Properties

Label 6003.2.a.t.1.14
Level 6003
Weight 2
Character 6003.1
Self dual Yes
Analytic conductor 47.934
Analytic rank 1
Dimension 22
CM No

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Newspace parameters

Level: \( N \) = \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(1\)
Dimension: \(22\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.289055 q^{2} -1.91645 q^{4} -0.894239 q^{5} +3.31166 q^{7} -1.13207 q^{8} +O(q^{10})\) \(q+0.289055 q^{2} -1.91645 q^{4} -0.894239 q^{5} +3.31166 q^{7} -1.13207 q^{8} -0.258484 q^{10} -3.47272 q^{11} +1.33472 q^{13} +0.957253 q^{14} +3.50566 q^{16} +4.10507 q^{17} -2.37402 q^{19} +1.71376 q^{20} -1.00381 q^{22} +1.00000 q^{23} -4.20034 q^{25} +0.385806 q^{26} -6.34663 q^{28} +1.00000 q^{29} -8.16928 q^{31} +3.27747 q^{32} +1.18659 q^{34} -2.96142 q^{35} -7.23767 q^{37} -0.686223 q^{38} +1.01234 q^{40} +2.74639 q^{41} +1.38389 q^{43} +6.65529 q^{44} +0.289055 q^{46} +2.36806 q^{47} +3.96711 q^{49} -1.21413 q^{50} -2.55791 q^{52} +1.52853 q^{53} +3.10545 q^{55} -3.74903 q^{56} +0.289055 q^{58} +15.2608 q^{59} +4.80702 q^{61} -2.36137 q^{62} -6.06396 q^{64} -1.19355 q^{65} -12.6857 q^{67} -7.86716 q^{68} -0.856013 q^{70} -0.717856 q^{71} -11.3827 q^{73} -2.09209 q^{74} +4.54969 q^{76} -11.5005 q^{77} +8.33380 q^{79} -3.13490 q^{80} +0.793858 q^{82} -0.376134 q^{83} -3.67092 q^{85} +0.400021 q^{86} +3.93136 q^{88} +17.2590 q^{89} +4.42013 q^{91} -1.91645 q^{92} +0.684501 q^{94} +2.12294 q^{95} +11.7592 q^{97} +1.14671 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} + O(q^{10}) \) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} - 12q^{10} - 28q^{13} - q^{14} + 3q^{16} - 10q^{17} - 8q^{19} - 11q^{22} + 22q^{23} + 11q^{26} - 21q^{28} + 22q^{29} - 18q^{31} + 5q^{32} - 33q^{34} + 2q^{35} - 28q^{37} + 14q^{38} - 30q^{40} - 10q^{41} - 14q^{43} + 37q^{44} - 3q^{46} - 18q^{47} + 2q^{49} + 7q^{50} - 57q^{52} + 20q^{53} - 42q^{55} - 2q^{56} - 3q^{58} - 20q^{59} - 38q^{61} + 4q^{62} - 24q^{64} + 12q^{65} - 50q^{67} + 11q^{68} - 48q^{70} + 12q^{71} - 46q^{73} - 6q^{74} - 16q^{76} - 14q^{77} - 20q^{79} - 58q^{80} - 42q^{82} + 22q^{83} - 66q^{85} + 22q^{86} - 68q^{88} - 14q^{89} - 16q^{91} + 17q^{92} - 27q^{94} - 20q^{95} - 48q^{97} - 28q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.289055 0.204393 0.102196 0.994764i \(-0.467413\pi\)
0.102196 + 0.994764i \(0.467413\pi\)
\(3\) 0 0
\(4\) −1.91645 −0.958224
\(5\) −0.894239 −0.399916 −0.199958 0.979804i \(-0.564081\pi\)
−0.199958 + 0.979804i \(0.564081\pi\)
\(6\) 0 0
\(7\) 3.31166 1.25169 0.625846 0.779947i \(-0.284754\pi\)
0.625846 + 0.779947i \(0.284754\pi\)
\(8\) −1.13207 −0.400247
\(9\) 0 0
\(10\) −0.258484 −0.0817400
\(11\) −3.47272 −1.04707 −0.523533 0.852005i \(-0.675386\pi\)
−0.523533 + 0.852005i \(0.675386\pi\)
\(12\) 0 0
\(13\) 1.33472 0.370183 0.185092 0.982721i \(-0.440742\pi\)
0.185092 + 0.982721i \(0.440742\pi\)
\(14\) 0.957253 0.255837
\(15\) 0 0
\(16\) 3.50566 0.876416
\(17\) 4.10507 0.995627 0.497813 0.867284i \(-0.334136\pi\)
0.497813 + 0.867284i \(0.334136\pi\)
\(18\) 0 0
\(19\) −2.37402 −0.544638 −0.272319 0.962207i \(-0.587791\pi\)
−0.272319 + 0.962207i \(0.587791\pi\)
\(20\) 1.71376 0.383209
\(21\) 0 0
\(22\) −1.00381 −0.214013
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −4.20034 −0.840067
\(26\) 0.385806 0.0756629
\(27\) 0 0
\(28\) −6.34663 −1.19940
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) −8.16928 −1.46725 −0.733623 0.679557i \(-0.762172\pi\)
−0.733623 + 0.679557i \(0.762172\pi\)
\(32\) 3.27747 0.579380
\(33\) 0 0
\(34\) 1.18659 0.203499
\(35\) −2.96142 −0.500571
\(36\) 0 0
\(37\) −7.23767 −1.18987 −0.594933 0.803775i \(-0.702821\pi\)
−0.594933 + 0.803775i \(0.702821\pi\)
\(38\) −0.686223 −0.111320
\(39\) 0 0
\(40\) 1.01234 0.160065
\(41\) 2.74639 0.428914 0.214457 0.976733i \(-0.431202\pi\)
0.214457 + 0.976733i \(0.431202\pi\)
\(42\) 0 0
\(43\) 1.38389 0.211041 0.105521 0.994417i \(-0.466349\pi\)
0.105521 + 0.994417i \(0.466349\pi\)
\(44\) 6.65529 1.00332
\(45\) 0 0
\(46\) 0.289055 0.0426189
\(47\) 2.36806 0.345417 0.172709 0.984973i \(-0.444748\pi\)
0.172709 + 0.984973i \(0.444748\pi\)
\(48\) 0 0
\(49\) 3.96711 0.566731
\(50\) −1.21413 −0.171704
\(51\) 0 0
\(52\) −2.55791 −0.354719
\(53\) 1.52853 0.209960 0.104980 0.994474i \(-0.466522\pi\)
0.104980 + 0.994474i \(0.466522\pi\)
\(54\) 0 0
\(55\) 3.10545 0.418738
\(56\) −3.74903 −0.500985
\(57\) 0 0
\(58\) 0.289055 0.0379548
\(59\) 15.2608 1.98679 0.993395 0.114745i \(-0.0366051\pi\)
0.993395 + 0.114745i \(0.0366051\pi\)
\(60\) 0 0
\(61\) 4.80702 0.615476 0.307738 0.951471i \(-0.400428\pi\)
0.307738 + 0.951471i \(0.400428\pi\)
\(62\) −2.36137 −0.299895
\(63\) 0 0
\(64\) −6.06396 −0.757995
\(65\) −1.19355 −0.148042
\(66\) 0 0
\(67\) −12.6857 −1.54980 −0.774900 0.632083i \(-0.782200\pi\)
−0.774900 + 0.632083i \(0.782200\pi\)
\(68\) −7.86716 −0.954033
\(69\) 0 0
\(70\) −0.856013 −0.102313
\(71\) −0.717856 −0.0851938 −0.0425969 0.999092i \(-0.513563\pi\)
−0.0425969 + 0.999092i \(0.513563\pi\)
\(72\) 0 0
\(73\) −11.3827 −1.33225 −0.666124 0.745841i \(-0.732048\pi\)
−0.666124 + 0.745841i \(0.732048\pi\)
\(74\) −2.09209 −0.243200
\(75\) 0 0
\(76\) 4.54969 0.521885
\(77\) −11.5005 −1.31060
\(78\) 0 0
\(79\) 8.33380 0.937625 0.468813 0.883298i \(-0.344682\pi\)
0.468813 + 0.883298i \(0.344682\pi\)
\(80\) −3.13490 −0.350493
\(81\) 0 0
\(82\) 0.793858 0.0876669
\(83\) −0.376134 −0.0412860 −0.0206430 0.999787i \(-0.506571\pi\)
−0.0206430 + 0.999787i \(0.506571\pi\)
\(84\) 0 0
\(85\) −3.67092 −0.398167
\(86\) 0.400021 0.0431353
\(87\) 0 0
\(88\) 3.93136 0.419085
\(89\) 17.2590 1.82945 0.914724 0.404079i \(-0.132408\pi\)
0.914724 + 0.404079i \(0.132408\pi\)
\(90\) 0 0
\(91\) 4.42013 0.463355
\(92\) −1.91645 −0.199803
\(93\) 0 0
\(94\) 0.684501 0.0706009
\(95\) 2.12294 0.217809
\(96\) 0 0
\(97\) 11.7592 1.19397 0.596984 0.802253i \(-0.296365\pi\)
0.596984 + 0.802253i \(0.296365\pi\)
\(98\) 1.14671 0.115836
\(99\) 0 0
\(100\) 8.04972 0.804972
\(101\) −3.08171 −0.306642 −0.153321 0.988176i \(-0.548997\pi\)
−0.153321 + 0.988176i \(0.548997\pi\)
\(102\) 0 0
\(103\) −7.26054 −0.715402 −0.357701 0.933836i \(-0.616439\pi\)
−0.357701 + 0.933836i \(0.616439\pi\)
\(104\) −1.51099 −0.148165
\(105\) 0 0
\(106\) 0.441831 0.0429144
\(107\) −7.59019 −0.733771 −0.366886 0.930266i \(-0.619576\pi\)
−0.366886 + 0.930266i \(0.619576\pi\)
\(108\) 0 0
\(109\) 0.347144 0.0332503 0.0166252 0.999862i \(-0.494708\pi\)
0.0166252 + 0.999862i \(0.494708\pi\)
\(110\) 0.897645 0.0855871
\(111\) 0 0
\(112\) 11.6096 1.09700
\(113\) −10.6630 −1.00309 −0.501546 0.865131i \(-0.667235\pi\)
−0.501546 + 0.865131i \(0.667235\pi\)
\(114\) 0 0
\(115\) −0.894239 −0.0833882
\(116\) −1.91645 −0.177938
\(117\) 0 0
\(118\) 4.41122 0.406086
\(119\) 13.5946 1.24622
\(120\) 0 0
\(121\) 1.05982 0.0963469
\(122\) 1.38949 0.125799
\(123\) 0 0
\(124\) 15.6560 1.40595
\(125\) 8.22730 0.735872
\(126\) 0 0
\(127\) −2.00396 −0.177823 −0.0889115 0.996040i \(-0.528339\pi\)
−0.0889115 + 0.996040i \(0.528339\pi\)
\(128\) −8.30776 −0.734309
\(129\) 0 0
\(130\) −0.345003 −0.0302588
\(131\) 0.854972 0.0746993 0.0373496 0.999302i \(-0.488108\pi\)
0.0373496 + 0.999302i \(0.488108\pi\)
\(132\) 0 0
\(133\) −7.86196 −0.681719
\(134\) −3.66686 −0.316768
\(135\) 0 0
\(136\) −4.64723 −0.398496
\(137\) −11.8624 −1.01347 −0.506736 0.862102i \(-0.669148\pi\)
−0.506736 + 0.862102i \(0.669148\pi\)
\(138\) 0 0
\(139\) 10.9558 0.929257 0.464628 0.885506i \(-0.346188\pi\)
0.464628 + 0.885506i \(0.346188\pi\)
\(140\) 5.67540 0.479659
\(141\) 0 0
\(142\) −0.207500 −0.0174130
\(143\) −4.63510 −0.387606
\(144\) 0 0
\(145\) −0.894239 −0.0742625
\(146\) −3.29023 −0.272302
\(147\) 0 0
\(148\) 13.8706 1.14016
\(149\) −21.5784 −1.76777 −0.883887 0.467700i \(-0.845083\pi\)
−0.883887 + 0.467700i \(0.845083\pi\)
\(150\) 0 0
\(151\) −14.0988 −1.14734 −0.573672 0.819085i \(-0.694482\pi\)
−0.573672 + 0.819085i \(0.694482\pi\)
\(152\) 2.68756 0.217990
\(153\) 0 0
\(154\) −3.32428 −0.267878
\(155\) 7.30529 0.586775
\(156\) 0 0
\(157\) −15.4088 −1.22976 −0.614878 0.788622i \(-0.710795\pi\)
−0.614878 + 0.788622i \(0.710795\pi\)
\(158\) 2.40893 0.191644
\(159\) 0 0
\(160\) −2.93084 −0.231703
\(161\) 3.31166 0.260996
\(162\) 0 0
\(163\) −4.10759 −0.321731 −0.160866 0.986976i \(-0.551429\pi\)
−0.160866 + 0.986976i \(0.551429\pi\)
\(164\) −5.26331 −0.410995
\(165\) 0 0
\(166\) −0.108723 −0.00843857
\(167\) −2.48477 −0.192277 −0.0961386 0.995368i \(-0.530649\pi\)
−0.0961386 + 0.995368i \(0.530649\pi\)
\(168\) 0 0
\(169\) −11.2185 −0.862964
\(170\) −1.06110 −0.0813825
\(171\) 0 0
\(172\) −2.65215 −0.202225
\(173\) −0.886694 −0.0674141 −0.0337070 0.999432i \(-0.510731\pi\)
−0.0337070 + 0.999432i \(0.510731\pi\)
\(174\) 0 0
\(175\) −13.9101 −1.05150
\(176\) −12.1742 −0.917665
\(177\) 0 0
\(178\) 4.98880 0.373926
\(179\) −19.6025 −1.46516 −0.732580 0.680681i \(-0.761684\pi\)
−0.732580 + 0.680681i \(0.761684\pi\)
\(180\) 0 0
\(181\) 0.855906 0.0636190 0.0318095 0.999494i \(-0.489873\pi\)
0.0318095 + 0.999494i \(0.489873\pi\)
\(182\) 1.27766 0.0947065
\(183\) 0 0
\(184\) −1.13207 −0.0834572
\(185\) 6.47221 0.475846
\(186\) 0 0
\(187\) −14.2558 −1.04249
\(188\) −4.53827 −0.330987
\(189\) 0 0
\(190\) 0.613648 0.0445187
\(191\) −22.0227 −1.59351 −0.796753 0.604305i \(-0.793451\pi\)
−0.796753 + 0.604305i \(0.793451\pi\)
\(192\) 0 0
\(193\) −17.3403 −1.24818 −0.624091 0.781352i \(-0.714530\pi\)
−0.624091 + 0.781352i \(0.714530\pi\)
\(194\) 3.39906 0.244039
\(195\) 0 0
\(196\) −7.60277 −0.543055
\(197\) −10.2972 −0.733645 −0.366822 0.930291i \(-0.619554\pi\)
−0.366822 + 0.930291i \(0.619554\pi\)
\(198\) 0 0
\(199\) −24.4201 −1.73109 −0.865546 0.500829i \(-0.833029\pi\)
−0.865546 + 0.500829i \(0.833029\pi\)
\(200\) 4.75507 0.336234
\(201\) 0 0
\(202\) −0.890785 −0.0626754
\(203\) 3.31166 0.232433
\(204\) 0 0
\(205\) −2.45593 −0.171529
\(206\) −2.09870 −0.146223
\(207\) 0 0
\(208\) 4.67906 0.324435
\(209\) 8.24433 0.570272
\(210\) 0 0
\(211\) 8.64080 0.594857 0.297429 0.954744i \(-0.403871\pi\)
0.297429 + 0.954744i \(0.403871\pi\)
\(212\) −2.92936 −0.201189
\(213\) 0 0
\(214\) −2.19398 −0.149978
\(215\) −1.23753 −0.0843988
\(216\) 0 0
\(217\) −27.0539 −1.83654
\(218\) 0.100344 0.00679613
\(219\) 0 0
\(220\) −5.95142 −0.401245
\(221\) 5.47911 0.368565
\(222\) 0 0
\(223\) 13.1563 0.881009 0.440505 0.897750i \(-0.354800\pi\)
0.440505 + 0.897750i \(0.354800\pi\)
\(224\) 10.8539 0.725205
\(225\) 0 0
\(226\) −3.08220 −0.205025
\(227\) 9.56440 0.634812 0.317406 0.948290i \(-0.397188\pi\)
0.317406 + 0.948290i \(0.397188\pi\)
\(228\) 0 0
\(229\) −0.877427 −0.0579820 −0.0289910 0.999580i \(-0.509229\pi\)
−0.0289910 + 0.999580i \(0.509229\pi\)
\(230\) −0.258484 −0.0170440
\(231\) 0 0
\(232\) −1.13207 −0.0743240
\(233\) 2.16205 0.141641 0.0708204 0.997489i \(-0.477438\pi\)
0.0708204 + 0.997489i \(0.477438\pi\)
\(234\) 0 0
\(235\) −2.11761 −0.138138
\(236\) −29.2466 −1.90379
\(237\) 0 0
\(238\) 3.92960 0.254718
\(239\) 27.0986 1.75286 0.876430 0.481529i \(-0.159918\pi\)
0.876430 + 0.481529i \(0.159918\pi\)
\(240\) 0 0
\(241\) 4.64431 0.299166 0.149583 0.988749i \(-0.452207\pi\)
0.149583 + 0.988749i \(0.452207\pi\)
\(242\) 0.306345 0.0196926
\(243\) 0 0
\(244\) −9.21240 −0.589763
\(245\) −3.54755 −0.226645
\(246\) 0 0
\(247\) −3.16864 −0.201616
\(248\) 9.24819 0.587261
\(249\) 0 0
\(250\) 2.37814 0.150407
\(251\) −0.336274 −0.0212254 −0.0106127 0.999944i \(-0.503378\pi\)
−0.0106127 + 0.999944i \(0.503378\pi\)
\(252\) 0 0
\(253\) −3.47272 −0.218328
\(254\) −0.579256 −0.0363458
\(255\) 0 0
\(256\) 9.72652 0.607907
\(257\) 4.19170 0.261471 0.130736 0.991417i \(-0.458266\pi\)
0.130736 + 0.991417i \(0.458266\pi\)
\(258\) 0 0
\(259\) −23.9687 −1.48934
\(260\) 2.28738 0.141858
\(261\) 0 0
\(262\) 0.247134 0.0152680
\(263\) 28.9512 1.78521 0.892605 0.450840i \(-0.148876\pi\)
0.892605 + 0.450840i \(0.148876\pi\)
\(264\) 0 0
\(265\) −1.36688 −0.0839665
\(266\) −2.27254 −0.139338
\(267\) 0 0
\(268\) 24.3114 1.48506
\(269\) −23.7525 −1.44822 −0.724108 0.689686i \(-0.757748\pi\)
−0.724108 + 0.689686i \(0.757748\pi\)
\(270\) 0 0
\(271\) 3.93157 0.238826 0.119413 0.992845i \(-0.461899\pi\)
0.119413 + 0.992845i \(0.461899\pi\)
\(272\) 14.3910 0.872583
\(273\) 0 0
\(274\) −3.42888 −0.207146
\(275\) 14.5866 0.879606
\(276\) 0 0
\(277\) 2.29969 0.138175 0.0690875 0.997611i \(-0.477991\pi\)
0.0690875 + 0.997611i \(0.477991\pi\)
\(278\) 3.16682 0.189933
\(279\) 0 0
\(280\) 3.35253 0.200352
\(281\) −6.10006 −0.363899 −0.181949 0.983308i \(-0.558241\pi\)
−0.181949 + 0.983308i \(0.558241\pi\)
\(282\) 0 0
\(283\) −10.0481 −0.597296 −0.298648 0.954363i \(-0.596536\pi\)
−0.298648 + 0.954363i \(0.596536\pi\)
\(284\) 1.37573 0.0816347
\(285\) 0 0
\(286\) −1.33980 −0.0792240
\(287\) 9.09511 0.536868
\(288\) 0 0
\(289\) −0.148368 −0.00872752
\(290\) −0.258484 −0.0151787
\(291\) 0 0
\(292\) 21.8144 1.27659
\(293\) −9.61185 −0.561530 −0.280765 0.959777i \(-0.590588\pi\)
−0.280765 + 0.959777i \(0.590588\pi\)
\(294\) 0 0
\(295\) −13.6468 −0.794549
\(296\) 8.19354 0.476240
\(297\) 0 0
\(298\) −6.23736 −0.361321
\(299\) 1.33472 0.0771886
\(300\) 0 0
\(301\) 4.58298 0.264158
\(302\) −4.07533 −0.234509
\(303\) 0 0
\(304\) −8.32253 −0.477330
\(305\) −4.29862 −0.246139
\(306\) 0 0
\(307\) −19.8876 −1.13505 −0.567523 0.823358i \(-0.692098\pi\)
−0.567523 + 0.823358i \(0.692098\pi\)
\(308\) 22.0401 1.25585
\(309\) 0 0
\(310\) 2.11163 0.119933
\(311\) −12.7548 −0.723257 −0.361629 0.932322i \(-0.617779\pi\)
−0.361629 + 0.932322i \(0.617779\pi\)
\(312\) 0 0
\(313\) −2.13988 −0.120953 −0.0604766 0.998170i \(-0.519262\pi\)
−0.0604766 + 0.998170i \(0.519262\pi\)
\(314\) −4.45399 −0.251353
\(315\) 0 0
\(316\) −15.9713 −0.898455
\(317\) −30.1388 −1.69276 −0.846381 0.532577i \(-0.821224\pi\)
−0.846381 + 0.532577i \(0.821224\pi\)
\(318\) 0 0
\(319\) −3.47272 −0.194435
\(320\) 5.42263 0.303134
\(321\) 0 0
\(322\) 0.957253 0.0533456
\(323\) −9.74554 −0.542256
\(324\) 0 0
\(325\) −5.60625 −0.310979
\(326\) −1.18732 −0.0657596
\(327\) 0 0
\(328\) −3.10910 −0.171671
\(329\) 7.84223 0.432356
\(330\) 0 0
\(331\) −5.18664 −0.285084 −0.142542 0.989789i \(-0.545528\pi\)
−0.142542 + 0.989789i \(0.545528\pi\)
\(332\) 0.720840 0.0395612
\(333\) 0 0
\(334\) −0.718235 −0.0393001
\(335\) 11.3440 0.619790
\(336\) 0 0
\(337\) 3.43321 0.187019 0.0935093 0.995618i \(-0.470192\pi\)
0.0935093 + 0.995618i \(0.470192\pi\)
\(338\) −3.24278 −0.176384
\(339\) 0 0
\(340\) 7.03512 0.381533
\(341\) 28.3697 1.53630
\(342\) 0 0
\(343\) −10.0439 −0.542319
\(344\) −1.56666 −0.0844686
\(345\) 0 0
\(346\) −0.256303 −0.0137790
\(347\) 28.6744 1.53932 0.769661 0.638453i \(-0.220425\pi\)
0.769661 + 0.638453i \(0.220425\pi\)
\(348\) 0 0
\(349\) −19.5605 −1.04705 −0.523524 0.852011i \(-0.675383\pi\)
−0.523524 + 0.852011i \(0.675383\pi\)
\(350\) −4.02079 −0.214920
\(351\) 0 0
\(352\) −11.3817 −0.606649
\(353\) 1.49472 0.0795560 0.0397780 0.999209i \(-0.487335\pi\)
0.0397780 + 0.999209i \(0.487335\pi\)
\(354\) 0 0
\(355\) 0.641935 0.0340704
\(356\) −33.0759 −1.75302
\(357\) 0 0
\(358\) −5.66621 −0.299468
\(359\) −3.55884 −0.187828 −0.0939142 0.995580i \(-0.529938\pi\)
−0.0939142 + 0.995580i \(0.529938\pi\)
\(360\) 0 0
\(361\) −13.3640 −0.703369
\(362\) 0.247404 0.0130033
\(363\) 0 0
\(364\) −8.47094 −0.443998
\(365\) 10.1789 0.532787
\(366\) 0 0
\(367\) 26.5002 1.38330 0.691649 0.722234i \(-0.256884\pi\)
0.691649 + 0.722234i \(0.256884\pi\)
\(368\) 3.50566 0.182745
\(369\) 0 0
\(370\) 1.87083 0.0972596
\(371\) 5.06199 0.262806
\(372\) 0 0
\(373\) −7.34016 −0.380059 −0.190030 0.981778i \(-0.560858\pi\)
−0.190030 + 0.981778i \(0.560858\pi\)
\(374\) −4.12071 −0.213077
\(375\) 0 0
\(376\) −2.68081 −0.138252
\(377\) 1.33472 0.0687413
\(378\) 0 0
\(379\) −23.6874 −1.21674 −0.608370 0.793654i \(-0.708176\pi\)
−0.608370 + 0.793654i \(0.708176\pi\)
\(380\) −4.06851 −0.208710
\(381\) 0 0
\(382\) −6.36577 −0.325701
\(383\) 0.481105 0.0245833 0.0122917 0.999924i \(-0.496087\pi\)
0.0122917 + 0.999924i \(0.496087\pi\)
\(384\) 0 0
\(385\) 10.2842 0.524131
\(386\) −5.01230 −0.255119
\(387\) 0 0
\(388\) −22.5359 −1.14409
\(389\) −24.1016 −1.22200 −0.610999 0.791631i \(-0.709232\pi\)
−0.610999 + 0.791631i \(0.709232\pi\)
\(390\) 0 0
\(391\) 4.10507 0.207603
\(392\) −4.49105 −0.226832
\(393\) 0 0
\(394\) −2.97646 −0.149952
\(395\) −7.45241 −0.374971
\(396\) 0 0
\(397\) −20.8364 −1.04575 −0.522874 0.852410i \(-0.675140\pi\)
−0.522874 + 0.852410i \(0.675140\pi\)
\(398\) −7.05875 −0.353823
\(399\) 0 0
\(400\) −14.7250 −0.736248
\(401\) 2.85890 0.142767 0.0713833 0.997449i \(-0.477259\pi\)
0.0713833 + 0.997449i \(0.477259\pi\)
\(402\) 0 0
\(403\) −10.9037 −0.543150
\(404\) 5.90594 0.293832
\(405\) 0 0
\(406\) 0.957253 0.0475077
\(407\) 25.1344 1.24587
\(408\) 0 0
\(409\) 17.0699 0.844051 0.422025 0.906584i \(-0.361319\pi\)
0.422025 + 0.906584i \(0.361319\pi\)
\(410\) −0.709899 −0.0350594
\(411\) 0 0
\(412\) 13.9144 0.685515
\(413\) 50.5387 2.48685
\(414\) 0 0
\(415\) 0.336353 0.0165109
\(416\) 4.37449 0.214477
\(417\) 0 0
\(418\) 2.38307 0.116560
\(419\) 14.0978 0.688722 0.344361 0.938837i \(-0.388096\pi\)
0.344361 + 0.938837i \(0.388096\pi\)
\(420\) 0 0
\(421\) 22.6436 1.10358 0.551791 0.833982i \(-0.313945\pi\)
0.551791 + 0.833982i \(0.313945\pi\)
\(422\) 2.49767 0.121585
\(423\) 0 0
\(424\) −1.73041 −0.0840360
\(425\) −17.2427 −0.836393
\(426\) 0 0
\(427\) 15.9192 0.770385
\(428\) 14.5462 0.703117
\(429\) 0 0
\(430\) −0.357714 −0.0172505
\(431\) −10.3999 −0.500945 −0.250472 0.968124i \(-0.580586\pi\)
−0.250472 + 0.968124i \(0.580586\pi\)
\(432\) 0 0
\(433\) 15.9738 0.767650 0.383825 0.923406i \(-0.374607\pi\)
0.383825 + 0.923406i \(0.374607\pi\)
\(434\) −7.82007 −0.375375
\(435\) 0 0
\(436\) −0.665282 −0.0318612
\(437\) −2.37402 −0.113565
\(438\) 0 0
\(439\) −31.9678 −1.52574 −0.762871 0.646551i \(-0.776211\pi\)
−0.762871 + 0.646551i \(0.776211\pi\)
\(440\) −3.51558 −0.167599
\(441\) 0 0
\(442\) 1.58376 0.0753320
\(443\) 7.99836 0.380014 0.190007 0.981783i \(-0.439149\pi\)
0.190007 + 0.981783i \(0.439149\pi\)
\(444\) 0 0
\(445\) −15.4337 −0.731625
\(446\) 3.80289 0.180072
\(447\) 0 0
\(448\) −20.0818 −0.948775
\(449\) −9.91225 −0.467788 −0.233894 0.972262i \(-0.575147\pi\)
−0.233894 + 0.972262i \(0.575147\pi\)
\(450\) 0 0
\(451\) −9.53745 −0.449101
\(452\) 20.4351 0.961186
\(453\) 0 0
\(454\) 2.76464 0.129751
\(455\) −3.95265 −0.185303
\(456\) 0 0
\(457\) −24.1434 −1.12938 −0.564690 0.825303i \(-0.691004\pi\)
−0.564690 + 0.825303i \(0.691004\pi\)
\(458\) −0.253625 −0.0118511
\(459\) 0 0
\(460\) 1.71376 0.0799046
\(461\) 24.3613 1.13462 0.567310 0.823505i \(-0.307984\pi\)
0.567310 + 0.823505i \(0.307984\pi\)
\(462\) 0 0
\(463\) 33.5748 1.56035 0.780177 0.625559i \(-0.215129\pi\)
0.780177 + 0.625559i \(0.215129\pi\)
\(464\) 3.50566 0.162746
\(465\) 0 0
\(466\) 0.624953 0.0289504
\(467\) −21.8840 −1.01267 −0.506336 0.862337i \(-0.669000\pi\)
−0.506336 + 0.862337i \(0.669000\pi\)
\(468\) 0 0
\(469\) −42.0107 −1.93987
\(470\) −0.612107 −0.0282344
\(471\) 0 0
\(472\) −17.2763 −0.795206
\(473\) −4.80587 −0.220974
\(474\) 0 0
\(475\) 9.97169 0.457533
\(476\) −26.0534 −1.19415
\(477\) 0 0
\(478\) 7.83298 0.358272
\(479\) −33.7604 −1.54255 −0.771277 0.636499i \(-0.780382\pi\)
−0.771277 + 0.636499i \(0.780382\pi\)
\(480\) 0 0
\(481\) −9.66023 −0.440469
\(482\) 1.34246 0.0611475
\(483\) 0 0
\(484\) −2.03108 −0.0923219
\(485\) −10.5156 −0.477487
\(486\) 0 0
\(487\) 23.9241 1.08410 0.542052 0.840345i \(-0.317647\pi\)
0.542052 + 0.840345i \(0.317647\pi\)
\(488\) −5.44188 −0.246342
\(489\) 0 0
\(490\) −1.02544 −0.0463245
\(491\) −38.6555 −1.74450 −0.872248 0.489063i \(-0.837339\pi\)
−0.872248 + 0.489063i \(0.837339\pi\)
\(492\) 0 0
\(493\) 4.10507 0.184883
\(494\) −0.915913 −0.0412089
\(495\) 0 0
\(496\) −28.6388 −1.28592
\(497\) −2.37730 −0.106636
\(498\) 0 0
\(499\) −17.6483 −0.790045 −0.395022 0.918672i \(-0.629263\pi\)
−0.395022 + 0.918672i \(0.629263\pi\)
\(500\) −15.7672 −0.705130
\(501\) 0 0
\(502\) −0.0972017 −0.00433833
\(503\) 8.02256 0.357708 0.178854 0.983876i \(-0.442761\pi\)
0.178854 + 0.983876i \(0.442761\pi\)
\(504\) 0 0
\(505\) 2.75579 0.122631
\(506\) −1.00381 −0.0446247
\(507\) 0 0
\(508\) 3.84049 0.170394
\(509\) 15.2539 0.676117 0.338059 0.941125i \(-0.390230\pi\)
0.338059 + 0.941125i \(0.390230\pi\)
\(510\) 0 0
\(511\) −37.6957 −1.66756
\(512\) 19.4270 0.858561
\(513\) 0 0
\(514\) 1.21163 0.0534428
\(515\) 6.49266 0.286101
\(516\) 0 0
\(517\) −8.22363 −0.361675
\(518\) −6.92828 −0.304411
\(519\) 0 0
\(520\) 1.35119 0.0592535
\(521\) −22.3514 −0.979231 −0.489615 0.871939i \(-0.662863\pi\)
−0.489615 + 0.871939i \(0.662863\pi\)
\(522\) 0 0
\(523\) 19.1215 0.836126 0.418063 0.908418i \(-0.362709\pi\)
0.418063 + 0.908418i \(0.362709\pi\)
\(524\) −1.63851 −0.0715786
\(525\) 0 0
\(526\) 8.36850 0.364884
\(527\) −33.5355 −1.46083
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) −0.395102 −0.0171621
\(531\) 0 0
\(532\) 15.0670 0.653239
\(533\) 3.66565 0.158777
\(534\) 0 0
\(535\) 6.78745 0.293447
\(536\) 14.3611 0.620303
\(537\) 0 0
\(538\) −6.86579 −0.296005
\(539\) −13.7767 −0.593404
\(540\) 0 0
\(541\) −16.4775 −0.708422 −0.354211 0.935166i \(-0.615251\pi\)
−0.354211 + 0.935166i \(0.615251\pi\)
\(542\) 1.13644 0.0488143
\(543\) 0 0
\(544\) 13.4543 0.576846
\(545\) −0.310429 −0.0132973
\(546\) 0 0
\(547\) −26.7313 −1.14295 −0.571475 0.820620i \(-0.693629\pi\)
−0.571475 + 0.820620i \(0.693629\pi\)
\(548\) 22.7336 0.971132
\(549\) 0 0
\(550\) 4.21633 0.179785
\(551\) −2.37402 −0.101137
\(552\) 0 0
\(553\) 27.5987 1.17362
\(554\) 0.664737 0.0282420
\(555\) 0 0
\(556\) −20.9962 −0.890436
\(557\) 14.1487 0.599502 0.299751 0.954018i \(-0.403096\pi\)
0.299751 + 0.954018i \(0.403096\pi\)
\(558\) 0 0
\(559\) 1.84710 0.0781240
\(560\) −10.3817 −0.438709
\(561\) 0 0
\(562\) −1.76325 −0.0743783
\(563\) 28.8148 1.21440 0.607200 0.794549i \(-0.292293\pi\)
0.607200 + 0.794549i \(0.292293\pi\)
\(564\) 0 0
\(565\) 9.53528 0.401152
\(566\) −2.90445 −0.122083
\(567\) 0 0
\(568\) 0.812663 0.0340986
\(569\) −3.94615 −0.165431 −0.0827156 0.996573i \(-0.526359\pi\)
−0.0827156 + 0.996573i \(0.526359\pi\)
\(570\) 0 0
\(571\) −14.6831 −0.614469 −0.307234 0.951634i \(-0.599404\pi\)
−0.307234 + 0.951634i \(0.599404\pi\)
\(572\) 8.88292 0.371414
\(573\) 0 0
\(574\) 2.62899 0.109732
\(575\) −4.20034 −0.175166
\(576\) 0 0
\(577\) −22.5062 −0.936944 −0.468472 0.883478i \(-0.655195\pi\)
−0.468472 + 0.883478i \(0.655195\pi\)
\(578\) −0.0428865 −0.00178384
\(579\) 0 0
\(580\) 1.71376 0.0711601
\(581\) −1.24563 −0.0516773
\(582\) 0 0
\(583\) −5.30818 −0.219842
\(584\) 12.8860 0.533228
\(585\) 0 0
\(586\) −2.77835 −0.114773
\(587\) −9.57987 −0.395403 −0.197702 0.980262i \(-0.563348\pi\)
−0.197702 + 0.980262i \(0.563348\pi\)
\(588\) 0 0
\(589\) 19.3941 0.799118
\(590\) −3.94469 −0.162400
\(591\) 0 0
\(592\) −25.3728 −1.04282
\(593\) 20.6846 0.849417 0.424708 0.905330i \(-0.360377\pi\)
0.424708 + 0.905330i \(0.360377\pi\)
\(594\) 0 0
\(595\) −12.1568 −0.498382
\(596\) 41.3539 1.69392
\(597\) 0 0
\(598\) 0.385806 0.0157768
\(599\) 25.3877 1.03731 0.518656 0.854983i \(-0.326432\pi\)
0.518656 + 0.854983i \(0.326432\pi\)
\(600\) 0 0
\(601\) 9.65156 0.393695 0.196848 0.980434i \(-0.436930\pi\)
0.196848 + 0.980434i \(0.436930\pi\)
\(602\) 1.32473 0.0539921
\(603\) 0 0
\(604\) 27.0196 1.09941
\(605\) −0.947729 −0.0385307
\(606\) 0 0
\(607\) −5.51354 −0.223788 −0.111894 0.993720i \(-0.535692\pi\)
−0.111894 + 0.993720i \(0.535692\pi\)
\(608\) −7.78078 −0.315552
\(609\) 0 0
\(610\) −1.24254 −0.0503090
\(611\) 3.16069 0.127868
\(612\) 0 0
\(613\) 29.9800 1.21088 0.605440 0.795891i \(-0.292997\pi\)
0.605440 + 0.795891i \(0.292997\pi\)
\(614\) −5.74862 −0.231995
\(615\) 0 0
\(616\) 13.0194 0.524565
\(617\) −22.8426 −0.919607 −0.459803 0.888021i \(-0.652080\pi\)
−0.459803 + 0.888021i \(0.652080\pi\)
\(618\) 0 0
\(619\) 8.68566 0.349106 0.174553 0.984648i \(-0.444152\pi\)
0.174553 + 0.984648i \(0.444152\pi\)
\(620\) −14.0002 −0.562262
\(621\) 0 0
\(622\) −3.68683 −0.147829
\(623\) 57.1559 2.28990
\(624\) 0 0
\(625\) 13.6445 0.545780
\(626\) −0.618544 −0.0247220
\(627\) 0 0
\(628\) 29.5302 1.17838
\(629\) −29.7112 −1.18466
\(630\) 0 0
\(631\) 32.6104 1.29820 0.649100 0.760703i \(-0.275146\pi\)
0.649100 + 0.760703i \(0.275146\pi\)
\(632\) −9.43443 −0.375282
\(633\) 0 0
\(634\) −8.71177 −0.345989
\(635\) 1.79202 0.0711143
\(636\) 0 0
\(637\) 5.29497 0.209794
\(638\) −1.00381 −0.0397412
\(639\) 0 0
\(640\) 7.42912 0.293662
\(641\) 35.2898 1.39386 0.696931 0.717138i \(-0.254548\pi\)
0.696931 + 0.717138i \(0.254548\pi\)
\(642\) 0 0
\(643\) −3.07557 −0.121289 −0.0606444 0.998159i \(-0.519316\pi\)
−0.0606444 + 0.998159i \(0.519316\pi\)
\(644\) −6.34663 −0.250092
\(645\) 0 0
\(646\) −2.81700 −0.110833
\(647\) −6.33211 −0.248941 −0.124470 0.992223i \(-0.539723\pi\)
−0.124470 + 0.992223i \(0.539723\pi\)
\(648\) 0 0
\(649\) −52.9966 −2.08030
\(650\) −1.62052 −0.0635619
\(651\) 0 0
\(652\) 7.87198 0.308290
\(653\) −37.9427 −1.48481 −0.742407 0.669949i \(-0.766316\pi\)
−0.742407 + 0.669949i \(0.766316\pi\)
\(654\) 0 0
\(655\) −0.764550 −0.0298734
\(656\) 9.62791 0.375907
\(657\) 0 0
\(658\) 2.26684 0.0883705
\(659\) −12.5938 −0.490586 −0.245293 0.969449i \(-0.578884\pi\)
−0.245293 + 0.969449i \(0.578884\pi\)
\(660\) 0 0
\(661\) −3.00472 −0.116870 −0.0584349 0.998291i \(-0.518611\pi\)
−0.0584349 + 0.998291i \(0.518611\pi\)
\(662\) −1.49923 −0.0582691
\(663\) 0 0
\(664\) 0.425809 0.0165246
\(665\) 7.03048 0.272630
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) 4.76193 0.184245
\(669\) 0 0
\(670\) 3.27905 0.126681
\(671\) −16.6935 −0.644444
\(672\) 0 0
\(673\) 13.1939 0.508588 0.254294 0.967127i \(-0.418157\pi\)
0.254294 + 0.967127i \(0.418157\pi\)
\(674\) 0.992386 0.0382253
\(675\) 0 0
\(676\) 21.4997 0.826913
\(677\) −31.7524 −1.22034 −0.610171 0.792270i \(-0.708899\pi\)
−0.610171 + 0.792270i \(0.708899\pi\)
\(678\) 0 0
\(679\) 38.9426 1.49448
\(680\) 4.15573 0.159365
\(681\) 0 0
\(682\) 8.20040 0.314009
\(683\) −36.3980 −1.39273 −0.696366 0.717687i \(-0.745201\pi\)
−0.696366 + 0.717687i \(0.745201\pi\)
\(684\) 0 0
\(685\) 10.6078 0.405303
\(686\) −2.90324 −0.110846
\(687\) 0 0
\(688\) 4.85145 0.184960
\(689\) 2.04016 0.0777238
\(690\) 0 0
\(691\) 3.06066 0.116433 0.0582165 0.998304i \(-0.481459\pi\)
0.0582165 + 0.998304i \(0.481459\pi\)
\(692\) 1.69930 0.0645978
\(693\) 0 0
\(694\) 8.28848 0.314626
\(695\) −9.79709 −0.371625
\(696\) 0 0
\(697\) 11.2741 0.427038
\(698\) −5.65405 −0.214009
\(699\) 0 0
\(700\) 26.6580 1.00758
\(701\) −7.42386 −0.280395 −0.140198 0.990124i \(-0.544774\pi\)
−0.140198 + 0.990124i \(0.544774\pi\)
\(702\) 0 0
\(703\) 17.1824 0.648046
\(704\) 21.0585 0.793671
\(705\) 0 0
\(706\) 0.432057 0.0162607
\(707\) −10.2056 −0.383821
\(708\) 0 0
\(709\) 12.1383 0.455863 0.227931 0.973677i \(-0.426804\pi\)
0.227931 + 0.973677i \(0.426804\pi\)
\(710\) 0.185555 0.00696374
\(711\) 0 0
\(712\) −19.5384 −0.732231
\(713\) −8.16928 −0.305942
\(714\) 0 0
\(715\) 4.14489 0.155010
\(716\) 37.5672 1.40395
\(717\) 0 0
\(718\) −1.02870 −0.0383908
\(719\) 39.1844 1.46133 0.730666 0.682735i \(-0.239210\pi\)
0.730666 + 0.682735i \(0.239210\pi\)
\(720\) 0 0
\(721\) −24.0445 −0.895462
\(722\) −3.86294 −0.143764
\(723\) 0 0
\(724\) −1.64030 −0.0609612
\(725\) −4.20034 −0.155997
\(726\) 0 0
\(727\) −47.9994 −1.78020 −0.890099 0.455768i \(-0.849365\pi\)
−0.890099 + 0.455768i \(0.849365\pi\)
\(728\) −5.00389 −0.185457
\(729\) 0 0
\(730\) 2.94226 0.108898
\(731\) 5.68097 0.210118
\(732\) 0 0
\(733\) 47.6003 1.75816 0.879078 0.476678i \(-0.158159\pi\)
0.879078 + 0.476678i \(0.158159\pi\)
\(734\) 7.66001 0.282736
\(735\) 0 0
\(736\) 3.27747 0.120809
\(737\) 44.0538 1.62274
\(738\) 0 0
\(739\) −49.1296 −1.80726 −0.903631 0.428311i \(-0.859109\pi\)
−0.903631 + 0.428311i \(0.859109\pi\)
\(740\) −12.4036 −0.455967
\(741\) 0 0
\(742\) 1.46319 0.0537156
\(743\) −28.0456 −1.02889 −0.514447 0.857522i \(-0.672003\pi\)
−0.514447 + 0.857522i \(0.672003\pi\)
\(744\) 0 0
\(745\) 19.2963 0.706961
\(746\) −2.12171 −0.0776814
\(747\) 0 0
\(748\) 27.3205 0.998935
\(749\) −25.1362 −0.918455
\(750\) 0 0
\(751\) −19.8878 −0.725716 −0.362858 0.931845i \(-0.618199\pi\)
−0.362858 + 0.931845i \(0.618199\pi\)
\(752\) 8.30163 0.302729
\(753\) 0 0
\(754\) 0.385806 0.0140502
\(755\) 12.6077 0.458841
\(756\) 0 0
\(757\) −18.4139 −0.669263 −0.334632 0.942349i \(-0.608612\pi\)
−0.334632 + 0.942349i \(0.608612\pi\)
\(758\) −6.84696 −0.248693
\(759\) 0 0
\(760\) −2.40332 −0.0871776
\(761\) 33.7274 1.22262 0.611309 0.791392i \(-0.290643\pi\)
0.611309 + 0.791392i \(0.290643\pi\)
\(762\) 0 0
\(763\) 1.14962 0.0416191
\(764\) 42.2053 1.52693
\(765\) 0 0
\(766\) 0.139066 0.00502466
\(767\) 20.3689 0.735477
\(768\) 0 0
\(769\) 8.03396 0.289712 0.144856 0.989453i \(-0.453728\pi\)
0.144856 + 0.989453i \(0.453728\pi\)
\(770\) 2.97270 0.107129
\(771\) 0 0
\(772\) 33.2317 1.19604
\(773\) −4.80753 −0.172915 −0.0864574 0.996256i \(-0.527555\pi\)
−0.0864574 + 0.996256i \(0.527555\pi\)
\(774\) 0 0
\(775\) 34.3137 1.23259
\(776\) −13.3123 −0.477882
\(777\) 0 0
\(778\) −6.96668 −0.249768
\(779\) −6.51999 −0.233603
\(780\) 0 0
\(781\) 2.49292 0.0892036
\(782\) 1.18659 0.0424325
\(783\) 0 0
\(784\) 13.9074 0.496692
\(785\) 13.7792 0.491799
\(786\) 0 0
\(787\) 11.4342 0.407586 0.203793 0.979014i \(-0.434673\pi\)
0.203793 + 0.979014i \(0.434673\pi\)
\(788\) 19.7340 0.702996
\(789\) 0 0
\(790\) −2.15416 −0.0766415
\(791\) −35.3123 −1.25556
\(792\) 0 0
\(793\) 6.41600 0.227839
\(794\) −6.02286 −0.213743
\(795\) 0 0
\(796\) 46.7998 1.65877
\(797\) 18.4342 0.652974 0.326487 0.945202i \(-0.394135\pi\)
0.326487 + 0.945202i \(0.394135\pi\)
\(798\) 0 0
\(799\) 9.72107 0.343907
\(800\) −13.7665 −0.486718
\(801\) 0 0
\(802\) 0.826380 0.0291805
\(803\) 39.5291 1.39495
\(804\) 0 0
\(805\) −2.96142 −0.104376
\(806\) −3.15176 −0.111016
\(807\) 0 0
\(808\) 3.48871 0.122733
\(809\) 12.2971 0.432345 0.216172 0.976355i \(-0.430643\pi\)
0.216172 + 0.976355i \(0.430643\pi\)
\(810\) 0 0
\(811\) 5.31716 0.186711 0.0933554 0.995633i \(-0.470241\pi\)
0.0933554 + 0.995633i \(0.470241\pi\)
\(812\) −6.34663 −0.222723
\(813\) 0 0
\(814\) 7.26524 0.254646
\(815\) 3.67317 0.128665
\(816\) 0 0
\(817\) −3.28539 −0.114941
\(818\) 4.93413 0.172518
\(819\) 0 0
\(820\) 4.70666 0.164364
\(821\) 42.5523 1.48509 0.742543 0.669799i \(-0.233620\pi\)
0.742543 + 0.669799i \(0.233620\pi\)
\(822\) 0 0
\(823\) 31.2256 1.08846 0.544229 0.838937i \(-0.316822\pi\)
0.544229 + 0.838937i \(0.316822\pi\)
\(824\) 8.21943 0.286337
\(825\) 0 0
\(826\) 14.6085 0.508294
\(827\) −25.7765 −0.896336 −0.448168 0.893949i \(-0.647923\pi\)
−0.448168 + 0.893949i \(0.647923\pi\)
\(828\) 0 0
\(829\) −20.3170 −0.705638 −0.352819 0.935692i \(-0.614777\pi\)
−0.352819 + 0.935692i \(0.614777\pi\)
\(830\) 0.0972247 0.00337472
\(831\) 0 0
\(832\) −8.09366 −0.280597
\(833\) 16.2853 0.564252
\(834\) 0 0
\(835\) 2.22198 0.0768947
\(836\) −15.7998 −0.546448
\(837\) 0 0
\(838\) 4.07504 0.140770
\(839\) 43.8024 1.51223 0.756113 0.654441i \(-0.227096\pi\)
0.756113 + 0.654441i \(0.227096\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 6.54525 0.225564
\(843\) 0 0
\(844\) −16.5596 −0.570006
\(845\) 10.0321 0.345113
\(846\) 0 0
\(847\) 3.50975 0.120597
\(848\) 5.35853 0.184013
\(849\) 0 0
\(850\) −4.98409 −0.170953
\(851\) −7.23767 −0.248104
\(852\) 0 0
\(853\) −1.50016 −0.0513644 −0.0256822 0.999670i \(-0.508176\pi\)
−0.0256822 + 0.999670i \(0.508176\pi\)
\(854\) 4.60153 0.157461
\(855\) 0 0
\(856\) 8.59262 0.293690
\(857\) 42.2557 1.44343 0.721713 0.692192i \(-0.243355\pi\)
0.721713 + 0.692192i \(0.243355\pi\)
\(858\) 0 0
\(859\) 26.1886 0.893543 0.446771 0.894648i \(-0.352574\pi\)
0.446771 + 0.894648i \(0.352574\pi\)
\(860\) 2.37166 0.0808729
\(861\) 0 0
\(862\) −3.00614 −0.102390
\(863\) −37.8785 −1.28940 −0.644700 0.764436i \(-0.723018\pi\)
−0.644700 + 0.764436i \(0.723018\pi\)
\(864\) 0 0
\(865\) 0.792916 0.0269600
\(866\) 4.61730 0.156902
\(867\) 0 0
\(868\) 51.8474 1.75981
\(869\) −28.9410 −0.981756
\(870\) 0 0
\(871\) −16.9318 −0.573711
\(872\) −0.392991 −0.0133083
\(873\) 0 0
\(874\) −0.686223 −0.0232119
\(875\) 27.2461 0.921085
\(876\) 0 0
\(877\) 55.5435 1.87557 0.937786 0.347214i \(-0.112872\pi\)
0.937786 + 0.347214i \(0.112872\pi\)
\(878\) −9.24047 −0.311851
\(879\) 0 0
\(880\) 10.8867 0.366989
\(881\) −53.4437 −1.80056 −0.900281 0.435309i \(-0.856639\pi\)
−0.900281 + 0.435309i \(0.856639\pi\)
\(882\) 0 0
\(883\) 22.3197 0.751118 0.375559 0.926798i \(-0.377451\pi\)
0.375559 + 0.926798i \(0.377451\pi\)
\(884\) −10.5004 −0.353167
\(885\) 0 0
\(886\) 2.31197 0.0776721
\(887\) 45.9912 1.54423 0.772116 0.635482i \(-0.219198\pi\)
0.772116 + 0.635482i \(0.219198\pi\)
\(888\) 0 0
\(889\) −6.63646 −0.222580
\(890\) −4.46118 −0.149539
\(891\) 0 0
\(892\) −25.2133 −0.844204
\(893\) −5.62183 −0.188128
\(894\) 0 0
\(895\) 17.5293 0.585941
\(896\) −27.5125 −0.919128
\(897\) 0 0
\(898\) −2.86519 −0.0956125
\(899\) −8.16928 −0.272461
\(900\) 0 0
\(901\) 6.27475 0.209042
\(902\) −2.75685 −0.0917930
\(903\) 0 0
\(904\) 12.0713 0.401484
\(905\) −0.765385 −0.0254423
\(906\) 0 0
\(907\) 35.4404 1.17678 0.588389 0.808578i \(-0.299762\pi\)
0.588389 + 0.808578i \(0.299762\pi\)
\(908\) −18.3297 −0.608291
\(909\) 0 0
\(910\) −1.14253 −0.0378746
\(911\) −0.877383 −0.0290690 −0.0145345 0.999894i \(-0.504627\pi\)
−0.0145345 + 0.999894i \(0.504627\pi\)
\(912\) 0 0
\(913\) 1.30621 0.0432292
\(914\) −6.97877 −0.230837
\(915\) 0 0
\(916\) 1.68154 0.0555597
\(917\) 2.83138 0.0935004
\(918\) 0 0
\(919\) −5.81102 −0.191688 −0.0958439 0.995396i \(-0.530555\pi\)
−0.0958439 + 0.995396i \(0.530555\pi\)
\(920\) 1.01234 0.0333759
\(921\) 0 0
\(922\) 7.04176 0.231908
\(923\) −0.958134 −0.0315374
\(924\) 0 0
\(925\) 30.4007 0.999567
\(926\) 9.70498 0.318925
\(927\) 0 0
\(928\) 3.27747 0.107588
\(929\) 49.6595 1.62928 0.814638 0.579970i \(-0.196936\pi\)
0.814638 + 0.579970i \(0.196936\pi\)
\(930\) 0 0
\(931\) −9.41802 −0.308663
\(932\) −4.14346 −0.135724
\(933\) 0 0
\(934\) −6.32568 −0.206983
\(935\) 12.7481 0.416907
\(936\) 0 0
\(937\) −11.7442 −0.383665 −0.191833 0.981428i \(-0.561443\pi\)
−0.191833 + 0.981428i \(0.561443\pi\)
\(938\) −12.1434 −0.396496
\(939\) 0 0
\(940\) 4.05830 0.132367
\(941\) −20.1855 −0.658028 −0.329014 0.944325i \(-0.606716\pi\)
−0.329014 + 0.944325i \(0.606716\pi\)
\(942\) 0 0
\(943\) 2.74639 0.0894347
\(944\) 53.4993 1.74125
\(945\) 0 0
\(946\) −1.38916 −0.0451655
\(947\) 7.76958 0.252478 0.126239 0.992000i \(-0.459709\pi\)
0.126239 + 0.992000i \(0.459709\pi\)
\(948\) 0 0
\(949\) −15.1927 −0.493176
\(950\) 2.88237 0.0935164
\(951\) 0 0
\(952\) −15.3901 −0.498795
\(953\) −4.69003 −0.151925 −0.0759625 0.997111i \(-0.524203\pi\)
−0.0759625 + 0.997111i \(0.524203\pi\)
\(954\) 0 0
\(955\) 19.6935 0.637268
\(956\) −51.9330 −1.67963
\(957\) 0 0
\(958\) −9.75863 −0.315287
\(959\) −39.2842 −1.26855
\(960\) 0 0
\(961\) 35.7372 1.15281
\(962\) −2.79234 −0.0900286
\(963\) 0 0
\(964\) −8.90058 −0.286668
\(965\) 15.5064 0.499167
\(966\) 0 0
\(967\) 35.8106 1.15159 0.575796 0.817593i \(-0.304692\pi\)
0.575796 + 0.817593i \(0.304692\pi\)
\(968\) −1.19979 −0.0385626
\(969\) 0 0
\(970\) −3.03958 −0.0975949
\(971\) −18.9838 −0.609220 −0.304610 0.952477i \(-0.598526\pi\)
−0.304610 + 0.952477i \(0.598526\pi\)
\(972\) 0 0
\(973\) 36.2818 1.16314
\(974\) 6.91539 0.221583
\(975\) 0 0
\(976\) 16.8518 0.539413
\(977\) −12.0941 −0.386923 −0.193462 0.981108i \(-0.561971\pi\)
−0.193462 + 0.981108i \(0.561971\pi\)
\(978\) 0 0
\(979\) −59.9357 −1.91555
\(980\) 6.79869 0.217176
\(981\) 0 0
\(982\) −11.1736 −0.356563
\(983\) −10.7348 −0.342387 −0.171193 0.985237i \(-0.554762\pi\)
−0.171193 + 0.985237i \(0.554762\pi\)
\(984\) 0 0
\(985\) 9.20815 0.293396
\(986\) 1.18659 0.0377888
\(987\) 0 0
\(988\) 6.07254 0.193193
\(989\) 1.38389 0.0440051
\(990\) 0 0
\(991\) 35.0246 1.11259 0.556297 0.830984i \(-0.312222\pi\)
0.556297 + 0.830984i \(0.312222\pi\)
\(992\) −26.7746 −0.850093
\(993\) 0 0
\(994\) −0.687170 −0.0217957
\(995\) 21.8374 0.692292
\(996\) 0 0
\(997\) −20.8820 −0.661340 −0.330670 0.943746i \(-0.607275\pi\)
−0.330670 + 0.943746i \(0.607275\pi\)
\(998\) −5.10132 −0.161479
\(999\) 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 \(a_p\))