52.1566 2.41611
\(467\) 38.5151 1.78227 0.891134 0.453740i \(-0.149911\pi\)
0.891134 + 0.453740i \(0.149911\pi\)
\(468\) −5.79958 −0.268085
\(469\) 11.9649 0.552486
\(470\) 16.2183 0.748094
\(471\) 9.68358 0.446196
\(472\) 85.8465 3.95140
\(473\) −14.6702 −0.674537
\(474\) 40.6900 1.86895
\(475\) 1.42477 0.0653729
\(476\) 22.1624 1.01581
\(477\) 0.635458 0.0290956
\(478\) −20.6634 −0.945121
\(479\) 27.0967 1.23808 0.619039 0.785360i \(-0.287522\pi\)
0.619039 + 0.785360i \(0.287522\pi\)
\(480\) 24.9463 1.13864
\(481\) −2.32960 −0.106221
\(482\) −1.72731 −0.0786768
\(483\) −8.05442 −0.366489
\(484\) −4.50641 −0.204837
\(485\) −19.7623 −0.897362
\(486\) −26.0113 −1.17990
\(487\) −18.3006 −0.829278 −0.414639 0.909986i \(-0.636092\pi\)
−0.414639 + 0.909986i \(0.636092\pi\)
\(488\) −90.4780 −4.09575
\(489\) 21.9101 0.990811
\(490\) 5.60245 0.253093
\(491\) 29.4340 1.32834 0.664169 0.747583i \(-0.268786\pi\)
0.664169 + 0.747583i \(0.268786\pi\)
\(492\) 37.9305 1.71004
\(493\) −42.1899 −1.90014
\(494\) 14.9946 0.674639
\(495\) −6.99943 −0.314601
\(496\) −26.6579 −1.19698
\(497\) −7.16977 −0.321608
\(498\) −9.24926 −0.414469
\(499\) 5.64540 0.252723 0.126361 0.991984i \(-0.459670\pi\)
0.126361 + 0.991984i \(0.459670\pi\)
\(500\) 53.7282 2.40280
\(501\) −9.37253 −0.418734
\(502\) −45.8464 −2.04623
\(503\) 11.9336 0.532091 0.266046 0.963960i \(-0.414283\pi\)
0.266046 + 0.963960i \(0.414283\pi\)
\(504\) 7.04710 0.313903
\(505\) −33.3676 −1.48484
\(506\) −46.8439 −2.08247
\(507\) −16.2125 −0.720024
\(508\) 39.2953 1.74345
\(509\) 9.50300 0.421213 0.210607 0.977571i \(-0.432456\pi\)
0.210607 + 0.977571i \(0.432456\pi\)
\(510\) 37.3695 1.65475
\(511\) 6.07721 0.268840
\(512\) 48.1792 2.12924
\(513\) 26.9721 1.19085
\(514\) −20.3870 −0.899232
\(515\) −20.8763 −0.919918
\(516\) 30.4798 1.34180
\(517\) −9.17097 −0.403339
\(518\) 4.94595 0.217312
\(519\) 14.9852 0.657777
\(520\) 18.2495 0.800292
\(521\) 14.5153 0.635929 0.317965 0.948103i \(-0.397001\pi\)
0.317965 + 0.948103i \(0.397001\pi\)
\(522\) −23.4400 −1.02594
\(523\) −27.1413 −1.18680 −0.593402 0.804906i \(-0.702216\pi\)
−0.593402 + 0.804906i \(0.702216\pi\)
\(524\) 79.2300 3.46118
\(525\) −0.420565 −0.0183550
\(526\) 29.9385 1.30538
\(527\) −14.8339 −0.646175
\(528\) −37.9750 −1.65265
\(529\) 9.74778 0.423817
\(530\) −3.49378 −0.151760
\(531\) 12.6489 0.548915
\(532\) −22.2985 −0.966762
\(533\) 7.01342 0.303785
\(534\) 32.5249 1.40749
\(535\) −10.4483 −0.451720
\(536\) −82.7462 −3.57409
\(537\) −20.5460 −0.886627
\(538\) −30.6318 −1.32063
\(539\) −3.16802 −0.136456
\(540\) 57.3568 2.46824
\(541\) −11.9558 −0.514019 −0.257010 0.966409i \(-0.582737\pi\)
−0.257010 + 0.966409i \(0.582737\pi\)
\(542\) −78.9583 −3.39155
\(543\) −34.9024 −1.49780
\(544\) −38.7395 −1.66094
\(545\) 10.1121 0.433155
\(546\) −4.42612 −0.189420
\(547\) 21.6130 0.924106 0.462053 0.886852i \(-0.347113\pi\)
0.462053 + 0.886852i \(0.347113\pi\)
\(548\) −14.7711 −0.630992
\(549\) −13.3313 −0.568966
\(550\) −2.44598 −0.104297
\(551\) 42.4490 1.80839
\(552\) 55.7025 2.37086
\(553\) −11.1885 −0.475782
\(554\) −51.3138 −2.18011
\(555\) 5.84148 0.247957
\(556\) −105.814 −4.48752
\(557\) 34.7922 1.47419 0.737096 0.675788i \(-0.236197\pi\)
0.737096 + 0.675788i \(0.236197\pi\)
\(558\) −8.24145 −0.348889
\(559\) 5.63578 0.238368
\(560\) −18.4659 −0.780327
\(561\) −21.1314 −0.892168
\(562\) 28.8070 1.21515
\(563\) 30.9153 1.30292 0.651462 0.758681i \(-0.274156\pi\)
0.651462 + 0.758681i \(0.274156\pi\)
\(564\) 19.0542 0.802326
\(565\) 20.5455 0.864354
\(566\) −5.88537 −0.247380
\(567\) −4.90469 −0.205977
\(568\) 49.5845 2.08052
\(569\) 16.4744 0.690644 0.345322 0.938484i \(-0.387770\pi\)
0.345322 + 0.938484i \(0.387770\pi\)
\(570\) −37.5990 −1.57485
\(571\) −30.5979 −1.28048 −0.640241 0.768174i \(-0.721166\pi\)
−0.640241 + 0.768174i \(0.721166\pi\)
\(572\) −18.0308 −0.753905
\(573\) 23.3430 0.975168
\(574\) −14.8901 −0.621502
\(575\) 1.70994 0.0713094
\(576\) −4.16631 −0.173596
\(577\) 29.5228 1.22905 0.614526 0.788897i \(-0.289347\pi\)
0.614526 + 0.788897i \(0.289347\pi\)
\(578\) −14.1057 −0.586721
\(579\) −12.7617 −0.530358
\(580\) 90.2686 3.74820
\(581\) 2.54325 0.105512
\(582\) −33.1476 −1.37401
\(583\) 1.97563 0.0818221
\(584\) −42.0285 −1.73915
\(585\) 2.68893 0.111174
\(586\) 32.0101 1.32233
\(587\) 18.6398 0.769348 0.384674 0.923053i \(-0.374314\pi\)
0.384674 + 0.923053i \(0.374314\pi\)
\(588\) 6.58209 0.271441
\(589\) 14.9250 0.614974
\(590\) −69.5441 −2.86308
\(591\) −3.71726 −0.152908
\(592\) −16.3020 −0.670010
\(593\) 4.46977 0.183551 0.0917757 0.995780i \(-0.470746\pi\)
0.0917757 + 0.995780i \(0.470746\pi\)
\(594\) −46.3045 −1.89989
\(595\) −10.2754 −0.421252
\(596\) −29.8788 −1.22389
\(597\) 25.9050 1.06022
\(598\) 17.9958 0.735903
\(599\) 23.2416 0.949627 0.474814 0.880086i \(-0.342516\pi\)
0.474814 + 0.880086i \(0.342516\pi\)
\(600\) 2.90853 0.118740
\(601\) 20.2537 0.826166 0.413083 0.910693i \(-0.364452\pi\)
0.413083 + 0.910693i \(0.364452\pi\)
\(602\) −11.9653 −0.487668
\(603\) −12.1921 −0.496500
\(604\) 95.1674 3.87230
\(605\) 2.08937 0.0849448
\(606\) −55.9678 −2.27354
\(607\) 15.8435 0.643067 0.321534 0.946898i \(-0.395802\pi\)
0.321534 + 0.946898i \(0.395802\pi\)
\(608\) 38.9774 1.58074
\(609\) −12.5301 −0.507747
\(610\) 73.2961 2.96767
\(611\) 3.52316 0.142532
\(612\) −22.5833 −0.912874
\(613\) −1.88452 −0.0761150 −0.0380575 0.999276i \(-0.512117\pi\)
−0.0380575 + 0.999276i \(0.512117\pi\)
\(614\) −31.6798 −1.27849
\(615\) −17.5862 −0.709144
\(616\) 21.9093 0.882751
\(617\) 37.1643 1.49618 0.748089 0.663599i \(-0.230972\pi\)
0.748089 + 0.663599i \(0.230972\pi\)
\(618\) −35.0160 −1.40855
\(619\) 8.30855 0.333949 0.166974 0.985961i \(-0.446600\pi\)
0.166974 + 0.985961i \(0.446600\pi\)
\(620\) 31.7383 1.27464
\(621\) 32.3706 1.29899
\(622\) −26.8030 −1.07470
\(623\) −8.94330 −0.358306
\(624\) 14.5887 0.584014
\(625\) −23.4167 −0.936667
\(626\) −26.6473 −1.06504
\(627\) 21.2611 0.849088
\(628\) 32.1746 1.28391
\(629\) −9.07134 −0.361698
\(630\) −5.70885 −0.227446
\(631\) 31.2650 1.24464 0.622321 0.782762i \(-0.286190\pi\)
0.622321 + 0.782762i \(0.286190\pi\)
\(632\) 77.3768 3.07788
\(633\) 26.7307 1.06245
\(634\) 75.8487 3.01234
\(635\) −18.2190 −0.723000
\(636\) −4.10469 −0.162762
\(637\) 1.21704 0.0482210
\(638\) −72.8744 −2.88512
\(639\) 7.30593 0.289018
\(640\) −12.5415 −0.495746
\(641\) −3.21887 −0.127138 −0.0635688 0.997977i \(-0.520248\pi\)
−0.0635688 + 0.997977i \(0.520248\pi\)
\(642\) −17.5251 −0.691660
\(643\) −18.0704 −0.712628 −0.356314 0.934366i \(-0.615967\pi\)
−0.356314 + 0.934366i \(0.615967\pi\)
\(644\) −26.7616 −1.05455
\(645\) −14.1317 −0.556436
\(646\) 58.3883 2.29726
\(647\) −27.3717 −1.07609 −0.538047 0.842915i \(-0.680838\pi\)
−0.538047 + 0.842915i \(0.680838\pi\)
\(648\) 33.9197 1.33249
\(649\) 39.3251 1.54365
\(650\) 0.939657 0.0368564
\(651\) −4.40558 −0.172668
\(652\) 72.7985 2.85101
\(653\) 23.0635 0.902543 0.451271 0.892387i \(-0.350971\pi\)
0.451271 + 0.892387i \(0.350971\pi\)
\(654\) 16.9611 0.663233
\(655\) −36.7344 −1.43533
\(656\) 49.0785 1.91619
\(657\) −6.19262 −0.241597
\(658\) −7.47999 −0.291600
\(659\) 10.5894 0.412503 0.206252 0.978499i \(-0.433873\pi\)
0.206252 + 0.978499i \(0.433873\pi\)
\(660\) 45.2122 1.75988
\(661\) −16.6479 −0.647528 −0.323764 0.946138i \(-0.604948\pi\)
−0.323764 + 0.946138i \(0.604948\pi\)
\(662\) 62.5778 2.43215
\(663\) 8.11793 0.315274
\(664\) −17.5885 −0.682568
\(665\) 10.3385 0.400911
\(666\) −5.03987 −0.195291
\(667\) 50.9452 1.97261
\(668\) −31.1411 −1.20488
\(669\) −32.3104 −1.24919
\(670\) 67.0326 2.58969
\(671\) −41.4468 −1.60004
\(672\) −11.5054 −0.443830
\(673\) 34.7365 1.33899 0.669496 0.742815i \(-0.266510\pi\)
0.669496 + 0.742815i \(0.266510\pi\)
\(674\) −45.5487 −1.75447
\(675\) 1.69025 0.0650576
\(676\) −53.8676 −2.07183
\(677\) −26.8774 −1.03298 −0.516492 0.856292i \(-0.672762\pi\)
−0.516492 + 0.856292i \(0.672762\pi\)
\(678\) 34.4611 1.32347
\(679\) 9.11453 0.349784
\(680\) 71.0625 2.72512
\(681\) 14.7918 0.566822
\(682\) −25.6225 −0.981138
\(683\) 23.4514 0.897345 0.448672 0.893696i \(-0.351897\pi\)
0.448672 + 0.893696i \(0.351897\pi\)
\(684\) 22.7219 0.868795
\(685\) 6.84854 0.261669
\(686\) −2.58389 −0.0986534
\(687\) 29.8051 1.13714
\(688\) 39.4380 1.50356
\(689\) −0.758966 −0.0289143
\(690\) −45.1245 −1.71786
\(691\) −40.4654 −1.53938 −0.769689 0.638419i \(-0.779589\pi\)
−0.769689 + 0.638419i \(0.779589\pi\)
\(692\) 49.7897 1.89272
\(693\) 3.22819 0.122629
\(694\) 37.4303 1.42083
\(695\) 49.0600 1.86095
\(696\) 86.6555 3.28467
\(697\) 27.3099 1.03444
\(698\) 74.9731 2.83777
\(699\) −28.4105 −1.07458
\(700\) −1.39737 −0.0528154
\(701\) 16.0954 0.607915 0.303957 0.952686i \(-0.401692\pi\)
0.303957 + 0.952686i \(0.401692\pi\)
\(702\) 17.7885 0.671385
\(703\) 9.12705 0.344233
\(704\) −12.9530 −0.488184
\(705\) −8.83434 −0.332721
\(706\) 50.7056 1.90833
\(707\) 15.3894 0.578777
\(708\) −81.7044 −3.07064
\(709\) −25.2079 −0.946703 −0.473352 0.880874i \(-0.656956\pi\)
−0.473352 + 0.880874i \(0.656956\pi\)
\(710\) −40.1683 −1.50749
\(711\) 11.4009 0.427568
\(712\) 61.8498 2.31792
\(713\) 17.9123 0.670820
\(714\) −17.2351 −0.645007
\(715\) 8.35984 0.312640
\(716\) −68.2661 −2.55122
\(717\) 11.2556 0.420350
\(718\) −91.0382 −3.39751
\(719\) 34.6652 1.29279 0.646397 0.763001i \(-0.276275\pi\)
0.646397 + 0.763001i \(0.276275\pi\)
\(720\) 18.8166 0.701253
\(721\) 9.62828 0.358576
\(722\) −9.65290 −0.359244
\(723\) 0.940891 0.0349921
\(724\) −115.966 −4.30985
\(725\) 2.66012 0.0987945
\(726\) 3.50452 0.130065
\(727\) 33.4073 1.23901 0.619505 0.784993i \(-0.287333\pi\)
0.619505 + 0.784993i \(0.287333\pi\)
\(728\) −8.41678 −0.311947
\(729\) 28.8828 1.06973
\(730\) 34.0473 1.26015
\(731\) 21.9454 0.811681
\(732\) 86.1125 3.18281
\(733\) −35.1577 −1.29858 −0.649289 0.760542i \(-0.724933\pi\)
−0.649289 + 0.760542i \(0.724933\pi\)
\(734\) −82.9863 −3.06308
\(735\) −3.05174 −0.112565
\(736\) 46.7788 1.72429
\(737\) −37.9050 −1.39625
\(738\) 15.1729 0.558522
\(739\) −29.9573 −1.10200 −0.550998 0.834506i \(-0.685753\pi\)
−0.550998 + 0.834506i \(0.685753\pi\)
\(740\) 19.4088 0.713483
\(741\) −8.16778 −0.300051
\(742\) 1.61135 0.0591547
\(743\) 38.5524 1.41435 0.707175 0.707039i \(-0.249969\pi\)
0.707175 + 0.707039i \(0.249969\pi\)
\(744\) 30.4679 1.11701
\(745\) 13.8531 0.507539
\(746\) −37.7943 −1.38375
\(747\) −2.59155 −0.0948199
\(748\) −70.2110 −2.56717
\(749\) 4.81884 0.176077
\(750\) −41.7830 −1.52570
\(751\) 10.7625 0.392729 0.196364 0.980531i \(-0.437086\pi\)
0.196364 + 0.980531i \(0.437086\pi\)
\(752\) 24.6543 0.899051
\(753\) 24.9732 0.910074
\(754\) 27.9958 1.01955
\(755\) −44.1237 −1.60583
\(756\) −26.4533 −0.962099
\(757\) 5.24608 0.190672 0.0953360 0.995445i \(-0.469607\pi\)
0.0953360 + 0.995445i \(0.469607\pi\)
\(758\) 78.5095 2.85159
\(759\) 25.5166 0.926193
\(760\) −71.4989 −2.59354
\(761\) 17.7460 0.643291 0.321646 0.946860i \(-0.395764\pi\)
0.321646 + 0.946860i \(0.395764\pi\)
\(762\) −30.5589 −1.10703
\(763\) −4.66377 −0.168840
\(764\) 77.5593 2.80600
\(765\) 10.4706 0.378564
\(766\) 82.5023 2.98093
\(767\) −15.1073 −0.545494
\(768\) −32.5454 −1.17438
\(769\) 12.5287 0.451798 0.225899 0.974151i \(-0.427468\pi\)
0.225899 + 0.974151i \(0.427468\pi\)
\(770\) −17.7487 −0.639619
\(771\) 11.1051 0.399940
\(772\) −42.4019 −1.52608
\(773\) 3.54616 0.127547 0.0637733 0.997964i \(-0.479687\pi\)
0.0637733 + 0.997964i \(0.479687\pi\)
\(774\) 12.1925 0.438250
\(775\) 0.935296 0.0335968
\(776\) −63.0340 −2.26279
\(777\) −2.69413 −0.0966514
\(778\) −23.6626 −0.848344
\(779\) −27.4776 −0.984489
\(780\) −17.3689 −0.621908
\(781\) 22.7140 0.812771
\(782\) 70.0747 2.50587
\(783\) 50.3585 1.79967
\(784\) 8.51660 0.304164
\(785\) −14.9175 −0.532429
\(786\) −61.6151 −2.19774
\(787\) −16.3250 −0.581924 −0.290962 0.956735i \(-0.593975\pi\)
−0.290962 + 0.956735i \(0.593975\pi\)
\(788\) −12.3510 −0.439984
\(789\) −16.3080 −0.580579
\(790\) −62.6828 −2.23016
\(791\) −9.47571 −0.336917
\(792\) −22.3254 −0.793298
\(793\) 15.9224 0.565421
\(794\) −77.9720 −2.76712
\(795\) 1.90311 0.0674964
\(796\) 86.0718 3.05074
\(797\) −23.2658 −0.824115 −0.412058 0.911158i \(-0.635190\pi\)
−0.412058 + 0.911158i \(0.635190\pi\)
\(798\) 17.3409 0.613863
\(799\) 13.7190 0.485344
\(800\) 2.44257 0.0863580
\(801\) 9.11314 0.321997
\(802\) 45.4137 1.60361
\(803\) −19.2527 −0.679414
\(804\) 78.7537 2.77743
\(805\) 12.4078 0.437318
\(806\) 9.84327 0.346714
\(807\) 16.6856 0.587361
\(808\) −106.429 −3.74417
\(809\) 52.5787 1.84857 0.924285 0.381704i \(-0.124662\pi\)
0.924285 + 0.381704i \(0.124662\pi\)
\(810\) −27.4783 −0.965488
\(811\) 13.1212 0.460749 0.230374 0.973102i \(-0.426005\pi\)
0.230374 + 0.973102i \(0.426005\pi\)
\(812\) −41.6325 −1.46101
\(813\) 43.0097 1.50842
\(814\) −15.6689 −0.549194
\(815\) −33.7525 −1.18230
\(816\) 56.8075 1.98866
\(817\) −22.0802 −0.772489
\(818\) −23.4787 −0.820914
\(819\) −1.24015 −0.0433345
\(820\) −58.4317 −2.04053
\(821\) −19.1866 −0.669617 −0.334809 0.942286i \(-0.608672\pi\)
−0.334809 + 0.942286i \(0.608672\pi\)
\(822\) 11.4871 0.400659
\(823\) −52.2064 −1.81980 −0.909900 0.414827i \(-0.863842\pi\)
−0.909900 + 0.414827i \(0.863842\pi\)
\(824\) −66.5869 −2.31967
\(825\) 1.33236 0.0463868
\(826\) 32.0742 1.11601
\(827\) −17.8820 −0.621819 −0.310909 0.950440i \(-0.600634\pi\)
−0.310909 + 0.950440i \(0.600634\pi\)
\(828\) 27.2698 0.947690
\(829\) −56.3134 −1.95584 −0.977922 0.208968i \(-0.932989\pi\)
−0.977922 + 0.208968i \(0.932989\pi\)
\(830\) 14.2485 0.494571
\(831\) 27.9514 0.969622
\(832\) 4.97608 0.172514
\(833\) 4.73910 0.164200
\(834\) 82.2889 2.84943
\(835\) 14.4383 0.499660
\(836\) 70.6421 2.44321
\(837\) 17.7060 0.612008
\(838\) −72.5107 −2.50484
\(839\) 20.2365 0.698642 0.349321 0.937003i \(-0.386412\pi\)
0.349321 + 0.937003i \(0.386412\pi\)
\(840\) 21.1051 0.728196
\(841\) 50.2546 1.73292
\(842\) 78.1855 2.69445
\(843\) −15.6916 −0.540447
\(844\) 88.8153 3.05715
\(845\) 24.9754 0.859178
\(846\) 7.62204 0.262051
\(847\) −0.963631 −0.0331107
\(848\) −5.31108 −0.182383
\(849\) 3.20584 0.110024
\(850\) 3.65898 0.125502
\(851\) 10.9538 0.375493
\(852\) −47.1921 −1.61677
\(853\) 0.939780 0.0321775 0.0160887 0.999871i \(-0.494879\pi\)
0.0160887 + 0.999871i \(0.494879\pi\)
\(854\) −33.8047 −1.15677
\(855\) −10.5349 −0.360285
\(856\) −33.3260 −1.13906
\(857\) 4.78546 0.163468 0.0817342 0.996654i \(-0.473954\pi\)
0.0817342 + 0.996654i \(0.473954\pi\)
\(858\) 14.0221 0.478705
\(859\) 12.6053 0.430086 0.215043 0.976605i \(-0.431011\pi\)
0.215043 + 0.976605i \(0.431011\pi\)
\(860\) −46.9540 −1.60112
\(861\) 8.11088 0.276418
\(862\) 75.4205 2.56883
\(863\) −1.00000 −0.0340404
\(864\) 46.2401 1.57312
\(865\) −23.0846 −0.784901
\(866\) −53.6729 −1.82388
\(867\) 7.68360 0.260949
\(868\) −14.6379 −0.496844
\(869\) 35.4453 1.20240
\(870\) −70.1995 −2.37999
\(871\) 14.5617 0.493406
\(872\) 32.2536 1.09224
\(873\) −9.28762 −0.314338
\(874\) −70.5051 −2.38487
\(875\) 11.4890 0.388399
\(876\) 40.0007 1.35150
\(877\) 17.9131 0.604881 0.302441 0.953168i \(-0.402199\pi\)
0.302441 + 0.953168i \(0.402199\pi\)
\(878\) −1.76812 −0.0596712
\(879\) −17.4364 −0.588115
\(880\) 58.5004 1.97205
\(881\) 33.5258 1.12951 0.564757 0.825258i \(-0.308970\pi\)
0.564757 + 0.825258i \(0.308970\pi\)
\(882\) 2.63296 0.0886564
\(883\) 12.0913 0.406904 0.203452 0.979085i \(-0.434784\pi\)
0.203452 + 0.979085i \(0.434784\pi\)
\(884\) 26.9726 0.907186
\(885\) 37.8817 1.27338
\(886\) −10.6069 −0.356346
\(887\) 24.5908 0.825680 0.412840 0.910804i \(-0.364537\pi\)
0.412840 + 0.910804i \(0.364537\pi\)
\(888\) 18.6320 0.625248
\(889\) 8.40274 0.281819
\(890\) −50.1044 −1.67950
\(891\) 15.5382 0.520548
\(892\) −107.354 −3.59449
\(893\) −13.8033 −0.461909
\(894\) 23.2360 0.777127
\(895\) 31.6511 1.05798
\(896\) 5.78423 0.193237
\(897\) −9.80257 −0.327298
\(898\) 73.7397 2.46072
\(899\) 27.8658 0.929377
\(900\) 1.42390 0.0474634
\(901\) −2.95538 −0.0984579
\(902\) 47.1723 1.57067
\(903\) 6.51765 0.216894
\(904\) 65.5318 2.17956
\(905\) 53.7670 1.78727
\(906\) −74.0091 −2.45879
\(907\) 46.2903 1.53705 0.768523 0.639822i \(-0.220992\pi\)
0.768523 + 0.639822i \(0.220992\pi\)
\(908\) 49.1470 1.63100
\(909\) −15.6816 −0.520127
\(910\) 6.81842 0.226029
\(911\) −41.3060 −1.36853 −0.684265 0.729233i \(-0.739877\pi\)
−0.684265 + 0.729233i \(0.739877\pi\)
\(912\) −57.1564 −1.89264
\(913\) −8.05708 −0.266651
\(914\) 100.612 3.32794
\(915\) −39.9255 −1.31990
\(916\) 99.0302 3.27205
\(917\) 16.9422 0.559480
\(918\) 69.2677 2.28617
\(919\) 1.96299 0.0647530 0.0323765 0.999476i \(-0.489692\pi\)
0.0323765 + 0.999476i \(0.489692\pi\)
\(920\) −85.8095 −2.82906
\(921\) 17.2565 0.568620
\(922\) 68.9237 2.26988
\(923\) −8.72592 −0.287217
\(924\) −20.8522 −0.685987
\(925\) 0.571959 0.0188059
\(926\) 4.41945 0.145232
\(927\) −9.81113 −0.322240
\(928\) 72.7730 2.38889
\(929\) 34.1404 1.12011 0.560054 0.828456i \(-0.310780\pi\)
0.560054 + 0.828456i \(0.310780\pi\)
\(930\) −24.6820 −0.809356
\(931\) −4.76821 −0.156272
\(932\) −94.3964 −3.09206
\(933\) 14.6000 0.477981
\(934\) −99.5189 −3.25636
\(935\) 32.5528 1.06459
\(936\) 8.57662 0.280336
\(937\) −38.4027 −1.25456 −0.627280 0.778794i \(-0.715832\pi\)
−0.627280 + 0.778794i \(0.715832\pi\)
\(938\) −30.9159 −1.00944
\(939\) 14.5152 0.473685
\(940\) −29.3529 −0.957387
\(941\) 26.2195 0.854730 0.427365 0.904079i \(-0.359442\pi\)
0.427365 + 0.904079i \(0.359442\pi\)
\(942\) −25.0213 −0.815238
\(943\) −32.9773 −1.07389
\(944\) −105.718 −3.44082
\(945\) 12.2649 0.398978
\(946\) 37.9062 1.23244
\(947\) −40.1010 −1.30311 −0.651554 0.758603i \(-0.725882\pi\)
−0.651554 + 0.758603i \(0.725882\pi\)
\(948\) −73.6434 −2.39183
\(949\) 7.39622 0.240091
\(950\) −3.68145 −0.119442
\(951\) −41.3159 −1.33976
\(952\) −32.7745 −1.06223
\(953\) 21.1875 0.686332 0.343166 0.939275i \(-0.388501\pi\)
0.343166 + 0.939275i \(0.388501\pi\)
\(954\) −1.64195 −0.0531602
\(955\) −35.9598 −1.16363
\(956\) 37.3979 1.20954
\(957\) 39.6957 1.28318
\(958\) −70.0148 −2.26208
\(959\) −3.15859 −0.101996
\(960\) −12.4775 −0.402711
\(961\) −21.2024 −0.683949
\(962\) 6.01943 0.194074
\(963\) −4.91035 −0.158234
\(964\) 3.12620 0.100688
\(965\) 19.6593 0.632857
\(966\) 20.8117 0.669607
\(967\) 7.11479 0.228796 0.114398 0.993435i \(-0.463506\pi\)
0.114398 + 0.993435i \(0.463506\pi\)
\(968\) 6.66425 0.214197
\(969\) −31.8049 −1.02172
\(970\) 51.0638 1.63956
\(971\) −1.50885 −0.0484213 −0.0242107 0.999707i \(-0.507707\pi\)
−0.0242107 + 0.999707i \(0.507707\pi\)
\(972\) 47.0770 1.50999
\(973\) −22.6268 −0.725383
\(974\) 47.2867 1.51516
\(975\) −0.511845 −0.0163922
\(976\) 111.422 3.56652
\(977\) 24.3726 0.779749 0.389874 0.920868i \(-0.372518\pi\)
0.389874 + 0.920868i \(0.372518\pi\)
\(978\) −56.6134 −1.81030
\(979\) 28.3326 0.905513
\(980\) −10.1397 −0.323900
\(981\) 4.75234 0.151730
\(982\) −76.0542 −2.42699
\(983\) −22.4254 −0.715261 −0.357630 0.933863i \(-0.616415\pi\)
−0.357630 + 0.933863i \(0.616415\pi\)
\(984\) −56.0929 −1.78818
\(985\) 5.72643 0.182459
\(986\) 109.014 3.47172
\(987\) 4.07446 0.129692
\(988\) −27.1382 −0.863381
\(989\) −26.4996 −0.842637
\(990\) 18.0858 0.574803
\(991\) 29.8617 0.948588 0.474294 0.880367i \(-0.342703\pi\)
0.474294 + 0.880367i \(0.342703\pi\)
\(992\) 25.5869 0.812385
\(993\) −34.0870 −1.08172
\(994\) 18.5259 0.587606
\(995\) −39.9066 −1.26512
\(996\) 16.7399 0.530424
\(997\) −29.8203 −0.944418 −0.472209 0.881487i \(-0.656543\pi\)
−0.472209 + 0.881487i \(0.656543\pi\)
\(998\) −14.5871 −0.461746
\(999\) 10.8277 0.342573
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 \(a_p\))