Properties

Label 619.2.a.b.1.4
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 1.4
Character \(\chi\) = 619.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.98324 q^{2} -1.72419 q^{3} +1.93325 q^{4} -1.05779 q^{5} +3.41948 q^{6} +3.75491 q^{7} +0.132389 q^{8} -0.0271814 q^{9} +O(q^{10})\) \(q-1.98324 q^{2} -1.72419 q^{3} +1.93325 q^{4} -1.05779 q^{5} +3.41948 q^{6} +3.75491 q^{7} +0.132389 q^{8} -0.0271814 q^{9} +2.09786 q^{10} +6.08342 q^{11} -3.33328 q^{12} -6.72402 q^{13} -7.44689 q^{14} +1.82383 q^{15} -4.12905 q^{16} -5.23542 q^{17} +0.0539073 q^{18} -0.354999 q^{19} -2.04497 q^{20} -6.47416 q^{21} -12.0649 q^{22} +6.00028 q^{23} -0.228263 q^{24} -3.88108 q^{25} +13.3354 q^{26} +5.21942 q^{27} +7.25916 q^{28} +6.90103 q^{29} -3.61709 q^{30} -5.33395 q^{31} +7.92413 q^{32} -10.4889 q^{33} +10.3831 q^{34} -3.97191 q^{35} -0.0525484 q^{36} +5.05059 q^{37} +0.704048 q^{38} +11.5935 q^{39} -0.140040 q^{40} +9.63715 q^{41} +12.8398 q^{42} -0.0907075 q^{43} +11.7607 q^{44} +0.0287523 q^{45} -11.9000 q^{46} -4.97845 q^{47} +7.11925 q^{48} +7.09934 q^{49} +7.69711 q^{50} +9.02684 q^{51} -12.9992 q^{52} -6.61252 q^{53} -10.3514 q^{54} -6.43498 q^{55} +0.497107 q^{56} +0.612084 q^{57} -13.6864 q^{58} +6.12048 q^{59} +3.52591 q^{60} +1.72186 q^{61} +10.5785 q^{62} -0.102064 q^{63} -7.45736 q^{64} +7.11261 q^{65} +20.8021 q^{66} +11.6947 q^{67} -10.1214 q^{68} -10.3456 q^{69} +7.87726 q^{70} +10.5001 q^{71} -0.00359851 q^{72} -5.79254 q^{73} -10.0165 q^{74} +6.69170 q^{75} -0.686300 q^{76} +22.8427 q^{77} -22.9926 q^{78} +12.9226 q^{79} +4.36768 q^{80} -8.91772 q^{81} -19.1128 q^{82} +0.184214 q^{83} -12.5162 q^{84} +5.53798 q^{85} +0.179895 q^{86} -11.8987 q^{87} +0.805375 q^{88} -7.11052 q^{89} -0.0570227 q^{90} -25.2481 q^{91} +11.6000 q^{92} +9.19672 q^{93} +9.87346 q^{94} +0.375514 q^{95} -13.6627 q^{96} +13.5999 q^{97} -14.0797 q^{98} -0.165356 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + O(q^{10}) \) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + 5q^{10} + 23q^{11} - 6q^{12} + 9q^{13} + 7q^{14} - 2q^{15} + 35q^{16} + 4q^{17} + 10q^{18} - q^{19} + 29q^{20} + 30q^{21} + 4q^{23} + 4q^{24} + 35q^{25} + q^{26} - 5q^{27} - 13q^{28} + 90q^{29} - 31q^{30} + 2q^{31} + 43q^{32} - 6q^{33} - 9q^{34} + 9q^{35} + 33q^{36} + 19q^{37} + 5q^{38} + 32q^{39} - 12q^{40} + 59q^{41} - 25q^{42} - 4q^{43} + 52q^{44} + 30q^{45} - q^{46} + 4q^{47} - 44q^{48} + 30q^{49} + 31q^{50} - 12q^{52} + 34q^{53} - 28q^{54} - 17q^{55} + 2q^{56} - 8q^{57} + 6q^{58} + 13q^{59} - 64q^{60} + 16q^{61} + 28q^{62} - 40q^{63} + 37q^{64} + 31q^{65} - 59q^{66} - 11q^{67} - 52q^{68} + 6q^{69} - 40q^{70} + 42q^{71} + 6q^{72} - 4q^{73} + 16q^{74} - 52q^{75} - 42q^{76} + 29q^{77} - 56q^{78} + 3q^{79} + 21q^{80} + 30q^{81} - 43q^{82} - 11q^{83} - 36q^{84} + 19q^{85} - 11q^{86} - 20q^{87} - 47q^{88} + 58q^{89} - 33q^{90} - 39q^{91} - 7q^{92} - 15q^{93} - 46q^{94} + 23q^{95} - 70q^{96} - 9q^{97} - 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.98324 −1.40236 −0.701182 0.712983i \(-0.747344\pi\)
−0.701182 + 0.712983i \(0.747344\pi\)
\(3\) −1.72419 −0.995459 −0.497730 0.867332i \(-0.665833\pi\)
−0.497730 + 0.867332i \(0.665833\pi\)
\(4\) 1.93325 0.966623
\(5\) −1.05779 −0.473059 −0.236529 0.971624i \(-0.576010\pi\)
−0.236529 + 0.971624i \(0.576010\pi\)
\(6\) 3.41948 1.39600
\(7\) 3.75491 1.41922 0.709611 0.704594i \(-0.248871\pi\)
0.709611 + 0.704594i \(0.248871\pi\)
\(8\) 0.132389 0.0468064
\(9\) −0.0271814 −0.00906047
\(10\) 2.09786 0.663400
\(11\) 6.08342 1.83422 0.917109 0.398636i \(-0.130516\pi\)
0.917109 + 0.398636i \(0.130516\pi\)
\(12\) −3.33328 −0.962234
\(13\) −6.72402 −1.86491 −0.932454 0.361288i \(-0.882337\pi\)
−0.932454 + 0.361288i \(0.882337\pi\)
\(14\) −7.44689 −1.99027
\(15\) 1.82383 0.470911
\(16\) −4.12905 −1.03226
\(17\) −5.23542 −1.26978 −0.634888 0.772604i \(-0.718954\pi\)
−0.634888 + 0.772604i \(0.718954\pi\)
\(18\) 0.0539073 0.0127061
\(19\) −0.354999 −0.0814423 −0.0407211 0.999171i \(-0.512966\pi\)
−0.0407211 + 0.999171i \(0.512966\pi\)
\(20\) −2.04497 −0.457270
\(21\) −6.47416 −1.41278
\(22\) −12.0649 −2.57224
\(23\) 6.00028 1.25115 0.625573 0.780166i \(-0.284865\pi\)
0.625573 + 0.780166i \(0.284865\pi\)
\(24\) −0.228263 −0.0465939
\(25\) −3.88108 −0.776215
\(26\) 13.3354 2.61528
\(27\) 5.21942 1.00448
\(28\) 7.25916 1.37185
\(29\) 6.90103 1.28149 0.640745 0.767754i \(-0.278626\pi\)
0.640745 + 0.767754i \(0.278626\pi\)
\(30\) −3.61709 −0.660388
\(31\) −5.33395 −0.958005 −0.479003 0.877814i \(-0.659002\pi\)
−0.479003 + 0.877814i \(0.659002\pi\)
\(32\) 7.92413 1.40080
\(33\) −10.4889 −1.82589
\(34\) 10.3831 1.78069
\(35\) −3.97191 −0.671375
\(36\) −0.0525484 −0.00875806
\(37\) 5.05059 0.830311 0.415156 0.909750i \(-0.363727\pi\)
0.415156 + 0.909750i \(0.363727\pi\)
\(38\) 0.704048 0.114212
\(39\) 11.5935 1.85644
\(40\) −0.140040 −0.0221422
\(41\) 9.63715 1.50507 0.752535 0.658552i \(-0.228831\pi\)
0.752535 + 0.658552i \(0.228831\pi\)
\(42\) 12.8398 1.98123
\(43\) −0.0907075 −0.0138328 −0.00691638 0.999976i \(-0.502202\pi\)
−0.00691638 + 0.999976i \(0.502202\pi\)
\(44\) 11.7607 1.77300
\(45\) 0.0287523 0.00428614
\(46\) −11.9000 −1.75456
\(47\) −4.97845 −0.726181 −0.363091 0.931754i \(-0.618278\pi\)
−0.363091 + 0.931754i \(0.618278\pi\)
\(48\) 7.11925 1.02758
\(49\) 7.09934 1.01419
\(50\) 7.69711 1.08854
\(51\) 9.02684 1.26401
\(52\) −12.9992 −1.80266
\(53\) −6.61252 −0.908300 −0.454150 0.890925i \(-0.650057\pi\)
−0.454150 + 0.890925i \(0.650057\pi\)
\(54\) −10.3514 −1.40864
\(55\) −6.43498 −0.867693
\(56\) 0.497107 0.0664287
\(57\) 0.612084 0.0810725
\(58\) −13.6864 −1.79711
\(59\) 6.12048 0.796819 0.398409 0.917208i \(-0.369562\pi\)
0.398409 + 0.917208i \(0.369562\pi\)
\(60\) 3.52591 0.455193
\(61\) 1.72186 0.220462 0.110231 0.993906i \(-0.464841\pi\)
0.110231 + 0.993906i \(0.464841\pi\)
\(62\) 10.5785 1.34347
\(63\) −0.102064 −0.0128588
\(64\) −7.45736 −0.932170
\(65\) 7.11261 0.882211
\(66\) 20.8021 2.56056
\(67\) 11.6947 1.42873 0.714367 0.699771i \(-0.246715\pi\)
0.714367 + 0.699771i \(0.246715\pi\)
\(68\) −10.1214 −1.22739
\(69\) −10.3456 −1.24546
\(70\) 7.87726 0.941512
\(71\) 10.5001 1.24613 0.623066 0.782169i \(-0.285887\pi\)
0.623066 + 0.782169i \(0.285887\pi\)
\(72\) −0.00359851 −0.000424089 0
\(73\) −5.79254 −0.677965 −0.338983 0.940793i \(-0.610083\pi\)
−0.338983 + 0.940793i \(0.610083\pi\)
\(74\) −10.0165 −1.16440
\(75\) 6.69170 0.772691
\(76\) −0.686300 −0.0787240
\(77\) 22.8427 2.60316
\(78\) −22.9926 −2.60340
\(79\) 12.9226 1.45391 0.726953 0.686687i \(-0.240936\pi\)
0.726953 + 0.686687i \(0.240936\pi\)
\(80\) 4.36768 0.488321
\(81\) −8.91772 −0.990857
\(82\) −19.1128 −2.11065
\(83\) 0.184214 0.0202201 0.0101101 0.999949i \(-0.496782\pi\)
0.0101101 + 0.999949i \(0.496782\pi\)
\(84\) −12.5162 −1.36562
\(85\) 5.53798 0.600678
\(86\) 0.179895 0.0193986
\(87\) −11.8987 −1.27567
\(88\) 0.805375 0.0858533
\(89\) −7.11052 −0.753714 −0.376857 0.926271i \(-0.622995\pi\)
−0.376857 + 0.926271i \(0.622995\pi\)
\(90\) −0.0570227 −0.00601072
\(91\) −25.2481 −2.64672
\(92\) 11.6000 1.20939
\(93\) 9.19672 0.953655
\(94\) 9.87346 1.01837
\(95\) 0.375514 0.0385270
\(96\) −13.6627 −1.39444
\(97\) 13.5999 1.38086 0.690432 0.723398i \(-0.257421\pi\)
0.690432 + 0.723398i \(0.257421\pi\)
\(98\) −14.0797 −1.42227
\(99\) −0.165356 −0.0166189
\(100\) −7.50308 −0.750308
\(101\) 13.8730 1.38041 0.690206 0.723613i \(-0.257520\pi\)
0.690206 + 0.723613i \(0.257520\pi\)
\(102\) −17.9024 −1.77260
\(103\) 5.85475 0.576886 0.288443 0.957497i \(-0.406862\pi\)
0.288443 + 0.957497i \(0.406862\pi\)
\(104\) −0.890184 −0.0872897
\(105\) 6.84831 0.668327
\(106\) 13.1142 1.27377
\(107\) 9.98693 0.965473 0.482737 0.875766i \(-0.339643\pi\)
0.482737 + 0.875766i \(0.339643\pi\)
\(108\) 10.0904 0.970952
\(109\) −4.85404 −0.464933 −0.232466 0.972604i \(-0.574680\pi\)
−0.232466 + 0.972604i \(0.574680\pi\)
\(110\) 12.7621 1.21682
\(111\) −8.70815 −0.826541
\(112\) −15.5042 −1.46501
\(113\) −3.36631 −0.316675 −0.158338 0.987385i \(-0.550613\pi\)
−0.158338 + 0.987385i \(0.550613\pi\)
\(114\) −1.21391 −0.113693
\(115\) −6.34705 −0.591865
\(116\) 13.3414 1.23872
\(117\) 0.182769 0.0168970
\(118\) −12.1384 −1.11743
\(119\) −19.6585 −1.80209
\(120\) 0.241454 0.0220417
\(121\) 26.0079 2.36436
\(122\) −3.41486 −0.309167
\(123\) −16.6162 −1.49824
\(124\) −10.3118 −0.926030
\(125\) 9.39433 0.840254
\(126\) 0.202417 0.0180327
\(127\) −7.17138 −0.636357 −0.318179 0.948031i \(-0.603071\pi\)
−0.318179 + 0.948031i \(0.603071\pi\)
\(128\) −1.05852 −0.0935608
\(129\) 0.156397 0.0137700
\(130\) −14.1060 −1.23718
\(131\) −8.12631 −0.709999 −0.354999 0.934867i \(-0.615519\pi\)
−0.354999 + 0.934867i \(0.615519\pi\)
\(132\) −20.2777 −1.76495
\(133\) −1.33299 −0.115585
\(134\) −23.1934 −2.00360
\(135\) −5.52106 −0.475177
\(136\) −0.693110 −0.0594337
\(137\) −7.70090 −0.657933 −0.328966 0.944342i \(-0.606700\pi\)
−0.328966 + 0.944342i \(0.606700\pi\)
\(138\) 20.5178 1.74659
\(139\) 10.6370 0.902221 0.451110 0.892468i \(-0.351028\pi\)
0.451110 + 0.892468i \(0.351028\pi\)
\(140\) −7.67868 −0.648967
\(141\) 8.58377 0.722884
\(142\) −20.8242 −1.74753
\(143\) −40.9050 −3.42065
\(144\) 0.112233 0.00935279
\(145\) −7.29985 −0.606220
\(146\) 11.4880 0.950754
\(147\) −12.2406 −1.00959
\(148\) 9.76403 0.802598
\(149\) 1.61152 0.132021 0.0660105 0.997819i \(-0.478973\pi\)
0.0660105 + 0.997819i \(0.478973\pi\)
\(150\) −13.2713 −1.08359
\(151\) 19.9654 1.62476 0.812381 0.583127i \(-0.198171\pi\)
0.812381 + 0.583127i \(0.198171\pi\)
\(152\) −0.0469978 −0.00381202
\(153\) 0.142306 0.0115048
\(154\) −45.3025 −3.65058
\(155\) 5.64220 0.453193
\(156\) 22.4130 1.79448
\(157\) 1.54108 0.122991 0.0614956 0.998107i \(-0.480413\pi\)
0.0614956 + 0.998107i \(0.480413\pi\)
\(158\) −25.6286 −2.03891
\(159\) 11.4012 0.904176
\(160\) −8.38207 −0.662661
\(161\) 22.5305 1.77565
\(162\) 17.6860 1.38954
\(163\) −3.56264 −0.279048 −0.139524 0.990219i \(-0.544557\pi\)
−0.139524 + 0.990219i \(0.544557\pi\)
\(164\) 18.6310 1.45484
\(165\) 11.0951 0.863753
\(166\) −0.365341 −0.0283559
\(167\) −1.11339 −0.0861566 −0.0430783 0.999072i \(-0.513716\pi\)
−0.0430783 + 0.999072i \(0.513716\pi\)
\(168\) −0.857106 −0.0661271
\(169\) 32.2125 2.47788
\(170\) −10.9832 −0.842369
\(171\) 0.00964937 0.000737906 0
\(172\) −0.175360 −0.0133711
\(173\) 2.42857 0.184641 0.0923203 0.995729i \(-0.470572\pi\)
0.0923203 + 0.995729i \(0.470572\pi\)
\(174\) 23.5979 1.78895
\(175\) −14.5731 −1.10162
\(176\) −25.1187 −1.89340
\(177\) −10.5528 −0.793201
\(178\) 14.1019 1.05698
\(179\) 20.2117 1.51069 0.755346 0.655326i \(-0.227469\pi\)
0.755346 + 0.655326i \(0.227469\pi\)
\(180\) 0.0555852 0.00414308
\(181\) 14.7095 1.09335 0.546676 0.837345i \(-0.315893\pi\)
0.546676 + 0.837345i \(0.315893\pi\)
\(182\) 50.0731 3.71166
\(183\) −2.96881 −0.219461
\(184\) 0.794369 0.0585617
\(185\) −5.34247 −0.392786
\(186\) −18.2393 −1.33737
\(187\) −31.8492 −2.32905
\(188\) −9.62457 −0.701944
\(189\) 19.5985 1.42558
\(190\) −0.744736 −0.0540288
\(191\) −16.9898 −1.22934 −0.614670 0.788784i \(-0.710711\pi\)
−0.614670 + 0.788784i \(0.710711\pi\)
\(192\) 12.8579 0.927937
\(193\) −24.0147 −1.72862 −0.864309 0.502961i \(-0.832244\pi\)
−0.864309 + 0.502961i \(0.832244\pi\)
\(194\) −26.9719 −1.93647
\(195\) −12.2635 −0.878205
\(196\) 13.7248 0.980341
\(197\) −3.25339 −0.231794 −0.115897 0.993261i \(-0.536974\pi\)
−0.115897 + 0.993261i \(0.536974\pi\)
\(198\) 0.327941 0.0233057
\(199\) −4.10164 −0.290758 −0.145379 0.989376i \(-0.546440\pi\)
−0.145379 + 0.989376i \(0.546440\pi\)
\(200\) −0.513810 −0.0363319
\(201\) −20.1638 −1.42225
\(202\) −27.5134 −1.93584
\(203\) 25.9128 1.81872
\(204\) 17.4511 1.22182
\(205\) −10.1941 −0.711986
\(206\) −11.6114 −0.809004
\(207\) −0.163096 −0.0113360
\(208\) 27.7638 1.92508
\(209\) −2.15960 −0.149383
\(210\) −13.5819 −0.937237
\(211\) 0.994439 0.0684600 0.0342300 0.999414i \(-0.489102\pi\)
0.0342300 + 0.999414i \(0.489102\pi\)
\(212\) −12.7836 −0.877984
\(213\) −18.1041 −1.24047
\(214\) −19.8065 −1.35394
\(215\) 0.0959496 0.00654371
\(216\) 0.690992 0.0470161
\(217\) −20.0285 −1.35962
\(218\) 9.62673 0.652005
\(219\) 9.98742 0.674887
\(220\) −12.4404 −0.838732
\(221\) 35.2031 2.36802
\(222\) 17.2704 1.15911
\(223\) 6.42942 0.430546 0.215273 0.976554i \(-0.430936\pi\)
0.215273 + 0.976554i \(0.430936\pi\)
\(224\) 29.7544 1.98805
\(225\) 0.105493 0.00703288
\(226\) 6.67620 0.444094
\(227\) 3.97251 0.263665 0.131832 0.991272i \(-0.457914\pi\)
0.131832 + 0.991272i \(0.457914\pi\)
\(228\) 1.18331 0.0783665
\(229\) −6.23389 −0.411947 −0.205974 0.978558i \(-0.566036\pi\)
−0.205974 + 0.978558i \(0.566036\pi\)
\(230\) 12.5877 0.830010
\(231\) −39.3850 −2.59134
\(232\) 0.913618 0.0599820
\(233\) 9.33323 0.611440 0.305720 0.952121i \(-0.401103\pi\)
0.305720 + 0.952121i \(0.401103\pi\)
\(234\) −0.362474 −0.0236957
\(235\) 5.26616 0.343526
\(236\) 11.8324 0.770223
\(237\) −22.2810 −1.44731
\(238\) 38.9876 2.52719
\(239\) 5.73841 0.371187 0.185594 0.982627i \(-0.440579\pi\)
0.185594 + 0.982627i \(0.440579\pi\)
\(240\) −7.53069 −0.486104
\(241\) −19.6426 −1.26529 −0.632644 0.774443i \(-0.718030\pi\)
−0.632644 + 0.774443i \(0.718030\pi\)
\(242\) −51.5800 −3.31569
\(243\) −0.282469 −0.0181204
\(244\) 3.32878 0.213103
\(245\) −7.50962 −0.479772
\(246\) 32.9540 2.10107
\(247\) 2.38702 0.151882
\(248\) −0.706154 −0.0448408
\(249\) −0.317619 −0.0201283
\(250\) −18.6312 −1.17834
\(251\) 7.09344 0.447734 0.223867 0.974620i \(-0.428132\pi\)
0.223867 + 0.974620i \(0.428132\pi\)
\(252\) −0.197314 −0.0124296
\(253\) 36.5022 2.29487
\(254\) 14.2226 0.892404
\(255\) −9.54851 −0.597951
\(256\) 17.0140 1.06338
\(257\) 19.4959 1.21612 0.608061 0.793890i \(-0.291948\pi\)
0.608061 + 0.793890i \(0.291948\pi\)
\(258\) −0.310172 −0.0193105
\(259\) 18.9645 1.17840
\(260\) 13.7504 0.852766
\(261\) −0.187580 −0.0116109
\(262\) 16.1164 0.995676
\(263\) 6.79551 0.419029 0.209514 0.977806i \(-0.432812\pi\)
0.209514 + 0.977806i \(0.432812\pi\)
\(264\) −1.38862 −0.0854634
\(265\) 6.99467 0.429679
\(266\) 2.64364 0.162092
\(267\) 12.2599 0.750292
\(268\) 22.6087 1.38105
\(269\) 18.6646 1.13800 0.569001 0.822337i \(-0.307330\pi\)
0.569001 + 0.822337i \(0.307330\pi\)
\(270\) 10.9496 0.666371
\(271\) −18.9261 −1.14968 −0.574840 0.818266i \(-0.694936\pi\)
−0.574840 + 0.818266i \(0.694936\pi\)
\(272\) 21.6173 1.31074
\(273\) 43.5324 2.63470
\(274\) 15.2727 0.922661
\(275\) −23.6102 −1.42375
\(276\) −20.0006 −1.20390
\(277\) −17.9961 −1.08128 −0.540640 0.841254i \(-0.681818\pi\)
−0.540640 + 0.841254i \(0.681818\pi\)
\(278\) −21.0958 −1.26524
\(279\) 0.144984 0.00867998
\(280\) −0.525836 −0.0314247
\(281\) −28.9297 −1.72580 −0.862900 0.505374i \(-0.831354\pi\)
−0.862900 + 0.505374i \(0.831354\pi\)
\(282\) −17.0237 −1.01375
\(283\) −28.9941 −1.72352 −0.861761 0.507315i \(-0.830638\pi\)
−0.861761 + 0.507315i \(0.830638\pi\)
\(284\) 20.2993 1.20454
\(285\) −0.647457 −0.0383520
\(286\) 81.1245 4.79699
\(287\) 36.1866 2.13603
\(288\) −0.215389 −0.0126919
\(289\) 10.4096 0.612330
\(290\) 14.4774 0.850141
\(291\) −23.4488 −1.37459
\(292\) −11.1984 −0.655337
\(293\) 9.64668 0.563565 0.281782 0.959478i \(-0.409074\pi\)
0.281782 + 0.959478i \(0.409074\pi\)
\(294\) 24.2760 1.41581
\(295\) −6.47419 −0.376942
\(296\) 0.668640 0.0388639
\(297\) 31.7519 1.84243
\(298\) −3.19604 −0.185142
\(299\) −40.3460 −2.33327
\(300\) 12.9367 0.746901
\(301\) −0.340598 −0.0196318
\(302\) −39.5962 −2.27851
\(303\) −23.9196 −1.37414
\(304\) 1.46581 0.0840698
\(305\) −1.82137 −0.104291
\(306\) −0.282227 −0.0161339
\(307\) 16.4730 0.940166 0.470083 0.882622i \(-0.344224\pi\)
0.470083 + 0.882622i \(0.344224\pi\)
\(308\) 44.1605 2.51628
\(309\) −10.0947 −0.574267
\(310\) −11.1899 −0.635541
\(311\) 24.5521 1.39222 0.696110 0.717935i \(-0.254913\pi\)
0.696110 + 0.717935i \(0.254913\pi\)
\(312\) 1.53484 0.0868934
\(313\) −13.2228 −0.747395 −0.373698 0.927551i \(-0.621910\pi\)
−0.373698 + 0.927551i \(0.621910\pi\)
\(314\) −3.05633 −0.172478
\(315\) 0.107962 0.00608298
\(316\) 24.9826 1.40538
\(317\) 11.4591 0.643607 0.321803 0.946807i \(-0.395711\pi\)
0.321803 + 0.946807i \(0.395711\pi\)
\(318\) −22.6114 −1.26798
\(319\) 41.9819 2.35053
\(320\) 7.88833 0.440971
\(321\) −17.2193 −0.961089
\(322\) −44.6835 −2.49011
\(323\) 1.85857 0.103413
\(324\) −17.2401 −0.957786
\(325\) 26.0965 1.44757
\(326\) 7.06558 0.391326
\(327\) 8.36927 0.462822
\(328\) 1.27585 0.0704470
\(329\) −18.6936 −1.03061
\(330\) −22.0043 −1.21130
\(331\) 26.1510 1.43739 0.718694 0.695326i \(-0.244740\pi\)
0.718694 + 0.695326i \(0.244740\pi\)
\(332\) 0.356131 0.0195452
\(333\) −0.137282 −0.00752302
\(334\) 2.20812 0.120823
\(335\) −12.3705 −0.675875
\(336\) 26.7322 1.45836
\(337\) 15.4634 0.842346 0.421173 0.906980i \(-0.361619\pi\)
0.421173 + 0.906980i \(0.361619\pi\)
\(338\) −63.8851 −3.47489
\(339\) 5.80414 0.315237
\(340\) 10.7063 0.580630
\(341\) −32.4486 −1.75719
\(342\) −0.0191370 −0.00103481
\(343\) 0.373019 0.0201411
\(344\) −0.0120086 −0.000647462 0
\(345\) 10.9435 0.589178
\(346\) −4.81644 −0.258933
\(347\) 33.8444 1.81686 0.908432 0.418032i \(-0.137280\pi\)
0.908432 + 0.418032i \(0.137280\pi\)
\(348\) −23.0031 −1.23309
\(349\) 26.7836 1.43369 0.716847 0.697230i \(-0.245584\pi\)
0.716847 + 0.697230i \(0.245584\pi\)
\(350\) 28.9020 1.54487
\(351\) −35.0955 −1.87326
\(352\) 48.2058 2.56938
\(353\) −24.0208 −1.27850 −0.639248 0.769000i \(-0.720754\pi\)
−0.639248 + 0.769000i \(0.720754\pi\)
\(354\) 20.9288 1.11236
\(355\) −11.1069 −0.589494
\(356\) −13.7464 −0.728557
\(357\) 33.8950 1.79391
\(358\) −40.0846 −2.11854
\(359\) −32.1070 −1.69454 −0.847271 0.531160i \(-0.821756\pi\)
−0.847271 + 0.531160i \(0.821756\pi\)
\(360\) 0.00380647 0.000200619 0
\(361\) −18.8740 −0.993367
\(362\) −29.1726 −1.53328
\(363\) −44.8425 −2.35362
\(364\) −48.8108 −2.55838
\(365\) 6.12730 0.320717
\(366\) 5.88786 0.307764
\(367\) −15.2200 −0.794479 −0.397240 0.917715i \(-0.630032\pi\)
−0.397240 + 0.917715i \(0.630032\pi\)
\(368\) −24.7755 −1.29151
\(369\) −0.261951 −0.0136366
\(370\) 10.5954 0.550829
\(371\) −24.8294 −1.28908
\(372\) 17.7795 0.921825
\(373\) −21.1126 −1.09317 −0.546585 0.837403i \(-0.684073\pi\)
−0.546585 + 0.837403i \(0.684073\pi\)
\(374\) 63.1647 3.26617
\(375\) −16.1976 −0.836439
\(376\) −0.659090 −0.0339900
\(377\) −46.4027 −2.38986
\(378\) −38.8685 −1.99918
\(379\) −10.1114 −0.519390 −0.259695 0.965691i \(-0.583622\pi\)
−0.259695 + 0.965691i \(0.583622\pi\)
\(380\) 0.725962 0.0372411
\(381\) 12.3648 0.633468
\(382\) 33.6949 1.72398
\(383\) −14.6121 −0.746644 −0.373322 0.927702i \(-0.621781\pi\)
−0.373322 + 0.927702i \(0.621781\pi\)
\(384\) 1.82508 0.0931359
\(385\) −24.1628 −1.23145
\(386\) 47.6270 2.42415
\(387\) 0.00246556 0.000125331 0
\(388\) 26.2920 1.33477
\(389\) 0.579277 0.0293705 0.0146853 0.999892i \(-0.495325\pi\)
0.0146853 + 0.999892i \(0.495325\pi\)
\(390\) 24.3214 1.23156
\(391\) −31.4140 −1.58867
\(392\) 0.939872 0.0474707
\(393\) 14.0113 0.706775
\(394\) 6.45225 0.325060
\(395\) −13.6694 −0.687783
\(396\) −0.319674 −0.0160642
\(397\) −31.2076 −1.56626 −0.783132 0.621855i \(-0.786379\pi\)
−0.783132 + 0.621855i \(0.786379\pi\)
\(398\) 8.13455 0.407748
\(399\) 2.29832 0.115060
\(400\) 16.0252 0.801258
\(401\) −10.9396 −0.546299 −0.273150 0.961972i \(-0.588065\pi\)
−0.273150 + 0.961972i \(0.588065\pi\)
\(402\) 39.9897 1.99451
\(403\) 35.8656 1.78659
\(404\) 26.8198 1.33434
\(405\) 9.43308 0.468734
\(406\) −51.3912 −2.55050
\(407\) 30.7248 1.52297
\(408\) 1.19505 0.0591638
\(409\) −5.13360 −0.253840 −0.126920 0.991913i \(-0.540509\pi\)
−0.126920 + 0.991913i \(0.540509\pi\)
\(410\) 20.2173 0.998464
\(411\) 13.2778 0.654945
\(412\) 11.3187 0.557631
\(413\) 22.9818 1.13086
\(414\) 0.323459 0.0158972
\(415\) −0.194860 −0.00956530
\(416\) −53.2820 −2.61237
\(417\) −18.3402 −0.898124
\(418\) 4.28302 0.209489
\(419\) 2.80692 0.137127 0.0685636 0.997647i \(-0.478158\pi\)
0.0685636 + 0.997647i \(0.478158\pi\)
\(420\) 13.2395 0.646020
\(421\) −22.1099 −1.07757 −0.538785 0.842443i \(-0.681116\pi\)
−0.538785 + 0.842443i \(0.681116\pi\)
\(422\) −1.97221 −0.0960059
\(423\) 0.135321 0.00657955
\(424\) −0.875423 −0.0425143
\(425\) 20.3191 0.985619
\(426\) 35.9049 1.73960
\(427\) 6.46543 0.312884
\(428\) 19.3072 0.933249
\(429\) 70.5279 3.40512
\(430\) −0.190291 −0.00917666
\(431\) 2.65789 0.128026 0.0640130 0.997949i \(-0.479610\pi\)
0.0640130 + 0.997949i \(0.479610\pi\)
\(432\) −21.5513 −1.03689
\(433\) 12.7709 0.613732 0.306866 0.951753i \(-0.400720\pi\)
0.306866 + 0.951753i \(0.400720\pi\)
\(434\) 39.7213 1.90668
\(435\) 12.5863 0.603467
\(436\) −9.38406 −0.449415
\(437\) −2.13009 −0.101896
\(438\) −19.8075 −0.946437
\(439\) −20.6371 −0.984954 −0.492477 0.870325i \(-0.663908\pi\)
−0.492477 + 0.870325i \(0.663908\pi\)
\(440\) −0.851919 −0.0406136
\(441\) −0.192970 −0.00918906
\(442\) −69.8162 −3.32082
\(443\) 18.9329 0.899529 0.449764 0.893147i \(-0.351508\pi\)
0.449764 + 0.893147i \(0.351508\pi\)
\(444\) −16.8350 −0.798954
\(445\) 7.52145 0.356551
\(446\) −12.7511 −0.603782
\(447\) −2.77857 −0.131422
\(448\) −28.0017 −1.32296
\(449\) −12.4002 −0.585203 −0.292602 0.956234i \(-0.594521\pi\)
−0.292602 + 0.956234i \(0.594521\pi\)
\(450\) −0.209218 −0.00986265
\(451\) 58.6268 2.76063
\(452\) −6.50790 −0.306106
\(453\) −34.4241 −1.61738
\(454\) −7.87845 −0.369754
\(455\) 26.7072 1.25205
\(456\) 0.0810329 0.00379471
\(457\) −31.1873 −1.45888 −0.729440 0.684045i \(-0.760219\pi\)
−0.729440 + 0.684045i \(0.760219\pi\)
\(458\) 12.3633 0.577700
\(459\) −27.3259 −1.27546
\(460\) −12.2704 −0.572111
\(461\) 34.4152 1.60288 0.801439 0.598077i \(-0.204068\pi\)
0.801439 + 0.598077i \(0.204068\pi\)
\(462\) 78.1100 3.63401
\(463\) 6.32091 0.293758 0.146879 0.989154i \(-0.453077\pi\)
0.146879 + 0.989154i \(0.453077\pi\)
\(464\) −28.4947 −1.32283
\(465\) −9.72821 −0.451135
\(466\) −18.5100 −0.857461
\(467\) −10.0959 −0.467185 −0.233592 0.972335i \(-0.575048\pi\)
−0.233592 + 0.972335i \(0.575048\pi\)
\(468\) 0.353337 0.0163330
\(469\) 43.9125 2.02769
\(470\) −10.4441 −0.481749
\(471\) −2.65710 −0.122433
\(472\) 0.810282 0.0372962
\(473\) −0.551811 −0.0253723
\(474\) 44.1886 2.02965
\(475\) 1.37778 0.0632167
\(476\) −38.0048 −1.74195
\(477\) 0.179738 0.00822963
\(478\) −11.3807 −0.520539
\(479\) 16.3802 0.748431 0.374216 0.927342i \(-0.377912\pi\)
0.374216 + 0.927342i \(0.377912\pi\)
\(480\) 14.4523 0.659652
\(481\) −33.9603 −1.54845
\(482\) 38.9559 1.77439
\(483\) −38.8468 −1.76759
\(484\) 50.2798 2.28544
\(485\) −14.3859 −0.653229
\(486\) 0.560204 0.0254114
\(487\) 15.6438 0.708887 0.354443 0.935077i \(-0.384670\pi\)
0.354443 + 0.935077i \(0.384670\pi\)
\(488\) 0.227955 0.0103190
\(489\) 6.14266 0.277781
\(490\) 14.8934 0.672815
\(491\) −25.0257 −1.12939 −0.564696 0.825299i \(-0.691007\pi\)
−0.564696 + 0.825299i \(0.691007\pi\)
\(492\) −32.1233 −1.44823
\(493\) −36.1298 −1.62720
\(494\) −4.73403 −0.212994
\(495\) 0.174912 0.00786171
\(496\) 22.0241 0.988913
\(497\) 39.4269 1.76854
\(498\) 0.629916 0.0282272
\(499\) −14.4100 −0.645081 −0.322541 0.946556i \(-0.604537\pi\)
−0.322541 + 0.946556i \(0.604537\pi\)
\(500\) 18.1615 0.812209
\(501\) 1.91969 0.0857654
\(502\) −14.0680 −0.627885
\(503\) 28.2401 1.25917 0.629583 0.776933i \(-0.283226\pi\)
0.629583 + 0.776933i \(0.283226\pi\)
\(504\) −0.0135121 −0.000601876 0
\(505\) −14.6747 −0.653015
\(506\) −72.3927 −3.21825
\(507\) −55.5403 −2.46663
\(508\) −13.8641 −0.615118
\(509\) 29.9612 1.32801 0.664003 0.747730i \(-0.268856\pi\)
0.664003 + 0.747730i \(0.268856\pi\)
\(510\) 18.9370 0.838545
\(511\) −21.7505 −0.962184
\(512\) −31.6259 −1.39768
\(513\) −1.85289 −0.0818070
\(514\) −38.6651 −1.70544
\(515\) −6.19311 −0.272901
\(516\) 0.302353 0.0133104
\(517\) −30.2860 −1.33198
\(518\) −37.6112 −1.65254
\(519\) −4.18730 −0.183802
\(520\) 0.941629 0.0412932
\(521\) −2.37228 −0.103931 −0.0519657 0.998649i \(-0.516549\pi\)
−0.0519657 + 0.998649i \(0.516549\pi\)
\(522\) 0.372016 0.0162827
\(523\) 10.0656 0.440137 0.220068 0.975484i \(-0.429372\pi\)
0.220068 + 0.975484i \(0.429372\pi\)
\(524\) −15.7102 −0.686301
\(525\) 25.1267 1.09662
\(526\) −13.4771 −0.587631
\(527\) 27.9254 1.21645
\(528\) 43.3094 1.88480
\(529\) 13.0034 0.565366
\(530\) −13.8721 −0.602566
\(531\) −0.166363 −0.00721955
\(532\) −2.57699 −0.111727
\(533\) −64.8004 −2.80682
\(534\) −24.3143 −1.05218
\(535\) −10.5641 −0.456726
\(536\) 1.54824 0.0668740
\(537\) −34.8487 −1.50383
\(538\) −37.0165 −1.59589
\(539\) 43.1882 1.86025
\(540\) −10.6736 −0.459318
\(541\) −12.6292 −0.542971 −0.271486 0.962443i \(-0.587515\pi\)
−0.271486 + 0.962443i \(0.587515\pi\)
\(542\) 37.5351 1.61227
\(543\) −25.3620 −1.08839
\(544\) −41.4861 −1.77870
\(545\) 5.13456 0.219941
\(546\) −86.3353 −3.69481
\(547\) 5.30868 0.226983 0.113491 0.993539i \(-0.463797\pi\)
0.113491 + 0.993539i \(0.463797\pi\)
\(548\) −14.8877 −0.635973
\(549\) −0.0468026 −0.00199749
\(550\) 46.8247 1.99661
\(551\) −2.44986 −0.104367
\(552\) −1.36964 −0.0582958
\(553\) 48.5232 2.06342
\(554\) 35.6906 1.51635
\(555\) 9.21141 0.391003
\(556\) 20.5640 0.872107
\(557\) −9.22500 −0.390876 −0.195438 0.980716i \(-0.562613\pi\)
−0.195438 + 0.980716i \(0.562613\pi\)
\(558\) −0.287539 −0.0121725
\(559\) 0.609919 0.0257968
\(560\) 16.4002 0.693036
\(561\) 54.9140 2.31847
\(562\) 57.3746 2.42020
\(563\) 28.4238 1.19792 0.598961 0.800778i \(-0.295581\pi\)
0.598961 + 0.800778i \(0.295581\pi\)
\(564\) 16.5945 0.698756
\(565\) 3.56085 0.149806
\(566\) 57.5023 2.41700
\(567\) −33.4852 −1.40625
\(568\) 1.39009 0.0583271
\(569\) −7.41846 −0.310998 −0.155499 0.987836i \(-0.549699\pi\)
−0.155499 + 0.987836i \(0.549699\pi\)
\(570\) 1.28406 0.0537835
\(571\) −16.7408 −0.700581 −0.350291 0.936641i \(-0.613917\pi\)
−0.350291 + 0.936641i \(0.613917\pi\)
\(572\) −79.0795 −3.30648
\(573\) 29.2936 1.22376
\(574\) −71.7668 −2.99549
\(575\) −23.2876 −0.971159
\(576\) 0.202702 0.00844590
\(577\) 9.51827 0.396251 0.198125 0.980177i \(-0.436515\pi\)
0.198125 + 0.980177i \(0.436515\pi\)
\(578\) −20.6448 −0.858709
\(579\) 41.4059 1.72077
\(580\) −14.1124 −0.585986
\(581\) 0.691707 0.0286968
\(582\) 46.5046 1.92768
\(583\) −40.2267 −1.66602
\(584\) −0.766866 −0.0317332
\(585\) −0.193331 −0.00799325
\(586\) −19.1317 −0.790323
\(587\) −43.0662 −1.77753 −0.888765 0.458362i \(-0.848436\pi\)
−0.888765 + 0.458362i \(0.848436\pi\)
\(588\) −23.6641 −0.975890
\(589\) 1.89354 0.0780221
\(590\) 12.8399 0.528610
\(591\) 5.60945 0.230742
\(592\) −20.8541 −0.857100
\(593\) 16.0330 0.658396 0.329198 0.944261i \(-0.393222\pi\)
0.329198 + 0.944261i \(0.393222\pi\)
\(594\) −62.9717 −2.58376
\(595\) 20.7946 0.852496
\(596\) 3.11547 0.127615
\(597\) 7.07200 0.289438
\(598\) 80.0159 3.27210
\(599\) −38.5861 −1.57659 −0.788293 0.615301i \(-0.789035\pi\)
−0.788293 + 0.615301i \(0.789035\pi\)
\(600\) 0.885905 0.0361669
\(601\) 7.61906 0.310788 0.155394 0.987853i \(-0.450335\pi\)
0.155394 + 0.987853i \(0.450335\pi\)
\(602\) 0.675489 0.0275309
\(603\) −0.317878 −0.0129450
\(604\) 38.5980 1.57053
\(605\) −27.5110 −1.11848
\(606\) 47.4383 1.92705
\(607\) −11.7127 −0.475402 −0.237701 0.971338i \(-0.576394\pi\)
−0.237701 + 0.971338i \(0.576394\pi\)
\(608\) −2.81305 −0.114084
\(609\) −44.6784 −1.81046
\(610\) 3.61221 0.146254
\(611\) 33.4752 1.35426
\(612\) 0.275113 0.0111208
\(613\) −19.9221 −0.804647 −0.402323 0.915498i \(-0.631797\pi\)
−0.402323 + 0.915498i \(0.631797\pi\)
\(614\) −32.6700 −1.31845
\(615\) 17.5765 0.708754
\(616\) 3.02411 0.121845
\(617\) 33.1161 1.33321 0.666603 0.745413i \(-0.267748\pi\)
0.666603 + 0.745413i \(0.267748\pi\)
\(618\) 20.0202 0.805331
\(619\) 1.00000 0.0401934
\(620\) 10.9078 0.438067
\(621\) 31.3180 1.25675
\(622\) −48.6927 −1.95240
\(623\) −26.6994 −1.06969
\(624\) −47.8700 −1.91633
\(625\) 9.46815 0.378726
\(626\) 26.2239 1.04812
\(627\) 3.72356 0.148705
\(628\) 2.97928 0.118886
\(629\) −26.4419 −1.05431
\(630\) −0.214115 −0.00853055
\(631\) −23.1947 −0.923364 −0.461682 0.887045i \(-0.652754\pi\)
−0.461682 + 0.887045i \(0.652754\pi\)
\(632\) 1.71081 0.0680522
\(633\) −1.71460 −0.0681492
\(634\) −22.7261 −0.902571
\(635\) 7.58583 0.301034
\(636\) 22.0414 0.873997
\(637\) −47.7361 −1.89137
\(638\) −83.2602 −3.29630
\(639\) −0.285408 −0.0112906
\(640\) 1.11969 0.0442597
\(641\) −37.7299 −1.49024 −0.745121 0.666930i \(-0.767608\pi\)
−0.745121 + 0.666930i \(0.767608\pi\)
\(642\) 34.1501 1.34780
\(643\) 30.6859 1.21013 0.605066 0.796175i \(-0.293147\pi\)
0.605066 + 0.796175i \(0.293147\pi\)
\(644\) 43.5570 1.71639
\(645\) −0.165435 −0.00651400
\(646\) −3.68599 −0.145023
\(647\) 16.7802 0.659697 0.329849 0.944034i \(-0.393002\pi\)
0.329849 + 0.944034i \(0.393002\pi\)
\(648\) −1.18060 −0.0463785
\(649\) 37.2334 1.46154
\(650\) −51.7556 −2.03002
\(651\) 34.5328 1.35345
\(652\) −6.88747 −0.269734
\(653\) −22.3619 −0.875087 −0.437544 0.899197i \(-0.644151\pi\)
−0.437544 + 0.899197i \(0.644151\pi\)
\(654\) −16.5983 −0.649044
\(655\) 8.59594 0.335871
\(656\) −39.7923 −1.55363
\(657\) 0.157449 0.00614269
\(658\) 37.0740 1.44529
\(659\) −18.9001 −0.736244 −0.368122 0.929777i \(-0.619999\pi\)
−0.368122 + 0.929777i \(0.619999\pi\)
\(660\) 21.4496 0.834924
\(661\) −3.11133 −0.121017 −0.0605084 0.998168i \(-0.519272\pi\)
−0.0605084 + 0.998168i \(0.519272\pi\)
\(662\) −51.8637 −2.01574
\(663\) −60.6967 −2.35726
\(664\) 0.0243878 0.000946432 0
\(665\) 1.41002 0.0546783
\(666\) 0.272264 0.0105500
\(667\) 41.4082 1.60333
\(668\) −2.15245 −0.0832809
\(669\) −11.0855 −0.428591
\(670\) 24.5338 0.947823
\(671\) 10.4748 0.404375
\(672\) −51.3021 −1.97902
\(673\) 2.56807 0.0989918 0.0494959 0.998774i \(-0.484239\pi\)
0.0494959 + 0.998774i \(0.484239\pi\)
\(674\) −30.6677 −1.18127
\(675\) −20.2570 −0.779692
\(676\) 62.2747 2.39518
\(677\) −22.1451 −0.851105 −0.425552 0.904934i \(-0.639920\pi\)
−0.425552 + 0.904934i \(0.639920\pi\)
\(678\) −11.5110 −0.442077
\(679\) 51.0665 1.95975
\(680\) 0.733166 0.0281156
\(681\) −6.84935 −0.262468
\(682\) 64.3534 2.46422
\(683\) 10.0367 0.384045 0.192023 0.981390i \(-0.438495\pi\)
0.192023 + 0.981390i \(0.438495\pi\)
\(684\) 0.0186546 0.000713277 0
\(685\) 8.14595 0.311241
\(686\) −0.739786 −0.0282452
\(687\) 10.7484 0.410077
\(688\) 0.374536 0.0142790
\(689\) 44.4628 1.69390
\(690\) −21.7036 −0.826242
\(691\) 46.8230 1.78123 0.890615 0.454759i \(-0.150275\pi\)
0.890615 + 0.454759i \(0.150275\pi\)
\(692\) 4.69502 0.178478
\(693\) −0.620896 −0.0235859
\(694\) −67.1217 −2.54790
\(695\) −11.2518 −0.426803
\(696\) −1.57525 −0.0597096
\(697\) −50.4545 −1.91110
\(698\) −53.1184 −2.01056
\(699\) −16.0922 −0.608664
\(700\) −28.1734 −1.06485
\(701\) −19.9414 −0.753178 −0.376589 0.926381i \(-0.622903\pi\)
−0.376589 + 0.926381i \(0.622903\pi\)
\(702\) 69.6029 2.62699
\(703\) −1.79295 −0.0676224
\(704\) −45.3662 −1.70980
\(705\) −9.07984 −0.341967
\(706\) 47.6390 1.79292
\(707\) 52.0917 1.95911
\(708\) −20.4013 −0.766726
\(709\) −24.8082 −0.931693 −0.465847 0.884865i \(-0.654250\pi\)
−0.465847 + 0.884865i \(0.654250\pi\)
\(710\) 22.0277 0.826685
\(711\) −0.351255 −0.0131731
\(712\) −0.941352 −0.0352787
\(713\) −32.0052 −1.19860
\(714\) −67.2219 −2.51572
\(715\) 43.2690 1.61817
\(716\) 39.0742 1.46027
\(717\) −9.89410 −0.369502
\(718\) 63.6759 2.37636
\(719\) 11.7629 0.438681 0.219341 0.975648i \(-0.429609\pi\)
0.219341 + 0.975648i \(0.429609\pi\)
\(720\) −0.118720 −0.00442442
\(721\) 21.9841 0.818730
\(722\) 37.4317 1.39306
\(723\) 33.8674 1.25954
\(724\) 28.4372 1.05686
\(725\) −26.7834 −0.994712
\(726\) 88.9336 3.30063
\(727\) 10.6858 0.396315 0.198158 0.980170i \(-0.436504\pi\)
0.198158 + 0.980170i \(0.436504\pi\)
\(728\) −3.34256 −0.123884
\(729\) 27.2402 1.00890
\(730\) −12.1519 −0.449762
\(731\) 0.474892 0.0175645
\(732\) −5.73944 −0.212136
\(733\) 7.03351 0.259789 0.129894 0.991528i \(-0.458536\pi\)
0.129894 + 0.991528i \(0.458536\pi\)
\(734\) 30.1850 1.11415
\(735\) 12.9480 0.477594
\(736\) 47.5470 1.75261
\(737\) 71.1437 2.62061
\(738\) 0.519513 0.0191235
\(739\) −31.3859 −1.15455 −0.577274 0.816550i \(-0.695884\pi\)
−0.577274 + 0.816550i \(0.695884\pi\)
\(740\) −10.3283 −0.379676
\(741\) −4.11567 −0.151193
\(742\) 49.2427 1.80776
\(743\) 11.7765 0.432037 0.216019 0.976389i \(-0.430693\pi\)
0.216019 + 0.976389i \(0.430693\pi\)
\(744\) 1.21754 0.0446372
\(745\) −1.70465 −0.0624537
\(746\) 41.8714 1.53302
\(747\) −0.00500720 −0.000183204 0
\(748\) −61.5724 −2.25131
\(749\) 37.5000 1.37022
\(750\) 32.1237 1.17299
\(751\) −39.3469 −1.43579 −0.717894 0.696152i \(-0.754894\pi\)
−0.717894 + 0.696152i \(0.754894\pi\)
\(752\) 20.5563 0.749610
\(753\) −12.2304 −0.445701
\(754\) 92.0278 3.35145
\(755\) −21.1192 −0.768608
\(756\) 37.8887 1.37800
\(757\) 34.7833 1.26422 0.632111 0.774878i \(-0.282189\pi\)
0.632111 + 0.774878i \(0.282189\pi\)
\(758\) 20.0534 0.728373
\(759\) −62.9366 −2.28445
\(760\) 0.0497138 0.00180331
\(761\) 15.7398 0.570568 0.285284 0.958443i \(-0.407912\pi\)
0.285284 + 0.958443i \(0.407912\pi\)
\(762\) −24.5224 −0.888352
\(763\) −18.2265 −0.659843
\(764\) −32.8455 −1.18831
\(765\) −0.150530 −0.00544243
\(766\) 28.9794 1.04707
\(767\) −41.1542 −1.48599
\(768\) −29.3353 −1.05855
\(769\) 21.2397 0.765924 0.382962 0.923764i \(-0.374904\pi\)
0.382962 + 0.923764i \(0.374904\pi\)
\(770\) 47.9206 1.72694
\(771\) −33.6146 −1.21060
\(772\) −46.4264 −1.67092
\(773\) 19.0417 0.684881 0.342441 0.939539i \(-0.388746\pi\)
0.342441 + 0.939539i \(0.388746\pi\)
\(774\) −0.00488980 −0.000175760 0
\(775\) 20.7015 0.743618
\(776\) 1.80048 0.0646333
\(777\) −32.6983 −1.17305
\(778\) −1.14885 −0.0411881
\(779\) −3.42117 −0.122576
\(780\) −23.7083 −0.848894
\(781\) 63.8765 2.28568
\(782\) 62.3015 2.22790
\(783\) 36.0194 1.28723
\(784\) −29.3135 −1.04691
\(785\) −1.63014 −0.0581821
\(786\) −27.7877 −0.991155
\(787\) 6.88251 0.245335 0.122668 0.992448i \(-0.460855\pi\)
0.122668 + 0.992448i \(0.460855\pi\)
\(788\) −6.28960 −0.224058
\(789\) −11.7167 −0.417126
\(790\) 27.1098 0.964522
\(791\) −12.6402 −0.449433
\(792\) −0.0218912 −0.000777871 0
\(793\) −11.5778 −0.411141
\(794\) 61.8922 2.19647
\(795\) −12.0601 −0.427728
\(796\) −7.92949 −0.281053
\(797\) −31.6062 −1.11955 −0.559774 0.828645i \(-0.689112\pi\)
−0.559774 + 0.828645i \(0.689112\pi\)
\(798\) −4.55812 −0.161356
\(799\) 26.0643 0.922087
\(800\) −30.7542 −1.08732
\(801\) 0.193274 0.00682901
\(802\) 21.6959 0.766110
\(803\) −35.2384 −1.24354
\(804\) −38.9817 −1.37478
\(805\) −23.8326 −0.839988
\(806\) −71.1301 −2.50545
\(807\) −32.1813 −1.13284
\(808\) 1.83662 0.0646121
\(809\) −3.63194 −0.127692 −0.0638460 0.997960i \(-0.520337\pi\)
−0.0638460 + 0.997960i \(0.520337\pi\)
\(810\) −18.7081 −0.657335
\(811\) −22.3667 −0.785402 −0.392701 0.919666i \(-0.628459\pi\)
−0.392701 + 0.919666i \(0.628459\pi\)
\(812\) 50.0957 1.75802
\(813\) 32.6322 1.14446
\(814\) −60.9347 −2.13576
\(815\) 3.76853 0.132006
\(816\) −37.2723 −1.30479
\(817\) 0.0322010 0.00112657
\(818\) 10.1812 0.355976
\(819\) 0.686279 0.0239805
\(820\) −19.7077 −0.688222
\(821\) 7.83461 0.273430 0.136715 0.990610i \(-0.456346\pi\)
0.136715 + 0.990610i \(0.456346\pi\)
\(822\) −26.3331 −0.918471
\(823\) 54.9563 1.91566 0.957829 0.287340i \(-0.0927708\pi\)
0.957829 + 0.287340i \(0.0927708\pi\)
\(824\) 0.775103 0.0270020
\(825\) 40.7084 1.41728
\(826\) −45.5785 −1.58588
\(827\) 39.2858 1.36610 0.683050 0.730371i \(-0.260653\pi\)
0.683050 + 0.730371i \(0.260653\pi\)
\(828\) −0.315305 −0.0109576
\(829\) 11.1466 0.387136 0.193568 0.981087i \(-0.437994\pi\)
0.193568 + 0.981087i \(0.437994\pi\)
\(830\) 0.386454 0.0134140
\(831\) 31.0286 1.07637
\(832\) 50.1434 1.73841
\(833\) −37.1680 −1.28780
\(834\) 36.3731 1.25950
\(835\) 1.17773 0.0407571
\(836\) −4.17505 −0.144397
\(837\) −27.8401 −0.962296
\(838\) −5.56681 −0.192302
\(839\) −30.3701 −1.04849 −0.524247 0.851566i \(-0.675653\pi\)
−0.524247 + 0.851566i \(0.675653\pi\)
\(840\) 0.906639 0.0312820
\(841\) 18.6243 0.642216
\(842\) 43.8492 1.51114
\(843\) 49.8802 1.71796
\(844\) 1.92250 0.0661751
\(845\) −34.0741 −1.17218
\(846\) −0.268375 −0.00922691
\(847\) 97.6575 3.35555
\(848\) 27.3034 0.937604
\(849\) 49.9913 1.71570
\(850\) −40.2976 −1.38220
\(851\) 30.3050 1.03884
\(852\) −34.9998 −1.19907
\(853\) 40.0751 1.37214 0.686072 0.727533i \(-0.259333\pi\)
0.686072 + 0.727533i \(0.259333\pi\)
\(854\) −12.8225 −0.438777
\(855\) −0.0102070 −0.000349073 0
\(856\) 1.32216 0.0451904
\(857\) 44.1508 1.50816 0.754081 0.656781i \(-0.228083\pi\)
0.754081 + 0.656781i \(0.228083\pi\)
\(858\) −139.874 −4.77521
\(859\) 0.132999 0.00453786 0.00226893 0.999997i \(-0.499278\pi\)
0.00226893 + 0.999997i \(0.499278\pi\)
\(860\) 0.185494 0.00632530
\(861\) −62.3925 −2.12633
\(862\) −5.27124 −0.179539
\(863\) −3.62727 −0.123474 −0.0617368 0.998092i \(-0.519664\pi\)
−0.0617368 + 0.998092i \(0.519664\pi\)
\(864\) 41.3594 1.40708
\(865\) −2.56892 −0.0873459
\(866\) −25.3279 −0.860675
\(867\) −17.9481 −0.609550
\(868\) −38.7200 −1.31424
\(869\) 78.6136 2.66678
\(870\) −24.9617 −0.846281
\(871\) −78.6354 −2.66446
\(872\) −0.642620 −0.0217619
\(873\) −0.369665 −0.0125113
\(874\) 4.22449 0.142895
\(875\) 35.2748 1.19251
\(876\) 19.3081 0.652362
\(877\) −19.8824 −0.671382 −0.335691 0.941972i \(-0.608970\pi\)
−0.335691 + 0.941972i \(0.608970\pi\)
\(878\) 40.9283 1.38126
\(879\) −16.6327 −0.561006
\(880\) 26.5704 0.895687
\(881\) −27.5924 −0.929613 −0.464807 0.885412i \(-0.653876\pi\)
−0.464807 + 0.885412i \(0.653876\pi\)
\(882\) 0.382706 0.0128864
\(883\) −29.7392 −1.00080 −0.500402 0.865793i \(-0.666815\pi\)
−0.500402 + 0.865793i \(0.666815\pi\)
\(884\) 68.0562 2.28898
\(885\) 11.1627 0.375230
\(886\) −37.5485 −1.26147
\(887\) 13.4684 0.452225 0.226113 0.974101i \(-0.427398\pi\)
0.226113 + 0.974101i \(0.427398\pi\)
\(888\) −1.15286 −0.0386875
\(889\) −26.9279 −0.903133
\(890\) −14.9169 −0.500014
\(891\) −54.2502 −1.81745
\(892\) 12.4297 0.416176
\(893\) 1.76734 0.0591418
\(894\) 5.51057 0.184301
\(895\) −21.3797 −0.714646
\(896\) −3.97464 −0.132783
\(897\) 69.5641 2.32268
\(898\) 24.5927 0.820668
\(899\) −36.8097 −1.22767
\(900\) 0.203944 0.00679814
\(901\) 34.6193 1.15334
\(902\) −116.271 −3.87140
\(903\) 0.587255 0.0195426
\(904\) −0.445660 −0.0148224
\(905\) −15.5596 −0.517219
\(906\) 68.2713 2.26816
\(907\) 42.2875 1.40413 0.702067 0.712111i \(-0.252261\pi\)
0.702067 + 0.712111i \(0.252261\pi\)
\(908\) 7.67985 0.254865
\(909\) −0.377087 −0.0125072
\(910\) −52.9669 −1.75583
\(911\) 12.6596 0.419432 0.209716 0.977762i \(-0.432746\pi\)
0.209716 + 0.977762i \(0.432746\pi\)
\(912\) −2.52733 −0.0836881
\(913\) 1.12065 0.0370881
\(914\) 61.8519 2.04588
\(915\) 3.14038 0.103818
\(916\) −12.0517 −0.398198
\(917\) −30.5135 −1.00765
\(918\) 54.1938 1.78866
\(919\) 22.2268 0.733195 0.366598 0.930380i \(-0.380523\pi\)
0.366598 + 0.930380i \(0.380523\pi\)
\(920\) −0.840277 −0.0277031
\(921\) −28.4026 −0.935897
\(922\) −68.2537 −2.24782
\(923\) −70.6029 −2.32392
\(924\) −76.1410 −2.50485
\(925\) −19.6017 −0.644501
\(926\) −12.5359 −0.411955
\(927\) −0.159141 −0.00522686
\(928\) 54.6847 1.79511
\(929\) 11.2819 0.370147 0.185074 0.982725i \(-0.440748\pi\)
0.185074 + 0.982725i \(0.440748\pi\)
\(930\) 19.2934 0.632655
\(931\) −2.52026 −0.0825981
\(932\) 18.0434 0.591032
\(933\) −42.3323 −1.38590
\(934\) 20.0227 0.655162
\(935\) 33.6898 1.10178
\(936\) 0.0241965 0.000790886 0
\(937\) 0.306358 0.0100083 0.00500413 0.999987i \(-0.498407\pi\)
0.00500413 + 0.999987i \(0.498407\pi\)
\(938\) −87.0891 −2.84356
\(939\) 22.7985 0.744001
\(940\) 10.1808 0.332061
\(941\) −8.83306 −0.287950 −0.143975 0.989581i \(-0.545988\pi\)
−0.143975 + 0.989581i \(0.545988\pi\)
\(942\) 5.26968 0.171695
\(943\) 57.8256 1.88306
\(944\) −25.2718 −0.822526
\(945\) −20.7311 −0.674382
\(946\) 1.09438 0.0355812
\(947\) −15.8861 −0.516230 −0.258115 0.966114i \(-0.583101\pi\)
−0.258115 + 0.966114i \(0.583101\pi\)
\(948\) −43.0746 −1.39900
\(949\) 38.9492 1.26434
\(950\) −2.73246 −0.0886528
\(951\) −19.7576 −0.640684
\(952\) −2.60256 −0.0843496
\(953\) −45.8789 −1.48616 −0.743081 0.669201i \(-0.766637\pi\)
−0.743081 + 0.669201i \(0.766637\pi\)
\(954\) −0.356463 −0.0115409
\(955\) 17.9717 0.581550
\(956\) 11.0938 0.358798
\(957\) −72.3845 −2.33986
\(958\) −32.4859 −1.04957
\(959\) −28.9162 −0.933752
\(960\) −13.6009 −0.438969
\(961\) −2.54901 −0.0822262
\(962\) 67.3514 2.17150
\(963\) −0.271459 −0.00874765
\(964\) −37.9739 −1.22306
\(965\) 25.4026 0.817738
\(966\) 77.0426 2.47881
\(967\) 48.9246 1.57331 0.786654 0.617394i \(-0.211812\pi\)
0.786654 + 0.617394i \(0.211812\pi\)
\(968\) 3.44316 0.110667
\(969\) −3.20451 −0.102944
\(970\) 28.5307 0.916065
\(971\) 32.6323 1.04722 0.523610 0.851958i \(-0.324585\pi\)
0.523610 + 0.851958i \(0.324585\pi\)
\(972\) −0.546082 −0.0175156
\(973\) 39.9411 1.28045
\(974\) −31.0254 −0.994117
\(975\) −44.9951 −1.44100
\(976\) −7.10965 −0.227574
\(977\) −7.75796 −0.248199 −0.124100 0.992270i \(-0.539604\pi\)
−0.124100 + 0.992270i \(0.539604\pi\)
\(978\) −12.1824 −0.389550
\(979\) −43.2563 −1.38248
\(980\) −14.5180 −0.463759
\(981\) 0.131940 0.00421251
\(982\) 49.6319 1.58382
\(983\) −0.898497 −0.0286576 −0.0143288 0.999897i \(-0.504561\pi\)
−0.0143288 + 0.999897i \(0.504561\pi\)
\(984\) −2.19980 −0.0701271
\(985\) 3.44141 0.109652
\(986\) 71.6541 2.28193
\(987\) 32.2313 1.02593
\(988\) 4.61470 0.146813
\(989\) −0.544271 −0.0173068
\(990\) −0.346893 −0.0110250
\(991\) 1.90886 0.0606369 0.0303185 0.999540i \(-0.490348\pi\)
0.0303185 + 0.999540i \(0.490348\pi\)
\(992\) −42.2669 −1.34197
\(993\) −45.0892 −1.43086
\(994\) −78.1931 −2.48014
\(995\) 4.33868 0.137545
\(996\) −0.614036 −0.0194565
\(997\) 20.8626 0.660724 0.330362 0.943854i \(-0.392829\pi\)
0.330362 + 0.943854i \(0.392829\pi\)
\(998\) 28.5786 0.904638
\(999\) 26.3612 0.834030
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 \(a_p\))