Properties

Label 4026.2.a.bc.1.6
Level 4026
Weight 2
Character 4026.1
Self dual Yes
Analytic conductor 32.148
Analytic rank 0
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1477718538\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-1.48002\)
Character \(\chi\) = 4026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+2.48002 q^{5}\) \(+1.00000 q^{6}\) \(+3.05465 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+2.48002 q^{5}\) \(+1.00000 q^{6}\) \(+3.05465 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+2.48002 q^{10}\) \(+1.00000 q^{11}\) \(+1.00000 q^{12}\) \(-0.563179 q^{13}\) \(+3.05465 q^{14}\) \(+2.48002 q^{15}\) \(+1.00000 q^{16}\) \(-7.92722 q^{17}\) \(+1.00000 q^{18}\) \(+2.52127 q^{19}\) \(+2.48002 q^{20}\) \(+3.05465 q^{21}\) \(+1.00000 q^{22}\) \(+5.23607 q^{23}\) \(+1.00000 q^{24}\) \(+1.15051 q^{25}\) \(-0.563179 q^{26}\) \(+1.00000 q^{27}\) \(+3.05465 q^{28}\) \(-6.06505 q^{29}\) \(+2.48002 q^{30}\) \(+9.71609 q^{31}\) \(+1.00000 q^{32}\) \(+1.00000 q^{33}\) \(-7.92722 q^{34}\) \(+7.57560 q^{35}\) \(+1.00000 q^{36}\) \(-0.209636 q^{37}\) \(+2.52127 q^{38}\) \(-0.563179 q^{39}\) \(+2.48002 q^{40}\) \(-8.94907 q^{41}\) \(+3.05465 q^{42}\) \(+11.5248 q^{43}\) \(+1.00000 q^{44}\) \(+2.48002 q^{45}\) \(+5.23607 q^{46}\) \(-11.1915 q^{47}\) \(+1.00000 q^{48}\) \(+2.33089 q^{49}\) \(+1.15051 q^{50}\) \(-7.92722 q^{51}\) \(-0.563179 q^{52}\) \(+10.0107 q^{53}\) \(+1.00000 q^{54}\) \(+2.48002 q^{55}\) \(+3.05465 q^{56}\) \(+2.52127 q^{57}\) \(-6.06505 q^{58}\) \(+6.44123 q^{59}\) \(+2.48002 q^{60}\) \(-1.00000 q^{61}\) \(+9.71609 q^{62}\) \(+3.05465 q^{63}\) \(+1.00000 q^{64}\) \(-1.39670 q^{65}\) \(+1.00000 q^{66}\) \(+0.884771 q^{67}\) \(-7.92722 q^{68}\) \(+5.23607 q^{69}\) \(+7.57560 q^{70}\) \(-0.510840 q^{71}\) \(+1.00000 q^{72}\) \(-9.15175 q^{73}\) \(-0.209636 q^{74}\) \(+1.15051 q^{75}\) \(+2.52127 q^{76}\) \(+3.05465 q^{77}\) \(-0.563179 q^{78}\) \(-11.7545 q^{79}\) \(+2.48002 q^{80}\) \(+1.00000 q^{81}\) \(-8.94907 q^{82}\) \(+9.91345 q^{83}\) \(+3.05465 q^{84}\) \(-19.6597 q^{85}\) \(+11.5248 q^{86}\) \(-6.06505 q^{87}\) \(+1.00000 q^{88}\) \(-6.04252 q^{89}\) \(+2.48002 q^{90}\) \(-1.72031 q^{91}\) \(+5.23607 q^{92}\) \(+9.71609 q^{93}\) \(-11.1915 q^{94}\) \(+6.25281 q^{95}\) \(+1.00000 q^{96}\) \(-1.64385 q^{97}\) \(+2.33089 q^{98}\) \(+1.00000 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(9q \) \(\mathstrut +\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut +\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 9q^{12} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 9q^{14} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 9q^{16} \) \(\mathstrut +\mathstrut q^{17} \) \(\mathstrut +\mathstrut 9q^{18} \) \(\mathstrut +\mathstrut 5q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut +\mathstrut 9q^{21} \) \(\mathstrut +\mathstrut 9q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 9q^{24} \) \(\mathstrut +\mathstrut 23q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut +\mathstrut 9q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut +\mathstrut 8q^{30} \) \(\mathstrut +\mathstrut 25q^{31} \) \(\mathstrut +\mathstrut 9q^{32} \) \(\mathstrut +\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 9q^{36} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut +\mathstrut 5q^{38} \) \(\mathstrut +\mathstrut 8q^{39} \) \(\mathstrut +\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 5q^{41} \) \(\mathstrut +\mathstrut 9q^{42} \) \(\mathstrut +\mathstrut 5q^{43} \) \(\mathstrut +\mathstrut 9q^{44} \) \(\mathstrut +\mathstrut 8q^{45} \) \(\mathstrut -\mathstrut q^{46} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 9q^{48} \) \(\mathstrut +\mathstrut 30q^{49} \) \(\mathstrut +\mathstrut 23q^{50} \) \(\mathstrut +\mathstrut q^{51} \) \(\mathstrut +\mathstrut 8q^{52} \) \(\mathstrut +\mathstrut q^{53} \) \(\mathstrut +\mathstrut 9q^{54} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut +\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 9q^{61} \) \(\mathstrut +\mathstrut 25q^{62} \) \(\mathstrut +\mathstrut 9q^{63} \) \(\mathstrut +\mathstrut 9q^{64} \) \(\mathstrut -\mathstrut 14q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut q^{68} \) \(\mathstrut -\mathstrut q^{69} \) \(\mathstrut +\mathstrut 5q^{70} \) \(\mathstrut +\mathstrut 20q^{71} \) \(\mathstrut +\mathstrut 9q^{72} \) \(\mathstrut +\mathstrut 15q^{73} \) \(\mathstrut +\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 5q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 8q^{78} \) \(\mathstrut -\mathstrut 2q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 9q^{81} \) \(\mathstrut +\mathstrut 5q^{82} \) \(\mathstrut +\mathstrut 21q^{83} \) \(\mathstrut +\mathstrut 9q^{84} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut +\mathstrut 5q^{86} \) \(\mathstrut -\mathstrut 14q^{87} \) \(\mathstrut +\mathstrut 9q^{88} \) \(\mathstrut +\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 8q^{90} \) \(\mathstrut -\mathstrut 19q^{91} \) \(\mathstrut -\mathstrut q^{92} \) \(\mathstrut +\mathstrut 25q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 3q^{97} \) \(\mathstrut +\mathstrut 30q^{98} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 2.48002 1.10910 0.554550 0.832151i \(-0.312890\pi\)
0.554550 + 0.832151i \(0.312890\pi\)
\(6\) 1.00000 0.408248
\(7\) 3.05465 1.15455 0.577275 0.816550i \(-0.304116\pi\)
0.577275 + 0.816550i \(0.304116\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 2.48002 0.784252
\(11\) 1.00000 0.301511
\(12\) 1.00000 0.288675
\(13\) −0.563179 −0.156198 −0.0780989 0.996946i \(-0.524885\pi\)
−0.0780989 + 0.996946i \(0.524885\pi\)
\(14\) 3.05465 0.816390
\(15\) 2.48002 0.640339
\(16\) 1.00000 0.250000
\(17\) −7.92722 −1.92263 −0.961317 0.275446i \(-0.911174\pi\)
−0.961317 + 0.275446i \(0.911174\pi\)
\(18\) 1.00000 0.235702
\(19\) 2.52127 0.578419 0.289210 0.957266i \(-0.406607\pi\)
0.289210 + 0.957266i \(0.406607\pi\)
\(20\) 2.48002 0.554550
\(21\) 3.05465 0.666579
\(22\) 1.00000 0.213201
\(23\) 5.23607 1.09180 0.545898 0.837852i \(-0.316189\pi\)
0.545898 + 0.837852i \(0.316189\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.15051 0.230102
\(26\) −0.563179 −0.110448
\(27\) 1.00000 0.192450
\(28\) 3.05465 0.577275
\(29\) −6.06505 −1.12625 −0.563126 0.826371i \(-0.690401\pi\)
−0.563126 + 0.826371i \(0.690401\pi\)
\(30\) 2.48002 0.452788
\(31\) 9.71609 1.74506 0.872531 0.488559i \(-0.162477\pi\)
0.872531 + 0.488559i \(0.162477\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.00000 0.174078
\(34\) −7.92722 −1.35951
\(35\) 7.57560 1.28051
\(36\) 1.00000 0.166667
\(37\) −0.209636 −0.0344640 −0.0172320 0.999852i \(-0.505485\pi\)
−0.0172320 + 0.999852i \(0.505485\pi\)
\(38\) 2.52127 0.409004
\(39\) −0.563179 −0.0901808
\(40\) 2.48002 0.392126
\(41\) −8.94907 −1.39761 −0.698805 0.715312i \(-0.746285\pi\)
−0.698805 + 0.715312i \(0.746285\pi\)
\(42\) 3.05465 0.471343
\(43\) 11.5248 1.75752 0.878761 0.477262i \(-0.158371\pi\)
0.878761 + 0.477262i \(0.158371\pi\)
\(44\) 1.00000 0.150756
\(45\) 2.48002 0.369700
\(46\) 5.23607 0.772016
\(47\) −11.1915 −1.63245 −0.816224 0.577735i \(-0.803937\pi\)
−0.816224 + 0.577735i \(0.803937\pi\)
\(48\) 1.00000 0.144338
\(49\) 2.33089 0.332984
\(50\) 1.15051 0.162707
\(51\) −7.92722 −1.11003
\(52\) −0.563179 −0.0780989
\(53\) 10.0107 1.37508 0.687539 0.726147i \(-0.258691\pi\)
0.687539 + 0.726147i \(0.258691\pi\)
\(54\) 1.00000 0.136083
\(55\) 2.48002 0.334406
\(56\) 3.05465 0.408195
\(57\) 2.52127 0.333951
\(58\) −6.06505 −0.796381
\(59\) 6.44123 0.838577 0.419288 0.907853i \(-0.362280\pi\)
0.419288 + 0.907853i \(0.362280\pi\)
\(60\) 2.48002 0.320170
\(61\) −1.00000 −0.128037
\(62\) 9.71609 1.23394
\(63\) 3.05465 0.384850
\(64\) 1.00000 0.125000
\(65\) −1.39670 −0.173239
\(66\) 1.00000 0.123091
\(67\) 0.884771 0.108092 0.0540460 0.998538i \(-0.482788\pi\)
0.0540460 + 0.998538i \(0.482788\pi\)
\(68\) −7.92722 −0.961317
\(69\) 5.23607 0.630348
\(70\) 7.57560 0.905458
\(71\) −0.510840 −0.0606256 −0.0303128 0.999540i \(-0.509650\pi\)
−0.0303128 + 0.999540i \(0.509650\pi\)
\(72\) 1.00000 0.117851
\(73\) −9.15175 −1.07113 −0.535566 0.844494i \(-0.679902\pi\)
−0.535566 + 0.844494i \(0.679902\pi\)
\(74\) −0.209636 −0.0243697
\(75\) 1.15051 0.132850
\(76\) 2.52127 0.289210
\(77\) 3.05465 0.348110
\(78\) −0.563179 −0.0637675
\(79\) −11.7545 −1.32248 −0.661242 0.750172i \(-0.729971\pi\)
−0.661242 + 0.750172i \(0.729971\pi\)
\(80\) 2.48002 0.277275
\(81\) 1.00000 0.111111
\(82\) −8.94907 −0.988260
\(83\) 9.91345 1.08814 0.544071 0.839039i \(-0.316882\pi\)
0.544071 + 0.839039i \(0.316882\pi\)
\(84\) 3.05465 0.333290
\(85\) −19.6597 −2.13239
\(86\) 11.5248 1.24276
\(87\) −6.06505 −0.650242
\(88\) 1.00000 0.106600
\(89\) −6.04252 −0.640505 −0.320253 0.947332i \(-0.603768\pi\)
−0.320253 + 0.947332i \(0.603768\pi\)
\(90\) 2.48002 0.261417
\(91\) −1.72031 −0.180338
\(92\) 5.23607 0.545898
\(93\) 9.71609 1.00751
\(94\) −11.1915 −1.15432
\(95\) 6.25281 0.641525
\(96\) 1.00000 0.102062
\(97\) −1.64385 −0.166908 −0.0834539 0.996512i \(-0.526595\pi\)
−0.0834539 + 0.996512i \(0.526595\pi\)
\(98\) 2.33089 0.235455
\(99\) 1.00000 0.100504
\(100\) 1.15051 0.115051
\(101\) 1.83614 0.182703 0.0913515 0.995819i \(-0.470881\pi\)
0.0913515 + 0.995819i \(0.470881\pi\)
\(102\) −7.92722 −0.784912
\(103\) 14.7996 1.45824 0.729122 0.684384i \(-0.239929\pi\)
0.729122 + 0.684384i \(0.239929\pi\)
\(104\) −0.563179 −0.0552242
\(105\) 7.57560 0.739303
\(106\) 10.0107 0.972327
\(107\) 8.98865 0.868965 0.434483 0.900680i \(-0.356931\pi\)
0.434483 + 0.900680i \(0.356931\pi\)
\(108\) 1.00000 0.0962250
\(109\) −3.15550 −0.302242 −0.151121 0.988515i \(-0.548288\pi\)
−0.151121 + 0.988515i \(0.548288\pi\)
\(110\) 2.48002 0.236461
\(111\) −0.209636 −0.0198978
\(112\) 3.05465 0.288637
\(113\) −18.7992 −1.76848 −0.884238 0.467036i \(-0.845322\pi\)
−0.884238 + 0.467036i \(0.845322\pi\)
\(114\) 2.52127 0.236139
\(115\) 12.9856 1.21091
\(116\) −6.06505 −0.563126
\(117\) −0.563179 −0.0520659
\(118\) 6.44123 0.592963
\(119\) −24.2149 −2.21977
\(120\) 2.48002 0.226394
\(121\) 1.00000 0.0909091
\(122\) −1.00000 −0.0905357
\(123\) −8.94907 −0.806911
\(124\) 9.71609 0.872531
\(125\) −9.54682 −0.853893
\(126\) 3.05465 0.272130
\(127\) −8.93785 −0.793106 −0.396553 0.918012i \(-0.629794\pi\)
−0.396553 + 0.918012i \(0.629794\pi\)
\(128\) 1.00000 0.0883883
\(129\) 11.5248 1.01471
\(130\) −1.39670 −0.122498
\(131\) −1.23327 −0.107751 −0.0538755 0.998548i \(-0.517157\pi\)
−0.0538755 + 0.998548i \(0.517157\pi\)
\(132\) 1.00000 0.0870388
\(133\) 7.70161 0.667814
\(134\) 0.884771 0.0764326
\(135\) 2.48002 0.213446
\(136\) −7.92722 −0.679753
\(137\) −12.5567 −1.07279 −0.536397 0.843966i \(-0.680215\pi\)
−0.536397 + 0.843966i \(0.680215\pi\)
\(138\) 5.23607 0.445724
\(139\) 1.69681 0.143922 0.0719608 0.997407i \(-0.477074\pi\)
0.0719608 + 0.997407i \(0.477074\pi\)
\(140\) 7.57560 0.640255
\(141\) −11.1915 −0.942495
\(142\) −0.510840 −0.0428688
\(143\) −0.563179 −0.0470954
\(144\) 1.00000 0.0833333
\(145\) −15.0415 −1.24913
\(146\) −9.15175 −0.757404
\(147\) 2.33089 0.192249
\(148\) −0.209636 −0.0172320
\(149\) −11.1537 −0.913750 −0.456875 0.889531i \(-0.651031\pi\)
−0.456875 + 0.889531i \(0.651031\pi\)
\(150\) 1.15051 0.0939388
\(151\) −24.0110 −1.95399 −0.976993 0.213272i \(-0.931588\pi\)
−0.976993 + 0.213272i \(0.931588\pi\)
\(152\) 2.52127 0.204502
\(153\) −7.92722 −0.640878
\(154\) 3.05465 0.246151
\(155\) 24.0961 1.93545
\(156\) −0.563179 −0.0450904
\(157\) 2.98169 0.237965 0.118982 0.992896i \(-0.462037\pi\)
0.118982 + 0.992896i \(0.462037\pi\)
\(158\) −11.7545 −0.935138
\(159\) 10.0107 0.793902
\(160\) 2.48002 0.196063
\(161\) 15.9944 1.26053
\(162\) 1.00000 0.0785674
\(163\) 0.137462 0.0107668 0.00538341 0.999986i \(-0.498286\pi\)
0.00538341 + 0.999986i \(0.498286\pi\)
\(164\) −8.94907 −0.698805
\(165\) 2.48002 0.193069
\(166\) 9.91345 0.769433
\(167\) −23.8724 −1.84730 −0.923651 0.383235i \(-0.874810\pi\)
−0.923651 + 0.383235i \(0.874810\pi\)
\(168\) 3.05465 0.235671
\(169\) −12.6828 −0.975602
\(170\) −19.6597 −1.50783
\(171\) 2.52127 0.192806
\(172\) 11.5248 0.878761
\(173\) 23.1350 1.75892 0.879462 0.475969i \(-0.157903\pi\)
0.879462 + 0.475969i \(0.157903\pi\)
\(174\) −6.06505 −0.459791
\(175\) 3.51441 0.265664
\(176\) 1.00000 0.0753778
\(177\) 6.44123 0.484152
\(178\) −6.04252 −0.452906
\(179\) 5.52363 0.412856 0.206428 0.978462i \(-0.433816\pi\)
0.206428 + 0.978462i \(0.433816\pi\)
\(180\) 2.48002 0.184850
\(181\) 13.7332 1.02078 0.510391 0.859943i \(-0.329501\pi\)
0.510391 + 0.859943i \(0.329501\pi\)
\(182\) −1.72031 −0.127518
\(183\) −1.00000 −0.0739221
\(184\) 5.23607 0.386008
\(185\) −0.519903 −0.0382240
\(186\) 9.71609 0.712418
\(187\) −7.92722 −0.579696
\(188\) −11.1915 −0.816224
\(189\) 3.05465 0.222193
\(190\) 6.25281 0.453627
\(191\) 3.16971 0.229352 0.114676 0.993403i \(-0.463417\pi\)
0.114676 + 0.993403i \(0.463417\pi\)
\(192\) 1.00000 0.0721688
\(193\) 12.5415 0.902758 0.451379 0.892332i \(-0.350932\pi\)
0.451379 + 0.892332i \(0.350932\pi\)
\(194\) −1.64385 −0.118022
\(195\) −1.39670 −0.100020
\(196\) 2.33089 0.166492
\(197\) −6.86021 −0.488769 −0.244385 0.969678i \(-0.578586\pi\)
−0.244385 + 0.969678i \(0.578586\pi\)
\(198\) 1.00000 0.0710669
\(199\) 15.1849 1.07643 0.538213 0.842809i \(-0.319100\pi\)
0.538213 + 0.842809i \(0.319100\pi\)
\(200\) 1.15051 0.0813534
\(201\) 0.884771 0.0624069
\(202\) 1.83614 0.129191
\(203\) −18.5266 −1.30031
\(204\) −7.92722 −0.555016
\(205\) −22.1939 −1.55009
\(206\) 14.7996 1.03113
\(207\) 5.23607 0.363932
\(208\) −0.563179 −0.0390494
\(209\) 2.52127 0.174400
\(210\) 7.57560 0.522766
\(211\) −12.8366 −0.883708 −0.441854 0.897087i \(-0.645679\pi\)
−0.441854 + 0.897087i \(0.645679\pi\)
\(212\) 10.0107 0.687539
\(213\) −0.510840 −0.0350022
\(214\) 8.98865 0.614451
\(215\) 28.5819 1.94927
\(216\) 1.00000 0.0680414
\(217\) 29.6793 2.01476
\(218\) −3.15550 −0.213717
\(219\) −9.15175 −0.618418
\(220\) 2.48002 0.167203
\(221\) 4.46444 0.300311
\(222\) −0.209636 −0.0140699
\(223\) −9.17245 −0.614233 −0.307116 0.951672i \(-0.599364\pi\)
−0.307116 + 0.951672i \(0.599364\pi\)
\(224\) 3.05465 0.204097
\(225\) 1.15051 0.0767007
\(226\) −18.7992 −1.25050
\(227\) −18.1194 −1.20263 −0.601314 0.799013i \(-0.705356\pi\)
−0.601314 + 0.799013i \(0.705356\pi\)
\(228\) 2.52127 0.166975
\(229\) −2.69696 −0.178220 −0.0891101 0.996022i \(-0.528402\pi\)
−0.0891101 + 0.996022i \(0.528402\pi\)
\(230\) 12.9856 0.856243
\(231\) 3.05465 0.200981
\(232\) −6.06505 −0.398190
\(233\) 23.2176 1.52104 0.760519 0.649315i \(-0.224945\pi\)
0.760519 + 0.649315i \(0.224945\pi\)
\(234\) −0.563179 −0.0368162
\(235\) −27.7552 −1.81055
\(236\) 6.44123 0.419288
\(237\) −11.7545 −0.763537
\(238\) −24.2149 −1.56962
\(239\) 1.27199 0.0822784 0.0411392 0.999153i \(-0.486901\pi\)
0.0411392 + 0.999153i \(0.486901\pi\)
\(240\) 2.48002 0.160085
\(241\) −3.69603 −0.238082 −0.119041 0.992889i \(-0.537982\pi\)
−0.119041 + 0.992889i \(0.537982\pi\)
\(242\) 1.00000 0.0642824
\(243\) 1.00000 0.0641500
\(244\) −1.00000 −0.0640184
\(245\) 5.78066 0.369313
\(246\) −8.94907 −0.570572
\(247\) −1.41993 −0.0903478
\(248\) 9.71609 0.616972
\(249\) 9.91345 0.628239
\(250\) −9.54682 −0.603794
\(251\) 14.6841 0.926855 0.463428 0.886135i \(-0.346619\pi\)
0.463428 + 0.886135i \(0.346619\pi\)
\(252\) 3.05465 0.192425
\(253\) 5.23607 0.329189
\(254\) −8.93785 −0.560811
\(255\) −19.6597 −1.23114
\(256\) 1.00000 0.0625000
\(257\) 14.5769 0.909284 0.454642 0.890674i \(-0.349767\pi\)
0.454642 + 0.890674i \(0.349767\pi\)
\(258\) 11.5248 0.717505
\(259\) −0.640365 −0.0397904
\(260\) −1.39670 −0.0866194
\(261\) −6.06505 −0.375417
\(262\) −1.23327 −0.0761915
\(263\) 5.61536 0.346258 0.173129 0.984899i \(-0.444612\pi\)
0.173129 + 0.984899i \(0.444612\pi\)
\(264\) 1.00000 0.0615457
\(265\) 24.8268 1.52510
\(266\) 7.70161 0.472216
\(267\) −6.04252 −0.369796
\(268\) 0.884771 0.0540460
\(269\) 2.38580 0.145465 0.0727324 0.997351i \(-0.476828\pi\)
0.0727324 + 0.997351i \(0.476828\pi\)
\(270\) 2.48002 0.150929
\(271\) 9.99441 0.607117 0.303559 0.952813i \(-0.401825\pi\)
0.303559 + 0.952813i \(0.401825\pi\)
\(272\) −7.92722 −0.480658
\(273\) −1.72031 −0.104118
\(274\) −12.5567 −0.758580
\(275\) 1.15051 0.0693784
\(276\) 5.23607 0.315174
\(277\) −23.6176 −1.41905 −0.709523 0.704682i \(-0.751090\pi\)
−0.709523 + 0.704682i \(0.751090\pi\)
\(278\) 1.69681 0.101768
\(279\) 9.71609 0.581687
\(280\) 7.57560 0.452729
\(281\) −3.30201 −0.196982 −0.0984908 0.995138i \(-0.531401\pi\)
−0.0984908 + 0.995138i \(0.531401\pi\)
\(282\) −11.1915 −0.666444
\(283\) 8.84256 0.525636 0.262818 0.964845i \(-0.415348\pi\)
0.262818 + 0.964845i \(0.415348\pi\)
\(284\) −0.510840 −0.0303128
\(285\) 6.25281 0.370385
\(286\) −0.563179 −0.0333015
\(287\) −27.3363 −1.61361
\(288\) 1.00000 0.0589256
\(289\) 45.8408 2.69652
\(290\) −15.0415 −0.883265
\(291\) −1.64385 −0.0963643
\(292\) −9.15175 −0.535566
\(293\) −9.08141 −0.530542 −0.265271 0.964174i \(-0.585461\pi\)
−0.265271 + 0.964174i \(0.585461\pi\)
\(294\) 2.33089 0.135940
\(295\) 15.9744 0.930065
\(296\) −0.209636 −0.0121849
\(297\) 1.00000 0.0580259
\(298\) −11.1537 −0.646119
\(299\) −2.94884 −0.170536
\(300\) 1.15051 0.0664248
\(301\) 35.2044 2.02915
\(302\) −24.0110 −1.38168
\(303\) 1.83614 0.105484
\(304\) 2.52127 0.144605
\(305\) −2.48002 −0.142006
\(306\) −7.92722 −0.453169
\(307\) 27.4504 1.56668 0.783338 0.621596i \(-0.213516\pi\)
0.783338 + 0.621596i \(0.213516\pi\)
\(308\) 3.05465 0.174055
\(309\) 14.7996 0.841918
\(310\) 24.0961 1.36857
\(311\) −18.8187 −1.06711 −0.533557 0.845764i \(-0.679145\pi\)
−0.533557 + 0.845764i \(0.679145\pi\)
\(312\) −0.563179 −0.0318837
\(313\) 3.52222 0.199087 0.0995437 0.995033i \(-0.468262\pi\)
0.0995437 + 0.995033i \(0.468262\pi\)
\(314\) 2.98169 0.168267
\(315\) 7.57560 0.426837
\(316\) −11.7545 −0.661242
\(317\) 5.11337 0.287196 0.143598 0.989636i \(-0.454133\pi\)
0.143598 + 0.989636i \(0.454133\pi\)
\(318\) 10.0107 0.561373
\(319\) −6.06505 −0.339578
\(320\) 2.48002 0.138637
\(321\) 8.98865 0.501697
\(322\) 15.9944 0.891331
\(323\) −19.9867 −1.11209
\(324\) 1.00000 0.0555556
\(325\) −0.647943 −0.0359414
\(326\) 0.137462 0.00761329
\(327\) −3.15550 −0.174500
\(328\) −8.94907 −0.494130
\(329\) −34.1861 −1.88474
\(330\) 2.48002 0.136521
\(331\) −3.31658 −0.182296 −0.0911478 0.995837i \(-0.529054\pi\)
−0.0911478 + 0.995837i \(0.529054\pi\)
\(332\) 9.91345 0.544071
\(333\) −0.209636 −0.0114880
\(334\) −23.8724 −1.30624
\(335\) 2.19425 0.119885
\(336\) 3.05465 0.166645
\(337\) 25.8047 1.40567 0.702836 0.711352i \(-0.251917\pi\)
0.702836 + 0.711352i \(0.251917\pi\)
\(338\) −12.6828 −0.689855
\(339\) −18.7992 −1.02103
\(340\) −19.6597 −1.06620
\(341\) 9.71609 0.526156
\(342\) 2.52127 0.136335
\(343\) −14.2625 −0.770103
\(344\) 11.5248 0.621378
\(345\) 12.9856 0.699119
\(346\) 23.1350 1.24375
\(347\) 10.6264 0.570454 0.285227 0.958460i \(-0.407931\pi\)
0.285227 + 0.958460i \(0.407931\pi\)
\(348\) −6.06505 −0.325121
\(349\) −8.05418 −0.431131 −0.215565 0.976489i \(-0.569159\pi\)
−0.215565 + 0.976489i \(0.569159\pi\)
\(350\) 3.51441 0.187853
\(351\) −0.563179 −0.0300603
\(352\) 1.00000 0.0533002
\(353\) 15.8575 0.844008 0.422004 0.906594i \(-0.361327\pi\)
0.422004 + 0.906594i \(0.361327\pi\)
\(354\) 6.44123 0.342347
\(355\) −1.26690 −0.0672398
\(356\) −6.04252 −0.320253
\(357\) −24.2149 −1.28159
\(358\) 5.52363 0.291933
\(359\) −22.9502 −1.21127 −0.605633 0.795744i \(-0.707080\pi\)
−0.605633 + 0.795744i \(0.707080\pi\)
\(360\) 2.48002 0.130709
\(361\) −12.6432 −0.665431
\(362\) 13.7332 0.721802
\(363\) 1.00000 0.0524864
\(364\) −1.72031 −0.0901690
\(365\) −22.6965 −1.18799
\(366\) −1.00000 −0.0522708
\(367\) −1.88699 −0.0985003 −0.0492501 0.998786i \(-0.515683\pi\)
−0.0492501 + 0.998786i \(0.515683\pi\)
\(368\) 5.23607 0.272949
\(369\) −8.94907 −0.465870
\(370\) −0.519903 −0.0270284
\(371\) 30.5792 1.58760
\(372\) 9.71609 0.503756
\(373\) −28.7332 −1.48775 −0.743875 0.668318i \(-0.767014\pi\)
−0.743875 + 0.668318i \(0.767014\pi\)
\(374\) −7.92722 −0.409907
\(375\) −9.54682 −0.492996
\(376\) −11.1915 −0.577158
\(377\) 3.41571 0.175918
\(378\) 3.05465 0.157114
\(379\) −20.4724 −1.05160 −0.525799 0.850609i \(-0.676234\pi\)
−0.525799 + 0.850609i \(0.676234\pi\)
\(380\) 6.25281 0.320762
\(381\) −8.93785 −0.457900
\(382\) 3.16971 0.162177
\(383\) −9.30271 −0.475346 −0.237673 0.971345i \(-0.576385\pi\)
−0.237673 + 0.971345i \(0.576385\pi\)
\(384\) 1.00000 0.0510310
\(385\) 7.57560 0.386088
\(386\) 12.5415 0.638346
\(387\) 11.5248 0.585841
\(388\) −1.64385 −0.0834539
\(389\) 18.7260 0.949446 0.474723 0.880135i \(-0.342548\pi\)
0.474723 + 0.880135i \(0.342548\pi\)
\(390\) −1.39670 −0.0707245
\(391\) −41.5075 −2.09912
\(392\) 2.33089 0.117728
\(393\) −1.23327 −0.0622101
\(394\) −6.86021 −0.345612
\(395\) −29.1514 −1.46677
\(396\) 1.00000 0.0502519
\(397\) 9.81052 0.492376 0.246188 0.969222i \(-0.420822\pi\)
0.246188 + 0.969222i \(0.420822\pi\)
\(398\) 15.1849 0.761148
\(399\) 7.70161 0.385563
\(400\) 1.15051 0.0575255
\(401\) −28.6037 −1.42840 −0.714199 0.699942i \(-0.753209\pi\)
−0.714199 + 0.699942i \(0.753209\pi\)
\(402\) 0.884771 0.0441284
\(403\) −5.47190 −0.272575
\(404\) 1.83614 0.0913515
\(405\) 2.48002 0.123233
\(406\) −18.5266 −0.919461
\(407\) −0.209636 −0.0103913
\(408\) −7.92722 −0.392456
\(409\) 22.5803 1.11652 0.558262 0.829665i \(-0.311468\pi\)
0.558262 + 0.829665i \(0.311468\pi\)
\(410\) −22.1939 −1.09608
\(411\) −12.5567 −0.619378
\(412\) 14.7996 0.729122
\(413\) 19.6757 0.968178
\(414\) 5.23607 0.257339
\(415\) 24.5856 1.20686
\(416\) −0.563179 −0.0276121
\(417\) 1.69681 0.0830931
\(418\) 2.52127 0.123319
\(419\) 10.5038 0.513142 0.256571 0.966525i \(-0.417407\pi\)
0.256571 + 0.966525i \(0.417407\pi\)
\(420\) 7.57560 0.369651
\(421\) 9.57254 0.466537 0.233269 0.972412i \(-0.425058\pi\)
0.233269 + 0.972412i \(0.425058\pi\)
\(422\) −12.8366 −0.624876
\(423\) −11.1915 −0.544150
\(424\) 10.0107 0.486164
\(425\) −9.12035 −0.442402
\(426\) −0.510840 −0.0247503
\(427\) −3.05465 −0.147825
\(428\) 8.98865 0.434483
\(429\) −0.563179 −0.0271905
\(430\) 28.5819 1.37834
\(431\) 22.8634 1.10129 0.550645 0.834740i \(-0.314382\pi\)
0.550645 + 0.834740i \(0.314382\pi\)
\(432\) 1.00000 0.0481125
\(433\) −24.8870 −1.19599 −0.597996 0.801499i \(-0.704036\pi\)
−0.597996 + 0.801499i \(0.704036\pi\)
\(434\) 29.6793 1.42465
\(435\) −15.0415 −0.721183
\(436\) −3.15550 −0.151121
\(437\) 13.2016 0.631516
\(438\) −9.15175 −0.437287
\(439\) 37.4005 1.78503 0.892514 0.451021i \(-0.148940\pi\)
0.892514 + 0.451021i \(0.148940\pi\)
\(440\) 2.48002 0.118230
\(441\) 2.33089 0.110995
\(442\) 4.46444 0.212352
\(443\) 4.65294 0.221068 0.110534 0.993872i \(-0.464744\pi\)
0.110534 + 0.993872i \(0.464744\pi\)
\(444\) −0.209636 −0.00994890
\(445\) −14.9856 −0.710384
\(446\) −9.17245 −0.434328
\(447\) −11.1537 −0.527554
\(448\) 3.05465 0.144319
\(449\) 7.34048 0.346419 0.173209 0.984885i \(-0.444586\pi\)
0.173209 + 0.984885i \(0.444586\pi\)
\(450\) 1.15051 0.0542356
\(451\) −8.94907 −0.421395
\(452\) −18.7992 −0.884238
\(453\) −24.0110 −1.12813
\(454\) −18.1194 −0.850387
\(455\) −4.26642 −0.200013
\(456\) 2.52127 0.118069
\(457\) −22.9286 −1.07256 −0.536278 0.844041i \(-0.680170\pi\)
−0.536278 + 0.844041i \(0.680170\pi\)
\(458\) −2.69696 −0.126021
\(459\) −7.92722 −0.370011
\(460\) 12.9856 0.605455
\(461\) −30.3009 −1.41125 −0.705627 0.708584i \(-0.749334\pi\)
−0.705627 + 0.708584i \(0.749334\pi\)
\(462\) 3.05465 0.142115
\(463\) −13.1614 −0.611661 −0.305831 0.952086i \(-0.598934\pi\)
−0.305831 + 0.952086i \(0.598934\pi\)
\(464\) −6.06505 −0.281563
\(465\) 24.0961 1.11743
\(466\) 23.2176 1.07554
\(467\) −39.2863 −1.81796 −0.908978 0.416845i \(-0.863136\pi\)
−0.908978 + 0.416845i \(0.863136\pi\)
\(468\) −0.563179 −0.0260330
\(469\) 2.70267 0.124798
\(470\) −27.7552 −1.28025
\(471\) 2.98169 0.137389
\(472\) 6.44123 0.296482
\(473\) 11.5248 0.529913
\(474\) −11.7545 −0.539902
\(475\) 2.90075 0.133096
\(476\) −24.2149 −1.10989
\(477\) 10.0107 0.458359
\(478\) 1.27199 0.0581796
\(479\) 27.5371 1.25820 0.629102 0.777323i \(-0.283423\pi\)
0.629102 + 0.777323i \(0.283423\pi\)
\(480\) 2.48002 0.113197
\(481\) 0.118063 0.00538320
\(482\) −3.69603 −0.168350
\(483\) 15.9944 0.727768
\(484\) 1.00000 0.0454545
\(485\) −4.07679 −0.185117
\(486\) 1.00000 0.0453609
\(487\) −23.3045 −1.05603 −0.528014 0.849236i \(-0.677063\pi\)
−0.528014 + 0.849236i \(0.677063\pi\)
\(488\) −1.00000 −0.0452679
\(489\) 0.137462 0.00621622
\(490\) 5.78066 0.261144
\(491\) 26.6058 1.20070 0.600352 0.799736i \(-0.295027\pi\)
0.600352 + 0.799736i \(0.295027\pi\)
\(492\) −8.94907 −0.403455
\(493\) 48.0790 2.16537
\(494\) −1.41993 −0.0638856
\(495\) 2.48002 0.111469
\(496\) 9.71609 0.436265
\(497\) −1.56044 −0.0699952
\(498\) 9.91345 0.444232
\(499\) 19.4279 0.869710 0.434855 0.900500i \(-0.356800\pi\)
0.434855 + 0.900500i \(0.356800\pi\)
\(500\) −9.54682 −0.426947
\(501\) −23.8724 −1.06654
\(502\) 14.6841 0.655386
\(503\) −1.34412 −0.0599315 −0.0299657 0.999551i \(-0.509540\pi\)
−0.0299657 + 0.999551i \(0.509540\pi\)
\(504\) 3.05465 0.136065
\(505\) 4.55368 0.202636
\(506\) 5.23607 0.232772
\(507\) −12.6828 −0.563264
\(508\) −8.93785 −0.396553
\(509\) −1.53645 −0.0681019 −0.0340509 0.999420i \(-0.510841\pi\)
−0.0340509 + 0.999420i \(0.510841\pi\)
\(510\) −19.6597 −0.870545
\(511\) −27.9554 −1.23667
\(512\) 1.00000 0.0441942
\(513\) 2.52127 0.111317
\(514\) 14.5769 0.642961
\(515\) 36.7032 1.61734
\(516\) 11.5248 0.507353
\(517\) −11.1915 −0.492202
\(518\) −0.640365 −0.0281360
\(519\) 23.1350 1.01552
\(520\) −1.39670 −0.0612492
\(521\) −8.24810 −0.361356 −0.180678 0.983542i \(-0.557829\pi\)
−0.180678 + 0.983542i \(0.557829\pi\)
\(522\) −6.06505 −0.265460
\(523\) 23.6098 1.03239 0.516193 0.856472i \(-0.327349\pi\)
0.516193 + 0.856472i \(0.327349\pi\)
\(524\) −1.23327 −0.0538755
\(525\) 3.51441 0.153381
\(526\) 5.61536 0.244841
\(527\) −77.0216 −3.35511
\(528\) 1.00000 0.0435194
\(529\) 4.41640 0.192018
\(530\) 24.8268 1.07841
\(531\) 6.44123 0.279526
\(532\) 7.70161 0.333907
\(533\) 5.03993 0.218304
\(534\) −6.04252 −0.261485
\(535\) 22.2920 0.963769
\(536\) 0.884771 0.0382163
\(537\) 5.52363 0.238362
\(538\) 2.38580 0.102859
\(539\) 2.33089 0.100399
\(540\) 2.48002 0.106723
\(541\) −6.18059 −0.265724 −0.132862 0.991135i \(-0.542417\pi\)
−0.132862 + 0.991135i \(0.542417\pi\)
\(542\) 9.99441 0.429297
\(543\) 13.7332 0.589349
\(544\) −7.92722 −0.339877
\(545\) −7.82571 −0.335217
\(546\) −1.72031 −0.0736227
\(547\) 31.9594 1.36649 0.683243 0.730191i \(-0.260569\pi\)
0.683243 + 0.730191i \(0.260569\pi\)
\(548\) −12.5567 −0.536397
\(549\) −1.00000 −0.0426790
\(550\) 1.15051 0.0490579
\(551\) −15.2917 −0.651446
\(552\) 5.23607 0.222862
\(553\) −35.9059 −1.52687
\(554\) −23.6176 −1.00342
\(555\) −0.519903 −0.0220686
\(556\) 1.69681 0.0719608
\(557\) 20.0481 0.849465 0.424732 0.905319i \(-0.360368\pi\)
0.424732 + 0.905319i \(0.360368\pi\)
\(558\) 9.71609 0.411315
\(559\) −6.49055 −0.274521
\(560\) 7.57560 0.320128
\(561\) −7.92722 −0.334687
\(562\) −3.30201 −0.139287
\(563\) −28.3156 −1.19336 −0.596681 0.802479i \(-0.703514\pi\)
−0.596681 + 0.802479i \(0.703514\pi\)
\(564\) −11.1915 −0.471247
\(565\) −46.6223 −1.96142
\(566\) 8.84256 0.371681
\(567\) 3.05465 0.128283
\(568\) −0.510840 −0.0214344
\(569\) −24.2313 −1.01583 −0.507915 0.861407i \(-0.669584\pi\)
−0.507915 + 0.861407i \(0.669584\pi\)
\(570\) 6.25281 0.261901
\(571\) 31.8198 1.33162 0.665809 0.746122i \(-0.268087\pi\)
0.665809 + 0.746122i \(0.268087\pi\)
\(572\) −0.563179 −0.0235477
\(573\) 3.16971 0.132417
\(574\) −27.3363 −1.14099
\(575\) 6.02415 0.251224
\(576\) 1.00000 0.0416667
\(577\) 26.1956 1.09054 0.545268 0.838262i \(-0.316428\pi\)
0.545268 + 0.838262i \(0.316428\pi\)
\(578\) 45.8408 1.90673
\(579\) 12.5415 0.521207
\(580\) −15.0415 −0.624563
\(581\) 30.2821 1.25631
\(582\) −1.64385 −0.0681399
\(583\) 10.0107 0.414602
\(584\) −9.15175 −0.378702
\(585\) −1.39670 −0.0577463
\(586\) −9.08141 −0.375150
\(587\) −30.5834 −1.26231 −0.631156 0.775656i \(-0.717419\pi\)
−0.631156 + 0.775656i \(0.717419\pi\)
\(588\) 2.33089 0.0961243
\(589\) 24.4969 1.00938
\(590\) 15.9744 0.657655
\(591\) −6.86021 −0.282191
\(592\) −0.209636 −0.00861600
\(593\) −28.1893 −1.15760 −0.578798 0.815471i \(-0.696478\pi\)
−0.578798 + 0.815471i \(0.696478\pi\)
\(594\) 1.00000 0.0410305
\(595\) −60.0535 −2.46195
\(596\) −11.1537 −0.456875
\(597\) 15.1849 0.621475
\(598\) −2.94884 −0.120587
\(599\) −12.5385 −0.512308 −0.256154 0.966636i \(-0.582455\pi\)
−0.256154 + 0.966636i \(0.582455\pi\)
\(600\) 1.15051 0.0469694
\(601\) 16.9268 0.690458 0.345229 0.938518i \(-0.387801\pi\)
0.345229 + 0.938518i \(0.387801\pi\)
\(602\) 35.2044 1.43482
\(603\) 0.884771 0.0360307
\(604\) −24.0110 −0.976993
\(605\) 2.48002 0.100827
\(606\) 1.83614 0.0745882
\(607\) 37.6087 1.52649 0.763245 0.646109i \(-0.223605\pi\)
0.763245 + 0.646109i \(0.223605\pi\)
\(608\) 2.52127 0.102251
\(609\) −18.5266 −0.750737
\(610\) −2.48002 −0.100413
\(611\) 6.30282 0.254985
\(612\) −7.92722 −0.320439
\(613\) −39.6419 −1.60112 −0.800561 0.599251i \(-0.795465\pi\)
−0.800561 + 0.599251i \(0.795465\pi\)
\(614\) 27.4504 1.10781
\(615\) −22.1939 −0.894944
\(616\) 3.05465 0.123075
\(617\) −43.0664 −1.73379 −0.866894 0.498493i \(-0.833887\pi\)
−0.866894 + 0.498493i \(0.833887\pi\)
\(618\) 14.7996 0.595326
\(619\) −14.0636 −0.565264 −0.282632 0.959228i \(-0.591208\pi\)
−0.282632 + 0.959228i \(0.591208\pi\)
\(620\) 24.0961 0.967723
\(621\) 5.23607 0.210116
\(622\) −18.8187 −0.754563
\(623\) −18.4578 −0.739495
\(624\) −0.563179 −0.0225452
\(625\) −29.4289 −1.17716
\(626\) 3.52222 0.140776
\(627\) 2.52127 0.100690
\(628\) 2.98169 0.118982
\(629\) 1.66183 0.0662616
\(630\) 7.57560 0.301819
\(631\) −2.98845 −0.118968 −0.0594841 0.998229i \(-0.518946\pi\)
−0.0594841 + 0.998229i \(0.518946\pi\)
\(632\) −11.7545 −0.467569
\(633\) −12.8366 −0.510209
\(634\) 5.11337 0.203078
\(635\) −22.1661 −0.879634
\(636\) 10.0107 0.396951
\(637\) −1.31271 −0.0520114
\(638\) −6.06505 −0.240118
\(639\) −0.510840 −0.0202085
\(640\) 2.48002 0.0980315
\(641\) 3.37291 0.133222 0.0666110 0.997779i \(-0.478781\pi\)
0.0666110 + 0.997779i \(0.478781\pi\)
\(642\) 8.98865 0.354754
\(643\) −32.4451 −1.27951 −0.639755 0.768579i \(-0.720964\pi\)
−0.639755 + 0.768579i \(0.720964\pi\)
\(644\) 15.9944 0.630266
\(645\) 28.5819 1.12541
\(646\) −19.9867 −0.786365
\(647\) 12.8345 0.504575 0.252288 0.967652i \(-0.418817\pi\)
0.252288 + 0.967652i \(0.418817\pi\)
\(648\) 1.00000 0.0392837
\(649\) 6.44123 0.252840
\(650\) −0.647943 −0.0254144
\(651\) 29.6793 1.16322
\(652\) 0.137462 0.00538341
\(653\) −27.5362 −1.07757 −0.538787 0.842442i \(-0.681117\pi\)
−0.538787 + 0.842442i \(0.681117\pi\)
\(654\) −3.15550 −0.123390
\(655\) −3.05853 −0.119507
\(656\) −8.94907 −0.349403
\(657\) −9.15175 −0.357044
\(658\) −34.1861 −1.33271
\(659\) 11.5977 0.451781 0.225891 0.974153i \(-0.427471\pi\)
0.225891 + 0.974153i \(0.427471\pi\)
\(660\) 2.48002 0.0965347
\(661\) 9.16858 0.356616 0.178308 0.983975i \(-0.442938\pi\)
0.178308 + 0.983975i \(0.442938\pi\)
\(662\) −3.31658 −0.128902
\(663\) 4.46444 0.173385
\(664\) 9.91345 0.384716
\(665\) 19.1002 0.740672
\(666\) −0.209636 −0.00812324
\(667\) −31.7570 −1.22964
\(668\) −23.8724 −0.923651
\(669\) −9.17245 −0.354627
\(670\) 2.19425 0.0847713
\(671\) −1.00000 −0.0386046
\(672\) 3.05465 0.117836
\(673\) −9.77653 −0.376857 −0.188429 0.982087i \(-0.560339\pi\)
−0.188429 + 0.982087i \(0.560339\pi\)
\(674\) 25.8047 0.993960
\(675\) 1.15051 0.0442832
\(676\) −12.6828 −0.487801
\(677\) −23.6193 −0.907764 −0.453882 0.891062i \(-0.649961\pi\)
−0.453882 + 0.891062i \(0.649961\pi\)
\(678\) −18.7992 −0.721978
\(679\) −5.02139 −0.192703
\(680\) −19.6597 −0.753914
\(681\) −18.1194 −0.694338
\(682\) 9.71609 0.372048
\(683\) 8.49649 0.325109 0.162554 0.986700i \(-0.448027\pi\)
0.162554 + 0.986700i \(0.448027\pi\)
\(684\) 2.52127 0.0964032
\(685\) −31.1410 −1.18983
\(686\) −14.2625 −0.544545
\(687\) −2.69696 −0.102895
\(688\) 11.5248 0.439381
\(689\) −5.63783 −0.214784
\(690\) 12.9856 0.494352
\(691\) 37.9056 1.44200 0.720999 0.692937i \(-0.243683\pi\)
0.720999 + 0.692937i \(0.243683\pi\)
\(692\) 23.1350 0.879462
\(693\) 3.05465 0.116037
\(694\) 10.6264 0.403372
\(695\) 4.20813 0.159623
\(696\) −6.06505 −0.229895
\(697\) 70.9413 2.68709
\(698\) −8.05418 −0.304855
\(699\) 23.2176 0.878172
\(700\) 3.51441 0.132832
\(701\) 17.5404 0.662491 0.331245 0.943545i \(-0.392531\pi\)
0.331245 + 0.943545i \(0.392531\pi\)
\(702\) −0.563179 −0.0212558
\(703\) −0.528550 −0.0199346
\(704\) 1.00000 0.0376889
\(705\) −27.7552 −1.04532
\(706\) 15.8575 0.596804
\(707\) 5.60877 0.210940
\(708\) 6.44123 0.242076
\(709\) 3.19203 0.119879 0.0599396 0.998202i \(-0.480909\pi\)
0.0599396 + 0.998202i \(0.480909\pi\)
\(710\) −1.26690 −0.0475457
\(711\) −11.7545 −0.440828
\(712\) −6.04252 −0.226453
\(713\) 50.8741 1.90525
\(714\) −24.2149 −0.906219
\(715\) −1.39670 −0.0522335
\(716\) 5.52363 0.206428
\(717\) 1.27199 0.0475035
\(718\) −22.9502 −0.856494
\(719\) −8.35794 −0.311699 −0.155849 0.987781i \(-0.549811\pi\)
−0.155849 + 0.987781i \(0.549811\pi\)
\(720\) 2.48002 0.0924250
\(721\) 45.2075 1.68361
\(722\) −12.6432 −0.470531
\(723\) −3.69603 −0.137457
\(724\) 13.7332 0.510391
\(725\) −6.97791 −0.259153
\(726\) 1.00000 0.0371135
\(727\) 9.05645 0.335885 0.167943 0.985797i \(-0.446288\pi\)
0.167943 + 0.985797i \(0.446288\pi\)
\(728\) −1.72031 −0.0637591
\(729\) 1.00000 0.0370370
\(730\) −22.6965 −0.840037
\(731\) −91.3600 −3.37907
\(732\) −1.00000 −0.0369611
\(733\) −42.4251 −1.56701 −0.783503 0.621388i \(-0.786569\pi\)
−0.783503 + 0.621388i \(0.786569\pi\)
\(734\) −1.88699 −0.0696502
\(735\) 5.78066 0.213223
\(736\) 5.23607 0.193004
\(737\) 0.884771 0.0325910
\(738\) −8.94907 −0.329420
\(739\) 1.48944 0.0547898 0.0273949 0.999625i \(-0.491279\pi\)
0.0273949 + 0.999625i \(0.491279\pi\)
\(740\) −0.519903 −0.0191120
\(741\) −1.41993 −0.0521623
\(742\) 30.5792 1.12260
\(743\) 2.22990 0.0818072 0.0409036 0.999163i \(-0.486976\pi\)
0.0409036 + 0.999163i \(0.486976\pi\)
\(744\) 9.71609 0.356209
\(745\) −27.6615 −1.01344
\(746\) −28.7332 −1.05200
\(747\) 9.91345 0.362714
\(748\) −7.92722 −0.289848
\(749\) 27.4572 1.00326
\(750\) −9.54682 −0.348601
\(751\) −39.7426 −1.45023 −0.725114 0.688629i \(-0.758213\pi\)
−0.725114 + 0.688629i \(0.758213\pi\)
\(752\) −11.1915 −0.408112
\(753\) 14.6841 0.535120
\(754\) 3.41571 0.124393
\(755\) −59.5478 −2.16716
\(756\) 3.05465 0.111097
\(757\) −4.74560 −0.172482 −0.0862409 0.996274i \(-0.527485\pi\)
−0.0862409 + 0.996274i \(0.527485\pi\)
\(758\) −20.4724 −0.743592
\(759\) 5.23607 0.190057
\(760\) 6.25281 0.226813
\(761\) −43.2710 −1.56857 −0.784285 0.620400i \(-0.786970\pi\)
−0.784285 + 0.620400i \(0.786970\pi\)
\(762\) −8.93785 −0.323784
\(763\) −9.63895 −0.348953
\(764\) 3.16971 0.114676
\(765\) −19.6597 −0.710797
\(766\) −9.30271 −0.336121
\(767\) −3.62756 −0.130984
\(768\) 1.00000 0.0360844
\(769\) −8.05143 −0.290342 −0.145171 0.989407i \(-0.546373\pi\)
−0.145171 + 0.989407i \(0.546373\pi\)
\(770\) 7.57560 0.273006
\(771\) 14.5769 0.524975
\(772\) 12.5415 0.451379
\(773\) 16.4522 0.591743 0.295871 0.955228i \(-0.404390\pi\)
0.295871 + 0.955228i \(0.404390\pi\)
\(774\) 11.5248 0.414252
\(775\) 11.1785 0.401542
\(776\) −1.64385 −0.0590108
\(777\) −0.640365 −0.0229730
\(778\) 18.7260 0.671359
\(779\) −22.5630 −0.808405
\(780\) −1.39670 −0.0500098
\(781\) −0.510840 −0.0182793
\(782\) −41.5075 −1.48430
\(783\) −6.06505 −0.216747
\(784\) 2.33089 0.0832461
\(785\) 7.39466 0.263927
\(786\) −1.23327 −0.0439892
\(787\) 7.94206 0.283104 0.141552 0.989931i \(-0.454791\pi\)
0.141552 + 0.989931i \(0.454791\pi\)
\(788\) −6.86021 −0.244385
\(789\) 5.61536 0.199912
\(790\) −29.1514 −1.03716
\(791\) −57.4249 −2.04179
\(792\) 1.00000 0.0355335
\(793\) 0.563179 0.0199991
\(794\) 9.81052 0.348162
\(795\) 24.8268 0.880516
\(796\) 15.1849 0.538213
\(797\) 15.9814 0.566089 0.283045 0.959107i \(-0.408656\pi\)
0.283045 + 0.959107i \(0.408656\pi\)
\(798\) 7.70161 0.272634
\(799\) 88.7175 3.13860
\(800\) 1.15051 0.0406767
\(801\) −6.04252 −0.213502
\(802\) −28.6037 −1.01003
\(803\) −9.15175 −0.322958
\(804\) 0.884771 0.0312035
\(805\) 39.6664 1.39806
\(806\) −5.47190 −0.192739
\(807\) 2.38580 0.0839841
\(808\) 1.83614 0.0645953
\(809\) −14.8680 −0.522730 −0.261365 0.965240i \(-0.584173\pi\)
−0.261365 + 0.965240i \(0.584173\pi\)
\(810\) 2.48002 0.0871391
\(811\) −2.72880 −0.0958212 −0.0479106 0.998852i \(-0.515256\pi\)
−0.0479106 + 0.998852i \(0.515256\pi\)
\(812\) −18.5266 −0.650157
\(813\) 9.99441 0.350519
\(814\) −0.209636 −0.00734775
\(815\) 0.340908 0.0119415
\(816\) −7.92722 −0.277508
\(817\) 29.0573 1.01659
\(818\) 22.5803 0.789502
\(819\) −1.72031 −0.0601127
\(820\) −22.1939 −0.775045
\(821\) −52.2326 −1.82293 −0.911465 0.411378i \(-0.865048\pi\)
−0.911465 + 0.411378i \(0.865048\pi\)
\(822\) −12.5567 −0.437966
\(823\) −16.5978 −0.578563 −0.289282 0.957244i \(-0.593416\pi\)
−0.289282 + 0.957244i \(0.593416\pi\)
\(824\) 14.7996 0.515567
\(825\) 1.15051 0.0400556
\(826\) 19.6757 0.684605
\(827\) −23.7169 −0.824718 −0.412359 0.911021i \(-0.635295\pi\)
−0.412359 + 0.911021i \(0.635295\pi\)
\(828\) 5.23607 0.181966
\(829\) 29.9201 1.03917 0.519585 0.854419i \(-0.326087\pi\)
0.519585 + 0.854419i \(0.326087\pi\)
\(830\) 24.5856 0.853378
\(831\) −23.6176 −0.819286
\(832\) −0.563179 −0.0195247
\(833\) −18.4775 −0.640206
\(834\) 1.69681 0.0587557
\(835\) −59.2041 −2.04884
\(836\) 2.52127 0.0872000
\(837\) 9.71609 0.335837
\(838\) 10.5038 0.362846
\(839\) 31.8873 1.10087 0.550435 0.834878i \(-0.314462\pi\)
0.550435 + 0.834878i \(0.314462\pi\)
\(840\) 7.57560 0.261383
\(841\) 7.78488 0.268444
\(842\) 9.57254 0.329892
\(843\) −3.30201 −0.113727
\(844\) −12.8366 −0.441854
\(845\) −31.4537 −1.08204
\(846\) −11.1915 −0.384772
\(847\) 3.05465 0.104959
\(848\) 10.0107 0.343770
\(849\) 8.84256 0.303476
\(850\) −9.12035 −0.312825
\(851\) −1.09767 −0.0376276
\(852\) −0.510840 −0.0175011
\(853\) 6.82860 0.233807 0.116903 0.993143i \(-0.462703\pi\)
0.116903 + 0.993143i \(0.462703\pi\)
\(854\) −3.05465 −0.104528
\(855\) 6.25281 0.213842
\(856\) 8.98865 0.307226
\(857\) 55.5248 1.89669 0.948345 0.317241i \(-0.102756\pi\)
0.948345 + 0.317241i \(0.102756\pi\)
\(858\) −0.563179 −0.0192266
\(859\) 40.5582 1.38383 0.691914 0.721980i \(-0.256768\pi\)
0.691914 + 0.721980i \(0.256768\pi\)
\(860\) 28.5819 0.974634
\(861\) −27.3363 −0.931618
\(862\) 22.8634 0.778729
\(863\) −37.9939 −1.29333 −0.646664 0.762775i \(-0.723836\pi\)
−0.646664 + 0.762775i \(0.723836\pi\)
\(864\) 1.00000 0.0340207
\(865\) 57.3754 1.95082
\(866\) −24.8870 −0.845694
\(867\) 45.8408 1.55684
\(868\) 29.6793 1.00738
\(869\) −11.7545 −0.398744
\(870\) −15.0415 −0.509954
\(871\) −0.498284 −0.0168837
\(872\) −3.15550 −0.106859
\(873\) −1.64385 −0.0556360
\(874\) 13.2016 0.446549
\(875\) −29.1622 −0.985862
\(876\) −9.15175 −0.309209
\(877\) −21.1864 −0.715415 −0.357708 0.933834i \(-0.616442\pi\)
−0.357708 + 0.933834i \(0.616442\pi\)
\(878\) 37.4005 1.26220
\(879\) −9.08141 −0.306308
\(880\) 2.48002 0.0836015
\(881\) 47.6282 1.60464 0.802318 0.596897i \(-0.203600\pi\)
0.802318 + 0.596897i \(0.203600\pi\)
\(882\) 2.33089 0.0784851
\(883\) 20.3471 0.684735 0.342367 0.939566i \(-0.388771\pi\)
0.342367 + 0.939566i \(0.388771\pi\)
\(884\) 4.46444 0.150155
\(885\) 15.9744 0.536973
\(886\) 4.65294 0.156319
\(887\) 10.3078 0.346101 0.173050 0.984913i \(-0.444638\pi\)
0.173050 + 0.984913i \(0.444638\pi\)
\(888\) −0.209636 −0.00703493
\(889\) −27.3020 −0.915680
\(890\) −14.9856 −0.502318
\(891\) 1.00000 0.0335013
\(892\) −9.17245 −0.307116
\(893\) −28.2168 −0.944240
\(894\) −11.1537 −0.373037
\(895\) 13.6987 0.457898
\(896\) 3.05465 0.102049
\(897\) −2.94884 −0.0984590
\(898\) 7.34048 0.244955
\(899\) −58.9286 −1.96538
\(900\) 1.15051 0.0383504
\(901\) −79.3572 −2.64377
\(902\) −8.94907 −0.297971
\(903\) 35.2044 1.17153
\(904\) −18.7992 −0.625251
\(905\) 34.0587 1.13215
\(906\) −24.0110 −0.797711
\(907\) −5.06282 −0.168108 −0.0840541 0.996461i \(-0.526787\pi\)
−0.0840541 + 0.996461i \(0.526787\pi\)
\(908\) −18.1194 −0.601314
\(909\) 1.83614 0.0609010
\(910\) −4.26642 −0.141430
\(911\) −25.5720 −0.847238 −0.423619 0.905840i \(-0.639240\pi\)
−0.423619 + 0.905840i \(0.639240\pi\)
\(912\) 2.52127 0.0834877
\(913\) 9.91345 0.328087
\(914\) −22.9286 −0.758412
\(915\) −2.48002 −0.0819870
\(916\) −2.69696 −0.0891101
\(917\) −3.76720 −0.124404
\(918\) −7.92722 −0.261637
\(919\) 31.4159 1.03631 0.518157 0.855285i \(-0.326618\pi\)
0.518157 + 0.855285i \(0.326618\pi\)
\(920\) 12.9856 0.428121
\(921\) 27.4504 0.904521
\(922\) −30.3009 −0.997907
\(923\) 0.287695 0.00946958
\(924\) 3.05465 0.100491
\(925\) −0.241189 −0.00793024
\(926\) −13.1614 −0.432510
\(927\) 14.7996 0.486081
\(928\) −6.06505 −0.199095
\(929\) 29.5591 0.969802 0.484901 0.874569i \(-0.338856\pi\)
0.484901 + 0.874569i \(0.338856\pi\)
\(930\) 24.0961 0.790143
\(931\) 5.87681 0.192605
\(932\) 23.2176 0.760519
\(933\) −18.8187 −0.616098
\(934\) −39.2863 −1.28549
\(935\) −19.6597 −0.642940
\(936\) −0.563179 −0.0184081
\(937\) 48.8881 1.59711 0.798553 0.601925i \(-0.205599\pi\)
0.798553 + 0.601925i \(0.205599\pi\)
\(938\) 2.70267 0.0882452
\(939\) 3.52222 0.114943
\(940\) −27.7552 −0.905274
\(941\) 47.8671 1.56042 0.780211 0.625516i \(-0.215111\pi\)
0.780211 + 0.625516i \(0.215111\pi\)
\(942\) 2.98169 0.0971488
\(943\) −46.8579 −1.52590
\(944\) 6.44123 0.209644
\(945\) 7.57560 0.246434
\(946\) 11.5248 0.374705
\(947\) 48.4058 1.57298 0.786489 0.617604i \(-0.211897\pi\)
0.786489 + 0.617604i \(0.211897\pi\)
\(948\) −11.7545 −0.381769
\(949\) 5.15407 0.167308
\(950\) 2.90075 0.0941128
\(951\) 5.11337 0.165813
\(952\) −24.2149 −0.784809
\(953\) −36.5601 −1.18430 −0.592149 0.805828i \(-0.701720\pi\)
−0.592149 + 0.805828i \(0.701720\pi\)
\(954\) 10.0107 0.324109
\(955\) 7.86095 0.254374
\(956\) 1.27199 0.0411392
\(957\) −6.06505 −0.196055
\(958\) 27.5371 0.889684
\(959\) −38.3564 −1.23859
\(960\) 2.48002 0.0800424
\(961\) 63.4024 2.04524
\(962\) 0.118063 0.00380650
\(963\) 8.98865 0.289655
\(964\) −3.69603 −0.119041
\(965\) 31.1032 1.00125
\(966\) 15.9944 0.514610
\(967\) 27.2489 0.876267 0.438133 0.898910i \(-0.355640\pi\)
0.438133 + 0.898910i \(0.355640\pi\)
\(968\) 1.00000 0.0321412
\(969\) −19.9867 −0.642065
\(970\) −4.07679 −0.130898
\(971\) −1.38132 −0.0443285 −0.0221643 0.999754i \(-0.507056\pi\)
−0.0221643 + 0.999754i \(0.507056\pi\)
\(972\) 1.00000 0.0320750
\(973\) 5.18316 0.166164
\(974\) −23.3045 −0.746724
\(975\) −0.647943 −0.0207508
\(976\) −1.00000 −0.0320092
\(977\) 9.30511 0.297697 0.148848 0.988860i \(-0.452443\pi\)
0.148848 + 0.988860i \(0.452443\pi\)
\(978\) 0.137462 0.00439553
\(979\) −6.04252 −0.193120
\(980\) 5.78066 0.184656
\(981\) −3.15550 −0.100747
\(982\) 26.6058 0.849025
\(983\) −10.3254 −0.329330 −0.164665 0.986350i \(-0.552654\pi\)
−0.164665 + 0.986350i \(0.552654\pi\)
\(984\) −8.94907 −0.285286
\(985\) −17.0135 −0.542094
\(986\) 48.0790 1.53115
\(987\) −34.1861 −1.08816
\(988\) −1.41993 −0.0451739
\(989\) 60.3449 1.91885
\(990\) 2.48002 0.0788203
\(991\) 49.4368 1.57041 0.785206 0.619234i \(-0.212557\pi\)
0.785206 + 0.619234i \(0.212557\pi\)
\(992\) 9.71609 0.308486
\(993\) −3.31658 −0.105248
\(994\) −1.56044 −0.0494941
\(995\) 37.6588 1.19386
\(996\) 9.91345 0.314120
\(997\) 12.9086 0.408820 0.204410 0.978885i \(-0.434472\pi\)
0.204410 + 0.978885i \(0.434472\pi\)
\(998\) 19.4279 0.614978
\(999\) −0.209636 −0.00663260
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 \(a_p\))