Properties

Label 619.2.a.b.1.7
Level 619
Weight 2
Character 619.1
Self dual Yes
Analytic conductor 4.943
Analytic rank 0
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 619.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(4.94273988512\)
Analytic rank: \(0\)
Dimension: \(30\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 619.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.45512 q^{2} +2.41034 q^{3} +0.117377 q^{4} -2.25507 q^{5} -3.50733 q^{6} -1.27109 q^{7} +2.73944 q^{8} +2.80973 q^{9} +O(q^{10})\) \(q-1.45512 q^{2} +2.41034 q^{3} +0.117377 q^{4} -2.25507 q^{5} -3.50733 q^{6} -1.27109 q^{7} +2.73944 q^{8} +2.80973 q^{9} +3.28140 q^{10} +2.81981 q^{11} +0.282919 q^{12} +1.19984 q^{13} +1.84959 q^{14} -5.43548 q^{15} -4.22098 q^{16} -3.27932 q^{17} -4.08850 q^{18} +4.87284 q^{19} -0.264693 q^{20} -3.06376 q^{21} -4.10317 q^{22} +9.08548 q^{23} +6.60299 q^{24} +0.0853300 q^{25} -1.74591 q^{26} -0.458606 q^{27} -0.149197 q^{28} +8.59083 q^{29} +7.90928 q^{30} +9.78712 q^{31} +0.663144 q^{32} +6.79670 q^{33} +4.77181 q^{34} +2.86640 q^{35} +0.329799 q^{36} -5.98121 q^{37} -7.09057 q^{38} +2.89202 q^{39} -6.17763 q^{40} -0.101904 q^{41} +4.45815 q^{42} +0.656035 q^{43} +0.330981 q^{44} -6.33614 q^{45} -13.2205 q^{46} +8.22008 q^{47} -10.1740 q^{48} -5.38432 q^{49} -0.124165 q^{50} -7.90427 q^{51} +0.140834 q^{52} +5.04461 q^{53} +0.667327 q^{54} -6.35886 q^{55} -3.48209 q^{56} +11.7452 q^{57} -12.5007 q^{58} -5.66022 q^{59} -0.638001 q^{60} +6.42480 q^{61} -14.2414 q^{62} -3.57143 q^{63} +7.47700 q^{64} -2.70572 q^{65} -9.89002 q^{66} +1.69588 q^{67} -0.384917 q^{68} +21.8991 q^{69} -4.17096 q^{70} +2.02566 q^{71} +7.69711 q^{72} -9.64772 q^{73} +8.70338 q^{74} +0.205674 q^{75} +0.571960 q^{76} -3.58424 q^{77} -4.20823 q^{78} -5.55932 q^{79} +9.51859 q^{80} -9.53460 q^{81} +0.148282 q^{82} +6.25367 q^{83} -0.359616 q^{84} +7.39509 q^{85} -0.954610 q^{86} +20.7068 q^{87} +7.72471 q^{88} +15.9399 q^{89} +9.21985 q^{90} -1.52511 q^{91} +1.06643 q^{92} +23.5903 q^{93} -11.9612 q^{94} -10.9886 q^{95} +1.59840 q^{96} -11.5366 q^{97} +7.83484 q^{98} +7.92292 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + O(q^{10}) \) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + 5q^{10} + 23q^{11} - 6q^{12} + 9q^{13} + 7q^{14} - 2q^{15} + 35q^{16} + 4q^{17} + 10q^{18} - q^{19} + 29q^{20} + 30q^{21} + 4q^{23} + 4q^{24} + 35q^{25} + q^{26} - 5q^{27} - 13q^{28} + 90q^{29} - 31q^{30} + 2q^{31} + 43q^{32} - 6q^{33} - 9q^{34} + 9q^{35} + 33q^{36} + 19q^{37} + 5q^{38} + 32q^{39} - 12q^{40} + 59q^{41} - 25q^{42} - 4q^{43} + 52q^{44} + 30q^{45} - q^{46} + 4q^{47} - 44q^{48} + 30q^{49} + 31q^{50} - 12q^{52} + 34q^{53} - 28q^{54} - 17q^{55} + 2q^{56} - 8q^{57} + 6q^{58} + 13q^{59} - 64q^{60} + 16q^{61} + 28q^{62} - 40q^{63} + 37q^{64} + 31q^{65} - 59q^{66} - 11q^{67} - 52q^{68} + 6q^{69} - 40q^{70} + 42q^{71} + 6q^{72} - 4q^{73} + 16q^{74} - 52q^{75} - 42q^{76} + 29q^{77} - 56q^{78} + 3q^{79} + 21q^{80} + 30q^{81} - 43q^{82} - 11q^{83} - 36q^{84} + 19q^{85} - 11q^{86} - 20q^{87} - 47q^{88} + 58q^{89} - 33q^{90} - 39q^{91} - 7q^{92} - 15q^{93} - 46q^{94} + 23q^{95} - 70q^{96} - 9q^{97} - 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.45512 −1.02893 −0.514463 0.857513i \(-0.672009\pi\)
−0.514463 + 0.857513i \(0.672009\pi\)
\(3\) 2.41034 1.39161 0.695805 0.718231i \(-0.255048\pi\)
0.695805 + 0.718231i \(0.255048\pi\)
\(4\) 0.117377 0.0586886
\(5\) −2.25507 −1.00850 −0.504248 0.863559i \(-0.668230\pi\)
−0.504248 + 0.863559i \(0.668230\pi\)
\(6\) −3.50733 −1.43186
\(7\) −1.27109 −0.480428 −0.240214 0.970720i \(-0.577218\pi\)
−0.240214 + 0.970720i \(0.577218\pi\)
\(8\) 2.73944 0.968540
\(9\) 2.80973 0.936578
\(10\) 3.28140 1.03767
\(11\) 2.81981 0.850205 0.425103 0.905145i \(-0.360238\pi\)
0.425103 + 0.905145i \(0.360238\pi\)
\(12\) 0.282919 0.0816716
\(13\) 1.19984 0.332775 0.166388 0.986060i \(-0.446790\pi\)
0.166388 + 0.986060i \(0.446790\pi\)
\(14\) 1.84959 0.494325
\(15\) −5.43548 −1.40343
\(16\) −4.22098 −1.05524
\(17\) −3.27932 −0.795352 −0.397676 0.917526i \(-0.630183\pi\)
−0.397676 + 0.917526i \(0.630183\pi\)
\(18\) −4.08850 −0.963669
\(19\) 4.87284 1.11791 0.558953 0.829199i \(-0.311203\pi\)
0.558953 + 0.829199i \(0.311203\pi\)
\(20\) −0.264693 −0.0591872
\(21\) −3.06376 −0.668568
\(22\) −4.10317 −0.874798
\(23\) 9.08548 1.89445 0.947227 0.320564i \(-0.103872\pi\)
0.947227 + 0.320564i \(0.103872\pi\)
\(24\) 6.60299 1.34783
\(25\) 0.0853300 0.0170660
\(26\) −1.74591 −0.342401
\(27\) −0.458606 −0.0882588
\(28\) −0.149197 −0.0281956
\(29\) 8.59083 1.59528 0.797638 0.603136i \(-0.206083\pi\)
0.797638 + 0.603136i \(0.206083\pi\)
\(30\) 7.90928 1.44403
\(31\) 9.78712 1.75782 0.878909 0.476989i \(-0.158272\pi\)
0.878909 + 0.476989i \(0.158272\pi\)
\(32\) 0.663144 0.117228
\(33\) 6.79670 1.18315
\(34\) 4.77181 0.818358
\(35\) 2.86640 0.484510
\(36\) 0.329799 0.0549664
\(37\) −5.98121 −0.983304 −0.491652 0.870792i \(-0.663607\pi\)
−0.491652 + 0.870792i \(0.663607\pi\)
\(38\) −7.09057 −1.15024
\(39\) 2.89202 0.463093
\(40\) −6.17763 −0.976769
\(41\) −0.101904 −0.0159147 −0.00795733 0.999968i \(-0.502533\pi\)
−0.00795733 + 0.999968i \(0.502533\pi\)
\(42\) 4.45815 0.687907
\(43\) 0.656035 0.100044 0.0500222 0.998748i \(-0.484071\pi\)
0.0500222 + 0.998748i \(0.484071\pi\)
\(44\) 0.330981 0.0498973
\(45\) −6.33614 −0.944536
\(46\) −13.2205 −1.94925
\(47\) 8.22008 1.19902 0.599511 0.800367i \(-0.295362\pi\)
0.599511 + 0.800367i \(0.295362\pi\)
\(48\) −10.1740 −1.46849
\(49\) −5.38432 −0.769189
\(50\) −0.124165 −0.0175596
\(51\) −7.90427 −1.10682
\(52\) 0.140834 0.0195301
\(53\) 5.04461 0.692931 0.346465 0.938063i \(-0.387382\pi\)
0.346465 + 0.938063i \(0.387382\pi\)
\(54\) 0.667327 0.0908118
\(55\) −6.35886 −0.857429
\(56\) −3.48209 −0.465314
\(57\) 11.7452 1.55569
\(58\) −12.5007 −1.64142
\(59\) −5.66022 −0.736898 −0.368449 0.929648i \(-0.620111\pi\)
−0.368449 + 0.929648i \(0.620111\pi\)
\(60\) −0.638001 −0.0823656
\(61\) 6.42480 0.822611 0.411305 0.911498i \(-0.365073\pi\)
0.411305 + 0.911498i \(0.365073\pi\)
\(62\) −14.2414 −1.80867
\(63\) −3.57143 −0.449958
\(64\) 7.47700 0.934625
\(65\) −2.70572 −0.335603
\(66\) −9.89002 −1.21738
\(67\) 1.69588 0.207184 0.103592 0.994620i \(-0.466966\pi\)
0.103592 + 0.994620i \(0.466966\pi\)
\(68\) −0.384917 −0.0466781
\(69\) 21.8991 2.63634
\(70\) −4.17096 −0.498525
\(71\) 2.02566 0.240402 0.120201 0.992750i \(-0.461646\pi\)
0.120201 + 0.992750i \(0.461646\pi\)
\(72\) 7.69711 0.907113
\(73\) −9.64772 −1.12918 −0.564590 0.825372i \(-0.690966\pi\)
−0.564590 + 0.825372i \(0.690966\pi\)
\(74\) 8.70338 1.01175
\(75\) 0.205674 0.0237492
\(76\) 0.571960 0.0656083
\(77\) −3.58424 −0.408462
\(78\) −4.20823 −0.476489
\(79\) −5.55932 −0.625472 −0.312736 0.949840i \(-0.601246\pi\)
−0.312736 + 0.949840i \(0.601246\pi\)
\(80\) 9.51859 1.06421
\(81\) −9.53460 −1.05940
\(82\) 0.148282 0.0163750
\(83\) 6.25367 0.686429 0.343215 0.939257i \(-0.388484\pi\)
0.343215 + 0.939257i \(0.388484\pi\)
\(84\) −0.359616 −0.0392373
\(85\) 7.39509 0.802110
\(86\) −0.954610 −0.102938
\(87\) 20.7068 2.22000
\(88\) 7.72471 0.823457
\(89\) 15.9399 1.68963 0.844813 0.535062i \(-0.179712\pi\)
0.844813 + 0.535062i \(0.179712\pi\)
\(90\) 9.21985 0.971858
\(91\) −1.52511 −0.159874
\(92\) 1.06643 0.111183
\(93\) 23.5903 2.44620
\(94\) −11.9612 −1.23370
\(95\) −10.9886 −1.12740
\(96\) 1.59840 0.163136
\(97\) −11.5366 −1.17136 −0.585681 0.810542i \(-0.699173\pi\)
−0.585681 + 0.810542i \(0.699173\pi\)
\(98\) 7.83484 0.791438
\(99\) 7.92292 0.796283
\(100\) 0.0100158 0.00100158
\(101\) −12.4750 −1.24131 −0.620653 0.784086i \(-0.713132\pi\)
−0.620653 + 0.784086i \(0.713132\pi\)
\(102\) 11.5017 1.13884
\(103\) 13.3216 1.31262 0.656308 0.754493i \(-0.272117\pi\)
0.656308 + 0.754493i \(0.272117\pi\)
\(104\) 3.28689 0.322306
\(105\) 6.90900 0.674249
\(106\) −7.34052 −0.712974
\(107\) 8.02008 0.775331 0.387665 0.921800i \(-0.373282\pi\)
0.387665 + 0.921800i \(0.373282\pi\)
\(108\) −0.0538299 −0.00517978
\(109\) −14.9962 −1.43637 −0.718187 0.695850i \(-0.755028\pi\)
−0.718187 + 0.695850i \(0.755028\pi\)
\(110\) 9.25292 0.882231
\(111\) −14.4167 −1.36838
\(112\) 5.36525 0.506969
\(113\) −1.99561 −0.187732 −0.0938658 0.995585i \(-0.529922\pi\)
−0.0938658 + 0.995585i \(0.529922\pi\)
\(114\) −17.0907 −1.60069
\(115\) −20.4884 −1.91055
\(116\) 1.00837 0.0936245
\(117\) 3.37123 0.311670
\(118\) 8.23631 0.758213
\(119\) 4.16832 0.382109
\(120\) −14.8902 −1.35928
\(121\) −3.04867 −0.277151
\(122\) −9.34886 −0.846406
\(123\) −0.245622 −0.0221470
\(124\) 1.14878 0.103164
\(125\) 11.0829 0.991286
\(126\) 5.19687 0.462974
\(127\) −8.25231 −0.732274 −0.366137 0.930561i \(-0.619320\pi\)
−0.366137 + 0.930561i \(0.619320\pi\)
\(128\) −12.2062 −1.07889
\(129\) 1.58127 0.139223
\(130\) 3.93714 0.345310
\(131\) 15.4250 1.34769 0.673843 0.738875i \(-0.264642\pi\)
0.673843 + 0.738875i \(0.264642\pi\)
\(132\) 0.797777 0.0694376
\(133\) −6.19383 −0.537073
\(134\) −2.46771 −0.213177
\(135\) 1.03419 0.0890087
\(136\) −8.98351 −0.770330
\(137\) −16.2510 −1.38841 −0.694207 0.719775i \(-0.744245\pi\)
−0.694207 + 0.719775i \(0.744245\pi\)
\(138\) −31.8658 −2.71260
\(139\) −4.38715 −0.372113 −0.186057 0.982539i \(-0.559571\pi\)
−0.186057 + 0.982539i \(0.559571\pi\)
\(140\) 0.336450 0.0284352
\(141\) 19.8132 1.66857
\(142\) −2.94759 −0.247356
\(143\) 3.38332 0.282927
\(144\) −11.8598 −0.988318
\(145\) −19.3729 −1.60883
\(146\) 14.0386 1.16184
\(147\) −12.9780 −1.07041
\(148\) −0.702057 −0.0577087
\(149\) 1.03300 0.0846265 0.0423132 0.999104i \(-0.486527\pi\)
0.0423132 + 0.999104i \(0.486527\pi\)
\(150\) −0.299281 −0.0244362
\(151\) 18.7956 1.52957 0.764783 0.644288i \(-0.222846\pi\)
0.764783 + 0.644288i \(0.222846\pi\)
\(152\) 13.3489 1.08274
\(153\) −9.21401 −0.744909
\(154\) 5.21551 0.420277
\(155\) −22.0706 −1.77275
\(156\) 0.339457 0.0271783
\(157\) −7.30975 −0.583381 −0.291691 0.956513i \(-0.594218\pi\)
−0.291691 + 0.956513i \(0.594218\pi\)
\(158\) 8.08948 0.643565
\(159\) 12.1592 0.964289
\(160\) −1.49543 −0.118224
\(161\) −11.5485 −0.910149
\(162\) 13.8740 1.09004
\(163\) −8.59779 −0.673431 −0.336715 0.941606i \(-0.609316\pi\)
−0.336715 + 0.941606i \(0.609316\pi\)
\(164\) −0.0119611 −0.000934009 0
\(165\) −15.3270 −1.19321
\(166\) −9.09985 −0.706285
\(167\) 2.32471 0.179892 0.0899459 0.995947i \(-0.471331\pi\)
0.0899459 + 0.995947i \(0.471331\pi\)
\(168\) −8.39301 −0.647535
\(169\) −11.5604 −0.889261
\(170\) −10.7607 −0.825312
\(171\) 13.6914 1.04701
\(172\) 0.0770035 0.00587146
\(173\) −26.1646 −1.98926 −0.994630 0.103499i \(-0.966996\pi\)
−0.994630 + 0.103499i \(0.966996\pi\)
\(174\) −30.1309 −2.28422
\(175\) −0.108462 −0.00819898
\(176\) −11.9024 −0.897174
\(177\) −13.6430 −1.02547
\(178\) −23.1945 −1.73850
\(179\) −17.0938 −1.27765 −0.638824 0.769353i \(-0.720579\pi\)
−0.638824 + 0.769353i \(0.720579\pi\)
\(180\) −0.743718 −0.0554335
\(181\) −20.3727 −1.51429 −0.757144 0.653248i \(-0.773406\pi\)
−0.757144 + 0.653248i \(0.773406\pi\)
\(182\) 2.21921 0.164499
\(183\) 15.4859 1.14475
\(184\) 24.8892 1.83485
\(185\) 13.4880 0.991659
\(186\) −34.3267 −2.51696
\(187\) −9.24706 −0.676212
\(188\) 0.964849 0.0703689
\(189\) 0.582931 0.0424020
\(190\) 15.9897 1.16002
\(191\) 13.3300 0.964529 0.482264 0.876026i \(-0.339815\pi\)
0.482264 + 0.876026i \(0.339815\pi\)
\(192\) 18.0221 1.30063
\(193\) 21.9679 1.58129 0.790644 0.612277i \(-0.209746\pi\)
0.790644 + 0.612277i \(0.209746\pi\)
\(194\) 16.7871 1.20524
\(195\) −6.52169 −0.467028
\(196\) −0.631996 −0.0451426
\(197\) 12.7697 0.909804 0.454902 0.890541i \(-0.349674\pi\)
0.454902 + 0.890541i \(0.349674\pi\)
\(198\) −11.5288 −0.819316
\(199\) −6.43943 −0.456479 −0.228240 0.973605i \(-0.573297\pi\)
−0.228240 + 0.973605i \(0.573297\pi\)
\(200\) 0.233757 0.0165291
\(201\) 4.08764 0.288320
\(202\) 18.1526 1.27721
\(203\) −10.9197 −0.766415
\(204\) −0.927781 −0.0649576
\(205\) 0.229799 0.0160499
\(206\) −19.3845 −1.35058
\(207\) 25.5278 1.77430
\(208\) −5.06449 −0.351159
\(209\) 13.7405 0.950449
\(210\) −10.0534 −0.693752
\(211\) 3.70816 0.255281 0.127640 0.991821i \(-0.459260\pi\)
0.127640 + 0.991821i \(0.459260\pi\)
\(212\) 0.592122 0.0406671
\(213\) 4.88254 0.334546
\(214\) −11.6702 −0.797758
\(215\) −1.47940 −0.100894
\(216\) −1.25633 −0.0854822
\(217\) −12.4403 −0.844505
\(218\) 21.8213 1.47792
\(219\) −23.2543 −1.57138
\(220\) −0.746385 −0.0503213
\(221\) −3.93465 −0.264673
\(222\) 20.9781 1.40796
\(223\) 1.57390 0.105396 0.0526982 0.998610i \(-0.483218\pi\)
0.0526982 + 0.998610i \(0.483218\pi\)
\(224\) −0.842918 −0.0563198
\(225\) 0.239754 0.0159836
\(226\) 2.90386 0.193162
\(227\) 1.07023 0.0710337 0.0355169 0.999369i \(-0.488692\pi\)
0.0355169 + 0.999369i \(0.488692\pi\)
\(228\) 1.37862 0.0913012
\(229\) 4.48075 0.296097 0.148048 0.988980i \(-0.452701\pi\)
0.148048 + 0.988980i \(0.452701\pi\)
\(230\) 29.8131 1.96582
\(231\) −8.63924 −0.568420
\(232\) 23.5341 1.54509
\(233\) −4.42879 −0.290140 −0.145070 0.989421i \(-0.546341\pi\)
−0.145070 + 0.989421i \(0.546341\pi\)
\(234\) −4.90554 −0.320685
\(235\) −18.5368 −1.20921
\(236\) −0.664381 −0.0432475
\(237\) −13.3998 −0.870413
\(238\) −6.06541 −0.393162
\(239\) 11.5886 0.749603 0.374802 0.927105i \(-0.377711\pi\)
0.374802 + 0.927105i \(0.377711\pi\)
\(240\) 22.9430 1.48097
\(241\) −12.9016 −0.831066 −0.415533 0.909578i \(-0.636405\pi\)
−0.415533 + 0.909578i \(0.636405\pi\)
\(242\) 4.43618 0.285168
\(243\) −21.6058 −1.38601
\(244\) 0.754124 0.0482779
\(245\) 12.1420 0.775725
\(246\) 0.357410 0.0227876
\(247\) 5.84662 0.372011
\(248\) 26.8113 1.70252
\(249\) 15.0735 0.955242
\(250\) −16.1270 −1.01996
\(251\) −20.1137 −1.26956 −0.634782 0.772691i \(-0.718910\pi\)
−0.634782 + 0.772691i \(0.718910\pi\)
\(252\) −0.419205 −0.0264074
\(253\) 25.6193 1.61067
\(254\) 12.0081 0.753455
\(255\) 17.8247 1.11622
\(256\) 2.80754 0.175471
\(257\) 3.79278 0.236587 0.118293 0.992979i \(-0.462258\pi\)
0.118293 + 0.992979i \(0.462258\pi\)
\(258\) −2.30093 −0.143250
\(259\) 7.60267 0.472407
\(260\) −0.317589 −0.0196960
\(261\) 24.1379 1.49410
\(262\) −22.4452 −1.38667
\(263\) −21.9708 −1.35478 −0.677388 0.735626i \(-0.736888\pi\)
−0.677388 + 0.735626i \(0.736888\pi\)
\(264\) 18.6192 1.14593
\(265\) −11.3759 −0.698818
\(266\) 9.01277 0.552609
\(267\) 38.4206 2.35130
\(268\) 0.199057 0.0121594
\(269\) 6.37593 0.388748 0.194374 0.980928i \(-0.437733\pi\)
0.194374 + 0.980928i \(0.437733\pi\)
\(270\) −1.50487 −0.0915834
\(271\) −9.29331 −0.564529 −0.282264 0.959337i \(-0.591086\pi\)
−0.282264 + 0.959337i \(0.591086\pi\)
\(272\) 13.8419 0.839290
\(273\) −3.67602 −0.222483
\(274\) 23.6471 1.42858
\(275\) 0.240614 0.0145096
\(276\) 2.57045 0.154723
\(277\) −1.86135 −0.111838 −0.0559189 0.998435i \(-0.517809\pi\)
−0.0559189 + 0.998435i \(0.517809\pi\)
\(278\) 6.38383 0.382877
\(279\) 27.4992 1.64633
\(280\) 7.85234 0.469267
\(281\) 18.5118 1.10432 0.552162 0.833737i \(-0.313803\pi\)
0.552162 + 0.833737i \(0.313803\pi\)
\(282\) −28.8306 −1.71683
\(283\) 6.10833 0.363102 0.181551 0.983381i \(-0.441888\pi\)
0.181551 + 0.983381i \(0.441888\pi\)
\(284\) 0.237767 0.0141089
\(285\) −26.4862 −1.56891
\(286\) −4.92313 −0.291111
\(287\) 0.129529 0.00764585
\(288\) 1.86326 0.109794
\(289\) −6.24607 −0.367416
\(290\) 28.1899 1.65537
\(291\) −27.8070 −1.63008
\(292\) −1.13242 −0.0662699
\(293\) −16.9613 −0.990889 −0.495445 0.868639i \(-0.664995\pi\)
−0.495445 + 0.868639i \(0.664995\pi\)
\(294\) 18.8846 1.10137
\(295\) 12.7642 0.743159
\(296\) −16.3852 −0.952369
\(297\) −1.29318 −0.0750381
\(298\) −1.50314 −0.0870744
\(299\) 10.9011 0.630427
\(300\) 0.0241414 0.00139381
\(301\) −0.833881 −0.0480641
\(302\) −27.3499 −1.57381
\(303\) −30.0689 −1.72741
\(304\) −20.5681 −1.17966
\(305\) −14.4884 −0.829601
\(306\) 13.4075 0.766456
\(307\) 10.4450 0.596129 0.298065 0.954546i \(-0.403659\pi\)
0.298065 + 0.954546i \(0.403659\pi\)
\(308\) −0.420708 −0.0239721
\(309\) 32.1096 1.82665
\(310\) 32.1154 1.82403
\(311\) 25.6027 1.45179 0.725897 0.687804i \(-0.241425\pi\)
0.725897 + 0.687804i \(0.241425\pi\)
\(312\) 7.92252 0.448524
\(313\) −12.0009 −0.678330 −0.339165 0.940727i \(-0.610144\pi\)
−0.339165 + 0.940727i \(0.610144\pi\)
\(314\) 10.6366 0.600256
\(315\) 8.05382 0.453781
\(316\) −0.652537 −0.0367081
\(317\) 9.21967 0.517828 0.258914 0.965900i \(-0.416635\pi\)
0.258914 + 0.965900i \(0.416635\pi\)
\(318\) −17.6931 −0.992182
\(319\) 24.2245 1.35631
\(320\) −16.8611 −0.942566
\(321\) 19.3311 1.07896
\(322\) 16.8045 0.936476
\(323\) −15.9796 −0.889129
\(324\) −1.11914 −0.0621747
\(325\) 0.102382 0.00567914
\(326\) 12.5108 0.692911
\(327\) −36.1459 −1.99887
\(328\) −0.279159 −0.0154140
\(329\) −10.4485 −0.576043
\(330\) 22.3027 1.22772
\(331\) 16.3162 0.896822 0.448411 0.893827i \(-0.351990\pi\)
0.448411 + 0.893827i \(0.351990\pi\)
\(332\) 0.734038 0.0402856
\(333\) −16.8056 −0.920941
\(334\) −3.38274 −0.185095
\(335\) −3.82432 −0.208945
\(336\) 12.9321 0.705503
\(337\) 33.7094 1.83627 0.918134 0.396269i \(-0.129695\pi\)
0.918134 + 0.396269i \(0.129695\pi\)
\(338\) 16.8218 0.914983
\(339\) −4.81011 −0.261249
\(340\) 0.868014 0.0470747
\(341\) 27.5978 1.49451
\(342\) −19.9226 −1.07729
\(343\) 15.7416 0.849968
\(344\) 1.79717 0.0968969
\(345\) −49.3839 −2.65874
\(346\) 38.0727 2.04680
\(347\) −11.6182 −0.623695 −0.311848 0.950132i \(-0.600948\pi\)
−0.311848 + 0.950132i \(0.600948\pi\)
\(348\) 2.43051 0.130289
\(349\) 28.4712 1.52403 0.762014 0.647560i \(-0.224211\pi\)
0.762014 + 0.647560i \(0.224211\pi\)
\(350\) 0.157826 0.00843614
\(351\) −0.550253 −0.0293703
\(352\) 1.86994 0.0996682
\(353\) −24.7286 −1.31617 −0.658086 0.752943i \(-0.728634\pi\)
−0.658086 + 0.752943i \(0.728634\pi\)
\(354\) 19.8523 1.05514
\(355\) −4.56801 −0.242445
\(356\) 1.87098 0.0991617
\(357\) 10.0471 0.531747
\(358\) 24.8735 1.31461
\(359\) 20.3672 1.07494 0.537469 0.843284i \(-0.319381\pi\)
0.537469 + 0.843284i \(0.319381\pi\)
\(360\) −17.3575 −0.914821
\(361\) 4.74457 0.249714
\(362\) 29.6447 1.55809
\(363\) −7.34832 −0.385687
\(364\) −0.179013 −0.00938281
\(365\) 21.7563 1.13877
\(366\) −22.5339 −1.17787
\(367\) 2.29419 0.119756 0.0598780 0.998206i \(-0.480929\pi\)
0.0598780 + 0.998206i \(0.480929\pi\)
\(368\) −38.3496 −1.99911
\(369\) −0.286322 −0.0149053
\(370\) −19.6267 −1.02034
\(371\) −6.41217 −0.332903
\(372\) 2.76896 0.143564
\(373\) 4.97209 0.257445 0.128723 0.991681i \(-0.458912\pi\)
0.128723 + 0.991681i \(0.458912\pi\)
\(374\) 13.4556 0.695772
\(375\) 26.7136 1.37948
\(376\) 22.5184 1.16130
\(377\) 10.3076 0.530868
\(378\) −0.848235 −0.0436285
\(379\) 20.6330 1.05985 0.529924 0.848045i \(-0.322220\pi\)
0.529924 + 0.848045i \(0.322220\pi\)
\(380\) −1.28981 −0.0661658
\(381\) −19.8909 −1.01904
\(382\) −19.3968 −0.992428
\(383\) −19.9239 −1.01806 −0.509032 0.860747i \(-0.669997\pi\)
−0.509032 + 0.860747i \(0.669997\pi\)
\(384\) −29.4211 −1.50139
\(385\) 8.08271 0.411933
\(386\) −31.9660 −1.62703
\(387\) 1.84328 0.0936993
\(388\) −1.35413 −0.0687455
\(389\) −24.4179 −1.23804 −0.619018 0.785377i \(-0.712469\pi\)
−0.619018 + 0.785377i \(0.712469\pi\)
\(390\) 9.48985 0.480537
\(391\) −29.7942 −1.50676
\(392\) −14.7501 −0.744990
\(393\) 37.1794 1.87545
\(394\) −18.5815 −0.936121
\(395\) 12.5366 0.630787
\(396\) 0.929970 0.0467327
\(397\) −13.0744 −0.656185 −0.328092 0.944646i \(-0.606406\pi\)
−0.328092 + 0.944646i \(0.606406\pi\)
\(398\) 9.37015 0.469683
\(399\) −14.9292 −0.747397
\(400\) −0.360176 −0.0180088
\(401\) 33.3744 1.66664 0.833318 0.552794i \(-0.186438\pi\)
0.833318 + 0.552794i \(0.186438\pi\)
\(402\) −5.94801 −0.296660
\(403\) 11.7430 0.584958
\(404\) −1.46428 −0.0728504
\(405\) 21.5012 1.06840
\(406\) 15.8895 0.788585
\(407\) −16.8659 −0.836010
\(408\) −21.6533 −1.07200
\(409\) 9.32317 0.461001 0.230501 0.973072i \(-0.425964\pi\)
0.230501 + 0.973072i \(0.425964\pi\)
\(410\) −0.334386 −0.0165141
\(411\) −39.1704 −1.93213
\(412\) 1.56365 0.0770356
\(413\) 7.19467 0.354026
\(414\) −37.1460 −1.82563
\(415\) −14.1024 −0.692262
\(416\) 0.795665 0.0390107
\(417\) −10.5745 −0.517836
\(418\) −19.9941 −0.977942
\(419\) −9.39551 −0.459001 −0.229500 0.973309i \(-0.573709\pi\)
−0.229500 + 0.973309i \(0.573709\pi\)
\(420\) 0.810958 0.0395707
\(421\) −28.8517 −1.40614 −0.703072 0.711118i \(-0.748189\pi\)
−0.703072 + 0.711118i \(0.748189\pi\)
\(422\) −5.39583 −0.262665
\(423\) 23.0962 1.12298
\(424\) 13.8194 0.671131
\(425\) −0.279824 −0.0135735
\(426\) −7.10468 −0.344223
\(427\) −8.16651 −0.395205
\(428\) 0.941375 0.0455031
\(429\) 8.15494 0.393724
\(430\) 2.15271 0.103813
\(431\) −22.2344 −1.07099 −0.535497 0.844537i \(-0.679876\pi\)
−0.535497 + 0.844537i \(0.679876\pi\)
\(432\) 1.93577 0.0931346
\(433\) −28.4182 −1.36569 −0.682846 0.730562i \(-0.739258\pi\)
−0.682846 + 0.730562i \(0.739258\pi\)
\(434\) 18.1022 0.868933
\(435\) −46.6952 −2.23887
\(436\) −1.76021 −0.0842988
\(437\) 44.2721 2.11782
\(438\) 33.8378 1.61683
\(439\) −23.5027 −1.12172 −0.560862 0.827910i \(-0.689530\pi\)
−0.560862 + 0.827910i \(0.689530\pi\)
\(440\) −17.4198 −0.830454
\(441\) −15.1285 −0.720405
\(442\) 5.72539 0.272329
\(443\) −6.64797 −0.315855 −0.157927 0.987451i \(-0.550481\pi\)
−0.157927 + 0.987451i \(0.550481\pi\)
\(444\) −1.69220 −0.0803080
\(445\) −35.9455 −1.70398
\(446\) −2.29022 −0.108445
\(447\) 2.48987 0.117767
\(448\) −9.50396 −0.449020
\(449\) 8.06570 0.380644 0.190322 0.981722i \(-0.439047\pi\)
0.190322 + 0.981722i \(0.439047\pi\)
\(450\) −0.348872 −0.0164460
\(451\) −0.287349 −0.0135307
\(452\) −0.234239 −0.0110177
\(453\) 45.3038 2.12856
\(454\) −1.55732 −0.0730884
\(455\) 3.43922 0.161233
\(456\) 32.1753 1.50675
\(457\) 22.7762 1.06543 0.532713 0.846296i \(-0.321173\pi\)
0.532713 + 0.846296i \(0.321173\pi\)
\(458\) −6.52004 −0.304661
\(459\) 1.50392 0.0701968
\(460\) −2.40487 −0.112128
\(461\) 38.7077 1.80280 0.901398 0.432992i \(-0.142542\pi\)
0.901398 + 0.432992i \(0.142542\pi\)
\(462\) 12.5711 0.584862
\(463\) 16.7000 0.776113 0.388056 0.921636i \(-0.373147\pi\)
0.388056 + 0.921636i \(0.373147\pi\)
\(464\) −36.2617 −1.68341
\(465\) −53.1977 −2.46698
\(466\) 6.44443 0.298532
\(467\) −9.30878 −0.430759 −0.215380 0.976530i \(-0.569099\pi\)
−0.215380 + 0.976530i \(0.569099\pi\)
\(468\) 0.395705 0.0182915
\(469\) −2.15562 −0.0995372
\(470\) 26.9733 1.24419
\(471\) −17.6190 −0.811839
\(472\) −15.5059 −0.713715
\(473\) 1.84989 0.0850582
\(474\) 19.4984 0.895591
\(475\) 0.415799 0.0190782
\(476\) 0.489265 0.0224254
\(477\) 14.1740 0.648984
\(478\) −16.8628 −0.771286
\(479\) −6.66857 −0.304695 −0.152347 0.988327i \(-0.548683\pi\)
−0.152347 + 0.988327i \(0.548683\pi\)
\(480\) −3.60450 −0.164522
\(481\) −7.17648 −0.327219
\(482\) 18.7734 0.855106
\(483\) −27.8358 −1.26657
\(484\) −0.357844 −0.0162656
\(485\) 26.0157 1.18131
\(486\) 31.4390 1.42610
\(487\) 10.6950 0.484636 0.242318 0.970197i \(-0.422092\pi\)
0.242318 + 0.970197i \(0.422092\pi\)
\(488\) 17.6004 0.796731
\(489\) −20.7236 −0.937153
\(490\) −17.6681 −0.798163
\(491\) 16.1788 0.730137 0.365068 0.930981i \(-0.381046\pi\)
0.365068 + 0.930981i \(0.381046\pi\)
\(492\) −0.0288304 −0.00129978
\(493\) −28.1721 −1.26881
\(494\) −8.50754 −0.382772
\(495\) −17.8667 −0.803049
\(496\) −41.3112 −1.85493
\(497\) −2.57481 −0.115496
\(498\) −21.9337 −0.982873
\(499\) −23.1743 −1.03742 −0.518712 0.854949i \(-0.673588\pi\)
−0.518712 + 0.854949i \(0.673588\pi\)
\(500\) 1.30088 0.0581772
\(501\) 5.60335 0.250339
\(502\) 29.2679 1.30629
\(503\) −31.5186 −1.40534 −0.702672 0.711514i \(-0.748010\pi\)
−0.702672 + 0.711514i \(0.748010\pi\)
\(504\) −9.78374 −0.435802
\(505\) 28.1319 1.25185
\(506\) −37.2792 −1.65726
\(507\) −27.8645 −1.23750
\(508\) −0.968632 −0.0429761
\(509\) 33.5085 1.48524 0.742618 0.669715i \(-0.233584\pi\)
0.742618 + 0.669715i \(0.233584\pi\)
\(510\) −25.9370 −1.14851
\(511\) 12.2631 0.542489
\(512\) 20.3271 0.898341
\(513\) −2.23471 −0.0986650
\(514\) −5.51895 −0.243430
\(515\) −30.0411 −1.32377
\(516\) 0.185604 0.00817078
\(517\) 23.1791 1.01941
\(518\) −11.0628 −0.486072
\(519\) −63.0656 −2.76827
\(520\) −7.41216 −0.325045
\(521\) −22.7960 −0.998712 −0.499356 0.866397i \(-0.666430\pi\)
−0.499356 + 0.866397i \(0.666430\pi\)
\(522\) −35.1236 −1.53732
\(523\) 29.8928 1.30712 0.653560 0.756874i \(-0.273275\pi\)
0.653560 + 0.756874i \(0.273275\pi\)
\(524\) 1.81054 0.0790938
\(525\) −0.261431 −0.0114098
\(526\) 31.9701 1.39396
\(527\) −32.0951 −1.39808
\(528\) −28.6887 −1.24852
\(529\) 59.5460 2.58896
\(530\) 16.5534 0.719032
\(531\) −15.9037 −0.690162
\(532\) −0.727014 −0.0315201
\(533\) −0.122268 −0.00529600
\(534\) −55.9066 −2.41931
\(535\) −18.0858 −0.781919
\(536\) 4.64576 0.200666
\(537\) −41.2018 −1.77799
\(538\) −9.27776 −0.399992
\(539\) −15.1828 −0.653968
\(540\) 0.121390 0.00522380
\(541\) 36.5305 1.57057 0.785283 0.619136i \(-0.212517\pi\)
0.785283 + 0.619136i \(0.212517\pi\)
\(542\) 13.5229 0.580858
\(543\) −49.1050 −2.10730
\(544\) −2.17466 −0.0932378
\(545\) 33.8174 1.44858
\(546\) 5.34906 0.228918
\(547\) −21.9611 −0.938987 −0.469493 0.882936i \(-0.655563\pi\)
−0.469493 + 0.882936i \(0.655563\pi\)
\(548\) −1.90749 −0.0814841
\(549\) 18.0520 0.770439
\(550\) −0.350123 −0.0149293
\(551\) 41.8617 1.78337
\(552\) 59.9913 2.55340
\(553\) 7.06641 0.300494
\(554\) 2.70849 0.115073
\(555\) 32.5107 1.38000
\(556\) −0.514951 −0.0218388
\(557\) 0.927328 0.0392922 0.0196461 0.999807i \(-0.493746\pi\)
0.0196461 + 0.999807i \(0.493746\pi\)
\(558\) −40.0147 −1.69396
\(559\) 0.787135 0.0332923
\(560\) −12.0990 −0.511276
\(561\) −22.2886 −0.941023
\(562\) −26.9370 −1.13627
\(563\) −13.4615 −0.567334 −0.283667 0.958923i \(-0.591551\pi\)
−0.283667 + 0.958923i \(0.591551\pi\)
\(564\) 2.32561 0.0979260
\(565\) 4.50024 0.189327
\(566\) −8.88836 −0.373606
\(567\) 12.1194 0.508965
\(568\) 5.54919 0.232839
\(569\) −17.9315 −0.751727 −0.375863 0.926675i \(-0.622654\pi\)
−0.375863 + 0.926675i \(0.622654\pi\)
\(570\) 38.5406 1.61429
\(571\) 10.3154 0.431688 0.215844 0.976428i \(-0.430750\pi\)
0.215844 + 0.976428i \(0.430750\pi\)
\(572\) 0.397124 0.0166046
\(573\) 32.1299 1.34225
\(574\) −0.188480 −0.00786701
\(575\) 0.775264 0.0323307
\(576\) 21.0084 0.875349
\(577\) −40.7762 −1.69754 −0.848768 0.528766i \(-0.822655\pi\)
−0.848768 + 0.528766i \(0.822655\pi\)
\(578\) 9.08878 0.378043
\(579\) 52.9502 2.20053
\(580\) −2.27393 −0.0944200
\(581\) −7.94900 −0.329780
\(582\) 40.4626 1.67723
\(583\) 14.2249 0.589133
\(584\) −26.4294 −1.09366
\(585\) −7.60234 −0.314318
\(586\) 24.6807 1.01955
\(587\) −23.5853 −0.973470 −0.486735 0.873550i \(-0.661812\pi\)
−0.486735 + 0.873550i \(0.661812\pi\)
\(588\) −1.52333 −0.0628209
\(589\) 47.6911 1.96508
\(590\) −18.5734 −0.764656
\(591\) 30.7793 1.26609
\(592\) 25.2465 1.03763
\(593\) 8.37847 0.344062 0.172031 0.985092i \(-0.444967\pi\)
0.172031 + 0.985092i \(0.444967\pi\)
\(594\) 1.88174 0.0772086
\(595\) −9.39984 −0.385356
\(596\) 0.121250 0.00496661
\(597\) −15.5212 −0.635241
\(598\) −15.8624 −0.648663
\(599\) 37.5552 1.53446 0.767232 0.641369i \(-0.221633\pi\)
0.767232 + 0.641369i \(0.221633\pi\)
\(600\) 0.563433 0.0230020
\(601\) 41.2307 1.68184 0.840918 0.541162i \(-0.182016\pi\)
0.840918 + 0.541162i \(0.182016\pi\)
\(602\) 1.21340 0.0494544
\(603\) 4.76497 0.194044
\(604\) 2.20618 0.0897680
\(605\) 6.87495 0.279506
\(606\) 43.7539 1.77738
\(607\) −30.0555 −1.21992 −0.609958 0.792434i \(-0.708814\pi\)
−0.609958 + 0.792434i \(0.708814\pi\)
\(608\) 3.23139 0.131050
\(609\) −26.3203 −1.06655
\(610\) 21.0823 0.853598
\(611\) 9.86276 0.399005
\(612\) −1.08151 −0.0437176
\(613\) −23.1151 −0.933608 −0.466804 0.884361i \(-0.654595\pi\)
−0.466804 + 0.884361i \(0.654595\pi\)
\(614\) −15.1988 −0.613373
\(615\) 0.553894 0.0223352
\(616\) −9.81883 −0.395612
\(617\) 20.3152 0.817858 0.408929 0.912566i \(-0.365902\pi\)
0.408929 + 0.912566i \(0.365902\pi\)
\(618\) −46.7233 −1.87949
\(619\) 1.00000 0.0401934
\(620\) −2.59059 −0.104040
\(621\) −4.16666 −0.167202
\(622\) −37.2550 −1.49379
\(623\) −20.2611 −0.811743
\(624\) −12.2071 −0.488676
\(625\) −25.4194 −1.01677
\(626\) 17.4627 0.697951
\(627\) 33.1192 1.32265
\(628\) −0.857997 −0.0342378
\(629\) 19.6143 0.782073
\(630\) −11.7193 −0.466908
\(631\) 12.3255 0.490672 0.245336 0.969438i \(-0.421102\pi\)
0.245336 + 0.969438i \(0.421102\pi\)
\(632\) −15.2294 −0.605795
\(633\) 8.93793 0.355251
\(634\) −13.4157 −0.532807
\(635\) 18.6095 0.738496
\(636\) 1.42722 0.0565928
\(637\) −6.46032 −0.255967
\(638\) −35.2496 −1.39554
\(639\) 5.69158 0.225155
\(640\) 27.5259 1.08806
\(641\) −8.05058 −0.317979 −0.158989 0.987280i \(-0.550824\pi\)
−0.158989 + 0.987280i \(0.550824\pi\)
\(642\) −28.1291 −1.11017
\(643\) −3.32324 −0.131056 −0.0655279 0.997851i \(-0.520873\pi\)
−0.0655279 + 0.997851i \(0.520873\pi\)
\(644\) −1.35553 −0.0534153
\(645\) −3.56586 −0.140406
\(646\) 23.2522 0.914847
\(647\) 12.5973 0.495250 0.247625 0.968856i \(-0.420350\pi\)
0.247625 + 0.968856i \(0.420350\pi\)
\(648\) −26.1195 −1.02607
\(649\) −15.9608 −0.626514
\(650\) −0.148978 −0.00584341
\(651\) −29.9854 −1.17522
\(652\) −1.00918 −0.0395227
\(653\) 29.3506 1.14858 0.574289 0.818653i \(-0.305279\pi\)
0.574289 + 0.818653i \(0.305279\pi\)
\(654\) 52.5967 2.05669
\(655\) −34.7844 −1.35914
\(656\) 0.430132 0.0167939
\(657\) −27.1075 −1.05756
\(658\) 15.2038 0.592706
\(659\) 6.74528 0.262759 0.131379 0.991332i \(-0.458059\pi\)
0.131379 + 0.991332i \(0.458059\pi\)
\(660\) −1.79904 −0.0700276
\(661\) −14.0612 −0.546918 −0.273459 0.961884i \(-0.588168\pi\)
−0.273459 + 0.961884i \(0.588168\pi\)
\(662\) −23.7421 −0.922764
\(663\) −9.48384 −0.368322
\(664\) 17.1316 0.664834
\(665\) 13.9675 0.541637
\(666\) 24.4542 0.947580
\(667\) 78.0518 3.02218
\(668\) 0.272868 0.0105576
\(669\) 3.79364 0.146671
\(670\) 5.56485 0.214989
\(671\) 18.1167 0.699388
\(672\) −2.03172 −0.0783752
\(673\) −34.2462 −1.32009 −0.660047 0.751224i \(-0.729464\pi\)
−0.660047 + 0.751224i \(0.729464\pi\)
\(674\) −49.0513 −1.88938
\(675\) −0.0391328 −0.00150622
\(676\) −1.35693 −0.0521894
\(677\) −15.8548 −0.609349 −0.304674 0.952457i \(-0.598548\pi\)
−0.304674 + 0.952457i \(0.598548\pi\)
\(678\) 6.99929 0.268806
\(679\) 14.6641 0.562755
\(680\) 20.2584 0.776875
\(681\) 2.57962 0.0988512
\(682\) −40.1582 −1.53774
\(683\) −18.6499 −0.713617 −0.356808 0.934178i \(-0.616135\pi\)
−0.356808 + 0.934178i \(0.616135\pi\)
\(684\) 1.60706 0.0614473
\(685\) 36.6471 1.40021
\(686\) −22.9060 −0.874554
\(687\) 10.8001 0.412051
\(688\) −2.76911 −0.105571
\(689\) 6.05272 0.230590
\(690\) 71.8596 2.73565
\(691\) 11.6482 0.443118 0.221559 0.975147i \(-0.428885\pi\)
0.221559 + 0.975147i \(0.428885\pi\)
\(692\) −3.07113 −0.116747
\(693\) −10.0708 −0.382557
\(694\) 16.9058 0.641736
\(695\) 9.89332 0.375275
\(696\) 56.7251 2.15016
\(697\) 0.334174 0.0126578
\(698\) −41.4290 −1.56811
\(699\) −10.6749 −0.403761
\(700\) −0.0127310 −0.000481186 0
\(701\) −13.3080 −0.502635 −0.251318 0.967905i \(-0.580864\pi\)
−0.251318 + 0.967905i \(0.580864\pi\)
\(702\) 0.800685 0.0302199
\(703\) −29.1455 −1.09924
\(704\) 21.0837 0.794623
\(705\) −44.6800 −1.68275
\(706\) 35.9831 1.35424
\(707\) 15.8568 0.596358
\(708\) −1.60138 −0.0601836
\(709\) −24.9024 −0.935229 −0.467615 0.883932i \(-0.654886\pi\)
−0.467615 + 0.883932i \(0.654886\pi\)
\(710\) 6.64701 0.249458
\(711\) −15.6202 −0.585803
\(712\) 43.6665 1.63647
\(713\) 88.9207 3.33011
\(714\) −14.6197 −0.547128
\(715\) −7.62961 −0.285331
\(716\) −2.00642 −0.0749834
\(717\) 27.9324 1.04316
\(718\) −29.6367 −1.10603
\(719\) −46.5236 −1.73504 −0.867519 0.497404i \(-0.834287\pi\)
−0.867519 + 0.497404i \(0.834287\pi\)
\(720\) 26.7447 0.996716
\(721\) −16.9330 −0.630618
\(722\) −6.90392 −0.256937
\(723\) −31.0973 −1.15652
\(724\) −2.39128 −0.0888714
\(725\) 0.733055 0.0272250
\(726\) 10.6927 0.396843
\(727\) −15.9297 −0.590801 −0.295401 0.955373i \(-0.595453\pi\)
−0.295401 + 0.955373i \(0.595453\pi\)
\(728\) −4.17794 −0.154845
\(729\) −23.4735 −0.869389
\(730\) −31.6580 −1.17171
\(731\) −2.15135 −0.0795704
\(732\) 1.81770 0.0671840
\(733\) 3.17341 0.117212 0.0586062 0.998281i \(-0.481334\pi\)
0.0586062 + 0.998281i \(0.481334\pi\)
\(734\) −3.33833 −0.123220
\(735\) 29.2664 1.07951
\(736\) 6.02498 0.222084
\(737\) 4.78206 0.176149
\(738\) 0.416633 0.0153365
\(739\) 12.2055 0.448986 0.224493 0.974476i \(-0.427927\pi\)
0.224493 + 0.974476i \(0.427927\pi\)
\(740\) 1.58319 0.0581991
\(741\) 14.0923 0.517695
\(742\) 9.33048 0.342533
\(743\) −4.89107 −0.179436 −0.0897181 0.995967i \(-0.528597\pi\)
−0.0897181 + 0.995967i \(0.528597\pi\)
\(744\) 64.6242 2.36924
\(745\) −2.32948 −0.0853455
\(746\) −7.23500 −0.264892
\(747\) 17.5711 0.642895
\(748\) −1.08539 −0.0396859
\(749\) −10.1943 −0.372491
\(750\) −38.8715 −1.41939
\(751\) −6.73617 −0.245806 −0.122903 0.992419i \(-0.539220\pi\)
−0.122903 + 0.992419i \(0.539220\pi\)
\(752\) −34.6967 −1.26526
\(753\) −48.4808 −1.76674
\(754\) −14.9988 −0.546224
\(755\) −42.3854 −1.54256
\(756\) 0.0684228 0.00248851
\(757\) −38.5115 −1.39972 −0.699862 0.714278i \(-0.746755\pi\)
−0.699862 + 0.714278i \(0.746755\pi\)
\(758\) −30.0236 −1.09050
\(759\) 61.7513 2.24143
\(760\) −30.1026 −1.09194
\(761\) 14.8273 0.537490 0.268745 0.963211i \(-0.413391\pi\)
0.268745 + 0.963211i \(0.413391\pi\)
\(762\) 28.9436 1.04852
\(763\) 19.0616 0.690075
\(764\) 1.56464 0.0566068
\(765\) 20.7782 0.751238
\(766\) 28.9917 1.04751
\(767\) −6.79135 −0.245221
\(768\) 6.76712 0.244187
\(769\) 0.228352 0.00823460 0.00411730 0.999992i \(-0.498689\pi\)
0.00411730 + 0.999992i \(0.498689\pi\)
\(770\) −11.7613 −0.423848
\(771\) 9.14188 0.329237
\(772\) 2.57853 0.0928035
\(773\) −25.7779 −0.927167 −0.463584 0.886053i \(-0.653437\pi\)
−0.463584 + 0.886053i \(0.653437\pi\)
\(774\) −2.68220 −0.0964096
\(775\) 0.835134 0.0299989
\(776\) −31.6038 −1.13451
\(777\) 18.3250 0.657406
\(778\) 35.5310 1.27385
\(779\) −0.496560 −0.0177911
\(780\) −0.765498 −0.0274092
\(781\) 5.71199 0.204391
\(782\) 43.3542 1.55034
\(783\) −3.93981 −0.140797
\(784\) 22.7271 0.811682
\(785\) 16.4840 0.588338
\(786\) −54.1005 −1.92970
\(787\) 7.22305 0.257474 0.128737 0.991679i \(-0.458908\pi\)
0.128737 + 0.991679i \(0.458908\pi\)
\(788\) 1.49887 0.0533951
\(789\) −52.9570 −1.88532
\(790\) −18.2423 −0.649033
\(791\) 2.53661 0.0901915
\(792\) 21.7044 0.771232
\(793\) 7.70872 0.273745
\(794\) 19.0248 0.675165
\(795\) −27.4199 −0.972483
\(796\) −0.755842 −0.0267901
\(797\) −43.2130 −1.53068 −0.765341 0.643625i \(-0.777430\pi\)
−0.765341 + 0.643625i \(0.777430\pi\)
\(798\) 21.7238 0.769016
\(799\) −26.9563 −0.953644
\(800\) 0.0565861 0.00200062
\(801\) 44.7869 1.58247
\(802\) −48.5637 −1.71484
\(803\) −27.2047 −0.960034
\(804\) 0.479796 0.0169211
\(805\) 26.0426 0.917882
\(806\) −17.0874 −0.601879
\(807\) 15.3682 0.540985
\(808\) −34.1745 −1.20225
\(809\) 21.2090 0.745668 0.372834 0.927898i \(-0.378386\pi\)
0.372834 + 0.927898i \(0.378386\pi\)
\(810\) −31.2868 −1.09931
\(811\) 21.3226 0.748738 0.374369 0.927280i \(-0.377859\pi\)
0.374369 + 0.927280i \(0.377859\pi\)
\(812\) −1.28173 −0.0449798
\(813\) −22.4000 −0.785604
\(814\) 24.5419 0.860193
\(815\) 19.3886 0.679153
\(816\) 33.3637 1.16796
\(817\) 3.19675 0.111840
\(818\) −13.5663 −0.474336
\(819\) −4.28514 −0.149735
\(820\) 0.0269732 0.000941945 0
\(821\) 2.54292 0.0887486 0.0443743 0.999015i \(-0.485871\pi\)
0.0443743 + 0.999015i \(0.485871\pi\)
\(822\) 56.9976 1.98802
\(823\) −56.7854 −1.97942 −0.989708 0.143100i \(-0.954293\pi\)
−0.989708 + 0.143100i \(0.954293\pi\)
\(824\) 36.4938 1.27132
\(825\) 0.579962 0.0201917
\(826\) −10.4691 −0.364267
\(827\) −41.8297 −1.45456 −0.727281 0.686340i \(-0.759216\pi\)
−0.727281 + 0.686340i \(0.759216\pi\)
\(828\) 2.99638 0.104131
\(829\) −34.0210 −1.18160 −0.590800 0.806818i \(-0.701188\pi\)
−0.590800 + 0.806818i \(0.701188\pi\)
\(830\) 20.5208 0.712286
\(831\) −4.48649 −0.155634
\(832\) 8.97119 0.311020
\(833\) 17.6569 0.611776
\(834\) 15.3872 0.532815
\(835\) −5.24239 −0.181420
\(836\) 1.61282 0.0557805
\(837\) −4.48843 −0.155143
\(838\) 13.6716 0.472278
\(839\) −29.1800 −1.00741 −0.503703 0.863877i \(-0.668029\pi\)
−0.503703 + 0.863877i \(0.668029\pi\)
\(840\) 18.9268 0.653037
\(841\) 44.8023 1.54491
\(842\) 41.9827 1.44682
\(843\) 44.6198 1.53679
\(844\) 0.435254 0.0149821
\(845\) 26.0695 0.896817
\(846\) −33.6078 −1.15546
\(847\) 3.87514 0.133151
\(848\) −21.2932 −0.731211
\(849\) 14.7231 0.505297
\(850\) 0.407178 0.0139661
\(851\) −54.3421 −1.86282
\(852\) 0.573098 0.0196340
\(853\) −28.9232 −0.990313 −0.495156 0.868804i \(-0.664889\pi\)
−0.495156 + 0.868804i \(0.664889\pi\)
\(854\) 11.8833 0.406637
\(855\) −30.8750 −1.05590
\(856\) 21.9706 0.750939
\(857\) 11.0508 0.377489 0.188744 0.982026i \(-0.439558\pi\)
0.188744 + 0.982026i \(0.439558\pi\)
\(858\) −11.8664 −0.405113
\(859\) 2.24428 0.0765739 0.0382870 0.999267i \(-0.487810\pi\)
0.0382870 + 0.999267i \(0.487810\pi\)
\(860\) −0.173648 −0.00592135
\(861\) 0.312208 0.0106400
\(862\) 32.3538 1.10197
\(863\) −48.1246 −1.63818 −0.819090 0.573665i \(-0.805521\pi\)
−0.819090 + 0.573665i \(0.805521\pi\)
\(864\) −0.304122 −0.0103464
\(865\) 59.0030 2.00616
\(866\) 41.3519 1.40520
\(867\) −15.0551 −0.511299
\(868\) −1.46021 −0.0495628
\(869\) −15.6762 −0.531780
\(870\) 67.9472 2.30363
\(871\) 2.03478 0.0689458
\(872\) −41.0812 −1.39119
\(873\) −32.4147 −1.09707
\(874\) −64.4213 −2.17908
\(875\) −14.0874 −0.476241
\(876\) −2.72952 −0.0922219
\(877\) −34.8726 −1.17756 −0.588782 0.808292i \(-0.700392\pi\)
−0.588782 + 0.808292i \(0.700392\pi\)
\(878\) 34.1993 1.15417
\(879\) −40.8825 −1.37893
\(880\) 26.8406 0.904797
\(881\) −40.8075 −1.37484 −0.687420 0.726261i \(-0.741257\pi\)
−0.687420 + 0.726261i \(0.741257\pi\)
\(882\) 22.0138 0.741244
\(883\) 18.5720 0.624998 0.312499 0.949918i \(-0.398834\pi\)
0.312499 + 0.949918i \(0.398834\pi\)
\(884\) −0.461838 −0.0155333
\(885\) 30.7660 1.03419
\(886\) 9.67361 0.324991
\(887\) −8.15171 −0.273708 −0.136854 0.990591i \(-0.543699\pi\)
−0.136854 + 0.990591i \(0.543699\pi\)
\(888\) −39.4938 −1.32533
\(889\) 10.4894 0.351805
\(890\) 52.3051 1.75327
\(891\) −26.8858 −0.900707
\(892\) 0.184740 0.00618557
\(893\) 40.0551 1.34039
\(894\) −3.62307 −0.121174
\(895\) 38.5476 1.28850
\(896\) 15.5152 0.518328
\(897\) 26.2754 0.877309
\(898\) −11.7366 −0.391654
\(899\) 84.0794 2.80421
\(900\) 0.0281417 0.000938056 0
\(901\) −16.5429 −0.551124
\(902\) 0.418127 0.0139221
\(903\) −2.00994 −0.0668865
\(904\) −5.46687 −0.181825
\(905\) 45.9417 1.52715
\(906\) −65.9225 −2.19013
\(907\) −32.6381 −1.08373 −0.541866 0.840465i \(-0.682282\pi\)
−0.541866 + 0.840465i \(0.682282\pi\)
\(908\) 0.125621 0.00416887
\(909\) −35.0513 −1.16258
\(910\) −5.00448 −0.165897
\(911\) −11.9018 −0.394324 −0.197162 0.980371i \(-0.563173\pi\)
−0.197162 + 0.980371i \(0.563173\pi\)
\(912\) −49.5762 −1.64163
\(913\) 17.6342 0.583606
\(914\) −33.1421 −1.09624
\(915\) −34.9218 −1.15448
\(916\) 0.525938 0.0173775
\(917\) −19.6066 −0.647466
\(918\) −2.18838 −0.0722273
\(919\) −15.2268 −0.502286 −0.251143 0.967950i \(-0.580806\pi\)
−0.251143 + 0.967950i \(0.580806\pi\)
\(920\) −56.1268 −1.85044
\(921\) 25.1761 0.829579
\(922\) −56.3243 −1.85494
\(923\) 2.43047 0.0799999
\(924\) −1.01405 −0.0333598
\(925\) −0.510376 −0.0167811
\(926\) −24.3004 −0.798562
\(927\) 37.4301 1.22937
\(928\) 5.69695 0.187012
\(929\) −47.7928 −1.56803 −0.784015 0.620742i \(-0.786832\pi\)
−0.784015 + 0.620742i \(0.786832\pi\)
\(930\) 77.4090 2.53834
\(931\) −26.2369 −0.859881
\(932\) −0.519839 −0.0170279
\(933\) 61.7111 2.02033
\(934\) 13.5454 0.443219
\(935\) 20.8527 0.681958
\(936\) 9.23528 0.301865
\(937\) −9.48310 −0.309799 −0.154900 0.987930i \(-0.549505\pi\)
−0.154900 + 0.987930i \(0.549505\pi\)
\(938\) 3.13669 0.102416
\(939\) −28.9262 −0.943970
\(940\) −2.17580 −0.0709668
\(941\) −4.95823 −0.161634 −0.0808168 0.996729i \(-0.525753\pi\)
−0.0808168 + 0.996729i \(0.525753\pi\)
\(942\) 25.6377 0.835323
\(943\) −0.925843 −0.0301496
\(944\) 23.8917 0.777607
\(945\) −1.31455 −0.0427623
\(946\) −2.69182 −0.0875186
\(947\) 15.6500 0.508558 0.254279 0.967131i \(-0.418162\pi\)
0.254279 + 0.967131i \(0.418162\pi\)
\(948\) −1.57284 −0.0510833
\(949\) −11.5757 −0.375763
\(950\) −0.605038 −0.0196300
\(951\) 22.2225 0.720615
\(952\) 11.4189 0.370088
\(953\) −11.1551 −0.361351 −0.180675 0.983543i \(-0.557828\pi\)
−0.180675 + 0.983543i \(0.557828\pi\)
\(954\) −20.6249 −0.667756
\(955\) −30.0602 −0.972724
\(956\) 1.36024 0.0439932
\(957\) 58.3893 1.88746
\(958\) 9.70358 0.313508
\(959\) 20.6565 0.667033
\(960\) −40.6411 −1.31168
\(961\) 64.7877 2.08993
\(962\) 10.4426 0.336684
\(963\) 22.5343 0.726158
\(964\) −1.51436 −0.0487741
\(965\) −49.5392 −1.59472
\(966\) 40.5044 1.30321
\(967\) 0.462563 0.0148750 0.00743752 0.999972i \(-0.497633\pi\)
0.00743752 + 0.999972i \(0.497633\pi\)
\(968\) −8.35165 −0.268432
\(969\) −38.5162 −1.23732
\(970\) −37.8561 −1.21548
\(971\) −2.43944 −0.0782854 −0.0391427 0.999234i \(-0.512463\pi\)
−0.0391427 + 0.999234i \(0.512463\pi\)
\(972\) −2.53603 −0.0813431
\(973\) 5.57648 0.178774
\(974\) −15.5625 −0.498655
\(975\) 0.246776 0.00790314
\(976\) −27.1189 −0.868056
\(977\) −47.8043 −1.52939 −0.764697 0.644390i \(-0.777111\pi\)
−0.764697 + 0.644390i \(0.777111\pi\)
\(978\) 30.1553 0.964261
\(979\) 44.9475 1.43653
\(980\) 1.42519 0.0455262
\(981\) −42.1353 −1.34528
\(982\) −23.5420 −0.751257
\(983\) −20.6062 −0.657236 −0.328618 0.944463i \(-0.606583\pi\)
−0.328618 + 0.944463i \(0.606583\pi\)
\(984\) −0.672868 −0.0214502
\(985\) −28.7966 −0.917535
\(986\) 40.9938 1.30551
\(987\) −25.1844 −0.801628
\(988\) 0.686259 0.0218328
\(989\) 5.96039 0.189529
\(990\) 25.9982 0.826278
\(991\) −35.4600 −1.12642 −0.563212 0.826312i \(-0.690435\pi\)
−0.563212 + 0.826312i \(0.690435\pi\)
\(992\) 6.49027 0.206066
\(993\) 39.3277 1.24803
\(994\) 3.74666 0.118837
\(995\) 14.5214 0.460358
\(996\) 1.76928 0.0560618
\(997\) 59.7846 1.89340 0.946698 0.322123i \(-0.104396\pi\)
0.946698 + 0.322123i \(0.104396\pi\)
\(998\) 33.7214 1.06743
\(999\) 2.74302 0.0867852
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 \(a_p\))