Properties

Label 8023.2.a.c.1.15
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 1.15
Character \(\chi\) = 8023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.49733 q^{2}\) \(-3.32636 q^{3}\) \(+4.23663 q^{4}\) \(-4.15753 q^{5}\) \(+8.30700 q^{6}\) \(-2.74619 q^{7}\) \(-5.58560 q^{8}\) \(+8.06465 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.49733 q^{2}\) \(-3.32636 q^{3}\) \(+4.23663 q^{4}\) \(-4.15753 q^{5}\) \(+8.30700 q^{6}\) \(-2.74619 q^{7}\) \(-5.58560 q^{8}\) \(+8.06465 q^{9}\) \(+10.3827 q^{10}\) \(+5.53369 q^{11}\) \(-14.0926 q^{12}\) \(+4.58517 q^{13}\) \(+6.85813 q^{14}\) \(+13.8294 q^{15}\) \(+5.47580 q^{16}\) \(+0.508478 q^{17}\) \(-20.1401 q^{18}\) \(-0.582777 q^{19}\) \(-17.6139 q^{20}\) \(+9.13481 q^{21}\) \(-13.8194 q^{22}\) \(-1.53472 q^{23}\) \(+18.5797 q^{24}\) \(+12.2851 q^{25}\) \(-11.4507 q^{26}\) \(-16.8468 q^{27}\) \(-11.6346 q^{28}\) \(+2.85183 q^{29}\) \(-34.5366 q^{30}\) \(+6.73575 q^{31}\) \(-2.50365 q^{32}\) \(-18.4070 q^{33}\) \(-1.26984 q^{34}\) \(+11.4174 q^{35}\) \(+34.1670 q^{36}\) \(+3.94226 q^{37}\) \(+1.45538 q^{38}\) \(-15.2519 q^{39}\) \(+23.2223 q^{40}\) \(-0.699012 q^{41}\) \(-22.8126 q^{42}\) \(+9.44515 q^{43}\) \(+23.4442 q^{44}\) \(-33.5291 q^{45}\) \(+3.83269 q^{46}\) \(+8.69809 q^{47}\) \(-18.2145 q^{48}\) \(+0.541563 q^{49}\) \(-30.6798 q^{50}\) \(-1.69138 q^{51}\) \(+19.4257 q^{52}\) \(-12.8066 q^{53}\) \(+42.0721 q^{54}\) \(-23.0065 q^{55}\) \(+15.3391 q^{56}\) \(+1.93852 q^{57}\) \(-7.12195 q^{58}\) \(-7.79089 q^{59}\) \(+58.5903 q^{60}\) \(+7.59599 q^{61}\) \(-16.8214 q^{62}\) \(-22.1471 q^{63}\) \(-4.69917 q^{64}\) \(-19.0630 q^{65}\) \(+45.9683 q^{66}\) \(-12.3897 q^{67}\) \(+2.15424 q^{68}\) \(+5.10502 q^{69}\) \(-28.5129 q^{70}\) \(-1.00000 q^{71}\) \(-45.0460 q^{72}\) \(-12.6786 q^{73}\) \(-9.84511 q^{74}\) \(-40.8646 q^{75}\) \(-2.46901 q^{76}\) \(-15.1966 q^{77}\) \(+38.0890 q^{78}\) \(-2.24538 q^{79}\) \(-22.7658 q^{80}\) \(+31.8447 q^{81}\) \(+1.74566 q^{82}\) \(+14.6900 q^{83}\) \(+38.7009 q^{84}\) \(-2.11401 q^{85}\) \(-23.5876 q^{86}\) \(-9.48621 q^{87}\) \(-30.9090 q^{88}\) \(-12.6291 q^{89}\) \(+83.7330 q^{90}\) \(-12.5917 q^{91}\) \(-6.50204 q^{92}\) \(-22.4055 q^{93}\) \(-21.7220 q^{94}\) \(+2.42291 q^{95}\) \(+8.32804 q^{96}\) \(+4.50089 q^{97}\) \(-1.35246 q^{98}\) \(+44.6273 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 46q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 27q^{14} \) \(\mathstrut -\mathstrut 41q^{15} \) \(\mathstrut +\mathstrut 150q^{16} \) \(\mathstrut -\mathstrut 137q^{17} \) \(\mathstrut -\mathstrut 67q^{18} \) \(\mathstrut -\mathstrut 42q^{19} \) \(\mathstrut -\mathstrut 66q^{20} \) \(\mathstrut -\mathstrut 46q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 48q^{24} \) \(\mathstrut +\mathstrut 129q^{25} \) \(\mathstrut -\mathstrut 67q^{26} \) \(\mathstrut -\mathstrut 89q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 79q^{29} \) \(\mathstrut -\mathstrut 11q^{30} \) \(\mathstrut +\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 147q^{32} \) \(\mathstrut -\mathstrut 112q^{33} \) \(\mathstrut -\mathstrut 28q^{34} \) \(\mathstrut -\mathstrut 53q^{35} \) \(\mathstrut +\mathstrut 141q^{36} \) \(\mathstrut -\mathstrut 60q^{37} \) \(\mathstrut -\mathstrut 53q^{38} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 48q^{40} \) \(\mathstrut -\mathstrut 128q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 63q^{43} \) \(\mathstrut -\mathstrut 88q^{45} \) \(\mathstrut -\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 92q^{47} \) \(\mathstrut -\mathstrut 131q^{48} \) \(\mathstrut +\mathstrut 122q^{49} \) \(\mathstrut -\mathstrut 116q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 89q^{52} \) \(\mathstrut -\mathstrut 94q^{53} \) \(\mathstrut -\mathstrut 71q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 104q^{56} \) \(\mathstrut -\mathstrut 93q^{57} \) \(\mathstrut -\mathstrut 65q^{58} \) \(\mathstrut -\mathstrut 54q^{59} \) \(\mathstrut -\mathstrut 12q^{60} \) \(\mathstrut +\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 97q^{62} \) \(\mathstrut -\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 163q^{64} \) \(\mathstrut -\mathstrut 163q^{65} \) \(\mathstrut -\mathstrut 65q^{66} \) \(\mathstrut -\mathstrut 35q^{67} \) \(\mathstrut -\mathstrut 217q^{68} \) \(\mathstrut -\mathstrut 46q^{69} \) \(\mathstrut -\mathstrut 79q^{70} \) \(\mathstrut -\mathstrut 158q^{71} \) \(\mathstrut -\mathstrut 99q^{72} \) \(\mathstrut -\mathstrut 165q^{73} \) \(\mathstrut -\mathstrut 94q^{75} \) \(\mathstrut -\mathstrut 93q^{76} \) \(\mathstrut -\mathstrut 140q^{77} \) \(\mathstrut +\mathstrut 25q^{78} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut 134q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 158q^{83} \) \(\mathstrut -\mathstrut 160q^{84} \) \(\mathstrut +\mathstrut 23q^{85} \) \(\mathstrut -\mathstrut 122q^{86} \) \(\mathstrut -\mathstrut 71q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 251q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut -\mathstrut 57q^{91} \) \(\mathstrut -\mathstrut 58q^{92} \) \(\mathstrut -\mathstrut 52q^{93} \) \(\mathstrut -\mathstrut 64q^{94} \) \(\mathstrut -\mathstrut 84q^{95} \) \(\mathstrut -\mathstrut 98q^{96} \) \(\mathstrut -\mathstrut 48q^{97} \) \(\mathstrut -\mathstrut 84q^{98} \) \(\mathstrut +\mathstrut 85q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.49733 −1.76588 −0.882938 0.469490i \(-0.844438\pi\)
−0.882938 + 0.469490i \(0.844438\pi\)
\(3\) −3.32636 −1.92047 −0.960237 0.279187i \(-0.909935\pi\)
−0.960237 + 0.279187i \(0.909935\pi\)
\(4\) 4.23663 2.11832
\(5\) −4.15753 −1.85931 −0.929653 0.368437i \(-0.879893\pi\)
−0.929653 + 0.368437i \(0.879893\pi\)
\(6\) 8.30700 3.39132
\(7\) −2.74619 −1.03796 −0.518981 0.854786i \(-0.673689\pi\)
−0.518981 + 0.854786i \(0.673689\pi\)
\(8\) −5.58560 −1.97481
\(9\) 8.06465 2.68822
\(10\) 10.3827 3.28330
\(11\) 5.53369 1.66847 0.834235 0.551409i \(-0.185910\pi\)
0.834235 + 0.551409i \(0.185910\pi\)
\(12\) −14.0926 −4.06817
\(13\) 4.58517 1.27170 0.635848 0.771814i \(-0.280650\pi\)
0.635848 + 0.771814i \(0.280650\pi\)
\(14\) 6.85813 1.83291
\(15\) 13.8294 3.57075
\(16\) 5.47580 1.36895
\(17\) 0.508478 0.123324 0.0616620 0.998097i \(-0.480360\pi\)
0.0616620 + 0.998097i \(0.480360\pi\)
\(18\) −20.1401 −4.74706
\(19\) −0.582777 −0.133698 −0.0668491 0.997763i \(-0.521295\pi\)
−0.0668491 + 0.997763i \(0.521295\pi\)
\(20\) −17.6139 −3.93860
\(21\) 9.13481 1.99338
\(22\) −13.8194 −2.94631
\(23\) −1.53472 −0.320011 −0.160006 0.987116i \(-0.551151\pi\)
−0.160006 + 0.987116i \(0.551151\pi\)
\(24\) 18.5797 3.79257
\(25\) 12.2851 2.45702
\(26\) −11.4507 −2.24566
\(27\) −16.8468 −3.24218
\(28\) −11.6346 −2.19873
\(29\) 2.85183 0.529572 0.264786 0.964307i \(-0.414699\pi\)
0.264786 + 0.964307i \(0.414699\pi\)
\(30\) −34.5366 −6.30549
\(31\) 6.73575 1.20978 0.604889 0.796310i \(-0.293218\pi\)
0.604889 + 0.796310i \(0.293218\pi\)
\(32\) −2.50365 −0.442588
\(33\) −18.4070 −3.20425
\(34\) −1.26984 −0.217775
\(35\) 11.4174 1.92989
\(36\) 34.1670 5.69450
\(37\) 3.94226 0.648104 0.324052 0.946039i \(-0.394955\pi\)
0.324052 + 0.946039i \(0.394955\pi\)
\(38\) 1.45538 0.236094
\(39\) −15.2519 −2.44226
\(40\) 23.2223 3.67177
\(41\) −0.699012 −0.109167 −0.0545837 0.998509i \(-0.517383\pi\)
−0.0545837 + 0.998509i \(0.517383\pi\)
\(42\) −22.8126 −3.52006
\(43\) 9.44515 1.44037 0.720186 0.693781i \(-0.244057\pi\)
0.720186 + 0.693781i \(0.244057\pi\)
\(44\) 23.4442 3.53435
\(45\) −33.5291 −4.99822
\(46\) 3.83269 0.565100
\(47\) 8.69809 1.26875 0.634373 0.773027i \(-0.281258\pi\)
0.634373 + 0.773027i \(0.281258\pi\)
\(48\) −18.2145 −2.62903
\(49\) 0.541563 0.0773662
\(50\) −30.6798 −4.33878
\(51\) −1.69138 −0.236841
\(52\) 19.4257 2.69386
\(53\) −12.8066 −1.75912 −0.879562 0.475784i \(-0.842165\pi\)
−0.879562 + 0.475784i \(0.842165\pi\)
\(54\) 42.0721 5.72528
\(55\) −23.0065 −3.10220
\(56\) 15.3391 2.04978
\(57\) 1.93852 0.256764
\(58\) −7.12195 −0.935158
\(59\) −7.79089 −1.01429 −0.507144 0.861861i \(-0.669299\pi\)
−0.507144 + 0.861861i \(0.669299\pi\)
\(60\) 58.5903 7.56397
\(61\) 7.59599 0.972566 0.486283 0.873801i \(-0.338352\pi\)
0.486283 + 0.873801i \(0.338352\pi\)
\(62\) −16.8214 −2.13632
\(63\) −22.1471 −2.79027
\(64\) −4.69917 −0.587396
\(65\) −19.0630 −2.36447
\(66\) 45.9683 5.65831
\(67\) −12.3897 −1.51364 −0.756822 0.653621i \(-0.773249\pi\)
−0.756822 + 0.653621i \(0.773249\pi\)
\(68\) 2.15424 0.261239
\(69\) 5.10502 0.614573
\(70\) −28.5129 −3.40794
\(71\) −1.00000 −0.118678
\(72\) −45.0460 −5.30872
\(73\) −12.6786 −1.48392 −0.741960 0.670444i \(-0.766103\pi\)
−0.741960 + 0.670444i \(0.766103\pi\)
\(74\) −9.84511 −1.14447
\(75\) −40.8646 −4.71863
\(76\) −2.46901 −0.283215
\(77\) −15.1966 −1.73181
\(78\) 38.0890 4.31273
\(79\) −2.24538 −0.252625 −0.126312 0.991991i \(-0.540314\pi\)
−0.126312 + 0.991991i \(0.540314\pi\)
\(80\) −22.7658 −2.54530
\(81\) 31.8447 3.53830
\(82\) 1.74566 0.192776
\(83\) 14.6900 1.61244 0.806218 0.591619i \(-0.201511\pi\)
0.806218 + 0.591619i \(0.201511\pi\)
\(84\) 38.7009 4.22261
\(85\) −2.11401 −0.229297
\(86\) −23.5876 −2.54352
\(87\) −9.48621 −1.01703
\(88\) −30.9090 −3.29491
\(89\) −12.6291 −1.33869 −0.669343 0.742953i \(-0.733424\pi\)
−0.669343 + 0.742953i \(0.733424\pi\)
\(90\) 83.7330 8.82623
\(91\) −12.5917 −1.31997
\(92\) −6.50204 −0.677885
\(93\) −22.4055 −2.32334
\(94\) −21.7220 −2.24045
\(95\) 2.42291 0.248586
\(96\) 8.32804 0.849978
\(97\) 4.50089 0.456996 0.228498 0.973544i \(-0.426619\pi\)
0.228498 + 0.973544i \(0.426619\pi\)
\(98\) −1.35246 −0.136619
\(99\) 44.6273 4.48521
\(100\) 52.0474 5.20474
\(101\) −15.1903 −1.51149 −0.755747 0.654864i \(-0.772726\pi\)
−0.755747 + 0.654864i \(0.772726\pi\)
\(102\) 4.22393 0.418231
\(103\) −13.9046 −1.37006 −0.685029 0.728516i \(-0.740210\pi\)
−0.685029 + 0.728516i \(0.740210\pi\)
\(104\) −25.6109 −2.51136
\(105\) −37.9783 −3.70630
\(106\) 31.9823 3.10640
\(107\) −3.40732 −0.329398 −0.164699 0.986344i \(-0.552665\pi\)
−0.164699 + 0.986344i \(0.552665\pi\)
\(108\) −71.3739 −6.86796
\(109\) 8.66056 0.829531 0.414765 0.909928i \(-0.363864\pi\)
0.414765 + 0.909928i \(0.363864\pi\)
\(110\) 57.4547 5.47809
\(111\) −13.1134 −1.24467
\(112\) −15.0376 −1.42092
\(113\) −1.00000 −0.0940721
\(114\) −4.84112 −0.453413
\(115\) 6.38064 0.594998
\(116\) 12.0822 1.12180
\(117\) 36.9778 3.41860
\(118\) 19.4564 1.79111
\(119\) −1.39638 −0.128006
\(120\) −77.2458 −7.05154
\(121\) 19.6217 1.78379
\(122\) −18.9696 −1.71743
\(123\) 2.32517 0.209653
\(124\) 28.5369 2.56269
\(125\) −30.2880 −2.70904
\(126\) 55.3085 4.92727
\(127\) 5.93990 0.527081 0.263541 0.964648i \(-0.415110\pi\)
0.263541 + 0.964648i \(0.415110\pi\)
\(128\) 16.7427 1.47986
\(129\) −31.4179 −2.76620
\(130\) 47.6065 4.17536
\(131\) 4.82393 0.421468 0.210734 0.977543i \(-0.432415\pi\)
0.210734 + 0.977543i \(0.432415\pi\)
\(132\) −77.9839 −6.78762
\(133\) 1.60042 0.138774
\(134\) 30.9411 2.67291
\(135\) 70.0413 6.02820
\(136\) −2.84016 −0.243541
\(137\) 7.70416 0.658211 0.329105 0.944293i \(-0.393253\pi\)
0.329105 + 0.944293i \(0.393253\pi\)
\(138\) −12.7489 −1.08526
\(139\) 10.0930 0.856079 0.428040 0.903760i \(-0.359204\pi\)
0.428040 + 0.903760i \(0.359204\pi\)
\(140\) 48.3713 4.08812
\(141\) −28.9330 −2.43659
\(142\) 2.49733 0.209571
\(143\) 25.3729 2.12179
\(144\) 44.1605 3.68004
\(145\) −11.8566 −0.984635
\(146\) 31.6626 2.62042
\(147\) −1.80143 −0.148580
\(148\) 16.7019 1.37289
\(149\) −1.51550 −0.124155 −0.0620773 0.998071i \(-0.519773\pi\)
−0.0620773 + 0.998071i \(0.519773\pi\)
\(150\) 102.052 8.33252
\(151\) 5.78386 0.470684 0.235342 0.971913i \(-0.424379\pi\)
0.235342 + 0.971913i \(0.424379\pi\)
\(152\) 3.25516 0.264028
\(153\) 4.10070 0.331522
\(154\) 37.9508 3.05816
\(155\) −28.0041 −2.24935
\(156\) −64.6167 −5.17348
\(157\) −8.46600 −0.675661 −0.337830 0.941207i \(-0.609693\pi\)
−0.337830 + 0.941207i \(0.609693\pi\)
\(158\) 5.60744 0.446104
\(159\) 42.5994 3.37835
\(160\) 10.4090 0.822905
\(161\) 4.21463 0.332159
\(162\) −79.5265 −6.24819
\(163\) −3.59691 −0.281732 −0.140866 0.990029i \(-0.544989\pi\)
−0.140866 + 0.990029i \(0.544989\pi\)
\(164\) −2.96146 −0.231251
\(165\) 76.5278 5.95768
\(166\) −36.6857 −2.84736
\(167\) −20.3539 −1.57503 −0.787515 0.616296i \(-0.788633\pi\)
−0.787515 + 0.616296i \(0.788633\pi\)
\(168\) −51.0234 −3.93654
\(169\) 8.02375 0.617211
\(170\) 5.27938 0.404910
\(171\) −4.69989 −0.359410
\(172\) 40.0156 3.05116
\(173\) −9.73791 −0.740359 −0.370180 0.928960i \(-0.620704\pi\)
−0.370180 + 0.928960i \(0.620704\pi\)
\(174\) 23.6901 1.79595
\(175\) −33.7372 −2.55029
\(176\) 30.3014 2.28405
\(177\) 25.9153 1.94791
\(178\) 31.5391 2.36395
\(179\) −20.2638 −1.51459 −0.757294 0.653074i \(-0.773479\pi\)
−0.757294 + 0.653074i \(0.773479\pi\)
\(180\) −142.050 −10.5878
\(181\) 23.3241 1.73366 0.866832 0.498601i \(-0.166153\pi\)
0.866832 + 0.498601i \(0.166153\pi\)
\(182\) 31.4457 2.33091
\(183\) −25.2670 −1.86779
\(184\) 8.57233 0.631961
\(185\) −16.3901 −1.20502
\(186\) 55.9539 4.10274
\(187\) 2.81376 0.205763
\(188\) 36.8506 2.68761
\(189\) 46.2647 3.36526
\(190\) −6.05080 −0.438971
\(191\) 4.47219 0.323596 0.161798 0.986824i \(-0.448271\pi\)
0.161798 + 0.986824i \(0.448271\pi\)
\(192\) 15.6311 1.12808
\(193\) 3.66691 0.263950 0.131975 0.991253i \(-0.457868\pi\)
0.131975 + 0.991253i \(0.457868\pi\)
\(194\) −11.2402 −0.806998
\(195\) 63.4103 4.54090
\(196\) 2.29440 0.163886
\(197\) 8.93248 0.636413 0.318206 0.948021i \(-0.396920\pi\)
0.318206 + 0.948021i \(0.396920\pi\)
\(198\) −111.449 −7.92033
\(199\) 1.47155 0.104315 0.0521576 0.998639i \(-0.483390\pi\)
0.0521576 + 0.998639i \(0.483390\pi\)
\(200\) −68.6196 −4.85214
\(201\) 41.2126 2.90691
\(202\) 37.9352 2.66911
\(203\) −7.83167 −0.549675
\(204\) −7.16576 −0.501703
\(205\) 2.90617 0.202976
\(206\) 34.7242 2.41935
\(207\) −12.3770 −0.860259
\(208\) 25.1075 1.74089
\(209\) −3.22491 −0.223071
\(210\) 94.8441 6.54487
\(211\) 26.7853 1.84398 0.921989 0.387215i \(-0.126563\pi\)
0.921989 + 0.387215i \(0.126563\pi\)
\(212\) −54.2570 −3.72638
\(213\) 3.32636 0.227918
\(214\) 8.50918 0.581676
\(215\) −39.2685 −2.67809
\(216\) 94.0998 6.40268
\(217\) −18.4977 −1.25570
\(218\) −21.6282 −1.46485
\(219\) 42.1736 2.84983
\(220\) −97.4701 −6.57143
\(221\) 2.33146 0.156831
\(222\) 32.7484 2.19793
\(223\) 6.06546 0.406173 0.203087 0.979161i \(-0.434903\pi\)
0.203087 + 0.979161i \(0.434903\pi\)
\(224\) 6.87551 0.459389
\(225\) 99.0749 6.60499
\(226\) 2.49733 0.166120
\(227\) −3.64474 −0.241910 −0.120955 0.992658i \(-0.538596\pi\)
−0.120955 + 0.992658i \(0.538596\pi\)
\(228\) 8.21282 0.543907
\(229\) −25.4298 −1.68045 −0.840226 0.542237i \(-0.817578\pi\)
−0.840226 + 0.542237i \(0.817578\pi\)
\(230\) −15.9345 −1.05069
\(231\) 50.5492 3.32589
\(232\) −15.9292 −1.04580
\(233\) 0.660938 0.0432995 0.0216497 0.999766i \(-0.493108\pi\)
0.0216497 + 0.999766i \(0.493108\pi\)
\(234\) −92.3455 −6.03682
\(235\) −36.1626 −2.35899
\(236\) −33.0072 −2.14858
\(237\) 7.46894 0.485160
\(238\) 3.48721 0.226042
\(239\) −17.9222 −1.15929 −0.579645 0.814869i \(-0.696809\pi\)
−0.579645 + 0.814869i \(0.696809\pi\)
\(240\) 75.7273 4.88818
\(241\) 0.123628 0.00796360 0.00398180 0.999992i \(-0.498733\pi\)
0.00398180 + 0.999992i \(0.498733\pi\)
\(242\) −49.0018 −3.14996
\(243\) −55.3862 −3.55303
\(244\) 32.1814 2.06020
\(245\) −2.25157 −0.143847
\(246\) −5.80669 −0.370221
\(247\) −2.67213 −0.170023
\(248\) −37.6233 −2.38908
\(249\) −48.8641 −3.09664
\(250\) 75.6389 4.78382
\(251\) 19.2444 1.21470 0.607349 0.794435i \(-0.292233\pi\)
0.607349 + 0.794435i \(0.292233\pi\)
\(252\) −93.8291 −5.91068
\(253\) −8.49266 −0.533929
\(254\) −14.8339 −0.930760
\(255\) 7.03197 0.440359
\(256\) −32.4135 −2.02585
\(257\) −18.9575 −1.18254 −0.591269 0.806474i \(-0.701373\pi\)
−0.591269 + 0.806474i \(0.701373\pi\)
\(258\) 78.4608 4.88476
\(259\) −10.8262 −0.672708
\(260\) −80.7629 −5.00870
\(261\) 22.9990 1.42360
\(262\) −12.0469 −0.744261
\(263\) 27.1592 1.67471 0.837353 0.546663i \(-0.184102\pi\)
0.837353 + 0.546663i \(0.184102\pi\)
\(264\) 102.814 6.32779
\(265\) 53.2439 3.27075
\(266\) −3.99676 −0.245057
\(267\) 42.0090 2.57091
\(268\) −52.4907 −3.20638
\(269\) −2.31502 −0.141149 −0.0705747 0.997506i \(-0.522483\pi\)
−0.0705747 + 0.997506i \(0.522483\pi\)
\(270\) −174.916 −10.6450
\(271\) 16.7506 1.01752 0.508762 0.860907i \(-0.330103\pi\)
0.508762 + 0.860907i \(0.330103\pi\)
\(272\) 2.78433 0.168825
\(273\) 41.8846 2.53497
\(274\) −19.2398 −1.16232
\(275\) 67.9818 4.09946
\(276\) 21.6281 1.30186
\(277\) −15.3416 −0.921788 −0.460894 0.887455i \(-0.652471\pi\)
−0.460894 + 0.887455i \(0.652471\pi\)
\(278\) −25.2056 −1.51173
\(279\) 54.3215 3.25214
\(280\) −63.7730 −3.81116
\(281\) −5.67678 −0.338648 −0.169324 0.985560i \(-0.554158\pi\)
−0.169324 + 0.985560i \(0.554158\pi\)
\(282\) 72.2550 4.30272
\(283\) −12.6112 −0.749658 −0.374829 0.927094i \(-0.622299\pi\)
−0.374829 + 0.927094i \(0.622299\pi\)
\(284\) −4.23663 −0.251398
\(285\) −8.05948 −0.477402
\(286\) −63.3644 −3.74681
\(287\) 1.91962 0.113312
\(288\) −20.1911 −1.18977
\(289\) −16.7415 −0.984791
\(290\) 29.6097 1.73874
\(291\) −14.9716 −0.877649
\(292\) −53.7147 −3.14341
\(293\) −21.8904 −1.27885 −0.639426 0.768853i \(-0.720828\pi\)
−0.639426 + 0.768853i \(0.720828\pi\)
\(294\) 4.49876 0.262373
\(295\) 32.3909 1.88587
\(296\) −22.0199 −1.27988
\(297\) −93.2252 −5.40948
\(298\) 3.78470 0.219242
\(299\) −7.03694 −0.406957
\(300\) −173.128 −9.99556
\(301\) −25.9382 −1.49505
\(302\) −14.4442 −0.831169
\(303\) 50.5284 2.90278
\(304\) −3.19117 −0.183026
\(305\) −31.5806 −1.80830
\(306\) −10.2408 −0.585427
\(307\) 14.9123 0.851089 0.425544 0.904938i \(-0.360083\pi\)
0.425544 + 0.904938i \(0.360083\pi\)
\(308\) −64.3823 −3.66852
\(309\) 46.2516 2.63116
\(310\) 69.9354 3.97206
\(311\) −5.59134 −0.317056 −0.158528 0.987355i \(-0.550675\pi\)
−0.158528 + 0.987355i \(0.550675\pi\)
\(312\) 85.1911 4.82300
\(313\) −8.50978 −0.481001 −0.240501 0.970649i \(-0.577312\pi\)
−0.240501 + 0.970649i \(0.577312\pi\)
\(314\) 21.1424 1.19313
\(315\) 92.0772 5.18796
\(316\) −9.51285 −0.535140
\(317\) −7.64247 −0.429244 −0.214622 0.976697i \(-0.568852\pi\)
−0.214622 + 0.976697i \(0.568852\pi\)
\(318\) −106.385 −5.96575
\(319\) 15.7811 0.883574
\(320\) 19.5369 1.09215
\(321\) 11.3340 0.632600
\(322\) −10.5253 −0.586552
\(323\) −0.296329 −0.0164882
\(324\) 134.914 7.49524
\(325\) 56.3291 3.12458
\(326\) 8.98267 0.497504
\(327\) −28.8081 −1.59309
\(328\) 3.90441 0.215585
\(329\) −23.8866 −1.31691
\(330\) −191.115 −10.5205
\(331\) −15.7379 −0.865035 −0.432517 0.901626i \(-0.642375\pi\)
−0.432517 + 0.901626i \(0.642375\pi\)
\(332\) 62.2361 3.41565
\(333\) 31.7930 1.74224
\(334\) 50.8302 2.78131
\(335\) 51.5106 2.81433
\(336\) 50.0204 2.72884
\(337\) 29.4154 1.60236 0.801179 0.598425i \(-0.204207\pi\)
0.801179 + 0.598425i \(0.204207\pi\)
\(338\) −20.0379 −1.08992
\(339\) 3.32636 0.180663
\(340\) −8.95631 −0.485724
\(341\) 37.2736 2.01848
\(342\) 11.7372 0.634673
\(343\) 17.7361 0.957659
\(344\) −52.7569 −2.84446
\(345\) −21.2243 −1.14268
\(346\) 24.3187 1.30738
\(347\) −5.33506 −0.286401 −0.143200 0.989694i \(-0.545739\pi\)
−0.143200 + 0.989694i \(0.545739\pi\)
\(348\) −40.1896 −2.15439
\(349\) 12.5401 0.671256 0.335628 0.941995i \(-0.391052\pi\)
0.335628 + 0.941995i \(0.391052\pi\)
\(350\) 84.2527 4.50350
\(351\) −77.2456 −4.12306
\(352\) −13.8544 −0.738444
\(353\) −35.1401 −1.87032 −0.935158 0.354230i \(-0.884743\pi\)
−0.935158 + 0.354230i \(0.884743\pi\)
\(354\) −64.7189 −3.43977
\(355\) 4.15753 0.220659
\(356\) −53.5051 −2.83576
\(357\) 4.64485 0.245832
\(358\) 50.6053 2.67457
\(359\) 21.6689 1.14364 0.571820 0.820379i \(-0.306238\pi\)
0.571820 + 0.820379i \(0.306238\pi\)
\(360\) 187.280 9.87053
\(361\) −18.6604 −0.982125
\(362\) −58.2478 −3.06143
\(363\) −65.2689 −3.42573
\(364\) −53.3466 −2.79612
\(365\) 52.7118 2.75906
\(366\) 63.0998 3.29828
\(367\) −4.16145 −0.217226 −0.108613 0.994084i \(-0.534641\pi\)
−0.108613 + 0.994084i \(0.534641\pi\)
\(368\) −8.40382 −0.438079
\(369\) −5.63729 −0.293466
\(370\) 40.9314 2.12792
\(371\) 35.1694 1.82591
\(372\) −94.9240 −4.92158
\(373\) 5.01960 0.259905 0.129953 0.991520i \(-0.458517\pi\)
0.129953 + 0.991520i \(0.458517\pi\)
\(374\) −7.02687 −0.363351
\(375\) 100.749 5.20263
\(376\) −48.5841 −2.50553
\(377\) 13.0761 0.673454
\(378\) −115.538 −5.94263
\(379\) −3.55125 −0.182416 −0.0912078 0.995832i \(-0.529073\pi\)
−0.0912078 + 0.995832i \(0.529073\pi\)
\(380\) 10.2650 0.526583
\(381\) −19.7582 −1.01225
\(382\) −11.1685 −0.571430
\(383\) −34.2682 −1.75102 −0.875511 0.483198i \(-0.839475\pi\)
−0.875511 + 0.483198i \(0.839475\pi\)
\(384\) −55.6921 −2.84202
\(385\) 63.1802 3.21996
\(386\) −9.15746 −0.466103
\(387\) 76.1718 3.87203
\(388\) 19.0686 0.968063
\(389\) 18.8182 0.954119 0.477060 0.878871i \(-0.341703\pi\)
0.477060 + 0.878871i \(0.341703\pi\)
\(390\) −158.356 −8.01867
\(391\) −0.780371 −0.0394651
\(392\) −3.02496 −0.152783
\(393\) −16.0461 −0.809419
\(394\) −22.3073 −1.12383
\(395\) 9.33524 0.469707
\(396\) 189.070 9.50110
\(397\) 1.56573 0.0785820 0.0392910 0.999228i \(-0.487490\pi\)
0.0392910 + 0.999228i \(0.487490\pi\)
\(398\) −3.67493 −0.184208
\(399\) −5.32356 −0.266511
\(400\) 67.2707 3.36353
\(401\) −12.5104 −0.624742 −0.312371 0.949960i \(-0.601123\pi\)
−0.312371 + 0.949960i \(0.601123\pi\)
\(402\) −102.921 −5.13325
\(403\) 30.8846 1.53847
\(404\) −64.3558 −3.20182
\(405\) −132.395 −6.57877
\(406\) 19.5582 0.970658
\(407\) 21.8153 1.08134
\(408\) 9.44738 0.467715
\(409\) −20.2039 −0.999016 −0.499508 0.866309i \(-0.666486\pi\)
−0.499508 + 0.866309i \(0.666486\pi\)
\(410\) −7.25765 −0.358430
\(411\) −25.6268 −1.26408
\(412\) −58.9086 −2.90222
\(413\) 21.3953 1.05279
\(414\) 30.9093 1.51911
\(415\) −61.0741 −2.99801
\(416\) −11.4797 −0.562837
\(417\) −33.5730 −1.64408
\(418\) 8.05364 0.393916
\(419\) 0.780137 0.0381122 0.0190561 0.999818i \(-0.493934\pi\)
0.0190561 + 0.999818i \(0.493934\pi\)
\(420\) −160.900 −7.85112
\(421\) −1.99035 −0.0970037 −0.0485018 0.998823i \(-0.515445\pi\)
−0.0485018 + 0.998823i \(0.515445\pi\)
\(422\) −66.8917 −3.25624
\(423\) 70.1471 3.41067
\(424\) 71.5327 3.47394
\(425\) 6.24669 0.303009
\(426\) −8.30700 −0.402475
\(427\) −20.8600 −1.00949
\(428\) −14.4356 −0.697769
\(429\) −84.3993 −4.07484
\(430\) 98.0663 4.72917
\(431\) 8.69931 0.419031 0.209516 0.977805i \(-0.432811\pi\)
0.209516 + 0.977805i \(0.432811\pi\)
\(432\) −92.2500 −4.43838
\(433\) −30.5003 −1.46575 −0.732875 0.680363i \(-0.761822\pi\)
−0.732875 + 0.680363i \(0.761822\pi\)
\(434\) 46.1947 2.21742
\(435\) 39.4392 1.89097
\(436\) 36.6916 1.75721
\(437\) 0.894399 0.0427849
\(438\) −105.321 −5.03244
\(439\) −11.0461 −0.527203 −0.263601 0.964632i \(-0.584910\pi\)
−0.263601 + 0.964632i \(0.584910\pi\)
\(440\) 128.505 6.12624
\(441\) 4.36752 0.207977
\(442\) −5.82241 −0.276944
\(443\) −16.3786 −0.778172 −0.389086 0.921201i \(-0.627209\pi\)
−0.389086 + 0.921201i \(0.627209\pi\)
\(444\) −55.5566 −2.63660
\(445\) 52.5061 2.48903
\(446\) −15.1474 −0.717251
\(447\) 5.04110 0.238436
\(448\) 12.9048 0.609695
\(449\) 10.6434 0.502294 0.251147 0.967949i \(-0.419192\pi\)
0.251147 + 0.967949i \(0.419192\pi\)
\(450\) −247.422 −11.6636
\(451\) −3.86812 −0.182143
\(452\) −4.23663 −0.199275
\(453\) −19.2392 −0.903935
\(454\) 9.10210 0.427183
\(455\) 52.3506 2.45423
\(456\) −10.8278 −0.507059
\(457\) 15.4957 0.724860 0.362430 0.932011i \(-0.381947\pi\)
0.362430 + 0.932011i \(0.381947\pi\)
\(458\) 63.5066 2.96747
\(459\) −8.56625 −0.399838
\(460\) 27.0325 1.26039
\(461\) −6.19068 −0.288329 −0.144164 0.989554i \(-0.546049\pi\)
−0.144164 + 0.989554i \(0.546049\pi\)
\(462\) −126.238 −5.87312
\(463\) −23.7363 −1.10312 −0.551560 0.834135i \(-0.685967\pi\)
−0.551560 + 0.834135i \(0.685967\pi\)
\(464\) 15.6161 0.724957
\(465\) 93.1517 4.31981
\(466\) −1.65058 −0.0764615
\(467\) −18.5039 −0.856259 −0.428129 0.903717i \(-0.640827\pi\)
−0.428129 + 0.903717i \(0.640827\pi\)
\(468\) 156.661 7.24167
\(469\) 34.0245 1.57111
\(470\) 90.3098 4.16568
\(471\) 28.1610 1.29759
\(472\) 43.5168 2.00303
\(473\) 52.2665 2.40322
\(474\) −18.6524 −0.856731
\(475\) −7.15946 −0.328498
\(476\) −5.91594 −0.271157
\(477\) −103.281 −4.72891
\(478\) 44.7576 2.04716
\(479\) −2.33657 −0.106761 −0.0533803 0.998574i \(-0.517000\pi\)
−0.0533803 + 0.998574i \(0.517000\pi\)
\(480\) −34.6241 −1.58037
\(481\) 18.0759 0.824191
\(482\) −0.308740 −0.0140627
\(483\) −14.0194 −0.637903
\(484\) 83.1301 3.77864
\(485\) −18.7126 −0.849695
\(486\) 138.317 6.27421
\(487\) 8.72371 0.395309 0.197655 0.980272i \(-0.436668\pi\)
0.197655 + 0.980272i \(0.436668\pi\)
\(488\) −42.4282 −1.92063
\(489\) 11.9646 0.541059
\(490\) 5.62289 0.254016
\(491\) −26.6140 −1.20107 −0.600536 0.799598i \(-0.705046\pi\)
−0.600536 + 0.799598i \(0.705046\pi\)
\(492\) 9.85087 0.444112
\(493\) 1.45009 0.0653089
\(494\) 6.67317 0.300240
\(495\) −185.539 −8.33938
\(496\) 36.8837 1.65613
\(497\) 2.74619 0.123183
\(498\) 122.030 5.46828
\(499\) 34.1636 1.52937 0.764686 0.644403i \(-0.222894\pi\)
0.764686 + 0.644403i \(0.222894\pi\)
\(500\) −128.319 −5.73860
\(501\) 67.7042 3.02480
\(502\) −48.0596 −2.14500
\(503\) −14.0370 −0.625878 −0.312939 0.949773i \(-0.601314\pi\)
−0.312939 + 0.949773i \(0.601314\pi\)
\(504\) 123.705 5.51025
\(505\) 63.1543 2.81033
\(506\) 21.2089 0.942852
\(507\) −26.6899 −1.18534
\(508\) 25.1652 1.11653
\(509\) −15.4094 −0.683009 −0.341505 0.939880i \(-0.610937\pi\)
−0.341505 + 0.939880i \(0.610937\pi\)
\(510\) −17.5611 −0.777619
\(511\) 34.8179 1.54025
\(512\) 47.4618 2.09754
\(513\) 9.81795 0.433473
\(514\) 47.3431 2.08821
\(515\) 57.8087 2.54736
\(516\) −133.106 −5.85968
\(517\) 48.1325 2.11687
\(518\) 27.0366 1.18792
\(519\) 32.3918 1.42184
\(520\) 106.478 4.66938
\(521\) −34.4747 −1.51036 −0.755181 0.655516i \(-0.772451\pi\)
−0.755181 + 0.655516i \(0.772451\pi\)
\(522\) −57.4360 −2.51391
\(523\) −26.2391 −1.14735 −0.573677 0.819082i \(-0.694484\pi\)
−0.573677 + 0.819082i \(0.694484\pi\)
\(524\) 20.4372 0.892804
\(525\) 112.222 4.89776
\(526\) −67.8253 −2.95732
\(527\) 3.42498 0.149195
\(528\) −100.793 −4.38646
\(529\) −20.6446 −0.897593
\(530\) −132.967 −5.77574
\(531\) −62.8309 −2.72663
\(532\) 6.78038 0.293967
\(533\) −3.20509 −0.138828
\(534\) −104.910 −4.53991
\(535\) 14.1660 0.612451
\(536\) 69.2040 2.98916
\(537\) 67.4046 2.90873
\(538\) 5.78136 0.249252
\(539\) 2.99684 0.129083
\(540\) 296.739 12.7696
\(541\) −33.9669 −1.46035 −0.730177 0.683258i \(-0.760562\pi\)
−0.730177 + 0.683258i \(0.760562\pi\)
\(542\) −41.8316 −1.79682
\(543\) −77.5841 −3.32945
\(544\) −1.27305 −0.0545817
\(545\) −36.0065 −1.54235
\(546\) −104.600 −4.47645
\(547\) 40.1183 1.71533 0.857667 0.514206i \(-0.171913\pi\)
0.857667 + 0.514206i \(0.171913\pi\)
\(548\) 32.6397 1.39430
\(549\) 61.2590 2.61447
\(550\) −169.773 −7.23913
\(551\) −1.66198 −0.0708027
\(552\) −28.5146 −1.21366
\(553\) 6.16624 0.262215
\(554\) 38.3130 1.62776
\(555\) 54.5193 2.31421
\(556\) 42.7605 1.81345
\(557\) 7.08731 0.300299 0.150150 0.988663i \(-0.452024\pi\)
0.150150 + 0.988663i \(0.452024\pi\)
\(558\) −135.659 −5.74288
\(559\) 43.3076 1.83172
\(560\) 62.5193 2.64192
\(561\) −9.35957 −0.395161
\(562\) 14.1768 0.598010
\(563\) 10.4475 0.440310 0.220155 0.975465i \(-0.429344\pi\)
0.220155 + 0.975465i \(0.429344\pi\)
\(564\) −122.578 −5.16148
\(565\) 4.15753 0.174909
\(566\) 31.4943 1.32380
\(567\) −87.4515 −3.67262
\(568\) 5.58560 0.234367
\(569\) 13.2137 0.553946 0.276973 0.960878i \(-0.410669\pi\)
0.276973 + 0.960878i \(0.410669\pi\)
\(570\) 20.1271 0.843033
\(571\) −22.6388 −0.947403 −0.473701 0.880686i \(-0.657082\pi\)
−0.473701 + 0.880686i \(0.657082\pi\)
\(572\) 107.496 4.49462
\(573\) −14.8761 −0.621458
\(574\) −4.79392 −0.200094
\(575\) −18.8541 −0.786272
\(576\) −37.8972 −1.57905
\(577\) −9.06755 −0.377487 −0.188743 0.982026i \(-0.560441\pi\)
−0.188743 + 0.982026i \(0.560441\pi\)
\(578\) 41.8088 1.73902
\(579\) −12.1974 −0.506909
\(580\) −50.2320 −2.08577
\(581\) −40.3415 −1.67365
\(582\) 37.3889 1.54982
\(583\) −70.8679 −2.93505
\(584\) 70.8177 2.93046
\(585\) −153.736 −6.35621
\(586\) 54.6675 2.25829
\(587\) 21.2743 0.878083 0.439041 0.898467i \(-0.355318\pi\)
0.439041 + 0.898467i \(0.355318\pi\)
\(588\) −7.63201 −0.314739
\(589\) −3.92544 −0.161745
\(590\) −80.8906 −3.33021
\(591\) −29.7126 −1.22221
\(592\) 21.5871 0.887222
\(593\) −0.00680874 −0.000279601 0 −0.000139801 1.00000i \(-0.500044\pi\)
−0.000139801 1.00000i \(0.500044\pi\)
\(594\) 232.814 9.55246
\(595\) 5.80549 0.238002
\(596\) −6.42062 −0.262999
\(597\) −4.89489 −0.200335
\(598\) 17.5735 0.718635
\(599\) −22.1529 −0.905141 −0.452571 0.891729i \(-0.649493\pi\)
−0.452571 + 0.891729i \(0.649493\pi\)
\(600\) 228.253 9.31840
\(601\) −46.4704 −1.89557 −0.947783 0.318915i \(-0.896681\pi\)
−0.947783 + 0.318915i \(0.896681\pi\)
\(602\) 64.7761 2.64008
\(603\) −99.9187 −4.06900
\(604\) 24.5041 0.997057
\(605\) −81.5780 −3.31662
\(606\) −126.186 −5.12595
\(607\) 28.2722 1.14753 0.573766 0.819019i \(-0.305482\pi\)
0.573766 + 0.819019i \(0.305482\pi\)
\(608\) 1.45907 0.0591731
\(609\) 26.0509 1.05564
\(610\) 78.8669 3.19323
\(611\) 39.8822 1.61346
\(612\) 17.3732 0.702269
\(613\) −2.86610 −0.115761 −0.0578803 0.998324i \(-0.518434\pi\)
−0.0578803 + 0.998324i \(0.518434\pi\)
\(614\) −37.2408 −1.50292
\(615\) −9.66695 −0.389809
\(616\) 84.8820 3.41999
\(617\) −36.8513 −1.48358 −0.741789 0.670633i \(-0.766022\pi\)
−0.741789 + 0.670633i \(0.766022\pi\)
\(618\) −115.505 −4.64630
\(619\) −13.3826 −0.537893 −0.268947 0.963155i \(-0.586676\pi\)
−0.268947 + 0.963155i \(0.586676\pi\)
\(620\) −118.643 −4.76483
\(621\) 25.8552 1.03753
\(622\) 13.9634 0.559881
\(623\) 34.6820 1.38951
\(624\) −83.5164 −3.34333
\(625\) 64.4978 2.57991
\(626\) 21.2517 0.849388
\(627\) 10.7272 0.428403
\(628\) −35.8674 −1.43126
\(629\) 2.00455 0.0799268
\(630\) −229.947 −9.16130
\(631\) −42.2000 −1.67996 −0.839978 0.542621i \(-0.817432\pi\)
−0.839978 + 0.542621i \(0.817432\pi\)
\(632\) 12.5418 0.498886
\(633\) −89.0976 −3.54131
\(634\) 19.0857 0.757992
\(635\) −24.6953 −0.980005
\(636\) 180.478 7.15642
\(637\) 2.48316 0.0983863
\(638\) −39.4107 −1.56028
\(639\) −8.06465 −0.319033
\(640\) −69.6082 −2.75150
\(641\) 23.1027 0.912502 0.456251 0.889851i \(-0.349192\pi\)
0.456251 + 0.889851i \(0.349192\pi\)
\(642\) −28.3046 −1.11709
\(643\) 34.9475 1.37819 0.689097 0.724670i \(-0.258008\pi\)
0.689097 + 0.724670i \(0.258008\pi\)
\(644\) 17.8559 0.703619
\(645\) 130.621 5.14320
\(646\) 0.740030 0.0291161
\(647\) 18.4251 0.724364 0.362182 0.932107i \(-0.382032\pi\)
0.362182 + 0.932107i \(0.382032\pi\)
\(648\) −177.872 −6.98746
\(649\) −43.1124 −1.69231
\(650\) −140.672 −5.51762
\(651\) 61.5298 2.41154
\(652\) −15.2388 −0.596798
\(653\) 31.5421 1.23434 0.617168 0.786831i \(-0.288280\pi\)
0.617168 + 0.786831i \(0.288280\pi\)
\(654\) 71.9432 2.81320
\(655\) −20.0556 −0.783638
\(656\) −3.82765 −0.149445
\(657\) −102.249 −3.98910
\(658\) 59.6526 2.32550
\(659\) −15.3148 −0.596578 −0.298289 0.954476i \(-0.596416\pi\)
−0.298289 + 0.954476i \(0.596416\pi\)
\(660\) 324.220 12.6203
\(661\) −2.33459 −0.0908049 −0.0454025 0.998969i \(-0.514457\pi\)
−0.0454025 + 0.998969i \(0.514457\pi\)
\(662\) 39.3027 1.52754
\(663\) −7.75526 −0.301189
\(664\) −82.0524 −3.18425
\(665\) −6.65378 −0.258023
\(666\) −79.3974 −3.07659
\(667\) −4.37676 −0.169469
\(668\) −86.2319 −3.33641
\(669\) −20.1759 −0.780045
\(670\) −128.639 −4.96975
\(671\) 42.0338 1.62270
\(672\) −22.8704 −0.882245
\(673\) −31.9052 −1.22986 −0.614928 0.788583i \(-0.710815\pi\)
−0.614928 + 0.788583i \(0.710815\pi\)
\(674\) −73.4598 −2.82956
\(675\) −206.965 −7.96608
\(676\) 33.9937 1.30745
\(677\) 46.1825 1.77494 0.887468 0.460869i \(-0.152462\pi\)
0.887468 + 0.460869i \(0.152462\pi\)
\(678\) −8.30700 −0.319028
\(679\) −12.3603 −0.474345
\(680\) 11.8080 0.452818
\(681\) 12.1237 0.464582
\(682\) −93.0843 −3.56438
\(683\) −19.2195 −0.735413 −0.367706 0.929942i \(-0.619857\pi\)
−0.367706 + 0.929942i \(0.619857\pi\)
\(684\) −19.9117 −0.761344
\(685\) −32.0303 −1.22381
\(686\) −44.2928 −1.69111
\(687\) 84.5888 3.22726
\(688\) 51.7198 1.97180
\(689\) −58.7205 −2.23707
\(690\) 53.0040 2.01783
\(691\) −43.1976 −1.64331 −0.821657 0.569982i \(-0.806950\pi\)
−0.821657 + 0.569982i \(0.806950\pi\)
\(692\) −41.2559 −1.56832
\(693\) −122.555 −4.65548
\(694\) 13.3234 0.505748
\(695\) −41.9621 −1.59171
\(696\) 52.9862 2.00844
\(697\) −0.355433 −0.0134630
\(698\) −31.3167 −1.18535
\(699\) −2.19851 −0.0831555
\(700\) −142.932 −5.40232
\(701\) 39.1331 1.47804 0.739018 0.673686i \(-0.235290\pi\)
0.739018 + 0.673686i \(0.235290\pi\)
\(702\) 192.907 7.28082
\(703\) −2.29746 −0.0866503
\(704\) −26.0037 −0.980053
\(705\) 120.290 4.53037
\(706\) 87.7562 3.30275
\(707\) 41.7155 1.56887
\(708\) 109.794 4.12630
\(709\) −36.3319 −1.36447 −0.682237 0.731131i \(-0.738993\pi\)
−0.682237 + 0.731131i \(0.738993\pi\)
\(710\) −10.3827 −0.389656
\(711\) −18.1082 −0.679111
\(712\) 70.5414 2.64365
\(713\) −10.3375 −0.387142
\(714\) −11.5997 −0.434108
\(715\) −105.489 −3.94505
\(716\) −85.8503 −3.20838
\(717\) 59.6156 2.22639
\(718\) −54.1142 −2.01953
\(719\) 28.4806 1.06215 0.531073 0.847326i \(-0.321789\pi\)
0.531073 + 0.847326i \(0.321789\pi\)
\(720\) −183.599 −6.84231
\(721\) 38.1846 1.42207
\(722\) 46.6010 1.73431
\(723\) −0.411232 −0.0152939
\(724\) 98.8155 3.67245
\(725\) 35.0350 1.30117
\(726\) 162.998 6.04941
\(727\) 7.69073 0.285233 0.142617 0.989778i \(-0.454448\pi\)
0.142617 + 0.989778i \(0.454448\pi\)
\(728\) 70.3325 2.60670
\(729\) 88.7004 3.28520
\(730\) −131.638 −4.87216
\(731\) 4.80265 0.177632
\(732\) −107.047 −3.95657
\(733\) 43.1288 1.59300 0.796499 0.604640i \(-0.206683\pi\)
0.796499 + 0.604640i \(0.206683\pi\)
\(734\) 10.3925 0.383594
\(735\) 7.48951 0.276255
\(736\) 3.84240 0.141633
\(737\) −68.5608 −2.52547
\(738\) 14.0782 0.518224
\(739\) 13.8586 0.509795 0.254898 0.966968i \(-0.417958\pi\)
0.254898 + 0.966968i \(0.417958\pi\)
\(740\) −69.4388 −2.55262
\(741\) 8.88845 0.326526
\(742\) −87.8295 −3.22432
\(743\) 20.1434 0.738990 0.369495 0.929233i \(-0.379531\pi\)
0.369495 + 0.929233i \(0.379531\pi\)
\(744\) 125.148 4.58816
\(745\) 6.30074 0.230841
\(746\) −12.5356 −0.458960
\(747\) 118.470 4.33458
\(748\) 11.9209 0.435870
\(749\) 9.35715 0.341903
\(750\) −251.602 −9.18720
\(751\) 43.1365 1.57407 0.787036 0.616907i \(-0.211614\pi\)
0.787036 + 0.616907i \(0.211614\pi\)
\(752\) 47.6290 1.73685
\(753\) −64.0138 −2.33279
\(754\) −32.6553 −1.18924
\(755\) −24.0466 −0.875144
\(756\) 196.006 7.12869
\(757\) 23.5363 0.855442 0.427721 0.903911i \(-0.359316\pi\)
0.427721 + 0.903911i \(0.359316\pi\)
\(758\) 8.86863 0.322123
\(759\) 28.2496 1.02540
\(760\) −13.5334 −0.490909
\(761\) −16.0878 −0.583184 −0.291592 0.956543i \(-0.594185\pi\)
−0.291592 + 0.956543i \(0.594185\pi\)
\(762\) 49.3428 1.78750
\(763\) −23.7835 −0.861022
\(764\) 18.9470 0.685479
\(765\) −17.0488 −0.616400
\(766\) 85.5788 3.09209
\(767\) −35.7225 −1.28987
\(768\) 107.819 3.89058
\(769\) 31.5671 1.13834 0.569169 0.822220i \(-0.307265\pi\)
0.569169 + 0.822220i \(0.307265\pi\)
\(770\) −157.782 −5.68605
\(771\) 63.0595 2.27103
\(772\) 15.5353 0.559129
\(773\) −19.2836 −0.693583 −0.346791 0.937942i \(-0.612729\pi\)
−0.346791 + 0.937942i \(0.612729\pi\)
\(774\) −190.226 −6.83753
\(775\) 82.7493 2.97244
\(776\) −25.1402 −0.902480
\(777\) 36.0118 1.29192
\(778\) −46.9951 −1.68486
\(779\) 0.407368 0.0145955
\(780\) 268.646 9.61908
\(781\) −5.53369 −0.198011
\(782\) 1.94884 0.0696904
\(783\) −48.0443 −1.71696
\(784\) 2.96549 0.105910
\(785\) 35.1977 1.25626
\(786\) 40.0723 1.42933
\(787\) 25.5050 0.909155 0.454577 0.890707i \(-0.349790\pi\)
0.454577 + 0.890707i \(0.349790\pi\)
\(788\) 37.8436 1.34812
\(789\) −90.3411 −3.21623
\(790\) −23.3131 −0.829444
\(791\) 2.74619 0.0976433
\(792\) −249.270 −8.85744
\(793\) 34.8289 1.23681
\(794\) −3.91015 −0.138766
\(795\) −177.108 −6.28139
\(796\) 6.23441 0.220973
\(797\) 40.3170 1.42810 0.714050 0.700095i \(-0.246859\pi\)
0.714050 + 0.700095i \(0.246859\pi\)
\(798\) 13.2947 0.470626
\(799\) 4.42279 0.156467
\(800\) −30.7576 −1.08744
\(801\) −101.850 −3.59868
\(802\) 31.2426 1.10322
\(803\) −70.1595 −2.47588
\(804\) 174.603 6.15776
\(805\) −17.5225 −0.617586
\(806\) −77.1288 −2.71675
\(807\) 7.70059 0.271074
\(808\) 84.8471 2.98491
\(809\) 2.58833 0.0910008 0.0455004 0.998964i \(-0.485512\pi\)
0.0455004 + 0.998964i \(0.485512\pi\)
\(810\) 330.634 11.6173
\(811\) −35.6481 −1.25177 −0.625887 0.779914i \(-0.715263\pi\)
−0.625887 + 0.779914i \(0.715263\pi\)
\(812\) −33.1799 −1.16439
\(813\) −55.7184 −1.95413
\(814\) −54.4798 −1.90952
\(815\) 14.9543 0.523826
\(816\) −9.26166 −0.324223
\(817\) −5.50441 −0.192575
\(818\) 50.4556 1.76414
\(819\) −101.548 −3.54838
\(820\) 12.3124 0.429967
\(821\) −26.2735 −0.916952 −0.458476 0.888707i \(-0.651604\pi\)
−0.458476 + 0.888707i \(0.651604\pi\)
\(822\) 63.9984 2.23220
\(823\) 5.73640 0.199958 0.0999792 0.994990i \(-0.468122\pi\)
0.0999792 + 0.994990i \(0.468122\pi\)
\(824\) 77.6654 2.70560
\(825\) −226.132 −7.87290
\(826\) −53.4310 −1.85910
\(827\) 43.3519 1.50749 0.753746 0.657165i \(-0.228245\pi\)
0.753746 + 0.657165i \(0.228245\pi\)
\(828\) −52.4367 −1.82230
\(829\) 33.2138 1.15356 0.576781 0.816899i \(-0.304309\pi\)
0.576781 + 0.816899i \(0.304309\pi\)
\(830\) 152.522 5.29411
\(831\) 51.0317 1.77027
\(832\) −21.5465 −0.746989
\(833\) 0.275373 0.00954111
\(834\) 83.8427 2.90324
\(835\) 84.6219 2.92846
\(836\) −13.6627 −0.472536
\(837\) −113.476 −3.92231
\(838\) −1.94826 −0.0673014
\(839\) −23.3145 −0.804908 −0.402454 0.915440i \(-0.631843\pi\)
−0.402454 + 0.915440i \(0.631843\pi\)
\(840\) 212.132 7.31924
\(841\) −20.8671 −0.719554
\(842\) 4.97055 0.171296
\(843\) 18.8830 0.650365
\(844\) 113.480 3.90613
\(845\) −33.3590 −1.14758
\(846\) −175.180 −6.02281
\(847\) −53.8850 −1.85151
\(848\) −70.1265 −2.40816
\(849\) 41.9493 1.43970
\(850\) −15.6000 −0.535077
\(851\) −6.05027 −0.207400
\(852\) 14.0926 0.482803
\(853\) 14.7429 0.504789 0.252394 0.967624i \(-0.418782\pi\)
0.252394 + 0.967624i \(0.418782\pi\)
\(854\) 52.0943 1.78263
\(855\) 19.5400 0.668252
\(856\) 19.0319 0.650498
\(857\) 30.3932 1.03821 0.519106 0.854710i \(-0.326265\pi\)
0.519106 + 0.854710i \(0.326265\pi\)
\(858\) 210.773 7.19565
\(859\) −18.6872 −0.637601 −0.318800 0.947822i \(-0.603280\pi\)
−0.318800 + 0.947822i \(0.603280\pi\)
\(860\) −166.366 −5.67304
\(861\) −6.38535 −0.217612
\(862\) −21.7250 −0.739957
\(863\) −1.08737 −0.0370147 −0.0185073 0.999829i \(-0.505891\pi\)
−0.0185073 + 0.999829i \(0.505891\pi\)
\(864\) 42.1787 1.43495
\(865\) 40.4857 1.37655
\(866\) 76.1691 2.58833
\(867\) 55.6880 1.89127
\(868\) −78.3679 −2.65998
\(869\) −12.4252 −0.421497
\(870\) −98.4925 −3.33921
\(871\) −56.8089 −1.92490
\(872\) −48.3744 −1.63817
\(873\) 36.2981 1.22851
\(874\) −2.23360 −0.0755528
\(875\) 83.1765 2.81188
\(876\) 178.674 6.03684
\(877\) −14.4087 −0.486546 −0.243273 0.969958i \(-0.578221\pi\)
−0.243273 + 0.969958i \(0.578221\pi\)
\(878\) 27.5858 0.930975
\(879\) 72.8154 2.45600
\(880\) −125.979 −4.24675
\(881\) 18.0172 0.607014 0.303507 0.952829i \(-0.401842\pi\)
0.303507 + 0.952829i \(0.401842\pi\)
\(882\) −10.9071 −0.367262
\(883\) 9.93478 0.334332 0.167166 0.985929i \(-0.446538\pi\)
0.167166 + 0.985929i \(0.446538\pi\)
\(884\) 9.87753 0.332217
\(885\) −107.744 −3.62176
\(886\) 40.9028 1.37415
\(887\) −6.18386 −0.207634 −0.103817 0.994596i \(-0.533106\pi\)
−0.103817 + 0.994596i \(0.533106\pi\)
\(888\) 73.2461 2.45798
\(889\) −16.3121 −0.547090
\(890\) −131.125 −4.39531
\(891\) 176.219 5.90354
\(892\) 25.6971 0.860404
\(893\) −5.06904 −0.169629
\(894\) −12.5893 −0.421048
\(895\) 84.2474 2.81608
\(896\) −45.9785 −1.53604
\(897\) 23.4074 0.781550
\(898\) −26.5801 −0.886989
\(899\) 19.2092 0.640664
\(900\) 419.744 13.9915
\(901\) −6.51189 −0.216942
\(902\) 9.65995 0.321641
\(903\) 86.2796 2.87121
\(904\) 5.58560 0.185774
\(905\) −96.9705 −3.22341
\(906\) 48.0465 1.59624
\(907\) −39.9220 −1.32559 −0.662793 0.748802i \(-0.730629\pi\)
−0.662793 + 0.748802i \(0.730629\pi\)
\(908\) −15.4414 −0.512442
\(909\) −122.505 −4.06322
\(910\) −130.736 −4.33387
\(911\) −14.9110 −0.494025 −0.247012 0.969012i \(-0.579449\pi\)
−0.247012 + 0.969012i \(0.579449\pi\)
\(912\) 10.6150 0.351497
\(913\) 81.2898 2.69030
\(914\) −38.6979 −1.28001
\(915\) 105.048 3.47279
\(916\) −107.737 −3.55973
\(917\) −13.2474 −0.437468
\(918\) 21.3927 0.706065
\(919\) −31.0823 −1.02531 −0.512655 0.858595i \(-0.671338\pi\)
−0.512655 + 0.858595i \(0.671338\pi\)
\(920\) −35.6398 −1.17501
\(921\) −49.6036 −1.63449
\(922\) 15.4601 0.509152
\(923\) −4.58517 −0.150923
\(924\) 214.159 7.04530
\(925\) 48.4310 1.59240
\(926\) 59.2773 1.94797
\(927\) −112.136 −3.68301
\(928\) −7.13999 −0.234382
\(929\) −41.2500 −1.35337 −0.676684 0.736273i \(-0.736584\pi\)
−0.676684 + 0.736273i \(0.736584\pi\)
\(930\) −232.630 −7.62824
\(931\) −0.315610 −0.0103437
\(932\) 2.80015 0.0917220
\(933\) 18.5988 0.608897
\(934\) 46.2103 1.51205
\(935\) −11.6983 −0.382575
\(936\) −206.543 −6.75108
\(937\) −8.76986 −0.286499 −0.143249 0.989687i \(-0.545755\pi\)
−0.143249 + 0.989687i \(0.545755\pi\)
\(938\) −84.9703 −2.77438
\(939\) 28.3066 0.923750
\(940\) −153.208 −4.99708
\(941\) −35.8810 −1.16969 −0.584844 0.811146i \(-0.698844\pi\)
−0.584844 + 0.811146i \(0.698844\pi\)
\(942\) −70.3271 −2.29138
\(943\) 1.07279 0.0349348
\(944\) −42.6614 −1.38851
\(945\) −192.347 −6.25704
\(946\) −130.527 −4.24378
\(947\) 43.4826 1.41299 0.706497 0.707716i \(-0.250274\pi\)
0.706497 + 0.707716i \(0.250274\pi\)
\(948\) 31.6431 1.02772
\(949\) −58.1336 −1.88709
\(950\) 17.8795 0.580088
\(951\) 25.4216 0.824352
\(952\) 7.79961 0.252787
\(953\) −30.7698 −0.996730 −0.498365 0.866967i \(-0.666066\pi\)
−0.498365 + 0.866967i \(0.666066\pi\)
\(954\) 257.926 8.35067
\(955\) −18.5933 −0.601664
\(956\) −75.9298 −2.45575
\(957\) −52.4937 −1.69688
\(958\) 5.83517 0.188526
\(959\) −21.1571 −0.683198
\(960\) −64.9869 −2.09744
\(961\) 14.3704 0.463561
\(962\) −45.1415 −1.45542
\(963\) −27.4788 −0.885493
\(964\) 0.523768 0.0168694
\(965\) −15.2453 −0.490763
\(966\) 35.0109 1.12646
\(967\) 19.9740 0.642319 0.321159 0.947025i \(-0.395927\pi\)
0.321159 + 0.947025i \(0.395927\pi\)
\(968\) −109.599 −3.52265
\(969\) 0.985697 0.0316651
\(970\) 46.7314 1.50046
\(971\) −52.9981 −1.70079 −0.850395 0.526145i \(-0.823637\pi\)
−0.850395 + 0.526145i \(0.823637\pi\)
\(972\) −234.651 −7.52644
\(973\) −27.7174 −0.888578
\(974\) −21.7859 −0.698067
\(975\) −187.371 −6.00067
\(976\) 41.5941 1.33140
\(977\) −60.3597 −1.93108 −0.965539 0.260259i \(-0.916192\pi\)
−0.965539 + 0.260259i \(0.916192\pi\)
\(978\) −29.8796 −0.955443
\(979\) −69.8858 −2.23356
\(980\) −9.53906 −0.304714
\(981\) 69.8444 2.22996
\(982\) 66.4637 2.12094
\(983\) 38.2268 1.21925 0.609623 0.792692i \(-0.291321\pi\)
0.609623 + 0.792692i \(0.291321\pi\)
\(984\) −12.9875 −0.414025
\(985\) −37.1371 −1.18329
\(986\) −3.62135 −0.115327
\(987\) 79.4554 2.52909
\(988\) −11.3208 −0.360164
\(989\) −14.4956 −0.460935
\(990\) 463.352 14.7263
\(991\) −0.385132 −0.0122341 −0.00611706 0.999981i \(-0.501947\pi\)
−0.00611706 + 0.999981i \(0.501947\pi\)
\(992\) −16.8640 −0.535432
\(993\) 52.3500 1.66128
\(994\) −6.85813 −0.217527
\(995\) −6.11801 −0.193954
\(996\) −207.020 −6.55966
\(997\) 12.4811 0.395280 0.197640 0.980275i \(-0.436672\pi\)
0.197640 + 0.980275i \(0.436672\pi\)
\(998\) −85.3176 −2.70068
\(999\) −66.4147 −2.10127
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 \(a_p\))