Properties

Label 8021.2.a.a.1.12
Level 8021
Weight 2
Character 8021.1
Self dual Yes
Analytic conductor 64.048
Analytic rank 1
Dimension 134
CM No

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Newspace parameters

Level: \( N \) = \( 8021 = 13 \cdot 617 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8021.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0480074613\)
Analytic rank: \(1\)
Dimension: \(134\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 8021.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.37815 q^{2}\) \(+2.24175 q^{3}\) \(+3.65561 q^{4}\) \(+2.50193 q^{5}\) \(-5.33123 q^{6}\) \(-3.50735 q^{7}\) \(-3.93730 q^{8}\) \(+2.02545 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.37815 q^{2}\) \(+2.24175 q^{3}\) \(+3.65561 q^{4}\) \(+2.50193 q^{5}\) \(-5.33123 q^{6}\) \(-3.50735 q^{7}\) \(-3.93730 q^{8}\) \(+2.02545 q^{9}\) \(-5.94998 q^{10}\) \(-4.72784 q^{11}\) \(+8.19497 q^{12}\) \(+1.00000 q^{13}\) \(+8.34103 q^{14}\) \(+5.60871 q^{15}\) \(+2.05228 q^{16}\) \(+0.105110 q^{17}\) \(-4.81683 q^{18}\) \(+2.87419 q^{19}\) \(+9.14610 q^{20}\) \(-7.86262 q^{21}\) \(+11.2435 q^{22}\) \(-5.90670 q^{23}\) \(-8.82645 q^{24}\) \(+1.25967 q^{25}\) \(-2.37815 q^{26}\) \(-2.18470 q^{27}\) \(-12.8215 q^{28}\) \(+8.85260 q^{29}\) \(-13.3384 q^{30}\) \(+5.66043 q^{31}\) \(+2.99397 q^{32}\) \(-10.5986 q^{33}\) \(-0.249968 q^{34}\) \(-8.77516 q^{35}\) \(+7.40426 q^{36}\) \(+6.18356 q^{37}\) \(-6.83528 q^{38}\) \(+2.24175 q^{39}\) \(-9.85086 q^{40}\) \(+5.52352 q^{41}\) \(+18.6985 q^{42}\) \(-7.13642 q^{43}\) \(-17.2832 q^{44}\) \(+5.06754 q^{45}\) \(+14.0470 q^{46}\) \(+3.13636 q^{47}\) \(+4.60069 q^{48}\) \(+5.30154 q^{49}\) \(-2.99568 q^{50}\) \(+0.235631 q^{51}\) \(+3.65561 q^{52}\) \(-4.15489 q^{53}\) \(+5.19555 q^{54}\) \(-11.8287 q^{55}\) \(+13.8095 q^{56}\) \(+6.44323 q^{57}\) \(-21.0528 q^{58}\) \(-6.63482 q^{59}\) \(+20.5033 q^{60}\) \(-10.7653 q^{61}\) \(-13.4614 q^{62}\) \(-7.10397 q^{63}\) \(-11.2247 q^{64}\) \(+2.50193 q^{65}\) \(+25.2052 q^{66}\) \(+3.63647 q^{67}\) \(+0.384242 q^{68}\) \(-13.2413 q^{69}\) \(+20.8687 q^{70}\) \(-0.128553 q^{71}\) \(-7.97481 q^{72}\) \(-4.52614 q^{73}\) \(-14.7054 q^{74}\) \(+2.82386 q^{75}\) \(+10.5069 q^{76}\) \(+16.5822 q^{77}\) \(-5.33123 q^{78}\) \(-4.46982 q^{79}\) \(+5.13466 q^{80}\) \(-10.9739 q^{81}\) \(-13.1358 q^{82}\) \(+9.21052 q^{83}\) \(-28.7427 q^{84}\) \(+0.262979 q^{85}\) \(+16.9715 q^{86}\) \(+19.8453 q^{87}\) \(+18.6149 q^{88}\) \(-2.90807 q^{89}\) \(-12.0514 q^{90}\) \(-3.50735 q^{91}\) \(-21.5926 q^{92}\) \(+12.6893 q^{93}\) \(-7.45875 q^{94}\) \(+7.19104 q^{95}\) \(+6.71174 q^{96}\) \(+0.930007 q^{97}\) \(-12.6079 q^{98}\) \(-9.57601 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 47q^{11} \) \(\mathstrut -\mathstrut 53q^{12} \) \(\mathstrut +\mathstrut 134q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 87q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 52q^{22} \) \(\mathstrut -\mathstrut 44q^{23} \) \(\mathstrut -\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 58q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 117q^{27} \) \(\mathstrut -\mathstrut 71q^{28} \) \(\mathstrut -\mathstrut 42q^{29} \) \(\mathstrut -\mathstrut 21q^{30} \) \(\mathstrut -\mathstrut 82q^{31} \) \(\mathstrut -\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 30q^{34} \) \(\mathstrut -\mathstrut 54q^{35} \) \(\mathstrut +\mathstrut 32q^{36} \) \(\mathstrut -\mathstrut 55q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut 33q^{39} \) \(\mathstrut -\mathstrut 86q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut +\mathstrut 6q^{42} \) \(\mathstrut -\mathstrut 148q^{43} \) \(\mathstrut -\mathstrut 54q^{44} \) \(\mathstrut -\mathstrut 24q^{45} \) \(\mathstrut -\mathstrut 57q^{46} \) \(\mathstrut -\mathstrut 21q^{47} \) \(\mathstrut -\mathstrut 82q^{48} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 17q^{50} \) \(\mathstrut -\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 98q^{52} \) \(\mathstrut -\mathstrut 17q^{53} \) \(\mathstrut -\mathstrut 10q^{54} \) \(\mathstrut -\mathstrut 148q^{55} \) \(\mathstrut -\mathstrut 47q^{56} \) \(\mathstrut -\mathstrut q^{57} \) \(\mathstrut -\mathstrut 58q^{58} \) \(\mathstrut -\mathstrut 64q^{59} \) \(\mathstrut -\mathstrut 16q^{60} \) \(\mathstrut -\mathstrut 112q^{61} \) \(\mathstrut -\mathstrut 15q^{62} \) \(\mathstrut -\mathstrut 58q^{63} \) \(\mathstrut -\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 20q^{66} \) \(\mathstrut -\mathstrut 110q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 40q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 28q^{72} \) \(\mathstrut -\mathstrut 43q^{73} \) \(\mathstrut -\mathstrut 52q^{74} \) \(\mathstrut -\mathstrut 150q^{75} \) \(\mathstrut -\mathstrut 96q^{76} \) \(\mathstrut -\mathstrut 24q^{77} \) \(\mathstrut -\mathstrut 16q^{78} \) \(\mathstrut -\mathstrut 228q^{79} \) \(\mathstrut +\mathstrut 20q^{80} \) \(\mathstrut +\mathstrut 54q^{81} \) \(\mathstrut -\mathstrut 89q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 77q^{87} \) \(\mathstrut -\mathstrut 95q^{88} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 46q^{90} \) \(\mathstrut -\mathstrut 32q^{91} \) \(\mathstrut -\mathstrut 62q^{92} \) \(\mathstrut -\mathstrut 9q^{93} \) \(\mathstrut -\mathstrut 87q^{94} \) \(\mathstrut -\mathstrut 61q^{95} \) \(\mathstrut -\mathstrut 54q^{96} \) \(\mathstrut -\mathstrut 38q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut -\mathstrut 193q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.37815 −1.68161 −0.840804 0.541340i \(-0.817917\pi\)
−0.840804 + 0.541340i \(0.817917\pi\)
\(3\) 2.24175 1.29428 0.647138 0.762373i \(-0.275966\pi\)
0.647138 + 0.762373i \(0.275966\pi\)
\(4\) 3.65561 1.82781
\(5\) 2.50193 1.11890 0.559449 0.828865i \(-0.311013\pi\)
0.559449 + 0.828865i \(0.311013\pi\)
\(6\) −5.33123 −2.17647
\(7\) −3.50735 −1.32566 −0.662828 0.748772i \(-0.730644\pi\)
−0.662828 + 0.748772i \(0.730644\pi\)
\(8\) −3.93730 −1.39205
\(9\) 2.02545 0.675150
\(10\) −5.94998 −1.88155
\(11\) −4.72784 −1.42550 −0.712749 0.701419i \(-0.752550\pi\)
−0.712749 + 0.701419i \(0.752550\pi\)
\(12\) 8.19497 2.36569
\(13\) 1.00000 0.277350
\(14\) 8.34103 2.22923
\(15\) 5.60871 1.44816
\(16\) 2.05228 0.513069
\(17\) 0.105110 0.0254930 0.0127465 0.999919i \(-0.495943\pi\)
0.0127465 + 0.999919i \(0.495943\pi\)
\(18\) −4.81683 −1.13534
\(19\) 2.87419 0.659386 0.329693 0.944088i \(-0.393055\pi\)
0.329693 + 0.944088i \(0.393055\pi\)
\(20\) 9.14610 2.04513
\(21\) −7.86262 −1.71576
\(22\) 11.2435 2.39713
\(23\) −5.90670 −1.23163 −0.615816 0.787890i \(-0.711173\pi\)
−0.615816 + 0.787890i \(0.711173\pi\)
\(24\) −8.82645 −1.80169
\(25\) 1.25967 0.251933
\(26\) −2.37815 −0.466394
\(27\) −2.18470 −0.420445
\(28\) −12.8215 −2.42304
\(29\) 8.85260 1.64389 0.821943 0.569569i \(-0.192890\pi\)
0.821943 + 0.569569i \(0.192890\pi\)
\(30\) −13.3384 −2.43524
\(31\) 5.66043 1.01664 0.508322 0.861167i \(-0.330266\pi\)
0.508322 + 0.861167i \(0.330266\pi\)
\(32\) 2.99397 0.529264
\(33\) −10.5986 −1.84499
\(34\) −0.249968 −0.0428692
\(35\) −8.77516 −1.48327
\(36\) 7.40426 1.23404
\(37\) 6.18356 1.01657 0.508285 0.861189i \(-0.330280\pi\)
0.508285 + 0.861189i \(0.330280\pi\)
\(38\) −6.83528 −1.10883
\(39\) 2.24175 0.358968
\(40\) −9.85086 −1.55756
\(41\) 5.52352 0.862629 0.431315 0.902202i \(-0.358050\pi\)
0.431315 + 0.902202i \(0.358050\pi\)
\(42\) 18.6985 2.88524
\(43\) −7.13642 −1.08829 −0.544147 0.838990i \(-0.683147\pi\)
−0.544147 + 0.838990i \(0.683147\pi\)
\(44\) −17.2832 −2.60553
\(45\) 5.06754 0.755424
\(46\) 14.0470 2.07112
\(47\) 3.13636 0.457485 0.228743 0.973487i \(-0.426539\pi\)
0.228743 + 0.973487i \(0.426539\pi\)
\(48\) 4.60069 0.664053
\(49\) 5.30154 0.757362
\(50\) −2.99568 −0.423653
\(51\) 0.235631 0.0329949
\(52\) 3.65561 0.506942
\(53\) −4.15489 −0.570717 −0.285359 0.958421i \(-0.592113\pi\)
−0.285359 + 0.958421i \(0.592113\pi\)
\(54\) 5.19555 0.707024
\(55\) −11.8287 −1.59499
\(56\) 13.8095 1.84537
\(57\) 6.44323 0.853427
\(58\) −21.0528 −2.76437
\(59\) −6.63482 −0.863780 −0.431890 0.901926i \(-0.642153\pi\)
−0.431890 + 0.901926i \(0.642153\pi\)
\(60\) 20.5033 2.64696
\(61\) −10.7653 −1.37835 −0.689175 0.724595i \(-0.742027\pi\)
−0.689175 + 0.724595i \(0.742027\pi\)
\(62\) −13.4614 −1.70960
\(63\) −7.10397 −0.895017
\(64\) −11.2247 −1.40308
\(65\) 2.50193 0.310327
\(66\) 25.2052 3.10255
\(67\) 3.63647 0.444265 0.222133 0.975016i \(-0.428698\pi\)
0.222133 + 0.975016i \(0.428698\pi\)
\(68\) 0.384242 0.0465962
\(69\) −13.2413 −1.59407
\(70\) 20.8687 2.49428
\(71\) −0.128553 −0.0152565 −0.00762823 0.999971i \(-0.502428\pi\)
−0.00762823 + 0.999971i \(0.502428\pi\)
\(72\) −7.97481 −0.939840
\(73\) −4.52614 −0.529745 −0.264873 0.964283i \(-0.585330\pi\)
−0.264873 + 0.964283i \(0.585330\pi\)
\(74\) −14.7054 −1.70947
\(75\) 2.82386 0.326071
\(76\) 10.5069 1.20523
\(77\) 16.5822 1.88972
\(78\) −5.33123 −0.603643
\(79\) −4.46982 −0.502894 −0.251447 0.967871i \(-0.580906\pi\)
−0.251447 + 0.967871i \(0.580906\pi\)
\(80\) 5.13466 0.574072
\(81\) −10.9739 −1.21932
\(82\) −13.1358 −1.45060
\(83\) 9.21052 1.01099 0.505493 0.862831i \(-0.331311\pi\)
0.505493 + 0.862831i \(0.331311\pi\)
\(84\) −28.7427 −3.13608
\(85\) 0.262979 0.0285240
\(86\) 16.9715 1.83008
\(87\) 19.8453 2.12764
\(88\) 18.6149 1.98436
\(89\) −2.90807 −0.308255 −0.154127 0.988051i \(-0.549257\pi\)
−0.154127 + 0.988051i \(0.549257\pi\)
\(90\) −12.0514 −1.27033
\(91\) −3.50735 −0.367671
\(92\) −21.5926 −2.25118
\(93\) 12.6893 1.31582
\(94\) −7.45875 −0.769311
\(95\) 7.19104 0.737785
\(96\) 6.71174 0.685014
\(97\) 0.930007 0.0944279 0.0472140 0.998885i \(-0.484966\pi\)
0.0472140 + 0.998885i \(0.484966\pi\)
\(98\) −12.6079 −1.27359
\(99\) −9.57601 −0.962425
\(100\) 4.60485 0.460485
\(101\) −16.0190 −1.59395 −0.796974 0.604014i \(-0.793567\pi\)
−0.796974 + 0.604014i \(0.793567\pi\)
\(102\) −0.560366 −0.0554845
\(103\) −19.0494 −1.87700 −0.938499 0.345283i \(-0.887783\pi\)
−0.938499 + 0.345283i \(0.887783\pi\)
\(104\) −3.93730 −0.386084
\(105\) −19.6717 −1.91977
\(106\) 9.88095 0.959723
\(107\) 17.8326 1.72394 0.861970 0.506960i \(-0.169231\pi\)
0.861970 + 0.506960i \(0.169231\pi\)
\(108\) −7.98641 −0.768492
\(109\) 6.46069 0.618822 0.309411 0.950928i \(-0.399868\pi\)
0.309411 + 0.950928i \(0.399868\pi\)
\(110\) 28.1306 2.68214
\(111\) 13.8620 1.31572
\(112\) −7.19806 −0.680153
\(113\) 12.0549 1.13403 0.567016 0.823707i \(-0.308098\pi\)
0.567016 + 0.823707i \(0.308098\pi\)
\(114\) −15.3230 −1.43513
\(115\) −14.7782 −1.37807
\(116\) 32.3617 3.00471
\(117\) 2.02545 0.187253
\(118\) 15.7786 1.45254
\(119\) −0.368659 −0.0337949
\(120\) −22.0832 −2.01591
\(121\) 11.3525 1.03205
\(122\) 25.6014 2.31785
\(123\) 12.3824 1.11648
\(124\) 20.6924 1.85823
\(125\) −9.35806 −0.837011
\(126\) 16.8943 1.50507
\(127\) 11.4918 1.01973 0.509866 0.860254i \(-0.329695\pi\)
0.509866 + 0.860254i \(0.329695\pi\)
\(128\) 20.7061 1.83017
\(129\) −15.9981 −1.40855
\(130\) −5.94998 −0.521848
\(131\) −14.1479 −1.23611 −0.618055 0.786135i \(-0.712079\pi\)
−0.618055 + 0.786135i \(0.712079\pi\)
\(132\) −38.7446 −3.37228
\(133\) −10.0808 −0.874118
\(134\) −8.64808 −0.747080
\(135\) −5.46597 −0.470435
\(136\) −0.413850 −0.0354874
\(137\) −15.4742 −1.32205 −0.661024 0.750365i \(-0.729878\pi\)
−0.661024 + 0.750365i \(0.729878\pi\)
\(138\) 31.4899 2.68060
\(139\) 5.79097 0.491184 0.245592 0.969373i \(-0.421018\pi\)
0.245592 + 0.969373i \(0.421018\pi\)
\(140\) −32.0786 −2.71114
\(141\) 7.03094 0.592112
\(142\) 0.305719 0.0256554
\(143\) −4.72784 −0.395362
\(144\) 4.15678 0.346399
\(145\) 22.1486 1.83934
\(146\) 10.7639 0.890824
\(147\) 11.8847 0.980236
\(148\) 22.6047 1.85809
\(149\) 1.69713 0.139035 0.0695173 0.997581i \(-0.477854\pi\)
0.0695173 + 0.997581i \(0.477854\pi\)
\(150\) −6.71557 −0.548324
\(151\) −0.191220 −0.0155612 −0.00778062 0.999970i \(-0.502477\pi\)
−0.00778062 + 0.999970i \(0.502477\pi\)
\(152\) −11.3166 −0.917895
\(153\) 0.212895 0.0172116
\(154\) −39.4351 −3.17777
\(155\) 14.1620 1.13752
\(156\) 8.19497 0.656123
\(157\) 15.1809 1.21157 0.605784 0.795629i \(-0.292860\pi\)
0.605784 + 0.795629i \(0.292860\pi\)
\(158\) 10.6299 0.845671
\(159\) −9.31422 −0.738666
\(160\) 7.49071 0.592193
\(161\) 20.7169 1.63272
\(162\) 26.0976 2.05042
\(163\) −2.83971 −0.222423 −0.111211 0.993797i \(-0.535473\pi\)
−0.111211 + 0.993797i \(0.535473\pi\)
\(164\) 20.1919 1.57672
\(165\) −26.5171 −2.06435
\(166\) −21.9040 −1.70008
\(167\) −8.32604 −0.644288 −0.322144 0.946691i \(-0.604404\pi\)
−0.322144 + 0.946691i \(0.604404\pi\)
\(168\) 30.9575 2.38842
\(169\) 1.00000 0.0769231
\(170\) −0.625403 −0.0479662
\(171\) 5.82154 0.445184
\(172\) −26.0880 −1.98919
\(173\) −15.9041 −1.20917 −0.604584 0.796541i \(-0.706661\pi\)
−0.604584 + 0.796541i \(0.706661\pi\)
\(174\) −47.1952 −3.57786
\(175\) −4.41810 −0.333977
\(176\) −9.70284 −0.731379
\(177\) −14.8736 −1.11797
\(178\) 6.91583 0.518364
\(179\) −20.6598 −1.54419 −0.772094 0.635508i \(-0.780791\pi\)
−0.772094 + 0.635508i \(0.780791\pi\)
\(180\) 18.5250 1.38077
\(181\) −10.9163 −0.811399 −0.405699 0.914007i \(-0.632972\pi\)
−0.405699 + 0.914007i \(0.632972\pi\)
\(182\) 8.34103 0.618278
\(183\) −24.1330 −1.78397
\(184\) 23.2564 1.71449
\(185\) 15.4708 1.13744
\(186\) −30.1771 −2.21269
\(187\) −0.496944 −0.0363402
\(188\) 11.4653 0.836194
\(189\) 7.66251 0.557366
\(190\) −17.1014 −1.24067
\(191\) −19.9101 −1.44065 −0.720323 0.693639i \(-0.756006\pi\)
−0.720323 + 0.693639i \(0.756006\pi\)
\(192\) −25.1629 −1.81598
\(193\) −17.5021 −1.25983 −0.629916 0.776664i \(-0.716911\pi\)
−0.629916 + 0.776664i \(0.716911\pi\)
\(194\) −2.21170 −0.158791
\(195\) 5.60871 0.401648
\(196\) 19.3804 1.38431
\(197\) 22.7279 1.61930 0.809648 0.586916i \(-0.199658\pi\)
0.809648 + 0.586916i \(0.199658\pi\)
\(198\) 22.7732 1.61842
\(199\) −17.6723 −1.25276 −0.626378 0.779519i \(-0.715463\pi\)
−0.626378 + 0.779519i \(0.715463\pi\)
\(200\) −4.95968 −0.350703
\(201\) 8.15206 0.575002
\(202\) 38.0956 2.68039
\(203\) −31.0492 −2.17923
\(204\) 0.861375 0.0603083
\(205\) 13.8195 0.965194
\(206\) 45.3025 3.15637
\(207\) −11.9637 −0.831536
\(208\) 2.05228 0.142300
\(209\) −13.5887 −0.939953
\(210\) 46.7824 3.22829
\(211\) −2.38955 −0.164503 −0.0822517 0.996612i \(-0.526211\pi\)
−0.0822517 + 0.996612i \(0.526211\pi\)
\(212\) −15.1887 −1.04316
\(213\) −0.288184 −0.0197461
\(214\) −42.4086 −2.89899
\(215\) −17.8548 −1.21769
\(216\) 8.60181 0.585279
\(217\) −19.8532 −1.34772
\(218\) −15.3645 −1.04062
\(219\) −10.1465 −0.685636
\(220\) −43.2413 −2.91533
\(221\) 0.105110 0.00707048
\(222\) −32.9660 −2.21253
\(223\) 0.0900022 0.00602699 0.00301350 0.999995i \(-0.499041\pi\)
0.00301350 + 0.999995i \(0.499041\pi\)
\(224\) −10.5009 −0.701622
\(225\) 2.55139 0.170093
\(226\) −28.6684 −1.90700
\(227\) −22.1818 −1.47226 −0.736128 0.676842i \(-0.763348\pi\)
−0.736128 + 0.676842i \(0.763348\pi\)
\(228\) 23.5540 1.55990
\(229\) −24.9623 −1.64955 −0.824777 0.565458i \(-0.808699\pi\)
−0.824777 + 0.565458i \(0.808699\pi\)
\(230\) 35.1447 2.31737
\(231\) 37.1732 2.44582
\(232\) −34.8553 −2.28837
\(233\) −6.55348 −0.429333 −0.214666 0.976687i \(-0.568866\pi\)
−0.214666 + 0.976687i \(0.568866\pi\)
\(234\) −4.81683 −0.314886
\(235\) 7.84696 0.511879
\(236\) −24.2543 −1.57882
\(237\) −10.0202 −0.650884
\(238\) 0.876727 0.0568298
\(239\) −6.71661 −0.434461 −0.217231 0.976120i \(-0.569702\pi\)
−0.217231 + 0.976120i \(0.569702\pi\)
\(240\) 11.5106 0.743008
\(241\) −2.99824 −0.193134 −0.0965669 0.995326i \(-0.530786\pi\)
−0.0965669 + 0.995326i \(0.530786\pi\)
\(242\) −26.9980 −1.73550
\(243\) −18.0467 −1.15769
\(244\) −39.3536 −2.51936
\(245\) 13.2641 0.847411
\(246\) −29.4472 −1.87748
\(247\) 2.87419 0.182881
\(248\) −22.2868 −1.41521
\(249\) 20.6477 1.30849
\(250\) 22.2549 1.40752
\(251\) −10.9778 −0.692912 −0.346456 0.938066i \(-0.612615\pi\)
−0.346456 + 0.938066i \(0.612615\pi\)
\(252\) −25.9694 −1.63592
\(253\) 27.9259 1.75569
\(254\) −27.3293 −1.71479
\(255\) 0.589533 0.0369180
\(256\) −26.7928 −1.67455
\(257\) 8.21707 0.512567 0.256284 0.966602i \(-0.417502\pi\)
0.256284 + 0.966602i \(0.417502\pi\)
\(258\) 38.0459 2.36863
\(259\) −21.6879 −1.34762
\(260\) 9.14610 0.567217
\(261\) 17.9305 1.10987
\(262\) 33.6460 2.07865
\(263\) −17.1376 −1.05675 −0.528376 0.849011i \(-0.677199\pi\)
−0.528376 + 0.849011i \(0.677199\pi\)
\(264\) 41.7301 2.56831
\(265\) −10.3952 −0.638575
\(266\) 23.9737 1.46992
\(267\) −6.51917 −0.398967
\(268\) 13.2935 0.812031
\(269\) −4.90970 −0.299350 −0.149675 0.988735i \(-0.547823\pi\)
−0.149675 + 0.988735i \(0.547823\pi\)
\(270\) 12.9989 0.791088
\(271\) −6.03044 −0.366323 −0.183162 0.983083i \(-0.558633\pi\)
−0.183162 + 0.983083i \(0.558633\pi\)
\(272\) 0.215715 0.0130797
\(273\) −7.86262 −0.475867
\(274\) 36.7999 2.22317
\(275\) −5.95550 −0.359130
\(276\) −48.4052 −2.91365
\(277\) −30.6866 −1.84378 −0.921890 0.387452i \(-0.873355\pi\)
−0.921890 + 0.387452i \(0.873355\pi\)
\(278\) −13.7718 −0.825979
\(279\) 11.4649 0.686387
\(280\) 34.5505 2.06478
\(281\) −5.60986 −0.334656 −0.167328 0.985901i \(-0.553514\pi\)
−0.167328 + 0.985901i \(0.553514\pi\)
\(282\) −16.7207 −0.995701
\(283\) 15.7660 0.937190 0.468595 0.883413i \(-0.344760\pi\)
0.468595 + 0.883413i \(0.344760\pi\)
\(284\) −0.469941 −0.0278859
\(285\) 16.1205 0.954898
\(286\) 11.2435 0.664844
\(287\) −19.3729 −1.14355
\(288\) 6.06414 0.357333
\(289\) −16.9890 −0.999350
\(290\) −52.6728 −3.09305
\(291\) 2.08484 0.122216
\(292\) −16.5458 −0.968271
\(293\) 33.2134 1.94035 0.970174 0.242411i \(-0.0779383\pi\)
0.970174 + 0.242411i \(0.0779383\pi\)
\(294\) −28.2637 −1.64837
\(295\) −16.5999 −0.966482
\(296\) −24.3465 −1.41511
\(297\) 10.3289 0.599344
\(298\) −4.03604 −0.233802
\(299\) −5.90670 −0.341593
\(300\) 10.3229 0.595995
\(301\) 25.0300 1.44270
\(302\) 0.454750 0.0261679
\(303\) −35.9106 −2.06301
\(304\) 5.89864 0.338310
\(305\) −26.9340 −1.54223
\(306\) −0.506298 −0.0289431
\(307\) −13.8893 −0.792704 −0.396352 0.918099i \(-0.629724\pi\)
−0.396352 + 0.918099i \(0.629724\pi\)
\(308\) 60.6182 3.45404
\(309\) −42.7041 −2.42935
\(310\) −33.6795 −1.91286
\(311\) 5.07844 0.287972 0.143986 0.989580i \(-0.454008\pi\)
0.143986 + 0.989580i \(0.454008\pi\)
\(312\) −8.82645 −0.499699
\(313\) 2.75156 0.155528 0.0777638 0.996972i \(-0.475222\pi\)
0.0777638 + 0.996972i \(0.475222\pi\)
\(314\) −36.1025 −2.03738
\(315\) −17.7737 −1.00143
\(316\) −16.3399 −0.919193
\(317\) −28.6464 −1.60894 −0.804471 0.593992i \(-0.797551\pi\)
−0.804471 + 0.593992i \(0.797551\pi\)
\(318\) 22.1506 1.24215
\(319\) −41.8537 −2.34336
\(320\) −28.0834 −1.56991
\(321\) 39.9762 2.23125
\(322\) −49.2679 −2.74559
\(323\) 0.302107 0.0168097
\(324\) −40.1163 −2.22868
\(325\) 1.25967 0.0698737
\(326\) 6.75325 0.374028
\(327\) 14.4833 0.800926
\(328\) −21.7478 −1.20082
\(329\) −11.0003 −0.606468
\(330\) 63.0617 3.47143
\(331\) −24.9743 −1.37271 −0.686356 0.727265i \(-0.740791\pi\)
−0.686356 + 0.727265i \(0.740791\pi\)
\(332\) 33.6701 1.84789
\(333\) 12.5245 0.686338
\(334\) 19.8006 1.08344
\(335\) 9.09820 0.497088
\(336\) −16.1363 −0.880306
\(337\) 28.9325 1.57605 0.788026 0.615642i \(-0.211103\pi\)
0.788026 + 0.615642i \(0.211103\pi\)
\(338\) −2.37815 −0.129354
\(339\) 27.0241 1.46775
\(340\) 0.961348 0.0521364
\(341\) −26.7616 −1.44922
\(342\) −13.8445 −0.748626
\(343\) 5.95712 0.321654
\(344\) 28.0982 1.51496
\(345\) −33.1289 −1.78360
\(346\) 37.8225 2.03335
\(347\) 7.03820 0.377830 0.188915 0.981993i \(-0.439503\pi\)
0.188915 + 0.981993i \(0.439503\pi\)
\(348\) 72.5468 3.88892
\(349\) −7.05133 −0.377449 −0.188725 0.982030i \(-0.560435\pi\)
−0.188725 + 0.982030i \(0.560435\pi\)
\(350\) 10.5069 0.561618
\(351\) −2.18470 −0.116611
\(352\) −14.1550 −0.754465
\(353\) 27.9622 1.48828 0.744139 0.668025i \(-0.232860\pi\)
0.744139 + 0.668025i \(0.232860\pi\)
\(354\) 35.3718 1.87999
\(355\) −0.321631 −0.0170704
\(356\) −10.6308 −0.563430
\(357\) −0.826441 −0.0437399
\(358\) 49.1322 2.59672
\(359\) 21.1097 1.11413 0.557064 0.830470i \(-0.311928\pi\)
0.557064 + 0.830470i \(0.311928\pi\)
\(360\) −19.9524 −1.05159
\(361\) −10.7390 −0.565211
\(362\) 25.9605 1.36445
\(363\) 25.4495 1.33575
\(364\) −12.8215 −0.672031
\(365\) −11.3241 −0.592731
\(366\) 57.3921 2.99993
\(367\) 14.7325 0.769031 0.384516 0.923118i \(-0.374368\pi\)
0.384516 + 0.923118i \(0.374368\pi\)
\(368\) −12.1222 −0.631912
\(369\) 11.1876 0.582404
\(370\) −36.7920 −1.91273
\(371\) 14.5727 0.756575
\(372\) 46.3871 2.40506
\(373\) 1.07397 0.0556080 0.0278040 0.999613i \(-0.491149\pi\)
0.0278040 + 0.999613i \(0.491149\pi\)
\(374\) 1.18181 0.0611099
\(375\) −20.9785 −1.08332
\(376\) −12.3488 −0.636840
\(377\) 8.85260 0.455932
\(378\) −18.2226 −0.937271
\(379\) −0.256521 −0.0131766 −0.00658831 0.999978i \(-0.502097\pi\)
−0.00658831 + 0.999978i \(0.502097\pi\)
\(380\) 26.2877 1.34853
\(381\) 25.7618 1.31982
\(382\) 47.3493 2.42260
\(383\) −29.2418 −1.49419 −0.747094 0.664719i \(-0.768551\pi\)
−0.747094 + 0.664719i \(0.768551\pi\)
\(384\) 46.4178 2.36875
\(385\) 41.4876 2.11440
\(386\) 41.6228 2.11854
\(387\) −14.4545 −0.734762
\(388\) 3.39975 0.172596
\(389\) −12.5029 −0.633922 −0.316961 0.948438i \(-0.602663\pi\)
−0.316961 + 0.948438i \(0.602663\pi\)
\(390\) −13.3384 −0.675415
\(391\) −0.620854 −0.0313979
\(392\) −20.8737 −1.05428
\(393\) −31.7162 −1.59987
\(394\) −54.0504 −2.72302
\(395\) −11.1832 −0.562687
\(396\) −35.0062 −1.75913
\(397\) 5.52599 0.277341 0.138671 0.990339i \(-0.455717\pi\)
0.138671 + 0.990339i \(0.455717\pi\)
\(398\) 42.0274 2.10665
\(399\) −22.5987 −1.13135
\(400\) 2.58518 0.129259
\(401\) 24.6712 1.23202 0.616010 0.787738i \(-0.288748\pi\)
0.616010 + 0.787738i \(0.288748\pi\)
\(402\) −19.3868 −0.966928
\(403\) 5.66043 0.281966
\(404\) −58.5591 −2.91343
\(405\) −27.4560 −1.36430
\(406\) 73.8398 3.66461
\(407\) −29.2349 −1.44912
\(408\) −0.927749 −0.0459304
\(409\) 2.85516 0.141178 0.0705892 0.997505i \(-0.477512\pi\)
0.0705892 + 0.997505i \(0.477512\pi\)
\(410\) −32.8648 −1.62308
\(411\) −34.6892 −1.71109
\(412\) −69.6374 −3.43079
\(413\) 23.2707 1.14508
\(414\) 28.4516 1.39832
\(415\) 23.0441 1.13119
\(416\) 2.99397 0.146792
\(417\) 12.9819 0.635727
\(418\) 32.3161 1.58063
\(419\) 38.7933 1.89518 0.947589 0.319491i \(-0.103512\pi\)
0.947589 + 0.319491i \(0.103512\pi\)
\(420\) −71.9123 −3.50896
\(421\) −18.6868 −0.910739 −0.455370 0.890302i \(-0.650493\pi\)
−0.455370 + 0.890302i \(0.650493\pi\)
\(422\) 5.68272 0.276630
\(423\) 6.35254 0.308871
\(424\) 16.3590 0.794465
\(425\) 0.132404 0.00642252
\(426\) 0.685347 0.0332052
\(427\) 37.7576 1.82722
\(428\) 65.1889 3.15103
\(429\) −10.5986 −0.511708
\(430\) 42.4616 2.04768
\(431\) 18.9446 0.912531 0.456266 0.889844i \(-0.349187\pi\)
0.456266 + 0.889844i \(0.349187\pi\)
\(432\) −4.48360 −0.215718
\(433\) −35.5309 −1.70750 −0.853752 0.520679i \(-0.825679\pi\)
−0.853752 + 0.520679i \(0.825679\pi\)
\(434\) 47.2138 2.26634
\(435\) 49.6517 2.38062
\(436\) 23.6178 1.13109
\(437\) −16.9770 −0.812120
\(438\) 24.1299 1.15297
\(439\) 36.3646 1.73559 0.867793 0.496926i \(-0.165538\pi\)
0.867793 + 0.496926i \(0.165538\pi\)
\(440\) 46.5733 2.22030
\(441\) 10.7380 0.511333
\(442\) −0.249968 −0.0118898
\(443\) 5.76070 0.273699 0.136849 0.990592i \(-0.456302\pi\)
0.136849 + 0.990592i \(0.456302\pi\)
\(444\) 50.6741 2.40489
\(445\) −7.27579 −0.344906
\(446\) −0.214039 −0.0101350
\(447\) 3.80455 0.179949
\(448\) 39.3689 1.86001
\(449\) 31.1123 1.46828 0.734139 0.678999i \(-0.237586\pi\)
0.734139 + 0.678999i \(0.237586\pi\)
\(450\) −6.06760 −0.286029
\(451\) −26.1143 −1.22968
\(452\) 44.0681 2.07279
\(453\) −0.428667 −0.0201405
\(454\) 52.7517 2.47576
\(455\) −8.77516 −0.411386
\(456\) −25.3689 −1.18801
\(457\) 1.76591 0.0826057 0.0413028 0.999147i \(-0.486849\pi\)
0.0413028 + 0.999147i \(0.486849\pi\)
\(458\) 59.3641 2.77390
\(459\) −0.229634 −0.0107184
\(460\) −54.0232 −2.51884
\(461\) −18.7198 −0.871870 −0.435935 0.899978i \(-0.643582\pi\)
−0.435935 + 0.899978i \(0.643582\pi\)
\(462\) −88.4036 −4.11291
\(463\) −21.2147 −0.985931 −0.492966 0.870049i \(-0.664087\pi\)
−0.492966 + 0.870049i \(0.664087\pi\)
\(464\) 18.1680 0.843427
\(465\) 31.7477 1.47227
\(466\) 15.5852 0.721970
\(467\) −7.66006 −0.354465 −0.177233 0.984169i \(-0.556715\pi\)
−0.177233 + 0.984169i \(0.556715\pi\)
\(468\) 7.40426 0.342262
\(469\) −12.7544 −0.588943
\(470\) −18.6613 −0.860781
\(471\) 34.0318 1.56810
\(472\) 26.1233 1.20242
\(473\) 33.7399 1.55136
\(474\) 23.8296 1.09453
\(475\) 3.62053 0.166121
\(476\) −1.34767 −0.0617705
\(477\) −8.41552 −0.385320
\(478\) 15.9731 0.730593
\(479\) −4.83577 −0.220952 −0.110476 0.993879i \(-0.535238\pi\)
−0.110476 + 0.993879i \(0.535238\pi\)
\(480\) 16.7923 0.766461
\(481\) 6.18356 0.281946
\(482\) 7.13028 0.324775
\(483\) 46.4421 2.11319
\(484\) 41.5003 1.88638
\(485\) 2.32681 0.105655
\(486\) 42.9177 1.94679
\(487\) −37.3725 −1.69351 −0.846754 0.531985i \(-0.821446\pi\)
−0.846754 + 0.531985i \(0.821446\pi\)
\(488\) 42.3861 1.91873
\(489\) −6.36591 −0.287877
\(490\) −31.5440 −1.42501
\(491\) −20.4687 −0.923739 −0.461870 0.886948i \(-0.652821\pi\)
−0.461870 + 0.886948i \(0.652821\pi\)
\(492\) 45.2651 2.04071
\(493\) 0.930498 0.0419075
\(494\) −6.83528 −0.307534
\(495\) −23.9585 −1.07686
\(496\) 11.6168 0.521609
\(497\) 0.450882 0.0202248
\(498\) −49.1034 −2.20037
\(499\) −22.5475 −1.00936 −0.504682 0.863305i \(-0.668390\pi\)
−0.504682 + 0.863305i \(0.668390\pi\)
\(500\) −34.2094 −1.52989
\(501\) −18.6649 −0.833887
\(502\) 26.1068 1.16521
\(503\) −1.06285 −0.0473904 −0.0236952 0.999719i \(-0.507543\pi\)
−0.0236952 + 0.999719i \(0.507543\pi\)
\(504\) 27.9705 1.24590
\(505\) −40.0784 −1.78346
\(506\) −66.4121 −2.95238
\(507\) 2.24175 0.0995597
\(508\) 42.0096 1.86387
\(509\) 26.6956 1.18326 0.591630 0.806209i \(-0.298484\pi\)
0.591630 + 0.806209i \(0.298484\pi\)
\(510\) −1.40200 −0.0620816
\(511\) 15.8748 0.702260
\(512\) 22.3053 0.985765
\(513\) −6.27925 −0.277236
\(514\) −19.5415 −0.861937
\(515\) −47.6604 −2.10017
\(516\) −58.4828 −2.57456
\(517\) −14.8282 −0.652144
\(518\) 51.5772 2.26617
\(519\) −35.6531 −1.56500
\(520\) −9.85086 −0.431989
\(521\) −6.61042 −0.289608 −0.144804 0.989460i \(-0.546255\pi\)
−0.144804 + 0.989460i \(0.546255\pi\)
\(522\) −42.6415 −1.86637
\(523\) −1.11548 −0.0487766 −0.0243883 0.999703i \(-0.507764\pi\)
−0.0243883 + 0.999703i \(0.507764\pi\)
\(524\) −51.7194 −2.25937
\(525\) −9.90427 −0.432258
\(526\) 40.7559 1.77704
\(527\) 0.594969 0.0259173
\(528\) −21.7514 −0.946606
\(529\) 11.8890 0.516915
\(530\) 24.7215 1.07383
\(531\) −13.4385 −0.583181
\(532\) −36.8516 −1.59772
\(533\) 5.52352 0.239250
\(534\) 15.5036 0.670906
\(535\) 44.6159 1.92891
\(536\) −14.3179 −0.618438
\(537\) −46.3142 −1.99861
\(538\) 11.6760 0.503389
\(539\) −25.0648 −1.07962
\(540\) −19.9815 −0.859865
\(541\) 22.7322 0.977334 0.488667 0.872470i \(-0.337483\pi\)
0.488667 + 0.872470i \(0.337483\pi\)
\(542\) 14.3413 0.616012
\(543\) −24.4715 −1.05017
\(544\) 0.314697 0.0134925
\(545\) 16.1642 0.692398
\(546\) 18.6985 0.800222
\(547\) 30.8568 1.31934 0.659671 0.751554i \(-0.270696\pi\)
0.659671 + 0.751554i \(0.270696\pi\)
\(548\) −56.5675 −2.41645
\(549\) −21.8045 −0.930594
\(550\) 14.1631 0.603917
\(551\) 25.4441 1.08396
\(552\) 52.1351 2.21902
\(553\) 15.6772 0.666664
\(554\) 72.9775 3.10052
\(555\) 34.6818 1.47216
\(556\) 21.1695 0.897789
\(557\) −1.53405 −0.0649998 −0.0324999 0.999472i \(-0.510347\pi\)
−0.0324999 + 0.999472i \(0.510347\pi\)
\(558\) −27.2654 −1.15423
\(559\) −7.13642 −0.301838
\(560\) −18.0091 −0.761022
\(561\) −1.11403 −0.0470342
\(562\) 13.3411 0.562761
\(563\) −1.48277 −0.0624913 −0.0312457 0.999512i \(-0.509947\pi\)
−0.0312457 + 0.999512i \(0.509947\pi\)
\(564\) 25.7024 1.08227
\(565\) 30.1606 1.26887
\(566\) −37.4939 −1.57599
\(567\) 38.4894 1.61640
\(568\) 0.506153 0.0212377
\(569\) −25.5034 −1.06916 −0.534579 0.845118i \(-0.679530\pi\)
−0.534579 + 0.845118i \(0.679530\pi\)
\(570\) −38.3371 −1.60576
\(571\) −8.53230 −0.357066 −0.178533 0.983934i \(-0.557135\pi\)
−0.178533 + 0.983934i \(0.557135\pi\)
\(572\) −17.2832 −0.722645
\(573\) −44.6335 −1.86459
\(574\) 46.0718 1.92300
\(575\) −7.44046 −0.310289
\(576\) −22.7350 −0.947293
\(577\) −19.3591 −0.805931 −0.402965 0.915215i \(-0.632021\pi\)
−0.402965 + 0.915215i \(0.632021\pi\)
\(578\) 40.4023 1.68052
\(579\) −39.2354 −1.63057
\(580\) 80.9667 3.36196
\(581\) −32.3045 −1.34022
\(582\) −4.95808 −0.205519
\(583\) 19.6436 0.813557
\(584\) 17.8208 0.737429
\(585\) 5.06754 0.209517
\(586\) −78.9865 −3.26290
\(587\) −40.7167 −1.68056 −0.840278 0.542156i \(-0.817608\pi\)
−0.840278 + 0.542156i \(0.817608\pi\)
\(588\) 43.4460 1.79168
\(589\) 16.2692 0.670360
\(590\) 39.4771 1.62524
\(591\) 50.9503 2.09582
\(592\) 12.6904 0.521571
\(593\) 15.7761 0.647847 0.323923 0.946083i \(-0.394998\pi\)
0.323923 + 0.946083i \(0.394998\pi\)
\(594\) −24.5637 −1.00786
\(595\) −0.922359 −0.0378130
\(596\) 6.20406 0.254128
\(597\) −39.6169 −1.62141
\(598\) 14.0470 0.574426
\(599\) 24.3147 0.993470 0.496735 0.867902i \(-0.334532\pi\)
0.496735 + 0.867902i \(0.334532\pi\)
\(600\) −11.1184 −0.453906
\(601\) 9.68715 0.395147 0.197573 0.980288i \(-0.436694\pi\)
0.197573 + 0.980288i \(0.436694\pi\)
\(602\) −59.5251 −2.42606
\(603\) 7.36549 0.299946
\(604\) −0.699025 −0.0284429
\(605\) 28.4032 1.15475
\(606\) 85.4008 3.46917
\(607\) −11.6975 −0.474788 −0.237394 0.971413i \(-0.576293\pi\)
−0.237394 + 0.971413i \(0.576293\pi\)
\(608\) 8.60526 0.348989
\(609\) −69.6046 −2.82052
\(610\) 64.0531 2.59343
\(611\) 3.13636 0.126884
\(612\) 0.778263 0.0314594
\(613\) −37.2724 −1.50542 −0.752709 0.658353i \(-0.771253\pi\)
−0.752709 + 0.658353i \(0.771253\pi\)
\(614\) 33.0309 1.33302
\(615\) 30.9798 1.24923
\(616\) −65.2892 −2.63058
\(617\) 1.00000 0.0402585
\(618\) 101.557 4.08522
\(619\) 12.3610 0.496829 0.248415 0.968654i \(-0.420090\pi\)
0.248415 + 0.968654i \(0.420090\pi\)
\(620\) 51.7709 2.07917
\(621\) 12.9043 0.517833
\(622\) −12.0773 −0.484256
\(623\) 10.1996 0.408640
\(624\) 4.60069 0.184175
\(625\) −29.7116 −1.18846
\(626\) −6.54364 −0.261537
\(627\) −30.4626 −1.21656
\(628\) 55.4955 2.21451
\(629\) 0.649955 0.0259154
\(630\) 42.2685 1.68402
\(631\) −43.1706 −1.71859 −0.859297 0.511478i \(-0.829098\pi\)
−0.859297 + 0.511478i \(0.829098\pi\)
\(632\) 17.5990 0.700052
\(633\) −5.35678 −0.212913
\(634\) 68.1255 2.70561
\(635\) 28.7517 1.14098
\(636\) −34.0492 −1.35014
\(637\) 5.30154 0.210055
\(638\) 99.5345 3.94061
\(639\) −0.260378 −0.0103004
\(640\) 51.8051 2.04778
\(641\) 38.9831 1.53974 0.769870 0.638201i \(-0.220321\pi\)
0.769870 + 0.638201i \(0.220321\pi\)
\(642\) −95.0695 −3.75209
\(643\) −38.9950 −1.53781 −0.768906 0.639362i \(-0.779199\pi\)
−0.768906 + 0.639362i \(0.779199\pi\)
\(644\) 75.7329 2.98429
\(645\) −40.0261 −1.57603
\(646\) −0.718457 −0.0282673
\(647\) 7.78946 0.306235 0.153118 0.988208i \(-0.451069\pi\)
0.153118 + 0.988208i \(0.451069\pi\)
\(648\) 43.2075 1.69735
\(649\) 31.3684 1.23132
\(650\) −2.99568 −0.117500
\(651\) −44.5058 −1.74432
\(652\) −10.3809 −0.406546
\(653\) 9.09892 0.356068 0.178034 0.984024i \(-0.443026\pi\)
0.178034 + 0.984024i \(0.443026\pi\)
\(654\) −34.4434 −1.34684
\(655\) −35.3972 −1.38308
\(656\) 11.3358 0.442588
\(657\) −9.16748 −0.357658
\(658\) 26.1605 1.01984
\(659\) 37.7491 1.47050 0.735248 0.677798i \(-0.237066\pi\)
0.735248 + 0.677798i \(0.237066\pi\)
\(660\) −96.9363 −3.77324
\(661\) 2.59922 0.101098 0.0505491 0.998722i \(-0.483903\pi\)
0.0505491 + 0.998722i \(0.483903\pi\)
\(662\) 59.3927 2.30836
\(663\) 0.235631 0.00915115
\(664\) −36.2646 −1.40734
\(665\) −25.2215 −0.978049
\(666\) −29.7852 −1.15415
\(667\) −52.2896 −2.02466
\(668\) −30.4368 −1.17763
\(669\) 0.201763 0.00780059
\(670\) −21.6369 −0.835907
\(671\) 50.8965 1.96484
\(672\) −23.5405 −0.908093
\(673\) −8.52553 −0.328635 −0.164318 0.986407i \(-0.552542\pi\)
−0.164318 + 0.986407i \(0.552542\pi\)
\(674\) −68.8059 −2.65030
\(675\) −2.75199 −0.105924
\(676\) 3.65561 0.140600
\(677\) 42.2460 1.62365 0.811823 0.583904i \(-0.198475\pi\)
0.811823 + 0.583904i \(0.198475\pi\)
\(678\) −64.2675 −2.46818
\(679\) −3.26186 −0.125179
\(680\) −1.03543 −0.0397068
\(681\) −49.7260 −1.90551
\(682\) 63.6433 2.43703
\(683\) 33.8343 1.29463 0.647316 0.762222i \(-0.275891\pi\)
0.647316 + 0.762222i \(0.275891\pi\)
\(684\) 21.2813 0.813711
\(685\) −38.7153 −1.47924
\(686\) −14.1669 −0.540896
\(687\) −55.9592 −2.13498
\(688\) −14.6459 −0.558370
\(689\) −4.15489 −0.158289
\(690\) 78.7857 2.99932
\(691\) −23.4453 −0.891903 −0.445952 0.895057i \(-0.647135\pi\)
−0.445952 + 0.895057i \(0.647135\pi\)
\(692\) −58.1393 −2.21013
\(693\) 33.5865 1.27584
\(694\) −16.7379 −0.635362
\(695\) 14.4886 0.549585
\(696\) −78.1370 −2.96178
\(697\) 0.580578 0.0219910
\(698\) 16.7691 0.634722
\(699\) −14.6913 −0.555675
\(700\) −16.1508 −0.610445
\(701\) 0.196821 0.00743381 0.00371691 0.999993i \(-0.498817\pi\)
0.00371691 + 0.999993i \(0.498817\pi\)
\(702\) 5.19555 0.196093
\(703\) 17.7728 0.670312
\(704\) 53.0685 2.00009
\(705\) 17.5909 0.662513
\(706\) −66.4984 −2.50270
\(707\) 56.1842 2.11302
\(708\) −54.3722 −2.04343
\(709\) 21.6522 0.813165 0.406583 0.913614i \(-0.366720\pi\)
0.406583 + 0.913614i \(0.366720\pi\)
\(710\) 0.764889 0.0287058
\(711\) −9.05340 −0.339529
\(712\) 11.4499 0.429105
\(713\) −33.4345 −1.25213
\(714\) 1.96540 0.0735534
\(715\) −11.8287 −0.442370
\(716\) −75.5243 −2.82248
\(717\) −15.0570 −0.562313
\(718\) −50.2021 −1.87353
\(719\) 34.4191 1.28362 0.641808 0.766866i \(-0.278185\pi\)
0.641808 + 0.766866i \(0.278185\pi\)
\(720\) 10.4000 0.387585
\(721\) 66.8131 2.48825
\(722\) 25.5390 0.950463
\(723\) −6.72131 −0.249968
\(724\) −39.9056 −1.48308
\(725\) 11.1513 0.414150
\(726\) −60.5228 −2.24621
\(727\) −45.8045 −1.69880 −0.849398 0.527753i \(-0.823035\pi\)
−0.849398 + 0.527753i \(0.823035\pi\)
\(728\) 13.8095 0.511814
\(729\) −7.53445 −0.279054
\(730\) 26.9305 0.996741
\(731\) −0.750111 −0.0277438
\(732\) −88.2211 −3.26074
\(733\) −2.80654 −0.103662 −0.0518310 0.998656i \(-0.516506\pi\)
−0.0518310 + 0.998656i \(0.516506\pi\)
\(734\) −35.0362 −1.29321
\(735\) 29.7348 1.09678
\(736\) −17.6845 −0.651858
\(737\) −17.1927 −0.633299
\(738\) −26.6059 −0.979376
\(739\) −50.0863 −1.84245 −0.921227 0.389025i \(-0.872812\pi\)
−0.921227 + 0.389025i \(0.872812\pi\)
\(740\) 56.5554 2.07902
\(741\) 6.44323 0.236698
\(742\) −34.6560 −1.27226
\(743\) −17.2495 −0.632823 −0.316412 0.948622i \(-0.602478\pi\)
−0.316412 + 0.948622i \(0.602478\pi\)
\(744\) −49.9615 −1.83168
\(745\) 4.24611 0.155566
\(746\) −2.55406 −0.0935108
\(747\) 18.6554 0.682567
\(748\) −1.81664 −0.0664228
\(749\) −62.5451 −2.28535
\(750\) 49.8900 1.82172
\(751\) 16.2520 0.593044 0.296522 0.955026i \(-0.404173\pi\)
0.296522 + 0.955026i \(0.404173\pi\)
\(752\) 6.43668 0.234722
\(753\) −24.6095 −0.896819
\(754\) −21.0528 −0.766699
\(755\) −0.478419 −0.0174114
\(756\) 28.0112 1.01876
\(757\) 27.1765 0.987748 0.493874 0.869533i \(-0.335580\pi\)
0.493874 + 0.869533i \(0.335580\pi\)
\(758\) 0.610047 0.0221579
\(759\) 62.6030 2.27234
\(760\) −28.3133 −1.02703
\(761\) 13.7248 0.497525 0.248763 0.968565i \(-0.419976\pi\)
0.248763 + 0.968565i \(0.419976\pi\)
\(762\) −61.2654 −2.21941
\(763\) −22.6599 −0.820344
\(764\) −72.7837 −2.63322
\(765\) 0.532650 0.0192580
\(766\) 69.5415 2.51264
\(767\) −6.63482 −0.239570
\(768\) −60.0628 −2.16733
\(769\) 38.3615 1.38335 0.691676 0.722208i \(-0.256872\pi\)
0.691676 + 0.722208i \(0.256872\pi\)
\(770\) −98.6639 −3.55560
\(771\) 18.4206 0.663403
\(772\) −63.9810 −2.30273
\(773\) 28.2532 1.01620 0.508099 0.861299i \(-0.330348\pi\)
0.508099 + 0.861299i \(0.330348\pi\)
\(774\) 34.3749 1.23558
\(775\) 7.13026 0.256126
\(776\) −3.66172 −0.131448
\(777\) −48.6190 −1.74420
\(778\) 29.7338 1.06601
\(779\) 15.8757 0.568805
\(780\) 20.5033 0.734135
\(781\) 0.607779 0.0217481
\(782\) 1.47649 0.0527990
\(783\) −19.3403 −0.691164
\(784\) 10.8802 0.388579
\(785\) 37.9816 1.35562
\(786\) 75.4259 2.69035
\(787\) 39.7752 1.41783 0.708917 0.705292i \(-0.249184\pi\)
0.708917 + 0.705292i \(0.249184\pi\)
\(788\) 83.0844 2.95976
\(789\) −38.4183 −1.36773
\(790\) 26.5953 0.946220
\(791\) −42.2809 −1.50333
\(792\) 37.7036 1.33974
\(793\) −10.7653 −0.382286
\(794\) −13.1416 −0.466379
\(795\) −23.3036 −0.826492
\(796\) −64.6031 −2.28980
\(797\) 44.9581 1.59250 0.796249 0.604969i \(-0.206814\pi\)
0.796249 + 0.604969i \(0.206814\pi\)
\(798\) 53.7432 1.90249
\(799\) 0.329663 0.0116627
\(800\) 3.77140 0.133339
\(801\) −5.89015 −0.208118
\(802\) −58.6718 −2.07177
\(803\) 21.3989 0.755151
\(804\) 29.8008 1.05099
\(805\) 51.8322 1.82685
\(806\) −13.4614 −0.474157
\(807\) −11.0063 −0.387441
\(808\) 63.0715 2.21885
\(809\) 19.0268 0.668948 0.334474 0.942405i \(-0.391441\pi\)
0.334474 + 0.942405i \(0.391441\pi\)
\(810\) 65.2945 2.29421
\(811\) −2.91892 −0.102497 −0.0512486 0.998686i \(-0.516320\pi\)
−0.0512486 + 0.998686i \(0.516320\pi\)
\(812\) −113.504 −3.98320
\(813\) −13.5187 −0.474123
\(814\) 69.5250 2.43685
\(815\) −7.10475 −0.248869
\(816\) 0.483580 0.0169287
\(817\) −20.5115 −0.717605
\(818\) −6.79000 −0.237407
\(819\) −7.10397 −0.248233
\(820\) 50.5186 1.76419
\(821\) 8.39898 0.293126 0.146563 0.989201i \(-0.453179\pi\)
0.146563 + 0.989201i \(0.453179\pi\)
\(822\) 82.4963 2.87739
\(823\) −4.44310 −0.154877 −0.0774384 0.996997i \(-0.524674\pi\)
−0.0774384 + 0.996997i \(0.524674\pi\)
\(824\) 75.0034 2.61287
\(825\) −13.3508 −0.464814
\(826\) −55.3412 −1.92557
\(827\) 10.3147 0.358678 0.179339 0.983787i \(-0.442604\pi\)
0.179339 + 0.983787i \(0.442604\pi\)
\(828\) −43.7347 −1.51989
\(829\) −1.40088 −0.0486546 −0.0243273 0.999704i \(-0.507744\pi\)
−0.0243273 + 0.999704i \(0.507744\pi\)
\(830\) −54.8024 −1.90222
\(831\) −68.7918 −2.38636
\(832\) −11.2247 −0.389146
\(833\) 0.557245 0.0193074
\(834\) −30.8730 −1.06904
\(835\) −20.8312 −0.720893
\(836\) −49.6752 −1.71805
\(837\) −12.3663 −0.427443
\(838\) −92.2565 −3.18695
\(839\) −15.2350 −0.525969 −0.262985 0.964800i \(-0.584707\pi\)
−0.262985 + 0.964800i \(0.584707\pi\)
\(840\) 77.4535 2.67240
\(841\) 49.3685 1.70236
\(842\) 44.4401 1.53151
\(843\) −12.5759 −0.433137
\(844\) −8.73527 −0.300680
\(845\) 2.50193 0.0860691
\(846\) −15.1073 −0.519400
\(847\) −39.8172 −1.36814
\(848\) −8.52697 −0.292818
\(849\) 35.3434 1.21298
\(850\) −0.314876 −0.0108002
\(851\) −36.5244 −1.25204
\(852\) −1.05349 −0.0360920
\(853\) 26.7644 0.916395 0.458197 0.888850i \(-0.348495\pi\)
0.458197 + 0.888850i \(0.348495\pi\)
\(854\) −89.7933 −3.07266
\(855\) 14.5651 0.498116
\(856\) −70.2122 −2.39980
\(857\) 21.5674 0.736730 0.368365 0.929681i \(-0.379918\pi\)
0.368365 + 0.929681i \(0.379918\pi\)
\(858\) 25.2052 0.860492
\(859\) 49.1853 1.67818 0.839091 0.543991i \(-0.183088\pi\)
0.839091 + 0.543991i \(0.183088\pi\)
\(860\) −65.2704 −2.22570
\(861\) −43.4293 −1.48007
\(862\) −45.0532 −1.53452
\(863\) 13.4745 0.458677 0.229338 0.973347i \(-0.426344\pi\)
0.229338 + 0.973347i \(0.426344\pi\)
\(864\) −6.54092 −0.222527
\(865\) −39.7911 −1.35294
\(866\) 84.4979 2.87135
\(867\) −38.0850 −1.29343
\(868\) −72.5754 −2.46337
\(869\) 21.1326 0.716875
\(870\) −118.079 −4.00326
\(871\) 3.63647 0.123217
\(872\) −25.4377 −0.861428
\(873\) 1.88368 0.0637530
\(874\) 40.3739 1.36567
\(875\) 32.8220 1.10959
\(876\) −37.0916 −1.25321
\(877\) 39.2319 1.32477 0.662383 0.749165i \(-0.269545\pi\)
0.662383 + 0.749165i \(0.269545\pi\)
\(878\) −86.4805 −2.91857
\(879\) 74.4562 2.51134
\(880\) −24.2759 −0.818339
\(881\) 50.6525 1.70653 0.853263 0.521480i \(-0.174620\pi\)
0.853263 + 0.521480i \(0.174620\pi\)
\(882\) −25.5366 −0.859862
\(883\) 12.4245 0.418118 0.209059 0.977903i \(-0.432960\pi\)
0.209059 + 0.977903i \(0.432960\pi\)
\(884\) 0.384242 0.0129235
\(885\) −37.2128 −1.25089
\(886\) −13.6998 −0.460254
\(887\) 17.6650 0.593132 0.296566 0.955012i \(-0.404158\pi\)
0.296566 + 0.955012i \(0.404158\pi\)
\(888\) −54.5789 −1.83155
\(889\) −40.3058 −1.35181
\(890\) 17.3030 0.579996
\(891\) 51.8829 1.73814
\(892\) 0.329013 0.0110162
\(893\) 9.01451 0.301659
\(894\) −9.04780 −0.302604
\(895\) −51.6895 −1.72779
\(896\) −72.6235 −2.42618
\(897\) −13.2413 −0.442116
\(898\) −73.9897 −2.46907
\(899\) 50.1096 1.67125
\(900\) 9.32690 0.310897
\(901\) −0.436721 −0.0145493
\(902\) 62.1039 2.06783
\(903\) 56.1110 1.86726
\(904\) −47.4638 −1.57862
\(905\) −27.3117 −0.907873
\(906\) 1.01944 0.0338685
\(907\) 13.6245 0.452396 0.226198 0.974081i \(-0.427370\pi\)
0.226198 + 0.974081i \(0.427370\pi\)
\(908\) −81.0880 −2.69100
\(909\) −32.4456 −1.07615
\(910\) 20.8687 0.691790
\(911\) −3.06188 −0.101444 −0.0507222 0.998713i \(-0.516152\pi\)
−0.0507222 + 0.998713i \(0.516152\pi\)
\(912\) 13.2233 0.437867
\(913\) −43.5459 −1.44116
\(914\) −4.19960 −0.138910
\(915\) −60.3792 −1.99608
\(916\) −91.2524 −3.01506
\(917\) 49.6218 1.63866
\(918\) 0.546105 0.0180241
\(919\) −46.5436 −1.53533 −0.767666 0.640850i \(-0.778582\pi\)
−0.767666 + 0.640850i \(0.778582\pi\)
\(920\) 58.1860 1.91834
\(921\) −31.1364 −1.02598
\(922\) 44.5186 1.46614
\(923\) −0.128553 −0.00423138
\(924\) 135.891 4.47048
\(925\) 7.78922 0.256108
\(926\) 50.4518 1.65795
\(927\) −38.5837 −1.26726
\(928\) 26.5044 0.870050
\(929\) 52.3846 1.71868 0.859341 0.511403i \(-0.170874\pi\)
0.859341 + 0.511403i \(0.170874\pi\)
\(930\) −75.5010 −2.47578
\(931\) 15.2376 0.499394
\(932\) −23.9570 −0.784737
\(933\) 11.3846 0.372715
\(934\) 18.2168 0.596072
\(935\) −1.24332 −0.0406610
\(936\) −7.97481 −0.260665
\(937\) −1.92038 −0.0627360 −0.0313680 0.999508i \(-0.509986\pi\)
−0.0313680 + 0.999508i \(0.509986\pi\)
\(938\) 30.3319 0.990371
\(939\) 6.16833 0.201296
\(940\) 28.6855 0.935616
\(941\) 24.0292 0.783329 0.391665 0.920108i \(-0.371899\pi\)
0.391665 + 0.920108i \(0.371899\pi\)
\(942\) −80.9328 −2.63693
\(943\) −32.6258 −1.06244
\(944\) −13.6165 −0.443179
\(945\) 19.1711 0.623635
\(946\) −80.2386 −2.60878
\(947\) −12.1843 −0.395937 −0.197969 0.980208i \(-0.563434\pi\)
−0.197969 + 0.980208i \(0.563434\pi\)
\(948\) −36.6301 −1.18969
\(949\) −4.52614 −0.146925
\(950\) −8.61017 −0.279351
\(951\) −64.2181 −2.08242
\(952\) 1.45152 0.0470440
\(953\) −42.0618 −1.36252 −0.681258 0.732043i \(-0.738567\pi\)
−0.681258 + 0.732043i \(0.738567\pi\)
\(954\) 20.0134 0.647957
\(955\) −49.8138 −1.61194
\(956\) −24.5533 −0.794111
\(957\) −93.8256 −3.03295
\(958\) 11.5002 0.371555
\(959\) 54.2734 1.75258
\(960\) −62.9560 −2.03189
\(961\) 1.04052 0.0335651
\(962\) −14.7054 −0.474123
\(963\) 36.1190 1.16392
\(964\) −10.9604 −0.353011
\(965\) −43.7892 −1.40962
\(966\) −110.446 −3.55355
\(967\) −16.3981 −0.527326 −0.263663 0.964615i \(-0.584931\pi\)
−0.263663 + 0.964615i \(0.584931\pi\)
\(968\) −44.6982 −1.43665
\(969\) 0.677249 0.0217564
\(970\) −5.53352 −0.177671
\(971\) −50.5242 −1.62140 −0.810700 0.585462i \(-0.800913\pi\)
−0.810700 + 0.585462i \(0.800913\pi\)
\(972\) −65.9716 −2.11604
\(973\) −20.3110 −0.651141
\(974\) 88.8774 2.84782
\(975\) 2.82386 0.0904359
\(976\) −22.0933 −0.707189
\(977\) −23.4779 −0.751124 −0.375562 0.926797i \(-0.622550\pi\)
−0.375562 + 0.926797i \(0.622550\pi\)
\(978\) 15.1391 0.484096
\(979\) 13.7489 0.439417
\(980\) 48.4884 1.54890
\(981\) 13.0858 0.417798
\(982\) 48.6777 1.55337
\(983\) 8.70841 0.277755 0.138878 0.990310i \(-0.455651\pi\)
0.138878 + 0.990310i \(0.455651\pi\)
\(984\) −48.7531 −1.55419
\(985\) 56.8637 1.81183
\(986\) −2.21287 −0.0704721
\(987\) −24.6600 −0.784937
\(988\) 10.5069 0.334270
\(989\) 42.1527 1.34038
\(990\) 56.9771 1.81085
\(991\) −23.9640 −0.761241 −0.380620 0.924731i \(-0.624290\pi\)
−0.380620 + 0.924731i \(0.624290\pi\)
\(992\) 16.9472 0.538073
\(993\) −55.9862 −1.77667
\(994\) −1.07227 −0.0340102
\(995\) −44.2149 −1.40171
\(996\) 75.4799 2.39167
\(997\) −44.3697 −1.40520 −0.702602 0.711583i \(-0.747978\pi\)
−0.702602 + 0.711583i \(0.747978\pi\)
\(998\) 53.6214 1.69735
\(999\) −13.5092 −0.427412
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 \(a_p\))