Properties

Label 9075.2.a.bm.1.2
Level $9075$
Weight $2$
Character 9075.1
Self dual yes
Analytic conductor $72.464$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9075.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(72.4642398343\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{15}) \)
Defining polynomial: \( x^{2} - 15 \) 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 1.2
Root \(3.87298\) of defining polynomial
Character \(\chi\) \(=\) 9075.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} -2.00000 q^{4} +3.87298 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -2.00000 q^{4} +3.87298 q^{7} +1.00000 q^{9} -2.00000 q^{12} -3.87298 q^{13} +4.00000 q^{16} -7.74597 q^{17} +3.87298 q^{19} +3.87298 q^{21} +6.00000 q^{23} +1.00000 q^{27} -7.74597 q^{28} +7.74597 q^{29} -5.00000 q^{31} -2.00000 q^{36} +2.00000 q^{37} -3.87298 q^{39} -7.74597 q^{41} +3.87298 q^{43} -12.0000 q^{47} +4.00000 q^{48} +8.00000 q^{49} -7.74597 q^{51} +7.74597 q^{52} +6.00000 q^{53} +3.87298 q^{57} +11.6190 q^{61} +3.87298 q^{63} -8.00000 q^{64} -7.00000 q^{67} +15.4919 q^{68} +6.00000 q^{69} +12.0000 q^{71} -7.74597 q^{76} +7.74597 q^{79} +1.00000 q^{81} +7.74597 q^{83} -7.74597 q^{84} +7.74597 q^{87} +6.00000 q^{89} -15.0000 q^{91} -12.0000 q^{92} -5.00000 q^{93} +7.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{3} - 4 q^{4} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{3} - 4 q^{4} + 2 q^{9} - 4 q^{12} + 8 q^{16} + 12 q^{23} + 2 q^{27} - 10 q^{31} - 4 q^{36} + 4 q^{37} - 24 q^{47} + 8 q^{48} + 16 q^{49} + 12 q^{53} - 16 q^{64} - 14 q^{67} + 12 q^{69} + 24 q^{71} + 2 q^{81} + 12 q^{89} - 30 q^{91} - 24 q^{92} - 10 q^{93} + 14 q^{97}+O(q^{100}) \) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(3\) 1.00000 0.577350
\(4\) −2.00000 −1.00000
\(5\) 0 0
\(6\) 0 0
\(7\) 3.87298 1.46385 0.731925 0.681385i \(-0.238622\pi\)
0.731925 + 0.681385i \(0.238622\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0 0
\(12\) −2.00000 −0.577350
\(13\) −3.87298 −1.07417 −0.537086 0.843527i \(-0.680475\pi\)
−0.537086 + 0.843527i \(0.680475\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 4.00000 1.00000
\(17\) −7.74597 −1.87867 −0.939336 0.342997i \(-0.888558\pi\)
−0.939336 + 0.342997i \(0.888558\pi\)
\(18\) 0 0
\(19\) 3.87298 0.888523 0.444262 0.895897i \(-0.353466\pi\)
0.444262 + 0.895897i \(0.353466\pi\)
\(20\) 0 0
\(21\) 3.87298 0.845154
\(22\) 0 0
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −7.74597 −1.46385
\(29\) 7.74597 1.43839 0.719195 0.694808i \(-0.244511\pi\)
0.719195 + 0.694808i \(0.244511\pi\)
\(30\) 0 0
\(31\) −5.00000 −0.898027 −0.449013 0.893525i \(-0.648224\pi\)
−0.449013 + 0.893525i \(0.648224\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0 0
\(39\) −3.87298 −0.620174
\(40\) 0 0
\(41\) −7.74597 −1.20972 −0.604858 0.796333i \(-0.706770\pi\)
−0.604858 + 0.796333i \(0.706770\pi\)
\(42\) 0 0
\(43\) 3.87298 0.590624 0.295312 0.955401i \(-0.404576\pi\)
0.295312 + 0.955401i \(0.404576\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −12.0000 −1.75038 −0.875190 0.483779i \(-0.839264\pi\)
−0.875190 + 0.483779i \(0.839264\pi\)
\(48\) 4.00000 0.577350
\(49\) 8.00000 1.14286
\(50\) 0 0
\(51\) −7.74597 −1.08465
\(52\) 7.74597 1.07417
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 3.87298 0.512989
\(58\) 0 0
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 11.6190 1.48765 0.743827 0.668372i \(-0.233009\pi\)
0.743827 + 0.668372i \(0.233009\pi\)
\(62\) 0 0
\(63\) 3.87298 0.487950
\(64\) −8.00000 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) −7.00000 −0.855186 −0.427593 0.903971i \(-0.640638\pi\)
−0.427593 + 0.903971i \(0.640638\pi\)
\(68\) 15.4919 1.87867
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −7.74597 −0.888523
\(77\) 0 0
\(78\) 0 0
\(79\) 7.74597 0.871489 0.435745 0.900070i \(-0.356485\pi\)
0.435745 + 0.900070i \(0.356485\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 7.74597 0.850230 0.425115 0.905139i \(-0.360234\pi\)
0.425115 + 0.905139i \(0.360234\pi\)
\(84\) −7.74597 −0.845154
\(85\) 0 0
\(86\) 0 0
\(87\) 7.74597 0.830455
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) −15.0000 −1.57243
\(92\) −12.0000 −1.25109
\(93\) −5.00000 −0.518476
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −15.4919 −1.54150 −0.770752 0.637135i \(-0.780120\pi\)
−0.770752 + 0.637135i \(0.780120\pi\)
\(102\) 0 0
\(103\) 16.0000 1.57653 0.788263 0.615338i \(-0.210980\pi\)
0.788263 + 0.615338i \(0.210980\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 7.74597 0.748831 0.374415 0.927261i \(-0.377843\pi\)
0.374415 + 0.927261i \(0.377843\pi\)
\(108\) −2.00000 −0.192450
\(109\) −3.87298 −0.370965 −0.185482 0.982648i \(-0.559385\pi\)
−0.185482 + 0.982648i \(0.559385\pi\)
\(110\) 0 0
\(111\) 2.00000 0.189832
\(112\) 15.4919 1.46385
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −15.4919 −1.43839
\(117\) −3.87298 −0.358057
\(118\) 0 0
\(119\) −30.0000 −2.75010
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) −7.74597 −0.698430
\(124\) 10.0000 0.898027
\(125\) 0 0
\(126\) 0 0
\(127\) 7.74597 0.687343 0.343672 0.939090i \(-0.388329\pi\)
0.343672 + 0.939090i \(0.388329\pi\)
\(128\) 0 0
\(129\) 3.87298 0.340997
\(130\) 0 0
\(131\) −7.74597 −0.676768 −0.338384 0.941008i \(-0.609880\pi\)
−0.338384 + 0.941008i \(0.609880\pi\)
\(132\) 0 0
\(133\) 15.0000 1.30066
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 12.0000 1.02523 0.512615 0.858619i \(-0.328677\pi\)
0.512615 + 0.858619i \(0.328677\pi\)
\(138\) 0 0
\(139\) −7.74597 −0.657004 −0.328502 0.944503i \(-0.606544\pi\)
−0.328502 + 0.944503i \(0.606544\pi\)
\(140\) 0 0
\(141\) −12.0000 −1.01058
\(142\) 0 0
\(143\) 0 0
\(144\) 4.00000 0.333333
\(145\) 0 0
\(146\) 0 0
\(147\) 8.00000 0.659829
\(148\) −4.00000 −0.328798
\(149\) −7.74597 −0.634574 −0.317287 0.948330i \(-0.602772\pi\)
−0.317287 + 0.948330i \(0.602772\pi\)
\(150\) 0 0
\(151\) 11.6190 0.945537 0.472768 0.881187i \(-0.343255\pi\)
0.472768 + 0.881187i \(0.343255\pi\)
\(152\) 0 0
\(153\) −7.74597 −0.626224
\(154\) 0 0
\(155\) 0 0
\(156\) 7.74597 0.620174
\(157\) −13.0000 −1.03751 −0.518756 0.854922i \(-0.673605\pi\)
−0.518756 + 0.854922i \(0.673605\pi\)
\(158\) 0 0
\(159\) 6.00000 0.475831
\(160\) 0 0
\(161\) 23.2379 1.83140
\(162\) 0 0
\(163\) −11.0000 −0.861586 −0.430793 0.902451i \(-0.641766\pi\)
−0.430793 + 0.902451i \(0.641766\pi\)
\(164\) 15.4919 1.20972
\(165\) 0 0
\(166\) 0 0
\(167\) −15.4919 −1.19880 −0.599401 0.800449i \(-0.704594\pi\)
−0.599401 + 0.800449i \(0.704594\pi\)
\(168\) 0 0
\(169\) 2.00000 0.153846
\(170\) 0 0
\(171\) 3.87298 0.296174
\(172\) −7.74597 −0.590624
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 6.00000 0.448461 0.224231 0.974536i \(-0.428013\pi\)
0.224231 + 0.974536i \(0.428013\pi\)
\(180\) 0 0
\(181\) 5.00000 0.371647 0.185824 0.982583i \(-0.440505\pi\)
0.185824 + 0.982583i \(0.440505\pi\)
\(182\) 0 0
\(183\) 11.6190 0.858898
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 24.0000 1.75038
\(189\) 3.87298 0.281718
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) −8.00000 −0.577350
\(193\) 11.6190 0.836350 0.418175 0.908366i \(-0.362670\pi\)
0.418175 + 0.908366i \(0.362670\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −16.0000 −1.14286
\(197\) −15.4919 −1.10375 −0.551877 0.833925i \(-0.686088\pi\)
−0.551877 + 0.833925i \(0.686088\pi\)
\(198\) 0 0
\(199\) 25.0000 1.77220 0.886102 0.463491i \(-0.153403\pi\)
0.886102 + 0.463491i \(0.153403\pi\)
\(200\) 0 0
\(201\) −7.00000 −0.493742
\(202\) 0 0
\(203\) 30.0000 2.10559
\(204\) 15.4919 1.08465
\(205\) 0 0
\(206\) 0 0
\(207\) 6.00000 0.417029
\(208\) −15.4919 −1.07417
\(209\) 0 0
\(210\) 0 0
\(211\) 19.3649 1.33314 0.666568 0.745444i \(-0.267763\pi\)
0.666568 + 0.745444i \(0.267763\pi\)
\(212\) −12.0000 −0.824163
\(213\) 12.0000 0.822226
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −19.3649 −1.31458
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 30.0000 2.01802
\(222\) 0 0
\(223\) 19.0000 1.27233 0.636167 0.771551i \(-0.280519\pi\)
0.636167 + 0.771551i \(0.280519\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 15.4919 1.02824 0.514118 0.857720i \(-0.328119\pi\)
0.514118 + 0.857720i \(0.328119\pi\)
\(228\) −7.74597 −0.512989
\(229\) −5.00000 −0.330409 −0.165205 0.986259i \(-0.552828\pi\)
−0.165205 + 0.986259i \(0.552828\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −15.4919 −1.01491 −0.507455 0.861678i \(-0.669414\pi\)
−0.507455 + 0.861678i \(0.669414\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 7.74597 0.503155
\(238\) 0 0
\(239\) −23.2379 −1.50313 −0.751567 0.659656i \(-0.770702\pi\)
−0.751567 + 0.659656i \(0.770702\pi\)
\(240\) 0 0
\(241\) 27.1109 1.74637 0.873183 0.487393i \(-0.162052\pi\)
0.873183 + 0.487393i \(0.162052\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) −23.2379 −1.48765
\(245\) 0 0
\(246\) 0 0
\(247\) −15.0000 −0.954427
\(248\) 0 0
\(249\) 7.74597 0.490881
\(250\) 0 0
\(251\) 18.0000 1.13615 0.568075 0.822977i \(-0.307688\pi\)
0.568075 + 0.822977i \(0.307688\pi\)
\(252\) −7.74597 −0.487950
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) −12.0000 −0.748539 −0.374270 0.927320i \(-0.622107\pi\)
−0.374270 + 0.927320i \(0.622107\pi\)
\(258\) 0 0
\(259\) 7.74597 0.481311
\(260\) 0 0
\(261\) 7.74597 0.479463
\(262\) 0 0
\(263\) 23.2379 1.43291 0.716455 0.697633i \(-0.245763\pi\)
0.716455 + 0.697633i \(0.245763\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 6.00000 0.367194
\(268\) 14.0000 0.855186
\(269\) 30.0000 1.82913 0.914566 0.404436i \(-0.132532\pi\)
0.914566 + 0.404436i \(0.132532\pi\)
\(270\) 0 0
\(271\) −23.2379 −1.41160 −0.705801 0.708410i \(-0.749413\pi\)
−0.705801 + 0.708410i \(0.749413\pi\)
\(272\) −30.9839 −1.87867
\(273\) −15.0000 −0.907841
\(274\) 0 0
\(275\) 0 0
\(276\) −12.0000 −0.722315
\(277\) −27.1109 −1.62894 −0.814468 0.580209i \(-0.802971\pi\)
−0.814468 + 0.580209i \(0.802971\pi\)
\(278\) 0 0
\(279\) −5.00000 −0.299342
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) 3.87298 0.230225 0.115112 0.993352i \(-0.463277\pi\)
0.115112 + 0.993352i \(0.463277\pi\)
\(284\) −24.0000 −1.42414
\(285\) 0 0
\(286\) 0 0
\(287\) −30.0000 −1.77084
\(288\) 0 0
\(289\) 43.0000 2.52941
\(290\) 0 0
\(291\) 7.00000 0.410347
\(292\) 0 0
\(293\) −23.2379 −1.35757 −0.678786 0.734336i \(-0.737494\pi\)
−0.678786 + 0.734336i \(0.737494\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −23.2379 −1.34388
\(300\) 0 0
\(301\) 15.0000 0.864586
\(302\) 0 0
\(303\) −15.4919 −0.889988
\(304\) 15.4919 0.888523
\(305\) 0 0
\(306\) 0 0
\(307\) 11.6190 0.663129 0.331564 0.943433i \(-0.392424\pi\)
0.331564 + 0.943433i \(0.392424\pi\)
\(308\) 0 0
\(309\) 16.0000 0.910208
\(310\) 0 0
\(311\) 18.0000 1.02069 0.510343 0.859971i \(-0.329518\pi\)
0.510343 + 0.859971i \(0.329518\pi\)
\(312\) 0 0
\(313\) −1.00000 −0.0565233 −0.0282617 0.999601i \(-0.508997\pi\)
−0.0282617 + 0.999601i \(0.508997\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −15.4919 −0.871489
\(317\) 18.0000 1.01098 0.505490 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 7.74597 0.432338
\(322\) 0 0
\(323\) −30.0000 −1.66924
\(324\) −2.00000 −0.111111
\(325\) 0 0
\(326\) 0 0
\(327\) −3.87298 −0.214176
\(328\) 0 0
\(329\) −46.4758 −2.56229
\(330\) 0 0
\(331\) 20.0000 1.09930 0.549650 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) −15.4919 −0.850230
\(333\) 2.00000 0.109599
\(334\) 0 0
\(335\) 0 0
\(336\) 15.4919 0.845154
\(337\) −19.3649 −1.05487 −0.527437 0.849594i \(-0.676847\pi\)
−0.527437 + 0.849594i \(0.676847\pi\)
\(338\) 0 0
\(339\) 6.00000 0.325875
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 3.87298 0.209121
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 15.4919 0.831651 0.415825 0.909445i \(-0.363493\pi\)
0.415825 + 0.909445i \(0.363493\pi\)
\(348\) −15.4919 −0.830455
\(349\) −15.4919 −0.829264 −0.414632 0.909989i \(-0.636090\pi\)
−0.414632 + 0.909989i \(0.636090\pi\)
\(350\) 0 0
\(351\) −3.87298 −0.206725
\(352\) 0 0
\(353\) 6.00000 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −12.0000 −0.635999
\(357\) −30.0000 −1.58777
\(358\) 0 0
\(359\) −15.4919 −0.817633 −0.408816 0.912617i \(-0.634058\pi\)
−0.408816 + 0.912617i \(0.634058\pi\)
\(360\) 0 0
\(361\) −4.00000 −0.210526
\(362\) 0 0
\(363\) 0 0
\(364\) 30.0000 1.57243
\(365\) 0 0
\(366\) 0 0
\(367\) 13.0000 0.678594 0.339297 0.940679i \(-0.389811\pi\)
0.339297 + 0.940679i \(0.389811\pi\)
\(368\) 24.0000 1.25109
\(369\) −7.74597 −0.403239
\(370\) 0 0
\(371\) 23.2379 1.20645
\(372\) 10.0000 0.518476
\(373\) 3.87298 0.200535 0.100268 0.994960i \(-0.468030\pi\)
0.100268 + 0.994960i \(0.468030\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −30.0000 −1.54508
\(378\) 0 0
\(379\) 5.00000 0.256833 0.128416 0.991720i \(-0.459011\pi\)
0.128416 + 0.991720i \(0.459011\pi\)
\(380\) 0 0
\(381\) 7.74597 0.396838
\(382\) 0 0
\(383\) −6.00000 −0.306586 −0.153293 0.988181i \(-0.548988\pi\)
−0.153293 + 0.988181i \(0.548988\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 3.87298 0.196875
\(388\) −14.0000 −0.710742
\(389\) 30.0000 1.52106 0.760530 0.649303i \(-0.224939\pi\)
0.760530 + 0.649303i \(0.224939\pi\)
\(390\) 0 0
\(391\) −46.4758 −2.35038
\(392\) 0 0
\(393\) −7.74597 −0.390732
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −23.0000 −1.15434 −0.577168 0.816625i \(-0.695842\pi\)
−0.577168 + 0.816625i \(0.695842\pi\)
\(398\) 0 0
\(399\) 15.0000 0.750939
\(400\) 0 0
\(401\) −30.0000 −1.49813 −0.749064 0.662497i \(-0.769497\pi\)
−0.749064 + 0.662497i \(0.769497\pi\)
\(402\) 0 0
\(403\) 19.3649 0.964635
\(404\) 30.9839 1.54150
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 27.1109 1.34055 0.670273 0.742114i \(-0.266177\pi\)
0.670273 + 0.742114i \(0.266177\pi\)
\(410\) 0 0
\(411\) 12.0000 0.591916
\(412\) −32.0000 −1.57653
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −7.74597 −0.379322
\(418\) 0 0
\(419\) 24.0000 1.17248 0.586238 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) 0 0
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) 0 0
\(423\) −12.0000 −0.583460
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 45.0000 2.17770
\(428\) −15.4919 −0.748831
\(429\) 0 0
\(430\) 0 0
\(431\) −7.74597 −0.373110 −0.186555 0.982445i \(-0.559732\pi\)
−0.186555 + 0.982445i \(0.559732\pi\)
\(432\) 4.00000 0.192450
\(433\) −11.0000 −0.528626 −0.264313 0.964437i \(-0.585145\pi\)
−0.264313 + 0.964437i \(0.585145\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 7.74597 0.370965
\(437\) 23.2379 1.11162
\(438\) 0 0
\(439\) 34.8569 1.66363 0.831813 0.555055i \(-0.187303\pi\)
0.831813 + 0.555055i \(0.187303\pi\)
\(440\) 0 0
\(441\) 8.00000 0.380952
\(442\) 0 0
\(443\) 6.00000 0.285069 0.142534 0.989790i \(-0.454475\pi\)
0.142534 + 0.989790i \(0.454475\pi\)
\(444\) −4.00000 −0.189832
\(445\) 0 0
\(446\) 0 0
\(447\) −7.74597 −0.366372
\(448\) −30.9839 −1.46385
\(449\) −36.0000 −1.69895 −0.849473 0.527633i \(-0.823080\pi\)
−0.849473 + 0.527633i \(0.823080\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −12.0000 −0.564433
\(453\) 11.6190 0.545906
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −15.4919 −0.724682 −0.362341 0.932046i \(-0.618022\pi\)
−0.362341 + 0.932046i \(0.618022\pi\)
\(458\) 0 0
\(459\) −7.74597 −0.361551
\(460\) 0 0
\(461\) −7.74597 −0.360766 −0.180383 0.983596i \(-0.557734\pi\)
−0.180383 + 0.983596i \(0.557734\pi\)
\(462\) 0 0
\(463\) 4.00000 0.185896 0.0929479 0.995671i \(-0.470371\pi\)
0.0929479 + 0.995671i \(0.470371\pi\)
\(464\) 30.9839 1.43839
\(465\) 0 0
\(466\) 0 0
\(467\) 42.0000 1.94353 0.971764 0.235954i \(-0.0758216\pi\)
0.971764 + 0.235954i \(0.0758216\pi\)
\(468\) 7.74597 0.358057
\(469\) −27.1109 −1.25186
\(470\) 0 0
\(471\) −13.0000 −0.599008
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 60.0000 2.75010
\(477\) 6.00000 0.274721
\(478\) 0 0
\(479\) 30.9839 1.41569 0.707845 0.706368i \(-0.249668\pi\)
0.707845 + 0.706368i \(0.249668\pi\)
\(480\) 0 0
\(481\) −7.74597 −0.353186
\(482\) 0 0
\(483\) 23.2379 1.05736
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 23.0000 1.04223 0.521115 0.853487i \(-0.325516\pi\)
0.521115 + 0.853487i \(0.325516\pi\)
\(488\) 0 0
\(489\) −11.0000 −0.497437
\(490\) 0 0
\(491\) −7.74597 −0.349571 −0.174785 0.984607i \(-0.555923\pi\)
−0.174785 + 0.984607i \(0.555923\pi\)
\(492\) 15.4919 0.698430
\(493\) −60.0000 −2.70226
\(494\) 0 0
\(495\) 0 0
\(496\) −20.0000 −0.898027
\(497\) 46.4758 2.08472
\(498\) 0 0
\(499\) 25.0000 1.11915 0.559577 0.828778i \(-0.310964\pi\)
0.559577 + 0.828778i \(0.310964\pi\)
\(500\) 0 0
\(501\) −15.4919 −0.692129
\(502\) 0 0
\(503\) 7.74597 0.345376 0.172688 0.984977i \(-0.444755\pi\)
0.172688 + 0.984977i \(0.444755\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 2.00000 0.0888231
\(508\) −15.4919 −0.687343
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 3.87298 0.170996
\(514\) 0 0
\(515\) 0 0
\(516\) −7.74597 −0.340997
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 30.0000 1.31432 0.657162 0.753749i \(-0.271757\pi\)
0.657162 + 0.753749i \(0.271757\pi\)
\(522\) 0 0
\(523\) −11.6190 −0.508061 −0.254031 0.967196i \(-0.581756\pi\)
−0.254031 + 0.967196i \(0.581756\pi\)
\(524\) 15.4919 0.676768
\(525\) 0 0
\(526\) 0 0
\(527\) 38.7298 1.68710
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 0 0
\(532\) −30.0000 −1.30066
\(533\) 30.0000 1.29944
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 6.00000 0.258919
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −42.6028 −1.83164 −0.915819 0.401591i \(-0.868457\pi\)
−0.915819 + 0.401591i \(0.868457\pi\)
\(542\) 0 0
\(543\) 5.00000 0.214571
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 23.2379 0.993581 0.496790 0.867871i \(-0.334512\pi\)
0.496790 + 0.867871i \(0.334512\pi\)
\(548\) −24.0000 −1.02523
\(549\) 11.6190 0.495885
\(550\) 0 0
\(551\) 30.0000 1.27804
\(552\) 0 0
\(553\) 30.0000 1.27573
\(554\) 0 0
\(555\) 0 0
\(556\) 15.4919 0.657004
\(557\) −15.4919 −0.656414 −0.328207 0.944606i \(-0.606444\pi\)
−0.328207 + 0.944606i \(0.606444\pi\)
\(558\) 0 0
\(559\) −15.0000 −0.634432
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 7.74597 0.326454 0.163227 0.986589i \(-0.447810\pi\)
0.163227 + 0.986589i \(0.447810\pi\)
\(564\) 24.0000 1.01058
\(565\) 0 0
\(566\) 0 0
\(567\) 3.87298 0.162650
\(568\) 0 0
\(569\) 23.2379 0.974183 0.487092 0.873351i \(-0.338058\pi\)
0.487092 + 0.873351i \(0.338058\pi\)
\(570\) 0 0
\(571\) −19.3649 −0.810397 −0.405198 0.914229i \(-0.632798\pi\)
−0.405198 + 0.914229i \(0.632798\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −8.00000 −0.333333
\(577\) −37.0000 −1.54033 −0.770165 0.637845i \(-0.779826\pi\)
−0.770165 + 0.637845i \(0.779826\pi\)
\(578\) 0 0
\(579\) 11.6190 0.482867
\(580\) 0 0
\(581\) 30.0000 1.24461
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −18.0000 −0.742940 −0.371470 0.928445i \(-0.621146\pi\)
−0.371470 + 0.928445i \(0.621146\pi\)
\(588\) −16.0000 −0.659829
\(589\) −19.3649 −0.797917
\(590\) 0 0
\(591\) −15.4919 −0.637253
\(592\) 8.00000 0.328798
\(593\) −23.2379 −0.954266 −0.477133 0.878831i \(-0.658324\pi\)
−0.477133 + 0.878831i \(0.658324\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 15.4919 0.634574
\(597\) 25.0000 1.02318
\(598\) 0 0
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) 0 0
\(601\) 27.1109 1.10588 0.552938 0.833222i \(-0.313507\pi\)
0.552938 + 0.833222i \(0.313507\pi\)
\(602\) 0 0
\(603\) −7.00000 −0.285062
\(604\) −23.2379 −0.945537
\(605\) 0 0
\(606\) 0 0
\(607\) 38.7298 1.57200 0.785998 0.618229i \(-0.212150\pi\)
0.785998 + 0.618229i \(0.212150\pi\)
\(608\) 0 0
\(609\) 30.0000 1.21566
\(610\) 0 0
\(611\) 46.4758 1.88021
\(612\) 15.4919 0.626224
\(613\) 46.4758 1.87714 0.938570 0.345089i \(-0.112151\pi\)
0.938570 + 0.345089i \(0.112151\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −12.0000 −0.483102 −0.241551 0.970388i \(-0.577656\pi\)
−0.241551 + 0.970388i \(0.577656\pi\)
\(618\) 0 0
\(619\) −1.00000 −0.0401934 −0.0200967 0.999798i \(-0.506397\pi\)
−0.0200967 + 0.999798i \(0.506397\pi\)
\(620\) 0 0
\(621\) 6.00000 0.240772
\(622\) 0 0
\(623\) 23.2379 0.931007
\(624\) −15.4919 −0.620174
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 26.0000 1.03751
\(629\) −15.4919 −0.617704
\(630\) 0 0
\(631\) 7.00000 0.278666 0.139333 0.990246i \(-0.455504\pi\)
0.139333 + 0.990246i \(0.455504\pi\)
\(632\) 0 0
\(633\) 19.3649 0.769686
\(634\) 0 0
\(635\) 0 0
\(636\) −12.0000 −0.475831
\(637\) −30.9839 −1.22763
\(638\) 0 0
\(639\) 12.0000 0.474713
\(640\) 0 0
\(641\) 30.0000 1.18493 0.592464 0.805597i \(-0.298155\pi\)
0.592464 + 0.805597i \(0.298155\pi\)
\(642\) 0 0
\(643\) 16.0000 0.630978 0.315489 0.948929i \(-0.397831\pi\)
0.315489 + 0.948929i \(0.397831\pi\)
\(644\) −46.4758 −1.83140
\(645\) 0 0
\(646\) 0 0
\(647\) −12.0000 −0.471769 −0.235884 0.971781i \(-0.575799\pi\)
−0.235884 + 0.971781i \(0.575799\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −19.3649 −0.758971
\(652\) 22.0000 0.861586
\(653\) −24.0000 −0.939193 −0.469596 0.882881i \(-0.655601\pi\)
−0.469596 + 0.882881i \(0.655601\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −30.9839 −1.20972
\(657\) 0 0
\(658\) 0 0
\(659\) 46.4758 1.81044 0.905220 0.424943i \(-0.139706\pi\)
0.905220 + 0.424943i \(0.139706\pi\)
\(660\) 0 0
\(661\) −2.00000 −0.0777910 −0.0388955 0.999243i \(-0.512384\pi\)
−0.0388955 + 0.999243i \(0.512384\pi\)
\(662\) 0 0
\(663\) 30.0000 1.16510
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 46.4758 1.79955
\(668\) 30.9839 1.19880
\(669\) 19.0000 0.734582
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 30.9839 1.19434 0.597170 0.802115i \(-0.296292\pi\)
0.597170 + 0.802115i \(0.296292\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −4.00000 −0.153846
\(677\) −23.2379 −0.893105 −0.446553 0.894757i \(-0.647348\pi\)
−0.446553 + 0.894757i \(0.647348\pi\)
\(678\) 0 0
\(679\) 27.1109 1.04042
\(680\) 0 0
\(681\) 15.4919 0.593652
\(682\) 0 0
\(683\) −6.00000 −0.229584 −0.114792 0.993390i \(-0.536620\pi\)
−0.114792 + 0.993390i \(0.536620\pi\)
\(684\) −7.74597 −0.296174
\(685\) 0 0
\(686\) 0 0
\(687\) −5.00000 −0.190762
\(688\) 15.4919 0.590624
\(689\) −23.2379 −0.885293
\(690\) 0 0
\(691\) −28.0000 −1.06517 −0.532585 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 60.0000 2.27266
\(698\) 0 0
\(699\) −15.4919 −0.585959
\(700\) 0 0
\(701\) −30.9839 −1.17024 −0.585122 0.810945i \(-0.698953\pi\)
−0.585122 + 0.810945i \(0.698953\pi\)
\(702\) 0 0
\(703\) 7.74597 0.292145
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −60.0000 −2.25653
\(708\) 0 0
\(709\) 19.0000 0.713560 0.356780 0.934188i \(-0.383875\pi\)
0.356780 + 0.934188i \(0.383875\pi\)
\(710\) 0 0
\(711\) 7.74597 0.290496
\(712\) 0 0
\(713\) −30.0000 −1.12351
\(714\) 0 0
\(715\) 0 0
\(716\) −12.0000 −0.448461
\(717\) −23.2379 −0.867835
\(718\) 0 0
\(719\) 6.00000 0.223762 0.111881 0.993722i \(-0.464312\pi\)
0.111881 + 0.993722i \(0.464312\pi\)
\(720\) 0 0
\(721\) 61.9677 2.30780
\(722\) 0 0
\(723\) 27.1109 1.00826
\(724\) −10.0000 −0.371647
\(725\) 0 0
\(726\) 0 0
\(727\) 17.0000 0.630495 0.315248 0.949009i \(-0.397912\pi\)
0.315248 + 0.949009i \(0.397912\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −30.0000 −1.10959
\(732\) −23.2379 −0.858898
\(733\) −30.9839 −1.14442 −0.572208 0.820109i \(-0.693913\pi\)
−0.572208 + 0.820109i \(0.693913\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −7.74597 −0.284940 −0.142470 0.989799i \(-0.545504\pi\)
−0.142470 + 0.989799i \(0.545504\pi\)
\(740\) 0 0
\(741\) −15.0000 −0.551039
\(742\) 0 0
\(743\) −23.2379 −0.852516 −0.426258 0.904602i \(-0.640168\pi\)
−0.426258 + 0.904602i \(0.640168\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 7.74597 0.283410
\(748\) 0 0
\(749\) 30.0000 1.09618
\(750\) 0 0
\(751\) −8.00000 −0.291924 −0.145962 0.989290i \(-0.546628\pi\)
−0.145962 + 0.989290i \(0.546628\pi\)
\(752\) −48.0000 −1.75038
\(753\) 18.0000 0.655956
\(754\) 0 0
\(755\) 0 0
\(756\) −7.74597 −0.281718
\(757\) 17.0000 0.617876 0.308938 0.951082i \(-0.400027\pi\)
0.308938 + 0.951082i \(0.400027\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 54.2218 1.96554 0.982769 0.184839i \(-0.0591765\pi\)
0.982769 + 0.184839i \(0.0591765\pi\)
\(762\) 0 0
\(763\) −15.0000 −0.543036
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 16.0000 0.577350
\(769\) −19.3649 −0.698317 −0.349158 0.937064i \(-0.613532\pi\)
−0.349158 + 0.937064i \(0.613532\pi\)
\(770\) 0 0
\(771\) −12.0000 −0.432169
\(772\) −23.2379 −0.836350
\(773\) −6.00000 −0.215805 −0.107903 0.994161i \(-0.534413\pi\)
−0.107903 + 0.994161i \(0.534413\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 7.74597 0.277885
\(778\) 0 0
\(779\) −30.0000 −1.07486
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 7.74597 0.276818
\(784\) 32.0000 1.14286
\(785\) 0 0
\(786\) 0 0
\(787\) −11.6190 −0.414171 −0.207085 0.978323i \(-0.566398\pi\)
−0.207085 + 0.978323i \(0.566398\pi\)
\(788\) 30.9839 1.10375
\(789\) 23.2379 0.827291
\(790\) 0 0
\(791\) 23.2379 0.826245
\(792\) 0 0
\(793\) −45.0000 −1.59800
\(794\) 0 0
\(795\) 0 0
\(796\) −50.0000 −1.77220
\(797\) 12.0000 0.425062 0.212531 0.977154i \(-0.431829\pi\)
0.212531 + 0.977154i \(0.431829\pi\)
\(798\) 0 0
\(799\) 92.9516 3.28839
\(800\) 0 0
\(801\) 6.00000 0.212000
\(802\) 0 0
\(803\) 0 0
\(804\) 14.0000 0.493742
\(805\) 0 0
\(806\) 0 0
\(807\) 30.0000 1.05605
\(808\) 0 0
\(809\) 15.4919 0.544667 0.272334 0.962203i \(-0.412205\pi\)
0.272334 + 0.962203i \(0.412205\pi\)
\(810\) 0 0
\(811\) 3.87298 0.135999 0.0679994 0.997685i \(-0.478338\pi\)
0.0679994 + 0.997685i \(0.478338\pi\)
\(812\) −60.0000 −2.10559
\(813\) −23.2379 −0.814989
\(814\) 0 0
\(815\) 0 0
\(816\) −30.9839 −1.08465
\(817\) 15.0000 0.524784
\(818\) 0 0
\(819\) −15.0000 −0.524142
\(820\) 0 0
\(821\) −46.4758 −1.62202 −0.811008 0.585035i \(-0.801081\pi\)
−0.811008 + 0.585035i \(0.801081\pi\)
\(822\) 0 0
\(823\) 31.0000 1.08059 0.540296 0.841475i \(-0.318312\pi\)
0.540296 + 0.841475i \(0.318312\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 23.2379 0.808061 0.404030 0.914746i \(-0.367609\pi\)
0.404030 + 0.914746i \(0.367609\pi\)
\(828\) −12.0000 −0.417029
\(829\) 14.0000 0.486240 0.243120 0.969996i \(-0.421829\pi\)
0.243120 + 0.969996i \(0.421829\pi\)
\(830\) 0 0
\(831\) −27.1109 −0.940466
\(832\) 30.9839 1.07417
\(833\) −61.9677 −2.14705
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −5.00000 −0.172825
\(838\) 0 0
\(839\) −30.0000 −1.03572 −0.517858 0.855467i \(-0.673270\pi\)
−0.517858 + 0.855467i \(0.673270\pi\)
\(840\) 0 0
\(841\) 31.0000 1.06897
\(842\) 0 0
\(843\) 0 0
\(844\) −38.7298 −1.33314
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 24.0000 0.824163
\(849\) 3.87298 0.132920
\(850\) 0 0
\(851\) 12.0000 0.411355
\(852\) −24.0000 −0.822226
\(853\) −11.6190 −0.397825 −0.198913 0.980017i \(-0.563741\pi\)
−0.198913 + 0.980017i \(0.563741\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −23.2379 −0.793792 −0.396896 0.917864i \(-0.629913\pi\)
−0.396896 + 0.917864i \(0.629913\pi\)
\(858\) 0 0
\(859\) 44.0000 1.50126 0.750630 0.660722i \(-0.229750\pi\)
0.750630 + 0.660722i \(0.229750\pi\)
\(860\) 0 0
\(861\) −30.0000 −1.02240
\(862\) 0 0
\(863\) −36.0000 −1.22545 −0.612727 0.790295i \(-0.709928\pi\)
−0.612727 + 0.790295i \(0.709928\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 43.0000 1.46036
\(868\) 38.7298 1.31458
\(869\) 0 0
\(870\) 0 0
\(871\) 27.1109 0.918617
\(872\) 0 0
\(873\) 7.00000 0.236914
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 19.3649 0.653907 0.326953 0.945040i \(-0.393978\pi\)
0.326953 + 0.945040i \(0.393978\pi\)
\(878\) 0 0
\(879\) −23.2379 −0.783795
\(880\) 0 0
\(881\) −18.0000 −0.606435 −0.303218 0.952921i \(-0.598061\pi\)
−0.303218 + 0.952921i \(0.598061\pi\)
\(882\) 0 0
\(883\) 29.0000 0.975928 0.487964 0.872864i \(-0.337740\pi\)
0.487964 + 0.872864i \(0.337740\pi\)
\(884\) −60.0000 −2.01802
\(885\) 0 0
\(886\) 0 0
\(887\) 7.74597 0.260084 0.130042 0.991508i \(-0.458489\pi\)
0.130042 + 0.991508i \(0.458489\pi\)
\(888\) 0 0
\(889\) 30.0000 1.00617
\(890\) 0 0
\(891\) 0 0
\(892\) −38.0000 −1.27233
\(893\) −46.4758 −1.55525
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −23.2379 −0.775891
\(898\) 0 0
\(899\) −38.7298 −1.29171
\(900\) 0 0
\(901\) −46.4758 −1.54833
\(902\) 0 0
\(903\) 15.0000 0.499169
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 28.0000 0.929725 0.464862 0.885383i \(-0.346104\pi\)
0.464862 + 0.885383i \(0.346104\pi\)
\(908\) −30.9839 −1.02824
\(909\) −15.4919 −0.513835
\(910\) 0 0
\(911\) 30.0000 0.993944 0.496972 0.867766i \(-0.334445\pi\)
0.496972 + 0.867766i \(0.334445\pi\)
\(912\) 15.4919 0.512989
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 10.0000 0.330409
\(917\) −30.0000 −0.990687
\(918\) 0 0
\(919\) −11.6190 −0.383274 −0.191637 0.981466i \(-0.561380\pi\)
−0.191637 + 0.981466i \(0.561380\pi\)
\(920\) 0 0
\(921\) 11.6190 0.382857
\(922\) 0 0
\(923\) −46.4758 −1.52977
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 16.0000 0.525509
\(928\) 0 0
\(929\) 60.0000 1.96854 0.984268 0.176682i \(-0.0565363\pi\)
0.984268 + 0.176682i \(0.0565363\pi\)
\(930\) 0 0
\(931\) 30.9839 1.01546
\(932\) 30.9839 1.01491
\(933\) 18.0000 0.589294
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −27.1109 −0.885674 −0.442837 0.896602i \(-0.646028\pi\)
−0.442837 + 0.896602i \(0.646028\pi\)
\(938\) 0 0
\(939\) −1.00000 −0.0326338
\(940\) 0 0
\(941\) −30.9839 −1.01005 −0.505023 0.863106i \(-0.668516\pi\)
−0.505023 + 0.863106i \(0.668516\pi\)
\(942\) 0 0
\(943\) −46.4758 −1.51346
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −18.0000 −0.584921 −0.292461 0.956278i \(-0.594474\pi\)
−0.292461 + 0.956278i \(0.594474\pi\)
\(948\) −15.4919 −0.503155
\(949\) 0 0
\(950\) 0 0
\(951\) 18.0000 0.583690
\(952\) 0 0
\(953\) 7.74597 0.250916 0.125458 0.992099i \(-0.459960\pi\)
0.125458 + 0.992099i \(0.459960\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 46.4758 1.50313
\(957\) 0 0
\(958\) 0 0
\(959\) 46.4758 1.50078
\(960\) 0 0
\(961\) −6.00000 −0.193548
\(962\) 0 0
\(963\) 7.74597 0.249610
\(964\) −54.2218 −1.74637
\(965\) 0 0
\(966\) 0 0
\(967\) 23.2379 0.747280 0.373640 0.927574i \(-0.378109\pi\)
0.373640 + 0.927574i \(0.378109\pi\)
\(968\) 0 0
\(969\) −30.0000 −0.963739
\(970\) 0 0
\(971\) −30.0000 −0.962746 −0.481373 0.876516i \(-0.659862\pi\)
−0.481373 + 0.876516i \(0.659862\pi\)
\(972\) −2.00000 −0.0641500
\(973\) −30.0000 −0.961756
\(974\) 0 0
\(975\) 0 0
\(976\) 46.4758 1.48765
\(977\) −42.0000 −1.34370 −0.671850 0.740688i \(-0.734500\pi\)
−0.671850 + 0.740688i \(0.734500\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −3.87298 −0.123655
\(982\) 0 0
\(983\) −24.0000 −0.765481 −0.382741 0.923856i \(-0.625020\pi\)
−0.382741 + 0.923856i \(0.625020\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −46.4758 −1.47934
\(988\) 30.0000 0.954427
\(989\) 23.2379 0.738922
\(990\) 0 0
\(991\) 55.0000 1.74713 0.873566 0.486705i \(-0.161801\pi\)
0.873566 + 0.486705i \(0.161801\pi\)
\(992\) 0 0
\(993\) 20.0000 0.634681
\(994\) 0 0
\(995\) 0 0
\(996\) −15.4919 −0.490881
\(997\) −46.4758 −1.47190 −0.735952 0.677034i \(-0.763265\pi\)
−0.735952 + 0.677034i \(0.763265\pi\)
\(998\) 0 0
\(999\) 2.00000 0.0632772
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 9075.2.a.bm.1.2 yes 2
5.4 even 2 9075.2.a.bf.1.1 2
11.10 odd 2 inner 9075.2.a.bm.1.1 yes 2
55.54 odd 2 9075.2.a.bf.1.2 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9075.2.a.bf.1.1 2 5.4 even 2
9075.2.a.bf.1.2 yes 2 55.54 odd 2
9075.2.a.bm.1.1 yes 2 11.10 odd 2 inner
9075.2.a.bm.1.2 yes 2 1.1 even 1 trivial