Properties

Label 6017.2.a.c.1.13
Level 6017
Weight 2
Character 6017.1
Self dual Yes
Analytic conductor 48.046
Analytic rank 1
Dimension 106
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(1\)
Dimension: \(106\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.37596 q^{2}\) \(+1.38475 q^{3}\) \(+3.64518 q^{4}\) \(+0.740241 q^{5}\) \(-3.29011 q^{6}\) \(-0.0236528 q^{7}\) \(-3.90889 q^{8}\) \(-1.08246 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.37596 q^{2}\) \(+1.38475 q^{3}\) \(+3.64518 q^{4}\) \(+0.740241 q^{5}\) \(-3.29011 q^{6}\) \(-0.0236528 q^{7}\) \(-3.90889 q^{8}\) \(-1.08246 q^{9}\) \(-1.75878 q^{10}\) \(+1.00000 q^{11}\) \(+5.04767 q^{12}\) \(-2.69585 q^{13}\) \(+0.0561980 q^{14}\) \(+1.02505 q^{15}\) \(+1.99699 q^{16}\) \(+0.455891 q^{17}\) \(+2.57189 q^{18}\) \(-1.92790 q^{19}\) \(+2.69831 q^{20}\) \(-0.0327532 q^{21}\) \(-2.37596 q^{22}\) \(+4.19781 q^{23}\) \(-5.41283 q^{24}\) \(-4.45204 q^{25}\) \(+6.40522 q^{26}\) \(-5.65320 q^{27}\) \(-0.0862186 q^{28}\) \(-6.59167 q^{29}\) \(-2.43547 q^{30}\) \(+8.95500 q^{31}\) \(+3.07301 q^{32}\) \(+1.38475 q^{33}\) \(-1.08318 q^{34}\) \(-0.0175087 q^{35}\) \(-3.94578 q^{36}\) \(+10.5100 q^{37}\) \(+4.58062 q^{38}\) \(-3.73308 q^{39}\) \(-2.89352 q^{40}\) \(-12.2011 q^{41}\) \(+0.0778202 q^{42}\) \(+8.91127 q^{43}\) \(+3.64518 q^{44}\) \(-0.801284 q^{45}\) \(-9.97383 q^{46}\) \(-6.38200 q^{47}\) \(+2.76533 q^{48}\) \(-6.99944 q^{49}\) \(+10.5779 q^{50}\) \(+0.631296 q^{51}\) \(-9.82685 q^{52}\) \(+12.7888 q^{53}\) \(+13.4318 q^{54}\) \(+0.740241 q^{55}\) \(+0.0924559 q^{56}\) \(-2.66967 q^{57}\) \(+15.6615 q^{58}\) \(-1.06255 q^{59}\) \(+3.73649 q^{60}\) \(+9.20916 q^{61}\) \(-21.2767 q^{62}\) \(+0.0256033 q^{63}\) \(-11.2953 q^{64}\) \(-1.99558 q^{65}\) \(-3.29011 q^{66}\) \(-12.8056 q^{67}\) \(+1.66181 q^{68}\) \(+5.81292 q^{69}\) \(+0.0416000 q^{70}\) \(+12.9039 q^{71}\) \(+4.23123 q^{72}\) \(-11.4506 q^{73}\) \(-24.9713 q^{74}\) \(-6.16497 q^{75}\) \(-7.02756 q^{76}\) \(-0.0236528 q^{77}\) \(+8.86964 q^{78}\) \(-7.58395 q^{79}\) \(+1.47825 q^{80}\) \(-4.58088 q^{81}\) \(+28.9892 q^{82}\) \(+14.3889 q^{83}\) \(-0.119391 q^{84}\) \(+0.337469 q^{85}\) \(-21.1728 q^{86}\) \(-9.12783 q^{87}\) \(-3.90889 q^{88}\) \(-9.90297 q^{89}\) \(+1.90382 q^{90}\) \(+0.0637642 q^{91}\) \(+15.3018 q^{92}\) \(+12.4004 q^{93}\) \(+15.1634 q^{94}\) \(-1.42711 q^{95}\) \(+4.25535 q^{96}\) \(+10.9611 q^{97}\) \(+16.6304 q^{98}\) \(-1.08246 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut -\mathstrut 30q^{10} \) \(\mathstrut +\mathstrut 106q^{11} \) \(\mathstrut -\mathstrut 26q^{12} \) \(\mathstrut -\mathstrut 72q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut -\mathstrut 46q^{15} \) \(\mathstrut +\mathstrut 75q^{16} \) \(\mathstrut -\mathstrut 65q^{17} \) \(\mathstrut -\mathstrut 37q^{18} \) \(\mathstrut -\mathstrut 63q^{19} \) \(\mathstrut -\mathstrut 25q^{20} \) \(\mathstrut -\mathstrut 27q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut -\mathstrut 56q^{24} \) \(\mathstrut +\mathstrut 74q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 54q^{27} \) \(\mathstrut -\mathstrut 115q^{28} \) \(\mathstrut -\mathstrut 45q^{29} \) \(\mathstrut -\mathstrut 14q^{30} \) \(\mathstrut -\mathstrut 89q^{31} \) \(\mathstrut -\mathstrut 96q^{32} \) \(\mathstrut -\mathstrut 15q^{33} \) \(\mathstrut -\mathstrut 26q^{34} \) \(\mathstrut -\mathstrut 52q^{35} \) \(\mathstrut +\mathstrut 91q^{36} \) \(\mathstrut -\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 7q^{38} \) \(\mathstrut -\mathstrut 34q^{39} \) \(\mathstrut -\mathstrut 74q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 94q^{43} \) \(\mathstrut +\mathstrut 93q^{44} \) \(\mathstrut -\mathstrut 46q^{45} \) \(\mathstrut -\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 105q^{47} \) \(\mathstrut -\mathstrut 57q^{48} \) \(\mathstrut +\mathstrut 80q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 36q^{51} \) \(\mathstrut -\mathstrut 137q^{52} \) \(\mathstrut -\mathstrut 61q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 32q^{56} \) \(\mathstrut -\mathstrut 71q^{57} \) \(\mathstrut -\mathstrut 28q^{58} \) \(\mathstrut -\mathstrut 15q^{59} \) \(\mathstrut -\mathstrut 21q^{60} \) \(\mathstrut -\mathstrut 80q^{61} \) \(\mathstrut -\mathstrut 84q^{62} \) \(\mathstrut -\mathstrut 182q^{63} \) \(\mathstrut +\mathstrut 55q^{64} \) \(\mathstrut -\mathstrut 73q^{65} \) \(\mathstrut -\mathstrut 22q^{66} \) \(\mathstrut -\mathstrut 58q^{67} \) \(\mathstrut -\mathstrut 145q^{68} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 39q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 100q^{72} \) \(\mathstrut -\mathstrut 155q^{73} \) \(\mathstrut -\mathstrut 15q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 132q^{76} \) \(\mathstrut -\mathstrut 66q^{77} \) \(\mathstrut -\mathstrut 45q^{78} \) \(\mathstrut -\mathstrut 50q^{79} \) \(\mathstrut -\mathstrut 28q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut -\mathstrut 57q^{82} \) \(\mathstrut -\mathstrut 96q^{83} \) \(\mathstrut -\mathstrut 27q^{84} \) \(\mathstrut -\mathstrut 74q^{85} \) \(\mathstrut +\mathstrut 54q^{86} \) \(\mathstrut -\mathstrut 182q^{87} \) \(\mathstrut -\mathstrut 39q^{88} \) \(\mathstrut +\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 53q^{90} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 49q^{95} \) \(\mathstrut -\mathstrut 56q^{96} \) \(\mathstrut -\mathstrut 102q^{97} \) \(\mathstrut -\mathstrut 76q^{98} \) \(\mathstrut +\mathstrut 97q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.37596 −1.68006 −0.840028 0.542542i \(-0.817462\pi\)
−0.840028 + 0.542542i \(0.817462\pi\)
\(3\) 1.38475 0.799486 0.399743 0.916627i \(-0.369099\pi\)
0.399743 + 0.916627i \(0.369099\pi\)
\(4\) 3.64518 1.82259
\(5\) 0.740241 0.331046 0.165523 0.986206i \(-0.447069\pi\)
0.165523 + 0.986206i \(0.447069\pi\)
\(6\) −3.29011 −1.34318
\(7\) −0.0236528 −0.00893990 −0.00446995 0.999990i \(-0.501423\pi\)
−0.00446995 + 0.999990i \(0.501423\pi\)
\(8\) −3.90889 −1.38200
\(9\) −1.08246 −0.360821
\(10\) −1.75878 −0.556176
\(11\) 1.00000 0.301511
\(12\) 5.04767 1.45714
\(13\) −2.69585 −0.747693 −0.373847 0.927491i \(-0.621961\pi\)
−0.373847 + 0.927491i \(0.621961\pi\)
\(14\) 0.0561980 0.0150195
\(15\) 1.02505 0.264667
\(16\) 1.99699 0.499247
\(17\) 0.455891 0.110570 0.0552849 0.998471i \(-0.482393\pi\)
0.0552849 + 0.998471i \(0.482393\pi\)
\(18\) 2.57189 0.606200
\(19\) −1.92790 −0.442292 −0.221146 0.975241i \(-0.570980\pi\)
−0.221146 + 0.975241i \(0.570980\pi\)
\(20\) 2.69831 0.603361
\(21\) −0.0327532 −0.00714733
\(22\) −2.37596 −0.506556
\(23\) 4.19781 0.875304 0.437652 0.899144i \(-0.355810\pi\)
0.437652 + 0.899144i \(0.355810\pi\)
\(24\) −5.41283 −1.10489
\(25\) −4.45204 −0.890409
\(26\) 6.40522 1.25617
\(27\) −5.65320 −1.08796
\(28\) −0.0862186 −0.0162938
\(29\) −6.59167 −1.22404 −0.612021 0.790841i \(-0.709643\pi\)
−0.612021 + 0.790841i \(0.709643\pi\)
\(30\) −2.43547 −0.444655
\(31\) 8.95500 1.60837 0.804183 0.594382i \(-0.202603\pi\)
0.804183 + 0.594382i \(0.202603\pi\)
\(32\) 3.07301 0.543236
\(33\) 1.38475 0.241054
\(34\) −1.08318 −0.185764
\(35\) −0.0175087 −0.00295952
\(36\) −3.94578 −0.657630
\(37\) 10.5100 1.72783 0.863916 0.503637i \(-0.168005\pi\)
0.863916 + 0.503637i \(0.168005\pi\)
\(38\) 4.58062 0.743075
\(39\) −3.73308 −0.597771
\(40\) −2.89352 −0.457505
\(41\) −12.2011 −1.90548 −0.952742 0.303781i \(-0.901751\pi\)
−0.952742 + 0.303781i \(0.901751\pi\)
\(42\) 0.0778202 0.0120079
\(43\) 8.91127 1.35896 0.679478 0.733696i \(-0.262206\pi\)
0.679478 + 0.733696i \(0.262206\pi\)
\(44\) 3.64518 0.549532
\(45\) −0.801284 −0.119448
\(46\) −9.97383 −1.47056
\(47\) −6.38200 −0.930910 −0.465455 0.885072i \(-0.654109\pi\)
−0.465455 + 0.885072i \(0.654109\pi\)
\(48\) 2.76533 0.399141
\(49\) −6.99944 −0.999920
\(50\) 10.5779 1.49594
\(51\) 0.631296 0.0883991
\(52\) −9.82685 −1.36274
\(53\) 12.7888 1.75667 0.878336 0.478044i \(-0.158654\pi\)
0.878336 + 0.478044i \(0.158654\pi\)
\(54\) 13.4318 1.82783
\(55\) 0.740241 0.0998140
\(56\) 0.0924559 0.0123549
\(57\) −2.66967 −0.353606
\(58\) 15.6615 2.05646
\(59\) −1.06255 −0.138333 −0.0691663 0.997605i \(-0.522034\pi\)
−0.0691663 + 0.997605i \(0.522034\pi\)
\(60\) 3.73649 0.482379
\(61\) 9.20916 1.17911 0.589556 0.807728i \(-0.299303\pi\)
0.589556 + 0.807728i \(0.299303\pi\)
\(62\) −21.2767 −2.70215
\(63\) 0.0256033 0.00322571
\(64\) −11.2953 −1.41191
\(65\) −1.99558 −0.247521
\(66\) −3.29011 −0.404985
\(67\) −12.8056 −1.56446 −0.782228 0.622992i \(-0.785917\pi\)
−0.782228 + 0.622992i \(0.785917\pi\)
\(68\) 1.66181 0.201524
\(69\) 5.81292 0.699794
\(70\) 0.0416000 0.00497215
\(71\) 12.9039 1.53141 0.765705 0.643192i \(-0.222390\pi\)
0.765705 + 0.643192i \(0.222390\pi\)
\(72\) 4.23123 0.498655
\(73\) −11.4506 −1.34020 −0.670098 0.742273i \(-0.733748\pi\)
−0.670098 + 0.742273i \(0.733748\pi\)
\(74\) −24.9713 −2.90285
\(75\) −6.16497 −0.711870
\(76\) −7.02756 −0.806117
\(77\) −0.0236528 −0.00269548
\(78\) 8.86964 1.00429
\(79\) −7.58395 −0.853261 −0.426631 0.904426i \(-0.640300\pi\)
−0.426631 + 0.904426i \(0.640300\pi\)
\(80\) 1.47825 0.165274
\(81\) −4.58088 −0.508986
\(82\) 28.9892 3.20132
\(83\) 14.3889 1.57938 0.789691 0.613505i \(-0.210241\pi\)
0.789691 + 0.613505i \(0.210241\pi\)
\(84\) −0.119391 −0.0130267
\(85\) 0.337469 0.0366037
\(86\) −21.1728 −2.28312
\(87\) −9.12783 −0.978606
\(88\) −3.90889 −0.416689
\(89\) −9.90297 −1.04971 −0.524856 0.851191i \(-0.675881\pi\)
−0.524856 + 0.851191i \(0.675881\pi\)
\(90\) 1.90382 0.200680
\(91\) 0.0637642 0.00668430
\(92\) 15.3018 1.59532
\(93\) 12.4004 1.28587
\(94\) 15.1634 1.56398
\(95\) −1.42711 −0.146419
\(96\) 4.25535 0.434310
\(97\) 10.9611 1.11293 0.556467 0.830870i \(-0.312157\pi\)
0.556467 + 0.830870i \(0.312157\pi\)
\(98\) 16.6304 1.67992
\(99\) −1.08246 −0.108792
\(100\) −16.2285 −1.62285
\(101\) −0.00336168 −0.000334500 0 −0.000167250 1.00000i \(-0.500053\pi\)
−0.000167250 1.00000i \(0.500053\pi\)
\(102\) −1.49993 −0.148516
\(103\) 4.33393 0.427035 0.213517 0.976939i \(-0.431508\pi\)
0.213517 + 0.976939i \(0.431508\pi\)
\(104\) 10.5378 1.03331
\(105\) −0.0242452 −0.00236609
\(106\) −30.3856 −2.95131
\(107\) 3.76297 0.363780 0.181890 0.983319i \(-0.441779\pi\)
0.181890 + 0.983319i \(0.441779\pi\)
\(108\) −20.6069 −1.98290
\(109\) −11.8950 −1.13933 −0.569666 0.821876i \(-0.692928\pi\)
−0.569666 + 0.821876i \(0.692928\pi\)
\(110\) −1.75878 −0.167693
\(111\) 14.5537 1.38138
\(112\) −0.0472343 −0.00446322
\(113\) −7.17418 −0.674890 −0.337445 0.941345i \(-0.609563\pi\)
−0.337445 + 0.941345i \(0.609563\pi\)
\(114\) 6.34302 0.594078
\(115\) 3.10739 0.289766
\(116\) −24.0278 −2.23093
\(117\) 2.91816 0.269784
\(118\) 2.52458 0.232407
\(119\) −0.0107831 −0.000988484 0
\(120\) −4.00680 −0.365769
\(121\) 1.00000 0.0909091
\(122\) −21.8806 −1.98097
\(123\) −16.8954 −1.52341
\(124\) 32.6426 2.93139
\(125\) −6.99679 −0.625812
\(126\) −0.0608323 −0.00541937
\(127\) −8.47494 −0.752029 −0.376015 0.926614i \(-0.622706\pi\)
−0.376015 + 0.926614i \(0.622706\pi\)
\(128\) 20.6912 1.82886
\(129\) 12.3399 1.08647
\(130\) 4.74140 0.415849
\(131\) −10.4785 −0.915511 −0.457756 0.889078i \(-0.651347\pi\)
−0.457756 + 0.889078i \(0.651347\pi\)
\(132\) 5.04767 0.439343
\(133\) 0.0456002 0.00395404
\(134\) 30.4256 2.62838
\(135\) −4.18473 −0.360164
\(136\) −1.78203 −0.152807
\(137\) −11.8644 −1.01365 −0.506824 0.862050i \(-0.669181\pi\)
−0.506824 + 0.862050i \(0.669181\pi\)
\(138\) −13.8113 −1.17569
\(139\) −4.94092 −0.419083 −0.209542 0.977800i \(-0.567197\pi\)
−0.209542 + 0.977800i \(0.567197\pi\)
\(140\) −0.0638225 −0.00539399
\(141\) −8.83748 −0.744250
\(142\) −30.6591 −2.57285
\(143\) −2.69585 −0.225438
\(144\) −2.16167 −0.180139
\(145\) −4.87942 −0.405214
\(146\) 27.2063 2.25161
\(147\) −9.69248 −0.799423
\(148\) 38.3108 3.14913
\(149\) 3.35133 0.274552 0.137276 0.990533i \(-0.456165\pi\)
0.137276 + 0.990533i \(0.456165\pi\)
\(150\) 14.6477 1.19598
\(151\) −8.26299 −0.672433 −0.336216 0.941785i \(-0.609147\pi\)
−0.336216 + 0.941785i \(0.609147\pi\)
\(152\) 7.53596 0.611247
\(153\) −0.493486 −0.0398960
\(154\) 0.0561980 0.00452856
\(155\) 6.62885 0.532442
\(156\) −13.6077 −1.08949
\(157\) −9.98978 −0.797271 −0.398636 0.917109i \(-0.630516\pi\)
−0.398636 + 0.917109i \(0.630516\pi\)
\(158\) 18.0192 1.43353
\(159\) 17.7093 1.40444
\(160\) 2.27477 0.179836
\(161\) −0.0992898 −0.00782513
\(162\) 10.8840 0.855126
\(163\) −24.1202 −1.88924 −0.944621 0.328162i \(-0.893571\pi\)
−0.944621 + 0.328162i \(0.893571\pi\)
\(164\) −44.4750 −3.47292
\(165\) 1.02505 0.0798000
\(166\) −34.1873 −2.65345
\(167\) 11.8559 0.917441 0.458720 0.888581i \(-0.348308\pi\)
0.458720 + 0.888581i \(0.348308\pi\)
\(168\) 0.128028 0.00987761
\(169\) −5.73241 −0.440955
\(170\) −0.801813 −0.0614963
\(171\) 2.08689 0.159588
\(172\) 32.4832 2.47682
\(173\) −23.8978 −1.81692 −0.908459 0.417973i \(-0.862741\pi\)
−0.908459 + 0.417973i \(0.862741\pi\)
\(174\) 21.6873 1.64411
\(175\) 0.105303 0.00796017
\(176\) 1.99699 0.150529
\(177\) −1.47137 −0.110595
\(178\) 23.5291 1.76358
\(179\) −18.5890 −1.38941 −0.694704 0.719296i \(-0.744465\pi\)
−0.694704 + 0.719296i \(0.744465\pi\)
\(180\) −2.92083 −0.217706
\(181\) −6.13112 −0.455722 −0.227861 0.973694i \(-0.573173\pi\)
−0.227861 + 0.973694i \(0.573173\pi\)
\(182\) −0.151501 −0.0112300
\(183\) 12.7524 0.942684
\(184\) −16.4088 −1.20967
\(185\) 7.77992 0.571991
\(186\) −29.4630 −2.16033
\(187\) 0.455891 0.0333381
\(188\) −23.2635 −1.69667
\(189\) 0.133714 0.00972624
\(190\) 3.39076 0.245992
\(191\) 12.4253 0.899061 0.449531 0.893265i \(-0.351591\pi\)
0.449531 + 0.893265i \(0.351591\pi\)
\(192\) −15.6412 −1.12881
\(193\) −26.0289 −1.87360 −0.936802 0.349859i \(-0.886229\pi\)
−0.936802 + 0.349859i \(0.886229\pi\)
\(194\) −26.0432 −1.86979
\(195\) −2.76337 −0.197889
\(196\) −25.5142 −1.82245
\(197\) −18.5248 −1.31983 −0.659917 0.751338i \(-0.729409\pi\)
−0.659917 + 0.751338i \(0.729409\pi\)
\(198\) 2.57189 0.182776
\(199\) 11.7367 0.831995 0.415997 0.909366i \(-0.363433\pi\)
0.415997 + 0.909366i \(0.363433\pi\)
\(200\) 17.4025 1.23054
\(201\) −17.7326 −1.25076
\(202\) 0.00798722 0.000561979 0
\(203\) 0.155911 0.0109428
\(204\) 2.30119 0.161115
\(205\) −9.03171 −0.630802
\(206\) −10.2972 −0.717443
\(207\) −4.54398 −0.315828
\(208\) −5.38357 −0.373284
\(209\) −1.92790 −0.133356
\(210\) 0.0576057 0.00397517
\(211\) −17.1680 −1.18190 −0.590949 0.806709i \(-0.701246\pi\)
−0.590949 + 0.806709i \(0.701246\pi\)
\(212\) 46.6174 3.20169
\(213\) 17.8687 1.22434
\(214\) −8.94065 −0.611171
\(215\) 6.59648 0.449876
\(216\) 22.0977 1.50356
\(217\) −0.211810 −0.0143786
\(218\) 28.2620 1.91414
\(219\) −15.8563 −1.07147
\(220\) 2.69831 0.181920
\(221\) −1.22901 −0.0826723
\(222\) −34.5790 −2.32079
\(223\) 6.32896 0.423819 0.211909 0.977289i \(-0.432032\pi\)
0.211909 + 0.977289i \(0.432032\pi\)
\(224\) −0.0726851 −0.00485648
\(225\) 4.81918 0.321279
\(226\) 17.0456 1.13385
\(227\) 3.14572 0.208789 0.104394 0.994536i \(-0.466710\pi\)
0.104394 + 0.994536i \(0.466710\pi\)
\(228\) −9.73142 −0.644479
\(229\) 8.98263 0.593589 0.296794 0.954941i \(-0.404082\pi\)
0.296794 + 0.954941i \(0.404082\pi\)
\(230\) −7.38303 −0.486823
\(231\) −0.0327532 −0.00215500
\(232\) 25.7661 1.69163
\(233\) −25.6478 −1.68025 −0.840123 0.542396i \(-0.817517\pi\)
−0.840123 + 0.542396i \(0.817517\pi\)
\(234\) −6.93342 −0.453252
\(235\) −4.72421 −0.308174
\(236\) −3.87320 −0.252124
\(237\) −10.5019 −0.682171
\(238\) 0.0256202 0.00166071
\(239\) 23.4249 1.51523 0.757616 0.652700i \(-0.226364\pi\)
0.757616 + 0.652700i \(0.226364\pi\)
\(240\) 2.04701 0.132134
\(241\) 6.89908 0.444409 0.222205 0.975000i \(-0.428675\pi\)
0.222205 + 0.975000i \(0.428675\pi\)
\(242\) −2.37596 −0.152732
\(243\) 10.6162 0.681030
\(244\) 33.5691 2.14904
\(245\) −5.18127 −0.331019
\(246\) 40.1428 2.55941
\(247\) 5.19733 0.330698
\(248\) −35.0041 −2.22276
\(249\) 19.9250 1.26269
\(250\) 16.6241 1.05140
\(251\) 14.0297 0.885544 0.442772 0.896634i \(-0.353995\pi\)
0.442772 + 0.896634i \(0.353995\pi\)
\(252\) 0.0933286 0.00587915
\(253\) 4.19781 0.263914
\(254\) 20.1361 1.26345
\(255\) 0.467311 0.0292641
\(256\) −26.5708 −1.66068
\(257\) −3.27357 −0.204200 −0.102100 0.994774i \(-0.532556\pi\)
−0.102100 + 0.994774i \(0.532556\pi\)
\(258\) −29.3191 −1.82533
\(259\) −0.248590 −0.0154466
\(260\) −7.27423 −0.451129
\(261\) 7.13525 0.441661
\(262\) 24.8965 1.53811
\(263\) 6.93509 0.427636 0.213818 0.976874i \(-0.431410\pi\)
0.213818 + 0.976874i \(0.431410\pi\)
\(264\) −5.41283 −0.333137
\(265\) 9.46676 0.581539
\(266\) −0.108344 −0.00664302
\(267\) −13.7131 −0.839231
\(268\) −46.6788 −2.85136
\(269\) −0.549062 −0.0334769 −0.0167384 0.999860i \(-0.505328\pi\)
−0.0167384 + 0.999860i \(0.505328\pi\)
\(270\) 9.94274 0.605096
\(271\) −15.7272 −0.955362 −0.477681 0.878533i \(-0.658523\pi\)
−0.477681 + 0.878533i \(0.658523\pi\)
\(272\) 0.910409 0.0552017
\(273\) 0.0882975 0.00534401
\(274\) 28.1894 1.70299
\(275\) −4.45204 −0.268468
\(276\) 21.1892 1.27544
\(277\) −8.10336 −0.486884 −0.243442 0.969915i \(-0.578277\pi\)
−0.243442 + 0.969915i \(0.578277\pi\)
\(278\) 11.7394 0.704084
\(279\) −9.69347 −0.580333
\(280\) 0.0684396 0.00409005
\(281\) −25.9155 −1.54599 −0.772994 0.634413i \(-0.781242\pi\)
−0.772994 + 0.634413i \(0.781242\pi\)
\(282\) 20.9975 1.25038
\(283\) −16.0686 −0.955182 −0.477591 0.878582i \(-0.658490\pi\)
−0.477591 + 0.878582i \(0.658490\pi\)
\(284\) 47.0370 2.79113
\(285\) −1.97620 −0.117060
\(286\) 6.40522 0.378749
\(287\) 0.288588 0.0170348
\(288\) −3.32642 −0.196011
\(289\) −16.7922 −0.987774
\(290\) 11.5933 0.680783
\(291\) 15.1784 0.889775
\(292\) −41.7397 −2.44263
\(293\) 28.0396 1.63809 0.819047 0.573727i \(-0.194503\pi\)
0.819047 + 0.573727i \(0.194503\pi\)
\(294\) 23.0289 1.34308
\(295\) −0.786545 −0.0457944
\(296\) −41.0823 −2.38786
\(297\) −5.65320 −0.328032
\(298\) −7.96262 −0.461262
\(299\) −11.3167 −0.654459
\(300\) −22.4724 −1.29745
\(301\) −0.210776 −0.0121489
\(302\) 19.6325 1.12973
\(303\) −0.00465509 −0.000267428 0
\(304\) −3.85000 −0.220813
\(305\) 6.81699 0.390340
\(306\) 1.17250 0.0670275
\(307\) 15.6188 0.891413 0.445706 0.895179i \(-0.352953\pi\)
0.445706 + 0.895179i \(0.352953\pi\)
\(308\) −0.0862186 −0.00491276
\(309\) 6.00141 0.341409
\(310\) −15.7499 −0.894533
\(311\) 26.6381 1.51051 0.755254 0.655433i \(-0.227514\pi\)
0.755254 + 0.655433i \(0.227514\pi\)
\(312\) 14.5922 0.826119
\(313\) −1.27151 −0.0718698 −0.0359349 0.999354i \(-0.511441\pi\)
−0.0359349 + 0.999354i \(0.511441\pi\)
\(314\) 23.7353 1.33946
\(315\) 0.0189526 0.00106786
\(316\) −27.6449 −1.55515
\(317\) −31.7844 −1.78519 −0.892594 0.450861i \(-0.851117\pi\)
−0.892594 + 0.450861i \(0.851117\pi\)
\(318\) −42.0765 −2.35953
\(319\) −6.59167 −0.369063
\(320\) −8.36125 −0.467408
\(321\) 5.21077 0.290837
\(322\) 0.235909 0.0131467
\(323\) −0.878915 −0.0489041
\(324\) −16.6981 −0.927674
\(325\) 12.0020 0.665753
\(326\) 57.3087 3.17404
\(327\) −16.4716 −0.910881
\(328\) 47.6925 2.63338
\(329\) 0.150952 0.00832224
\(330\) −2.43547 −0.134068
\(331\) 3.46925 0.190687 0.0953437 0.995444i \(-0.469605\pi\)
0.0953437 + 0.995444i \(0.469605\pi\)
\(332\) 52.4500 2.87857
\(333\) −11.3767 −0.623439
\(334\) −28.1692 −1.54135
\(335\) −9.47925 −0.517906
\(336\) −0.0654077 −0.00356828
\(337\) −21.8333 −1.18933 −0.594667 0.803972i \(-0.702716\pi\)
−0.594667 + 0.803972i \(0.702716\pi\)
\(338\) 13.6200 0.740829
\(339\) −9.93445 −0.539566
\(340\) 1.23014 0.0667135
\(341\) 8.95500 0.484940
\(342\) −4.95836 −0.268117
\(343\) 0.331125 0.0178791
\(344\) −34.8331 −1.87808
\(345\) 4.30296 0.231664
\(346\) 56.7803 3.05253
\(347\) 0.110564 0.00593538 0.00296769 0.999996i \(-0.499055\pi\)
0.00296769 + 0.999996i \(0.499055\pi\)
\(348\) −33.2726 −1.78360
\(349\) −20.4887 −1.09673 −0.548367 0.836238i \(-0.684750\pi\)
−0.548367 + 0.836238i \(0.684750\pi\)
\(350\) −0.250196 −0.0133735
\(351\) 15.2402 0.813459
\(352\) 3.07301 0.163792
\(353\) −0.114179 −0.00607714 −0.00303857 0.999995i \(-0.500967\pi\)
−0.00303857 + 0.999995i \(0.500967\pi\)
\(354\) 3.49592 0.185806
\(355\) 9.55198 0.506966
\(356\) −36.0981 −1.91320
\(357\) −0.0149319 −0.000790279 0
\(358\) 44.1667 2.33428
\(359\) 6.29292 0.332128 0.166064 0.986115i \(-0.446894\pi\)
0.166064 + 0.986115i \(0.446894\pi\)
\(360\) 3.13213 0.165078
\(361\) −15.2832 −0.804378
\(362\) 14.5673 0.765639
\(363\) 1.38475 0.0726806
\(364\) 0.232432 0.0121828
\(365\) −8.47623 −0.443666
\(366\) −30.2992 −1.58376
\(367\) −18.3331 −0.956981 −0.478490 0.878093i \(-0.658816\pi\)
−0.478490 + 0.878093i \(0.658816\pi\)
\(368\) 8.38298 0.436993
\(369\) 13.2072 0.687539
\(370\) −18.4848 −0.960978
\(371\) −0.302490 −0.0157045
\(372\) 45.2019 2.34361
\(373\) −13.8887 −0.719128 −0.359564 0.933120i \(-0.617075\pi\)
−0.359564 + 0.933120i \(0.617075\pi\)
\(374\) −1.08318 −0.0560098
\(375\) −9.68881 −0.500328
\(376\) 24.9465 1.28652
\(377\) 17.7701 0.915209
\(378\) −0.317698 −0.0163406
\(379\) −2.16780 −0.111353 −0.0556763 0.998449i \(-0.517731\pi\)
−0.0556763 + 0.998449i \(0.517731\pi\)
\(380\) −5.20209 −0.266861
\(381\) −11.7357 −0.601237
\(382\) −29.5219 −1.51047
\(383\) 23.7594 1.21405 0.607025 0.794683i \(-0.292363\pi\)
0.607025 + 0.794683i \(0.292363\pi\)
\(384\) 28.6522 1.46215
\(385\) −0.0175087 −0.000892328 0
\(386\) 61.8437 3.14776
\(387\) −9.64613 −0.490340
\(388\) 39.9553 2.02842
\(389\) 23.9556 1.21460 0.607299 0.794473i \(-0.292253\pi\)
0.607299 + 0.794473i \(0.292253\pi\)
\(390\) 6.56567 0.332465
\(391\) 1.91374 0.0967822
\(392\) 27.3600 1.38189
\(393\) −14.5101 −0.731939
\(394\) 44.0141 2.21740
\(395\) −5.61395 −0.282468
\(396\) −3.94578 −0.198283
\(397\) −3.14305 −0.157745 −0.0788727 0.996885i \(-0.525132\pi\)
−0.0788727 + 0.996885i \(0.525132\pi\)
\(398\) −27.8860 −1.39780
\(399\) 0.0631450 0.00316120
\(400\) −8.89068 −0.444534
\(401\) 33.8638 1.69108 0.845540 0.533913i \(-0.179279\pi\)
0.845540 + 0.533913i \(0.179279\pi\)
\(402\) 42.1319 2.10135
\(403\) −24.1413 −1.20256
\(404\) −0.0122539 −0.000609657 0
\(405\) −3.39095 −0.168498
\(406\) −0.370439 −0.0183846
\(407\) 10.5100 0.520961
\(408\) −2.46766 −0.122168
\(409\) 21.5966 1.06788 0.533942 0.845521i \(-0.320710\pi\)
0.533942 + 0.845521i \(0.320710\pi\)
\(410\) 21.4590 1.05978
\(411\) −16.4293 −0.810398
\(412\) 15.7980 0.778310
\(413\) 0.0251323 0.00123668
\(414\) 10.7963 0.530610
\(415\) 10.6512 0.522848
\(416\) −8.28436 −0.406174
\(417\) −6.84194 −0.335051
\(418\) 4.58062 0.224046
\(419\) 16.1028 0.786673 0.393336 0.919395i \(-0.371321\pi\)
0.393336 + 0.919395i \(0.371321\pi\)
\(420\) −0.0883783 −0.00431242
\(421\) −1.32384 −0.0645201 −0.0322600 0.999480i \(-0.510270\pi\)
−0.0322600 + 0.999480i \(0.510270\pi\)
\(422\) 40.7906 1.98565
\(423\) 6.90828 0.335892
\(424\) −49.9898 −2.42772
\(425\) −2.02965 −0.0984524
\(426\) −42.4552 −2.05696
\(427\) −0.217822 −0.0105411
\(428\) 13.7167 0.663022
\(429\) −3.73308 −0.180235
\(430\) −15.6730 −0.755818
\(431\) 40.3712 1.94461 0.972307 0.233708i \(-0.0750861\pi\)
0.972307 + 0.233708i \(0.0750861\pi\)
\(432\) −11.2894 −0.543160
\(433\) 15.1868 0.729831 0.364916 0.931041i \(-0.381098\pi\)
0.364916 + 0.931041i \(0.381098\pi\)
\(434\) 0.503253 0.0241569
\(435\) −6.75679 −0.323963
\(436\) −43.3594 −2.07654
\(437\) −8.09298 −0.387140
\(438\) 37.6739 1.80013
\(439\) −15.6349 −0.746215 −0.373108 0.927788i \(-0.621708\pi\)
−0.373108 + 0.927788i \(0.621708\pi\)
\(440\) −2.89352 −0.137943
\(441\) 7.57664 0.360793
\(442\) 2.92008 0.138894
\(443\) 0.200075 0.00950587 0.00475293 0.999989i \(-0.498487\pi\)
0.00475293 + 0.999989i \(0.498487\pi\)
\(444\) 53.0509 2.51769
\(445\) −7.33058 −0.347503
\(446\) −15.0374 −0.712040
\(447\) 4.64076 0.219500
\(448\) 0.267165 0.0126224
\(449\) 27.4542 1.29564 0.647822 0.761792i \(-0.275680\pi\)
0.647822 + 0.761792i \(0.275680\pi\)
\(450\) −11.4502 −0.539766
\(451\) −12.2011 −0.574525
\(452\) −26.1512 −1.23005
\(453\) −11.4422 −0.537601
\(454\) −7.47411 −0.350777
\(455\) 0.0472009 0.00221281
\(456\) 10.4354 0.488684
\(457\) 33.9830 1.58966 0.794829 0.606833i \(-0.207560\pi\)
0.794829 + 0.606833i \(0.207560\pi\)
\(458\) −21.3424 −0.997263
\(459\) −2.57724 −0.120295
\(460\) 11.3270 0.528124
\(461\) −8.86716 −0.412985 −0.206492 0.978448i \(-0.566205\pi\)
−0.206492 + 0.978448i \(0.566205\pi\)
\(462\) 0.0778202 0.00362052
\(463\) 11.9162 0.553795 0.276897 0.960899i \(-0.410694\pi\)
0.276897 + 0.960899i \(0.410694\pi\)
\(464\) −13.1635 −0.611100
\(465\) 9.17931 0.425680
\(466\) 60.9382 2.82291
\(467\) −9.43492 −0.436596 −0.218298 0.975882i \(-0.570050\pi\)
−0.218298 + 0.975882i \(0.570050\pi\)
\(468\) 10.6372 0.491705
\(469\) 0.302888 0.0139861
\(470\) 11.2245 0.517749
\(471\) −13.8334 −0.637407
\(472\) 4.15340 0.191176
\(473\) 8.91127 0.409741
\(474\) 24.9520 1.14609
\(475\) 8.58311 0.393820
\(476\) −0.0393063 −0.00180160
\(477\) −13.8434 −0.633845
\(478\) −55.6567 −2.54568
\(479\) −16.5305 −0.755300 −0.377650 0.925948i \(-0.623268\pi\)
−0.377650 + 0.925948i \(0.623268\pi\)
\(480\) 3.14999 0.143776
\(481\) −28.3333 −1.29189
\(482\) −16.3919 −0.746632
\(483\) −0.137492 −0.00625609
\(484\) 3.64518 0.165690
\(485\) 8.11387 0.368432
\(486\) −25.2237 −1.14417
\(487\) 4.75603 0.215516 0.107758 0.994177i \(-0.465633\pi\)
0.107758 + 0.994177i \(0.465633\pi\)
\(488\) −35.9975 −1.62953
\(489\) −33.4005 −1.51042
\(490\) 12.3105 0.556131
\(491\) 19.9136 0.898687 0.449343 0.893359i \(-0.351658\pi\)
0.449343 + 0.893359i \(0.351658\pi\)
\(492\) −61.5869 −2.77655
\(493\) −3.00509 −0.135342
\(494\) −12.3487 −0.555592
\(495\) −0.801284 −0.0360150
\(496\) 17.8830 0.802971
\(497\) −0.305212 −0.0136906
\(498\) −47.3410 −2.12140
\(499\) −27.8491 −1.24670 −0.623349 0.781944i \(-0.714228\pi\)
−0.623349 + 0.781944i \(0.714228\pi\)
\(500\) −25.5046 −1.14060
\(501\) 16.4175 0.733481
\(502\) −33.3339 −1.48776
\(503\) −16.3229 −0.727803 −0.363902 0.931437i \(-0.618556\pi\)
−0.363902 + 0.931437i \(0.618556\pi\)
\(504\) −0.100080 −0.00445793
\(505\) −0.00248845 −0.000110735 0
\(506\) −9.97383 −0.443391
\(507\) −7.93796 −0.352537
\(508\) −30.8927 −1.37064
\(509\) −25.8239 −1.14462 −0.572312 0.820036i \(-0.693953\pi\)
−0.572312 + 0.820036i \(0.693953\pi\)
\(510\) −1.11031 −0.0491654
\(511\) 0.270839 0.0119812
\(512\) 21.7488 0.961168
\(513\) 10.8988 0.481195
\(514\) 7.77787 0.343067
\(515\) 3.20815 0.141368
\(516\) 44.9811 1.98018
\(517\) −6.38200 −0.280680
\(518\) 0.590640 0.0259512
\(519\) −33.0925 −1.45260
\(520\) 7.80047 0.342073
\(521\) 35.9772 1.57619 0.788095 0.615554i \(-0.211068\pi\)
0.788095 + 0.615554i \(0.211068\pi\)
\(522\) −16.9531 −0.742015
\(523\) −26.0216 −1.13785 −0.568923 0.822391i \(-0.692640\pi\)
−0.568923 + 0.822391i \(0.692640\pi\)
\(524\) −38.1961 −1.66860
\(525\) 0.145819 0.00636405
\(526\) −16.4775 −0.718452
\(527\) 4.08250 0.177837
\(528\) 2.76533 0.120346
\(529\) −5.37838 −0.233843
\(530\) −22.4926 −0.977018
\(531\) 1.15018 0.0499134
\(532\) 0.166221 0.00720660
\(533\) 32.8922 1.42472
\(534\) 32.5819 1.40996
\(535\) 2.78550 0.120428
\(536\) 50.0557 2.16208
\(537\) −25.7411 −1.11081
\(538\) 1.30455 0.0562431
\(539\) −6.99944 −0.301487
\(540\) −15.2541 −0.656431
\(541\) −10.1232 −0.435229 −0.217615 0.976035i \(-0.569828\pi\)
−0.217615 + 0.976035i \(0.569828\pi\)
\(542\) 37.3673 1.60506
\(543\) −8.49007 −0.364344
\(544\) 1.40096 0.0600656
\(545\) −8.80515 −0.377171
\(546\) −0.209791 −0.00897824
\(547\) 1.00000 0.0427569
\(548\) −43.2481 −1.84747
\(549\) −9.96858 −0.425449
\(550\) 10.5779 0.451042
\(551\) 12.7081 0.541384
\(552\) −22.7221 −0.967115
\(553\) 0.179381 0.00762807
\(554\) 19.2533 0.817993
\(555\) 10.7733 0.457299
\(556\) −18.0105 −0.763817
\(557\) 6.08001 0.257618 0.128809 0.991669i \(-0.458885\pi\)
0.128809 + 0.991669i \(0.458885\pi\)
\(558\) 23.0313 0.974992
\(559\) −24.0234 −1.01608
\(560\) −0.0349647 −0.00147753
\(561\) 0.631296 0.0266533
\(562\) 61.5741 2.59735
\(563\) 11.1344 0.469258 0.234629 0.972085i \(-0.424612\pi\)
0.234629 + 0.972085i \(0.424612\pi\)
\(564\) −32.2142 −1.35646
\(565\) −5.31062 −0.223419
\(566\) 38.1784 1.60476
\(567\) 0.108350 0.00455029
\(568\) −50.4398 −2.11641
\(569\) −36.8049 −1.54294 −0.771470 0.636265i \(-0.780478\pi\)
−0.771470 + 0.636265i \(0.780478\pi\)
\(570\) 4.69536 0.196667
\(571\) 7.13030 0.298394 0.149197 0.988808i \(-0.452331\pi\)
0.149197 + 0.988808i \(0.452331\pi\)
\(572\) −9.82685 −0.410881
\(573\) 17.2059 0.718787
\(574\) −0.685674 −0.0286195
\(575\) −18.6888 −0.779378
\(576\) 12.2268 0.509449
\(577\) −38.6237 −1.60793 −0.803964 0.594678i \(-0.797279\pi\)
−0.803964 + 0.594678i \(0.797279\pi\)
\(578\) 39.8975 1.65952
\(579\) −36.0436 −1.49792
\(580\) −17.7864 −0.738540
\(581\) −0.340336 −0.0141195
\(582\) −36.0633 −1.49487
\(583\) 12.7888 0.529657
\(584\) 44.7592 1.85215
\(585\) 2.16014 0.0893107
\(586\) −66.6210 −2.75209
\(587\) 17.0231 0.702617 0.351308 0.936260i \(-0.385737\pi\)
0.351308 + 0.936260i \(0.385737\pi\)
\(588\) −35.3309 −1.45702
\(589\) −17.2644 −0.711366
\(590\) 1.86880 0.0769372
\(591\) −25.6522 −1.05519
\(592\) 20.9883 0.862615
\(593\) −22.9062 −0.940644 −0.470322 0.882495i \(-0.655862\pi\)
−0.470322 + 0.882495i \(0.655862\pi\)
\(594\) 13.4318 0.551112
\(595\) −0.00798208 −0.000327233 0
\(596\) 12.2162 0.500395
\(597\) 16.2524 0.665168
\(598\) 26.8879 1.09953
\(599\) −19.9739 −0.816112 −0.408056 0.912957i \(-0.633793\pi\)
−0.408056 + 0.912957i \(0.633793\pi\)
\(600\) 24.0982 0.983804
\(601\) 7.26975 0.296539 0.148270 0.988947i \(-0.452630\pi\)
0.148270 + 0.988947i \(0.452630\pi\)
\(602\) 0.500795 0.0204109
\(603\) 13.8616 0.564489
\(604\) −30.1201 −1.22557
\(605\) 0.740241 0.0300951
\(606\) 0.0110603 0.000449295 0
\(607\) 40.3674 1.63846 0.819231 0.573464i \(-0.194401\pi\)
0.819231 + 0.573464i \(0.194401\pi\)
\(608\) −5.92447 −0.240269
\(609\) 0.215898 0.00874864
\(610\) −16.1969 −0.655793
\(611\) 17.2049 0.696035
\(612\) −1.79885 −0.0727140
\(613\) −12.6973 −0.512841 −0.256420 0.966565i \(-0.582543\pi\)
−0.256420 + 0.966565i \(0.582543\pi\)
\(614\) −37.1097 −1.49762
\(615\) −12.5067 −0.504318
\(616\) 0.0924559 0.00372515
\(617\) −14.1349 −0.569051 −0.284525 0.958669i \(-0.591836\pi\)
−0.284525 + 0.958669i \(0.591836\pi\)
\(618\) −14.2591 −0.573586
\(619\) −10.6455 −0.427880 −0.213940 0.976847i \(-0.568630\pi\)
−0.213940 + 0.976847i \(0.568630\pi\)
\(620\) 24.1634 0.970425
\(621\) −23.7311 −0.952294
\(622\) −63.2910 −2.53774
\(623\) 0.234233 0.00938433
\(624\) −7.45491 −0.298435
\(625\) 17.0809 0.683237
\(626\) 3.02105 0.120745
\(627\) −2.66967 −0.106616
\(628\) −36.4146 −1.45310
\(629\) 4.79141 0.191046
\(630\) −0.0450305 −0.00179406
\(631\) −4.53215 −0.180422 −0.0902111 0.995923i \(-0.528754\pi\)
−0.0902111 + 0.995923i \(0.528754\pi\)
\(632\) 29.6448 1.17921
\(633\) −23.7735 −0.944911
\(634\) 75.5184 2.99922
\(635\) −6.27349 −0.248956
\(636\) 64.5535 2.55971
\(637\) 18.8694 0.747634
\(638\) 15.6615 0.620046
\(639\) −13.9680 −0.552565
\(640\) 15.3165 0.605437
\(641\) 23.3323 0.921569 0.460785 0.887512i \(-0.347568\pi\)
0.460785 + 0.887512i \(0.347568\pi\)
\(642\) −12.3806 −0.488623
\(643\) −26.1118 −1.02975 −0.514875 0.857265i \(-0.672162\pi\)
−0.514875 + 0.857265i \(0.672162\pi\)
\(644\) −0.361929 −0.0142620
\(645\) 9.13449 0.359670
\(646\) 2.08827 0.0821617
\(647\) 8.91290 0.350402 0.175201 0.984533i \(-0.443942\pi\)
0.175201 + 0.984533i \(0.443942\pi\)
\(648\) 17.9061 0.703419
\(649\) −1.06255 −0.0417088
\(650\) −28.5163 −1.11850
\(651\) −0.293305 −0.0114955
\(652\) −87.9226 −3.44332
\(653\) 9.94054 0.389003 0.194502 0.980902i \(-0.437691\pi\)
0.194502 + 0.980902i \(0.437691\pi\)
\(654\) 39.1358 1.53033
\(655\) −7.75662 −0.303076
\(656\) −24.3653 −0.951307
\(657\) 12.3949 0.483571
\(658\) −0.358655 −0.0139818
\(659\) −42.6225 −1.66034 −0.830168 0.557513i \(-0.811756\pi\)
−0.830168 + 0.557513i \(0.811756\pi\)
\(660\) 3.73649 0.145443
\(661\) −18.6726 −0.726280 −0.363140 0.931734i \(-0.618295\pi\)
−0.363140 + 0.931734i \(0.618295\pi\)
\(662\) −8.24280 −0.320366
\(663\) −1.70188 −0.0660954
\(664\) −56.2444 −2.18271
\(665\) 0.0337552 0.00130897
\(666\) 27.0305 1.04741
\(667\) −27.6706 −1.07141
\(668\) 43.2171 1.67212
\(669\) 8.76404 0.338837
\(670\) 22.5223 0.870112
\(671\) 9.20916 0.355516
\(672\) −0.100651 −0.00388269
\(673\) −9.88167 −0.380910 −0.190455 0.981696i \(-0.560996\pi\)
−0.190455 + 0.981696i \(0.560996\pi\)
\(674\) 51.8749 1.99815
\(675\) 25.1683 0.968728
\(676\) −20.8957 −0.803680
\(677\) −18.6069 −0.715121 −0.357561 0.933890i \(-0.616391\pi\)
−0.357561 + 0.933890i \(0.616391\pi\)
\(678\) 23.6039 0.906501
\(679\) −0.259261 −0.00994952
\(680\) −1.31913 −0.0505863
\(681\) 4.35604 0.166924
\(682\) −21.2767 −0.814727
\(683\) −29.0955 −1.11331 −0.556654 0.830744i \(-0.687915\pi\)
−0.556654 + 0.830744i \(0.687915\pi\)
\(684\) 7.60708 0.290864
\(685\) −8.78255 −0.335564
\(686\) −0.786740 −0.0300379
\(687\) 12.4387 0.474566
\(688\) 17.7957 0.678455
\(689\) −34.4765 −1.31345
\(690\) −10.2237 −0.389208
\(691\) 5.72111 0.217641 0.108821 0.994061i \(-0.465293\pi\)
0.108821 + 0.994061i \(0.465293\pi\)
\(692\) −87.1119 −3.31150
\(693\) 0.0256033 0.000972588 0
\(694\) −0.262695 −0.00997177
\(695\) −3.65747 −0.138736
\(696\) 35.6796 1.35243
\(697\) −5.56235 −0.210689
\(698\) 48.6803 1.84258
\(699\) −35.5159 −1.34333
\(700\) 0.383849 0.0145081
\(701\) −32.6620 −1.23363 −0.616814 0.787109i \(-0.711577\pi\)
−0.616814 + 0.787109i \(0.711577\pi\)
\(702\) −36.2100 −1.36666
\(703\) −20.2623 −0.764205
\(704\) −11.2953 −0.425708
\(705\) −6.54186 −0.246381
\(706\) 0.271285 0.0102099
\(707\) 7.95131e−5 0 2.99040e−6 0
\(708\) −5.36342 −0.201569
\(709\) 12.0320 0.451873 0.225936 0.974142i \(-0.427456\pi\)
0.225936 + 0.974142i \(0.427456\pi\)
\(710\) −22.6951 −0.851733
\(711\) 8.20935 0.307875
\(712\) 38.7096 1.45070
\(713\) 37.5914 1.40781
\(714\) 0.0354776 0.00132771
\(715\) −1.99558 −0.0746303
\(716\) −67.7603 −2.53232
\(717\) 32.4377 1.21141
\(718\) −14.9517 −0.557993
\(719\) 21.3720 0.797040 0.398520 0.917160i \(-0.369524\pi\)
0.398520 + 0.917160i \(0.369524\pi\)
\(720\) −1.60015 −0.0596342
\(721\) −0.102509 −0.00381765
\(722\) 36.3122 1.35140
\(723\) 9.55351 0.355299
\(724\) −22.3490 −0.830595
\(725\) 29.3464 1.08990
\(726\) −3.29011 −0.122108
\(727\) −9.21347 −0.341709 −0.170854 0.985296i \(-0.554653\pi\)
−0.170854 + 0.985296i \(0.554653\pi\)
\(728\) −0.249247 −0.00923771
\(729\) 28.4435 1.05346
\(730\) 20.1392 0.745384
\(731\) 4.06257 0.150260
\(732\) 46.4848 1.71813
\(733\) −46.2437 −1.70805 −0.854026 0.520231i \(-0.825846\pi\)
−0.854026 + 0.520231i \(0.825846\pi\)
\(734\) 43.5587 1.60778
\(735\) −7.17477 −0.264645
\(736\) 12.8999 0.475497
\(737\) −12.8056 −0.471701
\(738\) −31.3798 −1.15511
\(739\) 10.5290 0.387315 0.193657 0.981069i \(-0.437965\pi\)
0.193657 + 0.981069i \(0.437965\pi\)
\(740\) 28.3592 1.04251
\(741\) 7.19701 0.264389
\(742\) 0.718703 0.0263844
\(743\) −32.6415 −1.19750 −0.598750 0.800936i \(-0.704336\pi\)
−0.598750 + 0.800936i \(0.704336\pi\)
\(744\) −48.4719 −1.77707
\(745\) 2.48079 0.0908891
\(746\) 32.9989 1.20818
\(747\) −15.5754 −0.569875
\(748\) 1.66181 0.0607617
\(749\) −0.0890045 −0.00325215
\(750\) 23.0202 0.840579
\(751\) 7.21461 0.263265 0.131632 0.991299i \(-0.457978\pi\)
0.131632 + 0.991299i \(0.457978\pi\)
\(752\) −12.7448 −0.464754
\(753\) 19.4276 0.707981
\(754\) −42.2211 −1.53760
\(755\) −6.11660 −0.222606
\(756\) 0.487411 0.0177270
\(757\) 4.72327 0.171670 0.0858351 0.996309i \(-0.472644\pi\)
0.0858351 + 0.996309i \(0.472644\pi\)
\(758\) 5.15061 0.187079
\(759\) 5.81292 0.210996
\(760\) 5.57842 0.202351
\(761\) −18.0472 −0.654211 −0.327106 0.944988i \(-0.606073\pi\)
−0.327106 + 0.944988i \(0.606073\pi\)
\(762\) 27.8835 1.01011
\(763\) 0.281349 0.0101855
\(764\) 45.2924 1.63862
\(765\) −0.365298 −0.0132074
\(766\) −56.4514 −2.03967
\(767\) 2.86448 0.103430
\(768\) −36.7940 −1.32769
\(769\) −22.5757 −0.814099 −0.407050 0.913406i \(-0.633442\pi\)
−0.407050 + 0.913406i \(0.633442\pi\)
\(770\) 0.0416000 0.00149916
\(771\) −4.53308 −0.163255
\(772\) −94.8802 −3.41481
\(773\) −42.3119 −1.52185 −0.760927 0.648837i \(-0.775256\pi\)
−0.760927 + 0.648837i \(0.775256\pi\)
\(774\) 22.9188 0.823800
\(775\) −39.8680 −1.43210
\(776\) −42.8458 −1.53807
\(777\) −0.344236 −0.0123494
\(778\) −56.9176 −2.04060
\(779\) 23.5225 0.842779
\(780\) −10.0730 −0.360671
\(781\) 12.9039 0.461737
\(782\) −4.54698 −0.162600
\(783\) 37.2640 1.33171
\(784\) −13.9778 −0.499207
\(785\) −7.39484 −0.263933
\(786\) 34.4755 1.22970
\(787\) −28.3379 −1.01014 −0.505068 0.863080i \(-0.668533\pi\)
−0.505068 + 0.863080i \(0.668533\pi\)
\(788\) −67.5261 −2.40552
\(789\) 9.60337 0.341889
\(790\) 13.3385 0.474563
\(791\) 0.169689 0.00603345
\(792\) 4.23123 0.150350
\(793\) −24.8265 −0.881614
\(794\) 7.46777 0.265021
\(795\) 13.1091 0.464932
\(796\) 42.7825 1.51639
\(797\) 4.58337 0.162351 0.0811757 0.996700i \(-0.474133\pi\)
0.0811757 + 0.996700i \(0.474133\pi\)
\(798\) −0.150030 −0.00531100
\(799\) −2.90950 −0.102931
\(800\) −13.6812 −0.483702
\(801\) 10.7196 0.378759
\(802\) −80.4591 −2.84111
\(803\) −11.4506 −0.404084
\(804\) −64.6386 −2.27963
\(805\) −0.0734983 −0.00259048
\(806\) 57.3587 2.02038
\(807\) −0.760314 −0.0267643
\(808\) 0.0131404 0.000462279 0
\(809\) 32.7136 1.15015 0.575075 0.818101i \(-0.304973\pi\)
0.575075 + 0.818101i \(0.304973\pi\)
\(810\) 8.05676 0.283086
\(811\) 20.4644 0.718602 0.359301 0.933222i \(-0.383015\pi\)
0.359301 + 0.933222i \(0.383015\pi\)
\(812\) 0.568325 0.0199443
\(813\) −21.7783 −0.763799
\(814\) −24.9713 −0.875244
\(815\) −17.8548 −0.625426
\(816\) 1.26069 0.0441330
\(817\) −17.1801 −0.601055
\(818\) −51.3127 −1.79411
\(819\) −0.0690225 −0.00241184
\(820\) −32.9222 −1.14969
\(821\) 54.4837 1.90149 0.950747 0.309968i \(-0.100318\pi\)
0.950747 + 0.309968i \(0.100318\pi\)
\(822\) 39.0354 1.36151
\(823\) 0.912794 0.0318180 0.0159090 0.999873i \(-0.494936\pi\)
0.0159090 + 0.999873i \(0.494936\pi\)
\(824\) −16.9408 −0.590162
\(825\) −6.16497 −0.214637
\(826\) −0.0597133 −0.00207769
\(827\) 48.1650 1.67486 0.837430 0.546545i \(-0.184057\pi\)
0.837430 + 0.546545i \(0.184057\pi\)
\(828\) −16.5636 −0.575626
\(829\) 10.1069 0.351027 0.175514 0.984477i \(-0.443841\pi\)
0.175514 + 0.984477i \(0.443841\pi\)
\(830\) −25.3069 −0.878414
\(831\) −11.2211 −0.389257
\(832\) 30.4504 1.05568
\(833\) −3.19098 −0.110561
\(834\) 16.2562 0.562905
\(835\) 8.77625 0.303715
\(836\) −7.02756 −0.243053
\(837\) −50.6244 −1.74983
\(838\) −38.2596 −1.32166
\(839\) −2.71956 −0.0938897 −0.0469448 0.998897i \(-0.514949\pi\)
−0.0469448 + 0.998897i \(0.514949\pi\)
\(840\) 0.0947718 0.00326994
\(841\) 14.4501 0.498281
\(842\) 3.14539 0.108397
\(843\) −35.8865 −1.23600
\(844\) −62.5807 −2.15411
\(845\) −4.24336 −0.145976
\(846\) −16.4138 −0.564318
\(847\) −0.0236528 −0.000812718 0
\(848\) 25.5390 0.877013
\(849\) −22.2511 −0.763655
\(850\) 4.82236 0.165406
\(851\) 44.1189 1.51238
\(852\) 65.1346 2.23147
\(853\) 13.0713 0.447552 0.223776 0.974641i \(-0.428162\pi\)
0.223776 + 0.974641i \(0.428162\pi\)
\(854\) 0.517536 0.0177097
\(855\) 1.54480 0.0528310
\(856\) −14.7090 −0.502743
\(857\) −24.8268 −0.848068 −0.424034 0.905646i \(-0.639386\pi\)
−0.424034 + 0.905646i \(0.639386\pi\)
\(858\) 8.86964 0.302804
\(859\) −40.9652 −1.39771 −0.698857 0.715262i \(-0.746307\pi\)
−0.698857 + 0.715262i \(0.746307\pi\)
\(860\) 24.0454 0.819941
\(861\) 0.399623 0.0136191
\(862\) −95.9204 −3.26706
\(863\) −23.9378 −0.814852 −0.407426 0.913238i \(-0.633574\pi\)
−0.407426 + 0.913238i \(0.633574\pi\)
\(864\) −17.3723 −0.591019
\(865\) −17.6901 −0.601483
\(866\) −36.0832 −1.22616
\(867\) −23.2530 −0.789712
\(868\) −0.772087 −0.0262064
\(869\) −7.58395 −0.257268
\(870\) 16.0539 0.544277
\(871\) 34.5220 1.16973
\(872\) 46.4961 1.57456
\(873\) −11.8650 −0.401570
\(874\) 19.2286 0.650417
\(875\) 0.165493 0.00559469
\(876\) −57.7990 −1.95285
\(877\) 8.26172 0.278979 0.139489 0.990224i \(-0.455454\pi\)
0.139489 + 0.990224i \(0.455454\pi\)
\(878\) 37.1480 1.25368
\(879\) 38.8279 1.30963
\(880\) 1.47825 0.0498319
\(881\) −47.6116 −1.60408 −0.802038 0.597273i \(-0.796251\pi\)
−0.802038 + 0.597273i \(0.796251\pi\)
\(882\) −18.0018 −0.606152
\(883\) 25.6560 0.863394 0.431697 0.902019i \(-0.357915\pi\)
0.431697 + 0.902019i \(0.357915\pi\)
\(884\) −4.47997 −0.150678
\(885\) −1.08917 −0.0366120
\(886\) −0.475371 −0.0159704
\(887\) 36.2618 1.21755 0.608776 0.793342i \(-0.291661\pi\)
0.608776 + 0.793342i \(0.291661\pi\)
\(888\) −56.8888 −1.90906
\(889\) 0.200456 0.00672307
\(890\) 17.4172 0.583825
\(891\) −4.58088 −0.153465
\(892\) 23.0702 0.772448
\(893\) 12.3039 0.411734
\(894\) −11.0263 −0.368773
\(895\) −13.7603 −0.459957
\(896\) −0.489404 −0.0163498
\(897\) −15.6707 −0.523231
\(898\) −65.2301 −2.17676
\(899\) −59.0284 −1.96871
\(900\) 17.5668 0.585559
\(901\) 5.83029 0.194235
\(902\) 28.9892 0.965235
\(903\) −0.291872 −0.00971291
\(904\) 28.0430 0.932698
\(905\) −4.53850 −0.150865
\(906\) 27.1862 0.903200
\(907\) 11.7981 0.391748 0.195874 0.980629i \(-0.437246\pi\)
0.195874 + 0.980629i \(0.437246\pi\)
\(908\) 11.4667 0.380537
\(909\) 0.00363890 0.000120695 0
\(910\) −0.112147 −0.00371765
\(911\) −2.86242 −0.0948363 −0.0474182 0.998875i \(-0.515099\pi\)
−0.0474182 + 0.998875i \(0.515099\pi\)
\(912\) −5.33129 −0.176537
\(913\) 14.3889 0.476202
\(914\) −80.7423 −2.67072
\(915\) 9.43984 0.312071
\(916\) 32.7433 1.08187
\(917\) 0.247846 0.00818458
\(918\) 6.12342 0.202103
\(919\) 49.9337 1.64716 0.823581 0.567199i \(-0.191973\pi\)
0.823581 + 0.567199i \(0.191973\pi\)
\(920\) −12.1464 −0.400456
\(921\) 21.6282 0.712672
\(922\) 21.0680 0.693838
\(923\) −34.7869 −1.14502
\(924\) −0.119391 −0.00392769
\(925\) −46.7909 −1.53848
\(926\) −28.3125 −0.930407
\(927\) −4.69132 −0.154083
\(928\) −20.2563 −0.664945
\(929\) −13.9415 −0.457406 −0.228703 0.973496i \(-0.573448\pi\)
−0.228703 + 0.973496i \(0.573448\pi\)
\(930\) −21.8097 −0.715167
\(931\) 13.4943 0.442256
\(932\) −93.4911 −3.06240
\(933\) 36.8871 1.20763
\(934\) 22.4170 0.733506
\(935\) 0.337469 0.0110364
\(936\) −11.4067 −0.372841
\(937\) 5.58943 0.182599 0.0912993 0.995823i \(-0.470898\pi\)
0.0912993 + 0.995823i \(0.470898\pi\)
\(938\) −0.719650 −0.0234974
\(939\) −1.76072 −0.0574589
\(940\) −17.2206 −0.561675
\(941\) 49.2201 1.60453 0.802265 0.596968i \(-0.203628\pi\)
0.802265 + 0.596968i \(0.203628\pi\)
\(942\) 32.8675 1.07088
\(943\) −51.2177 −1.66788
\(944\) −2.12190 −0.0690621
\(945\) 0.0989803 0.00321983
\(946\) −21.1728 −0.688387
\(947\) 55.5109 1.80386 0.901931 0.431881i \(-0.142150\pi\)
0.901931 + 0.431881i \(0.142150\pi\)
\(948\) −38.2813 −1.24332
\(949\) 30.8692 1.00206
\(950\) −20.3931 −0.661640
\(951\) −44.0134 −1.42723
\(952\) 0.0421498 0.00136608
\(953\) −21.3410 −0.691304 −0.345652 0.938363i \(-0.612342\pi\)
−0.345652 + 0.938363i \(0.612342\pi\)
\(954\) 32.8913 1.06490
\(955\) 9.19769 0.297630
\(956\) 85.3881 2.76165
\(957\) −9.12783 −0.295061
\(958\) 39.2759 1.26895
\(959\) 0.280627 0.00906191
\(960\) −11.5783 −0.373687
\(961\) 49.1920 1.58684
\(962\) 67.3188 2.17044
\(963\) −4.07328 −0.131260
\(964\) 25.1484 0.809976
\(965\) −19.2677 −0.620249
\(966\) 0.326675 0.0105106
\(967\) 0.792195 0.0254753 0.0127376 0.999919i \(-0.495945\pi\)
0.0127376 + 0.999919i \(0.495945\pi\)
\(968\) −3.90889 −0.125636
\(969\) −1.21708 −0.0390982
\(970\) −19.2782 −0.618987
\(971\) −50.4127 −1.61782 −0.808910 0.587932i \(-0.799942\pi\)
−0.808910 + 0.587932i \(0.799942\pi\)
\(972\) 38.6980 1.24124
\(973\) 0.116866 0.00374656
\(974\) −11.3001 −0.362079
\(975\) 16.6198 0.532260
\(976\) 18.3906 0.588668
\(977\) 6.57833 0.210460 0.105230 0.994448i \(-0.466442\pi\)
0.105230 + 0.994448i \(0.466442\pi\)
\(978\) 79.3583 2.53760
\(979\) −9.90297 −0.316500
\(980\) −18.8867 −0.603313
\(981\) 12.8759 0.411096
\(982\) −47.3138 −1.50984
\(983\) −22.7119 −0.724396 −0.362198 0.932101i \(-0.617974\pi\)
−0.362198 + 0.932101i \(0.617974\pi\)
\(984\) 66.0423 2.10535
\(985\) −13.7128 −0.436926
\(986\) 7.13996 0.227383
\(987\) 0.209031 0.00665352
\(988\) 18.9452 0.602728
\(989\) 37.4078 1.18950
\(990\) 1.90382 0.0605073
\(991\) −26.2906 −0.835149 −0.417575 0.908643i \(-0.637120\pi\)
−0.417575 + 0.908643i \(0.637120\pi\)
\(992\) 27.5188 0.873723
\(993\) 4.80405 0.152452
\(994\) 0.725172 0.0230011
\(995\) 8.68800 0.275428
\(996\) 72.6302 2.30138
\(997\) −7.58425 −0.240196 −0.120098 0.992762i \(-0.538321\pi\)
−0.120098 + 0.992762i \(0.538321\pi\)
\(998\) 66.1684 2.09452
\(999\) −59.4150 −1.87981
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 \(a_p\))