Properties

Label 8048.2.a.p.1.5
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 10
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(0.208270\)
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.791730 q^{3}\) \(+0.178789 q^{5}\) \(+0.0809018 q^{7}\) \(-2.37316 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.791730 q^{3}\) \(+0.178789 q^{5}\) \(+0.0809018 q^{7}\) \(-2.37316 q^{9}\) \(+4.30391 q^{11}\) \(+1.10019 q^{13}\) \(+0.141552 q^{15}\) \(-3.06504 q^{17}\) \(+2.15853 q^{19}\) \(+0.0640524 q^{21}\) \(-9.15620 q^{23}\) \(-4.96803 q^{25}\) \(-4.25410 q^{27}\) \(-6.17849 q^{29}\) \(+9.82812 q^{31}\) \(+3.40754 q^{33}\) \(+0.0144643 q^{35}\) \(+4.08321 q^{37}\) \(+0.871056 q^{39}\) \(+4.58598 q^{41}\) \(-2.03126 q^{43}\) \(-0.424295 q^{45}\) \(+5.12836 q^{47}\) \(-6.99345 q^{49}\) \(-2.42668 q^{51}\) \(+2.69017 q^{53}\) \(+0.769491 q^{55}\) \(+1.70897 q^{57}\) \(-9.21598 q^{59}\) \(-14.0554 q^{61}\) \(-0.191993 q^{63}\) \(+0.196702 q^{65}\) \(-5.62801 q^{67}\) \(-7.24924 q^{69}\) \(+4.88191 q^{71}\) \(+10.9754 q^{73}\) \(-3.93334 q^{75}\) \(+0.348194 q^{77}\) \(-17.4356 q^{79}\) \(+3.75139 q^{81}\) \(+2.48372 q^{83}\) \(-0.547994 q^{85}\) \(-4.89170 q^{87}\) \(+5.57230 q^{89}\) \(+0.0890076 q^{91}\) \(+7.78122 q^{93}\) \(+0.385920 q^{95}\) \(-13.9731 q^{97}\) \(-10.2139 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(10q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(10q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut -\mathstrut 27q^{25} \) \(\mathstrut +\mathstrut 2q^{27} \) \(\mathstrut -\mathstrut 9q^{29} \) \(\mathstrut +\mathstrut 22q^{31} \) \(\mathstrut -\mathstrut 10q^{33} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut -\mathstrut 35q^{37} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 4q^{41} \) \(\mathstrut +\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 7q^{47} \) \(\mathstrut -\mathstrut 27q^{49} \) \(\mathstrut -\mathstrut 9q^{51} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut -\mathstrut 23q^{57} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 4q^{61} \) \(\mathstrut -\mathstrut 10q^{63} \) \(\mathstrut -\mathstrut 16q^{65} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut q^{71} \) \(\mathstrut -\mathstrut 31q^{73} \) \(\mathstrut -\mathstrut 30q^{75} \) \(\mathstrut +\mathstrut 3q^{77} \) \(\mathstrut +\mathstrut 10q^{79} \) \(\mathstrut -\mathstrut 6q^{81} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 25q^{87} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 6q^{93} \) \(\mathstrut -\mathstrut 39q^{95} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 35q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0.791730 0.457106 0.228553 0.973532i \(-0.426601\pi\)
0.228553 + 0.973532i \(0.426601\pi\)
\(4\) 0 0
\(5\) 0.178789 0.0799568 0.0399784 0.999201i \(-0.487271\pi\)
0.0399784 + 0.999201i \(0.487271\pi\)
\(6\) 0 0
\(7\) 0.0809018 0.0305780 0.0152890 0.999883i \(-0.495133\pi\)
0.0152890 + 0.999883i \(0.495133\pi\)
\(8\) 0 0
\(9\) −2.37316 −0.791054
\(10\) 0 0
\(11\) 4.30391 1.29768 0.648839 0.760926i \(-0.275255\pi\)
0.648839 + 0.760926i \(0.275255\pi\)
\(12\) 0 0
\(13\) 1.10019 0.305139 0.152569 0.988293i \(-0.451245\pi\)
0.152569 + 0.988293i \(0.451245\pi\)
\(14\) 0 0
\(15\) 0.141552 0.0365487
\(16\) 0 0
\(17\) −3.06504 −0.743381 −0.371690 0.928357i \(-0.621222\pi\)
−0.371690 + 0.928357i \(0.621222\pi\)
\(18\) 0 0
\(19\) 2.15853 0.495200 0.247600 0.968862i \(-0.420358\pi\)
0.247600 + 0.968862i \(0.420358\pi\)
\(20\) 0 0
\(21\) 0.0640524 0.0139774
\(22\) 0 0
\(23\) −9.15620 −1.90920 −0.954600 0.297892i \(-0.903716\pi\)
−0.954600 + 0.297892i \(0.903716\pi\)
\(24\) 0 0
\(25\) −4.96803 −0.993607
\(26\) 0 0
\(27\) −4.25410 −0.818701
\(28\) 0 0
\(29\) −6.17849 −1.14732 −0.573658 0.819095i \(-0.694476\pi\)
−0.573658 + 0.819095i \(0.694476\pi\)
\(30\) 0 0
\(31\) 9.82812 1.76518 0.882591 0.470141i \(-0.155797\pi\)
0.882591 + 0.470141i \(0.155797\pi\)
\(32\) 0 0
\(33\) 3.40754 0.593176
\(34\) 0 0
\(35\) 0.0144643 0.00244492
\(36\) 0 0
\(37\) 4.08321 0.671275 0.335637 0.941991i \(-0.391048\pi\)
0.335637 + 0.941991i \(0.391048\pi\)
\(38\) 0 0
\(39\) 0.871056 0.139481
\(40\) 0 0
\(41\) 4.58598 0.716210 0.358105 0.933681i \(-0.383423\pi\)
0.358105 + 0.933681i \(0.383423\pi\)
\(42\) 0 0
\(43\) −2.03126 −0.309764 −0.154882 0.987933i \(-0.549500\pi\)
−0.154882 + 0.987933i \(0.549500\pi\)
\(44\) 0 0
\(45\) −0.424295 −0.0632501
\(46\) 0 0
\(47\) 5.12836 0.748049 0.374024 0.927419i \(-0.377978\pi\)
0.374024 + 0.927419i \(0.377978\pi\)
\(48\) 0 0
\(49\) −6.99345 −0.999065
\(50\) 0 0
\(51\) −2.42668 −0.339804
\(52\) 0 0
\(53\) 2.69017 0.369523 0.184761 0.982783i \(-0.440849\pi\)
0.184761 + 0.982783i \(0.440849\pi\)
\(54\) 0 0
\(55\) 0.769491 0.103758
\(56\) 0 0
\(57\) 1.70897 0.226359
\(58\) 0 0
\(59\) −9.21598 −1.19982 −0.599909 0.800068i \(-0.704797\pi\)
−0.599909 + 0.800068i \(0.704797\pi\)
\(60\) 0 0
\(61\) −14.0554 −1.79961 −0.899805 0.436291i \(-0.856292\pi\)
−0.899805 + 0.436291i \(0.856292\pi\)
\(62\) 0 0
\(63\) −0.191993 −0.0241889
\(64\) 0 0
\(65\) 0.196702 0.0243979
\(66\) 0 0
\(67\) −5.62801 −0.687570 −0.343785 0.939048i \(-0.611709\pi\)
−0.343785 + 0.939048i \(0.611709\pi\)
\(68\) 0 0
\(69\) −7.24924 −0.872706
\(70\) 0 0
\(71\) 4.88191 0.579376 0.289688 0.957121i \(-0.406448\pi\)
0.289688 + 0.957121i \(0.406448\pi\)
\(72\) 0 0
\(73\) 10.9754 1.28457 0.642286 0.766465i \(-0.277986\pi\)
0.642286 + 0.766465i \(0.277986\pi\)
\(74\) 0 0
\(75\) −3.93334 −0.454183
\(76\) 0 0
\(77\) 0.348194 0.0396804
\(78\) 0 0
\(79\) −17.4356 −1.96166 −0.980828 0.194874i \(-0.937570\pi\)
−0.980828 + 0.194874i \(0.937570\pi\)
\(80\) 0 0
\(81\) 3.75139 0.416822
\(82\) 0 0
\(83\) 2.48372 0.272624 0.136312 0.990666i \(-0.456475\pi\)
0.136312 + 0.990666i \(0.456475\pi\)
\(84\) 0 0
\(85\) −0.547994 −0.0594383
\(86\) 0 0
\(87\) −4.89170 −0.524445
\(88\) 0 0
\(89\) 5.57230 0.590662 0.295331 0.955395i \(-0.404570\pi\)
0.295331 + 0.955395i \(0.404570\pi\)
\(90\) 0 0
\(91\) 0.0890076 0.00933053
\(92\) 0 0
\(93\) 7.78122 0.806875
\(94\) 0 0
\(95\) 0.385920 0.0395946
\(96\) 0 0
\(97\) −13.9731 −1.41876 −0.709379 0.704828i \(-0.751024\pi\)
−0.709379 + 0.704828i \(0.751024\pi\)
\(98\) 0 0
\(99\) −10.2139 −1.02653
\(100\) 0 0
\(101\) −7.98379 −0.794417 −0.397208 0.917728i \(-0.630021\pi\)
−0.397208 + 0.917728i \(0.630021\pi\)
\(102\) 0 0
\(103\) −10.5314 −1.03769 −0.518846 0.854868i \(-0.673638\pi\)
−0.518846 + 0.854868i \(0.673638\pi\)
\(104\) 0 0
\(105\) 0.0114518 0.00111759
\(106\) 0 0
\(107\) 3.31671 0.320638 0.160319 0.987065i \(-0.448748\pi\)
0.160319 + 0.987065i \(0.448748\pi\)
\(108\) 0 0
\(109\) −12.7956 −1.22559 −0.612797 0.790240i \(-0.709956\pi\)
−0.612797 + 0.790240i \(0.709956\pi\)
\(110\) 0 0
\(111\) 3.23280 0.306844
\(112\) 0 0
\(113\) −4.42086 −0.415880 −0.207940 0.978142i \(-0.566676\pi\)
−0.207940 + 0.978142i \(0.566676\pi\)
\(114\) 0 0
\(115\) −1.63702 −0.152653
\(116\) 0 0
\(117\) −2.61094 −0.241381
\(118\) 0 0
\(119\) −0.247967 −0.0227311
\(120\) 0 0
\(121\) 7.52364 0.683967
\(122\) 0 0
\(123\) 3.63086 0.327384
\(124\) 0 0
\(125\) −1.78217 −0.159402
\(126\) 0 0
\(127\) 17.5071 1.55351 0.776753 0.629806i \(-0.216865\pi\)
0.776753 + 0.629806i \(0.216865\pi\)
\(128\) 0 0
\(129\) −1.60821 −0.141595
\(130\) 0 0
\(131\) −11.8336 −1.03390 −0.516952 0.856014i \(-0.672934\pi\)
−0.516952 + 0.856014i \(0.672934\pi\)
\(132\) 0 0
\(133\) 0.174629 0.0151422
\(134\) 0 0
\(135\) −0.760584 −0.0654607
\(136\) 0 0
\(137\) −2.19499 −0.187530 −0.0937651 0.995594i \(-0.529890\pi\)
−0.0937651 + 0.995594i \(0.529890\pi\)
\(138\) 0 0
\(139\) −6.11773 −0.518899 −0.259450 0.965757i \(-0.583541\pi\)
−0.259450 + 0.965757i \(0.583541\pi\)
\(140\) 0 0
\(141\) 4.06028 0.341937
\(142\) 0 0
\(143\) 4.73513 0.395972
\(144\) 0 0
\(145\) −1.10464 −0.0917357
\(146\) 0 0
\(147\) −5.53693 −0.456678
\(148\) 0 0
\(149\) −17.3950 −1.42505 −0.712526 0.701646i \(-0.752449\pi\)
−0.712526 + 0.701646i \(0.752449\pi\)
\(150\) 0 0
\(151\) 21.9595 1.78704 0.893520 0.449024i \(-0.148228\pi\)
0.893520 + 0.449024i \(0.148228\pi\)
\(152\) 0 0
\(153\) 7.27383 0.588055
\(154\) 0 0
\(155\) 1.75716 0.141138
\(156\) 0 0
\(157\) −19.5736 −1.56214 −0.781070 0.624444i \(-0.785326\pi\)
−0.781070 + 0.624444i \(0.785326\pi\)
\(158\) 0 0
\(159\) 2.12989 0.168911
\(160\) 0 0
\(161\) −0.740753 −0.0583795
\(162\) 0 0
\(163\) 14.2549 1.11653 0.558265 0.829663i \(-0.311467\pi\)
0.558265 + 0.829663i \(0.311467\pi\)
\(164\) 0 0
\(165\) 0.609229 0.0474284
\(166\) 0 0
\(167\) 19.3555 1.49777 0.748886 0.662698i \(-0.230589\pi\)
0.748886 + 0.662698i \(0.230589\pi\)
\(168\) 0 0
\(169\) −11.7896 −0.906890
\(170\) 0 0
\(171\) −5.12254 −0.391730
\(172\) 0 0
\(173\) 24.1751 1.83800 0.919000 0.394258i \(-0.128998\pi\)
0.919000 + 0.394258i \(0.128998\pi\)
\(174\) 0 0
\(175\) −0.401923 −0.0303825
\(176\) 0 0
\(177\) −7.29657 −0.548444
\(178\) 0 0
\(179\) −11.7844 −0.880807 −0.440403 0.897800i \(-0.645165\pi\)
−0.440403 + 0.897800i \(0.645165\pi\)
\(180\) 0 0
\(181\) 0.193747 0.0144011 0.00720054 0.999974i \(-0.497708\pi\)
0.00720054 + 0.999974i \(0.497708\pi\)
\(182\) 0 0
\(183\) −11.1281 −0.822612
\(184\) 0 0
\(185\) 0.730031 0.0536730
\(186\) 0 0
\(187\) −13.1916 −0.964669
\(188\) 0 0
\(189\) −0.344164 −0.0250342
\(190\) 0 0
\(191\) 20.0106 1.44791 0.723957 0.689845i \(-0.242321\pi\)
0.723957 + 0.689845i \(0.242321\pi\)
\(192\) 0 0
\(193\) −16.4429 −1.18358 −0.591792 0.806091i \(-0.701579\pi\)
−0.591792 + 0.806091i \(0.701579\pi\)
\(194\) 0 0
\(195\) 0.155735 0.0111524
\(196\) 0 0
\(197\) 24.3311 1.73352 0.866761 0.498723i \(-0.166198\pi\)
0.866761 + 0.498723i \(0.166198\pi\)
\(198\) 0 0
\(199\) 16.2467 1.15170 0.575851 0.817555i \(-0.304671\pi\)
0.575851 + 0.817555i \(0.304671\pi\)
\(200\) 0 0
\(201\) −4.45586 −0.314292
\(202\) 0 0
\(203\) −0.499851 −0.0350827
\(204\) 0 0
\(205\) 0.819922 0.0572659
\(206\) 0 0
\(207\) 21.7292 1.51028
\(208\) 0 0
\(209\) 9.29010 0.642610
\(210\) 0 0
\(211\) −13.5844 −0.935189 −0.467594 0.883943i \(-0.654879\pi\)
−0.467594 + 0.883943i \(0.654879\pi\)
\(212\) 0 0
\(213\) 3.86515 0.264836
\(214\) 0 0
\(215\) −0.363166 −0.0247677
\(216\) 0 0
\(217\) 0.795113 0.0539758
\(218\) 0 0
\(219\) 8.68955 0.587185
\(220\) 0 0
\(221\) −3.37213 −0.226834
\(222\) 0 0
\(223\) −24.6725 −1.65219 −0.826096 0.563530i \(-0.809443\pi\)
−0.826096 + 0.563530i \(0.809443\pi\)
\(224\) 0 0
\(225\) 11.7900 0.785997
\(226\) 0 0
\(227\) −17.9854 −1.19373 −0.596866 0.802341i \(-0.703588\pi\)
−0.596866 + 0.802341i \(0.703588\pi\)
\(228\) 0 0
\(229\) 15.8558 1.04778 0.523891 0.851786i \(-0.324480\pi\)
0.523891 + 0.851786i \(0.324480\pi\)
\(230\) 0 0
\(231\) 0.275676 0.0181381
\(232\) 0 0
\(233\) 2.33607 0.153041 0.0765205 0.997068i \(-0.475619\pi\)
0.0765205 + 0.997068i \(0.475619\pi\)
\(234\) 0 0
\(235\) 0.916894 0.0598115
\(236\) 0 0
\(237\) −13.8043 −0.896684
\(238\) 0 0
\(239\) −4.84852 −0.313625 −0.156812 0.987628i \(-0.550122\pi\)
−0.156812 + 0.987628i \(0.550122\pi\)
\(240\) 0 0
\(241\) −3.42679 −0.220739 −0.110369 0.993891i \(-0.535203\pi\)
−0.110369 + 0.993891i \(0.535203\pi\)
\(242\) 0 0
\(243\) 15.7324 1.00923
\(244\) 0 0
\(245\) −1.25035 −0.0798820
\(246\) 0 0
\(247\) 2.37480 0.151105
\(248\) 0 0
\(249\) 1.96644 0.124618
\(250\) 0 0
\(251\) 25.7166 1.62321 0.811607 0.584204i \(-0.198593\pi\)
0.811607 + 0.584204i \(0.198593\pi\)
\(252\) 0 0
\(253\) −39.4074 −2.47753
\(254\) 0 0
\(255\) −0.433864 −0.0271696
\(256\) 0 0
\(257\) −24.1897 −1.50891 −0.754457 0.656350i \(-0.772100\pi\)
−0.754457 + 0.656350i \(0.772100\pi\)
\(258\) 0 0
\(259\) 0.330339 0.0205262
\(260\) 0 0
\(261\) 14.6626 0.907590
\(262\) 0 0
\(263\) −18.1779 −1.12089 −0.560447 0.828190i \(-0.689371\pi\)
−0.560447 + 0.828190i \(0.689371\pi\)
\(264\) 0 0
\(265\) 0.480972 0.0295458
\(266\) 0 0
\(267\) 4.41176 0.269995
\(268\) 0 0
\(269\) −5.69010 −0.346931 −0.173466 0.984840i \(-0.555497\pi\)
−0.173466 + 0.984840i \(0.555497\pi\)
\(270\) 0 0
\(271\) −16.4138 −0.997069 −0.498535 0.866870i \(-0.666128\pi\)
−0.498535 + 0.866870i \(0.666128\pi\)
\(272\) 0 0
\(273\) 0.0704700 0.00426504
\(274\) 0 0
\(275\) −21.3820 −1.28938
\(276\) 0 0
\(277\) −26.4497 −1.58921 −0.794605 0.607127i \(-0.792322\pi\)
−0.794605 + 0.607127i \(0.792322\pi\)
\(278\) 0 0
\(279\) −23.3237 −1.39636
\(280\) 0 0
\(281\) 3.32607 0.198417 0.0992084 0.995067i \(-0.468369\pi\)
0.0992084 + 0.995067i \(0.468369\pi\)
\(282\) 0 0
\(283\) 21.9817 1.30668 0.653339 0.757065i \(-0.273367\pi\)
0.653339 + 0.757065i \(0.273367\pi\)
\(284\) 0 0
\(285\) 0.305545 0.0180989
\(286\) 0 0
\(287\) 0.371014 0.0219003
\(288\) 0 0
\(289\) −7.60555 −0.447385
\(290\) 0 0
\(291\) −11.0630 −0.648522
\(292\) 0 0
\(293\) −6.54118 −0.382140 −0.191070 0.981576i \(-0.561196\pi\)
−0.191070 + 0.981576i \(0.561196\pi\)
\(294\) 0 0
\(295\) −1.64771 −0.0959336
\(296\) 0 0
\(297\) −18.3092 −1.06241
\(298\) 0 0
\(299\) −10.0736 −0.582570
\(300\) 0 0
\(301\) −0.164333 −0.00947197
\(302\) 0 0
\(303\) −6.32101 −0.363132
\(304\) 0 0
\(305\) −2.51295 −0.143891
\(306\) 0 0
\(307\) −15.6985 −0.895959 −0.447980 0.894044i \(-0.647856\pi\)
−0.447980 + 0.894044i \(0.647856\pi\)
\(308\) 0 0
\(309\) −8.33804 −0.474335
\(310\) 0 0
\(311\) −25.6166 −1.45258 −0.726292 0.687386i \(-0.758758\pi\)
−0.726292 + 0.687386i \(0.758758\pi\)
\(312\) 0 0
\(313\) 3.69793 0.209019 0.104510 0.994524i \(-0.466673\pi\)
0.104510 + 0.994524i \(0.466673\pi\)
\(314\) 0 0
\(315\) −0.0343262 −0.00193406
\(316\) 0 0
\(317\) 19.0196 1.06825 0.534124 0.845406i \(-0.320641\pi\)
0.534124 + 0.845406i \(0.320641\pi\)
\(318\) 0 0
\(319\) −26.5917 −1.48885
\(320\) 0 0
\(321\) 2.62594 0.146566
\(322\) 0 0
\(323\) −6.61597 −0.368122
\(324\) 0 0
\(325\) −5.46580 −0.303188
\(326\) 0 0
\(327\) −10.1306 −0.560226
\(328\) 0 0
\(329\) 0.414894 0.0228738
\(330\) 0 0
\(331\) 4.74934 0.261048 0.130524 0.991445i \(-0.458334\pi\)
0.130524 + 0.991445i \(0.458334\pi\)
\(332\) 0 0
\(333\) −9.69011 −0.531015
\(334\) 0 0
\(335\) −1.00622 −0.0549759
\(336\) 0 0
\(337\) −29.8451 −1.62576 −0.812882 0.582428i \(-0.802103\pi\)
−0.812882 + 0.582428i \(0.802103\pi\)
\(338\) 0 0
\(339\) −3.50013 −0.190101
\(340\) 0 0
\(341\) 42.2993 2.29064
\(342\) 0 0
\(343\) −1.13210 −0.0611274
\(344\) 0 0
\(345\) −1.29608 −0.0697787
\(346\) 0 0
\(347\) −15.3781 −0.825540 −0.412770 0.910835i \(-0.635439\pi\)
−0.412770 + 0.910835i \(0.635439\pi\)
\(348\) 0 0
\(349\) 6.64130 0.355501 0.177750 0.984076i \(-0.443118\pi\)
0.177750 + 0.984076i \(0.443118\pi\)
\(350\) 0 0
\(351\) −4.68033 −0.249817
\(352\) 0 0
\(353\) −33.7272 −1.79512 −0.897558 0.440896i \(-0.854661\pi\)
−0.897558 + 0.440896i \(0.854661\pi\)
\(354\) 0 0
\(355\) 0.872830 0.0463250
\(356\) 0 0
\(357\) −0.196323 −0.0103905
\(358\) 0 0
\(359\) 27.2110 1.43614 0.718071 0.695970i \(-0.245025\pi\)
0.718071 + 0.695970i \(0.245025\pi\)
\(360\) 0 0
\(361\) −14.3408 −0.754777
\(362\) 0 0
\(363\) 5.95669 0.312645
\(364\) 0 0
\(365\) 1.96228 0.102710
\(366\) 0 0
\(367\) −14.0523 −0.733525 −0.366763 0.930315i \(-0.619534\pi\)
−0.366763 + 0.930315i \(0.619534\pi\)
\(368\) 0 0
\(369\) −10.8833 −0.566561
\(370\) 0 0
\(371\) 0.217639 0.0112993
\(372\) 0 0
\(373\) 19.8673 1.02869 0.514345 0.857584i \(-0.328035\pi\)
0.514345 + 0.857584i \(0.328035\pi\)
\(374\) 0 0
\(375\) −1.41100 −0.0728637
\(376\) 0 0
\(377\) −6.79753 −0.350091
\(378\) 0 0
\(379\) 16.4863 0.846844 0.423422 0.905933i \(-0.360829\pi\)
0.423422 + 0.905933i \(0.360829\pi\)
\(380\) 0 0
\(381\) 13.8609 0.710116
\(382\) 0 0
\(383\) −22.2392 −1.13637 −0.568186 0.822900i \(-0.692355\pi\)
−0.568186 + 0.822900i \(0.692355\pi\)
\(384\) 0 0
\(385\) 0.0622532 0.00317272
\(386\) 0 0
\(387\) 4.82051 0.245040
\(388\) 0 0
\(389\) −10.3650 −0.525528 −0.262764 0.964860i \(-0.584634\pi\)
−0.262764 + 0.964860i \(0.584634\pi\)
\(390\) 0 0
\(391\) 28.0641 1.41926
\(392\) 0 0
\(393\) −9.36900 −0.472604
\(394\) 0 0
\(395\) −3.11729 −0.156848
\(396\) 0 0
\(397\) −2.54363 −0.127661 −0.0638306 0.997961i \(-0.520332\pi\)
−0.0638306 + 0.997961i \(0.520332\pi\)
\(398\) 0 0
\(399\) 0.138259 0.00692160
\(400\) 0 0
\(401\) 12.4246 0.620455 0.310227 0.950662i \(-0.399595\pi\)
0.310227 + 0.950662i \(0.399595\pi\)
\(402\) 0 0
\(403\) 10.8128 0.538625
\(404\) 0 0
\(405\) 0.670707 0.0333277
\(406\) 0 0
\(407\) 17.5738 0.871098
\(408\) 0 0
\(409\) 14.3575 0.709932 0.354966 0.934879i \(-0.384492\pi\)
0.354966 + 0.934879i \(0.384492\pi\)
\(410\) 0 0
\(411\) −1.73784 −0.0857211
\(412\) 0 0
\(413\) −0.745589 −0.0366880
\(414\) 0 0
\(415\) 0.444061 0.0217981
\(416\) 0 0
\(417\) −4.84359 −0.237192
\(418\) 0 0
\(419\) −15.6860 −0.766309 −0.383155 0.923684i \(-0.625162\pi\)
−0.383155 + 0.923684i \(0.625162\pi\)
\(420\) 0 0
\(421\) 0.689920 0.0336247 0.0168123 0.999859i \(-0.494648\pi\)
0.0168123 + 0.999859i \(0.494648\pi\)
\(422\) 0 0
\(423\) −12.1704 −0.591747
\(424\) 0 0
\(425\) 15.2272 0.738628
\(426\) 0 0
\(427\) −1.13711 −0.0550285
\(428\) 0 0
\(429\) 3.74895 0.181001
\(430\) 0 0
\(431\) −29.0858 −1.40102 −0.700508 0.713645i \(-0.747043\pi\)
−0.700508 + 0.713645i \(0.747043\pi\)
\(432\) 0 0
\(433\) 18.1169 0.870643 0.435321 0.900275i \(-0.356635\pi\)
0.435321 + 0.900275i \(0.356635\pi\)
\(434\) 0 0
\(435\) −0.874580 −0.0419329
\(436\) 0 0
\(437\) −19.7639 −0.945435
\(438\) 0 0
\(439\) −3.25712 −0.155454 −0.0777270 0.996975i \(-0.524766\pi\)
−0.0777270 + 0.996975i \(0.524766\pi\)
\(440\) 0 0
\(441\) 16.5966 0.790315
\(442\) 0 0
\(443\) 21.5717 1.02490 0.512451 0.858717i \(-0.328738\pi\)
0.512451 + 0.858717i \(0.328738\pi\)
\(444\) 0 0
\(445\) 0.996264 0.0472274
\(446\) 0 0
\(447\) −13.7721 −0.651399
\(448\) 0 0
\(449\) 18.9612 0.894834 0.447417 0.894325i \(-0.352344\pi\)
0.447417 + 0.894325i \(0.352344\pi\)
\(450\) 0 0
\(451\) 19.7377 0.929410
\(452\) 0 0
\(453\) 17.3860 0.816866
\(454\) 0 0
\(455\) 0.0159136 0.000746039 0
\(456\) 0 0
\(457\) 4.18789 0.195901 0.0979506 0.995191i \(-0.468771\pi\)
0.0979506 + 0.995191i \(0.468771\pi\)
\(458\) 0 0
\(459\) 13.0390 0.608607
\(460\) 0 0
\(461\) 13.7101 0.638543 0.319271 0.947663i \(-0.396562\pi\)
0.319271 + 0.947663i \(0.396562\pi\)
\(462\) 0 0
\(463\) −4.87808 −0.226703 −0.113352 0.993555i \(-0.536159\pi\)
−0.113352 + 0.993555i \(0.536159\pi\)
\(464\) 0 0
\(465\) 1.39119 0.0645151
\(466\) 0 0
\(467\) −12.3373 −0.570904 −0.285452 0.958393i \(-0.592144\pi\)
−0.285452 + 0.958393i \(0.592144\pi\)
\(468\) 0 0
\(469\) −0.455316 −0.0210245
\(470\) 0 0
\(471\) −15.4970 −0.714063
\(472\) 0 0
\(473\) −8.74236 −0.401974
\(474\) 0 0
\(475\) −10.7236 −0.492034
\(476\) 0 0
\(477\) −6.38421 −0.292313
\(478\) 0 0
\(479\) 3.56361 0.162826 0.0814128 0.996680i \(-0.474057\pi\)
0.0814128 + 0.996680i \(0.474057\pi\)
\(480\) 0 0
\(481\) 4.49231 0.204832
\(482\) 0 0
\(483\) −0.586476 −0.0266856
\(484\) 0 0
\(485\) −2.49824 −0.113439
\(486\) 0 0
\(487\) 5.09262 0.230769 0.115384 0.993321i \(-0.463190\pi\)
0.115384 + 0.993321i \(0.463190\pi\)
\(488\) 0 0
\(489\) 11.2860 0.510372
\(490\) 0 0
\(491\) −27.1049 −1.22323 −0.611614 0.791156i \(-0.709479\pi\)
−0.611614 + 0.791156i \(0.709479\pi\)
\(492\) 0 0
\(493\) 18.9373 0.852893
\(494\) 0 0
\(495\) −1.82613 −0.0820783
\(496\) 0 0
\(497\) 0.394955 0.0177162
\(498\) 0 0
\(499\) 4.49778 0.201348 0.100674 0.994919i \(-0.467900\pi\)
0.100674 + 0.994919i \(0.467900\pi\)
\(500\) 0 0
\(501\) 15.3243 0.684640
\(502\) 0 0
\(503\) 1.00000 0.0445878
\(504\) 0 0
\(505\) −1.42741 −0.0635190
\(506\) 0 0
\(507\) −9.33416 −0.414545
\(508\) 0 0
\(509\) −9.92656 −0.439987 −0.219993 0.975501i \(-0.570604\pi\)
−0.219993 + 0.975501i \(0.570604\pi\)
\(510\) 0 0
\(511\) 0.887929 0.0392797
\(512\) 0 0
\(513\) −9.18258 −0.405421
\(514\) 0 0
\(515\) −1.88290 −0.0829704
\(516\) 0 0
\(517\) 22.0720 0.970726
\(518\) 0 0
\(519\) 19.1402 0.840160
\(520\) 0 0
\(521\) −8.65790 −0.379309 −0.189655 0.981851i \(-0.560737\pi\)
−0.189655 + 0.981851i \(0.560737\pi\)
\(522\) 0 0
\(523\) −17.7111 −0.774451 −0.387226 0.921985i \(-0.626567\pi\)
−0.387226 + 0.921985i \(0.626567\pi\)
\(524\) 0 0
\(525\) −0.318215 −0.0138880
\(526\) 0 0
\(527\) −30.1236 −1.31220
\(528\) 0 0
\(529\) 60.8360 2.64504
\(530\) 0 0
\(531\) 21.8710 0.949122
\(532\) 0 0
\(533\) 5.04547 0.218543
\(534\) 0 0
\(535\) 0.592990 0.0256372
\(536\) 0 0
\(537\) −9.33006 −0.402622
\(538\) 0 0
\(539\) −30.0992 −1.29646
\(540\) 0 0
\(541\) −10.8187 −0.465131 −0.232565 0.972581i \(-0.574712\pi\)
−0.232565 + 0.972581i \(0.574712\pi\)
\(542\) 0 0
\(543\) 0.153395 0.00658282
\(544\) 0 0
\(545\) −2.28771 −0.0979945
\(546\) 0 0
\(547\) 33.1188 1.41606 0.708028 0.706184i \(-0.249585\pi\)
0.708028 + 0.706184i \(0.249585\pi\)
\(548\) 0 0
\(549\) 33.3558 1.42359
\(550\) 0 0
\(551\) −13.3364 −0.568151
\(552\) 0 0
\(553\) −1.41057 −0.0599835
\(554\) 0 0
\(555\) 0.577988 0.0245342
\(556\) 0 0
\(557\) 12.3324 0.522541 0.261270 0.965266i \(-0.415859\pi\)
0.261270 + 0.965266i \(0.415859\pi\)
\(558\) 0 0
\(559\) −2.23478 −0.0945210
\(560\) 0 0
\(561\) −10.4442 −0.440955
\(562\) 0 0
\(563\) −29.3356 −1.23635 −0.618174 0.786041i \(-0.712127\pi\)
−0.618174 + 0.786041i \(0.712127\pi\)
\(564\) 0 0
\(565\) −0.790400 −0.0332524
\(566\) 0 0
\(567\) 0.303495 0.0127456
\(568\) 0 0
\(569\) 0.339405 0.0142286 0.00711431 0.999975i \(-0.497735\pi\)
0.00711431 + 0.999975i \(0.497735\pi\)
\(570\) 0 0
\(571\) 16.5993 0.694658 0.347329 0.937743i \(-0.387089\pi\)
0.347329 + 0.937743i \(0.387089\pi\)
\(572\) 0 0
\(573\) 15.8430 0.661850
\(574\) 0 0
\(575\) 45.4883 1.89699
\(576\) 0 0
\(577\) −19.0207 −0.791840 −0.395920 0.918285i \(-0.629574\pi\)
−0.395920 + 0.918285i \(0.629574\pi\)
\(578\) 0 0
\(579\) −13.0183 −0.541023
\(580\) 0 0
\(581\) 0.200937 0.00833629
\(582\) 0 0
\(583\) 11.5782 0.479522
\(584\) 0 0
\(585\) −0.466806 −0.0193001
\(586\) 0 0
\(587\) −29.3939 −1.21322 −0.606609 0.795000i \(-0.707471\pi\)
−0.606609 + 0.795000i \(0.707471\pi\)
\(588\) 0 0
\(589\) 21.2143 0.874118
\(590\) 0 0
\(591\) 19.2637 0.792403
\(592\) 0 0
\(593\) −21.6941 −0.890871 −0.445436 0.895314i \(-0.646951\pi\)
−0.445436 + 0.895314i \(0.646951\pi\)
\(594\) 0 0
\(595\) −0.0443337 −0.00181751
\(596\) 0 0
\(597\) 12.8630 0.526449
\(598\) 0 0
\(599\) 7.41054 0.302786 0.151393 0.988474i \(-0.451624\pi\)
0.151393 + 0.988474i \(0.451624\pi\)
\(600\) 0 0
\(601\) −17.7208 −0.722848 −0.361424 0.932402i \(-0.617709\pi\)
−0.361424 + 0.932402i \(0.617709\pi\)
\(602\) 0 0
\(603\) 13.3562 0.543906
\(604\) 0 0
\(605\) 1.34514 0.0546878
\(606\) 0 0
\(607\) −37.0318 −1.50307 −0.751536 0.659692i \(-0.770687\pi\)
−0.751536 + 0.659692i \(0.770687\pi\)
\(608\) 0 0
\(609\) −0.395747 −0.0160365
\(610\) 0 0
\(611\) 5.64219 0.228259
\(612\) 0 0
\(613\) 37.6348 1.52005 0.760027 0.649891i \(-0.225185\pi\)
0.760027 + 0.649891i \(0.225185\pi\)
\(614\) 0 0
\(615\) 0.649157 0.0261765
\(616\) 0 0
\(617\) −8.73601 −0.351699 −0.175849 0.984417i \(-0.556267\pi\)
−0.175849 + 0.984417i \(0.556267\pi\)
\(618\) 0 0
\(619\) −17.0846 −0.686687 −0.343343 0.939210i \(-0.611559\pi\)
−0.343343 + 0.939210i \(0.611559\pi\)
\(620\) 0 0
\(621\) 38.9513 1.56306
\(622\) 0 0
\(623\) 0.450809 0.0180613
\(624\) 0 0
\(625\) 24.5215 0.980862
\(626\) 0 0
\(627\) 7.35526 0.293741
\(628\) 0 0
\(629\) −12.5152 −0.499013
\(630\) 0 0
\(631\) 38.0472 1.51464 0.757318 0.653046i \(-0.226509\pi\)
0.757318 + 0.653046i \(0.226509\pi\)
\(632\) 0 0
\(633\) −10.7552 −0.427480
\(634\) 0 0
\(635\) 3.13008 0.124213
\(636\) 0 0
\(637\) −7.69415 −0.304853
\(638\) 0 0
\(639\) −11.5856 −0.458318
\(640\) 0 0
\(641\) 27.5905 1.08976 0.544879 0.838514i \(-0.316575\pi\)
0.544879 + 0.838514i \(0.316575\pi\)
\(642\) 0 0
\(643\) −6.89268 −0.271821 −0.135910 0.990721i \(-0.543396\pi\)
−0.135910 + 0.990721i \(0.543396\pi\)
\(644\) 0 0
\(645\) −0.287530 −0.0113215
\(646\) 0 0
\(647\) −8.60822 −0.338424 −0.169212 0.985580i \(-0.554122\pi\)
−0.169212 + 0.985580i \(0.554122\pi\)
\(648\) 0 0
\(649\) −39.6647 −1.55698
\(650\) 0 0
\(651\) 0.629515 0.0246726
\(652\) 0 0
\(653\) 3.73378 0.146114 0.0730571 0.997328i \(-0.476724\pi\)
0.0730571 + 0.997328i \(0.476724\pi\)
\(654\) 0 0
\(655\) −2.11571 −0.0826677
\(656\) 0 0
\(657\) −26.0464 −1.01617
\(658\) 0 0
\(659\) −10.1373 −0.394893 −0.197447 0.980314i \(-0.563265\pi\)
−0.197447 + 0.980314i \(0.563265\pi\)
\(660\) 0 0
\(661\) −11.0003 −0.427863 −0.213932 0.976849i \(-0.568627\pi\)
−0.213932 + 0.976849i \(0.568627\pi\)
\(662\) 0 0
\(663\) −2.66982 −0.103687
\(664\) 0 0
\(665\) 0.0312216 0.00121072
\(666\) 0 0
\(667\) 56.5715 2.19046
\(668\) 0 0
\(669\) −19.5339 −0.755226
\(670\) 0 0
\(671\) −60.4932 −2.33531
\(672\) 0 0
\(673\) −44.9940 −1.73439 −0.867196 0.497967i \(-0.834080\pi\)
−0.867196 + 0.497967i \(0.834080\pi\)
\(674\) 0 0
\(675\) 21.1345 0.813467
\(676\) 0 0
\(677\) 15.4870 0.595213 0.297607 0.954689i \(-0.403812\pi\)
0.297607 + 0.954689i \(0.403812\pi\)
\(678\) 0 0
\(679\) −1.13045 −0.0433828
\(680\) 0 0
\(681\) −14.2396 −0.545661
\(682\) 0 0
\(683\) −33.7255 −1.29047 −0.645235 0.763984i \(-0.723241\pi\)
−0.645235 + 0.763984i \(0.723241\pi\)
\(684\) 0 0
\(685\) −0.392439 −0.0149943
\(686\) 0 0
\(687\) 12.5535 0.478947
\(688\) 0 0
\(689\) 2.95970 0.112756
\(690\) 0 0
\(691\) −13.5728 −0.516333 −0.258166 0.966100i \(-0.583118\pi\)
−0.258166 + 0.966100i \(0.583118\pi\)
\(692\) 0 0
\(693\) −0.826321 −0.0313894
\(694\) 0 0
\(695\) −1.09378 −0.0414895
\(696\) 0 0
\(697\) −14.0562 −0.532417
\(698\) 0 0
\(699\) 1.84954 0.0699559
\(700\) 0 0
\(701\) −34.7789 −1.31358 −0.656790 0.754074i \(-0.728086\pi\)
−0.656790 + 0.754074i \(0.728086\pi\)
\(702\) 0 0
\(703\) 8.81371 0.332415
\(704\) 0 0
\(705\) 0.725932 0.0273402
\(706\) 0 0
\(707\) −0.645903 −0.0242917
\(708\) 0 0
\(709\) −23.1752 −0.870362 −0.435181 0.900343i \(-0.643316\pi\)
−0.435181 + 0.900343i \(0.643316\pi\)
\(710\) 0 0
\(711\) 41.3775 1.55178
\(712\) 0 0
\(713\) −89.9882 −3.37009
\(714\) 0 0
\(715\) 0.846588 0.0316606
\(716\) 0 0
\(717\) −3.83872 −0.143360
\(718\) 0 0
\(719\) 39.5082 1.47341 0.736704 0.676215i \(-0.236381\pi\)
0.736704 + 0.676215i \(0.236381\pi\)
\(720\) 0 0
\(721\) −0.852011 −0.0317305
\(722\) 0 0
\(723\) −2.71309 −0.100901
\(724\) 0 0
\(725\) 30.6950 1.13998
\(726\) 0 0
\(727\) 5.75881 0.213583 0.106791 0.994281i \(-0.465942\pi\)
0.106791 + 0.994281i \(0.465942\pi\)
\(728\) 0 0
\(729\) 1.20162 0.0445043
\(730\) 0 0
\(731\) 6.22589 0.230273
\(732\) 0 0
\(733\) −41.9036 −1.54774 −0.773872 0.633343i \(-0.781682\pi\)
−0.773872 + 0.633343i \(0.781682\pi\)
\(734\) 0 0
\(735\) −0.989941 −0.0365145
\(736\) 0 0
\(737\) −24.2224 −0.892245
\(738\) 0 0
\(739\) 14.5650 0.535780 0.267890 0.963449i \(-0.413674\pi\)
0.267890 + 0.963449i \(0.413674\pi\)
\(740\) 0 0
\(741\) 1.88020 0.0690708
\(742\) 0 0
\(743\) 22.9633 0.842440 0.421220 0.906958i \(-0.361602\pi\)
0.421220 + 0.906958i \(0.361602\pi\)
\(744\) 0 0
\(745\) −3.11003 −0.113943
\(746\) 0 0
\(747\) −5.89427 −0.215660
\(748\) 0 0
\(749\) 0.268328 0.00980448
\(750\) 0 0
\(751\) 8.52609 0.311121 0.155561 0.987826i \(-0.450282\pi\)
0.155561 + 0.987826i \(0.450282\pi\)
\(752\) 0 0
\(753\) 20.3606 0.741980
\(754\) 0 0
\(755\) 3.92611 0.142886
\(756\) 0 0
\(757\) −19.7364 −0.717331 −0.358665 0.933466i \(-0.616768\pi\)
−0.358665 + 0.933466i \(0.616768\pi\)
\(758\) 0 0
\(759\) −31.2001 −1.13249
\(760\) 0 0
\(761\) 44.7253 1.62129 0.810646 0.585537i \(-0.199116\pi\)
0.810646 + 0.585537i \(0.199116\pi\)
\(762\) 0 0
\(763\) −1.03519 −0.0374762
\(764\) 0 0
\(765\) 1.30048 0.0470189
\(766\) 0 0
\(767\) −10.1394 −0.366111
\(768\) 0 0
\(769\) −28.1170 −1.01393 −0.506963 0.861968i \(-0.669232\pi\)
−0.506963 + 0.861968i \(0.669232\pi\)
\(770\) 0 0
\(771\) −19.1517 −0.689733
\(772\) 0 0
\(773\) 34.5978 1.24440 0.622199 0.782859i \(-0.286240\pi\)
0.622199 + 0.782859i \(0.286240\pi\)
\(774\) 0 0
\(775\) −48.8264 −1.75390
\(776\) 0 0
\(777\) 0.261539 0.00938266
\(778\) 0 0
\(779\) 9.89897 0.354667
\(780\) 0 0
\(781\) 21.0113 0.751843
\(782\) 0 0
\(783\) 26.2839 0.939310
\(784\) 0 0
\(785\) −3.49953 −0.124904
\(786\) 0 0
\(787\) 46.1869 1.64639 0.823193 0.567762i \(-0.192190\pi\)
0.823193 + 0.567762i \(0.192190\pi\)
\(788\) 0 0
\(789\) −14.3920 −0.512367
\(790\) 0 0
\(791\) −0.357656 −0.0127168
\(792\) 0 0
\(793\) −15.4637 −0.549131
\(794\) 0 0
\(795\) 0.380800 0.0135056
\(796\) 0 0
\(797\) 31.0936 1.10139 0.550695 0.834707i \(-0.314363\pi\)
0.550695 + 0.834707i \(0.314363\pi\)
\(798\) 0 0
\(799\) −15.7186 −0.556085
\(800\) 0 0
\(801\) −13.2240 −0.467246
\(802\) 0 0
\(803\) 47.2371 1.66696
\(804\) 0 0
\(805\) −0.132438 −0.00466784
\(806\) 0 0
\(807\) −4.50502 −0.158584
\(808\) 0 0
\(809\) −22.7451 −0.799676 −0.399838 0.916586i \(-0.630934\pi\)
−0.399838 + 0.916586i \(0.630934\pi\)
\(810\) 0 0
\(811\) 20.2514 0.711121 0.355561 0.934653i \(-0.384290\pi\)
0.355561 + 0.934653i \(0.384290\pi\)
\(812\) 0 0
\(813\) −12.9953 −0.455766
\(814\) 0 0
\(815\) 2.54862 0.0892741
\(816\) 0 0
\(817\) −4.38453 −0.153395
\(818\) 0 0
\(819\) −0.211230 −0.00738096
\(820\) 0 0
\(821\) 47.0787 1.64306 0.821529 0.570167i \(-0.193121\pi\)
0.821529 + 0.570167i \(0.193121\pi\)
\(822\) 0 0
\(823\) 3.97277 0.138482 0.0692411 0.997600i \(-0.477942\pi\)
0.0692411 + 0.997600i \(0.477942\pi\)
\(824\) 0 0
\(825\) −16.9288 −0.589384
\(826\) 0 0
\(827\) 12.1175 0.421366 0.210683 0.977554i \(-0.432431\pi\)
0.210683 + 0.977554i \(0.432431\pi\)
\(828\) 0 0
\(829\) 27.0304 0.938804 0.469402 0.882985i \(-0.344470\pi\)
0.469402 + 0.882985i \(0.344470\pi\)
\(830\) 0 0
\(831\) −20.9410 −0.726437
\(832\) 0 0
\(833\) 21.4352 0.742686
\(834\) 0 0
\(835\) 3.46054 0.119757
\(836\) 0 0
\(837\) −41.8098 −1.44516
\(838\) 0 0
\(839\) 21.4624 0.740964 0.370482 0.928840i \(-0.379193\pi\)
0.370482 + 0.928840i \(0.379193\pi\)
\(840\) 0 0
\(841\) 9.17374 0.316336
\(842\) 0 0
\(843\) 2.63335 0.0906974
\(844\) 0 0
\(845\) −2.10784 −0.0725120
\(846\) 0 0
\(847\) 0.608676 0.0209144
\(848\) 0 0
\(849\) 17.4036 0.597290
\(850\) 0 0
\(851\) −37.3866 −1.28160
\(852\) 0 0
\(853\) −20.5093 −0.702226 −0.351113 0.936333i \(-0.614197\pi\)
−0.351113 + 0.936333i \(0.614197\pi\)
\(854\) 0 0
\(855\) −0.915852 −0.0313215
\(856\) 0 0
\(857\) −23.2772 −0.795135 −0.397567 0.917573i \(-0.630146\pi\)
−0.397567 + 0.917573i \(0.630146\pi\)
\(858\) 0 0
\(859\) 3.80551 0.129842 0.0649212 0.997890i \(-0.479320\pi\)
0.0649212 + 0.997890i \(0.479320\pi\)
\(860\) 0 0
\(861\) 0.293743 0.0100107
\(862\) 0 0
\(863\) 35.9633 1.22420 0.612102 0.790779i \(-0.290324\pi\)
0.612102 + 0.790779i \(0.290324\pi\)
\(864\) 0 0
\(865\) 4.32224 0.146960
\(866\) 0 0
\(867\) −6.02154 −0.204502
\(868\) 0 0
\(869\) −75.0412 −2.54560
\(870\) 0 0
\(871\) −6.19189 −0.209804
\(872\) 0 0
\(873\) 33.1605 1.12231
\(874\) 0 0
\(875\) −0.144181 −0.00487421
\(876\) 0 0
\(877\) 14.2388 0.480810 0.240405 0.970673i \(-0.422720\pi\)
0.240405 + 0.970673i \(0.422720\pi\)
\(878\) 0 0
\(879\) −5.17885 −0.174678
\(880\) 0 0
\(881\) 27.4845 0.925976 0.462988 0.886365i \(-0.346777\pi\)
0.462988 + 0.886365i \(0.346777\pi\)
\(882\) 0 0
\(883\) −24.3360 −0.818973 −0.409487 0.912316i \(-0.634292\pi\)
−0.409487 + 0.912316i \(0.634292\pi\)
\(884\) 0 0
\(885\) −1.30454 −0.0438518
\(886\) 0 0
\(887\) 26.2023 0.879787 0.439893 0.898050i \(-0.355016\pi\)
0.439893 + 0.898050i \(0.355016\pi\)
\(888\) 0 0
\(889\) 1.41636 0.0475031
\(890\) 0 0
\(891\) 16.1457 0.540900
\(892\) 0 0
\(893\) 11.0697 0.370434
\(894\) 0 0
\(895\) −2.10692 −0.0704265
\(896\) 0 0
\(897\) −7.97556 −0.266296
\(898\) 0 0
\(899\) −60.7230 −2.02522
\(900\) 0 0
\(901\) −8.24546 −0.274696
\(902\) 0 0
\(903\) −0.130107 −0.00432969
\(904\) 0 0
\(905\) 0.0346397 0.00115146
\(906\) 0 0
\(907\) −58.2340 −1.93363 −0.966814 0.255482i \(-0.917766\pi\)
−0.966814 + 0.255482i \(0.917766\pi\)
\(908\) 0 0
\(909\) 18.9468 0.628427
\(910\) 0 0
\(911\) 30.4851 1.01002 0.505008 0.863114i \(-0.331489\pi\)
0.505008 + 0.863114i \(0.331489\pi\)
\(912\) 0 0
\(913\) 10.6897 0.353778
\(914\) 0 0
\(915\) −1.98958 −0.0657734
\(916\) 0 0
\(917\) −0.957358 −0.0316148
\(918\) 0 0
\(919\) 2.94915 0.0972833 0.0486417 0.998816i \(-0.484511\pi\)
0.0486417 + 0.998816i \(0.484511\pi\)
\(920\) 0 0
\(921\) −12.4290 −0.409548
\(922\) 0 0
\(923\) 5.37104 0.176790
\(924\) 0 0
\(925\) −20.2855 −0.666983
\(926\) 0 0
\(927\) 24.9928 0.820870
\(928\) 0 0
\(929\) 28.9881 0.951070 0.475535 0.879697i \(-0.342255\pi\)
0.475535 + 0.879697i \(0.342255\pi\)
\(930\) 0 0
\(931\) −15.0956 −0.494737
\(932\) 0 0
\(933\) −20.2814 −0.663984
\(934\) 0 0
\(935\) −2.35852 −0.0771318
\(936\) 0 0
\(937\) −27.5952 −0.901497 −0.450748 0.892651i \(-0.648843\pi\)
−0.450748 + 0.892651i \(0.648843\pi\)
\(938\) 0 0
\(939\) 2.92776 0.0955439
\(940\) 0 0
\(941\) 19.2064 0.626112 0.313056 0.949735i \(-0.398647\pi\)
0.313056 + 0.949735i \(0.398647\pi\)
\(942\) 0 0
\(943\) −41.9902 −1.36739
\(944\) 0 0
\(945\) −0.0615326 −0.00200166
\(946\) 0 0
\(947\) 41.2922 1.34182 0.670908 0.741541i \(-0.265905\pi\)
0.670908 + 0.741541i \(0.265905\pi\)
\(948\) 0 0
\(949\) 12.0750 0.391973
\(950\) 0 0
\(951\) 15.0584 0.488302
\(952\) 0 0
\(953\) −24.0272 −0.778317 −0.389158 0.921171i \(-0.627234\pi\)
−0.389158 + 0.921171i \(0.627234\pi\)
\(954\) 0 0
\(955\) 3.57767 0.115771
\(956\) 0 0
\(957\) −21.0534 −0.680561
\(958\) 0 0
\(959\) −0.177578 −0.00573430
\(960\) 0 0
\(961\) 65.5920 2.11587
\(962\) 0 0
\(963\) −7.87109 −0.253642
\(964\) 0 0
\(965\) −2.93980 −0.0946355
\(966\) 0 0
\(967\) 10.8553 0.349084 0.174542 0.984650i \(-0.444155\pi\)
0.174542 + 0.984650i \(0.444155\pi\)
\(968\) 0 0
\(969\) −5.23806 −0.168271
\(970\) 0 0
\(971\) 17.1111 0.549122 0.274561 0.961570i \(-0.411467\pi\)
0.274561 + 0.961570i \(0.411467\pi\)
\(972\) 0 0
\(973\) −0.494936 −0.0158669
\(974\) 0 0
\(975\) −4.32744 −0.138589
\(976\) 0 0
\(977\) 22.5277 0.720726 0.360363 0.932812i \(-0.382653\pi\)
0.360363 + 0.932812i \(0.382653\pi\)
\(978\) 0 0
\(979\) 23.9827 0.766489
\(980\) 0 0
\(981\) 30.3660 0.969512
\(982\) 0 0
\(983\) 27.0618 0.863138 0.431569 0.902080i \(-0.357960\pi\)
0.431569 + 0.902080i \(0.357960\pi\)
\(984\) 0 0
\(985\) 4.35014 0.138607
\(986\) 0 0
\(987\) 0.328484 0.0104558
\(988\) 0 0
\(989\) 18.5986 0.591401
\(990\) 0 0
\(991\) 19.8216 0.629655 0.314827 0.949149i \(-0.398053\pi\)
0.314827 + 0.949149i \(0.398053\pi\)
\(992\) 0 0
\(993\) 3.76020 0.119326
\(994\) 0 0
\(995\) 2.90473 0.0920863
\(996\) 0 0
\(997\) −23.1120 −0.731966 −0.365983 0.930622i \(-0.619267\pi\)
−0.365983 + 0.930622i \(0.619267\pi\)
\(998\) 0 0
\(999\) −17.3703 −0.549573
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 \(a_p\))