Properties

Label 6004.2.a.g.1.1
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 1
Dimension 27
CM No

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Newspace parameters

Level: \( N \) = \( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9421813736\)
Analytic rank: \(1\)
Dimension: \(27\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-3.35817 q^{3}\) \(-0.581328 q^{5}\) \(+3.25261 q^{7}\) \(+8.27730 q^{9}\) \(+O(q^{10})\) \(q\)\(-3.35817 q^{3}\) \(-0.581328 q^{5}\) \(+3.25261 q^{7}\) \(+8.27730 q^{9}\) \(+4.01989 q^{11}\) \(+4.26295 q^{13}\) \(+1.95220 q^{15}\) \(-2.04729 q^{17}\) \(+1.00000 q^{19}\) \(-10.9228 q^{21}\) \(+0.293401 q^{23}\) \(-4.66206 q^{25}\) \(-17.7221 q^{27}\) \(-6.94533 q^{29}\) \(-1.87612 q^{31}\) \(-13.4995 q^{33}\) \(-1.89084 q^{35}\) \(+8.28320 q^{37}\) \(-14.3157 q^{39}\) \(-6.21102 q^{41}\) \(-9.11192 q^{43}\) \(-4.81183 q^{45}\) \(-8.53931 q^{47}\) \(+3.57949 q^{49}\) \(+6.87514 q^{51}\) \(-14.3146 q^{53}\) \(-2.33688 q^{55}\) \(-3.35817 q^{57}\) \(+3.68459 q^{59}\) \(+1.48250 q^{61}\) \(+26.9229 q^{63}\) \(-2.47817 q^{65}\) \(+2.71154 q^{67}\) \(-0.985291 q^{69}\) \(-11.7082 q^{71}\) \(+9.47027 q^{73}\) \(+15.6560 q^{75}\) \(+13.0752 q^{77}\) \(-1.00000 q^{79}\) \(+34.6818 q^{81}\) \(+11.0452 q^{83}\) \(+1.19015 q^{85}\) \(+23.3236 q^{87}\) \(-7.66115 q^{89}\) \(+13.8657 q^{91}\) \(+6.30032 q^{93}\) \(-0.581328 q^{95}\) \(-18.9946 q^{97}\) \(+33.2739 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(27q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(27q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut -\mathstrut 11q^{23} \) \(\mathstrut +\mathstrut 13q^{25} \) \(\mathstrut -\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 39q^{29} \) \(\mathstrut -\mathstrut 27q^{31} \) \(\mathstrut -\mathstrut 18q^{33} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut -\mathstrut q^{37} \) \(\mathstrut -\mathstrut 22q^{39} \) \(\mathstrut -\mathstrut 36q^{41} \) \(\mathstrut -\mathstrut 2q^{43} \) \(\mathstrut -\mathstrut 18q^{45} \) \(\mathstrut -\mathstrut 12q^{47} \) \(\mathstrut +\mathstrut 15q^{49} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 28q^{53} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 30q^{59} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 32q^{65} \) \(\mathstrut +\mathstrut 13q^{67} \) \(\mathstrut -\mathstrut 27q^{69} \) \(\mathstrut -\mathstrut 59q^{71} \) \(\mathstrut -\mathstrut 30q^{73} \) \(\mathstrut -\mathstrut 21q^{75} \) \(\mathstrut -\mathstrut 39q^{77} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut -\mathstrut 5q^{81} \) \(\mathstrut +\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 56q^{89} \) \(\mathstrut -\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 38q^{93} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 30q^{97} \) \(\mathstrut +\mathstrut 31q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 0
\(3\) −3.35817 −1.93884 −0.969420 0.245407i \(-0.921078\pi\)
−0.969420 + 0.245407i \(0.921078\pi\)
\(4\) 0 0
\(5\) −0.581328 −0.259978 −0.129989 0.991515i \(-0.541494\pi\)
−0.129989 + 0.991515i \(0.541494\pi\)
\(6\) 0 0
\(7\) 3.25261 1.22937 0.614686 0.788772i \(-0.289283\pi\)
0.614686 + 0.788772i \(0.289283\pi\)
\(8\) 0 0
\(9\) 8.27730 2.75910
\(10\) 0 0
\(11\) 4.01989 1.21204 0.606022 0.795448i \(-0.292764\pi\)
0.606022 + 0.795448i \(0.292764\pi\)
\(12\) 0 0
\(13\) 4.26295 1.18233 0.591164 0.806551i \(-0.298669\pi\)
0.591164 + 0.806551i \(0.298669\pi\)
\(14\) 0 0
\(15\) 1.95220 0.504055
\(16\) 0 0
\(17\) −2.04729 −0.496540 −0.248270 0.968691i \(-0.579862\pi\)
−0.248270 + 0.968691i \(0.579862\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −10.9228 −2.38356
\(22\) 0 0
\(23\) 0.293401 0.0611784 0.0305892 0.999532i \(-0.490262\pi\)
0.0305892 + 0.999532i \(0.490262\pi\)
\(24\) 0 0
\(25\) −4.66206 −0.932412
\(26\) 0 0
\(27\) −17.7221 −3.41062
\(28\) 0 0
\(29\) −6.94533 −1.28972 −0.644858 0.764302i \(-0.723084\pi\)
−0.644858 + 0.764302i \(0.723084\pi\)
\(30\) 0 0
\(31\) −1.87612 −0.336961 −0.168480 0.985705i \(-0.553886\pi\)
−0.168480 + 0.985705i \(0.553886\pi\)
\(32\) 0 0
\(33\) −13.4995 −2.34996
\(34\) 0 0
\(35\) −1.89084 −0.319610
\(36\) 0 0
\(37\) 8.28320 1.36175 0.680875 0.732400i \(-0.261600\pi\)
0.680875 + 0.732400i \(0.261600\pi\)
\(38\) 0 0
\(39\) −14.3157 −2.29235
\(40\) 0 0
\(41\) −6.21102 −0.969999 −0.484999 0.874514i \(-0.661180\pi\)
−0.484999 + 0.874514i \(0.661180\pi\)
\(42\) 0 0
\(43\) −9.11192 −1.38956 −0.694778 0.719225i \(-0.744497\pi\)
−0.694778 + 0.719225i \(0.744497\pi\)
\(44\) 0 0
\(45\) −4.81183 −0.717305
\(46\) 0 0
\(47\) −8.53931 −1.24559 −0.622794 0.782386i \(-0.714002\pi\)
−0.622794 + 0.782386i \(0.714002\pi\)
\(48\) 0 0
\(49\) 3.57949 0.511356
\(50\) 0 0
\(51\) 6.87514 0.962712
\(52\) 0 0
\(53\) −14.3146 −1.96626 −0.983132 0.182899i \(-0.941452\pi\)
−0.983132 + 0.182899i \(0.941452\pi\)
\(54\) 0 0
\(55\) −2.33688 −0.315105
\(56\) 0 0
\(57\) −3.35817 −0.444800
\(58\) 0 0
\(59\) 3.68459 0.479692 0.239846 0.970811i \(-0.422903\pi\)
0.239846 + 0.970811i \(0.422903\pi\)
\(60\) 0 0
\(61\) 1.48250 0.189815 0.0949075 0.995486i \(-0.469744\pi\)
0.0949075 + 0.995486i \(0.469744\pi\)
\(62\) 0 0
\(63\) 26.9229 3.39196
\(64\) 0 0
\(65\) −2.47817 −0.307379
\(66\) 0 0
\(67\) 2.71154 0.331268 0.165634 0.986187i \(-0.447033\pi\)
0.165634 + 0.986187i \(0.447033\pi\)
\(68\) 0 0
\(69\) −0.985291 −0.118615
\(70\) 0 0
\(71\) −11.7082 −1.38951 −0.694757 0.719245i \(-0.744488\pi\)
−0.694757 + 0.719245i \(0.744488\pi\)
\(72\) 0 0
\(73\) 9.47027 1.10841 0.554206 0.832380i \(-0.313022\pi\)
0.554206 + 0.832380i \(0.313022\pi\)
\(74\) 0 0
\(75\) 15.6560 1.80780
\(76\) 0 0
\(77\) 13.0752 1.49005
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) 34.6818 3.85354
\(82\) 0 0
\(83\) 11.0452 1.21237 0.606186 0.795323i \(-0.292699\pi\)
0.606186 + 0.795323i \(0.292699\pi\)
\(84\) 0 0
\(85\) 1.19015 0.129089
\(86\) 0 0
\(87\) 23.3236 2.50055
\(88\) 0 0
\(89\) −7.66115 −0.812081 −0.406040 0.913855i \(-0.633091\pi\)
−0.406040 + 0.913855i \(0.633091\pi\)
\(90\) 0 0
\(91\) 13.8657 1.45352
\(92\) 0 0
\(93\) 6.30032 0.653313
\(94\) 0 0
\(95\) −0.581328 −0.0596430
\(96\) 0 0
\(97\) −18.9946 −1.92861 −0.964306 0.264789i \(-0.914698\pi\)
−0.964306 + 0.264789i \(0.914698\pi\)
\(98\) 0 0
\(99\) 33.2739 3.34415
\(100\) 0 0
\(101\) −6.30058 −0.626931 −0.313466 0.949600i \(-0.601490\pi\)
−0.313466 + 0.949600i \(0.601490\pi\)
\(102\) 0 0
\(103\) 4.58596 0.451868 0.225934 0.974143i \(-0.427457\pi\)
0.225934 + 0.974143i \(0.427457\pi\)
\(104\) 0 0
\(105\) 6.34975 0.619672
\(106\) 0 0
\(107\) 0.995018 0.0961920 0.0480960 0.998843i \(-0.484685\pi\)
0.0480960 + 0.998843i \(0.484685\pi\)
\(108\) 0 0
\(109\) −14.8584 −1.42318 −0.711588 0.702597i \(-0.752024\pi\)
−0.711588 + 0.702597i \(0.752024\pi\)
\(110\) 0 0
\(111\) −27.8164 −2.64021
\(112\) 0 0
\(113\) −14.9859 −1.40976 −0.704879 0.709328i \(-0.748999\pi\)
−0.704879 + 0.709328i \(0.748999\pi\)
\(114\) 0 0
\(115\) −0.170562 −0.0159050
\(116\) 0 0
\(117\) 35.2857 3.26216
\(118\) 0 0
\(119\) −6.65903 −0.610433
\(120\) 0 0
\(121\) 5.15955 0.469050
\(122\) 0 0
\(123\) 20.8577 1.88067
\(124\) 0 0
\(125\) 5.61683 0.502384
\(126\) 0 0
\(127\) −7.48987 −0.664618 −0.332309 0.943171i \(-0.607828\pi\)
−0.332309 + 0.943171i \(0.607828\pi\)
\(128\) 0 0
\(129\) 30.5994 2.69413
\(130\) 0 0
\(131\) −2.86391 −0.250221 −0.125110 0.992143i \(-0.539929\pi\)
−0.125110 + 0.992143i \(0.539929\pi\)
\(132\) 0 0
\(133\) 3.25261 0.282037
\(134\) 0 0
\(135\) 10.3023 0.886684
\(136\) 0 0
\(137\) −12.2269 −1.04461 −0.522306 0.852758i \(-0.674928\pi\)
−0.522306 + 0.852758i \(0.674928\pi\)
\(138\) 0 0
\(139\) −22.1261 −1.87671 −0.938356 0.345671i \(-0.887651\pi\)
−0.938356 + 0.345671i \(0.887651\pi\)
\(140\) 0 0
\(141\) 28.6765 2.41499
\(142\) 0 0
\(143\) 17.1366 1.43303
\(144\) 0 0
\(145\) 4.03752 0.335298
\(146\) 0 0
\(147\) −12.0205 −0.991438
\(148\) 0 0
\(149\) −22.1134 −1.81160 −0.905800 0.423706i \(-0.860729\pi\)
−0.905800 + 0.423706i \(0.860729\pi\)
\(150\) 0 0
\(151\) −8.12362 −0.661091 −0.330545 0.943790i \(-0.607233\pi\)
−0.330545 + 0.943790i \(0.607233\pi\)
\(152\) 0 0
\(153\) −16.9460 −1.37000
\(154\) 0 0
\(155\) 1.09064 0.0876023
\(156\) 0 0
\(157\) 22.8376 1.82264 0.911318 0.411703i \(-0.135066\pi\)
0.911318 + 0.411703i \(0.135066\pi\)
\(158\) 0 0
\(159\) 48.0709 3.81227
\(160\) 0 0
\(161\) 0.954321 0.0752110
\(162\) 0 0
\(163\) 19.4277 1.52170 0.760848 0.648930i \(-0.224783\pi\)
0.760848 + 0.648930i \(0.224783\pi\)
\(164\) 0 0
\(165\) 7.84763 0.610937
\(166\) 0 0
\(167\) 15.4108 1.19253 0.596263 0.802789i \(-0.296652\pi\)
0.596263 + 0.802789i \(0.296652\pi\)
\(168\) 0 0
\(169\) 5.17270 0.397900
\(170\) 0 0
\(171\) 8.27730 0.632981
\(172\) 0 0
\(173\) 2.34862 0.178562 0.0892812 0.996006i \(-0.471543\pi\)
0.0892812 + 0.996006i \(0.471543\pi\)
\(174\) 0 0
\(175\) −15.1639 −1.14628
\(176\) 0 0
\(177\) −12.3735 −0.930047
\(178\) 0 0
\(179\) 3.42505 0.256000 0.128000 0.991774i \(-0.459144\pi\)
0.128000 + 0.991774i \(0.459144\pi\)
\(180\) 0 0
\(181\) −0.166441 −0.0123714 −0.00618572 0.999981i \(-0.501969\pi\)
−0.00618572 + 0.999981i \(0.501969\pi\)
\(182\) 0 0
\(183\) −4.97849 −0.368021
\(184\) 0 0
\(185\) −4.81526 −0.354025
\(186\) 0 0
\(187\) −8.22988 −0.601828
\(188\) 0 0
\(189\) −57.6431 −4.19292
\(190\) 0 0
\(191\) 0.245961 0.0177971 0.00889856 0.999960i \(-0.497167\pi\)
0.00889856 + 0.999960i \(0.497167\pi\)
\(192\) 0 0
\(193\) −8.68586 −0.625222 −0.312611 0.949881i \(-0.601204\pi\)
−0.312611 + 0.949881i \(0.601204\pi\)
\(194\) 0 0
\(195\) 8.32211 0.595959
\(196\) 0 0
\(197\) −13.9003 −0.990354 −0.495177 0.868792i \(-0.664897\pi\)
−0.495177 + 0.868792i \(0.664897\pi\)
\(198\) 0 0
\(199\) −4.00929 −0.284211 −0.142106 0.989852i \(-0.545387\pi\)
−0.142106 + 0.989852i \(0.545387\pi\)
\(200\) 0 0
\(201\) −9.10582 −0.642275
\(202\) 0 0
\(203\) −22.5905 −1.58554
\(204\) 0 0
\(205\) 3.61064 0.252178
\(206\) 0 0
\(207\) 2.42857 0.168797
\(208\) 0 0
\(209\) 4.01989 0.278062
\(210\) 0 0
\(211\) 5.53336 0.380932 0.190466 0.981694i \(-0.439000\pi\)
0.190466 + 0.981694i \(0.439000\pi\)
\(212\) 0 0
\(213\) 39.3183 2.69404
\(214\) 0 0
\(215\) 5.29702 0.361254
\(216\) 0 0
\(217\) −6.10229 −0.414250
\(218\) 0 0
\(219\) −31.8028 −2.14903
\(220\) 0 0
\(221\) −8.72747 −0.587073
\(222\) 0 0
\(223\) −19.1233 −1.28059 −0.640296 0.768128i \(-0.721188\pi\)
−0.640296 + 0.768128i \(0.721188\pi\)
\(224\) 0 0
\(225\) −38.5893 −2.57262
\(226\) 0 0
\(227\) 22.0361 1.46259 0.731294 0.682062i \(-0.238917\pi\)
0.731294 + 0.682062i \(0.238917\pi\)
\(228\) 0 0
\(229\) 21.0639 1.39194 0.695969 0.718071i \(-0.254975\pi\)
0.695969 + 0.718071i \(0.254975\pi\)
\(230\) 0 0
\(231\) −43.9086 −2.88897
\(232\) 0 0
\(233\) −6.83099 −0.447513 −0.223756 0.974645i \(-0.571832\pi\)
−0.223756 + 0.974645i \(0.571832\pi\)
\(234\) 0 0
\(235\) 4.96414 0.323825
\(236\) 0 0
\(237\) 3.35817 0.218137
\(238\) 0 0
\(239\) 2.62776 0.169976 0.0849879 0.996382i \(-0.472915\pi\)
0.0849879 + 0.996382i \(0.472915\pi\)
\(240\) 0 0
\(241\) −22.0823 −1.42245 −0.711223 0.702967i \(-0.751858\pi\)
−0.711223 + 0.702967i \(0.751858\pi\)
\(242\) 0 0
\(243\) −63.3013 −4.06078
\(244\) 0 0
\(245\) −2.08086 −0.132941
\(246\) 0 0
\(247\) 4.26295 0.271245
\(248\) 0 0
\(249\) −37.0918 −2.35059
\(250\) 0 0
\(251\) 18.0587 1.13986 0.569928 0.821694i \(-0.306971\pi\)
0.569928 + 0.821694i \(0.306971\pi\)
\(252\) 0 0
\(253\) 1.17944 0.0741509
\(254\) 0 0
\(255\) −3.99671 −0.250284
\(256\) 0 0
\(257\) 16.5241 1.03074 0.515372 0.856966i \(-0.327654\pi\)
0.515372 + 0.856966i \(0.327654\pi\)
\(258\) 0 0
\(259\) 26.9420 1.67410
\(260\) 0 0
\(261\) −57.4886 −3.55846
\(262\) 0 0
\(263\) 0.570983 0.0352083 0.0176042 0.999845i \(-0.494396\pi\)
0.0176042 + 0.999845i \(0.494396\pi\)
\(264\) 0 0
\(265\) 8.32149 0.511185
\(266\) 0 0
\(267\) 25.7275 1.57449
\(268\) 0 0
\(269\) 9.83599 0.599711 0.299856 0.953985i \(-0.403062\pi\)
0.299856 + 0.953985i \(0.403062\pi\)
\(270\) 0 0
\(271\) 20.4824 1.24422 0.622109 0.782931i \(-0.286276\pi\)
0.622109 + 0.782931i \(0.286276\pi\)
\(272\) 0 0
\(273\) −46.5634 −2.81815
\(274\) 0 0
\(275\) −18.7410 −1.13012
\(276\) 0 0
\(277\) −3.56807 −0.214384 −0.107192 0.994238i \(-0.534186\pi\)
−0.107192 + 0.994238i \(0.534186\pi\)
\(278\) 0 0
\(279\) −15.5292 −0.929709
\(280\) 0 0
\(281\) 10.0631 0.600315 0.300157 0.953890i \(-0.402961\pi\)
0.300157 + 0.953890i \(0.402961\pi\)
\(282\) 0 0
\(283\) 4.08499 0.242828 0.121414 0.992602i \(-0.461257\pi\)
0.121414 + 0.992602i \(0.461257\pi\)
\(284\) 0 0
\(285\) 1.95220 0.115638
\(286\) 0 0
\(287\) −20.2021 −1.19249
\(288\) 0 0
\(289\) −12.8086 −0.753448
\(290\) 0 0
\(291\) 63.7872 3.73927
\(292\) 0 0
\(293\) −8.37505 −0.489276 −0.244638 0.969614i \(-0.578669\pi\)
−0.244638 + 0.969614i \(0.578669\pi\)
\(294\) 0 0
\(295\) −2.14195 −0.124709
\(296\) 0 0
\(297\) −71.2409 −4.13382
\(298\) 0 0
\(299\) 1.25075 0.0723329
\(300\) 0 0
\(301\) −29.6376 −1.70828
\(302\) 0 0
\(303\) 21.1584 1.21552
\(304\) 0 0
\(305\) −0.861820 −0.0493477
\(306\) 0 0
\(307\) 11.4283 0.652250 0.326125 0.945327i \(-0.394257\pi\)
0.326125 + 0.945327i \(0.394257\pi\)
\(308\) 0 0
\(309\) −15.4004 −0.876100
\(310\) 0 0
\(311\) −2.27135 −0.128797 −0.0643983 0.997924i \(-0.520513\pi\)
−0.0643983 + 0.997924i \(0.520513\pi\)
\(312\) 0 0
\(313\) −23.4656 −1.32636 −0.663178 0.748462i \(-0.730793\pi\)
−0.663178 + 0.748462i \(0.730793\pi\)
\(314\) 0 0
\(315\) −15.6510 −0.881835
\(316\) 0 0
\(317\) 0.250367 0.0140620 0.00703101 0.999975i \(-0.497762\pi\)
0.00703101 + 0.999975i \(0.497762\pi\)
\(318\) 0 0
\(319\) −27.9195 −1.56319
\(320\) 0 0
\(321\) −3.34144 −0.186501
\(322\) 0 0
\(323\) −2.04729 −0.113914
\(324\) 0 0
\(325\) −19.8741 −1.10242
\(326\) 0 0
\(327\) 49.8970 2.75931
\(328\) 0 0
\(329\) −27.7751 −1.53129
\(330\) 0 0
\(331\) −25.3484 −1.39328 −0.696638 0.717423i \(-0.745322\pi\)
−0.696638 + 0.717423i \(0.745322\pi\)
\(332\) 0 0
\(333\) 68.5625 3.75720
\(334\) 0 0
\(335\) −1.57630 −0.0861223
\(336\) 0 0
\(337\) −1.98944 −0.108372 −0.0541859 0.998531i \(-0.517256\pi\)
−0.0541859 + 0.998531i \(0.517256\pi\)
\(338\) 0 0
\(339\) 50.3253 2.73330
\(340\) 0 0
\(341\) −7.54180 −0.408411
\(342\) 0 0
\(343\) −11.1256 −0.600725
\(344\) 0 0
\(345\) 0.572778 0.0308373
\(346\) 0 0
\(347\) −13.0131 −0.698578 −0.349289 0.937015i \(-0.613577\pi\)
−0.349289 + 0.937015i \(0.613577\pi\)
\(348\) 0 0
\(349\) −32.6639 −1.74846 −0.874228 0.485515i \(-0.838632\pi\)
−0.874228 + 0.485515i \(0.838632\pi\)
\(350\) 0 0
\(351\) −75.5483 −4.03247
\(352\) 0 0
\(353\) −17.4045 −0.926346 −0.463173 0.886268i \(-0.653289\pi\)
−0.463173 + 0.886268i \(0.653289\pi\)
\(354\) 0 0
\(355\) 6.80633 0.361243
\(356\) 0 0
\(357\) 22.3622 1.18353
\(358\) 0 0
\(359\) 16.5104 0.871385 0.435693 0.900096i \(-0.356504\pi\)
0.435693 + 0.900096i \(0.356504\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −17.3267 −0.909413
\(364\) 0 0
\(365\) −5.50533 −0.288162
\(366\) 0 0
\(367\) 26.4740 1.38193 0.690966 0.722887i \(-0.257185\pi\)
0.690966 + 0.722887i \(0.257185\pi\)
\(368\) 0 0
\(369\) −51.4105 −2.67632
\(370\) 0 0
\(371\) −46.5599 −2.41727
\(372\) 0 0
\(373\) 30.1533 1.56128 0.780639 0.624982i \(-0.214894\pi\)
0.780639 + 0.624982i \(0.214894\pi\)
\(374\) 0 0
\(375\) −18.8623 −0.974043
\(376\) 0 0
\(377\) −29.6076 −1.52487
\(378\) 0 0
\(379\) 22.5182 1.15668 0.578341 0.815795i \(-0.303700\pi\)
0.578341 + 0.815795i \(0.303700\pi\)
\(380\) 0 0
\(381\) 25.1522 1.28859
\(382\) 0 0
\(383\) −2.04476 −0.104482 −0.0522411 0.998634i \(-0.516636\pi\)
−0.0522411 + 0.998634i \(0.516636\pi\)
\(384\) 0 0
\(385\) −7.60096 −0.387381
\(386\) 0 0
\(387\) −75.4222 −3.83392
\(388\) 0 0
\(389\) −16.0989 −0.816246 −0.408123 0.912927i \(-0.633816\pi\)
−0.408123 + 0.912927i \(0.633816\pi\)
\(390\) 0 0
\(391\) −0.600677 −0.0303775
\(392\) 0 0
\(393\) 9.61749 0.485138
\(394\) 0 0
\(395\) 0.581328 0.0292498
\(396\) 0 0
\(397\) −1.29730 −0.0651098 −0.0325549 0.999470i \(-0.510364\pi\)
−0.0325549 + 0.999470i \(0.510364\pi\)
\(398\) 0 0
\(399\) −10.9228 −0.546825
\(400\) 0 0
\(401\) −18.4883 −0.923263 −0.461631 0.887072i \(-0.652736\pi\)
−0.461631 + 0.887072i \(0.652736\pi\)
\(402\) 0 0
\(403\) −7.99779 −0.398398
\(404\) 0 0
\(405\) −20.1615 −1.00183
\(406\) 0 0
\(407\) 33.2976 1.65050
\(408\) 0 0
\(409\) 19.4062 0.959577 0.479788 0.877384i \(-0.340713\pi\)
0.479788 + 0.877384i \(0.340713\pi\)
\(410\) 0 0
\(411\) 41.0599 2.02533
\(412\) 0 0
\(413\) 11.9845 0.589720
\(414\) 0 0
\(415\) −6.42090 −0.315190
\(416\) 0 0
\(417\) 74.3032 3.63864
\(418\) 0 0
\(419\) 35.2757 1.72333 0.861666 0.507476i \(-0.169421\pi\)
0.861666 + 0.507476i \(0.169421\pi\)
\(420\) 0 0
\(421\) −19.4877 −0.949774 −0.474887 0.880047i \(-0.657511\pi\)
−0.474887 + 0.880047i \(0.657511\pi\)
\(422\) 0 0
\(423\) −70.6825 −3.43670
\(424\) 0 0
\(425\) 9.54457 0.462980
\(426\) 0 0
\(427\) 4.82201 0.233353
\(428\) 0 0
\(429\) −57.5476 −2.77842
\(430\) 0 0
\(431\) −22.9227 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(432\) 0 0
\(433\) 28.3208 1.36101 0.680505 0.732744i \(-0.261761\pi\)
0.680505 + 0.732744i \(0.261761\pi\)
\(434\) 0 0
\(435\) −13.5587 −0.650088
\(436\) 0 0
\(437\) 0.293401 0.0140353
\(438\) 0 0
\(439\) 28.0353 1.33805 0.669027 0.743238i \(-0.266711\pi\)
0.669027 + 0.743238i \(0.266711\pi\)
\(440\) 0 0
\(441\) 29.6286 1.41088
\(442\) 0 0
\(443\) −1.77220 −0.0841997 −0.0420999 0.999113i \(-0.513405\pi\)
−0.0420999 + 0.999113i \(0.513405\pi\)
\(444\) 0 0
\(445\) 4.45364 0.211123
\(446\) 0 0
\(447\) 74.2605 3.51240
\(448\) 0 0
\(449\) 3.60125 0.169953 0.0849767 0.996383i \(-0.472918\pi\)
0.0849767 + 0.996383i \(0.472918\pi\)
\(450\) 0 0
\(451\) −24.9677 −1.17568
\(452\) 0 0
\(453\) 27.2805 1.28175
\(454\) 0 0
\(455\) −8.06053 −0.377883
\(456\) 0 0
\(457\) 15.1957 0.710827 0.355413 0.934709i \(-0.384340\pi\)
0.355413 + 0.934709i \(0.384340\pi\)
\(458\) 0 0
\(459\) 36.2822 1.69351
\(460\) 0 0
\(461\) 29.9458 1.39471 0.697357 0.716724i \(-0.254359\pi\)
0.697357 + 0.716724i \(0.254359\pi\)
\(462\) 0 0
\(463\) −7.90812 −0.367521 −0.183761 0.982971i \(-0.558827\pi\)
−0.183761 + 0.982971i \(0.558827\pi\)
\(464\) 0 0
\(465\) −3.66255 −0.169847
\(466\) 0 0
\(467\) 14.0952 0.652250 0.326125 0.945327i \(-0.394257\pi\)
0.326125 + 0.945327i \(0.394257\pi\)
\(468\) 0 0
\(469\) 8.81960 0.407251
\(470\) 0 0
\(471\) −76.6924 −3.53380
\(472\) 0 0
\(473\) −36.6290 −1.68420
\(474\) 0 0
\(475\) −4.66206 −0.213910
\(476\) 0 0
\(477\) −118.486 −5.42512
\(478\) 0 0
\(479\) −8.80418 −0.402273 −0.201137 0.979563i \(-0.564463\pi\)
−0.201137 + 0.979563i \(0.564463\pi\)
\(480\) 0 0
\(481\) 35.3108 1.61003
\(482\) 0 0
\(483\) −3.20477 −0.145822
\(484\) 0 0
\(485\) 11.0421 0.501397
\(486\) 0 0
\(487\) −12.7351 −0.577083 −0.288541 0.957467i \(-0.593170\pi\)
−0.288541 + 0.957467i \(0.593170\pi\)
\(488\) 0 0
\(489\) −65.2416 −2.95033
\(490\) 0 0
\(491\) −25.4661 −1.14927 −0.574635 0.818410i \(-0.694856\pi\)
−0.574635 + 0.818410i \(0.694856\pi\)
\(492\) 0 0
\(493\) 14.2191 0.640396
\(494\) 0 0
\(495\) −19.3430 −0.869405
\(496\) 0 0
\(497\) −38.0824 −1.70823
\(498\) 0 0
\(499\) 1.05715 0.0473246 0.0236623 0.999720i \(-0.492467\pi\)
0.0236623 + 0.999720i \(0.492467\pi\)
\(500\) 0 0
\(501\) −51.7522 −2.31212
\(502\) 0 0
\(503\) 34.7788 1.55071 0.775355 0.631525i \(-0.217571\pi\)
0.775355 + 0.631525i \(0.217571\pi\)
\(504\) 0 0
\(505\) 3.66270 0.162988
\(506\) 0 0
\(507\) −17.3708 −0.771465
\(508\) 0 0
\(509\) −30.8250 −1.36629 −0.683146 0.730282i \(-0.739389\pi\)
−0.683146 + 0.730282i \(0.739389\pi\)
\(510\) 0 0
\(511\) 30.8031 1.36265
\(512\) 0 0
\(513\) −17.7221 −0.782449
\(514\) 0 0
\(515\) −2.66595 −0.117476
\(516\) 0 0
\(517\) −34.3271 −1.50971
\(518\) 0 0
\(519\) −7.88707 −0.346204
\(520\) 0 0
\(521\) −6.82843 −0.299159 −0.149579 0.988750i \(-0.547792\pi\)
−0.149579 + 0.988750i \(0.547792\pi\)
\(522\) 0 0
\(523\) −18.1587 −0.794026 −0.397013 0.917813i \(-0.629953\pi\)
−0.397013 + 0.917813i \(0.629953\pi\)
\(524\) 0 0
\(525\) 50.9229 2.22246
\(526\) 0 0
\(527\) 3.84095 0.167314
\(528\) 0 0
\(529\) −22.9139 −0.996257
\(530\) 0 0
\(531\) 30.4984 1.32352
\(532\) 0 0
\(533\) −26.4773 −1.14686
\(534\) 0 0
\(535\) −0.578432 −0.0250078
\(536\) 0 0
\(537\) −11.5019 −0.496343
\(538\) 0 0
\(539\) 14.3892 0.619786
\(540\) 0 0
\(541\) −7.64478 −0.328675 −0.164337 0.986404i \(-0.552549\pi\)
−0.164337 + 0.986404i \(0.552549\pi\)
\(542\) 0 0
\(543\) 0.558936 0.0239862
\(544\) 0 0
\(545\) 8.63760 0.369994
\(546\) 0 0
\(547\) 44.8156 1.91618 0.958089 0.286471i \(-0.0924822\pi\)
0.958089 + 0.286471i \(0.0924822\pi\)
\(548\) 0 0
\(549\) 12.2711 0.523719
\(550\) 0 0
\(551\) −6.94533 −0.295881
\(552\) 0 0
\(553\) −3.25261 −0.138315
\(554\) 0 0
\(555\) 16.1704 0.686397
\(556\) 0 0
\(557\) 33.5445 1.42133 0.710663 0.703532i \(-0.248395\pi\)
0.710663 + 0.703532i \(0.248395\pi\)
\(558\) 0 0
\(559\) −38.8436 −1.64291
\(560\) 0 0
\(561\) 27.6373 1.16685
\(562\) 0 0
\(563\) −7.31636 −0.308348 −0.154174 0.988044i \(-0.549272\pi\)
−0.154174 + 0.988044i \(0.549272\pi\)
\(564\) 0 0
\(565\) 8.71174 0.366506
\(566\) 0 0
\(567\) 112.807 4.73743
\(568\) 0 0
\(569\) −16.6777 −0.699167 −0.349584 0.936905i \(-0.613677\pi\)
−0.349584 + 0.936905i \(0.613677\pi\)
\(570\) 0 0
\(571\) 41.8203 1.75012 0.875062 0.484010i \(-0.160820\pi\)
0.875062 + 0.484010i \(0.160820\pi\)
\(572\) 0 0
\(573\) −0.825979 −0.0345058
\(574\) 0 0
\(575\) −1.36785 −0.0570434
\(576\) 0 0
\(577\) 34.0377 1.41701 0.708504 0.705706i \(-0.249370\pi\)
0.708504 + 0.705706i \(0.249370\pi\)
\(578\) 0 0
\(579\) 29.1686 1.21220
\(580\) 0 0
\(581\) 35.9259 1.49046
\(582\) 0 0
\(583\) −57.5432 −2.38320
\(584\) 0 0
\(585\) −20.5126 −0.848090
\(586\) 0 0
\(587\) 0.643931 0.0265779 0.0132889 0.999912i \(-0.495770\pi\)
0.0132889 + 0.999912i \(0.495770\pi\)
\(588\) 0 0
\(589\) −1.87612 −0.0773041
\(590\) 0 0
\(591\) 46.6795 1.92014
\(592\) 0 0
\(593\) −13.6058 −0.558722 −0.279361 0.960186i \(-0.590123\pi\)
−0.279361 + 0.960186i \(0.590123\pi\)
\(594\) 0 0
\(595\) 3.87108 0.158699
\(596\) 0 0
\(597\) 13.4639 0.551040
\(598\) 0 0
\(599\) −40.4635 −1.65330 −0.826648 0.562720i \(-0.809755\pi\)
−0.826648 + 0.562720i \(0.809755\pi\)
\(600\) 0 0
\(601\) 5.98704 0.244217 0.122108 0.992517i \(-0.461034\pi\)
0.122108 + 0.992517i \(0.461034\pi\)
\(602\) 0 0
\(603\) 22.4443 0.914001
\(604\) 0 0
\(605\) −2.99939 −0.121943
\(606\) 0 0
\(607\) −25.8342 −1.04858 −0.524289 0.851540i \(-0.675669\pi\)
−0.524289 + 0.851540i \(0.675669\pi\)
\(608\) 0 0
\(609\) 75.8627 3.07411
\(610\) 0 0
\(611\) −36.4026 −1.47269
\(612\) 0 0
\(613\) 18.7495 0.757287 0.378643 0.925543i \(-0.376391\pi\)
0.378643 + 0.925543i \(0.376391\pi\)
\(614\) 0 0
\(615\) −12.1251 −0.488933
\(616\) 0 0
\(617\) 32.3475 1.30226 0.651131 0.758965i \(-0.274295\pi\)
0.651131 + 0.758965i \(0.274295\pi\)
\(618\) 0 0
\(619\) −21.5896 −0.867761 −0.433881 0.900970i \(-0.642856\pi\)
−0.433881 + 0.900970i \(0.642856\pi\)
\(620\) 0 0
\(621\) −5.19968 −0.208656
\(622\) 0 0
\(623\) −24.9188 −0.998349
\(624\) 0 0
\(625\) 20.0451 0.801803
\(626\) 0 0
\(627\) −13.4995 −0.539118
\(628\) 0 0
\(629\) −16.9581 −0.676163
\(630\) 0 0
\(631\) 46.3066 1.84344 0.921718 0.387862i \(-0.126786\pi\)
0.921718 + 0.387862i \(0.126786\pi\)
\(632\) 0 0
\(633\) −18.5820 −0.738567
\(634\) 0 0
\(635\) 4.35407 0.172786
\(636\) 0 0
\(637\) 15.2592 0.604591
\(638\) 0 0
\(639\) −96.9127 −3.83381
\(640\) 0 0
\(641\) 41.0229 1.62031 0.810154 0.586217i \(-0.199383\pi\)
0.810154 + 0.586217i \(0.199383\pi\)
\(642\) 0 0
\(643\) −9.45471 −0.372857 −0.186429 0.982468i \(-0.559691\pi\)
−0.186429 + 0.982468i \(0.559691\pi\)
\(644\) 0 0
\(645\) −17.7883 −0.700413
\(646\) 0 0
\(647\) −12.9860 −0.510534 −0.255267 0.966871i \(-0.582163\pi\)
−0.255267 + 0.966871i \(0.582163\pi\)
\(648\) 0 0
\(649\) 14.8116 0.581408
\(650\) 0 0
\(651\) 20.4925 0.803165
\(652\) 0 0
\(653\) −40.9198 −1.60132 −0.800659 0.599121i \(-0.795517\pi\)
−0.800659 + 0.599121i \(0.795517\pi\)
\(654\) 0 0
\(655\) 1.66487 0.0650519
\(656\) 0 0
\(657\) 78.3883 3.05822
\(658\) 0 0
\(659\) 22.0483 0.858879 0.429439 0.903096i \(-0.358711\pi\)
0.429439 + 0.903096i \(0.358711\pi\)
\(660\) 0 0
\(661\) −12.5805 −0.489325 −0.244663 0.969608i \(-0.578677\pi\)
−0.244663 + 0.969608i \(0.578677\pi\)
\(662\) 0 0
\(663\) 29.3083 1.13824
\(664\) 0 0
\(665\) −1.89084 −0.0733235
\(666\) 0 0
\(667\) −2.03777 −0.0789028
\(668\) 0 0
\(669\) 64.2194 2.48286
\(670\) 0 0
\(671\) 5.95950 0.230064
\(672\) 0 0
\(673\) 19.3975 0.747719 0.373860 0.927485i \(-0.378034\pi\)
0.373860 + 0.927485i \(0.378034\pi\)
\(674\) 0 0
\(675\) 82.6214 3.18010
\(676\) 0 0
\(677\) −46.4270 −1.78434 −0.892168 0.451704i \(-0.850816\pi\)
−0.892168 + 0.451704i \(0.850816\pi\)
\(678\) 0 0
\(679\) −61.7822 −2.37098
\(680\) 0 0
\(681\) −74.0010 −2.83573
\(682\) 0 0
\(683\) −28.3473 −1.08468 −0.542339 0.840160i \(-0.682461\pi\)
−0.542339 + 0.840160i \(0.682461\pi\)
\(684\) 0 0
\(685\) 7.10782 0.271576
\(686\) 0 0
\(687\) −70.7360 −2.69875
\(688\) 0 0
\(689\) −61.0224 −2.32477
\(690\) 0 0
\(691\) 12.2941 0.467689 0.233844 0.972274i \(-0.424869\pi\)
0.233844 + 0.972274i \(0.424869\pi\)
\(692\) 0 0
\(693\) 108.227 4.11121
\(694\) 0 0
\(695\) 12.8625 0.487903
\(696\) 0 0
\(697\) 12.7157 0.481643
\(698\) 0 0
\(699\) 22.9396 0.867656
\(700\) 0 0
\(701\) 35.2348 1.33080 0.665400 0.746487i \(-0.268261\pi\)
0.665400 + 0.746487i \(0.268261\pi\)
\(702\) 0 0
\(703\) 8.28320 0.312407
\(704\) 0 0
\(705\) −16.6704 −0.627845
\(706\) 0 0
\(707\) −20.4933 −0.770732
\(708\) 0 0
\(709\) 23.9774 0.900490 0.450245 0.892905i \(-0.351337\pi\)
0.450245 + 0.892905i \(0.351337\pi\)
\(710\) 0 0
\(711\) −8.27730 −0.310423
\(712\) 0 0
\(713\) −0.550455 −0.0206147
\(714\) 0 0
\(715\) −9.96198 −0.372557
\(716\) 0 0
\(717\) −8.82447 −0.329556
\(718\) 0 0
\(719\) −4.45710 −0.166222 −0.0831108 0.996540i \(-0.526486\pi\)
−0.0831108 + 0.996540i \(0.526486\pi\)
\(720\) 0 0
\(721\) 14.9164 0.555514
\(722\) 0 0
\(723\) 74.1561 2.75789
\(724\) 0 0
\(725\) 32.3795 1.20255
\(726\) 0 0
\(727\) −42.5483 −1.57803 −0.789015 0.614374i \(-0.789408\pi\)
−0.789015 + 0.614374i \(0.789408\pi\)
\(728\) 0 0
\(729\) 108.531 4.01966
\(730\) 0 0
\(731\) 18.6547 0.689970
\(732\) 0 0
\(733\) −8.70291 −0.321449 −0.160725 0.986999i \(-0.551383\pi\)
−0.160725 + 0.986999i \(0.551383\pi\)
\(734\) 0 0
\(735\) 6.98788 0.257752
\(736\) 0 0
\(737\) 10.9001 0.401511
\(738\) 0 0
\(739\) −12.9269 −0.475523 −0.237761 0.971324i \(-0.576414\pi\)
−0.237761 + 0.971324i \(0.576414\pi\)
\(740\) 0 0
\(741\) −14.3157 −0.525900
\(742\) 0 0
\(743\) 15.4438 0.566579 0.283290 0.959034i \(-0.408574\pi\)
0.283290 + 0.959034i \(0.408574\pi\)
\(744\) 0 0
\(745\) 12.8551 0.470976
\(746\) 0 0
\(747\) 91.4247 3.34506
\(748\) 0 0
\(749\) 3.23641 0.118256
\(750\) 0 0
\(751\) −6.20609 −0.226463 −0.113232 0.993569i \(-0.536120\pi\)
−0.113232 + 0.993569i \(0.536120\pi\)
\(752\) 0 0
\(753\) −60.6443 −2.21000
\(754\) 0 0
\(755\) 4.72249 0.171869
\(756\) 0 0
\(757\) 45.9623 1.67053 0.835265 0.549848i \(-0.185314\pi\)
0.835265 + 0.549848i \(0.185314\pi\)
\(758\) 0 0
\(759\) −3.96077 −0.143767
\(760\) 0 0
\(761\) −44.9795 −1.63050 −0.815252 0.579106i \(-0.803402\pi\)
−0.815252 + 0.579106i \(0.803402\pi\)
\(762\) 0 0
\(763\) −48.3286 −1.74961
\(764\) 0 0
\(765\) 9.85119 0.356171
\(766\) 0 0
\(767\) 15.7072 0.567154
\(768\) 0 0
\(769\) 17.8468 0.643573 0.321787 0.946812i \(-0.395717\pi\)
0.321787 + 0.946812i \(0.395717\pi\)
\(770\) 0 0
\(771\) −55.4907 −1.99845
\(772\) 0 0
\(773\) 16.5750 0.596161 0.298080 0.954541i \(-0.403654\pi\)
0.298080 + 0.954541i \(0.403654\pi\)
\(774\) 0 0
\(775\) 8.74657 0.314186
\(776\) 0 0
\(777\) −90.4759 −3.24581
\(778\) 0 0
\(779\) −6.21102 −0.222533
\(780\) 0 0
\(781\) −47.0659 −1.68415
\(782\) 0 0
\(783\) 123.086 4.39873
\(784\) 0 0
\(785\) −13.2761 −0.473845
\(786\) 0 0
\(787\) −7.41270 −0.264234 −0.132117 0.991234i \(-0.542178\pi\)
−0.132117 + 0.991234i \(0.542178\pi\)
\(788\) 0 0
\(789\) −1.91746 −0.0682633
\(790\) 0 0
\(791\) −48.7434 −1.73312
\(792\) 0 0
\(793\) 6.31982 0.224424
\(794\) 0 0
\(795\) −27.9450 −0.991106
\(796\) 0 0
\(797\) 19.6949 0.697628 0.348814 0.937192i \(-0.386584\pi\)
0.348814 + 0.937192i \(0.386584\pi\)
\(798\) 0 0
\(799\) 17.4824 0.618484
\(800\) 0 0
\(801\) −63.4137 −2.24061
\(802\) 0 0
\(803\) 38.0695 1.34344
\(804\) 0 0
\(805\) −0.554774 −0.0195532
\(806\) 0 0
\(807\) −33.0309 −1.16274
\(808\) 0 0
\(809\) −1.74969 −0.0615158 −0.0307579 0.999527i \(-0.509792\pi\)
−0.0307579 + 0.999527i \(0.509792\pi\)
\(810\) 0 0
\(811\) −46.2599 −1.62441 −0.812203 0.583375i \(-0.801732\pi\)
−0.812203 + 0.583375i \(0.801732\pi\)
\(812\) 0 0
\(813\) −68.7834 −2.41234
\(814\) 0 0
\(815\) −11.2939 −0.395607
\(816\) 0 0
\(817\) −9.11192 −0.318786
\(818\) 0 0
\(819\) 114.771 4.01041
\(820\) 0 0
\(821\) −21.7094 −0.757663 −0.378832 0.925466i \(-0.623674\pi\)
−0.378832 + 0.925466i \(0.623674\pi\)
\(822\) 0 0
\(823\) 2.56169 0.0892950 0.0446475 0.999003i \(-0.485784\pi\)
0.0446475 + 0.999003i \(0.485784\pi\)
\(824\) 0 0
\(825\) 62.9354 2.19113
\(826\) 0 0
\(827\) 2.20009 0.0765045 0.0382522 0.999268i \(-0.487821\pi\)
0.0382522 + 0.999268i \(0.487821\pi\)
\(828\) 0 0
\(829\) 13.1400 0.456370 0.228185 0.973618i \(-0.426721\pi\)
0.228185 + 0.973618i \(0.426721\pi\)
\(830\) 0 0
\(831\) 11.9822 0.415657
\(832\) 0 0
\(833\) −7.32825 −0.253909
\(834\) 0 0
\(835\) −8.95875 −0.310030
\(836\) 0 0
\(837\) 33.2487 1.14924
\(838\) 0 0
\(839\) −31.1082 −1.07397 −0.536986 0.843591i \(-0.680437\pi\)
−0.536986 + 0.843591i \(0.680437\pi\)
\(840\) 0 0
\(841\) 19.2377 0.663368
\(842\) 0 0
\(843\) −33.7936 −1.16391
\(844\) 0 0
\(845\) −3.00704 −0.103445
\(846\) 0 0
\(847\) 16.7820 0.576637
\(848\) 0 0
\(849\) −13.7181 −0.470804
\(850\) 0 0
\(851\) 2.43030 0.0833096
\(852\) 0 0
\(853\) 30.4940 1.04409 0.522047 0.852917i \(-0.325169\pi\)
0.522047 + 0.852917i \(0.325169\pi\)
\(854\) 0 0
\(855\) −4.81183 −0.164561
\(856\) 0 0
\(857\) 48.1544 1.64492 0.822461 0.568821i \(-0.192600\pi\)
0.822461 + 0.568821i \(0.192600\pi\)
\(858\) 0 0
\(859\) −21.5553 −0.735459 −0.367730 0.929933i \(-0.619865\pi\)
−0.367730 + 0.929933i \(0.619865\pi\)
\(860\) 0 0
\(861\) 67.8419 2.31205
\(862\) 0 0
\(863\) −9.52724 −0.324311 −0.162156 0.986765i \(-0.551845\pi\)
−0.162156 + 0.986765i \(0.551845\pi\)
\(864\) 0 0
\(865\) −1.36532 −0.0464222
\(866\) 0 0
\(867\) 43.0135 1.46082
\(868\) 0 0
\(869\) −4.01989 −0.136366
\(870\) 0 0
\(871\) 11.5592 0.391667
\(872\) 0 0
\(873\) −157.224 −5.32124
\(874\) 0 0
\(875\) 18.2694 0.617617
\(876\) 0 0
\(877\) −9.68697 −0.327106 −0.163553 0.986535i \(-0.552295\pi\)
−0.163553 + 0.986535i \(0.552295\pi\)
\(878\) 0 0
\(879\) 28.1249 0.948628
\(880\) 0 0
\(881\) −48.1977 −1.62382 −0.811910 0.583782i \(-0.801572\pi\)
−0.811910 + 0.583782i \(0.801572\pi\)
\(882\) 0 0
\(883\) −25.9939 −0.874766 −0.437383 0.899275i \(-0.644095\pi\)
−0.437383 + 0.899275i \(0.644095\pi\)
\(884\) 0 0
\(885\) 7.19304 0.241791
\(886\) 0 0
\(887\) 47.4975 1.59481 0.797405 0.603444i \(-0.206205\pi\)
0.797405 + 0.603444i \(0.206205\pi\)
\(888\) 0 0
\(889\) −24.3616 −0.817063
\(890\) 0 0
\(891\) 139.417 4.67066
\(892\) 0 0
\(893\) −8.53931 −0.285757
\(894\) 0 0
\(895\) −1.99108 −0.0665543
\(896\) 0 0
\(897\) −4.20024 −0.140242
\(898\) 0 0
\(899\) 13.0303 0.434584
\(900\) 0 0
\(901\) 29.3061 0.976328
\(902\) 0 0
\(903\) 99.5280 3.31208
\(904\) 0 0
\(905\) 0.0967567 0.00321630
\(906\) 0 0
\(907\) 15.0849 0.500886 0.250443 0.968131i \(-0.419424\pi\)
0.250443 + 0.968131i \(0.419424\pi\)
\(908\) 0 0
\(909\) −52.1518 −1.72977
\(910\) 0 0
\(911\) −11.9463 −0.395800 −0.197900 0.980222i \(-0.563412\pi\)
−0.197900 + 0.980222i \(0.563412\pi\)
\(912\) 0 0
\(913\) 44.4007 1.46945
\(914\) 0 0
\(915\) 2.89414 0.0956772
\(916\) 0 0
\(917\) −9.31519 −0.307615
\(918\) 0 0
\(919\) 8.90417 0.293721 0.146861 0.989157i \(-0.453083\pi\)
0.146861 + 0.989157i \(0.453083\pi\)
\(920\) 0 0
\(921\) −38.3783 −1.26461
\(922\) 0 0
\(923\) −49.9116 −1.64286
\(924\) 0 0
\(925\) −38.6167 −1.26971
\(926\) 0 0
\(927\) 37.9594 1.24675
\(928\) 0 0
\(929\) 7.67807 0.251909 0.125955 0.992036i \(-0.459801\pi\)
0.125955 + 0.992036i \(0.459801\pi\)
\(930\) 0 0
\(931\) 3.57949 0.117313
\(932\) 0 0
\(933\) 7.62759 0.249716
\(934\) 0 0
\(935\) 4.78426 0.156462
\(936\) 0 0
\(937\) −54.1812 −1.77002 −0.885011 0.465570i \(-0.845850\pi\)
−0.885011 + 0.465570i \(0.845850\pi\)
\(938\) 0 0
\(939\) 78.8016 2.57159
\(940\) 0 0
\(941\) 7.53369 0.245591 0.122796 0.992432i \(-0.460814\pi\)
0.122796 + 0.992432i \(0.460814\pi\)
\(942\) 0 0
\(943\) −1.82232 −0.0593430
\(944\) 0 0
\(945\) 33.5095 1.09007
\(946\) 0 0
\(947\) 18.0610 0.586903 0.293452 0.955974i \(-0.405196\pi\)
0.293452 + 0.955974i \(0.405196\pi\)
\(948\) 0 0
\(949\) 40.3712 1.31051
\(950\) 0 0
\(951\) −0.840775 −0.0272640
\(952\) 0 0
\(953\) −54.9471 −1.77991 −0.889955 0.456047i \(-0.849265\pi\)
−0.889955 + 0.456047i \(0.849265\pi\)
\(954\) 0 0
\(955\) −0.142984 −0.00462686
\(956\) 0 0
\(957\) 93.7584 3.03078
\(958\) 0 0
\(959\) −39.7693 −1.28422
\(960\) 0 0
\(961\) −27.4802 −0.886457
\(962\) 0 0
\(963\) 8.23607 0.265404
\(964\) 0 0
\(965\) 5.04933 0.162544
\(966\) 0 0
\(967\) 40.3739 1.29834 0.649169 0.760644i \(-0.275117\pi\)
0.649169 + 0.760644i \(0.275117\pi\)
\(968\) 0 0
\(969\) 6.87514 0.220861
\(970\) 0 0
\(971\) 12.4426 0.399303 0.199651 0.979867i \(-0.436019\pi\)
0.199651 + 0.979867i \(0.436019\pi\)
\(972\) 0 0
\(973\) −71.9677 −2.30718
\(974\) 0 0
\(975\) 66.7406 2.13741
\(976\) 0 0
\(977\) 17.3752 0.555880 0.277940 0.960598i \(-0.410348\pi\)
0.277940 + 0.960598i \(0.410348\pi\)
\(978\) 0 0
\(979\) −30.7970 −0.984277
\(980\) 0 0
\(981\) −122.987 −3.92668
\(982\) 0 0
\(983\) 36.2478 1.15612 0.578062 0.815993i \(-0.303809\pi\)
0.578062 + 0.815993i \(0.303809\pi\)
\(984\) 0 0
\(985\) 8.08063 0.257470
\(986\) 0 0
\(987\) 93.2735 2.96893
\(988\) 0 0
\(989\) −2.67345 −0.0850108
\(990\) 0 0
\(991\) 19.1118 0.607107 0.303554 0.952814i \(-0.401827\pi\)
0.303554 + 0.952814i \(0.401827\pi\)
\(992\) 0 0
\(993\) 85.1243 2.70134
\(994\) 0 0
\(995\) 2.33071 0.0738886
\(996\) 0 0
\(997\) −35.0889 −1.11128 −0.555638 0.831424i \(-0.687526\pi\)
−0.555638 + 0.831424i \(0.687526\pi\)
\(998\) 0 0
\(999\) −146.795 −4.64440
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 \(a_p\))