Properties

Label 6026.2.a.i.1.6
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(25\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-2.34651 q^{3}\) \(+1.00000 q^{4}\) \(-0.801214 q^{5}\) \(+2.34651 q^{6}\) \(+2.16934 q^{7}\) \(-1.00000 q^{8}\) \(+2.50610 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-2.34651 q^{3}\) \(+1.00000 q^{4}\) \(-0.801214 q^{5}\) \(+2.34651 q^{6}\) \(+2.16934 q^{7}\) \(-1.00000 q^{8}\) \(+2.50610 q^{9}\) \(+0.801214 q^{10}\) \(+4.95686 q^{11}\) \(-2.34651 q^{12}\) \(-1.05384 q^{13}\) \(-2.16934 q^{14}\) \(+1.88006 q^{15}\) \(+1.00000 q^{16}\) \(-2.72459 q^{17}\) \(-2.50610 q^{18}\) \(+5.72094 q^{19}\) \(-0.801214 q^{20}\) \(-5.09038 q^{21}\) \(-4.95686 q^{22}\) \(+1.00000 q^{23}\) \(+2.34651 q^{24}\) \(-4.35806 q^{25}\) \(+1.05384 q^{26}\) \(+1.15893 q^{27}\) \(+2.16934 q^{28}\) \(-3.63101 q^{29}\) \(-1.88006 q^{30}\) \(-1.85326 q^{31}\) \(-1.00000 q^{32}\) \(-11.6313 q^{33}\) \(+2.72459 q^{34}\) \(-1.73811 q^{35}\) \(+2.50610 q^{36}\) \(+1.54837 q^{37}\) \(-5.72094 q^{38}\) \(+2.47285 q^{39}\) \(+0.801214 q^{40}\) \(-10.7572 q^{41}\) \(+5.09038 q^{42}\) \(-3.49752 q^{43}\) \(+4.95686 q^{44}\) \(-2.00793 q^{45}\) \(-1.00000 q^{46}\) \(+9.13800 q^{47}\) \(-2.34651 q^{48}\) \(-2.29395 q^{49}\) \(+4.35806 q^{50}\) \(+6.39327 q^{51}\) \(-1.05384 q^{52}\) \(+5.24949 q^{53}\) \(-1.15893 q^{54}\) \(-3.97151 q^{55}\) \(-2.16934 q^{56}\) \(-13.4242 q^{57}\) \(+3.63101 q^{58}\) \(-0.391725 q^{59}\) \(+1.88006 q^{60}\) \(-8.80009 q^{61}\) \(+1.85326 q^{62}\) \(+5.43660 q^{63}\) \(+1.00000 q^{64}\) \(+0.844354 q^{65}\) \(+11.6313 q^{66}\) \(-11.5468 q^{67}\) \(-2.72459 q^{68}\) \(-2.34651 q^{69}\) \(+1.73811 q^{70}\) \(-6.56429 q^{71}\) \(-2.50610 q^{72}\) \(-3.25034 q^{73}\) \(-1.54837 q^{74}\) \(+10.2262 q^{75}\) \(+5.72094 q^{76}\) \(+10.7531 q^{77}\) \(-2.47285 q^{78}\) \(-4.15930 q^{79}\) \(-0.801214 q^{80}\) \(-10.2378 q^{81}\) \(+10.7572 q^{82}\) \(-1.60729 q^{83}\) \(-5.09038 q^{84}\) \(+2.18298 q^{85}\) \(+3.49752 q^{86}\) \(+8.52020 q^{87}\) \(-4.95686 q^{88}\) \(-3.89493 q^{89}\) \(+2.00793 q^{90}\) \(-2.28615 q^{91}\) \(+1.00000 q^{92}\) \(+4.34870 q^{93}\) \(-9.13800 q^{94}\) \(-4.58370 q^{95}\) \(+2.34651 q^{96}\) \(-9.72957 q^{97}\) \(+2.29395 q^{98}\) \(+12.4224 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut 3q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 25q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut -\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 3q^{20} \) \(\mathstrut -\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 11q^{28} \) \(\mathstrut -\mathstrut 7q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 25q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut -\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 23q^{38} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 3q^{40} \) \(\mathstrut -\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut -\mathstrut 26q^{43} \) \(\mathstrut -\mathstrut 12q^{44} \) \(\mathstrut +\mathstrut 20q^{45} \) \(\mathstrut -\mathstrut 25q^{46} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 28q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 47q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 11q^{56} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut +\mathstrut 7q^{58} \) \(\mathstrut -\mathstrut 19q^{59} \) \(\mathstrut -\mathstrut 26q^{61} \) \(\mathstrut +\mathstrut 7q^{62} \) \(\mathstrut -\mathstrut 15q^{63} \) \(\mathstrut +\mathstrut 25q^{64} \) \(\mathstrut +\mathstrut 13q^{65} \) \(\mathstrut -\mathstrut 3q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut -\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 23q^{76} \) \(\mathstrut +\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 2q^{78} \) \(\mathstrut -\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 3q^{80} \) \(\mathstrut -\mathstrut 27q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 16q^{84} \) \(\mathstrut -\mathstrut 42q^{85} \) \(\mathstrut +\mathstrut 26q^{86} \) \(\mathstrut -\mathstrut 17q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 27q^{89} \) \(\mathstrut -\mathstrut 20q^{90} \) \(\mathstrut -\mathstrut 26q^{91} \) \(\mathstrut +\mathstrut 25q^{92} \) \(\mathstrut -\mathstrut 27q^{93} \) \(\mathstrut +\mathstrut 2q^{94} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 4q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut -\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.34651 −1.35476 −0.677379 0.735634i \(-0.736884\pi\)
−0.677379 + 0.735634i \(0.736884\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.801214 −0.358314 −0.179157 0.983820i \(-0.557337\pi\)
−0.179157 + 0.983820i \(0.557337\pi\)
\(6\) 2.34651 0.957958
\(7\) 2.16934 0.819935 0.409967 0.912100i \(-0.365540\pi\)
0.409967 + 0.912100i \(0.365540\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.50610 0.835368
\(10\) 0.801214 0.253366
\(11\) 4.95686 1.49455 0.747275 0.664515i \(-0.231362\pi\)
0.747275 + 0.664515i \(0.231362\pi\)
\(12\) −2.34651 −0.677379
\(13\) −1.05384 −0.292283 −0.146142 0.989264i \(-0.546686\pi\)
−0.146142 + 0.989264i \(0.546686\pi\)
\(14\) −2.16934 −0.579781
\(15\) 1.88006 0.485429
\(16\) 1.00000 0.250000
\(17\) −2.72459 −0.660809 −0.330405 0.943839i \(-0.607185\pi\)
−0.330405 + 0.943839i \(0.607185\pi\)
\(18\) −2.50610 −0.590695
\(19\) 5.72094 1.31247 0.656237 0.754555i \(-0.272147\pi\)
0.656237 + 0.754555i \(0.272147\pi\)
\(20\) −0.801214 −0.179157
\(21\) −5.09038 −1.11081
\(22\) −4.95686 −1.05681
\(23\) 1.00000 0.208514
\(24\) 2.34651 0.478979
\(25\) −4.35806 −0.871611
\(26\) 1.05384 0.206675
\(27\) 1.15893 0.223036
\(28\) 2.16934 0.409967
\(29\) −3.63101 −0.674262 −0.337131 0.941458i \(-0.609456\pi\)
−0.337131 + 0.941458i \(0.609456\pi\)
\(30\) −1.88006 −0.343250
\(31\) −1.85326 −0.332856 −0.166428 0.986054i \(-0.553223\pi\)
−0.166428 + 0.986054i \(0.553223\pi\)
\(32\) −1.00000 −0.176777
\(33\) −11.6313 −2.02475
\(34\) 2.72459 0.467263
\(35\) −1.73811 −0.293794
\(36\) 2.50610 0.417684
\(37\) 1.54837 0.254550 0.127275 0.991867i \(-0.459377\pi\)
0.127275 + 0.991867i \(0.459377\pi\)
\(38\) −5.72094 −0.928060
\(39\) 2.47285 0.395973
\(40\) 0.801214 0.126683
\(41\) −10.7572 −1.67999 −0.839993 0.542597i \(-0.817441\pi\)
−0.839993 + 0.542597i \(0.817441\pi\)
\(42\) 5.09038 0.785463
\(43\) −3.49752 −0.533367 −0.266684 0.963784i \(-0.585928\pi\)
−0.266684 + 0.963784i \(0.585928\pi\)
\(44\) 4.95686 0.747275
\(45\) −2.00793 −0.299324
\(46\) −1.00000 −0.147442
\(47\) 9.13800 1.33291 0.666457 0.745543i \(-0.267810\pi\)
0.666457 + 0.745543i \(0.267810\pi\)
\(48\) −2.34651 −0.338689
\(49\) −2.29395 −0.327707
\(50\) 4.35806 0.616322
\(51\) 6.39327 0.895236
\(52\) −1.05384 −0.146142
\(53\) 5.24949 0.721073 0.360536 0.932745i \(-0.382594\pi\)
0.360536 + 0.932745i \(0.382594\pi\)
\(54\) −1.15893 −0.157710
\(55\) −3.97151 −0.535518
\(56\) −2.16934 −0.289891
\(57\) −13.4242 −1.77808
\(58\) 3.63101 0.476775
\(59\) −0.391725 −0.0509982 −0.0254991 0.999675i \(-0.508117\pi\)
−0.0254991 + 0.999675i \(0.508117\pi\)
\(60\) 1.88006 0.242714
\(61\) −8.80009 −1.12674 −0.563368 0.826206i \(-0.690495\pi\)
−0.563368 + 0.826206i \(0.690495\pi\)
\(62\) 1.85326 0.235365
\(63\) 5.43660 0.684947
\(64\) 1.00000 0.125000
\(65\) 0.844354 0.104729
\(66\) 11.6313 1.43172
\(67\) −11.5468 −1.41067 −0.705336 0.708873i \(-0.749204\pi\)
−0.705336 + 0.708873i \(0.749204\pi\)
\(68\) −2.72459 −0.330405
\(69\) −2.34651 −0.282486
\(70\) 1.73811 0.207744
\(71\) −6.56429 −0.779038 −0.389519 0.921018i \(-0.627359\pi\)
−0.389519 + 0.921018i \(0.627359\pi\)
\(72\) −2.50610 −0.295347
\(73\) −3.25034 −0.380423 −0.190212 0.981743i \(-0.560917\pi\)
−0.190212 + 0.981743i \(0.560917\pi\)
\(74\) −1.54837 −0.179994
\(75\) 10.2262 1.18082
\(76\) 5.72094 0.656237
\(77\) 10.7531 1.22543
\(78\) −2.47285 −0.279995
\(79\) −4.15930 −0.467958 −0.233979 0.972242i \(-0.575175\pi\)
−0.233979 + 0.972242i \(0.575175\pi\)
\(80\) −0.801214 −0.0895785
\(81\) −10.2378 −1.13753
\(82\) 10.7572 1.18793
\(83\) −1.60729 −0.176423 −0.0882113 0.996102i \(-0.528115\pi\)
−0.0882113 + 0.996102i \(0.528115\pi\)
\(84\) −5.09038 −0.555406
\(85\) 2.18298 0.236777
\(86\) 3.49752 0.377148
\(87\) 8.52020 0.913461
\(88\) −4.95686 −0.528403
\(89\) −3.89493 −0.412862 −0.206431 0.978461i \(-0.566185\pi\)
−0.206431 + 0.978461i \(0.566185\pi\)
\(90\) 2.00793 0.211654
\(91\) −2.28615 −0.239653
\(92\) 1.00000 0.104257
\(93\) 4.34870 0.450939
\(94\) −9.13800 −0.942513
\(95\) −4.58370 −0.470278
\(96\) 2.34651 0.239490
\(97\) −9.72957 −0.987888 −0.493944 0.869494i \(-0.664445\pi\)
−0.493944 + 0.869494i \(0.664445\pi\)
\(98\) 2.29395 0.231724
\(99\) 12.4224 1.24850
\(100\) −4.35806 −0.435806
\(101\) 2.35792 0.234622 0.117311 0.993095i \(-0.462573\pi\)
0.117311 + 0.993095i \(0.462573\pi\)
\(102\) −6.39327 −0.633028
\(103\) 18.5109 1.82393 0.911966 0.410265i \(-0.134564\pi\)
0.911966 + 0.410265i \(0.134564\pi\)
\(104\) 1.05384 0.103338
\(105\) 4.07849 0.398020
\(106\) −5.24949 −0.509876
\(107\) 17.8100 1.72176 0.860878 0.508812i \(-0.169915\pi\)
0.860878 + 0.508812i \(0.169915\pi\)
\(108\) 1.15893 0.111518
\(109\) −4.57649 −0.438348 −0.219174 0.975686i \(-0.570336\pi\)
−0.219174 + 0.975686i \(0.570336\pi\)
\(110\) 3.97151 0.378669
\(111\) −3.63326 −0.344854
\(112\) 2.16934 0.204984
\(113\) 17.0840 1.60713 0.803564 0.595219i \(-0.202935\pi\)
0.803564 + 0.595219i \(0.202935\pi\)
\(114\) 13.4242 1.25730
\(115\) −0.801214 −0.0747136
\(116\) −3.63101 −0.337131
\(117\) −2.64104 −0.244164
\(118\) 0.391725 0.0360612
\(119\) −5.91056 −0.541820
\(120\) −1.88006 −0.171625
\(121\) 13.5705 1.23368
\(122\) 8.80009 0.796722
\(123\) 25.2418 2.27597
\(124\) −1.85326 −0.166428
\(125\) 7.49781 0.670624
\(126\) −5.43660 −0.484331
\(127\) −8.06876 −0.715987 −0.357993 0.933724i \(-0.616539\pi\)
−0.357993 + 0.933724i \(0.616539\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 8.20697 0.722583
\(130\) −0.844354 −0.0740547
\(131\) 1.00000 0.0873704
\(132\) −11.6313 −1.01238
\(133\) 12.4107 1.07614
\(134\) 11.5468 0.997496
\(135\) −0.928551 −0.0799170
\(136\) 2.72459 0.233631
\(137\) 15.0822 1.28856 0.644278 0.764792i \(-0.277158\pi\)
0.644278 + 0.764792i \(0.277158\pi\)
\(138\) 2.34651 0.199748
\(139\) −4.84350 −0.410820 −0.205410 0.978676i \(-0.565853\pi\)
−0.205410 + 0.978676i \(0.565853\pi\)
\(140\) −1.73811 −0.146897
\(141\) −21.4424 −1.80578
\(142\) 6.56429 0.550863
\(143\) −5.22375 −0.436832
\(144\) 2.50610 0.208842
\(145\) 2.90922 0.241597
\(146\) 3.25034 0.269000
\(147\) 5.38278 0.443964
\(148\) 1.54837 0.127275
\(149\) −20.2287 −1.65720 −0.828598 0.559844i \(-0.810861\pi\)
−0.828598 + 0.559844i \(0.810861\pi\)
\(150\) −10.2262 −0.834967
\(151\) −2.26969 −0.184705 −0.0923524 0.995726i \(-0.529439\pi\)
−0.0923524 + 0.995726i \(0.529439\pi\)
\(152\) −5.72094 −0.464030
\(153\) −6.82810 −0.552019
\(154\) −10.7531 −0.866513
\(155\) 1.48486 0.119267
\(156\) 2.47285 0.197986
\(157\) −22.4688 −1.79321 −0.896605 0.442832i \(-0.853974\pi\)
−0.896605 + 0.442832i \(0.853974\pi\)
\(158\) 4.15930 0.330896
\(159\) −12.3180 −0.976879
\(160\) 0.801214 0.0633416
\(161\) 2.16934 0.170968
\(162\) 10.2378 0.804354
\(163\) 7.86199 0.615799 0.307899 0.951419i \(-0.400374\pi\)
0.307899 + 0.951419i \(0.400374\pi\)
\(164\) −10.7572 −0.839993
\(165\) 9.31919 0.725498
\(166\) 1.60729 0.124750
\(167\) 13.9226 1.07736 0.538682 0.842509i \(-0.318923\pi\)
0.538682 + 0.842509i \(0.318923\pi\)
\(168\) 5.09038 0.392732
\(169\) −11.8894 −0.914570
\(170\) −2.18298 −0.167427
\(171\) 14.3373 1.09640
\(172\) −3.49752 −0.266684
\(173\) 4.50823 0.342755 0.171377 0.985205i \(-0.445178\pi\)
0.171377 + 0.985205i \(0.445178\pi\)
\(174\) −8.52020 −0.645914
\(175\) −9.45412 −0.714664
\(176\) 4.95686 0.373638
\(177\) 0.919185 0.0690902
\(178\) 3.89493 0.291938
\(179\) −10.9819 −0.820828 −0.410414 0.911899i \(-0.634616\pi\)
−0.410414 + 0.911899i \(0.634616\pi\)
\(180\) −2.00793 −0.149662
\(181\) 23.5272 1.74877 0.874383 0.485237i \(-0.161267\pi\)
0.874383 + 0.485237i \(0.161267\pi\)
\(182\) 2.28615 0.169460
\(183\) 20.6495 1.52645
\(184\) −1.00000 −0.0737210
\(185\) −1.24058 −0.0912089
\(186\) −4.34870 −0.318862
\(187\) −13.5054 −0.987613
\(188\) 9.13800 0.666457
\(189\) 2.51412 0.182875
\(190\) 4.58370 0.332537
\(191\) 15.6529 1.13261 0.566304 0.824197i \(-0.308373\pi\)
0.566304 + 0.824197i \(0.308373\pi\)
\(192\) −2.34651 −0.169345
\(193\) 6.04551 0.435165 0.217583 0.976042i \(-0.430183\pi\)
0.217583 + 0.976042i \(0.430183\pi\)
\(194\) 9.72957 0.698542
\(195\) −1.98128 −0.141883
\(196\) −2.29395 −0.163854
\(197\) −25.0561 −1.78517 −0.892587 0.450876i \(-0.851112\pi\)
−0.892587 + 0.450876i \(0.851112\pi\)
\(198\) −12.4224 −0.882823
\(199\) −14.5181 −1.02916 −0.514580 0.857443i \(-0.672052\pi\)
−0.514580 + 0.857443i \(0.672052\pi\)
\(200\) 4.35806 0.308161
\(201\) 27.0948 1.91112
\(202\) −2.35792 −0.165903
\(203\) −7.87691 −0.552850
\(204\) 6.39327 0.447618
\(205\) 8.61879 0.601963
\(206\) −18.5109 −1.28972
\(207\) 2.50610 0.174186
\(208\) −1.05384 −0.0730708
\(209\) 28.3579 1.96156
\(210\) −4.07849 −0.281442
\(211\) −4.54692 −0.313023 −0.156512 0.987676i \(-0.550025\pi\)
−0.156512 + 0.987676i \(0.550025\pi\)
\(212\) 5.24949 0.360536
\(213\) 15.4032 1.05541
\(214\) −17.8100 −1.21747
\(215\) 2.80227 0.191113
\(216\) −1.15893 −0.0788552
\(217\) −4.02036 −0.272920
\(218\) 4.57649 0.309959
\(219\) 7.62695 0.515382
\(220\) −3.97151 −0.267759
\(221\) 2.87128 0.193143
\(222\) 3.63326 0.243849
\(223\) 10.3638 0.694010 0.347005 0.937863i \(-0.387199\pi\)
0.347005 + 0.937863i \(0.387199\pi\)
\(224\) −2.16934 −0.144945
\(225\) −10.9217 −0.728116
\(226\) −17.0840 −1.13641
\(227\) −2.15095 −0.142764 −0.0713819 0.997449i \(-0.522741\pi\)
−0.0713819 + 0.997449i \(0.522741\pi\)
\(228\) −13.4242 −0.889042
\(229\) −6.99096 −0.461975 −0.230988 0.972957i \(-0.574196\pi\)
−0.230988 + 0.972957i \(0.574196\pi\)
\(230\) 0.801214 0.0528305
\(231\) −25.2323 −1.66017
\(232\) 3.63101 0.238387
\(233\) −20.8075 −1.36315 −0.681574 0.731750i \(-0.738704\pi\)
−0.681574 + 0.731750i \(0.738704\pi\)
\(234\) 2.64104 0.172650
\(235\) −7.32150 −0.477602
\(236\) −0.391725 −0.0254991
\(237\) 9.75983 0.633969
\(238\) 5.91056 0.383125
\(239\) −3.34023 −0.216061 −0.108031 0.994148i \(-0.534454\pi\)
−0.108031 + 0.994148i \(0.534454\pi\)
\(240\) 1.88006 0.121357
\(241\) −0.760361 −0.0489792 −0.0244896 0.999700i \(-0.507796\pi\)
−0.0244896 + 0.999700i \(0.507796\pi\)
\(242\) −13.5705 −0.872345
\(243\) 20.5462 1.31804
\(244\) −8.80009 −0.563368
\(245\) 1.83795 0.117422
\(246\) −25.2418 −1.60936
\(247\) −6.02897 −0.383614
\(248\) 1.85326 0.117682
\(249\) 3.77151 0.239010
\(250\) −7.49781 −0.474203
\(251\) 22.7890 1.43843 0.719213 0.694789i \(-0.244502\pi\)
0.719213 + 0.694789i \(0.244502\pi\)
\(252\) 5.43660 0.342474
\(253\) 4.95686 0.311635
\(254\) 8.06876 0.506279
\(255\) −5.12238 −0.320776
\(256\) 1.00000 0.0625000
\(257\) 26.7538 1.66885 0.834427 0.551118i \(-0.185799\pi\)
0.834427 + 0.551118i \(0.185799\pi\)
\(258\) −8.20697 −0.510943
\(259\) 3.35894 0.208715
\(260\) 0.844354 0.0523646
\(261\) −9.09969 −0.563257
\(262\) −1.00000 −0.0617802
\(263\) −26.0349 −1.60538 −0.802689 0.596398i \(-0.796598\pi\)
−0.802689 + 0.596398i \(0.796598\pi\)
\(264\) 11.6313 0.715859
\(265\) −4.20597 −0.258371
\(266\) −12.4107 −0.760948
\(267\) 9.13949 0.559328
\(268\) −11.5468 −0.705336
\(269\) −8.46523 −0.516134 −0.258067 0.966127i \(-0.583086\pi\)
−0.258067 + 0.966127i \(0.583086\pi\)
\(270\) 0.928551 0.0565098
\(271\) 1.12438 0.0683014 0.0341507 0.999417i \(-0.489127\pi\)
0.0341507 + 0.999417i \(0.489127\pi\)
\(272\) −2.72459 −0.165202
\(273\) 5.36446 0.324672
\(274\) −15.0822 −0.911146
\(275\) −21.6023 −1.30267
\(276\) −2.34651 −0.141243
\(277\) −6.25501 −0.375827 −0.187914 0.982186i \(-0.560172\pi\)
−0.187914 + 0.982186i \(0.560172\pi\)
\(278\) 4.84350 0.290494
\(279\) −4.64447 −0.278057
\(280\) 1.73811 0.103872
\(281\) 3.86835 0.230766 0.115383 0.993321i \(-0.463190\pi\)
0.115383 + 0.993321i \(0.463190\pi\)
\(282\) 21.4424 1.27688
\(283\) 16.9857 1.00970 0.504848 0.863208i \(-0.331548\pi\)
0.504848 + 0.863208i \(0.331548\pi\)
\(284\) −6.56429 −0.389519
\(285\) 10.7557 0.637113
\(286\) 5.22375 0.308887
\(287\) −23.3360 −1.37748
\(288\) −2.50610 −0.147674
\(289\) −9.57663 −0.563331
\(290\) −2.90922 −0.170835
\(291\) 22.8305 1.33835
\(292\) −3.25034 −0.190212
\(293\) 12.4103 0.725019 0.362509 0.931980i \(-0.381920\pi\)
0.362509 + 0.931980i \(0.381920\pi\)
\(294\) −5.38278 −0.313930
\(295\) 0.313855 0.0182734
\(296\) −1.54837 −0.0899971
\(297\) 5.74466 0.333339
\(298\) 20.2287 1.17181
\(299\) −1.05384 −0.0609453
\(300\) 10.2262 0.590411
\(301\) −7.58733 −0.437326
\(302\) 2.26969 0.130606
\(303\) −5.53289 −0.317856
\(304\) 5.72094 0.328119
\(305\) 7.05076 0.403725
\(306\) 6.82810 0.390336
\(307\) 9.16510 0.523080 0.261540 0.965193i \(-0.415770\pi\)
0.261540 + 0.965193i \(0.415770\pi\)
\(308\) 10.7531 0.612717
\(309\) −43.4360 −2.47099
\(310\) −1.48486 −0.0843344
\(311\) −34.9754 −1.98328 −0.991638 0.129052i \(-0.958806\pi\)
−0.991638 + 0.129052i \(0.958806\pi\)
\(312\) −2.47285 −0.139998
\(313\) 28.3096 1.60015 0.800076 0.599898i \(-0.204792\pi\)
0.800076 + 0.599898i \(0.204792\pi\)
\(314\) 22.4688 1.26799
\(315\) −4.35588 −0.245426
\(316\) −4.15930 −0.233979
\(317\) 21.2570 1.19391 0.596956 0.802274i \(-0.296377\pi\)
0.596956 + 0.802274i \(0.296377\pi\)
\(318\) 12.3180 0.690758
\(319\) −17.9984 −1.00772
\(320\) −0.801214 −0.0447893
\(321\) −41.7913 −2.33256
\(322\) −2.16934 −0.120893
\(323\) −15.5872 −0.867295
\(324\) −10.2378 −0.568764
\(325\) 4.59270 0.254757
\(326\) −7.86199 −0.435435
\(327\) 10.7388 0.593856
\(328\) 10.7572 0.593965
\(329\) 19.8235 1.09290
\(330\) −9.31919 −0.513004
\(331\) −13.9101 −0.764567 −0.382283 0.924045i \(-0.624862\pi\)
−0.382283 + 0.924045i \(0.624862\pi\)
\(332\) −1.60729 −0.0882113
\(333\) 3.88037 0.212643
\(334\) −13.9226 −0.761811
\(335\) 9.25150 0.505463
\(336\) −5.09038 −0.277703
\(337\) −32.6134 −1.77657 −0.888284 0.459295i \(-0.848102\pi\)
−0.888284 + 0.459295i \(0.848102\pi\)
\(338\) 11.8894 0.646699
\(339\) −40.0878 −2.17727
\(340\) 2.18298 0.118389
\(341\) −9.18637 −0.497470
\(342\) −14.3373 −0.775272
\(343\) −20.1618 −1.08863
\(344\) 3.49752 0.188574
\(345\) 1.88006 0.101219
\(346\) −4.50823 −0.242364
\(347\) 13.6324 0.731827 0.365914 0.930649i \(-0.380757\pi\)
0.365914 + 0.930649i \(0.380757\pi\)
\(348\) 8.52020 0.456730
\(349\) −31.6422 −1.69377 −0.846883 0.531779i \(-0.821524\pi\)
−0.846883 + 0.531779i \(0.821524\pi\)
\(350\) 9.45412 0.505344
\(351\) −1.22133 −0.0651897
\(352\) −4.95686 −0.264202
\(353\) 2.99798 0.159566 0.0797832 0.996812i \(-0.474577\pi\)
0.0797832 + 0.996812i \(0.474577\pi\)
\(354\) −0.919185 −0.0488541
\(355\) 5.25941 0.279140
\(356\) −3.89493 −0.206431
\(357\) 13.8692 0.734035
\(358\) 10.9819 0.580413
\(359\) −9.88532 −0.521727 −0.260864 0.965376i \(-0.584007\pi\)
−0.260864 + 0.965376i \(0.584007\pi\)
\(360\) 2.00793 0.105827
\(361\) 13.7292 0.722589
\(362\) −23.5272 −1.23656
\(363\) −31.8433 −1.67134
\(364\) −2.28615 −0.119827
\(365\) 2.60422 0.136311
\(366\) −20.6495 −1.07937
\(367\) 7.10593 0.370927 0.185463 0.982651i \(-0.440621\pi\)
0.185463 + 0.982651i \(0.440621\pi\)
\(368\) 1.00000 0.0521286
\(369\) −26.9586 −1.40341
\(370\) 1.24058 0.0644944
\(371\) 11.3879 0.591233
\(372\) 4.34870 0.225469
\(373\) −2.94518 −0.152496 −0.0762479 0.997089i \(-0.524294\pi\)
−0.0762479 + 0.997089i \(0.524294\pi\)
\(374\) 13.5054 0.698348
\(375\) −17.5937 −0.908534
\(376\) −9.13800 −0.471256
\(377\) 3.82651 0.197075
\(378\) −2.51412 −0.129312
\(379\) −27.5028 −1.41272 −0.706362 0.707851i \(-0.749665\pi\)
−0.706362 + 0.707851i \(0.749665\pi\)
\(380\) −4.58370 −0.235139
\(381\) 18.9334 0.969988
\(382\) −15.6529 −0.800874
\(383\) −29.9652 −1.53115 −0.765575 0.643347i \(-0.777545\pi\)
−0.765575 + 0.643347i \(0.777545\pi\)
\(384\) 2.34651 0.119745
\(385\) −8.61557 −0.439090
\(386\) −6.04551 −0.307708
\(387\) −8.76516 −0.445558
\(388\) −9.72957 −0.493944
\(389\) −19.3084 −0.978975 −0.489487 0.872010i \(-0.662816\pi\)
−0.489487 + 0.872010i \(0.662816\pi\)
\(390\) 1.98128 0.100326
\(391\) −2.72459 −0.137788
\(392\) 2.29395 0.115862
\(393\) −2.34651 −0.118366
\(394\) 25.0561 1.26231
\(395\) 3.33249 0.167676
\(396\) 12.4224 0.624250
\(397\) 14.7981 0.742697 0.371349 0.928493i \(-0.378895\pi\)
0.371349 + 0.928493i \(0.378895\pi\)
\(398\) 14.5181 0.727726
\(399\) −29.1218 −1.45791
\(400\) −4.35806 −0.217903
\(401\) −19.7159 −0.984567 −0.492283 0.870435i \(-0.663838\pi\)
−0.492283 + 0.870435i \(0.663838\pi\)
\(402\) −27.0948 −1.35136
\(403\) 1.95305 0.0972882
\(404\) 2.35792 0.117311
\(405\) 8.20264 0.407592
\(406\) 7.87691 0.390924
\(407\) 7.67505 0.380438
\(408\) −6.39327 −0.316514
\(409\) 7.73328 0.382386 0.191193 0.981552i \(-0.438764\pi\)
0.191193 + 0.981552i \(0.438764\pi\)
\(410\) −8.61879 −0.425652
\(411\) −35.3904 −1.74568
\(412\) 18.5109 0.911966
\(413\) −0.849785 −0.0418152
\(414\) −2.50610 −0.123168
\(415\) 1.28778 0.0632147
\(416\) 1.05384 0.0516689
\(417\) 11.3653 0.556562
\(418\) −28.3579 −1.38703
\(419\) 0.0658483 0.00321690 0.00160845 0.999999i \(-0.499488\pi\)
0.00160845 + 0.999999i \(0.499488\pi\)
\(420\) 4.07849 0.199010
\(421\) 29.7977 1.45225 0.726125 0.687563i \(-0.241319\pi\)
0.726125 + 0.687563i \(0.241319\pi\)
\(422\) 4.54692 0.221341
\(423\) 22.9008 1.11347
\(424\) −5.24949 −0.254938
\(425\) 11.8739 0.575969
\(426\) −15.4032 −0.746286
\(427\) −19.0904 −0.923850
\(428\) 17.8100 0.860878
\(429\) 12.2576 0.591802
\(430\) −2.80227 −0.135137
\(431\) −35.7277 −1.72094 −0.860472 0.509498i \(-0.829831\pi\)
−0.860472 + 0.509498i \(0.829831\pi\)
\(432\) 1.15893 0.0557590
\(433\) −3.20078 −0.153819 −0.0769097 0.997038i \(-0.524505\pi\)
−0.0769097 + 0.997038i \(0.524505\pi\)
\(434\) 4.02036 0.192984
\(435\) −6.82651 −0.327306
\(436\) −4.57649 −0.219174
\(437\) 5.72094 0.273670
\(438\) −7.62695 −0.364430
\(439\) 1.11275 0.0531086 0.0265543 0.999647i \(-0.491547\pi\)
0.0265543 + 0.999647i \(0.491547\pi\)
\(440\) 3.97151 0.189334
\(441\) −5.74888 −0.273756
\(442\) −2.87128 −0.136573
\(443\) −36.2757 −1.72351 −0.861755 0.507325i \(-0.830634\pi\)
−0.861755 + 0.507325i \(0.830634\pi\)
\(444\) −3.63326 −0.172427
\(445\) 3.12068 0.147934
\(446\) −10.3638 −0.490739
\(447\) 47.4667 2.24510
\(448\) 2.16934 0.102492
\(449\) −22.3452 −1.05454 −0.527268 0.849699i \(-0.676784\pi\)
−0.527268 + 0.849699i \(0.676784\pi\)
\(450\) 10.9217 0.514856
\(451\) −53.3218 −2.51082
\(452\) 17.0840 0.803564
\(453\) 5.32585 0.250230
\(454\) 2.15095 0.100949
\(455\) 1.83169 0.0858711
\(456\) 13.4242 0.628648
\(457\) −33.7980 −1.58100 −0.790502 0.612460i \(-0.790180\pi\)
−0.790502 + 0.612460i \(0.790180\pi\)
\(458\) 6.99096 0.326666
\(459\) −3.15760 −0.147384
\(460\) −0.801214 −0.0373568
\(461\) −32.0441 −1.49244 −0.746221 0.665698i \(-0.768134\pi\)
−0.746221 + 0.665698i \(0.768134\pi\)
\(462\) 25.2323 1.17391
\(463\) 38.1770 1.77424 0.887118 0.461543i \(-0.152704\pi\)
0.887118 + 0.461543i \(0.152704\pi\)
\(464\) −3.63101 −0.168565
\(465\) −3.48424 −0.161578
\(466\) 20.8075 0.963891
\(467\) −28.3122 −1.31013 −0.655067 0.755571i \(-0.727360\pi\)
−0.655067 + 0.755571i \(0.727360\pi\)
\(468\) −2.64104 −0.122082
\(469\) −25.0491 −1.15666
\(470\) 7.32150 0.337715
\(471\) 52.7234 2.42936
\(472\) 0.391725 0.0180306
\(473\) −17.3367 −0.797144
\(474\) −9.75983 −0.448284
\(475\) −24.9322 −1.14397
\(476\) −5.91056 −0.270910
\(477\) 13.1558 0.602362
\(478\) 3.34023 0.152778
\(479\) 13.2565 0.605704 0.302852 0.953038i \(-0.402061\pi\)
0.302852 + 0.953038i \(0.402061\pi\)
\(480\) −1.88006 −0.0858125
\(481\) −1.63174 −0.0744008
\(482\) 0.760361 0.0346335
\(483\) −5.09038 −0.231620
\(484\) 13.5705 0.616841
\(485\) 7.79547 0.353974
\(486\) −20.5462 −0.931994
\(487\) 3.81113 0.172699 0.0863493 0.996265i \(-0.472480\pi\)
0.0863493 + 0.996265i \(0.472480\pi\)
\(488\) 8.80009 0.398361
\(489\) −18.4482 −0.834258
\(490\) −1.83795 −0.0830299
\(491\) 30.2940 1.36715 0.683575 0.729880i \(-0.260424\pi\)
0.683575 + 0.729880i \(0.260424\pi\)
\(492\) 25.2418 1.13799
\(493\) 9.89300 0.445558
\(494\) 6.02897 0.271256
\(495\) −9.95302 −0.447355
\(496\) −1.85326 −0.0832140
\(497\) −14.2402 −0.638760
\(498\) −3.77151 −0.169005
\(499\) 9.88708 0.442606 0.221303 0.975205i \(-0.428969\pi\)
0.221303 + 0.975205i \(0.428969\pi\)
\(500\) 7.49781 0.335312
\(501\) −32.6695 −1.45957
\(502\) −22.7890 −1.01712
\(503\) −8.28046 −0.369208 −0.184604 0.982813i \(-0.559100\pi\)
−0.184604 + 0.982813i \(0.559100\pi\)
\(504\) −5.43660 −0.242165
\(505\) −1.88920 −0.0840684
\(506\) −4.95686 −0.220359
\(507\) 27.8986 1.23902
\(508\) −8.06876 −0.357993
\(509\) −13.9904 −0.620114 −0.310057 0.950718i \(-0.600348\pi\)
−0.310057 + 0.950718i \(0.600348\pi\)
\(510\) 5.12238 0.226823
\(511\) −7.05110 −0.311922
\(512\) −1.00000 −0.0441942
\(513\) 6.63017 0.292729
\(514\) −26.7538 −1.18006
\(515\) −14.8312 −0.653541
\(516\) 8.20697 0.361292
\(517\) 45.2958 1.99211
\(518\) −3.35894 −0.147583
\(519\) −10.5786 −0.464349
\(520\) −0.844354 −0.0370274
\(521\) 40.6942 1.78285 0.891424 0.453171i \(-0.149707\pi\)
0.891424 + 0.453171i \(0.149707\pi\)
\(522\) 9.09969 0.398283
\(523\) −27.2572 −1.19187 −0.595937 0.803032i \(-0.703219\pi\)
−0.595937 + 0.803032i \(0.703219\pi\)
\(524\) 1.00000 0.0436852
\(525\) 22.1842 0.968197
\(526\) 26.0349 1.13517
\(527\) 5.04937 0.219954
\(528\) −11.6313 −0.506188
\(529\) 1.00000 0.0434783
\(530\) 4.20597 0.182696
\(531\) −0.981703 −0.0426023
\(532\) 12.4107 0.538072
\(533\) 11.3364 0.491032
\(534\) −9.13949 −0.395505
\(535\) −14.2696 −0.616929
\(536\) 11.5468 0.498748
\(537\) 25.7692 1.11202
\(538\) 8.46523 0.364962
\(539\) −11.3708 −0.489775
\(540\) −0.928551 −0.0399585
\(541\) −42.8788 −1.84350 −0.921751 0.387782i \(-0.873241\pi\)
−0.921751 + 0.387782i \(0.873241\pi\)
\(542\) −1.12438 −0.0482963
\(543\) −55.2069 −2.36915
\(544\) 2.72459 0.116816
\(545\) 3.66675 0.157066
\(546\) −5.36446 −0.229578
\(547\) −37.9295 −1.62175 −0.810875 0.585219i \(-0.801008\pi\)
−0.810875 + 0.585219i \(0.801008\pi\)
\(548\) 15.0822 0.644278
\(549\) −22.0539 −0.941239
\(550\) 21.6023 0.921125
\(551\) −20.7728 −0.884951
\(552\) 2.34651 0.0998741
\(553\) −9.02295 −0.383695
\(554\) 6.25501 0.265750
\(555\) 2.91102 0.123566
\(556\) −4.84350 −0.205410
\(557\) 18.1271 0.768070 0.384035 0.923319i \(-0.374534\pi\)
0.384035 + 0.923319i \(0.374534\pi\)
\(558\) 4.64447 0.196616
\(559\) 3.68584 0.155894
\(560\) −1.73811 −0.0734485
\(561\) 31.6905 1.33798
\(562\) −3.86835 −0.163176
\(563\) −1.00248 −0.0422495 −0.0211247 0.999777i \(-0.506725\pi\)
−0.0211247 + 0.999777i \(0.506725\pi\)
\(564\) −21.4424 −0.902888
\(565\) −13.6880 −0.575856
\(566\) −16.9857 −0.713963
\(567\) −22.2092 −0.932699
\(568\) 6.56429 0.275432
\(569\) 40.4471 1.69563 0.847815 0.530292i \(-0.177918\pi\)
0.847815 + 0.530292i \(0.177918\pi\)
\(570\) −10.7557 −0.450507
\(571\) 10.8177 0.452708 0.226354 0.974045i \(-0.427319\pi\)
0.226354 + 0.974045i \(0.427319\pi\)
\(572\) −5.22375 −0.218416
\(573\) −36.7298 −1.53441
\(574\) 23.3360 0.974025
\(575\) −4.35806 −0.181743
\(576\) 2.50610 0.104421
\(577\) −1.81018 −0.0753589 −0.0376794 0.999290i \(-0.511997\pi\)
−0.0376794 + 0.999290i \(0.511997\pi\)
\(578\) 9.57663 0.398335
\(579\) −14.1858 −0.589544
\(580\) 2.90922 0.120799
\(581\) −3.48676 −0.144655
\(582\) −22.8305 −0.946355
\(583\) 26.0210 1.07768
\(584\) 3.25034 0.134500
\(585\) 2.11604 0.0874874
\(586\) −12.4103 −0.512666
\(587\) 9.46704 0.390746 0.195373 0.980729i \(-0.437408\pi\)
0.195373 + 0.980729i \(0.437408\pi\)
\(588\) 5.38278 0.221982
\(589\) −10.6024 −0.436865
\(590\) −0.313855 −0.0129212
\(591\) 58.7944 2.41848
\(592\) 1.54837 0.0636376
\(593\) 17.2800 0.709604 0.354802 0.934941i \(-0.384548\pi\)
0.354802 + 0.934941i \(0.384548\pi\)
\(594\) −5.74466 −0.235706
\(595\) 4.73563 0.194142
\(596\) −20.2287 −0.828598
\(597\) 34.0668 1.39426
\(598\) 1.05384 0.0430948
\(599\) 45.2397 1.84844 0.924221 0.381858i \(-0.124716\pi\)
0.924221 + 0.381858i \(0.124716\pi\)
\(600\) −10.2262 −0.417484
\(601\) −27.4082 −1.11800 −0.559002 0.829167i \(-0.688815\pi\)
−0.559002 + 0.829167i \(0.688815\pi\)
\(602\) 7.58733 0.309236
\(603\) −28.9376 −1.17843
\(604\) −2.26969 −0.0923524
\(605\) −10.8729 −0.442045
\(606\) 5.53289 0.224758
\(607\) −23.8072 −0.966304 −0.483152 0.875537i \(-0.660508\pi\)
−0.483152 + 0.875537i \(0.660508\pi\)
\(608\) −5.72094 −0.232015
\(609\) 18.4832 0.748978
\(610\) −7.05076 −0.285477
\(611\) −9.63001 −0.389589
\(612\) −6.82810 −0.276010
\(613\) −34.8656 −1.40821 −0.704104 0.710097i \(-0.748651\pi\)
−0.704104 + 0.710097i \(0.748651\pi\)
\(614\) −9.16510 −0.369873
\(615\) −20.2241 −0.815514
\(616\) −10.7531 −0.433256
\(617\) −18.4346 −0.742150 −0.371075 0.928603i \(-0.621011\pi\)
−0.371075 + 0.928603i \(0.621011\pi\)
\(618\) 43.4360 1.74725
\(619\) 10.1319 0.407235 0.203617 0.979051i \(-0.434730\pi\)
0.203617 + 0.979051i \(0.434730\pi\)
\(620\) 1.48486 0.0596334
\(621\) 1.15893 0.0465062
\(622\) 34.9754 1.40239
\(623\) −8.44944 −0.338520
\(624\) 2.47285 0.0989932
\(625\) 15.7829 0.631317
\(626\) −28.3096 −1.13148
\(627\) −66.5422 −2.65744
\(628\) −22.4688 −0.896605
\(629\) −4.21866 −0.168209
\(630\) 4.35588 0.173543
\(631\) −26.1719 −1.04189 −0.520944 0.853591i \(-0.674420\pi\)
−0.520944 + 0.853591i \(0.674420\pi\)
\(632\) 4.15930 0.165448
\(633\) 10.6694 0.424070
\(634\) −21.2570 −0.844223
\(635\) 6.46481 0.256548
\(636\) −12.3180 −0.488440
\(637\) 2.41746 0.0957833
\(638\) 17.9984 0.712564
\(639\) −16.4508 −0.650784
\(640\) 0.801214 0.0316708
\(641\) 17.9495 0.708964 0.354482 0.935063i \(-0.384657\pi\)
0.354482 + 0.935063i \(0.384657\pi\)
\(642\) 41.7913 1.64937
\(643\) −46.2363 −1.82338 −0.911692 0.410875i \(-0.865223\pi\)
−0.911692 + 0.410875i \(0.865223\pi\)
\(644\) 2.16934 0.0854841
\(645\) −6.57554 −0.258912
\(646\) 15.5872 0.613270
\(647\) 23.2982 0.915947 0.457973 0.888966i \(-0.348575\pi\)
0.457973 + 0.888966i \(0.348575\pi\)
\(648\) 10.2378 0.402177
\(649\) −1.94173 −0.0762194
\(650\) −4.59270 −0.180141
\(651\) 9.43382 0.369740
\(652\) 7.86199 0.307899
\(653\) −1.63158 −0.0638485 −0.0319242 0.999490i \(-0.510164\pi\)
−0.0319242 + 0.999490i \(0.510164\pi\)
\(654\) −10.7388 −0.419919
\(655\) −0.801214 −0.0313060
\(656\) −10.7572 −0.419997
\(657\) −8.14569 −0.317794
\(658\) −19.8235 −0.772799
\(659\) −11.8686 −0.462334 −0.231167 0.972914i \(-0.574254\pi\)
−0.231167 + 0.972914i \(0.574254\pi\)
\(660\) 9.31919 0.362749
\(661\) 26.1156 1.01578 0.507890 0.861422i \(-0.330426\pi\)
0.507890 + 0.861422i \(0.330426\pi\)
\(662\) 13.9101 0.540630
\(663\) −6.73749 −0.261663
\(664\) 1.60729 0.0623748
\(665\) −9.94362 −0.385597
\(666\) −3.88037 −0.150361
\(667\) −3.63101 −0.140593
\(668\) 13.9226 0.538682
\(669\) −24.3187 −0.940216
\(670\) −9.25150 −0.357417
\(671\) −43.6208 −1.68396
\(672\) 5.09038 0.196366
\(673\) 26.5063 1.02174 0.510872 0.859657i \(-0.329323\pi\)
0.510872 + 0.859657i \(0.329323\pi\)
\(674\) 32.6134 1.25622
\(675\) −5.05068 −0.194401
\(676\) −11.8894 −0.457285
\(677\) −22.5908 −0.868236 −0.434118 0.900856i \(-0.642940\pi\)
−0.434118 + 0.900856i \(0.642940\pi\)
\(678\) 40.0878 1.53956
\(679\) −21.1068 −0.810003
\(680\) −2.18298 −0.0837134
\(681\) 5.04723 0.193410
\(682\) 9.18637 0.351764
\(683\) −46.4146 −1.77600 −0.888002 0.459839i \(-0.847907\pi\)
−0.888002 + 0.459839i \(0.847907\pi\)
\(684\) 14.3373 0.548200
\(685\) −12.0840 −0.461707
\(686\) 20.1618 0.769780
\(687\) 16.4043 0.625865
\(688\) −3.49752 −0.133342
\(689\) −5.53214 −0.210758
\(690\) −1.88006 −0.0715725
\(691\) −13.3213 −0.506766 −0.253383 0.967366i \(-0.581543\pi\)
−0.253383 + 0.967366i \(0.581543\pi\)
\(692\) 4.50823 0.171377
\(693\) 26.9485 1.02369
\(694\) −13.6324 −0.517480
\(695\) 3.88068 0.147203
\(696\) −8.52020 −0.322957
\(697\) 29.3088 1.11015
\(698\) 31.6422 1.19767
\(699\) 48.8251 1.84673
\(700\) −9.45412 −0.357332
\(701\) −2.54850 −0.0962557 −0.0481279 0.998841i \(-0.515325\pi\)
−0.0481279 + 0.998841i \(0.515325\pi\)
\(702\) 1.22133 0.0460961
\(703\) 8.85813 0.334091
\(704\) 4.95686 0.186819
\(705\) 17.1800 0.647035
\(706\) −2.99798 −0.112830
\(707\) 5.11514 0.192375
\(708\) 0.919185 0.0345451
\(709\) 7.95334 0.298694 0.149347 0.988785i \(-0.452283\pi\)
0.149347 + 0.988785i \(0.452283\pi\)
\(710\) −5.25941 −0.197382
\(711\) −10.4236 −0.390917
\(712\) 3.89493 0.145969
\(713\) −1.85326 −0.0694052
\(714\) −13.8692 −0.519041
\(715\) 4.18535 0.156523
\(716\) −10.9819 −0.410414
\(717\) 7.83787 0.292711
\(718\) 9.88532 0.368917
\(719\) 23.0187 0.858453 0.429226 0.903197i \(-0.358786\pi\)
0.429226 + 0.903197i \(0.358786\pi\)
\(720\) −2.00793 −0.0748310
\(721\) 40.1565 1.49551
\(722\) −13.7292 −0.510948
\(723\) 1.78419 0.0663549
\(724\) 23.5272 0.874383
\(725\) 15.8241 0.587694
\(726\) 31.8433 1.18182
\(727\) 11.8822 0.440687 0.220344 0.975422i \(-0.429282\pi\)
0.220344 + 0.975422i \(0.429282\pi\)
\(728\) 2.28615 0.0847302
\(729\) −17.4986 −0.648095
\(730\) −2.60422 −0.0963865
\(731\) 9.52930 0.352454
\(732\) 20.6495 0.763227
\(733\) −39.1487 −1.44599 −0.722996 0.690852i \(-0.757235\pi\)
−0.722996 + 0.690852i \(0.757235\pi\)
\(734\) −7.10593 −0.262285
\(735\) −4.31276 −0.159078
\(736\) −1.00000 −0.0368605
\(737\) −57.2361 −2.10832
\(738\) 26.9586 0.992359
\(739\) 42.4684 1.56223 0.781113 0.624389i \(-0.214652\pi\)
0.781113 + 0.624389i \(0.214652\pi\)
\(740\) −1.24058 −0.0456045
\(741\) 14.1470 0.519704
\(742\) −11.3879 −0.418065
\(743\) 12.9776 0.476103 0.238051 0.971253i \(-0.423491\pi\)
0.238051 + 0.971253i \(0.423491\pi\)
\(744\) −4.34870 −0.159431
\(745\) 16.2075 0.593796
\(746\) 2.94518 0.107831
\(747\) −4.02803 −0.147378
\(748\) −13.5054 −0.493806
\(749\) 38.6360 1.41173
\(750\) 17.5937 0.642430
\(751\) −36.1688 −1.31982 −0.659909 0.751345i \(-0.729405\pi\)
−0.659909 + 0.751345i \(0.729405\pi\)
\(752\) 9.13800 0.333229
\(753\) −53.4745 −1.94872
\(754\) −3.82651 −0.139353
\(755\) 1.81851 0.0661823
\(756\) 2.51412 0.0914375
\(757\) 2.30039 0.0836090 0.0418045 0.999126i \(-0.486689\pi\)
0.0418045 + 0.999126i \(0.486689\pi\)
\(758\) 27.5028 0.998947
\(759\) −11.6313 −0.422190
\(760\) 4.58370 0.166268
\(761\) −7.05622 −0.255788 −0.127894 0.991788i \(-0.540822\pi\)
−0.127894 + 0.991788i \(0.540822\pi\)
\(762\) −18.9334 −0.685885
\(763\) −9.92798 −0.359417
\(764\) 15.6529 0.566304
\(765\) 5.47077 0.197796
\(766\) 29.9652 1.08269
\(767\) 0.412816 0.0149059
\(768\) −2.34651 −0.0846724
\(769\) −53.9520 −1.94556 −0.972780 0.231731i \(-0.925561\pi\)
−0.972780 + 0.231731i \(0.925561\pi\)
\(770\) 8.61557 0.310484
\(771\) −62.7780 −2.26089
\(772\) 6.04551 0.217583
\(773\) −37.7566 −1.35801 −0.679005 0.734134i \(-0.737588\pi\)
−0.679005 + 0.734134i \(0.737588\pi\)
\(774\) 8.76516 0.315057
\(775\) 8.07662 0.290121
\(776\) 9.72957 0.349271
\(777\) −7.88179 −0.282758
\(778\) 19.3084 0.692240
\(779\) −61.5411 −2.20494
\(780\) −1.98128 −0.0709413
\(781\) −32.5383 −1.16431
\(782\) 2.72459 0.0974310
\(783\) −4.20808 −0.150385
\(784\) −2.29395 −0.0819268
\(785\) 18.0024 0.642532
\(786\) 2.34651 0.0836972
\(787\) −44.1385 −1.57337 −0.786683 0.617357i \(-0.788203\pi\)
−0.786683 + 0.617357i \(0.788203\pi\)
\(788\) −25.0561 −0.892587
\(789\) 61.0910 2.17490
\(790\) −3.33249 −0.118565
\(791\) 37.0611 1.31774
\(792\) −12.4224 −0.441411
\(793\) 9.27390 0.329326
\(794\) −14.7981 −0.525166
\(795\) 9.86934 0.350029
\(796\) −14.5181 −0.514580
\(797\) −19.8010 −0.701386 −0.350693 0.936490i \(-0.614054\pi\)
−0.350693 + 0.936490i \(0.614054\pi\)
\(798\) 29.1218 1.03090
\(799\) −24.8973 −0.880802
\(800\) 4.35806 0.154081
\(801\) −9.76111 −0.344892
\(802\) 19.7159 0.696194
\(803\) −16.1115 −0.568562
\(804\) 27.0948 0.955559
\(805\) −1.73811 −0.0612603
\(806\) −1.95305 −0.0687931
\(807\) 19.8637 0.699237
\(808\) −2.35792 −0.0829514
\(809\) −6.78896 −0.238687 −0.119344 0.992853i \(-0.538079\pi\)
−0.119344 + 0.992853i \(0.538079\pi\)
\(810\) −8.20264 −0.288211
\(811\) 42.9659 1.50874 0.754368 0.656452i \(-0.227943\pi\)
0.754368 + 0.656452i \(0.227943\pi\)
\(812\) −7.87691 −0.276425
\(813\) −2.63837 −0.0925318
\(814\) −7.67505 −0.269010
\(815\) −6.29914 −0.220649
\(816\) 6.39327 0.223809
\(817\) −20.0091 −0.700031
\(818\) −7.73328 −0.270388
\(819\) −5.72932 −0.200199
\(820\) 8.61879 0.300981
\(821\) 46.9328 1.63797 0.818983 0.573817i \(-0.194538\pi\)
0.818983 + 0.573817i \(0.194538\pi\)
\(822\) 35.3904 1.23438
\(823\) 16.3680 0.570554 0.285277 0.958445i \(-0.407914\pi\)
0.285277 + 0.958445i \(0.407914\pi\)
\(824\) −18.5109 −0.644858
\(825\) 50.6900 1.76480
\(826\) 0.849785 0.0295678
\(827\) 1.97138 0.0685517 0.0342758 0.999412i \(-0.489088\pi\)
0.0342758 + 0.999412i \(0.489088\pi\)
\(828\) 2.50610 0.0870932
\(829\) 46.0931 1.60088 0.800439 0.599414i \(-0.204600\pi\)
0.800439 + 0.599414i \(0.204600\pi\)
\(830\) −1.28778 −0.0446995
\(831\) 14.6774 0.509155
\(832\) −1.05384 −0.0365354
\(833\) 6.25007 0.216552
\(834\) −11.3653 −0.393549
\(835\) −11.1550 −0.386034
\(836\) 28.3579 0.980780
\(837\) −2.14780 −0.0742389
\(838\) −0.0658483 −0.00227469
\(839\) 56.0780 1.93603 0.968014 0.250896i \(-0.0807253\pi\)
0.968014 + 0.250896i \(0.0807253\pi\)
\(840\) −4.07849 −0.140721
\(841\) −15.8158 −0.545371
\(842\) −29.7977 −1.02690
\(843\) −9.07712 −0.312633
\(844\) −4.54692 −0.156512
\(845\) 9.52597 0.327703
\(846\) −22.9008 −0.787345
\(847\) 29.4391 1.01154
\(848\) 5.24949 0.180268
\(849\) −39.8572 −1.36789
\(850\) −11.8739 −0.407271
\(851\) 1.54837 0.0530774
\(852\) 15.4032 0.527704
\(853\) −17.6307 −0.603662 −0.301831 0.953361i \(-0.597598\pi\)
−0.301831 + 0.953361i \(0.597598\pi\)
\(854\) 19.0904 0.653260
\(855\) −11.4872 −0.392855
\(856\) −17.8100 −0.608733
\(857\) 25.5825 0.873883 0.436941 0.899490i \(-0.356062\pi\)
0.436941 + 0.899490i \(0.356062\pi\)
\(858\) −12.2576 −0.418467
\(859\) −23.8615 −0.814145 −0.407072 0.913396i \(-0.633450\pi\)
−0.407072 + 0.913396i \(0.633450\pi\)
\(860\) 2.80227 0.0955565
\(861\) 54.7581 1.86615
\(862\) 35.7277 1.21689
\(863\) 41.8838 1.42574 0.712871 0.701295i \(-0.247394\pi\)
0.712871 + 0.701295i \(0.247394\pi\)
\(864\) −1.15893 −0.0394276
\(865\) −3.61206 −0.122814
\(866\) 3.20078 0.108767
\(867\) 22.4717 0.763177
\(868\) −4.02036 −0.136460
\(869\) −20.6171 −0.699386
\(870\) 6.82651 0.231440
\(871\) 12.1686 0.412316
\(872\) 4.57649 0.154980
\(873\) −24.3833 −0.825250
\(874\) −5.72094 −0.193514
\(875\) 16.2653 0.549868
\(876\) 7.62695 0.257691
\(877\) −2.29207 −0.0773977 −0.0386989 0.999251i \(-0.512321\pi\)
−0.0386989 + 0.999251i \(0.512321\pi\)
\(878\) −1.11275 −0.0375534
\(879\) −29.1209 −0.982225
\(880\) −3.97151 −0.133880
\(881\) 38.3660 1.29258 0.646291 0.763091i \(-0.276319\pi\)
0.646291 + 0.763091i \(0.276319\pi\)
\(882\) 5.74888 0.193575
\(883\) −22.7495 −0.765581 −0.382791 0.923835i \(-0.625037\pi\)
−0.382791 + 0.923835i \(0.625037\pi\)
\(884\) 2.87128 0.0965717
\(885\) −0.736464 −0.0247560
\(886\) 36.2757 1.21871
\(887\) −33.8641 −1.13704 −0.568522 0.822668i \(-0.692485\pi\)
−0.568522 + 0.822668i \(0.692485\pi\)
\(888\) 3.63326 0.121924
\(889\) −17.5039 −0.587062
\(890\) −3.12068 −0.104605
\(891\) −50.7471 −1.70009
\(892\) 10.3638 0.347005
\(893\) 52.2780 1.74942
\(894\) −47.4667 −1.58752
\(895\) 8.79888 0.294114
\(896\) −2.16934 −0.0724727
\(897\) 2.47285 0.0825661
\(898\) 22.3452 0.745670
\(899\) 6.72921 0.224432
\(900\) −10.9217 −0.364058
\(901\) −14.3027 −0.476492
\(902\) 53.3218 1.77542
\(903\) 17.8037 0.592471
\(904\) −17.0840 −0.568205
\(905\) −18.8504 −0.626607
\(906\) −5.32585 −0.176940
\(907\) 20.2556 0.672575 0.336287 0.941759i \(-0.390829\pi\)
0.336287 + 0.941759i \(0.390829\pi\)
\(908\) −2.15095 −0.0713819
\(909\) 5.90920 0.195996
\(910\) −1.83169 −0.0607200
\(911\) 18.5546 0.614741 0.307370 0.951590i \(-0.400551\pi\)
0.307370 + 0.951590i \(0.400551\pi\)
\(912\) −13.4242 −0.444521
\(913\) −7.96710 −0.263672
\(914\) 33.7980 1.11794
\(915\) −16.5447 −0.546950
\(916\) −6.99096 −0.230988
\(917\) 2.16934 0.0716380
\(918\) 3.15760 0.104216
\(919\) −11.0170 −0.363419 −0.181709 0.983352i \(-0.558163\pi\)
−0.181709 + 0.983352i \(0.558163\pi\)
\(920\) 0.801214 0.0264153
\(921\) −21.5060 −0.708646
\(922\) 32.0441 1.05532
\(923\) 6.91773 0.227700
\(924\) −25.2323 −0.830083
\(925\) −6.74788 −0.221869
\(926\) −38.1770 −1.25457
\(927\) 46.3902 1.52366
\(928\) 3.63101 0.119194
\(929\) 23.4114 0.768104 0.384052 0.923312i \(-0.374528\pi\)
0.384052 + 0.923312i \(0.374528\pi\)
\(930\) 3.48424 0.114253
\(931\) −13.1236 −0.430107
\(932\) −20.8075 −0.681574
\(933\) 82.0702 2.68686
\(934\) 28.3122 0.926405
\(935\) 10.8207 0.353876
\(936\) 2.64104 0.0863251
\(937\) −11.8029 −0.385583 −0.192791 0.981240i \(-0.561754\pi\)
−0.192791 + 0.981240i \(0.561754\pi\)
\(938\) 25.0491 0.817881
\(939\) −66.4287 −2.16782
\(940\) −7.32150 −0.238801
\(941\) 34.6407 1.12925 0.564627 0.825346i \(-0.309020\pi\)
0.564627 + 0.825346i \(0.309020\pi\)
\(942\) −52.7234 −1.71782
\(943\) −10.7572 −0.350301
\(944\) −0.391725 −0.0127495
\(945\) −2.01435 −0.0655267
\(946\) 17.3367 0.563666
\(947\) 5.24140 0.170323 0.0851613 0.996367i \(-0.472859\pi\)
0.0851613 + 0.996367i \(0.472859\pi\)
\(948\) 9.75983 0.316985
\(949\) 3.42535 0.111191
\(950\) 24.9322 0.808907
\(951\) −49.8797 −1.61746
\(952\) 5.91056 0.191562
\(953\) −46.1346 −1.49445 −0.747223 0.664573i \(-0.768614\pi\)
−0.747223 + 0.664573i \(0.768614\pi\)
\(954\) −13.1558 −0.425934
\(955\) −12.5414 −0.405829
\(956\) −3.34023 −0.108031
\(957\) 42.2335 1.36521
\(958\) −13.2565 −0.428297
\(959\) 32.7184 1.05653
\(960\) 1.88006 0.0606786
\(961\) −27.5654 −0.889207
\(962\) 1.63174 0.0526093
\(963\) 44.6337 1.43830
\(964\) −0.760361 −0.0244896
\(965\) −4.84375 −0.155926
\(966\) 5.09038 0.163780
\(967\) −56.9759 −1.83222 −0.916111 0.400925i \(-0.868689\pi\)
−0.916111 + 0.400925i \(0.868689\pi\)
\(968\) −13.5705 −0.436172
\(969\) 36.5755 1.17497
\(970\) −7.79547 −0.250297
\(971\) −32.3179 −1.03713 −0.518566 0.855038i \(-0.673534\pi\)
−0.518566 + 0.855038i \(0.673534\pi\)
\(972\) 20.5462 0.659019
\(973\) −10.5072 −0.336846
\(974\) −3.81113 −0.122116
\(975\) −10.7768 −0.345134
\(976\) −8.80009 −0.281684
\(977\) 33.7699 1.08040 0.540198 0.841538i \(-0.318349\pi\)
0.540198 + 0.841538i \(0.318349\pi\)
\(978\) 18.4482 0.589909
\(979\) −19.3066 −0.617043
\(980\) 1.83795 0.0587110
\(981\) −11.4692 −0.366182
\(982\) −30.2940 −0.966721
\(983\) 24.1219 0.769370 0.384685 0.923048i \(-0.374310\pi\)
0.384685 + 0.923048i \(0.374310\pi\)
\(984\) −25.2418 −0.804679
\(985\) 20.0753 0.639653
\(986\) −9.89300 −0.315057
\(987\) −46.5159 −1.48062
\(988\) −6.02897 −0.191807
\(989\) −3.49752 −0.111215
\(990\) 9.95302 0.316328
\(991\) −5.22611 −0.166013 −0.0830064 0.996549i \(-0.526452\pi\)
−0.0830064 + 0.996549i \(0.526452\pi\)
\(992\) 1.85326 0.0588411
\(993\) 32.6401 1.03580
\(994\) 14.2402 0.451672
\(995\) 11.6321 0.368762
\(996\) 3.77151 0.119505
\(997\) −16.2074 −0.513295 −0.256647 0.966505i \(-0.582618\pi\)
−0.256647 + 0.966505i \(0.582618\pi\)
\(998\) −9.88708 −0.312970
\(999\) 1.79445 0.0567739
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 \(a_p\))