Properties

Label 8011.2.a.b.1.19
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 1.19
Character \(\chi\) = 8011.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.56153 q^{2}\) \(+2.54144 q^{3}\) \(+4.56142 q^{4}\) \(-3.00625 q^{5}\) \(-6.50997 q^{6}\) \(-3.61687 q^{7}\) \(-6.56114 q^{8}\) \(+3.45892 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.56153 q^{2}\) \(+2.54144 q^{3}\) \(+4.56142 q^{4}\) \(-3.00625 q^{5}\) \(-6.50997 q^{6}\) \(-3.61687 q^{7}\) \(-6.56114 q^{8}\) \(+3.45892 q^{9}\) \(+7.70058 q^{10}\) \(+2.20426 q^{11}\) \(+11.5926 q^{12}\) \(-3.81806 q^{13}\) \(+9.26470 q^{14}\) \(-7.64019 q^{15}\) \(+7.68370 q^{16}\) \(-7.79644 q^{17}\) \(-8.86010 q^{18}\) \(+1.99752 q^{19}\) \(-13.7127 q^{20}\) \(-9.19204 q^{21}\) \(-5.64628 q^{22}\) \(+2.98541 q^{23}\) \(-16.6747 q^{24}\) \(+4.03751 q^{25}\) \(+9.78007 q^{26}\) \(+1.16631 q^{27}\) \(-16.4980 q^{28}\) \(+8.31482 q^{29}\) \(+19.5706 q^{30}\) \(-2.64647 q^{31}\) \(-6.55973 q^{32}\) \(+5.60200 q^{33}\) \(+19.9708 q^{34}\) \(+10.8732 q^{35}\) \(+15.7776 q^{36}\) \(-10.7166 q^{37}\) \(-5.11670 q^{38}\) \(-9.70338 q^{39}\) \(+19.7244 q^{40}\) \(-11.2502 q^{41}\) \(+23.5457 q^{42}\) \(+3.57514 q^{43}\) \(+10.0546 q^{44}\) \(-10.3983 q^{45}\) \(-7.64721 q^{46}\) \(-9.63306 q^{47}\) \(+19.5277 q^{48}\) \(+6.08171 q^{49}\) \(-10.3422 q^{50}\) \(-19.8142 q^{51}\) \(-17.4158 q^{52}\) \(+7.38262 q^{53}\) \(-2.98752 q^{54}\) \(-6.62656 q^{55}\) \(+23.7308 q^{56}\) \(+5.07658 q^{57}\) \(-21.2986 q^{58}\) \(-8.73893 q^{59}\) \(-34.8501 q^{60}\) \(+2.57776 q^{61}\) \(+6.77901 q^{62}\) \(-12.5104 q^{63}\) \(+1.43551 q^{64}\) \(+11.4780 q^{65}\) \(-14.3497 q^{66}\) \(-9.40824 q^{67}\) \(-35.5628 q^{68}\) \(+7.58725 q^{69}\) \(-27.8520 q^{70}\) \(+13.8414 q^{71}\) \(-22.6944 q^{72}\) \(-6.32605 q^{73}\) \(+27.4508 q^{74}\) \(+10.2611 q^{75}\) \(+9.11153 q^{76}\) \(-7.97252 q^{77}\) \(+24.8555 q^{78}\) \(+10.0733 q^{79}\) \(-23.0991 q^{80}\) \(-7.41265 q^{81}\) \(+28.8176 q^{82}\) \(+7.40492 q^{83}\) \(-41.9288 q^{84}\) \(+23.4380 q^{85}\) \(-9.15782 q^{86}\) \(+21.1316 q^{87}\) \(-14.4625 q^{88}\) \(-13.9660 q^{89}\) \(+26.6356 q^{90}\) \(+13.8094 q^{91}\) \(+13.6177 q^{92}\) \(-6.72585 q^{93}\) \(+24.6753 q^{94}\) \(-6.00504 q^{95}\) \(-16.6711 q^{96}\) \(-1.11229 q^{97}\) \(-15.5785 q^{98}\) \(+7.62436 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut 21q^{10} \) \(\mathstrut +\mathstrut 70q^{11} \) \(\mathstrut +\mathstrut 20q^{12} \) \(\mathstrut +\mathstrut 53q^{13} \) \(\mathstrut +\mathstrut 69q^{14} \) \(\mathstrut +\mathstrut 28q^{15} \) \(\mathstrut +\mathstrut 449q^{16} \) \(\mathstrut +\mathstrut 88q^{17} \) \(\mathstrut +\mathstrut 86q^{18} \) \(\mathstrut +\mathstrut 44q^{19} \) \(\mathstrut +\mathstrut 136q^{20} \) \(\mathstrut +\mathstrut 125q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 104q^{23} \) \(\mathstrut +\mathstrut 84q^{24} \) \(\mathstrut +\mathstrut 444q^{25} \) \(\mathstrut +\mathstrut 100q^{26} \) \(\mathstrut +\mathstrut 32q^{27} \) \(\mathstrut +\mathstrut 46q^{28} \) \(\mathstrut +\mathstrut 373q^{29} \) \(\mathstrut +\mathstrut 99q^{30} \) \(\mathstrut +\mathstrut 30q^{31} \) \(\mathstrut +\mathstrut 221q^{32} \) \(\mathstrut +\mathstrut 56q^{33} \) \(\mathstrut +\mathstrut 26q^{34} \) \(\mathstrut +\mathstrut 164q^{35} \) \(\mathstrut +\mathstrut 599q^{36} \) \(\mathstrut +\mathstrut 81q^{37} \) \(\mathstrut +\mathstrut 66q^{38} \) \(\mathstrut +\mathstrut 143q^{39} \) \(\mathstrut +\mathstrut 42q^{40} \) \(\mathstrut +\mathstrut 182q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut +\mathstrut 40q^{43} \) \(\mathstrut +\mathstrut 184q^{44} \) \(\mathstrut +\mathstrut 198q^{45} \) \(\mathstrut +\mathstrut 54q^{46} \) \(\mathstrut +\mathstrut 66q^{47} \) \(\mathstrut +\mathstrut 5q^{48} \) \(\mathstrut +\mathstrut 479q^{49} \) \(\mathstrut +\mathstrut 184q^{50} \) \(\mathstrut +\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 64q^{52} \) \(\mathstrut +\mathstrut 221q^{53} \) \(\mathstrut +\mathstrut 67q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 174q^{56} \) \(\mathstrut +\mathstrut 84q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut +\mathstrut 127q^{59} \) \(\mathstrut +\mathstrut 29q^{60} \) \(\mathstrut +\mathstrut 174q^{61} \) \(\mathstrut +\mathstrut 86q^{62} \) \(\mathstrut +\mathstrut 48q^{63} \) \(\mathstrut +\mathstrut 549q^{64} \) \(\mathstrut +\mathstrut 202q^{65} \) \(\mathstrut +\mathstrut 32q^{66} \) \(\mathstrut +\mathstrut 29q^{67} \) \(\mathstrut +\mathstrut 172q^{68} \) \(\mathstrut +\mathstrut 249q^{69} \) \(\mathstrut +\mathstrut 12q^{70} \) \(\mathstrut +\mathstrut 185q^{71} \) \(\mathstrut +\mathstrut 218q^{72} \) \(\mathstrut +\mathstrut 57q^{73} \) \(\mathstrut +\mathstrut 272q^{74} \) \(\mathstrut +\mathstrut 24q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 384q^{77} \) \(\mathstrut +\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 93q^{79} \) \(\mathstrut +\mathstrut 215q^{80} \) \(\mathstrut +\mathstrut 702q^{81} \) \(\mathstrut +\mathstrut 48q^{82} \) \(\mathstrut +\mathstrut 121q^{83} \) \(\mathstrut +\mathstrut 179q^{84} \) \(\mathstrut +\mathstrut 177q^{85} \) \(\mathstrut +\mathstrut 209q^{86} \) \(\mathstrut +\mathstrut 91q^{87} \) \(\mathstrut +\mathstrut 36q^{88} \) \(\mathstrut +\mathstrut 186q^{89} \) \(\mathstrut +\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut +\mathstrut 272q^{92} \) \(\mathstrut +\mathstrut 220q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 170q^{95} \) \(\mathstrut +\mathstrut 162q^{96} \) \(\mathstrut +\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 196q^{98} \) \(\mathstrut +\mathstrut 152q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.56153 −1.81127 −0.905636 0.424055i \(-0.860606\pi\)
−0.905636 + 0.424055i \(0.860606\pi\)
\(3\) 2.54144 1.46730 0.733650 0.679527i \(-0.237815\pi\)
0.733650 + 0.679527i \(0.237815\pi\)
\(4\) 4.56142 2.28071
\(5\) −3.00625 −1.34443 −0.672217 0.740354i \(-0.734658\pi\)
−0.672217 + 0.740354i \(0.734658\pi\)
\(6\) −6.50997 −2.65768
\(7\) −3.61687 −1.36705 −0.683523 0.729929i \(-0.739553\pi\)
−0.683523 + 0.729929i \(0.739553\pi\)
\(8\) −6.56114 −2.31971
\(9\) 3.45892 1.15297
\(10\) 7.70058 2.43514
\(11\) 2.20426 0.664610 0.332305 0.943172i \(-0.392174\pi\)
0.332305 + 0.943172i \(0.392174\pi\)
\(12\) 11.5926 3.34649
\(13\) −3.81806 −1.05894 −0.529470 0.848328i \(-0.677609\pi\)
−0.529470 + 0.848328i \(0.677609\pi\)
\(14\) 9.26470 2.47609
\(15\) −7.64019 −1.97269
\(16\) 7.68370 1.92093
\(17\) −7.79644 −1.89091 −0.945457 0.325746i \(-0.894384\pi\)
−0.945457 + 0.325746i \(0.894384\pi\)
\(18\) −8.86010 −2.08835
\(19\) 1.99752 0.458263 0.229131 0.973396i \(-0.426411\pi\)
0.229131 + 0.973396i \(0.426411\pi\)
\(20\) −13.7127 −3.06626
\(21\) −9.19204 −2.00587
\(22\) −5.64628 −1.20379
\(23\) 2.98541 0.622502 0.311251 0.950328i \(-0.399252\pi\)
0.311251 + 0.950328i \(0.399252\pi\)
\(24\) −16.6747 −3.40372
\(25\) 4.03751 0.807503
\(26\) 9.78007 1.91803
\(27\) 1.16631 0.224456
\(28\) −16.4980 −3.11784
\(29\) 8.31482 1.54402 0.772012 0.635608i \(-0.219251\pi\)
0.772012 + 0.635608i \(0.219251\pi\)
\(30\) 19.5706 3.57308
\(31\) −2.64647 −0.475320 −0.237660 0.971348i \(-0.576380\pi\)
−0.237660 + 0.971348i \(0.576380\pi\)
\(32\) −6.55973 −1.15961
\(33\) 5.60200 0.975183
\(34\) 19.9708 3.42496
\(35\) 10.8732 1.83790
\(36\) 15.7776 2.62959
\(37\) −10.7166 −1.76179 −0.880896 0.473310i \(-0.843059\pi\)
−0.880896 + 0.473310i \(0.843059\pi\)
\(38\) −5.11670 −0.830039
\(39\) −9.70338 −1.55378
\(40\) 19.7244 3.11870
\(41\) −11.2502 −1.75698 −0.878489 0.477762i \(-0.841448\pi\)
−0.878489 + 0.477762i \(0.841448\pi\)
\(42\) 23.5457 3.63318
\(43\) 3.57514 0.545204 0.272602 0.962127i \(-0.412116\pi\)
0.272602 + 0.962127i \(0.412116\pi\)
\(44\) 10.0546 1.51578
\(45\) −10.3983 −1.55009
\(46\) −7.64721 −1.12752
\(47\) −9.63306 −1.40513 −0.702563 0.711622i \(-0.747961\pi\)
−0.702563 + 0.711622i \(0.747961\pi\)
\(48\) 19.5277 2.81858
\(49\) 6.08171 0.868816
\(50\) −10.3422 −1.46261
\(51\) −19.8142 −2.77454
\(52\) −17.4158 −2.41514
\(53\) 7.38262 1.01408 0.507041 0.861922i \(-0.330739\pi\)
0.507041 + 0.861922i \(0.330739\pi\)
\(54\) −2.98752 −0.406550
\(55\) −6.62656 −0.893525
\(56\) 23.7308 3.17116
\(57\) 5.07658 0.672409
\(58\) −21.2986 −2.79665
\(59\) −8.73893 −1.13771 −0.568856 0.822437i \(-0.692614\pi\)
−0.568856 + 0.822437i \(0.692614\pi\)
\(60\) −34.8501 −4.49913
\(61\) 2.57776 0.330048 0.165024 0.986290i \(-0.447230\pi\)
0.165024 + 0.986290i \(0.447230\pi\)
\(62\) 6.77901 0.860935
\(63\) −12.5104 −1.57617
\(64\) 1.43551 0.179438
\(65\) 11.4780 1.42368
\(66\) −14.3497 −1.76632
\(67\) −9.40824 −1.14940 −0.574700 0.818364i \(-0.694881\pi\)
−0.574700 + 0.818364i \(0.694881\pi\)
\(68\) −35.5628 −4.31263
\(69\) 7.58725 0.913397
\(70\) −27.8520 −3.32895
\(71\) 13.8414 1.64267 0.821333 0.570449i \(-0.193231\pi\)
0.821333 + 0.570449i \(0.193231\pi\)
\(72\) −22.6944 −2.67456
\(73\) −6.32605 −0.740408 −0.370204 0.928950i \(-0.620712\pi\)
−0.370204 + 0.928950i \(0.620712\pi\)
\(74\) 27.4508 3.19109
\(75\) 10.2611 1.18485
\(76\) 9.11153 1.04516
\(77\) −7.97252 −0.908553
\(78\) 24.8555 2.81433
\(79\) 10.0733 1.13333 0.566666 0.823948i \(-0.308233\pi\)
0.566666 + 0.823948i \(0.308233\pi\)
\(80\) −23.0991 −2.58256
\(81\) −7.41265 −0.823628
\(82\) 28.8176 3.18237
\(83\) 7.40492 0.812796 0.406398 0.913696i \(-0.366785\pi\)
0.406398 + 0.913696i \(0.366785\pi\)
\(84\) −41.9288 −4.57480
\(85\) 23.4380 2.54221
\(86\) −9.15782 −0.987513
\(87\) 21.1316 2.26555
\(88\) −14.4625 −1.54171
\(89\) −13.9660 −1.48040 −0.740198 0.672389i \(-0.765268\pi\)
−0.740198 + 0.672389i \(0.765268\pi\)
\(90\) 26.6356 2.80764
\(91\) 13.8094 1.44762
\(92\) 13.6177 1.41975
\(93\) −6.72585 −0.697438
\(94\) 24.6753 2.54507
\(95\) −6.00504 −0.616104
\(96\) −16.6711 −1.70149
\(97\) −1.11229 −0.112936 −0.0564679 0.998404i \(-0.517984\pi\)
−0.0564679 + 0.998404i \(0.517984\pi\)
\(98\) −15.5785 −1.57366
\(99\) 7.62436 0.766277
\(100\) 18.4168 1.84168
\(101\) 16.7103 1.66274 0.831368 0.555723i \(-0.187558\pi\)
0.831368 + 0.555723i \(0.187558\pi\)
\(102\) 50.7546 5.02545
\(103\) −16.0534 −1.58179 −0.790894 0.611953i \(-0.790384\pi\)
−0.790894 + 0.611953i \(0.790384\pi\)
\(104\) 25.0509 2.45644
\(105\) 27.6335 2.69676
\(106\) −18.9108 −1.83678
\(107\) 3.00288 0.290299 0.145149 0.989410i \(-0.453634\pi\)
0.145149 + 0.989410i \(0.453634\pi\)
\(108\) 5.32001 0.511918
\(109\) 11.4788 1.09947 0.549733 0.835340i \(-0.314729\pi\)
0.549733 + 0.835340i \(0.314729\pi\)
\(110\) 16.9741 1.61842
\(111\) −27.2355 −2.58508
\(112\) −27.7909 −2.62599
\(113\) −1.71065 −0.160924 −0.0804621 0.996758i \(-0.525640\pi\)
−0.0804621 + 0.996758i \(0.525640\pi\)
\(114\) −13.0038 −1.21792
\(115\) −8.97488 −0.836912
\(116\) 37.9274 3.52147
\(117\) −13.2064 −1.22093
\(118\) 22.3850 2.06071
\(119\) 28.1987 2.58497
\(120\) 50.1284 4.57607
\(121\) −6.14122 −0.558293
\(122\) −6.60299 −0.597807
\(123\) −28.5916 −2.57802
\(124\) −12.0717 −1.08407
\(125\) 2.89347 0.258800
\(126\) 32.0458 2.85487
\(127\) −15.1212 −1.34179 −0.670896 0.741552i \(-0.734090\pi\)
−0.670896 + 0.741552i \(0.734090\pi\)
\(128\) 9.44237 0.834595
\(129\) 9.08601 0.799978
\(130\) −29.4013 −2.57867
\(131\) −22.2083 −1.94035 −0.970175 0.242404i \(-0.922064\pi\)
−0.970175 + 0.242404i \(0.922064\pi\)
\(132\) 25.5531 2.22411
\(133\) −7.22476 −0.626466
\(134\) 24.0995 2.08188
\(135\) −3.50620 −0.301766
\(136\) 51.1536 4.38638
\(137\) −1.16754 −0.0997500 −0.0498750 0.998755i \(-0.515882\pi\)
−0.0498750 + 0.998755i \(0.515882\pi\)
\(138\) −19.4349 −1.65441
\(139\) −3.10551 −0.263406 −0.131703 0.991289i \(-0.542044\pi\)
−0.131703 + 0.991289i \(0.542044\pi\)
\(140\) 49.5971 4.19172
\(141\) −24.4818 −2.06174
\(142\) −35.4550 −2.97532
\(143\) −8.41602 −0.703783
\(144\) 26.5773 2.21477
\(145\) −24.9964 −2.07584
\(146\) 16.2044 1.34108
\(147\) 15.4563 1.27481
\(148\) −48.8827 −4.01814
\(149\) 14.7707 1.21006 0.605029 0.796203i \(-0.293161\pi\)
0.605029 + 0.796203i \(0.293161\pi\)
\(150\) −26.2841 −2.14609
\(151\) 5.66785 0.461243 0.230622 0.973044i \(-0.425924\pi\)
0.230622 + 0.973044i \(0.425924\pi\)
\(152\) −13.1060 −1.06304
\(153\) −26.9672 −2.18017
\(154\) 20.4218 1.64564
\(155\) 7.95594 0.639037
\(156\) −44.2612 −3.54373
\(157\) −8.78474 −0.701099 −0.350549 0.936544i \(-0.614005\pi\)
−0.350549 + 0.936544i \(0.614005\pi\)
\(158\) −25.8030 −2.05277
\(159\) 18.7625 1.48796
\(160\) 19.7201 1.55901
\(161\) −10.7978 −0.850989
\(162\) 18.9877 1.49181
\(163\) 9.38215 0.734866 0.367433 0.930050i \(-0.380237\pi\)
0.367433 + 0.930050i \(0.380237\pi\)
\(164\) −51.3167 −4.00716
\(165\) −16.8410 −1.31107
\(166\) −18.9679 −1.47219
\(167\) 17.8900 1.38437 0.692185 0.721720i \(-0.256648\pi\)
0.692185 + 0.721720i \(0.256648\pi\)
\(168\) 60.3103 4.65304
\(169\) 1.57762 0.121355
\(170\) −60.0371 −4.60464
\(171\) 6.90925 0.528364
\(172\) 16.3077 1.24345
\(173\) 17.5847 1.33694 0.668471 0.743738i \(-0.266949\pi\)
0.668471 + 0.743738i \(0.266949\pi\)
\(174\) −54.1292 −4.10352
\(175\) −14.6031 −1.10389
\(176\) 16.9369 1.27667
\(177\) −22.2095 −1.66937
\(178\) 35.7743 2.68140
\(179\) −11.6772 −0.872796 −0.436398 0.899754i \(-0.643746\pi\)
−0.436398 + 0.899754i \(0.643746\pi\)
\(180\) −47.4312 −3.53531
\(181\) −0.837814 −0.0622742 −0.0311371 0.999515i \(-0.509913\pi\)
−0.0311371 + 0.999515i \(0.509913\pi\)
\(182\) −35.3732 −2.62204
\(183\) 6.55121 0.484280
\(184\) −19.5877 −1.44403
\(185\) 32.2166 2.36861
\(186\) 17.2284 1.26325
\(187\) −17.1854 −1.25672
\(188\) −43.9404 −3.20468
\(189\) −4.21837 −0.306841
\(190\) 15.3821 1.11593
\(191\) −7.66133 −0.554354 −0.277177 0.960819i \(-0.589399\pi\)
−0.277177 + 0.960819i \(0.589399\pi\)
\(192\) 3.64825 0.263290
\(193\) 13.9158 1.00168 0.500842 0.865539i \(-0.333024\pi\)
0.500842 + 0.865539i \(0.333024\pi\)
\(194\) 2.84916 0.204558
\(195\) 29.1707 2.08896
\(196\) 27.7412 1.98152
\(197\) −19.7394 −1.40637 −0.703186 0.711006i \(-0.748240\pi\)
−0.703186 + 0.711006i \(0.748240\pi\)
\(198\) −19.5300 −1.38794
\(199\) −1.56272 −0.110779 −0.0553893 0.998465i \(-0.517640\pi\)
−0.0553893 + 0.998465i \(0.517640\pi\)
\(200\) −26.4907 −1.87317
\(201\) −23.9105 −1.68652
\(202\) −42.8038 −3.01167
\(203\) −30.0736 −2.11075
\(204\) −90.3808 −6.32792
\(205\) 33.8207 2.36214
\(206\) 41.1212 2.86505
\(207\) 10.3263 0.717727
\(208\) −29.3369 −2.03415
\(209\) 4.40306 0.304566
\(210\) −70.7841 −4.88456
\(211\) −0.459529 −0.0316353 −0.0158176 0.999875i \(-0.505035\pi\)
−0.0158176 + 0.999875i \(0.505035\pi\)
\(212\) 33.6752 2.31282
\(213\) 35.1770 2.41029
\(214\) −7.69195 −0.525811
\(215\) −10.7478 −0.732991
\(216\) −7.65230 −0.520673
\(217\) 9.57193 0.649785
\(218\) −29.4032 −1.99143
\(219\) −16.0773 −1.08640
\(220\) −30.2265 −2.03787
\(221\) 29.7673 2.00237
\(222\) 69.7644 4.68228
\(223\) 21.1560 1.41671 0.708354 0.705857i \(-0.249438\pi\)
0.708354 + 0.705857i \(0.249438\pi\)
\(224\) 23.7256 1.58524
\(225\) 13.9654 0.931028
\(226\) 4.38187 0.291478
\(227\) 15.9982 1.06184 0.530920 0.847422i \(-0.321847\pi\)
0.530920 + 0.847422i \(0.321847\pi\)
\(228\) 23.1564 1.53357
\(229\) −27.4724 −1.81543 −0.907714 0.419590i \(-0.862174\pi\)
−0.907714 + 0.419590i \(0.862174\pi\)
\(230\) 22.9894 1.51588
\(231\) −20.2617 −1.33312
\(232\) −54.5547 −3.58169
\(233\) 0.954541 0.0625341 0.0312670 0.999511i \(-0.490046\pi\)
0.0312670 + 0.999511i \(0.490046\pi\)
\(234\) 33.8284 2.21143
\(235\) 28.9593 1.88910
\(236\) −39.8619 −2.59479
\(237\) 25.6006 1.66294
\(238\) −72.2317 −4.68208
\(239\) 11.2833 0.729856 0.364928 0.931036i \(-0.381094\pi\)
0.364928 + 0.931036i \(0.381094\pi\)
\(240\) −58.7050 −3.78939
\(241\) −18.4650 −1.18944 −0.594718 0.803934i \(-0.702736\pi\)
−0.594718 + 0.803934i \(0.702736\pi\)
\(242\) 15.7309 1.01122
\(243\) −22.3377 −1.43297
\(244\) 11.7582 0.752743
\(245\) −18.2831 −1.16807
\(246\) 73.2381 4.66949
\(247\) −7.62666 −0.485273
\(248\) 17.3639 1.10261
\(249\) 18.8192 1.19262
\(250\) −7.41171 −0.468758
\(251\) 27.3617 1.72706 0.863529 0.504299i \(-0.168249\pi\)
0.863529 + 0.504299i \(0.168249\pi\)
\(252\) −57.0653 −3.59478
\(253\) 6.58063 0.413721
\(254\) 38.7334 2.43035
\(255\) 59.5663 3.73019
\(256\) −27.0579 −1.69112
\(257\) 22.5196 1.40473 0.702367 0.711815i \(-0.252127\pi\)
0.702367 + 0.711815i \(0.252127\pi\)
\(258\) −23.2741 −1.44898
\(259\) 38.7604 2.40845
\(260\) 52.3561 3.24699
\(261\) 28.7603 1.78022
\(262\) 56.8872 3.51450
\(263\) 1.37032 0.0844976 0.0422488 0.999107i \(-0.486548\pi\)
0.0422488 + 0.999107i \(0.486548\pi\)
\(264\) −36.7555 −2.26215
\(265\) −22.1940 −1.36336
\(266\) 18.5064 1.13470
\(267\) −35.4938 −2.17219
\(268\) −42.9149 −2.62145
\(269\) 5.74852 0.350493 0.175247 0.984525i \(-0.443928\pi\)
0.175247 + 0.984525i \(0.443928\pi\)
\(270\) 8.98123 0.546580
\(271\) 25.7719 1.56553 0.782765 0.622317i \(-0.213809\pi\)
0.782765 + 0.622317i \(0.213809\pi\)
\(272\) −59.9055 −3.63231
\(273\) 35.0958 2.12410
\(274\) 2.99069 0.180674
\(275\) 8.89974 0.536674
\(276\) 34.6086 2.08319
\(277\) −16.3149 −0.980266 −0.490133 0.871648i \(-0.663052\pi\)
−0.490133 + 0.871648i \(0.663052\pi\)
\(278\) 7.95484 0.477099
\(279\) −9.15392 −0.548031
\(280\) −71.3405 −4.26341
\(281\) −11.2518 −0.671226 −0.335613 0.942000i \(-0.608943\pi\)
−0.335613 + 0.942000i \(0.608943\pi\)
\(282\) 62.7109 3.73438
\(283\) 19.2045 1.14159 0.570795 0.821093i \(-0.306635\pi\)
0.570795 + 0.821093i \(0.306635\pi\)
\(284\) 63.1362 3.74644
\(285\) −15.2614 −0.904010
\(286\) 21.5579 1.27474
\(287\) 40.6903 2.40187
\(288\) −22.6895 −1.33699
\(289\) 43.7845 2.57556
\(290\) 64.0289 3.75991
\(291\) −2.82682 −0.165711
\(292\) −28.8558 −1.68866
\(293\) −12.5841 −0.735172 −0.367586 0.929989i \(-0.619816\pi\)
−0.367586 + 0.929989i \(0.619816\pi\)
\(294\) −39.5917 −2.30904
\(295\) 26.2714 1.52958
\(296\) 70.3129 4.08685
\(297\) 2.57084 0.149175
\(298\) −37.8354 −2.19175
\(299\) −11.3985 −0.659192
\(300\) 46.8051 2.70230
\(301\) −12.9308 −0.745319
\(302\) −14.5183 −0.835437
\(303\) 42.4682 2.43973
\(304\) 15.3484 0.880289
\(305\) −7.74937 −0.443728
\(306\) 69.0773 3.94888
\(307\) −29.6428 −1.69180 −0.845902 0.533338i \(-0.820937\pi\)
−0.845902 + 0.533338i \(0.820937\pi\)
\(308\) −36.3660 −2.07215
\(309\) −40.7987 −2.32096
\(310\) −20.3794 −1.15747
\(311\) 7.71994 0.437757 0.218879 0.975752i \(-0.429760\pi\)
0.218879 + 0.975752i \(0.429760\pi\)
\(312\) 63.6653 3.60434
\(313\) 12.6853 0.717017 0.358508 0.933527i \(-0.383285\pi\)
0.358508 + 0.933527i \(0.383285\pi\)
\(314\) 22.5024 1.26988
\(315\) 37.6094 2.11905
\(316\) 45.9484 2.58480
\(317\) 15.5382 0.872712 0.436356 0.899774i \(-0.356269\pi\)
0.436356 + 0.899774i \(0.356269\pi\)
\(318\) −48.0606 −2.69511
\(319\) 18.3281 1.02617
\(320\) −4.31548 −0.241243
\(321\) 7.63163 0.425956
\(322\) 27.6589 1.54137
\(323\) −15.5736 −0.866536
\(324\) −33.8122 −1.87846
\(325\) −15.4155 −0.855097
\(326\) −24.0326 −1.33104
\(327\) 29.1726 1.61325
\(328\) 73.8138 4.07569
\(329\) 34.8415 1.92087
\(330\) 43.1386 2.37470
\(331\) 0.378075 0.0207809 0.0103904 0.999946i \(-0.496693\pi\)
0.0103904 + 0.999946i \(0.496693\pi\)
\(332\) 33.7769 1.85375
\(333\) −37.0677 −2.03130
\(334\) −45.8257 −2.50747
\(335\) 28.2835 1.54529
\(336\) −70.6289 −3.85312
\(337\) 10.4593 0.569752 0.284876 0.958564i \(-0.408048\pi\)
0.284876 + 0.958564i \(0.408048\pi\)
\(338\) −4.04111 −0.219808
\(339\) −4.34751 −0.236124
\(340\) 106.911 5.79804
\(341\) −5.83352 −0.315903
\(342\) −17.6982 −0.957011
\(343\) 3.32132 0.179334
\(344\) −23.4570 −1.26472
\(345\) −22.8091 −1.22800
\(346\) −45.0437 −2.42157
\(347\) 23.7289 1.27384 0.636918 0.770932i \(-0.280209\pi\)
0.636918 + 0.770932i \(0.280209\pi\)
\(348\) 96.3902 5.16705
\(349\) −9.93055 −0.531570 −0.265785 0.964032i \(-0.585631\pi\)
−0.265785 + 0.964032i \(0.585631\pi\)
\(350\) 37.4063 1.99945
\(351\) −4.45303 −0.237685
\(352\) −14.4594 −0.770686
\(353\) 11.0081 0.585902 0.292951 0.956127i \(-0.405363\pi\)
0.292951 + 0.956127i \(0.405363\pi\)
\(354\) 56.8901 3.02368
\(355\) −41.6105 −2.20846
\(356\) −63.7049 −3.37635
\(357\) 71.6652 3.79293
\(358\) 29.9115 1.58087
\(359\) 25.7066 1.35674 0.678372 0.734718i \(-0.262686\pi\)
0.678372 + 0.734718i \(0.262686\pi\)
\(360\) 68.2250 3.59578
\(361\) −15.0099 −0.789995
\(362\) 2.14608 0.112796
\(363\) −15.6076 −0.819184
\(364\) 62.9906 3.30160
\(365\) 19.0177 0.995430
\(366\) −16.7811 −0.877162
\(367\) 15.4100 0.804395 0.402197 0.915553i \(-0.368247\pi\)
0.402197 + 0.915553i \(0.368247\pi\)
\(368\) 22.9390 1.19578
\(369\) −38.9133 −2.02575
\(370\) −82.5237 −4.29020
\(371\) −26.7019 −1.38630
\(372\) −30.6794 −1.59065
\(373\) −1.50176 −0.0777582 −0.0388791 0.999244i \(-0.512379\pi\)
−0.0388791 + 0.999244i \(0.512379\pi\)
\(374\) 44.0209 2.27626
\(375\) 7.35359 0.379738
\(376\) 63.2039 3.25949
\(377\) −31.7465 −1.63503
\(378\) 10.8055 0.555773
\(379\) 14.6246 0.751217 0.375608 0.926778i \(-0.377434\pi\)
0.375608 + 0.926778i \(0.377434\pi\)
\(380\) −27.3915 −1.40515
\(381\) −38.4297 −1.96881
\(382\) 19.6247 1.00409
\(383\) −4.12778 −0.210920 −0.105460 0.994424i \(-0.533631\pi\)
−0.105460 + 0.994424i \(0.533631\pi\)
\(384\) 23.9972 1.22460
\(385\) 23.9674 1.22149
\(386\) −35.6458 −1.81432
\(387\) 12.3661 0.628605
\(388\) −5.07362 −0.257574
\(389\) −22.3662 −1.13401 −0.567006 0.823714i \(-0.691898\pi\)
−0.567006 + 0.823714i \(0.691898\pi\)
\(390\) −74.7216 −3.78368
\(391\) −23.2756 −1.17710
\(392\) −39.9030 −2.01541
\(393\) −56.4411 −2.84708
\(394\) 50.5630 2.54732
\(395\) −30.2827 −1.52369
\(396\) 34.7779 1.74765
\(397\) 6.41105 0.321762 0.160881 0.986974i \(-0.448567\pi\)
0.160881 + 0.986974i \(0.448567\pi\)
\(398\) 4.00296 0.200650
\(399\) −18.3613 −0.919215
\(400\) 31.0230 1.55115
\(401\) 1.93305 0.0965319 0.0482659 0.998835i \(-0.484631\pi\)
0.0482659 + 0.998835i \(0.484631\pi\)
\(402\) 61.2473 3.05474
\(403\) 10.1044 0.503336
\(404\) 76.2226 3.79222
\(405\) 22.2842 1.10731
\(406\) 77.0343 3.82315
\(407\) −23.6221 −1.17091
\(408\) 130.004 6.43614
\(409\) 3.27687 0.162031 0.0810153 0.996713i \(-0.474184\pi\)
0.0810153 + 0.996713i \(0.474184\pi\)
\(410\) −86.6327 −4.27848
\(411\) −2.96724 −0.146363
\(412\) −73.2263 −3.60760
\(413\) 31.6075 1.55531
\(414\) −26.4511 −1.30000
\(415\) −22.2610 −1.09275
\(416\) 25.0455 1.22795
\(417\) −7.89246 −0.386495
\(418\) −11.2786 −0.551652
\(419\) 34.7357 1.69695 0.848475 0.529236i \(-0.177521\pi\)
0.848475 + 0.529236i \(0.177521\pi\)
\(420\) 126.048 6.15052
\(421\) −29.7591 −1.45037 −0.725185 0.688554i \(-0.758246\pi\)
−0.725185 + 0.688554i \(0.758246\pi\)
\(422\) 1.17710 0.0573002
\(423\) −33.3199 −1.62007
\(424\) −48.4384 −2.35238
\(425\) −31.4782 −1.52692
\(426\) −90.1067 −4.36568
\(427\) −9.32340 −0.451191
\(428\) 13.6974 0.662087
\(429\) −21.3888 −1.03266
\(430\) 27.5307 1.32765
\(431\) 26.0204 1.25336 0.626680 0.779277i \(-0.284413\pi\)
0.626680 + 0.779277i \(0.284413\pi\)
\(432\) 8.96154 0.431162
\(433\) −19.6649 −0.945037 −0.472518 0.881321i \(-0.656655\pi\)
−0.472518 + 0.881321i \(0.656655\pi\)
\(434\) −24.5188 −1.17694
\(435\) −63.5268 −3.04588
\(436\) 52.3594 2.50756
\(437\) 5.96342 0.285269
\(438\) 41.1824 1.96777
\(439\) 28.5104 1.36073 0.680365 0.732874i \(-0.261821\pi\)
0.680365 + 0.732874i \(0.261821\pi\)
\(440\) 43.4778 2.07272
\(441\) 21.0361 1.00172
\(442\) −76.2498 −3.62683
\(443\) −0.529187 −0.0251424 −0.0125712 0.999921i \(-0.504002\pi\)
−0.0125712 + 0.999921i \(0.504002\pi\)
\(444\) −124.232 −5.89581
\(445\) 41.9853 1.99029
\(446\) −54.1916 −2.56605
\(447\) 37.5387 1.77552
\(448\) −5.19203 −0.245300
\(449\) 20.3954 0.962520 0.481260 0.876578i \(-0.340179\pi\)
0.481260 + 0.876578i \(0.340179\pi\)
\(450\) −35.7728 −1.68634
\(451\) −24.7983 −1.16771
\(452\) −7.80298 −0.367022
\(453\) 14.4045 0.676782
\(454\) −40.9799 −1.92328
\(455\) −41.5145 −1.94623
\(456\) −33.3082 −1.55980
\(457\) 1.88618 0.0882317 0.0441158 0.999026i \(-0.485953\pi\)
0.0441158 + 0.999026i \(0.485953\pi\)
\(458\) 70.3713 3.28823
\(459\) −9.09303 −0.424426
\(460\) −40.9382 −1.90875
\(461\) 17.2168 0.801864 0.400932 0.916108i \(-0.368686\pi\)
0.400932 + 0.916108i \(0.368686\pi\)
\(462\) 51.9008 2.41465
\(463\) 14.3910 0.668806 0.334403 0.942430i \(-0.391465\pi\)
0.334403 + 0.942430i \(0.391465\pi\)
\(464\) 63.8886 2.96595
\(465\) 20.2196 0.937659
\(466\) −2.44508 −0.113266
\(467\) 2.69015 0.124485 0.0622427 0.998061i \(-0.480175\pi\)
0.0622427 + 0.998061i \(0.480175\pi\)
\(468\) −60.2397 −2.78458
\(469\) 34.0284 1.57128
\(470\) −74.1801 −3.42167
\(471\) −22.3259 −1.02872
\(472\) 57.3374 2.63917
\(473\) 7.88055 0.362348
\(474\) −65.5767 −3.01204
\(475\) 8.06502 0.370048
\(476\) 128.626 5.89556
\(477\) 25.5359 1.16921
\(478\) −28.9025 −1.32197
\(479\) 19.0487 0.870357 0.435179 0.900344i \(-0.356685\pi\)
0.435179 + 0.900344i \(0.356685\pi\)
\(480\) 50.1176 2.28754
\(481\) 40.9165 1.86563
\(482\) 47.2986 2.15439
\(483\) −27.4420 −1.24866
\(484\) −28.0127 −1.27330
\(485\) 3.34381 0.151835
\(486\) 57.2187 2.59549
\(487\) −36.4665 −1.65245 −0.826227 0.563337i \(-0.809517\pi\)
−0.826227 + 0.563337i \(0.809517\pi\)
\(488\) −16.9130 −0.765617
\(489\) 23.8442 1.07827
\(490\) 46.8327 2.11569
\(491\) −22.7726 −1.02771 −0.513857 0.857876i \(-0.671784\pi\)
−0.513857 + 0.857876i \(0.671784\pi\)
\(492\) −130.418 −5.87971
\(493\) −64.8260 −2.91962
\(494\) 19.5359 0.878962
\(495\) −22.9207 −1.03021
\(496\) −20.3347 −0.913055
\(497\) −50.0623 −2.24560
\(498\) −48.2058 −2.16015
\(499\) 23.6318 1.05791 0.528953 0.848651i \(-0.322585\pi\)
0.528953 + 0.848651i \(0.322585\pi\)
\(500\) 13.1983 0.590248
\(501\) 45.4664 2.03129
\(502\) −70.0878 −3.12817
\(503\) −28.5638 −1.27360 −0.636799 0.771030i \(-0.719742\pi\)
−0.636799 + 0.771030i \(0.719742\pi\)
\(504\) 82.0827 3.65625
\(505\) −50.2352 −2.23544
\(506\) −16.8565 −0.749362
\(507\) 4.00942 0.178065
\(508\) −68.9742 −3.06024
\(509\) 1.67049 0.0740431 0.0370215 0.999314i \(-0.488213\pi\)
0.0370215 + 0.999314i \(0.488213\pi\)
\(510\) −152.581 −6.75638
\(511\) 22.8805 1.01217
\(512\) 50.4248 2.22848
\(513\) 2.32972 0.102860
\(514\) −57.6846 −2.54436
\(515\) 48.2605 2.12661
\(516\) 41.4451 1.82452
\(517\) −21.2338 −0.933861
\(518\) −99.2857 −4.36236
\(519\) 44.6905 1.96170
\(520\) −75.3091 −3.30252
\(521\) 40.1288 1.75808 0.879038 0.476752i \(-0.158186\pi\)
0.879038 + 0.476752i \(0.158186\pi\)
\(522\) −73.6702 −3.22446
\(523\) 26.8145 1.17252 0.586258 0.810124i \(-0.300601\pi\)
0.586258 + 0.810124i \(0.300601\pi\)
\(524\) −101.301 −4.42538
\(525\) −37.1130 −1.61974
\(526\) −3.51011 −0.153048
\(527\) 20.6331 0.898790
\(528\) 43.0441 1.87325
\(529\) −14.0873 −0.612492
\(530\) 56.8505 2.46943
\(531\) −30.2272 −1.31175
\(532\) −32.9552 −1.42879
\(533\) 42.9538 1.86054
\(534\) 90.9183 3.93442
\(535\) −9.02738 −0.390288
\(536\) 61.7288 2.66628
\(537\) −29.6769 −1.28065
\(538\) −14.7250 −0.634839
\(539\) 13.4057 0.577424
\(540\) −15.9932 −0.688240
\(541\) 23.4834 1.00963 0.504815 0.863227i \(-0.331561\pi\)
0.504815 + 0.863227i \(0.331561\pi\)
\(542\) −66.0154 −2.83560
\(543\) −2.12925 −0.0913750
\(544\) 51.1425 2.19272
\(545\) −34.5080 −1.47816
\(546\) −89.8989 −3.84732
\(547\) −14.8864 −0.636497 −0.318248 0.948007i \(-0.603095\pi\)
−0.318248 + 0.948007i \(0.603095\pi\)
\(548\) −5.32566 −0.227501
\(549\) 8.91624 0.380536
\(550\) −22.7969 −0.972064
\(551\) 16.6090 0.707568
\(552\) −49.7810 −2.11882
\(553\) −36.4337 −1.54932
\(554\) 41.7910 1.77553
\(555\) 81.8766 3.47547
\(556\) −14.1655 −0.600752
\(557\) −31.3251 −1.32729 −0.663643 0.748049i \(-0.730991\pi\)
−0.663643 + 0.748049i \(0.730991\pi\)
\(558\) 23.4480 0.992634
\(559\) −13.6501 −0.577339
\(560\) 83.5463 3.53048
\(561\) −43.6757 −1.84399
\(562\) 28.8218 1.21577
\(563\) 33.6511 1.41822 0.709112 0.705096i \(-0.249096\pi\)
0.709112 + 0.705096i \(0.249096\pi\)
\(564\) −111.672 −4.70224
\(565\) 5.14263 0.216352
\(566\) −49.1929 −2.06773
\(567\) 26.8106 1.12594
\(568\) −90.8151 −3.81052
\(569\) 27.4804 1.15204 0.576019 0.817436i \(-0.304605\pi\)
0.576019 + 0.817436i \(0.304605\pi\)
\(570\) 39.0926 1.63741
\(571\) −22.4223 −0.938346 −0.469173 0.883106i \(-0.655448\pi\)
−0.469173 + 0.883106i \(0.655448\pi\)
\(572\) −38.3890 −1.60512
\(573\) −19.4708 −0.813404
\(574\) −104.229 −4.35044
\(575\) 12.0536 0.502672
\(576\) 4.96529 0.206887
\(577\) −1.83229 −0.0762792 −0.0381396 0.999272i \(-0.512143\pi\)
−0.0381396 + 0.999272i \(0.512143\pi\)
\(578\) −112.155 −4.66504
\(579\) 35.3662 1.46977
\(580\) −114.019 −4.73438
\(581\) −26.7826 −1.11113
\(582\) 7.24096 0.300148
\(583\) 16.2732 0.673969
\(584\) 41.5061 1.71754
\(585\) 39.7016 1.64146
\(586\) 32.2346 1.33160
\(587\) 4.21437 0.173946 0.0869729 0.996211i \(-0.472281\pi\)
0.0869729 + 0.996211i \(0.472281\pi\)
\(588\) 70.5027 2.90748
\(589\) −5.28638 −0.217822
\(590\) −67.2948 −2.77048
\(591\) −50.1664 −2.06357
\(592\) −82.3429 −3.38427
\(593\) −35.3505 −1.45167 −0.725837 0.687867i \(-0.758547\pi\)
−0.725837 + 0.687867i \(0.758547\pi\)
\(594\) −6.58528 −0.270198
\(595\) −84.7721 −3.47532
\(596\) 67.3751 2.75979
\(597\) −3.97157 −0.162545
\(598\) 29.1976 1.19398
\(599\) 2.19553 0.0897070 0.0448535 0.998994i \(-0.485718\pi\)
0.0448535 + 0.998994i \(0.485718\pi\)
\(600\) −67.3245 −2.74851
\(601\) −10.8225 −0.441460 −0.220730 0.975335i \(-0.570844\pi\)
−0.220730 + 0.975335i \(0.570844\pi\)
\(602\) 33.1226 1.34998
\(603\) −32.5423 −1.32523
\(604\) 25.8534 1.05196
\(605\) 18.4620 0.750588
\(606\) −108.783 −4.41902
\(607\) 17.2143 0.698707 0.349353 0.936991i \(-0.386401\pi\)
0.349353 + 0.936991i \(0.386401\pi\)
\(608\) −13.1032 −0.531404
\(609\) −76.4302 −3.09711
\(610\) 19.8502 0.803712
\(611\) 36.7796 1.48794
\(612\) −123.009 −4.97234
\(613\) 14.1562 0.571763 0.285881 0.958265i \(-0.407714\pi\)
0.285881 + 0.958265i \(0.407714\pi\)
\(614\) 75.9309 3.06432
\(615\) 85.9533 3.46597
\(616\) 52.3088 2.10758
\(617\) −11.9955 −0.482922 −0.241461 0.970410i \(-0.577627\pi\)
−0.241461 + 0.970410i \(0.577627\pi\)
\(618\) 104.507 4.20389
\(619\) 8.40040 0.337641 0.168820 0.985647i \(-0.446004\pi\)
0.168820 + 0.985647i \(0.446004\pi\)
\(620\) 36.2904 1.45746
\(621\) 3.48190 0.139724
\(622\) −19.7748 −0.792898
\(623\) 50.5132 2.02377
\(624\) −74.5579 −2.98470
\(625\) −28.8861 −1.15544
\(626\) −32.4938 −1.29871
\(627\) 11.1901 0.446890
\(628\) −40.0709 −1.59900
\(629\) 83.5510 3.33140
\(630\) −96.3375 −3.83818
\(631\) 9.95363 0.396248 0.198124 0.980177i \(-0.436515\pi\)
0.198124 + 0.980177i \(0.436515\pi\)
\(632\) −66.0922 −2.62901
\(633\) −1.16787 −0.0464185
\(634\) −39.8015 −1.58072
\(635\) 45.4581 1.80395
\(636\) 85.5836 3.39361
\(637\) −23.2204 −0.920025
\(638\) −46.9478 −1.85868
\(639\) 47.8761 1.89395
\(640\) −28.3861 −1.12206
\(641\) 16.5800 0.654869 0.327435 0.944874i \(-0.393816\pi\)
0.327435 + 0.944874i \(0.393816\pi\)
\(642\) −19.5486 −0.771522
\(643\) −23.2968 −0.918736 −0.459368 0.888246i \(-0.651924\pi\)
−0.459368 + 0.888246i \(0.651924\pi\)
\(644\) −49.2535 −1.94086
\(645\) −27.3148 −1.07552
\(646\) 39.8921 1.56953
\(647\) −21.2826 −0.836706 −0.418353 0.908285i \(-0.637392\pi\)
−0.418353 + 0.908285i \(0.637392\pi\)
\(648\) 48.6355 1.91058
\(649\) −19.2629 −0.756135
\(650\) 39.4872 1.54881
\(651\) 24.3265 0.953430
\(652\) 42.7959 1.67602
\(653\) −27.4555 −1.07442 −0.537209 0.843449i \(-0.680521\pi\)
−0.537209 + 0.843449i \(0.680521\pi\)
\(654\) −74.7263 −2.92203
\(655\) 66.7637 2.60867
\(656\) −86.4428 −3.37503
\(657\) −21.8813 −0.853670
\(658\) −89.2474 −3.47922
\(659\) −19.1374 −0.745486 −0.372743 0.927935i \(-0.621583\pi\)
−0.372743 + 0.927935i \(0.621583\pi\)
\(660\) −76.8188 −2.99017
\(661\) −22.3987 −0.871209 −0.435604 0.900138i \(-0.643465\pi\)
−0.435604 + 0.900138i \(0.643465\pi\)
\(662\) −0.968450 −0.0376399
\(663\) 75.6518 2.93807
\(664\) −48.5847 −1.88545
\(665\) 21.7194 0.842243
\(666\) 94.9498 3.67923
\(667\) 24.8232 0.961157
\(668\) 81.6038 3.15735
\(669\) 53.7666 2.07874
\(670\) −72.4489 −2.79895
\(671\) 5.68205 0.219353
\(672\) 60.2973 2.32602
\(673\) 28.5580 1.10083 0.550414 0.834892i \(-0.314470\pi\)
0.550414 + 0.834892i \(0.314470\pi\)
\(674\) −26.7917 −1.03198
\(675\) 4.70897 0.181248
\(676\) 7.19618 0.276776
\(677\) −49.3503 −1.89669 −0.948343 0.317248i \(-0.897241\pi\)
−0.948343 + 0.317248i \(0.897241\pi\)
\(678\) 11.1363 0.427686
\(679\) 4.02300 0.154389
\(680\) −153.780 −5.89720
\(681\) 40.6585 1.55804
\(682\) 14.9427 0.572186
\(683\) −15.6337 −0.598205 −0.299103 0.954221i \(-0.596687\pi\)
−0.299103 + 0.954221i \(0.596687\pi\)
\(684\) 31.5160 1.20504
\(685\) 3.50992 0.134107
\(686\) −8.50764 −0.324823
\(687\) −69.8195 −2.66378
\(688\) 27.4703 1.04730
\(689\) −28.1873 −1.07385
\(690\) 58.4262 2.22425
\(691\) −26.3036 −1.00064 −0.500318 0.865842i \(-0.666783\pi\)
−0.500318 + 0.865842i \(0.666783\pi\)
\(692\) 80.2113 3.04918
\(693\) −27.5763 −1.04754
\(694\) −60.7823 −2.30726
\(695\) 9.33591 0.354131
\(696\) −138.648 −5.25542
\(697\) 87.7111 3.32230
\(698\) 25.4374 0.962818
\(699\) 2.42591 0.0917563
\(700\) −66.6110 −2.51766
\(701\) −2.53467 −0.0957332 −0.0478666 0.998854i \(-0.515242\pi\)
−0.0478666 + 0.998854i \(0.515242\pi\)
\(702\) 11.4066 0.430513
\(703\) −21.4066 −0.807364
\(704\) 3.16423 0.119256
\(705\) 73.5984 2.77188
\(706\) −28.1976 −1.06123
\(707\) −60.4389 −2.27304
\(708\) −101.307 −3.80734
\(709\) −17.9266 −0.673246 −0.336623 0.941639i \(-0.609285\pi\)
−0.336623 + 0.941639i \(0.609285\pi\)
\(710\) 106.586 4.00012
\(711\) 34.8426 1.30670
\(712\) 91.6331 3.43409
\(713\) −7.90081 −0.295888
\(714\) −183.572 −6.87002
\(715\) 25.3006 0.946190
\(716\) −53.2647 −1.99059
\(717\) 28.6758 1.07092
\(718\) −65.8482 −2.45743
\(719\) 42.6941 1.59222 0.796110 0.605152i \(-0.206888\pi\)
0.796110 + 0.605152i \(0.206888\pi\)
\(720\) −79.8978 −2.97762
\(721\) 58.0630 2.16238
\(722\) 38.4483 1.43090
\(723\) −46.9277 −1.74526
\(724\) −3.82162 −0.142029
\(725\) 33.5712 1.24680
\(726\) 39.9792 1.48377
\(727\) 37.8904 1.40528 0.702639 0.711546i \(-0.252005\pi\)
0.702639 + 0.711546i \(0.252005\pi\)
\(728\) −90.6056 −3.35807
\(729\) −34.5320 −1.27896
\(730\) −48.7143 −1.80300
\(731\) −27.8734 −1.03093
\(732\) 29.8828 1.10450
\(733\) −3.71487 −0.137212 −0.0686059 0.997644i \(-0.521855\pi\)
−0.0686059 + 0.997644i \(0.521855\pi\)
\(734\) −39.4731 −1.45698
\(735\) −46.4655 −1.71390
\(736\) −19.5835 −0.721857
\(737\) −20.7382 −0.763903
\(738\) 99.6775 3.66918
\(739\) 3.91332 0.143954 0.0719769 0.997406i \(-0.477069\pi\)
0.0719769 + 0.997406i \(0.477069\pi\)
\(740\) 146.953 5.40212
\(741\) −19.3827 −0.712041
\(742\) 68.3978 2.51096
\(743\) 7.39114 0.271155 0.135577 0.990767i \(-0.456711\pi\)
0.135577 + 0.990767i \(0.456711\pi\)
\(744\) 44.1292 1.61786
\(745\) −44.4042 −1.62684
\(746\) 3.84680 0.140841
\(747\) 25.6130 0.937131
\(748\) −78.3898 −2.86622
\(749\) −10.8610 −0.396852
\(750\) −18.8364 −0.687809
\(751\) −12.5849 −0.459230 −0.229615 0.973282i \(-0.573747\pi\)
−0.229615 + 0.973282i \(0.573747\pi\)
\(752\) −74.0176 −2.69914
\(753\) 69.5382 2.53411
\(754\) 81.3196 2.96148
\(755\) −17.0389 −0.620111
\(756\) −19.2417 −0.699816
\(757\) −15.5271 −0.564343 −0.282172 0.959364i \(-0.591055\pi\)
−0.282172 + 0.959364i \(0.591055\pi\)
\(758\) −37.4614 −1.36066
\(759\) 16.7243 0.607053
\(760\) 39.3999 1.42918
\(761\) 0.107011 0.00387916 0.00193958 0.999998i \(-0.499383\pi\)
0.00193958 + 0.999998i \(0.499383\pi\)
\(762\) 98.4386 3.56605
\(763\) −41.5171 −1.50302
\(764\) −34.9465 −1.26432
\(765\) 81.0701 2.93110
\(766\) 10.5734 0.382033
\(767\) 33.3658 1.20477
\(768\) −68.7660 −2.48138
\(769\) −17.8476 −0.643600 −0.321800 0.946808i \(-0.604288\pi\)
−0.321800 + 0.946808i \(0.604288\pi\)
\(770\) −61.3930 −2.21245
\(771\) 57.2322 2.06117
\(772\) 63.4759 2.28455
\(773\) 6.08433 0.218838 0.109419 0.993996i \(-0.465101\pi\)
0.109419 + 0.993996i \(0.465101\pi\)
\(774\) −31.6761 −1.13857
\(775\) −10.6852 −0.383822
\(776\) 7.29789 0.261979
\(777\) 98.5071 3.53392
\(778\) 57.2916 2.05400
\(779\) −22.4724 −0.805158
\(780\) 133.060 4.76431
\(781\) 30.5100 1.09173
\(782\) 59.6210 2.13204
\(783\) 9.69762 0.346565
\(784\) 46.7301 1.66893
\(785\) 26.4091 0.942581
\(786\) 144.575 5.15684
\(787\) 31.0249 1.10592 0.552959 0.833208i \(-0.313498\pi\)
0.552959 + 0.833208i \(0.313498\pi\)
\(788\) −90.0396 −3.20753
\(789\) 3.48259 0.123983
\(790\) 77.5701 2.75982
\(791\) 6.18719 0.219991
\(792\) −50.0245 −1.77754
\(793\) −9.84204 −0.349501
\(794\) −16.4221 −0.582798
\(795\) −56.4046 −2.00047
\(796\) −7.12823 −0.252654
\(797\) −20.5158 −0.726706 −0.363353 0.931652i \(-0.618368\pi\)
−0.363353 + 0.931652i \(0.618368\pi\)
\(798\) 47.0330 1.66495
\(799\) 75.1036 2.65697
\(800\) −26.4850 −0.936385
\(801\) −48.3073 −1.70685
\(802\) −4.95156 −0.174846
\(803\) −13.9443 −0.492083
\(804\) −109.066 −3.84645
\(805\) 32.4609 1.14410
\(806\) −25.8827 −0.911679
\(807\) 14.6095 0.514279
\(808\) −109.639 −3.85707
\(809\) 39.3255 1.38261 0.691305 0.722563i \(-0.257036\pi\)
0.691305 + 0.722563i \(0.257036\pi\)
\(810\) −57.0817 −2.00565
\(811\) 28.9904 1.01799 0.508995 0.860769i \(-0.330017\pi\)
0.508995 + 0.860769i \(0.330017\pi\)
\(812\) −137.178 −4.81401
\(813\) 65.4977 2.29710
\(814\) 60.5087 2.12083
\(815\) −28.2050 −0.987979
\(816\) −152.246 −5.32969
\(817\) 7.14142 0.249847
\(818\) −8.39378 −0.293482
\(819\) 47.7656 1.66907
\(820\) 154.270 5.38736
\(821\) 12.3105 0.429639 0.214819 0.976654i \(-0.431084\pi\)
0.214819 + 0.976654i \(0.431084\pi\)
\(822\) 7.60067 0.265104
\(823\) −6.01238 −0.209578 −0.104789 0.994494i \(-0.533417\pi\)
−0.104789 + 0.994494i \(0.533417\pi\)
\(824\) 105.329 3.66930
\(825\) 22.6181 0.787463
\(826\) −80.9635 −2.81708
\(827\) −38.1609 −1.32699 −0.663493 0.748183i \(-0.730927\pi\)
−0.663493 + 0.748183i \(0.730927\pi\)
\(828\) 47.1025 1.63693
\(829\) −6.76980 −0.235125 −0.117562 0.993066i \(-0.537508\pi\)
−0.117562 + 0.993066i \(0.537508\pi\)
\(830\) 57.0222 1.97927
\(831\) −41.4633 −1.43834
\(832\) −5.48085 −0.190014
\(833\) −47.4157 −1.64286
\(834\) 20.2167 0.700048
\(835\) −53.7817 −1.86119
\(836\) 20.0842 0.694627
\(837\) −3.08659 −0.106688
\(838\) −88.9764 −3.07364
\(839\) −36.7102 −1.26738 −0.633688 0.773589i \(-0.718460\pi\)
−0.633688 + 0.773589i \(0.718460\pi\)
\(840\) −181.308 −6.25571
\(841\) 40.1363 1.38401
\(842\) 76.2287 2.62702
\(843\) −28.5958 −0.984891
\(844\) −2.09611 −0.0721509
\(845\) −4.74271 −0.163154
\(846\) 85.3499 2.93439
\(847\) 22.2120 0.763213
\(848\) 56.7259 1.94797
\(849\) 48.8071 1.67506
\(850\) 80.6323 2.76567
\(851\) −31.9934 −1.09672
\(852\) 160.457 5.49716
\(853\) −0.511245 −0.0175047 −0.00875235 0.999962i \(-0.502786\pi\)
−0.00875235 + 0.999962i \(0.502786\pi\)
\(854\) 23.8821 0.817230
\(855\) −20.7709 −0.710350
\(856\) −19.7023 −0.673411
\(857\) 30.0453 1.02633 0.513164 0.858291i \(-0.328473\pi\)
0.513164 + 0.858291i \(0.328473\pi\)
\(858\) 54.7880 1.87043
\(859\) 23.6291 0.806215 0.403107 0.915153i \(-0.367930\pi\)
0.403107 + 0.915153i \(0.367930\pi\)
\(860\) −49.0250 −1.67174
\(861\) 103.412 3.52427
\(862\) −66.6520 −2.27018
\(863\) −48.2324 −1.64185 −0.820925 0.571036i \(-0.806542\pi\)
−0.820925 + 0.571036i \(0.806542\pi\)
\(864\) −7.65064 −0.260280
\(865\) −52.8640 −1.79743
\(866\) 50.3723 1.71172
\(867\) 111.276 3.77912
\(868\) 43.6616 1.48197
\(869\) 22.2042 0.753224
\(870\) 162.726 5.51692
\(871\) 35.9213 1.21715
\(872\) −75.3138 −2.55045
\(873\) −3.84731 −0.130212
\(874\) −15.2755 −0.516700
\(875\) −10.4653 −0.353792
\(876\) −73.3352 −2.47777
\(877\) 55.2702 1.86634 0.933171 0.359433i \(-0.117030\pi\)
0.933171 + 0.359433i \(0.117030\pi\)
\(878\) −73.0303 −2.46465
\(879\) −31.9818 −1.07872
\(880\) −50.9165 −1.71639
\(881\) −42.1938 −1.42154 −0.710772 0.703422i \(-0.751654\pi\)
−0.710772 + 0.703422i \(0.751654\pi\)
\(882\) −53.8846 −1.81439
\(883\) 44.5562 1.49944 0.749718 0.661758i \(-0.230189\pi\)
0.749718 + 0.661758i \(0.230189\pi\)
\(884\) 135.781 4.56682
\(885\) 66.7671 2.24435
\(886\) 1.35553 0.0455398
\(887\) 41.9321 1.40794 0.703971 0.710229i \(-0.251408\pi\)
0.703971 + 0.710229i \(0.251408\pi\)
\(888\) 178.696 5.99664
\(889\) 54.6914 1.83429
\(890\) −107.546 −3.60497
\(891\) −16.3394 −0.547392
\(892\) 96.5013 3.23110
\(893\) −19.2422 −0.643917
\(894\) −96.1564 −3.21595
\(895\) 35.1046 1.17342
\(896\) −34.1518 −1.14093
\(897\) −28.9686 −0.967233
\(898\) −52.2434 −1.74339
\(899\) −22.0049 −0.733906
\(900\) 63.7021 2.12340
\(901\) −57.5582 −1.91754
\(902\) 63.5215 2.11503
\(903\) −32.8629 −1.09361
\(904\) 11.2238 0.373298
\(905\) 2.51867 0.0837236
\(906\) −36.8975 −1.22584
\(907\) 32.7075 1.08604 0.543018 0.839721i \(-0.317282\pi\)
0.543018 + 0.839721i \(0.317282\pi\)
\(908\) 72.9746 2.42175
\(909\) 57.7995 1.91709
\(910\) 106.341 3.52516
\(911\) −42.1150 −1.39533 −0.697666 0.716423i \(-0.745778\pi\)
−0.697666 + 0.716423i \(0.745778\pi\)
\(912\) 39.0069 1.29165
\(913\) 16.3224 0.540192
\(914\) −4.83150 −0.159812
\(915\) −19.6946 −0.651082
\(916\) −125.313 −4.14046
\(917\) 80.3245 2.65255
\(918\) 23.2920 0.768752
\(919\) −47.3855 −1.56310 −0.781552 0.623840i \(-0.785572\pi\)
−0.781552 + 0.623840i \(0.785572\pi\)
\(920\) 58.8855 1.94140
\(921\) −75.3354 −2.48239
\(922\) −44.1012 −1.45239
\(923\) −52.8472 −1.73949
\(924\) −92.4220 −3.04046
\(925\) −43.2683 −1.42265
\(926\) −36.8629 −1.21139
\(927\) −55.5273 −1.82376
\(928\) −54.5429 −1.79046
\(929\) −53.5664 −1.75746 −0.878728 0.477323i \(-0.841607\pi\)
−0.878728 + 0.477323i \(0.841607\pi\)
\(930\) −51.7929 −1.69836
\(931\) 12.1484 0.398146
\(932\) 4.35406 0.142622
\(933\) 19.6197 0.642322
\(934\) −6.89090 −0.225477
\(935\) 51.6635 1.68958
\(936\) 86.6488 2.83221
\(937\) −37.0292 −1.20969 −0.604845 0.796343i \(-0.706765\pi\)
−0.604845 + 0.796343i \(0.706765\pi\)
\(938\) −87.1645 −2.84602
\(939\) 32.2390 1.05208
\(940\) 132.096 4.30849
\(941\) 42.6671 1.39091 0.695454 0.718570i \(-0.255203\pi\)
0.695454 + 0.718570i \(0.255203\pi\)
\(942\) 57.1884 1.86330
\(943\) −33.5863 −1.09372
\(944\) −67.1473 −2.18546
\(945\) 12.6815 0.412528
\(946\) −20.1862 −0.656312
\(947\) 29.0710 0.944682 0.472341 0.881416i \(-0.343409\pi\)
0.472341 + 0.881416i \(0.343409\pi\)
\(948\) 116.775 3.79268
\(949\) 24.1533 0.784049
\(950\) −20.6588 −0.670258
\(951\) 39.4894 1.28053
\(952\) −185.015 −5.99639
\(953\) −6.08784 −0.197205 −0.0986023 0.995127i \(-0.531437\pi\)
−0.0986023 + 0.995127i \(0.531437\pi\)
\(954\) −65.4108 −2.11775
\(955\) 23.0318 0.745292
\(956\) 51.4678 1.66459
\(957\) 46.5796 1.50571
\(958\) −48.7937 −1.57645
\(959\) 4.22285 0.136363
\(960\) −10.9675 −0.353976
\(961\) −23.9962 −0.774071
\(962\) −104.809 −3.37917
\(963\) 10.3867 0.334706
\(964\) −84.2267 −2.71276
\(965\) −41.8344 −1.34670
\(966\) 70.2935 2.26166
\(967\) −5.63642 −0.181255 −0.0906275 0.995885i \(-0.528887\pi\)
−0.0906275 + 0.995885i \(0.528887\pi\)
\(968\) 40.2934 1.29508
\(969\) −39.5792 −1.27147
\(970\) −8.56527 −0.275014
\(971\) −22.2430 −0.713812 −0.356906 0.934140i \(-0.616168\pi\)
−0.356906 + 0.934140i \(0.616168\pi\)
\(972\) −101.892 −3.26818
\(973\) 11.2322 0.360088
\(974\) 93.4099 2.99305
\(975\) −39.1775 −1.25468
\(976\) 19.8067 0.633997
\(977\) 22.6529 0.724731 0.362365 0.932036i \(-0.381969\pi\)
0.362365 + 0.932036i \(0.381969\pi\)
\(978\) −61.0774 −1.95304
\(979\) −30.7848 −0.983886
\(980\) −83.3970 −2.66402
\(981\) 39.7041 1.26765
\(982\) 58.3326 1.86147
\(983\) 34.2767 1.09326 0.546628 0.837375i \(-0.315911\pi\)
0.546628 + 0.837375i \(0.315911\pi\)
\(984\) 187.593 5.98026
\(985\) 59.3414 1.89078
\(986\) 166.054 5.28822
\(987\) 88.5475 2.81850
\(988\) −34.7884 −1.10677
\(989\) 10.6733 0.339390
\(990\) 58.7120 1.86599
\(991\) 11.7312 0.372655 0.186327 0.982488i \(-0.440341\pi\)
0.186327 + 0.982488i \(0.440341\pi\)
\(992\) 17.3601 0.551185
\(993\) 0.960855 0.0304918
\(994\) 128.236 4.06740
\(995\) 4.69793 0.148934
\(996\) 85.8421 2.72001
\(997\) −9.43404 −0.298779 −0.149389 0.988778i \(-0.547731\pi\)
−0.149389 + 0.988778i \(0.547731\pi\)
\(998\) −60.5335 −1.91616
\(999\) −12.4988 −0.395444
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 \(a_p\))