Properties

Label 8023.2.a.c.1.10
Level 8023
Weight 2
Character 8023.1
Self dual Yes
Analytic conductor 64.064
Analytic rank 1
Dimension 158
CM No

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Newspace parameters

Level: \( N \) = \( 8023 = 71 \cdot 113 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0639775417\)
Analytic rank: \(1\)
Dimension: \(158\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 8023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.65311 q^{2}\) \(+3.18762 q^{3}\) \(+5.03901 q^{4}\) \(+1.63340 q^{5}\) \(-8.45712 q^{6}\) \(-4.20358 q^{7}\) \(-8.06283 q^{8}\) \(+7.16092 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.65311 q^{2}\) \(+3.18762 q^{3}\) \(+5.03901 q^{4}\) \(+1.63340 q^{5}\) \(-8.45712 q^{6}\) \(-4.20358 q^{7}\) \(-8.06283 q^{8}\) \(+7.16092 q^{9}\) \(-4.33359 q^{10}\) \(+2.16758 q^{11}\) \(+16.0624 q^{12}\) \(-5.03410 q^{13}\) \(+11.1526 q^{14}\) \(+5.20666 q^{15}\) \(+11.3136 q^{16}\) \(-3.71761 q^{17}\) \(-18.9987 q^{18}\) \(-3.68579 q^{19}\) \(+8.23071 q^{20}\) \(-13.3994 q^{21}\) \(-5.75084 q^{22}\) \(+8.32475 q^{23}\) \(-25.7012 q^{24}\) \(-2.33201 q^{25}\) \(+13.3560 q^{26}\) \(+13.2634 q^{27}\) \(-21.1819 q^{28}\) \(+1.34136 q^{29}\) \(-13.8138 q^{30}\) \(-5.07756 q^{31}\) \(-13.8906 q^{32}\) \(+6.90943 q^{33}\) \(+9.86323 q^{34}\) \(-6.86613 q^{35}\) \(+36.0839 q^{36}\) \(-8.50610 q^{37}\) \(+9.77882 q^{38}\) \(-16.0468 q^{39}\) \(-13.1698 q^{40}\) \(+4.79784 q^{41}\) \(+35.5502 q^{42}\) \(+5.13540 q^{43}\) \(+10.9225 q^{44}\) \(+11.6966 q^{45}\) \(-22.0865 q^{46}\) \(+8.84448 q^{47}\) \(+36.0634 q^{48}\) \(+10.6701 q^{49}\) \(+6.18708 q^{50}\) \(-11.8503 q^{51}\) \(-25.3668 q^{52}\) \(-1.62659 q^{53}\) \(-35.1894 q^{54}\) \(+3.54053 q^{55}\) \(+33.8928 q^{56}\) \(-11.7489 q^{57}\) \(-3.55879 q^{58}\) \(-6.82868 q^{59}\) \(+26.2364 q^{60}\) \(+10.3494 q^{61}\) \(+13.4714 q^{62}\) \(-30.1015 q^{63}\) \(+14.2260 q^{64}\) \(-8.22269 q^{65}\) \(-18.3315 q^{66}\) \(-12.2664 q^{67}\) \(-18.7330 q^{68}\) \(+26.5361 q^{69}\) \(+18.2166 q^{70}\) \(-1.00000 q^{71}\) \(-57.7373 q^{72}\) \(-15.9852 q^{73}\) \(+22.5676 q^{74}\) \(-7.43356 q^{75}\) \(-18.5727 q^{76}\) \(-9.11161 q^{77}\) \(+42.5739 q^{78}\) \(-3.57000 q^{79}\) \(+18.4796 q^{80}\) \(+20.7961 q^{81}\) \(-12.7292 q^{82}\) \(-5.03437 q^{83}\) \(-67.5198 q^{84}\) \(-6.07233 q^{85}\) \(-13.6248 q^{86}\) \(+4.27575 q^{87}\) \(-17.4769 q^{88}\) \(-17.4561 q^{89}\) \(-31.0325 q^{90}\) \(+21.1612 q^{91}\) \(+41.9485 q^{92}\) \(-16.1853 q^{93}\) \(-23.4654 q^{94}\) \(-6.02037 q^{95}\) \(-44.2778 q^{96}\) \(+10.7728 q^{97}\) \(-28.3090 q^{98}\) \(+15.5219 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 46q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 27q^{14} \) \(\mathstrut -\mathstrut 41q^{15} \) \(\mathstrut +\mathstrut 150q^{16} \) \(\mathstrut -\mathstrut 137q^{17} \) \(\mathstrut -\mathstrut 67q^{18} \) \(\mathstrut -\mathstrut 42q^{19} \) \(\mathstrut -\mathstrut 66q^{20} \) \(\mathstrut -\mathstrut 46q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 48q^{24} \) \(\mathstrut +\mathstrut 129q^{25} \) \(\mathstrut -\mathstrut 67q^{26} \) \(\mathstrut -\mathstrut 89q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 79q^{29} \) \(\mathstrut -\mathstrut 11q^{30} \) \(\mathstrut +\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 147q^{32} \) \(\mathstrut -\mathstrut 112q^{33} \) \(\mathstrut -\mathstrut 28q^{34} \) \(\mathstrut -\mathstrut 53q^{35} \) \(\mathstrut +\mathstrut 141q^{36} \) \(\mathstrut -\mathstrut 60q^{37} \) \(\mathstrut -\mathstrut 53q^{38} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 48q^{40} \) \(\mathstrut -\mathstrut 128q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 63q^{43} \) \(\mathstrut -\mathstrut 88q^{45} \) \(\mathstrut -\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 92q^{47} \) \(\mathstrut -\mathstrut 131q^{48} \) \(\mathstrut +\mathstrut 122q^{49} \) \(\mathstrut -\mathstrut 116q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 89q^{52} \) \(\mathstrut -\mathstrut 94q^{53} \) \(\mathstrut -\mathstrut 71q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 104q^{56} \) \(\mathstrut -\mathstrut 93q^{57} \) \(\mathstrut -\mathstrut 65q^{58} \) \(\mathstrut -\mathstrut 54q^{59} \) \(\mathstrut -\mathstrut 12q^{60} \) \(\mathstrut +\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 97q^{62} \) \(\mathstrut -\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 163q^{64} \) \(\mathstrut -\mathstrut 163q^{65} \) \(\mathstrut -\mathstrut 65q^{66} \) \(\mathstrut -\mathstrut 35q^{67} \) \(\mathstrut -\mathstrut 217q^{68} \) \(\mathstrut -\mathstrut 46q^{69} \) \(\mathstrut -\mathstrut 79q^{70} \) \(\mathstrut -\mathstrut 158q^{71} \) \(\mathstrut -\mathstrut 99q^{72} \) \(\mathstrut -\mathstrut 165q^{73} \) \(\mathstrut -\mathstrut 94q^{75} \) \(\mathstrut -\mathstrut 93q^{76} \) \(\mathstrut -\mathstrut 140q^{77} \) \(\mathstrut +\mathstrut 25q^{78} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut 134q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 158q^{83} \) \(\mathstrut -\mathstrut 160q^{84} \) \(\mathstrut +\mathstrut 23q^{85} \) \(\mathstrut -\mathstrut 122q^{86} \) \(\mathstrut -\mathstrut 71q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 251q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut -\mathstrut 57q^{91} \) \(\mathstrut -\mathstrut 58q^{92} \) \(\mathstrut -\mathstrut 52q^{93} \) \(\mathstrut -\mathstrut 64q^{94} \) \(\mathstrut -\mathstrut 84q^{95} \) \(\mathstrut -\mathstrut 98q^{96} \) \(\mathstrut -\mathstrut 48q^{97} \) \(\mathstrut -\mathstrut 84q^{98} \) \(\mathstrut +\mathstrut 85q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.65311 −1.87603 −0.938017 0.346589i \(-0.887340\pi\)
−0.938017 + 0.346589i \(0.887340\pi\)
\(3\) 3.18762 1.84037 0.920187 0.391480i \(-0.128037\pi\)
0.920187 + 0.391480i \(0.128037\pi\)
\(4\) 5.03901 2.51950
\(5\) 1.63340 0.730478 0.365239 0.930914i \(-0.380987\pi\)
0.365239 + 0.930914i \(0.380987\pi\)
\(6\) −8.45712 −3.45260
\(7\) −4.20358 −1.58880 −0.794402 0.607392i \(-0.792216\pi\)
−0.794402 + 0.607392i \(0.792216\pi\)
\(8\) −8.06283 −2.85064
\(9\) 7.16092 2.38697
\(10\) −4.33359 −1.37040
\(11\) 2.16758 0.653551 0.326775 0.945102i \(-0.394038\pi\)
0.326775 + 0.945102i \(0.394038\pi\)
\(12\) 16.0624 4.63683
\(13\) −5.03410 −1.39621 −0.698103 0.715997i \(-0.745972\pi\)
−0.698103 + 0.715997i \(0.745972\pi\)
\(14\) 11.1526 2.98065
\(15\) 5.20666 1.34435
\(16\) 11.3136 2.82840
\(17\) −3.71761 −0.901652 −0.450826 0.892612i \(-0.648870\pi\)
−0.450826 + 0.892612i \(0.648870\pi\)
\(18\) −18.9987 −4.47805
\(19\) −3.68579 −0.845578 −0.422789 0.906228i \(-0.638949\pi\)
−0.422789 + 0.906228i \(0.638949\pi\)
\(20\) 8.23071 1.84044
\(21\) −13.3994 −2.92399
\(22\) −5.75084 −1.22608
\(23\) 8.32475 1.73583 0.867915 0.496713i \(-0.165460\pi\)
0.867915 + 0.496713i \(0.165460\pi\)
\(24\) −25.7012 −5.24624
\(25\) −2.33201 −0.466402
\(26\) 13.3560 2.61933
\(27\) 13.2634 2.55255
\(28\) −21.1819 −4.00300
\(29\) 1.34136 0.249085 0.124542 0.992214i \(-0.460254\pi\)
0.124542 + 0.992214i \(0.460254\pi\)
\(30\) −13.8138 −2.52205
\(31\) −5.07756 −0.911958 −0.455979 0.889991i \(-0.650711\pi\)
−0.455979 + 0.889991i \(0.650711\pi\)
\(32\) −13.8906 −2.45553
\(33\) 6.90943 1.20278
\(34\) 9.86323 1.69153
\(35\) −6.86613 −1.16059
\(36\) 36.0839 6.01399
\(37\) −8.50610 −1.39839 −0.699197 0.714929i \(-0.746459\pi\)
−0.699197 + 0.714929i \(0.746459\pi\)
\(38\) 9.77882 1.58633
\(39\) −16.0468 −2.56954
\(40\) −13.1698 −2.08233
\(41\) 4.79784 0.749297 0.374648 0.927167i \(-0.377763\pi\)
0.374648 + 0.927167i \(0.377763\pi\)
\(42\) 35.5502 5.48551
\(43\) 5.13540 0.783141 0.391570 0.920148i \(-0.371932\pi\)
0.391570 + 0.920148i \(0.371932\pi\)
\(44\) 10.9225 1.64662
\(45\) 11.6966 1.74363
\(46\) −22.0865 −3.25648
\(47\) 8.84448 1.29010 0.645050 0.764141i \(-0.276837\pi\)
0.645050 + 0.764141i \(0.276837\pi\)
\(48\) 36.0634 5.20530
\(49\) 10.6701 1.52430
\(50\) 6.18708 0.874985
\(51\) −11.8503 −1.65938
\(52\) −25.3668 −3.51775
\(53\) −1.62659 −0.223429 −0.111715 0.993740i \(-0.535634\pi\)
−0.111715 + 0.993740i \(0.535634\pi\)
\(54\) −35.1894 −4.78867
\(55\) 3.54053 0.477405
\(56\) 33.8928 4.52911
\(57\) −11.7489 −1.55618
\(58\) −3.55879 −0.467291
\(59\) −6.82868 −0.889019 −0.444509 0.895774i \(-0.646622\pi\)
−0.444509 + 0.895774i \(0.646622\pi\)
\(60\) 26.2364 3.38710
\(61\) 10.3494 1.32510 0.662552 0.749016i \(-0.269473\pi\)
0.662552 + 0.749016i \(0.269473\pi\)
\(62\) 13.4714 1.71086
\(63\) −30.1015 −3.79244
\(64\) 14.2260 1.77825
\(65\) −8.22269 −1.01990
\(66\) −18.3315 −2.25645
\(67\) −12.2664 −1.49858 −0.749288 0.662245i \(-0.769604\pi\)
−0.749288 + 0.662245i \(0.769604\pi\)
\(68\) −18.7330 −2.27172
\(69\) 26.5361 3.19457
\(70\) 18.2166 2.17730
\(71\) −1.00000 −0.118678
\(72\) −57.7373 −6.80441
\(73\) −15.9852 −1.87093 −0.935465 0.353420i \(-0.885018\pi\)
−0.935465 + 0.353420i \(0.885018\pi\)
\(74\) 22.5676 2.62344
\(75\) −7.43356 −0.858353
\(76\) −18.5727 −2.13044
\(77\) −9.11161 −1.03836
\(78\) 42.5739 4.82055
\(79\) −3.57000 −0.401656 −0.200828 0.979626i \(-0.564363\pi\)
−0.200828 + 0.979626i \(0.564363\pi\)
\(80\) 18.4796 2.06608
\(81\) 20.7961 2.31067
\(82\) −12.7292 −1.40571
\(83\) −5.03437 −0.552594 −0.276297 0.961072i \(-0.589107\pi\)
−0.276297 + 0.961072i \(0.589107\pi\)
\(84\) −67.5198 −7.36702
\(85\) −6.07233 −0.658637
\(86\) −13.6248 −1.46920
\(87\) 4.27575 0.458409
\(88\) −17.4769 −1.86304
\(89\) −17.4561 −1.85034 −0.925172 0.379549i \(-0.876079\pi\)
−0.925172 + 0.379549i \(0.876079\pi\)
\(90\) −31.0325 −3.27111
\(91\) 21.1612 2.21830
\(92\) 41.9485 4.37343
\(93\) −16.1853 −1.67834
\(94\) −23.4654 −2.42027
\(95\) −6.02037 −0.617677
\(96\) −44.2778 −4.51909
\(97\) 10.7728 1.09382 0.546908 0.837193i \(-0.315805\pi\)
0.546908 + 0.837193i \(0.315805\pi\)
\(98\) −28.3090 −2.85964
\(99\) 15.5219 1.56001
\(100\) −11.7510 −1.17510
\(101\) 16.4307 1.63491 0.817457 0.575990i \(-0.195383\pi\)
0.817457 + 0.575990i \(0.195383\pi\)
\(102\) 31.4402 3.11305
\(103\) −8.18039 −0.806038 −0.403019 0.915192i \(-0.632039\pi\)
−0.403019 + 0.915192i \(0.632039\pi\)
\(104\) 40.5891 3.98008
\(105\) −21.8866 −2.13591
\(106\) 4.31552 0.419161
\(107\) −15.2568 −1.47493 −0.737467 0.675383i \(-0.763978\pi\)
−0.737467 + 0.675383i \(0.763978\pi\)
\(108\) 66.8346 6.43116
\(109\) 4.92343 0.471580 0.235790 0.971804i \(-0.424232\pi\)
0.235790 + 0.971804i \(0.424232\pi\)
\(110\) −9.39342 −0.895627
\(111\) −27.1142 −2.57357
\(112\) −47.5576 −4.49377
\(113\) −1.00000 −0.0940721
\(114\) 31.1712 2.91945
\(115\) 13.5976 1.26799
\(116\) 6.75913 0.627570
\(117\) −36.0488 −3.33271
\(118\) 18.1173 1.66783
\(119\) 15.6273 1.43255
\(120\) −41.9804 −3.83227
\(121\) −6.30159 −0.572871
\(122\) −27.4581 −2.48594
\(123\) 15.2937 1.37899
\(124\) −25.5859 −2.29768
\(125\) −11.9761 −1.07117
\(126\) 79.8628 7.11474
\(127\) 2.87553 0.255162 0.127581 0.991828i \(-0.459279\pi\)
0.127581 + 0.991828i \(0.459279\pi\)
\(128\) −9.96218 −0.880541
\(129\) 16.3697 1.44127
\(130\) 21.8157 1.91336
\(131\) 16.2102 1.41629 0.708145 0.706067i \(-0.249532\pi\)
0.708145 + 0.706067i \(0.249532\pi\)
\(132\) 34.8167 3.03040
\(133\) 15.4935 1.34346
\(134\) 32.5441 2.81138
\(135\) 21.6645 1.86458
\(136\) 29.9744 2.57029
\(137\) −0.210990 −0.0180261 −0.00901306 0.999959i \(-0.502869\pi\)
−0.00901306 + 0.999959i \(0.502869\pi\)
\(138\) −70.4033 −5.99313
\(139\) −0.551847 −0.0468070 −0.0234035 0.999726i \(-0.507450\pi\)
−0.0234035 + 0.999726i \(0.507450\pi\)
\(140\) −34.5985 −2.92410
\(141\) 28.1928 2.37426
\(142\) 2.65311 0.222644
\(143\) −10.9118 −0.912492
\(144\) 81.0157 6.75131
\(145\) 2.19098 0.181951
\(146\) 42.4106 3.50993
\(147\) 34.0123 2.80528
\(148\) −42.8623 −3.52326
\(149\) −8.87298 −0.726903 −0.363452 0.931613i \(-0.618402\pi\)
−0.363452 + 0.931613i \(0.618402\pi\)
\(150\) 19.7221 1.61030
\(151\) −7.40506 −0.602615 −0.301308 0.953527i \(-0.597423\pi\)
−0.301308 + 0.953527i \(0.597423\pi\)
\(152\) 29.7179 2.41044
\(153\) −26.6215 −2.15222
\(154\) 24.1741 1.94801
\(155\) −8.29369 −0.666165
\(156\) −80.8599 −6.47397
\(157\) −3.00465 −0.239797 −0.119898 0.992786i \(-0.538257\pi\)
−0.119898 + 0.992786i \(0.538257\pi\)
\(158\) 9.47161 0.753521
\(159\) −5.18495 −0.411193
\(160\) −22.6888 −1.79371
\(161\) −34.9938 −2.75789
\(162\) −55.1743 −4.33490
\(163\) 6.98601 0.547186 0.273593 0.961846i \(-0.411788\pi\)
0.273593 + 0.961846i \(0.411788\pi\)
\(164\) 24.1764 1.88786
\(165\) 11.2859 0.878603
\(166\) 13.3568 1.03669
\(167\) 15.9892 1.23728 0.618639 0.785675i \(-0.287684\pi\)
0.618639 + 0.785675i \(0.287684\pi\)
\(168\) 108.037 8.33526
\(169\) 12.3421 0.949394
\(170\) 16.1106 1.23563
\(171\) −26.3937 −2.01837
\(172\) 25.8773 1.97313
\(173\) −16.1864 −1.23063 −0.615314 0.788282i \(-0.710971\pi\)
−0.615314 + 0.788282i \(0.710971\pi\)
\(174\) −11.3441 −0.859991
\(175\) 9.80279 0.741021
\(176\) 24.5231 1.84850
\(177\) −21.7672 −1.63613
\(178\) 46.3130 3.47131
\(179\) −22.5409 −1.68479 −0.842395 0.538861i \(-0.818855\pi\)
−0.842395 + 0.538861i \(0.818855\pi\)
\(180\) 58.9395 4.39309
\(181\) 7.21461 0.536257 0.268129 0.963383i \(-0.413595\pi\)
0.268129 + 0.963383i \(0.413595\pi\)
\(182\) −56.1432 −4.16161
\(183\) 32.9899 2.43869
\(184\) −67.1210 −4.94823
\(185\) −13.8939 −1.02150
\(186\) 42.9416 3.14863
\(187\) −8.05822 −0.589275
\(188\) 44.5674 3.25041
\(189\) −55.7540 −4.05551
\(190\) 15.9727 1.15878
\(191\) −8.84764 −0.640193 −0.320096 0.947385i \(-0.603715\pi\)
−0.320096 + 0.947385i \(0.603715\pi\)
\(192\) 45.3472 3.27265
\(193\) −0.0801491 −0.00576926 −0.00288463 0.999996i \(-0.500918\pi\)
−0.00288463 + 0.999996i \(0.500918\pi\)
\(194\) −28.5815 −2.05204
\(195\) −26.2108 −1.87699
\(196\) 53.7668 3.84048
\(197\) −20.5025 −1.46074 −0.730372 0.683049i \(-0.760653\pi\)
−0.730372 + 0.683049i \(0.760653\pi\)
\(198\) −41.1813 −2.92663
\(199\) −4.29022 −0.304125 −0.152063 0.988371i \(-0.548592\pi\)
−0.152063 + 0.988371i \(0.548592\pi\)
\(200\) 18.8026 1.32954
\(201\) −39.1005 −2.75794
\(202\) −43.5924 −3.06715
\(203\) −5.63853 −0.395747
\(204\) −59.7138 −4.18080
\(205\) 7.83679 0.547345
\(206\) 21.7035 1.51215
\(207\) 59.6129 4.14338
\(208\) −56.9537 −3.94903
\(209\) −7.98926 −0.552628
\(210\) 58.0676 4.00705
\(211\) −19.5231 −1.34402 −0.672012 0.740540i \(-0.734570\pi\)
−0.672012 + 0.740540i \(0.734570\pi\)
\(212\) −8.19639 −0.562930
\(213\) −3.18762 −0.218412
\(214\) 40.4781 2.76703
\(215\) 8.38815 0.572067
\(216\) −106.941 −7.27641
\(217\) 21.3440 1.44892
\(218\) −13.0624 −0.884699
\(219\) −50.9548 −3.44321
\(220\) 17.8407 1.20282
\(221\) 18.7148 1.25889
\(222\) 71.9371 4.82810
\(223\) −7.71790 −0.516829 −0.258415 0.966034i \(-0.583200\pi\)
−0.258415 + 0.966034i \(0.583200\pi\)
\(224\) 58.3901 3.90135
\(225\) −16.6993 −1.11329
\(226\) 2.65311 0.176482
\(227\) −23.0036 −1.52680 −0.763400 0.645926i \(-0.776471\pi\)
−0.763400 + 0.645926i \(0.776471\pi\)
\(228\) −59.2028 −3.92080
\(229\) 9.96613 0.658580 0.329290 0.944229i \(-0.393191\pi\)
0.329290 + 0.944229i \(0.393191\pi\)
\(230\) −36.0761 −2.37878
\(231\) −29.0444 −1.91098
\(232\) −10.8152 −0.710051
\(233\) 24.0838 1.57778 0.788890 0.614534i \(-0.210656\pi\)
0.788890 + 0.614534i \(0.210656\pi\)
\(234\) 95.6415 6.25228
\(235\) 14.4466 0.942390
\(236\) −34.4098 −2.23989
\(237\) −11.3798 −0.739198
\(238\) −41.4609 −2.68751
\(239\) −10.7836 −0.697532 −0.348766 0.937210i \(-0.613399\pi\)
−0.348766 + 0.937210i \(0.613399\pi\)
\(240\) 58.9059 3.80236
\(241\) −1.67148 −0.107669 −0.0538347 0.998550i \(-0.517144\pi\)
−0.0538347 + 0.998550i \(0.517144\pi\)
\(242\) 16.7188 1.07473
\(243\) 26.4996 1.69995
\(244\) 52.1507 3.33860
\(245\) 17.4285 1.11347
\(246\) −40.5759 −2.58702
\(247\) 18.5546 1.18060
\(248\) 40.9395 2.59966
\(249\) −16.0477 −1.01698
\(250\) 31.7739 2.00956
\(251\) −28.8956 −1.82388 −0.911938 0.410328i \(-0.865414\pi\)
−0.911938 + 0.410328i \(0.865414\pi\)
\(252\) −151.682 −9.55506
\(253\) 18.0446 1.13445
\(254\) −7.62909 −0.478692
\(255\) −19.3563 −1.21214
\(256\) −2.02129 −0.126331
\(257\) −0.195501 −0.0121950 −0.00609751 0.999981i \(-0.501941\pi\)
−0.00609751 + 0.999981i \(0.501941\pi\)
\(258\) −43.4306 −2.70387
\(259\) 35.7561 2.22178
\(260\) −41.4342 −2.56964
\(261\) 9.60539 0.594559
\(262\) −43.0074 −2.65701
\(263\) 6.13642 0.378388 0.189194 0.981940i \(-0.439413\pi\)
0.189194 + 0.981940i \(0.439413\pi\)
\(264\) −55.7096 −3.42869
\(265\) −2.65687 −0.163210
\(266\) −41.1061 −2.52038
\(267\) −55.6434 −3.40532
\(268\) −61.8103 −3.77567
\(269\) −9.97582 −0.608237 −0.304118 0.952634i \(-0.598362\pi\)
−0.304118 + 0.952634i \(0.598362\pi\)
\(270\) −57.4784 −3.49802
\(271\) 12.4706 0.757535 0.378768 0.925492i \(-0.376348\pi\)
0.378768 + 0.925492i \(0.376348\pi\)
\(272\) −42.0594 −2.55023
\(273\) 67.4540 4.08250
\(274\) 0.559781 0.0338176
\(275\) −5.05482 −0.304817
\(276\) 133.716 8.04874
\(277\) −30.0747 −1.80702 −0.903508 0.428572i \(-0.859017\pi\)
−0.903508 + 0.428572i \(0.859017\pi\)
\(278\) 1.46411 0.0878116
\(279\) −36.3601 −2.17682
\(280\) 55.3604 3.30842
\(281\) 23.9708 1.42998 0.714988 0.699137i \(-0.246432\pi\)
0.714988 + 0.699137i \(0.246432\pi\)
\(282\) −74.7988 −4.45420
\(283\) 1.38317 0.0822211 0.0411105 0.999155i \(-0.486910\pi\)
0.0411105 + 0.999155i \(0.486910\pi\)
\(284\) −5.03901 −0.299010
\(285\) −19.1906 −1.13676
\(286\) 28.9503 1.71187
\(287\) −20.1681 −1.19049
\(288\) −99.4692 −5.86128
\(289\) −3.17941 −0.187024
\(290\) −5.81292 −0.341346
\(291\) 34.3397 2.01303
\(292\) −80.5497 −4.71381
\(293\) 22.7327 1.32806 0.664030 0.747706i \(-0.268845\pi\)
0.664030 + 0.747706i \(0.268845\pi\)
\(294\) −90.2384 −5.26281
\(295\) −11.1540 −0.649409
\(296\) 68.5833 3.98632
\(297\) 28.7496 1.66822
\(298\) 23.5410 1.36369
\(299\) −41.9076 −2.42358
\(300\) −37.4577 −2.16262
\(301\) −21.5871 −1.24426
\(302\) 19.6465 1.13053
\(303\) 52.3748 3.00885
\(304\) −41.6995 −2.39163
\(305\) 16.9047 0.967959
\(306\) 70.6298 4.03764
\(307\) −8.24446 −0.470536 −0.235268 0.971931i \(-0.575597\pi\)
−0.235268 + 0.971931i \(0.575597\pi\)
\(308\) −45.9135 −2.61616
\(309\) −26.0760 −1.48341
\(310\) 22.0041 1.24975
\(311\) −2.81256 −0.159486 −0.0797429 0.996815i \(-0.525410\pi\)
−0.0797429 + 0.996815i \(0.525410\pi\)
\(312\) 129.383 7.32484
\(313\) −25.0286 −1.41470 −0.707351 0.706862i \(-0.750110\pi\)
−0.707351 + 0.706862i \(0.750110\pi\)
\(314\) 7.97167 0.449867
\(315\) −49.1678 −2.77029
\(316\) −17.9893 −1.01197
\(317\) −14.0682 −0.790152 −0.395076 0.918649i \(-0.629282\pi\)
−0.395076 + 0.918649i \(0.629282\pi\)
\(318\) 13.7562 0.771412
\(319\) 2.90751 0.162789
\(320\) 23.2368 1.29898
\(321\) −48.6330 −2.71443
\(322\) 92.8424 5.17390
\(323\) 13.7023 0.762417
\(324\) 104.791 5.82175
\(325\) 11.7395 0.651193
\(326\) −18.5347 −1.02654
\(327\) 15.6940 0.867882
\(328\) −38.6842 −2.13598
\(329\) −37.1785 −2.04972
\(330\) −29.9427 −1.64829
\(331\) 2.70772 0.148830 0.0744149 0.997227i \(-0.476291\pi\)
0.0744149 + 0.997227i \(0.476291\pi\)
\(332\) −25.3682 −1.39226
\(333\) −60.9115 −3.33793
\(334\) −42.4210 −2.32118
\(335\) −20.0359 −1.09468
\(336\) −151.596 −8.27021
\(337\) 11.9779 0.652477 0.326238 0.945288i \(-0.394219\pi\)
0.326238 + 0.945288i \(0.394219\pi\)
\(338\) −32.7450 −1.78109
\(339\) −3.18762 −0.173128
\(340\) −30.5985 −1.65944
\(341\) −11.0060 −0.596011
\(342\) 70.0254 3.78654
\(343\) −15.4276 −0.833012
\(344\) −41.4058 −2.23245
\(345\) 43.3441 2.33357
\(346\) 42.9443 2.30870
\(347\) −15.8771 −0.852329 −0.426164 0.904646i \(-0.640135\pi\)
−0.426164 + 0.904646i \(0.640135\pi\)
\(348\) 21.5456 1.15496
\(349\) −4.20634 −0.225160 −0.112580 0.993643i \(-0.535911\pi\)
−0.112580 + 0.993643i \(0.535911\pi\)
\(350\) −26.0079 −1.39018
\(351\) −66.7694 −3.56389
\(352\) −30.1089 −1.60481
\(353\) 3.21012 0.170858 0.0854288 0.996344i \(-0.472774\pi\)
0.0854288 + 0.996344i \(0.472774\pi\)
\(354\) 57.7510 3.06943
\(355\) −1.63340 −0.0866918
\(356\) −87.9615 −4.66195
\(357\) 49.8138 2.63642
\(358\) 59.8037 3.16072
\(359\) 5.27319 0.278308 0.139154 0.990271i \(-0.455562\pi\)
0.139154 + 0.990271i \(0.455562\pi\)
\(360\) −94.3081 −4.97047
\(361\) −5.41494 −0.284997
\(362\) −19.1412 −1.00604
\(363\) −20.0871 −1.05430
\(364\) 106.632 5.58902
\(365\) −26.1103 −1.36667
\(366\) −87.5260 −4.57506
\(367\) −33.5018 −1.74878 −0.874389 0.485225i \(-0.838738\pi\)
−0.874389 + 0.485225i \(0.838738\pi\)
\(368\) 94.1827 4.90961
\(369\) 34.3570 1.78855
\(370\) 36.8620 1.91636
\(371\) 6.83750 0.354985
\(372\) −81.5581 −4.22859
\(373\) −30.8460 −1.59714 −0.798572 0.601899i \(-0.794411\pi\)
−0.798572 + 0.601899i \(0.794411\pi\)
\(374\) 21.3794 1.10550
\(375\) −38.1752 −1.97136
\(376\) −71.3115 −3.67761
\(377\) −6.75254 −0.347774
\(378\) 147.922 7.60827
\(379\) −12.2344 −0.628438 −0.314219 0.949351i \(-0.601743\pi\)
−0.314219 + 0.949351i \(0.601743\pi\)
\(380\) −30.3367 −1.55624
\(381\) 9.16608 0.469593
\(382\) 23.4738 1.20102
\(383\) −28.8684 −1.47511 −0.737554 0.675289i \(-0.764019\pi\)
−0.737554 + 0.675289i \(0.764019\pi\)
\(384\) −31.7556 −1.62052
\(385\) −14.8829 −0.758503
\(386\) 0.212645 0.0108233
\(387\) 36.7742 1.86934
\(388\) 54.2844 2.75587
\(389\) 13.4361 0.681238 0.340619 0.940201i \(-0.389363\pi\)
0.340619 + 0.940201i \(0.389363\pi\)
\(390\) 69.5402 3.52131
\(391\) −30.9481 −1.56511
\(392\) −86.0313 −4.34524
\(393\) 51.6719 2.60650
\(394\) 54.3955 2.74041
\(395\) −5.83123 −0.293401
\(396\) 78.2149 3.93045
\(397\) 6.92657 0.347634 0.173817 0.984778i \(-0.444390\pi\)
0.173817 + 0.984778i \(0.444390\pi\)
\(398\) 11.3824 0.570549
\(399\) 49.3875 2.47247
\(400\) −26.3834 −1.31917
\(401\) 3.98177 0.198840 0.0994201 0.995046i \(-0.468301\pi\)
0.0994201 + 0.995046i \(0.468301\pi\)
\(402\) 103.738 5.17399
\(403\) 25.5609 1.27328
\(404\) 82.7943 4.11917
\(405\) 33.9683 1.68790
\(406\) 14.9596 0.742435
\(407\) −18.4377 −0.913922
\(408\) 95.5471 4.73029
\(409\) −31.1055 −1.53807 −0.769034 0.639207i \(-0.779263\pi\)
−0.769034 + 0.639207i \(0.779263\pi\)
\(410\) −20.7919 −1.02684
\(411\) −0.672557 −0.0331748
\(412\) −41.2210 −2.03082
\(413\) 28.7049 1.41248
\(414\) −158.160 −7.77312
\(415\) −8.22314 −0.403658
\(416\) 69.9264 3.42842
\(417\) −1.75908 −0.0861424
\(418\) 21.1964 1.03675
\(419\) 14.6888 0.717595 0.358797 0.933415i \(-0.383187\pi\)
0.358797 + 0.933415i \(0.383187\pi\)
\(420\) −110.287 −5.38144
\(421\) 38.7452 1.88832 0.944162 0.329480i \(-0.106874\pi\)
0.944162 + 0.329480i \(0.106874\pi\)
\(422\) 51.7969 2.52144
\(423\) 63.3346 3.07943
\(424\) 13.1149 0.636916
\(425\) 8.66949 0.420532
\(426\) 8.45712 0.409749
\(427\) −43.5045 −2.10533
\(428\) −76.8793 −3.71610
\(429\) −34.7827 −1.67933
\(430\) −22.2547 −1.07322
\(431\) 9.91713 0.477691 0.238846 0.971058i \(-0.423231\pi\)
0.238846 + 0.971058i \(0.423231\pi\)
\(432\) 150.057 7.21962
\(433\) 18.2435 0.876727 0.438363 0.898798i \(-0.355558\pi\)
0.438363 + 0.898798i \(0.355558\pi\)
\(434\) −56.6279 −2.71823
\(435\) 6.98401 0.334858
\(436\) 24.8092 1.18815
\(437\) −30.6833 −1.46778
\(438\) 135.189 6.45958
\(439\) −18.5053 −0.883209 −0.441604 0.897210i \(-0.645590\pi\)
−0.441604 + 0.897210i \(0.645590\pi\)
\(440\) −28.5467 −1.36091
\(441\) 76.4078 3.63847
\(442\) −49.6524 −2.36173
\(443\) 5.94598 0.282502 0.141251 0.989974i \(-0.454888\pi\)
0.141251 + 0.989974i \(0.454888\pi\)
\(444\) −136.629 −6.48411
\(445\) −28.5128 −1.35164
\(446\) 20.4765 0.969589
\(447\) −28.2837 −1.33777
\(448\) −59.8003 −2.82530
\(449\) 31.8811 1.50456 0.752280 0.658843i \(-0.228954\pi\)
0.752280 + 0.658843i \(0.228954\pi\)
\(450\) 44.3052 2.08857
\(451\) 10.3997 0.489703
\(452\) −5.03901 −0.237015
\(453\) −23.6045 −1.10904
\(454\) 61.0310 2.86433
\(455\) 34.5647 1.62042
\(456\) 94.7294 4.43611
\(457\) 19.6807 0.920622 0.460311 0.887758i \(-0.347738\pi\)
0.460311 + 0.887758i \(0.347738\pi\)
\(458\) −26.4413 −1.23552
\(459\) −49.3083 −2.30151
\(460\) 68.5186 3.19469
\(461\) 16.7739 0.781240 0.390620 0.920552i \(-0.372261\pi\)
0.390620 + 0.920552i \(0.372261\pi\)
\(462\) 77.0580 3.58506
\(463\) 12.7776 0.593828 0.296914 0.954904i \(-0.404043\pi\)
0.296914 + 0.954904i \(0.404043\pi\)
\(464\) 15.1756 0.704510
\(465\) −26.4371 −1.22599
\(466\) −63.8970 −2.95997
\(467\) 6.77405 0.313466 0.156733 0.987641i \(-0.449904\pi\)
0.156733 + 0.987641i \(0.449904\pi\)
\(468\) −181.650 −8.39678
\(469\) 51.5627 2.38094
\(470\) −38.3283 −1.76795
\(471\) −9.57767 −0.441316
\(472\) 55.0585 2.53427
\(473\) 11.1314 0.511822
\(474\) 30.1919 1.38676
\(475\) 8.59529 0.394379
\(476\) 78.7459 3.60931
\(477\) −11.6479 −0.533319
\(478\) 28.6101 1.30859
\(479\) 41.0926 1.87757 0.938784 0.344507i \(-0.111954\pi\)
0.938784 + 0.344507i \(0.111954\pi\)
\(480\) −72.3233 −3.30109
\(481\) 42.8205 1.95245
\(482\) 4.43462 0.201991
\(483\) −111.547 −5.07556
\(484\) −31.7537 −1.44335
\(485\) 17.5963 0.799009
\(486\) −70.3064 −3.18916
\(487\) −31.4162 −1.42360 −0.711802 0.702380i \(-0.752121\pi\)
−0.711802 + 0.702380i \(0.752121\pi\)
\(488\) −83.4454 −3.77739
\(489\) 22.2687 1.00703
\(490\) −46.2399 −2.08891
\(491\) 22.1114 0.997873 0.498937 0.866638i \(-0.333724\pi\)
0.498937 + 0.866638i \(0.333724\pi\)
\(492\) 77.0650 3.47436
\(493\) −4.98666 −0.224588
\(494\) −49.2275 −2.21485
\(495\) 25.3534 1.13955
\(496\) −57.4455 −2.57938
\(497\) 4.20358 0.188556
\(498\) 42.5763 1.90789
\(499\) −3.33469 −0.149281 −0.0746405 0.997211i \(-0.523781\pi\)
−0.0746405 + 0.997211i \(0.523781\pi\)
\(500\) −60.3476 −2.69883
\(501\) 50.9673 2.27705
\(502\) 76.6634 3.42165
\(503\) 15.4875 0.690555 0.345278 0.938501i \(-0.387785\pi\)
0.345278 + 0.938501i \(0.387785\pi\)
\(504\) 242.704 10.8109
\(505\) 26.8378 1.19427
\(506\) −47.8743 −2.12827
\(507\) 39.3420 1.74724
\(508\) 14.4898 0.642881
\(509\) −6.08134 −0.269551 −0.134775 0.990876i \(-0.543031\pi\)
−0.134775 + 0.990876i \(0.543031\pi\)
\(510\) 51.3544 2.27401
\(511\) 67.1952 2.97254
\(512\) 25.2871 1.11754
\(513\) −48.8863 −2.15838
\(514\) 0.518686 0.0228783
\(515\) −13.3618 −0.588793
\(516\) 82.4870 3.63129
\(517\) 19.1711 0.843145
\(518\) −94.8650 −4.16813
\(519\) −51.5960 −2.26481
\(520\) 66.2981 2.90737
\(521\) −13.4697 −0.590120 −0.295060 0.955479i \(-0.595340\pi\)
−0.295060 + 0.955479i \(0.595340\pi\)
\(522\) −25.4842 −1.11541
\(523\) −27.6027 −1.20698 −0.603491 0.797370i \(-0.706224\pi\)
−0.603491 + 0.797370i \(0.706224\pi\)
\(524\) 81.6832 3.56835
\(525\) 31.2476 1.36376
\(526\) −16.2806 −0.709869
\(527\) 18.8764 0.822268
\(528\) 78.1704 3.40193
\(529\) 46.3014 2.01310
\(530\) 7.04897 0.306188
\(531\) −48.8997 −2.12207
\(532\) 78.0720 3.38485
\(533\) −24.1528 −1.04617
\(534\) 147.628 6.38850
\(535\) −24.9205 −1.07741
\(536\) 98.9017 4.27190
\(537\) −71.8520 −3.10064
\(538\) 26.4670 1.14107
\(539\) 23.1283 0.996208
\(540\) 109.168 4.69782
\(541\) 29.9625 1.28819 0.644095 0.764946i \(-0.277234\pi\)
0.644095 + 0.764946i \(0.277234\pi\)
\(542\) −33.0859 −1.42116
\(543\) 22.9974 0.986914
\(544\) 51.6396 2.21403
\(545\) 8.04193 0.344479
\(546\) −178.963 −7.65891
\(547\) 14.3899 0.615268 0.307634 0.951505i \(-0.400463\pi\)
0.307634 + 0.951505i \(0.400463\pi\)
\(548\) −1.06318 −0.0454169
\(549\) 74.1112 3.16299
\(550\) 13.4110 0.571847
\(551\) −4.94398 −0.210621
\(552\) −213.956 −9.10659
\(553\) 15.0068 0.638154
\(554\) 79.7917 3.39002
\(555\) −44.2883 −1.87994
\(556\) −2.78076 −0.117931
\(557\) −28.3468 −1.20109 −0.600546 0.799591i \(-0.705050\pi\)
−0.600546 + 0.799591i \(0.705050\pi\)
\(558\) 96.4673 4.08379
\(559\) −25.8521 −1.09343
\(560\) −77.6805 −3.28260
\(561\) −25.6865 −1.08449
\(562\) −63.5971 −2.68268
\(563\) −32.8296 −1.38360 −0.691802 0.722087i \(-0.743183\pi\)
−0.691802 + 0.722087i \(0.743183\pi\)
\(564\) 142.064 5.98197
\(565\) −1.63340 −0.0687176
\(566\) −3.66971 −0.154249
\(567\) −87.4179 −3.67121
\(568\) 8.06283 0.338309
\(569\) −20.0665 −0.841231 −0.420616 0.907239i \(-0.638186\pi\)
−0.420616 + 0.907239i \(0.638186\pi\)
\(570\) 50.9149 2.13259
\(571\) 22.3214 0.934123 0.467061 0.884225i \(-0.345313\pi\)
0.467061 + 0.884225i \(0.345313\pi\)
\(572\) −54.9847 −2.29903
\(573\) −28.2029 −1.17819
\(574\) 53.5083 2.23339
\(575\) −19.4134 −0.809594
\(576\) 101.872 4.24465
\(577\) 9.36579 0.389903 0.194952 0.980813i \(-0.437545\pi\)
0.194952 + 0.980813i \(0.437545\pi\)
\(578\) 8.43533 0.350863
\(579\) −0.255485 −0.0106176
\(580\) 11.0404 0.458426
\(581\) 21.1624 0.877964
\(582\) −91.1071 −3.77651
\(583\) −3.52576 −0.146022
\(584\) 128.886 5.33335
\(585\) −58.8820 −2.43447
\(586\) −60.3125 −2.49149
\(587\) −30.0310 −1.23951 −0.619756 0.784795i \(-0.712768\pi\)
−0.619756 + 0.784795i \(0.712768\pi\)
\(588\) 171.388 7.06792
\(589\) 18.7148 0.771132
\(590\) 29.5927 1.21831
\(591\) −65.3543 −2.68832
\(592\) −96.2345 −3.95521
\(593\) −18.8196 −0.772827 −0.386414 0.922326i \(-0.626286\pi\)
−0.386414 + 0.922326i \(0.626286\pi\)
\(594\) −76.2760 −3.12964
\(595\) 25.5256 1.04645
\(596\) −44.7110 −1.83144
\(597\) −13.6756 −0.559704
\(598\) 111.186 4.54671
\(599\) 22.0322 0.900210 0.450105 0.892976i \(-0.351387\pi\)
0.450105 + 0.892976i \(0.351387\pi\)
\(600\) 59.9355 2.44686
\(601\) 15.5878 0.635841 0.317920 0.948117i \(-0.397016\pi\)
0.317920 + 0.948117i \(0.397016\pi\)
\(602\) 57.2729 2.33427
\(603\) −87.8385 −3.57706
\(604\) −37.3141 −1.51829
\(605\) −10.2930 −0.418470
\(606\) −138.956 −5.64471
\(607\) 24.3938 0.990113 0.495056 0.868861i \(-0.335147\pi\)
0.495056 + 0.868861i \(0.335147\pi\)
\(608\) 51.1977 2.07634
\(609\) −17.9735 −0.728322
\(610\) −44.8500 −1.81592
\(611\) −44.5239 −1.80125
\(612\) −134.146 −5.42253
\(613\) 32.7273 1.32184 0.660922 0.750454i \(-0.270165\pi\)
0.660922 + 0.750454i \(0.270165\pi\)
\(614\) 21.8735 0.882742
\(615\) 24.9807 1.00732
\(616\) 73.4654 2.96001
\(617\) −31.3596 −1.26249 −0.631244 0.775584i \(-0.717456\pi\)
−0.631244 + 0.775584i \(0.717456\pi\)
\(618\) 69.1825 2.78293
\(619\) 6.53679 0.262736 0.131368 0.991334i \(-0.458063\pi\)
0.131368 + 0.991334i \(0.458063\pi\)
\(620\) −41.7920 −1.67841
\(621\) 110.415 4.43079
\(622\) 7.46205 0.299201
\(623\) 73.3782 2.93984
\(624\) −181.547 −7.26768
\(625\) −7.90170 −0.316068
\(626\) 66.4038 2.65403
\(627\) −25.4667 −1.01704
\(628\) −15.1404 −0.604169
\(629\) 31.6223 1.26086
\(630\) 130.448 5.19716
\(631\) −2.05051 −0.0816297 −0.0408148 0.999167i \(-0.512995\pi\)
−0.0408148 + 0.999167i \(0.512995\pi\)
\(632\) 28.7843 1.14498
\(633\) −62.2322 −2.47351
\(634\) 37.3247 1.48235
\(635\) 4.69688 0.186390
\(636\) −26.1270 −1.03600
\(637\) −53.7143 −2.12824
\(638\) −7.71396 −0.305399
\(639\) −7.16092 −0.283282
\(640\) −16.2722 −0.643216
\(641\) 26.0642 1.02947 0.514736 0.857349i \(-0.327890\pi\)
0.514736 + 0.857349i \(0.327890\pi\)
\(642\) 129.029 5.09236
\(643\) 8.02091 0.316314 0.158157 0.987414i \(-0.449445\pi\)
0.158157 + 0.987414i \(0.449445\pi\)
\(644\) −176.334 −6.94853
\(645\) 26.7382 1.05282
\(646\) −36.3538 −1.43032
\(647\) −33.5034 −1.31716 −0.658578 0.752512i \(-0.728842\pi\)
−0.658578 + 0.752512i \(0.728842\pi\)
\(648\) −167.675 −6.58690
\(649\) −14.8017 −0.581019
\(650\) −31.1464 −1.22166
\(651\) 68.0365 2.66656
\(652\) 35.2025 1.37864
\(653\) 27.2781 1.06747 0.533736 0.845651i \(-0.320787\pi\)
0.533736 + 0.845651i \(0.320787\pi\)
\(654\) −41.6381 −1.62818
\(655\) 26.4777 1.03457
\(656\) 54.2808 2.11931
\(657\) −114.469 −4.46586
\(658\) 98.6387 3.84534
\(659\) 32.9389 1.28312 0.641559 0.767073i \(-0.278288\pi\)
0.641559 + 0.767073i \(0.278288\pi\)
\(660\) 56.8695 2.21364
\(661\) 3.84905 0.149711 0.0748554 0.997194i \(-0.476150\pi\)
0.0748554 + 0.997194i \(0.476150\pi\)
\(662\) −7.18389 −0.279210
\(663\) 59.6556 2.31683
\(664\) 40.5913 1.57525
\(665\) 25.3071 0.981368
\(666\) 161.605 6.26207
\(667\) 11.1665 0.432369
\(668\) 80.5695 3.11733
\(669\) −24.6017 −0.951158
\(670\) 53.1574 2.05365
\(671\) 22.4332 0.866022
\(672\) 186.125 7.17995
\(673\) −10.9814 −0.423300 −0.211650 0.977346i \(-0.567884\pi\)
−0.211650 + 0.977346i \(0.567884\pi\)
\(674\) −31.7787 −1.22407
\(675\) −30.9305 −1.19051
\(676\) 62.1920 2.39200
\(677\) 37.6395 1.44660 0.723301 0.690533i \(-0.242624\pi\)
0.723301 + 0.690533i \(0.242624\pi\)
\(678\) 8.45712 0.324794
\(679\) −45.2845 −1.73786
\(680\) 48.9602 1.87754
\(681\) −73.3266 −2.80988
\(682\) 29.2003 1.11814
\(683\) −3.96056 −0.151547 −0.0757733 0.997125i \(-0.524143\pi\)
−0.0757733 + 0.997125i \(0.524143\pi\)
\(684\) −132.998 −5.08530
\(685\) −0.344631 −0.0131677
\(686\) 40.9312 1.56276
\(687\) 31.7682 1.21203
\(688\) 58.0997 2.21503
\(689\) 8.18840 0.311953
\(690\) −114.997 −4.37785
\(691\) 23.8477 0.907208 0.453604 0.891203i \(-0.350138\pi\)
0.453604 + 0.891203i \(0.350138\pi\)
\(692\) −81.5633 −3.10057
\(693\) −65.2476 −2.47855
\(694\) 42.1238 1.59900
\(695\) −0.901386 −0.0341915
\(696\) −34.4747 −1.30676
\(697\) −17.8365 −0.675605
\(698\) 11.1599 0.422408
\(699\) 76.7699 2.90370
\(700\) 49.3963 1.86701
\(701\) −38.7044 −1.46185 −0.730923 0.682460i \(-0.760910\pi\)
−0.730923 + 0.682460i \(0.760910\pi\)
\(702\) 177.147 6.68598
\(703\) 31.3517 1.18245
\(704\) 30.8361 1.16218
\(705\) 46.0501 1.73435
\(706\) −8.51682 −0.320535
\(707\) −69.0677 −2.59756
\(708\) −109.685 −4.12223
\(709\) −6.74522 −0.253322 −0.126661 0.991946i \(-0.540426\pi\)
−0.126661 + 0.991946i \(0.540426\pi\)
\(710\) 4.33359 0.162637
\(711\) −25.5645 −0.958743
\(712\) 140.746 5.27467
\(713\) −42.2694 −1.58300
\(714\) −132.162 −4.94602
\(715\) −17.8234 −0.666556
\(716\) −113.584 −4.24483
\(717\) −34.3740 −1.28372
\(718\) −13.9904 −0.522116
\(719\) 37.0830 1.38296 0.691482 0.722394i \(-0.256958\pi\)
0.691482 + 0.722394i \(0.256958\pi\)
\(720\) 132.331 4.93168
\(721\) 34.3869 1.28064
\(722\) 14.3665 0.534664
\(723\) −5.32804 −0.198152
\(724\) 36.3545 1.35110
\(725\) −3.12807 −0.116173
\(726\) 53.2932 1.97790
\(727\) −16.6745 −0.618422 −0.309211 0.950993i \(-0.600065\pi\)
−0.309211 + 0.950993i \(0.600065\pi\)
\(728\) −170.619 −6.32358
\(729\) 22.0825 0.817869
\(730\) 69.2734 2.56393
\(731\) −19.0914 −0.706120
\(732\) 166.236 6.14428
\(733\) 28.5766 1.05550 0.527751 0.849399i \(-0.323035\pi\)
0.527751 + 0.849399i \(0.323035\pi\)
\(734\) 88.8840 3.28077
\(735\) 55.5556 2.04920
\(736\) −115.635 −4.26237
\(737\) −26.5884 −0.979395
\(738\) −91.1529 −3.35538
\(739\) 6.37684 0.234576 0.117288 0.993098i \(-0.462580\pi\)
0.117288 + 0.993098i \(0.462580\pi\)
\(740\) −70.0113 −2.57366
\(741\) 59.1451 2.17275
\(742\) −18.1407 −0.665964
\(743\) 34.9524 1.28228 0.641139 0.767425i \(-0.278462\pi\)
0.641139 + 0.767425i \(0.278462\pi\)
\(744\) 130.500 4.78435
\(745\) −14.4931 −0.530987
\(746\) 81.8378 2.99630
\(747\) −36.0507 −1.31903
\(748\) −40.6054 −1.48468
\(749\) 64.1334 2.34338
\(750\) 101.283 3.69834
\(751\) −47.6699 −1.73950 −0.869750 0.493493i \(-0.835720\pi\)
−0.869750 + 0.493493i \(0.835720\pi\)
\(752\) 100.063 3.64891
\(753\) −92.1083 −3.35661
\(754\) 17.9153 0.652435
\(755\) −12.0954 −0.440197
\(756\) −280.945 −10.2179
\(757\) 15.9954 0.581363 0.290681 0.956820i \(-0.406118\pi\)
0.290681 + 0.956820i \(0.406118\pi\)
\(758\) 32.4592 1.17897
\(759\) 57.5193 2.08782
\(760\) 48.5412 1.76077
\(761\) −3.36358 −0.121930 −0.0609648 0.998140i \(-0.519418\pi\)
−0.0609648 + 0.998140i \(0.519418\pi\)
\(762\) −24.3187 −0.880972
\(763\) −20.6961 −0.749248
\(764\) −44.5833 −1.61297
\(765\) −43.4835 −1.57215
\(766\) 76.5912 2.76735
\(767\) 34.3762 1.24125
\(768\) −6.44311 −0.232496
\(769\) 28.0621 1.01195 0.505973 0.862549i \(-0.331133\pi\)
0.505973 + 0.862549i \(0.331133\pi\)
\(770\) 39.4860 1.42298
\(771\) −0.623183 −0.0224434
\(772\) −0.403872 −0.0145357
\(773\) 46.3326 1.66647 0.833233 0.552922i \(-0.186487\pi\)
0.833233 + 0.552922i \(0.186487\pi\)
\(774\) −97.5661 −3.50694
\(775\) 11.8409 0.425338
\(776\) −86.8595 −3.11808
\(777\) 113.977 4.08890
\(778\) −35.6475 −1.27803
\(779\) −17.6838 −0.633589
\(780\) −132.076 −4.72910
\(781\) −2.16758 −0.0775622
\(782\) 82.1089 2.93621
\(783\) 17.7911 0.635801
\(784\) 120.717 4.31133
\(785\) −4.90779 −0.175166
\(786\) −137.091 −4.88989
\(787\) 44.1689 1.57445 0.787226 0.616665i \(-0.211517\pi\)
0.787226 + 0.616665i \(0.211517\pi\)
\(788\) −103.312 −3.68035
\(789\) 19.5606 0.696375
\(790\) 15.4709 0.550431
\(791\) 4.20358 0.149462
\(792\) −125.150 −4.44703
\(793\) −52.0998 −1.85012
\(794\) −18.3770 −0.652174
\(795\) −8.46908 −0.300367
\(796\) −21.6184 −0.766245
\(797\) −27.5301 −0.975167 −0.487584 0.873076i \(-0.662122\pi\)
−0.487584 + 0.873076i \(0.662122\pi\)
\(798\) −131.031 −4.63843
\(799\) −32.8803 −1.16322
\(800\) 32.3929 1.14526
\(801\) −125.002 −4.41672
\(802\) −10.5641 −0.373031
\(803\) −34.6493 −1.22275
\(804\) −197.028 −6.94864
\(805\) −57.1588 −2.01458
\(806\) −67.8161 −2.38872
\(807\) −31.7991 −1.11938
\(808\) −132.478 −4.66055
\(809\) 17.9031 0.629439 0.314720 0.949185i \(-0.398090\pi\)
0.314720 + 0.949185i \(0.398090\pi\)
\(810\) −90.1216 −3.16655
\(811\) −31.9472 −1.12182 −0.560909 0.827877i \(-0.689548\pi\)
−0.560909 + 0.827877i \(0.689548\pi\)
\(812\) −28.4126 −0.997086
\(813\) 39.7515 1.39415
\(814\) 48.9172 1.71455
\(815\) 11.4109 0.399708
\(816\) −134.070 −4.69337
\(817\) −18.9280 −0.662207
\(818\) 82.5264 2.88547
\(819\) 151.534 5.29503
\(820\) 39.4896 1.37904
\(821\) −0.620164 −0.0216439 −0.0108219 0.999941i \(-0.503445\pi\)
−0.0108219 + 0.999941i \(0.503445\pi\)
\(822\) 1.78437 0.0622370
\(823\) −19.4882 −0.679316 −0.339658 0.940549i \(-0.610311\pi\)
−0.339658 + 0.940549i \(0.610311\pi\)
\(824\) 65.9571 2.29772
\(825\) −16.1128 −0.560977
\(826\) −76.1574 −2.64986
\(827\) −10.1962 −0.354556 −0.177278 0.984161i \(-0.556729\pi\)
−0.177278 + 0.984161i \(0.556729\pi\)
\(828\) 300.390 10.4393
\(829\) −9.48036 −0.329266 −0.164633 0.986355i \(-0.552644\pi\)
−0.164633 + 0.986355i \(0.552644\pi\)
\(830\) 21.8169 0.757276
\(831\) −95.8668 −3.32558
\(832\) −71.6152 −2.48281
\(833\) −39.6673 −1.37439
\(834\) 4.66703 0.161606
\(835\) 26.1167 0.903804
\(836\) −40.2579 −1.39235
\(837\) −67.3460 −2.32782
\(838\) −38.9710 −1.34623
\(839\) 42.1445 1.45499 0.727495 0.686113i \(-0.240684\pi\)
0.727495 + 0.686113i \(0.240684\pi\)
\(840\) 176.468 6.08873
\(841\) −27.2007 −0.937957
\(842\) −102.795 −3.54256
\(843\) 76.4097 2.63169
\(844\) −98.3770 −3.38627
\(845\) 20.1596 0.693511
\(846\) −168.034 −5.77712
\(847\) 26.4892 0.910181
\(848\) −18.4025 −0.631946
\(849\) 4.40903 0.151317
\(850\) −23.0011 −0.788932
\(851\) −70.8111 −2.42737
\(852\) −16.0624 −0.550290
\(853\) 19.5852 0.670585 0.335293 0.942114i \(-0.391165\pi\)
0.335293 + 0.942114i \(0.391165\pi\)
\(854\) 115.422 3.94967
\(855\) −43.1114 −1.47438
\(856\) 123.013 4.20451
\(857\) −47.5609 −1.62465 −0.812325 0.583205i \(-0.801798\pi\)
−0.812325 + 0.583205i \(0.801798\pi\)
\(858\) 92.2825 3.15047
\(859\) 1.90388 0.0649595 0.0324797 0.999472i \(-0.489660\pi\)
0.0324797 + 0.999472i \(0.489660\pi\)
\(860\) 42.2680 1.44133
\(861\) −64.2883 −2.19094
\(862\) −26.3113 −0.896165
\(863\) 7.87449 0.268051 0.134025 0.990978i \(-0.457210\pi\)
0.134025 + 0.990978i \(0.457210\pi\)
\(864\) −184.237 −6.26786
\(865\) −26.4388 −0.898946
\(866\) −48.4021 −1.64477
\(867\) −10.1347 −0.344194
\(868\) 107.552 3.65057
\(869\) −7.73827 −0.262503
\(870\) −18.5294 −0.628204
\(871\) 61.7501 2.09232
\(872\) −39.6968 −1.34430
\(873\) 77.1434 2.61091
\(874\) 81.4062 2.75361
\(875\) 50.3425 1.70189
\(876\) −256.762 −8.67518
\(877\) 40.7578 1.37629 0.688147 0.725571i \(-0.258424\pi\)
0.688147 + 0.725571i \(0.258424\pi\)
\(878\) 49.0966 1.65693
\(879\) 72.4633 2.44413
\(880\) 40.0561 1.35029
\(881\) −13.5227 −0.455590 −0.227795 0.973709i \(-0.573152\pi\)
−0.227795 + 0.973709i \(0.573152\pi\)
\(882\) −202.719 −6.82589
\(883\) −12.7088 −0.427686 −0.213843 0.976868i \(-0.568598\pi\)
−0.213843 + 0.976868i \(0.568598\pi\)
\(884\) 94.3039 3.17178
\(885\) −35.5546 −1.19515
\(886\) −15.7754 −0.529983
\(887\) −11.7992 −0.396179 −0.198090 0.980184i \(-0.563474\pi\)
−0.198090 + 0.980184i \(0.563474\pi\)
\(888\) 218.617 7.33632
\(889\) −12.0875 −0.405402
\(890\) 75.6476 2.53571
\(891\) 45.0772 1.51014
\(892\) −38.8906 −1.30215
\(893\) −32.5989 −1.09088
\(894\) 75.0398 2.50971
\(895\) −36.8184 −1.23070
\(896\) 41.8768 1.39901
\(897\) −133.585 −4.46029
\(898\) −84.5840 −2.82261
\(899\) −6.81085 −0.227155
\(900\) −84.1480 −2.80493
\(901\) 6.04701 0.201455
\(902\) −27.5916 −0.918700
\(903\) −68.8114 −2.28990
\(904\) 8.06283 0.268166
\(905\) 11.7843 0.391724
\(906\) 62.6254 2.08059
\(907\) 40.2844 1.33762 0.668811 0.743433i \(-0.266804\pi\)
0.668811 + 0.743433i \(0.266804\pi\)
\(908\) −115.915 −3.84678
\(909\) 117.659 3.90250
\(910\) −91.7042 −3.03996
\(911\) 0.493027 0.0163347 0.00816736 0.999967i \(-0.497400\pi\)
0.00816736 + 0.999967i \(0.497400\pi\)
\(912\) −132.922 −4.40149
\(913\) −10.9124 −0.361148
\(914\) −52.2150 −1.72712
\(915\) 53.8857 1.78141
\(916\) 50.2194 1.65930
\(917\) −68.1408 −2.25021
\(918\) 130.820 4.31772
\(919\) 12.7766 0.421462 0.210731 0.977544i \(-0.432416\pi\)
0.210731 + 0.977544i \(0.432416\pi\)
\(920\) −109.635 −3.61457
\(921\) −26.2802 −0.865962
\(922\) −44.5031 −1.46563
\(923\) 5.03410 0.165699
\(924\) −146.355 −4.81472
\(925\) 19.8363 0.652213
\(926\) −33.9005 −1.11404
\(927\) −58.5791 −1.92399
\(928\) −18.6323 −0.611634
\(929\) −23.3053 −0.764623 −0.382311 0.924034i \(-0.624872\pi\)
−0.382311 + 0.924034i \(0.624872\pi\)
\(930\) 70.1407 2.30000
\(931\) −39.3278 −1.28892
\(932\) 121.358 3.97522
\(933\) −8.96539 −0.293514
\(934\) −17.9723 −0.588072
\(935\) −13.1623 −0.430453
\(936\) 290.655 9.50036
\(937\) 19.0057 0.620889 0.310444 0.950592i \(-0.399522\pi\)
0.310444 + 0.950592i \(0.399522\pi\)
\(938\) −136.802 −4.46673
\(939\) −79.7818 −2.60358
\(940\) 72.7963 2.37435
\(941\) 26.0101 0.847905 0.423953 0.905684i \(-0.360642\pi\)
0.423953 + 0.905684i \(0.360642\pi\)
\(942\) 25.4106 0.827924
\(943\) 39.9408 1.30065
\(944\) −77.2569 −2.51450
\(945\) −91.0685 −2.96246
\(946\) −29.5329 −0.960196
\(947\) 36.9855 1.20187 0.600934 0.799299i \(-0.294796\pi\)
0.600934 + 0.799299i \(0.294796\pi\)
\(948\) −57.3429 −1.86241
\(949\) 80.4712 2.61220
\(950\) −22.8043 −0.739869
\(951\) −44.8442 −1.45417
\(952\) −126.000 −4.08368
\(953\) −61.1788 −1.98178 −0.990888 0.134686i \(-0.956997\pi\)
−0.990888 + 0.134686i \(0.956997\pi\)
\(954\) 30.9031 1.00053
\(955\) −14.4517 −0.467647
\(956\) −54.3386 −1.75744
\(957\) 9.26805 0.299593
\(958\) −109.023 −3.52238
\(959\) 0.886915 0.0286400
\(960\) 74.0701 2.39060
\(961\) −5.21834 −0.168333
\(962\) −113.608 −3.66286
\(963\) −109.253 −3.52063
\(964\) −8.42259 −0.271273
\(965\) −0.130915 −0.00421432
\(966\) 295.946 9.52192
\(967\) 27.2888 0.877550 0.438775 0.898597i \(-0.355413\pi\)
0.438775 + 0.898597i \(0.355413\pi\)
\(968\) 50.8086 1.63305
\(969\) 43.6778 1.40313
\(970\) −46.6851 −1.49897
\(971\) 50.8894 1.63312 0.816560 0.577261i \(-0.195878\pi\)
0.816560 + 0.577261i \(0.195878\pi\)
\(972\) 133.532 4.28303
\(973\) 2.31973 0.0743673
\(974\) 83.3507 2.67073
\(975\) 37.4212 1.19844
\(976\) 117.089 3.74792
\(977\) −3.85414 −0.123305 −0.0616525 0.998098i \(-0.519637\pi\)
−0.0616525 + 0.998098i \(0.519637\pi\)
\(978\) −59.0815 −1.88922
\(979\) −37.8376 −1.20929
\(980\) 87.8226 2.80539
\(981\) 35.2563 1.12565
\(982\) −58.6640 −1.87204
\(983\) 0.663283 0.0211554 0.0105777 0.999944i \(-0.496633\pi\)
0.0105777 + 0.999944i \(0.496633\pi\)
\(984\) −123.310 −3.93099
\(985\) −33.4888 −1.06704
\(986\) 13.2302 0.421334
\(987\) −118.511 −3.77224
\(988\) 93.4969 2.97453
\(989\) 42.7509 1.35940
\(990\) −67.2656 −2.13784
\(991\) −18.4606 −0.586419 −0.293210 0.956048i \(-0.594723\pi\)
−0.293210 + 0.956048i \(0.594723\pi\)
\(992\) 70.5302 2.23934
\(993\) 8.63119 0.273903
\(994\) −11.1526 −0.353738
\(995\) −7.00763 −0.222157
\(996\) −80.8643 −2.56228
\(997\) −11.3310 −0.358858 −0.179429 0.983771i \(-0.557425\pi\)
−0.179429 + 0.983771i \(0.557425\pi\)
\(998\) 8.84730 0.280056
\(999\) −112.820 −3.56947
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 \(a_p\))