Properties

Label 195.2.a.a.1.1
Level 195
Weight 2
Character 195.1
Self dual Yes
Analytic conductor 1.557
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 195 = 3 \cdot 5 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 195.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.55708283941\)
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 \(\chi\) = 195.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{3}\) \(-1.00000 q^{4}\) \(+1.00000 q^{5}\) \(-1.00000 q^{6}\) \(+3.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{3}\) \(-1.00000 q^{4}\) \(+1.00000 q^{5}\) \(-1.00000 q^{6}\) \(+3.00000 q^{8}\) \(+1.00000 q^{9}\) \(-1.00000 q^{10}\) \(+4.00000 q^{11}\) \(-1.00000 q^{12}\) \(+1.00000 q^{13}\) \(+1.00000 q^{15}\) \(-1.00000 q^{16}\) \(+2.00000 q^{17}\) \(-1.00000 q^{18}\) \(-4.00000 q^{19}\) \(-1.00000 q^{20}\) \(-4.00000 q^{22}\) \(+8.00000 q^{23}\) \(+3.00000 q^{24}\) \(+1.00000 q^{25}\) \(-1.00000 q^{26}\) \(+1.00000 q^{27}\) \(-2.00000 q^{29}\) \(-1.00000 q^{30}\) \(-8.00000 q^{31}\) \(-5.00000 q^{32}\) \(+4.00000 q^{33}\) \(-2.00000 q^{34}\) \(-1.00000 q^{36}\) \(+6.00000 q^{37}\) \(+4.00000 q^{38}\) \(+1.00000 q^{39}\) \(+3.00000 q^{40}\) \(-6.00000 q^{41}\) \(-4.00000 q^{43}\) \(-4.00000 q^{44}\) \(+1.00000 q^{45}\) \(-8.00000 q^{46}\) \(-8.00000 q^{47}\) \(-1.00000 q^{48}\) \(-7.00000 q^{49}\) \(-1.00000 q^{50}\) \(+2.00000 q^{51}\) \(-1.00000 q^{52}\) \(+6.00000 q^{53}\) \(-1.00000 q^{54}\) \(+4.00000 q^{55}\) \(-4.00000 q^{57}\) \(+2.00000 q^{58}\) \(-12.0000 q^{59}\) \(-1.00000 q^{60}\) \(-2.00000 q^{61}\) \(+8.00000 q^{62}\) \(+7.00000 q^{64}\) \(+1.00000 q^{65}\) \(-4.00000 q^{66}\) \(-4.00000 q^{67}\) \(-2.00000 q^{68}\) \(+8.00000 q^{69}\) \(+3.00000 q^{72}\) \(-6.00000 q^{73}\) \(-6.00000 q^{74}\) \(+1.00000 q^{75}\) \(+4.00000 q^{76}\) \(-1.00000 q^{78}\) \(+16.0000 q^{79}\) \(-1.00000 q^{80}\) \(+1.00000 q^{81}\) \(+6.00000 q^{82}\) \(-4.00000 q^{83}\) \(+2.00000 q^{85}\) \(+4.00000 q^{86}\) \(-2.00000 q^{87}\) \(+12.0000 q^{88}\) \(+10.0000 q^{89}\) \(-1.00000 q^{90}\) \(-8.00000 q^{92}\) \(-8.00000 q^{93}\) \(+8.00000 q^{94}\) \(-4.00000 q^{95}\) \(-5.00000 q^{96}\) \(+18.0000 q^{97}\) \(+7.00000 q^{98}\) \(+4.00000 q^{99}\) \(+O(q^{100})\)

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 −0.353553 0.935414i \(-0.615027\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.00000 −0.500000
\(5\) 1.00000 0.447214
\(6\) −1.00000 −0.408248
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 3.00000 1.06066
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) 4.00000 1.20605 0.603023 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) −1.00000 −0.288675
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) −1.00000 −0.250000
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) −1.00000 −0.235702
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) −4.00000 −0.852803
\(23\) 8.00000 1.66812 0.834058 0.551677i \(-0.186012\pi\)
0.834058 + 0.551677i \(0.186012\pi\)
\(24\) 3.00000 0.612372
\(25\) 1.00000 0.200000
\(26\) −1.00000 −0.196116
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) −1.00000 −0.182574
\(31\) −8.00000 −1.43684 −0.718421 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) −5.00000 −0.883883
\(33\) 4.00000 0.696311
\(34\) −2.00000 −0.342997
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 6.00000 0.986394 0.493197 0.869918i \(-0.335828\pi\)
0.493197 + 0.869918i \(0.335828\pi\)
\(38\) 4.00000 0.648886
\(39\) 1.00000 0.160128
\(40\) 3.00000 0.474342
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) −4.00000 −0.603023
\(45\) 1.00000 0.149071
\(46\) −8.00000 −1.17954
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) −1.00000 −0.144338
\(49\) −7.00000 −1.00000
\(50\) −1.00000 −0.141421
\(51\) 2.00000 0.280056
\(52\) −1.00000 −0.138675
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) −1.00000 −0.136083
\(55\) 4.00000 0.539360
\(56\) 0 0
\(57\) −4.00000 −0.529813
\(58\) 2.00000 0.262613
\(59\) −12.0000 −1.56227 −0.781133 0.624364i \(-0.785358\pi\)
−0.781133 + 0.624364i \(0.785358\pi\)
\(60\) −1.00000 −0.129099
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 8.00000 1.01600
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) 1.00000 0.124035
\(66\) −4.00000 −0.492366
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) −2.00000 −0.242536
\(69\) 8.00000 0.963087
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 3.00000 0.353553
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) −6.00000 −0.697486
\(75\) 1.00000 0.115470
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) −1.00000 −0.113228
\(79\) 16.0000 1.80014 0.900070 0.435745i \(-0.143515\pi\)
0.900070 + 0.435745i \(0.143515\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) 6.00000 0.662589
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) 2.00000 0.216930
\(86\) 4.00000 0.431331
\(87\) −2.00000 −0.214423
\(88\) 12.0000 1.27920
\(89\) 10.0000 1.06000 0.529999 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) −1.00000 −0.105409
\(91\) 0 0
\(92\) −8.00000 −0.834058
\(93\) −8.00000 −0.829561
\(94\) 8.00000 0.825137
\(95\) −4.00000 −0.410391
\(96\) −5.00000 −0.510310
\(97\) 18.0000 1.82762 0.913812 0.406138i \(-0.133125\pi\)
0.913812 + 0.406138i \(0.133125\pi\)
\(98\) 7.00000 0.707107
\(99\) 4.00000 0.402015
\(100\) −1.00000 −0.100000
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) −2.00000 −0.198030
\(103\) −8.00000 −0.788263 −0.394132 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(104\) 3.00000 0.294174
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) −4.00000 −0.381385
\(111\) 6.00000 0.569495
\(112\) 0 0
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 4.00000 0.374634
\(115\) 8.00000 0.746004
\(116\) 2.00000 0.185695
\(117\) 1.00000 0.0924500
\(118\) 12.0000 1.10469
\(119\) 0 0
\(120\) 3.00000 0.273861
\(121\) 5.00000 0.454545
\(122\) 2.00000 0.181071
\(123\) −6.00000 −0.541002
\(124\) 8.00000 0.718421
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 3.00000 0.265165
\(129\) −4.00000 −0.352180
\(130\) −1.00000 −0.0877058
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) −4.00000 −0.348155
\(133\) 0 0
\(134\) 4.00000 0.345547
\(135\) 1.00000 0.0860663
\(136\) 6.00000 0.514496
\(137\) −6.00000 −0.512615 −0.256307 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) −8.00000 −0.681005
\(139\) −20.0000 −1.69638 −0.848189 0.529694i \(-0.822307\pi\)
−0.848189 + 0.529694i \(0.822307\pi\)
\(140\) 0 0
\(141\) −8.00000 −0.673722
\(142\) 0 0
\(143\) 4.00000 0.334497
\(144\) −1.00000 −0.0833333
\(145\) −2.00000 −0.166091
\(146\) 6.00000 0.496564
\(147\) −7.00000 −0.577350
\(148\) −6.00000 −0.493197
\(149\) −10.0000 −0.819232 −0.409616 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) −1.00000 −0.0816497
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) −12.0000 −0.973329
\(153\) 2.00000 0.161690
\(154\) 0 0
\(155\) −8.00000 −0.642575
\(156\) −1.00000 −0.0800641
\(157\) −2.00000 −0.159617 −0.0798087 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) −16.0000 −1.27289
\(159\) 6.00000 0.475831
\(160\) −5.00000 −0.395285
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) −20.0000 −1.56652 −0.783260 0.621694i \(-0.786445\pi\)
−0.783260 + 0.621694i \(0.786445\pi\)
\(164\) 6.00000 0.468521
\(165\) 4.00000 0.311400
\(166\) 4.00000 0.310460
\(167\) 16.0000 1.23812 0.619059 0.785345i \(-0.287514\pi\)
0.619059 + 0.785345i \(0.287514\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −2.00000 −0.153393
\(171\) −4.00000 −0.305888
\(172\) 4.00000 0.304997
\(173\) −2.00000 −0.152057 −0.0760286 0.997106i \(-0.524224\pi\)
−0.0760286 + 0.997106i \(0.524224\pi\)
\(174\) 2.00000 0.151620
\(175\) 0 0
\(176\) −4.00000 −0.301511
\(177\) −12.0000 −0.901975
\(178\) −10.0000 −0.749532
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) −1.00000 −0.0745356
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) 0 0
\(183\) −2.00000 −0.147844
\(184\) 24.0000 1.76930
\(185\) 6.00000 0.441129
\(186\) 8.00000 0.586588
\(187\) 8.00000 0.585018
\(188\) 8.00000 0.583460
\(189\) 0 0
\(190\) 4.00000 0.290191
\(191\) 16.0000 1.15772 0.578860 0.815427i \(-0.303498\pi\)
0.578860 + 0.815427i \(0.303498\pi\)
\(192\) 7.00000 0.505181
\(193\) −14.0000 −1.00774 −0.503871 0.863779i \(-0.668091\pi\)
−0.503871 + 0.863779i \(0.668091\pi\)
\(194\) −18.0000 −1.29232
\(195\) 1.00000 0.0716115
\(196\) 7.00000 0.500000
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) −4.00000 −0.284268
\(199\) −8.00000 −0.567105 −0.283552 0.958957i \(-0.591513\pi\)
−0.283552 + 0.958957i \(0.591513\pi\)
\(200\) 3.00000 0.212132
\(201\) −4.00000 −0.282138
\(202\) −6.00000 −0.422159
\(203\) 0 0
\(204\) −2.00000 −0.140028
\(205\) −6.00000 −0.419058
\(206\) 8.00000 0.557386
\(207\) 8.00000 0.556038
\(208\) −1.00000 −0.0693375
\(209\) −16.0000 −1.10674
\(210\) 0 0
\(211\) 20.0000 1.37686 0.688428 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) −6.00000 −0.412082
\(213\) 0 0
\(214\) −12.0000 −0.820303
\(215\) −4.00000 −0.272798
\(216\) 3.00000 0.204124
\(217\) 0 0
\(218\) 2.00000 0.135457
\(219\) −6.00000 −0.405442
\(220\) −4.00000 −0.269680
\(221\) 2.00000 0.134535
\(222\) −6.00000 −0.402694
\(223\) −24.0000 −1.60716 −0.803579 0.595198i \(-0.797074\pi\)
−0.803579 + 0.595198i \(0.797074\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) −2.00000 −0.133038
\(227\) 12.0000 0.796468 0.398234 0.917284i \(-0.369623\pi\)
0.398234 + 0.917284i \(0.369623\pi\)
\(228\) 4.00000 0.264906
\(229\) 22.0000 1.45380 0.726900 0.686743i \(-0.240960\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) −8.00000 −0.527504
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) 26.0000 1.70332 0.851658 0.524097i \(-0.175597\pi\)
0.851658 + 0.524097i \(0.175597\pi\)
\(234\) −1.00000 −0.0653720
\(235\) −8.00000 −0.521862
\(236\) 12.0000 0.781133
\(237\) 16.0000 1.03931
\(238\) 0 0
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) −1.00000 −0.0645497
\(241\) −14.0000 −0.901819 −0.450910 0.892570i \(-0.648900\pi\)
−0.450910 + 0.892570i \(0.648900\pi\)
\(242\) −5.00000 −0.321412
\(243\) 1.00000 0.0641500
\(244\) 2.00000 0.128037
\(245\) −7.00000 −0.447214
\(246\) 6.00000 0.382546
\(247\) −4.00000 −0.254514
\(248\) −24.0000 −1.52400
\(249\) −4.00000 −0.253490
\(250\) −1.00000 −0.0632456
\(251\) −4.00000 −0.252478 −0.126239 0.992000i \(-0.540291\pi\)
−0.126239 + 0.992000i \(0.540291\pi\)
\(252\) 0 0
\(253\) 32.0000 2.01182
\(254\) 16.0000 1.00393
\(255\) 2.00000 0.125245
\(256\) −17.0000 −1.06250
\(257\) 18.0000 1.12281 0.561405 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) 4.00000 0.249029
\(259\) 0 0
\(260\) −1.00000 −0.0620174
\(261\) −2.00000 −0.123797
\(262\) 12.0000 0.741362
\(263\) −24.0000 −1.47990 −0.739952 0.672660i \(-0.765152\pi\)
−0.739952 + 0.672660i \(0.765152\pi\)
\(264\) 12.0000 0.738549
\(265\) 6.00000 0.368577
\(266\) 0 0
\(267\) 10.0000 0.611990
\(268\) 4.00000 0.244339
\(269\) 14.0000 0.853595 0.426798 0.904347i \(-0.359642\pi\)
0.426798 + 0.904347i \(0.359642\pi\)
\(270\) −1.00000 −0.0608581
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) −2.00000 −0.121268
\(273\) 0 0
\(274\) 6.00000 0.362473
\(275\) 4.00000 0.241209
\(276\) −8.00000 −0.481543
\(277\) −10.0000 −0.600842 −0.300421 0.953807i \(-0.597127\pi\)
−0.300421 + 0.953807i \(0.597127\pi\)
\(278\) 20.0000 1.19952
\(279\) −8.00000 −0.478947
\(280\) 0 0
\(281\) −22.0000 −1.31241 −0.656205 0.754583i \(-0.727839\pi\)
−0.656205 + 0.754583i \(0.727839\pi\)
\(282\) 8.00000 0.476393
\(283\) −20.0000 −1.18888 −0.594438 0.804141i \(-0.702626\pi\)
−0.594438 + 0.804141i \(0.702626\pi\)
\(284\) 0 0
\(285\) −4.00000 −0.236940
\(286\) −4.00000 −0.236525
\(287\) 0 0
\(288\) −5.00000 −0.294628
\(289\) −13.0000 −0.764706
\(290\) 2.00000 0.117444
\(291\) 18.0000 1.05518
\(292\) 6.00000 0.351123
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 7.00000 0.408248
\(295\) −12.0000 −0.698667
\(296\) 18.0000 1.04623
\(297\) 4.00000 0.232104
\(298\) 10.0000 0.579284
\(299\) 8.00000 0.462652
\(300\) −1.00000 −0.0577350
\(301\) 0 0
\(302\) 0 0
\(303\) 6.00000 0.344691
\(304\) 4.00000 0.229416
\(305\) −2.00000 −0.114520
\(306\) −2.00000 −0.114332
\(307\) −4.00000 −0.228292 −0.114146 0.993464i \(-0.536413\pi\)
−0.114146 + 0.993464i \(0.536413\pi\)
\(308\) 0 0
\(309\) −8.00000 −0.455104
\(310\) 8.00000 0.454369
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 3.00000 0.169842
\(313\) 26.0000 1.46961 0.734803 0.678280i \(-0.237274\pi\)
0.734803 + 0.678280i \(0.237274\pi\)
\(314\) 2.00000 0.112867
\(315\) 0 0
\(316\) −16.0000 −0.900070
\(317\) 30.0000 1.68497 0.842484 0.538721i \(-0.181092\pi\)
0.842484 + 0.538721i \(0.181092\pi\)
\(318\) −6.00000 −0.336463
\(319\) −8.00000 −0.447914
\(320\) 7.00000 0.391312
\(321\) 12.0000 0.669775
\(322\) 0 0
\(323\) −8.00000 −0.445132
\(324\) −1.00000 −0.0555556
\(325\) 1.00000 0.0554700
\(326\) 20.0000 1.10770
\(327\) −2.00000 −0.110600
\(328\) −18.0000 −0.993884
\(329\) 0 0
\(330\) −4.00000 −0.220193
\(331\) 20.0000 1.09930 0.549650 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) 4.00000 0.219529
\(333\) 6.00000 0.328798
\(334\) −16.0000 −0.875481
\(335\) −4.00000 −0.218543
\(336\) 0 0
\(337\) −14.0000 −0.762629 −0.381314 0.924445i \(-0.624528\pi\)
−0.381314 + 0.924445i \(0.624528\pi\)
\(338\) −1.00000 −0.0543928
\(339\) 2.00000 0.108625
\(340\) −2.00000 −0.108465
\(341\) −32.0000 −1.73290
\(342\) 4.00000 0.216295
\(343\) 0 0
\(344\) −12.0000 −0.646997
\(345\) 8.00000 0.430706
\(346\) 2.00000 0.107521
\(347\) −4.00000 −0.214731 −0.107366 0.994220i \(-0.534242\pi\)
−0.107366 + 0.994220i \(0.534242\pi\)
\(348\) 2.00000 0.107211
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) 1.00000 0.0533761
\(352\) −20.0000 −1.06600
\(353\) −14.0000 −0.745145 −0.372572 0.928003i \(-0.621524\pi\)
−0.372572 + 0.928003i \(0.621524\pi\)
\(354\) 12.0000 0.637793
\(355\) 0 0
\(356\) −10.0000 −0.529999
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) 16.0000 0.844448 0.422224 0.906492i \(-0.361250\pi\)
0.422224 + 0.906492i \(0.361250\pi\)
\(360\) 3.00000 0.158114
\(361\) −3.00000 −0.157895
\(362\) −22.0000 −1.15629
\(363\) 5.00000 0.262432
\(364\) 0 0
\(365\) −6.00000 −0.314054
\(366\) 2.00000 0.104542
\(367\) −16.0000 −0.835193 −0.417597 0.908633i \(-0.637127\pi\)
−0.417597 + 0.908633i \(0.637127\pi\)
\(368\) −8.00000 −0.417029
\(369\) −6.00000 −0.312348
\(370\) −6.00000 −0.311925
\(371\) 0 0
\(372\) 8.00000 0.414781
\(373\) 22.0000 1.13912 0.569558 0.821951i \(-0.307114\pi\)
0.569558 + 0.821951i \(0.307114\pi\)
\(374\) −8.00000 −0.413670
\(375\) 1.00000 0.0516398
\(376\) −24.0000 −1.23771
\(377\) −2.00000 −0.103005
\(378\) 0 0
\(379\) 36.0000 1.84920 0.924598 0.380945i \(-0.124401\pi\)
0.924598 + 0.380945i \(0.124401\pi\)
\(380\) 4.00000 0.205196
\(381\) −16.0000 −0.819705
\(382\) −16.0000 −0.818631
\(383\) 24.0000 1.22634 0.613171 0.789950i \(-0.289894\pi\)
0.613171 + 0.789950i \(0.289894\pi\)
\(384\) 3.00000 0.153093
\(385\) 0 0
\(386\) 14.0000 0.712581
\(387\) −4.00000 −0.203331
\(388\) −18.0000 −0.913812
\(389\) 6.00000 0.304212 0.152106 0.988364i \(-0.451394\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(390\) −1.00000 −0.0506370
\(391\) 16.0000 0.809155
\(392\) −21.0000 −1.06066
\(393\) −12.0000 −0.605320
\(394\) −6.00000 −0.302276
\(395\) 16.0000 0.805047
\(396\) −4.00000 −0.201008
\(397\) 14.0000 0.702640 0.351320 0.936255i \(-0.385733\pi\)
0.351320 + 0.936255i \(0.385733\pi\)
\(398\) 8.00000 0.401004
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) −30.0000 −1.49813 −0.749064 0.662497i \(-0.769497\pi\)
−0.749064 + 0.662497i \(0.769497\pi\)
\(402\) 4.00000 0.199502
\(403\) −8.00000 −0.398508
\(404\) −6.00000 −0.298511
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 24.0000 1.18964
\(408\) 6.00000 0.297044
\(409\) −38.0000 −1.87898 −0.939490 0.342578i \(-0.888700\pi\)
−0.939490 + 0.342578i \(0.888700\pi\)
\(410\) 6.00000 0.296319
\(411\) −6.00000 −0.295958
\(412\) 8.00000 0.394132
\(413\) 0 0
\(414\) −8.00000 −0.393179
\(415\) −4.00000 −0.196352
\(416\) −5.00000 −0.245145
\(417\) −20.0000 −0.979404
\(418\) 16.0000 0.782586
\(419\) 20.0000 0.977064 0.488532 0.872546i \(-0.337533\pi\)
0.488532 + 0.872546i \(0.337533\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) −20.0000 −0.973585
\(423\) −8.00000 −0.388973
\(424\) 18.0000 0.874157
\(425\) 2.00000 0.0970143
\(426\) 0 0
\(427\) 0 0
\(428\) −12.0000 −0.580042
\(429\) 4.00000 0.193122
\(430\) 4.00000 0.192897
\(431\) 8.00000 0.385346 0.192673 0.981263i \(-0.438284\pi\)
0.192673 + 0.981263i \(0.438284\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 18.0000 0.865025 0.432512 0.901628i \(-0.357627\pi\)
0.432512 + 0.901628i \(0.357627\pi\)
\(434\) 0 0
\(435\) −2.00000 −0.0958927
\(436\) 2.00000 0.0957826
\(437\) −32.0000 −1.53077
\(438\) 6.00000 0.286691
\(439\) −24.0000 −1.14546 −0.572729 0.819745i \(-0.694115\pi\)
−0.572729 + 0.819745i \(0.694115\pi\)
\(440\) 12.0000 0.572078
\(441\) −7.00000 −0.333333
\(442\) −2.00000 −0.0951303
\(443\) −4.00000 −0.190046 −0.0950229 0.995475i \(-0.530292\pi\)
−0.0950229 + 0.995475i \(0.530292\pi\)
\(444\) −6.00000 −0.284747
\(445\) 10.0000 0.474045
\(446\) 24.0000 1.13643
\(447\) −10.0000 −0.472984
\(448\) 0 0
\(449\) 18.0000 0.849473 0.424736 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) −1.00000 −0.0471405
\(451\) −24.0000 −1.13012
\(452\) −2.00000 −0.0940721
\(453\) 0 0
\(454\) −12.0000 −0.563188
\(455\) 0 0
\(456\) −12.0000 −0.561951
\(457\) 26.0000 1.21623 0.608114 0.793849i \(-0.291926\pi\)
0.608114 + 0.793849i \(0.291926\pi\)
\(458\) −22.0000 −1.02799
\(459\) 2.00000 0.0933520
\(460\) −8.00000 −0.373002
\(461\) −18.0000 −0.838344 −0.419172 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) 2.00000 0.0928477
\(465\) −8.00000 −0.370991
\(466\) −26.0000 −1.20443
\(467\) 4.00000 0.185098 0.0925490 0.995708i \(-0.470499\pi\)
0.0925490 + 0.995708i \(0.470499\pi\)
\(468\) −1.00000 −0.0462250
\(469\) 0 0
\(470\) 8.00000 0.369012
\(471\) −2.00000 −0.0921551
\(472\) −36.0000 −1.65703
\(473\) −16.0000 −0.735681
\(474\) −16.0000 −0.734904
\(475\) −4.00000 −0.183533
\(476\) 0 0
\(477\) 6.00000 0.274721
\(478\) 24.0000 1.09773
\(479\) 8.00000 0.365529 0.182765 0.983157i \(-0.441495\pi\)
0.182765 + 0.983157i \(0.441495\pi\)
\(480\) −5.00000 −0.228218
\(481\) 6.00000 0.273576
\(482\) 14.0000 0.637683
\(483\) 0 0
\(484\) −5.00000 −0.227273
\(485\) 18.0000 0.817338
\(486\) −1.00000 −0.0453609
\(487\) 16.0000 0.725029 0.362515 0.931978i \(-0.381918\pi\)
0.362515 + 0.931978i \(0.381918\pi\)
\(488\) −6.00000 −0.271607
\(489\) −20.0000 −0.904431
\(490\) 7.00000 0.316228
\(491\) −20.0000 −0.902587 −0.451294 0.892375i \(-0.649037\pi\)
−0.451294 + 0.892375i \(0.649037\pi\)
\(492\) 6.00000 0.270501
\(493\) −4.00000 −0.180151
\(494\) 4.00000 0.179969
\(495\) 4.00000 0.179787
\(496\) 8.00000 0.359211
\(497\) 0 0
\(498\) 4.00000 0.179244
\(499\) 28.0000 1.25345 0.626726 0.779240i \(-0.284395\pi\)
0.626726 + 0.779240i \(0.284395\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 16.0000 0.714827
\(502\) 4.00000 0.178529
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) 6.00000 0.266996
\(506\) −32.0000 −1.42257
\(507\) 1.00000 0.0444116
\(508\) 16.0000 0.709885
\(509\) 30.0000 1.32973 0.664863 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(510\) −2.00000 −0.0885615
\(511\) 0 0
\(512\) 11.0000 0.486136
\(513\) −4.00000 −0.176604
\(514\) −18.0000 −0.793946
\(515\) −8.00000 −0.352522
\(516\) 4.00000 0.176090
\(517\) −32.0000 −1.40736
\(518\) 0 0
\(519\) −2.00000 −0.0877903
\(520\) 3.00000 0.131559
\(521\) −22.0000 −0.963837 −0.481919 0.876216i \(-0.660060\pi\)
−0.481919 + 0.876216i \(0.660060\pi\)
\(522\) 2.00000 0.0875376
\(523\) −20.0000 −0.874539 −0.437269 0.899331i \(-0.644054\pi\)
−0.437269 + 0.899331i \(0.644054\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) 24.0000 1.04645
\(527\) −16.0000 −0.696971
\(528\) −4.00000 −0.174078
\(529\) 41.0000 1.78261
\(530\) −6.00000 −0.260623
\(531\) −12.0000 −0.520756
\(532\) 0 0
\(533\) −6.00000 −0.259889
\(534\) −10.0000 −0.432742
\(535\) 12.0000 0.518805
\(536\) −12.0000 −0.518321
\(537\) −12.0000 −0.517838
\(538\) −14.0000 −0.603583
\(539\) −28.0000 −1.20605
\(540\) −1.00000 −0.0430331
\(541\) 14.0000 0.601907 0.300954 0.953639i \(-0.402695\pi\)
0.300954 + 0.953639i \(0.402695\pi\)
\(542\) 8.00000 0.343629
\(543\) 22.0000 0.944110
\(544\) −10.0000 −0.428746
\(545\) −2.00000 −0.0856706
\(546\) 0 0
\(547\) 36.0000 1.53925 0.769624 0.638497i \(-0.220443\pi\)
0.769624 + 0.638497i \(0.220443\pi\)
\(548\) 6.00000 0.256307
\(549\) −2.00000 −0.0853579
\(550\) −4.00000 −0.170561
\(551\) 8.00000 0.340811
\(552\) 24.0000 1.02151
\(553\) 0 0
\(554\) 10.0000 0.424859
\(555\) 6.00000 0.254686
\(556\) 20.0000 0.848189
\(557\) −18.0000 −0.762684 −0.381342 0.924434i \(-0.624538\pi\)
−0.381342 + 0.924434i \(0.624538\pi\)
\(558\) 8.00000 0.338667
\(559\) −4.00000 −0.169182
\(560\) 0 0
\(561\) 8.00000 0.337760
\(562\) 22.0000 0.928014
\(563\) 4.00000 0.168580 0.0842900 0.996441i \(-0.473138\pi\)
0.0842900 + 0.996441i \(0.473138\pi\)
\(564\) 8.00000 0.336861
\(565\) 2.00000 0.0841406
\(566\) 20.0000 0.840663
\(567\) 0 0
\(568\) 0 0
\(569\) −38.0000 −1.59304 −0.796521 0.604610i \(-0.793329\pi\)
−0.796521 + 0.604610i \(0.793329\pi\)
\(570\) 4.00000 0.167542
\(571\) 44.0000 1.84134 0.920671 0.390339i \(-0.127642\pi\)
0.920671 + 0.390339i \(0.127642\pi\)
\(572\) −4.00000 −0.167248
\(573\) 16.0000 0.668410
\(574\) 0 0
\(575\) 8.00000 0.333623
\(576\) 7.00000 0.291667
\(577\) 18.0000 0.749350 0.374675 0.927156i \(-0.377754\pi\)
0.374675 + 0.927156i \(0.377754\pi\)
\(578\) 13.0000 0.540729
\(579\) −14.0000 −0.581820
\(580\) 2.00000 0.0830455
\(581\) 0 0
\(582\) −18.0000 −0.746124
\(583\) 24.0000 0.993978
\(584\) −18.0000 −0.744845
\(585\) 1.00000 0.0413449
\(586\) −6.00000 −0.247858
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 7.00000 0.288675
\(589\) 32.0000 1.31854
\(590\) 12.0000 0.494032
\(591\) 6.00000 0.246807
\(592\) −6.00000 −0.246598
\(593\) −30.0000 −1.23195 −0.615976 0.787765i \(-0.711238\pi\)
−0.615976 + 0.787765i \(0.711238\pi\)
\(594\) −4.00000 −0.164122
\(595\) 0 0
\(596\) 10.0000 0.409616
\(597\) −8.00000 −0.327418
\(598\) −8.00000 −0.327144
\(599\) 40.0000 1.63436 0.817178 0.576386i \(-0.195537\pi\)
0.817178 + 0.576386i \(0.195537\pi\)
\(600\) 3.00000 0.122474
\(601\) −38.0000 −1.55005 −0.775026 0.631929i \(-0.782263\pi\)
−0.775026 + 0.631929i \(0.782263\pi\)
\(602\) 0 0
\(603\) −4.00000 −0.162893
\(604\) 0 0
\(605\) 5.00000 0.203279
\(606\) −6.00000 −0.243733
\(607\) 32.0000 1.29884 0.649420 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) 20.0000 0.811107
\(609\) 0 0
\(610\) 2.00000 0.0809776
\(611\) −8.00000 −0.323645
\(612\) −2.00000 −0.0808452
\(613\) 6.00000 0.242338 0.121169 0.992632i \(-0.461336\pi\)
0.121169 + 0.992632i \(0.461336\pi\)
\(614\) 4.00000 0.161427
\(615\) −6.00000 −0.241943
\(616\) 0 0
\(617\) −38.0000 −1.52982 −0.764911 0.644136i \(-0.777217\pi\)
−0.764911 + 0.644136i \(0.777217\pi\)
\(618\) 8.00000 0.321807
\(619\) 4.00000 0.160774 0.0803868 0.996764i \(-0.474384\pi\)
0.0803868 + 0.996764i \(0.474384\pi\)
\(620\) 8.00000 0.321288
\(621\) 8.00000 0.321029
\(622\) −24.0000 −0.962312
\(623\) 0 0
\(624\) −1.00000 −0.0400320
\(625\) 1.00000 0.0400000
\(626\) −26.0000 −1.03917
\(627\) −16.0000 −0.638978
\(628\) 2.00000 0.0798087
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 48.0000 1.90934
\(633\) 20.0000 0.794929
\(634\) −30.0000 −1.19145
\(635\) −16.0000 −0.634941
\(636\) −6.00000 −0.237915
\(637\) −7.00000 −0.277350
\(638\) 8.00000 0.316723
\(639\) 0 0
\(640\) 3.00000 0.118585
\(641\) −30.0000 −1.18493 −0.592464 0.805597i \(-0.701845\pi\)
−0.592464 + 0.805597i \(0.701845\pi\)
\(642\) −12.0000 −0.473602
\(643\) 28.0000 1.10421 0.552106 0.833774i \(-0.313824\pi\)
0.552106 + 0.833774i \(0.313824\pi\)
\(644\) 0 0
\(645\) −4.00000 −0.157500
\(646\) 8.00000 0.314756
\(647\) 24.0000 0.943537 0.471769 0.881722i \(-0.343616\pi\)
0.471769 + 0.881722i \(0.343616\pi\)
\(648\) 3.00000 0.117851
\(649\) −48.0000 −1.88416
\(650\) −1.00000 −0.0392232
\(651\) 0 0
\(652\) 20.0000 0.783260
\(653\) 30.0000 1.17399 0.586995 0.809590i \(-0.300311\pi\)
0.586995 + 0.809590i \(0.300311\pi\)
\(654\) 2.00000 0.0782062
\(655\) −12.0000 −0.468879
\(656\) 6.00000 0.234261
\(657\) −6.00000 −0.234082
\(658\) 0 0
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) −4.00000 −0.155700
\(661\) 38.0000 1.47803 0.739014 0.673690i \(-0.235292\pi\)
0.739014 + 0.673690i \(0.235292\pi\)
\(662\) −20.0000 −0.777322
\(663\) 2.00000 0.0776736
\(664\) −12.0000 −0.465690
\(665\) 0 0
\(666\) −6.00000 −0.232495
\(667\) −16.0000 −0.619522
\(668\) −16.0000 −0.619059
\(669\) −24.0000 −0.927894
\(670\) 4.00000 0.154533
\(671\) −8.00000 −0.308837
\(672\) 0 0
\(673\) 34.0000 1.31060 0.655302 0.755367i \(-0.272541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) 14.0000 0.539260
\(675\) 1.00000 0.0384900
\(676\) −1.00000 −0.0384615
\(677\) −10.0000 −0.384331 −0.192166 0.981363i \(-0.561551\pi\)
−0.192166 + 0.981363i \(0.561551\pi\)
\(678\) −2.00000 −0.0768095
\(679\) 0 0
\(680\) 6.00000 0.230089
\(681\) 12.0000 0.459841
\(682\) 32.0000 1.22534
\(683\) 4.00000 0.153056 0.0765279 0.997067i \(-0.475617\pi\)
0.0765279 + 0.997067i \(0.475617\pi\)
\(684\) 4.00000 0.152944
\(685\) −6.00000 −0.229248
\(686\) 0 0
\(687\) 22.0000 0.839352
\(688\) 4.00000 0.152499
\(689\) 6.00000 0.228582
\(690\) −8.00000 −0.304555
\(691\) −36.0000 −1.36950 −0.684752 0.728776i \(-0.740090\pi\)
−0.684752 + 0.728776i \(0.740090\pi\)
\(692\) 2.00000 0.0760286
\(693\) 0 0
\(694\) 4.00000 0.151838
\(695\) −20.0000 −0.758643
\(696\) −6.00000 −0.227429
\(697\) −12.0000 −0.454532
\(698\) −14.0000 −0.529908
\(699\) 26.0000 0.983410
\(700\) 0 0
\(701\) −34.0000 −1.28416 −0.642081 0.766637i \(-0.721929\pi\)
−0.642081 + 0.766637i \(0.721929\pi\)
\(702\) −1.00000 −0.0377426
\(703\) −24.0000 −0.905177
\(704\) 28.0000 1.05529
\(705\) −8.00000 −0.301297
\(706\) 14.0000 0.526897
\(707\) 0 0
\(708\) 12.0000 0.450988
\(709\) −10.0000 −0.375558 −0.187779 0.982211i \(-0.560129\pi\)
−0.187779 + 0.982211i \(0.560129\pi\)
\(710\) 0 0
\(711\) 16.0000 0.600047
\(712\) 30.0000 1.12430
\(713\) −64.0000 −2.39682
\(714\) 0 0
\(715\) 4.00000 0.149592
\(716\) 12.0000 0.448461
\(717\) −24.0000 −0.896296
\(718\) −16.0000 −0.597115
\(719\) −48.0000 −1.79010 −0.895049 0.445968i \(-0.852860\pi\)
−0.895049 + 0.445968i \(0.852860\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 0 0
\(722\) 3.00000 0.111648
\(723\) −14.0000 −0.520666
\(724\) −22.0000 −0.817624
\(725\) −2.00000 −0.0742781
\(726\) −5.00000 −0.185567
\(727\) −24.0000 −0.890111 −0.445055 0.895503i \(-0.646816\pi\)
−0.445055 + 0.895503i \(0.646816\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 6.00000 0.222070
\(731\) −8.00000 −0.295891
\(732\) 2.00000 0.0739221
\(733\) 30.0000 1.10808 0.554038 0.832492i \(-0.313086\pi\)
0.554038 + 0.832492i \(0.313086\pi\)
\(734\) 16.0000 0.590571
\(735\) −7.00000 −0.258199
\(736\) −40.0000 −1.47442
\(737\) −16.0000 −0.589368
\(738\) 6.00000 0.220863
\(739\) −4.00000 −0.147142 −0.0735712 0.997290i \(-0.523440\pi\)
−0.0735712 + 0.997290i \(0.523440\pi\)
\(740\) −6.00000 −0.220564
\(741\) −4.00000 −0.146944
\(742\) 0 0
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) −24.0000 −0.879883
\(745\) −10.0000 −0.366372
\(746\) −22.0000 −0.805477
\(747\) −4.00000 −0.146352
\(748\) −8.00000 −0.292509
\(749\) 0 0
\(750\) −1.00000 −0.0365148
\(751\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 8.00000 0.291730
\(753\) −4.00000 −0.145768
\(754\) 2.00000 0.0728357
\(755\) 0 0
\(756\) 0 0
\(757\) −42.0000 −1.52652 −0.763258 0.646094i \(-0.776401\pi\)
−0.763258 + 0.646094i \(0.776401\pi\)
\(758\) −36.0000 −1.30758
\(759\) 32.0000 1.16153
\(760\) −12.0000 −0.435286
\(761\) 10.0000 0.362500 0.181250 0.983437i \(-0.441986\pi\)
0.181250 + 0.983437i \(0.441986\pi\)
\(762\) 16.0000 0.579619
\(763\) 0 0
\(764\) −16.0000 −0.578860
\(765\) 2.00000 0.0723102
\(766\) −24.0000 −0.867155
\(767\) −12.0000 −0.433295
\(768\) −17.0000 −0.613435
\(769\) −30.0000 −1.08183 −0.540914 0.841078i \(-0.681921\pi\)
−0.540914 + 0.841078i \(0.681921\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) 14.0000 0.503871
\(773\) 6.00000 0.215805 0.107903 0.994161i \(-0.465587\pi\)
0.107903 + 0.994161i \(0.465587\pi\)
\(774\) 4.00000 0.143777
\(775\) −8.00000 −0.287368
\(776\) 54.0000 1.93849
\(777\) 0 0
\(778\) −6.00000 −0.215110
\(779\) 24.0000 0.859889
\(780\) −1.00000 −0.0358057
\(781\) 0 0
\(782\) −16.0000 −0.572159
\(783\) −2.00000 −0.0714742
\(784\) 7.00000 0.250000
\(785\) −2.00000 −0.0713831
\(786\) 12.0000 0.428026
\(787\) −4.00000 −0.142585 −0.0712923 0.997455i \(-0.522712\pi\)
−0.0712923 + 0.997455i \(0.522712\pi\)
\(788\) −6.00000 −0.213741
\(789\) −24.0000 −0.854423
\(790\) −16.0000 −0.569254
\(791\) 0 0
\(792\) 12.0000 0.426401
\(793\) −2.00000 −0.0710221
\(794\) −14.0000 −0.496841
\(795\) 6.00000 0.212798
\(796\) 8.00000 0.283552
\(797\) 46.0000 1.62940 0.814702 0.579880i \(-0.196901\pi\)
0.814702 + 0.579880i \(0.196901\pi\)
\(798\) 0 0
\(799\) −16.0000 −0.566039
\(800\) −5.00000 −0.176777
\(801\) 10.0000 0.353333
\(802\) 30.0000 1.05934
\(803\) −24.0000 −0.846942
\(804\) 4.00000 0.141069
\(805\) 0 0
\(806\) 8.00000 0.281788
\(807\) 14.0000 0.492823
\(808\) 18.0000 0.633238
\(809\) 42.0000 1.47664 0.738321 0.674450i \(-0.235619\pi\)
0.738321 + 0.674450i \(0.235619\pi\)
\(810\) −1.00000 −0.0351364
\(811\) 20.0000 0.702295 0.351147 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) 0 0
\(813\) −8.00000 −0.280572
\(814\) −24.0000 −0.841200
\(815\) −20.0000 −0.700569
\(816\) −2.00000 −0.0700140
\(817\) 16.0000 0.559769
\(818\) 38.0000 1.32864
\(819\) 0 0
\(820\) 6.00000 0.209529
\(821\) 22.0000 0.767805 0.383903 0.923374i \(-0.374580\pi\)
0.383903 + 0.923374i \(0.374580\pi\)
\(822\) 6.00000 0.209274
\(823\) −24.0000 −0.836587 −0.418294 0.908312i \(-0.637372\pi\)
−0.418294 + 0.908312i \(0.637372\pi\)
\(824\) −24.0000 −0.836080
\(825\) 4.00000 0.139262
\(826\) 0 0
\(827\) −12.0000 −0.417281 −0.208640 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) −8.00000 −0.278019
\(829\) −34.0000 −1.18087 −0.590434 0.807086i \(-0.701044\pi\)
−0.590434 + 0.807086i \(0.701044\pi\)
\(830\) 4.00000 0.138842
\(831\) −10.0000 −0.346896
\(832\) 7.00000 0.242681
\(833\) −14.0000 −0.485071
\(834\) 20.0000 0.692543
\(835\) 16.0000 0.553703
\(836\) 16.0000 0.553372
\(837\) −8.00000 −0.276520
\(838\) −20.0000 −0.690889
\(839\) 16.0000 0.552381 0.276191 0.961103i \(-0.410928\pi\)
0.276191 + 0.961103i \(0.410928\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) 10.0000 0.344623
\(843\) −22.0000 −0.757720
\(844\) −20.0000 −0.688428
\(845\) 1.00000 0.0344010
\(846\) 8.00000 0.275046
\(847\) 0 0
\(848\) −6.00000 −0.206041
\(849\) −20.0000 −0.686398
\(850\) −2.00000 −0.0685994
\(851\) 48.0000 1.64542
\(852\) 0 0
\(853\) −42.0000 −1.43805 −0.719026 0.694983i \(-0.755412\pi\)
−0.719026 + 0.694983i \(0.755412\pi\)
\(854\) 0 0
\(855\) −4.00000 −0.136797
\(856\) 36.0000 1.23045
\(857\) 10.0000 0.341593 0.170797 0.985306i \(-0.445366\pi\)
0.170797 + 0.985306i \(0.445366\pi\)
\(858\) −4.00000 −0.136558
\(859\) −4.00000 −0.136478 −0.0682391 0.997669i \(-0.521738\pi\)
−0.0682391 + 0.997669i \(0.521738\pi\)
\(860\) 4.00000 0.136399
\(861\) 0 0
\(862\) −8.00000 −0.272481
\(863\) −40.0000 −1.36162 −0.680808 0.732462i \(-0.738371\pi\)
−0.680808 + 0.732462i \(0.738371\pi\)
\(864\) −5.00000 −0.170103
\(865\) −2.00000 −0.0680020
\(866\) −18.0000 −0.611665
\(867\) −13.0000 −0.441503
\(868\) 0 0
\(869\) 64.0000 2.17105
\(870\) 2.00000 0.0678064
\(871\) −4.00000 −0.135535
\(872\) −6.00000 −0.203186
\(873\) 18.0000 0.609208
\(874\) 32.0000 1.08242
\(875\) 0 0
\(876\) 6.00000 0.202721
\(877\) −50.0000 −1.68838 −0.844190 0.536044i \(-0.819918\pi\)
−0.844190 + 0.536044i \(0.819918\pi\)
\(878\) 24.0000 0.809961
\(879\) 6.00000 0.202375
\(880\) −4.00000 −0.134840
\(881\) −14.0000 −0.471672 −0.235836 0.971793i \(-0.575783\pi\)
−0.235836 + 0.971793i \(0.575783\pi\)
\(882\) 7.00000 0.235702
\(883\) 36.0000 1.21150 0.605748 0.795656i \(-0.292874\pi\)
0.605748 + 0.795656i \(0.292874\pi\)
\(884\) −2.00000 −0.0672673
\(885\) −12.0000 −0.403376
\(886\) 4.00000 0.134383
\(887\) 24.0000 0.805841 0.402921 0.915235i \(-0.367995\pi\)
0.402921 + 0.915235i \(0.367995\pi\)
\(888\) 18.0000 0.604040
\(889\) 0 0
\(890\) −10.0000 −0.335201
\(891\) 4.00000 0.134005
\(892\) 24.0000 0.803579
\(893\) 32.0000 1.07084
\(894\) 10.0000 0.334450
\(895\) −12.0000 −0.401116
\(896\) 0 0
\(897\) 8.00000 0.267112
\(898\) −18.0000 −0.600668
\(899\) 16.0000 0.533630
\(900\) −1.00000 −0.0333333
\(901\) 12.0000 0.399778
\(902\) 24.0000 0.799113
\(903\) 0 0
\(904\) 6.00000 0.199557
\(905\) 22.0000 0.731305
\(906\) 0 0
\(907\) −4.00000 −0.132818 −0.0664089 0.997792i \(-0.521154\pi\)
−0.0664089 + 0.997792i \(0.521154\pi\)
\(908\) −12.0000 −0.398234
\(909\) 6.00000 0.199007
\(910\) 0 0
\(911\) 32.0000 1.06021 0.530104 0.847933i \(-0.322153\pi\)
0.530104 + 0.847933i \(0.322153\pi\)
\(912\) 4.00000 0.132453
\(913\) −16.0000 −0.529523
\(914\) −26.0000 −0.860004
\(915\) −2.00000 −0.0661180
\(916\) −22.0000 −0.726900
\(917\) 0 0
\(918\) −2.00000 −0.0660098
\(919\) −40.0000 −1.31948 −0.659739 0.751495i \(-0.729333\pi\)
−0.659739 + 0.751495i \(0.729333\pi\)
\(920\) 24.0000 0.791257
\(921\) −4.00000 −0.131804
\(922\) 18.0000 0.592798
\(923\) 0 0
\(924\) 0 0
\(925\) 6.00000 0.197279
\(926\) −8.00000 −0.262896
\(927\) −8.00000 −0.262754
\(928\) 10.0000 0.328266
\(929\) 18.0000 0.590561 0.295280 0.955411i \(-0.404587\pi\)
0.295280 + 0.955411i \(0.404587\pi\)
\(930\) 8.00000 0.262330
\(931\) 28.0000 0.917663
\(932\) −26.0000 −0.851658
\(933\) 24.0000 0.785725
\(934\) −4.00000 −0.130884
\(935\) 8.00000 0.261628
\(936\) 3.00000 0.0980581
\(937\) −22.0000 −0.718709 −0.359354 0.933201i \(-0.617003\pi\)
−0.359354 + 0.933201i \(0.617003\pi\)
\(938\) 0 0
\(939\) 26.0000 0.848478
\(940\) 8.00000 0.260931
\(941\) 46.0000 1.49956 0.749779 0.661689i \(-0.230160\pi\)
0.749779 + 0.661689i \(0.230160\pi\)
\(942\) 2.00000 0.0651635
\(943\) −48.0000 −1.56310
\(944\) 12.0000 0.390567
\(945\) 0 0
\(946\) 16.0000 0.520205
\(947\) 12.0000 0.389948 0.194974 0.980808i \(-0.437538\pi\)
0.194974 + 0.980808i \(0.437538\pi\)
\(948\) −16.0000 −0.519656
\(949\) −6.00000 −0.194768
\(950\) 4.00000 0.129777
\(951\) 30.0000 0.972817
\(952\) 0 0
\(953\) 10.0000 0.323932 0.161966 0.986796i \(-0.448217\pi\)
0.161966 + 0.986796i \(0.448217\pi\)
\(954\) −6.00000 −0.194257
\(955\) 16.0000 0.517748
\(956\) 24.0000 0.776215
\(957\) −8.00000 −0.258603
\(958\) −8.00000 −0.258468
\(959\) 0 0
\(960\) 7.00000 0.225924
\(961\) 33.0000 1.06452
\(962\) −6.00000 −0.193448
\(963\) 12.0000 0.386695
\(964\) 14.0000 0.450910
\(965\) −14.0000 −0.450676
\(966\) 0 0
\(967\) −16.0000 −0.514525 −0.257263 0.966342i \(-0.582821\pi\)
−0.257263 + 0.966342i \(0.582821\pi\)
\(968\) 15.0000 0.482118
\(969\) −8.00000 −0.256997
\(970\) −18.0000 −0.577945
\(971\) −36.0000 −1.15529 −0.577647 0.816286i \(-0.696029\pi\)
−0.577647 + 0.816286i \(0.696029\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 0 0
\(974\) −16.0000 −0.512673
\(975\) 1.00000 0.0320256
\(976\) 2.00000 0.0640184
\(977\) −30.0000 −0.959785 −0.479893 0.877327i \(-0.659324\pi\)
−0.479893 + 0.877327i \(0.659324\pi\)
\(978\) 20.0000 0.639529
\(979\) 40.0000 1.27841
\(980\) 7.00000 0.223607
\(981\) −2.00000 −0.0638551
\(982\) 20.0000 0.638226
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) −18.0000 −0.573819
\(985\) 6.00000 0.191176
\(986\) 4.00000 0.127386
\(987\) 0 0
\(988\) 4.00000 0.127257
\(989\) −32.0000 −1.01754
\(990\) −4.00000 −0.127128
\(991\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(992\) 40.0000 1.27000
\(993\) 20.0000 0.634681
\(994\) 0 0
\(995\) −8.00000 −0.253617
\(996\) 4.00000 0.126745
\(997\) 38.0000 1.20347 0.601736 0.798695i \(-0.294476\pi\)
0.601736 + 0.798695i \(0.294476\pi\)
\(998\) −28.0000 −0.886325
\(999\) 6.00000 0.189832
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 \(a_p\))