Properties

Label 8035.2.a.e.1.13
Level 8035
Weight 2
Character 8035.1
Self dual Yes
Analytic conductor 64.160
Analytic rank 0
Dimension 153
CM No

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Newspace parameters

Level: \( N \) = \( 8035 = 5 \cdot 1607 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8035.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1597980241\)
Analytic rank: \(0\)
Dimension: \(153\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 8035.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.41868 q^{2} +3.20867 q^{3} +3.85002 q^{4} +1.00000 q^{5} -7.76074 q^{6} -2.07887 q^{7} -4.47460 q^{8} +7.29555 q^{9} +O(q^{10})\) \(q-2.41868 q^{2} +3.20867 q^{3} +3.85002 q^{4} +1.00000 q^{5} -7.76074 q^{6} -2.07887 q^{7} -4.47460 q^{8} +7.29555 q^{9} -2.41868 q^{10} -4.56961 q^{11} +12.3534 q^{12} +3.08185 q^{13} +5.02812 q^{14} +3.20867 q^{15} +3.12259 q^{16} +3.05404 q^{17} -17.6456 q^{18} -0.524240 q^{19} +3.85002 q^{20} -6.67040 q^{21} +11.0524 q^{22} +7.45230 q^{23} -14.3575 q^{24} +1.00000 q^{25} -7.45401 q^{26} +13.7830 q^{27} -8.00367 q^{28} +2.84809 q^{29} -7.76074 q^{30} -6.26218 q^{31} +1.39665 q^{32} -14.6624 q^{33} -7.38676 q^{34} -2.07887 q^{35} +28.0880 q^{36} +5.05829 q^{37} +1.26797 q^{38} +9.88864 q^{39} -4.47460 q^{40} +1.86903 q^{41} +16.1336 q^{42} +7.79340 q^{43} -17.5931 q^{44} +7.29555 q^{45} -18.0247 q^{46} +2.35402 q^{47} +10.0194 q^{48} -2.67831 q^{49} -2.41868 q^{50} +9.79941 q^{51} +11.8652 q^{52} -7.65213 q^{53} -33.3367 q^{54} -4.56961 q^{55} +9.30210 q^{56} -1.68211 q^{57} -6.88861 q^{58} -1.36729 q^{59} +12.3534 q^{60} +4.00882 q^{61} +15.1462 q^{62} -15.1665 q^{63} -9.62322 q^{64} +3.08185 q^{65} +35.4636 q^{66} +3.62849 q^{67} +11.7581 q^{68} +23.9120 q^{69} +5.02812 q^{70} -9.13799 q^{71} -32.6447 q^{72} +16.3476 q^{73} -12.2344 q^{74} +3.20867 q^{75} -2.01833 q^{76} +9.49961 q^{77} -23.9175 q^{78} +2.32344 q^{79} +3.12259 q^{80} +22.3384 q^{81} -4.52059 q^{82} -6.26732 q^{83} -25.6811 q^{84} +3.05404 q^{85} -18.8497 q^{86} +9.13856 q^{87} +20.4472 q^{88} +6.63886 q^{89} -17.6456 q^{90} -6.40676 q^{91} +28.6915 q^{92} -20.0933 q^{93} -5.69363 q^{94} -0.524240 q^{95} +4.48137 q^{96} -6.71316 q^{97} +6.47797 q^{98} -33.3378 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153q + 18q^{2} + 7q^{3} + 176q^{4} + 153q^{5} + 19q^{6} + 5q^{7} + 57q^{8} + 206q^{9} + O(q^{10}) \) \( 153q + 18q^{2} + 7q^{3} + 176q^{4} + 153q^{5} + 19q^{6} + 5q^{7} + 57q^{8} + 206q^{9} + 18q^{10} + 38q^{11} + 14q^{12} + 28q^{13} + 53q^{14} + 7q^{15} + 214q^{16} + 50q^{17} + 47q^{18} + 65q^{19} + 176q^{20} + 109q^{21} + 13q^{22} + 52q^{23} + 66q^{24} + 153q^{25} + 36q^{26} + 19q^{27} + 26q^{28} + 172q^{29} + 19q^{30} + 60q^{31} + 107q^{32} + 4q^{33} + 40q^{34} + 5q^{35} + 241q^{36} + 65q^{37} + 29q^{38} + 56q^{39} + 57q^{40} + 152q^{41} - 19q^{42} + 22q^{43} + 97q^{44} + 206q^{45} + 86q^{46} + 37q^{47} - 4q^{48} + 260q^{49} + 18q^{50} + 102q^{51} - 6q^{52} + 169q^{53} + 64q^{54} + 38q^{55} + 146q^{56} + 40q^{57} - 9q^{58} + 64q^{59} + 14q^{60} + 164q^{61} + 12q^{62} + 19q^{63} + 259q^{64} + 28q^{65} + 6q^{66} + 5q^{67} + 112q^{68} + 119q^{69} + 53q^{70} + 100q^{71} + 77q^{72} + 10q^{73} + 98q^{74} + 7q^{75} + 126q^{76} + 80q^{77} - 4q^{78} + 110q^{79} + 214q^{80} + 305q^{81} - 27q^{82} + 36q^{83} + 172q^{84} + 50q^{85} + 44q^{86} + 23q^{87} + 47q^{88} + 143q^{89} + 47q^{90} + 82q^{91} + 130q^{92} + 31q^{93} + 77q^{94} + 65q^{95} + 57q^{96} + 11q^{97} + 29q^{98} + 99q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.41868 −1.71027 −0.855133 0.518409i \(-0.826524\pi\)
−0.855133 + 0.518409i \(0.826524\pi\)
\(3\) 3.20867 1.85253 0.926263 0.376878i \(-0.123002\pi\)
0.926263 + 0.376878i \(0.123002\pi\)
\(4\) 3.85002 1.92501
\(5\) 1.00000 0.447214
\(6\) −7.76074 −3.16831
\(7\) −2.07887 −0.785738 −0.392869 0.919594i \(-0.628517\pi\)
−0.392869 + 0.919594i \(0.628517\pi\)
\(8\) −4.47460 −1.58201
\(9\) 7.29555 2.43185
\(10\) −2.41868 −0.764854
\(11\) −4.56961 −1.37779 −0.688894 0.724862i \(-0.741904\pi\)
−0.688894 + 0.724862i \(0.741904\pi\)
\(12\) 12.3534 3.56613
\(13\) 3.08185 0.854752 0.427376 0.904074i \(-0.359438\pi\)
0.427376 + 0.904074i \(0.359438\pi\)
\(14\) 5.02812 1.34382
\(15\) 3.20867 0.828475
\(16\) 3.12259 0.780648
\(17\) 3.05404 0.740714 0.370357 0.928889i \(-0.379235\pi\)
0.370357 + 0.928889i \(0.379235\pi\)
\(18\) −17.6456 −4.15911
\(19\) −0.524240 −0.120269 −0.0601345 0.998190i \(-0.519153\pi\)
−0.0601345 + 0.998190i \(0.519153\pi\)
\(20\) 3.85002 0.860890
\(21\) −6.67040 −1.45560
\(22\) 11.0524 2.35638
\(23\) 7.45230 1.55391 0.776956 0.629555i \(-0.216763\pi\)
0.776956 + 0.629555i \(0.216763\pi\)
\(24\) −14.3575 −2.93071
\(25\) 1.00000 0.200000
\(26\) −7.45401 −1.46185
\(27\) 13.7830 2.65254
\(28\) −8.00367 −1.51255
\(29\) 2.84809 0.528876 0.264438 0.964403i \(-0.414814\pi\)
0.264438 + 0.964403i \(0.414814\pi\)
\(30\) −7.76074 −1.41691
\(31\) −6.26218 −1.12472 −0.562360 0.826892i \(-0.690107\pi\)
−0.562360 + 0.826892i \(0.690107\pi\)
\(32\) 1.39665 0.246894
\(33\) −14.6624 −2.55239
\(34\) −7.38676 −1.26682
\(35\) −2.07887 −0.351393
\(36\) 28.0880 4.68133
\(37\) 5.05829 0.831577 0.415789 0.909461i \(-0.363506\pi\)
0.415789 + 0.909461i \(0.363506\pi\)
\(38\) 1.26797 0.205692
\(39\) 9.88864 1.58345
\(40\) −4.47460 −0.707496
\(41\) 1.86903 0.291894 0.145947 0.989292i \(-0.453377\pi\)
0.145947 + 0.989292i \(0.453377\pi\)
\(42\) 16.1336 2.48946
\(43\) 7.79340 1.18848 0.594241 0.804287i \(-0.297452\pi\)
0.594241 + 0.804287i \(0.297452\pi\)
\(44\) −17.5931 −2.65225
\(45\) 7.29555 1.08756
\(46\) −18.0247 −2.65760
\(47\) 2.35402 0.343370 0.171685 0.985152i \(-0.445079\pi\)
0.171685 + 0.985152i \(0.445079\pi\)
\(48\) 10.0194 1.44617
\(49\) −2.67831 −0.382616
\(50\) −2.41868 −0.342053
\(51\) 9.79941 1.37219
\(52\) 11.8652 1.64540
\(53\) −7.65213 −1.05110 −0.525551 0.850762i \(-0.676141\pi\)
−0.525551 + 0.850762i \(0.676141\pi\)
\(54\) −33.3367 −4.53655
\(55\) −4.56961 −0.616166
\(56\) 9.30210 1.24304
\(57\) −1.68211 −0.222801
\(58\) −6.88861 −0.904519
\(59\) −1.36729 −0.178006 −0.0890032 0.996031i \(-0.528368\pi\)
−0.0890032 + 0.996031i \(0.528368\pi\)
\(60\) 12.3534 1.59482
\(61\) 4.00882 0.513277 0.256638 0.966507i \(-0.417385\pi\)
0.256638 + 0.966507i \(0.417385\pi\)
\(62\) 15.1462 1.92357
\(63\) −15.1665 −1.91080
\(64\) −9.62322 −1.20290
\(65\) 3.08185 0.382257
\(66\) 35.4636 4.36526
\(67\) 3.62849 0.443291 0.221646 0.975127i \(-0.428857\pi\)
0.221646 + 0.975127i \(0.428857\pi\)
\(68\) 11.7581 1.42588
\(69\) 23.9120 2.87866
\(70\) 5.02812 0.600975
\(71\) −9.13799 −1.08448 −0.542240 0.840224i \(-0.682424\pi\)
−0.542240 + 0.840224i \(0.682424\pi\)
\(72\) −32.6447 −3.84721
\(73\) 16.3476 1.91334 0.956669 0.291178i \(-0.0940473\pi\)
0.956669 + 0.291178i \(0.0940473\pi\)
\(74\) −12.2344 −1.42222
\(75\) 3.20867 0.370505
\(76\) −2.01833 −0.231519
\(77\) 9.49961 1.08258
\(78\) −23.9175 −2.70812
\(79\) 2.32344 0.261407 0.130704 0.991421i \(-0.458276\pi\)
0.130704 + 0.991421i \(0.458276\pi\)
\(80\) 3.12259 0.349116
\(81\) 22.3384 2.48205
\(82\) −4.52059 −0.499215
\(83\) −6.26732 −0.687928 −0.343964 0.938983i \(-0.611770\pi\)
−0.343964 + 0.938983i \(0.611770\pi\)
\(84\) −25.6811 −2.80204
\(85\) 3.05404 0.331258
\(86\) −18.8497 −2.03262
\(87\) 9.13856 0.979757
\(88\) 20.4472 2.17967
\(89\) 6.63886 0.703717 0.351859 0.936053i \(-0.385550\pi\)
0.351859 + 0.936053i \(0.385550\pi\)
\(90\) −17.6456 −1.86001
\(91\) −6.40676 −0.671611
\(92\) 28.6915 2.99129
\(93\) −20.0933 −2.08357
\(94\) −5.69363 −0.587254
\(95\) −0.524240 −0.0537859
\(96\) 4.48137 0.457378
\(97\) −6.71316 −0.681618 −0.340809 0.940133i \(-0.610701\pi\)
−0.340809 + 0.940133i \(0.610701\pi\)
\(98\) 6.47797 0.654374
\(99\) −33.3378 −3.35058
\(100\) 3.85002 0.385002
\(101\) 11.0639 1.10090 0.550450 0.834868i \(-0.314456\pi\)
0.550450 + 0.834868i \(0.314456\pi\)
\(102\) −23.7017 −2.34681
\(103\) −7.09138 −0.698734 −0.349367 0.936986i \(-0.613603\pi\)
−0.349367 + 0.936986i \(0.613603\pi\)
\(104\) −13.7900 −1.35222
\(105\) −6.67040 −0.650964
\(106\) 18.5081 1.79766
\(107\) 9.34656 0.903566 0.451783 0.892128i \(-0.350788\pi\)
0.451783 + 0.892128i \(0.350788\pi\)
\(108\) 53.0648 5.10616
\(109\) −11.6573 −1.11657 −0.558284 0.829650i \(-0.688540\pi\)
−0.558284 + 0.829650i \(0.688540\pi\)
\(110\) 11.0524 1.05381
\(111\) 16.2304 1.54052
\(112\) −6.49145 −0.613385
\(113\) −17.3684 −1.63388 −0.816939 0.576724i \(-0.804331\pi\)
−0.816939 + 0.576724i \(0.804331\pi\)
\(114\) 4.06849 0.381049
\(115\) 7.45230 0.694930
\(116\) 10.9652 1.01809
\(117\) 22.4838 2.07863
\(118\) 3.30704 0.304438
\(119\) −6.34895 −0.582008
\(120\) −14.3575 −1.31065
\(121\) 9.88133 0.898302
\(122\) −9.69606 −0.877840
\(123\) 5.99710 0.540740
\(124\) −24.1095 −2.16510
\(125\) 1.00000 0.0894427
\(126\) 36.6829 3.26797
\(127\) 3.99446 0.354451 0.177225 0.984170i \(-0.443288\pi\)
0.177225 + 0.984170i \(0.443288\pi\)
\(128\) 20.4822 1.81039
\(129\) 25.0064 2.20169
\(130\) −7.45401 −0.653760
\(131\) 3.18872 0.278600 0.139300 0.990250i \(-0.455515\pi\)
0.139300 + 0.990250i \(0.455515\pi\)
\(132\) −56.4503 −4.91337
\(133\) 1.08983 0.0944999
\(134\) −8.77617 −0.758145
\(135\) 13.7830 1.18625
\(136\) −13.6656 −1.17182
\(137\) −14.4679 −1.23608 −0.618038 0.786148i \(-0.712072\pi\)
−0.618038 + 0.786148i \(0.712072\pi\)
\(138\) −57.8354 −4.92327
\(139\) −4.85721 −0.411983 −0.205991 0.978554i \(-0.566042\pi\)
−0.205991 + 0.978554i \(0.566042\pi\)
\(140\) −8.00367 −0.676434
\(141\) 7.55329 0.636101
\(142\) 22.1019 1.85475
\(143\) −14.0829 −1.17767
\(144\) 22.7810 1.89842
\(145\) 2.84809 0.236521
\(146\) −39.5395 −3.27232
\(147\) −8.59380 −0.708805
\(148\) 19.4745 1.60079
\(149\) 7.53589 0.617365 0.308682 0.951165i \(-0.400112\pi\)
0.308682 + 0.951165i \(0.400112\pi\)
\(150\) −7.76074 −0.633662
\(151\) 2.85900 0.232662 0.116331 0.993210i \(-0.462887\pi\)
0.116331 + 0.993210i \(0.462887\pi\)
\(152\) 2.34576 0.190267
\(153\) 22.2809 1.80131
\(154\) −22.9765 −1.85150
\(155\) −6.26218 −0.502990
\(156\) 38.0714 3.04815
\(157\) −18.2262 −1.45461 −0.727305 0.686314i \(-0.759228\pi\)
−0.727305 + 0.686314i \(0.759228\pi\)
\(158\) −5.61966 −0.447076
\(159\) −24.5532 −1.94719
\(160\) 1.39665 0.110415
\(161\) −15.4923 −1.22097
\(162\) −54.0295 −4.24496
\(163\) −7.16288 −0.561040 −0.280520 0.959848i \(-0.590507\pi\)
−0.280520 + 0.959848i \(0.590507\pi\)
\(164\) 7.19580 0.561897
\(165\) −14.6624 −1.14146
\(166\) 15.1587 1.17654
\(167\) −6.18720 −0.478780 −0.239390 0.970923i \(-0.576947\pi\)
−0.239390 + 0.970923i \(0.576947\pi\)
\(168\) 29.8473 2.30277
\(169\) −3.50220 −0.269400
\(170\) −7.38676 −0.566538
\(171\) −3.82462 −0.292476
\(172\) 30.0047 2.28784
\(173\) 7.49442 0.569790 0.284895 0.958559i \(-0.408041\pi\)
0.284895 + 0.958559i \(0.408041\pi\)
\(174\) −22.1033 −1.67564
\(175\) −2.07887 −0.157148
\(176\) −14.2690 −1.07557
\(177\) −4.38719 −0.329761
\(178\) −16.0573 −1.20354
\(179\) 21.6911 1.62127 0.810634 0.585553i \(-0.199123\pi\)
0.810634 + 0.585553i \(0.199123\pi\)
\(180\) 28.0880 2.09356
\(181\) 9.80379 0.728710 0.364355 0.931260i \(-0.381289\pi\)
0.364355 + 0.931260i \(0.381289\pi\)
\(182\) 15.4959 1.14863
\(183\) 12.8630 0.950859
\(184\) −33.3460 −2.45830
\(185\) 5.05829 0.371893
\(186\) 48.5992 3.56346
\(187\) −13.9558 −1.02055
\(188\) 9.06303 0.660990
\(189\) −28.6530 −2.08420
\(190\) 1.26797 0.0919882
\(191\) 23.0035 1.66447 0.832237 0.554420i \(-0.187060\pi\)
0.832237 + 0.554420i \(0.187060\pi\)
\(192\) −30.8777 −2.22841
\(193\) −22.9828 −1.65434 −0.827168 0.561954i \(-0.810050\pi\)
−0.827168 + 0.561954i \(0.810050\pi\)
\(194\) 16.2370 1.16575
\(195\) 9.88864 0.708140
\(196\) −10.3115 −0.736538
\(197\) 17.1115 1.21914 0.609570 0.792732i \(-0.291342\pi\)
0.609570 + 0.792732i \(0.291342\pi\)
\(198\) 80.6336 5.73038
\(199\) 7.00526 0.496590 0.248295 0.968685i \(-0.420130\pi\)
0.248295 + 0.968685i \(0.420130\pi\)
\(200\) −4.47460 −0.316402
\(201\) 11.6426 0.821208
\(202\) −26.7601 −1.88283
\(203\) −5.92079 −0.415558
\(204\) 37.7279 2.64148
\(205\) 1.86903 0.130539
\(206\) 17.1518 1.19502
\(207\) 54.3686 3.77888
\(208\) 9.62336 0.667260
\(209\) 2.39557 0.165705
\(210\) 16.1336 1.11332
\(211\) −14.2337 −0.979887 −0.489944 0.871754i \(-0.662983\pi\)
−0.489944 + 0.871754i \(0.662983\pi\)
\(212\) −29.4608 −2.02338
\(213\) −29.3208 −2.00903
\(214\) −22.6064 −1.54534
\(215\) 7.79340 0.531506
\(216\) −61.6734 −4.19634
\(217\) 13.0182 0.883736
\(218\) 28.1953 1.90963
\(219\) 52.4539 3.54451
\(220\) −17.5931 −1.18612
\(221\) 9.41211 0.633127
\(222\) −39.2561 −2.63470
\(223\) −5.36588 −0.359326 −0.179663 0.983728i \(-0.557501\pi\)
−0.179663 + 0.983728i \(0.557501\pi\)
\(224\) −2.90344 −0.193994
\(225\) 7.29555 0.486370
\(226\) 42.0085 2.79436
\(227\) 14.3492 0.952392 0.476196 0.879339i \(-0.342015\pi\)
0.476196 + 0.879339i \(0.342015\pi\)
\(228\) −6.47616 −0.428894
\(229\) 17.9188 1.18411 0.592054 0.805899i \(-0.298317\pi\)
0.592054 + 0.805899i \(0.298317\pi\)
\(230\) −18.0247 −1.18852
\(231\) 30.4811 2.00551
\(232\) −12.7440 −0.836687
\(233\) 5.33613 0.349582 0.174791 0.984606i \(-0.444075\pi\)
0.174791 + 0.984606i \(0.444075\pi\)
\(234\) −54.3811 −3.55501
\(235\) 2.35402 0.153560
\(236\) −5.26410 −0.342664
\(237\) 7.45515 0.484264
\(238\) 15.3561 0.995387
\(239\) −6.48503 −0.419482 −0.209741 0.977757i \(-0.567262\pi\)
−0.209741 + 0.977757i \(0.567262\pi\)
\(240\) 10.0194 0.646747
\(241\) 20.2686 1.30561 0.652807 0.757524i \(-0.273591\pi\)
0.652807 + 0.757524i \(0.273591\pi\)
\(242\) −23.8998 −1.53634
\(243\) 30.3276 1.94552
\(244\) 15.4340 0.988062
\(245\) −2.67831 −0.171111
\(246\) −14.5051 −0.924809
\(247\) −1.61563 −0.102800
\(248\) 28.0207 1.77932
\(249\) −20.1098 −1.27440
\(250\) −2.41868 −0.152971
\(251\) −5.24465 −0.331039 −0.165520 0.986207i \(-0.552930\pi\)
−0.165520 + 0.986207i \(0.552930\pi\)
\(252\) −58.3912 −3.67830
\(253\) −34.0541 −2.14096
\(254\) −9.66131 −0.606205
\(255\) 9.79941 0.613663
\(256\) −30.2935 −1.89334
\(257\) 18.1737 1.13365 0.566823 0.823839i \(-0.308172\pi\)
0.566823 + 0.823839i \(0.308172\pi\)
\(258\) −60.4826 −3.76548
\(259\) −10.5155 −0.653402
\(260\) 11.8652 0.735847
\(261\) 20.7784 1.28615
\(262\) −7.71249 −0.476479
\(263\) 11.5009 0.709176 0.354588 0.935023i \(-0.384621\pi\)
0.354588 + 0.935023i \(0.384621\pi\)
\(264\) 65.6082 4.03790
\(265\) −7.65213 −0.470067
\(266\) −2.63594 −0.161620
\(267\) 21.3019 1.30365
\(268\) 13.9698 0.853339
\(269\) 6.68235 0.407430 0.203715 0.979030i \(-0.434698\pi\)
0.203715 + 0.979030i \(0.434698\pi\)
\(270\) −33.3367 −2.02881
\(271\) 3.76727 0.228845 0.114423 0.993432i \(-0.463498\pi\)
0.114423 + 0.993432i \(0.463498\pi\)
\(272\) 9.53653 0.578237
\(273\) −20.5572 −1.24418
\(274\) 34.9933 2.11402
\(275\) −4.56961 −0.275558
\(276\) 92.0614 5.54144
\(277\) −10.4187 −0.626001 −0.313001 0.949753i \(-0.601334\pi\)
−0.313001 + 0.949753i \(0.601334\pi\)
\(278\) 11.7480 0.704600
\(279\) −45.6861 −2.73515
\(280\) 9.30210 0.555907
\(281\) 27.4287 1.63626 0.818129 0.575035i \(-0.195012\pi\)
0.818129 + 0.575035i \(0.195012\pi\)
\(282\) −18.2690 −1.08790
\(283\) 21.2660 1.26413 0.632067 0.774913i \(-0.282207\pi\)
0.632067 + 0.774913i \(0.282207\pi\)
\(284\) −35.1814 −2.08763
\(285\) −1.68211 −0.0996398
\(286\) 34.0619 2.01412
\(287\) −3.88547 −0.229352
\(288\) 10.1893 0.600411
\(289\) −7.67282 −0.451342
\(290\) −6.88861 −0.404513
\(291\) −21.5403 −1.26272
\(292\) 62.9384 3.68319
\(293\) 2.12681 0.124250 0.0621248 0.998068i \(-0.480212\pi\)
0.0621248 + 0.998068i \(0.480212\pi\)
\(294\) 20.7857 1.21224
\(295\) −1.36729 −0.0796069
\(296\) −22.6338 −1.31556
\(297\) −62.9829 −3.65464
\(298\) −18.2269 −1.05586
\(299\) 22.9669 1.32821
\(300\) 12.3534 0.713225
\(301\) −16.2014 −0.933836
\(302\) −6.91501 −0.397914
\(303\) 35.5004 2.03945
\(304\) −1.63699 −0.0938877
\(305\) 4.00882 0.229544
\(306\) −53.8905 −3.08071
\(307\) 32.5608 1.85834 0.929170 0.369652i \(-0.120523\pi\)
0.929170 + 0.369652i \(0.120523\pi\)
\(308\) 36.5737 2.08398
\(309\) −22.7539 −1.29442
\(310\) 15.1462 0.860247
\(311\) 28.2988 1.60468 0.802339 0.596868i \(-0.203589\pi\)
0.802339 + 0.596868i \(0.203589\pi\)
\(312\) −44.2477 −2.50503
\(313\) 20.3450 1.14997 0.574983 0.818165i \(-0.305009\pi\)
0.574983 + 0.818165i \(0.305009\pi\)
\(314\) 44.0834 2.48777
\(315\) −15.1665 −0.854535
\(316\) 8.94528 0.503211
\(317\) 23.1495 1.30021 0.650104 0.759846i \(-0.274725\pi\)
0.650104 + 0.759846i \(0.274725\pi\)
\(318\) 59.3862 3.33022
\(319\) −13.0146 −0.728680
\(320\) −9.62322 −0.537954
\(321\) 29.9900 1.67388
\(322\) 37.4710 2.08818
\(323\) −1.60105 −0.0890850
\(324\) 86.0033 4.77796
\(325\) 3.08185 0.170950
\(326\) 17.3247 0.959528
\(327\) −37.4044 −2.06847
\(328\) −8.36316 −0.461778
\(329\) −4.89371 −0.269799
\(330\) 35.4636 1.95221
\(331\) −16.2276 −0.891947 −0.445974 0.895046i \(-0.647142\pi\)
−0.445974 + 0.895046i \(0.647142\pi\)
\(332\) −24.1293 −1.32427
\(333\) 36.9030 2.02227
\(334\) 14.9649 0.818841
\(335\) 3.62849 0.198246
\(336\) −20.8289 −1.13631
\(337\) −7.54943 −0.411244 −0.205622 0.978632i \(-0.565922\pi\)
−0.205622 + 0.978632i \(0.565922\pi\)
\(338\) 8.47070 0.460745
\(339\) −55.7293 −3.02680
\(340\) 11.7581 0.637673
\(341\) 28.6157 1.54963
\(342\) 9.25054 0.500212
\(343\) 20.1199 1.08637
\(344\) −34.8723 −1.88019
\(345\) 23.9120 1.28738
\(346\) −18.1266 −0.974492
\(347\) 7.01011 0.376323 0.188161 0.982138i \(-0.439747\pi\)
0.188161 + 0.982138i \(0.439747\pi\)
\(348\) 35.1836 1.88604
\(349\) 25.3886 1.35902 0.679509 0.733667i \(-0.262193\pi\)
0.679509 + 0.733667i \(0.262193\pi\)
\(350\) 5.02812 0.268764
\(351\) 42.4772 2.26726
\(352\) −6.38213 −0.340168
\(353\) −2.32093 −0.123531 −0.0617654 0.998091i \(-0.519673\pi\)
−0.0617654 + 0.998091i \(0.519673\pi\)
\(354\) 10.6112 0.563979
\(355\) −9.13799 −0.484994
\(356\) 25.5597 1.35466
\(357\) −20.3717 −1.07818
\(358\) −52.4638 −2.77280
\(359\) 31.2488 1.64925 0.824625 0.565680i \(-0.191386\pi\)
0.824625 + 0.565680i \(0.191386\pi\)
\(360\) −32.6447 −1.72052
\(361\) −18.7252 −0.985535
\(362\) −23.7122 −1.24629
\(363\) 31.7059 1.66413
\(364\) −24.6661 −1.29286
\(365\) 16.3476 0.855671
\(366\) −31.1114 −1.62622
\(367\) −10.4243 −0.544143 −0.272071 0.962277i \(-0.587709\pi\)
−0.272071 + 0.962277i \(0.587709\pi\)
\(368\) 23.2705 1.21306
\(369\) 13.6356 0.709842
\(370\) −12.2344 −0.636035
\(371\) 15.9078 0.825890
\(372\) −77.3593 −4.01090
\(373\) −20.1508 −1.04337 −0.521683 0.853139i \(-0.674696\pi\)
−0.521683 + 0.853139i \(0.674696\pi\)
\(374\) 33.7546 1.74541
\(375\) 3.20867 0.165695
\(376\) −10.5333 −0.543214
\(377\) 8.77737 0.452058
\(378\) 69.3026 3.56454
\(379\) 20.6357 1.05999 0.529994 0.848002i \(-0.322194\pi\)
0.529994 + 0.848002i \(0.322194\pi\)
\(380\) −2.01833 −0.103538
\(381\) 12.8169 0.656629
\(382\) −55.6381 −2.84669
\(383\) 1.81219 0.0925987 0.0462994 0.998928i \(-0.485257\pi\)
0.0462994 + 0.998928i \(0.485257\pi\)
\(384\) 65.7206 3.35379
\(385\) 9.49961 0.484145
\(386\) 55.5880 2.82935
\(387\) 56.8572 2.89021
\(388\) −25.8458 −1.31212
\(389\) −0.775387 −0.0393137 −0.0196568 0.999807i \(-0.506257\pi\)
−0.0196568 + 0.999807i \(0.506257\pi\)
\(390\) −23.9175 −1.21111
\(391\) 22.7596 1.15100
\(392\) 11.9844 0.605301
\(393\) 10.2315 0.516113
\(394\) −41.3871 −2.08505
\(395\) 2.32344 0.116905
\(396\) −128.351 −6.44989
\(397\) −29.1485 −1.46292 −0.731460 0.681885i \(-0.761161\pi\)
−0.731460 + 0.681885i \(0.761161\pi\)
\(398\) −16.9435 −0.849300
\(399\) 3.49689 0.175064
\(400\) 3.12259 0.156130
\(401\) −2.92900 −0.146267 −0.0731336 0.997322i \(-0.523300\pi\)
−0.0731336 + 0.997322i \(0.523300\pi\)
\(402\) −28.1598 −1.40448
\(403\) −19.2991 −0.961357
\(404\) 42.5962 2.11924
\(405\) 22.3384 1.11001
\(406\) 14.3205 0.710715
\(407\) −23.1144 −1.14574
\(408\) −43.8484 −2.17082
\(409\) 12.5090 0.618532 0.309266 0.950976i \(-0.399917\pi\)
0.309266 + 0.950976i \(0.399917\pi\)
\(410\) −4.52059 −0.223256
\(411\) −46.4227 −2.28986
\(412\) −27.3019 −1.34507
\(413\) 2.84242 0.139866
\(414\) −131.500 −6.46289
\(415\) −6.26732 −0.307651
\(416\) 4.30425 0.211033
\(417\) −15.5852 −0.763209
\(418\) −5.79413 −0.283400
\(419\) 21.2780 1.03950 0.519750 0.854318i \(-0.326025\pi\)
0.519750 + 0.854318i \(0.326025\pi\)
\(420\) −25.6811 −1.25311
\(421\) 24.7633 1.20689 0.603445 0.797405i \(-0.293794\pi\)
0.603445 + 0.797405i \(0.293794\pi\)
\(422\) 34.4267 1.67587
\(423\) 17.1739 0.835024
\(424\) 34.2402 1.66285
\(425\) 3.05404 0.148143
\(426\) 70.9176 3.43597
\(427\) −8.33381 −0.403301
\(428\) 35.9844 1.73937
\(429\) −45.1872 −2.18166
\(430\) −18.8497 −0.909016
\(431\) −13.1762 −0.634674 −0.317337 0.948313i \(-0.602789\pi\)
−0.317337 + 0.948313i \(0.602789\pi\)
\(432\) 43.0387 2.07070
\(433\) 32.2915 1.55183 0.775916 0.630836i \(-0.217288\pi\)
0.775916 + 0.630836i \(0.217288\pi\)
\(434\) −31.4870 −1.51142
\(435\) 9.13856 0.438160
\(436\) −44.8808 −2.14940
\(437\) −3.90679 −0.186887
\(438\) −126.869 −6.06205
\(439\) 7.69188 0.367114 0.183557 0.983009i \(-0.441239\pi\)
0.183557 + 0.983009i \(0.441239\pi\)
\(440\) 20.4472 0.974780
\(441\) −19.5397 −0.930464
\(442\) −22.7649 −1.08281
\(443\) −7.75332 −0.368371 −0.184186 0.982891i \(-0.558965\pi\)
−0.184186 + 0.982891i \(0.558965\pi\)
\(444\) 62.4872 2.96551
\(445\) 6.63886 0.314712
\(446\) 12.9783 0.614542
\(447\) 24.1802 1.14368
\(448\) 20.0054 0.945167
\(449\) −33.3073 −1.57187 −0.785935 0.618310i \(-0.787818\pi\)
−0.785935 + 0.618310i \(0.787818\pi\)
\(450\) −17.6456 −0.831822
\(451\) −8.54074 −0.402168
\(452\) −66.8684 −3.14523
\(453\) 9.17358 0.431012
\(454\) −34.7062 −1.62884
\(455\) −6.40676 −0.300354
\(456\) 7.52678 0.352474
\(457\) 8.52564 0.398813 0.199406 0.979917i \(-0.436099\pi\)
0.199406 + 0.979917i \(0.436099\pi\)
\(458\) −43.3398 −2.02514
\(459\) 42.0939 1.96478
\(460\) 28.6915 1.33775
\(461\) −6.52883 −0.304078 −0.152039 0.988375i \(-0.548584\pi\)
−0.152039 + 0.988375i \(0.548584\pi\)
\(462\) −73.7241 −3.42995
\(463\) −39.4131 −1.83168 −0.915841 0.401541i \(-0.868475\pi\)
−0.915841 + 0.401541i \(0.868475\pi\)
\(464\) 8.89340 0.412866
\(465\) −20.0933 −0.931802
\(466\) −12.9064 −0.597877
\(467\) 8.60565 0.398222 0.199111 0.979977i \(-0.436195\pi\)
0.199111 + 0.979977i \(0.436195\pi\)
\(468\) 86.5630 4.00138
\(469\) −7.54316 −0.348311
\(470\) −5.69363 −0.262628
\(471\) −58.4819 −2.69470
\(472\) 6.11809 0.281608
\(473\) −35.6128 −1.63748
\(474\) −18.0316 −0.828220
\(475\) −0.524240 −0.0240538
\(476\) −24.4436 −1.12037
\(477\) −55.8265 −2.55612
\(478\) 15.6852 0.717425
\(479\) −2.29903 −0.105045 −0.0525226 0.998620i \(-0.516726\pi\)
−0.0525226 + 0.998620i \(0.516726\pi\)
\(480\) 4.48137 0.204546
\(481\) 15.5889 0.710792
\(482\) −49.0232 −2.23295
\(483\) −49.7098 −2.26187
\(484\) 38.0433 1.72924
\(485\) −6.71316 −0.304829
\(486\) −73.3528 −3.32735
\(487\) 26.9406 1.22080 0.610398 0.792095i \(-0.291010\pi\)
0.610398 + 0.792095i \(0.291010\pi\)
\(488\) −17.9379 −0.812009
\(489\) −22.9833 −1.03934
\(490\) 6.47797 0.292645
\(491\) −40.1734 −1.81300 −0.906501 0.422205i \(-0.861256\pi\)
−0.906501 + 0.422205i \(0.861256\pi\)
\(492\) 23.0889 1.04093
\(493\) 8.69818 0.391746
\(494\) 3.90769 0.175815
\(495\) −33.3378 −1.49842
\(496\) −19.5542 −0.878010
\(497\) 18.9967 0.852117
\(498\) 48.6391 2.17957
\(499\) −23.0032 −1.02977 −0.514883 0.857261i \(-0.672165\pi\)
−0.514883 + 0.857261i \(0.672165\pi\)
\(500\) 3.85002 0.172178
\(501\) −19.8527 −0.886952
\(502\) 12.6851 0.566165
\(503\) −13.6086 −0.606778 −0.303389 0.952867i \(-0.598118\pi\)
−0.303389 + 0.952867i \(0.598118\pi\)
\(504\) 67.8639 3.02290
\(505\) 11.0639 0.492338
\(506\) 82.3660 3.66161
\(507\) −11.2374 −0.499070
\(508\) 15.3787 0.682320
\(509\) −4.84045 −0.214549 −0.107275 0.994229i \(-0.534212\pi\)
−0.107275 + 0.994229i \(0.534212\pi\)
\(510\) −23.7017 −1.04953
\(511\) −33.9844 −1.50338
\(512\) 32.3058 1.42773
\(513\) −7.22561 −0.319018
\(514\) −43.9565 −1.93884
\(515\) −7.09138 −0.312483
\(516\) 96.2752 4.23828
\(517\) −10.7570 −0.473091
\(518\) 25.4337 1.11749
\(519\) 24.0471 1.05555
\(520\) −13.7900 −0.604733
\(521\) 30.2522 1.32537 0.662686 0.748897i \(-0.269416\pi\)
0.662686 + 0.748897i \(0.269416\pi\)
\(522\) −50.2562 −2.19965
\(523\) 14.2555 0.623350 0.311675 0.950189i \(-0.399110\pi\)
0.311675 + 0.950189i \(0.399110\pi\)
\(524\) 12.2766 0.536306
\(525\) −6.67040 −0.291120
\(526\) −27.8170 −1.21288
\(527\) −19.1250 −0.833097
\(528\) −45.7845 −1.99252
\(529\) 32.5367 1.41464
\(530\) 18.5081 0.803939
\(531\) −9.97516 −0.432885
\(532\) 4.19585 0.181913
\(533\) 5.76007 0.249496
\(534\) −51.5225 −2.22959
\(535\) 9.34656 0.404087
\(536\) −16.2360 −0.701290
\(537\) 69.5995 3.00344
\(538\) −16.1625 −0.696814
\(539\) 12.2388 0.527163
\(540\) 53.0648 2.28355
\(541\) −36.9524 −1.58871 −0.794354 0.607456i \(-0.792190\pi\)
−0.794354 + 0.607456i \(0.792190\pi\)
\(542\) −9.11182 −0.391386
\(543\) 31.4571 1.34995
\(544\) 4.26542 0.182878
\(545\) −11.6573 −0.499344
\(546\) 49.7212 2.12787
\(547\) −30.3372 −1.29713 −0.648563 0.761161i \(-0.724630\pi\)
−0.648563 + 0.761161i \(0.724630\pi\)
\(548\) −55.7017 −2.37946
\(549\) 29.2466 1.24821
\(550\) 11.0524 0.471277
\(551\) −1.49308 −0.0636074
\(552\) −106.996 −4.55407
\(553\) −4.83012 −0.205398
\(554\) 25.1996 1.07063
\(555\) 16.2304 0.688941
\(556\) −18.7003 −0.793070
\(557\) −3.80562 −0.161249 −0.0806247 0.996745i \(-0.525692\pi\)
−0.0806247 + 0.996745i \(0.525692\pi\)
\(558\) 110.500 4.67784
\(559\) 24.0181 1.01586
\(560\) −6.49145 −0.274314
\(561\) −44.7795 −1.89059
\(562\) −66.3412 −2.79843
\(563\) −40.8938 −1.72347 −0.861735 0.507359i \(-0.830622\pi\)
−0.861735 + 0.507359i \(0.830622\pi\)
\(564\) 29.0803 1.22450
\(565\) −17.3684 −0.730692
\(566\) −51.4358 −2.16201
\(567\) −46.4387 −1.95024
\(568\) 40.8888 1.71566
\(569\) 7.97790 0.334451 0.167225 0.985919i \(-0.446519\pi\)
0.167225 + 0.985919i \(0.446519\pi\)
\(570\) 4.06849 0.170410
\(571\) −41.2854 −1.72774 −0.863870 0.503714i \(-0.831966\pi\)
−0.863870 + 0.503714i \(0.831966\pi\)
\(572\) −54.2192 −2.26702
\(573\) 73.8105 3.08348
\(574\) 9.39771 0.392253
\(575\) 7.45230 0.310782
\(576\) −70.2067 −2.92528
\(577\) 21.5844 0.898571 0.449285 0.893388i \(-0.351679\pi\)
0.449285 + 0.893388i \(0.351679\pi\)
\(578\) 18.5581 0.771915
\(579\) −73.7441 −3.06470
\(580\) 10.9652 0.455304
\(581\) 13.0289 0.540531
\(582\) 52.0991 2.15958
\(583\) 34.9673 1.44820
\(584\) −73.1488 −3.02692
\(585\) 22.4838 0.929591
\(586\) −5.14407 −0.212500
\(587\) −14.4554 −0.596639 −0.298319 0.954466i \(-0.596426\pi\)
−0.298319 + 0.954466i \(0.596426\pi\)
\(588\) −33.0863 −1.36446
\(589\) 3.28289 0.135269
\(590\) 3.30704 0.136149
\(591\) 54.9050 2.25849
\(592\) 15.7950 0.649169
\(593\) 23.3477 0.958776 0.479388 0.877603i \(-0.340859\pi\)
0.479388 + 0.877603i \(0.340859\pi\)
\(594\) 152.336 6.25041
\(595\) −6.34895 −0.260282
\(596\) 29.0133 1.18843
\(597\) 22.4775 0.919945
\(598\) −55.5495 −2.27159
\(599\) 2.35020 0.0960266 0.0480133 0.998847i \(-0.484711\pi\)
0.0480133 + 0.998847i \(0.484711\pi\)
\(600\) −14.3575 −0.586142
\(601\) 30.9849 1.26390 0.631950 0.775009i \(-0.282255\pi\)
0.631950 + 0.775009i \(0.282255\pi\)
\(602\) 39.1861 1.59711
\(603\) 26.4719 1.07802
\(604\) 11.0072 0.447876
\(605\) 9.88133 0.401733
\(606\) −85.8642 −3.48799
\(607\) −36.8369 −1.49516 −0.747582 0.664169i \(-0.768785\pi\)
−0.747582 + 0.664169i \(0.768785\pi\)
\(608\) −0.732178 −0.0296937
\(609\) −18.9979 −0.769832
\(610\) −9.69606 −0.392582
\(611\) 7.25475 0.293496
\(612\) 85.7820 3.46753
\(613\) −9.13529 −0.368971 −0.184485 0.982835i \(-0.559062\pi\)
−0.184485 + 0.982835i \(0.559062\pi\)
\(614\) −78.7541 −3.17826
\(615\) 5.99710 0.241826
\(616\) −42.5069 −1.71265
\(617\) 22.8004 0.917908 0.458954 0.888460i \(-0.348224\pi\)
0.458954 + 0.888460i \(0.348224\pi\)
\(618\) 55.0344 2.21381
\(619\) −31.3972 −1.26196 −0.630980 0.775799i \(-0.717347\pi\)
−0.630980 + 0.775799i \(0.717347\pi\)
\(620\) −24.1095 −0.968260
\(621\) 102.715 4.12181
\(622\) −68.4458 −2.74443
\(623\) −13.8013 −0.552938
\(624\) 30.8782 1.23612
\(625\) 1.00000 0.0400000
\(626\) −49.2080 −1.96675
\(627\) 7.68660 0.306973
\(628\) −70.1712 −2.80014
\(629\) 15.4482 0.615961
\(630\) 36.6829 1.46148
\(631\) 24.9187 0.991996 0.495998 0.868324i \(-0.334802\pi\)
0.495998 + 0.868324i \(0.334802\pi\)
\(632\) −10.3965 −0.413549
\(633\) −45.6712 −1.81527
\(634\) −55.9913 −2.22370
\(635\) 3.99446 0.158515
\(636\) −94.5300 −3.74836
\(637\) −8.25415 −0.327041
\(638\) 31.4782 1.24624
\(639\) −66.6667 −2.63729
\(640\) 20.4822 0.809630
\(641\) −45.3830 −1.79252 −0.896260 0.443529i \(-0.853726\pi\)
−0.896260 + 0.443529i \(0.853726\pi\)
\(642\) −72.5363 −2.86278
\(643\) 17.3675 0.684907 0.342454 0.939535i \(-0.388742\pi\)
0.342454 + 0.939535i \(0.388742\pi\)
\(644\) −59.6458 −2.35037
\(645\) 25.0064 0.984628
\(646\) 3.87244 0.152359
\(647\) 13.6988 0.538556 0.269278 0.963062i \(-0.413215\pi\)
0.269278 + 0.963062i \(0.413215\pi\)
\(648\) −99.9555 −3.92662
\(649\) 6.24799 0.245255
\(650\) −7.45401 −0.292370
\(651\) 41.7712 1.63714
\(652\) −27.5772 −1.08001
\(653\) 34.1028 1.33455 0.667273 0.744813i \(-0.267462\pi\)
0.667273 + 0.744813i \(0.267462\pi\)
\(654\) 90.4694 3.53763
\(655\) 3.18872 0.124594
\(656\) 5.83622 0.227866
\(657\) 119.265 4.65295
\(658\) 11.8363 0.461428
\(659\) −42.3915 −1.65134 −0.825669 0.564155i \(-0.809202\pi\)
−0.825669 + 0.564155i \(0.809202\pi\)
\(660\) −56.4503 −2.19733
\(661\) −0.955563 −0.0371671 −0.0185836 0.999827i \(-0.505916\pi\)
−0.0185836 + 0.999827i \(0.505916\pi\)
\(662\) 39.2493 1.52547
\(663\) 30.2003 1.17288
\(664\) 28.0438 1.08831
\(665\) 1.08983 0.0422616
\(666\) −89.2566 −3.45862
\(667\) 21.2248 0.821827
\(668\) −23.8208 −0.921656
\(669\) −17.2173 −0.665660
\(670\) −8.77617 −0.339053
\(671\) −18.3187 −0.707187
\(672\) −9.31618 −0.359380
\(673\) −3.53237 −0.136163 −0.0680814 0.997680i \(-0.521688\pi\)
−0.0680814 + 0.997680i \(0.521688\pi\)
\(674\) 18.2597 0.703336
\(675\) 13.7830 0.530508
\(676\) −13.4835 −0.518597
\(677\) 33.5824 1.29068 0.645339 0.763896i \(-0.276716\pi\)
0.645339 + 0.763896i \(0.276716\pi\)
\(678\) 134.791 5.17663
\(679\) 13.9558 0.535573
\(680\) −13.6656 −0.524052
\(681\) 46.0419 1.76433
\(682\) −69.2123 −2.65027
\(683\) −17.6851 −0.676702 −0.338351 0.941020i \(-0.609869\pi\)
−0.338351 + 0.941020i \(0.609869\pi\)
\(684\) −14.7249 −0.563019
\(685\) −14.4679 −0.552790
\(686\) −48.6637 −1.85799
\(687\) 57.4955 2.19359
\(688\) 24.3356 0.927786
\(689\) −23.5827 −0.898430
\(690\) −57.8354 −2.20175
\(691\) −26.3266 −1.00151 −0.500755 0.865589i \(-0.666944\pi\)
−0.500755 + 0.865589i \(0.666944\pi\)
\(692\) 28.8536 1.09685
\(693\) 69.3049 2.63268
\(694\) −16.9552 −0.643611
\(695\) −4.85721 −0.184244
\(696\) −40.8914 −1.54998
\(697\) 5.70810 0.216210
\(698\) −61.4068 −2.32428
\(699\) 17.1219 0.647609
\(700\) −8.00367 −0.302510
\(701\) −5.22791 −0.197455 −0.0987277 0.995114i \(-0.531477\pi\)
−0.0987277 + 0.995114i \(0.531477\pi\)
\(702\) −102.739 −3.87762
\(703\) −2.65176 −0.100013
\(704\) 43.9744 1.65735
\(705\) 7.55329 0.284473
\(706\) 5.61359 0.211270
\(707\) −23.0004 −0.865019
\(708\) −16.8908 −0.634793
\(709\) 12.3423 0.463525 0.231763 0.972772i \(-0.425551\pi\)
0.231763 + 0.972772i \(0.425551\pi\)
\(710\) 22.1019 0.829469
\(711\) 16.9508 0.635704
\(712\) −29.7062 −1.11329
\(713\) −46.6676 −1.74772
\(714\) 49.2726 1.84398
\(715\) −14.0829 −0.526669
\(716\) 83.5111 3.12095
\(717\) −20.8083 −0.777101
\(718\) −75.5809 −2.82065
\(719\) 1.13009 0.0421452 0.0210726 0.999778i \(-0.493292\pi\)
0.0210726 + 0.999778i \(0.493292\pi\)
\(720\) 22.7810 0.848999
\(721\) 14.7420 0.549022
\(722\) 45.2902 1.68553
\(723\) 65.0351 2.41868
\(724\) 37.7447 1.40277
\(725\) 2.84809 0.105775
\(726\) −76.6864 −2.84610
\(727\) −41.5701 −1.54175 −0.770875 0.636986i \(-0.780181\pi\)
−0.770875 + 0.636986i \(0.780181\pi\)
\(728\) 28.6677 1.06249
\(729\) 30.2960 1.12207
\(730\) −39.5395 −1.46342
\(731\) 23.8014 0.880326
\(732\) 49.5227 1.83041
\(733\) −6.40419 −0.236544 −0.118272 0.992981i \(-0.537735\pi\)
−0.118272 + 0.992981i \(0.537735\pi\)
\(734\) 25.2130 0.930628
\(735\) −8.59380 −0.316987
\(736\) 10.4082 0.383652
\(737\) −16.5808 −0.610761
\(738\) −32.9802 −1.21402
\(739\) −15.5457 −0.571858 −0.285929 0.958251i \(-0.592302\pi\)
−0.285929 + 0.958251i \(0.592302\pi\)
\(740\) 19.4745 0.715896
\(741\) −5.18402 −0.190440
\(742\) −38.4758 −1.41249
\(743\) −14.8375 −0.544335 −0.272167 0.962250i \(-0.587740\pi\)
−0.272167 + 0.962250i \(0.587740\pi\)
\(744\) 89.9092 3.29623
\(745\) 7.53589 0.276094
\(746\) 48.7382 1.78443
\(747\) −45.7236 −1.67294
\(748\) −53.7300 −1.96456
\(749\) −19.4303 −0.709967
\(750\) −7.76074 −0.283382
\(751\) −50.5683 −1.84526 −0.922631 0.385683i \(-0.873966\pi\)
−0.922631 + 0.385683i \(0.873966\pi\)
\(752\) 7.35066 0.268051
\(753\) −16.8283 −0.613259
\(754\) −21.2297 −0.773139
\(755\) 2.85900 0.104050
\(756\) −110.315 −4.01211
\(757\) −10.1071 −0.367348 −0.183674 0.982987i \(-0.558799\pi\)
−0.183674 + 0.982987i \(0.558799\pi\)
\(758\) −49.9113 −1.81286
\(759\) −109.268 −3.96619
\(760\) 2.34576 0.0850898
\(761\) 51.5532 1.86880 0.934400 0.356224i \(-0.115936\pi\)
0.934400 + 0.356224i \(0.115936\pi\)
\(762\) −31.0000 −1.12301
\(763\) 24.2340 0.877330
\(764\) 88.5638 3.20412
\(765\) 22.2809 0.805569
\(766\) −4.38312 −0.158368
\(767\) −4.21379 −0.152151
\(768\) −97.2017 −3.50746
\(769\) −27.7346 −1.00013 −0.500067 0.865987i \(-0.666691\pi\)
−0.500067 + 0.865987i \(0.666691\pi\)
\(770\) −22.9765 −0.828017
\(771\) 58.3135 2.10011
\(772\) −88.4841 −3.18461
\(773\) 16.3729 0.588892 0.294446 0.955668i \(-0.404865\pi\)
0.294446 + 0.955668i \(0.404865\pi\)
\(774\) −137.519 −4.94303
\(775\) −6.26218 −0.224944
\(776\) 30.0387 1.07833
\(777\) −33.7408 −1.21044
\(778\) 1.87541 0.0672368
\(779\) −0.979821 −0.0351057
\(780\) 38.0714 1.36318
\(781\) 41.7571 1.49418
\(782\) −55.0483 −1.96852
\(783\) 39.2552 1.40287
\(784\) −8.36326 −0.298688
\(785\) −18.2262 −0.650522
\(786\) −24.7468 −0.882690
\(787\) −26.9931 −0.962200 −0.481100 0.876666i \(-0.659763\pi\)
−0.481100 + 0.876666i \(0.659763\pi\)
\(788\) 65.8794 2.34685
\(789\) 36.9026 1.31377
\(790\) −5.61966 −0.199938
\(791\) 36.1065 1.28380
\(792\) 149.173 5.30064
\(793\) 12.3546 0.438724
\(794\) 70.5008 2.50198
\(795\) −24.5532 −0.870811
\(796\) 26.9704 0.955939
\(797\) 25.8694 0.916343 0.458171 0.888864i \(-0.348505\pi\)
0.458171 + 0.888864i \(0.348505\pi\)
\(798\) −8.45786 −0.299405
\(799\) 7.18929 0.254339
\(800\) 1.39665 0.0493789
\(801\) 48.4341 1.71134
\(802\) 7.08431 0.250156
\(803\) −74.7020 −2.63618
\(804\) 44.8243 1.58083
\(805\) −15.4923 −0.546033
\(806\) 46.6784 1.64417
\(807\) 21.4415 0.754775
\(808\) −49.5066 −1.74163
\(809\) 3.11806 0.109625 0.0548126 0.998497i \(-0.482544\pi\)
0.0548126 + 0.998497i \(0.482544\pi\)
\(810\) −54.0295 −1.89840
\(811\) 18.9745 0.666285 0.333143 0.942876i \(-0.391891\pi\)
0.333143 + 0.942876i \(0.391891\pi\)
\(812\) −22.7951 −0.799953
\(813\) 12.0879 0.423942
\(814\) 55.9063 1.95952
\(815\) −7.16288 −0.250905
\(816\) 30.5996 1.07120
\(817\) −4.08561 −0.142938
\(818\) −30.2554 −1.05785
\(819\) −46.7409 −1.63326
\(820\) 7.19580 0.251288
\(821\) −24.6619 −0.860708 −0.430354 0.902660i \(-0.641611\pi\)
−0.430354 + 0.902660i \(0.641611\pi\)
\(822\) 112.282 3.91628
\(823\) −51.5756 −1.79781 −0.898906 0.438142i \(-0.855637\pi\)
−0.898906 + 0.438142i \(0.855637\pi\)
\(824\) 31.7311 1.10540
\(825\) −14.6624 −0.510478
\(826\) −6.87491 −0.239209
\(827\) −10.6889 −0.371691 −0.185846 0.982579i \(-0.559502\pi\)
−0.185846 + 0.982579i \(0.559502\pi\)
\(828\) 209.320 7.27438
\(829\) −33.0486 −1.14783 −0.573913 0.818916i \(-0.694575\pi\)
−0.573913 + 0.818916i \(0.694575\pi\)
\(830\) 15.1587 0.526165
\(831\) −33.4303 −1.15968
\(832\) −29.6573 −1.02818
\(833\) −8.17967 −0.283409
\(834\) 37.6955 1.30529
\(835\) −6.18720 −0.214117
\(836\) 9.22299 0.318984
\(837\) −86.3116 −2.98337
\(838\) −51.4648 −1.77782
\(839\) 10.6417 0.367392 0.183696 0.982983i \(-0.441194\pi\)
0.183696 + 0.982983i \(0.441194\pi\)
\(840\) 29.8473 1.02983
\(841\) −20.8884 −0.720290
\(842\) −59.8945 −2.06410
\(843\) 88.0095 3.03121
\(844\) −54.7999 −1.88629
\(845\) −3.50220 −0.120479
\(846\) −41.5382 −1.42811
\(847\) −20.5420 −0.705830
\(848\) −23.8945 −0.820540
\(849\) 68.2357 2.34184
\(850\) −7.38676 −0.253364
\(851\) 37.6959 1.29220
\(852\) −112.885 −3.86739
\(853\) −17.5451 −0.600732 −0.300366 0.953824i \(-0.597109\pi\)
−0.300366 + 0.953824i \(0.597109\pi\)
\(854\) 20.1568 0.689752
\(855\) −3.82462 −0.130799
\(856\) −41.8221 −1.42945
\(857\) −23.0552 −0.787551 −0.393775 0.919207i \(-0.628831\pi\)
−0.393775 + 0.919207i \(0.628831\pi\)
\(858\) 109.293 3.73122
\(859\) −38.8993 −1.32723 −0.663614 0.748075i \(-0.730978\pi\)
−0.663614 + 0.748075i \(0.730978\pi\)
\(860\) 30.0047 1.02315
\(861\) −12.4672 −0.424880
\(862\) 31.8690 1.08546
\(863\) 41.6221 1.41683 0.708416 0.705795i \(-0.249410\pi\)
0.708416 + 0.705795i \(0.249410\pi\)
\(864\) 19.2500 0.654898
\(865\) 7.49442 0.254818
\(866\) −78.1029 −2.65404
\(867\) −24.6195 −0.836123
\(868\) 50.1204 1.70120
\(869\) −10.6172 −0.360164
\(870\) −22.1033 −0.749371
\(871\) 11.1825 0.378904
\(872\) 52.1618 1.76642
\(873\) −48.9762 −1.65759
\(874\) 9.44929 0.319627
\(875\) −2.07887 −0.0702786
\(876\) 201.948 6.82320
\(877\) −39.4937 −1.33361 −0.666803 0.745234i \(-0.732338\pi\)
−0.666803 + 0.745234i \(0.732338\pi\)
\(878\) −18.6042 −0.627862
\(879\) 6.82423 0.230175
\(880\) −14.2690 −0.481008
\(881\) −32.6211 −1.09903 −0.549517 0.835483i \(-0.685188\pi\)
−0.549517 + 0.835483i \(0.685188\pi\)
\(882\) 47.2604 1.59134
\(883\) −28.8237 −0.969995 −0.484998 0.874515i \(-0.661180\pi\)
−0.484998 + 0.874515i \(0.661180\pi\)
\(884\) 36.2368 1.21877
\(885\) −4.38719 −0.147474
\(886\) 18.7528 0.630013
\(887\) 25.2813 0.848864 0.424432 0.905460i \(-0.360474\pi\)
0.424432 + 0.905460i \(0.360474\pi\)
\(888\) −72.6244 −2.43711
\(889\) −8.30395 −0.278505
\(890\) −16.0573 −0.538241
\(891\) −102.078 −3.41974
\(892\) −20.6587 −0.691705
\(893\) −1.23407 −0.0412967
\(894\) −58.4841 −1.95600
\(895\) 21.6911 0.725053
\(896\) −42.5798 −1.42249
\(897\) 73.6931 2.46054
\(898\) 80.5597 2.68831
\(899\) −17.8352 −0.594838
\(900\) 28.0880 0.936267
\(901\) −23.3699 −0.778566
\(902\) 20.6573 0.687814
\(903\) −51.9851 −1.72996
\(904\) 77.7164 2.58481
\(905\) 9.80379 0.325889
\(906\) −22.1880 −0.737146
\(907\) 53.1095 1.76347 0.881737 0.471742i \(-0.156375\pi\)
0.881737 + 0.471742i \(0.156375\pi\)
\(908\) 55.2448 1.83336
\(909\) 80.7174 2.67723
\(910\) 15.4959 0.513684
\(911\) 25.6482 0.849761 0.424881 0.905249i \(-0.360316\pi\)
0.424881 + 0.905249i \(0.360316\pi\)
\(912\) −5.25255 −0.173929
\(913\) 28.6392 0.947820
\(914\) −20.6208 −0.682076
\(915\) 12.8630 0.425237
\(916\) 68.9876 2.27942
\(917\) −6.62892 −0.218906
\(918\) −101.812 −3.36029
\(919\) 1.15059 0.0379544 0.0189772 0.999820i \(-0.493959\pi\)
0.0189772 + 0.999820i \(0.493959\pi\)
\(920\) −33.3460 −1.09939
\(921\) 104.477 3.44262
\(922\) 15.7912 0.520054
\(923\) −28.1619 −0.926961
\(924\) 117.353 3.86062
\(925\) 5.05829 0.166315
\(926\) 95.3277 3.13266
\(927\) −51.7355 −1.69922
\(928\) 3.97777 0.130577
\(929\) 44.0573 1.44547 0.722737 0.691123i \(-0.242884\pi\)
0.722737 + 0.691123i \(0.242884\pi\)
\(930\) 48.5992 1.59363
\(931\) 1.40408 0.0460168
\(932\) 20.5442 0.672948
\(933\) 90.8015 2.97271
\(934\) −20.8143 −0.681065
\(935\) −13.9558 −0.456403
\(936\) −100.606 −3.28841
\(937\) 51.6634 1.68777 0.843885 0.536524i \(-0.180263\pi\)
0.843885 + 0.536524i \(0.180263\pi\)
\(938\) 18.2445 0.595704
\(939\) 65.2803 2.13034
\(940\) 9.06303 0.295604
\(941\) −1.85595 −0.0605021 −0.0302510 0.999542i \(-0.509631\pi\)
−0.0302510 + 0.999542i \(0.509631\pi\)
\(942\) 141.449 4.60866
\(943\) 13.9286 0.453577
\(944\) −4.26950 −0.138960
\(945\) −28.6530 −0.932084
\(946\) 86.1360 2.80052
\(947\) −22.1760 −0.720622 −0.360311 0.932832i \(-0.617329\pi\)
−0.360311 + 0.932832i \(0.617329\pi\)
\(948\) 28.7024 0.932212
\(949\) 50.3807 1.63543
\(950\) 1.26797 0.0411384
\(951\) 74.2792 2.40867
\(952\) 28.4090 0.920741
\(953\) 44.7958 1.45108 0.725540 0.688180i \(-0.241590\pi\)
0.725540 + 0.688180i \(0.241590\pi\)
\(954\) 135.027 4.37165
\(955\) 23.0035 0.744375
\(956\) −24.9675 −0.807506
\(957\) −41.7596 −1.34990
\(958\) 5.56061 0.179655
\(959\) 30.0769 0.971233
\(960\) −30.8777 −0.996574
\(961\) 8.21488 0.264996
\(962\) −37.7045 −1.21564
\(963\) 68.1884 2.19734
\(964\) 78.0343 2.51332
\(965\) −22.9828 −0.739842
\(966\) 120.232 3.86840
\(967\) 36.9652 1.18872 0.594361 0.804199i \(-0.297405\pi\)
0.594361 + 0.804199i \(0.297405\pi\)
\(968\) −44.2150 −1.42112
\(969\) −5.13725 −0.165032
\(970\) 16.2370 0.521338
\(971\) −45.0408 −1.44543 −0.722715 0.691146i \(-0.757106\pi\)
−0.722715 + 0.691146i \(0.757106\pi\)
\(972\) 116.762 3.74514
\(973\) 10.0975 0.323711
\(974\) −65.1608 −2.08789
\(975\) 9.88864 0.316690
\(976\) 12.5179 0.400688
\(977\) 23.5274 0.752709 0.376354 0.926476i \(-0.377178\pi\)
0.376354 + 0.926476i \(0.377178\pi\)
\(978\) 55.5893 1.77755
\(979\) −30.3370 −0.969574
\(980\) −10.3115 −0.329390
\(981\) −85.0465 −2.71533
\(982\) 97.1667 3.10071
\(983\) −33.5789 −1.07100 −0.535501 0.844535i \(-0.679877\pi\)
−0.535501 + 0.844535i \(0.679877\pi\)
\(984\) −26.8346 −0.855456
\(985\) 17.1115 0.545216
\(986\) −21.0381 −0.669990
\(987\) −15.7023 −0.499809
\(988\) −6.22020 −0.197891
\(989\) 58.0787 1.84680
\(990\) 80.6336 2.56270
\(991\) −6.92238 −0.219897 −0.109948 0.993937i \(-0.535069\pi\)
−0.109948 + 0.993937i \(0.535069\pi\)
\(992\) −8.74605 −0.277687
\(993\) −52.0689 −1.65236
\(994\) −45.9469 −1.45735
\(995\) 7.00526 0.222082
\(996\) −77.4229 −2.45324
\(997\) 42.5962 1.34904 0.674518 0.738258i \(-0.264351\pi\)
0.674518 + 0.738258i \(0.264351\pi\)
\(998\) 55.6374 1.76117
\(999\) 69.7184 2.20579
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 \(a_p\))