Properties

Label 6010.2.a.c.1.14
Level 6010
Weight 2
Character 6010.1
Self dual Yes
Analytic conductor 47.990
Analytic rank 1
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6010 = 2 \cdot 5 \cdot 601 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9900916148\)
Analytic rank: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Root \(2.41044\)
Character \(\chi\) = 6010.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.41044 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{5}\) \(+1.41044 q^{6}\) \(-3.15104 q^{7}\) \(+1.00000 q^{8}\) \(-1.01066 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.41044 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{5}\) \(+1.41044 q^{6}\) \(-3.15104 q^{7}\) \(+1.00000 q^{8}\) \(-1.01066 q^{9}\) \(+1.00000 q^{10}\) \(-1.04069 q^{11}\) \(+1.41044 q^{12}\) \(-3.01659 q^{13}\) \(-3.15104 q^{14}\) \(+1.41044 q^{15}\) \(+1.00000 q^{16}\) \(+2.09209 q^{17}\) \(-1.01066 q^{18}\) \(+3.54717 q^{19}\) \(+1.00000 q^{20}\) \(-4.44435 q^{21}\) \(-1.04069 q^{22}\) \(-1.80458 q^{23}\) \(+1.41044 q^{24}\) \(+1.00000 q^{25}\) \(-3.01659 q^{26}\) \(-5.65679 q^{27}\) \(-3.15104 q^{28}\) \(-0.429786 q^{29}\) \(+1.41044 q^{30}\) \(-9.55437 q^{31}\) \(+1.00000 q^{32}\) \(-1.46783 q^{33}\) \(+2.09209 q^{34}\) \(-3.15104 q^{35}\) \(-1.01066 q^{36}\) \(+7.40717 q^{37}\) \(+3.54717 q^{38}\) \(-4.25473 q^{39}\) \(+1.00000 q^{40}\) \(-9.28453 q^{41}\) \(-4.44435 q^{42}\) \(-7.43486 q^{43}\) \(-1.04069 q^{44}\) \(-1.01066 q^{45}\) \(-1.80458 q^{46}\) \(-10.5989 q^{47}\) \(+1.41044 q^{48}\) \(+2.92903 q^{49}\) \(+1.00000 q^{50}\) \(+2.95077 q^{51}\) \(-3.01659 q^{52}\) \(-7.88673 q^{53}\) \(-5.65679 q^{54}\) \(-1.04069 q^{55}\) \(-3.15104 q^{56}\) \(+5.00308 q^{57}\) \(-0.429786 q^{58}\) \(+3.06070 q^{59}\) \(+1.41044 q^{60}\) \(-4.36339 q^{61}\) \(-9.55437 q^{62}\) \(+3.18461 q^{63}\) \(+1.00000 q^{64}\) \(-3.01659 q^{65}\) \(-1.46783 q^{66}\) \(+11.1448 q^{67}\) \(+2.09209 q^{68}\) \(-2.54525 q^{69}\) \(-3.15104 q^{70}\) \(+8.28515 q^{71}\) \(-1.01066 q^{72}\) \(-5.43760 q^{73}\) \(+7.40717 q^{74}\) \(+1.41044 q^{75}\) \(+3.54717 q^{76}\) \(+3.27926 q^{77}\) \(-4.25473 q^{78}\) \(+9.01031 q^{79}\) \(+1.00000 q^{80}\) \(-4.94661 q^{81}\) \(-9.28453 q^{82}\) \(+8.94926 q^{83}\) \(-4.44435 q^{84}\) \(+2.09209 q^{85}\) \(-7.43486 q^{86}\) \(-0.606188 q^{87}\) \(-1.04069 q^{88}\) \(-8.34070 q^{89}\) \(-1.01066 q^{90}\) \(+9.50540 q^{91}\) \(-1.80458 q^{92}\) \(-13.4759 q^{93}\) \(-10.5989 q^{94}\) \(+3.54717 q^{95}\) \(+1.41044 q^{96}\) \(+6.35468 q^{97}\) \(+2.92903 q^{98}\) \(+1.05178 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(16q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 8q^{12} \) \(\mathstrut -\mathstrut 20q^{13} \) \(\mathstrut -\mathstrut 10q^{14} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut -\mathstrut 27q^{17} \) \(\mathstrut -\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut 17q^{19} \) \(\mathstrut +\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 14q^{22} \) \(\mathstrut -\mathstrut 9q^{23} \) \(\mathstrut -\mathstrut 8q^{24} \) \(\mathstrut +\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 20q^{26} \) \(\mathstrut -\mathstrut 11q^{27} \) \(\mathstrut -\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 23q^{29} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 16q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut -\mathstrut 27q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut -\mathstrut 2q^{36} \) \(\mathstrut -\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 17q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut -\mathstrut 35q^{41} \) \(\mathstrut -\mathstrut 12q^{42} \) \(\mathstrut +\mathstrut 3q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut -\mathstrut 25q^{47} \) \(\mathstrut -\mathstrut 8q^{48} \) \(\mathstrut -\mathstrut 24q^{49} \) \(\mathstrut +\mathstrut 16q^{50} \) \(\mathstrut -\mathstrut q^{51} \) \(\mathstrut -\mathstrut 20q^{52} \) \(\mathstrut -\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 11q^{54} \) \(\mathstrut -\mathstrut 14q^{55} \) \(\mathstrut -\mathstrut 10q^{56} \) \(\mathstrut -\mathstrut 6q^{57} \) \(\mathstrut -\mathstrut 23q^{58} \) \(\mathstrut -\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 21q^{62} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 16q^{64} \) \(\mathstrut -\mathstrut 20q^{65} \) \(\mathstrut -\mathstrut 9q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut -\mathstrut 25q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 16q^{71} \) \(\mathstrut -\mathstrut 2q^{72} \) \(\mathstrut -\mathstrut 17q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 17q^{76} \) \(\mathstrut -\mathstrut 34q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 40q^{79} \) \(\mathstrut +\mathstrut 16q^{80} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut -\mathstrut 35q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 12q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut +\mathstrut 3q^{86} \) \(\mathstrut +\mathstrut 10q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut -\mathstrut q^{91} \) \(\mathstrut -\mathstrut 9q^{92} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut -\mathstrut 25q^{94} \) \(\mathstrut -\mathstrut 17q^{95} \) \(\mathstrut -\mathstrut 8q^{96} \) \(\mathstrut -\mathstrut 21q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 15q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.41044 0.814318 0.407159 0.913357i \(-0.366519\pi\)
0.407159 + 0.913357i \(0.366519\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 1.41044 0.575810
\(7\) −3.15104 −1.19098 −0.595490 0.803363i \(-0.703042\pi\)
−0.595490 + 0.803363i \(0.703042\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.01066 −0.336885
\(10\) 1.00000 0.316228
\(11\) −1.04069 −0.313780 −0.156890 0.987616i \(-0.550147\pi\)
−0.156890 + 0.987616i \(0.550147\pi\)
\(12\) 1.41044 0.407159
\(13\) −3.01659 −0.836653 −0.418326 0.908297i \(-0.637383\pi\)
−0.418326 + 0.908297i \(0.637383\pi\)
\(14\) −3.15104 −0.842150
\(15\) 1.41044 0.364174
\(16\) 1.00000 0.250000
\(17\) 2.09209 0.507406 0.253703 0.967282i \(-0.418351\pi\)
0.253703 + 0.967282i \(0.418351\pi\)
\(18\) −1.01066 −0.238214
\(19\) 3.54717 0.813778 0.406889 0.913478i \(-0.366614\pi\)
0.406889 + 0.913478i \(0.366614\pi\)
\(20\) 1.00000 0.223607
\(21\) −4.44435 −0.969837
\(22\) −1.04069 −0.221876
\(23\) −1.80458 −0.376281 −0.188141 0.982142i \(-0.560246\pi\)
−0.188141 + 0.982142i \(0.560246\pi\)
\(24\) 1.41044 0.287905
\(25\) 1.00000 0.200000
\(26\) −3.01659 −0.591603
\(27\) −5.65679 −1.08865
\(28\) −3.15104 −0.595490
\(29\) −0.429786 −0.0798093 −0.0399047 0.999203i \(-0.512705\pi\)
−0.0399047 + 0.999203i \(0.512705\pi\)
\(30\) 1.41044 0.257510
\(31\) −9.55437 −1.71602 −0.858008 0.513637i \(-0.828298\pi\)
−0.858008 + 0.513637i \(0.828298\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.46783 −0.255517
\(34\) 2.09209 0.358790
\(35\) −3.15104 −0.532622
\(36\) −1.01066 −0.168443
\(37\) 7.40717 1.21773 0.608866 0.793273i \(-0.291625\pi\)
0.608866 + 0.793273i \(0.291625\pi\)
\(38\) 3.54717 0.575428
\(39\) −4.25473 −0.681302
\(40\) 1.00000 0.158114
\(41\) −9.28453 −1.45000 −0.725000 0.688749i \(-0.758160\pi\)
−0.725000 + 0.688749i \(0.758160\pi\)
\(42\) −4.44435 −0.685778
\(43\) −7.43486 −1.13381 −0.566903 0.823785i \(-0.691858\pi\)
−0.566903 + 0.823785i \(0.691858\pi\)
\(44\) −1.04069 −0.156890
\(45\) −1.01066 −0.150660
\(46\) −1.80458 −0.266071
\(47\) −10.5989 −1.54601 −0.773006 0.634399i \(-0.781248\pi\)
−0.773006 + 0.634399i \(0.781248\pi\)
\(48\) 1.41044 0.203580
\(49\) 2.92903 0.418433
\(50\) 1.00000 0.141421
\(51\) 2.95077 0.413190
\(52\) −3.01659 −0.418326
\(53\) −7.88673 −1.08333 −0.541663 0.840596i \(-0.682205\pi\)
−0.541663 + 0.840596i \(0.682205\pi\)
\(54\) −5.65679 −0.769792
\(55\) −1.04069 −0.140327
\(56\) −3.15104 −0.421075
\(57\) 5.00308 0.662674
\(58\) −0.429786 −0.0564337
\(59\) 3.06070 0.398469 0.199235 0.979952i \(-0.436154\pi\)
0.199235 + 0.979952i \(0.436154\pi\)
\(60\) 1.41044 0.182087
\(61\) −4.36339 −0.558675 −0.279337 0.960193i \(-0.590115\pi\)
−0.279337 + 0.960193i \(0.590115\pi\)
\(62\) −9.55437 −1.21341
\(63\) 3.18461 0.401224
\(64\) 1.00000 0.125000
\(65\) −3.01659 −0.374162
\(66\) −1.46783 −0.180678
\(67\) 11.1448 1.36155 0.680774 0.732493i \(-0.261643\pi\)
0.680774 + 0.732493i \(0.261643\pi\)
\(68\) 2.09209 0.253703
\(69\) −2.54525 −0.306413
\(70\) −3.15104 −0.376621
\(71\) 8.28515 0.983266 0.491633 0.870802i \(-0.336400\pi\)
0.491633 + 0.870802i \(0.336400\pi\)
\(72\) −1.01066 −0.119107
\(73\) −5.43760 −0.636423 −0.318212 0.948020i \(-0.603082\pi\)
−0.318212 + 0.948020i \(0.603082\pi\)
\(74\) 7.40717 0.861066
\(75\) 1.41044 0.162864
\(76\) 3.54717 0.406889
\(77\) 3.27926 0.373706
\(78\) −4.25473 −0.481753
\(79\) 9.01031 1.01374 0.506869 0.862023i \(-0.330803\pi\)
0.506869 + 0.862023i \(0.330803\pi\)
\(80\) 1.00000 0.111803
\(81\) −4.94661 −0.549623
\(82\) −9.28453 −1.02531
\(83\) 8.94926 0.982309 0.491154 0.871073i \(-0.336575\pi\)
0.491154 + 0.871073i \(0.336575\pi\)
\(84\) −4.44435 −0.484918
\(85\) 2.09209 0.226919
\(86\) −7.43486 −0.801721
\(87\) −0.606188 −0.0649902
\(88\) −1.04069 −0.110938
\(89\) −8.34070 −0.884112 −0.442056 0.896987i \(-0.645751\pi\)
−0.442056 + 0.896987i \(0.645751\pi\)
\(90\) −1.01066 −0.106533
\(91\) 9.50540 0.996436
\(92\) −1.80458 −0.188141
\(93\) −13.4759 −1.39738
\(94\) −10.5989 −1.09320
\(95\) 3.54717 0.363932
\(96\) 1.41044 0.143953
\(97\) 6.35468 0.645220 0.322610 0.946532i \(-0.395440\pi\)
0.322610 + 0.946532i \(0.395440\pi\)
\(98\) 2.92903 0.295877
\(99\) 1.05178 0.105708
\(100\) 1.00000 0.100000
\(101\) −4.10281 −0.408245 −0.204122 0.978945i \(-0.565434\pi\)
−0.204122 + 0.978945i \(0.565434\pi\)
\(102\) 2.95077 0.292170
\(103\) −8.66854 −0.854136 −0.427068 0.904219i \(-0.640454\pi\)
−0.427068 + 0.904219i \(0.640454\pi\)
\(104\) −3.01659 −0.295801
\(105\) −4.44435 −0.433724
\(106\) −7.88673 −0.766027
\(107\) −15.3045 −1.47954 −0.739770 0.672860i \(-0.765066\pi\)
−0.739770 + 0.672860i \(0.765066\pi\)
\(108\) −5.65679 −0.544325
\(109\) −13.5541 −1.29825 −0.649126 0.760681i \(-0.724865\pi\)
−0.649126 + 0.760681i \(0.724865\pi\)
\(110\) −1.04069 −0.0992261
\(111\) 10.4474 0.991621
\(112\) −3.15104 −0.297745
\(113\) 16.1227 1.51670 0.758349 0.651849i \(-0.226006\pi\)
0.758349 + 0.651849i \(0.226006\pi\)
\(114\) 5.00308 0.468581
\(115\) −1.80458 −0.168278
\(116\) −0.429786 −0.0399047
\(117\) 3.04874 0.281856
\(118\) 3.06070 0.281760
\(119\) −6.59225 −0.604311
\(120\) 1.41044 0.128755
\(121\) −9.91696 −0.901542
\(122\) −4.36339 −0.395043
\(123\) −13.0953 −1.18076
\(124\) −9.55437 −0.858008
\(125\) 1.00000 0.0894427
\(126\) 3.18461 0.283708
\(127\) 12.6071 1.11870 0.559351 0.828931i \(-0.311050\pi\)
0.559351 + 0.828931i \(0.311050\pi\)
\(128\) 1.00000 0.0883883
\(129\) −10.4864 −0.923278
\(130\) −3.01659 −0.264573
\(131\) 9.23835 0.807158 0.403579 0.914945i \(-0.367766\pi\)
0.403579 + 0.914945i \(0.367766\pi\)
\(132\) −1.46783 −0.127759
\(133\) −11.1773 −0.969193
\(134\) 11.1448 0.962760
\(135\) −5.65679 −0.486859
\(136\) 2.09209 0.179395
\(137\) −22.3754 −1.91166 −0.955829 0.293925i \(-0.905038\pi\)
−0.955829 + 0.293925i \(0.905038\pi\)
\(138\) −2.54525 −0.216666
\(139\) −14.1367 −1.19906 −0.599529 0.800353i \(-0.704646\pi\)
−0.599529 + 0.800353i \(0.704646\pi\)
\(140\) −3.15104 −0.266311
\(141\) −14.9492 −1.25895
\(142\) 8.28515 0.695274
\(143\) 3.13935 0.262525
\(144\) −1.01066 −0.0842214
\(145\) −0.429786 −0.0356918
\(146\) −5.43760 −0.450019
\(147\) 4.13122 0.340738
\(148\) 7.40717 0.608866
\(149\) −7.35152 −0.602260 −0.301130 0.953583i \(-0.597364\pi\)
−0.301130 + 0.953583i \(0.597364\pi\)
\(150\) 1.41044 0.115162
\(151\) 16.3564 1.33107 0.665533 0.746368i \(-0.268204\pi\)
0.665533 + 0.746368i \(0.268204\pi\)
\(152\) 3.54717 0.287714
\(153\) −2.11438 −0.170938
\(154\) 3.27926 0.264250
\(155\) −9.55437 −0.767425
\(156\) −4.25473 −0.340651
\(157\) −7.76589 −0.619785 −0.309893 0.950772i \(-0.600293\pi\)
−0.309893 + 0.950772i \(0.600293\pi\)
\(158\) 9.01031 0.716822
\(159\) −11.1238 −0.882172
\(160\) 1.00000 0.0790569
\(161\) 5.68630 0.448143
\(162\) −4.94661 −0.388642
\(163\) 15.3338 1.20104 0.600519 0.799610i \(-0.294961\pi\)
0.600519 + 0.799610i \(0.294961\pi\)
\(164\) −9.28453 −0.725000
\(165\) −1.46783 −0.114271
\(166\) 8.94926 0.694597
\(167\) −20.5909 −1.59337 −0.796686 0.604393i \(-0.793416\pi\)
−0.796686 + 0.604393i \(0.793416\pi\)
\(168\) −4.44435 −0.342889
\(169\) −3.90016 −0.300012
\(170\) 2.09209 0.160456
\(171\) −3.58497 −0.274150
\(172\) −7.43486 −0.566903
\(173\) 9.79839 0.744958 0.372479 0.928041i \(-0.378508\pi\)
0.372479 + 0.928041i \(0.378508\pi\)
\(174\) −0.606188 −0.0459550
\(175\) −3.15104 −0.238196
\(176\) −1.04069 −0.0784451
\(177\) 4.31694 0.324481
\(178\) −8.34070 −0.625162
\(179\) 11.9994 0.896877 0.448439 0.893814i \(-0.351980\pi\)
0.448439 + 0.893814i \(0.351980\pi\)
\(180\) −1.01066 −0.0753299
\(181\) 0.246164 0.0182972 0.00914860 0.999958i \(-0.497088\pi\)
0.00914860 + 0.999958i \(0.497088\pi\)
\(182\) 9.50540 0.704587
\(183\) −6.15430 −0.454939
\(184\) −1.80458 −0.133035
\(185\) 7.40717 0.544586
\(186\) −13.4759 −0.988099
\(187\) −2.17722 −0.159214
\(188\) −10.5989 −0.773006
\(189\) 17.8248 1.29656
\(190\) 3.54717 0.257339
\(191\) 20.4010 1.47617 0.738084 0.674709i \(-0.235731\pi\)
0.738084 + 0.674709i \(0.235731\pi\)
\(192\) 1.41044 0.101790
\(193\) 2.54753 0.183375 0.0916875 0.995788i \(-0.470774\pi\)
0.0916875 + 0.995788i \(0.470774\pi\)
\(194\) 6.35468 0.456240
\(195\) −4.25473 −0.304687
\(196\) 2.92903 0.209216
\(197\) −3.59037 −0.255803 −0.127901 0.991787i \(-0.540824\pi\)
−0.127901 + 0.991787i \(0.540824\pi\)
\(198\) 1.05178 0.0747469
\(199\) −22.6077 −1.60262 −0.801308 0.598251i \(-0.795862\pi\)
−0.801308 + 0.598251i \(0.795862\pi\)
\(200\) 1.00000 0.0707107
\(201\) 15.7190 1.10873
\(202\) −4.10281 −0.288673
\(203\) 1.35427 0.0950513
\(204\) 2.95077 0.206595
\(205\) −9.28453 −0.648460
\(206\) −8.66854 −0.603966
\(207\) 1.82381 0.126764
\(208\) −3.01659 −0.209163
\(209\) −3.69152 −0.255348
\(210\) −4.44435 −0.306689
\(211\) −0.563633 −0.0388021 −0.0194011 0.999812i \(-0.506176\pi\)
−0.0194011 + 0.999812i \(0.506176\pi\)
\(212\) −7.88673 −0.541663
\(213\) 11.6857 0.800692
\(214\) −15.3045 −1.04619
\(215\) −7.43486 −0.507053
\(216\) −5.65679 −0.384896
\(217\) 30.1062 2.04374
\(218\) −13.5541 −0.918002
\(219\) −7.66942 −0.518251
\(220\) −1.04069 −0.0701634
\(221\) −6.31099 −0.424523
\(222\) 10.4474 0.701182
\(223\) −9.19193 −0.615537 −0.307769 0.951461i \(-0.599582\pi\)
−0.307769 + 0.951461i \(0.599582\pi\)
\(224\) −3.15104 −0.210537
\(225\) −1.01066 −0.0673771
\(226\) 16.1227 1.07247
\(227\) −4.76633 −0.316353 −0.158176 0.987411i \(-0.550561\pi\)
−0.158176 + 0.987411i \(0.550561\pi\)
\(228\) 5.00308 0.331337
\(229\) −11.9104 −0.787060 −0.393530 0.919312i \(-0.628746\pi\)
−0.393530 + 0.919312i \(0.628746\pi\)
\(230\) −1.80458 −0.118991
\(231\) 4.62520 0.304316
\(232\) −0.429786 −0.0282169
\(233\) 15.3681 1.00680 0.503398 0.864055i \(-0.332083\pi\)
0.503398 + 0.864055i \(0.332083\pi\)
\(234\) 3.04874 0.199302
\(235\) −10.5989 −0.691398
\(236\) 3.06070 0.199235
\(237\) 12.7085 0.825506
\(238\) −6.59225 −0.427312
\(239\) −8.67620 −0.561217 −0.280608 0.959822i \(-0.590536\pi\)
−0.280608 + 0.959822i \(0.590536\pi\)
\(240\) 1.41044 0.0910436
\(241\) −11.9235 −0.768063 −0.384031 0.923320i \(-0.625465\pi\)
−0.384031 + 0.923320i \(0.625465\pi\)
\(242\) −9.91696 −0.637486
\(243\) 9.99349 0.641082
\(244\) −4.36339 −0.279337
\(245\) 2.92903 0.187129
\(246\) −13.0953 −0.834925
\(247\) −10.7004 −0.680849
\(248\) −9.55437 −0.606703
\(249\) 12.6224 0.799912
\(250\) 1.00000 0.0632456
\(251\) −11.7240 −0.740015 −0.370008 0.929029i \(-0.620645\pi\)
−0.370008 + 0.929029i \(0.620645\pi\)
\(252\) 3.18461 0.200612
\(253\) 1.87801 0.118070
\(254\) 12.6071 0.791042
\(255\) 2.95077 0.184784
\(256\) 1.00000 0.0625000
\(257\) 16.6262 1.03712 0.518558 0.855042i \(-0.326469\pi\)
0.518558 + 0.855042i \(0.326469\pi\)
\(258\) −10.4864 −0.652856
\(259\) −23.3403 −1.45029
\(260\) −3.01659 −0.187081
\(261\) 0.434366 0.0268866
\(262\) 9.23835 0.570747
\(263\) 17.0636 1.05219 0.526094 0.850426i \(-0.323656\pi\)
0.526094 + 0.850426i \(0.323656\pi\)
\(264\) −1.46783 −0.0903390
\(265\) −7.88673 −0.484478
\(266\) −11.1773 −0.685323
\(267\) −11.7641 −0.719949
\(268\) 11.1448 0.680774
\(269\) −7.54805 −0.460213 −0.230106 0.973165i \(-0.573907\pi\)
−0.230106 + 0.973165i \(0.573907\pi\)
\(270\) −5.65679 −0.344262
\(271\) 2.98704 0.181450 0.0907249 0.995876i \(-0.471082\pi\)
0.0907249 + 0.995876i \(0.471082\pi\)
\(272\) 2.09209 0.126852
\(273\) 13.4068 0.811417
\(274\) −22.3754 −1.35175
\(275\) −1.04069 −0.0627561
\(276\) −2.54525 −0.153206
\(277\) −0.626895 −0.0376665 −0.0188332 0.999823i \(-0.505995\pi\)
−0.0188332 + 0.999823i \(0.505995\pi\)
\(278\) −14.1367 −0.847862
\(279\) 9.65618 0.578101
\(280\) −3.15104 −0.188310
\(281\) 23.0483 1.37495 0.687473 0.726210i \(-0.258720\pi\)
0.687473 + 0.726210i \(0.258720\pi\)
\(282\) −14.9492 −0.890209
\(283\) 1.83831 0.109276 0.0546381 0.998506i \(-0.482599\pi\)
0.0546381 + 0.998506i \(0.482599\pi\)
\(284\) 8.28515 0.491633
\(285\) 5.00308 0.296357
\(286\) 3.13935 0.185633
\(287\) 29.2559 1.72692
\(288\) −1.01066 −0.0595535
\(289\) −12.6232 −0.742539
\(290\) −0.429786 −0.0252379
\(291\) 8.96291 0.525415
\(292\) −5.43760 −0.318212
\(293\) −11.1006 −0.648504 −0.324252 0.945971i \(-0.605113\pi\)
−0.324252 + 0.945971i \(0.605113\pi\)
\(294\) 4.13122 0.240938
\(295\) 3.06070 0.178201
\(296\) 7.40717 0.430533
\(297\) 5.88698 0.341597
\(298\) −7.35152 −0.425862
\(299\) 5.44369 0.314817
\(300\) 1.41044 0.0814318
\(301\) 23.4275 1.35034
\(302\) 16.3564 0.941206
\(303\) −5.78677 −0.332441
\(304\) 3.54717 0.203444
\(305\) −4.36339 −0.249847
\(306\) −2.11438 −0.120871
\(307\) 10.5173 0.600255 0.300128 0.953899i \(-0.402971\pi\)
0.300128 + 0.953899i \(0.402971\pi\)
\(308\) 3.27926 0.186853
\(309\) −12.2265 −0.695539
\(310\) −9.55437 −0.542652
\(311\) 9.81794 0.556725 0.278362 0.960476i \(-0.410208\pi\)
0.278362 + 0.960476i \(0.410208\pi\)
\(312\) −4.25473 −0.240877
\(313\) 26.9734 1.52463 0.762314 0.647208i \(-0.224063\pi\)
0.762314 + 0.647208i \(0.224063\pi\)
\(314\) −7.76589 −0.438254
\(315\) 3.18461 0.179433
\(316\) 9.01031 0.506869
\(317\) 9.77743 0.549155 0.274578 0.961565i \(-0.411462\pi\)
0.274578 + 0.961565i \(0.411462\pi\)
\(318\) −11.1238 −0.623790
\(319\) 0.447275 0.0250426
\(320\) 1.00000 0.0559017
\(321\) −21.5861 −1.20482
\(322\) 5.68630 0.316885
\(323\) 7.42101 0.412916
\(324\) −4.94661 −0.274811
\(325\) −3.01659 −0.167331
\(326\) 15.3338 0.849262
\(327\) −19.1173 −1.05719
\(328\) −9.28453 −0.512653
\(329\) 33.3976 1.84127
\(330\) −1.46783 −0.0808016
\(331\) 9.21802 0.506668 0.253334 0.967379i \(-0.418473\pi\)
0.253334 + 0.967379i \(0.418473\pi\)
\(332\) 8.94926 0.491154
\(333\) −7.48610 −0.410236
\(334\) −20.5909 −1.12668
\(335\) 11.1448 0.608903
\(336\) −4.44435 −0.242459
\(337\) −3.83268 −0.208779 −0.104390 0.994536i \(-0.533289\pi\)
−0.104390 + 0.994536i \(0.533289\pi\)
\(338\) −3.90016 −0.212141
\(339\) 22.7401 1.23508
\(340\) 2.09209 0.113460
\(341\) 9.94316 0.538452
\(342\) −3.58497 −0.193853
\(343\) 12.8278 0.692635
\(344\) −7.43486 −0.400861
\(345\) −2.54525 −0.137032
\(346\) 9.79839 0.526765
\(347\) 28.8686 1.54975 0.774875 0.632115i \(-0.217813\pi\)
0.774875 + 0.632115i \(0.217813\pi\)
\(348\) −0.606188 −0.0324951
\(349\) 26.4828 1.41759 0.708795 0.705414i \(-0.249239\pi\)
0.708795 + 0.705414i \(0.249239\pi\)
\(350\) −3.15104 −0.168430
\(351\) 17.0643 0.910822
\(352\) −1.04069 −0.0554691
\(353\) −17.6764 −0.940818 −0.470409 0.882449i \(-0.655894\pi\)
−0.470409 + 0.882449i \(0.655894\pi\)
\(354\) 4.31694 0.229443
\(355\) 8.28515 0.439730
\(356\) −8.34070 −0.442056
\(357\) −9.29798 −0.492101
\(358\) 11.9994 0.634188
\(359\) −17.0247 −0.898528 −0.449264 0.893399i \(-0.648314\pi\)
−0.449264 + 0.893399i \(0.648314\pi\)
\(360\) −1.01066 −0.0532663
\(361\) −6.41755 −0.337766
\(362\) 0.246164 0.0129381
\(363\) −13.9873 −0.734142
\(364\) 9.50540 0.498218
\(365\) −5.43760 −0.284617
\(366\) −6.15430 −0.321691
\(367\) −36.4460 −1.90247 −0.951233 0.308474i \(-0.900182\pi\)
−0.951233 + 0.308474i \(0.900182\pi\)
\(368\) −1.80458 −0.0940703
\(369\) 9.38347 0.488484
\(370\) 7.40717 0.385080
\(371\) 24.8514 1.29022
\(372\) −13.4759 −0.698692
\(373\) −15.9187 −0.824239 −0.412119 0.911130i \(-0.635211\pi\)
−0.412119 + 0.911130i \(0.635211\pi\)
\(374\) −2.17722 −0.112581
\(375\) 1.41044 0.0728349
\(376\) −10.5989 −0.546598
\(377\) 1.29649 0.0667727
\(378\) 17.8248 0.916807
\(379\) −9.80431 −0.503614 −0.251807 0.967778i \(-0.581025\pi\)
−0.251807 + 0.967778i \(0.581025\pi\)
\(380\) 3.54717 0.181966
\(381\) 17.7816 0.910980
\(382\) 20.4010 1.04381
\(383\) −9.63675 −0.492415 −0.246207 0.969217i \(-0.579184\pi\)
−0.246207 + 0.969217i \(0.579184\pi\)
\(384\) 1.41044 0.0719763
\(385\) 3.27926 0.167126
\(386\) 2.54753 0.129666
\(387\) 7.51408 0.381962
\(388\) 6.35468 0.322610
\(389\) 10.6926 0.542137 0.271069 0.962560i \(-0.412623\pi\)
0.271069 + 0.962560i \(0.412623\pi\)
\(390\) −4.25473 −0.215447
\(391\) −3.77534 −0.190927
\(392\) 2.92903 0.147938
\(393\) 13.0301 0.657284
\(394\) −3.59037 −0.180880
\(395\) 9.01031 0.453358
\(396\) 1.05178 0.0528540
\(397\) 3.69620 0.185507 0.0927534 0.995689i \(-0.470433\pi\)
0.0927534 + 0.995689i \(0.470433\pi\)
\(398\) −22.6077 −1.13322
\(399\) −15.7649 −0.789232
\(400\) 1.00000 0.0500000
\(401\) 2.95099 0.147366 0.0736828 0.997282i \(-0.476525\pi\)
0.0736828 + 0.997282i \(0.476525\pi\)
\(402\) 15.7190 0.783994
\(403\) 28.8217 1.43571
\(404\) −4.10281 −0.204122
\(405\) −4.94661 −0.245799
\(406\) 1.35427 0.0672114
\(407\) −7.70858 −0.382100
\(408\) 2.95077 0.146085
\(409\) 34.2197 1.69205 0.846027 0.533141i \(-0.178988\pi\)
0.846027 + 0.533141i \(0.178988\pi\)
\(410\) −9.28453 −0.458530
\(411\) −31.5591 −1.55670
\(412\) −8.66854 −0.427068
\(413\) −9.64438 −0.474569
\(414\) 1.82381 0.0896354
\(415\) 8.94926 0.439302
\(416\) −3.01659 −0.147901
\(417\) −19.9390 −0.976416
\(418\) −3.69152 −0.180558
\(419\) −29.3149 −1.43213 −0.716064 0.698035i \(-0.754058\pi\)
−0.716064 + 0.698035i \(0.754058\pi\)
\(420\) −4.44435 −0.216862
\(421\) −11.7698 −0.573623 −0.286812 0.957987i \(-0.592595\pi\)
−0.286812 + 0.957987i \(0.592595\pi\)
\(422\) −0.563633 −0.0274372
\(423\) 10.7119 0.520829
\(424\) −7.88673 −0.383013
\(425\) 2.09209 0.101481
\(426\) 11.6857 0.566175
\(427\) 13.7492 0.665370
\(428\) −15.3045 −0.739770
\(429\) 4.42786 0.213779
\(430\) −7.43486 −0.358541
\(431\) 17.6035 0.847932 0.423966 0.905678i \(-0.360638\pi\)
0.423966 + 0.905678i \(0.360638\pi\)
\(432\) −5.65679 −0.272163
\(433\) 19.7338 0.948348 0.474174 0.880431i \(-0.342747\pi\)
0.474174 + 0.880431i \(0.342747\pi\)
\(434\) 30.1062 1.44514
\(435\) −0.606188 −0.0290645
\(436\) −13.5541 −0.649126
\(437\) −6.40116 −0.306209
\(438\) −7.66942 −0.366459
\(439\) −20.8591 −0.995553 −0.497776 0.867305i \(-0.665850\pi\)
−0.497776 + 0.867305i \(0.665850\pi\)
\(440\) −1.04069 −0.0496130
\(441\) −2.96024 −0.140964
\(442\) −6.31099 −0.300183
\(443\) −21.5858 −1.02557 −0.512785 0.858517i \(-0.671386\pi\)
−0.512785 + 0.858517i \(0.671386\pi\)
\(444\) 10.4474 0.495810
\(445\) −8.34070 −0.395387
\(446\) −9.19193 −0.435251
\(447\) −10.3689 −0.490432
\(448\) −3.15104 −0.148872
\(449\) 15.1846 0.716608 0.358304 0.933605i \(-0.383355\pi\)
0.358304 + 0.933605i \(0.383355\pi\)
\(450\) −1.01066 −0.0476428
\(451\) 9.66234 0.454982
\(452\) 16.1227 0.758349
\(453\) 23.0698 1.08391
\(454\) −4.76633 −0.223695
\(455\) 9.50540 0.445620
\(456\) 5.00308 0.234291
\(457\) 10.6088 0.496257 0.248129 0.968727i \(-0.420184\pi\)
0.248129 + 0.968727i \(0.420184\pi\)
\(458\) −11.9104 −0.556536
\(459\) −11.8345 −0.552388
\(460\) −1.80458 −0.0841390
\(461\) −3.89885 −0.181588 −0.0907938 0.995870i \(-0.528940\pi\)
−0.0907938 + 0.995870i \(0.528940\pi\)
\(462\) 4.62520 0.215184
\(463\) 3.98126 0.185025 0.0925125 0.995712i \(-0.470510\pi\)
0.0925125 + 0.995712i \(0.470510\pi\)
\(464\) −0.429786 −0.0199523
\(465\) −13.4759 −0.624929
\(466\) 15.3681 0.711912
\(467\) 12.8211 0.593291 0.296646 0.954988i \(-0.404132\pi\)
0.296646 + 0.954988i \(0.404132\pi\)
\(468\) 3.04874 0.140928
\(469\) −35.1175 −1.62158
\(470\) −10.5989 −0.488892
\(471\) −10.9533 −0.504703
\(472\) 3.06070 0.140880
\(473\) 7.73740 0.355766
\(474\) 12.7085 0.583721
\(475\) 3.54717 0.162756
\(476\) −6.59225 −0.302155
\(477\) 7.97077 0.364956
\(478\) −8.67620 −0.396840
\(479\) −21.5439 −0.984367 −0.492184 0.870491i \(-0.663801\pi\)
−0.492184 + 0.870491i \(0.663801\pi\)
\(480\) 1.41044 0.0643775
\(481\) −22.3444 −1.01882
\(482\) −11.9235 −0.543103
\(483\) 8.02019 0.364931
\(484\) −9.91696 −0.450771
\(485\) 6.35468 0.288551
\(486\) 9.99349 0.453314
\(487\) 31.2923 1.41799 0.708994 0.705215i \(-0.249149\pi\)
0.708994 + 0.705215i \(0.249149\pi\)
\(488\) −4.36339 −0.197521
\(489\) 21.6275 0.978028
\(490\) 2.92903 0.132320
\(491\) 16.7735 0.756978 0.378489 0.925606i \(-0.376444\pi\)
0.378489 + 0.925606i \(0.376444\pi\)
\(492\) −13.0953 −0.590381
\(493\) −0.899152 −0.0404958
\(494\) −10.7004 −0.481433
\(495\) 1.05178 0.0472741
\(496\) −9.55437 −0.429004
\(497\) −26.1068 −1.17105
\(498\) 12.6224 0.565623
\(499\) 10.5285 0.471320 0.235660 0.971836i \(-0.424275\pi\)
0.235660 + 0.971836i \(0.424275\pi\)
\(500\) 1.00000 0.0447214
\(501\) −29.0423 −1.29751
\(502\) −11.7240 −0.523270
\(503\) 6.54465 0.291811 0.145906 0.989299i \(-0.453390\pi\)
0.145906 + 0.989299i \(0.453390\pi\)
\(504\) 3.18461 0.141854
\(505\) −4.10281 −0.182573
\(506\) 1.87801 0.0834878
\(507\) −5.50094 −0.244305
\(508\) 12.6071 0.559351
\(509\) 16.4367 0.728545 0.364272 0.931292i \(-0.381318\pi\)
0.364272 + 0.931292i \(0.381318\pi\)
\(510\) 2.95077 0.130662
\(511\) 17.1341 0.757967
\(512\) 1.00000 0.0441942
\(513\) −20.0656 −0.885920
\(514\) 16.6262 0.733352
\(515\) −8.66854 −0.381981
\(516\) −10.4864 −0.461639
\(517\) 11.0302 0.485108
\(518\) −23.3403 −1.02551
\(519\) 13.8201 0.606633
\(520\) −3.01659 −0.132286
\(521\) 31.6137 1.38502 0.692510 0.721408i \(-0.256505\pi\)
0.692510 + 0.721408i \(0.256505\pi\)
\(522\) 0.434366 0.0190117
\(523\) −11.3152 −0.494781 −0.247390 0.968916i \(-0.579573\pi\)
−0.247390 + 0.968916i \(0.579573\pi\)
\(524\) 9.23835 0.403579
\(525\) −4.44435 −0.193967
\(526\) 17.0636 0.744009
\(527\) −19.9886 −0.870717
\(528\) −1.46783 −0.0638793
\(529\) −19.7435 −0.858413
\(530\) −7.88673 −0.342578
\(531\) −3.09332 −0.134239
\(532\) −11.1773 −0.484596
\(533\) 28.0077 1.21315
\(534\) −11.7641 −0.509081
\(535\) −15.3045 −0.661671
\(536\) 11.1448 0.481380
\(537\) 16.9244 0.730344
\(538\) −7.54805 −0.325420
\(539\) −3.04822 −0.131296
\(540\) −5.65679 −0.243430
\(541\) −35.4631 −1.52468 −0.762338 0.647179i \(-0.775949\pi\)
−0.762338 + 0.647179i \(0.775949\pi\)
\(542\) 2.98704 0.128304
\(543\) 0.347199 0.0148998
\(544\) 2.09209 0.0896976
\(545\) −13.5541 −0.580596
\(546\) 13.4068 0.573758
\(547\) 11.7442 0.502147 0.251073 0.967968i \(-0.419216\pi\)
0.251073 + 0.967968i \(0.419216\pi\)
\(548\) −22.3754 −0.955829
\(549\) 4.40989 0.188209
\(550\) −1.04069 −0.0443753
\(551\) −1.52453 −0.0649471
\(552\) −2.54525 −0.108333
\(553\) −28.3918 −1.20734
\(554\) −0.626895 −0.0266342
\(555\) 10.4474 0.443466
\(556\) −14.1367 −0.599529
\(557\) 6.71231 0.284410 0.142205 0.989837i \(-0.454581\pi\)
0.142205 + 0.989837i \(0.454581\pi\)
\(558\) 9.65618 0.408779
\(559\) 22.4279 0.948601
\(560\) −3.15104 −0.133156
\(561\) −3.07084 −0.129651
\(562\) 23.0483 0.972233
\(563\) −3.19238 −0.134543 −0.0672713 0.997735i \(-0.521429\pi\)
−0.0672713 + 0.997735i \(0.521429\pi\)
\(564\) −14.9492 −0.629473
\(565\) 16.1227 0.678288
\(566\) 1.83831 0.0772699
\(567\) 15.5869 0.654590
\(568\) 8.28515 0.347637
\(569\) −40.2457 −1.68719 −0.843593 0.536983i \(-0.819564\pi\)
−0.843593 + 0.536983i \(0.819564\pi\)
\(570\) 5.00308 0.209556
\(571\) −9.96583 −0.417057 −0.208529 0.978016i \(-0.566867\pi\)
−0.208529 + 0.978016i \(0.566867\pi\)
\(572\) 3.13935 0.131263
\(573\) 28.7745 1.20207
\(574\) 29.2559 1.22112
\(575\) −1.80458 −0.0752562
\(576\) −1.01066 −0.0421107
\(577\) −29.0788 −1.21057 −0.605284 0.796010i \(-0.706940\pi\)
−0.605284 + 0.796010i \(0.706940\pi\)
\(578\) −12.6232 −0.525054
\(579\) 3.59314 0.149326
\(580\) −0.429786 −0.0178459
\(581\) −28.1994 −1.16991
\(582\) 8.96291 0.371524
\(583\) 8.20765 0.339926
\(584\) −5.43760 −0.225010
\(585\) 3.04874 0.126050
\(586\) −11.1006 −0.458562
\(587\) 6.93147 0.286092 0.143046 0.989716i \(-0.454310\pi\)
0.143046 + 0.989716i \(0.454310\pi\)
\(588\) 4.13122 0.170369
\(589\) −33.8910 −1.39646
\(590\) 3.06070 0.126007
\(591\) −5.06400 −0.208305
\(592\) 7.40717 0.304433
\(593\) −40.2143 −1.65140 −0.825701 0.564108i \(-0.809220\pi\)
−0.825701 + 0.564108i \(0.809220\pi\)
\(594\) 5.88698 0.241546
\(595\) −6.59225 −0.270256
\(596\) −7.35152 −0.301130
\(597\) −31.8868 −1.30504
\(598\) 5.44369 0.222609
\(599\) 39.7203 1.62293 0.811464 0.584402i \(-0.198671\pi\)
0.811464 + 0.584402i \(0.198671\pi\)
\(600\) 1.41044 0.0575810
\(601\) −1.00000 −0.0407909
\(602\) 23.4275 0.954834
\(603\) −11.2635 −0.458686
\(604\) 16.3564 0.665533
\(605\) −9.91696 −0.403182
\(606\) −5.78677 −0.235071
\(607\) −1.07765 −0.0437405 −0.0218702 0.999761i \(-0.506962\pi\)
−0.0218702 + 0.999761i \(0.506962\pi\)
\(608\) 3.54717 0.143857
\(609\) 1.91012 0.0774020
\(610\) −4.36339 −0.176668
\(611\) 31.9727 1.29348
\(612\) −2.11438 −0.0854689
\(613\) 16.2193 0.655091 0.327546 0.944835i \(-0.393778\pi\)
0.327546 + 0.944835i \(0.393778\pi\)
\(614\) 10.5173 0.424444
\(615\) −13.0953 −0.528053
\(616\) 3.27926 0.132125
\(617\) 35.2021 1.41718 0.708591 0.705619i \(-0.249331\pi\)
0.708591 + 0.705619i \(0.249331\pi\)
\(618\) −12.2265 −0.491820
\(619\) 39.2335 1.57693 0.788463 0.615082i \(-0.210877\pi\)
0.788463 + 0.615082i \(0.210877\pi\)
\(620\) −9.55437 −0.383713
\(621\) 10.2081 0.409638
\(622\) 9.81794 0.393664
\(623\) 26.2818 1.05296
\(624\) −4.25473 −0.170325
\(625\) 1.00000 0.0400000
\(626\) 26.9734 1.07807
\(627\) −5.20667 −0.207934
\(628\) −7.76589 −0.309893
\(629\) 15.4965 0.617884
\(630\) 3.18461 0.126878
\(631\) 35.7483 1.42312 0.711558 0.702628i \(-0.247990\pi\)
0.711558 + 0.702628i \(0.247990\pi\)
\(632\) 9.01031 0.358411
\(633\) −0.794972 −0.0315973
\(634\) 9.77743 0.388311
\(635\) 12.6071 0.500299
\(636\) −11.1238 −0.441086
\(637\) −8.83569 −0.350083
\(638\) 0.447275 0.0177078
\(639\) −8.37344 −0.331248
\(640\) 1.00000 0.0395285
\(641\) −12.6490 −0.499604 −0.249802 0.968297i \(-0.580366\pi\)
−0.249802 + 0.968297i \(0.580366\pi\)
\(642\) −21.5861 −0.851934
\(643\) 17.2681 0.680987 0.340494 0.940247i \(-0.389406\pi\)
0.340494 + 0.940247i \(0.389406\pi\)
\(644\) 5.68630 0.224072
\(645\) −10.4864 −0.412903
\(646\) 7.42101 0.291976
\(647\) −10.9293 −0.429677 −0.214838 0.976650i \(-0.568922\pi\)
−0.214838 + 0.976650i \(0.568922\pi\)
\(648\) −4.94661 −0.194321
\(649\) −3.18525 −0.125032
\(650\) −3.01659 −0.118321
\(651\) 42.4630 1.66426
\(652\) 15.3338 0.600519
\(653\) −10.2745 −0.402071 −0.201036 0.979584i \(-0.564431\pi\)
−0.201036 + 0.979584i \(0.564431\pi\)
\(654\) −19.1173 −0.747546
\(655\) 9.23835 0.360972
\(656\) −9.28453 −0.362500
\(657\) 5.49555 0.214402
\(658\) 33.3976 1.30197
\(659\) −1.44077 −0.0561245 −0.0280623 0.999606i \(-0.508934\pi\)
−0.0280623 + 0.999606i \(0.508934\pi\)
\(660\) −1.46783 −0.0571354
\(661\) −15.7992 −0.614518 −0.307259 0.951626i \(-0.599412\pi\)
−0.307259 + 0.951626i \(0.599412\pi\)
\(662\) 9.21802 0.358268
\(663\) −8.90127 −0.345697
\(664\) 8.94926 0.347299
\(665\) −11.1773 −0.433436
\(666\) −7.48610 −0.290081
\(667\) 0.775584 0.0300307
\(668\) −20.5909 −0.796686
\(669\) −12.9647 −0.501244
\(670\) 11.1448 0.430559
\(671\) 4.54094 0.175301
\(672\) −4.44435 −0.171445
\(673\) 38.0739 1.46764 0.733821 0.679343i \(-0.237735\pi\)
0.733821 + 0.679343i \(0.237735\pi\)
\(674\) −3.83268 −0.147629
\(675\) −5.65679 −0.217730
\(676\) −3.90016 −0.150006
\(677\) −34.5726 −1.32873 −0.664366 0.747407i \(-0.731298\pi\)
−0.664366 + 0.747407i \(0.731298\pi\)
\(678\) 22.7401 0.873330
\(679\) −20.0238 −0.768444
\(680\) 2.09209 0.0802280
\(681\) −6.72263 −0.257612
\(682\) 9.94316 0.380743
\(683\) 30.5658 1.16957 0.584784 0.811189i \(-0.301179\pi\)
0.584784 + 0.811189i \(0.301179\pi\)
\(684\) −3.58497 −0.137075
\(685\) −22.3754 −0.854919
\(686\) 12.8278 0.489767
\(687\) −16.7989 −0.640918
\(688\) −7.43486 −0.283451
\(689\) 23.7911 0.906367
\(690\) −2.54525 −0.0968962
\(691\) −20.9029 −0.795184 −0.397592 0.917562i \(-0.630154\pi\)
−0.397592 + 0.917562i \(0.630154\pi\)
\(692\) 9.79839 0.372479
\(693\) −3.31420 −0.125896
\(694\) 28.8686 1.09584
\(695\) −14.1367 −0.536235
\(696\) −0.606188 −0.0229775
\(697\) −19.4241 −0.735739
\(698\) 26.4828 1.00239
\(699\) 21.6758 0.819852
\(700\) −3.15104 −0.119098
\(701\) −23.0749 −0.871526 −0.435763 0.900061i \(-0.643521\pi\)
−0.435763 + 0.900061i \(0.643521\pi\)
\(702\) 17.0643 0.644049
\(703\) 26.2745 0.990962
\(704\) −1.04069 −0.0392226
\(705\) −14.9492 −0.563018
\(706\) −17.6764 −0.665259
\(707\) 12.9281 0.486211
\(708\) 4.31694 0.162241
\(709\) −38.6734 −1.45241 −0.726204 0.687479i \(-0.758717\pi\)
−0.726204 + 0.687479i \(0.758717\pi\)
\(710\) 8.28515 0.310936
\(711\) −9.10632 −0.341514
\(712\) −8.34070 −0.312581
\(713\) 17.2416 0.645704
\(714\) −9.29798 −0.347968
\(715\) 3.13935 0.117405
\(716\) 11.9994 0.448439
\(717\) −12.2373 −0.457009
\(718\) −17.0247 −0.635356
\(719\) 25.4717 0.949935 0.474968 0.880003i \(-0.342460\pi\)
0.474968 + 0.880003i \(0.342460\pi\)
\(720\) −1.01066 −0.0376649
\(721\) 27.3149 1.01726
\(722\) −6.41755 −0.238837
\(723\) −16.8175 −0.625448
\(724\) 0.246164 0.00914860
\(725\) −0.429786 −0.0159619
\(726\) −13.9873 −0.519117
\(727\) 23.5111 0.871977 0.435989 0.899952i \(-0.356399\pi\)
0.435989 + 0.899952i \(0.356399\pi\)
\(728\) 9.50540 0.352293
\(729\) 28.9350 1.07167
\(730\) −5.43760 −0.201255
\(731\) −15.5544 −0.575300
\(732\) −6.15430 −0.227470
\(733\) −5.37759 −0.198626 −0.0993129 0.995056i \(-0.531664\pi\)
−0.0993129 + 0.995056i \(0.531664\pi\)
\(734\) −36.4460 −1.34525
\(735\) 4.13122 0.152382
\(736\) −1.80458 −0.0665177
\(737\) −11.5983 −0.427227
\(738\) 9.38347 0.345410
\(739\) −15.8932 −0.584642 −0.292321 0.956320i \(-0.594427\pi\)
−0.292321 + 0.956320i \(0.594427\pi\)
\(740\) 7.40717 0.272293
\(741\) −15.0923 −0.554428
\(742\) 24.8514 0.912322
\(743\) 12.1988 0.447530 0.223765 0.974643i \(-0.428165\pi\)
0.223765 + 0.974643i \(0.428165\pi\)
\(744\) −13.4759 −0.494050
\(745\) −7.35152 −0.269339
\(746\) −15.9187 −0.582825
\(747\) −9.04462 −0.330926
\(748\) −2.17722 −0.0796071
\(749\) 48.2250 1.76210
\(750\) 1.41044 0.0515020
\(751\) 38.6497 1.41035 0.705173 0.709035i \(-0.250869\pi\)
0.705173 + 0.709035i \(0.250869\pi\)
\(752\) −10.5989 −0.386503
\(753\) −16.5361 −0.602608
\(754\) 1.29649 0.0472154
\(755\) 16.3564 0.595271
\(756\) 17.8248 0.648280
\(757\) −1.02975 −0.0374268 −0.0187134 0.999825i \(-0.505957\pi\)
−0.0187134 + 0.999825i \(0.505957\pi\)
\(758\) −9.80431 −0.356109
\(759\) 2.64883 0.0961463
\(760\) 3.54717 0.128670
\(761\) 22.6429 0.820806 0.410403 0.911904i \(-0.365388\pi\)
0.410403 + 0.911904i \(0.365388\pi\)
\(762\) 17.7816 0.644160
\(763\) 42.7096 1.54619
\(764\) 20.4010 0.738084
\(765\) −2.11438 −0.0764457
\(766\) −9.63675 −0.348190
\(767\) −9.23290 −0.333381
\(768\) 1.41044 0.0508949
\(769\) 0.211541 0.00762835 0.00381417 0.999993i \(-0.498786\pi\)
0.00381417 + 0.999993i \(0.498786\pi\)
\(770\) 3.27926 0.118176
\(771\) 23.4503 0.844543
\(772\) 2.54753 0.0916875
\(773\) 6.41109 0.230591 0.115295 0.993331i \(-0.463219\pi\)
0.115295 + 0.993331i \(0.463219\pi\)
\(774\) 7.51408 0.270088
\(775\) −9.55437 −0.343203
\(776\) 6.35468 0.228120
\(777\) −32.9201 −1.18100
\(778\) 10.6926 0.383349
\(779\) −32.9339 −1.17998
\(780\) −4.25473 −0.152344
\(781\) −8.62229 −0.308530
\(782\) −3.77534 −0.135006
\(783\) 2.43121 0.0868845
\(784\) 2.92903 0.104608
\(785\) −7.76589 −0.277176
\(786\) 13.0301 0.464770
\(787\) 15.8847 0.566227 0.283114 0.959086i \(-0.408633\pi\)
0.283114 + 0.959086i \(0.408633\pi\)
\(788\) −3.59037 −0.127901
\(789\) 24.0672 0.856816
\(790\) 9.01031 0.320572
\(791\) −50.8033 −1.80636
\(792\) 1.05178 0.0373734
\(793\) 13.1626 0.467417
\(794\) 3.69620 0.131173
\(795\) −11.1238 −0.394519
\(796\) −22.6077 −0.801308
\(797\) −20.6779 −0.732449 −0.366225 0.930526i \(-0.619350\pi\)
−0.366225 + 0.930526i \(0.619350\pi\)
\(798\) −15.7649 −0.558071
\(799\) −22.1739 −0.784456
\(800\) 1.00000 0.0353553
\(801\) 8.42958 0.297845
\(802\) 2.95099 0.104203
\(803\) 5.65887 0.199697
\(804\) 15.7190 0.554367
\(805\) 5.68630 0.200416
\(806\) 28.8217 1.01520
\(807\) −10.6461 −0.374760
\(808\) −4.10281 −0.144336
\(809\) −44.6175 −1.56867 −0.784334 0.620339i \(-0.786995\pi\)
−0.784334 + 0.620339i \(0.786995\pi\)
\(810\) −4.94661 −0.173806
\(811\) −2.34123 −0.0822119 −0.0411059 0.999155i \(-0.513088\pi\)
−0.0411059 + 0.999155i \(0.513088\pi\)
\(812\) 1.35427 0.0475257
\(813\) 4.21304 0.147758
\(814\) −7.70858 −0.270186
\(815\) 15.3338 0.537121
\(816\) 2.95077 0.103298
\(817\) −26.3727 −0.922665
\(818\) 34.2197 1.19646
\(819\) −9.60669 −0.335685
\(820\) −9.28453 −0.324230
\(821\) 20.3297 0.709510 0.354755 0.934959i \(-0.384564\pi\)
0.354755 + 0.934959i \(0.384564\pi\)
\(822\) −31.5591 −1.10075
\(823\) −33.4109 −1.16463 −0.582316 0.812963i \(-0.697853\pi\)
−0.582316 + 0.812963i \(0.697853\pi\)
\(824\) −8.66854 −0.301983
\(825\) −1.46783 −0.0511034
\(826\) −9.64438 −0.335571
\(827\) 14.0651 0.489092 0.244546 0.969638i \(-0.421361\pi\)
0.244546 + 0.969638i \(0.421361\pi\)
\(828\) 1.82381 0.0633818
\(829\) −27.2410 −0.946119 −0.473060 0.881030i \(-0.656850\pi\)
−0.473060 + 0.881030i \(0.656850\pi\)
\(830\) 8.94926 0.310633
\(831\) −0.884198 −0.0306725
\(832\) −3.01659 −0.104582
\(833\) 6.12779 0.212315
\(834\) −19.9390 −0.690430
\(835\) −20.5909 −0.712578
\(836\) −3.69152 −0.127674
\(837\) 54.0471 1.86814
\(838\) −29.3149 −1.01267
\(839\) −24.1273 −0.832968 −0.416484 0.909143i \(-0.636738\pi\)
−0.416484 + 0.909143i \(0.636738\pi\)
\(840\) −4.44435 −0.153345
\(841\) −28.8153 −0.993630
\(842\) −11.7698 −0.405613
\(843\) 32.5082 1.11964
\(844\) −0.563633 −0.0194011
\(845\) −3.90016 −0.134170
\(846\) 10.7119 0.368282
\(847\) 31.2487 1.07372
\(848\) −7.88673 −0.270831
\(849\) 2.59283 0.0889856
\(850\) 2.09209 0.0717581
\(851\) −13.3668 −0.458209
\(852\) 11.6857 0.400346
\(853\) −21.3206 −0.730002 −0.365001 0.931007i \(-0.618931\pi\)
−0.365001 + 0.931007i \(0.618931\pi\)
\(854\) 13.7492 0.470488
\(855\) −3.58497 −0.122604
\(856\) −15.3045 −0.523096
\(857\) 37.7178 1.28842 0.644208 0.764850i \(-0.277187\pi\)
0.644208 + 0.764850i \(0.277187\pi\)
\(858\) 4.42786 0.151165
\(859\) 21.5115 0.733963 0.366982 0.930228i \(-0.380391\pi\)
0.366982 + 0.930228i \(0.380391\pi\)
\(860\) −7.43486 −0.253527
\(861\) 41.2637 1.40626
\(862\) 17.6035 0.599578
\(863\) 3.67152 0.124980 0.0624900 0.998046i \(-0.480096\pi\)
0.0624900 + 0.998046i \(0.480096\pi\)
\(864\) −5.65679 −0.192448
\(865\) 9.79839 0.333155
\(866\) 19.7338 0.670583
\(867\) −17.8042 −0.604663
\(868\) 30.1062 1.02187
\(869\) −9.37696 −0.318091
\(870\) −0.606188 −0.0205517
\(871\) −33.6192 −1.13914
\(872\) −13.5541 −0.459001
\(873\) −6.42240 −0.217365
\(874\) −6.40116 −0.216523
\(875\) −3.15104 −0.106524
\(876\) −7.66942 −0.259126
\(877\) −55.2201 −1.86465 −0.932325 0.361620i \(-0.882224\pi\)
−0.932325 + 0.361620i \(0.882224\pi\)
\(878\) −20.8591 −0.703962
\(879\) −15.6568 −0.528089
\(880\) −1.04069 −0.0350817
\(881\) −30.9841 −1.04388 −0.521940 0.852982i \(-0.674792\pi\)
−0.521940 + 0.852982i \(0.674792\pi\)
\(882\) −2.96024 −0.0996765
\(883\) −5.21387 −0.175461 −0.0877304 0.996144i \(-0.527961\pi\)
−0.0877304 + 0.996144i \(0.527961\pi\)
\(884\) −6.31099 −0.212261
\(885\) 4.31694 0.145112
\(886\) −21.5858 −0.725188
\(887\) 3.86782 0.129869 0.0649343 0.997890i \(-0.479316\pi\)
0.0649343 + 0.997890i \(0.479316\pi\)
\(888\) 10.4474 0.350591
\(889\) −39.7255 −1.33235
\(890\) −8.34070 −0.279581
\(891\) 5.14789 0.172461
\(892\) −9.19193 −0.307769
\(893\) −37.5962 −1.25811
\(894\) −10.3689 −0.346787
\(895\) 11.9994 0.401096
\(896\) −3.15104 −0.105269
\(897\) 7.67800 0.256361
\(898\) 15.1846 0.506718
\(899\) 4.10634 0.136954
\(900\) −1.01066 −0.0336885
\(901\) −16.4997 −0.549686
\(902\) 9.66234 0.321721
\(903\) 33.0431 1.09961
\(904\) 16.1227 0.536234
\(905\) 0.246164 0.00818276
\(906\) 23.0698 0.766441
\(907\) −46.4004 −1.54070 −0.770350 0.637622i \(-0.779918\pi\)
−0.770350 + 0.637622i \(0.779918\pi\)
\(908\) −4.76633 −0.158176
\(909\) 4.14653 0.137532
\(910\) 9.50540 0.315101
\(911\) −31.7722 −1.05266 −0.526330 0.850280i \(-0.676432\pi\)
−0.526330 + 0.850280i \(0.676432\pi\)
\(912\) 5.00308 0.165669
\(913\) −9.31342 −0.308229
\(914\) 10.6088 0.350907
\(915\) −6.15430 −0.203455
\(916\) −11.9104 −0.393530
\(917\) −29.1104 −0.961309
\(918\) −11.8345 −0.390597
\(919\) −38.7173 −1.27717 −0.638584 0.769553i \(-0.720479\pi\)
−0.638584 + 0.769553i \(0.720479\pi\)
\(920\) −1.80458 −0.0594953
\(921\) 14.8341 0.488799
\(922\) −3.89885 −0.128402
\(923\) −24.9929 −0.822652
\(924\) 4.62520 0.152158
\(925\) 7.40717 0.243546
\(926\) 3.98126 0.130832
\(927\) 8.76091 0.287746
\(928\) −0.429786 −0.0141084
\(929\) −21.4597 −0.704071 −0.352035 0.935987i \(-0.614510\pi\)
−0.352035 + 0.935987i \(0.614510\pi\)
\(930\) −13.4759 −0.441891
\(931\) 10.3898 0.340511
\(932\) 15.3681 0.503398
\(933\) 13.8476 0.453351
\(934\) 12.8211 0.419520
\(935\) −2.17722 −0.0712027
\(936\) 3.04874 0.0996512
\(937\) 7.45122 0.243421 0.121710 0.992566i \(-0.461162\pi\)
0.121710 + 0.992566i \(0.461162\pi\)
\(938\) −35.1175 −1.14663
\(939\) 38.0444 1.24153
\(940\) −10.5989 −0.345699
\(941\) 37.2907 1.21564 0.607822 0.794073i \(-0.292044\pi\)
0.607822 + 0.794073i \(0.292044\pi\)
\(942\) −10.9533 −0.356879
\(943\) 16.7547 0.545608
\(944\) 3.06070 0.0996174
\(945\) 17.8248 0.579840
\(946\) 7.73740 0.251564
\(947\) −47.3493 −1.53865 −0.769323 0.638859i \(-0.779407\pi\)
−0.769323 + 0.638859i \(0.779407\pi\)
\(948\) 12.7085 0.412753
\(949\) 16.4030 0.532465
\(950\) 3.54717 0.115086
\(951\) 13.7905 0.447187
\(952\) −6.59225 −0.213656
\(953\) 29.2932 0.948899 0.474450 0.880283i \(-0.342647\pi\)
0.474450 + 0.880283i \(0.342647\pi\)
\(954\) 7.97077 0.258063
\(955\) 20.4010 0.660162
\(956\) −8.67620 −0.280608
\(957\) 0.630855 0.0203927
\(958\) −21.5439 −0.696053
\(959\) 70.5056 2.27674
\(960\) 1.41044 0.0455218
\(961\) 60.2860 1.94471
\(962\) −22.3444 −0.720413
\(963\) 15.4676 0.498436
\(964\) −11.9235 −0.384031
\(965\) 2.54753 0.0820078
\(966\) 8.02019 0.258045
\(967\) −40.1468 −1.29103 −0.645517 0.763746i \(-0.723358\pi\)
−0.645517 + 0.763746i \(0.723358\pi\)
\(968\) −9.91696 −0.318743
\(969\) 10.4669 0.336245
\(970\) 6.35468 0.204037
\(971\) 16.4345 0.527410 0.263705 0.964603i \(-0.415056\pi\)
0.263705 + 0.964603i \(0.415056\pi\)
\(972\) 9.99349 0.320541
\(973\) 44.5452 1.42805
\(974\) 31.2923 1.00267
\(975\) −4.25473 −0.136260
\(976\) −4.36339 −0.139669
\(977\) 35.9031 1.14864 0.574322 0.818630i \(-0.305266\pi\)
0.574322 + 0.818630i \(0.305266\pi\)
\(978\) 21.6275 0.691570
\(979\) 8.68010 0.277417
\(980\) 2.92903 0.0935644
\(981\) 13.6986 0.437362
\(982\) 16.7735 0.535265
\(983\) −23.9468 −0.763785 −0.381893 0.924207i \(-0.624728\pi\)
−0.381893 + 0.924207i \(0.624728\pi\)
\(984\) −13.0953 −0.417462
\(985\) −3.59037 −0.114399
\(986\) −0.899152 −0.0286348
\(987\) 47.1053 1.49938
\(988\) −10.7004 −0.340425
\(989\) 13.4168 0.426629
\(990\) 1.05178 0.0334278
\(991\) 37.5903 1.19410 0.597048 0.802205i \(-0.296340\pi\)
0.597048 + 0.802205i \(0.296340\pi\)
\(992\) −9.55437 −0.303352
\(993\) 13.0015 0.412589
\(994\) −26.1068 −0.828057
\(995\) −22.6077 −0.716712
\(996\) 12.6224 0.399956
\(997\) −0.824218 −0.0261033 −0.0130516 0.999915i \(-0.504155\pi\)
−0.0130516 + 0.999915i \(0.504155\pi\)
\(998\) 10.5285 0.333273
\(999\) −41.9008 −1.32568
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 \(a_p\))