Properties

Label 4031.2.a.c.1.14
Level 4031
Weight 2
Character 4031.1
Self dual Yes
Analytic conductor 32.188
Analytic rank 1
Dimension 61
CM No

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Newspace parameters

Level: \( N \) = \( 4031 = 29 \cdot 139 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4031.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1876970548\)
Analytic rank: \(1\)
Dimension: \(61\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 4031.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.73344 q^{2}\) \(-1.78807 q^{3}\) \(+1.00480 q^{4}\) \(-2.76512 q^{5}\) \(+3.09951 q^{6}\) \(-4.11682 q^{7}\) \(+1.72512 q^{8}\) \(+0.197207 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.73344 q^{2}\) \(-1.78807 q^{3}\) \(+1.00480 q^{4}\) \(-2.76512 q^{5}\) \(+3.09951 q^{6}\) \(-4.11682 q^{7}\) \(+1.72512 q^{8}\) \(+0.197207 q^{9}\) \(+4.79315 q^{10}\) \(-1.99041 q^{11}\) \(-1.79665 q^{12}\) \(-4.67393 q^{13}\) \(+7.13623 q^{14}\) \(+4.94423 q^{15}\) \(-4.99998 q^{16}\) \(-2.57995 q^{17}\) \(-0.341846 q^{18}\) \(-2.14491 q^{19}\) \(-2.77838 q^{20}\) \(+7.36117 q^{21}\) \(+3.45025 q^{22}\) \(-1.75275 q^{23}\) \(-3.08464 q^{24}\) \(+2.64587 q^{25}\) \(+8.10195 q^{26}\) \(+5.01160 q^{27}\) \(-4.13657 q^{28}\) \(-1.00000 q^{29}\) \(-8.57050 q^{30}\) \(+6.89231 q^{31}\) \(+5.21690 q^{32}\) \(+3.55900 q^{33}\) \(+4.47218 q^{34}\) \(+11.3835 q^{35}\) \(+0.198153 q^{36}\) \(+5.25840 q^{37}\) \(+3.71806 q^{38}\) \(+8.35733 q^{39}\) \(-4.77016 q^{40}\) \(-6.91323 q^{41}\) \(-12.7601 q^{42}\) \(-4.92517 q^{43}\) \(-1.99996 q^{44}\) \(-0.545301 q^{45}\) \(+3.03828 q^{46}\) \(-4.03679 q^{47}\) \(+8.94033 q^{48}\) \(+9.94817 q^{49}\) \(-4.58644 q^{50}\) \(+4.61314 q^{51}\) \(-4.69635 q^{52}\) \(+6.90102 q^{53}\) \(-8.68728 q^{54}\) \(+5.50372 q^{55}\) \(-7.10200 q^{56}\) \(+3.83526 q^{57}\) \(+1.73344 q^{58}\) \(-11.1107 q^{59}\) \(+4.96795 q^{60}\) \(-3.54169 q^{61}\) \(-11.9474 q^{62}\) \(-0.811866 q^{63}\) \(+0.956800 q^{64}\) \(+12.9240 q^{65}\) \(-6.16929 q^{66}\) \(+8.82546 q^{67}\) \(-2.59233 q^{68}\) \(+3.13405 q^{69}\) \(-19.7325 q^{70}\) \(+1.32126 q^{71}\) \(+0.340206 q^{72}\) \(+1.21852 q^{73}\) \(-9.11510 q^{74}\) \(-4.73101 q^{75}\) \(-2.15520 q^{76}\) \(+8.19415 q^{77}\) \(-14.4869 q^{78}\) \(-13.8652 q^{79}\) \(+13.8255 q^{80}\) \(-9.55273 q^{81}\) \(+11.9836 q^{82}\) \(+14.0747 q^{83}\) \(+7.39648 q^{84}\) \(+7.13386 q^{85}\) \(+8.53746 q^{86}\) \(+1.78807 q^{87}\) \(-3.43369 q^{88}\) \(+7.91115 q^{89}\) \(+0.945244 q^{90}\) \(+19.2417 q^{91}\) \(-1.76116 q^{92}\) \(-12.3240 q^{93}\) \(+6.99752 q^{94}\) \(+5.93093 q^{95}\) \(-9.32820 q^{96}\) \(+17.0121 q^{97}\) \(-17.2445 q^{98}\) \(-0.392523 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 11q^{16} \) \(\mathstrut -\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 17q^{18} \) \(\mathstrut -\mathstrut 36q^{19} \) \(\mathstrut -\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 42q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 28q^{24} \) \(\mathstrut -\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut -\mathstrut 10q^{27} \) \(\mathstrut -\mathstrut 25q^{28} \) \(\mathstrut -\mathstrut 61q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 18q^{31} \) \(\mathstrut -\mathstrut 3q^{32} \) \(\mathstrut -\mathstrut 42q^{33} \) \(\mathstrut -\mathstrut 22q^{34} \) \(\mathstrut -\mathstrut 29q^{35} \) \(\mathstrut -\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 30q^{37} \) \(\mathstrut -\mathstrut 27q^{38} \) \(\mathstrut -\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut 22q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 58q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 31q^{45} \) \(\mathstrut -\mathstrut 40q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 37q^{48} \) \(\mathstrut -\mathstrut 37q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 43q^{52} \) \(\mathstrut -\mathstrut 27q^{53} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut -\mathstrut 22q^{56} \) \(\mathstrut -\mathstrut 50q^{57} \) \(\mathstrut +\mathstrut q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 76q^{61} \) \(\mathstrut -\mathstrut 17q^{62} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 60q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 7q^{66} \) \(\mathstrut -\mathstrut 45q^{67} \) \(\mathstrut -\mathstrut 31q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 28q^{71} \) \(\mathstrut -\mathstrut 40q^{72} \) \(\mathstrut -\mathstrut 50q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 35q^{75} \) \(\mathstrut -\mathstrut 100q^{76} \) \(\mathstrut +\mathstrut q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 66q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut -\mathstrut 63q^{81} \) \(\mathstrut -\mathstrut 5q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 62q^{88} \) \(\mathstrut -\mathstrut 30q^{89} \) \(\mathstrut +\mathstrut 50q^{90} \) \(\mathstrut -\mathstrut 52q^{91} \) \(\mathstrut -\mathstrut 53q^{92} \) \(\mathstrut -\mathstrut 42q^{93} \) \(\mathstrut -\mathstrut 92q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut -\mathstrut 47q^{96} \) \(\mathstrut -\mathstrut 34q^{97} \) \(\mathstrut +\mathstrut 36q^{98} \) \(\mathstrut -\mathstrut 29q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.73344 −1.22572 −0.612862 0.790190i \(-0.709982\pi\)
−0.612862 + 0.790190i \(0.709982\pi\)
\(3\) −1.78807 −1.03234 −0.516172 0.856485i \(-0.672644\pi\)
−0.516172 + 0.856485i \(0.672644\pi\)
\(4\) 1.00480 0.502399
\(5\) −2.76512 −1.23660 −0.618299 0.785943i \(-0.712178\pi\)
−0.618299 + 0.785943i \(0.712178\pi\)
\(6\) 3.09951 1.26537
\(7\) −4.11682 −1.55601 −0.778005 0.628258i \(-0.783768\pi\)
−0.778005 + 0.628258i \(0.783768\pi\)
\(8\) 1.72512 0.609922
\(9\) 0.197207 0.0657357
\(10\) 4.79315 1.51573
\(11\) −1.99041 −0.600131 −0.300066 0.953919i \(-0.597009\pi\)
−0.300066 + 0.953919i \(0.597009\pi\)
\(12\) −1.79665 −0.518649
\(13\) −4.67393 −1.29631 −0.648157 0.761506i \(-0.724460\pi\)
−0.648157 + 0.761506i \(0.724460\pi\)
\(14\) 7.13623 1.90724
\(15\) 4.94423 1.27660
\(16\) −4.99998 −1.24999
\(17\) −2.57995 −0.625730 −0.312865 0.949798i \(-0.601289\pi\)
−0.312865 + 0.949798i \(0.601289\pi\)
\(18\) −0.341846 −0.0805738
\(19\) −2.14491 −0.492076 −0.246038 0.969260i \(-0.579129\pi\)
−0.246038 + 0.969260i \(0.579129\pi\)
\(20\) −2.77838 −0.621265
\(21\) 7.36117 1.60634
\(22\) 3.45025 0.735595
\(23\) −1.75275 −0.365474 −0.182737 0.983162i \(-0.558496\pi\)
−0.182737 + 0.983162i \(0.558496\pi\)
\(24\) −3.08464 −0.629649
\(25\) 2.64587 0.529174
\(26\) 8.10195 1.58892
\(27\) 5.01160 0.964483
\(28\) −4.13657 −0.781738
\(29\) −1.00000 −0.185695
\(30\) −8.57050 −1.56475
\(31\) 6.89231 1.23790 0.618948 0.785432i \(-0.287559\pi\)
0.618948 + 0.785432i \(0.287559\pi\)
\(32\) 5.21690 0.922226
\(33\) 3.55900 0.619542
\(34\) 4.47218 0.766972
\(35\) 11.3835 1.92416
\(36\) 0.198153 0.0330255
\(37\) 5.25840 0.864476 0.432238 0.901759i \(-0.357724\pi\)
0.432238 + 0.901759i \(0.357724\pi\)
\(38\) 3.71806 0.603149
\(39\) 8.35733 1.33824
\(40\) −4.77016 −0.754228
\(41\) −6.91323 −1.07967 −0.539833 0.841772i \(-0.681513\pi\)
−0.539833 + 0.841772i \(0.681513\pi\)
\(42\) −12.7601 −1.96893
\(43\) −4.92517 −0.751081 −0.375541 0.926806i \(-0.622543\pi\)
−0.375541 + 0.926806i \(0.622543\pi\)
\(44\) −1.99996 −0.301505
\(45\) −0.545301 −0.0812886
\(46\) 3.03828 0.447970
\(47\) −4.03679 −0.588827 −0.294413 0.955678i \(-0.595124\pi\)
−0.294413 + 0.955678i \(0.595124\pi\)
\(48\) 8.94033 1.29043
\(49\) 9.94817 1.42117
\(50\) −4.58644 −0.648621
\(51\) 4.61314 0.645969
\(52\) −4.69635 −0.651267
\(53\) 6.90102 0.947928 0.473964 0.880544i \(-0.342823\pi\)
0.473964 + 0.880544i \(0.342823\pi\)
\(54\) −8.68728 −1.18219
\(55\) 5.50372 0.742121
\(56\) −7.10200 −0.949044
\(57\) 3.83526 0.507992
\(58\) 1.73344 0.227611
\(59\) −11.1107 −1.44649 −0.723243 0.690594i \(-0.757349\pi\)
−0.723243 + 0.690594i \(0.757349\pi\)
\(60\) 4.96795 0.641360
\(61\) −3.54169 −0.453467 −0.226734 0.973957i \(-0.572805\pi\)
−0.226734 + 0.973957i \(0.572805\pi\)
\(62\) −11.9474 −1.51732
\(63\) −0.811866 −0.102285
\(64\) 0.956800 0.119600
\(65\) 12.9240 1.60302
\(66\) −6.16929 −0.759388
\(67\) 8.82546 1.07820 0.539101 0.842241i \(-0.318764\pi\)
0.539101 + 0.842241i \(0.318764\pi\)
\(68\) −2.59233 −0.314366
\(69\) 3.13405 0.377295
\(70\) −19.7325 −2.35849
\(71\) 1.32126 0.156805 0.0784025 0.996922i \(-0.475018\pi\)
0.0784025 + 0.996922i \(0.475018\pi\)
\(72\) 0.340206 0.0400936
\(73\) 1.21852 0.142616 0.0713082 0.997454i \(-0.477283\pi\)
0.0713082 + 0.997454i \(0.477283\pi\)
\(74\) −9.11510 −1.05961
\(75\) −4.73101 −0.546290
\(76\) −2.15520 −0.247218
\(77\) 8.19415 0.933810
\(78\) −14.4869 −1.64032
\(79\) −13.8652 −1.55996 −0.779981 0.625804i \(-0.784771\pi\)
−0.779981 + 0.625804i \(0.784771\pi\)
\(80\) 13.8255 1.54574
\(81\) −9.55273 −1.06141
\(82\) 11.9836 1.32337
\(83\) 14.0747 1.54490 0.772451 0.635075i \(-0.219031\pi\)
0.772451 + 0.635075i \(0.219031\pi\)
\(84\) 7.39648 0.807023
\(85\) 7.13386 0.773776
\(86\) 8.53746 0.920618
\(87\) 1.78807 0.191702
\(88\) −3.43369 −0.366033
\(89\) 7.91115 0.838580 0.419290 0.907852i \(-0.362279\pi\)
0.419290 + 0.907852i \(0.362279\pi\)
\(90\) 0.945244 0.0996374
\(91\) 19.2417 2.01708
\(92\) −1.76116 −0.183614
\(93\) −12.3240 −1.27793
\(94\) 6.99752 0.721739
\(95\) 5.93093 0.608500
\(96\) −9.32820 −0.952055
\(97\) 17.0121 1.72731 0.863657 0.504079i \(-0.168168\pi\)
0.863657 + 0.504079i \(0.168168\pi\)
\(98\) −17.2445 −1.74196
\(99\) −0.392523 −0.0394501
\(100\) 2.65856 0.265856
\(101\) 1.60717 0.159919 0.0799596 0.996798i \(-0.474521\pi\)
0.0799596 + 0.996798i \(0.474521\pi\)
\(102\) −7.99658 −0.791780
\(103\) 8.06634 0.794800 0.397400 0.917646i \(-0.369913\pi\)
0.397400 + 0.917646i \(0.369913\pi\)
\(104\) −8.06308 −0.790650
\(105\) −20.3545 −1.98639
\(106\) −11.9625 −1.16190
\(107\) 12.4805 1.20654 0.603270 0.797537i \(-0.293864\pi\)
0.603270 + 0.797537i \(0.293864\pi\)
\(108\) 5.03564 0.484555
\(109\) −6.69103 −0.640884 −0.320442 0.947268i \(-0.603831\pi\)
−0.320442 + 0.947268i \(0.603831\pi\)
\(110\) −9.54033 −0.909635
\(111\) −9.40241 −0.892438
\(112\) 20.5840 1.94500
\(113\) 16.2832 1.53179 0.765897 0.642964i \(-0.222295\pi\)
0.765897 + 0.642964i \(0.222295\pi\)
\(114\) −6.64817 −0.622658
\(115\) 4.84656 0.451944
\(116\) −1.00480 −0.0932931
\(117\) −0.921732 −0.0852142
\(118\) 19.2596 1.77299
\(119\) 10.6212 0.973642
\(120\) 8.52939 0.778623
\(121\) −7.03827 −0.639843
\(122\) 6.13929 0.555825
\(123\) 12.3614 1.11459
\(124\) 6.92537 0.621917
\(125\) 6.50945 0.582223
\(126\) 1.40732 0.125374
\(127\) −1.13446 −0.100667 −0.0503337 0.998732i \(-0.516028\pi\)
−0.0503337 + 0.998732i \(0.516028\pi\)
\(128\) −12.0923 −1.06882
\(129\) 8.80656 0.775375
\(130\) −22.4028 −1.96486
\(131\) −17.6223 −1.53967 −0.769834 0.638244i \(-0.779661\pi\)
−0.769834 + 0.638244i \(0.779661\pi\)
\(132\) 3.57607 0.311257
\(133\) 8.83020 0.765675
\(134\) −15.2984 −1.32158
\(135\) −13.8577 −1.19268
\(136\) −4.45072 −0.381646
\(137\) −16.1735 −1.38180 −0.690898 0.722952i \(-0.742785\pi\)
−0.690898 + 0.722952i \(0.742785\pi\)
\(138\) −5.43267 −0.462460
\(139\) −1.00000 −0.0848189
\(140\) 11.4381 0.966695
\(141\) 7.21808 0.607872
\(142\) −2.29032 −0.192200
\(143\) 9.30303 0.777959
\(144\) −0.986031 −0.0821693
\(145\) 2.76512 0.229630
\(146\) −2.11222 −0.174808
\(147\) −17.7881 −1.46713
\(148\) 5.28363 0.434312
\(149\) 4.67382 0.382895 0.191447 0.981503i \(-0.438682\pi\)
0.191447 + 0.981503i \(0.438682\pi\)
\(150\) 8.20089 0.669600
\(151\) 2.36916 0.192799 0.0963996 0.995343i \(-0.469267\pi\)
0.0963996 + 0.995343i \(0.469267\pi\)
\(152\) −3.70023 −0.300128
\(153\) −0.508785 −0.0411328
\(154\) −14.2040 −1.14459
\(155\) −19.0580 −1.53078
\(156\) 8.39742 0.672332
\(157\) 9.65761 0.770761 0.385381 0.922758i \(-0.374070\pi\)
0.385381 + 0.922758i \(0.374070\pi\)
\(158\) 24.0345 1.91208
\(159\) −12.3395 −0.978589
\(160\) −14.4253 −1.14042
\(161\) 7.21575 0.568681
\(162\) 16.5590 1.30100
\(163\) 1.40430 0.109994 0.0549968 0.998487i \(-0.482485\pi\)
0.0549968 + 0.998487i \(0.482485\pi\)
\(164\) −6.94640 −0.542423
\(165\) −9.84105 −0.766125
\(166\) −24.3976 −1.89362
\(167\) 23.2591 1.79984 0.899922 0.436050i \(-0.143623\pi\)
0.899922 + 0.436050i \(0.143623\pi\)
\(168\) 12.6989 0.979741
\(169\) 8.84561 0.680432
\(170\) −12.3661 −0.948436
\(171\) −0.422992 −0.0323470
\(172\) −4.94880 −0.377342
\(173\) 3.38728 0.257530 0.128765 0.991675i \(-0.458899\pi\)
0.128765 + 0.991675i \(0.458899\pi\)
\(174\) −3.09951 −0.234973
\(175\) −10.8926 −0.823400
\(176\) 9.95200 0.750161
\(177\) 19.8667 1.49327
\(178\) −13.7135 −1.02787
\(179\) 15.7211 1.17505 0.587524 0.809207i \(-0.300103\pi\)
0.587524 + 0.809207i \(0.300103\pi\)
\(180\) −0.547917 −0.0408393
\(181\) −17.1928 −1.27793 −0.638965 0.769236i \(-0.720637\pi\)
−0.638965 + 0.769236i \(0.720637\pi\)
\(182\) −33.3542 −2.47238
\(183\) 6.33280 0.468134
\(184\) −3.02370 −0.222910
\(185\) −14.5401 −1.06901
\(186\) 21.3628 1.56639
\(187\) 5.13516 0.375520
\(188\) −4.05616 −0.295826
\(189\) −20.6318 −1.50075
\(190\) −10.2809 −0.745853
\(191\) 4.86513 0.352028 0.176014 0.984388i \(-0.443680\pi\)
0.176014 + 0.984388i \(0.443680\pi\)
\(192\) −1.71083 −0.123468
\(193\) −25.5427 −1.83860 −0.919302 0.393553i \(-0.871246\pi\)
−0.919302 + 0.393553i \(0.871246\pi\)
\(194\) −29.4893 −2.11721
\(195\) −23.1090 −1.65487
\(196\) 9.99590 0.713993
\(197\) −3.93826 −0.280590 −0.140295 0.990110i \(-0.544805\pi\)
−0.140295 + 0.990110i \(0.544805\pi\)
\(198\) 0.680413 0.0483549
\(199\) 8.92493 0.632671 0.316336 0.948647i \(-0.397547\pi\)
0.316336 + 0.948647i \(0.397547\pi\)
\(200\) 4.56444 0.322755
\(201\) −15.7806 −1.11308
\(202\) −2.78592 −0.196017
\(203\) 4.11682 0.288944
\(204\) 4.63527 0.324534
\(205\) 19.1159 1.33511
\(206\) −13.9825 −0.974205
\(207\) −0.345655 −0.0240247
\(208\) 23.3695 1.62039
\(209\) 4.26925 0.295310
\(210\) 35.2832 2.43477
\(211\) −16.7727 −1.15468 −0.577341 0.816503i \(-0.695910\pi\)
−0.577341 + 0.816503i \(0.695910\pi\)
\(212\) 6.93413 0.476238
\(213\) −2.36252 −0.161877
\(214\) −21.6342 −1.47888
\(215\) 13.6187 0.928785
\(216\) 8.64561 0.588259
\(217\) −28.3744 −1.92618
\(218\) 11.5985 0.785547
\(219\) −2.17879 −0.147229
\(220\) 5.53012 0.372841
\(221\) 12.0585 0.811143
\(222\) 16.2985 1.09388
\(223\) −9.42187 −0.630935 −0.315468 0.948936i \(-0.602161\pi\)
−0.315468 + 0.948936i \(0.602161\pi\)
\(224\) −21.4770 −1.43499
\(225\) 0.521784 0.0347856
\(226\) −28.2258 −1.87756
\(227\) −18.5748 −1.23285 −0.616426 0.787413i \(-0.711420\pi\)
−0.616426 + 0.787413i \(0.711420\pi\)
\(228\) 3.85366 0.255215
\(229\) −0.969783 −0.0640851 −0.0320425 0.999487i \(-0.510201\pi\)
−0.0320425 + 0.999487i \(0.510201\pi\)
\(230\) −8.40120 −0.553959
\(231\) −14.6517 −0.964014
\(232\) −1.72512 −0.113260
\(233\) −9.93912 −0.651134 −0.325567 0.945519i \(-0.605555\pi\)
−0.325567 + 0.945519i \(0.605555\pi\)
\(234\) 1.59776 0.104449
\(235\) 11.1622 0.728142
\(236\) −11.1640 −0.726713
\(237\) 24.7921 1.61042
\(238\) −18.4111 −1.19342
\(239\) −11.8610 −0.767227 −0.383613 0.923494i \(-0.625320\pi\)
−0.383613 + 0.923494i \(0.625320\pi\)
\(240\) −24.7210 −1.59574
\(241\) 7.98266 0.514208 0.257104 0.966384i \(-0.417232\pi\)
0.257104 + 0.966384i \(0.417232\pi\)
\(242\) 12.2004 0.784270
\(243\) 2.04619 0.131263
\(244\) −3.55868 −0.227821
\(245\) −27.5079 −1.75741
\(246\) −21.4276 −1.36618
\(247\) 10.0252 0.637885
\(248\) 11.8901 0.755019
\(249\) −25.1666 −1.59487
\(250\) −11.2837 −0.713644
\(251\) 20.3390 1.28379 0.641893 0.766794i \(-0.278149\pi\)
0.641893 + 0.766794i \(0.278149\pi\)
\(252\) −0.815761 −0.0513881
\(253\) 3.48869 0.219332
\(254\) 1.96652 0.123390
\(255\) −12.7559 −0.798804
\(256\) 19.0477 1.19048
\(257\) 23.5156 1.46686 0.733432 0.679762i \(-0.237917\pi\)
0.733432 + 0.679762i \(0.237917\pi\)
\(258\) −15.2656 −0.950395
\(259\) −21.6479 −1.34513
\(260\) 12.9860 0.805355
\(261\) −0.197207 −0.0122068
\(262\) 30.5471 1.88721
\(263\) −18.5188 −1.14192 −0.570958 0.820979i \(-0.693428\pi\)
−0.570958 + 0.820979i \(0.693428\pi\)
\(264\) 6.13970 0.377872
\(265\) −19.0821 −1.17221
\(266\) −15.3066 −0.938507
\(267\) −14.1457 −0.865704
\(268\) 8.86780 0.541687
\(269\) 25.9852 1.58434 0.792171 0.610299i \(-0.208951\pi\)
0.792171 + 0.610299i \(0.208951\pi\)
\(270\) 24.0213 1.46189
\(271\) −20.3772 −1.23783 −0.618913 0.785459i \(-0.712427\pi\)
−0.618913 + 0.785459i \(0.712427\pi\)
\(272\) 12.8997 0.782159
\(273\) −34.4056 −2.08232
\(274\) 28.0357 1.69370
\(275\) −5.26636 −0.317574
\(276\) 3.14908 0.189553
\(277\) 1.82620 0.109726 0.0548628 0.998494i \(-0.482528\pi\)
0.0548628 + 0.998494i \(0.482528\pi\)
\(278\) 1.73344 0.103965
\(279\) 1.35921 0.0813739
\(280\) 19.6378 1.17359
\(281\) 3.64692 0.217557 0.108778 0.994066i \(-0.465306\pi\)
0.108778 + 0.994066i \(0.465306\pi\)
\(282\) −12.5121 −0.745083
\(283\) −1.75521 −0.104337 −0.0521683 0.998638i \(-0.516613\pi\)
−0.0521683 + 0.998638i \(0.516613\pi\)
\(284\) 1.32760 0.0787787
\(285\) −10.6049 −0.628182
\(286\) −16.1262 −0.953563
\(287\) 28.4605 1.67997
\(288\) 1.02881 0.0606232
\(289\) −10.3439 −0.608462
\(290\) −4.79315 −0.281463
\(291\) −30.4188 −1.78318
\(292\) 1.22436 0.0716503
\(293\) 10.6127 0.620003 0.310002 0.950736i \(-0.399670\pi\)
0.310002 + 0.950736i \(0.399670\pi\)
\(294\) 30.8345 1.79830
\(295\) 30.7223 1.78872
\(296\) 9.07137 0.527263
\(297\) −9.97514 −0.578816
\(298\) −8.10177 −0.469323
\(299\) 8.19224 0.473769
\(300\) −4.75370 −0.274455
\(301\) 20.2760 1.16869
\(302\) −4.10678 −0.236319
\(303\) −2.87373 −0.165092
\(304\) 10.7245 0.615092
\(305\) 9.79319 0.560756
\(306\) 0.881946 0.0504175
\(307\) −0.258382 −0.0147467 −0.00737333 0.999973i \(-0.502347\pi\)
−0.00737333 + 0.999973i \(0.502347\pi\)
\(308\) 8.23346 0.469145
\(309\) −14.4232 −0.820507
\(310\) 33.0359 1.87631
\(311\) 24.4312 1.38536 0.692682 0.721243i \(-0.256429\pi\)
0.692682 + 0.721243i \(0.256429\pi\)
\(312\) 14.4174 0.816224
\(313\) 10.9772 0.620467 0.310234 0.950660i \(-0.399593\pi\)
0.310234 + 0.950660i \(0.399593\pi\)
\(314\) −16.7408 −0.944741
\(315\) 2.24490 0.126486
\(316\) −13.9318 −0.783723
\(317\) −26.5903 −1.49346 −0.746729 0.665129i \(-0.768377\pi\)
−0.746729 + 0.665129i \(0.768377\pi\)
\(318\) 21.3898 1.19948
\(319\) 1.99041 0.111442
\(320\) −2.64566 −0.147897
\(321\) −22.3161 −1.24556
\(322\) −12.5080 −0.697046
\(323\) 5.53376 0.307907
\(324\) −9.59856 −0.533253
\(325\) −12.3666 −0.685976
\(326\) −2.43427 −0.134822
\(327\) 11.9641 0.661614
\(328\) −11.9262 −0.658512
\(329\) 16.6187 0.916220
\(330\) 17.0588 0.939057
\(331\) −23.1894 −1.27461 −0.637304 0.770613i \(-0.719950\pi\)
−0.637304 + 0.770613i \(0.719950\pi\)
\(332\) 14.1422 0.776156
\(333\) 1.03700 0.0568270
\(334\) −40.3182 −2.20611
\(335\) −24.4034 −1.33330
\(336\) −36.8057 −2.00791
\(337\) 12.7774 0.696029 0.348015 0.937489i \(-0.386856\pi\)
0.348015 + 0.937489i \(0.386856\pi\)
\(338\) −15.3333 −0.834021
\(339\) −29.1155 −1.58134
\(340\) 7.16809 0.388744
\(341\) −13.7185 −0.742899
\(342\) 0.733229 0.0396485
\(343\) −12.1371 −0.655341
\(344\) −8.49650 −0.458101
\(345\) −8.66601 −0.466562
\(346\) −5.87164 −0.315661
\(347\) −16.1604 −0.867536 −0.433768 0.901025i \(-0.642816\pi\)
−0.433768 + 0.901025i \(0.642816\pi\)
\(348\) 1.79665 0.0963106
\(349\) −27.3766 −1.46544 −0.732719 0.680531i \(-0.761749\pi\)
−0.732719 + 0.680531i \(0.761749\pi\)
\(350\) 18.8815 1.00926
\(351\) −23.4239 −1.25027
\(352\) −10.3838 −0.553457
\(353\) −8.09900 −0.431066 −0.215533 0.976497i \(-0.569149\pi\)
−0.215533 + 0.976497i \(0.569149\pi\)
\(354\) −34.4376 −1.83034
\(355\) −3.65345 −0.193905
\(356\) 7.94910 0.421302
\(357\) −18.9915 −1.00513
\(358\) −27.2515 −1.44028
\(359\) 4.45481 0.235116 0.117558 0.993066i \(-0.462493\pi\)
0.117558 + 0.993066i \(0.462493\pi\)
\(360\) −0.940709 −0.0495797
\(361\) −14.3994 −0.757861
\(362\) 29.8026 1.56639
\(363\) 12.5849 0.660538
\(364\) 19.3340 1.01338
\(365\) −3.36934 −0.176359
\(366\) −10.9775 −0.573803
\(367\) −1.13040 −0.0590064 −0.0295032 0.999565i \(-0.509393\pi\)
−0.0295032 + 0.999565i \(0.509393\pi\)
\(368\) 8.76372 0.456840
\(369\) −1.36334 −0.0709726
\(370\) 25.2043 1.31031
\(371\) −28.4102 −1.47499
\(372\) −12.3831 −0.642033
\(373\) −21.0857 −1.09178 −0.545889 0.837857i \(-0.683808\pi\)
−0.545889 + 0.837857i \(0.683808\pi\)
\(374\) −8.90147 −0.460284
\(375\) −11.6394 −0.601055
\(376\) −6.96395 −0.359138
\(377\) 4.67393 0.240720
\(378\) 35.7639 1.83950
\(379\) 35.6204 1.82970 0.914848 0.403798i \(-0.132310\pi\)
0.914848 + 0.403798i \(0.132310\pi\)
\(380\) 5.95938 0.305710
\(381\) 2.02850 0.103923
\(382\) −8.43339 −0.431490
\(383\) −1.78014 −0.0909608 −0.0454804 0.998965i \(-0.514482\pi\)
−0.0454804 + 0.998965i \(0.514482\pi\)
\(384\) 21.6220 1.10339
\(385\) −22.6578 −1.15475
\(386\) 44.2766 2.25362
\(387\) −0.971279 −0.0493729
\(388\) 17.0937 0.867801
\(389\) 1.43693 0.0728552 0.0364276 0.999336i \(-0.488402\pi\)
0.0364276 + 0.999336i \(0.488402\pi\)
\(390\) 40.0579 2.02841
\(391\) 4.52201 0.228688
\(392\) 17.1618 0.866801
\(393\) 31.5100 1.58947
\(394\) 6.82673 0.343926
\(395\) 38.3390 1.92904
\(396\) −0.394406 −0.0198197
\(397\) −38.4081 −1.92765 −0.963823 0.266543i \(-0.914119\pi\)
−0.963823 + 0.266543i \(0.914119\pi\)
\(398\) −15.4708 −0.775480
\(399\) −15.7890 −0.790441
\(400\) −13.2293 −0.661464
\(401\) −15.8959 −0.793804 −0.396902 0.917861i \(-0.629915\pi\)
−0.396902 + 0.917861i \(0.629915\pi\)
\(402\) 27.3546 1.36432
\(403\) −32.2142 −1.60470
\(404\) 1.61488 0.0803432
\(405\) 26.4144 1.31254
\(406\) −7.13623 −0.354165
\(407\) −10.4664 −0.518799
\(408\) 7.95822 0.393991
\(409\) −6.52618 −0.322699 −0.161349 0.986897i \(-0.551585\pi\)
−0.161349 + 0.986897i \(0.551585\pi\)
\(410\) −33.1362 −1.63648
\(411\) 28.9194 1.42649
\(412\) 8.10503 0.399306
\(413\) 45.7406 2.25075
\(414\) 0.599171 0.0294476
\(415\) −38.9182 −1.91042
\(416\) −24.3834 −1.19549
\(417\) 1.78807 0.0875623
\(418\) −7.40047 −0.361969
\(419\) 17.4463 0.852308 0.426154 0.904651i \(-0.359868\pi\)
0.426154 + 0.904651i \(0.359868\pi\)
\(420\) −20.4521 −0.997962
\(421\) 21.5524 1.05040 0.525201 0.850978i \(-0.323990\pi\)
0.525201 + 0.850978i \(0.323990\pi\)
\(422\) 29.0744 1.41532
\(423\) −0.796084 −0.0387069
\(424\) 11.9051 0.578162
\(425\) −6.82621 −0.331120
\(426\) 4.09527 0.198416
\(427\) 14.5805 0.705599
\(428\) 12.5404 0.606164
\(429\) −16.6345 −0.803122
\(430\) −23.6071 −1.13843
\(431\) −17.7399 −0.854501 −0.427250 0.904133i \(-0.640518\pi\)
−0.427250 + 0.904133i \(0.640518\pi\)
\(432\) −25.0579 −1.20560
\(433\) −33.3143 −1.60098 −0.800492 0.599344i \(-0.795428\pi\)
−0.800492 + 0.599344i \(0.795428\pi\)
\(434\) 49.1851 2.36096
\(435\) −4.94423 −0.237058
\(436\) −6.72313 −0.321979
\(437\) 3.75949 0.179841
\(438\) 3.77680 0.180462
\(439\) 39.5485 1.88754 0.943772 0.330596i \(-0.107250\pi\)
0.943772 + 0.330596i \(0.107250\pi\)
\(440\) 9.49456 0.452636
\(441\) 1.96185 0.0934215
\(442\) −20.9026 −0.994237
\(443\) 35.8764 1.70454 0.852269 0.523104i \(-0.175226\pi\)
0.852269 + 0.523104i \(0.175226\pi\)
\(444\) −9.44752 −0.448360
\(445\) −21.8753 −1.03699
\(446\) 16.3322 0.773352
\(447\) −8.35714 −0.395279
\(448\) −3.93897 −0.186099
\(449\) −28.0027 −1.32153 −0.660765 0.750592i \(-0.729768\pi\)
−0.660765 + 0.750592i \(0.729768\pi\)
\(450\) −0.904479 −0.0426376
\(451\) 13.7602 0.647941
\(452\) 16.3613 0.769571
\(453\) −4.23623 −0.199035
\(454\) 32.1982 1.51114
\(455\) −53.2056 −2.49431
\(456\) 6.61628 0.309835
\(457\) −17.0996 −0.799885 −0.399942 0.916540i \(-0.630970\pi\)
−0.399942 + 0.916540i \(0.630970\pi\)
\(458\) 1.68106 0.0785506
\(459\) −12.9297 −0.603506
\(460\) 4.86981 0.227056
\(461\) 16.1459 0.751990 0.375995 0.926622i \(-0.377301\pi\)
0.375995 + 0.926622i \(0.377301\pi\)
\(462\) 25.3979 1.18161
\(463\) −10.3594 −0.481444 −0.240722 0.970594i \(-0.577384\pi\)
−0.240722 + 0.970594i \(0.577384\pi\)
\(464\) 4.99998 0.232118
\(465\) 34.0772 1.58029
\(466\) 17.2288 0.798110
\(467\) 10.9627 0.507291 0.253646 0.967297i \(-0.418370\pi\)
0.253646 + 0.967297i \(0.418370\pi\)
\(468\) −0.926154 −0.0428115
\(469\) −36.3328 −1.67769
\(470\) −19.3489 −0.892500
\(471\) −17.2685 −0.795692
\(472\) −19.1672 −0.882243
\(473\) 9.80310 0.450747
\(474\) −42.9754 −1.97393
\(475\) −5.67515 −0.260394
\(476\) 10.6721 0.489157
\(477\) 1.36093 0.0623127
\(478\) 20.5603 0.940408
\(479\) 30.5134 1.39419 0.697096 0.716978i \(-0.254475\pi\)
0.697096 + 0.716978i \(0.254475\pi\)
\(480\) 25.7936 1.17731
\(481\) −24.5774 −1.12063
\(482\) −13.8374 −0.630277
\(483\) −12.9023 −0.587075
\(484\) −7.07203 −0.321456
\(485\) −47.0404 −2.13599
\(486\) −3.54693 −0.160892
\(487\) 12.1141 0.548942 0.274471 0.961595i \(-0.411497\pi\)
0.274471 + 0.961595i \(0.411497\pi\)
\(488\) −6.10984 −0.276579
\(489\) −2.51100 −0.113551
\(490\) 47.6831 2.15410
\(491\) 22.9920 1.03762 0.518808 0.854891i \(-0.326376\pi\)
0.518808 + 0.854891i \(0.326376\pi\)
\(492\) 12.4207 0.559967
\(493\) 2.57995 0.116195
\(494\) −17.3780 −0.781871
\(495\) 1.08537 0.0487839
\(496\) −34.4614 −1.54736
\(497\) −5.43940 −0.243990
\(498\) 43.6247 1.95487
\(499\) 1.13345 0.0507403 0.0253702 0.999678i \(-0.491924\pi\)
0.0253702 + 0.999678i \(0.491924\pi\)
\(500\) 6.54068 0.292508
\(501\) −41.5890 −1.85806
\(502\) −35.2564 −1.57357
\(503\) −11.3333 −0.505329 −0.252664 0.967554i \(-0.581307\pi\)
−0.252664 + 0.967554i \(0.581307\pi\)
\(504\) −1.40056 −0.0623861
\(505\) −4.44401 −0.197756
\(506\) −6.04742 −0.268841
\(507\) −15.8166 −0.702440
\(508\) −1.13991 −0.0505751
\(509\) 31.3002 1.38735 0.693677 0.720286i \(-0.255989\pi\)
0.693677 + 0.720286i \(0.255989\pi\)
\(510\) 22.1115 0.979113
\(511\) −5.01640 −0.221913
\(512\) −8.83326 −0.390378
\(513\) −10.7494 −0.474599
\(514\) −40.7628 −1.79797
\(515\) −22.3044 −0.982847
\(516\) 8.84881 0.389547
\(517\) 8.03487 0.353373
\(518\) 37.5252 1.64876
\(519\) −6.05671 −0.265860
\(520\) 22.2954 0.977716
\(521\) 25.8744 1.13358 0.566788 0.823863i \(-0.308186\pi\)
0.566788 + 0.823863i \(0.308186\pi\)
\(522\) 0.341846 0.0149622
\(523\) −15.6465 −0.684173 −0.342086 0.939668i \(-0.611134\pi\)
−0.342086 + 0.939668i \(0.611134\pi\)
\(524\) −17.7068 −0.773527
\(525\) 19.4767 0.850032
\(526\) 32.1011 1.39967
\(527\) −17.7818 −0.774588
\(528\) −17.7949 −0.774424
\(529\) −19.9279 −0.866429
\(530\) 33.0776 1.43680
\(531\) −2.19110 −0.0950858
\(532\) 8.87256 0.384674
\(533\) 32.3120 1.39959
\(534\) 24.5207 1.06111
\(535\) −34.5101 −1.49200
\(536\) 15.2250 0.657618
\(537\) −28.1104 −1.21305
\(538\) −45.0436 −1.94197
\(539\) −19.8009 −0.852887
\(540\) −13.9241 −0.599199
\(541\) −29.2020 −1.25549 −0.627746 0.778418i \(-0.716022\pi\)
−0.627746 + 0.778418i \(0.716022\pi\)
\(542\) 35.3226 1.51723
\(543\) 30.7420 1.31926
\(544\) −13.4593 −0.577064
\(545\) 18.5015 0.792516
\(546\) 59.6398 2.55235
\(547\) 4.68008 0.200106 0.100053 0.994982i \(-0.468099\pi\)
0.100053 + 0.994982i \(0.468099\pi\)
\(548\) −16.2511 −0.694213
\(549\) −0.698447 −0.0298090
\(550\) 9.12890 0.389258
\(551\) 2.14491 0.0913762
\(552\) 5.40661 0.230120
\(553\) 57.0806 2.42732
\(554\) −3.16560 −0.134493
\(555\) 25.9988 1.10359
\(556\) −1.00480 −0.0426129
\(557\) −3.30413 −0.140001 −0.0700003 0.997547i \(-0.522300\pi\)
−0.0700003 + 0.997547i \(0.522300\pi\)
\(558\) −2.35611 −0.0997420
\(559\) 23.0199 0.973637
\(560\) −56.9171 −2.40519
\(561\) −9.18204 −0.387666
\(562\) −6.32170 −0.266665
\(563\) 12.0632 0.508404 0.254202 0.967151i \(-0.418187\pi\)
0.254202 + 0.967151i \(0.418187\pi\)
\(564\) 7.25271 0.305394
\(565\) −45.0249 −1.89421
\(566\) 3.04255 0.127888
\(567\) 39.3268 1.65157
\(568\) 2.27934 0.0956388
\(569\) −40.9608 −1.71717 −0.858584 0.512673i \(-0.828655\pi\)
−0.858584 + 0.512673i \(0.828655\pi\)
\(570\) 18.3830 0.769978
\(571\) 2.49342 0.104346 0.0521731 0.998638i \(-0.483385\pi\)
0.0521731 + 0.998638i \(0.483385\pi\)
\(572\) 9.34767 0.390846
\(573\) −8.69921 −0.363415
\(574\) −49.3344 −2.05918
\(575\) −4.63755 −0.193399
\(576\) 0.188688 0.00786199
\(577\) 25.4492 1.05946 0.529732 0.848165i \(-0.322292\pi\)
0.529732 + 0.848165i \(0.322292\pi\)
\(578\) 17.9304 0.745806
\(579\) 45.6722 1.89807
\(580\) 2.77838 0.115366
\(581\) −57.9430 −2.40388
\(582\) 52.7291 2.18569
\(583\) −13.7359 −0.568881
\(584\) 2.10208 0.0869848
\(585\) 2.54870 0.105376
\(586\) −18.3965 −0.759953
\(587\) 29.2319 1.20653 0.603264 0.797542i \(-0.293867\pi\)
0.603264 + 0.797542i \(0.293867\pi\)
\(588\) −17.8734 −0.737087
\(589\) −14.7834 −0.609139
\(590\) −53.2551 −2.19248
\(591\) 7.04191 0.289665
\(592\) −26.2919 −1.08059
\(593\) 28.0472 1.15176 0.575880 0.817534i \(-0.304659\pi\)
0.575880 + 0.817534i \(0.304659\pi\)
\(594\) 17.2913 0.709469
\(595\) −29.3688 −1.20400
\(596\) 4.69625 0.192366
\(597\) −15.9584 −0.653135
\(598\) −14.2007 −0.580710
\(599\) 24.6296 1.00634 0.503169 0.864188i \(-0.332167\pi\)
0.503169 + 0.864188i \(0.332167\pi\)
\(600\) −8.16155 −0.333194
\(601\) −35.0948 −1.43155 −0.715774 0.698332i \(-0.753926\pi\)
−0.715774 + 0.698332i \(0.753926\pi\)
\(602\) −35.1471 −1.43249
\(603\) 1.74044 0.0708763
\(604\) 2.38052 0.0968621
\(605\) 19.4616 0.791228
\(606\) 4.98143 0.202357
\(607\) 14.8389 0.602293 0.301147 0.953578i \(-0.402631\pi\)
0.301147 + 0.953578i \(0.402631\pi\)
\(608\) −11.1898 −0.453805
\(609\) −7.36117 −0.298290
\(610\) −16.9759 −0.687332
\(611\) 18.8677 0.763304
\(612\) −0.511226 −0.0206651
\(613\) 27.5300 1.11193 0.555963 0.831207i \(-0.312350\pi\)
0.555963 + 0.831207i \(0.312350\pi\)
\(614\) 0.447889 0.0180753
\(615\) −34.1806 −1.37830
\(616\) 14.1359 0.569551
\(617\) −27.9004 −1.12323 −0.561613 0.827400i \(-0.689819\pi\)
−0.561613 + 0.827400i \(0.689819\pi\)
\(618\) 25.0017 1.00572
\(619\) 16.9797 0.682470 0.341235 0.939978i \(-0.389155\pi\)
0.341235 + 0.939978i \(0.389155\pi\)
\(620\) −19.1495 −0.769061
\(621\) −8.78409 −0.352493
\(622\) −42.3498 −1.69807
\(623\) −32.5688 −1.30484
\(624\) −41.7865 −1.67280
\(625\) −31.2287 −1.24915
\(626\) −19.0282 −0.760521
\(627\) −7.63373 −0.304862
\(628\) 9.70395 0.387230
\(629\) −13.5664 −0.540929
\(630\) −3.89139 −0.155037
\(631\) 0.523279 0.0208314 0.0104157 0.999946i \(-0.496685\pi\)
0.0104157 + 0.999946i \(0.496685\pi\)
\(632\) −23.9192 −0.951454
\(633\) 29.9909 1.19203
\(634\) 46.0925 1.83057
\(635\) 3.13692 0.124485
\(636\) −12.3987 −0.491642
\(637\) −46.4971 −1.84228
\(638\) −3.45025 −0.136597
\(639\) 0.260563 0.0103077
\(640\) 33.4367 1.32170
\(641\) −13.3609 −0.527726 −0.263863 0.964560i \(-0.584997\pi\)
−0.263863 + 0.964560i \(0.584997\pi\)
\(642\) 38.6836 1.52672
\(643\) −9.81732 −0.387157 −0.193579 0.981085i \(-0.562009\pi\)
−0.193579 + 0.981085i \(0.562009\pi\)
\(644\) 7.25037 0.285705
\(645\) −24.3512 −0.958826
\(646\) −9.59242 −0.377409
\(647\) 6.90779 0.271573 0.135787 0.990738i \(-0.456644\pi\)
0.135787 + 0.990738i \(0.456644\pi\)
\(648\) −16.4796 −0.647380
\(649\) 22.1148 0.868081
\(650\) 21.4367 0.840817
\(651\) 50.7355 1.98848
\(652\) 1.41104 0.0552607
\(653\) 13.6257 0.533214 0.266607 0.963805i \(-0.414097\pi\)
0.266607 + 0.963805i \(0.414097\pi\)
\(654\) −20.7389 −0.810956
\(655\) 48.7277 1.90395
\(656\) 34.5660 1.34958
\(657\) 0.240300 0.00937499
\(658\) −28.8075 −1.12303
\(659\) −13.6298 −0.530942 −0.265471 0.964119i \(-0.585527\pi\)
−0.265471 + 0.964119i \(0.585527\pi\)
\(660\) −9.88826 −0.384900
\(661\) 29.9549 1.16511 0.582556 0.812791i \(-0.302053\pi\)
0.582556 + 0.812791i \(0.302053\pi\)
\(662\) 40.1974 1.56232
\(663\) −21.5615 −0.837379
\(664\) 24.2806 0.942269
\(665\) −24.4165 −0.946832
\(666\) −1.79756 −0.0696542
\(667\) 1.75275 0.0678668
\(668\) 23.3707 0.904240
\(669\) 16.8470 0.651343
\(670\) 42.3017 1.63426
\(671\) 7.04942 0.272140
\(672\) 38.4025 1.48141
\(673\) −10.3738 −0.399882 −0.199941 0.979808i \(-0.564075\pi\)
−0.199941 + 0.979808i \(0.564075\pi\)
\(674\) −22.1488 −0.853139
\(675\) 13.2600 0.510379
\(676\) 8.88805 0.341848
\(677\) −12.4111 −0.476997 −0.238498 0.971143i \(-0.576655\pi\)
−0.238498 + 0.971143i \(0.576655\pi\)
\(678\) 50.4699 1.93828
\(679\) −70.0356 −2.68772
\(680\) 12.3068 0.471943
\(681\) 33.2131 1.27273
\(682\) 23.7802 0.910590
\(683\) 37.1084 1.41991 0.709956 0.704246i \(-0.248715\pi\)
0.709956 + 0.704246i \(0.248715\pi\)
\(684\) −0.425021 −0.0162511
\(685\) 44.7216 1.70873
\(686\) 21.0388 0.803267
\(687\) 1.73404 0.0661579
\(688\) 24.6257 0.938847
\(689\) −32.2549 −1.22881
\(690\) 15.0220 0.571876
\(691\) 15.0165 0.571253 0.285627 0.958341i \(-0.407798\pi\)
0.285627 + 0.958341i \(0.407798\pi\)
\(692\) 3.40353 0.129383
\(693\) 1.61595 0.0613847
\(694\) 28.0130 1.06336
\(695\) 2.76512 0.104887
\(696\) 3.08464 0.116923
\(697\) 17.8358 0.675579
\(698\) 47.4556 1.79622
\(699\) 17.7719 0.672194
\(700\) −10.9448 −0.413675
\(701\) −32.5487 −1.22935 −0.614673 0.788782i \(-0.710712\pi\)
−0.614673 + 0.788782i \(0.710712\pi\)
\(702\) 40.6037 1.53249
\(703\) −11.2788 −0.425388
\(704\) −1.90442 −0.0717757
\(705\) −19.9588 −0.751693
\(706\) 14.0391 0.528368
\(707\) −6.61641 −0.248836
\(708\) 19.9620 0.750218
\(709\) 39.9748 1.50128 0.750642 0.660709i \(-0.229744\pi\)
0.750642 + 0.660709i \(0.229744\pi\)
\(710\) 6.33301 0.237674
\(711\) −2.73433 −0.102545
\(712\) 13.6477 0.511468
\(713\) −12.0805 −0.452418
\(714\) 32.9205 1.23202
\(715\) −25.7240 −0.962022
\(716\) 15.7965 0.590343
\(717\) 21.2084 0.792043
\(718\) −7.72213 −0.288187
\(719\) 0.921437 0.0343638 0.0171819 0.999852i \(-0.494531\pi\)
0.0171819 + 0.999852i \(0.494531\pi\)
\(720\) 2.72649 0.101610
\(721\) −33.2076 −1.23672
\(722\) 24.9604 0.928928
\(723\) −14.2736 −0.530840
\(724\) −17.2753 −0.642031
\(725\) −2.64587 −0.0982651
\(726\) −21.8152 −0.809637
\(727\) 21.5936 0.800862 0.400431 0.916327i \(-0.368860\pi\)
0.400431 + 0.916327i \(0.368860\pi\)
\(728\) 33.1942 1.23026
\(729\) 24.9995 0.925906
\(730\) 5.84053 0.216168
\(731\) 12.7067 0.469974
\(732\) 6.36319 0.235190
\(733\) −22.0973 −0.816183 −0.408092 0.912941i \(-0.633806\pi\)
−0.408092 + 0.912941i \(0.633806\pi\)
\(734\) 1.95947 0.0723255
\(735\) 49.1861 1.81426
\(736\) −9.14392 −0.337050
\(737\) −17.5663 −0.647062
\(738\) 2.36326 0.0869928
\(739\) 42.3637 1.55837 0.779187 0.626792i \(-0.215632\pi\)
0.779187 + 0.626792i \(0.215632\pi\)
\(740\) −14.6099 −0.537069
\(741\) −17.9257 −0.658518
\(742\) 49.2473 1.80792
\(743\) 2.31320 0.0848630 0.0424315 0.999099i \(-0.486490\pi\)
0.0424315 + 0.999099i \(0.486490\pi\)
\(744\) −21.2603 −0.779440
\(745\) −12.9237 −0.473486
\(746\) 36.5508 1.33822
\(747\) 2.77564 0.101555
\(748\) 5.15980 0.188661
\(749\) −51.3801 −1.87739
\(750\) 20.1761 0.736727
\(751\) −18.2167 −0.664736 −0.332368 0.943150i \(-0.607848\pi\)
−0.332368 + 0.943150i \(0.607848\pi\)
\(752\) 20.1839 0.736030
\(753\) −36.3676 −1.32531
\(754\) −8.10195 −0.295056
\(755\) −6.55100 −0.238415
\(756\) −20.7308 −0.753972
\(757\) 12.5485 0.456083 0.228041 0.973651i \(-0.426768\pi\)
0.228041 + 0.973651i \(0.426768\pi\)
\(758\) −61.7456 −2.24270
\(759\) −6.23804 −0.226427
\(760\) 10.2316 0.371137
\(761\) 24.6831 0.894763 0.447382 0.894343i \(-0.352357\pi\)
0.447382 + 0.894343i \(0.352357\pi\)
\(762\) −3.51628 −0.127381
\(763\) 27.5457 0.997223
\(764\) 4.88847 0.176859
\(765\) 1.40685 0.0508647
\(766\) 3.08575 0.111493
\(767\) 51.9305 1.87510
\(768\) −34.0587 −1.22899
\(769\) −35.7018 −1.28744 −0.643720 0.765261i \(-0.722610\pi\)
−0.643720 + 0.765261i \(0.722610\pi\)
\(770\) 39.2758 1.41540
\(771\) −42.0477 −1.51431
\(772\) −25.6652 −0.923712
\(773\) −7.51031 −0.270127 −0.135064 0.990837i \(-0.543124\pi\)
−0.135064 + 0.990837i \(0.543124\pi\)
\(774\) 1.68365 0.0605175
\(775\) 18.2361 0.655062
\(776\) 29.3479 1.05353
\(777\) 38.7080 1.38864
\(778\) −2.49082 −0.0893003
\(779\) 14.8283 0.531278
\(780\) −23.2199 −0.831404
\(781\) −2.62986 −0.0941036
\(782\) −7.83862 −0.280308
\(783\) −5.01160 −0.179100
\(784\) −49.7406 −1.77645
\(785\) −26.7044 −0.953122
\(786\) −54.6205 −1.94825
\(787\) 4.92388 0.175518 0.0877588 0.996142i \(-0.472030\pi\)
0.0877588 + 0.996142i \(0.472030\pi\)
\(788\) −3.95716 −0.140968
\(789\) 33.1129 1.17885
\(790\) −66.4582 −2.36448
\(791\) −67.0349 −2.38349
\(792\) −0.677149 −0.0240614
\(793\) 16.5536 0.587836
\(794\) 66.5779 2.36276
\(795\) 34.1202 1.21012
\(796\) 8.96774 0.317853
\(797\) −44.0689 −1.56100 −0.780499 0.625157i \(-0.785035\pi\)
−0.780499 + 0.625157i \(0.785035\pi\)
\(798\) 27.3693 0.968862
\(799\) 10.4147 0.368446
\(800\) 13.8032 0.488018
\(801\) 1.56014 0.0551247
\(802\) 27.5545 0.972985
\(803\) −2.42534 −0.0855885
\(804\) −15.8563 −0.559208
\(805\) −19.9524 −0.703230
\(806\) 55.8412 1.96692
\(807\) −46.4634 −1.63559
\(808\) 2.77256 0.0975382
\(809\) 35.8140 1.25915 0.629577 0.776938i \(-0.283228\pi\)
0.629577 + 0.776938i \(0.283228\pi\)
\(810\) −45.7877 −1.60881
\(811\) −28.5435 −1.00230 −0.501149 0.865361i \(-0.667089\pi\)
−0.501149 + 0.865361i \(0.667089\pi\)
\(812\) 4.13657 0.145165
\(813\) 36.4359 1.27786
\(814\) 18.1428 0.635905
\(815\) −3.88307 −0.136018
\(816\) −23.0656 −0.807458
\(817\) 10.5640 0.369589
\(818\) 11.3127 0.395540
\(819\) 3.79460 0.132594
\(820\) 19.2076 0.670759
\(821\) 0.641300 0.0223815 0.0111908 0.999937i \(-0.496438\pi\)
0.0111908 + 0.999937i \(0.496438\pi\)
\(822\) −50.1300 −1.74848
\(823\) 17.8126 0.620907 0.310453 0.950589i \(-0.399519\pi\)
0.310453 + 0.950589i \(0.399519\pi\)
\(824\) 13.9154 0.484766
\(825\) 9.41664 0.327845
\(826\) −79.2883 −2.75879
\(827\) 38.6438 1.34378 0.671889 0.740652i \(-0.265483\pi\)
0.671889 + 0.740652i \(0.265483\pi\)
\(828\) −0.347313 −0.0120700
\(829\) 39.9589 1.38783 0.693916 0.720056i \(-0.255884\pi\)
0.693916 + 0.720056i \(0.255884\pi\)
\(830\) 67.4622 2.34165
\(831\) −3.26538 −0.113275
\(832\) −4.47202 −0.155039
\(833\) −25.6658 −0.889267
\(834\) −3.09951 −0.107327
\(835\) −64.3142 −2.22568
\(836\) 4.28973 0.148363
\(837\) 34.5415 1.19393
\(838\) −30.2420 −1.04469
\(839\) −1.46409 −0.0505462 −0.0252731 0.999681i \(-0.508046\pi\)
−0.0252731 + 0.999681i \(0.508046\pi\)
\(840\) −35.1139 −1.21155
\(841\) 1.00000 0.0344828
\(842\) −37.3598 −1.28750
\(843\) −6.52096 −0.224594
\(844\) −16.8532 −0.580111
\(845\) −24.4591 −0.841420
\(846\) 1.37996 0.0474440
\(847\) 28.9753 0.995602
\(848\) −34.5049 −1.18490
\(849\) 3.13845 0.107711
\(850\) 11.8328 0.405861
\(851\) −9.21668 −0.315944
\(852\) −2.37385 −0.0813268
\(853\) 57.5784 1.97145 0.985723 0.168376i \(-0.0538522\pi\)
0.985723 + 0.168376i \(0.0538522\pi\)
\(854\) −25.2743 −0.864870
\(855\) 1.16962 0.0400002
\(856\) 21.5304 0.735894
\(857\) 8.96067 0.306091 0.153045 0.988219i \(-0.451092\pi\)
0.153045 + 0.988219i \(0.451092\pi\)
\(858\) 28.8348 0.984405
\(859\) −37.8543 −1.29157 −0.645786 0.763518i \(-0.723470\pi\)
−0.645786 + 0.763518i \(0.723470\pi\)
\(860\) 13.6840 0.466620
\(861\) −50.8895 −1.73431
\(862\) 30.7510 1.04738
\(863\) 14.1478 0.481596 0.240798 0.970575i \(-0.422591\pi\)
0.240798 + 0.970575i \(0.422591\pi\)
\(864\) 26.1450 0.889471
\(865\) −9.36623 −0.318461
\(866\) 57.7482 1.96236
\(867\) 18.4956 0.628142
\(868\) −28.5105 −0.967709
\(869\) 27.5975 0.936182
\(870\) 8.57050 0.290567
\(871\) −41.2496 −1.39769
\(872\) −11.5428 −0.390889
\(873\) 3.35490 0.113546
\(874\) −6.51684 −0.220435
\(875\) −26.7982 −0.905944
\(876\) −2.18925 −0.0739678
\(877\) 1.85034 0.0624817 0.0312408 0.999512i \(-0.490054\pi\)
0.0312408 + 0.999512i \(0.490054\pi\)
\(878\) −68.5547 −2.31361
\(879\) −18.9764 −0.640057
\(880\) −27.5184 −0.927647
\(881\) −53.7460 −1.81075 −0.905375 0.424613i \(-0.860410\pi\)
−0.905375 + 0.424613i \(0.860410\pi\)
\(882\) −3.40074 −0.114509
\(883\) 28.7143 0.966312 0.483156 0.875534i \(-0.339490\pi\)
0.483156 + 0.875534i \(0.339490\pi\)
\(884\) 12.1164 0.407517
\(885\) −54.9337 −1.84658
\(886\) −62.1894 −2.08929
\(887\) −13.0560 −0.438377 −0.219188 0.975683i \(-0.570341\pi\)
−0.219188 + 0.975683i \(0.570341\pi\)
\(888\) −16.2203 −0.544317
\(889\) 4.67038 0.156639
\(890\) 37.9193 1.27106
\(891\) 19.0139 0.636988
\(892\) −9.46708 −0.316981
\(893\) 8.65856 0.289748
\(894\) 14.4866 0.484503
\(895\) −43.4706 −1.45306
\(896\) 49.7820 1.66310
\(897\) −14.6483 −0.489093
\(898\) 48.5409 1.61983
\(899\) −6.89231 −0.229871
\(900\) 0.524288 0.0174763
\(901\) −17.8043 −0.593147
\(902\) −23.8524 −0.794197
\(903\) −36.2550 −1.20649
\(904\) 28.0904 0.934274
\(905\) 47.5401 1.58029
\(906\) 7.34323 0.243962
\(907\) 43.7318 1.45209 0.726045 0.687648i \(-0.241357\pi\)
0.726045 + 0.687648i \(0.241357\pi\)
\(908\) −18.6639 −0.619383
\(909\) 0.316945 0.0105124
\(910\) 92.2284 3.05734
\(911\) −5.69697 −0.188749 −0.0943746 0.995537i \(-0.530085\pi\)
−0.0943746 + 0.995537i \(0.530085\pi\)
\(912\) −19.1762 −0.634987
\(913\) −28.0145 −0.927143
\(914\) 29.6410 0.980438
\(915\) −17.5109 −0.578894
\(916\) −0.974435 −0.0321962
\(917\) 72.5478 2.39574
\(918\) 22.4128 0.739732
\(919\) 29.1840 0.962691 0.481345 0.876531i \(-0.340148\pi\)
0.481345 + 0.876531i \(0.340148\pi\)
\(920\) 8.36090 0.275651
\(921\) 0.462007 0.0152236
\(922\) −27.9879 −0.921732
\(923\) −6.17549 −0.203269
\(924\) −14.7220 −0.484319
\(925\) 13.9130 0.457458
\(926\) 17.9574 0.590117
\(927\) 1.59074 0.0522467
\(928\) −5.21690 −0.171253
\(929\) 27.8507 0.913750 0.456875 0.889531i \(-0.348969\pi\)
0.456875 + 0.889531i \(0.348969\pi\)
\(930\) −59.0706 −1.93700
\(931\) −21.3379 −0.699323
\(932\) −9.98681 −0.327129
\(933\) −43.6847 −1.43017
\(934\) −19.0031 −0.621799
\(935\) −14.1993 −0.464367
\(936\) −1.59010 −0.0519740
\(937\) −13.5946 −0.444116 −0.222058 0.975033i \(-0.571277\pi\)
−0.222058 + 0.975033i \(0.571277\pi\)
\(938\) 62.9805 2.05639
\(939\) −19.6280 −0.640536
\(940\) 11.2157 0.365817
\(941\) 47.4444 1.54664 0.773322 0.634014i \(-0.218594\pi\)
0.773322 + 0.634014i \(0.218594\pi\)
\(942\) 29.9339 0.975298
\(943\) 12.1172 0.394590
\(944\) 55.5531 1.80810
\(945\) 57.0494 1.85582
\(946\) −16.9930 −0.552492
\(947\) 31.7174 1.03068 0.515338 0.856987i \(-0.327666\pi\)
0.515338 + 0.856987i \(0.327666\pi\)
\(948\) 24.9110 0.809072
\(949\) −5.69525 −0.184876
\(950\) 9.83750 0.319171
\(951\) 47.5453 1.54176
\(952\) 18.3228 0.593846
\(953\) −3.23737 −0.104869 −0.0524343 0.998624i \(-0.516698\pi\)
−0.0524343 + 0.998624i \(0.516698\pi\)
\(954\) −2.35909 −0.0763782
\(955\) −13.4527 −0.435318
\(956\) −11.9179 −0.385454
\(957\) −3.55900 −0.115046
\(958\) −52.8930 −1.70889
\(959\) 66.5834 2.15009
\(960\) 4.73064 0.152681
\(961\) 16.5039 0.532384
\(962\) 42.6033 1.37359
\(963\) 2.46125 0.0793127
\(964\) 8.02095 0.258338
\(965\) 70.6285 2.27361
\(966\) 22.3653 0.719592
\(967\) 41.2621 1.32690 0.663450 0.748221i \(-0.269092\pi\)
0.663450 + 0.748221i \(0.269092\pi\)
\(968\) −12.1419 −0.390254
\(969\) −9.89478 −0.317866
\(970\) 81.5414 2.61814
\(971\) 14.4091 0.462411 0.231206 0.972905i \(-0.425733\pi\)
0.231206 + 0.972905i \(0.425733\pi\)
\(972\) 2.05600 0.0659463
\(973\) 4.11682 0.131979
\(974\) −20.9990 −0.672851
\(975\) 22.1124 0.708163
\(976\) 17.7084 0.566831
\(977\) 43.1375 1.38009 0.690045 0.723766i \(-0.257591\pi\)
0.690045 + 0.723766i \(0.257591\pi\)
\(978\) 4.35266 0.139183
\(979\) −15.7464 −0.503258
\(980\) −27.6398 −0.882922
\(981\) −1.31952 −0.0421290
\(982\) −39.8552 −1.27183
\(983\) −23.1476 −0.738293 −0.369146 0.929371i \(-0.620350\pi\)
−0.369146 + 0.929371i \(0.620350\pi\)
\(984\) 21.3248 0.679811
\(985\) 10.8898 0.346977
\(986\) −4.47218 −0.142423
\(987\) −29.7155 −0.945855
\(988\) 10.0733 0.320473
\(989\) 8.63259 0.274501
\(990\) −1.88142 −0.0597955
\(991\) −32.6835 −1.03823 −0.519113 0.854706i \(-0.673738\pi\)
−0.519113 + 0.854706i \(0.673738\pi\)
\(992\) 35.9565 1.14162
\(993\) 41.4644 1.31583
\(994\) 9.42884 0.299065
\(995\) −24.6785 −0.782360
\(996\) −25.2874 −0.801261
\(997\) 18.0248 0.570852 0.285426 0.958401i \(-0.407865\pi\)
0.285426 + 0.958401i \(0.407865\pi\)
\(998\) −1.96477 −0.0621936
\(999\) 26.3530 0.833773
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 \(a_p\))