Properties

Label 6034.2.a.n.1.16
Level 6034
Weight 2
Character 6034.1
Self dual Yes
Analytic conductor 48.182
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6034.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1817325796\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 6034.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.44853 q^{3}\) \(+1.00000 q^{4}\) \(-1.26403 q^{5}\) \(-1.44853 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(-0.901751 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.44853 q^{3}\) \(+1.00000 q^{4}\) \(-1.26403 q^{5}\) \(-1.44853 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(-0.901751 q^{9}\) \(+1.26403 q^{10}\) \(-3.22511 q^{11}\) \(+1.44853 q^{12}\) \(-2.31777 q^{13}\) \(+1.00000 q^{14}\) \(-1.83098 q^{15}\) \(+1.00000 q^{16}\) \(+3.60165 q^{17}\) \(+0.901751 q^{18}\) \(+5.33546 q^{19}\) \(-1.26403 q^{20}\) \(-1.44853 q^{21}\) \(+3.22511 q^{22}\) \(-7.66129 q^{23}\) \(-1.44853 q^{24}\) \(-3.40224 q^{25}\) \(+2.31777 q^{26}\) \(-5.65182 q^{27}\) \(-1.00000 q^{28}\) \(-0.214755 q^{29}\) \(+1.83098 q^{30}\) \(-5.47162 q^{31}\) \(-1.00000 q^{32}\) \(-4.67167 q^{33}\) \(-3.60165 q^{34}\) \(+1.26403 q^{35}\) \(-0.901751 q^{36}\) \(+0.154141 q^{37}\) \(-5.33546 q^{38}\) \(-3.35737 q^{39}\) \(+1.26403 q^{40}\) \(+3.69908 q^{41}\) \(+1.44853 q^{42}\) \(+7.50104 q^{43}\) \(-3.22511 q^{44}\) \(+1.13984 q^{45}\) \(+7.66129 q^{46}\) \(+0.101562 q^{47}\) \(+1.44853 q^{48}\) \(+1.00000 q^{49}\) \(+3.40224 q^{50}\) \(+5.21710 q^{51}\) \(-2.31777 q^{52}\) \(+9.39083 q^{53}\) \(+5.65182 q^{54}\) \(+4.07662 q^{55}\) \(+1.00000 q^{56}\) \(+7.72860 q^{57}\) \(+0.214755 q^{58}\) \(+11.8493 q^{59}\) \(-1.83098 q^{60}\) \(+5.95759 q^{61}\) \(+5.47162 q^{62}\) \(+0.901751 q^{63}\) \(+1.00000 q^{64}\) \(+2.92972 q^{65}\) \(+4.67167 q^{66}\) \(-2.95438 q^{67}\) \(+3.60165 q^{68}\) \(-11.0976 q^{69}\) \(-1.26403 q^{70}\) \(+10.7018 q^{71}\) \(+0.901751 q^{72}\) \(-15.7336 q^{73}\) \(-0.154141 q^{74}\) \(-4.92826 q^{75}\) \(+5.33546 q^{76}\) \(+3.22511 q^{77}\) \(+3.35737 q^{78}\) \(-13.6695 q^{79}\) \(-1.26403 q^{80}\) \(-5.48159 q^{81}\) \(-3.69908 q^{82}\) \(-1.96725 q^{83}\) \(-1.44853 q^{84}\) \(-4.55257 q^{85}\) \(-7.50104 q^{86}\) \(-0.311080 q^{87}\) \(+3.22511 q^{88}\) \(-0.350463 q^{89}\) \(-1.13984 q^{90}\) \(+2.31777 q^{91}\) \(-7.66129 q^{92}\) \(-7.92583 q^{93}\) \(-0.101562 q^{94}\) \(-6.74416 q^{95}\) \(-1.44853 q^{96}\) \(-17.6621 q^{97}\) \(-1.00000 q^{98}\) \(+2.90824 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut -\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 15q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut +\mathstrut 24q^{14} \) \(\mathstrut +\mathstrut 13q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut +\mathstrut 6q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut -\mathstrut 7q^{21} \) \(\mathstrut -\mathstrut 15q^{22} \) \(\mathstrut +\mathstrut 3q^{23} \) \(\mathstrut -\mathstrut 7q^{24} \) \(\mathstrut +\mathstrut 12q^{25} \) \(\mathstrut +\mathstrut 7q^{26} \) \(\mathstrut +\mathstrut 22q^{27} \) \(\mathstrut -\mathstrut 24q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 13q^{30} \) \(\mathstrut +\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 6q^{38} \) \(\mathstrut +\mathstrut 7q^{39} \) \(\mathstrut -\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 7q^{42} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 41q^{45} \) \(\mathstrut -\mathstrut 3q^{46} \) \(\mathstrut +\mathstrut 35q^{47} \) \(\mathstrut +\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 24q^{49} \) \(\mathstrut -\mathstrut 12q^{50} \) \(\mathstrut +\mathstrut 31q^{51} \) \(\mathstrut -\mathstrut 7q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 14q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 5q^{58} \) \(\mathstrut +\mathstrut 35q^{59} \) \(\mathstrut +\mathstrut 13q^{60} \) \(\mathstrut -\mathstrut 7q^{61} \) \(\mathstrut -\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut +\mathstrut 10q^{67} \) \(\mathstrut -\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut +\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 58q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut +\mathstrut 9q^{73} \) \(\mathstrut -\mathstrut 2q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 6q^{76} \) \(\mathstrut -\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 7q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut -\mathstrut 25q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut -\mathstrut 7q^{84} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 15q^{86} \) \(\mathstrut +\mathstrut 30q^{87} \) \(\mathstrut -\mathstrut 15q^{88} \) \(\mathstrut +\mathstrut 45q^{89} \) \(\mathstrut -\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 7q^{91} \) \(\mathstrut +\mathstrut 3q^{92} \) \(\mathstrut +\mathstrut 25q^{93} \) \(\mathstrut -\mathstrut 35q^{94} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 7q^{96} \) \(\mathstrut -\mathstrut 9q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 64q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.44853 0.836311 0.418156 0.908375i \(-0.362677\pi\)
0.418156 + 0.908375i \(0.362677\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.26403 −0.565289 −0.282645 0.959225i \(-0.591212\pi\)
−0.282645 + 0.959225i \(0.591212\pi\)
\(6\) −1.44853 −0.591361
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) −0.901751 −0.300584
\(10\) 1.26403 0.399720
\(11\) −3.22511 −0.972406 −0.486203 0.873846i \(-0.661618\pi\)
−0.486203 + 0.873846i \(0.661618\pi\)
\(12\) 1.44853 0.418156
\(13\) −2.31777 −0.642835 −0.321417 0.946938i \(-0.604159\pi\)
−0.321417 + 0.946938i \(0.604159\pi\)
\(14\) 1.00000 0.267261
\(15\) −1.83098 −0.472758
\(16\) 1.00000 0.250000
\(17\) 3.60165 0.873527 0.436764 0.899576i \(-0.356125\pi\)
0.436764 + 0.899576i \(0.356125\pi\)
\(18\) 0.901751 0.212545
\(19\) 5.33546 1.22404 0.612020 0.790843i \(-0.290357\pi\)
0.612020 + 0.790843i \(0.290357\pi\)
\(20\) −1.26403 −0.282645
\(21\) −1.44853 −0.316096
\(22\) 3.22511 0.687595
\(23\) −7.66129 −1.59749 −0.798745 0.601670i \(-0.794502\pi\)
−0.798745 + 0.601670i \(0.794502\pi\)
\(24\) −1.44853 −0.295681
\(25\) −3.40224 −0.680448
\(26\) 2.31777 0.454553
\(27\) −5.65182 −1.08769
\(28\) −1.00000 −0.188982
\(29\) −0.214755 −0.0398791 −0.0199395 0.999801i \(-0.506347\pi\)
−0.0199395 + 0.999801i \(0.506347\pi\)
\(30\) 1.83098 0.334290
\(31\) −5.47162 −0.982732 −0.491366 0.870953i \(-0.663502\pi\)
−0.491366 + 0.870953i \(0.663502\pi\)
\(32\) −1.00000 −0.176777
\(33\) −4.67167 −0.813234
\(34\) −3.60165 −0.617677
\(35\) 1.26403 0.213659
\(36\) −0.901751 −0.150292
\(37\) 0.154141 0.0253407 0.0126703 0.999920i \(-0.495967\pi\)
0.0126703 + 0.999920i \(0.495967\pi\)
\(38\) −5.33546 −0.865526
\(39\) −3.35737 −0.537610
\(40\) 1.26403 0.199860
\(41\) 3.69908 0.577699 0.288850 0.957374i \(-0.406727\pi\)
0.288850 + 0.957374i \(0.406727\pi\)
\(42\) 1.44853 0.223514
\(43\) 7.50104 1.14390 0.571949 0.820289i \(-0.306188\pi\)
0.571949 + 0.820289i \(0.306188\pi\)
\(44\) −3.22511 −0.486203
\(45\) 1.13984 0.169917
\(46\) 7.66129 1.12960
\(47\) 0.101562 0.0148144 0.00740720 0.999973i \(-0.497642\pi\)
0.00740720 + 0.999973i \(0.497642\pi\)
\(48\) 1.44853 0.209078
\(49\) 1.00000 0.142857
\(50\) 3.40224 0.481149
\(51\) 5.21710 0.730541
\(52\) −2.31777 −0.321417
\(53\) 9.39083 1.28993 0.644965 0.764212i \(-0.276872\pi\)
0.644965 + 0.764212i \(0.276872\pi\)
\(54\) 5.65182 0.769115
\(55\) 4.07662 0.549691
\(56\) 1.00000 0.133631
\(57\) 7.72860 1.02368
\(58\) 0.214755 0.0281988
\(59\) 11.8493 1.54264 0.771322 0.636445i \(-0.219596\pi\)
0.771322 + 0.636445i \(0.219596\pi\)
\(60\) −1.83098 −0.236379
\(61\) 5.95759 0.762792 0.381396 0.924412i \(-0.375443\pi\)
0.381396 + 0.924412i \(0.375443\pi\)
\(62\) 5.47162 0.694897
\(63\) 0.901751 0.113610
\(64\) 1.00000 0.125000
\(65\) 2.92972 0.363388
\(66\) 4.67167 0.575043
\(67\) −2.95438 −0.360935 −0.180467 0.983581i \(-0.557761\pi\)
−0.180467 + 0.983581i \(0.557761\pi\)
\(68\) 3.60165 0.436764
\(69\) −11.0976 −1.33600
\(70\) −1.26403 −0.151080
\(71\) 10.7018 1.27007 0.635035 0.772483i \(-0.280986\pi\)
0.635035 + 0.772483i \(0.280986\pi\)
\(72\) 0.901751 0.106272
\(73\) −15.7336 −1.84148 −0.920739 0.390179i \(-0.872413\pi\)
−0.920739 + 0.390179i \(0.872413\pi\)
\(74\) −0.154141 −0.0179186
\(75\) −4.92826 −0.569066
\(76\) 5.33546 0.612020
\(77\) 3.22511 0.367535
\(78\) 3.35737 0.380147
\(79\) −13.6695 −1.53794 −0.768970 0.639285i \(-0.779230\pi\)
−0.768970 + 0.639285i \(0.779230\pi\)
\(80\) −1.26403 −0.141322
\(81\) −5.48159 −0.609066
\(82\) −3.69908 −0.408495
\(83\) −1.96725 −0.215934 −0.107967 0.994154i \(-0.534434\pi\)
−0.107967 + 0.994154i \(0.534434\pi\)
\(84\) −1.44853 −0.158048
\(85\) −4.55257 −0.493796
\(86\) −7.50104 −0.808857
\(87\) −0.311080 −0.0333513
\(88\) 3.22511 0.343797
\(89\) −0.350463 −0.0371490 −0.0185745 0.999827i \(-0.505913\pi\)
−0.0185745 + 0.999827i \(0.505913\pi\)
\(90\) −1.13984 −0.120149
\(91\) 2.31777 0.242969
\(92\) −7.66129 −0.798745
\(93\) −7.92583 −0.821870
\(94\) −0.101562 −0.0104754
\(95\) −6.74416 −0.691936
\(96\) −1.44853 −0.147840
\(97\) −17.6621 −1.79332 −0.896659 0.442723i \(-0.854013\pi\)
−0.896659 + 0.442723i \(0.854013\pi\)
\(98\) −1.00000 −0.101015
\(99\) 2.90824 0.292289
\(100\) −3.40224 −0.340224
\(101\) 8.91473 0.887049 0.443524 0.896262i \(-0.353728\pi\)
0.443524 + 0.896262i \(0.353728\pi\)
\(102\) −5.21710 −0.516570
\(103\) 9.46770 0.932880 0.466440 0.884553i \(-0.345536\pi\)
0.466440 + 0.884553i \(0.345536\pi\)
\(104\) 2.31777 0.227276
\(105\) 1.83098 0.178686
\(106\) −9.39083 −0.912118
\(107\) 17.0234 1.64571 0.822856 0.568250i \(-0.192380\pi\)
0.822856 + 0.568250i \(0.192380\pi\)
\(108\) −5.65182 −0.543846
\(109\) 19.5460 1.87217 0.936086 0.351773i \(-0.114421\pi\)
0.936086 + 0.351773i \(0.114421\pi\)
\(110\) −4.07662 −0.388690
\(111\) 0.223279 0.0211927
\(112\) −1.00000 −0.0944911
\(113\) −14.8821 −1.39999 −0.699997 0.714146i \(-0.746815\pi\)
−0.699997 + 0.714146i \(0.746815\pi\)
\(114\) −7.72860 −0.723849
\(115\) 9.68407 0.903044
\(116\) −0.214755 −0.0199395
\(117\) 2.09005 0.193226
\(118\) −11.8493 −1.09081
\(119\) −3.60165 −0.330162
\(120\) 1.83098 0.167145
\(121\) −0.598690 −0.0544264
\(122\) −5.95759 −0.539375
\(123\) 5.35824 0.483136
\(124\) −5.47162 −0.491366
\(125\) 10.6206 0.949939
\(126\) −0.901751 −0.0803344
\(127\) 7.87038 0.698383 0.349191 0.937051i \(-0.386456\pi\)
0.349191 + 0.937051i \(0.386456\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 10.8655 0.956654
\(130\) −2.92972 −0.256954
\(131\) −0.0345986 −0.00302290 −0.00151145 0.999999i \(-0.500481\pi\)
−0.00151145 + 0.999999i \(0.500481\pi\)
\(132\) −4.67167 −0.406617
\(133\) −5.33546 −0.462643
\(134\) 2.95438 0.255219
\(135\) 7.14404 0.614861
\(136\) −3.60165 −0.308839
\(137\) −2.39977 −0.205026 −0.102513 0.994732i \(-0.532688\pi\)
−0.102513 + 0.994732i \(0.532688\pi\)
\(138\) 11.0976 0.944694
\(139\) −13.1736 −1.11737 −0.558683 0.829381i \(-0.688693\pi\)
−0.558683 + 0.829381i \(0.688693\pi\)
\(140\) 1.26403 0.106830
\(141\) 0.147116 0.0123894
\(142\) −10.7018 −0.898075
\(143\) 7.47506 0.625096
\(144\) −0.901751 −0.0751459
\(145\) 0.271456 0.0225432
\(146\) 15.7336 1.30212
\(147\) 1.44853 0.119473
\(148\) 0.154141 0.0126703
\(149\) 14.8747 1.21859 0.609293 0.792945i \(-0.291453\pi\)
0.609293 + 0.792945i \(0.291453\pi\)
\(150\) 4.92826 0.402390
\(151\) 24.1404 1.96452 0.982259 0.187530i \(-0.0600480\pi\)
0.982259 + 0.187530i \(0.0600480\pi\)
\(152\) −5.33546 −0.432763
\(153\) −3.24779 −0.262568
\(154\) −3.22511 −0.259886
\(155\) 6.91627 0.555528
\(156\) −3.35737 −0.268805
\(157\) 6.06502 0.484041 0.242021 0.970271i \(-0.422190\pi\)
0.242021 + 0.970271i \(0.422190\pi\)
\(158\) 13.6695 1.08749
\(159\) 13.6029 1.07878
\(160\) 1.26403 0.0999300
\(161\) 7.66129 0.603794
\(162\) 5.48159 0.430674
\(163\) 10.5901 0.829477 0.414738 0.909941i \(-0.363873\pi\)
0.414738 + 0.909941i \(0.363873\pi\)
\(164\) 3.69908 0.288850
\(165\) 5.90512 0.459713
\(166\) 1.96725 0.152688
\(167\) 3.80166 0.294181 0.147091 0.989123i \(-0.453009\pi\)
0.147091 + 0.989123i \(0.453009\pi\)
\(168\) 1.44853 0.111757
\(169\) −7.62793 −0.586764
\(170\) 4.55257 0.349166
\(171\) −4.81126 −0.367926
\(172\) 7.50104 0.571949
\(173\) 16.4571 1.25121 0.625605 0.780140i \(-0.284852\pi\)
0.625605 + 0.780140i \(0.284852\pi\)
\(174\) 0.311080 0.0235829
\(175\) 3.40224 0.257185
\(176\) −3.22511 −0.243102
\(177\) 17.1641 1.29013
\(178\) 0.350463 0.0262683
\(179\) 19.1032 1.42784 0.713921 0.700227i \(-0.246918\pi\)
0.713921 + 0.700227i \(0.246918\pi\)
\(180\) 1.13984 0.0849584
\(181\) 15.4524 1.14857 0.574285 0.818655i \(-0.305280\pi\)
0.574285 + 0.818655i \(0.305280\pi\)
\(182\) −2.31777 −0.171805
\(183\) 8.62977 0.637931
\(184\) 7.66129 0.564798
\(185\) −0.194839 −0.0143248
\(186\) 7.92583 0.581150
\(187\) −11.6157 −0.849423
\(188\) 0.101562 0.00740720
\(189\) 5.65182 0.411109
\(190\) 6.74416 0.489273
\(191\) 4.74568 0.343385 0.171692 0.985151i \(-0.445076\pi\)
0.171692 + 0.985151i \(0.445076\pi\)
\(192\) 1.44853 0.104539
\(193\) 4.37571 0.314970 0.157485 0.987521i \(-0.449661\pi\)
0.157485 + 0.987521i \(0.449661\pi\)
\(194\) 17.6621 1.26807
\(195\) 4.24380 0.303905
\(196\) 1.00000 0.0714286
\(197\) 3.06798 0.218585 0.109292 0.994010i \(-0.465142\pi\)
0.109292 + 0.994010i \(0.465142\pi\)
\(198\) −2.90824 −0.206680
\(199\) −26.2836 −1.86320 −0.931599 0.363488i \(-0.881586\pi\)
−0.931599 + 0.363488i \(0.881586\pi\)
\(200\) 3.40224 0.240575
\(201\) −4.27951 −0.301854
\(202\) −8.91473 −0.627238
\(203\) 0.214755 0.0150729
\(204\) 5.21710 0.365270
\(205\) −4.67573 −0.326567
\(206\) −9.46770 −0.659646
\(207\) 6.90858 0.480179
\(208\) −2.31777 −0.160709
\(209\) −17.2074 −1.19026
\(210\) −1.83098 −0.126350
\(211\) −8.94228 −0.615612 −0.307806 0.951449i \(-0.599595\pi\)
−0.307806 + 0.951449i \(0.599595\pi\)
\(212\) 9.39083 0.644965
\(213\) 15.5019 1.06217
\(214\) −17.0234 −1.16369
\(215\) −9.48150 −0.646633
\(216\) 5.65182 0.384557
\(217\) 5.47162 0.371438
\(218\) −19.5460 −1.32382
\(219\) −22.7906 −1.54005
\(220\) 4.07662 0.274845
\(221\) −8.34780 −0.561534
\(222\) −0.223279 −0.0149855
\(223\) −27.0980 −1.81461 −0.907307 0.420470i \(-0.861865\pi\)
−0.907307 + 0.420470i \(0.861865\pi\)
\(224\) 1.00000 0.0668153
\(225\) 3.06797 0.204532
\(226\) 14.8821 0.989946
\(227\) 0.799865 0.0530889 0.0265444 0.999648i \(-0.491550\pi\)
0.0265444 + 0.999648i \(0.491550\pi\)
\(228\) 7.72860 0.511839
\(229\) −1.41408 −0.0934453 −0.0467227 0.998908i \(-0.514878\pi\)
−0.0467227 + 0.998908i \(0.514878\pi\)
\(230\) −9.68407 −0.638549
\(231\) 4.67167 0.307374
\(232\) 0.214755 0.0140994
\(233\) 2.30009 0.150684 0.0753419 0.997158i \(-0.475995\pi\)
0.0753419 + 0.997158i \(0.475995\pi\)
\(234\) −2.09005 −0.136631
\(235\) −0.128377 −0.00837442
\(236\) 11.8493 0.771322
\(237\) −19.8007 −1.28620
\(238\) 3.60165 0.233460
\(239\) 9.46668 0.612349 0.306174 0.951975i \(-0.400951\pi\)
0.306174 + 0.951975i \(0.400951\pi\)
\(240\) −1.83098 −0.118189
\(241\) 15.2642 0.983254 0.491627 0.870806i \(-0.336402\pi\)
0.491627 + 0.870806i \(0.336402\pi\)
\(242\) 0.598690 0.0384853
\(243\) 9.01518 0.578324
\(244\) 5.95759 0.381396
\(245\) −1.26403 −0.0807556
\(246\) −5.35824 −0.341629
\(247\) −12.3664 −0.786855
\(248\) 5.47162 0.347448
\(249\) −2.84963 −0.180588
\(250\) −10.6206 −0.671709
\(251\) 1.32168 0.0834237 0.0417118 0.999130i \(-0.486719\pi\)
0.0417118 + 0.999130i \(0.486719\pi\)
\(252\) 0.901751 0.0568050
\(253\) 24.7085 1.55341
\(254\) −7.87038 −0.493831
\(255\) −6.59455 −0.412967
\(256\) 1.00000 0.0625000
\(257\) −9.58020 −0.597597 −0.298798 0.954316i \(-0.596586\pi\)
−0.298798 + 0.954316i \(0.596586\pi\)
\(258\) −10.8655 −0.676456
\(259\) −0.154141 −0.00957788
\(260\) 2.92972 0.181694
\(261\) 0.193656 0.0119870
\(262\) 0.0345986 0.00213751
\(263\) 26.9818 1.66377 0.831885 0.554947i \(-0.187262\pi\)
0.831885 + 0.554947i \(0.187262\pi\)
\(264\) 4.67167 0.287522
\(265\) −11.8703 −0.729184
\(266\) 5.33546 0.327138
\(267\) −0.507657 −0.0310681
\(268\) −2.95438 −0.180467
\(269\) −7.60283 −0.463553 −0.231776 0.972769i \(-0.574454\pi\)
−0.231776 + 0.972769i \(0.574454\pi\)
\(270\) −7.14404 −0.434773
\(271\) 23.1724 1.40763 0.703813 0.710386i \(-0.251479\pi\)
0.703813 + 0.710386i \(0.251479\pi\)
\(272\) 3.60165 0.218382
\(273\) 3.35737 0.203197
\(274\) 2.39977 0.144976
\(275\) 10.9726 0.661672
\(276\) −11.0976 −0.667999
\(277\) 21.5203 1.29303 0.646515 0.762902i \(-0.276226\pi\)
0.646515 + 0.762902i \(0.276226\pi\)
\(278\) 13.1736 0.790098
\(279\) 4.93404 0.295393
\(280\) −1.26403 −0.0755400
\(281\) −29.3424 −1.75042 −0.875210 0.483742i \(-0.839277\pi\)
−0.875210 + 0.483742i \(0.839277\pi\)
\(282\) −0.147116 −0.00876066
\(283\) −30.0854 −1.78839 −0.894197 0.447674i \(-0.852253\pi\)
−0.894197 + 0.447674i \(0.852253\pi\)
\(284\) 10.7018 0.635035
\(285\) −9.76914 −0.578674
\(286\) −7.47506 −0.442010
\(287\) −3.69908 −0.218350
\(288\) 0.901751 0.0531362
\(289\) −4.02815 −0.236950
\(290\) −0.271456 −0.0159405
\(291\) −25.5842 −1.49977
\(292\) −15.7336 −0.920739
\(293\) 19.2131 1.12244 0.561221 0.827666i \(-0.310332\pi\)
0.561221 + 0.827666i \(0.310332\pi\)
\(294\) −1.44853 −0.0844802
\(295\) −14.9778 −0.872040
\(296\) −0.154141 −0.00895929
\(297\) 18.2277 1.05768
\(298\) −14.8747 −0.861671
\(299\) 17.7571 1.02692
\(300\) −4.92826 −0.284533
\(301\) −7.50104 −0.432352
\(302\) −24.1404 −1.38912
\(303\) 12.9133 0.741849
\(304\) 5.33546 0.306010
\(305\) −7.53055 −0.431198
\(306\) 3.24779 0.185664
\(307\) −2.60073 −0.148431 −0.0742156 0.997242i \(-0.523645\pi\)
−0.0742156 + 0.997242i \(0.523645\pi\)
\(308\) 3.22511 0.183767
\(309\) 13.7143 0.780178
\(310\) −6.91627 −0.392818
\(311\) −10.9513 −0.620991 −0.310495 0.950575i \(-0.600495\pi\)
−0.310495 + 0.950575i \(0.600495\pi\)
\(312\) 3.35737 0.190074
\(313\) 21.0786 1.19143 0.595717 0.803195i \(-0.296868\pi\)
0.595717 + 0.803195i \(0.296868\pi\)
\(314\) −6.06502 −0.342269
\(315\) −1.13984 −0.0642225
\(316\) −13.6695 −0.768970
\(317\) −3.41278 −0.191681 −0.0958403 0.995397i \(-0.530554\pi\)
−0.0958403 + 0.995397i \(0.530554\pi\)
\(318\) −13.6029 −0.762815
\(319\) 0.692609 0.0387787
\(320\) −1.26403 −0.0706612
\(321\) 24.6589 1.37633
\(322\) −7.66129 −0.426947
\(323\) 19.2164 1.06923
\(324\) −5.48159 −0.304533
\(325\) 7.88562 0.437415
\(326\) −10.5901 −0.586529
\(327\) 28.3131 1.56572
\(328\) −3.69908 −0.204248
\(329\) −0.101562 −0.00559931
\(330\) −5.90512 −0.325066
\(331\) 1.05122 0.0577806 0.0288903 0.999583i \(-0.490803\pi\)
0.0288903 + 0.999583i \(0.490803\pi\)
\(332\) −1.96725 −0.107967
\(333\) −0.138997 −0.00761700
\(334\) −3.80166 −0.208018
\(335\) 3.73441 0.204033
\(336\) −1.44853 −0.0790240
\(337\) 8.35437 0.455092 0.227546 0.973767i \(-0.426930\pi\)
0.227546 + 0.973767i \(0.426930\pi\)
\(338\) 7.62793 0.414905
\(339\) −21.5573 −1.17083
\(340\) −4.55257 −0.246898
\(341\) 17.6466 0.955615
\(342\) 4.81126 0.260163
\(343\) −1.00000 −0.0539949
\(344\) −7.50104 −0.404429
\(345\) 14.0277 0.755226
\(346\) −16.4571 −0.884739
\(347\) −7.54630 −0.405107 −0.202553 0.979271i \(-0.564924\pi\)
−0.202553 + 0.979271i \(0.564924\pi\)
\(348\) −0.311080 −0.0166757
\(349\) 2.03679 0.109027 0.0545133 0.998513i \(-0.482639\pi\)
0.0545133 + 0.998513i \(0.482639\pi\)
\(350\) −3.40224 −0.181857
\(351\) 13.0996 0.699206
\(352\) 3.22511 0.171899
\(353\) −29.7876 −1.58544 −0.792718 0.609589i \(-0.791334\pi\)
−0.792718 + 0.609589i \(0.791334\pi\)
\(354\) −17.1641 −0.912260
\(355\) −13.5273 −0.717957
\(356\) −0.350463 −0.0185745
\(357\) −5.21710 −0.276118
\(358\) −19.1032 −1.00964
\(359\) 11.9211 0.629173 0.314586 0.949229i \(-0.398134\pi\)
0.314586 + 0.949229i \(0.398134\pi\)
\(360\) −1.13984 −0.0600747
\(361\) 9.46716 0.498272
\(362\) −15.4524 −0.812162
\(363\) −0.867223 −0.0455174
\(364\) 2.31777 0.121484
\(365\) 19.8877 1.04097
\(366\) −8.62977 −0.451085
\(367\) 35.9106 1.87452 0.937260 0.348632i \(-0.113354\pi\)
0.937260 + 0.348632i \(0.113354\pi\)
\(368\) −7.66129 −0.399372
\(369\) −3.33565 −0.173647
\(370\) 0.194839 0.0101292
\(371\) −9.39083 −0.487548
\(372\) −7.92583 −0.410935
\(373\) 1.76229 0.0912480 0.0456240 0.998959i \(-0.485472\pi\)
0.0456240 + 0.998959i \(0.485472\pi\)
\(374\) 11.6157 0.600633
\(375\) 15.3844 0.794445
\(376\) −0.101562 −0.00523768
\(377\) 0.497754 0.0256356
\(378\) −5.65182 −0.290698
\(379\) −6.08120 −0.312370 −0.156185 0.987728i \(-0.549920\pi\)
−0.156185 + 0.987728i \(0.549920\pi\)
\(380\) −6.74416 −0.345968
\(381\) 11.4005 0.584065
\(382\) −4.74568 −0.242810
\(383\) −10.3380 −0.528248 −0.264124 0.964489i \(-0.585083\pi\)
−0.264124 + 0.964489i \(0.585083\pi\)
\(384\) −1.44853 −0.0739202
\(385\) −4.07662 −0.207764
\(386\) −4.37571 −0.222718
\(387\) −6.76407 −0.343837
\(388\) −17.6621 −0.896659
\(389\) −29.5639 −1.49895 −0.749474 0.662033i \(-0.769694\pi\)
−0.749474 + 0.662033i \(0.769694\pi\)
\(390\) −4.24380 −0.214893
\(391\) −27.5933 −1.39545
\(392\) −1.00000 −0.0505076
\(393\) −0.0501173 −0.00252808
\(394\) −3.06798 −0.154563
\(395\) 17.2786 0.869381
\(396\) 2.90824 0.146145
\(397\) −2.23532 −0.112188 −0.0560938 0.998426i \(-0.517865\pi\)
−0.0560938 + 0.998426i \(0.517865\pi\)
\(398\) 26.2836 1.31748
\(399\) −7.72860 −0.386914
\(400\) −3.40224 −0.170112
\(401\) 11.2737 0.562979 0.281490 0.959564i \(-0.409171\pi\)
0.281490 + 0.959564i \(0.409171\pi\)
\(402\) 4.27951 0.213443
\(403\) 12.6820 0.631734
\(404\) 8.91473 0.443524
\(405\) 6.92887 0.344298
\(406\) −0.214755 −0.0106581
\(407\) −0.497123 −0.0246414
\(408\) −5.21710 −0.258285
\(409\) 32.5916 1.61155 0.805777 0.592220i \(-0.201748\pi\)
0.805777 + 0.592220i \(0.201748\pi\)
\(410\) 4.67573 0.230918
\(411\) −3.47615 −0.171466
\(412\) 9.46770 0.466440
\(413\) −11.8493 −0.583065
\(414\) −6.90858 −0.339538
\(415\) 2.48666 0.122065
\(416\) 2.31777 0.113638
\(417\) −19.0823 −0.934466
\(418\) 17.2074 0.841643
\(419\) 16.8439 0.822880 0.411440 0.911437i \(-0.365026\pi\)
0.411440 + 0.911437i \(0.365026\pi\)
\(420\) 1.83098 0.0893428
\(421\) −0.753904 −0.0367430 −0.0183715 0.999831i \(-0.505848\pi\)
−0.0183715 + 0.999831i \(0.505848\pi\)
\(422\) 8.94228 0.435304
\(423\) −0.0915840 −0.00445297
\(424\) −9.39083 −0.456059
\(425\) −12.2537 −0.594390
\(426\) −15.5019 −0.751070
\(427\) −5.95759 −0.288308
\(428\) 17.0234 0.822856
\(429\) 10.8279 0.522775
\(430\) 9.48150 0.457239
\(431\) 1.00000 0.0481683
\(432\) −5.65182 −0.271923
\(433\) −13.5708 −0.652171 −0.326086 0.945340i \(-0.605730\pi\)
−0.326086 + 0.945340i \(0.605730\pi\)
\(434\) −5.47162 −0.262646
\(435\) 0.393213 0.0188531
\(436\) 19.5460 0.936086
\(437\) −40.8765 −1.95539
\(438\) 22.7906 1.08898
\(439\) −10.6671 −0.509114 −0.254557 0.967058i \(-0.581930\pi\)
−0.254557 + 0.967058i \(0.581930\pi\)
\(440\) −4.07662 −0.194345
\(441\) −0.901751 −0.0429405
\(442\) 8.34780 0.397064
\(443\) 10.5775 0.502553 0.251277 0.967915i \(-0.419150\pi\)
0.251277 + 0.967915i \(0.419150\pi\)
\(444\) 0.223279 0.0105964
\(445\) 0.442994 0.0209999
\(446\) 27.0980 1.28313
\(447\) 21.5466 1.01912
\(448\) −1.00000 −0.0472456
\(449\) −22.5821 −1.06572 −0.532859 0.846204i \(-0.678882\pi\)
−0.532859 + 0.846204i \(0.678882\pi\)
\(450\) −3.06797 −0.144626
\(451\) −11.9299 −0.561758
\(452\) −14.8821 −0.699997
\(453\) 34.9682 1.64295
\(454\) −0.799865 −0.0375395
\(455\) −2.92972 −0.137348
\(456\) −7.72860 −0.361925
\(457\) −4.14872 −0.194069 −0.0970345 0.995281i \(-0.530936\pi\)
−0.0970345 + 0.995281i \(0.530936\pi\)
\(458\) 1.41408 0.0660758
\(459\) −20.3558 −0.950129
\(460\) 9.68407 0.451522
\(461\) 25.6956 1.19676 0.598382 0.801211i \(-0.295811\pi\)
0.598382 + 0.801211i \(0.295811\pi\)
\(462\) −4.67167 −0.217346
\(463\) 19.0380 0.884773 0.442386 0.896825i \(-0.354132\pi\)
0.442386 + 0.896825i \(0.354132\pi\)
\(464\) −0.214755 −0.00996977
\(465\) 10.0184 0.464594
\(466\) −2.30009 −0.106549
\(467\) −2.34262 −0.108404 −0.0542018 0.998530i \(-0.517261\pi\)
−0.0542018 + 0.998530i \(0.517261\pi\)
\(468\) 2.09005 0.0966128
\(469\) 2.95438 0.136420
\(470\) 0.128377 0.00592161
\(471\) 8.78538 0.404809
\(472\) −11.8493 −0.545407
\(473\) −24.1916 −1.11233
\(474\) 19.8007 0.909478
\(475\) −18.1525 −0.832895
\(476\) −3.60165 −0.165081
\(477\) −8.46819 −0.387732
\(478\) −9.46668 −0.432996
\(479\) 6.41867 0.293277 0.146638 0.989190i \(-0.453155\pi\)
0.146638 + 0.989190i \(0.453155\pi\)
\(480\) 1.83098 0.0835726
\(481\) −0.357265 −0.0162899
\(482\) −15.2642 −0.695266
\(483\) 11.0976 0.504960
\(484\) −0.598690 −0.0272132
\(485\) 22.3254 1.01374
\(486\) −9.01518 −0.408937
\(487\) −0.883066 −0.0400155 −0.0200078 0.999800i \(-0.506369\pi\)
−0.0200078 + 0.999800i \(0.506369\pi\)
\(488\) −5.95759 −0.269688
\(489\) 15.3400 0.693701
\(490\) 1.26403 0.0571029
\(491\) −22.4448 −1.01292 −0.506460 0.862263i \(-0.669046\pi\)
−0.506460 + 0.862263i \(0.669046\pi\)
\(492\) 5.35824 0.241568
\(493\) −0.773473 −0.0348355
\(494\) 12.3664 0.556390
\(495\) −3.67609 −0.165228
\(496\) −5.47162 −0.245683
\(497\) −10.7018 −0.480041
\(498\) 2.84963 0.127695
\(499\) 19.9212 0.891796 0.445898 0.895084i \(-0.352884\pi\)
0.445898 + 0.895084i \(0.352884\pi\)
\(500\) 10.6206 0.474970
\(501\) 5.50683 0.246027
\(502\) −1.32168 −0.0589895
\(503\) 3.31834 0.147958 0.0739788 0.997260i \(-0.476430\pi\)
0.0739788 + 0.997260i \(0.476430\pi\)
\(504\) −0.901751 −0.0401672
\(505\) −11.2684 −0.501439
\(506\) −24.7085 −1.09843
\(507\) −11.0493 −0.490717
\(508\) 7.87038 0.349191
\(509\) 23.8167 1.05566 0.527829 0.849351i \(-0.323006\pi\)
0.527829 + 0.849351i \(0.323006\pi\)
\(510\) 6.59455 0.292012
\(511\) 15.7336 0.696013
\(512\) −1.00000 −0.0441942
\(513\) −30.1551 −1.33138
\(514\) 9.58020 0.422565
\(515\) −11.9674 −0.527347
\(516\) 10.8655 0.478327
\(517\) −0.327549 −0.0144056
\(518\) 0.154141 0.00677259
\(519\) 23.8386 1.04640
\(520\) −2.92972 −0.128477
\(521\) 21.2943 0.932920 0.466460 0.884542i \(-0.345529\pi\)
0.466460 + 0.884542i \(0.345529\pi\)
\(522\) −0.193656 −0.00847609
\(523\) −0.989607 −0.0432725 −0.0216362 0.999766i \(-0.506888\pi\)
−0.0216362 + 0.999766i \(0.506888\pi\)
\(524\) −0.0345986 −0.00151145
\(525\) 4.92826 0.215087
\(526\) −26.9818 −1.17646
\(527\) −19.7068 −0.858443
\(528\) −4.67167 −0.203309
\(529\) 35.6954 1.55197
\(530\) 11.8703 0.515611
\(531\) −10.6851 −0.463694
\(532\) −5.33546 −0.231322
\(533\) −8.57363 −0.371365
\(534\) 0.507657 0.0219685
\(535\) −21.5180 −0.930303
\(536\) 2.95438 0.127610
\(537\) 27.6716 1.19412
\(538\) 7.60283 0.327781
\(539\) −3.22511 −0.138915
\(540\) 7.14404 0.307431
\(541\) 29.7230 1.27789 0.638947 0.769251i \(-0.279370\pi\)
0.638947 + 0.769251i \(0.279370\pi\)
\(542\) −23.1724 −0.995341
\(543\) 22.3834 0.960563
\(544\) −3.60165 −0.154419
\(545\) −24.7067 −1.05832
\(546\) −3.35737 −0.143682
\(547\) −18.7571 −0.801997 −0.400998 0.916079i \(-0.631337\pi\)
−0.400998 + 0.916079i \(0.631337\pi\)
\(548\) −2.39977 −0.102513
\(549\) −5.37227 −0.229283
\(550\) −10.9726 −0.467872
\(551\) −1.14582 −0.0488135
\(552\) 11.0976 0.472347
\(553\) 13.6695 0.581287
\(554\) −21.5203 −0.914310
\(555\) −0.282230 −0.0119800
\(556\) −13.1736 −0.558683
\(557\) −3.12542 −0.132428 −0.0662142 0.997805i \(-0.521092\pi\)
−0.0662142 + 0.997805i \(0.521092\pi\)
\(558\) −4.93404 −0.208875
\(559\) −17.3857 −0.735337
\(560\) 1.26403 0.0534148
\(561\) −16.8257 −0.710382
\(562\) 29.3424 1.23773
\(563\) 32.6668 1.37674 0.688371 0.725359i \(-0.258326\pi\)
0.688371 + 0.725359i \(0.258326\pi\)
\(564\) 0.147116 0.00619472
\(565\) 18.8114 0.791402
\(566\) 30.0854 1.26459
\(567\) 5.48159 0.230205
\(568\) −10.7018 −0.449037
\(569\) 12.7210 0.533293 0.266647 0.963794i \(-0.414084\pi\)
0.266647 + 0.963794i \(0.414084\pi\)
\(570\) 9.76914 0.409184
\(571\) −7.60141 −0.318109 −0.159055 0.987270i \(-0.550845\pi\)
−0.159055 + 0.987270i \(0.550845\pi\)
\(572\) 7.47506 0.312548
\(573\) 6.87427 0.287177
\(574\) 3.69908 0.154397
\(575\) 26.0655 1.08701
\(576\) −0.901751 −0.0375730
\(577\) 13.7678 0.573159 0.286579 0.958056i \(-0.407482\pi\)
0.286579 + 0.958056i \(0.407482\pi\)
\(578\) 4.02815 0.167549
\(579\) 6.33836 0.263413
\(580\) 0.271456 0.0112716
\(581\) 1.96725 0.0816154
\(582\) 25.5842 1.06050
\(583\) −30.2864 −1.25434
\(584\) 15.7336 0.651061
\(585\) −2.64188 −0.109228
\(586\) −19.2131 −0.793687
\(587\) −20.6386 −0.851844 −0.425922 0.904760i \(-0.640050\pi\)
−0.425922 + 0.904760i \(0.640050\pi\)
\(588\) 1.44853 0.0597365
\(589\) −29.1936 −1.20290
\(590\) 14.9778 0.616626
\(591\) 4.44408 0.182805
\(592\) 0.154141 0.00633517
\(593\) 39.6214 1.62706 0.813528 0.581525i \(-0.197544\pi\)
0.813528 + 0.581525i \(0.197544\pi\)
\(594\) −18.2277 −0.747892
\(595\) 4.55257 0.186637
\(596\) 14.8747 0.609293
\(597\) −38.0727 −1.55821
\(598\) −17.7571 −0.726143
\(599\) −12.5956 −0.514643 −0.257321 0.966326i \(-0.582840\pi\)
−0.257321 + 0.966326i \(0.582840\pi\)
\(600\) 4.92826 0.201195
\(601\) −18.3882 −0.750072 −0.375036 0.927010i \(-0.622370\pi\)
−0.375036 + 0.927010i \(0.622370\pi\)
\(602\) 7.50104 0.305719
\(603\) 2.66411 0.108491
\(604\) 24.1404 0.982259
\(605\) 0.756760 0.0307667
\(606\) −12.9133 −0.524566
\(607\) −23.2820 −0.944988 −0.472494 0.881334i \(-0.656646\pi\)
−0.472494 + 0.881334i \(0.656646\pi\)
\(608\) −5.33546 −0.216382
\(609\) 0.311080 0.0126056
\(610\) 7.53055 0.304903
\(611\) −0.235398 −0.00952320
\(612\) −3.24779 −0.131284
\(613\) −27.5399 −1.11233 −0.556163 0.831073i \(-0.687727\pi\)
−0.556163 + 0.831073i \(0.687727\pi\)
\(614\) 2.60073 0.104957
\(615\) −6.77295 −0.273112
\(616\) −3.22511 −0.129943
\(617\) −8.33362 −0.335499 −0.167749 0.985830i \(-0.553650\pi\)
−0.167749 + 0.985830i \(0.553650\pi\)
\(618\) −13.7143 −0.551669
\(619\) 47.6877 1.91673 0.958366 0.285542i \(-0.0921737\pi\)
0.958366 + 0.285542i \(0.0921737\pi\)
\(620\) 6.91627 0.277764
\(621\) 43.3002 1.73758
\(622\) 10.9513 0.439107
\(623\) 0.350463 0.0140410
\(624\) −3.35737 −0.134402
\(625\) 3.58643 0.143457
\(626\) −21.0786 −0.842471
\(627\) −24.9255 −0.995430
\(628\) 6.06502 0.242021
\(629\) 0.555163 0.0221358
\(630\) 1.13984 0.0454122
\(631\) 9.06920 0.361039 0.180520 0.983571i \(-0.442222\pi\)
0.180520 + 0.983571i \(0.442222\pi\)
\(632\) 13.6695 0.543744
\(633\) −12.9532 −0.514843
\(634\) 3.41278 0.135539
\(635\) −9.94836 −0.394789
\(636\) 13.6029 0.539391
\(637\) −2.31777 −0.0918335
\(638\) −0.692609 −0.0274206
\(639\) −9.65036 −0.381762
\(640\) 1.26403 0.0499650
\(641\) −8.20148 −0.323939 −0.161969 0.986796i \(-0.551785\pi\)
−0.161969 + 0.986796i \(0.551785\pi\)
\(642\) −24.6589 −0.973210
\(643\) 38.6839 1.52554 0.762772 0.646667i \(-0.223838\pi\)
0.762772 + 0.646667i \(0.223838\pi\)
\(644\) 7.66129 0.301897
\(645\) −13.7343 −0.540786
\(646\) −19.2164 −0.756061
\(647\) 14.5250 0.571038 0.285519 0.958373i \(-0.407834\pi\)
0.285519 + 0.958373i \(0.407834\pi\)
\(648\) 5.48159 0.215337
\(649\) −38.2152 −1.50008
\(650\) −7.88562 −0.309299
\(651\) 7.92583 0.310638
\(652\) 10.5901 0.414738
\(653\) 33.1727 1.29815 0.649074 0.760725i \(-0.275157\pi\)
0.649074 + 0.760725i \(0.275157\pi\)
\(654\) −28.3131 −1.10713
\(655\) 0.0437336 0.00170881
\(656\) 3.69908 0.144425
\(657\) 14.1878 0.553518
\(658\) 0.101562 0.00395931
\(659\) 2.38108 0.0927539 0.0463769 0.998924i \(-0.485232\pi\)
0.0463769 + 0.998924i \(0.485232\pi\)
\(660\) 5.90512 0.229856
\(661\) −35.0387 −1.36285 −0.681423 0.731890i \(-0.738639\pi\)
−0.681423 + 0.731890i \(0.738639\pi\)
\(662\) −1.05122 −0.0408570
\(663\) −12.0921 −0.469617
\(664\) 1.96725 0.0763442
\(665\) 6.74416 0.261527
\(666\) 0.138997 0.00538603
\(667\) 1.64530 0.0637064
\(668\) 3.80166 0.147091
\(669\) −39.2523 −1.51758
\(670\) −3.73441 −0.144273
\(671\) −19.2139 −0.741743
\(672\) 1.44853 0.0558784
\(673\) −23.1260 −0.891440 −0.445720 0.895172i \(-0.647052\pi\)
−0.445720 + 0.895172i \(0.647052\pi\)
\(674\) −8.35437 −0.321798
\(675\) 19.2288 0.740118
\(676\) −7.62793 −0.293382
\(677\) −1.52519 −0.0586177 −0.0293089 0.999570i \(-0.509331\pi\)
−0.0293089 + 0.999570i \(0.509331\pi\)
\(678\) 21.5573 0.827903
\(679\) 17.6621 0.677810
\(680\) 4.55257 0.174583
\(681\) 1.15863 0.0443988
\(682\) −17.6466 −0.675722
\(683\) −29.1688 −1.11611 −0.558057 0.829803i \(-0.688453\pi\)
−0.558057 + 0.829803i \(0.688453\pi\)
\(684\) −4.81126 −0.183963
\(685\) 3.03337 0.115899
\(686\) 1.00000 0.0381802
\(687\) −2.04835 −0.0781494
\(688\) 7.50104 0.285974
\(689\) −21.7658 −0.829211
\(690\) −14.0277 −0.534025
\(691\) −30.5639 −1.16271 −0.581353 0.813652i \(-0.697476\pi\)
−0.581353 + 0.813652i \(0.697476\pi\)
\(692\) 16.4571 0.625605
\(693\) −2.90824 −0.110475
\(694\) 7.54630 0.286454
\(695\) 16.6517 0.631636
\(696\) 0.311080 0.0117915
\(697\) 13.3228 0.504636
\(698\) −2.03679 −0.0770935
\(699\) 3.33175 0.126018
\(700\) 3.40224 0.128593
\(701\) 35.7765 1.35126 0.675629 0.737242i \(-0.263872\pi\)
0.675629 + 0.737242i \(0.263872\pi\)
\(702\) −13.0996 −0.494414
\(703\) 0.822416 0.0310180
\(704\) −3.22511 −0.121551
\(705\) −0.185959 −0.00700362
\(706\) 29.7876 1.12107
\(707\) −8.91473 −0.335273
\(708\) 17.1641 0.645065
\(709\) −46.5856 −1.74956 −0.874779 0.484523i \(-0.838993\pi\)
−0.874779 + 0.484523i \(0.838993\pi\)
\(710\) 13.5273 0.507672
\(711\) 12.3265 0.462280
\(712\) 0.350463 0.0131342
\(713\) 41.9197 1.56990
\(714\) 5.21710 0.195245
\(715\) −9.44867 −0.353360
\(716\) 19.1032 0.713921
\(717\) 13.7128 0.512114
\(718\) −11.9211 −0.444892
\(719\) 22.9733 0.856760 0.428380 0.903599i \(-0.359084\pi\)
0.428380 + 0.903599i \(0.359084\pi\)
\(720\) 1.13984 0.0424792
\(721\) −9.46770 −0.352596
\(722\) −9.46716 −0.352331
\(723\) 22.1107 0.822306
\(724\) 15.4524 0.574285
\(725\) 0.730649 0.0271356
\(726\) 0.867223 0.0321856
\(727\) −45.7342 −1.69619 −0.848094 0.529846i \(-0.822250\pi\)
−0.848094 + 0.529846i \(0.822250\pi\)
\(728\) −2.31777 −0.0859024
\(729\) 29.5036 1.09272
\(730\) −19.8877 −0.736076
\(731\) 27.0161 0.999225
\(732\) 8.62977 0.318966
\(733\) 16.4772 0.608599 0.304299 0.952576i \(-0.401578\pi\)
0.304299 + 0.952576i \(0.401578\pi\)
\(734\) −35.9106 −1.32549
\(735\) −1.83098 −0.0675368
\(736\) 7.66129 0.282399
\(737\) 9.52818 0.350975
\(738\) 3.33565 0.122787
\(739\) 7.07809 0.260372 0.130186 0.991490i \(-0.458443\pi\)
0.130186 + 0.991490i \(0.458443\pi\)
\(740\) −0.194839 −0.00716241
\(741\) −17.9131 −0.658055
\(742\) 9.39083 0.344748
\(743\) 37.7294 1.38416 0.692078 0.721823i \(-0.256695\pi\)
0.692078 + 0.721823i \(0.256695\pi\)
\(744\) 7.92583 0.290575
\(745\) −18.8021 −0.688854
\(746\) −1.76229 −0.0645221
\(747\) 1.77397 0.0649063
\(748\) −11.6157 −0.424712
\(749\) −17.0234 −0.622020
\(750\) −15.3844 −0.561757
\(751\) −22.3861 −0.816879 −0.408439 0.912785i \(-0.633927\pi\)
−0.408439 + 0.912785i \(0.633927\pi\)
\(752\) 0.101562 0.00370360
\(753\) 1.91450 0.0697682
\(754\) −0.497754 −0.0181271
\(755\) −30.5141 −1.11052
\(756\) 5.65182 0.205555
\(757\) −39.3845 −1.43146 −0.715728 0.698379i \(-0.753905\pi\)
−0.715728 + 0.698379i \(0.753905\pi\)
\(758\) 6.08120 0.220879
\(759\) 35.7911 1.29913
\(760\) 6.74416 0.244636
\(761\) −4.36983 −0.158406 −0.0792031 0.996858i \(-0.525238\pi\)
−0.0792031 + 0.996858i \(0.525238\pi\)
\(762\) −11.4005 −0.412997
\(763\) −19.5460 −0.707614
\(764\) 4.74568 0.171692
\(765\) 4.10529 0.148427
\(766\) 10.3380 0.373527
\(767\) −27.4639 −0.991665
\(768\) 1.44853 0.0522694
\(769\) 1.36858 0.0493524 0.0246762 0.999695i \(-0.492145\pi\)
0.0246762 + 0.999695i \(0.492145\pi\)
\(770\) 4.07662 0.146911
\(771\) −13.8772 −0.499777
\(772\) 4.37571 0.157485
\(773\) −33.0732 −1.18956 −0.594781 0.803888i \(-0.702761\pi\)
−0.594781 + 0.803888i \(0.702761\pi\)
\(774\) 6.76407 0.243129
\(775\) 18.6158 0.668698
\(776\) 17.6621 0.634033
\(777\) −0.223279 −0.00801009
\(778\) 29.5639 1.05992
\(779\) 19.7363 0.707126
\(780\) 4.24380 0.151953
\(781\) −34.5144 −1.23502
\(782\) 27.5933 0.986733
\(783\) 1.21376 0.0433762
\(784\) 1.00000 0.0357143
\(785\) −7.66634 −0.273623
\(786\) 0.0501173 0.00178762
\(787\) −16.8755 −0.601547 −0.300773 0.953696i \(-0.597245\pi\)
−0.300773 + 0.953696i \(0.597245\pi\)
\(788\) 3.06798 0.109292
\(789\) 39.0841 1.39143
\(790\) −17.2786 −0.614745
\(791\) 14.8821 0.529148
\(792\) −2.90824 −0.103340
\(793\) −13.8083 −0.490349
\(794\) 2.23532 0.0793286
\(795\) −17.1945 −0.609824
\(796\) −26.2836 −0.931599
\(797\) −22.6911 −0.803761 −0.401881 0.915692i \(-0.631643\pi\)
−0.401881 + 0.915692i \(0.631643\pi\)
\(798\) 7.72860 0.273589
\(799\) 0.365792 0.0129408
\(800\) 3.40224 0.120287
\(801\) 0.316030 0.0111664
\(802\) −11.2737 −0.398087
\(803\) 50.7425 1.79066
\(804\) −4.27951 −0.150927
\(805\) −9.68407 −0.341319
\(806\) −12.6820 −0.446704
\(807\) −11.0130 −0.387674
\(808\) −8.91473 −0.313619
\(809\) 18.2557 0.641835 0.320917 0.947107i \(-0.396009\pi\)
0.320917 + 0.947107i \(0.396009\pi\)
\(810\) −6.92887 −0.243456
\(811\) 10.7230 0.376535 0.188267 0.982118i \(-0.439713\pi\)
0.188267 + 0.982118i \(0.439713\pi\)
\(812\) 0.214755 0.00753644
\(813\) 33.5660 1.17721
\(814\) 0.497123 0.0174241
\(815\) −13.3861 −0.468895
\(816\) 5.21710 0.182635
\(817\) 40.0215 1.40017
\(818\) −32.5916 −1.13954
\(819\) −2.09005 −0.0730324
\(820\) −4.67573 −0.163284
\(821\) 25.1558 0.877942 0.438971 0.898501i \(-0.355343\pi\)
0.438971 + 0.898501i \(0.355343\pi\)
\(822\) 3.47615 0.121245
\(823\) −22.6642 −0.790025 −0.395012 0.918676i \(-0.629260\pi\)
−0.395012 + 0.918676i \(0.629260\pi\)
\(824\) −9.46770 −0.329823
\(825\) 15.8942 0.553363
\(826\) 11.8493 0.412289
\(827\) −46.7646 −1.62617 −0.813083 0.582148i \(-0.802212\pi\)
−0.813083 + 0.582148i \(0.802212\pi\)
\(828\) 6.90858 0.240090
\(829\) −3.07344 −0.106745 −0.0533725 0.998575i \(-0.516997\pi\)
−0.0533725 + 0.998575i \(0.516997\pi\)
\(830\) −2.48666 −0.0863132
\(831\) 31.1729 1.08137
\(832\) −2.31777 −0.0803543
\(833\) 3.60165 0.124790
\(834\) 19.0823 0.660768
\(835\) −4.80540 −0.166298
\(836\) −17.2074 −0.595132
\(837\) 30.9246 1.06891
\(838\) −16.8439 −0.581864
\(839\) 20.3451 0.702391 0.351196 0.936302i \(-0.385775\pi\)
0.351196 + 0.936302i \(0.385775\pi\)
\(840\) −1.83098 −0.0631749
\(841\) −28.9539 −0.998410
\(842\) 0.753904 0.0259812
\(843\) −42.5034 −1.46390
\(844\) −8.94228 −0.307806
\(845\) 9.64190 0.331691
\(846\) 0.0915840 0.00314872
\(847\) 0.598690 0.0205712
\(848\) 9.39083 0.322482
\(849\) −43.5798 −1.49565
\(850\) 12.2537 0.420297
\(851\) −1.18092 −0.0404815
\(852\) 15.5019 0.531087
\(853\) 6.13553 0.210076 0.105038 0.994468i \(-0.466504\pi\)
0.105038 + 0.994468i \(0.466504\pi\)
\(854\) 5.95759 0.203865
\(855\) 6.08156 0.207985
\(856\) −17.0234 −0.581847
\(857\) 32.3955 1.10661 0.553305 0.832979i \(-0.313366\pi\)
0.553305 + 0.832979i \(0.313366\pi\)
\(858\) −10.8279 −0.369658
\(859\) 21.0123 0.716929 0.358465 0.933543i \(-0.383300\pi\)
0.358465 + 0.933543i \(0.383300\pi\)
\(860\) −9.48150 −0.323317
\(861\) −5.35824 −0.182608
\(862\) −1.00000 −0.0340601
\(863\) 8.12612 0.276616 0.138308 0.990389i \(-0.455834\pi\)
0.138308 + 0.990389i \(0.455834\pi\)
\(864\) 5.65182 0.192279
\(865\) −20.8022 −0.707296
\(866\) 13.5708 0.461155
\(867\) −5.83491 −0.198164
\(868\) 5.47162 0.185719
\(869\) 44.0856 1.49550
\(870\) −0.393213 −0.0133312
\(871\) 6.84758 0.232021
\(872\) −19.5460 −0.661912
\(873\) 15.9268 0.539042
\(874\) 40.8765 1.38267
\(875\) −10.6206 −0.359043
\(876\) −22.7906 −0.770024
\(877\) 39.3833 1.32988 0.664940 0.746896i \(-0.268457\pi\)
0.664940 + 0.746896i \(0.268457\pi\)
\(878\) 10.6671 0.359998
\(879\) 27.8308 0.938711
\(880\) 4.07662 0.137423
\(881\) −13.7834 −0.464375 −0.232187 0.972671i \(-0.574588\pi\)
−0.232187 + 0.972671i \(0.574588\pi\)
\(882\) 0.901751 0.0303635
\(883\) 42.7783 1.43960 0.719802 0.694179i \(-0.244232\pi\)
0.719802 + 0.694179i \(0.244232\pi\)
\(884\) −8.34780 −0.280767
\(885\) −21.6958 −0.729297
\(886\) −10.5775 −0.355359
\(887\) 19.9689 0.670489 0.335244 0.942131i \(-0.391181\pi\)
0.335244 + 0.942131i \(0.391181\pi\)
\(888\) −0.223279 −0.00749275
\(889\) −7.87038 −0.263964
\(890\) −0.442994 −0.0148492
\(891\) 17.6787 0.592259
\(892\) −27.0980 −0.907307
\(893\) 0.541882 0.0181334
\(894\) −21.5466 −0.720625
\(895\) −24.1470 −0.807144
\(896\) 1.00000 0.0334077
\(897\) 25.7218 0.858826
\(898\) 22.5821 0.753576
\(899\) 1.17506 0.0391904
\(900\) 3.06797 0.102266
\(901\) 33.8224 1.12679
\(902\) 11.9299 0.397223
\(903\) −10.8655 −0.361581
\(904\) 14.8821 0.494973
\(905\) −19.5323 −0.649275
\(906\) −34.9682 −1.16174
\(907\) −29.8320 −0.990554 −0.495277 0.868735i \(-0.664933\pi\)
−0.495277 + 0.868735i \(0.664933\pi\)
\(908\) 0.799865 0.0265444
\(909\) −8.03887 −0.266632
\(910\) 2.92972 0.0971194
\(911\) 13.0430 0.432134 0.216067 0.976379i \(-0.430677\pi\)
0.216067 + 0.976379i \(0.430677\pi\)
\(912\) 7.72860 0.255919
\(913\) 6.34460 0.209976
\(914\) 4.14872 0.137228
\(915\) −10.9083 −0.360616
\(916\) −1.41408 −0.0467227
\(917\) 0.0345986 0.00114255
\(918\) 20.3558 0.671843
\(919\) −51.8241 −1.70952 −0.854760 0.519024i \(-0.826295\pi\)
−0.854760 + 0.519024i \(0.826295\pi\)
\(920\) −9.68407 −0.319274
\(921\) −3.76724 −0.124135
\(922\) −25.6956 −0.846240
\(923\) −24.8043 −0.816445
\(924\) 4.67167 0.153687
\(925\) −0.524426 −0.0172430
\(926\) −19.0380 −0.625629
\(927\) −8.53751 −0.280409
\(928\) 0.214755 0.00704969
\(929\) 20.6123 0.676266 0.338133 0.941098i \(-0.390205\pi\)
0.338133 + 0.941098i \(0.390205\pi\)
\(930\) −10.0184 −0.328518
\(931\) 5.33546 0.174863
\(932\) 2.30009 0.0753419
\(933\) −15.8633 −0.519341
\(934\) 2.34262 0.0766529
\(935\) 14.6825 0.480170
\(936\) −2.09005 −0.0683156
\(937\) −10.7696 −0.351829 −0.175914 0.984405i \(-0.556288\pi\)
−0.175914 + 0.984405i \(0.556288\pi\)
\(938\) −2.95438 −0.0964638
\(939\) 30.5331 0.996409
\(940\) −0.128377 −0.00418721
\(941\) −31.6617 −1.03214 −0.516070 0.856546i \(-0.672606\pi\)
−0.516070 + 0.856546i \(0.672606\pi\)
\(942\) −8.78538 −0.286243
\(943\) −28.3397 −0.922869
\(944\) 11.8493 0.385661
\(945\) −7.14404 −0.232396
\(946\) 24.1916 0.786538
\(947\) −29.7484 −0.966693 −0.483346 0.875429i \(-0.660579\pi\)
−0.483346 + 0.875429i \(0.660579\pi\)
\(948\) −19.8007 −0.643098
\(949\) 36.4669 1.18377
\(950\) 18.1525 0.588946
\(951\) −4.94352 −0.160305
\(952\) 3.60165 0.116730
\(953\) −14.4958 −0.469565 −0.234783 0.972048i \(-0.575438\pi\)
−0.234783 + 0.972048i \(0.575438\pi\)
\(954\) 8.46819 0.274168
\(955\) −5.99866 −0.194112
\(956\) 9.46668 0.306174
\(957\) 1.00327 0.0324310
\(958\) −6.41867 −0.207378
\(959\) 2.39977 0.0774927
\(960\) −1.83098 −0.0590947
\(961\) −1.06136 −0.0342376
\(962\) 0.357265 0.0115187
\(963\) −15.3508 −0.494674
\(964\) 15.2642 0.491627
\(965\) −5.53101 −0.178049
\(966\) −11.0976 −0.357061
\(967\) 19.6733 0.632649 0.316325 0.948651i \(-0.397551\pi\)
0.316325 + 0.948651i \(0.397551\pi\)
\(968\) 0.598690 0.0192426
\(969\) 27.8357 0.894210
\(970\) −22.3254 −0.716825
\(971\) 50.1679 1.60996 0.804982 0.593299i \(-0.202175\pi\)
0.804982 + 0.593299i \(0.202175\pi\)
\(972\) 9.01518 0.289162
\(973\) 13.1736 0.422325
\(974\) 0.883066 0.0282952
\(975\) 11.4226 0.365815
\(976\) 5.95759 0.190698
\(977\) 46.9127 1.50087 0.750435 0.660944i \(-0.229844\pi\)
0.750435 + 0.660944i \(0.229844\pi\)
\(978\) −15.3400 −0.490521
\(979\) 1.13028 0.0361239
\(980\) −1.26403 −0.0403778
\(981\) −17.6257 −0.562744
\(982\) 22.4448 0.716243
\(983\) 34.9309 1.11412 0.557062 0.830471i \(-0.311929\pi\)
0.557062 + 0.830471i \(0.311929\pi\)
\(984\) −5.35824 −0.170814
\(985\) −3.87801 −0.123564
\(986\) 0.773473 0.0246324
\(987\) −0.147116 −0.00468277
\(988\) −12.3664 −0.393427
\(989\) −57.4676 −1.82736
\(990\) 3.67609 0.116834
\(991\) 32.8605 1.04385 0.521924 0.852992i \(-0.325214\pi\)
0.521924 + 0.852992i \(0.325214\pi\)
\(992\) 5.47162 0.173724
\(993\) 1.52273 0.0483225
\(994\) 10.7018 0.339440
\(995\) 33.2232 1.05325
\(996\) −2.84963 −0.0902941
\(997\) 31.3910 0.994163 0.497081 0.867704i \(-0.334405\pi\)
0.497081 + 0.867704i \(0.334405\pi\)
\(998\) −19.9212 −0.630595
\(999\) −0.871179 −0.0275629
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 \(a_p\))