Properties

Label 4005.2.a.p.1.4
Level 4005
Weight 2
Character 4005.1
Self dual Yes
Analytic conductor 31.980
Analytic rank 1
Dimension 8
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4005 = 3^{2} \cdot 5 \cdot 89 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4005.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9800860095\)
Analytic rank: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(0.217002\)
Character \(\chi\) = 4005.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.217002 q^{2} -1.95291 q^{4} +1.00000 q^{5} -2.89958 q^{7} +0.857790 q^{8} +O(q^{10})\) \(q-0.217002 q^{2} -1.95291 q^{4} +1.00000 q^{5} -2.89958 q^{7} +0.857790 q^{8} -0.217002 q^{10} -3.07479 q^{11} +0.0854942 q^{13} +0.629215 q^{14} +3.71968 q^{16} +2.13219 q^{17} +2.44475 q^{19} -1.95291 q^{20} +0.667236 q^{22} -2.98507 q^{23} +1.00000 q^{25} -0.0185524 q^{26} +5.66262 q^{28} +6.39489 q^{29} +7.97229 q^{31} -2.52276 q^{32} -0.462689 q^{34} -2.89958 q^{35} -1.01070 q^{37} -0.530516 q^{38} +0.857790 q^{40} +4.08276 q^{41} -1.92193 q^{43} +6.00479 q^{44} +0.647767 q^{46} -8.73550 q^{47} +1.40756 q^{49} -0.217002 q^{50} -0.166962 q^{52} +6.19276 q^{53} -3.07479 q^{55} -2.48723 q^{56} -1.38770 q^{58} -11.6153 q^{59} +10.7793 q^{61} -1.73000 q^{62} -6.89191 q^{64} +0.0854942 q^{65} -4.48372 q^{67} -4.16397 q^{68} +0.629215 q^{70} -9.54118 q^{71} +1.45652 q^{73} +0.219325 q^{74} -4.77437 q^{76} +8.91560 q^{77} -12.8611 q^{79} +3.71968 q^{80} -0.885968 q^{82} -4.61282 q^{83} +2.13219 q^{85} +0.417062 q^{86} -2.63752 q^{88} -1.00000 q^{89} -0.247897 q^{91} +5.82958 q^{92} +1.89562 q^{94} +2.44475 q^{95} +2.35298 q^{97} -0.305442 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - q^{2} + 7q^{4} + 8q^{5} - 6q^{7} - 3q^{8} + O(q^{10}) \) \( 8q - q^{2} + 7q^{4} + 8q^{5} - 6q^{7} - 3q^{8} - q^{10} - 14q^{11} - 7q^{13} - 15q^{14} + 9q^{16} - 17q^{17} + 17q^{19} + 7q^{20} + 2q^{22} + q^{23} + 8q^{25} - 3q^{26} - 29q^{28} - 10q^{29} + q^{31} - 2q^{32} - 16q^{34} - 6q^{35} - 11q^{37} + 30q^{38} - 3q^{40} - 15q^{41} - 5q^{43} - 7q^{44} - 12q^{46} - 12q^{47} + 4q^{49} - q^{50} - 14q^{52} + q^{53} - 14q^{55} - 3q^{56} - 37q^{58} - 26q^{59} + 13q^{61} - 22q^{62} - 15q^{64} - 7q^{65} - 25q^{67} - 23q^{68} - 15q^{70} - 28q^{71} - 17q^{73} + 5q^{74} + 8q^{76} - 7q^{79} + 9q^{80} + 5q^{82} - 44q^{83} - 17q^{85} + 13q^{86} - 66q^{88} - 8q^{89} + 27q^{91} - 15q^{92} - 27q^{94} + 17q^{95} + q^{97} + 34q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.217002 −0.153444 −0.0767218 0.997053i \(-0.524445\pi\)
−0.0767218 + 0.997053i \(0.524445\pi\)
\(3\) 0 0
\(4\) −1.95291 −0.976455
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −2.89958 −1.09594 −0.547969 0.836499i \(-0.684599\pi\)
−0.547969 + 0.836499i \(0.684599\pi\)
\(8\) 0.857790 0.303274
\(9\) 0 0
\(10\) −0.217002 −0.0686221
\(11\) −3.07479 −0.927085 −0.463542 0.886075i \(-0.653422\pi\)
−0.463542 + 0.886075i \(0.653422\pi\)
\(12\) 0 0
\(13\) 0.0854942 0.0237118 0.0118559 0.999930i \(-0.496226\pi\)
0.0118559 + 0.999930i \(0.496226\pi\)
\(14\) 0.629215 0.168165
\(15\) 0 0
\(16\) 3.71968 0.929920
\(17\) 2.13219 0.517132 0.258566 0.965994i \(-0.416750\pi\)
0.258566 + 0.965994i \(0.416750\pi\)
\(18\) 0 0
\(19\) 2.44475 0.560864 0.280432 0.959874i \(-0.409522\pi\)
0.280432 + 0.959874i \(0.409522\pi\)
\(20\) −1.95291 −0.436684
\(21\) 0 0
\(22\) 0.667236 0.142255
\(23\) −2.98507 −0.622431 −0.311215 0.950339i \(-0.600736\pi\)
−0.311215 + 0.950339i \(0.600736\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −0.0185524 −0.00363843
\(27\) 0 0
\(28\) 5.66262 1.07013
\(29\) 6.39489 1.18750 0.593750 0.804649i \(-0.297647\pi\)
0.593750 + 0.804649i \(0.297647\pi\)
\(30\) 0 0
\(31\) 7.97229 1.43186 0.715932 0.698170i \(-0.246002\pi\)
0.715932 + 0.698170i \(0.246002\pi\)
\(32\) −2.52276 −0.445965
\(33\) 0 0
\(34\) −0.462689 −0.0793506
\(35\) −2.89958 −0.490118
\(36\) 0 0
\(37\) −1.01070 −0.166158 −0.0830792 0.996543i \(-0.526475\pi\)
−0.0830792 + 0.996543i \(0.526475\pi\)
\(38\) −0.530516 −0.0860610
\(39\) 0 0
\(40\) 0.857790 0.135628
\(41\) 4.08276 0.637621 0.318810 0.947819i \(-0.396717\pi\)
0.318810 + 0.947819i \(0.396717\pi\)
\(42\) 0 0
\(43\) −1.92193 −0.293091 −0.146546 0.989204i \(-0.546816\pi\)
−0.146546 + 0.989204i \(0.546816\pi\)
\(44\) 6.00479 0.905256
\(45\) 0 0
\(46\) 0.647767 0.0955080
\(47\) −8.73550 −1.27420 −0.637102 0.770780i \(-0.719867\pi\)
−0.637102 + 0.770780i \(0.719867\pi\)
\(48\) 0 0
\(49\) 1.40756 0.201079
\(50\) −0.217002 −0.0306887
\(51\) 0 0
\(52\) −0.166962 −0.0231535
\(53\) 6.19276 0.850641 0.425321 0.905043i \(-0.360161\pi\)
0.425321 + 0.905043i \(0.360161\pi\)
\(54\) 0 0
\(55\) −3.07479 −0.414605
\(56\) −2.48723 −0.332370
\(57\) 0 0
\(58\) −1.38770 −0.182214
\(59\) −11.6153 −1.51219 −0.756094 0.654463i \(-0.772895\pi\)
−0.756094 + 0.654463i \(0.772895\pi\)
\(60\) 0 0
\(61\) 10.7793 1.38014 0.690072 0.723740i \(-0.257579\pi\)
0.690072 + 0.723740i \(0.257579\pi\)
\(62\) −1.73000 −0.219711
\(63\) 0 0
\(64\) −6.89191 −0.861489
\(65\) 0.0854942 0.0106042
\(66\) 0 0
\(67\) −4.48372 −0.547774 −0.273887 0.961762i \(-0.588309\pi\)
−0.273887 + 0.961762i \(0.588309\pi\)
\(68\) −4.16397 −0.504956
\(69\) 0 0
\(70\) 0.629215 0.0752055
\(71\) −9.54118 −1.13233 −0.566165 0.824292i \(-0.691574\pi\)
−0.566165 + 0.824292i \(0.691574\pi\)
\(72\) 0 0
\(73\) 1.45652 0.170473 0.0852363 0.996361i \(-0.472835\pi\)
0.0852363 + 0.996361i \(0.472835\pi\)
\(74\) 0.219325 0.0254960
\(75\) 0 0
\(76\) −4.77437 −0.547658
\(77\) 8.91560 1.01603
\(78\) 0 0
\(79\) −12.8611 −1.44699 −0.723493 0.690332i \(-0.757464\pi\)
−0.723493 + 0.690332i \(0.757464\pi\)
\(80\) 3.71968 0.415873
\(81\) 0 0
\(82\) −0.885968 −0.0978388
\(83\) −4.61282 −0.506322 −0.253161 0.967424i \(-0.581470\pi\)
−0.253161 + 0.967424i \(0.581470\pi\)
\(84\) 0 0
\(85\) 2.13219 0.231268
\(86\) 0.417062 0.0449730
\(87\) 0 0
\(88\) −2.63752 −0.281161
\(89\) −1.00000 −0.106000
\(90\) 0 0
\(91\) −0.247897 −0.0259867
\(92\) 5.82958 0.607776
\(93\) 0 0
\(94\) 1.89562 0.195518
\(95\) 2.44475 0.250826
\(96\) 0 0
\(97\) 2.35298 0.238909 0.119454 0.992840i \(-0.461886\pi\)
0.119454 + 0.992840i \(0.461886\pi\)
\(98\) −0.305442 −0.0308543
\(99\) 0 0
\(100\) −1.95291 −0.195291
\(101\) −12.5683 −1.25059 −0.625296 0.780388i \(-0.715022\pi\)
−0.625296 + 0.780388i \(0.715022\pi\)
\(102\) 0 0
\(103\) −2.14879 −0.211727 −0.105863 0.994381i \(-0.533761\pi\)
−0.105863 + 0.994381i \(0.533761\pi\)
\(104\) 0.0733360 0.00719119
\(105\) 0 0
\(106\) −1.34384 −0.130526
\(107\) 2.32018 0.224301 0.112150 0.993691i \(-0.464226\pi\)
0.112150 + 0.993691i \(0.464226\pi\)
\(108\) 0 0
\(109\) 17.7443 1.69960 0.849798 0.527108i \(-0.176724\pi\)
0.849798 + 0.527108i \(0.176724\pi\)
\(110\) 0.667236 0.0636185
\(111\) 0 0
\(112\) −10.7855 −1.01913
\(113\) −5.47285 −0.514842 −0.257421 0.966299i \(-0.582873\pi\)
−0.257421 + 0.966299i \(0.582873\pi\)
\(114\) 0 0
\(115\) −2.98507 −0.278359
\(116\) −12.4886 −1.15954
\(117\) 0 0
\(118\) 2.52055 0.232036
\(119\) −6.18245 −0.566744
\(120\) 0 0
\(121\) −1.54566 −0.140514
\(122\) −2.33912 −0.211774
\(123\) 0 0
\(124\) −15.5692 −1.39815
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −4.94804 −0.439067 −0.219534 0.975605i \(-0.570454\pi\)
−0.219534 + 0.975605i \(0.570454\pi\)
\(128\) 6.54107 0.578155
\(129\) 0 0
\(130\) −0.0185524 −0.00162715
\(131\) −4.76457 −0.416282 −0.208141 0.978099i \(-0.566741\pi\)
−0.208141 + 0.978099i \(0.566741\pi\)
\(132\) 0 0
\(133\) −7.08874 −0.614672
\(134\) 0.972977 0.0840524
\(135\) 0 0
\(136\) 1.82897 0.156833
\(137\) −16.4896 −1.40881 −0.704403 0.709801i \(-0.748785\pi\)
−0.704403 + 0.709801i \(0.748785\pi\)
\(138\) 0 0
\(139\) 15.7987 1.34003 0.670013 0.742349i \(-0.266289\pi\)
0.670013 + 0.742349i \(0.266289\pi\)
\(140\) 5.66262 0.478578
\(141\) 0 0
\(142\) 2.07046 0.173749
\(143\) −0.262877 −0.0219829
\(144\) 0 0
\(145\) 6.39489 0.531066
\(146\) −0.316068 −0.0261579
\(147\) 0 0
\(148\) 1.97381 0.162246
\(149\) −20.2146 −1.65604 −0.828022 0.560696i \(-0.810534\pi\)
−0.828022 + 0.560696i \(0.810534\pi\)
\(150\) 0 0
\(151\) −11.1576 −0.907990 −0.453995 0.891004i \(-0.650002\pi\)
−0.453995 + 0.891004i \(0.650002\pi\)
\(152\) 2.09708 0.170096
\(153\) 0 0
\(154\) −1.93470 −0.155903
\(155\) 7.97229 0.640349
\(156\) 0 0
\(157\) −10.4281 −0.832253 −0.416127 0.909307i \(-0.636613\pi\)
−0.416127 + 0.909307i \(0.636613\pi\)
\(158\) 2.79088 0.222031
\(159\) 0 0
\(160\) −2.52276 −0.199441
\(161\) 8.65545 0.682145
\(162\) 0 0
\(163\) 21.8735 1.71326 0.856631 0.515930i \(-0.172553\pi\)
0.856631 + 0.515930i \(0.172553\pi\)
\(164\) −7.97327 −0.622608
\(165\) 0 0
\(166\) 1.00099 0.0776919
\(167\) −9.51097 −0.735981 −0.367990 0.929830i \(-0.619954\pi\)
−0.367990 + 0.929830i \(0.619954\pi\)
\(168\) 0 0
\(169\) −12.9927 −0.999438
\(170\) −0.462689 −0.0354867
\(171\) 0 0
\(172\) 3.75335 0.286190
\(173\) 11.7120 0.890447 0.445224 0.895419i \(-0.353124\pi\)
0.445224 + 0.895419i \(0.353124\pi\)
\(174\) 0 0
\(175\) −2.89958 −0.219188
\(176\) −11.4372 −0.862114
\(177\) 0 0
\(178\) 0.217002 0.0162650
\(179\) −10.5402 −0.787808 −0.393904 0.919152i \(-0.628876\pi\)
−0.393904 + 0.919152i \(0.628876\pi\)
\(180\) 0 0
\(181\) −14.4072 −1.07088 −0.535439 0.844574i \(-0.679854\pi\)
−0.535439 + 0.844574i \(0.679854\pi\)
\(182\) 0.0537942 0.00398749
\(183\) 0 0
\(184\) −2.56056 −0.188767
\(185\) −1.01070 −0.0743083
\(186\) 0 0
\(187\) −6.55604 −0.479425
\(188\) 17.0596 1.24420
\(189\) 0 0
\(190\) −0.530516 −0.0384876
\(191\) 13.9019 1.00590 0.502952 0.864314i \(-0.332247\pi\)
0.502952 + 0.864314i \(0.332247\pi\)
\(192\) 0 0
\(193\) 17.4291 1.25457 0.627287 0.778788i \(-0.284165\pi\)
0.627287 + 0.778788i \(0.284165\pi\)
\(194\) −0.510601 −0.0366590
\(195\) 0 0
\(196\) −2.74883 −0.196345
\(197\) −15.6196 −1.11285 −0.556426 0.830897i \(-0.687828\pi\)
−0.556426 + 0.830897i \(0.687828\pi\)
\(198\) 0 0
\(199\) 14.9293 1.05831 0.529155 0.848525i \(-0.322509\pi\)
0.529155 + 0.848525i \(0.322509\pi\)
\(200\) 0.857790 0.0606549
\(201\) 0 0
\(202\) 2.72735 0.191895
\(203\) −18.5425 −1.30143
\(204\) 0 0
\(205\) 4.08276 0.285153
\(206\) 0.466292 0.0324881
\(207\) 0 0
\(208\) 0.318011 0.0220501
\(209\) −7.51709 −0.519968
\(210\) 0 0
\(211\) −7.92872 −0.545835 −0.272918 0.962037i \(-0.587989\pi\)
−0.272918 + 0.962037i \(0.587989\pi\)
\(212\) −12.0939 −0.830613
\(213\) 0 0
\(214\) −0.503485 −0.0344175
\(215\) −1.92193 −0.131074
\(216\) 0 0
\(217\) −23.1163 −1.56923
\(218\) −3.85055 −0.260792
\(219\) 0 0
\(220\) 6.00479 0.404843
\(221\) 0.182290 0.0122621
\(222\) 0 0
\(223\) −20.6302 −1.38150 −0.690751 0.723093i \(-0.742720\pi\)
−0.690751 + 0.723093i \(0.742720\pi\)
\(224\) 7.31493 0.488749
\(225\) 0 0
\(226\) 1.18762 0.0789993
\(227\) −14.5245 −0.964027 −0.482013 0.876164i \(-0.660094\pi\)
−0.482013 + 0.876164i \(0.660094\pi\)
\(228\) 0 0
\(229\) −3.90028 −0.257738 −0.128869 0.991662i \(-0.541135\pi\)
−0.128869 + 0.991662i \(0.541135\pi\)
\(230\) 0.647767 0.0427125
\(231\) 0 0
\(232\) 5.48547 0.360139
\(233\) −6.62860 −0.434254 −0.217127 0.976143i \(-0.569669\pi\)
−0.217127 + 0.976143i \(0.569669\pi\)
\(234\) 0 0
\(235\) −8.73550 −0.569841
\(236\) 22.6837 1.47658
\(237\) 0 0
\(238\) 1.34160 0.0869633
\(239\) 19.2676 1.24632 0.623159 0.782095i \(-0.285849\pi\)
0.623159 + 0.782095i \(0.285849\pi\)
\(240\) 0 0
\(241\) 19.6370 1.26493 0.632465 0.774589i \(-0.282043\pi\)
0.632465 + 0.774589i \(0.282043\pi\)
\(242\) 0.335411 0.0215610
\(243\) 0 0
\(244\) −21.0510 −1.34765
\(245\) 1.40756 0.0899254
\(246\) 0 0
\(247\) 0.209012 0.0132991
\(248\) 6.83854 0.434248
\(249\) 0 0
\(250\) −0.217002 −0.0137244
\(251\) 15.7920 0.996783 0.498392 0.866952i \(-0.333924\pi\)
0.498392 + 0.866952i \(0.333924\pi\)
\(252\) 0 0
\(253\) 9.17848 0.577046
\(254\) 1.07373 0.0673721
\(255\) 0 0
\(256\) 12.3644 0.772775
\(257\) −20.2283 −1.26181 −0.630903 0.775862i \(-0.717315\pi\)
−0.630903 + 0.775862i \(0.717315\pi\)
\(258\) 0 0
\(259\) 2.93061 0.182099
\(260\) −0.166962 −0.0103546
\(261\) 0 0
\(262\) 1.03392 0.0638759
\(263\) −6.98711 −0.430843 −0.215422 0.976521i \(-0.569113\pi\)
−0.215422 + 0.976521i \(0.569113\pi\)
\(264\) 0 0
\(265\) 6.19276 0.380418
\(266\) 1.53827 0.0943175
\(267\) 0 0
\(268\) 8.75631 0.534877
\(269\) 10.8371 0.660749 0.330375 0.943850i \(-0.392825\pi\)
0.330375 + 0.943850i \(0.392825\pi\)
\(270\) 0 0
\(271\) −13.3936 −0.813601 −0.406801 0.913517i \(-0.633356\pi\)
−0.406801 + 0.913517i \(0.633356\pi\)
\(272\) 7.93106 0.480891
\(273\) 0 0
\(274\) 3.57829 0.216172
\(275\) −3.07479 −0.185417
\(276\) 0 0
\(277\) −20.2556 −1.21704 −0.608520 0.793539i \(-0.708236\pi\)
−0.608520 + 0.793539i \(0.708236\pi\)
\(278\) −3.42834 −0.205618
\(279\) 0 0
\(280\) −2.48723 −0.148640
\(281\) −17.8054 −1.06218 −0.531090 0.847315i \(-0.678218\pi\)
−0.531090 + 0.847315i \(0.678218\pi\)
\(282\) 0 0
\(283\) 12.8718 0.765150 0.382575 0.923924i \(-0.375037\pi\)
0.382575 + 0.923924i \(0.375037\pi\)
\(284\) 18.6331 1.10567
\(285\) 0 0
\(286\) 0.0570448 0.00337313
\(287\) −11.8383 −0.698793
\(288\) 0 0
\(289\) −12.4538 −0.732575
\(290\) −1.38770 −0.0814888
\(291\) 0 0
\(292\) −2.84445 −0.166459
\(293\) −23.9695 −1.40031 −0.700156 0.713990i \(-0.746886\pi\)
−0.700156 + 0.713990i \(0.746886\pi\)
\(294\) 0 0
\(295\) −11.6153 −0.676271
\(296\) −0.866970 −0.0503916
\(297\) 0 0
\(298\) 4.38661 0.254109
\(299\) −0.255206 −0.0147590
\(300\) 0 0
\(301\) 5.57278 0.321210
\(302\) 2.42122 0.139325
\(303\) 0 0
\(304\) 9.09368 0.521558
\(305\) 10.7793 0.617219
\(306\) 0 0
\(307\) 24.2471 1.38385 0.691927 0.721967i \(-0.256762\pi\)
0.691927 + 0.721967i \(0.256762\pi\)
\(308\) −17.4114 −0.992105
\(309\) 0 0
\(310\) −1.73000 −0.0982575
\(311\) 2.02464 0.114807 0.0574034 0.998351i \(-0.481718\pi\)
0.0574034 + 0.998351i \(0.481718\pi\)
\(312\) 0 0
\(313\) −13.7597 −0.777746 −0.388873 0.921291i \(-0.627136\pi\)
−0.388873 + 0.921291i \(0.627136\pi\)
\(314\) 2.26292 0.127704
\(315\) 0 0
\(316\) 25.1165 1.41292
\(317\) 25.9557 1.45782 0.728909 0.684611i \(-0.240028\pi\)
0.728909 + 0.684611i \(0.240028\pi\)
\(318\) 0 0
\(319\) −19.6629 −1.10091
\(320\) −6.89191 −0.385270
\(321\) 0 0
\(322\) −1.87825 −0.104671
\(323\) 5.21267 0.290041
\(324\) 0 0
\(325\) 0.0854942 0.00474236
\(326\) −4.74659 −0.262889
\(327\) 0 0
\(328\) 3.50215 0.193374
\(329\) 25.3293 1.39645
\(330\) 0 0
\(331\) −14.7062 −0.808325 −0.404163 0.914687i \(-0.632437\pi\)
−0.404163 + 0.914687i \(0.632437\pi\)
\(332\) 9.00842 0.494401
\(333\) 0 0
\(334\) 2.06390 0.112932
\(335\) −4.48372 −0.244972
\(336\) 0 0
\(337\) −21.7701 −1.18589 −0.592947 0.805242i \(-0.702036\pi\)
−0.592947 + 0.805242i \(0.702036\pi\)
\(338\) 2.81944 0.153357
\(339\) 0 0
\(340\) −4.16397 −0.225823
\(341\) −24.5131 −1.32746
\(342\) 0 0
\(343\) 16.2157 0.875567
\(344\) −1.64861 −0.0888871
\(345\) 0 0
\(346\) −2.54153 −0.136633
\(347\) −28.7105 −1.54126 −0.770629 0.637284i \(-0.780058\pi\)
−0.770629 + 0.637284i \(0.780058\pi\)
\(348\) 0 0
\(349\) −5.52078 −0.295520 −0.147760 0.989023i \(-0.547206\pi\)
−0.147760 + 0.989023i \(0.547206\pi\)
\(350\) 0.629215 0.0336329
\(351\) 0 0
\(352\) 7.75695 0.413447
\(353\) 19.8488 1.05645 0.528223 0.849106i \(-0.322858\pi\)
0.528223 + 0.849106i \(0.322858\pi\)
\(354\) 0 0
\(355\) −9.54118 −0.506394
\(356\) 1.95291 0.103504
\(357\) 0 0
\(358\) 2.28723 0.120884
\(359\) 7.11756 0.375651 0.187825 0.982202i \(-0.439856\pi\)
0.187825 + 0.982202i \(0.439856\pi\)
\(360\) 0 0
\(361\) −13.0232 −0.685432
\(362\) 3.12639 0.164319
\(363\) 0 0
\(364\) 0.484121 0.0253748
\(365\) 1.45652 0.0762377
\(366\) 0 0
\(367\) −29.6237 −1.54635 −0.773173 0.634195i \(-0.781332\pi\)
−0.773173 + 0.634195i \(0.781332\pi\)
\(368\) −11.1035 −0.578810
\(369\) 0 0
\(370\) 0.219325 0.0114021
\(371\) −17.9564 −0.932250
\(372\) 0 0
\(373\) 28.3346 1.46711 0.733556 0.679629i \(-0.237859\pi\)
0.733556 + 0.679629i \(0.237859\pi\)
\(374\) 1.42267 0.0735647
\(375\) 0 0
\(376\) −7.49322 −0.386433
\(377\) 0.546725 0.0281578
\(378\) 0 0
\(379\) −7.10576 −0.364999 −0.182499 0.983206i \(-0.558419\pi\)
−0.182499 + 0.983206i \(0.558419\pi\)
\(380\) −4.77437 −0.244920
\(381\) 0 0
\(382\) −3.01673 −0.154350
\(383\) −13.5263 −0.691160 −0.345580 0.938389i \(-0.612318\pi\)
−0.345580 + 0.938389i \(0.612318\pi\)
\(384\) 0 0
\(385\) 8.91560 0.454381
\(386\) −3.78215 −0.192506
\(387\) 0 0
\(388\) −4.59515 −0.233283
\(389\) −35.5717 −1.80356 −0.901779 0.432198i \(-0.857738\pi\)
−0.901779 + 0.432198i \(0.857738\pi\)
\(390\) 0 0
\(391\) −6.36474 −0.321879
\(392\) 1.20739 0.0609822
\(393\) 0 0
\(394\) 3.38949 0.170760
\(395\) −12.8611 −0.647111
\(396\) 0 0
\(397\) −28.5754 −1.43416 −0.717078 0.696993i \(-0.754521\pi\)
−0.717078 + 0.696993i \(0.754521\pi\)
\(398\) −3.23969 −0.162391
\(399\) 0 0
\(400\) 3.71968 0.185984
\(401\) 15.5212 0.775094 0.387547 0.921850i \(-0.373323\pi\)
0.387547 + 0.921850i \(0.373323\pi\)
\(402\) 0 0
\(403\) 0.681584 0.0339521
\(404\) 24.5448 1.22115
\(405\) 0 0
\(406\) 4.02376 0.199696
\(407\) 3.10770 0.154043
\(408\) 0 0
\(409\) 32.6342 1.61366 0.806830 0.590784i \(-0.201181\pi\)
0.806830 + 0.590784i \(0.201181\pi\)
\(410\) −0.885968 −0.0437549
\(411\) 0 0
\(412\) 4.19640 0.206742
\(413\) 33.6796 1.65726
\(414\) 0 0
\(415\) −4.61282 −0.226434
\(416\) −0.215681 −0.0105746
\(417\) 0 0
\(418\) 1.63122 0.0797858
\(419\) −12.9971 −0.634950 −0.317475 0.948267i \(-0.602835\pi\)
−0.317475 + 0.948267i \(0.602835\pi\)
\(420\) 0 0
\(421\) −18.2329 −0.888617 −0.444309 0.895874i \(-0.646551\pi\)
−0.444309 + 0.895874i \(0.646551\pi\)
\(422\) 1.72055 0.0837550
\(423\) 0 0
\(424\) 5.31209 0.257978
\(425\) 2.13219 0.103426
\(426\) 0 0
\(427\) −31.2553 −1.51255
\(428\) −4.53111 −0.219019
\(429\) 0 0
\(430\) 0.417062 0.0201125
\(431\) −8.50370 −0.409609 −0.204804 0.978803i \(-0.565656\pi\)
−0.204804 + 0.978803i \(0.565656\pi\)
\(432\) 0 0
\(433\) −12.5444 −0.602846 −0.301423 0.953491i \(-0.597462\pi\)
−0.301423 + 0.953491i \(0.597462\pi\)
\(434\) 5.01628 0.240789
\(435\) 0 0
\(436\) −34.6530 −1.65958
\(437\) −7.29775 −0.349099
\(438\) 0 0
\(439\) −11.3997 −0.544079 −0.272040 0.962286i \(-0.587698\pi\)
−0.272040 + 0.962286i \(0.587698\pi\)
\(440\) −2.63752 −0.125739
\(441\) 0 0
\(442\) −0.0395572 −0.00188155
\(443\) 1.45229 0.0690005 0.0345002 0.999405i \(-0.489016\pi\)
0.0345002 + 0.999405i \(0.489016\pi\)
\(444\) 0 0
\(445\) −1.00000 −0.0474045
\(446\) 4.47680 0.211983
\(447\) 0 0
\(448\) 19.9836 0.944138
\(449\) 33.3724 1.57494 0.787471 0.616351i \(-0.211390\pi\)
0.787471 + 0.616351i \(0.211390\pi\)
\(450\) 0 0
\(451\) −12.5537 −0.591128
\(452\) 10.6880 0.502720
\(453\) 0 0
\(454\) 3.15185 0.147924
\(455\) −0.247897 −0.0116216
\(456\) 0 0
\(457\) −17.8566 −0.835294 −0.417647 0.908609i \(-0.637145\pi\)
−0.417647 + 0.908609i \(0.637145\pi\)
\(458\) 0.846368 0.0395482
\(459\) 0 0
\(460\) 5.82958 0.271806
\(461\) 36.8041 1.71414 0.857068 0.515203i \(-0.172284\pi\)
0.857068 + 0.515203i \(0.172284\pi\)
\(462\) 0 0
\(463\) −35.0568 −1.62923 −0.814615 0.580002i \(-0.803052\pi\)
−0.814615 + 0.580002i \(0.803052\pi\)
\(464\) 23.7869 1.10428
\(465\) 0 0
\(466\) 1.43842 0.0666335
\(467\) −5.50869 −0.254912 −0.127456 0.991844i \(-0.540681\pi\)
−0.127456 + 0.991844i \(0.540681\pi\)
\(468\) 0 0
\(469\) 13.0009 0.600326
\(470\) 1.89562 0.0874385
\(471\) 0 0
\(472\) −9.96352 −0.458608
\(473\) 5.90953 0.271720
\(474\) 0 0
\(475\) 2.44475 0.112173
\(476\) 12.0738 0.553400
\(477\) 0 0
\(478\) −4.18111 −0.191239
\(479\) 7.72431 0.352933 0.176466 0.984307i \(-0.443533\pi\)
0.176466 + 0.984307i \(0.443533\pi\)
\(480\) 0 0
\(481\) −0.0864092 −0.00393992
\(482\) −4.26127 −0.194095
\(483\) 0 0
\(484\) 3.01853 0.137206
\(485\) 2.35298 0.106843
\(486\) 0 0
\(487\) 27.1768 1.23150 0.615749 0.787943i \(-0.288854\pi\)
0.615749 + 0.787943i \(0.288854\pi\)
\(488\) 9.24635 0.418563
\(489\) 0 0
\(490\) −0.305442 −0.0137985
\(491\) −19.3503 −0.873266 −0.436633 0.899640i \(-0.643829\pi\)
−0.436633 + 0.899640i \(0.643829\pi\)
\(492\) 0 0
\(493\) 13.6351 0.614094
\(494\) −0.0453560 −0.00204066
\(495\) 0 0
\(496\) 29.6543 1.33152
\(497\) 27.6654 1.24096
\(498\) 0 0
\(499\) 17.3273 0.775678 0.387839 0.921727i \(-0.373222\pi\)
0.387839 + 0.921727i \(0.373222\pi\)
\(500\) −1.95291 −0.0873368
\(501\) 0 0
\(502\) −3.42690 −0.152950
\(503\) −27.1992 −1.21275 −0.606376 0.795178i \(-0.707377\pi\)
−0.606376 + 0.795178i \(0.707377\pi\)
\(504\) 0 0
\(505\) −12.5683 −0.559282
\(506\) −1.99175 −0.0885440
\(507\) 0 0
\(508\) 9.66307 0.428730
\(509\) 1.73289 0.0768091 0.0384046 0.999262i \(-0.487772\pi\)
0.0384046 + 0.999262i \(0.487772\pi\)
\(510\) 0 0
\(511\) −4.22329 −0.186827
\(512\) −15.7652 −0.696732
\(513\) 0 0
\(514\) 4.38958 0.193616
\(515\) −2.14879 −0.0946871
\(516\) 0 0
\(517\) 26.8598 1.18129
\(518\) −0.635949 −0.0279420
\(519\) 0 0
\(520\) 0.0733360 0.00321600
\(521\) 4.23423 0.185505 0.0927524 0.995689i \(-0.470433\pi\)
0.0927524 + 0.995689i \(0.470433\pi\)
\(522\) 0 0
\(523\) 34.3472 1.50190 0.750949 0.660360i \(-0.229596\pi\)
0.750949 + 0.660360i \(0.229596\pi\)
\(524\) 9.30478 0.406481
\(525\) 0 0
\(526\) 1.51622 0.0661102
\(527\) 16.9984 0.740463
\(528\) 0 0
\(529\) −14.0893 −0.612580
\(530\) −1.34384 −0.0583728
\(531\) 0 0
\(532\) 13.8437 0.600199
\(533\) 0.349053 0.0151191
\(534\) 0 0
\(535\) 2.32018 0.100310
\(536\) −3.84609 −0.166126
\(537\) 0 0
\(538\) −2.35167 −0.101388
\(539\) −4.32794 −0.186418
\(540\) 0 0
\(541\) 29.2111 1.25588 0.627942 0.778260i \(-0.283897\pi\)
0.627942 + 0.778260i \(0.283897\pi\)
\(542\) 2.90643 0.124842
\(543\) 0 0
\(544\) −5.37899 −0.230622
\(545\) 17.7443 0.760083
\(546\) 0 0
\(547\) −12.7289 −0.544248 −0.272124 0.962262i \(-0.587726\pi\)
−0.272124 + 0.962262i \(0.587726\pi\)
\(548\) 32.2028 1.37564
\(549\) 0 0
\(550\) 0.667236 0.0284510
\(551\) 15.6339 0.666026
\(552\) 0 0
\(553\) 37.2917 1.58581
\(554\) 4.39550 0.186747
\(555\) 0 0
\(556\) −30.8534 −1.30848
\(557\) −28.9428 −1.22635 −0.613173 0.789949i \(-0.710107\pi\)
−0.613173 + 0.789949i \(0.710107\pi\)
\(558\) 0 0
\(559\) −0.164314 −0.00694973
\(560\) −10.7855 −0.455771
\(561\) 0 0
\(562\) 3.86381 0.162985
\(563\) 22.9924 0.969016 0.484508 0.874787i \(-0.338999\pi\)
0.484508 + 0.874787i \(0.338999\pi\)
\(564\) 0 0
\(565\) −5.47285 −0.230244
\(566\) −2.79321 −0.117407
\(567\) 0 0
\(568\) −8.18433 −0.343407
\(569\) 13.8257 0.579604 0.289802 0.957087i \(-0.406411\pi\)
0.289802 + 0.957087i \(0.406411\pi\)
\(570\) 0 0
\(571\) −2.42140 −0.101332 −0.0506662 0.998716i \(-0.516134\pi\)
−0.0506662 + 0.998716i \(0.516134\pi\)
\(572\) 0.513375 0.0214653
\(573\) 0 0
\(574\) 2.56893 0.107225
\(575\) −2.98507 −0.124486
\(576\) 0 0
\(577\) 44.7007 1.86091 0.930456 0.366403i \(-0.119411\pi\)
0.930456 + 0.366403i \(0.119411\pi\)
\(578\) 2.70249 0.112409
\(579\) 0 0
\(580\) −12.4886 −0.518563
\(581\) 13.3752 0.554898
\(582\) 0 0
\(583\) −19.0415 −0.788617
\(584\) 1.24939 0.0517000
\(585\) 0 0
\(586\) 5.20143 0.214869
\(587\) −29.3215 −1.21023 −0.605113 0.796139i \(-0.706872\pi\)
−0.605113 + 0.796139i \(0.706872\pi\)
\(588\) 0 0
\(589\) 19.4902 0.803081
\(590\) 2.52055 0.103770
\(591\) 0 0
\(592\) −3.75949 −0.154514
\(593\) −44.0890 −1.81052 −0.905260 0.424858i \(-0.860324\pi\)
−0.905260 + 0.424858i \(0.860324\pi\)
\(594\) 0 0
\(595\) −6.18245 −0.253456
\(596\) 39.4773 1.61705
\(597\) 0 0
\(598\) 0.0553803 0.00226467
\(599\) 18.2067 0.743907 0.371953 0.928251i \(-0.378688\pi\)
0.371953 + 0.928251i \(0.378688\pi\)
\(600\) 0 0
\(601\) 13.2451 0.540279 0.270139 0.962821i \(-0.412930\pi\)
0.270139 + 0.962821i \(0.412930\pi\)
\(602\) −1.20931 −0.0492876
\(603\) 0 0
\(604\) 21.7897 0.886612
\(605\) −1.54566 −0.0628399
\(606\) 0 0
\(607\) 39.4524 1.60132 0.800662 0.599116i \(-0.204481\pi\)
0.800662 + 0.599116i \(0.204481\pi\)
\(608\) −6.16751 −0.250125
\(609\) 0 0
\(610\) −2.33912 −0.0947084
\(611\) −0.746834 −0.0302137
\(612\) 0 0
\(613\) 32.7000 1.32074 0.660370 0.750940i \(-0.270399\pi\)
0.660370 + 0.750940i \(0.270399\pi\)
\(614\) −5.26167 −0.212344
\(615\) 0 0
\(616\) 7.64771 0.308135
\(617\) 9.43966 0.380026 0.190013 0.981782i \(-0.439147\pi\)
0.190013 + 0.981782i \(0.439147\pi\)
\(618\) 0 0
\(619\) 34.8324 1.40003 0.700016 0.714127i \(-0.253176\pi\)
0.700016 + 0.714127i \(0.253176\pi\)
\(620\) −15.5692 −0.625272
\(621\) 0 0
\(622\) −0.439351 −0.0176164
\(623\) 2.89958 0.116169
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 2.98589 0.119340
\(627\) 0 0
\(628\) 20.3652 0.812658
\(629\) −2.15501 −0.0859258
\(630\) 0 0
\(631\) −29.5893 −1.17793 −0.588965 0.808159i \(-0.700464\pi\)
−0.588965 + 0.808159i \(0.700464\pi\)
\(632\) −11.0321 −0.438834
\(633\) 0 0
\(634\) −5.63244 −0.223693
\(635\) −4.94804 −0.196357
\(636\) 0 0
\(637\) 0.120338 0.00476796
\(638\) 4.26690 0.168928
\(639\) 0 0
\(640\) 6.54107 0.258559
\(641\) −42.2095 −1.66718 −0.833588 0.552387i \(-0.813717\pi\)
−0.833588 + 0.552387i \(0.813717\pi\)
\(642\) 0 0
\(643\) 8.60054 0.339172 0.169586 0.985515i \(-0.445757\pi\)
0.169586 + 0.985515i \(0.445757\pi\)
\(644\) −16.9033 −0.666084
\(645\) 0 0
\(646\) −1.13116 −0.0445049
\(647\) −7.36546 −0.289566 −0.144783 0.989463i \(-0.546248\pi\)
−0.144783 + 0.989463i \(0.546248\pi\)
\(648\) 0 0
\(649\) 35.7148 1.40193
\(650\) −0.0185524 −0.000727685 0
\(651\) 0 0
\(652\) −42.7169 −1.67292
\(653\) −46.8039 −1.83158 −0.915790 0.401658i \(-0.868434\pi\)
−0.915790 + 0.401658i \(0.868434\pi\)
\(654\) 0 0
\(655\) −4.76457 −0.186167
\(656\) 15.1866 0.592936
\(657\) 0 0
\(658\) −5.49650 −0.214276
\(659\) 5.79198 0.225623 0.112812 0.993616i \(-0.464014\pi\)
0.112812 + 0.993616i \(0.464014\pi\)
\(660\) 0 0
\(661\) −17.2823 −0.672205 −0.336102 0.941825i \(-0.609109\pi\)
−0.336102 + 0.941825i \(0.609109\pi\)
\(662\) 3.19127 0.124032
\(663\) 0 0
\(664\) −3.95683 −0.153555
\(665\) −7.08874 −0.274890
\(666\) 0 0
\(667\) −19.0892 −0.739137
\(668\) 18.5741 0.718652
\(669\) 0 0
\(670\) 0.972977 0.0375894
\(671\) −33.1440 −1.27951
\(672\) 0 0
\(673\) −29.0530 −1.11991 −0.559955 0.828523i \(-0.689182\pi\)
−0.559955 + 0.828523i \(0.689182\pi\)
\(674\) 4.72416 0.181968
\(675\) 0 0
\(676\) 25.3736 0.975906
\(677\) 0.715159 0.0274858 0.0137429 0.999906i \(-0.495625\pi\)
0.0137429 + 0.999906i \(0.495625\pi\)
\(678\) 0 0
\(679\) −6.82264 −0.261829
\(680\) 1.82897 0.0701378
\(681\) 0 0
\(682\) 5.31940 0.203690
\(683\) −31.4207 −1.20228 −0.601141 0.799143i \(-0.705287\pi\)
−0.601141 + 0.799143i \(0.705287\pi\)
\(684\) 0 0
\(685\) −16.4896 −0.630037
\(686\) −3.51885 −0.134350
\(687\) 0 0
\(688\) −7.14895 −0.272551
\(689\) 0.529445 0.0201703
\(690\) 0 0
\(691\) −4.95338 −0.188435 −0.0942177 0.995552i \(-0.530035\pi\)
−0.0942177 + 0.995552i \(0.530035\pi\)
\(692\) −22.8725 −0.869482
\(693\) 0 0
\(694\) 6.23023 0.236496
\(695\) 15.7987 0.599278
\(696\) 0 0
\(697\) 8.70523 0.329734
\(698\) 1.19802 0.0453457
\(699\) 0 0
\(700\) 5.66262 0.214027
\(701\) −17.4064 −0.657432 −0.328716 0.944429i \(-0.606616\pi\)
−0.328716 + 0.944429i \(0.606616\pi\)
\(702\) 0 0
\(703\) −2.47091 −0.0931923
\(704\) 21.1912 0.798673
\(705\) 0 0
\(706\) −4.30724 −0.162105
\(707\) 36.4428 1.37057
\(708\) 0 0
\(709\) 36.6600 1.37679 0.688397 0.725334i \(-0.258315\pi\)
0.688397 + 0.725334i \(0.258315\pi\)
\(710\) 2.07046 0.0777029
\(711\) 0 0
\(712\) −0.857790 −0.0321470
\(713\) −23.7979 −0.891237
\(714\) 0 0
\(715\) −0.262877 −0.00983103
\(716\) 20.5840 0.769259
\(717\) 0 0
\(718\) −1.54453 −0.0576412
\(719\) 7.06178 0.263360 0.131680 0.991292i \(-0.457963\pi\)
0.131680 + 0.991292i \(0.457963\pi\)
\(720\) 0 0
\(721\) 6.23059 0.232039
\(722\) 2.82606 0.105175
\(723\) 0 0
\(724\) 28.1360 1.04566
\(725\) 6.39489 0.237500
\(726\) 0 0
\(727\) 1.55147 0.0575408 0.0287704 0.999586i \(-0.490841\pi\)
0.0287704 + 0.999586i \(0.490841\pi\)
\(728\) −0.212643 −0.00788109
\(729\) 0 0
\(730\) −0.316068 −0.0116982
\(731\) −4.09791 −0.151567
\(732\) 0 0
\(733\) −25.3100 −0.934844 −0.467422 0.884034i \(-0.654817\pi\)
−0.467422 + 0.884034i \(0.654817\pi\)
\(734\) 6.42841 0.237277
\(735\) 0 0
\(736\) 7.53061 0.277582
\(737\) 13.7865 0.507833
\(738\) 0 0
\(739\) −37.5699 −1.38203 −0.691016 0.722839i \(-0.742837\pi\)
−0.691016 + 0.722839i \(0.742837\pi\)
\(740\) 1.97381 0.0725587
\(741\) 0 0
\(742\) 3.89658 0.143048
\(743\) 34.4271 1.26301 0.631503 0.775373i \(-0.282438\pi\)
0.631503 + 0.775373i \(0.282438\pi\)
\(744\) 0 0
\(745\) −20.2146 −0.740605
\(746\) −6.14867 −0.225119
\(747\) 0 0
\(748\) 12.8034 0.468137
\(749\) −6.72756 −0.245820
\(750\) 0 0
\(751\) 21.2041 0.773748 0.386874 0.922133i \(-0.373555\pi\)
0.386874 + 0.922133i \(0.373555\pi\)
\(752\) −32.4933 −1.18491
\(753\) 0 0
\(754\) −0.118641 −0.00432063
\(755\) −11.1576 −0.406066
\(756\) 0 0
\(757\) −5.17722 −0.188169 −0.0940846 0.995564i \(-0.529992\pi\)
−0.0940846 + 0.995564i \(0.529992\pi\)
\(758\) 1.54197 0.0560067
\(759\) 0 0
\(760\) 2.09708 0.0760691
\(761\) −1.46516 −0.0531121 −0.0265561 0.999647i \(-0.508454\pi\)
−0.0265561 + 0.999647i \(0.508454\pi\)
\(762\) 0 0
\(763\) −51.4510 −1.86265
\(764\) −27.1491 −0.982220
\(765\) 0 0
\(766\) 2.93523 0.106054
\(767\) −0.993044 −0.0358567
\(768\) 0 0
\(769\) 14.6373 0.527836 0.263918 0.964545i \(-0.414985\pi\)
0.263918 + 0.964545i \(0.414985\pi\)
\(770\) −1.93470 −0.0697219
\(771\) 0 0
\(772\) −34.0375 −1.22503
\(773\) 9.55856 0.343797 0.171899 0.985115i \(-0.445010\pi\)
0.171899 + 0.985115i \(0.445010\pi\)
\(774\) 0 0
\(775\) 7.97229 0.286373
\(776\) 2.01836 0.0724549
\(777\) 0 0
\(778\) 7.71914 0.276744
\(779\) 9.98133 0.357618
\(780\) 0 0
\(781\) 29.3372 1.04977
\(782\) 1.38116 0.0493902
\(783\) 0 0
\(784\) 5.23565 0.186988
\(785\) −10.4281 −0.372195
\(786\) 0 0
\(787\) 34.2818 1.22201 0.611007 0.791625i \(-0.290765\pi\)
0.611007 + 0.791625i \(0.290765\pi\)
\(788\) 30.5037 1.08665
\(789\) 0 0
\(790\) 2.79088 0.0992951
\(791\) 15.8690 0.564235
\(792\) 0 0
\(793\) 0.921565 0.0327257
\(794\) 6.20091 0.220062
\(795\) 0 0
\(796\) −29.1556 −1.03339
\(797\) 20.5514 0.727969 0.363985 0.931405i \(-0.381416\pi\)
0.363985 + 0.931405i \(0.381416\pi\)
\(798\) 0 0
\(799\) −18.6257 −0.658931
\(800\) −2.52276 −0.0891929
\(801\) 0 0
\(802\) −3.36814 −0.118933
\(803\) −4.47849 −0.158043
\(804\) 0 0
\(805\) 8.65545 0.305065
\(806\) −0.147905 −0.00520973
\(807\) 0 0
\(808\) −10.7810 −0.379273
\(809\) 2.35755 0.0828871 0.0414435 0.999141i \(-0.486804\pi\)
0.0414435 + 0.999141i \(0.486804\pi\)
\(810\) 0 0
\(811\) −2.02279 −0.0710298 −0.0355149 0.999369i \(-0.511307\pi\)
−0.0355149 + 0.999369i \(0.511307\pi\)
\(812\) 36.2118 1.27078
\(813\) 0 0
\(814\) −0.674377 −0.0236369
\(815\) 21.8735 0.766194
\(816\) 0 0
\(817\) −4.69863 −0.164384
\(818\) −7.08170 −0.247606
\(819\) 0 0
\(820\) −7.97327 −0.278439
\(821\) 38.4774 1.34287 0.671435 0.741064i \(-0.265678\pi\)
0.671435 + 0.741064i \(0.265678\pi\)
\(822\) 0 0
\(823\) 48.6469 1.69572 0.847862 0.530216i \(-0.177889\pi\)
0.847862 + 0.530216i \(0.177889\pi\)
\(824\) −1.84321 −0.0642113
\(825\) 0 0
\(826\) −7.30854 −0.254297
\(827\) −50.5027 −1.75615 −0.878076 0.478521i \(-0.841173\pi\)
−0.878076 + 0.478521i \(0.841173\pi\)
\(828\) 0 0
\(829\) −13.0462 −0.453113 −0.226557 0.973998i \(-0.572747\pi\)
−0.226557 + 0.973998i \(0.572747\pi\)
\(830\) 1.00099 0.0347449
\(831\) 0 0
\(832\) −0.589218 −0.0204275
\(833\) 3.00117 0.103985
\(834\) 0 0
\(835\) −9.51097 −0.329141
\(836\) 14.6802 0.507726
\(837\) 0 0
\(838\) 2.82040 0.0974290
\(839\) −56.2774 −1.94291 −0.971455 0.237222i \(-0.923763\pi\)
−0.971455 + 0.237222i \(0.923763\pi\)
\(840\) 0 0
\(841\) 11.8946 0.410158
\(842\) 3.95658 0.136353
\(843\) 0 0
\(844\) 15.4841 0.532984
\(845\) −12.9927 −0.446962
\(846\) 0 0
\(847\) 4.48175 0.153995
\(848\) 23.0351 0.791028
\(849\) 0 0
\(850\) −0.462689 −0.0158701
\(851\) 3.01702 0.103422
\(852\) 0 0
\(853\) 22.0873 0.756253 0.378127 0.925754i \(-0.376568\pi\)
0.378127 + 0.925754i \(0.376568\pi\)
\(854\) 6.78248 0.232092
\(855\) 0 0
\(856\) 1.99023 0.0680247
\(857\) 41.4385 1.41551 0.707756 0.706457i \(-0.249708\pi\)
0.707756 + 0.706457i \(0.249708\pi\)
\(858\) 0 0
\(859\) 48.6370 1.65947 0.829737 0.558154i \(-0.188490\pi\)
0.829737 + 0.558154i \(0.188490\pi\)
\(860\) 3.75335 0.127988
\(861\) 0 0
\(862\) 1.84532 0.0628518
\(863\) 39.8223 1.35557 0.677784 0.735261i \(-0.262940\pi\)
0.677784 + 0.735261i \(0.262940\pi\)
\(864\) 0 0
\(865\) 11.7120 0.398220
\(866\) 2.72216 0.0925028
\(867\) 0 0
\(868\) 45.1440 1.53229
\(869\) 39.5452 1.34148
\(870\) 0 0
\(871\) −0.383332 −0.0129887
\(872\) 15.2209 0.515444
\(873\) 0 0
\(874\) 1.58363 0.0535670
\(875\) −2.89958 −0.0980236
\(876\) 0 0
\(877\) −22.1393 −0.747590 −0.373795 0.927511i \(-0.621944\pi\)
−0.373795 + 0.927511i \(0.621944\pi\)
\(878\) 2.47376 0.0834855
\(879\) 0 0
\(880\) −11.4372 −0.385549
\(881\) 8.16284 0.275013 0.137507 0.990501i \(-0.456091\pi\)
0.137507 + 0.990501i \(0.456091\pi\)
\(882\) 0 0
\(883\) −13.9344 −0.468929 −0.234465 0.972125i \(-0.575334\pi\)
−0.234465 + 0.972125i \(0.575334\pi\)
\(884\) −0.355995 −0.0119734
\(885\) 0 0
\(886\) −0.315150 −0.0105877
\(887\) −12.6081 −0.423339 −0.211669 0.977341i \(-0.567890\pi\)
−0.211669 + 0.977341i \(0.567890\pi\)
\(888\) 0 0
\(889\) 14.3472 0.481191
\(890\) 0.217002 0.00727393
\(891\) 0 0
\(892\) 40.2890 1.34897
\(893\) −21.3561 −0.714655
\(894\) 0 0
\(895\) −10.5402 −0.352318
\(896\) −18.9664 −0.633621
\(897\) 0 0
\(898\) −7.24189 −0.241665
\(899\) 50.9819 1.70034
\(900\) 0 0
\(901\) 13.2041 0.439894
\(902\) 2.72417 0.0907049
\(903\) 0 0
\(904\) −4.69455 −0.156139
\(905\) −14.4072 −0.478911
\(906\) 0 0
\(907\) −20.2619 −0.672784 −0.336392 0.941722i \(-0.609207\pi\)
−0.336392 + 0.941722i \(0.609207\pi\)
\(908\) 28.3651 0.941329
\(909\) 0 0
\(910\) 0.0537942 0.00178326
\(911\) −22.2785 −0.738119 −0.369059 0.929406i \(-0.620320\pi\)
−0.369059 + 0.929406i \(0.620320\pi\)
\(912\) 0 0
\(913\) 14.1834 0.469404
\(914\) 3.87491 0.128171
\(915\) 0 0
\(916\) 7.61689 0.251669
\(917\) 13.8152 0.456220
\(918\) 0 0
\(919\) 55.7446 1.83884 0.919422 0.393271i \(-0.128657\pi\)
0.919422 + 0.393271i \(0.128657\pi\)
\(920\) −2.56056 −0.0844193
\(921\) 0 0
\(922\) −7.98656 −0.263023
\(923\) −0.815716 −0.0268496
\(924\) 0 0
\(925\) −1.01070 −0.0332317
\(926\) 7.60741 0.249995
\(927\) 0 0
\(928\) −16.1327 −0.529583
\(929\) −1.15202 −0.0377967 −0.0188983 0.999821i \(-0.506016\pi\)
−0.0188983 + 0.999821i \(0.506016\pi\)
\(930\) 0 0
\(931\) 3.44112 0.112778
\(932\) 12.9451 0.424030
\(933\) 0 0
\(934\) 1.19540 0.0391146
\(935\) −6.55604 −0.214405
\(936\) 0 0
\(937\) −44.8375 −1.46478 −0.732388 0.680887i \(-0.761594\pi\)
−0.732388 + 0.680887i \(0.761594\pi\)
\(938\) −2.82122 −0.0921162
\(939\) 0 0
\(940\) 17.0596 0.556424
\(941\) 1.24362 0.0405408 0.0202704 0.999795i \(-0.493547\pi\)
0.0202704 + 0.999795i \(0.493547\pi\)
\(942\) 0 0
\(943\) −12.1873 −0.396875
\(944\) −43.2053 −1.40621
\(945\) 0 0
\(946\) −1.28238 −0.0416938
\(947\) −39.5512 −1.28524 −0.642621 0.766185i \(-0.722153\pi\)
−0.642621 + 0.766185i \(0.722153\pi\)
\(948\) 0 0
\(949\) 0.124524 0.00404222
\(950\) −0.530516 −0.0172122
\(951\) 0 0
\(952\) −5.30324 −0.171879
\(953\) −43.1091 −1.39644 −0.698221 0.715883i \(-0.746024\pi\)
−0.698221 + 0.715883i \(0.746024\pi\)
\(954\) 0 0
\(955\) 13.9019 0.449854
\(956\) −37.6279 −1.21697
\(957\) 0 0
\(958\) −1.67619 −0.0541553
\(959\) 47.8130 1.54396
\(960\) 0 0
\(961\) 32.5573 1.05024
\(962\) 0.0187510 0.000604555 0
\(963\) 0 0
\(964\) −38.3493 −1.23515
\(965\) 17.4291 0.561062
\(966\) 0 0
\(967\) 9.21109 0.296209 0.148104 0.988972i \(-0.452683\pi\)
0.148104 + 0.988972i \(0.452683\pi\)
\(968\) −1.32585 −0.0426144
\(969\) 0 0
\(970\) −0.510601 −0.0163944
\(971\) 35.7097 1.14598 0.572990 0.819562i \(-0.305783\pi\)
0.572990 + 0.819562i \(0.305783\pi\)
\(972\) 0 0
\(973\) −45.8095 −1.46858
\(974\) −5.89742 −0.188965
\(975\) 0 0
\(976\) 40.0954 1.28342
\(977\) 27.4614 0.878569 0.439284 0.898348i \(-0.355232\pi\)
0.439284 + 0.898348i \(0.355232\pi\)
\(978\) 0 0
\(979\) 3.07479 0.0982708
\(980\) −2.74883 −0.0878081
\(981\) 0 0
\(982\) 4.19905 0.133997
\(983\) 53.3643 1.70206 0.851029 0.525118i \(-0.175979\pi\)
0.851029 + 0.525118i \(0.175979\pi\)
\(984\) 0 0
\(985\) −15.6196 −0.497683
\(986\) −2.95885 −0.0942289
\(987\) 0 0
\(988\) −0.408181 −0.0129860
\(989\) 5.73710 0.182429
\(990\) 0 0
\(991\) 0.953902 0.0303017 0.0151509 0.999885i \(-0.495177\pi\)
0.0151509 + 0.999885i \(0.495177\pi\)
\(992\) −20.1121 −0.638561
\(993\) 0 0
\(994\) −6.00345 −0.190418
\(995\) 14.9293 0.473290
\(996\) 0 0
\(997\) −23.3821 −0.740519 −0.370260 0.928928i \(-0.620731\pi\)
−0.370260 + 0.928928i \(0.620731\pi\)
\(998\) −3.76007 −0.119023
\(999\) 0 0
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 \(a_p\))