Properties

Label 6012.2.a.f.1.2
Level 6012
Weight 2
Character 6012.1
Self dual yes
Analytic conductor 48.006
Analytic rank 0
Dimension 5
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6012.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.0060616952\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.161121.1
Defining polynomial: \(x^{5} - x^{4} - 6 x^{3} + 3 x^{2} + 5 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 2004)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-2.07823\) of defining polynomial
Character \(\chi\) \(=\) 6012.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.614948 q^{5} -3.46328 q^{7} +O(q^{10})\) \(q+0.614948 q^{5} -3.46328 q^{7} -3.80906 q^{11} -2.93060 q^{13} -3.15646 q^{17} -5.58256 q^{19} +0.574360 q^{23} -4.62184 q^{25} +3.25128 q^{29} -1.74532 q^{31} -2.12974 q^{35} -4.35964 q^{37} +1.51130 q^{41} +9.97984 q^{43} +8.29318 q^{47} +4.99433 q^{49} -0.465048 q^{53} -2.34237 q^{55} +9.58387 q^{59} -6.22999 q^{61} -1.80217 q^{65} +3.41132 q^{67} +8.58319 q^{71} -9.90115 q^{73} +13.1918 q^{77} +10.2406 q^{79} +8.39859 q^{83} -1.94106 q^{85} +7.12992 q^{89} +10.1495 q^{91} -3.43299 q^{95} +4.70410 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + 7q^{5} - 2q^{7} + O(q^{10}) \) \( 5q + 7q^{5} - 2q^{7} + 5q^{11} - 8q^{13} + 7q^{17} + 2q^{19} + 13q^{23} + 2q^{25} + 11q^{29} - 12q^{31} + 12q^{35} - 7q^{37} + 12q^{41} + 19q^{47} - 9q^{49} + 21q^{53} - q^{55} + 7q^{59} - 6q^{61} - 14q^{65} + 10q^{67} + 35q^{71} - 8q^{73} + 6q^{77} + 11q^{83} + 5q^{85} + 32q^{89} + 5q^{91} + 19q^{95} + 11q^{97} + O(q^{100}) \)

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 0
\(4\) 0 0
\(5\) 0.614948 0.275013 0.137507 0.990501i \(-0.456091\pi\)
0.137507 + 0.990501i \(0.456091\pi\)
\(6\) 0 0
\(7\) −3.46328 −1.30900 −0.654499 0.756063i \(-0.727120\pi\)
−0.654499 + 0.756063i \(0.727120\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −3.80906 −1.14847 −0.574237 0.818689i \(-0.694701\pi\)
−0.574237 + 0.818689i \(0.694701\pi\)
\(12\) 0 0
\(13\) −2.93060 −0.812801 −0.406401 0.913695i \(-0.633216\pi\)
−0.406401 + 0.913695i \(0.633216\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.15646 −0.765555 −0.382778 0.923841i \(-0.625032\pi\)
−0.382778 + 0.923841i \(0.625032\pi\)
\(18\) 0 0
\(19\) −5.58256 −1.28073 −0.640363 0.768072i \(-0.721216\pi\)
−0.640363 + 0.768072i \(0.721216\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.574360 0.119762 0.0598811 0.998206i \(-0.480928\pi\)
0.0598811 + 0.998206i \(0.480928\pi\)
\(24\) 0 0
\(25\) −4.62184 −0.924368
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3.25128 0.603748 0.301874 0.953348i \(-0.402388\pi\)
0.301874 + 0.953348i \(0.402388\pi\)
\(30\) 0 0
\(31\) −1.74532 −0.313468 −0.156734 0.987641i \(-0.550097\pi\)
−0.156734 + 0.987641i \(0.550097\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2.12974 −0.359992
\(36\) 0 0
\(37\) −4.35964 −0.716720 −0.358360 0.933583i \(-0.616664\pi\)
−0.358360 + 0.933583i \(0.616664\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.51130 0.236026 0.118013 0.993012i \(-0.462348\pi\)
0.118013 + 0.993012i \(0.462348\pi\)
\(42\) 0 0
\(43\) 9.97984 1.52191 0.760956 0.648804i \(-0.224730\pi\)
0.760956 + 0.648804i \(0.224730\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 8.29318 1.20968 0.604842 0.796345i \(-0.293236\pi\)
0.604842 + 0.796345i \(0.293236\pi\)
\(48\) 0 0
\(49\) 4.99433 0.713476
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.465048 −0.0638792 −0.0319396 0.999490i \(-0.510168\pi\)
−0.0319396 + 0.999490i \(0.510168\pi\)
\(54\) 0 0
\(55\) −2.34237 −0.315845
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 9.58387 1.24771 0.623857 0.781539i \(-0.285565\pi\)
0.623857 + 0.781539i \(0.285565\pi\)
\(60\) 0 0
\(61\) −6.22999 −0.797668 −0.398834 0.917023i \(-0.630585\pi\)
−0.398834 + 0.917023i \(0.630585\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.80217 −0.223531
\(66\) 0 0
\(67\) 3.41132 0.416759 0.208380 0.978048i \(-0.433181\pi\)
0.208380 + 0.978048i \(0.433181\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8.58319 1.01864 0.509319 0.860578i \(-0.329897\pi\)
0.509319 + 0.860578i \(0.329897\pi\)
\(72\) 0 0
\(73\) −9.90115 −1.15884 −0.579421 0.815028i \(-0.696721\pi\)
−0.579421 + 0.815028i \(0.696721\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 13.1918 1.50335
\(78\) 0 0
\(79\) 10.2406 1.15216 0.576078 0.817395i \(-0.304583\pi\)
0.576078 + 0.817395i \(0.304583\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 8.39859 0.921865 0.460932 0.887435i \(-0.347515\pi\)
0.460932 + 0.887435i \(0.347515\pi\)
\(84\) 0 0
\(85\) −1.94106 −0.210538
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 7.12992 0.755770 0.377885 0.925853i \(-0.376652\pi\)
0.377885 + 0.925853i \(0.376652\pi\)
\(90\) 0 0
\(91\) 10.1495 1.06396
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −3.43299 −0.352217
\(96\) 0 0
\(97\) 4.70410 0.477629 0.238815 0.971065i \(-0.423241\pi\)
0.238815 + 0.971065i \(0.423241\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 6.74351 0.671004 0.335502 0.942039i \(-0.391094\pi\)
0.335502 + 0.942039i \(0.391094\pi\)
\(102\) 0 0
\(103\) −3.37572 −0.332620 −0.166310 0.986074i \(-0.553185\pi\)
−0.166310 + 0.986074i \(0.553185\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.87891 0.665010 0.332505 0.943102i \(-0.392106\pi\)
0.332505 + 0.943102i \(0.392106\pi\)
\(108\) 0 0
\(109\) −12.2964 −1.17778 −0.588891 0.808213i \(-0.700435\pi\)
−0.588891 + 0.808213i \(0.700435\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −5.04942 −0.475009 −0.237505 0.971386i \(-0.576329\pi\)
−0.237505 + 0.971386i \(0.576329\pi\)
\(114\) 0 0
\(115\) 0.353202 0.0329362
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 10.9317 1.00211
\(120\) 0 0
\(121\) 3.50891 0.318992
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −5.91693 −0.529227
\(126\) 0 0
\(127\) 8.43089 0.748121 0.374060 0.927404i \(-0.377965\pi\)
0.374060 + 0.927404i \(0.377965\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −7.65327 −0.668669 −0.334335 0.942454i \(-0.608512\pi\)
−0.334335 + 0.942454i \(0.608512\pi\)
\(132\) 0 0
\(133\) 19.3340 1.67647
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 5.27810 0.450938 0.225469 0.974250i \(-0.427609\pi\)
0.225469 + 0.974250i \(0.427609\pi\)
\(138\) 0 0
\(139\) 5.53478 0.469454 0.234727 0.972061i \(-0.424580\pi\)
0.234727 + 0.972061i \(0.424580\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 11.1628 0.933481
\(144\) 0 0
\(145\) 1.99937 0.166039
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −13.1803 −1.07977 −0.539886 0.841738i \(-0.681533\pi\)
−0.539886 + 0.841738i \(0.681533\pi\)
\(150\) 0 0
\(151\) −2.29363 −0.186653 −0.0933266 0.995636i \(-0.529750\pi\)
−0.0933266 + 0.995636i \(0.529750\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.07328 −0.0862080
\(156\) 0 0
\(157\) −14.6203 −1.16682 −0.583412 0.812177i \(-0.698283\pi\)
−0.583412 + 0.812177i \(0.698283\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1.98917 −0.156769
\(162\) 0 0
\(163\) 15.6158 1.22312 0.611560 0.791198i \(-0.290542\pi\)
0.611560 + 0.791198i \(0.290542\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) −4.41160 −0.339354
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −13.8874 −1.05584 −0.527919 0.849295i \(-0.677028\pi\)
−0.527919 + 0.849295i \(0.677028\pi\)
\(174\) 0 0
\(175\) 16.0067 1.21000
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3.21586 −0.240364 −0.120182 0.992752i \(-0.538348\pi\)
−0.120182 + 0.992752i \(0.538348\pi\)
\(180\) 0 0
\(181\) 7.33183 0.544971 0.272485 0.962160i \(-0.412154\pi\)
0.272485 + 0.962160i \(0.412154\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2.68095 −0.197107
\(186\) 0 0
\(187\) 12.0231 0.879220
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2.33599 −0.169026 −0.0845130 0.996422i \(-0.526933\pi\)
−0.0845130 + 0.996422i \(0.526933\pi\)
\(192\) 0 0
\(193\) 9.73301 0.700597 0.350299 0.936638i \(-0.386080\pi\)
0.350299 + 0.936638i \(0.386080\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 19.0432 1.35677 0.678386 0.734705i \(-0.262680\pi\)
0.678386 + 0.734705i \(0.262680\pi\)
\(198\) 0 0
\(199\) 5.26986 0.373570 0.186785 0.982401i \(-0.440193\pi\)
0.186785 + 0.982401i \(0.440193\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −11.2601 −0.790305
\(204\) 0 0
\(205\) 0.929372 0.0649102
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 21.2643 1.47088
\(210\) 0 0
\(211\) −1.49086 −0.102635 −0.0513176 0.998682i \(-0.516342\pi\)
−0.0513176 + 0.998682i \(0.516342\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 6.13709 0.418546
\(216\) 0 0
\(217\) 6.04453 0.410330
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 9.25032 0.622244
\(222\) 0 0
\(223\) −0.343506 −0.0230029 −0.0115014 0.999934i \(-0.503661\pi\)
−0.0115014 + 0.999934i \(0.503661\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −8.12470 −0.539256 −0.269628 0.962965i \(-0.586901\pi\)
−0.269628 + 0.962965i \(0.586901\pi\)
\(228\) 0 0
\(229\) 5.95619 0.393596 0.196798 0.980444i \(-0.436946\pi\)
0.196798 + 0.980444i \(0.436946\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.870260 −0.0570126 −0.0285063 0.999594i \(-0.509075\pi\)
−0.0285063 + 0.999594i \(0.509075\pi\)
\(234\) 0 0
\(235\) 5.09988 0.332679
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −13.0177 −0.842046 −0.421023 0.907050i \(-0.638329\pi\)
−0.421023 + 0.907050i \(0.638329\pi\)
\(240\) 0 0
\(241\) −2.82934 −0.182254 −0.0911270 0.995839i \(-0.529047\pi\)
−0.0911270 + 0.995839i \(0.529047\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3.07126 0.196215
\(246\) 0 0
\(247\) 16.3602 1.04098
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 16.4580 1.03882 0.519410 0.854525i \(-0.326152\pi\)
0.519410 + 0.854525i \(0.326152\pi\)
\(252\) 0 0
\(253\) −2.18777 −0.137544
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −24.5773 −1.53309 −0.766545 0.642191i \(-0.778026\pi\)
−0.766545 + 0.642191i \(0.778026\pi\)
\(258\) 0 0
\(259\) 15.0987 0.938185
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −24.6483 −1.51988 −0.759939 0.649994i \(-0.774771\pi\)
−0.759939 + 0.649994i \(0.774771\pi\)
\(264\) 0 0
\(265\) −0.285980 −0.0175676
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4.52549 0.275924 0.137962 0.990438i \(-0.455945\pi\)
0.137962 + 0.990438i \(0.455945\pi\)
\(270\) 0 0
\(271\) −22.1048 −1.34277 −0.671385 0.741109i \(-0.734300\pi\)
−0.671385 + 0.741109i \(0.734300\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 17.6048 1.06161
\(276\) 0 0
\(277\) −14.4555 −0.868548 −0.434274 0.900781i \(-0.642995\pi\)
−0.434274 + 0.900781i \(0.642995\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −3.60180 −0.214866 −0.107433 0.994212i \(-0.534263\pi\)
−0.107433 + 0.994212i \(0.534263\pi\)
\(282\) 0 0
\(283\) −22.0928 −1.31328 −0.656639 0.754205i \(-0.728023\pi\)
−0.656639 + 0.754205i \(0.728023\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −5.23407 −0.308957
\(288\) 0 0
\(289\) −7.03673 −0.413926
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0.403322 0.0235623 0.0117812 0.999931i \(-0.496250\pi\)
0.0117812 + 0.999931i \(0.496250\pi\)
\(294\) 0 0
\(295\) 5.89358 0.343138
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.68322 −0.0973430
\(300\) 0 0
\(301\) −34.5630 −1.99218
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −3.83112 −0.219369
\(306\) 0 0
\(307\) 28.5615 1.63009 0.815045 0.579397i \(-0.196712\pi\)
0.815045 + 0.579397i \(0.196712\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 14.0740 0.798061 0.399031 0.916938i \(-0.369347\pi\)
0.399031 + 0.916938i \(0.369347\pi\)
\(312\) 0 0
\(313\) 13.3132 0.752504 0.376252 0.926517i \(-0.377213\pi\)
0.376252 + 0.926517i \(0.377213\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 23.0614 1.29526 0.647630 0.761955i \(-0.275760\pi\)
0.647630 + 0.761955i \(0.275760\pi\)
\(318\) 0 0
\(319\) −12.3843 −0.693388
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 17.6211 0.980467
\(324\) 0 0
\(325\) 13.5447 0.751327
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −28.7216 −1.58347
\(330\) 0 0
\(331\) 31.1825 1.71394 0.856972 0.515363i \(-0.172343\pi\)
0.856972 + 0.515363i \(0.172343\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2.09779 0.114614
\(336\) 0 0
\(337\) −0.817442 −0.0445289 −0.0222645 0.999752i \(-0.507088\pi\)
−0.0222645 + 0.999752i \(0.507088\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 6.64802 0.360010
\(342\) 0 0
\(343\) 6.94619 0.375059
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 9.97471 0.535471 0.267735 0.963492i \(-0.413725\pi\)
0.267735 + 0.963492i \(0.413725\pi\)
\(348\) 0 0
\(349\) −13.6700 −0.731740 −0.365870 0.930666i \(-0.619229\pi\)
−0.365870 + 0.930666i \(0.619229\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0.0887759 0.00472506 0.00236253 0.999997i \(-0.499248\pi\)
0.00236253 + 0.999997i \(0.499248\pi\)
\(354\) 0 0
\(355\) 5.27822 0.280139
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 6.69628 0.353416 0.176708 0.984263i \(-0.443455\pi\)
0.176708 + 0.984263i \(0.443455\pi\)
\(360\) 0 0
\(361\) 12.1650 0.640261
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −6.08870 −0.318697
\(366\) 0 0
\(367\) 26.5833 1.38764 0.693819 0.720150i \(-0.255927\pi\)
0.693819 + 0.720150i \(0.255927\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.61059 0.0836178
\(372\) 0 0
\(373\) 25.1865 1.30411 0.652053 0.758173i \(-0.273908\pi\)
0.652053 + 0.758173i \(0.273908\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −9.52820 −0.490727
\(378\) 0 0
\(379\) −15.4647 −0.794370 −0.397185 0.917739i \(-0.630013\pi\)
−0.397185 + 0.917739i \(0.630013\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −30.0700 −1.53651 −0.768253 0.640147i \(-0.778874\pi\)
−0.768253 + 0.640147i \(0.778874\pi\)
\(384\) 0 0
\(385\) 8.11230 0.413441
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 26.8151 1.35958 0.679790 0.733407i \(-0.262071\pi\)
0.679790 + 0.733407i \(0.262071\pi\)
\(390\) 0 0
\(391\) −1.81295 −0.0916846
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 6.29743 0.316858
\(396\) 0 0
\(397\) −10.7692 −0.540490 −0.270245 0.962792i \(-0.587105\pi\)
−0.270245 + 0.962792i \(0.587105\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −17.6845 −0.883121 −0.441561 0.897231i \(-0.645575\pi\)
−0.441561 + 0.897231i \(0.645575\pi\)
\(402\) 0 0
\(403\) 5.11483 0.254788
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 16.6061 0.823134
\(408\) 0 0
\(409\) −20.1733 −0.997506 −0.498753 0.866744i \(-0.666209\pi\)
−0.498753 + 0.866744i \(0.666209\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −33.1917 −1.63325
\(414\) 0 0
\(415\) 5.16470 0.253525
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −7.91248 −0.386550 −0.193275 0.981145i \(-0.561911\pi\)
−0.193275 + 0.981145i \(0.561911\pi\)
\(420\) 0 0
\(421\) 7.95900 0.387898 0.193949 0.981012i \(-0.437870\pi\)
0.193949 + 0.981012i \(0.437870\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 14.5887 0.707654
\(426\) 0 0
\(427\) 21.5762 1.04415
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −6.43209 −0.309823 −0.154912 0.987928i \(-0.549509\pi\)
−0.154912 + 0.987928i \(0.549509\pi\)
\(432\) 0 0
\(433\) 25.3350 1.21752 0.608761 0.793354i \(-0.291667\pi\)
0.608761 + 0.793354i \(0.291667\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −3.20640 −0.153383
\(438\) 0 0
\(439\) −5.63416 −0.268904 −0.134452 0.990920i \(-0.542927\pi\)
−0.134452 + 0.990920i \(0.542927\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −34.5091 −1.63958 −0.819789 0.572666i \(-0.805909\pi\)
−0.819789 + 0.572666i \(0.805909\pi\)
\(444\) 0 0
\(445\) 4.38453 0.207847
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 37.4839 1.76897 0.884487 0.466565i \(-0.154509\pi\)
0.884487 + 0.466565i \(0.154509\pi\)
\(450\) 0 0
\(451\) −5.75663 −0.271069
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 6.24141 0.292602
\(456\) 0 0
\(457\) 8.87783 0.415287 0.207644 0.978205i \(-0.433421\pi\)
0.207644 + 0.978205i \(0.433421\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −9.67760 −0.450731 −0.225365 0.974274i \(-0.572358\pi\)
−0.225365 + 0.974274i \(0.572358\pi\)
\(462\) 0 0
\(463\) 8.66347 0.402626 0.201313 0.979527i \(-0.435479\pi\)
0.201313 + 0.979527i \(0.435479\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −31.1541 −1.44164 −0.720819 0.693124i \(-0.756234\pi\)
−0.720819 + 0.693124i \(0.756234\pi\)
\(468\) 0 0
\(469\) −11.8144 −0.545537
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −38.0138 −1.74787
\(474\) 0 0
\(475\) 25.8017 1.18386
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −6.78094 −0.309829 −0.154915 0.987928i \(-0.549510\pi\)
−0.154915 + 0.987928i \(0.549510\pi\)
\(480\) 0 0
\(481\) 12.7763 0.582551
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2.89278 0.131354
\(486\) 0 0
\(487\) 3.19422 0.144744 0.0723719 0.997378i \(-0.476943\pi\)
0.0723719 + 0.997378i \(0.476943\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −36.1947 −1.63344 −0.816722 0.577031i \(-0.804211\pi\)
−0.816722 + 0.577031i \(0.804211\pi\)
\(492\) 0 0
\(493\) −10.2626 −0.462202
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −29.7260 −1.33339
\(498\) 0 0
\(499\) −19.5019 −0.873026 −0.436513 0.899698i \(-0.643787\pi\)
−0.436513 + 0.899698i \(0.643787\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 23.7924 1.06085 0.530426 0.847731i \(-0.322032\pi\)
0.530426 + 0.847731i \(0.322032\pi\)
\(504\) 0 0
\(505\) 4.14691 0.184535
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 17.6743 0.783399 0.391700 0.920093i \(-0.371887\pi\)
0.391700 + 0.920093i \(0.371887\pi\)
\(510\) 0 0
\(511\) 34.2905 1.51692
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −2.07589 −0.0914748
\(516\) 0 0
\(517\) −31.5892 −1.38929
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 41.0601 1.79887 0.899437 0.437050i \(-0.143977\pi\)
0.899437 + 0.437050i \(0.143977\pi\)
\(522\) 0 0
\(523\) 2.50620 0.109588 0.0547942 0.998498i \(-0.482550\pi\)
0.0547942 + 0.998498i \(0.482550\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 5.50904 0.239977
\(528\) 0 0
\(529\) −22.6701 −0.985657
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −4.42902 −0.191842
\(534\) 0 0
\(535\) 4.23018 0.182886
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −19.0237 −0.819409
\(540\) 0 0
\(541\) 36.2521 1.55860 0.779299 0.626652i \(-0.215575\pi\)
0.779299 + 0.626652i \(0.215575\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −7.56165 −0.323906
\(546\) 0 0
\(547\) 10.5354 0.450461 0.225230 0.974306i \(-0.427686\pi\)
0.225230 + 0.974306i \(0.427686\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −18.1505 −0.773236
\(552\) 0 0
\(553\) −35.4660 −1.50817
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 17.9650 0.761200 0.380600 0.924740i \(-0.375717\pi\)
0.380600 + 0.924740i \(0.375717\pi\)
\(558\) 0 0
\(559\) −29.2469 −1.23701
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 9.50941 0.400774 0.200387 0.979717i \(-0.435780\pi\)
0.200387 + 0.979717i \(0.435780\pi\)
\(564\) 0 0
\(565\) −3.10513 −0.130634
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 18.4813 0.774778 0.387389 0.921916i \(-0.373377\pi\)
0.387389 + 0.921916i \(0.373377\pi\)
\(570\) 0 0
\(571\) 12.7478 0.533478 0.266739 0.963769i \(-0.414054\pi\)
0.266739 + 0.963769i \(0.414054\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −2.65460 −0.110704
\(576\) 0 0
\(577\) −36.1464 −1.50480 −0.752398 0.658709i \(-0.771103\pi\)
−0.752398 + 0.658709i \(0.771103\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −29.0867 −1.20672
\(582\) 0 0
\(583\) 1.77139 0.0733636
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 44.8985 1.85316 0.926580 0.376098i \(-0.122734\pi\)
0.926580 + 0.376098i \(0.122734\pi\)
\(588\) 0 0
\(589\) 9.74334 0.401468
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 24.0796 0.988832 0.494416 0.869225i \(-0.335382\pi\)
0.494416 + 0.869225i \(0.335382\pi\)
\(594\) 0 0
\(595\) 6.72245 0.275594
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −4.07062 −0.166321 −0.0831604 0.996536i \(-0.526501\pi\)
−0.0831604 + 0.996536i \(0.526501\pi\)
\(600\) 0 0
\(601\) −13.0899 −0.533949 −0.266974 0.963704i \(-0.586024\pi\)
−0.266974 + 0.963704i \(0.586024\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2.15780 0.0877269
\(606\) 0 0
\(607\) 29.3314 1.19053 0.595263 0.803531i \(-0.297048\pi\)
0.595263 + 0.803531i \(0.297048\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −24.3040 −0.983233
\(612\) 0 0
\(613\) −0.550896 −0.0222505 −0.0111252 0.999938i \(-0.503541\pi\)
−0.0111252 + 0.999938i \(0.503541\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 47.2384 1.90175 0.950874 0.309578i \(-0.100188\pi\)
0.950874 + 0.309578i \(0.100188\pi\)
\(618\) 0 0
\(619\) −2.51048 −0.100905 −0.0504524 0.998726i \(-0.516066\pi\)
−0.0504524 + 0.998726i \(0.516066\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −24.6929 −0.989301
\(624\) 0 0
\(625\) 19.4706 0.778823
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 13.7610 0.548689
\(630\) 0 0
\(631\) 42.8135 1.70438 0.852190 0.523233i \(-0.175274\pi\)
0.852190 + 0.523233i \(0.175274\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 5.18456 0.205743
\(636\) 0 0
\(637\) −14.6364 −0.579915
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 38.7594 1.53090 0.765452 0.643493i \(-0.222515\pi\)
0.765452 + 0.643493i \(0.222515\pi\)
\(642\) 0 0
\(643\) 30.1097 1.18741 0.593705 0.804682i \(-0.297664\pi\)
0.593705 + 0.804682i \(0.297664\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −14.3050 −0.562389 −0.281195 0.959651i \(-0.590731\pi\)
−0.281195 + 0.959651i \(0.590731\pi\)
\(648\) 0 0
\(649\) −36.5055 −1.43297
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −21.0547 −0.823933 −0.411966 0.911199i \(-0.635158\pi\)
−0.411966 + 0.911199i \(0.635158\pi\)
\(654\) 0 0
\(655\) −4.70637 −0.183893
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 4.02197 0.156674 0.0783368 0.996927i \(-0.475039\pi\)
0.0783368 + 0.996927i \(0.475039\pi\)
\(660\) 0 0
\(661\) 19.5974 0.762252 0.381126 0.924523i \(-0.375536\pi\)
0.381126 + 0.924523i \(0.375536\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 11.8894 0.461051
\(666\) 0 0
\(667\) 1.86741 0.0723062
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 23.7304 0.916101
\(672\) 0 0
\(673\) −18.6277 −0.718046 −0.359023 0.933329i \(-0.616890\pi\)
−0.359023 + 0.933329i \(0.616890\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 19.2425 0.739549 0.369774 0.929122i \(-0.379435\pi\)
0.369774 + 0.929122i \(0.379435\pi\)
\(678\) 0 0
\(679\) −16.2916 −0.625216
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −36.3752 −1.39186 −0.695929 0.718111i \(-0.745007\pi\)
−0.695929 + 0.718111i \(0.745007\pi\)
\(684\) 0 0
\(685\) 3.24576 0.124014
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.36287 0.0519211
\(690\) 0 0
\(691\) −31.4677 −1.19709 −0.598543 0.801091i \(-0.704254\pi\)
−0.598543 + 0.801091i \(0.704254\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 3.40360 0.129106
\(696\) 0 0
\(697\) −4.77037 −0.180691
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 38.1706 1.44168 0.720841 0.693100i \(-0.243756\pi\)
0.720841 + 0.693100i \(0.243756\pi\)
\(702\) 0 0
\(703\) 24.3379 0.917922
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −23.3547 −0.878343
\(708\) 0 0
\(709\) 12.0061 0.450900 0.225450 0.974255i \(-0.427615\pi\)
0.225450 + 0.974255i \(0.427615\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1.00244 −0.0375417
\(714\) 0 0
\(715\) 6.86455 0.256720
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −18.4358 −0.687539 −0.343769 0.939054i \(-0.611704\pi\)
−0.343769 + 0.939054i \(0.611704\pi\)
\(720\) 0 0
\(721\) 11.6911 0.435399
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −15.0269 −0.558085
\(726\) 0 0
\(727\) −14.4468 −0.535802 −0.267901 0.963446i \(-0.586330\pi\)
−0.267901 + 0.963446i \(0.586330\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −31.5010 −1.16511
\(732\) 0 0
\(733\) 44.5104 1.64403 0.822014 0.569467i \(-0.192850\pi\)
0.822014 + 0.569467i \(0.192850\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −12.9939 −0.478637
\(738\) 0 0
\(739\) 29.3056 1.07802 0.539011 0.842298i \(-0.318798\pi\)
0.539011 + 0.842298i \(0.318798\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −9.42691 −0.345840 −0.172920 0.984936i \(-0.555320\pi\)
−0.172920 + 0.984936i \(0.555320\pi\)
\(744\) 0 0
\(745\) −8.10520 −0.296951
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −23.8236 −0.870496
\(750\) 0 0
\(751\) 32.0724 1.17034 0.585170 0.810911i \(-0.301028\pi\)
0.585170 + 0.810911i \(0.301028\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.41047 −0.0513321
\(756\) 0 0
\(757\) −17.9811 −0.653533 −0.326767 0.945105i \(-0.605959\pi\)
−0.326767 + 0.945105i \(0.605959\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −34.0598 −1.23467 −0.617333 0.786702i \(-0.711787\pi\)
−0.617333 + 0.786702i \(0.711787\pi\)
\(762\) 0 0
\(763\) 42.5859 1.54171
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −28.0865 −1.01414
\(768\) 0 0
\(769\) 1.20670 0.0435147 0.0217574 0.999763i \(-0.493074\pi\)
0.0217574 + 0.999763i \(0.493074\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 15.9957 0.575327 0.287663 0.957732i \(-0.407122\pi\)
0.287663 + 0.957732i \(0.407122\pi\)
\(774\) 0 0
\(775\) 8.06658 0.289760
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −8.43693 −0.302284
\(780\) 0 0
\(781\) −32.6938 −1.16988
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −8.99070 −0.320892
\(786\) 0 0
\(787\) −32.7244 −1.16650 −0.583250 0.812292i \(-0.698219\pi\)
−0.583250 + 0.812292i \(0.698219\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 17.4876 0.621786
\(792\) 0 0
\(793\) 18.2576 0.648346
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 31.2345 1.10638 0.553191 0.833054i \(-0.313410\pi\)
0.553191 + 0.833054i \(0.313410\pi\)
\(798\) 0 0
\(799\) −26.1771 −0.926080
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 37.7140 1.33090
\(804\) 0 0
\(805\) −1.22324 −0.0431135
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 46.8880 1.64849 0.824247 0.566230i \(-0.191599\pi\)
0.824247 + 0.566230i \(0.191599\pi\)
\(810\) 0 0
\(811\) −40.2325 −1.41275 −0.706377 0.707836i \(-0.749672\pi\)
−0.706377 + 0.707836i \(0.749672\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 9.60288 0.336374
\(816\) 0 0
\(817\) −55.7130 −1.94915
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −39.3186 −1.37223 −0.686115 0.727494i \(-0.740685\pi\)
−0.686115 + 0.727494i \(0.740685\pi\)
\(822\) 0 0
\(823\) −4.64345 −0.161860 −0.0809302 0.996720i \(-0.525789\pi\)
−0.0809302 + 0.996720i \(0.525789\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −19.5624 −0.680251 −0.340125 0.940380i \(-0.610470\pi\)
−0.340125 + 0.940380i \(0.610470\pi\)
\(828\) 0 0
\(829\) 3.01629 0.104760 0.0523801 0.998627i \(-0.483319\pi\)
0.0523801 + 0.998627i \(0.483319\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −15.7644 −0.546205
\(834\) 0 0
\(835\) 0.614948 0.0212812
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 25.4908 0.880041 0.440020 0.897988i \(-0.354971\pi\)
0.440020 + 0.897988i \(0.354971\pi\)
\(840\) 0 0
\(841\) −18.4292 −0.635489
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −2.71291 −0.0933268
\(846\) 0 0
\(847\) −12.1523 −0.417559
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −2.50400 −0.0858360
\(852\) 0 0
\(853\) 22.8504 0.782382 0.391191 0.920310i \(-0.372063\pi\)
0.391191 + 0.920310i \(0.372063\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −13.9103 −0.475167 −0.237584 0.971367i \(-0.576355\pi\)
−0.237584 + 0.971367i \(0.576355\pi\)
\(858\) 0 0
\(859\) −33.0864 −1.12889 −0.564447 0.825469i \(-0.690910\pi\)
−0.564447 + 0.825469i \(0.690910\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 48.6677 1.65667 0.828334 0.560234i \(-0.189289\pi\)
0.828334 + 0.560234i \(0.189289\pi\)
\(864\) 0 0
\(865\) −8.54002 −0.290369
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −39.0069 −1.32322
\(870\) 0 0
\(871\) −9.99721 −0.338742
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 20.4920 0.692757
\(876\) 0 0
\(877\) 21.5965 0.729264 0.364632 0.931152i \(-0.381195\pi\)
0.364632 + 0.931152i \(0.381195\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 1.38305 0.0465960 0.0232980 0.999729i \(-0.492583\pi\)
0.0232980 + 0.999729i \(0.492583\pi\)
\(882\) 0 0
\(883\) −24.0085 −0.807951 −0.403976 0.914770i \(-0.632372\pi\)
−0.403976 + 0.914770i \(0.632372\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 38.6184 1.29668 0.648339 0.761352i \(-0.275464\pi\)
0.648339 + 0.761352i \(0.275464\pi\)
\(888\) 0 0
\(889\) −29.1986 −0.979289
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −46.2972 −1.54928
\(894\) 0 0
\(895\) −1.97759 −0.0661034
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −5.67452 −0.189256
\(900\) 0 0
\(901\) 1.46791 0.0489030
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 4.50870 0.149874
\(906\) 0 0
\(907\) 33.3349 1.10687 0.553433 0.832893i \(-0.313317\pi\)
0.553433 + 0.832893i \(0.313317\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 10.7100 0.354838 0.177419 0.984135i \(-0.443225\pi\)
0.177419 + 0.984135i \(0.443225\pi\)
\(912\) 0 0
\(913\) −31.9907 −1.05874
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 26.5054 0.875287
\(918\) 0 0
\(919\) −56.1186 −1.85118 −0.925591 0.378525i \(-0.876431\pi\)
−0.925591 + 0.378525i \(0.876431\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −25.1539 −0.827950
\(924\) 0 0
\(925\) 20.1495 0.662513
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −29.8268 −0.978587 −0.489293 0.872119i \(-0.662745\pi\)
−0.489293 + 0.872119i \(0.662745\pi\)
\(930\) 0 0
\(931\) −27.8812 −0.913768
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 7.39361 0.241797
\(936\) 0 0
\(937\) 23.8975 0.780696 0.390348 0.920667i \(-0.372355\pi\)
0.390348 + 0.920667i \(0.372355\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −15.7999 −0.515061 −0.257530 0.966270i \(-0.582909\pi\)
−0.257530 + 0.966270i \(0.582909\pi\)
\(942\) 0 0
\(943\) 0.868031 0.0282670
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 50.5289 1.64197 0.820985 0.570950i \(-0.193425\pi\)
0.820985 + 0.570950i \(0.193425\pi\)
\(948\) 0 0
\(949\) 29.0163 0.941909
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 14.2502 0.461609 0.230804 0.973000i \(-0.425864\pi\)
0.230804 + 0.973000i \(0.425864\pi\)
\(954\) 0 0
\(955\) −1.43651 −0.0464844
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −18.2795 −0.590277
\(960\) 0 0
\(961\) −27.9539 −0.901738
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 5.98530 0.192673
\(966\) 0 0
\(967\) 25.5040 0.820152 0.410076 0.912051i \(-0.365502\pi\)
0.410076 + 0.912051i \(0.365502\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 6.48205 0.208019 0.104009 0.994576i \(-0.466833\pi\)
0.104009 + 0.994576i \(0.466833\pi\)
\(972\) 0 0
\(973\) −19.1685 −0.614514
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 17.9008 0.572698 0.286349 0.958125i \(-0.407558\pi\)
0.286349 + 0.958125i \(0.407558\pi\)
\(978\) 0 0
\(979\) −27.1582 −0.867981
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 54.4682 1.73727 0.868634 0.495455i \(-0.164999\pi\)
0.868634 + 0.495455i \(0.164999\pi\)
\(984\) 0 0
\(985\) 11.7106 0.373130
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 5.73202 0.182268
\(990\) 0 0
\(991\) −39.3981 −1.25152 −0.625760 0.780016i \(-0.715211\pi\)
−0.625760 + 0.780016i \(0.715211\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 3.24069 0.102737
\(996\) 0 0
\(997\) 14.2166 0.450245 0.225122 0.974331i \(-0.427722\pi\)
0.225122 + 0.974331i \(0.427722\pi\)
\(998\) 0 0
\(999\) 0 0
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 6012.2.a.f.1.2 5
3.2 odd 2 2004.2.a.b.1.4 5
12.11 even 2 8016.2.a.q.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2004.2.a.b.1.4 5 3.2 odd 2
6012.2.a.f.1.2 5 1.1 even 1 trivial
8016.2.a.q.1.4 5 12.11 even 2