Properties

Label 7448.2.a.bn.1.2
Level $7448$
Weight $2$
Character 7448.1
Self dual yes
Analytic conductor $59.473$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7448 = 2^{3} \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7448.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(59.4725794254\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.98211824.1
Defining polynomial: \(x^{6} - 3 x^{5} - 6 x^{4} + 15 x^{3} + 8 x^{2} - 9 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.15897\) of defining polynomial
Character \(\chi\) \(=\) 7448.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.15897 q^{3} +1.74190 q^{5} -1.65679 q^{9} +O(q^{10})\) \(q-1.15897 q^{3} +1.74190 q^{5} -1.65679 q^{9} -5.45213 q^{11} -3.91531 q^{13} -2.01881 q^{15} -1.01881 q^{17} -1.00000 q^{19} +7.27914 q^{23} -1.96579 q^{25} +5.39708 q^{27} +3.52394 q^{29} -5.06969 q^{31} +6.31886 q^{33} -2.61756 q^{37} +4.53773 q^{39} -11.4218 q^{41} -2.55126 q^{43} -2.88596 q^{45} +0.536392 q^{47} +1.18077 q^{51} -1.33771 q^{53} -9.49706 q^{55} +1.15897 q^{57} +10.6368 q^{59} -3.90221 q^{61} -6.82008 q^{65} -13.9146 q^{67} -8.43630 q^{69} +7.41290 q^{71} +6.92561 q^{73} +2.27829 q^{75} +0.214460 q^{79} -1.28469 q^{81} +10.9949 q^{83} -1.77466 q^{85} -4.08414 q^{87} -5.26815 q^{89} +5.87562 q^{93} -1.74190 q^{95} +7.06281 q^{97} +9.03303 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{3} + q^{5} + 3 q^{9} + O(q^{10}) \) \( 6 q + 3 q^{3} + q^{5} + 3 q^{9} + 3 q^{11} + 6 q^{13} - 8 q^{15} - 2 q^{17} - 6 q^{19} + 2 q^{23} + 5 q^{25} + 6 q^{27} - q^{29} + 14 q^{31} + 19 q^{33} - 7 q^{37} + 22 q^{39} - 21 q^{41} + q^{43} - 4 q^{45} + 23 q^{47} + 2 q^{51} - 15 q^{53} + 2 q^{55} - 3 q^{57} + 25 q^{59} + 21 q^{61} + 6 q^{65} + 2 q^{67} - 20 q^{69} + 13 q^{71} - 2 q^{73} + 24 q^{75} - 17 q^{79} - 2 q^{81} + 4 q^{83} + 40 q^{85} + 30 q^{87} - q^{89} + 6 q^{93} - q^{95} - 13 q^{97} + 41 q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.15897 −0.669132 −0.334566 0.942372i \(-0.608590\pi\)
−0.334566 + 0.942372i \(0.608590\pi\)
\(4\) 0 0
\(5\) 1.74190 0.779001 0.389500 0.921026i \(-0.372648\pi\)
0.389500 + 0.921026i \(0.372648\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −1.65679 −0.552263
\(10\) 0 0
\(11\) −5.45213 −1.64388 −0.821940 0.569575i \(-0.807108\pi\)
−0.821940 + 0.569575i \(0.807108\pi\)
\(12\) 0 0
\(13\) −3.91531 −1.08591 −0.542956 0.839761i \(-0.682695\pi\)
−0.542956 + 0.839761i \(0.682695\pi\)
\(14\) 0 0
\(15\) −2.01881 −0.521254
\(16\) 0 0
\(17\) −1.01881 −0.247097 −0.123549 0.992339i \(-0.539427\pi\)
−0.123549 + 0.992339i \(0.539427\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 7.27914 1.51781 0.758903 0.651204i \(-0.225736\pi\)
0.758903 + 0.651204i \(0.225736\pi\)
\(24\) 0 0
\(25\) −1.96579 −0.393158
\(26\) 0 0
\(27\) 5.39708 1.03867
\(28\) 0 0
\(29\) 3.52394 0.654379 0.327189 0.944959i \(-0.393898\pi\)
0.327189 + 0.944959i \(0.393898\pi\)
\(30\) 0 0
\(31\) −5.06969 −0.910544 −0.455272 0.890352i \(-0.650458\pi\)
−0.455272 + 0.890352i \(0.650458\pi\)
\(32\) 0 0
\(33\) 6.31886 1.09997
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2.61756 −0.430325 −0.215162 0.976578i \(-0.569028\pi\)
−0.215162 + 0.976578i \(0.569028\pi\)
\(38\) 0 0
\(39\) 4.53773 0.726619
\(40\) 0 0
\(41\) −11.4218 −1.78379 −0.891896 0.452240i \(-0.850625\pi\)
−0.891896 + 0.452240i \(0.850625\pi\)
\(42\) 0 0
\(43\) −2.55126 −0.389064 −0.194532 0.980896i \(-0.562319\pi\)
−0.194532 + 0.980896i \(0.562319\pi\)
\(44\) 0 0
\(45\) −2.88596 −0.430213
\(46\) 0 0
\(47\) 0.536392 0.0782409 0.0391204 0.999235i \(-0.487544\pi\)
0.0391204 + 0.999235i \(0.487544\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 1.18077 0.165341
\(52\) 0 0
\(53\) −1.33771 −0.183748 −0.0918740 0.995771i \(-0.529286\pi\)
−0.0918740 + 0.995771i \(0.529286\pi\)
\(54\) 0 0
\(55\) −9.49706 −1.28058
\(56\) 0 0
\(57\) 1.15897 0.153509
\(58\) 0 0
\(59\) 10.6368 1.38479 0.692396 0.721517i \(-0.256555\pi\)
0.692396 + 0.721517i \(0.256555\pi\)
\(60\) 0 0
\(61\) −3.90221 −0.499626 −0.249813 0.968294i \(-0.580369\pi\)
−0.249813 + 0.968294i \(0.580369\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −6.82008 −0.845927
\(66\) 0 0
\(67\) −13.9146 −1.69993 −0.849967 0.526837i \(-0.823378\pi\)
−0.849967 + 0.526837i \(0.823378\pi\)
\(68\) 0 0
\(69\) −8.43630 −1.01561
\(70\) 0 0
\(71\) 7.41290 0.879750 0.439875 0.898059i \(-0.355023\pi\)
0.439875 + 0.898059i \(0.355023\pi\)
\(72\) 0 0
\(73\) 6.92561 0.810581 0.405290 0.914188i \(-0.367170\pi\)
0.405290 + 0.914188i \(0.367170\pi\)
\(74\) 0 0
\(75\) 2.27829 0.263074
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0.214460 0.0241287 0.0120643 0.999927i \(-0.496160\pi\)
0.0120643 + 0.999927i \(0.496160\pi\)
\(80\) 0 0
\(81\) −1.28469 −0.142743
\(82\) 0 0
\(83\) 10.9949 1.20684 0.603422 0.797422i \(-0.293803\pi\)
0.603422 + 0.797422i \(0.293803\pi\)
\(84\) 0 0
\(85\) −1.77466 −0.192489
\(86\) 0 0
\(87\) −4.08414 −0.437866
\(88\) 0 0
\(89\) −5.26815 −0.558423 −0.279212 0.960230i \(-0.590073\pi\)
−0.279212 + 0.960230i \(0.590073\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 5.87562 0.609274
\(94\) 0 0
\(95\) −1.74190 −0.178715
\(96\) 0 0
\(97\) 7.06281 0.717119 0.358560 0.933507i \(-0.383268\pi\)
0.358560 + 0.933507i \(0.383268\pi\)
\(98\) 0 0
\(99\) 9.03303 0.907853
\(100\) 0 0
\(101\) 18.0830 1.79932 0.899661 0.436590i \(-0.143814\pi\)
0.899661 + 0.436590i \(0.143814\pi\)
\(102\) 0 0
\(103\) 11.3179 1.11519 0.557593 0.830115i \(-0.311725\pi\)
0.557593 + 0.830115i \(0.311725\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 14.9021 1.44064 0.720322 0.693640i \(-0.243994\pi\)
0.720322 + 0.693640i \(0.243994\pi\)
\(108\) 0 0
\(109\) −11.2146 −1.07417 −0.537084 0.843529i \(-0.680474\pi\)
−0.537084 + 0.843529i \(0.680474\pi\)
\(110\) 0 0
\(111\) 3.03368 0.287944
\(112\) 0 0
\(113\) −10.7219 −1.00863 −0.504317 0.863519i \(-0.668256\pi\)
−0.504317 + 0.863519i \(0.668256\pi\)
\(114\) 0 0
\(115\) 12.6795 1.18237
\(116\) 0 0
\(117\) 6.48685 0.599709
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 18.7257 1.70234
\(122\) 0 0
\(123\) 13.2376 1.19359
\(124\) 0 0
\(125\) −12.1337 −1.08527
\(126\) 0 0
\(127\) −13.6962 −1.21534 −0.607670 0.794189i \(-0.707896\pi\)
−0.607670 + 0.794189i \(0.707896\pi\)
\(128\) 0 0
\(129\) 2.95684 0.260335
\(130\) 0 0
\(131\) 13.3514 1.16651 0.583257 0.812287i \(-0.301778\pi\)
0.583257 + 0.812287i \(0.301778\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 9.40116 0.809123
\(136\) 0 0
\(137\) −4.51449 −0.385699 −0.192850 0.981228i \(-0.561773\pi\)
−0.192850 + 0.981228i \(0.561773\pi\)
\(138\) 0 0
\(139\) 17.3162 1.46875 0.734373 0.678747i \(-0.237477\pi\)
0.734373 + 0.678747i \(0.237477\pi\)
\(140\) 0 0
\(141\) −0.621663 −0.0523534
\(142\) 0 0
\(143\) 21.3468 1.78511
\(144\) 0 0
\(145\) 6.13834 0.509762
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 4.79098 0.392492 0.196246 0.980555i \(-0.437125\pi\)
0.196246 + 0.980555i \(0.437125\pi\)
\(150\) 0 0
\(151\) −1.22460 −0.0996568 −0.0498284 0.998758i \(-0.515867\pi\)
−0.0498284 + 0.998758i \(0.515867\pi\)
\(152\) 0 0
\(153\) 1.68795 0.136463
\(154\) 0 0
\(155\) −8.83089 −0.709314
\(156\) 0 0
\(157\) −10.6980 −0.853791 −0.426896 0.904301i \(-0.640393\pi\)
−0.426896 + 0.904301i \(0.640393\pi\)
\(158\) 0 0
\(159\) 1.55036 0.122952
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −6.22523 −0.487598 −0.243799 0.969826i \(-0.578394\pi\)
−0.243799 + 0.969826i \(0.578394\pi\)
\(164\) 0 0
\(165\) 11.0068 0.856879
\(166\) 0 0
\(167\) −19.1481 −1.48172 −0.740861 0.671658i \(-0.765582\pi\)
−0.740861 + 0.671658i \(0.765582\pi\)
\(168\) 0 0
\(169\) 2.32968 0.179206
\(170\) 0 0
\(171\) 1.65679 0.126698
\(172\) 0 0
\(173\) 21.2360 1.61454 0.807271 0.590181i \(-0.200944\pi\)
0.807271 + 0.590181i \(0.200944\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −12.3277 −0.926609
\(178\) 0 0
\(179\) 12.5546 0.938377 0.469189 0.883098i \(-0.344546\pi\)
0.469189 + 0.883098i \(0.344546\pi\)
\(180\) 0 0
\(181\) 18.2194 1.35424 0.677119 0.735874i \(-0.263228\pi\)
0.677119 + 0.735874i \(0.263228\pi\)
\(182\) 0 0
\(183\) 4.52254 0.334316
\(184\) 0 0
\(185\) −4.55953 −0.335223
\(186\) 0 0
\(187\) 5.55468 0.406198
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 11.5319 0.834421 0.417211 0.908810i \(-0.363008\pi\)
0.417211 + 0.908810i \(0.363008\pi\)
\(192\) 0 0
\(193\) −3.33145 −0.239803 −0.119902 0.992786i \(-0.538258\pi\)
−0.119902 + 0.992786i \(0.538258\pi\)
\(194\) 0 0
\(195\) 7.90427 0.566036
\(196\) 0 0
\(197\) −16.1096 −1.14776 −0.573879 0.818940i \(-0.694562\pi\)
−0.573879 + 0.818940i \(0.694562\pi\)
\(198\) 0 0
\(199\) 15.3330 1.08693 0.543465 0.839432i \(-0.317112\pi\)
0.543465 + 0.839432i \(0.317112\pi\)
\(200\) 0 0
\(201\) 16.1265 1.13748
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −19.8957 −1.38958
\(206\) 0 0
\(207\) −12.0600 −0.838227
\(208\) 0 0
\(209\) 5.45213 0.377132
\(210\) 0 0
\(211\) 16.6714 1.14771 0.573853 0.818959i \(-0.305448\pi\)
0.573853 + 0.818959i \(0.305448\pi\)
\(212\) 0 0
\(213\) −8.59133 −0.588669
\(214\) 0 0
\(215\) −4.44404 −0.303081
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −8.02657 −0.542385
\(220\) 0 0
\(221\) 3.98895 0.268326
\(222\) 0 0
\(223\) −1.05554 −0.0706840 −0.0353420 0.999375i \(-0.511252\pi\)
−0.0353420 + 0.999375i \(0.511252\pi\)
\(224\) 0 0
\(225\) 3.25690 0.217126
\(226\) 0 0
\(227\) 6.20712 0.411981 0.205990 0.978554i \(-0.433958\pi\)
0.205990 + 0.978554i \(0.433958\pi\)
\(228\) 0 0
\(229\) 1.44789 0.0956793 0.0478397 0.998855i \(-0.484766\pi\)
0.0478397 + 0.998855i \(0.484766\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −23.3805 −1.53170 −0.765852 0.643016i \(-0.777683\pi\)
−0.765852 + 0.643016i \(0.777683\pi\)
\(234\) 0 0
\(235\) 0.934341 0.0609497
\(236\) 0 0
\(237\) −0.248553 −0.0161452
\(238\) 0 0
\(239\) −12.2577 −0.792888 −0.396444 0.918059i \(-0.629756\pi\)
−0.396444 + 0.918059i \(0.629756\pi\)
\(240\) 0 0
\(241\) 6.60037 0.425167 0.212583 0.977143i \(-0.431812\pi\)
0.212583 + 0.977143i \(0.431812\pi\)
\(242\) 0 0
\(243\) −14.7023 −0.943154
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 3.91531 0.249125
\(248\) 0 0
\(249\) −12.7427 −0.807538
\(250\) 0 0
\(251\) −19.6376 −1.23952 −0.619758 0.784793i \(-0.712769\pi\)
−0.619758 + 0.784793i \(0.712769\pi\)
\(252\) 0 0
\(253\) −39.6868 −2.49509
\(254\) 0 0
\(255\) 2.05678 0.128800
\(256\) 0 0
\(257\) 9.88504 0.616612 0.308306 0.951287i \(-0.400238\pi\)
0.308306 + 0.951287i \(0.400238\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −5.83842 −0.361389
\(262\) 0 0
\(263\) −5.84626 −0.360496 −0.180248 0.983621i \(-0.557690\pi\)
−0.180248 + 0.983621i \(0.557690\pi\)
\(264\) 0 0
\(265\) −2.33015 −0.143140
\(266\) 0 0
\(267\) 6.10563 0.373659
\(268\) 0 0
\(269\) 9.64384 0.587995 0.293998 0.955806i \(-0.405014\pi\)
0.293998 + 0.955806i \(0.405014\pi\)
\(270\) 0 0
\(271\) 17.5016 1.06315 0.531574 0.847012i \(-0.321601\pi\)
0.531574 + 0.847012i \(0.321601\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 10.7177 0.646304
\(276\) 0 0
\(277\) 2.52578 0.151759 0.0758796 0.997117i \(-0.475824\pi\)
0.0758796 + 0.997117i \(0.475824\pi\)
\(278\) 0 0
\(279\) 8.39941 0.502859
\(280\) 0 0
\(281\) 25.7152 1.53404 0.767019 0.641625i \(-0.221739\pi\)
0.767019 + 0.641625i \(0.221739\pi\)
\(282\) 0 0
\(283\) 18.4402 1.09616 0.548078 0.836427i \(-0.315360\pi\)
0.548078 + 0.836427i \(0.315360\pi\)
\(284\) 0 0
\(285\) 2.01881 0.119584
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −15.9620 −0.938943
\(290\) 0 0
\(291\) −8.18558 −0.479847
\(292\) 0 0
\(293\) −25.9767 −1.51758 −0.758788 0.651338i \(-0.774208\pi\)
−0.758788 + 0.651338i \(0.774208\pi\)
\(294\) 0 0
\(295\) 18.5282 1.07875
\(296\) 0 0
\(297\) −29.4256 −1.70744
\(298\) 0 0
\(299\) −28.5001 −1.64820
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −20.9576 −1.20398
\(304\) 0 0
\(305\) −6.79725 −0.389209
\(306\) 0 0
\(307\) −0.121059 −0.00690918 −0.00345459 0.999994i \(-0.501100\pi\)
−0.00345459 + 0.999994i \(0.501100\pi\)
\(308\) 0 0
\(309\) −13.1171 −0.746206
\(310\) 0 0
\(311\) 7.14728 0.405285 0.202642 0.979253i \(-0.435047\pi\)
0.202642 + 0.979253i \(0.435047\pi\)
\(312\) 0 0
\(313\) 1.29570 0.0732372 0.0366186 0.999329i \(-0.488341\pi\)
0.0366186 + 0.999329i \(0.488341\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.93181 0.164667 0.0823333 0.996605i \(-0.473763\pi\)
0.0823333 + 0.996605i \(0.473763\pi\)
\(318\) 0 0
\(319\) −19.2130 −1.07572
\(320\) 0 0
\(321\) −17.2711 −0.963981
\(322\) 0 0
\(323\) 1.01881 0.0566880
\(324\) 0 0
\(325\) 7.69668 0.426935
\(326\) 0 0
\(327\) 12.9974 0.718760
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 5.47990 0.301203 0.150601 0.988595i \(-0.451879\pi\)
0.150601 + 0.988595i \(0.451879\pi\)
\(332\) 0 0
\(333\) 4.33675 0.237652
\(334\) 0 0
\(335\) −24.2377 −1.32425
\(336\) 0 0
\(337\) 20.1683 1.09864 0.549319 0.835613i \(-0.314887\pi\)
0.549319 + 0.835613i \(0.314887\pi\)
\(338\) 0 0
\(339\) 12.4264 0.674909
\(340\) 0 0
\(341\) 27.6406 1.49682
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −14.6952 −0.791162
\(346\) 0 0
\(347\) 24.0352 1.29028 0.645139 0.764065i \(-0.276800\pi\)
0.645139 + 0.764065i \(0.276800\pi\)
\(348\) 0 0
\(349\) −26.1496 −1.39976 −0.699879 0.714261i \(-0.746763\pi\)
−0.699879 + 0.714261i \(0.746763\pi\)
\(350\) 0 0
\(351\) −21.1313 −1.12790
\(352\) 0 0
\(353\) −3.97407 −0.211518 −0.105759 0.994392i \(-0.533727\pi\)
−0.105759 + 0.994392i \(0.533727\pi\)
\(354\) 0 0
\(355\) 12.9125 0.685326
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −30.7706 −1.62401 −0.812005 0.583650i \(-0.801624\pi\)
−0.812005 + 0.583650i \(0.801624\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −21.7025 −1.13909
\(364\) 0 0
\(365\) 12.0637 0.631443
\(366\) 0 0
\(367\) −2.77758 −0.144988 −0.0724942 0.997369i \(-0.523096\pi\)
−0.0724942 + 0.997369i \(0.523096\pi\)
\(368\) 0 0
\(369\) 18.9236 0.985122
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 31.5603 1.63413 0.817065 0.576546i \(-0.195600\pi\)
0.817065 + 0.576546i \(0.195600\pi\)
\(374\) 0 0
\(375\) 14.0626 0.726189
\(376\) 0 0
\(377\) −13.7973 −0.710598
\(378\) 0 0
\(379\) 9.53802 0.489935 0.244968 0.969531i \(-0.421223\pi\)
0.244968 + 0.969531i \(0.421223\pi\)
\(380\) 0 0
\(381\) 15.8735 0.813223
\(382\) 0 0
\(383\) 1.54697 0.0790462 0.0395231 0.999219i \(-0.487416\pi\)
0.0395231 + 0.999219i \(0.487416\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 4.22690 0.214865
\(388\) 0 0
\(389\) 35.6869 1.80940 0.904699 0.426052i \(-0.140096\pi\)
0.904699 + 0.426052i \(0.140096\pi\)
\(390\) 0 0
\(391\) −7.41605 −0.375046
\(392\) 0 0
\(393\) −15.4738 −0.780552
\(394\) 0 0
\(395\) 0.373568 0.0187962
\(396\) 0 0
\(397\) 25.5296 1.28129 0.640647 0.767835i \(-0.278666\pi\)
0.640647 + 0.767835i \(0.278666\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 34.2571 1.71072 0.855359 0.518035i \(-0.173336\pi\)
0.855359 + 0.518035i \(0.173336\pi\)
\(402\) 0 0
\(403\) 19.8494 0.988771
\(404\) 0 0
\(405\) −2.23779 −0.111197
\(406\) 0 0
\(407\) 14.2713 0.707402
\(408\) 0 0
\(409\) −29.3744 −1.45247 −0.726236 0.687445i \(-0.758732\pi\)
−0.726236 + 0.687445i \(0.758732\pi\)
\(410\) 0 0
\(411\) 5.23216 0.258083
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 19.1520 0.940133
\(416\) 0 0
\(417\) −20.0690 −0.982784
\(418\) 0 0
\(419\) 28.7692 1.40547 0.702735 0.711452i \(-0.251962\pi\)
0.702735 + 0.711452i \(0.251962\pi\)
\(420\) 0 0
\(421\) −33.3082 −1.62334 −0.811671 0.584114i \(-0.801442\pi\)
−0.811671 + 0.584114i \(0.801442\pi\)
\(422\) 0 0
\(423\) −0.888689 −0.0432095
\(424\) 0 0
\(425\) 2.00276 0.0971482
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −24.7403 −1.19447
\(430\) 0 0
\(431\) 24.1705 1.16425 0.582126 0.813099i \(-0.302221\pi\)
0.582126 + 0.813099i \(0.302221\pi\)
\(432\) 0 0
\(433\) 29.0858 1.39778 0.698888 0.715232i \(-0.253679\pi\)
0.698888 + 0.715232i \(0.253679\pi\)
\(434\) 0 0
\(435\) −7.11415 −0.341098
\(436\) 0 0
\(437\) −7.27914 −0.348208
\(438\) 0 0
\(439\) 6.18898 0.295384 0.147692 0.989033i \(-0.452816\pi\)
0.147692 + 0.989033i \(0.452816\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −37.8146 −1.79662 −0.898312 0.439358i \(-0.855206\pi\)
−0.898312 + 0.439358i \(0.855206\pi\)
\(444\) 0 0
\(445\) −9.17659 −0.435012
\(446\) 0 0
\(447\) −5.55260 −0.262629
\(448\) 0 0
\(449\) −10.2594 −0.484171 −0.242085 0.970255i \(-0.577831\pi\)
−0.242085 + 0.970255i \(0.577831\pi\)
\(450\) 0 0
\(451\) 62.2734 2.93234
\(452\) 0 0
\(453\) 1.41928 0.0666836
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 20.8390 0.974809 0.487404 0.873176i \(-0.337944\pi\)
0.487404 + 0.873176i \(0.337944\pi\)
\(458\) 0 0
\(459\) −5.49859 −0.256652
\(460\) 0 0
\(461\) −35.7831 −1.66658 −0.833292 0.552833i \(-0.813547\pi\)
−0.833292 + 0.552833i \(0.813547\pi\)
\(462\) 0 0
\(463\) 6.54002 0.303941 0.151970 0.988385i \(-0.451438\pi\)
0.151970 + 0.988385i \(0.451438\pi\)
\(464\) 0 0
\(465\) 10.2347 0.474625
\(466\) 0 0
\(467\) 1.39826 0.0647037 0.0323518 0.999477i \(-0.489700\pi\)
0.0323518 + 0.999477i \(0.489700\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 12.3986 0.571299
\(472\) 0 0
\(473\) 13.9098 0.639574
\(474\) 0 0
\(475\) 1.96579 0.0901966
\(476\) 0 0
\(477\) 2.21630 0.101477
\(478\) 0 0
\(479\) −11.6232 −0.531076 −0.265538 0.964100i \(-0.585549\pi\)
−0.265538 + 0.964100i \(0.585549\pi\)
\(480\) 0 0
\(481\) 10.2486 0.467295
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 12.3027 0.558636
\(486\) 0 0
\(487\) −25.4177 −1.15178 −0.575892 0.817526i \(-0.695345\pi\)
−0.575892 + 0.817526i \(0.695345\pi\)
\(488\) 0 0
\(489\) 7.21485 0.326267
\(490\) 0 0
\(491\) 3.49578 0.157762 0.0788812 0.996884i \(-0.474865\pi\)
0.0788812 + 0.996884i \(0.474865\pi\)
\(492\) 0 0
\(493\) −3.59022 −0.161695
\(494\) 0 0
\(495\) 15.7346 0.707218
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −18.4993 −0.828143 −0.414072 0.910244i \(-0.635894\pi\)
−0.414072 + 0.910244i \(0.635894\pi\)
\(500\) 0 0
\(501\) 22.1920 0.991467
\(502\) 0 0
\(503\) 40.5993 1.81023 0.905116 0.425165i \(-0.139784\pi\)
0.905116 + 0.425165i \(0.139784\pi\)
\(504\) 0 0
\(505\) 31.4987 1.40167
\(506\) 0 0
\(507\) −2.70003 −0.119913
\(508\) 0 0
\(509\) 8.37357 0.371152 0.185576 0.982630i \(-0.440585\pi\)
0.185576 + 0.982630i \(0.440585\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −5.39708 −0.238287
\(514\) 0 0
\(515\) 19.7146 0.868730
\(516\) 0 0
\(517\) −2.92448 −0.128619
\(518\) 0 0
\(519\) −24.6119 −1.08034
\(520\) 0 0
\(521\) −42.4863 −1.86136 −0.930679 0.365836i \(-0.880783\pi\)
−0.930679 + 0.365836i \(0.880783\pi\)
\(522\) 0 0
\(523\) 19.4417 0.850125 0.425063 0.905164i \(-0.360252\pi\)
0.425063 + 0.905164i \(0.360252\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 5.16505 0.224993
\(528\) 0 0
\(529\) 29.9859 1.30373
\(530\) 0 0
\(531\) −17.6229 −0.764770
\(532\) 0 0
\(533\) 44.7201 1.93704
\(534\) 0 0
\(535\) 25.9580 1.12226
\(536\) 0 0
\(537\) −14.5504 −0.627898
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −46.1121 −1.98252 −0.991258 0.131938i \(-0.957880\pi\)
−0.991258 + 0.131938i \(0.957880\pi\)
\(542\) 0 0
\(543\) −21.1157 −0.906163
\(544\) 0 0
\(545\) −19.5348 −0.836778
\(546\) 0 0
\(547\) 4.29879 0.183803 0.0919016 0.995768i \(-0.470705\pi\)
0.0919016 + 0.995768i \(0.470705\pi\)
\(548\) 0 0
\(549\) 6.46513 0.275925
\(550\) 0 0
\(551\) −3.52394 −0.150125
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 5.28436 0.224309
\(556\) 0 0
\(557\) 38.9723 1.65131 0.825656 0.564174i \(-0.190805\pi\)
0.825656 + 0.564174i \(0.190805\pi\)
\(558\) 0 0
\(559\) 9.98899 0.422489
\(560\) 0 0
\(561\) −6.43770 −0.271800
\(562\) 0 0
\(563\) 27.0802 1.14130 0.570648 0.821195i \(-0.306692\pi\)
0.570648 + 0.821195i \(0.306692\pi\)
\(564\) 0 0
\(565\) −18.6765 −0.785727
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 30.7718 1.29002 0.645011 0.764173i \(-0.276853\pi\)
0.645011 + 0.764173i \(0.276853\pi\)
\(570\) 0 0
\(571\) −12.3229 −0.515696 −0.257848 0.966185i \(-0.583013\pi\)
−0.257848 + 0.966185i \(0.583013\pi\)
\(572\) 0 0
\(573\) −13.3652 −0.558338
\(574\) 0 0
\(575\) −14.3093 −0.596737
\(576\) 0 0
\(577\) 23.3163 0.970672 0.485336 0.874328i \(-0.338697\pi\)
0.485336 + 0.874328i \(0.338697\pi\)
\(578\) 0 0
\(579\) 3.86105 0.160460
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 7.29335 0.302059
\(584\) 0 0
\(585\) 11.2994 0.467174
\(586\) 0 0
\(587\) 11.1401 0.459803 0.229901 0.973214i \(-0.426160\pi\)
0.229901 + 0.973214i \(0.426160\pi\)
\(588\) 0 0
\(589\) 5.06969 0.208893
\(590\) 0 0
\(591\) 18.6705 0.768001
\(592\) 0 0
\(593\) −2.14637 −0.0881409 −0.0440705 0.999028i \(-0.514033\pi\)
−0.0440705 + 0.999028i \(0.514033\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −17.7705 −0.727299
\(598\) 0 0
\(599\) −21.3811 −0.873609 −0.436804 0.899556i \(-0.643890\pi\)
−0.436804 + 0.899556i \(0.643890\pi\)
\(600\) 0 0
\(601\) 13.7457 0.560701 0.280350 0.959898i \(-0.409549\pi\)
0.280350 + 0.959898i \(0.409549\pi\)
\(602\) 0 0
\(603\) 23.0535 0.938810
\(604\) 0 0
\(605\) 32.6183 1.32612
\(606\) 0 0
\(607\) −21.0041 −0.852529 −0.426264 0.904599i \(-0.640171\pi\)
−0.426264 + 0.904599i \(0.640171\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2.10014 −0.0849627
\(612\) 0 0
\(613\) −19.7824 −0.799005 −0.399502 0.916732i \(-0.630817\pi\)
−0.399502 + 0.916732i \(0.630817\pi\)
\(614\) 0 0
\(615\) 23.0585 0.929809
\(616\) 0 0
\(617\) 10.8866 0.438278 0.219139 0.975694i \(-0.429675\pi\)
0.219139 + 0.975694i \(0.429675\pi\)
\(618\) 0 0
\(619\) 40.1046 1.61194 0.805971 0.591955i \(-0.201644\pi\)
0.805971 + 0.591955i \(0.201644\pi\)
\(620\) 0 0
\(621\) 39.2861 1.57650
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −11.3067 −0.452269
\(626\) 0 0
\(627\) −6.31886 −0.252351
\(628\) 0 0
\(629\) 2.66680 0.106332
\(630\) 0 0
\(631\) 22.4234 0.892660 0.446330 0.894868i \(-0.352731\pi\)
0.446330 + 0.894868i \(0.352731\pi\)
\(632\) 0 0
\(633\) −19.3216 −0.767966
\(634\) 0 0
\(635\) −23.8574 −0.946751
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −12.2816 −0.485853
\(640\) 0 0
\(641\) −17.9934 −0.710696 −0.355348 0.934734i \(-0.615638\pi\)
−0.355348 + 0.934734i \(0.615638\pi\)
\(642\) 0 0
\(643\) 16.8909 0.666114 0.333057 0.942907i \(-0.391920\pi\)
0.333057 + 0.942907i \(0.391920\pi\)
\(644\) 0 0
\(645\) 5.15051 0.202801
\(646\) 0 0
\(647\) −16.6995 −0.656525 −0.328263 0.944587i \(-0.606463\pi\)
−0.328263 + 0.944587i \(0.606463\pi\)
\(648\) 0 0
\(649\) −57.9932 −2.27643
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 17.2314 0.674315 0.337158 0.941448i \(-0.390534\pi\)
0.337158 + 0.941448i \(0.390534\pi\)
\(654\) 0 0
\(655\) 23.2567 0.908716
\(656\) 0 0
\(657\) −11.4743 −0.447654
\(658\) 0 0
\(659\) −30.0457 −1.17041 −0.585207 0.810884i \(-0.698987\pi\)
−0.585207 + 0.810884i \(0.698987\pi\)
\(660\) 0 0
\(661\) −1.55903 −0.0606393 −0.0303196 0.999540i \(-0.509653\pi\)
−0.0303196 + 0.999540i \(0.509653\pi\)
\(662\) 0 0
\(663\) −4.62308 −0.179545
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 25.6512 0.993220
\(668\) 0 0
\(669\) 1.22334 0.0472969
\(670\) 0 0
\(671\) 21.2753 0.821326
\(672\) 0 0
\(673\) −17.5500 −0.676504 −0.338252 0.941056i \(-0.609836\pi\)
−0.338252 + 0.941056i \(0.609836\pi\)
\(674\) 0 0
\(675\) −10.6095 −0.408361
\(676\) 0 0
\(677\) −37.4505 −1.43934 −0.719669 0.694317i \(-0.755707\pi\)
−0.719669 + 0.694317i \(0.755707\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −7.19386 −0.275669
\(682\) 0 0
\(683\) −11.2872 −0.431892 −0.215946 0.976405i \(-0.569283\pi\)
−0.215946 + 0.976405i \(0.569283\pi\)
\(684\) 0 0
\(685\) −7.86379 −0.300460
\(686\) 0 0
\(687\) −1.67806 −0.0640221
\(688\) 0 0
\(689\) 5.23754 0.199534
\(690\) 0 0
\(691\) 31.6804 1.20518 0.602589 0.798052i \(-0.294136\pi\)
0.602589 + 0.798052i \(0.294136\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 30.1632 1.14415
\(696\) 0 0
\(697\) 11.6367 0.440770
\(698\) 0 0
\(699\) 27.0973 1.02491
\(700\) 0 0
\(701\) −0.469405 −0.0177292 −0.00886459 0.999961i \(-0.502822\pi\)
−0.00886459 + 0.999961i \(0.502822\pi\)
\(702\) 0 0
\(703\) 2.61756 0.0987233
\(704\) 0 0
\(705\) −1.08287 −0.0407834
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 12.8409 0.482251 0.241126 0.970494i \(-0.422483\pi\)
0.241126 + 0.970494i \(0.422483\pi\)
\(710\) 0 0
\(711\) −0.355315 −0.0133254
\(712\) 0 0
\(713\) −36.9030 −1.38203
\(714\) 0 0
\(715\) 37.1840 1.39060
\(716\) 0 0
\(717\) 14.2064 0.530546
\(718\) 0 0
\(719\) 24.2164 0.903120 0.451560 0.892241i \(-0.350868\pi\)
0.451560 + 0.892241i \(0.350868\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −7.64963 −0.284493
\(724\) 0 0
\(725\) −6.92732 −0.257274
\(726\) 0 0
\(727\) 21.7727 0.807505 0.403753 0.914868i \(-0.367706\pi\)
0.403753 + 0.914868i \(0.367706\pi\)
\(728\) 0 0
\(729\) 20.8936 0.773837
\(730\) 0 0
\(731\) 2.59925 0.0961366
\(732\) 0 0
\(733\) 48.7308 1.79991 0.899956 0.435981i \(-0.143598\pi\)
0.899956 + 0.435981i \(0.143598\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 75.8639 2.79448
\(738\) 0 0
\(739\) 38.9231 1.43181 0.715905 0.698197i \(-0.246014\pi\)
0.715905 + 0.698197i \(0.246014\pi\)
\(740\) 0 0
\(741\) −4.53773 −0.166698
\(742\) 0 0
\(743\) 20.8849 0.766192 0.383096 0.923709i \(-0.374858\pi\)
0.383096 + 0.923709i \(0.374858\pi\)
\(744\) 0 0
\(745\) 8.34540 0.305752
\(746\) 0 0
\(747\) −18.2162 −0.666495
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −29.0940 −1.06165 −0.530827 0.847480i \(-0.678119\pi\)
−0.530827 + 0.847480i \(0.678119\pi\)
\(752\) 0 0
\(753\) 22.7594 0.829399
\(754\) 0 0
\(755\) −2.13314 −0.0776328
\(756\) 0 0
\(757\) 33.8924 1.23184 0.615920 0.787808i \(-0.288784\pi\)
0.615920 + 0.787808i \(0.288784\pi\)
\(758\) 0 0
\(759\) 45.9958 1.66954
\(760\) 0 0
\(761\) 5.46397 0.198069 0.0990344 0.995084i \(-0.468425\pi\)
0.0990344 + 0.995084i \(0.468425\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 2.94024 0.106305
\(766\) 0 0
\(767\) −41.6464 −1.50376
\(768\) 0 0
\(769\) −31.6212 −1.14029 −0.570145 0.821544i \(-0.693113\pi\)
−0.570145 + 0.821544i \(0.693113\pi\)
\(770\) 0 0
\(771\) −11.4565 −0.412595
\(772\) 0 0
\(773\) −30.3820 −1.09277 −0.546383 0.837535i \(-0.683996\pi\)
−0.546383 + 0.837535i \(0.683996\pi\)
\(774\) 0 0
\(775\) 9.96595 0.357987
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 11.4218 0.409230
\(780\) 0 0
\(781\) −40.4161 −1.44620
\(782\) 0 0
\(783\) 19.0190 0.679682
\(784\) 0 0
\(785\) −18.6348 −0.665104
\(786\) 0 0
\(787\) −49.8241 −1.77604 −0.888020 0.459806i \(-0.847919\pi\)
−0.888020 + 0.459806i \(0.847919\pi\)
\(788\) 0 0
\(789\) 6.77564 0.241219
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 15.2784 0.542551
\(794\) 0 0
\(795\) 2.70057 0.0957794
\(796\) 0 0
\(797\) 3.52663 0.124920 0.0624598 0.998047i \(-0.480105\pi\)
0.0624598 + 0.998047i \(0.480105\pi\)
\(798\) 0 0
\(799\) −0.546481 −0.0193331
\(800\) 0 0
\(801\) 8.72821 0.308396
\(802\) 0 0
\(803\) −37.7593 −1.33250
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −11.1769 −0.393446
\(808\) 0 0
\(809\) −19.2422 −0.676519 −0.338259 0.941053i \(-0.609838\pi\)
−0.338259 + 0.941053i \(0.609838\pi\)
\(810\) 0 0
\(811\) −42.7925 −1.50265 −0.751324 0.659934i \(-0.770584\pi\)
−0.751324 + 0.659934i \(0.770584\pi\)
\(812\) 0 0
\(813\) −20.2839 −0.711386
\(814\) 0 0
\(815\) −10.8437 −0.379839
\(816\) 0 0
\(817\) 2.55126 0.0892573
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −35.6682 −1.24483 −0.622414 0.782688i \(-0.713848\pi\)
−0.622414 + 0.782688i \(0.713848\pi\)
\(822\) 0 0
\(823\) −26.3256 −0.917653 −0.458826 0.888526i \(-0.651730\pi\)
−0.458826 + 0.888526i \(0.651730\pi\)
\(824\) 0 0
\(825\) −12.4215 −0.432462
\(826\) 0 0
\(827\) 24.1983 0.841458 0.420729 0.907186i \(-0.361774\pi\)
0.420729 + 0.907186i \(0.361774\pi\)
\(828\) 0 0
\(829\) −2.91616 −0.101283 −0.0506413 0.998717i \(-0.516127\pi\)
−0.0506413 + 0.998717i \(0.516127\pi\)
\(830\) 0 0
\(831\) −2.92730 −0.101547
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −33.3540 −1.15426
\(836\) 0 0
\(837\) −27.3615 −0.945753
\(838\) 0 0
\(839\) 30.3903 1.04919 0.524595 0.851352i \(-0.324217\pi\)
0.524595 + 0.851352i \(0.324217\pi\)
\(840\) 0 0
\(841\) −16.5819 −0.571788
\(842\) 0 0
\(843\) −29.8031 −1.02647
\(844\) 0 0
\(845\) 4.05807 0.139602
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −21.3716 −0.733473
\(850\) 0 0
\(851\) −19.0536 −0.653149
\(852\) 0 0
\(853\) 34.4884 1.18086 0.590430 0.807089i \(-0.298958\pi\)
0.590430 + 0.807089i \(0.298958\pi\)
\(854\) 0 0
\(855\) 2.88596 0.0986977
\(856\) 0 0
\(857\) −40.2979 −1.37655 −0.688274 0.725451i \(-0.741631\pi\)
−0.688274 + 0.725451i \(0.741631\pi\)
\(858\) 0 0
\(859\) 1.45229 0.0495516 0.0247758 0.999693i \(-0.492113\pi\)
0.0247758 + 0.999693i \(0.492113\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −12.6326 −0.430020 −0.215010 0.976612i \(-0.568978\pi\)
−0.215010 + 0.976612i \(0.568978\pi\)
\(864\) 0 0
\(865\) 36.9909 1.25773
\(866\) 0 0
\(867\) 18.4995 0.628276
\(868\) 0 0
\(869\) −1.16926 −0.0396646
\(870\) 0 0
\(871\) 54.4798 1.84598
\(872\) 0 0
\(873\) −11.7016 −0.396038
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 7.16028 0.241786 0.120893 0.992666i \(-0.461424\pi\)
0.120893 + 0.992666i \(0.461424\pi\)
\(878\) 0 0
\(879\) 30.1062 1.01546
\(880\) 0 0
\(881\) 1.95742 0.0659472 0.0329736 0.999456i \(-0.489502\pi\)
0.0329736 + 0.999456i \(0.489502\pi\)
\(882\) 0 0
\(883\) −20.3489 −0.684796 −0.342398 0.939555i \(-0.611239\pi\)
−0.342398 + 0.939555i \(0.611239\pi\)
\(884\) 0 0
\(885\) −21.4737 −0.721829
\(886\) 0 0
\(887\) 8.10888 0.272270 0.136135 0.990690i \(-0.456532\pi\)
0.136135 + 0.990690i \(0.456532\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 7.00428 0.234652
\(892\) 0 0
\(893\) −0.536392 −0.0179497
\(894\) 0 0
\(895\) 21.8689 0.730997
\(896\) 0 0
\(897\) 33.0308 1.10287
\(898\) 0 0
\(899\) −17.8653 −0.595841
\(900\) 0 0
\(901\) 1.36287 0.0454036
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 31.7364 1.05495
\(906\) 0 0
\(907\) 29.7288 0.987129 0.493565 0.869709i \(-0.335694\pi\)
0.493565 + 0.869709i \(0.335694\pi\)
\(908\) 0 0
\(909\) −29.9596 −0.993698
\(910\) 0 0
\(911\) −30.1074 −0.997501 −0.498751 0.866746i \(-0.666208\pi\)
−0.498751 + 0.866746i \(0.666208\pi\)
\(912\) 0 0
\(913\) −59.9455 −1.98391
\(914\) 0 0
\(915\) 7.87781 0.260432
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −4.12477 −0.136064 −0.0680318 0.997683i \(-0.521672\pi\)
−0.0680318 + 0.997683i \(0.521672\pi\)
\(920\) 0 0
\(921\) 0.140303 0.00462315
\(922\) 0 0
\(923\) −29.0238 −0.955332
\(924\) 0 0
\(925\) 5.14558 0.169186
\(926\) 0 0
\(927\) −18.7514 −0.615876
\(928\) 0 0
\(929\) 35.9094 1.17815 0.589075 0.808078i \(-0.299492\pi\)
0.589075 + 0.808078i \(0.299492\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −8.28348 −0.271189
\(934\) 0 0
\(935\) 9.67568 0.316429
\(936\) 0 0
\(937\) 24.0332 0.785130 0.392565 0.919724i \(-0.371588\pi\)
0.392565 + 0.919724i \(0.371588\pi\)
\(938\) 0 0
\(939\) −1.50168 −0.0490053
\(940\) 0 0
\(941\) −7.78796 −0.253880 −0.126940 0.991910i \(-0.540516\pi\)
−0.126940 + 0.991910i \(0.540516\pi\)
\(942\) 0 0
\(943\) −83.1412 −2.70745
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −20.1844 −0.655904 −0.327952 0.944694i \(-0.606358\pi\)
−0.327952 + 0.944694i \(0.606358\pi\)
\(948\) 0 0
\(949\) −27.1159 −0.880220
\(950\) 0 0
\(951\) −3.39788 −0.110184
\(952\) 0 0
\(953\) 2.08018 0.0673838 0.0336919 0.999432i \(-0.489274\pi\)
0.0336919 + 0.999432i \(0.489274\pi\)
\(954\) 0 0
\(955\) 20.0875 0.650015
\(956\) 0 0
\(957\) 22.2673 0.719798
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −5.29821 −0.170910
\(962\) 0 0
\(963\) −24.6897 −0.795614
\(964\) 0 0
\(965\) −5.80305 −0.186807
\(966\) 0 0
\(967\) 21.0053 0.675484 0.337742 0.941239i \(-0.390337\pi\)
0.337742 + 0.941239i \(0.390337\pi\)
\(968\) 0 0
\(969\) −1.18077 −0.0379317
\(970\) 0 0
\(971\) 34.2931 1.10052 0.550260 0.834994i \(-0.314529\pi\)
0.550260 + 0.834994i \(0.314529\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −8.92022 −0.285676
\(976\) 0 0
\(977\) 8.43730 0.269933 0.134967 0.990850i \(-0.456907\pi\)
0.134967 + 0.990850i \(0.456907\pi\)
\(978\) 0 0
\(979\) 28.7226 0.917980
\(980\) 0 0
\(981\) 18.5803 0.593223
\(982\) 0 0
\(983\) −51.7499 −1.65056 −0.825282 0.564721i \(-0.808984\pi\)
−0.825282 + 0.564721i \(0.808984\pi\)
\(984\) 0 0
\(985\) −28.0612 −0.894104
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −18.5710 −0.590523
\(990\) 0 0
\(991\) −6.15109 −0.195396 −0.0976979 0.995216i \(-0.531148\pi\)
−0.0976979 + 0.995216i \(0.531148\pi\)
\(992\) 0 0
\(993\) −6.35104 −0.201544
\(994\) 0 0
\(995\) 26.7086 0.846719
\(996\) 0 0
\(997\) 26.0839 0.826085 0.413043 0.910712i \(-0.364466\pi\)
0.413043 + 0.910712i \(0.364466\pi\)
\(998\) 0 0
\(999\) −14.1272 −0.446965
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 7448.2.a.bn.1.2 yes 6
7.6 odd 2 7448.2.a.bm.1.5 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7448.2.a.bm.1.5 6 7.6 odd 2
7448.2.a.bn.1.2 yes 6 1.1 even 1 trivial