Properties

Label 4015.2.a.h.1.19
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 1.19
Character \(\chi\) = 4015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.132711 q^{2}\) \(+1.97030 q^{3}\) \(-1.98239 q^{4}\) \(+1.00000 q^{5}\) \(+0.261480 q^{6}\) \(+2.54454 q^{7}\) \(-0.528506 q^{8}\) \(+0.882080 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.132711 q^{2}\) \(+1.97030 q^{3}\) \(-1.98239 q^{4}\) \(+1.00000 q^{5}\) \(+0.261480 q^{6}\) \(+2.54454 q^{7}\) \(-0.528506 q^{8}\) \(+0.882080 q^{9}\) \(+0.132711 q^{10}\) \(+1.00000 q^{11}\) \(-3.90590 q^{12}\) \(+3.82891 q^{13}\) \(+0.337688 q^{14}\) \(+1.97030 q^{15}\) \(+3.89464 q^{16}\) \(+3.23514 q^{17}\) \(+0.117062 q^{18}\) \(+3.88348 q^{19}\) \(-1.98239 q^{20}\) \(+5.01351 q^{21}\) \(+0.132711 q^{22}\) \(-0.671050 q^{23}\) \(-1.04132 q^{24}\) \(+1.00000 q^{25}\) \(+0.508138 q^{26}\) \(-4.17294 q^{27}\) \(-5.04427 q^{28}\) \(-4.15859 q^{29}\) \(+0.261480 q^{30}\) \(-1.65403 q^{31}\) \(+1.57387 q^{32}\) \(+1.97030 q^{33}\) \(+0.429338 q^{34}\) \(+2.54454 q^{35}\) \(-1.74862 q^{36}\) \(+11.2450 q^{37}\) \(+0.515380 q^{38}\) \(+7.54410 q^{39}\) \(-0.528506 q^{40}\) \(-5.91398 q^{41}\) \(+0.665347 q^{42}\) \(-8.13054 q^{43}\) \(-1.98239 q^{44}\) \(+0.882080 q^{45}\) \(-0.0890556 q^{46}\) \(-2.25578 q^{47}\) \(+7.67360 q^{48}\) \(-0.525313 q^{49}\) \(+0.132711 q^{50}\) \(+6.37420 q^{51}\) \(-7.59039 q^{52}\) \(+10.1295 q^{53}\) \(-0.553794 q^{54}\) \(+1.00000 q^{55}\) \(-1.34481 q^{56}\) \(+7.65162 q^{57}\) \(-0.551890 q^{58}\) \(+4.81921 q^{59}\) \(-3.90590 q^{60}\) \(+4.97900 q^{61}\) \(-0.219508 q^{62}\) \(+2.24449 q^{63}\) \(-7.58040 q^{64}\) \(+3.82891 q^{65}\) \(+0.261480 q^{66}\) \(-14.5608 q^{67}\) \(-6.41330 q^{68}\) \(-1.32217 q^{69}\) \(+0.337688 q^{70}\) \(+9.53201 q^{71}\) \(-0.466185 q^{72}\) \(+1.00000 q^{73}\) \(+1.49233 q^{74}\) \(+1.97030 q^{75}\) \(-7.69856 q^{76}\) \(+2.54454 q^{77}\) \(+1.00118 q^{78}\) \(-8.85321 q^{79}\) \(+3.89464 q^{80}\) \(-10.8682 q^{81}\) \(-0.784849 q^{82}\) \(-1.15591 q^{83}\) \(-9.93871 q^{84}\) \(+3.23514 q^{85}\) \(-1.07901 q^{86}\) \(-8.19367 q^{87}\) \(-0.528506 q^{88}\) \(-1.34094 q^{89}\) \(+0.117062 q^{90}\) \(+9.74282 q^{91}\) \(+1.33028 q^{92}\) \(-3.25894 q^{93}\) \(-0.299367 q^{94}\) \(+3.88348 q^{95}\) \(+3.10100 q^{96}\) \(+6.93229 q^{97}\) \(-0.0697148 q^{98}\) \(+0.882080 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 37q^{11} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 11q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 43q^{16} \) \(\mathstrut +\mathstrut 38q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 43q^{20} \) \(\mathstrut +\mathstrut 39q^{21} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 9q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 14q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 20q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 15q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 62q^{41} \) \(\mathstrut -\mathstrut 13q^{42} \) \(\mathstrut +\mathstrut 30q^{43} \) \(\mathstrut +\mathstrut 43q^{44} \) \(\mathstrut +\mathstrut 50q^{45} \) \(\mathstrut +\mathstrut 31q^{46} \) \(\mathstrut +\mathstrut 5q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 59q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut +\mathstrut 37q^{55} \) \(\mathstrut +\mathstrut 22q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 40q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 57q^{61} \) \(\mathstrut +\mathstrut 20q^{62} \) \(\mathstrut -\mathstrut 29q^{63} \) \(\mathstrut +\mathstrut 10q^{64} \) \(\mathstrut +\mathstrut 11q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 53q^{68} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 11q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut +\mathstrut 59q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 42q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 61q^{81} \) \(\mathstrut -\mathstrut 22q^{82} \) \(\mathstrut +\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 66q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut -\mathstrut q^{86} \) \(\mathstrut -\mathstrut 26q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 69q^{89} \) \(\mathstrut +\mathstrut 11q^{90} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 21q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut +\mathstrut 34q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 15q^{98} \) \(\mathstrut +\mathstrut 50q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.132711 0.0938407 0.0469204 0.998899i \(-0.485059\pi\)
0.0469204 + 0.998899i \(0.485059\pi\)
\(3\) 1.97030 1.13755 0.568776 0.822492i \(-0.307417\pi\)
0.568776 + 0.822492i \(0.307417\pi\)
\(4\) −1.98239 −0.991194
\(5\) 1.00000 0.447214
\(6\) 0.261480 0.106749
\(7\) 2.54454 0.961746 0.480873 0.876790i \(-0.340320\pi\)
0.480873 + 0.876790i \(0.340320\pi\)
\(8\) −0.528506 −0.186855
\(9\) 0.882080 0.294027
\(10\) 0.132711 0.0419669
\(11\) 1.00000 0.301511
\(12\) −3.90590 −1.12754
\(13\) 3.82891 1.06195 0.530974 0.847388i \(-0.321826\pi\)
0.530974 + 0.847388i \(0.321826\pi\)
\(14\) 0.337688 0.0902510
\(15\) 1.97030 0.508729
\(16\) 3.89464 0.973659
\(17\) 3.23514 0.784637 0.392318 0.919829i \(-0.371673\pi\)
0.392318 + 0.919829i \(0.371673\pi\)
\(18\) 0.117062 0.0275917
\(19\) 3.88348 0.890931 0.445466 0.895299i \(-0.353038\pi\)
0.445466 + 0.895299i \(0.353038\pi\)
\(20\) −1.98239 −0.443275
\(21\) 5.01351 1.09404
\(22\) 0.132711 0.0282940
\(23\) −0.671050 −0.139924 −0.0699618 0.997550i \(-0.522288\pi\)
−0.0699618 + 0.997550i \(0.522288\pi\)
\(24\) −1.04132 −0.212558
\(25\) 1.00000 0.200000
\(26\) 0.508138 0.0996541
\(27\) −4.17294 −0.803082
\(28\) −5.04427 −0.953277
\(29\) −4.15859 −0.772231 −0.386116 0.922450i \(-0.626183\pi\)
−0.386116 + 0.922450i \(0.626183\pi\)
\(30\) 0.261480 0.0477395
\(31\) −1.65403 −0.297073 −0.148537 0.988907i \(-0.547456\pi\)
−0.148537 + 0.988907i \(0.547456\pi\)
\(32\) 1.57387 0.278224
\(33\) 1.97030 0.342985
\(34\) 0.429338 0.0736309
\(35\) 2.54454 0.430106
\(36\) −1.74862 −0.291437
\(37\) 11.2450 1.84866 0.924332 0.381590i \(-0.124623\pi\)
0.924332 + 0.381590i \(0.124623\pi\)
\(38\) 0.515380 0.0836056
\(39\) 7.54410 1.20802
\(40\) −0.528506 −0.0835642
\(41\) −5.91398 −0.923608 −0.461804 0.886982i \(-0.652798\pi\)
−0.461804 + 0.886982i \(0.652798\pi\)
\(42\) 0.665347 0.102665
\(43\) −8.13054 −1.23990 −0.619948 0.784643i \(-0.712846\pi\)
−0.619948 + 0.784643i \(0.712846\pi\)
\(44\) −1.98239 −0.298856
\(45\) 0.882080 0.131493
\(46\) −0.0890556 −0.0131305
\(47\) −2.25578 −0.329040 −0.164520 0.986374i \(-0.552607\pi\)
−0.164520 + 0.986374i \(0.552607\pi\)
\(48\) 7.67360 1.10759
\(49\) −0.525313 −0.0750448
\(50\) 0.132711 0.0187681
\(51\) 6.37420 0.892566
\(52\) −7.59039 −1.05260
\(53\) 10.1295 1.39140 0.695698 0.718334i \(-0.255095\pi\)
0.695698 + 0.718334i \(0.255095\pi\)
\(54\) −0.553794 −0.0753618
\(55\) 1.00000 0.134840
\(56\) −1.34481 −0.179707
\(57\) 7.65162 1.01348
\(58\) −0.551890 −0.0724668
\(59\) 4.81921 0.627407 0.313704 0.949521i \(-0.398430\pi\)
0.313704 + 0.949521i \(0.398430\pi\)
\(60\) −3.90590 −0.504249
\(61\) 4.97900 0.637496 0.318748 0.947839i \(-0.396738\pi\)
0.318748 + 0.947839i \(0.396738\pi\)
\(62\) −0.219508 −0.0278776
\(63\) 2.24449 0.282779
\(64\) −7.58040 −0.947551
\(65\) 3.82891 0.474918
\(66\) 0.261480 0.0321860
\(67\) −14.5608 −1.77889 −0.889445 0.457043i \(-0.848909\pi\)
−0.889445 + 0.457043i \(0.848909\pi\)
\(68\) −6.41330 −0.777727
\(69\) −1.32217 −0.159170
\(70\) 0.337688 0.0403615
\(71\) 9.53201 1.13124 0.565621 0.824665i \(-0.308637\pi\)
0.565621 + 0.824665i \(0.308637\pi\)
\(72\) −0.466185 −0.0549404
\(73\) 1.00000 0.117041
\(74\) 1.49233 0.173480
\(75\) 1.97030 0.227511
\(76\) −7.69856 −0.883085
\(77\) 2.54454 0.289977
\(78\) 1.00118 0.113362
\(79\) −8.85321 −0.996064 −0.498032 0.867159i \(-0.665944\pi\)
−0.498032 + 0.867159i \(0.665944\pi\)
\(80\) 3.89464 0.435434
\(81\) −10.8682 −1.20757
\(82\) −0.784849 −0.0866721
\(83\) −1.15591 −0.126878 −0.0634388 0.997986i \(-0.520207\pi\)
−0.0634388 + 0.997986i \(0.520207\pi\)
\(84\) −9.93871 −1.08440
\(85\) 3.23514 0.350900
\(86\) −1.07901 −0.116353
\(87\) −8.19367 −0.878454
\(88\) −0.528506 −0.0563389
\(89\) −1.34094 −0.142140 −0.0710699 0.997471i \(-0.522641\pi\)
−0.0710699 + 0.997471i \(0.522641\pi\)
\(90\) 0.117062 0.0123394
\(91\) 9.74282 1.02132
\(92\) 1.33028 0.138691
\(93\) −3.25894 −0.337936
\(94\) −0.299367 −0.0308773
\(95\) 3.88348 0.398437
\(96\) 3.10100 0.316495
\(97\) 6.93229 0.703867 0.351933 0.936025i \(-0.385524\pi\)
0.351933 + 0.936025i \(0.385524\pi\)
\(98\) −0.0697148 −0.00704226
\(99\) 0.882080 0.0886524
\(100\) −1.98239 −0.198239
\(101\) 8.49613 0.845397 0.422698 0.906270i \(-0.361083\pi\)
0.422698 + 0.906270i \(0.361083\pi\)
\(102\) 0.845925 0.0837590
\(103\) −0.217970 −0.0214772 −0.0107386 0.999942i \(-0.503418\pi\)
−0.0107386 + 0.999942i \(0.503418\pi\)
\(104\) −2.02360 −0.198431
\(105\) 5.01351 0.489268
\(106\) 1.34430 0.130570
\(107\) 3.99697 0.386401 0.193201 0.981159i \(-0.438113\pi\)
0.193201 + 0.981159i \(0.438113\pi\)
\(108\) 8.27238 0.796010
\(109\) 6.58915 0.631126 0.315563 0.948905i \(-0.397807\pi\)
0.315563 + 0.948905i \(0.397807\pi\)
\(110\) 0.132711 0.0126535
\(111\) 22.1560 2.10295
\(112\) 9.91006 0.936413
\(113\) 19.4398 1.82874 0.914372 0.404875i \(-0.132685\pi\)
0.914372 + 0.404875i \(0.132685\pi\)
\(114\) 1.01545 0.0951058
\(115\) −0.671050 −0.0625757
\(116\) 8.24394 0.765431
\(117\) 3.37740 0.312241
\(118\) 0.639561 0.0588764
\(119\) 8.23195 0.754621
\(120\) −1.04132 −0.0950586
\(121\) 1.00000 0.0909091
\(122\) 0.660768 0.0598231
\(123\) −11.6523 −1.05065
\(124\) 3.27894 0.294457
\(125\) 1.00000 0.0894427
\(126\) 0.297868 0.0265362
\(127\) 9.38206 0.832523 0.416261 0.909245i \(-0.363340\pi\)
0.416261 + 0.909245i \(0.363340\pi\)
\(128\) −4.15375 −0.367143
\(129\) −16.0196 −1.41045
\(130\) 0.508138 0.0445666
\(131\) 8.55103 0.747107 0.373554 0.927609i \(-0.378139\pi\)
0.373554 + 0.927609i \(0.378139\pi\)
\(132\) −3.90590 −0.339965
\(133\) 9.88167 0.856849
\(134\) −1.93238 −0.166932
\(135\) −4.17294 −0.359149
\(136\) −1.70979 −0.146613
\(137\) 8.40839 0.718377 0.359189 0.933265i \(-0.383053\pi\)
0.359189 + 0.933265i \(0.383053\pi\)
\(138\) −0.175466 −0.0149367
\(139\) −16.1906 −1.37327 −0.686634 0.727004i \(-0.740912\pi\)
−0.686634 + 0.727004i \(0.740912\pi\)
\(140\) −5.04427 −0.426318
\(141\) −4.44457 −0.374300
\(142\) 1.26500 0.106157
\(143\) 3.82891 0.320190
\(144\) 3.43538 0.286282
\(145\) −4.15859 −0.345352
\(146\) 0.132711 0.0109832
\(147\) −1.03502 −0.0853674
\(148\) −22.2919 −1.83238
\(149\) −13.8410 −1.13390 −0.566951 0.823751i \(-0.691877\pi\)
−0.566951 + 0.823751i \(0.691877\pi\)
\(150\) 0.261480 0.0213498
\(151\) 10.6531 0.866939 0.433470 0.901168i \(-0.357289\pi\)
0.433470 + 0.901168i \(0.357289\pi\)
\(152\) −2.05244 −0.166475
\(153\) 2.85365 0.230704
\(154\) 0.337688 0.0272117
\(155\) −1.65403 −0.132855
\(156\) −14.9553 −1.19738
\(157\) 1.34322 0.107201 0.0536005 0.998562i \(-0.482930\pi\)
0.0536005 + 0.998562i \(0.482930\pi\)
\(158\) −1.17492 −0.0934714
\(159\) 19.9582 1.58279
\(160\) 1.57387 0.124426
\(161\) −1.70751 −0.134571
\(162\) −1.44232 −0.113320
\(163\) 11.7586 0.921003 0.460501 0.887659i \(-0.347670\pi\)
0.460501 + 0.887659i \(0.347670\pi\)
\(164\) 11.7238 0.915475
\(165\) 1.97030 0.153388
\(166\) −0.153402 −0.0119063
\(167\) 8.00639 0.619553 0.309776 0.950809i \(-0.399746\pi\)
0.309776 + 0.950809i \(0.399746\pi\)
\(168\) −2.64967 −0.204426
\(169\) 1.66055 0.127735
\(170\) 0.429338 0.0329287
\(171\) 3.42554 0.261957
\(172\) 16.1179 1.22898
\(173\) 17.1620 1.30481 0.652403 0.757872i \(-0.273761\pi\)
0.652403 + 0.757872i \(0.273761\pi\)
\(174\) −1.08739 −0.0824348
\(175\) 2.54454 0.192349
\(176\) 3.89464 0.293569
\(177\) 9.49528 0.713709
\(178\) −0.177958 −0.0133385
\(179\) −22.4630 −1.67896 −0.839481 0.543389i \(-0.817141\pi\)
−0.839481 + 0.543389i \(0.817141\pi\)
\(180\) −1.74862 −0.130335
\(181\) 5.63145 0.418583 0.209291 0.977853i \(-0.432884\pi\)
0.209291 + 0.977853i \(0.432884\pi\)
\(182\) 1.29298 0.0958419
\(183\) 9.81013 0.725186
\(184\) 0.354654 0.0261454
\(185\) 11.2450 0.826747
\(186\) −0.432497 −0.0317122
\(187\) 3.23514 0.236577
\(188\) 4.47183 0.326142
\(189\) −10.6182 −0.772361
\(190\) 0.515380 0.0373896
\(191\) 8.04571 0.582167 0.291084 0.956698i \(-0.405984\pi\)
0.291084 + 0.956698i \(0.405984\pi\)
\(192\) −14.9357 −1.07789
\(193\) −20.9449 −1.50764 −0.753822 0.657079i \(-0.771792\pi\)
−0.753822 + 0.657079i \(0.771792\pi\)
\(194\) 0.919989 0.0660514
\(195\) 7.54410 0.540244
\(196\) 1.04137 0.0743839
\(197\) 18.4399 1.31379 0.656894 0.753983i \(-0.271870\pi\)
0.656894 + 0.753983i \(0.271870\pi\)
\(198\) 0.117062 0.00831920
\(199\) −9.26236 −0.656591 −0.328296 0.944575i \(-0.606474\pi\)
−0.328296 + 0.944575i \(0.606474\pi\)
\(200\) −0.528506 −0.0373710
\(201\) −28.6892 −2.02358
\(202\) 1.12753 0.0793327
\(203\) −10.5817 −0.742690
\(204\) −12.6361 −0.884706
\(205\) −5.91398 −0.413050
\(206\) −0.0289270 −0.00201544
\(207\) −0.591919 −0.0411412
\(208\) 14.9122 1.03398
\(209\) 3.88348 0.268626
\(210\) 0.665347 0.0459133
\(211\) −25.1125 −1.72881 −0.864407 0.502792i \(-0.832306\pi\)
−0.864407 + 0.502792i \(0.832306\pi\)
\(212\) −20.0806 −1.37914
\(213\) 18.7809 1.28685
\(214\) 0.530441 0.0362602
\(215\) −8.13054 −0.554498
\(216\) 2.20542 0.150060
\(217\) −4.20876 −0.285709
\(218\) 0.874451 0.0592253
\(219\) 1.97030 0.133140
\(220\) −1.98239 −0.133653
\(221\) 12.3871 0.833244
\(222\) 2.94034 0.197343
\(223\) −13.7294 −0.919388 −0.459694 0.888077i \(-0.652041\pi\)
−0.459694 + 0.888077i \(0.652041\pi\)
\(224\) 4.00478 0.267581
\(225\) 0.882080 0.0588053
\(226\) 2.57988 0.171611
\(227\) 12.6613 0.840362 0.420181 0.907440i \(-0.361967\pi\)
0.420181 + 0.907440i \(0.361967\pi\)
\(228\) −15.1685 −1.00456
\(229\) 4.59839 0.303870 0.151935 0.988390i \(-0.451450\pi\)
0.151935 + 0.988390i \(0.451450\pi\)
\(230\) −0.0890556 −0.00587215
\(231\) 5.01351 0.329865
\(232\) 2.19784 0.144295
\(233\) 1.72131 0.112767 0.0563834 0.998409i \(-0.482043\pi\)
0.0563834 + 0.998409i \(0.482043\pi\)
\(234\) 0.448218 0.0293009
\(235\) −2.25578 −0.147151
\(236\) −9.55354 −0.621882
\(237\) −17.4435 −1.13308
\(238\) 1.09247 0.0708142
\(239\) −21.1154 −1.36584 −0.682922 0.730492i \(-0.739291\pi\)
−0.682922 + 0.730492i \(0.739291\pi\)
\(240\) 7.67360 0.495329
\(241\) −3.67870 −0.236966 −0.118483 0.992956i \(-0.537803\pi\)
−0.118483 + 0.992956i \(0.537803\pi\)
\(242\) 0.132711 0.00853098
\(243\) −8.89475 −0.570598
\(244\) −9.87032 −0.631882
\(245\) −0.525313 −0.0335610
\(246\) −1.54639 −0.0985941
\(247\) 14.8695 0.946123
\(248\) 0.874167 0.0555096
\(249\) −2.27749 −0.144330
\(250\) 0.132711 0.00839337
\(251\) −6.09989 −0.385021 −0.192511 0.981295i \(-0.561663\pi\)
−0.192511 + 0.981295i \(0.561663\pi\)
\(252\) −4.44945 −0.280289
\(253\) −0.671050 −0.0421885
\(254\) 1.24510 0.0781246
\(255\) 6.37420 0.399168
\(256\) 14.6096 0.913098
\(257\) −3.13747 −0.195710 −0.0978549 0.995201i \(-0.531198\pi\)
−0.0978549 + 0.995201i \(0.531198\pi\)
\(258\) −2.12597 −0.132357
\(259\) 28.6133 1.77794
\(260\) −7.59039 −0.470736
\(261\) −3.66821 −0.227057
\(262\) 1.13481 0.0701091
\(263\) −2.68651 −0.165657 −0.0828286 0.996564i \(-0.526395\pi\)
−0.0828286 + 0.996564i \(0.526395\pi\)
\(264\) −1.04132 −0.0640885
\(265\) 10.1295 0.622252
\(266\) 1.31140 0.0804074
\(267\) −2.64206 −0.161692
\(268\) 28.8652 1.76322
\(269\) −10.5332 −0.642218 −0.321109 0.947042i \(-0.604056\pi\)
−0.321109 + 0.947042i \(0.604056\pi\)
\(270\) −0.553794 −0.0337028
\(271\) 13.2890 0.807252 0.403626 0.914924i \(-0.367750\pi\)
0.403626 + 0.914924i \(0.367750\pi\)
\(272\) 12.5997 0.763969
\(273\) 19.1963 1.16181
\(274\) 1.11588 0.0674130
\(275\) 1.00000 0.0603023
\(276\) 2.62105 0.157769
\(277\) −24.6994 −1.48404 −0.742022 0.670376i \(-0.766133\pi\)
−0.742022 + 0.670376i \(0.766133\pi\)
\(278\) −2.14867 −0.128868
\(279\) −1.45899 −0.0873474
\(280\) −1.34481 −0.0803675
\(281\) −25.3659 −1.51320 −0.756600 0.653878i \(-0.773141\pi\)
−0.756600 + 0.653878i \(0.773141\pi\)
\(282\) −0.589842 −0.0351246
\(283\) 25.5812 1.52065 0.760323 0.649545i \(-0.225041\pi\)
0.760323 + 0.649545i \(0.225041\pi\)
\(284\) −18.8961 −1.12128
\(285\) 7.65162 0.453243
\(286\) 0.508138 0.0300468
\(287\) −15.0484 −0.888277
\(288\) 1.38828 0.0818053
\(289\) −6.53387 −0.384345
\(290\) −0.551890 −0.0324081
\(291\) 13.6587 0.800686
\(292\) −1.98239 −0.116010
\(293\) −4.53296 −0.264818 −0.132409 0.991195i \(-0.542271\pi\)
−0.132409 + 0.991195i \(0.542271\pi\)
\(294\) −0.137359 −0.00801094
\(295\) 4.81921 0.280585
\(296\) −5.94304 −0.345432
\(297\) −4.17294 −0.242138
\(298\) −1.83686 −0.106406
\(299\) −2.56939 −0.148592
\(300\) −3.90590 −0.225507
\(301\) −20.6885 −1.19246
\(302\) 1.41379 0.0813542
\(303\) 16.7399 0.961684
\(304\) 15.1247 0.867463
\(305\) 4.97900 0.285097
\(306\) 0.378711 0.0216494
\(307\) 13.3064 0.759438 0.379719 0.925102i \(-0.376021\pi\)
0.379719 + 0.925102i \(0.376021\pi\)
\(308\) −5.04427 −0.287424
\(309\) −0.429466 −0.0244315
\(310\) −0.219508 −0.0124672
\(311\) −15.8864 −0.900836 −0.450418 0.892818i \(-0.648725\pi\)
−0.450418 + 0.892818i \(0.648725\pi\)
\(312\) −3.98710 −0.225725
\(313\) 2.54881 0.144067 0.0720336 0.997402i \(-0.477051\pi\)
0.0720336 + 0.997402i \(0.477051\pi\)
\(314\) 0.178260 0.0100598
\(315\) 2.24449 0.126463
\(316\) 17.5505 0.987292
\(317\) 33.6871 1.89206 0.946028 0.324086i \(-0.105057\pi\)
0.946028 + 0.324086i \(0.105057\pi\)
\(318\) 2.64867 0.148530
\(319\) −4.15859 −0.232837
\(320\) −7.58040 −0.423757
\(321\) 7.87522 0.439552
\(322\) −0.226606 −0.0126282
\(323\) 12.5636 0.699057
\(324\) 21.5449 1.19694
\(325\) 3.82891 0.212390
\(326\) 1.56049 0.0864276
\(327\) 12.9826 0.717939
\(328\) 3.12557 0.172581
\(329\) −5.73993 −0.316452
\(330\) 0.261480 0.0143940
\(331\) 5.72012 0.314406 0.157203 0.987566i \(-0.449752\pi\)
0.157203 + 0.987566i \(0.449752\pi\)
\(332\) 2.29146 0.125760
\(333\) 9.91897 0.543556
\(334\) 1.06253 0.0581393
\(335\) −14.5608 −0.795544
\(336\) 19.5258 1.06522
\(337\) 3.76158 0.204906 0.102453 0.994738i \(-0.467331\pi\)
0.102453 + 0.994738i \(0.467331\pi\)
\(338\) 0.220374 0.0119867
\(339\) 38.3023 2.08029
\(340\) −6.41330 −0.347810
\(341\) −1.65403 −0.0895709
\(342\) 0.454606 0.0245823
\(343\) −19.1485 −1.03392
\(344\) 4.29704 0.231681
\(345\) −1.32217 −0.0711832
\(346\) 2.27759 0.122444
\(347\) −4.79279 −0.257290 −0.128645 0.991691i \(-0.541063\pi\)
−0.128645 + 0.991691i \(0.541063\pi\)
\(348\) 16.2430 0.870718
\(349\) −30.9852 −1.65860 −0.829300 0.558804i \(-0.811261\pi\)
−0.829300 + 0.558804i \(0.811261\pi\)
\(350\) 0.337688 0.0180502
\(351\) −15.9778 −0.852832
\(352\) 1.57387 0.0838877
\(353\) 21.3880 1.13837 0.569185 0.822210i \(-0.307259\pi\)
0.569185 + 0.822210i \(0.307259\pi\)
\(354\) 1.26013 0.0669750
\(355\) 9.53201 0.505907
\(356\) 2.65827 0.140888
\(357\) 16.2194 0.858422
\(358\) −2.98108 −0.157555
\(359\) 6.98654 0.368736 0.184368 0.982857i \(-0.440976\pi\)
0.184368 + 0.982857i \(0.440976\pi\)
\(360\) −0.466185 −0.0245701
\(361\) −3.91859 −0.206242
\(362\) 0.747355 0.0392801
\(363\) 1.97030 0.103414
\(364\) −19.3140 −1.01233
\(365\) 1.00000 0.0523424
\(366\) 1.30191 0.0680520
\(367\) −13.3010 −0.694309 −0.347154 0.937808i \(-0.612852\pi\)
−0.347154 + 0.937808i \(0.612852\pi\)
\(368\) −2.61350 −0.136238
\(369\) −5.21660 −0.271565
\(370\) 1.49233 0.0775826
\(371\) 25.7750 1.33817
\(372\) 6.46049 0.334961
\(373\) 19.3542 1.00212 0.501060 0.865413i \(-0.332944\pi\)
0.501060 + 0.865413i \(0.332944\pi\)
\(374\) 0.429338 0.0222006
\(375\) 1.97030 0.101746
\(376\) 1.19219 0.0614827
\(377\) −15.9229 −0.820070
\(378\) −1.40915 −0.0724789
\(379\) −7.41176 −0.380717 −0.190358 0.981715i \(-0.560965\pi\)
−0.190358 + 0.981715i \(0.560965\pi\)
\(380\) −7.69856 −0.394928
\(381\) 18.4855 0.947039
\(382\) 1.06775 0.0546310
\(383\) −22.8099 −1.16553 −0.582765 0.812641i \(-0.698029\pi\)
−0.582765 + 0.812641i \(0.698029\pi\)
\(384\) −8.18413 −0.417644
\(385\) 2.54454 0.129682
\(386\) −2.77961 −0.141478
\(387\) −7.17178 −0.364562
\(388\) −13.7425 −0.697669
\(389\) −10.1628 −0.515275 −0.257638 0.966242i \(-0.582944\pi\)
−0.257638 + 0.966242i \(0.582944\pi\)
\(390\) 1.00118 0.0506969
\(391\) −2.17094 −0.109789
\(392\) 0.277631 0.0140225
\(393\) 16.8481 0.849874
\(394\) 2.44717 0.123287
\(395\) −8.85321 −0.445453
\(396\) −1.74862 −0.0878717
\(397\) −6.89456 −0.346028 −0.173014 0.984919i \(-0.555351\pi\)
−0.173014 + 0.984919i \(0.555351\pi\)
\(398\) −1.22922 −0.0616150
\(399\) 19.4698 0.974711
\(400\) 3.89464 0.194732
\(401\) 20.0054 0.999022 0.499511 0.866308i \(-0.333513\pi\)
0.499511 + 0.866308i \(0.333513\pi\)
\(402\) −3.80737 −0.189894
\(403\) −6.33315 −0.315476
\(404\) −16.8426 −0.837952
\(405\) −10.8682 −0.540044
\(406\) −1.40431 −0.0696946
\(407\) 11.2450 0.557393
\(408\) −3.36880 −0.166780
\(409\) 1.48384 0.0733710 0.0366855 0.999327i \(-0.488320\pi\)
0.0366855 + 0.999327i \(0.488320\pi\)
\(410\) −0.784849 −0.0387609
\(411\) 16.5670 0.817192
\(412\) 0.432101 0.0212881
\(413\) 12.2627 0.603406
\(414\) −0.0785541 −0.00386072
\(415\) −1.15591 −0.0567414
\(416\) 6.02622 0.295460
\(417\) −31.9003 −1.56216
\(418\) 0.515380 0.0252080
\(419\) 18.7532 0.916152 0.458076 0.888913i \(-0.348539\pi\)
0.458076 + 0.888913i \(0.348539\pi\)
\(420\) −9.93871 −0.484960
\(421\) −19.6952 −0.959887 −0.479944 0.877299i \(-0.659343\pi\)
−0.479944 + 0.877299i \(0.659343\pi\)
\(422\) −3.33270 −0.162233
\(423\) −1.98978 −0.0967464
\(424\) −5.35351 −0.259990
\(425\) 3.23514 0.156927
\(426\) 2.49243 0.120759
\(427\) 12.6693 0.613109
\(428\) −7.92354 −0.382999
\(429\) 7.54410 0.364233
\(430\) −1.07901 −0.0520345
\(431\) −14.4097 −0.694091 −0.347045 0.937848i \(-0.612815\pi\)
−0.347045 + 0.937848i \(0.612815\pi\)
\(432\) −16.2521 −0.781928
\(433\) −5.42227 −0.260578 −0.130289 0.991476i \(-0.541590\pi\)
−0.130289 + 0.991476i \(0.541590\pi\)
\(434\) −0.558548 −0.0268111
\(435\) −8.19367 −0.392857
\(436\) −13.0622 −0.625568
\(437\) −2.60601 −0.124662
\(438\) 0.261480 0.0124940
\(439\) 19.6784 0.939197 0.469599 0.882880i \(-0.344399\pi\)
0.469599 + 0.882880i \(0.344399\pi\)
\(440\) −0.528506 −0.0251955
\(441\) −0.463368 −0.0220652
\(442\) 1.64390 0.0781922
\(443\) −19.5849 −0.930508 −0.465254 0.885177i \(-0.654037\pi\)
−0.465254 + 0.885177i \(0.654037\pi\)
\(444\) −43.9217 −2.08443
\(445\) −1.34094 −0.0635668
\(446\) −1.82204 −0.0862761
\(447\) −27.2710 −1.28987
\(448\) −19.2886 −0.911303
\(449\) −22.9616 −1.08362 −0.541812 0.840500i \(-0.682261\pi\)
−0.541812 + 0.840500i \(0.682261\pi\)
\(450\) 0.117062 0.00551834
\(451\) −5.91398 −0.278478
\(452\) −38.5373 −1.81264
\(453\) 20.9898 0.986189
\(454\) 1.68030 0.0788602
\(455\) 9.74282 0.456750
\(456\) −4.04393 −0.189374
\(457\) −6.57865 −0.307736 −0.153868 0.988091i \(-0.549173\pi\)
−0.153868 + 0.988091i \(0.549173\pi\)
\(458\) 0.610256 0.0285154
\(459\) −13.5000 −0.630128
\(460\) 1.33028 0.0620247
\(461\) 28.2952 1.31784 0.658920 0.752213i \(-0.271013\pi\)
0.658920 + 0.752213i \(0.271013\pi\)
\(462\) 0.665347 0.0309547
\(463\) −23.5149 −1.09283 −0.546415 0.837514i \(-0.684008\pi\)
−0.546415 + 0.837514i \(0.684008\pi\)
\(464\) −16.1962 −0.751890
\(465\) −3.25894 −0.151130
\(466\) 0.228437 0.0105821
\(467\) −11.1027 −0.513774 −0.256887 0.966441i \(-0.582697\pi\)
−0.256887 + 0.966441i \(0.582697\pi\)
\(468\) −6.69533 −0.309492
\(469\) −37.0506 −1.71084
\(470\) −0.299367 −0.0138088
\(471\) 2.64655 0.121947
\(472\) −2.54698 −0.117234
\(473\) −8.13054 −0.373843
\(474\) −2.31494 −0.106329
\(475\) 3.88348 0.178186
\(476\) −16.3189 −0.747976
\(477\) 8.93505 0.409108
\(478\) −2.80225 −0.128172
\(479\) −18.1299 −0.828375 −0.414188 0.910192i \(-0.635934\pi\)
−0.414188 + 0.910192i \(0.635934\pi\)
\(480\) 3.10100 0.141541
\(481\) 43.0560 1.96319
\(482\) −0.488203 −0.0222371
\(483\) −3.36431 −0.153082
\(484\) −1.98239 −0.0901085
\(485\) 6.93229 0.314779
\(486\) −1.18043 −0.0535454
\(487\) −14.3673 −0.651045 −0.325522 0.945534i \(-0.605540\pi\)
−0.325522 + 0.945534i \(0.605540\pi\)
\(488\) −2.63143 −0.119119
\(489\) 23.1679 1.04769
\(490\) −0.0697148 −0.00314939
\(491\) 2.80368 0.126528 0.0632642 0.997997i \(-0.479849\pi\)
0.0632642 + 0.997997i \(0.479849\pi\)
\(492\) 23.0994 1.04140
\(493\) −13.4536 −0.605921
\(494\) 1.97334 0.0887849
\(495\) 0.882080 0.0396465
\(496\) −6.44186 −0.289248
\(497\) 24.2546 1.08797
\(498\) −0.302248 −0.0135440
\(499\) 9.81848 0.439535 0.219768 0.975552i \(-0.429470\pi\)
0.219768 + 0.975552i \(0.429470\pi\)
\(500\) −1.98239 −0.0886551
\(501\) 15.7750 0.704774
\(502\) −0.809521 −0.0361307
\(503\) 4.01730 0.179123 0.0895613 0.995981i \(-0.471453\pi\)
0.0895613 + 0.995981i \(0.471453\pi\)
\(504\) −1.18623 −0.0528387
\(505\) 8.49613 0.378073
\(506\) −0.0890556 −0.00395900
\(507\) 3.27179 0.145305
\(508\) −18.5989 −0.825192
\(509\) −39.4244 −1.74746 −0.873728 0.486416i \(-0.838304\pi\)
−0.873728 + 0.486416i \(0.838304\pi\)
\(510\) 0.845925 0.0374582
\(511\) 2.54454 0.112564
\(512\) 10.2463 0.452829
\(513\) −16.2055 −0.715491
\(514\) −0.416376 −0.0183656
\(515\) −0.217970 −0.00960490
\(516\) 31.7570 1.39803
\(517\) −2.25578 −0.0992092
\(518\) 3.79730 0.166844
\(519\) 33.8144 1.48429
\(520\) −2.02360 −0.0887408
\(521\) −2.83163 −0.124056 −0.0620279 0.998074i \(-0.519757\pi\)
−0.0620279 + 0.998074i \(0.519757\pi\)
\(522\) −0.486811 −0.0213072
\(523\) 6.86181 0.300046 0.150023 0.988683i \(-0.452065\pi\)
0.150023 + 0.988683i \(0.452065\pi\)
\(524\) −16.9515 −0.740528
\(525\) 5.01351 0.218807
\(526\) −0.356529 −0.0155454
\(527\) −5.35103 −0.233095
\(528\) 7.67360 0.333951
\(529\) −22.5497 −0.980421
\(530\) 1.34430 0.0583925
\(531\) 4.25093 0.184474
\(532\) −19.5893 −0.849304
\(533\) −22.6441 −0.980825
\(534\) −0.350630 −0.0151733
\(535\) 3.99697 0.172804
\(536\) 7.69549 0.332395
\(537\) −44.2588 −1.90991
\(538\) −1.39786 −0.0602662
\(539\) −0.525313 −0.0226269
\(540\) 8.27238 0.355987
\(541\) 8.15603 0.350655 0.175328 0.984510i \(-0.443902\pi\)
0.175328 + 0.984510i \(0.443902\pi\)
\(542\) 1.76360 0.0757531
\(543\) 11.0957 0.476160
\(544\) 5.09170 0.218305
\(545\) 6.58915 0.282248
\(546\) 2.54755 0.109025
\(547\) 38.8849 1.66260 0.831300 0.555824i \(-0.187597\pi\)
0.831300 + 0.555824i \(0.187597\pi\)
\(548\) −16.6687 −0.712051
\(549\) 4.39188 0.187441
\(550\) 0.132711 0.00565881
\(551\) −16.1498 −0.688005
\(552\) 0.698774 0.0297418
\(553\) −22.5273 −0.957960
\(554\) −3.27788 −0.139264
\(555\) 22.1560 0.940469
\(556\) 32.0960 1.36117
\(557\) 29.9230 1.26788 0.633939 0.773383i \(-0.281437\pi\)
0.633939 + 0.773383i \(0.281437\pi\)
\(558\) −0.193624 −0.00819675
\(559\) −31.1311 −1.31671
\(560\) 9.91006 0.418777
\(561\) 6.37420 0.269119
\(562\) −3.36632 −0.142000
\(563\) −25.1222 −1.05877 −0.529387 0.848380i \(-0.677578\pi\)
−0.529387 + 0.848380i \(0.677578\pi\)
\(564\) 8.81085 0.371004
\(565\) 19.4398 0.817839
\(566\) 3.39491 0.142699
\(567\) −27.6545 −1.16138
\(568\) −5.03773 −0.211378
\(569\) 29.3653 1.23106 0.615529 0.788114i \(-0.288942\pi\)
0.615529 + 0.788114i \(0.288942\pi\)
\(570\) 1.01545 0.0425326
\(571\) 14.4976 0.606705 0.303352 0.952878i \(-0.401894\pi\)
0.303352 + 0.952878i \(0.401894\pi\)
\(572\) −7.59039 −0.317370
\(573\) 15.8525 0.662246
\(574\) −1.99708 −0.0833565
\(575\) −0.671050 −0.0279847
\(576\) −6.68652 −0.278605
\(577\) −4.09019 −0.170277 −0.0851384 0.996369i \(-0.527133\pi\)
−0.0851384 + 0.996369i \(0.527133\pi\)
\(578\) −0.867115 −0.0360672
\(579\) −41.2676 −1.71502
\(580\) 8.24394 0.342311
\(581\) −2.94126 −0.122024
\(582\) 1.81265 0.0751370
\(583\) 10.1295 0.419522
\(584\) −0.528506 −0.0218697
\(585\) 3.37740 0.139638
\(586\) −0.601573 −0.0248507
\(587\) −22.4572 −0.926907 −0.463453 0.886121i \(-0.653390\pi\)
−0.463453 + 0.886121i \(0.653390\pi\)
\(588\) 2.05182 0.0846156
\(589\) −6.42340 −0.264672
\(590\) 0.639561 0.0263303
\(591\) 36.3321 1.49450
\(592\) 43.7951 1.79997
\(593\) 15.0724 0.618949 0.309474 0.950908i \(-0.399847\pi\)
0.309474 + 0.950908i \(0.399847\pi\)
\(594\) −0.553794 −0.0227224
\(595\) 8.23195 0.337477
\(596\) 27.4383 1.12392
\(597\) −18.2496 −0.746907
\(598\) −0.340986 −0.0139439
\(599\) 16.6594 0.680687 0.340343 0.940301i \(-0.389457\pi\)
0.340343 + 0.940301i \(0.389457\pi\)
\(600\) −1.04132 −0.0425115
\(601\) −22.3272 −0.910744 −0.455372 0.890301i \(-0.650494\pi\)
−0.455372 + 0.890301i \(0.650494\pi\)
\(602\) −2.74559 −0.111902
\(603\) −12.8438 −0.523041
\(604\) −21.1186 −0.859305
\(605\) 1.00000 0.0406558
\(606\) 2.22157 0.0902451
\(607\) −20.7008 −0.840220 −0.420110 0.907473i \(-0.638008\pi\)
−0.420110 + 0.907473i \(0.638008\pi\)
\(608\) 6.11210 0.247878
\(609\) −20.8491 −0.844850
\(610\) 0.660768 0.0267537
\(611\) −8.63719 −0.349423
\(612\) −5.65704 −0.228672
\(613\) −5.03455 −0.203344 −0.101672 0.994818i \(-0.532419\pi\)
−0.101672 + 0.994818i \(0.532419\pi\)
\(614\) 1.76591 0.0712662
\(615\) −11.6523 −0.469866
\(616\) −1.34481 −0.0541837
\(617\) −20.8441 −0.839154 −0.419577 0.907720i \(-0.637822\pi\)
−0.419577 + 0.907720i \(0.637822\pi\)
\(618\) −0.0569948 −0.00229267
\(619\) −21.1408 −0.849720 −0.424860 0.905259i \(-0.639677\pi\)
−0.424860 + 0.905259i \(0.639677\pi\)
\(620\) 3.27894 0.131685
\(621\) 2.80025 0.112370
\(622\) −2.10830 −0.0845351
\(623\) −3.41209 −0.136702
\(624\) 29.3815 1.17620
\(625\) 1.00000 0.0400000
\(626\) 0.338254 0.0135194
\(627\) 7.65162 0.305576
\(628\) −2.66279 −0.106257
\(629\) 36.3791 1.45053
\(630\) 0.297868 0.0118673
\(631\) 16.5259 0.657887 0.328943 0.944350i \(-0.393307\pi\)
0.328943 + 0.944350i \(0.393307\pi\)
\(632\) 4.67897 0.186120
\(633\) −49.4791 −1.96662
\(634\) 4.47064 0.177552
\(635\) 9.38206 0.372316
\(636\) −39.5649 −1.56885
\(637\) −2.01138 −0.0796937
\(638\) −0.551890 −0.0218496
\(639\) 8.40800 0.332615
\(640\) −4.15375 −0.164191
\(641\) −4.49477 −0.177533 −0.0887663 0.996052i \(-0.528292\pi\)
−0.0887663 + 0.996052i \(0.528292\pi\)
\(642\) 1.04513 0.0412479
\(643\) −33.2692 −1.31201 −0.656004 0.754757i \(-0.727755\pi\)
−0.656004 + 0.754757i \(0.727755\pi\)
\(644\) 3.38495 0.133386
\(645\) −16.0196 −0.630771
\(646\) 1.66733 0.0656001
\(647\) 28.6260 1.12540 0.562702 0.826660i \(-0.309762\pi\)
0.562702 + 0.826660i \(0.309762\pi\)
\(648\) 5.74390 0.225642
\(649\) 4.81921 0.189170
\(650\) 0.508138 0.0199308
\(651\) −8.29251 −0.325009
\(652\) −23.3101 −0.912892
\(653\) −26.8504 −1.05074 −0.525369 0.850874i \(-0.676073\pi\)
−0.525369 + 0.850874i \(0.676073\pi\)
\(654\) 1.72293 0.0673719
\(655\) 8.55103 0.334117
\(656\) −23.0328 −0.899280
\(657\) 0.882080 0.0344132
\(658\) −0.761751 −0.0296961
\(659\) 9.00813 0.350907 0.175453 0.984488i \(-0.443861\pi\)
0.175453 + 0.984488i \(0.443861\pi\)
\(660\) −3.90590 −0.152037
\(661\) −11.7105 −0.455487 −0.227743 0.973721i \(-0.573135\pi\)
−0.227743 + 0.973721i \(0.573135\pi\)
\(662\) 0.759123 0.0295041
\(663\) 24.4062 0.947859
\(664\) 0.610906 0.0237077
\(665\) 9.88167 0.383195
\(666\) 1.31636 0.0510077
\(667\) 2.79062 0.108053
\(668\) −15.8718 −0.614097
\(669\) −27.0510 −1.04585
\(670\) −1.93238 −0.0746544
\(671\) 4.97900 0.192212
\(672\) 7.89062 0.304387
\(673\) −31.9276 −1.23072 −0.615360 0.788246i \(-0.710989\pi\)
−0.615360 + 0.788246i \(0.710989\pi\)
\(674\) 0.499203 0.0192286
\(675\) −4.17294 −0.160616
\(676\) −3.29186 −0.126610
\(677\) 1.00170 0.0384983 0.0192492 0.999815i \(-0.493872\pi\)
0.0192492 + 0.999815i \(0.493872\pi\)
\(678\) 5.08313 0.195216
\(679\) 17.6395 0.676941
\(680\) −1.70979 −0.0655675
\(681\) 24.9466 0.955957
\(682\) −0.219508 −0.00840540
\(683\) 35.6127 1.36268 0.681341 0.731967i \(-0.261397\pi\)
0.681341 + 0.731967i \(0.261397\pi\)
\(684\) −6.79074 −0.259651
\(685\) 8.40839 0.321268
\(686\) −2.54121 −0.0970238
\(687\) 9.06020 0.345668
\(688\) −31.6655 −1.20724
\(689\) 38.7850 1.47759
\(690\) −0.175466 −0.00667988
\(691\) −49.8893 −1.89788 −0.948939 0.315460i \(-0.897841\pi\)
−0.948939 + 0.315460i \(0.897841\pi\)
\(692\) −34.0218 −1.29332
\(693\) 2.24449 0.0852610
\(694\) −0.636055 −0.0241443
\(695\) −16.1906 −0.614144
\(696\) 4.33041 0.164144
\(697\) −19.1326 −0.724697
\(698\) −4.11207 −0.155644
\(699\) 3.39150 0.128278
\(700\) −5.04427 −0.190655
\(701\) −13.4608 −0.508408 −0.254204 0.967151i \(-0.581813\pi\)
−0.254204 + 0.967151i \(0.581813\pi\)
\(702\) −2.12043 −0.0800304
\(703\) 43.6696 1.64703
\(704\) −7.58040 −0.285697
\(705\) −4.44457 −0.167392
\(706\) 2.83842 0.106825
\(707\) 21.6188 0.813057
\(708\) −18.8233 −0.707424
\(709\) −37.9966 −1.42699 −0.713497 0.700658i \(-0.752890\pi\)
−0.713497 + 0.700658i \(0.752890\pi\)
\(710\) 1.26500 0.0474747
\(711\) −7.80924 −0.292869
\(712\) 0.708697 0.0265595
\(713\) 1.10994 0.0415675
\(714\) 2.15249 0.0805549
\(715\) 3.82891 0.143193
\(716\) 44.5303 1.66418
\(717\) −41.6037 −1.55372
\(718\) 0.927190 0.0346024
\(719\) −20.7668 −0.774469 −0.387235 0.921981i \(-0.626570\pi\)
−0.387235 + 0.921981i \(0.626570\pi\)
\(720\) 3.43538 0.128029
\(721\) −0.554633 −0.0206556
\(722\) −0.520040 −0.0193539
\(723\) −7.24814 −0.269561
\(724\) −11.1637 −0.414897
\(725\) −4.15859 −0.154446
\(726\) 0.261480 0.00970444
\(727\) 45.1957 1.67621 0.838107 0.545506i \(-0.183662\pi\)
0.838107 + 0.545506i \(0.183662\pi\)
\(728\) −5.14914 −0.190840
\(729\) 15.0792 0.558489
\(730\) 0.132711 0.00491185
\(731\) −26.3034 −0.972867
\(732\) −19.4475 −0.718800
\(733\) 51.7668 1.91205 0.956025 0.293287i \(-0.0947490\pi\)
0.956025 + 0.293287i \(0.0947490\pi\)
\(734\) −1.76519 −0.0651545
\(735\) −1.03502 −0.0381775
\(736\) −1.05615 −0.0389301
\(737\) −14.5608 −0.536355
\(738\) −0.692300 −0.0254839
\(739\) 21.0525 0.774429 0.387214 0.921990i \(-0.373437\pi\)
0.387214 + 0.921990i \(0.373437\pi\)
\(740\) −22.2919 −0.819467
\(741\) 29.2974 1.07627
\(742\) 3.42062 0.125575
\(743\) −21.0814 −0.773401 −0.386700 0.922205i \(-0.626385\pi\)
−0.386700 + 0.922205i \(0.626385\pi\)
\(744\) 1.72237 0.0631452
\(745\) −13.8410 −0.507097
\(746\) 2.56851 0.0940397
\(747\) −1.01961 −0.0373054
\(748\) −6.41330 −0.234494
\(749\) 10.1704 0.371620
\(750\) 0.261480 0.00954790
\(751\) −20.2110 −0.737509 −0.368755 0.929527i \(-0.620216\pi\)
−0.368755 + 0.929527i \(0.620216\pi\)
\(752\) −8.78545 −0.320372
\(753\) −12.0186 −0.437982
\(754\) −2.11314 −0.0769560
\(755\) 10.6531 0.387707
\(756\) 21.0494 0.765559
\(757\) 30.3677 1.10373 0.551866 0.833933i \(-0.313916\pi\)
0.551866 + 0.833933i \(0.313916\pi\)
\(758\) −0.983621 −0.0357267
\(759\) −1.32217 −0.0479917
\(760\) −2.05244 −0.0744499
\(761\) 2.49497 0.0904426 0.0452213 0.998977i \(-0.485601\pi\)
0.0452213 + 0.998977i \(0.485601\pi\)
\(762\) 2.45322 0.0888708
\(763\) 16.7663 0.606983
\(764\) −15.9497 −0.577041
\(765\) 2.85365 0.103174
\(766\) −3.02712 −0.109374
\(767\) 18.4523 0.666274
\(768\) 28.7852 1.03870
\(769\) 5.78286 0.208535 0.104268 0.994549i \(-0.466750\pi\)
0.104268 + 0.994549i \(0.466750\pi\)
\(770\) 0.337688 0.0121694
\(771\) −6.18175 −0.222630
\(772\) 41.5208 1.49437
\(773\) −12.9793 −0.466834 −0.233417 0.972377i \(-0.574991\pi\)
−0.233417 + 0.972377i \(0.574991\pi\)
\(774\) −0.951773 −0.0342108
\(775\) −1.65403 −0.0594146
\(776\) −3.66375 −0.131521
\(777\) 56.3768 2.02251
\(778\) −1.34872 −0.0483538
\(779\) −22.9668 −0.822871
\(780\) −14.9553 −0.535487
\(781\) 9.53201 0.341082
\(782\) −0.288107 −0.0103027
\(783\) 17.3535 0.620165
\(784\) −2.04591 −0.0730680
\(785\) 1.34322 0.0479417
\(786\) 2.23593 0.0797528
\(787\) 34.7102 1.23729 0.618643 0.785673i \(-0.287683\pi\)
0.618643 + 0.785673i \(0.287683\pi\)
\(788\) −36.5550 −1.30222
\(789\) −5.29323 −0.188444
\(790\) −1.17492 −0.0418017
\(791\) 49.4654 1.75879
\(792\) −0.466185 −0.0165651
\(793\) 19.0642 0.676988
\(794\) −0.914982 −0.0324715
\(795\) 19.9582 0.707844
\(796\) 18.3616 0.650809
\(797\) −24.9100 −0.882357 −0.441178 0.897419i \(-0.645439\pi\)
−0.441178 + 0.897419i \(0.645439\pi\)
\(798\) 2.58386 0.0914677
\(799\) −7.29777 −0.258177
\(800\) 1.57387 0.0556448
\(801\) −1.18282 −0.0417929
\(802\) 2.65493 0.0937490
\(803\) 1.00000 0.0352892
\(804\) 56.8731 2.00576
\(805\) −1.70751 −0.0601819
\(806\) −0.840477 −0.0296045
\(807\) −20.7535 −0.730556
\(808\) −4.49026 −0.157967
\(809\) −25.9432 −0.912113 −0.456057 0.889951i \(-0.650739\pi\)
−0.456057 + 0.889951i \(0.650739\pi\)
\(810\) −1.44232 −0.0506781
\(811\) 0.676194 0.0237444 0.0118722 0.999930i \(-0.496221\pi\)
0.0118722 + 0.999930i \(0.496221\pi\)
\(812\) 20.9771 0.736150
\(813\) 26.1834 0.918292
\(814\) 1.49233 0.0523062
\(815\) 11.7586 0.411885
\(816\) 24.8252 0.869055
\(817\) −31.5748 −1.10466
\(818\) 0.196921 0.00688519
\(819\) 8.59394 0.300297
\(820\) 11.7238 0.409413
\(821\) 46.4905 1.62253 0.811264 0.584680i \(-0.198780\pi\)
0.811264 + 0.584680i \(0.198780\pi\)
\(822\) 2.19863 0.0766859
\(823\) 40.0098 1.39465 0.697326 0.716754i \(-0.254373\pi\)
0.697326 + 0.716754i \(0.254373\pi\)
\(824\) 0.115198 0.00401313
\(825\) 1.97030 0.0685970
\(826\) 1.62739 0.0566241
\(827\) −25.1725 −0.875333 −0.437667 0.899137i \(-0.644195\pi\)
−0.437667 + 0.899137i \(0.644195\pi\)
\(828\) 1.17341 0.0407789
\(829\) 37.1449 1.29009 0.645047 0.764143i \(-0.276838\pi\)
0.645047 + 0.764143i \(0.276838\pi\)
\(830\) −0.153402 −0.00532466
\(831\) −48.6652 −1.68818
\(832\) −29.0247 −1.00625
\(833\) −1.69946 −0.0588829
\(834\) −4.23351 −0.146595
\(835\) 8.00639 0.277072
\(836\) −7.69856 −0.266260
\(837\) 6.90218 0.238574
\(838\) 2.48875 0.0859724
\(839\) 6.15310 0.212429 0.106214 0.994343i \(-0.466127\pi\)
0.106214 + 0.994343i \(0.466127\pi\)
\(840\) −2.64967 −0.0914223
\(841\) −11.7061 −0.403659
\(842\) −2.61377 −0.0900765
\(843\) −49.9783 −1.72135
\(844\) 49.7827 1.71359
\(845\) 1.66055 0.0571248
\(846\) −0.264065 −0.00907875
\(847\) 2.54454 0.0874314
\(848\) 39.4508 1.35475
\(849\) 50.4027 1.72982
\(850\) 0.429338 0.0147262
\(851\) −7.54594 −0.258672
\(852\) −37.2311 −1.27552
\(853\) −38.4435 −1.31628 −0.658141 0.752895i \(-0.728657\pi\)
−0.658141 + 0.752895i \(0.728657\pi\)
\(854\) 1.68135 0.0575346
\(855\) 3.42554 0.117151
\(856\) −2.11242 −0.0722011
\(857\) −1.66089 −0.0567349 −0.0283675 0.999598i \(-0.509031\pi\)
−0.0283675 + 0.999598i \(0.509031\pi\)
\(858\) 1.00118 0.0341799
\(859\) −17.7609 −0.605995 −0.302998 0.952991i \(-0.597987\pi\)
−0.302998 + 0.952991i \(0.597987\pi\)
\(860\) 16.1179 0.549615
\(861\) −29.6498 −1.01046
\(862\) −1.91232 −0.0651340
\(863\) −22.1899 −0.755354 −0.377677 0.925937i \(-0.623277\pi\)
−0.377677 + 0.925937i \(0.623277\pi\)
\(864\) −6.56767 −0.223437
\(865\) 17.1620 0.583527
\(866\) −0.719594 −0.0244528
\(867\) −12.8737 −0.437213
\(868\) 8.34339 0.283193
\(869\) −8.85321 −0.300324
\(870\) −1.08739 −0.0368660
\(871\) −55.7521 −1.88909
\(872\) −3.48240 −0.117929
\(873\) 6.11483 0.206956
\(874\) −0.345845 −0.0116984
\(875\) 2.54454 0.0860212
\(876\) −3.90590 −0.131968
\(877\) −35.5037 −1.19887 −0.599437 0.800422i \(-0.704609\pi\)
−0.599437 + 0.800422i \(0.704609\pi\)
\(878\) 2.61153 0.0881350
\(879\) −8.93129 −0.301245
\(880\) 3.89464 0.131288
\(881\) 5.64538 0.190198 0.0950988 0.995468i \(-0.469683\pi\)
0.0950988 + 0.995468i \(0.469683\pi\)
\(882\) −0.0614940 −0.00207061
\(883\) 9.39336 0.316112 0.158056 0.987430i \(-0.449477\pi\)
0.158056 + 0.987430i \(0.449477\pi\)
\(884\) −24.5560 −0.825906
\(885\) 9.49528 0.319180
\(886\) −2.59913 −0.0873196
\(887\) −18.5335 −0.622296 −0.311148 0.950362i \(-0.600713\pi\)
−0.311148 + 0.950362i \(0.600713\pi\)
\(888\) −11.7096 −0.392947
\(889\) 23.8730 0.800676
\(890\) −0.177958 −0.00596516
\(891\) −10.8682 −0.364098
\(892\) 27.2170 0.911292
\(893\) −8.76028 −0.293152
\(894\) −3.61916 −0.121043
\(895\) −22.4630 −0.750854
\(896\) −10.5694 −0.353098
\(897\) −5.06247 −0.169031
\(898\) −3.04725 −0.101688
\(899\) 6.87845 0.229409
\(900\) −1.74862 −0.0582875
\(901\) 32.7704 1.09174
\(902\) −0.784849 −0.0261326
\(903\) −40.7625 −1.35649
\(904\) −10.2741 −0.341710
\(905\) 5.63145 0.187196
\(906\) 2.78558 0.0925447
\(907\) −41.0922 −1.36444 −0.682222 0.731145i \(-0.738986\pi\)
−0.682222 + 0.731145i \(0.738986\pi\)
\(908\) −25.0997 −0.832962
\(909\) 7.49427 0.248569
\(910\) 1.29298 0.0428618
\(911\) 39.7424 1.31673 0.658363 0.752701i \(-0.271249\pi\)
0.658363 + 0.752701i \(0.271249\pi\)
\(912\) 29.8003 0.986785
\(913\) −1.15591 −0.0382551
\(914\) −0.873058 −0.0288782
\(915\) 9.81013 0.324313
\(916\) −9.11579 −0.301194
\(917\) 21.7585 0.718527
\(918\) −1.79160 −0.0591317
\(919\) 29.9968 0.989502 0.494751 0.869035i \(-0.335259\pi\)
0.494751 + 0.869035i \(0.335259\pi\)
\(920\) 0.354654 0.0116926
\(921\) 26.2176 0.863900
\(922\) 3.75509 0.123667
\(923\) 36.4972 1.20132
\(924\) −9.93871 −0.326960
\(925\) 11.2450 0.369733
\(926\) −3.12068 −0.102552
\(927\) −0.192267 −0.00631487
\(928\) −6.54510 −0.214853
\(929\) −56.6461 −1.85850 −0.929249 0.369455i \(-0.879544\pi\)
−0.929249 + 0.369455i \(0.879544\pi\)
\(930\) −0.432497 −0.0141821
\(931\) −2.04004 −0.0668597
\(932\) −3.41231 −0.111774
\(933\) −31.3010 −1.02475
\(934\) −1.47345 −0.0482129
\(935\) 3.23514 0.105800
\(936\) −1.78498 −0.0583439
\(937\) 1.09346 0.0357219 0.0178610 0.999840i \(-0.494314\pi\)
0.0178610 + 0.999840i \(0.494314\pi\)
\(938\) −4.91702 −0.160546
\(939\) 5.02191 0.163884
\(940\) 4.47183 0.145855
\(941\) 7.32395 0.238754 0.119377 0.992849i \(-0.461910\pi\)
0.119377 + 0.992849i \(0.461910\pi\)
\(942\) 0.351226 0.0114436
\(943\) 3.96857 0.129235
\(944\) 18.7691 0.610881
\(945\) −10.6182 −0.345410
\(946\) −1.07901 −0.0350817
\(947\) −5.17883 −0.168289 −0.0841446 0.996454i \(-0.526816\pi\)
−0.0841446 + 0.996454i \(0.526816\pi\)
\(948\) 34.5797 1.12310
\(949\) 3.82891 0.124292
\(950\) 0.515380 0.0167211
\(951\) 66.3736 2.15231
\(952\) −4.35063 −0.141005
\(953\) −33.6364 −1.08959 −0.544796 0.838569i \(-0.683393\pi\)
−0.544796 + 0.838569i \(0.683393\pi\)
\(954\) 1.18578 0.0383910
\(955\) 8.04571 0.260353
\(956\) 41.8590 1.35382
\(957\) −8.19367 −0.264864
\(958\) −2.40603 −0.0777354
\(959\) 21.3955 0.690896
\(960\) −14.9357 −0.482047
\(961\) −28.2642 −0.911748
\(962\) 5.71400 0.184227
\(963\) 3.52564 0.113612
\(964\) 7.29261 0.234879
\(965\) −20.9449 −0.674239
\(966\) −0.446481 −0.0143653
\(967\) 8.09327 0.260262 0.130131 0.991497i \(-0.458460\pi\)
0.130131 + 0.991497i \(0.458460\pi\)
\(968\) −0.528506 −0.0169868
\(969\) 24.7541 0.795215
\(970\) 0.919989 0.0295391
\(971\) −13.7786 −0.442177 −0.221088 0.975254i \(-0.570961\pi\)
−0.221088 + 0.975254i \(0.570961\pi\)
\(972\) 17.6328 0.565574
\(973\) −41.1976 −1.32073
\(974\) −1.90670 −0.0610945
\(975\) 7.54410 0.241605
\(976\) 19.3914 0.620704
\(977\) −32.4506 −1.03819 −0.519093 0.854718i \(-0.673730\pi\)
−0.519093 + 0.854718i \(0.673730\pi\)
\(978\) 3.07463 0.0983160
\(979\) −1.34094 −0.0428568
\(980\) 1.04137 0.0332655
\(981\) 5.81215 0.185568
\(982\) 0.372079 0.0118735
\(983\) −46.2118 −1.47393 −0.736964 0.675932i \(-0.763741\pi\)
−0.736964 + 0.675932i \(0.763741\pi\)
\(984\) 6.15832 0.196320
\(985\) 18.4399 0.587544
\(986\) −1.78544 −0.0568601
\(987\) −11.3094 −0.359981
\(988\) −29.4771 −0.937791
\(989\) 5.45599 0.173491
\(990\) 0.117062 0.00372046
\(991\) −26.2698 −0.834487 −0.417243 0.908795i \(-0.637004\pi\)
−0.417243 + 0.908795i \(0.637004\pi\)
\(992\) −2.60324 −0.0826529
\(993\) 11.2704 0.357654
\(994\) 3.21885 0.102096
\(995\) −9.26236 −0.293637
\(996\) 4.51487 0.143059
\(997\) −41.7385 −1.32187 −0.660936 0.750442i \(-0.729840\pi\)
−0.660936 + 0.750442i \(0.729840\pi\)
\(998\) 1.30302 0.0412463
\(999\) −46.9246 −1.48463
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 \(a_p\))