Properties

Label 8011.2.a.b.1.10
Level 8011
Weight 2
Character 8011.1
Self dual Yes
Analytic conductor 63.968
Analytic rank 0
Dimension 358
CM No

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Newspace parameters

Level: \( N \) = \( 8011 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8011.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9681570592\)
Analytic rank: \(0\)
Dimension: \(358\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 8011.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.66752 q^{2}\) \(+1.67561 q^{3}\) \(+5.11568 q^{4}\) \(-2.95924 q^{5}\) \(-4.46972 q^{6}\) \(-2.28368 q^{7}\) \(-8.31114 q^{8}\) \(-0.192344 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.66752 q^{2}\) \(+1.67561 q^{3}\) \(+5.11568 q^{4}\) \(-2.95924 q^{5}\) \(-4.46972 q^{6}\) \(-2.28368 q^{7}\) \(-8.31114 q^{8}\) \(-0.192344 q^{9}\) \(+7.89385 q^{10}\) \(-3.02794 q^{11}\) \(+8.57186 q^{12}\) \(+0.947331 q^{13}\) \(+6.09176 q^{14}\) \(-4.95853 q^{15}\) \(+11.9388 q^{16}\) \(+5.89642 q^{17}\) \(+0.513081 q^{18}\) \(-7.66287 q^{19}\) \(-15.1385 q^{20}\) \(-3.82654 q^{21}\) \(+8.07710 q^{22}\) \(-1.63367 q^{23}\) \(-13.9262 q^{24}\) \(+3.75713 q^{25}\) \(-2.52703 q^{26}\) \(-5.34911 q^{27}\) \(-11.6825 q^{28}\) \(+7.16324 q^{29}\) \(+13.2270 q^{30}\) \(-3.55148 q^{31}\) \(-15.2247 q^{32}\) \(-5.07364 q^{33}\) \(-15.7288 q^{34}\) \(+6.75795 q^{35}\) \(-0.983968 q^{36}\) \(-6.75814 q^{37}\) \(+20.4409 q^{38}\) \(+1.58735 q^{39}\) \(+24.5947 q^{40}\) \(-2.81195 q^{41}\) \(+10.2074 q^{42}\) \(-12.3624 q^{43}\) \(-15.4900 q^{44}\) \(+0.569192 q^{45}\) \(+4.35784 q^{46}\) \(-4.25096 q^{47}\) \(+20.0047 q^{48}\) \(-1.78483 q^{49}\) \(-10.0222 q^{50}\) \(+9.88007 q^{51}\) \(+4.84624 q^{52}\) \(-3.22130 q^{53}\) \(+14.2689 q^{54}\) \(+8.96042 q^{55}\) \(+18.9799 q^{56}\) \(-12.8400 q^{57}\) \(-19.1081 q^{58}\) \(-3.55040 q^{59}\) \(-25.3662 q^{60}\) \(-8.64493 q^{61}\) \(+9.47364 q^{62}\) \(+0.439250 q^{63}\) \(+16.7347 q^{64}\) \(-2.80338 q^{65}\) \(+13.5340 q^{66}\) \(+9.86666 q^{67}\) \(+30.1642 q^{68}\) \(-2.73738 q^{69}\) \(-18.0270 q^{70}\) \(+6.24835 q^{71}\) \(+1.59859 q^{72}\) \(+8.63808 q^{73}\) \(+18.0275 q^{74}\) \(+6.29546 q^{75}\) \(-39.2008 q^{76}\) \(+6.91483 q^{77}\) \(-4.23430 q^{78}\) \(-6.90866 q^{79}\) \(-35.3298 q^{80}\) \(-8.38597 q^{81}\) \(+7.50094 q^{82}\) \(+3.20341 q^{83}\) \(-19.5753 q^{84}\) \(-17.4489 q^{85}\) \(+32.9769 q^{86}\) \(+12.0028 q^{87}\) \(+25.1656 q^{88}\) \(+8.25139 q^{89}\) \(-1.51833 q^{90}\) \(-2.16340 q^{91}\) \(-8.35731 q^{92}\) \(-5.95088 q^{93}\) \(+11.3395 q^{94}\) \(+22.6763 q^{95}\) \(-25.5107 q^{96}\) \(-8.96631 q^{97}\) \(+4.76107 q^{98}\) \(+0.582405 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut 21q^{10} \) \(\mathstrut +\mathstrut 70q^{11} \) \(\mathstrut +\mathstrut 20q^{12} \) \(\mathstrut +\mathstrut 53q^{13} \) \(\mathstrut +\mathstrut 69q^{14} \) \(\mathstrut +\mathstrut 28q^{15} \) \(\mathstrut +\mathstrut 449q^{16} \) \(\mathstrut +\mathstrut 88q^{17} \) \(\mathstrut +\mathstrut 86q^{18} \) \(\mathstrut +\mathstrut 44q^{19} \) \(\mathstrut +\mathstrut 136q^{20} \) \(\mathstrut +\mathstrut 125q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 104q^{23} \) \(\mathstrut +\mathstrut 84q^{24} \) \(\mathstrut +\mathstrut 444q^{25} \) \(\mathstrut +\mathstrut 100q^{26} \) \(\mathstrut +\mathstrut 32q^{27} \) \(\mathstrut +\mathstrut 46q^{28} \) \(\mathstrut +\mathstrut 373q^{29} \) \(\mathstrut +\mathstrut 99q^{30} \) \(\mathstrut +\mathstrut 30q^{31} \) \(\mathstrut +\mathstrut 221q^{32} \) \(\mathstrut +\mathstrut 56q^{33} \) \(\mathstrut +\mathstrut 26q^{34} \) \(\mathstrut +\mathstrut 164q^{35} \) \(\mathstrut +\mathstrut 599q^{36} \) \(\mathstrut +\mathstrut 81q^{37} \) \(\mathstrut +\mathstrut 66q^{38} \) \(\mathstrut +\mathstrut 143q^{39} \) \(\mathstrut +\mathstrut 42q^{40} \) \(\mathstrut +\mathstrut 182q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut +\mathstrut 40q^{43} \) \(\mathstrut +\mathstrut 184q^{44} \) \(\mathstrut +\mathstrut 198q^{45} \) \(\mathstrut +\mathstrut 54q^{46} \) \(\mathstrut +\mathstrut 66q^{47} \) \(\mathstrut +\mathstrut 5q^{48} \) \(\mathstrut +\mathstrut 479q^{49} \) \(\mathstrut +\mathstrut 184q^{50} \) \(\mathstrut +\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 64q^{52} \) \(\mathstrut +\mathstrut 221q^{53} \) \(\mathstrut +\mathstrut 67q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 174q^{56} \) \(\mathstrut +\mathstrut 84q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut +\mathstrut 127q^{59} \) \(\mathstrut +\mathstrut 29q^{60} \) \(\mathstrut +\mathstrut 174q^{61} \) \(\mathstrut +\mathstrut 86q^{62} \) \(\mathstrut +\mathstrut 48q^{63} \) \(\mathstrut +\mathstrut 549q^{64} \) \(\mathstrut +\mathstrut 202q^{65} \) \(\mathstrut +\mathstrut 32q^{66} \) \(\mathstrut +\mathstrut 29q^{67} \) \(\mathstrut +\mathstrut 172q^{68} \) \(\mathstrut +\mathstrut 249q^{69} \) \(\mathstrut +\mathstrut 12q^{70} \) \(\mathstrut +\mathstrut 185q^{71} \) \(\mathstrut +\mathstrut 218q^{72} \) \(\mathstrut +\mathstrut 57q^{73} \) \(\mathstrut +\mathstrut 272q^{74} \) \(\mathstrut +\mathstrut 24q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 384q^{77} \) \(\mathstrut +\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 93q^{79} \) \(\mathstrut +\mathstrut 215q^{80} \) \(\mathstrut +\mathstrut 702q^{81} \) \(\mathstrut +\mathstrut 48q^{82} \) \(\mathstrut +\mathstrut 121q^{83} \) \(\mathstrut +\mathstrut 179q^{84} \) \(\mathstrut +\mathstrut 177q^{85} \) \(\mathstrut +\mathstrut 209q^{86} \) \(\mathstrut +\mathstrut 91q^{87} \) \(\mathstrut +\mathstrut 36q^{88} \) \(\mathstrut +\mathstrut 186q^{89} \) \(\mathstrut +\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut +\mathstrut 272q^{92} \) \(\mathstrut +\mathstrut 220q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 170q^{95} \) \(\mathstrut +\mathstrut 162q^{96} \) \(\mathstrut +\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 196q^{98} \) \(\mathstrut +\mathstrut 152q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.66752 −1.88622 −0.943112 0.332476i \(-0.892116\pi\)
−0.943112 + 0.332476i \(0.892116\pi\)
\(3\) 1.67561 0.967412 0.483706 0.875231i \(-0.339290\pi\)
0.483706 + 0.875231i \(0.339290\pi\)
\(4\) 5.11568 2.55784
\(5\) −2.95924 −1.32341 −0.661707 0.749762i \(-0.730168\pi\)
−0.661707 + 0.749762i \(0.730168\pi\)
\(6\) −4.46972 −1.82475
\(7\) −2.28368 −0.863148 −0.431574 0.902078i \(-0.642042\pi\)
−0.431574 + 0.902078i \(0.642042\pi\)
\(8\) −8.31114 −2.93843
\(9\) −0.192344 −0.0641145
\(10\) 7.89385 2.49625
\(11\) −3.02794 −0.912958 −0.456479 0.889734i \(-0.650890\pi\)
−0.456479 + 0.889734i \(0.650890\pi\)
\(12\) 8.57186 2.47448
\(13\) 0.947331 0.262742 0.131371 0.991333i \(-0.458062\pi\)
0.131371 + 0.991333i \(0.458062\pi\)
\(14\) 6.09176 1.62809
\(15\) −4.95853 −1.28029
\(16\) 11.9388 2.98470
\(17\) 5.89642 1.43009 0.715046 0.699078i \(-0.246406\pi\)
0.715046 + 0.699078i \(0.246406\pi\)
\(18\) 0.513081 0.120934
\(19\) −7.66287 −1.75798 −0.878992 0.476837i \(-0.841783\pi\)
−0.878992 + 0.476837i \(0.841783\pi\)
\(20\) −15.1385 −3.38508
\(21\) −3.82654 −0.835020
\(22\) 8.07710 1.72204
\(23\) −1.63367 −0.340643 −0.170322 0.985389i \(-0.554481\pi\)
−0.170322 + 0.985389i \(0.554481\pi\)
\(24\) −13.9262 −2.84267
\(25\) 3.75713 0.751425
\(26\) −2.52703 −0.495590
\(27\) −5.34911 −1.02944
\(28\) −11.6825 −2.20779
\(29\) 7.16324 1.33018 0.665091 0.746763i \(-0.268393\pi\)
0.665091 + 0.746763i \(0.268393\pi\)
\(30\) 13.2270 2.41491
\(31\) −3.55148 −0.637864 −0.318932 0.947778i \(-0.603324\pi\)
−0.318932 + 0.947778i \(0.603324\pi\)
\(32\) −15.2247 −2.69138
\(33\) −5.07364 −0.883207
\(34\) −15.7288 −2.69747
\(35\) 6.75795 1.14230
\(36\) −0.983968 −0.163995
\(37\) −6.75814 −1.11103 −0.555516 0.831506i \(-0.687479\pi\)
−0.555516 + 0.831506i \(0.687479\pi\)
\(38\) 20.4409 3.31595
\(39\) 1.58735 0.254180
\(40\) 24.5947 3.88876
\(41\) −2.81195 −0.439153 −0.219576 0.975595i \(-0.570468\pi\)
−0.219576 + 0.975595i \(0.570468\pi\)
\(42\) 10.2074 1.57503
\(43\) −12.3624 −1.88524 −0.942621 0.333865i \(-0.891647\pi\)
−0.942621 + 0.333865i \(0.891647\pi\)
\(44\) −15.4900 −2.33520
\(45\) 0.569192 0.0848501
\(46\) 4.35784 0.642529
\(47\) −4.25096 −0.620067 −0.310033 0.950726i \(-0.600340\pi\)
−0.310033 + 0.950726i \(0.600340\pi\)
\(48\) 20.0047 2.88743
\(49\) −1.78483 −0.254975
\(50\) −10.0222 −1.41736
\(51\) 9.88007 1.38349
\(52\) 4.84624 0.672052
\(53\) −3.22130 −0.442480 −0.221240 0.975219i \(-0.571010\pi\)
−0.221240 + 0.975219i \(0.571010\pi\)
\(54\) 14.2689 1.94175
\(55\) 8.96042 1.20822
\(56\) 18.9799 2.53630
\(57\) −12.8400 −1.70069
\(58\) −19.1081 −2.50902
\(59\) −3.55040 −0.462223 −0.231112 0.972927i \(-0.574236\pi\)
−0.231112 + 0.972927i \(0.574236\pi\)
\(60\) −25.3662 −3.27477
\(61\) −8.64493 −1.10687 −0.553435 0.832892i \(-0.686683\pi\)
−0.553435 + 0.832892i \(0.686683\pi\)
\(62\) 9.47364 1.20315
\(63\) 0.439250 0.0553403
\(64\) 16.7347 2.09184
\(65\) −2.80338 −0.347717
\(66\) 13.5340 1.66593
\(67\) 9.86666 1.20540 0.602702 0.797966i \(-0.294091\pi\)
0.602702 + 0.797966i \(0.294091\pi\)
\(68\) 30.1642 3.65794
\(69\) −2.73738 −0.329542
\(70\) −18.0270 −2.15464
\(71\) 6.24835 0.741542 0.370771 0.928724i \(-0.379093\pi\)
0.370771 + 0.928724i \(0.379093\pi\)
\(72\) 1.59859 0.188396
\(73\) 8.63808 1.01101 0.505506 0.862823i \(-0.331306\pi\)
0.505506 + 0.862823i \(0.331306\pi\)
\(74\) 18.0275 2.09565
\(75\) 6.29546 0.726937
\(76\) −39.2008 −4.49664
\(77\) 6.91483 0.788018
\(78\) −4.23430 −0.479440
\(79\) −6.90866 −0.777285 −0.388642 0.921389i \(-0.627056\pi\)
−0.388642 + 0.921389i \(0.627056\pi\)
\(80\) −35.3298 −3.94999
\(81\) −8.38597 −0.931775
\(82\) 7.50094 0.828341
\(83\) 3.20341 0.351620 0.175810 0.984424i \(-0.443746\pi\)
0.175810 + 0.984424i \(0.443746\pi\)
\(84\) −19.5753 −2.13585
\(85\) −17.4489 −1.89260
\(86\) 32.9769 3.55599
\(87\) 12.0028 1.28683
\(88\) 25.1656 2.68267
\(89\) 8.25139 0.874646 0.437323 0.899305i \(-0.355927\pi\)
0.437323 + 0.899305i \(0.355927\pi\)
\(90\) −1.51833 −0.160046
\(91\) −2.16340 −0.226785
\(92\) −8.35731 −0.871310
\(93\) −5.95088 −0.617077
\(94\) 11.3395 1.16958
\(95\) 22.6763 2.32654
\(96\) −25.5107 −2.60367
\(97\) −8.96631 −0.910391 −0.455196 0.890391i \(-0.650431\pi\)
−0.455196 + 0.890391i \(0.650431\pi\)
\(98\) 4.76107 0.480940
\(99\) 0.582405 0.0585339
\(100\) 19.2202 1.92202
\(101\) 4.03848 0.401844 0.200922 0.979607i \(-0.435606\pi\)
0.200922 + 0.979607i \(0.435606\pi\)
\(102\) −26.3553 −2.60957
\(103\) 11.3163 1.11502 0.557512 0.830169i \(-0.311756\pi\)
0.557512 + 0.830169i \(0.311756\pi\)
\(104\) −7.87340 −0.772050
\(105\) 11.3237 1.10508
\(106\) 8.59290 0.834616
\(107\) −9.41035 −0.909733 −0.454866 0.890560i \(-0.650313\pi\)
−0.454866 + 0.890560i \(0.650313\pi\)
\(108\) −27.3643 −2.63313
\(109\) −18.6652 −1.78780 −0.893902 0.448263i \(-0.852043\pi\)
−0.893902 + 0.448263i \(0.852043\pi\)
\(110\) −23.9021 −2.27898
\(111\) −11.3240 −1.07482
\(112\) −27.2643 −2.57624
\(113\) 3.91702 0.368482 0.184241 0.982881i \(-0.441017\pi\)
0.184241 + 0.982881i \(0.441017\pi\)
\(114\) 34.2509 3.20789
\(115\) 4.83442 0.450812
\(116\) 36.6448 3.40239
\(117\) −0.182213 −0.0168456
\(118\) 9.47078 0.871856
\(119\) −13.4655 −1.23438
\(120\) 41.2110 3.76203
\(121\) −1.83158 −0.166507
\(122\) 23.0605 2.08780
\(123\) −4.71172 −0.424842
\(124\) −18.1682 −1.63155
\(125\) 3.67797 0.328968
\(126\) −1.17171 −0.104384
\(127\) −16.4276 −1.45771 −0.728855 0.684668i \(-0.759947\pi\)
−0.728855 + 0.684668i \(0.759947\pi\)
\(128\) −14.1908 −1.25430
\(129\) −20.7144 −1.82381
\(130\) 7.47809 0.655871
\(131\) −1.69660 −0.148233 −0.0741164 0.997250i \(-0.523614\pi\)
−0.0741164 + 0.997250i \(0.523614\pi\)
\(132\) −25.9551 −2.25910
\(133\) 17.4995 1.51740
\(134\) −26.3195 −2.27366
\(135\) 15.8293 1.36237
\(136\) −49.0060 −4.20223
\(137\) −22.5290 −1.92478 −0.962391 0.271667i \(-0.912425\pi\)
−0.962391 + 0.271667i \(0.912425\pi\)
\(138\) 7.30203 0.621590
\(139\) 16.1229 1.36753 0.683763 0.729704i \(-0.260342\pi\)
0.683763 + 0.729704i \(0.260342\pi\)
\(140\) 34.5715 2.92183
\(141\) −7.12294 −0.599860
\(142\) −16.6676 −1.39871
\(143\) −2.86846 −0.239873
\(144\) −2.29635 −0.191363
\(145\) −21.1978 −1.76038
\(146\) −23.0423 −1.90699
\(147\) −2.99067 −0.246666
\(148\) −34.5725 −2.84184
\(149\) −16.9777 −1.39086 −0.695432 0.718592i \(-0.744787\pi\)
−0.695432 + 0.718592i \(0.744787\pi\)
\(150\) −16.7933 −1.37117
\(151\) −15.3917 −1.25256 −0.626279 0.779599i \(-0.715423\pi\)
−0.626279 + 0.779599i \(0.715423\pi\)
\(152\) 63.6872 5.16571
\(153\) −1.13414 −0.0916896
\(154\) −18.4455 −1.48638
\(155\) 10.5097 0.844158
\(156\) 8.12039 0.650151
\(157\) 18.8211 1.50209 0.751045 0.660251i \(-0.229550\pi\)
0.751045 + 0.660251i \(0.229550\pi\)
\(158\) 18.4290 1.46613
\(159\) −5.39763 −0.428060
\(160\) 45.0537 3.56181
\(161\) 3.73076 0.294025
\(162\) 22.3698 1.75754
\(163\) −18.2232 −1.42735 −0.713677 0.700475i \(-0.752972\pi\)
−0.713677 + 0.700475i \(0.752972\pi\)
\(164\) −14.3850 −1.12328
\(165\) 15.0141 1.16885
\(166\) −8.54518 −0.663234
\(167\) −5.14879 −0.398426 −0.199213 0.979956i \(-0.563839\pi\)
−0.199213 + 0.979956i \(0.563839\pi\)
\(168\) 31.8029 2.45365
\(169\) −12.1026 −0.930967
\(170\) 46.5454 3.56987
\(171\) 1.47390 0.112712
\(172\) −63.2418 −4.82215
\(173\) 5.86979 0.446272 0.223136 0.974787i \(-0.428371\pi\)
0.223136 + 0.974787i \(0.428371\pi\)
\(174\) −32.0177 −2.42725
\(175\) −8.58005 −0.648591
\(176\) −36.1500 −2.72491
\(177\) −5.94908 −0.447160
\(178\) −22.0108 −1.64978
\(179\) −12.6060 −0.942213 −0.471107 0.882076i \(-0.656145\pi\)
−0.471107 + 0.882076i \(0.656145\pi\)
\(180\) 2.91180 0.217033
\(181\) 18.1081 1.34596 0.672981 0.739660i \(-0.265014\pi\)
0.672981 + 0.739660i \(0.265014\pi\)
\(182\) 5.77091 0.427768
\(183\) −14.4855 −1.07080
\(184\) 13.5776 1.00096
\(185\) 19.9990 1.47035
\(186\) 15.8741 1.16395
\(187\) −17.8540 −1.30561
\(188\) −21.7466 −1.58603
\(189\) 12.2156 0.888557
\(190\) −60.4896 −4.38837
\(191\) −1.74370 −0.126170 −0.0630848 0.998008i \(-0.520094\pi\)
−0.0630848 + 0.998008i \(0.520094\pi\)
\(192\) 28.0408 2.02367
\(193\) 2.25746 0.162495 0.0812477 0.996694i \(-0.474110\pi\)
0.0812477 + 0.996694i \(0.474110\pi\)
\(194\) 23.9178 1.71720
\(195\) −4.69736 −0.336385
\(196\) −9.13060 −0.652186
\(197\) 5.47249 0.389898 0.194949 0.980813i \(-0.437546\pi\)
0.194949 + 0.980813i \(0.437546\pi\)
\(198\) −1.55358 −0.110408
\(199\) 1.28842 0.0913338 0.0456669 0.998957i \(-0.485459\pi\)
0.0456669 + 0.998957i \(0.485459\pi\)
\(200\) −31.2260 −2.20801
\(201\) 16.5326 1.16612
\(202\) −10.7727 −0.757967
\(203\) −16.3585 −1.14814
\(204\) 50.5433 3.53874
\(205\) 8.32125 0.581181
\(206\) −30.1864 −2.10319
\(207\) 0.314225 0.0218402
\(208\) 11.3100 0.784207
\(209\) 23.2027 1.60497
\(210\) −30.2061 −2.08442
\(211\) 3.27165 0.225230 0.112615 0.993639i \(-0.464077\pi\)
0.112615 + 0.993639i \(0.464077\pi\)
\(212\) −16.4791 −1.13179
\(213\) 10.4698 0.717377
\(214\) 25.1023 1.71596
\(215\) 36.5832 2.49496
\(216\) 44.4572 3.02493
\(217\) 8.11042 0.550571
\(218\) 49.7899 3.37220
\(219\) 14.4740 0.978064
\(220\) 45.8386 3.09044
\(221\) 5.58586 0.375745
\(222\) 30.2070 2.02736
\(223\) −12.5804 −0.842448 −0.421224 0.906957i \(-0.638399\pi\)
−0.421224 + 0.906957i \(0.638399\pi\)
\(224\) 34.7684 2.32306
\(225\) −0.722659 −0.0481773
\(226\) −10.4487 −0.695040
\(227\) 28.8962 1.91791 0.958955 0.283558i \(-0.0915149\pi\)
0.958955 + 0.283558i \(0.0915149\pi\)
\(228\) −65.6851 −4.35010
\(229\) 1.04679 0.0691738 0.0345869 0.999402i \(-0.488988\pi\)
0.0345869 + 0.999402i \(0.488988\pi\)
\(230\) −12.8959 −0.850332
\(231\) 11.5865 0.762338
\(232\) −59.5347 −3.90865
\(233\) 11.6114 0.760685 0.380343 0.924846i \(-0.375806\pi\)
0.380343 + 0.924846i \(0.375806\pi\)
\(234\) 0.486057 0.0317746
\(235\) 12.5796 0.820605
\(236\) −18.1627 −1.18229
\(237\) −11.5762 −0.751954
\(238\) 35.9195 2.32832
\(239\) 4.91271 0.317777 0.158888 0.987297i \(-0.449209\pi\)
0.158888 + 0.987297i \(0.449209\pi\)
\(240\) −59.1989 −3.82127
\(241\) 22.7747 1.46704 0.733522 0.679665i \(-0.237875\pi\)
0.733522 + 0.679665i \(0.237875\pi\)
\(242\) 4.88577 0.314069
\(243\) 1.99574 0.128027
\(244\) −44.2247 −2.83119
\(245\) 5.28174 0.337438
\(246\) 12.5686 0.801346
\(247\) −7.25927 −0.461896
\(248\) 29.5168 1.87432
\(249\) 5.36766 0.340162
\(250\) −9.81107 −0.620506
\(251\) −11.1052 −0.700957 −0.350479 0.936571i \(-0.613981\pi\)
−0.350479 + 0.936571i \(0.613981\pi\)
\(252\) 2.24706 0.141552
\(253\) 4.94665 0.310993
\(254\) 43.8209 2.74957
\(255\) −29.2376 −1.83093
\(256\) 4.38484 0.274052
\(257\) 14.4664 0.902386 0.451193 0.892426i \(-0.350999\pi\)
0.451193 + 0.892426i \(0.350999\pi\)
\(258\) 55.2563 3.44010
\(259\) 15.4334 0.958985
\(260\) −14.3412 −0.889403
\(261\) −1.37780 −0.0852839
\(262\) 4.52572 0.279600
\(263\) −26.0580 −1.60680 −0.803402 0.595437i \(-0.796979\pi\)
−0.803402 + 0.595437i \(0.796979\pi\)
\(264\) 42.1677 2.59524
\(265\) 9.53262 0.585584
\(266\) −46.6803 −2.86216
\(267\) 13.8261 0.846142
\(268\) 50.4746 3.08323
\(269\) 0.895258 0.0545848 0.0272924 0.999627i \(-0.491311\pi\)
0.0272924 + 0.999627i \(0.491311\pi\)
\(270\) −42.2251 −2.56974
\(271\) −0.566173 −0.0343926 −0.0171963 0.999852i \(-0.505474\pi\)
−0.0171963 + 0.999852i \(0.505474\pi\)
\(272\) 70.3961 4.26839
\(273\) −3.62500 −0.219395
\(274\) 60.0966 3.63057
\(275\) −11.3764 −0.686020
\(276\) −14.0036 −0.842916
\(277\) −8.10132 −0.486761 −0.243381 0.969931i \(-0.578256\pi\)
−0.243381 + 0.969931i \(0.578256\pi\)
\(278\) −43.0082 −2.57946
\(279\) 0.683104 0.0408964
\(280\) −56.1663 −3.35658
\(281\) 9.16231 0.546578 0.273289 0.961932i \(-0.411889\pi\)
0.273289 + 0.961932i \(0.411889\pi\)
\(282\) 19.0006 1.13147
\(283\) −21.9242 −1.30326 −0.651628 0.758538i \(-0.725914\pi\)
−0.651628 + 0.758538i \(0.725914\pi\)
\(284\) 31.9645 1.89675
\(285\) 37.9966 2.25072
\(286\) 7.65168 0.452454
\(287\) 6.42158 0.379054
\(288\) 2.92838 0.172557
\(289\) 17.7677 1.04516
\(290\) 56.5456 3.32047
\(291\) −15.0240 −0.880723
\(292\) 44.1896 2.58600
\(293\) −7.44075 −0.434693 −0.217347 0.976094i \(-0.569740\pi\)
−0.217347 + 0.976094i \(0.569740\pi\)
\(294\) 7.97767 0.465267
\(295\) 10.5065 0.611713
\(296\) 56.1678 3.26469
\(297\) 16.1968 0.939833
\(298\) 45.2883 2.62348
\(299\) −1.54762 −0.0895013
\(300\) 32.2056 1.85939
\(301\) 28.2316 1.62724
\(302\) 41.0577 2.36260
\(303\) 6.76690 0.388749
\(304\) −91.4855 −5.24705
\(305\) 25.5825 1.46485
\(306\) 3.02534 0.172947
\(307\) −12.2830 −0.701028 −0.350514 0.936557i \(-0.613993\pi\)
−0.350514 + 0.936557i \(0.613993\pi\)
\(308\) 35.3741 2.01562
\(309\) 18.9616 1.07869
\(310\) −28.0348 −1.59227
\(311\) 19.9688 1.13233 0.566164 0.824293i \(-0.308427\pi\)
0.566164 + 0.824293i \(0.308427\pi\)
\(312\) −13.1927 −0.746890
\(313\) 6.40673 0.362130 0.181065 0.983471i \(-0.442046\pi\)
0.181065 + 0.983471i \(0.442046\pi\)
\(314\) −50.2058 −2.83328
\(315\) −1.29985 −0.0732382
\(316\) −35.3425 −1.98817
\(317\) −7.96801 −0.447528 −0.223764 0.974643i \(-0.571834\pi\)
−0.223764 + 0.974643i \(0.571834\pi\)
\(318\) 14.3983 0.807417
\(319\) −21.6899 −1.21440
\(320\) −49.5222 −2.76837
\(321\) −15.7680 −0.880086
\(322\) −9.95190 −0.554598
\(323\) −45.1835 −2.51408
\(324\) −42.8999 −2.38333
\(325\) 3.55924 0.197431
\(326\) 48.6109 2.69231
\(327\) −31.2756 −1.72954
\(328\) 23.3705 1.29042
\(329\) 9.70782 0.535210
\(330\) −40.0505 −2.20471
\(331\) 9.40042 0.516694 0.258347 0.966052i \(-0.416822\pi\)
0.258347 + 0.966052i \(0.416822\pi\)
\(332\) 16.3876 0.899388
\(333\) 1.29988 0.0712333
\(334\) 13.7345 0.751520
\(335\) −29.1979 −1.59525
\(336\) −45.6843 −2.49228
\(337\) −8.67640 −0.472634 −0.236317 0.971676i \(-0.575940\pi\)
−0.236317 + 0.971676i \(0.575940\pi\)
\(338\) 32.2839 1.75601
\(339\) 6.56338 0.356474
\(340\) −89.2631 −4.84097
\(341\) 10.7537 0.582343
\(342\) −3.93167 −0.212601
\(343\) 20.0617 1.08323
\(344\) 102.745 5.53966
\(345\) 8.10058 0.436121
\(346\) −15.6578 −0.841768
\(347\) 9.07737 0.487299 0.243649 0.969863i \(-0.421655\pi\)
0.243649 + 0.969863i \(0.421655\pi\)
\(348\) 61.4023 3.29151
\(349\) 34.0324 1.82171 0.910857 0.412723i \(-0.135422\pi\)
0.910857 + 0.412723i \(0.135422\pi\)
\(350\) 22.8875 1.22339
\(351\) −5.06738 −0.270477
\(352\) 46.0996 2.45712
\(353\) −1.92632 −0.102528 −0.0512639 0.998685i \(-0.516325\pi\)
−0.0512639 + 0.998685i \(0.516325\pi\)
\(354\) 15.8693 0.843444
\(355\) −18.4904 −0.981368
\(356\) 42.2114 2.23720
\(357\) −22.5629 −1.19415
\(358\) 33.6267 1.77722
\(359\) −12.6811 −0.669283 −0.334641 0.942346i \(-0.608615\pi\)
−0.334641 + 0.942346i \(0.608615\pi\)
\(360\) −4.73063 −0.249326
\(361\) 39.7196 2.09051
\(362\) −48.3037 −2.53878
\(363\) −3.06900 −0.161081
\(364\) −11.0672 −0.580081
\(365\) −25.5622 −1.33799
\(366\) 38.6404 2.01977
\(367\) −12.8098 −0.668667 −0.334334 0.942455i \(-0.608511\pi\)
−0.334334 + 0.942455i \(0.608511\pi\)
\(368\) −19.5040 −1.01672
\(369\) 0.540861 0.0281561
\(370\) −53.3477 −2.77342
\(371\) 7.35641 0.381926
\(372\) −30.4428 −1.57838
\(373\) −12.6473 −0.654852 −0.327426 0.944877i \(-0.606181\pi\)
−0.327426 + 0.944877i \(0.606181\pi\)
\(374\) 47.6260 2.46268
\(375\) 6.16283 0.318247
\(376\) 35.3304 1.82202
\(377\) 6.78596 0.349495
\(378\) −32.5855 −1.67602
\(379\) 30.0712 1.54465 0.772327 0.635225i \(-0.219093\pi\)
0.772327 + 0.635225i \(0.219093\pi\)
\(380\) 116.005 5.95091
\(381\) −27.5261 −1.41021
\(382\) 4.65136 0.237984
\(383\) 31.8222 1.62604 0.813018 0.582238i \(-0.197823\pi\)
0.813018 + 0.582238i \(0.197823\pi\)
\(384\) −23.7782 −1.21343
\(385\) −20.4627 −1.04287
\(386\) −6.02182 −0.306503
\(387\) 2.37782 0.120871
\(388\) −45.8688 −2.32863
\(389\) −0.700445 −0.0355140 −0.0177570 0.999842i \(-0.505653\pi\)
−0.0177570 + 0.999842i \(0.505653\pi\)
\(390\) 12.5303 0.634498
\(391\) −9.63278 −0.487151
\(392\) 14.8339 0.749227
\(393\) −2.84284 −0.143402
\(394\) −14.5980 −0.735436
\(395\) 20.4444 1.02867
\(396\) 2.97940 0.149720
\(397\) 38.4405 1.92927 0.964637 0.263581i \(-0.0849037\pi\)
0.964637 + 0.263581i \(0.0849037\pi\)
\(398\) −3.43689 −0.172276
\(399\) 29.3223 1.46795
\(400\) 44.8556 2.24278
\(401\) −20.3458 −1.01602 −0.508010 0.861351i \(-0.669619\pi\)
−0.508010 + 0.861351i \(0.669619\pi\)
\(402\) −44.1012 −2.19957
\(403\) −3.36442 −0.167594
\(404\) 20.6596 1.02785
\(405\) 24.8161 1.23312
\(406\) 43.6367 2.16565
\(407\) 20.4632 1.01433
\(408\) −82.1147 −4.06528
\(409\) 8.89191 0.439677 0.219838 0.975536i \(-0.429447\pi\)
0.219838 + 0.975536i \(0.429447\pi\)
\(410\) −22.1971 −1.09624
\(411\) −37.7497 −1.86206
\(412\) 57.8903 2.85205
\(413\) 8.10797 0.398967
\(414\) −0.838203 −0.0411954
\(415\) −9.47968 −0.465339
\(416\) −14.4229 −0.707139
\(417\) 27.0156 1.32296
\(418\) −61.8938 −3.02732
\(419\) −14.8732 −0.726603 −0.363301 0.931672i \(-0.618350\pi\)
−0.363301 + 0.931672i \(0.618350\pi\)
\(420\) 57.9282 2.82661
\(421\) −1.42604 −0.0695008 −0.0347504 0.999396i \(-0.511064\pi\)
−0.0347504 + 0.999396i \(0.511064\pi\)
\(422\) −8.72720 −0.424834
\(423\) 0.817646 0.0397553
\(424\) 26.7727 1.30020
\(425\) 22.1536 1.07461
\(426\) −27.9283 −1.35313
\(427\) 19.7422 0.955393
\(428\) −48.1403 −2.32695
\(429\) −4.80641 −0.232056
\(430\) −97.5866 −4.70604
\(431\) −10.4355 −0.502660 −0.251330 0.967901i \(-0.580868\pi\)
−0.251330 + 0.967901i \(0.580868\pi\)
\(432\) −63.8620 −3.07256
\(433\) −23.0379 −1.10713 −0.553565 0.832806i \(-0.686733\pi\)
−0.553565 + 0.832806i \(0.686733\pi\)
\(434\) −21.6347 −1.03850
\(435\) −35.5191 −1.70301
\(436\) −95.4852 −4.57291
\(437\) 12.5186 0.598845
\(438\) −38.6098 −1.84485
\(439\) −15.7702 −0.752669 −0.376334 0.926484i \(-0.622816\pi\)
−0.376334 + 0.926484i \(0.622816\pi\)
\(440\) −74.4713 −3.55028
\(441\) 0.343300 0.0163476
\(442\) −14.9004 −0.708740
\(443\) −13.9520 −0.662882 −0.331441 0.943476i \(-0.607535\pi\)
−0.331441 + 0.943476i \(0.607535\pi\)
\(444\) −57.9298 −2.74923
\(445\) −24.4179 −1.15752
\(446\) 33.5586 1.58904
\(447\) −28.4479 −1.34554
\(448\) −38.2167 −1.80557
\(449\) −0.593025 −0.0279866 −0.0139933 0.999902i \(-0.504454\pi\)
−0.0139933 + 0.999902i \(0.504454\pi\)
\(450\) 1.92771 0.0908731
\(451\) 8.51442 0.400928
\(452\) 20.0382 0.942518
\(453\) −25.7904 −1.21174
\(454\) −77.0813 −3.61761
\(455\) 6.40201 0.300131
\(456\) 106.715 4.99737
\(457\) 13.4204 0.627779 0.313890 0.949459i \(-0.398368\pi\)
0.313890 + 0.949459i \(0.398368\pi\)
\(458\) −2.79233 −0.130477
\(459\) −31.5406 −1.47219
\(460\) 24.7313 1.15310
\(461\) 20.2794 0.944504 0.472252 0.881463i \(-0.343441\pi\)
0.472252 + 0.881463i \(0.343441\pi\)
\(462\) −30.9074 −1.43794
\(463\) −41.0949 −1.90984 −0.954921 0.296861i \(-0.904060\pi\)
−0.954921 + 0.296861i \(0.904060\pi\)
\(464\) 85.5205 3.97019
\(465\) 17.6101 0.816649
\(466\) −30.9736 −1.43482
\(467\) 22.0758 1.02155 0.510773 0.859716i \(-0.329359\pi\)
0.510773 + 0.859716i \(0.329359\pi\)
\(468\) −0.932143 −0.0430883
\(469\) −22.5322 −1.04044
\(470\) −33.5565 −1.54784
\(471\) 31.5368 1.45314
\(472\) 29.5079 1.35821
\(473\) 37.4325 1.72115
\(474\) 30.8797 1.41835
\(475\) −28.7904 −1.32099
\(476\) −68.8852 −3.15735
\(477\) 0.619597 0.0283694
\(478\) −13.1048 −0.599398
\(479\) 15.1393 0.691734 0.345867 0.938284i \(-0.387585\pi\)
0.345867 + 0.938284i \(0.387585\pi\)
\(480\) 75.4923 3.44574
\(481\) −6.40219 −0.291915
\(482\) −60.7519 −2.76717
\(483\) 6.25129 0.284444
\(484\) −9.36975 −0.425898
\(485\) 26.5335 1.20482
\(486\) −5.32369 −0.241488
\(487\) −5.66374 −0.256649 −0.128324 0.991732i \(-0.540960\pi\)
−0.128324 + 0.991732i \(0.540960\pi\)
\(488\) 71.8492 3.25246
\(489\) −30.5350 −1.38084
\(490\) −14.0892 −0.636483
\(491\) −10.3558 −0.467351 −0.233676 0.972315i \(-0.575075\pi\)
−0.233676 + 0.972315i \(0.575075\pi\)
\(492\) −24.1037 −1.08668
\(493\) 42.2375 1.90228
\(494\) 19.3643 0.871240
\(495\) −1.72348 −0.0774646
\(496\) −42.4004 −1.90383
\(497\) −14.2692 −0.640061
\(498\) −14.3184 −0.641621
\(499\) 37.0368 1.65799 0.828997 0.559253i \(-0.188912\pi\)
0.828997 + 0.559253i \(0.188912\pi\)
\(500\) 18.8153 0.841446
\(501\) −8.62735 −0.385442
\(502\) 29.6235 1.32216
\(503\) 22.9747 1.02439 0.512195 0.858869i \(-0.328832\pi\)
0.512195 + 0.858869i \(0.328832\pi\)
\(504\) −3.65067 −0.162614
\(505\) −11.9509 −0.531806
\(506\) −13.1953 −0.586602
\(507\) −20.2791 −0.900628
\(508\) −84.0381 −3.72859
\(509\) 25.8533 1.14593 0.572964 0.819581i \(-0.305793\pi\)
0.572964 + 0.819581i \(0.305793\pi\)
\(510\) 77.9918 3.45354
\(511\) −19.7266 −0.872652
\(512\) 16.6850 0.737378
\(513\) 40.9896 1.80973
\(514\) −38.5893 −1.70210
\(515\) −33.4876 −1.47564
\(516\) −105.968 −4.66500
\(517\) 12.8717 0.566095
\(518\) −41.1689 −1.80886
\(519\) 9.83545 0.431728
\(520\) 23.2993 1.02174
\(521\) −10.8019 −0.473239 −0.236619 0.971602i \(-0.576039\pi\)
−0.236619 + 0.971602i \(0.576039\pi\)
\(522\) 3.67532 0.160865
\(523\) 14.7037 0.642946 0.321473 0.946919i \(-0.395822\pi\)
0.321473 + 0.946919i \(0.395822\pi\)
\(524\) −8.67927 −0.379156
\(525\) −14.3768 −0.627455
\(526\) 69.5103 3.03079
\(527\) −20.9410 −0.912204
\(528\) −60.5731 −2.63611
\(529\) −20.3311 −0.883962
\(530\) −25.4285 −1.10454
\(531\) 0.682898 0.0296352
\(532\) 89.5219 3.88126
\(533\) −2.66385 −0.115384
\(534\) −36.8814 −1.59601
\(535\) 27.8475 1.20395
\(536\) −82.0032 −3.54200
\(537\) −21.1226 −0.911508
\(538\) −2.38812 −0.102959
\(539\) 5.40435 0.232782
\(540\) 80.9777 3.48473
\(541\) 10.8235 0.465337 0.232669 0.972556i \(-0.425254\pi\)
0.232669 + 0.972556i \(0.425254\pi\)
\(542\) 1.51028 0.0648721
\(543\) 30.3420 1.30210
\(544\) −89.7714 −3.84892
\(545\) 55.2349 2.36600
\(546\) 9.66977 0.413828
\(547\) 38.6655 1.65322 0.826609 0.562777i \(-0.190267\pi\)
0.826609 + 0.562777i \(0.190267\pi\)
\(548\) −115.251 −4.92328
\(549\) 1.66280 0.0709664
\(550\) 30.3467 1.29399
\(551\) −54.8910 −2.33844
\(552\) 22.7508 0.968337
\(553\) 15.7771 0.670912
\(554\) 21.6105 0.918140
\(555\) 33.5104 1.42244
\(556\) 82.4795 3.49791
\(557\) 11.4708 0.486033 0.243017 0.970022i \(-0.421863\pi\)
0.243017 + 0.970022i \(0.421863\pi\)
\(558\) −1.82219 −0.0771397
\(559\) −11.7112 −0.495333
\(560\) 80.6818 3.40943
\(561\) −29.9163 −1.26307
\(562\) −24.4407 −1.03097
\(563\) −19.1123 −0.805486 −0.402743 0.915313i \(-0.631943\pi\)
−0.402743 + 0.915313i \(0.631943\pi\)
\(564\) −36.4387 −1.53435
\(565\) −11.5914 −0.487654
\(566\) 58.4832 2.45823
\(567\) 19.1508 0.804260
\(568\) −51.9309 −2.17897
\(569\) 38.9786 1.63407 0.817034 0.576589i \(-0.195617\pi\)
0.817034 + 0.576589i \(0.195617\pi\)
\(570\) −101.357 −4.24536
\(571\) 2.17452 0.0910008 0.0455004 0.998964i \(-0.485512\pi\)
0.0455004 + 0.998964i \(0.485512\pi\)
\(572\) −14.6741 −0.613556
\(573\) −2.92175 −0.122058
\(574\) −17.1297 −0.714981
\(575\) −6.13789 −0.255968
\(576\) −3.21882 −0.134117
\(577\) −14.4405 −0.601165 −0.300583 0.953756i \(-0.597181\pi\)
−0.300583 + 0.953756i \(0.597181\pi\)
\(578\) −47.3959 −1.97141
\(579\) 3.78261 0.157200
\(580\) −108.441 −4.50277
\(581\) −7.31556 −0.303500
\(582\) 40.0769 1.66124
\(583\) 9.75391 0.403966
\(584\) −71.7923 −2.97079
\(585\) 0.539213 0.0222937
\(586\) 19.8484 0.819929
\(587\) −20.6851 −0.853763 −0.426882 0.904307i \(-0.640388\pi\)
−0.426882 + 0.904307i \(0.640388\pi\)
\(588\) −15.2993 −0.630932
\(589\) 27.2145 1.12135
\(590\) −28.0264 −1.15383
\(591\) 9.16973 0.377192
\(592\) −80.6841 −3.31609
\(593\) 30.9756 1.27202 0.636009 0.771682i \(-0.280584\pi\)
0.636009 + 0.771682i \(0.280584\pi\)
\(594\) −43.2053 −1.77274
\(595\) 39.8477 1.63360
\(596\) −86.8522 −3.55761
\(597\) 2.15889 0.0883574
\(598\) 4.12832 0.168819
\(599\) 14.0833 0.575428 0.287714 0.957716i \(-0.407105\pi\)
0.287714 + 0.957716i \(0.407105\pi\)
\(600\) −52.3225 −2.13606
\(601\) −31.6167 −1.28967 −0.644837 0.764320i \(-0.723075\pi\)
−0.644837 + 0.764320i \(0.723075\pi\)
\(602\) −75.3085 −3.06934
\(603\) −1.89779 −0.0772839
\(604\) −78.7389 −3.20384
\(605\) 5.42008 0.220358
\(606\) −18.0509 −0.733267
\(607\) 8.12864 0.329931 0.164966 0.986299i \(-0.447249\pi\)
0.164966 + 0.986299i \(0.447249\pi\)
\(608\) 116.665 4.73140
\(609\) −27.4104 −1.11073
\(610\) −68.2418 −2.76303
\(611\) −4.02707 −0.162918
\(612\) −5.80189 −0.234527
\(613\) 24.7448 0.999434 0.499717 0.866189i \(-0.333437\pi\)
0.499717 + 0.866189i \(0.333437\pi\)
\(614\) 32.7652 1.32230
\(615\) 13.9431 0.562242
\(616\) −57.4701 −2.31554
\(617\) −42.0895 −1.69446 −0.847229 0.531228i \(-0.821731\pi\)
−0.847229 + 0.531228i \(0.821731\pi\)
\(618\) −50.5805 −2.03465
\(619\) 48.8247 1.96243 0.981216 0.192913i \(-0.0617936\pi\)
0.981216 + 0.192913i \(0.0617936\pi\)
\(620\) 53.7642 2.15922
\(621\) 8.73867 0.350671
\(622\) −53.2673 −2.13582
\(623\) −18.8435 −0.754949
\(624\) 18.9511 0.758651
\(625\) −29.6696 −1.18679
\(626\) −17.0901 −0.683057
\(627\) 38.8786 1.55266
\(628\) 96.2828 3.84210
\(629\) −39.8488 −1.58888
\(630\) 3.46738 0.138144
\(631\) −42.3507 −1.68595 −0.842977 0.537949i \(-0.819199\pi\)
−0.842977 + 0.537949i \(0.819199\pi\)
\(632\) 57.4188 2.28400
\(633\) 5.48200 0.217890
\(634\) 21.2548 0.844137
\(635\) 48.6132 1.92915
\(636\) −27.6126 −1.09491
\(637\) −1.69082 −0.0669928
\(638\) 57.8582 2.29063
\(639\) −1.20183 −0.0475436
\(640\) 41.9941 1.65996
\(641\) −47.9125 −1.89243 −0.946215 0.323537i \(-0.895128\pi\)
−0.946215 + 0.323537i \(0.895128\pi\)
\(642\) 42.0616 1.66004
\(643\) −33.1186 −1.30607 −0.653036 0.757327i \(-0.726505\pi\)
−0.653036 + 0.757327i \(0.726505\pi\)
\(644\) 19.0854 0.752070
\(645\) 61.2991 2.41365
\(646\) 120.528 4.74211
\(647\) 22.6387 0.890018 0.445009 0.895526i \(-0.353201\pi\)
0.445009 + 0.895526i \(0.353201\pi\)
\(648\) 69.6970 2.73796
\(649\) 10.7504 0.421991
\(650\) −9.49435 −0.372399
\(651\) 13.5899 0.532629
\(652\) −93.2242 −3.65094
\(653\) −31.0970 −1.21692 −0.608460 0.793584i \(-0.708213\pi\)
−0.608460 + 0.793584i \(0.708213\pi\)
\(654\) 83.4282 3.26230
\(655\) 5.02066 0.196173
\(656\) −33.5713 −1.31074
\(657\) −1.66148 −0.0648205
\(658\) −25.8958 −1.00952
\(659\) 24.1812 0.941966 0.470983 0.882142i \(-0.343899\pi\)
0.470983 + 0.882142i \(0.343899\pi\)
\(660\) 76.8074 2.98973
\(661\) 14.0027 0.544640 0.272320 0.962207i \(-0.412209\pi\)
0.272320 + 0.962207i \(0.412209\pi\)
\(662\) −25.0758 −0.974600
\(663\) 9.35970 0.363500
\(664\) −26.6240 −1.03321
\(665\) −51.7853 −2.00815
\(666\) −3.46747 −0.134362
\(667\) −11.7024 −0.453117
\(668\) −26.3396 −1.01911
\(669\) −21.0798 −0.814994
\(670\) 77.8859 3.00900
\(671\) 26.1763 1.01053
\(672\) 58.2581 2.24735
\(673\) −37.4592 −1.44394 −0.721972 0.691922i \(-0.756764\pi\)
−0.721972 + 0.691922i \(0.756764\pi\)
\(674\) 23.1445 0.891493
\(675\) −20.0973 −0.773545
\(676\) −61.9128 −2.38126
\(677\) 43.5235 1.67274 0.836371 0.548163i \(-0.184673\pi\)
0.836371 + 0.548163i \(0.184673\pi\)
\(678\) −17.5080 −0.672389
\(679\) 20.4761 0.785802
\(680\) 145.021 5.56129
\(681\) 48.4187 1.85541
\(682\) −28.6856 −1.09843
\(683\) −17.6853 −0.676708 −0.338354 0.941019i \(-0.609870\pi\)
−0.338354 + 0.941019i \(0.609870\pi\)
\(684\) 7.54002 0.288300
\(685\) 66.6688 2.54728
\(686\) −53.5150 −2.04321
\(687\) 1.75401 0.0669195
\(688\) −147.592 −5.62688
\(689\) −3.05164 −0.116258
\(690\) −21.6085 −0.822621
\(691\) −19.6308 −0.746791 −0.373395 0.927672i \(-0.621807\pi\)
−0.373395 + 0.927672i \(0.621807\pi\)
\(692\) 30.0279 1.14149
\(693\) −1.33002 −0.0505234
\(694\) −24.2141 −0.919154
\(695\) −47.7116 −1.80980
\(696\) −99.7568 −3.78127
\(697\) −16.5804 −0.628029
\(698\) −90.7822 −3.43616
\(699\) 19.4561 0.735896
\(700\) −43.8928 −1.65899
\(701\) 12.2379 0.462220 0.231110 0.972928i \(-0.425764\pi\)
0.231110 + 0.972928i \(0.425764\pi\)
\(702\) 13.5173 0.510179
\(703\) 51.7868 1.95317
\(704\) −50.6718 −1.90976
\(705\) 21.0785 0.793863
\(706\) 5.13851 0.193390
\(707\) −9.22258 −0.346851
\(708\) −30.4336 −1.14376
\(709\) 17.1224 0.643046 0.321523 0.946902i \(-0.395805\pi\)
0.321523 + 0.946902i \(0.395805\pi\)
\(710\) 49.3235 1.85108
\(711\) 1.32884 0.0498352
\(712\) −68.5785 −2.57009
\(713\) 5.80193 0.217284
\(714\) 60.1870 2.25244
\(715\) 8.48847 0.317451
\(716\) −64.4880 −2.41003
\(717\) 8.23177 0.307421
\(718\) 33.8271 1.26242
\(719\) 41.8356 1.56020 0.780102 0.625653i \(-0.215167\pi\)
0.780102 + 0.625653i \(0.215167\pi\)
\(720\) 6.79547 0.253252
\(721\) −25.8427 −0.962431
\(722\) −105.953 −3.94316
\(723\) 38.1614 1.41924
\(724\) 92.6350 3.44275
\(725\) 26.9132 0.999531
\(726\) 8.18663 0.303834
\(727\) −45.0775 −1.67183 −0.835916 0.548857i \(-0.815063\pi\)
−0.835916 + 0.548857i \(0.815063\pi\)
\(728\) 17.9803 0.666394
\(729\) 28.5020 1.05563
\(730\) 68.1877 2.52374
\(731\) −72.8936 −2.69607
\(732\) −74.1031 −2.73893
\(733\) 15.1009 0.557764 0.278882 0.960325i \(-0.410036\pi\)
0.278882 + 0.960325i \(0.410036\pi\)
\(734\) 34.1705 1.26126
\(735\) 8.85012 0.326441
\(736\) 24.8721 0.916800
\(737\) −29.8757 −1.10048
\(738\) −1.44276 −0.0531087
\(739\) 39.8828 1.46711 0.733557 0.679628i \(-0.237859\pi\)
0.733557 + 0.679628i \(0.237859\pi\)
\(740\) 102.308 3.76093
\(741\) −12.1637 −0.446844
\(742\) −19.6234 −0.720397
\(743\) 20.7790 0.762306 0.381153 0.924512i \(-0.375527\pi\)
0.381153 + 0.924512i \(0.375527\pi\)
\(744\) 49.4586 1.81324
\(745\) 50.2410 1.84069
\(746\) 33.7369 1.23520
\(747\) −0.616156 −0.0225440
\(748\) −91.3353 −3.33955
\(749\) 21.4902 0.785234
\(750\) −16.4395 −0.600285
\(751\) −10.5944 −0.386596 −0.193298 0.981140i \(-0.561918\pi\)
−0.193298 + 0.981140i \(0.561918\pi\)
\(752\) −50.7514 −1.85071
\(753\) −18.6080 −0.678114
\(754\) −18.1017 −0.659225
\(755\) 45.5478 1.65765
\(756\) 62.4912 2.27278
\(757\) 27.3635 0.994543 0.497271 0.867595i \(-0.334335\pi\)
0.497271 + 0.867595i \(0.334335\pi\)
\(758\) −80.2156 −2.91356
\(759\) 8.28863 0.300858
\(760\) −188.466 −6.83638
\(761\) 19.1211 0.693139 0.346569 0.938024i \(-0.387347\pi\)
0.346569 + 0.938024i \(0.387347\pi\)
\(762\) 73.4266 2.65996
\(763\) 42.6253 1.54314
\(764\) −8.92020 −0.322722
\(765\) 3.35619 0.121343
\(766\) −84.8863 −3.06707
\(767\) −3.36341 −0.121446
\(768\) 7.34726 0.265121
\(769\) −3.91719 −0.141258 −0.0706288 0.997503i \(-0.522501\pi\)
−0.0706288 + 0.997503i \(0.522501\pi\)
\(770\) 54.5847 1.96709
\(771\) 24.2399 0.872979
\(772\) 11.5484 0.415637
\(773\) 4.52051 0.162591 0.0812957 0.996690i \(-0.474094\pi\)
0.0812957 + 0.996690i \(0.474094\pi\)
\(774\) −6.34289 −0.227991
\(775\) −13.3433 −0.479307
\(776\) 74.5203 2.67512
\(777\) 25.8603 0.927733
\(778\) 1.86845 0.0669873
\(779\) 21.5476 0.772024
\(780\) −24.0302 −0.860419
\(781\) −18.9196 −0.676997
\(782\) 25.6957 0.918875
\(783\) −38.3170 −1.36934
\(784\) −21.3087 −0.761025
\(785\) −55.6963 −1.98789
\(786\) 7.58333 0.270489
\(787\) 32.7245 1.16650 0.583251 0.812292i \(-0.301780\pi\)
0.583251 + 0.812292i \(0.301780\pi\)
\(788\) 27.9955 0.997297
\(789\) −43.6629 −1.55444
\(790\) −54.5359 −1.94030
\(791\) −8.94520 −0.318055
\(792\) −4.84045 −0.171998
\(793\) −8.18961 −0.290821
\(794\) −102.541 −3.63904
\(795\) 15.9729 0.566501
\(796\) 6.59115 0.233617
\(797\) −24.1889 −0.856814 −0.428407 0.903586i \(-0.640925\pi\)
−0.428407 + 0.903586i \(0.640925\pi\)
\(798\) −78.2179 −2.76888
\(799\) −25.0655 −0.886752
\(800\) −57.2012 −2.02237
\(801\) −1.58710 −0.0560775
\(802\) 54.2729 1.91644
\(803\) −26.1556 −0.923011
\(804\) 84.5756 2.98275
\(805\) −11.0402 −0.389117
\(806\) 8.97467 0.316119
\(807\) 1.50010 0.0528060
\(808\) −33.5644 −1.18079
\(809\) 4.80521 0.168942 0.0844712 0.996426i \(-0.473080\pi\)
0.0844712 + 0.996426i \(0.473080\pi\)
\(810\) −66.1976 −2.32595
\(811\) −30.3017 −1.06404 −0.532018 0.846733i \(-0.678566\pi\)
−0.532018 + 0.846733i \(0.678566\pi\)
\(812\) −83.6849 −2.93677
\(813\) −0.948684 −0.0332718
\(814\) −54.5862 −1.91324
\(815\) 53.9270 1.88898
\(816\) 117.956 4.12929
\(817\) 94.7312 3.31422
\(818\) −23.7194 −0.829328
\(819\) 0.416115 0.0145402
\(820\) 42.5688 1.48657
\(821\) −38.5463 −1.34528 −0.672638 0.739972i \(-0.734839\pi\)
−0.672638 + 0.739972i \(0.734839\pi\)
\(822\) 100.698 3.51226
\(823\) −2.65886 −0.0926819 −0.0463410 0.998926i \(-0.514756\pi\)
−0.0463410 + 0.998926i \(0.514756\pi\)
\(824\) −94.0510 −3.27642
\(825\) −19.0623 −0.663664
\(826\) −21.6282 −0.752541
\(827\) −9.74827 −0.338981 −0.169490 0.985532i \(-0.554212\pi\)
−0.169490 + 0.985532i \(0.554212\pi\)
\(828\) 1.60748 0.0558636
\(829\) 49.1290 1.70632 0.853161 0.521648i \(-0.174682\pi\)
0.853161 + 0.521648i \(0.174682\pi\)
\(830\) 25.2873 0.877734
\(831\) −13.5746 −0.470898
\(832\) 15.8533 0.549615
\(833\) −10.5241 −0.364638
\(834\) −72.0648 −2.49540
\(835\) 15.2365 0.527282
\(836\) 118.698 4.10524
\(837\) 18.9972 0.656641
\(838\) 39.6746 1.37054
\(839\) −17.6872 −0.610630 −0.305315 0.952251i \(-0.598762\pi\)
−0.305315 + 0.952251i \(0.598762\pi\)
\(840\) −94.1126 −3.24719
\(841\) 22.3121 0.769382
\(842\) 3.80399 0.131094
\(843\) 15.3524 0.528766
\(844\) 16.7367 0.576101
\(845\) 35.8144 1.23205
\(846\) −2.18109 −0.0749874
\(847\) 4.18272 0.143720
\(848\) −38.4585 −1.32067
\(849\) −36.7363 −1.26079
\(850\) −59.0952 −2.02695
\(851\) 11.0405 0.378465
\(852\) 53.5600 1.83493
\(853\) 6.64201 0.227418 0.113709 0.993514i \(-0.463727\pi\)
0.113709 + 0.993514i \(0.463727\pi\)
\(854\) −52.6628 −1.80208
\(855\) −4.36164 −0.149165
\(856\) 78.2107 2.67319
\(857\) −17.1577 −0.586097 −0.293049 0.956098i \(-0.594670\pi\)
−0.293049 + 0.956098i \(0.594670\pi\)
\(858\) 12.8212 0.437709
\(859\) 5.19035 0.177092 0.0885462 0.996072i \(-0.471778\pi\)
0.0885462 + 0.996072i \(0.471778\pi\)
\(860\) 187.148 6.38170
\(861\) 10.7600 0.366701
\(862\) 27.8369 0.948129
\(863\) 0.869663 0.0296037 0.0148018 0.999890i \(-0.495288\pi\)
0.0148018 + 0.999890i \(0.495288\pi\)
\(864\) 81.4388 2.77060
\(865\) −17.3701 −0.590602
\(866\) 61.4541 2.08830
\(867\) 29.7717 1.01110
\(868\) 41.4903 1.40827
\(869\) 20.9190 0.709629
\(870\) 94.7481 3.21226
\(871\) 9.34699 0.316711
\(872\) 155.129 5.25334
\(873\) 1.72461 0.0583693
\(874\) −33.3936 −1.12956
\(875\) −8.39929 −0.283948
\(876\) 74.0444 2.50173
\(877\) 14.5132 0.490075 0.245038 0.969514i \(-0.421200\pi\)
0.245038 + 0.969514i \(0.421200\pi\)
\(878\) 42.0673 1.41970
\(879\) −12.4678 −0.420527
\(880\) 106.977 3.60618
\(881\) −28.5486 −0.961828 −0.480914 0.876768i \(-0.659695\pi\)
−0.480914 + 0.876768i \(0.659695\pi\)
\(882\) −0.915761 −0.0308353
\(883\) −12.0171 −0.404409 −0.202205 0.979343i \(-0.564811\pi\)
−0.202205 + 0.979343i \(0.564811\pi\)
\(884\) 28.5754 0.961096
\(885\) 17.6048 0.591778
\(886\) 37.2174 1.25034
\(887\) −16.9674 −0.569710 −0.284855 0.958571i \(-0.591945\pi\)
−0.284855 + 0.958571i \(0.591945\pi\)
\(888\) 94.1152 3.15830
\(889\) 37.5152 1.25822
\(890\) 65.1352 2.18334
\(891\) 25.3922 0.850672
\(892\) −64.3574 −2.15485
\(893\) 32.5746 1.09007
\(894\) 75.8853 2.53799
\(895\) 37.3041 1.24694
\(896\) 32.4072 1.08265
\(897\) −2.59321 −0.0865846
\(898\) 1.58191 0.0527890
\(899\) −25.4401 −0.848475
\(900\) −3.69689 −0.123230
\(901\) −18.9941 −0.632787
\(902\) −22.7124 −0.756240
\(903\) 47.3051 1.57421
\(904\) −32.5549 −1.08276
\(905\) −53.5862 −1.78126
\(906\) 68.7965 2.28561
\(907\) 22.6963 0.753617 0.376809 0.926291i \(-0.377021\pi\)
0.376809 + 0.926291i \(0.377021\pi\)
\(908\) 147.824 4.90570
\(909\) −0.776776 −0.0257640
\(910\) −17.0775 −0.566114
\(911\) 38.6284 1.27982 0.639908 0.768451i \(-0.278972\pi\)
0.639908 + 0.768451i \(0.278972\pi\)
\(912\) −153.294 −5.07606
\(913\) −9.69975 −0.321015
\(914\) −35.7992 −1.18413
\(915\) 42.8661 1.41711
\(916\) 5.35504 0.176935
\(917\) 3.87449 0.127947
\(918\) 84.1352 2.77688
\(919\) −21.9472 −0.723970 −0.361985 0.932184i \(-0.617901\pi\)
−0.361985 + 0.932184i \(0.617901\pi\)
\(920\) −40.1795 −1.32468
\(921\) −20.5815 −0.678183
\(922\) −54.0957 −1.78155
\(923\) 5.91925 0.194834
\(924\) 59.2730 1.94994
\(925\) −25.3912 −0.834857
\(926\) 109.622 3.60239
\(927\) −2.17661 −0.0714893
\(928\) −109.059 −3.58002
\(929\) 55.6957 1.82732 0.913658 0.406483i \(-0.133245\pi\)
0.913658 + 0.406483i \(0.133245\pi\)
\(930\) −46.9753 −1.54038
\(931\) 13.6769 0.448242
\(932\) 59.3999 1.94571
\(933\) 33.4599 1.09543
\(934\) −58.8876 −1.92686
\(935\) 52.8344 1.72787
\(936\) 1.51440 0.0494996
\(937\) −4.37763 −0.143011 −0.0715054 0.997440i \(-0.522780\pi\)
−0.0715054 + 0.997440i \(0.522780\pi\)
\(938\) 60.1053 1.96251
\(939\) 10.7351 0.350328
\(940\) 64.3534 2.09898
\(941\) 23.6834 0.772055 0.386028 0.922487i \(-0.373847\pi\)
0.386028 + 0.922487i \(0.373847\pi\)
\(942\) −84.1251 −2.74095
\(943\) 4.59379 0.149594
\(944\) −42.3876 −1.37960
\(945\) −36.1490 −1.17593
\(946\) −99.8520 −3.24647
\(947\) −7.08558 −0.230250 −0.115125 0.993351i \(-0.536727\pi\)
−0.115125 + 0.993351i \(0.536727\pi\)
\(948\) −59.2200 −1.92338
\(949\) 8.18312 0.265635
\(950\) 76.7990 2.49169
\(951\) −13.3512 −0.432944
\(952\) 111.914 3.62714
\(953\) 38.8102 1.25719 0.628593 0.777734i \(-0.283631\pi\)
0.628593 + 0.777734i \(0.283631\pi\)
\(954\) −1.65279 −0.0535110
\(955\) 5.16003 0.166975
\(956\) 25.1319 0.812822
\(957\) −36.3437 −1.17482
\(958\) −40.3845 −1.30477
\(959\) 51.4489 1.66137
\(960\) −82.9796 −2.67816
\(961\) −18.3870 −0.593130
\(962\) 17.0780 0.550617
\(963\) 1.81002 0.0583271
\(964\) 116.508 3.75246
\(965\) −6.68037 −0.215049
\(966\) −16.6755 −0.536524
\(967\) 6.82336 0.219424 0.109712 0.993963i \(-0.465007\pi\)
0.109712 + 0.993963i \(0.465007\pi\)
\(968\) 15.2225 0.489269
\(969\) −75.7097 −2.43215
\(970\) −70.7787 −2.27257
\(971\) −1.33232 −0.0427562 −0.0213781 0.999771i \(-0.506805\pi\)
−0.0213781 + 0.999771i \(0.506805\pi\)
\(972\) 10.2096 0.327472
\(973\) −36.8194 −1.18038
\(974\) 15.1082 0.484097
\(975\) 5.96388 0.190997
\(976\) −103.210 −3.30367
\(977\) −4.93022 −0.157732 −0.0788658 0.996885i \(-0.525130\pi\)
−0.0788658 + 0.996885i \(0.525130\pi\)
\(978\) 81.4527 2.60457
\(979\) −24.9847 −0.798515
\(980\) 27.0197 0.863112
\(981\) 3.59014 0.114624
\(982\) 27.6244 0.881529
\(983\) −14.5594 −0.464373 −0.232186 0.972671i \(-0.574588\pi\)
−0.232186 + 0.972671i \(0.574588\pi\)
\(984\) 39.1598 1.24837
\(985\) −16.1944 −0.515997
\(986\) −112.669 −3.58813
\(987\) 16.2665 0.517768
\(988\) −37.1361 −1.18146
\(989\) 20.1960 0.642195
\(990\) 4.59742 0.146116
\(991\) 37.1791 1.18103 0.590517 0.807025i \(-0.298924\pi\)
0.590517 + 0.807025i \(0.298924\pi\)
\(992\) 54.0703 1.71673
\(993\) 15.7514 0.499856
\(994\) 38.0634 1.20730
\(995\) −3.81275 −0.120872
\(996\) 27.4592 0.870078
\(997\) 35.6219 1.12816 0.564079 0.825721i \(-0.309231\pi\)
0.564079 + 0.825721i \(0.309231\pi\)
\(998\) −98.7965 −3.12735
\(999\) 36.1500 1.14374
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 \(a_p\))