Properties

Label 8011.2.a.b.1.20
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 1.20
Character \(\chi\) = 8011.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.55695 q^{2}\) \(-3.16452 q^{3}\) \(+4.53798 q^{4}\) \(-0.685875 q^{5}\) \(+8.09151 q^{6}\) \(+1.59461 q^{7}\) \(-6.48950 q^{8}\) \(+7.01419 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.55695 q^{2}\) \(-3.16452 q^{3}\) \(+4.53798 q^{4}\) \(-0.685875 q^{5}\) \(+8.09151 q^{6}\) \(+1.59461 q^{7}\) \(-6.48950 q^{8}\) \(+7.01419 q^{9}\) \(+1.75375 q^{10}\) \(+5.60348 q^{11}\) \(-14.3605 q^{12}\) \(+6.89011 q^{13}\) \(-4.07733 q^{14}\) \(+2.17047 q^{15}\) \(+7.51733 q^{16}\) \(-4.01448 q^{17}\) \(-17.9349 q^{18}\) \(-0.308996 q^{19}\) \(-3.11249 q^{20}\) \(-5.04617 q^{21}\) \(-14.3278 q^{22}\) \(+1.61927 q^{23}\) \(+20.5361 q^{24}\) \(-4.52958 q^{25}\) \(-17.6177 q^{26}\) \(-12.7030 q^{27}\) \(+7.23631 q^{28}\) \(+7.76524 q^{29}\) \(-5.54977 q^{30}\) \(-0.885352 q^{31}\) \(-6.24245 q^{32}\) \(-17.7323 q^{33}\) \(+10.2648 q^{34}\) \(-1.09370 q^{35}\) \(+31.8303 q^{36}\) \(-8.39723 q^{37}\) \(+0.790088 q^{38}\) \(-21.8039 q^{39}\) \(+4.45098 q^{40}\) \(+6.70304 q^{41}\) \(+12.9028 q^{42}\) \(-9.78400 q^{43}\) \(+25.4285 q^{44}\) \(-4.81086 q^{45}\) \(-4.14038 q^{46}\) \(+1.40397 q^{47}\) \(-23.7888 q^{48}\) \(-4.45722 q^{49}\) \(+11.5819 q^{50}\) \(+12.7039 q^{51}\) \(+31.2672 q^{52}\) \(+0.875914 q^{53}\) \(+32.4809 q^{54}\) \(-3.84329 q^{55}\) \(-10.3482 q^{56}\) \(+0.977825 q^{57}\) \(-19.8553 q^{58}\) \(-1.30650 q^{59}\) \(+9.84954 q^{60}\) \(+5.98955 q^{61}\) \(+2.26380 q^{62}\) \(+11.1849 q^{63}\) \(+0.926941 q^{64}\) \(-4.72576 q^{65}\) \(+45.3406 q^{66}\) \(+0.601968 q^{67}\) \(-18.2177 q^{68}\) \(-5.12420 q^{69}\) \(+2.79654 q^{70}\) \(+8.18935 q^{71}\) \(-45.5185 q^{72}\) \(+15.1959 q^{73}\) \(+21.4713 q^{74}\) \(+14.3339 q^{75}\) \(-1.40222 q^{76}\) \(+8.93535 q^{77}\) \(+55.7514 q^{78}\) \(+7.71395 q^{79}\) \(-5.15595 q^{80}\) \(+19.1563 q^{81}\) \(-17.1393 q^{82}\) \(+9.63593 q^{83}\) \(-22.8994 q^{84}\) \(+2.75343 q^{85}\) \(+25.0172 q^{86}\) \(-24.5733 q^{87}\) \(-36.3638 q^{88}\) \(-0.465576 q^{89}\) \(+12.3011 q^{90}\) \(+10.9870 q^{91}\) \(+7.34821 q^{92}\) \(+2.80171 q^{93}\) \(-3.58989 q^{94}\) \(+0.211933 q^{95}\) \(+19.7543 q^{96}\) \(-14.9417 q^{97}\) \(+11.3969 q^{98}\) \(+39.3039 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut 21q^{10} \) \(\mathstrut +\mathstrut 70q^{11} \) \(\mathstrut +\mathstrut 20q^{12} \) \(\mathstrut +\mathstrut 53q^{13} \) \(\mathstrut +\mathstrut 69q^{14} \) \(\mathstrut +\mathstrut 28q^{15} \) \(\mathstrut +\mathstrut 449q^{16} \) \(\mathstrut +\mathstrut 88q^{17} \) \(\mathstrut +\mathstrut 86q^{18} \) \(\mathstrut +\mathstrut 44q^{19} \) \(\mathstrut +\mathstrut 136q^{20} \) \(\mathstrut +\mathstrut 125q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 104q^{23} \) \(\mathstrut +\mathstrut 84q^{24} \) \(\mathstrut +\mathstrut 444q^{25} \) \(\mathstrut +\mathstrut 100q^{26} \) \(\mathstrut +\mathstrut 32q^{27} \) \(\mathstrut +\mathstrut 46q^{28} \) \(\mathstrut +\mathstrut 373q^{29} \) \(\mathstrut +\mathstrut 99q^{30} \) \(\mathstrut +\mathstrut 30q^{31} \) \(\mathstrut +\mathstrut 221q^{32} \) \(\mathstrut +\mathstrut 56q^{33} \) \(\mathstrut +\mathstrut 26q^{34} \) \(\mathstrut +\mathstrut 164q^{35} \) \(\mathstrut +\mathstrut 599q^{36} \) \(\mathstrut +\mathstrut 81q^{37} \) \(\mathstrut +\mathstrut 66q^{38} \) \(\mathstrut +\mathstrut 143q^{39} \) \(\mathstrut +\mathstrut 42q^{40} \) \(\mathstrut +\mathstrut 182q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut +\mathstrut 40q^{43} \) \(\mathstrut +\mathstrut 184q^{44} \) \(\mathstrut +\mathstrut 198q^{45} \) \(\mathstrut +\mathstrut 54q^{46} \) \(\mathstrut +\mathstrut 66q^{47} \) \(\mathstrut +\mathstrut 5q^{48} \) \(\mathstrut +\mathstrut 479q^{49} \) \(\mathstrut +\mathstrut 184q^{50} \) \(\mathstrut +\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 64q^{52} \) \(\mathstrut +\mathstrut 221q^{53} \) \(\mathstrut +\mathstrut 67q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 174q^{56} \) \(\mathstrut +\mathstrut 84q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut +\mathstrut 127q^{59} \) \(\mathstrut +\mathstrut 29q^{60} \) \(\mathstrut +\mathstrut 174q^{61} \) \(\mathstrut +\mathstrut 86q^{62} \) \(\mathstrut +\mathstrut 48q^{63} \) \(\mathstrut +\mathstrut 549q^{64} \) \(\mathstrut +\mathstrut 202q^{65} \) \(\mathstrut +\mathstrut 32q^{66} \) \(\mathstrut +\mathstrut 29q^{67} \) \(\mathstrut +\mathstrut 172q^{68} \) \(\mathstrut +\mathstrut 249q^{69} \) \(\mathstrut +\mathstrut 12q^{70} \) \(\mathstrut +\mathstrut 185q^{71} \) \(\mathstrut +\mathstrut 218q^{72} \) \(\mathstrut +\mathstrut 57q^{73} \) \(\mathstrut +\mathstrut 272q^{74} \) \(\mathstrut +\mathstrut 24q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 384q^{77} \) \(\mathstrut +\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 93q^{79} \) \(\mathstrut +\mathstrut 215q^{80} \) \(\mathstrut +\mathstrut 702q^{81} \) \(\mathstrut +\mathstrut 48q^{82} \) \(\mathstrut +\mathstrut 121q^{83} \) \(\mathstrut +\mathstrut 179q^{84} \) \(\mathstrut +\mathstrut 177q^{85} \) \(\mathstrut +\mathstrut 209q^{86} \) \(\mathstrut +\mathstrut 91q^{87} \) \(\mathstrut +\mathstrut 36q^{88} \) \(\mathstrut +\mathstrut 186q^{89} \) \(\mathstrut +\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut +\mathstrut 272q^{92} \) \(\mathstrut +\mathstrut 220q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 170q^{95} \) \(\mathstrut +\mathstrut 162q^{96} \) \(\mathstrut +\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 196q^{98} \) \(\mathstrut +\mathstrut 152q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.55695 −1.80804 −0.904018 0.427495i \(-0.859396\pi\)
−0.904018 + 0.427495i \(0.859396\pi\)
\(3\) −3.16452 −1.82704 −0.913518 0.406798i \(-0.866645\pi\)
−0.913518 + 0.406798i \(0.866645\pi\)
\(4\) 4.53798 2.26899
\(5\) −0.685875 −0.306733 −0.153366 0.988169i \(-0.549011\pi\)
−0.153366 + 0.988169i \(0.549011\pi\)
\(6\) 8.09151 3.30335
\(7\) 1.59461 0.602705 0.301353 0.953513i \(-0.402562\pi\)
0.301353 + 0.953513i \(0.402562\pi\)
\(8\) −6.48950 −2.29438
\(9\) 7.01419 2.33806
\(10\) 1.75375 0.554583
\(11\) 5.60348 1.68951 0.844756 0.535151i \(-0.179745\pi\)
0.844756 + 0.535151i \(0.179745\pi\)
\(12\) −14.3605 −4.14553
\(13\) 6.89011 1.91097 0.955487 0.295034i \(-0.0953310\pi\)
0.955487 + 0.295034i \(0.0953310\pi\)
\(14\) −4.07733 −1.08971
\(15\) 2.17047 0.560412
\(16\) 7.51733 1.87933
\(17\) −4.01448 −0.973656 −0.486828 0.873498i \(-0.661846\pi\)
−0.486828 + 0.873498i \(0.661846\pi\)
\(18\) −17.9349 −4.22730
\(19\) −0.308996 −0.0708886 −0.0354443 0.999372i \(-0.511285\pi\)
−0.0354443 + 0.999372i \(0.511285\pi\)
\(20\) −3.11249 −0.695974
\(21\) −5.04617 −1.10116
\(22\) −14.3278 −3.05470
\(23\) 1.61927 0.337641 0.168820 0.985647i \(-0.446004\pi\)
0.168820 + 0.985647i \(0.446004\pi\)
\(24\) 20.5361 4.19192
\(25\) −4.52958 −0.905915
\(26\) −17.6177 −3.45511
\(27\) −12.7030 −2.44469
\(28\) 7.23631 1.36753
\(29\) 7.76524 1.44197 0.720984 0.692951i \(-0.243690\pi\)
0.720984 + 0.692951i \(0.243690\pi\)
\(30\) −5.54977 −1.01324
\(31\) −0.885352 −0.159014 −0.0795069 0.996834i \(-0.525335\pi\)
−0.0795069 + 0.996834i \(0.525335\pi\)
\(32\) −6.24245 −1.10352
\(33\) −17.7323 −3.08680
\(34\) 10.2648 1.76040
\(35\) −1.09370 −0.184869
\(36\) 31.8303 5.30505
\(37\) −8.39723 −1.38050 −0.690248 0.723573i \(-0.742499\pi\)
−0.690248 + 0.723573i \(0.742499\pi\)
\(38\) 0.790088 0.128169
\(39\) −21.8039 −3.49142
\(40\) 4.45098 0.703762
\(41\) 6.70304 1.04684 0.523419 0.852075i \(-0.324656\pi\)
0.523419 + 0.852075i \(0.324656\pi\)
\(42\) 12.9028 1.99094
\(43\) −9.78400 −1.49205 −0.746023 0.665920i \(-0.768039\pi\)
−0.746023 + 0.665920i \(0.768039\pi\)
\(44\) 25.4285 3.83349
\(45\) −4.81086 −0.717160
\(46\) −4.14038 −0.610466
\(47\) 1.40397 0.204790 0.102395 0.994744i \(-0.467349\pi\)
0.102395 + 0.994744i \(0.467349\pi\)
\(48\) −23.7888 −3.43361
\(49\) −4.45722 −0.636746
\(50\) 11.5819 1.63793
\(51\) 12.7039 1.77890
\(52\) 31.2672 4.33598
\(53\) 0.875914 0.120316 0.0601580 0.998189i \(-0.480840\pi\)
0.0601580 + 0.998189i \(0.480840\pi\)
\(54\) 32.4809 4.42009
\(55\) −3.84329 −0.518229
\(56\) −10.3482 −1.38284
\(57\) 0.977825 0.129516
\(58\) −19.8553 −2.60713
\(59\) −1.30650 −0.170092 −0.0850460 0.996377i \(-0.527104\pi\)
−0.0850460 + 0.996377i \(0.527104\pi\)
\(60\) 9.84954 1.27157
\(61\) 5.98955 0.766883 0.383441 0.923565i \(-0.374739\pi\)
0.383441 + 0.923565i \(0.374739\pi\)
\(62\) 2.26380 0.287503
\(63\) 11.1849 1.40916
\(64\) 0.926941 0.115868
\(65\) −4.72576 −0.586158
\(66\) 45.3406 5.58105
\(67\) 0.601968 0.0735421 0.0367710 0.999324i \(-0.488293\pi\)
0.0367710 + 0.999324i \(0.488293\pi\)
\(68\) −18.2177 −2.20922
\(69\) −5.12420 −0.616882
\(70\) 2.79654 0.334250
\(71\) 8.18935 0.971897 0.485948 0.873988i \(-0.338474\pi\)
0.485948 + 0.873988i \(0.338474\pi\)
\(72\) −45.5185 −5.36441
\(73\) 15.1959 1.77855 0.889273 0.457377i \(-0.151211\pi\)
0.889273 + 0.457377i \(0.151211\pi\)
\(74\) 21.4713 2.49599
\(75\) 14.3339 1.65514
\(76\) −1.40222 −0.160846
\(77\) 8.93535 1.01828
\(78\) 55.7514 6.31261
\(79\) 7.71395 0.867887 0.433944 0.900940i \(-0.357122\pi\)
0.433944 + 0.900940i \(0.357122\pi\)
\(80\) −5.15595 −0.576453
\(81\) 19.1563 2.12848
\(82\) −17.1393 −1.89272
\(83\) 9.63593 1.05768 0.528840 0.848721i \(-0.322627\pi\)
0.528840 + 0.848721i \(0.322627\pi\)
\(84\) −22.8994 −2.49853
\(85\) 2.75343 0.298652
\(86\) 25.0172 2.69767
\(87\) −24.5733 −2.63453
\(88\) −36.3638 −3.87639
\(89\) −0.465576 −0.0493509 −0.0246755 0.999696i \(-0.507855\pi\)
−0.0246755 + 0.999696i \(0.507855\pi\)
\(90\) 12.3011 1.29665
\(91\) 10.9870 1.15175
\(92\) 7.34821 0.766104
\(93\) 2.80171 0.290524
\(94\) −3.58989 −0.370268
\(95\) 0.211933 0.0217438
\(96\) 19.7543 2.01617
\(97\) −14.9417 −1.51710 −0.758550 0.651615i \(-0.774092\pi\)
−0.758550 + 0.651615i \(0.774092\pi\)
\(98\) 11.3969 1.15126
\(99\) 39.3039 3.95019
\(100\) −20.5551 −2.05551
\(101\) −2.11472 −0.210422 −0.105211 0.994450i \(-0.533552\pi\)
−0.105211 + 0.994450i \(0.533552\pi\)
\(102\) −32.4833 −3.21632
\(103\) −11.0743 −1.09118 −0.545592 0.838051i \(-0.683695\pi\)
−0.545592 + 0.838051i \(0.683695\pi\)
\(104\) −44.7134 −4.38451
\(105\) 3.46104 0.337763
\(106\) −2.23967 −0.217536
\(107\) 6.31380 0.610378 0.305189 0.952292i \(-0.401280\pi\)
0.305189 + 0.952292i \(0.401280\pi\)
\(108\) −57.6459 −5.54698
\(109\) −18.0659 −1.73040 −0.865201 0.501426i \(-0.832809\pi\)
−0.865201 + 0.501426i \(0.832809\pi\)
\(110\) 9.82708 0.936976
\(111\) 26.5732 2.52222
\(112\) 11.9872 1.13268
\(113\) 11.9289 1.12218 0.561088 0.827756i \(-0.310383\pi\)
0.561088 + 0.827756i \(0.310383\pi\)
\(114\) −2.50025 −0.234170
\(115\) −1.11061 −0.103565
\(116\) 35.2385 3.27182
\(117\) 48.3286 4.46798
\(118\) 3.34065 0.307532
\(119\) −6.40153 −0.586827
\(120\) −14.0852 −1.28580
\(121\) 20.3990 1.85445
\(122\) −15.3150 −1.38655
\(123\) −21.2119 −1.91261
\(124\) −4.01771 −0.360801
\(125\) 6.53610 0.584606
\(126\) −28.5992 −2.54782
\(127\) −6.90290 −0.612534 −0.306267 0.951946i \(-0.599080\pi\)
−0.306267 + 0.951946i \(0.599080\pi\)
\(128\) 10.1148 0.894026
\(129\) 30.9617 2.72602
\(130\) 12.0835 1.05979
\(131\) −15.4243 −1.34762 −0.673812 0.738902i \(-0.735344\pi\)
−0.673812 + 0.738902i \(0.735344\pi\)
\(132\) −80.4690 −7.00393
\(133\) −0.492728 −0.0427249
\(134\) −1.53920 −0.132967
\(135\) 8.71266 0.749866
\(136\) 26.0520 2.23394
\(137\) 14.3025 1.22194 0.610972 0.791653i \(-0.290779\pi\)
0.610972 + 0.791653i \(0.290779\pi\)
\(138\) 13.1023 1.11534
\(139\) −7.08158 −0.600652 −0.300326 0.953837i \(-0.597095\pi\)
−0.300326 + 0.953837i \(0.597095\pi\)
\(140\) −4.96320 −0.419467
\(141\) −4.44290 −0.374160
\(142\) −20.9397 −1.75722
\(143\) 38.6086 3.22861
\(144\) 52.7280 4.39400
\(145\) −5.32598 −0.442299
\(146\) −38.8551 −3.21567
\(147\) 14.1050 1.16336
\(148\) −38.1065 −3.13233
\(149\) 15.1424 1.24051 0.620257 0.784399i \(-0.287028\pi\)
0.620257 + 0.784399i \(0.287028\pi\)
\(150\) −36.6511 −2.99255
\(151\) 15.4004 1.25327 0.626635 0.779313i \(-0.284432\pi\)
0.626635 + 0.779313i \(0.284432\pi\)
\(152\) 2.00523 0.162646
\(153\) −28.1584 −2.27647
\(154\) −22.8472 −1.84108
\(155\) 0.607240 0.0487747
\(156\) −98.9458 −7.92200
\(157\) 4.06649 0.324541 0.162271 0.986746i \(-0.448118\pi\)
0.162271 + 0.986746i \(0.448118\pi\)
\(158\) −19.7242 −1.56917
\(159\) −2.77185 −0.219822
\(160\) 4.28154 0.338485
\(161\) 2.58210 0.203498
\(162\) −48.9816 −3.84836
\(163\) 4.53658 0.355332 0.177666 0.984091i \(-0.443145\pi\)
0.177666 + 0.984091i \(0.443145\pi\)
\(164\) 30.4183 2.37527
\(165\) 12.1622 0.946823
\(166\) −24.6386 −1.91232
\(167\) 0.431081 0.0333580 0.0166790 0.999861i \(-0.494691\pi\)
0.0166790 + 0.999861i \(0.494691\pi\)
\(168\) 32.7471 2.52649
\(169\) 34.4737 2.65182
\(170\) −7.04039 −0.539973
\(171\) −2.16736 −0.165742
\(172\) −44.3996 −3.38544
\(173\) 0.0803178 0.00610645 0.00305322 0.999995i \(-0.499028\pi\)
0.00305322 + 0.999995i \(0.499028\pi\)
\(174\) 62.8326 4.76332
\(175\) −7.22290 −0.546000
\(176\) 42.1232 3.17516
\(177\) 4.13445 0.310764
\(178\) 1.19045 0.0892283
\(179\) −17.9420 −1.34105 −0.670526 0.741886i \(-0.733931\pi\)
−0.670526 + 0.741886i \(0.733931\pi\)
\(180\) −21.8316 −1.62723
\(181\) 13.9061 1.03363 0.516817 0.856096i \(-0.327117\pi\)
0.516817 + 0.856096i \(0.327117\pi\)
\(182\) −28.0933 −2.08241
\(183\) −18.9540 −1.40112
\(184\) −10.5082 −0.774677
\(185\) 5.75945 0.423443
\(186\) −7.16384 −0.525278
\(187\) −22.4951 −1.64500
\(188\) 6.37121 0.464668
\(189\) −20.2563 −1.47343
\(190\) −0.541901 −0.0393137
\(191\) −2.71070 −0.196139 −0.0980695 0.995180i \(-0.531267\pi\)
−0.0980695 + 0.995180i \(0.531267\pi\)
\(192\) −2.93332 −0.211694
\(193\) −11.7498 −0.845770 −0.422885 0.906183i \(-0.638983\pi\)
−0.422885 + 0.906183i \(0.638983\pi\)
\(194\) 38.2052 2.74297
\(195\) 14.9547 1.07093
\(196\) −20.2268 −1.44477
\(197\) −2.98441 −0.212631 −0.106315 0.994332i \(-0.533905\pi\)
−0.106315 + 0.994332i \(0.533905\pi\)
\(198\) −100.498 −7.14208
\(199\) 6.35937 0.450804 0.225402 0.974266i \(-0.427631\pi\)
0.225402 + 0.974266i \(0.427631\pi\)
\(200\) 29.3947 2.07852
\(201\) −1.90494 −0.134364
\(202\) 5.40722 0.380451
\(203\) 12.3825 0.869082
\(204\) 57.6502 4.03632
\(205\) −4.59744 −0.321099
\(206\) 28.3164 1.97290
\(207\) 11.3578 0.789425
\(208\) 51.7953 3.59136
\(209\) −1.73145 −0.119767
\(210\) −8.84971 −0.610688
\(211\) 25.1148 1.72897 0.864487 0.502656i \(-0.167644\pi\)
0.864487 + 0.502656i \(0.167644\pi\)
\(212\) 3.97489 0.272996
\(213\) −25.9154 −1.77569
\(214\) −16.1441 −1.10359
\(215\) 6.71060 0.457659
\(216\) 82.4359 5.60906
\(217\) −1.41179 −0.0958385
\(218\) 46.1936 3.12863
\(219\) −48.0877 −3.24947
\(220\) −17.4408 −1.17586
\(221\) −27.6603 −1.86063
\(222\) −67.9463 −4.56026
\(223\) 6.82434 0.456992 0.228496 0.973545i \(-0.426619\pi\)
0.228496 + 0.973545i \(0.426619\pi\)
\(224\) −9.95426 −0.665097
\(225\) −31.7713 −2.11809
\(226\) −30.5016 −2.02894
\(227\) 1.15143 0.0764234 0.0382117 0.999270i \(-0.487834\pi\)
0.0382117 + 0.999270i \(0.487834\pi\)
\(228\) 4.43736 0.293871
\(229\) −9.13828 −0.603875 −0.301937 0.953328i \(-0.597633\pi\)
−0.301937 + 0.953328i \(0.597633\pi\)
\(230\) 2.83978 0.187250
\(231\) −28.2761 −1.86043
\(232\) −50.3925 −3.30843
\(233\) 6.40479 0.419592 0.209796 0.977745i \(-0.432720\pi\)
0.209796 + 0.977745i \(0.432720\pi\)
\(234\) −123.574 −8.07826
\(235\) −0.962950 −0.0628159
\(236\) −5.92888 −0.385937
\(237\) −24.4110 −1.58566
\(238\) 16.3684 1.06100
\(239\) 10.1014 0.653404 0.326702 0.945127i \(-0.394063\pi\)
0.326702 + 0.945127i \(0.394063\pi\)
\(240\) 16.3161 1.05320
\(241\) −13.0351 −0.839667 −0.419833 0.907601i \(-0.637911\pi\)
−0.419833 + 0.907601i \(0.637911\pi\)
\(242\) −52.1591 −3.35292
\(243\) −22.5115 −1.44411
\(244\) 27.1805 1.74005
\(245\) 3.05710 0.195311
\(246\) 54.2377 3.45807
\(247\) −2.12902 −0.135466
\(248\) 5.74549 0.364839
\(249\) −30.4931 −1.93242
\(250\) −16.7125 −1.05699
\(251\) 29.4731 1.86032 0.930161 0.367151i \(-0.119667\pi\)
0.930161 + 0.367151i \(0.119667\pi\)
\(252\) 50.7568 3.19738
\(253\) 9.07353 0.570448
\(254\) 17.6504 1.10748
\(255\) −8.71330 −0.545648
\(256\) −27.7168 −1.73230
\(257\) 15.3686 0.958665 0.479333 0.877633i \(-0.340879\pi\)
0.479333 + 0.877633i \(0.340879\pi\)
\(258\) −79.1674 −4.92875
\(259\) −13.3903 −0.832032
\(260\) −21.4454 −1.32999
\(261\) 54.4669 3.37141
\(262\) 39.4391 2.43655
\(263\) −17.8395 −1.10003 −0.550014 0.835156i \(-0.685378\pi\)
−0.550014 + 0.835156i \(0.685378\pi\)
\(264\) 115.074 7.08230
\(265\) −0.600768 −0.0369049
\(266\) 1.25988 0.0772482
\(267\) 1.47332 0.0901660
\(268\) 2.73172 0.166866
\(269\) −5.25562 −0.320441 −0.160221 0.987081i \(-0.551221\pi\)
−0.160221 + 0.987081i \(0.551221\pi\)
\(270\) −22.2778 −1.35578
\(271\) −11.0816 −0.673160 −0.336580 0.941655i \(-0.609270\pi\)
−0.336580 + 0.941655i \(0.609270\pi\)
\(272\) −30.1782 −1.82982
\(273\) −34.7687 −2.10430
\(274\) −36.5707 −2.20932
\(275\) −25.3814 −1.53055
\(276\) −23.2536 −1.39970
\(277\) 24.3915 1.46554 0.732772 0.680475i \(-0.238226\pi\)
0.732772 + 0.680475i \(0.238226\pi\)
\(278\) 18.1072 1.08600
\(279\) −6.21002 −0.371784
\(280\) 7.09757 0.424161
\(281\) −1.93276 −0.115299 −0.0576495 0.998337i \(-0.518361\pi\)
−0.0576495 + 0.998337i \(0.518361\pi\)
\(282\) 11.3603 0.676494
\(283\) −1.65407 −0.0983243 −0.0491621 0.998791i \(-0.515655\pi\)
−0.0491621 + 0.998791i \(0.515655\pi\)
\(284\) 37.1631 2.20523
\(285\) −0.670666 −0.0397268
\(286\) −98.7202 −5.83745
\(287\) 10.6887 0.630935
\(288\) −43.7857 −2.58010
\(289\) −0.883914 −0.0519949
\(290\) 13.6183 0.799692
\(291\) 47.2833 2.77180
\(292\) 68.9588 4.03551
\(293\) −24.6754 −1.44155 −0.720775 0.693169i \(-0.756214\pi\)
−0.720775 + 0.693169i \(0.756214\pi\)
\(294\) −36.0657 −2.10339
\(295\) 0.896096 0.0521727
\(296\) 54.4938 3.16739
\(297\) −71.1809 −4.13033
\(298\) −38.7183 −2.24289
\(299\) 11.1569 0.645222
\(300\) 65.0472 3.75550
\(301\) −15.6016 −0.899264
\(302\) −39.3781 −2.26596
\(303\) 6.69206 0.384449
\(304\) −2.32283 −0.133223
\(305\) −4.10808 −0.235228
\(306\) 71.9995 4.11593
\(307\) −4.15070 −0.236893 −0.118446 0.992960i \(-0.537791\pi\)
−0.118446 + 0.992960i \(0.537791\pi\)
\(308\) 40.5485 2.31047
\(309\) 35.0449 1.99363
\(310\) −1.55268 −0.0881864
\(311\) 32.6683 1.85245 0.926226 0.376969i \(-0.123034\pi\)
0.926226 + 0.376969i \(0.123034\pi\)
\(312\) 141.496 8.01065
\(313\) 14.7376 0.833021 0.416511 0.909131i \(-0.363253\pi\)
0.416511 + 0.909131i \(0.363253\pi\)
\(314\) −10.3978 −0.586782
\(315\) −7.67143 −0.432236
\(316\) 35.0058 1.96923
\(317\) −13.2619 −0.744861 −0.372431 0.928060i \(-0.621476\pi\)
−0.372431 + 0.928060i \(0.621476\pi\)
\(318\) 7.08747 0.397446
\(319\) 43.5124 2.43622
\(320\) −0.635766 −0.0355404
\(321\) −19.9802 −1.11518
\(322\) −6.60229 −0.367931
\(323\) 1.24046 0.0690211
\(324\) 86.9309 4.82949
\(325\) −31.2093 −1.73118
\(326\) −11.5998 −0.642453
\(327\) 57.1700 3.16151
\(328\) −43.4993 −2.40185
\(329\) 2.23879 0.123428
\(330\) −31.0980 −1.71189
\(331\) −26.7393 −1.46973 −0.734864 0.678215i \(-0.762754\pi\)
−0.734864 + 0.678215i \(0.762754\pi\)
\(332\) 43.7277 2.39987
\(333\) −58.8997 −3.22769
\(334\) −1.10225 −0.0603125
\(335\) −0.412875 −0.0225577
\(336\) −37.9338 −2.06946
\(337\) −3.33553 −0.181698 −0.0908491 0.995865i \(-0.528958\pi\)
−0.0908491 + 0.995865i \(0.528958\pi\)
\(338\) −88.1473 −4.79458
\(339\) −37.7493 −2.05026
\(340\) 12.4950 0.677639
\(341\) −4.96105 −0.268656
\(342\) 5.54182 0.299667
\(343\) −18.2698 −0.986476
\(344\) 63.4932 3.42332
\(345\) 3.51456 0.189218
\(346\) −0.205368 −0.0110407
\(347\) −15.7284 −0.844342 −0.422171 0.906516i \(-0.638732\pi\)
−0.422171 + 0.906516i \(0.638732\pi\)
\(348\) −111.513 −5.97773
\(349\) 1.83999 0.0984922 0.0492461 0.998787i \(-0.484318\pi\)
0.0492461 + 0.998787i \(0.484318\pi\)
\(350\) 18.4686 0.987187
\(351\) −87.5250 −4.67174
\(352\) −34.9794 −1.86441
\(353\) 3.73006 0.198531 0.0992655 0.995061i \(-0.468351\pi\)
0.0992655 + 0.995061i \(0.468351\pi\)
\(354\) −10.5716 −0.561873
\(355\) −5.61687 −0.298112
\(356\) −2.11278 −0.111977
\(357\) 20.2578 1.07216
\(358\) 45.8769 2.42467
\(359\) −7.39270 −0.390172 −0.195086 0.980786i \(-0.562499\pi\)
−0.195086 + 0.980786i \(0.562499\pi\)
\(360\) 31.2200 1.64544
\(361\) −18.9045 −0.994975
\(362\) −35.5572 −1.86885
\(363\) −64.5530 −3.38815
\(364\) 49.8590 2.61332
\(365\) −10.4225 −0.545538
\(366\) 48.4645 2.53328
\(367\) −1.67650 −0.0875128 −0.0437564 0.999042i \(-0.513933\pi\)
−0.0437564 + 0.999042i \(0.513933\pi\)
\(368\) 12.1726 0.634539
\(369\) 47.0164 2.44757
\(370\) −14.7266 −0.765600
\(371\) 1.39674 0.0725152
\(372\) 12.7141 0.659197
\(373\) 1.88315 0.0975059 0.0487530 0.998811i \(-0.484475\pi\)
0.0487530 + 0.998811i \(0.484475\pi\)
\(374\) 57.5188 2.97422
\(375\) −20.6836 −1.06810
\(376\) −9.11107 −0.469868
\(377\) 53.5034 2.75556
\(378\) 51.7943 2.66401
\(379\) 17.0710 0.876880 0.438440 0.898760i \(-0.355531\pi\)
0.438440 + 0.898760i \(0.355531\pi\)
\(380\) 0.961748 0.0493366
\(381\) 21.8444 1.11912
\(382\) 6.93111 0.354626
\(383\) 22.3103 1.14000 0.570002 0.821643i \(-0.306942\pi\)
0.570002 + 0.821643i \(0.306942\pi\)
\(384\) −32.0083 −1.63342
\(385\) −6.12854 −0.312339
\(386\) 30.0437 1.52918
\(387\) −68.6268 −3.48850
\(388\) −67.8052 −3.44229
\(389\) 8.43356 0.427599 0.213799 0.976878i \(-0.431416\pi\)
0.213799 + 0.976878i \(0.431416\pi\)
\(390\) −38.2385 −1.93628
\(391\) −6.50052 −0.328746
\(392\) 28.9251 1.46094
\(393\) 48.8104 2.46216
\(394\) 7.63099 0.384444
\(395\) −5.29081 −0.266209
\(396\) 178.360 8.96294
\(397\) 19.8297 0.995224 0.497612 0.867400i \(-0.334210\pi\)
0.497612 + 0.867400i \(0.334210\pi\)
\(398\) −16.2606 −0.815069
\(399\) 1.55925 0.0780600
\(400\) −34.0503 −1.70252
\(401\) 14.8971 0.743928 0.371964 0.928247i \(-0.378685\pi\)
0.371964 + 0.928247i \(0.378685\pi\)
\(402\) 4.87083 0.242935
\(403\) −6.10017 −0.303871
\(404\) −9.59655 −0.477446
\(405\) −13.1388 −0.652873
\(406\) −31.6615 −1.57133
\(407\) −47.0537 −2.33236
\(408\) −82.4420 −4.08149
\(409\) −17.1802 −0.849508 −0.424754 0.905309i \(-0.639639\pi\)
−0.424754 + 0.905309i \(0.639639\pi\)
\(410\) 11.7554 0.580559
\(411\) −45.2605 −2.23254
\(412\) −50.2550 −2.47589
\(413\) −2.08336 −0.102515
\(414\) −29.0414 −1.42731
\(415\) −6.60904 −0.324425
\(416\) −43.0112 −2.10880
\(417\) 22.4098 1.09741
\(418\) 4.42724 0.216543
\(419\) −30.6253 −1.49614 −0.748072 0.663617i \(-0.769020\pi\)
−0.748072 + 0.663617i \(0.769020\pi\)
\(420\) 15.7062 0.766382
\(421\) 31.9474 1.55702 0.778511 0.627631i \(-0.215975\pi\)
0.778511 + 0.627631i \(0.215975\pi\)
\(422\) −64.2172 −3.12604
\(423\) 9.84773 0.478813
\(424\) −5.68424 −0.276051
\(425\) 18.1839 0.882049
\(426\) 66.2642 3.21051
\(427\) 9.55098 0.462204
\(428\) 28.6519 1.38494
\(429\) −122.178 −5.89880
\(430\) −17.1587 −0.827464
\(431\) 31.0625 1.49623 0.748115 0.663569i \(-0.230959\pi\)
0.748115 + 0.663569i \(0.230959\pi\)
\(432\) −95.4926 −4.59439
\(433\) 28.9902 1.39318 0.696591 0.717468i \(-0.254699\pi\)
0.696591 + 0.717468i \(0.254699\pi\)
\(434\) 3.60987 0.173279
\(435\) 16.8542 0.808096
\(436\) −81.9829 −3.92627
\(437\) −0.500348 −0.0239349
\(438\) 122.958 5.87516
\(439\) −16.1118 −0.768976 −0.384488 0.923130i \(-0.625622\pi\)
−0.384488 + 0.923130i \(0.625622\pi\)
\(440\) 24.9410 1.18901
\(441\) −31.2638 −1.48875
\(442\) 70.7258 3.36408
\(443\) −31.4474 −1.49411 −0.747056 0.664762i \(-0.768533\pi\)
−0.747056 + 0.664762i \(0.768533\pi\)
\(444\) 120.589 5.72289
\(445\) 0.319327 0.0151375
\(446\) −17.4495 −0.826257
\(447\) −47.9184 −2.26646
\(448\) 1.47811 0.0698340
\(449\) 32.0885 1.51435 0.757176 0.653211i \(-0.226579\pi\)
0.757176 + 0.653211i \(0.226579\pi\)
\(450\) 81.2376 3.82958
\(451\) 37.5603 1.76865
\(452\) 54.1332 2.54621
\(453\) −48.7350 −2.28977
\(454\) −2.94416 −0.138176
\(455\) −7.53573 −0.353280
\(456\) −6.34559 −0.297160
\(457\) −6.65419 −0.311270 −0.155635 0.987815i \(-0.549742\pi\)
−0.155635 + 0.987815i \(0.549742\pi\)
\(458\) 23.3661 1.09183
\(459\) 50.9959 2.38029
\(460\) −5.03995 −0.234989
\(461\) 6.43037 0.299492 0.149746 0.988724i \(-0.452154\pi\)
0.149746 + 0.988724i \(0.452154\pi\)
\(462\) 72.3006 3.36373
\(463\) −11.5754 −0.537953 −0.268976 0.963147i \(-0.586685\pi\)
−0.268976 + 0.963147i \(0.586685\pi\)
\(464\) 58.3739 2.70994
\(465\) −1.92162 −0.0891132
\(466\) −16.3767 −0.758637
\(467\) −40.3956 −1.86928 −0.934642 0.355589i \(-0.884280\pi\)
−0.934642 + 0.355589i \(0.884280\pi\)
\(468\) 219.314 10.1378
\(469\) 0.959903 0.0443242
\(470\) 2.46221 0.113573
\(471\) −12.8685 −0.592949
\(472\) 8.47853 0.390256
\(473\) −54.8244 −2.52083
\(474\) 62.4176 2.86693
\(475\) 1.39962 0.0642191
\(476\) −29.0500 −1.33151
\(477\) 6.14383 0.281307
\(478\) −25.8287 −1.18138
\(479\) −31.8996 −1.45753 −0.728764 0.684765i \(-0.759905\pi\)
−0.728764 + 0.684765i \(0.759905\pi\)
\(480\) −13.5490 −0.618425
\(481\) −57.8578 −2.63809
\(482\) 33.3302 1.51815
\(483\) −8.17110 −0.371798
\(484\) 92.5702 4.20774
\(485\) 10.2481 0.465344
\(486\) 57.5607 2.61101
\(487\) 32.6997 1.48176 0.740882 0.671635i \(-0.234408\pi\)
0.740882 + 0.671635i \(0.234408\pi\)
\(488\) −38.8691 −1.75952
\(489\) −14.3561 −0.649205
\(490\) −7.81684 −0.353129
\(491\) 14.1986 0.640773 0.320386 0.947287i \(-0.396187\pi\)
0.320386 + 0.947287i \(0.396187\pi\)
\(492\) −96.2592 −4.33970
\(493\) −31.1734 −1.40398
\(494\) 5.44379 0.244928
\(495\) −26.9575 −1.21165
\(496\) −6.65548 −0.298840
\(497\) 13.0588 0.585767
\(498\) 77.9693 3.49389
\(499\) 35.4197 1.58560 0.792802 0.609480i \(-0.208622\pi\)
0.792802 + 0.609480i \(0.208622\pi\)
\(500\) 29.6607 1.32647
\(501\) −1.36416 −0.0609464
\(502\) −75.3611 −3.36353
\(503\) −32.7936 −1.46219 −0.731097 0.682274i \(-0.760991\pi\)
−0.731097 + 0.682274i \(0.760991\pi\)
\(504\) −72.5843 −3.23316
\(505\) 1.45043 0.0645433
\(506\) −23.2005 −1.03139
\(507\) −109.093 −4.84497
\(508\) −31.3253 −1.38983
\(509\) −10.9396 −0.484888 −0.242444 0.970165i \(-0.577949\pi\)
−0.242444 + 0.970165i \(0.577949\pi\)
\(510\) 22.2795 0.986551
\(511\) 24.2315 1.07194
\(512\) 50.6409 2.23803
\(513\) 3.92517 0.173301
\(514\) −39.2966 −1.73330
\(515\) 7.59559 0.334702
\(516\) 140.504 6.18532
\(517\) 7.86713 0.345996
\(518\) 34.2383 1.50434
\(519\) −0.254167 −0.0111567
\(520\) 30.6678 1.34487
\(521\) −18.1101 −0.793420 −0.396710 0.917944i \(-0.629848\pi\)
−0.396710 + 0.917944i \(0.629848\pi\)
\(522\) −139.269 −6.09564
\(523\) −25.0849 −1.09689 −0.548443 0.836188i \(-0.684779\pi\)
−0.548443 + 0.836188i \(0.684779\pi\)
\(524\) −69.9951 −3.05775
\(525\) 22.8570 0.997562
\(526\) 45.6146 1.98889
\(527\) 3.55423 0.154825
\(528\) −133.300 −5.80113
\(529\) −20.3780 −0.885999
\(530\) 1.53613 0.0667253
\(531\) −9.16404 −0.397686
\(532\) −2.23599 −0.0969426
\(533\) 46.1847 2.00048
\(534\) −3.76721 −0.163023
\(535\) −4.33048 −0.187223
\(536\) −3.90647 −0.168734
\(537\) 56.7780 2.45015
\(538\) 13.4384 0.579369
\(539\) −24.9760 −1.07579
\(540\) 39.5379 1.70144
\(541\) 28.8653 1.24102 0.620509 0.784200i \(-0.286926\pi\)
0.620509 + 0.784200i \(0.286926\pi\)
\(542\) 28.3351 1.21710
\(543\) −44.0062 −1.88849
\(544\) 25.0602 1.07445
\(545\) 12.3910 0.530771
\(546\) 88.9017 3.80464
\(547\) 15.0940 0.645374 0.322687 0.946506i \(-0.395414\pi\)
0.322687 + 0.946506i \(0.395414\pi\)
\(548\) 64.9044 2.77258
\(549\) 42.0118 1.79302
\(550\) 64.8989 2.76730
\(551\) −2.39943 −0.102219
\(552\) 33.2535 1.41536
\(553\) 12.3007 0.523080
\(554\) −62.3678 −2.64975
\(555\) −18.2259 −0.773646
\(556\) −32.1361 −1.36287
\(557\) 29.6601 1.25674 0.628370 0.777915i \(-0.283722\pi\)
0.628370 + 0.777915i \(0.283722\pi\)
\(558\) 15.8787 0.672199
\(559\) −67.4129 −2.85126
\(560\) −8.22172 −0.347431
\(561\) 71.1861 3.00548
\(562\) 4.94198 0.208465
\(563\) −15.7220 −0.662603 −0.331302 0.943525i \(-0.607488\pi\)
−0.331302 + 0.943525i \(0.607488\pi\)
\(564\) −20.1618 −0.848965
\(565\) −8.18174 −0.344208
\(566\) 4.22937 0.177774
\(567\) 30.5468 1.28284
\(568\) −53.1447 −2.22990
\(569\) −34.5504 −1.44843 −0.724215 0.689574i \(-0.757798\pi\)
−0.724215 + 0.689574i \(0.757798\pi\)
\(570\) 1.71486 0.0718275
\(571\) 25.1686 1.05327 0.526636 0.850091i \(-0.323453\pi\)
0.526636 + 0.850091i \(0.323453\pi\)
\(572\) 175.205 7.32570
\(573\) 8.57805 0.358353
\(574\) −27.3305 −1.14075
\(575\) −7.33459 −0.305874
\(576\) 6.50174 0.270906
\(577\) 34.8624 1.45134 0.725670 0.688043i \(-0.241530\pi\)
0.725670 + 0.688043i \(0.241530\pi\)
\(578\) 2.26012 0.0940087
\(579\) 37.1825 1.54525
\(580\) −24.1692 −1.00357
\(581\) 15.3655 0.637470
\(582\) −120.901 −5.01151
\(583\) 4.90817 0.203276
\(584\) −98.6138 −4.08067
\(585\) −33.1473 −1.37047
\(586\) 63.0936 2.60637
\(587\) 28.9981 1.19688 0.598440 0.801168i \(-0.295788\pi\)
0.598440 + 0.801168i \(0.295788\pi\)
\(588\) 64.0082 2.63965
\(589\) 0.273570 0.0112723
\(590\) −2.29127 −0.0943302
\(591\) 9.44423 0.388484
\(592\) −63.1248 −2.59441
\(593\) 35.1555 1.44366 0.721832 0.692069i \(-0.243300\pi\)
0.721832 + 0.692069i \(0.243300\pi\)
\(594\) 182.006 7.46779
\(595\) 4.39065 0.179999
\(596\) 68.7160 2.81472
\(597\) −20.1244 −0.823635
\(598\) −28.5277 −1.16658
\(599\) −10.5538 −0.431216 −0.215608 0.976480i \(-0.569173\pi\)
−0.215608 + 0.976480i \(0.569173\pi\)
\(600\) −93.0200 −3.79753
\(601\) −28.8849 −1.17824 −0.589120 0.808045i \(-0.700526\pi\)
−0.589120 + 0.808045i \(0.700526\pi\)
\(602\) 39.8926 1.62590
\(603\) 4.22232 0.171946
\(604\) 69.8870 2.84366
\(605\) −13.9911 −0.568821
\(606\) −17.1113 −0.695097
\(607\) −3.69585 −0.150010 −0.0750049 0.997183i \(-0.523897\pi\)
−0.0750049 + 0.997183i \(0.523897\pi\)
\(608\) 1.92889 0.0782269
\(609\) −39.1847 −1.58785
\(610\) 10.5041 0.425300
\(611\) 9.67353 0.391349
\(612\) −127.782 −5.16529
\(613\) 25.0764 1.01283 0.506413 0.862291i \(-0.330971\pi\)
0.506413 + 0.862291i \(0.330971\pi\)
\(614\) 10.6131 0.428310
\(615\) 14.5487 0.586660
\(616\) −57.9859 −2.33632
\(617\) −29.1513 −1.17359 −0.586793 0.809737i \(-0.699610\pi\)
−0.586793 + 0.809737i \(0.699610\pi\)
\(618\) −89.6079 −3.60456
\(619\) 3.08358 0.123940 0.0619699 0.998078i \(-0.480262\pi\)
0.0619699 + 0.998078i \(0.480262\pi\)
\(620\) 2.75565 0.110669
\(621\) −20.5695 −0.825426
\(622\) −83.5313 −3.34930
\(623\) −0.742411 −0.0297441
\(624\) −163.907 −6.56154
\(625\) 18.1649 0.726597
\(626\) −37.6834 −1.50613
\(627\) 5.47922 0.218819
\(628\) 18.4537 0.736382
\(629\) 33.7105 1.34413
\(630\) 19.6155 0.781498
\(631\) 43.1286 1.71692 0.858460 0.512880i \(-0.171421\pi\)
0.858460 + 0.512880i \(0.171421\pi\)
\(632\) −50.0597 −1.99127
\(633\) −79.4762 −3.15890
\(634\) 33.9099 1.34674
\(635\) 4.73453 0.187884
\(636\) −12.5786 −0.498774
\(637\) −30.7108 −1.21681
\(638\) −111.259 −4.40478
\(639\) 57.4416 2.27236
\(640\) −6.93745 −0.274227
\(641\) 1.10483 0.0436382 0.0218191 0.999762i \(-0.493054\pi\)
0.0218191 + 0.999762i \(0.493054\pi\)
\(642\) 51.0882 2.01629
\(643\) 34.3139 1.35321 0.676605 0.736346i \(-0.263450\pi\)
0.676605 + 0.736346i \(0.263450\pi\)
\(644\) 11.7175 0.461735
\(645\) −21.2358 −0.836160
\(646\) −3.17179 −0.124793
\(647\) 0.210590 0.00827913 0.00413956 0.999991i \(-0.498682\pi\)
0.00413956 + 0.999991i \(0.498682\pi\)
\(648\) −124.315 −4.88354
\(649\) −7.32095 −0.287372
\(650\) 79.8005 3.13003
\(651\) 4.46764 0.175100
\(652\) 20.5869 0.806246
\(653\) 43.0947 1.68643 0.843213 0.537579i \(-0.180661\pi\)
0.843213 + 0.537579i \(0.180661\pi\)
\(654\) −146.181 −5.71612
\(655\) 10.5791 0.413360
\(656\) 50.3890 1.96736
\(657\) 106.587 4.15835
\(658\) −5.72446 −0.223163
\(659\) −40.8938 −1.59299 −0.796497 0.604642i \(-0.793316\pi\)
−0.796497 + 0.604642i \(0.793316\pi\)
\(660\) 55.1917 2.14833
\(661\) 1.03269 0.0401672 0.0200836 0.999798i \(-0.493607\pi\)
0.0200836 + 0.999798i \(0.493607\pi\)
\(662\) 68.3711 2.65732
\(663\) 87.5314 3.39944
\(664\) −62.5323 −2.42672
\(665\) 0.337950 0.0131051
\(666\) 150.604 5.83577
\(667\) 12.5740 0.486867
\(668\) 1.95624 0.0756891
\(669\) −21.5958 −0.834941
\(670\) 1.05570 0.0407852
\(671\) 33.5623 1.29566
\(672\) 31.5004 1.21516
\(673\) 9.75914 0.376187 0.188094 0.982151i \(-0.439769\pi\)
0.188094 + 0.982151i \(0.439769\pi\)
\(674\) 8.52879 0.328517
\(675\) 57.5391 2.21468
\(676\) 156.441 6.01696
\(677\) −37.4418 −1.43901 −0.719503 0.694489i \(-0.755630\pi\)
−0.719503 + 0.694489i \(0.755630\pi\)
\(678\) 96.5229 3.70694
\(679\) −23.8262 −0.914364
\(680\) −17.8684 −0.685222
\(681\) −3.64374 −0.139628
\(682\) 12.6851 0.485739
\(683\) −33.6556 −1.28780 −0.643898 0.765112i \(-0.722684\pi\)
−0.643898 + 0.765112i \(0.722684\pi\)
\(684\) −9.83544 −0.376067
\(685\) −9.80971 −0.374810
\(686\) 46.7149 1.78358
\(687\) 28.9183 1.10330
\(688\) −73.5496 −2.80405
\(689\) 6.03515 0.229921
\(690\) −8.98656 −0.342112
\(691\) 15.9719 0.607600 0.303800 0.952736i \(-0.401745\pi\)
0.303800 + 0.952736i \(0.401745\pi\)
\(692\) 0.364481 0.0138555
\(693\) 62.6743 2.38080
\(694\) 40.2166 1.52660
\(695\) 4.85708 0.184239
\(696\) 159.468 6.04462
\(697\) −26.9092 −1.01926
\(698\) −4.70475 −0.178077
\(699\) −20.2681 −0.766610
\(700\) −32.7774 −1.23887
\(701\) −1.91053 −0.0721598 −0.0360799 0.999349i \(-0.511487\pi\)
−0.0360799 + 0.999349i \(0.511487\pi\)
\(702\) 223.797 8.44667
\(703\) 2.59471 0.0978614
\(704\) 5.19409 0.195760
\(705\) 3.04727 0.114767
\(706\) −9.53756 −0.358951
\(707\) −3.37214 −0.126823
\(708\) 18.7621 0.705121
\(709\) 25.9578 0.974865 0.487432 0.873161i \(-0.337934\pi\)
0.487432 + 0.873161i \(0.337934\pi\)
\(710\) 14.3620 0.538998
\(711\) 54.1071 2.02918
\(712\) 3.02135 0.113230
\(713\) −1.43362 −0.0536895
\(714\) −51.7981 −1.93849
\(715\) −26.4807 −0.990321
\(716\) −81.4207 −3.04283
\(717\) −31.9660 −1.19379
\(718\) 18.9027 0.705444
\(719\) 17.0348 0.635290 0.317645 0.948210i \(-0.397108\pi\)
0.317645 + 0.948210i \(0.397108\pi\)
\(720\) −36.1648 −1.34778
\(721\) −17.6592 −0.657662
\(722\) 48.3379 1.79895
\(723\) 41.2499 1.53410
\(724\) 63.1058 2.34531
\(725\) −35.1732 −1.30630
\(726\) 165.059 6.12590
\(727\) −13.5285 −0.501743 −0.250871 0.968020i \(-0.580717\pi\)
−0.250871 + 0.968020i \(0.580717\pi\)
\(728\) −71.3003 −2.64256
\(729\) 13.7692 0.509971
\(730\) 26.6498 0.986352
\(731\) 39.2777 1.45274
\(732\) −86.0131 −3.17914
\(733\) −23.8537 −0.881056 −0.440528 0.897739i \(-0.645209\pi\)
−0.440528 + 0.897739i \(0.645209\pi\)
\(734\) 4.28673 0.158226
\(735\) −9.67425 −0.356840
\(736\) −10.1082 −0.372593
\(737\) 3.37311 0.124250
\(738\) −120.218 −4.42530
\(739\) 21.9798 0.808539 0.404269 0.914640i \(-0.367526\pi\)
0.404269 + 0.914640i \(0.367526\pi\)
\(740\) 26.1363 0.960789
\(741\) 6.73733 0.247502
\(742\) −3.57139 −0.131110
\(743\) 16.8472 0.618065 0.309032 0.951052i \(-0.399995\pi\)
0.309032 + 0.951052i \(0.399995\pi\)
\(744\) −18.1817 −0.666574
\(745\) −10.3858 −0.380506
\(746\) −4.81512 −0.176294
\(747\) 67.5882 2.47292
\(748\) −102.082 −3.73250
\(749\) 10.0680 0.367878
\(750\) 52.8869 1.93116
\(751\) −21.2671 −0.776048 −0.388024 0.921649i \(-0.626842\pi\)
−0.388024 + 0.921649i \(0.626842\pi\)
\(752\) 10.5541 0.384870
\(753\) −93.2681 −3.39888
\(754\) −136.805 −4.98216
\(755\) −10.5628 −0.384419
\(756\) −91.9227 −3.34320
\(757\) 16.9532 0.616175 0.308087 0.951358i \(-0.400311\pi\)
0.308087 + 0.951358i \(0.400311\pi\)
\(758\) −43.6498 −1.58543
\(759\) −28.7134 −1.04223
\(760\) −1.37534 −0.0498887
\(761\) −0.541203 −0.0196186 −0.00980929 0.999952i \(-0.503122\pi\)
−0.00980929 + 0.999952i \(0.503122\pi\)
\(762\) −55.8549 −2.02341
\(763\) −28.8081 −1.04292
\(764\) −12.3011 −0.445038
\(765\) 19.3131 0.698267
\(766\) −57.0464 −2.06117
\(767\) −9.00194 −0.325041
\(768\) 87.7103 3.16497
\(769\) 7.63415 0.275295 0.137647 0.990481i \(-0.456046\pi\)
0.137647 + 0.990481i \(0.456046\pi\)
\(770\) 15.6703 0.564720
\(771\) −48.6342 −1.75152
\(772\) −53.3205 −1.91905
\(773\) −6.34313 −0.228147 −0.114073 0.993472i \(-0.536390\pi\)
−0.114073 + 0.993472i \(0.536390\pi\)
\(774\) 175.475 6.30733
\(775\) 4.01027 0.144053
\(776\) 96.9641 3.48081
\(777\) 42.3738 1.52015
\(778\) −21.5642 −0.773114
\(779\) −2.07121 −0.0742089
\(780\) 67.8644 2.42994
\(781\) 45.8888 1.64203
\(782\) 16.6215 0.594384
\(783\) −98.6417 −3.52517
\(784\) −33.5064 −1.19666
\(785\) −2.78910 −0.0995474
\(786\) −124.806 −4.45167
\(787\) −40.4199 −1.44081 −0.720407 0.693552i \(-0.756045\pi\)
−0.720407 + 0.693552i \(0.756045\pi\)
\(788\) −13.5432 −0.482457
\(789\) 56.4533 2.00979
\(790\) 13.5283 0.481316
\(791\) 19.0219 0.676342
\(792\) −255.062 −9.06324
\(793\) 41.2686 1.46549
\(794\) −50.7035 −1.79940
\(795\) 1.90114 0.0674265
\(796\) 28.8587 1.02287
\(797\) 32.4008 1.14770 0.573848 0.818962i \(-0.305450\pi\)
0.573848 + 0.818962i \(0.305450\pi\)
\(798\) −3.98692 −0.141135
\(799\) −5.63623 −0.199395
\(800\) 28.2756 0.999694
\(801\) −3.26564 −0.115386
\(802\) −38.0912 −1.34505
\(803\) 85.1499 3.00488
\(804\) −8.64458 −0.304871
\(805\) −1.77100 −0.0624194
\(806\) 15.5978 0.549410
\(807\) 16.6315 0.585457
\(808\) 13.7234 0.482789
\(809\) 45.9212 1.61450 0.807252 0.590207i \(-0.200954\pi\)
0.807252 + 0.590207i \(0.200954\pi\)
\(810\) 33.5953 1.18042
\(811\) −9.02458 −0.316896 −0.158448 0.987367i \(-0.550649\pi\)
−0.158448 + 0.987367i \(0.550649\pi\)
\(812\) 56.1917 1.97194
\(813\) 35.0680 1.22989
\(814\) 120.314 4.21700
\(815\) −3.11152 −0.108992
\(816\) 95.4996 3.34315
\(817\) 3.02322 0.105769
\(818\) 43.9290 1.53594
\(819\) 77.0651 2.69287
\(820\) −20.8631 −0.728572
\(821\) 38.4902 1.34332 0.671658 0.740861i \(-0.265582\pi\)
0.671658 + 0.740861i \(0.265582\pi\)
\(822\) 115.729 4.03650
\(823\) −20.9030 −0.728633 −0.364317 0.931275i \(-0.618697\pi\)
−0.364317 + 0.931275i \(0.618697\pi\)
\(824\) 71.8667 2.50359
\(825\) 80.3199 2.79638
\(826\) 5.32704 0.185351
\(827\) −11.4353 −0.397643 −0.198821 0.980036i \(-0.563711\pi\)
−0.198821 + 0.980036i \(0.563711\pi\)
\(828\) 51.5417 1.79120
\(829\) −0.407809 −0.0141638 −0.00708189 0.999975i \(-0.502254\pi\)
−0.00708189 + 0.999975i \(0.502254\pi\)
\(830\) 16.8990 0.586572
\(831\) −77.1874 −2.67760
\(832\) 6.38673 0.221420
\(833\) 17.8935 0.619972
\(834\) −57.3007 −1.98416
\(835\) −0.295668 −0.0102320
\(836\) −7.85731 −0.271751
\(837\) 11.2466 0.388740
\(838\) 78.3073 2.70508
\(839\) −6.28097 −0.216843 −0.108422 0.994105i \(-0.534580\pi\)
−0.108422 + 0.994105i \(0.534580\pi\)
\(840\) −22.4604 −0.774958
\(841\) 31.2990 1.07927
\(842\) −81.6879 −2.81515
\(843\) 6.11627 0.210656
\(844\) 113.971 3.92303
\(845\) −23.6446 −0.813399
\(846\) −25.1801 −0.865711
\(847\) 32.5284 1.11769
\(848\) 6.58454 0.226114
\(849\) 5.23434 0.179642
\(850\) −46.4953 −1.59478
\(851\) −13.5974 −0.466111
\(852\) −117.603 −4.02903
\(853\) 25.8926 0.886545 0.443273 0.896387i \(-0.353817\pi\)
0.443273 + 0.896387i \(0.353817\pi\)
\(854\) −24.4214 −0.835682
\(855\) 1.48654 0.0508385
\(856\) −40.9734 −1.40044
\(857\) 23.6126 0.806591 0.403296 0.915070i \(-0.367865\pi\)
0.403296 + 0.915070i \(0.367865\pi\)
\(858\) 312.402 10.6652
\(859\) −4.22371 −0.144111 −0.0720556 0.997401i \(-0.522956\pi\)
−0.0720556 + 0.997401i \(0.522956\pi\)
\(860\) 30.4526 1.03842
\(861\) −33.8247 −1.15274
\(862\) −79.4253 −2.70524
\(863\) −15.6758 −0.533611 −0.266805 0.963750i \(-0.585968\pi\)
−0.266805 + 0.963750i \(0.585968\pi\)
\(864\) 79.2977 2.69776
\(865\) −0.0550879 −0.00187305
\(866\) −74.1265 −2.51892
\(867\) 2.79716 0.0949966
\(868\) −6.40668 −0.217457
\(869\) 43.2250 1.46631
\(870\) −43.0953 −1.46107
\(871\) 4.14763 0.140537
\(872\) 117.239 3.97020
\(873\) −104.804 −3.54708
\(874\) 1.27936 0.0432751
\(875\) 10.4225 0.352345
\(876\) −218.221 −7.37302
\(877\) 8.14788 0.275134 0.137567 0.990492i \(-0.456072\pi\)
0.137567 + 0.990492i \(0.456072\pi\)
\(878\) 41.1971 1.39034
\(879\) 78.0857 2.63376
\(880\) −28.8913 −0.973924
\(881\) 50.8584 1.71346 0.856732 0.515763i \(-0.172491\pi\)
0.856732 + 0.515763i \(0.172491\pi\)
\(882\) 79.9399 2.69172
\(883\) 3.86244 0.129981 0.0649906 0.997886i \(-0.479298\pi\)
0.0649906 + 0.997886i \(0.479298\pi\)
\(884\) −125.522 −4.22175
\(885\) −2.83571 −0.0953215
\(886\) 80.4094 2.70141
\(887\) −0.993274 −0.0333509 −0.0166754 0.999861i \(-0.505308\pi\)
−0.0166754 + 0.999861i \(0.505308\pi\)
\(888\) −172.447 −5.78693
\(889\) −11.0074 −0.369177
\(890\) −0.816502 −0.0273692
\(891\) 107.342 3.59609
\(892\) 30.9688 1.03691
\(893\) −0.433822 −0.0145173
\(894\) 122.525 4.09785
\(895\) 12.3060 0.411344
\(896\) 16.1291 0.538834
\(897\) −35.3063 −1.17884
\(898\) −82.0487 −2.73800
\(899\) −6.87497 −0.229293
\(900\) −144.178 −4.80592
\(901\) −3.51634 −0.117146
\(902\) −96.0398 −3.19778
\(903\) 49.3717 1.64299
\(904\) −77.4126 −2.57470
\(905\) −9.53786 −0.317049
\(906\) 124.613 4.13999
\(907\) 2.66865 0.0886112 0.0443056 0.999018i \(-0.485892\pi\)
0.0443056 + 0.999018i \(0.485892\pi\)
\(908\) 5.22519 0.173404
\(909\) −14.8330 −0.491980
\(910\) 19.2685 0.638744
\(911\) −45.8384 −1.51869 −0.759346 0.650687i \(-0.774481\pi\)
−0.759346 + 0.650687i \(0.774481\pi\)
\(912\) 7.35064 0.243404
\(913\) 53.9947 1.78696
\(914\) 17.0144 0.562787
\(915\) 13.0001 0.429770
\(916\) −41.4694 −1.37019
\(917\) −24.5957 −0.812221
\(918\) −130.394 −4.30364
\(919\) 12.8826 0.424958 0.212479 0.977166i \(-0.431846\pi\)
0.212479 + 0.977166i \(0.431846\pi\)
\(920\) 7.20733 0.237619
\(921\) 13.1350 0.432812
\(922\) −16.4421 −0.541493
\(923\) 56.4255 1.85727
\(924\) −128.317 −4.22130
\(925\) 38.0359 1.25061
\(926\) 29.5976 0.972638
\(927\) −77.6773 −2.55126
\(928\) −48.4741 −1.59124
\(929\) 15.8814 0.521052 0.260526 0.965467i \(-0.416104\pi\)
0.260526 + 0.965467i \(0.416104\pi\)
\(930\) 4.91350 0.161120
\(931\) 1.37727 0.0451381
\(932\) 29.0648 0.952050
\(933\) −103.380 −3.38450
\(934\) 103.289 3.37973
\(935\) 15.4288 0.504576
\(936\) −313.628 −10.2512
\(937\) 44.0335 1.43851 0.719256 0.694745i \(-0.244483\pi\)
0.719256 + 0.694745i \(0.244483\pi\)
\(938\) −2.45442 −0.0801397
\(939\) −46.6376 −1.52196
\(940\) −4.36985 −0.142529
\(941\) −5.54300 −0.180696 −0.0903482 0.995910i \(-0.528798\pi\)
−0.0903482 + 0.995910i \(0.528798\pi\)
\(942\) 32.9041 1.07207
\(943\) 10.8540 0.353455
\(944\) −9.82140 −0.319659
\(945\) 13.8933 0.451948
\(946\) 140.183 4.55775
\(947\) 32.8534 1.06759 0.533796 0.845614i \(-0.320765\pi\)
0.533796 + 0.845614i \(0.320765\pi\)
\(948\) −110.777 −3.59785
\(949\) 104.701 3.39875
\(950\) −3.57876 −0.116110
\(951\) 41.9675 1.36089
\(952\) 41.5427 1.34641
\(953\) −23.2944 −0.754580 −0.377290 0.926095i \(-0.623144\pi\)
−0.377290 + 0.926095i \(0.623144\pi\)
\(954\) −15.7095 −0.508612
\(955\) 1.85920 0.0601622
\(956\) 45.8399 1.48257
\(957\) −137.696 −4.45107
\(958\) 81.5655 2.63526
\(959\) 22.8069 0.736472
\(960\) 2.01189 0.0649336
\(961\) −30.2162 −0.974715
\(962\) 147.940 4.76976
\(963\) 44.2862 1.42710
\(964\) −59.1532 −1.90520
\(965\) 8.05890 0.259425
\(966\) 20.8931 0.672224
\(967\) −10.0153 −0.322070 −0.161035 0.986949i \(-0.551483\pi\)
−0.161035 + 0.986949i \(0.551483\pi\)
\(968\) −132.379 −4.25482
\(969\) −3.92546 −0.126104
\(970\) −26.2040 −0.841359
\(971\) −27.5079 −0.882771 −0.441386 0.897318i \(-0.645513\pi\)
−0.441386 + 0.897318i \(0.645513\pi\)
\(972\) −102.157 −3.27668
\(973\) −11.2923 −0.362016
\(974\) −83.6114 −2.67908
\(975\) 98.7624 3.16293
\(976\) 45.0254 1.44123
\(977\) 2.14839 0.0687330 0.0343665 0.999409i \(-0.489059\pi\)
0.0343665 + 0.999409i \(0.489059\pi\)
\(978\) 36.7078 1.17379
\(979\) −2.60884 −0.0833790
\(980\) 13.8731 0.443159
\(981\) −126.718 −4.04579
\(982\) −36.3050 −1.15854
\(983\) −51.1773 −1.63230 −0.816150 0.577839i \(-0.803896\pi\)
−0.816150 + 0.577839i \(0.803896\pi\)
\(984\) 137.654 4.38826
\(985\) 2.04693 0.0652207
\(986\) 79.7089 2.53845
\(987\) −7.08468 −0.225508
\(988\) −9.66146 −0.307372
\(989\) −15.8429 −0.503775
\(990\) 68.9290 2.19071
\(991\) −15.3919 −0.488938 −0.244469 0.969657i \(-0.578614\pi\)
−0.244469 + 0.969657i \(0.578614\pi\)
\(992\) 5.52676 0.175475
\(993\) 84.6172 2.68525
\(994\) −33.3907 −1.05909
\(995\) −4.36173 −0.138276
\(996\) −138.377 −4.38465
\(997\) 38.1850 1.20933 0.604666 0.796479i \(-0.293307\pi\)
0.604666 + 0.796479i \(0.293307\pi\)
\(998\) −90.5663 −2.86683
\(999\) 106.670 3.37488
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 \(a_p\))