Properties

Label 4010.2.a.e.1.1
Level 4010
Weight 2
Character 4010.1
Self dual Yes
Analytic conductor 32.020
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0200112105\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\)
Character \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +3.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +3.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +1.00000 q^{10} -3.00000 q^{11} -1.00000 q^{12} +4.00000 q^{13} +3.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -7.00000 q^{17} -2.00000 q^{18} +1.00000 q^{20} -3.00000 q^{21} -3.00000 q^{22} -6.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} +4.00000 q^{26} +5.00000 q^{27} +3.00000 q^{28} +10.0000 q^{29} -1.00000 q^{30} +7.00000 q^{31} +1.00000 q^{32} +3.00000 q^{33} -7.00000 q^{34} +3.00000 q^{35} -2.00000 q^{36} +8.00000 q^{37} -4.00000 q^{39} +1.00000 q^{40} +2.00000 q^{41} -3.00000 q^{42} +4.00000 q^{43} -3.00000 q^{44} -2.00000 q^{45} -6.00000 q^{46} +8.00000 q^{47} -1.00000 q^{48} +2.00000 q^{49} +1.00000 q^{50} +7.00000 q^{51} +4.00000 q^{52} +14.0000 q^{53} +5.00000 q^{54} -3.00000 q^{55} +3.00000 q^{56} +10.0000 q^{58} -10.0000 q^{59} -1.00000 q^{60} +2.00000 q^{61} +7.00000 q^{62} -6.00000 q^{63} +1.00000 q^{64} +4.00000 q^{65} +3.00000 q^{66} +3.00000 q^{67} -7.00000 q^{68} +6.00000 q^{69} +3.00000 q^{70} -3.00000 q^{71} -2.00000 q^{72} -6.00000 q^{73} +8.00000 q^{74} -1.00000 q^{75} -9.00000 q^{77} -4.00000 q^{78} +1.00000 q^{80} +1.00000 q^{81} +2.00000 q^{82} +14.0000 q^{83} -3.00000 q^{84} -7.00000 q^{85} +4.00000 q^{86} -10.0000 q^{87} -3.00000 q^{88} -10.0000 q^{89} -2.00000 q^{90} +12.0000 q^{91} -6.00000 q^{92} -7.00000 q^{93} +8.00000 q^{94} -1.00000 q^{96} +3.00000 q^{97} +2.00000 q^{98} +6.00000 q^{99} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.00000 −0.577350 −0.288675 0.957427i \(-0.593215\pi\)
−0.288675 + 0.957427i \(0.593215\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −1.00000 −0.408248
\(7\) 3.00000 1.13389 0.566947 0.823754i \(-0.308125\pi\)
0.566947 + 0.823754i \(0.308125\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.00000 −0.666667
\(10\) 1.00000 0.316228
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) −1.00000 −0.288675
\(13\) 4.00000 1.10940 0.554700 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 3.00000 0.801784
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) −7.00000 −1.69775 −0.848875 0.528594i \(-0.822719\pi\)
−0.848875 + 0.528594i \(0.822719\pi\)
\(18\) −2.00000 −0.471405
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 1.00000 0.223607
\(21\) −3.00000 −0.654654
\(22\) −3.00000 −0.639602
\(23\) −6.00000 −1.25109 −0.625543 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) −1.00000 −0.204124
\(25\) 1.00000 0.200000
\(26\) 4.00000 0.784465
\(27\) 5.00000 0.962250
\(28\) 3.00000 0.566947
\(29\) 10.0000 1.85695 0.928477 0.371391i \(-0.121119\pi\)
0.928477 + 0.371391i \(0.121119\pi\)
\(30\) −1.00000 −0.182574
\(31\) 7.00000 1.25724 0.628619 0.777714i \(-0.283621\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) 1.00000 0.176777
\(33\) 3.00000 0.522233
\(34\) −7.00000 −1.20049
\(35\) 3.00000 0.507093
\(36\) −2.00000 −0.333333
\(37\) 8.00000 1.31519 0.657596 0.753371i \(-0.271573\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) 0 0
\(39\) −4.00000 −0.640513
\(40\) 1.00000 0.158114
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) −3.00000 −0.462910
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) −3.00000 −0.452267
\(45\) −2.00000 −0.298142
\(46\) −6.00000 −0.884652
\(47\) 8.00000 1.16692 0.583460 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) −1.00000 −0.144338
\(49\) 2.00000 0.285714
\(50\) 1.00000 0.141421
\(51\) 7.00000 0.980196
\(52\) 4.00000 0.554700
\(53\) 14.0000 1.92305 0.961524 0.274721i \(-0.0885855\pi\)
0.961524 + 0.274721i \(0.0885855\pi\)
\(54\) 5.00000 0.680414
\(55\) −3.00000 −0.404520
\(56\) 3.00000 0.400892
\(57\) 0 0
\(58\) 10.0000 1.31306
\(59\) −10.0000 −1.30189 −0.650945 0.759125i \(-0.725627\pi\)
−0.650945 + 0.759125i \(0.725627\pi\)
\(60\) −1.00000 −0.129099
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 7.00000 0.889001
\(63\) −6.00000 −0.755929
\(64\) 1.00000 0.125000
\(65\) 4.00000 0.496139
\(66\) 3.00000 0.369274
\(67\) 3.00000 0.366508 0.183254 0.983066i \(-0.441337\pi\)
0.183254 + 0.983066i \(0.441337\pi\)
\(68\) −7.00000 −0.848875
\(69\) 6.00000 0.722315
\(70\) 3.00000 0.358569
\(71\) −3.00000 −0.356034 −0.178017 0.984027i \(-0.556968\pi\)
−0.178017 + 0.984027i \(0.556968\pi\)
\(72\) −2.00000 −0.235702
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) 8.00000 0.929981
\(75\) −1.00000 −0.115470
\(76\) 0 0
\(77\) −9.00000 −1.02565
\(78\) −4.00000 −0.452911
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) 2.00000 0.220863
\(83\) 14.0000 1.53670 0.768350 0.640030i \(-0.221078\pi\)
0.768350 + 0.640030i \(0.221078\pi\)
\(84\) −3.00000 −0.327327
\(85\) −7.00000 −0.759257
\(86\) 4.00000 0.431331
\(87\) −10.0000 −1.07211
\(88\) −3.00000 −0.319801
\(89\) −10.0000 −1.06000 −0.529999 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) −2.00000 −0.210819
\(91\) 12.0000 1.25794
\(92\) −6.00000 −0.625543
\(93\) −7.00000 −0.725866
\(94\) 8.00000 0.825137
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) 3.00000 0.304604 0.152302 0.988334i \(-0.451331\pi\)
0.152302 + 0.988334i \(0.451331\pi\)
\(98\) 2.00000 0.202031
\(99\) 6.00000 0.603023
\(100\) 1.00000 0.100000
\(101\) 2.00000 0.199007 0.0995037 0.995037i \(-0.468274\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) 7.00000 0.693103
\(103\) 9.00000 0.886796 0.443398 0.896325i \(-0.353773\pi\)
0.443398 + 0.896325i \(0.353773\pi\)
\(104\) 4.00000 0.392232
\(105\) −3.00000 −0.292770
\(106\) 14.0000 1.35980
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 5.00000 0.481125
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) −3.00000 −0.286039
\(111\) −8.00000 −0.759326
\(112\) 3.00000 0.283473
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) −6.00000 −0.559503
\(116\) 10.0000 0.928477
\(117\) −8.00000 −0.739600
\(118\) −10.0000 −0.920575
\(119\) −21.0000 −1.92507
\(120\) −1.00000 −0.0912871
\(121\) −2.00000 −0.181818
\(122\) 2.00000 0.181071
\(123\) −2.00000 −0.180334
\(124\) 7.00000 0.628619
\(125\) 1.00000 0.0894427
\(126\) −6.00000 −0.534522
\(127\) −12.0000 −1.06483 −0.532414 0.846484i \(-0.678715\pi\)
−0.532414 + 0.846484i \(0.678715\pi\)
\(128\) 1.00000 0.0883883
\(129\) −4.00000 −0.352180
\(130\) 4.00000 0.350823
\(131\) 2.00000 0.174741 0.0873704 0.996176i \(-0.472154\pi\)
0.0873704 + 0.996176i \(0.472154\pi\)
\(132\) 3.00000 0.261116
\(133\) 0 0
\(134\) 3.00000 0.259161
\(135\) 5.00000 0.430331
\(136\) −7.00000 −0.600245
\(137\) 13.0000 1.11066 0.555332 0.831628i \(-0.312591\pi\)
0.555332 + 0.831628i \(0.312591\pi\)
\(138\) 6.00000 0.510754
\(139\) 10.0000 0.848189 0.424094 0.905618i \(-0.360592\pi\)
0.424094 + 0.905618i \(0.360592\pi\)
\(140\) 3.00000 0.253546
\(141\) −8.00000 −0.673722
\(142\) −3.00000 −0.251754
\(143\) −12.0000 −1.00349
\(144\) −2.00000 −0.166667
\(145\) 10.0000 0.830455
\(146\) −6.00000 −0.496564
\(147\) −2.00000 −0.164957
\(148\) 8.00000 0.657596
\(149\) −20.0000 −1.63846 −0.819232 0.573462i \(-0.805600\pi\)
−0.819232 + 0.573462i \(0.805600\pi\)
\(150\) −1.00000 −0.0816497
\(151\) 12.0000 0.976546 0.488273 0.872691i \(-0.337627\pi\)
0.488273 + 0.872691i \(0.337627\pi\)
\(152\) 0 0
\(153\) 14.0000 1.13183
\(154\) −9.00000 −0.725241
\(155\) 7.00000 0.562254
\(156\) −4.00000 −0.320256
\(157\) 18.0000 1.43656 0.718278 0.695756i \(-0.244931\pi\)
0.718278 + 0.695756i \(0.244931\pi\)
\(158\) 0 0
\(159\) −14.0000 −1.11027
\(160\) 1.00000 0.0790569
\(161\) −18.0000 −1.41860
\(162\) 1.00000 0.0785674
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 2.00000 0.156174
\(165\) 3.00000 0.233550
\(166\) 14.0000 1.08661
\(167\) 8.00000 0.619059 0.309529 0.950890i \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) −3.00000 −0.231455
\(169\) 3.00000 0.230769
\(170\) −7.00000 −0.536875
\(171\) 0 0
\(172\) 4.00000 0.304997
\(173\) −11.0000 −0.836315 −0.418157 0.908375i \(-0.637324\pi\)
−0.418157 + 0.908375i \(0.637324\pi\)
\(174\) −10.0000 −0.758098
\(175\) 3.00000 0.226779
\(176\) −3.00000 −0.226134
\(177\) 10.0000 0.751646
\(178\) −10.0000 −0.749532
\(179\) 5.00000 0.373718 0.186859 0.982387i \(-0.440169\pi\)
0.186859 + 0.982387i \(0.440169\pi\)
\(180\) −2.00000 −0.149071
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 12.0000 0.889499
\(183\) −2.00000 −0.147844
\(184\) −6.00000 −0.442326
\(185\) 8.00000 0.588172
\(186\) −7.00000 −0.513265
\(187\) 21.0000 1.53567
\(188\) 8.00000 0.583460
\(189\) 15.0000 1.09109
\(190\) 0 0
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) 3.00000 0.215387
\(195\) −4.00000 −0.286446
\(196\) 2.00000 0.142857
\(197\) 3.00000 0.213741 0.106871 0.994273i \(-0.465917\pi\)
0.106871 + 0.994273i \(0.465917\pi\)
\(198\) 6.00000 0.426401
\(199\) 5.00000 0.354441 0.177220 0.984171i \(-0.443289\pi\)
0.177220 + 0.984171i \(0.443289\pi\)
\(200\) 1.00000 0.0707107
\(201\) −3.00000 −0.211604
\(202\) 2.00000 0.140720
\(203\) 30.0000 2.10559
\(204\) 7.00000 0.490098
\(205\) 2.00000 0.139686
\(206\) 9.00000 0.627060
\(207\) 12.0000 0.834058
\(208\) 4.00000 0.277350
\(209\) 0 0
\(210\) −3.00000 −0.207020
\(211\) 22.0000 1.51454 0.757271 0.653101i \(-0.226532\pi\)
0.757271 + 0.653101i \(0.226532\pi\)
\(212\) 14.0000 0.961524
\(213\) 3.00000 0.205557
\(214\) −12.0000 −0.820303
\(215\) 4.00000 0.272798
\(216\) 5.00000 0.340207
\(217\) 21.0000 1.42557
\(218\) 10.0000 0.677285
\(219\) 6.00000 0.405442
\(220\) −3.00000 −0.202260
\(221\) −28.0000 −1.88348
\(222\) −8.00000 −0.536925
\(223\) −1.00000 −0.0669650 −0.0334825 0.999439i \(-0.510660\pi\)
−0.0334825 + 0.999439i \(0.510660\pi\)
\(224\) 3.00000 0.200446
\(225\) −2.00000 −0.133333
\(226\) −6.00000 −0.399114
\(227\) 13.0000 0.862840 0.431420 0.902151i \(-0.358013\pi\)
0.431420 + 0.902151i \(0.358013\pi\)
\(228\) 0 0
\(229\) 20.0000 1.32164 0.660819 0.750546i \(-0.270209\pi\)
0.660819 + 0.750546i \(0.270209\pi\)
\(230\) −6.00000 −0.395628
\(231\) 9.00000 0.592157
\(232\) 10.0000 0.656532
\(233\) −21.0000 −1.37576 −0.687878 0.725826i \(-0.741458\pi\)
−0.687878 + 0.725826i \(0.741458\pi\)
\(234\) −8.00000 −0.522976
\(235\) 8.00000 0.521862
\(236\) −10.0000 −0.650945
\(237\) 0 0
\(238\) −21.0000 −1.36123
\(239\) −30.0000 −1.94054 −0.970269 0.242028i \(-0.922188\pi\)
−0.970269 + 0.242028i \(0.922188\pi\)
\(240\) −1.00000 −0.0645497
\(241\) −13.0000 −0.837404 −0.418702 0.908124i \(-0.637515\pi\)
−0.418702 + 0.908124i \(0.637515\pi\)
\(242\) −2.00000 −0.128565
\(243\) −16.0000 −1.02640
\(244\) 2.00000 0.128037
\(245\) 2.00000 0.127775
\(246\) −2.00000 −0.127515
\(247\) 0 0
\(248\) 7.00000 0.444500
\(249\) −14.0000 −0.887214
\(250\) 1.00000 0.0632456
\(251\) 2.00000 0.126239 0.0631194 0.998006i \(-0.479895\pi\)
0.0631194 + 0.998006i \(0.479895\pi\)
\(252\) −6.00000 −0.377964
\(253\) 18.0000 1.13165
\(254\) −12.0000 −0.752947
\(255\) 7.00000 0.438357
\(256\) 1.00000 0.0625000
\(257\) 8.00000 0.499026 0.249513 0.968371i \(-0.419729\pi\)
0.249513 + 0.968371i \(0.419729\pi\)
\(258\) −4.00000 −0.249029
\(259\) 24.0000 1.49129
\(260\) 4.00000 0.248069
\(261\) −20.0000 −1.23797
\(262\) 2.00000 0.123560
\(263\) −21.0000 −1.29492 −0.647458 0.762101i \(-0.724168\pi\)
−0.647458 + 0.762101i \(0.724168\pi\)
\(264\) 3.00000 0.184637
\(265\) 14.0000 0.860013
\(266\) 0 0
\(267\) 10.0000 0.611990
\(268\) 3.00000 0.183254
\(269\) −15.0000 −0.914566 −0.457283 0.889321i \(-0.651177\pi\)
−0.457283 + 0.889321i \(0.651177\pi\)
\(270\) 5.00000 0.304290
\(271\) −28.0000 −1.70088 −0.850439 0.526073i \(-0.823664\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) −7.00000 −0.424437
\(273\) −12.0000 −0.726273
\(274\) 13.0000 0.785359
\(275\) −3.00000 −0.180907
\(276\) 6.00000 0.361158
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) 10.0000 0.599760
\(279\) −14.0000 −0.838158
\(280\) 3.00000 0.179284
\(281\) 22.0000 1.31241 0.656205 0.754583i \(-0.272161\pi\)
0.656205 + 0.754583i \(0.272161\pi\)
\(282\) −8.00000 −0.476393
\(283\) −21.0000 −1.24832 −0.624160 0.781296i \(-0.714559\pi\)
−0.624160 + 0.781296i \(0.714559\pi\)
\(284\) −3.00000 −0.178017
\(285\) 0 0
\(286\) −12.0000 −0.709575
\(287\) 6.00000 0.354169
\(288\) −2.00000 −0.117851
\(289\) 32.0000 1.88235
\(290\) 10.0000 0.587220
\(291\) −3.00000 −0.175863
\(292\) −6.00000 −0.351123
\(293\) 4.00000 0.233682 0.116841 0.993151i \(-0.462723\pi\)
0.116841 + 0.993151i \(0.462723\pi\)
\(294\) −2.00000 −0.116642
\(295\) −10.0000 −0.582223
\(296\) 8.00000 0.464991
\(297\) −15.0000 −0.870388
\(298\) −20.0000 −1.15857
\(299\) −24.0000 −1.38796
\(300\) −1.00000 −0.0577350
\(301\) 12.0000 0.691669
\(302\) 12.0000 0.690522
\(303\) −2.00000 −0.114897
\(304\) 0 0
\(305\) 2.00000 0.114520
\(306\) 14.0000 0.800327
\(307\) −22.0000 −1.25561 −0.627803 0.778372i \(-0.716046\pi\)
−0.627803 + 0.778372i \(0.716046\pi\)
\(308\) −9.00000 −0.512823
\(309\) −9.00000 −0.511992
\(310\) 7.00000 0.397573
\(311\) 12.0000 0.680458 0.340229 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) −4.00000 −0.226455
\(313\) −16.0000 −0.904373 −0.452187 0.891923i \(-0.649356\pi\)
−0.452187 + 0.891923i \(0.649356\pi\)
\(314\) 18.0000 1.01580
\(315\) −6.00000 −0.338062
\(316\) 0 0
\(317\) 18.0000 1.01098 0.505490 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) −14.0000 −0.785081
\(319\) −30.0000 −1.67968
\(320\) 1.00000 0.0559017
\(321\) 12.0000 0.669775
\(322\) −18.0000 −1.00310
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 4.00000 0.221880
\(326\) −16.0000 −0.886158
\(327\) −10.0000 −0.553001
\(328\) 2.00000 0.110432
\(329\) 24.0000 1.32316
\(330\) 3.00000 0.165145
\(331\) −13.0000 −0.714545 −0.357272 0.934000i \(-0.616293\pi\)
−0.357272 + 0.934000i \(0.616293\pi\)
\(332\) 14.0000 0.768350
\(333\) −16.0000 −0.876795
\(334\) 8.00000 0.437741
\(335\) 3.00000 0.163908
\(336\) −3.00000 −0.163663
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 3.00000 0.163178
\(339\) 6.00000 0.325875
\(340\) −7.00000 −0.379628
\(341\) −21.0000 −1.13721
\(342\) 0 0
\(343\) −15.0000 −0.809924
\(344\) 4.00000 0.215666
\(345\) 6.00000 0.323029
\(346\) −11.0000 −0.591364
\(347\) −7.00000 −0.375780 −0.187890 0.982190i \(-0.560165\pi\)
−0.187890 + 0.982190i \(0.560165\pi\)
\(348\) −10.0000 −0.536056
\(349\) 35.0000 1.87351 0.936754 0.349990i \(-0.113815\pi\)
0.936754 + 0.349990i \(0.113815\pi\)
\(350\) 3.00000 0.160357
\(351\) 20.0000 1.06752
\(352\) −3.00000 −0.159901
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 10.0000 0.531494
\(355\) −3.00000 −0.159223
\(356\) −10.0000 −0.529999
\(357\) 21.0000 1.11144
\(358\) 5.00000 0.264258
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) −2.00000 −0.105409
\(361\) −19.0000 −1.00000
\(362\) 2.00000 0.105118
\(363\) 2.00000 0.104973
\(364\) 12.0000 0.628971
\(365\) −6.00000 −0.314054
\(366\) −2.00000 −0.104542
\(367\) −2.00000 −0.104399 −0.0521996 0.998637i \(-0.516623\pi\)
−0.0521996 + 0.998637i \(0.516623\pi\)
\(368\) −6.00000 −0.312772
\(369\) −4.00000 −0.208232
\(370\) 8.00000 0.415900
\(371\) 42.0000 2.18053
\(372\) −7.00000 −0.362933
\(373\) −31.0000 −1.60512 −0.802560 0.596572i \(-0.796529\pi\)
−0.802560 + 0.596572i \(0.796529\pi\)
\(374\) 21.0000 1.08588
\(375\) −1.00000 −0.0516398
\(376\) 8.00000 0.412568
\(377\) 40.0000 2.06010
\(378\) 15.0000 0.771517
\(379\) −25.0000 −1.28416 −0.642082 0.766636i \(-0.721929\pi\)
−0.642082 + 0.766636i \(0.721929\pi\)
\(380\) 0 0
\(381\) 12.0000 0.614779
\(382\) 12.0000 0.613973
\(383\) −21.0000 −1.07305 −0.536525 0.843884i \(-0.680263\pi\)
−0.536525 + 0.843884i \(0.680263\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −9.00000 −0.458682
\(386\) 14.0000 0.712581
\(387\) −8.00000 −0.406663
\(388\) 3.00000 0.152302
\(389\) 5.00000 0.253510 0.126755 0.991934i \(-0.459544\pi\)
0.126755 + 0.991934i \(0.459544\pi\)
\(390\) −4.00000 −0.202548
\(391\) 42.0000 2.12403
\(392\) 2.00000 0.101015
\(393\) −2.00000 −0.100887
\(394\) 3.00000 0.151138
\(395\) 0 0
\(396\) 6.00000 0.301511
\(397\) 13.0000 0.652451 0.326226 0.945292i \(-0.394223\pi\)
0.326226 + 0.945292i \(0.394223\pi\)
\(398\) 5.00000 0.250627
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 1.00000 0.0499376
\(402\) −3.00000 −0.149626
\(403\) 28.0000 1.39478
\(404\) 2.00000 0.0995037
\(405\) 1.00000 0.0496904
\(406\) 30.0000 1.48888
\(407\) −24.0000 −1.18964
\(408\) 7.00000 0.346552
\(409\) 30.0000 1.48340 0.741702 0.670729i \(-0.234019\pi\)
0.741702 + 0.670729i \(0.234019\pi\)
\(410\) 2.00000 0.0987730
\(411\) −13.0000 −0.641243
\(412\) 9.00000 0.443398
\(413\) −30.0000 −1.47620
\(414\) 12.0000 0.589768
\(415\) 14.0000 0.687233
\(416\) 4.00000 0.196116
\(417\) −10.0000 −0.489702
\(418\) 0 0
\(419\) −5.00000 −0.244266 −0.122133 0.992514i \(-0.538973\pi\)
−0.122133 + 0.992514i \(0.538973\pi\)
\(420\) −3.00000 −0.146385
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) 22.0000 1.07094
\(423\) −16.0000 −0.777947
\(424\) 14.0000 0.679900
\(425\) −7.00000 −0.339550
\(426\) 3.00000 0.145350
\(427\) 6.00000 0.290360
\(428\) −12.0000 −0.580042
\(429\) 12.0000 0.579365
\(430\) 4.00000 0.192897
\(431\) 17.0000 0.818861 0.409431 0.912341i \(-0.365727\pi\)
0.409431 + 0.912341i \(0.365727\pi\)
\(432\) 5.00000 0.240563
\(433\) 4.00000 0.192228 0.0961139 0.995370i \(-0.469359\pi\)
0.0961139 + 0.995370i \(0.469359\pi\)
\(434\) 21.0000 1.00803
\(435\) −10.0000 −0.479463
\(436\) 10.0000 0.478913
\(437\) 0 0
\(438\) 6.00000 0.286691
\(439\) −35.0000 −1.67046 −0.835229 0.549902i \(-0.814665\pi\)
−0.835229 + 0.549902i \(0.814665\pi\)
\(440\) −3.00000 −0.143019
\(441\) −4.00000 −0.190476
\(442\) −28.0000 −1.33182
\(443\) 4.00000 0.190046 0.0950229 0.995475i \(-0.469708\pi\)
0.0950229 + 0.995475i \(0.469708\pi\)
\(444\) −8.00000 −0.379663
\(445\) −10.0000 −0.474045
\(446\) −1.00000 −0.0473514
\(447\) 20.0000 0.945968
\(448\) 3.00000 0.141737
\(449\) −20.0000 −0.943858 −0.471929 0.881636i \(-0.656442\pi\)
−0.471929 + 0.881636i \(0.656442\pi\)
\(450\) −2.00000 −0.0942809
\(451\) −6.00000 −0.282529
\(452\) −6.00000 −0.282216
\(453\) −12.0000 −0.563809
\(454\) 13.0000 0.610120
\(455\) 12.0000 0.562569
\(456\) 0 0
\(457\) −2.00000 −0.0935561 −0.0467780 0.998905i \(-0.514895\pi\)
−0.0467780 + 0.998905i \(0.514895\pi\)
\(458\) 20.0000 0.934539
\(459\) −35.0000 −1.63366
\(460\) −6.00000 −0.279751
\(461\) −13.0000 −0.605470 −0.302735 0.953075i \(-0.597900\pi\)
−0.302735 + 0.953075i \(0.597900\pi\)
\(462\) 9.00000 0.418718
\(463\) 14.0000 0.650635 0.325318 0.945605i \(-0.394529\pi\)
0.325318 + 0.945605i \(0.394529\pi\)
\(464\) 10.0000 0.464238
\(465\) −7.00000 −0.324617
\(466\) −21.0000 −0.972806
\(467\) −27.0000 −1.24941 −0.624705 0.780860i \(-0.714781\pi\)
−0.624705 + 0.780860i \(0.714781\pi\)
\(468\) −8.00000 −0.369800
\(469\) 9.00000 0.415581
\(470\) 8.00000 0.369012
\(471\) −18.0000 −0.829396
\(472\) −10.0000 −0.460287
\(473\) −12.0000 −0.551761
\(474\) 0 0
\(475\) 0 0
\(476\) −21.0000 −0.962533
\(477\) −28.0000 −1.28203
\(478\) −30.0000 −1.37217
\(479\) 10.0000 0.456912 0.228456 0.973554i \(-0.426632\pi\)
0.228456 + 0.973554i \(0.426632\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 32.0000 1.45907
\(482\) −13.0000 −0.592134
\(483\) 18.0000 0.819028
\(484\) −2.00000 −0.0909091
\(485\) 3.00000 0.136223
\(486\) −16.0000 −0.725775
\(487\) 8.00000 0.362515 0.181257 0.983436i \(-0.441983\pi\)
0.181257 + 0.983436i \(0.441983\pi\)
\(488\) 2.00000 0.0905357
\(489\) 16.0000 0.723545
\(490\) 2.00000 0.0903508
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) −2.00000 −0.0901670
\(493\) −70.0000 −3.15264
\(494\) 0 0
\(495\) 6.00000 0.269680
\(496\) 7.00000 0.314309
\(497\) −9.00000 −0.403705
\(498\) −14.0000 −0.627355
\(499\) 20.0000 0.895323 0.447661 0.894203i \(-0.352257\pi\)
0.447661 + 0.894203i \(0.352257\pi\)
\(500\) 1.00000 0.0447214
\(501\) −8.00000 −0.357414
\(502\) 2.00000 0.0892644
\(503\) −21.0000 −0.936344 −0.468172 0.883637i \(-0.655087\pi\)
−0.468172 + 0.883637i \(0.655087\pi\)
\(504\) −6.00000 −0.267261
\(505\) 2.00000 0.0889988
\(506\) 18.0000 0.800198
\(507\) −3.00000 −0.133235
\(508\) −12.0000 −0.532414
\(509\) 5.00000 0.221621 0.110811 0.993842i \(-0.464655\pi\)
0.110811 + 0.993842i \(0.464655\pi\)
\(510\) 7.00000 0.309965
\(511\) −18.0000 −0.796273
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 8.00000 0.352865
\(515\) 9.00000 0.396587
\(516\) −4.00000 −0.176090
\(517\) −24.0000 −1.05552
\(518\) 24.0000 1.05450
\(519\) 11.0000 0.482846
\(520\) 4.00000 0.175412
\(521\) 42.0000 1.84005 0.920027 0.391856i \(-0.128167\pi\)
0.920027 + 0.391856i \(0.128167\pi\)
\(522\) −20.0000 −0.875376
\(523\) −11.0000 −0.480996 −0.240498 0.970650i \(-0.577311\pi\)
−0.240498 + 0.970650i \(0.577311\pi\)
\(524\) 2.00000 0.0873704
\(525\) −3.00000 −0.130931
\(526\) −21.0000 −0.915644
\(527\) −49.0000 −2.13447
\(528\) 3.00000 0.130558
\(529\) 13.0000 0.565217
\(530\) 14.0000 0.608121
\(531\) 20.0000 0.867926
\(532\) 0 0
\(533\) 8.00000 0.346518
\(534\) 10.0000 0.432742
\(535\) −12.0000 −0.518805
\(536\) 3.00000 0.129580
\(537\) −5.00000 −0.215766
\(538\) −15.0000 −0.646696
\(539\) −6.00000 −0.258438
\(540\) 5.00000 0.215166
\(541\) −28.0000 −1.20381 −0.601907 0.798566i \(-0.705592\pi\)
−0.601907 + 0.798566i \(0.705592\pi\)
\(542\) −28.0000 −1.20270
\(543\) −2.00000 −0.0858282
\(544\) −7.00000 −0.300123
\(545\) 10.0000 0.428353
\(546\) −12.0000 −0.513553
\(547\) 18.0000 0.769624 0.384812 0.922995i \(-0.374266\pi\)
0.384812 + 0.922995i \(0.374266\pi\)
\(548\) 13.0000 0.555332
\(549\) −4.00000 −0.170716
\(550\) −3.00000 −0.127920
\(551\) 0 0
\(552\) 6.00000 0.255377
\(553\) 0 0
\(554\) −2.00000 −0.0849719
\(555\) −8.00000 −0.339581
\(556\) 10.0000 0.424094
\(557\) 33.0000 1.39825 0.699127 0.714997i \(-0.253572\pi\)
0.699127 + 0.714997i \(0.253572\pi\)
\(558\) −14.0000 −0.592667
\(559\) 16.0000 0.676728
\(560\) 3.00000 0.126773
\(561\) −21.0000 −0.886621
\(562\) 22.0000 0.928014
\(563\) −16.0000 −0.674320 −0.337160 0.941447i \(-0.609466\pi\)
−0.337160 + 0.941447i \(0.609466\pi\)
\(564\) −8.00000 −0.336861
\(565\) −6.00000 −0.252422
\(566\) −21.0000 −0.882696
\(567\) 3.00000 0.125988
\(568\) −3.00000 −0.125877
\(569\) −10.0000 −0.419222 −0.209611 0.977785i \(-0.567220\pi\)
−0.209611 + 0.977785i \(0.567220\pi\)
\(570\) 0 0
\(571\) −38.0000 −1.59025 −0.795125 0.606445i \(-0.792595\pi\)
−0.795125 + 0.606445i \(0.792595\pi\)
\(572\) −12.0000 −0.501745
\(573\) −12.0000 −0.501307
\(574\) 6.00000 0.250435
\(575\) −6.00000 −0.250217
\(576\) −2.00000 −0.0833333
\(577\) −42.0000 −1.74848 −0.874241 0.485491i \(-0.838641\pi\)
−0.874241 + 0.485491i \(0.838641\pi\)
\(578\) 32.0000 1.33102
\(579\) −14.0000 −0.581820
\(580\) 10.0000 0.415227
\(581\) 42.0000 1.74245
\(582\) −3.00000 −0.124354
\(583\) −42.0000 −1.73946
\(584\) −6.00000 −0.248282
\(585\) −8.00000 −0.330759
\(586\) 4.00000 0.165238
\(587\) −22.0000 −0.908037 −0.454019 0.890992i \(-0.650010\pi\)
−0.454019 + 0.890992i \(0.650010\pi\)
\(588\) −2.00000 −0.0824786
\(589\) 0 0
\(590\) −10.0000 −0.411693
\(591\) −3.00000 −0.123404
\(592\) 8.00000 0.328798
\(593\) 39.0000 1.60154 0.800769 0.598973i \(-0.204424\pi\)
0.800769 + 0.598973i \(0.204424\pi\)
\(594\) −15.0000 −0.615457
\(595\) −21.0000 −0.860916
\(596\) −20.0000 −0.819232
\(597\) −5.00000 −0.204636
\(598\) −24.0000 −0.981433
\(599\) 30.0000 1.22577 0.612883 0.790173i \(-0.290010\pi\)
0.612883 + 0.790173i \(0.290010\pi\)
\(600\) −1.00000 −0.0408248
\(601\) 17.0000 0.693444 0.346722 0.937968i \(-0.387295\pi\)
0.346722 + 0.937968i \(0.387295\pi\)
\(602\) 12.0000 0.489083
\(603\) −6.00000 −0.244339
\(604\) 12.0000 0.488273
\(605\) −2.00000 −0.0813116
\(606\) −2.00000 −0.0812444
\(607\) −27.0000 −1.09590 −0.547948 0.836512i \(-0.684591\pi\)
−0.547948 + 0.836512i \(0.684591\pi\)
\(608\) 0 0
\(609\) −30.0000 −1.21566
\(610\) 2.00000 0.0809776
\(611\) 32.0000 1.29458
\(612\) 14.0000 0.565916
\(613\) 4.00000 0.161558 0.0807792 0.996732i \(-0.474259\pi\)
0.0807792 + 0.996732i \(0.474259\pi\)
\(614\) −22.0000 −0.887848
\(615\) −2.00000 −0.0806478
\(616\) −9.00000 −0.362620
\(617\) −22.0000 −0.885687 −0.442843 0.896599i \(-0.646030\pi\)
−0.442843 + 0.896599i \(0.646030\pi\)
\(618\) −9.00000 −0.362033
\(619\) 25.0000 1.00483 0.502417 0.864625i \(-0.332444\pi\)
0.502417 + 0.864625i \(0.332444\pi\)
\(620\) 7.00000 0.281127
\(621\) −30.0000 −1.20386
\(622\) 12.0000 0.481156
\(623\) −30.0000 −1.20192
\(624\) −4.00000 −0.160128
\(625\) 1.00000 0.0400000
\(626\) −16.0000 −0.639489
\(627\) 0 0
\(628\) 18.0000 0.718278
\(629\) −56.0000 −2.23287
\(630\) −6.00000 −0.239046
\(631\) −8.00000 −0.318475 −0.159237 0.987240i \(-0.550904\pi\)
−0.159237 + 0.987240i \(0.550904\pi\)
\(632\) 0 0
\(633\) −22.0000 −0.874421
\(634\) 18.0000 0.714871
\(635\) −12.0000 −0.476205
\(636\) −14.0000 −0.555136
\(637\) 8.00000 0.316972
\(638\) −30.0000 −1.18771
\(639\) 6.00000 0.237356
\(640\) 1.00000 0.0395285
\(641\) −8.00000 −0.315981 −0.157991 0.987441i \(-0.550502\pi\)
−0.157991 + 0.987441i \(0.550502\pi\)
\(642\) 12.0000 0.473602
\(643\) 34.0000 1.34083 0.670415 0.741987i \(-0.266116\pi\)
0.670415 + 0.741987i \(0.266116\pi\)
\(644\) −18.0000 −0.709299
\(645\) −4.00000 −0.157500
\(646\) 0 0
\(647\) 18.0000 0.707653 0.353827 0.935311i \(-0.384880\pi\)
0.353827 + 0.935311i \(0.384880\pi\)
\(648\) 1.00000 0.0392837
\(649\) 30.0000 1.17760
\(650\) 4.00000 0.156893
\(651\) −21.0000 −0.823055
\(652\) −16.0000 −0.626608
\(653\) 19.0000 0.743527 0.371764 0.928327i \(-0.378753\pi\)
0.371764 + 0.928327i \(0.378753\pi\)
\(654\) −10.0000 −0.391031
\(655\) 2.00000 0.0781465
\(656\) 2.00000 0.0780869
\(657\) 12.0000 0.468165
\(658\) 24.0000 0.935617
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 3.00000 0.116775
\(661\) −38.0000 −1.47803 −0.739014 0.673690i \(-0.764708\pi\)
−0.739014 + 0.673690i \(0.764708\pi\)
\(662\) −13.0000 −0.505259
\(663\) 28.0000 1.08743
\(664\) 14.0000 0.543305
\(665\) 0 0
\(666\) −16.0000 −0.619987
\(667\) −60.0000 −2.32321
\(668\) 8.00000 0.309529
\(669\) 1.00000 0.0386622
\(670\) 3.00000 0.115900
\(671\) −6.00000 −0.231627
\(672\) −3.00000 −0.115728
\(673\) −6.00000 −0.231283 −0.115642 0.993291i \(-0.536892\pi\)
−0.115642 + 0.993291i \(0.536892\pi\)
\(674\) 18.0000 0.693334
\(675\) 5.00000 0.192450
\(676\) 3.00000 0.115385
\(677\) 3.00000 0.115299 0.0576497 0.998337i \(-0.481639\pi\)
0.0576497 + 0.998337i \(0.481639\pi\)
\(678\) 6.00000 0.230429
\(679\) 9.00000 0.345388
\(680\) −7.00000 −0.268438
\(681\) −13.0000 −0.498161
\(682\) −21.0000 −0.804132
\(683\) −36.0000 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) 0 0
\(685\) 13.0000 0.496704
\(686\) −15.0000 −0.572703
\(687\) −20.0000 −0.763048
\(688\) 4.00000 0.152499
\(689\) 56.0000 2.13343
\(690\) 6.00000 0.228416
\(691\) 17.0000 0.646710 0.323355 0.946278i \(-0.395189\pi\)
0.323355 + 0.946278i \(0.395189\pi\)
\(692\) −11.0000 −0.418157
\(693\) 18.0000 0.683763
\(694\) −7.00000 −0.265716
\(695\) 10.0000 0.379322
\(696\) −10.0000 −0.379049
\(697\) −14.0000 −0.530288
\(698\) 35.0000 1.32477
\(699\) 21.0000 0.794293
\(700\) 3.00000 0.113389
\(701\) 27.0000 1.01978 0.509888 0.860241i \(-0.329687\pi\)
0.509888 + 0.860241i \(0.329687\pi\)
\(702\) 20.0000 0.754851
\(703\) 0 0
\(704\) −3.00000 −0.113067
\(705\) −8.00000 −0.301297
\(706\) −6.00000 −0.225813
\(707\) 6.00000 0.225653
\(708\) 10.0000 0.375823
\(709\) 10.0000 0.375558 0.187779 0.982211i \(-0.439871\pi\)
0.187779 + 0.982211i \(0.439871\pi\)
\(710\) −3.00000 −0.112588
\(711\) 0 0
\(712\) −10.0000 −0.374766
\(713\) −42.0000 −1.57291
\(714\) 21.0000 0.785905
\(715\) −12.0000 −0.448775
\(716\) 5.00000 0.186859
\(717\) 30.0000 1.12037
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) −2.00000 −0.0745356
\(721\) 27.0000 1.00553
\(722\) −19.0000 −0.707107
\(723\) 13.0000 0.483475
\(724\) 2.00000 0.0743294
\(725\) 10.0000 0.371391
\(726\) 2.00000 0.0742270
\(727\) −2.00000 −0.0741759 −0.0370879 0.999312i \(-0.511808\pi\)
−0.0370879 + 0.999312i \(0.511808\pi\)
\(728\) 12.0000 0.444750
\(729\) 13.0000 0.481481
\(730\) −6.00000 −0.222070
\(731\) −28.0000 −1.03562
\(732\) −2.00000 −0.0739221
\(733\) −31.0000 −1.14501 −0.572506 0.819901i \(-0.694029\pi\)
−0.572506 + 0.819901i \(0.694029\pi\)
\(734\) −2.00000 −0.0738213
\(735\) −2.00000 −0.0737711
\(736\) −6.00000 −0.221163
\(737\) −9.00000 −0.331519
\(738\) −4.00000 −0.147242
\(739\) −15.0000 −0.551784 −0.275892 0.961189i \(-0.588973\pi\)
−0.275892 + 0.961189i \(0.588973\pi\)
\(740\) 8.00000 0.294086
\(741\) 0 0
\(742\) 42.0000 1.54187
\(743\) −16.0000 −0.586983 −0.293492 0.955962i \(-0.594817\pi\)
−0.293492 + 0.955962i \(0.594817\pi\)
\(744\) −7.00000 −0.256632
\(745\) −20.0000 −0.732743
\(746\) −31.0000 −1.13499
\(747\) −28.0000 −1.02447
\(748\) 21.0000 0.767836
\(749\) −36.0000 −1.31541
\(750\) −1.00000 −0.0365148
\(751\) −48.0000 −1.75154 −0.875772 0.482724i \(-0.839647\pi\)
−0.875772 + 0.482724i \(0.839647\pi\)
\(752\) 8.00000 0.291730
\(753\) −2.00000 −0.0728841
\(754\) 40.0000 1.45671
\(755\) 12.0000 0.436725
\(756\) 15.0000 0.545545
\(757\) 13.0000 0.472493 0.236247 0.971693i \(-0.424083\pi\)
0.236247 + 0.971693i \(0.424083\pi\)
\(758\) −25.0000 −0.908041
\(759\) −18.0000 −0.653359
\(760\) 0 0
\(761\) 42.0000 1.52250 0.761249 0.648459i \(-0.224586\pi\)
0.761249 + 0.648459i \(0.224586\pi\)
\(762\) 12.0000 0.434714
\(763\) 30.0000 1.08607
\(764\) 12.0000 0.434145
\(765\) 14.0000 0.506171
\(766\) −21.0000 −0.758761
\(767\) −40.0000 −1.44432
\(768\) −1.00000 −0.0360844
\(769\) −20.0000 −0.721218 −0.360609 0.932717i \(-0.617431\pi\)
−0.360609 + 0.932717i \(0.617431\pi\)
\(770\) −9.00000 −0.324337
\(771\) −8.00000 −0.288113
\(772\) 14.0000 0.503871
\(773\) −21.0000 −0.755318 −0.377659 0.925945i \(-0.623271\pi\)
−0.377659 + 0.925945i \(0.623271\pi\)
\(774\) −8.00000 −0.287554
\(775\) 7.00000 0.251447
\(776\) 3.00000 0.107694
\(777\) −24.0000 −0.860995
\(778\) 5.00000 0.179259
\(779\) 0 0
\(780\) −4.00000 −0.143223
\(781\) 9.00000 0.322045
\(782\) 42.0000 1.50192
\(783\) 50.0000 1.78685
\(784\) 2.00000 0.0714286
\(785\) 18.0000 0.642448
\(786\) −2.00000 −0.0713376
\(787\) −47.0000 −1.67537 −0.837685 0.546154i \(-0.816091\pi\)
−0.837685 + 0.546154i \(0.816091\pi\)
\(788\) 3.00000 0.106871
\(789\) 21.0000 0.747620
\(790\) 0 0
\(791\) −18.0000 −0.640006
\(792\) 6.00000 0.213201
\(793\) 8.00000 0.284088
\(794\) 13.0000 0.461353
\(795\) −14.0000 −0.496529
\(796\) 5.00000 0.177220
\(797\) −42.0000 −1.48772 −0.743858 0.668338i \(-0.767006\pi\)
−0.743858 + 0.668338i \(0.767006\pi\)
\(798\) 0 0
\(799\) −56.0000 −1.98114
\(800\) 1.00000 0.0353553
\(801\) 20.0000 0.706665
\(802\) 1.00000 0.0353112
\(803\) 18.0000 0.635206
\(804\) −3.00000 −0.105802
\(805\) −18.0000 −0.634417
\(806\) 28.0000 0.986258
\(807\) 15.0000 0.528025
\(808\) 2.00000 0.0703598
\(809\) −15.0000 −0.527372 −0.263686 0.964609i \(-0.584938\pi\)
−0.263686 + 0.964609i \(0.584938\pi\)
\(810\) 1.00000 0.0351364
\(811\) 12.0000 0.421377 0.210688 0.977553i \(-0.432429\pi\)
0.210688 + 0.977553i \(0.432429\pi\)
\(812\) 30.0000 1.05279
\(813\) 28.0000 0.982003
\(814\) −24.0000 −0.841200
\(815\) −16.0000 −0.560456
\(816\) 7.00000 0.245049
\(817\) 0 0
\(818\) 30.0000 1.04893
\(819\) −24.0000 −0.838628
\(820\) 2.00000 0.0698430
\(821\) 27.0000 0.942306 0.471153 0.882051i \(-0.343838\pi\)
0.471153 + 0.882051i \(0.343838\pi\)
\(822\) −13.0000 −0.453427
\(823\) −26.0000 −0.906303 −0.453152 0.891434i \(-0.649700\pi\)
−0.453152 + 0.891434i \(0.649700\pi\)
\(824\) 9.00000 0.313530
\(825\) 3.00000 0.104447
\(826\) −30.0000 −1.04383
\(827\) −22.0000 −0.765015 −0.382507 0.923952i \(-0.624939\pi\)
−0.382507 + 0.923952i \(0.624939\pi\)
\(828\) 12.0000 0.417029
\(829\) 45.0000 1.56291 0.781457 0.623959i \(-0.214477\pi\)
0.781457 + 0.623959i \(0.214477\pi\)
\(830\) 14.0000 0.485947
\(831\) 2.00000 0.0693792
\(832\) 4.00000 0.138675
\(833\) −14.0000 −0.485071
\(834\) −10.0000 −0.346272
\(835\) 8.00000 0.276851
\(836\) 0 0
\(837\) 35.0000 1.20978
\(838\) −5.00000 −0.172722
\(839\) 45.0000 1.55357 0.776786 0.629764i \(-0.216849\pi\)
0.776786 + 0.629764i \(0.216849\pi\)
\(840\) −3.00000 −0.103510
\(841\) 71.0000 2.44828
\(842\) 22.0000 0.758170
\(843\) −22.0000 −0.757720
\(844\) 22.0000 0.757271
\(845\) 3.00000 0.103203
\(846\) −16.0000 −0.550091
\(847\) −6.00000 −0.206162
\(848\) 14.0000 0.480762
\(849\) 21.0000 0.720718
\(850\) −7.00000 −0.240098
\(851\) −48.0000 −1.64542
\(852\) 3.00000 0.102778
\(853\) −46.0000 −1.57501 −0.787505 0.616308i \(-0.788628\pi\)
−0.787505 + 0.616308i \(0.788628\pi\)
\(854\) 6.00000 0.205316
\(855\) 0 0
\(856\) −12.0000 −0.410152
\(857\) 28.0000 0.956462 0.478231 0.878234i \(-0.341278\pi\)
0.478231 + 0.878234i \(0.341278\pi\)
\(858\) 12.0000 0.409673
\(859\) −25.0000 −0.852989 −0.426494 0.904490i \(-0.640252\pi\)
−0.426494 + 0.904490i \(0.640252\pi\)
\(860\) 4.00000 0.136399
\(861\) −6.00000 −0.204479
\(862\) 17.0000 0.579022
\(863\) −56.0000 −1.90626 −0.953131 0.302558i \(-0.902160\pi\)
−0.953131 + 0.302558i \(0.902160\pi\)
\(864\) 5.00000 0.170103
\(865\) −11.0000 −0.374011
\(866\) 4.00000 0.135926
\(867\) −32.0000 −1.08678
\(868\) 21.0000 0.712786
\(869\) 0 0
\(870\) −10.0000 −0.339032
\(871\) 12.0000 0.406604
\(872\) 10.0000 0.338643
\(873\) −6.00000 −0.203069
\(874\) 0 0
\(875\) 3.00000 0.101419
\(876\) 6.00000 0.202721
\(877\) 28.0000 0.945493 0.472746 0.881199i \(-0.343263\pi\)
0.472746 + 0.881199i \(0.343263\pi\)
\(878\) −35.0000 −1.18119
\(879\) −4.00000 −0.134917
\(880\) −3.00000 −0.101130
\(881\) −38.0000 −1.28025 −0.640126 0.768270i \(-0.721118\pi\)
−0.640126 + 0.768270i \(0.721118\pi\)
\(882\) −4.00000 −0.134687
\(883\) 4.00000 0.134611 0.0673054 0.997732i \(-0.478560\pi\)
0.0673054 + 0.997732i \(0.478560\pi\)
\(884\) −28.0000 −0.941742
\(885\) 10.0000 0.336146
\(886\) 4.00000 0.134383
\(887\) −12.0000 −0.402921 −0.201460 0.979497i \(-0.564569\pi\)
−0.201460 + 0.979497i \(0.564569\pi\)
\(888\) −8.00000 −0.268462
\(889\) −36.0000 −1.20740
\(890\) −10.0000 −0.335201
\(891\) −3.00000 −0.100504
\(892\) −1.00000 −0.0334825
\(893\) 0 0
\(894\) 20.0000 0.668900
\(895\) 5.00000 0.167132
\(896\) 3.00000 0.100223
\(897\) 24.0000 0.801337
\(898\) −20.0000 −0.667409
\(899\) 70.0000 2.33463
\(900\) −2.00000 −0.0666667
\(901\) −98.0000 −3.26485
\(902\) −6.00000 −0.199778
\(903\) −12.0000 −0.399335
\(904\) −6.00000 −0.199557
\(905\) 2.00000 0.0664822
\(906\) −12.0000 −0.398673
\(907\) 28.0000 0.929725 0.464862 0.885383i \(-0.346104\pi\)
0.464862 + 0.885383i \(0.346104\pi\)
\(908\) 13.0000 0.431420
\(909\) −4.00000 −0.132672
\(910\) 12.0000 0.397796
\(911\) 52.0000 1.72284 0.861418 0.507896i \(-0.169577\pi\)
0.861418 + 0.507896i \(0.169577\pi\)
\(912\) 0 0
\(913\) −42.0000 −1.39000
\(914\) −2.00000 −0.0661541
\(915\) −2.00000 −0.0661180
\(916\) 20.0000 0.660819
\(917\) 6.00000 0.198137
\(918\) −35.0000 −1.15517
\(919\) −5.00000 −0.164935 −0.0824674 0.996594i \(-0.526280\pi\)
−0.0824674 + 0.996594i \(0.526280\pi\)
\(920\) −6.00000 −0.197814
\(921\) 22.0000 0.724925
\(922\) −13.0000 −0.428132
\(923\) −12.0000 −0.394985
\(924\) 9.00000 0.296078
\(925\) 8.00000 0.263038
\(926\) 14.0000 0.460069
\(927\) −18.0000 −0.591198
\(928\) 10.0000 0.328266
\(929\) 40.0000 1.31236 0.656179 0.754606i \(-0.272172\pi\)
0.656179 + 0.754606i \(0.272172\pi\)
\(930\) −7.00000 −0.229539
\(931\) 0 0
\(932\) −21.0000 −0.687878
\(933\) −12.0000 −0.392862
\(934\) −27.0000 −0.883467
\(935\) 21.0000 0.686773
\(936\) −8.00000 −0.261488
\(937\) 38.0000 1.24141 0.620703 0.784046i \(-0.286847\pi\)
0.620703 + 0.784046i \(0.286847\pi\)
\(938\) 9.00000 0.293860
\(939\) 16.0000 0.522140
\(940\) 8.00000 0.260931
\(941\) −58.0000 −1.89075 −0.945373 0.325991i \(-0.894302\pi\)
−0.945373 + 0.325991i \(0.894302\pi\)
\(942\) −18.0000 −0.586472
\(943\) −12.0000 −0.390774
\(944\) −10.0000 −0.325472
\(945\) 15.0000 0.487950
\(946\) −12.0000 −0.390154
\(947\) −22.0000 −0.714904 −0.357452 0.933932i \(-0.616354\pi\)
−0.357452 + 0.933932i \(0.616354\pi\)
\(948\) 0 0
\(949\) −24.0000 −0.779073
\(950\) 0 0
\(951\) −18.0000 −0.583690
\(952\) −21.0000 −0.680614
\(953\) −36.0000 −1.16615 −0.583077 0.812417i \(-0.698151\pi\)
−0.583077 + 0.812417i \(0.698151\pi\)
\(954\) −28.0000 −0.906533
\(955\) 12.0000 0.388311
\(956\) −30.0000 −0.970269
\(957\) 30.0000 0.969762
\(958\) 10.0000 0.323085
\(959\) 39.0000 1.25938
\(960\) −1.00000 −0.0322749
\(961\) 18.0000 0.580645
\(962\) 32.0000 1.03172
\(963\) 24.0000 0.773389
\(964\) −13.0000 −0.418702
\(965\) 14.0000 0.450676
\(966\) 18.0000 0.579141
\(967\) −52.0000 −1.67221 −0.836104 0.548572i \(-0.815172\pi\)
−0.836104 + 0.548572i \(0.815172\pi\)
\(968\) −2.00000 −0.0642824
\(969\) 0 0
\(970\) 3.00000 0.0963242
\(971\) −8.00000 −0.256732 −0.128366 0.991727i \(-0.540973\pi\)
−0.128366 + 0.991727i \(0.540973\pi\)
\(972\) −16.0000 −0.513200
\(973\) 30.0000 0.961756
\(974\) 8.00000 0.256337
\(975\) −4.00000 −0.128103
\(976\) 2.00000 0.0640184
\(977\) 38.0000 1.21573 0.607864 0.794041i \(-0.292027\pi\)
0.607864 + 0.794041i \(0.292027\pi\)
\(978\) 16.0000 0.511624
\(979\) 30.0000 0.958804
\(980\) 2.00000 0.0638877
\(981\) −20.0000 −0.638551
\(982\) 12.0000 0.382935
\(983\) −11.0000 −0.350846 −0.175423 0.984493i \(-0.556129\pi\)
−0.175423 + 0.984493i \(0.556129\pi\)
\(984\) −2.00000 −0.0637577
\(985\) 3.00000 0.0955879
\(986\) −70.0000 −2.22925
\(987\) −24.0000 −0.763928
\(988\) 0 0
\(989\) −24.0000 −0.763156
\(990\) 6.00000 0.190693
\(991\) 7.00000 0.222362 0.111181 0.993800i \(-0.464537\pi\)
0.111181 + 0.993800i \(0.464537\pi\)
\(992\) 7.00000 0.222250
\(993\) 13.0000 0.412543
\(994\) −9.00000 −0.285463
\(995\) 5.00000 0.158511
\(996\) −14.0000 −0.443607
\(997\) 38.0000 1.20347 0.601736 0.798695i \(-0.294476\pi\)
0.601736 + 0.798695i \(0.294476\pi\)
\(998\) 20.0000 0.633089
\(999\) 40.0000 1.26554
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 \(a_p\))