Properties

Label 4015.2.a.h.1.7
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 1.7
Character \(\chi\) = 4015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.93175 q^{2}\) \(-1.55022 q^{3}\) \(+1.73167 q^{4}\) \(+1.00000 q^{5}\) \(+2.99464 q^{6}\) \(+5.03826 q^{7}\) \(+0.518349 q^{8}\) \(-0.596820 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.93175 q^{2}\) \(-1.55022 q^{3}\) \(+1.73167 q^{4}\) \(+1.00000 q^{5}\) \(+2.99464 q^{6}\) \(+5.03826 q^{7}\) \(+0.518349 q^{8}\) \(-0.596820 q^{9}\) \(-1.93175 q^{10}\) \(+1.00000 q^{11}\) \(-2.68447 q^{12}\) \(+4.93475 q^{13}\) \(-9.73267 q^{14}\) \(-1.55022 q^{15}\) \(-4.46466 q^{16}\) \(-1.88345 q^{17}\) \(+1.15291 q^{18}\) \(-5.80475 q^{19}\) \(+1.73167 q^{20}\) \(-7.81041 q^{21}\) \(-1.93175 q^{22}\) \(+2.09112 q^{23}\) \(-0.803554 q^{24}\) \(+1.00000 q^{25}\) \(-9.53271 q^{26}\) \(+5.57586 q^{27}\) \(+8.72460 q^{28}\) \(+7.08062 q^{29}\) \(+2.99464 q^{30}\) \(+0.155442 q^{31}\) \(+7.58792 q^{32}\) \(-1.55022 q^{33}\) \(+3.63837 q^{34}\) \(+5.03826 q^{35}\) \(-1.03349 q^{36}\) \(-2.57766 q^{37}\) \(+11.2134 q^{38}\) \(-7.64994 q^{39}\) \(+0.518349 q^{40}\) \(+3.66097 q^{41}\) \(+15.0878 q^{42}\) \(-6.60752 q^{43}\) \(+1.73167 q^{44}\) \(-0.596820 q^{45}\) \(-4.03952 q^{46}\) \(+0.494115 q^{47}\) \(+6.92120 q^{48}\) \(+18.3841 q^{49}\) \(-1.93175 q^{50}\) \(+2.91977 q^{51}\) \(+8.54535 q^{52}\) \(-0.831913 q^{53}\) \(-10.7712 q^{54}\) \(+1.00000 q^{55}\) \(+2.61157 q^{56}\) \(+8.99864 q^{57}\) \(-13.6780 q^{58}\) \(+7.98834 q^{59}\) \(-2.68447 q^{60}\) \(+12.2714 q^{61}\) \(-0.300275 q^{62}\) \(-3.00693 q^{63}\) \(-5.72867 q^{64}\) \(+4.93475 q^{65}\) \(+2.99464 q^{66}\) \(+4.93466 q^{67}\) \(-3.26152 q^{68}\) \(-3.24169 q^{69}\) \(-9.73267 q^{70}\) \(+8.14192 q^{71}\) \(-0.309361 q^{72}\) \(+1.00000 q^{73}\) \(+4.97939 q^{74}\) \(-1.55022 q^{75}\) \(-10.0519 q^{76}\) \(+5.03826 q^{77}\) \(+14.7778 q^{78}\) \(-10.7148 q^{79}\) \(-4.46466 q^{80}\) \(-6.85335 q^{81}\) \(-7.07208 q^{82}\) \(+2.33014 q^{83}\) \(-13.5250 q^{84}\) \(-1.88345 q^{85}\) \(+12.7641 q^{86}\) \(-10.9765 q^{87}\) \(+0.518349 q^{88}\) \(-6.49569 q^{89}\) \(+1.15291 q^{90}\) \(+24.8625 q^{91}\) \(+3.62112 q^{92}\) \(-0.240969 q^{93}\) \(-0.954507 q^{94}\) \(-5.80475 q^{95}\) \(-11.7629 q^{96}\) \(-11.1355 q^{97}\) \(-35.5135 q^{98}\) \(-0.596820 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 37q^{11} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 11q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 43q^{16} \) \(\mathstrut +\mathstrut 38q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 43q^{20} \) \(\mathstrut +\mathstrut 39q^{21} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 9q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 14q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 20q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 15q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 62q^{41} \) \(\mathstrut -\mathstrut 13q^{42} \) \(\mathstrut +\mathstrut 30q^{43} \) \(\mathstrut +\mathstrut 43q^{44} \) \(\mathstrut +\mathstrut 50q^{45} \) \(\mathstrut +\mathstrut 31q^{46} \) \(\mathstrut +\mathstrut 5q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 59q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut +\mathstrut 37q^{55} \) \(\mathstrut +\mathstrut 22q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 40q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 57q^{61} \) \(\mathstrut +\mathstrut 20q^{62} \) \(\mathstrut -\mathstrut 29q^{63} \) \(\mathstrut +\mathstrut 10q^{64} \) \(\mathstrut +\mathstrut 11q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 53q^{68} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 11q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut +\mathstrut 59q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 42q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 61q^{81} \) \(\mathstrut -\mathstrut 22q^{82} \) \(\mathstrut +\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 66q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut -\mathstrut q^{86} \) \(\mathstrut -\mathstrut 26q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 69q^{89} \) \(\mathstrut +\mathstrut 11q^{90} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 21q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut +\mathstrut 34q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 15q^{98} \) \(\mathstrut +\mathstrut 50q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.93175 −1.36596 −0.682978 0.730439i \(-0.739315\pi\)
−0.682978 + 0.730439i \(0.739315\pi\)
\(3\) −1.55022 −0.895020 −0.447510 0.894279i \(-0.647689\pi\)
−0.447510 + 0.894279i \(0.647689\pi\)
\(4\) 1.73167 0.865835
\(5\) 1.00000 0.447214
\(6\) 2.99464 1.22256
\(7\) 5.03826 1.90428 0.952142 0.305657i \(-0.0988762\pi\)
0.952142 + 0.305657i \(0.0988762\pi\)
\(8\) 0.518349 0.183264
\(9\) −0.596820 −0.198940
\(10\) −1.93175 −0.610874
\(11\) 1.00000 0.301511
\(12\) −2.68447 −0.774939
\(13\) 4.93475 1.36865 0.684326 0.729176i \(-0.260096\pi\)
0.684326 + 0.729176i \(0.260096\pi\)
\(14\) −9.73267 −2.60117
\(15\) −1.55022 −0.400265
\(16\) −4.46466 −1.11616
\(17\) −1.88345 −0.456805 −0.228402 0.973567i \(-0.573350\pi\)
−0.228402 + 0.973567i \(0.573350\pi\)
\(18\) 1.15291 0.271743
\(19\) −5.80475 −1.33170 −0.665851 0.746085i \(-0.731931\pi\)
−0.665851 + 0.746085i \(0.731931\pi\)
\(20\) 1.73167 0.387213
\(21\) −7.81041 −1.70437
\(22\) −1.93175 −0.411851
\(23\) 2.09112 0.436028 0.218014 0.975946i \(-0.430042\pi\)
0.218014 + 0.975946i \(0.430042\pi\)
\(24\) −0.803554 −0.164025
\(25\) 1.00000 0.200000
\(26\) −9.53271 −1.86952
\(27\) 5.57586 1.07307
\(28\) 8.72460 1.64879
\(29\) 7.08062 1.31484 0.657420 0.753525i \(-0.271648\pi\)
0.657420 + 0.753525i \(0.271648\pi\)
\(30\) 2.99464 0.546744
\(31\) 0.155442 0.0279182 0.0139591 0.999903i \(-0.495557\pi\)
0.0139591 + 0.999903i \(0.495557\pi\)
\(32\) 7.58792 1.34137
\(33\) −1.55022 −0.269859
\(34\) 3.63837 0.623975
\(35\) 5.03826 0.851621
\(36\) −1.03349 −0.172249
\(37\) −2.57766 −0.423764 −0.211882 0.977295i \(-0.567959\pi\)
−0.211882 + 0.977295i \(0.567959\pi\)
\(38\) 11.2134 1.81905
\(39\) −7.64994 −1.22497
\(40\) 0.518349 0.0819581
\(41\) 3.66097 0.571747 0.285873 0.958267i \(-0.407716\pi\)
0.285873 + 0.958267i \(0.407716\pi\)
\(42\) 15.0878 2.32809
\(43\) −6.60752 −1.00764 −0.503818 0.863810i \(-0.668072\pi\)
−0.503818 + 0.863810i \(0.668072\pi\)
\(44\) 1.73167 0.261059
\(45\) −0.596820 −0.0889686
\(46\) −4.03952 −0.595595
\(47\) 0.494115 0.0720740 0.0360370 0.999350i \(-0.488527\pi\)
0.0360370 + 0.999350i \(0.488527\pi\)
\(48\) 6.92120 0.998990
\(49\) 18.3841 2.62629
\(50\) −1.93175 −0.273191
\(51\) 2.91977 0.408849
\(52\) 8.54535 1.18503
\(53\) −0.831913 −0.114272 −0.0571361 0.998366i \(-0.518197\pi\)
−0.0571361 + 0.998366i \(0.518197\pi\)
\(54\) −10.7712 −1.46577
\(55\) 1.00000 0.134840
\(56\) 2.61157 0.348986
\(57\) 8.99864 1.19190
\(58\) −13.6780 −1.79601
\(59\) 7.98834 1.03999 0.519996 0.854168i \(-0.325933\pi\)
0.519996 + 0.854168i \(0.325933\pi\)
\(60\) −2.68447 −0.346563
\(61\) 12.2714 1.57119 0.785594 0.618742i \(-0.212358\pi\)
0.785594 + 0.618742i \(0.212358\pi\)
\(62\) −0.300275 −0.0381350
\(63\) −3.00693 −0.378838
\(64\) −5.72867 −0.716084
\(65\) 4.93475 0.612080
\(66\) 2.99464 0.368615
\(67\) 4.93466 0.602865 0.301432 0.953488i \(-0.402535\pi\)
0.301432 + 0.953488i \(0.402535\pi\)
\(68\) −3.26152 −0.395517
\(69\) −3.24169 −0.390254
\(70\) −9.73267 −1.16328
\(71\) 8.14192 0.966269 0.483134 0.875546i \(-0.339498\pi\)
0.483134 + 0.875546i \(0.339498\pi\)
\(72\) −0.309361 −0.0364585
\(73\) 1.00000 0.117041
\(74\) 4.97939 0.578843
\(75\) −1.55022 −0.179004
\(76\) −10.0519 −1.15303
\(77\) 5.03826 0.574163
\(78\) 14.7778 1.67326
\(79\) −10.7148 −1.20550 −0.602752 0.797928i \(-0.705929\pi\)
−0.602752 + 0.797928i \(0.705929\pi\)
\(80\) −4.46466 −0.499164
\(81\) −6.85335 −0.761483
\(82\) −7.07208 −0.780981
\(83\) 2.33014 0.255766 0.127883 0.991789i \(-0.459182\pi\)
0.127883 + 0.991789i \(0.459182\pi\)
\(84\) −13.5250 −1.47570
\(85\) −1.88345 −0.204289
\(86\) 12.7641 1.37639
\(87\) −10.9765 −1.17681
\(88\) 0.518349 0.0552561
\(89\) −6.49569 −0.688541 −0.344271 0.938870i \(-0.611874\pi\)
−0.344271 + 0.938870i \(0.611874\pi\)
\(90\) 1.15291 0.121527
\(91\) 24.8625 2.60630
\(92\) 3.62112 0.377528
\(93\) −0.240969 −0.0249873
\(94\) −0.954507 −0.0984499
\(95\) −5.80475 −0.595555
\(96\) −11.7629 −1.20055
\(97\) −11.1355 −1.13064 −0.565320 0.824872i \(-0.691247\pi\)
−0.565320 + 0.824872i \(0.691247\pi\)
\(98\) −35.5135 −3.58740
\(99\) −0.596820 −0.0599826
\(100\) 1.73167 0.173167
\(101\) −6.87548 −0.684136 −0.342068 0.939675i \(-0.611127\pi\)
−0.342068 + 0.939675i \(0.611127\pi\)
\(102\) −5.64027 −0.558470
\(103\) −1.32182 −0.130243 −0.0651216 0.997877i \(-0.520744\pi\)
−0.0651216 + 0.997877i \(0.520744\pi\)
\(104\) 2.55792 0.250825
\(105\) −7.81041 −0.762218
\(106\) 1.60705 0.156091
\(107\) 5.62131 0.543433 0.271716 0.962377i \(-0.412409\pi\)
0.271716 + 0.962377i \(0.412409\pi\)
\(108\) 9.65555 0.929105
\(109\) −7.60288 −0.728224 −0.364112 0.931355i \(-0.618627\pi\)
−0.364112 + 0.931355i \(0.618627\pi\)
\(110\) −1.93175 −0.184185
\(111\) 3.99593 0.379277
\(112\) −22.4941 −2.12549
\(113\) 12.0398 1.13261 0.566305 0.824196i \(-0.308372\pi\)
0.566305 + 0.824196i \(0.308372\pi\)
\(114\) −17.3832 −1.62808
\(115\) 2.09112 0.194998
\(116\) 12.2613 1.13843
\(117\) −2.94515 −0.272280
\(118\) −15.4315 −1.42058
\(119\) −9.48933 −0.869886
\(120\) −0.803554 −0.0733541
\(121\) 1.00000 0.0909091
\(122\) −23.7053 −2.14617
\(123\) −5.67530 −0.511725
\(124\) 0.269174 0.0241725
\(125\) 1.00000 0.0894427
\(126\) 5.80865 0.517476
\(127\) −10.9666 −0.973124 −0.486562 0.873646i \(-0.661749\pi\)
−0.486562 + 0.873646i \(0.661749\pi\)
\(128\) −4.10947 −0.363229
\(129\) 10.2431 0.901855
\(130\) −9.53271 −0.836074
\(131\) 20.4822 1.78954 0.894769 0.446530i \(-0.147340\pi\)
0.894769 + 0.446530i \(0.147340\pi\)
\(132\) −2.68447 −0.233653
\(133\) −29.2459 −2.53594
\(134\) −9.53255 −0.823487
\(135\) 5.57586 0.479894
\(136\) −0.976286 −0.0837158
\(137\) 11.3844 0.972639 0.486319 0.873781i \(-0.338339\pi\)
0.486319 + 0.873781i \(0.338339\pi\)
\(138\) 6.26214 0.533069
\(139\) −13.6259 −1.15573 −0.577865 0.816132i \(-0.696114\pi\)
−0.577865 + 0.816132i \(0.696114\pi\)
\(140\) 8.72460 0.737363
\(141\) −0.765986 −0.0645077
\(142\) −15.7282 −1.31988
\(143\) 4.93475 0.412664
\(144\) 2.66460 0.222050
\(145\) 7.08062 0.588014
\(146\) −1.93175 −0.159873
\(147\) −28.4993 −2.35059
\(148\) −4.46365 −0.366909
\(149\) 8.90186 0.729269 0.364635 0.931151i \(-0.381194\pi\)
0.364635 + 0.931151i \(0.381194\pi\)
\(150\) 2.99464 0.244511
\(151\) −17.8913 −1.45597 −0.727986 0.685592i \(-0.759543\pi\)
−0.727986 + 0.685592i \(0.759543\pi\)
\(152\) −3.00889 −0.244053
\(153\) 1.12408 0.0908767
\(154\) −9.73267 −0.784281
\(155\) 0.155442 0.0124854
\(156\) −13.2472 −1.06062
\(157\) −6.52351 −0.520633 −0.260317 0.965523i \(-0.583827\pi\)
−0.260317 + 0.965523i \(0.583827\pi\)
\(158\) 20.6983 1.64667
\(159\) 1.28965 0.102276
\(160\) 7.58792 0.599878
\(161\) 10.5356 0.830321
\(162\) 13.2390 1.04015
\(163\) 14.5035 1.13600 0.567999 0.823029i \(-0.307718\pi\)
0.567999 + 0.823029i \(0.307718\pi\)
\(164\) 6.33958 0.495038
\(165\) −1.55022 −0.120684
\(166\) −4.50125 −0.349365
\(167\) 2.45982 0.190347 0.0951733 0.995461i \(-0.469659\pi\)
0.0951733 + 0.995461i \(0.469659\pi\)
\(168\) −4.04851 −0.312350
\(169\) 11.3517 0.873209
\(170\) 3.63837 0.279050
\(171\) 3.46439 0.264929
\(172\) −11.4420 −0.872447
\(173\) −20.2070 −1.53631 −0.768156 0.640263i \(-0.778825\pi\)
−0.768156 + 0.640263i \(0.778825\pi\)
\(174\) 21.2039 1.60747
\(175\) 5.03826 0.380857
\(176\) −4.46466 −0.336536
\(177\) −12.3837 −0.930814
\(178\) 12.5481 0.940517
\(179\) −13.6978 −1.02382 −0.511910 0.859039i \(-0.671062\pi\)
−0.511910 + 0.859039i \(0.671062\pi\)
\(180\) −1.03349 −0.0770321
\(181\) 19.9045 1.47949 0.739743 0.672889i \(-0.234947\pi\)
0.739743 + 0.672889i \(0.234947\pi\)
\(182\) −48.0283 −3.56009
\(183\) −19.0233 −1.40624
\(184\) 1.08393 0.0799082
\(185\) −2.57766 −0.189513
\(186\) 0.465493 0.0341316
\(187\) −1.88345 −0.137732
\(188\) 0.855643 0.0624042
\(189\) 28.0926 2.04344
\(190\) 11.2134 0.813502
\(191\) −4.80342 −0.347563 −0.173782 0.984784i \(-0.555599\pi\)
−0.173782 + 0.984784i \(0.555599\pi\)
\(192\) 8.88070 0.640909
\(193\) −13.6923 −0.985596 −0.492798 0.870144i \(-0.664026\pi\)
−0.492798 + 0.870144i \(0.664026\pi\)
\(194\) 21.5110 1.54440
\(195\) −7.64994 −0.547824
\(196\) 31.8351 2.27394
\(197\) 12.9944 0.925815 0.462907 0.886407i \(-0.346806\pi\)
0.462907 + 0.886407i \(0.346806\pi\)
\(198\) 1.15291 0.0819336
\(199\) 10.4918 0.743747 0.371873 0.928283i \(-0.378716\pi\)
0.371873 + 0.928283i \(0.378716\pi\)
\(200\) 0.518349 0.0366528
\(201\) −7.64981 −0.539576
\(202\) 13.2817 0.934499
\(203\) 35.6740 2.50383
\(204\) 5.05607 0.353996
\(205\) 3.66097 0.255693
\(206\) 2.55344 0.177906
\(207\) −1.24802 −0.0867434
\(208\) −22.0320 −1.52764
\(209\) −5.80475 −0.401523
\(210\) 15.0878 1.04116
\(211\) 20.6162 1.41928 0.709639 0.704566i \(-0.248858\pi\)
0.709639 + 0.704566i \(0.248858\pi\)
\(212\) −1.44060 −0.0989407
\(213\) −12.6218 −0.864829
\(214\) −10.8590 −0.742305
\(215\) −6.60752 −0.450629
\(216\) 2.89024 0.196656
\(217\) 0.783156 0.0531641
\(218\) 14.6869 0.994721
\(219\) −1.55022 −0.104754
\(220\) 1.73167 0.116749
\(221\) −9.29437 −0.625207
\(222\) −7.71915 −0.518076
\(223\) −0.515177 −0.0344988 −0.0172494 0.999851i \(-0.505491\pi\)
−0.0172494 + 0.999851i \(0.505491\pi\)
\(224\) 38.2299 2.55434
\(225\) −0.596820 −0.0397880
\(226\) −23.2579 −1.54710
\(227\) −28.9941 −1.92441 −0.962204 0.272329i \(-0.912206\pi\)
−0.962204 + 0.272329i \(0.912206\pi\)
\(228\) 15.5827 1.03199
\(229\) −18.8631 −1.24651 −0.623254 0.782019i \(-0.714190\pi\)
−0.623254 + 0.782019i \(0.714190\pi\)
\(230\) −4.03952 −0.266358
\(231\) −7.81041 −0.513887
\(232\) 3.67023 0.240962
\(233\) 11.2385 0.736259 0.368129 0.929775i \(-0.379998\pi\)
0.368129 + 0.929775i \(0.379998\pi\)
\(234\) 5.68931 0.371922
\(235\) 0.494115 0.0322325
\(236\) 13.8332 0.900462
\(237\) 16.6102 1.07895
\(238\) 18.3310 1.18823
\(239\) 29.2160 1.88983 0.944915 0.327317i \(-0.106145\pi\)
0.944915 + 0.327317i \(0.106145\pi\)
\(240\) 6.92120 0.446762
\(241\) 15.4868 0.997595 0.498797 0.866719i \(-0.333775\pi\)
0.498797 + 0.866719i \(0.333775\pi\)
\(242\) −1.93175 −0.124178
\(243\) −6.10339 −0.391533
\(244\) 21.2500 1.36039
\(245\) 18.3841 1.17451
\(246\) 10.9633 0.698993
\(247\) −28.6450 −1.82264
\(248\) 0.0805731 0.00511639
\(249\) −3.61223 −0.228916
\(250\) −1.93175 −0.122175
\(251\) 16.8859 1.06583 0.532915 0.846169i \(-0.321096\pi\)
0.532915 + 0.846169i \(0.321096\pi\)
\(252\) −5.20701 −0.328011
\(253\) 2.09112 0.131467
\(254\) 21.1847 1.32924
\(255\) 2.91977 0.182843
\(256\) 19.3958 1.21224
\(257\) 3.41553 0.213055 0.106527 0.994310i \(-0.466027\pi\)
0.106527 + 0.994310i \(0.466027\pi\)
\(258\) −19.7871 −1.23189
\(259\) −12.9869 −0.806966
\(260\) 8.54535 0.529960
\(261\) −4.22586 −0.261574
\(262\) −39.5665 −2.44443
\(263\) −20.8884 −1.28804 −0.644018 0.765010i \(-0.722734\pi\)
−0.644018 + 0.765010i \(0.722734\pi\)
\(264\) −0.803554 −0.0494553
\(265\) −0.831913 −0.0511040
\(266\) 56.4958 3.46398
\(267\) 10.0697 0.616258
\(268\) 8.54520 0.521981
\(269\) 6.76940 0.412738 0.206369 0.978474i \(-0.433835\pi\)
0.206369 + 0.978474i \(0.433835\pi\)
\(270\) −10.7712 −0.655513
\(271\) 8.18356 0.497116 0.248558 0.968617i \(-0.420043\pi\)
0.248558 + 0.968617i \(0.420043\pi\)
\(272\) 8.40898 0.509869
\(273\) −38.5424 −2.33269
\(274\) −21.9919 −1.32858
\(275\) 1.00000 0.0603023
\(276\) −5.61354 −0.337895
\(277\) −18.5592 −1.11511 −0.557557 0.830138i \(-0.688261\pi\)
−0.557557 + 0.830138i \(0.688261\pi\)
\(278\) 26.3218 1.57868
\(279\) −0.0927708 −0.00555404
\(280\) 2.61157 0.156071
\(281\) 1.44112 0.0859699 0.0429850 0.999076i \(-0.486313\pi\)
0.0429850 + 0.999076i \(0.486313\pi\)
\(282\) 1.47970 0.0881146
\(283\) 17.6781 1.05085 0.525426 0.850839i \(-0.323906\pi\)
0.525426 + 0.850839i \(0.323906\pi\)
\(284\) 14.0991 0.836629
\(285\) 8.99864 0.533034
\(286\) −9.53271 −0.563681
\(287\) 18.4449 1.08877
\(288\) −4.52862 −0.266852
\(289\) −13.4526 −0.791329
\(290\) −13.6780 −0.803201
\(291\) 17.2625 1.01194
\(292\) 1.73167 0.101338
\(293\) −20.6008 −1.20351 −0.601755 0.798680i \(-0.705532\pi\)
−0.601755 + 0.798680i \(0.705532\pi\)
\(294\) 55.0537 3.21079
\(295\) 7.98834 0.465099
\(296\) −1.33612 −0.0776606
\(297\) 5.57586 0.323544
\(298\) −17.1962 −0.996149
\(299\) 10.3191 0.596771
\(300\) −2.68447 −0.154988
\(301\) −33.2904 −1.91883
\(302\) 34.5615 1.98879
\(303\) 10.6585 0.612315
\(304\) 25.9163 1.48640
\(305\) 12.2714 0.702657
\(306\) −2.17145 −0.124134
\(307\) 4.01236 0.228997 0.114499 0.993423i \(-0.463474\pi\)
0.114499 + 0.993423i \(0.463474\pi\)
\(308\) 8.72460 0.497130
\(309\) 2.04912 0.116570
\(310\) −0.300275 −0.0170545
\(311\) −19.3873 −1.09935 −0.549677 0.835377i \(-0.685249\pi\)
−0.549677 + 0.835377i \(0.685249\pi\)
\(312\) −3.96533 −0.224493
\(313\) −21.2151 −1.19915 −0.599575 0.800319i \(-0.704664\pi\)
−0.599575 + 0.800319i \(0.704664\pi\)
\(314\) 12.6018 0.711162
\(315\) −3.00693 −0.169421
\(316\) −18.5544 −1.04377
\(317\) 19.5399 1.09747 0.548734 0.835997i \(-0.315110\pi\)
0.548734 + 0.835997i \(0.315110\pi\)
\(318\) −2.49128 −0.139704
\(319\) 7.08062 0.396439
\(320\) −5.72867 −0.320243
\(321\) −8.71426 −0.486383
\(322\) −20.3522 −1.13418
\(323\) 10.9330 0.608328
\(324\) −11.8677 −0.659318
\(325\) 4.93475 0.273730
\(326\) −28.0171 −1.55172
\(327\) 11.7861 0.651774
\(328\) 1.89766 0.104781
\(329\) 2.48948 0.137249
\(330\) 2.99464 0.164850
\(331\) −26.3665 −1.44923 −0.724617 0.689151i \(-0.757984\pi\)
−0.724617 + 0.689151i \(0.757984\pi\)
\(332\) 4.03503 0.221451
\(333\) 1.53840 0.0843036
\(334\) −4.75177 −0.260005
\(335\) 4.93466 0.269609
\(336\) 34.8708 1.90236
\(337\) 12.1864 0.663834 0.331917 0.943309i \(-0.392305\pi\)
0.331917 + 0.943309i \(0.392305\pi\)
\(338\) −21.9287 −1.19277
\(339\) −18.6644 −1.01371
\(340\) −3.26152 −0.176881
\(341\) 0.155442 0.00841765
\(342\) −6.69235 −0.361881
\(343\) 57.3559 3.09693
\(344\) −3.42500 −0.184663
\(345\) −3.24169 −0.174527
\(346\) 39.0350 2.09853
\(347\) −7.37707 −0.396022 −0.198011 0.980200i \(-0.563448\pi\)
−0.198011 + 0.980200i \(0.563448\pi\)
\(348\) −19.0077 −1.01892
\(349\) −2.44699 −0.130984 −0.0654921 0.997853i \(-0.520862\pi\)
−0.0654921 + 0.997853i \(0.520862\pi\)
\(350\) −9.73267 −0.520233
\(351\) 27.5155 1.46867
\(352\) 7.58792 0.404438
\(353\) 11.5591 0.615228 0.307614 0.951511i \(-0.400469\pi\)
0.307614 + 0.951511i \(0.400469\pi\)
\(354\) 23.9222 1.27145
\(355\) 8.14192 0.432128
\(356\) −11.2484 −0.596163
\(357\) 14.7105 0.778565
\(358\) 26.4607 1.39849
\(359\) 20.3984 1.07659 0.538293 0.842758i \(-0.319069\pi\)
0.538293 + 0.842758i \(0.319069\pi\)
\(360\) −0.309361 −0.0163047
\(361\) 14.6952 0.773430
\(362\) −38.4505 −2.02091
\(363\) −1.55022 −0.0813654
\(364\) 43.0537 2.25663
\(365\) 1.00000 0.0523424
\(366\) 36.7483 1.92087
\(367\) 31.4652 1.64247 0.821234 0.570592i \(-0.193286\pi\)
0.821234 + 0.570592i \(0.193286\pi\)
\(368\) −9.33613 −0.486679
\(369\) −2.18494 −0.113743
\(370\) 4.97939 0.258866
\(371\) −4.19140 −0.217606
\(372\) −0.417279 −0.0216349
\(373\) −9.05849 −0.469031 −0.234516 0.972112i \(-0.575350\pi\)
−0.234516 + 0.972112i \(0.575350\pi\)
\(374\) 3.63837 0.188136
\(375\) −1.55022 −0.0800530
\(376\) 0.256124 0.0132086
\(377\) 34.9411 1.79956
\(378\) −54.2680 −2.79125
\(379\) −4.54049 −0.233229 −0.116615 0.993177i \(-0.537204\pi\)
−0.116615 + 0.993177i \(0.537204\pi\)
\(380\) −10.0519 −0.515652
\(381\) 17.0006 0.870965
\(382\) 9.27902 0.474756
\(383\) 13.7088 0.700487 0.350244 0.936659i \(-0.386099\pi\)
0.350244 + 0.936659i \(0.386099\pi\)
\(384\) 6.37057 0.325097
\(385\) 5.03826 0.256773
\(386\) 26.4502 1.34628
\(387\) 3.94350 0.200459
\(388\) −19.2830 −0.978947
\(389\) −6.70658 −0.340037 −0.170019 0.985441i \(-0.554383\pi\)
−0.170019 + 0.985441i \(0.554383\pi\)
\(390\) 14.7778 0.748303
\(391\) −3.93852 −0.199180
\(392\) 9.52935 0.481305
\(393\) −31.7519 −1.60167
\(394\) −25.1020 −1.26462
\(395\) −10.7148 −0.539118
\(396\) −1.03349 −0.0519350
\(397\) 1.51931 0.0762521 0.0381261 0.999273i \(-0.487861\pi\)
0.0381261 + 0.999273i \(0.487861\pi\)
\(398\) −20.2676 −1.01593
\(399\) 45.3375 2.26971
\(400\) −4.46466 −0.223233
\(401\) 8.98064 0.448472 0.224236 0.974535i \(-0.428011\pi\)
0.224236 + 0.974535i \(0.428011\pi\)
\(402\) 14.7775 0.737037
\(403\) 0.767066 0.0382103
\(404\) −11.9061 −0.592348
\(405\) −6.85335 −0.340546
\(406\) −68.9134 −3.42011
\(407\) −2.57766 −0.127770
\(408\) 1.51346 0.0749273
\(409\) 18.8030 0.929747 0.464874 0.885377i \(-0.346100\pi\)
0.464874 + 0.885377i \(0.346100\pi\)
\(410\) −7.07208 −0.349265
\(411\) −17.6484 −0.870531
\(412\) −2.28896 −0.112769
\(413\) 40.2473 1.98044
\(414\) 2.41087 0.118488
\(415\) 2.33014 0.114382
\(416\) 37.4445 1.83587
\(417\) 21.1231 1.03440
\(418\) 11.2134 0.548463
\(419\) −36.2214 −1.76953 −0.884766 0.466035i \(-0.845682\pi\)
−0.884766 + 0.466035i \(0.845682\pi\)
\(420\) −13.5250 −0.659955
\(421\) 29.7990 1.45231 0.726156 0.687530i \(-0.241305\pi\)
0.726156 + 0.687530i \(0.241305\pi\)
\(422\) −39.8254 −1.93867
\(423\) −0.294897 −0.0143384
\(424\) −0.431221 −0.0209419
\(425\) −1.88345 −0.0913609
\(426\) 24.3821 1.18132
\(427\) 61.8264 2.99199
\(428\) 9.73425 0.470523
\(429\) −7.64994 −0.369343
\(430\) 12.7641 0.615539
\(431\) 29.1183 1.40258 0.701291 0.712876i \(-0.252608\pi\)
0.701291 + 0.712876i \(0.252608\pi\)
\(432\) −24.8943 −1.19773
\(433\) 5.29947 0.254676 0.127338 0.991859i \(-0.459357\pi\)
0.127338 + 0.991859i \(0.459357\pi\)
\(434\) −1.51286 −0.0726198
\(435\) −10.9765 −0.526284
\(436\) −13.1657 −0.630521
\(437\) −12.1384 −0.580659
\(438\) 2.99464 0.143089
\(439\) 0.706813 0.0337344 0.0168672 0.999858i \(-0.494631\pi\)
0.0168672 + 0.999858i \(0.494631\pi\)
\(440\) 0.518349 0.0247113
\(441\) −10.9720 −0.522475
\(442\) 17.9544 0.854005
\(443\) −7.82679 −0.371862 −0.185931 0.982563i \(-0.559530\pi\)
−0.185931 + 0.982563i \(0.559530\pi\)
\(444\) 6.91963 0.328391
\(445\) −6.49569 −0.307925
\(446\) 0.995195 0.0471238
\(447\) −13.7998 −0.652710
\(448\) −28.8625 −1.36363
\(449\) 24.0263 1.13387 0.566935 0.823762i \(-0.308129\pi\)
0.566935 + 0.823762i \(0.308129\pi\)
\(450\) 1.15291 0.0543486
\(451\) 3.66097 0.172388
\(452\) 20.8490 0.980653
\(453\) 27.7354 1.30312
\(454\) 56.0095 2.62866
\(455\) 24.8625 1.16557
\(456\) 4.66443 0.218432
\(457\) 22.4896 1.05202 0.526008 0.850479i \(-0.323688\pi\)
0.526008 + 0.850479i \(0.323688\pi\)
\(458\) 36.4388 1.70267
\(459\) −10.5019 −0.490186
\(460\) 3.62112 0.168836
\(461\) −0.829128 −0.0386163 −0.0193082 0.999814i \(-0.506146\pi\)
−0.0193082 + 0.999814i \(0.506146\pi\)
\(462\) 15.0878 0.701947
\(463\) 20.7013 0.962073 0.481036 0.876701i \(-0.340260\pi\)
0.481036 + 0.876701i \(0.340260\pi\)
\(464\) −31.6126 −1.46758
\(465\) −0.240969 −0.0111747
\(466\) −21.7100 −1.00570
\(467\) −12.9160 −0.597679 −0.298840 0.954303i \(-0.596600\pi\)
−0.298840 + 0.954303i \(0.596600\pi\)
\(468\) −5.10003 −0.235749
\(469\) 24.8621 1.14803
\(470\) −0.954507 −0.0440281
\(471\) 10.1129 0.465977
\(472\) 4.14074 0.190593
\(473\) −6.60752 −0.303814
\(474\) −32.0869 −1.47380
\(475\) −5.80475 −0.266340
\(476\) −16.4324 −0.753177
\(477\) 0.496502 0.0227333
\(478\) −56.4382 −2.58142
\(479\) −30.7438 −1.40472 −0.702360 0.711822i \(-0.747870\pi\)
−0.702360 + 0.711822i \(0.747870\pi\)
\(480\) −11.7629 −0.536903
\(481\) −12.7201 −0.579985
\(482\) −29.9167 −1.36267
\(483\) −16.3325 −0.743153
\(484\) 1.73167 0.0787122
\(485\) −11.1355 −0.505637
\(486\) 11.7902 0.534816
\(487\) −2.24109 −0.101554 −0.0507768 0.998710i \(-0.516170\pi\)
−0.0507768 + 0.998710i \(0.516170\pi\)
\(488\) 6.36085 0.287942
\(489\) −22.4835 −1.01674
\(490\) −35.5135 −1.60433
\(491\) −26.5097 −1.19637 −0.598183 0.801360i \(-0.704110\pi\)
−0.598183 + 0.801360i \(0.704110\pi\)
\(492\) −9.82774 −0.443069
\(493\) −13.3360 −0.600625
\(494\) 55.3350 2.48964
\(495\) −0.596820 −0.0268251
\(496\) −0.693995 −0.0311613
\(497\) 41.0211 1.84005
\(498\) 6.97793 0.312689
\(499\) −16.7668 −0.750583 −0.375292 0.926907i \(-0.622457\pi\)
−0.375292 + 0.926907i \(0.622457\pi\)
\(500\) 1.73167 0.0774426
\(501\) −3.81326 −0.170364
\(502\) −32.6195 −1.45588
\(503\) −18.2376 −0.813175 −0.406588 0.913612i \(-0.633281\pi\)
−0.406588 + 0.913612i \(0.633281\pi\)
\(504\) −1.55864 −0.0694273
\(505\) −6.87548 −0.305955
\(506\) −4.03952 −0.179579
\(507\) −17.5977 −0.781539
\(508\) −18.9904 −0.842564
\(509\) 5.26211 0.233239 0.116620 0.993177i \(-0.462794\pi\)
0.116620 + 0.993177i \(0.462794\pi\)
\(510\) −5.64027 −0.249755
\(511\) 5.03826 0.222879
\(512\) −29.2490 −1.29264
\(513\) −32.3665 −1.42902
\(514\) −6.59795 −0.291023
\(515\) −1.32182 −0.0582465
\(516\) 17.7377 0.780857
\(517\) 0.494115 0.0217311
\(518\) 25.0875 1.10228
\(519\) 31.3253 1.37503
\(520\) 2.55792 0.112172
\(521\) 30.3204 1.32836 0.664181 0.747572i \(-0.268780\pi\)
0.664181 + 0.747572i \(0.268780\pi\)
\(522\) 8.16331 0.357298
\(523\) 1.53755 0.0672325 0.0336163 0.999435i \(-0.489298\pi\)
0.0336163 + 0.999435i \(0.489298\pi\)
\(524\) 35.4684 1.54944
\(525\) −7.81041 −0.340874
\(526\) 40.3513 1.75940
\(527\) −0.292768 −0.0127532
\(528\) 6.92120 0.301207
\(529\) −18.6272 −0.809880
\(530\) 1.60705 0.0698058
\(531\) −4.76760 −0.206896
\(532\) −50.6442 −2.19570
\(533\) 18.0659 0.782523
\(534\) −19.4522 −0.841781
\(535\) 5.62131 0.243030
\(536\) 2.55788 0.110483
\(537\) 21.2346 0.916340
\(538\) −13.0768 −0.563781
\(539\) 18.3841 0.791858
\(540\) 9.65555 0.415509
\(541\) 5.17801 0.222620 0.111310 0.993786i \(-0.464495\pi\)
0.111310 + 0.993786i \(0.464495\pi\)
\(542\) −15.8086 −0.679038
\(543\) −30.8563 −1.32417
\(544\) −14.2915 −0.612743
\(545\) −7.60288 −0.325671
\(546\) 74.4544 3.18635
\(547\) −16.2447 −0.694572 −0.347286 0.937759i \(-0.612897\pi\)
−0.347286 + 0.937759i \(0.612897\pi\)
\(548\) 19.7141 0.842144
\(549\) −7.32380 −0.312572
\(550\) −1.93175 −0.0823702
\(551\) −41.1013 −1.75097
\(552\) −1.68033 −0.0715194
\(553\) −53.9837 −2.29562
\(554\) 35.8518 1.52320
\(555\) 3.99593 0.169618
\(556\) −23.5955 −1.00067
\(557\) 7.56535 0.320554 0.160277 0.987072i \(-0.448761\pi\)
0.160277 + 0.987072i \(0.448761\pi\)
\(558\) 0.179210 0.00758657
\(559\) −32.6064 −1.37910
\(560\) −22.4941 −0.950550
\(561\) 2.91977 0.123273
\(562\) −2.78388 −0.117431
\(563\) 29.7103 1.25214 0.626070 0.779767i \(-0.284662\pi\)
0.626070 + 0.779767i \(0.284662\pi\)
\(564\) −1.32643 −0.0558530
\(565\) 12.0398 0.506519
\(566\) −34.1497 −1.43542
\(567\) −34.5289 −1.45008
\(568\) 4.22035 0.177082
\(569\) 36.1059 1.51364 0.756819 0.653624i \(-0.226752\pi\)
0.756819 + 0.653624i \(0.226752\pi\)
\(570\) −17.3832 −0.728100
\(571\) 14.4335 0.604022 0.302011 0.953304i \(-0.402342\pi\)
0.302011 + 0.953304i \(0.402342\pi\)
\(572\) 8.54535 0.357299
\(573\) 7.44635 0.311076
\(574\) −35.6310 −1.48721
\(575\) 2.09112 0.0872056
\(576\) 3.41898 0.142458
\(577\) −32.8442 −1.36732 −0.683660 0.729801i \(-0.739613\pi\)
−0.683660 + 0.729801i \(0.739613\pi\)
\(578\) 25.9871 1.08092
\(579\) 21.2261 0.882128
\(580\) 12.2613 0.509123
\(581\) 11.7398 0.487051
\(582\) −33.3468 −1.38227
\(583\) −0.831913 −0.0344543
\(584\) 0.518349 0.0214494
\(585\) −2.94515 −0.121767
\(586\) 39.7956 1.64394
\(587\) −21.8084 −0.900130 −0.450065 0.892996i \(-0.648599\pi\)
−0.450065 + 0.892996i \(0.648599\pi\)
\(588\) −49.3514 −2.03522
\(589\) −0.902302 −0.0371787
\(590\) −15.4315 −0.635304
\(591\) −20.1442 −0.828623
\(592\) 11.5084 0.472990
\(593\) 2.68288 0.110173 0.0550863 0.998482i \(-0.482457\pi\)
0.0550863 + 0.998482i \(0.482457\pi\)
\(594\) −10.7712 −0.441947
\(595\) −9.48933 −0.389025
\(596\) 15.4151 0.631426
\(597\) −16.2647 −0.665668
\(598\) −19.9340 −0.815162
\(599\) −11.9206 −0.487063 −0.243531 0.969893i \(-0.578306\pi\)
−0.243531 + 0.969893i \(0.578306\pi\)
\(600\) −0.803554 −0.0328050
\(601\) 40.4224 1.64886 0.824431 0.565962i \(-0.191495\pi\)
0.824431 + 0.565962i \(0.191495\pi\)
\(602\) 64.3088 2.62103
\(603\) −2.94510 −0.119934
\(604\) −30.9818 −1.26063
\(605\) 1.00000 0.0406558
\(606\) −20.5896 −0.836395
\(607\) −22.6150 −0.917914 −0.458957 0.888458i \(-0.651777\pi\)
−0.458957 + 0.888458i \(0.651777\pi\)
\(608\) −44.0460 −1.78630
\(609\) −55.3026 −2.24097
\(610\) −23.7053 −0.959798
\(611\) 2.43833 0.0986443
\(612\) 1.94654 0.0786842
\(613\) 16.9075 0.682888 0.341444 0.939902i \(-0.389084\pi\)
0.341444 + 0.939902i \(0.389084\pi\)
\(614\) −7.75089 −0.312800
\(615\) −5.67530 −0.228850
\(616\) 2.61157 0.105223
\(617\) 16.0878 0.647672 0.323836 0.946113i \(-0.395027\pi\)
0.323836 + 0.946113i \(0.395027\pi\)
\(618\) −3.95839 −0.159230
\(619\) −26.1103 −1.04946 −0.524730 0.851269i \(-0.675834\pi\)
−0.524730 + 0.851269i \(0.675834\pi\)
\(620\) 0.269174 0.0108103
\(621\) 11.6598 0.467891
\(622\) 37.4515 1.50167
\(623\) −32.7270 −1.31118
\(624\) 34.1544 1.36727
\(625\) 1.00000 0.0400000
\(626\) 40.9824 1.63799
\(627\) 8.99864 0.359371
\(628\) −11.2966 −0.450782
\(629\) 4.85490 0.193577
\(630\) 5.80865 0.231422
\(631\) −7.64708 −0.304425 −0.152213 0.988348i \(-0.548640\pi\)
−0.152213 + 0.988348i \(0.548640\pi\)
\(632\) −5.55398 −0.220925
\(633\) −31.9596 −1.27028
\(634\) −37.7462 −1.49909
\(635\) −10.9666 −0.435194
\(636\) 2.23324 0.0885539
\(637\) 90.7207 3.59448
\(638\) −13.6780 −0.541518
\(639\) −4.85926 −0.192229
\(640\) −4.10947 −0.162441
\(641\) −29.0050 −1.14563 −0.572815 0.819685i \(-0.694149\pi\)
−0.572815 + 0.819685i \(0.694149\pi\)
\(642\) 16.8338 0.664377
\(643\) 39.1775 1.54501 0.772506 0.635008i \(-0.219003\pi\)
0.772506 + 0.635008i \(0.219003\pi\)
\(644\) 18.2442 0.718921
\(645\) 10.2431 0.403322
\(646\) −21.1198 −0.830949
\(647\) 42.1918 1.65873 0.829365 0.558708i \(-0.188703\pi\)
0.829365 + 0.558708i \(0.188703\pi\)
\(648\) −3.55242 −0.139552
\(649\) 7.98834 0.313570
\(650\) −9.53271 −0.373904
\(651\) −1.21406 −0.0475829
\(652\) 25.1152 0.983587
\(653\) −30.7023 −1.20147 −0.600736 0.799447i \(-0.705126\pi\)
−0.600736 + 0.799447i \(0.705126\pi\)
\(654\) −22.7679 −0.890295
\(655\) 20.4822 0.800306
\(656\) −16.3450 −0.638164
\(657\) −0.596820 −0.0232842
\(658\) −4.80906 −0.187476
\(659\) 34.9234 1.36042 0.680211 0.733016i \(-0.261888\pi\)
0.680211 + 0.733016i \(0.261888\pi\)
\(660\) −2.68447 −0.104493
\(661\) 22.9407 0.892291 0.446145 0.894961i \(-0.352796\pi\)
0.446145 + 0.894961i \(0.352796\pi\)
\(662\) 50.9336 1.97959
\(663\) 14.4083 0.559572
\(664\) 1.20782 0.0468727
\(665\) −29.2459 −1.13411
\(666\) −2.97180 −0.115155
\(667\) 14.8064 0.573307
\(668\) 4.25960 0.164809
\(669\) 0.798638 0.0308771
\(670\) −9.53255 −0.368274
\(671\) 12.2714 0.473731
\(672\) −59.2648 −2.28619
\(673\) 30.9844 1.19436 0.597180 0.802107i \(-0.296288\pi\)
0.597180 + 0.802107i \(0.296288\pi\)
\(674\) −23.5411 −0.906768
\(675\) 5.57586 0.214615
\(676\) 19.6574 0.756055
\(677\) 47.8263 1.83811 0.919057 0.394126i \(-0.128953\pi\)
0.919057 + 0.394126i \(0.128953\pi\)
\(678\) 36.0549 1.38468
\(679\) −56.1036 −2.15306
\(680\) −0.976286 −0.0374388
\(681\) 44.9473 1.72238
\(682\) −0.300275 −0.0114981
\(683\) −2.35139 −0.0899733 −0.0449867 0.998988i \(-0.514325\pi\)
−0.0449867 + 0.998988i \(0.514325\pi\)
\(684\) 5.99918 0.229384
\(685\) 11.3844 0.434977
\(686\) −110.797 −4.23026
\(687\) 29.2419 1.11565
\(688\) 29.5003 1.12469
\(689\) −4.10528 −0.156399
\(690\) 6.26214 0.238396
\(691\) −36.4761 −1.38762 −0.693808 0.720160i \(-0.744068\pi\)
−0.693808 + 0.720160i \(0.744068\pi\)
\(692\) −34.9919 −1.33019
\(693\) −3.00693 −0.114224
\(694\) 14.2507 0.540949
\(695\) −13.6259 −0.516858
\(696\) −5.68966 −0.215666
\(697\) −6.89526 −0.261177
\(698\) 4.72697 0.178918
\(699\) −17.4221 −0.658966
\(700\) 8.72460 0.329759
\(701\) −1.95771 −0.0739417 −0.0369709 0.999316i \(-0.511771\pi\)
−0.0369709 + 0.999316i \(0.511771\pi\)
\(702\) −53.1531 −2.00613
\(703\) 14.9627 0.564327
\(704\) −5.72867 −0.215907
\(705\) −0.765986 −0.0288487
\(706\) −22.3293 −0.840374
\(707\) −34.6404 −1.30279
\(708\) −21.4444 −0.805931
\(709\) −22.7895 −0.855877 −0.427939 0.903808i \(-0.640760\pi\)
−0.427939 + 0.903808i \(0.640760\pi\)
\(710\) −15.7282 −0.590268
\(711\) 6.39478 0.239823
\(712\) −3.36703 −0.126185
\(713\) 0.325047 0.0121731
\(714\) −28.4171 −1.06348
\(715\) 4.93475 0.184549
\(716\) −23.7200 −0.886459
\(717\) −45.2913 −1.69143
\(718\) −39.4047 −1.47057
\(719\) −28.1303 −1.04908 −0.524541 0.851385i \(-0.675763\pi\)
−0.524541 + 0.851385i \(0.675763\pi\)
\(720\) 2.66460 0.0993037
\(721\) −6.65969 −0.248020
\(722\) −28.3874 −1.05647
\(723\) −24.0080 −0.892867
\(724\) 34.4679 1.28099
\(725\) 7.08062 0.262968
\(726\) 2.99464 0.111142
\(727\) 13.7962 0.511673 0.255837 0.966720i \(-0.417649\pi\)
0.255837 + 0.966720i \(0.417649\pi\)
\(728\) 12.8875 0.477641
\(729\) 30.0216 1.11191
\(730\) −1.93175 −0.0714974
\(731\) 12.4450 0.460293
\(732\) −32.9421 −1.21757
\(733\) 25.4547 0.940190 0.470095 0.882616i \(-0.344220\pi\)
0.470095 + 0.882616i \(0.344220\pi\)
\(734\) −60.7829 −2.24354
\(735\) −28.4993 −1.05121
\(736\) 15.8672 0.584874
\(737\) 4.93466 0.181771
\(738\) 4.22076 0.155368
\(739\) −51.2472 −1.88516 −0.942579 0.333984i \(-0.891607\pi\)
−0.942579 + 0.333984i \(0.891607\pi\)
\(740\) −4.46365 −0.164087
\(741\) 44.4060 1.63130
\(742\) 8.09674 0.297241
\(743\) −23.3817 −0.857791 −0.428896 0.903354i \(-0.641097\pi\)
−0.428896 + 0.903354i \(0.641097\pi\)
\(744\) −0.124906 −0.00457927
\(745\) 8.90186 0.326139
\(746\) 17.4988 0.640676
\(747\) −1.39067 −0.0508821
\(748\) −3.26152 −0.119253
\(749\) 28.3216 1.03485
\(750\) 2.99464 0.109349
\(751\) 38.4156 1.40181 0.700903 0.713257i \(-0.252781\pi\)
0.700903 + 0.713257i \(0.252781\pi\)
\(752\) −2.20605 −0.0804465
\(753\) −26.1769 −0.953939
\(754\) −67.4975 −2.45812
\(755\) −17.8913 −0.651130
\(756\) 48.6471 1.76928
\(757\) −19.8109 −0.720040 −0.360020 0.932945i \(-0.617230\pi\)
−0.360020 + 0.932945i \(0.617230\pi\)
\(758\) 8.77110 0.318581
\(759\) −3.24169 −0.117666
\(760\) −3.00889 −0.109144
\(761\) 34.5569 1.25269 0.626343 0.779547i \(-0.284551\pi\)
0.626343 + 0.779547i \(0.284551\pi\)
\(762\) −32.8409 −1.18970
\(763\) −38.3053 −1.38674
\(764\) −8.31793 −0.300932
\(765\) 1.12408 0.0406413
\(766\) −26.4820 −0.956834
\(767\) 39.4204 1.42339
\(768\) −30.0678 −1.08498
\(769\) 25.3529 0.914249 0.457124 0.889403i \(-0.348879\pi\)
0.457124 + 0.889403i \(0.348879\pi\)
\(770\) −9.73267 −0.350741
\(771\) −5.29482 −0.190688
\(772\) −23.7106 −0.853363
\(773\) −41.7998 −1.50343 −0.751717 0.659486i \(-0.770774\pi\)
−0.751717 + 0.659486i \(0.770774\pi\)
\(774\) −7.61786 −0.273818
\(775\) 0.155442 0.00558364
\(776\) −5.77207 −0.207205
\(777\) 20.1325 0.722251
\(778\) 12.9555 0.464476
\(779\) −21.2510 −0.761396
\(780\) −13.2472 −0.474325
\(781\) 8.14192 0.291341
\(782\) 7.60825 0.272071
\(783\) 39.4806 1.41092
\(784\) −82.0786 −2.93138
\(785\) −6.52351 −0.232834
\(786\) 61.3368 2.18781
\(787\) 9.97500 0.355570 0.177785 0.984069i \(-0.443107\pi\)
0.177785 + 0.984069i \(0.443107\pi\)
\(788\) 22.5021 0.801603
\(789\) 32.3817 1.15282
\(790\) 20.6983 0.736411
\(791\) 60.6597 2.15681
\(792\) −0.309361 −0.0109927
\(793\) 60.5561 2.15041
\(794\) −2.93494 −0.104157
\(795\) 1.28965 0.0457391
\(796\) 18.1684 0.643962
\(797\) −36.3482 −1.28752 −0.643759 0.765228i \(-0.722626\pi\)
−0.643759 + 0.765228i \(0.722626\pi\)
\(798\) −87.5808 −3.10033
\(799\) −0.930642 −0.0329237
\(800\) 7.58792 0.268274
\(801\) 3.87675 0.136978
\(802\) −17.3484 −0.612592
\(803\) 1.00000 0.0352892
\(804\) −13.2469 −0.467184
\(805\) 10.5356 0.371331
\(806\) −1.48178 −0.0521936
\(807\) −10.4941 −0.369408
\(808\) −3.56389 −0.125377
\(809\) −18.4730 −0.649474 −0.324737 0.945804i \(-0.605276\pi\)
−0.324737 + 0.945804i \(0.605276\pi\)
\(810\) 13.2390 0.465170
\(811\) 19.6901 0.691412 0.345706 0.938343i \(-0.387639\pi\)
0.345706 + 0.938343i \(0.387639\pi\)
\(812\) 61.7756 2.16790
\(813\) −12.6863 −0.444928
\(814\) 4.97939 0.174528
\(815\) 14.5035 0.508034
\(816\) −13.0358 −0.456343
\(817\) 38.3550 1.34187
\(818\) −36.3227 −1.26999
\(819\) −14.8385 −0.518497
\(820\) 6.33958 0.221388
\(821\) 45.5502 1.58971 0.794856 0.606798i \(-0.207546\pi\)
0.794856 + 0.606798i \(0.207546\pi\)
\(822\) 34.0923 1.18911
\(823\) −18.9055 −0.659005 −0.329502 0.944155i \(-0.606881\pi\)
−0.329502 + 0.944155i \(0.606881\pi\)
\(824\) −0.685165 −0.0238689
\(825\) −1.55022 −0.0539717
\(826\) −77.7479 −2.70519
\(827\) 27.0676 0.941232 0.470616 0.882338i \(-0.344032\pi\)
0.470616 + 0.882338i \(0.344032\pi\)
\(828\) −2.16116 −0.0751054
\(829\) −0.0508846 −0.00176730 −0.000883648 1.00000i \(-0.500281\pi\)
−0.000883648 1.00000i \(0.500281\pi\)
\(830\) −4.50125 −0.156241
\(831\) 28.7708 0.998050
\(832\) −28.2695 −0.980070
\(833\) −34.6255 −1.19970
\(834\) −40.8046 −1.41295
\(835\) 2.45982 0.0851256
\(836\) −10.0519 −0.347653
\(837\) 0.866722 0.0299583
\(838\) 69.9709 2.41710
\(839\) 10.0560 0.347171 0.173586 0.984819i \(-0.444465\pi\)
0.173586 + 0.984819i \(0.444465\pi\)
\(840\) −4.04851 −0.139687
\(841\) 21.1352 0.728802
\(842\) −57.5642 −1.98379
\(843\) −2.23405 −0.0769448
\(844\) 35.7004 1.22886
\(845\) 11.3517 0.390511
\(846\) 0.569669 0.0195856
\(847\) 5.03826 0.173117
\(848\) 3.71421 0.127547
\(849\) −27.4049 −0.940534
\(850\) 3.63837 0.124795
\(851\) −5.39018 −0.184773
\(852\) −21.8567 −0.748799
\(853\) −41.4409 −1.41891 −0.709455 0.704751i \(-0.751059\pi\)
−0.709455 + 0.704751i \(0.751059\pi\)
\(854\) −119.433 −4.08692
\(855\) 3.46439 0.118480
\(856\) 2.91380 0.0995916
\(857\) 1.42104 0.0485419 0.0242709 0.999705i \(-0.492274\pi\)
0.0242709 + 0.999705i \(0.492274\pi\)
\(858\) 14.7778 0.504506
\(859\) −17.0378 −0.581322 −0.290661 0.956826i \(-0.593875\pi\)
−0.290661 + 0.956826i \(0.593875\pi\)
\(860\) −11.4420 −0.390170
\(861\) −28.5936 −0.974469
\(862\) −56.2494 −1.91586
\(863\) −34.3440 −1.16908 −0.584541 0.811364i \(-0.698725\pi\)
−0.584541 + 0.811364i \(0.698725\pi\)
\(864\) 42.3092 1.43939
\(865\) −20.2070 −0.687059
\(866\) −10.2373 −0.347877
\(867\) 20.8545 0.708255
\(868\) 1.35617 0.0460313
\(869\) −10.7148 −0.363473
\(870\) 21.2039 0.718881
\(871\) 24.3513 0.825113
\(872\) −3.94094 −0.133457
\(873\) 6.64589 0.224929
\(874\) 23.4484 0.793155
\(875\) 5.03826 0.170324
\(876\) −2.68447 −0.0906998
\(877\) −10.7392 −0.362636 −0.181318 0.983424i \(-0.558036\pi\)
−0.181318 + 0.983424i \(0.558036\pi\)
\(878\) −1.36539 −0.0460796
\(879\) 31.9357 1.07717
\(880\) −4.46466 −0.150504
\(881\) 35.0429 1.18063 0.590313 0.807174i \(-0.299004\pi\)
0.590313 + 0.807174i \(0.299004\pi\)
\(882\) 21.1951 0.713677
\(883\) −42.7549 −1.43882 −0.719409 0.694587i \(-0.755587\pi\)
−0.719409 + 0.694587i \(0.755587\pi\)
\(884\) −16.0948 −0.541326
\(885\) −12.3837 −0.416273
\(886\) 15.1194 0.507947
\(887\) −4.46323 −0.149861 −0.0749303 0.997189i \(-0.523873\pi\)
−0.0749303 + 0.997189i \(0.523873\pi\)
\(888\) 2.07129 0.0695078
\(889\) −55.2523 −1.85310
\(890\) 12.5481 0.420612
\(891\) −6.85335 −0.229596
\(892\) −0.892117 −0.0298703
\(893\) −2.86821 −0.0959811
\(894\) 26.6579 0.891573
\(895\) −13.6978 −0.457867
\(896\) −20.7046 −0.691691
\(897\) −15.9969 −0.534122
\(898\) −46.4129 −1.54882
\(899\) 1.10063 0.0367079
\(900\) −1.03349 −0.0344498
\(901\) 1.56687 0.0522000
\(902\) −7.07208 −0.235475
\(903\) 51.6074 1.71739
\(904\) 6.24082 0.207567
\(905\) 19.9045 0.661646
\(906\) −53.5779 −1.78001
\(907\) 35.2083 1.16907 0.584537 0.811367i \(-0.301276\pi\)
0.584537 + 0.811367i \(0.301276\pi\)
\(908\) −50.2083 −1.66622
\(909\) 4.10342 0.136102
\(910\) −48.0283 −1.59212
\(911\) 45.5719 1.50986 0.754932 0.655803i \(-0.227670\pi\)
0.754932 + 0.655803i \(0.227670\pi\)
\(912\) −40.1759 −1.33036
\(913\) 2.33014 0.0771164
\(914\) −43.4443 −1.43701
\(915\) −19.0233 −0.628891
\(916\) −32.6646 −1.07927
\(917\) 103.195 3.40779
\(918\) 20.2870 0.669572
\(919\) −13.0262 −0.429695 −0.214847 0.976648i \(-0.568925\pi\)
−0.214847 + 0.976648i \(0.568925\pi\)
\(920\) 1.08393 0.0357360
\(921\) −6.22004 −0.204957
\(922\) 1.60167 0.0527482
\(923\) 40.1783 1.32249
\(924\) −13.5250 −0.444941
\(925\) −2.57766 −0.0847528
\(926\) −39.9899 −1.31415
\(927\) 0.788890 0.0259106
\(928\) 53.7272 1.76368
\(929\) 58.7904 1.92885 0.964425 0.264355i \(-0.0851591\pi\)
0.964425 + 0.264355i \(0.0851591\pi\)
\(930\) 0.465493 0.0152641
\(931\) −106.715 −3.49744
\(932\) 19.4614 0.637478
\(933\) 30.0546 0.983943
\(934\) 24.9504 0.816404
\(935\) −1.88345 −0.0615955
\(936\) −1.52662 −0.0498990
\(937\) 5.56584 0.181828 0.0909141 0.995859i \(-0.471021\pi\)
0.0909141 + 0.995859i \(0.471021\pi\)
\(938\) −48.0275 −1.56815
\(939\) 32.8881 1.07326
\(940\) 0.855643 0.0279080
\(941\) 6.16795 0.201069 0.100535 0.994934i \(-0.467945\pi\)
0.100535 + 0.994934i \(0.467945\pi\)
\(942\) −19.5356 −0.636504
\(943\) 7.65551 0.249298
\(944\) −35.6652 −1.16080
\(945\) 28.0926 0.913853
\(946\) 12.7641 0.414996
\(947\) −42.4764 −1.38030 −0.690149 0.723667i \(-0.742455\pi\)
−0.690149 + 0.723667i \(0.742455\pi\)
\(948\) 28.7634 0.934193
\(949\) 4.93475 0.160189
\(950\) 11.2134 0.363809
\(951\) −30.2911 −0.982256
\(952\) −4.91878 −0.159419
\(953\) −50.8495 −1.64718 −0.823588 0.567188i \(-0.808031\pi\)
−0.823588 + 0.567188i \(0.808031\pi\)
\(954\) −0.959120 −0.0310527
\(955\) −4.80342 −0.155435
\(956\) 50.5925 1.63628
\(957\) −10.9765 −0.354821
\(958\) 59.3895 1.91879
\(959\) 57.3578 1.85218
\(960\) 8.88070 0.286623
\(961\) −30.9758 −0.999221
\(962\) 24.5720 0.792234
\(963\) −3.35491 −0.108110
\(964\) 26.8181 0.863752
\(965\) −13.6923 −0.440772
\(966\) 31.5503 1.01511
\(967\) −35.1896 −1.13162 −0.565811 0.824535i \(-0.691437\pi\)
−0.565811 + 0.824535i \(0.691437\pi\)
\(968\) 0.518349 0.0166604
\(969\) −16.9485 −0.544465
\(970\) 21.5110 0.690678
\(971\) −7.12227 −0.228565 −0.114282 0.993448i \(-0.536457\pi\)
−0.114282 + 0.993448i \(0.536457\pi\)
\(972\) −10.5690 −0.339002
\(973\) −68.6506 −2.20084
\(974\) 4.32924 0.138718
\(975\) −7.64994 −0.244994
\(976\) −54.7875 −1.75371
\(977\) 29.1255 0.931808 0.465904 0.884835i \(-0.345729\pi\)
0.465904 + 0.884835i \(0.345729\pi\)
\(978\) 43.4326 1.38882
\(979\) −6.49569 −0.207603
\(980\) 31.8351 1.01694
\(981\) 4.53755 0.144873
\(982\) 51.2102 1.63418
\(983\) −18.5931 −0.593028 −0.296514 0.955028i \(-0.595824\pi\)
−0.296514 + 0.955028i \(0.595824\pi\)
\(984\) −2.94178 −0.0937806
\(985\) 12.9944 0.414037
\(986\) 25.7619 0.820427
\(987\) −3.85924 −0.122841
\(988\) −49.6036 −1.57810
\(989\) −13.8171 −0.439358
\(990\) 1.15291 0.0366418
\(991\) 41.2954 1.31179 0.655896 0.754851i \(-0.272291\pi\)
0.655896 + 0.754851i \(0.272291\pi\)
\(992\) 1.17948 0.0374486
\(993\) 40.8739 1.29709
\(994\) −79.2427 −2.51343
\(995\) 10.4918 0.332614
\(996\) −6.25518 −0.198203
\(997\) −7.10600 −0.225049 −0.112525 0.993649i \(-0.535894\pi\)
−0.112525 + 0.993649i \(0.535894\pi\)
\(998\) 32.3892 1.02526
\(999\) −14.3726 −0.454730
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 \(a_p\))