Properties

Label 8041.2.a.j.1.2
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 82
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(0\)
Dimension: \(82\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.70525 q^{2}\) \(-2.86444 q^{3}\) \(+5.31840 q^{4}\) \(+1.46004 q^{5}\) \(+7.74904 q^{6}\) \(-3.90191 q^{7}\) \(-8.97712 q^{8}\) \(+5.20501 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.70525 q^{2}\) \(-2.86444 q^{3}\) \(+5.31840 q^{4}\) \(+1.46004 q^{5}\) \(+7.74904 q^{6}\) \(-3.90191 q^{7}\) \(-8.97712 q^{8}\) \(+5.20501 q^{9}\) \(-3.94978 q^{10}\) \(+1.00000 q^{11}\) \(-15.2342 q^{12}\) \(-2.79985 q^{13}\) \(+10.5557 q^{14}\) \(-4.18220 q^{15}\) \(+13.6486 q^{16}\) \(+1.00000 q^{17}\) \(-14.0809 q^{18}\) \(+0.0854401 q^{19}\) \(+7.76508 q^{20}\) \(+11.1768 q^{21}\) \(-2.70525 q^{22}\) \(+2.41012 q^{23}\) \(+25.7144 q^{24}\) \(-2.86828 q^{25}\) \(+7.57432 q^{26}\) \(-6.31612 q^{27}\) \(-20.7519 q^{28}\) \(-3.04090 q^{29}\) \(+11.3139 q^{30}\) \(+10.3818 q^{31}\) \(-18.9686 q^{32}\) \(-2.86444 q^{33}\) \(-2.70525 q^{34}\) \(-5.69695 q^{35}\) \(+27.6823 q^{36}\) \(+8.69439 q^{37}\) \(-0.231137 q^{38}\) \(+8.02001 q^{39}\) \(-13.1070 q^{40}\) \(+3.21483 q^{41}\) \(-30.2360 q^{42}\) \(+1.00000 q^{43}\) \(+5.31840 q^{44}\) \(+7.59953 q^{45}\) \(-6.51998 q^{46}\) \(+5.14653 q^{47}\) \(-39.0955 q^{48}\) \(+8.22490 q^{49}\) \(+7.75943 q^{50}\) \(-2.86444 q^{51}\) \(-14.8907 q^{52}\) \(-8.25146 q^{53}\) \(+17.0867 q^{54}\) \(+1.46004 q^{55}\) \(+35.0279 q^{56}\) \(-0.244738 q^{57}\) \(+8.22640 q^{58}\) \(-1.57918 q^{59}\) \(-22.2426 q^{60}\) \(+4.41140 q^{61}\) \(-28.0854 q^{62}\) \(-20.3095 q^{63}\) \(+24.0179 q^{64}\) \(-4.08790 q^{65}\) \(+7.74904 q^{66}\) \(+11.0950 q^{67}\) \(+5.31840 q^{68}\) \(-6.90364 q^{69}\) \(+15.4117 q^{70}\) \(-6.21684 q^{71}\) \(-46.7260 q^{72}\) \(-13.0490 q^{73}\) \(-23.5205 q^{74}\) \(+8.21601 q^{75}\) \(+0.454405 q^{76}\) \(-3.90191 q^{77}\) \(-21.6962 q^{78}\) \(-13.3929 q^{79}\) \(+19.9275 q^{80}\) \(+2.47710 q^{81}\) \(-8.69693 q^{82}\) \(+4.11226 q^{83}\) \(+59.4426 q^{84}\) \(+1.46004 q^{85}\) \(-2.70525 q^{86}\) \(+8.71046 q^{87}\) \(-8.97712 q^{88}\) \(+2.09674 q^{89}\) \(-20.5587 q^{90}\) \(+10.9248 q^{91}\) \(+12.8180 q^{92}\) \(-29.7380 q^{93}\) \(-13.9227 q^{94}\) \(+0.124746 q^{95}\) \(+54.3345 q^{96}\) \(-8.47364 q^{97}\) \(-22.2504 q^{98}\) \(+5.20501 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 82q^{11} \) \(\mathstrut +\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 26q^{13} \) \(\mathstrut +\mathstrut 17q^{14} \) \(\mathstrut +\mathstrut 66q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut +\mathstrut 82q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 9q^{20} \) \(\mathstrut +\mathstrut 22q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 117q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 30q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 26q^{30} \) \(\mathstrut +\mathstrut 40q^{31} \) \(\mathstrut +\mathstrut 58q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 160q^{36} \) \(\mathstrut +\mathstrut 31q^{37} \) \(\mathstrut +\mathstrut 18q^{38} \) \(\mathstrut +\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 29q^{40} \) \(\mathstrut +\mathstrut 42q^{41} \) \(\mathstrut -\mathstrut 51q^{42} \) \(\mathstrut +\mathstrut 82q^{43} \) \(\mathstrut +\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 84q^{47} \) \(\mathstrut -\mathstrut 46q^{48} \) \(\mathstrut +\mathstrut 136q^{49} \) \(\mathstrut +\mathstrut 59q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut +\mathstrut 83q^{53} \) \(\mathstrut +\mathstrut 24q^{54} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 23q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 96q^{59} \) \(\mathstrut +\mathstrut 184q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 148q^{64} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut +\mathstrut 10q^{66} \) \(\mathstrut +\mathstrut 78q^{67} \) \(\mathstrut +\mathstrut 98q^{68} \) \(\mathstrut +\mathstrut 61q^{69} \) \(\mathstrut -\mathstrut 3q^{70} \) \(\mathstrut +\mathstrut 155q^{71} \) \(\mathstrut +\mathstrut 50q^{72} \) \(\mathstrut -\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 10q^{74} \) \(\mathstrut -\mathstrut 19q^{75} \) \(\mathstrut +\mathstrut 44q^{76} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 27q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 19q^{80} \) \(\mathstrut +\mathstrut 150q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 54q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 11q^{85} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 81q^{90} \) \(\mathstrut -\mathstrut 14q^{91} \) \(\mathstrut +\mathstrut 60q^{92} \) \(\mathstrut +\mathstrut 36q^{93} \) \(\mathstrut +\mathstrut 19q^{94} \) \(\mathstrut +\mathstrut 111q^{95} \) \(\mathstrut -\mathstrut 6q^{96} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 5q^{98} \) \(\mathstrut +\mathstrut 108q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.70525 −1.91290 −0.956452 0.291890i \(-0.905716\pi\)
−0.956452 + 0.291890i \(0.905716\pi\)
\(3\) −2.86444 −1.65378 −0.826892 0.562360i \(-0.809893\pi\)
−0.826892 + 0.562360i \(0.809893\pi\)
\(4\) 5.31840 2.65920
\(5\) 1.46004 0.652950 0.326475 0.945206i \(-0.394139\pi\)
0.326475 + 0.945206i \(0.394139\pi\)
\(6\) 7.74904 3.16353
\(7\) −3.90191 −1.47478 −0.737392 0.675466i \(-0.763943\pi\)
−0.737392 + 0.675466i \(0.763943\pi\)
\(8\) −8.97712 −3.17389
\(9\) 5.20501 1.73500
\(10\) −3.94978 −1.24903
\(11\) 1.00000 0.301511
\(12\) −15.2342 −4.39774
\(13\) −2.79985 −0.776540 −0.388270 0.921546i \(-0.626927\pi\)
−0.388270 + 0.921546i \(0.626927\pi\)
\(14\) 10.5557 2.82112
\(15\) −4.18220 −1.07984
\(16\) 13.6486 3.41215
\(17\) 1.00000 0.242536
\(18\) −14.0809 −3.31889
\(19\) 0.0854401 0.0196013 0.00980066 0.999952i \(-0.496880\pi\)
0.00980066 + 0.999952i \(0.496880\pi\)
\(20\) 7.76508 1.73633
\(21\) 11.1768 2.43897
\(22\) −2.70525 −0.576762
\(23\) 2.41012 0.502544 0.251272 0.967916i \(-0.419151\pi\)
0.251272 + 0.967916i \(0.419151\pi\)
\(24\) 25.7144 5.24893
\(25\) −2.86828 −0.573656
\(26\) 7.57432 1.48545
\(27\) −6.31612 −1.21554
\(28\) −20.7519 −3.92174
\(29\) −3.04090 −0.564680 −0.282340 0.959314i \(-0.591111\pi\)
−0.282340 + 0.959314i \(0.591111\pi\)
\(30\) 11.3139 2.06563
\(31\) 10.3818 1.86463 0.932313 0.361652i \(-0.117787\pi\)
0.932313 + 0.361652i \(0.117787\pi\)
\(32\) −18.9686 −3.35322
\(33\) −2.86444 −0.498635
\(34\) −2.70525 −0.463947
\(35\) −5.69695 −0.962960
\(36\) 27.6823 4.61372
\(37\) 8.69439 1.42935 0.714675 0.699457i \(-0.246575\pi\)
0.714675 + 0.699457i \(0.246575\pi\)
\(38\) −0.231137 −0.0374954
\(39\) 8.02001 1.28423
\(40\) −13.1070 −2.07239
\(41\) 3.21483 0.502072 0.251036 0.967978i \(-0.419229\pi\)
0.251036 + 0.967978i \(0.419229\pi\)
\(42\) −30.2360 −4.66552
\(43\) 1.00000 0.152499
\(44\) 5.31840 0.801779
\(45\) 7.59953 1.13287
\(46\) −6.51998 −0.961319
\(47\) 5.14653 0.750698 0.375349 0.926884i \(-0.377523\pi\)
0.375349 + 0.926884i \(0.377523\pi\)
\(48\) −39.0955 −5.64295
\(49\) 8.22490 1.17499
\(50\) 7.75943 1.09735
\(51\) −2.86444 −0.401102
\(52\) −14.8907 −2.06497
\(53\) −8.25146 −1.13342 −0.566712 0.823916i \(-0.691785\pi\)
−0.566712 + 0.823916i \(0.691785\pi\)
\(54\) 17.0867 2.32521
\(55\) 1.46004 0.196872
\(56\) 35.0279 4.68080
\(57\) −0.244738 −0.0324163
\(58\) 8.22640 1.08018
\(59\) −1.57918 −0.205592 −0.102796 0.994702i \(-0.532779\pi\)
−0.102796 + 0.994702i \(0.532779\pi\)
\(60\) −22.2426 −2.87151
\(61\) 4.41140 0.564822 0.282411 0.959293i \(-0.408866\pi\)
0.282411 + 0.959293i \(0.408866\pi\)
\(62\) −28.0854 −3.56685
\(63\) −20.3095 −2.55875
\(64\) 24.0179 3.00223
\(65\) −4.08790 −0.507042
\(66\) 7.74904 0.953840
\(67\) 11.0950 1.35547 0.677737 0.735305i \(-0.262961\pi\)
0.677737 + 0.735305i \(0.262961\pi\)
\(68\) 5.31840 0.644951
\(69\) −6.90364 −0.831100
\(70\) 15.4117 1.84205
\(71\) −6.21684 −0.737803 −0.368901 0.929469i \(-0.620266\pi\)
−0.368901 + 0.929469i \(0.620266\pi\)
\(72\) −46.7260 −5.50671
\(73\) −13.0490 −1.52727 −0.763636 0.645647i \(-0.776588\pi\)
−0.763636 + 0.645647i \(0.776588\pi\)
\(74\) −23.5205 −2.73421
\(75\) 8.21601 0.948703
\(76\) 0.454405 0.0521238
\(77\) −3.90191 −0.444664
\(78\) −21.6962 −2.45661
\(79\) −13.3929 −1.50681 −0.753407 0.657554i \(-0.771591\pi\)
−0.753407 + 0.657554i \(0.771591\pi\)
\(80\) 19.9275 2.22796
\(81\) 2.47710 0.275233
\(82\) −8.69693 −0.960416
\(83\) 4.11226 0.451379 0.225690 0.974199i \(-0.427536\pi\)
0.225690 + 0.974199i \(0.427536\pi\)
\(84\) 59.4426 6.48572
\(85\) 1.46004 0.158364
\(86\) −2.70525 −0.291715
\(87\) 8.71046 0.933860
\(88\) −8.97712 −0.956964
\(89\) 2.09674 0.222254 0.111127 0.993806i \(-0.464554\pi\)
0.111127 + 0.993806i \(0.464554\pi\)
\(90\) −20.5587 −2.16707
\(91\) 10.9248 1.14523
\(92\) 12.8180 1.33637
\(93\) −29.7380 −3.08369
\(94\) −13.9227 −1.43601
\(95\) 0.124746 0.0127987
\(96\) 54.3345 5.54550
\(97\) −8.47364 −0.860368 −0.430184 0.902741i \(-0.641551\pi\)
−0.430184 + 0.902741i \(0.641551\pi\)
\(98\) −22.2504 −2.24763
\(99\) 5.20501 0.523123
\(100\) −15.2547 −1.52547
\(101\) −10.8536 −1.07997 −0.539986 0.841674i \(-0.681570\pi\)
−0.539986 + 0.841674i \(0.681570\pi\)
\(102\) 7.74904 0.767269
\(103\) 18.9072 1.86298 0.931492 0.363762i \(-0.118508\pi\)
0.931492 + 0.363762i \(0.118508\pi\)
\(104\) 25.1346 2.46465
\(105\) 16.3186 1.59253
\(106\) 22.3223 2.16813
\(107\) 12.1714 1.17665 0.588325 0.808625i \(-0.299788\pi\)
0.588325 + 0.808625i \(0.299788\pi\)
\(108\) −33.5916 −3.23236
\(109\) 8.96218 0.858421 0.429211 0.903204i \(-0.358792\pi\)
0.429211 + 0.903204i \(0.358792\pi\)
\(110\) −3.94978 −0.376597
\(111\) −24.9046 −2.36384
\(112\) −53.2555 −5.03217
\(113\) 15.6036 1.46786 0.733930 0.679226i \(-0.237684\pi\)
0.733930 + 0.679226i \(0.237684\pi\)
\(114\) 0.662079 0.0620094
\(115\) 3.51887 0.328136
\(116\) −16.1727 −1.50160
\(117\) −14.5733 −1.34730
\(118\) 4.27209 0.393277
\(119\) −3.90191 −0.357687
\(120\) 37.5441 3.42729
\(121\) 1.00000 0.0909091
\(122\) −11.9340 −1.08045
\(123\) −9.20869 −0.830319
\(124\) 55.2146 4.95842
\(125\) −11.4880 −1.02752
\(126\) 54.9423 4.89465
\(127\) −4.09351 −0.363240 −0.181620 0.983369i \(-0.558134\pi\)
−0.181620 + 0.983369i \(0.558134\pi\)
\(128\) −27.0371 −2.38977
\(129\) −2.86444 −0.252200
\(130\) 11.0588 0.969922
\(131\) 5.03598 0.439996 0.219998 0.975500i \(-0.429395\pi\)
0.219998 + 0.975500i \(0.429395\pi\)
\(132\) −15.2342 −1.32597
\(133\) −0.333380 −0.0289077
\(134\) −30.0149 −2.59289
\(135\) −9.22179 −0.793685
\(136\) −8.97712 −0.769781
\(137\) −19.0186 −1.62487 −0.812436 0.583050i \(-0.801859\pi\)
−0.812436 + 0.583050i \(0.801859\pi\)
\(138\) 18.6761 1.58981
\(139\) 14.1586 1.20092 0.600460 0.799655i \(-0.294984\pi\)
0.600460 + 0.799655i \(0.294984\pi\)
\(140\) −30.2986 −2.56070
\(141\) −14.7419 −1.24149
\(142\) 16.8181 1.41135
\(143\) −2.79985 −0.234136
\(144\) 71.0410 5.92008
\(145\) −4.43983 −0.368708
\(146\) 35.3009 2.92152
\(147\) −23.5597 −1.94317
\(148\) 46.2403 3.80093
\(149\) 5.96756 0.488882 0.244441 0.969664i \(-0.421396\pi\)
0.244441 + 0.969664i \(0.421396\pi\)
\(150\) −22.2264 −1.81478
\(151\) −1.83128 −0.149028 −0.0745138 0.997220i \(-0.523740\pi\)
−0.0745138 + 0.997220i \(0.523740\pi\)
\(152\) −0.767006 −0.0622124
\(153\) 5.20501 0.420800
\(154\) 10.5557 0.850599
\(155\) 15.1579 1.21751
\(156\) 42.6536 3.41502
\(157\) −13.6927 −1.09280 −0.546400 0.837524i \(-0.684002\pi\)
−0.546400 + 0.837524i \(0.684002\pi\)
\(158\) 36.2311 2.88239
\(159\) 23.6358 1.87444
\(160\) −27.6950 −2.18948
\(161\) −9.40406 −0.741144
\(162\) −6.70118 −0.526494
\(163\) −10.9932 −0.861057 −0.430528 0.902577i \(-0.641673\pi\)
−0.430528 + 0.902577i \(0.641673\pi\)
\(164\) 17.0978 1.33511
\(165\) −4.18220 −0.325584
\(166\) −11.1247 −0.863445
\(167\) −0.717479 −0.0555202 −0.0277601 0.999615i \(-0.508837\pi\)
−0.0277601 + 0.999615i \(0.508837\pi\)
\(168\) −100.335 −7.74103
\(169\) −5.16082 −0.396986
\(170\) −3.94978 −0.302934
\(171\) 0.444717 0.0340083
\(172\) 5.31840 0.405524
\(173\) 14.3090 1.08790 0.543948 0.839119i \(-0.316929\pi\)
0.543948 + 0.839119i \(0.316929\pi\)
\(174\) −23.5640 −1.78638
\(175\) 11.1918 0.846018
\(176\) 13.6486 1.02880
\(177\) 4.52347 0.340005
\(178\) −5.67222 −0.425151
\(179\) 21.7483 1.62554 0.812772 0.582582i \(-0.197958\pi\)
0.812772 + 0.582582i \(0.197958\pi\)
\(180\) 40.4173 3.01253
\(181\) −2.64099 −0.196303 −0.0981515 0.995171i \(-0.531293\pi\)
−0.0981515 + 0.995171i \(0.531293\pi\)
\(182\) −29.5543 −2.19071
\(183\) −12.6362 −0.934094
\(184\) −21.6359 −1.59502
\(185\) 12.6942 0.933294
\(186\) 80.4489 5.89880
\(187\) 1.00000 0.0731272
\(188\) 27.3713 1.99626
\(189\) 24.6449 1.79265
\(190\) −0.337470 −0.0244826
\(191\) 13.3372 0.965049 0.482525 0.875882i \(-0.339720\pi\)
0.482525 + 0.875882i \(0.339720\pi\)
\(192\) −68.7977 −4.96504
\(193\) −4.69011 −0.337602 −0.168801 0.985650i \(-0.553989\pi\)
−0.168801 + 0.985650i \(0.553989\pi\)
\(194\) 22.9234 1.64580
\(195\) 11.7095 0.838538
\(196\) 43.7433 3.12452
\(197\) −5.93508 −0.422857 −0.211428 0.977393i \(-0.567812\pi\)
−0.211428 + 0.977393i \(0.567812\pi\)
\(198\) −14.0809 −1.00068
\(199\) −1.90194 −0.134825 −0.0674124 0.997725i \(-0.521474\pi\)
−0.0674124 + 0.997725i \(0.521474\pi\)
\(200\) 25.7489 1.82072
\(201\) −31.7810 −2.24166
\(202\) 29.3617 2.06588
\(203\) 11.8653 0.832781
\(204\) −15.2342 −1.06661
\(205\) 4.69378 0.327828
\(206\) −51.1488 −3.56371
\(207\) 12.5447 0.871916
\(208\) −38.2140 −2.64967
\(209\) 0.0854401 0.00591002
\(210\) −44.1458 −3.04635
\(211\) −23.3274 −1.60593 −0.802963 0.596028i \(-0.796745\pi\)
−0.802963 + 0.596028i \(0.796745\pi\)
\(212\) −43.8845 −3.01400
\(213\) 17.8077 1.22017
\(214\) −32.9266 −2.25082
\(215\) 1.46004 0.0995740
\(216\) 56.7005 3.85798
\(217\) −40.5088 −2.74992
\(218\) −24.2450 −1.64208
\(219\) 37.3781 2.52578
\(220\) 7.76508 0.523522
\(221\) −2.79985 −0.188339
\(222\) 67.3731 4.52179
\(223\) 0.170281 0.0114029 0.00570144 0.999984i \(-0.498185\pi\)
0.00570144 + 0.999984i \(0.498185\pi\)
\(224\) 74.0139 4.94527
\(225\) −14.9294 −0.995295
\(226\) −42.2116 −2.80787
\(227\) −13.9926 −0.928721 −0.464360 0.885646i \(-0.653716\pi\)
−0.464360 + 0.885646i \(0.653716\pi\)
\(228\) −1.30162 −0.0862016
\(229\) −10.3592 −0.684554 −0.342277 0.939599i \(-0.611198\pi\)
−0.342277 + 0.939599i \(0.611198\pi\)
\(230\) −9.51944 −0.627693
\(231\) 11.1768 0.735378
\(232\) 27.2985 1.79223
\(233\) 21.2870 1.39455 0.697277 0.716801i \(-0.254395\pi\)
0.697277 + 0.716801i \(0.254395\pi\)
\(234\) 39.4244 2.57725
\(235\) 7.51414 0.490168
\(236\) −8.39872 −0.546710
\(237\) 38.3630 2.49195
\(238\) 10.5557 0.684222
\(239\) 18.4546 1.19373 0.596866 0.802341i \(-0.296413\pi\)
0.596866 + 0.802341i \(0.296413\pi\)
\(240\) −57.0811 −3.68457
\(241\) 11.8870 0.765706 0.382853 0.923809i \(-0.374942\pi\)
0.382853 + 0.923809i \(0.374942\pi\)
\(242\) −2.70525 −0.173900
\(243\) 11.8529 0.760361
\(244\) 23.4616 1.50198
\(245\) 12.0087 0.767207
\(246\) 24.9118 1.58832
\(247\) −0.239220 −0.0152212
\(248\) −93.1986 −5.91812
\(249\) −11.7793 −0.746484
\(250\) 31.0780 1.96554
\(251\) 3.39419 0.214239 0.107120 0.994246i \(-0.465837\pi\)
0.107120 + 0.994246i \(0.465837\pi\)
\(252\) −108.014 −6.80424
\(253\) 2.41012 0.151523
\(254\) 11.0740 0.694844
\(255\) −4.18220 −0.261899
\(256\) 25.1065 1.56916
\(257\) −17.9527 −1.11986 −0.559930 0.828540i \(-0.689172\pi\)
−0.559930 + 0.828540i \(0.689172\pi\)
\(258\) 7.74904 0.482434
\(259\) −33.9247 −2.10798
\(260\) −21.7411 −1.34833
\(261\) −15.8279 −0.979722
\(262\) −13.6236 −0.841670
\(263\) 15.7554 0.971522 0.485761 0.874092i \(-0.338543\pi\)
0.485761 + 0.874092i \(0.338543\pi\)
\(264\) 25.7144 1.58261
\(265\) −12.0475 −0.740070
\(266\) 0.901877 0.0552976
\(267\) −6.00599 −0.367560
\(268\) 59.0078 3.60447
\(269\) −5.23879 −0.319415 −0.159707 0.987164i \(-0.551055\pi\)
−0.159707 + 0.987164i \(0.551055\pi\)
\(270\) 24.9473 1.51824
\(271\) 21.1346 1.28384 0.641918 0.766773i \(-0.278139\pi\)
0.641918 + 0.766773i \(0.278139\pi\)
\(272\) 13.6486 0.827567
\(273\) −31.2934 −1.89396
\(274\) 51.4503 3.10822
\(275\) −2.86828 −0.172964
\(276\) −36.7163 −2.21006
\(277\) −20.3154 −1.22063 −0.610316 0.792158i \(-0.708958\pi\)
−0.610316 + 0.792158i \(0.708958\pi\)
\(278\) −38.3027 −2.29725
\(279\) 54.0374 3.23513
\(280\) 51.1422 3.05633
\(281\) 11.7689 0.702076 0.351038 0.936361i \(-0.385829\pi\)
0.351038 + 0.936361i \(0.385829\pi\)
\(282\) 39.8806 2.37486
\(283\) −19.3526 −1.15039 −0.575195 0.818016i \(-0.695074\pi\)
−0.575195 + 0.818016i \(0.695074\pi\)
\(284\) −33.0636 −1.96196
\(285\) −0.357328 −0.0211663
\(286\) 7.57432 0.447879
\(287\) −12.5440 −0.740448
\(288\) −98.7320 −5.81784
\(289\) 1.00000 0.0588235
\(290\) 12.0109 0.705303
\(291\) 24.2722 1.42286
\(292\) −69.3999 −4.06132
\(293\) −1.26343 −0.0738103 −0.0369051 0.999319i \(-0.511750\pi\)
−0.0369051 + 0.999319i \(0.511750\pi\)
\(294\) 63.7350 3.71710
\(295\) −2.30567 −0.134241
\(296\) −78.0506 −4.53660
\(297\) −6.31612 −0.366498
\(298\) −16.1438 −0.935183
\(299\) −6.74798 −0.390246
\(300\) 43.6960 2.52279
\(301\) −3.90191 −0.224902
\(302\) 4.95408 0.285075
\(303\) 31.0894 1.78604
\(304\) 1.16614 0.0668825
\(305\) 6.44083 0.368801
\(306\) −14.0809 −0.804950
\(307\) −17.3585 −0.990701 −0.495351 0.868693i \(-0.664960\pi\)
−0.495351 + 0.868693i \(0.664960\pi\)
\(308\) −20.7519 −1.18245
\(309\) −54.1586 −3.08097
\(310\) −41.0059 −2.32898
\(311\) −4.55666 −0.258384 −0.129192 0.991620i \(-0.541238\pi\)
−0.129192 + 0.991620i \(0.541238\pi\)
\(312\) −71.9966 −4.07600
\(313\) −22.5999 −1.27742 −0.638711 0.769447i \(-0.720532\pi\)
−0.638711 + 0.769447i \(0.720532\pi\)
\(314\) 37.0423 2.09042
\(315\) −29.6527 −1.67074
\(316\) −71.2286 −4.00692
\(317\) −20.3039 −1.14038 −0.570189 0.821513i \(-0.693130\pi\)
−0.570189 + 0.821513i \(0.693130\pi\)
\(318\) −63.9408 −3.58562
\(319\) −3.04090 −0.170258
\(320\) 35.0671 1.96031
\(321\) −34.8641 −1.94592
\(322\) 25.4404 1.41774
\(323\) 0.0854401 0.00475402
\(324\) 13.1742 0.731900
\(325\) 8.03077 0.445467
\(326\) 29.7395 1.64712
\(327\) −25.6716 −1.41964
\(328\) −28.8599 −1.59352
\(329\) −20.0813 −1.10712
\(330\) 11.3139 0.622810
\(331\) −10.0546 −0.552650 −0.276325 0.961064i \(-0.589117\pi\)
−0.276325 + 0.961064i \(0.589117\pi\)
\(332\) 21.8707 1.20031
\(333\) 45.2544 2.47993
\(334\) 1.94096 0.106205
\(335\) 16.1992 0.885057
\(336\) 152.547 8.32213
\(337\) −8.61303 −0.469182 −0.234591 0.972094i \(-0.575375\pi\)
−0.234591 + 0.972094i \(0.575375\pi\)
\(338\) 13.9613 0.759396
\(339\) −44.6954 −2.42752
\(340\) 7.76508 0.421121
\(341\) 10.3818 0.562206
\(342\) −1.20307 −0.0650547
\(343\) −4.77943 −0.258065
\(344\) −8.97712 −0.484014
\(345\) −10.0796 −0.542667
\(346\) −38.7096 −2.08104
\(347\) 2.19565 0.117869 0.0589343 0.998262i \(-0.481230\pi\)
0.0589343 + 0.998262i \(0.481230\pi\)
\(348\) 46.3257 2.48332
\(349\) −14.0518 −0.752174 −0.376087 0.926584i \(-0.622731\pi\)
−0.376087 + 0.926584i \(0.622731\pi\)
\(350\) −30.2766 −1.61835
\(351\) 17.6842 0.943913
\(352\) −18.9686 −1.01103
\(353\) −10.2950 −0.547950 −0.273975 0.961737i \(-0.588339\pi\)
−0.273975 + 0.961737i \(0.588339\pi\)
\(354\) −12.2371 −0.650396
\(355\) −9.07683 −0.481748
\(356\) 11.1513 0.591018
\(357\) 11.1768 0.591538
\(358\) −58.8347 −3.10951
\(359\) −31.1739 −1.64529 −0.822647 0.568553i \(-0.807503\pi\)
−0.822647 + 0.568553i \(0.807503\pi\)
\(360\) −68.2218 −3.59561
\(361\) −18.9927 −0.999616
\(362\) 7.14454 0.375509
\(363\) −2.86444 −0.150344
\(364\) 58.1023 3.04539
\(365\) −19.0521 −0.997233
\(366\) 34.1841 1.78683
\(367\) −24.1619 −1.26124 −0.630620 0.776092i \(-0.717199\pi\)
−0.630620 + 0.776092i \(0.717199\pi\)
\(368\) 32.8947 1.71475
\(369\) 16.7332 0.871097
\(370\) −34.3410 −1.78530
\(371\) 32.1964 1.67156
\(372\) −158.159 −8.20015
\(373\) 2.28471 0.118298 0.0591488 0.998249i \(-0.481161\pi\)
0.0591488 + 0.998249i \(0.481161\pi\)
\(374\) −2.70525 −0.139885
\(375\) 32.9067 1.69930
\(376\) −46.2010 −2.38263
\(377\) 8.51407 0.438497
\(378\) −66.6707 −3.42917
\(379\) −23.1819 −1.19077 −0.595387 0.803439i \(-0.703001\pi\)
−0.595387 + 0.803439i \(0.703001\pi\)
\(380\) 0.663450 0.0340343
\(381\) 11.7256 0.600721
\(382\) −36.0806 −1.84605
\(383\) −21.3515 −1.09101 −0.545504 0.838108i \(-0.683662\pi\)
−0.545504 + 0.838108i \(0.683662\pi\)
\(384\) 77.4461 3.95216
\(385\) −5.69695 −0.290343
\(386\) 12.6879 0.645799
\(387\) 5.20501 0.264586
\(388\) −45.0662 −2.28789
\(389\) 15.3077 0.776129 0.388065 0.921632i \(-0.373144\pi\)
0.388065 + 0.921632i \(0.373144\pi\)
\(390\) −31.6773 −1.60404
\(391\) 2.41012 0.121885
\(392\) −73.8358 −3.72927
\(393\) −14.4253 −0.727659
\(394\) 16.0559 0.808885
\(395\) −19.5541 −0.983875
\(396\) 27.6823 1.39109
\(397\) 15.0866 0.757175 0.378588 0.925565i \(-0.376410\pi\)
0.378588 + 0.925565i \(0.376410\pi\)
\(398\) 5.14522 0.257907
\(399\) 0.954946 0.0478071
\(400\) −39.1480 −1.95740
\(401\) 15.0482 0.751471 0.375736 0.926727i \(-0.377390\pi\)
0.375736 + 0.926727i \(0.377390\pi\)
\(402\) 85.9758 4.28808
\(403\) −29.0675 −1.44796
\(404\) −57.7237 −2.87186
\(405\) 3.61666 0.179713
\(406\) −32.0987 −1.59303
\(407\) 8.69439 0.430965
\(408\) 25.7144 1.27305
\(409\) 14.0337 0.693922 0.346961 0.937880i \(-0.387214\pi\)
0.346961 + 0.937880i \(0.387214\pi\)
\(410\) −12.6979 −0.627104
\(411\) 54.4777 2.68719
\(412\) 100.556 4.95405
\(413\) 6.16182 0.303203
\(414\) −33.9366 −1.66789
\(415\) 6.00407 0.294728
\(416\) 53.1095 2.60391
\(417\) −40.5566 −1.98606
\(418\) −0.231137 −0.0113053
\(419\) −4.61075 −0.225250 −0.112625 0.993638i \(-0.535926\pi\)
−0.112625 + 0.993638i \(0.535926\pi\)
\(420\) 86.7886 4.23485
\(421\) −11.8350 −0.576802 −0.288401 0.957510i \(-0.593124\pi\)
−0.288401 + 0.957510i \(0.593124\pi\)
\(422\) 63.1066 3.07198
\(423\) 26.7877 1.30246
\(424\) 74.0743 3.59737
\(425\) −2.86828 −0.139132
\(426\) −48.1745 −2.33406
\(427\) −17.2129 −0.832990
\(428\) 64.7322 3.12895
\(429\) 8.02001 0.387210
\(430\) −3.94978 −0.190475
\(431\) 30.1359 1.45160 0.725799 0.687907i \(-0.241470\pi\)
0.725799 + 0.687907i \(0.241470\pi\)
\(432\) −86.2060 −4.14759
\(433\) 16.5008 0.792978 0.396489 0.918039i \(-0.370228\pi\)
0.396489 + 0.918039i \(0.370228\pi\)
\(434\) 109.587 5.26033
\(435\) 12.7176 0.609764
\(436\) 47.6645 2.28271
\(437\) 0.205921 0.00985053
\(438\) −101.117 −4.83157
\(439\) −36.3938 −1.73698 −0.868491 0.495705i \(-0.834910\pi\)
−0.868491 + 0.495705i \(0.834910\pi\)
\(440\) −13.1070 −0.624850
\(441\) 42.8107 2.03860
\(442\) 7.57432 0.360274
\(443\) 20.5084 0.974382 0.487191 0.873295i \(-0.338022\pi\)
0.487191 + 0.873295i \(0.338022\pi\)
\(444\) −132.452 −6.28591
\(445\) 3.06133 0.145121
\(446\) −0.460654 −0.0218126
\(447\) −17.0937 −0.808505
\(448\) −93.7155 −4.42764
\(449\) 25.1863 1.18862 0.594308 0.804238i \(-0.297426\pi\)
0.594308 + 0.804238i \(0.297426\pi\)
\(450\) 40.3879 1.90390
\(451\) 3.21483 0.151380
\(452\) 82.9860 3.90333
\(453\) 5.24560 0.246460
\(454\) 37.8535 1.77655
\(455\) 15.9506 0.747777
\(456\) 2.19704 0.102886
\(457\) −24.2591 −1.13479 −0.567397 0.823444i \(-0.692050\pi\)
−0.567397 + 0.823444i \(0.692050\pi\)
\(458\) 28.0242 1.30949
\(459\) −6.31612 −0.294811
\(460\) 18.7148 0.872580
\(461\) −5.33259 −0.248363 −0.124182 0.992259i \(-0.539631\pi\)
−0.124182 + 0.992259i \(0.539631\pi\)
\(462\) −30.2360 −1.40671
\(463\) 39.9014 1.85438 0.927188 0.374595i \(-0.122218\pi\)
0.927188 + 0.374595i \(0.122218\pi\)
\(464\) −41.5039 −1.92677
\(465\) −43.4188 −2.01350
\(466\) −57.5866 −2.66765
\(467\) 32.5132 1.50453 0.752267 0.658859i \(-0.228960\pi\)
0.752267 + 0.658859i \(0.228960\pi\)
\(468\) −77.5065 −3.58274
\(469\) −43.2918 −1.99903
\(470\) −20.3277 −0.937645
\(471\) 39.2220 1.80726
\(472\) 14.1765 0.652526
\(473\) 1.00000 0.0459800
\(474\) −103.782 −4.76685
\(475\) −0.245066 −0.0112444
\(476\) −20.7519 −0.951162
\(477\) −42.9489 −1.96650
\(478\) −49.9245 −2.28349
\(479\) 11.1410 0.509044 0.254522 0.967067i \(-0.418082\pi\)
0.254522 + 0.967067i \(0.418082\pi\)
\(480\) 79.3307 3.62093
\(481\) −24.3430 −1.10995
\(482\) −32.1572 −1.46472
\(483\) 26.9374 1.22569
\(484\) 5.31840 0.241745
\(485\) −12.3719 −0.561778
\(486\) −32.0650 −1.45450
\(487\) −20.6799 −0.937096 −0.468548 0.883438i \(-0.655223\pi\)
−0.468548 + 0.883438i \(0.655223\pi\)
\(488\) −39.6017 −1.79268
\(489\) 31.4895 1.42400
\(490\) −32.4865 −1.46759
\(491\) −30.4785 −1.37548 −0.687738 0.725959i \(-0.741396\pi\)
−0.687738 + 0.725959i \(0.741396\pi\)
\(492\) −48.9755 −2.20798
\(493\) −3.04090 −0.136955
\(494\) 0.647151 0.0291167
\(495\) 7.59953 0.341573
\(496\) 141.697 6.36238
\(497\) 24.2575 1.08810
\(498\) 31.8661 1.42795
\(499\) −9.37777 −0.419807 −0.209903 0.977722i \(-0.567315\pi\)
−0.209903 + 0.977722i \(0.567315\pi\)
\(500\) −61.0978 −2.73238
\(501\) 2.05517 0.0918184
\(502\) −9.18214 −0.409819
\(503\) 0.115930 0.00516908 0.00258454 0.999997i \(-0.499177\pi\)
0.00258454 + 0.999997i \(0.499177\pi\)
\(504\) 182.321 8.12120
\(505\) −15.8467 −0.705168
\(506\) −6.51998 −0.289849
\(507\) 14.7828 0.656529
\(508\) −21.7709 −0.965929
\(509\) 13.4272 0.595150 0.297575 0.954698i \(-0.403822\pi\)
0.297575 + 0.954698i \(0.403822\pi\)
\(510\) 11.3139 0.500988
\(511\) 50.9161 2.25240
\(512\) −13.8453 −0.611884
\(513\) −0.539650 −0.0238261
\(514\) 48.5666 2.14218
\(515\) 27.6053 1.21644
\(516\) −15.2342 −0.670650
\(517\) 5.14653 0.226344
\(518\) 91.7750 4.03236
\(519\) −40.9873 −1.79914
\(520\) 36.6976 1.60930
\(521\) −37.5304 −1.64424 −0.822119 0.569316i \(-0.807208\pi\)
−0.822119 + 0.569316i \(0.807208\pi\)
\(522\) 42.8185 1.87411
\(523\) 30.8897 1.35071 0.675356 0.737492i \(-0.263990\pi\)
0.675356 + 0.737492i \(0.263990\pi\)
\(524\) 26.7834 1.17004
\(525\) −32.0581 −1.39913
\(526\) −42.6225 −1.85843
\(527\) 10.3818 0.452238
\(528\) −39.0955 −1.70141
\(529\) −17.1913 −0.747449
\(530\) 32.5915 1.41568
\(531\) −8.21965 −0.356703
\(532\) −1.77305 −0.0768713
\(533\) −9.00106 −0.389879
\(534\) 16.2477 0.703108
\(535\) 17.7707 0.768294
\(536\) −99.6013 −4.30212
\(537\) −62.2967 −2.68830
\(538\) 14.1723 0.611010
\(539\) 8.22490 0.354271
\(540\) −49.0452 −2.11057
\(541\) −11.2165 −0.482233 −0.241117 0.970496i \(-0.577514\pi\)
−0.241117 + 0.970496i \(0.577514\pi\)
\(542\) −57.1745 −2.45585
\(543\) 7.56494 0.324643
\(544\) −18.9686 −0.813274
\(545\) 13.0852 0.560506
\(546\) 84.6565 3.62296
\(547\) 38.1870 1.63276 0.816379 0.577517i \(-0.195978\pi\)
0.816379 + 0.577517i \(0.195978\pi\)
\(548\) −101.149 −4.32086
\(549\) 22.9614 0.979968
\(550\) 7.75943 0.330863
\(551\) −0.259815 −0.0110685
\(552\) 61.9747 2.63782
\(553\) 52.2577 2.22222
\(554\) 54.9583 2.33495
\(555\) −36.3617 −1.54347
\(556\) 75.3013 3.19349
\(557\) −19.7566 −0.837114 −0.418557 0.908190i \(-0.637464\pi\)
−0.418557 + 0.908190i \(0.637464\pi\)
\(558\) −146.185 −6.18850
\(559\) −2.79985 −0.118421
\(560\) −77.7553 −3.28576
\(561\) −2.86444 −0.120937
\(562\) −31.8380 −1.34300
\(563\) 34.7217 1.46335 0.731673 0.681655i \(-0.238740\pi\)
0.731673 + 0.681655i \(0.238740\pi\)
\(564\) −78.4034 −3.30138
\(565\) 22.7818 0.958439
\(566\) 52.3536 2.20059
\(567\) −9.66541 −0.405909
\(568\) 55.8093 2.34170
\(569\) 6.48624 0.271917 0.135959 0.990715i \(-0.456589\pi\)
0.135959 + 0.990715i \(0.456589\pi\)
\(570\) 0.966662 0.0404890
\(571\) −21.4098 −0.895973 −0.447987 0.894040i \(-0.647859\pi\)
−0.447987 + 0.894040i \(0.647859\pi\)
\(572\) −14.8907 −0.622613
\(573\) −38.2037 −1.59598
\(574\) 33.9346 1.41640
\(575\) −6.91289 −0.288288
\(576\) 125.013 5.20888
\(577\) 24.2099 1.00787 0.503936 0.863741i \(-0.331885\pi\)
0.503936 + 0.863741i \(0.331885\pi\)
\(578\) −2.70525 −0.112524
\(579\) 13.4345 0.558320
\(580\) −23.6128 −0.980469
\(581\) −16.0457 −0.665687
\(582\) −65.6626 −2.72180
\(583\) −8.25146 −0.341740
\(584\) 117.143 4.84739
\(585\) −21.2776 −0.879719
\(586\) 3.41789 0.141192
\(587\) −14.3756 −0.593346 −0.296673 0.954979i \(-0.595877\pi\)
−0.296673 + 0.954979i \(0.595877\pi\)
\(588\) −125.300 −5.16728
\(589\) 0.887023 0.0365491
\(590\) 6.23742 0.256791
\(591\) 17.0007 0.699314
\(592\) 118.666 4.87715
\(593\) −12.6413 −0.519117 −0.259559 0.965727i \(-0.583577\pi\)
−0.259559 + 0.965727i \(0.583577\pi\)
\(594\) 17.0867 0.701076
\(595\) −5.69695 −0.233552
\(596\) 31.7379 1.30003
\(597\) 5.44798 0.222971
\(598\) 18.2550 0.746502
\(599\) 10.6326 0.434438 0.217219 0.976123i \(-0.430301\pi\)
0.217219 + 0.976123i \(0.430301\pi\)
\(600\) −73.7561 −3.01108
\(601\) 30.4403 1.24169 0.620843 0.783935i \(-0.286790\pi\)
0.620843 + 0.783935i \(0.286790\pi\)
\(602\) 10.5557 0.430216
\(603\) 57.7497 2.35175
\(604\) −9.73949 −0.396294
\(605\) 1.46004 0.0593591
\(606\) −84.1048 −3.41652
\(607\) 29.3697 1.19208 0.596039 0.802955i \(-0.296740\pi\)
0.596039 + 0.802955i \(0.296740\pi\)
\(608\) −1.62068 −0.0657274
\(609\) −33.9874 −1.37724
\(610\) −17.4241 −0.705480
\(611\) −14.4095 −0.582947
\(612\) 27.6823 1.11899
\(613\) −16.3021 −0.658438 −0.329219 0.944254i \(-0.606785\pi\)
−0.329219 + 0.944254i \(0.606785\pi\)
\(614\) 46.9591 1.89512
\(615\) −13.4451 −0.542157
\(616\) 35.0279 1.41131
\(617\) 19.4734 0.783968 0.391984 0.919972i \(-0.371789\pi\)
0.391984 + 0.919972i \(0.371789\pi\)
\(618\) 146.513 5.89361
\(619\) −25.0258 −1.00587 −0.502935 0.864324i \(-0.667747\pi\)
−0.502935 + 0.864324i \(0.667747\pi\)
\(620\) 80.6156 3.23760
\(621\) −15.2226 −0.610861
\(622\) 12.3269 0.494264
\(623\) −8.18129 −0.327777
\(624\) 109.462 4.38198
\(625\) −2.43157 −0.0972628
\(626\) 61.1385 2.44359
\(627\) −0.244738 −0.00977390
\(628\) −72.8235 −2.90597
\(629\) 8.69439 0.346668
\(630\) 80.2180 3.19596
\(631\) −36.8409 −1.46661 −0.733306 0.679898i \(-0.762024\pi\)
−0.733306 + 0.679898i \(0.762024\pi\)
\(632\) 120.229 4.78246
\(633\) 66.8200 2.65586
\(634\) 54.9271 2.18143
\(635\) −5.97670 −0.237178
\(636\) 125.705 4.98451
\(637\) −23.0285 −0.912423
\(638\) 8.22640 0.325686
\(639\) −32.3587 −1.28009
\(640\) −39.4753 −1.56040
\(641\) 16.6208 0.656484 0.328242 0.944594i \(-0.393544\pi\)
0.328242 + 0.944594i \(0.393544\pi\)
\(642\) 94.3163 3.72237
\(643\) 28.0723 1.10706 0.553532 0.832828i \(-0.313280\pi\)
0.553532 + 0.832828i \(0.313280\pi\)
\(644\) −50.0146 −1.97085
\(645\) −4.18220 −0.164674
\(646\) −0.231137 −0.00909398
\(647\) −43.4375 −1.70771 −0.853853 0.520514i \(-0.825740\pi\)
−0.853853 + 0.520514i \(0.825740\pi\)
\(648\) −22.2372 −0.873559
\(649\) −1.57918 −0.0619883
\(650\) −21.7253 −0.852135
\(651\) 116.035 4.54777
\(652\) −58.4664 −2.28972
\(653\) 42.0792 1.64669 0.823344 0.567543i \(-0.192106\pi\)
0.823344 + 0.567543i \(0.192106\pi\)
\(654\) 69.4483 2.71564
\(655\) 7.35274 0.287295
\(656\) 43.8779 1.71314
\(657\) −67.9203 −2.64982
\(658\) 54.3250 2.11781
\(659\) −36.7559 −1.43181 −0.715904 0.698199i \(-0.753985\pi\)
−0.715904 + 0.698199i \(0.753985\pi\)
\(660\) −22.2426 −0.865792
\(661\) 33.7598 1.31310 0.656552 0.754281i \(-0.272014\pi\)
0.656552 + 0.754281i \(0.272014\pi\)
\(662\) 27.2002 1.05717
\(663\) 8.02001 0.311471
\(664\) −36.9162 −1.43263
\(665\) −0.486748 −0.0188753
\(666\) −122.425 −4.74386
\(667\) −7.32892 −0.283777
\(668\) −3.81584 −0.147639
\(669\) −0.487760 −0.0188579
\(670\) −43.8229 −1.69303
\(671\) 4.41140 0.170300
\(672\) −212.008 −8.17840
\(673\) 27.9838 1.07870 0.539348 0.842083i \(-0.318671\pi\)
0.539348 + 0.842083i \(0.318671\pi\)
\(674\) 23.3004 0.897500
\(675\) 18.1164 0.697300
\(676\) −27.4473 −1.05566
\(677\) 22.1185 0.850082 0.425041 0.905174i \(-0.360260\pi\)
0.425041 + 0.905174i \(0.360260\pi\)
\(678\) 120.912 4.64362
\(679\) 33.0634 1.26886
\(680\) −13.1070 −0.502629
\(681\) 40.0809 1.53590
\(682\) −28.0854 −1.07545
\(683\) −35.8050 −1.37004 −0.685019 0.728525i \(-0.740206\pi\)
−0.685019 + 0.728525i \(0.740206\pi\)
\(684\) 2.36518 0.0904350
\(685\) −27.7680 −1.06096
\(686\) 12.9296 0.493654
\(687\) 29.6732 1.13210
\(688\) 13.6486 0.520347
\(689\) 23.1029 0.880149
\(690\) 27.2679 1.03807
\(691\) −23.0727 −0.877727 −0.438864 0.898554i \(-0.644619\pi\)
−0.438864 + 0.898554i \(0.644619\pi\)
\(692\) 76.1011 2.89293
\(693\) −20.3095 −0.771493
\(694\) −5.93979 −0.225471
\(695\) 20.6722 0.784141
\(696\) −78.1948 −2.96397
\(697\) 3.21483 0.121770
\(698\) 38.0136 1.43884
\(699\) −60.9752 −2.30629
\(700\) 59.5223 2.24973
\(701\) 14.8196 0.559728 0.279864 0.960040i \(-0.409711\pi\)
0.279864 + 0.960040i \(0.409711\pi\)
\(702\) −47.8403 −1.80561
\(703\) 0.742850 0.0280171
\(704\) 24.0179 0.905207
\(705\) −21.5238 −0.810633
\(706\) 27.8507 1.04818
\(707\) 42.3497 1.59272
\(708\) 24.0576 0.904141
\(709\) 31.8550 1.19634 0.598170 0.801369i \(-0.295895\pi\)
0.598170 + 0.801369i \(0.295895\pi\)
\(710\) 24.5551 0.921538
\(711\) −69.7100 −2.61433
\(712\) −18.8227 −0.705410
\(713\) 25.0214 0.937058
\(714\) −30.2360 −1.13156
\(715\) −4.08790 −0.152879
\(716\) 115.666 4.32265
\(717\) −52.8622 −1.97417
\(718\) 84.3332 3.14729
\(719\) 24.8189 0.925588 0.462794 0.886466i \(-0.346847\pi\)
0.462794 + 0.886466i \(0.346847\pi\)
\(720\) 103.723 3.86552
\(721\) −73.7743 −2.74750
\(722\) 51.3801 1.91217
\(723\) −34.0495 −1.26631
\(724\) −14.0458 −0.522009
\(725\) 8.72214 0.323932
\(726\) 7.74904 0.287594
\(727\) 26.8024 0.994046 0.497023 0.867737i \(-0.334427\pi\)
0.497023 + 0.867737i \(0.334427\pi\)
\(728\) −98.0730 −3.63483
\(729\) −41.3831 −1.53271
\(730\) 51.5408 1.90761
\(731\) 1.00000 0.0369863
\(732\) −67.2043 −2.48394
\(733\) 17.0206 0.628672 0.314336 0.949312i \(-0.398218\pi\)
0.314336 + 0.949312i \(0.398218\pi\)
\(734\) 65.3641 2.41263
\(735\) −34.3981 −1.26879
\(736\) −45.7167 −1.68514
\(737\) 11.0950 0.408691
\(738\) −45.2676 −1.66632
\(739\) −22.8259 −0.839665 −0.419832 0.907602i \(-0.637911\pi\)
−0.419832 + 0.907602i \(0.637911\pi\)
\(740\) 67.5127 2.48181
\(741\) 0.685231 0.0251726
\(742\) −87.0995 −3.19752
\(743\) 23.8125 0.873594 0.436797 0.899560i \(-0.356113\pi\)
0.436797 + 0.899560i \(0.356113\pi\)
\(744\) 266.962 9.78730
\(745\) 8.71288 0.319215
\(746\) −6.18072 −0.226292
\(747\) 21.4044 0.783145
\(748\) 5.31840 0.194460
\(749\) −47.4915 −1.73530
\(750\) −89.0210 −3.25059
\(751\) −17.3823 −0.634289 −0.317144 0.948377i \(-0.602724\pi\)
−0.317144 + 0.948377i \(0.602724\pi\)
\(752\) 70.2428 2.56149
\(753\) −9.72244 −0.354305
\(754\) −23.0327 −0.838802
\(755\) −2.67375 −0.0973076
\(756\) 131.071 4.76702
\(757\) 36.2301 1.31680 0.658402 0.752666i \(-0.271233\pi\)
0.658402 + 0.752666i \(0.271233\pi\)
\(758\) 62.7129 2.27784
\(759\) −6.90364 −0.250586
\(760\) −1.11986 −0.0406216
\(761\) 27.2543 0.987969 0.493984 0.869471i \(-0.335540\pi\)
0.493984 + 0.869471i \(0.335540\pi\)
\(762\) −31.7208 −1.14912
\(763\) −34.9696 −1.26599
\(764\) 70.9328 2.56626
\(765\) 7.59953 0.274762
\(766\) 57.7611 2.08699
\(767\) 4.42148 0.159650
\(768\) −71.9161 −2.59505
\(769\) 26.8922 0.969759 0.484880 0.874581i \(-0.338863\pi\)
0.484880 + 0.874581i \(0.338863\pi\)
\(770\) 15.4117 0.555399
\(771\) 51.4244 1.85201
\(772\) −24.9439 −0.897750
\(773\) 14.2146 0.511264 0.255632 0.966774i \(-0.417717\pi\)
0.255632 + 0.966774i \(0.417717\pi\)
\(774\) −14.0809 −0.506127
\(775\) −29.7779 −1.06965
\(776\) 76.0689 2.73071
\(777\) 97.1753 3.48614
\(778\) −41.4111 −1.48466
\(779\) 0.274676 0.00984127
\(780\) 62.2761 2.22984
\(781\) −6.21684 −0.222456
\(782\) −6.51998 −0.233154
\(783\) 19.2067 0.686390
\(784\) 112.258 4.00922
\(785\) −19.9920 −0.713544
\(786\) 39.0240 1.39194
\(787\) 33.6463 1.19936 0.599681 0.800239i \(-0.295294\pi\)
0.599681 + 0.800239i \(0.295294\pi\)
\(788\) −31.5651 −1.12446
\(789\) −45.1305 −1.60669
\(790\) 52.8989 1.88206
\(791\) −60.8837 −2.16477
\(792\) −46.7260 −1.66034
\(793\) −12.3513 −0.438607
\(794\) −40.8131 −1.44840
\(795\) 34.5092 1.22392
\(796\) −10.1153 −0.358526
\(797\) 22.7785 0.806856 0.403428 0.915011i \(-0.367819\pi\)
0.403428 + 0.915011i \(0.367819\pi\)
\(798\) −2.58337 −0.0914503
\(799\) 5.14653 0.182071
\(800\) 54.4074 1.92359
\(801\) 10.9136 0.385612
\(802\) −40.7092 −1.43749
\(803\) −13.0490 −0.460490
\(804\) −169.024 −5.96102
\(805\) −13.7303 −0.483930
\(806\) 78.6351 2.76980
\(807\) 15.0062 0.528243
\(808\) 97.4339 3.42771
\(809\) −0.776410 −0.0272971 −0.0136486 0.999907i \(-0.504345\pi\)
−0.0136486 + 0.999907i \(0.504345\pi\)
\(810\) −9.78399 −0.343774
\(811\) 14.7897 0.519337 0.259669 0.965698i \(-0.416387\pi\)
0.259669 + 0.965698i \(0.416387\pi\)
\(812\) 63.1044 2.21453
\(813\) −60.5388 −2.12319
\(814\) −23.5205 −0.824394
\(815\) −16.0506 −0.562227
\(816\) −39.0955 −1.36862
\(817\) 0.0854401 0.00298917
\(818\) −37.9647 −1.32741
\(819\) 56.8636 1.98697
\(820\) 24.9634 0.871761
\(821\) −18.2421 −0.636653 −0.318327 0.947981i \(-0.603121\pi\)
−0.318327 + 0.947981i \(0.603121\pi\)
\(822\) −147.376 −5.14033
\(823\) −23.2228 −0.809496 −0.404748 0.914428i \(-0.632641\pi\)
−0.404748 + 0.914428i \(0.632641\pi\)
\(824\) −169.732 −5.91291
\(825\) 8.21601 0.286045
\(826\) −16.6693 −0.579999
\(827\) −38.2993 −1.33180 −0.665899 0.746042i \(-0.731952\pi\)
−0.665899 + 0.746042i \(0.731952\pi\)
\(828\) 66.7177 2.31860
\(829\) 8.96084 0.311223 0.155611 0.987818i \(-0.450265\pi\)
0.155611 + 0.987818i \(0.450265\pi\)
\(830\) −16.2425 −0.563787
\(831\) 58.1922 2.01866
\(832\) −67.2465 −2.33135
\(833\) 8.22490 0.284976
\(834\) 109.716 3.79915
\(835\) −1.04755 −0.0362519
\(836\) 0.454405 0.0157159
\(837\) −65.5727 −2.26652
\(838\) 12.4732 0.430881
\(839\) −38.2289 −1.31981 −0.659904 0.751349i \(-0.729403\pi\)
−0.659904 + 0.751349i \(0.729403\pi\)
\(840\) −146.494 −5.05451
\(841\) −19.7529 −0.681136
\(842\) 32.0166 1.10337
\(843\) −33.7114 −1.16108
\(844\) −124.065 −4.27048
\(845\) −7.53500 −0.259212
\(846\) −72.4676 −2.49149
\(847\) −3.90191 −0.134071
\(848\) −112.621 −3.86741
\(849\) 55.4342 1.90250
\(850\) 7.75943 0.266146
\(851\) 20.9545 0.718311
\(852\) 94.7087 3.24467
\(853\) −50.1829 −1.71823 −0.859114 0.511784i \(-0.828985\pi\)
−0.859114 + 0.511784i \(0.828985\pi\)
\(854\) 46.5653 1.59343
\(855\) 0.649305 0.0222058
\(856\) −109.264 −3.73456
\(857\) 45.4847 1.55373 0.776864 0.629669i \(-0.216809\pi\)
0.776864 + 0.629669i \(0.216809\pi\)
\(858\) −21.6962 −0.740695
\(859\) 27.3259 0.932348 0.466174 0.884693i \(-0.345632\pi\)
0.466174 + 0.884693i \(0.345632\pi\)
\(860\) 7.76508 0.264787
\(861\) 35.9315 1.22454
\(862\) −81.5254 −2.77677
\(863\) −7.09436 −0.241495 −0.120747 0.992683i \(-0.538529\pi\)
−0.120747 + 0.992683i \(0.538529\pi\)
\(864\) 119.808 4.07596
\(865\) 20.8918 0.710341
\(866\) −44.6389 −1.51689
\(867\) −2.86444 −0.0972814
\(868\) −215.442 −7.31259
\(869\) −13.3929 −0.454322
\(870\) −34.4044 −1.16642
\(871\) −31.0645 −1.05258
\(872\) −80.4545 −2.72453
\(873\) −44.1054 −1.49274
\(874\) −0.557068 −0.0188431
\(875\) 44.8252 1.51537
\(876\) 198.792 6.71655
\(877\) 49.8966 1.68489 0.842444 0.538784i \(-0.181116\pi\)
0.842444 + 0.538784i \(0.181116\pi\)
\(878\) 98.4545 3.32268
\(879\) 3.61901 0.122066
\(880\) 19.9275 0.671756
\(881\) 42.7205 1.43929 0.719645 0.694342i \(-0.244304\pi\)
0.719645 + 0.694342i \(0.244304\pi\)
\(882\) −115.814 −3.89965
\(883\) −16.1800 −0.544500 −0.272250 0.962227i \(-0.587768\pi\)
−0.272250 + 0.962227i \(0.587768\pi\)
\(884\) −14.8907 −0.500830
\(885\) 6.60445 0.222006
\(886\) −55.4804 −1.86390
\(887\) −15.6534 −0.525589 −0.262794 0.964852i \(-0.584644\pi\)
−0.262794 + 0.964852i \(0.584644\pi\)
\(888\) 223.571 7.50255
\(889\) 15.9725 0.535701
\(890\) −8.28167 −0.277602
\(891\) 2.47710 0.0829859
\(892\) 0.905624 0.0303225
\(893\) 0.439720 0.0147147
\(894\) 46.2428 1.54659
\(895\) 31.7534 1.06140
\(896\) 105.496 3.52439
\(897\) 19.3292 0.645382
\(898\) −68.1354 −2.27371
\(899\) −31.5700 −1.05292
\(900\) −79.4007 −2.64669
\(901\) −8.25146 −0.274896
\(902\) −8.69693 −0.289576
\(903\) 11.1768 0.371940
\(904\) −140.075 −4.65882
\(905\) −3.85595 −0.128176
\(906\) −14.1907 −0.471453
\(907\) 28.9493 0.961244 0.480622 0.876928i \(-0.340411\pi\)
0.480622 + 0.876928i \(0.340411\pi\)
\(908\) −74.4182 −2.46965
\(909\) −56.4930 −1.87375
\(910\) −43.1505 −1.43042
\(911\) 19.4549 0.644569 0.322284 0.946643i \(-0.395549\pi\)
0.322284 + 0.946643i \(0.395549\pi\)
\(912\) −3.34033 −0.110609
\(913\) 4.11226 0.136096
\(914\) 65.6271 2.17075
\(915\) −18.4494 −0.609917
\(916\) −55.0943 −1.82037
\(917\) −19.6500 −0.648899
\(918\) 17.0867 0.563945
\(919\) 34.5423 1.13944 0.569722 0.821837i \(-0.307051\pi\)
0.569722 + 0.821837i \(0.307051\pi\)
\(920\) −31.5893 −1.04147
\(921\) 49.7223 1.63841
\(922\) 14.4260 0.475095
\(923\) 17.4062 0.572933
\(924\) 59.4426 1.95552
\(925\) −24.9379 −0.819955
\(926\) −107.944 −3.54724
\(927\) 98.4123 3.23228
\(928\) 57.6817 1.89349
\(929\) −20.7106 −0.679493 −0.339746 0.940517i \(-0.610341\pi\)
−0.339746 + 0.940517i \(0.610341\pi\)
\(930\) 117.459 3.85162
\(931\) 0.702736 0.0230313
\(932\) 113.213 3.70840
\(933\) 13.0523 0.427312
\(934\) −87.9566 −2.87803
\(935\) 1.46004 0.0477484
\(936\) 130.826 4.27618
\(937\) −41.4977 −1.35567 −0.677835 0.735214i \(-0.737082\pi\)
−0.677835 + 0.735214i \(0.737082\pi\)
\(938\) 117.115 3.82395
\(939\) 64.7360 2.11258
\(940\) 39.9632 1.30346
\(941\) −3.43324 −0.111920 −0.0559602 0.998433i \(-0.517822\pi\)
−0.0559602 + 0.998433i \(0.517822\pi\)
\(942\) −106.106 −3.45710
\(943\) 7.74812 0.252314
\(944\) −21.5536 −0.701509
\(945\) 35.9826 1.17051
\(946\) −2.70525 −0.0879554
\(947\) 32.4824 1.05554 0.527768 0.849388i \(-0.323029\pi\)
0.527768 + 0.849388i \(0.323029\pi\)
\(948\) 204.030 6.62658
\(949\) 36.5354 1.18599
\(950\) 0.662967 0.0215095
\(951\) 58.1592 1.88594
\(952\) 35.0279 1.13526
\(953\) 21.3202 0.690630 0.345315 0.938487i \(-0.387772\pi\)
0.345315 + 0.938487i \(0.387772\pi\)
\(954\) 116.188 3.76172
\(955\) 19.4729 0.630129
\(956\) 98.1491 3.17437
\(957\) 8.71046 0.281569
\(958\) −30.1391 −0.973752
\(959\) 74.2090 2.39633
\(960\) −100.447 −3.24193
\(961\) 76.7818 2.47683
\(962\) 65.8541 2.12322
\(963\) 63.3520 2.04149
\(964\) 63.2196 2.03617
\(965\) −6.84775 −0.220437
\(966\) −72.8724 −2.34463
\(967\) 15.3744 0.494409 0.247204 0.968963i \(-0.420488\pi\)
0.247204 + 0.968963i \(0.420488\pi\)
\(968\) −8.97712 −0.288535
\(969\) −0.244738 −0.00786212
\(970\) 33.4691 1.07463
\(971\) 6.79781 0.218152 0.109076 0.994033i \(-0.465211\pi\)
0.109076 + 0.994033i \(0.465211\pi\)
\(972\) 63.0382 2.02195
\(973\) −55.2457 −1.77110
\(974\) 55.9444 1.79257
\(975\) −23.0036 −0.736706
\(976\) 60.2094 1.92726
\(977\) 10.5447 0.337355 0.168678 0.985671i \(-0.446050\pi\)
0.168678 + 0.985671i \(0.446050\pi\)
\(978\) −85.1870 −2.72398
\(979\) 2.09674 0.0670121
\(980\) 63.8670 2.04016
\(981\) 46.6482 1.48936
\(982\) 82.4521 2.63115
\(983\) 3.58198 0.114248 0.0571238 0.998367i \(-0.481807\pi\)
0.0571238 + 0.998367i \(0.481807\pi\)
\(984\) 82.6674 2.63534
\(985\) −8.66546 −0.276105
\(986\) 8.22640 0.261982
\(987\) 57.5216 1.83093
\(988\) −1.27227 −0.0404762
\(989\) 2.41012 0.0766373
\(990\) −20.5587 −0.653397
\(991\) −31.3561 −0.996059 −0.498029 0.867160i \(-0.665943\pi\)
−0.498029 + 0.867160i \(0.665943\pi\)
\(992\) −196.929 −6.25249
\(993\) 28.8007 0.913963
\(994\) −65.6228 −2.08143
\(995\) −2.77691 −0.0880338
\(996\) −62.6471 −1.98505
\(997\) −49.7996 −1.57717 −0.788584 0.614927i \(-0.789186\pi\)
−0.788584 + 0.614927i \(0.789186\pi\)
\(998\) 25.3692 0.803050
\(999\) −54.9148 −1.73743
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 \(a_p\))