Properties

Label 4008.2.a.l.1.6
Level 4008
Weight 2
Character 4008.1
Self dual Yes
Analytic conductor 32.004
Analytic rank 0
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4008 = 2^{3} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0040411301\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-0.619387\)
Character \(\chi\) = 4008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-0.619387 q^{5}\) \(+0.954126 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-0.619387 q^{5}\) \(+0.954126 q^{7}\) \(+1.00000 q^{9}\) \(+6.25107 q^{11}\) \(+2.92641 q^{13}\) \(-0.619387 q^{15}\) \(+5.33666 q^{17}\) \(+2.94423 q^{19}\) \(+0.954126 q^{21}\) \(-2.33637 q^{23}\) \(-4.61636 q^{25}\) \(+1.00000 q^{27}\) \(+4.47124 q^{29}\) \(-3.45595 q^{31}\) \(+6.25107 q^{33}\) \(-0.590974 q^{35}\) \(+4.26640 q^{37}\) \(+2.92641 q^{39}\) \(-10.8203 q^{41}\) \(-1.32390 q^{43}\) \(-0.619387 q^{45}\) \(+3.37095 q^{47}\) \(-6.08964 q^{49}\) \(+5.33666 q^{51}\) \(+5.72269 q^{53}\) \(-3.87184 q^{55}\) \(+2.94423 q^{57}\) \(-10.0347 q^{59}\) \(+11.8490 q^{61}\) \(+0.954126 q^{63}\) \(-1.81258 q^{65}\) \(+0.604492 q^{67}\) \(-2.33637 q^{69}\) \(-9.74739 q^{71}\) \(-11.1654 q^{73}\) \(-4.61636 q^{75}\) \(+5.96431 q^{77}\) \(+6.74411 q^{79}\) \(+1.00000 q^{81}\) \(+0.00272570 q^{83}\) \(-3.30546 q^{85}\) \(+4.47124 q^{87}\) \(+9.85457 q^{89}\) \(+2.79217 q^{91}\) \(-3.45595 q^{93}\) \(-1.82362 q^{95}\) \(-8.92479 q^{97}\) \(+6.25107 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut q^{11} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 7q^{23} \) \(\mathstrut +\mathstrut 18q^{25} \) \(\mathstrut +\mathstrut 12q^{27} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 33q^{31} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut +\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut +\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 4q^{45} \) \(\mathstrut +\mathstrut 18q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut +\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 20q^{53} \) \(\mathstrut +\mathstrut 39q^{55} \) \(\mathstrut +\mathstrut 12q^{57} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 10q^{61} \) \(\mathstrut +\mathstrut 11q^{63} \) \(\mathstrut +\mathstrut 9q^{67} \) \(\mathstrut +\mathstrut 7q^{69} \) \(\mathstrut +\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 18q^{75} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 12q^{81} \) \(\mathstrut +\mathstrut 26q^{83} \) \(\mathstrut +\mathstrut 15q^{85} \) \(\mathstrut +\mathstrut 5q^{87} \) \(\mathstrut -\mathstrut 15q^{89} \) \(\mathstrut +\mathstrut 11q^{91} \) \(\mathstrut +\mathstrut 33q^{93} \) \(\mathstrut +\mathstrut 3q^{95} \) \(\mathstrut +\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −0.619387 −0.276999 −0.138499 0.990363i \(-0.544228\pi\)
−0.138499 + 0.990363i \(0.544228\pi\)
\(6\) 0 0
\(7\) 0.954126 0.360626 0.180313 0.983609i \(-0.442289\pi\)
0.180313 + 0.983609i \(0.442289\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 6.25107 1.88477 0.942385 0.334531i \(-0.108578\pi\)
0.942385 + 0.334531i \(0.108578\pi\)
\(12\) 0 0
\(13\) 2.92641 0.811641 0.405820 0.913953i \(-0.366986\pi\)
0.405820 + 0.913953i \(0.366986\pi\)
\(14\) 0 0
\(15\) −0.619387 −0.159925
\(16\) 0 0
\(17\) 5.33666 1.29433 0.647165 0.762350i \(-0.275954\pi\)
0.647165 + 0.762350i \(0.275954\pi\)
\(18\) 0 0
\(19\) 2.94423 0.675454 0.337727 0.941244i \(-0.390342\pi\)
0.337727 + 0.941244i \(0.390342\pi\)
\(20\) 0 0
\(21\) 0.954126 0.208207
\(22\) 0 0
\(23\) −2.33637 −0.487167 −0.243583 0.969880i \(-0.578323\pi\)
−0.243583 + 0.969880i \(0.578323\pi\)
\(24\) 0 0
\(25\) −4.61636 −0.923272
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 4.47124 0.830289 0.415144 0.909756i \(-0.363731\pi\)
0.415144 + 0.909756i \(0.363731\pi\)
\(30\) 0 0
\(31\) −3.45595 −0.620707 −0.310353 0.950621i \(-0.600447\pi\)
−0.310353 + 0.950621i \(0.600447\pi\)
\(32\) 0 0
\(33\) 6.25107 1.08817
\(34\) 0 0
\(35\) −0.590974 −0.0998928
\(36\) 0 0
\(37\) 4.26640 0.701392 0.350696 0.936489i \(-0.385945\pi\)
0.350696 + 0.936489i \(0.385945\pi\)
\(38\) 0 0
\(39\) 2.92641 0.468601
\(40\) 0 0
\(41\) −10.8203 −1.68985 −0.844925 0.534885i \(-0.820355\pi\)
−0.844925 + 0.534885i \(0.820355\pi\)
\(42\) 0 0
\(43\) −1.32390 −0.201893 −0.100947 0.994892i \(-0.532187\pi\)
−0.100947 + 0.994892i \(0.532187\pi\)
\(44\) 0 0
\(45\) −0.619387 −0.0923328
\(46\) 0 0
\(47\) 3.37095 0.491704 0.245852 0.969307i \(-0.420932\pi\)
0.245852 + 0.969307i \(0.420932\pi\)
\(48\) 0 0
\(49\) −6.08964 −0.869949
\(50\) 0 0
\(51\) 5.33666 0.747282
\(52\) 0 0
\(53\) 5.72269 0.786072 0.393036 0.919523i \(-0.371425\pi\)
0.393036 + 0.919523i \(0.371425\pi\)
\(54\) 0 0
\(55\) −3.87184 −0.522078
\(56\) 0 0
\(57\) 2.94423 0.389973
\(58\) 0 0
\(59\) −10.0347 −1.30641 −0.653204 0.757182i \(-0.726575\pi\)
−0.653204 + 0.757182i \(0.726575\pi\)
\(60\) 0 0
\(61\) 11.8490 1.51711 0.758556 0.651608i \(-0.225905\pi\)
0.758556 + 0.651608i \(0.225905\pi\)
\(62\) 0 0
\(63\) 0.954126 0.120209
\(64\) 0 0
\(65\) −1.81258 −0.224823
\(66\) 0 0
\(67\) 0.604492 0.0738505 0.0369252 0.999318i \(-0.488244\pi\)
0.0369252 + 0.999318i \(0.488244\pi\)
\(68\) 0 0
\(69\) −2.33637 −0.281266
\(70\) 0 0
\(71\) −9.74739 −1.15680 −0.578401 0.815752i \(-0.696323\pi\)
−0.578401 + 0.815752i \(0.696323\pi\)
\(72\) 0 0
\(73\) −11.1654 −1.30681 −0.653404 0.757009i \(-0.726660\pi\)
−0.653404 + 0.757009i \(0.726660\pi\)
\(74\) 0 0
\(75\) −4.61636 −0.533051
\(76\) 0 0
\(77\) 5.96431 0.679697
\(78\) 0 0
\(79\) 6.74411 0.758772 0.379386 0.925239i \(-0.376135\pi\)
0.379386 + 0.925239i \(0.376135\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 0.00272570 0.000299184 0 0.000149592 1.00000i \(-0.499952\pi\)
0.000149592 1.00000i \(0.499952\pi\)
\(84\) 0 0
\(85\) −3.30546 −0.358528
\(86\) 0 0
\(87\) 4.47124 0.479367
\(88\) 0 0
\(89\) 9.85457 1.04458 0.522291 0.852767i \(-0.325077\pi\)
0.522291 + 0.852767i \(0.325077\pi\)
\(90\) 0 0
\(91\) 2.79217 0.292699
\(92\) 0 0
\(93\) −3.45595 −0.358365
\(94\) 0 0
\(95\) −1.82362 −0.187100
\(96\) 0 0
\(97\) −8.92479 −0.906175 −0.453088 0.891466i \(-0.649678\pi\)
−0.453088 + 0.891466i \(0.649678\pi\)
\(98\) 0 0
\(99\) 6.25107 0.628256
\(100\) 0 0
\(101\) 1.91531 0.190580 0.0952901 0.995450i \(-0.469622\pi\)
0.0952901 + 0.995450i \(0.469622\pi\)
\(102\) 0 0
\(103\) 5.90694 0.582028 0.291014 0.956719i \(-0.406007\pi\)
0.291014 + 0.956719i \(0.406007\pi\)
\(104\) 0 0
\(105\) −0.590974 −0.0576732
\(106\) 0 0
\(107\) −7.36790 −0.712282 −0.356141 0.934432i \(-0.615908\pi\)
−0.356141 + 0.934432i \(0.615908\pi\)
\(108\) 0 0
\(109\) 9.19031 0.880272 0.440136 0.897931i \(-0.354930\pi\)
0.440136 + 0.897931i \(0.354930\pi\)
\(110\) 0 0
\(111\) 4.26640 0.404949
\(112\) 0 0
\(113\) −12.9146 −1.21490 −0.607451 0.794357i \(-0.707808\pi\)
−0.607451 + 0.794357i \(0.707808\pi\)
\(114\) 0 0
\(115\) 1.44712 0.134944
\(116\) 0 0
\(117\) 2.92641 0.270547
\(118\) 0 0
\(119\) 5.09185 0.466769
\(120\) 0 0
\(121\) 28.0759 2.55236
\(122\) 0 0
\(123\) −10.8203 −0.975635
\(124\) 0 0
\(125\) 5.95625 0.532743
\(126\) 0 0
\(127\) 9.28542 0.823948 0.411974 0.911196i \(-0.364839\pi\)
0.411974 + 0.911196i \(0.364839\pi\)
\(128\) 0 0
\(129\) −1.32390 −0.116563
\(130\) 0 0
\(131\) −2.24628 −0.196259 −0.0981293 0.995174i \(-0.531286\pi\)
−0.0981293 + 0.995174i \(0.531286\pi\)
\(132\) 0 0
\(133\) 2.80917 0.243586
\(134\) 0 0
\(135\) −0.619387 −0.0533084
\(136\) 0 0
\(137\) −0.893884 −0.0763696 −0.0381848 0.999271i \(-0.512158\pi\)
−0.0381848 + 0.999271i \(0.512158\pi\)
\(138\) 0 0
\(139\) 1.11800 0.0948276 0.0474138 0.998875i \(-0.484902\pi\)
0.0474138 + 0.998875i \(0.484902\pi\)
\(140\) 0 0
\(141\) 3.37095 0.283885
\(142\) 0 0
\(143\) 18.2932 1.52976
\(144\) 0 0
\(145\) −2.76943 −0.229989
\(146\) 0 0
\(147\) −6.08964 −0.502265
\(148\) 0 0
\(149\) −10.8738 −0.890814 −0.445407 0.895328i \(-0.646941\pi\)
−0.445407 + 0.895328i \(0.646941\pi\)
\(150\) 0 0
\(151\) 23.9232 1.94684 0.973421 0.229023i \(-0.0735530\pi\)
0.973421 + 0.229023i \(0.0735530\pi\)
\(152\) 0 0
\(153\) 5.33666 0.431443
\(154\) 0 0
\(155\) 2.14057 0.171935
\(156\) 0 0
\(157\) 10.4595 0.834758 0.417379 0.908733i \(-0.362949\pi\)
0.417379 + 0.908733i \(0.362949\pi\)
\(158\) 0 0
\(159\) 5.72269 0.453839
\(160\) 0 0
\(161\) −2.22919 −0.175685
\(162\) 0 0
\(163\) −1.79788 −0.140821 −0.0704103 0.997518i \(-0.522431\pi\)
−0.0704103 + 0.997518i \(0.522431\pi\)
\(164\) 0 0
\(165\) −3.87184 −0.301422
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) −4.43611 −0.341240
\(170\) 0 0
\(171\) 2.94423 0.225151
\(172\) 0 0
\(173\) 6.35455 0.483127 0.241564 0.970385i \(-0.422340\pi\)
0.241564 + 0.970385i \(0.422340\pi\)
\(174\) 0 0
\(175\) −4.40459 −0.332956
\(176\) 0 0
\(177\) −10.0347 −0.754255
\(178\) 0 0
\(179\) 15.3384 1.14645 0.573224 0.819399i \(-0.305693\pi\)
0.573224 + 0.819399i \(0.305693\pi\)
\(180\) 0 0
\(181\) 2.95349 0.219531 0.109766 0.993958i \(-0.464990\pi\)
0.109766 + 0.993958i \(0.464990\pi\)
\(182\) 0 0
\(183\) 11.8490 0.875904
\(184\) 0 0
\(185\) −2.64256 −0.194285
\(186\) 0 0
\(187\) 33.3598 2.43951
\(188\) 0 0
\(189\) 0.954126 0.0694025
\(190\) 0 0
\(191\) 1.76766 0.127903 0.0639515 0.997953i \(-0.479630\pi\)
0.0639515 + 0.997953i \(0.479630\pi\)
\(192\) 0 0
\(193\) −11.2653 −0.810897 −0.405448 0.914118i \(-0.632885\pi\)
−0.405448 + 0.914118i \(0.632885\pi\)
\(194\) 0 0
\(195\) −1.81258 −0.129802
\(196\) 0 0
\(197\) −20.9384 −1.49180 −0.745901 0.666057i \(-0.767981\pi\)
−0.745901 + 0.666057i \(0.767981\pi\)
\(198\) 0 0
\(199\) 12.8279 0.909347 0.454674 0.890658i \(-0.349756\pi\)
0.454674 + 0.890658i \(0.349756\pi\)
\(200\) 0 0
\(201\) 0.604492 0.0426376
\(202\) 0 0
\(203\) 4.26613 0.299424
\(204\) 0 0
\(205\) 6.70197 0.468086
\(206\) 0 0
\(207\) −2.33637 −0.162389
\(208\) 0 0
\(209\) 18.4046 1.27307
\(210\) 0 0
\(211\) −8.08886 −0.556860 −0.278430 0.960457i \(-0.589814\pi\)
−0.278430 + 0.960457i \(0.589814\pi\)
\(212\) 0 0
\(213\) −9.74739 −0.667880
\(214\) 0 0
\(215\) 0.820009 0.0559242
\(216\) 0 0
\(217\) −3.29741 −0.223843
\(218\) 0 0
\(219\) −11.1654 −0.754486
\(220\) 0 0
\(221\) 15.6173 1.05053
\(222\) 0 0
\(223\) 24.7517 1.65750 0.828749 0.559620i \(-0.189053\pi\)
0.828749 + 0.559620i \(0.189053\pi\)
\(224\) 0 0
\(225\) −4.61636 −0.307757
\(226\) 0 0
\(227\) −1.26183 −0.0837504 −0.0418752 0.999123i \(-0.513333\pi\)
−0.0418752 + 0.999123i \(0.513333\pi\)
\(228\) 0 0
\(229\) 12.5768 0.831096 0.415548 0.909571i \(-0.363590\pi\)
0.415548 + 0.909571i \(0.363590\pi\)
\(230\) 0 0
\(231\) 5.96431 0.392423
\(232\) 0 0
\(233\) 15.6215 1.02340 0.511698 0.859165i \(-0.329017\pi\)
0.511698 + 0.859165i \(0.329017\pi\)
\(234\) 0 0
\(235\) −2.08793 −0.136201
\(236\) 0 0
\(237\) 6.74411 0.438077
\(238\) 0 0
\(239\) −27.8379 −1.80068 −0.900341 0.435185i \(-0.856683\pi\)
−0.900341 + 0.435185i \(0.856683\pi\)
\(240\) 0 0
\(241\) −31.0024 −1.99704 −0.998521 0.0543633i \(-0.982687\pi\)
−0.998521 + 0.0543633i \(0.982687\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 3.77185 0.240975
\(246\) 0 0
\(247\) 8.61604 0.548226
\(248\) 0 0
\(249\) 0.00272570 0.000172734 0
\(250\) 0 0
\(251\) 2.88623 0.182177 0.0910885 0.995843i \(-0.470965\pi\)
0.0910885 + 0.995843i \(0.470965\pi\)
\(252\) 0 0
\(253\) −14.6048 −0.918197
\(254\) 0 0
\(255\) −3.30546 −0.206996
\(256\) 0 0
\(257\) −10.5265 −0.656626 −0.328313 0.944569i \(-0.606480\pi\)
−0.328313 + 0.944569i \(0.606480\pi\)
\(258\) 0 0
\(259\) 4.07069 0.252940
\(260\) 0 0
\(261\) 4.47124 0.276763
\(262\) 0 0
\(263\) −13.9049 −0.857415 −0.428708 0.903443i \(-0.641031\pi\)
−0.428708 + 0.903443i \(0.641031\pi\)
\(264\) 0 0
\(265\) −3.54456 −0.217741
\(266\) 0 0
\(267\) 9.85457 0.603090
\(268\) 0 0
\(269\) 8.54423 0.520951 0.260475 0.965480i \(-0.416121\pi\)
0.260475 + 0.965480i \(0.416121\pi\)
\(270\) 0 0
\(271\) 3.35225 0.203635 0.101817 0.994803i \(-0.467534\pi\)
0.101817 + 0.994803i \(0.467534\pi\)
\(272\) 0 0
\(273\) 2.79217 0.168990
\(274\) 0 0
\(275\) −28.8572 −1.74015
\(276\) 0 0
\(277\) −11.5788 −0.695700 −0.347850 0.937550i \(-0.613088\pi\)
−0.347850 + 0.937550i \(0.613088\pi\)
\(278\) 0 0
\(279\) −3.45595 −0.206902
\(280\) 0 0
\(281\) −7.10103 −0.423612 −0.211806 0.977312i \(-0.567935\pi\)
−0.211806 + 0.977312i \(0.567935\pi\)
\(282\) 0 0
\(283\) −3.58868 −0.213325 −0.106662 0.994295i \(-0.534016\pi\)
−0.106662 + 0.994295i \(0.534016\pi\)
\(284\) 0 0
\(285\) −1.82362 −0.108022
\(286\) 0 0
\(287\) −10.3240 −0.609404
\(288\) 0 0
\(289\) 11.4799 0.675291
\(290\) 0 0
\(291\) −8.92479 −0.523180
\(292\) 0 0
\(293\) −23.4842 −1.37196 −0.685982 0.727619i \(-0.740627\pi\)
−0.685982 + 0.727619i \(0.740627\pi\)
\(294\) 0 0
\(295\) 6.21537 0.361873
\(296\) 0 0
\(297\) 6.25107 0.362724
\(298\) 0 0
\(299\) −6.83718 −0.395404
\(300\) 0 0
\(301\) −1.26317 −0.0728080
\(302\) 0 0
\(303\) 1.91531 0.110031
\(304\) 0 0
\(305\) −7.33913 −0.420237
\(306\) 0 0
\(307\) 3.96744 0.226433 0.113217 0.993570i \(-0.463885\pi\)
0.113217 + 0.993570i \(0.463885\pi\)
\(308\) 0 0
\(309\) 5.90694 0.336034
\(310\) 0 0
\(311\) 1.69973 0.0963829 0.0481915 0.998838i \(-0.484654\pi\)
0.0481915 + 0.998838i \(0.484654\pi\)
\(312\) 0 0
\(313\) 9.65206 0.545566 0.272783 0.962076i \(-0.412056\pi\)
0.272783 + 0.962076i \(0.412056\pi\)
\(314\) 0 0
\(315\) −0.590974 −0.0332976
\(316\) 0 0
\(317\) −8.58465 −0.482162 −0.241081 0.970505i \(-0.577502\pi\)
−0.241081 + 0.970505i \(0.577502\pi\)
\(318\) 0 0
\(319\) 27.9501 1.56490
\(320\) 0 0
\(321\) −7.36790 −0.411236
\(322\) 0 0
\(323\) 15.7124 0.874260
\(324\) 0 0
\(325\) −13.5094 −0.749365
\(326\) 0 0
\(327\) 9.19031 0.508225
\(328\) 0 0
\(329\) 3.21631 0.177321
\(330\) 0 0
\(331\) 13.0207 0.715683 0.357841 0.933782i \(-0.383513\pi\)
0.357841 + 0.933782i \(0.383513\pi\)
\(332\) 0 0
\(333\) 4.26640 0.233797
\(334\) 0 0
\(335\) −0.374415 −0.0204565
\(336\) 0 0
\(337\) 1.58095 0.0861199 0.0430600 0.999072i \(-0.486289\pi\)
0.0430600 + 0.999072i \(0.486289\pi\)
\(338\) 0 0
\(339\) −12.9146 −0.701424
\(340\) 0 0
\(341\) −21.6034 −1.16989
\(342\) 0 0
\(343\) −12.4892 −0.674352
\(344\) 0 0
\(345\) 1.44712 0.0779102
\(346\) 0 0
\(347\) 20.4617 1.09844 0.549220 0.835678i \(-0.314925\pi\)
0.549220 + 0.835678i \(0.314925\pi\)
\(348\) 0 0
\(349\) 3.71699 0.198966 0.0994831 0.995039i \(-0.468281\pi\)
0.0994831 + 0.995039i \(0.468281\pi\)
\(350\) 0 0
\(351\) 2.92641 0.156200
\(352\) 0 0
\(353\) 22.2105 1.18214 0.591072 0.806619i \(-0.298705\pi\)
0.591072 + 0.806619i \(0.298705\pi\)
\(354\) 0 0
\(355\) 6.03741 0.320433
\(356\) 0 0
\(357\) 5.09185 0.269489
\(358\) 0 0
\(359\) −3.53420 −0.186528 −0.0932640 0.995641i \(-0.529730\pi\)
−0.0932640 + 0.995641i \(0.529730\pi\)
\(360\) 0 0
\(361\) −10.3315 −0.543762
\(362\) 0 0
\(363\) 28.0759 1.47360
\(364\) 0 0
\(365\) 6.91569 0.361984
\(366\) 0 0
\(367\) 10.2786 0.536537 0.268268 0.963344i \(-0.413549\pi\)
0.268268 + 0.963344i \(0.413549\pi\)
\(368\) 0 0
\(369\) −10.8203 −0.563283
\(370\) 0 0
\(371\) 5.46017 0.283478
\(372\) 0 0
\(373\) −22.5828 −1.16929 −0.584647 0.811288i \(-0.698767\pi\)
−0.584647 + 0.811288i \(0.698767\pi\)
\(374\) 0 0
\(375\) 5.95625 0.307580
\(376\) 0 0
\(377\) 13.0847 0.673896
\(378\) 0 0
\(379\) 10.3926 0.533834 0.266917 0.963720i \(-0.413995\pi\)
0.266917 + 0.963720i \(0.413995\pi\)
\(380\) 0 0
\(381\) 9.28542 0.475707
\(382\) 0 0
\(383\) 6.01014 0.307104 0.153552 0.988141i \(-0.450929\pi\)
0.153552 + 0.988141i \(0.450929\pi\)
\(384\) 0 0
\(385\) −3.69422 −0.188275
\(386\) 0 0
\(387\) −1.32390 −0.0672978
\(388\) 0 0
\(389\) −22.9823 −1.16525 −0.582626 0.812741i \(-0.697975\pi\)
−0.582626 + 0.812741i \(0.697975\pi\)
\(390\) 0 0
\(391\) −12.4684 −0.630555
\(392\) 0 0
\(393\) −2.24628 −0.113310
\(394\) 0 0
\(395\) −4.17722 −0.210179
\(396\) 0 0
\(397\) −38.2310 −1.91876 −0.959381 0.282115i \(-0.908964\pi\)
−0.959381 + 0.282115i \(0.908964\pi\)
\(398\) 0 0
\(399\) 2.80917 0.140634
\(400\) 0 0
\(401\) −22.9593 −1.14653 −0.573266 0.819370i \(-0.694324\pi\)
−0.573266 + 0.819370i \(0.694324\pi\)
\(402\) 0 0
\(403\) −10.1135 −0.503791
\(404\) 0 0
\(405\) −0.619387 −0.0307776
\(406\) 0 0
\(407\) 26.6696 1.32196
\(408\) 0 0
\(409\) 21.3129 1.05386 0.526928 0.849910i \(-0.323344\pi\)
0.526928 + 0.849910i \(0.323344\pi\)
\(410\) 0 0
\(411\) −0.893884 −0.0440920
\(412\) 0 0
\(413\) −9.57438 −0.471124
\(414\) 0 0
\(415\) −0.00168826 −8.28736e−5 0
\(416\) 0 0
\(417\) 1.11800 0.0547487
\(418\) 0 0
\(419\) −31.8211 −1.55456 −0.777281 0.629154i \(-0.783402\pi\)
−0.777281 + 0.629154i \(0.783402\pi\)
\(420\) 0 0
\(421\) −0.234009 −0.0114049 −0.00570245 0.999984i \(-0.501815\pi\)
−0.00570245 + 0.999984i \(0.501815\pi\)
\(422\) 0 0
\(423\) 3.37095 0.163901
\(424\) 0 0
\(425\) −24.6359 −1.19502
\(426\) 0 0
\(427\) 11.3055 0.547110
\(428\) 0 0
\(429\) 18.2932 0.883205
\(430\) 0 0
\(431\) −9.97830 −0.480638 −0.240319 0.970694i \(-0.577252\pi\)
−0.240319 + 0.970694i \(0.577252\pi\)
\(432\) 0 0
\(433\) 31.2262 1.50064 0.750318 0.661077i \(-0.229901\pi\)
0.750318 + 0.661077i \(0.229901\pi\)
\(434\) 0 0
\(435\) −2.76943 −0.132784
\(436\) 0 0
\(437\) −6.87882 −0.329059
\(438\) 0 0
\(439\) −15.4486 −0.737320 −0.368660 0.929564i \(-0.620183\pi\)
−0.368660 + 0.929564i \(0.620183\pi\)
\(440\) 0 0
\(441\) −6.08964 −0.289983
\(442\) 0 0
\(443\) −4.04906 −0.192377 −0.0961883 0.995363i \(-0.530665\pi\)
−0.0961883 + 0.995363i \(0.530665\pi\)
\(444\) 0 0
\(445\) −6.10380 −0.289348
\(446\) 0 0
\(447\) −10.8738 −0.514312
\(448\) 0 0
\(449\) −3.16361 −0.149300 −0.0746500 0.997210i \(-0.523784\pi\)
−0.0746500 + 0.997210i \(0.523784\pi\)
\(450\) 0 0
\(451\) −67.6386 −3.18498
\(452\) 0 0
\(453\) 23.9232 1.12401
\(454\) 0 0
\(455\) −1.72943 −0.0810771
\(456\) 0 0
\(457\) −21.9553 −1.02702 −0.513512 0.858083i \(-0.671656\pi\)
−0.513512 + 0.858083i \(0.671656\pi\)
\(458\) 0 0
\(459\) 5.33666 0.249094
\(460\) 0 0
\(461\) −25.4993 −1.18762 −0.593811 0.804604i \(-0.702378\pi\)
−0.593811 + 0.804604i \(0.702378\pi\)
\(462\) 0 0
\(463\) 0.891709 0.0414412 0.0207206 0.999785i \(-0.493404\pi\)
0.0207206 + 0.999785i \(0.493404\pi\)
\(464\) 0 0
\(465\) 2.14057 0.0992666
\(466\) 0 0
\(467\) 30.2712 1.40079 0.700393 0.713758i \(-0.253008\pi\)
0.700393 + 0.713758i \(0.253008\pi\)
\(468\) 0 0
\(469\) 0.576762 0.0266324
\(470\) 0 0
\(471\) 10.4595 0.481948
\(472\) 0 0
\(473\) −8.27582 −0.380523
\(474\) 0 0
\(475\) −13.5916 −0.623627
\(476\) 0 0
\(477\) 5.72269 0.262024
\(478\) 0 0
\(479\) −1.73323 −0.0791932 −0.0395966 0.999216i \(-0.512607\pi\)
−0.0395966 + 0.999216i \(0.512607\pi\)
\(480\) 0 0
\(481\) 12.4852 0.569278
\(482\) 0 0
\(483\) −2.22919 −0.101432
\(484\) 0 0
\(485\) 5.52790 0.251009
\(486\) 0 0
\(487\) 41.7612 1.89238 0.946190 0.323612i \(-0.104897\pi\)
0.946190 + 0.323612i \(0.104897\pi\)
\(488\) 0 0
\(489\) −1.79788 −0.0813029
\(490\) 0 0
\(491\) 34.6055 1.56173 0.780863 0.624703i \(-0.214780\pi\)
0.780863 + 0.624703i \(0.214780\pi\)
\(492\) 0 0
\(493\) 23.8615 1.07467
\(494\) 0 0
\(495\) −3.87184 −0.174026
\(496\) 0 0
\(497\) −9.30024 −0.417173
\(498\) 0 0
\(499\) 17.8402 0.798636 0.399318 0.916813i \(-0.369247\pi\)
0.399318 + 0.916813i \(0.369247\pi\)
\(500\) 0 0
\(501\) 1.00000 0.0446767
\(502\) 0 0
\(503\) −25.0372 −1.11635 −0.558176 0.829722i \(-0.688499\pi\)
−0.558176 + 0.829722i \(0.688499\pi\)
\(504\) 0 0
\(505\) −1.18632 −0.0527904
\(506\) 0 0
\(507\) −4.43611 −0.197015
\(508\) 0 0
\(509\) −16.2180 −0.718852 −0.359426 0.933174i \(-0.617027\pi\)
−0.359426 + 0.933174i \(0.617027\pi\)
\(510\) 0 0
\(511\) −10.6532 −0.471269
\(512\) 0 0
\(513\) 2.94423 0.129991
\(514\) 0 0
\(515\) −3.65868 −0.161221
\(516\) 0 0
\(517\) 21.0721 0.926748
\(518\) 0 0
\(519\) 6.35455 0.278934
\(520\) 0 0
\(521\) −23.8985 −1.04701 −0.523506 0.852022i \(-0.675376\pi\)
−0.523506 + 0.852022i \(0.675376\pi\)
\(522\) 0 0
\(523\) −7.56408 −0.330754 −0.165377 0.986230i \(-0.552884\pi\)
−0.165377 + 0.986230i \(0.552884\pi\)
\(524\) 0 0
\(525\) −4.40459 −0.192232
\(526\) 0 0
\(527\) −18.4432 −0.803399
\(528\) 0 0
\(529\) −17.5414 −0.762669
\(530\) 0 0
\(531\) −10.0347 −0.435469
\(532\) 0 0
\(533\) −31.6647 −1.37155
\(534\) 0 0
\(535\) 4.56358 0.197301
\(536\) 0 0
\(537\) 15.3384 0.661901
\(538\) 0 0
\(539\) −38.0668 −1.63965
\(540\) 0 0
\(541\) 5.93874 0.255326 0.127663 0.991818i \(-0.459252\pi\)
0.127663 + 0.991818i \(0.459252\pi\)
\(542\) 0 0
\(543\) 2.95349 0.126746
\(544\) 0 0
\(545\) −5.69236 −0.243834
\(546\) 0 0
\(547\) −14.2274 −0.608319 −0.304159 0.952621i \(-0.598376\pi\)
−0.304159 + 0.952621i \(0.598376\pi\)
\(548\) 0 0
\(549\) 11.8490 0.505704
\(550\) 0 0
\(551\) 13.1644 0.560822
\(552\) 0 0
\(553\) 6.43473 0.273633
\(554\) 0 0
\(555\) −2.64256 −0.112170
\(556\) 0 0
\(557\) 43.7728 1.85471 0.927356 0.374179i \(-0.122076\pi\)
0.927356 + 0.374179i \(0.122076\pi\)
\(558\) 0 0
\(559\) −3.87429 −0.163865
\(560\) 0 0
\(561\) 33.3598 1.40845
\(562\) 0 0
\(563\) 1.51748 0.0639541 0.0319770 0.999489i \(-0.489820\pi\)
0.0319770 + 0.999489i \(0.489820\pi\)
\(564\) 0 0
\(565\) 7.99913 0.336526
\(566\) 0 0
\(567\) 0.954126 0.0400695
\(568\) 0 0
\(569\) 31.3447 1.31404 0.657019 0.753874i \(-0.271817\pi\)
0.657019 + 0.753874i \(0.271817\pi\)
\(570\) 0 0
\(571\) −32.7936 −1.37237 −0.686184 0.727428i \(-0.740716\pi\)
−0.686184 + 0.727428i \(0.740716\pi\)
\(572\) 0 0
\(573\) 1.76766 0.0738449
\(574\) 0 0
\(575\) 10.7855 0.449787
\(576\) 0 0
\(577\) 17.2365 0.717565 0.358782 0.933421i \(-0.383192\pi\)
0.358782 + 0.933421i \(0.383192\pi\)
\(578\) 0 0
\(579\) −11.2653 −0.468171
\(580\) 0 0
\(581\) 0.00260066 0.000107894 0
\(582\) 0 0
\(583\) 35.7729 1.48156
\(584\) 0 0
\(585\) −1.81258 −0.0749411
\(586\) 0 0
\(587\) 14.9256 0.616045 0.308023 0.951379i \(-0.400333\pi\)
0.308023 + 0.951379i \(0.400333\pi\)
\(588\) 0 0
\(589\) −10.1751 −0.419259
\(590\) 0 0
\(591\) −20.9384 −0.861293
\(592\) 0 0
\(593\) −1.00970 −0.0414635 −0.0207318 0.999785i \(-0.506600\pi\)
−0.0207318 + 0.999785i \(0.506600\pi\)
\(594\) 0 0
\(595\) −3.15383 −0.129294
\(596\) 0 0
\(597\) 12.8279 0.525012
\(598\) 0 0
\(599\) 1.66824 0.0681624 0.0340812 0.999419i \(-0.489150\pi\)
0.0340812 + 0.999419i \(0.489150\pi\)
\(600\) 0 0
\(601\) −21.4063 −0.873182 −0.436591 0.899660i \(-0.643814\pi\)
−0.436591 + 0.899660i \(0.643814\pi\)
\(602\) 0 0
\(603\) 0.604492 0.0246168
\(604\) 0 0
\(605\) −17.3899 −0.706999
\(606\) 0 0
\(607\) 36.1471 1.46716 0.733582 0.679601i \(-0.237847\pi\)
0.733582 + 0.679601i \(0.237847\pi\)
\(608\) 0 0
\(609\) 4.26613 0.172872
\(610\) 0 0
\(611\) 9.86479 0.399087
\(612\) 0 0
\(613\) −27.3272 −1.10373 −0.551867 0.833932i \(-0.686084\pi\)
−0.551867 + 0.833932i \(0.686084\pi\)
\(614\) 0 0
\(615\) 6.70197 0.270250
\(616\) 0 0
\(617\) 15.4624 0.622491 0.311246 0.950330i \(-0.399254\pi\)
0.311246 + 0.950330i \(0.399254\pi\)
\(618\) 0 0
\(619\) 9.42786 0.378938 0.189469 0.981887i \(-0.439323\pi\)
0.189469 + 0.981887i \(0.439323\pi\)
\(620\) 0 0
\(621\) −2.33637 −0.0937553
\(622\) 0 0
\(623\) 9.40251 0.376704
\(624\) 0 0
\(625\) 19.3926 0.775703
\(626\) 0 0
\(627\) 18.4046 0.735010
\(628\) 0 0
\(629\) 22.7683 0.907833
\(630\) 0 0
\(631\) −3.25940 −0.129755 −0.0648774 0.997893i \(-0.520666\pi\)
−0.0648774 + 0.997893i \(0.520666\pi\)
\(632\) 0 0
\(633\) −8.08886 −0.321503
\(634\) 0 0
\(635\) −5.75127 −0.228232
\(636\) 0 0
\(637\) −17.8208 −0.706086
\(638\) 0 0
\(639\) −9.74739 −0.385601
\(640\) 0 0
\(641\) −32.6986 −1.29152 −0.645758 0.763542i \(-0.723458\pi\)
−0.645758 + 0.763542i \(0.723458\pi\)
\(642\) 0 0
\(643\) 43.9513 1.73327 0.866635 0.498943i \(-0.166278\pi\)
0.866635 + 0.498943i \(0.166278\pi\)
\(644\) 0 0
\(645\) 0.820009 0.0322878
\(646\) 0 0
\(647\) −37.4757 −1.47332 −0.736661 0.676262i \(-0.763599\pi\)
−0.736661 + 0.676262i \(0.763599\pi\)
\(648\) 0 0
\(649\) −62.7277 −2.46228
\(650\) 0 0
\(651\) −3.29741 −0.129236
\(652\) 0 0
\(653\) −32.0885 −1.25572 −0.627860 0.778326i \(-0.716069\pi\)
−0.627860 + 0.778326i \(0.716069\pi\)
\(654\) 0 0
\(655\) 1.39132 0.0543633
\(656\) 0 0
\(657\) −11.1654 −0.435603
\(658\) 0 0
\(659\) 48.8689 1.90366 0.951831 0.306623i \(-0.0991990\pi\)
0.951831 + 0.306623i \(0.0991990\pi\)
\(660\) 0 0
\(661\) −1.28040 −0.0498018 −0.0249009 0.999690i \(-0.507927\pi\)
−0.0249009 + 0.999690i \(0.507927\pi\)
\(662\) 0 0
\(663\) 15.6173 0.606524
\(664\) 0 0
\(665\) −1.73997 −0.0674730
\(666\) 0 0
\(667\) −10.4465 −0.404489
\(668\) 0 0
\(669\) 24.7517 0.956957
\(670\) 0 0
\(671\) 74.0691 2.85940
\(672\) 0 0
\(673\) 7.53994 0.290643 0.145322 0.989384i \(-0.453578\pi\)
0.145322 + 0.989384i \(0.453578\pi\)
\(674\) 0 0
\(675\) −4.61636 −0.177684
\(676\) 0 0
\(677\) −29.9878 −1.15253 −0.576263 0.817264i \(-0.695490\pi\)
−0.576263 + 0.817264i \(0.695490\pi\)
\(678\) 0 0
\(679\) −8.51538 −0.326790
\(680\) 0 0
\(681\) −1.26183 −0.0483533
\(682\) 0 0
\(683\) 18.5606 0.710201 0.355100 0.934828i \(-0.384447\pi\)
0.355100 + 0.934828i \(0.384447\pi\)
\(684\) 0 0
\(685\) 0.553660 0.0211543
\(686\) 0 0
\(687\) 12.5768 0.479834
\(688\) 0 0
\(689\) 16.7469 0.638008
\(690\) 0 0
\(691\) −25.4157 −0.966857 −0.483429 0.875384i \(-0.660609\pi\)
−0.483429 + 0.875384i \(0.660609\pi\)
\(692\) 0 0
\(693\) 5.96431 0.226566
\(694\) 0 0
\(695\) −0.692476 −0.0262671
\(696\) 0 0
\(697\) −57.7444 −2.18722
\(698\) 0 0
\(699\) 15.6215 0.590858
\(700\) 0 0
\(701\) −1.05383 −0.0398026 −0.0199013 0.999802i \(-0.506335\pi\)
−0.0199013 + 0.999802i \(0.506335\pi\)
\(702\) 0 0
\(703\) 12.5613 0.473758
\(704\) 0 0
\(705\) −2.08793 −0.0786358
\(706\) 0 0
\(707\) 1.82744 0.0687281
\(708\) 0 0
\(709\) −1.33736 −0.0502257 −0.0251129 0.999685i \(-0.507995\pi\)
−0.0251129 + 0.999685i \(0.507995\pi\)
\(710\) 0 0
\(711\) 6.74411 0.252924
\(712\) 0 0
\(713\) 8.07437 0.302388
\(714\) 0 0
\(715\) −11.3306 −0.423740
\(716\) 0 0
\(717\) −27.8379 −1.03962
\(718\) 0 0
\(719\) 6.81276 0.254073 0.127037 0.991898i \(-0.459453\pi\)
0.127037 + 0.991898i \(0.459453\pi\)
\(720\) 0 0
\(721\) 5.63597 0.209894
\(722\) 0 0
\(723\) −31.0024 −1.15299
\(724\) 0 0
\(725\) −20.6409 −0.766582
\(726\) 0 0
\(727\) 20.6649 0.766419 0.383210 0.923661i \(-0.374819\pi\)
0.383210 + 0.923661i \(0.374819\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −7.06522 −0.261317
\(732\) 0 0
\(733\) −36.2674 −1.33957 −0.669784 0.742556i \(-0.733613\pi\)
−0.669784 + 0.742556i \(0.733613\pi\)
\(734\) 0 0
\(735\) 3.77185 0.139127
\(736\) 0 0
\(737\) 3.77872 0.139191
\(738\) 0 0
\(739\) 16.6388 0.612069 0.306034 0.952020i \(-0.400998\pi\)
0.306034 + 0.952020i \(0.400998\pi\)
\(740\) 0 0
\(741\) 8.61604 0.316518
\(742\) 0 0
\(743\) 4.04095 0.148248 0.0741241 0.997249i \(-0.476384\pi\)
0.0741241 + 0.997249i \(0.476384\pi\)
\(744\) 0 0
\(745\) 6.73508 0.246754
\(746\) 0 0
\(747\) 0.00272570 9.97281e−5 0
\(748\) 0 0
\(749\) −7.02991 −0.256867
\(750\) 0 0
\(751\) −25.2195 −0.920272 −0.460136 0.887849i \(-0.652199\pi\)
−0.460136 + 0.887849i \(0.652199\pi\)
\(752\) 0 0
\(753\) 2.88623 0.105180
\(754\) 0 0
\(755\) −14.8177 −0.539272
\(756\) 0 0
\(757\) 22.8414 0.830184 0.415092 0.909779i \(-0.363749\pi\)
0.415092 + 0.909779i \(0.363749\pi\)
\(758\) 0 0
\(759\) −14.6048 −0.530121
\(760\) 0 0
\(761\) −30.8230 −1.11733 −0.558666 0.829392i \(-0.688687\pi\)
−0.558666 + 0.829392i \(0.688687\pi\)
\(762\) 0 0
\(763\) 8.76872 0.317449
\(764\) 0 0
\(765\) −3.30546 −0.119509
\(766\) 0 0
\(767\) −29.3657 −1.06033
\(768\) 0 0
\(769\) −22.8669 −0.824600 −0.412300 0.911048i \(-0.635274\pi\)
−0.412300 + 0.911048i \(0.635274\pi\)
\(770\) 0 0
\(771\) −10.5265 −0.379103
\(772\) 0 0
\(773\) −31.4906 −1.13264 −0.566320 0.824186i \(-0.691633\pi\)
−0.566320 + 0.824186i \(0.691633\pi\)
\(774\) 0 0
\(775\) 15.9539 0.573081
\(776\) 0 0
\(777\) 4.07069 0.146035
\(778\) 0 0
\(779\) −31.8576 −1.14142
\(780\) 0 0
\(781\) −60.9317 −2.18031
\(782\) 0 0
\(783\) 4.47124 0.159789
\(784\) 0 0
\(785\) −6.47848 −0.231227
\(786\) 0 0
\(787\) −17.5858 −0.626866 −0.313433 0.949610i \(-0.601479\pi\)
−0.313433 + 0.949610i \(0.601479\pi\)
\(788\) 0 0
\(789\) −13.9049 −0.495029
\(790\) 0 0
\(791\) −12.3221 −0.438125
\(792\) 0 0
\(793\) 34.6751 1.23135
\(794\) 0 0
\(795\) −3.54456 −0.125713
\(796\) 0 0
\(797\) 18.0559 0.639573 0.319787 0.947490i \(-0.396389\pi\)
0.319787 + 0.947490i \(0.396389\pi\)
\(798\) 0 0
\(799\) 17.9896 0.636427
\(800\) 0 0
\(801\) 9.85457 0.348194
\(802\) 0 0
\(803\) −69.7955 −2.46303
\(804\) 0 0
\(805\) 1.38073 0.0486645
\(806\) 0 0
\(807\) 8.54423 0.300771
\(808\) 0 0
\(809\) 46.6237 1.63920 0.819600 0.572936i \(-0.194195\pi\)
0.819600 + 0.572936i \(0.194195\pi\)
\(810\) 0 0
\(811\) 17.3725 0.610030 0.305015 0.952348i \(-0.401339\pi\)
0.305015 + 0.952348i \(0.401339\pi\)
\(812\) 0 0
\(813\) 3.35225 0.117569
\(814\) 0 0
\(815\) 1.11358 0.0390071
\(816\) 0 0
\(817\) −3.89788 −0.136370
\(818\) 0 0
\(819\) 2.79217 0.0975662
\(820\) 0 0
\(821\) −6.23612 −0.217642 −0.108821 0.994061i \(-0.534708\pi\)
−0.108821 + 0.994061i \(0.534708\pi\)
\(822\) 0 0
\(823\) −18.4109 −0.641762 −0.320881 0.947120i \(-0.603979\pi\)
−0.320881 + 0.947120i \(0.603979\pi\)
\(824\) 0 0
\(825\) −28.8572 −1.00468
\(826\) 0 0
\(827\) −2.54468 −0.0884873 −0.0442436 0.999021i \(-0.514088\pi\)
−0.0442436 + 0.999021i \(0.514088\pi\)
\(828\) 0 0
\(829\) 40.5243 1.40747 0.703734 0.710463i \(-0.251515\pi\)
0.703734 + 0.710463i \(0.251515\pi\)
\(830\) 0 0
\(831\) −11.5788 −0.401663
\(832\) 0 0
\(833\) −32.4984 −1.12600
\(834\) 0 0
\(835\) −0.619387 −0.0214348
\(836\) 0 0
\(837\) −3.45595 −0.119455
\(838\) 0 0
\(839\) 21.9352 0.757287 0.378643 0.925543i \(-0.376391\pi\)
0.378643 + 0.925543i \(0.376391\pi\)
\(840\) 0 0
\(841\) −9.00799 −0.310620
\(842\) 0 0
\(843\) −7.10103 −0.244573
\(844\) 0 0
\(845\) 2.74767 0.0945228
\(846\) 0 0
\(847\) 26.7880 0.920445
\(848\) 0 0
\(849\) −3.58868 −0.123163
\(850\) 0 0
\(851\) −9.96789 −0.341695
\(852\) 0 0
\(853\) 7.93334 0.271632 0.135816 0.990734i \(-0.456634\pi\)
0.135816 + 0.990734i \(0.456634\pi\)
\(854\) 0 0
\(855\) −1.82362 −0.0623666
\(856\) 0 0
\(857\) −45.3773 −1.55006 −0.775029 0.631926i \(-0.782265\pi\)
−0.775029 + 0.631926i \(0.782265\pi\)
\(858\) 0 0
\(859\) 16.9407 0.578010 0.289005 0.957328i \(-0.406676\pi\)
0.289005 + 0.957328i \(0.406676\pi\)
\(860\) 0 0
\(861\) −10.3240 −0.351839
\(862\) 0 0
\(863\) −23.2827 −0.792551 −0.396275 0.918132i \(-0.629697\pi\)
−0.396275 + 0.918132i \(0.629697\pi\)
\(864\) 0 0
\(865\) −3.93593 −0.133826
\(866\) 0 0
\(867\) 11.4799 0.389879
\(868\) 0 0
\(869\) 42.1579 1.43011
\(870\) 0 0
\(871\) 1.76899 0.0599400
\(872\) 0 0
\(873\) −8.92479 −0.302058
\(874\) 0 0
\(875\) 5.68302 0.192121
\(876\) 0 0
\(877\) 32.5659 1.09967 0.549836 0.835272i \(-0.314690\pi\)
0.549836 + 0.835272i \(0.314690\pi\)
\(878\) 0 0
\(879\) −23.4842 −0.792104
\(880\) 0 0
\(881\) 20.9764 0.706712 0.353356 0.935489i \(-0.385040\pi\)
0.353356 + 0.935489i \(0.385040\pi\)
\(882\) 0 0
\(883\) 30.1958 1.01617 0.508084 0.861307i \(-0.330354\pi\)
0.508084 + 0.861307i \(0.330354\pi\)
\(884\) 0 0
\(885\) 6.21537 0.208927
\(886\) 0 0
\(887\) −37.7926 −1.26895 −0.634475 0.772943i \(-0.718784\pi\)
−0.634475 + 0.772943i \(0.718784\pi\)
\(888\) 0 0
\(889\) 8.85947 0.297137
\(890\) 0 0
\(891\) 6.25107 0.209419
\(892\) 0 0
\(893\) 9.92487 0.332123
\(894\) 0 0
\(895\) −9.50042 −0.317564
\(896\) 0 0
\(897\) −6.83718 −0.228287
\(898\) 0 0
\(899\) −15.4524 −0.515366
\(900\) 0 0
\(901\) 30.5400 1.01744
\(902\) 0 0
\(903\) −1.26317 −0.0420357
\(904\) 0 0
\(905\) −1.82935 −0.0608098
\(906\) 0 0
\(907\) −16.2201 −0.538581 −0.269291 0.963059i \(-0.586789\pi\)
−0.269291 + 0.963059i \(0.586789\pi\)
\(908\) 0 0
\(909\) 1.91531 0.0635267
\(910\) 0 0
\(911\) −36.1700 −1.19837 −0.599183 0.800612i \(-0.704508\pi\)
−0.599183 + 0.800612i \(0.704508\pi\)
\(912\) 0 0
\(913\) 0.0170385 0.000563894 0
\(914\) 0 0
\(915\) −7.33913 −0.242624
\(916\) 0 0
\(917\) −2.14324 −0.0707759
\(918\) 0 0
\(919\) 46.1395 1.52200 0.761000 0.648752i \(-0.224709\pi\)
0.761000 + 0.648752i \(0.224709\pi\)
\(920\) 0 0
\(921\) 3.96744 0.130731
\(922\) 0 0
\(923\) −28.5249 −0.938908
\(924\) 0 0
\(925\) −19.6952 −0.647576
\(926\) 0 0
\(927\) 5.90694 0.194009
\(928\) 0 0
\(929\) −38.7751 −1.27217 −0.636084 0.771619i \(-0.719447\pi\)
−0.636084 + 0.771619i \(0.719447\pi\)
\(930\) 0 0
\(931\) −17.9293 −0.587610
\(932\) 0 0
\(933\) 1.69973 0.0556467
\(934\) 0 0
\(935\) −20.6627 −0.675742
\(936\) 0 0
\(937\) −11.0137 −0.359802 −0.179901 0.983685i \(-0.557578\pi\)
−0.179901 + 0.983685i \(0.557578\pi\)
\(938\) 0 0
\(939\) 9.65206 0.314983
\(940\) 0 0
\(941\) 59.1291 1.92755 0.963776 0.266713i \(-0.0859374\pi\)
0.963776 + 0.266713i \(0.0859374\pi\)
\(942\) 0 0
\(943\) 25.2803 0.823239
\(944\) 0 0
\(945\) −0.590974 −0.0192244
\(946\) 0 0
\(947\) −30.8243 −1.00165 −0.500827 0.865547i \(-0.666971\pi\)
−0.500827 + 0.865547i \(0.666971\pi\)
\(948\) 0 0
\(949\) −32.6745 −1.06066
\(950\) 0 0
\(951\) −8.58465 −0.278376
\(952\) 0 0
\(953\) −18.3635 −0.594852 −0.297426 0.954745i \(-0.596128\pi\)
−0.297426 + 0.954745i \(0.596128\pi\)
\(954\) 0 0
\(955\) −1.09486 −0.0354290
\(956\) 0 0
\(957\) 27.9501 0.903497
\(958\) 0 0
\(959\) −0.852878 −0.0275409
\(960\) 0 0
\(961\) −19.0564 −0.614723
\(962\) 0 0
\(963\) −7.36790 −0.237427
\(964\) 0 0
\(965\) 6.97761 0.224617
\(966\) 0 0
\(967\) −5.11727 −0.164560 −0.0822802 0.996609i \(-0.526220\pi\)
−0.0822802 + 0.996609i \(0.526220\pi\)
\(968\) 0 0
\(969\) 15.7124 0.504754
\(970\) 0 0
\(971\) −56.0924 −1.80009 −0.900045 0.435797i \(-0.856467\pi\)
−0.900045 + 0.435797i \(0.856467\pi\)
\(972\) 0 0
\(973\) 1.06671 0.0341973
\(974\) 0 0
\(975\) −13.5094 −0.432646
\(976\) 0 0
\(977\) −9.10703 −0.291360 −0.145680 0.989332i \(-0.546537\pi\)
−0.145680 + 0.989332i \(0.546537\pi\)
\(978\) 0 0
\(979\) 61.6016 1.96880
\(980\) 0 0
\(981\) 9.19031 0.293424
\(982\) 0 0
\(983\) −37.4710 −1.19514 −0.597570 0.801817i \(-0.703867\pi\)
−0.597570 + 0.801817i \(0.703867\pi\)
\(984\) 0 0
\(985\) 12.9690 0.413227
\(986\) 0 0
\(987\) 3.21631 0.102376
\(988\) 0 0
\(989\) 3.09313 0.0983558
\(990\) 0 0
\(991\) −33.6068 −1.06756 −0.533778 0.845625i \(-0.679228\pi\)
−0.533778 + 0.845625i \(0.679228\pi\)
\(992\) 0 0
\(993\) 13.0207 0.413200
\(994\) 0 0
\(995\) −7.94546 −0.251888
\(996\) 0 0
\(997\) −10.8355 −0.343164 −0.171582 0.985170i \(-0.554888\pi\)
−0.171582 + 0.985170i \(0.554888\pi\)
\(998\) 0 0
\(999\) 4.26640 0.134983
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 \(a_p\))