Properties

Label 4009.2.a.c.1.11
Level 4009
Weight 2
Character 4009.1
Self dual Yes
Analytic conductor 32.012
Analytic rank 1
Dimension 71
CM No

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Newspace parameters

Level: \( N \) = \( 4009 = 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4009.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0120261703\)
Analytic rank: \(1\)
Dimension: \(71\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 4009.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.28791 q^{2}\) \(-0.433636 q^{3}\) \(+3.23453 q^{4}\) \(+1.92947 q^{5}\) \(+0.992121 q^{6}\) \(+3.12765 q^{7}\) \(-2.82450 q^{8}\) \(-2.81196 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.28791 q^{2}\) \(-0.433636 q^{3}\) \(+3.23453 q^{4}\) \(+1.92947 q^{5}\) \(+0.992121 q^{6}\) \(+3.12765 q^{7}\) \(-2.82450 q^{8}\) \(-2.81196 q^{9}\) \(-4.41445 q^{10}\) \(+3.32297 q^{11}\) \(-1.40261 q^{12}\) \(-6.14688 q^{13}\) \(-7.15577 q^{14}\) \(-0.836688 q^{15}\) \(-0.00686423 q^{16}\) \(+0.414157 q^{17}\) \(+6.43351 q^{18}\) \(+1.00000 q^{19}\) \(+6.24093 q^{20}\) \(-1.35626 q^{21}\) \(-7.60265 q^{22}\) \(-1.43364 q^{23}\) \(+1.22481 q^{24}\) \(-1.27715 q^{25}\) \(+14.0635 q^{26}\) \(+2.52028 q^{27}\) \(+10.1165 q^{28}\) \(+5.96085 q^{29}\) \(+1.91427 q^{30}\) \(-4.07439 q^{31}\) \(+5.66470 q^{32}\) \(-1.44096 q^{33}\) \(-0.947555 q^{34}\) \(+6.03469 q^{35}\) \(-9.09538 q^{36}\) \(-5.79741 q^{37}\) \(-2.28791 q^{38}\) \(+2.66551 q^{39}\) \(-5.44978 q^{40}\) \(-2.66125 q^{41}\) \(+3.10300 q^{42}\) \(+9.79443 q^{43}\) \(+10.7482 q^{44}\) \(-5.42559 q^{45}\) \(+3.28005 q^{46}\) \(-1.77055 q^{47}\) \(+0.00297658 q^{48}\) \(+2.78217 q^{49}\) \(+2.92200 q^{50}\) \(-0.179594 q^{51}\) \(-19.8823 q^{52}\) \(-8.51997 q^{53}\) \(-5.76616 q^{54}\) \(+6.41156 q^{55}\) \(-8.83403 q^{56}\) \(-0.433636 q^{57}\) \(-13.6379 q^{58}\) \(-15.1036 q^{59}\) \(-2.70629 q^{60}\) \(-9.57471 q^{61}\) \(+9.32184 q^{62}\) \(-8.79481 q^{63}\) \(-12.9466 q^{64}\) \(-11.8602 q^{65}\) \(+3.29678 q^{66}\) \(+0.513387 q^{67}\) \(+1.33961 q^{68}\) \(+0.621679 q^{69}\) \(-13.8068 q^{70}\) \(-6.51152 q^{71}\) \(+7.94238 q^{72}\) \(-1.35387 q^{73}\) \(+13.2639 q^{74}\) \(+0.553818 q^{75}\) \(+3.23453 q^{76}\) \(+10.3931 q^{77}\) \(-6.09845 q^{78}\) \(+10.5946 q^{79}\) \(-0.0132443 q^{80}\) \(+7.34300 q^{81}\) \(+6.08870 q^{82}\) \(+5.31145 q^{83}\) \(-4.38687 q^{84}\) \(+0.799104 q^{85}\) \(-22.4088 q^{86}\) \(-2.58484 q^{87}\) \(-9.38571 q^{88}\) \(-10.1959 q^{89}\) \(+12.4133 q^{90}\) \(-19.2253 q^{91}\) \(-4.63716 q^{92}\) \(+1.76680 q^{93}\) \(+4.05086 q^{94}\) \(+1.92947 q^{95}\) \(-2.45642 q^{96}\) \(-11.1926 q^{97}\) \(-6.36535 q^{98}\) \(-9.34405 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 9q^{12} \) \(\mathstrut -\mathstrut 15q^{13} \) \(\mathstrut -\mathstrut 53q^{14} \) \(\mathstrut -\mathstrut 33q^{15} \) \(\mathstrut +\mathstrut 53q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut +\mathstrut 71q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 38q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 65q^{23} \) \(\mathstrut -\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 51q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 23q^{27} \) \(\mathstrut -\mathstrut 29q^{28} \) \(\mathstrut -\mathstrut 97q^{29} \) \(\mathstrut -\mathstrut 27q^{30} \) \(\mathstrut -\mathstrut 53q^{31} \) \(\mathstrut -\mathstrut 78q^{32} \) \(\mathstrut -\mathstrut 17q^{33} \) \(\mathstrut -\mathstrut 24q^{34} \) \(\mathstrut -\mathstrut 38q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 33q^{37} \) \(\mathstrut -\mathstrut 15q^{38} \) \(\mathstrut -\mathstrut 86q^{39} \) \(\mathstrut +\mathstrut 25q^{40} \) \(\mathstrut -\mathstrut 69q^{41} \) \(\mathstrut +\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 94q^{44} \) \(\mathstrut -\mathstrut 34q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut 74q^{49} \) \(\mathstrut -\mathstrut 41q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 30q^{52} \) \(\mathstrut -\mathstrut 50q^{53} \) \(\mathstrut -\mathstrut 17q^{54} \) \(\mathstrut -\mathstrut 30q^{55} \) \(\mathstrut -\mathstrut 116q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 11q^{58} \) \(\mathstrut -\mathstrut 93q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut -\mathstrut 84q^{63} \) \(\mathstrut +\mathstrut 93q^{64} \) \(\mathstrut -\mathstrut 78q^{65} \) \(\mathstrut -\mathstrut 53q^{66} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 9q^{68} \) \(\mathstrut -\mathstrut 69q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 221q^{71} \) \(\mathstrut -\mathstrut 73q^{72} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 58q^{74} \) \(\mathstrut -\mathstrut 70q^{75} \) \(\mathstrut +\mathstrut 69q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 68q^{79} \) \(\mathstrut -\mathstrut 71q^{80} \) \(\mathstrut +\mathstrut 39q^{81} \) \(\mathstrut +\mathstrut 26q^{82} \) \(\mathstrut -\mathstrut 45q^{83} \) \(\mathstrut -\mathstrut 10q^{84} \) \(\mathstrut -\mathstrut 44q^{85} \) \(\mathstrut -\mathstrut 80q^{86} \) \(\mathstrut -\mathstrut 7q^{87} \) \(\mathstrut -\mathstrut 46q^{88} \) \(\mathstrut -\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 46q^{92} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut +\mathstrut 41q^{94} \) \(\mathstrut -\mathstrut 18q^{95} \) \(\mathstrut -\mathstrut 140q^{96} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 97q^{98} \) \(\mathstrut -\mathstrut 142q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.28791 −1.61780 −0.808898 0.587948i \(-0.799936\pi\)
−0.808898 + 0.587948i \(0.799936\pi\)
\(3\) −0.433636 −0.250360 −0.125180 0.992134i \(-0.539951\pi\)
−0.125180 + 0.992134i \(0.539951\pi\)
\(4\) 3.23453 1.61727
\(5\) 1.92947 0.862885 0.431442 0.902140i \(-0.358005\pi\)
0.431442 + 0.902140i \(0.358005\pi\)
\(6\) 0.992121 0.405032
\(7\) 3.12765 1.18214 0.591069 0.806621i \(-0.298706\pi\)
0.591069 + 0.806621i \(0.298706\pi\)
\(8\) −2.82450 −0.998611
\(9\) −2.81196 −0.937320
\(10\) −4.41445 −1.39597
\(11\) 3.32297 1.00191 0.500956 0.865473i \(-0.332982\pi\)
0.500956 + 0.865473i \(0.332982\pi\)
\(12\) −1.40261 −0.404899
\(13\) −6.14688 −1.70484 −0.852419 0.522859i \(-0.824865\pi\)
−0.852419 + 0.522859i \(0.824865\pi\)
\(14\) −7.15577 −1.91246
\(15\) −0.836688 −0.216032
\(16\) −0.00686423 −0.00171606
\(17\) 0.414157 0.100448 0.0502240 0.998738i \(-0.484006\pi\)
0.0502240 + 0.998738i \(0.484006\pi\)
\(18\) 6.43351 1.51639
\(19\) 1.00000 0.229416
\(20\) 6.24093 1.39551
\(21\) −1.35626 −0.295960
\(22\) −7.60265 −1.62089
\(23\) −1.43364 −0.298935 −0.149468 0.988767i \(-0.547756\pi\)
−0.149468 + 0.988767i \(0.547756\pi\)
\(24\) 1.22481 0.250012
\(25\) −1.27715 −0.255430
\(26\) 14.0635 2.75808
\(27\) 2.52028 0.485027
\(28\) 10.1165 1.91183
\(29\) 5.96085 1.10690 0.553451 0.832882i \(-0.313311\pi\)
0.553451 + 0.832882i \(0.313311\pi\)
\(30\) 1.91427 0.349496
\(31\) −4.07439 −0.731782 −0.365891 0.930658i \(-0.619236\pi\)
−0.365891 + 0.930658i \(0.619236\pi\)
\(32\) 5.66470 1.00139
\(33\) −1.44096 −0.250839
\(34\) −0.947555 −0.162504
\(35\) 6.03469 1.02005
\(36\) −9.09538 −1.51590
\(37\) −5.79741 −0.953088 −0.476544 0.879151i \(-0.658111\pi\)
−0.476544 + 0.879151i \(0.658111\pi\)
\(38\) −2.28791 −0.371148
\(39\) 2.66551 0.426823
\(40\) −5.44978 −0.861687
\(41\) −2.66125 −0.415617 −0.207809 0.978169i \(-0.566633\pi\)
−0.207809 + 0.978169i \(0.566633\pi\)
\(42\) 3.10300 0.478804
\(43\) 9.79443 1.49364 0.746818 0.665028i \(-0.231581\pi\)
0.746818 + 0.665028i \(0.231581\pi\)
\(44\) 10.7482 1.62036
\(45\) −5.42559 −0.808799
\(46\) 3.28005 0.483616
\(47\) −1.77055 −0.258261 −0.129131 0.991628i \(-0.541219\pi\)
−0.129131 + 0.991628i \(0.541219\pi\)
\(48\) 0.00297658 0.000429632 0
\(49\) 2.78217 0.397452
\(50\) 2.92200 0.413234
\(51\) −0.179594 −0.0251481
\(52\) −19.8823 −2.75718
\(53\) −8.51997 −1.17031 −0.585154 0.810922i \(-0.698966\pi\)
−0.585154 + 0.810922i \(0.698966\pi\)
\(54\) −5.76616 −0.784676
\(55\) 6.41156 0.864534
\(56\) −8.83403 −1.18050
\(57\) −0.433636 −0.0574365
\(58\) −13.6379 −1.79074
\(59\) −15.1036 −1.96632 −0.983162 0.182734i \(-0.941505\pi\)
−0.983162 + 0.182734i \(0.941505\pi\)
\(60\) −2.70629 −0.349381
\(61\) −9.57471 −1.22592 −0.612958 0.790115i \(-0.710021\pi\)
−0.612958 + 0.790115i \(0.710021\pi\)
\(62\) 9.32184 1.18387
\(63\) −8.79481 −1.10804
\(64\) −12.9466 −1.61833
\(65\) −11.8602 −1.47108
\(66\) 3.29678 0.405806
\(67\) 0.513387 0.0627202 0.0313601 0.999508i \(-0.490016\pi\)
0.0313601 + 0.999508i \(0.490016\pi\)
\(68\) 1.33961 0.162451
\(69\) 0.621679 0.0748414
\(70\) −13.8068 −1.65023
\(71\) −6.51152 −0.772776 −0.386388 0.922336i \(-0.626277\pi\)
−0.386388 + 0.922336i \(0.626277\pi\)
\(72\) 7.94238 0.936018
\(73\) −1.35387 −0.158459 −0.0792293 0.996856i \(-0.525246\pi\)
−0.0792293 + 0.996856i \(0.525246\pi\)
\(74\) 13.2639 1.54190
\(75\) 0.553818 0.0639494
\(76\) 3.23453 0.371026
\(77\) 10.3931 1.18440
\(78\) −6.09845 −0.690513
\(79\) 10.5946 1.19199 0.595995 0.802988i \(-0.296758\pi\)
0.595995 + 0.802988i \(0.296758\pi\)
\(80\) −0.0132443 −0.00148076
\(81\) 7.34300 0.815888
\(82\) 6.08870 0.672384
\(83\) 5.31145 0.583008 0.291504 0.956570i \(-0.405844\pi\)
0.291504 + 0.956570i \(0.405844\pi\)
\(84\) −4.38687 −0.478647
\(85\) 0.799104 0.0866750
\(86\) −22.4088 −2.41640
\(87\) −2.58484 −0.277124
\(88\) −9.38571 −1.00052
\(89\) −10.1959 −1.08076 −0.540382 0.841420i \(-0.681720\pi\)
−0.540382 + 0.841420i \(0.681720\pi\)
\(90\) 12.4133 1.30847
\(91\) −19.2253 −2.01536
\(92\) −4.63716 −0.483458
\(93\) 1.76680 0.183209
\(94\) 4.05086 0.417814
\(95\) 1.92947 0.197959
\(96\) −2.45642 −0.250707
\(97\) −11.1926 −1.13643 −0.568217 0.822879i \(-0.692366\pi\)
−0.568217 + 0.822879i \(0.692366\pi\)
\(98\) −6.36535 −0.642997
\(99\) −9.34405 −0.939112
\(100\) −4.13098 −0.413098
\(101\) −11.4371 −1.13803 −0.569017 0.822326i \(-0.692676\pi\)
−0.569017 + 0.822326i \(0.692676\pi\)
\(102\) 0.410894 0.0406846
\(103\) 11.8303 1.16567 0.582836 0.812590i \(-0.301943\pi\)
0.582836 + 0.812590i \(0.301943\pi\)
\(104\) 17.3619 1.70247
\(105\) −2.61686 −0.255380
\(106\) 19.4929 1.89332
\(107\) 2.94013 0.284233 0.142116 0.989850i \(-0.454609\pi\)
0.142116 + 0.989850i \(0.454609\pi\)
\(108\) 8.15191 0.784418
\(109\) −6.31183 −0.604564 −0.302282 0.953219i \(-0.597748\pi\)
−0.302282 + 0.953219i \(0.597748\pi\)
\(110\) −14.6691 −1.39864
\(111\) 2.51397 0.238615
\(112\) −0.0214689 −0.00202862
\(113\) −2.39064 −0.224893 −0.112446 0.993658i \(-0.535869\pi\)
−0.112446 + 0.993658i \(0.535869\pi\)
\(114\) 0.992121 0.0929206
\(115\) −2.76617 −0.257947
\(116\) 19.2806 1.79015
\(117\) 17.2848 1.59798
\(118\) 34.5557 3.18111
\(119\) 1.29534 0.118743
\(120\) 2.36322 0.215732
\(121\) 0.0421006 0.00382733
\(122\) 21.9061 1.98328
\(123\) 1.15401 0.104054
\(124\) −13.1787 −1.18349
\(125\) −12.1116 −1.08329
\(126\) 20.1217 1.79259
\(127\) −10.8008 −0.958412 −0.479206 0.877702i \(-0.659075\pi\)
−0.479206 + 0.877702i \(0.659075\pi\)
\(128\) 18.2913 1.61673
\(129\) −4.24722 −0.373947
\(130\) 27.1351 2.37991
\(131\) 6.67408 0.583117 0.291559 0.956553i \(-0.405826\pi\)
0.291559 + 0.956553i \(0.405826\pi\)
\(132\) −4.66083 −0.405673
\(133\) 3.12765 0.271201
\(134\) −1.17458 −0.101468
\(135\) 4.86279 0.418523
\(136\) −1.16979 −0.100308
\(137\) −16.9404 −1.44732 −0.723660 0.690157i \(-0.757542\pi\)
−0.723660 + 0.690157i \(0.757542\pi\)
\(138\) −1.42235 −0.121078
\(139\) 22.2056 1.88346 0.941729 0.336372i \(-0.109200\pi\)
0.941729 + 0.336372i \(0.109200\pi\)
\(140\) 19.5194 1.64969
\(141\) 0.767774 0.0646583
\(142\) 14.8978 1.25019
\(143\) −20.4259 −1.70810
\(144\) 0.0193019 0.00160850
\(145\) 11.5013 0.955129
\(146\) 3.09753 0.256354
\(147\) −1.20645 −0.0995062
\(148\) −18.7519 −1.54140
\(149\) −21.1259 −1.73070 −0.865351 0.501166i \(-0.832904\pi\)
−0.865351 + 0.501166i \(0.832904\pi\)
\(150\) −1.26709 −0.103457
\(151\) 16.5480 1.34666 0.673329 0.739343i \(-0.264864\pi\)
0.673329 + 0.739343i \(0.264864\pi\)
\(152\) −2.82450 −0.229097
\(153\) −1.16459 −0.0941518
\(154\) −23.7784 −1.91612
\(155\) −7.86141 −0.631444
\(156\) 8.62168 0.690287
\(157\) −7.26961 −0.580178 −0.290089 0.957000i \(-0.593685\pi\)
−0.290089 + 0.957000i \(0.593685\pi\)
\(158\) −24.2396 −1.92840
\(159\) 3.69457 0.292998
\(160\) 10.9299 0.864082
\(161\) −4.48393 −0.353383
\(162\) −16.8001 −1.31994
\(163\) 10.8741 0.851729 0.425864 0.904787i \(-0.359970\pi\)
0.425864 + 0.904787i \(0.359970\pi\)
\(164\) −8.60790 −0.672164
\(165\) −2.78028 −0.216445
\(166\) −12.1521 −0.943188
\(167\) −6.37658 −0.493434 −0.246717 0.969088i \(-0.579352\pi\)
−0.246717 + 0.969088i \(0.579352\pi\)
\(168\) 3.83076 0.295549
\(169\) 24.7841 1.90647
\(170\) −1.82828 −0.140223
\(171\) −2.81196 −0.215036
\(172\) 31.6804 2.41561
\(173\) 16.4117 1.24776 0.623880 0.781520i \(-0.285555\pi\)
0.623880 + 0.781520i \(0.285555\pi\)
\(174\) 5.91388 0.448330
\(175\) −3.99447 −0.301954
\(176\) −0.0228096 −0.00171934
\(177\) 6.54948 0.492289
\(178\) 23.3273 1.74846
\(179\) −10.2673 −0.767410 −0.383705 0.923456i \(-0.625352\pi\)
−0.383705 + 0.923456i \(0.625352\pi\)
\(180\) −17.5492 −1.30804
\(181\) −0.0275621 −0.00204868 −0.00102434 0.999999i \(-0.500326\pi\)
−0.00102434 + 0.999999i \(0.500326\pi\)
\(182\) 43.9857 3.26044
\(183\) 4.15194 0.306920
\(184\) 4.04932 0.298520
\(185\) −11.1859 −0.822405
\(186\) −4.04229 −0.296395
\(187\) 1.37623 0.100640
\(188\) −5.72690 −0.417677
\(189\) 7.88253 0.573370
\(190\) −4.41445 −0.320258
\(191\) 3.94185 0.285222 0.142611 0.989779i \(-0.454450\pi\)
0.142611 + 0.989779i \(0.454450\pi\)
\(192\) 5.61412 0.405164
\(193\) 12.8805 0.927159 0.463579 0.886055i \(-0.346565\pi\)
0.463579 + 0.886055i \(0.346565\pi\)
\(194\) 25.6076 1.83852
\(195\) 5.14302 0.368299
\(196\) 8.99901 0.642786
\(197\) 1.62358 0.115675 0.0578375 0.998326i \(-0.481579\pi\)
0.0578375 + 0.998326i \(0.481579\pi\)
\(198\) 21.3783 1.51929
\(199\) 15.0475 1.06669 0.533345 0.845898i \(-0.320935\pi\)
0.533345 + 0.845898i \(0.320935\pi\)
\(200\) 3.60731 0.255075
\(201\) −0.222623 −0.0157026
\(202\) 26.1671 1.84111
\(203\) 18.6434 1.30851
\(204\) −0.580901 −0.0406712
\(205\) −5.13480 −0.358630
\(206\) −27.0666 −1.88582
\(207\) 4.03135 0.280198
\(208\) 0.0421936 0.00292560
\(209\) 3.32297 0.229854
\(210\) 5.98714 0.413152
\(211\) 1.00000 0.0688428
\(212\) −27.5581 −1.89270
\(213\) 2.82363 0.193472
\(214\) −6.72675 −0.459831
\(215\) 18.8980 1.28884
\(216\) −7.11852 −0.484354
\(217\) −12.7432 −0.865068
\(218\) 14.4409 0.978062
\(219\) 0.587087 0.0396717
\(220\) 20.7384 1.39818
\(221\) −2.54578 −0.171247
\(222\) −5.75173 −0.386031
\(223\) −12.9664 −0.868298 −0.434149 0.900841i \(-0.642951\pi\)
−0.434149 + 0.900841i \(0.642951\pi\)
\(224\) 17.7172 1.18378
\(225\) 3.59129 0.239420
\(226\) 5.46957 0.363831
\(227\) 1.56235 0.103697 0.0518484 0.998655i \(-0.483489\pi\)
0.0518484 + 0.998655i \(0.483489\pi\)
\(228\) −1.40261 −0.0928901
\(229\) −20.7640 −1.37213 −0.686063 0.727542i \(-0.740663\pi\)
−0.686063 + 0.727542i \(0.740663\pi\)
\(230\) 6.32875 0.417305
\(231\) −4.50681 −0.296526
\(232\) −16.8364 −1.10536
\(233\) 0.126027 0.00825634 0.00412817 0.999991i \(-0.498686\pi\)
0.00412817 + 0.999991i \(0.498686\pi\)
\(234\) −39.5460 −2.58520
\(235\) −3.41622 −0.222850
\(236\) −48.8532 −3.18007
\(237\) −4.59422 −0.298426
\(238\) −2.96362 −0.192103
\(239\) −25.3406 −1.63915 −0.819573 0.572975i \(-0.805789\pi\)
−0.819573 + 0.572975i \(0.805789\pi\)
\(240\) 0.00574322 0.000370723 0
\(241\) 19.3994 1.24962 0.624812 0.780775i \(-0.285176\pi\)
0.624812 + 0.780775i \(0.285176\pi\)
\(242\) −0.0963225 −0.00619184
\(243\) −10.7450 −0.689293
\(244\) −30.9697 −1.98263
\(245\) 5.36810 0.342956
\(246\) −2.64028 −0.168338
\(247\) −6.14688 −0.391117
\(248\) 11.5081 0.730766
\(249\) −2.30324 −0.145962
\(250\) 27.7102 1.75255
\(251\) 11.4789 0.724539 0.362270 0.932073i \(-0.382002\pi\)
0.362270 + 0.932073i \(0.382002\pi\)
\(252\) −28.4471 −1.79200
\(253\) −4.76395 −0.299507
\(254\) 24.7112 1.55052
\(255\) −0.346520 −0.0216999
\(256\) −15.9555 −0.997222
\(257\) 18.4453 1.15058 0.575292 0.817948i \(-0.304888\pi\)
0.575292 + 0.817948i \(0.304888\pi\)
\(258\) 9.71725 0.604970
\(259\) −18.1322 −1.12668
\(260\) −38.3623 −2.37913
\(261\) −16.7617 −1.03752
\(262\) −15.2697 −0.943365
\(263\) 9.32046 0.574724 0.287362 0.957822i \(-0.407222\pi\)
0.287362 + 0.957822i \(0.407222\pi\)
\(264\) 4.06999 0.250490
\(265\) −16.4390 −1.00984
\(266\) −7.15577 −0.438749
\(267\) 4.42132 0.270580
\(268\) 1.66057 0.101435
\(269\) −29.0995 −1.77423 −0.887113 0.461552i \(-0.847293\pi\)
−0.887113 + 0.461552i \(0.847293\pi\)
\(270\) −11.1256 −0.677085
\(271\) −5.36920 −0.326155 −0.163078 0.986613i \(-0.552142\pi\)
−0.163078 + 0.986613i \(0.552142\pi\)
\(272\) −0.00284287 −0.000172374 0
\(273\) 8.33677 0.504564
\(274\) 38.7582 2.34147
\(275\) −4.24392 −0.255918
\(276\) 2.01084 0.121038
\(277\) −12.2510 −0.736090 −0.368045 0.929808i \(-0.619973\pi\)
−0.368045 + 0.929808i \(0.619973\pi\)
\(278\) −50.8045 −3.04705
\(279\) 11.4570 0.685914
\(280\) −17.0450 −1.01863
\(281\) −24.0484 −1.43461 −0.717303 0.696762i \(-0.754623\pi\)
−0.717303 + 0.696762i \(0.754623\pi\)
\(282\) −1.75660 −0.104604
\(283\) 12.9639 0.770627 0.385313 0.922786i \(-0.374093\pi\)
0.385313 + 0.922786i \(0.374093\pi\)
\(284\) −21.0617 −1.24978
\(285\) −0.836688 −0.0495611
\(286\) 46.7326 2.76335
\(287\) −8.32345 −0.491317
\(288\) −15.9289 −0.938621
\(289\) −16.8285 −0.989910
\(290\) −26.3139 −1.54520
\(291\) 4.85350 0.284517
\(292\) −4.37914 −0.256270
\(293\) 1.83619 0.107272 0.0536358 0.998561i \(-0.482919\pi\)
0.0536358 + 0.998561i \(0.482919\pi\)
\(294\) 2.76024 0.160981
\(295\) −29.1420 −1.69671
\(296\) 16.3748 0.951764
\(297\) 8.37479 0.485955
\(298\) 48.3342 2.79992
\(299\) 8.81243 0.509636
\(300\) 1.79134 0.103423
\(301\) 30.6335 1.76569
\(302\) −37.8604 −2.17862
\(303\) 4.95954 0.284918
\(304\) −0.00686423 −0.000393691 0
\(305\) −18.4741 −1.05782
\(306\) 2.66449 0.152319
\(307\) −28.2677 −1.61332 −0.806661 0.591015i \(-0.798728\pi\)
−0.806661 + 0.591015i \(0.798728\pi\)
\(308\) 33.6167 1.91549
\(309\) −5.13004 −0.291838
\(310\) 17.9862 1.02155
\(311\) 5.04129 0.285865 0.142933 0.989732i \(-0.454347\pi\)
0.142933 + 0.989732i \(0.454347\pi\)
\(312\) −7.52873 −0.426230
\(313\) 2.83741 0.160380 0.0801900 0.996780i \(-0.474447\pi\)
0.0801900 + 0.996780i \(0.474447\pi\)
\(314\) 16.6322 0.938611
\(315\) −16.9693 −0.956113
\(316\) 34.2687 1.92776
\(317\) 2.00520 0.112623 0.0563117 0.998413i \(-0.482066\pi\)
0.0563117 + 0.998413i \(0.482066\pi\)
\(318\) −8.45284 −0.474012
\(319\) 19.8077 1.10902
\(320\) −24.9801 −1.39643
\(321\) −1.27495 −0.0711605
\(322\) 10.2588 0.571702
\(323\) 0.414157 0.0230443
\(324\) 23.7512 1.31951
\(325\) 7.85049 0.435467
\(326\) −24.8791 −1.37792
\(327\) 2.73704 0.151359
\(328\) 7.51670 0.415040
\(329\) −5.53765 −0.305301
\(330\) 6.36104 0.350164
\(331\) 7.43302 0.408556 0.204278 0.978913i \(-0.434515\pi\)
0.204278 + 0.978913i \(0.434515\pi\)
\(332\) 17.1801 0.942878
\(333\) 16.3021 0.893348
\(334\) 14.5890 0.798276
\(335\) 0.990564 0.0541203
\(336\) 0.00930968 0.000507885 0
\(337\) −12.5642 −0.684417 −0.342209 0.939624i \(-0.611175\pi\)
−0.342209 + 0.939624i \(0.611175\pi\)
\(338\) −56.7039 −3.08429
\(339\) 1.03667 0.0563041
\(340\) 2.58473 0.140177
\(341\) −13.5391 −0.733181
\(342\) 6.43351 0.347884
\(343\) −13.1919 −0.712295
\(344\) −27.6644 −1.49156
\(345\) 1.19951 0.0645795
\(346\) −37.5485 −2.01862
\(347\) 4.27954 0.229738 0.114869 0.993381i \(-0.463355\pi\)
0.114869 + 0.993381i \(0.463355\pi\)
\(348\) −8.36075 −0.448183
\(349\) 29.5194 1.58014 0.790070 0.613017i \(-0.210044\pi\)
0.790070 + 0.613017i \(0.210044\pi\)
\(350\) 9.13899 0.488500
\(351\) −15.4918 −0.826893
\(352\) 18.8236 1.00330
\(353\) 33.5425 1.78528 0.892642 0.450766i \(-0.148849\pi\)
0.892642 + 0.450766i \(0.148849\pi\)
\(354\) −14.9846 −0.796424
\(355\) −12.5638 −0.666816
\(356\) −32.9790 −1.74788
\(357\) −0.561705 −0.0297286
\(358\) 23.4906 1.24151
\(359\) 29.4401 1.55379 0.776895 0.629631i \(-0.216794\pi\)
0.776895 + 0.629631i \(0.216794\pi\)
\(360\) 15.3246 0.807676
\(361\) 1.00000 0.0526316
\(362\) 0.0630596 0.00331434
\(363\) −0.0182564 −0.000958210 0
\(364\) −62.1847 −3.25937
\(365\) −2.61225 −0.136731
\(366\) −9.49927 −0.496535
\(367\) −15.2551 −0.796312 −0.398156 0.917318i \(-0.630350\pi\)
−0.398156 + 0.917318i \(0.630350\pi\)
\(368\) 0.00984086 0.000512990 0
\(369\) 7.48333 0.389566
\(370\) 25.5924 1.33048
\(371\) −26.6474 −1.38347
\(372\) 5.71478 0.296298
\(373\) −14.4505 −0.748220 −0.374110 0.927384i \(-0.622052\pi\)
−0.374110 + 0.927384i \(0.622052\pi\)
\(374\) −3.14869 −0.162815
\(375\) 5.25201 0.271213
\(376\) 5.00092 0.257903
\(377\) −36.6406 −1.88709
\(378\) −18.0345 −0.927596
\(379\) −1.98740 −0.102086 −0.0510429 0.998696i \(-0.516255\pi\)
−0.0510429 + 0.998696i \(0.516255\pi\)
\(380\) 6.24093 0.320153
\(381\) 4.68360 0.239948
\(382\) −9.01860 −0.461432
\(383\) 11.2057 0.572585 0.286292 0.958142i \(-0.407577\pi\)
0.286292 + 0.958142i \(0.407577\pi\)
\(384\) −7.93175 −0.404766
\(385\) 20.0531 1.02200
\(386\) −29.4694 −1.49995
\(387\) −27.5415 −1.40001
\(388\) −36.2027 −1.83792
\(389\) −18.1661 −0.921057 −0.460528 0.887645i \(-0.652340\pi\)
−0.460528 + 0.887645i \(0.652340\pi\)
\(390\) −11.7668 −0.595833
\(391\) −0.593754 −0.0300274
\(392\) −7.85823 −0.396900
\(393\) −2.89412 −0.145989
\(394\) −3.71460 −0.187139
\(395\) 20.4420 1.02855
\(396\) −30.2236 −1.51879
\(397\) 3.10587 0.155879 0.0779396 0.996958i \(-0.475166\pi\)
0.0779396 + 0.996958i \(0.475166\pi\)
\(398\) −34.4274 −1.72569
\(399\) −1.35626 −0.0678979
\(400\) 0.00876665 0.000438333 0
\(401\) 4.21538 0.210506 0.105253 0.994445i \(-0.466435\pi\)
0.105253 + 0.994445i \(0.466435\pi\)
\(402\) 0.509341 0.0254036
\(403\) 25.0448 1.24757
\(404\) −36.9937 −1.84050
\(405\) 14.1681 0.704018
\(406\) −42.6545 −2.11691
\(407\) −19.2646 −0.954910
\(408\) 0.507262 0.0251132
\(409\) 4.00260 0.197916 0.0989580 0.995092i \(-0.468449\pi\)
0.0989580 + 0.995092i \(0.468449\pi\)
\(410\) 11.7480 0.580190
\(411\) 7.34599 0.362351
\(412\) 38.2654 1.88520
\(413\) −47.2388 −2.32447
\(414\) −9.22336 −0.453303
\(415\) 10.2483 0.503068
\(416\) −34.8203 −1.70720
\(417\) −9.62917 −0.471542
\(418\) −7.60265 −0.371858
\(419\) −33.7660 −1.64958 −0.824789 0.565440i \(-0.808706\pi\)
−0.824789 + 0.565440i \(0.808706\pi\)
\(420\) −8.46433 −0.413017
\(421\) 0.542851 0.0264569 0.0132285 0.999913i \(-0.495789\pi\)
0.0132285 + 0.999913i \(0.495789\pi\)
\(422\) −2.28791 −0.111374
\(423\) 4.97871 0.242073
\(424\) 24.0647 1.16868
\(425\) −0.528941 −0.0256574
\(426\) −6.46022 −0.312998
\(427\) −29.9463 −1.44920
\(428\) 9.50994 0.459680
\(429\) 8.85740 0.427639
\(430\) −43.2370 −2.08507
\(431\) −29.5803 −1.42483 −0.712417 0.701757i \(-0.752399\pi\)
−0.712417 + 0.701757i \(0.752399\pi\)
\(432\) −0.0172998 −0.000832335 0
\(433\) 16.5113 0.793482 0.396741 0.917931i \(-0.370141\pi\)
0.396741 + 0.917931i \(0.370141\pi\)
\(434\) 29.1554 1.39950
\(435\) −4.98737 −0.239126
\(436\) −20.4158 −0.977741
\(437\) −1.43364 −0.0685804
\(438\) −1.34320 −0.0641807
\(439\) 22.6708 1.08202 0.541010 0.841016i \(-0.318042\pi\)
0.541010 + 0.841016i \(0.318042\pi\)
\(440\) −18.1094 −0.863334
\(441\) −7.82334 −0.372540
\(442\) 5.82451 0.277044
\(443\) 29.6849 1.41037 0.705186 0.709022i \(-0.250863\pi\)
0.705186 + 0.709022i \(0.250863\pi\)
\(444\) 8.13150 0.385904
\(445\) −19.6727 −0.932575
\(446\) 29.6661 1.40473
\(447\) 9.16096 0.433298
\(448\) −40.4924 −1.91309
\(449\) −28.1898 −1.33036 −0.665179 0.746684i \(-0.731645\pi\)
−0.665179 + 0.746684i \(0.731645\pi\)
\(450\) −8.21656 −0.387332
\(451\) −8.84324 −0.416412
\(452\) −7.73261 −0.363711
\(453\) −7.17582 −0.337149
\(454\) −3.57451 −0.167760
\(455\) −37.0946 −1.73902
\(456\) 1.22481 0.0573568
\(457\) −0.358204 −0.0167561 −0.00837803 0.999965i \(-0.502667\pi\)
−0.00837803 + 0.999965i \(0.502667\pi\)
\(458\) 47.5062 2.21982
\(459\) 1.04379 0.0487200
\(460\) −8.94726 −0.417168
\(461\) −25.3002 −1.17835 −0.589174 0.808006i \(-0.700547\pi\)
−0.589174 + 0.808006i \(0.700547\pi\)
\(462\) 10.3112 0.479719
\(463\) −5.62977 −0.261638 −0.130819 0.991406i \(-0.541761\pi\)
−0.130819 + 0.991406i \(0.541761\pi\)
\(464\) −0.0409166 −0.00189951
\(465\) 3.40899 0.158088
\(466\) −0.288340 −0.0133571
\(467\) 36.6216 1.69465 0.847323 0.531078i \(-0.178213\pi\)
0.847323 + 0.531078i \(0.178213\pi\)
\(468\) 55.9082 2.58436
\(469\) 1.60569 0.0741439
\(470\) 7.81601 0.360526
\(471\) 3.15237 0.145253
\(472\) 42.6602 1.96359
\(473\) 32.5465 1.49649
\(474\) 10.5112 0.482793
\(475\) −1.27715 −0.0585996
\(476\) 4.18981 0.192040
\(477\) 23.9578 1.09695
\(478\) 57.9770 2.65181
\(479\) 0.363547 0.0166109 0.00830544 0.999966i \(-0.497356\pi\)
0.00830544 + 0.999966i \(0.497356\pi\)
\(480\) −4.73959 −0.216332
\(481\) 35.6360 1.62486
\(482\) −44.3840 −2.02164
\(483\) 1.94439 0.0884729
\(484\) 0.136176 0.00618981
\(485\) −21.5957 −0.980611
\(486\) 24.5836 1.11514
\(487\) −10.4494 −0.473508 −0.236754 0.971570i \(-0.576083\pi\)
−0.236754 + 0.971570i \(0.576083\pi\)
\(488\) 27.0438 1.22421
\(489\) −4.71542 −0.213239
\(490\) −12.2817 −0.554832
\(491\) −36.9990 −1.66974 −0.834872 0.550445i \(-0.814458\pi\)
−0.834872 + 0.550445i \(0.814458\pi\)
\(492\) 3.73270 0.168283
\(493\) 2.46873 0.111186
\(494\) 14.0635 0.632747
\(495\) −18.0290 −0.810345
\(496\) 0.0279676 0.00125578
\(497\) −20.3657 −0.913528
\(498\) 5.26960 0.236136
\(499\) −20.2733 −0.907558 −0.453779 0.891114i \(-0.649924\pi\)
−0.453779 + 0.891114i \(0.649924\pi\)
\(500\) −39.1753 −1.75197
\(501\) 2.76511 0.123536
\(502\) −26.2626 −1.17216
\(503\) −24.7611 −1.10404 −0.552022 0.833829i \(-0.686144\pi\)
−0.552022 + 0.833829i \(0.686144\pi\)
\(504\) 24.8409 1.10650
\(505\) −22.0675 −0.981992
\(506\) 10.8995 0.484541
\(507\) −10.7473 −0.477304
\(508\) −34.9354 −1.55001
\(509\) −3.39562 −0.150508 −0.0752541 0.997164i \(-0.523977\pi\)
−0.0752541 + 0.997164i \(0.523977\pi\)
\(510\) 0.792807 0.0351061
\(511\) −4.23443 −0.187320
\(512\) −0.0776599 −0.00343211
\(513\) 2.52028 0.111273
\(514\) −42.2011 −1.86141
\(515\) 22.8262 1.00584
\(516\) −13.7378 −0.604771
\(517\) −5.88348 −0.258755
\(518\) 41.4849 1.82274
\(519\) −7.11671 −0.312389
\(520\) 33.4992 1.46904
\(521\) −0.754794 −0.0330681 −0.0165341 0.999863i \(-0.505263\pi\)
−0.0165341 + 0.999863i \(0.505263\pi\)
\(522\) 38.3492 1.67850
\(523\) 9.11617 0.398622 0.199311 0.979936i \(-0.436130\pi\)
0.199311 + 0.979936i \(0.436130\pi\)
\(524\) 21.5875 0.943056
\(525\) 1.73215 0.0755971
\(526\) −21.3244 −0.929787
\(527\) −1.68744 −0.0735060
\(528\) 0.00989107 0.000430454 0
\(529\) −20.9447 −0.910638
\(530\) 37.6110 1.63372
\(531\) 42.4708 1.84308
\(532\) 10.1165 0.438605
\(533\) 16.3584 0.708560
\(534\) −10.1156 −0.437744
\(535\) 5.67288 0.245260
\(536\) −1.45006 −0.0626331
\(537\) 4.45225 0.192129
\(538\) 66.5770 2.87034
\(539\) 9.24504 0.398212
\(540\) 15.7289 0.676863
\(541\) −20.9768 −0.901861 −0.450930 0.892559i \(-0.648908\pi\)
−0.450930 + 0.892559i \(0.648908\pi\)
\(542\) 12.2842 0.527653
\(543\) 0.0119519 0.000512906 0
\(544\) 2.34608 0.100587
\(545\) −12.1785 −0.521669
\(546\) −19.0738 −0.816282
\(547\) −45.1326 −1.92973 −0.964865 0.262745i \(-0.915372\pi\)
−0.964865 + 0.262745i \(0.915372\pi\)
\(548\) −54.7944 −2.34070
\(549\) 26.9237 1.14908
\(550\) 9.70972 0.414024
\(551\) 5.96085 0.253941
\(552\) −1.75593 −0.0747375
\(553\) 33.1363 1.40910
\(554\) 28.0291 1.19084
\(555\) 4.85062 0.205897
\(556\) 71.8249 3.04605
\(557\) −11.2775 −0.477843 −0.238922 0.971039i \(-0.576794\pi\)
−0.238922 + 0.971039i \(0.576794\pi\)
\(558\) −26.2126 −1.10967
\(559\) −60.2052 −2.54641
\(560\) −0.0414235 −0.00175046
\(561\) −0.596784 −0.0251962
\(562\) 55.0205 2.32090
\(563\) −23.6175 −0.995358 −0.497679 0.867361i \(-0.665814\pi\)
−0.497679 + 0.867361i \(0.665814\pi\)
\(564\) 2.48339 0.104570
\(565\) −4.61267 −0.194056
\(566\) −29.6603 −1.24672
\(567\) 22.9663 0.964493
\(568\) 18.3918 0.771703
\(569\) 22.2960 0.934697 0.467348 0.884073i \(-0.345209\pi\)
0.467348 + 0.884073i \(0.345209\pi\)
\(570\) 1.91427 0.0801798
\(571\) −17.1415 −0.717348 −0.358674 0.933463i \(-0.616771\pi\)
−0.358674 + 0.933463i \(0.616771\pi\)
\(572\) −66.0682 −2.76245
\(573\) −1.70933 −0.0714083
\(574\) 19.0433 0.794852
\(575\) 1.83098 0.0763570
\(576\) 36.4053 1.51689
\(577\) −5.43556 −0.226285 −0.113143 0.993579i \(-0.536092\pi\)
−0.113143 + 0.993579i \(0.536092\pi\)
\(578\) 38.5020 1.60147
\(579\) −5.58545 −0.232123
\(580\) 37.2012 1.54470
\(581\) 16.6123 0.689196
\(582\) −11.1044 −0.460291
\(583\) −28.3116 −1.17255
\(584\) 3.82401 0.158239
\(585\) 33.3505 1.37887
\(586\) −4.20105 −0.173544
\(587\) 36.6084 1.51099 0.755495 0.655154i \(-0.227396\pi\)
0.755495 + 0.655154i \(0.227396\pi\)
\(588\) −3.90230 −0.160928
\(589\) −4.07439 −0.167882
\(590\) 66.6742 2.74493
\(591\) −0.704041 −0.0289604
\(592\) 0.0397947 0.00163555
\(593\) −34.3256 −1.40958 −0.704791 0.709415i \(-0.748959\pi\)
−0.704791 + 0.709415i \(0.748959\pi\)
\(594\) −19.1608 −0.786176
\(595\) 2.49931 0.102462
\(596\) −68.3324 −2.79901
\(597\) −6.52515 −0.267057
\(598\) −20.1621 −0.824488
\(599\) −38.1948 −1.56060 −0.780298 0.625408i \(-0.784932\pi\)
−0.780298 + 0.625408i \(0.784932\pi\)
\(600\) −1.56426 −0.0638606
\(601\) 28.6278 1.16775 0.583877 0.811842i \(-0.301535\pi\)
0.583877 + 0.811842i \(0.301535\pi\)
\(602\) −70.0867 −2.85652
\(603\) −1.44362 −0.0587889
\(604\) 53.5251 2.17790
\(605\) 0.0812319 0.00330255
\(606\) −11.3470 −0.460940
\(607\) 24.1016 0.978255 0.489128 0.872212i \(-0.337315\pi\)
0.489128 + 0.872212i \(0.337315\pi\)
\(608\) 5.66470 0.229734
\(609\) −8.08446 −0.327599
\(610\) 42.2671 1.71135
\(611\) 10.8834 0.440294
\(612\) −3.76692 −0.152269
\(613\) 32.1756 1.29956 0.649779 0.760123i \(-0.274861\pi\)
0.649779 + 0.760123i \(0.274861\pi\)
\(614\) 64.6739 2.61003
\(615\) 2.22663 0.0897866
\(616\) −29.3552 −1.18275
\(617\) 9.13019 0.367568 0.183784 0.982967i \(-0.441165\pi\)
0.183784 + 0.982967i \(0.441165\pi\)
\(618\) 11.7371 0.472134
\(619\) 18.4061 0.739804 0.369902 0.929071i \(-0.379391\pi\)
0.369902 + 0.929071i \(0.379391\pi\)
\(620\) −25.4280 −1.02121
\(621\) −3.61318 −0.144992
\(622\) −11.5340 −0.462472
\(623\) −31.8892 −1.27761
\(624\) −0.0182967 −0.000732453 0
\(625\) −16.9831 −0.679326
\(626\) −6.49174 −0.259462
\(627\) −1.44096 −0.0575463
\(628\) −23.5138 −0.938303
\(629\) −2.40104 −0.0957357
\(630\) 38.8243 1.54680
\(631\) −11.1359 −0.443314 −0.221657 0.975125i \(-0.571147\pi\)
−0.221657 + 0.975125i \(0.571147\pi\)
\(632\) −29.9245 −1.19033
\(633\) −0.433636 −0.0172355
\(634\) −4.58772 −0.182202
\(635\) −20.8397 −0.826999
\(636\) 11.9502 0.473856
\(637\) −17.1016 −0.677592
\(638\) −45.3182 −1.79417
\(639\) 18.3101 0.724338
\(640\) 35.2924 1.39506
\(641\) −7.03126 −0.277718 −0.138859 0.990312i \(-0.544343\pi\)
−0.138859 + 0.990312i \(0.544343\pi\)
\(642\) 2.91696 0.115123
\(643\) 38.9204 1.53487 0.767434 0.641127i \(-0.221533\pi\)
0.767434 + 0.641127i \(0.221533\pi\)
\(644\) −14.5034 −0.571514
\(645\) −8.19487 −0.322673
\(646\) −0.947555 −0.0372811
\(647\) 0.954552 0.0375273 0.0187637 0.999824i \(-0.494027\pi\)
0.0187637 + 0.999824i \(0.494027\pi\)
\(648\) −20.7403 −0.814756
\(649\) −50.1888 −1.97008
\(650\) −17.9612 −0.704496
\(651\) 5.52593 0.216578
\(652\) 35.1728 1.37747
\(653\) −31.9323 −1.24961 −0.624804 0.780781i \(-0.714821\pi\)
−0.624804 + 0.780781i \(0.714821\pi\)
\(654\) −6.26210 −0.244867
\(655\) 12.8774 0.503163
\(656\) 0.0182674 0.000713223 0
\(657\) 3.80703 0.148526
\(658\) 12.6697 0.493914
\(659\) −1.96616 −0.0765908 −0.0382954 0.999266i \(-0.512193\pi\)
−0.0382954 + 0.999266i \(0.512193\pi\)
\(660\) −8.99292 −0.350049
\(661\) −48.5702 −1.88916 −0.944582 0.328276i \(-0.893532\pi\)
−0.944582 + 0.328276i \(0.893532\pi\)
\(662\) −17.0061 −0.660961
\(663\) 1.10394 0.0428735
\(664\) −15.0022 −0.582198
\(665\) 6.03469 0.234015
\(666\) −37.2977 −1.44526
\(667\) −8.54573 −0.330892
\(668\) −20.6252 −0.798015
\(669\) 5.62272 0.217387
\(670\) −2.26632 −0.0875556
\(671\) −31.8164 −1.22826
\(672\) −7.68281 −0.296371
\(673\) −2.66734 −0.102818 −0.0514092 0.998678i \(-0.516371\pi\)
−0.0514092 + 0.998678i \(0.516371\pi\)
\(674\) 28.7458 1.10725
\(675\) −3.21877 −0.123890
\(676\) 80.1651 3.08327
\(677\) 5.39660 0.207408 0.103704 0.994608i \(-0.466931\pi\)
0.103704 + 0.994608i \(0.466931\pi\)
\(678\) −2.37180 −0.0910886
\(679\) −35.0064 −1.34342
\(680\) −2.25707 −0.0865546
\(681\) −0.677491 −0.0259615
\(682\) 30.9761 1.18614
\(683\) 40.2981 1.54196 0.770981 0.636858i \(-0.219766\pi\)
0.770981 + 0.636858i \(0.219766\pi\)
\(684\) −9.09538 −0.347770
\(685\) −32.6861 −1.24887
\(686\) 30.1819 1.15235
\(687\) 9.00403 0.343525
\(688\) −0.0672312 −0.00256317
\(689\) 52.3712 1.99519
\(690\) −2.74437 −0.104477
\(691\) 14.2210 0.540993 0.270497 0.962721i \(-0.412812\pi\)
0.270497 + 0.962721i \(0.412812\pi\)
\(692\) 53.0842 2.01796
\(693\) −29.2249 −1.11016
\(694\) −9.79120 −0.371669
\(695\) 42.8451 1.62521
\(696\) 7.30088 0.276739
\(697\) −1.10218 −0.0417479
\(698\) −67.5378 −2.55634
\(699\) −0.0546501 −0.00206706
\(700\) −12.9202 −0.488339
\(701\) −9.93859 −0.375375 −0.187688 0.982229i \(-0.560099\pi\)
−0.187688 + 0.982229i \(0.560099\pi\)
\(702\) 35.4439 1.33774
\(703\) −5.79741 −0.218653
\(704\) −43.0211 −1.62142
\(705\) 1.48140 0.0557926
\(706\) −76.7421 −2.88823
\(707\) −35.7712 −1.34531
\(708\) 21.1845 0.796162
\(709\) 21.3935 0.803451 0.401725 0.915760i \(-0.368411\pi\)
0.401725 + 0.915760i \(0.368411\pi\)
\(710\) 28.7448 1.07877
\(711\) −29.7917 −1.11728
\(712\) 28.7983 1.07926
\(713\) 5.84122 0.218755
\(714\) 1.28513 0.0480948
\(715\) −39.4111 −1.47389
\(716\) −33.2098 −1.24111
\(717\) 10.9886 0.410377
\(718\) −67.3563 −2.51372
\(719\) 29.1510 1.08715 0.543574 0.839361i \(-0.317071\pi\)
0.543574 + 0.839361i \(0.317071\pi\)
\(720\) 0.0372425 0.00138795
\(721\) 37.0009 1.37799
\(722\) −2.28791 −0.0851472
\(723\) −8.41227 −0.312856
\(724\) −0.0891506 −0.00331325
\(725\) −7.61289 −0.282736
\(726\) 0.0417689 0.00155019
\(727\) −7.77117 −0.288217 −0.144108 0.989562i \(-0.546031\pi\)
−0.144108 + 0.989562i \(0.546031\pi\)
\(728\) 54.3018 2.01256
\(729\) −17.3696 −0.643317
\(730\) 5.97660 0.221204
\(731\) 4.05643 0.150033
\(732\) 13.4296 0.496372
\(733\) −36.8697 −1.36181 −0.680906 0.732370i \(-0.738414\pi\)
−0.680906 + 0.732370i \(0.738414\pi\)
\(734\) 34.9024 1.28827
\(735\) −2.32780 −0.0858623
\(736\) −8.12116 −0.299350
\(737\) 1.70597 0.0628401
\(738\) −17.1212 −0.630239
\(739\) 9.28480 0.341547 0.170773 0.985310i \(-0.445373\pi\)
0.170773 + 0.985310i \(0.445373\pi\)
\(740\) −36.1812 −1.33005
\(741\) 2.66551 0.0979200
\(742\) 60.9670 2.23817
\(743\) −18.2761 −0.670484 −0.335242 0.942132i \(-0.608818\pi\)
−0.335242 + 0.942132i \(0.608818\pi\)
\(744\) −4.99033 −0.182954
\(745\) −40.7618 −1.49340
\(746\) 33.0615 1.21047
\(747\) −14.9356 −0.546465
\(748\) 4.45146 0.162762
\(749\) 9.19567 0.336003
\(750\) −12.0161 −0.438767
\(751\) 21.2805 0.776535 0.388267 0.921547i \(-0.373074\pi\)
0.388267 + 0.921547i \(0.373074\pi\)
\(752\) 0.0121535 0.000443191 0
\(753\) −4.97765 −0.181396
\(754\) 83.8305 3.05293
\(755\) 31.9289 1.16201
\(756\) 25.4963 0.927291
\(757\) 0.280839 0.0102073 0.00510364 0.999987i \(-0.498375\pi\)
0.00510364 + 0.999987i \(0.498375\pi\)
\(758\) 4.54699 0.165154
\(759\) 2.06582 0.0749845
\(760\) −5.44978 −0.197684
\(761\) 51.7868 1.87727 0.938635 0.344912i \(-0.112091\pi\)
0.938635 + 0.344912i \(0.112091\pi\)
\(762\) −10.7156 −0.388187
\(763\) −19.7412 −0.714679
\(764\) 12.7500 0.461281
\(765\) −2.24705 −0.0812422
\(766\) −25.6376 −0.926326
\(767\) 92.8402 3.35227
\(768\) 6.91890 0.249664
\(769\) −15.6573 −0.564618 −0.282309 0.959324i \(-0.591100\pi\)
−0.282309 + 0.959324i \(0.591100\pi\)
\(770\) −45.8797 −1.65339
\(771\) −7.99854 −0.288060
\(772\) 41.6624 1.49946
\(773\) −18.7346 −0.673838 −0.336919 0.941534i \(-0.609385\pi\)
−0.336919 + 0.941534i \(0.609385\pi\)
\(774\) 63.0125 2.26494
\(775\) 5.20360 0.186919
\(776\) 31.6134 1.13486
\(777\) 7.86279 0.282076
\(778\) 41.5623 1.49008
\(779\) −2.66125 −0.0953492
\(780\) 16.6353 0.595638
\(781\) −21.6376 −0.774253
\(782\) 1.35846 0.0485783
\(783\) 15.0230 0.536878
\(784\) −0.0190974 −0.000682051 0
\(785\) −14.0265 −0.500627
\(786\) 6.62149 0.236181
\(787\) −46.5132 −1.65802 −0.829009 0.559235i \(-0.811095\pi\)
−0.829009 + 0.559235i \(0.811095\pi\)
\(788\) 5.25151 0.187077
\(789\) −4.04169 −0.143888
\(790\) −46.7695 −1.66398
\(791\) −7.47708 −0.265854
\(792\) 26.3923 0.937808
\(793\) 58.8546 2.08999
\(794\) −7.10595 −0.252181
\(795\) 7.12855 0.252824
\(796\) 48.6717 1.72512
\(797\) 32.8054 1.16203 0.581013 0.813894i \(-0.302656\pi\)
0.581013 + 0.813894i \(0.302656\pi\)
\(798\) 3.10300 0.109845
\(799\) −0.733286 −0.0259418
\(800\) −7.23467 −0.255784
\(801\) 28.6705 1.01302
\(802\) −9.64441 −0.340556
\(803\) −4.49887 −0.158762
\(804\) −0.720081 −0.0253953
\(805\) −8.65160 −0.304929
\(806\) −57.3002 −2.01831
\(807\) 12.6186 0.444195
\(808\) 32.3041 1.13645
\(809\) 8.27972 0.291099 0.145550 0.989351i \(-0.453505\pi\)
0.145550 + 0.989351i \(0.453505\pi\)
\(810\) −32.4153 −1.13896
\(811\) 6.45437 0.226644 0.113322 0.993558i \(-0.463851\pi\)
0.113322 + 0.993558i \(0.463851\pi\)
\(812\) 60.3027 2.11621
\(813\) 2.32828 0.0816562
\(814\) 44.0756 1.54485
\(815\) 20.9813 0.734944
\(816\) 0.00123277 4.31557e−5 0
\(817\) 9.79443 0.342664
\(818\) −9.15760 −0.320188
\(819\) 54.0607 1.88903
\(820\) −16.6087 −0.580000
\(821\) −3.90894 −0.136423 −0.0682115 0.997671i \(-0.521729\pi\)
−0.0682115 + 0.997671i \(0.521729\pi\)
\(822\) −16.8070 −0.586210
\(823\) −3.61262 −0.125928 −0.0629639 0.998016i \(-0.520055\pi\)
−0.0629639 + 0.998016i \(0.520055\pi\)
\(824\) −33.4146 −1.16405
\(825\) 1.84032 0.0640717
\(826\) 108.078 3.76052
\(827\) 25.1855 0.875785 0.437892 0.899027i \(-0.355725\pi\)
0.437892 + 0.899027i \(0.355725\pi\)
\(828\) 13.0395 0.453155
\(829\) 33.9331 1.17855 0.589273 0.807934i \(-0.299414\pi\)
0.589273 + 0.807934i \(0.299414\pi\)
\(830\) −23.4471 −0.813862
\(831\) 5.31247 0.184287
\(832\) 79.5812 2.75898
\(833\) 1.15225 0.0399233
\(834\) 22.0307 0.762860
\(835\) −12.3034 −0.425777
\(836\) 10.7482 0.371736
\(837\) −10.2686 −0.354934
\(838\) 77.2536 2.66868
\(839\) 1.77048 0.0611238 0.0305619 0.999533i \(-0.490270\pi\)
0.0305619 + 0.999533i \(0.490270\pi\)
\(840\) 7.39133 0.255025
\(841\) 6.53171 0.225231
\(842\) −1.24199 −0.0428019
\(843\) 10.4282 0.359168
\(844\) 3.23453 0.111337
\(845\) 47.8202 1.64507
\(846\) −11.3909 −0.391626
\(847\) 0.131676 0.00452444
\(848\) 0.0584830 0.00200832
\(849\) −5.62164 −0.192934
\(850\) 1.21017 0.0415085
\(851\) 8.31141 0.284911
\(852\) 9.13313 0.312896
\(853\) −43.9146 −1.50361 −0.751804 0.659386i \(-0.770816\pi\)
−0.751804 + 0.659386i \(0.770816\pi\)
\(854\) 68.5145 2.34452
\(855\) −5.42559 −0.185551
\(856\) −8.30439 −0.283838
\(857\) 18.9573 0.647568 0.323784 0.946131i \(-0.395045\pi\)
0.323784 + 0.946131i \(0.395045\pi\)
\(858\) −20.2649 −0.691833
\(859\) 6.81862 0.232648 0.116324 0.993211i \(-0.462889\pi\)
0.116324 + 0.993211i \(0.462889\pi\)
\(860\) 61.1263 2.08439
\(861\) 3.60935 0.123006
\(862\) 67.6771 2.30509
\(863\) 24.4917 0.833707 0.416853 0.908974i \(-0.363133\pi\)
0.416853 + 0.908974i \(0.363133\pi\)
\(864\) 14.2766 0.485700
\(865\) 31.6659 1.07667
\(866\) −37.7763 −1.28369
\(867\) 7.29743 0.247834
\(868\) −41.2184 −1.39905
\(869\) 35.2056 1.19427
\(870\) 11.4106 0.386857
\(871\) −3.15573 −0.106928
\(872\) 17.8278 0.603724
\(873\) 31.4731 1.06520
\(874\) 3.28005 0.110949
\(875\) −37.8807 −1.28060
\(876\) 1.89895 0.0641597
\(877\) −5.60868 −0.189392 −0.0946958 0.995506i \(-0.530188\pi\)
−0.0946958 + 0.995506i \(0.530188\pi\)
\(878\) −51.8688 −1.75049
\(879\) −0.796240 −0.0268565
\(880\) −0.0440104 −0.00148359
\(881\) −39.3862 −1.32696 −0.663478 0.748196i \(-0.730920\pi\)
−0.663478 + 0.748196i \(0.730920\pi\)
\(882\) 17.8991 0.602694
\(883\) −12.9715 −0.436526 −0.218263 0.975890i \(-0.570039\pi\)
−0.218263 + 0.975890i \(0.570039\pi\)
\(884\) −8.23440 −0.276953
\(885\) 12.6370 0.424789
\(886\) −67.9164 −2.28170
\(887\) 19.6718 0.660516 0.330258 0.943891i \(-0.392864\pi\)
0.330258 + 0.943891i \(0.392864\pi\)
\(888\) −7.10069 −0.238284
\(889\) −33.7809 −1.13298
\(890\) 45.0094 1.50872
\(891\) 24.4005 0.817448
\(892\) −41.9404 −1.40427
\(893\) −1.77055 −0.0592492
\(894\) −20.9594 −0.700989
\(895\) −19.8103 −0.662187
\(896\) 57.2086 1.91120
\(897\) −3.82139 −0.127592
\(898\) 64.4957 2.15225
\(899\) −24.2868 −0.810011
\(900\) 11.6162 0.387205
\(901\) −3.52861 −0.117555
\(902\) 20.2325 0.673670
\(903\) −13.2838 −0.442057
\(904\) 6.75237 0.224580
\(905\) −0.0531802 −0.00176777
\(906\) 16.4176 0.545439
\(907\) 23.6875 0.786529 0.393265 0.919425i \(-0.371346\pi\)
0.393265 + 0.919425i \(0.371346\pi\)
\(908\) 5.05347 0.167705
\(909\) 32.1607 1.06670
\(910\) 84.8690 2.81338
\(911\) −59.3177 −1.96528 −0.982641 0.185518i \(-0.940604\pi\)
−0.982641 + 0.185518i \(0.940604\pi\)
\(912\) 0.00297658 9.85644e−5 0
\(913\) 17.6498 0.584122
\(914\) 0.819538 0.0271079
\(915\) 8.01104 0.264837
\(916\) −67.1619 −2.21909
\(917\) 20.8742 0.689325
\(918\) −2.38810 −0.0788190
\(919\) −38.4131 −1.26713 −0.633566 0.773689i \(-0.718410\pi\)
−0.633566 + 0.773689i \(0.718410\pi\)
\(920\) 7.81304 0.257588
\(921\) 12.2579 0.403911
\(922\) 57.8846 1.90633
\(923\) 40.0256 1.31746
\(924\) −14.5774 −0.479562
\(925\) 7.40415 0.243447
\(926\) 12.8804 0.423277
\(927\) −33.2663 −1.09261
\(928\) 33.7664 1.10844
\(929\) −43.1954 −1.41719 −0.708597 0.705613i \(-0.750672\pi\)
−0.708597 + 0.705613i \(0.750672\pi\)
\(930\) −7.79946 −0.255755
\(931\) 2.78217 0.0911818
\(932\) 0.407640 0.0133527
\(933\) −2.18609 −0.0715693
\(934\) −83.7870 −2.74159
\(935\) 2.65539 0.0868407
\(936\) −48.8209 −1.59576
\(937\) 40.1404 1.31133 0.655666 0.755051i \(-0.272388\pi\)
0.655666 + 0.755051i \(0.272388\pi\)
\(938\) −3.67368 −0.119950
\(939\) −1.23040 −0.0401527
\(940\) −11.0499 −0.360407
\(941\) 20.0028 0.652072 0.326036 0.945357i \(-0.394287\pi\)
0.326036 + 0.945357i \(0.394287\pi\)
\(942\) −7.21233 −0.234990
\(943\) 3.81528 0.124243
\(944\) 0.103675 0.00337433
\(945\) 15.2091 0.494752
\(946\) −74.4636 −2.42102
\(947\) −13.6086 −0.442220 −0.221110 0.975249i \(-0.570968\pi\)
−0.221110 + 0.975249i \(0.570968\pi\)
\(948\) −14.8601 −0.482635
\(949\) 8.32208 0.270146
\(950\) 2.92200 0.0948023
\(951\) −0.869528 −0.0281964
\(952\) −3.65868 −0.118579
\(953\) 55.8908 1.81048 0.905241 0.424899i \(-0.139691\pi\)
0.905241 + 0.424899i \(0.139691\pi\)
\(954\) −54.8133 −1.77465
\(955\) 7.60568 0.246114
\(956\) −81.9649 −2.65094
\(957\) −8.58933 −0.277654
\(958\) −0.831762 −0.0268730
\(959\) −52.9837 −1.71093
\(960\) 10.8323 0.349610
\(961\) −14.3993 −0.464495
\(962\) −81.5319 −2.62869
\(963\) −8.26752 −0.266417
\(964\) 62.7479 2.02097
\(965\) 24.8525 0.800031
\(966\) −4.44860 −0.143131
\(967\) 19.3635 0.622689 0.311344 0.950297i \(-0.399221\pi\)
0.311344 + 0.950297i \(0.399221\pi\)
\(968\) −0.118913 −0.00382202
\(969\) −0.179594 −0.00576938
\(970\) 49.4091 1.58643
\(971\) 27.8321 0.893175 0.446588 0.894740i \(-0.352639\pi\)
0.446588 + 0.894740i \(0.352639\pi\)
\(972\) −34.7551 −1.11477
\(973\) 69.4514 2.22651
\(974\) 23.9073 0.766039
\(975\) −3.40425 −0.109023
\(976\) 0.0657231 0.00210374
\(977\) −32.5766 −1.04222 −0.521108 0.853491i \(-0.674481\pi\)
−0.521108 + 0.853491i \(0.674481\pi\)
\(978\) 10.7885 0.344977
\(979\) −33.8807 −1.08283
\(980\) 17.3633 0.554650
\(981\) 17.7486 0.566670
\(982\) 84.6505 2.70131
\(983\) −17.3041 −0.551915 −0.275958 0.961170i \(-0.588995\pi\)
−0.275958 + 0.961170i \(0.588995\pi\)
\(984\) −3.25951 −0.103909
\(985\) 3.13264 0.0998142
\(986\) −5.64823 −0.179876
\(987\) 2.40133 0.0764351
\(988\) −19.8823 −0.632540
\(989\) −14.0417 −0.446500
\(990\) 41.2488 1.31097
\(991\) 56.7783 1.80362 0.901811 0.432130i \(-0.142238\pi\)
0.901811 + 0.432130i \(0.142238\pi\)
\(992\) −23.0802 −0.732797
\(993\) −3.22323 −0.102286
\(994\) 46.5950 1.47790
\(995\) 29.0337 0.920431
\(996\) −7.44990 −0.236059
\(997\) −28.4672 −0.901565 −0.450783 0.892634i \(-0.648855\pi\)
−0.450783 + 0.892634i \(0.648855\pi\)
\(998\) 46.3835 1.46824
\(999\) −14.6111 −0.462274
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 \(a_p\))