Properties

Label 4015.2.a.h.1.20
Level 4015
Weight 2
Character 4015.1
Self dual Yes
Analytic conductor 32.060
Analytic rank 0
Dimension 37
CM No

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Newspace parameters

Level: \( N \) = \( 4015 = 5 \cdot 11 \cdot 73 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0599364115\)
Analytic rank: \(0\)
Dimension: \(37\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 4015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.503541 q^{2}\) \(+0.0692183 q^{3}\) \(-1.74645 q^{4}\) \(+1.00000 q^{5}\) \(+0.0348542 q^{6}\) \(-2.92313 q^{7}\) \(-1.88649 q^{8}\) \(-2.99521 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.503541 q^{2}\) \(+0.0692183 q^{3}\) \(-1.74645 q^{4}\) \(+1.00000 q^{5}\) \(+0.0348542 q^{6}\) \(-2.92313 q^{7}\) \(-1.88649 q^{8}\) \(-2.99521 q^{9}\) \(+0.503541 q^{10}\) \(+1.00000 q^{11}\) \(-0.120886 q^{12}\) \(+5.73426 q^{13}\) \(-1.47192 q^{14}\) \(+0.0692183 q^{15}\) \(+2.54297 q^{16}\) \(+0.148278 q^{17}\) \(-1.50821 q^{18}\) \(-4.90526 q^{19}\) \(-1.74645 q^{20}\) \(-0.202334 q^{21}\) \(+0.503541 q^{22}\) \(-6.36870 q^{23}\) \(-0.130579 q^{24}\) \(+1.00000 q^{25}\) \(+2.88743 q^{26}\) \(-0.414978 q^{27}\) \(+5.10510 q^{28}\) \(-1.48132 q^{29}\) \(+0.0348542 q^{30}\) \(+6.03969 q^{31}\) \(+5.05347 q^{32}\) \(+0.0692183 q^{33}\) \(+0.0746642 q^{34}\) \(-2.92313 q^{35}\) \(+5.23097 q^{36}\) \(-6.02102 q^{37}\) \(-2.47000 q^{38}\) \(+0.396915 q^{39}\) \(-1.88649 q^{40}\) \(+1.06629 q^{41}\) \(-0.101884 q^{42}\) \(+0.407031 q^{43}\) \(-1.74645 q^{44}\) \(-2.99521 q^{45}\) \(-3.20690 q^{46}\) \(-3.78321 q^{47}\) \(+0.176020 q^{48}\) \(+1.54472 q^{49}\) \(+0.503541 q^{50}\) \(+0.0102636 q^{51}\) \(-10.0146 q^{52}\) \(+0.702635 q^{53}\) \(-0.208958 q^{54}\) \(+1.00000 q^{55}\) \(+5.51446 q^{56}\) \(-0.339533 q^{57}\) \(-0.745903 q^{58}\) \(+4.46036 q^{59}\) \(-0.120886 q^{60}\) \(-2.17639 q^{61}\) \(+3.04123 q^{62}\) \(+8.75540 q^{63}\) \(-2.54131 q^{64}\) \(+5.73426 q^{65}\) \(+0.0348542 q^{66}\) \(+4.71801 q^{67}\) \(-0.258960 q^{68}\) \(-0.440831 q^{69}\) \(-1.47192 q^{70}\) \(+6.20880 q^{71}\) \(+5.65043 q^{72}\) \(+1.00000 q^{73}\) \(-3.03183 q^{74}\) \(+0.0692183 q^{75}\) \(+8.56677 q^{76}\) \(-2.92313 q^{77}\) \(+0.199863 q^{78}\) \(-7.70643 q^{79}\) \(+2.54297 q^{80}\) \(+8.95690 q^{81}\) \(+0.536922 q^{82}\) \(+15.6514 q^{83}\) \(+0.353366 q^{84}\) \(+0.148278 q^{85}\) \(+0.204957 q^{86}\) \(-0.102534 q^{87}\) \(-1.88649 q^{88}\) \(+3.63060 q^{89}\) \(-1.50821 q^{90}\) \(-16.7620 q^{91}\) \(+11.1226 q^{92}\) \(+0.418057 q^{93}\) \(-1.90500 q^{94}\) \(-4.90526 q^{95}\) \(+0.349792 q^{96}\) \(+17.1806 q^{97}\) \(+0.777827 q^{98}\) \(-2.99521 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 37q^{11} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 11q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 43q^{16} \) \(\mathstrut +\mathstrut 38q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 43q^{20} \) \(\mathstrut +\mathstrut 39q^{21} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 9q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 14q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 20q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 15q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 62q^{41} \) \(\mathstrut -\mathstrut 13q^{42} \) \(\mathstrut +\mathstrut 30q^{43} \) \(\mathstrut +\mathstrut 43q^{44} \) \(\mathstrut +\mathstrut 50q^{45} \) \(\mathstrut +\mathstrut 31q^{46} \) \(\mathstrut +\mathstrut 5q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 59q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut +\mathstrut 37q^{55} \) \(\mathstrut +\mathstrut 22q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 40q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 57q^{61} \) \(\mathstrut +\mathstrut 20q^{62} \) \(\mathstrut -\mathstrut 29q^{63} \) \(\mathstrut +\mathstrut 10q^{64} \) \(\mathstrut +\mathstrut 11q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 53q^{68} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 11q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut +\mathstrut 59q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 42q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 61q^{81} \) \(\mathstrut -\mathstrut 22q^{82} \) \(\mathstrut +\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 66q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut -\mathstrut q^{86} \) \(\mathstrut -\mathstrut 26q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 69q^{89} \) \(\mathstrut +\mathstrut 11q^{90} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 21q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut +\mathstrut 34q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 15q^{98} \) \(\mathstrut +\mathstrut 50q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.503541 0.356057 0.178029 0.984025i \(-0.443028\pi\)
0.178029 + 0.984025i \(0.443028\pi\)
\(3\) 0.0692183 0.0399632 0.0199816 0.999800i \(-0.493639\pi\)
0.0199816 + 0.999800i \(0.493639\pi\)
\(4\) −1.74645 −0.873223
\(5\) 1.00000 0.447214
\(6\) 0.0348542 0.0142292
\(7\) −2.92313 −1.10484 −0.552421 0.833566i \(-0.686296\pi\)
−0.552421 + 0.833566i \(0.686296\pi\)
\(8\) −1.88649 −0.666975
\(9\) −2.99521 −0.998403
\(10\) 0.503541 0.159234
\(11\) 1.00000 0.301511
\(12\) −0.120886 −0.0348968
\(13\) 5.73426 1.59040 0.795198 0.606350i \(-0.207367\pi\)
0.795198 + 0.606350i \(0.207367\pi\)
\(14\) −1.47192 −0.393387
\(15\) 0.0692183 0.0178721
\(16\) 2.54297 0.635742
\(17\) 0.148278 0.0359628 0.0179814 0.999838i \(-0.494276\pi\)
0.0179814 + 0.999838i \(0.494276\pi\)
\(18\) −1.50821 −0.355488
\(19\) −4.90526 −1.12534 −0.562671 0.826681i \(-0.690226\pi\)
−0.562671 + 0.826681i \(0.690226\pi\)
\(20\) −1.74645 −0.390517
\(21\) −0.202334 −0.0441530
\(22\) 0.503541 0.107355
\(23\) −6.36870 −1.32797 −0.663983 0.747747i \(-0.731135\pi\)
−0.663983 + 0.747747i \(0.731135\pi\)
\(24\) −0.130579 −0.0266544
\(25\) 1.00000 0.200000
\(26\) 2.88743 0.566272
\(27\) −0.414978 −0.0798625
\(28\) 5.10510 0.964773
\(29\) −1.48132 −0.275073 −0.137537 0.990497i \(-0.543918\pi\)
−0.137537 + 0.990497i \(0.543918\pi\)
\(30\) 0.0348542 0.00636348
\(31\) 6.03969 1.08476 0.542381 0.840133i \(-0.317523\pi\)
0.542381 + 0.840133i \(0.317523\pi\)
\(32\) 5.05347 0.893335
\(33\) 0.0692183 0.0120494
\(34\) 0.0746642 0.0128048
\(35\) −2.92313 −0.494100
\(36\) 5.23097 0.871829
\(37\) −6.02102 −0.989850 −0.494925 0.868936i \(-0.664804\pi\)
−0.494925 + 0.868936i \(0.664804\pi\)
\(38\) −2.47000 −0.400686
\(39\) 0.396915 0.0635573
\(40\) −1.88649 −0.298280
\(41\) 1.06629 0.166527 0.0832635 0.996528i \(-0.473466\pi\)
0.0832635 + 0.996528i \(0.473466\pi\)
\(42\) −0.101884 −0.0157210
\(43\) 0.407031 0.0620717 0.0310358 0.999518i \(-0.490119\pi\)
0.0310358 + 0.999518i \(0.490119\pi\)
\(44\) −1.74645 −0.263287
\(45\) −2.99521 −0.446499
\(46\) −3.20690 −0.472832
\(47\) −3.78321 −0.551838 −0.275919 0.961181i \(-0.588982\pi\)
−0.275919 + 0.961181i \(0.588982\pi\)
\(48\) 0.176020 0.0254063
\(49\) 1.54472 0.220674
\(50\) 0.503541 0.0712114
\(51\) 0.0102636 0.00143719
\(52\) −10.0146 −1.38877
\(53\) 0.702635 0.0965143 0.0482572 0.998835i \(-0.484633\pi\)
0.0482572 + 0.998835i \(0.484633\pi\)
\(54\) −0.208958 −0.0284356
\(55\) 1.00000 0.134840
\(56\) 5.51446 0.736901
\(57\) −0.339533 −0.0449723
\(58\) −0.745903 −0.0979418
\(59\) 4.46036 0.580690 0.290345 0.956922i \(-0.406230\pi\)
0.290345 + 0.956922i \(0.406230\pi\)
\(60\) −0.120886 −0.0156063
\(61\) −2.17639 −0.278658 −0.139329 0.990246i \(-0.544495\pi\)
−0.139329 + 0.990246i \(0.544495\pi\)
\(62\) 3.04123 0.386237
\(63\) 8.75540 1.10308
\(64\) −2.54131 −0.317664
\(65\) 5.73426 0.711247
\(66\) 0.0348542 0.00429026
\(67\) 4.71801 0.576396 0.288198 0.957571i \(-0.406944\pi\)
0.288198 + 0.957571i \(0.406944\pi\)
\(68\) −0.258960 −0.0314035
\(69\) −0.440831 −0.0530698
\(70\) −1.47192 −0.175928
\(71\) 6.20880 0.736849 0.368424 0.929658i \(-0.379897\pi\)
0.368424 + 0.929658i \(0.379897\pi\)
\(72\) 5.65043 0.665909
\(73\) 1.00000 0.117041
\(74\) −3.03183 −0.352443
\(75\) 0.0692183 0.00799264
\(76\) 8.56677 0.982676
\(77\) −2.92313 −0.333122
\(78\) 0.199863 0.0226300
\(79\) −7.70643 −0.867041 −0.433520 0.901144i \(-0.642729\pi\)
−0.433520 + 0.901144i \(0.642729\pi\)
\(80\) 2.54297 0.284313
\(81\) 8.95690 0.995211
\(82\) 0.536922 0.0592931
\(83\) 15.6514 1.71797 0.858984 0.512002i \(-0.171096\pi\)
0.858984 + 0.512002i \(0.171096\pi\)
\(84\) 0.353366 0.0385554
\(85\) 0.148278 0.0160830
\(86\) 0.204957 0.0221011
\(87\) −0.102534 −0.0109928
\(88\) −1.88649 −0.201100
\(89\) 3.63060 0.384842 0.192421 0.981312i \(-0.438366\pi\)
0.192421 + 0.981312i \(0.438366\pi\)
\(90\) −1.50821 −0.158979
\(91\) −16.7620 −1.75714
\(92\) 11.1226 1.15961
\(93\) 0.418057 0.0433505
\(94\) −1.90500 −0.196486
\(95\) −4.90526 −0.503269
\(96\) 0.349792 0.0357005
\(97\) 17.1806 1.74443 0.872215 0.489122i \(-0.162683\pi\)
0.872215 + 0.489122i \(0.162683\pi\)
\(98\) 0.777827 0.0785724
\(99\) −2.99521 −0.301030
\(100\) −1.74645 −0.174645
\(101\) 12.4499 1.23882 0.619408 0.785070i \(-0.287373\pi\)
0.619408 + 0.785070i \(0.287373\pi\)
\(102\) 0.00516813 0.000511721 0
\(103\) 12.1754 1.19967 0.599837 0.800122i \(-0.295232\pi\)
0.599837 + 0.800122i \(0.295232\pi\)
\(104\) −10.8176 −1.06075
\(105\) −0.202334 −0.0197458
\(106\) 0.353805 0.0343646
\(107\) 2.78463 0.269200 0.134600 0.990900i \(-0.457025\pi\)
0.134600 + 0.990900i \(0.457025\pi\)
\(108\) 0.724737 0.0697378
\(109\) 2.97959 0.285393 0.142696 0.989767i \(-0.454423\pi\)
0.142696 + 0.989767i \(0.454423\pi\)
\(110\) 0.503541 0.0480107
\(111\) −0.416765 −0.0395576
\(112\) −7.43344 −0.702394
\(113\) 5.56265 0.523290 0.261645 0.965164i \(-0.415735\pi\)
0.261645 + 0.965164i \(0.415735\pi\)
\(114\) −0.170969 −0.0160127
\(115\) −6.36870 −0.593885
\(116\) 2.58704 0.240200
\(117\) −17.1753 −1.58786
\(118\) 2.24598 0.206759
\(119\) −0.433438 −0.0397332
\(120\) −0.130579 −0.0119202
\(121\) 1.00000 0.0909091
\(122\) −1.09590 −0.0992181
\(123\) 0.0738069 0.00665495
\(124\) −10.5480 −0.947239
\(125\) 1.00000 0.0894427
\(126\) 4.40870 0.392758
\(127\) 9.87999 0.876708 0.438354 0.898802i \(-0.355562\pi\)
0.438354 + 0.898802i \(0.355562\pi\)
\(128\) −11.3866 −1.00644
\(129\) 0.0281740 0.00248058
\(130\) 2.88743 0.253245
\(131\) −0.0462060 −0.00403703 −0.00201852 0.999998i \(-0.500643\pi\)
−0.00201852 + 0.999998i \(0.500643\pi\)
\(132\) −0.120886 −0.0105218
\(133\) 14.3387 1.24333
\(134\) 2.37571 0.205230
\(135\) −0.414978 −0.0357156
\(136\) −0.279726 −0.0239863
\(137\) 13.6843 1.16913 0.584564 0.811348i \(-0.301266\pi\)
0.584564 + 0.811348i \(0.301266\pi\)
\(138\) −0.221976 −0.0188959
\(139\) 1.26747 0.107505 0.0537526 0.998554i \(-0.482882\pi\)
0.0537526 + 0.998554i \(0.482882\pi\)
\(140\) 5.10510 0.431460
\(141\) −0.261867 −0.0220532
\(142\) 3.12638 0.262360
\(143\) 5.73426 0.479523
\(144\) −7.61672 −0.634727
\(145\) −1.48132 −0.123017
\(146\) 0.503541 0.0416733
\(147\) 0.106923 0.00881882
\(148\) 10.5154 0.864360
\(149\) 13.6738 1.12020 0.560099 0.828426i \(-0.310763\pi\)
0.560099 + 0.828426i \(0.310763\pi\)
\(150\) 0.0348542 0.00284583
\(151\) −1.73480 −0.141176 −0.0705882 0.997506i \(-0.522488\pi\)
−0.0705882 + 0.997506i \(0.522488\pi\)
\(152\) 9.25371 0.750575
\(153\) −0.444125 −0.0359054
\(154\) −1.47192 −0.118611
\(155\) 6.03969 0.485120
\(156\) −0.693191 −0.0554997
\(157\) 4.58342 0.365797 0.182898 0.983132i \(-0.441452\pi\)
0.182898 + 0.983132i \(0.441452\pi\)
\(158\) −3.88050 −0.308716
\(159\) 0.0486352 0.00385702
\(160\) 5.05347 0.399512
\(161\) 18.6166 1.46719
\(162\) 4.51017 0.354352
\(163\) −19.5809 −1.53370 −0.766848 0.641829i \(-0.778176\pi\)
−0.766848 + 0.641829i \(0.778176\pi\)
\(164\) −1.86222 −0.145415
\(165\) 0.0692183 0.00538863
\(166\) 7.88114 0.611695
\(167\) −1.67099 −0.129305 −0.0646524 0.997908i \(-0.520594\pi\)
−0.0646524 + 0.997908i \(0.520594\pi\)
\(168\) 0.381701 0.0294489
\(169\) 19.8817 1.52936
\(170\) 0.0746642 0.00572648
\(171\) 14.6923 1.12355
\(172\) −0.710858 −0.0542024
\(173\) −16.9382 −1.28778 −0.643892 0.765116i \(-0.722681\pi\)
−0.643892 + 0.765116i \(0.722681\pi\)
\(174\) −0.0516301 −0.00391407
\(175\) −2.92313 −0.220968
\(176\) 2.54297 0.191684
\(177\) 0.308739 0.0232062
\(178\) 1.82815 0.137026
\(179\) 2.65541 0.198475 0.0992374 0.995064i \(-0.468360\pi\)
0.0992374 + 0.995064i \(0.468360\pi\)
\(180\) 5.23097 0.389894
\(181\) −10.5568 −0.784679 −0.392340 0.919820i \(-0.628334\pi\)
−0.392340 + 0.919820i \(0.628334\pi\)
\(182\) −8.44035 −0.625641
\(183\) −0.150646 −0.0111360
\(184\) 12.0145 0.885720
\(185\) −6.02102 −0.442674
\(186\) 0.210509 0.0154353
\(187\) 0.148278 0.0108432
\(188\) 6.60717 0.481878
\(189\) 1.21304 0.0882354
\(190\) −2.47000 −0.179192
\(191\) 7.27263 0.526229 0.263114 0.964765i \(-0.415250\pi\)
0.263114 + 0.964765i \(0.415250\pi\)
\(192\) −0.175905 −0.0126949
\(193\) 21.0373 1.51430 0.757150 0.653241i \(-0.226591\pi\)
0.757150 + 0.653241i \(0.226591\pi\)
\(194\) 8.65116 0.621117
\(195\) 0.396915 0.0284237
\(196\) −2.69776 −0.192697
\(197\) 11.8782 0.846284 0.423142 0.906063i \(-0.360927\pi\)
0.423142 + 0.906063i \(0.360927\pi\)
\(198\) −1.50821 −0.107184
\(199\) 23.6215 1.67448 0.837241 0.546835i \(-0.184167\pi\)
0.837241 + 0.546835i \(0.184167\pi\)
\(200\) −1.88649 −0.133395
\(201\) 0.326572 0.0230346
\(202\) 6.26905 0.441089
\(203\) 4.33008 0.303912
\(204\) −0.0179248 −0.00125499
\(205\) 1.06629 0.0744731
\(206\) 6.13079 0.427153
\(207\) 19.0756 1.32585
\(208\) 14.5820 1.01108
\(209\) −4.90526 −0.339304
\(210\) −0.101884 −0.00703063
\(211\) 23.0822 1.58904 0.794521 0.607237i \(-0.207722\pi\)
0.794521 + 0.607237i \(0.207722\pi\)
\(212\) −1.22711 −0.0842786
\(213\) 0.429762 0.0294468
\(214\) 1.40217 0.0958507
\(215\) 0.407031 0.0277593
\(216\) 0.782851 0.0532663
\(217\) −17.6548 −1.19849
\(218\) 1.50034 0.101616
\(219\) 0.0692183 0.00467734
\(220\) −1.74645 −0.117745
\(221\) 0.850266 0.0571951
\(222\) −0.209858 −0.0140847
\(223\) −9.46907 −0.634096 −0.317048 0.948410i \(-0.602692\pi\)
−0.317048 + 0.948410i \(0.602692\pi\)
\(224\) −14.7720 −0.986993
\(225\) −2.99521 −0.199681
\(226\) 2.80102 0.186321
\(227\) −14.7932 −0.981860 −0.490930 0.871199i \(-0.663343\pi\)
−0.490930 + 0.871199i \(0.663343\pi\)
\(228\) 0.592977 0.0392708
\(229\) −10.3786 −0.685840 −0.342920 0.939365i \(-0.611416\pi\)
−0.342920 + 0.939365i \(0.611416\pi\)
\(230\) −3.20690 −0.211457
\(231\) −0.202334 −0.0133126
\(232\) 2.79448 0.183467
\(233\) −6.44758 −0.422395 −0.211198 0.977443i \(-0.567736\pi\)
−0.211198 + 0.977443i \(0.567736\pi\)
\(234\) −8.64846 −0.565368
\(235\) −3.78321 −0.246789
\(236\) −7.78979 −0.507072
\(237\) −0.533425 −0.0346497
\(238\) −0.218254 −0.0141473
\(239\) −14.5254 −0.939568 −0.469784 0.882781i \(-0.655668\pi\)
−0.469784 + 0.882781i \(0.655668\pi\)
\(240\) 0.176020 0.0113620
\(241\) 3.36384 0.216684 0.108342 0.994114i \(-0.465446\pi\)
0.108342 + 0.994114i \(0.465446\pi\)
\(242\) 0.503541 0.0323688
\(243\) 1.86491 0.119634
\(244\) 3.80094 0.243330
\(245\) 1.54472 0.0986883
\(246\) 0.0371648 0.00236954
\(247\) −28.1280 −1.78974
\(248\) −11.3938 −0.723508
\(249\) 1.08337 0.0686555
\(250\) 0.503541 0.0318467
\(251\) −25.7115 −1.62289 −0.811447 0.584426i \(-0.801320\pi\)
−0.811447 + 0.584426i \(0.801320\pi\)
\(252\) −15.2908 −0.963232
\(253\) −6.36870 −0.400397
\(254\) 4.97498 0.312158
\(255\) 0.0102636 0.000642730 0
\(256\) −0.650989 −0.0406868
\(257\) 12.9607 0.808469 0.404234 0.914655i \(-0.367538\pi\)
0.404234 + 0.914655i \(0.367538\pi\)
\(258\) 0.0141868 0.000883229 0
\(259\) 17.6003 1.09363
\(260\) −10.0146 −0.621077
\(261\) 4.43685 0.274634
\(262\) −0.0232666 −0.00143741
\(263\) −29.5752 −1.82368 −0.911842 0.410542i \(-0.865339\pi\)
−0.911842 + 0.410542i \(0.865339\pi\)
\(264\) −0.130579 −0.00803661
\(265\) 0.702635 0.0431625
\(266\) 7.22013 0.442695
\(267\) 0.251303 0.0153795
\(268\) −8.23975 −0.503323
\(269\) 22.6119 1.37867 0.689336 0.724442i \(-0.257902\pi\)
0.689336 + 0.724442i \(0.257902\pi\)
\(270\) −0.208958 −0.0127168
\(271\) −25.5167 −1.55003 −0.775015 0.631943i \(-0.782258\pi\)
−0.775015 + 0.631943i \(0.782258\pi\)
\(272\) 0.377067 0.0228631
\(273\) −1.16024 −0.0702207
\(274\) 6.89060 0.416276
\(275\) 1.00000 0.0603023
\(276\) 0.769887 0.0463418
\(277\) 18.5524 1.11471 0.557353 0.830275i \(-0.311817\pi\)
0.557353 + 0.830275i \(0.311817\pi\)
\(278\) 0.638221 0.0382780
\(279\) −18.0901 −1.08303
\(280\) 5.51446 0.329552
\(281\) 14.8603 0.886491 0.443245 0.896400i \(-0.353827\pi\)
0.443245 + 0.896400i \(0.353827\pi\)
\(282\) −0.131861 −0.00785219
\(283\) 6.14254 0.365136 0.182568 0.983193i \(-0.441559\pi\)
0.182568 + 0.983193i \(0.441559\pi\)
\(284\) −10.8433 −0.643433
\(285\) −0.339533 −0.0201122
\(286\) 2.88743 0.170737
\(287\) −3.11692 −0.183986
\(288\) −15.1362 −0.891908
\(289\) −16.9780 −0.998707
\(290\) −0.745903 −0.0438009
\(291\) 1.18921 0.0697130
\(292\) −1.74645 −0.102203
\(293\) −11.8885 −0.694535 −0.347268 0.937766i \(-0.612890\pi\)
−0.347268 + 0.937766i \(0.612890\pi\)
\(294\) 0.0538399 0.00314000
\(295\) 4.46036 0.259692
\(296\) 11.3586 0.660205
\(297\) −0.414978 −0.0240795
\(298\) 6.88530 0.398855
\(299\) −36.5198 −2.11199
\(300\) −0.120886 −0.00697936
\(301\) −1.18981 −0.0685793
\(302\) −0.873545 −0.0502669
\(303\) 0.861763 0.0495070
\(304\) −12.4739 −0.715428
\(305\) −2.17639 −0.124620
\(306\) −0.223635 −0.0127844
\(307\) −32.7128 −1.86702 −0.933508 0.358557i \(-0.883269\pi\)
−0.933508 + 0.358557i \(0.883269\pi\)
\(308\) 5.10510 0.290890
\(309\) 0.842758 0.0479428
\(310\) 3.04123 0.172730
\(311\) −16.1358 −0.914978 −0.457489 0.889215i \(-0.651251\pi\)
−0.457489 + 0.889215i \(0.651251\pi\)
\(312\) −0.748776 −0.0423911
\(313\) 12.1415 0.686280 0.343140 0.939284i \(-0.388510\pi\)
0.343140 + 0.939284i \(0.388510\pi\)
\(314\) 2.30794 0.130244
\(315\) 8.75540 0.493311
\(316\) 13.4589 0.757120
\(317\) 6.37854 0.358255 0.179127 0.983826i \(-0.442673\pi\)
0.179127 + 0.983826i \(0.442673\pi\)
\(318\) 0.0244898 0.00137332
\(319\) −1.48132 −0.0829377
\(320\) −2.54131 −0.142064
\(321\) 0.192747 0.0107581
\(322\) 9.37421 0.522404
\(323\) −0.727343 −0.0404705
\(324\) −15.6428 −0.869042
\(325\) 5.73426 0.318079
\(326\) −9.85979 −0.546083
\(327\) 0.206242 0.0114052
\(328\) −2.01155 −0.111069
\(329\) 11.0588 0.609693
\(330\) 0.0348542 0.00191866
\(331\) −6.05625 −0.332882 −0.166441 0.986051i \(-0.553227\pi\)
−0.166441 + 0.986051i \(0.553227\pi\)
\(332\) −27.3344 −1.50017
\(333\) 18.0342 0.988269
\(334\) −0.841410 −0.0460399
\(335\) 4.71801 0.257772
\(336\) −0.514530 −0.0280699
\(337\) −26.4455 −1.44058 −0.720288 0.693675i \(-0.755991\pi\)
−0.720288 + 0.693675i \(0.755991\pi\)
\(338\) 10.0112 0.544540
\(339\) 0.385037 0.0209123
\(340\) −0.258960 −0.0140441
\(341\) 6.03969 0.327068
\(342\) 7.39816 0.400046
\(343\) 15.9465 0.861032
\(344\) −0.767860 −0.0414002
\(345\) −0.440831 −0.0237335
\(346\) −8.52905 −0.458525
\(347\) −27.9460 −1.50022 −0.750111 0.661312i \(-0.770000\pi\)
−0.750111 + 0.661312i \(0.770000\pi\)
\(348\) 0.179070 0.00959917
\(349\) 34.5706 1.85052 0.925261 0.379331i \(-0.123846\pi\)
0.925261 + 0.379331i \(0.123846\pi\)
\(350\) −1.47192 −0.0786773
\(351\) −2.37959 −0.127013
\(352\) 5.05347 0.269351
\(353\) 1.60102 0.0852139 0.0426070 0.999092i \(-0.486434\pi\)
0.0426070 + 0.999092i \(0.486434\pi\)
\(354\) 0.155463 0.00826274
\(355\) 6.20880 0.329529
\(356\) −6.34064 −0.336053
\(357\) −0.0300018 −0.00158786
\(358\) 1.33711 0.0706684
\(359\) 4.41178 0.232845 0.116422 0.993200i \(-0.462857\pi\)
0.116422 + 0.993200i \(0.462857\pi\)
\(360\) 5.65043 0.297804
\(361\) 5.06154 0.266397
\(362\) −5.31577 −0.279391
\(363\) 0.0692183 0.00363302
\(364\) 29.2739 1.53437
\(365\) 1.00000 0.0523424
\(366\) −0.0758562 −0.00396507
\(367\) −24.5704 −1.28256 −0.641282 0.767305i \(-0.721597\pi\)
−0.641282 + 0.767305i \(0.721597\pi\)
\(368\) −16.1954 −0.844245
\(369\) −3.19377 −0.166261
\(370\) −3.03183 −0.157617
\(371\) −2.05390 −0.106633
\(372\) −0.730114 −0.0378547
\(373\) 34.2164 1.77166 0.885830 0.464010i \(-0.153590\pi\)
0.885830 + 0.464010i \(0.153590\pi\)
\(374\) 0.0746642 0.00386080
\(375\) 0.0692183 0.00357442
\(376\) 7.13698 0.368062
\(377\) −8.49424 −0.437476
\(378\) 0.610813 0.0314168
\(379\) 9.46370 0.486118 0.243059 0.970012i \(-0.421849\pi\)
0.243059 + 0.970012i \(0.421849\pi\)
\(380\) 8.56677 0.439466
\(381\) 0.683876 0.0350360
\(382\) 3.66206 0.187368
\(383\) 31.9424 1.63218 0.816090 0.577925i \(-0.196137\pi\)
0.816090 + 0.577925i \(0.196137\pi\)
\(384\) −0.788160 −0.0402206
\(385\) −2.92313 −0.148977
\(386\) 10.5932 0.539177
\(387\) −1.21914 −0.0619726
\(388\) −30.0051 −1.52328
\(389\) −27.7993 −1.40948 −0.704741 0.709465i \(-0.748937\pi\)
−0.704741 + 0.709465i \(0.748937\pi\)
\(390\) 0.199863 0.0101205
\(391\) −0.944341 −0.0477574
\(392\) −2.91409 −0.147184
\(393\) −0.00319830 −0.000161333 0
\(394\) 5.98114 0.301325
\(395\) −7.70643 −0.387752
\(396\) 5.23097 0.262866
\(397\) 22.9262 1.15063 0.575316 0.817931i \(-0.304879\pi\)
0.575316 + 0.817931i \(0.304879\pi\)
\(398\) 11.8944 0.596211
\(399\) 0.992501 0.0496872
\(400\) 2.54297 0.127148
\(401\) −4.82523 −0.240960 −0.120480 0.992716i \(-0.538443\pi\)
−0.120480 + 0.992716i \(0.538443\pi\)
\(402\) 0.164442 0.00820164
\(403\) 34.6332 1.72520
\(404\) −21.7432 −1.08176
\(405\) 8.95690 0.445072
\(406\) 2.18037 0.108210
\(407\) −6.02102 −0.298451
\(408\) −0.0193621 −0.000958567 0
\(409\) 6.11712 0.302472 0.151236 0.988498i \(-0.451675\pi\)
0.151236 + 0.988498i \(0.451675\pi\)
\(410\) 0.536922 0.0265167
\(411\) 0.947203 0.0467221
\(412\) −21.2636 −1.04758
\(413\) −13.0382 −0.641570
\(414\) 9.60534 0.472077
\(415\) 15.6514 0.768299
\(416\) 28.9779 1.42076
\(417\) 0.0877319 0.00429625
\(418\) −2.47000 −0.120811
\(419\) 24.3574 1.18994 0.594968 0.803750i \(-0.297165\pi\)
0.594968 + 0.803750i \(0.297165\pi\)
\(420\) 0.353366 0.0172425
\(421\) −23.4906 −1.14486 −0.572430 0.819954i \(-0.693999\pi\)
−0.572430 + 0.819954i \(0.693999\pi\)
\(422\) 11.6228 0.565790
\(423\) 11.3315 0.550956
\(424\) −1.32551 −0.0643726
\(425\) 0.148278 0.00719256
\(426\) 0.216403 0.0104847
\(427\) 6.36187 0.307872
\(428\) −4.86321 −0.235072
\(429\) 0.396915 0.0191632
\(430\) 0.204957 0.00988390
\(431\) 29.6527 1.42832 0.714160 0.699982i \(-0.246809\pi\)
0.714160 + 0.699982i \(0.246809\pi\)
\(432\) −1.05528 −0.0507720
\(433\) 31.5416 1.51579 0.757895 0.652376i \(-0.226228\pi\)
0.757895 + 0.652376i \(0.226228\pi\)
\(434\) −8.88993 −0.426730
\(435\) −0.102534 −0.00491613
\(436\) −5.20369 −0.249212
\(437\) 31.2401 1.49442
\(438\) 0.0348542 0.00166540
\(439\) 22.1450 1.05692 0.528462 0.848957i \(-0.322769\pi\)
0.528462 + 0.848957i \(0.322769\pi\)
\(440\) −1.88649 −0.0899348
\(441\) −4.62675 −0.220321
\(442\) 0.428144 0.0203647
\(443\) −19.8277 −0.942043 −0.471021 0.882122i \(-0.656115\pi\)
−0.471021 + 0.882122i \(0.656115\pi\)
\(444\) 0.727857 0.0345426
\(445\) 3.63060 0.172107
\(446\) −4.76806 −0.225774
\(447\) 0.946474 0.0447667
\(448\) 7.42860 0.350968
\(449\) −26.1829 −1.23565 −0.617823 0.786318i \(-0.711985\pi\)
−0.617823 + 0.786318i \(0.711985\pi\)
\(450\) −1.50821 −0.0710977
\(451\) 1.06629 0.0502098
\(452\) −9.71488 −0.456949
\(453\) −0.120080 −0.00564186
\(454\) −7.44899 −0.349598
\(455\) −16.7620 −0.785815
\(456\) 0.640526 0.0299954
\(457\) −19.3732 −0.906241 −0.453120 0.891449i \(-0.649689\pi\)
−0.453120 + 0.891449i \(0.649689\pi\)
\(458\) −5.22607 −0.244198
\(459\) −0.0615323 −0.00287208
\(460\) 11.1226 0.518594
\(461\) 30.2137 1.40719 0.703595 0.710601i \(-0.251577\pi\)
0.703595 + 0.710601i \(0.251577\pi\)
\(462\) −0.101884 −0.00474005
\(463\) −6.26645 −0.291227 −0.145613 0.989342i \(-0.546516\pi\)
−0.145613 + 0.989342i \(0.546516\pi\)
\(464\) −3.76694 −0.174876
\(465\) 0.418057 0.0193869
\(466\) −3.24662 −0.150397
\(467\) 21.4366 0.991968 0.495984 0.868332i \(-0.334807\pi\)
0.495984 + 0.868332i \(0.334807\pi\)
\(468\) 29.9957 1.38655
\(469\) −13.7914 −0.636826
\(470\) −1.90500 −0.0878711
\(471\) 0.317256 0.0146184
\(472\) −8.41443 −0.387305
\(473\) 0.407031 0.0187153
\(474\) −0.268601 −0.0123373
\(475\) −4.90526 −0.225069
\(476\) 0.756976 0.0346959
\(477\) −2.10454 −0.0963602
\(478\) −7.31412 −0.334540
\(479\) −8.25086 −0.376991 −0.188496 0.982074i \(-0.560361\pi\)
−0.188496 + 0.982074i \(0.560361\pi\)
\(480\) 0.349792 0.0159658
\(481\) −34.5261 −1.57425
\(482\) 1.69383 0.0771519
\(483\) 1.28861 0.0586337
\(484\) −1.74645 −0.0793839
\(485\) 17.1806 0.780133
\(486\) 0.939061 0.0425967
\(487\) −2.22229 −0.100701 −0.0503507 0.998732i \(-0.516034\pi\)
−0.0503507 + 0.998732i \(0.516034\pi\)
\(488\) 4.10573 0.185858
\(489\) −1.35536 −0.0612913
\(490\) 0.777827 0.0351387
\(491\) 41.6526 1.87976 0.939879 0.341509i \(-0.110938\pi\)
0.939879 + 0.341509i \(0.110938\pi\)
\(492\) −0.128900 −0.00581125
\(493\) −0.219647 −0.00989240
\(494\) −14.1636 −0.637250
\(495\) −2.99521 −0.134625
\(496\) 15.3588 0.689628
\(497\) −18.1491 −0.814100
\(498\) 0.545519 0.0244453
\(499\) 4.61368 0.206537 0.103268 0.994654i \(-0.467070\pi\)
0.103268 + 0.994654i \(0.467070\pi\)
\(500\) −1.74645 −0.0781035
\(501\) −0.115663 −0.00516743
\(502\) −12.9468 −0.577843
\(503\) −6.36777 −0.283925 −0.141962 0.989872i \(-0.545341\pi\)
−0.141962 + 0.989872i \(0.545341\pi\)
\(504\) −16.5170 −0.735724
\(505\) 12.4499 0.554015
\(506\) −3.20690 −0.142564
\(507\) 1.37618 0.0611181
\(508\) −17.2549 −0.765562
\(509\) −2.36511 −0.104832 −0.0524158 0.998625i \(-0.516692\pi\)
−0.0524158 + 0.998625i \(0.516692\pi\)
\(510\) 0.00516813 0.000228849 0
\(511\) −2.92313 −0.129312
\(512\) 22.4454 0.991955
\(513\) 2.03557 0.0898727
\(514\) 6.52626 0.287861
\(515\) 12.1754 0.536511
\(516\) −0.0492044 −0.00216610
\(517\) −3.78321 −0.166385
\(518\) 8.86245 0.389394
\(519\) −1.17243 −0.0514640
\(520\) −10.8176 −0.474384
\(521\) −22.6602 −0.992762 −0.496381 0.868105i \(-0.665338\pi\)
−0.496381 + 0.868105i \(0.665338\pi\)
\(522\) 2.23413 0.0977854
\(523\) −8.73652 −0.382021 −0.191011 0.981588i \(-0.561176\pi\)
−0.191011 + 0.981588i \(0.561176\pi\)
\(524\) 0.0806963 0.00352523
\(525\) −0.202334 −0.00883059
\(526\) −14.8923 −0.649335
\(527\) 0.895556 0.0390110
\(528\) 0.176020 0.00766028
\(529\) 17.5604 0.763496
\(530\) 0.353805 0.0153683
\(531\) −13.3597 −0.579763
\(532\) −25.0418 −1.08570
\(533\) 6.11440 0.264844
\(534\) 0.126542 0.00547599
\(535\) 2.78463 0.120390
\(536\) −8.90047 −0.384442
\(537\) 0.183803 0.00793168
\(538\) 11.3860 0.490886
\(539\) 1.54472 0.0665356
\(540\) 0.724737 0.0311877
\(541\) −1.05163 −0.0452131 −0.0226065 0.999744i \(-0.507196\pi\)
−0.0226065 + 0.999744i \(0.507196\pi\)
\(542\) −12.8487 −0.551899
\(543\) −0.730722 −0.0313583
\(544\) 0.749320 0.0321268
\(545\) 2.97959 0.127632
\(546\) −0.584226 −0.0250026
\(547\) 31.6544 1.35345 0.676723 0.736238i \(-0.263399\pi\)
0.676723 + 0.736238i \(0.263399\pi\)
\(548\) −23.8989 −1.02091
\(549\) 6.51873 0.278213
\(550\) 0.503541 0.0214711
\(551\) 7.26623 0.309552
\(552\) 0.831622 0.0353962
\(553\) 22.5269 0.957942
\(554\) 9.34190 0.396899
\(555\) −0.416765 −0.0176907
\(556\) −2.21356 −0.0938760
\(557\) 7.01070 0.297053 0.148526 0.988908i \(-0.452547\pi\)
0.148526 + 0.988908i \(0.452547\pi\)
\(558\) −9.10913 −0.385620
\(559\) 2.33402 0.0987186
\(560\) −7.43344 −0.314120
\(561\) 0.0102636 0.000433328 0
\(562\) 7.48276 0.315641
\(563\) −17.9652 −0.757144 −0.378572 0.925572i \(-0.623585\pi\)
−0.378572 + 0.925572i \(0.623585\pi\)
\(564\) 0.457337 0.0192574
\(565\) 5.56265 0.234023
\(566\) 3.09302 0.130009
\(567\) −26.1822 −1.09955
\(568\) −11.7128 −0.491459
\(569\) 13.8524 0.580725 0.290362 0.956917i \(-0.406224\pi\)
0.290362 + 0.956917i \(0.406224\pi\)
\(570\) −0.170969 −0.00716110
\(571\) 31.3483 1.31189 0.655943 0.754811i \(-0.272271\pi\)
0.655943 + 0.754811i \(0.272271\pi\)
\(572\) −10.0146 −0.418730
\(573\) 0.503398 0.0210298
\(574\) −1.56950 −0.0655095
\(575\) −6.36870 −0.265593
\(576\) 7.61176 0.317157
\(577\) −45.8827 −1.91012 −0.955061 0.296410i \(-0.904210\pi\)
−0.955061 + 0.296410i \(0.904210\pi\)
\(578\) −8.54912 −0.355597
\(579\) 1.45617 0.0605163
\(580\) 2.58704 0.107421
\(581\) −45.7513 −1.89808
\(582\) 0.598818 0.0248218
\(583\) 0.702635 0.0291002
\(584\) −1.88649 −0.0780635
\(585\) −17.1753 −0.710111
\(586\) −5.98636 −0.247294
\(587\) −7.47689 −0.308604 −0.154302 0.988024i \(-0.549313\pi\)
−0.154302 + 0.988024i \(0.549313\pi\)
\(588\) −0.186734 −0.00770080
\(589\) −29.6262 −1.22073
\(590\) 2.24598 0.0924654
\(591\) 0.822185 0.0338202
\(592\) −15.3113 −0.629290
\(593\) −9.67487 −0.397299 −0.198650 0.980071i \(-0.563656\pi\)
−0.198650 + 0.980071i \(0.563656\pi\)
\(594\) −0.208958 −0.00857366
\(595\) −0.433438 −0.0177692
\(596\) −23.8805 −0.978183
\(597\) 1.63504 0.0669176
\(598\) −18.3892 −0.751990
\(599\) 36.6763 1.49855 0.749276 0.662257i \(-0.230401\pi\)
0.749276 + 0.662257i \(0.230401\pi\)
\(600\) −0.130579 −0.00533088
\(601\) 1.06165 0.0433056 0.0216528 0.999766i \(-0.493107\pi\)
0.0216528 + 0.999766i \(0.493107\pi\)
\(602\) −0.599116 −0.0244182
\(603\) −14.1314 −0.575476
\(604\) 3.02974 0.123279
\(605\) 1.00000 0.0406558
\(606\) 0.433933 0.0176273
\(607\) −12.9975 −0.527553 −0.263776 0.964584i \(-0.584968\pi\)
−0.263776 + 0.964584i \(0.584968\pi\)
\(608\) −24.7885 −1.00531
\(609\) 0.299721 0.0121453
\(610\) −1.09590 −0.0443717
\(611\) −21.6939 −0.877641
\(612\) 0.775640 0.0313534
\(613\) −9.18222 −0.370866 −0.185433 0.982657i \(-0.559369\pi\)
−0.185433 + 0.982657i \(0.559369\pi\)
\(614\) −16.4722 −0.664764
\(615\) 0.0738069 0.00297618
\(616\) 5.51446 0.222184
\(617\) 2.00272 0.0806265 0.0403133 0.999187i \(-0.487164\pi\)
0.0403133 + 0.999187i \(0.487164\pi\)
\(618\) 0.424363 0.0170704
\(619\) 5.49082 0.220695 0.110347 0.993893i \(-0.464804\pi\)
0.110347 + 0.993893i \(0.464804\pi\)
\(620\) −10.5480 −0.423618
\(621\) 2.64287 0.106055
\(622\) −8.12504 −0.325784
\(623\) −10.6127 −0.425190
\(624\) 1.00934 0.0404061
\(625\) 1.00000 0.0400000
\(626\) 6.11375 0.244355
\(627\) −0.339533 −0.0135597
\(628\) −8.00469 −0.319422
\(629\) −0.892788 −0.0355978
\(630\) 4.40870 0.175647
\(631\) −35.3593 −1.40763 −0.703815 0.710383i \(-0.748522\pi\)
−0.703815 + 0.710383i \(0.748522\pi\)
\(632\) 14.5381 0.578294
\(633\) 1.59771 0.0635031
\(634\) 3.21186 0.127559
\(635\) 9.87999 0.392076
\(636\) −0.0849387 −0.00336804
\(637\) 8.85779 0.350959
\(638\) −0.745903 −0.0295306
\(639\) −18.5966 −0.735672
\(640\) −11.3866 −0.450094
\(641\) 28.8580 1.13982 0.569911 0.821706i \(-0.306978\pi\)
0.569911 + 0.821706i \(0.306978\pi\)
\(642\) 0.0970561 0.00383050
\(643\) 22.9963 0.906887 0.453443 0.891285i \(-0.350195\pi\)
0.453443 + 0.891285i \(0.350195\pi\)
\(644\) −32.5129 −1.28119
\(645\) 0.0281740 0.00110935
\(646\) −0.366247 −0.0144098
\(647\) −22.7153 −0.893029 −0.446515 0.894776i \(-0.647335\pi\)
−0.446515 + 0.894776i \(0.647335\pi\)
\(648\) −16.8971 −0.663781
\(649\) 4.46036 0.175085
\(650\) 2.88743 0.113254
\(651\) −1.22204 −0.0478954
\(652\) 34.1970 1.33926
\(653\) 26.5444 1.03876 0.519382 0.854542i \(-0.326162\pi\)
0.519382 + 0.854542i \(0.326162\pi\)
\(654\) 0.103851 0.00406090
\(655\) −0.0462060 −0.00180542
\(656\) 2.71155 0.105868
\(657\) −2.99521 −0.116854
\(658\) 5.56857 0.217085
\(659\) 24.4136 0.951018 0.475509 0.879711i \(-0.342264\pi\)
0.475509 + 0.879711i \(0.342264\pi\)
\(660\) −0.120886 −0.00470548
\(661\) 10.6242 0.413233 0.206616 0.978422i \(-0.433755\pi\)
0.206616 + 0.978422i \(0.433755\pi\)
\(662\) −3.04957 −0.118525
\(663\) 0.0588539 0.00228570
\(664\) −29.5263 −1.14584
\(665\) 14.3387 0.556032
\(666\) 9.08097 0.351880
\(667\) 9.43406 0.365288
\(668\) 2.91829 0.112912
\(669\) −0.655432 −0.0253405
\(670\) 2.37571 0.0917816
\(671\) −2.17639 −0.0840185
\(672\) −1.02249 −0.0394434
\(673\) 49.2143 1.89707 0.948535 0.316672i \(-0.102565\pi\)
0.948535 + 0.316672i \(0.102565\pi\)
\(674\) −13.3164 −0.512928
\(675\) −0.414978 −0.0159725
\(676\) −34.7223 −1.33547
\(677\) −7.71267 −0.296422 −0.148211 0.988956i \(-0.547351\pi\)
−0.148211 + 0.988956i \(0.547351\pi\)
\(678\) 0.193882 0.00744599
\(679\) −50.2213 −1.92732
\(680\) −0.279726 −0.0107270
\(681\) −1.02396 −0.0392383
\(682\) 3.04123 0.116455
\(683\) −25.3815 −0.971195 −0.485597 0.874183i \(-0.661398\pi\)
−0.485597 + 0.874183i \(0.661398\pi\)
\(684\) −25.6593 −0.981106
\(685\) 13.6843 0.522850
\(686\) 8.02973 0.306576
\(687\) −0.718391 −0.0274083
\(688\) 1.03507 0.0394616
\(689\) 4.02909 0.153496
\(690\) −0.221976 −0.00845049
\(691\) −3.74986 −0.142651 −0.0713256 0.997453i \(-0.522723\pi\)
−0.0713256 + 0.997453i \(0.522723\pi\)
\(692\) 29.5816 1.12452
\(693\) 8.75540 0.332590
\(694\) −14.0720 −0.534164
\(695\) 1.26747 0.0480778
\(696\) 0.193429 0.00733192
\(697\) 0.158108 0.00598877
\(698\) 17.4077 0.658892
\(699\) −0.446290 −0.0168802
\(700\) 5.10510 0.192955
\(701\) 2.89554 0.109363 0.0546816 0.998504i \(-0.482586\pi\)
0.0546816 + 0.998504i \(0.482586\pi\)
\(702\) −1.19822 −0.0452239
\(703\) 29.5347 1.11392
\(704\) −2.54131 −0.0957793
\(705\) −0.261867 −0.00986248
\(706\) 0.806181 0.0303410
\(707\) −36.3928 −1.36869
\(708\) −0.539196 −0.0202642
\(709\) −20.6188 −0.774356 −0.387178 0.922005i \(-0.626550\pi\)
−0.387178 + 0.922005i \(0.626550\pi\)
\(710\) 3.12638 0.117331
\(711\) 23.0824 0.865656
\(712\) −6.84908 −0.256680
\(713\) −38.4650 −1.44053
\(714\) −0.0151071 −0.000565370 0
\(715\) 5.73426 0.214449
\(716\) −4.63753 −0.173313
\(717\) −1.00542 −0.0375481
\(718\) 2.22151 0.0829060
\(719\) −5.36575 −0.200109 −0.100054 0.994982i \(-0.531902\pi\)
−0.100054 + 0.994982i \(0.531902\pi\)
\(720\) −7.61672 −0.283859
\(721\) −35.5902 −1.32545
\(722\) 2.54869 0.0948525
\(723\) 0.232839 0.00865938
\(724\) 18.4368 0.685200
\(725\) −1.48132 −0.0550147
\(726\) 0.0348542 0.00129356
\(727\) −24.7930 −0.919520 −0.459760 0.888043i \(-0.652065\pi\)
−0.459760 + 0.888043i \(0.652065\pi\)
\(728\) 31.6213 1.17196
\(729\) −26.7416 −0.990430
\(730\) 0.503541 0.0186369
\(731\) 0.0603539 0.00223227
\(732\) 0.263095 0.00972426
\(733\) −39.2809 −1.45087 −0.725436 0.688289i \(-0.758362\pi\)
−0.725436 + 0.688289i \(0.758362\pi\)
\(734\) −12.3722 −0.456666
\(735\) 0.106923 0.00394390
\(736\) −32.1840 −1.18632
\(737\) 4.71801 0.173790
\(738\) −1.60819 −0.0591984
\(739\) 24.7129 0.909078 0.454539 0.890727i \(-0.349804\pi\)
0.454539 + 0.890727i \(0.349804\pi\)
\(740\) 10.5154 0.386554
\(741\) −1.94697 −0.0715238
\(742\) −1.03422 −0.0379674
\(743\) −5.78402 −0.212195 −0.106098 0.994356i \(-0.533836\pi\)
−0.106098 + 0.994356i \(0.533836\pi\)
\(744\) −0.788660 −0.0289137
\(745\) 13.6738 0.500968
\(746\) 17.2294 0.630812
\(747\) −46.8793 −1.71523
\(748\) −0.258960 −0.00946853
\(749\) −8.13985 −0.297423
\(750\) 0.0348542 0.00127270
\(751\) 37.6508 1.37390 0.686948 0.726707i \(-0.258950\pi\)
0.686948 + 0.726707i \(0.258950\pi\)
\(752\) −9.62058 −0.350827
\(753\) −1.77970 −0.0648560
\(754\) −4.27720 −0.155766
\(755\) −1.73480 −0.0631360
\(756\) −2.11850 −0.0770492
\(757\) 37.3917 1.35902 0.679512 0.733664i \(-0.262192\pi\)
0.679512 + 0.733664i \(0.262192\pi\)
\(758\) 4.76536 0.173086
\(759\) −0.440831 −0.0160011
\(760\) 9.25371 0.335667
\(761\) 6.93789 0.251498 0.125749 0.992062i \(-0.459867\pi\)
0.125749 + 0.992062i \(0.459867\pi\)
\(762\) 0.344359 0.0124748
\(763\) −8.70974 −0.315314
\(764\) −12.7013 −0.459515
\(765\) −0.444125 −0.0160574
\(766\) 16.0843 0.581149
\(767\) 25.5769 0.923527
\(768\) −0.0450603 −0.00162597
\(769\) −8.74815 −0.315466 −0.157733 0.987482i \(-0.550419\pi\)
−0.157733 + 0.987482i \(0.550419\pi\)
\(770\) −1.47192 −0.0530442
\(771\) 0.897120 0.0323090
\(772\) −36.7406 −1.32232
\(773\) −45.8116 −1.64773 −0.823864 0.566788i \(-0.808186\pi\)
−0.823864 + 0.566788i \(0.808186\pi\)
\(774\) −0.613889 −0.0220658
\(775\) 6.03969 0.216952
\(776\) −32.4111 −1.16349
\(777\) 1.21826 0.0437048
\(778\) −13.9981 −0.501856
\(779\) −5.23044 −0.187400
\(780\) −0.693191 −0.0248202
\(781\) 6.20880 0.222168
\(782\) −0.475514 −0.0170044
\(783\) 0.614713 0.0219681
\(784\) 3.92816 0.140292
\(785\) 4.58342 0.163589
\(786\) −0.00161047 −5.74437e−5 0
\(787\) 2.08207 0.0742179 0.0371089 0.999311i \(-0.488185\pi\)
0.0371089 + 0.999311i \(0.488185\pi\)
\(788\) −20.7446 −0.738994
\(789\) −2.04714 −0.0728802
\(790\) −3.88050 −0.138062
\(791\) −16.2604 −0.578153
\(792\) 5.65043 0.200779
\(793\) −12.4800 −0.443176
\(794\) 11.5443 0.409691
\(795\) 0.0486352 0.00172491
\(796\) −41.2536 −1.46220
\(797\) 23.1135 0.818722 0.409361 0.912372i \(-0.365752\pi\)
0.409361 + 0.912372i \(0.365752\pi\)
\(798\) 0.499765 0.0176915
\(799\) −0.560968 −0.0198456
\(800\) 5.05347 0.178667
\(801\) −10.8744 −0.384228
\(802\) −2.42970 −0.0857957
\(803\) 1.00000 0.0352892
\(804\) −0.570341 −0.0201144
\(805\) 18.6166 0.656148
\(806\) 17.4392 0.614270
\(807\) 1.56516 0.0550961
\(808\) −23.4867 −0.826258
\(809\) −7.46910 −0.262600 −0.131300 0.991343i \(-0.541915\pi\)
−0.131300 + 0.991343i \(0.541915\pi\)
\(810\) 4.51017 0.158471
\(811\) 2.00979 0.0705732 0.0352866 0.999377i \(-0.488766\pi\)
0.0352866 + 0.999377i \(0.488766\pi\)
\(812\) −7.56226 −0.265383
\(813\) −1.76622 −0.0619441
\(814\) −3.03183 −0.106266
\(815\) −19.5809 −0.685889
\(816\) 0.0260999 0.000913681 0
\(817\) −1.99659 −0.0698519
\(818\) 3.08022 0.107697
\(819\) 50.2057 1.75433
\(820\) −1.86222 −0.0650317
\(821\) 51.5046 1.79752 0.898762 0.438437i \(-0.144468\pi\)
0.898762 + 0.438437i \(0.144468\pi\)
\(822\) 0.476955 0.0166357
\(823\) −11.1764 −0.389586 −0.194793 0.980844i \(-0.562403\pi\)
−0.194793 + 0.980844i \(0.562403\pi\)
\(824\) −22.9687 −0.800152
\(825\) 0.0692183 0.00240987
\(826\) −6.56529 −0.228436
\(827\) −51.5815 −1.79367 −0.896833 0.442370i \(-0.854138\pi\)
−0.896833 + 0.442370i \(0.854138\pi\)
\(828\) −33.3145 −1.15776
\(829\) −3.50380 −0.121692 −0.0608460 0.998147i \(-0.519380\pi\)
−0.0608460 + 0.998147i \(0.519380\pi\)
\(830\) 7.88114 0.273558
\(831\) 1.28417 0.0445472
\(832\) −14.5725 −0.505212
\(833\) 0.229048 0.00793604
\(834\) 0.0441766 0.00152971
\(835\) −1.67099 −0.0578268
\(836\) 8.56677 0.296288
\(837\) −2.50634 −0.0866318
\(838\) 12.2649 0.423685
\(839\) −4.04675 −0.139709 −0.0698547 0.997557i \(-0.522254\pi\)
−0.0698547 + 0.997557i \(0.522254\pi\)
\(840\) 0.381701 0.0131699
\(841\) −26.8057 −0.924335
\(842\) −11.8285 −0.407636
\(843\) 1.02860 0.0354270
\(844\) −40.3118 −1.38759
\(845\) 19.8817 0.683951
\(846\) 5.70587 0.196172
\(847\) −2.92313 −0.100440
\(848\) 1.78678 0.0613583
\(849\) 0.425176 0.0145920
\(850\) 0.0746642 0.00256096
\(851\) 38.3461 1.31449
\(852\) −0.750556 −0.0257136
\(853\) −12.0050 −0.411044 −0.205522 0.978652i \(-0.565889\pi\)
−0.205522 + 0.978652i \(0.565889\pi\)
\(854\) 3.20346 0.109620
\(855\) 14.6923 0.502465
\(856\) −5.25317 −0.179550
\(857\) 4.73993 0.161913 0.0809565 0.996718i \(-0.474203\pi\)
0.0809565 + 0.996718i \(0.474203\pi\)
\(858\) 0.199863 0.00682321
\(859\) 42.0669 1.43530 0.717651 0.696403i \(-0.245217\pi\)
0.717651 + 0.696403i \(0.245217\pi\)
\(860\) −0.710858 −0.0242401
\(861\) −0.215748 −0.00735266
\(862\) 14.9313 0.508564
\(863\) 28.5115 0.970541 0.485271 0.874364i \(-0.338721\pi\)
0.485271 + 0.874364i \(0.338721\pi\)
\(864\) −2.09708 −0.0713440
\(865\) −16.9382 −0.575915
\(866\) 15.8825 0.539708
\(867\) −1.17519 −0.0399115
\(868\) 30.8332 1.04655
\(869\) −7.70643 −0.261423
\(870\) −0.0516301 −0.00175042
\(871\) 27.0543 0.916698
\(872\) −5.62096 −0.190350
\(873\) −51.4596 −1.74164
\(874\) 15.7307 0.532098
\(875\) −2.92313 −0.0988200
\(876\) −0.120886 −0.00408436
\(877\) 30.6410 1.03467 0.517337 0.855782i \(-0.326923\pi\)
0.517337 + 0.855782i \(0.326923\pi\)
\(878\) 11.1509 0.376326
\(879\) −0.822903 −0.0277558
\(880\) 2.54297 0.0857235
\(881\) −0.352856 −0.0118880 −0.00594402 0.999982i \(-0.501892\pi\)
−0.00594402 + 0.999982i \(0.501892\pi\)
\(882\) −2.32976 −0.0784469
\(883\) −22.9728 −0.773097 −0.386548 0.922269i \(-0.626333\pi\)
−0.386548 + 0.922269i \(0.626333\pi\)
\(884\) −1.48494 −0.0499441
\(885\) 0.308739 0.0103781
\(886\) −9.98406 −0.335421
\(887\) −7.48394 −0.251286 −0.125643 0.992076i \(-0.540099\pi\)
−0.125643 + 0.992076i \(0.540099\pi\)
\(888\) 0.786222 0.0263839
\(889\) −28.8806 −0.968623
\(890\) 1.82815 0.0612798
\(891\) 8.95690 0.300068
\(892\) 16.5372 0.553707
\(893\) 18.5576 0.621007
\(894\) 0.476588 0.0159395
\(895\) 2.65541 0.0887606
\(896\) 33.2845 1.11196
\(897\) −2.52784 −0.0844020
\(898\) −13.1841 −0.439960
\(899\) −8.94669 −0.298389
\(900\) 5.23097 0.174366
\(901\) 0.104186 0.00347093
\(902\) 0.536922 0.0178775
\(903\) −0.0823564 −0.00274065
\(904\) −10.4939 −0.349021
\(905\) −10.5568 −0.350919
\(906\) −0.0604653 −0.00200882
\(907\) −35.5524 −1.18050 −0.590249 0.807222i \(-0.700970\pi\)
−0.590249 + 0.807222i \(0.700970\pi\)
\(908\) 25.8356 0.857383
\(909\) −37.2902 −1.23684
\(910\) −8.44035 −0.279795
\(911\) 50.4252 1.67066 0.835331 0.549747i \(-0.185276\pi\)
0.835331 + 0.549747i \(0.185276\pi\)
\(912\) −0.863423 −0.0285908
\(913\) 15.6514 0.517987
\(914\) −9.75520 −0.322673
\(915\) −0.150646 −0.00498019
\(916\) 18.1257 0.598891
\(917\) 0.135066 0.00446028
\(918\) −0.0309840 −0.00102262
\(919\) −10.0332 −0.330964 −0.165482 0.986213i \(-0.552918\pi\)
−0.165482 + 0.986213i \(0.552918\pi\)
\(920\) 12.0145 0.396106
\(921\) −2.26432 −0.0746119
\(922\) 15.2138 0.501040
\(923\) 35.6028 1.17188
\(924\) 0.353366 0.0116249
\(925\) −6.02102 −0.197970
\(926\) −3.15542 −0.103693
\(927\) −36.4678 −1.19776
\(928\) −7.48578 −0.245733
\(929\) −25.9326 −0.850821 −0.425410 0.905001i \(-0.639870\pi\)
−0.425410 + 0.905001i \(0.639870\pi\)
\(930\) 0.210509 0.00690286
\(931\) −7.57723 −0.248334
\(932\) 11.2604 0.368845
\(933\) −1.11689 −0.0365654
\(934\) 10.7942 0.353197
\(935\) 0.148278 0.00484922
\(936\) 32.4010 1.05906
\(937\) −5.36428 −0.175243 −0.0876217 0.996154i \(-0.527927\pi\)
−0.0876217 + 0.996154i \(0.527927\pi\)
\(938\) −6.94452 −0.226746
\(939\) 0.840415 0.0274259
\(940\) 6.60717 0.215502
\(941\) 16.7528 0.546124 0.273062 0.961996i \(-0.411964\pi\)
0.273062 + 0.961996i \(0.411964\pi\)
\(942\) 0.159751 0.00520498
\(943\) −6.79090 −0.221142
\(944\) 11.3426 0.369169
\(945\) 1.21304 0.0394601
\(946\) 0.204957 0.00666372
\(947\) −25.8379 −0.839617 −0.419809 0.907613i \(-0.637903\pi\)
−0.419809 + 0.907613i \(0.637903\pi\)
\(948\) 0.931599 0.0302569
\(949\) 5.73426 0.186142
\(950\) −2.47000 −0.0801373
\(951\) 0.441512 0.0143170
\(952\) 0.817675 0.0265010
\(953\) 5.62062 0.182070 0.0910349 0.995848i \(-0.470983\pi\)
0.0910349 + 0.995848i \(0.470983\pi\)
\(954\) −1.05972 −0.0343097
\(955\) 7.27263 0.235337
\(956\) 25.3678 0.820453
\(957\) −0.102534 −0.00331445
\(958\) −4.15464 −0.134230
\(959\) −40.0010 −1.29170
\(960\) −0.175905 −0.00567731
\(961\) 5.47790 0.176707
\(962\) −17.3853 −0.560524
\(963\) −8.34055 −0.268770
\(964\) −5.87477 −0.189214
\(965\) 21.0373 0.677216
\(966\) 0.648866 0.0208769
\(967\) −37.2610 −1.19823 −0.599117 0.800662i \(-0.704481\pi\)
−0.599117 + 0.800662i \(0.704481\pi\)
\(968\) −1.88649 −0.0606340
\(969\) −0.0503454 −0.00161733
\(970\) 8.65116 0.277772
\(971\) −49.2881 −1.58173 −0.790866 0.611990i \(-0.790369\pi\)
−0.790866 + 0.611990i \(0.790369\pi\)
\(972\) −3.25697 −0.104467
\(973\) −3.70498 −0.118776
\(974\) −1.11901 −0.0358555
\(975\) 0.396915 0.0127115
\(976\) −5.53448 −0.177154
\(977\) 13.0956 0.418967 0.209483 0.977812i \(-0.432822\pi\)
0.209483 + 0.977812i \(0.432822\pi\)
\(978\) −0.682477 −0.0218232
\(979\) 3.63060 0.116034
\(980\) −2.69776 −0.0861769
\(981\) −8.92449 −0.284937
\(982\) 20.9738 0.669301
\(983\) 14.7098 0.469170 0.234585 0.972096i \(-0.424627\pi\)
0.234585 + 0.972096i \(0.424627\pi\)
\(984\) −0.139236 −0.00443868
\(985\) 11.8782 0.378469
\(986\) −0.110601 −0.00352226
\(987\) 0.765473 0.0243653
\(988\) 49.1240 1.56284
\(989\) −2.59226 −0.0824291
\(990\) −1.50821 −0.0479341
\(991\) 24.4908 0.777976 0.388988 0.921243i \(-0.372825\pi\)
0.388988 + 0.921243i \(0.372825\pi\)
\(992\) 30.5214 0.969055
\(993\) −0.419203 −0.0133030
\(994\) −9.13884 −0.289866
\(995\) 23.6215 0.748851
\(996\) −1.89204 −0.0599516
\(997\) 41.1570 1.30346 0.651728 0.758453i \(-0.274044\pi\)
0.651728 + 0.758453i \(0.274044\pi\)
\(998\) 2.32318 0.0735389
\(999\) 2.49859 0.0790519
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 \(a_p\))