Properties

Label 4008.2.a.i.1.1
Level 4008
Weight 2
Character 4008.1
Self dual Yes
Analytic conductor 32.004
Analytic rank 1
Dimension 9
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: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
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 1.1
Root \(-3.17025\)
Character \(\chi\) = 4008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-4.17025 q^{5}\) \(-1.78655 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-4.17025 q^{5}\) \(-1.78655 q^{7}\) \(+1.00000 q^{9}\) \(+4.35038 q^{11}\) \(+2.54982 q^{13}\) \(-4.17025 q^{15}\) \(+0.0716370 q^{17}\) \(-7.16710 q^{19}\) \(-1.78655 q^{21}\) \(-2.75103 q^{23}\) \(+12.3910 q^{25}\) \(+1.00000 q^{27}\) \(+5.44140 q^{29}\) \(+3.34520 q^{31}\) \(+4.35038 q^{33}\) \(+7.45034 q^{35}\) \(-6.04022 q^{37}\) \(+2.54982 q^{39}\) \(+3.33471 q^{41}\) \(+3.47637 q^{43}\) \(-4.17025 q^{45}\) \(+1.84888 q^{47}\) \(-3.80826 q^{49}\) \(+0.0716370 q^{51}\) \(-10.4810 q^{53}\) \(-18.1422 q^{55}\) \(-7.16710 q^{57}\) \(+7.84697 q^{59}\) \(-6.59987 q^{61}\) \(-1.78655 q^{63}\) \(-10.6334 q^{65}\) \(+3.06798 q^{67}\) \(-2.75103 q^{69}\) \(-9.41046 q^{71}\) \(-8.85175 q^{73}\) \(+12.3910 q^{75}\) \(-7.77214 q^{77}\) \(+0.0583476 q^{79}\) \(+1.00000 q^{81}\) \(+0.584902 q^{83}\) \(-0.298744 q^{85}\) \(+5.44140 q^{87}\) \(-3.61449 q^{89}\) \(-4.55536 q^{91}\) \(+3.34520 q^{93}\) \(+29.8886 q^{95}\) \(+0.334815 q^{97}\) \(+4.35038 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(9q \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut q^{11} \) \(\mathstrut -\mathstrut 4q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut -\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut -\mathstrut 7q^{23} \) \(\mathstrut -\mathstrut q^{25} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 9q^{29} \) \(\mathstrut -\mathstrut 25q^{31} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 24q^{43} \) \(\mathstrut -\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 4q^{49} \) \(\mathstrut -\mathstrut 9q^{51} \) \(\mathstrut -\mathstrut 26q^{53} \) \(\mathstrut -\mathstrut 29q^{55} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut -\mathstrut 4q^{59} \) \(\mathstrut -\mathstrut 20q^{61} \) \(\mathstrut -\mathstrut 11q^{63} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 25q^{67} \) \(\mathstrut -\mathstrut 7q^{69} \) \(\mathstrut -\mathstrut 15q^{71} \) \(\mathstrut -\mathstrut 10q^{73} \) \(\mathstrut -\mathstrut q^{75} \) \(\mathstrut -\mathstrut 20q^{77} \) \(\mathstrut -\mathstrut 34q^{79} \) \(\mathstrut +\mathstrut 9q^{81} \) \(\mathstrut -\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 13q^{85} \) \(\mathstrut -\mathstrut 9q^{87} \) \(\mathstrut +\mathstrut 13q^{89} \) \(\mathstrut -\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 25q^{93} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut -\mathstrut 4q^{97} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −4.17025 −1.86499 −0.932496 0.361180i \(-0.882374\pi\)
−0.932496 + 0.361180i \(0.882374\pi\)
\(6\) 0 0
\(7\) −1.78655 −0.675251 −0.337625 0.941281i \(-0.609624\pi\)
−0.337625 + 0.941281i \(0.609624\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 4.35038 1.31169 0.655844 0.754897i \(-0.272313\pi\)
0.655844 + 0.754897i \(0.272313\pi\)
\(12\) 0 0
\(13\) 2.54982 0.707192 0.353596 0.935398i \(-0.384959\pi\)
0.353596 + 0.935398i \(0.384959\pi\)
\(14\) 0 0
\(15\) −4.17025 −1.07675
\(16\) 0 0
\(17\) 0.0716370 0.0173745 0.00868726 0.999962i \(-0.497235\pi\)
0.00868726 + 0.999962i \(0.497235\pi\)
\(18\) 0 0
\(19\) −7.16710 −1.64425 −0.822123 0.569310i \(-0.807211\pi\)
−0.822123 + 0.569310i \(0.807211\pi\)
\(20\) 0 0
\(21\) −1.78655 −0.389856
\(22\) 0 0
\(23\) −2.75103 −0.573630 −0.286815 0.957986i \(-0.592596\pi\)
−0.286815 + 0.957986i \(0.592596\pi\)
\(24\) 0 0
\(25\) 12.3910 2.47820
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 5.44140 1.01044 0.505222 0.862990i \(-0.331411\pi\)
0.505222 + 0.862990i \(0.331411\pi\)
\(30\) 0 0
\(31\) 3.34520 0.600816 0.300408 0.953811i \(-0.402877\pi\)
0.300408 + 0.953811i \(0.402877\pi\)
\(32\) 0 0
\(33\) 4.35038 0.757303
\(34\) 0 0
\(35\) 7.45034 1.25934
\(36\) 0 0
\(37\) −6.04022 −0.993005 −0.496503 0.868035i \(-0.665383\pi\)
−0.496503 + 0.868035i \(0.665383\pi\)
\(38\) 0 0
\(39\) 2.54982 0.408298
\(40\) 0 0
\(41\) 3.33471 0.520794 0.260397 0.965502i \(-0.416147\pi\)
0.260397 + 0.965502i \(0.416147\pi\)
\(42\) 0 0
\(43\) 3.47637 0.530142 0.265071 0.964229i \(-0.414605\pi\)
0.265071 + 0.964229i \(0.414605\pi\)
\(44\) 0 0
\(45\) −4.17025 −0.621664
\(46\) 0 0
\(47\) 1.84888 0.269687 0.134843 0.990867i \(-0.456947\pi\)
0.134843 + 0.990867i \(0.456947\pi\)
\(48\) 0 0
\(49\) −3.80826 −0.544036
\(50\) 0 0
\(51\) 0.0716370 0.0100312
\(52\) 0 0
\(53\) −10.4810 −1.43968 −0.719838 0.694142i \(-0.755784\pi\)
−0.719838 + 0.694142i \(0.755784\pi\)
\(54\) 0 0
\(55\) −18.1422 −2.44629
\(56\) 0 0
\(57\) −7.16710 −0.949306
\(58\) 0 0
\(59\) 7.84697 1.02159 0.510794 0.859703i \(-0.329351\pi\)
0.510794 + 0.859703i \(0.329351\pi\)
\(60\) 0 0
\(61\) −6.59987 −0.845026 −0.422513 0.906357i \(-0.638852\pi\)
−0.422513 + 0.906357i \(0.638852\pi\)
\(62\) 0 0
\(63\) −1.78655 −0.225084
\(64\) 0 0
\(65\) −10.6334 −1.31891
\(66\) 0 0
\(67\) 3.06798 0.374814 0.187407 0.982282i \(-0.439992\pi\)
0.187407 + 0.982282i \(0.439992\pi\)
\(68\) 0 0
\(69\) −2.75103 −0.331185
\(70\) 0 0
\(71\) −9.41046 −1.11682 −0.558408 0.829566i \(-0.688588\pi\)
−0.558408 + 0.829566i \(0.688588\pi\)
\(72\) 0 0
\(73\) −8.85175 −1.03602 −0.518009 0.855375i \(-0.673327\pi\)
−0.518009 + 0.855375i \(0.673327\pi\)
\(74\) 0 0
\(75\) 12.3910 1.43079
\(76\) 0 0
\(77\) −7.77214 −0.885718
\(78\) 0 0
\(79\) 0.0583476 0.00656462 0.00328231 0.999995i \(-0.498955\pi\)
0.00328231 + 0.999995i \(0.498955\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 0.584902 0.0642013 0.0321007 0.999485i \(-0.489780\pi\)
0.0321007 + 0.999485i \(0.489780\pi\)
\(84\) 0 0
\(85\) −0.298744 −0.0324033
\(86\) 0 0
\(87\) 5.44140 0.583380
\(88\) 0 0
\(89\) −3.61449 −0.383135 −0.191567 0.981479i \(-0.561357\pi\)
−0.191567 + 0.981479i \(0.561357\pi\)
\(90\) 0 0
\(91\) −4.55536 −0.477532
\(92\) 0 0
\(93\) 3.34520 0.346881
\(94\) 0 0
\(95\) 29.8886 3.06651
\(96\) 0 0
\(97\) 0.334815 0.0339953 0.0169976 0.999856i \(-0.494589\pi\)
0.0169976 + 0.999856i \(0.494589\pi\)
\(98\) 0 0
\(99\) 4.35038 0.437229
\(100\) 0 0
\(101\) 4.71758 0.469416 0.234708 0.972066i \(-0.424587\pi\)
0.234708 + 0.972066i \(0.424587\pi\)
\(102\) 0 0
\(103\) −20.2182 −1.99216 −0.996081 0.0884418i \(-0.971811\pi\)
−0.996081 + 0.0884418i \(0.971811\pi\)
\(104\) 0 0
\(105\) 7.45034 0.727079
\(106\) 0 0
\(107\) 4.02095 0.388719 0.194360 0.980930i \(-0.437737\pi\)
0.194360 + 0.980930i \(0.437737\pi\)
\(108\) 0 0
\(109\) 7.32526 0.701633 0.350816 0.936444i \(-0.385904\pi\)
0.350816 + 0.936444i \(0.385904\pi\)
\(110\) 0 0
\(111\) −6.04022 −0.573312
\(112\) 0 0
\(113\) −14.8947 −1.40118 −0.700590 0.713564i \(-0.747080\pi\)
−0.700590 + 0.713564i \(0.747080\pi\)
\(114\) 0 0
\(115\) 11.4725 1.06981
\(116\) 0 0
\(117\) 2.54982 0.235731
\(118\) 0 0
\(119\) −0.127983 −0.0117322
\(120\) 0 0
\(121\) 7.92577 0.720525
\(122\) 0 0
\(123\) 3.33471 0.300681
\(124\) 0 0
\(125\) −30.8222 −2.75683
\(126\) 0 0
\(127\) −18.8761 −1.67498 −0.837490 0.546453i \(-0.815978\pi\)
−0.837490 + 0.546453i \(0.815978\pi\)
\(128\) 0 0
\(129\) 3.47637 0.306078
\(130\) 0 0
\(131\) 0.342949 0.0299636 0.0149818 0.999888i \(-0.495231\pi\)
0.0149818 + 0.999888i \(0.495231\pi\)
\(132\) 0 0
\(133\) 12.8044 1.11028
\(134\) 0 0
\(135\) −4.17025 −0.358918
\(136\) 0 0
\(137\) 11.5389 0.985833 0.492917 0.870077i \(-0.335931\pi\)
0.492917 + 0.870077i \(0.335931\pi\)
\(138\) 0 0
\(139\) −15.7651 −1.33718 −0.668591 0.743630i \(-0.733102\pi\)
−0.668591 + 0.743630i \(0.733102\pi\)
\(140\) 0 0
\(141\) 1.84888 0.155704
\(142\) 0 0
\(143\) 11.0927 0.927615
\(144\) 0 0
\(145\) −22.6920 −1.88447
\(146\) 0 0
\(147\) −3.80826 −0.314100
\(148\) 0 0
\(149\) 0.883298 0.0723626 0.0361813 0.999345i \(-0.488481\pi\)
0.0361813 + 0.999345i \(0.488481\pi\)
\(150\) 0 0
\(151\) −4.06988 −0.331202 −0.165601 0.986193i \(-0.552956\pi\)
−0.165601 + 0.986193i \(0.552956\pi\)
\(152\) 0 0
\(153\) 0.0716370 0.00579151
\(154\) 0 0
\(155\) −13.9503 −1.12052
\(156\) 0 0
\(157\) −12.5877 −1.00461 −0.502304 0.864691i \(-0.667514\pi\)
−0.502304 + 0.864691i \(0.667514\pi\)
\(158\) 0 0
\(159\) −10.4810 −0.831198
\(160\) 0 0
\(161\) 4.91484 0.387344
\(162\) 0 0
\(163\) −10.2085 −0.799593 −0.399797 0.916604i \(-0.630919\pi\)
−0.399797 + 0.916604i \(0.630919\pi\)
\(164\) 0 0
\(165\) −18.1422 −1.41236
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) −6.49843 −0.499879
\(170\) 0 0
\(171\) −7.16710 −0.548082
\(172\) 0 0
\(173\) −24.5779 −1.86862 −0.934310 0.356461i \(-0.883983\pi\)
−0.934310 + 0.356461i \(0.883983\pi\)
\(174\) 0 0
\(175\) −22.1371 −1.67340
\(176\) 0 0
\(177\) 7.84697 0.589814
\(178\) 0 0
\(179\) −14.2545 −1.06543 −0.532717 0.846293i \(-0.678829\pi\)
−0.532717 + 0.846293i \(0.678829\pi\)
\(180\) 0 0
\(181\) 22.8429 1.69790 0.848948 0.528476i \(-0.177236\pi\)
0.848948 + 0.528476i \(0.177236\pi\)
\(182\) 0 0
\(183\) −6.59987 −0.487876
\(184\) 0 0
\(185\) 25.1892 1.85195
\(186\) 0 0
\(187\) 0.311648 0.0227899
\(188\) 0 0
\(189\) −1.78655 −0.129952
\(190\) 0 0
\(191\) 1.42405 0.103041 0.0515203 0.998672i \(-0.483593\pi\)
0.0515203 + 0.998672i \(0.483593\pi\)
\(192\) 0 0
\(193\) −13.9804 −1.00633 −0.503166 0.864190i \(-0.667831\pi\)
−0.503166 + 0.864190i \(0.667831\pi\)
\(194\) 0 0
\(195\) −10.6334 −0.761472
\(196\) 0 0
\(197\) 14.2442 1.01486 0.507428 0.861694i \(-0.330596\pi\)
0.507428 + 0.861694i \(0.330596\pi\)
\(198\) 0 0
\(199\) −16.6866 −1.18288 −0.591441 0.806348i \(-0.701441\pi\)
−0.591441 + 0.806348i \(0.701441\pi\)
\(200\) 0 0
\(201\) 3.06798 0.216399
\(202\) 0 0
\(203\) −9.72131 −0.682302
\(204\) 0 0
\(205\) −13.9066 −0.971277
\(206\) 0 0
\(207\) −2.75103 −0.191210
\(208\) 0 0
\(209\) −31.1796 −2.15674
\(210\) 0 0
\(211\) −8.11871 −0.558915 −0.279458 0.960158i \(-0.590155\pi\)
−0.279458 + 0.960158i \(0.590155\pi\)
\(212\) 0 0
\(213\) −9.41046 −0.644794
\(214\) 0 0
\(215\) −14.4973 −0.988711
\(216\) 0 0
\(217\) −5.97636 −0.405701
\(218\) 0 0
\(219\) −8.85175 −0.598146
\(220\) 0 0
\(221\) 0.182661 0.0122871
\(222\) 0 0
\(223\) −10.7903 −0.722574 −0.361287 0.932455i \(-0.617662\pi\)
−0.361287 + 0.932455i \(0.617662\pi\)
\(224\) 0 0
\(225\) 12.3910 0.826066
\(226\) 0 0
\(227\) −0.189331 −0.0125664 −0.00628318 0.999980i \(-0.502000\pi\)
−0.00628318 + 0.999980i \(0.502000\pi\)
\(228\) 0 0
\(229\) −14.4062 −0.951987 −0.475993 0.879449i \(-0.657911\pi\)
−0.475993 + 0.879449i \(0.657911\pi\)
\(230\) 0 0
\(231\) −7.77214 −0.511370
\(232\) 0 0
\(233\) 29.7817 1.95107 0.975533 0.219854i \(-0.0705582\pi\)
0.975533 + 0.219854i \(0.0705582\pi\)
\(234\) 0 0
\(235\) −7.71029 −0.502964
\(236\) 0 0
\(237\) 0.0583476 0.00379008
\(238\) 0 0
\(239\) 7.50122 0.485213 0.242607 0.970125i \(-0.421998\pi\)
0.242607 + 0.970125i \(0.421998\pi\)
\(240\) 0 0
\(241\) 15.6609 1.00881 0.504404 0.863468i \(-0.331712\pi\)
0.504404 + 0.863468i \(0.331712\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 15.8814 1.01462
\(246\) 0 0
\(247\) −18.2748 −1.16280
\(248\) 0 0
\(249\) 0.584902 0.0370667
\(250\) 0 0
\(251\) −7.02486 −0.443405 −0.221703 0.975114i \(-0.571161\pi\)
−0.221703 + 0.975114i \(0.571161\pi\)
\(252\) 0 0
\(253\) −11.9680 −0.752423
\(254\) 0 0
\(255\) −0.298744 −0.0187081
\(256\) 0 0
\(257\) 8.17803 0.510132 0.255066 0.966924i \(-0.417903\pi\)
0.255066 + 0.966924i \(0.417903\pi\)
\(258\) 0 0
\(259\) 10.7911 0.670528
\(260\) 0 0
\(261\) 5.44140 0.336814
\(262\) 0 0
\(263\) 22.1033 1.36295 0.681473 0.731843i \(-0.261340\pi\)
0.681473 + 0.731843i \(0.261340\pi\)
\(264\) 0 0
\(265\) 43.7084 2.68499
\(266\) 0 0
\(267\) −3.61449 −0.221203
\(268\) 0 0
\(269\) −14.4088 −0.878519 −0.439259 0.898360i \(-0.644759\pi\)
−0.439259 + 0.898360i \(0.644759\pi\)
\(270\) 0 0
\(271\) −4.72029 −0.286737 −0.143369 0.989669i \(-0.545793\pi\)
−0.143369 + 0.989669i \(0.545793\pi\)
\(272\) 0 0
\(273\) −4.55536 −0.275703
\(274\) 0 0
\(275\) 53.9054 3.25062
\(276\) 0 0
\(277\) −27.9962 −1.68213 −0.841063 0.540937i \(-0.818070\pi\)
−0.841063 + 0.540937i \(0.818070\pi\)
\(278\) 0 0
\(279\) 3.34520 0.200272
\(280\) 0 0
\(281\) −21.2473 −1.26751 −0.633755 0.773534i \(-0.718487\pi\)
−0.633755 + 0.773534i \(0.718487\pi\)
\(282\) 0 0
\(283\) −6.07839 −0.361322 −0.180661 0.983545i \(-0.557824\pi\)
−0.180661 + 0.983545i \(0.557824\pi\)
\(284\) 0 0
\(285\) 29.8886 1.77045
\(286\) 0 0
\(287\) −5.95761 −0.351666
\(288\) 0 0
\(289\) −16.9949 −0.999698
\(290\) 0 0
\(291\) 0.334815 0.0196272
\(292\) 0 0
\(293\) 15.5348 0.907553 0.453777 0.891115i \(-0.350076\pi\)
0.453777 + 0.891115i \(0.350076\pi\)
\(294\) 0 0
\(295\) −32.7238 −1.90525
\(296\) 0 0
\(297\) 4.35038 0.252434
\(298\) 0 0
\(299\) −7.01463 −0.405666
\(300\) 0 0
\(301\) −6.21070 −0.357979
\(302\) 0 0
\(303\) 4.71758 0.271018
\(304\) 0 0
\(305\) 27.5231 1.57597
\(306\) 0 0
\(307\) −7.05233 −0.402498 −0.201249 0.979540i \(-0.564500\pi\)
−0.201249 + 0.979540i \(0.564500\pi\)
\(308\) 0 0
\(309\) −20.2182 −1.15018
\(310\) 0 0
\(311\) 26.0059 1.47466 0.737330 0.675532i \(-0.236086\pi\)
0.737330 + 0.675532i \(0.236086\pi\)
\(312\) 0 0
\(313\) 17.5377 0.991287 0.495644 0.868526i \(-0.334932\pi\)
0.495644 + 0.868526i \(0.334932\pi\)
\(314\) 0 0
\(315\) 7.45034 0.419779
\(316\) 0 0
\(317\) 20.8460 1.17083 0.585413 0.810735i \(-0.300932\pi\)
0.585413 + 0.810735i \(0.300932\pi\)
\(318\) 0 0
\(319\) 23.6721 1.32539
\(320\) 0 0
\(321\) 4.02095 0.224427
\(322\) 0 0
\(323\) −0.513430 −0.0285680
\(324\) 0 0
\(325\) 31.5947 1.75256
\(326\) 0 0
\(327\) 7.32526 0.405088
\(328\) 0 0
\(329\) −3.30311 −0.182106
\(330\) 0 0
\(331\) 27.8470 1.53061 0.765305 0.643667i \(-0.222588\pi\)
0.765305 + 0.643667i \(0.222588\pi\)
\(332\) 0 0
\(333\) −6.04022 −0.331002
\(334\) 0 0
\(335\) −12.7943 −0.699025
\(336\) 0 0
\(337\) 7.22298 0.393461 0.196731 0.980458i \(-0.436968\pi\)
0.196731 + 0.980458i \(0.436968\pi\)
\(338\) 0 0
\(339\) −14.8947 −0.808971
\(340\) 0 0
\(341\) 14.5529 0.788083
\(342\) 0 0
\(343\) 19.3094 1.04261
\(344\) 0 0
\(345\) 11.4725 0.617658
\(346\) 0 0
\(347\) 14.7990 0.794452 0.397226 0.917721i \(-0.369973\pi\)
0.397226 + 0.917721i \(0.369973\pi\)
\(348\) 0 0
\(349\) −1.40557 −0.0752384 −0.0376192 0.999292i \(-0.511977\pi\)
−0.0376192 + 0.999292i \(0.511977\pi\)
\(350\) 0 0
\(351\) 2.54982 0.136099
\(352\) 0 0
\(353\) −11.8156 −0.628883 −0.314442 0.949277i \(-0.601817\pi\)
−0.314442 + 0.949277i \(0.601817\pi\)
\(354\) 0 0
\(355\) 39.2440 2.08285
\(356\) 0 0
\(357\) −0.127983 −0.00677356
\(358\) 0 0
\(359\) −5.61217 −0.296199 −0.148099 0.988972i \(-0.547316\pi\)
−0.148099 + 0.988972i \(0.547316\pi\)
\(360\) 0 0
\(361\) 32.3674 1.70355
\(362\) 0 0
\(363\) 7.92577 0.415995
\(364\) 0 0
\(365\) 36.9140 1.93217
\(366\) 0 0
\(367\) −31.0874 −1.62275 −0.811374 0.584527i \(-0.801280\pi\)
−0.811374 + 0.584527i \(0.801280\pi\)
\(368\) 0 0
\(369\) 3.33471 0.173598
\(370\) 0 0
\(371\) 18.7248 0.972143
\(372\) 0 0
\(373\) −1.78421 −0.0923828 −0.0461914 0.998933i \(-0.514708\pi\)
−0.0461914 + 0.998933i \(0.514708\pi\)
\(374\) 0 0
\(375\) −30.8222 −1.59165
\(376\) 0 0
\(377\) 13.8746 0.714577
\(378\) 0 0
\(379\) 8.79107 0.451567 0.225783 0.974178i \(-0.427506\pi\)
0.225783 + 0.974178i \(0.427506\pi\)
\(380\) 0 0
\(381\) −18.8761 −0.967050
\(382\) 0 0
\(383\) −19.5651 −0.999729 −0.499865 0.866103i \(-0.666617\pi\)
−0.499865 + 0.866103i \(0.666617\pi\)
\(384\) 0 0
\(385\) 32.4118 1.65186
\(386\) 0 0
\(387\) 3.47637 0.176714
\(388\) 0 0
\(389\) −19.6033 −0.993927 −0.496963 0.867772i \(-0.665552\pi\)
−0.496963 + 0.867772i \(0.665552\pi\)
\(390\) 0 0
\(391\) −0.197075 −0.00996654
\(392\) 0 0
\(393\) 0.342949 0.0172995
\(394\) 0 0
\(395\) −0.243324 −0.0122430
\(396\) 0 0
\(397\) −8.41521 −0.422347 −0.211174 0.977449i \(-0.567729\pi\)
−0.211174 + 0.977449i \(0.567729\pi\)
\(398\) 0 0
\(399\) 12.8044 0.641020
\(400\) 0 0
\(401\) 1.30360 0.0650989 0.0325494 0.999470i \(-0.489637\pi\)
0.0325494 + 0.999470i \(0.489637\pi\)
\(402\) 0 0
\(403\) 8.52965 0.424892
\(404\) 0 0
\(405\) −4.17025 −0.207221
\(406\) 0 0
\(407\) −26.2772 −1.30251
\(408\) 0 0
\(409\) 10.4075 0.514616 0.257308 0.966329i \(-0.417165\pi\)
0.257308 + 0.966329i \(0.417165\pi\)
\(410\) 0 0
\(411\) 11.5389 0.569171
\(412\) 0 0
\(413\) −14.0190 −0.689828
\(414\) 0 0
\(415\) −2.43919 −0.119735
\(416\) 0 0
\(417\) −15.7651 −0.772022
\(418\) 0 0
\(419\) 8.00995 0.391312 0.195656 0.980673i \(-0.437316\pi\)
0.195656 + 0.980673i \(0.437316\pi\)
\(420\) 0 0
\(421\) 23.1739 1.12943 0.564714 0.825287i \(-0.308986\pi\)
0.564714 + 0.825287i \(0.308986\pi\)
\(422\) 0 0
\(423\) 1.84888 0.0898956
\(424\) 0 0
\(425\) 0.887653 0.0430575
\(426\) 0 0
\(427\) 11.7910 0.570605
\(428\) 0 0
\(429\) 11.0927 0.535559
\(430\) 0 0
\(431\) −36.5254 −1.75937 −0.879684 0.475559i \(-0.842246\pi\)
−0.879684 + 0.475559i \(0.842246\pi\)
\(432\) 0 0
\(433\) −11.3450 −0.545207 −0.272603 0.962127i \(-0.587885\pi\)
−0.272603 + 0.962127i \(0.587885\pi\)
\(434\) 0 0
\(435\) −22.6920 −1.08800
\(436\) 0 0
\(437\) 19.7169 0.943188
\(438\) 0 0
\(439\) 1.47796 0.0705391 0.0352696 0.999378i \(-0.488771\pi\)
0.0352696 + 0.999378i \(0.488771\pi\)
\(440\) 0 0
\(441\) −3.80826 −0.181345
\(442\) 0 0
\(443\) −30.7173 −1.45943 −0.729713 0.683754i \(-0.760346\pi\)
−0.729713 + 0.683754i \(0.760346\pi\)
\(444\) 0 0
\(445\) 15.0733 0.714544
\(446\) 0 0
\(447\) 0.883298 0.0417786
\(448\) 0 0
\(449\) 13.5252 0.638292 0.319146 0.947705i \(-0.396604\pi\)
0.319146 + 0.947705i \(0.396604\pi\)
\(450\) 0 0
\(451\) 14.5072 0.683119
\(452\) 0 0
\(453\) −4.06988 −0.191220
\(454\) 0 0
\(455\) 18.9970 0.890593
\(456\) 0 0
\(457\) 18.2676 0.854523 0.427262 0.904128i \(-0.359478\pi\)
0.427262 + 0.904128i \(0.359478\pi\)
\(458\) 0 0
\(459\) 0.0716370 0.00334373
\(460\) 0 0
\(461\) 21.1705 0.986007 0.493003 0.870027i \(-0.335899\pi\)
0.493003 + 0.870027i \(0.335899\pi\)
\(462\) 0 0
\(463\) −25.4679 −1.18359 −0.591796 0.806088i \(-0.701581\pi\)
−0.591796 + 0.806088i \(0.701581\pi\)
\(464\) 0 0
\(465\) −13.9503 −0.646931
\(466\) 0 0
\(467\) −18.1847 −0.841488 −0.420744 0.907179i \(-0.638231\pi\)
−0.420744 + 0.907179i \(0.638231\pi\)
\(468\) 0 0
\(469\) −5.48109 −0.253093
\(470\) 0 0
\(471\) −12.5877 −0.580010
\(472\) 0 0
\(473\) 15.1235 0.695381
\(474\) 0 0
\(475\) −88.8075 −4.07477
\(476\) 0 0
\(477\) −10.4810 −0.479892
\(478\) 0 0
\(479\) −31.4363 −1.43636 −0.718182 0.695856i \(-0.755025\pi\)
−0.718182 + 0.695856i \(0.755025\pi\)
\(480\) 0 0
\(481\) −15.4014 −0.702246
\(482\) 0 0
\(483\) 4.91484 0.223633
\(484\) 0 0
\(485\) −1.39626 −0.0634009
\(486\) 0 0
\(487\) 7.63846 0.346132 0.173066 0.984910i \(-0.444633\pi\)
0.173066 + 0.984910i \(0.444633\pi\)
\(488\) 0 0
\(489\) −10.2085 −0.461645
\(490\) 0 0
\(491\) 2.60219 0.117435 0.0587176 0.998275i \(-0.481299\pi\)
0.0587176 + 0.998275i \(0.481299\pi\)
\(492\) 0 0
\(493\) 0.389806 0.0175560
\(494\) 0 0
\(495\) −18.1422 −0.815429
\(496\) 0 0
\(497\) 16.8122 0.754131
\(498\) 0 0
\(499\) −11.7781 −0.527261 −0.263631 0.964624i \(-0.584920\pi\)
−0.263631 + 0.964624i \(0.584920\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) 19.8128 0.883410 0.441705 0.897160i \(-0.354374\pi\)
0.441705 + 0.897160i \(0.354374\pi\)
\(504\) 0 0
\(505\) −19.6735 −0.875458
\(506\) 0 0
\(507\) −6.49843 −0.288606
\(508\) 0 0
\(509\) 41.0164 1.81802 0.909010 0.416774i \(-0.136839\pi\)
0.909010 + 0.416774i \(0.136839\pi\)
\(510\) 0 0
\(511\) 15.8140 0.699572
\(512\) 0 0
\(513\) −7.16710 −0.316435
\(514\) 0 0
\(515\) 84.3151 3.71537
\(516\) 0 0
\(517\) 8.04332 0.353745
\(518\) 0 0
\(519\) −24.5779 −1.07885
\(520\) 0 0
\(521\) −24.5419 −1.07520 −0.537599 0.843201i \(-0.680669\pi\)
−0.537599 + 0.843201i \(0.680669\pi\)
\(522\) 0 0
\(523\) 42.2257 1.84640 0.923201 0.384318i \(-0.125563\pi\)
0.923201 + 0.384318i \(0.125563\pi\)
\(524\) 0 0
\(525\) −22.1371 −0.966140
\(526\) 0 0
\(527\) 0.239640 0.0104389
\(528\) 0 0
\(529\) −15.4318 −0.670949
\(530\) 0 0
\(531\) 7.84697 0.340530
\(532\) 0 0
\(533\) 8.50290 0.368301
\(534\) 0 0
\(535\) −16.7683 −0.724959
\(536\) 0 0
\(537\) −14.2545 −0.615129
\(538\) 0 0
\(539\) −16.5673 −0.713606
\(540\) 0 0
\(541\) 39.1790 1.68444 0.842219 0.539135i \(-0.181249\pi\)
0.842219 + 0.539135i \(0.181249\pi\)
\(542\) 0 0
\(543\) 22.8429 0.980281
\(544\) 0 0
\(545\) −30.5482 −1.30854
\(546\) 0 0
\(547\) 30.0775 1.28602 0.643010 0.765858i \(-0.277685\pi\)
0.643010 + 0.765858i \(0.277685\pi\)
\(548\) 0 0
\(549\) −6.59987 −0.281675
\(550\) 0 0
\(551\) −38.9991 −1.66142
\(552\) 0 0
\(553\) −0.104241 −0.00443276
\(554\) 0 0
\(555\) 25.1892 1.06922
\(556\) 0 0
\(557\) 37.0920 1.57164 0.785819 0.618456i \(-0.212242\pi\)
0.785819 + 0.618456i \(0.212242\pi\)
\(558\) 0 0
\(559\) 8.86412 0.374912
\(560\) 0 0
\(561\) 0.311648 0.0131578
\(562\) 0 0
\(563\) −41.1589 −1.73464 −0.867321 0.497749i \(-0.834160\pi\)
−0.867321 + 0.497749i \(0.834160\pi\)
\(564\) 0 0
\(565\) 62.1148 2.61319
\(566\) 0 0
\(567\) −1.78655 −0.0750279
\(568\) 0 0
\(569\) 14.7976 0.620347 0.310173 0.950680i \(-0.399613\pi\)
0.310173 + 0.950680i \(0.399613\pi\)
\(570\) 0 0
\(571\) −19.6533 −0.822464 −0.411232 0.911531i \(-0.634901\pi\)
−0.411232 + 0.911531i \(0.634901\pi\)
\(572\) 0 0
\(573\) 1.42405 0.0594906
\(574\) 0 0
\(575\) −34.0880 −1.42157
\(576\) 0 0
\(577\) 34.3832 1.43139 0.715696 0.698412i \(-0.246109\pi\)
0.715696 + 0.698412i \(0.246109\pi\)
\(578\) 0 0
\(579\) −13.9804 −0.581006
\(580\) 0 0
\(581\) −1.04495 −0.0433520
\(582\) 0 0
\(583\) −45.5963 −1.88841
\(584\) 0 0
\(585\) −10.6334 −0.439636
\(586\) 0 0
\(587\) −11.7539 −0.485135 −0.242567 0.970135i \(-0.577990\pi\)
−0.242567 + 0.970135i \(0.577990\pi\)
\(588\) 0 0
\(589\) −23.9754 −0.987889
\(590\) 0 0
\(591\) 14.2442 0.585928
\(592\) 0 0
\(593\) −30.1475 −1.23801 −0.619005 0.785387i \(-0.712464\pi\)
−0.619005 + 0.785387i \(0.712464\pi\)
\(594\) 0 0
\(595\) 0.533720 0.0218804
\(596\) 0 0
\(597\) −16.6866 −0.682938
\(598\) 0 0
\(599\) 39.4902 1.61353 0.806764 0.590874i \(-0.201217\pi\)
0.806764 + 0.590874i \(0.201217\pi\)
\(600\) 0 0
\(601\) −8.04132 −0.328012 −0.164006 0.986459i \(-0.552442\pi\)
−0.164006 + 0.986459i \(0.552442\pi\)
\(602\) 0 0
\(603\) 3.06798 0.124938
\(604\) 0 0
\(605\) −33.0524 −1.34377
\(606\) 0 0
\(607\) 2.36619 0.0960408 0.0480204 0.998846i \(-0.484709\pi\)
0.0480204 + 0.998846i \(0.484709\pi\)
\(608\) 0 0
\(609\) −9.72131 −0.393927
\(610\) 0 0
\(611\) 4.71430 0.190720
\(612\) 0 0
\(613\) 38.3389 1.54849 0.774247 0.632884i \(-0.218129\pi\)
0.774247 + 0.632884i \(0.218129\pi\)
\(614\) 0 0
\(615\) −13.9066 −0.560767
\(616\) 0 0
\(617\) 23.7019 0.954201 0.477100 0.878849i \(-0.341688\pi\)
0.477100 + 0.878849i \(0.341688\pi\)
\(618\) 0 0
\(619\) 21.6224 0.869078 0.434539 0.900653i \(-0.356911\pi\)
0.434539 + 0.900653i \(0.356911\pi\)
\(620\) 0 0
\(621\) −2.75103 −0.110395
\(622\) 0 0
\(623\) 6.45745 0.258712
\(624\) 0 0
\(625\) 66.5816 2.66326
\(626\) 0 0
\(627\) −31.1796 −1.24519
\(628\) 0 0
\(629\) −0.432703 −0.0172530
\(630\) 0 0
\(631\) −22.0461 −0.877643 −0.438822 0.898574i \(-0.644604\pi\)
−0.438822 + 0.898574i \(0.644604\pi\)
\(632\) 0 0
\(633\) −8.11871 −0.322690
\(634\) 0 0
\(635\) 78.7179 3.12383
\(636\) 0 0
\(637\) −9.71036 −0.384738
\(638\) 0 0
\(639\) −9.41046 −0.372272
\(640\) 0 0
\(641\) −2.39872 −0.0947438 −0.0473719 0.998877i \(-0.515085\pi\)
−0.0473719 + 0.998877i \(0.515085\pi\)
\(642\) 0 0
\(643\) 4.16347 0.164191 0.0820957 0.996624i \(-0.473839\pi\)
0.0820957 + 0.996624i \(0.473839\pi\)
\(644\) 0 0
\(645\) −14.4973 −0.570832
\(646\) 0 0
\(647\) −18.0107 −0.708072 −0.354036 0.935232i \(-0.615191\pi\)
−0.354036 + 0.935232i \(0.615191\pi\)
\(648\) 0 0
\(649\) 34.1373 1.34001
\(650\) 0 0
\(651\) −5.97636 −0.234232
\(652\) 0 0
\(653\) −12.0581 −0.471871 −0.235935 0.971769i \(-0.575815\pi\)
−0.235935 + 0.971769i \(0.575815\pi\)
\(654\) 0 0
\(655\) −1.43018 −0.0558819
\(656\) 0 0
\(657\) −8.85175 −0.345340
\(658\) 0 0
\(659\) 3.11754 0.121442 0.0607211 0.998155i \(-0.480660\pi\)
0.0607211 + 0.998155i \(0.480660\pi\)
\(660\) 0 0
\(661\) 6.44996 0.250874 0.125437 0.992102i \(-0.459967\pi\)
0.125437 + 0.992102i \(0.459967\pi\)
\(662\) 0 0
\(663\) 0.182661 0.00709397
\(664\) 0 0
\(665\) −53.3974 −2.07066
\(666\) 0 0
\(667\) −14.9695 −0.579620
\(668\) 0 0
\(669\) −10.7903 −0.417178
\(670\) 0 0
\(671\) −28.7119 −1.10841
\(672\) 0 0
\(673\) −49.1326 −1.89392 −0.946960 0.321350i \(-0.895863\pi\)
−0.946960 + 0.321350i \(0.895863\pi\)
\(674\) 0 0
\(675\) 12.3910 0.476929
\(676\) 0 0
\(677\) −12.1529 −0.467074 −0.233537 0.972348i \(-0.575030\pi\)
−0.233537 + 0.972348i \(0.575030\pi\)
\(678\) 0 0
\(679\) −0.598161 −0.0229553
\(680\) 0 0
\(681\) −0.189331 −0.00725519
\(682\) 0 0
\(683\) 34.4616 1.31863 0.659317 0.751865i \(-0.270845\pi\)
0.659317 + 0.751865i \(0.270845\pi\)
\(684\) 0 0
\(685\) −48.1200 −1.83857
\(686\) 0 0
\(687\) −14.4062 −0.549630
\(688\) 0 0
\(689\) −26.7247 −1.01813
\(690\) 0 0
\(691\) −3.60365 −0.137089 −0.0685446 0.997648i \(-0.521836\pi\)
−0.0685446 + 0.997648i \(0.521836\pi\)
\(692\) 0 0
\(693\) −7.77214 −0.295239
\(694\) 0 0
\(695\) 65.7446 2.49383
\(696\) 0 0
\(697\) 0.238888 0.00904854
\(698\) 0 0
\(699\) 29.7817 1.12645
\(700\) 0 0
\(701\) 40.8273 1.54203 0.771013 0.636819i \(-0.219750\pi\)
0.771013 + 0.636819i \(0.219750\pi\)
\(702\) 0 0
\(703\) 43.2909 1.63275
\(704\) 0 0
\(705\) −7.71029 −0.290386
\(706\) 0 0
\(707\) −8.42816 −0.316974
\(708\) 0 0
\(709\) 29.4473 1.10592 0.552959 0.833209i \(-0.313499\pi\)
0.552959 + 0.833209i \(0.313499\pi\)
\(710\) 0 0
\(711\) 0.0583476 0.00218821
\(712\) 0 0
\(713\) −9.20275 −0.344646
\(714\) 0 0
\(715\) −46.2592 −1.73000
\(716\) 0 0
\(717\) 7.50122 0.280138
\(718\) 0 0
\(719\) −15.9152 −0.593535 −0.296768 0.954950i \(-0.595909\pi\)
−0.296768 + 0.954950i \(0.595909\pi\)
\(720\) 0 0
\(721\) 36.1208 1.34521
\(722\) 0 0
\(723\) 15.6609 0.582435
\(724\) 0 0
\(725\) 67.4243 2.50408
\(726\) 0 0
\(727\) −52.3345 −1.94098 −0.970490 0.241142i \(-0.922478\pi\)
−0.970490 + 0.241142i \(0.922478\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0.249037 0.00921096
\(732\) 0 0
\(733\) −25.8494 −0.954771 −0.477385 0.878694i \(-0.658415\pi\)
−0.477385 + 0.878694i \(0.658415\pi\)
\(734\) 0 0
\(735\) 15.8814 0.585793
\(736\) 0 0
\(737\) 13.3469 0.491639
\(738\) 0 0
\(739\) −15.9750 −0.587650 −0.293825 0.955859i \(-0.594928\pi\)
−0.293825 + 0.955859i \(0.594928\pi\)
\(740\) 0 0
\(741\) −18.2748 −0.671342
\(742\) 0 0
\(743\) −23.6409 −0.867302 −0.433651 0.901081i \(-0.642775\pi\)
−0.433651 + 0.901081i \(0.642775\pi\)
\(744\) 0 0
\(745\) −3.68357 −0.134956
\(746\) 0 0
\(747\) 0.584902 0.0214004
\(748\) 0 0
\(749\) −7.18360 −0.262483
\(750\) 0 0
\(751\) −20.1018 −0.733526 −0.366763 0.930314i \(-0.619534\pi\)
−0.366763 + 0.930314i \(0.619534\pi\)
\(752\) 0 0
\(753\) −7.02486 −0.256000
\(754\) 0 0
\(755\) 16.9724 0.617689
\(756\) 0 0
\(757\) 4.43011 0.161015 0.0805075 0.996754i \(-0.474346\pi\)
0.0805075 + 0.996754i \(0.474346\pi\)
\(758\) 0 0
\(759\) −11.9680 −0.434412
\(760\) 0 0
\(761\) 12.1245 0.439512 0.219756 0.975555i \(-0.429474\pi\)
0.219756 + 0.975555i \(0.429474\pi\)
\(762\) 0 0
\(763\) −13.0869 −0.473778
\(764\) 0 0
\(765\) −0.298744 −0.0108011
\(766\) 0 0
\(767\) 20.0083 0.722459
\(768\) 0 0
\(769\) −27.8010 −1.00253 −0.501265 0.865294i \(-0.667132\pi\)
−0.501265 + 0.865294i \(0.667132\pi\)
\(770\) 0 0
\(771\) 8.17803 0.294525
\(772\) 0 0
\(773\) 23.2674 0.836869 0.418435 0.908247i \(-0.362579\pi\)
0.418435 + 0.908247i \(0.362579\pi\)
\(774\) 0 0
\(775\) 41.4503 1.48894
\(776\) 0 0
\(777\) 10.7911 0.387129
\(778\) 0 0
\(779\) −23.9002 −0.856313
\(780\) 0 0
\(781\) −40.9390 −1.46491
\(782\) 0 0
\(783\) 5.44140 0.194460
\(784\) 0 0
\(785\) 52.4938 1.87358
\(786\) 0 0
\(787\) −51.5377 −1.83712 −0.918560 0.395282i \(-0.870647\pi\)
−0.918560 + 0.395282i \(0.870647\pi\)
\(788\) 0 0
\(789\) 22.1033 0.786897
\(790\) 0 0
\(791\) 26.6101 0.946148
\(792\) 0 0
\(793\) −16.8285 −0.597596
\(794\) 0 0
\(795\) 43.7084 1.55018
\(796\) 0 0
\(797\) −5.11408 −0.181150 −0.0905750 0.995890i \(-0.528870\pi\)
−0.0905750 + 0.995890i \(0.528870\pi\)
\(798\) 0 0
\(799\) 0.132448 0.00468568
\(800\) 0 0
\(801\) −3.61449 −0.127712
\(802\) 0 0
\(803\) −38.5084 −1.35893
\(804\) 0 0
\(805\) −20.4961 −0.722393
\(806\) 0 0
\(807\) −14.4088 −0.507213
\(808\) 0 0
\(809\) 36.7775 1.29303 0.646514 0.762902i \(-0.276226\pi\)
0.646514 + 0.762902i \(0.276226\pi\)
\(810\) 0 0
\(811\) 38.7923 1.36218 0.681090 0.732200i \(-0.261506\pi\)
0.681090 + 0.732200i \(0.261506\pi\)
\(812\) 0 0
\(813\) −4.72029 −0.165548
\(814\) 0 0
\(815\) 42.5721 1.49124
\(816\) 0 0
\(817\) −24.9155 −0.871684
\(818\) 0 0
\(819\) −4.55536 −0.159177
\(820\) 0 0
\(821\) −26.0951 −0.910725 −0.455363 0.890306i \(-0.650490\pi\)
−0.455363 + 0.890306i \(0.650490\pi\)
\(822\) 0 0
\(823\) 41.9826 1.46342 0.731710 0.681616i \(-0.238723\pi\)
0.731710 + 0.681616i \(0.238723\pi\)
\(824\) 0 0
\(825\) 53.9054 1.87675
\(826\) 0 0
\(827\) −8.82167 −0.306759 −0.153380 0.988167i \(-0.549016\pi\)
−0.153380 + 0.988167i \(0.549016\pi\)
\(828\) 0 0
\(829\) −27.5764 −0.957768 −0.478884 0.877878i \(-0.658959\pi\)
−0.478884 + 0.877878i \(0.658959\pi\)
\(830\) 0 0
\(831\) −27.9962 −0.971176
\(832\) 0 0
\(833\) −0.272812 −0.00945237
\(834\) 0 0
\(835\) 4.17025 0.144317
\(836\) 0 0
\(837\) 3.34520 0.115627
\(838\) 0 0
\(839\) −35.2189 −1.21589 −0.607945 0.793979i \(-0.708006\pi\)
−0.607945 + 0.793979i \(0.708006\pi\)
\(840\) 0 0
\(841\) 0.608865 0.0209953
\(842\) 0 0
\(843\) −21.2473 −0.731797
\(844\) 0 0
\(845\) 27.1001 0.932271
\(846\) 0 0
\(847\) −14.1598 −0.486535
\(848\) 0 0
\(849\) −6.07839 −0.208610
\(850\) 0 0
\(851\) 16.6168 0.569617
\(852\) 0 0
\(853\) −0.579339 −0.0198362 −0.00991810 0.999951i \(-0.503157\pi\)
−0.00991810 + 0.999951i \(0.503157\pi\)
\(854\) 0 0
\(855\) 29.8886 1.02217
\(856\) 0 0
\(857\) −11.0178 −0.376359 −0.188180 0.982135i \(-0.560259\pi\)
−0.188180 + 0.982135i \(0.560259\pi\)
\(858\) 0 0
\(859\) −18.7589 −0.640045 −0.320022 0.947410i \(-0.603690\pi\)
−0.320022 + 0.947410i \(0.603690\pi\)
\(860\) 0 0
\(861\) −5.95761 −0.203035
\(862\) 0 0
\(863\) −5.38140 −0.183185 −0.0915925 0.995797i \(-0.529196\pi\)
−0.0915925 + 0.995797i \(0.529196\pi\)
\(864\) 0 0
\(865\) 102.496 3.48496
\(866\) 0 0
\(867\) −16.9949 −0.577176
\(868\) 0 0
\(869\) 0.253834 0.00861073
\(870\) 0 0
\(871\) 7.82280 0.265065
\(872\) 0 0
\(873\) 0.334815 0.0113318
\(874\) 0 0
\(875\) 55.0653 1.86155
\(876\) 0 0
\(877\) −7.93120 −0.267818 −0.133909 0.990994i \(-0.542753\pi\)
−0.133909 + 0.990994i \(0.542753\pi\)
\(878\) 0 0
\(879\) 15.5348 0.523976
\(880\) 0 0
\(881\) −27.7441 −0.934721 −0.467361 0.884067i \(-0.654795\pi\)
−0.467361 + 0.884067i \(0.654795\pi\)
\(882\) 0 0
\(883\) 10.6482 0.358340 0.179170 0.983818i \(-0.442659\pi\)
0.179170 + 0.983818i \(0.442659\pi\)
\(884\) 0 0
\(885\) −32.7238 −1.10000
\(886\) 0 0
\(887\) −41.5610 −1.39548 −0.697741 0.716350i \(-0.745811\pi\)
−0.697741 + 0.716350i \(0.745811\pi\)
\(888\) 0 0
\(889\) 33.7230 1.13103
\(890\) 0 0
\(891\) 4.35038 0.145743
\(892\) 0 0
\(893\) −13.2511 −0.443431
\(894\) 0 0
\(895\) 59.4450 1.98703
\(896\) 0 0
\(897\) −7.01463 −0.234212
\(898\) 0 0
\(899\) 18.2026 0.607090
\(900\) 0 0
\(901\) −0.750828 −0.0250137
\(902\) 0 0
\(903\) −6.21070 −0.206679
\(904\) 0 0
\(905\) −95.2604 −3.16656
\(906\) 0 0
\(907\) 58.4184 1.93975 0.969876 0.243599i \(-0.0783280\pi\)
0.969876 + 0.243599i \(0.0783280\pi\)
\(908\) 0 0
\(909\) 4.71758 0.156472
\(910\) 0 0
\(911\) −21.0024 −0.695840 −0.347920 0.937524i \(-0.613112\pi\)
−0.347920 + 0.937524i \(0.613112\pi\)
\(912\) 0 0
\(913\) 2.54454 0.0842121
\(914\) 0 0
\(915\) 27.5231 0.909885
\(916\) 0 0
\(917\) −0.612695 −0.0202330
\(918\) 0 0
\(919\) −10.2975 −0.339683 −0.169842 0.985471i \(-0.554326\pi\)
−0.169842 + 0.985471i \(0.554326\pi\)
\(920\) 0 0
\(921\) −7.05233 −0.232382
\(922\) 0 0
\(923\) −23.9950 −0.789804
\(924\) 0 0
\(925\) −74.8442 −2.46086
\(926\) 0 0
\(927\) −20.2182 −0.664054
\(928\) 0 0
\(929\) −47.3424 −1.55325 −0.776627 0.629960i \(-0.783071\pi\)
−0.776627 + 0.629960i \(0.783071\pi\)
\(930\) 0 0
\(931\) 27.2942 0.894530
\(932\) 0 0
\(933\) 26.0059 0.851396
\(934\) 0 0
\(935\) −1.29965 −0.0425031
\(936\) 0 0
\(937\) 33.2393 1.08588 0.542941 0.839771i \(-0.317311\pi\)
0.542941 + 0.839771i \(0.317311\pi\)
\(938\) 0 0
\(939\) 17.5377 0.572320
\(940\) 0 0
\(941\) 50.1401 1.63452 0.817260 0.576270i \(-0.195492\pi\)
0.817260 + 0.576270i \(0.195492\pi\)
\(942\) 0 0
\(943\) −9.17388 −0.298743
\(944\) 0 0
\(945\) 7.45034 0.242360
\(946\) 0 0
\(947\) 16.5748 0.538609 0.269304 0.963055i \(-0.413206\pi\)
0.269304 + 0.963055i \(0.413206\pi\)
\(948\) 0 0
\(949\) −22.5703 −0.732664
\(950\) 0 0
\(951\) 20.8460 0.675977
\(952\) 0 0
\(953\) −26.0587 −0.844123 −0.422062 0.906567i \(-0.638693\pi\)
−0.422062 + 0.906567i \(0.638693\pi\)
\(954\) 0 0
\(955\) −5.93865 −0.192170
\(956\) 0 0
\(957\) 23.6721 0.765212
\(958\) 0 0
\(959\) −20.6147 −0.665685
\(960\) 0 0
\(961\) −19.8096 −0.639020
\(962\) 0 0
\(963\) 4.02095 0.129573
\(964\) 0 0
\(965\) 58.3018 1.87680
\(966\) 0 0
\(967\) −12.6689 −0.407403 −0.203702 0.979033i \(-0.565297\pi\)
−0.203702 + 0.979033i \(0.565297\pi\)
\(968\) 0 0
\(969\) −0.513430 −0.0164937
\(970\) 0 0
\(971\) −49.9738 −1.60373 −0.801867 0.597502i \(-0.796160\pi\)
−0.801867 + 0.597502i \(0.796160\pi\)
\(972\) 0 0
\(973\) 28.1651 0.902933
\(974\) 0 0
\(975\) 31.5947 1.01184
\(976\) 0 0
\(977\) 33.0974 1.05888 0.529440 0.848347i \(-0.322402\pi\)
0.529440 + 0.848347i \(0.322402\pi\)
\(978\) 0 0
\(979\) −15.7244 −0.502553
\(980\) 0 0
\(981\) 7.32526 0.233878
\(982\) 0 0
\(983\) −39.4423 −1.25801 −0.629007 0.777400i \(-0.716538\pi\)
−0.629007 + 0.777400i \(0.716538\pi\)
\(984\) 0 0
\(985\) −59.4018 −1.89270
\(986\) 0 0
\(987\) −3.30311 −0.105139
\(988\) 0 0
\(989\) −9.56361 −0.304105
\(990\) 0 0
\(991\) 53.1881 1.68957 0.844787 0.535102i \(-0.179727\pi\)
0.844787 + 0.535102i \(0.179727\pi\)
\(992\) 0 0
\(993\) 27.8470 0.883698
\(994\) 0 0
\(995\) 69.5874 2.20607
\(996\) 0 0
\(997\) −30.5032 −0.966046 −0.483023 0.875608i \(-0.660461\pi\)
−0.483023 + 0.875608i \(0.660461\pi\)
\(998\) 0 0
\(999\) −6.04022 −0.191104
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 \(a_p\))