Properties

Label 4031.2.a.c.1.5
Level 4031
Weight 2
Character 4031.1
Self dual Yes
Analytic conductor 32.188
Analytic rank 1
Dimension 61
CM No

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Newspace parameters

Level: \( N \) = \( 4031 = 29 \cdot 139 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4031.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1876970548\)
Analytic rank: \(1\)
Dimension: \(61\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 4031.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.42000 q^{2}\) \(-2.29529 q^{3}\) \(+3.85639 q^{4}\) \(+1.32254 q^{5}\) \(+5.55461 q^{6}\) \(+0.993943 q^{7}\) \(-4.49245 q^{8}\) \(+2.26837 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.42000 q^{2}\) \(-2.29529 q^{3}\) \(+3.85639 q^{4}\) \(+1.32254 q^{5}\) \(+5.55461 q^{6}\) \(+0.993943 q^{7}\) \(-4.49245 q^{8}\) \(+2.26837 q^{9}\) \(-3.20054 q^{10}\) \(+2.10381 q^{11}\) \(-8.85154 q^{12}\) \(+3.07912 q^{13}\) \(-2.40534 q^{14}\) \(-3.03561 q^{15}\) \(+3.15895 q^{16}\) \(+6.60217 q^{17}\) \(-5.48946 q^{18}\) \(-0.0631268 q^{19}\) \(+5.10022 q^{20}\) \(-2.28139 q^{21}\) \(-5.09121 q^{22}\) \(-5.94544 q^{23}\) \(+10.3115 q^{24}\) \(-3.25089 q^{25}\) \(-7.45147 q^{26}\) \(+1.67929 q^{27}\) \(+3.83303 q^{28}\) \(-1.00000 q^{29}\) \(+7.34618 q^{30}\) \(+5.42341 q^{31}\) \(+1.34025 q^{32}\) \(-4.82886 q^{33}\) \(-15.9772 q^{34}\) \(+1.31453 q^{35}\) \(+8.74773 q^{36}\) \(-5.88877 q^{37}\) \(+0.152767 q^{38}\) \(-7.06749 q^{39}\) \(-5.94144 q^{40}\) \(-5.46764 q^{41}\) \(+5.52096 q^{42}\) \(+0.835709 q^{43}\) \(+8.11310 q^{44}\) \(+3.00001 q^{45}\) \(+14.3880 q^{46}\) \(-0.379470 q^{47}\) \(-7.25073 q^{48}\) \(-6.01208 q^{49}\) \(+7.86715 q^{50}\) \(-15.1539 q^{51}\) \(+11.8743 q^{52}\) \(-2.25880 q^{53}\) \(-4.06389 q^{54}\) \(+2.78237 q^{55}\) \(-4.46524 q^{56}\) \(+0.144895 q^{57}\) \(+2.42000 q^{58}\) \(-7.33926 q^{59}\) \(-11.7065 q^{60}\) \(-4.55335 q^{61}\) \(-13.1246 q^{62}\) \(+2.25464 q^{63}\) \(-9.56131 q^{64}\) \(+4.07226 q^{65}\) \(+11.6858 q^{66}\) \(-8.31257 q^{67}\) \(+25.4605 q^{68}\) \(+13.6465 q^{69}\) \(-3.18115 q^{70}\) \(-7.18358 q^{71}\) \(-10.1906 q^{72}\) \(-15.1404 q^{73}\) \(+14.2508 q^{74}\) \(+7.46175 q^{75}\) \(-0.243442 q^{76}\) \(+2.09106 q^{77}\) \(+17.1033 q^{78}\) \(-1.93701 q^{79}\) \(+4.17784 q^{80}\) \(-10.6596 q^{81}\) \(+13.2317 q^{82}\) \(+7.16441 q^{83}\) \(-8.79793 q^{84}\) \(+8.73162 q^{85}\) \(-2.02241 q^{86}\) \(+2.29529 q^{87}\) \(-9.45126 q^{88}\) \(-3.20563 q^{89}\) \(-7.26002 q^{90}\) \(+3.06047 q^{91}\) \(-22.9279 q^{92}\) \(-12.4483 q^{93}\) \(+0.918316 q^{94}\) \(-0.0834877 q^{95}\) \(-3.07627 q^{96}\) \(-4.74236 q^{97}\) \(+14.5492 q^{98}\) \(+4.77222 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 11q^{16} \) \(\mathstrut -\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 17q^{18} \) \(\mathstrut -\mathstrut 36q^{19} \) \(\mathstrut -\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 42q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 28q^{24} \) \(\mathstrut -\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut -\mathstrut 10q^{27} \) \(\mathstrut -\mathstrut 25q^{28} \) \(\mathstrut -\mathstrut 61q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 18q^{31} \) \(\mathstrut -\mathstrut 3q^{32} \) \(\mathstrut -\mathstrut 42q^{33} \) \(\mathstrut -\mathstrut 22q^{34} \) \(\mathstrut -\mathstrut 29q^{35} \) \(\mathstrut -\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 30q^{37} \) \(\mathstrut -\mathstrut 27q^{38} \) \(\mathstrut -\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut 22q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 58q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 31q^{45} \) \(\mathstrut -\mathstrut 40q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 37q^{48} \) \(\mathstrut -\mathstrut 37q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 43q^{52} \) \(\mathstrut -\mathstrut 27q^{53} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut -\mathstrut 22q^{56} \) \(\mathstrut -\mathstrut 50q^{57} \) \(\mathstrut +\mathstrut q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 76q^{61} \) \(\mathstrut -\mathstrut 17q^{62} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 60q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 7q^{66} \) \(\mathstrut -\mathstrut 45q^{67} \) \(\mathstrut -\mathstrut 31q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 28q^{71} \) \(\mathstrut -\mathstrut 40q^{72} \) \(\mathstrut -\mathstrut 50q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 35q^{75} \) \(\mathstrut -\mathstrut 100q^{76} \) \(\mathstrut +\mathstrut q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 66q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut -\mathstrut 63q^{81} \) \(\mathstrut -\mathstrut 5q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 62q^{88} \) \(\mathstrut -\mathstrut 30q^{89} \) \(\mathstrut +\mathstrut 50q^{90} \) \(\mathstrut -\mathstrut 52q^{91} \) \(\mathstrut -\mathstrut 53q^{92} \) \(\mathstrut -\mathstrut 42q^{93} \) \(\mathstrut -\mathstrut 92q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut -\mathstrut 47q^{96} \) \(\mathstrut -\mathstrut 34q^{97} \) \(\mathstrut +\mathstrut 36q^{98} \) \(\mathstrut -\mathstrut 29q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.42000 −1.71120 −0.855598 0.517640i \(-0.826811\pi\)
−0.855598 + 0.517640i \(0.826811\pi\)
\(3\) −2.29529 −1.32519 −0.662594 0.748978i \(-0.730545\pi\)
−0.662594 + 0.748978i \(0.730545\pi\)
\(4\) 3.85639 1.92819
\(5\) 1.32254 0.591457 0.295729 0.955272i \(-0.404438\pi\)
0.295729 + 0.955272i \(0.404438\pi\)
\(6\) 5.55461 2.26766
\(7\) 0.993943 0.375675 0.187838 0.982200i \(-0.439852\pi\)
0.187838 + 0.982200i \(0.439852\pi\)
\(8\) −4.49245 −1.58832
\(9\) 2.26837 0.756125
\(10\) −3.20054 −1.01210
\(11\) 2.10381 0.634322 0.317161 0.948372i \(-0.397270\pi\)
0.317161 + 0.948372i \(0.397270\pi\)
\(12\) −8.85154 −2.55522
\(13\) 3.07912 0.853995 0.426997 0.904253i \(-0.359571\pi\)
0.426997 + 0.904253i \(0.359571\pi\)
\(14\) −2.40534 −0.642854
\(15\) −3.03561 −0.783792
\(16\) 3.15895 0.789738
\(17\) 6.60217 1.60126 0.800630 0.599159i \(-0.204498\pi\)
0.800630 + 0.599159i \(0.204498\pi\)
\(18\) −5.48946 −1.29388
\(19\) −0.0631268 −0.0144823 −0.00724114 0.999974i \(-0.502305\pi\)
−0.00724114 + 0.999974i \(0.502305\pi\)
\(20\) 5.10022 1.14044
\(21\) −2.28139 −0.497841
\(22\) −5.09121 −1.08545
\(23\) −5.94544 −1.23971 −0.619855 0.784716i \(-0.712809\pi\)
−0.619855 + 0.784716i \(0.712809\pi\)
\(24\) 10.3115 2.10483
\(25\) −3.25089 −0.650178
\(26\) −7.45147 −1.46135
\(27\) 1.67929 0.323180
\(28\) 3.83303 0.724375
\(29\) −1.00000 −0.185695
\(30\) 7.34618 1.34122
\(31\) 5.42341 0.974073 0.487036 0.873382i \(-0.338078\pi\)
0.487036 + 0.873382i \(0.338078\pi\)
\(32\) 1.34025 0.236925
\(33\) −4.82886 −0.840596
\(34\) −15.9772 −2.74007
\(35\) 1.31453 0.222196
\(36\) 8.74773 1.45796
\(37\) −5.88877 −0.968109 −0.484054 0.875038i \(-0.660836\pi\)
−0.484054 + 0.875038i \(0.660836\pi\)
\(38\) 0.152767 0.0247820
\(39\) −7.06749 −1.13170
\(40\) −5.94144 −0.939425
\(41\) −5.46764 −0.853902 −0.426951 0.904275i \(-0.640412\pi\)
−0.426951 + 0.904275i \(0.640412\pi\)
\(42\) 5.52096 0.851903
\(43\) 0.835709 0.127444 0.0637222 0.997968i \(-0.479703\pi\)
0.0637222 + 0.997968i \(0.479703\pi\)
\(44\) 8.11310 1.22310
\(45\) 3.00001 0.447216
\(46\) 14.3880 2.12139
\(47\) −0.379470 −0.0553514 −0.0276757 0.999617i \(-0.508811\pi\)
−0.0276757 + 0.999617i \(0.508811\pi\)
\(48\) −7.25073 −1.04655
\(49\) −6.01208 −0.858868
\(50\) 7.86715 1.11258
\(51\) −15.1539 −2.12197
\(52\) 11.8743 1.64667
\(53\) −2.25880 −0.310270 −0.155135 0.987893i \(-0.549581\pi\)
−0.155135 + 0.987893i \(0.549581\pi\)
\(54\) −4.06389 −0.553025
\(55\) 2.78237 0.375174
\(56\) −4.46524 −0.596693
\(57\) 0.144895 0.0191918
\(58\) 2.42000 0.317761
\(59\) −7.33926 −0.955490 −0.477745 0.878499i \(-0.658546\pi\)
−0.477745 + 0.878499i \(0.658546\pi\)
\(60\) −11.7065 −1.51130
\(61\) −4.55335 −0.582996 −0.291498 0.956571i \(-0.594154\pi\)
−0.291498 + 0.956571i \(0.594154\pi\)
\(62\) −13.1246 −1.66683
\(63\) 2.25464 0.284057
\(64\) −9.56131 −1.19516
\(65\) 4.07226 0.505101
\(66\) 11.6858 1.43842
\(67\) −8.31257 −1.01554 −0.507771 0.861492i \(-0.669530\pi\)
−0.507771 + 0.861492i \(0.669530\pi\)
\(68\) 25.4605 3.08754
\(69\) 13.6465 1.64285
\(70\) −3.18115 −0.380221
\(71\) −7.18358 −0.852535 −0.426267 0.904597i \(-0.640172\pi\)
−0.426267 + 0.904597i \(0.640172\pi\)
\(72\) −10.1906 −1.20097
\(73\) −15.1404 −1.77205 −0.886026 0.463635i \(-0.846545\pi\)
−0.886026 + 0.463635i \(0.846545\pi\)
\(74\) 14.2508 1.65662
\(75\) 7.46175 0.861609
\(76\) −0.243442 −0.0279247
\(77\) 2.09106 0.238299
\(78\) 17.1033 1.93657
\(79\) −1.93701 −0.217930 −0.108965 0.994046i \(-0.534754\pi\)
−0.108965 + 0.994046i \(0.534754\pi\)
\(80\) 4.17784 0.467096
\(81\) −10.6596 −1.18440
\(82\) 13.2317 1.46119
\(83\) 7.16441 0.786396 0.393198 0.919454i \(-0.371369\pi\)
0.393198 + 0.919454i \(0.371369\pi\)
\(84\) −8.79793 −0.959933
\(85\) 8.73162 0.947077
\(86\) −2.02241 −0.218083
\(87\) 2.29529 0.246081
\(88\) −9.45126 −1.00751
\(89\) −3.20563 −0.339796 −0.169898 0.985462i \(-0.554344\pi\)
−0.169898 + 0.985462i \(0.554344\pi\)
\(90\) −7.26002 −0.765274
\(91\) 3.06047 0.320825
\(92\) −22.9279 −2.39040
\(93\) −12.4483 −1.29083
\(94\) 0.918316 0.0947171
\(95\) −0.0834877 −0.00856565
\(96\) −3.07627 −0.313971
\(97\) −4.74236 −0.481514 −0.240757 0.970585i \(-0.577396\pi\)
−0.240757 + 0.970585i \(0.577396\pi\)
\(98\) 14.5492 1.46969
\(99\) 4.77222 0.479626
\(100\) −12.5367 −1.25367
\(101\) −13.7873 −1.37189 −0.685943 0.727655i \(-0.740610\pi\)
−0.685943 + 0.727655i \(0.740610\pi\)
\(102\) 36.6724 3.63111
\(103\) −7.19163 −0.708613 −0.354306 0.935129i \(-0.615283\pi\)
−0.354306 + 0.935129i \(0.615283\pi\)
\(104\) −13.8328 −1.35642
\(105\) −3.01723 −0.294451
\(106\) 5.46628 0.530932
\(107\) 9.55918 0.924121 0.462060 0.886848i \(-0.347110\pi\)
0.462060 + 0.886848i \(0.347110\pi\)
\(108\) 6.47601 0.623155
\(109\) −7.46758 −0.715264 −0.357632 0.933863i \(-0.616416\pi\)
−0.357632 + 0.933863i \(0.616416\pi\)
\(110\) −6.73332 −0.641997
\(111\) 13.5165 1.28293
\(112\) 3.13982 0.296685
\(113\) 5.21525 0.490610 0.245305 0.969446i \(-0.421112\pi\)
0.245305 + 0.969446i \(0.421112\pi\)
\(114\) −0.350645 −0.0328409
\(115\) −7.86308 −0.733236
\(116\) −3.85639 −0.358057
\(117\) 6.98460 0.645727
\(118\) 17.7610 1.63503
\(119\) 6.56218 0.601554
\(120\) 13.6374 1.24492
\(121\) −6.57400 −0.597636
\(122\) 11.0191 0.997622
\(123\) 12.5498 1.13158
\(124\) 20.9148 1.87820
\(125\) −10.9121 −0.976010
\(126\) −5.45621 −0.486078
\(127\) 15.9418 1.41460 0.707301 0.706913i \(-0.249913\pi\)
0.707301 + 0.706913i \(0.249913\pi\)
\(128\) 20.4578 1.80824
\(129\) −1.91820 −0.168888
\(130\) −9.85485 −0.864328
\(131\) 8.12307 0.709716 0.354858 0.934920i \(-0.384529\pi\)
0.354858 + 0.934920i \(0.384529\pi\)
\(132\) −18.6219 −1.62083
\(133\) −0.0627445 −0.00544064
\(134\) 20.1164 1.73779
\(135\) 2.22093 0.191147
\(136\) −29.6599 −2.54332
\(137\) 13.2174 1.12924 0.564621 0.825350i \(-0.309022\pi\)
0.564621 + 0.825350i \(0.309022\pi\)
\(138\) −33.0246 −2.81124
\(139\) −1.00000 −0.0848189
\(140\) 5.06933 0.428437
\(141\) 0.870995 0.0733510
\(142\) 17.3843 1.45885
\(143\) 6.47788 0.541707
\(144\) 7.16569 0.597141
\(145\) −1.32254 −0.109831
\(146\) 36.6398 3.03233
\(147\) 13.7995 1.13816
\(148\) −22.7094 −1.86670
\(149\) −15.3222 −1.25524 −0.627621 0.778519i \(-0.715971\pi\)
−0.627621 + 0.778519i \(0.715971\pi\)
\(150\) −18.0574 −1.47438
\(151\) 10.3431 0.841711 0.420855 0.907128i \(-0.361730\pi\)
0.420855 + 0.907128i \(0.361730\pi\)
\(152\) 0.283594 0.0230025
\(153\) 14.9762 1.21075
\(154\) −5.06037 −0.407776
\(155\) 7.17267 0.576122
\(156\) −27.2550 −2.18215
\(157\) −10.2141 −0.815174 −0.407587 0.913166i \(-0.633630\pi\)
−0.407587 + 0.913166i \(0.633630\pi\)
\(158\) 4.68755 0.372922
\(159\) 5.18460 0.411166
\(160\) 1.77253 0.140131
\(161\) −5.90943 −0.465728
\(162\) 25.7962 2.02674
\(163\) −2.60802 −0.204276 −0.102138 0.994770i \(-0.532568\pi\)
−0.102138 + 0.994770i \(0.532568\pi\)
\(164\) −21.0853 −1.64649
\(165\) −6.38635 −0.497176
\(166\) −17.3378 −1.34568
\(167\) 13.1116 1.01461 0.507305 0.861767i \(-0.330642\pi\)
0.507305 + 0.861767i \(0.330642\pi\)
\(168\) 10.2490 0.790731
\(169\) −3.51901 −0.270693
\(170\) −21.1305 −1.62064
\(171\) −0.143195 −0.0109504
\(172\) 3.22282 0.245738
\(173\) −3.00964 −0.228819 −0.114409 0.993434i \(-0.536498\pi\)
−0.114409 + 0.993434i \(0.536498\pi\)
\(174\) −5.55461 −0.421094
\(175\) −3.23120 −0.244256
\(176\) 6.64583 0.500948
\(177\) 16.8458 1.26620
\(178\) 7.75763 0.581459
\(179\) −11.3054 −0.845002 −0.422501 0.906362i \(-0.638848\pi\)
−0.422501 + 0.906362i \(0.638848\pi\)
\(180\) 11.5692 0.862318
\(181\) −1.18911 −0.0883860 −0.0441930 0.999023i \(-0.514072\pi\)
−0.0441930 + 0.999023i \(0.514072\pi\)
\(182\) −7.40634 −0.548994
\(183\) 10.4513 0.772580
\(184\) 26.7096 1.96906
\(185\) −7.78813 −0.572595
\(186\) 30.1249 2.20886
\(187\) 13.8897 1.01571
\(188\) −1.46338 −0.106728
\(189\) 1.66912 0.121411
\(190\) 0.202040 0.0146575
\(191\) 10.9855 0.794880 0.397440 0.917628i \(-0.369899\pi\)
0.397440 + 0.917628i \(0.369899\pi\)
\(192\) 21.9460 1.58382
\(193\) 21.9625 1.58089 0.790446 0.612531i \(-0.209849\pi\)
0.790446 + 0.612531i \(0.209849\pi\)
\(194\) 11.4765 0.823965
\(195\) −9.34703 −0.669355
\(196\) −23.1849 −1.65606
\(197\) 18.2380 1.29940 0.649702 0.760189i \(-0.274893\pi\)
0.649702 + 0.760189i \(0.274893\pi\)
\(198\) −11.5488 −0.820735
\(199\) −9.54505 −0.676631 −0.338315 0.941033i \(-0.609857\pi\)
−0.338315 + 0.941033i \(0.609857\pi\)
\(200\) 14.6045 1.03269
\(201\) 19.0798 1.34578
\(202\) 33.3652 2.34757
\(203\) −0.993943 −0.0697611
\(204\) −58.4394 −4.09157
\(205\) −7.23117 −0.505047
\(206\) 17.4037 1.21258
\(207\) −13.4865 −0.937376
\(208\) 9.72680 0.674432
\(209\) −0.132807 −0.00918643
\(210\) 7.30169 0.503864
\(211\) −1.12096 −0.0771700 −0.0385850 0.999255i \(-0.512285\pi\)
−0.0385850 + 0.999255i \(0.512285\pi\)
\(212\) −8.71080 −0.598260
\(213\) 16.4884 1.12977
\(214\) −23.1332 −1.58135
\(215\) 1.10526 0.0753779
\(216\) −7.54416 −0.513315
\(217\) 5.39056 0.365935
\(218\) 18.0715 1.22396
\(219\) 34.7517 2.34830
\(220\) 10.7299 0.723409
\(221\) 20.3289 1.36747
\(222\) −32.7098 −2.19534
\(223\) 0.555399 0.0371923 0.0185961 0.999827i \(-0.494080\pi\)
0.0185961 + 0.999827i \(0.494080\pi\)
\(224\) 1.33213 0.0890069
\(225\) −7.37424 −0.491616
\(226\) −12.6209 −0.839530
\(227\) −9.06931 −0.601951 −0.300975 0.953632i \(-0.597312\pi\)
−0.300975 + 0.953632i \(0.597312\pi\)
\(228\) 0.558770 0.0370054
\(229\) −6.88442 −0.454936 −0.227468 0.973786i \(-0.573045\pi\)
−0.227468 + 0.973786i \(0.573045\pi\)
\(230\) 19.0286 1.25471
\(231\) −4.79961 −0.315791
\(232\) 4.49245 0.294944
\(233\) −4.09828 −0.268487 −0.134243 0.990948i \(-0.542860\pi\)
−0.134243 + 0.990948i \(0.542860\pi\)
\(234\) −16.9027 −1.10497
\(235\) −0.501864 −0.0327380
\(236\) −28.3030 −1.84237
\(237\) 4.44600 0.288799
\(238\) −15.8805 −1.02938
\(239\) 13.7817 0.891461 0.445731 0.895167i \(-0.352944\pi\)
0.445731 + 0.895167i \(0.352944\pi\)
\(240\) −9.58936 −0.618991
\(241\) 14.6615 0.944429 0.472214 0.881484i \(-0.343455\pi\)
0.472214 + 0.881484i \(0.343455\pi\)
\(242\) 15.9091 1.02267
\(243\) 19.4290 1.24637
\(244\) −17.5595 −1.12413
\(245\) −7.95120 −0.507984
\(246\) −30.3706 −1.93636
\(247\) −0.194375 −0.0123678
\(248\) −24.3644 −1.54714
\(249\) −16.4444 −1.04212
\(250\) 26.4073 1.67014
\(251\) 14.5009 0.915292 0.457646 0.889135i \(-0.348693\pi\)
0.457646 + 0.889135i \(0.348693\pi\)
\(252\) 8.69475 0.547718
\(253\) −12.5081 −0.786375
\(254\) −38.5790 −2.42066
\(255\) −20.0416 −1.25506
\(256\) −30.3853 −1.89908
\(257\) 8.45239 0.527246 0.263623 0.964626i \(-0.415083\pi\)
0.263623 + 0.964626i \(0.415083\pi\)
\(258\) 4.64204 0.289001
\(259\) −5.85311 −0.363694
\(260\) 15.7042 0.973933
\(261\) −2.26837 −0.140409
\(262\) −19.6578 −1.21446
\(263\) −0.0694720 −0.00428383 −0.00214191 0.999998i \(-0.500682\pi\)
−0.00214191 + 0.999998i \(0.500682\pi\)
\(264\) 21.6934 1.33514
\(265\) −2.98735 −0.183511
\(266\) 0.151842 0.00931000
\(267\) 7.35787 0.450294
\(268\) −32.0565 −1.95816
\(269\) −20.5705 −1.25421 −0.627103 0.778936i \(-0.715760\pi\)
−0.627103 + 0.778936i \(0.715760\pi\)
\(270\) −5.37465 −0.327091
\(271\) −22.6403 −1.37530 −0.687651 0.726042i \(-0.741358\pi\)
−0.687651 + 0.726042i \(0.741358\pi\)
\(272\) 20.8559 1.26458
\(273\) −7.02468 −0.425153
\(274\) −31.9862 −1.93235
\(275\) −6.83925 −0.412422
\(276\) 52.6263 3.16773
\(277\) −16.4296 −0.987161 −0.493580 0.869700i \(-0.664312\pi\)
−0.493580 + 0.869700i \(0.664312\pi\)
\(278\) 2.42000 0.145142
\(279\) 12.3023 0.736521
\(280\) −5.90546 −0.352919
\(281\) 1.40158 0.0836115 0.0418057 0.999126i \(-0.486689\pi\)
0.0418057 + 0.999126i \(0.486689\pi\)
\(282\) −2.10781 −0.125518
\(283\) −29.8875 −1.77663 −0.888313 0.459239i \(-0.848122\pi\)
−0.888313 + 0.459239i \(0.848122\pi\)
\(284\) −27.7027 −1.64385
\(285\) 0.191629 0.0113511
\(286\) −15.6764 −0.926968
\(287\) −5.43452 −0.320790
\(288\) 3.04019 0.179145
\(289\) 26.5886 1.56404
\(290\) 3.20054 0.187942
\(291\) 10.8851 0.638097
\(292\) −58.3873 −3.41686
\(293\) 19.9743 1.16691 0.583456 0.812145i \(-0.301700\pi\)
0.583456 + 0.812145i \(0.301700\pi\)
\(294\) −33.3947 −1.94762
\(295\) −9.70645 −0.565131
\(296\) 26.4551 1.53767
\(297\) 3.53291 0.205000
\(298\) 37.0796 2.14797
\(299\) −18.3067 −1.05871
\(300\) 28.7754 1.66135
\(301\) 0.830648 0.0478777
\(302\) −25.0303 −1.44033
\(303\) 31.6459 1.81801
\(304\) −0.199415 −0.0114372
\(305\) −6.02198 −0.344817
\(306\) −36.2423 −2.07184
\(307\) −1.31117 −0.0748326 −0.0374163 0.999300i \(-0.511913\pi\)
−0.0374163 + 0.999300i \(0.511913\pi\)
\(308\) 8.06396 0.459487
\(309\) 16.5069 0.939046
\(310\) −17.3578 −0.985859
\(311\) −8.29311 −0.470259 −0.235129 0.971964i \(-0.575551\pi\)
−0.235129 + 0.971964i \(0.575551\pi\)
\(312\) 31.7504 1.79751
\(313\) −25.6938 −1.45230 −0.726149 0.687537i \(-0.758692\pi\)
−0.726149 + 0.687537i \(0.758692\pi\)
\(314\) 24.7181 1.39492
\(315\) 2.98184 0.168008
\(316\) −7.46985 −0.420212
\(317\) −19.1223 −1.07402 −0.537008 0.843577i \(-0.680446\pi\)
−0.537008 + 0.843577i \(0.680446\pi\)
\(318\) −12.5467 −0.703585
\(319\) −2.10381 −0.117791
\(320\) −12.6452 −0.706888
\(321\) −21.9411 −1.22463
\(322\) 14.3008 0.796953
\(323\) −0.416774 −0.0231899
\(324\) −41.1076 −2.28375
\(325\) −10.0099 −0.555249
\(326\) 6.31140 0.349556
\(327\) 17.1403 0.947860
\(328\) 24.5631 1.35627
\(329\) −0.377172 −0.0207941
\(330\) 15.4549 0.850767
\(331\) −11.8325 −0.650371 −0.325185 0.945650i \(-0.605427\pi\)
−0.325185 + 0.945650i \(0.605427\pi\)
\(332\) 27.6287 1.51632
\(333\) −13.3579 −0.732011
\(334\) −31.7302 −1.73620
\(335\) −10.9937 −0.600649
\(336\) −7.20681 −0.393164
\(337\) 4.99610 0.272155 0.136078 0.990698i \(-0.456550\pi\)
0.136078 + 0.990698i \(0.456550\pi\)
\(338\) 8.51599 0.463209
\(339\) −11.9705 −0.650151
\(340\) 33.6725 1.82615
\(341\) 11.4098 0.617875
\(342\) 0.346532 0.0187383
\(343\) −12.9333 −0.698331
\(344\) −3.75439 −0.202423
\(345\) 18.0481 0.971676
\(346\) 7.28333 0.391554
\(347\) 15.5398 0.834218 0.417109 0.908856i \(-0.363043\pi\)
0.417109 + 0.908856i \(0.363043\pi\)
\(348\) 8.85154 0.474493
\(349\) −10.6995 −0.572732 −0.286366 0.958120i \(-0.592447\pi\)
−0.286366 + 0.958120i \(0.592447\pi\)
\(350\) 7.81950 0.417970
\(351\) 5.17075 0.275994
\(352\) 2.81963 0.150287
\(353\) −22.3963 −1.19203 −0.596017 0.802972i \(-0.703251\pi\)
−0.596017 + 0.802972i \(0.703251\pi\)
\(354\) −40.7667 −2.16672
\(355\) −9.50057 −0.504238
\(356\) −12.3622 −0.655194
\(357\) −15.0621 −0.797172
\(358\) 27.3589 1.44597
\(359\) 16.4105 0.866111 0.433056 0.901367i \(-0.357435\pi\)
0.433056 + 0.901367i \(0.357435\pi\)
\(360\) −13.4774 −0.710323
\(361\) −18.9960 −0.999790
\(362\) 2.87765 0.151246
\(363\) 15.0893 0.791980
\(364\) 11.8024 0.618612
\(365\) −20.0238 −1.04809
\(366\) −25.2921 −1.32204
\(367\) −32.5064 −1.69682 −0.848411 0.529338i \(-0.822441\pi\)
−0.848411 + 0.529338i \(0.822441\pi\)
\(368\) −18.7814 −0.979047
\(369\) −12.4027 −0.645657
\(370\) 18.8473 0.979822
\(371\) −2.24512 −0.116561
\(372\) −48.0055 −2.48897
\(373\) 18.2762 0.946304 0.473152 0.880981i \(-0.343116\pi\)
0.473152 + 0.880981i \(0.343116\pi\)
\(374\) −33.6130 −1.73809
\(375\) 25.0465 1.29340
\(376\) 1.70475 0.0879158
\(377\) −3.07912 −0.158583
\(378\) −4.03928 −0.207758
\(379\) −5.15184 −0.264632 −0.132316 0.991208i \(-0.542241\pi\)
−0.132316 + 0.991208i \(0.542241\pi\)
\(380\) −0.321961 −0.0165162
\(381\) −36.5910 −1.87461
\(382\) −26.5848 −1.36020
\(383\) −24.5106 −1.25244 −0.626218 0.779648i \(-0.715398\pi\)
−0.626218 + 0.779648i \(0.715398\pi\)
\(384\) −46.9568 −2.39625
\(385\) 2.76551 0.140944
\(386\) −53.1491 −2.70522
\(387\) 1.89570 0.0963639
\(388\) −18.2884 −0.928452
\(389\) 4.22748 0.214342 0.107171 0.994241i \(-0.465821\pi\)
0.107171 + 0.994241i \(0.465821\pi\)
\(390\) 22.6198 1.14540
\(391\) −39.2528 −1.98510
\(392\) 27.0090 1.36416
\(393\) −18.6448 −0.940508
\(394\) −44.1360 −2.22354
\(395\) −2.56177 −0.128897
\(396\) 18.4035 0.924813
\(397\) −0.130869 −0.00656810 −0.00328405 0.999995i \(-0.501045\pi\)
−0.00328405 + 0.999995i \(0.501045\pi\)
\(398\) 23.0990 1.15785
\(399\) 0.144017 0.00720987
\(400\) −10.2694 −0.513471
\(401\) 1.40604 0.0702141 0.0351071 0.999384i \(-0.488823\pi\)
0.0351071 + 0.999384i \(0.488823\pi\)
\(402\) −46.1730 −2.30290
\(403\) 16.6993 0.831853
\(404\) −53.1691 −2.64526
\(405\) −14.0977 −0.700522
\(406\) 2.40534 0.119375
\(407\) −12.3888 −0.614092
\(408\) 68.0783 3.37038
\(409\) 1.30490 0.0645232 0.0322616 0.999479i \(-0.489729\pi\)
0.0322616 + 0.999479i \(0.489729\pi\)
\(410\) 17.4994 0.864234
\(411\) −30.3379 −1.49646
\(412\) −27.7337 −1.36634
\(413\) −7.29481 −0.358954
\(414\) 32.6373 1.60403
\(415\) 9.47520 0.465119
\(416\) 4.12680 0.202333
\(417\) 2.29529 0.112401
\(418\) 0.321392 0.0157198
\(419\) 32.6894 1.59698 0.798491 0.602006i \(-0.205632\pi\)
0.798491 + 0.602006i \(0.205632\pi\)
\(420\) −11.6356 −0.567759
\(421\) 11.3690 0.554092 0.277046 0.960857i \(-0.410645\pi\)
0.277046 + 0.960857i \(0.410645\pi\)
\(422\) 2.71272 0.132053
\(423\) −0.860780 −0.0418526
\(424\) 10.1475 0.492808
\(425\) −21.4629 −1.04110
\(426\) −39.9020 −1.93326
\(427\) −4.52577 −0.219017
\(428\) 36.8639 1.78188
\(429\) −14.8686 −0.717864
\(430\) −2.67472 −0.128986
\(431\) 17.6376 0.849574 0.424787 0.905293i \(-0.360349\pi\)
0.424787 + 0.905293i \(0.360349\pi\)
\(432\) 5.30481 0.255228
\(433\) 0.471773 0.0226720 0.0113360 0.999936i \(-0.496392\pi\)
0.0113360 + 0.999936i \(0.496392\pi\)
\(434\) −13.0451 −0.626187
\(435\) 3.03561 0.145547
\(436\) −28.7979 −1.37917
\(437\) 0.375317 0.0179538
\(438\) −84.0991 −4.01841
\(439\) 11.0842 0.529019 0.264510 0.964383i \(-0.414790\pi\)
0.264510 + 0.964383i \(0.414790\pi\)
\(440\) −12.4997 −0.595898
\(441\) −13.6376 −0.649412
\(442\) −49.1958 −2.34001
\(443\) −38.7939 −1.84316 −0.921578 0.388194i \(-0.873099\pi\)
−0.921578 + 0.388194i \(0.873099\pi\)
\(444\) 52.1248 2.47373
\(445\) −4.23957 −0.200975
\(446\) −1.34406 −0.0636433
\(447\) 35.1689 1.66343
\(448\) −9.50340 −0.448993
\(449\) −21.3325 −1.00674 −0.503371 0.864070i \(-0.667907\pi\)
−0.503371 + 0.864070i \(0.667907\pi\)
\(450\) 17.8456 0.841252
\(451\) −11.5029 −0.541649
\(452\) 20.1120 0.945991
\(453\) −23.7405 −1.11543
\(454\) 21.9477 1.03006
\(455\) 4.04759 0.189754
\(456\) −0.650933 −0.0304827
\(457\) −1.35756 −0.0635042 −0.0317521 0.999496i \(-0.510109\pi\)
−0.0317521 + 0.999496i \(0.510109\pi\)
\(458\) 16.6603 0.778484
\(459\) 11.0870 0.517496
\(460\) −30.3231 −1.41382
\(461\) 20.1214 0.937149 0.468574 0.883424i \(-0.344768\pi\)
0.468574 + 0.883424i \(0.344768\pi\)
\(462\) 11.6150 0.540381
\(463\) −23.3357 −1.08450 −0.542252 0.840216i \(-0.682428\pi\)
−0.542252 + 0.840216i \(0.682428\pi\)
\(464\) −3.15895 −0.146651
\(465\) −16.4634 −0.763471
\(466\) 9.91782 0.459434
\(467\) 3.22537 0.149252 0.0746262 0.997212i \(-0.476224\pi\)
0.0746262 + 0.997212i \(0.476224\pi\)
\(468\) 26.9353 1.24509
\(469\) −8.26222 −0.381514
\(470\) 1.21451 0.0560211
\(471\) 23.4444 1.08026
\(472\) 32.9713 1.51763
\(473\) 1.75817 0.0808408
\(474\) −10.7593 −0.494192
\(475\) 0.205219 0.00941607
\(476\) 25.3063 1.15991
\(477\) −5.12380 −0.234603
\(478\) −33.3516 −1.52547
\(479\) 9.40374 0.429668 0.214834 0.976651i \(-0.431079\pi\)
0.214834 + 0.976651i \(0.431079\pi\)
\(480\) −4.06849 −0.185700
\(481\) −18.1323 −0.826760
\(482\) −35.4807 −1.61610
\(483\) 13.5639 0.617178
\(484\) −25.3519 −1.15236
\(485\) −6.27195 −0.284795
\(486\) −47.0182 −2.13279
\(487\) 25.1250 1.13852 0.569262 0.822156i \(-0.307229\pi\)
0.569262 + 0.822156i \(0.307229\pi\)
\(488\) 20.4557 0.925986
\(489\) 5.98617 0.270704
\(490\) 19.2419 0.869260
\(491\) 26.0291 1.17468 0.587339 0.809341i \(-0.300176\pi\)
0.587339 + 0.809341i \(0.300176\pi\)
\(492\) 48.3971 2.18191
\(493\) −6.60217 −0.297347
\(494\) 0.470388 0.0211637
\(495\) 6.31145 0.283679
\(496\) 17.1323 0.769262
\(497\) −7.14007 −0.320276
\(498\) 39.7955 1.78328
\(499\) −37.8778 −1.69564 −0.847821 0.530282i \(-0.822086\pi\)
−0.847821 + 0.530282i \(0.822086\pi\)
\(500\) −42.0814 −1.88194
\(501\) −30.0951 −1.34455
\(502\) −35.0923 −1.56624
\(503\) 32.1149 1.43193 0.715966 0.698135i \(-0.245986\pi\)
0.715966 + 0.698135i \(0.245986\pi\)
\(504\) −10.1288 −0.451175
\(505\) −18.2342 −0.811412
\(506\) 30.2695 1.34564
\(507\) 8.07716 0.358719
\(508\) 61.4776 2.72763
\(509\) −21.7665 −0.964783 −0.482392 0.875956i \(-0.660232\pi\)
−0.482392 + 0.875956i \(0.660232\pi\)
\(510\) 48.5007 2.14765
\(511\) −15.0487 −0.665716
\(512\) 32.6167 1.44147
\(513\) −0.106009 −0.00468039
\(514\) −20.4548 −0.902221
\(515\) −9.51121 −0.419114
\(516\) −7.39732 −0.325649
\(517\) −0.798331 −0.0351106
\(518\) 14.1645 0.622353
\(519\) 6.90801 0.303228
\(520\) −18.2944 −0.802264
\(521\) −10.1407 −0.444274 −0.222137 0.975015i \(-0.571303\pi\)
−0.222137 + 0.975015i \(0.571303\pi\)
\(522\) 5.48946 0.240267
\(523\) −3.77378 −0.165016 −0.0825080 0.996590i \(-0.526293\pi\)
−0.0825080 + 0.996590i \(0.526293\pi\)
\(524\) 31.3257 1.36847
\(525\) 7.41656 0.323685
\(526\) 0.168122 0.00733048
\(527\) 35.8062 1.55974
\(528\) −15.2541 −0.663851
\(529\) 12.3483 0.536882
\(530\) 7.22937 0.314024
\(531\) −16.6482 −0.722470
\(532\) −0.241967 −0.0104906
\(533\) −16.8355 −0.729228
\(534\) −17.8060 −0.770542
\(535\) 12.6424 0.546578
\(536\) 37.3438 1.61301
\(537\) 25.9491 1.11979
\(538\) 49.7806 2.14619
\(539\) −12.6482 −0.544799
\(540\) 8.56478 0.368569
\(541\) −32.0384 −1.37744 −0.688719 0.725028i \(-0.741827\pi\)
−0.688719 + 0.725028i \(0.741827\pi\)
\(542\) 54.7895 2.35341
\(543\) 2.72936 0.117128
\(544\) 8.84856 0.379379
\(545\) −9.87616 −0.423048
\(546\) 16.9997 0.727521
\(547\) 32.9681 1.40962 0.704808 0.709398i \(-0.251033\pi\)
0.704808 + 0.709398i \(0.251033\pi\)
\(548\) 50.9716 2.17740
\(549\) −10.3287 −0.440818
\(550\) 16.5510 0.705736
\(551\) 0.0631268 0.00268929
\(552\) −61.3065 −2.60938
\(553\) −1.92528 −0.0818711
\(554\) 39.7597 1.68923
\(555\) 17.8761 0.758796
\(556\) −3.85639 −0.163547
\(557\) −2.28887 −0.0969827 −0.0484914 0.998824i \(-0.515441\pi\)
−0.0484914 + 0.998824i \(0.515441\pi\)
\(558\) −29.7716 −1.26033
\(559\) 2.57325 0.108837
\(560\) 4.15253 0.175477
\(561\) −31.8809 −1.34601
\(562\) −3.39183 −0.143076
\(563\) 25.6742 1.08204 0.541020 0.841010i \(-0.318038\pi\)
0.541020 + 0.841010i \(0.318038\pi\)
\(564\) 3.35889 0.141435
\(565\) 6.89738 0.290175
\(566\) 72.3276 3.04016
\(567\) −10.5950 −0.444950
\(568\) 32.2719 1.35410
\(569\) 16.8490 0.706348 0.353174 0.935558i \(-0.385102\pi\)
0.353174 + 0.935558i \(0.385102\pi\)
\(570\) −0.463741 −0.0194240
\(571\) −31.7691 −1.32950 −0.664748 0.747068i \(-0.731461\pi\)
−0.664748 + 0.747068i \(0.731461\pi\)
\(572\) 24.9812 1.04452
\(573\) −25.2149 −1.05337
\(574\) 13.1515 0.548935
\(575\) 19.3280 0.806033
\(576\) −21.6886 −0.903693
\(577\) −6.81810 −0.283841 −0.141921 0.989878i \(-0.545328\pi\)
−0.141921 + 0.989878i \(0.545328\pi\)
\(578\) −64.3443 −2.67637
\(579\) −50.4103 −2.09498
\(580\) −5.10022 −0.211775
\(581\) 7.12101 0.295429
\(582\) −26.3419 −1.09191
\(583\) −4.75207 −0.196811
\(584\) 68.0177 2.81459
\(585\) 9.23741 0.381920
\(586\) −48.3378 −1.99682
\(587\) 13.7641 0.568106 0.284053 0.958809i \(-0.408321\pi\)
0.284053 + 0.958809i \(0.408321\pi\)
\(588\) 53.2162 2.19460
\(589\) −0.342363 −0.0141068
\(590\) 23.4896 0.967051
\(591\) −41.8616 −1.72196
\(592\) −18.6024 −0.764552
\(593\) −10.7738 −0.442427 −0.221213 0.975225i \(-0.571002\pi\)
−0.221213 + 0.975225i \(0.571002\pi\)
\(594\) −8.54964 −0.350796
\(595\) 8.67873 0.355793
\(596\) −59.0883 −2.42035
\(597\) 21.9087 0.896663
\(598\) 44.3023 1.81165
\(599\) −17.9555 −0.733642 −0.366821 0.930291i \(-0.619554\pi\)
−0.366821 + 0.930291i \(0.619554\pi\)
\(600\) −33.5216 −1.36851
\(601\) −19.2342 −0.784579 −0.392290 0.919842i \(-0.628317\pi\)
−0.392290 + 0.919842i \(0.628317\pi\)
\(602\) −2.01016 −0.0819282
\(603\) −18.8560 −0.767876
\(604\) 39.8871 1.62298
\(605\) −8.69436 −0.353476
\(606\) −76.5829 −3.11097
\(607\) 26.8813 1.09108 0.545539 0.838085i \(-0.316325\pi\)
0.545539 + 0.838085i \(0.316325\pi\)
\(608\) −0.0846058 −0.00343122
\(609\) 2.28139 0.0924467
\(610\) 14.5732 0.590050
\(611\) −1.16843 −0.0472698
\(612\) 57.7540 2.33457
\(613\) 37.0311 1.49567 0.747836 0.663884i \(-0.231093\pi\)
0.747836 + 0.663884i \(0.231093\pi\)
\(614\) 3.17304 0.128053
\(615\) 16.5977 0.669282
\(616\) −9.39401 −0.378496
\(617\) −42.1368 −1.69636 −0.848182 0.529705i \(-0.822303\pi\)
−0.848182 + 0.529705i \(0.822303\pi\)
\(618\) −39.9467 −1.60689
\(619\) 31.4965 1.26595 0.632975 0.774172i \(-0.281834\pi\)
0.632975 + 0.774172i \(0.281834\pi\)
\(620\) 27.6606 1.11088
\(621\) −9.98415 −0.400650
\(622\) 20.0693 0.804706
\(623\) −3.18622 −0.127653
\(624\) −22.3259 −0.893750
\(625\) 1.82276 0.0729103
\(626\) 62.1789 2.48517
\(627\) 0.304830 0.0121738
\(628\) −39.3895 −1.57181
\(629\) −38.8787 −1.55019
\(630\) −7.21605 −0.287494
\(631\) −38.5253 −1.53367 −0.766833 0.641846i \(-0.778169\pi\)
−0.766833 + 0.641846i \(0.778169\pi\)
\(632\) 8.70192 0.346144
\(633\) 2.57293 0.102265
\(634\) 46.2760 1.83785
\(635\) 21.0836 0.836676
\(636\) 19.9938 0.792807
\(637\) −18.5119 −0.733469
\(638\) 5.09121 0.201563
\(639\) −16.2951 −0.644623
\(640\) 27.0563 1.06949
\(641\) 44.8125 1.76999 0.884994 0.465602i \(-0.154162\pi\)
0.884994 + 0.465602i \(0.154162\pi\)
\(642\) 53.0975 2.09559
\(643\) 1.57148 0.0619733 0.0309866 0.999520i \(-0.490135\pi\)
0.0309866 + 0.999520i \(0.490135\pi\)
\(644\) −22.7891 −0.898015
\(645\) −2.53689 −0.0998900
\(646\) 1.00859 0.0396825
\(647\) 32.1307 1.26319 0.631593 0.775300i \(-0.282401\pi\)
0.631593 + 0.775300i \(0.282401\pi\)
\(648\) 47.8878 1.88121
\(649\) −15.4404 −0.606088
\(650\) 24.2239 0.950140
\(651\) −12.3729 −0.484933
\(652\) −10.0575 −0.393883
\(653\) 17.1292 0.670319 0.335159 0.942161i \(-0.391210\pi\)
0.335159 + 0.942161i \(0.391210\pi\)
\(654\) −41.4795 −1.62198
\(655\) 10.7431 0.419767
\(656\) −17.2720 −0.674359
\(657\) −34.3442 −1.33989
\(658\) 0.912754 0.0355829
\(659\) −34.5549 −1.34607 −0.673035 0.739611i \(-0.735010\pi\)
−0.673035 + 0.739611i \(0.735010\pi\)
\(660\) −24.6282 −0.958653
\(661\) 35.5387 1.38230 0.691148 0.722714i \(-0.257105\pi\)
0.691148 + 0.722714i \(0.257105\pi\)
\(662\) 28.6345 1.11291
\(663\) −46.6607 −1.81215
\(664\) −32.1858 −1.24905
\(665\) −0.0829820 −0.00321790
\(666\) 32.3262 1.25261
\(667\) 5.94544 0.230208
\(668\) 50.5636 1.95636
\(669\) −1.27480 −0.0492867
\(670\) 26.6047 1.02783
\(671\) −9.57936 −0.369807
\(672\) −3.05764 −0.117951
\(673\) 13.7134 0.528612 0.264306 0.964439i \(-0.414857\pi\)
0.264306 + 0.964439i \(0.414857\pi\)
\(674\) −12.0906 −0.465711
\(675\) −5.45921 −0.210125
\(676\) −13.5707 −0.521948
\(677\) 31.6369 1.21590 0.607952 0.793973i \(-0.291991\pi\)
0.607952 + 0.793973i \(0.291991\pi\)
\(678\) 28.9687 1.11254
\(679\) −4.71364 −0.180893
\(680\) −39.2264 −1.50426
\(681\) 20.8167 0.797699
\(682\) −27.6117 −1.05731
\(683\) −29.1284 −1.11457 −0.557284 0.830322i \(-0.688157\pi\)
−0.557284 + 0.830322i \(0.688157\pi\)
\(684\) −0.552217 −0.0211145
\(685\) 17.4806 0.667898
\(686\) 31.2985 1.19498
\(687\) 15.8018 0.602875
\(688\) 2.63997 0.100648
\(689\) −6.95511 −0.264969
\(690\) −43.6763 −1.66273
\(691\) 19.3505 0.736129 0.368065 0.929800i \(-0.380021\pi\)
0.368065 + 0.929800i \(0.380021\pi\)
\(692\) −11.6063 −0.441207
\(693\) 4.74332 0.180184
\(694\) −37.6062 −1.42751
\(695\) −1.32254 −0.0501667
\(696\) −10.3115 −0.390857
\(697\) −36.0983 −1.36732
\(698\) 25.8928 0.980057
\(699\) 9.40675 0.355796
\(700\) −12.4608 −0.470973
\(701\) −6.91265 −0.261087 −0.130544 0.991443i \(-0.541672\pi\)
−0.130544 + 0.991443i \(0.541672\pi\)
\(702\) −12.5132 −0.472281
\(703\) 0.371740 0.0140204
\(704\) −20.1152 −0.758118
\(705\) 1.15192 0.0433840
\(706\) 54.1989 2.03980
\(707\) −13.7038 −0.515384
\(708\) 64.9638 2.44149
\(709\) 44.1605 1.65848 0.829241 0.558891i \(-0.188773\pi\)
0.829241 + 0.558891i \(0.188773\pi\)
\(710\) 22.9913 0.862850
\(711\) −4.39386 −0.164783
\(712\) 14.4012 0.539706
\(713\) −32.2446 −1.20757
\(714\) 36.4503 1.36412
\(715\) 8.56724 0.320397
\(716\) −43.5979 −1.62933
\(717\) −31.6330 −1.18135
\(718\) −39.7133 −1.48209
\(719\) −36.3925 −1.35721 −0.678605 0.734503i \(-0.737415\pi\)
−0.678605 + 0.734503i \(0.737415\pi\)
\(720\) 9.47690 0.353183
\(721\) −7.14808 −0.266208
\(722\) 45.9703 1.71084
\(723\) −33.6524 −1.25155
\(724\) −4.58568 −0.170425
\(725\) 3.25089 0.120735
\(726\) −36.5160 −1.35523
\(727\) −2.63607 −0.0977664 −0.0488832 0.998805i \(-0.515566\pi\)
−0.0488832 + 0.998805i \(0.515566\pi\)
\(728\) −13.7490 −0.509573
\(729\) −12.6165 −0.467279
\(730\) 48.4575 1.79349
\(731\) 5.51749 0.204072
\(732\) 40.3042 1.48968
\(733\) −22.0550 −0.814620 −0.407310 0.913290i \(-0.633533\pi\)
−0.407310 + 0.913290i \(0.633533\pi\)
\(734\) 78.6655 2.90360
\(735\) 18.2503 0.673174
\(736\) −7.96839 −0.293719
\(737\) −17.4880 −0.644180
\(738\) 30.0144 1.10485
\(739\) 27.7896 1.02226 0.511129 0.859504i \(-0.329227\pi\)
0.511129 + 0.859504i \(0.329227\pi\)
\(740\) −30.0341 −1.10407
\(741\) 0.446148 0.0163897
\(742\) 5.43317 0.199458
\(743\) −43.2896 −1.58814 −0.794071 0.607825i \(-0.792042\pi\)
−0.794071 + 0.607825i \(0.792042\pi\)
\(744\) 55.9235 2.05025
\(745\) −20.2642 −0.742422
\(746\) −44.2283 −1.61931
\(747\) 16.2516 0.594613
\(748\) 53.5640 1.95849
\(749\) 9.50128 0.347169
\(750\) −60.6125 −2.21326
\(751\) −28.8839 −1.05399 −0.526995 0.849868i \(-0.676681\pi\)
−0.526995 + 0.849868i \(0.676681\pi\)
\(752\) −1.19873 −0.0437131
\(753\) −33.2839 −1.21293
\(754\) 7.45147 0.271366
\(755\) 13.6792 0.497836
\(756\) 6.43679 0.234104
\(757\) 14.6830 0.533662 0.266831 0.963743i \(-0.414023\pi\)
0.266831 + 0.963743i \(0.414023\pi\)
\(758\) 12.4674 0.452838
\(759\) 28.7097 1.04210
\(760\) 0.375065 0.0136050
\(761\) −40.2124 −1.45770 −0.728850 0.684674i \(-0.759945\pi\)
−0.728850 + 0.684674i \(0.759945\pi\)
\(762\) 88.5501 3.20783
\(763\) −7.42235 −0.268707
\(764\) 42.3642 1.53268
\(765\) 19.8066 0.716109
\(766\) 59.3157 2.14316
\(767\) −22.5985 −0.815983
\(768\) 69.7432 2.51664
\(769\) −47.9126 −1.72777 −0.863887 0.503686i \(-0.831977\pi\)
−0.863887 + 0.503686i \(0.831977\pi\)
\(770\) −6.69254 −0.241182
\(771\) −19.4007 −0.698700
\(772\) 84.6958 3.04827
\(773\) 50.4137 1.81326 0.906628 0.421932i \(-0.138648\pi\)
0.906628 + 0.421932i \(0.138648\pi\)
\(774\) −4.58759 −0.164898
\(775\) −17.6309 −0.633321
\(776\) 21.3048 0.764799
\(777\) 13.4346 0.481964
\(778\) −10.2305 −0.366781
\(779\) 0.345155 0.0123665
\(780\) −36.0458 −1.29065
\(781\) −15.1129 −0.540781
\(782\) 94.9917 3.39690
\(783\) −1.67929 −0.0600131
\(784\) −18.9919 −0.678281
\(785\) −13.5085 −0.482141
\(786\) 45.1205 1.60939
\(787\) 30.9280 1.10246 0.551232 0.834352i \(-0.314158\pi\)
0.551232 + 0.834352i \(0.314158\pi\)
\(788\) 70.3329 2.50550
\(789\) 0.159459 0.00567688
\(790\) 6.19947 0.220567
\(791\) 5.18367 0.184310
\(792\) −21.4390 −0.761801
\(793\) −14.0203 −0.497876
\(794\) 0.316702 0.0112393
\(795\) 6.85684 0.243187
\(796\) −36.8094 −1.30468
\(797\) −1.30169 −0.0461083 −0.0230541 0.999734i \(-0.507339\pi\)
−0.0230541 + 0.999734i \(0.507339\pi\)
\(798\) −0.348521 −0.0123375
\(799\) −2.50532 −0.0886320
\(800\) −4.35701 −0.154044
\(801\) −7.27158 −0.256929
\(802\) −3.40260 −0.120150
\(803\) −31.8525 −1.12405
\(804\) 73.5791 2.59493
\(805\) −7.81545 −0.275458
\(806\) −40.4123 −1.42346
\(807\) 47.2154 1.66206
\(808\) 61.9387 2.17900
\(809\) −11.2088 −0.394080 −0.197040 0.980395i \(-0.563133\pi\)
−0.197040 + 0.980395i \(0.563133\pi\)
\(810\) 34.1165 1.19873
\(811\) −48.3721 −1.69857 −0.849287 0.527931i \(-0.822968\pi\)
−0.849287 + 0.527931i \(0.822968\pi\)
\(812\) −3.83303 −0.134513
\(813\) 51.9662 1.82253
\(814\) 29.9810 1.05083
\(815\) −3.44921 −0.120820
\(816\) −47.8705 −1.67580
\(817\) −0.0527557 −0.00184569
\(818\) −3.15786 −0.110412
\(819\) 6.94230 0.242584
\(820\) −27.8862 −0.973828
\(821\) 21.9970 0.767701 0.383851 0.923395i \(-0.374598\pi\)
0.383851 + 0.923395i \(0.374598\pi\)
\(822\) 73.4176 2.56073
\(823\) 43.5196 1.51700 0.758500 0.651674i \(-0.225933\pi\)
0.758500 + 0.651674i \(0.225933\pi\)
\(824\) 32.3081 1.12551
\(825\) 15.6981 0.546537
\(826\) 17.6534 0.614241
\(827\) 39.8202 1.38468 0.692341 0.721570i \(-0.256579\pi\)
0.692341 + 0.721570i \(0.256579\pi\)
\(828\) −52.0091 −1.80744
\(829\) 38.3913 1.33339 0.666693 0.745333i \(-0.267709\pi\)
0.666693 + 0.745333i \(0.267709\pi\)
\(830\) −22.9300 −0.795911
\(831\) 37.7108 1.30817
\(832\) −29.4404 −1.02066
\(833\) −39.6927 −1.37527
\(834\) −5.55461 −0.192340
\(835\) 17.3407 0.600098
\(836\) −0.512154 −0.0177132
\(837\) 9.10750 0.314801
\(838\) −79.1083 −2.73275
\(839\) −43.9201 −1.51629 −0.758146 0.652085i \(-0.773895\pi\)
−0.758146 + 0.652085i \(0.773895\pi\)
\(840\) 13.5548 0.467684
\(841\) 1.00000 0.0344828
\(842\) −27.5130 −0.948161
\(843\) −3.21705 −0.110801
\(844\) −4.32285 −0.148799
\(845\) −4.65402 −0.160103
\(846\) 2.08309 0.0716180
\(847\) −6.53418 −0.224517
\(848\) −7.13543 −0.245032
\(849\) 68.6005 2.35436
\(850\) 51.9402 1.78154
\(851\) 35.0114 1.20017
\(852\) 63.5858 2.17841
\(853\) 26.1199 0.894328 0.447164 0.894452i \(-0.352434\pi\)
0.447164 + 0.894452i \(0.352434\pi\)
\(854\) 10.9523 0.374782
\(855\) −0.189381 −0.00647671
\(856\) −42.9442 −1.46780
\(857\) −41.6365 −1.42228 −0.711138 0.703053i \(-0.751820\pi\)
−0.711138 + 0.703053i \(0.751820\pi\)
\(858\) 35.9821 1.22841
\(859\) −16.8512 −0.574954 −0.287477 0.957788i \(-0.592816\pi\)
−0.287477 + 0.957788i \(0.592816\pi\)
\(860\) 4.26230 0.145343
\(861\) 12.4738 0.425107
\(862\) −42.6830 −1.45379
\(863\) 35.9569 1.22399 0.611993 0.790863i \(-0.290368\pi\)
0.611993 + 0.790863i \(0.290368\pi\)
\(864\) 2.25068 0.0765696
\(865\) −3.98037 −0.135337
\(866\) −1.14169 −0.0387962
\(867\) −61.0287 −2.07264
\(868\) 20.7881 0.705594
\(869\) −4.07509 −0.138238
\(870\) −7.34618 −0.249059
\(871\) −25.5954 −0.867267
\(872\) 33.5478 1.13607
\(873\) −10.7575 −0.364085
\(874\) −0.908266 −0.0307226
\(875\) −10.8460 −0.366663
\(876\) 134.016 4.52799
\(877\) −11.6984 −0.395027 −0.197514 0.980300i \(-0.563287\pi\)
−0.197514 + 0.980300i \(0.563287\pi\)
\(878\) −26.8237 −0.905256
\(879\) −45.8469 −1.54638
\(880\) 8.78936 0.296289
\(881\) −21.5111 −0.724728 −0.362364 0.932037i \(-0.618030\pi\)
−0.362364 + 0.932037i \(0.618030\pi\)
\(882\) 33.0031 1.11127
\(883\) −2.67443 −0.0900019 −0.0450009 0.998987i \(-0.514329\pi\)
−0.0450009 + 0.998987i \(0.514329\pi\)
\(884\) 78.3960 2.63674
\(885\) 22.2792 0.748906
\(886\) 93.8812 3.15400
\(887\) −30.1820 −1.01341 −0.506707 0.862118i \(-0.669137\pi\)
−0.506707 + 0.862118i \(0.669137\pi\)
\(888\) −60.7221 −2.03770
\(889\) 15.8452 0.531431
\(890\) 10.2598 0.343908
\(891\) −22.4257 −0.751291
\(892\) 2.14183 0.0717139
\(893\) 0.0239547 0.000801615 0
\(894\) −85.1087 −2.84646
\(895\) −14.9518 −0.499783
\(896\) 20.3339 0.679309
\(897\) 42.0194 1.40299
\(898\) 51.6246 1.72273
\(899\) −5.42341 −0.180881
\(900\) −28.4379 −0.947931
\(901\) −14.9130 −0.496822
\(902\) 27.8369 0.926867
\(903\) −1.90658 −0.0634470
\(904\) −23.4293 −0.779247
\(905\) −1.57265 −0.0522765
\(906\) 57.4519 1.90871
\(907\) −16.1485 −0.536203 −0.268102 0.963391i \(-0.586396\pi\)
−0.268102 + 0.963391i \(0.586396\pi\)
\(908\) −34.9748 −1.16068
\(909\) −31.2747 −1.03732
\(910\) −9.79516 −0.324707
\(911\) −19.0676 −0.631739 −0.315869 0.948803i \(-0.602296\pi\)
−0.315869 + 0.948803i \(0.602296\pi\)
\(912\) 0.457715 0.0151565
\(913\) 15.0725 0.498828
\(914\) 3.28530 0.108668
\(915\) 13.8222 0.456948
\(916\) −26.5490 −0.877204
\(917\) 8.07387 0.266623
\(918\) −26.8305 −0.885538
\(919\) −48.5107 −1.60022 −0.800110 0.599854i \(-0.795226\pi\)
−0.800110 + 0.599854i \(0.795226\pi\)
\(920\) 35.3245 1.16461
\(921\) 3.00953 0.0991673
\(922\) −48.6938 −1.60365
\(923\) −22.1191 −0.728060
\(924\) −18.5092 −0.608906
\(925\) 19.1438 0.629443
\(926\) 56.4724 1.85580
\(927\) −16.3133 −0.535800
\(928\) −1.34025 −0.0439959
\(929\) −5.06627 −0.166219 −0.0831095 0.996540i \(-0.526485\pi\)
−0.0831095 + 0.996540i \(0.526485\pi\)
\(930\) 39.8413 1.30645
\(931\) 0.379523 0.0124384
\(932\) −15.8045 −0.517695
\(933\) 19.0351 0.623182
\(934\) −7.80539 −0.255400
\(935\) 18.3696 0.600752
\(936\) −31.3780 −1.02562
\(937\) 48.6089 1.58798 0.793992 0.607929i \(-0.207999\pi\)
0.793992 + 0.607929i \(0.207999\pi\)
\(938\) 19.9945 0.652845
\(939\) 58.9748 1.92457
\(940\) −1.93538 −0.0631252
\(941\) −10.5540 −0.344051 −0.172025 0.985093i \(-0.555031\pi\)
−0.172025 + 0.985093i \(0.555031\pi\)
\(942\) −56.7353 −1.84854
\(943\) 32.5075 1.05859
\(944\) −23.1844 −0.754587
\(945\) 2.20748 0.0718093
\(946\) −4.25477 −0.138334
\(947\) 30.1059 0.978310 0.489155 0.872197i \(-0.337305\pi\)
0.489155 + 0.872197i \(0.337305\pi\)
\(948\) 17.1455 0.556860
\(949\) −46.6192 −1.51332
\(950\) −0.496628 −0.0161128
\(951\) 43.8914 1.42327
\(952\) −29.4803 −0.955462
\(953\) 24.3969 0.790294 0.395147 0.918618i \(-0.370694\pi\)
0.395147 + 0.918618i \(0.370694\pi\)
\(954\) 12.3996 0.401451
\(955\) 14.5287 0.470138
\(956\) 53.1474 1.71891
\(957\) 4.82886 0.156095
\(958\) −22.7570 −0.735246
\(959\) 13.1374 0.424228
\(960\) 29.0245 0.936760
\(961\) −1.58665 −0.0511823
\(962\) 43.8800 1.41475
\(963\) 21.6838 0.698751
\(964\) 56.5404 1.82104
\(965\) 29.0462 0.935030
\(966\) −32.8246 −1.05611
\(967\) −17.7460 −0.570674 −0.285337 0.958427i \(-0.592106\pi\)
−0.285337 + 0.958427i \(0.592106\pi\)
\(968\) 29.5334 0.949239
\(969\) 0.956619 0.0307310
\(970\) 15.1781 0.487340
\(971\) 22.4187 0.719452 0.359726 0.933058i \(-0.382870\pi\)
0.359726 + 0.933058i \(0.382870\pi\)
\(972\) 74.9259 2.40325
\(973\) −0.993943 −0.0318644
\(974\) −60.8025 −1.94824
\(975\) 22.9756 0.735810
\(976\) −14.3838 −0.460415
\(977\) −51.0740 −1.63400 −0.817001 0.576637i \(-0.804365\pi\)
−0.817001 + 0.576637i \(0.804365\pi\)
\(978\) −14.4865 −0.463228
\(979\) −6.74403 −0.215540
\(980\) −30.6629 −0.979491
\(981\) −16.9393 −0.540829
\(982\) −62.9904 −2.01010
\(983\) 5.71547 0.182295 0.0911476 0.995837i \(-0.470946\pi\)
0.0911476 + 0.995837i \(0.470946\pi\)
\(984\) −56.3796 −1.79732
\(985\) 24.1205 0.768542
\(986\) 15.9772 0.508819
\(987\) 0.865720 0.0275562
\(988\) −0.749586 −0.0238475
\(989\) −4.96866 −0.157994
\(990\) −15.2737 −0.485430
\(991\) 19.9731 0.634465 0.317233 0.948348i \(-0.397246\pi\)
0.317233 + 0.948348i \(0.397246\pi\)
\(992\) 7.26873 0.230782
\(993\) 27.1590 0.861864
\(994\) 17.2790 0.548055
\(995\) −12.6237 −0.400198
\(996\) −63.4161 −2.00941
\(997\) 31.6745 1.00314 0.501571 0.865116i \(-0.332755\pi\)
0.501571 + 0.865116i \(0.332755\pi\)
\(998\) 91.6641 2.90158
\(999\) −9.88899 −0.312874
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 \(a_p\))