Properties

Label 4012.2.a.g.1.5
Level 4012
Weight 2
Character 4012.1
Self dual Yes
Analytic conductor 32.036
Analytic rank 1
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4012 = 2^{2} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4012.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0359812909\)
Analytic rank: \(1\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(1.18762\)
Character \(\chi\) = 4012.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.18762 q^{3}\) \(+1.03337 q^{5}\) \(+2.52681 q^{7}\) \(-1.58957 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.18762 q^{3}\) \(+1.03337 q^{5}\) \(+2.52681 q^{7}\) \(-1.58957 q^{9}\) \(+4.63016 q^{11}\) \(-5.51519 q^{13}\) \(-1.22725 q^{15}\) \(-1.00000 q^{17}\) \(+4.35203 q^{19}\) \(-3.00088 q^{21}\) \(-4.68684 q^{23}\) \(-3.93214 q^{25}\) \(+5.45065 q^{27}\) \(-8.15402 q^{29}\) \(-0.288042 q^{31}\) \(-5.49885 q^{33}\) \(+2.61113 q^{35}\) \(-8.28324 q^{37}\) \(+6.54993 q^{39}\) \(+5.92083 q^{41}\) \(-4.48394 q^{43}\) \(-1.64261 q^{45}\) \(-5.50830 q^{47}\) \(-0.615243 q^{49}\) \(+1.18762 q^{51}\) \(+3.79017 q^{53}\) \(+4.78467 q^{55}\) \(-5.16854 q^{57}\) \(+1.00000 q^{59}\) \(+0.623587 q^{61}\) \(-4.01653 q^{63}\) \(-5.69924 q^{65}\) \(-10.7757 q^{67}\) \(+5.56616 q^{69}\) \(+1.81909 q^{71}\) \(+0.894382 q^{73}\) \(+4.66988 q^{75}\) \(+11.6995 q^{77}\) \(+0.647603 q^{79}\) \(-1.70457 q^{81}\) \(+5.53842 q^{83}\) \(-1.03337 q^{85}\) \(+9.68384 q^{87}\) \(-1.18899 q^{89}\) \(-13.9358 q^{91}\) \(+0.342084 q^{93}\) \(+4.49726 q^{95}\) \(-9.08803 q^{97}\) \(-7.35995 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 9q^{13} \) \(\mathstrut -\mathstrut 16q^{15} \) \(\mathstrut -\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut 15q^{19} \) \(\mathstrut +\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut -\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 33q^{33} \) \(\mathstrut -\mathstrut 9q^{35} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut -\mathstrut 18q^{41} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 30q^{45} \) \(\mathstrut -\mathstrut 60q^{47} \) \(\mathstrut +\mathstrut 10q^{49} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 41q^{57} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 23q^{63} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 4q^{73} \) \(\mathstrut -\mathstrut 62q^{75} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 48q^{79} \) \(\mathstrut +\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 20q^{83} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 13q^{87} \) \(\mathstrut -\mathstrut 29q^{89} \) \(\mathstrut -\mathstrut 28q^{91} \) \(\mathstrut -\mathstrut 31q^{93} \) \(\mathstrut -\mathstrut 48q^{95} \) \(\mathstrut -\mathstrut 26q^{97} \) \(\mathstrut -\mathstrut 3q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.18762 −0.685671 −0.342835 0.939396i \(-0.611387\pi\)
−0.342835 + 0.939396i \(0.611387\pi\)
\(4\) 0 0
\(5\) 1.03337 0.462138 0.231069 0.972937i \(-0.425778\pi\)
0.231069 + 0.972937i \(0.425778\pi\)
\(6\) 0 0
\(7\) 2.52681 0.955044 0.477522 0.878620i \(-0.341535\pi\)
0.477522 + 0.878620i \(0.341535\pi\)
\(8\) 0 0
\(9\) −1.58957 −0.529856
\(10\) 0 0
\(11\) 4.63016 1.39605 0.698023 0.716076i \(-0.254063\pi\)
0.698023 + 0.716076i \(0.254063\pi\)
\(12\) 0 0
\(13\) −5.51519 −1.52964 −0.764820 0.644245i \(-0.777172\pi\)
−0.764820 + 0.644245i \(0.777172\pi\)
\(14\) 0 0
\(15\) −1.22725 −0.316874
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) 4.35203 0.998424 0.499212 0.866480i \(-0.333623\pi\)
0.499212 + 0.866480i \(0.333623\pi\)
\(20\) 0 0
\(21\) −3.00088 −0.654845
\(22\) 0 0
\(23\) −4.68684 −0.977273 −0.488636 0.872488i \(-0.662506\pi\)
−0.488636 + 0.872488i \(0.662506\pi\)
\(24\) 0 0
\(25\) −3.93214 −0.786429
\(26\) 0 0
\(27\) 5.45065 1.04898
\(28\) 0 0
\(29\) −8.15402 −1.51416 −0.757081 0.653321i \(-0.773375\pi\)
−0.757081 + 0.653321i \(0.773375\pi\)
\(30\) 0 0
\(31\) −0.288042 −0.0517339 −0.0258670 0.999665i \(-0.508235\pi\)
−0.0258670 + 0.999665i \(0.508235\pi\)
\(32\) 0 0
\(33\) −5.49885 −0.957227
\(34\) 0 0
\(35\) 2.61113 0.441362
\(36\) 0 0
\(37\) −8.28324 −1.36176 −0.680878 0.732397i \(-0.738402\pi\)
−0.680878 + 0.732397i \(0.738402\pi\)
\(38\) 0 0
\(39\) 6.54993 1.04883
\(40\) 0 0
\(41\) 5.92083 0.924679 0.462339 0.886703i \(-0.347010\pi\)
0.462339 + 0.886703i \(0.347010\pi\)
\(42\) 0 0
\(43\) −4.48394 −0.683794 −0.341897 0.939737i \(-0.611069\pi\)
−0.341897 + 0.939737i \(0.611069\pi\)
\(44\) 0 0
\(45\) −1.64261 −0.244866
\(46\) 0 0
\(47\) −5.50830 −0.803467 −0.401734 0.915757i \(-0.631592\pi\)
−0.401734 + 0.915757i \(0.631592\pi\)
\(48\) 0 0
\(49\) −0.615243 −0.0878919
\(50\) 0 0
\(51\) 1.18762 0.166300
\(52\) 0 0
\(53\) 3.79017 0.520620 0.260310 0.965525i \(-0.416175\pi\)
0.260310 + 0.965525i \(0.416175\pi\)
\(54\) 0 0
\(55\) 4.78467 0.645165
\(56\) 0 0
\(57\) −5.16854 −0.684590
\(58\) 0 0
\(59\) 1.00000 0.130189
\(60\) 0 0
\(61\) 0.623587 0.0798421 0.0399210 0.999203i \(-0.487289\pi\)
0.0399210 + 0.999203i \(0.487289\pi\)
\(62\) 0 0
\(63\) −4.01653 −0.506035
\(64\) 0 0
\(65\) −5.69924 −0.706904
\(66\) 0 0
\(67\) −10.7757 −1.31646 −0.658229 0.752818i \(-0.728694\pi\)
−0.658229 + 0.752818i \(0.728694\pi\)
\(68\) 0 0
\(69\) 5.56616 0.670087
\(70\) 0 0
\(71\) 1.81909 0.215886 0.107943 0.994157i \(-0.465574\pi\)
0.107943 + 0.994157i \(0.465574\pi\)
\(72\) 0 0
\(73\) 0.894382 0.104680 0.0523398 0.998629i \(-0.483332\pi\)
0.0523398 + 0.998629i \(0.483332\pi\)
\(74\) 0 0
\(75\) 4.66988 0.539231
\(76\) 0 0
\(77\) 11.6995 1.33328
\(78\) 0 0
\(79\) 0.647603 0.0728610 0.0364305 0.999336i \(-0.488401\pi\)
0.0364305 + 0.999336i \(0.488401\pi\)
\(80\) 0 0
\(81\) −1.70457 −0.189397
\(82\) 0 0
\(83\) 5.53842 0.607920 0.303960 0.952685i \(-0.401691\pi\)
0.303960 + 0.952685i \(0.401691\pi\)
\(84\) 0 0
\(85\) −1.03337 −0.112085
\(86\) 0 0
\(87\) 9.68384 1.03822
\(88\) 0 0
\(89\) −1.18899 −0.126033 −0.0630166 0.998012i \(-0.520072\pi\)
−0.0630166 + 0.998012i \(0.520072\pi\)
\(90\) 0 0
\(91\) −13.9358 −1.46087
\(92\) 0 0
\(93\) 0.342084 0.0354724
\(94\) 0 0
\(95\) 4.49726 0.461409
\(96\) 0 0
\(97\) −9.08803 −0.922749 −0.461375 0.887205i \(-0.652644\pi\)
−0.461375 + 0.887205i \(0.652644\pi\)
\(98\) 0 0
\(99\) −7.35995 −0.739703
\(100\) 0 0
\(101\) −2.33733 −0.232573 −0.116286 0.993216i \(-0.537099\pi\)
−0.116286 + 0.993216i \(0.537099\pi\)
\(102\) 0 0
\(103\) 6.01022 0.592204 0.296102 0.955156i \(-0.404313\pi\)
0.296102 + 0.955156i \(0.404313\pi\)
\(104\) 0 0
\(105\) −3.10102 −0.302629
\(106\) 0 0
\(107\) −19.5086 −1.88597 −0.942984 0.332838i \(-0.891994\pi\)
−0.942984 + 0.332838i \(0.891994\pi\)
\(108\) 0 0
\(109\) 19.1263 1.83197 0.915983 0.401217i \(-0.131413\pi\)
0.915983 + 0.401217i \(0.131413\pi\)
\(110\) 0 0
\(111\) 9.83731 0.933716
\(112\) 0 0
\(113\) −5.29162 −0.497794 −0.248897 0.968530i \(-0.580068\pi\)
−0.248897 + 0.968530i \(0.580068\pi\)
\(114\) 0 0
\(115\) −4.84324 −0.451634
\(116\) 0 0
\(117\) 8.76677 0.810488
\(118\) 0 0
\(119\) −2.52681 −0.231632
\(120\) 0 0
\(121\) 10.4384 0.948943
\(122\) 0 0
\(123\) −7.03168 −0.634025
\(124\) 0 0
\(125\) −9.23022 −0.825576
\(126\) 0 0
\(127\) 14.5684 1.29274 0.646370 0.763024i \(-0.276286\pi\)
0.646370 + 0.763024i \(0.276286\pi\)
\(128\) 0 0
\(129\) 5.32520 0.468858
\(130\) 0 0
\(131\) −1.64696 −0.143896 −0.0719479 0.997408i \(-0.522922\pi\)
−0.0719479 + 0.997408i \(0.522922\pi\)
\(132\) 0 0
\(133\) 10.9967 0.953538
\(134\) 0 0
\(135\) 5.63254 0.484772
\(136\) 0 0
\(137\) 1.99828 0.170725 0.0853625 0.996350i \(-0.472795\pi\)
0.0853625 + 0.996350i \(0.472795\pi\)
\(138\) 0 0
\(139\) −16.6631 −1.41335 −0.706673 0.707540i \(-0.749805\pi\)
−0.706673 + 0.707540i \(0.749805\pi\)
\(140\) 0 0
\(141\) 6.54174 0.550914
\(142\) 0 0
\(143\) −25.5362 −2.13545
\(144\) 0 0
\(145\) −8.42613 −0.699752
\(146\) 0 0
\(147\) 0.730673 0.0602649
\(148\) 0 0
\(149\) −13.2853 −1.08837 −0.544187 0.838964i \(-0.683162\pi\)
−0.544187 + 0.838964i \(0.683162\pi\)
\(150\) 0 0
\(151\) −9.45570 −0.769494 −0.384747 0.923022i \(-0.625711\pi\)
−0.384747 + 0.923022i \(0.625711\pi\)
\(152\) 0 0
\(153\) 1.58957 0.128509
\(154\) 0 0
\(155\) −0.297655 −0.0239082
\(156\) 0 0
\(157\) 12.1686 0.971160 0.485580 0.874192i \(-0.338608\pi\)
0.485580 + 0.874192i \(0.338608\pi\)
\(158\) 0 0
\(159\) −4.50127 −0.356974
\(160\) 0 0
\(161\) −11.8427 −0.933338
\(162\) 0 0
\(163\) −23.6966 −1.85606 −0.928030 0.372506i \(-0.878499\pi\)
−0.928030 + 0.372506i \(0.878499\pi\)
\(164\) 0 0
\(165\) −5.68236 −0.442371
\(166\) 0 0
\(167\) 15.1640 1.17343 0.586713 0.809795i \(-0.300422\pi\)
0.586713 + 0.809795i \(0.300422\pi\)
\(168\) 0 0
\(169\) 17.4173 1.33980
\(170\) 0 0
\(171\) −6.91784 −0.529021
\(172\) 0 0
\(173\) 13.1395 0.998978 0.499489 0.866320i \(-0.333521\pi\)
0.499489 + 0.866320i \(0.333521\pi\)
\(174\) 0 0
\(175\) −9.93577 −0.751074
\(176\) 0 0
\(177\) −1.18762 −0.0892667
\(178\) 0 0
\(179\) 13.9694 1.04412 0.522059 0.852909i \(-0.325164\pi\)
0.522059 + 0.852909i \(0.325164\pi\)
\(180\) 0 0
\(181\) 6.23709 0.463599 0.231799 0.972764i \(-0.425539\pi\)
0.231799 + 0.972764i \(0.425539\pi\)
\(182\) 0 0
\(183\) −0.740581 −0.0547454
\(184\) 0 0
\(185\) −8.55966 −0.629319
\(186\) 0 0
\(187\) −4.63016 −0.338591
\(188\) 0 0
\(189\) 13.7727 1.00182
\(190\) 0 0
\(191\) 6.28159 0.454520 0.227260 0.973834i \(-0.427023\pi\)
0.227260 + 0.973834i \(0.427023\pi\)
\(192\) 0 0
\(193\) −18.1330 −1.30524 −0.652621 0.757684i \(-0.726331\pi\)
−0.652621 + 0.757684i \(0.726331\pi\)
\(194\) 0 0
\(195\) 6.76851 0.484703
\(196\) 0 0
\(197\) −12.3431 −0.879411 −0.439706 0.898142i \(-0.644917\pi\)
−0.439706 + 0.898142i \(0.644917\pi\)
\(198\) 0 0
\(199\) −7.76295 −0.550301 −0.275151 0.961401i \(-0.588728\pi\)
−0.275151 + 0.961401i \(0.588728\pi\)
\(200\) 0 0
\(201\) 12.7974 0.902657
\(202\) 0 0
\(203\) −20.6036 −1.44609
\(204\) 0 0
\(205\) 6.11842 0.427329
\(206\) 0 0
\(207\) 7.45004 0.517814
\(208\) 0 0
\(209\) 20.1506 1.39385
\(210\) 0 0
\(211\) 12.9000 0.888074 0.444037 0.896009i \(-0.353546\pi\)
0.444037 + 0.896009i \(0.353546\pi\)
\(212\) 0 0
\(213\) −2.16038 −0.148027
\(214\) 0 0
\(215\) −4.63357 −0.316007
\(216\) 0 0
\(217\) −0.727828 −0.0494082
\(218\) 0 0
\(219\) −1.06218 −0.0717757
\(220\) 0 0
\(221\) 5.51519 0.370992
\(222\) 0 0
\(223\) −14.9830 −1.00333 −0.501667 0.865061i \(-0.667280\pi\)
−0.501667 + 0.865061i \(0.667280\pi\)
\(224\) 0 0
\(225\) 6.25041 0.416694
\(226\) 0 0
\(227\) −3.65735 −0.242747 −0.121374 0.992607i \(-0.538730\pi\)
−0.121374 + 0.992607i \(0.538730\pi\)
\(228\) 0 0
\(229\) 10.3092 0.681249 0.340624 0.940199i \(-0.389362\pi\)
0.340624 + 0.940199i \(0.389362\pi\)
\(230\) 0 0
\(231\) −13.8945 −0.914194
\(232\) 0 0
\(233\) −24.6674 −1.61602 −0.808009 0.589171i \(-0.799455\pi\)
−0.808009 + 0.589171i \(0.799455\pi\)
\(234\) 0 0
\(235\) −5.69211 −0.371313
\(236\) 0 0
\(237\) −0.769103 −0.0499586
\(238\) 0 0
\(239\) −5.11018 −0.330550 −0.165275 0.986248i \(-0.552851\pi\)
−0.165275 + 0.986248i \(0.552851\pi\)
\(240\) 0 0
\(241\) −18.4630 −1.18930 −0.594652 0.803983i \(-0.702710\pi\)
−0.594652 + 0.803983i \(0.702710\pi\)
\(242\) 0 0
\(243\) −14.3276 −0.919113
\(244\) 0 0
\(245\) −0.635774 −0.0406181
\(246\) 0 0
\(247\) −24.0023 −1.52723
\(248\) 0 0
\(249\) −6.57751 −0.416833
\(250\) 0 0
\(251\) 7.44336 0.469821 0.234910 0.972017i \(-0.424520\pi\)
0.234910 + 0.972017i \(0.424520\pi\)
\(252\) 0 0
\(253\) −21.7008 −1.36432
\(254\) 0 0
\(255\) 1.22725 0.0768533
\(256\) 0 0
\(257\) −5.58926 −0.348649 −0.174324 0.984688i \(-0.555774\pi\)
−0.174324 + 0.984688i \(0.555774\pi\)
\(258\) 0 0
\(259\) −20.9302 −1.30054
\(260\) 0 0
\(261\) 12.9614 0.802288
\(262\) 0 0
\(263\) −8.41046 −0.518611 −0.259305 0.965795i \(-0.583494\pi\)
−0.259305 + 0.965795i \(0.583494\pi\)
\(264\) 0 0
\(265\) 3.91666 0.240598
\(266\) 0 0
\(267\) 1.41207 0.0864172
\(268\) 0 0
\(269\) −6.36903 −0.388327 −0.194163 0.980969i \(-0.562199\pi\)
−0.194163 + 0.980969i \(0.562199\pi\)
\(270\) 0 0
\(271\) 21.6443 1.31480 0.657398 0.753544i \(-0.271657\pi\)
0.657398 + 0.753544i \(0.271657\pi\)
\(272\) 0 0
\(273\) 16.5504 1.00168
\(274\) 0 0
\(275\) −18.2065 −1.09789
\(276\) 0 0
\(277\) −24.4894 −1.47142 −0.735712 0.677295i \(-0.763152\pi\)
−0.735712 + 0.677295i \(0.763152\pi\)
\(278\) 0 0
\(279\) 0.457863 0.0274115
\(280\) 0 0
\(281\) −0.662298 −0.0395094 −0.0197547 0.999805i \(-0.506289\pi\)
−0.0197547 + 0.999805i \(0.506289\pi\)
\(282\) 0 0
\(283\) 1.52952 0.0909208 0.0454604 0.998966i \(-0.485525\pi\)
0.0454604 + 0.998966i \(0.485525\pi\)
\(284\) 0 0
\(285\) −5.34102 −0.316375
\(286\) 0 0
\(287\) 14.9608 0.883108
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 10.7931 0.632702
\(292\) 0 0
\(293\) −13.2926 −0.776564 −0.388282 0.921541i \(-0.626931\pi\)
−0.388282 + 0.921541i \(0.626931\pi\)
\(294\) 0 0
\(295\) 1.03337 0.0601652
\(296\) 0 0
\(297\) 25.2374 1.46442
\(298\) 0 0
\(299\) 25.8488 1.49487
\(300\) 0 0
\(301\) −11.3301 −0.653053
\(302\) 0 0
\(303\) 2.77585 0.159468
\(304\) 0 0
\(305\) 0.644396 0.0368980
\(306\) 0 0
\(307\) −14.3656 −0.819887 −0.409944 0.912111i \(-0.634452\pi\)
−0.409944 + 0.912111i \(0.634452\pi\)
\(308\) 0 0
\(309\) −7.13783 −0.406057
\(310\) 0 0
\(311\) −17.6746 −1.00223 −0.501117 0.865380i \(-0.667077\pi\)
−0.501117 + 0.865380i \(0.667077\pi\)
\(312\) 0 0
\(313\) −23.2229 −1.31264 −0.656318 0.754484i \(-0.727887\pi\)
−0.656318 + 0.754484i \(0.727887\pi\)
\(314\) 0 0
\(315\) −4.15057 −0.233858
\(316\) 0 0
\(317\) 8.36278 0.469700 0.234850 0.972032i \(-0.424540\pi\)
0.234850 + 0.972032i \(0.424540\pi\)
\(318\) 0 0
\(319\) −37.7544 −2.11384
\(320\) 0 0
\(321\) 23.1687 1.29315
\(322\) 0 0
\(323\) −4.35203 −0.242153
\(324\) 0 0
\(325\) 21.6865 1.20295
\(326\) 0 0
\(327\) −22.7147 −1.25612
\(328\) 0 0
\(329\) −13.9184 −0.767346
\(330\) 0 0
\(331\) −22.2097 −1.22076 −0.610379 0.792110i \(-0.708983\pi\)
−0.610379 + 0.792110i \(0.708983\pi\)
\(332\) 0 0
\(333\) 13.1668 0.721535
\(334\) 0 0
\(335\) −11.1353 −0.608385
\(336\) 0 0
\(337\) 24.1815 1.31725 0.658625 0.752471i \(-0.271138\pi\)
0.658625 + 0.752471i \(0.271138\pi\)
\(338\) 0 0
\(339\) 6.28442 0.341323
\(340\) 0 0
\(341\) −1.33368 −0.0722229
\(342\) 0 0
\(343\) −19.2423 −1.03898
\(344\) 0 0
\(345\) 5.75191 0.309672
\(346\) 0 0
\(347\) 21.7712 1.16874 0.584370 0.811487i \(-0.301342\pi\)
0.584370 + 0.811487i \(0.301342\pi\)
\(348\) 0 0
\(349\) −0.197978 −0.0105975 −0.00529877 0.999986i \(-0.501687\pi\)
−0.00529877 + 0.999986i \(0.501687\pi\)
\(350\) 0 0
\(351\) −30.0614 −1.60456
\(352\) 0 0
\(353\) −27.6504 −1.47168 −0.735841 0.677154i \(-0.763213\pi\)
−0.735841 + 0.677154i \(0.763213\pi\)
\(354\) 0 0
\(355\) 1.87980 0.0997692
\(356\) 0 0
\(357\) 3.00088 0.158823
\(358\) 0 0
\(359\) −14.5218 −0.766429 −0.383214 0.923659i \(-0.625183\pi\)
−0.383214 + 0.923659i \(0.625183\pi\)
\(360\) 0 0
\(361\) −0.0598483 −0.00314991
\(362\) 0 0
\(363\) −12.3968 −0.650662
\(364\) 0 0
\(365\) 0.924229 0.0483763
\(366\) 0 0
\(367\) 24.0002 1.25280 0.626401 0.779501i \(-0.284527\pi\)
0.626401 + 0.779501i \(0.284527\pi\)
\(368\) 0 0
\(369\) −9.41157 −0.489947
\(370\) 0 0
\(371\) 9.57704 0.497215
\(372\) 0 0
\(373\) −10.6393 −0.550881 −0.275441 0.961318i \(-0.588824\pi\)
−0.275441 + 0.961318i \(0.588824\pi\)
\(374\) 0 0
\(375\) 10.9620 0.566073
\(376\) 0 0
\(377\) 44.9710 2.31612
\(378\) 0 0
\(379\) 3.06460 0.157418 0.0787089 0.996898i \(-0.474920\pi\)
0.0787089 + 0.996898i \(0.474920\pi\)
\(380\) 0 0
\(381\) −17.3017 −0.886394
\(382\) 0 0
\(383\) −29.1353 −1.48874 −0.744372 0.667765i \(-0.767251\pi\)
−0.744372 + 0.667765i \(0.767251\pi\)
\(384\) 0 0
\(385\) 12.0899 0.616161
\(386\) 0 0
\(387\) 7.12753 0.362313
\(388\) 0 0
\(389\) 17.8129 0.903150 0.451575 0.892233i \(-0.350862\pi\)
0.451575 + 0.892233i \(0.350862\pi\)
\(390\) 0 0
\(391\) 4.68684 0.237023
\(392\) 0 0
\(393\) 1.95596 0.0986651
\(394\) 0 0
\(395\) 0.669214 0.0336718
\(396\) 0 0
\(397\) 35.9205 1.80280 0.901400 0.432988i \(-0.142541\pi\)
0.901400 + 0.432988i \(0.142541\pi\)
\(398\) 0 0
\(399\) −13.0599 −0.653813
\(400\) 0 0
\(401\) −32.0902 −1.60251 −0.801255 0.598323i \(-0.795834\pi\)
−0.801255 + 0.598323i \(0.795834\pi\)
\(402\) 0 0
\(403\) 1.58861 0.0791342
\(404\) 0 0
\(405\) −1.76145 −0.0875274
\(406\) 0 0
\(407\) −38.3527 −1.90107
\(408\) 0 0
\(409\) −32.6614 −1.61500 −0.807500 0.589867i \(-0.799180\pi\)
−0.807500 + 0.589867i \(0.799180\pi\)
\(410\) 0 0
\(411\) −2.37320 −0.117061
\(412\) 0 0
\(413\) 2.52681 0.124336
\(414\) 0 0
\(415\) 5.72324 0.280943
\(416\) 0 0
\(417\) 19.7894 0.969090
\(418\) 0 0
\(419\) −16.6891 −0.815314 −0.407657 0.913135i \(-0.633654\pi\)
−0.407657 + 0.913135i \(0.633654\pi\)
\(420\) 0 0
\(421\) 12.8125 0.624441 0.312221 0.950010i \(-0.398927\pi\)
0.312221 + 0.950010i \(0.398927\pi\)
\(422\) 0 0
\(423\) 8.75581 0.425722
\(424\) 0 0
\(425\) 3.93214 0.190737
\(426\) 0 0
\(427\) 1.57568 0.0762527
\(428\) 0 0
\(429\) 30.3272 1.46421
\(430\) 0 0
\(431\) 13.5966 0.654927 0.327463 0.944864i \(-0.393806\pi\)
0.327463 + 0.944864i \(0.393806\pi\)
\(432\) 0 0
\(433\) 28.9831 1.39284 0.696420 0.717634i \(-0.254775\pi\)
0.696420 + 0.717634i \(0.254775\pi\)
\(434\) 0 0
\(435\) 10.0070 0.479799
\(436\) 0 0
\(437\) −20.3972 −0.975732
\(438\) 0 0
\(439\) −14.8551 −0.708997 −0.354498 0.935057i \(-0.615348\pi\)
−0.354498 + 0.935057i \(0.615348\pi\)
\(440\) 0 0
\(441\) 0.977970 0.0465700
\(442\) 0 0
\(443\) −4.99505 −0.237322 −0.118661 0.992935i \(-0.537860\pi\)
−0.118661 + 0.992935i \(0.537860\pi\)
\(444\) 0 0
\(445\) −1.22867 −0.0582447
\(446\) 0 0
\(447\) 15.7778 0.746266
\(448\) 0 0
\(449\) 32.6933 1.54289 0.771445 0.636296i \(-0.219534\pi\)
0.771445 + 0.636296i \(0.219534\pi\)
\(450\) 0 0
\(451\) 27.4144 1.29089
\(452\) 0 0
\(453\) 11.2297 0.527619
\(454\) 0 0
\(455\) −14.4009 −0.675124
\(456\) 0 0
\(457\) 29.8505 1.39635 0.698174 0.715928i \(-0.253996\pi\)
0.698174 + 0.715928i \(0.253996\pi\)
\(458\) 0 0
\(459\) −5.45065 −0.254414
\(460\) 0 0
\(461\) −23.9016 −1.11321 −0.556604 0.830778i \(-0.687896\pi\)
−0.556604 + 0.830778i \(0.687896\pi\)
\(462\) 0 0
\(463\) 33.1565 1.54091 0.770457 0.637492i \(-0.220028\pi\)
0.770457 + 0.637492i \(0.220028\pi\)
\(464\) 0 0
\(465\) 0.353499 0.0163931
\(466\) 0 0
\(467\) 25.0742 1.16030 0.580149 0.814511i \(-0.302994\pi\)
0.580149 + 0.814511i \(0.302994\pi\)
\(468\) 0 0
\(469\) −27.2281 −1.25728
\(470\) 0 0
\(471\) −14.4516 −0.665896
\(472\) 0 0
\(473\) −20.7614 −0.954608
\(474\) 0 0
\(475\) −17.1128 −0.785189
\(476\) 0 0
\(477\) −6.02474 −0.275854
\(478\) 0 0
\(479\) 6.64989 0.303841 0.151921 0.988393i \(-0.451454\pi\)
0.151921 + 0.988393i \(0.451454\pi\)
\(480\) 0 0
\(481\) 45.6837 2.08300
\(482\) 0 0
\(483\) 14.0646 0.639962
\(484\) 0 0
\(485\) −9.39131 −0.426437
\(486\) 0 0
\(487\) 20.5561 0.931487 0.465744 0.884920i \(-0.345787\pi\)
0.465744 + 0.884920i \(0.345787\pi\)
\(488\) 0 0
\(489\) 28.1424 1.27265
\(490\) 0 0
\(491\) −21.1923 −0.956393 −0.478197 0.878253i \(-0.658709\pi\)
−0.478197 + 0.878253i \(0.658709\pi\)
\(492\) 0 0
\(493\) 8.15402 0.367238
\(494\) 0 0
\(495\) −7.60556 −0.341845
\(496\) 0 0
\(497\) 4.59649 0.206181
\(498\) 0 0
\(499\) −19.2403 −0.861313 −0.430656 0.902516i \(-0.641718\pi\)
−0.430656 + 0.902516i \(0.641718\pi\)
\(500\) 0 0
\(501\) −18.0090 −0.804583
\(502\) 0 0
\(503\) −13.3508 −0.595285 −0.297642 0.954677i \(-0.596200\pi\)
−0.297642 + 0.954677i \(0.596200\pi\)
\(504\) 0 0
\(505\) −2.41533 −0.107481
\(506\) 0 0
\(507\) −20.6851 −0.918659
\(508\) 0 0
\(509\) 37.7144 1.67166 0.835832 0.548986i \(-0.184986\pi\)
0.835832 + 0.548986i \(0.184986\pi\)
\(510\) 0 0
\(511\) 2.25993 0.0999735
\(512\) 0 0
\(513\) 23.7214 1.04732
\(514\) 0 0
\(515\) 6.21078 0.273680
\(516\) 0 0
\(517\) −25.5043 −1.12168
\(518\) 0 0
\(519\) −15.6047 −0.684970
\(520\) 0 0
\(521\) 5.26252 0.230555 0.115277 0.993333i \(-0.463224\pi\)
0.115277 + 0.993333i \(0.463224\pi\)
\(522\) 0 0
\(523\) −8.41943 −0.368156 −0.184078 0.982912i \(-0.558930\pi\)
−0.184078 + 0.982912i \(0.558930\pi\)
\(524\) 0 0
\(525\) 11.7999 0.514989
\(526\) 0 0
\(527\) 0.288042 0.0125473
\(528\) 0 0
\(529\) −1.03358 −0.0449381
\(530\) 0 0
\(531\) −1.58957 −0.0689814
\(532\) 0 0
\(533\) −32.6545 −1.41442
\(534\) 0 0
\(535\) −20.1596 −0.871577
\(536\) 0 0
\(537\) −16.5902 −0.715921
\(538\) 0 0
\(539\) −2.84867 −0.122701
\(540\) 0 0
\(541\) 20.0821 0.863398 0.431699 0.902018i \(-0.357914\pi\)
0.431699 + 0.902018i \(0.357914\pi\)
\(542\) 0 0
\(543\) −7.40726 −0.317876
\(544\) 0 0
\(545\) 19.7646 0.846620
\(546\) 0 0
\(547\) 2.01168 0.0860131 0.0430066 0.999075i \(-0.486306\pi\)
0.0430066 + 0.999075i \(0.486306\pi\)
\(548\) 0 0
\(549\) −0.991233 −0.0423048
\(550\) 0 0
\(551\) −35.4865 −1.51178
\(552\) 0 0
\(553\) 1.63637 0.0695854
\(554\) 0 0
\(555\) 10.1656 0.431505
\(556\) 0 0
\(557\) 21.1857 0.897668 0.448834 0.893615i \(-0.351840\pi\)
0.448834 + 0.893615i \(0.351840\pi\)
\(558\) 0 0
\(559\) 24.7298 1.04596
\(560\) 0 0
\(561\) 5.49885 0.232162
\(562\) 0 0
\(563\) −13.3745 −0.563667 −0.281834 0.959463i \(-0.590943\pi\)
−0.281834 + 0.959463i \(0.590943\pi\)
\(564\) 0 0
\(565\) −5.46821 −0.230049
\(566\) 0 0
\(567\) −4.30712 −0.180882
\(568\) 0 0
\(569\) 22.8533 0.958060 0.479030 0.877799i \(-0.340988\pi\)
0.479030 + 0.877799i \(0.340988\pi\)
\(570\) 0 0
\(571\) 11.3829 0.476359 0.238179 0.971221i \(-0.423449\pi\)
0.238179 + 0.971221i \(0.423449\pi\)
\(572\) 0 0
\(573\) −7.46011 −0.311651
\(574\) 0 0
\(575\) 18.4293 0.768555
\(576\) 0 0
\(577\) −20.1452 −0.838655 −0.419328 0.907835i \(-0.637734\pi\)
−0.419328 + 0.907835i \(0.637734\pi\)
\(578\) 0 0
\(579\) 21.5351 0.894967
\(580\) 0 0
\(581\) 13.9945 0.580590
\(582\) 0 0
\(583\) 17.5491 0.726810
\(584\) 0 0
\(585\) 9.05933 0.374557
\(586\) 0 0
\(587\) 11.3827 0.469816 0.234908 0.972018i \(-0.424521\pi\)
0.234908 + 0.972018i \(0.424521\pi\)
\(588\) 0 0
\(589\) −1.25357 −0.0516524
\(590\) 0 0
\(591\) 14.6589 0.602986
\(592\) 0 0
\(593\) −42.7338 −1.75487 −0.877433 0.479699i \(-0.840746\pi\)
−0.877433 + 0.479699i \(0.840746\pi\)
\(594\) 0 0
\(595\) −2.61113 −0.107046
\(596\) 0 0
\(597\) 9.21941 0.377325
\(598\) 0 0
\(599\) 30.7320 1.25568 0.627839 0.778344i \(-0.283940\pi\)
0.627839 + 0.778344i \(0.283940\pi\)
\(600\) 0 0
\(601\) −30.1861 −1.23132 −0.615658 0.788014i \(-0.711110\pi\)
−0.615658 + 0.788014i \(0.711110\pi\)
\(602\) 0 0
\(603\) 17.1287 0.697533
\(604\) 0 0
\(605\) 10.7867 0.438542
\(606\) 0 0
\(607\) 21.0474 0.854288 0.427144 0.904184i \(-0.359520\pi\)
0.427144 + 0.904184i \(0.359520\pi\)
\(608\) 0 0
\(609\) 24.4692 0.991542
\(610\) 0 0
\(611\) 30.3793 1.22902
\(612\) 0 0
\(613\) 22.4809 0.907995 0.453998 0.891003i \(-0.349997\pi\)
0.453998 + 0.891003i \(0.349997\pi\)
\(614\) 0 0
\(615\) −7.26633 −0.293007
\(616\) 0 0
\(617\) −47.7816 −1.92361 −0.961806 0.273730i \(-0.911742\pi\)
−0.961806 + 0.273730i \(0.911742\pi\)
\(618\) 0 0
\(619\) −1.12745 −0.0453161 −0.0226580 0.999743i \(-0.507213\pi\)
−0.0226580 + 0.999743i \(0.507213\pi\)
\(620\) 0 0
\(621\) −25.5463 −1.02514
\(622\) 0 0
\(623\) −3.00436 −0.120367
\(624\) 0 0
\(625\) 10.1225 0.404899
\(626\) 0 0
\(627\) −23.9312 −0.955719
\(628\) 0 0
\(629\) 8.28324 0.330274
\(630\) 0 0
\(631\) −10.8411 −0.431576 −0.215788 0.976440i \(-0.569232\pi\)
−0.215788 + 0.976440i \(0.569232\pi\)
\(632\) 0 0
\(633\) −15.3203 −0.608926
\(634\) 0 0
\(635\) 15.0546 0.597424
\(636\) 0 0
\(637\) 3.39318 0.134443
\(638\) 0 0
\(639\) −2.89157 −0.114389
\(640\) 0 0
\(641\) 17.4969 0.691086 0.345543 0.938403i \(-0.387695\pi\)
0.345543 + 0.938403i \(0.387695\pi\)
\(642\) 0 0
\(643\) 39.7035 1.56575 0.782877 0.622176i \(-0.213751\pi\)
0.782877 + 0.622176i \(0.213751\pi\)
\(644\) 0 0
\(645\) 5.50291 0.216677
\(646\) 0 0
\(647\) −17.0242 −0.669290 −0.334645 0.942344i \(-0.608616\pi\)
−0.334645 + 0.942344i \(0.608616\pi\)
\(648\) 0 0
\(649\) 4.63016 0.181750
\(650\) 0 0
\(651\) 0.864380 0.0338777
\(652\) 0 0
\(653\) 40.7887 1.59618 0.798092 0.602536i \(-0.205843\pi\)
0.798092 + 0.602536i \(0.205843\pi\)
\(654\) 0 0
\(655\) −1.70192 −0.0664996
\(656\) 0 0
\(657\) −1.42168 −0.0554651
\(658\) 0 0
\(659\) −7.20821 −0.280792 −0.140396 0.990095i \(-0.544838\pi\)
−0.140396 + 0.990095i \(0.544838\pi\)
\(660\) 0 0
\(661\) 34.9067 1.35771 0.678857 0.734270i \(-0.262475\pi\)
0.678857 + 0.734270i \(0.262475\pi\)
\(662\) 0 0
\(663\) −6.54993 −0.254378
\(664\) 0 0
\(665\) 11.3637 0.440666
\(666\) 0 0
\(667\) 38.2165 1.47975
\(668\) 0 0
\(669\) 17.7940 0.687957
\(670\) 0 0
\(671\) 2.88730 0.111463
\(672\) 0 0
\(673\) −6.96846 −0.268614 −0.134307 0.990940i \(-0.542881\pi\)
−0.134307 + 0.990940i \(0.542881\pi\)
\(674\) 0 0
\(675\) −21.4327 −0.824946
\(676\) 0 0
\(677\) 28.8553 1.10900 0.554500 0.832184i \(-0.312910\pi\)
0.554500 + 0.832184i \(0.312910\pi\)
\(678\) 0 0
\(679\) −22.9637 −0.881266
\(680\) 0 0
\(681\) 4.34353 0.166445
\(682\) 0 0
\(683\) 40.0525 1.53257 0.766283 0.642503i \(-0.222104\pi\)
0.766283 + 0.642503i \(0.222104\pi\)
\(684\) 0 0
\(685\) 2.06497 0.0788984
\(686\) 0 0
\(687\) −12.2433 −0.467112
\(688\) 0 0
\(689\) −20.9035 −0.796361
\(690\) 0 0
\(691\) −10.5665 −0.401969 −0.200985 0.979594i \(-0.564414\pi\)
−0.200985 + 0.979594i \(0.564414\pi\)
\(692\) 0 0
\(693\) −18.5972 −0.706449
\(694\) 0 0
\(695\) −17.2192 −0.653161
\(696\) 0 0
\(697\) −5.92083 −0.224268
\(698\) 0 0
\(699\) 29.2954 1.10806
\(700\) 0 0
\(701\) −35.6541 −1.34664 −0.673319 0.739352i \(-0.735132\pi\)
−0.673319 + 0.739352i \(0.735132\pi\)
\(702\) 0 0
\(703\) −36.0489 −1.35961
\(704\) 0 0
\(705\) 6.76005 0.254598
\(706\) 0 0
\(707\) −5.90598 −0.222117
\(708\) 0 0
\(709\) −13.2597 −0.497979 −0.248990 0.968506i \(-0.580098\pi\)
−0.248990 + 0.968506i \(0.580098\pi\)
\(710\) 0 0
\(711\) −1.02941 −0.0386058
\(712\) 0 0
\(713\) 1.35001 0.0505582
\(714\) 0 0
\(715\) −26.3884 −0.986870
\(716\) 0 0
\(717\) 6.06893 0.226648
\(718\) 0 0
\(719\) −35.7261 −1.33236 −0.666180 0.745791i \(-0.732072\pi\)
−0.666180 + 0.745791i \(0.732072\pi\)
\(720\) 0 0
\(721\) 15.1867 0.565581
\(722\) 0 0
\(723\) 21.9269 0.815471
\(724\) 0 0
\(725\) 32.0628 1.19078
\(726\) 0 0
\(727\) 45.6976 1.69483 0.847415 0.530932i \(-0.178158\pi\)
0.847415 + 0.530932i \(0.178158\pi\)
\(728\) 0 0
\(729\) 22.1294 0.819606
\(730\) 0 0
\(731\) 4.48394 0.165845
\(732\) 0 0
\(733\) −25.7661 −0.951691 −0.475846 0.879529i \(-0.657858\pi\)
−0.475846 + 0.879529i \(0.657858\pi\)
\(734\) 0 0
\(735\) 0.755056 0.0278507
\(736\) 0 0
\(737\) −49.8931 −1.83784
\(738\) 0 0
\(739\) 25.5492 0.939843 0.469922 0.882708i \(-0.344282\pi\)
0.469922 + 0.882708i \(0.344282\pi\)
\(740\) 0 0
\(741\) 28.5055 1.04718
\(742\) 0 0
\(743\) 44.7258 1.64083 0.820415 0.571769i \(-0.193743\pi\)
0.820415 + 0.571769i \(0.193743\pi\)
\(744\) 0 0
\(745\) −13.7286 −0.502978
\(746\) 0 0
\(747\) −8.80369 −0.322110
\(748\) 0 0
\(749\) −49.2945 −1.80118
\(750\) 0 0
\(751\) 27.4166 1.00045 0.500224 0.865896i \(-0.333251\pi\)
0.500224 + 0.865896i \(0.333251\pi\)
\(752\) 0 0
\(753\) −8.83985 −0.322142
\(754\) 0 0
\(755\) −9.77124 −0.355612
\(756\) 0 0
\(757\) 26.8335 0.975280 0.487640 0.873045i \(-0.337858\pi\)
0.487640 + 0.873045i \(0.337858\pi\)
\(758\) 0 0
\(759\) 25.7722 0.935472
\(760\) 0 0
\(761\) −37.6103 −1.36337 −0.681686 0.731645i \(-0.738753\pi\)
−0.681686 + 0.731645i \(0.738753\pi\)
\(762\) 0 0
\(763\) 48.3284 1.74961
\(764\) 0 0
\(765\) 1.64261 0.0593888
\(766\) 0 0
\(767\) −5.51519 −0.199142
\(768\) 0 0
\(769\) 33.0477 1.19173 0.595866 0.803084i \(-0.296809\pi\)
0.595866 + 0.803084i \(0.296809\pi\)
\(770\) 0 0
\(771\) 6.63790 0.239058
\(772\) 0 0
\(773\) −28.1772 −1.01347 −0.506733 0.862103i \(-0.669147\pi\)
−0.506733 + 0.862103i \(0.669147\pi\)
\(774\) 0 0
\(775\) 1.13262 0.0406851
\(776\) 0 0
\(777\) 24.8570 0.891740
\(778\) 0 0
\(779\) 25.7676 0.923221
\(780\) 0 0
\(781\) 8.42268 0.301387
\(782\) 0 0
\(783\) −44.4446 −1.58832
\(784\) 0 0
\(785\) 12.5747 0.448810
\(786\) 0 0
\(787\) 14.5459 0.518507 0.259253 0.965809i \(-0.416524\pi\)
0.259253 + 0.965809i \(0.416524\pi\)
\(788\) 0 0
\(789\) 9.98839 0.355596
\(790\) 0 0
\(791\) −13.3709 −0.475415
\(792\) 0 0
\(793\) −3.43920 −0.122130
\(794\) 0 0
\(795\) −4.65148 −0.164971
\(796\) 0 0
\(797\) 22.5698 0.799462 0.399731 0.916633i \(-0.369104\pi\)
0.399731 + 0.916633i \(0.369104\pi\)
\(798\) 0 0
\(799\) 5.50830 0.194869
\(800\) 0 0
\(801\) 1.88999 0.0667794
\(802\) 0 0
\(803\) 4.14113 0.146137
\(804\) 0 0
\(805\) −12.2379 −0.431331
\(806\) 0 0
\(807\) 7.56396 0.266264
\(808\) 0 0
\(809\) 3.61148 0.126973 0.0634865 0.997983i \(-0.479778\pi\)
0.0634865 + 0.997983i \(0.479778\pi\)
\(810\) 0 0
\(811\) 33.7605 1.18549 0.592746 0.805390i \(-0.298044\pi\)
0.592746 + 0.805390i \(0.298044\pi\)
\(812\) 0 0
\(813\) −25.7051 −0.901517
\(814\) 0 0
\(815\) −24.4874 −0.857755
\(816\) 0 0
\(817\) −19.5142 −0.682717
\(818\) 0 0
\(819\) 22.1519 0.774052
\(820\) 0 0
\(821\) −7.93314 −0.276869 −0.138434 0.990372i \(-0.544207\pi\)
−0.138434 + 0.990372i \(0.544207\pi\)
\(822\) 0 0
\(823\) −12.6073 −0.439463 −0.219731 0.975560i \(-0.570518\pi\)
−0.219731 + 0.975560i \(0.570518\pi\)
\(824\) 0 0
\(825\) 21.6223 0.752791
\(826\) 0 0
\(827\) 44.0830 1.53292 0.766458 0.642294i \(-0.222017\pi\)
0.766458 + 0.642294i \(0.222017\pi\)
\(828\) 0 0
\(829\) −17.4568 −0.606300 −0.303150 0.952943i \(-0.598038\pi\)
−0.303150 + 0.952943i \(0.598038\pi\)
\(830\) 0 0
\(831\) 29.0840 1.00891
\(832\) 0 0
\(833\) 0.615243 0.0213169
\(834\) 0 0
\(835\) 15.6700 0.542284
\(836\) 0 0
\(837\) −1.57002 −0.0542677
\(838\) 0 0
\(839\) −52.3730 −1.80812 −0.904058 0.427410i \(-0.859426\pi\)
−0.904058 + 0.427410i \(0.859426\pi\)
\(840\) 0 0
\(841\) 37.4880 1.29269
\(842\) 0 0
\(843\) 0.786555 0.0270904
\(844\) 0 0
\(845\) 17.9986 0.619170
\(846\) 0 0
\(847\) 26.3758 0.906282
\(848\) 0 0
\(849\) −1.81649 −0.0623417
\(850\) 0 0
\(851\) 38.8222 1.33081
\(852\) 0 0
\(853\) 47.1584 1.61467 0.807336 0.590092i \(-0.200909\pi\)
0.807336 + 0.590092i \(0.200909\pi\)
\(854\) 0 0
\(855\) −7.14870 −0.244480
\(856\) 0 0
\(857\) −9.84517 −0.336305 −0.168152 0.985761i \(-0.553780\pi\)
−0.168152 + 0.985761i \(0.553780\pi\)
\(858\) 0 0
\(859\) 16.2690 0.555091 0.277546 0.960712i \(-0.410479\pi\)
0.277546 + 0.960712i \(0.410479\pi\)
\(860\) 0 0
\(861\) −17.7677 −0.605521
\(862\) 0 0
\(863\) 18.7237 0.637362 0.318681 0.947862i \(-0.396760\pi\)
0.318681 + 0.947862i \(0.396760\pi\)
\(864\) 0 0
\(865\) 13.5780 0.461665
\(866\) 0 0
\(867\) −1.18762 −0.0403336
\(868\) 0 0
\(869\) 2.99850 0.101717
\(870\) 0 0
\(871\) 59.4299 2.01371
\(872\) 0 0
\(873\) 14.4460 0.488924
\(874\) 0 0
\(875\) −23.3230 −0.788461
\(876\) 0 0
\(877\) 47.9591 1.61946 0.809732 0.586799i \(-0.199612\pi\)
0.809732 + 0.586799i \(0.199612\pi\)
\(878\) 0 0
\(879\) 15.7865 0.532467
\(880\) 0 0
\(881\) −36.3116 −1.22337 −0.611685 0.791102i \(-0.709508\pi\)
−0.611685 + 0.791102i \(0.709508\pi\)
\(882\) 0 0
\(883\) 14.7832 0.497493 0.248746 0.968569i \(-0.419981\pi\)
0.248746 + 0.968569i \(0.419981\pi\)
\(884\) 0 0
\(885\) −1.22725 −0.0412535
\(886\) 0 0
\(887\) −17.5647 −0.589765 −0.294882 0.955534i \(-0.595281\pi\)
−0.294882 + 0.955534i \(0.595281\pi\)
\(888\) 0 0
\(889\) 36.8117 1.23462
\(890\) 0 0
\(891\) −7.89244 −0.264407
\(892\) 0 0
\(893\) −23.9723 −0.802201
\(894\) 0 0
\(895\) 14.4355 0.482526
\(896\) 0 0
\(897\) −30.6985 −1.02499
\(898\) 0 0
\(899\) 2.34870 0.0783336
\(900\) 0 0
\(901\) −3.79017 −0.126269
\(902\) 0 0
\(903\) 13.4558 0.447779
\(904\) 0 0
\(905\) 6.44522 0.214247
\(906\) 0 0
\(907\) −26.9853 −0.896034 −0.448017 0.894025i \(-0.647870\pi\)
−0.448017 + 0.894025i \(0.647870\pi\)
\(908\) 0 0
\(909\) 3.71534 0.123230
\(910\) 0 0
\(911\) 15.0678 0.499217 0.249609 0.968347i \(-0.419698\pi\)
0.249609 + 0.968347i \(0.419698\pi\)
\(912\) 0 0
\(913\) 25.6437 0.848684
\(914\) 0 0
\(915\) −0.765296 −0.0252999
\(916\) 0 0
\(917\) −4.16156 −0.137427
\(918\) 0 0
\(919\) 46.0500 1.51905 0.759524 0.650479i \(-0.225432\pi\)
0.759524 + 0.650479i \(0.225432\pi\)
\(920\) 0 0
\(921\) 17.0608 0.562172
\(922\) 0 0
\(923\) −10.0326 −0.330228
\(924\) 0 0
\(925\) 32.5709 1.07092
\(926\) 0 0
\(927\) −9.55365 −0.313783
\(928\) 0 0
\(929\) −18.6977 −0.613451 −0.306725 0.951798i \(-0.599233\pi\)
−0.306725 + 0.951798i \(0.599233\pi\)
\(930\) 0 0
\(931\) −2.67755 −0.0877533
\(932\) 0 0
\(933\) 20.9906 0.687202
\(934\) 0 0
\(935\) −4.78467 −0.156476
\(936\) 0 0
\(937\) −3.18701 −0.104115 −0.0520576 0.998644i \(-0.516578\pi\)
−0.0520576 + 0.998644i \(0.516578\pi\)
\(938\) 0 0
\(939\) 27.5799 0.900036
\(940\) 0 0
\(941\) 13.3743 0.435989 0.217994 0.975950i \(-0.430049\pi\)
0.217994 + 0.975950i \(0.430049\pi\)
\(942\) 0 0
\(943\) −27.7500 −0.903663
\(944\) 0 0
\(945\) 14.2323 0.462978
\(946\) 0 0
\(947\) 26.1771 0.850641 0.425321 0.905043i \(-0.360161\pi\)
0.425321 + 0.905043i \(0.360161\pi\)
\(948\) 0 0
\(949\) −4.93269 −0.160122
\(950\) 0 0
\(951\) −9.93177 −0.322060
\(952\) 0 0
\(953\) −44.8044 −1.45136 −0.725679 0.688034i \(-0.758474\pi\)
−0.725679 + 0.688034i \(0.758474\pi\)
\(954\) 0 0
\(955\) 6.49121 0.210051
\(956\) 0 0
\(957\) 44.8377 1.44940
\(958\) 0 0
\(959\) 5.04928 0.163050
\(960\) 0 0
\(961\) −30.9170 −0.997324
\(962\) 0 0
\(963\) 31.0103 0.999291
\(964\) 0 0
\(965\) −18.7381 −0.603202
\(966\) 0 0
\(967\) 14.2867 0.459430 0.229715 0.973258i \(-0.426221\pi\)
0.229715 + 0.973258i \(0.426221\pi\)
\(968\) 0 0
\(969\) 5.16854 0.166037
\(970\) 0 0
\(971\) 33.2314 1.06645 0.533224 0.845974i \(-0.320980\pi\)
0.533224 + 0.845974i \(0.320980\pi\)
\(972\) 0 0
\(973\) −42.1045 −1.34981
\(974\) 0 0
\(975\) −25.7553 −0.824829
\(976\) 0 0
\(977\) −7.86530 −0.251633 −0.125817 0.992054i \(-0.540155\pi\)
−0.125817 + 0.992054i \(0.540155\pi\)
\(978\) 0 0
\(979\) −5.50523 −0.175948
\(980\) 0 0
\(981\) −30.4025 −0.970678
\(982\) 0 0
\(983\) −60.8191 −1.93983 −0.969914 0.243447i \(-0.921722\pi\)
−0.969914 + 0.243447i \(0.921722\pi\)
\(984\) 0 0
\(985\) −12.7550 −0.406409
\(986\) 0 0
\(987\) 16.5297 0.526147
\(988\) 0 0
\(989\) 21.0155 0.668254
\(990\) 0 0
\(991\) −12.1698 −0.386588 −0.193294 0.981141i \(-0.561917\pi\)
−0.193294 + 0.981141i \(0.561917\pi\)
\(992\) 0 0
\(993\) 26.3766 0.837037
\(994\) 0 0
\(995\) −8.02201 −0.254315
\(996\) 0 0
\(997\) −50.0742 −1.58587 −0.792933 0.609308i \(-0.791447\pi\)
−0.792933 + 0.609308i \(0.791447\pi\)
\(998\) 0 0
\(999\) −45.1490 −1.42845
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 \(a_p\))