Properties

Label 6036.2.a.i.1.11
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 0
Dimension 26
CM No

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Newspace parameters

Level: \( N \) = \( 6036 = 2^{2} \cdot 3 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.19770266\)
Analytic rank: \(0\)
Dimension: \(26\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(-0.461317 q^{5}\) \(-3.07386 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(-0.461317 q^{5}\) \(-3.07386 q^{7}\) \(+1.00000 q^{9}\) \(-5.13061 q^{11}\) \(+6.80493 q^{13}\) \(+0.461317 q^{15}\) \(+1.28513 q^{17}\) \(+6.12411 q^{19}\) \(+3.07386 q^{21}\) \(-8.36756 q^{23}\) \(-4.78719 q^{25}\) \(-1.00000 q^{27}\) \(+0.615911 q^{29}\) \(-3.68978 q^{31}\) \(+5.13061 q^{33}\) \(+1.41803 q^{35}\) \(+10.6984 q^{37}\) \(-6.80493 q^{39}\) \(-10.4321 q^{41}\) \(-0.274161 q^{43}\) \(-0.461317 q^{45}\) \(+7.41573 q^{47}\) \(+2.44862 q^{49}\) \(-1.28513 q^{51}\) \(-6.05978 q^{53}\) \(+2.36684 q^{55}\) \(-6.12411 q^{57}\) \(-13.1942 q^{59}\) \(+4.72241 q^{61}\) \(-3.07386 q^{63}\) \(-3.13923 q^{65}\) \(+8.57481 q^{67}\) \(+8.36756 q^{69}\) \(-9.71053 q^{71}\) \(-12.1190 q^{73}\) \(+4.78719 q^{75}\) \(+15.7708 q^{77}\) \(-10.4083 q^{79}\) \(+1.00000 q^{81}\) \(-0.536826 q^{83}\) \(-0.592854 q^{85}\) \(-0.615911 q^{87}\) \(+13.8744 q^{89}\) \(-20.9174 q^{91}\) \(+3.68978 q^{93}\) \(-2.82516 q^{95}\) \(+13.4725 q^{97}\) \(-5.13061 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 13q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 48q^{25} \) \(\mathstrut -\mathstrut 26q^{27} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 19q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 21q^{35} \) \(\mathstrut +\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 13q^{39} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 67q^{49} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut +\mathstrut 20q^{55} \) \(\mathstrut +\mathstrut q^{57} \) \(\mathstrut -\mathstrut 18q^{59} \) \(\mathstrut +\mathstrut 43q^{61} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 41q^{65} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 22q^{69} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 48q^{75} \) \(\mathstrut +\mathstrut 23q^{77} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 26q^{81} \) \(\mathstrut -\mathstrut 19q^{83} \) \(\mathstrut +\mathstrut 29q^{85} \) \(\mathstrut -\mathstrut 6q^{87} \) \(\mathstrut +\mathstrut 49q^{89} \) \(\mathstrut -\mathstrut 13q^{91} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 26q^{95} \) \(\mathstrut +\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) −0.461317 −0.206307 −0.103154 0.994665i \(-0.532893\pi\)
−0.103154 + 0.994665i \(0.532893\pi\)
\(6\) 0 0
\(7\) −3.07386 −1.16181 −0.580905 0.813971i \(-0.697301\pi\)
−0.580905 + 0.813971i \(0.697301\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −5.13061 −1.54694 −0.773469 0.633834i \(-0.781480\pi\)
−0.773469 + 0.633834i \(0.781480\pi\)
\(12\) 0 0
\(13\) 6.80493 1.88735 0.943673 0.330878i \(-0.107345\pi\)
0.943673 + 0.330878i \(0.107345\pi\)
\(14\) 0 0
\(15\) 0.461317 0.119112
\(16\) 0 0
\(17\) 1.28513 0.311690 0.155845 0.987781i \(-0.450190\pi\)
0.155845 + 0.987781i \(0.450190\pi\)
\(18\) 0 0
\(19\) 6.12411 1.40497 0.702484 0.711700i \(-0.252074\pi\)
0.702484 + 0.711700i \(0.252074\pi\)
\(20\) 0 0
\(21\) 3.07386 0.670771
\(22\) 0 0
\(23\) −8.36756 −1.74476 −0.872379 0.488831i \(-0.837424\pi\)
−0.872379 + 0.488831i \(0.837424\pi\)
\(24\) 0 0
\(25\) −4.78719 −0.957437
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 0.615911 0.114372 0.0571859 0.998364i \(-0.481787\pi\)
0.0571859 + 0.998364i \(0.481787\pi\)
\(30\) 0 0
\(31\) −3.68978 −0.662704 −0.331352 0.943507i \(-0.607505\pi\)
−0.331352 + 0.943507i \(0.607505\pi\)
\(32\) 0 0
\(33\) 5.13061 0.893125
\(34\) 0 0
\(35\) 1.41803 0.239690
\(36\) 0 0
\(37\) 10.6984 1.75881 0.879403 0.476078i \(-0.157942\pi\)
0.879403 + 0.476078i \(0.157942\pi\)
\(38\) 0 0
\(39\) −6.80493 −1.08966
\(40\) 0 0
\(41\) −10.4321 −1.62922 −0.814612 0.580006i \(-0.803050\pi\)
−0.814612 + 0.580006i \(0.803050\pi\)
\(42\) 0 0
\(43\) −0.274161 −0.0418091 −0.0209045 0.999781i \(-0.506655\pi\)
−0.0209045 + 0.999781i \(0.506655\pi\)
\(44\) 0 0
\(45\) −0.461317 −0.0687691
\(46\) 0 0
\(47\) 7.41573 1.08169 0.540847 0.841121i \(-0.318104\pi\)
0.540847 + 0.841121i \(0.318104\pi\)
\(48\) 0 0
\(49\) 2.44862 0.349803
\(50\) 0 0
\(51\) −1.28513 −0.179955
\(52\) 0 0
\(53\) −6.05978 −0.832374 −0.416187 0.909279i \(-0.636634\pi\)
−0.416187 + 0.909279i \(0.636634\pi\)
\(54\) 0 0
\(55\) 2.36684 0.319145
\(56\) 0 0
\(57\) −6.12411 −0.811158
\(58\) 0 0
\(59\) −13.1942 −1.71774 −0.858870 0.512194i \(-0.828833\pi\)
−0.858870 + 0.512194i \(0.828833\pi\)
\(60\) 0 0
\(61\) 4.72241 0.604642 0.302321 0.953206i \(-0.402239\pi\)
0.302321 + 0.953206i \(0.402239\pi\)
\(62\) 0 0
\(63\) −3.07386 −0.387270
\(64\) 0 0
\(65\) −3.13923 −0.389374
\(66\) 0 0
\(67\) 8.57481 1.04758 0.523790 0.851847i \(-0.324518\pi\)
0.523790 + 0.851847i \(0.324518\pi\)
\(68\) 0 0
\(69\) 8.36756 1.00734
\(70\) 0 0
\(71\) −9.71053 −1.15243 −0.576214 0.817299i \(-0.695471\pi\)
−0.576214 + 0.817299i \(0.695471\pi\)
\(72\) 0 0
\(73\) −12.1190 −1.41842 −0.709211 0.704996i \(-0.750949\pi\)
−0.709211 + 0.704996i \(0.750949\pi\)
\(74\) 0 0
\(75\) 4.78719 0.552777
\(76\) 0 0
\(77\) 15.7708 1.79725
\(78\) 0 0
\(79\) −10.4083 −1.17103 −0.585513 0.810663i \(-0.699107\pi\)
−0.585513 + 0.810663i \(0.699107\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −0.536826 −0.0589244 −0.0294622 0.999566i \(-0.509379\pi\)
−0.0294622 + 0.999566i \(0.509379\pi\)
\(84\) 0 0
\(85\) −0.592854 −0.0643040
\(86\) 0 0
\(87\) −0.615911 −0.0660326
\(88\) 0 0
\(89\) 13.8744 1.47068 0.735342 0.677696i \(-0.237021\pi\)
0.735342 + 0.677696i \(0.237021\pi\)
\(90\) 0 0
\(91\) −20.9174 −2.19274
\(92\) 0 0
\(93\) 3.68978 0.382612
\(94\) 0 0
\(95\) −2.82516 −0.289855
\(96\) 0 0
\(97\) 13.4725 1.36792 0.683960 0.729519i \(-0.260256\pi\)
0.683960 + 0.729519i \(0.260256\pi\)
\(98\) 0 0
\(99\) −5.13061 −0.515646
\(100\) 0 0
\(101\) −3.25530 −0.323915 −0.161957 0.986798i \(-0.551781\pi\)
−0.161957 + 0.986798i \(0.551781\pi\)
\(102\) 0 0
\(103\) 4.08644 0.402649 0.201324 0.979525i \(-0.435475\pi\)
0.201324 + 0.979525i \(0.435475\pi\)
\(104\) 0 0
\(105\) −1.41803 −0.138385
\(106\) 0 0
\(107\) 12.2673 1.18592 0.592960 0.805232i \(-0.297959\pi\)
0.592960 + 0.805232i \(0.297959\pi\)
\(108\) 0 0
\(109\) 1.40696 0.134762 0.0673811 0.997727i \(-0.478536\pi\)
0.0673811 + 0.997727i \(0.478536\pi\)
\(110\) 0 0
\(111\) −10.6984 −1.01545
\(112\) 0 0
\(113\) −4.51084 −0.424344 −0.212172 0.977232i \(-0.568054\pi\)
−0.212172 + 0.977232i \(0.568054\pi\)
\(114\) 0 0
\(115\) 3.86010 0.359956
\(116\) 0 0
\(117\) 6.80493 0.629116
\(118\) 0 0
\(119\) −3.95032 −0.362125
\(120\) 0 0
\(121\) 15.3232 1.39302
\(122\) 0 0
\(123\) 10.4321 0.940633
\(124\) 0 0
\(125\) 4.51500 0.403834
\(126\) 0 0
\(127\) −6.67912 −0.592676 −0.296338 0.955083i \(-0.595765\pi\)
−0.296338 + 0.955083i \(0.595765\pi\)
\(128\) 0 0
\(129\) 0.274161 0.0241385
\(130\) 0 0
\(131\) 1.22326 0.106877 0.0534383 0.998571i \(-0.482982\pi\)
0.0534383 + 0.998571i \(0.482982\pi\)
\(132\) 0 0
\(133\) −18.8247 −1.63231
\(134\) 0 0
\(135\) 0.461317 0.0397039
\(136\) 0 0
\(137\) 13.0509 1.11502 0.557508 0.830171i \(-0.311757\pi\)
0.557508 + 0.830171i \(0.311757\pi\)
\(138\) 0 0
\(139\) 11.6783 0.990545 0.495272 0.868738i \(-0.335068\pi\)
0.495272 + 0.868738i \(0.335068\pi\)
\(140\) 0 0
\(141\) −7.41573 −0.624517
\(142\) 0 0
\(143\) −34.9134 −2.91961
\(144\) 0 0
\(145\) −0.284130 −0.0235957
\(146\) 0 0
\(147\) −2.44862 −0.201959
\(148\) 0 0
\(149\) 9.05393 0.741727 0.370863 0.928687i \(-0.379062\pi\)
0.370863 + 0.928687i \(0.379062\pi\)
\(150\) 0 0
\(151\) −7.35196 −0.598294 −0.299147 0.954207i \(-0.596702\pi\)
−0.299147 + 0.954207i \(0.596702\pi\)
\(152\) 0 0
\(153\) 1.28513 0.103897
\(154\) 0 0
\(155\) 1.70216 0.136721
\(156\) 0 0
\(157\) −9.62422 −0.768097 −0.384048 0.923313i \(-0.625470\pi\)
−0.384048 + 0.923313i \(0.625470\pi\)
\(158\) 0 0
\(159\) 6.05978 0.480571
\(160\) 0 0
\(161\) 25.7207 2.02708
\(162\) 0 0
\(163\) 23.6560 1.85288 0.926441 0.376439i \(-0.122852\pi\)
0.926441 + 0.376439i \(0.122852\pi\)
\(164\) 0 0
\(165\) −2.36684 −0.184258
\(166\) 0 0
\(167\) −7.71310 −0.596857 −0.298429 0.954432i \(-0.596463\pi\)
−0.298429 + 0.954432i \(0.596463\pi\)
\(168\) 0 0
\(169\) 33.3070 2.56208
\(170\) 0 0
\(171\) 6.12411 0.468322
\(172\) 0 0
\(173\) −3.79746 −0.288716 −0.144358 0.989526i \(-0.546112\pi\)
−0.144358 + 0.989526i \(0.546112\pi\)
\(174\) 0 0
\(175\) 14.7151 1.11236
\(176\) 0 0
\(177\) 13.1942 0.991737
\(178\) 0 0
\(179\) 14.5568 1.08803 0.544014 0.839076i \(-0.316904\pi\)
0.544014 + 0.839076i \(0.316904\pi\)
\(180\) 0 0
\(181\) 20.0492 1.49025 0.745124 0.666927i \(-0.232391\pi\)
0.745124 + 0.666927i \(0.232391\pi\)
\(182\) 0 0
\(183\) −4.72241 −0.349090
\(184\) 0 0
\(185\) −4.93536 −0.362855
\(186\) 0 0
\(187\) −6.59352 −0.482166
\(188\) 0 0
\(189\) 3.07386 0.223590
\(190\) 0 0
\(191\) 18.1938 1.31646 0.658230 0.752817i \(-0.271305\pi\)
0.658230 + 0.752817i \(0.271305\pi\)
\(192\) 0 0
\(193\) −8.34471 −0.600665 −0.300333 0.953835i \(-0.597098\pi\)
−0.300333 + 0.953835i \(0.597098\pi\)
\(194\) 0 0
\(195\) 3.13923 0.224805
\(196\) 0 0
\(197\) 15.4128 1.09812 0.549059 0.835784i \(-0.314986\pi\)
0.549059 + 0.835784i \(0.314986\pi\)
\(198\) 0 0
\(199\) −21.3584 −1.51406 −0.757030 0.653380i \(-0.773350\pi\)
−0.757030 + 0.653380i \(0.773350\pi\)
\(200\) 0 0
\(201\) −8.57481 −0.604820
\(202\) 0 0
\(203\) −1.89322 −0.132878
\(204\) 0 0
\(205\) 4.81252 0.336121
\(206\) 0 0
\(207\) −8.36756 −0.581586
\(208\) 0 0
\(209\) −31.4204 −2.17340
\(210\) 0 0
\(211\) 9.36018 0.644382 0.322191 0.946675i \(-0.395581\pi\)
0.322191 + 0.946675i \(0.395581\pi\)
\(212\) 0 0
\(213\) 9.71053 0.665355
\(214\) 0 0
\(215\) 0.126475 0.00862553
\(216\) 0 0
\(217\) 11.3419 0.769936
\(218\) 0 0
\(219\) 12.1190 0.818926
\(220\) 0 0
\(221\) 8.74523 0.588268
\(222\) 0 0
\(223\) 21.8101 1.46051 0.730256 0.683174i \(-0.239401\pi\)
0.730256 + 0.683174i \(0.239401\pi\)
\(224\) 0 0
\(225\) −4.78719 −0.319146
\(226\) 0 0
\(227\) 20.8387 1.38311 0.691555 0.722323i \(-0.256926\pi\)
0.691555 + 0.722323i \(0.256926\pi\)
\(228\) 0 0
\(229\) −5.84901 −0.386513 −0.193257 0.981148i \(-0.561905\pi\)
−0.193257 + 0.981148i \(0.561905\pi\)
\(230\) 0 0
\(231\) −15.7708 −1.03764
\(232\) 0 0
\(233\) 22.7228 1.48862 0.744309 0.667835i \(-0.232779\pi\)
0.744309 + 0.667835i \(0.232779\pi\)
\(234\) 0 0
\(235\) −3.42100 −0.223162
\(236\) 0 0
\(237\) 10.4083 0.676092
\(238\) 0 0
\(239\) 2.60578 0.168554 0.0842768 0.996442i \(-0.473142\pi\)
0.0842768 + 0.996442i \(0.473142\pi\)
\(240\) 0 0
\(241\) −11.7532 −0.757090 −0.378545 0.925583i \(-0.623576\pi\)
−0.378545 + 0.925583i \(0.623576\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −1.12959 −0.0721669
\(246\) 0 0
\(247\) 41.6741 2.65166
\(248\) 0 0
\(249\) 0.536826 0.0340200
\(250\) 0 0
\(251\) 28.6050 1.80553 0.902764 0.430135i \(-0.141534\pi\)
0.902764 + 0.430135i \(0.141534\pi\)
\(252\) 0 0
\(253\) 42.9307 2.69903
\(254\) 0 0
\(255\) 0.592854 0.0371260
\(256\) 0 0
\(257\) −22.8951 −1.42816 −0.714079 0.700065i \(-0.753154\pi\)
−0.714079 + 0.700065i \(0.753154\pi\)
\(258\) 0 0
\(259\) −32.8854 −2.04340
\(260\) 0 0
\(261\) 0.615911 0.0381239
\(262\) 0 0
\(263\) 14.7911 0.912057 0.456029 0.889965i \(-0.349271\pi\)
0.456029 + 0.889965i \(0.349271\pi\)
\(264\) 0 0
\(265\) 2.79548 0.171725
\(266\) 0 0
\(267\) −13.8744 −0.849100
\(268\) 0 0
\(269\) 4.32434 0.263660 0.131830 0.991272i \(-0.457915\pi\)
0.131830 + 0.991272i \(0.457915\pi\)
\(270\) 0 0
\(271\) 7.47343 0.453979 0.226989 0.973897i \(-0.427112\pi\)
0.226989 + 0.973897i \(0.427112\pi\)
\(272\) 0 0
\(273\) 20.9174 1.26598
\(274\) 0 0
\(275\) 24.5612 1.48110
\(276\) 0 0
\(277\) −29.6405 −1.78093 −0.890463 0.455055i \(-0.849620\pi\)
−0.890463 + 0.455055i \(0.849620\pi\)
\(278\) 0 0
\(279\) −3.68978 −0.220901
\(280\) 0 0
\(281\) 10.1234 0.603913 0.301956 0.953322i \(-0.402360\pi\)
0.301956 + 0.953322i \(0.402360\pi\)
\(282\) 0 0
\(283\) −12.0125 −0.714071 −0.357036 0.934091i \(-0.616213\pi\)
−0.357036 + 0.934091i \(0.616213\pi\)
\(284\) 0 0
\(285\) 2.82516 0.167348
\(286\) 0 0
\(287\) 32.0669 1.89285
\(288\) 0 0
\(289\) −15.3484 −0.902849
\(290\) 0 0
\(291\) −13.4725 −0.789769
\(292\) 0 0
\(293\) 17.6680 1.03217 0.516087 0.856536i \(-0.327388\pi\)
0.516087 + 0.856536i \(0.327388\pi\)
\(294\) 0 0
\(295\) 6.08672 0.354382
\(296\) 0 0
\(297\) 5.13061 0.297708
\(298\) 0 0
\(299\) −56.9406 −3.29296
\(300\) 0 0
\(301\) 0.842731 0.0485742
\(302\) 0 0
\(303\) 3.25530 0.187012
\(304\) 0 0
\(305\) −2.17853 −0.124742
\(306\) 0 0
\(307\) −8.32687 −0.475240 −0.237620 0.971358i \(-0.576367\pi\)
−0.237620 + 0.971358i \(0.576367\pi\)
\(308\) 0 0
\(309\) −4.08644 −0.232469
\(310\) 0 0
\(311\) −4.53924 −0.257397 −0.128698 0.991684i \(-0.541080\pi\)
−0.128698 + 0.991684i \(0.541080\pi\)
\(312\) 0 0
\(313\) −6.70186 −0.378811 −0.189406 0.981899i \(-0.560656\pi\)
−0.189406 + 0.981899i \(0.560656\pi\)
\(314\) 0 0
\(315\) 1.41803 0.0798967
\(316\) 0 0
\(317\) −16.3726 −0.919574 −0.459787 0.888029i \(-0.652074\pi\)
−0.459787 + 0.888029i \(0.652074\pi\)
\(318\) 0 0
\(319\) −3.16000 −0.176926
\(320\) 0 0
\(321\) −12.2673 −0.684691
\(322\) 0 0
\(323\) 7.87029 0.437915
\(324\) 0 0
\(325\) −32.5764 −1.80702
\(326\) 0 0
\(327\) −1.40696 −0.0778050
\(328\) 0 0
\(329\) −22.7949 −1.25672
\(330\) 0 0
\(331\) −32.0668 −1.76255 −0.881276 0.472602i \(-0.843315\pi\)
−0.881276 + 0.472602i \(0.843315\pi\)
\(332\) 0 0
\(333\) 10.6984 0.586269
\(334\) 0 0
\(335\) −3.95571 −0.216123
\(336\) 0 0
\(337\) −7.75418 −0.422397 −0.211199 0.977443i \(-0.567737\pi\)
−0.211199 + 0.977443i \(0.567737\pi\)
\(338\) 0 0
\(339\) 4.51084 0.244995
\(340\) 0 0
\(341\) 18.9308 1.02516
\(342\) 0 0
\(343\) 13.9903 0.755406
\(344\) 0 0
\(345\) −3.86010 −0.207821
\(346\) 0 0
\(347\) 20.1726 1.08292 0.541461 0.840726i \(-0.317871\pi\)
0.541461 + 0.840726i \(0.317871\pi\)
\(348\) 0 0
\(349\) 17.7203 0.948548 0.474274 0.880377i \(-0.342711\pi\)
0.474274 + 0.880377i \(0.342711\pi\)
\(350\) 0 0
\(351\) −6.80493 −0.363220
\(352\) 0 0
\(353\) −19.7886 −1.05324 −0.526620 0.850101i \(-0.676541\pi\)
−0.526620 + 0.850101i \(0.676541\pi\)
\(354\) 0 0
\(355\) 4.47964 0.237754
\(356\) 0 0
\(357\) 3.95032 0.209073
\(358\) 0 0
\(359\) 32.4867 1.71458 0.857291 0.514833i \(-0.172146\pi\)
0.857291 + 0.514833i \(0.172146\pi\)
\(360\) 0 0
\(361\) 18.5047 0.973933
\(362\) 0 0
\(363\) −15.3232 −0.804259
\(364\) 0 0
\(365\) 5.59071 0.292631
\(366\) 0 0
\(367\) 2.28220 0.119130 0.0595649 0.998224i \(-0.481029\pi\)
0.0595649 + 0.998224i \(0.481029\pi\)
\(368\) 0 0
\(369\) −10.4321 −0.543075
\(370\) 0 0
\(371\) 18.6269 0.967061
\(372\) 0 0
\(373\) −6.60328 −0.341905 −0.170953 0.985279i \(-0.554684\pi\)
−0.170953 + 0.985279i \(0.554684\pi\)
\(374\) 0 0
\(375\) −4.51500 −0.233154
\(376\) 0 0
\(377\) 4.19123 0.215859
\(378\) 0 0
\(379\) 20.3031 1.04290 0.521451 0.853281i \(-0.325391\pi\)
0.521451 + 0.853281i \(0.325391\pi\)
\(380\) 0 0
\(381\) 6.67912 0.342181
\(382\) 0 0
\(383\) −38.9538 −1.99045 −0.995223 0.0976309i \(-0.968874\pi\)
−0.995223 + 0.0976309i \(0.968874\pi\)
\(384\) 0 0
\(385\) −7.27534 −0.370786
\(386\) 0 0
\(387\) −0.274161 −0.0139364
\(388\) 0 0
\(389\) 5.74843 0.291457 0.145729 0.989325i \(-0.453447\pi\)
0.145729 + 0.989325i \(0.453447\pi\)
\(390\) 0 0
\(391\) −10.7534 −0.543824
\(392\) 0 0
\(393\) −1.22326 −0.0617053
\(394\) 0 0
\(395\) 4.80153 0.241591
\(396\) 0 0
\(397\) 11.6885 0.586628 0.293314 0.956016i \(-0.405242\pi\)
0.293314 + 0.956016i \(0.405242\pi\)
\(398\) 0 0
\(399\) 18.8247 0.942412
\(400\) 0 0
\(401\) 17.2400 0.860925 0.430462 0.902609i \(-0.358351\pi\)
0.430462 + 0.902609i \(0.358351\pi\)
\(402\) 0 0
\(403\) −25.1087 −1.25075
\(404\) 0 0
\(405\) −0.461317 −0.0229230
\(406\) 0 0
\(407\) −54.8894 −2.72077
\(408\) 0 0
\(409\) 14.3836 0.711225 0.355613 0.934633i \(-0.384272\pi\)
0.355613 + 0.934633i \(0.384272\pi\)
\(410\) 0 0
\(411\) −13.0509 −0.643755
\(412\) 0 0
\(413\) 40.5572 1.99569
\(414\) 0 0
\(415\) 0.247647 0.0121565
\(416\) 0 0
\(417\) −11.6783 −0.571891
\(418\) 0 0
\(419\) −29.3061 −1.43170 −0.715848 0.698256i \(-0.753960\pi\)
−0.715848 + 0.698256i \(0.753960\pi\)
\(420\) 0 0
\(421\) 15.8552 0.772734 0.386367 0.922345i \(-0.373730\pi\)
0.386367 + 0.922345i \(0.373730\pi\)
\(422\) 0 0
\(423\) 7.41573 0.360565
\(424\) 0 0
\(425\) −6.15217 −0.298424
\(426\) 0 0
\(427\) −14.5160 −0.702480
\(428\) 0 0
\(429\) 34.9134 1.68564
\(430\) 0 0
\(431\) −15.7460 −0.758459 −0.379230 0.925303i \(-0.623811\pi\)
−0.379230 + 0.925303i \(0.623811\pi\)
\(432\) 0 0
\(433\) −21.5465 −1.03546 −0.517730 0.855544i \(-0.673223\pi\)
−0.517730 + 0.855544i \(0.673223\pi\)
\(434\) 0 0
\(435\) 0.284130 0.0136230
\(436\) 0 0
\(437\) −51.2439 −2.45133
\(438\) 0 0
\(439\) 13.7705 0.657228 0.328614 0.944464i \(-0.393418\pi\)
0.328614 + 0.944464i \(0.393418\pi\)
\(440\) 0 0
\(441\) 2.44862 0.116601
\(442\) 0 0
\(443\) −31.1748 −1.48116 −0.740580 0.671968i \(-0.765449\pi\)
−0.740580 + 0.671968i \(0.765449\pi\)
\(444\) 0 0
\(445\) −6.40051 −0.303413
\(446\) 0 0
\(447\) −9.05393 −0.428236
\(448\) 0 0
\(449\) −19.9758 −0.942716 −0.471358 0.881942i \(-0.656236\pi\)
−0.471358 + 0.881942i \(0.656236\pi\)
\(450\) 0 0
\(451\) 53.5232 2.52031
\(452\) 0 0
\(453\) 7.35196 0.345425
\(454\) 0 0
\(455\) 9.64956 0.452378
\(456\) 0 0
\(457\) 27.5948 1.29083 0.645415 0.763832i \(-0.276684\pi\)
0.645415 + 0.763832i \(0.276684\pi\)
\(458\) 0 0
\(459\) −1.28513 −0.0599849
\(460\) 0 0
\(461\) 30.2912 1.41080 0.705400 0.708809i \(-0.250767\pi\)
0.705400 + 0.708809i \(0.250767\pi\)
\(462\) 0 0
\(463\) 31.1019 1.44543 0.722714 0.691147i \(-0.242894\pi\)
0.722714 + 0.691147i \(0.242894\pi\)
\(464\) 0 0
\(465\) −1.70216 −0.0789357
\(466\) 0 0
\(467\) −16.6015 −0.768225 −0.384113 0.923286i \(-0.625493\pi\)
−0.384113 + 0.923286i \(0.625493\pi\)
\(468\) 0 0
\(469\) −26.3578 −1.21709
\(470\) 0 0
\(471\) 9.62422 0.443461
\(472\) 0 0
\(473\) 1.40661 0.0646761
\(474\) 0 0
\(475\) −29.3173 −1.34517
\(476\) 0 0
\(477\) −6.05978 −0.277458
\(478\) 0 0
\(479\) 42.2558 1.93072 0.965358 0.260929i \(-0.0840288\pi\)
0.965358 + 0.260929i \(0.0840288\pi\)
\(480\) 0 0
\(481\) 72.8018 3.31948
\(482\) 0 0
\(483\) −25.7207 −1.17033
\(484\) 0 0
\(485\) −6.21508 −0.282212
\(486\) 0 0
\(487\) 32.0611 1.45283 0.726414 0.687258i \(-0.241186\pi\)
0.726414 + 0.687258i \(0.241186\pi\)
\(488\) 0 0
\(489\) −23.6560 −1.06976
\(490\) 0 0
\(491\) 19.2699 0.869638 0.434819 0.900518i \(-0.356812\pi\)
0.434819 + 0.900518i \(0.356812\pi\)
\(492\) 0 0
\(493\) 0.791527 0.0356486
\(494\) 0 0
\(495\) 2.36684 0.106382
\(496\) 0 0
\(497\) 29.8488 1.33890
\(498\) 0 0
\(499\) 22.8034 1.02082 0.510410 0.859931i \(-0.329494\pi\)
0.510410 + 0.859931i \(0.329494\pi\)
\(500\) 0 0
\(501\) 7.71310 0.344596
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 1.50173 0.0668260
\(506\) 0 0
\(507\) −33.3070 −1.47922
\(508\) 0 0
\(509\) 11.0516 0.489855 0.244927 0.969541i \(-0.421236\pi\)
0.244927 + 0.969541i \(0.421236\pi\)
\(510\) 0 0
\(511\) 37.2521 1.64794
\(512\) 0 0
\(513\) −6.12411 −0.270386
\(514\) 0 0
\(515\) −1.88515 −0.0830695
\(516\) 0 0
\(517\) −38.0472 −1.67332
\(518\) 0 0
\(519\) 3.79746 0.166690
\(520\) 0 0
\(521\) 13.3139 0.583294 0.291647 0.956526i \(-0.405797\pi\)
0.291647 + 0.956526i \(0.405797\pi\)
\(522\) 0 0
\(523\) 15.6565 0.684612 0.342306 0.939589i \(-0.388792\pi\)
0.342306 + 0.939589i \(0.388792\pi\)
\(524\) 0 0
\(525\) −14.7151 −0.642222
\(526\) 0 0
\(527\) −4.74185 −0.206558
\(528\) 0 0
\(529\) 47.0161 2.04418
\(530\) 0 0
\(531\) −13.1942 −0.572580
\(532\) 0 0
\(533\) −70.9898 −3.07491
\(534\) 0 0
\(535\) −5.65910 −0.244664
\(536\) 0 0
\(537\) −14.5568 −0.628173
\(538\) 0 0
\(539\) −12.5629 −0.541124
\(540\) 0 0
\(541\) 14.3601 0.617389 0.308695 0.951161i \(-0.400108\pi\)
0.308695 + 0.951161i \(0.400108\pi\)
\(542\) 0 0
\(543\) −20.0492 −0.860395
\(544\) 0 0
\(545\) −0.649054 −0.0278024
\(546\) 0 0
\(547\) 40.6563 1.73834 0.869168 0.494517i \(-0.164655\pi\)
0.869168 + 0.494517i \(0.164655\pi\)
\(548\) 0 0
\(549\) 4.72241 0.201547
\(550\) 0 0
\(551\) 3.77191 0.160689
\(552\) 0 0
\(553\) 31.9937 1.36051
\(554\) 0 0
\(555\) 4.93536 0.209494
\(556\) 0 0
\(557\) −7.61895 −0.322825 −0.161413 0.986887i \(-0.551605\pi\)
−0.161413 + 0.986887i \(0.551605\pi\)
\(558\) 0 0
\(559\) −1.86564 −0.0789083
\(560\) 0 0
\(561\) 6.59352 0.278379
\(562\) 0 0
\(563\) 23.7344 1.00029 0.500143 0.865943i \(-0.333281\pi\)
0.500143 + 0.865943i \(0.333281\pi\)
\(564\) 0 0
\(565\) 2.08093 0.0875453
\(566\) 0 0
\(567\) −3.07386 −0.129090
\(568\) 0 0
\(569\) 22.8041 0.955998 0.477999 0.878360i \(-0.341362\pi\)
0.477999 + 0.878360i \(0.341362\pi\)
\(570\) 0 0
\(571\) 40.9778 1.71487 0.857433 0.514596i \(-0.172058\pi\)
0.857433 + 0.514596i \(0.172058\pi\)
\(572\) 0 0
\(573\) −18.1938 −0.760059
\(574\) 0 0
\(575\) 40.0571 1.67050
\(576\) 0 0
\(577\) 18.5156 0.770814 0.385407 0.922747i \(-0.374061\pi\)
0.385407 + 0.922747i \(0.374061\pi\)
\(578\) 0 0
\(579\) 8.34471 0.346794
\(580\) 0 0
\(581\) 1.65013 0.0684589
\(582\) 0 0
\(583\) 31.0904 1.28763
\(584\) 0 0
\(585\) −3.13923 −0.129791
\(586\) 0 0
\(587\) −25.1993 −1.04009 −0.520044 0.854139i \(-0.674084\pi\)
−0.520044 + 0.854139i \(0.674084\pi\)
\(588\) 0 0
\(589\) −22.5966 −0.931077
\(590\) 0 0
\(591\) −15.4128 −0.633999
\(592\) 0 0
\(593\) −29.4690 −1.21015 −0.605073 0.796170i \(-0.706856\pi\)
−0.605073 + 0.796170i \(0.706856\pi\)
\(594\) 0 0
\(595\) 1.82235 0.0747091
\(596\) 0 0
\(597\) 21.3584 0.874143
\(598\) 0 0
\(599\) −41.9027 −1.71210 −0.856050 0.516893i \(-0.827088\pi\)
−0.856050 + 0.516893i \(0.827088\pi\)
\(600\) 0 0
\(601\) −47.5334 −1.93893 −0.969465 0.245231i \(-0.921136\pi\)
−0.969465 + 0.245231i \(0.921136\pi\)
\(602\) 0 0
\(603\) 8.57481 0.349193
\(604\) 0 0
\(605\) −7.06886 −0.287390
\(606\) 0 0
\(607\) −3.30800 −0.134267 −0.0671337 0.997744i \(-0.521385\pi\)
−0.0671337 + 0.997744i \(0.521385\pi\)
\(608\) 0 0
\(609\) 1.89322 0.0767173
\(610\) 0 0
\(611\) 50.4635 2.04153
\(612\) 0 0
\(613\) −36.1428 −1.45979 −0.729897 0.683557i \(-0.760432\pi\)
−0.729897 + 0.683557i \(0.760432\pi\)
\(614\) 0 0
\(615\) −4.81252 −0.194060
\(616\) 0 0
\(617\) 1.12404 0.0452520 0.0226260 0.999744i \(-0.492797\pi\)
0.0226260 + 0.999744i \(0.492797\pi\)
\(618\) 0 0
\(619\) 11.5300 0.463429 0.231714 0.972784i \(-0.425567\pi\)
0.231714 + 0.972784i \(0.425567\pi\)
\(620\) 0 0
\(621\) 8.36756 0.335779
\(622\) 0 0
\(623\) −42.6480 −1.70866
\(624\) 0 0
\(625\) 21.8531 0.874123
\(626\) 0 0
\(627\) 31.4204 1.25481
\(628\) 0 0
\(629\) 13.7489 0.548203
\(630\) 0 0
\(631\) 13.5715 0.540274 0.270137 0.962822i \(-0.412931\pi\)
0.270137 + 0.962822i \(0.412931\pi\)
\(632\) 0 0
\(633\) −9.36018 −0.372034
\(634\) 0 0
\(635\) 3.08119 0.122273
\(636\) 0 0
\(637\) 16.6627 0.660200
\(638\) 0 0
\(639\) −9.71053 −0.384143
\(640\) 0 0
\(641\) 41.9101 1.65535 0.827675 0.561207i \(-0.189663\pi\)
0.827675 + 0.561207i \(0.189663\pi\)
\(642\) 0 0
\(643\) −30.6894 −1.21027 −0.605135 0.796123i \(-0.706881\pi\)
−0.605135 + 0.796123i \(0.706881\pi\)
\(644\) 0 0
\(645\) −0.126475 −0.00497995
\(646\) 0 0
\(647\) 29.5672 1.16241 0.581204 0.813758i \(-0.302582\pi\)
0.581204 + 0.813758i \(0.302582\pi\)
\(648\) 0 0
\(649\) 67.6944 2.65724
\(650\) 0 0
\(651\) −11.3419 −0.444523
\(652\) 0 0
\(653\) −0.892383 −0.0349217 −0.0174608 0.999848i \(-0.505558\pi\)
−0.0174608 + 0.999848i \(0.505558\pi\)
\(654\) 0 0
\(655\) −0.564311 −0.0220494
\(656\) 0 0
\(657\) −12.1190 −0.472807
\(658\) 0 0
\(659\) 2.10258 0.0819048 0.0409524 0.999161i \(-0.486961\pi\)
0.0409524 + 0.999161i \(0.486961\pi\)
\(660\) 0 0
\(661\) 4.25531 0.165512 0.0827562 0.996570i \(-0.473628\pi\)
0.0827562 + 0.996570i \(0.473628\pi\)
\(662\) 0 0
\(663\) −8.74523 −0.339637
\(664\) 0 0
\(665\) 8.68414 0.336757
\(666\) 0 0
\(667\) −5.15367 −0.199551
\(668\) 0 0
\(669\) −21.8101 −0.843227
\(670\) 0 0
\(671\) −24.2288 −0.935344
\(672\) 0 0
\(673\) −43.1845 −1.66464 −0.832320 0.554296i \(-0.812988\pi\)
−0.832320 + 0.554296i \(0.812988\pi\)
\(674\) 0 0
\(675\) 4.78719 0.184259
\(676\) 0 0
\(677\) 30.3438 1.16621 0.583103 0.812398i \(-0.301839\pi\)
0.583103 + 0.812398i \(0.301839\pi\)
\(678\) 0 0
\(679\) −41.4125 −1.58926
\(680\) 0 0
\(681\) −20.8387 −0.798539
\(682\) 0 0
\(683\) −14.0190 −0.536424 −0.268212 0.963360i \(-0.586433\pi\)
−0.268212 + 0.963360i \(0.586433\pi\)
\(684\) 0 0
\(685\) −6.02062 −0.230036
\(686\) 0 0
\(687\) 5.84901 0.223154
\(688\) 0 0
\(689\) −41.2363 −1.57098
\(690\) 0 0
\(691\) −11.4584 −0.435900 −0.217950 0.975960i \(-0.569937\pi\)
−0.217950 + 0.975960i \(0.569937\pi\)
\(692\) 0 0
\(693\) 15.7708 0.599083
\(694\) 0 0
\(695\) −5.38742 −0.204357
\(696\) 0 0
\(697\) −13.4067 −0.507814
\(698\) 0 0
\(699\) −22.7228 −0.859454
\(700\) 0 0
\(701\) −38.3826 −1.44969 −0.724845 0.688912i \(-0.758089\pi\)
−0.724845 + 0.688912i \(0.758089\pi\)
\(702\) 0 0
\(703\) 65.5182 2.47107
\(704\) 0 0
\(705\) 3.42100 0.128842
\(706\) 0 0
\(707\) 10.0063 0.376327
\(708\) 0 0
\(709\) −51.6664 −1.94037 −0.970186 0.242364i \(-0.922077\pi\)
−0.970186 + 0.242364i \(0.922077\pi\)
\(710\) 0 0
\(711\) −10.4083 −0.390342
\(712\) 0 0
\(713\) 30.8744 1.15626
\(714\) 0 0
\(715\) 16.1062 0.602337
\(716\) 0 0
\(717\) −2.60578 −0.0973145
\(718\) 0 0
\(719\) 20.7992 0.775681 0.387840 0.921727i \(-0.373221\pi\)
0.387840 + 0.921727i \(0.373221\pi\)
\(720\) 0 0
\(721\) −12.5612 −0.467802
\(722\) 0 0
\(723\) 11.7532 0.437106
\(724\) 0 0
\(725\) −2.94848 −0.109504
\(726\) 0 0
\(727\) 21.4030 0.793792 0.396896 0.917864i \(-0.370087\pi\)
0.396896 + 0.917864i \(0.370087\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −0.352333 −0.0130315
\(732\) 0 0
\(733\) −27.7510 −1.02501 −0.512504 0.858685i \(-0.671282\pi\)
−0.512504 + 0.858685i \(0.671282\pi\)
\(734\) 0 0
\(735\) 1.12959 0.0416656
\(736\) 0 0
\(737\) −43.9940 −1.62054
\(738\) 0 0
\(739\) 30.3211 1.11538 0.557690 0.830050i \(-0.311688\pi\)
0.557690 + 0.830050i \(0.311688\pi\)
\(740\) 0 0
\(741\) −41.6741 −1.53094
\(742\) 0 0
\(743\) −49.5720 −1.81862 −0.909311 0.416117i \(-0.863391\pi\)
−0.909311 + 0.416117i \(0.863391\pi\)
\(744\) 0 0
\(745\) −4.17673 −0.153024
\(746\) 0 0
\(747\) −0.536826 −0.0196415
\(748\) 0 0
\(749\) −37.7078 −1.37781
\(750\) 0 0
\(751\) −23.1097 −0.843286 −0.421643 0.906762i \(-0.638546\pi\)
−0.421643 + 0.906762i \(0.638546\pi\)
\(752\) 0 0
\(753\) −28.6050 −1.04242
\(754\) 0 0
\(755\) 3.39159 0.123432
\(756\) 0 0
\(757\) 43.6602 1.58686 0.793429 0.608663i \(-0.208294\pi\)
0.793429 + 0.608663i \(0.208294\pi\)
\(758\) 0 0
\(759\) −42.9307 −1.55829
\(760\) 0 0
\(761\) −26.2561 −0.951784 −0.475892 0.879504i \(-0.657875\pi\)
−0.475892 + 0.879504i \(0.657875\pi\)
\(762\) 0 0
\(763\) −4.32479 −0.156568
\(764\) 0 0
\(765\) −0.592854 −0.0214347
\(766\) 0 0
\(767\) −89.7856 −3.24197
\(768\) 0 0
\(769\) 29.2830 1.05597 0.527986 0.849253i \(-0.322947\pi\)
0.527986 + 0.849253i \(0.322947\pi\)
\(770\) 0 0
\(771\) 22.8951 0.824548
\(772\) 0 0
\(773\) 29.6109 1.06503 0.532515 0.846420i \(-0.321247\pi\)
0.532515 + 0.846420i \(0.321247\pi\)
\(774\) 0 0
\(775\) 17.6637 0.634497
\(776\) 0 0
\(777\) 32.8854 1.17976
\(778\) 0 0
\(779\) −63.8875 −2.28901
\(780\) 0 0
\(781\) 49.8210 1.78274
\(782\) 0 0
\(783\) −0.615911 −0.0220109
\(784\) 0 0
\(785\) 4.43982 0.158464
\(786\) 0 0
\(787\) −39.4862 −1.40753 −0.703766 0.710432i \(-0.748499\pi\)
−0.703766 + 0.710432i \(0.748499\pi\)
\(788\) 0 0
\(789\) −14.7911 −0.526577
\(790\) 0 0
\(791\) 13.8657 0.493007
\(792\) 0 0
\(793\) 32.1356 1.14117
\(794\) 0 0
\(795\) −2.79548 −0.0991454
\(796\) 0 0
\(797\) 22.1648 0.785118 0.392559 0.919727i \(-0.371590\pi\)
0.392559 + 0.919727i \(0.371590\pi\)
\(798\) 0 0
\(799\) 9.53019 0.337154
\(800\) 0 0
\(801\) 13.8744 0.490228
\(802\) 0 0
\(803\) 62.1779 2.19421
\(804\) 0 0
\(805\) −11.8654 −0.418201
\(806\) 0 0
\(807\) −4.32434 −0.152224
\(808\) 0 0
\(809\) −33.2730 −1.16982 −0.584908 0.811099i \(-0.698870\pi\)
−0.584908 + 0.811099i \(0.698870\pi\)
\(810\) 0 0
\(811\) 0.556963 0.0195576 0.00977881 0.999952i \(-0.496887\pi\)
0.00977881 + 0.999952i \(0.496887\pi\)
\(812\) 0 0
\(813\) −7.47343 −0.262105
\(814\) 0 0
\(815\) −10.9129 −0.382263
\(816\) 0 0
\(817\) −1.67899 −0.0587404
\(818\) 0 0
\(819\) −20.9174 −0.730913
\(820\) 0 0
\(821\) 4.00401 0.139741 0.0698704 0.997556i \(-0.477741\pi\)
0.0698704 + 0.997556i \(0.477741\pi\)
\(822\) 0 0
\(823\) 12.5663 0.438033 0.219016 0.975721i \(-0.429715\pi\)
0.219016 + 0.975721i \(0.429715\pi\)
\(824\) 0 0
\(825\) −24.5612 −0.855111
\(826\) 0 0
\(827\) −33.9485 −1.18051 −0.590253 0.807218i \(-0.700972\pi\)
−0.590253 + 0.807218i \(0.700972\pi\)
\(828\) 0 0
\(829\) 19.7090 0.684521 0.342261 0.939605i \(-0.388807\pi\)
0.342261 + 0.939605i \(0.388807\pi\)
\(830\) 0 0
\(831\) 29.6405 1.02822
\(832\) 0 0
\(833\) 3.14680 0.109030
\(834\) 0 0
\(835\) 3.55819 0.123136
\(836\) 0 0
\(837\) 3.68978 0.127537
\(838\) 0 0
\(839\) 9.95135 0.343559 0.171779 0.985135i \(-0.445048\pi\)
0.171779 + 0.985135i \(0.445048\pi\)
\(840\) 0 0
\(841\) −28.6207 −0.986919
\(842\) 0 0
\(843\) −10.1234 −0.348669
\(844\) 0 0
\(845\) −15.3651 −0.528576
\(846\) 0 0
\(847\) −47.1014 −1.61842
\(848\) 0 0
\(849\) 12.0125 0.412269
\(850\) 0 0
\(851\) −89.5195 −3.06869
\(852\) 0 0
\(853\) 49.4240 1.69224 0.846122 0.532988i \(-0.178931\pi\)
0.846122 + 0.532988i \(0.178931\pi\)
\(854\) 0 0
\(855\) −2.82516 −0.0966184
\(856\) 0 0
\(857\) 28.5986 0.976909 0.488455 0.872589i \(-0.337561\pi\)
0.488455 + 0.872589i \(0.337561\pi\)
\(858\) 0 0
\(859\) −3.16739 −0.108070 −0.0540349 0.998539i \(-0.517208\pi\)
−0.0540349 + 0.998539i \(0.517208\pi\)
\(860\) 0 0
\(861\) −32.0669 −1.09284
\(862\) 0 0
\(863\) −27.5485 −0.937762 −0.468881 0.883261i \(-0.655343\pi\)
−0.468881 + 0.883261i \(0.655343\pi\)
\(864\) 0 0
\(865\) 1.75184 0.0595642
\(866\) 0 0
\(867\) 15.3484 0.521260
\(868\) 0 0
\(869\) 53.4010 1.81150
\(870\) 0 0
\(871\) 58.3509 1.97715
\(872\) 0 0
\(873\) 13.4725 0.455974
\(874\) 0 0
\(875\) −13.8785 −0.469178
\(876\) 0 0
\(877\) 18.9871 0.641149 0.320574 0.947223i \(-0.396124\pi\)
0.320574 + 0.947223i \(0.396124\pi\)
\(878\) 0 0
\(879\) −17.6680 −0.595926
\(880\) 0 0
\(881\) −3.69188 −0.124383 −0.0621913 0.998064i \(-0.519809\pi\)
−0.0621913 + 0.998064i \(0.519809\pi\)
\(882\) 0 0
\(883\) 47.4959 1.59837 0.799183 0.601088i \(-0.205266\pi\)
0.799183 + 0.601088i \(0.205266\pi\)
\(884\) 0 0
\(885\) −6.08672 −0.204603
\(886\) 0 0
\(887\) 29.9946 1.00712 0.503560 0.863960i \(-0.332023\pi\)
0.503560 + 0.863960i \(0.332023\pi\)
\(888\) 0 0
\(889\) 20.5307 0.688577
\(890\) 0 0
\(891\) −5.13061 −0.171882
\(892\) 0 0
\(893\) 45.4147 1.51975
\(894\) 0 0
\(895\) −6.71531 −0.224468
\(896\) 0 0
\(897\) 56.9406 1.90119
\(898\) 0 0
\(899\) −2.27257 −0.0757946
\(900\) 0 0
\(901\) −7.78762 −0.259443
\(902\) 0 0
\(903\) −0.842731 −0.0280443
\(904\) 0 0
\(905\) −9.24905 −0.307449
\(906\) 0 0
\(907\) −51.3261 −1.70425 −0.852127 0.523335i \(-0.824688\pi\)
−0.852127 + 0.523335i \(0.824688\pi\)
\(908\) 0 0
\(909\) −3.25530 −0.107972
\(910\) 0 0
\(911\) 18.1307 0.600697 0.300349 0.953830i \(-0.402897\pi\)
0.300349 + 0.953830i \(0.402897\pi\)
\(912\) 0 0
\(913\) 2.75425 0.0911523
\(914\) 0 0
\(915\) 2.17853 0.0720199
\(916\) 0 0
\(917\) −3.76013 −0.124170
\(918\) 0 0
\(919\) 45.7329 1.50859 0.754294 0.656537i \(-0.227979\pi\)
0.754294 + 0.656537i \(0.227979\pi\)
\(920\) 0 0
\(921\) 8.32687 0.274380
\(922\) 0 0
\(923\) −66.0795 −2.17503
\(924\) 0 0
\(925\) −51.2152 −1.68395
\(926\) 0 0
\(927\) 4.08644 0.134216
\(928\) 0 0
\(929\) 41.4296 1.35926 0.679630 0.733555i \(-0.262140\pi\)
0.679630 + 0.733555i \(0.262140\pi\)
\(930\) 0 0
\(931\) 14.9956 0.491462
\(932\) 0 0
\(933\) 4.53924 0.148608
\(934\) 0 0
\(935\) 3.04170 0.0994744
\(936\) 0 0
\(937\) −22.9436 −0.749534 −0.374767 0.927119i \(-0.622277\pi\)
−0.374767 + 0.927119i \(0.622277\pi\)
\(938\) 0 0
\(939\) 6.70186 0.218707
\(940\) 0 0
\(941\) −11.0310 −0.359602 −0.179801 0.983703i \(-0.557545\pi\)
−0.179801 + 0.983703i \(0.557545\pi\)
\(942\) 0 0
\(943\) 87.2915 2.84260
\(944\) 0 0
\(945\) −1.41803 −0.0461284
\(946\) 0 0
\(947\) 0.911573 0.0296221 0.0148111 0.999890i \(-0.495285\pi\)
0.0148111 + 0.999890i \(0.495285\pi\)
\(948\) 0 0
\(949\) −82.4689 −2.67705
\(950\) 0 0
\(951\) 16.3726 0.530916
\(952\) 0 0
\(953\) 12.2543 0.396955 0.198478 0.980105i \(-0.436400\pi\)
0.198478 + 0.980105i \(0.436400\pi\)
\(954\) 0 0
\(955\) −8.39313 −0.271595
\(956\) 0 0
\(957\) 3.16000 0.102148
\(958\) 0 0
\(959\) −40.1168 −1.29544
\(960\) 0 0
\(961\) −17.3855 −0.560824
\(962\) 0 0
\(963\) 12.2673 0.395307
\(964\) 0 0
\(965\) 3.84956 0.123922
\(966\) 0 0
\(967\) −5.11612 −0.164523 −0.0822617 0.996611i \(-0.526214\pi\)
−0.0822617 + 0.996611i \(0.526214\pi\)
\(968\) 0 0
\(969\) −7.87029 −0.252830
\(970\) 0 0
\(971\) −24.0116 −0.770567 −0.385284 0.922798i \(-0.625896\pi\)
−0.385284 + 0.922798i \(0.625896\pi\)
\(972\) 0 0
\(973\) −35.8976 −1.15082
\(974\) 0 0
\(975\) 32.5764 1.04328
\(976\) 0 0
\(977\) 15.4229 0.493422 0.246711 0.969089i \(-0.420650\pi\)
0.246711 + 0.969089i \(0.420650\pi\)
\(978\) 0 0
\(979\) −71.1842 −2.27506
\(980\) 0 0
\(981\) 1.40696 0.0449207
\(982\) 0 0
\(983\) −25.9914 −0.828998 −0.414499 0.910050i \(-0.636043\pi\)
−0.414499 + 0.910050i \(0.636043\pi\)
\(984\) 0 0
\(985\) −7.11020 −0.226550
\(986\) 0 0
\(987\) 22.7949 0.725570
\(988\) 0 0
\(989\) 2.29406 0.0729467
\(990\) 0 0
\(991\) 55.7510 1.77099 0.885495 0.464650i \(-0.153820\pi\)
0.885495 + 0.464650i \(0.153820\pi\)
\(992\) 0 0
\(993\) 32.0668 1.01761
\(994\) 0 0
\(995\) 9.85302 0.312362
\(996\) 0 0
\(997\) 20.9362 0.663057 0.331528 0.943445i \(-0.392436\pi\)
0.331528 + 0.943445i \(0.392436\pi\)
\(998\) 0 0
\(999\) −10.6984 −0.338482
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 \(a_p\))