Properties

Label 8016.2.a.ba.1.1
Level $8016$
Weight $2$
Character 8016.1
Self dual yes
Analytic conductor $64.008$
Analytic rank $0$
Dimension $9$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8016.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.0080822603\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Defining polynomial: \(x^{9} - 3 x^{8} - 16 x^{7} + 45 x^{6} + 67 x^{5} - 166 x^{4} - 83 x^{3} + 152 x^{2} + 51 x - 10\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 4008)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-3.17025\) of defining polynomial
Character \(\chi\) \(=\) 8016.1

$q$-expansion

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 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 \(-0.390376\pi\)
0.337625 + 0.941281i \(0.390376\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −4.35038 −1.31169 −0.655844 0.754897i \(-0.727687\pi\)
−0.655844 + 0.754897i \(0.727687\pi\)
\(12\) 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 \(-0.192789\pi\)
0.822123 + 0.569310i \(0.192789\pi\)
\(20\) 0 0
\(21\) −1.78655 −0.389856
\(22\) 0 0
\(23\) 2.75103 0.573630 0.286815 0.957986i \(-0.407404\pi\)
0.286815 + 0.957986i \(0.407404\pi\)
\(24\) 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 \(-0.597123\pi\)
−0.300408 + 0.953811i \(0.597123\pi\)
\(32\) 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 \(-0.585395\pi\)
−0.265071 + 0.964229i \(0.585395\pi\)
\(44\) 0 0
\(45\) −4.17025 −0.621664
\(46\) 0 0
\(47\) −1.84888 −0.269687 −0.134843 0.990867i \(-0.543053\pi\)
−0.134843 + 0.990867i \(0.543053\pi\)
\(48\) 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 \(-0.670649\pi\)
−0.510794 + 0.859703i \(0.670649\pi\)
\(60\) 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 \(-0.560008\pi\)
−0.187407 + 0.982282i \(0.560008\pi\)
\(68\) 0 0
\(69\) −2.75103 −0.331185
\(70\) 0 0
\(71\) 9.41046 1.11682 0.558408 0.829566i \(-0.311412\pi\)
0.558408 + 0.829566i \(0.311412\pi\)
\(72\) 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 \(-0.501045\pi\)
−0.00328231 + 0.999995i \(0.501045\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −0.584902 −0.0642013 −0.0321007 0.999485i \(-0.510220\pi\)
−0.0321007 + 0.999485i \(0.510220\pi\)
\(84\) 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 \(-0.0281887\pi\)
0.996081 + 0.0884418i \(0.0281887\pi\)
\(104\) 0 0
\(105\) 7.45034 0.727079
\(106\) 0 0
\(107\) −4.02095 −0.388719 −0.194360 0.980930i \(-0.562263\pi\)
−0.194360 + 0.980930i \(0.562263\pi\)
\(108\) 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 \(-0.184022\pi\)
0.837490 + 0.546453i \(0.184022\pi\)
\(128\) 0 0
\(129\) 3.47637 0.306078
\(130\) 0 0
\(131\) −0.342949 −0.0299636 −0.0149818 0.999888i \(-0.504769\pi\)
−0.0149818 + 0.999888i \(0.504769\pi\)
\(132\) 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 \(-0.266898\pi\)
0.668591 + 0.743630i \(0.266898\pi\)
\(140\) 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 \(-0.447044\pi\)
0.165601 + 0.986193i \(0.447044\pi\)
\(152\) 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 \(-0.369081\pi\)
0.399797 + 0.916604i \(0.369081\pi\)
\(164\) 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 \(-0.321171\pi\)
0.532717 + 0.846293i \(0.321171\pi\)
\(180\) 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 \(-0.516407\pi\)
−0.0515203 + 0.998672i \(0.516407\pi\)
\(192\) 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 \(-0.298559\pi\)
0.591441 + 0.806348i \(0.298559\pi\)
\(200\) 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 \(-0.409845\pi\)
0.279458 + 0.960158i \(0.409845\pi\)
\(212\) 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 \(-0.382338\pi\)
0.361287 + 0.932455i \(0.382338\pi\)
\(224\) 0 0
\(225\) 12.3910 0.826066
\(226\) 0 0
\(227\) 0.189331 0.0125664 0.00628318 0.999980i \(-0.498000\pi\)
0.00628318 + 0.999980i \(0.498000\pi\)
\(228\) 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 \(-0.578002\pi\)
−0.242607 + 0.970125i \(0.578002\pi\)
\(240\) 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 \(-0.428839\pi\)
0.221703 + 0.975114i \(0.428839\pi\)
\(252\) 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 \(-0.738660\pi\)
−0.681473 + 0.731843i \(0.738660\pi\)
\(264\) 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 \(-0.454207\pi\)
0.143369 + 0.989669i \(0.454207\pi\)
\(272\) 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 \(-0.442176\pi\)
0.180661 + 0.983545i \(0.442176\pi\)
\(284\) 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 \(-0.435500\pi\)
0.201249 + 0.979540i \(0.435500\pi\)
\(308\) 0 0
\(309\) −20.2182 −1.15018
\(310\) 0 0
\(311\) −26.0059 −1.47466 −0.737330 0.675532i \(-0.763914\pi\)
−0.737330 + 0.675532i \(0.763914\pi\)
\(312\) 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 \(-0.777412\pi\)
−0.765305 + 0.643667i \(0.777412\pi\)
\(332\) 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 \(-0.630027\pi\)
−0.397226 + 0.917721i \(0.630027\pi\)
\(348\) 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 \(-0.452684\pi\)
0.148099 + 0.988972i \(0.452684\pi\)
\(360\) 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 \(-0.198720\pi\)
0.811374 + 0.584527i \(0.198720\pi\)
\(368\) 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 \(-0.572494\pi\)
−0.225783 + 0.974178i \(0.572494\pi\)
\(380\) 0 0
\(381\) −18.8761 −0.967050
\(382\) 0 0
\(383\) 19.5651 0.999729 0.499865 0.866103i \(-0.333383\pi\)
0.499865 + 0.866103i \(0.333383\pi\)
\(384\) 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 \(-0.562684\pi\)
−0.195656 + 0.980673i \(0.562684\pi\)
\(420\) 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 \(-0.157754\pi\)
0.879684 + 0.475559i \(0.157754\pi\)
\(432\) 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 \(-0.511229\pi\)
−0.0352696 + 0.999378i \(0.511229\pi\)
\(440\) 0 0
\(441\) −3.80826 −0.181345
\(442\) 0 0
\(443\) 30.7173 1.45943 0.729713 0.683754i \(-0.239654\pi\)
0.729713 + 0.683754i \(0.239654\pi\)
\(444\) 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 \(-0.298419\pi\)
0.591796 + 0.806088i \(0.298419\pi\)
\(464\) 0 0
\(465\) −13.9503 −0.646931
\(466\) 0 0
\(467\) 18.1847 0.841488 0.420744 0.907179i \(-0.361769\pi\)
0.420744 + 0.907179i \(0.361769\pi\)
\(468\) 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 \(-0.244975\pi\)
0.718182 + 0.695856i \(0.244975\pi\)
\(480\) 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 \(-0.555367\pi\)
−0.173066 + 0.984910i \(0.555367\pi\)
\(488\) 0 0
\(489\) −10.2085 −0.461645
\(490\) 0 0
\(491\) −2.60219 −0.117435 −0.0587176 0.998275i \(-0.518701\pi\)
−0.0587176 + 0.998275i \(0.518701\pi\)
\(492\) 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 \(-0.415080\pi\)
0.263631 + 0.964624i \(0.415080\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) −19.8128 −0.883410 −0.441705 0.897160i \(-0.645626\pi\)
−0.441705 + 0.897160i \(0.645626\pi\)
\(504\) 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 \(-0.874437\pi\)
−0.923201 + 0.384318i \(0.874437\pi\)
\(524\) 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 \(-0.722315\pi\)
−0.643010 + 0.765858i \(0.722315\pi\)
\(548\) 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 \(-0.165840\pi\)
0.867321 + 0.497749i \(0.165840\pi\)
\(564\) 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 \(-0.365099\pi\)
0.411232 + 0.911531i \(0.365099\pi\)
\(572\) 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 \(-0.422010\pi\)
0.242567 + 0.970135i \(0.422010\pi\)
\(588\) 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 \(-0.798783\pi\)
−0.806764 + 0.590874i \(0.798783\pi\)
\(600\) 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 \(-0.515291\pi\)
−0.0480204 + 0.998846i \(0.515291\pi\)
\(608\) 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 \(-0.643089\pi\)
−0.434539 + 0.900653i \(0.643089\pi\)
\(620\) 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 \(-0.355396\pi\)
0.438822 + 0.898574i \(0.355396\pi\)
\(632\) 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 \(-0.526161\pi\)
−0.0820957 + 0.996624i \(0.526161\pi\)
\(644\) 0 0
\(645\) −14.4973 −0.570832
\(646\) 0 0
\(647\) 18.0107 0.708072 0.354036 0.935232i \(-0.384809\pi\)
0.354036 + 0.935232i \(0.384809\pi\)
\(648\) 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 \(-0.519340\pi\)
−0.0607211 + 0.998155i \(0.519340\pi\)
\(660\) 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 \(-0.729155\pi\)
−0.659317 + 0.751865i \(0.729155\pi\)
\(684\) 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 \(-0.478164\pi\)
0.0685446 + 0.997648i \(0.478164\pi\)
\(692\) 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 \(-0.404091\pi\)
0.296768 + 0.954950i \(0.404091\pi\)
\(720\) 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 \(-0.0775219\pi\)
0.970490 + 0.241142i \(0.0775219\pi\)
\(728\) 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 \(-0.405072\pi\)
0.293825 + 0.955859i \(0.405072\pi\)
\(740\) 0 0
\(741\) −18.2748 −0.671342
\(742\) 0 0
\(743\) 23.6409 0.867302 0.433651 0.901081i \(-0.357225\pi\)
0.433651 + 0.901081i \(0.357225\pi\)
\(744\) 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 \(-0.380466\pi\)
0.366763 + 0.930314i \(0.380466\pi\)
\(752\) 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 \(-0.129353\pi\)
0.918560 + 0.395282i \(0.129353\pi\)
\(788\) 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 \(-0.738494\pi\)
−0.681090 + 0.732200i \(0.738494\pi\)
\(812\) 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 \(-0.761277\pi\)
−0.731710 + 0.681616i \(0.761277\pi\)
\(824\) 0 0
\(825\) 53.9054 1.87675
\(826\) 0 0
\(827\) 8.82167 0.306759 0.153380 0.988167i \(-0.450984\pi\)
0.153380 + 0.988167i \(0.450984\pi\)
\(828\) 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 \(-0.291994\pi\)
0.607945 + 0.793979i \(0.291994\pi\)
\(840\) 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 \(-0.396310\pi\)
0.320022 + 0.947410i \(0.396310\pi\)
\(860\) 0 0
\(861\) −5.95761 −0.203035
\(862\) 0 0
\(863\) 5.38140 0.183185 0.0915925 0.995797i \(-0.470804\pi\)
0.0915925 + 0.995797i \(0.470804\pi\)
\(864\) 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 \(-0.557341\pi\)
−0.179170 + 0.983818i \(0.557341\pi\)
\(884\) 0 0
\(885\) −32.7238 −1.10000
\(886\) 0 0
\(887\) 41.5610 1.39548 0.697741 0.716350i \(-0.254189\pi\)
0.697741 + 0.716350i \(0.254189\pi\)
\(888\) 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 \(-0.921672\pi\)
−0.969876 + 0.243599i \(0.921672\pi\)
\(908\) 0 0
\(909\) 4.71758 0.156472
\(910\) 0 0
\(911\) 21.0024 0.695840 0.347920 0.937524i \(-0.386888\pi\)
0.347920 + 0.937524i \(0.386888\pi\)
\(912\) 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 \(-0.445674\pi\)
0.169842 + 0.985471i \(0.445674\pi\)
\(920\) 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 \(-0.586794\pi\)
−0.269304 + 0.963055i \(0.586794\pi\)
\(948\) 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 \(-0.434703\pi\)
0.203702 + 0.979033i \(0.434703\pi\)
\(968\) 0 0
\(969\) −0.513430 −0.0164937
\(970\) 0 0
\(971\) 49.9738 1.60373 0.801867 0.597502i \(-0.203840\pi\)
0.801867 + 0.597502i \(0.203840\pi\)
\(972\) 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 \(-0.283462\pi\)
0.629007 + 0.777400i \(0.283462\pi\)
\(984\) 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 \(-0.820273\pi\)
−0.844787 + 0.535102i \(0.820273\pi\)
\(992\) 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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 8016.2.a.ba.1.1 9
4.3 odd 2 4008.2.a.i.1.1 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4008.2.a.i.1.1 9 4.3 odd 2
8016.2.a.ba.1.1 9 1.1 even 1 trivial