Properties

Label 8023.2.a.c.1.18
Level 8023
Weight 2
Character 8023.1
Self dual Yes
Analytic conductor 64.064
Analytic rank 1
Dimension 158
CM No

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Newspace parameters

Level: \( N \) = \( 8023 = 71 \cdot 113 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0639775417\)
Analytic rank: \(1\)
Dimension: \(158\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 8023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.43745 q^{2}\) \(-0.327529 q^{3}\) \(+3.94116 q^{4}\) \(-2.07610 q^{5}\) \(+0.798335 q^{6}\) \(-0.184041 q^{7}\) \(-4.73147 q^{8}\) \(-2.89272 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.43745 q^{2}\) \(-0.327529 q^{3}\) \(+3.94116 q^{4}\) \(-2.07610 q^{5}\) \(+0.798335 q^{6}\) \(-0.184041 q^{7}\) \(-4.73147 q^{8}\) \(-2.89272 q^{9}\) \(+5.06038 q^{10}\) \(+6.19257 q^{11}\) \(-1.29084 q^{12}\) \(+5.93759 q^{13}\) \(+0.448592 q^{14}\) \(+0.679982 q^{15}\) \(+3.65040 q^{16}\) \(-1.22386 q^{17}\) \(+7.05087 q^{18}\) \(+6.79540 q^{19}\) \(-8.18222 q^{20}\) \(+0.0602789 q^{21}\) \(-15.0941 q^{22}\) \(+4.78804 q^{23}\) \(+1.54969 q^{24}\) \(-0.689820 q^{25}\) \(-14.4726 q^{26}\) \(+1.93004 q^{27}\) \(-0.725336 q^{28}\) \(-1.27393 q^{29}\) \(-1.65742 q^{30}\) \(-3.43925 q^{31}\) \(+0.565277 q^{32}\) \(-2.02824 q^{33}\) \(+2.98309 q^{34}\) \(+0.382088 q^{35}\) \(-11.4007 q^{36}\) \(+6.19766 q^{37}\) \(-16.5634 q^{38}\) \(-1.94473 q^{39}\) \(+9.82299 q^{40}\) \(-10.3441 q^{41}\) \(-0.146927 q^{42}\) \(-4.48759 q^{43}\) \(+24.4059 q^{44}\) \(+6.00558 q^{45}\) \(-11.6706 q^{46}\) \(-11.8515 q^{47}\) \(-1.19561 q^{48}\) \(-6.96613 q^{49}\) \(+1.68140 q^{50}\) \(+0.400848 q^{51}\) \(+23.4010 q^{52}\) \(-12.2832 q^{53}\) \(-4.70437 q^{54}\) \(-12.8564 q^{55}\) \(+0.870786 q^{56}\) \(-2.22569 q^{57}\) \(+3.10514 q^{58}\) \(+0.000567193 q^{59}\) \(+2.67991 q^{60}\) \(-3.47475 q^{61}\) \(+8.38300 q^{62}\) \(+0.532381 q^{63}\) \(-8.67863 q^{64}\) \(-12.3270 q^{65}\) \(+4.94374 q^{66}\) \(+0.649522 q^{67}\) \(-4.82341 q^{68}\) \(-1.56822 q^{69}\) \(-0.931320 q^{70}\) \(-1.00000 q^{71}\) \(+13.6868 q^{72}\) \(+14.5453 q^{73}\) \(-15.1065 q^{74}\) \(+0.225936 q^{75}\) \(+26.7817 q^{76}\) \(-1.13969 q^{77}\) \(+4.74019 q^{78}\) \(-10.4879 q^{79}\) \(-7.57858 q^{80}\) \(+8.04603 q^{81}\) \(+25.2132 q^{82}\) \(-13.4124 q^{83}\) \(+0.237569 q^{84}\) \(+2.54084 q^{85}\) \(+10.9383 q^{86}\) \(+0.417250 q^{87}\) \(-29.2999 q^{88}\) \(-0.0342642 q^{89}\) \(-14.6383 q^{90}\) \(-1.09276 q^{91}\) \(+18.8704 q^{92}\) \(+1.12645 q^{93}\) \(+28.8874 q^{94}\) \(-14.1079 q^{95}\) \(-0.185145 q^{96}\) \(-4.90882 q^{97}\) \(+16.9796 q^{98}\) \(-17.9134 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 46q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 27q^{14} \) \(\mathstrut -\mathstrut 41q^{15} \) \(\mathstrut +\mathstrut 150q^{16} \) \(\mathstrut -\mathstrut 137q^{17} \) \(\mathstrut -\mathstrut 67q^{18} \) \(\mathstrut -\mathstrut 42q^{19} \) \(\mathstrut -\mathstrut 66q^{20} \) \(\mathstrut -\mathstrut 46q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 48q^{24} \) \(\mathstrut +\mathstrut 129q^{25} \) \(\mathstrut -\mathstrut 67q^{26} \) \(\mathstrut -\mathstrut 89q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 79q^{29} \) \(\mathstrut -\mathstrut 11q^{30} \) \(\mathstrut +\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 147q^{32} \) \(\mathstrut -\mathstrut 112q^{33} \) \(\mathstrut -\mathstrut 28q^{34} \) \(\mathstrut -\mathstrut 53q^{35} \) \(\mathstrut +\mathstrut 141q^{36} \) \(\mathstrut -\mathstrut 60q^{37} \) \(\mathstrut -\mathstrut 53q^{38} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 48q^{40} \) \(\mathstrut -\mathstrut 128q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 63q^{43} \) \(\mathstrut -\mathstrut 88q^{45} \) \(\mathstrut -\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 92q^{47} \) \(\mathstrut -\mathstrut 131q^{48} \) \(\mathstrut +\mathstrut 122q^{49} \) \(\mathstrut -\mathstrut 116q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 89q^{52} \) \(\mathstrut -\mathstrut 94q^{53} \) \(\mathstrut -\mathstrut 71q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 104q^{56} \) \(\mathstrut -\mathstrut 93q^{57} \) \(\mathstrut -\mathstrut 65q^{58} \) \(\mathstrut -\mathstrut 54q^{59} \) \(\mathstrut -\mathstrut 12q^{60} \) \(\mathstrut +\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 97q^{62} \) \(\mathstrut -\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 163q^{64} \) \(\mathstrut -\mathstrut 163q^{65} \) \(\mathstrut -\mathstrut 65q^{66} \) \(\mathstrut -\mathstrut 35q^{67} \) \(\mathstrut -\mathstrut 217q^{68} \) \(\mathstrut -\mathstrut 46q^{69} \) \(\mathstrut -\mathstrut 79q^{70} \) \(\mathstrut -\mathstrut 158q^{71} \) \(\mathstrut -\mathstrut 99q^{72} \) \(\mathstrut -\mathstrut 165q^{73} \) \(\mathstrut -\mathstrut 94q^{75} \) \(\mathstrut -\mathstrut 93q^{76} \) \(\mathstrut -\mathstrut 140q^{77} \) \(\mathstrut +\mathstrut 25q^{78} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut 134q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 158q^{83} \) \(\mathstrut -\mathstrut 160q^{84} \) \(\mathstrut +\mathstrut 23q^{85} \) \(\mathstrut -\mathstrut 122q^{86} \) \(\mathstrut -\mathstrut 71q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 251q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut -\mathstrut 57q^{91} \) \(\mathstrut -\mathstrut 58q^{92} \) \(\mathstrut -\mathstrut 52q^{93} \) \(\mathstrut -\mathstrut 64q^{94} \) \(\mathstrut -\mathstrut 84q^{95} \) \(\mathstrut -\mathstrut 98q^{96} \) \(\mathstrut -\mathstrut 48q^{97} \) \(\mathstrut -\mathstrut 84q^{98} \) \(\mathstrut +\mathstrut 85q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.43745 −1.72354 −0.861768 0.507302i \(-0.830643\pi\)
−0.861768 + 0.507302i \(0.830643\pi\)
\(3\) −0.327529 −0.189099 −0.0945495 0.995520i \(-0.530141\pi\)
−0.0945495 + 0.995520i \(0.530141\pi\)
\(4\) 3.94116 1.97058
\(5\) −2.07610 −0.928459 −0.464229 0.885715i \(-0.653669\pi\)
−0.464229 + 0.885715i \(0.653669\pi\)
\(6\) 0.798335 0.325919
\(7\) −0.184041 −0.0695611 −0.0347806 0.999395i \(-0.511073\pi\)
−0.0347806 + 0.999395i \(0.511073\pi\)
\(8\) −4.73147 −1.67283
\(9\) −2.89272 −0.964242
\(10\) 5.06038 1.60023
\(11\) 6.19257 1.86713 0.933565 0.358409i \(-0.116681\pi\)
0.933565 + 0.358409i \(0.116681\pi\)
\(12\) −1.29084 −0.372634
\(13\) 5.93759 1.64679 0.823396 0.567468i \(-0.192077\pi\)
0.823396 + 0.567468i \(0.192077\pi\)
\(14\) 0.448592 0.119891
\(15\) 0.679982 0.175571
\(16\) 3.65040 0.912600
\(17\) −1.22386 −0.296829 −0.148414 0.988925i \(-0.547417\pi\)
−0.148414 + 0.988925i \(0.547417\pi\)
\(18\) 7.05087 1.66191
\(19\) 6.79540 1.55897 0.779485 0.626420i \(-0.215481\pi\)
0.779485 + 0.626420i \(0.215481\pi\)
\(20\) −8.18222 −1.82960
\(21\) 0.0602789 0.0131539
\(22\) −15.0941 −3.21806
\(23\) 4.78804 0.998375 0.499187 0.866494i \(-0.333632\pi\)
0.499187 + 0.866494i \(0.333632\pi\)
\(24\) 1.54969 0.316330
\(25\) −0.689820 −0.137964
\(26\) −14.4726 −2.83830
\(27\) 1.93004 0.371436
\(28\) −0.725336 −0.137076
\(29\) −1.27393 −0.236563 −0.118282 0.992980i \(-0.537739\pi\)
−0.118282 + 0.992980i \(0.537739\pi\)
\(30\) −1.65742 −0.302602
\(31\) −3.43925 −0.617708 −0.308854 0.951110i \(-0.599945\pi\)
−0.308854 + 0.951110i \(0.599945\pi\)
\(32\) 0.565277 0.0999278
\(33\) −2.02824 −0.353072
\(34\) 2.98309 0.511595
\(35\) 0.382088 0.0645846
\(36\) −11.4007 −1.90011
\(37\) 6.19766 1.01889 0.509444 0.860504i \(-0.329851\pi\)
0.509444 + 0.860504i \(0.329851\pi\)
\(38\) −16.5634 −2.68694
\(39\) −1.94473 −0.311406
\(40\) 9.82299 1.55315
\(41\) −10.3441 −1.61548 −0.807738 0.589541i \(-0.799308\pi\)
−0.807738 + 0.589541i \(0.799308\pi\)
\(42\) −0.146927 −0.0226713
\(43\) −4.48759 −0.684351 −0.342176 0.939636i \(-0.611164\pi\)
−0.342176 + 0.939636i \(0.611164\pi\)
\(44\) 24.4059 3.67932
\(45\) 6.00558 0.895259
\(46\) −11.6706 −1.72073
\(47\) −11.8515 −1.72872 −0.864359 0.502876i \(-0.832275\pi\)
−0.864359 + 0.502876i \(0.832275\pi\)
\(48\) −1.19561 −0.172572
\(49\) −6.96613 −0.995161
\(50\) 1.68140 0.237786
\(51\) 0.400848 0.0561300
\(52\) 23.4010 3.24513
\(53\) −12.2832 −1.68723 −0.843615 0.536949i \(-0.819577\pi\)
−0.843615 + 0.536949i \(0.819577\pi\)
\(54\) −4.70437 −0.640183
\(55\) −12.8564 −1.73355
\(56\) 0.870786 0.116364
\(57\) −2.22569 −0.294800
\(58\) 3.10514 0.407725
\(59\) 0.000567193 0 7.38422e−5 0 3.69211e−5 1.00000i \(-0.499988\pi\)
3.69211e−5 1.00000i \(0.499988\pi\)
\(60\) 2.67991 0.345976
\(61\) −3.47475 −0.444896 −0.222448 0.974945i \(-0.571405\pi\)
−0.222448 + 0.974945i \(0.571405\pi\)
\(62\) 8.38300 1.06464
\(63\) 0.532381 0.0670737
\(64\) −8.67863 −1.08483
\(65\) −12.3270 −1.52898
\(66\) 4.94374 0.608533
\(67\) 0.649522 0.0793517 0.0396759 0.999213i \(-0.487367\pi\)
0.0396759 + 0.999213i \(0.487367\pi\)
\(68\) −4.82341 −0.584924
\(69\) −1.56822 −0.188792
\(70\) −0.931320 −0.111314
\(71\) −1.00000 −0.118678
\(72\) 13.6868 1.61301
\(73\) 14.5453 1.70239 0.851197 0.524846i \(-0.175877\pi\)
0.851197 + 0.524846i \(0.175877\pi\)
\(74\) −15.1065 −1.75609
\(75\) 0.225936 0.0260888
\(76\) 26.7817 3.07207
\(77\) −1.13969 −0.129880
\(78\) 4.74019 0.536720
\(79\) −10.4879 −1.17999 −0.589993 0.807408i \(-0.700870\pi\)
−0.589993 + 0.807408i \(0.700870\pi\)
\(80\) −7.57858 −0.847311
\(81\) 8.04603 0.894003
\(82\) 25.2132 2.78433
\(83\) −13.4124 −1.47220 −0.736102 0.676871i \(-0.763336\pi\)
−0.736102 + 0.676871i \(0.763336\pi\)
\(84\) 0.237569 0.0259209
\(85\) 2.54084 0.275593
\(86\) 10.9383 1.17950
\(87\) 0.417250 0.0447339
\(88\) −29.2999 −3.12338
\(89\) −0.0342642 −0.00363200 −0.00181600 0.999998i \(-0.500578\pi\)
−0.00181600 + 0.999998i \(0.500578\pi\)
\(90\) −14.6383 −1.54301
\(91\) −1.09276 −0.114553
\(92\) 18.8704 1.96737
\(93\) 1.12645 0.116808
\(94\) 28.8874 2.97951
\(95\) −14.1079 −1.44744
\(96\) −0.185145 −0.0188962
\(97\) −4.90882 −0.498415 −0.249208 0.968450i \(-0.580170\pi\)
−0.249208 + 0.968450i \(0.580170\pi\)
\(98\) 16.9796 1.71520
\(99\) −17.9134 −1.80036
\(100\) −2.71869 −0.271869
\(101\) −8.16140 −0.812089 −0.406045 0.913853i \(-0.633092\pi\)
−0.406045 + 0.913853i \(0.633092\pi\)
\(102\) −0.977047 −0.0967421
\(103\) 3.00531 0.296122 0.148061 0.988978i \(-0.452697\pi\)
0.148061 + 0.988978i \(0.452697\pi\)
\(104\) −28.0935 −2.75480
\(105\) −0.125145 −0.0122129
\(106\) 29.9397 2.90800
\(107\) 9.98915 0.965688 0.482844 0.875706i \(-0.339604\pi\)
0.482844 + 0.875706i \(0.339604\pi\)
\(108\) 7.60658 0.731944
\(109\) −3.20416 −0.306903 −0.153452 0.988156i \(-0.549039\pi\)
−0.153452 + 0.988156i \(0.549039\pi\)
\(110\) 31.3367 2.98784
\(111\) −2.02991 −0.192671
\(112\) −0.671825 −0.0634815
\(113\) −1.00000 −0.0940721
\(114\) 5.42500 0.508098
\(115\) −9.94043 −0.926950
\(116\) −5.02077 −0.466166
\(117\) −17.1758 −1.58790
\(118\) −0.00138250 −0.000127270 0
\(119\) 0.225240 0.0206477
\(120\) −3.21731 −0.293699
\(121\) 27.3479 2.48617
\(122\) 8.46952 0.766794
\(123\) 3.38799 0.305485
\(124\) −13.5546 −1.21724
\(125\) 11.8126 1.05655
\(126\) −1.29765 −0.115604
\(127\) −6.73100 −0.597280 −0.298640 0.954366i \(-0.596533\pi\)
−0.298640 + 0.954366i \(0.596533\pi\)
\(128\) 20.0232 1.76981
\(129\) 1.46982 0.129410
\(130\) 30.0465 2.63525
\(131\) 12.1022 1.05738 0.528688 0.848816i \(-0.322684\pi\)
0.528688 + 0.848816i \(0.322684\pi\)
\(132\) −7.99363 −0.695756
\(133\) −1.25063 −0.108444
\(134\) −1.58318 −0.136766
\(135\) −4.00695 −0.344863
\(136\) 5.79063 0.496543
\(137\) −18.3870 −1.57091 −0.785455 0.618919i \(-0.787571\pi\)
−0.785455 + 0.618919i \(0.787571\pi\)
\(138\) 3.82246 0.325389
\(139\) 17.1306 1.45300 0.726499 0.687168i \(-0.241146\pi\)
0.726499 + 0.687168i \(0.241146\pi\)
\(140\) 1.50587 0.127269
\(141\) 3.88171 0.326899
\(142\) 2.43745 0.204546
\(143\) 36.7689 3.07477
\(144\) −10.5596 −0.879967
\(145\) 2.64481 0.219639
\(146\) −35.4533 −2.93414
\(147\) 2.28161 0.188184
\(148\) 24.4259 2.00780
\(149\) 20.7798 1.70235 0.851173 0.524885i \(-0.175892\pi\)
0.851173 + 0.524885i \(0.175892\pi\)
\(150\) −0.550707 −0.0449651
\(151\) 3.33021 0.271008 0.135504 0.990777i \(-0.456735\pi\)
0.135504 + 0.990777i \(0.456735\pi\)
\(152\) −32.1522 −2.60789
\(153\) 3.54028 0.286215
\(154\) 2.77793 0.223852
\(155\) 7.14022 0.573516
\(156\) −7.66449 −0.613651
\(157\) −4.18589 −0.334071 −0.167035 0.985951i \(-0.553419\pi\)
−0.167035 + 0.985951i \(0.553419\pi\)
\(158\) 25.5638 2.03375
\(159\) 4.02311 0.319053
\(160\) −1.17357 −0.0927788
\(161\) −0.881197 −0.0694481
\(162\) −19.6118 −1.54085
\(163\) −9.81851 −0.769045 −0.384523 0.923116i \(-0.625634\pi\)
−0.384523 + 0.923116i \(0.625634\pi\)
\(164\) −40.7677 −3.18342
\(165\) 4.21083 0.327813
\(166\) 32.6921 2.53740
\(167\) 18.9979 1.47010 0.735051 0.678012i \(-0.237158\pi\)
0.735051 + 0.678012i \(0.237158\pi\)
\(168\) −0.285208 −0.0220042
\(169\) 22.2550 1.71192
\(170\) −6.19318 −0.474995
\(171\) −19.6572 −1.50322
\(172\) −17.6863 −1.34857
\(173\) −22.4767 −1.70887 −0.854436 0.519557i \(-0.826097\pi\)
−0.854436 + 0.519557i \(0.826097\pi\)
\(174\) −1.01702 −0.0771004
\(175\) 0.126955 0.00959693
\(176\) 22.6053 1.70394
\(177\) −0.000185772 0 −1.39635e−5 0
\(178\) 0.0835172 0.00625988
\(179\) −4.58668 −0.342824 −0.171412 0.985199i \(-0.554833\pi\)
−0.171412 + 0.985199i \(0.554833\pi\)
\(180\) 23.6689 1.76418
\(181\) −7.91386 −0.588233 −0.294116 0.955770i \(-0.595025\pi\)
−0.294116 + 0.955770i \(0.595025\pi\)
\(182\) 2.66355 0.197436
\(183\) 1.13808 0.0841293
\(184\) −22.6544 −1.67011
\(185\) −12.8669 −0.945997
\(186\) −2.74567 −0.201323
\(187\) −7.57881 −0.554217
\(188\) −46.7086 −3.40657
\(189\) −0.355207 −0.0258375
\(190\) 34.3873 2.49472
\(191\) −0.843412 −0.0610271 −0.0305136 0.999534i \(-0.509714\pi\)
−0.0305136 + 0.999534i \(0.509714\pi\)
\(192\) 2.84250 0.205140
\(193\) −11.7935 −0.848914 −0.424457 0.905448i \(-0.639535\pi\)
−0.424457 + 0.905448i \(0.639535\pi\)
\(194\) 11.9650 0.859037
\(195\) 4.03745 0.289128
\(196\) −27.4546 −1.96104
\(197\) 13.5337 0.964237 0.482118 0.876106i \(-0.339868\pi\)
0.482118 + 0.876106i \(0.339868\pi\)
\(198\) 43.6630 3.10299
\(199\) −1.57055 −0.111333 −0.0556666 0.998449i \(-0.517728\pi\)
−0.0556666 + 0.998449i \(0.517728\pi\)
\(200\) 3.26386 0.230790
\(201\) −0.212737 −0.0150053
\(202\) 19.8930 1.39967
\(203\) 0.234456 0.0164556
\(204\) 1.57981 0.110608
\(205\) 21.4753 1.49990
\(206\) −7.32528 −0.510376
\(207\) −13.8505 −0.962674
\(208\) 21.6746 1.50286
\(209\) 42.0809 2.91080
\(210\) 0.305034 0.0210494
\(211\) −18.8975 −1.30096 −0.650479 0.759524i \(-0.725432\pi\)
−0.650479 + 0.759524i \(0.725432\pi\)
\(212\) −48.4101 −3.32482
\(213\) 0.327529 0.0224419
\(214\) −24.3480 −1.66440
\(215\) 9.31668 0.635392
\(216\) −9.13191 −0.621348
\(217\) 0.632964 0.0429684
\(218\) 7.80998 0.528959
\(219\) −4.76399 −0.321921
\(220\) −50.6690 −3.41610
\(221\) −7.26675 −0.488815
\(222\) 4.94781 0.332075
\(223\) 2.89326 0.193747 0.0968734 0.995297i \(-0.469116\pi\)
0.0968734 + 0.995297i \(0.469116\pi\)
\(224\) −0.104034 −0.00695109
\(225\) 1.99546 0.133031
\(226\) 2.43745 0.162137
\(227\) −19.3822 −1.28644 −0.643221 0.765680i \(-0.722402\pi\)
−0.643221 + 0.765680i \(0.722402\pi\)
\(228\) −8.77179 −0.580926
\(229\) 5.47946 0.362093 0.181047 0.983475i \(-0.442052\pi\)
0.181047 + 0.983475i \(0.442052\pi\)
\(230\) 24.2293 1.59763
\(231\) 0.373281 0.0245601
\(232\) 6.02757 0.395729
\(233\) −8.03005 −0.526066 −0.263033 0.964787i \(-0.584723\pi\)
−0.263033 + 0.964787i \(0.584723\pi\)
\(234\) 41.8652 2.73681
\(235\) 24.6048 1.60504
\(236\) 0.00223540 0.000145512 0
\(237\) 3.43511 0.223134
\(238\) −0.549011 −0.0355871
\(239\) 11.2863 0.730048 0.365024 0.930998i \(-0.381061\pi\)
0.365024 + 0.930998i \(0.381061\pi\)
\(240\) 2.48221 0.160226
\(241\) 9.04283 0.582500 0.291250 0.956647i \(-0.405929\pi\)
0.291250 + 0.956647i \(0.405929\pi\)
\(242\) −66.6591 −4.28501
\(243\) −8.42542 −0.540491
\(244\) −13.6945 −0.876702
\(245\) 14.4624 0.923966
\(246\) −8.25805 −0.526514
\(247\) 40.3483 2.56730
\(248\) 16.2727 1.03332
\(249\) 4.39296 0.278392
\(250\) −28.7927 −1.82101
\(251\) −18.1978 −1.14863 −0.574317 0.818633i \(-0.694732\pi\)
−0.574317 + 0.818633i \(0.694732\pi\)
\(252\) 2.09820 0.132174
\(253\) 29.6502 1.86409
\(254\) 16.4065 1.02943
\(255\) −0.832200 −0.0521144
\(256\) −31.4482 −1.96551
\(257\) −19.6031 −1.22281 −0.611404 0.791318i \(-0.709395\pi\)
−0.611404 + 0.791318i \(0.709395\pi\)
\(258\) −3.58260 −0.223043
\(259\) −1.14063 −0.0708751
\(260\) −48.5827 −3.01297
\(261\) 3.68514 0.228104
\(262\) −29.4985 −1.82243
\(263\) −26.8647 −1.65655 −0.828275 0.560322i \(-0.810677\pi\)
−0.828275 + 0.560322i \(0.810677\pi\)
\(264\) 9.59658 0.590628
\(265\) 25.5012 1.56652
\(266\) 3.04836 0.186907
\(267\) 0.0112225 0.000686807 0
\(268\) 2.55987 0.156369
\(269\) −12.7425 −0.776927 −0.388463 0.921464i \(-0.626994\pi\)
−0.388463 + 0.921464i \(0.626994\pi\)
\(270\) 9.76673 0.594384
\(271\) −7.91223 −0.480634 −0.240317 0.970694i \(-0.577251\pi\)
−0.240317 + 0.970694i \(0.577251\pi\)
\(272\) −4.46756 −0.270886
\(273\) 0.357911 0.0216618
\(274\) 44.8174 2.70752
\(275\) −4.27176 −0.257597
\(276\) −6.18060 −0.372028
\(277\) −3.35145 −0.201369 −0.100685 0.994918i \(-0.532103\pi\)
−0.100685 + 0.994918i \(0.532103\pi\)
\(278\) −41.7549 −2.50429
\(279\) 9.94880 0.595619
\(280\) −1.80784 −0.108039
\(281\) 24.3984 1.45549 0.727743 0.685850i \(-0.240569\pi\)
0.727743 + 0.685850i \(0.240569\pi\)
\(282\) −9.46146 −0.563422
\(283\) −2.71240 −0.161236 −0.0806178 0.996745i \(-0.525689\pi\)
−0.0806178 + 0.996745i \(0.525689\pi\)
\(284\) −3.94116 −0.233865
\(285\) 4.62075 0.273709
\(286\) −89.6224 −5.29948
\(287\) 1.90374 0.112374
\(288\) −1.63519 −0.0963545
\(289\) −15.5022 −0.911893
\(290\) −6.44658 −0.378556
\(291\) 1.60778 0.0942498
\(292\) 57.3252 3.35470
\(293\) −3.00508 −0.175559 −0.0877793 0.996140i \(-0.527977\pi\)
−0.0877793 + 0.996140i \(0.527977\pi\)
\(294\) −5.56130 −0.324342
\(295\) −0.00117755 −6.85595e−5 0
\(296\) −29.3240 −1.70442
\(297\) 11.9519 0.693519
\(298\) −50.6497 −2.93406
\(299\) 28.4294 1.64411
\(300\) 0.890449 0.0514101
\(301\) 0.825903 0.0476042
\(302\) −8.11721 −0.467093
\(303\) 2.67309 0.153565
\(304\) 24.8059 1.42272
\(305\) 7.21391 0.413068
\(306\) −8.62925 −0.493301
\(307\) −18.2840 −1.04353 −0.521763 0.853091i \(-0.674725\pi\)
−0.521763 + 0.853091i \(0.674725\pi\)
\(308\) −4.49169 −0.255938
\(309\) −0.984325 −0.0559963
\(310\) −17.4039 −0.988476
\(311\) −27.3112 −1.54868 −0.774339 0.632770i \(-0.781918\pi\)
−0.774339 + 0.632770i \(0.781918\pi\)
\(312\) 9.20144 0.520929
\(313\) −1.40525 −0.0794293 −0.0397147 0.999211i \(-0.512645\pi\)
−0.0397147 + 0.999211i \(0.512645\pi\)
\(314\) 10.2029 0.575783
\(315\) −1.10528 −0.0622752
\(316\) −41.3346 −2.32526
\(317\) −15.9962 −0.898435 −0.449217 0.893422i \(-0.648297\pi\)
−0.449217 + 0.893422i \(0.648297\pi\)
\(318\) −9.80612 −0.549900
\(319\) −7.88891 −0.441694
\(320\) 18.0177 1.00722
\(321\) −3.27174 −0.182610
\(322\) 2.14787 0.119696
\(323\) −8.31659 −0.462747
\(324\) 31.7107 1.76170
\(325\) −4.09587 −0.227198
\(326\) 23.9321 1.32548
\(327\) 1.04946 0.0580350
\(328\) 48.9428 2.70241
\(329\) 2.18116 0.120252
\(330\) −10.2637 −0.564998
\(331\) −27.7606 −1.52586 −0.762930 0.646481i \(-0.776240\pi\)
−0.762930 + 0.646481i \(0.776240\pi\)
\(332\) −52.8604 −2.90109
\(333\) −17.9281 −0.982455
\(334\) −46.3064 −2.53378
\(335\) −1.34847 −0.0736748
\(336\) 0.220042 0.0120043
\(337\) −19.6789 −1.07198 −0.535989 0.844225i \(-0.680061\pi\)
−0.535989 + 0.844225i \(0.680061\pi\)
\(338\) −54.2454 −2.95056
\(339\) 0.327529 0.0177889
\(340\) 10.0139 0.543078
\(341\) −21.2978 −1.15334
\(342\) 47.9134 2.59086
\(343\) 2.57035 0.138786
\(344\) 21.2329 1.14480
\(345\) 3.25578 0.175285
\(346\) 54.7858 2.94530
\(347\) 7.03330 0.377567 0.188784 0.982019i \(-0.439545\pi\)
0.188784 + 0.982019i \(0.439545\pi\)
\(348\) 1.64445 0.0881516
\(349\) 22.4973 1.20425 0.602127 0.798400i \(-0.294320\pi\)
0.602127 + 0.798400i \(0.294320\pi\)
\(350\) −0.309447 −0.0165407
\(351\) 11.4598 0.611677
\(352\) 3.50051 0.186578
\(353\) −26.2014 −1.39456 −0.697279 0.716800i \(-0.745606\pi\)
−0.697279 + 0.716800i \(0.745606\pi\)
\(354\) 0.000452810 0 2.40666e−5 0
\(355\) 2.07610 0.110188
\(356\) −0.135041 −0.00715714
\(357\) −0.0737727 −0.00390446
\(358\) 11.1798 0.590870
\(359\) −7.54083 −0.397990 −0.198995 0.980001i \(-0.563768\pi\)
−0.198995 + 0.980001i \(0.563768\pi\)
\(360\) −28.4152 −1.49761
\(361\) 27.1774 1.43039
\(362\) 19.2896 1.01384
\(363\) −8.95722 −0.470132
\(364\) −4.30675 −0.225735
\(365\) −30.1974 −1.58060
\(366\) −2.77401 −0.145000
\(367\) −15.4682 −0.807431 −0.403716 0.914885i \(-0.632281\pi\)
−0.403716 + 0.914885i \(0.632281\pi\)
\(368\) 17.4782 0.911116
\(369\) 29.9226 1.55771
\(370\) 31.3625 1.63046
\(371\) 2.26062 0.117366
\(372\) 4.43953 0.230179
\(373\) 19.9834 1.03470 0.517351 0.855773i \(-0.326918\pi\)
0.517351 + 0.855773i \(0.326918\pi\)
\(374\) 18.4730 0.955214
\(375\) −3.86897 −0.199793
\(376\) 56.0749 2.89184
\(377\) −7.56409 −0.389570
\(378\) 0.865799 0.0445319
\(379\) 8.52459 0.437879 0.218939 0.975738i \(-0.429740\pi\)
0.218939 + 0.975738i \(0.429740\pi\)
\(380\) −55.6015 −2.85229
\(381\) 2.20460 0.112945
\(382\) 2.05577 0.105182
\(383\) −23.9332 −1.22293 −0.611464 0.791272i \(-0.709419\pi\)
−0.611464 + 0.791272i \(0.709419\pi\)
\(384\) −6.55817 −0.334670
\(385\) 2.36610 0.120588
\(386\) 28.7460 1.46314
\(387\) 12.9814 0.659880
\(388\) −19.3464 −0.982166
\(389\) 0.337116 0.0170924 0.00854622 0.999963i \(-0.497280\pi\)
0.00854622 + 0.999963i \(0.497280\pi\)
\(390\) −9.84109 −0.498323
\(391\) −5.85987 −0.296346
\(392\) 32.9600 1.66473
\(393\) −3.96383 −0.199949
\(394\) −32.9877 −1.66190
\(395\) 21.7740 1.09557
\(396\) −70.5995 −3.54776
\(397\) 31.6081 1.58637 0.793183 0.608984i \(-0.208423\pi\)
0.793183 + 0.608984i \(0.208423\pi\)
\(398\) 3.82813 0.191887
\(399\) 0.409619 0.0205066
\(400\) −2.51812 −0.125906
\(401\) 5.59058 0.279180 0.139590 0.990209i \(-0.455422\pi\)
0.139590 + 0.990209i \(0.455422\pi\)
\(402\) 0.518536 0.0258622
\(403\) −20.4209 −1.01724
\(404\) −32.1653 −1.60029
\(405\) −16.7043 −0.830045
\(406\) −0.571475 −0.0283618
\(407\) 38.3794 1.90240
\(408\) −1.89660 −0.0938957
\(409\) 39.3861 1.94752 0.973759 0.227583i \(-0.0730823\pi\)
0.973759 + 0.227583i \(0.0730823\pi\)
\(410\) −52.3451 −2.58514
\(411\) 6.02228 0.297057
\(412\) 11.8444 0.583531
\(413\) −0.000104387 0 −5.13655e−6 0
\(414\) 33.7598 1.65920
\(415\) 27.8455 1.36688
\(416\) 3.35638 0.164560
\(417\) −5.61076 −0.274760
\(418\) −102.570 −5.01687
\(419\) −37.0310 −1.80908 −0.904541 0.426386i \(-0.859787\pi\)
−0.904541 + 0.426386i \(0.859787\pi\)
\(420\) −0.493215 −0.0240664
\(421\) 23.6758 1.15389 0.576943 0.816784i \(-0.304245\pi\)
0.576943 + 0.816784i \(0.304245\pi\)
\(422\) 46.0617 2.24225
\(423\) 34.2831 1.66690
\(424\) 58.1177 2.82244
\(425\) 0.844240 0.0409517
\(426\) −0.798335 −0.0386795
\(427\) 0.639498 0.0309475
\(428\) 39.3688 1.90296
\(429\) −12.0429 −0.581436
\(430\) −22.7089 −1.09512
\(431\) 1.75821 0.0846901 0.0423450 0.999103i \(-0.486517\pi\)
0.0423450 + 0.999103i \(0.486517\pi\)
\(432\) 7.04541 0.338972
\(433\) −21.8231 −1.04875 −0.524375 0.851487i \(-0.675701\pi\)
−0.524375 + 0.851487i \(0.675701\pi\)
\(434\) −1.54282 −0.0740577
\(435\) −0.866251 −0.0415335
\(436\) −12.6281 −0.604776
\(437\) 32.5366 1.55644
\(438\) 11.6120 0.554842
\(439\) 22.3437 1.06641 0.533204 0.845987i \(-0.320988\pi\)
0.533204 + 0.845987i \(0.320988\pi\)
\(440\) 60.8295 2.89993
\(441\) 20.1511 0.959576
\(442\) 17.7123 0.842490
\(443\) −39.5121 −1.87727 −0.938637 0.344906i \(-0.887911\pi\)
−0.938637 + 0.344906i \(0.887911\pi\)
\(444\) −8.00020 −0.379673
\(445\) 0.0711358 0.00337216
\(446\) −7.05216 −0.333930
\(447\) −6.80598 −0.321912
\(448\) 1.59723 0.0754619
\(449\) 13.9786 0.659690 0.329845 0.944035i \(-0.393003\pi\)
0.329845 + 0.944035i \(0.393003\pi\)
\(450\) −4.86383 −0.229283
\(451\) −64.0565 −3.01630
\(452\) −3.94116 −0.185376
\(453\) −1.09074 −0.0512474
\(454\) 47.2431 2.21723
\(455\) 2.26868 0.106357
\(456\) 10.5308 0.493149
\(457\) 32.9067 1.53931 0.769655 0.638460i \(-0.220428\pi\)
0.769655 + 0.638460i \(0.220428\pi\)
\(458\) −13.3559 −0.624081
\(459\) −2.36209 −0.110253
\(460\) −39.1768 −1.82663
\(461\) 25.5739 1.19109 0.595547 0.803320i \(-0.296935\pi\)
0.595547 + 0.803320i \(0.296935\pi\)
\(462\) −0.909853 −0.0423302
\(463\) 36.6531 1.70341 0.851706 0.524020i \(-0.175568\pi\)
0.851706 + 0.524020i \(0.175568\pi\)
\(464\) −4.65036 −0.215888
\(465\) −2.33863 −0.108451
\(466\) 19.5728 0.906694
\(467\) 37.0449 1.71424 0.857118 0.515120i \(-0.172253\pi\)
0.857118 + 0.515120i \(0.172253\pi\)
\(468\) −67.6926 −3.12909
\(469\) −0.119539 −0.00551980
\(470\) −59.9730 −2.76635
\(471\) 1.37100 0.0631724
\(472\) −0.00268366 −0.000123525 0
\(473\) −27.7897 −1.27777
\(474\) −8.37290 −0.384580
\(475\) −4.68760 −0.215082
\(476\) 0.887707 0.0406880
\(477\) 35.5320 1.62690
\(478\) −27.5097 −1.25826
\(479\) 6.38969 0.291952 0.145976 0.989288i \(-0.453368\pi\)
0.145976 + 0.989288i \(0.453368\pi\)
\(480\) 0.384378 0.0175444
\(481\) 36.7992 1.67790
\(482\) −22.0414 −1.00396
\(483\) 0.288618 0.0131326
\(484\) 107.782 4.89919
\(485\) 10.1912 0.462758
\(486\) 20.5365 0.931556
\(487\) −4.39420 −0.199120 −0.0995601 0.995032i \(-0.531744\pi\)
−0.0995601 + 0.995032i \(0.531744\pi\)
\(488\) 16.4407 0.744234
\(489\) 3.21585 0.145426
\(490\) −35.2513 −1.59249
\(491\) −35.4352 −1.59917 −0.799583 0.600555i \(-0.794946\pi\)
−0.799583 + 0.600555i \(0.794946\pi\)
\(492\) 13.3526 0.601982
\(493\) 1.55911 0.0702187
\(494\) −98.3469 −4.42483
\(495\) 37.1899 1.67156
\(496\) −12.5546 −0.563720
\(497\) 0.184041 0.00825539
\(498\) −10.7076 −0.479819
\(499\) −15.0927 −0.675642 −0.337821 0.941210i \(-0.609690\pi\)
−0.337821 + 0.941210i \(0.609690\pi\)
\(500\) 46.5554 2.08202
\(501\) −6.22237 −0.277995
\(502\) 44.3562 1.97971
\(503\) −15.3291 −0.683493 −0.341746 0.939792i \(-0.611018\pi\)
−0.341746 + 0.939792i \(0.611018\pi\)
\(504\) −2.51894 −0.112203
\(505\) 16.9439 0.753992
\(506\) −72.2709 −3.21283
\(507\) −7.28915 −0.323722
\(508\) −26.5279 −1.17699
\(509\) 10.3928 0.460653 0.230327 0.973113i \(-0.426021\pi\)
0.230327 + 0.973113i \(0.426021\pi\)
\(510\) 2.02844 0.0898210
\(511\) −2.67693 −0.118420
\(512\) 36.6070 1.61782
\(513\) 13.1154 0.579058
\(514\) 47.7816 2.10756
\(515\) −6.23931 −0.274937
\(516\) 5.79277 0.255013
\(517\) −73.3911 −3.22774
\(518\) 2.78022 0.122156
\(519\) 7.36177 0.323146
\(520\) 58.3249 2.55771
\(521\) 20.3842 0.893049 0.446524 0.894772i \(-0.352662\pi\)
0.446524 + 0.894772i \(0.352662\pi\)
\(522\) −8.98233 −0.393146
\(523\) 34.0338 1.48819 0.744097 0.668071i \(-0.232880\pi\)
0.744097 + 0.668071i \(0.232880\pi\)
\(524\) 47.6967 2.08364
\(525\) −0.0415816 −0.00181477
\(526\) 65.4814 2.85512
\(527\) 4.20915 0.183353
\(528\) −7.40390 −0.322213
\(529\) −0.0747118 −0.00324834
\(530\) −62.1578 −2.69996
\(531\) −0.00164073 −7.12018e−5 0
\(532\) −4.92895 −0.213697
\(533\) −61.4190 −2.66035
\(534\) −0.0273543 −0.00118374
\(535\) −20.7384 −0.896601
\(536\) −3.07319 −0.132742
\(537\) 1.50227 0.0648277
\(538\) 31.0593 1.33906
\(539\) −43.1382 −1.85809
\(540\) −15.7920 −0.679580
\(541\) 44.7146 1.92243 0.961216 0.275796i \(-0.0889413\pi\)
0.961216 + 0.275796i \(0.0889413\pi\)
\(542\) 19.2857 0.828390
\(543\) 2.59202 0.111234
\(544\) −0.691817 −0.0296614
\(545\) 6.65215 0.284947
\(546\) −0.872391 −0.0373349
\(547\) −7.24815 −0.309909 −0.154954 0.987922i \(-0.549523\pi\)
−0.154954 + 0.987922i \(0.549523\pi\)
\(548\) −72.4662 −3.09560
\(549\) 10.0515 0.428987
\(550\) 10.4122 0.443977
\(551\) −8.65687 −0.368795
\(552\) 7.41998 0.315816
\(553\) 1.93022 0.0820812
\(554\) 8.16899 0.347067
\(555\) 4.21430 0.178887
\(556\) 67.5143 2.86325
\(557\) 3.01891 0.127915 0.0639577 0.997953i \(-0.479628\pi\)
0.0639577 + 0.997953i \(0.479628\pi\)
\(558\) −24.2497 −1.02657
\(559\) −26.6455 −1.12698
\(560\) 1.39477 0.0589399
\(561\) 2.48228 0.104802
\(562\) −59.4698 −2.50858
\(563\) −13.9953 −0.589830 −0.294915 0.955524i \(-0.595291\pi\)
−0.294915 + 0.955524i \(0.595291\pi\)
\(564\) 15.2984 0.644179
\(565\) 2.07610 0.0873421
\(566\) 6.61135 0.277896
\(567\) −1.48080 −0.0621879
\(568\) 4.73147 0.198528
\(569\) 5.84200 0.244909 0.122455 0.992474i \(-0.460923\pi\)
0.122455 + 0.992474i \(0.460923\pi\)
\(570\) −11.2628 −0.471748
\(571\) 14.3015 0.598499 0.299249 0.954175i \(-0.403264\pi\)
0.299249 + 0.954175i \(0.403264\pi\)
\(572\) 144.912 6.05908
\(573\) 0.276242 0.0115402
\(574\) −4.64027 −0.193681
\(575\) −3.30288 −0.137740
\(576\) 25.1049 1.04604
\(577\) −23.1355 −0.963143 −0.481572 0.876407i \(-0.659934\pi\)
−0.481572 + 0.876407i \(0.659934\pi\)
\(578\) 37.7858 1.57168
\(579\) 3.86271 0.160529
\(580\) 10.4236 0.432816
\(581\) 2.46844 0.102408
\(582\) −3.91888 −0.162443
\(583\) −76.0646 −3.15028
\(584\) −68.8205 −2.84781
\(585\) 35.6587 1.47430
\(586\) 7.32472 0.302582
\(587\) 0.156411 0.00645575 0.00322788 0.999995i \(-0.498973\pi\)
0.00322788 + 0.999995i \(0.498973\pi\)
\(588\) 8.99218 0.370831
\(589\) −23.3711 −0.962988
\(590\) 0.00287021 0.000118165 0
\(591\) −4.43268 −0.182336
\(592\) 22.6239 0.929838
\(593\) −35.9541 −1.47646 −0.738228 0.674551i \(-0.764337\pi\)
−0.738228 + 0.674551i \(0.764337\pi\)
\(594\) −29.1321 −1.19531
\(595\) −0.467621 −0.0191706
\(596\) 81.8964 3.35461
\(597\) 0.514400 0.0210530
\(598\) −69.2952 −2.83369
\(599\) 34.5138 1.41019 0.705097 0.709111i \(-0.250903\pi\)
0.705097 + 0.709111i \(0.250903\pi\)
\(600\) −1.06901 −0.0436421
\(601\) 29.9584 1.22203 0.611014 0.791620i \(-0.290762\pi\)
0.611014 + 0.791620i \(0.290762\pi\)
\(602\) −2.01310 −0.0820477
\(603\) −1.87889 −0.0765143
\(604\) 13.1249 0.534043
\(605\) −56.7769 −2.30831
\(606\) −6.51553 −0.264675
\(607\) −24.0552 −0.976371 −0.488185 0.872740i \(-0.662341\pi\)
−0.488185 + 0.872740i \(0.662341\pi\)
\(608\) 3.84128 0.155785
\(609\) −0.0767912 −0.00311174
\(610\) −17.5835 −0.711937
\(611\) −70.3693 −2.84684
\(612\) 13.9528 0.564008
\(613\) −16.2217 −0.655188 −0.327594 0.944819i \(-0.606238\pi\)
−0.327594 + 0.944819i \(0.606238\pi\)
\(614\) 44.5664 1.79855
\(615\) −7.03380 −0.283630
\(616\) 5.39240 0.217266
\(617\) −33.8823 −1.36405 −0.682026 0.731328i \(-0.738901\pi\)
−0.682026 + 0.731328i \(0.738901\pi\)
\(618\) 2.39924 0.0965116
\(619\) −6.46819 −0.259979 −0.129989 0.991515i \(-0.541494\pi\)
−0.129989 + 0.991515i \(0.541494\pi\)
\(620\) 28.1407 1.13016
\(621\) 9.24109 0.370832
\(622\) 66.5698 2.66920
\(623\) 0.00630603 0.000252646 0
\(624\) −7.09905 −0.284189
\(625\) −21.0750 −0.843002
\(626\) 3.42522 0.136899
\(627\) −13.7827 −0.550429
\(628\) −16.4973 −0.658312
\(629\) −7.58504 −0.302435
\(630\) 2.69405 0.107334
\(631\) 1.74216 0.0693545 0.0346772 0.999399i \(-0.488960\pi\)
0.0346772 + 0.999399i \(0.488960\pi\)
\(632\) 49.6234 1.97391
\(633\) 6.18948 0.246010
\(634\) 38.9899 1.54849
\(635\) 13.9742 0.554549
\(636\) 15.8557 0.628719
\(637\) −41.3620 −1.63882
\(638\) 19.2288 0.761276
\(639\) 2.89272 0.114434
\(640\) −41.5700 −1.64320
\(641\) −16.6102 −0.656065 −0.328033 0.944666i \(-0.606386\pi\)
−0.328033 + 0.944666i \(0.606386\pi\)
\(642\) 7.97469 0.314736
\(643\) 48.7587 1.92286 0.961428 0.275056i \(-0.0886965\pi\)
0.961428 + 0.275056i \(0.0886965\pi\)
\(644\) −3.47293 −0.136853
\(645\) −3.05148 −0.120152
\(646\) 20.2713 0.797562
\(647\) 30.0439 1.18115 0.590574 0.806983i \(-0.298901\pi\)
0.590574 + 0.806983i \(0.298901\pi\)
\(648\) −38.0695 −1.49551
\(649\) 0.00351238 0.000137873 0
\(650\) 9.98347 0.391584
\(651\) −0.207314 −0.00812528
\(652\) −38.6963 −1.51546
\(653\) 7.59203 0.297099 0.148550 0.988905i \(-0.452540\pi\)
0.148550 + 0.988905i \(0.452540\pi\)
\(654\) −2.55799 −0.100025
\(655\) −25.1254 −0.981730
\(656\) −37.7601 −1.47428
\(657\) −42.0754 −1.64152
\(658\) −5.31648 −0.207258
\(659\) −9.73993 −0.379414 −0.189707 0.981841i \(-0.560754\pi\)
−0.189707 + 0.981841i \(0.560754\pi\)
\(660\) 16.5956 0.645981
\(661\) −17.2422 −0.670643 −0.335322 0.942104i \(-0.608845\pi\)
−0.335322 + 0.942104i \(0.608845\pi\)
\(662\) 67.6650 2.62988
\(663\) 2.38007 0.0924343
\(664\) 63.4604 2.46274
\(665\) 2.59644 0.100686
\(666\) 43.6989 1.69330
\(667\) −6.09963 −0.236179
\(668\) 74.8737 2.89695
\(669\) −0.947625 −0.0366373
\(670\) 3.28683 0.126981
\(671\) −21.5176 −0.830678
\(672\) 0.0340743 0.00131444
\(673\) 42.6402 1.64366 0.821830 0.569732i \(-0.192953\pi\)
0.821830 + 0.569732i \(0.192953\pi\)
\(674\) 47.9663 1.84759
\(675\) −1.33138 −0.0512448
\(676\) 87.7103 3.37347
\(677\) 32.6847 1.25618 0.628088 0.778142i \(-0.283838\pi\)
0.628088 + 0.778142i \(0.283838\pi\)
\(678\) −0.798335 −0.0306599
\(679\) 0.903426 0.0346703
\(680\) −12.0219 −0.461020
\(681\) 6.34823 0.243265
\(682\) 51.9123 1.98782
\(683\) −47.4081 −1.81402 −0.907010 0.421109i \(-0.861641\pi\)
−0.907010 + 0.421109i \(0.861641\pi\)
\(684\) −77.4721 −2.96222
\(685\) 38.1733 1.45853
\(686\) −6.26509 −0.239202
\(687\) −1.79468 −0.0684714
\(688\) −16.3815 −0.624539
\(689\) −72.9327 −2.77851
\(690\) −7.93579 −0.302110
\(691\) 20.3203 0.773020 0.386510 0.922285i \(-0.373680\pi\)
0.386510 + 0.922285i \(0.373680\pi\)
\(692\) −88.5842 −3.36747
\(693\) 3.29681 0.125235
\(694\) −17.1433 −0.650751
\(695\) −35.5648 −1.34905
\(696\) −1.97420 −0.0748320
\(697\) 12.6597 0.479520
\(698\) −54.8361 −2.07558
\(699\) 2.63007 0.0994786
\(700\) 0.500351 0.0189115
\(701\) −21.0342 −0.794452 −0.397226 0.917721i \(-0.630027\pi\)
−0.397226 + 0.917721i \(0.630027\pi\)
\(702\) −27.9326 −1.05425
\(703\) 42.1156 1.58842
\(704\) −53.7430 −2.02552
\(705\) −8.05880 −0.303512
\(706\) 63.8645 2.40357
\(707\) 1.50203 0.0564898
\(708\) −0.000732157 0 −2.75161e−5 0
\(709\) −39.8120 −1.49517 −0.747585 0.664166i \(-0.768787\pi\)
−0.747585 + 0.664166i \(0.768787\pi\)
\(710\) −5.06038 −0.189913
\(711\) 30.3387 1.13779
\(712\) 0.162120 0.00607570
\(713\) −16.4673 −0.616703
\(714\) 0.179817 0.00672949
\(715\) −76.3359 −2.85480
\(716\) −18.0768 −0.675562
\(717\) −3.69658 −0.138051
\(718\) 18.3804 0.685950
\(719\) 13.3455 0.497705 0.248852 0.968541i \(-0.419947\pi\)
0.248852 + 0.968541i \(0.419947\pi\)
\(720\) 21.9228 0.817013
\(721\) −0.553101 −0.0205986
\(722\) −66.2436 −2.46533
\(723\) −2.96179 −0.110150
\(724\) −31.1898 −1.15916
\(725\) 0.878784 0.0326372
\(726\) 21.8328 0.810290
\(727\) −12.0974 −0.448669 −0.224334 0.974512i \(-0.572021\pi\)
−0.224334 + 0.974512i \(0.572021\pi\)
\(728\) 5.17037 0.191627
\(729\) −21.3785 −0.791797
\(730\) 73.6046 2.72423
\(731\) 5.49216 0.203135
\(732\) 4.48535 0.165783
\(733\) −22.9649 −0.848226 −0.424113 0.905609i \(-0.639414\pi\)
−0.424113 + 0.905609i \(0.639414\pi\)
\(734\) 37.7028 1.39164
\(735\) −4.73684 −0.174721
\(736\) 2.70657 0.0997654
\(737\) 4.02221 0.148160
\(738\) −72.9349 −2.68477
\(739\) 14.5386 0.534811 0.267405 0.963584i \(-0.413834\pi\)
0.267405 + 0.963584i \(0.413834\pi\)
\(740\) −50.7106 −1.86416
\(741\) −13.2152 −0.485474
\(742\) −5.51015 −0.202284
\(743\) −19.3507 −0.709909 −0.354954 0.934884i \(-0.615504\pi\)
−0.354954 + 0.934884i \(0.615504\pi\)
\(744\) −5.32978 −0.195399
\(745\) −43.1409 −1.58056
\(746\) −48.7086 −1.78335
\(747\) 38.7984 1.41956
\(748\) −29.8693 −1.09213
\(749\) −1.83842 −0.0671743
\(750\) 9.43043 0.344351
\(751\) −17.3043 −0.631444 −0.315722 0.948852i \(-0.602247\pi\)
−0.315722 + 0.948852i \(0.602247\pi\)
\(752\) −43.2627 −1.57763
\(753\) 5.96030 0.217205
\(754\) 18.4371 0.671439
\(755\) −6.91383 −0.251620
\(756\) −1.39993 −0.0509148
\(757\) 16.1487 0.586934 0.293467 0.955969i \(-0.405191\pi\)
0.293467 + 0.955969i \(0.405191\pi\)
\(758\) −20.7783 −0.754700
\(759\) −9.71131 −0.352498
\(760\) 66.7511 2.42132
\(761\) −33.5310 −1.21550 −0.607749 0.794129i \(-0.707927\pi\)
−0.607749 + 0.794129i \(0.707927\pi\)
\(762\) −5.37359 −0.194665
\(763\) 0.589698 0.0213485
\(764\) −3.32402 −0.120259
\(765\) −7.34996 −0.265738
\(766\) 58.3359 2.10776
\(767\) 0.00336776 0.000121603 0
\(768\) 10.3002 0.371676
\(769\) 47.4454 1.71093 0.855463 0.517863i \(-0.173272\pi\)
0.855463 + 0.517863i \(0.173272\pi\)
\(770\) −5.76726 −0.207838
\(771\) 6.42059 0.231232
\(772\) −46.4800 −1.67285
\(773\) −39.9719 −1.43769 −0.718845 0.695171i \(-0.755329\pi\)
−0.718845 + 0.695171i \(0.755329\pi\)
\(774\) −31.6414 −1.13733
\(775\) 2.37246 0.0852214
\(776\) 23.2259 0.833762
\(777\) 0.373588 0.0134024
\(778\) −0.821702 −0.0294595
\(779\) −70.2922 −2.51848
\(780\) 15.9122 0.569749
\(781\) −6.19257 −0.221587
\(782\) 14.2831 0.510763
\(783\) −2.45874 −0.0878681
\(784\) −25.4291 −0.908184
\(785\) 8.69032 0.310171
\(786\) 9.66162 0.344619
\(787\) −49.9378 −1.78009 −0.890046 0.455871i \(-0.849328\pi\)
−0.890046 + 0.455871i \(0.849328\pi\)
\(788\) 53.3384 1.90010
\(789\) 8.79897 0.313252
\(790\) −53.0730 −1.88825
\(791\) 0.184041 0.00654376
\(792\) 84.7566 3.01170
\(793\) −20.6316 −0.732650
\(794\) −77.0431 −2.73416
\(795\) −8.35237 −0.296228
\(796\) −6.18978 −0.219391
\(797\) −9.91488 −0.351203 −0.175601 0.984461i \(-0.556187\pi\)
−0.175601 + 0.984461i \(0.556187\pi\)
\(798\) −0.998425 −0.0353439
\(799\) 14.5045 0.513133
\(800\) −0.389939 −0.0137864
\(801\) 0.0991169 0.00350212
\(802\) −13.6268 −0.481177
\(803\) 90.0725 3.17859
\(804\) −0.838431 −0.0295692
\(805\) 1.82945 0.0644797
\(806\) 49.7748 1.75324
\(807\) 4.17355 0.146916
\(808\) 38.6154 1.35848
\(809\) 33.7817 1.18770 0.593851 0.804575i \(-0.297607\pi\)
0.593851 + 0.804575i \(0.297607\pi\)
\(810\) 40.7160 1.43061
\(811\) −38.1556 −1.33983 −0.669913 0.742440i \(-0.733669\pi\)
−0.669913 + 0.742440i \(0.733669\pi\)
\(812\) 0.924029 0.0324271
\(813\) 2.59149 0.0908874
\(814\) −93.5479 −3.27885
\(815\) 20.3842 0.714027
\(816\) 1.46326 0.0512242
\(817\) −30.4950 −1.06688
\(818\) −96.0016 −3.35662
\(819\) 3.16106 0.110456
\(820\) 84.6377 2.95568
\(821\) −26.6886 −0.931440 −0.465720 0.884932i \(-0.654205\pi\)
−0.465720 + 0.884932i \(0.654205\pi\)
\(822\) −14.6790 −0.511989
\(823\) −54.1423 −1.88728 −0.943640 0.330972i \(-0.892623\pi\)
−0.943640 + 0.330972i \(0.892623\pi\)
\(824\) −14.2195 −0.495360
\(825\) 1.39912 0.0487112
\(826\) 0.000254438 0 8.85303e−6 0
\(827\) 41.6673 1.44891 0.724456 0.689321i \(-0.242091\pi\)
0.724456 + 0.689321i \(0.242091\pi\)
\(828\) −54.5869 −1.89702
\(829\) −53.9328 −1.87316 −0.936582 0.350450i \(-0.886029\pi\)
−0.936582 + 0.350450i \(0.886029\pi\)
\(830\) −67.8719 −2.35587
\(831\) 1.09770 0.0380787
\(832\) −51.5301 −1.78649
\(833\) 8.52554 0.295392
\(834\) 13.6759 0.473559
\(835\) −39.4415 −1.36493
\(836\) 165.848 5.73596
\(837\) −6.63788 −0.229439
\(838\) 90.2612 3.11802
\(839\) 24.3030 0.839034 0.419517 0.907747i \(-0.362199\pi\)
0.419517 + 0.907747i \(0.362199\pi\)
\(840\) 0.592119 0.0204300
\(841\) −27.3771 −0.944038
\(842\) −57.7085 −1.98877
\(843\) −7.99118 −0.275231
\(844\) −74.4781 −2.56364
\(845\) −46.2035 −1.58945
\(846\) −83.5633 −2.87296
\(847\) −5.03314 −0.172941
\(848\) −44.8386 −1.53977
\(849\) 0.888391 0.0304895
\(850\) −2.05779 −0.0705817
\(851\) 29.6746 1.01723
\(852\) 1.29084 0.0442235
\(853\) −33.2930 −1.13993 −0.569965 0.821669i \(-0.693043\pi\)
−0.569965 + 0.821669i \(0.693043\pi\)
\(854\) −1.55874 −0.0533391
\(855\) 40.8103 1.39568
\(856\) −47.2634 −1.61543
\(857\) 4.61700 0.157714 0.0788569 0.996886i \(-0.474873\pi\)
0.0788569 + 0.996886i \(0.474873\pi\)
\(858\) 29.3539 1.00213
\(859\) 8.18929 0.279415 0.139708 0.990193i \(-0.455384\pi\)
0.139708 + 0.990193i \(0.455384\pi\)
\(860\) 36.7185 1.25209
\(861\) −0.623531 −0.0212499
\(862\) −4.28555 −0.145966
\(863\) 26.1352 0.889654 0.444827 0.895617i \(-0.353265\pi\)
0.444827 + 0.895617i \(0.353265\pi\)
\(864\) 1.09101 0.0371168
\(865\) 46.6638 1.58662
\(866\) 53.1926 1.80756
\(867\) 5.07741 0.172438
\(868\) 2.49461 0.0846726
\(869\) −64.9473 −2.20319
\(870\) 2.11144 0.0715846
\(871\) 3.85660 0.130676
\(872\) 15.1604 0.513396
\(873\) 14.1999 0.480593
\(874\) −79.3063 −2.68258
\(875\) −2.17401 −0.0734950
\(876\) −18.7756 −0.634370
\(877\) 26.4964 0.894718 0.447359 0.894354i \(-0.352365\pi\)
0.447359 + 0.894354i \(0.352365\pi\)
\(878\) −54.4617 −1.83799
\(879\) 0.984250 0.0331979
\(880\) −46.9309 −1.58204
\(881\) −3.90597 −0.131595 −0.0657977 0.997833i \(-0.520959\pi\)
−0.0657977 + 0.997833i \(0.520959\pi\)
\(882\) −49.1173 −1.65386
\(883\) −24.9050 −0.838119 −0.419059 0.907959i \(-0.637640\pi\)
−0.419059 + 0.907959i \(0.637640\pi\)
\(884\) −28.6394 −0.963248
\(885\) 0.000385681 0 1.29645e−5 0
\(886\) 96.3086 3.23555
\(887\) 22.7565 0.764088 0.382044 0.924144i \(-0.375220\pi\)
0.382044 + 0.924144i \(0.375220\pi\)
\(888\) 9.60447 0.322305
\(889\) 1.23878 0.0415474
\(890\) −0.173390 −0.00581204
\(891\) 49.8256 1.66922
\(892\) 11.4028 0.381793
\(893\) −80.5356 −2.69502
\(894\) 16.5892 0.554827
\(895\) 9.52239 0.318298
\(896\) −3.68509 −0.123110
\(897\) −9.31145 −0.310900
\(898\) −34.0721 −1.13700
\(899\) 4.38137 0.146127
\(900\) 7.86442 0.262147
\(901\) 15.0329 0.500818
\(902\) 156.134 5.19871
\(903\) −0.270507 −0.00900191
\(904\) 4.73147 0.157366
\(905\) 16.4299 0.546150
\(906\) 2.65862 0.0883268
\(907\) −41.5772 −1.38055 −0.690273 0.723549i \(-0.742510\pi\)
−0.690273 + 0.723549i \(0.742510\pi\)
\(908\) −76.3883 −2.53504
\(909\) 23.6087 0.783050
\(910\) −5.52979 −0.183311
\(911\) 7.66058 0.253806 0.126903 0.991915i \(-0.459496\pi\)
0.126903 + 0.991915i \(0.459496\pi\)
\(912\) −8.12465 −0.269034
\(913\) −83.0573 −2.74880
\(914\) −80.2083 −2.65306
\(915\) −2.36277 −0.0781106
\(916\) 21.5954 0.713533
\(917\) −2.22731 −0.0735522
\(918\) 5.75747 0.190025
\(919\) 45.2128 1.49143 0.745716 0.666264i \(-0.232107\pi\)
0.745716 + 0.666264i \(0.232107\pi\)
\(920\) 47.0328 1.55063
\(921\) 5.98855 0.197330
\(922\) −62.3350 −2.05290
\(923\) −5.93759 −0.195438
\(924\) 1.47116 0.0483976
\(925\) −4.27527 −0.140570
\(926\) −89.3399 −2.93589
\(927\) −8.69352 −0.285533
\(928\) −0.720124 −0.0236392
\(929\) 16.4780 0.540627 0.270314 0.962772i \(-0.412873\pi\)
0.270314 + 0.962772i \(0.412873\pi\)
\(930\) 5.70029 0.186920
\(931\) −47.3376 −1.55143
\(932\) −31.6477 −1.03665
\(933\) 8.94522 0.292853
\(934\) −90.2951 −2.95455
\(935\) 15.7343 0.514568
\(936\) 81.2668 2.65629
\(937\) −25.5293 −0.834006 −0.417003 0.908905i \(-0.636920\pi\)
−0.417003 + 0.908905i \(0.636920\pi\)
\(938\) 0.291370 0.00951357
\(939\) 0.460259 0.0150200
\(940\) 96.9715 3.16286
\(941\) −5.57361 −0.181694 −0.0908472 0.995865i \(-0.528957\pi\)
−0.0908472 + 0.995865i \(0.528957\pi\)
\(942\) −3.34175 −0.108880
\(943\) −49.5279 −1.61285
\(944\) 0.00207048 6.73884e−5 0
\(945\) 0.737444 0.0239891
\(946\) 67.7360 2.20229
\(947\) −5.41184 −0.175861 −0.0879306 0.996127i \(-0.528025\pi\)
−0.0879306 + 0.996127i \(0.528025\pi\)
\(948\) 13.5383 0.439703
\(949\) 86.3638 2.80349
\(950\) 11.4258 0.370701
\(951\) 5.23921 0.169893
\(952\) −1.06572 −0.0345401
\(953\) 32.1253 1.04064 0.520320 0.853972i \(-0.325813\pi\)
0.520320 + 0.853972i \(0.325813\pi\)
\(954\) −86.6073 −2.80402
\(955\) 1.75100 0.0566612
\(956\) 44.4809 1.43862
\(957\) 2.58385 0.0835239
\(958\) −15.5745 −0.503190
\(959\) 3.38398 0.109274
\(960\) −5.90131 −0.190464
\(961\) −19.1716 −0.618437
\(962\) −89.6961 −2.89192
\(963\) −28.8959 −0.931156
\(964\) 35.6392 1.14786
\(965\) 24.4844 0.788182
\(966\) −0.703490 −0.0226344
\(967\) 10.5398 0.338938 0.169469 0.985535i \(-0.445795\pi\)
0.169469 + 0.985535i \(0.445795\pi\)
\(968\) −129.396 −4.15893
\(969\) 2.72392 0.0875050
\(970\) −24.8405 −0.797580
\(971\) 17.8853 0.573968 0.286984 0.957935i \(-0.407347\pi\)
0.286984 + 0.957935i \(0.407347\pi\)
\(972\) −33.2059 −1.06508
\(973\) −3.15274 −0.101072
\(974\) 10.7106 0.343191
\(975\) 1.34152 0.0429629
\(976\) −12.6842 −0.406012
\(977\) 59.1835 1.89345 0.946725 0.322044i \(-0.104370\pi\)
0.946725 + 0.322044i \(0.104370\pi\)
\(978\) −7.83846 −0.250646
\(979\) −0.212183 −0.00678141
\(980\) 56.9984 1.82075
\(981\) 9.26876 0.295929
\(982\) 86.3714 2.75622
\(983\) −7.59683 −0.242301 −0.121151 0.992634i \(-0.538658\pi\)
−0.121151 + 0.992634i \(0.538658\pi\)
\(984\) −16.0302 −0.511023
\(985\) −28.0973 −0.895254
\(986\) −3.80025 −0.121025
\(987\) −0.714395 −0.0227394
\(988\) 159.019 5.05906
\(989\) −21.4867 −0.683239
\(990\) −90.6486 −2.88100
\(991\) −4.38131 −0.139177 −0.0695885 0.997576i \(-0.522169\pi\)
−0.0695885 + 0.997576i \(0.522169\pi\)
\(992\) −1.94413 −0.0617261
\(993\) 9.09240 0.288539
\(994\) −0.448592 −0.0142285
\(995\) 3.26061 0.103368
\(996\) 17.3133 0.548594
\(997\) −15.6397 −0.495315 −0.247658 0.968848i \(-0.579661\pi\)
−0.247658 + 0.968848i \(0.579661\pi\)
\(998\) 36.7877 1.16449
\(999\) 11.9617 0.378452
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 \(a_p\))