Properties

Label 4015.2.a.h.1.3
Level 4015
Weight 2
Character 4015.1
Self dual Yes
Analytic conductor 32.060
Analytic rank 0
Dimension 37
CM No

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Newspace parameters

Level: \( N \) = \( 4015 = 5 \cdot 11 \cdot 73 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0599364115\)
Analytic rank: \(0\)
Dimension: \(37\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 4015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.53170 q^{2}\) \(+2.11924 q^{3}\) \(+4.40953 q^{4}\) \(+1.00000 q^{5}\) \(-5.36530 q^{6}\) \(+2.19751 q^{7}\) \(-6.10021 q^{8}\) \(+1.49120 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.53170 q^{2}\) \(+2.11924 q^{3}\) \(+4.40953 q^{4}\) \(+1.00000 q^{5}\) \(-5.36530 q^{6}\) \(+2.19751 q^{7}\) \(-6.10021 q^{8}\) \(+1.49120 q^{9}\) \(-2.53170 q^{10}\) \(+1.00000 q^{11}\) \(+9.34487 q^{12}\) \(+4.02246 q^{13}\) \(-5.56346 q^{14}\) \(+2.11924 q^{15}\) \(+6.62488 q^{16}\) \(+6.58165 q^{17}\) \(-3.77528 q^{18}\) \(-4.95999 q^{19}\) \(+4.40953 q^{20}\) \(+4.65707 q^{21}\) \(-2.53170 q^{22}\) \(-2.67405 q^{23}\) \(-12.9278 q^{24}\) \(+1.00000 q^{25}\) \(-10.1837 q^{26}\) \(-3.19752 q^{27}\) \(+9.69000 q^{28}\) \(+9.82049 q^{29}\) \(-5.36530 q^{30}\) \(+6.06636 q^{31}\) \(-4.57181 q^{32}\) \(+2.11924 q^{33}\) \(-16.6628 q^{34}\) \(+2.19751 q^{35}\) \(+6.57548 q^{36}\) \(+0.228684 q^{37}\) \(+12.5572 q^{38}\) \(+8.52457 q^{39}\) \(-6.10021 q^{40}\) \(-1.39905 q^{41}\) \(-11.7903 q^{42}\) \(-4.42714 q^{43}\) \(+4.40953 q^{44}\) \(+1.49120 q^{45}\) \(+6.76992 q^{46}\) \(+6.69577 q^{47}\) \(+14.0397 q^{48}\) \(-2.17093 q^{49}\) \(-2.53170 q^{50}\) \(+13.9481 q^{51}\) \(+17.7371 q^{52}\) \(+9.42814 q^{53}\) \(+8.09517 q^{54}\) \(+1.00000 q^{55}\) \(-13.4053 q^{56}\) \(-10.5114 q^{57}\) \(-24.8626 q^{58}\) \(-7.06927 q^{59}\) \(+9.34487 q^{60}\) \(-3.47486 q^{61}\) \(-15.3582 q^{62}\) \(+3.27693 q^{63}\) \(-1.67529 q^{64}\) \(+4.02246 q^{65}\) \(-5.36530 q^{66}\) \(-16.1062 q^{67}\) \(+29.0220 q^{68}\) \(-5.66698 q^{69}\) \(-5.56346 q^{70}\) \(-11.3863 q^{71}\) \(-9.09663 q^{72}\) \(+1.00000 q^{73}\) \(-0.578961 q^{74}\) \(+2.11924 q^{75}\) \(-21.8712 q^{76}\) \(+2.19751 q^{77}\) \(-21.5817 q^{78}\) \(+6.89054 q^{79}\) \(+6.62488 q^{80}\) \(-11.2499 q^{81}\) \(+3.54198 q^{82}\) \(+14.5032 q^{83}\) \(+20.5355 q^{84}\) \(+6.58165 q^{85}\) \(+11.2082 q^{86}\) \(+20.8120 q^{87}\) \(-6.10021 q^{88}\) \(+12.9726 q^{89}\) \(-3.77528 q^{90}\) \(+8.83941 q^{91}\) \(-11.7913 q^{92}\) \(+12.8561 q^{93}\) \(-16.9517 q^{94}\) \(-4.95999 q^{95}\) \(-9.68878 q^{96}\) \(+5.76060 q^{97}\) \(+5.49615 q^{98}\) \(+1.49120 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 37q^{11} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 11q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 43q^{16} \) \(\mathstrut +\mathstrut 38q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 43q^{20} \) \(\mathstrut +\mathstrut 39q^{21} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 9q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 14q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 20q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 15q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 62q^{41} \) \(\mathstrut -\mathstrut 13q^{42} \) \(\mathstrut +\mathstrut 30q^{43} \) \(\mathstrut +\mathstrut 43q^{44} \) \(\mathstrut +\mathstrut 50q^{45} \) \(\mathstrut +\mathstrut 31q^{46} \) \(\mathstrut +\mathstrut 5q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 59q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut +\mathstrut 37q^{55} \) \(\mathstrut +\mathstrut 22q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 40q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 57q^{61} \) \(\mathstrut +\mathstrut 20q^{62} \) \(\mathstrut -\mathstrut 29q^{63} \) \(\mathstrut +\mathstrut 10q^{64} \) \(\mathstrut +\mathstrut 11q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 53q^{68} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 11q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut +\mathstrut 59q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 42q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 61q^{81} \) \(\mathstrut -\mathstrut 22q^{82} \) \(\mathstrut +\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 66q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut -\mathstrut q^{86} \) \(\mathstrut -\mathstrut 26q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 69q^{89} \) \(\mathstrut +\mathstrut 11q^{90} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 21q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut +\mathstrut 34q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 15q^{98} \) \(\mathstrut +\mathstrut 50q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.53170 −1.79019 −0.895093 0.445880i \(-0.852891\pi\)
−0.895093 + 0.445880i \(0.852891\pi\)
\(3\) 2.11924 1.22355 0.611773 0.791033i \(-0.290456\pi\)
0.611773 + 0.791033i \(0.290456\pi\)
\(4\) 4.40953 2.20476
\(5\) 1.00000 0.447214
\(6\) −5.36530 −2.19038
\(7\) 2.19751 0.830582 0.415291 0.909689i \(-0.363680\pi\)
0.415291 + 0.909689i \(0.363680\pi\)
\(8\) −6.10021 −2.15675
\(9\) 1.49120 0.497066
\(10\) −2.53170 −0.800595
\(11\) 1.00000 0.301511
\(12\) 9.34487 2.69763
\(13\) 4.02246 1.11563 0.557814 0.829966i \(-0.311640\pi\)
0.557814 + 0.829966i \(0.311640\pi\)
\(14\) −5.56346 −1.48690
\(15\) 2.11924 0.547187
\(16\) 6.62488 1.65622
\(17\) 6.58165 1.59629 0.798143 0.602468i \(-0.205816\pi\)
0.798143 + 0.602468i \(0.205816\pi\)
\(18\) −3.77528 −0.889841
\(19\) −4.95999 −1.13790 −0.568950 0.822372i \(-0.692650\pi\)
−0.568950 + 0.822372i \(0.692650\pi\)
\(20\) 4.40953 0.986000
\(21\) 4.65707 1.01626
\(22\) −2.53170 −0.539761
\(23\) −2.67405 −0.557579 −0.278789 0.960352i \(-0.589933\pi\)
−0.278789 + 0.960352i \(0.589933\pi\)
\(24\) −12.9278 −2.63888
\(25\) 1.00000 0.200000
\(26\) −10.1837 −1.99718
\(27\) −3.19752 −0.615363
\(28\) 9.69000 1.83124
\(29\) 9.82049 1.82362 0.911810 0.410613i \(-0.134685\pi\)
0.911810 + 0.410613i \(0.134685\pi\)
\(30\) −5.36530 −0.979566
\(31\) 6.06636 1.08955 0.544775 0.838582i \(-0.316615\pi\)
0.544775 + 0.838582i \(0.316615\pi\)
\(32\) −4.57181 −0.808189
\(33\) 2.11924 0.368913
\(34\) −16.6628 −2.85765
\(35\) 2.19751 0.371448
\(36\) 6.57548 1.09591
\(37\) 0.228684 0.0375955 0.0187977 0.999823i \(-0.494016\pi\)
0.0187977 + 0.999823i \(0.494016\pi\)
\(38\) 12.5572 2.03705
\(39\) 8.52457 1.36502
\(40\) −6.10021 −0.964528
\(41\) −1.39905 −0.218495 −0.109248 0.994015i \(-0.534844\pi\)
−0.109248 + 0.994015i \(0.534844\pi\)
\(42\) −11.7903 −1.81929
\(43\) −4.42714 −0.675132 −0.337566 0.941302i \(-0.609604\pi\)
−0.337566 + 0.941302i \(0.609604\pi\)
\(44\) 4.40953 0.664761
\(45\) 1.49120 0.222295
\(46\) 6.76992 0.998170
\(47\) 6.69577 0.976678 0.488339 0.872654i \(-0.337603\pi\)
0.488339 + 0.872654i \(0.337603\pi\)
\(48\) 14.0397 2.02646
\(49\) −2.17093 −0.310133
\(50\) −2.53170 −0.358037
\(51\) 13.9481 1.95313
\(52\) 17.7371 2.45970
\(53\) 9.42814 1.29505 0.647527 0.762042i \(-0.275803\pi\)
0.647527 + 0.762042i \(0.275803\pi\)
\(54\) 8.09517 1.10161
\(55\) 1.00000 0.134840
\(56\) −13.4053 −1.79136
\(57\) −10.5114 −1.39227
\(58\) −24.8626 −3.26462
\(59\) −7.06927 −0.920340 −0.460170 0.887831i \(-0.652212\pi\)
−0.460170 + 0.887831i \(0.652212\pi\)
\(60\) 9.34487 1.20642
\(61\) −3.47486 −0.444911 −0.222455 0.974943i \(-0.571407\pi\)
−0.222455 + 0.974943i \(0.571407\pi\)
\(62\) −15.3582 −1.95050
\(63\) 3.27693 0.412855
\(64\) −1.67529 −0.209411
\(65\) 4.02246 0.498924
\(66\) −5.36530 −0.660423
\(67\) −16.1062 −1.96769 −0.983844 0.179026i \(-0.942705\pi\)
−0.983844 + 0.179026i \(0.942705\pi\)
\(68\) 29.0220 3.51943
\(69\) −5.66698 −0.682224
\(70\) −5.56346 −0.664960
\(71\) −11.3863 −1.35131 −0.675655 0.737218i \(-0.736139\pi\)
−0.675655 + 0.737218i \(0.736139\pi\)
\(72\) −9.09663 −1.07205
\(73\) 1.00000 0.117041
\(74\) −0.578961 −0.0673028
\(75\) 2.11924 0.244709
\(76\) −21.8712 −2.50880
\(77\) 2.19751 0.250430
\(78\) −21.5817 −2.44365
\(79\) 6.89054 0.775246 0.387623 0.921818i \(-0.373296\pi\)
0.387623 + 0.921818i \(0.373296\pi\)
\(80\) 6.62488 0.740684
\(81\) −11.2499 −1.24999
\(82\) 3.54198 0.391147
\(83\) 14.5032 1.59193 0.795964 0.605344i \(-0.206964\pi\)
0.795964 + 0.605344i \(0.206964\pi\)
\(84\) 20.5355 2.24061
\(85\) 6.58165 0.713881
\(86\) 11.2082 1.20861
\(87\) 20.8120 2.23128
\(88\) −6.10021 −0.650285
\(89\) 12.9726 1.37509 0.687544 0.726143i \(-0.258689\pi\)
0.687544 + 0.726143i \(0.258689\pi\)
\(90\) −3.77528 −0.397949
\(91\) 8.83941 0.926622
\(92\) −11.7913 −1.22933
\(93\) 12.8561 1.33312
\(94\) −16.9517 −1.74843
\(95\) −4.95999 −0.508884
\(96\) −9.68878 −0.988857
\(97\) 5.76060 0.584900 0.292450 0.956281i \(-0.405529\pi\)
0.292450 + 0.956281i \(0.405529\pi\)
\(98\) 5.49615 0.555195
\(99\) 1.49120 0.149871
\(100\) 4.40953 0.440953
\(101\) −1.63236 −0.162426 −0.0812131 0.996697i \(-0.525879\pi\)
−0.0812131 + 0.996697i \(0.525879\pi\)
\(102\) −35.3126 −3.49646
\(103\) −18.3587 −1.80894 −0.904468 0.426542i \(-0.859732\pi\)
−0.904468 + 0.426542i \(0.859732\pi\)
\(104\) −24.5378 −2.40613
\(105\) 4.65707 0.454484
\(106\) −23.8693 −2.31839
\(107\) 3.07728 0.297492 0.148746 0.988875i \(-0.452476\pi\)
0.148746 + 0.988875i \(0.452476\pi\)
\(108\) −14.0995 −1.35673
\(109\) 17.5992 1.68569 0.842847 0.538153i \(-0.180878\pi\)
0.842847 + 0.538153i \(0.180878\pi\)
\(110\) −2.53170 −0.241389
\(111\) 0.484638 0.0459998
\(112\) 14.5583 1.37563
\(113\) −4.49663 −0.423007 −0.211504 0.977377i \(-0.567836\pi\)
−0.211504 + 0.977377i \(0.567836\pi\)
\(114\) 26.6119 2.49243
\(115\) −2.67405 −0.249357
\(116\) 43.3037 4.02065
\(117\) 5.99829 0.554542
\(118\) 17.8973 1.64758
\(119\) 14.4633 1.32585
\(120\) −12.9278 −1.18015
\(121\) 1.00000 0.0909091
\(122\) 8.79733 0.796472
\(123\) −2.96493 −0.267339
\(124\) 26.7498 2.40220
\(125\) 1.00000 0.0894427
\(126\) −8.29622 −0.739086
\(127\) −18.3157 −1.62525 −0.812627 0.582784i \(-0.801964\pi\)
−0.812627 + 0.582784i \(0.801964\pi\)
\(128\) 13.3849 1.18307
\(129\) −9.38219 −0.826056
\(130\) −10.1837 −0.893167
\(131\) −3.39963 −0.297027 −0.148513 0.988910i \(-0.547449\pi\)
−0.148513 + 0.988910i \(0.547449\pi\)
\(132\) 9.34487 0.813366
\(133\) −10.8997 −0.945120
\(134\) 40.7762 3.52253
\(135\) −3.19752 −0.275199
\(136\) −40.1495 −3.44279
\(137\) 13.0457 1.11457 0.557285 0.830321i \(-0.311843\pi\)
0.557285 + 0.830321i \(0.311843\pi\)
\(138\) 14.3471 1.22131
\(139\) 4.06813 0.345054 0.172527 0.985005i \(-0.444807\pi\)
0.172527 + 0.985005i \(0.444807\pi\)
\(140\) 9.69000 0.818955
\(141\) 14.1900 1.19501
\(142\) 28.8269 2.41910
\(143\) 4.02246 0.336375
\(144\) 9.87901 0.823251
\(145\) 9.82049 0.815547
\(146\) −2.53170 −0.209525
\(147\) −4.60073 −0.379462
\(148\) 1.00839 0.0828891
\(149\) 15.5117 1.27077 0.635383 0.772197i \(-0.280842\pi\)
0.635383 + 0.772197i \(0.280842\pi\)
\(150\) −5.36530 −0.438075
\(151\) 17.5705 1.42987 0.714936 0.699190i \(-0.246456\pi\)
0.714936 + 0.699190i \(0.246456\pi\)
\(152\) 30.2570 2.45417
\(153\) 9.81456 0.793460
\(154\) −5.56346 −0.448316
\(155\) 6.06636 0.487262
\(156\) 37.5893 3.00956
\(157\) 10.7588 0.858649 0.429324 0.903150i \(-0.358752\pi\)
0.429324 + 0.903150i \(0.358752\pi\)
\(158\) −17.4448 −1.38783
\(159\) 19.9805 1.58456
\(160\) −4.57181 −0.361433
\(161\) −5.87627 −0.463115
\(162\) 28.4815 2.23772
\(163\) −19.5362 −1.53019 −0.765097 0.643915i \(-0.777309\pi\)
−0.765097 + 0.643915i \(0.777309\pi\)
\(164\) −6.16915 −0.481730
\(165\) 2.11924 0.164983
\(166\) −36.7177 −2.84985
\(167\) −13.9145 −1.07673 −0.538367 0.842711i \(-0.680958\pi\)
−0.538367 + 0.842711i \(0.680958\pi\)
\(168\) −28.4091 −2.19181
\(169\) 3.18016 0.244628
\(170\) −16.6628 −1.27798
\(171\) −7.39634 −0.565612
\(172\) −19.5216 −1.48851
\(173\) 6.22956 0.473624 0.236812 0.971555i \(-0.423897\pi\)
0.236812 + 0.971555i \(0.423897\pi\)
\(174\) −52.6899 −3.99441
\(175\) 2.19751 0.166116
\(176\) 6.62488 0.499369
\(177\) −14.9815 −1.12608
\(178\) −32.8427 −2.46166
\(179\) −16.8483 −1.25930 −0.629652 0.776877i \(-0.716803\pi\)
−0.629652 + 0.776877i \(0.716803\pi\)
\(180\) 6.57548 0.490108
\(181\) 11.0877 0.824139 0.412070 0.911152i \(-0.364806\pi\)
0.412070 + 0.911152i \(0.364806\pi\)
\(182\) −22.3788 −1.65882
\(183\) −7.36409 −0.544369
\(184\) 16.3123 1.20256
\(185\) 0.228684 0.0168132
\(186\) −32.5479 −2.38653
\(187\) 6.58165 0.481298
\(188\) 29.5252 2.15334
\(189\) −7.02659 −0.511109
\(190\) 12.5572 0.910998
\(191\) −15.1883 −1.09898 −0.549492 0.835499i \(-0.685179\pi\)
−0.549492 + 0.835499i \(0.685179\pi\)
\(192\) −3.55034 −0.256224
\(193\) −19.1609 −1.37923 −0.689615 0.724176i \(-0.742220\pi\)
−0.689615 + 0.724176i \(0.742220\pi\)
\(194\) −14.5841 −1.04708
\(195\) 8.52457 0.610457
\(196\) −9.57277 −0.683769
\(197\) −0.658409 −0.0469097 −0.0234548 0.999725i \(-0.507467\pi\)
−0.0234548 + 0.999725i \(0.507467\pi\)
\(198\) −3.77528 −0.268297
\(199\) 6.11287 0.433330 0.216665 0.976246i \(-0.430482\pi\)
0.216665 + 0.976246i \(0.430482\pi\)
\(200\) −6.10021 −0.431350
\(201\) −34.1330 −2.40756
\(202\) 4.13266 0.290773
\(203\) 21.5807 1.51467
\(204\) 61.5047 4.30619
\(205\) −1.39905 −0.0977140
\(206\) 46.4788 3.23833
\(207\) −3.98755 −0.277154
\(208\) 26.6483 1.84773
\(209\) −4.95999 −0.343090
\(210\) −11.7903 −0.813610
\(211\) −12.5868 −0.866514 −0.433257 0.901270i \(-0.642636\pi\)
−0.433257 + 0.901270i \(0.642636\pi\)
\(212\) 41.5736 2.85529
\(213\) −24.1305 −1.65339
\(214\) −7.79077 −0.532566
\(215\) −4.42714 −0.301928
\(216\) 19.5055 1.32718
\(217\) 13.3309 0.904962
\(218\) −44.5559 −3.01771
\(219\) 2.11924 0.143205
\(220\) 4.40953 0.297290
\(221\) 26.4744 1.78086
\(222\) −1.22696 −0.0823482
\(223\) 3.33426 0.223278 0.111639 0.993749i \(-0.464390\pi\)
0.111639 + 0.993749i \(0.464390\pi\)
\(224\) −10.0466 −0.671268
\(225\) 1.49120 0.0994133
\(226\) 11.3841 0.757261
\(227\) −25.2482 −1.67578 −0.837891 0.545837i \(-0.816212\pi\)
−0.837891 + 0.545837i \(0.816212\pi\)
\(228\) −46.3505 −3.06964
\(229\) 24.0408 1.58866 0.794330 0.607487i \(-0.207822\pi\)
0.794330 + 0.607487i \(0.207822\pi\)
\(230\) 6.76992 0.446395
\(231\) 4.65707 0.306413
\(232\) −59.9071 −3.93309
\(233\) −20.8263 −1.36438 −0.682188 0.731177i \(-0.738972\pi\)
−0.682188 + 0.731177i \(0.738972\pi\)
\(234\) −15.1859 −0.992732
\(235\) 6.69577 0.436784
\(236\) −31.1721 −2.02913
\(237\) 14.6027 0.948550
\(238\) −36.6167 −2.37351
\(239\) 12.9257 0.836095 0.418048 0.908425i \(-0.362715\pi\)
0.418048 + 0.908425i \(0.362715\pi\)
\(240\) 14.0397 0.906261
\(241\) −6.34423 −0.408668 −0.204334 0.978901i \(-0.565503\pi\)
−0.204334 + 0.978901i \(0.565503\pi\)
\(242\) −2.53170 −0.162744
\(243\) −14.2488 −0.914060
\(244\) −15.3225 −0.980923
\(245\) −2.17093 −0.138696
\(246\) 7.50633 0.478586
\(247\) −19.9514 −1.26947
\(248\) −37.0061 −2.34989
\(249\) 30.7357 1.94780
\(250\) −2.53170 −0.160119
\(251\) −21.1044 −1.33210 −0.666048 0.745909i \(-0.732016\pi\)
−0.666048 + 0.745909i \(0.732016\pi\)
\(252\) 14.4497 0.910247
\(253\) −2.67405 −0.168116
\(254\) 46.3699 2.90951
\(255\) 13.9481 0.873466
\(256\) −30.5362 −1.90851
\(257\) 12.0366 0.750825 0.375413 0.926858i \(-0.377501\pi\)
0.375413 + 0.926858i \(0.377501\pi\)
\(258\) 23.7529 1.47879
\(259\) 0.502537 0.0312261
\(260\) 17.7371 1.10001
\(261\) 14.6443 0.906460
\(262\) 8.60685 0.531733
\(263\) 27.2915 1.68287 0.841434 0.540360i \(-0.181712\pi\)
0.841434 + 0.540360i \(0.181712\pi\)
\(264\) −12.9278 −0.795654
\(265\) 9.42814 0.579166
\(266\) 27.5947 1.69194
\(267\) 27.4920 1.68248
\(268\) −71.0208 −4.33829
\(269\) 4.86328 0.296520 0.148260 0.988948i \(-0.452633\pi\)
0.148260 + 0.988948i \(0.452633\pi\)
\(270\) 8.09517 0.492656
\(271\) −2.76163 −0.167757 −0.0838785 0.996476i \(-0.526731\pi\)
−0.0838785 + 0.996476i \(0.526731\pi\)
\(272\) 43.6026 2.64380
\(273\) 18.7329 1.13377
\(274\) −33.0279 −1.99529
\(275\) 1.00000 0.0603023
\(276\) −24.9887 −1.50414
\(277\) 11.9544 0.718272 0.359136 0.933285i \(-0.383071\pi\)
0.359136 + 0.933285i \(0.383071\pi\)
\(278\) −10.2993 −0.617711
\(279\) 9.04615 0.541579
\(280\) −13.4053 −0.801120
\(281\) 28.4992 1.70012 0.850061 0.526684i \(-0.176565\pi\)
0.850061 + 0.526684i \(0.176565\pi\)
\(282\) −35.9248 −2.13929
\(283\) −31.9118 −1.89696 −0.948479 0.316840i \(-0.897378\pi\)
−0.948479 + 0.316840i \(0.897378\pi\)
\(284\) −50.2084 −2.97932
\(285\) −10.5114 −0.622644
\(286\) −10.1837 −0.602173
\(287\) −3.07444 −0.181478
\(288\) −6.81748 −0.401724
\(289\) 26.3182 1.54813
\(290\) −24.8626 −1.45998
\(291\) 12.2081 0.715653
\(292\) 4.40953 0.258048
\(293\) −11.3079 −0.660615 −0.330308 0.943873i \(-0.607152\pi\)
−0.330308 + 0.943873i \(0.607152\pi\)
\(294\) 11.6477 0.679307
\(295\) −7.06927 −0.411589
\(296\) −1.39502 −0.0810840
\(297\) −3.19752 −0.185539
\(298\) −39.2710 −2.27491
\(299\) −10.7563 −0.622051
\(300\) 9.34487 0.539526
\(301\) −9.72870 −0.560753
\(302\) −44.4834 −2.55973
\(303\) −3.45938 −0.198736
\(304\) −32.8593 −1.88461
\(305\) −3.47486 −0.198970
\(306\) −24.8476 −1.42044
\(307\) −17.2953 −0.987096 −0.493548 0.869719i \(-0.664300\pi\)
−0.493548 + 0.869719i \(0.664300\pi\)
\(308\) 9.69000 0.552139
\(309\) −38.9066 −2.21332
\(310\) −15.3582 −0.872289
\(311\) 5.94804 0.337282 0.168641 0.985678i \(-0.446062\pi\)
0.168641 + 0.985678i \(0.446062\pi\)
\(312\) −52.0017 −2.94402
\(313\) −26.6362 −1.50557 −0.752785 0.658267i \(-0.771290\pi\)
−0.752785 + 0.658267i \(0.771290\pi\)
\(314\) −27.2382 −1.53714
\(315\) 3.27693 0.184634
\(316\) 30.3840 1.70923
\(317\) 6.59539 0.370434 0.185217 0.982698i \(-0.440701\pi\)
0.185217 + 0.982698i \(0.440701\pi\)
\(318\) −50.5848 −2.83666
\(319\) 9.82049 0.549842
\(320\) −1.67529 −0.0936514
\(321\) 6.52152 0.363996
\(322\) 14.8770 0.829062
\(323\) −32.6449 −1.81641
\(324\) −49.6068 −2.75594
\(325\) 4.02246 0.223126
\(326\) 49.4599 2.73933
\(327\) 37.2969 2.06253
\(328\) 8.53451 0.471239
\(329\) 14.7140 0.811212
\(330\) −5.36530 −0.295350
\(331\) 29.3404 1.61270 0.806348 0.591441i \(-0.201441\pi\)
0.806348 + 0.591441i \(0.201441\pi\)
\(332\) 63.9521 3.50983
\(333\) 0.341014 0.0186874
\(334\) 35.2273 1.92755
\(335\) −16.1062 −0.879977
\(336\) 30.8525 1.68314
\(337\) 17.9441 0.977480 0.488740 0.872429i \(-0.337457\pi\)
0.488740 + 0.872429i \(0.337457\pi\)
\(338\) −8.05123 −0.437929
\(339\) −9.52946 −0.517569
\(340\) 29.0220 1.57394
\(341\) 6.06636 0.328512
\(342\) 18.7253 1.01255
\(343\) −20.1533 −1.08817
\(344\) 27.0065 1.45609
\(345\) −5.66698 −0.305100
\(346\) −15.7714 −0.847875
\(347\) 1.93240 0.103737 0.0518684 0.998654i \(-0.483482\pi\)
0.0518684 + 0.998654i \(0.483482\pi\)
\(348\) 91.7712 4.91945
\(349\) −7.81487 −0.418320 −0.209160 0.977881i \(-0.567073\pi\)
−0.209160 + 0.977881i \(0.567073\pi\)
\(350\) −5.56346 −0.297379
\(351\) −12.8619 −0.686516
\(352\) −4.57181 −0.243678
\(353\) −7.04133 −0.374772 −0.187386 0.982286i \(-0.560002\pi\)
−0.187386 + 0.982286i \(0.560002\pi\)
\(354\) 37.9288 2.01589
\(355\) −11.3863 −0.604324
\(356\) 57.2028 3.03174
\(357\) 30.6512 1.62224
\(358\) 42.6550 2.25439
\(359\) −23.1301 −1.22076 −0.610381 0.792108i \(-0.708984\pi\)
−0.610381 + 0.792108i \(0.708984\pi\)
\(360\) −9.09663 −0.479435
\(361\) 5.60152 0.294817
\(362\) −28.0707 −1.47536
\(363\) 2.11924 0.111232
\(364\) 38.9776 2.04298
\(365\) 1.00000 0.0523424
\(366\) 18.6437 0.974521
\(367\) −17.9411 −0.936517 −0.468258 0.883592i \(-0.655118\pi\)
−0.468258 + 0.883592i \(0.655118\pi\)
\(368\) −17.7153 −0.923473
\(369\) −2.08626 −0.108607
\(370\) −0.578961 −0.0300987
\(371\) 20.7185 1.07565
\(372\) 56.6894 2.93921
\(373\) −23.8875 −1.23685 −0.618424 0.785845i \(-0.712228\pi\)
−0.618424 + 0.785845i \(0.712228\pi\)
\(374\) −16.6628 −0.861613
\(375\) 2.11924 0.109437
\(376\) −40.8456 −2.10645
\(377\) 39.5025 2.03448
\(378\) 17.7893 0.914981
\(379\) 24.6953 1.26851 0.634256 0.773123i \(-0.281306\pi\)
0.634256 + 0.773123i \(0.281306\pi\)
\(380\) −21.8712 −1.12197
\(381\) −38.8154 −1.98857
\(382\) 38.4522 1.96739
\(383\) 2.98296 0.152422 0.0762111 0.997092i \(-0.475718\pi\)
0.0762111 + 0.997092i \(0.475718\pi\)
\(384\) 28.3660 1.44755
\(385\) 2.19751 0.111996
\(386\) 48.5097 2.46908
\(387\) −6.60174 −0.335585
\(388\) 25.4015 1.28957
\(389\) 4.02022 0.203833 0.101917 0.994793i \(-0.467503\pi\)
0.101917 + 0.994793i \(0.467503\pi\)
\(390\) −21.5817 −1.09283
\(391\) −17.5997 −0.890055
\(392\) 13.2431 0.668879
\(393\) −7.20464 −0.363426
\(394\) 1.66690 0.0839770
\(395\) 6.89054 0.346701
\(396\) 6.57548 0.330430
\(397\) 5.60003 0.281057 0.140529 0.990077i \(-0.455120\pi\)
0.140529 + 0.990077i \(0.455120\pi\)
\(398\) −15.4760 −0.775741
\(399\) −23.0990 −1.15640
\(400\) 6.62488 0.331244
\(401\) −37.5251 −1.87392 −0.936958 0.349443i \(-0.886371\pi\)
−0.936958 + 0.349443i \(0.886371\pi\)
\(402\) 86.4148 4.30998
\(403\) 24.4017 1.21553
\(404\) −7.19795 −0.358111
\(405\) −11.2499 −0.559013
\(406\) −54.6359 −2.71153
\(407\) 0.228684 0.0113355
\(408\) −85.0866 −4.21241
\(409\) 24.2622 1.19969 0.599844 0.800117i \(-0.295229\pi\)
0.599844 + 0.800117i \(0.295229\pi\)
\(410\) 3.54198 0.174926
\(411\) 27.6471 1.36373
\(412\) −80.9531 −3.98827
\(413\) −15.5348 −0.764418
\(414\) 10.0953 0.496157
\(415\) 14.5032 0.711932
\(416\) −18.3899 −0.901639
\(417\) 8.62136 0.422190
\(418\) 12.5572 0.614194
\(419\) 12.4559 0.608513 0.304256 0.952590i \(-0.401592\pi\)
0.304256 + 0.952590i \(0.401592\pi\)
\(420\) 20.5355 1.00203
\(421\) −23.1694 −1.12921 −0.564604 0.825362i \(-0.690971\pi\)
−0.564604 + 0.825362i \(0.690971\pi\)
\(422\) 31.8662 1.55122
\(423\) 9.98472 0.485474
\(424\) −57.5137 −2.79311
\(425\) 6.58165 0.319257
\(426\) 61.0912 2.95988
\(427\) −7.63606 −0.369535
\(428\) 13.5694 0.655900
\(429\) 8.52457 0.411570
\(430\) 11.2082 0.540508
\(431\) 24.3161 1.17126 0.585632 0.810577i \(-0.300846\pi\)
0.585632 + 0.810577i \(0.300846\pi\)
\(432\) −21.1832 −1.01918
\(433\) −32.4704 −1.56043 −0.780214 0.625513i \(-0.784890\pi\)
−0.780214 + 0.625513i \(0.784890\pi\)
\(434\) −33.7499 −1.62005
\(435\) 20.8120 0.997860
\(436\) 77.6040 3.71656
\(437\) 13.2633 0.634469
\(438\) −5.36530 −0.256364
\(439\) 19.7767 0.943891 0.471945 0.881628i \(-0.343552\pi\)
0.471945 + 0.881628i \(0.343552\pi\)
\(440\) −6.10021 −0.290816
\(441\) −3.23729 −0.154157
\(442\) −67.0254 −3.18807
\(443\) 1.94369 0.0923473 0.0461736 0.998933i \(-0.485297\pi\)
0.0461736 + 0.998933i \(0.485297\pi\)
\(444\) 2.13702 0.101419
\(445\) 12.9726 0.614958
\(446\) −8.44136 −0.399710
\(447\) 32.8730 1.55484
\(448\) −3.68147 −0.173933
\(449\) 14.4782 0.683268 0.341634 0.939833i \(-0.389020\pi\)
0.341634 + 0.939833i \(0.389020\pi\)
\(450\) −3.77528 −0.177968
\(451\) −1.39905 −0.0658787
\(452\) −19.8280 −0.932631
\(453\) 37.2363 1.74951
\(454\) 63.9210 2.99996
\(455\) 8.83941 0.414398
\(456\) 64.1220 3.00279
\(457\) 15.4855 0.724382 0.362191 0.932104i \(-0.382029\pi\)
0.362191 + 0.932104i \(0.382029\pi\)
\(458\) −60.8642 −2.84400
\(459\) −21.0450 −0.982295
\(460\) −11.7913 −0.549773
\(461\) −34.1818 −1.59201 −0.796003 0.605293i \(-0.793056\pi\)
−0.796003 + 0.605293i \(0.793056\pi\)
\(462\) −11.7903 −0.548536
\(463\) 19.2318 0.893778 0.446889 0.894589i \(-0.352532\pi\)
0.446889 + 0.894589i \(0.352532\pi\)
\(464\) 65.0595 3.02031
\(465\) 12.8561 0.596188
\(466\) 52.7260 2.44249
\(467\) 13.4116 0.620617 0.310308 0.950636i \(-0.399568\pi\)
0.310308 + 0.950636i \(0.399568\pi\)
\(468\) 26.4496 1.22263
\(469\) −35.3937 −1.63433
\(470\) −16.9517 −0.781924
\(471\) 22.8006 1.05060
\(472\) 43.1240 1.98494
\(473\) −4.42714 −0.203560
\(474\) −36.9698 −1.69808
\(475\) −4.95999 −0.227580
\(476\) 63.7762 2.92318
\(477\) 14.0592 0.643728
\(478\) −32.7241 −1.49677
\(479\) 12.2562 0.560000 0.280000 0.960000i \(-0.409666\pi\)
0.280000 + 0.960000i \(0.409666\pi\)
\(480\) −9.68878 −0.442230
\(481\) 0.919873 0.0419426
\(482\) 16.0617 0.731591
\(483\) −12.4533 −0.566643
\(484\) 4.40953 0.200433
\(485\) 5.76060 0.261575
\(486\) 36.0737 1.63634
\(487\) 20.6788 0.937046 0.468523 0.883451i \(-0.344786\pi\)
0.468523 + 0.883451i \(0.344786\pi\)
\(488\) 21.1974 0.959561
\(489\) −41.4020 −1.87226
\(490\) 5.49615 0.248291
\(491\) 8.04376 0.363010 0.181505 0.983390i \(-0.441903\pi\)
0.181505 + 0.983390i \(0.441903\pi\)
\(492\) −13.0739 −0.589419
\(493\) 64.6351 2.91102
\(494\) 50.5109 2.27259
\(495\) 1.49120 0.0670244
\(496\) 40.1889 1.80453
\(497\) −25.0217 −1.12237
\(498\) −77.8138 −3.48692
\(499\) 2.35660 0.105496 0.0527479 0.998608i \(-0.483202\pi\)
0.0527479 + 0.998608i \(0.483202\pi\)
\(500\) 4.40953 0.197200
\(501\) −29.4881 −1.31743
\(502\) 53.4301 2.38470
\(503\) 32.0592 1.42945 0.714724 0.699406i \(-0.246552\pi\)
0.714724 + 0.699406i \(0.246552\pi\)
\(504\) −19.9900 −0.890424
\(505\) −1.63236 −0.0726392
\(506\) 6.76992 0.300959
\(507\) 6.73955 0.299314
\(508\) −80.7635 −3.58330
\(509\) 12.8603 0.570024 0.285012 0.958524i \(-0.408002\pi\)
0.285012 + 0.958524i \(0.408002\pi\)
\(510\) −35.3126 −1.56367
\(511\) 2.19751 0.0972123
\(512\) 50.5386 2.23351
\(513\) 15.8597 0.700221
\(514\) −30.4732 −1.34412
\(515\) −18.3587 −0.808980
\(516\) −41.3710 −1.82126
\(517\) 6.69577 0.294480
\(518\) −1.27227 −0.0559006
\(519\) 13.2020 0.579502
\(520\) −24.5378 −1.07606
\(521\) 23.8421 1.04454 0.522271 0.852780i \(-0.325085\pi\)
0.522271 + 0.852780i \(0.325085\pi\)
\(522\) −37.0751 −1.62273
\(523\) 18.7856 0.821437 0.410718 0.911762i \(-0.365278\pi\)
0.410718 + 0.911762i \(0.365278\pi\)
\(524\) −14.9907 −0.654874
\(525\) 4.65707 0.203251
\(526\) −69.0941 −3.01265
\(527\) 39.9267 1.73923
\(528\) 14.0397 0.611001
\(529\) −15.8494 −0.689106
\(530\) −23.8693 −1.03681
\(531\) −10.5417 −0.457470
\(532\) −48.0623 −2.08377
\(533\) −5.62762 −0.243759
\(534\) −69.6017 −3.01196
\(535\) 3.07728 0.133043
\(536\) 98.2514 4.24381
\(537\) −35.7058 −1.54082
\(538\) −12.3124 −0.530825
\(539\) −2.17093 −0.0935086
\(540\) −14.0995 −0.606748
\(541\) 22.1772 0.953474 0.476737 0.879046i \(-0.341819\pi\)
0.476737 + 0.879046i \(0.341819\pi\)
\(542\) 6.99163 0.300316
\(543\) 23.4975 1.00837
\(544\) −30.0901 −1.29010
\(545\) 17.5992 0.753865
\(546\) −47.4261 −2.02965
\(547\) 12.5284 0.535677 0.267839 0.963464i \(-0.413691\pi\)
0.267839 + 0.963464i \(0.413691\pi\)
\(548\) 57.5254 2.45736
\(549\) −5.18171 −0.221150
\(550\) −2.53170 −0.107952
\(551\) −48.7096 −2.07510
\(552\) 34.5698 1.47139
\(553\) 15.1421 0.643906
\(554\) −30.2651 −1.28584
\(555\) 0.484638 0.0205717
\(556\) 17.9385 0.760762
\(557\) −35.7557 −1.51502 −0.757508 0.652826i \(-0.773583\pi\)
−0.757508 + 0.652826i \(0.773583\pi\)
\(558\) −22.9022 −0.969527
\(559\) −17.8080 −0.753197
\(560\) 14.5583 0.615199
\(561\) 13.9481 0.588891
\(562\) −72.1517 −3.04353
\(563\) 41.7470 1.75943 0.879714 0.475504i \(-0.157734\pi\)
0.879714 + 0.475504i \(0.157734\pi\)
\(564\) 62.5711 2.63472
\(565\) −4.49663 −0.189175
\(566\) 80.7912 3.39591
\(567\) −24.7219 −1.03822
\(568\) 69.4591 2.91444
\(569\) −41.9732 −1.75961 −0.879803 0.475338i \(-0.842326\pi\)
−0.879803 + 0.475338i \(0.842326\pi\)
\(570\) 26.6119 1.11465
\(571\) 1.00640 0.0421167 0.0210583 0.999778i \(-0.493296\pi\)
0.0210583 + 0.999778i \(0.493296\pi\)
\(572\) 17.7371 0.741627
\(573\) −32.1877 −1.34466
\(574\) 7.78356 0.324880
\(575\) −2.67405 −0.111516
\(576\) −2.49819 −0.104091
\(577\) −30.6626 −1.27650 −0.638251 0.769828i \(-0.720342\pi\)
−0.638251 + 0.769828i \(0.720342\pi\)
\(578\) −66.6298 −2.77143
\(579\) −40.6066 −1.68755
\(580\) 43.3037 1.79809
\(581\) 31.8709 1.32223
\(582\) −30.9074 −1.28115
\(583\) 9.42814 0.390474
\(584\) −6.10021 −0.252429
\(585\) 5.99829 0.247999
\(586\) 28.6283 1.18262
\(587\) 3.85705 0.159198 0.0795988 0.996827i \(-0.474636\pi\)
0.0795988 + 0.996827i \(0.474636\pi\)
\(588\) −20.2871 −0.836624
\(589\) −30.0891 −1.23980
\(590\) 17.8973 0.736820
\(591\) −1.39533 −0.0573962
\(592\) 1.51500 0.0622663
\(593\) 16.8870 0.693464 0.346732 0.937964i \(-0.387291\pi\)
0.346732 + 0.937964i \(0.387291\pi\)
\(594\) 8.09517 0.332149
\(595\) 14.4633 0.592937
\(596\) 68.3991 2.80174
\(597\) 12.9547 0.530200
\(598\) 27.2317 1.11359
\(599\) 26.9023 1.09920 0.549599 0.835429i \(-0.314781\pi\)
0.549599 + 0.835429i \(0.314781\pi\)
\(600\) −12.9278 −0.527777
\(601\) −4.21138 −0.171786 −0.0858930 0.996304i \(-0.527374\pi\)
−0.0858930 + 0.996304i \(0.527374\pi\)
\(602\) 24.6302 1.00385
\(603\) −24.0176 −0.978072
\(604\) 77.4778 3.15253
\(605\) 1.00000 0.0406558
\(606\) 8.75812 0.355774
\(607\) 46.6747 1.89447 0.947233 0.320546i \(-0.103866\pi\)
0.947233 + 0.320546i \(0.103866\pi\)
\(608\) 22.6761 0.919639
\(609\) 45.7347 1.85326
\(610\) 8.79733 0.356193
\(611\) 26.9334 1.08961
\(612\) 43.2776 1.74939
\(613\) 8.06688 0.325818 0.162909 0.986641i \(-0.447912\pi\)
0.162909 + 0.986641i \(0.447912\pi\)
\(614\) 43.7866 1.76708
\(615\) −2.96493 −0.119558
\(616\) −13.4053 −0.540115
\(617\) −29.9207 −1.20456 −0.602280 0.798285i \(-0.705741\pi\)
−0.602280 + 0.798285i \(0.705741\pi\)
\(618\) 98.4999 3.96225
\(619\) 5.02350 0.201912 0.100956 0.994891i \(-0.467810\pi\)
0.100956 + 0.994891i \(0.467810\pi\)
\(620\) 26.7498 1.07430
\(621\) 8.55034 0.343113
\(622\) −15.0587 −0.603798
\(623\) 28.5074 1.14212
\(624\) 56.4742 2.26078
\(625\) 1.00000 0.0400000
\(626\) 67.4351 2.69525
\(627\) −10.5114 −0.419786
\(628\) 47.4414 1.89312
\(629\) 1.50512 0.0600131
\(630\) −8.29622 −0.330529
\(631\) −27.8508 −1.10872 −0.554361 0.832276i \(-0.687037\pi\)
−0.554361 + 0.832276i \(0.687037\pi\)
\(632\) −42.0337 −1.67201
\(633\) −26.6746 −1.06022
\(634\) −16.6976 −0.663146
\(635\) −18.3157 −0.726836
\(636\) 88.1047 3.49358
\(637\) −8.73247 −0.345993
\(638\) −24.8626 −0.984319
\(639\) −16.9793 −0.671691
\(640\) 13.3849 0.529087
\(641\) −6.48488 −0.256137 −0.128069 0.991765i \(-0.540878\pi\)
−0.128069 + 0.991765i \(0.540878\pi\)
\(642\) −16.5106 −0.651620
\(643\) 1.27801 0.0503997 0.0251999 0.999682i \(-0.491978\pi\)
0.0251999 + 0.999682i \(0.491978\pi\)
\(644\) −25.9116 −1.02106
\(645\) −9.38219 −0.369423
\(646\) 82.6474 3.25172
\(647\) 4.30310 0.169172 0.0845862 0.996416i \(-0.473043\pi\)
0.0845862 + 0.996416i \(0.473043\pi\)
\(648\) 68.6269 2.69592
\(649\) −7.06927 −0.277493
\(650\) −10.1837 −0.399437
\(651\) 28.2515 1.10726
\(652\) −86.1454 −3.37372
\(653\) −19.0853 −0.746867 −0.373433 0.927657i \(-0.621820\pi\)
−0.373433 + 0.927657i \(0.621820\pi\)
\(654\) −94.4248 −3.69230
\(655\) −3.39963 −0.132834
\(656\) −9.26854 −0.361876
\(657\) 1.49120 0.0581772
\(658\) −37.2516 −1.45222
\(659\) −19.2115 −0.748374 −0.374187 0.927353i \(-0.622078\pi\)
−0.374187 + 0.927353i \(0.622078\pi\)
\(660\) 9.34487 0.363749
\(661\) 10.6760 0.415250 0.207625 0.978209i \(-0.433427\pi\)
0.207625 + 0.978209i \(0.433427\pi\)
\(662\) −74.2813 −2.88703
\(663\) 56.1058 2.17897
\(664\) −88.4723 −3.43339
\(665\) −10.8997 −0.422671
\(666\) −0.863346 −0.0334540
\(667\) −26.2605 −1.01681
\(668\) −61.3562 −2.37394
\(669\) 7.06611 0.273192
\(670\) 40.7762 1.57532
\(671\) −3.47486 −0.134146
\(672\) −21.2912 −0.821327
\(673\) 46.3295 1.78587 0.892936 0.450183i \(-0.148641\pi\)
0.892936 + 0.450183i \(0.148641\pi\)
\(674\) −45.4293 −1.74987
\(675\) −3.19752 −0.123073
\(676\) 14.0230 0.539347
\(677\) −9.35049 −0.359368 −0.179684 0.983724i \(-0.557508\pi\)
−0.179684 + 0.983724i \(0.557508\pi\)
\(678\) 24.1258 0.926545
\(679\) 12.6590 0.485808
\(680\) −40.1495 −1.53966
\(681\) −53.5071 −2.05040
\(682\) −15.3582 −0.588097
\(683\) −48.6180 −1.86031 −0.930157 0.367161i \(-0.880330\pi\)
−0.930157 + 0.367161i \(0.880330\pi\)
\(684\) −32.6143 −1.24704
\(685\) 13.0457 0.498451
\(686\) 51.0221 1.94803
\(687\) 50.9483 1.94380
\(688\) −29.3292 −1.11817
\(689\) 37.9243 1.44480
\(690\) 14.3471 0.546185
\(691\) 22.0934 0.840474 0.420237 0.907414i \(-0.361947\pi\)
0.420237 + 0.907414i \(0.361947\pi\)
\(692\) 27.4694 1.04423
\(693\) 3.27693 0.124480
\(694\) −4.89227 −0.185708
\(695\) 4.06813 0.154313
\(696\) −126.958 −4.81232
\(697\) −9.20807 −0.348781
\(698\) 19.7849 0.748871
\(699\) −44.1360 −1.66938
\(700\) 9.69000 0.366248
\(701\) −40.5304 −1.53081 −0.765405 0.643548i \(-0.777462\pi\)
−0.765405 + 0.643548i \(0.777462\pi\)
\(702\) 32.5625 1.22899
\(703\) −1.13427 −0.0427799
\(704\) −1.67529 −0.0631397
\(705\) 14.1900 0.534425
\(706\) 17.8266 0.670912
\(707\) −3.58714 −0.134908
\(708\) −66.0614 −2.48274
\(709\) 0.694305 0.0260752 0.0130376 0.999915i \(-0.495850\pi\)
0.0130376 + 0.999915i \(0.495850\pi\)
\(710\) 28.8269 1.08185
\(711\) 10.2752 0.385349
\(712\) −79.1353 −2.96572
\(713\) −16.2218 −0.607511
\(714\) −77.5999 −2.90410
\(715\) 4.02246 0.150431
\(716\) −74.2932 −2.77647
\(717\) 27.3928 1.02300
\(718\) 58.5587 2.18539
\(719\) 47.7151 1.77947 0.889736 0.456476i \(-0.150888\pi\)
0.889736 + 0.456476i \(0.150888\pi\)
\(720\) 9.87901 0.368169
\(721\) −40.3435 −1.50247
\(722\) −14.1814 −0.527777
\(723\) −13.4450 −0.500024
\(724\) 48.8913 1.81703
\(725\) 9.82049 0.364724
\(726\) −5.36530 −0.199125
\(727\) −14.0176 −0.519885 −0.259943 0.965624i \(-0.583704\pi\)
−0.259943 + 0.965624i \(0.583704\pi\)
\(728\) −53.9223 −1.99849
\(729\) 3.55310 0.131596
\(730\) −2.53170 −0.0937026
\(731\) −29.1379 −1.07770
\(732\) −32.4721 −1.20020
\(733\) 24.8247 0.916920 0.458460 0.888715i \(-0.348401\pi\)
0.458460 + 0.888715i \(0.348401\pi\)
\(734\) 45.4215 1.67654
\(735\) −4.60073 −0.169701
\(736\) 12.2253 0.450629
\(737\) −16.1062 −0.593280
\(738\) 5.28180 0.194426
\(739\) 12.0878 0.444658 0.222329 0.974972i \(-0.428634\pi\)
0.222329 + 0.974972i \(0.428634\pi\)
\(740\) 1.00839 0.0370691
\(741\) −42.2818 −1.55326
\(742\) −52.4531 −1.92561
\(743\) 7.47764 0.274328 0.137164 0.990548i \(-0.456201\pi\)
0.137164 + 0.990548i \(0.456201\pi\)
\(744\) −78.4250 −2.87520
\(745\) 15.5117 0.568304
\(746\) 60.4761 2.21419
\(747\) 21.6271 0.791294
\(748\) 29.0220 1.06115
\(749\) 6.76238 0.247092
\(750\) −5.36530 −0.195913
\(751\) −21.3092 −0.777583 −0.388792 0.921326i \(-0.627107\pi\)
−0.388792 + 0.921326i \(0.627107\pi\)
\(752\) 44.3586 1.61759
\(753\) −44.7254 −1.62988
\(754\) −100.009 −3.64210
\(755\) 17.5705 0.639458
\(756\) −30.9840 −1.12688
\(757\) −4.95336 −0.180033 −0.0900165 0.995940i \(-0.528692\pi\)
−0.0900165 + 0.995940i \(0.528692\pi\)
\(758\) −62.5212 −2.27087
\(759\) −5.66698 −0.205698
\(760\) 30.2570 1.09754
\(761\) 2.58107 0.0935636 0.0467818 0.998905i \(-0.485103\pi\)
0.0467818 + 0.998905i \(0.485103\pi\)
\(762\) 98.2692 3.55992
\(763\) 38.6744 1.40011
\(764\) −66.9731 −2.42300
\(765\) 9.81456 0.354846
\(766\) −7.55197 −0.272864
\(767\) −28.4358 −1.02676
\(768\) −64.7136 −2.33515
\(769\) 5.16842 0.186378 0.0931890 0.995648i \(-0.470294\pi\)
0.0931890 + 0.995648i \(0.470294\pi\)
\(770\) −5.56346 −0.200493
\(771\) 25.5086 0.918670
\(772\) −84.4904 −3.04088
\(773\) 0.486616 0.0175024 0.00875119 0.999962i \(-0.497214\pi\)
0.00875119 + 0.999962i \(0.497214\pi\)
\(774\) 16.7137 0.600760
\(775\) 6.06636 0.217910
\(776\) −35.1409 −1.26148
\(777\) 1.06500 0.0382066
\(778\) −10.1780 −0.364899
\(779\) 6.93928 0.248626
\(780\) 37.5893 1.34591
\(781\) −11.3863 −0.407435
\(782\) 44.5572 1.59336
\(783\) −31.4012 −1.12219
\(784\) −14.3821 −0.513648
\(785\) 10.7588 0.383999
\(786\) 18.2400 0.650600
\(787\) −35.3471 −1.25999 −0.629994 0.776600i \(-0.716943\pi\)
−0.629994 + 0.776600i \(0.716943\pi\)
\(788\) −2.90327 −0.103425
\(789\) 57.8374 2.05907
\(790\) −17.4448 −0.620658
\(791\) −9.88141 −0.351342
\(792\) −9.09663 −0.323235
\(793\) −13.9775 −0.496355
\(794\) −14.1776 −0.503145
\(795\) 19.9805 0.708637
\(796\) 26.9549 0.955390
\(797\) 3.85250 0.136463 0.0682313 0.997670i \(-0.478264\pi\)
0.0682313 + 0.997670i \(0.478264\pi\)
\(798\) 58.4799 2.07017
\(799\) 44.0692 1.55906
\(800\) −4.57181 −0.161638
\(801\) 19.3447 0.683510
\(802\) 95.0025 3.35466
\(803\) 1.00000 0.0352892
\(804\) −150.511 −5.30810
\(805\) −5.87627 −0.207111
\(806\) −61.7778 −2.17603
\(807\) 10.3065 0.362806
\(808\) 9.95776 0.350313
\(809\) −9.04985 −0.318176 −0.159088 0.987264i \(-0.550855\pi\)
−0.159088 + 0.987264i \(0.550855\pi\)
\(810\) 28.4815 1.00074
\(811\) −21.4746 −0.754076 −0.377038 0.926198i \(-0.623057\pi\)
−0.377038 + 0.926198i \(0.623057\pi\)
\(812\) 95.1606 3.33948
\(813\) −5.85257 −0.205258
\(814\) −0.578961 −0.0202926
\(815\) −19.5362 −0.684323
\(816\) 92.4047 3.23481
\(817\) 21.9586 0.768233
\(818\) −61.4247 −2.14766
\(819\) 13.1813 0.460593
\(820\) −6.16915 −0.215436
\(821\) 45.0516 1.57231 0.786156 0.618028i \(-0.212068\pi\)
0.786156 + 0.618028i \(0.212068\pi\)
\(822\) −69.9942 −2.44133
\(823\) −35.6951 −1.24425 −0.622126 0.782917i \(-0.713731\pi\)
−0.622126 + 0.782917i \(0.713731\pi\)
\(824\) 111.992 3.90142
\(825\) 2.11924 0.0737826
\(826\) 39.3296 1.36845
\(827\) 42.2943 1.47072 0.735358 0.677678i \(-0.237014\pi\)
0.735358 + 0.677678i \(0.237014\pi\)
\(828\) −17.5832 −0.611059
\(829\) −31.9342 −1.10912 −0.554561 0.832143i \(-0.687114\pi\)
−0.554561 + 0.832143i \(0.687114\pi\)
\(830\) −36.7177 −1.27449
\(831\) 25.3343 0.878839
\(832\) −6.73877 −0.233625
\(833\) −14.2883 −0.495060
\(834\) −21.8267 −0.755798
\(835\) −13.9145 −0.481530
\(836\) −21.8712 −0.756432
\(837\) −19.3973 −0.670469
\(838\) −31.5348 −1.08935
\(839\) 0.187256 0.00646479 0.00323239 0.999995i \(-0.498971\pi\)
0.00323239 + 0.999995i \(0.498971\pi\)
\(840\) −28.4091 −0.980208
\(841\) 67.4420 2.32559
\(842\) 58.6581 2.02149
\(843\) 60.3969 2.08018
\(844\) −55.5020 −1.91046
\(845\) 3.18016 0.109401
\(846\) −25.2784 −0.869088
\(847\) 2.19751 0.0755075
\(848\) 62.4603 2.14489
\(849\) −67.6289 −2.32102
\(850\) −16.6628 −0.571529
\(851\) −0.611514 −0.0209624
\(852\) −106.404 −3.64534
\(853\) −34.5935 −1.18446 −0.592230 0.805769i \(-0.701752\pi\)
−0.592230 + 0.805769i \(0.701752\pi\)
\(854\) 19.3323 0.661536
\(855\) −7.39634 −0.252949
\(856\) −18.7721 −0.641617
\(857\) −44.0430 −1.50448 −0.752240 0.658889i \(-0.771027\pi\)
−0.752240 + 0.658889i \(0.771027\pi\)
\(858\) −21.5817 −0.736787
\(859\) −35.0611 −1.19627 −0.598134 0.801396i \(-0.704091\pi\)
−0.598134 + 0.801396i \(0.704091\pi\)
\(860\) −19.5216 −0.665680
\(861\) −6.51548 −0.222047
\(862\) −61.5611 −2.09678
\(863\) 42.6150 1.45063 0.725315 0.688417i \(-0.241694\pi\)
0.725315 + 0.688417i \(0.241694\pi\)
\(864\) 14.6184 0.497329
\(865\) 6.22956 0.211811
\(866\) 82.2054 2.79345
\(867\) 55.7746 1.89421
\(868\) 58.7831 1.99523
\(869\) 6.89054 0.233745
\(870\) −52.6899 −1.78635
\(871\) −64.7866 −2.19521
\(872\) −107.359 −3.63562
\(873\) 8.59020 0.290734
\(874\) −33.5787 −1.13582
\(875\) 2.19751 0.0742896
\(876\) 9.34487 0.315734
\(877\) −30.2501 −1.02147 −0.510737 0.859737i \(-0.670628\pi\)
−0.510737 + 0.859737i \(0.670628\pi\)
\(878\) −50.0688 −1.68974
\(879\) −23.9642 −0.808293
\(880\) 6.62488 0.223325
\(881\) −2.93721 −0.0989573 −0.0494786 0.998775i \(-0.515756\pi\)
−0.0494786 + 0.998775i \(0.515756\pi\)
\(882\) 8.19586 0.275969
\(883\) −15.8623 −0.533808 −0.266904 0.963723i \(-0.586001\pi\)
−0.266904 + 0.963723i \(0.586001\pi\)
\(884\) 116.740 3.92638
\(885\) −14.9815 −0.503598
\(886\) −4.92084 −0.165319
\(887\) −8.04592 −0.270156 −0.135078 0.990835i \(-0.543128\pi\)
−0.135078 + 0.990835i \(0.543128\pi\)
\(888\) −2.95639 −0.0992101
\(889\) −40.2490 −1.34991
\(890\) −32.8427 −1.10089
\(891\) −11.2499 −0.376887
\(892\) 14.7025 0.492276
\(893\) −33.2110 −1.11136
\(894\) −83.2248 −2.78345
\(895\) −16.8483 −0.563178
\(896\) 29.4136 0.982640
\(897\) −22.7952 −0.761109
\(898\) −36.6545 −1.22318
\(899\) 59.5746 1.98693
\(900\) 6.57548 0.219183
\(901\) 62.0528 2.06728
\(902\) 3.54198 0.117935
\(903\) −20.6175 −0.686107
\(904\) 27.4304 0.912321
\(905\) 11.0877 0.368566
\(906\) −94.2713 −3.13195
\(907\) 39.5218 1.31230 0.656150 0.754631i \(-0.272184\pi\)
0.656150 + 0.754631i \(0.272184\pi\)
\(908\) −111.333 −3.69470
\(909\) −2.43418 −0.0807366
\(910\) −22.3788 −0.741849
\(911\) −25.2132 −0.835351 −0.417676 0.908596i \(-0.637155\pi\)
−0.417676 + 0.908596i \(0.637155\pi\)
\(912\) −69.6370 −2.30591
\(913\) 14.5032 0.479984
\(914\) −39.2048 −1.29678
\(915\) −7.36409 −0.243449
\(916\) 106.008 3.50262
\(917\) −7.47073 −0.246705
\(918\) 53.2796 1.75849
\(919\) −43.0647 −1.42057 −0.710287 0.703912i \(-0.751435\pi\)
−0.710287 + 0.703912i \(0.751435\pi\)
\(920\) 16.3123 0.537801
\(921\) −36.6530 −1.20776
\(922\) 86.5383 2.84999
\(923\) −45.8011 −1.50756
\(924\) 20.5355 0.675568
\(925\) 0.228684 0.00751909
\(926\) −48.6893 −1.60003
\(927\) −27.3765 −0.899161
\(928\) −44.8974 −1.47383
\(929\) 57.7294 1.89404 0.947021 0.321172i \(-0.104077\pi\)
0.947021 + 0.321172i \(0.104077\pi\)
\(930\) −32.5479 −1.06729
\(931\) 10.7678 0.352900
\(932\) −91.8342 −3.00813
\(933\) 12.6053 0.412681
\(934\) −33.9543 −1.11102
\(935\) 6.58165 0.215243
\(936\) −36.5908 −1.19601
\(937\) −50.9207 −1.66351 −0.831754 0.555144i \(-0.812663\pi\)
−0.831754 + 0.555144i \(0.812663\pi\)
\(938\) 89.6063 2.92575
\(939\) −56.4487 −1.84213
\(940\) 29.5252 0.963005
\(941\) −0.322576 −0.0105157 −0.00525784 0.999986i \(-0.501674\pi\)
−0.00525784 + 0.999986i \(0.501674\pi\)
\(942\) −57.7244 −1.88076
\(943\) 3.74114 0.121828
\(944\) −46.8330 −1.52429
\(945\) −7.02659 −0.228575
\(946\) 11.2082 0.364410
\(947\) 18.9973 0.617328 0.308664 0.951171i \(-0.400118\pi\)
0.308664 + 0.951171i \(0.400118\pi\)
\(948\) 64.3912 2.09133
\(949\) 4.02246 0.130574
\(950\) 12.5572 0.407410
\(951\) 13.9773 0.453243
\(952\) −88.2291 −2.85952
\(953\) −48.0159 −1.55539 −0.777694 0.628643i \(-0.783611\pi\)
−0.777694 + 0.628643i \(0.783611\pi\)
\(954\) −35.5938 −1.15239
\(955\) −15.1883 −0.491481
\(956\) 56.9963 1.84339
\(957\) 20.8120 0.672757
\(958\) −31.0291 −1.00250
\(959\) 28.6681 0.925742
\(960\) −3.55034 −0.114587
\(961\) 5.80074 0.187121
\(962\) −2.32885 −0.0750850
\(963\) 4.58884 0.147873
\(964\) −27.9751 −0.901016
\(965\) −19.1609 −0.616811
\(966\) 31.5280 1.01440
\(967\) 18.9562 0.609592 0.304796 0.952418i \(-0.401412\pi\)
0.304796 + 0.952418i \(0.401412\pi\)
\(968\) −6.10021 −0.196068
\(969\) −69.1826 −2.22247
\(970\) −14.5841 −0.468269
\(971\) 5.96892 0.191552 0.0957759 0.995403i \(-0.469467\pi\)
0.0957759 + 0.995403i \(0.469467\pi\)
\(972\) −62.8304 −2.01529
\(973\) 8.93977 0.286596
\(974\) −52.3526 −1.67749
\(975\) 8.52457 0.273005
\(976\) −23.0205 −0.736869
\(977\) 19.5208 0.624525 0.312262 0.949996i \(-0.398913\pi\)
0.312262 + 0.949996i \(0.398913\pi\)
\(978\) 104.818 3.35170
\(979\) 12.9726 0.414605
\(980\) −9.57277 −0.305791
\(981\) 26.2439 0.837902
\(982\) −20.3644 −0.649855
\(983\) −22.4505 −0.716061 −0.358031 0.933710i \(-0.616552\pi\)
−0.358031 + 0.933710i \(0.616552\pi\)
\(984\) 18.0867 0.576583
\(985\) −0.658409 −0.0209787
\(986\) −163.637 −5.21126
\(987\) 31.1827 0.992555
\(988\) −87.9761 −2.79889
\(989\) 11.8384 0.376439
\(990\) −3.77528 −0.119986
\(991\) 5.43339 0.172597 0.0862986 0.996269i \(-0.472496\pi\)
0.0862986 + 0.996269i \(0.472496\pi\)
\(992\) −27.7342 −0.880563
\(993\) 62.1796 1.97321
\(994\) 63.3474 2.00926
\(995\) 6.11287 0.193791
\(996\) 135.530 4.29444
\(997\) 51.6642 1.63622 0.818111 0.575060i \(-0.195021\pi\)
0.818111 + 0.575060i \(0.195021\pi\)
\(998\) −5.96621 −0.188857
\(999\) −0.731222 −0.0231348
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 \(a_p\))