Properties

Label 6001.2.a.b.1.7
Level 6001
Weight 2
Character 6001.1
Self dual Yes
Analytic conductor 47.918
Analytic rank 1
Dimension 114
CM No

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Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.918226253\)
Analytic rank: \(1\)
Dimension: \(114\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.61975 q^{2}\) \(-2.31872 q^{3}\) \(+4.86309 q^{4}\) \(+0.216177 q^{5}\) \(+6.07447 q^{6}\) \(+3.38406 q^{7}\) \(-7.50057 q^{8}\) \(+2.37647 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.61975 q^{2}\) \(-2.31872 q^{3}\) \(+4.86309 q^{4}\) \(+0.216177 q^{5}\) \(+6.07447 q^{6}\) \(+3.38406 q^{7}\) \(-7.50057 q^{8}\) \(+2.37647 q^{9}\) \(-0.566328 q^{10}\) \(+0.605807 q^{11}\) \(-11.2761 q^{12}\) \(-3.04846 q^{13}\) \(-8.86539 q^{14}\) \(-0.501253 q^{15}\) \(+9.92345 q^{16}\) \(+1.00000 q^{17}\) \(-6.22574 q^{18}\) \(+4.98478 q^{19}\) \(+1.05129 q^{20}\) \(-7.84669 q^{21}\) \(-1.58706 q^{22}\) \(+1.60592 q^{23}\) \(+17.3917 q^{24}\) \(-4.95327 q^{25}\) \(+7.98621 q^{26}\) \(+1.44580 q^{27}\) \(+16.4570 q^{28}\) \(-10.5141 q^{29}\) \(+1.31316 q^{30}\) \(+5.87827 q^{31}\) \(-10.9958 q^{32}\) \(-1.40470 q^{33}\) \(-2.61975 q^{34}\) \(+0.731555 q^{35}\) \(+11.5570 q^{36}\) \(-3.75203 q^{37}\) \(-13.0589 q^{38}\) \(+7.06853 q^{39}\) \(-1.62145 q^{40}\) \(-0.864890 q^{41}\) \(+20.5564 q^{42}\) \(+6.40616 q^{43}\) \(+2.94609 q^{44}\) \(+0.513736 q^{45}\) \(-4.20712 q^{46}\) \(+0.621685 q^{47}\) \(-23.0097 q^{48}\) \(+4.45187 q^{49}\) \(+12.9763 q^{50}\) \(-2.31872 q^{51}\) \(-14.8249 q^{52}\) \(+9.64958 q^{53}\) \(-3.78764 q^{54}\) \(+0.130961 q^{55}\) \(-25.3824 q^{56}\) \(-11.5583 q^{57}\) \(+27.5443 q^{58}\) \(-5.81342 q^{59}\) \(-2.43764 q^{60}\) \(-6.34225 q^{61}\) \(-15.3996 q^{62}\) \(+8.04211 q^{63}\) \(+8.95936 q^{64}\) \(-0.659006 q^{65}\) \(+3.67995 q^{66}\) \(+8.53186 q^{67}\) \(+4.86309 q^{68}\) \(-3.72369 q^{69}\) \(-1.91649 q^{70}\) \(-12.8904 q^{71}\) \(-17.8249 q^{72}\) \(+16.5475 q^{73}\) \(+9.82938 q^{74}\) \(+11.4852 q^{75}\) \(+24.2414 q^{76}\) \(+2.05009 q^{77}\) \(-18.5178 q^{78}\) \(+0.298557 q^{79}\) \(+2.14522 q^{80}\) \(-10.4818 q^{81}\) \(+2.26579 q^{82}\) \(+3.17470 q^{83}\) \(-38.1592 q^{84}\) \(+0.216177 q^{85}\) \(-16.7825 q^{86}\) \(+24.3793 q^{87}\) \(-4.54390 q^{88}\) \(-6.23133 q^{89}\) \(-1.34586 q^{90}\) \(-10.3162 q^{91}\) \(+7.80974 q^{92}\) \(-13.6301 q^{93}\) \(-1.62866 q^{94}\) \(+1.07759 q^{95}\) \(+25.4962 q^{96}\) \(-18.2172 q^{97}\) \(-11.6628 q^{98}\) \(+1.43968 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut -\mathstrut 19q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 49q^{12} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 110q^{16} \) \(\mathstrut +\mathstrut 114q^{17} \) \(\mathstrut -\mathstrut 21q^{18} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 88q^{20} \) \(\mathstrut -\mathstrut 30q^{21} \) \(\mathstrut -\mathstrut 36q^{22} \) \(\mathstrut -\mathstrut 77q^{23} \) \(\mathstrut -\mathstrut 72q^{24} \) \(\mathstrut +\mathstrut 119q^{25} \) \(\mathstrut -\mathstrut 79q^{26} \) \(\mathstrut -\mathstrut 77q^{27} \) \(\mathstrut -\mathstrut 92q^{28} \) \(\mathstrut -\mathstrut 65q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 131q^{31} \) \(\mathstrut -\mathstrut 30q^{32} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 33q^{35} \) \(\mathstrut +\mathstrut 109q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 14q^{38} \) \(\mathstrut -\mathstrut 83q^{39} \) \(\mathstrut -\mathstrut 42q^{40} \) \(\mathstrut -\mathstrut 99q^{41} \) \(\mathstrut +\mathstrut 29q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 73q^{45} \) \(\mathstrut -\mathstrut 35q^{46} \) \(\mathstrut -\mathstrut 113q^{47} \) \(\mathstrut -\mathstrut 86q^{48} \) \(\mathstrut +\mathstrut 101q^{49} \) \(\mathstrut -\mathstrut 44q^{50} \) \(\mathstrut -\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut 3q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 78q^{54} \) \(\mathstrut -\mathstrut 63q^{55} \) \(\mathstrut -\mathstrut 117q^{56} \) \(\mathstrut -\mathstrut 64q^{57} \) \(\mathstrut -\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 134q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 30q^{61} \) \(\mathstrut -\mathstrut 30q^{62} \) \(\mathstrut -\mathstrut 154q^{63} \) \(\mathstrut +\mathstrut 117q^{64} \) \(\mathstrut -\mathstrut 66q^{65} \) \(\mathstrut -\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 110q^{68} \) \(\mathstrut -\mathstrut 35q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 233q^{71} \) \(\mathstrut +\mathstrut 16q^{72} \) \(\mathstrut -\mathstrut 56q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 100q^{75} \) \(\mathstrut -\mathstrut 64q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 50q^{78} \) \(\mathstrut -\mathstrut 154q^{79} \) \(\mathstrut -\mathstrut 128q^{80} \) \(\mathstrut +\mathstrut 118q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 53q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut -\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 52q^{88} \) \(\mathstrut -\mathstrut 118q^{89} \) \(\mathstrut -\mathstrut 5q^{90} \) \(\mathstrut -\mathstrut 95q^{91} \) \(\mathstrut -\mathstrut 102q^{92} \) \(\mathstrut +\mathstrut 47q^{93} \) \(\mathstrut -\mathstrut 3q^{94} \) \(\mathstrut -\mathstrut 158q^{95} \) \(\mathstrut -\mathstrut 144q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut -\mathstrut 131q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.61975 −1.85244 −0.926221 0.376980i \(-0.876963\pi\)
−0.926221 + 0.376980i \(0.876963\pi\)
\(3\) −2.31872 −1.33871 −0.669357 0.742941i \(-0.733430\pi\)
−0.669357 + 0.742941i \(0.733430\pi\)
\(4\) 4.86309 2.43154
\(5\) 0.216177 0.0966771 0.0483385 0.998831i \(-0.484607\pi\)
0.0483385 + 0.998831i \(0.484607\pi\)
\(6\) 6.07447 2.47989
\(7\) 3.38406 1.27905 0.639527 0.768768i \(-0.279130\pi\)
0.639527 + 0.768768i \(0.279130\pi\)
\(8\) −7.50057 −2.65185
\(9\) 2.37647 0.792155
\(10\) −0.566328 −0.179089
\(11\) 0.605807 0.182658 0.0913288 0.995821i \(-0.470889\pi\)
0.0913288 + 0.995821i \(0.470889\pi\)
\(12\) −11.2761 −3.25514
\(13\) −3.04846 −0.845491 −0.422746 0.906248i \(-0.638934\pi\)
−0.422746 + 0.906248i \(0.638934\pi\)
\(14\) −8.86539 −2.36938
\(15\) −0.501253 −0.129423
\(16\) 9.92345 2.48086
\(17\) 1.00000 0.242536
\(18\) −6.22574 −1.46742
\(19\) 4.98478 1.14359 0.571793 0.820398i \(-0.306248\pi\)
0.571793 + 0.820398i \(0.306248\pi\)
\(20\) 1.05129 0.235075
\(21\) −7.84669 −1.71229
\(22\) −1.58706 −0.338363
\(23\) 1.60592 0.334858 0.167429 0.985884i \(-0.446453\pi\)
0.167429 + 0.985884i \(0.446453\pi\)
\(24\) 17.3917 3.55007
\(25\) −4.95327 −0.990654
\(26\) 7.98621 1.56622
\(27\) 1.44580 0.278245
\(28\) 16.4570 3.11008
\(29\) −10.5141 −1.95242 −0.976211 0.216824i \(-0.930430\pi\)
−0.976211 + 0.216824i \(0.930430\pi\)
\(30\) 1.31316 0.239749
\(31\) 5.87827 1.05577 0.527884 0.849317i \(-0.322986\pi\)
0.527884 + 0.849317i \(0.322986\pi\)
\(32\) −10.9958 −1.94380
\(33\) −1.40470 −0.244526
\(34\) −2.61975 −0.449283
\(35\) 0.731555 0.123655
\(36\) 11.5570 1.92616
\(37\) −3.75203 −0.616830 −0.308415 0.951252i \(-0.599799\pi\)
−0.308415 + 0.951252i \(0.599799\pi\)
\(38\) −13.0589 −2.11843
\(39\) 7.06853 1.13187
\(40\) −1.62145 −0.256373
\(41\) −0.864890 −0.135073 −0.0675366 0.997717i \(-0.521514\pi\)
−0.0675366 + 0.997717i \(0.521514\pi\)
\(42\) 20.5564 3.17192
\(43\) 6.40616 0.976930 0.488465 0.872583i \(-0.337557\pi\)
0.488465 + 0.872583i \(0.337557\pi\)
\(44\) 2.94609 0.444140
\(45\) 0.513736 0.0765832
\(46\) −4.20712 −0.620305
\(47\) 0.621685 0.0906821 0.0453411 0.998972i \(-0.485563\pi\)
0.0453411 + 0.998972i \(0.485563\pi\)
\(48\) −23.0097 −3.32117
\(49\) 4.45187 0.635982
\(50\) 12.9763 1.83513
\(51\) −2.31872 −0.324686
\(52\) −14.8249 −2.05585
\(53\) 9.64958 1.32547 0.662736 0.748853i \(-0.269395\pi\)
0.662736 + 0.748853i \(0.269395\pi\)
\(54\) −3.78764 −0.515432
\(55\) 0.130961 0.0176588
\(56\) −25.3824 −3.39187
\(57\) −11.5583 −1.53094
\(58\) 27.5443 3.61675
\(59\) −5.81342 −0.756843 −0.378422 0.925633i \(-0.623533\pi\)
−0.378422 + 0.925633i \(0.623533\pi\)
\(60\) −2.43764 −0.314698
\(61\) −6.34225 −0.812042 −0.406021 0.913864i \(-0.633084\pi\)
−0.406021 + 0.913864i \(0.633084\pi\)
\(62\) −15.3996 −1.95575
\(63\) 8.04211 1.01321
\(64\) 8.95936 1.11992
\(65\) −0.659006 −0.0817396
\(66\) 3.67995 0.452971
\(67\) 8.53186 1.04233 0.521166 0.853455i \(-0.325497\pi\)
0.521166 + 0.853455i \(0.325497\pi\)
\(68\) 4.86309 0.589736
\(69\) −3.72369 −0.448279
\(70\) −1.91649 −0.229064
\(71\) −12.8904 −1.52981 −0.764904 0.644144i \(-0.777214\pi\)
−0.764904 + 0.644144i \(0.777214\pi\)
\(72\) −17.8249 −2.10068
\(73\) 16.5475 1.93673 0.968367 0.249530i \(-0.0802762\pi\)
0.968367 + 0.249530i \(0.0802762\pi\)
\(74\) 9.82938 1.14264
\(75\) 11.4852 1.32620
\(76\) 24.2414 2.78068
\(77\) 2.05009 0.233629
\(78\) −18.5178 −2.09673
\(79\) 0.298557 0.0335902 0.0167951 0.999859i \(-0.494654\pi\)
0.0167951 + 0.999859i \(0.494654\pi\)
\(80\) 2.14522 0.239843
\(81\) −10.4818 −1.16465
\(82\) 2.26579 0.250215
\(83\) 3.17470 0.348468 0.174234 0.984704i \(-0.444255\pi\)
0.174234 + 0.984704i \(0.444255\pi\)
\(84\) −38.1592 −4.16351
\(85\) 0.216177 0.0234476
\(86\) −16.7825 −1.80971
\(87\) 24.3793 2.61373
\(88\) −4.54390 −0.484381
\(89\) −6.23133 −0.660520 −0.330260 0.943890i \(-0.607136\pi\)
−0.330260 + 0.943890i \(0.607136\pi\)
\(90\) −1.34586 −0.141866
\(91\) −10.3162 −1.08143
\(92\) 7.80974 0.814222
\(93\) −13.6301 −1.41337
\(94\) −1.62866 −0.167983
\(95\) 1.07759 0.110559
\(96\) 25.4962 2.60220
\(97\) −18.2172 −1.84967 −0.924837 0.380363i \(-0.875799\pi\)
−0.924837 + 0.380363i \(0.875799\pi\)
\(98\) −11.6628 −1.17812
\(99\) 1.43968 0.144693
\(100\) −24.0882 −2.40882
\(101\) −14.5345 −1.44624 −0.723119 0.690724i \(-0.757292\pi\)
−0.723119 + 0.690724i \(0.757292\pi\)
\(102\) 6.07447 0.601462
\(103\) −4.71810 −0.464888 −0.232444 0.972610i \(-0.574672\pi\)
−0.232444 + 0.972610i \(0.574672\pi\)
\(104\) 22.8652 2.24212
\(105\) −1.69627 −0.165539
\(106\) −25.2795 −2.45536
\(107\) −15.4790 −1.49642 −0.748208 0.663465i \(-0.769085\pi\)
−0.748208 + 0.663465i \(0.769085\pi\)
\(108\) 7.03106 0.676564
\(109\) −17.9470 −1.71902 −0.859508 0.511123i \(-0.829230\pi\)
−0.859508 + 0.511123i \(0.829230\pi\)
\(110\) −0.343085 −0.0327119
\(111\) 8.69991 0.825759
\(112\) 33.5816 3.17316
\(113\) −6.04866 −0.569010 −0.284505 0.958675i \(-0.591829\pi\)
−0.284505 + 0.958675i \(0.591829\pi\)
\(114\) 30.2799 2.83597
\(115\) 0.347163 0.0323731
\(116\) −51.1310 −4.74740
\(117\) −7.24457 −0.669760
\(118\) 15.2297 1.40201
\(119\) 3.38406 0.310216
\(120\) 3.75968 0.343211
\(121\) −10.6330 −0.966636
\(122\) 16.6151 1.50426
\(123\) 2.00544 0.180824
\(124\) 28.5865 2.56715
\(125\) −2.15166 −0.192451
\(126\) −21.0683 −1.87691
\(127\) −15.5307 −1.37812 −0.689062 0.724702i \(-0.741977\pi\)
−0.689062 + 0.724702i \(0.741977\pi\)
\(128\) −1.47967 −0.130786
\(129\) −14.8541 −1.30783
\(130\) 1.72643 0.151418
\(131\) 2.50539 0.218897 0.109449 0.993992i \(-0.465091\pi\)
0.109449 + 0.993992i \(0.465091\pi\)
\(132\) −6.83116 −0.594576
\(133\) 16.8688 1.46271
\(134\) −22.3513 −1.93086
\(135\) 0.312548 0.0268999
\(136\) −7.50057 −0.643169
\(137\) 13.0927 1.11859 0.559294 0.828969i \(-0.311072\pi\)
0.559294 + 0.828969i \(0.311072\pi\)
\(138\) 9.75513 0.830411
\(139\) 15.5926 1.32254 0.661272 0.750146i \(-0.270017\pi\)
0.661272 + 0.750146i \(0.270017\pi\)
\(140\) 3.55761 0.300673
\(141\) −1.44151 −0.121397
\(142\) 33.7696 2.83388
\(143\) −1.84678 −0.154435
\(144\) 23.5827 1.96523
\(145\) −2.27290 −0.188754
\(146\) −43.3502 −3.58769
\(147\) −10.3226 −0.851398
\(148\) −18.2465 −1.49985
\(149\) −16.3563 −1.33996 −0.669979 0.742380i \(-0.733697\pi\)
−0.669979 + 0.742380i \(0.733697\pi\)
\(150\) −30.0885 −2.45671
\(151\) 8.22364 0.669230 0.334615 0.942355i \(-0.391394\pi\)
0.334615 + 0.942355i \(0.391394\pi\)
\(152\) −37.3887 −3.03263
\(153\) 2.37647 0.192126
\(154\) −5.37071 −0.432784
\(155\) 1.27074 0.102069
\(156\) 34.3749 2.75219
\(157\) 8.76181 0.699269 0.349634 0.936886i \(-0.386306\pi\)
0.349634 + 0.936886i \(0.386306\pi\)
\(158\) −0.782144 −0.0622240
\(159\) −22.3747 −1.77443
\(160\) −2.37704 −0.187921
\(161\) 5.43454 0.428302
\(162\) 27.4597 2.15744
\(163\) 21.0887 1.65179 0.825896 0.563823i \(-0.190670\pi\)
0.825896 + 0.563823i \(0.190670\pi\)
\(164\) −4.20604 −0.328436
\(165\) −0.303662 −0.0236401
\(166\) −8.31691 −0.645517
\(167\) 2.81554 0.217873 0.108937 0.994049i \(-0.465255\pi\)
0.108937 + 0.994049i \(0.465255\pi\)
\(168\) 58.8547 4.54074
\(169\) −3.70688 −0.285144
\(170\) −0.566328 −0.0434354
\(171\) 11.8462 0.905898
\(172\) 31.1537 2.37545
\(173\) 21.6542 1.64634 0.823170 0.567795i \(-0.192203\pi\)
0.823170 + 0.567795i \(0.192203\pi\)
\(174\) −63.8676 −4.84179
\(175\) −16.7622 −1.26710
\(176\) 6.01169 0.453148
\(177\) 13.4797 1.01320
\(178\) 16.3245 1.22358
\(179\) 21.6382 1.61732 0.808659 0.588277i \(-0.200194\pi\)
0.808659 + 0.588277i \(0.200194\pi\)
\(180\) 2.49834 0.186216
\(181\) 13.4427 0.999187 0.499594 0.866260i \(-0.333483\pi\)
0.499594 + 0.866260i \(0.333483\pi\)
\(182\) 27.0258 2.00329
\(183\) 14.7059 1.08709
\(184\) −12.0453 −0.887994
\(185\) −0.811101 −0.0596333
\(186\) 35.7073 2.61819
\(187\) 0.605807 0.0443010
\(188\) 3.02331 0.220498
\(189\) 4.89268 0.355890
\(190\) −2.82302 −0.204804
\(191\) −17.6388 −1.27630 −0.638148 0.769914i \(-0.720299\pi\)
−0.638148 + 0.769914i \(0.720299\pi\)
\(192\) −20.7743 −1.49925
\(193\) −13.6671 −0.983779 −0.491890 0.870658i \(-0.663694\pi\)
−0.491890 + 0.870658i \(0.663694\pi\)
\(194\) 47.7244 3.42642
\(195\) 1.52805 0.109426
\(196\) 21.6498 1.54642
\(197\) −22.5607 −1.60738 −0.803691 0.595046i \(-0.797134\pi\)
−0.803691 + 0.595046i \(0.797134\pi\)
\(198\) −3.77160 −0.268036
\(199\) −18.0931 −1.28259 −0.641294 0.767295i \(-0.721602\pi\)
−0.641294 + 0.767295i \(0.721602\pi\)
\(200\) 37.1524 2.62707
\(201\) −19.7830 −1.39538
\(202\) 38.0768 2.67907
\(203\) −35.5804 −2.49725
\(204\) −11.2761 −0.789488
\(205\) −0.186969 −0.0130585
\(206\) 12.3602 0.861179
\(207\) 3.81642 0.265260
\(208\) −30.2513 −2.09755
\(209\) 3.01981 0.208885
\(210\) 4.44380 0.306652
\(211\) 20.1155 1.38481 0.692403 0.721511i \(-0.256552\pi\)
0.692403 + 0.721511i \(0.256552\pi\)
\(212\) 46.9268 3.22294
\(213\) 29.8892 2.04798
\(214\) 40.5512 2.77202
\(215\) 1.38486 0.0944468
\(216\) −10.8443 −0.737864
\(217\) 19.8924 1.35038
\(218\) 47.0168 3.18438
\(219\) −38.3689 −2.59273
\(220\) 0.636876 0.0429382
\(221\) −3.04846 −0.205062
\(222\) −22.7916 −1.52967
\(223\) −6.23690 −0.417653 −0.208827 0.977953i \(-0.566964\pi\)
−0.208827 + 0.977953i \(0.566964\pi\)
\(224\) −37.2105 −2.48623
\(225\) −11.7713 −0.784751
\(226\) 15.8460 1.05406
\(227\) 13.0031 0.863049 0.431524 0.902101i \(-0.357976\pi\)
0.431524 + 0.902101i \(0.357976\pi\)
\(228\) −56.2091 −3.72254
\(229\) 13.9959 0.924878 0.462439 0.886651i \(-0.346974\pi\)
0.462439 + 0.886651i \(0.346974\pi\)
\(230\) −0.909480 −0.0599693
\(231\) −4.75358 −0.312763
\(232\) 78.8619 5.17754
\(233\) −17.3041 −1.13363 −0.566815 0.823845i \(-0.691825\pi\)
−0.566815 + 0.823845i \(0.691825\pi\)
\(234\) 18.9790 1.24069
\(235\) 0.134394 0.00876688
\(236\) −28.2712 −1.84030
\(237\) −0.692270 −0.0449677
\(238\) −8.86539 −0.574658
\(239\) 29.9641 1.93822 0.969109 0.246634i \(-0.0793247\pi\)
0.969109 + 0.246634i \(0.0793247\pi\)
\(240\) −4.97416 −0.321081
\(241\) 27.1082 1.74619 0.873097 0.487546i \(-0.162108\pi\)
0.873097 + 0.487546i \(0.162108\pi\)
\(242\) 27.8558 1.79064
\(243\) 19.9670 1.28088
\(244\) −30.8429 −1.97452
\(245\) 0.962390 0.0614848
\(246\) −5.25375 −0.334967
\(247\) −15.1959 −0.966893
\(248\) −44.0904 −2.79974
\(249\) −7.36123 −0.466499
\(250\) 5.63682 0.356504
\(251\) 3.10278 0.195846 0.0979228 0.995194i \(-0.468780\pi\)
0.0979228 + 0.995194i \(0.468780\pi\)
\(252\) 39.1095 2.46366
\(253\) 0.972879 0.0611644
\(254\) 40.6865 2.55290
\(255\) −0.501253 −0.0313897
\(256\) −14.0424 −0.877647
\(257\) −3.18613 −0.198745 −0.0993726 0.995050i \(-0.531684\pi\)
−0.0993726 + 0.995050i \(0.531684\pi\)
\(258\) 38.9140 2.42268
\(259\) −12.6971 −0.788960
\(260\) −3.20480 −0.198754
\(261\) −24.9864 −1.54662
\(262\) −6.56351 −0.405495
\(263\) −0.0320315 −0.00197515 −0.000987573 1.00000i \(-0.500314\pi\)
−0.000987573 1.00000i \(0.500314\pi\)
\(264\) 10.5360 0.648448
\(265\) 2.08601 0.128143
\(266\) −44.1920 −2.70959
\(267\) 14.4487 0.884247
\(268\) 41.4912 2.53448
\(269\) −12.0236 −0.733094 −0.366547 0.930399i \(-0.619460\pi\)
−0.366547 + 0.930399i \(0.619460\pi\)
\(270\) −0.818799 −0.0498305
\(271\) −7.27379 −0.441851 −0.220926 0.975291i \(-0.570908\pi\)
−0.220926 + 0.975291i \(0.570908\pi\)
\(272\) 9.92345 0.601698
\(273\) 23.9204 1.44773
\(274\) −34.2997 −2.07212
\(275\) −3.00072 −0.180950
\(276\) −18.1086 −1.09001
\(277\) 15.7552 0.946640 0.473320 0.880891i \(-0.343055\pi\)
0.473320 + 0.880891i \(0.343055\pi\)
\(278\) −40.8486 −2.44994
\(279\) 13.9695 0.836332
\(280\) −5.48708 −0.327916
\(281\) −16.0943 −0.960108 −0.480054 0.877239i \(-0.659383\pi\)
−0.480054 + 0.877239i \(0.659383\pi\)
\(282\) 3.77641 0.224882
\(283\) −13.7318 −0.816272 −0.408136 0.912921i \(-0.633821\pi\)
−0.408136 + 0.912921i \(0.633821\pi\)
\(284\) −62.6871 −3.71980
\(285\) −2.49864 −0.148006
\(286\) 4.83810 0.286083
\(287\) −2.92684 −0.172766
\(288\) −26.1312 −1.53979
\(289\) 1.00000 0.0588235
\(290\) 5.95444 0.349657
\(291\) 42.2405 2.47618
\(292\) 80.4718 4.70925
\(293\) 15.4912 0.905005 0.452502 0.891763i \(-0.350531\pi\)
0.452502 + 0.891763i \(0.350531\pi\)
\(294\) 27.0427 1.57717
\(295\) −1.25673 −0.0731694
\(296\) 28.1424 1.63574
\(297\) 0.875876 0.0508235
\(298\) 42.8493 2.48219
\(299\) −4.89560 −0.283120
\(300\) 55.8538 3.22472
\(301\) 21.6788 1.24955
\(302\) −21.5439 −1.23971
\(303\) 33.7015 1.93610
\(304\) 49.4662 2.83708
\(305\) −1.37105 −0.0785059
\(306\) −6.22574 −0.355902
\(307\) 10.4733 0.597743 0.298872 0.954293i \(-0.403390\pi\)
0.298872 + 0.954293i \(0.403390\pi\)
\(308\) 9.96975 0.568079
\(309\) 10.9400 0.622352
\(310\) −3.32903 −0.189076
\(311\) −8.12547 −0.460753 −0.230377 0.973102i \(-0.573996\pi\)
−0.230377 + 0.973102i \(0.573996\pi\)
\(312\) −53.0181 −3.00156
\(313\) −9.96182 −0.563075 −0.281538 0.959550i \(-0.590844\pi\)
−0.281538 + 0.959550i \(0.590844\pi\)
\(314\) −22.9537 −1.29535
\(315\) 1.73851 0.0979542
\(316\) 1.45191 0.0816762
\(317\) 15.0746 0.846671 0.423336 0.905973i \(-0.360859\pi\)
0.423336 + 0.905973i \(0.360859\pi\)
\(318\) 58.6161 3.28703
\(319\) −6.36952 −0.356625
\(320\) 1.93680 0.108271
\(321\) 35.8916 2.00327
\(322\) −14.2371 −0.793405
\(323\) 4.98478 0.277361
\(324\) −50.9740 −2.83189
\(325\) 15.0999 0.837589
\(326\) −55.2470 −3.05985
\(327\) 41.6142 2.30127
\(328\) 6.48717 0.358194
\(329\) 2.10382 0.115987
\(330\) 0.795519 0.0437919
\(331\) 33.4525 1.83872 0.919359 0.393420i \(-0.128708\pi\)
0.919359 + 0.393420i \(0.128708\pi\)
\(332\) 15.4388 0.847316
\(333\) −8.91657 −0.488625
\(334\) −7.37601 −0.403597
\(335\) 1.84439 0.100770
\(336\) −77.8663 −4.24795
\(337\) −20.3557 −1.10885 −0.554423 0.832235i \(-0.687061\pi\)
−0.554423 + 0.832235i \(0.687061\pi\)
\(338\) 9.71109 0.528213
\(339\) 14.0252 0.761742
\(340\) 1.05129 0.0570140
\(341\) 3.56109 0.192844
\(342\) −31.0340 −1.67812
\(343\) −8.62302 −0.465600
\(344\) −48.0499 −2.59068
\(345\) −0.804973 −0.0433383
\(346\) −56.7286 −3.04975
\(347\) −7.32242 −0.393088 −0.196544 0.980495i \(-0.562972\pi\)
−0.196544 + 0.980495i \(0.562972\pi\)
\(348\) 118.559 6.35541
\(349\) 16.7811 0.898271 0.449136 0.893464i \(-0.351732\pi\)
0.449136 + 0.893464i \(0.351732\pi\)
\(350\) 43.9127 2.34723
\(351\) −4.40747 −0.235254
\(352\) −6.66133 −0.355050
\(353\) 1.00000 0.0532246
\(354\) −35.3135 −1.87689
\(355\) −2.78660 −0.147897
\(356\) −30.3035 −1.60608
\(357\) −7.84669 −0.415291
\(358\) −56.6868 −2.99599
\(359\) −30.3103 −1.59972 −0.799859 0.600189i \(-0.795092\pi\)
−0.799859 + 0.600189i \(0.795092\pi\)
\(360\) −3.85332 −0.203088
\(361\) 5.84803 0.307791
\(362\) −35.2165 −1.85094
\(363\) 24.6550 1.29405
\(364\) −50.1685 −2.62954
\(365\) 3.57717 0.187238
\(366\) −38.5258 −2.01378
\(367\) −32.4415 −1.69343 −0.846717 0.532043i \(-0.821424\pi\)
−0.846717 + 0.532043i \(0.821424\pi\)
\(368\) 15.9363 0.830737
\(369\) −2.05538 −0.106999
\(370\) 2.12488 0.110467
\(371\) 32.6548 1.69535
\(372\) −66.2842 −3.43667
\(373\) −33.0668 −1.71214 −0.856068 0.516864i \(-0.827099\pi\)
−0.856068 + 0.516864i \(0.827099\pi\)
\(374\) −1.58706 −0.0820650
\(375\) 4.98910 0.257636
\(376\) −4.66300 −0.240476
\(377\) 32.0519 1.65076
\(378\) −12.8176 −0.659266
\(379\) −18.7297 −0.962082 −0.481041 0.876698i \(-0.659741\pi\)
−0.481041 + 0.876698i \(0.659741\pi\)
\(380\) 5.24043 0.268828
\(381\) 36.0113 1.84491
\(382\) 46.2091 2.36426
\(383\) −31.5763 −1.61347 −0.806737 0.590911i \(-0.798769\pi\)
−0.806737 + 0.590911i \(0.798769\pi\)
\(384\) 3.43094 0.175085
\(385\) 0.443181 0.0225866
\(386\) 35.8044 1.82239
\(387\) 15.2240 0.773880
\(388\) −88.5917 −4.49756
\(389\) 2.38448 0.120898 0.0604489 0.998171i \(-0.480747\pi\)
0.0604489 + 0.998171i \(0.480747\pi\)
\(390\) −4.00311 −0.202705
\(391\) 1.60592 0.0812150
\(392\) −33.3916 −1.68653
\(393\) −5.80931 −0.293041
\(394\) 59.1034 2.97758
\(395\) 0.0645409 0.00324741
\(396\) 7.00128 0.351828
\(397\) 24.2645 1.21780 0.608900 0.793247i \(-0.291611\pi\)
0.608900 + 0.793247i \(0.291611\pi\)
\(398\) 47.3995 2.37592
\(399\) −39.1140 −1.95815
\(400\) −49.1535 −2.45768
\(401\) 20.7258 1.03500 0.517498 0.855684i \(-0.326863\pi\)
0.517498 + 0.855684i \(0.326863\pi\)
\(402\) 51.8265 2.58487
\(403\) −17.9197 −0.892642
\(404\) −70.6826 −3.51659
\(405\) −2.26592 −0.112595
\(406\) 93.2117 4.62602
\(407\) −2.27301 −0.112669
\(408\) 17.3917 0.861019
\(409\) −14.0876 −0.696585 −0.348292 0.937386i \(-0.613238\pi\)
−0.348292 + 0.937386i \(0.613238\pi\)
\(410\) 0.489812 0.0241901
\(411\) −30.3584 −1.49747
\(412\) −22.9445 −1.13040
\(413\) −19.6730 −0.968044
\(414\) −9.99807 −0.491378
\(415\) 0.686295 0.0336889
\(416\) 33.5203 1.64347
\(417\) −36.1548 −1.77051
\(418\) −7.91115 −0.386947
\(419\) 10.5781 0.516773 0.258386 0.966042i \(-0.416809\pi\)
0.258386 + 0.966042i \(0.416809\pi\)
\(420\) −8.24911 −0.402516
\(421\) −21.1281 −1.02972 −0.514860 0.857274i \(-0.672156\pi\)
−0.514860 + 0.857274i \(0.672156\pi\)
\(422\) −52.6975 −2.56528
\(423\) 1.47741 0.0718343
\(424\) −72.3774 −3.51496
\(425\) −4.95327 −0.240269
\(426\) −78.3023 −3.79376
\(427\) −21.4626 −1.03865
\(428\) −75.2759 −3.63860
\(429\) 4.28216 0.206745
\(430\) −3.62799 −0.174957
\(431\) −29.5237 −1.42211 −0.711054 0.703138i \(-0.751782\pi\)
−0.711054 + 0.703138i \(0.751782\pi\)
\(432\) 14.3473 0.690287
\(433\) −23.1646 −1.11322 −0.556609 0.830774i \(-0.687898\pi\)
−0.556609 + 0.830774i \(0.687898\pi\)
\(434\) −52.1131 −2.50151
\(435\) 5.27023 0.252688
\(436\) −87.2781 −4.17986
\(437\) 8.00517 0.382939
\(438\) 100.517 4.80289
\(439\) 31.8923 1.52214 0.761068 0.648672i \(-0.224675\pi\)
0.761068 + 0.648672i \(0.224675\pi\)
\(440\) −0.982284 −0.0468285
\(441\) 10.5797 0.503796
\(442\) 7.98621 0.379865
\(443\) −30.0347 −1.42699 −0.713497 0.700658i \(-0.752890\pi\)
−0.713497 + 0.700658i \(0.752890\pi\)
\(444\) 42.3084 2.00787
\(445\) −1.34707 −0.0638571
\(446\) 16.3391 0.773679
\(447\) 37.9256 1.79382
\(448\) 30.3190 1.43244
\(449\) −32.2392 −1.52146 −0.760732 0.649066i \(-0.775160\pi\)
−0.760732 + 0.649066i \(0.775160\pi\)
\(450\) 30.8378 1.45371
\(451\) −0.523956 −0.0246721
\(452\) −29.4152 −1.38357
\(453\) −19.0683 −0.895908
\(454\) −34.0650 −1.59875
\(455\) −2.23012 −0.104549
\(456\) 86.6940 4.05982
\(457\) 40.0897 1.87532 0.937658 0.347560i \(-0.112990\pi\)
0.937658 + 0.347560i \(0.112990\pi\)
\(458\) −36.6659 −1.71328
\(459\) 1.44580 0.0674843
\(460\) 1.68828 0.0787166
\(461\) −37.9134 −1.76580 −0.882901 0.469559i \(-0.844413\pi\)
−0.882901 + 0.469559i \(0.844413\pi\)
\(462\) 12.4532 0.579375
\(463\) −4.18769 −0.194618 −0.0973092 0.995254i \(-0.531024\pi\)
−0.0973092 + 0.995254i \(0.531024\pi\)
\(464\) −104.336 −4.84369
\(465\) −2.94650 −0.136641
\(466\) 45.3324 2.09998
\(467\) 10.6805 0.494236 0.247118 0.968985i \(-0.420517\pi\)
0.247118 + 0.968985i \(0.420517\pi\)
\(468\) −35.2310 −1.62855
\(469\) 28.8723 1.33320
\(470\) −0.352078 −0.0162401
\(471\) −20.3162 −0.936121
\(472\) 43.6040 2.00704
\(473\) 3.88089 0.178444
\(474\) 1.81357 0.0833002
\(475\) −24.6909 −1.13290
\(476\) 16.4570 0.754305
\(477\) 22.9319 1.04998
\(478\) −78.4985 −3.59044
\(479\) 21.8653 0.999051 0.499525 0.866299i \(-0.333508\pi\)
0.499525 + 0.866299i \(0.333508\pi\)
\(480\) 5.51168 0.251573
\(481\) 11.4379 0.521525
\(482\) −71.0168 −3.23473
\(483\) −12.6012 −0.573374
\(484\) −51.7092 −2.35042
\(485\) −3.93813 −0.178821
\(486\) −52.3085 −2.37276
\(487\) 27.2950 1.23685 0.618427 0.785842i \(-0.287770\pi\)
0.618427 + 0.785842i \(0.287770\pi\)
\(488\) 47.5705 2.15342
\(489\) −48.8987 −2.21128
\(490\) −2.52122 −0.113897
\(491\) 1.76167 0.0795031 0.0397516 0.999210i \(-0.487343\pi\)
0.0397516 + 0.999210i \(0.487343\pi\)
\(492\) 9.75262 0.439682
\(493\) −10.5141 −0.473532
\(494\) 39.8095 1.79111
\(495\) 0.311225 0.0139885
\(496\) 58.3327 2.61921
\(497\) −43.6219 −1.95671
\(498\) 19.2846 0.864163
\(499\) 24.6671 1.10425 0.552126 0.833761i \(-0.313817\pi\)
0.552126 + 0.833761i \(0.313817\pi\)
\(500\) −10.4637 −0.467952
\(501\) −6.52845 −0.291670
\(502\) −8.12850 −0.362793
\(503\) 20.7548 0.925409 0.462704 0.886513i \(-0.346879\pi\)
0.462704 + 0.886513i \(0.346879\pi\)
\(504\) −60.3204 −2.68688
\(505\) −3.14202 −0.139818
\(506\) −2.54870 −0.113303
\(507\) 8.59521 0.381727
\(508\) −75.5270 −3.35097
\(509\) −34.9462 −1.54896 −0.774481 0.632597i \(-0.781989\pi\)
−0.774481 + 0.632597i \(0.781989\pi\)
\(510\) 1.31316 0.0581476
\(511\) 55.9976 2.47719
\(512\) 39.7468 1.75658
\(513\) 7.20701 0.318197
\(514\) 8.34686 0.368164
\(515\) −1.01994 −0.0449440
\(516\) −72.2368 −3.18005
\(517\) 0.376621 0.0165638
\(518\) 33.2632 1.46150
\(519\) −50.2101 −2.20398
\(520\) 4.94292 0.216762
\(521\) 14.1237 0.618771 0.309385 0.950937i \(-0.399877\pi\)
0.309385 + 0.950937i \(0.399877\pi\)
\(522\) 65.4582 2.86503
\(523\) −2.80695 −0.122739 −0.0613697 0.998115i \(-0.519547\pi\)
−0.0613697 + 0.998115i \(0.519547\pi\)
\(524\) 12.1840 0.532259
\(525\) 38.8668 1.69628
\(526\) 0.0839145 0.00365885
\(527\) 5.87827 0.256061
\(528\) −13.9394 −0.606636
\(529\) −20.4210 −0.887870
\(530\) −5.46483 −0.237377
\(531\) −13.8154 −0.599537
\(532\) 82.0345 3.55665
\(533\) 2.63658 0.114203
\(534\) −37.8520 −1.63802
\(535\) −3.34620 −0.144669
\(536\) −63.9938 −2.76411
\(537\) −50.1730 −2.16513
\(538\) 31.4989 1.35802
\(539\) 2.69697 0.116167
\(540\) 1.51995 0.0654083
\(541\) −21.7805 −0.936418 −0.468209 0.883618i \(-0.655100\pi\)
−0.468209 + 0.883618i \(0.655100\pi\)
\(542\) 19.0555 0.818504
\(543\) −31.1698 −1.33763
\(544\) −10.9958 −0.471441
\(545\) −3.87973 −0.166189
\(546\) −62.6653 −2.68183
\(547\) 17.0651 0.729651 0.364825 0.931076i \(-0.381129\pi\)
0.364825 + 0.931076i \(0.381129\pi\)
\(548\) 63.6712 2.71990
\(549\) −15.0721 −0.643264
\(550\) 7.86114 0.335200
\(551\) −52.4105 −2.23276
\(552\) 27.9298 1.18877
\(553\) 1.01033 0.0429638
\(554\) −41.2748 −1.75360
\(555\) 1.88072 0.0798320
\(556\) 75.8280 3.21582
\(557\) 40.2072 1.70363 0.851816 0.523840i \(-0.175501\pi\)
0.851816 + 0.523840i \(0.175501\pi\)
\(558\) −36.5966 −1.54926
\(559\) −19.5289 −0.825986
\(560\) 7.25955 0.306772
\(561\) −1.40470 −0.0593063
\(562\) 42.1632 1.77855
\(563\) −6.67822 −0.281453 −0.140727 0.990048i \(-0.544944\pi\)
−0.140727 + 0.990048i \(0.544944\pi\)
\(564\) −7.01021 −0.295183
\(565\) −1.30758 −0.0550103
\(566\) 35.9739 1.51210
\(567\) −35.4711 −1.48965
\(568\) 96.6853 4.05683
\(569\) −0.960867 −0.0402816 −0.0201408 0.999797i \(-0.506411\pi\)
−0.0201408 + 0.999797i \(0.506411\pi\)
\(570\) 6.54580 0.274173
\(571\) 10.5338 0.440827 0.220414 0.975407i \(-0.429259\pi\)
0.220414 + 0.975407i \(0.429259\pi\)
\(572\) −8.98105 −0.375517
\(573\) 40.8993 1.70859
\(574\) 7.66759 0.320039
\(575\) −7.95457 −0.331728
\(576\) 21.2916 0.887151
\(577\) 27.7951 1.15712 0.578562 0.815638i \(-0.303614\pi\)
0.578562 + 0.815638i \(0.303614\pi\)
\(578\) −2.61975 −0.108967
\(579\) 31.6902 1.31700
\(580\) −11.0533 −0.458965
\(581\) 10.7434 0.445710
\(582\) −110.660 −4.58699
\(583\) 5.84578 0.242107
\(584\) −124.115 −5.13593
\(585\) −1.56611 −0.0647505
\(586\) −40.5830 −1.67647
\(587\) 16.9858 0.701081 0.350540 0.936548i \(-0.385998\pi\)
0.350540 + 0.936548i \(0.385998\pi\)
\(588\) −50.1999 −2.07021
\(589\) 29.3019 1.20736
\(590\) 3.29231 0.135542
\(591\) 52.3120 2.15183
\(592\) −37.2331 −1.53027
\(593\) −5.88610 −0.241713 −0.120857 0.992670i \(-0.538564\pi\)
−0.120857 + 0.992670i \(0.538564\pi\)
\(594\) −2.29458 −0.0941476
\(595\) 0.731555 0.0299908
\(596\) −79.5419 −3.25816
\(597\) 41.9529 1.71702
\(598\) 12.8252 0.524463
\(599\) 39.5784 1.61713 0.808565 0.588407i \(-0.200245\pi\)
0.808565 + 0.588407i \(0.200245\pi\)
\(600\) −86.1459 −3.51689
\(601\) −10.2614 −0.418573 −0.209286 0.977854i \(-0.567114\pi\)
−0.209286 + 0.977854i \(0.567114\pi\)
\(602\) −56.7931 −2.31472
\(603\) 20.2757 0.825689
\(604\) 39.9923 1.62726
\(605\) −2.29860 −0.0934516
\(606\) −88.2894 −3.58651
\(607\) −33.6135 −1.36433 −0.682164 0.731199i \(-0.738961\pi\)
−0.682164 + 0.731199i \(0.738961\pi\)
\(608\) −54.8117 −2.22291
\(609\) 82.5010 3.34311
\(610\) 3.59180 0.145428
\(611\) −1.89518 −0.0766709
\(612\) 11.5570 0.467163
\(613\) 1.09646 0.0442858 0.0221429 0.999755i \(-0.492951\pi\)
0.0221429 + 0.999755i \(0.492951\pi\)
\(614\) −27.4374 −1.10728
\(615\) 0.433529 0.0174816
\(616\) −15.3768 −0.619550
\(617\) 21.2959 0.857341 0.428670 0.903461i \(-0.358982\pi\)
0.428670 + 0.903461i \(0.358982\pi\)
\(618\) −28.6599 −1.15287
\(619\) −1.95401 −0.0785383 −0.0392691 0.999229i \(-0.512503\pi\)
−0.0392691 + 0.999229i \(0.512503\pi\)
\(620\) 6.17973 0.248184
\(621\) 2.32185 0.0931725
\(622\) 21.2867 0.853519
\(623\) −21.0872 −0.844841
\(624\) 70.1442 2.80802
\(625\) 24.3012 0.972048
\(626\) 26.0975 1.04306
\(627\) −7.00210 −0.279637
\(628\) 42.6095 1.70030
\(629\) −3.75203 −0.149603
\(630\) −4.55447 −0.181455
\(631\) −3.11124 −0.123857 −0.0619283 0.998081i \(-0.519725\pi\)
−0.0619283 + 0.998081i \(0.519725\pi\)
\(632\) −2.23935 −0.0890764
\(633\) −46.6422 −1.85386
\(634\) −39.4916 −1.56841
\(635\) −3.35737 −0.133233
\(636\) −108.810 −4.31460
\(637\) −13.5714 −0.537717
\(638\) 16.6865 0.660627
\(639\) −30.6336 −1.21185
\(640\) −0.319870 −0.0126440
\(641\) −2.50666 −0.0990071 −0.0495036 0.998774i \(-0.515764\pi\)
−0.0495036 + 0.998774i \(0.515764\pi\)
\(642\) −94.0269 −3.71095
\(643\) 31.7764 1.25314 0.626570 0.779365i \(-0.284458\pi\)
0.626570 + 0.779365i \(0.284458\pi\)
\(644\) 26.4287 1.04143
\(645\) −3.21111 −0.126437
\(646\) −13.0589 −0.513795
\(647\) −28.3128 −1.11309 −0.556546 0.830816i \(-0.687874\pi\)
−0.556546 + 0.830816i \(0.687874\pi\)
\(648\) 78.6196 3.08847
\(649\) −3.52181 −0.138243
\(650\) −39.5578 −1.55159
\(651\) −46.1249 −1.80778
\(652\) 102.556 4.01640
\(653\) −27.6210 −1.08089 −0.540447 0.841378i \(-0.681745\pi\)
−0.540447 + 0.841378i \(0.681745\pi\)
\(654\) −109.019 −4.26297
\(655\) 0.541607 0.0211624
\(656\) −8.58269 −0.335098
\(657\) 39.3245 1.53419
\(658\) −5.51148 −0.214860
\(659\) 2.81302 0.109580 0.0547899 0.998498i \(-0.482551\pi\)
0.0547899 + 0.998498i \(0.482551\pi\)
\(660\) −1.47674 −0.0574819
\(661\) −3.28095 −0.127614 −0.0638070 0.997962i \(-0.520324\pi\)
−0.0638070 + 0.997962i \(0.520324\pi\)
\(662\) −87.6373 −3.40612
\(663\) 7.06853 0.274519
\(664\) −23.8120 −0.924086
\(665\) 3.64664 0.141411
\(666\) 23.3592 0.905150
\(667\) −16.8848 −0.653784
\(668\) 13.6922 0.529768
\(669\) 14.4616 0.559118
\(670\) −4.83183 −0.186670
\(671\) −3.84218 −0.148326
\(672\) 86.2807 3.32835
\(673\) −11.7832 −0.454208 −0.227104 0.973871i \(-0.572926\pi\)
−0.227104 + 0.973871i \(0.572926\pi\)
\(674\) 53.3269 2.05407
\(675\) −7.16144 −0.275644
\(676\) −18.0269 −0.693341
\(677\) −42.7536 −1.64315 −0.821577 0.570097i \(-0.806906\pi\)
−0.821577 + 0.570097i \(0.806906\pi\)
\(678\) −36.7424 −1.41108
\(679\) −61.6480 −2.36583
\(680\) −1.62145 −0.0621797
\(681\) −30.1506 −1.15538
\(682\) −9.32917 −0.357232
\(683\) 13.4457 0.514486 0.257243 0.966347i \(-0.417186\pi\)
0.257243 + 0.966347i \(0.417186\pi\)
\(684\) 57.6089 2.20273
\(685\) 2.83034 0.108142
\(686\) 22.5902 0.862496
\(687\) −32.4527 −1.23815
\(688\) 63.5712 2.42363
\(689\) −29.4164 −1.12067
\(690\) 2.10883 0.0802817
\(691\) −36.2653 −1.37960 −0.689798 0.724002i \(-0.742301\pi\)
−0.689798 + 0.724002i \(0.742301\pi\)
\(692\) 105.306 4.00315
\(693\) 4.87196 0.185070
\(694\) 19.1829 0.728173
\(695\) 3.37075 0.127860
\(696\) −182.859 −6.93124
\(697\) −0.864890 −0.0327600
\(698\) −43.9623 −1.66400
\(699\) 40.1234 1.51761
\(700\) −81.5159 −3.08101
\(701\) 2.98235 0.112642 0.0563210 0.998413i \(-0.482063\pi\)
0.0563210 + 0.998413i \(0.482063\pi\)
\(702\) 11.5465 0.435794
\(703\) −18.7031 −0.705399
\(704\) 5.42764 0.204562
\(705\) −0.311622 −0.0117363
\(706\) −2.61975 −0.0985956
\(707\) −49.1857 −1.84982
\(708\) 65.5530 2.46363
\(709\) 27.2729 1.02426 0.512128 0.858909i \(-0.328857\pi\)
0.512128 + 0.858909i \(0.328857\pi\)
\(710\) 7.30019 0.273971
\(711\) 0.709510 0.0266087
\(712\) 46.7386 1.75160
\(713\) 9.44004 0.353532
\(714\) 20.5564 0.769303
\(715\) −0.399230 −0.0149304
\(716\) 105.229 3.93258
\(717\) −69.4784 −2.59472
\(718\) 79.4054 2.96338
\(719\) 8.97679 0.334778 0.167389 0.985891i \(-0.446466\pi\)
0.167389 + 0.985891i \(0.446466\pi\)
\(720\) 5.09803 0.189993
\(721\) −15.9663 −0.594618
\(722\) −15.3204 −0.570165
\(723\) −62.8564 −2.33766
\(724\) 65.3730 2.42957
\(725\) 52.0792 1.93417
\(726\) −64.5898 −2.39715
\(727\) −45.6766 −1.69405 −0.847025 0.531553i \(-0.821609\pi\)
−0.847025 + 0.531553i \(0.821609\pi\)
\(728\) 77.3773 2.86779
\(729\) −14.8524 −0.550090
\(730\) −9.37130 −0.346847
\(731\) 6.40616 0.236940
\(732\) 71.5162 2.64331
\(733\) −6.77664 −0.250301 −0.125150 0.992138i \(-0.539941\pi\)
−0.125150 + 0.992138i \(0.539941\pi\)
\(734\) 84.9887 3.13699
\(735\) −2.23151 −0.0823106
\(736\) −17.6584 −0.650898
\(737\) 5.16866 0.190390
\(738\) 5.38458 0.198209
\(739\) −26.2113 −0.964197 −0.482099 0.876117i \(-0.660125\pi\)
−0.482099 + 0.876117i \(0.660125\pi\)
\(740\) −3.94446 −0.145001
\(741\) 35.2351 1.29439
\(742\) −85.5473 −3.14054
\(743\) −49.0933 −1.80106 −0.900529 0.434796i \(-0.856820\pi\)
−0.900529 + 0.434796i \(0.856820\pi\)
\(744\) 102.233 3.74805
\(745\) −3.53584 −0.129543
\(746\) 86.6268 3.17163
\(747\) 7.54456 0.276041
\(748\) 2.94609 0.107720
\(749\) −52.3820 −1.91400
\(750\) −13.0702 −0.477256
\(751\) −47.5002 −1.73331 −0.866654 0.498910i \(-0.833734\pi\)
−0.866654 + 0.498910i \(0.833734\pi\)
\(752\) 6.16926 0.224970
\(753\) −7.19447 −0.262181
\(754\) −83.9679 −3.05793
\(755\) 1.77776 0.0646992
\(756\) 23.7935 0.865363
\(757\) 11.3486 0.412471 0.206235 0.978502i \(-0.433879\pi\)
0.206235 + 0.978502i \(0.433879\pi\)
\(758\) 49.0672 1.78220
\(759\) −2.25583 −0.0818816
\(760\) −8.08256 −0.293185
\(761\) 17.2748 0.626213 0.313106 0.949718i \(-0.398630\pi\)
0.313106 + 0.949718i \(0.398630\pi\)
\(762\) −94.3405 −3.41760
\(763\) −60.7339 −2.19871
\(764\) −85.7788 −3.10337
\(765\) 0.513736 0.0185742
\(766\) 82.7220 2.98887
\(767\) 17.7220 0.639905
\(768\) 32.5603 1.17492
\(769\) 26.1758 0.943924 0.471962 0.881619i \(-0.343546\pi\)
0.471962 + 0.881619i \(0.343546\pi\)
\(770\) −1.16102 −0.0418403
\(771\) 7.38774 0.266063
\(772\) −66.4643 −2.39210
\(773\) 4.03438 0.145107 0.0725533 0.997365i \(-0.476885\pi\)
0.0725533 + 0.997365i \(0.476885\pi\)
\(774\) −39.8831 −1.43357
\(775\) −29.1166 −1.04590
\(776\) 136.639 4.90507
\(777\) 29.4410 1.05619
\(778\) −6.24674 −0.223956
\(779\) −4.31129 −0.154468
\(780\) 7.43105 0.266074
\(781\) −7.80908 −0.279431
\(782\) −4.20712 −0.150446
\(783\) −15.2013 −0.543251
\(784\) 44.1779 1.57778
\(785\) 1.89410 0.0676032
\(786\) 15.2189 0.542842
\(787\) −39.5086 −1.40833 −0.704165 0.710036i \(-0.748679\pi\)
−0.704165 + 0.710036i \(0.748679\pi\)
\(788\) −109.715 −3.90842
\(789\) 0.0742721 0.00264416
\(790\) −0.169081 −0.00601564
\(791\) −20.4690 −0.727795
\(792\) −10.7984 −0.383705
\(793\) 19.3341 0.686575
\(794\) −63.5669 −2.25590
\(795\) −4.83688 −0.171546
\(796\) −87.9885 −3.11867
\(797\) −23.1479 −0.819940 −0.409970 0.912099i \(-0.634461\pi\)
−0.409970 + 0.912099i \(0.634461\pi\)
\(798\) 102.469 3.62736
\(799\) 0.621685 0.0219936
\(800\) 54.4652 1.92563
\(801\) −14.8085 −0.523234
\(802\) −54.2964 −1.91727
\(803\) 10.0246 0.353759
\(804\) −96.2064 −3.39294
\(805\) 1.17482 0.0414070
\(806\) 46.9451 1.65357
\(807\) 27.8795 0.981404
\(808\) 109.017 3.83521
\(809\) −12.0620 −0.424077 −0.212038 0.977261i \(-0.568010\pi\)
−0.212038 + 0.977261i \(0.568010\pi\)
\(810\) 5.93614 0.208575
\(811\) −16.9298 −0.594484 −0.297242 0.954802i \(-0.596067\pi\)
−0.297242 + 0.954802i \(0.596067\pi\)
\(812\) −173.031 −6.07218
\(813\) 16.8659 0.591512
\(814\) 5.95471 0.208712
\(815\) 4.55887 0.159690
\(816\) −23.0097 −0.805501
\(817\) 31.9333 1.11720
\(818\) 36.9059 1.29038
\(819\) −24.5161 −0.856660
\(820\) −0.909246 −0.0317523
\(821\) 32.5308 1.13533 0.567666 0.823259i \(-0.307847\pi\)
0.567666 + 0.823259i \(0.307847\pi\)
\(822\) 79.5315 2.77398
\(823\) −36.8163 −1.28334 −0.641668 0.766983i \(-0.721757\pi\)
−0.641668 + 0.766983i \(0.721757\pi\)
\(824\) 35.3885 1.23282
\(825\) 6.95784 0.242241
\(826\) 51.5383 1.79325
\(827\) 27.8455 0.968283 0.484142 0.874990i \(-0.339132\pi\)
0.484142 + 0.874990i \(0.339132\pi\)
\(828\) 18.5596 0.644990
\(829\) −34.8659 −1.21094 −0.605471 0.795868i \(-0.707015\pi\)
−0.605471 + 0.795868i \(0.707015\pi\)
\(830\) −1.79792 −0.0624067
\(831\) −36.5320 −1.26728
\(832\) −27.3123 −0.946883
\(833\) 4.45187 0.154248
\(834\) 94.7165 3.27976
\(835\) 0.608654 0.0210633
\(836\) 14.6856 0.507913
\(837\) 8.49881 0.293762
\(838\) −27.7119 −0.957292
\(839\) −9.84127 −0.339759 −0.169879 0.985465i \(-0.554338\pi\)
−0.169879 + 0.985465i \(0.554338\pi\)
\(840\) 12.7230 0.438985
\(841\) 81.5465 2.81195
\(842\) 55.3503 1.90750
\(843\) 37.3183 1.28531
\(844\) 97.8234 3.36722
\(845\) −0.801339 −0.0275669
\(846\) −3.87045 −0.133069
\(847\) −35.9827 −1.23638
\(848\) 95.7571 3.28831
\(849\) 31.8403 1.09275
\(850\) 12.9763 0.445084
\(851\) −6.02547 −0.206551
\(852\) 145.354 4.97974
\(853\) −15.8307 −0.542033 −0.271016 0.962575i \(-0.587360\pi\)
−0.271016 + 0.962575i \(0.587360\pi\)
\(854\) 56.2266 1.92403
\(855\) 2.56086 0.0875796
\(856\) 116.102 3.96827
\(857\) 3.53704 0.120823 0.0604114 0.998174i \(-0.480759\pi\)
0.0604114 + 0.998174i \(0.480759\pi\)
\(858\) −11.2182 −0.382983
\(859\) −0.251805 −0.00859147 −0.00429573 0.999991i \(-0.501367\pi\)
−0.00429573 + 0.999991i \(0.501367\pi\)
\(860\) 6.73470 0.229651
\(861\) 6.78653 0.231284
\(862\) 77.3447 2.63437
\(863\) −27.1322 −0.923591 −0.461796 0.886986i \(-0.652795\pi\)
−0.461796 + 0.886986i \(0.652795\pi\)
\(864\) −15.8978 −0.540853
\(865\) 4.68113 0.159163
\(866\) 60.6854 2.06217
\(867\) −2.31872 −0.0787479
\(868\) 96.7385 3.28352
\(869\) 0.180868 0.00613551
\(870\) −13.8067 −0.468090
\(871\) −26.0090 −0.881283
\(872\) 134.613 4.55858
\(873\) −43.2925 −1.46523
\(874\) −20.9715 −0.709373
\(875\) −7.28136 −0.246155
\(876\) −186.592 −6.30434
\(877\) 31.9378 1.07846 0.539231 0.842158i \(-0.318715\pi\)
0.539231 + 0.842158i \(0.318715\pi\)
\(878\) −83.5498 −2.81967
\(879\) −35.9197 −1.21154
\(880\) 1.29959 0.0438091
\(881\) −2.65980 −0.0896110 −0.0448055 0.998996i \(-0.514267\pi\)
−0.0448055 + 0.998996i \(0.514267\pi\)
\(882\) −27.7162 −0.933254
\(883\) −17.9088 −0.602678 −0.301339 0.953517i \(-0.597434\pi\)
−0.301339 + 0.953517i \(0.597434\pi\)
\(884\) −14.8249 −0.498617
\(885\) 2.91400 0.0979529
\(886\) 78.6835 2.64342
\(887\) 49.1193 1.64927 0.824633 0.565668i \(-0.191382\pi\)
0.824633 + 0.565668i \(0.191382\pi\)
\(888\) −65.2543 −2.18979
\(889\) −52.5567 −1.76270
\(890\) 3.52898 0.118292
\(891\) −6.34995 −0.212731
\(892\) −30.3306 −1.01554
\(893\) 3.09896 0.103703
\(894\) −99.3556 −3.32295
\(895\) 4.67768 0.156358
\(896\) −5.00730 −0.167282
\(897\) 11.3515 0.379016
\(898\) 84.4587 2.81842
\(899\) −61.8047 −2.06130
\(900\) −57.2447 −1.90816
\(901\) 9.64958 0.321474
\(902\) 1.37263 0.0457037
\(903\) −50.2672 −1.67279
\(904\) 45.3684 1.50893
\(905\) 2.90599 0.0965985
\(906\) 49.9542 1.65962
\(907\) −12.9245 −0.429150 −0.214575 0.976708i \(-0.568837\pi\)
−0.214575 + 0.976708i \(0.568837\pi\)
\(908\) 63.2354 2.09854
\(909\) −34.5408 −1.14564
\(910\) 5.84235 0.193672
\(911\) −23.5415 −0.779966 −0.389983 0.920822i \(-0.627519\pi\)
−0.389983 + 0.920822i \(0.627519\pi\)
\(912\) −114.698 −3.79804
\(913\) 1.92325 0.0636503
\(914\) −105.025 −3.47391
\(915\) 3.17907 0.105097
\(916\) 68.0635 2.24888
\(917\) 8.47841 0.279982
\(918\) −3.78764 −0.125011
\(919\) −30.5981 −1.00934 −0.504670 0.863312i \(-0.668386\pi\)
−0.504670 + 0.863312i \(0.668386\pi\)
\(920\) −2.60392 −0.0858487
\(921\) −24.2847 −0.800207
\(922\) 99.3236 3.27105
\(923\) 39.2959 1.29344
\(924\) −23.1171 −0.760496
\(925\) 18.5848 0.611065
\(926\) 10.9707 0.360519
\(927\) −11.2124 −0.368264
\(928\) 115.611 3.79512
\(929\) 8.54374 0.280311 0.140155 0.990130i \(-0.455240\pi\)
0.140155 + 0.990130i \(0.455240\pi\)
\(930\) 7.71909 0.253119
\(931\) 22.1916 0.727300
\(932\) −84.1514 −2.75647
\(933\) 18.8407 0.616817
\(934\) −27.9803 −0.915543
\(935\) 0.130961 0.00428289
\(936\) 54.3384 1.77611
\(937\) −10.6927 −0.349315 −0.174657 0.984629i \(-0.555882\pi\)
−0.174657 + 0.984629i \(0.555882\pi\)
\(938\) −75.6383 −2.46968
\(939\) 23.0987 0.753797
\(940\) 0.653569 0.0213171
\(941\) −27.1679 −0.885648 −0.442824 0.896609i \(-0.646023\pi\)
−0.442824 + 0.896609i \(0.646023\pi\)
\(942\) 53.2233 1.73411
\(943\) −1.38895 −0.0452303
\(944\) −57.6892 −1.87762
\(945\) 1.05768 0.0344064
\(946\) −10.1670 −0.330557
\(947\) 1.95002 0.0633671 0.0316835 0.999498i \(-0.489913\pi\)
0.0316835 + 0.999498i \(0.489913\pi\)
\(948\) −3.36657 −0.109341
\(949\) −50.4443 −1.63749
\(950\) 64.6841 2.09863
\(951\) −34.9537 −1.13345
\(952\) −25.3824 −0.822648
\(953\) 55.5344 1.79893 0.899467 0.436988i \(-0.143955\pi\)
0.899467 + 0.436988i \(0.143955\pi\)
\(954\) −60.0758 −1.94503
\(955\) −3.81308 −0.123389
\(956\) 145.718 4.71286
\(957\) 14.7691 0.477418
\(958\) −57.2816 −1.85068
\(959\) 44.3067 1.43074
\(960\) −4.49091 −0.144943
\(961\) 3.55400 0.114645
\(962\) −29.9645 −0.966095
\(963\) −36.7854 −1.18539
\(964\) 131.830 4.24595
\(965\) −2.95451 −0.0951089
\(966\) 33.0119 1.06214
\(967\) 34.5966 1.11255 0.556276 0.830998i \(-0.312230\pi\)
0.556276 + 0.830998i \(0.312230\pi\)
\(968\) 79.7536 2.56338
\(969\) −11.5583 −0.371306
\(970\) 10.3169 0.331256
\(971\) −12.5948 −0.404188 −0.202094 0.979366i \(-0.564775\pi\)
−0.202094 + 0.979366i \(0.564775\pi\)
\(972\) 97.1012 3.11452
\(973\) 52.7662 1.69161
\(974\) −71.5060 −2.29120
\(975\) −35.0123 −1.12129
\(976\) −62.9370 −2.01457
\(977\) 22.4304 0.717612 0.358806 0.933412i \(-0.383184\pi\)
0.358806 + 0.933412i \(0.383184\pi\)
\(978\) 128.102 4.09626
\(979\) −3.77498 −0.120649
\(980\) 4.68019 0.149503
\(981\) −42.6505 −1.36173
\(982\) −4.61514 −0.147275
\(983\) 18.6869 0.596020 0.298010 0.954563i \(-0.403677\pi\)
0.298010 + 0.954563i \(0.403677\pi\)
\(984\) −15.0419 −0.479519
\(985\) −4.87709 −0.155397
\(986\) 27.5443 0.877190
\(987\) −4.87817 −0.155274
\(988\) −73.8991 −2.35104
\(989\) 10.2878 0.327133
\(990\) −0.815331 −0.0259129
\(991\) −25.3301 −0.804639 −0.402319 0.915499i \(-0.631796\pi\)
−0.402319 + 0.915499i \(0.631796\pi\)
\(992\) −64.6363 −2.05220
\(993\) −77.5671 −2.46152
\(994\) 114.278 3.62469
\(995\) −3.91131 −0.123997
\(996\) −35.7983 −1.13431
\(997\) 13.6496 0.432286 0.216143 0.976362i \(-0.430652\pi\)
0.216143 + 0.976362i \(0.430652\pi\)
\(998\) −64.6216 −2.04556
\(999\) −5.42470 −0.171630
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 \(a_p\))