Properties

Label 3800.2.a.ba.1.4
Level $3800$
Weight $2$
Character 3800.1
Self dual yes
Analytic conductor $30.343$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3800.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(30.3431527681\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Defining polynomial: \( x^{6} - 2x^{5} - 10x^{4} + 16x^{3} + 15x^{2} - 14x - 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-0.185519\) of defining polynomial
Character \(\chi\) \(=\) 3800.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.185519 q^{3} +4.45651 q^{7} -2.96558 q^{9} +O(q^{10})\) \(q+0.185519 q^{3} +4.45651 q^{7} -2.96558 q^{9} +2.64623 q^{11} -1.30142 q^{13} +3.51716 q^{17} -1.00000 q^{19} +0.826767 q^{21} +6.52882 q^{23} -1.10673 q^{27} -5.20946 q^{29} +10.8219 q^{31} +0.490925 q^{33} -2.04607 q^{37} -0.241439 q^{39} -3.80044 q^{41} -4.77089 q^{43} -1.49093 q^{47} +12.8605 q^{49} +0.652501 q^{51} -0.225583 q^{53} -0.185519 q^{57} -2.86056 q^{59} -6.31449 q^{61} -13.2161 q^{63} +13.1831 q^{67} +1.21122 q^{69} +12.3310 q^{71} +5.42276 q^{73} +11.7929 q^{77} +14.9688 q^{79} +8.69143 q^{81} -3.84470 q^{83} -0.966455 q^{87} +1.67666 q^{89} -5.79981 q^{91} +2.00768 q^{93} -9.48523 q^{97} -7.84760 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 2 q^{3} - 2 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 2 q^{3} - 2 q^{7} + 6 q^{9} + 3 q^{11} + q^{13} + 14 q^{17} - 6 q^{19} + 15 q^{21} - 12 q^{23} - 8 q^{27} + 9 q^{29} + 5 q^{31} - 2 q^{33} + 8 q^{37} + 12 q^{39} + 3 q^{41} - 15 q^{43} - 4 q^{47} + 22 q^{49} + 33 q^{51} - 13 q^{53} + 2 q^{57} + 9 q^{61} - 21 q^{63} + 3 q^{67} - 11 q^{69} + 19 q^{71} - 3 q^{73} + 36 q^{77} - 16 q^{79} + 26 q^{81} - 31 q^{83} + 25 q^{87} + 14 q^{89} + 42 q^{91} - 39 q^{93} + 11 q^{97} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) 0.185519 0.107109 0.0535547 0.998565i \(-0.482945\pi\)
0.0535547 + 0.998565i \(0.482945\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 4.45651 1.68440 0.842201 0.539164i \(-0.181260\pi\)
0.842201 + 0.539164i \(0.181260\pi\)
\(8\) 0 0
\(9\) −2.96558 −0.988528
\(10\) 0 0
\(11\) 2.64623 0.797867 0.398934 0.916980i \(-0.369380\pi\)
0.398934 + 0.916980i \(0.369380\pi\)
\(12\) 0 0
\(13\) −1.30142 −0.360950 −0.180475 0.983580i \(-0.557764\pi\)
−0.180475 + 0.983580i \(0.557764\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.51716 0.853037 0.426519 0.904479i \(-0.359740\pi\)
0.426519 + 0.904479i \(0.359740\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 0.826767 0.180415
\(22\) 0 0
\(23\) 6.52882 1.36135 0.680677 0.732584i \(-0.261686\pi\)
0.680677 + 0.732584i \(0.261686\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.10673 −0.212990
\(28\) 0 0
\(29\) −5.20946 −0.967373 −0.483686 0.875241i \(-0.660702\pi\)
−0.483686 + 0.875241i \(0.660702\pi\)
\(30\) 0 0
\(31\) 10.8219 1.94368 0.971839 0.235646i \(-0.0757207\pi\)
0.971839 + 0.235646i \(0.0757207\pi\)
\(32\) 0 0
\(33\) 0.490925 0.0854591
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2.04607 −0.336373 −0.168186 0.985755i \(-0.553791\pi\)
−0.168186 + 0.985755i \(0.553791\pi\)
\(38\) 0 0
\(39\) −0.241439 −0.0386612
\(40\) 0 0
\(41\) −3.80044 −0.593529 −0.296764 0.954951i \(-0.595908\pi\)
−0.296764 + 0.954951i \(0.595908\pi\)
\(42\) 0 0
\(43\) −4.77089 −0.727554 −0.363777 0.931486i \(-0.618513\pi\)
−0.363777 + 0.931486i \(0.618513\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.49093 −0.217474 −0.108737 0.994071i \(-0.534681\pi\)
−0.108737 + 0.994071i \(0.534681\pi\)
\(48\) 0 0
\(49\) 12.8605 1.83721
\(50\) 0 0
\(51\) 0.652501 0.0913684
\(52\) 0 0
\(53\) −0.225583 −0.0309862 −0.0154931 0.999880i \(-0.504932\pi\)
−0.0154931 + 0.999880i \(0.504932\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −0.185519 −0.0245726
\(58\) 0 0
\(59\) −2.86056 −0.372413 −0.186206 0.982511i \(-0.559619\pi\)
−0.186206 + 0.982511i \(0.559619\pi\)
\(60\) 0 0
\(61\) −6.31449 −0.808488 −0.404244 0.914651i \(-0.632465\pi\)
−0.404244 + 0.914651i \(0.632465\pi\)
\(62\) 0 0
\(63\) −13.2161 −1.66508
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 13.1831 1.61058 0.805288 0.592884i \(-0.202011\pi\)
0.805288 + 0.592884i \(0.202011\pi\)
\(68\) 0 0
\(69\) 1.21122 0.145814
\(70\) 0 0
\(71\) 12.3310 1.46342 0.731711 0.681615i \(-0.238722\pi\)
0.731711 + 0.681615i \(0.238722\pi\)
\(72\) 0 0
\(73\) 5.42276 0.634686 0.317343 0.948311i \(-0.397209\pi\)
0.317343 + 0.948311i \(0.397209\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 11.7929 1.34393
\(78\) 0 0
\(79\) 14.9688 1.68413 0.842063 0.539379i \(-0.181341\pi\)
0.842063 + 0.539379i \(0.181341\pi\)
\(80\) 0 0
\(81\) 8.69143 0.965714
\(82\) 0 0
\(83\) −3.84470 −0.422011 −0.211005 0.977485i \(-0.567674\pi\)
−0.211005 + 0.977485i \(0.567674\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −0.966455 −0.103615
\(88\) 0 0
\(89\) 1.67666 0.177726 0.0888629 0.996044i \(-0.471677\pi\)
0.0888629 + 0.996044i \(0.471677\pi\)
\(90\) 0 0
\(91\) −5.79981 −0.607985
\(92\) 0 0
\(93\) 2.00768 0.208186
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −9.48523 −0.963079 −0.481539 0.876424i \(-0.659922\pi\)
−0.481539 + 0.876424i \(0.659922\pi\)
\(98\) 0 0
\(99\) −7.84760 −0.788714
\(100\) 0 0
\(101\) −6.39100 −0.635928 −0.317964 0.948103i \(-0.602999\pi\)
−0.317964 + 0.948103i \(0.602999\pi\)
\(102\) 0 0
\(103\) −4.14301 −0.408223 −0.204112 0.978948i \(-0.565431\pi\)
−0.204112 + 0.978948i \(0.565431\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −7.27597 −0.703394 −0.351697 0.936114i \(-0.614395\pi\)
−0.351697 + 0.936114i \(0.614395\pi\)
\(108\) 0 0
\(109\) 14.1077 1.35127 0.675637 0.737235i \(-0.263869\pi\)
0.675637 + 0.737235i \(0.263869\pi\)
\(110\) 0 0
\(111\) −0.379586 −0.0360287
\(112\) 0 0
\(113\) −7.03290 −0.661600 −0.330800 0.943701i \(-0.607319\pi\)
−0.330800 + 0.943701i \(0.607319\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 3.85948 0.356809
\(118\) 0 0
\(119\) 15.6743 1.43686
\(120\) 0 0
\(121\) −3.99749 −0.363408
\(122\) 0 0
\(123\) −0.705053 −0.0635725
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −13.6240 −1.20893 −0.604467 0.796630i \(-0.706614\pi\)
−0.604467 + 0.796630i \(0.706614\pi\)
\(128\) 0 0
\(129\) −0.885090 −0.0779279
\(130\) 0 0
\(131\) 22.3345 1.95137 0.975685 0.219177i \(-0.0703373\pi\)
0.975685 + 0.219177i \(0.0703373\pi\)
\(132\) 0 0
\(133\) −4.45651 −0.386428
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 5.55578 0.474662 0.237331 0.971429i \(-0.423727\pi\)
0.237331 + 0.971429i \(0.423727\pi\)
\(138\) 0 0
\(139\) −11.0452 −0.936841 −0.468420 0.883506i \(-0.655177\pi\)
−0.468420 + 0.883506i \(0.655177\pi\)
\(140\) 0 0
\(141\) −0.276595 −0.0232935
\(142\) 0 0
\(143\) −3.44386 −0.287990
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 2.38586 0.196782
\(148\) 0 0
\(149\) 17.6003 1.44188 0.720938 0.693000i \(-0.243711\pi\)
0.720938 + 0.693000i \(0.243711\pi\)
\(150\) 0 0
\(151\) 5.24140 0.426539 0.213269 0.976993i \(-0.431589\pi\)
0.213269 + 0.976993i \(0.431589\pi\)
\(152\) 0 0
\(153\) −10.4304 −0.843251
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 18.7965 1.50012 0.750061 0.661368i \(-0.230024\pi\)
0.750061 + 0.661368i \(0.230024\pi\)
\(158\) 0 0
\(159\) −0.0418499 −0.00331891
\(160\) 0 0
\(161\) 29.0957 2.29307
\(162\) 0 0
\(163\) −12.1669 −0.952982 −0.476491 0.879179i \(-0.658092\pi\)
−0.476491 + 0.879179i \(0.658092\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −7.46393 −0.577576 −0.288788 0.957393i \(-0.593252\pi\)
−0.288788 + 0.957393i \(0.593252\pi\)
\(168\) 0 0
\(169\) −11.3063 −0.869715
\(170\) 0 0
\(171\) 2.96558 0.226784
\(172\) 0 0
\(173\) −17.8070 −1.35384 −0.676921 0.736055i \(-0.736686\pi\)
−0.676921 + 0.736055i \(0.736686\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −0.530688 −0.0398889
\(178\) 0 0
\(179\) −9.48154 −0.708684 −0.354342 0.935116i \(-0.615295\pi\)
−0.354342 + 0.935116i \(0.615295\pi\)
\(180\) 0 0
\(181\) 4.32832 0.321721 0.160861 0.986977i \(-0.448573\pi\)
0.160861 + 0.986977i \(0.448573\pi\)
\(182\) 0 0
\(183\) −1.17146 −0.0865967
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 9.30720 0.680610
\(188\) 0 0
\(189\) −4.93215 −0.358761
\(190\) 0 0
\(191\) −8.21414 −0.594355 −0.297177 0.954822i \(-0.596045\pi\)
−0.297177 + 0.954822i \(0.596045\pi\)
\(192\) 0 0
\(193\) −2.89738 −0.208558 −0.104279 0.994548i \(-0.533253\pi\)
−0.104279 + 0.994548i \(0.533253\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 22.4118 1.59678 0.798388 0.602143i \(-0.205686\pi\)
0.798388 + 0.602143i \(0.205686\pi\)
\(198\) 0 0
\(199\) 2.68542 0.190364 0.0951821 0.995460i \(-0.469657\pi\)
0.0951821 + 0.995460i \(0.469657\pi\)
\(200\) 0 0
\(201\) 2.44572 0.172508
\(202\) 0 0
\(203\) −23.2160 −1.62944
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −19.3618 −1.34573
\(208\) 0 0
\(209\) −2.64623 −0.183043
\(210\) 0 0
\(211\) 7.22869 0.497644 0.248822 0.968549i \(-0.419957\pi\)
0.248822 + 0.968549i \(0.419957\pi\)
\(212\) 0 0
\(213\) 2.28764 0.156746
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 48.2281 3.27393
\(218\) 0 0
\(219\) 1.00603 0.0679809
\(220\) 0 0
\(221\) −4.57732 −0.307904
\(222\) 0 0
\(223\) −6.86629 −0.459801 −0.229900 0.973214i \(-0.573840\pi\)
−0.229900 + 0.973214i \(0.573840\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −19.2176 −1.27552 −0.637758 0.770237i \(-0.720138\pi\)
−0.637758 + 0.770237i \(0.720138\pi\)
\(228\) 0 0
\(229\) 25.2205 1.66661 0.833307 0.552810i \(-0.186445\pi\)
0.833307 + 0.552810i \(0.186445\pi\)
\(230\) 0 0
\(231\) 2.18781 0.143947
\(232\) 0 0
\(233\) 24.1123 1.57965 0.789825 0.613332i \(-0.210171\pi\)
0.789825 + 0.613332i \(0.210171\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 2.77701 0.180386
\(238\) 0 0
\(239\) 4.34082 0.280784 0.140392 0.990096i \(-0.455164\pi\)
0.140392 + 0.990096i \(0.455164\pi\)
\(240\) 0 0
\(241\) 21.9630 1.41476 0.707380 0.706834i \(-0.249877\pi\)
0.707380 + 0.706834i \(0.249877\pi\)
\(242\) 0 0
\(243\) 4.93261 0.316427
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 1.30142 0.0828077
\(248\) 0 0
\(249\) −0.713265 −0.0452013
\(250\) 0 0
\(251\) 4.41214 0.278492 0.139246 0.990258i \(-0.455532\pi\)
0.139246 + 0.990258i \(0.455532\pi\)
\(252\) 0 0
\(253\) 17.2767 1.08618
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 11.9112 0.743000 0.371500 0.928433i \(-0.378844\pi\)
0.371500 + 0.928433i \(0.378844\pi\)
\(258\) 0 0
\(259\) −9.11835 −0.566587
\(260\) 0 0
\(261\) 15.4491 0.956275
\(262\) 0 0
\(263\) 13.7779 0.849581 0.424790 0.905292i \(-0.360348\pi\)
0.424790 + 0.905292i \(0.360348\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0.311053 0.0190361
\(268\) 0 0
\(269\) −2.30474 −0.140522 −0.0702612 0.997529i \(-0.522383\pi\)
−0.0702612 + 0.997529i \(0.522383\pi\)
\(270\) 0 0
\(271\) −20.1878 −1.22632 −0.613161 0.789958i \(-0.710102\pi\)
−0.613161 + 0.789958i \(0.710102\pi\)
\(272\) 0 0
\(273\) −1.07597 −0.0651210
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 10.7021 0.643024 0.321512 0.946905i \(-0.395809\pi\)
0.321512 + 0.946905i \(0.395809\pi\)
\(278\) 0 0
\(279\) −32.0934 −1.92138
\(280\) 0 0
\(281\) −2.28603 −0.136373 −0.0681865 0.997673i \(-0.521721\pi\)
−0.0681865 + 0.997673i \(0.521721\pi\)
\(282\) 0 0
\(283\) 25.6515 1.52482 0.762411 0.647093i \(-0.224016\pi\)
0.762411 + 0.647093i \(0.224016\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −16.9367 −0.999741
\(288\) 0 0
\(289\) −4.62957 −0.272328
\(290\) 0 0
\(291\) −1.75969 −0.103155
\(292\) 0 0
\(293\) −19.6027 −1.14520 −0.572602 0.819833i \(-0.694066\pi\)
−0.572602 + 0.819833i \(0.694066\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −2.92866 −0.169938
\(298\) 0 0
\(299\) −8.49677 −0.491381
\(300\) 0 0
\(301\) −21.2615 −1.22549
\(302\) 0 0
\(303\) −1.18565 −0.0681139
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 31.6679 1.80738 0.903692 0.428183i \(-0.140846\pi\)
0.903692 + 0.428183i \(0.140846\pi\)
\(308\) 0 0
\(309\) −0.768608 −0.0437246
\(310\) 0 0
\(311\) 14.8957 0.844655 0.422328 0.906443i \(-0.361213\pi\)
0.422328 + 0.906443i \(0.361213\pi\)
\(312\) 0 0
\(313\) 0.288235 0.0162920 0.00814601 0.999967i \(-0.497407\pi\)
0.00814601 + 0.999967i \(0.497407\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −21.9612 −1.23347 −0.616733 0.787173i \(-0.711544\pi\)
−0.616733 + 0.787173i \(0.711544\pi\)
\(318\) 0 0
\(319\) −13.7854 −0.771835
\(320\) 0 0
\(321\) −1.34983 −0.0753402
\(322\) 0 0
\(323\) −3.51716 −0.195700
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 2.61725 0.144734
\(328\) 0 0
\(329\) −6.64432 −0.366313
\(330\) 0 0
\(331\) 24.0905 1.32413 0.662066 0.749445i \(-0.269680\pi\)
0.662066 + 0.749445i \(0.269680\pi\)
\(332\) 0 0
\(333\) 6.06780 0.332514
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −17.7090 −0.964673 −0.482337 0.875986i \(-0.660212\pi\)
−0.482337 + 0.875986i \(0.660212\pi\)
\(338\) 0 0
\(339\) −1.30474 −0.0708636
\(340\) 0 0
\(341\) 28.6373 1.55080
\(342\) 0 0
\(343\) 26.1172 1.41020
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −0.158465 −0.00850687 −0.00425344 0.999991i \(-0.501354\pi\)
−0.00425344 + 0.999991i \(0.501354\pi\)
\(348\) 0 0
\(349\) 27.3776 1.46549 0.732745 0.680503i \(-0.238239\pi\)
0.732745 + 0.680503i \(0.238239\pi\)
\(350\) 0 0
\(351\) 1.44032 0.0768788
\(352\) 0 0
\(353\) 18.3221 0.975185 0.487592 0.873071i \(-0.337875\pi\)
0.487592 + 0.873071i \(0.337875\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 2.90787 0.153901
\(358\) 0 0
\(359\) 35.6265 1.88030 0.940148 0.340767i \(-0.110687\pi\)
0.940148 + 0.340767i \(0.110687\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −0.741610 −0.0389245
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −3.03379 −0.158362 −0.0791812 0.996860i \(-0.525231\pi\)
−0.0791812 + 0.996860i \(0.525231\pi\)
\(368\) 0 0
\(369\) 11.2705 0.586719
\(370\) 0 0
\(371\) −1.00531 −0.0521932
\(372\) 0 0
\(373\) −9.43451 −0.488500 −0.244250 0.969712i \(-0.578542\pi\)
−0.244250 + 0.969712i \(0.578542\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 6.77972 0.349173
\(378\) 0 0
\(379\) −10.1522 −0.521486 −0.260743 0.965408i \(-0.583967\pi\)
−0.260743 + 0.965408i \(0.583967\pi\)
\(380\) 0 0
\(381\) −2.52751 −0.129488
\(382\) 0 0
\(383\) −19.0699 −0.974428 −0.487214 0.873283i \(-0.661987\pi\)
−0.487214 + 0.873283i \(0.661987\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 14.1485 0.719207
\(388\) 0 0
\(389\) −38.6448 −1.95937 −0.979685 0.200544i \(-0.935729\pi\)
−0.979685 + 0.200544i \(0.935729\pi\)
\(390\) 0 0
\(391\) 22.9629 1.16128
\(392\) 0 0
\(393\) 4.14347 0.209010
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −10.5339 −0.528679 −0.264339 0.964430i \(-0.585154\pi\)
−0.264339 + 0.964430i \(0.585154\pi\)
\(398\) 0 0
\(399\) −0.826767 −0.0413901
\(400\) 0 0
\(401\) −10.6994 −0.534304 −0.267152 0.963654i \(-0.586083\pi\)
−0.267152 + 0.963654i \(0.586083\pi\)
\(402\) 0 0
\(403\) −14.0839 −0.701571
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −5.41438 −0.268381
\(408\) 0 0
\(409\) 39.1036 1.93355 0.966775 0.255627i \(-0.0822819\pi\)
0.966775 + 0.255627i \(0.0822819\pi\)
\(410\) 0 0
\(411\) 1.03070 0.0508408
\(412\) 0 0
\(413\) −12.7481 −0.627292
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −2.04909 −0.100345
\(418\) 0 0
\(419\) 5.00833 0.244673 0.122336 0.992489i \(-0.460961\pi\)
0.122336 + 0.992489i \(0.460961\pi\)
\(420\) 0 0
\(421\) −12.7557 −0.621674 −0.310837 0.950463i \(-0.600609\pi\)
−0.310837 + 0.950463i \(0.600609\pi\)
\(422\) 0 0
\(423\) 4.42146 0.214979
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −28.1406 −1.36182
\(428\) 0 0
\(429\) −0.638902 −0.0308465
\(430\) 0 0
\(431\) 13.7140 0.660580 0.330290 0.943879i \(-0.392853\pi\)
0.330290 + 0.943879i \(0.392853\pi\)
\(432\) 0 0
\(433\) −1.49408 −0.0718007 −0.0359003 0.999355i \(-0.511430\pi\)
−0.0359003 + 0.999355i \(0.511430\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −6.52882 −0.312316
\(438\) 0 0
\(439\) 5.78568 0.276136 0.138068 0.990423i \(-0.455911\pi\)
0.138068 + 0.990423i \(0.455911\pi\)
\(440\) 0 0
\(441\) −38.1388 −1.81613
\(442\) 0 0
\(443\) −9.78426 −0.464864 −0.232432 0.972613i \(-0.574668\pi\)
−0.232432 + 0.972613i \(0.574668\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 3.26520 0.154439
\(448\) 0 0
\(449\) −38.0631 −1.79631 −0.898154 0.439682i \(-0.855091\pi\)
−0.898154 + 0.439682i \(0.855091\pi\)
\(450\) 0 0
\(451\) −10.0568 −0.473557
\(452\) 0 0
\(453\) 0.972379 0.0456864
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −18.3179 −0.856874 −0.428437 0.903572i \(-0.640936\pi\)
−0.428437 + 0.903572i \(0.640936\pi\)
\(458\) 0 0
\(459\) −3.89255 −0.181688
\(460\) 0 0
\(461\) −35.8641 −1.67036 −0.835179 0.549977i \(-0.814636\pi\)
−0.835179 + 0.549977i \(0.814636\pi\)
\(462\) 0 0
\(463\) 35.3540 1.64304 0.821519 0.570181i \(-0.193127\pi\)
0.821519 + 0.570181i \(0.193127\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −33.5118 −1.55074 −0.775371 0.631506i \(-0.782437\pi\)
−0.775371 + 0.631506i \(0.782437\pi\)
\(468\) 0 0
\(469\) 58.7507 2.71286
\(470\) 0 0
\(471\) 3.48711 0.160677
\(472\) 0 0
\(473\) −12.6248 −0.580491
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0.668984 0.0306307
\(478\) 0 0
\(479\) −21.1784 −0.967667 −0.483834 0.875160i \(-0.660756\pi\)
−0.483834 + 0.875160i \(0.660756\pi\)
\(480\) 0 0
\(481\) 2.66281 0.121414
\(482\) 0 0
\(483\) 5.39781 0.245609
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −35.2032 −1.59521 −0.797605 0.603180i \(-0.793900\pi\)
−0.797605 + 0.603180i \(0.793900\pi\)
\(488\) 0 0
\(489\) −2.25719 −0.102073
\(490\) 0 0
\(491\) −42.7908 −1.93112 −0.965561 0.260177i \(-0.916219\pi\)
−0.965561 + 0.260177i \(0.916219\pi\)
\(492\) 0 0
\(493\) −18.3225 −0.825205
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 54.9533 2.46499
\(498\) 0 0
\(499\) 18.3564 0.821747 0.410874 0.911692i \(-0.365224\pi\)
0.410874 + 0.911692i \(0.365224\pi\)
\(500\) 0 0
\(501\) −1.38470 −0.0618639
\(502\) 0 0
\(503\) −38.3650 −1.71061 −0.855305 0.518125i \(-0.826630\pi\)
−0.855305 + 0.518125i \(0.826630\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −2.09753 −0.0931547
\(508\) 0 0
\(509\) 1.73845 0.0770556 0.0385278 0.999258i \(-0.487733\pi\)
0.0385278 + 0.999258i \(0.487733\pi\)
\(510\) 0 0
\(511\) 24.1666 1.06907
\(512\) 0 0
\(513\) 1.10673 0.0488633
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −3.94532 −0.173515
\(518\) 0 0
\(519\) −3.30354 −0.145009
\(520\) 0 0
\(521\) −39.3764 −1.72511 −0.862556 0.505961i \(-0.831138\pi\)
−0.862556 + 0.505961i \(0.831138\pi\)
\(522\) 0 0
\(523\) −43.7296 −1.91216 −0.956080 0.293105i \(-0.905311\pi\)
−0.956080 + 0.293105i \(0.905311\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 38.0625 1.65803
\(528\) 0 0
\(529\) 19.6255 0.853282
\(530\) 0 0
\(531\) 8.48321 0.368140
\(532\) 0 0
\(533\) 4.94598 0.214234
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −1.75901 −0.0759067
\(538\) 0 0
\(539\) 34.0317 1.46585
\(540\) 0 0
\(541\) −17.8936 −0.769305 −0.384652 0.923061i \(-0.625679\pi\)
−0.384652 + 0.923061i \(0.625679\pi\)
\(542\) 0 0
\(543\) 0.802985 0.0344594
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 4.91310 0.210069 0.105034 0.994469i \(-0.466505\pi\)
0.105034 + 0.994469i \(0.466505\pi\)
\(548\) 0 0
\(549\) 18.7261 0.799212
\(550\) 0 0
\(551\) 5.20946 0.221931
\(552\) 0 0
\(553\) 66.7088 2.83675
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −38.6114 −1.63602 −0.818008 0.575206i \(-0.804922\pi\)
−0.818008 + 0.575206i \(0.804922\pi\)
\(558\) 0 0
\(559\) 6.20895 0.262611
\(560\) 0 0
\(561\) 1.72666 0.0728998
\(562\) 0 0
\(563\) −12.2697 −0.517105 −0.258553 0.965997i \(-0.583246\pi\)
−0.258553 + 0.965997i \(0.583246\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 38.7334 1.62665
\(568\) 0 0
\(569\) −32.0919 −1.34536 −0.672682 0.739932i \(-0.734858\pi\)
−0.672682 + 0.739932i \(0.734858\pi\)
\(570\) 0 0
\(571\) 6.85246 0.286767 0.143383 0.989667i \(-0.454202\pi\)
0.143383 + 0.989667i \(0.454202\pi\)
\(572\) 0 0
\(573\) −1.52388 −0.0636610
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 20.8983 0.870006 0.435003 0.900429i \(-0.356747\pi\)
0.435003 + 0.900429i \(0.356747\pi\)
\(578\) 0 0
\(579\) −0.537519 −0.0223385
\(580\) 0 0
\(581\) −17.1339 −0.710835
\(582\) 0 0
\(583\) −0.596943 −0.0247228
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −16.5692 −0.683883 −0.341942 0.939721i \(-0.611085\pi\)
−0.341942 + 0.939721i \(0.611085\pi\)
\(588\) 0 0
\(589\) −10.8219 −0.445910
\(590\) 0 0
\(591\) 4.15782 0.171030
\(592\) 0 0
\(593\) −6.96253 −0.285917 −0.142958 0.989729i \(-0.545662\pi\)
−0.142958 + 0.989729i \(0.545662\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0.498196 0.0203898
\(598\) 0 0
\(599\) −23.8154 −0.973072 −0.486536 0.873660i \(-0.661740\pi\)
−0.486536 + 0.873660i \(0.661740\pi\)
\(600\) 0 0
\(601\) 10.1339 0.413372 0.206686 0.978407i \(-0.433732\pi\)
0.206686 + 0.978407i \(0.433732\pi\)
\(602\) 0 0
\(603\) −39.0957 −1.59210
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −37.1179 −1.50657 −0.753286 0.657694i \(-0.771532\pi\)
−0.753286 + 0.657694i \(0.771532\pi\)
\(608\) 0 0
\(609\) −4.30701 −0.174529
\(610\) 0 0
\(611\) 1.94033 0.0784972
\(612\) 0 0
\(613\) −3.21621 −0.129901 −0.0649507 0.997888i \(-0.520689\pi\)
−0.0649507 + 0.997888i \(0.520689\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −4.80395 −0.193400 −0.0967000 0.995314i \(-0.530829\pi\)
−0.0967000 + 0.995314i \(0.530829\pi\)
\(618\) 0 0
\(619\) −10.3640 −0.416564 −0.208282 0.978069i \(-0.566787\pi\)
−0.208282 + 0.978069i \(0.566787\pi\)
\(620\) 0 0
\(621\) −7.22564 −0.289955
\(622\) 0 0
\(623\) 7.47205 0.299362
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −0.490925 −0.0196057
\(628\) 0 0
\(629\) −7.19638 −0.286938
\(630\) 0 0
\(631\) −0.213288 −0.00849084 −0.00424542 0.999991i \(-0.501351\pi\)
−0.00424542 + 0.999991i \(0.501351\pi\)
\(632\) 0 0
\(633\) 1.34106 0.0533024
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −16.7369 −0.663141
\(638\) 0 0
\(639\) −36.5686 −1.44663
\(640\) 0 0
\(641\) 4.44567 0.175593 0.0877967 0.996138i \(-0.472017\pi\)
0.0877967 + 0.996138i \(0.472017\pi\)
\(642\) 0 0
\(643\) 20.0788 0.791830 0.395915 0.918287i \(-0.370427\pi\)
0.395915 + 0.918287i \(0.370427\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 26.5734 1.04471 0.522353 0.852729i \(-0.325054\pi\)
0.522353 + 0.852729i \(0.325054\pi\)
\(648\) 0 0
\(649\) −7.56968 −0.297136
\(650\) 0 0
\(651\) 8.94722 0.350669
\(652\) 0 0
\(653\) 0.0209494 0.000819814 0 0.000409907 1.00000i \(-0.499870\pi\)
0.000409907 1.00000i \(0.499870\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −16.0816 −0.627405
\(658\) 0 0
\(659\) −30.9236 −1.20461 −0.602307 0.798265i \(-0.705752\pi\)
−0.602307 + 0.798265i \(0.705752\pi\)
\(660\) 0 0
\(661\) −26.7194 −1.03927 −0.519633 0.854390i \(-0.673931\pi\)
−0.519633 + 0.854390i \(0.673931\pi\)
\(662\) 0 0
\(663\) −0.849180 −0.0329794
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −34.0116 −1.31694
\(668\) 0 0
\(669\) −1.27383 −0.0492490
\(670\) 0 0
\(671\) −16.7096 −0.645066
\(672\) 0 0
\(673\) 17.3676 0.669472 0.334736 0.942312i \(-0.391353\pi\)
0.334736 + 0.942312i \(0.391353\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 45.7712 1.75913 0.879565 0.475779i \(-0.157834\pi\)
0.879565 + 0.475779i \(0.157834\pi\)
\(678\) 0 0
\(679\) −42.2710 −1.62221
\(680\) 0 0
\(681\) −3.56523 −0.136620
\(682\) 0 0
\(683\) 36.4020 1.39288 0.696441 0.717614i \(-0.254766\pi\)
0.696441 + 0.717614i \(0.254766\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 4.67887 0.178510
\(688\) 0 0
\(689\) 0.293579 0.0111845
\(690\) 0 0
\(691\) −20.3322 −0.773472 −0.386736 0.922190i \(-0.626398\pi\)
−0.386736 + 0.922190i \(0.626398\pi\)
\(692\) 0 0
\(693\) −34.9729 −1.32851
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −13.3668 −0.506302
\(698\) 0 0
\(699\) 4.47329 0.169196
\(700\) 0 0
\(701\) −19.4294 −0.733840 −0.366920 0.930253i \(-0.619588\pi\)
−0.366920 + 0.930253i \(0.619588\pi\)
\(702\) 0 0
\(703\) 2.04607 0.0771692
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −28.4815 −1.07116
\(708\) 0 0
\(709\) −13.0978 −0.491899 −0.245950 0.969283i \(-0.579100\pi\)
−0.245950 + 0.969283i \(0.579100\pi\)
\(710\) 0 0
\(711\) −44.3913 −1.66481
\(712\) 0 0
\(713\) 70.6545 2.64603
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0.805305 0.0300747
\(718\) 0 0
\(719\) 0.214142 0.00798615 0.00399308 0.999992i \(-0.498729\pi\)
0.00399308 + 0.999992i \(0.498729\pi\)
\(720\) 0 0
\(721\) −18.4634 −0.687612
\(722\) 0 0
\(723\) 4.07455 0.151534
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −10.2004 −0.378310 −0.189155 0.981947i \(-0.560575\pi\)
−0.189155 + 0.981947i \(0.560575\pi\)
\(728\) 0 0
\(729\) −25.1592 −0.931822
\(730\) 0 0
\(731\) −16.7800 −0.620630
\(732\) 0 0
\(733\) 31.0210 1.14579 0.572894 0.819630i \(-0.305821\pi\)
0.572894 + 0.819630i \(0.305821\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 34.8855 1.28503
\(738\) 0 0
\(739\) 35.2371 1.29622 0.648108 0.761548i \(-0.275560\pi\)
0.648108 + 0.761548i \(0.275560\pi\)
\(740\) 0 0
\(741\) 0.241439 0.00886948
\(742\) 0 0
\(743\) −7.82541 −0.287086 −0.143543 0.989644i \(-0.545850\pi\)
−0.143543 + 0.989644i \(0.545850\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 11.4018 0.417169
\(748\) 0 0
\(749\) −32.4254 −1.18480
\(750\) 0 0
\(751\) −24.2499 −0.884892 −0.442446 0.896795i \(-0.645889\pi\)
−0.442446 + 0.896795i \(0.645889\pi\)
\(752\) 0 0
\(753\) 0.818535 0.0298291
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −36.4717 −1.32559 −0.662793 0.748802i \(-0.730629\pi\)
−0.662793 + 0.748802i \(0.730629\pi\)
\(758\) 0 0
\(759\) 3.20516 0.116340
\(760\) 0 0
\(761\) 24.6495 0.893544 0.446772 0.894648i \(-0.352573\pi\)
0.446772 + 0.894648i \(0.352573\pi\)
\(762\) 0 0
\(763\) 62.8711 2.27609
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 3.72280 0.134422
\(768\) 0 0
\(769\) 14.3625 0.517927 0.258963 0.965887i \(-0.416619\pi\)
0.258963 + 0.965887i \(0.416619\pi\)
\(770\) 0 0
\(771\) 2.20976 0.0795824
\(772\) 0 0
\(773\) 24.1630 0.869081 0.434541 0.900652i \(-0.356911\pi\)
0.434541 + 0.900652i \(0.356911\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −1.69163 −0.0606868
\(778\) 0 0
\(779\) 3.80044 0.136165
\(780\) 0 0
\(781\) 32.6306 1.16762
\(782\) 0 0
\(783\) 5.76546 0.206041
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 29.6852 1.05816 0.529082 0.848571i \(-0.322537\pi\)
0.529082 + 0.848571i \(0.322537\pi\)
\(788\) 0 0
\(789\) 2.55606 0.0909981
\(790\) 0 0
\(791\) −31.3422 −1.11440
\(792\) 0 0
\(793\) 8.21783 0.291824
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −42.0735 −1.49032 −0.745160 0.666886i \(-0.767627\pi\)
−0.745160 + 0.666886i \(0.767627\pi\)
\(798\) 0 0
\(799\) −5.24383 −0.185513
\(800\) 0 0
\(801\) −4.97228 −0.175687
\(802\) 0 0
\(803\) 14.3498 0.506395
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −0.427573 −0.0150513
\(808\) 0 0
\(809\) 27.8348 0.978620 0.489310 0.872110i \(-0.337249\pi\)
0.489310 + 0.872110i \(0.337249\pi\)
\(810\) 0 0
\(811\) 14.9245 0.524069 0.262035 0.965059i \(-0.415607\pi\)
0.262035 + 0.965059i \(0.415607\pi\)
\(812\) 0 0
\(813\) −3.74522 −0.131351
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 4.77089 0.166912
\(818\) 0 0
\(819\) 17.1998 0.601010
\(820\) 0 0
\(821\) 0.503399 0.0175688 0.00878438 0.999961i \(-0.497204\pi\)
0.00878438 + 0.999961i \(0.497204\pi\)
\(822\) 0 0
\(823\) 20.7905 0.724713 0.362356 0.932040i \(-0.381972\pi\)
0.362356 + 0.932040i \(0.381972\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −37.3359 −1.29829 −0.649147 0.760663i \(-0.724874\pi\)
−0.649147 + 0.760663i \(0.724874\pi\)
\(828\) 0 0
\(829\) −20.5586 −0.714029 −0.357014 0.934099i \(-0.616205\pi\)
−0.357014 + 0.934099i \(0.616205\pi\)
\(830\) 0 0
\(831\) 1.98543 0.0688740
\(832\) 0 0
\(833\) 45.2323 1.56721
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −11.9770 −0.413984
\(838\) 0 0
\(839\) −8.13209 −0.280751 −0.140375 0.990098i \(-0.544831\pi\)
−0.140375 + 0.990098i \(0.544831\pi\)
\(840\) 0 0
\(841\) −1.86150 −0.0641896
\(842\) 0 0
\(843\) −0.424102 −0.0146068
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −17.8148 −0.612125
\(848\) 0 0
\(849\) 4.75884 0.163323
\(850\) 0 0
\(851\) −13.3585 −0.457922
\(852\) 0 0
\(853\) −32.7714 −1.12207 −0.561035 0.827792i \(-0.689597\pi\)
−0.561035 + 0.827792i \(0.689597\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −6.21619 −0.212341 −0.106170 0.994348i \(-0.533859\pi\)
−0.106170 + 0.994348i \(0.533859\pi\)
\(858\) 0 0
\(859\) 21.2194 0.723996 0.361998 0.932179i \(-0.382095\pi\)
0.361998 + 0.932179i \(0.382095\pi\)
\(860\) 0 0
\(861\) −3.14208 −0.107082
\(862\) 0 0
\(863\) −19.4411 −0.661784 −0.330892 0.943669i \(-0.607350\pi\)
−0.330892 + 0.943669i \(0.607350\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −0.858873 −0.0291689
\(868\) 0 0
\(869\) 39.6109 1.34371
\(870\) 0 0
\(871\) −17.1569 −0.581338
\(872\) 0 0
\(873\) 28.1292 0.952030
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −41.4953 −1.40120 −0.700599 0.713555i \(-0.747084\pi\)
−0.700599 + 0.713555i \(0.747084\pi\)
\(878\) 0 0
\(879\) −3.63668 −0.122662
\(880\) 0 0
\(881\) −15.6473 −0.527171 −0.263585 0.964636i \(-0.584905\pi\)
−0.263585 + 0.964636i \(0.584905\pi\)
\(882\) 0 0
\(883\) 45.4821 1.53059 0.765297 0.643677i \(-0.222592\pi\)
0.765297 + 0.643677i \(0.222592\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 12.9690 0.435457 0.217729 0.976009i \(-0.430135\pi\)
0.217729 + 0.976009i \(0.430135\pi\)
\(888\) 0 0
\(889\) −60.7155 −2.03633
\(890\) 0 0
\(891\) 22.9995 0.770512
\(892\) 0 0
\(893\) 1.49093 0.0498919
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −1.57631 −0.0526315
\(898\) 0 0
\(899\) −56.3765 −1.88026
\(900\) 0 0
\(901\) −0.793411 −0.0264324
\(902\) 0 0
\(903\) −3.94441 −0.131262
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −2.07053 −0.0687508 −0.0343754 0.999409i \(-0.510944\pi\)
−0.0343754 + 0.999409i \(0.510944\pi\)
\(908\) 0 0
\(909\) 18.9530 0.628633
\(910\) 0 0
\(911\) 25.5409 0.846207 0.423104 0.906081i \(-0.360941\pi\)
0.423104 + 0.906081i \(0.360941\pi\)
\(912\) 0 0
\(913\) −10.1739 −0.336708
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 99.5337 3.28689
\(918\) 0 0
\(919\) 25.0300 0.825664 0.412832 0.910807i \(-0.364540\pi\)
0.412832 + 0.910807i \(0.364540\pi\)
\(920\) 0 0
\(921\) 5.87500 0.193588
\(922\) 0 0
\(923\) −16.0479 −0.528223
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 12.2865 0.403540
\(928\) 0 0
\(929\) −16.4704 −0.540377 −0.270188 0.962807i \(-0.587086\pi\)
−0.270188 + 0.962807i \(0.587086\pi\)
\(930\) 0 0
\(931\) −12.8605 −0.421485
\(932\) 0 0
\(933\) 2.76343 0.0904706
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −4.56119 −0.149008 −0.0745039 0.997221i \(-0.523737\pi\)
−0.0745039 + 0.997221i \(0.523737\pi\)
\(938\) 0 0
\(939\) 0.0534732 0.00174503
\(940\) 0 0
\(941\) −10.3721 −0.338119 −0.169060 0.985606i \(-0.554073\pi\)
−0.169060 + 0.985606i \(0.554073\pi\)
\(942\) 0 0
\(943\) −24.8124 −0.808002
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −1.70431 −0.0553828 −0.0276914 0.999617i \(-0.508816\pi\)
−0.0276914 + 0.999617i \(0.508816\pi\)
\(948\) 0 0
\(949\) −7.05731 −0.229090
\(950\) 0 0
\(951\) −4.07422 −0.132116
\(952\) 0 0
\(953\) −18.5324 −0.600322 −0.300161 0.953888i \(-0.597040\pi\)
−0.300161 + 0.953888i \(0.597040\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −2.55746 −0.0826708
\(958\) 0 0
\(959\) 24.7594 0.799522
\(960\) 0 0
\(961\) 86.1144 2.77788
\(962\) 0 0
\(963\) 21.5775 0.695325
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −43.7127 −1.40570 −0.702852 0.711336i \(-0.748091\pi\)
−0.702852 + 0.711336i \(0.748091\pi\)
\(968\) 0 0
\(969\) −0.652501 −0.0209613
\(970\) 0 0
\(971\) −32.5273 −1.04385 −0.521925 0.852992i \(-0.674786\pi\)
−0.521925 + 0.852992i \(0.674786\pi\)
\(972\) 0 0
\(973\) −49.2230 −1.57802
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −2.03542 −0.0651187 −0.0325594 0.999470i \(-0.510366\pi\)
−0.0325594 + 0.999470i \(0.510366\pi\)
\(978\) 0 0
\(979\) 4.43682 0.141802
\(980\) 0 0
\(981\) −41.8376 −1.33577
\(982\) 0 0
\(983\) 19.2872 0.615166 0.307583 0.951521i \(-0.400480\pi\)
0.307583 + 0.951521i \(0.400480\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −1.23265 −0.0392356
\(988\) 0 0
\(989\) −31.1483 −0.990457
\(990\) 0 0
\(991\) −0.611835 −0.0194356 −0.00971778 0.999953i \(-0.503093\pi\)
−0.00971778 + 0.999953i \(0.503093\pi\)
\(992\) 0 0
\(993\) 4.46924 0.141827
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −58.8380 −1.86342 −0.931709 0.363207i \(-0.881682\pi\)
−0.931709 + 0.363207i \(0.881682\pi\)
\(998\) 0 0
\(999\) 2.26445 0.0716441
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 3800.2.a.ba.1.4 6
4.3 odd 2 7600.2.a.cl.1.3 6
5.2 odd 4 3800.2.d.q.3649.6 12
5.3 odd 4 3800.2.d.q.3649.7 12
5.4 even 2 3800.2.a.bc.1.3 yes 6
20.19 odd 2 7600.2.a.ch.1.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3800.2.a.ba.1.4 6 1.1 even 1 trivial
3800.2.a.bc.1.3 yes 6 5.4 even 2
3800.2.d.q.3649.6 12 5.2 odd 4
3800.2.d.q.3649.7 12 5.3 odd 4
7600.2.a.ch.1.4 6 20.19 odd 2
7600.2.a.cl.1.3 6 4.3 odd 2