Properties

Label 8015.2.a.l.1.32
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.32
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.159746 q^{2} -1.47853 q^{3} -1.97448 q^{4} -1.00000 q^{5} -0.236189 q^{6} -1.00000 q^{7} -0.634908 q^{8} -0.813953 q^{9} +O(q^{10})\) \(q+0.159746 q^{2} -1.47853 q^{3} -1.97448 q^{4} -1.00000 q^{5} -0.236189 q^{6} -1.00000 q^{7} -0.634908 q^{8} -0.813953 q^{9} -0.159746 q^{10} +4.75271 q^{11} +2.91933 q^{12} -0.0580750 q^{13} -0.159746 q^{14} +1.47853 q^{15} +3.84754 q^{16} +4.36259 q^{17} -0.130026 q^{18} +3.34416 q^{19} +1.97448 q^{20} +1.47853 q^{21} +0.759226 q^{22} -3.41396 q^{23} +0.938729 q^{24} +1.00000 q^{25} -0.00927726 q^{26} +5.63904 q^{27} +1.97448 q^{28} +6.44554 q^{29} +0.236189 q^{30} -2.13401 q^{31} +1.88444 q^{32} -7.02702 q^{33} +0.696907 q^{34} +1.00000 q^{35} +1.60713 q^{36} -10.9458 q^{37} +0.534216 q^{38} +0.0858656 q^{39} +0.634908 q^{40} -3.88048 q^{41} +0.236189 q^{42} +4.24610 q^{43} -9.38413 q^{44} +0.813953 q^{45} -0.545366 q^{46} +12.0801 q^{47} -5.68870 q^{48} +1.00000 q^{49} +0.159746 q^{50} -6.45022 q^{51} +0.114668 q^{52} -3.29849 q^{53} +0.900814 q^{54} -4.75271 q^{55} +0.634908 q^{56} -4.94443 q^{57} +1.02965 q^{58} -5.51131 q^{59} -2.91933 q^{60} -1.47783 q^{61} -0.340899 q^{62} +0.813953 q^{63} -7.39404 q^{64} +0.0580750 q^{65} -1.12254 q^{66} +15.1741 q^{67} -8.61385 q^{68} +5.04764 q^{69} +0.159746 q^{70} -4.33053 q^{71} +0.516785 q^{72} -6.31946 q^{73} -1.74854 q^{74} -1.47853 q^{75} -6.60298 q^{76} -4.75271 q^{77} +0.0137167 q^{78} -5.97180 q^{79} -3.84754 q^{80} -5.89562 q^{81} -0.619891 q^{82} +8.45930 q^{83} -2.91933 q^{84} -4.36259 q^{85} +0.678297 q^{86} -9.52992 q^{87} -3.01753 q^{88} -10.3162 q^{89} +0.130026 q^{90} +0.0580750 q^{91} +6.74080 q^{92} +3.15519 q^{93} +1.92975 q^{94} -3.34416 q^{95} -2.78620 q^{96} +1.33005 q^{97} +0.159746 q^{98} -3.86848 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.159746 0.112957 0.0564787 0.998404i \(-0.482013\pi\)
0.0564787 + 0.998404i \(0.482013\pi\)
\(3\) −1.47853 −0.853629 −0.426814 0.904339i \(-0.640364\pi\)
−0.426814 + 0.904339i \(0.640364\pi\)
\(4\) −1.97448 −0.987241
\(5\) −1.00000 −0.447214
\(6\) −0.236189 −0.0964238
\(7\) −1.00000 −0.377964
\(8\) −0.634908 −0.224474
\(9\) −0.813953 −0.271318
\(10\) −0.159746 −0.0505161
\(11\) 4.75271 1.43300 0.716498 0.697589i \(-0.245744\pi\)
0.716498 + 0.697589i \(0.245744\pi\)
\(12\) 2.91933 0.842737
\(13\) −0.0580750 −0.0161071 −0.00805356 0.999968i \(-0.502564\pi\)
−0.00805356 + 0.999968i \(0.502564\pi\)
\(14\) −0.159746 −0.0426939
\(15\) 1.47853 0.381754
\(16\) 3.84754 0.961885
\(17\) 4.36259 1.05808 0.529042 0.848596i \(-0.322551\pi\)
0.529042 + 0.848596i \(0.322551\pi\)
\(18\) −0.130026 −0.0306474
\(19\) 3.34416 0.767203 0.383601 0.923499i \(-0.374684\pi\)
0.383601 + 0.923499i \(0.374684\pi\)
\(20\) 1.97448 0.441507
\(21\) 1.47853 0.322641
\(22\) 0.759226 0.161868
\(23\) −3.41396 −0.711860 −0.355930 0.934513i \(-0.615836\pi\)
−0.355930 + 0.934513i \(0.615836\pi\)
\(24\) 0.938729 0.191617
\(25\) 1.00000 0.200000
\(26\) −0.00927726 −0.00181942
\(27\) 5.63904 1.08523
\(28\) 1.97448 0.373142
\(29\) 6.44554 1.19691 0.598454 0.801157i \(-0.295782\pi\)
0.598454 + 0.801157i \(0.295782\pi\)
\(30\) 0.236189 0.0431220
\(31\) −2.13401 −0.383279 −0.191640 0.981465i \(-0.561380\pi\)
−0.191640 + 0.981465i \(0.561380\pi\)
\(32\) 1.88444 0.333126
\(33\) −7.02702 −1.22325
\(34\) 0.696907 0.119518
\(35\) 1.00000 0.169031
\(36\) 1.60713 0.267856
\(37\) −10.9458 −1.79947 −0.899735 0.436436i \(-0.856241\pi\)
−0.899735 + 0.436436i \(0.856241\pi\)
\(38\) 0.534216 0.0866613
\(39\) 0.0858656 0.0137495
\(40\) 0.634908 0.100388
\(41\) −3.88048 −0.606028 −0.303014 0.952986i \(-0.597993\pi\)
−0.303014 + 0.952986i \(0.597993\pi\)
\(42\) 0.236189 0.0364448
\(43\) 4.24610 0.647524 0.323762 0.946139i \(-0.395052\pi\)
0.323762 + 0.946139i \(0.395052\pi\)
\(44\) −9.38413 −1.41471
\(45\) 0.813953 0.121337
\(46\) −0.545366 −0.0804099
\(47\) 12.0801 1.76206 0.881031 0.473058i \(-0.156850\pi\)
0.881031 + 0.473058i \(0.156850\pi\)
\(48\) −5.68870 −0.821093
\(49\) 1.00000 0.142857
\(50\) 0.159746 0.0225915
\(51\) −6.45022 −0.903211
\(52\) 0.114668 0.0159016
\(53\) −3.29849 −0.453083 −0.226542 0.974002i \(-0.572742\pi\)
−0.226542 + 0.974002i \(0.572742\pi\)
\(54\) 0.900814 0.122585
\(55\) −4.75271 −0.640855
\(56\) 0.634908 0.0848431
\(57\) −4.94443 −0.654906
\(58\) 1.02965 0.135200
\(59\) −5.51131 −0.717512 −0.358756 0.933431i \(-0.616799\pi\)
−0.358756 + 0.933431i \(0.616799\pi\)
\(60\) −2.91933 −0.376884
\(61\) −1.47783 −0.189217 −0.0946084 0.995515i \(-0.530160\pi\)
−0.0946084 + 0.995515i \(0.530160\pi\)
\(62\) −0.340899 −0.0432942
\(63\) 0.813953 0.102548
\(64\) −7.39404 −0.924256
\(65\) 0.0580750 0.00720332
\(66\) −1.12254 −0.138175
\(67\) 15.1741 1.85381 0.926904 0.375299i \(-0.122460\pi\)
0.926904 + 0.375299i \(0.122460\pi\)
\(68\) −8.61385 −1.04458
\(69\) 5.04764 0.607664
\(70\) 0.159746 0.0190933
\(71\) −4.33053 −0.513939 −0.256970 0.966419i \(-0.582724\pi\)
−0.256970 + 0.966419i \(0.582724\pi\)
\(72\) 0.516785 0.0609037
\(73\) −6.31946 −0.739637 −0.369819 0.929104i \(-0.620580\pi\)
−0.369819 + 0.929104i \(0.620580\pi\)
\(74\) −1.74854 −0.203264
\(75\) −1.47853 −0.170726
\(76\) −6.60298 −0.757414
\(77\) −4.75271 −0.541621
\(78\) 0.0137167 0.00155311
\(79\) −5.97180 −0.671880 −0.335940 0.941883i \(-0.609054\pi\)
−0.335940 + 0.941883i \(0.609054\pi\)
\(80\) −3.84754 −0.430168
\(81\) −5.89562 −0.655069
\(82\) −0.619891 −0.0684555
\(83\) 8.45930 0.928529 0.464264 0.885697i \(-0.346319\pi\)
0.464264 + 0.885697i \(0.346319\pi\)
\(84\) −2.91933 −0.318525
\(85\) −4.36259 −0.473189
\(86\) 0.678297 0.0731427
\(87\) −9.52992 −1.02171
\(88\) −3.01753 −0.321670
\(89\) −10.3162 −1.09352 −0.546759 0.837290i \(-0.684138\pi\)
−0.546759 + 0.837290i \(0.684138\pi\)
\(90\) 0.130026 0.0137059
\(91\) 0.0580750 0.00608792
\(92\) 6.74080 0.702777
\(93\) 3.15519 0.327178
\(94\) 1.92975 0.199038
\(95\) −3.34416 −0.343103
\(96\) −2.78620 −0.284366
\(97\) 1.33005 0.135046 0.0675232 0.997718i \(-0.478490\pi\)
0.0675232 + 0.997718i \(0.478490\pi\)
\(98\) 0.159746 0.0161368
\(99\) −3.86848 −0.388797
\(100\) −1.97448 −0.197448
\(101\) −15.6516 −1.55739 −0.778697 0.627400i \(-0.784119\pi\)
−0.778697 + 0.627400i \(0.784119\pi\)
\(102\) −1.03040 −0.102024
\(103\) −14.8919 −1.46734 −0.733670 0.679506i \(-0.762194\pi\)
−0.733670 + 0.679506i \(0.762194\pi\)
\(104\) 0.0368723 0.00361562
\(105\) −1.47853 −0.144290
\(106\) −0.526921 −0.0511791
\(107\) 17.4104 1.68313 0.841564 0.540157i \(-0.181635\pi\)
0.841564 + 0.540157i \(0.181635\pi\)
\(108\) −11.1342 −1.07139
\(109\) 16.3258 1.56373 0.781866 0.623446i \(-0.214268\pi\)
0.781866 + 0.623446i \(0.214268\pi\)
\(110\) −0.759226 −0.0723894
\(111\) 16.1836 1.53608
\(112\) −3.84754 −0.363558
\(113\) −1.47043 −0.138326 −0.0691630 0.997605i \(-0.522033\pi\)
−0.0691630 + 0.997605i \(0.522033\pi\)
\(114\) −0.789854 −0.0739766
\(115\) 3.41396 0.318353
\(116\) −12.7266 −1.18164
\(117\) 0.0472703 0.00437014
\(118\) −0.880410 −0.0810483
\(119\) −4.36259 −0.399918
\(120\) −0.938729 −0.0856939
\(121\) 11.5882 1.05348
\(122\) −0.236077 −0.0213734
\(123\) 5.73739 0.517323
\(124\) 4.21356 0.378389
\(125\) −1.00000 −0.0894427
\(126\) 0.130026 0.0115836
\(127\) −18.1014 −1.60624 −0.803121 0.595816i \(-0.796829\pi\)
−0.803121 + 0.595816i \(0.796829\pi\)
\(128\) −4.95006 −0.437527
\(129\) −6.27798 −0.552745
\(130\) 0.00927726 0.000813669 0
\(131\) 1.83833 0.160616 0.0803078 0.996770i \(-0.474410\pi\)
0.0803078 + 0.996770i \(0.474410\pi\)
\(132\) 13.8747 1.20764
\(133\) −3.34416 −0.289975
\(134\) 2.42400 0.209401
\(135\) −5.63904 −0.485331
\(136\) −2.76984 −0.237512
\(137\) 17.1057 1.46143 0.730717 0.682680i \(-0.239186\pi\)
0.730717 + 0.682680i \(0.239186\pi\)
\(138\) 0.806340 0.0686402
\(139\) 5.47133 0.464072 0.232036 0.972707i \(-0.425461\pi\)
0.232036 + 0.972707i \(0.425461\pi\)
\(140\) −1.97448 −0.166874
\(141\) −17.8608 −1.50415
\(142\) −0.691785 −0.0580533
\(143\) −0.276014 −0.0230814
\(144\) −3.13171 −0.260976
\(145\) −6.44554 −0.535273
\(146\) −1.00951 −0.0835476
\(147\) −1.47853 −0.121947
\(148\) 21.6122 1.77651
\(149\) −13.4587 −1.10258 −0.551290 0.834314i \(-0.685864\pi\)
−0.551290 + 0.834314i \(0.685864\pi\)
\(150\) −0.236189 −0.0192848
\(151\) −17.8102 −1.44938 −0.724689 0.689076i \(-0.758016\pi\)
−0.724689 + 0.689076i \(0.758016\pi\)
\(152\) −2.12323 −0.172217
\(153\) −3.55094 −0.287077
\(154\) −0.759226 −0.0611802
\(155\) 2.13401 0.171408
\(156\) −0.169540 −0.0135741
\(157\) −10.9663 −0.875206 −0.437603 0.899168i \(-0.644172\pi\)
−0.437603 + 0.899168i \(0.644172\pi\)
\(158\) −0.953972 −0.0758939
\(159\) 4.87692 0.386765
\(160\) −1.88444 −0.148978
\(161\) 3.41396 0.269058
\(162\) −0.941802 −0.0739950
\(163\) −2.89044 −0.226397 −0.113198 0.993572i \(-0.536110\pi\)
−0.113198 + 0.993572i \(0.536110\pi\)
\(164\) 7.66193 0.598296
\(165\) 7.02702 0.547053
\(166\) 1.35134 0.104884
\(167\) 4.33629 0.335552 0.167776 0.985825i \(-0.446341\pi\)
0.167776 + 0.985825i \(0.446341\pi\)
\(168\) −0.938729 −0.0724245
\(169\) −12.9966 −0.999741
\(170\) −0.696907 −0.0534503
\(171\) −2.72199 −0.208156
\(172\) −8.38384 −0.639262
\(173\) 23.3083 1.77210 0.886049 0.463592i \(-0.153440\pi\)
0.886049 + 0.463592i \(0.153440\pi\)
\(174\) −1.52237 −0.115410
\(175\) −1.00000 −0.0755929
\(176\) 18.2862 1.37838
\(177\) 8.14863 0.612489
\(178\) −1.64798 −0.123521
\(179\) 22.9899 1.71834 0.859172 0.511687i \(-0.170979\pi\)
0.859172 + 0.511687i \(0.170979\pi\)
\(180\) −1.60713 −0.119789
\(181\) −5.50437 −0.409136 −0.204568 0.978852i \(-0.565579\pi\)
−0.204568 + 0.978852i \(0.565579\pi\)
\(182\) 0.00927726 0.000687676 0
\(183\) 2.18501 0.161521
\(184\) 2.16755 0.159794
\(185\) 10.9458 0.804748
\(186\) 0.504029 0.0369572
\(187\) 20.7341 1.51623
\(188\) −23.8519 −1.73958
\(189\) −5.63904 −0.410180
\(190\) −0.534216 −0.0387561
\(191\) −4.51929 −0.327005 −0.163502 0.986543i \(-0.552279\pi\)
−0.163502 + 0.986543i \(0.552279\pi\)
\(192\) 10.9323 0.788971
\(193\) 15.0299 1.08187 0.540937 0.841063i \(-0.318070\pi\)
0.540937 + 0.841063i \(0.318070\pi\)
\(194\) 0.212471 0.0152545
\(195\) −0.0858656 −0.00614896
\(196\) −1.97448 −0.141034
\(197\) 10.7333 0.764719 0.382360 0.924014i \(-0.375112\pi\)
0.382360 + 0.924014i \(0.375112\pi\)
\(198\) −0.617974 −0.0439175
\(199\) 19.5730 1.38750 0.693748 0.720218i \(-0.255958\pi\)
0.693748 + 0.720218i \(0.255958\pi\)
\(200\) −0.634908 −0.0448947
\(201\) −22.4353 −1.58246
\(202\) −2.50028 −0.175919
\(203\) −6.44554 −0.452388
\(204\) 12.7358 0.891686
\(205\) 3.88048 0.271024
\(206\) −2.37892 −0.165747
\(207\) 2.77880 0.193140
\(208\) −0.223446 −0.0154932
\(209\) 15.8938 1.09940
\(210\) −0.236189 −0.0162986
\(211\) 4.99039 0.343553 0.171776 0.985136i \(-0.445049\pi\)
0.171776 + 0.985136i \(0.445049\pi\)
\(212\) 6.51282 0.447302
\(213\) 6.40281 0.438713
\(214\) 2.78125 0.190122
\(215\) −4.24610 −0.289582
\(216\) −3.58027 −0.243606
\(217\) 2.13401 0.144866
\(218\) 2.60799 0.176635
\(219\) 9.34351 0.631376
\(220\) 9.38413 0.632678
\(221\) −0.253358 −0.0170427
\(222\) 2.58527 0.173512
\(223\) −1.21294 −0.0812243 −0.0406121 0.999175i \(-0.512931\pi\)
−0.0406121 + 0.999175i \(0.512931\pi\)
\(224\) −1.88444 −0.125910
\(225\) −0.813953 −0.0542635
\(226\) −0.234895 −0.0156250
\(227\) 21.4605 1.42438 0.712192 0.701985i \(-0.247702\pi\)
0.712192 + 0.701985i \(0.247702\pi\)
\(228\) 9.76269 0.646550
\(229\) 1.00000 0.0660819
\(230\) 0.545366 0.0359604
\(231\) 7.02702 0.462344
\(232\) −4.09232 −0.268674
\(233\) 8.28070 0.542486 0.271243 0.962511i \(-0.412565\pi\)
0.271243 + 0.962511i \(0.412565\pi\)
\(234\) 0.00755125 0.000493640 0
\(235\) −12.0801 −0.788018
\(236\) 10.8820 0.708357
\(237\) 8.82948 0.573537
\(238\) −0.696907 −0.0451737
\(239\) −18.6568 −1.20681 −0.603405 0.797435i \(-0.706190\pi\)
−0.603405 + 0.797435i \(0.706190\pi\)
\(240\) 5.68870 0.367204
\(241\) 16.5944 1.06894 0.534469 0.845188i \(-0.320512\pi\)
0.534469 + 0.845188i \(0.320512\pi\)
\(242\) 1.85118 0.118998
\(243\) −8.20027 −0.526047
\(244\) 2.91795 0.186802
\(245\) −1.00000 −0.0638877
\(246\) 0.916526 0.0584356
\(247\) −0.194212 −0.0123574
\(248\) 1.35490 0.0860361
\(249\) −12.5073 −0.792619
\(250\) −0.159746 −0.0101032
\(251\) −4.90982 −0.309905 −0.154952 0.987922i \(-0.549522\pi\)
−0.154952 + 0.987922i \(0.549522\pi\)
\(252\) −1.60713 −0.101240
\(253\) −16.2256 −1.02009
\(254\) −2.89163 −0.181437
\(255\) 6.45022 0.403928
\(256\) 13.9973 0.874834
\(257\) 24.8189 1.54816 0.774079 0.633089i \(-0.218213\pi\)
0.774079 + 0.633089i \(0.218213\pi\)
\(258\) −1.00288 −0.0624367
\(259\) 10.9458 0.680136
\(260\) −0.114668 −0.00711141
\(261\) −5.24637 −0.324742
\(262\) 0.293666 0.0181427
\(263\) −26.8328 −1.65458 −0.827290 0.561775i \(-0.810119\pi\)
−0.827290 + 0.561775i \(0.810119\pi\)
\(264\) 4.46151 0.274587
\(265\) 3.29849 0.202625
\(266\) −0.534216 −0.0327549
\(267\) 15.2528 0.933458
\(268\) −29.9609 −1.83015
\(269\) 16.3660 0.997855 0.498927 0.866644i \(-0.333727\pi\)
0.498927 + 0.866644i \(0.333727\pi\)
\(270\) −0.900814 −0.0548218
\(271\) −2.24089 −0.136124 −0.0680621 0.997681i \(-0.521682\pi\)
−0.0680621 + 0.997681i \(0.521682\pi\)
\(272\) 16.7852 1.01775
\(273\) −0.0858656 −0.00519682
\(274\) 2.73256 0.165080
\(275\) 4.75271 0.286599
\(276\) −9.96646 −0.599911
\(277\) −28.0439 −1.68500 −0.842498 0.538699i \(-0.818916\pi\)
−0.842498 + 0.538699i \(0.818916\pi\)
\(278\) 0.874023 0.0524204
\(279\) 1.73698 0.103990
\(280\) −0.634908 −0.0379430
\(281\) −1.03182 −0.0615534 −0.0307767 0.999526i \(-0.509798\pi\)
−0.0307767 + 0.999526i \(0.509798\pi\)
\(282\) −2.85319 −0.169905
\(283\) 18.9214 1.12476 0.562379 0.826880i \(-0.309886\pi\)
0.562379 + 0.826880i \(0.309886\pi\)
\(284\) 8.55055 0.507382
\(285\) 4.94443 0.292883
\(286\) −0.0440921 −0.00260722
\(287\) 3.88048 0.229057
\(288\) −1.53385 −0.0903829
\(289\) 2.03220 0.119541
\(290\) −1.02965 −0.0604631
\(291\) −1.96652 −0.115280
\(292\) 12.4777 0.730200
\(293\) −8.20791 −0.479511 −0.239756 0.970833i \(-0.577067\pi\)
−0.239756 + 0.970833i \(0.577067\pi\)
\(294\) −0.236189 −0.0137748
\(295\) 5.51131 0.320881
\(296\) 6.94954 0.403934
\(297\) 26.8007 1.55513
\(298\) −2.14997 −0.124545
\(299\) 0.198266 0.0114660
\(300\) 2.91933 0.168547
\(301\) −4.24610 −0.244741
\(302\) −2.84512 −0.163718
\(303\) 23.1414 1.32944
\(304\) 12.8668 0.737960
\(305\) 1.47783 0.0846203
\(306\) −0.567249 −0.0324275
\(307\) −14.2145 −0.811264 −0.405632 0.914036i \(-0.632949\pi\)
−0.405632 + 0.914036i \(0.632949\pi\)
\(308\) 9.38413 0.534711
\(309\) 22.0181 1.25256
\(310\) 0.340899 0.0193618
\(311\) 13.4016 0.759934 0.379967 0.925000i \(-0.375935\pi\)
0.379967 + 0.925000i \(0.375935\pi\)
\(312\) −0.0545167 −0.00308640
\(313\) −5.29159 −0.299098 −0.149549 0.988754i \(-0.547782\pi\)
−0.149549 + 0.988754i \(0.547782\pi\)
\(314\) −1.75182 −0.0988611
\(315\) −0.813953 −0.0458610
\(316\) 11.7912 0.663308
\(317\) −20.6933 −1.16225 −0.581124 0.813815i \(-0.697387\pi\)
−0.581124 + 0.813815i \(0.697387\pi\)
\(318\) 0.779068 0.0436880
\(319\) 30.6338 1.71516
\(320\) 7.39404 0.413340
\(321\) −25.7418 −1.43677
\(322\) 0.545366 0.0303921
\(323\) 14.5892 0.811765
\(324\) 11.6408 0.646711
\(325\) −0.0580750 −0.00322142
\(326\) −0.461736 −0.0255732
\(327\) −24.1382 −1.33485
\(328\) 2.46374 0.136037
\(329\) −12.0801 −0.665997
\(330\) 1.12254 0.0617937
\(331\) 1.13907 0.0626090 0.0313045 0.999510i \(-0.490034\pi\)
0.0313045 + 0.999510i \(0.490034\pi\)
\(332\) −16.7027 −0.916681
\(333\) 8.90933 0.488228
\(334\) 0.692705 0.0379031
\(335\) −15.1741 −0.829048
\(336\) 5.68870 0.310344
\(337\) 0.408569 0.0222562 0.0111281 0.999938i \(-0.496458\pi\)
0.0111281 + 0.999938i \(0.496458\pi\)
\(338\) −2.07616 −0.112928
\(339\) 2.17407 0.118079
\(340\) 8.61385 0.467152
\(341\) −10.1423 −0.549237
\(342\) −0.434827 −0.0235127
\(343\) −1.00000 −0.0539949
\(344\) −2.69588 −0.145352
\(345\) −5.04764 −0.271756
\(346\) 3.72341 0.200172
\(347\) 14.1032 0.757099 0.378550 0.925581i \(-0.376423\pi\)
0.378550 + 0.925581i \(0.376423\pi\)
\(348\) 18.8167 1.00868
\(349\) 10.0733 0.539212 0.269606 0.962971i \(-0.413107\pi\)
0.269606 + 0.962971i \(0.413107\pi\)
\(350\) −0.159746 −0.00853878
\(351\) −0.327487 −0.0174800
\(352\) 8.95621 0.477368
\(353\) 15.5983 0.830213 0.415106 0.909773i \(-0.363744\pi\)
0.415106 + 0.909773i \(0.363744\pi\)
\(354\) 1.30171 0.0691852
\(355\) 4.33053 0.229841
\(356\) 20.3692 1.07956
\(357\) 6.45022 0.341382
\(358\) 3.67254 0.194100
\(359\) 19.6334 1.03621 0.518106 0.855316i \(-0.326637\pi\)
0.518106 + 0.855316i \(0.326637\pi\)
\(360\) −0.516785 −0.0272369
\(361\) −7.81660 −0.411400
\(362\) −0.879301 −0.0462150
\(363\) −17.1335 −0.899278
\(364\) −0.114668 −0.00601024
\(365\) 6.31946 0.330776
\(366\) 0.349047 0.0182450
\(367\) 31.1137 1.62412 0.812061 0.583572i \(-0.198345\pi\)
0.812061 + 0.583572i \(0.198345\pi\)
\(368\) −13.1353 −0.684727
\(369\) 3.15852 0.164426
\(370\) 1.74854 0.0909023
\(371\) 3.29849 0.171249
\(372\) −6.22987 −0.323004
\(373\) 23.7019 1.22724 0.613618 0.789603i \(-0.289714\pi\)
0.613618 + 0.789603i \(0.289714\pi\)
\(374\) 3.31219 0.171269
\(375\) 1.47853 0.0763509
\(376\) −7.66974 −0.395537
\(377\) −0.374325 −0.0192787
\(378\) −0.900814 −0.0463329
\(379\) −21.2814 −1.09315 −0.546577 0.837409i \(-0.684069\pi\)
−0.546577 + 0.837409i \(0.684069\pi\)
\(380\) 6.60298 0.338726
\(381\) 26.7635 1.37114
\(382\) −0.721939 −0.0369376
\(383\) 3.49249 0.178458 0.0892290 0.996011i \(-0.471560\pi\)
0.0892290 + 0.996011i \(0.471560\pi\)
\(384\) 7.31880 0.373486
\(385\) 4.75271 0.242220
\(386\) 2.40096 0.122206
\(387\) −3.45612 −0.175685
\(388\) −2.62617 −0.133323
\(389\) −9.56486 −0.484958 −0.242479 0.970157i \(-0.577961\pi\)
−0.242479 + 0.970157i \(0.577961\pi\)
\(390\) −0.0137167 −0.000694572 0
\(391\) −14.8937 −0.753207
\(392\) −0.634908 −0.0320677
\(393\) −2.71802 −0.137106
\(394\) 1.71461 0.0863807
\(395\) 5.97180 0.300474
\(396\) 7.63824 0.383836
\(397\) 0.337383 0.0169328 0.00846639 0.999964i \(-0.497305\pi\)
0.00846639 + 0.999964i \(0.497305\pi\)
\(398\) 3.12672 0.156728
\(399\) 4.94443 0.247531
\(400\) 3.84754 0.192377
\(401\) 9.95891 0.497324 0.248662 0.968590i \(-0.420009\pi\)
0.248662 + 0.968590i \(0.420009\pi\)
\(402\) −3.58395 −0.178751
\(403\) 0.123933 0.00617352
\(404\) 30.9038 1.53752
\(405\) 5.89562 0.292956
\(406\) −1.02965 −0.0511007
\(407\) −52.0220 −2.57863
\(408\) 4.09529 0.202747
\(409\) 4.42521 0.218812 0.109406 0.993997i \(-0.465105\pi\)
0.109406 + 0.993997i \(0.465105\pi\)
\(410\) 0.619891 0.0306142
\(411\) −25.2912 −1.24752
\(412\) 29.4037 1.44862
\(413\) 5.51131 0.271194
\(414\) 0.443902 0.0218166
\(415\) −8.45930 −0.415251
\(416\) −0.109439 −0.00536570
\(417\) −8.08952 −0.396145
\(418\) 2.53897 0.124185
\(419\) 3.84514 0.187848 0.0939238 0.995579i \(-0.470059\pi\)
0.0939238 + 0.995579i \(0.470059\pi\)
\(420\) 2.91933 0.142449
\(421\) 26.1696 1.27543 0.637715 0.770273i \(-0.279880\pi\)
0.637715 + 0.770273i \(0.279880\pi\)
\(422\) 0.797195 0.0388068
\(423\) −9.83262 −0.478079
\(424\) 2.09424 0.101705
\(425\) 4.36259 0.211617
\(426\) 1.02282 0.0495560
\(427\) 1.47783 0.0715172
\(428\) −34.3765 −1.66165
\(429\) 0.408094 0.0197030
\(430\) −0.678297 −0.0327104
\(431\) −33.5690 −1.61696 −0.808481 0.588522i \(-0.799710\pi\)
−0.808481 + 0.588522i \(0.799710\pi\)
\(432\) 21.6964 1.04387
\(433\) −28.2818 −1.35914 −0.679568 0.733613i \(-0.737833\pi\)
−0.679568 + 0.733613i \(0.737833\pi\)
\(434\) 0.340899 0.0163637
\(435\) 9.52992 0.456925
\(436\) −32.2351 −1.54378
\(437\) −11.4168 −0.546141
\(438\) 1.49259 0.0713186
\(439\) 18.7753 0.896096 0.448048 0.894009i \(-0.352119\pi\)
0.448048 + 0.894009i \(0.352119\pi\)
\(440\) 3.01753 0.143855
\(441\) −0.813953 −0.0387597
\(442\) −0.0404729 −0.00192510
\(443\) −7.92798 −0.376669 −0.188335 0.982105i \(-0.560309\pi\)
−0.188335 + 0.982105i \(0.560309\pi\)
\(444\) −31.9542 −1.51648
\(445\) 10.3162 0.489036
\(446\) −0.193762 −0.00917489
\(447\) 19.8991 0.941194
\(448\) 7.39404 0.349336
\(449\) 14.8159 0.699206 0.349603 0.936898i \(-0.386317\pi\)
0.349603 + 0.936898i \(0.386317\pi\)
\(450\) −0.130026 −0.00612947
\(451\) −18.4428 −0.868436
\(452\) 2.90333 0.136561
\(453\) 26.3330 1.23723
\(454\) 3.42823 0.160895
\(455\) −0.0580750 −0.00272260
\(456\) 3.13926 0.147009
\(457\) 13.6412 0.638110 0.319055 0.947736i \(-0.396635\pi\)
0.319055 + 0.947736i \(0.396635\pi\)
\(458\) 0.159746 0.00746444
\(459\) 24.6008 1.14827
\(460\) −6.74080 −0.314291
\(461\) 29.8106 1.38842 0.694210 0.719773i \(-0.255754\pi\)
0.694210 + 0.719773i \(0.255754\pi\)
\(462\) 1.12254 0.0522252
\(463\) −5.05076 −0.234729 −0.117364 0.993089i \(-0.537445\pi\)
−0.117364 + 0.993089i \(0.537445\pi\)
\(464\) 24.7995 1.15129
\(465\) −3.15519 −0.146319
\(466\) 1.32281 0.0612779
\(467\) 34.0421 1.57528 0.787641 0.616134i \(-0.211302\pi\)
0.787641 + 0.616134i \(0.211302\pi\)
\(468\) −0.0933344 −0.00431438
\(469\) −15.1741 −0.700673
\(470\) −1.92975 −0.0890126
\(471\) 16.2140 0.747101
\(472\) 3.49917 0.161063
\(473\) 20.1805 0.927899
\(474\) 1.41047 0.0647853
\(475\) 3.34416 0.153441
\(476\) 8.61385 0.394815
\(477\) 2.68482 0.122929
\(478\) −2.98036 −0.136318
\(479\) 7.92487 0.362096 0.181048 0.983474i \(-0.442051\pi\)
0.181048 + 0.983474i \(0.442051\pi\)
\(480\) 2.78620 0.127172
\(481\) 0.635675 0.0289843
\(482\) 2.65089 0.120745
\(483\) −5.04764 −0.229675
\(484\) −22.8808 −1.04003
\(485\) −1.33005 −0.0603946
\(486\) −1.30996 −0.0594210
\(487\) −29.0238 −1.31519 −0.657597 0.753369i \(-0.728427\pi\)
−0.657597 + 0.753369i \(0.728427\pi\)
\(488\) 0.938285 0.0424742
\(489\) 4.27360 0.193259
\(490\) −0.159746 −0.00721659
\(491\) 1.64632 0.0742973 0.0371486 0.999310i \(-0.488172\pi\)
0.0371486 + 0.999310i \(0.488172\pi\)
\(492\) −11.3284 −0.510723
\(493\) 28.1193 1.26643
\(494\) −0.0310246 −0.00139586
\(495\) 3.86848 0.173875
\(496\) −8.21068 −0.368670
\(497\) 4.33053 0.194251
\(498\) −1.99799 −0.0895323
\(499\) −10.8448 −0.485479 −0.242740 0.970091i \(-0.578046\pi\)
−0.242740 + 0.970091i \(0.578046\pi\)
\(500\) 1.97448 0.0883015
\(501\) −6.41133 −0.286437
\(502\) −0.784324 −0.0350061
\(503\) −25.3078 −1.12842 −0.564210 0.825632i \(-0.690819\pi\)
−0.564210 + 0.825632i \(0.690819\pi\)
\(504\) −0.516785 −0.0230194
\(505\) 15.6516 0.696488
\(506\) −2.59197 −0.115227
\(507\) 19.2159 0.853408
\(508\) 35.7409 1.58575
\(509\) −26.7371 −1.18510 −0.592549 0.805534i \(-0.701879\pi\)
−0.592549 + 0.805534i \(0.701879\pi\)
\(510\) 1.03040 0.0456267
\(511\) 6.31946 0.279557
\(512\) 12.1361 0.536346
\(513\) 18.8578 0.832594
\(514\) 3.96472 0.174876
\(515\) 14.8919 0.656214
\(516\) 12.3958 0.545693
\(517\) 57.4132 2.52503
\(518\) 1.74854 0.0768265
\(519\) −34.4620 −1.51271
\(520\) −0.0368723 −0.00161696
\(521\) −33.4348 −1.46481 −0.732403 0.680871i \(-0.761601\pi\)
−0.732403 + 0.680871i \(0.761601\pi\)
\(522\) −0.838086 −0.0366820
\(523\) −5.76180 −0.251946 −0.125973 0.992034i \(-0.540205\pi\)
−0.125973 + 0.992034i \(0.540205\pi\)
\(524\) −3.62975 −0.158566
\(525\) 1.47853 0.0645283
\(526\) −4.28643 −0.186897
\(527\) −9.30980 −0.405541
\(528\) −27.0367 −1.17662
\(529\) −11.3449 −0.493256
\(530\) 0.526921 0.0228880
\(531\) 4.48595 0.194674
\(532\) 6.60298 0.286275
\(533\) 0.225359 0.00976137
\(534\) 2.43658 0.105441
\(535\) −17.4104 −0.752718
\(536\) −9.63413 −0.416131
\(537\) −33.9912 −1.46683
\(538\) 2.61441 0.112715
\(539\) 4.75271 0.204714
\(540\) 11.1342 0.479139
\(541\) 4.21360 0.181157 0.0905784 0.995889i \(-0.471128\pi\)
0.0905784 + 0.995889i \(0.471128\pi\)
\(542\) −0.357973 −0.0153762
\(543\) 8.13836 0.349251
\(544\) 8.22106 0.352475
\(545\) −16.3258 −0.699322
\(546\) −0.0137167 −0.000587020 0
\(547\) −13.9530 −0.596588 −0.298294 0.954474i \(-0.596418\pi\)
−0.298294 + 0.954474i \(0.596418\pi\)
\(548\) −33.7748 −1.44279
\(549\) 1.20288 0.0513378
\(550\) 0.759226 0.0323735
\(551\) 21.5549 0.918270
\(552\) −3.20478 −0.136405
\(553\) 5.97180 0.253947
\(554\) −4.47991 −0.190333
\(555\) −16.1836 −0.686956
\(556\) −10.8030 −0.458151
\(557\) 15.1591 0.642311 0.321156 0.947026i \(-0.395929\pi\)
0.321156 + 0.947026i \(0.395929\pi\)
\(558\) 0.277476 0.0117465
\(559\) −0.246592 −0.0104297
\(560\) 3.84754 0.162588
\(561\) −30.6560 −1.29430
\(562\) −0.164830 −0.00695292
\(563\) 5.51360 0.232370 0.116185 0.993228i \(-0.462933\pi\)
0.116185 + 0.993228i \(0.462933\pi\)
\(564\) 35.2657 1.48496
\(565\) 1.47043 0.0618613
\(566\) 3.02261 0.127050
\(567\) 5.89562 0.247593
\(568\) 2.74949 0.115366
\(569\) −4.44384 −0.186295 −0.0931477 0.995652i \(-0.529693\pi\)
−0.0931477 + 0.995652i \(0.529693\pi\)
\(570\) 0.789854 0.0330833
\(571\) 44.6599 1.86896 0.934480 0.356017i \(-0.115865\pi\)
0.934480 + 0.356017i \(0.115865\pi\)
\(572\) 0.544984 0.0227869
\(573\) 6.68191 0.279141
\(574\) 0.619891 0.0258737
\(575\) −3.41396 −0.142372
\(576\) 6.01840 0.250767
\(577\) 8.76563 0.364918 0.182459 0.983213i \(-0.441594\pi\)
0.182459 + 0.983213i \(0.441594\pi\)
\(578\) 0.324636 0.0135031
\(579\) −22.2221 −0.923520
\(580\) 12.7266 0.528444
\(581\) −8.45930 −0.350951
\(582\) −0.314144 −0.0130217
\(583\) −15.6768 −0.649266
\(584\) 4.01227 0.166029
\(585\) −0.0472703 −0.00195439
\(586\) −1.31118 −0.0541644
\(587\) 26.9779 1.11350 0.556748 0.830681i \(-0.312049\pi\)
0.556748 + 0.830681i \(0.312049\pi\)
\(588\) 2.91933 0.120391
\(589\) −7.13646 −0.294053
\(590\) 0.880410 0.0362459
\(591\) −15.8696 −0.652786
\(592\) −42.1142 −1.73088
\(593\) −6.84484 −0.281084 −0.140542 0.990075i \(-0.544884\pi\)
−0.140542 + 0.990075i \(0.544884\pi\)
\(594\) 4.28131 0.175664
\(595\) 4.36259 0.178849
\(596\) 26.5739 1.08851
\(597\) −28.9393 −1.18441
\(598\) 0.0316722 0.00129517
\(599\) 34.8421 1.42361 0.711805 0.702378i \(-0.247878\pi\)
0.711805 + 0.702378i \(0.247878\pi\)
\(600\) 0.938729 0.0383235
\(601\) −38.1667 −1.55685 −0.778426 0.627737i \(-0.783981\pi\)
−0.778426 + 0.627737i \(0.783981\pi\)
\(602\) −0.678297 −0.0276453
\(603\) −12.3510 −0.502971
\(604\) 35.1660 1.43088
\(605\) −11.5882 −0.471129
\(606\) 3.69674 0.150170
\(607\) 9.69449 0.393487 0.196744 0.980455i \(-0.436963\pi\)
0.196744 + 0.980455i \(0.436963\pi\)
\(608\) 6.30188 0.255575
\(609\) 9.52992 0.386172
\(610\) 0.236077 0.00955850
\(611\) −0.701552 −0.0283817
\(612\) 7.01127 0.283414
\(613\) 18.3526 0.741253 0.370627 0.928782i \(-0.379143\pi\)
0.370627 + 0.928782i \(0.379143\pi\)
\(614\) −2.27071 −0.0916384
\(615\) −5.73739 −0.231354
\(616\) 3.01753 0.121580
\(617\) 11.3820 0.458222 0.229111 0.973400i \(-0.426418\pi\)
0.229111 + 0.973400i \(0.426418\pi\)
\(618\) 3.51730 0.141487
\(619\) −29.3186 −1.17841 −0.589207 0.807982i \(-0.700560\pi\)
−0.589207 + 0.807982i \(0.700560\pi\)
\(620\) −4.21356 −0.169221
\(621\) −19.2514 −0.772534
\(622\) 2.14085 0.0858402
\(623\) 10.3162 0.413311
\(624\) 0.330371 0.0132254
\(625\) 1.00000 0.0400000
\(626\) −0.845310 −0.0337854
\(627\) −23.4995 −0.938478
\(628\) 21.6527 0.864039
\(629\) −47.7519 −1.90399
\(630\) −0.130026 −0.00518035
\(631\) −13.7781 −0.548497 −0.274248 0.961659i \(-0.588429\pi\)
−0.274248 + 0.961659i \(0.588429\pi\)
\(632\) 3.79154 0.150819
\(633\) −7.37843 −0.293266
\(634\) −3.30567 −0.131285
\(635\) 18.1014 0.718334
\(636\) −9.62938 −0.381830
\(637\) −0.0580750 −0.00230102
\(638\) 4.89363 0.193741
\(639\) 3.52485 0.139441
\(640\) 4.95006 0.195668
\(641\) 40.9215 1.61630 0.808150 0.588976i \(-0.200469\pi\)
0.808150 + 0.588976i \(0.200469\pi\)
\(642\) −4.11215 −0.162294
\(643\) 20.5903 0.812001 0.406001 0.913873i \(-0.366923\pi\)
0.406001 + 0.913873i \(0.366923\pi\)
\(644\) −6.74080 −0.265625
\(645\) 6.27798 0.247195
\(646\) 2.33057 0.0916949
\(647\) 3.30656 0.129994 0.0649971 0.997885i \(-0.479296\pi\)
0.0649971 + 0.997885i \(0.479296\pi\)
\(648\) 3.74318 0.147046
\(649\) −26.1937 −1.02819
\(650\) −0.00927726 −0.000363884 0
\(651\) −3.15519 −0.123662
\(652\) 5.70712 0.223508
\(653\) 29.7186 1.16298 0.581490 0.813554i \(-0.302470\pi\)
0.581490 + 0.813554i \(0.302470\pi\)
\(654\) −3.85599 −0.150781
\(655\) −1.83833 −0.0718294
\(656\) −14.9303 −0.582929
\(657\) 5.14374 0.200677
\(658\) −1.92975 −0.0752294
\(659\) −7.97907 −0.310821 −0.155410 0.987850i \(-0.549670\pi\)
−0.155410 + 0.987850i \(0.549670\pi\)
\(660\) −13.8747 −0.540072
\(661\) 22.5312 0.876362 0.438181 0.898887i \(-0.355623\pi\)
0.438181 + 0.898887i \(0.355623\pi\)
\(662\) 0.181962 0.00707216
\(663\) 0.374597 0.0145481
\(664\) −5.37087 −0.208430
\(665\) 3.34416 0.129681
\(666\) 1.42323 0.0551490
\(667\) −22.0048 −0.852030
\(668\) −8.56192 −0.331271
\(669\) 1.79336 0.0693354
\(670\) −2.42400 −0.0936472
\(671\) −7.02370 −0.271147
\(672\) 2.78620 0.107480
\(673\) −10.1480 −0.391176 −0.195588 0.980686i \(-0.562661\pi\)
−0.195588 + 0.980686i \(0.562661\pi\)
\(674\) 0.0652673 0.00251400
\(675\) 5.63904 0.217047
\(676\) 25.6616 0.986984
\(677\) −44.2824 −1.70191 −0.850956 0.525237i \(-0.823977\pi\)
−0.850956 + 0.525237i \(0.823977\pi\)
\(678\) 0.347299 0.0133379
\(679\) −1.33005 −0.0510428
\(680\) 2.76984 0.106219
\(681\) −31.7300 −1.21590
\(682\) −1.62019 −0.0620405
\(683\) 38.6526 1.47900 0.739500 0.673157i \(-0.235062\pi\)
0.739500 + 0.673157i \(0.235062\pi\)
\(684\) 5.37451 0.205500
\(685\) −17.1057 −0.653574
\(686\) −0.159746 −0.00609913
\(687\) −1.47853 −0.0564094
\(688\) 16.3370 0.622843
\(689\) 0.191560 0.00729786
\(690\) −0.806340 −0.0306968
\(691\) −5.53294 −0.210483 −0.105241 0.994447i \(-0.533562\pi\)
−0.105241 + 0.994447i \(0.533562\pi\)
\(692\) −46.0218 −1.74949
\(693\) 3.86848 0.146951
\(694\) 2.25293 0.0855200
\(695\) −5.47133 −0.207539
\(696\) 6.05062 0.229348
\(697\) −16.9289 −0.641229
\(698\) 1.60917 0.0609080
\(699\) −12.2432 −0.463082
\(700\) 1.97448 0.0746284
\(701\) 16.9679 0.640867 0.320434 0.947271i \(-0.396171\pi\)
0.320434 + 0.947271i \(0.396171\pi\)
\(702\) −0.0523148 −0.00197450
\(703\) −36.6043 −1.38056
\(704\) −35.1417 −1.32445
\(705\) 17.8608 0.672675
\(706\) 2.49176 0.0937788
\(707\) 15.6516 0.588639
\(708\) −16.0893 −0.604674
\(709\) −25.6482 −0.963238 −0.481619 0.876381i \(-0.659951\pi\)
−0.481619 + 0.876381i \(0.659951\pi\)
\(710\) 0.691785 0.0259622
\(711\) 4.86077 0.182293
\(712\) 6.54985 0.245466
\(713\) 7.28541 0.272841
\(714\) 1.03040 0.0385616
\(715\) 0.276014 0.0103223
\(716\) −45.3931 −1.69642
\(717\) 27.5847 1.03017
\(718\) 3.13636 0.117048
\(719\) −43.5534 −1.62427 −0.812133 0.583472i \(-0.801694\pi\)
−0.812133 + 0.583472i \(0.801694\pi\)
\(720\) 3.13171 0.116712
\(721\) 14.8919 0.554602
\(722\) −1.24867 −0.0464707
\(723\) −24.5353 −0.912476
\(724\) 10.8683 0.403916
\(725\) 6.44554 0.239381
\(726\) −2.73702 −0.101580
\(727\) 34.5254 1.28047 0.640237 0.768177i \(-0.278836\pi\)
0.640237 + 0.768177i \(0.278836\pi\)
\(728\) −0.0368723 −0.00136658
\(729\) 29.8112 1.10412
\(730\) 1.00951 0.0373636
\(731\) 18.5240 0.685135
\(732\) −4.31427 −0.159460
\(733\) 13.1700 0.486446 0.243223 0.969970i \(-0.421795\pi\)
0.243223 + 0.969970i \(0.421795\pi\)
\(734\) 4.97029 0.183457
\(735\) 1.47853 0.0545364
\(736\) −6.43341 −0.237139
\(737\) 72.1179 2.65650
\(738\) 0.504562 0.0185732
\(739\) −16.9601 −0.623886 −0.311943 0.950101i \(-0.600980\pi\)
−0.311943 + 0.950101i \(0.600980\pi\)
\(740\) −21.6122 −0.794480
\(741\) 0.287148 0.0105487
\(742\) 0.526921 0.0193439
\(743\) −8.27151 −0.303452 −0.151726 0.988423i \(-0.548483\pi\)
−0.151726 + 0.988423i \(0.548483\pi\)
\(744\) −2.00326 −0.0734429
\(745\) 13.4587 0.493089
\(746\) 3.78628 0.138625
\(747\) −6.88547 −0.251926
\(748\) −40.9391 −1.49688
\(749\) −17.4104 −0.636163
\(750\) 0.236189 0.00862441
\(751\) 21.2591 0.775756 0.387878 0.921711i \(-0.373208\pi\)
0.387878 + 0.921711i \(0.373208\pi\)
\(752\) 46.4786 1.69490
\(753\) 7.25931 0.264544
\(754\) −0.0597970 −0.00217768
\(755\) 17.8102 0.648181
\(756\) 11.1342 0.404946
\(757\) −13.7496 −0.499738 −0.249869 0.968280i \(-0.580388\pi\)
−0.249869 + 0.968280i \(0.580388\pi\)
\(758\) −3.39962 −0.123480
\(759\) 23.9899 0.870780
\(760\) 2.12323 0.0770177
\(761\) −36.5443 −1.32473 −0.662365 0.749181i \(-0.730447\pi\)
−0.662365 + 0.749181i \(0.730447\pi\)
\(762\) 4.27536 0.154880
\(763\) −16.3258 −0.591035
\(764\) 8.92326 0.322832
\(765\) 3.55094 0.128385
\(766\) 0.557911 0.0201582
\(767\) 0.320070 0.0115570
\(768\) −20.6955 −0.746783
\(769\) −0.352002 −0.0126935 −0.00634675 0.999980i \(-0.502020\pi\)
−0.00634675 + 0.999980i \(0.502020\pi\)
\(770\) 0.759226 0.0273606
\(771\) −36.6954 −1.32155
\(772\) −29.6762 −1.06807
\(773\) 11.1063 0.399467 0.199733 0.979850i \(-0.435992\pi\)
0.199733 + 0.979850i \(0.435992\pi\)
\(774\) −0.552102 −0.0198449
\(775\) −2.13401 −0.0766558
\(776\) −0.844461 −0.0303144
\(777\) −16.1836 −0.580584
\(778\) −1.52795 −0.0547796
\(779\) −12.9769 −0.464947
\(780\) 0.169540 0.00607051
\(781\) −20.5817 −0.736473
\(782\) −2.37921 −0.0850804
\(783\) 36.3467 1.29892
\(784\) 3.84754 0.137412
\(785\) 10.9663 0.391404
\(786\) −0.434193 −0.0154872
\(787\) −23.8536 −0.850288 −0.425144 0.905126i \(-0.639777\pi\)
−0.425144 + 0.905126i \(0.639777\pi\)
\(788\) −21.1928 −0.754962
\(789\) 39.6730 1.41240
\(790\) 0.953972 0.0339408
\(791\) 1.47043 0.0522824
\(792\) 2.45613 0.0872747
\(793\) 0.0858250 0.00304774
\(794\) 0.0538956 0.00191268
\(795\) −4.87692 −0.172966
\(796\) −38.6466 −1.36979
\(797\) 54.5186 1.93115 0.965575 0.260126i \(-0.0837641\pi\)
0.965575 + 0.260126i \(0.0837641\pi\)
\(798\) 0.789854 0.0279605
\(799\) 52.7005 1.86441
\(800\) 1.88444 0.0666252
\(801\) 8.39692 0.296690
\(802\) 1.59090 0.0561765
\(803\) −30.0346 −1.05990
\(804\) 44.2981 1.56227
\(805\) −3.41396 −0.120326
\(806\) 0.0197977 0.000697345 0
\(807\) −24.1977 −0.851798
\(808\) 9.93733 0.349594
\(809\) −28.9252 −1.01696 −0.508478 0.861075i \(-0.669792\pi\)
−0.508478 + 0.861075i \(0.669792\pi\)
\(810\) 0.941802 0.0330916
\(811\) 34.9451 1.22709 0.613544 0.789660i \(-0.289743\pi\)
0.613544 + 0.789660i \(0.289743\pi\)
\(812\) 12.7266 0.446616
\(813\) 3.31322 0.116200
\(814\) −8.31031 −0.291276
\(815\) 2.89044 0.101248
\(816\) −24.8175 −0.868785
\(817\) 14.1996 0.496782
\(818\) 0.706909 0.0247165
\(819\) −0.0472703 −0.00165176
\(820\) −7.66193 −0.267566
\(821\) 37.6696 1.31468 0.657339 0.753595i \(-0.271682\pi\)
0.657339 + 0.753595i \(0.271682\pi\)
\(822\) −4.04017 −0.140917
\(823\) 5.24874 0.182960 0.0914798 0.995807i \(-0.470840\pi\)
0.0914798 + 0.995807i \(0.470840\pi\)
\(824\) 9.45497 0.329379
\(825\) −7.02702 −0.244649
\(826\) 0.880410 0.0306334
\(827\) −38.6477 −1.34391 −0.671956 0.740591i \(-0.734546\pi\)
−0.671956 + 0.740591i \(0.734546\pi\)
\(828\) −5.48669 −0.190676
\(829\) 31.8406 1.10587 0.552935 0.833224i \(-0.313508\pi\)
0.552935 + 0.833224i \(0.313508\pi\)
\(830\) −1.35134 −0.0469057
\(831\) 41.4638 1.43836
\(832\) 0.429409 0.0148871
\(833\) 4.36259 0.151155
\(834\) −1.29227 −0.0447476
\(835\) −4.33629 −0.150063
\(836\) −31.3820 −1.08537
\(837\) −12.0338 −0.415947
\(838\) 0.614246 0.0212188
\(839\) 38.0045 1.31206 0.656031 0.754734i \(-0.272234\pi\)
0.656031 + 0.754734i \(0.272234\pi\)
\(840\) 0.938729 0.0323892
\(841\) 12.5450 0.432587
\(842\) 4.18049 0.144069
\(843\) 1.52558 0.0525438
\(844\) −9.85343 −0.339169
\(845\) 12.9966 0.447098
\(846\) −1.57072 −0.0540026
\(847\) −11.5882 −0.398177
\(848\) −12.6911 −0.435814
\(849\) −27.9758 −0.960126
\(850\) 0.696907 0.0239037
\(851\) 37.3684 1.28097
\(852\) −12.6422 −0.433116
\(853\) 49.1986 1.68453 0.842263 0.539067i \(-0.181223\pi\)
0.842263 + 0.539067i \(0.181223\pi\)
\(854\) 0.236077 0.00807840
\(855\) 2.72199 0.0930900
\(856\) −11.0540 −0.377818
\(857\) 48.4228 1.65409 0.827046 0.562135i \(-0.190020\pi\)
0.827046 + 0.562135i \(0.190020\pi\)
\(858\) 0.0651914 0.00222560
\(859\) 10.8987 0.371860 0.185930 0.982563i \(-0.440470\pi\)
0.185930 + 0.982563i \(0.440470\pi\)
\(860\) 8.38384 0.285887
\(861\) −5.73739 −0.195530
\(862\) −5.36252 −0.182648
\(863\) −24.3339 −0.828335 −0.414167 0.910201i \(-0.635927\pi\)
−0.414167 + 0.910201i \(0.635927\pi\)
\(864\) 10.6265 0.361519
\(865\) −23.3083 −0.792506
\(866\) −4.51790 −0.153525
\(867\) −3.00467 −0.102044
\(868\) −4.21356 −0.143017
\(869\) −28.3822 −0.962802
\(870\) 1.52237 0.0516131
\(871\) −0.881235 −0.0298595
\(872\) −10.3654 −0.351017
\(873\) −1.08260 −0.0366405
\(874\) −1.82379 −0.0616907
\(875\) 1.00000 0.0338062
\(876\) −18.4486 −0.623320
\(877\) −29.3768 −0.991984 −0.495992 0.868327i \(-0.665196\pi\)
−0.495992 + 0.868327i \(0.665196\pi\)
\(878\) 2.99928 0.101221
\(879\) 12.1356 0.409325
\(880\) −18.2862 −0.616429
\(881\) 33.3076 1.12216 0.561080 0.827761i \(-0.310386\pi\)
0.561080 + 0.827761i \(0.310386\pi\)
\(882\) −0.130026 −0.00437819
\(883\) 8.77265 0.295223 0.147612 0.989045i \(-0.452841\pi\)
0.147612 + 0.989045i \(0.452841\pi\)
\(884\) 0.500250 0.0168252
\(885\) −8.14863 −0.273913
\(886\) −1.26646 −0.0425476
\(887\) 55.2610 1.85548 0.927742 0.373222i \(-0.121747\pi\)
0.927742 + 0.373222i \(0.121747\pi\)
\(888\) −10.2751 −0.344810
\(889\) 18.1014 0.607103
\(890\) 1.64798 0.0552403
\(891\) −28.0202 −0.938711
\(892\) 2.39492 0.0801879
\(893\) 40.3977 1.35186
\(894\) 3.17880 0.106315
\(895\) −22.9899 −0.768467
\(896\) 4.95006 0.165370
\(897\) −0.293142 −0.00978771
\(898\) 2.36678 0.0789805
\(899\) −13.7548 −0.458750
\(900\) 1.60713 0.0535711
\(901\) −14.3900 −0.479400
\(902\) −2.94616 −0.0980964
\(903\) 6.27798 0.208918
\(904\) 0.933585 0.0310506
\(905\) 5.50437 0.182971
\(906\) 4.20659 0.139754
\(907\) 56.3406 1.87076 0.935379 0.353648i \(-0.115059\pi\)
0.935379 + 0.353648i \(0.115059\pi\)
\(908\) −42.3734 −1.40621
\(909\) 12.7397 0.422548
\(910\) −0.00927726 −0.000307538 0
\(911\) −41.0937 −1.36149 −0.680747 0.732519i \(-0.738345\pi\)
−0.680747 + 0.732519i \(0.738345\pi\)
\(912\) −19.0239 −0.629944
\(913\) 40.2046 1.33058
\(914\) 2.17913 0.0720793
\(915\) −2.18501 −0.0722343
\(916\) −1.97448 −0.0652387
\(917\) −1.83833 −0.0607070
\(918\) 3.92988 0.129705
\(919\) −31.6676 −1.04462 −0.522308 0.852757i \(-0.674929\pi\)
−0.522308 + 0.852757i \(0.674929\pi\)
\(920\) −2.16755 −0.0714620
\(921\) 21.0165 0.692518
\(922\) 4.76213 0.156832
\(923\) 0.251496 0.00827808
\(924\) −13.8747 −0.456445
\(925\) −10.9458 −0.359894
\(926\) −0.806838 −0.0265143
\(927\) 12.1213 0.398115
\(928\) 12.1463 0.398721
\(929\) −26.3785 −0.865450 −0.432725 0.901526i \(-0.642448\pi\)
−0.432725 + 0.901526i \(0.642448\pi\)
\(930\) −0.504029 −0.0165278
\(931\) 3.34416 0.109600
\(932\) −16.3501 −0.535565
\(933\) −19.8146 −0.648701
\(934\) 5.43810 0.177940
\(935\) −20.7341 −0.678078
\(936\) −0.0300123 −0.000980982 0
\(937\) 50.7960 1.65943 0.829717 0.558185i \(-0.188502\pi\)
0.829717 + 0.558185i \(0.188502\pi\)
\(938\) −2.42400 −0.0791463
\(939\) 7.82376 0.255319
\(940\) 23.8519 0.777964
\(941\) 34.8829 1.13715 0.568576 0.822631i \(-0.307495\pi\)
0.568576 + 0.822631i \(0.307495\pi\)
\(942\) 2.59012 0.0843907
\(943\) 13.2478 0.431407
\(944\) −21.2050 −0.690163
\(945\) 5.63904 0.183438
\(946\) 3.22375 0.104813
\(947\) −31.3911 −1.02008 −0.510038 0.860152i \(-0.670369\pi\)
−0.510038 + 0.860152i \(0.670369\pi\)
\(948\) −17.4336 −0.566219
\(949\) 0.367003 0.0119134
\(950\) 0.534216 0.0173323
\(951\) 30.5956 0.992129
\(952\) 2.76984 0.0897711
\(953\) −13.8047 −0.447177 −0.223589 0.974684i \(-0.571777\pi\)
−0.223589 + 0.974684i \(0.571777\pi\)
\(954\) 0.428889 0.0138858
\(955\) 4.51929 0.146241
\(956\) 36.8376 1.19141
\(957\) −45.2929 −1.46411
\(958\) 1.26597 0.0409015
\(959\) −17.1057 −0.552370
\(960\) −10.9323 −0.352839
\(961\) −26.4460 −0.853097
\(962\) 0.101547 0.00327399
\(963\) −14.1713 −0.456662
\(964\) −32.7653 −1.05530
\(965\) −15.0299 −0.483829
\(966\) −0.806340 −0.0259436
\(967\) −10.3419 −0.332572 −0.166286 0.986078i \(-0.553178\pi\)
−0.166286 + 0.986078i \(0.553178\pi\)
\(968\) −7.35746 −0.236478
\(969\) −21.5705 −0.692946
\(970\) −0.212471 −0.00682202
\(971\) −10.5322 −0.337996 −0.168998 0.985616i \(-0.554053\pi\)
−0.168998 + 0.985616i \(0.554053\pi\)
\(972\) 16.1913 0.519335
\(973\) −5.47133 −0.175403
\(974\) −4.63644 −0.148561
\(975\) 0.0858656 0.00274990
\(976\) −5.68601 −0.182005
\(977\) 27.0688 0.866006 0.433003 0.901392i \(-0.357454\pi\)
0.433003 + 0.901392i \(0.357454\pi\)
\(978\) 0.682690 0.0218300
\(979\) −49.0300 −1.56701
\(980\) 1.97448 0.0630725
\(981\) −13.2885 −0.424268
\(982\) 0.262993 0.00839243
\(983\) 0.0672239 0.00214411 0.00107205 0.999999i \(-0.499659\pi\)
0.00107205 + 0.999999i \(0.499659\pi\)
\(984\) −3.64272 −0.116126
\(985\) −10.7333 −0.341993
\(986\) 4.49194 0.143053
\(987\) 17.8608 0.568514
\(988\) 0.383468 0.0121997
\(989\) −14.4960 −0.460946
\(990\) 0.617974 0.0196405
\(991\) −3.30485 −0.104982 −0.0524910 0.998621i \(-0.516716\pi\)
−0.0524910 + 0.998621i \(0.516716\pi\)
\(992\) −4.02142 −0.127680
\(993\) −1.68415 −0.0534449
\(994\) 0.691785 0.0219421
\(995\) −19.5730 −0.620507
\(996\) 24.6955 0.782506
\(997\) 37.0108 1.17214 0.586071 0.810260i \(-0.300674\pi\)
0.586071 + 0.810260i \(0.300674\pi\)
\(998\) −1.73241 −0.0548385
\(999\) −61.7235 −1.95285
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 \(a_p\))