Properties

Label 6017.2.a.c.1.17
Level 6017
Weight 2
Character 6017.1
Self dual Yes
Analytic conductor 48.046
Analytic rank 1
Dimension 106
CM No

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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 1.17
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.16812 q^{2}\) \(-0.750565 q^{3}\) \(+2.70073 q^{4}\) \(-2.22726 q^{5}\) \(+1.62731 q^{6}\) \(+3.66777 q^{7}\) \(-1.51925 q^{8}\) \(-2.43665 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.16812 q^{2}\) \(-0.750565 q^{3}\) \(+2.70073 q^{4}\) \(-2.22726 q^{5}\) \(+1.62731 q^{6}\) \(+3.66777 q^{7}\) \(-1.51925 q^{8}\) \(-2.43665 q^{9}\) \(+4.82897 q^{10}\) \(+1.00000 q^{11}\) \(-2.02707 q^{12}\) \(-5.53446 q^{13}\) \(-7.95214 q^{14}\) \(+1.67171 q^{15}\) \(-2.10753 q^{16}\) \(+0.526283 q^{17}\) \(+5.28294 q^{18}\) \(-3.67540 q^{19}\) \(-6.01523 q^{20}\) \(-2.75290 q^{21}\) \(-2.16812 q^{22}\) \(-1.72453 q^{23}\) \(+1.14030 q^{24}\) \(-0.0392908 q^{25}\) \(+11.9993 q^{26}\) \(+4.08056 q^{27}\) \(+9.90563 q^{28}\) \(+5.60414 q^{29}\) \(-3.62445 q^{30}\) \(+3.40223 q^{31}\) \(+7.60788 q^{32}\) \(-0.750565 q^{33}\) \(-1.14104 q^{34}\) \(-8.16909 q^{35}\) \(-6.58073 q^{36}\) \(+6.79662 q^{37}\) \(+7.96869 q^{38}\) \(+4.15397 q^{39}\) \(+3.38378 q^{40}\) \(+2.64528 q^{41}\) \(+5.96860 q^{42}\) \(+5.66180 q^{43}\) \(+2.70073 q^{44}\) \(+5.42707 q^{45}\) \(+3.73897 q^{46}\) \(+0.658614 q^{47}\) \(+1.58184 q^{48}\) \(+6.45251 q^{49}\) \(+0.0851870 q^{50}\) \(-0.395010 q^{51}\) \(-14.9470 q^{52}\) \(-2.76317 q^{53}\) \(-8.84713 q^{54}\) \(-2.22726 q^{55}\) \(-5.57226 q^{56}\) \(+2.75862 q^{57}\) \(-12.1504 q^{58}\) \(+3.85275 q^{59}\) \(+4.51482 q^{60}\) \(-5.20538 q^{61}\) \(-7.37643 q^{62}\) \(-8.93707 q^{63}\) \(-12.2797 q^{64}\) \(+12.3267 q^{65}\) \(+1.62731 q^{66}\) \(-11.2392 q^{67}\) \(+1.42135 q^{68}\) \(+1.29437 q^{69}\) \(+17.7115 q^{70}\) \(-1.31749 q^{71}\) \(+3.70189 q^{72}\) \(-4.46428 q^{73}\) \(-14.7359 q^{74}\) \(+0.0294903 q^{75}\) \(-9.92624 q^{76}\) \(+3.66777 q^{77}\) \(-9.00628 q^{78}\) \(+0.912121 q^{79}\) \(+4.69404 q^{80}\) \(+4.24723 q^{81}\) \(-5.73528 q^{82}\) \(+11.7779 q^{83}\) \(-7.43482 q^{84}\) \(-1.17217 q^{85}\) \(-12.2754 q^{86}\) \(-4.20627 q^{87}\) \(-1.51925 q^{88}\) \(-10.4548 q^{89}\) \(-11.7665 q^{90}\) \(-20.2991 q^{91}\) \(-4.65747 q^{92}\) \(-2.55359 q^{93}\) \(-1.42795 q^{94}\) \(+8.18609 q^{95}\) \(-5.71021 q^{96}\) \(-7.47645 q^{97}\) \(-13.9898 q^{98}\) \(-2.43665 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut -\mathstrut 30q^{10} \) \(\mathstrut +\mathstrut 106q^{11} \) \(\mathstrut -\mathstrut 26q^{12} \) \(\mathstrut -\mathstrut 72q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut -\mathstrut 46q^{15} \) \(\mathstrut +\mathstrut 75q^{16} \) \(\mathstrut -\mathstrut 65q^{17} \) \(\mathstrut -\mathstrut 37q^{18} \) \(\mathstrut -\mathstrut 63q^{19} \) \(\mathstrut -\mathstrut 25q^{20} \) \(\mathstrut -\mathstrut 27q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut -\mathstrut 56q^{24} \) \(\mathstrut +\mathstrut 74q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 54q^{27} \) \(\mathstrut -\mathstrut 115q^{28} \) \(\mathstrut -\mathstrut 45q^{29} \) \(\mathstrut -\mathstrut 14q^{30} \) \(\mathstrut -\mathstrut 89q^{31} \) \(\mathstrut -\mathstrut 96q^{32} \) \(\mathstrut -\mathstrut 15q^{33} \) \(\mathstrut -\mathstrut 26q^{34} \) \(\mathstrut -\mathstrut 52q^{35} \) \(\mathstrut +\mathstrut 91q^{36} \) \(\mathstrut -\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 7q^{38} \) \(\mathstrut -\mathstrut 34q^{39} \) \(\mathstrut -\mathstrut 74q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 94q^{43} \) \(\mathstrut +\mathstrut 93q^{44} \) \(\mathstrut -\mathstrut 46q^{45} \) \(\mathstrut -\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 105q^{47} \) \(\mathstrut -\mathstrut 57q^{48} \) \(\mathstrut +\mathstrut 80q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 36q^{51} \) \(\mathstrut -\mathstrut 137q^{52} \) \(\mathstrut -\mathstrut 61q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 32q^{56} \) \(\mathstrut -\mathstrut 71q^{57} \) \(\mathstrut -\mathstrut 28q^{58} \) \(\mathstrut -\mathstrut 15q^{59} \) \(\mathstrut -\mathstrut 21q^{60} \) \(\mathstrut -\mathstrut 80q^{61} \) \(\mathstrut -\mathstrut 84q^{62} \) \(\mathstrut -\mathstrut 182q^{63} \) \(\mathstrut +\mathstrut 55q^{64} \) \(\mathstrut -\mathstrut 73q^{65} \) \(\mathstrut -\mathstrut 22q^{66} \) \(\mathstrut -\mathstrut 58q^{67} \) \(\mathstrut -\mathstrut 145q^{68} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 39q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 100q^{72} \) \(\mathstrut -\mathstrut 155q^{73} \) \(\mathstrut -\mathstrut 15q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 132q^{76} \) \(\mathstrut -\mathstrut 66q^{77} \) \(\mathstrut -\mathstrut 45q^{78} \) \(\mathstrut -\mathstrut 50q^{79} \) \(\mathstrut -\mathstrut 28q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut -\mathstrut 57q^{82} \) \(\mathstrut -\mathstrut 96q^{83} \) \(\mathstrut -\mathstrut 27q^{84} \) \(\mathstrut -\mathstrut 74q^{85} \) \(\mathstrut +\mathstrut 54q^{86} \) \(\mathstrut -\mathstrut 182q^{87} \) \(\mathstrut -\mathstrut 39q^{88} \) \(\mathstrut +\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 53q^{90} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 49q^{95} \) \(\mathstrut -\mathstrut 56q^{96} \) \(\mathstrut -\mathstrut 102q^{97} \) \(\mathstrut -\mathstrut 76q^{98} \) \(\mathstrut +\mathstrut 97q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.16812 −1.53309 −0.766545 0.642191i \(-0.778026\pi\)
−0.766545 + 0.642191i \(0.778026\pi\)
\(3\) −0.750565 −0.433339 −0.216669 0.976245i \(-0.569519\pi\)
−0.216669 + 0.976245i \(0.569519\pi\)
\(4\) 2.70073 1.35036
\(5\) −2.22726 −0.996063 −0.498032 0.867159i \(-0.665944\pi\)
−0.498032 + 0.867159i \(0.665944\pi\)
\(6\) 1.62731 0.664347
\(7\) 3.66777 1.38629 0.693143 0.720800i \(-0.256226\pi\)
0.693143 + 0.720800i \(0.256226\pi\)
\(8\) −1.51925 −0.537137
\(9\) −2.43665 −0.812217
\(10\) 4.82897 1.52705
\(11\) 1.00000 0.301511
\(12\) −2.02707 −0.585165
\(13\) −5.53446 −1.53498 −0.767491 0.641060i \(-0.778495\pi\)
−0.767491 + 0.641060i \(0.778495\pi\)
\(14\) −7.95214 −2.12530
\(15\) 1.67171 0.431633
\(16\) −2.10753 −0.526884
\(17\) 0.526283 0.127642 0.0638212 0.997961i \(-0.479671\pi\)
0.0638212 + 0.997961i \(0.479671\pi\)
\(18\) 5.28294 1.24520
\(19\) −3.67540 −0.843194 −0.421597 0.906783i \(-0.638530\pi\)
−0.421597 + 0.906783i \(0.638530\pi\)
\(20\) −6.01523 −1.34505
\(21\) −2.75290 −0.600731
\(22\) −2.16812 −0.462244
\(23\) −1.72453 −0.359589 −0.179794 0.983704i \(-0.557543\pi\)
−0.179794 + 0.983704i \(0.557543\pi\)
\(24\) 1.14030 0.232762
\(25\) −0.0392908 −0.00785816
\(26\) 11.9993 2.35326
\(27\) 4.08056 0.785304
\(28\) 9.90563 1.87199
\(29\) 5.60414 1.04066 0.520331 0.853965i \(-0.325809\pi\)
0.520331 + 0.853965i \(0.325809\pi\)
\(30\) −3.62445 −0.661732
\(31\) 3.40223 0.611059 0.305529 0.952183i \(-0.401167\pi\)
0.305529 + 0.952183i \(0.401167\pi\)
\(32\) 7.60788 1.34490
\(33\) −0.750565 −0.130657
\(34\) −1.14104 −0.195687
\(35\) −8.16909 −1.38083
\(36\) −6.58073 −1.09679
\(37\) 6.79662 1.11736 0.558679 0.829384i \(-0.311308\pi\)
0.558679 + 0.829384i \(0.311308\pi\)
\(38\) 7.96869 1.29269
\(39\) 4.15397 0.665167
\(40\) 3.38378 0.535022
\(41\) 2.64528 0.413124 0.206562 0.978434i \(-0.433773\pi\)
0.206562 + 0.978434i \(0.433773\pi\)
\(42\) 5.96860 0.920975
\(43\) 5.66180 0.863416 0.431708 0.902013i \(-0.357911\pi\)
0.431708 + 0.902013i \(0.357911\pi\)
\(44\) 2.70073 0.407150
\(45\) 5.42707 0.809020
\(46\) 3.73897 0.551281
\(47\) 0.658614 0.0960687 0.0480344 0.998846i \(-0.484704\pi\)
0.0480344 + 0.998846i \(0.484704\pi\)
\(48\) 1.58184 0.228319
\(49\) 6.45251 0.921787
\(50\) 0.0851870 0.0120473
\(51\) −0.395010 −0.0553124
\(52\) −14.9470 −2.07278
\(53\) −2.76317 −0.379551 −0.189775 0.981828i \(-0.560776\pi\)
−0.189775 + 0.981828i \(0.560776\pi\)
\(54\) −8.84713 −1.20394
\(55\) −2.22726 −0.300324
\(56\) −5.57226 −0.744625
\(57\) 2.75862 0.365389
\(58\) −12.1504 −1.59543
\(59\) 3.85275 0.501585 0.250792 0.968041i \(-0.419309\pi\)
0.250792 + 0.968041i \(0.419309\pi\)
\(60\) 4.51482 0.582861
\(61\) −5.20538 −0.666481 −0.333241 0.942842i \(-0.608142\pi\)
−0.333241 + 0.942842i \(0.608142\pi\)
\(62\) −7.37643 −0.936807
\(63\) −8.93707 −1.12597
\(64\) −12.2797 −1.53496
\(65\) 12.3267 1.52894
\(66\) 1.62731 0.200308
\(67\) −11.2392 −1.37308 −0.686542 0.727090i \(-0.740872\pi\)
−0.686542 + 0.727090i \(0.740872\pi\)
\(68\) 1.42135 0.172363
\(69\) 1.29437 0.155824
\(70\) 17.7115 2.11693
\(71\) −1.31749 −0.156357 −0.0781785 0.996939i \(-0.524910\pi\)
−0.0781785 + 0.996939i \(0.524910\pi\)
\(72\) 3.70189 0.436272
\(73\) −4.46428 −0.522504 −0.261252 0.965271i \(-0.584135\pi\)
−0.261252 + 0.965271i \(0.584135\pi\)
\(74\) −14.7359 −1.71301
\(75\) 0.0294903 0.00340525
\(76\) −9.92624 −1.13862
\(77\) 3.66777 0.417981
\(78\) −9.00628 −1.01976
\(79\) 0.912121 0.102622 0.0513108 0.998683i \(-0.483660\pi\)
0.0513108 + 0.998683i \(0.483660\pi\)
\(80\) 4.69404 0.524809
\(81\) 4.24723 0.471915
\(82\) −5.73528 −0.633355
\(83\) 11.7779 1.29280 0.646398 0.763000i \(-0.276274\pi\)
0.646398 + 0.763000i \(0.276274\pi\)
\(84\) −7.43482 −0.811205
\(85\) −1.17217 −0.127140
\(86\) −12.2754 −1.32369
\(87\) −4.20627 −0.450959
\(88\) −1.51925 −0.161953
\(89\) −10.4548 −1.10820 −0.554101 0.832449i \(-0.686938\pi\)
−0.554101 + 0.832449i \(0.686938\pi\)
\(90\) −11.7665 −1.24030
\(91\) −20.2991 −2.12792
\(92\) −4.65747 −0.485575
\(93\) −2.55359 −0.264795
\(94\) −1.42795 −0.147282
\(95\) 8.18609 0.839875
\(96\) −5.71021 −0.582796
\(97\) −7.47645 −0.759119 −0.379559 0.925167i \(-0.623924\pi\)
−0.379559 + 0.925167i \(0.623924\pi\)
\(98\) −13.9898 −1.41318
\(99\) −2.43665 −0.244893
\(100\) −0.106114 −0.0106114
\(101\) −8.62240 −0.857961 −0.428980 0.903314i \(-0.641127\pi\)
−0.428980 + 0.903314i \(0.641127\pi\)
\(102\) 0.856426 0.0847988
\(103\) −11.7955 −1.16225 −0.581125 0.813815i \(-0.697387\pi\)
−0.581125 + 0.813815i \(0.697387\pi\)
\(104\) 8.40824 0.824496
\(105\) 6.13143 0.598366
\(106\) 5.99087 0.581885
\(107\) 12.8117 1.23856 0.619279 0.785171i \(-0.287425\pi\)
0.619279 + 0.785171i \(0.287425\pi\)
\(108\) 11.0205 1.06045
\(109\) 11.7958 1.12983 0.564915 0.825149i \(-0.308909\pi\)
0.564915 + 0.825149i \(0.308909\pi\)
\(110\) 4.82897 0.460424
\(111\) −5.10130 −0.484194
\(112\) −7.72994 −0.730411
\(113\) 4.12435 0.387986 0.193993 0.981003i \(-0.437856\pi\)
0.193993 + 0.981003i \(0.437856\pi\)
\(114\) −5.98102 −0.560174
\(115\) 3.84098 0.358173
\(116\) 15.1352 1.40527
\(117\) 13.4855 1.24674
\(118\) −8.35320 −0.768974
\(119\) 1.93028 0.176949
\(120\) −2.53975 −0.231846
\(121\) 1.00000 0.0909091
\(122\) 11.2859 1.02177
\(123\) −1.98546 −0.179022
\(124\) 9.18849 0.825151
\(125\) 11.2238 1.00389
\(126\) 19.3766 1.72620
\(127\) 0.966178 0.0857345 0.0428672 0.999081i \(-0.486351\pi\)
0.0428672 + 0.999081i \(0.486351\pi\)
\(128\) 11.4080 1.00834
\(129\) −4.24955 −0.374152
\(130\) −26.7257 −2.34400
\(131\) 1.08921 0.0951650 0.0475825 0.998867i \(-0.484848\pi\)
0.0475825 + 0.998867i \(0.484848\pi\)
\(132\) −2.02707 −0.176434
\(133\) −13.4805 −1.16891
\(134\) 24.3678 2.10506
\(135\) −9.08849 −0.782213
\(136\) −0.799557 −0.0685615
\(137\) 9.00793 0.769600 0.384800 0.923000i \(-0.374270\pi\)
0.384800 + 0.923000i \(0.374270\pi\)
\(138\) −2.80634 −0.238892
\(139\) 12.9830 1.10120 0.550602 0.834768i \(-0.314398\pi\)
0.550602 + 0.834768i \(0.314398\pi\)
\(140\) −22.0625 −1.86462
\(141\) −0.494332 −0.0416303
\(142\) 2.85646 0.239709
\(143\) −5.53446 −0.462814
\(144\) 5.13533 0.427944
\(145\) −12.4819 −1.03657
\(146\) 9.67907 0.801046
\(147\) −4.84302 −0.399446
\(148\) 18.3558 1.50884
\(149\) −8.44046 −0.691469 −0.345735 0.938332i \(-0.612370\pi\)
−0.345735 + 0.938332i \(0.612370\pi\)
\(150\) −0.0639384 −0.00522054
\(151\) 1.90073 0.154679 0.0773396 0.997005i \(-0.475357\pi\)
0.0773396 + 0.997005i \(0.475357\pi\)
\(152\) 5.58386 0.452911
\(153\) −1.28237 −0.103673
\(154\) −7.95214 −0.640802
\(155\) −7.57767 −0.608653
\(156\) 11.2187 0.898217
\(157\) −12.6551 −1.00999 −0.504994 0.863123i \(-0.668505\pi\)
−0.504994 + 0.863123i \(0.668505\pi\)
\(158\) −1.97758 −0.157328
\(159\) 2.07394 0.164474
\(160\) −16.9448 −1.33960
\(161\) −6.32516 −0.498492
\(162\) −9.20849 −0.723487
\(163\) 22.4177 1.75589 0.877943 0.478765i \(-0.158915\pi\)
0.877943 + 0.478765i \(0.158915\pi\)
\(164\) 7.14418 0.557867
\(165\) 1.67171 0.130142
\(166\) −25.5359 −1.98197
\(167\) 4.59803 0.355806 0.177903 0.984048i \(-0.443069\pi\)
0.177903 + 0.984048i \(0.443069\pi\)
\(168\) 4.18235 0.322675
\(169\) 17.6302 1.35617
\(170\) 2.54140 0.194917
\(171\) 8.95567 0.684857
\(172\) 15.2910 1.16593
\(173\) 12.2366 0.930333 0.465166 0.885223i \(-0.345995\pi\)
0.465166 + 0.885223i \(0.345995\pi\)
\(174\) 9.11968 0.691361
\(175\) −0.144109 −0.0108936
\(176\) −2.10753 −0.158861
\(177\) −2.89174 −0.217356
\(178\) 22.6671 1.69897
\(179\) 20.3948 1.52438 0.762189 0.647355i \(-0.224125\pi\)
0.762189 + 0.647355i \(0.224125\pi\)
\(180\) 14.6570 1.09247
\(181\) −26.2929 −1.95433 −0.977166 0.212476i \(-0.931847\pi\)
−0.977166 + 0.212476i \(0.931847\pi\)
\(182\) 44.0108 3.26229
\(183\) 3.90698 0.288812
\(184\) 2.61999 0.193148
\(185\) −15.1379 −1.11296
\(186\) 5.53649 0.405955
\(187\) 0.526283 0.0384856
\(188\) 1.77874 0.129728
\(189\) 14.9665 1.08866
\(190\) −17.7484 −1.28760
\(191\) −3.19724 −0.231344 −0.115672 0.993287i \(-0.536902\pi\)
−0.115672 + 0.993287i \(0.536902\pi\)
\(192\) 9.21671 0.665159
\(193\) 8.22263 0.591878 0.295939 0.955207i \(-0.404367\pi\)
0.295939 + 0.955207i \(0.404367\pi\)
\(194\) 16.2098 1.16380
\(195\) −9.25199 −0.662549
\(196\) 17.4264 1.24475
\(197\) −7.12564 −0.507680 −0.253840 0.967246i \(-0.581694\pi\)
−0.253840 + 0.967246i \(0.581694\pi\)
\(198\) 5.28294 0.375442
\(199\) −1.40097 −0.0993119 −0.0496560 0.998766i \(-0.515812\pi\)
−0.0496560 + 0.998766i \(0.515812\pi\)
\(200\) 0.0596927 0.00422091
\(201\) 8.43573 0.595011
\(202\) 18.6944 1.31533
\(203\) 20.5547 1.44265
\(204\) −1.06681 −0.0746918
\(205\) −5.89174 −0.411497
\(206\) 25.5741 1.78183
\(207\) 4.20207 0.292064
\(208\) 11.6641 0.808757
\(209\) −3.67540 −0.254233
\(210\) −13.2936 −0.917349
\(211\) 18.4251 1.26844 0.634219 0.773153i \(-0.281322\pi\)
0.634219 + 0.773153i \(0.281322\pi\)
\(212\) −7.46256 −0.512531
\(213\) 0.988859 0.0677555
\(214\) −27.7773 −1.89882
\(215\) −12.6103 −0.860017
\(216\) −6.19940 −0.421816
\(217\) 12.4786 0.847101
\(218\) −25.5746 −1.73213
\(219\) 3.35073 0.226421
\(220\) −6.01523 −0.405547
\(221\) −2.91269 −0.195929
\(222\) 11.0602 0.742313
\(223\) −6.36478 −0.426217 −0.213109 0.977029i \(-0.568359\pi\)
−0.213109 + 0.977029i \(0.568359\pi\)
\(224\) 27.9039 1.86441
\(225\) 0.0957380 0.00638253
\(226\) −8.94207 −0.594818
\(227\) 6.89072 0.457353 0.228677 0.973502i \(-0.426560\pi\)
0.228677 + 0.973502i \(0.426560\pi\)
\(228\) 7.45029 0.493407
\(229\) −20.2722 −1.33962 −0.669811 0.742532i \(-0.733625\pi\)
−0.669811 + 0.742532i \(0.733625\pi\)
\(230\) −8.32768 −0.549111
\(231\) −2.75290 −0.181127
\(232\) −8.51410 −0.558978
\(233\) 3.63481 0.238125 0.119062 0.992887i \(-0.462011\pi\)
0.119062 + 0.992887i \(0.462011\pi\)
\(234\) −29.2382 −1.91136
\(235\) −1.46691 −0.0956905
\(236\) 10.4052 0.677321
\(237\) −0.684606 −0.0444699
\(238\) −4.18508 −0.271278
\(239\) 11.5631 0.747958 0.373979 0.927437i \(-0.377993\pi\)
0.373979 + 0.927437i \(0.377993\pi\)
\(240\) −3.52318 −0.227420
\(241\) −11.2110 −0.722167 −0.361084 0.932533i \(-0.617593\pi\)
−0.361084 + 0.932533i \(0.617593\pi\)
\(242\) −2.16812 −0.139372
\(243\) −15.4295 −0.989803
\(244\) −14.0583 −0.899991
\(245\) −14.3714 −0.918158
\(246\) 4.30470 0.274457
\(247\) 20.3413 1.29429
\(248\) −5.16885 −0.328222
\(249\) −8.84011 −0.560219
\(250\) −24.3346 −1.53905
\(251\) −10.9324 −0.690044 −0.345022 0.938595i \(-0.612129\pi\)
−0.345022 + 0.938595i \(0.612129\pi\)
\(252\) −24.1366 −1.52046
\(253\) −1.72453 −0.108420
\(254\) −2.09479 −0.131439
\(255\) 0.879791 0.0550946
\(256\) −0.174559 −0.0109100
\(257\) −23.7766 −1.48315 −0.741573 0.670872i \(-0.765920\pi\)
−0.741573 + 0.670872i \(0.765920\pi\)
\(258\) 9.21351 0.573608
\(259\) 24.9284 1.54898
\(260\) 33.2910 2.06462
\(261\) −13.6553 −0.845244
\(262\) −2.36154 −0.145896
\(263\) 13.3940 0.825907 0.412953 0.910752i \(-0.364497\pi\)
0.412953 + 0.910752i \(0.364497\pi\)
\(264\) 1.14030 0.0701805
\(265\) 6.15431 0.378056
\(266\) 29.2273 1.79204
\(267\) 7.84698 0.480227
\(268\) −30.3539 −1.85416
\(269\) −3.49436 −0.213055 −0.106527 0.994310i \(-0.533973\pi\)
−0.106527 + 0.994310i \(0.533973\pi\)
\(270\) 19.7049 1.19920
\(271\) −9.84073 −0.597782 −0.298891 0.954287i \(-0.596617\pi\)
−0.298891 + 0.954287i \(0.596617\pi\)
\(272\) −1.10916 −0.0672527
\(273\) 15.2358 0.922111
\(274\) −19.5302 −1.17986
\(275\) −0.0392908 −0.00236932
\(276\) 3.49573 0.210418
\(277\) −0.328363 −0.0197294 −0.00986472 0.999951i \(-0.503140\pi\)
−0.00986472 + 0.999951i \(0.503140\pi\)
\(278\) −28.1487 −1.68825
\(279\) −8.29005 −0.496312
\(280\) 12.4109 0.741694
\(281\) −21.9982 −1.31230 −0.656152 0.754629i \(-0.727817\pi\)
−0.656152 + 0.754629i \(0.727817\pi\)
\(282\) 1.07177 0.0638230
\(283\) −14.5127 −0.862692 −0.431346 0.902186i \(-0.641961\pi\)
−0.431346 + 0.902186i \(0.641961\pi\)
\(284\) −3.55817 −0.211139
\(285\) −6.14419 −0.363950
\(286\) 11.9993 0.709536
\(287\) 9.70227 0.572707
\(288\) −18.5378 −1.09235
\(289\) −16.7230 −0.983707
\(290\) 27.0622 1.58915
\(291\) 5.61156 0.328956
\(292\) −12.0568 −0.705570
\(293\) −17.1760 −1.00344 −0.501718 0.865031i \(-0.667298\pi\)
−0.501718 + 0.865031i \(0.667298\pi\)
\(294\) 10.5002 0.612386
\(295\) −8.58109 −0.499610
\(296\) −10.3258 −0.600174
\(297\) 4.08056 0.236778
\(298\) 18.2999 1.06008
\(299\) 9.54431 0.551962
\(300\) 0.0796452 0.00459832
\(301\) 20.7662 1.19694
\(302\) −4.12100 −0.237137
\(303\) 6.47167 0.371788
\(304\) 7.74603 0.444265
\(305\) 11.5938 0.663857
\(306\) 2.78032 0.158941
\(307\) −3.36688 −0.192158 −0.0960791 0.995374i \(-0.530630\pi\)
−0.0960791 + 0.995374i \(0.530630\pi\)
\(308\) 9.90563 0.564425
\(309\) 8.85332 0.503648
\(310\) 16.4293 0.933119
\(311\) 14.5059 0.822555 0.411277 0.911510i \(-0.365083\pi\)
0.411277 + 0.911510i \(0.365083\pi\)
\(312\) −6.31093 −0.357286
\(313\) −4.56542 −0.258053 −0.129026 0.991641i \(-0.541185\pi\)
−0.129026 + 0.991641i \(0.541185\pi\)
\(314\) 27.4378 1.54840
\(315\) 19.9052 1.12153
\(316\) 2.46339 0.138576
\(317\) 8.55964 0.480757 0.240379 0.970679i \(-0.422728\pi\)
0.240379 + 0.970679i \(0.422728\pi\)
\(318\) −4.49654 −0.252153
\(319\) 5.60414 0.313771
\(320\) 27.3502 1.52892
\(321\) −9.61604 −0.536715
\(322\) 13.7137 0.764233
\(323\) −1.93430 −0.107627
\(324\) 11.4706 0.637256
\(325\) 0.217453 0.0120621
\(326\) −48.6041 −2.69193
\(327\) −8.85349 −0.489599
\(328\) −4.01885 −0.221904
\(329\) 2.41564 0.133179
\(330\) −3.62445 −0.199520
\(331\) −25.9079 −1.42403 −0.712014 0.702165i \(-0.752217\pi\)
−0.712014 + 0.702165i \(0.752217\pi\)
\(332\) 31.8090 1.74574
\(333\) −16.5610 −0.907537
\(334\) −9.96906 −0.545483
\(335\) 25.0326 1.36768
\(336\) 5.80182 0.316515
\(337\) −25.3650 −1.38172 −0.690861 0.722988i \(-0.742768\pi\)
−0.690861 + 0.722988i \(0.742768\pi\)
\(338\) −38.2243 −2.07913
\(339\) −3.09559 −0.168130
\(340\) −3.16571 −0.171685
\(341\) 3.40223 0.184241
\(342\) −19.4169 −1.04995
\(343\) −2.00808 −0.108426
\(344\) −8.60171 −0.463773
\(345\) −2.88290 −0.155210
\(346\) −26.5304 −1.42628
\(347\) −22.5982 −1.21314 −0.606569 0.795031i \(-0.707454\pi\)
−0.606569 + 0.795031i \(0.707454\pi\)
\(348\) −11.3600 −0.608959
\(349\) −13.6111 −0.728585 −0.364292 0.931285i \(-0.618689\pi\)
−0.364292 + 0.931285i \(0.618689\pi\)
\(350\) 0.312446 0.0167009
\(351\) −22.5837 −1.20543
\(352\) 7.60788 0.405502
\(353\) 21.8040 1.16051 0.580255 0.814435i \(-0.302953\pi\)
0.580255 + 0.814435i \(0.302953\pi\)
\(354\) 6.26962 0.333226
\(355\) 2.93439 0.155741
\(356\) −28.2354 −1.49648
\(357\) −1.44880 −0.0766788
\(358\) −44.2182 −2.33701
\(359\) 24.6872 1.30294 0.651470 0.758674i \(-0.274152\pi\)
0.651470 + 0.758674i \(0.274152\pi\)
\(360\) −8.24509 −0.434555
\(361\) −5.49145 −0.289024
\(362\) 57.0060 2.99617
\(363\) −0.750565 −0.0393944
\(364\) −54.8223 −2.87347
\(365\) 9.94313 0.520447
\(366\) −8.47078 −0.442775
\(367\) 22.7843 1.18933 0.594665 0.803973i \(-0.297285\pi\)
0.594665 + 0.803973i \(0.297285\pi\)
\(368\) 3.63450 0.189461
\(369\) −6.44563 −0.335546
\(370\) 32.8207 1.70627
\(371\) −10.1347 −0.526165
\(372\) −6.89656 −0.357570
\(373\) −24.3435 −1.26046 −0.630229 0.776409i \(-0.717039\pi\)
−0.630229 + 0.776409i \(0.717039\pi\)
\(374\) −1.14104 −0.0590019
\(375\) −8.42422 −0.435025
\(376\) −1.00060 −0.0516021
\(377\) −31.0159 −1.59740
\(378\) −32.4492 −1.66901
\(379\) 22.5194 1.15674 0.578372 0.815773i \(-0.303688\pi\)
0.578372 + 0.815773i \(0.303688\pi\)
\(380\) 22.1084 1.13414
\(381\) −0.725180 −0.0371521
\(382\) 6.93199 0.354671
\(383\) 4.26662 0.218014 0.109007 0.994041i \(-0.465233\pi\)
0.109007 + 0.994041i \(0.465233\pi\)
\(384\) −8.56248 −0.436952
\(385\) −8.16909 −0.416335
\(386\) −17.8276 −0.907402
\(387\) −13.7958 −0.701282
\(388\) −20.1918 −1.02509
\(389\) 20.4773 1.03824 0.519119 0.854702i \(-0.326260\pi\)
0.519119 + 0.854702i \(0.326260\pi\)
\(390\) 20.0594 1.01575
\(391\) −0.907589 −0.0458987
\(392\) −9.80299 −0.495126
\(393\) −0.817525 −0.0412387
\(394\) 15.4492 0.778319
\(395\) −2.03153 −0.102218
\(396\) −6.58073 −0.330694
\(397\) −19.4244 −0.974881 −0.487440 0.873156i \(-0.662069\pi\)
−0.487440 + 0.873156i \(0.662069\pi\)
\(398\) 3.03746 0.152254
\(399\) 10.1180 0.506533
\(400\) 0.0828067 0.00414033
\(401\) −35.6975 −1.78265 −0.891323 0.453368i \(-0.850222\pi\)
−0.891323 + 0.453368i \(0.850222\pi\)
\(402\) −18.2896 −0.912204
\(403\) −18.8295 −0.937964
\(404\) −23.2867 −1.15856
\(405\) −9.45971 −0.470057
\(406\) −44.5649 −2.21172
\(407\) 6.79662 0.336896
\(408\) 0.600119 0.0297103
\(409\) 22.2105 1.09824 0.549120 0.835743i \(-0.314963\pi\)
0.549120 + 0.835743i \(0.314963\pi\)
\(410\) 12.7740 0.630862
\(411\) −6.76104 −0.333497
\(412\) −31.8565 −1.56946
\(413\) 14.1310 0.695340
\(414\) −9.11057 −0.447760
\(415\) −26.2326 −1.28771
\(416\) −42.1055 −2.06439
\(417\) −9.74459 −0.477195
\(418\) 7.96869 0.389761
\(419\) −15.4531 −0.754933 −0.377466 0.926023i \(-0.623205\pi\)
−0.377466 + 0.926023i \(0.623205\pi\)
\(420\) 16.5593 0.808011
\(421\) 15.3680 0.748990 0.374495 0.927229i \(-0.377816\pi\)
0.374495 + 0.927229i \(0.377816\pi\)
\(422\) −39.9478 −1.94463
\(423\) −1.60481 −0.0780287
\(424\) 4.19795 0.203871
\(425\) −0.0206781 −0.00100303
\(426\) −2.14396 −0.103875
\(427\) −19.0921 −0.923933
\(428\) 34.6010 1.67250
\(429\) 4.15397 0.200555
\(430\) 27.3406 1.31848
\(431\) −7.27807 −0.350572 −0.175286 0.984518i \(-0.556085\pi\)
−0.175286 + 0.984518i \(0.556085\pi\)
\(432\) −8.59992 −0.413764
\(433\) −18.7803 −0.902524 −0.451262 0.892392i \(-0.649026\pi\)
−0.451262 + 0.892392i \(0.649026\pi\)
\(434\) −27.0550 −1.29868
\(435\) 9.36848 0.449184
\(436\) 31.8571 1.52568
\(437\) 6.33832 0.303203
\(438\) −7.26477 −0.347124
\(439\) −15.7530 −0.751852 −0.375926 0.926650i \(-0.622675\pi\)
−0.375926 + 0.926650i \(0.622675\pi\)
\(440\) 3.38378 0.161315
\(441\) −15.7225 −0.748691
\(442\) 6.31505 0.300376
\(443\) 15.6043 0.741384 0.370692 0.928756i \(-0.379121\pi\)
0.370692 + 0.928756i \(0.379121\pi\)
\(444\) −13.7772 −0.653838
\(445\) 23.2855 1.10384
\(446\) 13.7996 0.653429
\(447\) 6.33511 0.299641
\(448\) −45.0391 −2.12790
\(449\) −11.8845 −0.560865 −0.280432 0.959874i \(-0.590478\pi\)
−0.280432 + 0.959874i \(0.590478\pi\)
\(450\) −0.207571 −0.00978499
\(451\) 2.64528 0.124561
\(452\) 11.1387 0.523922
\(453\) −1.42662 −0.0670285
\(454\) −14.9399 −0.701163
\(455\) 45.2114 2.11955
\(456\) −4.19105 −0.196264
\(457\) −6.54730 −0.306270 −0.153135 0.988205i \(-0.548937\pi\)
−0.153135 + 0.988205i \(0.548937\pi\)
\(458\) 43.9524 2.05376
\(459\) 2.14753 0.100238
\(460\) 10.3734 0.483663
\(461\) 17.4877 0.814482 0.407241 0.913321i \(-0.366491\pi\)
0.407241 + 0.913321i \(0.366491\pi\)
\(462\) 5.96860 0.277684
\(463\) −26.3093 −1.22270 −0.611348 0.791362i \(-0.709372\pi\)
−0.611348 + 0.791362i \(0.709372\pi\)
\(464\) −11.8109 −0.548308
\(465\) 5.68753 0.263753
\(466\) −7.88070 −0.365066
\(467\) −20.3555 −0.941942 −0.470971 0.882149i \(-0.656096\pi\)
−0.470971 + 0.882149i \(0.656096\pi\)
\(468\) 36.4207 1.68355
\(469\) −41.2227 −1.90349
\(470\) 3.18043 0.146702
\(471\) 9.49849 0.437667
\(472\) −5.85330 −0.269420
\(473\) 5.66180 0.260330
\(474\) 1.48430 0.0681764
\(475\) 0.144409 0.00662595
\(476\) 5.21316 0.238945
\(477\) 6.73288 0.308278
\(478\) −25.0702 −1.14669
\(479\) 17.4532 0.797455 0.398727 0.917069i \(-0.369452\pi\)
0.398727 + 0.917069i \(0.369452\pi\)
\(480\) 12.7182 0.580502
\(481\) −37.6156 −1.71512
\(482\) 24.3068 1.10715
\(483\) 4.74744 0.216016
\(484\) 2.70073 0.122760
\(485\) 16.6520 0.756130
\(486\) 33.4529 1.51746
\(487\) 6.71867 0.304452 0.152226 0.988346i \(-0.451356\pi\)
0.152226 + 0.988346i \(0.451356\pi\)
\(488\) 7.90829 0.357992
\(489\) −16.8259 −0.760894
\(490\) 31.1589 1.40762
\(491\) −2.90298 −0.131010 −0.0655048 0.997852i \(-0.520866\pi\)
−0.0655048 + 0.997852i \(0.520866\pi\)
\(492\) −5.36217 −0.241745
\(493\) 2.94936 0.132833
\(494\) −44.1023 −1.98426
\(495\) 5.42707 0.243929
\(496\) −7.17032 −0.321957
\(497\) −4.83223 −0.216755
\(498\) 19.1664 0.858866
\(499\) 42.2982 1.89353 0.946763 0.321930i \(-0.104332\pi\)
0.946763 + 0.321930i \(0.104332\pi\)
\(500\) 30.3125 1.35562
\(501\) −3.45112 −0.154185
\(502\) 23.7026 1.05790
\(503\) 34.6211 1.54368 0.771839 0.635818i \(-0.219337\pi\)
0.771839 + 0.635818i \(0.219337\pi\)
\(504\) 13.5777 0.604798
\(505\) 19.2044 0.854583
\(506\) 3.73897 0.166218
\(507\) −13.2326 −0.587681
\(508\) 2.60938 0.115773
\(509\) 44.2777 1.96257 0.981287 0.192549i \(-0.0616754\pi\)
0.981287 + 0.192549i \(0.0616754\pi\)
\(510\) −1.90749 −0.0844650
\(511\) −16.3739 −0.724340
\(512\) −22.4376 −0.991612
\(513\) −14.9977 −0.662164
\(514\) 51.5505 2.27379
\(515\) 26.2718 1.15767
\(516\) −11.4769 −0.505241
\(517\) 0.658614 0.0289658
\(518\) −54.0477 −2.37472
\(519\) −9.18437 −0.403149
\(520\) −18.7274 −0.821250
\(521\) 12.9666 0.568077 0.284039 0.958813i \(-0.408326\pi\)
0.284039 + 0.958813i \(0.408326\pi\)
\(522\) 29.6063 1.29583
\(523\) −29.1335 −1.27392 −0.636959 0.770898i \(-0.719808\pi\)
−0.636959 + 0.770898i \(0.719808\pi\)
\(524\) 2.94167 0.128507
\(525\) 0.108163 0.00472064
\(526\) −29.0397 −1.26619
\(527\) 1.79054 0.0779970
\(528\) 1.58184 0.0688408
\(529\) −20.0260 −0.870696
\(530\) −13.3433 −0.579594
\(531\) −9.38780 −0.407396
\(532\) −36.4071 −1.57845
\(533\) −14.6402 −0.634137
\(534\) −17.0132 −0.736231
\(535\) −28.5351 −1.23368
\(536\) 17.0752 0.737534
\(537\) −15.3076 −0.660572
\(538\) 7.57617 0.326632
\(539\) 6.45251 0.277929
\(540\) −24.5455 −1.05627
\(541\) 3.02481 0.130047 0.0650233 0.997884i \(-0.479288\pi\)
0.0650233 + 0.997884i \(0.479288\pi\)
\(542\) 21.3358 0.916452
\(543\) 19.7345 0.846888
\(544\) 4.00390 0.171666
\(545\) −26.2723 −1.12538
\(546\) −33.0329 −1.41368
\(547\) 1.00000 0.0427569
\(548\) 24.3279 1.03924
\(549\) 12.6837 0.541328
\(550\) 0.0851870 0.00363239
\(551\) −20.5974 −0.877480
\(552\) −1.96647 −0.0836987
\(553\) 3.34545 0.142263
\(554\) 0.711930 0.0302470
\(555\) 11.3620 0.482288
\(556\) 35.0635 1.48703
\(557\) −30.3839 −1.28741 −0.643703 0.765276i \(-0.722603\pi\)
−0.643703 + 0.765276i \(0.722603\pi\)
\(558\) 17.9738 0.760891
\(559\) −31.3350 −1.32533
\(560\) 17.2166 0.727535
\(561\) −0.395010 −0.0166773
\(562\) 47.6947 2.01188
\(563\) −12.6324 −0.532394 −0.266197 0.963919i \(-0.585767\pi\)
−0.266197 + 0.963919i \(0.585767\pi\)
\(564\) −1.33506 −0.0562160
\(565\) −9.18603 −0.386459
\(566\) 31.4653 1.32258
\(567\) 15.5779 0.654208
\(568\) 2.00160 0.0839851
\(569\) −3.49728 −0.146613 −0.0733067 0.997309i \(-0.523355\pi\)
−0.0733067 + 0.997309i \(0.523355\pi\)
\(570\) 13.3213 0.557968
\(571\) 20.3992 0.853680 0.426840 0.904327i \(-0.359627\pi\)
0.426840 + 0.904327i \(0.359627\pi\)
\(572\) −14.9470 −0.624967
\(573\) 2.39974 0.100250
\(574\) −21.0356 −0.878011
\(575\) 0.0677580 0.00282570
\(576\) 29.9214 1.24672
\(577\) −0.992716 −0.0413273 −0.0206636 0.999786i \(-0.506578\pi\)
−0.0206636 + 0.999786i \(0.506578\pi\)
\(578\) 36.2575 1.50811
\(579\) −6.17162 −0.256484
\(580\) −33.7102 −1.39974
\(581\) 43.1987 1.79218
\(582\) −12.1665 −0.504318
\(583\) −2.76317 −0.114439
\(584\) 6.78237 0.280656
\(585\) −30.0359 −1.24183
\(586\) 37.2397 1.53836
\(587\) 24.2975 1.00286 0.501432 0.865197i \(-0.332807\pi\)
0.501432 + 0.865197i \(0.332807\pi\)
\(588\) −13.0797 −0.539397
\(589\) −12.5045 −0.515241
\(590\) 18.6048 0.765947
\(591\) 5.34825 0.219998
\(592\) −14.3241 −0.588717
\(593\) −16.3073 −0.669659 −0.334830 0.942279i \(-0.608679\pi\)
−0.334830 + 0.942279i \(0.608679\pi\)
\(594\) −8.84713 −0.363002
\(595\) −4.29925 −0.176252
\(596\) −22.7954 −0.933734
\(597\) 1.05152 0.0430357
\(598\) −20.6932 −0.846207
\(599\) −13.1853 −0.538736 −0.269368 0.963037i \(-0.586815\pi\)
−0.269368 + 0.963037i \(0.586815\pi\)
\(600\) −0.0448032 −0.00182908
\(601\) −18.1390 −0.739906 −0.369953 0.929050i \(-0.620626\pi\)
−0.369953 + 0.929050i \(0.620626\pi\)
\(602\) −45.0234 −1.83502
\(603\) 27.3860 1.11524
\(604\) 5.13335 0.208873
\(605\) −2.22726 −0.0905512
\(606\) −14.0313 −0.569984
\(607\) 17.5641 0.712904 0.356452 0.934314i \(-0.383986\pi\)
0.356452 + 0.934314i \(0.383986\pi\)
\(608\) −27.9620 −1.13401
\(609\) −15.4276 −0.625158
\(610\) −25.1366 −1.01775
\(611\) −3.64507 −0.147464
\(612\) −3.46333 −0.139997
\(613\) −4.24330 −0.171385 −0.0856926 0.996322i \(-0.527310\pi\)
−0.0856926 + 0.996322i \(0.527310\pi\)
\(614\) 7.29980 0.294596
\(615\) 4.42214 0.178318
\(616\) −5.57226 −0.224513
\(617\) −30.1821 −1.21509 −0.607543 0.794287i \(-0.707845\pi\)
−0.607543 + 0.794287i \(0.707845\pi\)
\(618\) −19.1950 −0.772137
\(619\) 34.0647 1.36918 0.684589 0.728930i \(-0.259982\pi\)
0.684589 + 0.728930i \(0.259982\pi\)
\(620\) −20.4652 −0.821902
\(621\) −7.03703 −0.282386
\(622\) −31.4505 −1.26105
\(623\) −38.3456 −1.53628
\(624\) −8.75463 −0.350466
\(625\) −24.8020 −0.992080
\(626\) 9.89836 0.395618
\(627\) 2.75862 0.110169
\(628\) −34.1780 −1.36385
\(629\) 3.57695 0.142622
\(630\) −43.1568 −1.71941
\(631\) 1.17670 0.0468436 0.0234218 0.999726i \(-0.492544\pi\)
0.0234218 + 0.999726i \(0.492544\pi\)
\(632\) −1.38574 −0.0551219
\(633\) −13.8293 −0.549664
\(634\) −18.5583 −0.737044
\(635\) −2.15194 −0.0853969
\(636\) 5.60114 0.222100
\(637\) −35.7111 −1.41493
\(638\) −12.1504 −0.481040
\(639\) 3.21026 0.126996
\(640\) −25.4087 −1.00437
\(641\) 11.8699 0.468834 0.234417 0.972136i \(-0.424682\pi\)
0.234417 + 0.972136i \(0.424682\pi\)
\(642\) 20.8487 0.822832
\(643\) −4.88951 −0.192823 −0.0964117 0.995342i \(-0.530737\pi\)
−0.0964117 + 0.995342i \(0.530737\pi\)
\(644\) −17.0825 −0.673145
\(645\) 9.46487 0.372679
\(646\) 4.19379 0.165002
\(647\) −42.5562 −1.67306 −0.836528 0.547924i \(-0.815418\pi\)
−0.836528 + 0.547924i \(0.815418\pi\)
\(648\) −6.45262 −0.253483
\(649\) 3.85275 0.151233
\(650\) −0.471464 −0.0184923
\(651\) −9.36599 −0.367082
\(652\) 60.5439 2.37108
\(653\) −1.14247 −0.0447083 −0.0223541 0.999750i \(-0.507116\pi\)
−0.0223541 + 0.999750i \(0.507116\pi\)
\(654\) 19.1954 0.750599
\(655\) −2.42597 −0.0947904
\(656\) −5.57502 −0.217668
\(657\) 10.8779 0.424387
\(658\) −5.23739 −0.204175
\(659\) −32.5666 −1.26861 −0.634307 0.773081i \(-0.718715\pi\)
−0.634307 + 0.773081i \(0.718715\pi\)
\(660\) 4.51482 0.175739
\(661\) 40.2416 1.56522 0.782608 0.622515i \(-0.213889\pi\)
0.782608 + 0.622515i \(0.213889\pi\)
\(662\) 56.1714 2.18316
\(663\) 2.18616 0.0849035
\(664\) −17.8937 −0.694409
\(665\) 30.0246 1.16431
\(666\) 35.9062 1.39134
\(667\) −9.66448 −0.374210
\(668\) 12.4180 0.480468
\(669\) 4.77718 0.184697
\(670\) −54.2736 −2.09677
\(671\) −5.20538 −0.200952
\(672\) −20.9437 −0.807921
\(673\) −42.2389 −1.62819 −0.814094 0.580733i \(-0.802766\pi\)
−0.814094 + 0.580733i \(0.802766\pi\)
\(674\) 54.9943 2.11830
\(675\) −0.160328 −0.00617105
\(676\) 47.6143 1.83132
\(677\) −5.24802 −0.201698 −0.100849 0.994902i \(-0.532156\pi\)
−0.100849 + 0.994902i \(0.532156\pi\)
\(678\) 6.71161 0.257758
\(679\) −27.4219 −1.05235
\(680\) 1.78083 0.0682915
\(681\) −5.17193 −0.198189
\(682\) −7.37643 −0.282458
\(683\) 4.26017 0.163011 0.0815054 0.996673i \(-0.474027\pi\)
0.0815054 + 0.996673i \(0.474027\pi\)
\(684\) 24.1868 0.924805
\(685\) −20.0631 −0.766570
\(686\) 4.35375 0.166227
\(687\) 15.2156 0.580510
\(688\) −11.9324 −0.454920
\(689\) 15.2926 0.582603
\(690\) 6.25046 0.237951
\(691\) −37.9833 −1.44495 −0.722476 0.691396i \(-0.756996\pi\)
−0.722476 + 0.691396i \(0.756996\pi\)
\(692\) 33.0477 1.25629
\(693\) −8.93707 −0.339491
\(694\) 48.9956 1.85985
\(695\) −28.9166 −1.09687
\(696\) 6.39039 0.242227
\(697\) 1.39217 0.0527321
\(698\) 29.5104 1.11699
\(699\) −2.72816 −0.103189
\(700\) −0.389200 −0.0147104
\(701\) −6.31743 −0.238606 −0.119303 0.992858i \(-0.538066\pi\)
−0.119303 + 0.992858i \(0.538066\pi\)
\(702\) 48.9640 1.84803
\(703\) −24.9803 −0.942149
\(704\) −12.2797 −0.462809
\(705\) 1.10101 0.0414664
\(706\) −47.2736 −1.77917
\(707\) −31.6249 −1.18938
\(708\) −7.80978 −0.293510
\(709\) 13.9420 0.523605 0.261802 0.965122i \(-0.415683\pi\)
0.261802 + 0.965122i \(0.415683\pi\)
\(710\) −6.36210 −0.238765
\(711\) −2.22252 −0.0833511
\(712\) 15.8834 0.595257
\(713\) −5.86723 −0.219730
\(714\) 3.14117 0.117555
\(715\) 12.3267 0.460992
\(716\) 55.0807 2.05846
\(717\) −8.67889 −0.324119
\(718\) −53.5247 −1.99752
\(719\) −19.0983 −0.712247 −0.356124 0.934439i \(-0.615902\pi\)
−0.356124 + 0.934439i \(0.615902\pi\)
\(720\) −11.4377 −0.426259
\(721\) −43.2633 −1.61121
\(722\) 11.9061 0.443099
\(723\) 8.41462 0.312943
\(724\) −71.0098 −2.63906
\(725\) −0.220191 −0.00817769
\(726\) 1.62731 0.0603952
\(727\) −17.1201 −0.634950 −0.317475 0.948267i \(-0.602835\pi\)
−0.317475 + 0.948267i \(0.602835\pi\)
\(728\) 30.8394 1.14299
\(729\) −1.16085 −0.0429945
\(730\) −21.5579 −0.797892
\(731\) 2.97971 0.110209
\(732\) 10.5517 0.390001
\(733\) −38.8717 −1.43576 −0.717880 0.696167i \(-0.754887\pi\)
−0.717880 + 0.696167i \(0.754887\pi\)
\(734\) −49.3990 −1.82335
\(735\) 10.7867 0.397873
\(736\) −13.1200 −0.483609
\(737\) −11.2392 −0.414000
\(738\) 13.9749 0.514422
\(739\) 5.89050 0.216686 0.108343 0.994114i \(-0.465446\pi\)
0.108343 + 0.994114i \(0.465446\pi\)
\(740\) −40.8832 −1.50290
\(741\) −15.2675 −0.560865
\(742\) 21.9731 0.806658
\(743\) 13.5219 0.496070 0.248035 0.968751i \(-0.420215\pi\)
0.248035 + 0.968751i \(0.420215\pi\)
\(744\) 3.87956 0.142231
\(745\) 18.7991 0.688747
\(746\) 52.7795 1.93240
\(747\) −28.6987 −1.05003
\(748\) 1.42135 0.0519696
\(749\) 46.9905 1.71699
\(750\) 18.2647 0.666932
\(751\) −22.8846 −0.835071 −0.417535 0.908661i \(-0.637106\pi\)
−0.417535 + 0.908661i \(0.637106\pi\)
\(752\) −1.38805 −0.0506170
\(753\) 8.20544 0.299023
\(754\) 67.2460 2.44895
\(755\) −4.23343 −0.154070
\(756\) 40.4205 1.47008
\(757\) −5.01203 −0.182165 −0.0910826 0.995843i \(-0.529033\pi\)
−0.0910826 + 0.995843i \(0.529033\pi\)
\(758\) −48.8247 −1.77339
\(759\) 1.29437 0.0469826
\(760\) −12.4367 −0.451128
\(761\) −42.0491 −1.52428 −0.762139 0.647413i \(-0.775851\pi\)
−0.762139 + 0.647413i \(0.775851\pi\)
\(762\) 1.57227 0.0569574
\(763\) 43.2641 1.56627
\(764\) −8.63487 −0.312399
\(765\) 2.85618 0.103265
\(766\) −9.25054 −0.334235
\(767\) −21.3228 −0.769923
\(768\) 0.131018 0.00472771
\(769\) −3.08597 −0.111283 −0.0556414 0.998451i \(-0.517720\pi\)
−0.0556414 + 0.998451i \(0.517720\pi\)
\(770\) 17.7115 0.638279
\(771\) 17.8459 0.642705
\(772\) 22.2071 0.799250
\(773\) −28.7452 −1.03389 −0.516947 0.856017i \(-0.672932\pi\)
−0.516947 + 0.856017i \(0.672932\pi\)
\(774\) 29.9110 1.07513
\(775\) −0.133676 −0.00480179
\(776\) 11.3586 0.407751
\(777\) −18.7104 −0.671232
\(778\) −44.3971 −1.59171
\(779\) −9.72246 −0.348343
\(780\) −24.9871 −0.894681
\(781\) −1.31749 −0.0471434
\(782\) 1.96776 0.0703669
\(783\) 22.8680 0.817236
\(784\) −13.5989 −0.485674
\(785\) 28.1863 1.00601
\(786\) 1.77249 0.0632226
\(787\) 15.4042 0.549099 0.274550 0.961573i \(-0.411471\pi\)
0.274550 + 0.961573i \(0.411471\pi\)
\(788\) −19.2444 −0.685553
\(789\) −10.0530 −0.357898
\(790\) 4.40460 0.156709
\(791\) 15.1272 0.537860
\(792\) 3.70189 0.131541
\(793\) 28.8090 1.02304
\(794\) 42.1143 1.49458
\(795\) −4.61921 −0.163827
\(796\) −3.78363 −0.134107
\(797\) 11.5401 0.408772 0.204386 0.978890i \(-0.434480\pi\)
0.204386 + 0.978890i \(0.434480\pi\)
\(798\) −21.9370 −0.776560
\(799\) 0.346617 0.0122624
\(800\) −0.298920 −0.0105684
\(801\) 25.4746 0.900102
\(802\) 77.3962 2.73296
\(803\) −4.46428 −0.157541
\(804\) 22.7826 0.803480
\(805\) 14.0878 0.496530
\(806\) 40.8245 1.43798
\(807\) 2.62274 0.0923248
\(808\) 13.0996 0.460843
\(809\) −31.7221 −1.11529 −0.557645 0.830080i \(-0.688295\pi\)
−0.557645 + 0.830080i \(0.688295\pi\)
\(810\) 20.5097 0.720639
\(811\) 19.1680 0.673080 0.336540 0.941669i \(-0.390743\pi\)
0.336540 + 0.941669i \(0.390743\pi\)
\(812\) 55.5125 1.94811
\(813\) 7.38610 0.259042
\(814\) −14.7359 −0.516492
\(815\) −49.9301 −1.74897
\(816\) 0.832496 0.0291432
\(817\) −20.8094 −0.728028
\(818\) −48.1550 −1.68370
\(819\) 49.4618 1.72834
\(820\) −15.9120 −0.555670
\(821\) −11.5761 −0.404008 −0.202004 0.979385i \(-0.564745\pi\)
−0.202004 + 0.979385i \(0.564745\pi\)
\(822\) 14.6587 0.511281
\(823\) −25.3856 −0.884888 −0.442444 0.896796i \(-0.645888\pi\)
−0.442444 + 0.896796i \(0.645888\pi\)
\(824\) 17.9204 0.624287
\(825\) 0.0294903 0.00102672
\(826\) −30.6376 −1.06602
\(827\) −27.3636 −0.951524 −0.475762 0.879574i \(-0.657828\pi\)
−0.475762 + 0.879574i \(0.657828\pi\)
\(828\) 11.3486 0.394392
\(829\) −3.75176 −0.130304 −0.0651521 0.997875i \(-0.520753\pi\)
−0.0651521 + 0.997875i \(0.520753\pi\)
\(830\) 56.8753 1.97417
\(831\) 0.246458 0.00854953
\(832\) 67.9615 2.35614
\(833\) 3.39584 0.117659
\(834\) 21.1274 0.731582
\(835\) −10.2410 −0.354406
\(836\) −9.92624 −0.343306
\(837\) 13.8830 0.479867
\(838\) 33.5041 1.15738
\(839\) 46.6639 1.61102 0.805508 0.592585i \(-0.201892\pi\)
0.805508 + 0.592585i \(0.201892\pi\)
\(840\) −9.31519 −0.321405
\(841\) 2.40636 0.0829780
\(842\) −33.3196 −1.14827
\(843\) 16.5111 0.568672
\(844\) 49.7612 1.71285
\(845\) −39.2671 −1.35083
\(846\) 3.47942 0.119625
\(847\) 3.66777 0.126026
\(848\) 5.82348 0.199979
\(849\) 10.8927 0.373838
\(850\) 0.0448325 0.00153774
\(851\) −11.7209 −0.401789
\(852\) 2.67064 0.0914945
\(853\) −9.01516 −0.308673 −0.154337 0.988018i \(-0.549324\pi\)
−0.154337 + 0.988018i \(0.549324\pi\)
\(854\) 41.3939 1.41647
\(855\) −19.9466 −0.682161
\(856\) −19.4643 −0.665275
\(857\) −16.2536 −0.555212 −0.277606 0.960695i \(-0.589541\pi\)
−0.277606 + 0.960695i \(0.589541\pi\)
\(858\) −9.00628 −0.307469
\(859\) 40.2552 1.37349 0.686744 0.726899i \(-0.259039\pi\)
0.686744 + 0.726899i \(0.259039\pi\)
\(860\) −34.0570 −1.16134
\(861\) −7.28219 −0.248176
\(862\) 15.7797 0.537459
\(863\) −6.55780 −0.223230 −0.111615 0.993752i \(-0.535602\pi\)
−0.111615 + 0.993752i \(0.535602\pi\)
\(864\) 31.0444 1.05615
\(865\) −27.2542 −0.926670
\(866\) 40.7179 1.38365
\(867\) 12.5517 0.426279
\(868\) 33.7012 1.14389
\(869\) 0.912121 0.0309416
\(870\) −20.3119 −0.688639
\(871\) 62.2027 2.10766
\(872\) −17.9208 −0.606873
\(873\) 18.2175 0.616569
\(874\) −13.7422 −0.464837
\(875\) 41.1664 1.39168
\(876\) 9.04940 0.305751
\(877\) −37.2577 −1.25810 −0.629051 0.777364i \(-0.716556\pi\)
−0.629051 + 0.777364i \(0.716556\pi\)
\(878\) 34.1544 1.15266
\(879\) 12.8917 0.434827
\(880\) 4.69404 0.158236
\(881\) 21.1519 0.712626 0.356313 0.934367i \(-0.384034\pi\)
0.356313 + 0.934367i \(0.384034\pi\)
\(882\) 34.0882 1.14781
\(883\) −40.8229 −1.37380 −0.686899 0.726753i \(-0.741029\pi\)
−0.686899 + 0.726753i \(0.741029\pi\)
\(884\) −7.86638 −0.264575
\(885\) 6.44066 0.216500
\(886\) −33.8320 −1.13661
\(887\) −19.4412 −0.652772 −0.326386 0.945237i \(-0.605831\pi\)
−0.326386 + 0.945237i \(0.605831\pi\)
\(888\) 7.75017 0.260079
\(889\) 3.54372 0.118852
\(890\) −50.4857 −1.69229
\(891\) 4.24723 0.142288
\(892\) −17.1895 −0.575548
\(893\) −2.42067 −0.0810046
\(894\) −13.7353 −0.459376
\(895\) −45.4246 −1.51838
\(896\) 41.8420 1.39784
\(897\) −7.16363 −0.239186
\(898\) 25.7670 0.859856
\(899\) 19.0666 0.635906
\(900\) 0.258562 0.00861873
\(901\) −1.45421 −0.0484467
\(902\) −5.73528 −0.190964
\(903\) −15.5863 −0.518681
\(904\) −6.26594 −0.208402
\(905\) 58.5612 1.94664
\(906\) 3.09308 0.102761
\(907\) −8.54748 −0.283815 −0.141907 0.989880i \(-0.545323\pi\)
−0.141907 + 0.989880i \(0.545323\pi\)
\(908\) 18.6099 0.617592
\(909\) 21.0098 0.696851
\(910\) −98.0236 −3.24945
\(911\) 9.45569 0.313281 0.156640 0.987656i \(-0.449934\pi\)
0.156640 + 0.987656i \(0.449934\pi\)
\(912\) −5.81390 −0.192517
\(913\) 11.7779 0.389793
\(914\) 14.1953 0.469539
\(915\) −8.70187 −0.287675
\(916\) −54.7495 −1.80898
\(917\) 3.99498 0.131926
\(918\) −4.65609 −0.153674
\(919\) −51.3133 −1.69267 −0.846335 0.532652i \(-0.821196\pi\)
−0.846335 + 0.532652i \(0.821196\pi\)
\(920\) −5.83541 −0.192388
\(921\) 2.52707 0.0832696
\(922\) −37.9153 −1.24867
\(923\) 7.29157 0.240005
\(924\) −7.43482 −0.244587
\(925\) −0.267045 −0.00878037
\(926\) 57.0415 1.87450
\(927\) 28.7416 0.943999
\(928\) 42.6356 1.39958
\(929\) 30.7015 1.00728 0.503642 0.863912i \(-0.331993\pi\)
0.503642 + 0.863912i \(0.331993\pi\)
\(930\) −12.3312 −0.404357
\(931\) −23.7155 −0.777245
\(932\) 9.81663 0.321555
\(933\) −10.8876 −0.356445
\(934\) 44.1332 1.44408
\(935\) −1.17217 −0.0383341
\(936\) −20.4880 −0.669670
\(937\) −25.5083 −0.833319 −0.416659 0.909063i \(-0.636799\pi\)
−0.416659 + 0.909063i \(0.636799\pi\)
\(938\) 89.3755 2.91821
\(939\) 3.42664 0.111824
\(940\) −3.96171 −0.129217
\(941\) 4.61499 0.150444 0.0752221 0.997167i \(-0.476033\pi\)
0.0752221 + 0.997167i \(0.476033\pi\)
\(942\) −20.5938 −0.670983
\(943\) −4.56186 −0.148554
\(944\) −8.11979 −0.264277
\(945\) −33.3344 −1.08437
\(946\) −12.2754 −0.399109
\(947\) 1.08975 0.0354121 0.0177060 0.999843i \(-0.494364\pi\)
0.0177060 + 0.999843i \(0.494364\pi\)
\(948\) −1.84893 −0.0600505
\(949\) 24.7073 0.802034
\(950\) −0.313096 −0.0101582
\(951\) −6.42457 −0.208331
\(952\) −2.93259 −0.0950457
\(953\) −22.0713 −0.714958 −0.357479 0.933921i \(-0.616364\pi\)
−0.357479 + 0.933921i \(0.616364\pi\)
\(954\) −14.5977 −0.472617
\(955\) 7.12110 0.230433
\(956\) 31.2289 1.01001
\(957\) −4.20627 −0.135969
\(958\) −37.8405 −1.22257
\(959\) 33.0390 1.06688
\(960\) −20.5281 −0.662540
\(961\) −19.4248 −0.626607
\(962\) 81.5550 2.62944
\(963\) −31.2178 −1.00598
\(964\) −30.2780 −0.975187
\(965\) −18.3140 −0.589548
\(966\) −10.2930 −0.331172
\(967\) −10.0099 −0.321895 −0.160948 0.986963i \(-0.551455\pi\)
−0.160948 + 0.986963i \(0.551455\pi\)
\(968\) −1.51925 −0.0488306
\(969\) 1.45182 0.0466391
\(970\) −36.1035 −1.15921
\(971\) −20.8142 −0.667960 −0.333980 0.942580i \(-0.608392\pi\)
−0.333980 + 0.942580i \(0.608392\pi\)
\(972\) −41.6708 −1.33659
\(973\) 47.6186 1.52658
\(974\) −14.5669 −0.466752
\(975\) −0.163213 −0.00522699
\(976\) 10.9705 0.351158
\(977\) −5.00340 −0.160073 −0.0800364 0.996792i \(-0.525504\pi\)
−0.0800364 + 0.996792i \(0.525504\pi\)
\(978\) 36.4805 1.16652
\(979\) −10.4548 −0.334136
\(980\) −38.8133 −1.23985
\(981\) −28.7422 −0.917667
\(982\) 6.29399 0.200849
\(983\) −8.54761 −0.272626 −0.136313 0.990666i \(-0.543525\pi\)
−0.136313 + 0.990666i \(0.543525\pi\)
\(984\) 3.01641 0.0961596
\(985\) 15.8707 0.505682
\(986\) −6.39456 −0.203644
\(987\) −1.81310 −0.0577115
\(988\) 54.9363 1.74776
\(989\) −9.76392 −0.310475
\(990\) −11.7665 −0.373964
\(991\) −5.42039 −0.172184 −0.0860922 0.996287i \(-0.527438\pi\)
−0.0860922 + 0.996287i \(0.527438\pi\)
\(992\) 25.8838 0.821810
\(993\) 19.4456 0.617087
\(994\) 10.4768 0.332305
\(995\) 3.12033 0.0989210
\(996\) −23.8747 −0.756499
\(997\) 48.3550 1.53142 0.765709 0.643187i \(-0.222388\pi\)
0.765709 + 0.643187i \(0.222388\pi\)
\(998\) −91.7074 −2.90295
\(999\) 27.7340 0.877466
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 \(a_p\))