Properties

Label 6026.2.a.i.1.9
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(25\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-1.05724 q^{3}\) \(+1.00000 q^{4}\) \(-2.13811 q^{5}\) \(+1.05724 q^{6}\) \(+3.42578 q^{7}\) \(-1.00000 q^{8}\) \(-1.88224 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-1.05724 q^{3}\) \(+1.00000 q^{4}\) \(-2.13811 q^{5}\) \(+1.05724 q^{6}\) \(+3.42578 q^{7}\) \(-1.00000 q^{8}\) \(-1.88224 q^{9}\) \(+2.13811 q^{10}\) \(-2.88880 q^{11}\) \(-1.05724 q^{12}\) \(+1.88300 q^{13}\) \(-3.42578 q^{14}\) \(+2.26050 q^{15}\) \(+1.00000 q^{16}\) \(+4.09799 q^{17}\) \(+1.88224 q^{18}\) \(-3.98884 q^{19}\) \(-2.13811 q^{20}\) \(-3.62188 q^{21}\) \(+2.88880 q^{22}\) \(+1.00000 q^{23}\) \(+1.05724 q^{24}\) \(-0.428488 q^{25}\) \(-1.88300 q^{26}\) \(+5.16171 q^{27}\) \(+3.42578 q^{28}\) \(+7.47426 q^{29}\) \(-2.26050 q^{30}\) \(-8.99847 q^{31}\) \(-1.00000 q^{32}\) \(+3.05415 q^{33}\) \(-4.09799 q^{34}\) \(-7.32470 q^{35}\) \(-1.88224 q^{36}\) \(-5.04641 q^{37}\) \(+3.98884 q^{38}\) \(-1.99079 q^{39}\) \(+2.13811 q^{40}\) \(+8.18175 q^{41}\) \(+3.62188 q^{42}\) \(+0.248678 q^{43}\) \(-2.88880 q^{44}\) \(+4.02444 q^{45}\) \(-1.00000 q^{46}\) \(-6.96367 q^{47}\) \(-1.05724 q^{48}\) \(+4.73599 q^{49}\) \(+0.428488 q^{50}\) \(-4.33257 q^{51}\) \(+1.88300 q^{52}\) \(+6.38409 q^{53}\) \(-5.16171 q^{54}\) \(+6.17656 q^{55}\) \(-3.42578 q^{56}\) \(+4.21717 q^{57}\) \(-7.47426 q^{58}\) \(+11.2269 q^{59}\) \(+2.26050 q^{60}\) \(-1.76733 q^{61}\) \(+8.99847 q^{62}\) \(-6.44815 q^{63}\) \(+1.00000 q^{64}\) \(-4.02606 q^{65}\) \(-3.05415 q^{66}\) \(-15.5338 q^{67}\) \(+4.09799 q^{68}\) \(-1.05724 q^{69}\) \(+7.32470 q^{70}\) \(+9.84931 q^{71}\) \(+1.88224 q^{72}\) \(+2.29095 q^{73}\) \(+5.04641 q^{74}\) \(+0.453015 q^{75}\) \(-3.98884 q^{76}\) \(-9.89639 q^{77}\) \(+1.99079 q^{78}\) \(+0.874389 q^{79}\) \(-2.13811 q^{80}\) \(+0.189559 q^{81}\) \(-8.18175 q^{82}\) \(-9.68880 q^{83}\) \(-3.62188 q^{84}\) \(-8.76196 q^{85}\) \(-0.248678 q^{86}\) \(-7.90209 q^{87}\) \(+2.88880 q^{88}\) \(-0.610099 q^{89}\) \(-4.02444 q^{90}\) \(+6.45075 q^{91}\) \(+1.00000 q^{92}\) \(+9.51355 q^{93}\) \(+6.96367 q^{94}\) \(+8.52858 q^{95}\) \(+1.05724 q^{96}\) \(+5.60934 q^{97}\) \(-4.73599 q^{98}\) \(+5.43741 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut 3q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 25q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut -\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 3q^{20} \) \(\mathstrut -\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 11q^{28} \) \(\mathstrut -\mathstrut 7q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 25q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut -\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 23q^{38} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 3q^{40} \) \(\mathstrut -\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut -\mathstrut 26q^{43} \) \(\mathstrut -\mathstrut 12q^{44} \) \(\mathstrut +\mathstrut 20q^{45} \) \(\mathstrut -\mathstrut 25q^{46} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 28q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 47q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 11q^{56} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut +\mathstrut 7q^{58} \) \(\mathstrut -\mathstrut 19q^{59} \) \(\mathstrut -\mathstrut 26q^{61} \) \(\mathstrut +\mathstrut 7q^{62} \) \(\mathstrut -\mathstrut 15q^{63} \) \(\mathstrut +\mathstrut 25q^{64} \) \(\mathstrut +\mathstrut 13q^{65} \) \(\mathstrut -\mathstrut 3q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut -\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 23q^{76} \) \(\mathstrut +\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 2q^{78} \) \(\mathstrut -\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 3q^{80} \) \(\mathstrut -\mathstrut 27q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 16q^{84} \) \(\mathstrut -\mathstrut 42q^{85} \) \(\mathstrut +\mathstrut 26q^{86} \) \(\mathstrut -\mathstrut 17q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 27q^{89} \) \(\mathstrut -\mathstrut 20q^{90} \) \(\mathstrut -\mathstrut 26q^{91} \) \(\mathstrut +\mathstrut 25q^{92} \) \(\mathstrut -\mathstrut 27q^{93} \) \(\mathstrut +\mathstrut 2q^{94} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 4q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut -\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.05724 −0.610398 −0.305199 0.952289i \(-0.598723\pi\)
−0.305199 + 0.952289i \(0.598723\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.13811 −0.956192 −0.478096 0.878308i \(-0.658673\pi\)
−0.478096 + 0.878308i \(0.658673\pi\)
\(6\) 1.05724 0.431617
\(7\) 3.42578 1.29482 0.647412 0.762140i \(-0.275851\pi\)
0.647412 + 0.762140i \(0.275851\pi\)
\(8\) −1.00000 −0.353553
\(9\) −1.88224 −0.627414
\(10\) 2.13811 0.676130
\(11\) −2.88880 −0.871005 −0.435503 0.900188i \(-0.643429\pi\)
−0.435503 + 0.900188i \(0.643429\pi\)
\(12\) −1.05724 −0.305199
\(13\) 1.88300 0.522251 0.261125 0.965305i \(-0.415906\pi\)
0.261125 + 0.965305i \(0.415906\pi\)
\(14\) −3.42578 −0.915579
\(15\) 2.26050 0.583658
\(16\) 1.00000 0.250000
\(17\) 4.09799 0.993909 0.496955 0.867777i \(-0.334452\pi\)
0.496955 + 0.867777i \(0.334452\pi\)
\(18\) 1.88224 0.443649
\(19\) −3.98884 −0.915103 −0.457552 0.889183i \(-0.651273\pi\)
−0.457552 + 0.889183i \(0.651273\pi\)
\(20\) −2.13811 −0.478096
\(21\) −3.62188 −0.790359
\(22\) 2.88880 0.615894
\(23\) 1.00000 0.208514
\(24\) 1.05724 0.215808
\(25\) −0.428488 −0.0856975
\(26\) −1.88300 −0.369287
\(27\) 5.16171 0.993371
\(28\) 3.42578 0.647412
\(29\) 7.47426 1.38794 0.693968 0.720006i \(-0.255861\pi\)
0.693968 + 0.720006i \(0.255861\pi\)
\(30\) −2.26050 −0.412708
\(31\) −8.99847 −1.61617 −0.808087 0.589064i \(-0.799497\pi\)
−0.808087 + 0.589064i \(0.799497\pi\)
\(32\) −1.00000 −0.176777
\(33\) 3.05415 0.531660
\(34\) −4.09799 −0.702800
\(35\) −7.32470 −1.23810
\(36\) −1.88224 −0.313707
\(37\) −5.04641 −0.829625 −0.414813 0.909907i \(-0.636153\pi\)
−0.414813 + 0.909907i \(0.636153\pi\)
\(38\) 3.98884 0.647076
\(39\) −1.99079 −0.318781
\(40\) 2.13811 0.338065
\(41\) 8.18175 1.27777 0.638887 0.769301i \(-0.279395\pi\)
0.638887 + 0.769301i \(0.279395\pi\)
\(42\) 3.62188 0.558868
\(43\) 0.248678 0.0379230 0.0189615 0.999820i \(-0.493964\pi\)
0.0189615 + 0.999820i \(0.493964\pi\)
\(44\) −2.88880 −0.435503
\(45\) 4.02444 0.599928
\(46\) −1.00000 −0.147442
\(47\) −6.96367 −1.01576 −0.507878 0.861429i \(-0.669570\pi\)
−0.507878 + 0.861429i \(0.669570\pi\)
\(48\) −1.05724 −0.152600
\(49\) 4.73599 0.676570
\(50\) 0.428488 0.0605973
\(51\) −4.33257 −0.606681
\(52\) 1.88300 0.261125
\(53\) 6.38409 0.876922 0.438461 0.898750i \(-0.355524\pi\)
0.438461 + 0.898750i \(0.355524\pi\)
\(54\) −5.16171 −0.702419
\(55\) 6.17656 0.832848
\(56\) −3.42578 −0.457789
\(57\) 4.21717 0.558577
\(58\) −7.47426 −0.981418
\(59\) 11.2269 1.46161 0.730806 0.682585i \(-0.239144\pi\)
0.730806 + 0.682585i \(0.239144\pi\)
\(60\) 2.26050 0.291829
\(61\) −1.76733 −0.226283 −0.113141 0.993579i \(-0.536091\pi\)
−0.113141 + 0.993579i \(0.536091\pi\)
\(62\) 8.99847 1.14281
\(63\) −6.44815 −0.812391
\(64\) 1.00000 0.125000
\(65\) −4.02606 −0.499372
\(66\) −3.05415 −0.375940
\(67\) −15.5338 −1.89776 −0.948880 0.315638i \(-0.897782\pi\)
−0.948880 + 0.315638i \(0.897782\pi\)
\(68\) 4.09799 0.496955
\(69\) −1.05724 −0.127277
\(70\) 7.32470 0.875469
\(71\) 9.84931 1.16890 0.584449 0.811430i \(-0.301311\pi\)
0.584449 + 0.811430i \(0.301311\pi\)
\(72\) 1.88224 0.221824
\(73\) 2.29095 0.268135 0.134068 0.990972i \(-0.457196\pi\)
0.134068 + 0.990972i \(0.457196\pi\)
\(74\) 5.04641 0.586634
\(75\) 0.453015 0.0523096
\(76\) −3.98884 −0.457552
\(77\) −9.89639 −1.12780
\(78\) 1.99079 0.225412
\(79\) 0.874389 0.0983765 0.0491883 0.998790i \(-0.484337\pi\)
0.0491883 + 0.998790i \(0.484337\pi\)
\(80\) −2.13811 −0.239048
\(81\) 0.189559 0.0210621
\(82\) −8.18175 −0.903523
\(83\) −9.68880 −1.06348 −0.531742 0.846906i \(-0.678462\pi\)
−0.531742 + 0.846906i \(0.678462\pi\)
\(84\) −3.62188 −0.395179
\(85\) −8.76196 −0.950368
\(86\) −0.248678 −0.0268156
\(87\) −7.90209 −0.847193
\(88\) 2.88880 0.307947
\(89\) −0.610099 −0.0646704 −0.0323352 0.999477i \(-0.510294\pi\)
−0.0323352 + 0.999477i \(0.510294\pi\)
\(90\) −4.02444 −0.424213
\(91\) 6.45075 0.676223
\(92\) 1.00000 0.104257
\(93\) 9.51355 0.986510
\(94\) 6.96367 0.718248
\(95\) 8.52858 0.875014
\(96\) 1.05724 0.107904
\(97\) 5.60934 0.569542 0.284771 0.958596i \(-0.408082\pi\)
0.284771 + 0.958596i \(0.408082\pi\)
\(98\) −4.73599 −0.478407
\(99\) 5.43741 0.546481
\(100\) −0.428488 −0.0428488
\(101\) −1.95082 −0.194113 −0.0970567 0.995279i \(-0.530943\pi\)
−0.0970567 + 0.995279i \(0.530943\pi\)
\(102\) 4.33257 0.428988
\(103\) 13.6416 1.34414 0.672072 0.740485i \(-0.265404\pi\)
0.672072 + 0.740485i \(0.265404\pi\)
\(104\) −1.88300 −0.184643
\(105\) 7.74397 0.755734
\(106\) −6.38409 −0.620077
\(107\) −9.13236 −0.882859 −0.441430 0.897296i \(-0.645528\pi\)
−0.441430 + 0.897296i \(0.645528\pi\)
\(108\) 5.16171 0.496685
\(109\) −0.273264 −0.0261739 −0.0130870 0.999914i \(-0.504166\pi\)
−0.0130870 + 0.999914i \(0.504166\pi\)
\(110\) −6.17656 −0.588912
\(111\) 5.33527 0.506402
\(112\) 3.42578 0.323706
\(113\) −2.15872 −0.203075 −0.101538 0.994832i \(-0.532376\pi\)
−0.101538 + 0.994832i \(0.532376\pi\)
\(114\) −4.21717 −0.394974
\(115\) −2.13811 −0.199380
\(116\) 7.47426 0.693968
\(117\) −3.54426 −0.327667
\(118\) −11.2269 −1.03352
\(119\) 14.0388 1.28694
\(120\) −2.26050 −0.206354
\(121\) −2.65485 −0.241350
\(122\) 1.76733 0.160006
\(123\) −8.65008 −0.779951
\(124\) −8.99847 −0.808087
\(125\) 11.6067 1.03813
\(126\) 6.44815 0.574447
\(127\) 9.72670 0.863105 0.431552 0.902088i \(-0.357966\pi\)
0.431552 + 0.902088i \(0.357966\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −0.262912 −0.0231481
\(130\) 4.02606 0.353109
\(131\) 1.00000 0.0873704
\(132\) 3.05415 0.265830
\(133\) −13.6649 −1.18490
\(134\) 15.5338 1.34192
\(135\) −11.0363 −0.949853
\(136\) −4.09799 −0.351400
\(137\) 16.4538 1.40574 0.702871 0.711318i \(-0.251901\pi\)
0.702871 + 0.711318i \(0.251901\pi\)
\(138\) 1.05724 0.0899983
\(139\) −15.7089 −1.33241 −0.666206 0.745768i \(-0.732083\pi\)
−0.666206 + 0.745768i \(0.732083\pi\)
\(140\) −7.32470 −0.619050
\(141\) 7.36228 0.620015
\(142\) −9.84931 −0.826536
\(143\) −5.43961 −0.454883
\(144\) −1.88224 −0.156853
\(145\) −15.9808 −1.32713
\(146\) −2.29095 −0.189600
\(147\) −5.00708 −0.412977
\(148\) −5.04641 −0.414813
\(149\) 10.0073 0.819827 0.409914 0.912124i \(-0.365559\pi\)
0.409914 + 0.912124i \(0.365559\pi\)
\(150\) −0.453015 −0.0369885
\(151\) −3.07867 −0.250539 −0.125269 0.992123i \(-0.539980\pi\)
−0.125269 + 0.992123i \(0.539980\pi\)
\(152\) 3.98884 0.323538
\(153\) −7.71341 −0.623592
\(154\) 9.89639 0.797474
\(155\) 19.2397 1.54537
\(156\) −1.99079 −0.159390
\(157\) −11.6045 −0.926143 −0.463072 0.886321i \(-0.653253\pi\)
−0.463072 + 0.886321i \(0.653253\pi\)
\(158\) −0.874389 −0.0695627
\(159\) −6.74952 −0.535272
\(160\) 2.13811 0.169032
\(161\) 3.42578 0.269990
\(162\) −0.189559 −0.0148931
\(163\) −12.1993 −0.955520 −0.477760 0.878491i \(-0.658551\pi\)
−0.477760 + 0.878491i \(0.658551\pi\)
\(164\) 8.18175 0.638887
\(165\) −6.53012 −0.508369
\(166\) 9.68880 0.751997
\(167\) −19.8800 −1.53836 −0.769180 0.639032i \(-0.779335\pi\)
−0.769180 + 0.639032i \(0.779335\pi\)
\(168\) 3.62188 0.279434
\(169\) −9.45431 −0.727254
\(170\) 8.76196 0.672011
\(171\) 7.50796 0.574148
\(172\) 0.248678 0.0189615
\(173\) −13.0623 −0.993106 −0.496553 0.868006i \(-0.665401\pi\)
−0.496553 + 0.868006i \(0.665401\pi\)
\(174\) 7.90209 0.599056
\(175\) −1.46791 −0.110963
\(176\) −2.88880 −0.217751
\(177\) −11.8695 −0.892166
\(178\) 0.610099 0.0457289
\(179\) −4.59658 −0.343565 −0.171782 0.985135i \(-0.554953\pi\)
−0.171782 + 0.985135i \(0.554953\pi\)
\(180\) 4.02444 0.299964
\(181\) −6.40419 −0.476020 −0.238010 0.971263i \(-0.576495\pi\)
−0.238010 + 0.971263i \(0.576495\pi\)
\(182\) −6.45075 −0.478162
\(183\) 1.86849 0.138123
\(184\) −1.00000 −0.0737210
\(185\) 10.7898 0.793281
\(186\) −9.51355 −0.697568
\(187\) −11.8383 −0.865700
\(188\) −6.96367 −0.507878
\(189\) 17.6829 1.28624
\(190\) −8.52858 −0.618728
\(191\) 8.96653 0.648795 0.324398 0.945921i \(-0.394838\pi\)
0.324398 + 0.945921i \(0.394838\pi\)
\(192\) −1.05724 −0.0762998
\(193\) 19.7194 1.41944 0.709718 0.704486i \(-0.248822\pi\)
0.709718 + 0.704486i \(0.248822\pi\)
\(194\) −5.60934 −0.402727
\(195\) 4.25652 0.304816
\(196\) 4.73599 0.338285
\(197\) −21.0521 −1.49990 −0.749950 0.661495i \(-0.769922\pi\)
−0.749950 + 0.661495i \(0.769922\pi\)
\(198\) −5.43741 −0.386420
\(199\) 10.0749 0.714188 0.357094 0.934068i \(-0.383768\pi\)
0.357094 + 0.934068i \(0.383768\pi\)
\(200\) 0.428488 0.0302986
\(201\) 16.4230 1.15839
\(202\) 1.95082 0.137259
\(203\) 25.6052 1.79713
\(204\) −4.33257 −0.303340
\(205\) −17.4935 −1.22180
\(206\) −13.6416 −0.950454
\(207\) −1.88224 −0.130825
\(208\) 1.88300 0.130563
\(209\) 11.5230 0.797059
\(210\) −7.74397 −0.534385
\(211\) 9.93841 0.684188 0.342094 0.939666i \(-0.388864\pi\)
0.342094 + 0.939666i \(0.388864\pi\)
\(212\) 6.38409 0.438461
\(213\) −10.4131 −0.713494
\(214\) 9.13236 0.624276
\(215\) −0.531700 −0.0362616
\(216\) −5.16171 −0.351210
\(217\) −30.8268 −2.09266
\(218\) 0.273264 0.0185078
\(219\) −2.42208 −0.163669
\(220\) 6.17656 0.416424
\(221\) 7.71653 0.519070
\(222\) −5.33527 −0.358080
\(223\) −1.24087 −0.0830947 −0.0415474 0.999137i \(-0.513229\pi\)
−0.0415474 + 0.999137i \(0.513229\pi\)
\(224\) −3.42578 −0.228895
\(225\) 0.806517 0.0537678
\(226\) 2.15872 0.143596
\(227\) 27.6748 1.83684 0.918419 0.395609i \(-0.129467\pi\)
0.918419 + 0.395609i \(0.129467\pi\)
\(228\) 4.21717 0.279289
\(229\) 27.1412 1.79354 0.896772 0.442494i \(-0.145906\pi\)
0.896772 + 0.442494i \(0.145906\pi\)
\(230\) 2.13811 0.140983
\(231\) 10.4629 0.688406
\(232\) −7.47426 −0.490709
\(233\) −10.2090 −0.668812 −0.334406 0.942429i \(-0.608536\pi\)
−0.334406 + 0.942429i \(0.608536\pi\)
\(234\) 3.54426 0.231696
\(235\) 14.8891 0.971257
\(236\) 11.2269 0.730806
\(237\) −0.924440 −0.0600489
\(238\) −14.0388 −0.910002
\(239\) −0.963565 −0.0623278 −0.0311639 0.999514i \(-0.509921\pi\)
−0.0311639 + 0.999514i \(0.509921\pi\)
\(240\) 2.26050 0.145914
\(241\) 8.62238 0.555417 0.277708 0.960665i \(-0.410425\pi\)
0.277708 + 0.960665i \(0.410425\pi\)
\(242\) 2.65485 0.170660
\(243\) −15.6855 −1.00623
\(244\) −1.76733 −0.113141
\(245\) −10.1261 −0.646930
\(246\) 8.65008 0.551509
\(247\) −7.51099 −0.477913
\(248\) 8.99847 0.571404
\(249\) 10.2434 0.649149
\(250\) −11.6067 −0.734072
\(251\) 4.66001 0.294137 0.147069 0.989126i \(-0.453016\pi\)
0.147069 + 0.989126i \(0.453016\pi\)
\(252\) −6.44815 −0.406195
\(253\) −2.88880 −0.181617
\(254\) −9.72670 −0.610307
\(255\) 9.26350 0.580103
\(256\) 1.00000 0.0625000
\(257\) 9.82881 0.613104 0.306552 0.951854i \(-0.400825\pi\)
0.306552 + 0.951854i \(0.400825\pi\)
\(258\) 0.262912 0.0163682
\(259\) −17.2879 −1.07422
\(260\) −4.02606 −0.249686
\(261\) −14.0684 −0.870810
\(262\) −1.00000 −0.0617802
\(263\) 17.8668 1.10171 0.550857 0.834599i \(-0.314301\pi\)
0.550857 + 0.834599i \(0.314301\pi\)
\(264\) −3.05415 −0.187970
\(265\) −13.6499 −0.838505
\(266\) 13.6649 0.837849
\(267\) 0.645022 0.0394747
\(268\) −15.5338 −0.948880
\(269\) −12.9576 −0.790040 −0.395020 0.918672i \(-0.629262\pi\)
−0.395020 + 0.918672i \(0.629262\pi\)
\(270\) 11.0363 0.671647
\(271\) −14.2166 −0.863595 −0.431797 0.901971i \(-0.642120\pi\)
−0.431797 + 0.901971i \(0.642120\pi\)
\(272\) 4.09799 0.248477
\(273\) −6.82000 −0.412765
\(274\) −16.4538 −0.994009
\(275\) 1.23781 0.0746430
\(276\) −1.05724 −0.0636384
\(277\) 20.6973 1.24358 0.621790 0.783184i \(-0.286406\pi\)
0.621790 + 0.783184i \(0.286406\pi\)
\(278\) 15.7089 0.942157
\(279\) 16.9373 1.01401
\(280\) 7.32470 0.437734
\(281\) −31.3920 −1.87269 −0.936344 0.351084i \(-0.885813\pi\)
−0.936344 + 0.351084i \(0.885813\pi\)
\(282\) −7.36228 −0.438417
\(283\) 6.28213 0.373434 0.186717 0.982414i \(-0.440215\pi\)
0.186717 + 0.982414i \(0.440215\pi\)
\(284\) 9.84931 0.584449
\(285\) −9.01676 −0.534107
\(286\) 5.43961 0.321651
\(287\) 28.0289 1.65449
\(288\) 1.88224 0.110912
\(289\) −0.206455 −0.0121444
\(290\) 15.9808 0.938424
\(291\) −5.93042 −0.347647
\(292\) 2.29095 0.134068
\(293\) −22.8404 −1.33435 −0.667175 0.744901i \(-0.732497\pi\)
−0.667175 + 0.744901i \(0.732497\pi\)
\(294\) 5.00708 0.292019
\(295\) −24.0043 −1.39758
\(296\) 5.04641 0.293317
\(297\) −14.9111 −0.865231
\(298\) −10.0073 −0.579705
\(299\) 1.88300 0.108897
\(300\) 0.453015 0.0261548
\(301\) 0.851915 0.0491036
\(302\) 3.07867 0.177158
\(303\) 2.06248 0.118486
\(304\) −3.98884 −0.228776
\(305\) 3.77873 0.216370
\(306\) 7.71341 0.440946
\(307\) −21.2908 −1.21513 −0.607564 0.794271i \(-0.707853\pi\)
−0.607564 + 0.794271i \(0.707853\pi\)
\(308\) −9.89639 −0.563899
\(309\) −14.4224 −0.820464
\(310\) −19.2397 −1.09274
\(311\) 1.17285 0.0665065 0.0332532 0.999447i \(-0.489413\pi\)
0.0332532 + 0.999447i \(0.489413\pi\)
\(312\) 1.99079 0.112706
\(313\) −7.39068 −0.417746 −0.208873 0.977943i \(-0.566980\pi\)
−0.208873 + 0.977943i \(0.566980\pi\)
\(314\) 11.6045 0.654882
\(315\) 13.7869 0.776801
\(316\) 0.874389 0.0491883
\(317\) −17.9224 −1.00662 −0.503311 0.864105i \(-0.667885\pi\)
−0.503311 + 0.864105i \(0.667885\pi\)
\(318\) 6.74952 0.378494
\(319\) −21.5916 −1.20890
\(320\) −2.13811 −0.119524
\(321\) 9.65511 0.538896
\(322\) −3.42578 −0.190911
\(323\) −16.3462 −0.909529
\(324\) 0.189559 0.0105310
\(325\) −0.806843 −0.0447556
\(326\) 12.1993 0.675654
\(327\) 0.288906 0.0159765
\(328\) −8.18175 −0.451761
\(329\) −23.8560 −1.31522
\(330\) 6.53012 0.359471
\(331\) −26.2243 −1.44142 −0.720708 0.693238i \(-0.756183\pi\)
−0.720708 + 0.693238i \(0.756183\pi\)
\(332\) −9.68880 −0.531742
\(333\) 9.49857 0.520518
\(334\) 19.8800 1.08779
\(335\) 33.2130 1.81462
\(336\) −3.62188 −0.197590
\(337\) −20.9240 −1.13980 −0.569901 0.821713i \(-0.693019\pi\)
−0.569901 + 0.821713i \(0.693019\pi\)
\(338\) 9.45431 0.514246
\(339\) 2.28228 0.123957
\(340\) −8.76196 −0.475184
\(341\) 25.9948 1.40770
\(342\) −7.50796 −0.405984
\(343\) −7.75601 −0.418785
\(344\) −0.248678 −0.0134078
\(345\) 2.26050 0.121701
\(346\) 13.0623 0.702232
\(347\) 20.5743 1.10449 0.552243 0.833683i \(-0.313772\pi\)
0.552243 + 0.833683i \(0.313772\pi\)
\(348\) −7.90209 −0.423597
\(349\) −12.3675 −0.662015 −0.331008 0.943628i \(-0.607389\pi\)
−0.331008 + 0.943628i \(0.607389\pi\)
\(350\) 1.46791 0.0784628
\(351\) 9.71950 0.518788
\(352\) 2.88880 0.153973
\(353\) 12.8737 0.685198 0.342599 0.939482i \(-0.388693\pi\)
0.342599 + 0.939482i \(0.388693\pi\)
\(354\) 11.8695 0.630857
\(355\) −21.0589 −1.11769
\(356\) −0.610099 −0.0323352
\(357\) −14.8424 −0.785545
\(358\) 4.59658 0.242937
\(359\) 20.2210 1.06722 0.533612 0.845730i \(-0.320834\pi\)
0.533612 + 0.845730i \(0.320834\pi\)
\(360\) −4.02444 −0.212107
\(361\) −3.08914 −0.162586
\(362\) 6.40419 0.336597
\(363\) 2.80682 0.147320
\(364\) 6.45075 0.338111
\(365\) −4.89830 −0.256389
\(366\) −1.86849 −0.0976675
\(367\) −17.6959 −0.923720 −0.461860 0.886953i \(-0.652818\pi\)
−0.461860 + 0.886953i \(0.652818\pi\)
\(368\) 1.00000 0.0521286
\(369\) −15.4000 −0.801693
\(370\) −10.7898 −0.560934
\(371\) 21.8705 1.13546
\(372\) 9.51355 0.493255
\(373\) −18.3029 −0.947688 −0.473844 0.880609i \(-0.657134\pi\)
−0.473844 + 0.880609i \(0.657134\pi\)
\(374\) 11.8383 0.612142
\(375\) −12.2711 −0.633676
\(376\) 6.96367 0.359124
\(377\) 14.0740 0.724850
\(378\) −17.6829 −0.909509
\(379\) −30.3097 −1.55690 −0.778451 0.627705i \(-0.783994\pi\)
−0.778451 + 0.627705i \(0.783994\pi\)
\(380\) 8.52858 0.437507
\(381\) −10.2835 −0.526838
\(382\) −8.96653 −0.458768
\(383\) −33.3270 −1.70293 −0.851464 0.524413i \(-0.824285\pi\)
−0.851464 + 0.524413i \(0.824285\pi\)
\(384\) 1.05724 0.0539521
\(385\) 21.1596 1.07839
\(386\) −19.7194 −1.00369
\(387\) −0.468071 −0.0237934
\(388\) 5.60934 0.284771
\(389\) −31.9039 −1.61759 −0.808795 0.588090i \(-0.799880\pi\)
−0.808795 + 0.588090i \(0.799880\pi\)
\(390\) −4.25652 −0.215537
\(391\) 4.09799 0.207244
\(392\) −4.73599 −0.239204
\(393\) −1.05724 −0.0533307
\(394\) 21.0521 1.06059
\(395\) −1.86954 −0.0940668
\(396\) 5.43741 0.273240
\(397\) −26.3120 −1.32056 −0.660280 0.751020i \(-0.729562\pi\)
−0.660280 + 0.751020i \(0.729562\pi\)
\(398\) −10.0749 −0.505007
\(399\) 14.4471 0.723259
\(400\) −0.428488 −0.0214244
\(401\) −11.2889 −0.563740 −0.281870 0.959453i \(-0.590955\pi\)
−0.281870 + 0.959453i \(0.590955\pi\)
\(402\) −16.4230 −0.819105
\(403\) −16.9441 −0.844048
\(404\) −1.95082 −0.0970567
\(405\) −0.405297 −0.0201394
\(406\) −25.6052 −1.27076
\(407\) 14.5781 0.722608
\(408\) 4.33257 0.214494
\(409\) −17.6148 −0.870995 −0.435498 0.900190i \(-0.643428\pi\)
−0.435498 + 0.900190i \(0.643428\pi\)
\(410\) 17.4935 0.863941
\(411\) −17.3956 −0.858062
\(412\) 13.6416 0.672072
\(413\) 38.4608 1.89253
\(414\) 1.88224 0.0925071
\(415\) 20.7157 1.01689
\(416\) −1.88300 −0.0923217
\(417\) 16.6081 0.813302
\(418\) −11.5230 −0.563606
\(419\) −9.48791 −0.463515 −0.231757 0.972774i \(-0.574448\pi\)
−0.231757 + 0.972774i \(0.574448\pi\)
\(420\) 7.74397 0.377867
\(421\) 37.8882 1.84656 0.923279 0.384131i \(-0.125499\pi\)
0.923279 + 0.384131i \(0.125499\pi\)
\(422\) −9.93841 −0.483794
\(423\) 13.1073 0.637299
\(424\) −6.38409 −0.310039
\(425\) −1.75594 −0.0851755
\(426\) 10.4131 0.504516
\(427\) −6.05447 −0.292996
\(428\) −9.13236 −0.441430
\(429\) 5.75098 0.277660
\(430\) 0.531700 0.0256408
\(431\) −30.4416 −1.46632 −0.733159 0.680057i \(-0.761955\pi\)
−0.733159 + 0.680057i \(0.761955\pi\)
\(432\) 5.16171 0.248343
\(433\) −23.7947 −1.14350 −0.571751 0.820427i \(-0.693736\pi\)
−0.571751 + 0.820427i \(0.693736\pi\)
\(434\) 30.8268 1.47973
\(435\) 16.8955 0.810079
\(436\) −0.273264 −0.0130870
\(437\) −3.98884 −0.190812
\(438\) 2.42208 0.115732
\(439\) −24.4063 −1.16485 −0.582424 0.812885i \(-0.697896\pi\)
−0.582424 + 0.812885i \(0.697896\pi\)
\(440\) −6.17656 −0.294456
\(441\) −8.91427 −0.424489
\(442\) −7.71653 −0.367038
\(443\) −8.82371 −0.419227 −0.209614 0.977784i \(-0.567221\pi\)
−0.209614 + 0.977784i \(0.567221\pi\)
\(444\) 5.33527 0.253201
\(445\) 1.30446 0.0618373
\(446\) 1.24087 0.0587569
\(447\) −10.5801 −0.500421
\(448\) 3.42578 0.161853
\(449\) 32.3312 1.52580 0.762902 0.646515i \(-0.223774\pi\)
0.762902 + 0.646515i \(0.223774\pi\)
\(450\) −0.806517 −0.0380196
\(451\) −23.6354 −1.11295
\(452\) −2.15872 −0.101538
\(453\) 3.25490 0.152929
\(454\) −27.6748 −1.29884
\(455\) −13.7924 −0.646599
\(456\) −4.21717 −0.197487
\(457\) 0.481915 0.0225430 0.0112715 0.999936i \(-0.496412\pi\)
0.0112715 + 0.999936i \(0.496412\pi\)
\(458\) −27.1412 −1.26823
\(459\) 21.1526 0.987320
\(460\) −2.13811 −0.0996899
\(461\) −11.0216 −0.513329 −0.256664 0.966501i \(-0.582623\pi\)
−0.256664 + 0.966501i \(0.582623\pi\)
\(462\) −10.4629 −0.486777
\(463\) −16.3035 −0.757690 −0.378845 0.925460i \(-0.623679\pi\)
−0.378845 + 0.925460i \(0.623679\pi\)
\(464\) 7.47426 0.346984
\(465\) −20.3410 −0.943292
\(466\) 10.2090 0.472921
\(467\) −5.72416 −0.264883 −0.132441 0.991191i \(-0.542282\pi\)
−0.132441 + 0.991191i \(0.542282\pi\)
\(468\) −3.54426 −0.163834
\(469\) −53.2155 −2.45727
\(470\) −14.8891 −0.686782
\(471\) 12.2688 0.565316
\(472\) −11.2269 −0.516758
\(473\) −0.718379 −0.0330311
\(474\) 0.924440 0.0424610
\(475\) 1.70917 0.0784220
\(476\) 14.0388 0.643469
\(477\) −12.0164 −0.550193
\(478\) 0.963565 0.0440724
\(479\) −19.4595 −0.889129 −0.444564 0.895747i \(-0.646641\pi\)
−0.444564 + 0.895747i \(0.646641\pi\)
\(480\) −2.26050 −0.103177
\(481\) −9.50240 −0.433272
\(482\) −8.62238 −0.392739
\(483\) −3.62188 −0.164801
\(484\) −2.65485 −0.120675
\(485\) −11.9934 −0.544591
\(486\) 15.6855 0.711510
\(487\) −25.7071 −1.16490 −0.582449 0.812867i \(-0.697905\pi\)
−0.582449 + 0.812867i \(0.697905\pi\)
\(488\) 1.76733 0.0800031
\(489\) 12.8976 0.583248
\(490\) 10.1261 0.457449
\(491\) 31.0924 1.40318 0.701590 0.712580i \(-0.252474\pi\)
0.701590 + 0.712580i \(0.252474\pi\)
\(492\) −8.65008 −0.389976
\(493\) 30.6295 1.37948
\(494\) 7.51099 0.337936
\(495\) −11.6258 −0.522540
\(496\) −8.99847 −0.404043
\(497\) 33.7416 1.51352
\(498\) −10.2434 −0.459017
\(499\) 41.1280 1.84114 0.920572 0.390573i \(-0.127723\pi\)
0.920572 + 0.390573i \(0.127723\pi\)
\(500\) 11.6067 0.519067
\(501\) 21.0180 0.939013
\(502\) −4.66001 −0.207987
\(503\) 19.8371 0.884491 0.442245 0.896894i \(-0.354182\pi\)
0.442245 + 0.896894i \(0.354182\pi\)
\(504\) 6.44815 0.287223
\(505\) 4.17106 0.185610
\(506\) 2.88880 0.128423
\(507\) 9.99548 0.443915
\(508\) 9.72670 0.431552
\(509\) −38.2365 −1.69480 −0.847401 0.530954i \(-0.821834\pi\)
−0.847401 + 0.530954i \(0.821834\pi\)
\(510\) −9.26350 −0.410195
\(511\) 7.84829 0.347188
\(512\) −1.00000 −0.0441942
\(513\) −20.5892 −0.909037
\(514\) −9.82881 −0.433530
\(515\) −29.1672 −1.28526
\(516\) −0.262912 −0.0115741
\(517\) 20.1166 0.884728
\(518\) 17.2879 0.759587
\(519\) 13.8100 0.606191
\(520\) 4.02606 0.176555
\(521\) 0.456619 0.0200048 0.0100024 0.999950i \(-0.496816\pi\)
0.0100024 + 0.999950i \(0.496816\pi\)
\(522\) 14.0684 0.615756
\(523\) 6.95728 0.304221 0.152110 0.988364i \(-0.451393\pi\)
0.152110 + 0.988364i \(0.451393\pi\)
\(524\) 1.00000 0.0436852
\(525\) 1.55193 0.0677318
\(526\) −17.8668 −0.779030
\(527\) −36.8757 −1.60633
\(528\) 3.05415 0.132915
\(529\) 1.00000 0.0434783
\(530\) 13.6499 0.592913
\(531\) −21.1317 −0.917036
\(532\) −13.6649 −0.592449
\(533\) 15.4062 0.667318
\(534\) −0.645022 −0.0279128
\(535\) 19.5260 0.844182
\(536\) 15.5338 0.670959
\(537\) 4.85970 0.209711
\(538\) 12.9576 0.558643
\(539\) −13.6813 −0.589296
\(540\) −11.0363 −0.474926
\(541\) 11.4234 0.491128 0.245564 0.969380i \(-0.421027\pi\)
0.245564 + 0.969380i \(0.421027\pi\)
\(542\) 14.2166 0.610654
\(543\) 6.77078 0.290562
\(544\) −4.09799 −0.175700
\(545\) 0.584268 0.0250273
\(546\) 6.82000 0.291869
\(547\) 20.4916 0.876156 0.438078 0.898937i \(-0.355659\pi\)
0.438078 + 0.898937i \(0.355659\pi\)
\(548\) 16.4538 0.702871
\(549\) 3.32653 0.141973
\(550\) −1.23781 −0.0527805
\(551\) −29.8136 −1.27010
\(552\) 1.05724 0.0449992
\(553\) 2.99547 0.127380
\(554\) −20.6973 −0.879343
\(555\) −11.4074 −0.484217
\(556\) −15.7089 −0.666206
\(557\) 34.4423 1.45937 0.729684 0.683784i \(-0.239667\pi\)
0.729684 + 0.683784i \(0.239667\pi\)
\(558\) −16.9373 −0.717013
\(559\) 0.468260 0.0198053
\(560\) −7.32470 −0.309525
\(561\) 12.5159 0.528422
\(562\) 31.3920 1.32419
\(563\) −38.3357 −1.61566 −0.807829 0.589416i \(-0.799358\pi\)
−0.807829 + 0.589416i \(0.799358\pi\)
\(564\) 7.36228 0.310008
\(565\) 4.61558 0.194179
\(566\) −6.28213 −0.264058
\(567\) 0.649387 0.0272717
\(568\) −9.84931 −0.413268
\(569\) −43.3728 −1.81828 −0.909141 0.416488i \(-0.863261\pi\)
−0.909141 + 0.416488i \(0.863261\pi\)
\(570\) 9.01676 0.377671
\(571\) 10.9007 0.456182 0.228091 0.973640i \(-0.426752\pi\)
0.228091 + 0.973640i \(0.426752\pi\)
\(572\) −5.43961 −0.227441
\(573\) −9.47978 −0.396024
\(574\) −28.0289 −1.16990
\(575\) −0.428488 −0.0178692
\(576\) −1.88224 −0.0784267
\(577\) −2.45423 −0.102171 −0.0510855 0.998694i \(-0.516268\pi\)
−0.0510855 + 0.998694i \(0.516268\pi\)
\(578\) 0.206455 0.00858740
\(579\) −20.8482 −0.866421
\(580\) −15.9808 −0.663566
\(581\) −33.1917 −1.37702
\(582\) 5.93042 0.245824
\(583\) −18.4423 −0.763803
\(584\) −2.29095 −0.0948001
\(585\) 7.57802 0.313313
\(586\) 22.8404 0.943528
\(587\) 10.3726 0.428125 0.214062 0.976820i \(-0.431330\pi\)
0.214062 + 0.976820i \(0.431330\pi\)
\(588\) −5.00708 −0.206489
\(589\) 35.8935 1.47897
\(590\) 24.0043 0.988240
\(591\) 22.2571 0.915536
\(592\) −5.04641 −0.207406
\(593\) 31.5489 1.29556 0.647779 0.761828i \(-0.275698\pi\)
0.647779 + 0.761828i \(0.275698\pi\)
\(594\) 14.9111 0.611811
\(595\) −30.0166 −1.23056
\(596\) 10.0073 0.409914
\(597\) −10.6516 −0.435939
\(598\) −1.88300 −0.0770017
\(599\) −41.5870 −1.69920 −0.849599 0.527429i \(-0.823156\pi\)
−0.849599 + 0.527429i \(0.823156\pi\)
\(600\) −0.453015 −0.0184942
\(601\) 11.8948 0.485199 0.242599 0.970127i \(-0.422000\pi\)
0.242599 + 0.970127i \(0.422000\pi\)
\(602\) −0.851915 −0.0347215
\(603\) 29.2384 1.19068
\(604\) −3.07867 −0.125269
\(605\) 5.67637 0.230777
\(606\) −2.06248 −0.0837826
\(607\) −4.77299 −0.193730 −0.0968648 0.995298i \(-0.530881\pi\)
−0.0968648 + 0.995298i \(0.530881\pi\)
\(608\) 3.98884 0.161769
\(609\) −27.0709 −1.09697
\(610\) −3.77873 −0.152997
\(611\) −13.1126 −0.530479
\(612\) −7.71341 −0.311796
\(613\) 12.8111 0.517434 0.258717 0.965953i \(-0.416700\pi\)
0.258717 + 0.965953i \(0.416700\pi\)
\(614\) 21.2908 0.859225
\(615\) 18.4948 0.745783
\(616\) 9.89639 0.398737
\(617\) −34.1863 −1.37629 −0.688144 0.725574i \(-0.741574\pi\)
−0.688144 + 0.725574i \(0.741574\pi\)
\(618\) 14.4224 0.580155
\(619\) −17.0595 −0.685678 −0.342839 0.939394i \(-0.611389\pi\)
−0.342839 + 0.939394i \(0.611389\pi\)
\(620\) 19.2397 0.772686
\(621\) 5.16171 0.207132
\(622\) −1.17285 −0.0470272
\(623\) −2.09007 −0.0837368
\(624\) −1.99079 −0.0796952
\(625\) −22.6740 −0.906958
\(626\) 7.39068 0.295391
\(627\) −12.1825 −0.486524
\(628\) −11.6045 −0.463072
\(629\) −20.6802 −0.824572
\(630\) −13.7869 −0.549281
\(631\) 7.17481 0.285625 0.142812 0.989750i \(-0.454385\pi\)
0.142812 + 0.989750i \(0.454385\pi\)
\(632\) −0.874389 −0.0347813
\(633\) −10.5073 −0.417627
\(634\) 17.9224 0.711790
\(635\) −20.7967 −0.825294
\(636\) −6.74952 −0.267636
\(637\) 8.91787 0.353339
\(638\) 21.5916 0.854820
\(639\) −18.5388 −0.733383
\(640\) 2.13811 0.0845162
\(641\) 2.70971 0.107027 0.0535135 0.998567i \(-0.482958\pi\)
0.0535135 + 0.998567i \(0.482958\pi\)
\(642\) −9.65511 −0.381057
\(643\) −49.2001 −1.94026 −0.970132 0.242577i \(-0.922007\pi\)
−0.970132 + 0.242577i \(0.922007\pi\)
\(644\) 3.42578 0.134995
\(645\) 0.562135 0.0221340
\(646\) 16.3462 0.643134
\(647\) −36.8361 −1.44818 −0.724089 0.689707i \(-0.757739\pi\)
−0.724089 + 0.689707i \(0.757739\pi\)
\(648\) −0.189559 −0.00744657
\(649\) −32.4321 −1.27307
\(650\) 0.806843 0.0316470
\(651\) 32.5914 1.27736
\(652\) −12.1993 −0.477760
\(653\) −28.7965 −1.12689 −0.563447 0.826152i \(-0.690525\pi\)
−0.563447 + 0.826152i \(0.690525\pi\)
\(654\) −0.288906 −0.0112971
\(655\) −2.13811 −0.0835429
\(656\) 8.18175 0.319443
\(657\) −4.31212 −0.168232
\(658\) 23.8560 0.930004
\(659\) −36.0407 −1.40395 −0.701973 0.712203i \(-0.747697\pi\)
−0.701973 + 0.712203i \(0.747697\pi\)
\(660\) −6.53012 −0.254184
\(661\) −13.7737 −0.535736 −0.267868 0.963456i \(-0.586319\pi\)
−0.267868 + 0.963456i \(0.586319\pi\)
\(662\) 26.2243 1.01924
\(663\) −8.15823 −0.316839
\(664\) 9.68880 0.375998
\(665\) 29.2171 1.13299
\(666\) −9.49857 −0.368062
\(667\) 7.47426 0.289404
\(668\) −19.8800 −0.769180
\(669\) 1.31190 0.0507209
\(670\) −33.2130 −1.28313
\(671\) 5.10544 0.197093
\(672\) 3.62188 0.139717
\(673\) −6.37154 −0.245605 −0.122802 0.992431i \(-0.539188\pi\)
−0.122802 + 0.992431i \(0.539188\pi\)
\(674\) 20.9240 0.805962
\(675\) −2.21173 −0.0851294
\(676\) −9.45431 −0.363627
\(677\) −12.2470 −0.470689 −0.235345 0.971912i \(-0.575622\pi\)
−0.235345 + 0.971912i \(0.575622\pi\)
\(678\) −2.28228 −0.0876506
\(679\) 19.2164 0.737457
\(680\) 8.76196 0.336006
\(681\) −29.2589 −1.12120
\(682\) −25.9948 −0.995391
\(683\) −35.7312 −1.36722 −0.683608 0.729849i \(-0.739590\pi\)
−0.683608 + 0.729849i \(0.739590\pi\)
\(684\) 7.50796 0.287074
\(685\) −35.1800 −1.34416
\(686\) 7.75601 0.296126
\(687\) −28.6948 −1.09478
\(688\) 0.248678 0.00948074
\(689\) 12.0212 0.457973
\(690\) −2.26050 −0.0860556
\(691\) −15.4716 −0.588568 −0.294284 0.955718i \(-0.595081\pi\)
−0.294284 + 0.955718i \(0.595081\pi\)
\(692\) −13.0623 −0.496553
\(693\) 18.6274 0.707596
\(694\) −20.5743 −0.780990
\(695\) 33.5874 1.27404
\(696\) 7.90209 0.299528
\(697\) 33.5287 1.26999
\(698\) 12.3675 0.468116
\(699\) 10.7933 0.408242
\(700\) −1.46791 −0.0554816
\(701\) 28.4299 1.07378 0.536892 0.843651i \(-0.319598\pi\)
0.536892 + 0.843651i \(0.319598\pi\)
\(702\) −9.71950 −0.366839
\(703\) 20.1293 0.759193
\(704\) −2.88880 −0.108876
\(705\) −15.7414 −0.592854
\(706\) −12.8737 −0.484508
\(707\) −6.68307 −0.251343
\(708\) −11.8695 −0.446083
\(709\) −24.8867 −0.934641 −0.467321 0.884088i \(-0.654781\pi\)
−0.467321 + 0.884088i \(0.654781\pi\)
\(710\) 21.0589 0.790327
\(711\) −1.64581 −0.0617228
\(712\) 0.610099 0.0228644
\(713\) −8.99847 −0.336995
\(714\) 14.8424 0.555464
\(715\) 11.6305 0.434955
\(716\) −4.59658 −0.171782
\(717\) 1.01872 0.0380448
\(718\) −20.2210 −0.754641
\(719\) 5.40032 0.201398 0.100699 0.994917i \(-0.467892\pi\)
0.100699 + 0.994917i \(0.467892\pi\)
\(720\) 4.02444 0.149982
\(721\) 46.7331 1.74043
\(722\) 3.08914 0.114966
\(723\) −9.11594 −0.339025
\(724\) −6.40419 −0.238010
\(725\) −3.20263 −0.118943
\(726\) −2.80682 −0.104171
\(727\) 19.7868 0.733850 0.366925 0.930250i \(-0.380410\pi\)
0.366925 + 0.930250i \(0.380410\pi\)
\(728\) −6.45075 −0.239081
\(729\) 16.0147 0.593137
\(730\) 4.89830 0.181294
\(731\) 1.01908 0.0376920
\(732\) 1.86849 0.0690613
\(733\) −27.2188 −1.00535 −0.502675 0.864475i \(-0.667651\pi\)
−0.502675 + 0.864475i \(0.667651\pi\)
\(734\) 17.6959 0.653169
\(735\) 10.7057 0.394885
\(736\) −1.00000 −0.0368605
\(737\) 44.8741 1.65296
\(738\) 15.4000 0.566883
\(739\) 13.4289 0.493991 0.246995 0.969017i \(-0.420557\pi\)
0.246995 + 0.969017i \(0.420557\pi\)
\(740\) 10.7898 0.396640
\(741\) 7.94093 0.291717
\(742\) −21.8705 −0.802891
\(743\) 18.8940 0.693153 0.346576 0.938022i \(-0.387344\pi\)
0.346576 + 0.938022i \(0.387344\pi\)
\(744\) −9.51355 −0.348784
\(745\) −21.3966 −0.783912
\(746\) 18.3029 0.670117
\(747\) 18.2367 0.667244
\(748\) −11.8383 −0.432850
\(749\) −31.2855 −1.14315
\(750\) 12.2711 0.448076
\(751\) −0.708626 −0.0258581 −0.0129291 0.999916i \(-0.504116\pi\)
−0.0129291 + 0.999916i \(0.504116\pi\)
\(752\) −6.96367 −0.253939
\(753\) −4.92676 −0.179541
\(754\) −14.0740 −0.512546
\(755\) 6.58254 0.239563
\(756\) 17.6829 0.643120
\(757\) −13.2334 −0.480976 −0.240488 0.970652i \(-0.577307\pi\)
−0.240488 + 0.970652i \(0.577307\pi\)
\(758\) 30.3097 1.10090
\(759\) 3.05415 0.110859
\(760\) −8.52858 −0.309364
\(761\) 49.8216 1.80603 0.903016 0.429606i \(-0.141348\pi\)
0.903016 + 0.429606i \(0.141348\pi\)
\(762\) 10.2835 0.372531
\(763\) −0.936142 −0.0338906
\(764\) 8.96653 0.324398
\(765\) 16.4921 0.596274
\(766\) 33.3270 1.20415
\(767\) 21.1402 0.763328
\(768\) −1.05724 −0.0381499
\(769\) 51.8616 1.87018 0.935089 0.354413i \(-0.115319\pi\)
0.935089 + 0.354413i \(0.115319\pi\)
\(770\) −21.1596 −0.762538
\(771\) −10.3914 −0.374238
\(772\) 19.7194 0.709718
\(773\) −6.66148 −0.239597 −0.119798 0.992798i \(-0.538225\pi\)
−0.119798 + 0.992798i \(0.538225\pi\)
\(774\) 0.468071 0.0168245
\(775\) 3.85573 0.138502
\(776\) −5.60934 −0.201363
\(777\) 18.2775 0.655701
\(778\) 31.9039 1.14381
\(779\) −32.6357 −1.16929
\(780\) 4.25652 0.152408
\(781\) −28.4527 −1.01812
\(782\) −4.09799 −0.146544
\(783\) 38.5799 1.37873
\(784\) 4.73599 0.169142
\(785\) 24.8118 0.885570
\(786\) 1.05724 0.0377105
\(787\) 14.4552 0.515270 0.257635 0.966242i \(-0.417057\pi\)
0.257635 + 0.966242i \(0.417057\pi\)
\(788\) −21.0521 −0.749950
\(789\) −18.8895 −0.672485
\(790\) 1.86954 0.0665153
\(791\) −7.39530 −0.262947
\(792\) −5.43741 −0.193210
\(793\) −3.32788 −0.118176
\(794\) 26.3120 0.933776
\(795\) 14.4312 0.511822
\(796\) 10.0749 0.357094
\(797\) 24.4618 0.866482 0.433241 0.901278i \(-0.357370\pi\)
0.433241 + 0.901278i \(0.357370\pi\)
\(798\) −14.4471 −0.511422
\(799\) −28.5371 −1.00957
\(800\) 0.428488 0.0151493
\(801\) 1.14835 0.0405751
\(802\) 11.2889 0.398624
\(803\) −6.61809 −0.233547
\(804\) 16.4230 0.579195
\(805\) −7.32470 −0.258162
\(806\) 16.9441 0.596832
\(807\) 13.6993 0.482239
\(808\) 1.95082 0.0686295
\(809\) −10.3920 −0.365363 −0.182682 0.983172i \(-0.558478\pi\)
−0.182682 + 0.983172i \(0.558478\pi\)
\(810\) 0.405297 0.0142407
\(811\) 4.30770 0.151264 0.0756319 0.997136i \(-0.475903\pi\)
0.0756319 + 0.997136i \(0.475903\pi\)
\(812\) 25.6052 0.898566
\(813\) 15.0303 0.527137
\(814\) −14.5781 −0.510961
\(815\) 26.0833 0.913660
\(816\) −4.33257 −0.151670
\(817\) −0.991935 −0.0347034
\(818\) 17.6148 0.615887
\(819\) −12.1419 −0.424272
\(820\) −17.4935 −0.610898
\(821\) 1.10610 0.0386031 0.0193016 0.999814i \(-0.493856\pi\)
0.0193016 + 0.999814i \(0.493856\pi\)
\(822\) 17.3956 0.606741
\(823\) −44.3392 −1.54557 −0.772783 0.634670i \(-0.781136\pi\)
−0.772783 + 0.634670i \(0.781136\pi\)
\(824\) −13.6416 −0.475227
\(825\) −1.30867 −0.0455619
\(826\) −38.4608 −1.33822
\(827\) 1.51438 0.0526600 0.0263300 0.999653i \(-0.491618\pi\)
0.0263300 + 0.999653i \(0.491618\pi\)
\(828\) −1.88224 −0.0654124
\(829\) 11.9940 0.416567 0.208284 0.978068i \(-0.433212\pi\)
0.208284 + 0.978068i \(0.433212\pi\)
\(830\) −20.7157 −0.719053
\(831\) −21.8820 −0.759079
\(832\) 1.88300 0.0652813
\(833\) 19.4080 0.672449
\(834\) −16.6081 −0.575091
\(835\) 42.5056 1.47097
\(836\) 11.5230 0.398530
\(837\) −46.4475 −1.60546
\(838\) 9.48791 0.327754
\(839\) −29.6034 −1.02202 −0.511012 0.859574i \(-0.670729\pi\)
−0.511012 + 0.859574i \(0.670729\pi\)
\(840\) −7.74397 −0.267192
\(841\) 26.8646 0.926364
\(842\) −37.8882 −1.30571
\(843\) 33.1889 1.14309
\(844\) 9.93841 0.342094
\(845\) 20.2143 0.695394
\(846\) −13.1073 −0.450639
\(847\) −9.09495 −0.312506
\(848\) 6.38409 0.219230
\(849\) −6.64173 −0.227944
\(850\) 1.75594 0.0602282
\(851\) −5.04641 −0.172989
\(852\) −10.4131 −0.356747
\(853\) −20.4826 −0.701311 −0.350656 0.936505i \(-0.614041\pi\)
−0.350656 + 0.936505i \(0.614041\pi\)
\(854\) 6.05447 0.207180
\(855\) −16.0528 −0.548996
\(856\) 9.13236 0.312138
\(857\) 45.7255 1.56195 0.780976 0.624561i \(-0.214722\pi\)
0.780976 + 0.624561i \(0.214722\pi\)
\(858\) −5.75098 −0.196335
\(859\) 9.25702 0.315845 0.157923 0.987451i \(-0.449520\pi\)
0.157923 + 0.987451i \(0.449520\pi\)
\(860\) −0.531700 −0.0181308
\(861\) −29.6333 −1.00990
\(862\) 30.4416 1.03684
\(863\) −49.0948 −1.67121 −0.835603 0.549334i \(-0.814881\pi\)
−0.835603 + 0.549334i \(0.814881\pi\)
\(864\) −5.16171 −0.175605
\(865\) 27.9286 0.949600
\(866\) 23.7947 0.808578
\(867\) 0.218273 0.00741294
\(868\) −30.8268 −1.04633
\(869\) −2.52593 −0.0856864
\(870\) −16.8955 −0.572812
\(871\) −29.2502 −0.991106
\(872\) 0.273264 0.00925388
\(873\) −10.5581 −0.357339
\(874\) 3.98884 0.134925
\(875\) 39.7620 1.34420
\(876\) −2.42208 −0.0818347
\(877\) −50.5971 −1.70854 −0.854272 0.519827i \(-0.825996\pi\)
−0.854272 + 0.519827i \(0.825996\pi\)
\(878\) 24.4063 0.823672
\(879\) 24.1478 0.814485
\(880\) 6.17656 0.208212
\(881\) 27.7363 0.934459 0.467229 0.884136i \(-0.345252\pi\)
0.467229 + 0.884136i \(0.345252\pi\)
\(882\) 8.91427 0.300159
\(883\) 27.8821 0.938306 0.469153 0.883117i \(-0.344559\pi\)
0.469153 + 0.883117i \(0.344559\pi\)
\(884\) 7.71653 0.259535
\(885\) 25.3783 0.853082
\(886\) 8.82371 0.296438
\(887\) 47.1150 1.58197 0.790984 0.611837i \(-0.209569\pi\)
0.790984 + 0.611837i \(0.209569\pi\)
\(888\) −5.33527 −0.179040
\(889\) 33.3216 1.11757
\(890\) −1.30446 −0.0437255
\(891\) −0.547597 −0.0183452
\(892\) −1.24087 −0.0415474
\(893\) 27.7770 0.929521
\(894\) 10.5801 0.353851
\(895\) 9.82800 0.328514
\(896\) −3.42578 −0.114447
\(897\) −1.99079 −0.0664704
\(898\) −32.3312 −1.07891
\(899\) −67.2569 −2.24314
\(900\) 0.806517 0.0268839
\(901\) 26.1619 0.871581
\(902\) 23.6354 0.786973
\(903\) −0.900680 −0.0299727
\(904\) 2.15872 0.0717979
\(905\) 13.6929 0.455166
\(906\) −3.25490 −0.108137
\(907\) 44.1631 1.46641 0.733207 0.680006i \(-0.238023\pi\)
0.733207 + 0.680006i \(0.238023\pi\)
\(908\) 27.6748 0.918419
\(909\) 3.67191 0.121789
\(910\) 13.7924 0.457214
\(911\) 17.0393 0.564538 0.282269 0.959335i \(-0.408913\pi\)
0.282269 + 0.959335i \(0.408913\pi\)
\(912\) 4.21717 0.139644
\(913\) 27.9890 0.926300
\(914\) −0.481915 −0.0159403
\(915\) −3.99503 −0.132072
\(916\) 27.1412 0.896772
\(917\) 3.42578 0.113129
\(918\) −21.1526 −0.698141
\(919\) −44.1611 −1.45674 −0.728371 0.685183i \(-0.759722\pi\)
−0.728371 + 0.685183i \(0.759722\pi\)
\(920\) 2.13811 0.0704914
\(921\) 22.5095 0.741712
\(922\) 11.0216 0.362978
\(923\) 18.5463 0.610458
\(924\) 10.4629 0.344203
\(925\) 2.16233 0.0710968
\(926\) 16.3035 0.535768
\(927\) −25.6768 −0.843335
\(928\) −7.47426 −0.245355
\(929\) 47.3416 1.55323 0.776613 0.629978i \(-0.216936\pi\)
0.776613 + 0.629978i \(0.216936\pi\)
\(930\) 20.3410 0.667008
\(931\) −18.8911 −0.619131
\(932\) −10.2090 −0.334406
\(933\) −1.23999 −0.0405954
\(934\) 5.72416 0.187300
\(935\) 25.3115 0.827775
\(936\) 3.54426 0.115848
\(937\) 3.19381 0.104337 0.0521686 0.998638i \(-0.483387\pi\)
0.0521686 + 0.998638i \(0.483387\pi\)
\(938\) 53.2155 1.73755
\(939\) 7.81373 0.254991
\(940\) 14.8891 0.485629
\(941\) −42.9033 −1.39861 −0.699304 0.714825i \(-0.746506\pi\)
−0.699304 + 0.714825i \(0.746506\pi\)
\(942\) −12.2688 −0.399739
\(943\) 8.18175 0.266434
\(944\) 11.2269 0.365403
\(945\) −37.8079 −1.22989
\(946\) 0.718379 0.0233565
\(947\) −28.5902 −0.929057 −0.464528 0.885558i \(-0.653776\pi\)
−0.464528 + 0.885558i \(0.653776\pi\)
\(948\) −0.924440 −0.0300244
\(949\) 4.31386 0.140034
\(950\) −1.70917 −0.0554528
\(951\) 18.9483 0.614441
\(952\) −14.0388 −0.455001
\(953\) −45.5680 −1.47609 −0.738047 0.674749i \(-0.764252\pi\)
−0.738047 + 0.674749i \(0.764252\pi\)
\(954\) 12.0164 0.389045
\(955\) −19.1714 −0.620373
\(956\) −0.963565 −0.0311639
\(957\) 22.8275 0.737910
\(958\) 19.4595 0.628709
\(959\) 56.3671 1.82019
\(960\) 2.26050 0.0729572
\(961\) 49.9725 1.61202
\(962\) 9.50240 0.306370
\(963\) 17.1893 0.553918
\(964\) 8.62238 0.277708
\(965\) −42.1623 −1.35725
\(966\) 3.62188 0.116532
\(967\) 8.85805 0.284856 0.142428 0.989805i \(-0.454509\pi\)
0.142428 + 0.989805i \(0.454509\pi\)
\(968\) 2.65485 0.0853302
\(969\) 17.2819 0.555175
\(970\) 11.9934 0.385084
\(971\) 27.7455 0.890394 0.445197 0.895433i \(-0.353134\pi\)
0.445197 + 0.895433i \(0.353134\pi\)
\(972\) −15.6855 −0.503113
\(973\) −53.8153 −1.72524
\(974\) 25.7071 0.823707
\(975\) 0.853027 0.0273187
\(976\) −1.76733 −0.0565707
\(977\) 48.7651 1.56013 0.780067 0.625696i \(-0.215185\pi\)
0.780067 + 0.625696i \(0.215185\pi\)
\(978\) −12.8976 −0.412418
\(979\) 1.76245 0.0563282
\(980\) −10.1261 −0.323465
\(981\) 0.514348 0.0164219
\(982\) −31.0924 −0.992199
\(983\) 32.6228 1.04051 0.520253 0.854012i \(-0.325837\pi\)
0.520253 + 0.854012i \(0.325837\pi\)
\(984\) 8.65008 0.275754
\(985\) 45.0117 1.43419
\(986\) −30.6295 −0.975441
\(987\) 25.2216 0.802811
\(988\) −7.51099 −0.238957
\(989\) 0.248678 0.00790749
\(990\) 11.6258 0.369492
\(991\) 48.1910 1.53084 0.765419 0.643532i \(-0.222532\pi\)
0.765419 + 0.643532i \(0.222532\pi\)
\(992\) 8.99847 0.285702
\(993\) 27.7254 0.879838
\(994\) −33.7416 −1.07022
\(995\) −21.5412 −0.682900
\(996\) 10.2434 0.324574
\(997\) 19.8878 0.629853 0.314927 0.949116i \(-0.398020\pi\)
0.314927 + 0.949116i \(0.398020\pi\)
\(998\) −41.1280 −1.30189
\(999\) −26.0481 −0.824125
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 \(a_p\))