Properties

Label 7600.2.a.cb.1.3
Level $7600$
Weight $2$
Character 7600.1
Self dual yes
Analytic conductor $60.686$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7600.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(60.6863055362\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.257.1
Defining polynomial: \(x^{3} - x^{2} - 4 x + 3\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 950)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(0.713538\) of defining polynomial
Character \(\chi\) \(=\) 7600.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.77733 q^{3} -4.69527 q^{7} +4.71354 q^{9} +O(q^{10})\) \(q+2.77733 q^{3} -4.69527 q^{7} +4.71354 q^{9} -6.40880 q^{11} -1.06379 q^{13} -1.91794 q^{17} +1.00000 q^{19} -13.0403 q^{21} +1.79560 q^{23} +4.75905 q^{27} +2.93621 q^{29} +5.55465 q^{31} -17.7993 q^{33} +11.4088 q^{37} -2.95449 q^{39} -1.14585 q^{41} -3.55465 q^{43} +10.8359 q^{47} +15.0455 q^{49} -5.32674 q^{51} +8.69527 q^{53} +2.77733 q^{57} +5.63148 q^{59} -3.39053 q^{61} -22.1313 q^{63} -8.82284 q^{67} +4.98696 q^{69} +1.42708 q^{71} +12.6132 q^{73} +30.0910 q^{77} +1.96345 q^{79} -0.923174 q^{81} +16.2447 q^{83} +8.15482 q^{87} -10.0000 q^{89} +4.99477 q^{91} +15.4271 q^{93} +14.9452 q^{97} -30.2081 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 2q^{3} + 2q^{7} + 13q^{9} + O(q^{10}) \) \( 3q + 2q^{3} + 2q^{7} + 13q^{9} - 2q^{11} + 2q^{13} + 4q^{17} + 3q^{19} - 11q^{21} + 14q^{23} - 7q^{27} + 14q^{29} + 4q^{31} - 4q^{33} + 17q^{37} - 29q^{39} - 8q^{41} + 2q^{43} + 13q^{47} + 25q^{49} + 11q^{51} + 10q^{53} + 2q^{57} + 6q^{59} + 22q^{61} + 2q^{63} + 8q^{69} + 2q^{71} + 12q^{73} + 50q^{77} - 24q^{79} - q^{81} + 12q^{83} - 21q^{87} - 30q^{89} + 7q^{91} + 44q^{93} - 24q^{99} + O(q^{100}) \)

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
\(3\) 2.77733 1.60349 0.801745 0.597666i \(-0.203905\pi\)
0.801745 + 0.597666i \(0.203905\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −4.69527 −1.77464 −0.887322 0.461151i \(-0.847437\pi\)
−0.887322 + 0.461151i \(0.847437\pi\)
\(8\) 0 0
\(9\) 4.71354 1.57118
\(10\) 0 0
\(11\) −6.40880 −1.93233 −0.966163 0.257931i \(-0.916959\pi\)
−0.966163 + 0.257931i \(0.916959\pi\)
\(12\) 0 0
\(13\) −1.06379 −0.295042 −0.147521 0.989059i \(-0.547129\pi\)
−0.147521 + 0.989059i \(0.547129\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.91794 −0.465169 −0.232584 0.972576i \(-0.574718\pi\)
−0.232584 + 0.972576i \(0.574718\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −13.0403 −2.84562
\(22\) 0 0
\(23\) 1.79560 0.374408 0.187204 0.982321i \(-0.440057\pi\)
0.187204 + 0.982321i \(0.440057\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 4.75905 0.915880
\(28\) 0 0
\(29\) 2.93621 0.545241 0.272620 0.962122i \(-0.412110\pi\)
0.272620 + 0.962122i \(0.412110\pi\)
\(30\) 0 0
\(31\) 5.55465 0.997645 0.498822 0.866704i \(-0.333766\pi\)
0.498822 + 0.866704i \(0.333766\pi\)
\(32\) 0 0
\(33\) −17.7993 −3.09847
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 11.4088 1.87560 0.937798 0.347182i \(-0.112861\pi\)
0.937798 + 0.347182i \(0.112861\pi\)
\(38\) 0 0
\(39\) −2.95449 −0.473096
\(40\) 0 0
\(41\) −1.14585 −0.178951 −0.0894757 0.995989i \(-0.528519\pi\)
−0.0894757 + 0.995989i \(0.528519\pi\)
\(42\) 0 0
\(43\) −3.55465 −0.542079 −0.271040 0.962568i \(-0.587367\pi\)
−0.271040 + 0.962568i \(0.587367\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10.8359 1.58058 0.790288 0.612736i \(-0.209931\pi\)
0.790288 + 0.612736i \(0.209931\pi\)
\(48\) 0 0
\(49\) 15.0455 2.14936
\(50\) 0 0
\(51\) −5.32674 −0.745893
\(52\) 0 0
\(53\) 8.69527 1.19439 0.597193 0.802097i \(-0.296283\pi\)
0.597193 + 0.802097i \(0.296283\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 2.77733 0.367866
\(58\) 0 0
\(59\) 5.63148 0.733156 0.366578 0.930387i \(-0.380529\pi\)
0.366578 + 0.930387i \(0.380529\pi\)
\(60\) 0 0
\(61\) −3.39053 −0.434113 −0.217056 0.976159i \(-0.569646\pi\)
−0.217056 + 0.976159i \(0.569646\pi\)
\(62\) 0 0
\(63\) −22.1313 −2.78828
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −8.82284 −1.07788 −0.538941 0.842344i \(-0.681175\pi\)
−0.538941 + 0.842344i \(0.681175\pi\)
\(68\) 0 0
\(69\) 4.98696 0.600360
\(70\) 0 0
\(71\) 1.42708 0.169363 0.0846814 0.996408i \(-0.473013\pi\)
0.0846814 + 0.996408i \(0.473013\pi\)
\(72\) 0 0
\(73\) 12.6132 1.47626 0.738132 0.674656i \(-0.235708\pi\)
0.738132 + 0.674656i \(0.235708\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 30.0910 3.42919
\(78\) 0 0
\(79\) 1.96345 0.220906 0.110453 0.993881i \(-0.464770\pi\)
0.110453 + 0.993881i \(0.464770\pi\)
\(80\) 0 0
\(81\) −0.923174 −0.102575
\(82\) 0 0
\(83\) 16.2447 1.78309 0.891543 0.452937i \(-0.149624\pi\)
0.891543 + 0.452937i \(0.149624\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 8.15482 0.874288
\(88\) 0 0
\(89\) −10.0000 −1.06000 −0.529999 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 0 0
\(91\) 4.99477 0.523594
\(92\) 0 0
\(93\) 15.4271 1.59971
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 14.9452 1.51745 0.758727 0.651409i \(-0.225822\pi\)
0.758727 + 0.651409i \(0.225822\pi\)
\(98\) 0 0
\(99\) −30.2081 −3.03603
\(100\) 0 0
\(101\) 10.5364 1.04841 0.524204 0.851592i \(-0.324363\pi\)
0.524204 + 0.851592i \(0.324363\pi\)
\(102\) 0 0
\(103\) −16.9817 −1.67326 −0.836630 0.547769i \(-0.815477\pi\)
−0.836630 + 0.547769i \(0.815477\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.79036 −0.173081 −0.0865405 0.996248i \(-0.527581\pi\)
−0.0865405 + 0.996248i \(0.527581\pi\)
\(108\) 0 0
\(109\) 2.41404 0.231223 0.115611 0.993295i \(-0.463117\pi\)
0.115611 + 0.993295i \(0.463117\pi\)
\(110\) 0 0
\(111\) 31.6860 3.00750
\(112\) 0 0
\(113\) −7.14585 −0.672225 −0.336112 0.941822i \(-0.609112\pi\)
−0.336112 + 0.941822i \(0.609112\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −5.01420 −0.463563
\(118\) 0 0
\(119\) 9.00523 0.825508
\(120\) 0 0
\(121\) 30.0728 2.73389
\(122\) 0 0
\(123\) −3.18239 −0.286947
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 9.26295 0.821954 0.410977 0.911646i \(-0.365188\pi\)
0.410977 + 0.911646i \(0.365188\pi\)
\(128\) 0 0
\(129\) −9.87242 −0.869219
\(130\) 0 0
\(131\) −11.5181 −1.00634 −0.503171 0.864187i \(-0.667833\pi\)
−0.503171 + 0.864187i \(0.667833\pi\)
\(132\) 0 0
\(133\) −4.69527 −0.407131
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −15.1041 −1.29043 −0.645214 0.764002i \(-0.723232\pi\)
−0.645214 + 0.764002i \(0.723232\pi\)
\(138\) 0 0
\(139\) 0.700500 0.0594156 0.0297078 0.999559i \(-0.490542\pi\)
0.0297078 + 0.999559i \(0.490542\pi\)
\(140\) 0 0
\(141\) 30.0948 2.53444
\(142\) 0 0
\(143\) 6.81761 0.570117
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 41.7863 3.44648
\(148\) 0 0
\(149\) 12.9452 1.06051 0.530255 0.847838i \(-0.322096\pi\)
0.530255 + 0.847838i \(0.322096\pi\)
\(150\) 0 0
\(151\) −5.70830 −0.464535 −0.232268 0.972652i \(-0.574615\pi\)
−0.232268 + 0.972652i \(0.574615\pi\)
\(152\) 0 0
\(153\) −9.04028 −0.730863
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −9.26295 −0.739264 −0.369632 0.929178i \(-0.620516\pi\)
−0.369632 + 0.929178i \(0.620516\pi\)
\(158\) 0 0
\(159\) 24.1496 1.91519
\(160\) 0 0
\(161\) −8.43081 −0.664441
\(162\) 0 0
\(163\) 4.28123 0.335332 0.167666 0.985844i \(-0.446377\pi\)
0.167666 + 0.985844i \(0.446377\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −15.2264 −1.17825 −0.589127 0.808040i \(-0.700528\pi\)
−0.589127 + 0.808040i \(0.700528\pi\)
\(168\) 0 0
\(169\) −11.8684 −0.912950
\(170\) 0 0
\(171\) 4.71354 0.360453
\(172\) 0 0
\(173\) 12.2630 0.932335 0.466168 0.884696i \(-0.345634\pi\)
0.466168 + 0.884696i \(0.345634\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 15.6404 1.17561
\(178\) 0 0
\(179\) 1.57292 0.117566 0.0587829 0.998271i \(-0.481278\pi\)
0.0587829 + 0.998271i \(0.481278\pi\)
\(180\) 0 0
\(181\) 11.4088 0.848010 0.424005 0.905660i \(-0.360624\pi\)
0.424005 + 0.905660i \(0.360624\pi\)
\(182\) 0 0
\(183\) −9.41661 −0.696096
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 12.2917 0.898858
\(188\) 0 0
\(189\) −22.3450 −1.62536
\(190\) 0 0
\(191\) 6.35805 0.460053 0.230026 0.973184i \(-0.426119\pi\)
0.230026 + 0.973184i \(0.426119\pi\)
\(192\) 0 0
\(193\) −14.4998 −1.04372 −0.521860 0.853031i \(-0.674762\pi\)
−0.521860 + 0.853031i \(0.674762\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 5.14585 0.366627 0.183313 0.983055i \(-0.441318\pi\)
0.183313 + 0.983055i \(0.441318\pi\)
\(198\) 0 0
\(199\) −3.87766 −0.274880 −0.137440 0.990510i \(-0.543887\pi\)
−0.137440 + 0.990510i \(0.543887\pi\)
\(200\) 0 0
\(201\) −24.5039 −1.72837
\(202\) 0 0
\(203\) −13.7863 −0.967608
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 8.46362 0.588262
\(208\) 0 0
\(209\) −6.40880 −0.443306
\(210\) 0 0
\(211\) −17.1496 −1.18063 −0.590313 0.807174i \(-0.700996\pi\)
−0.590313 + 0.807174i \(0.700996\pi\)
\(212\) 0 0
\(213\) 3.96345 0.271571
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −26.0806 −1.77046
\(218\) 0 0
\(219\) 35.0310 2.36717
\(220\) 0 0
\(221\) 2.04028 0.137244
\(222\) 0 0
\(223\) 7.84635 0.525430 0.262715 0.964873i \(-0.415382\pi\)
0.262715 + 0.964873i \(0.415382\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.28646 0.417247 0.208624 0.977996i \(-0.433102\pi\)
0.208624 + 0.977996i \(0.433102\pi\)
\(228\) 0 0
\(229\) −3.14585 −0.207884 −0.103942 0.994583i \(-0.533146\pi\)
−0.103942 + 0.994583i \(0.533146\pi\)
\(230\) 0 0
\(231\) 83.5726 5.49867
\(232\) 0 0
\(233\) −0.182394 −0.0119490 −0.00597451 0.999982i \(-0.501902\pi\)
−0.00597451 + 0.999982i \(0.501902\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 5.45315 0.354220
\(238\) 0 0
\(239\) 11.5039 0.744126 0.372063 0.928208i \(-0.378651\pi\)
0.372063 + 0.928208i \(0.378651\pi\)
\(240\) 0 0
\(241\) −0.445349 −0.0286874 −0.0143437 0.999897i \(-0.504566\pi\)
−0.0143437 + 0.999897i \(0.504566\pi\)
\(242\) 0 0
\(243\) −16.8411 −1.08036
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −1.06379 −0.0676872
\(248\) 0 0
\(249\) 45.1168 2.85916
\(250\) 0 0
\(251\) −13.2630 −0.837150 −0.418575 0.908182i \(-0.637470\pi\)
−0.418575 + 0.908182i \(0.637470\pi\)
\(252\) 0 0
\(253\) −11.5076 −0.723479
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 23.4816 1.46474 0.732370 0.680907i \(-0.238414\pi\)
0.732370 + 0.680907i \(0.238414\pi\)
\(258\) 0 0
\(259\) −53.5674 −3.32851
\(260\) 0 0
\(261\) 13.8399 0.856671
\(262\) 0 0
\(263\) 27.9269 1.72205 0.861023 0.508565i \(-0.169824\pi\)
0.861023 + 0.508565i \(0.169824\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −27.7733 −1.69970
\(268\) 0 0
\(269\) 16.4816 1.00490 0.502449 0.864607i \(-0.332432\pi\)
0.502449 + 0.864607i \(0.332432\pi\)
\(270\) 0 0
\(271\) 1.46736 0.0891356 0.0445678 0.999006i \(-0.485809\pi\)
0.0445678 + 0.999006i \(0.485809\pi\)
\(272\) 0 0
\(273\) 13.8721 0.839577
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −15.8359 −0.951486 −0.475743 0.879584i \(-0.657821\pi\)
−0.475743 + 0.879584i \(0.657821\pi\)
\(278\) 0 0
\(279\) 26.1821 1.56748
\(280\) 0 0
\(281\) −6.25515 −0.373151 −0.186576 0.982441i \(-0.559739\pi\)
−0.186576 + 0.982441i \(0.559739\pi\)
\(282\) 0 0
\(283\) −16.7005 −0.992742 −0.496371 0.868111i \(-0.665334\pi\)
−0.496371 + 0.868111i \(0.665334\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 5.38006 0.317575
\(288\) 0 0
\(289\) −13.3215 −0.783618
\(290\) 0 0
\(291\) 41.5076 2.43322
\(292\) 0 0
\(293\) −0.644516 −0.0376530 −0.0188265 0.999823i \(-0.505993\pi\)
−0.0188265 + 0.999823i \(0.505993\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −30.4998 −1.76978
\(298\) 0 0
\(299\) −1.91014 −0.110466
\(300\) 0 0
\(301\) 16.6900 0.961997
\(302\) 0 0
\(303\) 29.2630 1.68111
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 26.6457 1.52075 0.760375 0.649485i \(-0.225015\pi\)
0.760375 + 0.649485i \(0.225015\pi\)
\(308\) 0 0
\(309\) −47.1638 −2.68305
\(310\) 0 0
\(311\) −11.5494 −0.654907 −0.327454 0.944867i \(-0.606191\pi\)
−0.327454 + 0.944867i \(0.606191\pi\)
\(312\) 0 0
\(313\) 23.0638 1.30364 0.651821 0.758373i \(-0.274005\pi\)
0.651821 + 0.758373i \(0.274005\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 13.9232 0.782003 0.391002 0.920390i \(-0.372129\pi\)
0.391002 + 0.920390i \(0.372129\pi\)
\(318\) 0 0
\(319\) −18.8176 −1.05358
\(320\) 0 0
\(321\) −4.97242 −0.277534
\(322\) 0 0
\(323\) −1.91794 −0.106717
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 6.70457 0.370763
\(328\) 0 0
\(329\) −50.8773 −2.80496
\(330\) 0 0
\(331\) 0.735546 0.0404292 0.0202146 0.999796i \(-0.493565\pi\)
0.0202146 + 0.999796i \(0.493565\pi\)
\(332\) 0 0
\(333\) 53.7758 2.94690
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 2.28123 0.124266 0.0621332 0.998068i \(-0.480210\pi\)
0.0621332 + 0.998068i \(0.480210\pi\)
\(338\) 0 0
\(339\) −19.8463 −1.07791
\(340\) 0 0
\(341\) −35.5987 −1.92778
\(342\) 0 0
\(343\) −37.7758 −2.03970
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2.56246 −0.137560 −0.0687799 0.997632i \(-0.521911\pi\)
−0.0687799 + 0.997632i \(0.521911\pi\)
\(348\) 0 0
\(349\) −5.67176 −0.303602 −0.151801 0.988411i \(-0.548507\pi\)
−0.151801 + 0.988411i \(0.548507\pi\)
\(350\) 0 0
\(351\) −5.06262 −0.270223
\(352\) 0 0
\(353\) 23.6665 1.25964 0.629821 0.776740i \(-0.283128\pi\)
0.629821 + 0.776740i \(0.283128\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 25.0105 1.32369
\(358\) 0 0
\(359\) −31.9724 −1.68744 −0.843720 0.536784i \(-0.819639\pi\)
−0.843720 + 0.536784i \(0.819639\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 83.5218 4.38376
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 1.14585 0.0598128 0.0299064 0.999553i \(-0.490479\pi\)
0.0299064 + 0.999553i \(0.490479\pi\)
\(368\) 0 0
\(369\) −5.40100 −0.281165
\(370\) 0 0
\(371\) −40.8266 −2.11961
\(372\) 0 0
\(373\) −32.8579 −1.70132 −0.850658 0.525719i \(-0.823796\pi\)
−0.850658 + 0.525719i \(0.823796\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −3.12351 −0.160869
\(378\) 0 0
\(379\) 18.2865 0.939312 0.469656 0.882849i \(-0.344378\pi\)
0.469656 + 0.882849i \(0.344378\pi\)
\(380\) 0 0
\(381\) 25.7262 1.31800
\(382\) 0 0
\(383\) 20.8542 1.06560 0.532799 0.846242i \(-0.321140\pi\)
0.532799 + 0.846242i \(0.321140\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −16.7550 −0.851704
\(388\) 0 0
\(389\) −24.9086 −1.26292 −0.631459 0.775409i \(-0.717544\pi\)
−0.631459 + 0.775409i \(0.717544\pi\)
\(390\) 0 0
\(391\) −3.44385 −0.174163
\(392\) 0 0
\(393\) −31.9895 −1.61366
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 24.7445 1.24189 0.620946 0.783853i \(-0.286749\pi\)
0.620946 + 0.783853i \(0.286749\pi\)
\(398\) 0 0
\(399\) −13.0403 −0.652831
\(400\) 0 0
\(401\) 15.6457 0.781308 0.390654 0.920538i \(-0.372249\pi\)
0.390654 + 0.920538i \(0.372249\pi\)
\(402\) 0 0
\(403\) −5.90897 −0.294347
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −73.1168 −3.62426
\(408\) 0 0
\(409\) 30.5804 1.51210 0.756052 0.654512i \(-0.227126\pi\)
0.756052 + 0.654512i \(0.227126\pi\)
\(410\) 0 0
\(411\) −41.9489 −2.06919
\(412\) 0 0
\(413\) −26.4413 −1.30109
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 1.94552 0.0952723
\(418\) 0 0
\(419\) −1.96345 −0.0959210 −0.0479605 0.998849i \(-0.515272\pi\)
−0.0479605 + 0.998849i \(0.515272\pi\)
\(420\) 0 0
\(421\) −25.5949 −1.24742 −0.623710 0.781656i \(-0.714376\pi\)
−0.623710 + 0.781656i \(0.714376\pi\)
\(422\) 0 0
\(423\) 51.0753 2.48337
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 15.9194 0.770396
\(428\) 0 0
\(429\) 18.9347 0.914177
\(430\) 0 0
\(431\) 15.3540 0.739575 0.369788 0.929116i \(-0.379430\pi\)
0.369788 + 0.929116i \(0.379430\pi\)
\(432\) 0 0
\(433\) −16.6640 −0.800819 −0.400409 0.916336i \(-0.631132\pi\)
−0.400409 + 0.916336i \(0.631132\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.79560 0.0858951
\(438\) 0 0
\(439\) 19.5987 0.935393 0.467697 0.883889i \(-0.345084\pi\)
0.467697 + 0.883889i \(0.345084\pi\)
\(440\) 0 0
\(441\) 70.9176 3.37703
\(442\) 0 0
\(443\) 13.0183 0.618517 0.309258 0.950978i \(-0.399919\pi\)
0.309258 + 0.950978i \(0.399919\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 35.9530 1.70052
\(448\) 0 0
\(449\) 6.77359 0.319666 0.159833 0.987144i \(-0.448905\pi\)
0.159833 + 0.987144i \(0.448905\pi\)
\(450\) 0 0
\(451\) 7.34352 0.345793
\(452\) 0 0
\(453\) −15.8538 −0.744877
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 27.3189 1.27793 0.638963 0.769237i \(-0.279364\pi\)
0.638963 + 0.769237i \(0.279364\pi\)
\(458\) 0 0
\(459\) −9.12758 −0.426039
\(460\) 0 0
\(461\) −27.7993 −1.29474 −0.647372 0.762174i \(-0.724132\pi\)
−0.647372 + 0.762174i \(0.724132\pi\)
\(462\) 0 0
\(463\) 38.2369 1.77702 0.888509 0.458859i \(-0.151742\pi\)
0.888509 + 0.458859i \(0.151742\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 23.4711 1.08611 0.543056 0.839696i \(-0.317267\pi\)
0.543056 + 0.839696i \(0.317267\pi\)
\(468\) 0 0
\(469\) 41.4256 1.91286
\(470\) 0 0
\(471\) −25.7262 −1.18540
\(472\) 0 0
\(473\) 22.7811 1.04747
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 40.9855 1.87660
\(478\) 0 0
\(479\) 19.6900 0.899660 0.449830 0.893114i \(-0.351484\pi\)
0.449830 + 0.893114i \(0.351484\pi\)
\(480\) 0 0
\(481\) −12.1365 −0.553379
\(482\) 0 0
\(483\) −23.4151 −1.06542
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 16.3357 0.740242 0.370121 0.928984i \(-0.379316\pi\)
0.370121 + 0.928984i \(0.379316\pi\)
\(488\) 0 0
\(489\) 11.8904 0.537701
\(490\) 0 0
\(491\) −27.1093 −1.22343 −0.611713 0.791080i \(-0.709519\pi\)
−0.611713 + 0.791080i \(0.709519\pi\)
\(492\) 0 0
\(493\) −5.63148 −0.253629
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −6.70050 −0.300558
\(498\) 0 0
\(499\) 4.69003 0.209955 0.104977 0.994475i \(-0.466523\pi\)
0.104977 + 0.994475i \(0.466523\pi\)
\(500\) 0 0
\(501\) −42.2887 −1.88932
\(502\) 0 0
\(503\) 5.19136 0.231471 0.115736 0.993280i \(-0.463077\pi\)
0.115736 + 0.993280i \(0.463077\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −32.9623 −1.46391
\(508\) 0 0
\(509\) −4.51811 −0.200262 −0.100131 0.994974i \(-0.531926\pi\)
−0.100131 + 0.994974i \(0.531926\pi\)
\(510\) 0 0
\(511\) −59.2223 −2.61984
\(512\) 0 0
\(513\) 4.75905 0.210117
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −69.4450 −3.05419
\(518\) 0 0
\(519\) 34.0582 1.49499
\(520\) 0 0
\(521\) 14.4453 0.632862 0.316431 0.948615i \(-0.397515\pi\)
0.316431 + 0.948615i \(0.397515\pi\)
\(522\) 0 0
\(523\) −18.2134 −0.796415 −0.398208 0.917295i \(-0.630368\pi\)
−0.398208 + 0.917295i \(0.630368\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −10.6535 −0.464073
\(528\) 0 0
\(529\) −19.7758 −0.859819
\(530\) 0 0
\(531\) 26.5442 1.15192
\(532\) 0 0
\(533\) 1.21894 0.0527981
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 4.36852 0.188516
\(538\) 0 0
\(539\) −96.4237 −4.15326
\(540\) 0 0
\(541\) 37.3905 1.60754 0.803772 0.594937i \(-0.202823\pi\)
0.803772 + 0.594937i \(0.202823\pi\)
\(542\) 0 0
\(543\) 31.6860 1.35977
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 29.5621 1.26399 0.631993 0.774974i \(-0.282237\pi\)
0.631993 + 0.774974i \(0.282237\pi\)
\(548\) 0 0
\(549\) −15.9814 −0.682069
\(550\) 0 0
\(551\) 2.93621 0.125087
\(552\) 0 0
\(553\) −9.21894 −0.392029
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −14.3723 −0.608972 −0.304486 0.952517i \(-0.598485\pi\)
−0.304486 + 0.952517i \(0.598485\pi\)
\(558\) 0 0
\(559\) 3.78139 0.159936
\(560\) 0 0
\(561\) 34.1380 1.44131
\(562\) 0 0
\(563\) −6.39053 −0.269329 −0.134664 0.990891i \(-0.542996\pi\)
−0.134664 + 0.990891i \(0.542996\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 4.33455 0.182034
\(568\) 0 0
\(569\) −44.9086 −1.88267 −0.941334 0.337476i \(-0.890427\pi\)
−0.941334 + 0.337476i \(0.890427\pi\)
\(570\) 0 0
\(571\) −12.4193 −0.519730 −0.259865 0.965645i \(-0.583678\pi\)
−0.259865 + 0.965645i \(0.583678\pi\)
\(572\) 0 0
\(573\) 17.6584 0.737690
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 4.20440 0.175032 0.0875158 0.996163i \(-0.472107\pi\)
0.0875158 + 0.996163i \(0.472107\pi\)
\(578\) 0 0
\(579\) −40.2708 −1.67360
\(580\) 0 0
\(581\) −76.2731 −3.16434
\(582\) 0 0
\(583\) −55.7262 −2.30795
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 24.7915 1.02326 0.511628 0.859207i \(-0.329043\pi\)
0.511628 + 0.859207i \(0.329043\pi\)
\(588\) 0 0
\(589\) 5.55465 0.228875
\(590\) 0 0
\(591\) 14.2917 0.587882
\(592\) 0 0
\(593\) −4.67176 −0.191846 −0.0959231 0.995389i \(-0.530580\pi\)
−0.0959231 + 0.995389i \(0.530580\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −10.7695 −0.440767
\(598\) 0 0
\(599\) −39.2369 −1.60318 −0.801588 0.597877i \(-0.796011\pi\)
−0.801588 + 0.597877i \(0.796011\pi\)
\(600\) 0 0
\(601\) −42.4267 −1.73062 −0.865311 0.501235i \(-0.832879\pi\)
−0.865311 + 0.501235i \(0.832879\pi\)
\(602\) 0 0
\(603\) −41.5868 −1.69355
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −2.98173 −0.121025 −0.0605123 0.998167i \(-0.519273\pi\)
−0.0605123 + 0.998167i \(0.519273\pi\)
\(608\) 0 0
\(609\) −38.2890 −1.55155
\(610\) 0 0
\(611\) −11.5271 −0.466336
\(612\) 0 0
\(613\) 28.9452 1.16908 0.584542 0.811363i \(-0.301274\pi\)
0.584542 + 0.811363i \(0.301274\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 15.0365 0.605349 0.302674 0.953094i \(-0.402121\pi\)
0.302674 + 0.953094i \(0.402121\pi\)
\(618\) 0 0
\(619\) −8.25515 −0.331803 −0.165901 0.986142i \(-0.553053\pi\)
−0.165901 + 0.986142i \(0.553053\pi\)
\(620\) 0 0
\(621\) 8.54535 0.342913
\(622\) 0 0
\(623\) 46.9527 1.88112
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −17.7993 −0.710837
\(628\) 0 0
\(629\) −21.8814 −0.872468
\(630\) 0 0
\(631\) 9.09103 0.361908 0.180954 0.983492i \(-0.442081\pi\)
0.180954 + 0.983492i \(0.442081\pi\)
\(632\) 0 0
\(633\) −47.6300 −1.89312
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −16.0052 −0.634150
\(638\) 0 0
\(639\) 6.72658 0.266099
\(640\) 0 0
\(641\) 30.1171 1.18955 0.594777 0.803891i \(-0.297240\pi\)
0.594777 + 0.803891i \(0.297240\pi\)
\(642\) 0 0
\(643\) −35.3174 −1.39278 −0.696392 0.717662i \(-0.745212\pi\)
−0.696392 + 0.717662i \(0.745212\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 4.12234 0.162066 0.0810330 0.996711i \(-0.474178\pi\)
0.0810330 + 0.996711i \(0.474178\pi\)
\(648\) 0 0
\(649\) −36.0910 −1.41670
\(650\) 0 0
\(651\) −72.4342 −2.83892
\(652\) 0 0
\(653\) −8.62741 −0.337617 −0.168808 0.985649i \(-0.553992\pi\)
−0.168808 + 0.985649i \(0.553992\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 59.4528 2.31948
\(658\) 0 0
\(659\) 37.3853 1.45632 0.728162 0.685405i \(-0.240375\pi\)
0.728162 + 0.685405i \(0.240375\pi\)
\(660\) 0 0
\(661\) −12.8997 −0.501739 −0.250869 0.968021i \(-0.580716\pi\)
−0.250869 + 0.968021i \(0.580716\pi\)
\(662\) 0 0
\(663\) 5.66652 0.220070
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 5.27226 0.204143
\(668\) 0 0
\(669\) 21.7919 0.842522
\(670\) 0 0
\(671\) 21.7292 0.838848
\(672\) 0 0
\(673\) −10.4349 −0.402235 −0.201118 0.979567i \(-0.564457\pi\)
−0.201118 + 0.979567i \(0.564457\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −12.4401 −0.478112 −0.239056 0.971006i \(-0.576838\pi\)
−0.239056 + 0.971006i \(0.576838\pi\)
\(678\) 0 0
\(679\) −70.1716 −2.69294
\(680\) 0 0
\(681\) 17.4596 0.669052
\(682\) 0 0
\(683\) 17.5364 0.671011 0.335505 0.942038i \(-0.391093\pi\)
0.335505 + 0.942038i \(0.391093\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −8.73705 −0.333339
\(688\) 0 0
\(689\) −9.24992 −0.352394
\(690\) 0 0
\(691\) 25.2734 0.961446 0.480723 0.876872i \(-0.340374\pi\)
0.480723 + 0.876872i \(0.340374\pi\)
\(692\) 0 0
\(693\) 141.835 5.38787
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 2.19767 0.0832426
\(698\) 0 0
\(699\) −0.506567 −0.0191601
\(700\) 0 0
\(701\) −16.0545 −0.606370 −0.303185 0.952932i \(-0.598050\pi\)
−0.303185 + 0.952932i \(0.598050\pi\)
\(702\) 0 0
\(703\) 11.4088 0.430291
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −49.4711 −1.86055
\(708\) 0 0
\(709\) 13.5076 0.507290 0.253645 0.967297i \(-0.418371\pi\)
0.253645 + 0.967297i \(0.418371\pi\)
\(710\) 0 0
\(711\) 9.25482 0.347083
\(712\) 0 0
\(713\) 9.97392 0.373526
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 31.9501 1.19320
\(718\) 0 0
\(719\) −0.803402 −0.0299619 −0.0149809 0.999888i \(-0.504769\pi\)
−0.0149809 + 0.999888i \(0.504769\pi\)
\(720\) 0 0
\(721\) 79.7337 2.96944
\(722\) 0 0
\(723\) −1.23688 −0.0460000
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 51.6860 1.91693 0.958463 0.285217i \(-0.0920655\pi\)
0.958463 + 0.285217i \(0.0920655\pi\)
\(728\) 0 0
\(729\) −44.0037 −1.62977
\(730\) 0 0
\(731\) 6.81761 0.252158
\(732\) 0 0
\(733\) 22.3723 0.826338 0.413169 0.910654i \(-0.364422\pi\)
0.413169 + 0.910654i \(0.364422\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 56.5438 2.08282
\(738\) 0 0
\(739\) −33.4271 −1.22963 −0.614817 0.788669i \(-0.710770\pi\)
−0.614817 + 0.788669i \(0.710770\pi\)
\(740\) 0 0
\(741\) −2.95449 −0.108536
\(742\) 0 0
\(743\) 14.4998 0.531947 0.265974 0.963980i \(-0.414307\pi\)
0.265974 + 0.963980i \(0.414307\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 76.5699 2.80155
\(748\) 0 0
\(749\) 8.40623 0.307157
\(750\) 0 0
\(751\) 26.6169 0.971266 0.485633 0.874163i \(-0.338589\pi\)
0.485633 + 0.874163i \(0.338589\pi\)
\(752\) 0 0
\(753\) −36.8355 −1.34236
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 31.0362 1.12803 0.564015 0.825764i \(-0.309256\pi\)
0.564015 + 0.825764i \(0.309256\pi\)
\(758\) 0 0
\(759\) −31.9605 −1.16009
\(760\) 0 0
\(761\) −27.8083 −1.00805 −0.504025 0.863689i \(-0.668148\pi\)
−0.504025 + 0.863689i \(0.668148\pi\)
\(762\) 0 0
\(763\) −11.3345 −0.410338
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −5.99070 −0.216312
\(768\) 0 0
\(769\) −19.2279 −0.693376 −0.346688 0.937980i \(-0.612694\pi\)
−0.346688 + 0.937980i \(0.612694\pi\)
\(770\) 0 0
\(771\) 65.2159 2.34869
\(772\) 0 0
\(773\) −6.00373 −0.215939 −0.107970 0.994154i \(-0.534435\pi\)
−0.107970 + 0.994154i \(0.534435\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −148.774 −5.33724
\(778\) 0 0
\(779\) −1.14585 −0.0410543
\(780\) 0 0
\(781\) −9.14585 −0.327264
\(782\) 0 0
\(783\) 13.9736 0.499375
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 22.2797 0.794187 0.397093 0.917778i \(-0.370019\pi\)
0.397093 + 0.917778i \(0.370019\pi\)
\(788\) 0 0
\(789\) 77.5621 2.76128
\(790\) 0 0
\(791\) 33.5517 1.19296
\(792\) 0 0
\(793\) 3.60680 0.128081
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −26.6259 −0.943138 −0.471569 0.881829i \(-0.656312\pi\)
−0.471569 + 0.881829i \(0.656312\pi\)
\(798\) 0 0
\(799\) −20.7826 −0.735234
\(800\) 0 0
\(801\) −47.1354 −1.66545
\(802\) 0 0
\(803\) −80.8355 −2.85262
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 45.7747 1.61134
\(808\) 0 0
\(809\) 0.651250 0.0228967 0.0114484 0.999934i \(-0.496356\pi\)
0.0114484 + 0.999934i \(0.496356\pi\)
\(810\) 0 0
\(811\) 13.0780 0.459230 0.229615 0.973281i \(-0.426253\pi\)
0.229615 + 0.973281i \(0.426253\pi\)
\(812\) 0 0
\(813\) 4.07533 0.142928
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −3.55465 −0.124362
\(818\) 0 0
\(819\) 23.5430 0.822660
\(820\) 0 0
\(821\) 14.6640 0.511776 0.255888 0.966706i \(-0.417632\pi\)
0.255888 + 0.966706i \(0.417632\pi\)
\(822\) 0 0
\(823\) −18.2850 −0.637374 −0.318687 0.947860i \(-0.603242\pi\)
−0.318687 + 0.947860i \(0.603242\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 40.1910 1.39758 0.698790 0.715327i \(-0.253722\pi\)
0.698790 + 0.715327i \(0.253722\pi\)
\(828\) 0 0
\(829\) 28.3760 0.985539 0.492769 0.870160i \(-0.335985\pi\)
0.492769 + 0.870160i \(0.335985\pi\)
\(830\) 0 0
\(831\) −43.9814 −1.52570
\(832\) 0 0
\(833\) −28.8564 −0.999815
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 26.4349 0.913723
\(838\) 0 0
\(839\) −6.93471 −0.239413 −0.119706 0.992809i \(-0.538195\pi\)
−0.119706 + 0.992809i \(0.538195\pi\)
\(840\) 0 0
\(841\) −20.3787 −0.702712
\(842\) 0 0
\(843\) −17.3726 −0.598344
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −141.200 −4.85167
\(848\) 0 0
\(849\) −46.3827 −1.59185
\(850\) 0 0
\(851\) 20.4856 0.702238
\(852\) 0 0
\(853\) −21.9739 −0.752373 −0.376186 0.926544i \(-0.622765\pi\)
−0.376186 + 0.926544i \(0.622765\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −13.6091 −0.464879 −0.232440 0.972611i \(-0.574671\pi\)
−0.232440 + 0.972611i \(0.574671\pi\)
\(858\) 0 0
\(859\) −5.17192 −0.176464 −0.0882319 0.996100i \(-0.528122\pi\)
−0.0882319 + 0.996100i \(0.528122\pi\)
\(860\) 0 0
\(861\) 14.9422 0.509228
\(862\) 0 0
\(863\) 15.9635 0.543402 0.271701 0.962382i \(-0.412414\pi\)
0.271701 + 0.962382i \(0.412414\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −36.9982 −1.25652
\(868\) 0 0
\(869\) −12.5834 −0.426862
\(870\) 0 0
\(871\) 9.38563 0.318020
\(872\) 0 0
\(873\) 70.4447 2.38419
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 15.8866 0.536453 0.268227 0.963356i \(-0.413562\pi\)
0.268227 + 0.963356i \(0.413562\pi\)
\(878\) 0 0
\(879\) −1.79003 −0.0603762
\(880\) 0 0
\(881\) −16.1458 −0.543967 −0.271984 0.962302i \(-0.587680\pi\)
−0.271984 + 0.962302i \(0.587680\pi\)
\(882\) 0 0
\(883\) 38.2887 1.28852 0.644259 0.764808i \(-0.277166\pi\)
0.644259 + 0.764808i \(0.277166\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 19.2809 0.647389 0.323695 0.946162i \(-0.395075\pi\)
0.323695 + 0.946162i \(0.395075\pi\)
\(888\) 0 0
\(889\) −43.4920 −1.45868
\(890\) 0 0
\(891\) 5.91644 0.198208
\(892\) 0 0
\(893\) 10.8359 0.362609
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −5.30507 −0.177131
\(898\) 0 0
\(899\) 16.3096 0.543957
\(900\) 0 0
\(901\) −16.6770 −0.555591
\(902\) 0 0
\(903\) 46.3537 1.54255
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 43.0205 1.42847 0.714236 0.699905i \(-0.246774\pi\)
0.714236 + 0.699905i \(0.246774\pi\)
\(908\) 0 0
\(909\) 49.6636 1.64724
\(910\) 0 0
\(911\) 25.7733 0.853906 0.426953 0.904274i \(-0.359587\pi\)
0.426953 + 0.904274i \(0.359587\pi\)
\(912\) 0 0
\(913\) −104.109 −3.44550
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 54.0806 1.78590
\(918\) 0 0
\(919\) 29.5897 0.976074 0.488037 0.872823i \(-0.337713\pi\)
0.488037 + 0.872823i \(0.337713\pi\)
\(920\) 0 0
\(921\) 74.0037 2.43851
\(922\) 0 0
\(923\) −1.51811 −0.0499691
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −80.0440 −2.62899
\(928\) 0 0
\(929\) −1.42334 −0.0466983 −0.0233491 0.999727i \(-0.507433\pi\)
−0.0233491 + 0.999727i \(0.507433\pi\)
\(930\) 0 0
\(931\) 15.0455 0.493097
\(932\) 0 0
\(933\) −32.0765 −1.05014
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −28.2276 −0.922155 −0.461077 0.887360i \(-0.652537\pi\)
−0.461077 + 0.887360i \(0.652537\pi\)
\(938\) 0 0
\(939\) 64.0556 2.09038
\(940\) 0 0
\(941\) −15.8672 −0.517256 −0.258628 0.965977i \(-0.583270\pi\)
−0.258628 + 0.965977i \(0.583270\pi\)
\(942\) 0 0
\(943\) −2.05748 −0.0670009
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 43.6718 1.41914 0.709571 0.704634i \(-0.248889\pi\)
0.709571 + 0.704634i \(0.248889\pi\)
\(948\) 0 0
\(949\) −13.4178 −0.435559
\(950\) 0 0
\(951\) 38.6692 1.25393
\(952\) 0 0
\(953\) −16.0261 −0.519136 −0.259568 0.965725i \(-0.583580\pi\)
−0.259568 + 0.965725i \(0.583580\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −52.2626 −1.68941
\(958\) 0 0
\(959\) 70.9176 2.29005
\(960\) 0 0
\(961\) −0.145848 −0.00470478
\(962\) 0 0
\(963\) −8.43895 −0.271941
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −11.5987 −0.372988 −0.186494 0.982456i \(-0.559712\pi\)
−0.186494 + 0.982456i \(0.559712\pi\)
\(968\) 0 0
\(969\) −5.32674 −0.171120
\(970\) 0 0
\(971\) 27.0362 0.867633 0.433817 0.901001i \(-0.357167\pi\)
0.433817 + 0.901001i \(0.357167\pi\)
\(972\) 0 0
\(973\) −3.28903 −0.105442
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −14.1537 −0.452815 −0.226408 0.974033i \(-0.572698\pi\)
−0.226408 + 0.974033i \(0.572698\pi\)
\(978\) 0 0
\(979\) 64.0880 2.04826
\(980\) 0 0
\(981\) 11.3787 0.363293
\(982\) 0 0
\(983\) −32.8542 −1.04788 −0.523942 0.851754i \(-0.675539\pi\)
−0.523942 + 0.851754i \(0.675539\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −141.303 −4.49772
\(988\) 0 0
\(989\) −6.38273 −0.202959
\(990\) 0 0
\(991\) −47.9709 −1.52385 −0.761923 0.647667i \(-0.775745\pi\)
−0.761923 + 0.647667i \(0.775745\pi\)
\(992\) 0 0
\(993\) 2.04285 0.0648279
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −44.1716 −1.39893 −0.699464 0.714668i \(-0.746578\pi\)
−0.699464 + 0.714668i \(0.746578\pi\)
\(998\) 0 0
\(999\) 54.2951 1.71782
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 7600.2.a.cb.1.3 3
4.3 odd 2 950.2.a.k.1.1 3
5.4 even 2 7600.2.a.bm.1.1 3
12.11 even 2 8550.2.a.co.1.3 3
20.3 even 4 950.2.b.g.799.4 6
20.7 even 4 950.2.b.g.799.3 6
20.19 odd 2 950.2.a.m.1.3 yes 3
60.59 even 2 8550.2.a.cj.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.a.k.1.1 3 4.3 odd 2
950.2.a.m.1.3 yes 3 20.19 odd 2
950.2.b.g.799.3 6 20.7 even 4
950.2.b.g.799.4 6 20.3 even 4
7600.2.a.bm.1.1 3 5.4 even 2
7600.2.a.cb.1.3 3 1.1 even 1 trivial
8550.2.a.cj.1.1 3 60.59 even 2
8550.2.a.co.1.3 3 12.11 even 2