Properties

Label 6026.2.a.h.1.8
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(24\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-1.04677 q^{3}\) \(+1.00000 q^{4}\) \(+3.02542 q^{5}\) \(+1.04677 q^{6}\) \(-3.14954 q^{7}\) \(-1.00000 q^{8}\) \(-1.90427 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-1.04677 q^{3}\) \(+1.00000 q^{4}\) \(+3.02542 q^{5}\) \(+1.04677 q^{6}\) \(-3.14954 q^{7}\) \(-1.00000 q^{8}\) \(-1.90427 q^{9}\) \(-3.02542 q^{10}\) \(+5.21999 q^{11}\) \(-1.04677 q^{12}\) \(-5.14076 q^{13}\) \(+3.14954 q^{14}\) \(-3.16692 q^{15}\) \(+1.00000 q^{16}\) \(+3.04404 q^{17}\) \(+1.90427 q^{18}\) \(-1.27389 q^{19}\) \(+3.02542 q^{20}\) \(+3.29684 q^{21}\) \(-5.21999 q^{22}\) \(-1.00000 q^{23}\) \(+1.04677 q^{24}\) \(+4.15319 q^{25}\) \(+5.14076 q^{26}\) \(+5.13364 q^{27}\) \(-3.14954 q^{28}\) \(-2.37446 q^{29}\) \(+3.16692 q^{30}\) \(-3.86161 q^{31}\) \(-1.00000 q^{32}\) \(-5.46412 q^{33}\) \(-3.04404 q^{34}\) \(-9.52869 q^{35}\) \(-1.90427 q^{36}\) \(+10.8947 q^{37}\) \(+1.27389 q^{38}\) \(+5.38118 q^{39}\) \(-3.02542 q^{40}\) \(-2.37418 q^{41}\) \(-3.29684 q^{42}\) \(-9.52894 q^{43}\) \(+5.21999 q^{44}\) \(-5.76124 q^{45}\) \(+1.00000 q^{46}\) \(+13.1179 q^{47}\) \(-1.04677 q^{48}\) \(+2.91960 q^{49}\) \(-4.15319 q^{50}\) \(-3.18641 q^{51}\) \(-5.14076 q^{52}\) \(-0.167248 q^{53}\) \(-5.13364 q^{54}\) \(+15.7927 q^{55}\) \(+3.14954 q^{56}\) \(+1.33347 q^{57}\) \(+2.37446 q^{58}\) \(-7.58569 q^{59}\) \(-3.16692 q^{60}\) \(-0.958220 q^{61}\) \(+3.86161 q^{62}\) \(+5.99759 q^{63}\) \(+1.00000 q^{64}\) \(-15.5530 q^{65}\) \(+5.46412 q^{66}\) \(+13.0601 q^{67}\) \(+3.04404 q^{68}\) \(+1.04677 q^{69}\) \(+9.52869 q^{70}\) \(+0.625838 q^{71}\) \(+1.90427 q^{72}\) \(+6.70674 q^{73}\) \(-10.8947 q^{74}\) \(-4.34743 q^{75}\) \(-1.27389 q^{76}\) \(-16.4406 q^{77}\) \(-5.38118 q^{78}\) \(+1.23334 q^{79}\) \(+3.02542 q^{80}\) \(+0.339086 q^{81}\) \(+2.37418 q^{82}\) \(-17.6984 q^{83}\) \(+3.29684 q^{84}\) \(+9.20952 q^{85}\) \(+9.52894 q^{86}\) \(+2.48551 q^{87}\) \(-5.21999 q^{88}\) \(-16.6964 q^{89}\) \(+5.76124 q^{90}\) \(+16.1910 q^{91}\) \(-1.00000 q^{92}\) \(+4.04221 q^{93}\) \(-13.1179 q^{94}\) \(-3.85407 q^{95}\) \(+1.04677 q^{96}\) \(+18.5688 q^{97}\) \(-2.91960 q^{98}\) \(-9.94029 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 27q^{18} \) \(\mathstrut -\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut q^{20} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut -\mathstrut 7q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 23q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 27q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 20q^{38} \) \(\mathstrut -\mathstrut 39q^{39} \) \(\mathstrut +\mathstrut q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut -\mathstrut 44q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 13q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 32q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut -\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut +\mathstrut 21q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut -\mathstrut 13q^{55} \) \(\mathstrut +\mathstrut 7q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 6q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 40q^{61} \) \(\mathstrut +\mathstrut 23q^{62} \) \(\mathstrut -\mathstrut 54q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 29q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 17q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 5q^{70} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 27q^{72} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut +\mathstrut 6q^{74} \) \(\mathstrut -\mathstrut 36q^{75} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 39q^{78} \) \(\mathstrut -\mathstrut 53q^{79} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut +\mathstrut 24q^{81} \) \(\mathstrut +\mathstrut q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 37q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 7q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut +\mathstrut 13q^{90} \) \(\mathstrut -\mathstrut 44q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 23q^{93} \) \(\mathstrut -\mathstrut 32q^{94} \) \(\mathstrut +\mathstrut 28q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut -\mathstrut 20q^{97} \) \(\mathstrut +\mathstrut 13q^{98} \) \(\mathstrut -\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.04677 −0.604352 −0.302176 0.953252i \(-0.597713\pi\)
−0.302176 + 0.953252i \(0.597713\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.02542 1.35301 0.676505 0.736438i \(-0.263494\pi\)
0.676505 + 0.736438i \(0.263494\pi\)
\(6\) 1.04677 0.427342
\(7\) −3.14954 −1.19041 −0.595207 0.803572i \(-0.702930\pi\)
−0.595207 + 0.803572i \(0.702930\pi\)
\(8\) −1.00000 −0.353553
\(9\) −1.90427 −0.634758
\(10\) −3.02542 −0.956723
\(11\) 5.21999 1.57389 0.786943 0.617026i \(-0.211663\pi\)
0.786943 + 0.617026i \(0.211663\pi\)
\(12\) −1.04677 −0.302176
\(13\) −5.14076 −1.42579 −0.712895 0.701271i \(-0.752616\pi\)
−0.712895 + 0.701271i \(0.752616\pi\)
\(14\) 3.14954 0.841750
\(15\) −3.16692 −0.817695
\(16\) 1.00000 0.250000
\(17\) 3.04404 0.738289 0.369145 0.929372i \(-0.379651\pi\)
0.369145 + 0.929372i \(0.379651\pi\)
\(18\) 1.90427 0.448842
\(19\) −1.27389 −0.292251 −0.146126 0.989266i \(-0.546680\pi\)
−0.146126 + 0.989266i \(0.546680\pi\)
\(20\) 3.02542 0.676505
\(21\) 3.29684 0.719430
\(22\) −5.21999 −1.11291
\(23\) −1.00000 −0.208514
\(24\) 1.04677 0.213671
\(25\) 4.15319 0.830638
\(26\) 5.14076 1.00819
\(27\) 5.13364 0.987970
\(28\) −3.14954 −0.595207
\(29\) −2.37446 −0.440926 −0.220463 0.975395i \(-0.570757\pi\)
−0.220463 + 0.975395i \(0.570757\pi\)
\(30\) 3.16692 0.578198
\(31\) −3.86161 −0.693565 −0.346782 0.937946i \(-0.612726\pi\)
−0.346782 + 0.937946i \(0.612726\pi\)
\(32\) −1.00000 −0.176777
\(33\) −5.46412 −0.951181
\(34\) −3.04404 −0.522049
\(35\) −9.52869 −1.61064
\(36\) −1.90427 −0.317379
\(37\) 10.8947 1.79108 0.895540 0.444981i \(-0.146790\pi\)
0.895540 + 0.444981i \(0.146790\pi\)
\(38\) 1.27389 0.206653
\(39\) 5.38118 0.861679
\(40\) −3.02542 −0.478361
\(41\) −2.37418 −0.370785 −0.185393 0.982665i \(-0.559356\pi\)
−0.185393 + 0.982665i \(0.559356\pi\)
\(42\) −3.29684 −0.508714
\(43\) −9.52894 −1.45315 −0.726575 0.687087i \(-0.758889\pi\)
−0.726575 + 0.687087i \(0.758889\pi\)
\(44\) 5.21999 0.786943
\(45\) −5.76124 −0.858835
\(46\) 1.00000 0.147442
\(47\) 13.1179 1.91345 0.956725 0.290995i \(-0.0939863\pi\)
0.956725 + 0.290995i \(0.0939863\pi\)
\(48\) −1.04677 −0.151088
\(49\) 2.91960 0.417086
\(50\) −4.15319 −0.587350
\(51\) −3.18641 −0.446187
\(52\) −5.14076 −0.712895
\(53\) −0.167248 −0.0229733 −0.0114867 0.999934i \(-0.503656\pi\)
−0.0114867 + 0.999934i \(0.503656\pi\)
\(54\) −5.13364 −0.698600
\(55\) 15.7927 2.12948
\(56\) 3.14954 0.420875
\(57\) 1.33347 0.176623
\(58\) 2.37446 0.311782
\(59\) −7.58569 −0.987573 −0.493786 0.869583i \(-0.664387\pi\)
−0.493786 + 0.869583i \(0.664387\pi\)
\(60\) −3.16692 −0.408848
\(61\) −0.958220 −0.122687 −0.0613437 0.998117i \(-0.519539\pi\)
−0.0613437 + 0.998117i \(0.519539\pi\)
\(62\) 3.86161 0.490424
\(63\) 5.99759 0.755625
\(64\) 1.00000 0.125000
\(65\) −15.5530 −1.92911
\(66\) 5.46412 0.672587
\(67\) 13.0601 1.59555 0.797774 0.602956i \(-0.206011\pi\)
0.797774 + 0.602956i \(0.206011\pi\)
\(68\) 3.04404 0.369145
\(69\) 1.04677 0.126016
\(70\) 9.52869 1.13890
\(71\) 0.625838 0.0742733 0.0371366 0.999310i \(-0.488176\pi\)
0.0371366 + 0.999310i \(0.488176\pi\)
\(72\) 1.90427 0.224421
\(73\) 6.70674 0.784964 0.392482 0.919760i \(-0.371616\pi\)
0.392482 + 0.919760i \(0.371616\pi\)
\(74\) −10.8947 −1.26648
\(75\) −4.34743 −0.501998
\(76\) −1.27389 −0.146126
\(77\) −16.4406 −1.87358
\(78\) −5.38118 −0.609299
\(79\) 1.23334 0.138762 0.0693809 0.997590i \(-0.477898\pi\)
0.0693809 + 0.997590i \(0.477898\pi\)
\(80\) 3.02542 0.338253
\(81\) 0.339086 0.0376762
\(82\) 2.37418 0.262185
\(83\) −17.6984 −1.94265 −0.971325 0.237757i \(-0.923588\pi\)
−0.971325 + 0.237757i \(0.923588\pi\)
\(84\) 3.29684 0.359715
\(85\) 9.20952 0.998913
\(86\) 9.52894 1.02753
\(87\) 2.48551 0.266474
\(88\) −5.21999 −0.556453
\(89\) −16.6964 −1.76982 −0.884908 0.465766i \(-0.845779\pi\)
−0.884908 + 0.465766i \(0.845779\pi\)
\(90\) 5.76124 0.607288
\(91\) 16.1910 1.69728
\(92\) −1.00000 −0.104257
\(93\) 4.04221 0.419158
\(94\) −13.1179 −1.35301
\(95\) −3.85407 −0.395419
\(96\) 1.04677 0.106835
\(97\) 18.5688 1.88537 0.942686 0.333682i \(-0.108291\pi\)
0.942686 + 0.333682i \(0.108291\pi\)
\(98\) −2.91960 −0.294924
\(99\) −9.94029 −0.999037
\(100\) 4.15319 0.415319
\(101\) −4.09930 −0.407895 −0.203948 0.978982i \(-0.565377\pi\)
−0.203948 + 0.978982i \(0.565377\pi\)
\(102\) 3.18641 0.315502
\(103\) 2.13595 0.210461 0.105230 0.994448i \(-0.466442\pi\)
0.105230 + 0.994448i \(0.466442\pi\)
\(104\) 5.14076 0.504093
\(105\) 9.97434 0.973396
\(106\) 0.167248 0.0162446
\(107\) −10.9910 −1.06254 −0.531271 0.847202i \(-0.678285\pi\)
−0.531271 + 0.847202i \(0.678285\pi\)
\(108\) 5.13364 0.493985
\(109\) −18.2661 −1.74958 −0.874789 0.484503i \(-0.839000\pi\)
−0.874789 + 0.484503i \(0.839000\pi\)
\(110\) −15.7927 −1.50577
\(111\) −11.4043 −1.08244
\(112\) −3.14954 −0.297604
\(113\) 7.36243 0.692600 0.346300 0.938124i \(-0.387438\pi\)
0.346300 + 0.938124i \(0.387438\pi\)
\(114\) −1.33347 −0.124891
\(115\) −3.02542 −0.282122
\(116\) −2.37446 −0.220463
\(117\) 9.78941 0.905031
\(118\) 7.58569 0.698319
\(119\) −9.58734 −0.878870
\(120\) 3.16692 0.289099
\(121\) 16.2483 1.47712
\(122\) 0.958220 0.0867531
\(123\) 2.48522 0.224085
\(124\) −3.86161 −0.346782
\(125\) −2.56196 −0.229149
\(126\) −5.99759 −0.534308
\(127\) −8.81708 −0.782389 −0.391195 0.920308i \(-0.627938\pi\)
−0.391195 + 0.920308i \(0.627938\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 9.97460 0.878214
\(130\) 15.5530 1.36409
\(131\) −1.00000 −0.0873704
\(132\) −5.46412 −0.475591
\(133\) 4.01218 0.347900
\(134\) −13.0601 −1.12822
\(135\) 15.5314 1.33673
\(136\) −3.04404 −0.261025
\(137\) −9.26831 −0.791845 −0.395923 0.918284i \(-0.629575\pi\)
−0.395923 + 0.918284i \(0.629575\pi\)
\(138\) −1.04677 −0.0891069
\(139\) 2.50308 0.212308 0.106154 0.994350i \(-0.466146\pi\)
0.106154 + 0.994350i \(0.466146\pi\)
\(140\) −9.52869 −0.805321
\(141\) −13.7315 −1.15640
\(142\) −0.625838 −0.0525191
\(143\) −26.8347 −2.24403
\(144\) −1.90427 −0.158690
\(145\) −7.18374 −0.596577
\(146\) −6.70674 −0.555054
\(147\) −3.05615 −0.252067
\(148\) 10.8947 0.895540
\(149\) −4.75376 −0.389443 −0.194722 0.980859i \(-0.562380\pi\)
−0.194722 + 0.980859i \(0.562380\pi\)
\(150\) 4.34743 0.354966
\(151\) −12.1325 −0.987328 −0.493664 0.869653i \(-0.664343\pi\)
−0.493664 + 0.869653i \(0.664343\pi\)
\(152\) 1.27389 0.103326
\(153\) −5.79670 −0.468635
\(154\) 16.4406 1.32482
\(155\) −11.6830 −0.938400
\(156\) 5.38118 0.430840
\(157\) −10.9164 −0.871223 −0.435612 0.900135i \(-0.643468\pi\)
−0.435612 + 0.900135i \(0.643468\pi\)
\(158\) −1.23334 −0.0981194
\(159\) 0.175070 0.0138840
\(160\) −3.02542 −0.239181
\(161\) 3.14954 0.248219
\(162\) −0.339086 −0.0266411
\(163\) −13.2609 −1.03867 −0.519336 0.854570i \(-0.673821\pi\)
−0.519336 + 0.854570i \(0.673821\pi\)
\(164\) −2.37418 −0.185393
\(165\) −16.5313 −1.28696
\(166\) 17.6984 1.37366
\(167\) −23.6252 −1.82818 −0.914088 0.405516i \(-0.867092\pi\)
−0.914088 + 0.405516i \(0.867092\pi\)
\(168\) −3.29684 −0.254357
\(169\) 13.4274 1.03288
\(170\) −9.20952 −0.706338
\(171\) 2.42584 0.185509
\(172\) −9.52894 −0.726575
\(173\) 19.8326 1.50784 0.753921 0.656965i \(-0.228160\pi\)
0.753921 + 0.656965i \(0.228160\pi\)
\(174\) −2.48551 −0.188426
\(175\) −13.0806 −0.988803
\(176\) 5.21999 0.393471
\(177\) 7.94046 0.596842
\(178\) 16.6964 1.25145
\(179\) −16.7626 −1.25289 −0.626447 0.779464i \(-0.715491\pi\)
−0.626447 + 0.779464i \(0.715491\pi\)
\(180\) −5.76124 −0.429417
\(181\) 7.59423 0.564475 0.282237 0.959345i \(-0.408923\pi\)
0.282237 + 0.959345i \(0.408923\pi\)
\(182\) −16.1910 −1.20016
\(183\) 1.00303 0.0741465
\(184\) 1.00000 0.0737210
\(185\) 32.9611 2.42335
\(186\) −4.04221 −0.296389
\(187\) 15.8899 1.16198
\(188\) 13.1179 0.956725
\(189\) −16.1686 −1.17609
\(190\) 3.85407 0.279603
\(191\) 22.6661 1.64006 0.820029 0.572321i \(-0.193957\pi\)
0.820029 + 0.572321i \(0.193957\pi\)
\(192\) −1.04677 −0.0755440
\(193\) −7.92638 −0.570553 −0.285277 0.958445i \(-0.592085\pi\)
−0.285277 + 0.958445i \(0.592085\pi\)
\(194\) −18.5688 −1.33316
\(195\) 16.2804 1.16586
\(196\) 2.91960 0.208543
\(197\) 15.4109 1.09798 0.548991 0.835829i \(-0.315012\pi\)
0.548991 + 0.835829i \(0.315012\pi\)
\(198\) 9.94029 0.706426
\(199\) −20.8953 −1.48123 −0.740613 0.671932i \(-0.765465\pi\)
−0.740613 + 0.671932i \(0.765465\pi\)
\(200\) −4.15319 −0.293675
\(201\) −13.6709 −0.964273
\(202\) 4.09930 0.288426
\(203\) 7.47845 0.524884
\(204\) −3.18641 −0.223093
\(205\) −7.18291 −0.501676
\(206\) −2.13595 −0.148818
\(207\) 1.90427 0.132356
\(208\) −5.14076 −0.356447
\(209\) −6.64971 −0.459970
\(210\) −9.97434 −0.688295
\(211\) 5.23930 0.360689 0.180344 0.983604i \(-0.442279\pi\)
0.180344 + 0.983604i \(0.442279\pi\)
\(212\) −0.167248 −0.0114867
\(213\) −0.655107 −0.0448872
\(214\) 10.9910 0.751330
\(215\) −28.8291 −1.96613
\(216\) −5.13364 −0.349300
\(217\) 12.1623 0.825629
\(218\) 18.2661 1.23714
\(219\) −7.02041 −0.474395
\(220\) 15.7927 1.06474
\(221\) −15.6487 −1.05264
\(222\) 11.4043 0.765403
\(223\) 14.0674 0.942023 0.471012 0.882127i \(-0.343889\pi\)
0.471012 + 0.882127i \(0.343889\pi\)
\(224\) 3.14954 0.210437
\(225\) −7.90881 −0.527254
\(226\) −7.36243 −0.489742
\(227\) 8.01412 0.531916 0.265958 0.963985i \(-0.414312\pi\)
0.265958 + 0.963985i \(0.414312\pi\)
\(228\) 1.33347 0.0883114
\(229\) 1.99324 0.131717 0.0658584 0.997829i \(-0.479021\pi\)
0.0658584 + 0.997829i \(0.479021\pi\)
\(230\) 3.02542 0.199491
\(231\) 17.2095 1.13230
\(232\) 2.37446 0.155891
\(233\) 22.3493 1.46415 0.732075 0.681224i \(-0.238552\pi\)
0.732075 + 0.681224i \(0.238552\pi\)
\(234\) −9.78941 −0.639954
\(235\) 39.6873 2.58892
\(236\) −7.58569 −0.493786
\(237\) −1.29102 −0.0838610
\(238\) 9.58734 0.621455
\(239\) −20.8519 −1.34880 −0.674400 0.738366i \(-0.735598\pi\)
−0.674400 + 0.738366i \(0.735598\pi\)
\(240\) −3.16692 −0.204424
\(241\) 23.7143 1.52757 0.763786 0.645469i \(-0.223338\pi\)
0.763786 + 0.645469i \(0.223338\pi\)
\(242\) −16.2483 −1.04448
\(243\) −15.7559 −1.01074
\(244\) −0.958220 −0.0613437
\(245\) 8.83303 0.564322
\(246\) −2.48522 −0.158452
\(247\) 6.54878 0.416689
\(248\) 3.86161 0.245212
\(249\) 18.5261 1.17404
\(250\) 2.56196 0.162033
\(251\) −4.83713 −0.305317 −0.152658 0.988279i \(-0.548783\pi\)
−0.152658 + 0.988279i \(0.548783\pi\)
\(252\) 5.99759 0.377813
\(253\) −5.21999 −0.328178
\(254\) 8.81708 0.553233
\(255\) −9.64024 −0.603696
\(256\) 1.00000 0.0625000
\(257\) −14.7777 −0.921809 −0.460904 0.887450i \(-0.652475\pi\)
−0.460904 + 0.887450i \(0.652475\pi\)
\(258\) −9.97460 −0.620991
\(259\) −34.3133 −2.13213
\(260\) −15.5530 −0.964554
\(261\) 4.52162 0.279881
\(262\) 1.00000 0.0617802
\(263\) 8.81903 0.543805 0.271902 0.962325i \(-0.412347\pi\)
0.271902 + 0.962325i \(0.412347\pi\)
\(264\) 5.46412 0.336293
\(265\) −0.505997 −0.0310832
\(266\) −4.01218 −0.246002
\(267\) 17.4773 1.06959
\(268\) 13.0601 0.797774
\(269\) 30.6979 1.87168 0.935841 0.352421i \(-0.114642\pi\)
0.935841 + 0.352421i \(0.114642\pi\)
\(270\) −15.5314 −0.945214
\(271\) −30.0589 −1.82595 −0.912975 0.408016i \(-0.866221\pi\)
−0.912975 + 0.408016i \(0.866221\pi\)
\(272\) 3.04404 0.184572
\(273\) −16.9483 −1.02576
\(274\) 9.26831 0.559919
\(275\) 21.6796 1.30733
\(276\) 1.04677 0.0630081
\(277\) −30.1294 −1.81030 −0.905150 0.425093i \(-0.860241\pi\)
−0.905150 + 0.425093i \(0.860241\pi\)
\(278\) −2.50308 −0.150125
\(279\) 7.35356 0.440246
\(280\) 9.52869 0.569448
\(281\) 0.152255 0.00908275 0.00454137 0.999990i \(-0.498554\pi\)
0.00454137 + 0.999990i \(0.498554\pi\)
\(282\) 13.7315 0.817697
\(283\) −14.5431 −0.864499 −0.432250 0.901754i \(-0.642280\pi\)
−0.432250 + 0.901754i \(0.642280\pi\)
\(284\) 0.625838 0.0371366
\(285\) 4.03432 0.238972
\(286\) 26.8347 1.58677
\(287\) 7.47758 0.441388
\(288\) 1.90427 0.112210
\(289\) −7.73379 −0.454929
\(290\) 7.18374 0.421844
\(291\) −19.4372 −1.13943
\(292\) 6.70674 0.392482
\(293\) 26.8655 1.56950 0.784750 0.619813i \(-0.212791\pi\)
0.784750 + 0.619813i \(0.212791\pi\)
\(294\) 3.05615 0.178238
\(295\) −22.9499 −1.33620
\(296\) −10.8947 −0.633242
\(297\) 26.7976 1.55495
\(298\) 4.75376 0.275378
\(299\) 5.14076 0.297298
\(300\) −4.34743 −0.250999
\(301\) 30.0118 1.72985
\(302\) 12.1325 0.698147
\(303\) 4.29102 0.246513
\(304\) −1.27389 −0.0730628
\(305\) −2.89902 −0.165997
\(306\) 5.79670 0.331375
\(307\) −7.51874 −0.429117 −0.214559 0.976711i \(-0.568831\pi\)
−0.214559 + 0.976711i \(0.568831\pi\)
\(308\) −16.4406 −0.936788
\(309\) −2.23584 −0.127193
\(310\) 11.6830 0.663549
\(311\) −16.2277 −0.920189 −0.460094 0.887870i \(-0.652184\pi\)
−0.460094 + 0.887870i \(0.652184\pi\)
\(312\) −5.38118 −0.304650
\(313\) −18.0804 −1.02196 −0.510981 0.859592i \(-0.670718\pi\)
−0.510981 + 0.859592i \(0.670718\pi\)
\(314\) 10.9164 0.616048
\(315\) 18.1452 1.02237
\(316\) 1.23334 0.0693809
\(317\) −10.9186 −0.613249 −0.306625 0.951831i \(-0.599200\pi\)
−0.306625 + 0.951831i \(0.599200\pi\)
\(318\) −0.175070 −0.00981746
\(319\) −12.3946 −0.693966
\(320\) 3.02542 0.169126
\(321\) 11.5051 0.642149
\(322\) −3.14954 −0.175517
\(323\) −3.87779 −0.215766
\(324\) 0.339086 0.0188381
\(325\) −21.3505 −1.18431
\(326\) 13.2609 0.734451
\(327\) 19.1204 1.05736
\(328\) 2.37418 0.131092
\(329\) −41.3155 −2.27780
\(330\) 16.5313 0.910017
\(331\) 7.35143 0.404071 0.202036 0.979378i \(-0.435244\pi\)
0.202036 + 0.979378i \(0.435244\pi\)
\(332\) −17.6984 −0.971325
\(333\) −20.7465 −1.13690
\(334\) 23.6252 1.29272
\(335\) 39.5124 2.15879
\(336\) 3.29684 0.179857
\(337\) −24.7369 −1.34751 −0.673753 0.738957i \(-0.735319\pi\)
−0.673753 + 0.738957i \(0.735319\pi\)
\(338\) −13.4274 −0.730353
\(339\) −7.70677 −0.418574
\(340\) 9.20952 0.499457
\(341\) −20.1575 −1.09159
\(342\) −2.42584 −0.131175
\(343\) 12.8514 0.693909
\(344\) 9.52894 0.513766
\(345\) 3.16692 0.170501
\(346\) −19.8326 −1.06621
\(347\) 2.02795 0.108866 0.0544330 0.998517i \(-0.482665\pi\)
0.0544330 + 0.998517i \(0.482665\pi\)
\(348\) 2.48551 0.133237
\(349\) −29.6327 −1.58620 −0.793101 0.609090i \(-0.791535\pi\)
−0.793101 + 0.609090i \(0.791535\pi\)
\(350\) 13.0806 0.699189
\(351\) −26.3908 −1.40864
\(352\) −5.21999 −0.278226
\(353\) −0.0127493 −0.000678578 0 −0.000339289 1.00000i \(-0.500108\pi\)
−0.000339289 1.00000i \(0.500108\pi\)
\(354\) −7.94046 −0.422031
\(355\) 1.89342 0.100493
\(356\) −16.6964 −0.884908
\(357\) 10.0357 0.531147
\(358\) 16.7626 0.885929
\(359\) −8.48428 −0.447783 −0.223892 0.974614i \(-0.571876\pi\)
−0.223892 + 0.974614i \(0.571876\pi\)
\(360\) 5.76124 0.303644
\(361\) −17.3772 −0.914589
\(362\) −7.59423 −0.399144
\(363\) −17.0082 −0.892698
\(364\) 16.1910 0.848640
\(365\) 20.2907 1.06207
\(366\) −1.00303 −0.0524295
\(367\) 13.2569 0.692007 0.346003 0.938233i \(-0.387539\pi\)
0.346003 + 0.938233i \(0.387539\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 4.52110 0.235359
\(370\) −32.9611 −1.71357
\(371\) 0.526755 0.0273478
\(372\) 4.04221 0.209579
\(373\) 20.5034 1.06163 0.530813 0.847489i \(-0.321887\pi\)
0.530813 + 0.847489i \(0.321887\pi\)
\(374\) −15.8899 −0.821646
\(375\) 2.68178 0.138487
\(376\) −13.1179 −0.676506
\(377\) 12.2065 0.628667
\(378\) 16.1686 0.831624
\(379\) 8.74897 0.449405 0.224702 0.974427i \(-0.427859\pi\)
0.224702 + 0.974427i \(0.427859\pi\)
\(380\) −3.85407 −0.197710
\(381\) 9.22945 0.472839
\(382\) −22.6661 −1.15970
\(383\) 9.41680 0.481176 0.240588 0.970627i \(-0.422660\pi\)
0.240588 + 0.970627i \(0.422660\pi\)
\(384\) 1.04677 0.0534177
\(385\) −49.7397 −2.53497
\(386\) 7.92638 0.403442
\(387\) 18.1457 0.922399
\(388\) 18.5688 0.942686
\(389\) −18.5320 −0.939612 −0.469806 0.882770i \(-0.655676\pi\)
−0.469806 + 0.882770i \(0.655676\pi\)
\(390\) −16.2804 −0.824388
\(391\) −3.04404 −0.153944
\(392\) −2.91960 −0.147462
\(393\) 1.04677 0.0528025
\(394\) −15.4109 −0.776390
\(395\) 3.73138 0.187746
\(396\) −9.94029 −0.499518
\(397\) 8.99391 0.451392 0.225696 0.974198i \(-0.427534\pi\)
0.225696 + 0.974198i \(0.427534\pi\)
\(398\) 20.8953 1.04739
\(399\) −4.19982 −0.210254
\(400\) 4.15319 0.207659
\(401\) 6.04775 0.302010 0.151005 0.988533i \(-0.451749\pi\)
0.151005 + 0.988533i \(0.451749\pi\)
\(402\) 13.6709 0.681844
\(403\) 19.8516 0.988877
\(404\) −4.09930 −0.203948
\(405\) 1.02588 0.0509763
\(406\) −7.47845 −0.371149
\(407\) 56.8703 2.81896
\(408\) 3.18641 0.157751
\(409\) 4.90714 0.242642 0.121321 0.992613i \(-0.461287\pi\)
0.121321 + 0.992613i \(0.461287\pi\)
\(410\) 7.18291 0.354739
\(411\) 9.70178 0.478553
\(412\) 2.13595 0.105230
\(413\) 23.8914 1.17562
\(414\) −1.90427 −0.0935900
\(415\) −53.5451 −2.62843
\(416\) 5.14076 0.252046
\(417\) −2.62014 −0.128309
\(418\) 6.64971 0.325248
\(419\) −25.7798 −1.25942 −0.629712 0.776828i \(-0.716827\pi\)
−0.629712 + 0.776828i \(0.716827\pi\)
\(420\) 9.97434 0.486698
\(421\) −20.2967 −0.989201 −0.494600 0.869120i \(-0.664686\pi\)
−0.494600 + 0.869120i \(0.664686\pi\)
\(422\) −5.23930 −0.255045
\(423\) −24.9802 −1.21458
\(424\) 0.167248 0.00812230
\(425\) 12.6425 0.613251
\(426\) 0.655107 0.0317401
\(427\) 3.01795 0.146049
\(428\) −10.9910 −0.531271
\(429\) 28.0897 1.35618
\(430\) 28.8291 1.39026
\(431\) −23.0821 −1.11183 −0.555914 0.831240i \(-0.687632\pi\)
−0.555914 + 0.831240i \(0.687632\pi\)
\(432\) 5.13364 0.246993
\(433\) 36.2582 1.74246 0.871229 0.490876i \(-0.163323\pi\)
0.871229 + 0.490876i \(0.163323\pi\)
\(434\) −12.1623 −0.583808
\(435\) 7.51972 0.360543
\(436\) −18.2661 −0.874789
\(437\) 1.27389 0.0609386
\(438\) 7.02041 0.335448
\(439\) −14.4607 −0.690169 −0.345085 0.938572i \(-0.612150\pi\)
−0.345085 + 0.938572i \(0.612150\pi\)
\(440\) −15.7927 −0.752886
\(441\) −5.55972 −0.264749
\(442\) 15.6487 0.744332
\(443\) −22.1585 −1.05278 −0.526391 0.850242i \(-0.676455\pi\)
−0.526391 + 0.850242i \(0.676455\pi\)
\(444\) −11.4043 −0.541222
\(445\) −50.5137 −2.39458
\(446\) −14.0674 −0.666111
\(447\) 4.97609 0.235361
\(448\) −3.14954 −0.148802
\(449\) −31.8227 −1.50181 −0.750904 0.660412i \(-0.770382\pi\)
−0.750904 + 0.660412i \(0.770382\pi\)
\(450\) 7.90881 0.372825
\(451\) −12.3932 −0.583573
\(452\) 7.36243 0.346300
\(453\) 12.6999 0.596694
\(454\) −8.01412 −0.376121
\(455\) 48.9847 2.29644
\(456\) −1.33347 −0.0624456
\(457\) 16.0212 0.749441 0.374720 0.927138i \(-0.377739\pi\)
0.374720 + 0.927138i \(0.377739\pi\)
\(458\) −1.99324 −0.0931379
\(459\) 15.6270 0.729408
\(460\) −3.02542 −0.141061
\(461\) −19.3391 −0.900712 −0.450356 0.892849i \(-0.648703\pi\)
−0.450356 + 0.892849i \(0.648703\pi\)
\(462\) −17.2095 −0.800657
\(463\) −9.86263 −0.458355 −0.229178 0.973385i \(-0.573604\pi\)
−0.229178 + 0.973385i \(0.573604\pi\)
\(464\) −2.37446 −0.110231
\(465\) 12.2294 0.567125
\(466\) −22.3493 −1.03531
\(467\) −36.7936 −1.70260 −0.851302 0.524675i \(-0.824187\pi\)
−0.851302 + 0.524675i \(0.824187\pi\)
\(468\) 9.78941 0.452516
\(469\) −41.1334 −1.89936
\(470\) −39.6873 −1.83064
\(471\) 11.4269 0.526526
\(472\) 7.58569 0.349160
\(473\) −49.7410 −2.28709
\(474\) 1.29102 0.0592987
\(475\) −5.29072 −0.242755
\(476\) −9.58734 −0.439435
\(477\) 0.318487 0.0145825
\(478\) 20.8519 0.953746
\(479\) −8.67563 −0.396400 −0.198200 0.980162i \(-0.563510\pi\)
−0.198200 + 0.980162i \(0.563510\pi\)
\(480\) 3.16692 0.144549
\(481\) −56.0071 −2.55370
\(482\) −23.7143 −1.08016
\(483\) −3.29684 −0.150011
\(484\) 16.2483 0.738558
\(485\) 56.1783 2.55093
\(486\) 15.7559 0.714701
\(487\) 22.9577 1.04031 0.520156 0.854071i \(-0.325874\pi\)
0.520156 + 0.854071i \(0.325874\pi\)
\(488\) 0.958220 0.0433766
\(489\) 13.8811 0.627723
\(490\) −8.83303 −0.399036
\(491\) 18.4917 0.834518 0.417259 0.908788i \(-0.362991\pi\)
0.417259 + 0.908788i \(0.362991\pi\)
\(492\) 2.48522 0.112042
\(493\) −7.22795 −0.325531
\(494\) −6.54878 −0.294643
\(495\) −30.0736 −1.35171
\(496\) −3.86161 −0.173391
\(497\) −1.97110 −0.0884159
\(498\) −18.5261 −0.830175
\(499\) 24.6607 1.10396 0.551982 0.833856i \(-0.313872\pi\)
0.551982 + 0.833856i \(0.313872\pi\)
\(500\) −2.56196 −0.114575
\(501\) 24.7302 1.10486
\(502\) 4.83713 0.215892
\(503\) −28.3611 −1.26456 −0.632280 0.774740i \(-0.717881\pi\)
−0.632280 + 0.774740i \(0.717881\pi\)
\(504\) −5.99759 −0.267154
\(505\) −12.4021 −0.551887
\(506\) 5.21999 0.232057
\(507\) −14.0554 −0.624221
\(508\) −8.81708 −0.391195
\(509\) 14.8103 0.656456 0.328228 0.944598i \(-0.393549\pi\)
0.328228 + 0.944598i \(0.393549\pi\)
\(510\) 9.64024 0.426877
\(511\) −21.1231 −0.934433
\(512\) −1.00000 −0.0441942
\(513\) −6.53972 −0.288735
\(514\) 14.7777 0.651817
\(515\) 6.46214 0.284756
\(516\) 9.97460 0.439107
\(517\) 68.4755 3.01155
\(518\) 34.3133 1.50764
\(519\) −20.7601 −0.911268
\(520\) 15.5530 0.682043
\(521\) 18.7169 0.820001 0.410000 0.912085i \(-0.365529\pi\)
0.410000 + 0.912085i \(0.365529\pi\)
\(522\) −4.52162 −0.197906
\(523\) −32.1793 −1.40710 −0.703550 0.710645i \(-0.748403\pi\)
−0.703550 + 0.710645i \(0.748403\pi\)
\(524\) −1.00000 −0.0436852
\(525\) 13.6924 0.597585
\(526\) −8.81903 −0.384528
\(527\) −11.7549 −0.512051
\(528\) −5.46412 −0.237795
\(529\) 1.00000 0.0434783
\(530\) 0.505997 0.0219791
\(531\) 14.4452 0.626870
\(532\) 4.01218 0.173950
\(533\) 12.2051 0.528661
\(534\) −17.4773 −0.756316
\(535\) −33.2525 −1.43763
\(536\) −13.0601 −0.564111
\(537\) 17.5465 0.757189
\(538\) −30.6979 −1.32348
\(539\) 15.2403 0.656445
\(540\) 15.5314 0.668367
\(541\) −7.02657 −0.302096 −0.151048 0.988526i \(-0.548265\pi\)
−0.151048 + 0.988526i \(0.548265\pi\)
\(542\) 30.0589 1.29114
\(543\) −7.94941 −0.341142
\(544\) −3.04404 −0.130512
\(545\) −55.2628 −2.36720
\(546\) 16.9483 0.725318
\(547\) 21.4386 0.916647 0.458324 0.888785i \(-0.348450\pi\)
0.458324 + 0.888785i \(0.348450\pi\)
\(548\) −9.26831 −0.395923
\(549\) 1.82471 0.0778769
\(550\) −21.6796 −0.924421
\(551\) 3.02481 0.128861
\(552\) −1.04677 −0.0445534
\(553\) −3.88446 −0.165184
\(554\) 30.1294 1.28008
\(555\) −34.5027 −1.46456
\(556\) 2.50308 0.106154
\(557\) −4.96603 −0.210417 −0.105209 0.994450i \(-0.533551\pi\)
−0.105209 + 0.994450i \(0.533551\pi\)
\(558\) −7.35356 −0.311301
\(559\) 48.9860 2.07189
\(560\) −9.52869 −0.402661
\(561\) −16.6330 −0.702247
\(562\) −0.152255 −0.00642247
\(563\) 10.1665 0.428466 0.214233 0.976783i \(-0.431275\pi\)
0.214233 + 0.976783i \(0.431275\pi\)
\(564\) −13.7315 −0.578199
\(565\) 22.2745 0.937095
\(566\) 14.5431 0.611293
\(567\) −1.06796 −0.0448503
\(568\) −0.625838 −0.0262596
\(569\) 46.9043 1.96633 0.983166 0.182716i \(-0.0584888\pi\)
0.983166 + 0.182716i \(0.0584888\pi\)
\(570\) −4.03432 −0.168979
\(571\) −25.9001 −1.08389 −0.541943 0.840415i \(-0.682311\pi\)
−0.541943 + 0.840415i \(0.682311\pi\)
\(572\) −26.8347 −1.12201
\(573\) −23.7261 −0.991173
\(574\) −7.47758 −0.312108
\(575\) −4.15319 −0.173200
\(576\) −1.90427 −0.0793448
\(577\) −35.1868 −1.46484 −0.732422 0.680851i \(-0.761610\pi\)
−0.732422 + 0.680851i \(0.761610\pi\)
\(578\) 7.73379 0.321683
\(579\) 8.29709 0.344815
\(580\) −7.18374 −0.298289
\(581\) 55.7417 2.31256
\(582\) 19.4372 0.805698
\(583\) −0.873034 −0.0361574
\(584\) −6.70674 −0.277527
\(585\) 29.6171 1.22452
\(586\) −26.8655 −1.10980
\(587\) −16.0124 −0.660901 −0.330451 0.943823i \(-0.607201\pi\)
−0.330451 + 0.943823i \(0.607201\pi\)
\(588\) −3.05615 −0.126033
\(589\) 4.91927 0.202695
\(590\) 22.9499 0.944833
\(591\) −16.1317 −0.663567
\(592\) 10.8947 0.447770
\(593\) −7.64727 −0.314036 −0.157018 0.987596i \(-0.550188\pi\)
−0.157018 + 0.987596i \(0.550188\pi\)
\(594\) −26.7976 −1.09952
\(595\) −29.0058 −1.18912
\(596\) −4.75376 −0.194722
\(597\) 21.8725 0.895183
\(598\) −5.14076 −0.210221
\(599\) −37.1777 −1.51904 −0.759519 0.650485i \(-0.774566\pi\)
−0.759519 + 0.650485i \(0.774566\pi\)
\(600\) 4.34743 0.177483
\(601\) −6.46405 −0.263674 −0.131837 0.991271i \(-0.542088\pi\)
−0.131837 + 0.991271i \(0.542088\pi\)
\(602\) −30.0118 −1.22319
\(603\) −24.8701 −1.01279
\(604\) −12.1325 −0.493664
\(605\) 49.1579 1.99855
\(606\) −4.29102 −0.174311
\(607\) 25.0979 1.01869 0.509346 0.860562i \(-0.329887\pi\)
0.509346 + 0.860562i \(0.329887\pi\)
\(608\) 1.27389 0.0516632
\(609\) −7.82821 −0.317215
\(610\) 2.89902 0.117378
\(611\) −67.4362 −2.72818
\(612\) −5.79670 −0.234318
\(613\) 22.4318 0.906010 0.453005 0.891508i \(-0.350352\pi\)
0.453005 + 0.891508i \(0.350352\pi\)
\(614\) 7.51874 0.303432
\(615\) 7.51885 0.303189
\(616\) 16.4406 0.662409
\(617\) 2.35749 0.0949090 0.0474545 0.998873i \(-0.484889\pi\)
0.0474545 + 0.998873i \(0.484889\pi\)
\(618\) 2.23584 0.0899388
\(619\) −6.32247 −0.254122 −0.127061 0.991895i \(-0.540554\pi\)
−0.127061 + 0.991895i \(0.540554\pi\)
\(620\) −11.6830 −0.469200
\(621\) −5.13364 −0.206006
\(622\) 16.2277 0.650672
\(623\) 52.5860 2.10681
\(624\) 5.38118 0.215420
\(625\) −28.5170 −1.14068
\(626\) 18.0804 0.722637
\(627\) 6.96071 0.277984
\(628\) −10.9164 −0.435612
\(629\) 33.1640 1.32234
\(630\) −18.1452 −0.722924
\(631\) 6.31491 0.251393 0.125696 0.992069i \(-0.459884\pi\)
0.125696 + 0.992069i \(0.459884\pi\)
\(632\) −1.23334 −0.0490597
\(633\) −5.48434 −0.217983
\(634\) 10.9186 0.433633
\(635\) −26.6754 −1.05858
\(636\) 0.175070 0.00694199
\(637\) −15.0090 −0.594677
\(638\) 12.3946 0.490708
\(639\) −1.19177 −0.0471456
\(640\) −3.02542 −0.119590
\(641\) −43.8331 −1.73130 −0.865652 0.500647i \(-0.833096\pi\)
−0.865652 + 0.500647i \(0.833096\pi\)
\(642\) −11.5051 −0.454068
\(643\) 28.1706 1.11094 0.555471 0.831536i \(-0.312538\pi\)
0.555471 + 0.831536i \(0.312538\pi\)
\(644\) 3.14954 0.124109
\(645\) 30.1774 1.18823
\(646\) 3.87779 0.152570
\(647\) −42.6719 −1.67761 −0.838803 0.544435i \(-0.816744\pi\)
−0.838803 + 0.544435i \(0.816744\pi\)
\(648\) −0.339086 −0.0133205
\(649\) −39.5972 −1.55433
\(650\) 21.3505 0.837437
\(651\) −12.7311 −0.498971
\(652\) −13.2609 −0.519336
\(653\) −46.2071 −1.80822 −0.904112 0.427297i \(-0.859466\pi\)
−0.904112 + 0.427297i \(0.859466\pi\)
\(654\) −19.1204 −0.747668
\(655\) −3.02542 −0.118213
\(656\) −2.37418 −0.0926963
\(657\) −12.7715 −0.498263
\(658\) 41.3155 1.61065
\(659\) −32.6540 −1.27202 −0.636010 0.771681i \(-0.719416\pi\)
−0.636010 + 0.771681i \(0.719416\pi\)
\(660\) −16.5313 −0.643479
\(661\) −0.184289 −0.00716800 −0.00358400 0.999994i \(-0.501141\pi\)
−0.00358400 + 0.999994i \(0.501141\pi\)
\(662\) −7.35143 −0.285722
\(663\) 16.3806 0.636168
\(664\) 17.6984 0.686830
\(665\) 12.1385 0.470712
\(666\) 20.7465 0.803912
\(667\) 2.37446 0.0919394
\(668\) −23.6252 −0.914088
\(669\) −14.7253 −0.569314
\(670\) −39.5124 −1.52650
\(671\) −5.00190 −0.193096
\(672\) −3.29684 −0.127178
\(673\) −48.7096 −1.87762 −0.938808 0.344441i \(-0.888069\pi\)
−0.938808 + 0.344441i \(0.888069\pi\)
\(674\) 24.7369 0.952830
\(675\) 21.3210 0.820645
\(676\) 13.4274 0.516438
\(677\) −10.1269 −0.389207 −0.194604 0.980882i \(-0.562342\pi\)
−0.194604 + 0.980882i \(0.562342\pi\)
\(678\) 7.70677 0.295977
\(679\) −58.4830 −2.24437
\(680\) −9.20952 −0.353169
\(681\) −8.38893 −0.321465
\(682\) 20.1575 0.771872
\(683\) −47.3889 −1.81329 −0.906643 0.421899i \(-0.861364\pi\)
−0.906643 + 0.421899i \(0.861364\pi\)
\(684\) 2.42584 0.0927544
\(685\) −28.0406 −1.07137
\(686\) −12.8514 −0.490668
\(687\) −2.08646 −0.0796034
\(688\) −9.52894 −0.363287
\(689\) 0.859783 0.0327551
\(690\) −3.16692 −0.120563
\(691\) −22.1019 −0.840797 −0.420399 0.907339i \(-0.638110\pi\)
−0.420399 + 0.907339i \(0.638110\pi\)
\(692\) 19.8326 0.753921
\(693\) 31.3073 1.18927
\(694\) −2.02795 −0.0769799
\(695\) 7.57287 0.287255
\(696\) −2.48551 −0.0942129
\(697\) −7.22712 −0.273747
\(698\) 29.6327 1.12161
\(699\) −23.3945 −0.884863
\(700\) −13.0806 −0.494401
\(701\) −1.60571 −0.0606467 −0.0303234 0.999540i \(-0.509654\pi\)
−0.0303234 + 0.999540i \(0.509654\pi\)
\(702\) 26.3908 0.996057
\(703\) −13.8787 −0.523445
\(704\) 5.21999 0.196736
\(705\) −41.5435 −1.56462
\(706\) 0.0127493 0.000479827 0
\(707\) 12.9109 0.485564
\(708\) 7.94046 0.298421
\(709\) 11.3865 0.427628 0.213814 0.976874i \(-0.431411\pi\)
0.213814 + 0.976874i \(0.431411\pi\)
\(710\) −1.89342 −0.0710589
\(711\) −2.34862 −0.0880802
\(712\) 16.6964 0.625725
\(713\) 3.86161 0.144618
\(714\) −10.0357 −0.375578
\(715\) −81.1863 −3.03620
\(716\) −16.7626 −0.626447
\(717\) 21.8272 0.815150
\(718\) 8.48428 0.316631
\(719\) −29.0379 −1.08293 −0.541466 0.840722i \(-0.682131\pi\)
−0.541466 + 0.840722i \(0.682131\pi\)
\(720\) −5.76124 −0.214709
\(721\) −6.72725 −0.250536
\(722\) 17.3772 0.646712
\(723\) −24.8234 −0.923192
\(724\) 7.59423 0.282237
\(725\) −9.86157 −0.366249
\(726\) 17.0082 0.631233
\(727\) 8.16869 0.302960 0.151480 0.988460i \(-0.451596\pi\)
0.151480 + 0.988460i \(0.451596\pi\)
\(728\) −16.1910 −0.600079
\(729\) 15.4755 0.573167
\(730\) −20.2907 −0.750993
\(731\) −29.0065 −1.07284
\(732\) 1.00303 0.0370732
\(733\) −25.4395 −0.939629 −0.469814 0.882765i \(-0.655679\pi\)
−0.469814 + 0.882765i \(0.655679\pi\)
\(734\) −13.2569 −0.489323
\(735\) −9.24614 −0.341049
\(736\) 1.00000 0.0368605
\(737\) 68.1737 2.51121
\(738\) −4.52110 −0.166424
\(739\) −49.7902 −1.83156 −0.915781 0.401677i \(-0.868427\pi\)
−0.915781 + 0.401677i \(0.868427\pi\)
\(740\) 32.9611 1.21168
\(741\) −6.85506 −0.251827
\(742\) −0.526755 −0.0193378
\(743\) −1.10791 −0.0406453 −0.0203226 0.999793i \(-0.506469\pi\)
−0.0203226 + 0.999793i \(0.506469\pi\)
\(744\) −4.04221 −0.148195
\(745\) −14.3821 −0.526921
\(746\) −20.5034 −0.750683
\(747\) 33.7026 1.23311
\(748\) 15.8899 0.580991
\(749\) 34.6166 1.26486
\(750\) −2.68178 −0.0979249
\(751\) 32.3284 1.17968 0.589840 0.807520i \(-0.299191\pi\)
0.589840 + 0.807520i \(0.299191\pi\)
\(752\) 13.1179 0.478362
\(753\) 5.06335 0.184519
\(754\) −12.2065 −0.444535
\(755\) −36.7059 −1.33587
\(756\) −16.1686 −0.588047
\(757\) 50.0016 1.81734 0.908669 0.417516i \(-0.137099\pi\)
0.908669 + 0.417516i \(0.137099\pi\)
\(758\) −8.74897 −0.317777
\(759\) 5.46412 0.198335
\(760\) 3.85407 0.139802
\(761\) 10.9462 0.396799 0.198400 0.980121i \(-0.436426\pi\)
0.198400 + 0.980121i \(0.436426\pi\)
\(762\) −9.22945 −0.334348
\(763\) 57.5299 2.08272
\(764\) 22.6661 0.820029
\(765\) −17.5375 −0.634068
\(766\) −9.41680 −0.340243
\(767\) 38.9962 1.40807
\(768\) −1.04677 −0.0377720
\(769\) 0.585405 0.0211102 0.0105551 0.999944i \(-0.496640\pi\)
0.0105551 + 0.999944i \(0.496640\pi\)
\(770\) 49.7397 1.79249
\(771\) 15.4689 0.557097
\(772\) −7.92638 −0.285277
\(773\) −13.5638 −0.487856 −0.243928 0.969793i \(-0.578436\pi\)
−0.243928 + 0.969793i \(0.578436\pi\)
\(774\) −18.1457 −0.652234
\(775\) −16.0380 −0.576101
\(776\) −18.5688 −0.666579
\(777\) 35.9181 1.28856
\(778\) 18.5320 0.664406
\(779\) 3.02446 0.108362
\(780\) 16.2804 0.582931
\(781\) 3.26686 0.116898
\(782\) 3.04404 0.108855
\(783\) −12.1896 −0.435621
\(784\) 2.91960 0.104271
\(785\) −33.0267 −1.17877
\(786\) −1.04677 −0.0373370
\(787\) 55.7855 1.98854 0.994269 0.106907i \(-0.0340947\pi\)
0.994269 + 0.106907i \(0.0340947\pi\)
\(788\) 15.4109 0.548991
\(789\) −9.23149 −0.328650
\(790\) −3.73138 −0.132757
\(791\) −23.1883 −0.824480
\(792\) 9.94029 0.353213
\(793\) 4.92597 0.174926
\(794\) −8.99391 −0.319182
\(795\) 0.529662 0.0187852
\(796\) −20.8953 −0.740613
\(797\) 53.7424 1.90365 0.951826 0.306637i \(-0.0992039\pi\)
0.951826 + 0.306637i \(0.0992039\pi\)
\(798\) 4.19982 0.148672
\(799\) 39.9316 1.41268
\(800\) −4.15319 −0.146837
\(801\) 31.7946 1.12341
\(802\) −6.04775 −0.213553
\(803\) 35.0091 1.23544
\(804\) −13.6709 −0.482137
\(805\) 9.52869 0.335842
\(806\) −19.8516 −0.699242
\(807\) −32.1336 −1.13116
\(808\) 4.09930 0.144213
\(809\) −47.9366 −1.68536 −0.842681 0.538413i \(-0.819024\pi\)
−0.842681 + 0.538413i \(0.819024\pi\)
\(810\) −1.02588 −0.0360457
\(811\) 14.8844 0.522660 0.261330 0.965249i \(-0.415839\pi\)
0.261330 + 0.965249i \(0.415839\pi\)
\(812\) 7.47845 0.262442
\(813\) 31.4647 1.10352
\(814\) −56.8703 −1.99330
\(815\) −40.1197 −1.40533
\(816\) −3.18641 −0.111547
\(817\) 12.1389 0.424685
\(818\) −4.90714 −0.171574
\(819\) −30.8321 −1.07736
\(820\) −7.18291 −0.250838
\(821\) 45.3610 1.58311 0.791555 0.611097i \(-0.209272\pi\)
0.791555 + 0.611097i \(0.209272\pi\)
\(822\) −9.70178 −0.338388
\(823\) −10.9617 −0.382099 −0.191050 0.981580i \(-0.561189\pi\)
−0.191050 + 0.981580i \(0.561189\pi\)
\(824\) −2.13595 −0.0744092
\(825\) −22.6935 −0.790087
\(826\) −23.8914 −0.831289
\(827\) −24.6882 −0.858491 −0.429246 0.903188i \(-0.641221\pi\)
−0.429246 + 0.903188i \(0.641221\pi\)
\(828\) 1.90427 0.0661781
\(829\) 21.5198 0.747413 0.373707 0.927547i \(-0.378087\pi\)
0.373707 + 0.927547i \(0.378087\pi\)
\(830\) 53.5451 1.85858
\(831\) 31.5385 1.09406
\(832\) −5.14076 −0.178224
\(833\) 8.88739 0.307930
\(834\) 2.62014 0.0907282
\(835\) −71.4764 −2.47354
\(836\) −6.64971 −0.229985
\(837\) −19.8241 −0.685221
\(838\) 25.7798 0.890548
\(839\) 40.8920 1.41175 0.705874 0.708338i \(-0.250555\pi\)
0.705874 + 0.708338i \(0.250555\pi\)
\(840\) −9.97434 −0.344147
\(841\) −23.3620 −0.805585
\(842\) 20.2967 0.699471
\(843\) −0.159375 −0.00548918
\(844\) 5.23930 0.180344
\(845\) 40.6235 1.39749
\(846\) 24.9802 0.858836
\(847\) −51.1746 −1.75838
\(848\) −0.167248 −0.00574333
\(849\) 15.2233 0.522462
\(850\) −12.6425 −0.433634
\(851\) −10.8947 −0.373466
\(852\) −0.655107 −0.0224436
\(853\) 49.4139 1.69190 0.845951 0.533261i \(-0.179034\pi\)
0.845951 + 0.533261i \(0.179034\pi\)
\(854\) −3.01795 −0.103272
\(855\) 7.33920 0.250995
\(856\) 10.9910 0.375665
\(857\) −32.6474 −1.11521 −0.557607 0.830105i \(-0.688280\pi\)
−0.557607 + 0.830105i \(0.688280\pi\)
\(858\) −28.0897 −0.958967
\(859\) 3.49690 0.119313 0.0596564 0.998219i \(-0.480999\pi\)
0.0596564 + 0.998219i \(0.480999\pi\)
\(860\) −28.8291 −0.983063
\(861\) −7.82730 −0.266754
\(862\) 23.0821 0.786181
\(863\) 18.0762 0.615322 0.307661 0.951496i \(-0.400454\pi\)
0.307661 + 0.951496i \(0.400454\pi\)
\(864\) −5.13364 −0.174650
\(865\) 60.0019 2.04013
\(866\) −36.2582 −1.23210
\(867\) 8.09550 0.274937
\(868\) 12.1623 0.412815
\(869\) 6.43803 0.218395
\(870\) −7.51972 −0.254942
\(871\) −67.1389 −2.27492
\(872\) 18.2661 0.618570
\(873\) −35.3600 −1.19675
\(874\) −1.27389 −0.0430901
\(875\) 8.06901 0.272782
\(876\) −7.02041 −0.237198
\(877\) −22.0629 −0.745012 −0.372506 0.928030i \(-0.621501\pi\)
−0.372506 + 0.928030i \(0.621501\pi\)
\(878\) 14.4607 0.488023
\(879\) −28.1220 −0.948531
\(880\) 15.7927 0.532371
\(881\) 47.7843 1.60989 0.804947 0.593347i \(-0.202194\pi\)
0.804947 + 0.593347i \(0.202194\pi\)
\(882\) 5.55972 0.187206
\(883\) −51.2459 −1.72456 −0.862282 0.506429i \(-0.830965\pi\)
−0.862282 + 0.506429i \(0.830965\pi\)
\(884\) −15.6487 −0.526322
\(885\) 24.0233 0.807533
\(886\) 22.1585 0.744430
\(887\) −35.8793 −1.20471 −0.602355 0.798229i \(-0.705771\pi\)
−0.602355 + 0.798229i \(0.705771\pi\)
\(888\) 11.4043 0.382702
\(889\) 27.7697 0.931367
\(890\) 50.5137 1.69322
\(891\) 1.77002 0.0592980
\(892\) 14.0674 0.471012
\(893\) −16.7109 −0.559208
\(894\) −4.97609 −0.166425
\(895\) −50.7139 −1.69518
\(896\) 3.14954 0.105219
\(897\) −5.38118 −0.179673
\(898\) 31.8227 1.06194
\(899\) 9.16922 0.305810
\(900\) −7.90881 −0.263627
\(901\) −0.509111 −0.0169610
\(902\) 12.3932 0.412649
\(903\) −31.4154 −1.04544
\(904\) −7.36243 −0.244871
\(905\) 22.9758 0.763741
\(906\) −12.6999 −0.421927
\(907\) −19.8016 −0.657501 −0.328750 0.944417i \(-0.606627\pi\)
−0.328750 + 0.944417i \(0.606627\pi\)
\(908\) 8.01412 0.265958
\(909\) 7.80619 0.258915
\(910\) −48.9847 −1.62383
\(911\) 13.0534 0.432480 0.216240 0.976340i \(-0.430621\pi\)
0.216240 + 0.976340i \(0.430621\pi\)
\(912\) 1.33347 0.0441557
\(913\) −92.3853 −3.05751
\(914\) −16.0212 −0.529935
\(915\) 3.03460 0.100321
\(916\) 1.99324 0.0658584
\(917\) 3.14954 0.104007
\(918\) −15.6270 −0.515769
\(919\) −5.96660 −0.196820 −0.0984099 0.995146i \(-0.531376\pi\)
−0.0984099 + 0.995146i \(0.531376\pi\)
\(920\) 3.02542 0.0997453
\(921\) 7.87039 0.259338
\(922\) 19.3391 0.636900
\(923\) −3.21728 −0.105898
\(924\) 17.2095 0.566150
\(925\) 45.2478 1.48774
\(926\) 9.86263 0.324106
\(927\) −4.06743 −0.133592
\(928\) 2.37446 0.0779454
\(929\) 33.0383 1.08395 0.541976 0.840394i \(-0.317676\pi\)
0.541976 + 0.840394i \(0.317676\pi\)
\(930\) −12.2294 −0.401018
\(931\) −3.71926 −0.121894
\(932\) 22.3493 0.732075
\(933\) 16.9867 0.556118
\(934\) 36.7936 1.20392
\(935\) 48.0736 1.57217
\(936\) −9.78941 −0.319977
\(937\) 43.3951 1.41766 0.708828 0.705382i \(-0.249224\pi\)
0.708828 + 0.705382i \(0.249224\pi\)
\(938\) 41.1334 1.34305
\(939\) 18.9260 0.617626
\(940\) 39.6873 1.29446
\(941\) −8.46701 −0.276017 −0.138008 0.990431i \(-0.544070\pi\)
−0.138008 + 0.990431i \(0.544070\pi\)
\(942\) −11.4269 −0.372310
\(943\) 2.37418 0.0773140
\(944\) −7.58569 −0.246893
\(945\) −48.9169 −1.59127
\(946\) 49.7410 1.61722
\(947\) 30.9014 1.00416 0.502080 0.864821i \(-0.332568\pi\)
0.502080 + 0.864821i \(0.332568\pi\)
\(948\) −1.29102 −0.0419305
\(949\) −34.4777 −1.11919
\(950\) 5.29072 0.171654
\(951\) 11.4292 0.370619
\(952\) 9.58734 0.310727
\(953\) 28.7499 0.931299 0.465650 0.884969i \(-0.345821\pi\)
0.465650 + 0.884969i \(0.345821\pi\)
\(954\) −0.318487 −0.0103114
\(955\) 68.5744 2.21902
\(956\) −20.8519 −0.674400
\(957\) 12.9743 0.419400
\(958\) 8.67563 0.280297
\(959\) 29.1909 0.942624
\(960\) −3.16692 −0.102212
\(961\) −16.0880 −0.518968
\(962\) 56.0071 1.80574
\(963\) 20.9299 0.674457
\(964\) 23.7143 0.763786
\(965\) −23.9807 −0.771965
\(966\) 3.29684 0.106074
\(967\) −24.7389 −0.795548 −0.397774 0.917483i \(-0.630217\pi\)
−0.397774 + 0.917483i \(0.630217\pi\)
\(968\) −16.2483 −0.522239
\(969\) 4.05915 0.130399
\(970\) −56.1783 −1.80378
\(971\) −7.37370 −0.236633 −0.118317 0.992976i \(-0.537750\pi\)
−0.118317 + 0.992976i \(0.537750\pi\)
\(972\) −15.7559 −0.505370
\(973\) −7.88354 −0.252735
\(974\) −22.9577 −0.735612
\(975\) 22.3491 0.715743
\(976\) −0.958220 −0.0306719
\(977\) 7.63827 0.244370 0.122185 0.992507i \(-0.461010\pi\)
0.122185 + 0.992507i \(0.461010\pi\)
\(978\) −13.8811 −0.443867
\(979\) −87.1551 −2.78549
\(980\) 8.83303 0.282161
\(981\) 34.7837 1.11056
\(982\) −18.4917 −0.590093
\(983\) −30.9979 −0.988678 −0.494339 0.869269i \(-0.664590\pi\)
−0.494339 + 0.869269i \(0.664590\pi\)
\(984\) −2.48522 −0.0792260
\(985\) 46.6245 1.48558
\(986\) 7.22795 0.230185
\(987\) 43.2478 1.37659
\(988\) 6.54878 0.208344
\(989\) 9.52894 0.303003
\(990\) 30.0736 0.955801
\(991\) 49.4681 1.57141 0.785703 0.618604i \(-0.212301\pi\)
0.785703 + 0.618604i \(0.212301\pi\)
\(992\) 3.86161 0.122606
\(993\) −7.69525 −0.244202
\(994\) 1.97110 0.0625195
\(995\) −63.2170 −2.00411
\(996\) 18.5261 0.587022
\(997\) −31.5266 −0.998458 −0.499229 0.866470i \(-0.666383\pi\)
−0.499229 + 0.866470i \(0.666383\pi\)
\(998\) −24.6607 −0.780620
\(999\) 55.9296 1.76953
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 \(a_p\))