Properties

Label 8027.2.a.f.1.6
Level 8027
Weight 2
Character 8027.1
Self dual Yes
Analytic conductor 64.096
Analytic rank 0
Dimension 176
CM No

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Newspace parameters

Level: \( N \) = \( 8027 = 23 \cdot 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0959177025\)
Analytic rank: \(0\)
Dimension: \(176\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 8027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.66575 q^{2} -2.58411 q^{3} +5.10620 q^{4} +3.82950 q^{5} +6.88858 q^{6} -0.0815082 q^{7} -8.28034 q^{8} +3.67762 q^{9} +O(q^{10})\) \(q-2.66575 q^{2} -2.58411 q^{3} +5.10620 q^{4} +3.82950 q^{5} +6.88858 q^{6} -0.0815082 q^{7} -8.28034 q^{8} +3.67762 q^{9} -10.2085 q^{10} -5.27584 q^{11} -13.1950 q^{12} -1.39263 q^{13} +0.217280 q^{14} -9.89583 q^{15} +11.8609 q^{16} +5.32569 q^{17} -9.80360 q^{18} -6.49744 q^{19} +19.5542 q^{20} +0.210626 q^{21} +14.0640 q^{22} +1.00000 q^{23} +21.3973 q^{24} +9.66503 q^{25} +3.71240 q^{26} -1.75104 q^{27} -0.416197 q^{28} +7.22284 q^{29} +26.3798 q^{30} +7.84095 q^{31} -15.0574 q^{32} +13.6333 q^{33} -14.1969 q^{34} -0.312135 q^{35} +18.7787 q^{36} +4.66717 q^{37} +17.3205 q^{38} +3.59871 q^{39} -31.7095 q^{40} -2.06103 q^{41} -0.561476 q^{42} +0.0993810 q^{43} -26.9395 q^{44} +14.0834 q^{45} -2.66575 q^{46} +0.534447 q^{47} -30.6498 q^{48} -6.99336 q^{49} -25.7645 q^{50} -13.7622 q^{51} -7.11106 q^{52} +0.809749 q^{53} +4.66784 q^{54} -20.2038 q^{55} +0.674916 q^{56} +16.7901 q^{57} -19.2543 q^{58} +11.8358 q^{59} -50.5301 q^{60} +5.44642 q^{61} -20.9020 q^{62} -0.299756 q^{63} +16.4175 q^{64} -5.33308 q^{65} -36.3430 q^{66} -1.74709 q^{67} +27.1940 q^{68} -2.58411 q^{69} +0.832073 q^{70} +8.14606 q^{71} -30.4519 q^{72} -1.58643 q^{73} -12.4415 q^{74} -24.9755 q^{75} -33.1772 q^{76} +0.430024 q^{77} -9.59326 q^{78} -8.81922 q^{79} +45.4212 q^{80} -6.50797 q^{81} +5.49418 q^{82} +3.59595 q^{83} +1.07550 q^{84} +20.3947 q^{85} -0.264924 q^{86} -18.6646 q^{87} +43.6857 q^{88} -6.68289 q^{89} -37.5428 q^{90} +0.113511 q^{91} +5.10620 q^{92} -20.2619 q^{93} -1.42470 q^{94} -24.8819 q^{95} +38.9100 q^{96} +6.48504 q^{97} +18.6425 q^{98} -19.4025 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + O(q^{10}) \) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + 18q^{10} + 11q^{11} + 46q^{12} + 87q^{13} - 6q^{14} + 29q^{15} + 257q^{16} + 14q^{17} + 72q^{18} + 34q^{19} + 45q^{20} + 23q^{21} + 62q^{22} + 176q^{23} + 33q^{24} + 272q^{25} + 31q^{26} + 82q^{27} + 80q^{28} + 75q^{29} - 30q^{30} + 73q^{31} + 71q^{32} + 30q^{33} + 23q^{34} + 44q^{35} + 264q^{36} + 236q^{37} - 21q^{38} + 17q^{39} + 43q^{40} + 51q^{41} + 38q^{42} + 51q^{43} + 12q^{44} + 127q^{45} + 19q^{46} + 45q^{47} + 61q^{48} + 268q^{49} + 55q^{50} - 3q^{51} + 166q^{52} + 63q^{53} - 32q^{54} + 11q^{55} - 9q^{56} + 72q^{57} + 98q^{58} + 95q^{59} - 7q^{60} + 73q^{61} + 12q^{62} + 19q^{63} + 365q^{64} + 19q^{65} - 28q^{66} + 138q^{67} + 16q^{68} + 22q^{69} + 100q^{70} + 85q^{71} + 129q^{72} + 118q^{73} - 21q^{74} - 12q^{75} + 52q^{76} + 75q^{77} + 97q^{78} + 74q^{79} + 8q^{80} + 280q^{81} + 67q^{82} + 10q^{83} - 51q^{84} + 169q^{85} - 39q^{86} - 6q^{87} + 159q^{88} + 38q^{89} + 22q^{90} + 90q^{91} + 203q^{92} + 230q^{93} + 63q^{94} + 30q^{95} + 107q^{96} + 161q^{97} + 58q^{98} + 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.66575 −1.88497 −0.942483 0.334253i \(-0.891516\pi\)
−0.942483 + 0.334253i \(0.891516\pi\)
\(3\) −2.58411 −1.49194 −0.745968 0.665982i \(-0.768013\pi\)
−0.745968 + 0.665982i \(0.768013\pi\)
\(4\) 5.10620 2.55310
\(5\) 3.82950 1.71260 0.856301 0.516477i \(-0.172757\pi\)
0.856301 + 0.516477i \(0.172757\pi\)
\(6\) 6.88858 2.81225
\(7\) −0.0815082 −0.0308072 −0.0154036 0.999881i \(-0.504903\pi\)
−0.0154036 + 0.999881i \(0.504903\pi\)
\(8\) −8.28034 −2.92754
\(9\) 3.67762 1.22587
\(10\) −10.2085 −3.22820
\(11\) −5.27584 −1.59073 −0.795363 0.606134i \(-0.792720\pi\)
−0.795363 + 0.606134i \(0.792720\pi\)
\(12\) −13.1950 −3.80906
\(13\) −1.39263 −0.386247 −0.193123 0.981174i \(-0.561862\pi\)
−0.193123 + 0.981174i \(0.561862\pi\)
\(14\) 0.217280 0.0580706
\(15\) −9.89583 −2.55509
\(16\) 11.8609 2.96522
\(17\) 5.32569 1.29167 0.645835 0.763477i \(-0.276509\pi\)
0.645835 + 0.763477i \(0.276509\pi\)
\(18\) −9.80360 −2.31073
\(19\) −6.49744 −1.49061 −0.745307 0.666721i \(-0.767697\pi\)
−0.745307 + 0.666721i \(0.767697\pi\)
\(20\) 19.5542 4.37245
\(21\) 0.210626 0.0459624
\(22\) 14.0640 2.99846
\(23\) 1.00000 0.208514
\(24\) 21.3973 4.36771
\(25\) 9.66503 1.93301
\(26\) 3.71240 0.728062
\(27\) −1.75104 −0.336989
\(28\) −0.416197 −0.0786539
\(29\) 7.22284 1.34125 0.670624 0.741798i \(-0.266026\pi\)
0.670624 + 0.741798i \(0.266026\pi\)
\(30\) 26.3798 4.81627
\(31\) 7.84095 1.40828 0.704138 0.710063i \(-0.251333\pi\)
0.704138 + 0.710063i \(0.251333\pi\)
\(32\) −15.0574 −2.66180
\(33\) 13.6333 2.37326
\(34\) −14.1969 −2.43475
\(35\) −0.312135 −0.0527605
\(36\) 18.7787 3.12978
\(37\) 4.66717 0.767279 0.383639 0.923483i \(-0.374671\pi\)
0.383639 + 0.923483i \(0.374671\pi\)
\(38\) 17.3205 2.80976
\(39\) 3.59871 0.576256
\(40\) −31.7095 −5.01372
\(41\) −2.06103 −0.321879 −0.160939 0.986964i \(-0.551452\pi\)
−0.160939 + 0.986964i \(0.551452\pi\)
\(42\) −0.561476 −0.0866376
\(43\) 0.0993810 0.0151555 0.00757773 0.999971i \(-0.497588\pi\)
0.00757773 + 0.999971i \(0.497588\pi\)
\(44\) −26.9395 −4.06128
\(45\) 14.0834 2.09943
\(46\) −2.66575 −0.393043
\(47\) 0.534447 0.0779571 0.0389786 0.999240i \(-0.487590\pi\)
0.0389786 + 0.999240i \(0.487590\pi\)
\(48\) −30.6498 −4.42392
\(49\) −6.99336 −0.999051
\(50\) −25.7645 −3.64365
\(51\) −13.7622 −1.92709
\(52\) −7.11106 −0.986127
\(53\) 0.809749 0.111228 0.0556138 0.998452i \(-0.482288\pi\)
0.0556138 + 0.998452i \(0.482288\pi\)
\(54\) 4.66784 0.635212
\(55\) −20.2038 −2.72428
\(56\) 0.674916 0.0901894
\(57\) 16.7901 2.22390
\(58\) −19.2543 −2.52821
\(59\) 11.8358 1.54089 0.770443 0.637509i \(-0.220035\pi\)
0.770443 + 0.637509i \(0.220035\pi\)
\(60\) −50.5301 −6.52341
\(61\) 5.44642 0.697342 0.348671 0.937245i \(-0.386633\pi\)
0.348671 + 0.937245i \(0.386633\pi\)
\(62\) −20.9020 −2.65456
\(63\) −0.299756 −0.0377657
\(64\) 16.4175 2.05218
\(65\) −5.33308 −0.661487
\(66\) −36.3430 −4.47352
\(67\) −1.74709 −0.213441 −0.106720 0.994289i \(-0.534035\pi\)
−0.106720 + 0.994289i \(0.534035\pi\)
\(68\) 27.1940 3.29776
\(69\) −2.58411 −0.311090
\(70\) 0.832073 0.0994518
\(71\) 8.14606 0.966760 0.483380 0.875411i \(-0.339409\pi\)
0.483380 + 0.875411i \(0.339409\pi\)
\(72\) −30.4519 −3.58880
\(73\) −1.58643 −0.185677 −0.0928386 0.995681i \(-0.529594\pi\)
−0.0928386 + 0.995681i \(0.529594\pi\)
\(74\) −12.4415 −1.44629
\(75\) −24.9755 −2.88392
\(76\) −33.1772 −3.80569
\(77\) 0.430024 0.0490058
\(78\) −9.59326 −1.08622
\(79\) −8.81922 −0.992240 −0.496120 0.868254i \(-0.665242\pi\)
−0.496120 + 0.868254i \(0.665242\pi\)
\(80\) 45.4212 5.07824
\(81\) −6.50797 −0.723108
\(82\) 5.49418 0.606731
\(83\) 3.59595 0.394707 0.197353 0.980332i \(-0.436765\pi\)
0.197353 + 0.980332i \(0.436765\pi\)
\(84\) 1.07550 0.117347
\(85\) 20.3947 2.21212
\(86\) −0.264924 −0.0285675
\(87\) −18.6646 −2.00106
\(88\) 43.6857 4.65692
\(89\) −6.68289 −0.708385 −0.354192 0.935173i \(-0.615244\pi\)
−0.354192 + 0.935173i \(0.615244\pi\)
\(90\) −37.5428 −3.95736
\(91\) 0.113511 0.0118992
\(92\) 5.10620 0.532358
\(93\) −20.2619 −2.10106
\(94\) −1.42470 −0.146947
\(95\) −24.8819 −2.55283
\(96\) 38.9100 3.97123
\(97\) 6.48504 0.658456 0.329228 0.944250i \(-0.393212\pi\)
0.329228 + 0.944250i \(0.393212\pi\)
\(98\) 18.6425 1.88318
\(99\) −19.4025 −1.95003
\(100\) 49.3516 4.93516
\(101\) −8.54543 −0.850302 −0.425151 0.905122i \(-0.639779\pi\)
−0.425151 + 0.905122i \(0.639779\pi\)
\(102\) 36.6864 3.63250
\(103\) 8.41543 0.829197 0.414599 0.910004i \(-0.363922\pi\)
0.414599 + 0.910004i \(0.363922\pi\)
\(104\) 11.5315 1.13075
\(105\) 0.806592 0.0787153
\(106\) −2.15858 −0.209660
\(107\) −5.20146 −0.502844 −0.251422 0.967878i \(-0.580898\pi\)
−0.251422 + 0.967878i \(0.580898\pi\)
\(108\) −8.94118 −0.860365
\(109\) 0.741143 0.0709886 0.0354943 0.999370i \(-0.488699\pi\)
0.0354943 + 0.999370i \(0.488699\pi\)
\(110\) 53.8582 5.13518
\(111\) −12.0605 −1.14473
\(112\) −0.966759 −0.0913501
\(113\) −20.9429 −1.97015 −0.985073 0.172139i \(-0.944932\pi\)
−0.985073 + 0.172139i \(0.944932\pi\)
\(114\) −44.7581 −4.19198
\(115\) 3.82950 0.357102
\(116\) 36.8813 3.42434
\(117\) −5.12157 −0.473490
\(118\) −31.5512 −2.90452
\(119\) −0.434088 −0.0397927
\(120\) 81.9409 7.48014
\(121\) 16.8345 1.53041
\(122\) −14.5188 −1.31447
\(123\) 5.32593 0.480223
\(124\) 40.0375 3.59547
\(125\) 17.8647 1.59787
\(126\) 0.799074 0.0711872
\(127\) 14.5128 1.28780 0.643900 0.765109i \(-0.277315\pi\)
0.643900 + 0.765109i \(0.277315\pi\)
\(128\) −13.6500 −1.20650
\(129\) −0.256811 −0.0226110
\(130\) 14.2166 1.24688
\(131\) −18.2729 −1.59651 −0.798254 0.602321i \(-0.794243\pi\)
−0.798254 + 0.602321i \(0.794243\pi\)
\(132\) 69.6146 6.05917
\(133\) 0.529595 0.0459217
\(134\) 4.65730 0.402329
\(135\) −6.70561 −0.577127
\(136\) −44.0985 −3.78142
\(137\) −3.15018 −0.269138 −0.134569 0.990904i \(-0.542965\pi\)
−0.134569 + 0.990904i \(0.542965\pi\)
\(138\) 6.88858 0.586395
\(139\) 0.471167 0.0399639 0.0199819 0.999800i \(-0.493639\pi\)
0.0199819 + 0.999800i \(0.493639\pi\)
\(140\) −1.59383 −0.134703
\(141\) −1.38107 −0.116307
\(142\) −21.7153 −1.82231
\(143\) 7.34731 0.614413
\(144\) 43.6198 3.63498
\(145\) 27.6598 2.29702
\(146\) 4.22901 0.349995
\(147\) 18.0716 1.49052
\(148\) 23.8315 1.95894
\(149\) −20.5405 −1.68275 −0.841374 0.540454i \(-0.818253\pi\)
−0.841374 + 0.540454i \(0.818253\pi\)
\(150\) 66.5783 5.43610
\(151\) 11.1393 0.906500 0.453250 0.891383i \(-0.350264\pi\)
0.453250 + 0.891383i \(0.350264\pi\)
\(152\) 53.8010 4.36384
\(153\) 19.5859 1.58342
\(154\) −1.14634 −0.0923743
\(155\) 30.0269 2.41182
\(156\) 18.3758 1.47124
\(157\) 14.9918 1.19648 0.598238 0.801318i \(-0.295868\pi\)
0.598238 + 0.801318i \(0.295868\pi\)
\(158\) 23.5098 1.87034
\(159\) −2.09248 −0.165944
\(160\) −57.6623 −4.55860
\(161\) −0.0815082 −0.00642375
\(162\) 17.3486 1.36303
\(163\) 17.8388 1.39724 0.698622 0.715490i \(-0.253797\pi\)
0.698622 + 0.715490i \(0.253797\pi\)
\(164\) −10.5240 −0.821789
\(165\) 52.2088 4.06445
\(166\) −9.58589 −0.744010
\(167\) 8.80636 0.681457 0.340728 0.940162i \(-0.389326\pi\)
0.340728 + 0.940162i \(0.389326\pi\)
\(168\) −1.74406 −0.134557
\(169\) −11.0606 −0.850813
\(170\) −54.3671 −4.16977
\(171\) −23.8951 −1.82730
\(172\) 0.507459 0.0386934
\(173\) 12.1499 0.923741 0.461870 0.886947i \(-0.347179\pi\)
0.461870 + 0.886947i \(0.347179\pi\)
\(174\) 49.7551 3.77192
\(175\) −0.787780 −0.0595505
\(176\) −62.5761 −4.71685
\(177\) −30.5849 −2.29890
\(178\) 17.8149 1.33528
\(179\) −16.8562 −1.25989 −0.629946 0.776639i \(-0.716923\pi\)
−0.629946 + 0.776639i \(0.716923\pi\)
\(180\) 71.9128 5.36006
\(181\) 19.3918 1.44138 0.720692 0.693256i \(-0.243824\pi\)
0.720692 + 0.693256i \(0.243824\pi\)
\(182\) −0.302591 −0.0224296
\(183\) −14.0741 −1.04039
\(184\) −8.28034 −0.610435
\(185\) 17.8729 1.31404
\(186\) 54.0130 3.96043
\(187\) −28.0975 −2.05469
\(188\) 2.72899 0.199032
\(189\) 0.142724 0.0103817
\(190\) 66.3288 4.81200
\(191\) −14.9036 −1.07839 −0.539193 0.842182i \(-0.681271\pi\)
−0.539193 + 0.842182i \(0.681271\pi\)
\(192\) −42.4245 −3.06173
\(193\) −10.5594 −0.760084 −0.380042 0.924969i \(-0.624090\pi\)
−0.380042 + 0.924969i \(0.624090\pi\)
\(194\) −17.2875 −1.24117
\(195\) 13.7813 0.986897
\(196\) −35.7095 −2.55068
\(197\) 12.4171 0.884683 0.442342 0.896847i \(-0.354148\pi\)
0.442342 + 0.896847i \(0.354148\pi\)
\(198\) 51.7222 3.67574
\(199\) −13.7366 −0.973765 −0.486882 0.873467i \(-0.661866\pi\)
−0.486882 + 0.873467i \(0.661866\pi\)
\(200\) −80.0298 −5.65896
\(201\) 4.51467 0.318440
\(202\) 22.7799 1.60279
\(203\) −0.588721 −0.0413201
\(204\) −70.2724 −4.92005
\(205\) −7.89271 −0.551251
\(206\) −22.4334 −1.56301
\(207\) 3.67762 0.255612
\(208\) −16.5178 −1.14531
\(209\) 34.2794 2.37116
\(210\) −2.15017 −0.148376
\(211\) −23.0962 −1.59001 −0.795003 0.606606i \(-0.792531\pi\)
−0.795003 + 0.606606i \(0.792531\pi\)
\(212\) 4.13474 0.283975
\(213\) −21.0503 −1.44234
\(214\) 13.8658 0.947845
\(215\) 0.380579 0.0259553
\(216\) 14.4992 0.986548
\(217\) −0.639102 −0.0433851
\(218\) −1.97570 −0.133811
\(219\) 4.09950 0.277018
\(220\) −103.165 −6.95536
\(221\) −7.41673 −0.498903
\(222\) 32.1502 2.15778
\(223\) −25.5626 −1.71180 −0.855900 0.517141i \(-0.826996\pi\)
−0.855900 + 0.517141i \(0.826996\pi\)
\(224\) 1.22730 0.0820026
\(225\) 35.5443 2.36962
\(226\) 55.8285 3.71366
\(227\) −8.14130 −0.540357 −0.270179 0.962810i \(-0.587083\pi\)
−0.270179 + 0.962810i \(0.587083\pi\)
\(228\) 85.7335 5.67784
\(229\) 11.9423 0.789168 0.394584 0.918860i \(-0.370889\pi\)
0.394584 + 0.918860i \(0.370889\pi\)
\(230\) −10.2085 −0.673126
\(231\) −1.11123 −0.0731135
\(232\) −59.8076 −3.92656
\(233\) 3.34280 0.218994 0.109497 0.993987i \(-0.465076\pi\)
0.109497 + 0.993987i \(0.465076\pi\)
\(234\) 13.6528 0.892512
\(235\) 2.04666 0.133510
\(236\) 60.4358 3.93404
\(237\) 22.7898 1.48036
\(238\) 1.15717 0.0750080
\(239\) −21.4295 −1.38616 −0.693079 0.720861i \(-0.743747\pi\)
−0.693079 + 0.720861i \(0.743747\pi\)
\(240\) −117.373 −7.57641
\(241\) 15.4937 0.998040 0.499020 0.866591i \(-0.333693\pi\)
0.499020 + 0.866591i \(0.333693\pi\)
\(242\) −44.8764 −2.88477
\(243\) 22.0704 1.41582
\(244\) 27.8105 1.78038
\(245\) −26.7810 −1.71098
\(246\) −14.1976 −0.905204
\(247\) 9.04854 0.575745
\(248\) −64.9258 −4.12279
\(249\) −9.29233 −0.588878
\(250\) −47.6228 −3.01193
\(251\) 10.8668 0.685904 0.342952 0.939353i \(-0.388573\pi\)
0.342952 + 0.939353i \(0.388573\pi\)
\(252\) −1.53062 −0.0964197
\(253\) −5.27584 −0.331689
\(254\) −38.6874 −2.42746
\(255\) −52.7022 −3.30034
\(256\) 3.55241 0.222025
\(257\) −19.5127 −1.21717 −0.608584 0.793489i \(-0.708262\pi\)
−0.608584 + 0.793489i \(0.708262\pi\)
\(258\) 0.684594 0.0426209
\(259\) −0.380413 −0.0236377
\(260\) −27.2318 −1.68884
\(261\) 26.5629 1.64420
\(262\) 48.7108 3.00937
\(263\) −13.6333 −0.840665 −0.420333 0.907370i \(-0.638087\pi\)
−0.420333 + 0.907370i \(0.638087\pi\)
\(264\) −112.889 −6.94782
\(265\) 3.10093 0.190489
\(266\) −1.41176 −0.0865608
\(267\) 17.2693 1.05687
\(268\) −8.92099 −0.544936
\(269\) 24.2554 1.47888 0.739440 0.673223i \(-0.235090\pi\)
0.739440 + 0.673223i \(0.235090\pi\)
\(270\) 17.8755 1.08787
\(271\) −15.1768 −0.921923 −0.460962 0.887420i \(-0.652495\pi\)
−0.460962 + 0.887420i \(0.652495\pi\)
\(272\) 63.1674 3.83008
\(273\) −0.293325 −0.0177528
\(274\) 8.39758 0.507316
\(275\) −50.9912 −3.07488
\(276\) −13.1950 −0.794244
\(277\) −5.34590 −0.321204 −0.160602 0.987019i \(-0.551344\pi\)
−0.160602 + 0.987019i \(0.551344\pi\)
\(278\) −1.25601 −0.0753306
\(279\) 28.8360 1.72637
\(280\) 2.58459 0.154459
\(281\) 31.1392 1.85761 0.928806 0.370567i \(-0.120837\pi\)
0.928806 + 0.370567i \(0.120837\pi\)
\(282\) 3.68158 0.219235
\(283\) 4.75351 0.282567 0.141284 0.989969i \(-0.454877\pi\)
0.141284 + 0.989969i \(0.454877\pi\)
\(284\) 41.5954 2.46823
\(285\) 64.2976 3.80866
\(286\) −19.5860 −1.15815
\(287\) 0.167991 0.00991619
\(288\) −55.3754 −3.26303
\(289\) 11.3630 0.668411
\(290\) −73.7341 −4.32981
\(291\) −16.7580 −0.982374
\(292\) −8.10061 −0.474052
\(293\) 17.1833 1.00386 0.501931 0.864908i \(-0.332623\pi\)
0.501931 + 0.864908i \(0.332623\pi\)
\(294\) −48.1743 −2.80958
\(295\) 45.3250 2.63893
\(296\) −38.6458 −2.24624
\(297\) 9.23822 0.536056
\(298\) 54.7559 3.17192
\(299\) −1.39263 −0.0805380
\(300\) −127.530 −7.36294
\(301\) −0.00810037 −0.000466897 0
\(302\) −29.6944 −1.70872
\(303\) 22.0823 1.26860
\(304\) −77.0653 −4.42000
\(305\) 20.8570 1.19427
\(306\) −52.2109 −2.98470
\(307\) 5.60189 0.319717 0.159858 0.987140i \(-0.448896\pi\)
0.159858 + 0.987140i \(0.448896\pi\)
\(308\) 2.19579 0.125117
\(309\) −21.7464 −1.23711
\(310\) −80.0441 −4.54620
\(311\) 12.0853 0.685292 0.342646 0.939465i \(-0.388677\pi\)
0.342646 + 0.939465i \(0.388677\pi\)
\(312\) −29.7986 −1.68701
\(313\) 18.4171 1.04099 0.520497 0.853864i \(-0.325747\pi\)
0.520497 + 0.853864i \(0.325747\pi\)
\(314\) −39.9644 −2.25532
\(315\) −1.14792 −0.0646777
\(316\) −45.0327 −2.53329
\(317\) 2.65768 0.149270 0.0746352 0.997211i \(-0.476221\pi\)
0.0746352 + 0.997211i \(0.476221\pi\)
\(318\) 5.57802 0.312800
\(319\) −38.1065 −2.13356
\(320\) 62.8706 3.51457
\(321\) 13.4411 0.750211
\(322\) 0.217280 0.0121086
\(323\) −34.6033 −1.92538
\(324\) −33.2310 −1.84617
\(325\) −13.4598 −0.746618
\(326\) −47.5538 −2.63376
\(327\) −1.91519 −0.105910
\(328\) 17.0660 0.942314
\(329\) −0.0435618 −0.00240164
\(330\) −139.175 −7.66136
\(331\) 3.65090 0.200672 0.100336 0.994954i \(-0.468008\pi\)
0.100336 + 0.994954i \(0.468008\pi\)
\(332\) 18.3616 1.00773
\(333\) 17.1641 0.940586
\(334\) −23.4755 −1.28452
\(335\) −6.69047 −0.365539
\(336\) 2.49821 0.136289
\(337\) 21.9355 1.19490 0.597450 0.801906i \(-0.296180\pi\)
0.597450 + 0.801906i \(0.296180\pi\)
\(338\) 29.4847 1.60376
\(339\) 54.1188 2.93933
\(340\) 104.139 5.64776
\(341\) −41.3676 −2.24018
\(342\) 63.6983 3.44441
\(343\) 1.14057 0.0615852
\(344\) −0.822908 −0.0443682
\(345\) −9.89583 −0.532774
\(346\) −32.3886 −1.74122
\(347\) −1.93887 −0.104084 −0.0520420 0.998645i \(-0.516573\pi\)
−0.0520420 + 0.998645i \(0.516573\pi\)
\(348\) −95.3052 −5.10890
\(349\) −1.00000 −0.0535288
\(350\) 2.10002 0.112251
\(351\) 2.43856 0.130161
\(352\) 79.4405 4.23419
\(353\) 14.3814 0.765444 0.382722 0.923864i \(-0.374987\pi\)
0.382722 + 0.923864i \(0.374987\pi\)
\(354\) 81.5316 4.33336
\(355\) 31.1953 1.65568
\(356\) −34.1242 −1.80858
\(357\) 1.12173 0.0593682
\(358\) 44.9343 2.37485
\(359\) −9.04464 −0.477358 −0.238679 0.971099i \(-0.576714\pi\)
−0.238679 + 0.971099i \(0.576714\pi\)
\(360\) −116.616 −6.14618
\(361\) 23.2167 1.22193
\(362\) −51.6937 −2.71696
\(363\) −43.5021 −2.28327
\(364\) 0.579610 0.0303798
\(365\) −6.07521 −0.317991
\(366\) 37.5181 1.96110
\(367\) −4.46087 −0.232855 −0.116428 0.993199i \(-0.537144\pi\)
−0.116428 + 0.993199i \(0.537144\pi\)
\(368\) 11.8609 0.618291
\(369\) −7.57969 −0.394583
\(370\) −47.6447 −2.47693
\(371\) −0.0660012 −0.00342661
\(372\) −103.461 −5.36421
\(373\) 30.2512 1.56635 0.783175 0.621801i \(-0.213599\pi\)
0.783175 + 0.621801i \(0.213599\pi\)
\(374\) 74.9008 3.87303
\(375\) −46.1644 −2.38392
\(376\) −4.42540 −0.228223
\(377\) −10.0588 −0.518053
\(378\) −0.380467 −0.0195691
\(379\) −24.9774 −1.28300 −0.641501 0.767122i \(-0.721688\pi\)
−0.641501 + 0.767122i \(0.721688\pi\)
\(380\) −127.052 −6.51763
\(381\) −37.5026 −1.92132
\(382\) 39.7292 2.03272
\(383\) 33.1013 1.69140 0.845700 0.533659i \(-0.179183\pi\)
0.845700 + 0.533659i \(0.179183\pi\)
\(384\) 35.2730 1.80002
\(385\) 1.64678 0.0839275
\(386\) 28.1487 1.43273
\(387\) 0.365485 0.0185787
\(388\) 33.1139 1.68110
\(389\) −15.0250 −0.761799 −0.380900 0.924616i \(-0.624386\pi\)
−0.380900 + 0.924616i \(0.624386\pi\)
\(390\) −36.7373 −1.86027
\(391\) 5.32569 0.269332
\(392\) 57.9074 2.92476
\(393\) 47.2191 2.38189
\(394\) −33.1009 −1.66760
\(395\) −33.7732 −1.69931
\(396\) −99.0732 −4.97862
\(397\) 1.40240 0.0703846 0.0351923 0.999381i \(-0.488796\pi\)
0.0351923 + 0.999381i \(0.488796\pi\)
\(398\) 36.6184 1.83551
\(399\) −1.36853 −0.0685122
\(400\) 114.636 5.73179
\(401\) 13.5860 0.678450 0.339225 0.940705i \(-0.389835\pi\)
0.339225 + 0.940705i \(0.389835\pi\)
\(402\) −12.0350 −0.600249
\(403\) −10.9196 −0.543942
\(404\) −43.6347 −2.17091
\(405\) −24.9222 −1.23840
\(406\) 1.56938 0.0778870
\(407\) −24.6233 −1.22053
\(408\) 113.955 5.64163
\(409\) −25.0607 −1.23917 −0.619587 0.784928i \(-0.712700\pi\)
−0.619587 + 0.784928i \(0.712700\pi\)
\(410\) 21.0400 1.03909
\(411\) 8.14041 0.401537
\(412\) 42.9709 2.11702
\(413\) −0.964713 −0.0474704
\(414\) −9.80360 −0.481821
\(415\) 13.7707 0.675976
\(416\) 20.9694 1.02811
\(417\) −1.21755 −0.0596235
\(418\) −91.3803 −4.46955
\(419\) 2.43725 0.119068 0.0595338 0.998226i \(-0.481039\pi\)
0.0595338 + 0.998226i \(0.481039\pi\)
\(420\) 4.11862 0.200968
\(421\) 32.1163 1.56525 0.782625 0.622493i \(-0.213880\pi\)
0.782625 + 0.622493i \(0.213880\pi\)
\(422\) 61.5685 2.99711
\(423\) 1.96549 0.0955656
\(424\) −6.70499 −0.325623
\(425\) 51.4730 2.49681
\(426\) 56.1148 2.71877
\(427\) −0.443928 −0.0214832
\(428\) −26.5597 −1.28381
\(429\) −18.9862 −0.916664
\(430\) −1.01453 −0.0489248
\(431\) 19.0155 0.915943 0.457971 0.888967i \(-0.348576\pi\)
0.457971 + 0.888967i \(0.348576\pi\)
\(432\) −20.7689 −0.999245
\(433\) 23.3980 1.12444 0.562218 0.826989i \(-0.309948\pi\)
0.562218 + 0.826989i \(0.309948\pi\)
\(434\) 1.70368 0.0817794
\(435\) −71.4760 −3.42701
\(436\) 3.78442 0.181241
\(437\) −6.49744 −0.310815
\(438\) −10.9282 −0.522171
\(439\) −9.87946 −0.471521 −0.235760 0.971811i \(-0.575758\pi\)
−0.235760 + 0.971811i \(0.575758\pi\)
\(440\) 167.294 7.97544
\(441\) −25.7189 −1.22471
\(442\) 19.7711 0.940416
\(443\) 30.0851 1.42938 0.714692 0.699439i \(-0.246567\pi\)
0.714692 + 0.699439i \(0.246567\pi\)
\(444\) −61.5833 −2.92261
\(445\) −25.5921 −1.21318
\(446\) 68.1435 3.22669
\(447\) 53.0790 2.51055
\(448\) −1.33816 −0.0632220
\(449\) −40.7064 −1.92105 −0.960526 0.278190i \(-0.910265\pi\)
−0.960526 + 0.278190i \(0.910265\pi\)
\(450\) −94.7521 −4.46666
\(451\) 10.8737 0.512021
\(452\) −106.939 −5.02998
\(453\) −28.7851 −1.35244
\(454\) 21.7026 1.01856
\(455\) 0.434690 0.0203786
\(456\) −139.028 −6.51057
\(457\) 1.61931 0.0757479 0.0378740 0.999283i \(-0.487941\pi\)
0.0378740 + 0.999283i \(0.487941\pi\)
\(458\) −31.8351 −1.48756
\(459\) −9.32552 −0.435278
\(460\) 19.5542 0.911718
\(461\) −21.2793 −0.991077 −0.495539 0.868586i \(-0.665029\pi\)
−0.495539 + 0.868586i \(0.665029\pi\)
\(462\) 2.96226 0.137817
\(463\) −7.43494 −0.345531 −0.172766 0.984963i \(-0.555270\pi\)
−0.172766 + 0.984963i \(0.555270\pi\)
\(464\) 85.6692 3.97709
\(465\) −77.5928 −3.59828
\(466\) −8.91105 −0.412797
\(467\) −4.86079 −0.224930 −0.112465 0.993656i \(-0.535875\pi\)
−0.112465 + 0.993656i \(0.535875\pi\)
\(468\) −26.1518 −1.20887
\(469\) 0.142402 0.00657552
\(470\) −5.45588 −0.251661
\(471\) −38.7405 −1.78507
\(472\) −98.0042 −4.51101
\(473\) −0.524318 −0.0241082
\(474\) −60.7519 −2.79043
\(475\) −62.7980 −2.88137
\(476\) −2.21654 −0.101595
\(477\) 2.97795 0.136351
\(478\) 57.1256 2.61286
\(479\) −20.9271 −0.956185 −0.478092 0.878310i \(-0.658672\pi\)
−0.478092 + 0.878310i \(0.658672\pi\)
\(480\) 149.006 6.80114
\(481\) −6.49966 −0.296359
\(482\) −41.3024 −1.88127
\(483\) 0.210626 0.00958382
\(484\) 85.9602 3.90728
\(485\) 24.8344 1.12767
\(486\) −58.8342 −2.66877
\(487\) 34.1201 1.54613 0.773064 0.634327i \(-0.218723\pi\)
0.773064 + 0.634327i \(0.218723\pi\)
\(488\) −45.0982 −2.04150
\(489\) −46.0975 −2.08460
\(490\) 71.3914 3.22513
\(491\) −30.3656 −1.37038 −0.685191 0.728363i \(-0.740281\pi\)
−0.685191 + 0.728363i \(0.740281\pi\)
\(492\) 27.1953 1.22606
\(493\) 38.4666 1.73245
\(494\) −24.1211 −1.08526
\(495\) −74.3019 −3.33962
\(496\) 93.0006 4.17585
\(497\) −0.663971 −0.0297832
\(498\) 24.7710 1.11001
\(499\) 29.8874 1.33794 0.668972 0.743288i \(-0.266735\pi\)
0.668972 + 0.743288i \(0.266735\pi\)
\(500\) 91.2209 4.07952
\(501\) −22.7566 −1.01669
\(502\) −28.9680 −1.29291
\(503\) 5.00538 0.223179 0.111589 0.993754i \(-0.464406\pi\)
0.111589 + 0.993754i \(0.464406\pi\)
\(504\) 2.48208 0.110561
\(505\) −32.7247 −1.45623
\(506\) 14.0640 0.625223
\(507\) 28.5817 1.26936
\(508\) 74.1051 3.28788
\(509\) −15.1497 −0.671500 −0.335750 0.941951i \(-0.608990\pi\)
−0.335750 + 0.941951i \(0.608990\pi\)
\(510\) 140.491 6.22103
\(511\) 0.129307 0.00572019
\(512\) 17.8301 0.787987
\(513\) 11.3773 0.502320
\(514\) 52.0159 2.29432
\(515\) 32.2269 1.42009
\(516\) −1.31133 −0.0577281
\(517\) −2.81966 −0.124008
\(518\) 1.01408 0.0445563
\(519\) −31.3967 −1.37816
\(520\) 44.1597 1.93653
\(521\) −6.42035 −0.281280 −0.140640 0.990061i \(-0.544916\pi\)
−0.140640 + 0.990061i \(0.544916\pi\)
\(522\) −70.8098 −3.09926
\(523\) 10.8136 0.472844 0.236422 0.971650i \(-0.424025\pi\)
0.236422 + 0.971650i \(0.424025\pi\)
\(524\) −93.3050 −4.07605
\(525\) 2.03571 0.0888456
\(526\) 36.3429 1.58463
\(527\) 41.7585 1.81903
\(528\) 161.703 7.03724
\(529\) 1.00000 0.0434783
\(530\) −8.26629 −0.359065
\(531\) 43.5275 1.88893
\(532\) 2.70422 0.117243
\(533\) 2.87026 0.124325
\(534\) −46.0356 −1.99216
\(535\) −19.9190 −0.861172
\(536\) 14.4665 0.624857
\(537\) 43.5583 1.87968
\(538\) −64.6588 −2.78764
\(539\) 36.8958 1.58922
\(540\) −34.2402 −1.47346
\(541\) 40.6434 1.74740 0.873698 0.486468i \(-0.161715\pi\)
0.873698 + 0.486468i \(0.161715\pi\)
\(542\) 40.4574 1.73780
\(543\) −50.1106 −2.15045
\(544\) −80.1911 −3.43817
\(545\) 2.83820 0.121575
\(546\) 0.781929 0.0334635
\(547\) −20.8107 −0.889803 −0.444902 0.895580i \(-0.646761\pi\)
−0.444902 + 0.895580i \(0.646761\pi\)
\(548\) −16.0854 −0.687136
\(549\) 20.0298 0.854853
\(550\) 135.929 5.79605
\(551\) −46.9300 −1.99928
\(552\) 21.3973 0.910730
\(553\) 0.718839 0.0305682
\(554\) 14.2508 0.605459
\(555\) −46.1856 −1.96047
\(556\) 2.40587 0.102032
\(557\) −1.62632 −0.0689095 −0.0344548 0.999406i \(-0.510969\pi\)
−0.0344548 + 0.999406i \(0.510969\pi\)
\(558\) −76.8696 −3.25415
\(559\) −0.138401 −0.00585375
\(560\) −3.70220 −0.156446
\(561\) 72.6070 3.06547
\(562\) −83.0093 −3.50154
\(563\) 28.8410 1.21550 0.607751 0.794127i \(-0.292072\pi\)
0.607751 + 0.794127i \(0.292072\pi\)
\(564\) −7.05202 −0.296944
\(565\) −80.2009 −3.37408
\(566\) −12.6717 −0.532629
\(567\) 0.530453 0.0222769
\(568\) −67.4522 −2.83023
\(569\) 4.55057 0.190770 0.0953850 0.995440i \(-0.469592\pi\)
0.0953850 + 0.995440i \(0.469592\pi\)
\(570\) −171.401 −7.17920
\(571\) 25.7621 1.07811 0.539054 0.842271i \(-0.318782\pi\)
0.539054 + 0.842271i \(0.318782\pi\)
\(572\) 37.5168 1.56866
\(573\) 38.5125 1.60888
\(574\) −0.447821 −0.0186917
\(575\) 9.66503 0.403060
\(576\) 60.3772 2.51572
\(577\) 6.44218 0.268192 0.134096 0.990968i \(-0.457187\pi\)
0.134096 + 0.990968i \(0.457187\pi\)
\(578\) −30.2908 −1.25993
\(579\) 27.2867 1.13400
\(580\) 141.237 5.86453
\(581\) −0.293100 −0.0121598
\(582\) 44.6727 1.85174
\(583\) −4.27210 −0.176932
\(584\) 13.1361 0.543578
\(585\) −19.6130 −0.810899
\(586\) −45.8064 −1.89225
\(587\) 36.4265 1.50348 0.751741 0.659458i \(-0.229214\pi\)
0.751741 + 0.659458i \(0.229214\pi\)
\(588\) 92.2772 3.80545
\(589\) −50.9461 −2.09920
\(590\) −120.825 −4.97429
\(591\) −32.0872 −1.31989
\(592\) 55.3568 2.27515
\(593\) −45.2862 −1.85968 −0.929841 0.367961i \(-0.880056\pi\)
−0.929841 + 0.367961i \(0.880056\pi\)
\(594\) −24.6268 −1.01045
\(595\) −1.66234 −0.0681491
\(596\) −104.884 −4.29622
\(597\) 35.4970 1.45280
\(598\) 3.71240 0.151812
\(599\) 20.4669 0.836253 0.418127 0.908389i \(-0.362687\pi\)
0.418127 + 0.908389i \(0.362687\pi\)
\(600\) 206.806 8.44281
\(601\) 15.1597 0.618377 0.309188 0.951001i \(-0.399943\pi\)
0.309188 + 0.951001i \(0.399943\pi\)
\(602\) 0.0215935 0.000880086 0
\(603\) −6.42513 −0.261652
\(604\) 56.8793 2.31439
\(605\) 64.4676 2.62098
\(606\) −58.8659 −2.39126
\(607\) −11.2314 −0.455869 −0.227934 0.973677i \(-0.573197\pi\)
−0.227934 + 0.973677i \(0.573197\pi\)
\(608\) 97.8346 3.96772
\(609\) 1.52132 0.0616469
\(610\) −55.5995 −2.25116
\(611\) −0.744289 −0.0301107
\(612\) 100.009 4.04264
\(613\) 41.0310 1.65723 0.828613 0.559822i \(-0.189131\pi\)
0.828613 + 0.559822i \(0.189131\pi\)
\(614\) −14.9332 −0.602656
\(615\) 20.3956 0.822431
\(616\) −3.56075 −0.143467
\(617\) −25.4016 −1.02263 −0.511314 0.859394i \(-0.670841\pi\)
−0.511314 + 0.859394i \(0.670841\pi\)
\(618\) 57.9704 2.33191
\(619\) −38.2963 −1.53926 −0.769629 0.638491i \(-0.779559\pi\)
−0.769629 + 0.638491i \(0.779559\pi\)
\(620\) 153.323 6.15761
\(621\) −1.75104 −0.0702670
\(622\) −32.2162 −1.29175
\(623\) 0.544710 0.0218234
\(624\) 42.6839 1.70872
\(625\) 20.0877 0.803509
\(626\) −49.0952 −1.96224
\(627\) −88.5818 −3.53762
\(628\) 76.5512 3.05473
\(629\) 24.8559 0.991071
\(630\) 3.06005 0.121915
\(631\) 13.9775 0.556436 0.278218 0.960518i \(-0.410256\pi\)
0.278218 + 0.960518i \(0.410256\pi\)
\(632\) 73.0262 2.90483
\(633\) 59.6830 2.37219
\(634\) −7.08471 −0.281370
\(635\) 55.5766 2.20549
\(636\) −10.6846 −0.423673
\(637\) 9.73918 0.385880
\(638\) 101.582 4.02168
\(639\) 29.9581 1.18513
\(640\) −52.2725 −2.06625
\(641\) −32.2541 −1.27396 −0.636979 0.770881i \(-0.719816\pi\)
−0.636979 + 0.770881i \(0.719816\pi\)
\(642\) −35.8307 −1.41412
\(643\) −14.3131 −0.564452 −0.282226 0.959348i \(-0.591073\pi\)
−0.282226 + 0.959348i \(0.591073\pi\)
\(644\) −0.416197 −0.0164005
\(645\) −0.983458 −0.0387236
\(646\) 92.2437 3.62928
\(647\) 13.9962 0.550246 0.275123 0.961409i \(-0.411281\pi\)
0.275123 + 0.961409i \(0.411281\pi\)
\(648\) 53.8882 2.11693
\(649\) −62.4436 −2.45113
\(650\) 35.8805 1.40735
\(651\) 1.65151 0.0647278
\(652\) 91.0886 3.56731
\(653\) 16.8225 0.658316 0.329158 0.944275i \(-0.393235\pi\)
0.329158 + 0.944275i \(0.393235\pi\)
\(654\) 5.10542 0.199638
\(655\) −69.9759 −2.73418
\(656\) −24.4456 −0.954442
\(657\) −5.83427 −0.227617
\(658\) 0.116125 0.00452702
\(659\) 3.48427 0.135728 0.0678640 0.997695i \(-0.478382\pi\)
0.0678640 + 0.997695i \(0.478382\pi\)
\(660\) 266.589 10.3770
\(661\) 44.8868 1.74589 0.872947 0.487815i \(-0.162206\pi\)
0.872947 + 0.487815i \(0.162206\pi\)
\(662\) −9.73237 −0.378259
\(663\) 19.1656 0.744332
\(664\) −29.7757 −1.15552
\(665\) 2.02808 0.0786456
\(666\) −45.7551 −1.77297
\(667\) 7.22284 0.279669
\(668\) 44.9671 1.73983
\(669\) 66.0566 2.55390
\(670\) 17.8351 0.689030
\(671\) −28.7344 −1.10928
\(672\) −3.17148 −0.122343
\(673\) 27.0875 1.04415 0.522073 0.852901i \(-0.325159\pi\)
0.522073 + 0.852901i \(0.325159\pi\)
\(674\) −58.4744 −2.25235
\(675\) −16.9239 −0.651401
\(676\) −56.4775 −2.17221
\(677\) −24.1492 −0.928129 −0.464064 0.885802i \(-0.653609\pi\)
−0.464064 + 0.885802i \(0.653609\pi\)
\(678\) −144.267 −5.54054
\(679\) −0.528584 −0.0202852
\(680\) −168.875 −6.47606
\(681\) 21.0380 0.806178
\(682\) 110.276 4.22267
\(683\) 34.9350 1.33675 0.668376 0.743824i \(-0.266990\pi\)
0.668376 + 0.743824i \(0.266990\pi\)
\(684\) −122.013 −4.66529
\(685\) −12.0636 −0.460926
\(686\) −3.04048 −0.116086
\(687\) −30.8602 −1.17739
\(688\) 1.17875 0.0449393
\(689\) −1.12768 −0.0429613
\(690\) 26.3798 1.00426
\(691\) 18.3266 0.697178 0.348589 0.937276i \(-0.386661\pi\)
0.348589 + 0.937276i \(0.386661\pi\)
\(692\) 62.0399 2.35840
\(693\) 1.58147 0.0600749
\(694\) 5.16854 0.196195
\(695\) 1.80433 0.0684422
\(696\) 154.549 5.85818
\(697\) −10.9764 −0.415761
\(698\) 2.66575 0.100900
\(699\) −8.63816 −0.326725
\(700\) −4.02256 −0.152039
\(701\) 33.1286 1.25125 0.625626 0.780123i \(-0.284844\pi\)
0.625626 + 0.780123i \(0.284844\pi\)
\(702\) −6.50058 −0.245349
\(703\) −30.3247 −1.14372
\(704\) −86.6159 −3.26446
\(705\) −5.28880 −0.199188
\(706\) −38.3371 −1.44284
\(707\) 0.696523 0.0261954
\(708\) −156.173 −5.86933
\(709\) 26.3230 0.988580 0.494290 0.869297i \(-0.335428\pi\)
0.494290 + 0.869297i \(0.335428\pi\)
\(710\) −83.1588 −3.12089
\(711\) −32.4338 −1.21636
\(712\) 55.3366 2.07383
\(713\) 7.84095 0.293646
\(714\) −2.99025 −0.111907
\(715\) 28.1365 1.05224
\(716\) −86.0711 −3.21663
\(717\) 55.3762 2.06806
\(718\) 24.1107 0.899804
\(719\) 47.8069 1.78290 0.891448 0.453123i \(-0.149690\pi\)
0.891448 + 0.453123i \(0.149690\pi\)
\(720\) 167.042 6.22528
\(721\) −0.685927 −0.0255453
\(722\) −61.8898 −2.30330
\(723\) −40.0375 −1.48901
\(724\) 99.0185 3.68000
\(725\) 69.8090 2.59264
\(726\) 115.966 4.30389
\(727\) −42.4811 −1.57554 −0.787769 0.615971i \(-0.788764\pi\)
−0.787769 + 0.615971i \(0.788764\pi\)
\(728\) −0.939910 −0.0348354
\(729\) −37.5085 −1.38920
\(730\) 16.1950 0.599403
\(731\) 0.529272 0.0195758
\(732\) −71.8653 −2.65622
\(733\) 33.4133 1.23415 0.617075 0.786905i \(-0.288318\pi\)
0.617075 + 0.786905i \(0.288318\pi\)
\(734\) 11.8915 0.438925
\(735\) 69.2051 2.55267
\(736\) −15.0574 −0.555023
\(737\) 9.21736 0.339526
\(738\) 20.2055 0.743776
\(739\) 48.5329 1.78531 0.892656 0.450738i \(-0.148839\pi\)
0.892656 + 0.450738i \(0.148839\pi\)
\(740\) 91.2627 3.35488
\(741\) −23.3824 −0.858975
\(742\) 0.175942 0.00645905
\(743\) −17.3928 −0.638081 −0.319040 0.947741i \(-0.603361\pi\)
−0.319040 + 0.947741i \(0.603361\pi\)
\(744\) 167.775 6.15094
\(745\) −78.6599 −2.88188
\(746\) −80.6421 −2.95252
\(747\) 13.2245 0.483861
\(748\) −143.471 −5.24583
\(749\) 0.423962 0.0154912
\(750\) 123.063 4.49361
\(751\) 4.51639 0.164805 0.0824027 0.996599i \(-0.473741\pi\)
0.0824027 + 0.996599i \(0.473741\pi\)
\(752\) 6.33901 0.231160
\(753\) −28.0809 −1.02332
\(754\) 26.8141 0.976512
\(755\) 42.6577 1.55247
\(756\) 0.728780 0.0265055
\(757\) −6.38700 −0.232139 −0.116070 0.993241i \(-0.537030\pi\)
−0.116070 + 0.993241i \(0.537030\pi\)
\(758\) 66.5833 2.41842
\(759\) 13.6333 0.494859
\(760\) 206.031 7.47352
\(761\) −35.0503 −1.27057 −0.635286 0.772277i \(-0.719118\pi\)
−0.635286 + 0.772277i \(0.719118\pi\)
\(762\) 99.9724 3.62162
\(763\) −0.0604092 −0.00218696
\(764\) −76.1007 −2.75323
\(765\) 75.0040 2.71177
\(766\) −88.2398 −3.18823
\(767\) −16.4829 −0.595162
\(768\) −9.17980 −0.331248
\(769\) −5.95980 −0.214916 −0.107458 0.994210i \(-0.534271\pi\)
−0.107458 + 0.994210i \(0.534271\pi\)
\(770\) −4.38989 −0.158200
\(771\) 50.4230 1.81594
\(772\) −53.9185 −1.94057
\(773\) −0.385305 −0.0138584 −0.00692922 0.999976i \(-0.502206\pi\)
−0.00692922 + 0.999976i \(0.502206\pi\)
\(774\) −0.974291 −0.0350202
\(775\) 75.7831 2.72221
\(776\) −53.6983 −1.92766
\(777\) 0.983029 0.0352660
\(778\) 40.0529 1.43597
\(779\) 13.3914 0.479797
\(780\) 70.3699 2.51965
\(781\) −42.9773 −1.53785
\(782\) −14.1969 −0.507681
\(783\) −12.6475 −0.451985
\(784\) −82.9474 −2.96241
\(785\) 57.4111 2.04909
\(786\) −125.874 −4.48978
\(787\) −7.84030 −0.279476 −0.139738 0.990188i \(-0.544626\pi\)
−0.139738 + 0.990188i \(0.544626\pi\)
\(788\) 63.4043 2.25868
\(789\) 35.2299 1.25422
\(790\) 90.0307 3.20315
\(791\) 1.70702 0.0606947
\(792\) 160.660 5.70879
\(793\) −7.58486 −0.269346
\(794\) −3.73845 −0.132673
\(795\) −8.01314 −0.284197
\(796\) −70.1421 −2.48612
\(797\) −44.1213 −1.56286 −0.781428 0.623995i \(-0.785508\pi\)
−0.781428 + 0.623995i \(0.785508\pi\)
\(798\) 3.64815 0.129143
\(799\) 2.84630 0.100695
\(800\) −145.530 −5.14528
\(801\) −24.5771 −0.868390
\(802\) −36.2167 −1.27886
\(803\) 8.36973 0.295361
\(804\) 23.0528 0.813010
\(805\) −0.312135 −0.0110013
\(806\) 29.1088 1.02531
\(807\) −62.6787 −2.20639
\(808\) 70.7591 2.48929
\(809\) 41.5418 1.46053 0.730266 0.683163i \(-0.239396\pi\)
0.730266 + 0.683163i \(0.239396\pi\)
\(810\) 66.4364 2.33434
\(811\) −54.3388 −1.90809 −0.954047 0.299659i \(-0.903127\pi\)
−0.954047 + 0.299659i \(0.903127\pi\)
\(812\) −3.00613 −0.105494
\(813\) 39.2184 1.37545
\(814\) 65.6393 2.30066
\(815\) 68.3137 2.39293
\(816\) −163.231 −5.71424
\(817\) −0.645722 −0.0225909
\(818\) 66.8055 2.33580
\(819\) 0.417450 0.0145869
\(820\) −40.3017 −1.40740
\(821\) −12.1937 −0.425563 −0.212782 0.977100i \(-0.568252\pi\)
−0.212782 + 0.977100i \(0.568252\pi\)
\(822\) −21.7003 −0.756883
\(823\) 6.13549 0.213870 0.106935 0.994266i \(-0.465896\pi\)
0.106935 + 0.994266i \(0.465896\pi\)
\(824\) −69.6827 −2.42751
\(825\) 131.767 4.58753
\(826\) 2.57168 0.0894801
\(827\) −29.8981 −1.03966 −0.519830 0.854270i \(-0.674005\pi\)
−0.519830 + 0.854270i \(0.674005\pi\)
\(828\) 18.7787 0.652604
\(829\) 31.8990 1.10790 0.553948 0.832551i \(-0.313121\pi\)
0.553948 + 0.832551i \(0.313121\pi\)
\(830\) −36.7091 −1.27419
\(831\) 13.8144 0.479216
\(832\) −22.8635 −0.792649
\(833\) −37.2445 −1.29044
\(834\) 3.24567 0.112388
\(835\) 33.7239 1.16706
\(836\) 175.038 6.05380
\(837\) −13.7299 −0.474573
\(838\) −6.49710 −0.224439
\(839\) 18.8566 0.651001 0.325500 0.945542i \(-0.394467\pi\)
0.325500 + 0.945542i \(0.394467\pi\)
\(840\) −6.67885 −0.230442
\(841\) 23.1694 0.798946
\(842\) −85.6138 −2.95045
\(843\) −80.4672 −2.77144
\(844\) −117.934 −4.05944
\(845\) −42.3564 −1.45711
\(846\) −5.23951 −0.180138
\(847\) −1.37215 −0.0471476
\(848\) 9.60433 0.329814
\(849\) −12.2836 −0.421572
\(850\) −137.214 −4.70640
\(851\) 4.66717 0.159989
\(852\) −107.487 −3.68245
\(853\) −0.158682 −0.00543318 −0.00271659 0.999996i \(-0.500865\pi\)
−0.00271659 + 0.999996i \(0.500865\pi\)
\(854\) 1.18340 0.0404950
\(855\) −91.5062 −3.12945
\(856\) 43.0699 1.47210
\(857\) −36.3170 −1.24057 −0.620283 0.784378i \(-0.712982\pi\)
−0.620283 + 0.784378i \(0.712982\pi\)
\(858\) 50.6125 1.72788
\(859\) 39.8576 1.35992 0.679962 0.733247i \(-0.261996\pi\)
0.679962 + 0.733247i \(0.261996\pi\)
\(860\) 1.94331 0.0662664
\(861\) −0.434107 −0.0147943
\(862\) −50.6904 −1.72652
\(863\) −19.2445 −0.655091 −0.327546 0.944835i \(-0.606221\pi\)
−0.327546 + 0.944835i \(0.606221\pi\)
\(864\) 26.3662 0.896996
\(865\) 46.5280 1.58200
\(866\) −62.3732 −2.11953
\(867\) −29.3632 −0.997226
\(868\) −3.26338 −0.110766
\(869\) 46.5288 1.57838
\(870\) 190.537 6.45981
\(871\) 2.43305 0.0824409
\(872\) −6.13692 −0.207822
\(873\) 23.8495 0.807183
\(874\) 17.3205 0.585875
\(875\) −1.45612 −0.0492259
\(876\) 20.9329 0.707256
\(877\) −30.0245 −1.01386 −0.506928 0.861988i \(-0.669219\pi\)
−0.506928 + 0.861988i \(0.669219\pi\)
\(878\) 26.3361 0.888801
\(879\) −44.4036 −1.49770
\(880\) −239.635 −8.07809
\(881\) −40.5363 −1.36570 −0.682852 0.730557i \(-0.739261\pi\)
−0.682852 + 0.730557i \(0.739261\pi\)
\(882\) 68.5601 2.30854
\(883\) −8.47099 −0.285071 −0.142536 0.989790i \(-0.545526\pi\)
−0.142536 + 0.989790i \(0.545526\pi\)
\(884\) −37.8713 −1.27375
\(885\) −117.125 −3.93711
\(886\) −80.1991 −2.69434
\(887\) −1.67384 −0.0562020 −0.0281010 0.999605i \(-0.508946\pi\)
−0.0281010 + 0.999605i \(0.508946\pi\)
\(888\) 99.8649 3.35125
\(889\) −1.18291 −0.0396735
\(890\) 68.2220 2.28681
\(891\) 34.3350 1.15027
\(892\) −130.528 −4.37040
\(893\) −3.47254 −0.116204
\(894\) −141.495 −4.73231
\(895\) −64.5507 −2.15769
\(896\) 1.11258 0.0371688
\(897\) 3.59871 0.120158
\(898\) 108.513 3.62112
\(899\) 56.6340 1.88885
\(900\) 181.496 6.04988
\(901\) 4.31247 0.143669
\(902\) −28.9864 −0.965143
\(903\) 0.0209322 0.000696581 0
\(904\) 173.415 5.76768
\(905\) 74.2609 2.46852
\(906\) 76.7337 2.54931
\(907\) 10.9074 0.362175 0.181087 0.983467i \(-0.442038\pi\)
0.181087 + 0.983467i \(0.442038\pi\)
\(908\) −41.5711 −1.37959
\(909\) −31.4268 −1.04236
\(910\) −1.15877 −0.0384129
\(911\) −23.0359 −0.763213 −0.381606 0.924325i \(-0.624629\pi\)
−0.381606 + 0.924325i \(0.624629\pi\)
\(912\) 199.145 6.59436
\(913\) −18.9717 −0.627870
\(914\) −4.31666 −0.142782
\(915\) −53.8968 −1.78177
\(916\) 60.9797 2.01483
\(917\) 1.48939 0.0491840
\(918\) 24.8595 0.820484
\(919\) −24.5438 −0.809627 −0.404813 0.914399i \(-0.632663\pi\)
−0.404813 + 0.914399i \(0.632663\pi\)
\(920\) −31.7095 −1.04543
\(921\) −14.4759 −0.476997
\(922\) 56.7253 1.86815
\(923\) −11.3445 −0.373408
\(924\) −5.67416 −0.186666
\(925\) 45.1084 1.48316
\(926\) 19.8197 0.651315
\(927\) 30.9488 1.01649
\(928\) −108.757 −3.57013
\(929\) −58.7238 −1.92667 −0.963333 0.268308i \(-0.913535\pi\)
−0.963333 + 0.268308i \(0.913535\pi\)
\(930\) 206.843 6.78264
\(931\) 45.4389 1.48920
\(932\) 17.0690 0.559114
\(933\) −31.2296 −1.02241
\(934\) 12.9576 0.423986
\(935\) −107.599 −3.51887
\(936\) 42.4084 1.38616
\(937\) 43.3543 1.41632 0.708162 0.706050i \(-0.249525\pi\)
0.708162 + 0.706050i \(0.249525\pi\)
\(938\) −0.379608 −0.0123946
\(939\) −47.5917 −1.55310
\(940\) 10.4507 0.340863
\(941\) 30.3458 0.989244 0.494622 0.869108i \(-0.335307\pi\)
0.494622 + 0.869108i \(0.335307\pi\)
\(942\) 103.272 3.36479
\(943\) −2.06103 −0.0671164
\(944\) 140.383 4.56907
\(945\) 0.546563 0.0177797
\(946\) 1.39770 0.0454431
\(947\) 21.5319 0.699693 0.349846 0.936807i \(-0.386234\pi\)
0.349846 + 0.936807i \(0.386234\pi\)
\(948\) 116.369 3.77950
\(949\) 2.20931 0.0717172
\(950\) 167.403 5.43128
\(951\) −6.86774 −0.222702
\(952\) 3.59439 0.116495
\(953\) −16.1237 −0.522298 −0.261149 0.965298i \(-0.584101\pi\)
−0.261149 + 0.965298i \(0.584101\pi\)
\(954\) −7.93845 −0.257017
\(955\) −57.0732 −1.84685
\(956\) −109.423 −3.53900
\(957\) 98.4715 3.18313
\(958\) 55.7864 1.80238
\(959\) 0.256765 0.00829139
\(960\) −162.464 −5.24352
\(961\) 30.4805 0.983243
\(962\) 17.3264 0.558627
\(963\) −19.1290 −0.616423
\(964\) 79.1142 2.54810
\(965\) −40.4373 −1.30172
\(966\) −0.561476 −0.0180652
\(967\) −18.5513 −0.596571 −0.298285 0.954477i \(-0.596415\pi\)
−0.298285 + 0.954477i \(0.596415\pi\)
\(968\) −139.395 −4.48033
\(969\) 89.4188 2.87255
\(970\) −66.2023 −2.12563
\(971\) 54.4186 1.74638 0.873188 0.487384i \(-0.162049\pi\)
0.873188 + 0.487384i \(0.162049\pi\)
\(972\) 112.696 3.61473
\(973\) −0.0384040 −0.00123117
\(974\) −90.9555 −2.91440
\(975\) 34.7817 1.11391
\(976\) 64.5993 2.06777
\(977\) −46.5569 −1.48949 −0.744744 0.667351i \(-0.767428\pi\)
−0.744744 + 0.667351i \(0.767428\pi\)
\(978\) 122.884 3.92940
\(979\) 35.2579 1.12685
\(980\) −136.749 −4.36830
\(981\) 2.72564 0.0870231
\(982\) 80.9471 2.58312
\(983\) 47.6652 1.52028 0.760142 0.649757i \(-0.225130\pi\)
0.760142 + 0.649757i \(0.225130\pi\)
\(984\) −44.1005 −1.40587
\(985\) 47.5513 1.51511
\(986\) −102.542 −3.26561
\(987\) 0.112569 0.00358310
\(988\) 46.2037 1.46993
\(989\) 0.0993810 0.00316013
\(990\) 198.070 6.29508
\(991\) 1.49095 0.0473614 0.0236807 0.999720i \(-0.492461\pi\)
0.0236807 + 0.999720i \(0.492461\pi\)
\(992\) −118.064 −3.74855
\(993\) −9.43432 −0.299389
\(994\) 1.76998 0.0561403
\(995\) −52.6044 −1.66767
\(996\) −47.4485 −1.50346
\(997\) −15.9636 −0.505573 −0.252786 0.967522i \(-0.581347\pi\)
−0.252786 + 0.967522i \(0.581347\pi\)
\(998\) −79.6722 −2.52198
\(999\) −8.17243 −0.258564
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 \(a_p\))