Properties

Label 8002.2.a.d.1.16
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 1
Dimension 69
CM No

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Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.04234 q^{3}\) \(+1.00000 q^{4}\) \(-4.37946 q^{5}\) \(-2.04234 q^{6}\) \(-3.34038 q^{7}\) \(+1.00000 q^{8}\) \(+1.17114 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.04234 q^{3}\) \(+1.00000 q^{4}\) \(-4.37946 q^{5}\) \(-2.04234 q^{6}\) \(-3.34038 q^{7}\) \(+1.00000 q^{8}\) \(+1.17114 q^{9}\) \(-4.37946 q^{10}\) \(-6.47165 q^{11}\) \(-2.04234 q^{12}\) \(+2.30446 q^{13}\) \(-3.34038 q^{14}\) \(+8.94433 q^{15}\) \(+1.00000 q^{16}\) \(-1.94500 q^{17}\) \(+1.17114 q^{18}\) \(+0.497927 q^{19}\) \(-4.37946 q^{20}\) \(+6.82218 q^{21}\) \(-6.47165 q^{22}\) \(+9.13451 q^{23}\) \(-2.04234 q^{24}\) \(+14.1797 q^{25}\) \(+2.30446 q^{26}\) \(+3.73514 q^{27}\) \(-3.34038 q^{28}\) \(-8.73359 q^{29}\) \(+8.94433 q^{30}\) \(+0.749179 q^{31}\) \(+1.00000 q^{32}\) \(+13.2173 q^{33}\) \(-1.94500 q^{34}\) \(+14.6291 q^{35}\) \(+1.17114 q^{36}\) \(+4.43414 q^{37}\) \(+0.497927 q^{38}\) \(-4.70648 q^{39}\) \(-4.37946 q^{40}\) \(+6.22772 q^{41}\) \(+6.82218 q^{42}\) \(+3.60194 q^{43}\) \(-6.47165 q^{44}\) \(-5.12897 q^{45}\) \(+9.13451 q^{46}\) \(-7.36820 q^{47}\) \(-2.04234 q^{48}\) \(+4.15813 q^{49}\) \(+14.1797 q^{50}\) \(+3.97235 q^{51}\) \(+2.30446 q^{52}\) \(+1.69540 q^{53}\) \(+3.73514 q^{54}\) \(+28.3423 q^{55}\) \(-3.34038 q^{56}\) \(-1.01694 q^{57}\) \(-8.73359 q^{58}\) \(-13.4470 q^{59}\) \(+8.94433 q^{60}\) \(-3.81707 q^{61}\) \(+0.749179 q^{62}\) \(-3.91206 q^{63}\) \(+1.00000 q^{64}\) \(-10.0923 q^{65}\) \(+13.2173 q^{66}\) \(+11.9649 q^{67}\) \(-1.94500 q^{68}\) \(-18.6557 q^{69}\) \(+14.6291 q^{70}\) \(+1.43259 q^{71}\) \(+1.17114 q^{72}\) \(+1.41227 q^{73}\) \(+4.43414 q^{74}\) \(-28.9597 q^{75}\) \(+0.497927 q^{76}\) \(+21.6178 q^{77}\) \(-4.70648 q^{78}\) \(+12.5869 q^{79}\) \(-4.37946 q^{80}\) \(-11.1419 q^{81}\) \(+6.22772 q^{82}\) \(-5.82838 q^{83}\) \(+6.82218 q^{84}\) \(+8.51805 q^{85}\) \(+3.60194 q^{86}\) \(+17.8369 q^{87}\) \(-6.47165 q^{88}\) \(+15.3847 q^{89}\) \(-5.12897 q^{90}\) \(-7.69776 q^{91}\) \(+9.13451 q^{92}\) \(-1.53008 q^{93}\) \(-7.36820 q^{94}\) \(-2.18065 q^{95}\) \(-2.04234 q^{96}\) \(-9.69510 q^{97}\) \(+4.15813 q^{98}\) \(-7.57922 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 30q^{11} \) \(\mathstrut -\mathstrut 25q^{12} \) \(\mathstrut -\mathstrut 58q^{13} \) \(\mathstrut -\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 69q^{16} \) \(\mathstrut -\mathstrut 80q^{17} \) \(\mathstrut +\mathstrut 54q^{18} \) \(\mathstrut -\mathstrut 40q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 32q^{21} \) \(\mathstrut -\mathstrut 30q^{22} \) \(\mathstrut -\mathstrut 45q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 42q^{25} \) \(\mathstrut -\mathstrut 58q^{26} \) \(\mathstrut -\mathstrut 76q^{27} \) \(\mathstrut -\mathstrut 19q^{28} \) \(\mathstrut -\mathstrut 44q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 69q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 80q^{34} \) \(\mathstrut -\mathstrut 49q^{35} \) \(\mathstrut +\mathstrut 54q^{36} \) \(\mathstrut -\mathstrut 47q^{37} \) \(\mathstrut -\mathstrut 40q^{38} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 33q^{40} \) \(\mathstrut -\mathstrut 94q^{41} \) \(\mathstrut -\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 30q^{44} \) \(\mathstrut -\mathstrut 89q^{45} \) \(\mathstrut -\mathstrut 45q^{46} \) \(\mathstrut -\mathstrut 85q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut +\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 10q^{51} \) \(\mathstrut -\mathstrut 58q^{52} \) \(\mathstrut -\mathstrut 41q^{53} \) \(\mathstrut -\mathstrut 76q^{54} \) \(\mathstrut -\mathstrut 27q^{55} \) \(\mathstrut -\mathstrut 19q^{56} \) \(\mathstrut -\mathstrut 72q^{57} \) \(\mathstrut -\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 75q^{59} \) \(\mathstrut +\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 98q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 69q^{64} \) \(\mathstrut -\mathstrut 47q^{65} \) \(\mathstrut -\mathstrut 41q^{66} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 80q^{68} \) \(\mathstrut -\mathstrut 74q^{69} \) \(\mathstrut -\mathstrut 49q^{70} \) \(\mathstrut -\mathstrut 22q^{71} \) \(\mathstrut +\mathstrut 54q^{72} \) \(\mathstrut -\mathstrut 129q^{73} \) \(\mathstrut -\mathstrut 47q^{74} \) \(\mathstrut -\mathstrut 106q^{75} \) \(\mathstrut -\mathstrut 40q^{76} \) \(\mathstrut -\mathstrut 108q^{77} \) \(\mathstrut -\mathstrut 14q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 33q^{80} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 94q^{82} \) \(\mathstrut -\mathstrut 111q^{83} \) \(\mathstrut -\mathstrut 32q^{84} \) \(\mathstrut -\mathstrut 67q^{85} \) \(\mathstrut -\mathstrut 10q^{86} \) \(\mathstrut -\mathstrut 38q^{87} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 89q^{90} \) \(\mathstrut -\mathstrut 55q^{91} \) \(\mathstrut -\mathstrut 45q^{92} \) \(\mathstrut -\mathstrut 90q^{93} \) \(\mathstrut -\mathstrut 85q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 25q^{96} \) \(\mathstrut -\mathstrut 98q^{97} \) \(\mathstrut +\mathstrut 32q^{98} \) \(\mathstrut -\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.04234 −1.17914 −0.589572 0.807716i \(-0.700704\pi\)
−0.589572 + 0.807716i \(0.700704\pi\)
\(4\) 1.00000 0.500000
\(5\) −4.37946 −1.95855 −0.979277 0.202527i \(-0.935085\pi\)
−0.979277 + 0.202527i \(0.935085\pi\)
\(6\) −2.04234 −0.833781
\(7\) −3.34038 −1.26254 −0.631272 0.775561i \(-0.717467\pi\)
−0.631272 + 0.775561i \(0.717467\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.17114 0.390381
\(10\) −4.37946 −1.38491
\(11\) −6.47165 −1.95127 −0.975637 0.219389i \(-0.929594\pi\)
−0.975637 + 0.219389i \(0.929594\pi\)
\(12\) −2.04234 −0.589572
\(13\) 2.30446 0.639141 0.319571 0.947562i \(-0.396461\pi\)
0.319571 + 0.947562i \(0.396461\pi\)
\(14\) −3.34038 −0.892754
\(15\) 8.94433 2.30942
\(16\) 1.00000 0.250000
\(17\) −1.94500 −0.471732 −0.235866 0.971786i \(-0.575793\pi\)
−0.235866 + 0.971786i \(0.575793\pi\)
\(18\) 1.17114 0.276041
\(19\) 0.497927 0.114232 0.0571162 0.998368i \(-0.481809\pi\)
0.0571162 + 0.998368i \(0.481809\pi\)
\(20\) −4.37946 −0.979277
\(21\) 6.82218 1.48872
\(22\) −6.47165 −1.37976
\(23\) 9.13451 1.90468 0.952338 0.305044i \(-0.0986711\pi\)
0.952338 + 0.305044i \(0.0986711\pi\)
\(24\) −2.04234 −0.416890
\(25\) 14.1797 2.83593
\(26\) 2.30446 0.451941
\(27\) 3.73514 0.718829
\(28\) −3.34038 −0.631272
\(29\) −8.73359 −1.62179 −0.810894 0.585193i \(-0.801019\pi\)
−0.810894 + 0.585193i \(0.801019\pi\)
\(30\) 8.94433 1.63300
\(31\) 0.749179 0.134556 0.0672782 0.997734i \(-0.478568\pi\)
0.0672782 + 0.997734i \(0.478568\pi\)
\(32\) 1.00000 0.176777
\(33\) 13.2173 2.30083
\(34\) −1.94500 −0.333565
\(35\) 14.6291 2.47276
\(36\) 1.17114 0.195190
\(37\) 4.43414 0.728968 0.364484 0.931210i \(-0.381245\pi\)
0.364484 + 0.931210i \(0.381245\pi\)
\(38\) 0.497927 0.0807744
\(39\) −4.70648 −0.753640
\(40\) −4.37946 −0.692453
\(41\) 6.22772 0.972607 0.486303 0.873790i \(-0.338345\pi\)
0.486303 + 0.873790i \(0.338345\pi\)
\(42\) 6.82218 1.05269
\(43\) 3.60194 0.549291 0.274645 0.961546i \(-0.411440\pi\)
0.274645 + 0.961546i \(0.411440\pi\)
\(44\) −6.47165 −0.975637
\(45\) −5.12897 −0.764582
\(46\) 9.13451 1.34681
\(47\) −7.36820 −1.07476 −0.537382 0.843339i \(-0.680586\pi\)
−0.537382 + 0.843339i \(0.680586\pi\)
\(48\) −2.04234 −0.294786
\(49\) 4.15813 0.594019
\(50\) 14.1797 2.00531
\(51\) 3.97235 0.556240
\(52\) 2.30446 0.319571
\(53\) 1.69540 0.232881 0.116440 0.993198i \(-0.462852\pi\)
0.116440 + 0.993198i \(0.462852\pi\)
\(54\) 3.73514 0.508289
\(55\) 28.3423 3.82168
\(56\) −3.34038 −0.446377
\(57\) −1.01694 −0.134696
\(58\) −8.73359 −1.14678
\(59\) −13.4470 −1.75065 −0.875323 0.483539i \(-0.839351\pi\)
−0.875323 + 0.483539i \(0.839351\pi\)
\(60\) 8.94433 1.15471
\(61\) −3.81707 −0.488726 −0.244363 0.969684i \(-0.578579\pi\)
−0.244363 + 0.969684i \(0.578579\pi\)
\(62\) 0.749179 0.0951458
\(63\) −3.91206 −0.492873
\(64\) 1.00000 0.125000
\(65\) −10.0923 −1.25179
\(66\) 13.2173 1.62694
\(67\) 11.9649 1.46174 0.730871 0.682515i \(-0.239114\pi\)
0.730871 + 0.682515i \(0.239114\pi\)
\(68\) −1.94500 −0.235866
\(69\) −18.6557 −2.24589
\(70\) 14.6291 1.74851
\(71\) 1.43259 0.170018 0.0850089 0.996380i \(-0.472908\pi\)
0.0850089 + 0.996380i \(0.472908\pi\)
\(72\) 1.17114 0.138021
\(73\) 1.41227 0.165293 0.0826466 0.996579i \(-0.473663\pi\)
0.0826466 + 0.996579i \(0.473663\pi\)
\(74\) 4.43414 0.515458
\(75\) −28.9597 −3.34397
\(76\) 0.497927 0.0571162
\(77\) 21.6178 2.46357
\(78\) −4.70648 −0.532904
\(79\) 12.5869 1.41614 0.708070 0.706142i \(-0.249566\pi\)
0.708070 + 0.706142i \(0.249566\pi\)
\(80\) −4.37946 −0.489638
\(81\) −11.1419 −1.23798
\(82\) 6.22772 0.687737
\(83\) −5.82838 −0.639748 −0.319874 0.947460i \(-0.603641\pi\)
−0.319874 + 0.947460i \(0.603641\pi\)
\(84\) 6.82218 0.744361
\(85\) 8.51805 0.923913
\(86\) 3.60194 0.388407
\(87\) 17.8369 1.91232
\(88\) −6.47165 −0.689880
\(89\) 15.3847 1.63077 0.815386 0.578918i \(-0.196525\pi\)
0.815386 + 0.578918i \(0.196525\pi\)
\(90\) −5.12897 −0.540641
\(91\) −7.69776 −0.806945
\(92\) 9.13451 0.952338
\(93\) −1.53008 −0.158661
\(94\) −7.36820 −0.759972
\(95\) −2.18065 −0.223730
\(96\) −2.04234 −0.208445
\(97\) −9.69510 −0.984388 −0.492194 0.870486i \(-0.663805\pi\)
−0.492194 + 0.870486i \(0.663805\pi\)
\(98\) 4.15813 0.420035
\(99\) −7.57922 −0.761741
\(100\) 14.1797 1.41797
\(101\) −7.02597 −0.699110 −0.349555 0.936916i \(-0.613667\pi\)
−0.349555 + 0.936916i \(0.613667\pi\)
\(102\) 3.97235 0.393321
\(103\) 18.7509 1.84758 0.923789 0.382901i \(-0.125075\pi\)
0.923789 + 0.382901i \(0.125075\pi\)
\(104\) 2.30446 0.225971
\(105\) −29.8775 −2.91574
\(106\) 1.69540 0.164672
\(107\) 6.44341 0.622908 0.311454 0.950261i \(-0.399184\pi\)
0.311454 + 0.950261i \(0.399184\pi\)
\(108\) 3.73514 0.359414
\(109\) −7.54936 −0.723097 −0.361549 0.932353i \(-0.617752\pi\)
−0.361549 + 0.932353i \(0.617752\pi\)
\(110\) 28.3423 2.70233
\(111\) −9.05601 −0.859558
\(112\) −3.34038 −0.315636
\(113\) −9.24288 −0.869497 −0.434748 0.900552i \(-0.643163\pi\)
−0.434748 + 0.900552i \(0.643163\pi\)
\(114\) −1.01694 −0.0952447
\(115\) −40.0042 −3.73041
\(116\) −8.73359 −0.810894
\(117\) 2.69885 0.249509
\(118\) −13.4470 −1.23789
\(119\) 6.49704 0.595583
\(120\) 8.94433 0.816502
\(121\) 30.8822 2.80747
\(122\) −3.81707 −0.345581
\(123\) −12.7191 −1.14684
\(124\) 0.749179 0.0672782
\(125\) −40.2019 −3.59577
\(126\) −3.91206 −0.348514
\(127\) −1.60403 −0.142334 −0.0711672 0.997464i \(-0.522672\pi\)
−0.0711672 + 0.997464i \(0.522672\pi\)
\(128\) 1.00000 0.0883883
\(129\) −7.35637 −0.647693
\(130\) −10.0923 −0.885151
\(131\) −21.5751 −1.88502 −0.942511 0.334175i \(-0.891542\pi\)
−0.942511 + 0.334175i \(0.891542\pi\)
\(132\) 13.2173 1.15042
\(133\) −1.66327 −0.144223
\(134\) 11.9649 1.03361
\(135\) −16.3579 −1.40786
\(136\) −1.94500 −0.166783
\(137\) −10.2572 −0.876328 −0.438164 0.898895i \(-0.644371\pi\)
−0.438164 + 0.898895i \(0.644371\pi\)
\(138\) −18.6557 −1.58808
\(139\) 9.99255 0.847557 0.423779 0.905766i \(-0.360703\pi\)
0.423779 + 0.905766i \(0.360703\pi\)
\(140\) 14.6291 1.23638
\(141\) 15.0484 1.26730
\(142\) 1.43259 0.120221
\(143\) −14.9136 −1.24714
\(144\) 1.17114 0.0975952
\(145\) 38.2484 3.17636
\(146\) 1.41227 0.116880
\(147\) −8.49231 −0.700434
\(148\) 4.43414 0.364484
\(149\) 11.5562 0.946718 0.473359 0.880870i \(-0.343041\pi\)
0.473359 + 0.880870i \(0.343041\pi\)
\(150\) −28.9597 −2.36455
\(151\) −16.9180 −1.37677 −0.688383 0.725348i \(-0.741679\pi\)
−0.688383 + 0.725348i \(0.741679\pi\)
\(152\) 0.497927 0.0403872
\(153\) −2.27787 −0.184155
\(154\) 21.6178 1.74201
\(155\) −3.28100 −0.263536
\(156\) −4.70648 −0.376820
\(157\) 20.2628 1.61715 0.808574 0.588395i \(-0.200240\pi\)
0.808574 + 0.588395i \(0.200240\pi\)
\(158\) 12.5869 1.00136
\(159\) −3.46258 −0.274600
\(160\) −4.37946 −0.346227
\(161\) −30.5127 −2.40474
\(162\) −11.1419 −0.875387
\(163\) −5.60012 −0.438635 −0.219318 0.975654i \(-0.570383\pi\)
−0.219318 + 0.975654i \(0.570383\pi\)
\(164\) 6.22772 0.486303
\(165\) −57.8846 −4.50631
\(166\) −5.82838 −0.452370
\(167\) −1.79995 −0.139284 −0.0696420 0.997572i \(-0.522186\pi\)
−0.0696420 + 0.997572i \(0.522186\pi\)
\(168\) 6.82218 0.526343
\(169\) −7.68948 −0.591498
\(170\) 8.51805 0.653305
\(171\) 0.583144 0.0445941
\(172\) 3.60194 0.274645
\(173\) −4.24598 −0.322816 −0.161408 0.986888i \(-0.551604\pi\)
−0.161408 + 0.986888i \(0.551604\pi\)
\(174\) 17.8369 1.35222
\(175\) −47.3654 −3.58049
\(176\) −6.47165 −0.487819
\(177\) 27.4632 2.06426
\(178\) 15.3847 1.15313
\(179\) 9.28123 0.693712 0.346856 0.937918i \(-0.387249\pi\)
0.346856 + 0.937918i \(0.387249\pi\)
\(180\) −5.12897 −0.382291
\(181\) −25.2680 −1.87816 −0.939078 0.343704i \(-0.888318\pi\)
−0.939078 + 0.343704i \(0.888318\pi\)
\(182\) −7.69776 −0.570596
\(183\) 7.79575 0.576278
\(184\) 9.13451 0.673405
\(185\) −19.4191 −1.42772
\(186\) −1.53008 −0.112191
\(187\) 12.5874 0.920479
\(188\) −7.36820 −0.537382
\(189\) −12.4768 −0.907553
\(190\) −2.18065 −0.158201
\(191\) 12.8689 0.931162 0.465581 0.885005i \(-0.345845\pi\)
0.465581 + 0.885005i \(0.345845\pi\)
\(192\) −2.04234 −0.147393
\(193\) −18.5606 −1.33602 −0.668010 0.744152i \(-0.732854\pi\)
−0.668010 + 0.744152i \(0.732854\pi\)
\(194\) −9.69510 −0.696067
\(195\) 20.6118 1.47604
\(196\) 4.15813 0.297009
\(197\) 1.00470 0.0715819 0.0357909 0.999359i \(-0.488605\pi\)
0.0357909 + 0.999359i \(0.488605\pi\)
\(198\) −7.57922 −0.538632
\(199\) −3.89656 −0.276220 −0.138110 0.990417i \(-0.544103\pi\)
−0.138110 + 0.990417i \(0.544103\pi\)
\(200\) 14.1797 1.00265
\(201\) −24.4363 −1.72361
\(202\) −7.02597 −0.494345
\(203\) 29.1735 2.04758
\(204\) 3.97235 0.278120
\(205\) −27.2741 −1.90490
\(206\) 18.7509 1.30644
\(207\) 10.6978 0.743549
\(208\) 2.30446 0.159785
\(209\) −3.22241 −0.222899
\(210\) −29.8775 −2.06174
\(211\) 4.21378 0.290088 0.145044 0.989425i \(-0.453668\pi\)
0.145044 + 0.989425i \(0.453668\pi\)
\(212\) 1.69540 0.116440
\(213\) −2.92584 −0.200475
\(214\) 6.44341 0.440462
\(215\) −15.7745 −1.07581
\(216\) 3.73514 0.254144
\(217\) −2.50254 −0.169884
\(218\) −7.54936 −0.511307
\(219\) −2.88432 −0.194905
\(220\) 28.3423 1.91084
\(221\) −4.48217 −0.301504
\(222\) −9.05601 −0.607800
\(223\) 18.8200 1.26028 0.630140 0.776482i \(-0.282998\pi\)
0.630140 + 0.776482i \(0.282998\pi\)
\(224\) −3.34038 −0.223188
\(225\) 16.6064 1.10709
\(226\) −9.24288 −0.614827
\(227\) 2.50659 0.166368 0.0831842 0.996534i \(-0.473491\pi\)
0.0831842 + 0.996534i \(0.473491\pi\)
\(228\) −1.01694 −0.0673482
\(229\) 4.64419 0.306897 0.153448 0.988157i \(-0.450962\pi\)
0.153448 + 0.988157i \(0.450962\pi\)
\(230\) −40.0042 −2.63780
\(231\) −44.1507 −2.90491
\(232\) −8.73359 −0.573389
\(233\) 18.2942 1.19849 0.599247 0.800564i \(-0.295467\pi\)
0.599247 + 0.800564i \(0.295467\pi\)
\(234\) 2.69885 0.176429
\(235\) 32.2687 2.10498
\(236\) −13.4470 −0.875323
\(237\) −25.7067 −1.66983
\(238\) 6.49704 0.421141
\(239\) 14.5962 0.944153 0.472076 0.881558i \(-0.343505\pi\)
0.472076 + 0.881558i \(0.343505\pi\)
\(240\) 8.94433 0.577354
\(241\) 24.1313 1.55443 0.777215 0.629235i \(-0.216632\pi\)
0.777215 + 0.629235i \(0.216632\pi\)
\(242\) 30.8822 1.98518
\(243\) 11.5500 0.740932
\(244\) −3.81707 −0.244363
\(245\) −18.2104 −1.16342
\(246\) −12.7191 −0.810941
\(247\) 1.14745 0.0730106
\(248\) 0.749179 0.0475729
\(249\) 11.9035 0.754355
\(250\) −40.2019 −2.54259
\(251\) 9.69901 0.612196 0.306098 0.952000i \(-0.400976\pi\)
0.306098 + 0.952000i \(0.400976\pi\)
\(252\) −3.91206 −0.246437
\(253\) −59.1153 −3.71655
\(254\) −1.60403 −0.100646
\(255\) −17.3967 −1.08943
\(256\) 1.00000 0.0625000
\(257\) 25.4077 1.58489 0.792444 0.609945i \(-0.208808\pi\)
0.792444 + 0.609945i \(0.208808\pi\)
\(258\) −7.35637 −0.457988
\(259\) −14.8117 −0.920355
\(260\) −10.0923 −0.625896
\(261\) −10.2283 −0.633115
\(262\) −21.5751 −1.33291
\(263\) 8.23917 0.508049 0.254025 0.967198i \(-0.418246\pi\)
0.254025 + 0.967198i \(0.418246\pi\)
\(264\) 13.2173 0.813468
\(265\) −7.42493 −0.456110
\(266\) −1.66327 −0.101981
\(267\) −31.4207 −1.92292
\(268\) 11.9649 0.730871
\(269\) 17.6001 1.07310 0.536549 0.843869i \(-0.319728\pi\)
0.536549 + 0.843869i \(0.319728\pi\)
\(270\) −16.3579 −0.995511
\(271\) −22.6100 −1.37346 −0.686730 0.726912i \(-0.740955\pi\)
−0.686730 + 0.726912i \(0.740955\pi\)
\(272\) −1.94500 −0.117933
\(273\) 15.7214 0.951504
\(274\) −10.2572 −0.619657
\(275\) −91.7657 −5.53368
\(276\) −18.6557 −1.12294
\(277\) 5.92295 0.355876 0.177938 0.984042i \(-0.443057\pi\)
0.177938 + 0.984042i \(0.443057\pi\)
\(278\) 9.99255 0.599313
\(279\) 0.877395 0.0525283
\(280\) 14.6291 0.874253
\(281\) −5.70819 −0.340522 −0.170261 0.985399i \(-0.554461\pi\)
−0.170261 + 0.985399i \(0.554461\pi\)
\(282\) 15.0484 0.896117
\(283\) 21.3512 1.26920 0.634598 0.772842i \(-0.281166\pi\)
0.634598 + 0.772842i \(0.281166\pi\)
\(284\) 1.43259 0.0850089
\(285\) 4.45363 0.263810
\(286\) −14.9136 −0.881862
\(287\) −20.8030 −1.22796
\(288\) 1.17114 0.0690103
\(289\) −13.2170 −0.777469
\(290\) 38.2484 2.24602
\(291\) 19.8007 1.16074
\(292\) 1.41227 0.0826466
\(293\) −28.4207 −1.66035 −0.830176 0.557501i \(-0.811760\pi\)
−0.830176 + 0.557501i \(0.811760\pi\)
\(294\) −8.49231 −0.495281
\(295\) 58.8904 3.42873
\(296\) 4.43414 0.257729
\(297\) −24.1725 −1.40263
\(298\) 11.5562 0.669431
\(299\) 21.0501 1.21736
\(300\) −28.9597 −1.67199
\(301\) −12.0318 −0.693504
\(302\) −16.9180 −0.973520
\(303\) 14.3494 0.824351
\(304\) 0.497927 0.0285581
\(305\) 16.7167 0.957196
\(306\) −2.27787 −0.130217
\(307\) 25.6219 1.46232 0.731159 0.682207i \(-0.238980\pi\)
0.731159 + 0.682207i \(0.238980\pi\)
\(308\) 21.6178 1.23179
\(309\) −38.2956 −2.17856
\(310\) −3.28100 −0.186348
\(311\) −6.99098 −0.396422 −0.198211 0.980159i \(-0.563513\pi\)
−0.198211 + 0.980159i \(0.563513\pi\)
\(312\) −4.70648 −0.266452
\(313\) −19.5500 −1.10503 −0.552517 0.833502i \(-0.686333\pi\)
−0.552517 + 0.833502i \(0.686333\pi\)
\(314\) 20.2628 1.14350
\(315\) 17.1327 0.965319
\(316\) 12.5869 0.708070
\(317\) −5.35610 −0.300829 −0.150414 0.988623i \(-0.548061\pi\)
−0.150414 + 0.988623i \(0.548061\pi\)
\(318\) −3.46258 −0.194172
\(319\) 56.5207 3.16455
\(320\) −4.37946 −0.244819
\(321\) −13.1596 −0.734498
\(322\) −30.5127 −1.70041
\(323\) −0.968469 −0.0538871
\(324\) −11.1419 −0.618992
\(325\) 32.6764 1.81256
\(326\) −5.60012 −0.310162
\(327\) 15.4183 0.852636
\(328\) 6.22772 0.343868
\(329\) 24.6126 1.35694
\(330\) −57.8846 −3.18644
\(331\) −15.1757 −0.834133 −0.417066 0.908876i \(-0.636942\pi\)
−0.417066 + 0.908876i \(0.636942\pi\)
\(332\) −5.82838 −0.319874
\(333\) 5.19301 0.284575
\(334\) −1.79995 −0.0984886
\(335\) −52.3997 −2.86290
\(336\) 6.82218 0.372181
\(337\) 3.37094 0.183627 0.0918134 0.995776i \(-0.470734\pi\)
0.0918134 + 0.995776i \(0.470734\pi\)
\(338\) −7.68948 −0.418252
\(339\) 18.8771 1.02526
\(340\) 8.51805 0.461956
\(341\) −4.84842 −0.262557
\(342\) 0.583144 0.0315328
\(343\) 9.49292 0.512569
\(344\) 3.60194 0.194204
\(345\) 81.7021 4.39869
\(346\) −4.24598 −0.228265
\(347\) 12.5778 0.675214 0.337607 0.941287i \(-0.390382\pi\)
0.337607 + 0.941287i \(0.390382\pi\)
\(348\) 17.8369 0.956161
\(349\) −12.6349 −0.676330 −0.338165 0.941087i \(-0.609806\pi\)
−0.338165 + 0.941087i \(0.609806\pi\)
\(350\) −47.3654 −2.53179
\(351\) 8.60748 0.459433
\(352\) −6.47165 −0.344940
\(353\) 32.8797 1.75001 0.875005 0.484113i \(-0.160858\pi\)
0.875005 + 0.484113i \(0.160858\pi\)
\(354\) 27.4632 1.45965
\(355\) −6.27399 −0.332989
\(356\) 15.3847 0.815386
\(357\) −13.2692 −0.702278
\(358\) 9.28123 0.490528
\(359\) 14.2910 0.754249 0.377125 0.926163i \(-0.376913\pi\)
0.377125 + 0.926163i \(0.376913\pi\)
\(360\) −5.12897 −0.270321
\(361\) −18.7521 −0.986951
\(362\) −25.2680 −1.32806
\(363\) −63.0719 −3.31042
\(364\) −7.69776 −0.403472
\(365\) −6.18496 −0.323736
\(366\) 7.79575 0.407490
\(367\) −5.15525 −0.269102 −0.134551 0.990907i \(-0.542959\pi\)
−0.134551 + 0.990907i \(0.542959\pi\)
\(368\) 9.13451 0.476169
\(369\) 7.29355 0.379687
\(370\) −19.4191 −1.00955
\(371\) −5.66327 −0.294023
\(372\) −1.53008 −0.0793307
\(373\) −5.87609 −0.304252 −0.152126 0.988361i \(-0.548612\pi\)
−0.152126 + 0.988361i \(0.548612\pi\)
\(374\) 12.5874 0.650877
\(375\) 82.1059 4.23993
\(376\) −7.36820 −0.379986
\(377\) −20.1262 −1.03655
\(378\) −12.4768 −0.641737
\(379\) 3.68032 0.189045 0.0945227 0.995523i \(-0.469867\pi\)
0.0945227 + 0.995523i \(0.469867\pi\)
\(380\) −2.18065 −0.111865
\(381\) 3.27596 0.167833
\(382\) 12.8689 0.658431
\(383\) −16.3448 −0.835182 −0.417591 0.908635i \(-0.637125\pi\)
−0.417591 + 0.908635i \(0.637125\pi\)
\(384\) −2.04234 −0.104223
\(385\) −94.6741 −4.82504
\(386\) −18.5606 −0.944709
\(387\) 4.21838 0.214433
\(388\) −9.69510 −0.492194
\(389\) −11.4399 −0.580027 −0.290013 0.957023i \(-0.593660\pi\)
−0.290013 + 0.957023i \(0.593660\pi\)
\(390\) 20.6118 1.04372
\(391\) −17.7666 −0.898497
\(392\) 4.15813 0.210017
\(393\) 44.0636 2.22271
\(394\) 1.00470 0.0506160
\(395\) −55.1239 −2.77359
\(396\) −7.57922 −0.380870
\(397\) 13.7570 0.690446 0.345223 0.938521i \(-0.387803\pi\)
0.345223 + 0.938521i \(0.387803\pi\)
\(398\) −3.89656 −0.195317
\(399\) 3.39695 0.170060
\(400\) 14.1797 0.708983
\(401\) −7.04530 −0.351825 −0.175913 0.984406i \(-0.556288\pi\)
−0.175913 + 0.984406i \(0.556288\pi\)
\(402\) −24.4363 −1.21877
\(403\) 1.72645 0.0860006
\(404\) −7.02597 −0.349555
\(405\) 48.7953 2.42466
\(406\) 29.1735 1.44786
\(407\) −28.6962 −1.42242
\(408\) 3.97235 0.196661
\(409\) −28.1091 −1.38990 −0.694952 0.719056i \(-0.744574\pi\)
−0.694952 + 0.719056i \(0.744574\pi\)
\(410\) −27.2741 −1.34697
\(411\) 20.9486 1.03332
\(412\) 18.7509 0.923789
\(413\) 44.9180 2.21027
\(414\) 10.6978 0.525769
\(415\) 25.5252 1.25298
\(416\) 2.30446 0.112985
\(417\) −20.4082 −0.999392
\(418\) −3.22241 −0.157613
\(419\) −7.71131 −0.376722 −0.188361 0.982100i \(-0.560318\pi\)
−0.188361 + 0.982100i \(0.560318\pi\)
\(420\) −29.8775 −1.45787
\(421\) −26.3788 −1.28562 −0.642812 0.766024i \(-0.722233\pi\)
−0.642812 + 0.766024i \(0.722233\pi\)
\(422\) 4.21378 0.205124
\(423\) −8.62922 −0.419567
\(424\) 1.69540 0.0823358
\(425\) −27.5795 −1.33780
\(426\) −2.92584 −0.141758
\(427\) 12.7505 0.617038
\(428\) 6.44341 0.311454
\(429\) 30.4587 1.47056
\(430\) −15.7745 −0.760716
\(431\) 17.6942 0.852301 0.426150 0.904652i \(-0.359869\pi\)
0.426150 + 0.904652i \(0.359869\pi\)
\(432\) 3.73514 0.179707
\(433\) 2.40132 0.115400 0.0576999 0.998334i \(-0.481623\pi\)
0.0576999 + 0.998334i \(0.481623\pi\)
\(434\) −2.50254 −0.120126
\(435\) −78.1162 −3.74538
\(436\) −7.54936 −0.361549
\(437\) 4.54832 0.217576
\(438\) −2.88432 −0.137818
\(439\) 22.4515 1.07155 0.535775 0.844361i \(-0.320020\pi\)
0.535775 + 0.844361i \(0.320020\pi\)
\(440\) 28.3423 1.35117
\(441\) 4.86977 0.231894
\(442\) −4.48217 −0.213195
\(443\) 19.7224 0.937041 0.468521 0.883453i \(-0.344787\pi\)
0.468521 + 0.883453i \(0.344787\pi\)
\(444\) −9.05601 −0.429779
\(445\) −67.3765 −3.19395
\(446\) 18.8200 0.891152
\(447\) −23.6016 −1.11632
\(448\) −3.34038 −0.157818
\(449\) 4.72949 0.223198 0.111599 0.993753i \(-0.464403\pi\)
0.111599 + 0.993753i \(0.464403\pi\)
\(450\) 16.6064 0.782834
\(451\) −40.3036 −1.89782
\(452\) −9.24288 −0.434748
\(453\) 34.5522 1.62340
\(454\) 2.50659 0.117640
\(455\) 33.7120 1.58044
\(456\) −1.01694 −0.0476224
\(457\) 8.44358 0.394974 0.197487 0.980306i \(-0.436722\pi\)
0.197487 + 0.980306i \(0.436722\pi\)
\(458\) 4.64419 0.217009
\(459\) −7.26486 −0.339095
\(460\) −40.0042 −1.86521
\(461\) −3.02639 −0.140953 −0.0704765 0.997513i \(-0.522452\pi\)
−0.0704765 + 0.997513i \(0.522452\pi\)
\(462\) −44.1507 −2.05408
\(463\) 13.8911 0.645576 0.322788 0.946471i \(-0.395380\pi\)
0.322788 + 0.946471i \(0.395380\pi\)
\(464\) −8.73359 −0.405447
\(465\) 6.70090 0.310747
\(466\) 18.2942 0.847464
\(467\) −18.8979 −0.874491 −0.437245 0.899342i \(-0.644046\pi\)
−0.437245 + 0.899342i \(0.644046\pi\)
\(468\) 2.69885 0.124754
\(469\) −39.9672 −1.84552
\(470\) 32.2687 1.48845
\(471\) −41.3835 −1.90685
\(472\) −13.4470 −0.618947
\(473\) −23.3105 −1.07182
\(474\) −25.7067 −1.18075
\(475\) 7.06044 0.323955
\(476\) 6.49704 0.297791
\(477\) 1.98555 0.0909123
\(478\) 14.5962 0.667617
\(479\) −15.6279 −0.714056 −0.357028 0.934094i \(-0.616210\pi\)
−0.357028 + 0.934094i \(0.616210\pi\)
\(480\) 8.94433 0.408251
\(481\) 10.2183 0.465914
\(482\) 24.1313 1.09915
\(483\) 62.3173 2.83553
\(484\) 30.8822 1.40374
\(485\) 42.4593 1.92798
\(486\) 11.5500 0.523918
\(487\) 27.5791 1.24973 0.624864 0.780734i \(-0.285155\pi\)
0.624864 + 0.780734i \(0.285155\pi\)
\(488\) −3.81707 −0.172791
\(489\) 11.4373 0.517214
\(490\) −18.2104 −0.822660
\(491\) 19.0538 0.859887 0.429944 0.902856i \(-0.358533\pi\)
0.429944 + 0.902856i \(0.358533\pi\)
\(492\) −12.7191 −0.573422
\(493\) 16.9869 0.765049
\(494\) 1.14745 0.0516263
\(495\) 33.1929 1.49191
\(496\) 0.749179 0.0336391
\(497\) −4.78541 −0.214655
\(498\) 11.9035 0.533410
\(499\) −15.5409 −0.695706 −0.347853 0.937549i \(-0.613089\pi\)
−0.347853 + 0.937549i \(0.613089\pi\)
\(500\) −40.2019 −1.79789
\(501\) 3.67610 0.164236
\(502\) 9.69901 0.432888
\(503\) −26.3741 −1.17596 −0.587981 0.808875i \(-0.700077\pi\)
−0.587981 + 0.808875i \(0.700077\pi\)
\(504\) −3.91206 −0.174257
\(505\) 30.7699 1.36924
\(506\) −59.1153 −2.62800
\(507\) 15.7045 0.697462
\(508\) −1.60403 −0.0711672
\(509\) 20.7416 0.919357 0.459679 0.888085i \(-0.347965\pi\)
0.459679 + 0.888085i \(0.347965\pi\)
\(510\) −17.3967 −0.770341
\(511\) −4.71750 −0.208690
\(512\) 1.00000 0.0441942
\(513\) 1.85983 0.0821135
\(514\) 25.4077 1.12068
\(515\) −82.1187 −3.61858
\(516\) −7.35637 −0.323846
\(517\) 47.6844 2.09716
\(518\) −14.8117 −0.650789
\(519\) 8.67173 0.380647
\(520\) −10.0923 −0.442576
\(521\) 17.1214 0.750103 0.375051 0.927004i \(-0.377625\pi\)
0.375051 + 0.927004i \(0.377625\pi\)
\(522\) −10.2283 −0.447680
\(523\) 2.44924 0.107098 0.0535490 0.998565i \(-0.482947\pi\)
0.0535490 + 0.998565i \(0.482947\pi\)
\(524\) −21.5751 −0.942511
\(525\) 96.7362 4.22191
\(526\) 8.23917 0.359245
\(527\) −1.45715 −0.0634746
\(528\) 13.2173 0.575209
\(529\) 60.4392 2.62779
\(530\) −7.42493 −0.322518
\(531\) −15.7483 −0.683419
\(532\) −1.66327 −0.0721117
\(533\) 14.3515 0.621633
\(534\) −31.4207 −1.35971
\(535\) −28.2186 −1.22000
\(536\) 11.9649 0.516804
\(537\) −18.9554 −0.817986
\(538\) 17.6001 0.758794
\(539\) −26.9100 −1.15909
\(540\) −16.3579 −0.703932
\(541\) −32.0947 −1.37986 −0.689929 0.723877i \(-0.742358\pi\)
−0.689929 + 0.723877i \(0.742358\pi\)
\(542\) −22.6100 −0.971183
\(543\) 51.6058 2.21462
\(544\) −1.94500 −0.0833913
\(545\) 33.0621 1.41622
\(546\) 15.7214 0.672815
\(547\) −26.3157 −1.12518 −0.562589 0.826737i \(-0.690195\pi\)
−0.562589 + 0.826737i \(0.690195\pi\)
\(548\) −10.2572 −0.438164
\(549\) −4.47034 −0.190789
\(550\) −91.7657 −3.91290
\(551\) −4.34869 −0.185261
\(552\) −18.6557 −0.794041
\(553\) −42.0451 −1.78794
\(554\) 5.92295 0.251642
\(555\) 39.6604 1.68349
\(556\) 9.99255 0.423779
\(557\) 25.5775 1.08375 0.541877 0.840458i \(-0.317714\pi\)
0.541877 + 0.840458i \(0.317714\pi\)
\(558\) 0.877395 0.0371431
\(559\) 8.30051 0.351074
\(560\) 14.6291 0.618190
\(561\) −25.7076 −1.08538
\(562\) −5.70819 −0.240785
\(563\) 8.63895 0.364088 0.182044 0.983290i \(-0.441729\pi\)
0.182044 + 0.983290i \(0.441729\pi\)
\(564\) 15.0484 0.633650
\(565\) 40.4788 1.70296
\(566\) 21.3512 0.897457
\(567\) 37.2180 1.56301
\(568\) 1.43259 0.0601103
\(569\) −29.6846 −1.24444 −0.622222 0.782841i \(-0.713770\pi\)
−0.622222 + 0.782841i \(0.713770\pi\)
\(570\) 4.45363 0.186542
\(571\) 38.0107 1.59070 0.795350 0.606150i \(-0.207287\pi\)
0.795350 + 0.606150i \(0.207287\pi\)
\(572\) −14.9136 −0.623570
\(573\) −26.2827 −1.09797
\(574\) −20.8030 −0.868298
\(575\) 129.524 5.40153
\(576\) 1.17114 0.0487976
\(577\) −30.6860 −1.27748 −0.638738 0.769424i \(-0.720543\pi\)
−0.638738 + 0.769424i \(0.720543\pi\)
\(578\) −13.2170 −0.549753
\(579\) 37.9070 1.57536
\(580\) 38.2484 1.58818
\(581\) 19.4690 0.807711
\(582\) 19.8007 0.820764
\(583\) −10.9720 −0.454415
\(584\) 1.41227 0.0584400
\(585\) −11.8195 −0.488676
\(586\) −28.4207 −1.17405
\(587\) −34.8650 −1.43903 −0.719516 0.694476i \(-0.755636\pi\)
−0.719516 + 0.694476i \(0.755636\pi\)
\(588\) −8.49231 −0.350217
\(589\) 0.373036 0.0153707
\(590\) 58.8904 2.42448
\(591\) −2.05194 −0.0844053
\(592\) 4.43414 0.182242
\(593\) −32.9455 −1.35291 −0.676456 0.736483i \(-0.736485\pi\)
−0.676456 + 0.736483i \(0.736485\pi\)
\(594\) −24.1725 −0.991811
\(595\) −28.4535 −1.16648
\(596\) 11.5562 0.473359
\(597\) 7.95809 0.325703
\(598\) 21.0501 0.860802
\(599\) −12.0595 −0.492736 −0.246368 0.969176i \(-0.579237\pi\)
−0.246368 + 0.969176i \(0.579237\pi\)
\(600\) −28.9597 −1.18227
\(601\) −31.0655 −1.26719 −0.633594 0.773665i \(-0.718421\pi\)
−0.633594 + 0.773665i \(0.718421\pi\)
\(602\) −12.0318 −0.490381
\(603\) 14.0126 0.570636
\(604\) −16.9180 −0.688383
\(605\) −135.247 −5.49859
\(606\) 14.3494 0.582904
\(607\) 18.2721 0.741640 0.370820 0.928705i \(-0.379077\pi\)
0.370820 + 0.928705i \(0.379077\pi\)
\(608\) 0.497927 0.0201936
\(609\) −59.5822 −2.41439
\(610\) 16.7167 0.676840
\(611\) −16.9797 −0.686926
\(612\) −2.27787 −0.0920776
\(613\) 39.7285 1.60462 0.802309 0.596909i \(-0.203605\pi\)
0.802309 + 0.596909i \(0.203605\pi\)
\(614\) 25.6219 1.03402
\(615\) 55.7028 2.24615
\(616\) 21.6178 0.871004
\(617\) −28.2368 −1.13677 −0.568385 0.822763i \(-0.692431\pi\)
−0.568385 + 0.822763i \(0.692431\pi\)
\(618\) −38.2956 −1.54048
\(619\) −30.5843 −1.22929 −0.614644 0.788805i \(-0.710700\pi\)
−0.614644 + 0.788805i \(0.710700\pi\)
\(620\) −3.28100 −0.131768
\(621\) 34.1187 1.36914
\(622\) −6.99098 −0.280313
\(623\) −51.3906 −2.05892
\(624\) −4.70648 −0.188410
\(625\) 105.164 4.20658
\(626\) −19.5500 −0.781377
\(627\) 6.58125 0.262830
\(628\) 20.2628 0.808574
\(629\) −8.62441 −0.343878
\(630\) 17.1327 0.682583
\(631\) −0.331266 −0.0131875 −0.00659374 0.999978i \(-0.502099\pi\)
−0.00659374 + 0.999978i \(0.502099\pi\)
\(632\) 12.5869 0.500681
\(633\) −8.60596 −0.342056
\(634\) −5.35610 −0.212718
\(635\) 7.02477 0.278769
\(636\) −3.46258 −0.137300
\(637\) 9.58224 0.379662
\(638\) 56.5207 2.23768
\(639\) 1.67777 0.0663717
\(640\) −4.37946 −0.173113
\(641\) −46.8651 −1.85106 −0.925531 0.378673i \(-0.876381\pi\)
−0.925531 + 0.378673i \(0.876381\pi\)
\(642\) −13.1596 −0.519368
\(643\) −37.4873 −1.47836 −0.739178 0.673510i \(-0.764786\pi\)
−0.739178 + 0.673510i \(0.764786\pi\)
\(644\) −30.5127 −1.20237
\(645\) 32.2169 1.26854
\(646\) −0.968469 −0.0381039
\(647\) −36.0169 −1.41597 −0.707984 0.706228i \(-0.750395\pi\)
−0.707984 + 0.706228i \(0.750395\pi\)
\(648\) −11.1419 −0.437693
\(649\) 87.0240 3.41599
\(650\) 32.6764 1.28167
\(651\) 5.11103 0.200317
\(652\) −5.60012 −0.219318
\(653\) −48.2071 −1.88649 −0.943245 0.332098i \(-0.892244\pi\)
−0.943245 + 0.332098i \(0.892244\pi\)
\(654\) 15.4183 0.602905
\(655\) 94.4871 3.69192
\(656\) 6.22772 0.243152
\(657\) 1.65397 0.0645273
\(658\) 24.6126 0.959499
\(659\) −5.71394 −0.222584 −0.111292 0.993788i \(-0.535499\pi\)
−0.111292 + 0.993788i \(0.535499\pi\)
\(660\) −57.8846 −2.25315
\(661\) −2.24297 −0.0872412 −0.0436206 0.999048i \(-0.513889\pi\)
−0.0436206 + 0.999048i \(0.513889\pi\)
\(662\) −15.1757 −0.589821
\(663\) 9.15411 0.355516
\(664\) −5.82838 −0.226185
\(665\) 7.28420 0.282469
\(666\) 5.19301 0.201225
\(667\) −79.7771 −3.08898
\(668\) −1.79995 −0.0696420
\(669\) −38.4368 −1.48605
\(670\) −52.3997 −2.02438
\(671\) 24.7027 0.953639
\(672\) 6.82218 0.263171
\(673\) 30.7983 1.18719 0.593595 0.804764i \(-0.297708\pi\)
0.593595 + 0.804764i \(0.297708\pi\)
\(674\) 3.37094 0.129844
\(675\) 52.9631 2.03855
\(676\) −7.68948 −0.295749
\(677\) 23.5843 0.906418 0.453209 0.891404i \(-0.350279\pi\)
0.453209 + 0.891404i \(0.350279\pi\)
\(678\) 18.8771 0.724970
\(679\) 32.3853 1.24283
\(680\) 8.51805 0.326652
\(681\) −5.11931 −0.196172
\(682\) −4.84842 −0.185656
\(683\) 44.9004 1.71806 0.859032 0.511922i \(-0.171066\pi\)
0.859032 + 0.511922i \(0.171066\pi\)
\(684\) 0.583144 0.0222971
\(685\) 44.9208 1.71633
\(686\) 9.49292 0.362441
\(687\) −9.48501 −0.361876
\(688\) 3.60194 0.137323
\(689\) 3.90697 0.148844
\(690\) 81.7021 3.11035
\(691\) 5.98698 0.227755 0.113878 0.993495i \(-0.463673\pi\)
0.113878 + 0.993495i \(0.463673\pi\)
\(692\) −4.24598 −0.161408
\(693\) 25.3175 0.961731
\(694\) 12.5778 0.477449
\(695\) −43.7620 −1.65999
\(696\) 17.8369 0.676108
\(697\) −12.1129 −0.458810
\(698\) −12.6349 −0.478238
\(699\) −37.3630 −1.41320
\(700\) −47.3654 −1.79025
\(701\) 44.3162 1.67380 0.836899 0.547357i \(-0.184366\pi\)
0.836899 + 0.547357i \(0.184366\pi\)
\(702\) 8.60748 0.324868
\(703\) 2.20788 0.0832717
\(704\) −6.47165 −0.243909
\(705\) −65.9037 −2.48208
\(706\) 32.8797 1.23744
\(707\) 23.4694 0.882657
\(708\) 27.4632 1.03213
\(709\) −6.36586 −0.239075 −0.119537 0.992830i \(-0.538141\pi\)
−0.119537 + 0.992830i \(0.538141\pi\)
\(710\) −6.27399 −0.235459
\(711\) 14.7411 0.552834
\(712\) 15.3847 0.576565
\(713\) 6.84338 0.256287
\(714\) −13.2692 −0.496586
\(715\) 65.3136 2.44259
\(716\) 9.28123 0.346856
\(717\) −29.8105 −1.11329
\(718\) 14.2910 0.533335
\(719\) −12.3566 −0.460822 −0.230411 0.973093i \(-0.574007\pi\)
−0.230411 + 0.973093i \(0.574007\pi\)
\(720\) −5.12897 −0.191145
\(721\) −62.6350 −2.33265
\(722\) −18.7521 −0.697880
\(723\) −49.2842 −1.83290
\(724\) −25.2680 −0.939078
\(725\) −123.839 −4.59928
\(726\) −63.0719 −2.34082
\(727\) −49.2605 −1.82697 −0.913485 0.406873i \(-0.866619\pi\)
−0.913485 + 0.406873i \(0.866619\pi\)
\(728\) −7.69776 −0.285298
\(729\) 9.83657 0.364317
\(730\) −6.18496 −0.228916
\(731\) −7.00578 −0.259118
\(732\) 7.79575 0.288139
\(733\) −38.1606 −1.40949 −0.704747 0.709458i \(-0.748940\pi\)
−0.704747 + 0.709458i \(0.748940\pi\)
\(734\) −5.15525 −0.190284
\(735\) 37.1917 1.37184
\(736\) 9.13451 0.336702
\(737\) −77.4325 −2.85226
\(738\) 7.29355 0.268479
\(739\) −3.94406 −0.145085 −0.0725423 0.997365i \(-0.523111\pi\)
−0.0725423 + 0.997365i \(0.523111\pi\)
\(740\) −19.4191 −0.713861
\(741\) −2.34348 −0.0860900
\(742\) −5.66327 −0.207905
\(743\) 5.13388 0.188344 0.0941719 0.995556i \(-0.469980\pi\)
0.0941719 + 0.995556i \(0.469980\pi\)
\(744\) −1.53008 −0.0560953
\(745\) −50.6097 −1.85420
\(746\) −5.87609 −0.215139
\(747\) −6.82587 −0.249746
\(748\) 12.5874 0.460240
\(749\) −21.5234 −0.786449
\(750\) 82.1059 2.99808
\(751\) −9.80426 −0.357762 −0.178881 0.983871i \(-0.557248\pi\)
−0.178881 + 0.983871i \(0.557248\pi\)
\(752\) −7.36820 −0.268691
\(753\) −19.8086 −0.721867
\(754\) −20.1262 −0.732953
\(755\) 74.0916 2.69647
\(756\) −12.4768 −0.453777
\(757\) 44.1375 1.60421 0.802103 0.597186i \(-0.203715\pi\)
0.802103 + 0.597186i \(0.203715\pi\)
\(758\) 3.68032 0.133675
\(759\) 120.733 4.38235
\(760\) −2.18065 −0.0791005
\(761\) −9.97185 −0.361479 −0.180740 0.983531i \(-0.557849\pi\)
−0.180740 + 0.983531i \(0.557849\pi\)
\(762\) 3.27596 0.118676
\(763\) 25.2177 0.912942
\(764\) 12.8689 0.465581
\(765\) 9.97586 0.360678
\(766\) −16.3448 −0.590563
\(767\) −30.9880 −1.11891
\(768\) −2.04234 −0.0736965
\(769\) −32.6905 −1.17885 −0.589424 0.807824i \(-0.700645\pi\)
−0.589424 + 0.807824i \(0.700645\pi\)
\(770\) −94.6741 −3.41182
\(771\) −51.8911 −1.86881
\(772\) −18.5606 −0.668010
\(773\) −8.10816 −0.291630 −0.145815 0.989312i \(-0.546580\pi\)
−0.145815 + 0.989312i \(0.546580\pi\)
\(774\) 4.21838 0.151627
\(775\) 10.6231 0.381593
\(776\) −9.69510 −0.348034
\(777\) 30.2505 1.08523
\(778\) −11.4399 −0.410141
\(779\) 3.10095 0.111103
\(780\) 20.6118 0.738022
\(781\) −9.27125 −0.331751
\(782\) −17.7666 −0.635334
\(783\) −32.6212 −1.16579
\(784\) 4.15813 0.148505
\(785\) −88.7401 −3.16727
\(786\) 44.0636 1.57170
\(787\) 23.2504 0.828786 0.414393 0.910098i \(-0.363994\pi\)
0.414393 + 0.910098i \(0.363994\pi\)
\(788\) 1.00470 0.0357909
\(789\) −16.8272 −0.599063
\(790\) −55.1239 −1.96122
\(791\) 30.8747 1.09778
\(792\) −7.57922 −0.269316
\(793\) −8.79628 −0.312365
\(794\) 13.7570 0.488219
\(795\) 15.1642 0.537819
\(796\) −3.89656 −0.138110
\(797\) 8.72336 0.308997 0.154499 0.987993i \(-0.450624\pi\)
0.154499 + 0.987993i \(0.450624\pi\)
\(798\) 3.39695 0.120251
\(799\) 14.3312 0.507000
\(800\) 14.1797 0.501327
\(801\) 18.0177 0.636622
\(802\) −7.04530 −0.248778
\(803\) −9.13969 −0.322533
\(804\) −24.4363 −0.861803
\(805\) 133.629 4.70981
\(806\) 1.72645 0.0608116
\(807\) −35.9454 −1.26534
\(808\) −7.02597 −0.247173
\(809\) 14.3716 0.505277 0.252639 0.967561i \(-0.418702\pi\)
0.252639 + 0.967561i \(0.418702\pi\)
\(810\) 48.7953 1.71449
\(811\) −2.24050 −0.0786747 −0.0393373 0.999226i \(-0.512525\pi\)
−0.0393373 + 0.999226i \(0.512525\pi\)
\(812\) 29.1735 1.02379
\(813\) 46.1773 1.61951
\(814\) −28.6962 −1.00580
\(815\) 24.5255 0.859091
\(816\) 3.97235 0.139060
\(817\) 1.79350 0.0627467
\(818\) −28.1091 −0.982810
\(819\) −9.01518 −0.315016
\(820\) −27.2741 −0.952451
\(821\) 15.1105 0.527358 0.263679 0.964610i \(-0.415064\pi\)
0.263679 + 0.964610i \(0.415064\pi\)
\(822\) 20.9486 0.730665
\(823\) −49.7631 −1.73463 −0.867316 0.497757i \(-0.834157\pi\)
−0.867316 + 0.497757i \(0.834157\pi\)
\(824\) 18.7509 0.653218
\(825\) 187.417 6.52501
\(826\) 44.9180 1.56290
\(827\) −6.10476 −0.212283 −0.106142 0.994351i \(-0.533850\pi\)
−0.106142 + 0.994351i \(0.533850\pi\)
\(828\) 10.6978 0.371775
\(829\) −38.8927 −1.35080 −0.675400 0.737451i \(-0.736029\pi\)
−0.675400 + 0.737451i \(0.736029\pi\)
\(830\) 25.5252 0.885992
\(831\) −12.0967 −0.419629
\(832\) 2.30446 0.0798927
\(833\) −8.08757 −0.280218
\(834\) −20.4082 −0.706677
\(835\) 7.88279 0.272795
\(836\) −3.22241 −0.111449
\(837\) 2.79829 0.0967230
\(838\) −7.71131 −0.266383
\(839\) −31.4935 −1.08728 −0.543639 0.839319i \(-0.682954\pi\)
−0.543639 + 0.839319i \(0.682954\pi\)
\(840\) −29.8775 −1.03087
\(841\) 47.2757 1.63020
\(842\) −26.3788 −0.909074
\(843\) 11.6580 0.401524
\(844\) 4.21378 0.145044
\(845\) 33.6757 1.15848
\(846\) −8.62922 −0.296679
\(847\) −103.158 −3.54456
\(848\) 1.69540 0.0582202
\(849\) −43.6063 −1.49657
\(850\) −27.5795 −0.945968
\(851\) 40.5037 1.38845
\(852\) −2.92584 −0.100238
\(853\) 12.3807 0.423906 0.211953 0.977280i \(-0.432018\pi\)
0.211953 + 0.977280i \(0.432018\pi\)
\(854\) 12.7505 0.436312
\(855\) −2.55385 −0.0873400
\(856\) 6.44341 0.220231
\(857\) 26.6706 0.911050 0.455525 0.890223i \(-0.349452\pi\)
0.455525 + 0.890223i \(0.349452\pi\)
\(858\) 30.4587 1.03984
\(859\) −16.1083 −0.549608 −0.274804 0.961500i \(-0.588613\pi\)
−0.274804 + 0.961500i \(0.588613\pi\)
\(860\) −15.7745 −0.537907
\(861\) 42.4867 1.44794
\(862\) 17.6942 0.602668
\(863\) 24.2202 0.824464 0.412232 0.911079i \(-0.364749\pi\)
0.412232 + 0.911079i \(0.364749\pi\)
\(864\) 3.73514 0.127072
\(865\) 18.5951 0.632253
\(866\) 2.40132 0.0816000
\(867\) 26.9935 0.916748
\(868\) −2.50254 −0.0849418
\(869\) −81.4581 −2.76328
\(870\) −78.1162 −2.64839
\(871\) 27.5726 0.934260
\(872\) −7.54936 −0.255653
\(873\) −11.3543 −0.384286
\(874\) 4.54832 0.153849
\(875\) 134.290 4.53982
\(876\) −2.88432 −0.0974523
\(877\) 10.6456 0.359476 0.179738 0.983715i \(-0.442475\pi\)
0.179738 + 0.983715i \(0.442475\pi\)
\(878\) 22.4515 0.757700
\(879\) 58.0446 1.95780
\(880\) 28.3423 0.955419
\(881\) 46.2810 1.55925 0.779623 0.626249i \(-0.215410\pi\)
0.779623 + 0.626249i \(0.215410\pi\)
\(882\) 4.86977 0.163974
\(883\) −38.8860 −1.30862 −0.654309 0.756228i \(-0.727040\pi\)
−0.654309 + 0.756228i \(0.727040\pi\)
\(884\) −4.48217 −0.150752
\(885\) −120.274 −4.04297
\(886\) 19.7224 0.662588
\(887\) 2.99547 0.100578 0.0502890 0.998735i \(-0.483986\pi\)
0.0502890 + 0.998735i \(0.483986\pi\)
\(888\) −9.05601 −0.303900
\(889\) 5.35806 0.179703
\(890\) −67.3765 −2.25847
\(891\) 72.1061 2.41565
\(892\) 18.8200 0.630140
\(893\) −3.66883 −0.122773
\(894\) −23.6016 −0.789355
\(895\) −40.6468 −1.35867
\(896\) −3.34038 −0.111594
\(897\) −42.9914 −1.43544
\(898\) 4.72949 0.157825
\(899\) −6.54302 −0.218222
\(900\) 16.6064 0.553547
\(901\) −3.29755 −0.109857
\(902\) −40.3036 −1.34196
\(903\) 24.5731 0.817741
\(904\) −9.24288 −0.307414
\(905\) 110.660 3.67847
\(906\) 34.5522 1.14792
\(907\) 40.0753 1.33068 0.665339 0.746542i \(-0.268287\pi\)
0.665339 + 0.746542i \(0.268287\pi\)
\(908\) 2.50659 0.0831842
\(909\) −8.22841 −0.272919
\(910\) 33.7120 1.11754
\(911\) −10.6188 −0.351818 −0.175909 0.984406i \(-0.556286\pi\)
−0.175909 + 0.984406i \(0.556286\pi\)
\(912\) −1.01694 −0.0336741
\(913\) 37.7192 1.24832
\(914\) 8.44358 0.279289
\(915\) −34.1412 −1.12867
\(916\) 4.64419 0.153448
\(917\) 72.0689 2.37992
\(918\) −7.26486 −0.239776
\(919\) 49.7138 1.63991 0.819953 0.572431i \(-0.194000\pi\)
0.819953 + 0.572431i \(0.194000\pi\)
\(920\) −40.0042 −1.31890
\(921\) −52.3286 −1.72428
\(922\) −3.02639 −0.0996689
\(923\) 3.30135 0.108665
\(924\) −44.1507 −1.45245
\(925\) 62.8746 2.06730
\(926\) 13.8911 0.456491
\(927\) 21.9600 0.721260
\(928\) −8.73359 −0.286694
\(929\) −14.7596 −0.484247 −0.242123 0.970245i \(-0.577844\pi\)
−0.242123 + 0.970245i \(0.577844\pi\)
\(930\) 6.70090 0.219731
\(931\) 2.07045 0.0678561
\(932\) 18.2942 0.599247
\(933\) 14.2779 0.467439
\(934\) −18.8979 −0.618358
\(935\) −55.1258 −1.80281
\(936\) 2.69885 0.0882146
\(937\) 7.00193 0.228743 0.114372 0.993438i \(-0.463515\pi\)
0.114372 + 0.993438i \(0.463515\pi\)
\(938\) −39.9672 −1.30498
\(939\) 39.9278 1.30299
\(940\) 32.2687 1.05249
\(941\) 43.3572 1.41340 0.706701 0.707512i \(-0.250182\pi\)
0.706701 + 0.707512i \(0.250182\pi\)
\(942\) −41.3835 −1.34835
\(943\) 56.8872 1.85250
\(944\) −13.4470 −0.437661
\(945\) 54.6416 1.77749
\(946\) −23.3105 −0.757889
\(947\) −45.4850 −1.47806 −0.739031 0.673671i \(-0.764716\pi\)
−0.739031 + 0.673671i \(0.764716\pi\)
\(948\) −25.7067 −0.834916
\(949\) 3.25451 0.105646
\(950\) 7.06044 0.229071
\(951\) 10.9390 0.354720
\(952\) 6.49704 0.210570
\(953\) −34.6300 −1.12178 −0.560888 0.827892i \(-0.689540\pi\)
−0.560888 + 0.827892i \(0.689540\pi\)
\(954\) 1.98555 0.0642847
\(955\) −56.3589 −1.82373
\(956\) 14.5962 0.472076
\(957\) −115.434 −3.73146
\(958\) −15.6279 −0.504914
\(959\) 34.2628 1.10640
\(960\) 8.94433 0.288677
\(961\) −30.4387 −0.981895
\(962\) 10.2183 0.329451
\(963\) 7.54615 0.243171
\(964\) 24.1313 0.777215
\(965\) 81.2853 2.61667
\(966\) 62.3173 2.00503
\(967\) 41.4357 1.33248 0.666242 0.745736i \(-0.267902\pi\)
0.666242 + 0.745736i \(0.267902\pi\)
\(968\) 30.8822 0.992592
\(969\) 1.97794 0.0635406
\(970\) 42.4593 1.36329
\(971\) 38.0429 1.22085 0.610427 0.792072i \(-0.290998\pi\)
0.610427 + 0.792072i \(0.290998\pi\)
\(972\) 11.5500 0.370466
\(973\) −33.3789 −1.07008
\(974\) 27.5791 0.883691
\(975\) −66.7363 −2.13727
\(976\) −3.81707 −0.122181
\(977\) −15.1038 −0.483212 −0.241606 0.970374i \(-0.577674\pi\)
−0.241606 + 0.970374i \(0.577674\pi\)
\(978\) 11.4373 0.365726
\(979\) −99.5642 −3.18208
\(980\) −18.2104 −0.581709
\(981\) −8.84138 −0.282283
\(982\) 19.0538 0.608032
\(983\) −0.502919 −0.0160406 −0.00802031 0.999968i \(-0.502553\pi\)
−0.00802031 + 0.999968i \(0.502553\pi\)
\(984\) −12.7191 −0.405470
\(985\) −4.40004 −0.140197
\(986\) 16.9869 0.540972
\(987\) −50.2672 −1.60002
\(988\) 1.14745 0.0365053
\(989\) 32.9019 1.04622
\(990\) 33.1929 1.05494
\(991\) 12.1409 0.385668 0.192834 0.981231i \(-0.438232\pi\)
0.192834 + 0.981231i \(0.438232\pi\)
\(992\) 0.749179 0.0237864
\(993\) 30.9939 0.983563
\(994\) −4.78541 −0.151784
\(995\) 17.0648 0.540991
\(996\) 11.9035 0.377178
\(997\) −48.3450 −1.53110 −0.765550 0.643376i \(-0.777533\pi\)
−0.765550 + 0.643376i \(0.777533\pi\)
\(998\) −15.5409 −0.491939
\(999\) 16.5621 0.524003
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 \(a_p\))