Properties

Label 8042.2.a.c.1.18
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 0
Dimension 86
CM No

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Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(0\)
Dimension: \(86\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-2.00326 q^{3}\) \(+1.00000 q^{4}\) \(+3.10974 q^{5}\) \(+2.00326 q^{6}\) \(+0.986750 q^{7}\) \(-1.00000 q^{8}\) \(+1.01305 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-2.00326 q^{3}\) \(+1.00000 q^{4}\) \(+3.10974 q^{5}\) \(+2.00326 q^{6}\) \(+0.986750 q^{7}\) \(-1.00000 q^{8}\) \(+1.01305 q^{9}\) \(-3.10974 q^{10}\) \(+3.67333 q^{11}\) \(-2.00326 q^{12}\) \(+3.31892 q^{13}\) \(-0.986750 q^{14}\) \(-6.22962 q^{15}\) \(+1.00000 q^{16}\) \(+0.586675 q^{17}\) \(-1.01305 q^{18}\) \(+4.79483 q^{19}\) \(+3.10974 q^{20}\) \(-1.97672 q^{21}\) \(-3.67333 q^{22}\) \(-5.09332 q^{23}\) \(+2.00326 q^{24}\) \(+4.67048 q^{25}\) \(-3.31892 q^{26}\) \(+3.98037 q^{27}\) \(+0.986750 q^{28}\) \(+7.37813 q^{29}\) \(+6.22962 q^{30}\) \(+2.75789 q^{31}\) \(-1.00000 q^{32}\) \(-7.35864 q^{33}\) \(-0.586675 q^{34}\) \(+3.06853 q^{35}\) \(+1.01305 q^{36}\) \(-1.95094 q^{37}\) \(-4.79483 q^{38}\) \(-6.64866 q^{39}\) \(-3.10974 q^{40}\) \(+0.441491 q^{41}\) \(+1.97672 q^{42}\) \(+13.0457 q^{43}\) \(+3.67333 q^{44}\) \(+3.15033 q^{45}\) \(+5.09332 q^{46}\) \(-1.25308 q^{47}\) \(-2.00326 q^{48}\) \(-6.02632 q^{49}\) \(-4.67048 q^{50}\) \(-1.17526 q^{51}\) \(+3.31892 q^{52}\) \(-1.69088 q^{53}\) \(-3.98037 q^{54}\) \(+11.4231 q^{55}\) \(-0.986750 q^{56}\) \(-9.60530 q^{57}\) \(-7.37813 q^{58}\) \(-9.28498 q^{59}\) \(-6.22962 q^{60}\) \(+2.23525 q^{61}\) \(-2.75789 q^{62}\) \(+0.999629 q^{63}\) \(+1.00000 q^{64}\) \(+10.3210 q^{65}\) \(+7.35864 q^{66}\) \(+1.27723 q^{67}\) \(+0.586675 q^{68}\) \(+10.2033 q^{69}\) \(-3.06853 q^{70}\) \(+12.5663 q^{71}\) \(-1.01305 q^{72}\) \(+12.9485 q^{73}\) \(+1.95094 q^{74}\) \(-9.35619 q^{75}\) \(+4.79483 q^{76}\) \(+3.62466 q^{77}\) \(+6.64866 q^{78}\) \(+2.95821 q^{79}\) \(+3.10974 q^{80}\) \(-11.0129 q^{81}\) \(-0.441491 q^{82}\) \(-5.28601 q^{83}\) \(-1.97672 q^{84}\) \(+1.82441 q^{85}\) \(-13.0457 q^{86}\) \(-14.7803 q^{87}\) \(-3.67333 q^{88}\) \(-11.6601 q^{89}\) \(-3.15033 q^{90}\) \(+3.27494 q^{91}\) \(-5.09332 q^{92}\) \(-5.52477 q^{93}\) \(+1.25308 q^{94}\) \(+14.9107 q^{95}\) \(+2.00326 q^{96}\) \(+3.93094 q^{97}\) \(+6.02632 q^{98}\) \(+3.72127 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 45q^{13} \) \(\mathstrut -\mathstrut 35q^{14} \) \(\mathstrut +\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 86q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 72q^{18} \) \(\mathstrut +\mathstrut 47q^{19} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 12q^{24} \) \(\mathstrut +\mathstrut 112q^{25} \) \(\mathstrut -\mathstrut 45q^{26} \) \(\mathstrut +\mathstrut 51q^{27} \) \(\mathstrut +\mathstrut 35q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut -\mathstrut 17q^{30} \) \(\mathstrut +\mathstrut 24q^{31} \) \(\mathstrut -\mathstrut 86q^{32} \) \(\mathstrut +\mathstrut 43q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 42q^{35} \) \(\mathstrut +\mathstrut 72q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut -\mathstrut 15q^{42} \) \(\mathstrut +\mathstrut 72q^{43} \) \(\mathstrut +\mathstrut 13q^{44} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut +\mathstrut 12q^{48} \) \(\mathstrut +\mathstrut 89q^{49} \) \(\mathstrut -\mathstrut 112q^{50} \) \(\mathstrut +\mathstrut 56q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut -\mathstrut 7q^{53} \) \(\mathstrut -\mathstrut 51q^{54} \) \(\mathstrut +\mathstrut 48q^{55} \) \(\mathstrut -\mathstrut 35q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 31q^{61} \) \(\mathstrut -\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 98q^{63} \) \(\mathstrut +\mathstrut 86q^{64} \) \(\mathstrut -\mathstrut 9q^{65} \) \(\mathstrut -\mathstrut 43q^{66} \) \(\mathstrut +\mathstrut 157q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 42q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 72q^{72} \) \(\mathstrut +\mathstrut 74q^{73} \) \(\mathstrut -\mathstrut 61q^{74} \) \(\mathstrut +\mathstrut 76q^{75} \) \(\mathstrut +\mathstrut 47q^{76} \) \(\mathstrut -\mathstrut 13q^{77} \) \(\mathstrut -\mathstrut 20q^{78} \) \(\mathstrut +\mathstrut 57q^{79} \) \(\mathstrut -\mathstrut 4q^{80} \) \(\mathstrut +\mathstrut 34q^{81} \) \(\mathstrut +\mathstrut 16q^{82} \) \(\mathstrut +\mathstrut 65q^{83} \) \(\mathstrut +\mathstrut 15q^{84} \) \(\mathstrut +\mathstrut 102q^{85} \) \(\mathstrut -\mathstrut 72q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 91q^{91} \) \(\mathstrut +\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 57q^{93} \) \(\mathstrut -\mathstrut 11q^{94} \) \(\mathstrut -\mathstrut 13q^{95} \) \(\mathstrut -\mathstrut 12q^{96} \) \(\mathstrut +\mathstrut 64q^{97} \) \(\mathstrut -\mathstrut 89q^{98} \) \(\mathstrut +\mathstrut 56q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.00326 −1.15658 −0.578291 0.815830i \(-0.696280\pi\)
−0.578291 + 0.815830i \(0.696280\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.10974 1.39072 0.695359 0.718663i \(-0.255245\pi\)
0.695359 + 0.718663i \(0.255245\pi\)
\(6\) 2.00326 0.817828
\(7\) 0.986750 0.372956 0.186478 0.982459i \(-0.440293\pi\)
0.186478 + 0.982459i \(0.440293\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.01305 0.337684
\(10\) −3.10974 −0.983386
\(11\) 3.67333 1.10755 0.553775 0.832666i \(-0.313187\pi\)
0.553775 + 0.832666i \(0.313187\pi\)
\(12\) −2.00326 −0.578291
\(13\) 3.31892 0.920503 0.460251 0.887789i \(-0.347759\pi\)
0.460251 + 0.887789i \(0.347759\pi\)
\(14\) −0.986750 −0.263720
\(15\) −6.22962 −1.60848
\(16\) 1.00000 0.250000
\(17\) 0.586675 0.142290 0.0711448 0.997466i \(-0.477335\pi\)
0.0711448 + 0.997466i \(0.477335\pi\)
\(18\) −1.01305 −0.238779
\(19\) 4.79483 1.10001 0.550005 0.835161i \(-0.314626\pi\)
0.550005 + 0.835161i \(0.314626\pi\)
\(20\) 3.10974 0.695359
\(21\) −1.97672 −0.431355
\(22\) −3.67333 −0.783157
\(23\) −5.09332 −1.06203 −0.531016 0.847362i \(-0.678190\pi\)
−0.531016 + 0.847362i \(0.678190\pi\)
\(24\) 2.00326 0.408914
\(25\) 4.67048 0.934096
\(26\) −3.31892 −0.650894
\(27\) 3.98037 0.766023
\(28\) 0.986750 0.186478
\(29\) 7.37813 1.37008 0.685042 0.728504i \(-0.259784\pi\)
0.685042 + 0.728504i \(0.259784\pi\)
\(30\) 6.22962 1.13737
\(31\) 2.75789 0.495331 0.247666 0.968846i \(-0.420337\pi\)
0.247666 + 0.968846i \(0.420337\pi\)
\(32\) −1.00000 −0.176777
\(33\) −7.35864 −1.28097
\(34\) −0.586675 −0.100614
\(35\) 3.06853 0.518677
\(36\) 1.01305 0.168842
\(37\) −1.95094 −0.320732 −0.160366 0.987058i \(-0.551267\pi\)
−0.160366 + 0.987058i \(0.551267\pi\)
\(38\) −4.79483 −0.777825
\(39\) −6.64866 −1.06464
\(40\) −3.10974 −0.491693
\(41\) 0.441491 0.0689494 0.0344747 0.999406i \(-0.489024\pi\)
0.0344747 + 0.999406i \(0.489024\pi\)
\(42\) 1.97672 0.305014
\(43\) 13.0457 1.98946 0.994729 0.102543i \(-0.0326979\pi\)
0.994729 + 0.102543i \(0.0326979\pi\)
\(44\) 3.67333 0.553775
\(45\) 3.15033 0.469623
\(46\) 5.09332 0.750970
\(47\) −1.25308 −0.182781 −0.0913903 0.995815i \(-0.529131\pi\)
−0.0913903 + 0.995815i \(0.529131\pi\)
\(48\) −2.00326 −0.289146
\(49\) −6.02632 −0.860904
\(50\) −4.67048 −0.660506
\(51\) −1.17526 −0.164570
\(52\) 3.31892 0.460251
\(53\) −1.69088 −0.232260 −0.116130 0.993234i \(-0.537049\pi\)
−0.116130 + 0.993234i \(0.537049\pi\)
\(54\) −3.98037 −0.541660
\(55\) 11.4231 1.54029
\(56\) −0.986750 −0.131860
\(57\) −9.60530 −1.27225
\(58\) −7.37813 −0.968796
\(59\) −9.28498 −1.20880 −0.604401 0.796680i \(-0.706587\pi\)
−0.604401 + 0.796680i \(0.706587\pi\)
\(60\) −6.22962 −0.804240
\(61\) 2.23525 0.286195 0.143097 0.989709i \(-0.454294\pi\)
0.143097 + 0.989709i \(0.454294\pi\)
\(62\) −2.75789 −0.350252
\(63\) 0.999629 0.125941
\(64\) 1.00000 0.125000
\(65\) 10.3210 1.28016
\(66\) 7.35864 0.905786
\(67\) 1.27723 0.156039 0.0780193 0.996952i \(-0.475140\pi\)
0.0780193 + 0.996952i \(0.475140\pi\)
\(68\) 0.586675 0.0711448
\(69\) 10.2033 1.22833
\(70\) −3.06853 −0.366760
\(71\) 12.5663 1.49134 0.745672 0.666313i \(-0.232129\pi\)
0.745672 + 0.666313i \(0.232129\pi\)
\(72\) −1.01305 −0.119389
\(73\) 12.9485 1.51551 0.757754 0.652540i \(-0.226296\pi\)
0.757754 + 0.652540i \(0.226296\pi\)
\(74\) 1.95094 0.226792
\(75\) −9.35619 −1.08036
\(76\) 4.79483 0.550005
\(77\) 3.62466 0.413068
\(78\) 6.64866 0.752813
\(79\) 2.95821 0.332825 0.166412 0.986056i \(-0.446782\pi\)
0.166412 + 0.986056i \(0.446782\pi\)
\(80\) 3.10974 0.347679
\(81\) −11.0129 −1.22365
\(82\) −0.441491 −0.0487546
\(83\) −5.28601 −0.580215 −0.290108 0.956994i \(-0.593691\pi\)
−0.290108 + 0.956994i \(0.593691\pi\)
\(84\) −1.97672 −0.215677
\(85\) 1.82441 0.197885
\(86\) −13.0457 −1.40676
\(87\) −14.7803 −1.58462
\(88\) −3.67333 −0.391578
\(89\) −11.6601 −1.23597 −0.617985 0.786190i \(-0.712051\pi\)
−0.617985 + 0.786190i \(0.712051\pi\)
\(90\) −3.15033 −0.332074
\(91\) 3.27494 0.343307
\(92\) −5.09332 −0.531016
\(93\) −5.52477 −0.572892
\(94\) 1.25308 0.129245
\(95\) 14.9107 1.52980
\(96\) 2.00326 0.204457
\(97\) 3.93094 0.399126 0.199563 0.979885i \(-0.436048\pi\)
0.199563 + 0.979885i \(0.436048\pi\)
\(98\) 6.02632 0.608751
\(99\) 3.72127 0.374002
\(100\) 4.67048 0.467048
\(101\) −0.733382 −0.0729743 −0.0364871 0.999334i \(-0.511617\pi\)
−0.0364871 + 0.999334i \(0.511617\pi\)
\(102\) 1.17526 0.116368
\(103\) 8.76624 0.863763 0.431881 0.901930i \(-0.357850\pi\)
0.431881 + 0.901930i \(0.357850\pi\)
\(104\) −3.31892 −0.325447
\(105\) −6.14707 −0.599893
\(106\) 1.69088 0.164233
\(107\) 15.2066 1.47008 0.735038 0.678026i \(-0.237165\pi\)
0.735038 + 0.678026i \(0.237165\pi\)
\(108\) 3.98037 0.383012
\(109\) −14.0280 −1.34364 −0.671819 0.740715i \(-0.734487\pi\)
−0.671819 + 0.740715i \(0.734487\pi\)
\(110\) −11.4231 −1.08915
\(111\) 3.90823 0.370953
\(112\) 0.986750 0.0932391
\(113\) 10.2797 0.967031 0.483515 0.875336i \(-0.339360\pi\)
0.483515 + 0.875336i \(0.339360\pi\)
\(114\) 9.60530 0.899618
\(115\) −15.8389 −1.47699
\(116\) 7.37813 0.685042
\(117\) 3.36224 0.310839
\(118\) 9.28498 0.854752
\(119\) 0.578902 0.0530678
\(120\) 6.22962 0.568684
\(121\) 2.49336 0.226669
\(122\) −2.23525 −0.202370
\(123\) −0.884422 −0.0797457
\(124\) 2.75789 0.247666
\(125\) −1.02472 −0.0916540
\(126\) −0.999629 −0.0890540
\(127\) 13.1015 1.16257 0.581286 0.813700i \(-0.302550\pi\)
0.581286 + 0.813700i \(0.302550\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −26.1340 −2.30097
\(130\) −10.3210 −0.905209
\(131\) 7.20966 0.629911 0.314955 0.949106i \(-0.398010\pi\)
0.314955 + 0.949106i \(0.398010\pi\)
\(132\) −7.35864 −0.640487
\(133\) 4.73130 0.410256
\(134\) −1.27723 −0.110336
\(135\) 12.3779 1.06532
\(136\) −0.586675 −0.0503070
\(137\) 13.6352 1.16493 0.582467 0.812854i \(-0.302087\pi\)
0.582467 + 0.812854i \(0.302087\pi\)
\(138\) −10.2033 −0.868559
\(139\) −20.4265 −1.73255 −0.866276 0.499565i \(-0.833493\pi\)
−0.866276 + 0.499565i \(0.833493\pi\)
\(140\) 3.06853 0.259339
\(141\) 2.51025 0.211401
\(142\) −12.5663 −1.05454
\(143\) 12.1915 1.01950
\(144\) 1.01305 0.0844210
\(145\) 22.9441 1.90540
\(146\) −12.9485 −1.07163
\(147\) 12.0723 0.995706
\(148\) −1.95094 −0.160366
\(149\) −15.5351 −1.27269 −0.636343 0.771407i \(-0.719554\pi\)
−0.636343 + 0.771407i \(0.719554\pi\)
\(150\) 9.35619 0.763929
\(151\) −10.4311 −0.848869 −0.424434 0.905459i \(-0.639527\pi\)
−0.424434 + 0.905459i \(0.639527\pi\)
\(152\) −4.79483 −0.388912
\(153\) 0.594332 0.0480489
\(154\) −3.62466 −0.292083
\(155\) 8.57631 0.688866
\(156\) −6.64866 −0.532319
\(157\) 8.77366 0.700214 0.350107 0.936710i \(-0.386145\pi\)
0.350107 + 0.936710i \(0.386145\pi\)
\(158\) −2.95821 −0.235343
\(159\) 3.38727 0.268628
\(160\) −3.10974 −0.245846
\(161\) −5.02584 −0.396091
\(162\) 11.0129 0.865254
\(163\) 13.2439 1.03735 0.518673 0.854973i \(-0.326426\pi\)
0.518673 + 0.854973i \(0.326426\pi\)
\(164\) 0.441491 0.0344747
\(165\) −22.8834 −1.78147
\(166\) 5.28601 0.410274
\(167\) −4.45704 −0.344896 −0.172448 0.985019i \(-0.555168\pi\)
−0.172448 + 0.985019i \(0.555168\pi\)
\(168\) 1.97672 0.152507
\(169\) −1.98477 −0.152675
\(170\) −1.82441 −0.139926
\(171\) 4.85741 0.371456
\(172\) 13.0457 0.994729
\(173\) −10.1950 −0.775114 −0.387557 0.921846i \(-0.626681\pi\)
−0.387557 + 0.921846i \(0.626681\pi\)
\(174\) 14.7803 1.12049
\(175\) 4.60859 0.348377
\(176\) 3.67333 0.276888
\(177\) 18.6002 1.39808
\(178\) 11.6601 0.873963
\(179\) −6.27565 −0.469064 −0.234532 0.972108i \(-0.575356\pi\)
−0.234532 + 0.972108i \(0.575356\pi\)
\(180\) 3.15033 0.234811
\(181\) 7.07477 0.525863 0.262932 0.964814i \(-0.415311\pi\)
0.262932 + 0.964814i \(0.415311\pi\)
\(182\) −3.27494 −0.242755
\(183\) −4.47779 −0.331008
\(184\) 5.09332 0.375485
\(185\) −6.06690 −0.446048
\(186\) 5.52477 0.405096
\(187\) 2.15505 0.157593
\(188\) −1.25308 −0.0913903
\(189\) 3.92763 0.285693
\(190\) −14.9107 −1.08173
\(191\) 3.08074 0.222914 0.111457 0.993769i \(-0.464448\pi\)
0.111457 + 0.993769i \(0.464448\pi\)
\(192\) −2.00326 −0.144573
\(193\) −18.9600 −1.36477 −0.682385 0.730993i \(-0.739057\pi\)
−0.682385 + 0.730993i \(0.739057\pi\)
\(194\) −3.93094 −0.282225
\(195\) −20.6756 −1.48061
\(196\) −6.02632 −0.430452
\(197\) −9.82651 −0.700110 −0.350055 0.936729i \(-0.613837\pi\)
−0.350055 + 0.936729i \(0.613837\pi\)
\(198\) −3.72127 −0.264459
\(199\) 0.877522 0.0622059 0.0311029 0.999516i \(-0.490098\pi\)
0.0311029 + 0.999516i \(0.490098\pi\)
\(200\) −4.67048 −0.330253
\(201\) −2.55863 −0.180471
\(202\) 0.733382 0.0516006
\(203\) 7.28037 0.510982
\(204\) −1.17526 −0.0822849
\(205\) 1.37292 0.0958891
\(206\) −8.76624 −0.610773
\(207\) −5.15980 −0.358631
\(208\) 3.31892 0.230126
\(209\) 17.6130 1.21832
\(210\) 6.14707 0.424188
\(211\) −1.34276 −0.0924397 −0.0462199 0.998931i \(-0.514717\pi\)
−0.0462199 + 0.998931i \(0.514717\pi\)
\(212\) −1.69088 −0.116130
\(213\) −25.1736 −1.72486
\(214\) −15.2066 −1.03950
\(215\) 40.5689 2.76677
\(216\) −3.98037 −0.270830
\(217\) 2.72135 0.184737
\(218\) 14.0280 0.950095
\(219\) −25.9392 −1.75281
\(220\) 11.4231 0.770145
\(221\) 1.94713 0.130978
\(222\) −3.90823 −0.262303
\(223\) −2.78870 −0.186745 −0.0933725 0.995631i \(-0.529765\pi\)
−0.0933725 + 0.995631i \(0.529765\pi\)
\(224\) −0.986750 −0.0659300
\(225\) 4.73144 0.315429
\(226\) −10.2797 −0.683794
\(227\) −10.6267 −0.705322 −0.352661 0.935751i \(-0.614723\pi\)
−0.352661 + 0.935751i \(0.614723\pi\)
\(228\) −9.60530 −0.636126
\(229\) 15.0417 0.993982 0.496991 0.867756i \(-0.334438\pi\)
0.496991 + 0.867756i \(0.334438\pi\)
\(230\) 15.8389 1.04439
\(231\) −7.26113 −0.477748
\(232\) −7.37813 −0.484398
\(233\) 8.59287 0.562938 0.281469 0.959570i \(-0.409178\pi\)
0.281469 + 0.959570i \(0.409178\pi\)
\(234\) −3.36224 −0.219796
\(235\) −3.89676 −0.254196
\(236\) −9.28498 −0.604401
\(237\) −5.92607 −0.384940
\(238\) −0.578902 −0.0375246
\(239\) 17.9819 1.16316 0.581578 0.813491i \(-0.302436\pi\)
0.581578 + 0.813491i \(0.302436\pi\)
\(240\) −6.22962 −0.402120
\(241\) −4.28822 −0.276229 −0.138114 0.990416i \(-0.544104\pi\)
−0.138114 + 0.990416i \(0.544104\pi\)
\(242\) −2.49336 −0.160279
\(243\) 10.1205 0.649233
\(244\) 2.23525 0.143097
\(245\) −18.7403 −1.19727
\(246\) 0.884422 0.0563887
\(247\) 15.9137 1.01256
\(248\) −2.75789 −0.175126
\(249\) 10.5893 0.671067
\(250\) 1.02472 0.0648092
\(251\) −25.8562 −1.63203 −0.816015 0.578031i \(-0.803821\pi\)
−0.816015 + 0.578031i \(0.803821\pi\)
\(252\) 0.999629 0.0629707
\(253\) −18.7095 −1.17625
\(254\) −13.1015 −0.822062
\(255\) −3.65476 −0.228870
\(256\) 1.00000 0.0625000
\(257\) −23.1747 −1.44560 −0.722798 0.691060i \(-0.757144\pi\)
−0.722798 + 0.691060i \(0.757144\pi\)
\(258\) 26.1340 1.62703
\(259\) −1.92509 −0.119619
\(260\) 10.3210 0.640080
\(261\) 7.47442 0.462655
\(262\) −7.20966 −0.445414
\(263\) −17.4947 −1.07877 −0.539384 0.842060i \(-0.681343\pi\)
−0.539384 + 0.842060i \(0.681343\pi\)
\(264\) 7.35864 0.452893
\(265\) −5.25819 −0.323008
\(266\) −4.73130 −0.290095
\(267\) 23.3582 1.42950
\(268\) 1.27723 0.0780193
\(269\) −5.07663 −0.309527 −0.154764 0.987952i \(-0.549462\pi\)
−0.154764 + 0.987952i \(0.549462\pi\)
\(270\) −12.3779 −0.753297
\(271\) −26.3832 −1.60266 −0.801332 0.598220i \(-0.795875\pi\)
−0.801332 + 0.598220i \(0.795875\pi\)
\(272\) 0.586675 0.0355724
\(273\) −6.56056 −0.397063
\(274\) −13.6352 −0.823733
\(275\) 17.1562 1.03456
\(276\) 10.2033 0.614164
\(277\) −29.5079 −1.77296 −0.886478 0.462771i \(-0.846855\pi\)
−0.886478 + 0.462771i \(0.846855\pi\)
\(278\) 20.4265 1.22510
\(279\) 2.79388 0.167265
\(280\) −3.06853 −0.183380
\(281\) −23.4890 −1.40124 −0.700618 0.713536i \(-0.747092\pi\)
−0.700618 + 0.713536i \(0.747092\pi\)
\(282\) −2.51025 −0.149483
\(283\) 1.67740 0.0997113 0.0498557 0.998756i \(-0.484124\pi\)
0.0498557 + 0.998756i \(0.484124\pi\)
\(284\) 12.5663 0.745672
\(285\) −29.8700 −1.76934
\(286\) −12.1915 −0.720898
\(287\) 0.435642 0.0257151
\(288\) −1.01305 −0.0596946
\(289\) −16.6558 −0.979754
\(290\) −22.9441 −1.34732
\(291\) −7.87469 −0.461623
\(292\) 12.9485 0.757754
\(293\) 31.1202 1.81806 0.909029 0.416732i \(-0.136825\pi\)
0.909029 + 0.416732i \(0.136825\pi\)
\(294\) −12.0723 −0.704071
\(295\) −28.8739 −1.68110
\(296\) 1.95094 0.113396
\(297\) 14.6212 0.848410
\(298\) 15.5351 0.899924
\(299\) −16.9043 −0.977603
\(300\) −9.35619 −0.540180
\(301\) 12.8729 0.741981
\(302\) 10.4311 0.600241
\(303\) 1.46916 0.0844008
\(304\) 4.79483 0.275002
\(305\) 6.95105 0.398016
\(306\) −0.594332 −0.0339757
\(307\) −9.48668 −0.541434 −0.270717 0.962659i \(-0.587261\pi\)
−0.270717 + 0.962659i \(0.587261\pi\)
\(308\) 3.62466 0.206534
\(309\) −17.5611 −0.999013
\(310\) −8.57631 −0.487102
\(311\) 16.8993 0.958274 0.479137 0.877740i \(-0.340950\pi\)
0.479137 + 0.877740i \(0.340950\pi\)
\(312\) 6.64866 0.376406
\(313\) 21.9903 1.24296 0.621482 0.783428i \(-0.286531\pi\)
0.621482 + 0.783428i \(0.286531\pi\)
\(314\) −8.77366 −0.495126
\(315\) 3.10858 0.175149
\(316\) 2.95821 0.166412
\(317\) −12.1933 −0.684846 −0.342423 0.939546i \(-0.611248\pi\)
−0.342423 + 0.939546i \(0.611248\pi\)
\(318\) −3.38727 −0.189949
\(319\) 27.1023 1.51744
\(320\) 3.10974 0.173840
\(321\) −30.4627 −1.70026
\(322\) 5.02584 0.280079
\(323\) 2.81301 0.156520
\(324\) −11.0129 −0.611827
\(325\) 15.5009 0.859838
\(326\) −13.2439 −0.733514
\(327\) 28.1017 1.55403
\(328\) −0.441491 −0.0243773
\(329\) −1.23648 −0.0681692
\(330\) 22.8834 1.25969
\(331\) 14.2850 0.785176 0.392588 0.919714i \(-0.371580\pi\)
0.392588 + 0.919714i \(0.371580\pi\)
\(332\) −5.28601 −0.290108
\(333\) −1.97640 −0.108306
\(334\) 4.45704 0.243879
\(335\) 3.97185 0.217006
\(336\) −1.97672 −0.107839
\(337\) 3.68631 0.200806 0.100403 0.994947i \(-0.467987\pi\)
0.100403 + 0.994947i \(0.467987\pi\)
\(338\) 1.98477 0.107957
\(339\) −20.5929 −1.11845
\(340\) 1.82441 0.0989424
\(341\) 10.1306 0.548605
\(342\) −4.85741 −0.262659
\(343\) −12.8537 −0.694036
\(344\) −13.0457 −0.703379
\(345\) 31.7295 1.70826
\(346\) 10.1950 0.548089
\(347\) 13.6127 0.730770 0.365385 0.930857i \(-0.380937\pi\)
0.365385 + 0.930857i \(0.380937\pi\)
\(348\) −14.7803 −0.792308
\(349\) 0.786364 0.0420931 0.0210466 0.999778i \(-0.493300\pi\)
0.0210466 + 0.999778i \(0.493300\pi\)
\(350\) −4.60859 −0.246340
\(351\) 13.2105 0.705127
\(352\) −3.67333 −0.195789
\(353\) 3.24232 0.172571 0.0862857 0.996270i \(-0.472500\pi\)
0.0862857 + 0.996270i \(0.472500\pi\)
\(354\) −18.6002 −0.988591
\(355\) 39.0779 2.07404
\(356\) −11.6601 −0.617985
\(357\) −1.15969 −0.0613773
\(358\) 6.27565 0.331679
\(359\) 26.5650 1.40205 0.701023 0.713139i \(-0.252727\pi\)
0.701023 + 0.713139i \(0.252727\pi\)
\(360\) −3.15033 −0.166037
\(361\) 3.99042 0.210022
\(362\) −7.07477 −0.371842
\(363\) −4.99484 −0.262161
\(364\) 3.27494 0.171654
\(365\) 40.2665 2.10765
\(366\) 4.47779 0.234058
\(367\) −7.21298 −0.376514 −0.188257 0.982120i \(-0.560284\pi\)
−0.188257 + 0.982120i \(0.560284\pi\)
\(368\) −5.09332 −0.265508
\(369\) 0.447254 0.0232831
\(370\) 6.06690 0.315403
\(371\) −1.66847 −0.0866229
\(372\) −5.52477 −0.286446
\(373\) −16.3495 −0.846544 −0.423272 0.906003i \(-0.639119\pi\)
−0.423272 + 0.906003i \(0.639119\pi\)
\(374\) −2.15505 −0.111435
\(375\) 2.05279 0.106005
\(376\) 1.25308 0.0646227
\(377\) 24.4874 1.26117
\(378\) −3.92763 −0.202016
\(379\) 4.15838 0.213602 0.106801 0.994280i \(-0.465939\pi\)
0.106801 + 0.994280i \(0.465939\pi\)
\(380\) 14.9107 0.764902
\(381\) −26.2457 −1.34461
\(382\) −3.08074 −0.157624
\(383\) 13.0712 0.667906 0.333953 0.942590i \(-0.391617\pi\)
0.333953 + 0.942590i \(0.391617\pi\)
\(384\) 2.00326 0.102228
\(385\) 11.2717 0.574461
\(386\) 18.9600 0.965038
\(387\) 13.2160 0.671808
\(388\) 3.93094 0.199563
\(389\) −19.3391 −0.980532 −0.490266 0.871573i \(-0.663100\pi\)
−0.490266 + 0.871573i \(0.663100\pi\)
\(390\) 20.6756 1.04695
\(391\) −2.98813 −0.151116
\(392\) 6.02632 0.304375
\(393\) −14.4428 −0.728544
\(394\) 9.82651 0.495052
\(395\) 9.19927 0.462866
\(396\) 3.72127 0.187001
\(397\) −13.5300 −0.679050 −0.339525 0.940597i \(-0.610266\pi\)
−0.339525 + 0.940597i \(0.610266\pi\)
\(398\) −0.877522 −0.0439862
\(399\) −9.47803 −0.474495
\(400\) 4.67048 0.233524
\(401\) −19.8452 −0.991023 −0.495511 0.868601i \(-0.665019\pi\)
−0.495511 + 0.868601i \(0.665019\pi\)
\(402\) 2.55863 0.127613
\(403\) 9.15321 0.455954
\(404\) −0.733382 −0.0364871
\(405\) −34.2472 −1.70176
\(406\) −7.28037 −0.361319
\(407\) −7.16643 −0.355227
\(408\) 1.17526 0.0581842
\(409\) −7.04946 −0.348573 −0.174287 0.984695i \(-0.555762\pi\)
−0.174287 + 0.984695i \(0.555762\pi\)
\(410\) −1.37292 −0.0678039
\(411\) −27.3149 −1.34734
\(412\) 8.76624 0.431881
\(413\) −9.16195 −0.450830
\(414\) 5.15980 0.253590
\(415\) −16.4381 −0.806916
\(416\) −3.31892 −0.162723
\(417\) 40.9196 2.00384
\(418\) −17.6130 −0.861480
\(419\) −14.1122 −0.689428 −0.344714 0.938708i \(-0.612024\pi\)
−0.344714 + 0.938708i \(0.612024\pi\)
\(420\) −6.14707 −0.299946
\(421\) −23.4000 −1.14044 −0.570222 0.821491i \(-0.693143\pi\)
−0.570222 + 0.821491i \(0.693143\pi\)
\(422\) 1.34276 0.0653648
\(423\) −1.26944 −0.0617221
\(424\) 1.69088 0.0821163
\(425\) 2.74005 0.132912
\(426\) 25.1736 1.21966
\(427\) 2.20563 0.106738
\(428\) 15.2066 0.735038
\(429\) −24.4227 −1.17914
\(430\) −40.5689 −1.95640
\(431\) −2.29736 −0.110660 −0.0553300 0.998468i \(-0.517621\pi\)
−0.0553300 + 0.998468i \(0.517621\pi\)
\(432\) 3.98037 0.191506
\(433\) −12.0838 −0.580711 −0.290355 0.956919i \(-0.593774\pi\)
−0.290355 + 0.956919i \(0.593774\pi\)
\(434\) −2.72135 −0.130629
\(435\) −45.9629 −2.20375
\(436\) −14.0280 −0.671819
\(437\) −24.4216 −1.16825
\(438\) 25.9392 1.23942
\(439\) 26.7375 1.27611 0.638056 0.769990i \(-0.279739\pi\)
0.638056 + 0.769990i \(0.279739\pi\)
\(440\) −11.4231 −0.544575
\(441\) −6.10498 −0.290713
\(442\) −1.94713 −0.0926154
\(443\) 16.4053 0.779440 0.389720 0.920933i \(-0.372572\pi\)
0.389720 + 0.920933i \(0.372572\pi\)
\(444\) 3.90823 0.185477
\(445\) −36.2599 −1.71889
\(446\) 2.78870 0.132049
\(447\) 31.1209 1.47197
\(448\) 0.986750 0.0466195
\(449\) 38.7506 1.82876 0.914378 0.404862i \(-0.132680\pi\)
0.914378 + 0.404862i \(0.132680\pi\)
\(450\) −4.73144 −0.223042
\(451\) 1.62174 0.0763649
\(452\) 10.2797 0.483515
\(453\) 20.8962 0.981787
\(454\) 10.6267 0.498738
\(455\) 10.1842 0.477444
\(456\) 9.60530 0.449809
\(457\) −15.6397 −0.731596 −0.365798 0.930694i \(-0.619204\pi\)
−0.365798 + 0.930694i \(0.619204\pi\)
\(458\) −15.0417 −0.702852
\(459\) 2.33519 0.108997
\(460\) −15.8389 −0.738493
\(461\) −21.4138 −0.997339 −0.498670 0.866792i \(-0.666178\pi\)
−0.498670 + 0.866792i \(0.666178\pi\)
\(462\) 7.26113 0.337819
\(463\) 32.4214 1.50675 0.753375 0.657591i \(-0.228425\pi\)
0.753375 + 0.657591i \(0.228425\pi\)
\(464\) 7.37813 0.342521
\(465\) −17.1806 −0.796731
\(466\) −8.59287 −0.398057
\(467\) −4.54075 −0.210121 −0.105060 0.994466i \(-0.533504\pi\)
−0.105060 + 0.994466i \(0.533504\pi\)
\(468\) 3.36224 0.155419
\(469\) 1.26031 0.0581956
\(470\) 3.89676 0.179744
\(471\) −17.5759 −0.809856
\(472\) 9.28498 0.427376
\(473\) 47.9213 2.20342
\(474\) 5.92607 0.272193
\(475\) 22.3942 1.02751
\(476\) 0.578902 0.0265339
\(477\) −1.71295 −0.0784305
\(478\) −17.9819 −0.822475
\(479\) −19.0114 −0.868652 −0.434326 0.900756i \(-0.643013\pi\)
−0.434326 + 0.900756i \(0.643013\pi\)
\(480\) 6.22962 0.284342
\(481\) −6.47500 −0.295235
\(482\) 4.28822 0.195323
\(483\) 10.0681 0.458113
\(484\) 2.49336 0.113334
\(485\) 12.2242 0.555072
\(486\) −10.1205 −0.459077
\(487\) 14.5666 0.660077 0.330038 0.943968i \(-0.392938\pi\)
0.330038 + 0.943968i \(0.392938\pi\)
\(488\) −2.23525 −0.101185
\(489\) −26.5311 −1.19978
\(490\) 18.7403 0.846600
\(491\) −10.0491 −0.453508 −0.226754 0.973952i \(-0.572811\pi\)
−0.226754 + 0.973952i \(0.572811\pi\)
\(492\) −0.884422 −0.0398728
\(493\) 4.32857 0.194949
\(494\) −15.9137 −0.715990
\(495\) 11.5722 0.520131
\(496\) 2.75789 0.123833
\(497\) 12.3998 0.556206
\(498\) −10.5893 −0.474516
\(499\) 10.1008 0.452175 0.226087 0.974107i \(-0.427407\pi\)
0.226087 + 0.974107i \(0.427407\pi\)
\(500\) −1.02472 −0.0458270
\(501\) 8.92862 0.398901
\(502\) 25.8562 1.15402
\(503\) −23.4457 −1.04539 −0.522696 0.852519i \(-0.675074\pi\)
−0.522696 + 0.852519i \(0.675074\pi\)
\(504\) −0.999629 −0.0445270
\(505\) −2.28063 −0.101487
\(506\) 18.7095 0.831737
\(507\) 3.97601 0.176581
\(508\) 13.1015 0.581286
\(509\) −0.304784 −0.0135093 −0.00675465 0.999977i \(-0.502150\pi\)
−0.00675465 + 0.999977i \(0.502150\pi\)
\(510\) 3.65476 0.161836
\(511\) 12.7769 0.565219
\(512\) −1.00000 −0.0441942
\(513\) 19.0852 0.842633
\(514\) 23.1747 1.02219
\(515\) 27.2607 1.20125
\(516\) −26.1340 −1.15049
\(517\) −4.60298 −0.202439
\(518\) 1.92509 0.0845834
\(519\) 20.4233 0.896484
\(520\) −10.3210 −0.452605
\(521\) 22.4166 0.982087 0.491044 0.871135i \(-0.336616\pi\)
0.491044 + 0.871135i \(0.336616\pi\)
\(522\) −7.47442 −0.327147
\(523\) 17.7356 0.775525 0.387763 0.921759i \(-0.373248\pi\)
0.387763 + 0.921759i \(0.373248\pi\)
\(524\) 7.20966 0.314955
\(525\) −9.23221 −0.402927
\(526\) 17.4947 0.762804
\(527\) 1.61798 0.0704805
\(528\) −7.35864 −0.320244
\(529\) 2.94195 0.127911
\(530\) 5.25819 0.228401
\(531\) −9.40617 −0.408193
\(532\) 4.73130 0.205128
\(533\) 1.46527 0.0634681
\(534\) −23.3582 −1.01081
\(535\) 47.2885 2.04446
\(536\) −1.27723 −0.0551680
\(537\) 12.5718 0.542512
\(538\) 5.07663 0.218869
\(539\) −22.1367 −0.953494
\(540\) 12.3779 0.532661
\(541\) −3.00067 −0.129009 −0.0645044 0.997917i \(-0.520547\pi\)
−0.0645044 + 0.997917i \(0.520547\pi\)
\(542\) 26.3832 1.13325
\(543\) −14.1726 −0.608205
\(544\) −0.586675 −0.0251535
\(545\) −43.6234 −1.86862
\(546\) 6.56056 0.280766
\(547\) 7.40176 0.316477 0.158238 0.987401i \(-0.449419\pi\)
0.158238 + 0.987401i \(0.449419\pi\)
\(548\) 13.6352 0.582467
\(549\) 2.26443 0.0966433
\(550\) −17.1562 −0.731543
\(551\) 35.3769 1.50711
\(552\) −10.2033 −0.434279
\(553\) 2.91902 0.124129
\(554\) 29.5079 1.25367
\(555\) 12.1536 0.515891
\(556\) −20.4265 −0.866276
\(557\) −14.8240 −0.628114 −0.314057 0.949404i \(-0.601688\pi\)
−0.314057 + 0.949404i \(0.601688\pi\)
\(558\) −2.79388 −0.118274
\(559\) 43.2978 1.83130
\(560\) 3.06853 0.129669
\(561\) −4.31713 −0.182269
\(562\) 23.4890 0.990824
\(563\) −16.4780 −0.694466 −0.347233 0.937779i \(-0.612879\pi\)
−0.347233 + 0.937779i \(0.612879\pi\)
\(564\) 2.51025 0.105701
\(565\) 31.9671 1.34487
\(566\) −1.67740 −0.0705065
\(567\) −10.8670 −0.456369
\(568\) −12.5663 −0.527270
\(569\) 23.4956 0.984985 0.492492 0.870317i \(-0.336086\pi\)
0.492492 + 0.870317i \(0.336086\pi\)
\(570\) 29.8700 1.25112
\(571\) 2.41274 0.100970 0.0504851 0.998725i \(-0.483923\pi\)
0.0504851 + 0.998725i \(0.483923\pi\)
\(572\) 12.1915 0.509752
\(573\) −6.17152 −0.257819
\(574\) −0.435642 −0.0181833
\(575\) −23.7883 −0.992039
\(576\) 1.01305 0.0422105
\(577\) 0.0199972 0.000832494 0 0.000416247 1.00000i \(-0.499868\pi\)
0.000416247 1.00000i \(0.499868\pi\)
\(578\) 16.6558 0.692790
\(579\) 37.9818 1.57847
\(580\) 22.9441 0.952700
\(581\) −5.21597 −0.216395
\(582\) 7.87469 0.326416
\(583\) −6.21116 −0.257240
\(584\) −12.9485 −0.535813
\(585\) 10.4557 0.432289
\(586\) −31.1202 −1.28556
\(587\) 1.69077 0.0697856 0.0348928 0.999391i \(-0.488891\pi\)
0.0348928 + 0.999391i \(0.488891\pi\)
\(588\) 12.0723 0.497853
\(589\) 13.2236 0.544869
\(590\) 28.8739 1.18872
\(591\) 19.6851 0.809735
\(592\) −1.95094 −0.0801830
\(593\) 29.0262 1.19196 0.595981 0.802999i \(-0.296764\pi\)
0.595981 + 0.802999i \(0.296764\pi\)
\(594\) −14.6212 −0.599916
\(595\) 1.80023 0.0738024
\(596\) −15.5351 −0.636343
\(597\) −1.75790 −0.0719463
\(598\) 16.9043 0.691270
\(599\) −9.40753 −0.384381 −0.192191 0.981358i \(-0.561559\pi\)
−0.192191 + 0.981358i \(0.561559\pi\)
\(600\) 9.35619 0.381965
\(601\) −21.6330 −0.882428 −0.441214 0.897402i \(-0.645452\pi\)
−0.441214 + 0.897402i \(0.645452\pi\)
\(602\) −12.8729 −0.524660
\(603\) 1.29390 0.0526917
\(604\) −10.4311 −0.424434
\(605\) 7.75369 0.315232
\(606\) −1.46916 −0.0596804
\(607\) 27.0003 1.09591 0.547954 0.836508i \(-0.315407\pi\)
0.547954 + 0.836508i \(0.315407\pi\)
\(608\) −4.79483 −0.194456
\(609\) −14.5845 −0.590993
\(610\) −6.95105 −0.281440
\(611\) −4.15888 −0.168250
\(612\) 0.594332 0.0240245
\(613\) 23.4495 0.947115 0.473557 0.880763i \(-0.342970\pi\)
0.473557 + 0.880763i \(0.342970\pi\)
\(614\) 9.48668 0.382851
\(615\) −2.75032 −0.110904
\(616\) −3.62466 −0.146042
\(617\) 40.1023 1.61446 0.807229 0.590239i \(-0.200966\pi\)
0.807229 + 0.590239i \(0.200966\pi\)
\(618\) 17.5611 0.706409
\(619\) 40.1000 1.61176 0.805878 0.592082i \(-0.201694\pi\)
0.805878 + 0.592082i \(0.201694\pi\)
\(620\) 8.57631 0.344433
\(621\) −20.2733 −0.813541
\(622\) −16.8993 −0.677602
\(623\) −11.5056 −0.460963
\(624\) −6.64866 −0.266159
\(625\) −26.5390 −1.06156
\(626\) −21.9903 −0.878908
\(627\) −35.2834 −1.40908
\(628\) 8.77366 0.350107
\(629\) −1.14457 −0.0456368
\(630\) −3.10858 −0.123849
\(631\) −5.84092 −0.232523 −0.116262 0.993219i \(-0.537091\pi\)
−0.116262 + 0.993219i \(0.537091\pi\)
\(632\) −2.95821 −0.117671
\(633\) 2.68991 0.106914
\(634\) 12.1933 0.484259
\(635\) 40.7423 1.61681
\(636\) 3.38727 0.134314
\(637\) −20.0009 −0.792464
\(638\) −27.1023 −1.07299
\(639\) 12.7303 0.503603
\(640\) −3.10974 −0.122923
\(641\) 14.7294 0.581777 0.290888 0.956757i \(-0.406049\pi\)
0.290888 + 0.956757i \(0.406049\pi\)
\(642\) 30.4627 1.20227
\(643\) 33.6970 1.32888 0.664440 0.747341i \(-0.268670\pi\)
0.664440 + 0.747341i \(0.268670\pi\)
\(644\) −5.02584 −0.198046
\(645\) −81.2700 −3.20000
\(646\) −2.81301 −0.110676
\(647\) −41.5603 −1.63390 −0.816952 0.576706i \(-0.804338\pi\)
−0.816952 + 0.576706i \(0.804338\pi\)
\(648\) 11.0129 0.432627
\(649\) −34.1068 −1.33881
\(650\) −15.5009 −0.607997
\(651\) −5.45156 −0.213664
\(652\) 13.2439 0.518673
\(653\) 29.1947 1.14248 0.571239 0.820784i \(-0.306463\pi\)
0.571239 + 0.820784i \(0.306463\pi\)
\(654\) −28.1017 −1.09886
\(655\) 22.4202 0.876028
\(656\) 0.441491 0.0172373
\(657\) 13.1175 0.511763
\(658\) 1.23648 0.0482029
\(659\) −7.00600 −0.272915 −0.136457 0.990646i \(-0.543572\pi\)
−0.136457 + 0.990646i \(0.543572\pi\)
\(660\) −22.8834 −0.890737
\(661\) 23.2413 0.903980 0.451990 0.892023i \(-0.350714\pi\)
0.451990 + 0.892023i \(0.350714\pi\)
\(662\) −14.2850 −0.555203
\(663\) −3.90060 −0.151487
\(664\) 5.28601 0.205137
\(665\) 14.7131 0.570550
\(666\) 1.97640 0.0765839
\(667\) −37.5792 −1.45507
\(668\) −4.45704 −0.172448
\(669\) 5.58649 0.215986
\(670\) −3.97185 −0.153446
\(671\) 8.21082 0.316975
\(672\) 1.97672 0.0762535
\(673\) 47.2433 1.82110 0.910548 0.413403i \(-0.135660\pi\)
0.910548 + 0.413403i \(0.135660\pi\)
\(674\) −3.68631 −0.141991
\(675\) 18.5903 0.715539
\(676\) −1.98477 −0.0763374
\(677\) −17.8290 −0.685222 −0.342611 0.939477i \(-0.611311\pi\)
−0.342611 + 0.939477i \(0.611311\pi\)
\(678\) 20.5929 0.790865
\(679\) 3.87885 0.148857
\(680\) −1.82441 −0.0699628
\(681\) 21.2881 0.815763
\(682\) −10.1306 −0.387922
\(683\) −28.2164 −1.07967 −0.539836 0.841770i \(-0.681514\pi\)
−0.539836 + 0.841770i \(0.681514\pi\)
\(684\) 4.85741 0.185728
\(685\) 42.4019 1.62009
\(686\) 12.8537 0.490757
\(687\) −30.1324 −1.14962
\(688\) 13.0457 0.497364
\(689\) −5.61189 −0.213796
\(690\) −31.7295 −1.20792
\(691\) 15.3161 0.582653 0.291327 0.956624i \(-0.405903\pi\)
0.291327 + 0.956624i \(0.405903\pi\)
\(692\) −10.1950 −0.387557
\(693\) 3.67197 0.139486
\(694\) −13.6127 −0.516732
\(695\) −63.5211 −2.40949
\(696\) 14.7803 0.560246
\(697\) 0.259012 0.00981078
\(698\) −0.786364 −0.0297643
\(699\) −17.2138 −0.651084
\(700\) 4.60859 0.174189
\(701\) −33.7381 −1.27427 −0.637134 0.770753i \(-0.719880\pi\)
−0.637134 + 0.770753i \(0.719880\pi\)
\(702\) −13.2105 −0.498600
\(703\) −9.35441 −0.352808
\(704\) 3.67333 0.138444
\(705\) 7.80622 0.293999
\(706\) −3.24232 −0.122026
\(707\) −0.723665 −0.0272162
\(708\) 18.6002 0.699040
\(709\) 3.61380 0.135719 0.0678596 0.997695i \(-0.478383\pi\)
0.0678596 + 0.997695i \(0.478383\pi\)
\(710\) −39.0779 −1.46657
\(711\) 2.99682 0.112390
\(712\) 11.6601 0.436981
\(713\) −14.0468 −0.526057
\(714\) 1.15969 0.0434003
\(715\) 37.9124 1.41784
\(716\) −6.27565 −0.234532
\(717\) −36.0225 −1.34529
\(718\) −26.5650 −0.991396
\(719\) 33.0840 1.23382 0.616912 0.787032i \(-0.288384\pi\)
0.616912 + 0.787032i \(0.288384\pi\)
\(720\) 3.15033 0.117406
\(721\) 8.65008 0.322146
\(722\) −3.99042 −0.148508
\(723\) 8.59043 0.319481
\(724\) 7.07477 0.262932
\(725\) 34.4594 1.27979
\(726\) 4.99484 0.185376
\(727\) 24.3914 0.904626 0.452313 0.891859i \(-0.350599\pi\)
0.452313 + 0.891859i \(0.350599\pi\)
\(728\) −3.27494 −0.121377
\(729\) 12.7646 0.472762
\(730\) −40.2665 −1.49033
\(731\) 7.65361 0.283079
\(732\) −4.47779 −0.165504
\(733\) −17.5641 −0.648747 −0.324373 0.945929i \(-0.605153\pi\)
−0.324373 + 0.945929i \(0.605153\pi\)
\(734\) 7.21298 0.266236
\(735\) 37.5417 1.38475
\(736\) 5.09332 0.187742
\(737\) 4.69169 0.172821
\(738\) −0.447254 −0.0164636
\(739\) −19.2090 −0.706614 −0.353307 0.935507i \(-0.614943\pi\)
−0.353307 + 0.935507i \(0.614943\pi\)
\(740\) −6.06690 −0.223024
\(741\) −31.8792 −1.17111
\(742\) 1.66847 0.0612516
\(743\) −8.65367 −0.317472 −0.158736 0.987321i \(-0.550742\pi\)
−0.158736 + 0.987321i \(0.550742\pi\)
\(744\) 5.52477 0.202548
\(745\) −48.3101 −1.76995
\(746\) 16.3495 0.598597
\(747\) −5.35500 −0.195929
\(748\) 2.15505 0.0787965
\(749\) 15.0051 0.548274
\(750\) −2.05279 −0.0749572
\(751\) −0.766965 −0.0279870 −0.0139935 0.999902i \(-0.504454\pi\)
−0.0139935 + 0.999902i \(0.504454\pi\)
\(752\) −1.25308 −0.0456952
\(753\) 51.7967 1.88758
\(754\) −24.4874 −0.891779
\(755\) −32.4379 −1.18054
\(756\) 3.92763 0.142847
\(757\) −20.6390 −0.750136 −0.375068 0.926997i \(-0.622381\pi\)
−0.375068 + 0.926997i \(0.622381\pi\)
\(758\) −4.15838 −0.151039
\(759\) 37.4799 1.36044
\(760\) −14.9107 −0.540867
\(761\) 4.92869 0.178665 0.0893324 0.996002i \(-0.471527\pi\)
0.0893324 + 0.996002i \(0.471527\pi\)
\(762\) 26.2457 0.950783
\(763\) −13.8421 −0.501118
\(764\) 3.08074 0.111457
\(765\) 1.84822 0.0668225
\(766\) −13.0712 −0.472281
\(767\) −30.8161 −1.11271
\(768\) −2.00326 −0.0722864
\(769\) 44.0414 1.58817 0.794086 0.607805i \(-0.207950\pi\)
0.794086 + 0.607805i \(0.207950\pi\)
\(770\) −11.2717 −0.406205
\(771\) 46.4249 1.67195
\(772\) −18.9600 −0.682385
\(773\) 1.98061 0.0712374 0.0356187 0.999365i \(-0.488660\pi\)
0.0356187 + 0.999365i \(0.488660\pi\)
\(774\) −13.2160 −0.475040
\(775\) 12.8807 0.462687
\(776\) −3.93094 −0.141112
\(777\) 3.85645 0.138349
\(778\) 19.3391 0.693341
\(779\) 2.11688 0.0758450
\(780\) −20.6756 −0.740305
\(781\) 46.1601 1.65174
\(782\) 2.98813 0.106855
\(783\) 29.3677 1.04952
\(784\) −6.02632 −0.215226
\(785\) 27.2838 0.973800
\(786\) 14.4428 0.515158
\(787\) −7.40914 −0.264107 −0.132054 0.991243i \(-0.542157\pi\)
−0.132054 + 0.991243i \(0.542157\pi\)
\(788\) −9.82651 −0.350055
\(789\) 35.0464 1.24768
\(790\) −9.19927 −0.327295
\(791\) 10.1435 0.360660
\(792\) −3.72127 −0.132230
\(793\) 7.41862 0.263443
\(794\) 13.5300 0.480161
\(795\) 10.5335 0.373586
\(796\) 0.877522 0.0311029
\(797\) 11.1178 0.393812 0.196906 0.980422i \(-0.436911\pi\)
0.196906 + 0.980422i \(0.436911\pi\)
\(798\) 9.47803 0.335518
\(799\) −0.735152 −0.0260078
\(800\) −4.67048 −0.165126
\(801\) −11.8123 −0.417367
\(802\) 19.8452 0.700759
\(803\) 47.5642 1.67850
\(804\) −2.55863 −0.0902357
\(805\) −15.6290 −0.550851
\(806\) −9.15321 −0.322408
\(807\) 10.1698 0.357994
\(808\) 0.733382 0.0258003
\(809\) 9.46997 0.332947 0.166473 0.986046i \(-0.446762\pi\)
0.166473 + 0.986046i \(0.446762\pi\)
\(810\) 34.2472 1.20332
\(811\) 35.9524 1.26246 0.631230 0.775595i \(-0.282550\pi\)
0.631230 + 0.775595i \(0.282550\pi\)
\(812\) 7.28037 0.255491
\(813\) 52.8523 1.85361
\(814\) 7.16643 0.251183
\(815\) 41.1852 1.44265
\(816\) −1.17526 −0.0411424
\(817\) 62.5522 2.18842
\(818\) 7.04946 0.246479
\(819\) 3.31769 0.115929
\(820\) 1.37292 0.0479446
\(821\) 36.5795 1.27663 0.638316 0.769774i \(-0.279631\pi\)
0.638316 + 0.769774i \(0.279631\pi\)
\(822\) 27.3149 0.952715
\(823\) −22.6521 −0.789601 −0.394801 0.918767i \(-0.629186\pi\)
−0.394801 + 0.918767i \(0.629186\pi\)
\(824\) −8.76624 −0.305386
\(825\) −34.3684 −1.19655
\(826\) 9.16195 0.318785
\(827\) 40.8837 1.42166 0.710832 0.703362i \(-0.248319\pi\)
0.710832 + 0.703362i \(0.248319\pi\)
\(828\) −5.15980 −0.179315
\(829\) 1.12226 0.0389776 0.0194888 0.999810i \(-0.493796\pi\)
0.0194888 + 0.999810i \(0.493796\pi\)
\(830\) 16.4381 0.570576
\(831\) 59.1119 2.05057
\(832\) 3.31892 0.115063
\(833\) −3.53550 −0.122498
\(834\) −40.9196 −1.41693
\(835\) −13.8602 −0.479654
\(836\) 17.6130 0.609158
\(837\) 10.9774 0.379435
\(838\) 14.1122 0.487499
\(839\) −19.5416 −0.674649 −0.337325 0.941388i \(-0.609522\pi\)
−0.337325 + 0.941388i \(0.609522\pi\)
\(840\) 6.14707 0.212094
\(841\) 25.4368 0.877130
\(842\) 23.4000 0.806416
\(843\) 47.0546 1.62065
\(844\) −1.34276 −0.0462199
\(845\) −6.17212 −0.212327
\(846\) 1.26944 0.0436441
\(847\) 2.46032 0.0845376
\(848\) −1.69088 −0.0580650
\(849\) −3.36028 −0.115324
\(850\) −2.74005 −0.0939831
\(851\) 9.93675 0.340627
\(852\) −25.1736 −0.862432
\(853\) 0.0204900 0.000701564 0 0.000350782 1.00000i \(-0.499888\pi\)
0.000350782 1.00000i \(0.499888\pi\)
\(854\) −2.20563 −0.0754753
\(855\) 15.1053 0.516590
\(856\) −15.2066 −0.519750
\(857\) 14.1231 0.482435 0.241217 0.970471i \(-0.422453\pi\)
0.241217 + 0.970471i \(0.422453\pi\)
\(858\) 24.4227 0.833778
\(859\) −0.0401696 −0.00137057 −0.000685285 1.00000i \(-0.500218\pi\)
−0.000685285 1.00000i \(0.500218\pi\)
\(860\) 40.5689 1.38339
\(861\) −0.872704 −0.0297417
\(862\) 2.29736 0.0782485
\(863\) −51.6369 −1.75774 −0.878871 0.477059i \(-0.841703\pi\)
−0.878871 + 0.477059i \(0.841703\pi\)
\(864\) −3.98037 −0.135415
\(865\) −31.7039 −1.07797
\(866\) 12.0838 0.410624
\(867\) 33.3659 1.13317
\(868\) 2.72135 0.0923685
\(869\) 10.8665 0.368621
\(870\) 45.9629 1.55829
\(871\) 4.23903 0.143634
\(872\) 14.0280 0.475048
\(873\) 3.98224 0.134778
\(874\) 24.4216 0.826074
\(875\) −1.01115 −0.0341830
\(876\) −25.9392 −0.876406
\(877\) −26.6415 −0.899621 −0.449810 0.893124i \(-0.648508\pi\)
−0.449810 + 0.893124i \(0.648508\pi\)
\(878\) −26.7375 −0.902348
\(879\) −62.3418 −2.10274
\(880\) 11.4231 0.385073
\(881\) 43.0148 1.44921 0.724603 0.689167i \(-0.242023\pi\)
0.724603 + 0.689167i \(0.242023\pi\)
\(882\) 6.10498 0.205565
\(883\) 55.4412 1.86575 0.932873 0.360205i \(-0.117293\pi\)
0.932873 + 0.360205i \(0.117293\pi\)
\(884\) 1.94713 0.0654890
\(885\) 57.8419 1.94433
\(886\) −16.4053 −0.551148
\(887\) −17.3681 −0.583165 −0.291582 0.956546i \(-0.594182\pi\)
−0.291582 + 0.956546i \(0.594182\pi\)
\(888\) −3.90823 −0.131152
\(889\) 12.9279 0.433588
\(890\) 36.2599 1.21544
\(891\) −40.4540 −1.35526
\(892\) −2.78870 −0.0933725
\(893\) −6.00831 −0.201061
\(894\) −31.1209 −1.04084
\(895\) −19.5157 −0.652336
\(896\) −0.986750 −0.0329650
\(897\) 33.8638 1.13068
\(898\) −38.7506 −1.29313
\(899\) 20.3481 0.678645
\(900\) 4.73144 0.157715
\(901\) −0.991997 −0.0330482
\(902\) −1.62174 −0.0539982
\(903\) −25.7877 −0.858162
\(904\) −10.2797 −0.341897
\(905\) 22.0007 0.731328
\(906\) −20.8962 −0.694228
\(907\) −3.11891 −0.103562 −0.0517809 0.998658i \(-0.516490\pi\)
−0.0517809 + 0.998658i \(0.516490\pi\)
\(908\) −10.6267 −0.352661
\(909\) −0.742954 −0.0246422
\(910\) −10.1842 −0.337604
\(911\) −26.5284 −0.878925 −0.439463 0.898261i \(-0.644831\pi\)
−0.439463 + 0.898261i \(0.644831\pi\)
\(912\) −9.60530 −0.318063
\(913\) −19.4173 −0.642618
\(914\) 15.6397 0.517316
\(915\) −13.9248 −0.460339
\(916\) 15.0417 0.496991
\(917\) 7.11413 0.234929
\(918\) −2.33519 −0.0770727
\(919\) 32.7715 1.08103 0.540515 0.841334i \(-0.318229\pi\)
0.540515 + 0.841334i \(0.318229\pi\)
\(920\) 15.8389 0.522193
\(921\) 19.0043 0.626213
\(922\) 21.4138 0.705225
\(923\) 41.7065 1.37279
\(924\) −7.26113 −0.238874
\(925\) −9.11181 −0.299594
\(926\) −32.4214 −1.06543
\(927\) 8.88065 0.291679
\(928\) −7.37813 −0.242199
\(929\) −53.2898 −1.74838 −0.874191 0.485581i \(-0.838608\pi\)
−0.874191 + 0.485581i \(0.838608\pi\)
\(930\) 17.1806 0.563374
\(931\) −28.8952 −0.947002
\(932\) 8.59287 0.281469
\(933\) −33.8538 −1.10832
\(934\) 4.54075 0.148578
\(935\) 6.70165 0.219167
\(936\) −3.36224 −0.109898
\(937\) 16.9016 0.552150 0.276075 0.961136i \(-0.410966\pi\)
0.276075 + 0.961136i \(0.410966\pi\)
\(938\) −1.26031 −0.0411505
\(939\) −44.0523 −1.43759
\(940\) −3.89676 −0.127098
\(941\) 56.4315 1.83961 0.919807 0.392372i \(-0.128345\pi\)
0.919807 + 0.392372i \(0.128345\pi\)
\(942\) 17.5759 0.572655
\(943\) −2.24866 −0.0732264
\(944\) −9.28498 −0.302200
\(945\) 12.2139 0.397319
\(946\) −47.9213 −1.55806
\(947\) 21.2049 0.689068 0.344534 0.938774i \(-0.388037\pi\)
0.344534 + 0.938774i \(0.388037\pi\)
\(948\) −5.92607 −0.192470
\(949\) 42.9751 1.39503
\(950\) −22.3942 −0.726563
\(951\) 24.4264 0.792081
\(952\) −0.578902 −0.0187623
\(953\) −4.16784 −0.135010 −0.0675048 0.997719i \(-0.521504\pi\)
−0.0675048 + 0.997719i \(0.521504\pi\)
\(954\) 1.71295 0.0554587
\(955\) 9.58029 0.310011
\(956\) 17.9819 0.581578
\(957\) −54.2930 −1.75504
\(958\) 19.0114 0.614230
\(959\) 13.4545 0.434470
\(960\) −6.22962 −0.201060
\(961\) −23.3941 −0.754647
\(962\) 6.47500 0.208762
\(963\) 15.4050 0.496421
\(964\) −4.28822 −0.138114
\(965\) −58.9606 −1.89801
\(966\) −10.0681 −0.323934
\(967\) −6.15020 −0.197777 −0.0988885 0.995099i \(-0.531529\pi\)
−0.0988885 + 0.995099i \(0.531529\pi\)
\(968\) −2.49336 −0.0801395
\(969\) −5.63519 −0.181028
\(970\) −12.2242 −0.392495
\(971\) 5.48322 0.175965 0.0879825 0.996122i \(-0.471958\pi\)
0.0879825 + 0.996122i \(0.471958\pi\)
\(972\) 10.1205 0.324617
\(973\) −20.1558 −0.646166
\(974\) −14.5666 −0.466745
\(975\) −31.0524 −0.994474
\(976\) 2.23525 0.0715487
\(977\) −17.3234 −0.554223 −0.277112 0.960838i \(-0.589377\pi\)
−0.277112 + 0.960838i \(0.589377\pi\)
\(978\) 26.5311 0.848370
\(979\) −42.8315 −1.36890
\(980\) −18.7403 −0.598637
\(981\) −14.2111 −0.453725
\(982\) 10.0491 0.320678
\(983\) 54.0642 1.72438 0.862189 0.506586i \(-0.169093\pi\)
0.862189 + 0.506586i \(0.169093\pi\)
\(984\) 0.884422 0.0281944
\(985\) −30.5579 −0.973655
\(986\) −4.32857 −0.137850
\(987\) 2.47699 0.0788434
\(988\) 15.9137 0.506281
\(989\) −66.4462 −2.11287
\(990\) −11.5722 −0.367788
\(991\) 48.3787 1.53680 0.768400 0.639970i \(-0.221053\pi\)
0.768400 + 0.639970i \(0.221053\pi\)
\(992\) −2.75789 −0.0875630
\(993\) −28.6166 −0.908121
\(994\) −12.3998 −0.393297
\(995\) 2.72886 0.0865108
\(996\) 10.5893 0.335534
\(997\) −45.7129 −1.44774 −0.723871 0.689935i \(-0.757639\pi\)
−0.723871 + 0.689935i \(0.757639\pi\)
\(998\) −10.1008 −0.319736
\(999\) −7.76546 −0.245688
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 \(a_p\))