Properties

Label 8023.2.a.c.1.20
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 1.20
Character \(\chi\) = 8023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.36619 q^{2}\) \(-2.12839 q^{3}\) \(+3.59886 q^{4}\) \(+0.442767 q^{5}\) \(+5.03618 q^{6}\) \(-4.08071 q^{7}\) \(-3.78320 q^{8}\) \(+1.53005 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.36619 q^{2}\) \(-2.12839 q^{3}\) \(+3.59886 q^{4}\) \(+0.442767 q^{5}\) \(+5.03618 q^{6}\) \(-4.08071 q^{7}\) \(-3.78320 q^{8}\) \(+1.53005 q^{9}\) \(-1.04767 q^{10}\) \(+6.07255 q^{11}\) \(-7.65978 q^{12}\) \(-2.05816 q^{13}\) \(+9.65574 q^{14}\) \(-0.942382 q^{15}\) \(+1.75406 q^{16}\) \(-7.35382 q^{17}\) \(-3.62039 q^{18}\) \(-7.65712 q^{19}\) \(+1.59346 q^{20}\) \(+8.68535 q^{21}\) \(-14.3688 q^{22}\) \(+3.46771 q^{23}\) \(+8.05214 q^{24}\) \(-4.80396 q^{25}\) \(+4.87000 q^{26}\) \(+3.12863 q^{27}\) \(-14.6859 q^{28}\) \(+1.30887 q^{29}\) \(+2.22986 q^{30}\) \(+2.51535 q^{31}\) \(+3.41596 q^{32}\) \(-12.9248 q^{33}\) \(+17.4005 q^{34}\) \(-1.80681 q^{35}\) \(+5.50644 q^{36}\) \(+8.78489 q^{37}\) \(+18.1182 q^{38}\) \(+4.38058 q^{39}\) \(-1.67508 q^{40}\) \(+1.66699 q^{41}\) \(-20.5512 q^{42}\) \(-12.6010 q^{43}\) \(+21.8542 q^{44}\) \(+0.677457 q^{45}\) \(-8.20527 q^{46}\) \(+0.421122 q^{47}\) \(-3.73333 q^{48}\) \(+9.65220 q^{49}\) \(+11.3671 q^{50}\) \(+15.6518 q^{51}\) \(-7.40703 q^{52}\) \(+11.6200 q^{53}\) \(-7.40293 q^{54}\) \(+2.68873 q^{55}\) \(+15.4382 q^{56}\) \(+16.2973 q^{57}\) \(-3.09703 q^{58}\) \(+12.7502 q^{59}\) \(-3.39150 q^{60}\) \(-3.33656 q^{61}\) \(-5.95179 q^{62}\) \(-6.24370 q^{63}\) \(-11.5909 q^{64}\) \(-0.911287 q^{65}\) \(+30.5824 q^{66}\) \(-10.2681 q^{67}\) \(-26.4653 q^{68}\) \(-7.38065 q^{69}\) \(+4.27525 q^{70}\) \(-1.00000 q^{71}\) \(-5.78850 q^{72}\) \(-8.36381 q^{73}\) \(-20.7867 q^{74}\) \(+10.2247 q^{75}\) \(-27.5569 q^{76}\) \(-24.7803 q^{77}\) \(-10.3653 q^{78}\) \(+6.19979 q^{79}\) \(+0.776642 q^{80}\) \(-11.2491 q^{81}\) \(-3.94441 q^{82}\) \(-5.89730 q^{83}\) \(+31.2573 q^{84}\) \(-3.25603 q^{85}\) \(+29.8163 q^{86}\) \(-2.78578 q^{87}\) \(-22.9737 q^{88}\) \(+10.3247 q^{89}\) \(-1.60299 q^{90}\) \(+8.39877 q^{91}\) \(+12.4798 q^{92}\) \(-5.35364 q^{93}\) \(-0.996455 q^{94}\) \(-3.39032 q^{95}\) \(-7.27050 q^{96}\) \(+12.9648 q^{97}\) \(-22.8390 q^{98}\) \(+9.29131 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 46q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 27q^{14} \) \(\mathstrut -\mathstrut 41q^{15} \) \(\mathstrut +\mathstrut 150q^{16} \) \(\mathstrut -\mathstrut 137q^{17} \) \(\mathstrut -\mathstrut 67q^{18} \) \(\mathstrut -\mathstrut 42q^{19} \) \(\mathstrut -\mathstrut 66q^{20} \) \(\mathstrut -\mathstrut 46q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 48q^{24} \) \(\mathstrut +\mathstrut 129q^{25} \) \(\mathstrut -\mathstrut 67q^{26} \) \(\mathstrut -\mathstrut 89q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 79q^{29} \) \(\mathstrut -\mathstrut 11q^{30} \) \(\mathstrut +\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 147q^{32} \) \(\mathstrut -\mathstrut 112q^{33} \) \(\mathstrut -\mathstrut 28q^{34} \) \(\mathstrut -\mathstrut 53q^{35} \) \(\mathstrut +\mathstrut 141q^{36} \) \(\mathstrut -\mathstrut 60q^{37} \) \(\mathstrut -\mathstrut 53q^{38} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 48q^{40} \) \(\mathstrut -\mathstrut 128q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 63q^{43} \) \(\mathstrut -\mathstrut 88q^{45} \) \(\mathstrut -\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 92q^{47} \) \(\mathstrut -\mathstrut 131q^{48} \) \(\mathstrut +\mathstrut 122q^{49} \) \(\mathstrut -\mathstrut 116q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 89q^{52} \) \(\mathstrut -\mathstrut 94q^{53} \) \(\mathstrut -\mathstrut 71q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 104q^{56} \) \(\mathstrut -\mathstrut 93q^{57} \) \(\mathstrut -\mathstrut 65q^{58} \) \(\mathstrut -\mathstrut 54q^{59} \) \(\mathstrut -\mathstrut 12q^{60} \) \(\mathstrut +\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 97q^{62} \) \(\mathstrut -\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 163q^{64} \) \(\mathstrut -\mathstrut 163q^{65} \) \(\mathstrut -\mathstrut 65q^{66} \) \(\mathstrut -\mathstrut 35q^{67} \) \(\mathstrut -\mathstrut 217q^{68} \) \(\mathstrut -\mathstrut 46q^{69} \) \(\mathstrut -\mathstrut 79q^{70} \) \(\mathstrut -\mathstrut 158q^{71} \) \(\mathstrut -\mathstrut 99q^{72} \) \(\mathstrut -\mathstrut 165q^{73} \) \(\mathstrut -\mathstrut 94q^{75} \) \(\mathstrut -\mathstrut 93q^{76} \) \(\mathstrut -\mathstrut 140q^{77} \) \(\mathstrut +\mathstrut 25q^{78} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut 134q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 158q^{83} \) \(\mathstrut -\mathstrut 160q^{84} \) \(\mathstrut +\mathstrut 23q^{85} \) \(\mathstrut -\mathstrut 122q^{86} \) \(\mathstrut -\mathstrut 71q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 251q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut -\mathstrut 57q^{91} \) \(\mathstrut -\mathstrut 58q^{92} \) \(\mathstrut -\mathstrut 52q^{93} \) \(\mathstrut -\mathstrut 64q^{94} \) \(\mathstrut -\mathstrut 84q^{95} \) \(\mathstrut -\mathstrut 98q^{96} \) \(\mathstrut -\mathstrut 48q^{97} \) \(\mathstrut -\mathstrut 84q^{98} \) \(\mathstrut +\mathstrut 85q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.36619 −1.67315 −0.836575 0.547853i \(-0.815445\pi\)
−0.836575 + 0.547853i \(0.815445\pi\)
\(3\) −2.12839 −1.22883 −0.614414 0.788984i \(-0.710607\pi\)
−0.614414 + 0.788984i \(0.710607\pi\)
\(4\) 3.59886 1.79943
\(5\) 0.442767 0.198012 0.0990058 0.995087i \(-0.468434\pi\)
0.0990058 + 0.995087i \(0.468434\pi\)
\(6\) 5.03618 2.05601
\(7\) −4.08071 −1.54236 −0.771182 0.636615i \(-0.780334\pi\)
−0.771182 + 0.636615i \(0.780334\pi\)
\(8\) −3.78320 −1.33756
\(9\) 1.53005 0.510017
\(10\) −1.04767 −0.331303
\(11\) 6.07255 1.83094 0.915471 0.402384i \(-0.131818\pi\)
0.915471 + 0.402384i \(0.131818\pi\)
\(12\) −7.65978 −2.21119
\(13\) −2.05816 −0.570831 −0.285416 0.958404i \(-0.592132\pi\)
−0.285416 + 0.958404i \(0.592132\pi\)
\(14\) 9.65574 2.58061
\(15\) −0.942382 −0.243322
\(16\) 1.75406 0.438516
\(17\) −7.35382 −1.78356 −0.891781 0.452467i \(-0.850544\pi\)
−0.891781 + 0.452467i \(0.850544\pi\)
\(18\) −3.62039 −0.853335
\(19\) −7.65712 −1.75666 −0.878332 0.478052i \(-0.841343\pi\)
−0.878332 + 0.478052i \(0.841343\pi\)
\(20\) 1.59346 0.356308
\(21\) 8.68535 1.89530
\(22\) −14.3688 −3.06344
\(23\) 3.46771 0.723068 0.361534 0.932359i \(-0.382253\pi\)
0.361534 + 0.932359i \(0.382253\pi\)
\(24\) 8.05214 1.64364
\(25\) −4.80396 −0.960791
\(26\) 4.87000 0.955086
\(27\) 3.12863 0.602104
\(28\) −14.6859 −2.77537
\(29\) 1.30887 0.243051 0.121525 0.992588i \(-0.461221\pi\)
0.121525 + 0.992588i \(0.461221\pi\)
\(30\) 2.22986 0.407114
\(31\) 2.51535 0.451770 0.225885 0.974154i \(-0.427473\pi\)
0.225885 + 0.974154i \(0.427473\pi\)
\(32\) 3.41596 0.603862
\(33\) −12.9248 −2.24991
\(34\) 17.4005 2.98417
\(35\) −1.80681 −0.305406
\(36\) 5.50644 0.917740
\(37\) 8.78489 1.44423 0.722114 0.691774i \(-0.243171\pi\)
0.722114 + 0.691774i \(0.243171\pi\)
\(38\) 18.1182 2.93916
\(39\) 4.38058 0.701453
\(40\) −1.67508 −0.264853
\(41\) 1.66699 0.260340 0.130170 0.991492i \(-0.458448\pi\)
0.130170 + 0.991492i \(0.458448\pi\)
\(42\) −20.5512 −3.17112
\(43\) −12.6010 −1.92163 −0.960814 0.277193i \(-0.910596\pi\)
−0.960814 + 0.277193i \(0.910596\pi\)
\(44\) 21.8542 3.29465
\(45\) 0.677457 0.100989
\(46\) −8.20527 −1.20980
\(47\) 0.421122 0.0614270 0.0307135 0.999528i \(-0.490222\pi\)
0.0307135 + 0.999528i \(0.490222\pi\)
\(48\) −3.73333 −0.538860
\(49\) 9.65220 1.37889
\(50\) 11.3671 1.60755
\(51\) 15.6518 2.19169
\(52\) −7.40703 −1.02717
\(53\) 11.6200 1.59612 0.798062 0.602576i \(-0.205859\pi\)
0.798062 + 0.602576i \(0.205859\pi\)
\(54\) −7.40293 −1.00741
\(55\) 2.68873 0.362548
\(56\) 15.4382 2.06301
\(57\) 16.2973 2.15864
\(58\) −3.09703 −0.406660
\(59\) 12.7502 1.65994 0.829970 0.557808i \(-0.188357\pi\)
0.829970 + 0.557808i \(0.188357\pi\)
\(60\) −3.39150 −0.437841
\(61\) −3.33656 −0.427203 −0.213601 0.976921i \(-0.568519\pi\)
−0.213601 + 0.976921i \(0.568519\pi\)
\(62\) −5.95179 −0.755878
\(63\) −6.24370 −0.786632
\(64\) −11.5909 −1.44887
\(65\) −0.911287 −0.113031
\(66\) 30.5824 3.76444
\(67\) −10.2681 −1.25444 −0.627222 0.778840i \(-0.715808\pi\)
−0.627222 + 0.778840i \(0.715808\pi\)
\(68\) −26.4653 −3.20939
\(69\) −7.38065 −0.888526
\(70\) 4.27525 0.510990
\(71\) −1.00000 −0.118678
\(72\) −5.78850 −0.682181
\(73\) −8.36381 −0.978910 −0.489455 0.872029i \(-0.662804\pi\)
−0.489455 + 0.872029i \(0.662804\pi\)
\(74\) −20.7867 −2.41641
\(75\) 10.2247 1.18065
\(76\) −27.5569 −3.16099
\(77\) −24.7803 −2.82398
\(78\) −10.3653 −1.17364
\(79\) 6.19979 0.697531 0.348766 0.937210i \(-0.386601\pi\)
0.348766 + 0.937210i \(0.386601\pi\)
\(80\) 0.776642 0.0868312
\(81\) −11.2491 −1.24990
\(82\) −3.94441 −0.435588
\(83\) −5.89730 −0.647313 −0.323657 0.946175i \(-0.604912\pi\)
−0.323657 + 0.946175i \(0.604912\pi\)
\(84\) 31.2573 3.41046
\(85\) −3.25603 −0.353166
\(86\) 29.8163 3.21517
\(87\) −2.78578 −0.298667
\(88\) −22.9737 −2.44900
\(89\) 10.3247 1.09442 0.547210 0.836995i \(-0.315690\pi\)
0.547210 + 0.836995i \(0.315690\pi\)
\(90\) −1.60299 −0.168970
\(91\) 8.39877 0.880430
\(92\) 12.4798 1.30111
\(93\) −5.35364 −0.555147
\(94\) −0.996455 −0.102777
\(95\) −3.39032 −0.347840
\(96\) −7.27050 −0.742042
\(97\) 12.9648 1.31638 0.658189 0.752852i \(-0.271323\pi\)
0.658189 + 0.752852i \(0.271323\pi\)
\(98\) −22.8390 −2.30708
\(99\) 9.29131 0.933812
\(100\) −17.2888 −1.72888
\(101\) −13.2816 −1.32157 −0.660783 0.750577i \(-0.729776\pi\)
−0.660783 + 0.750577i \(0.729776\pi\)
\(102\) −37.0352 −3.66703
\(103\) −8.06131 −0.794305 −0.397152 0.917753i \(-0.630002\pi\)
−0.397152 + 0.917753i \(0.630002\pi\)
\(104\) 7.78645 0.763524
\(105\) 3.84559 0.375291
\(106\) −27.4950 −2.67055
\(107\) 8.88851 0.859285 0.429642 0.902999i \(-0.358640\pi\)
0.429642 + 0.902999i \(0.358640\pi\)
\(108\) 11.2595 1.08344
\(109\) 10.0984 0.967253 0.483627 0.875274i \(-0.339319\pi\)
0.483627 + 0.875274i \(0.339319\pi\)
\(110\) −6.36204 −0.606596
\(111\) −18.6977 −1.77471
\(112\) −7.15783 −0.676351
\(113\) −1.00000 −0.0940721
\(114\) −38.5626 −3.61172
\(115\) 1.53539 0.143176
\(116\) 4.71043 0.437352
\(117\) −3.14909 −0.291134
\(118\) −30.1695 −2.77733
\(119\) 30.0088 2.75090
\(120\) 3.56522 0.325459
\(121\) 25.8758 2.35235
\(122\) 7.89493 0.714774
\(123\) −3.54801 −0.319913
\(124\) 9.05238 0.812927
\(125\) −4.34087 −0.388259
\(126\) 14.7738 1.31615
\(127\) −6.65856 −0.590852 −0.295426 0.955366i \(-0.595462\pi\)
−0.295426 + 0.955366i \(0.595462\pi\)
\(128\) 20.5944 1.82031
\(129\) 26.8198 2.36135
\(130\) 2.15628 0.189118
\(131\) 9.11938 0.796764 0.398382 0.917220i \(-0.369572\pi\)
0.398382 + 0.917220i \(0.369572\pi\)
\(132\) −46.5144 −4.04856
\(133\) 31.2465 2.70941
\(134\) 24.2962 2.09887
\(135\) 1.38525 0.119224
\(136\) 27.8210 2.38563
\(137\) 5.12922 0.438219 0.219109 0.975700i \(-0.429685\pi\)
0.219109 + 0.975700i \(0.429685\pi\)
\(138\) 17.4640 1.48664
\(139\) 3.16049 0.268069 0.134034 0.990977i \(-0.457207\pi\)
0.134034 + 0.990977i \(0.457207\pi\)
\(140\) −6.50244 −0.549556
\(141\) −0.896313 −0.0754832
\(142\) 2.36619 0.198566
\(143\) −12.4983 −1.04516
\(144\) 2.68381 0.223651
\(145\) 0.579524 0.0481268
\(146\) 19.7904 1.63786
\(147\) −20.5437 −1.69441
\(148\) 31.6156 2.59879
\(149\) 17.2508 1.41324 0.706620 0.707593i \(-0.250219\pi\)
0.706620 + 0.707593i \(0.250219\pi\)
\(150\) −24.1936 −1.97540
\(151\) −13.1367 −1.06905 −0.534526 0.845152i \(-0.679510\pi\)
−0.534526 + 0.845152i \(0.679510\pi\)
\(152\) 28.9684 2.34965
\(153\) −11.2517 −0.909648
\(154\) 58.6349 4.72494
\(155\) 1.11371 0.0894556
\(156\) 15.7651 1.26222
\(157\) −13.5724 −1.08319 −0.541597 0.840639i \(-0.682180\pi\)
−0.541597 + 0.840639i \(0.682180\pi\)
\(158\) −14.6699 −1.16707
\(159\) −24.7318 −1.96136
\(160\) 1.51247 0.119572
\(161\) −14.1507 −1.11523
\(162\) 26.6175 2.09127
\(163\) 12.6027 0.987120 0.493560 0.869712i \(-0.335695\pi\)
0.493560 + 0.869712i \(0.335695\pi\)
\(164\) 5.99926 0.468463
\(165\) −5.72266 −0.445508
\(166\) 13.9541 1.08305
\(167\) 0.771686 0.0597149 0.0298574 0.999554i \(-0.490495\pi\)
0.0298574 + 0.999554i \(0.490495\pi\)
\(168\) −32.8585 −2.53508
\(169\) −8.76397 −0.674151
\(170\) 7.70439 0.590899
\(171\) −11.7158 −0.895929
\(172\) −45.3491 −3.45783
\(173\) −12.5847 −0.956796 −0.478398 0.878143i \(-0.658782\pi\)
−0.478398 + 0.878143i \(0.658782\pi\)
\(174\) 6.59170 0.499715
\(175\) 19.6036 1.48189
\(176\) 10.6516 0.802897
\(177\) −27.1375 −2.03978
\(178\) −24.4303 −1.83113
\(179\) 2.97475 0.222343 0.111172 0.993801i \(-0.464540\pi\)
0.111172 + 0.993801i \(0.464540\pi\)
\(180\) 2.43807 0.181723
\(181\) −14.3982 −1.07021 −0.535106 0.844785i \(-0.679728\pi\)
−0.535106 + 0.844785i \(0.679728\pi\)
\(182\) −19.8731 −1.47309
\(183\) 7.10150 0.524958
\(184\) −13.1191 −0.967150
\(185\) 3.88966 0.285974
\(186\) 12.6677 0.928844
\(187\) −44.6564 −3.26560
\(188\) 1.51556 0.110534
\(189\) −12.7670 −0.928664
\(190\) 8.02215 0.581988
\(191\) −17.7644 −1.28539 −0.642695 0.766122i \(-0.722184\pi\)
−0.642695 + 0.766122i \(0.722184\pi\)
\(192\) 24.6700 1.78041
\(193\) −4.14988 −0.298715 −0.149358 0.988783i \(-0.547721\pi\)
−0.149358 + 0.988783i \(0.547721\pi\)
\(194\) −30.6773 −2.20250
\(195\) 1.93958 0.138896
\(196\) 34.7369 2.48121
\(197\) 19.1210 1.36231 0.681157 0.732138i \(-0.261477\pi\)
0.681157 + 0.732138i \(0.261477\pi\)
\(198\) −21.9850 −1.56241
\(199\) 8.73906 0.619496 0.309748 0.950819i \(-0.399755\pi\)
0.309748 + 0.950819i \(0.399755\pi\)
\(200\) 18.1743 1.28512
\(201\) 21.8545 1.54150
\(202\) 31.4268 2.21118
\(203\) −5.34111 −0.374873
\(204\) 56.3286 3.94379
\(205\) 0.738088 0.0515503
\(206\) 19.0746 1.32899
\(207\) 5.30578 0.368777
\(208\) −3.61015 −0.250319
\(209\) −46.4982 −3.21635
\(210\) −9.09940 −0.627918
\(211\) 9.50402 0.654284 0.327142 0.944975i \(-0.393915\pi\)
0.327142 + 0.944975i \(0.393915\pi\)
\(212\) 41.8186 2.87211
\(213\) 2.12839 0.145835
\(214\) −21.0319 −1.43771
\(215\) −5.57929 −0.380505
\(216\) −11.8362 −0.805353
\(217\) −10.2644 −0.696793
\(218\) −23.8948 −1.61836
\(219\) 17.8015 1.20291
\(220\) 9.67634 0.652379
\(221\) 15.1353 1.01811
\(222\) 44.2423 2.96935
\(223\) 22.6442 1.51637 0.758185 0.652039i \(-0.226086\pi\)
0.758185 + 0.652039i \(0.226086\pi\)
\(224\) −13.9395 −0.931374
\(225\) −7.35030 −0.490020
\(226\) 2.36619 0.157397
\(227\) 23.4338 1.55536 0.777679 0.628661i \(-0.216397\pi\)
0.777679 + 0.628661i \(0.216397\pi\)
\(228\) 58.6518 3.88431
\(229\) −10.4501 −0.690562 −0.345281 0.938499i \(-0.612216\pi\)
−0.345281 + 0.938499i \(0.612216\pi\)
\(230\) −3.63302 −0.239555
\(231\) 52.7422 3.47018
\(232\) −4.95171 −0.325096
\(233\) −0.628158 −0.0411520 −0.0205760 0.999788i \(-0.506550\pi\)
−0.0205760 + 0.999788i \(0.506550\pi\)
\(234\) 7.45136 0.487110
\(235\) 0.186459 0.0121633
\(236\) 45.8863 2.98694
\(237\) −13.1956 −0.857146
\(238\) −71.0065 −4.60267
\(239\) 12.5760 0.813475 0.406737 0.913545i \(-0.366666\pi\)
0.406737 + 0.913545i \(0.366666\pi\)
\(240\) −1.65300 −0.106701
\(241\) 12.6444 0.814499 0.407250 0.913317i \(-0.366488\pi\)
0.407250 + 0.913317i \(0.366488\pi\)
\(242\) −61.2271 −3.93583
\(243\) 14.5566 0.933807
\(244\) −12.0078 −0.768721
\(245\) 4.27368 0.273035
\(246\) 8.39526 0.535262
\(247\) 15.7596 1.00276
\(248\) −9.51607 −0.604271
\(249\) 12.5518 0.795436
\(250\) 10.2713 0.649616
\(251\) 24.1268 1.52287 0.761434 0.648243i \(-0.224496\pi\)
0.761434 + 0.648243i \(0.224496\pi\)
\(252\) −22.4702 −1.41549
\(253\) 21.0579 1.32390
\(254\) 15.7554 0.988584
\(255\) 6.93011 0.433980
\(256\) −25.5485 −1.59678
\(257\) −2.28458 −0.142508 −0.0712542 0.997458i \(-0.522700\pi\)
−0.0712542 + 0.997458i \(0.522700\pi\)
\(258\) −63.4607 −3.95089
\(259\) −35.8486 −2.22752
\(260\) −3.27959 −0.203392
\(261\) 2.00264 0.123960
\(262\) −21.5782 −1.33311
\(263\) −6.37142 −0.392879 −0.196439 0.980516i \(-0.562938\pi\)
−0.196439 + 0.980516i \(0.562938\pi\)
\(264\) 48.8970 3.00940
\(265\) 5.14493 0.316051
\(266\) −73.9352 −4.53325
\(267\) −21.9751 −1.34485
\(268\) −36.9533 −2.25728
\(269\) −14.6742 −0.894701 −0.447351 0.894359i \(-0.647632\pi\)
−0.447351 + 0.894359i \(0.647632\pi\)
\(270\) −3.27777 −0.199479
\(271\) −4.61315 −0.280229 −0.140115 0.990135i \(-0.544747\pi\)
−0.140115 + 0.990135i \(0.544747\pi\)
\(272\) −12.8991 −0.782120
\(273\) −17.8759 −1.08190
\(274\) −12.1367 −0.733205
\(275\) −29.1723 −1.75915
\(276\) −26.5619 −1.59884
\(277\) 31.6588 1.90219 0.951095 0.308898i \(-0.0999603\pi\)
0.951095 + 0.308898i \(0.0999603\pi\)
\(278\) −7.47831 −0.448519
\(279\) 3.84861 0.230410
\(280\) 6.83551 0.408500
\(281\) 4.80563 0.286680 0.143340 0.989674i \(-0.454216\pi\)
0.143340 + 0.989674i \(0.454216\pi\)
\(282\) 2.12085 0.126295
\(283\) −20.3995 −1.21262 −0.606311 0.795228i \(-0.707351\pi\)
−0.606311 + 0.795228i \(0.707351\pi\)
\(284\) −3.59886 −0.213553
\(285\) 7.21593 0.427435
\(286\) 29.5733 1.74871
\(287\) −6.80250 −0.401539
\(288\) 5.22659 0.307980
\(289\) 37.0786 2.18110
\(290\) −1.37126 −0.0805234
\(291\) −27.5942 −1.61760
\(292\) −30.1002 −1.76148
\(293\) 12.9704 0.757740 0.378870 0.925450i \(-0.376313\pi\)
0.378870 + 0.925450i \(0.376313\pi\)
\(294\) 48.6102 2.83501
\(295\) 5.64539 0.328687
\(296\) −33.2350 −1.93175
\(297\) 18.9987 1.10242
\(298\) −40.8186 −2.36456
\(299\) −7.13712 −0.412750
\(300\) 36.7973 2.12449
\(301\) 51.4209 2.96385
\(302\) 31.0840 1.78868
\(303\) 28.2684 1.62398
\(304\) −13.4311 −0.770325
\(305\) −1.47732 −0.0845910
\(306\) 26.6237 1.52198
\(307\) 20.9522 1.19580 0.597902 0.801569i \(-0.296001\pi\)
0.597902 + 0.801569i \(0.296001\pi\)
\(308\) −89.1808 −5.08155
\(309\) 17.1576 0.976064
\(310\) −2.63526 −0.149673
\(311\) −2.33388 −0.132342 −0.0661711 0.997808i \(-0.521078\pi\)
−0.0661711 + 0.997808i \(0.521078\pi\)
\(312\) −16.5726 −0.938239
\(313\) −21.6269 −1.22242 −0.611212 0.791467i \(-0.709318\pi\)
−0.611212 + 0.791467i \(0.709318\pi\)
\(314\) 32.1148 1.81234
\(315\) −2.76451 −0.155762
\(316\) 22.3122 1.25516
\(317\) −33.5458 −1.88412 −0.942061 0.335442i \(-0.891114\pi\)
−0.942061 + 0.335442i \(0.891114\pi\)
\(318\) 58.5202 3.28165
\(319\) 7.94816 0.445012
\(320\) −5.13209 −0.286892
\(321\) −18.9182 −1.05591
\(322\) 33.4833 1.86595
\(323\) 56.3090 3.13312
\(324\) −40.4839 −2.24911
\(325\) 9.88732 0.548450
\(326\) −29.8204 −1.65160
\(327\) −21.4934 −1.18859
\(328\) −6.30656 −0.348221
\(329\) −1.71848 −0.0947428
\(330\) 13.5409 0.745402
\(331\) 35.2081 1.93521 0.967605 0.252467i \(-0.0812420\pi\)
0.967605 + 0.252467i \(0.0812420\pi\)
\(332\) −21.2236 −1.16479
\(333\) 13.4413 0.736581
\(334\) −1.82596 −0.0999119
\(335\) −4.54637 −0.248395
\(336\) 15.2347 0.831119
\(337\) 8.92467 0.486157 0.243079 0.970007i \(-0.421843\pi\)
0.243079 + 0.970007i \(0.421843\pi\)
\(338\) 20.7372 1.12796
\(339\) 2.12839 0.115598
\(340\) −11.7180 −0.635497
\(341\) 15.2746 0.827164
\(342\) 27.7218 1.49902
\(343\) −10.8229 −0.584380
\(344\) 47.6720 2.57030
\(345\) −3.26791 −0.175938
\(346\) 29.7778 1.60086
\(347\) −16.0283 −0.860445 −0.430223 0.902723i \(-0.641565\pi\)
−0.430223 + 0.902723i \(0.641565\pi\)
\(348\) −10.0256 −0.537431
\(349\) −12.4523 −0.666559 −0.333279 0.942828i \(-0.608155\pi\)
−0.333279 + 0.942828i \(0.608155\pi\)
\(350\) −46.3858 −2.47942
\(351\) −6.43922 −0.343700
\(352\) 20.7436 1.10564
\(353\) 3.79464 0.201968 0.100984 0.994888i \(-0.467801\pi\)
0.100984 + 0.994888i \(0.467801\pi\)
\(354\) 64.2125 3.41286
\(355\) −0.442767 −0.0234996
\(356\) 37.1573 1.96933
\(357\) −63.8705 −3.38038
\(358\) −7.03883 −0.372013
\(359\) 32.8685 1.73473 0.867366 0.497671i \(-0.165811\pi\)
0.867366 + 0.497671i \(0.165811\pi\)
\(360\) −2.56296 −0.135080
\(361\) 39.6315 2.08587
\(362\) 34.0690 1.79062
\(363\) −55.0739 −2.89063
\(364\) 30.2260 1.58427
\(365\) −3.70322 −0.193835
\(366\) −16.8035 −0.878334
\(367\) 5.35795 0.279683 0.139841 0.990174i \(-0.455341\pi\)
0.139841 + 0.990174i \(0.455341\pi\)
\(368\) 6.08259 0.317077
\(369\) 2.55058 0.132778
\(370\) −9.20369 −0.478477
\(371\) −47.4177 −2.46180
\(372\) −19.2670 −0.998948
\(373\) −21.9639 −1.13725 −0.568623 0.822598i \(-0.692524\pi\)
−0.568623 + 0.822598i \(0.692524\pi\)
\(374\) 105.666 5.46384
\(375\) 9.23907 0.477104
\(376\) −1.59319 −0.0821625
\(377\) −2.69386 −0.138741
\(378\) 30.2092 1.55379
\(379\) 2.02462 0.103998 0.0519989 0.998647i \(-0.483441\pi\)
0.0519989 + 0.998647i \(0.483441\pi\)
\(380\) −12.2013 −0.625913
\(381\) 14.1720 0.726055
\(382\) 42.0341 2.15065
\(383\) −5.91063 −0.302019 −0.151010 0.988532i \(-0.548252\pi\)
−0.151010 + 0.988532i \(0.548252\pi\)
\(384\) −43.8330 −2.23685
\(385\) −10.9719 −0.559180
\(386\) 9.81942 0.499795
\(387\) −19.2801 −0.980064
\(388\) 46.6586 2.36873
\(389\) −32.5830 −1.65202 −0.826011 0.563653i \(-0.809395\pi\)
−0.826011 + 0.563653i \(0.809395\pi\)
\(390\) −4.58941 −0.232394
\(391\) −25.5009 −1.28964
\(392\) −36.5162 −1.84435
\(393\) −19.4096 −0.979086
\(394\) −45.2439 −2.27935
\(395\) 2.74507 0.138119
\(396\) 33.4381 1.68033
\(397\) −7.99867 −0.401442 −0.200721 0.979648i \(-0.564328\pi\)
−0.200721 + 0.979648i \(0.564328\pi\)
\(398\) −20.6783 −1.03651
\(399\) −66.5048 −3.32940
\(400\) −8.42645 −0.421322
\(401\) −17.5912 −0.878463 −0.439232 0.898374i \(-0.644749\pi\)
−0.439232 + 0.898374i \(0.644749\pi\)
\(402\) −51.7119 −2.57915
\(403\) −5.17699 −0.257884
\(404\) −47.7985 −2.37807
\(405\) −4.98073 −0.247495
\(406\) 12.6381 0.627218
\(407\) 53.3467 2.64430
\(408\) −59.2140 −2.93153
\(409\) −12.6318 −0.624602 −0.312301 0.949983i \(-0.601100\pi\)
−0.312301 + 0.949983i \(0.601100\pi\)
\(410\) −1.74646 −0.0862514
\(411\) −10.9170 −0.538495
\(412\) −29.0115 −1.42930
\(413\) −52.0301 −2.56023
\(414\) −12.5545 −0.617019
\(415\) −2.61113 −0.128176
\(416\) −7.03060 −0.344703
\(417\) −6.72675 −0.329410
\(418\) 110.024 5.38143
\(419\) 9.63409 0.470656 0.235328 0.971916i \(-0.424384\pi\)
0.235328 + 0.971916i \(0.424384\pi\)
\(420\) 13.8397 0.675310
\(421\) 17.1770 0.837157 0.418578 0.908181i \(-0.362529\pi\)
0.418578 + 0.908181i \(0.362529\pi\)
\(422\) −22.4883 −1.09471
\(423\) 0.644339 0.0313288
\(424\) −43.9606 −2.13492
\(425\) 35.3274 1.71363
\(426\) −5.03618 −0.244004
\(427\) 13.6155 0.658902
\(428\) 31.9885 1.54622
\(429\) 26.6013 1.28432
\(430\) 13.2017 0.636641
\(431\) 10.8666 0.523423 0.261712 0.965146i \(-0.415713\pi\)
0.261712 + 0.965146i \(0.415713\pi\)
\(432\) 5.48781 0.264032
\(433\) 14.6337 0.703250 0.351625 0.936141i \(-0.385629\pi\)
0.351625 + 0.936141i \(0.385629\pi\)
\(434\) 24.2875 1.16584
\(435\) −1.23345 −0.0591396
\(436\) 36.3428 1.74050
\(437\) −26.5527 −1.27019
\(438\) −42.1217 −2.01265
\(439\) 17.7050 0.845012 0.422506 0.906360i \(-0.361150\pi\)
0.422506 + 0.906360i \(0.361150\pi\)
\(440\) −10.1720 −0.484931
\(441\) 14.7684 0.703256
\(442\) −35.8131 −1.70346
\(443\) 16.7633 0.796449 0.398225 0.917288i \(-0.369626\pi\)
0.398225 + 0.917288i \(0.369626\pi\)
\(444\) −67.2904 −3.19346
\(445\) 4.57146 0.216708
\(446\) −53.5806 −2.53711
\(447\) −36.7164 −1.73663
\(448\) 47.2993 2.23468
\(449\) 13.5333 0.638677 0.319339 0.947641i \(-0.396539\pi\)
0.319339 + 0.947641i \(0.396539\pi\)
\(450\) 17.3922 0.819877
\(451\) 10.1229 0.476667
\(452\) −3.59886 −0.169276
\(453\) 27.9601 1.31368
\(454\) −55.4489 −2.60235
\(455\) 3.71870 0.174335
\(456\) −61.6562 −2.88732
\(457\) −37.9060 −1.77317 −0.886585 0.462567i \(-0.846929\pi\)
−0.886585 + 0.462567i \(0.846929\pi\)
\(458\) 24.7269 1.15541
\(459\) −23.0073 −1.07389
\(460\) 5.52565 0.257635
\(461\) −0.753289 −0.0350841 −0.0175421 0.999846i \(-0.505584\pi\)
−0.0175421 + 0.999846i \(0.505584\pi\)
\(462\) −124.798 −5.80613
\(463\) 27.9872 1.30067 0.650337 0.759645i \(-0.274627\pi\)
0.650337 + 0.759645i \(0.274627\pi\)
\(464\) 2.29584 0.106582
\(465\) −2.37042 −0.109925
\(466\) 1.48634 0.0688534
\(467\) 35.1515 1.62662 0.813310 0.581831i \(-0.197664\pi\)
0.813310 + 0.581831i \(0.197664\pi\)
\(468\) −11.3331 −0.523875
\(469\) 41.9010 1.93481
\(470\) −0.441198 −0.0203509
\(471\) 28.8873 1.33106
\(472\) −48.2368 −2.22028
\(473\) −76.5199 −3.51839
\(474\) 31.2233 1.43413
\(475\) 36.7845 1.68779
\(476\) 107.997 4.95005
\(477\) 17.7791 0.814050
\(478\) −29.7572 −1.36106
\(479\) −4.71072 −0.215238 −0.107619 0.994192i \(-0.534323\pi\)
−0.107619 + 0.994192i \(0.534323\pi\)
\(480\) −3.21914 −0.146933
\(481\) −18.0807 −0.824411
\(482\) −29.9191 −1.36278
\(483\) 30.1183 1.37043
\(484\) 93.1234 4.23288
\(485\) 5.74040 0.260658
\(486\) −34.4437 −1.56240
\(487\) 40.4490 1.83292 0.916459 0.400129i \(-0.131035\pi\)
0.916459 + 0.400129i \(0.131035\pi\)
\(488\) 12.6229 0.571411
\(489\) −26.8235 −1.21300
\(490\) −10.1123 −0.456829
\(491\) −18.8191 −0.849293 −0.424647 0.905359i \(-0.639602\pi\)
−0.424647 + 0.905359i \(0.639602\pi\)
\(492\) −12.7688 −0.575661
\(493\) −9.62517 −0.433496
\(494\) −37.2902 −1.67777
\(495\) 4.11389 0.184906
\(496\) 4.41208 0.198108
\(497\) 4.08071 0.183045
\(498\) −29.6999 −1.33088
\(499\) −39.0292 −1.74719 −0.873593 0.486657i \(-0.838216\pi\)
−0.873593 + 0.486657i \(0.838216\pi\)
\(500\) −15.6222 −0.698645
\(501\) −1.64245 −0.0733793
\(502\) −57.0885 −2.54799
\(503\) −16.8751 −0.752423 −0.376212 0.926534i \(-0.622773\pi\)
−0.376212 + 0.926534i \(0.622773\pi\)
\(504\) 23.6212 1.05217
\(505\) −5.88065 −0.261685
\(506\) −49.8269 −2.21508
\(507\) 18.6532 0.828416
\(508\) −23.9632 −1.06320
\(509\) 9.70641 0.430229 0.215115 0.976589i \(-0.430988\pi\)
0.215115 + 0.976589i \(0.430988\pi\)
\(510\) −16.3980 −0.726114
\(511\) 34.1303 1.50984
\(512\) 19.2638 0.851346
\(513\) −23.9563 −1.05769
\(514\) 5.40576 0.238438
\(515\) −3.56929 −0.157282
\(516\) 96.5206 4.24908
\(517\) 2.55728 0.112469
\(518\) 84.8247 3.72698
\(519\) 26.7852 1.17574
\(520\) 3.44758 0.151187
\(521\) 30.8855 1.35312 0.676559 0.736389i \(-0.263471\pi\)
0.676559 + 0.736389i \(0.263471\pi\)
\(522\) −4.73862 −0.207404
\(523\) −34.9363 −1.52766 −0.763828 0.645420i \(-0.776682\pi\)
−0.763828 + 0.645420i \(0.776682\pi\)
\(524\) 32.8194 1.43372
\(525\) −41.7241 −1.82099
\(526\) 15.0760 0.657345
\(527\) −18.4974 −0.805759
\(528\) −22.6708 −0.986622
\(529\) −10.9750 −0.477172
\(530\) −12.1739 −0.528800
\(531\) 19.5085 0.846598
\(532\) 112.452 4.87540
\(533\) −3.43093 −0.148610
\(534\) 51.9972 2.25014
\(535\) 3.93554 0.170148
\(536\) 38.8462 1.67790
\(537\) −6.33143 −0.273221
\(538\) 34.7219 1.49697
\(539\) 58.6135 2.52466
\(540\) 4.98533 0.214534
\(541\) −26.3746 −1.13393 −0.566965 0.823742i \(-0.691883\pi\)
−0.566965 + 0.823742i \(0.691883\pi\)
\(542\) 10.9156 0.468865
\(543\) 30.6451 1.31511
\(544\) −25.1203 −1.07703
\(545\) 4.47125 0.191527
\(546\) 42.2977 1.81017
\(547\) −26.8385 −1.14753 −0.573766 0.819019i \(-0.694518\pi\)
−0.573766 + 0.819019i \(0.694518\pi\)
\(548\) 18.4593 0.788543
\(549\) −5.10511 −0.217881
\(550\) 69.0271 2.94333
\(551\) −10.0222 −0.426958
\(552\) 27.9225 1.18846
\(553\) −25.2996 −1.07585
\(554\) −74.9106 −3.18265
\(555\) −8.27873 −0.351412
\(556\) 11.3741 0.482371
\(557\) 11.2130 0.475109 0.237554 0.971374i \(-0.423654\pi\)
0.237554 + 0.971374i \(0.423654\pi\)
\(558\) −9.10655 −0.385511
\(559\) 25.9348 1.09693
\(560\) −3.16925 −0.133925
\(561\) 95.0463 4.01286
\(562\) −11.3710 −0.479658
\(563\) −29.7705 −1.25468 −0.627338 0.778747i \(-0.715856\pi\)
−0.627338 + 0.778747i \(0.715856\pi\)
\(564\) −3.22570 −0.135827
\(565\) −0.442767 −0.0186274
\(566\) 48.2690 2.02890
\(567\) 45.9043 1.92780
\(568\) 3.78320 0.158740
\(569\) −7.74289 −0.324599 −0.162299 0.986742i \(-0.551891\pi\)
−0.162299 + 0.986742i \(0.551891\pi\)
\(570\) −17.0743 −0.715163
\(571\) −13.2941 −0.556343 −0.278171 0.960531i \(-0.589728\pi\)
−0.278171 + 0.960531i \(0.589728\pi\)
\(572\) −44.9796 −1.88069
\(573\) 37.8097 1.57952
\(574\) 16.0960 0.671835
\(575\) −16.6587 −0.694718
\(576\) −17.7347 −0.738947
\(577\) 15.7063 0.653860 0.326930 0.945049i \(-0.393986\pi\)
0.326930 + 0.945049i \(0.393986\pi\)
\(578\) −87.7351 −3.64930
\(579\) 8.83258 0.367069
\(580\) 2.08562 0.0866008
\(581\) 24.0652 0.998393
\(582\) 65.2932 2.70649
\(583\) 70.5627 2.92241
\(584\) 31.6420 1.30935
\(585\) −1.39432 −0.0576479
\(586\) −30.6905 −1.26781
\(587\) 39.8682 1.64554 0.822768 0.568377i \(-0.192428\pi\)
0.822768 + 0.568377i \(0.192428\pi\)
\(588\) −73.9338 −3.04898
\(589\) −19.2603 −0.793607
\(590\) −13.3581 −0.549943
\(591\) −40.6969 −1.67405
\(592\) 15.4093 0.633317
\(593\) −16.1606 −0.663636 −0.331818 0.943343i \(-0.607662\pi\)
−0.331818 + 0.943343i \(0.607662\pi\)
\(594\) −44.9546 −1.84451
\(595\) 13.2869 0.544710
\(596\) 62.0831 2.54302
\(597\) −18.6001 −0.761253
\(598\) 16.8878 0.690593
\(599\) −9.69394 −0.396084 −0.198042 0.980194i \(-0.563458\pi\)
−0.198042 + 0.980194i \(0.563458\pi\)
\(600\) −38.6821 −1.57919
\(601\) 27.1552 1.10768 0.553841 0.832622i \(-0.313161\pi\)
0.553841 + 0.832622i \(0.313161\pi\)
\(602\) −121.672 −4.95897
\(603\) −15.7107 −0.639788
\(604\) −47.2772 −1.92368
\(605\) 11.4570 0.465792
\(606\) −66.8885 −2.71716
\(607\) 15.5194 0.629912 0.314956 0.949106i \(-0.398010\pi\)
0.314956 + 0.949106i \(0.398010\pi\)
\(608\) −26.1564 −1.06078
\(609\) 11.3680 0.460654
\(610\) 3.49562 0.141533
\(611\) −0.866738 −0.0350645
\(612\) −40.4933 −1.63685
\(613\) 40.0318 1.61687 0.808435 0.588585i \(-0.200315\pi\)
0.808435 + 0.588585i \(0.200315\pi\)
\(614\) −49.5769 −2.00076
\(615\) −1.57094 −0.0633465
\(616\) 93.7489 3.77725
\(617\) 9.15416 0.368533 0.184266 0.982876i \(-0.441009\pi\)
0.184266 + 0.982876i \(0.441009\pi\)
\(618\) −40.5982 −1.63310
\(619\) −22.7056 −0.912617 −0.456308 0.889822i \(-0.650829\pi\)
−0.456308 + 0.889822i \(0.650829\pi\)
\(620\) 4.00810 0.160969
\(621\) 10.8492 0.435363
\(622\) 5.52240 0.221428
\(623\) −42.1323 −1.68799
\(624\) 7.68381 0.307598
\(625\) 22.0978 0.883912
\(626\) 51.1734 2.04530
\(627\) 98.9664 3.95234
\(628\) −48.8450 −1.94913
\(629\) −64.6025 −2.57587
\(630\) 6.54135 0.260613
\(631\) 3.81869 0.152020 0.0760099 0.997107i \(-0.475782\pi\)
0.0760099 + 0.997107i \(0.475782\pi\)
\(632\) −23.4551 −0.932993
\(633\) −20.2283 −0.804002
\(634\) 79.3758 3.15242
\(635\) −2.94819 −0.116996
\(636\) −89.0063 −3.52933
\(637\) −19.8658 −0.787112
\(638\) −18.8069 −0.744571
\(639\) −1.53005 −0.0605279
\(640\) 9.11855 0.360442
\(641\) 29.3557 1.15948 0.579740 0.814801i \(-0.303154\pi\)
0.579740 + 0.814801i \(0.303154\pi\)
\(642\) 44.7641 1.76670
\(643\) −29.3639 −1.15800 −0.578999 0.815329i \(-0.696556\pi\)
−0.578999 + 0.815329i \(0.696556\pi\)
\(644\) −50.9265 −2.00678
\(645\) 11.8749 0.467575
\(646\) −133.238 −5.24218
\(647\) 35.3270 1.38885 0.694423 0.719567i \(-0.255660\pi\)
0.694423 + 0.719567i \(0.255660\pi\)
\(648\) 42.5576 1.67182
\(649\) 77.4265 3.03925
\(650\) −23.3953 −0.917639
\(651\) 21.8467 0.856239
\(652\) 45.3553 1.77625
\(653\) −45.1762 −1.76788 −0.883940 0.467601i \(-0.845119\pi\)
−0.883940 + 0.467601i \(0.845119\pi\)
\(654\) 50.8575 1.98868
\(655\) 4.03776 0.157768
\(656\) 2.92401 0.114163
\(657\) −12.7971 −0.499261
\(658\) 4.06625 0.158519
\(659\) 6.73244 0.262259 0.131129 0.991365i \(-0.458140\pi\)
0.131129 + 0.991365i \(0.458140\pi\)
\(660\) −20.5950 −0.801661
\(661\) −30.5092 −1.18667 −0.593336 0.804955i \(-0.702189\pi\)
−0.593336 + 0.804955i \(0.702189\pi\)
\(662\) −83.3090 −3.23790
\(663\) −32.2140 −1.25109
\(664\) 22.3107 0.865823
\(665\) 13.8349 0.536495
\(666\) −31.8048 −1.23241
\(667\) 4.53878 0.175742
\(668\) 2.77719 0.107453
\(669\) −48.1958 −1.86336
\(670\) 10.7576 0.415601
\(671\) −20.2614 −0.782183
\(672\) 29.6688 1.14450
\(673\) −44.9978 −1.73454 −0.867268 0.497841i \(-0.834126\pi\)
−0.867268 + 0.497841i \(0.834126\pi\)
\(674\) −21.1175 −0.813414
\(675\) −15.0298 −0.578497
\(676\) −31.5403 −1.21309
\(677\) −31.0734 −1.19425 −0.597125 0.802149i \(-0.703690\pi\)
−0.597125 + 0.802149i \(0.703690\pi\)
\(678\) −5.03618 −0.193413
\(679\) −52.9057 −2.03033
\(680\) 12.3182 0.472382
\(681\) −49.8764 −1.91127
\(682\) −36.1425 −1.38397
\(683\) 15.9081 0.608708 0.304354 0.952559i \(-0.401559\pi\)
0.304354 + 0.952559i \(0.401559\pi\)
\(684\) −42.1635 −1.61216
\(685\) 2.27105 0.0867723
\(686\) 25.6090 0.977756
\(687\) 22.2419 0.848582
\(688\) −22.1029 −0.842665
\(689\) −23.9157 −0.911117
\(690\) 7.73250 0.294371
\(691\) −5.80557 −0.220854 −0.110427 0.993884i \(-0.535222\pi\)
−0.110427 + 0.993884i \(0.535222\pi\)
\(692\) −45.2905 −1.72169
\(693\) −37.9152 −1.44028
\(694\) 37.9261 1.43965
\(695\) 1.39936 0.0530807
\(696\) 10.5392 0.399487
\(697\) −12.2587 −0.464333
\(698\) 29.4646 1.11525
\(699\) 1.33697 0.0505687
\(700\) 70.5504 2.66656
\(701\) −13.4768 −0.509012 −0.254506 0.967071i \(-0.581913\pi\)
−0.254506 + 0.967071i \(0.581913\pi\)
\(702\) 15.2364 0.575062
\(703\) −67.2670 −2.53702
\(704\) −70.3865 −2.65279
\(705\) −0.396858 −0.0149465
\(706\) −8.97884 −0.337923
\(707\) 54.1983 2.03834
\(708\) −97.6641 −3.67044
\(709\) −14.4289 −0.541887 −0.270943 0.962595i \(-0.587336\pi\)
−0.270943 + 0.962595i \(0.587336\pi\)
\(710\) 1.04767 0.0393184
\(711\) 9.48600 0.355753
\(712\) −39.0606 −1.46386
\(713\) 8.72250 0.326660
\(714\) 151.130 5.65589
\(715\) −5.53383 −0.206954
\(716\) 10.7057 0.400091
\(717\) −26.7667 −0.999620
\(718\) −77.7731 −2.90246
\(719\) −49.9060 −1.86118 −0.930590 0.366064i \(-0.880705\pi\)
−0.930590 + 0.366064i \(0.880705\pi\)
\(720\) 1.18830 0.0442854
\(721\) 32.8959 1.22511
\(722\) −93.7756 −3.48997
\(723\) −26.9123 −1.00088
\(724\) −51.8172 −1.92577
\(725\) −6.28775 −0.233521
\(726\) 130.315 4.83646
\(727\) −12.2743 −0.455229 −0.227615 0.973751i \(-0.573093\pi\)
−0.227615 + 0.973751i \(0.573093\pi\)
\(728\) −31.7742 −1.17763
\(729\) 2.76513 0.102412
\(730\) 8.76253 0.324316
\(731\) 92.6652 3.42735
\(732\) 25.5573 0.944625
\(733\) −24.4649 −0.903633 −0.451817 0.892111i \(-0.649224\pi\)
−0.451817 + 0.892111i \(0.649224\pi\)
\(734\) −12.6779 −0.467951
\(735\) −9.09606 −0.335513
\(736\) 11.8456 0.436633
\(737\) −62.3534 −2.29682
\(738\) −6.03516 −0.222157
\(739\) −21.2934 −0.783289 −0.391645 0.920117i \(-0.628094\pi\)
−0.391645 + 0.920117i \(0.628094\pi\)
\(740\) 13.9983 0.514589
\(741\) −33.5426 −1.23222
\(742\) 112.199 4.11896
\(743\) −29.2966 −1.07479 −0.537394 0.843331i \(-0.680591\pi\)
−0.537394 + 0.843331i \(0.680591\pi\)
\(744\) 20.2539 0.742545
\(745\) 7.63808 0.279838
\(746\) 51.9707 1.90278
\(747\) −9.02318 −0.330141
\(748\) −160.712 −5.87621
\(749\) −36.2714 −1.32533
\(750\) −21.8614 −0.798266
\(751\) −13.5655 −0.495011 −0.247505 0.968887i \(-0.579611\pi\)
−0.247505 + 0.968887i \(0.579611\pi\)
\(752\) 0.738675 0.0269367
\(753\) −51.3512 −1.87134
\(754\) 6.37419 0.232134
\(755\) −5.81651 −0.211685
\(756\) −45.9467 −1.67107
\(757\) 14.8883 0.541125 0.270563 0.962702i \(-0.412790\pi\)
0.270563 + 0.962702i \(0.412790\pi\)
\(758\) −4.79064 −0.174004
\(759\) −44.8194 −1.62684
\(760\) 12.8263 0.465258
\(761\) −20.8990 −0.757589 −0.378795 0.925481i \(-0.623661\pi\)
−0.378795 + 0.925481i \(0.623661\pi\)
\(762\) −33.5337 −1.21480
\(763\) −41.2087 −1.49186
\(764\) −63.9317 −2.31297
\(765\) −4.98189 −0.180121
\(766\) 13.9857 0.505323
\(767\) −26.2421 −0.947546
\(768\) 54.3772 1.96217
\(769\) −28.2988 −1.02048 −0.510241 0.860031i \(-0.670444\pi\)
−0.510241 + 0.860031i \(0.670444\pi\)
\(770\) 25.9616 0.935592
\(771\) 4.86249 0.175118
\(772\) −14.9348 −0.537517
\(773\) −29.1467 −1.04833 −0.524166 0.851616i \(-0.675623\pi\)
−0.524166 + 0.851616i \(0.675623\pi\)
\(774\) 45.6204 1.63979
\(775\) −12.0836 −0.434056
\(776\) −49.0486 −1.76074
\(777\) 76.2999 2.73724
\(778\) 77.0976 2.76408
\(779\) −12.7643 −0.457330
\(780\) 6.98026 0.249933
\(781\) −6.07255 −0.217293
\(782\) 60.3401 2.15776
\(783\) 4.09496 0.146342
\(784\) 16.9306 0.604663
\(785\) −6.00940 −0.214485
\(786\) 45.9269 1.63816
\(787\) 17.5048 0.623978 0.311989 0.950086i \(-0.399005\pi\)
0.311989 + 0.950086i \(0.399005\pi\)
\(788\) 68.8137 2.45139
\(789\) 13.5609 0.482780
\(790\) −6.49535 −0.231094
\(791\) 4.08071 0.145093
\(792\) −35.1509 −1.24903
\(793\) 6.86718 0.243861
\(794\) 18.9264 0.671672
\(795\) −10.9504 −0.388372
\(796\) 31.4506 1.11474
\(797\) 11.2022 0.396801 0.198401 0.980121i \(-0.436425\pi\)
0.198401 + 0.980121i \(0.436425\pi\)
\(798\) 157.363 5.57059
\(799\) −3.09686 −0.109559
\(800\) −16.4101 −0.580185
\(801\) 15.7974 0.558173
\(802\) 41.6242 1.46980
\(803\) −50.7896 −1.79233
\(804\) 78.6512 2.77381
\(805\) −6.26548 −0.220829
\(806\) 12.2497 0.431479
\(807\) 31.2324 1.09943
\(808\) 50.2469 1.76768
\(809\) 28.3606 0.997106 0.498553 0.866859i \(-0.333865\pi\)
0.498553 + 0.866859i \(0.333865\pi\)
\(810\) 11.7854 0.414095
\(811\) 43.2481 1.51865 0.759323 0.650714i \(-0.225530\pi\)
0.759323 + 0.650714i \(0.225530\pi\)
\(812\) −19.2219 −0.674557
\(813\) 9.81859 0.344353
\(814\) −126.228 −4.42430
\(815\) 5.58006 0.195461
\(816\) 27.4543 0.961091
\(817\) 96.4871 3.37566
\(818\) 29.8892 1.04505
\(819\) 12.8505 0.449034
\(820\) 2.65628 0.0927612
\(821\) −41.6063 −1.45207 −0.726036 0.687657i \(-0.758639\pi\)
−0.726036 + 0.687657i \(0.758639\pi\)
\(822\) 25.8317 0.900983
\(823\) 17.8613 0.622606 0.311303 0.950311i \(-0.399235\pi\)
0.311303 + 0.950311i \(0.399235\pi\)
\(824\) 30.4976 1.06243
\(825\) 62.0900 2.16170
\(826\) 123.113 4.28365
\(827\) −36.9493 −1.28485 −0.642427 0.766347i \(-0.722072\pi\)
−0.642427 + 0.766347i \(0.722072\pi\)
\(828\) 19.0947 0.663588
\(829\) −2.88194 −0.100094 −0.0500469 0.998747i \(-0.515937\pi\)
−0.0500469 + 0.998747i \(0.515937\pi\)
\(830\) 6.17844 0.214457
\(831\) −67.3822 −2.33746
\(832\) 23.8560 0.827059
\(833\) −70.9805 −2.45933
\(834\) 15.9168 0.551153
\(835\) 0.341678 0.0118242
\(836\) −167.340 −5.78759
\(837\) 7.86958 0.272012
\(838\) −22.7961 −0.787478
\(839\) −50.3066 −1.73678 −0.868388 0.495885i \(-0.834844\pi\)
−0.868388 + 0.495885i \(0.834844\pi\)
\(840\) −14.5486 −0.501976
\(841\) −27.2869 −0.940926
\(842\) −40.6441 −1.40069
\(843\) −10.2283 −0.352280
\(844\) 34.2036 1.17734
\(845\) −3.88040 −0.133490
\(846\) −1.52463 −0.0524178
\(847\) −105.592 −3.62818
\(848\) 20.3821 0.699925
\(849\) 43.4180 1.49010
\(850\) −83.5914 −2.86716
\(851\) 30.4635 1.04428
\(852\) 7.65978 0.262420
\(853\) 1.14137 0.0390797 0.0195399 0.999809i \(-0.493780\pi\)
0.0195399 + 0.999809i \(0.493780\pi\)
\(854\) −32.2169 −1.10244
\(855\) −5.18737 −0.177404
\(856\) −33.6270 −1.14935
\(857\) 22.3373 0.763028 0.381514 0.924363i \(-0.375403\pi\)
0.381514 + 0.924363i \(0.375403\pi\)
\(858\) −62.9436 −2.14886
\(859\) −46.2928 −1.57949 −0.789745 0.613435i \(-0.789787\pi\)
−0.789745 + 0.613435i \(0.789787\pi\)
\(860\) −20.0791 −0.684691
\(861\) 14.4784 0.493422
\(862\) −25.7123 −0.875766
\(863\) 30.6372 1.04290 0.521451 0.853281i \(-0.325391\pi\)
0.521451 + 0.853281i \(0.325391\pi\)
\(864\) 10.6873 0.363588
\(865\) −5.57209 −0.189457
\(866\) −34.6261 −1.17664
\(867\) −78.9178 −2.68019
\(868\) −36.9401 −1.25383
\(869\) 37.6485 1.27714
\(870\) 2.91859 0.0989494
\(871\) 21.1334 0.716077
\(872\) −38.2044 −1.29376
\(873\) 19.8369 0.671376
\(874\) 62.8287 2.12521
\(875\) 17.7138 0.598837
\(876\) 64.0649 2.16455
\(877\) 30.4664 1.02878 0.514388 0.857558i \(-0.328019\pi\)
0.514388 + 0.857558i \(0.328019\pi\)
\(878\) −41.8934 −1.41383
\(879\) −27.6061 −0.931131
\(880\) 4.71619 0.158983
\(881\) 39.1199 1.31798 0.658991 0.752151i \(-0.270983\pi\)
0.658991 + 0.752151i \(0.270983\pi\)
\(882\) −34.9448 −1.17665
\(883\) −49.0245 −1.64981 −0.824903 0.565275i \(-0.808770\pi\)
−0.824903 + 0.565275i \(0.808770\pi\)
\(884\) 54.4700 1.83202
\(885\) −12.0156 −0.403900
\(886\) −39.6652 −1.33258
\(887\) −2.47273 −0.0830260 −0.0415130 0.999138i \(-0.513218\pi\)
−0.0415130 + 0.999138i \(0.513218\pi\)
\(888\) 70.7372 2.37378
\(889\) 27.1717 0.911309
\(890\) −10.8169 −0.362584
\(891\) −68.3107 −2.28849
\(892\) 81.4934 2.72860
\(893\) −3.22458 −0.107907
\(894\) 86.8781 2.90564
\(895\) 1.31712 0.0440265
\(896\) −84.0400 −2.80758
\(897\) 15.1906 0.507199
\(898\) −32.0224 −1.06860
\(899\) 3.29226 0.109803
\(900\) −26.4527 −0.881756
\(901\) −85.4510 −2.84679
\(902\) −23.9526 −0.797536
\(903\) −109.444 −3.64206
\(904\) 3.78320 0.125827
\(905\) −6.37506 −0.211914
\(906\) −66.1589 −2.19798
\(907\) −8.09294 −0.268722 −0.134361 0.990932i \(-0.542898\pi\)
−0.134361 + 0.990932i \(0.542898\pi\)
\(908\) 84.3351 2.79876
\(909\) −20.3215 −0.674022
\(910\) −8.79915 −0.291689
\(911\) 40.8838 1.35454 0.677271 0.735734i \(-0.263162\pi\)
0.677271 + 0.735734i \(0.263162\pi\)
\(912\) 28.5866 0.946596
\(913\) −35.8117 −1.18519
\(914\) 89.6929 2.96678
\(915\) 3.14431 0.103948
\(916\) −37.6084 −1.24262
\(917\) −37.2136 −1.22890
\(918\) 54.4398 1.79678
\(919\) 8.89358 0.293372 0.146686 0.989183i \(-0.453139\pi\)
0.146686 + 0.989183i \(0.453139\pi\)
\(920\) −5.80869 −0.191507
\(921\) −44.5945 −1.46944
\(922\) 1.78242 0.0587010
\(923\) 2.05816 0.0677452
\(924\) 189.812 6.24435
\(925\) −42.2023 −1.38760
\(926\) −66.2230 −2.17622
\(927\) −12.3342 −0.405109
\(928\) 4.47104 0.146769
\(929\) −40.2545 −1.32071 −0.660354 0.750955i \(-0.729594\pi\)
−0.660354 + 0.750955i \(0.729594\pi\)
\(930\) 5.60886 0.183922
\(931\) −73.9081 −2.42224
\(932\) −2.26065 −0.0740501
\(933\) 4.96741 0.162626
\(934\) −83.1752 −2.72158
\(935\) −19.7724 −0.646626
\(936\) 11.9137 0.389410
\(937\) −39.6863 −1.29650 −0.648248 0.761430i \(-0.724498\pi\)
−0.648248 + 0.761430i \(0.724498\pi\)
\(938\) −99.1459 −3.23723
\(939\) 46.0305 1.50215
\(940\) 0.671040 0.0218869
\(941\) 34.2656 1.11703 0.558514 0.829495i \(-0.311372\pi\)
0.558514 + 0.829495i \(0.311372\pi\)
\(942\) −68.3529 −2.22706
\(943\) 5.78064 0.188244
\(944\) 22.3647 0.727910
\(945\) −5.65282 −0.183886
\(946\) 181.061 5.88679
\(947\) −36.4741 −1.18525 −0.592625 0.805478i \(-0.701908\pi\)
−0.592625 + 0.805478i \(0.701908\pi\)
\(948\) −47.4890 −1.54237
\(949\) 17.2141 0.558793
\(950\) −87.0391 −2.82392
\(951\) 71.3987 2.31526
\(952\) −113.529 −3.67951
\(953\) −12.0291 −0.389660 −0.194830 0.980837i \(-0.562415\pi\)
−0.194830 + 0.980837i \(0.562415\pi\)
\(954\) −42.0688 −1.36203
\(955\) −7.86551 −0.254522
\(956\) 45.2593 1.46379
\(957\) −16.9168 −0.546843
\(958\) 11.1465 0.360126
\(959\) −20.9309 −0.675893
\(960\) 10.9231 0.352541
\(961\) −24.6730 −0.795904
\(962\) 42.7825 1.37936
\(963\) 13.5999 0.438250
\(964\) 45.5055 1.46563
\(965\) −1.83743 −0.0591490
\(966\) −71.2657 −2.29293
\(967\) −13.0230 −0.418790 −0.209395 0.977831i \(-0.567150\pi\)
−0.209395 + 0.977831i \(0.567150\pi\)
\(968\) −97.8935 −3.14642
\(969\) −119.848 −3.85006
\(970\) −13.5829 −0.436120
\(971\) 8.32769 0.267248 0.133624 0.991032i \(-0.457338\pi\)
0.133624 + 0.991032i \(0.457338\pi\)
\(972\) 52.3872 1.68032
\(973\) −12.8970 −0.413460
\(974\) −95.7100 −3.06674
\(975\) −21.0441 −0.673950
\(976\) −5.85254 −0.187335
\(977\) 21.2680 0.680424 0.340212 0.940349i \(-0.389501\pi\)
0.340212 + 0.940349i \(0.389501\pi\)
\(978\) 63.4695 2.02953
\(979\) 62.6974 2.00382
\(980\) 15.3804 0.491308
\(981\) 15.4511 0.493316
\(982\) 44.5295 1.42099
\(983\) −36.4184 −1.16157 −0.580783 0.814058i \(-0.697253\pi\)
−0.580783 + 0.814058i \(0.697253\pi\)
\(984\) 13.4228 0.427904
\(985\) 8.46614 0.269754
\(986\) 22.7750 0.725304
\(987\) 3.65759 0.116423
\(988\) 56.7165 1.80439
\(989\) −43.6965 −1.38947
\(990\) −9.73424 −0.309375
\(991\) −9.99182 −0.317401 −0.158700 0.987327i \(-0.550730\pi\)
−0.158700 + 0.987327i \(0.550730\pi\)
\(992\) 8.59232 0.272806
\(993\) −74.9366 −2.37804
\(994\) −9.65574 −0.306261
\(995\) 3.86937 0.122667
\(996\) 45.1721 1.43133
\(997\) −7.06723 −0.223821 −0.111911 0.993718i \(-0.535697\pi\)
−0.111911 + 0.993718i \(0.535697\pi\)
\(998\) 92.3505 2.92330
\(999\) 27.4846 0.869576
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 \(a_p\))