Properties

Label 8013.2.a.d.1.16
Level 8013
Weight 2
Character 8013.1
Self dual Yes
Analytic conductor 63.984
Analytic rank 0
Dimension 129
CM No

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Newspace parameters

Level: \( N \) = \( 8013 = 3 \cdot 2671 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9841271397\)
Analytic rank: \(0\)
Dimension: \(129\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 8013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.21092 q^{2}\) \(+1.00000 q^{3}\) \(+2.88816 q^{4}\) \(+1.51753 q^{5}\) \(-2.21092 q^{6}\) \(+0.0486600 q^{7}\) \(-1.96364 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.21092 q^{2}\) \(+1.00000 q^{3}\) \(+2.88816 q^{4}\) \(+1.51753 q^{5}\) \(-2.21092 q^{6}\) \(+0.0486600 q^{7}\) \(-1.96364 q^{8}\) \(+1.00000 q^{9}\) \(-3.35514 q^{10}\) \(+6.56010 q^{11}\) \(+2.88816 q^{12}\) \(+0.517879 q^{13}\) \(-0.107583 q^{14}\) \(+1.51753 q^{15}\) \(-1.43486 q^{16}\) \(-4.76722 q^{17}\) \(-2.21092 q^{18}\) \(-0.00792509 q^{19}\) \(+4.38287 q^{20}\) \(+0.0486600 q^{21}\) \(-14.5038 q^{22}\) \(+4.25244 q^{23}\) \(-1.96364 q^{24}\) \(-2.69710 q^{25}\) \(-1.14499 q^{26}\) \(+1.00000 q^{27}\) \(+0.140538 q^{28}\) \(-7.88822 q^{29}\) \(-3.35514 q^{30}\) \(-3.05936 q^{31}\) \(+7.09965 q^{32}\) \(+6.56010 q^{33}\) \(+10.5399 q^{34}\) \(+0.0738431 q^{35}\) \(+2.88816 q^{36}\) \(+7.82698 q^{37}\) \(+0.0175217 q^{38}\) \(+0.517879 q^{39}\) \(-2.97989 q^{40}\) \(-7.47610 q^{41}\) \(-0.107583 q^{42}\) \(-8.77561 q^{43}\) \(+18.9466 q^{44}\) \(+1.51753 q^{45}\) \(-9.40180 q^{46}\) \(+1.80651 q^{47}\) \(-1.43486 q^{48}\) \(-6.99763 q^{49}\) \(+5.96306 q^{50}\) \(-4.76722 q^{51}\) \(+1.49571 q^{52}\) \(+5.72962 q^{53}\) \(-2.21092 q^{54}\) \(+9.95516 q^{55}\) \(-0.0955509 q^{56}\) \(-0.00792509 q^{57}\) \(+17.4402 q^{58}\) \(+0.207025 q^{59}\) \(+4.38287 q^{60}\) \(+12.1014 q^{61}\) \(+6.76400 q^{62}\) \(+0.0486600 q^{63}\) \(-12.8270 q^{64}\) \(+0.785897 q^{65}\) \(-14.5038 q^{66}\) \(-8.59573 q^{67}\) \(-13.7685 q^{68}\) \(+4.25244 q^{69}\) \(-0.163261 q^{70}\) \(+0.245324 q^{71}\) \(-1.96364 q^{72}\) \(+9.82368 q^{73}\) \(-17.3048 q^{74}\) \(-2.69710 q^{75}\) \(-0.0228889 q^{76}\) \(+0.319215 q^{77}\) \(-1.14499 q^{78}\) \(+16.6551 q^{79}\) \(-2.17745 q^{80}\) \(+1.00000 q^{81}\) \(+16.5290 q^{82}\) \(+6.64959 q^{83}\) \(+0.140538 q^{84}\) \(-7.23440 q^{85}\) \(+19.4022 q^{86}\) \(-7.88822 q^{87}\) \(-12.8817 q^{88}\) \(+14.6852 q^{89}\) \(-3.35514 q^{90}\) \(+0.0252000 q^{91}\) \(+12.2817 q^{92}\) \(-3.05936 q^{93}\) \(-3.99404 q^{94}\) \(-0.0120266 q^{95}\) \(+7.09965 q^{96}\) \(+12.1718 q^{97}\) \(+15.4712 q^{98}\) \(+6.56010 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut 41q^{10} \) \(\mathstrut +\mathstrut 51q^{11} \) \(\mathstrut +\mathstrut 151q^{12} \) \(\mathstrut +\mathstrut 56q^{13} \) \(\mathstrut +\mathstrut 5q^{14} \) \(\mathstrut +\mathstrut 16q^{15} \) \(\mathstrut +\mathstrut 195q^{16} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 15q^{18} \) \(\mathstrut +\mathstrut 93q^{19} \) \(\mathstrut +\mathstrut 44q^{20} \) \(\mathstrut +\mathstrut 61q^{21} \) \(\mathstrut +\mathstrut 46q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 42q^{24} \) \(\mathstrut +\mathstrut 193q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut +\mathstrut 129q^{27} \) \(\mathstrut +\mathstrut 145q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 41q^{30} \) \(\mathstrut +\mathstrut 67q^{31} \) \(\mathstrut +\mathstrut 89q^{32} \) \(\mathstrut +\mathstrut 51q^{33} \) \(\mathstrut +\mathstrut 73q^{34} \) \(\mathstrut +\mathstrut 56q^{35} \) \(\mathstrut +\mathstrut 151q^{36} \) \(\mathstrut +\mathstrut 95q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 103q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 5q^{42} \) \(\mathstrut +\mathstrut 150q^{43} \) \(\mathstrut +\mathstrut 69q^{44} \) \(\mathstrut +\mathstrut 16q^{45} \) \(\mathstrut +\mathstrut 72q^{46} \) \(\mathstrut +\mathstrut 53q^{47} \) \(\mathstrut +\mathstrut 195q^{48} \) \(\mathstrut +\mathstrut 240q^{49} \) \(\mathstrut +\mathstrut 17q^{50} \) \(\mathstrut +\mathstrut 18q^{51} \) \(\mathstrut +\mathstrut 124q^{52} \) \(\mathstrut +\mathstrut 34q^{53} \) \(\mathstrut +\mathstrut 15q^{54} \) \(\mathstrut +\mathstrut 66q^{55} \) \(\mathstrut -\mathstrut 17q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 57q^{58} \) \(\mathstrut +\mathstrut 49q^{59} \) \(\mathstrut +\mathstrut 44q^{60} \) \(\mathstrut +\mathstrut 113q^{61} \) \(\mathstrut +\mathstrut 27q^{62} \) \(\mathstrut +\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 262q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 46q^{66} \) \(\mathstrut +\mathstrut 185q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut +\mathstrut 50q^{69} \) \(\mathstrut +\mathstrut 25q^{70} \) \(\mathstrut +\mathstrut 41q^{71} \) \(\mathstrut +\mathstrut 42q^{72} \) \(\mathstrut +\mathstrut 153q^{73} \) \(\mathstrut -\mathstrut q^{74} \) \(\mathstrut +\mathstrut 193q^{75} \) \(\mathstrut +\mathstrut 190q^{76} \) \(\mathstrut +\mathstrut 39q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 101q^{79} \) \(\mathstrut +\mathstrut 48q^{80} \) \(\mathstrut +\mathstrut 129q^{81} \) \(\mathstrut +\mathstrut 15q^{82} \) \(\mathstrut +\mathstrut 162q^{83} \) \(\mathstrut +\mathstrut 145q^{84} \) \(\mathstrut +\mathstrut 99q^{85} \) \(\mathstrut +\mathstrut 13q^{86} \) \(\mathstrut +\mathstrut 24q^{87} \) \(\mathstrut +\mathstrut 86q^{88} \) \(\mathstrut -\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 117q^{91} \) \(\mathstrut +\mathstrut 56q^{92} \) \(\mathstrut +\mathstrut 67q^{93} \) \(\mathstrut +\mathstrut 49q^{94} \) \(\mathstrut +\mathstrut 71q^{95} \) \(\mathstrut +\mathstrut 89q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut +\mathstrut 40q^{98} \) \(\mathstrut +\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.21092 −1.56335 −0.781677 0.623683i \(-0.785636\pi\)
−0.781677 + 0.623683i \(0.785636\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.88816 1.44408
\(5\) 1.51753 0.678661 0.339330 0.940667i \(-0.389800\pi\)
0.339330 + 0.940667i \(0.389800\pi\)
\(6\) −2.21092 −0.902603
\(7\) 0.0486600 0.0183918 0.00919588 0.999958i \(-0.497073\pi\)
0.00919588 + 0.999958i \(0.497073\pi\)
\(8\) −1.96364 −0.694253
\(9\) 1.00000 0.333333
\(10\) −3.35514 −1.06099
\(11\) 6.56010 1.97794 0.988972 0.148100i \(-0.0473157\pi\)
0.988972 + 0.148100i \(0.0473157\pi\)
\(12\) 2.88816 0.833739
\(13\) 0.517879 0.143634 0.0718168 0.997418i \(-0.477120\pi\)
0.0718168 + 0.997418i \(0.477120\pi\)
\(14\) −0.107583 −0.0287528
\(15\) 1.51753 0.391825
\(16\) −1.43486 −0.358715
\(17\) −4.76722 −1.15622 −0.578110 0.815959i \(-0.696210\pi\)
−0.578110 + 0.815959i \(0.696210\pi\)
\(18\) −2.21092 −0.521118
\(19\) −0.00792509 −0.00181814 −0.000909070 1.00000i \(-0.500289\pi\)
−0.000909070 1.00000i \(0.500289\pi\)
\(20\) 4.38287 0.980040
\(21\) 0.0486600 0.0106185
\(22\) −14.5038 −3.09223
\(23\) 4.25244 0.886695 0.443348 0.896350i \(-0.353791\pi\)
0.443348 + 0.896350i \(0.353791\pi\)
\(24\) −1.96364 −0.400827
\(25\) −2.69710 −0.539420
\(26\) −1.14499 −0.224550
\(27\) 1.00000 0.192450
\(28\) 0.140538 0.0265591
\(29\) −7.88822 −1.46480 −0.732402 0.680872i \(-0.761601\pi\)
−0.732402 + 0.680872i \(0.761601\pi\)
\(30\) −3.35514 −0.612562
\(31\) −3.05936 −0.549477 −0.274739 0.961519i \(-0.588591\pi\)
−0.274739 + 0.961519i \(0.588591\pi\)
\(32\) 7.09965 1.25505
\(33\) 6.56010 1.14197
\(34\) 10.5399 1.80758
\(35\) 0.0738431 0.0124818
\(36\) 2.88816 0.481360
\(37\) 7.82698 1.28675 0.643374 0.765552i \(-0.277534\pi\)
0.643374 + 0.765552i \(0.277534\pi\)
\(38\) 0.0175217 0.00284240
\(39\) 0.517879 0.0829269
\(40\) −2.97989 −0.471162
\(41\) −7.47610 −1.16757 −0.583785 0.811908i \(-0.698429\pi\)
−0.583785 + 0.811908i \(0.698429\pi\)
\(42\) −0.107583 −0.0166005
\(43\) −8.77561 −1.33827 −0.669134 0.743142i \(-0.733335\pi\)
−0.669134 + 0.743142i \(0.733335\pi\)
\(44\) 18.9466 2.85631
\(45\) 1.51753 0.226220
\(46\) −9.40180 −1.38622
\(47\) 1.80651 0.263506 0.131753 0.991283i \(-0.457939\pi\)
0.131753 + 0.991283i \(0.457939\pi\)
\(48\) −1.43486 −0.207104
\(49\) −6.99763 −0.999662
\(50\) 5.96306 0.843304
\(51\) −4.76722 −0.667544
\(52\) 1.49571 0.207418
\(53\) 5.72962 0.787024 0.393512 0.919319i \(-0.371260\pi\)
0.393512 + 0.919319i \(0.371260\pi\)
\(54\) −2.21092 −0.300868
\(55\) 9.95516 1.34235
\(56\) −0.0955509 −0.0127685
\(57\) −0.00792509 −0.00104970
\(58\) 17.4402 2.29001
\(59\) 0.207025 0.0269524 0.0134762 0.999909i \(-0.495710\pi\)
0.0134762 + 0.999909i \(0.495710\pi\)
\(60\) 4.38287 0.565826
\(61\) 12.1014 1.54943 0.774713 0.632313i \(-0.217894\pi\)
0.774713 + 0.632313i \(0.217894\pi\)
\(62\) 6.76400 0.859028
\(63\) 0.0486600 0.00613058
\(64\) −12.8270 −1.60338
\(65\) 0.785897 0.0974785
\(66\) −14.5038 −1.78530
\(67\) −8.59573 −1.05014 −0.525068 0.851060i \(-0.675960\pi\)
−0.525068 + 0.851060i \(0.675960\pi\)
\(68\) −13.7685 −1.66967
\(69\) 4.25244 0.511934
\(70\) −0.163261 −0.0195134
\(71\) 0.245324 0.0291147 0.0145573 0.999894i \(-0.495366\pi\)
0.0145573 + 0.999894i \(0.495366\pi\)
\(72\) −1.96364 −0.231418
\(73\) 9.82368 1.14977 0.574887 0.818233i \(-0.305046\pi\)
0.574887 + 0.818233i \(0.305046\pi\)
\(74\) −17.3048 −2.01164
\(75\) −2.69710 −0.311434
\(76\) −0.0228889 −0.00262554
\(77\) 0.319215 0.0363779
\(78\) −1.14499 −0.129644
\(79\) 16.6551 1.87385 0.936924 0.349534i \(-0.113660\pi\)
0.936924 + 0.349534i \(0.113660\pi\)
\(80\) −2.17745 −0.243446
\(81\) 1.00000 0.111111
\(82\) 16.5290 1.82533
\(83\) 6.64959 0.729887 0.364944 0.931030i \(-0.381088\pi\)
0.364944 + 0.931030i \(0.381088\pi\)
\(84\) 0.140538 0.0153339
\(85\) −7.23440 −0.784681
\(86\) 19.4022 2.09219
\(87\) −7.88822 −0.845706
\(88\) −12.8817 −1.37319
\(89\) 14.6852 1.55663 0.778314 0.627876i \(-0.216075\pi\)
0.778314 + 0.627876i \(0.216075\pi\)
\(90\) −3.35514 −0.353663
\(91\) 0.0252000 0.00264167
\(92\) 12.2817 1.28046
\(93\) −3.05936 −0.317241
\(94\) −3.99404 −0.411953
\(95\) −0.0120266 −0.00123390
\(96\) 7.09965 0.724605
\(97\) 12.1718 1.23585 0.617927 0.786235i \(-0.287973\pi\)
0.617927 + 0.786235i \(0.287973\pi\)
\(98\) 15.4712 1.56283
\(99\) 6.56010 0.659315
\(100\) −7.78964 −0.778964
\(101\) 11.2638 1.12079 0.560393 0.828227i \(-0.310650\pi\)
0.560393 + 0.828227i \(0.310650\pi\)
\(102\) 10.5399 1.04361
\(103\) 2.01512 0.198556 0.0992779 0.995060i \(-0.468347\pi\)
0.0992779 + 0.995060i \(0.468347\pi\)
\(104\) −1.01693 −0.0997181
\(105\) 0.0738431 0.00720635
\(106\) −12.6677 −1.23040
\(107\) 3.71150 0.358804 0.179402 0.983776i \(-0.442584\pi\)
0.179402 + 0.983776i \(0.442584\pi\)
\(108\) 2.88816 0.277913
\(109\) −0.616748 −0.0590738 −0.0295369 0.999564i \(-0.509403\pi\)
−0.0295369 + 0.999564i \(0.509403\pi\)
\(110\) −22.0100 −2.09858
\(111\) 7.82698 0.742904
\(112\) −0.0698203 −0.00659740
\(113\) −15.6247 −1.46985 −0.734923 0.678150i \(-0.762782\pi\)
−0.734923 + 0.678150i \(0.762782\pi\)
\(114\) 0.0175217 0.00164106
\(115\) 6.45321 0.601765
\(116\) −22.7824 −2.11529
\(117\) 0.517879 0.0478779
\(118\) −0.457715 −0.0421361
\(119\) −0.231973 −0.0212649
\(120\) −2.97989 −0.272026
\(121\) 32.0349 2.91227
\(122\) −26.7552 −2.42230
\(123\) −7.47610 −0.674097
\(124\) −8.83592 −0.793489
\(125\) −11.6806 −1.04474
\(126\) −0.107583 −0.00958428
\(127\) 11.6821 1.03662 0.518310 0.855193i \(-0.326561\pi\)
0.518310 + 0.855193i \(0.326561\pi\)
\(128\) 14.1602 1.25159
\(129\) −8.77561 −0.772649
\(130\) −1.73755 −0.152394
\(131\) 0.423746 0.0370229 0.0185114 0.999829i \(-0.494107\pi\)
0.0185114 + 0.999829i \(0.494107\pi\)
\(132\) 18.9466 1.64909
\(133\) −0.000385635 0 −3.34388e−5 0
\(134\) 19.0044 1.64173
\(135\) 1.51753 0.130608
\(136\) 9.36112 0.802709
\(137\) −11.1143 −0.949556 −0.474778 0.880105i \(-0.657472\pi\)
−0.474778 + 0.880105i \(0.657472\pi\)
\(138\) −9.40180 −0.800334
\(139\) −4.99898 −0.424008 −0.212004 0.977269i \(-0.567999\pi\)
−0.212004 + 0.977269i \(0.567999\pi\)
\(140\) 0.213270 0.0180246
\(141\) 1.80651 0.152135
\(142\) −0.542392 −0.0455166
\(143\) 3.39734 0.284099
\(144\) −1.43486 −0.119572
\(145\) −11.9706 −0.994106
\(146\) −21.7193 −1.79751
\(147\) −6.99763 −0.577155
\(148\) 22.6056 1.85817
\(149\) 19.7415 1.61729 0.808643 0.588299i \(-0.200202\pi\)
0.808643 + 0.588299i \(0.200202\pi\)
\(150\) 5.96306 0.486882
\(151\) 17.1896 1.39887 0.699434 0.714697i \(-0.253435\pi\)
0.699434 + 0.714697i \(0.253435\pi\)
\(152\) 0.0155621 0.00126225
\(153\) −4.76722 −0.385407
\(154\) −0.705757 −0.0568715
\(155\) −4.64268 −0.372909
\(156\) 1.49571 0.119753
\(157\) 17.1097 1.36550 0.682752 0.730650i \(-0.260783\pi\)
0.682752 + 0.730650i \(0.260783\pi\)
\(158\) −36.8231 −2.92949
\(159\) 5.72962 0.454389
\(160\) 10.7739 0.851755
\(161\) 0.206924 0.0163079
\(162\) −2.21092 −0.173706
\(163\) 10.6059 0.830720 0.415360 0.909657i \(-0.363656\pi\)
0.415360 + 0.909657i \(0.363656\pi\)
\(164\) −21.5922 −1.68606
\(165\) 9.95516 0.775008
\(166\) −14.7017 −1.14107
\(167\) −9.14480 −0.707646 −0.353823 0.935312i \(-0.615119\pi\)
−0.353823 + 0.935312i \(0.615119\pi\)
\(168\) −0.0955509 −0.00737191
\(169\) −12.7318 −0.979369
\(170\) 15.9947 1.22674
\(171\) −0.00792509 −0.000606047 0
\(172\) −25.3453 −1.93256
\(173\) 19.9013 1.51307 0.756534 0.653955i \(-0.226891\pi\)
0.756534 + 0.653955i \(0.226891\pi\)
\(174\) 17.4402 1.32214
\(175\) −0.131241 −0.00992087
\(176\) −9.41283 −0.709519
\(177\) 0.207025 0.0155610
\(178\) −32.4678 −2.43356
\(179\) −19.8729 −1.48537 −0.742684 0.669642i \(-0.766447\pi\)
−0.742684 + 0.669642i \(0.766447\pi\)
\(180\) 4.38287 0.326680
\(181\) 0.0914433 0.00679693 0.00339846 0.999994i \(-0.498918\pi\)
0.00339846 + 0.999994i \(0.498918\pi\)
\(182\) −0.0557151 −0.00412988
\(183\) 12.1014 0.894561
\(184\) −8.35028 −0.615591
\(185\) 11.8777 0.873265
\(186\) 6.76400 0.495960
\(187\) −31.2734 −2.28694
\(188\) 5.21747 0.380523
\(189\) 0.0486600 0.00353949
\(190\) 0.0265898 0.00192902
\(191\) 19.5935 1.41774 0.708869 0.705340i \(-0.249206\pi\)
0.708869 + 0.705340i \(0.249206\pi\)
\(192\) −12.8270 −0.925710
\(193\) 17.7064 1.27454 0.637268 0.770642i \(-0.280065\pi\)
0.637268 + 0.770642i \(0.280065\pi\)
\(194\) −26.9108 −1.93208
\(195\) 0.785897 0.0562793
\(196\) −20.2103 −1.44359
\(197\) −4.40320 −0.313715 −0.156857 0.987621i \(-0.550136\pi\)
−0.156857 + 0.987621i \(0.550136\pi\)
\(198\) −14.5038 −1.03074
\(199\) −7.26491 −0.514996 −0.257498 0.966279i \(-0.582898\pi\)
−0.257498 + 0.966279i \(0.582898\pi\)
\(200\) 5.29614 0.374494
\(201\) −8.59573 −0.606296
\(202\) −24.9033 −1.75219
\(203\) −0.383841 −0.0269403
\(204\) −13.7685 −0.963986
\(205\) −11.3452 −0.792384
\(206\) −4.45527 −0.310413
\(207\) 4.25244 0.295565
\(208\) −0.743084 −0.0515236
\(209\) −0.0519894 −0.00359618
\(210\) −0.163261 −0.0112661
\(211\) 25.8895 1.78231 0.891155 0.453699i \(-0.149896\pi\)
0.891155 + 0.453699i \(0.149896\pi\)
\(212\) 16.5480 1.13652
\(213\) 0.245324 0.0168094
\(214\) −8.20583 −0.560939
\(215\) −13.3173 −0.908230
\(216\) −1.96364 −0.133609
\(217\) −0.148869 −0.0101059
\(218\) 1.36358 0.0923533
\(219\) 9.82368 0.663823
\(220\) 28.7521 1.93846
\(221\) −2.46884 −0.166072
\(222\) −17.3048 −1.16142
\(223\) −26.2779 −1.75970 −0.879850 0.475252i \(-0.842357\pi\)
−0.879850 + 0.475252i \(0.842357\pi\)
\(224\) 0.345469 0.0230826
\(225\) −2.69710 −0.179807
\(226\) 34.5449 2.29789
\(227\) 5.41646 0.359503 0.179752 0.983712i \(-0.442471\pi\)
0.179752 + 0.983712i \(0.442471\pi\)
\(228\) −0.0228889 −0.00151586
\(229\) 17.2949 1.14288 0.571440 0.820644i \(-0.306385\pi\)
0.571440 + 0.820644i \(0.306385\pi\)
\(230\) −14.2675 −0.940772
\(231\) 0.319215 0.0210028
\(232\) 15.4896 1.01694
\(233\) −6.86948 −0.450034 −0.225017 0.974355i \(-0.572244\pi\)
−0.225017 + 0.974355i \(0.572244\pi\)
\(234\) −1.14499 −0.0748501
\(235\) 2.74143 0.178831
\(236\) 0.597921 0.0389213
\(237\) 16.6551 1.08187
\(238\) 0.512873 0.0332446
\(239\) −4.77560 −0.308908 −0.154454 0.988000i \(-0.549362\pi\)
−0.154454 + 0.988000i \(0.549362\pi\)
\(240\) −2.17745 −0.140554
\(241\) 14.1647 0.912428 0.456214 0.889870i \(-0.349205\pi\)
0.456214 + 0.889870i \(0.349205\pi\)
\(242\) −70.8266 −4.55291
\(243\) 1.00000 0.0641500
\(244\) 34.9507 2.23749
\(245\) −10.6191 −0.678431
\(246\) 16.5290 1.05385
\(247\) −0.00410423 −0.000261146 0
\(248\) 6.00749 0.381476
\(249\) 6.64959 0.421401
\(250\) 25.8248 1.63331
\(251\) 15.7111 0.991676 0.495838 0.868415i \(-0.334861\pi\)
0.495838 + 0.868415i \(0.334861\pi\)
\(252\) 0.140538 0.00885305
\(253\) 27.8964 1.75383
\(254\) −25.8282 −1.62060
\(255\) −7.23440 −0.453036
\(256\) −5.65297 −0.353310
\(257\) −0.410524 −0.0256078 −0.0128039 0.999918i \(-0.504076\pi\)
−0.0128039 + 0.999918i \(0.504076\pi\)
\(258\) 19.4022 1.20793
\(259\) 0.380861 0.0236655
\(260\) 2.26979 0.140767
\(261\) −7.88822 −0.488268
\(262\) −0.936868 −0.0578799
\(263\) 10.6161 0.654618 0.327309 0.944917i \(-0.393858\pi\)
0.327309 + 0.944917i \(0.393858\pi\)
\(264\) −12.8817 −0.792814
\(265\) 8.69488 0.534122
\(266\) 0.000852607 0 5.22767e−5 0
\(267\) 14.6852 0.898719
\(268\) −24.8258 −1.51648
\(269\) −14.4471 −0.880853 −0.440427 0.897789i \(-0.645173\pi\)
−0.440427 + 0.897789i \(0.645173\pi\)
\(270\) −3.35514 −0.204187
\(271\) 23.7878 1.44501 0.722503 0.691368i \(-0.242991\pi\)
0.722503 + 0.691368i \(0.242991\pi\)
\(272\) 6.84030 0.414754
\(273\) 0.0252000 0.00152517
\(274\) 24.5727 1.48449
\(275\) −17.6932 −1.06694
\(276\) 12.2817 0.739272
\(277\) 16.6659 1.00136 0.500678 0.865634i \(-0.333084\pi\)
0.500678 + 0.865634i \(0.333084\pi\)
\(278\) 11.0523 0.662875
\(279\) −3.05936 −0.183159
\(280\) −0.145002 −0.00866550
\(281\) −21.2038 −1.26491 −0.632455 0.774597i \(-0.717953\pi\)
−0.632455 + 0.774597i \(0.717953\pi\)
\(282\) −3.99404 −0.237841
\(283\) 21.0479 1.25117 0.625584 0.780157i \(-0.284861\pi\)
0.625584 + 0.780157i \(0.284861\pi\)
\(284\) 0.708536 0.0420439
\(285\) −0.0120266 −0.000712393 0
\(286\) −7.51123 −0.444148
\(287\) −0.363787 −0.0214737
\(288\) 7.09965 0.418351
\(289\) 5.72637 0.336845
\(290\) 26.4661 1.55414
\(291\) 12.1718 0.713521
\(292\) 28.3723 1.66036
\(293\) 14.3585 0.838835 0.419417 0.907794i \(-0.362234\pi\)
0.419417 + 0.907794i \(0.362234\pi\)
\(294\) 15.4712 0.902298
\(295\) 0.314167 0.0182915
\(296\) −15.3694 −0.893328
\(297\) 6.56010 0.380656
\(298\) −43.6468 −2.52839
\(299\) 2.20225 0.127359
\(300\) −7.78964 −0.449735
\(301\) −0.427021 −0.0246131
\(302\) −38.0048 −2.18693
\(303\) 11.2638 0.647087
\(304\) 0.0113714 0.000652195 0
\(305\) 18.3643 1.05153
\(306\) 10.5399 0.602528
\(307\) −15.4896 −0.884039 −0.442019 0.897006i \(-0.645738\pi\)
−0.442019 + 0.897006i \(0.645738\pi\)
\(308\) 0.921942 0.0525325
\(309\) 2.01512 0.114636
\(310\) 10.2646 0.582989
\(311\) −4.07764 −0.231222 −0.115611 0.993295i \(-0.536883\pi\)
−0.115611 + 0.993295i \(0.536883\pi\)
\(312\) −1.01693 −0.0575723
\(313\) −16.5977 −0.938155 −0.469077 0.883157i \(-0.655413\pi\)
−0.469077 + 0.883157i \(0.655413\pi\)
\(314\) −37.8282 −2.13477
\(315\) 0.0738431 0.00416059
\(316\) 48.1026 2.70598
\(317\) 9.72846 0.546405 0.273202 0.961957i \(-0.411917\pi\)
0.273202 + 0.961957i \(0.411917\pi\)
\(318\) −12.6677 −0.710371
\(319\) −51.7475 −2.89730
\(320\) −19.4654 −1.08815
\(321\) 3.71150 0.207156
\(322\) −0.457491 −0.0254950
\(323\) 0.0377806 0.00210217
\(324\) 2.88816 0.160453
\(325\) −1.39677 −0.0774788
\(326\) −23.4488 −1.29871
\(327\) −0.616748 −0.0341063
\(328\) 14.6804 0.810589
\(329\) 0.0879046 0.00484634
\(330\) −22.0100 −1.21161
\(331\) 4.23416 0.232731 0.116365 0.993206i \(-0.462876\pi\)
0.116365 + 0.993206i \(0.462876\pi\)
\(332\) 19.2051 1.05401
\(333\) 7.82698 0.428916
\(334\) 20.2184 1.10630
\(335\) −13.0443 −0.712686
\(336\) −0.0698203 −0.00380901
\(337\) 29.5595 1.61021 0.805105 0.593133i \(-0.202109\pi\)
0.805105 + 0.593133i \(0.202109\pi\)
\(338\) 28.1490 1.53110
\(339\) −15.6247 −0.848616
\(340\) −20.8941 −1.13314
\(341\) −20.0697 −1.08684
\(342\) 0.0175217 0.000947466 0
\(343\) −0.681125 −0.0367773
\(344\) 17.2322 0.929096
\(345\) 6.45321 0.347429
\(346\) −44.0001 −2.36546
\(347\) −13.1968 −0.708440 −0.354220 0.935162i \(-0.615254\pi\)
−0.354220 + 0.935162i \(0.615254\pi\)
\(348\) −22.7824 −1.22127
\(349\) −21.0082 −1.12454 −0.562272 0.826953i \(-0.690072\pi\)
−0.562272 + 0.826953i \(0.690072\pi\)
\(350\) 0.290163 0.0155098
\(351\) 0.517879 0.0276423
\(352\) 46.5744 2.48242
\(353\) 7.10103 0.377950 0.188975 0.981982i \(-0.439484\pi\)
0.188975 + 0.981982i \(0.439484\pi\)
\(354\) −0.457715 −0.0243273
\(355\) 0.372288 0.0197590
\(356\) 42.4131 2.24789
\(357\) −0.231973 −0.0122773
\(358\) 43.9373 2.32216
\(359\) −12.6459 −0.667424 −0.333712 0.942675i \(-0.608301\pi\)
−0.333712 + 0.942675i \(0.608301\pi\)
\(360\) −2.97989 −0.157054
\(361\) −18.9999 −0.999997
\(362\) −0.202174 −0.0106260
\(363\) 32.0349 1.68140
\(364\) 0.0727815 0.00381479
\(365\) 14.9077 0.780307
\(366\) −26.7552 −1.39852
\(367\) −13.9430 −0.727820 −0.363910 0.931434i \(-0.618559\pi\)
−0.363910 + 0.931434i \(0.618559\pi\)
\(368\) −6.10166 −0.318071
\(369\) −7.47610 −0.389190
\(370\) −26.2606 −1.36522
\(371\) 0.278803 0.0144748
\(372\) −8.83592 −0.458121
\(373\) 35.5550 1.84097 0.920483 0.390783i \(-0.127796\pi\)
0.920483 + 0.390783i \(0.127796\pi\)
\(374\) 69.1430 3.57530
\(375\) −11.6806 −0.603183
\(376\) −3.54733 −0.182940
\(377\) −4.08514 −0.210395
\(378\) −0.107583 −0.00553349
\(379\) 5.72818 0.294237 0.147118 0.989119i \(-0.453000\pi\)
0.147118 + 0.989119i \(0.453000\pi\)
\(380\) −0.0347346 −0.00178185
\(381\) 11.6821 0.598493
\(382\) −43.3197 −2.21643
\(383\) −28.8842 −1.47591 −0.737957 0.674848i \(-0.764209\pi\)
−0.737957 + 0.674848i \(0.764209\pi\)
\(384\) 14.1602 0.722609
\(385\) 0.484418 0.0246882
\(386\) −39.1474 −1.99255
\(387\) −8.77561 −0.446089
\(388\) 35.1539 1.78467
\(389\) −3.49871 −0.177391 −0.0886957 0.996059i \(-0.528270\pi\)
−0.0886957 + 0.996059i \(0.528270\pi\)
\(390\) −1.73755 −0.0879844
\(391\) −20.2723 −1.02521
\(392\) 13.7409 0.694018
\(393\) 0.423746 0.0213752
\(394\) 9.73510 0.490447
\(395\) 25.2747 1.27171
\(396\) 18.9466 0.952103
\(397\) 7.78680 0.390808 0.195404 0.980723i \(-0.437398\pi\)
0.195404 + 0.980723i \(0.437398\pi\)
\(398\) 16.0621 0.805121
\(399\) −0.000385635 0 −1.93059e−5 0
\(400\) 3.86996 0.193498
\(401\) −31.3985 −1.56797 −0.783983 0.620782i \(-0.786815\pi\)
−0.783983 + 0.620782i \(0.786815\pi\)
\(402\) 19.0044 0.947856
\(403\) −1.58438 −0.0789235
\(404\) 32.5315 1.61850
\(405\) 1.51753 0.0754067
\(406\) 0.848640 0.0421173
\(407\) 51.3458 2.54512
\(408\) 9.36112 0.463444
\(409\) 2.38174 0.117769 0.0588846 0.998265i \(-0.481246\pi\)
0.0588846 + 0.998265i \(0.481246\pi\)
\(410\) 25.0833 1.23878
\(411\) −11.1143 −0.548227
\(412\) 5.81999 0.286730
\(413\) 0.0100738 0.000495701 0
\(414\) −9.40180 −0.462073
\(415\) 10.0910 0.495346
\(416\) 3.67675 0.180268
\(417\) −4.99898 −0.244801
\(418\) 0.114944 0.00562211
\(419\) 1.79343 0.0876145 0.0438073 0.999040i \(-0.486051\pi\)
0.0438073 + 0.999040i \(0.486051\pi\)
\(420\) 0.213270 0.0104065
\(421\) 8.14268 0.396850 0.198425 0.980116i \(-0.436417\pi\)
0.198425 + 0.980116i \(0.436417\pi\)
\(422\) −57.2397 −2.78638
\(423\) 1.80651 0.0878353
\(424\) −11.2509 −0.546394
\(425\) 12.8577 0.623688
\(426\) −0.542392 −0.0262790
\(427\) 0.588854 0.0284967
\(428\) 10.7194 0.518142
\(429\) 3.39734 0.164025
\(430\) 29.4434 1.41989
\(431\) 1.98300 0.0955177 0.0477589 0.998859i \(-0.484792\pi\)
0.0477589 + 0.998859i \(0.484792\pi\)
\(432\) −1.43486 −0.0690348
\(433\) 6.78933 0.326275 0.163137 0.986603i \(-0.447839\pi\)
0.163137 + 0.986603i \(0.447839\pi\)
\(434\) 0.329136 0.0157990
\(435\) −11.9706 −0.573947
\(436\) −1.78127 −0.0853072
\(437\) −0.0337010 −0.00161214
\(438\) −21.7193 −1.03779
\(439\) 29.1166 1.38966 0.694829 0.719175i \(-0.255480\pi\)
0.694829 + 0.719175i \(0.255480\pi\)
\(440\) −19.5484 −0.931933
\(441\) −6.99763 −0.333221
\(442\) 5.45840 0.259630
\(443\) −14.7084 −0.698818 −0.349409 0.936970i \(-0.613618\pi\)
−0.349409 + 0.936970i \(0.613618\pi\)
\(444\) 22.6056 1.07281
\(445\) 22.2852 1.05642
\(446\) 58.0983 2.75103
\(447\) 19.7415 0.933741
\(448\) −0.624163 −0.0294889
\(449\) −25.1731 −1.18799 −0.593996 0.804468i \(-0.702450\pi\)
−0.593996 + 0.804468i \(0.702450\pi\)
\(450\) 5.96306 0.281101
\(451\) −49.0440 −2.30939
\(452\) −45.1265 −2.12257
\(453\) 17.1896 0.807637
\(454\) −11.9753 −0.562031
\(455\) 0.0382418 0.00179280
\(456\) 0.0155621 0.000728760 0
\(457\) −6.08006 −0.284413 −0.142207 0.989837i \(-0.545420\pi\)
−0.142207 + 0.989837i \(0.545420\pi\)
\(458\) −38.2376 −1.78673
\(459\) −4.76722 −0.222515
\(460\) 18.6379 0.868996
\(461\) −11.5469 −0.537795 −0.268897 0.963169i \(-0.586659\pi\)
−0.268897 + 0.963169i \(0.586659\pi\)
\(462\) −0.705757 −0.0328348
\(463\) −14.2169 −0.660715 −0.330358 0.943856i \(-0.607169\pi\)
−0.330358 + 0.943856i \(0.607169\pi\)
\(464\) 11.3185 0.525448
\(465\) −4.64268 −0.215299
\(466\) 15.1879 0.703564
\(467\) 22.8859 1.05903 0.529516 0.848300i \(-0.322373\pi\)
0.529516 + 0.848300i \(0.322373\pi\)
\(468\) 1.49571 0.0691394
\(469\) −0.418268 −0.0193138
\(470\) −6.06108 −0.279577
\(471\) 17.1097 0.788374
\(472\) −0.406523 −0.0187118
\(473\) −57.5689 −2.64702
\(474\) −36.8231 −1.69134
\(475\) 0.0213747 0.000980741 0
\(476\) −0.669974 −0.0307082
\(477\) 5.72962 0.262341
\(478\) 10.5585 0.482933
\(479\) −31.6380 −1.44558 −0.722788 0.691070i \(-0.757140\pi\)
−0.722788 + 0.691070i \(0.757140\pi\)
\(480\) 10.7739 0.491761
\(481\) 4.05343 0.184820
\(482\) −31.3170 −1.42645
\(483\) 0.206924 0.00941536
\(484\) 92.5219 4.20554
\(485\) 18.4710 0.838726
\(486\) −2.21092 −0.100289
\(487\) −24.3308 −1.10253 −0.551266 0.834329i \(-0.685855\pi\)
−0.551266 + 0.834329i \(0.685855\pi\)
\(488\) −23.7628 −1.07569
\(489\) 10.6059 0.479617
\(490\) 23.4780 1.06063
\(491\) −27.6273 −1.24680 −0.623402 0.781901i \(-0.714250\pi\)
−0.623402 + 0.781901i \(0.714250\pi\)
\(492\) −21.5922 −0.973450
\(493\) 37.6049 1.69364
\(494\) 0.00907412 0.000408264 0
\(495\) 9.95516 0.447451
\(496\) 4.38976 0.197106
\(497\) 0.0119375 0.000535470 0
\(498\) −14.7017 −0.658799
\(499\) −22.3250 −0.999404 −0.499702 0.866197i \(-0.666557\pi\)
−0.499702 + 0.866197i \(0.666557\pi\)
\(500\) −33.7354 −1.50869
\(501\) −9.14480 −0.408560
\(502\) −34.7360 −1.55034
\(503\) −16.2498 −0.724542 −0.362271 0.932073i \(-0.617999\pi\)
−0.362271 + 0.932073i \(0.617999\pi\)
\(504\) −0.0955509 −0.00425618
\(505\) 17.0931 0.760634
\(506\) −61.6767 −2.74186
\(507\) −12.7318 −0.565439
\(508\) 33.7398 1.49696
\(509\) −26.0708 −1.15557 −0.577785 0.816189i \(-0.696083\pi\)
−0.577785 + 0.816189i \(0.696083\pi\)
\(510\) 15.9947 0.708256
\(511\) 0.478020 0.0211464
\(512\) −15.8221 −0.699245
\(513\) −0.00792509 −0.000349901 0
\(514\) 0.907636 0.0400341
\(515\) 3.05801 0.134752
\(516\) −25.3453 −1.11577
\(517\) 11.8509 0.521200
\(518\) −0.842052 −0.0369977
\(519\) 19.9013 0.873570
\(520\) −1.54322 −0.0676747
\(521\) 3.39487 0.148732 0.0743660 0.997231i \(-0.476307\pi\)
0.0743660 + 0.997231i \(0.476307\pi\)
\(522\) 17.4402 0.763337
\(523\) −13.5447 −0.592268 −0.296134 0.955146i \(-0.595698\pi\)
−0.296134 + 0.955146i \(0.595698\pi\)
\(524\) 1.22385 0.0534640
\(525\) −0.131241 −0.00572782
\(526\) −23.4714 −1.02340
\(527\) 14.5846 0.635317
\(528\) −9.41283 −0.409641
\(529\) −4.91675 −0.213772
\(530\) −19.2237 −0.835023
\(531\) 0.207025 0.00898412
\(532\) −0.00111377 −4.82882e−5 0
\(533\) −3.87171 −0.167702
\(534\) −32.4678 −1.40502
\(535\) 5.63232 0.243506
\(536\) 16.8789 0.729059
\(537\) −19.8729 −0.857577
\(538\) 31.9413 1.37709
\(539\) −45.9052 −1.97728
\(540\) 4.38287 0.188609
\(541\) −22.4670 −0.965932 −0.482966 0.875639i \(-0.660441\pi\)
−0.482966 + 0.875639i \(0.660441\pi\)
\(542\) −52.5929 −2.25906
\(543\) 0.0914433 0.00392421
\(544\) −33.8456 −1.45112
\(545\) −0.935935 −0.0400911
\(546\) −0.0557151 −0.00238438
\(547\) −21.3346 −0.912203 −0.456101 0.889928i \(-0.650755\pi\)
−0.456101 + 0.889928i \(0.650755\pi\)
\(548\) −32.0998 −1.37123
\(549\) 12.1014 0.516475
\(550\) 39.1183 1.66801
\(551\) 0.0625148 0.00266322
\(552\) −8.35028 −0.355411
\(553\) 0.810438 0.0344633
\(554\) −36.8469 −1.56547
\(555\) 11.8777 0.504180
\(556\) −14.4379 −0.612301
\(557\) 0.733346 0.0310729 0.0155364 0.999879i \(-0.495054\pi\)
0.0155364 + 0.999879i \(0.495054\pi\)
\(558\) 6.76400 0.286343
\(559\) −4.54470 −0.192220
\(560\) −0.105955 −0.00447740
\(561\) −31.2734 −1.32037
\(562\) 46.8798 1.97750
\(563\) 13.2132 0.556869 0.278435 0.960455i \(-0.410184\pi\)
0.278435 + 0.960455i \(0.410184\pi\)
\(564\) 5.21747 0.219695
\(565\) −23.7109 −0.997527
\(566\) −46.5352 −1.95602
\(567\) 0.0486600 0.00204353
\(568\) −0.481730 −0.0202129
\(569\) 15.0982 0.632951 0.316475 0.948601i \(-0.397501\pi\)
0.316475 + 0.948601i \(0.397501\pi\)
\(570\) 0.0265898 0.00111372
\(571\) −44.3027 −1.85401 −0.927005 0.375049i \(-0.877626\pi\)
−0.927005 + 0.375049i \(0.877626\pi\)
\(572\) 9.81204 0.410262
\(573\) 19.5935 0.818531
\(574\) 0.804303 0.0335710
\(575\) −11.4692 −0.478301
\(576\) −12.8270 −0.534459
\(577\) 25.5653 1.06430 0.532149 0.846650i \(-0.321384\pi\)
0.532149 + 0.846650i \(0.321384\pi\)
\(578\) −12.6605 −0.526609
\(579\) 17.7064 0.735853
\(580\) −34.5730 −1.43557
\(581\) 0.323569 0.0134239
\(582\) −26.9108 −1.11549
\(583\) 37.5869 1.55669
\(584\) −19.2902 −0.798234
\(585\) 0.785897 0.0324928
\(586\) −31.7455 −1.31140
\(587\) 28.5191 1.17711 0.588555 0.808457i \(-0.299697\pi\)
0.588555 + 0.808457i \(0.299697\pi\)
\(588\) −20.2103 −0.833457
\(589\) 0.0242457 0.000999027 0
\(590\) −0.694598 −0.0285961
\(591\) −4.40320 −0.181123
\(592\) −11.2306 −0.461576
\(593\) −0.865407 −0.0355380 −0.0177690 0.999842i \(-0.505656\pi\)
−0.0177690 + 0.999842i \(0.505656\pi\)
\(594\) −14.5038 −0.595100
\(595\) −0.352026 −0.0144317
\(596\) 57.0166 2.33549
\(597\) −7.26491 −0.297333
\(598\) −4.86899 −0.199108
\(599\) −38.0892 −1.55628 −0.778140 0.628090i \(-0.783837\pi\)
−0.778140 + 0.628090i \(0.783837\pi\)
\(600\) 5.29614 0.216214
\(601\) 2.33696 0.0953266 0.0476633 0.998863i \(-0.484823\pi\)
0.0476633 + 0.998863i \(0.484823\pi\)
\(602\) 0.944109 0.0384790
\(603\) −8.59573 −0.350045
\(604\) 49.6462 2.02008
\(605\) 48.6140 1.97644
\(606\) −24.9033 −1.01163
\(607\) 6.65273 0.270026 0.135013 0.990844i \(-0.456892\pi\)
0.135013 + 0.990844i \(0.456892\pi\)
\(608\) −0.0562653 −0.00228186
\(609\) −0.383841 −0.0155540
\(610\) −40.6019 −1.64392
\(611\) 0.935551 0.0378483
\(612\) −13.7685 −0.556558
\(613\) 35.9524 1.45211 0.726053 0.687639i \(-0.241353\pi\)
0.726053 + 0.687639i \(0.241353\pi\)
\(614\) 34.2462 1.38207
\(615\) −11.3452 −0.457483
\(616\) −0.626824 −0.0252554
\(617\) 45.7483 1.84176 0.920879 0.389849i \(-0.127473\pi\)
0.920879 + 0.389849i \(0.127473\pi\)
\(618\) −4.45527 −0.179217
\(619\) 15.3104 0.615376 0.307688 0.951487i \(-0.400445\pi\)
0.307688 + 0.951487i \(0.400445\pi\)
\(620\) −13.4088 −0.538510
\(621\) 4.25244 0.170645
\(622\) 9.01532 0.361482
\(623\) 0.714582 0.0286291
\(624\) −0.743084 −0.0297472
\(625\) −4.24017 −0.169607
\(626\) 36.6960 1.46667
\(627\) −0.0519894 −0.00207626
\(628\) 49.4156 1.97190
\(629\) −37.3129 −1.48776
\(630\) −0.163261 −0.00650447
\(631\) −32.1331 −1.27920 −0.639600 0.768708i \(-0.720900\pi\)
−0.639600 + 0.768708i \(0.720900\pi\)
\(632\) −32.7047 −1.30092
\(633\) 25.8895 1.02902
\(634\) −21.5088 −0.854224
\(635\) 17.7280 0.703513
\(636\) 16.5480 0.656173
\(637\) −3.62392 −0.143585
\(638\) 114.409 4.52951
\(639\) 0.245324 0.00970489
\(640\) 21.4885 0.849408
\(641\) 17.5518 0.693255 0.346627 0.938003i \(-0.387327\pi\)
0.346627 + 0.938003i \(0.387327\pi\)
\(642\) −8.20583 −0.323858
\(643\) 17.7933 0.701699 0.350849 0.936432i \(-0.385893\pi\)
0.350849 + 0.936432i \(0.385893\pi\)
\(644\) 0.597628 0.0235499
\(645\) −13.3173 −0.524367
\(646\) −0.0835299 −0.00328644
\(647\) 23.2101 0.912481 0.456241 0.889856i \(-0.349196\pi\)
0.456241 + 0.889856i \(0.349196\pi\)
\(648\) −1.96364 −0.0771392
\(649\) 1.35811 0.0533103
\(650\) 3.08814 0.121127
\(651\) −0.148869 −0.00583462
\(652\) 30.6316 1.19963
\(653\) 1.42891 0.0559174 0.0279587 0.999609i \(-0.491099\pi\)
0.0279587 + 0.999609i \(0.491099\pi\)
\(654\) 1.36358 0.0533202
\(655\) 0.643048 0.0251260
\(656\) 10.7272 0.418825
\(657\) 9.82368 0.383258
\(658\) −0.194350 −0.00757655
\(659\) −24.6133 −0.958798 −0.479399 0.877597i \(-0.659145\pi\)
−0.479399 + 0.877597i \(0.659145\pi\)
\(660\) 28.7521 1.11917
\(661\) 0.564346 0.0219505 0.0109753 0.999940i \(-0.496506\pi\)
0.0109753 + 0.999940i \(0.496506\pi\)
\(662\) −9.36138 −0.363840
\(663\) −2.46884 −0.0958818
\(664\) −13.0574 −0.506726
\(665\) −0.000585213 0 −2.26936e−5 0
\(666\) −17.3048 −0.670548
\(667\) −33.5442 −1.29884
\(668\) −26.4116 −1.02190
\(669\) −26.2779 −1.01596
\(670\) 28.8399 1.11418
\(671\) 79.3864 3.06468
\(672\) 0.345469 0.0133267
\(673\) −12.0503 −0.464504 −0.232252 0.972656i \(-0.574609\pi\)
−0.232252 + 0.972656i \(0.574609\pi\)
\(674\) −65.3536 −2.51733
\(675\) −2.69710 −0.103811
\(676\) −36.7715 −1.41429
\(677\) 5.32663 0.204719 0.102359 0.994747i \(-0.467361\pi\)
0.102359 + 0.994747i \(0.467361\pi\)
\(678\) 34.5449 1.32669
\(679\) 0.592278 0.0227295
\(680\) 14.2058 0.544767
\(681\) 5.41646 0.207559
\(682\) 44.3725 1.69911
\(683\) 19.8034 0.757757 0.378879 0.925446i \(-0.376310\pi\)
0.378879 + 0.925446i \(0.376310\pi\)
\(684\) −0.0228889 −0.000875179 0
\(685\) −16.8663 −0.644427
\(686\) 1.50591 0.0574960
\(687\) 17.2949 0.659842
\(688\) 12.5918 0.480057
\(689\) 2.96725 0.113043
\(690\) −14.2675 −0.543155
\(691\) −40.6129 −1.54499 −0.772493 0.635023i \(-0.780991\pi\)
−0.772493 + 0.635023i \(0.780991\pi\)
\(692\) 57.4781 2.18499
\(693\) 0.319215 0.0121260
\(694\) 29.1770 1.10754
\(695\) −7.58611 −0.287758
\(696\) 15.4896 0.587133
\(697\) 35.6402 1.34997
\(698\) 46.4474 1.75806
\(699\) −6.86948 −0.259828
\(700\) −0.379044 −0.0143265
\(701\) 4.20374 0.158773 0.0793866 0.996844i \(-0.474704\pi\)
0.0793866 + 0.996844i \(0.474704\pi\)
\(702\) −1.14499 −0.0432147
\(703\) −0.0620295 −0.00233949
\(704\) −84.1465 −3.17139
\(705\) 2.74143 0.103248
\(706\) −15.6998 −0.590870
\(707\) 0.548095 0.0206132
\(708\) 0.597921 0.0224712
\(709\) −1.39593 −0.0524254 −0.0262127 0.999656i \(-0.508345\pi\)
−0.0262127 + 0.999656i \(0.508345\pi\)
\(710\) −0.823097 −0.0308903
\(711\) 16.6551 0.624616
\(712\) −28.8365 −1.08069
\(713\) −13.0097 −0.487219
\(714\) 0.512873 0.0191938
\(715\) 5.15556 0.192807
\(716\) −57.3960 −2.14499
\(717\) −4.77560 −0.178348
\(718\) 27.9590 1.04342
\(719\) 36.6266 1.36594 0.682970 0.730446i \(-0.260688\pi\)
0.682970 + 0.730446i \(0.260688\pi\)
\(720\) −2.17745 −0.0811486
\(721\) 0.0980558 0.00365179
\(722\) 42.0073 1.56335
\(723\) 14.1647 0.526790
\(724\) 0.264103 0.00981530
\(725\) 21.2753 0.790145
\(726\) −70.8266 −2.62862
\(727\) 10.3952 0.385537 0.192769 0.981244i \(-0.438253\pi\)
0.192769 + 0.981244i \(0.438253\pi\)
\(728\) −0.0494838 −0.00183399
\(729\) 1.00000 0.0370370
\(730\) −32.9598 −1.21990
\(731\) 41.8353 1.54733
\(732\) 34.9507 1.29182
\(733\) 13.4529 0.496896 0.248448 0.968645i \(-0.420080\pi\)
0.248448 + 0.968645i \(0.420080\pi\)
\(734\) 30.8269 1.13784
\(735\) −10.6191 −0.391692
\(736\) 30.1908 1.11285
\(737\) −56.3888 −2.07711
\(738\) 16.5290 0.608442
\(739\) 22.6655 0.833764 0.416882 0.908961i \(-0.363123\pi\)
0.416882 + 0.908961i \(0.363123\pi\)
\(740\) 34.3046 1.26106
\(741\) −0.00410423 −0.000150773 0
\(742\) −0.616411 −0.0226292
\(743\) 12.7971 0.469479 0.234740 0.972058i \(-0.424576\pi\)
0.234740 + 0.972058i \(0.424576\pi\)
\(744\) 6.00749 0.220245
\(745\) 29.9584 1.09759
\(746\) −78.6091 −2.87808
\(747\) 6.64959 0.243296
\(748\) −90.3226 −3.30252
\(749\) 0.180602 0.00659904
\(750\) 25.8248 0.942989
\(751\) 15.7404 0.574375 0.287187 0.957874i \(-0.407280\pi\)
0.287187 + 0.957874i \(0.407280\pi\)
\(752\) −2.59208 −0.0945236
\(753\) 15.7111 0.572544
\(754\) 9.03190 0.328923
\(755\) 26.0857 0.949357
\(756\) 0.140538 0.00511131
\(757\) −31.9693 −1.16195 −0.580973 0.813923i \(-0.697328\pi\)
−0.580973 + 0.813923i \(0.697328\pi\)
\(758\) −12.6645 −0.459997
\(759\) 27.8964 1.01258
\(760\) 0.0236159 0.000856639 0
\(761\) 49.4640 1.79307 0.896534 0.442976i \(-0.146077\pi\)
0.896534 + 0.442976i \(0.146077\pi\)
\(762\) −25.8282 −0.935656
\(763\) −0.0300110 −0.00108647
\(764\) 56.5892 2.04732
\(765\) −7.23440 −0.261560
\(766\) 63.8606 2.30738
\(767\) 0.107214 0.00387127
\(768\) −5.65297 −0.203984
\(769\) 10.8605 0.391640 0.195820 0.980640i \(-0.437263\pi\)
0.195820 + 0.980640i \(0.437263\pi\)
\(770\) −1.07101 −0.0385965
\(771\) −0.410524 −0.0147847
\(772\) 51.1389 1.84053
\(773\) −39.5604 −1.42289 −0.711444 0.702743i \(-0.751958\pi\)
−0.711444 + 0.702743i \(0.751958\pi\)
\(774\) 19.4022 0.697396
\(775\) 8.25140 0.296399
\(776\) −23.9010 −0.857995
\(777\) 0.380861 0.0136633
\(778\) 7.73535 0.277326
\(779\) 0.0592488 0.00212281
\(780\) 2.26979 0.0812717
\(781\) 1.60935 0.0575872
\(782\) 44.8204 1.60277
\(783\) −7.88822 −0.281902
\(784\) 10.0406 0.358594
\(785\) 25.9645 0.926714
\(786\) −0.936868 −0.0334170
\(787\) −15.1489 −0.540000 −0.270000 0.962860i \(-0.587024\pi\)
−0.270000 + 0.962860i \(0.587024\pi\)
\(788\) −12.7171 −0.453029
\(789\) 10.6161 0.377944
\(790\) −55.8802 −1.98813
\(791\) −0.760297 −0.0270330
\(792\) −12.8817 −0.457731
\(793\) 6.26705 0.222550
\(794\) −17.2160 −0.610972
\(795\) 8.69488 0.308376
\(796\) −20.9822 −0.743695
\(797\) −47.6030 −1.68618 −0.843092 0.537769i \(-0.819267\pi\)
−0.843092 + 0.537769i \(0.819267\pi\)
\(798\) 0.000852607 0 3.01820e−5 0
\(799\) −8.61201 −0.304671
\(800\) −19.1484 −0.677000
\(801\) 14.6852 0.518876
\(802\) 69.4195 2.45129
\(803\) 64.4443 2.27419
\(804\) −24.8258 −0.875539
\(805\) 0.314013 0.0110675
\(806\) 3.50293 0.123385
\(807\) −14.4471 −0.508561
\(808\) −22.1180 −0.778109
\(809\) 19.4279 0.683049 0.341524 0.939873i \(-0.389057\pi\)
0.341524 + 0.939873i \(0.389057\pi\)
\(810\) −3.35514 −0.117888
\(811\) −25.0850 −0.880854 −0.440427 0.897788i \(-0.645173\pi\)
−0.440427 + 0.897788i \(0.645173\pi\)
\(812\) −1.10859 −0.0389040
\(813\) 23.7878 0.834275
\(814\) −113.521 −3.97892
\(815\) 16.0948 0.563777
\(816\) 6.84030 0.239458
\(817\) 0.0695475 0.00243316
\(818\) −5.26582 −0.184115
\(819\) 0.0252000 0.000880558 0
\(820\) −32.7668 −1.14427
\(821\) 28.4946 0.994468 0.497234 0.867617i \(-0.334349\pi\)
0.497234 + 0.867617i \(0.334349\pi\)
\(822\) 24.5727 0.857073
\(823\) 43.0968 1.50226 0.751130 0.660154i \(-0.229509\pi\)
0.751130 + 0.660154i \(0.229509\pi\)
\(824\) −3.95698 −0.137848
\(825\) −17.6932 −0.615999
\(826\) −0.0222724 −0.000774957 0
\(827\) −6.73989 −0.234369 −0.117185 0.993110i \(-0.537387\pi\)
−0.117185 + 0.993110i \(0.537387\pi\)
\(828\) 12.2817 0.426819
\(829\) −20.1494 −0.699816 −0.349908 0.936784i \(-0.613787\pi\)
−0.349908 + 0.936784i \(0.613787\pi\)
\(830\) −22.3103 −0.774401
\(831\) 16.6659 0.578133
\(832\) −6.64283 −0.230299
\(833\) 33.3592 1.15583
\(834\) 11.0523 0.382711
\(835\) −13.8775 −0.480252
\(836\) −0.150154 −0.00519317
\(837\) −3.05936 −0.105747
\(838\) −3.96512 −0.136973
\(839\) −30.7280 −1.06085 −0.530423 0.847733i \(-0.677967\pi\)
−0.530423 + 0.847733i \(0.677967\pi\)
\(840\) −0.145002 −0.00500303
\(841\) 33.2240 1.14565
\(842\) −18.0028 −0.620417
\(843\) −21.2038 −0.730297
\(844\) 74.7731 2.57380
\(845\) −19.3209 −0.664660
\(846\) −3.99404 −0.137318
\(847\) 1.55882 0.0535617
\(848\) −8.22121 −0.282318
\(849\) 21.0479 0.722362
\(850\) −28.4272 −0.975046
\(851\) 33.2838 1.14095
\(852\) 0.708536 0.0242740
\(853\) −42.4080 −1.45202 −0.726012 0.687682i \(-0.758628\pi\)
−0.726012 + 0.687682i \(0.758628\pi\)
\(854\) −1.30191 −0.0445504
\(855\) −0.0120266 −0.000411300 0
\(856\) −7.28807 −0.249101
\(857\) 1.17247 0.0400507 0.0200253 0.999799i \(-0.493625\pi\)
0.0200253 + 0.999799i \(0.493625\pi\)
\(858\) −7.51123 −0.256429
\(859\) −3.43890 −0.117334 −0.0586670 0.998278i \(-0.518685\pi\)
−0.0586670 + 0.998278i \(0.518685\pi\)
\(860\) −38.4624 −1.31156
\(861\) −0.363787 −0.0123978
\(862\) −4.38425 −0.149328
\(863\) −43.5007 −1.48078 −0.740391 0.672176i \(-0.765360\pi\)
−0.740391 + 0.672176i \(0.765360\pi\)
\(864\) 7.09965 0.241535
\(865\) 30.2008 1.02686
\(866\) −15.0107 −0.510083
\(867\) 5.72637 0.194478
\(868\) −0.429956 −0.0145936
\(869\) 109.259 3.70637
\(870\) 26.4661 0.897283
\(871\) −4.45154 −0.150835
\(872\) 1.21107 0.0410121
\(873\) 12.1718 0.411952
\(874\) 0.0745101 0.00252034
\(875\) −0.568378 −0.0192147
\(876\) 28.3723 0.958612
\(877\) 19.9045 0.672128 0.336064 0.941839i \(-0.390904\pi\)
0.336064 + 0.941839i \(0.390904\pi\)
\(878\) −64.3743 −2.17253
\(879\) 14.3585 0.484302
\(880\) −14.2843 −0.481523
\(881\) −18.8910 −0.636454 −0.318227 0.948014i \(-0.603087\pi\)
−0.318227 + 0.948014i \(0.603087\pi\)
\(882\) 15.4712 0.520942
\(883\) −44.9266 −1.51190 −0.755950 0.654630i \(-0.772825\pi\)
−0.755950 + 0.654630i \(0.772825\pi\)
\(884\) −7.13040 −0.239821
\(885\) 0.314167 0.0105606
\(886\) 32.5191 1.09250
\(887\) −2.15229 −0.0722670 −0.0361335 0.999347i \(-0.511504\pi\)
−0.0361335 + 0.999347i \(0.511504\pi\)
\(888\) −15.3694 −0.515763
\(889\) 0.568451 0.0190652
\(890\) −49.2708 −1.65156
\(891\) 6.56010 0.219772
\(892\) −75.8948 −2.54114
\(893\) −0.0143167 −0.000479091 0
\(894\) −43.6468 −1.45977
\(895\) −30.1577 −1.00806
\(896\) 0.689034 0.0230190
\(897\) 2.20225 0.0735309
\(898\) 55.6556 1.85725
\(899\) 24.1329 0.804877
\(900\) −7.78964 −0.259655
\(901\) −27.3144 −0.909973
\(902\) 108.432 3.61040
\(903\) −0.427021 −0.0142104
\(904\) 30.6813 1.02044
\(905\) 0.138768 0.00461281
\(906\) −38.0048 −1.26262
\(907\) 7.25645 0.240946 0.120473 0.992717i \(-0.461559\pi\)
0.120473 + 0.992717i \(0.461559\pi\)
\(908\) 15.6436 0.519151
\(909\) 11.2638 0.373596
\(910\) −0.0845494 −0.00280278
\(911\) 15.6873 0.519742 0.259871 0.965643i \(-0.416320\pi\)
0.259871 + 0.965643i \(0.416320\pi\)
\(912\) 0.0113714 0.000376545 0
\(913\) 43.6220 1.44368
\(914\) 13.4425 0.444639
\(915\) 18.3643 0.607104
\(916\) 49.9504 1.65041
\(917\) 0.0206195 0.000680916 0
\(918\) 10.5399 0.347869
\(919\) −13.7237 −0.452704 −0.226352 0.974046i \(-0.572680\pi\)
−0.226352 + 0.974046i \(0.572680\pi\)
\(920\) −12.6718 −0.417777
\(921\) −15.4896 −0.510400
\(922\) 25.5293 0.840764
\(923\) 0.127048 0.00418185
\(924\) 0.921942 0.0303297
\(925\) −21.1101 −0.694097
\(926\) 31.4324 1.03293
\(927\) 2.01512 0.0661853
\(928\) −56.0035 −1.83841
\(929\) −45.0360 −1.47758 −0.738792 0.673934i \(-0.764603\pi\)
−0.738792 + 0.673934i \(0.764603\pi\)
\(930\) 10.2646 0.336589
\(931\) 0.0554569 0.00181753
\(932\) −19.8401 −0.649885
\(933\) −4.07764 −0.133496
\(934\) −50.5988 −1.65564
\(935\) −47.4584 −1.55206
\(936\) −1.01693 −0.0332394
\(937\) 17.3038 0.565291 0.282646 0.959224i \(-0.408788\pi\)
0.282646 + 0.959224i \(0.408788\pi\)
\(938\) 0.924757 0.0301944
\(939\) −16.5977 −0.541644
\(940\) 7.91768 0.258246
\(941\) −42.0530 −1.37089 −0.685445 0.728125i \(-0.740392\pi\)
−0.685445 + 0.728125i \(0.740392\pi\)
\(942\) −37.8282 −1.23251
\(943\) −31.7917 −1.03528
\(944\) −0.297052 −0.00966822
\(945\) 0.0738431 0.00240212
\(946\) 127.280 4.13823
\(947\) 45.1348 1.46668 0.733341 0.679861i \(-0.237960\pi\)
0.733341 + 0.679861i \(0.237960\pi\)
\(948\) 48.1026 1.56230
\(949\) 5.08747 0.165146
\(950\) −0.0472578 −0.00153325
\(951\) 9.72846 0.315467
\(952\) 0.455512 0.0147632
\(953\) 26.2750 0.851131 0.425565 0.904928i \(-0.360075\pi\)
0.425565 + 0.904928i \(0.360075\pi\)
\(954\) −12.6677 −0.410133
\(955\) 29.7338 0.962163
\(956\) −13.7927 −0.446087
\(957\) −51.7475 −1.67276
\(958\) 69.9489 2.25995
\(959\) −0.540821 −0.0174640
\(960\) −19.4654 −0.628243
\(961\) −21.6403 −0.698075
\(962\) −8.96179 −0.288940
\(963\) 3.71150 0.119601
\(964\) 40.9099 1.31762
\(965\) 26.8700 0.864977
\(966\) −0.457491 −0.0147195
\(967\) −35.7448 −1.14948 −0.574738 0.818337i \(-0.694896\pi\)
−0.574738 + 0.818337i \(0.694896\pi\)
\(968\) −62.9052 −2.02185
\(969\) 0.0377806 0.00121369
\(970\) −40.8379 −1.31123
\(971\) −3.11135 −0.0998478 −0.0499239 0.998753i \(-0.515898\pi\)
−0.0499239 + 0.998753i \(0.515898\pi\)
\(972\) 2.88816 0.0926377
\(973\) −0.243251 −0.00779825
\(974\) 53.7933 1.72365
\(975\) −1.39677 −0.0447324
\(976\) −17.3638 −0.555802
\(977\) 24.5561 0.785621 0.392810 0.919620i \(-0.371503\pi\)
0.392810 + 0.919620i \(0.371503\pi\)
\(978\) −23.4488 −0.749811
\(979\) 96.3363 3.07892
\(980\) −30.6697 −0.979708
\(981\) −0.616748 −0.0196913
\(982\) 61.0818 1.94920
\(983\) 56.7505 1.81006 0.905030 0.425347i \(-0.139848\pi\)
0.905030 + 0.425347i \(0.139848\pi\)
\(984\) 14.6804 0.467994
\(985\) −6.68199 −0.212906
\(986\) −83.1412 −2.64776
\(987\) 0.0879046 0.00279803
\(988\) −0.0118537 −0.000377116 0
\(989\) −37.3178 −1.18664
\(990\) −22.0100 −0.699525
\(991\) 31.4474 0.998960 0.499480 0.866325i \(-0.333524\pi\)
0.499480 + 0.866325i \(0.333524\pi\)
\(992\) −21.7204 −0.689623
\(993\) 4.23416 0.134367
\(994\) −0.0263928 −0.000837129 0
\(995\) −11.0247 −0.349507
\(996\) 19.2051 0.608536
\(997\) 25.5631 0.809591 0.404795 0.914407i \(-0.367343\pi\)
0.404795 + 0.914407i \(0.367343\pi\)
\(998\) 49.3587 1.56242
\(999\) 7.82698 0.247635
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 \(a_p\))