Properties

Label 7448.2.a.bq.1.7
Level $7448$
Weight $2$
Character 7448.1
Self dual yes
Analytic conductor $59.473$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - 15 x^{6} - x^{5} + 66 x^{4} + 4 x^{3} - 76 x^{2} + 8 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 1064)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(2.39016\) of defining polynomial
Character \(\chi\) \(=\) 7448.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.39016 q^{3} +3.25179 q^{5} +2.71288 q^{9} +O(q^{10})\) \(q+2.39016 q^{3} +3.25179 q^{5} +2.71288 q^{9} -0.402893 q^{11} -1.63029 q^{13} +7.77230 q^{15} +4.43555 q^{17} +1.00000 q^{19} +0.837228 q^{23} +5.57412 q^{25} -0.686255 q^{27} -5.33215 q^{29} +3.16041 q^{31} -0.962981 q^{33} +11.4262 q^{37} -3.89665 q^{39} -2.00000 q^{41} +1.93761 q^{43} +8.82172 q^{45} +12.6484 q^{47} +10.6017 q^{51} -11.5064 q^{53} -1.31012 q^{55} +2.39016 q^{57} +5.16962 q^{59} +0.126407 q^{61} -5.30134 q^{65} -2.47276 q^{67} +2.00111 q^{69} -2.17338 q^{71} +12.5196 q^{73} +13.3231 q^{75} -4.40025 q^{79} -9.77891 q^{81} -1.87386 q^{83} +14.4235 q^{85} -12.7447 q^{87} +14.5852 q^{89} +7.55389 q^{93} +3.25179 q^{95} -7.50694 q^{97} -1.09300 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - q^{5} + 6q^{9} + O(q^{10}) \) \( 8q - q^{5} + 6q^{9} + 9q^{11} + 8q^{15} + 4q^{17} + 8q^{19} + 25q^{23} + 15q^{25} + 3q^{27} + 6q^{29} + 8q^{33} + 13q^{37} - 11q^{39} - 16q^{41} + 17q^{43} + 17q^{45} - 24q^{47} + 5q^{51} + 2q^{53} + 5q^{55} + 2q^{59} - 13q^{61} - 26q^{65} + 2q^{67} - 11q^{69} + 10q^{71} + 5q^{73} - 20q^{75} + 16q^{79} - 12q^{81} - 43q^{83} + 24q^{85} + 20q^{87} + 8q^{89} + 2q^{93} - q^{95} - 12q^{97} + 37q^{99} + O(q^{100}) \)

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
\(3\) 2.39016 1.37996 0.689981 0.723828i \(-0.257619\pi\)
0.689981 + 0.723828i \(0.257619\pi\)
\(4\) 0 0
\(5\) 3.25179 1.45424 0.727122 0.686509i \(-0.240858\pi\)
0.727122 + 0.686509i \(0.240858\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 2.71288 0.904295
\(10\) 0 0
\(11\) −0.402893 −0.121477 −0.0607385 0.998154i \(-0.519346\pi\)
−0.0607385 + 0.998154i \(0.519346\pi\)
\(12\) 0 0
\(13\) −1.63029 −0.452160 −0.226080 0.974109i \(-0.572591\pi\)
−0.226080 + 0.974109i \(0.572591\pi\)
\(14\) 0 0
\(15\) 7.77230 2.00680
\(16\) 0 0
\(17\) 4.43555 1.07578 0.537890 0.843015i \(-0.319222\pi\)
0.537890 + 0.843015i \(0.319222\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.837228 0.174574 0.0872870 0.996183i \(-0.472180\pi\)
0.0872870 + 0.996183i \(0.472180\pi\)
\(24\) 0 0
\(25\) 5.57412 1.11482
\(26\) 0 0
\(27\) −0.686255 −0.132070
\(28\) 0 0
\(29\) −5.33215 −0.990156 −0.495078 0.868849i \(-0.664860\pi\)
−0.495078 + 0.868849i \(0.664860\pi\)
\(30\) 0 0
\(31\) 3.16041 0.567626 0.283813 0.958880i \(-0.408401\pi\)
0.283813 + 0.958880i \(0.408401\pi\)
\(32\) 0 0
\(33\) −0.962981 −0.167634
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 11.4262 1.87846 0.939230 0.343289i \(-0.111541\pi\)
0.939230 + 0.343289i \(0.111541\pi\)
\(38\) 0 0
\(39\) −3.89665 −0.623963
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) 1.93761 0.295483 0.147742 0.989026i \(-0.452800\pi\)
0.147742 + 0.989026i \(0.452800\pi\)
\(44\) 0 0
\(45\) 8.82172 1.31506
\(46\) 0 0
\(47\) 12.6484 1.84496 0.922479 0.386048i \(-0.126160\pi\)
0.922479 + 0.386048i \(0.126160\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 10.6017 1.48453
\(52\) 0 0
\(53\) −11.5064 −1.58053 −0.790263 0.612768i \(-0.790056\pi\)
−0.790263 + 0.612768i \(0.790056\pi\)
\(54\) 0 0
\(55\) −1.31012 −0.176657
\(56\) 0 0
\(57\) 2.39016 0.316585
\(58\) 0 0
\(59\) 5.16962 0.673027 0.336514 0.941679i \(-0.390752\pi\)
0.336514 + 0.941679i \(0.390752\pi\)
\(60\) 0 0
\(61\) 0.126407 0.0161848 0.00809239 0.999967i \(-0.497424\pi\)
0.00809239 + 0.999967i \(0.497424\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −5.30134 −0.657550
\(66\) 0 0
\(67\) −2.47276 −0.302096 −0.151048 0.988526i \(-0.548265\pi\)
−0.151048 + 0.988526i \(0.548265\pi\)
\(68\) 0 0
\(69\) 2.00111 0.240906
\(70\) 0 0
\(71\) −2.17338 −0.257932 −0.128966 0.991649i \(-0.541166\pi\)
−0.128966 + 0.991649i \(0.541166\pi\)
\(72\) 0 0
\(73\) 12.5196 1.46531 0.732657 0.680598i \(-0.238280\pi\)
0.732657 + 0.680598i \(0.238280\pi\)
\(74\) 0 0
\(75\) 13.3231 1.53841
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −4.40025 −0.495067 −0.247533 0.968879i \(-0.579620\pi\)
−0.247533 + 0.968879i \(0.579620\pi\)
\(80\) 0 0
\(81\) −9.77891 −1.08655
\(82\) 0 0
\(83\) −1.87386 −0.205683 −0.102841 0.994698i \(-0.532793\pi\)
−0.102841 + 0.994698i \(0.532793\pi\)
\(84\) 0 0
\(85\) 14.4235 1.56445
\(86\) 0 0
\(87\) −12.7447 −1.36638
\(88\) 0 0
\(89\) 14.5852 1.54603 0.773016 0.634386i \(-0.218747\pi\)
0.773016 + 0.634386i \(0.218747\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 7.55389 0.783302
\(94\) 0 0
\(95\) 3.25179 0.333626
\(96\) 0 0
\(97\) −7.50694 −0.762215 −0.381107 0.924531i \(-0.624457\pi\)
−0.381107 + 0.924531i \(0.624457\pi\)
\(98\) 0 0
\(99\) −1.09300 −0.109851
\(100\) 0 0
\(101\) −3.20460 −0.318869 −0.159435 0.987208i \(-0.550967\pi\)
−0.159435 + 0.987208i \(0.550967\pi\)
\(102\) 0 0
\(103\) 5.83695 0.575132 0.287566 0.957761i \(-0.407154\pi\)
0.287566 + 0.957761i \(0.407154\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 15.3526 1.48419 0.742096 0.670294i \(-0.233832\pi\)
0.742096 + 0.670294i \(0.233832\pi\)
\(108\) 0 0
\(109\) 11.9238 1.14209 0.571046 0.820918i \(-0.306538\pi\)
0.571046 + 0.820918i \(0.306538\pi\)
\(110\) 0 0
\(111\) 27.3106 2.59220
\(112\) 0 0
\(113\) −19.0112 −1.78842 −0.894210 0.447648i \(-0.852262\pi\)
−0.894210 + 0.447648i \(0.852262\pi\)
\(114\) 0 0
\(115\) 2.72249 0.253873
\(116\) 0 0
\(117\) −4.42277 −0.408886
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −10.8377 −0.985243
\(122\) 0 0
\(123\) −4.78033 −0.431028
\(124\) 0 0
\(125\) 1.86692 0.166982
\(126\) 0 0
\(127\) 7.16086 0.635424 0.317712 0.948187i \(-0.397086\pi\)
0.317712 + 0.948187i \(0.397086\pi\)
\(128\) 0 0
\(129\) 4.63122 0.407756
\(130\) 0 0
\(131\) −1.96032 −0.171274 −0.0856370 0.996326i \(-0.527293\pi\)
−0.0856370 + 0.996326i \(0.527293\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −2.23155 −0.192062
\(136\) 0 0
\(137\) −16.1077 −1.37618 −0.688088 0.725627i \(-0.741550\pi\)
−0.688088 + 0.725627i \(0.741550\pi\)
\(138\) 0 0
\(139\) −2.58462 −0.219224 −0.109612 0.993974i \(-0.534961\pi\)
−0.109612 + 0.993974i \(0.534961\pi\)
\(140\) 0 0
\(141\) 30.2317 2.54597
\(142\) 0 0
\(143\) 0.656831 0.0549270
\(144\) 0 0
\(145\) −17.3390 −1.43993
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −9.68077 −0.793079 −0.396540 0.918018i \(-0.629789\pi\)
−0.396540 + 0.918018i \(0.629789\pi\)
\(150\) 0 0
\(151\) 3.90440 0.317735 0.158868 0.987300i \(-0.449216\pi\)
0.158868 + 0.987300i \(0.449216\pi\)
\(152\) 0 0
\(153\) 12.0331 0.972822
\(154\) 0 0
\(155\) 10.2770 0.825466
\(156\) 0 0
\(157\) 15.0349 1.19991 0.599956 0.800033i \(-0.295185\pi\)
0.599956 + 0.800033i \(0.295185\pi\)
\(158\) 0 0
\(159\) −27.5022 −2.18106
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −17.1071 −1.33993 −0.669964 0.742394i \(-0.733691\pi\)
−0.669964 + 0.742394i \(0.733691\pi\)
\(164\) 0 0
\(165\) −3.13141 −0.243780
\(166\) 0 0
\(167\) 9.06642 0.701580 0.350790 0.936454i \(-0.385913\pi\)
0.350790 + 0.936454i \(0.385913\pi\)
\(168\) 0 0
\(169\) −10.3422 −0.795552
\(170\) 0 0
\(171\) 2.71288 0.207459
\(172\) 0 0
\(173\) 11.2856 0.858025 0.429013 0.903299i \(-0.358862\pi\)
0.429013 + 0.903299i \(0.358862\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 12.3562 0.928752
\(178\) 0 0
\(179\) 23.4591 1.75342 0.876709 0.481022i \(-0.159734\pi\)
0.876709 + 0.481022i \(0.159734\pi\)
\(180\) 0 0
\(181\) −5.24897 −0.390153 −0.195076 0.980788i \(-0.562495\pi\)
−0.195076 + 0.980788i \(0.562495\pi\)
\(182\) 0 0
\(183\) 0.302134 0.0223344
\(184\) 0 0
\(185\) 37.1557 2.73174
\(186\) 0 0
\(187\) −1.78705 −0.130682
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −19.4213 −1.40528 −0.702640 0.711546i \(-0.747995\pi\)
−0.702640 + 0.711546i \(0.747995\pi\)
\(192\) 0 0
\(193\) −5.89056 −0.424012 −0.212006 0.977268i \(-0.568000\pi\)
−0.212006 + 0.977268i \(0.568000\pi\)
\(194\) 0 0
\(195\) −12.6711 −0.907394
\(196\) 0 0
\(197\) 0.994596 0.0708620 0.0354310 0.999372i \(-0.488720\pi\)
0.0354310 + 0.999372i \(0.488720\pi\)
\(198\) 0 0
\(199\) 0.596351 0.0422742 0.0211371 0.999777i \(-0.493271\pi\)
0.0211371 + 0.999777i \(0.493271\pi\)
\(200\) 0 0
\(201\) −5.91031 −0.416881
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −6.50357 −0.454229
\(206\) 0 0
\(207\) 2.27130 0.157866
\(208\) 0 0
\(209\) −0.402893 −0.0278687
\(210\) 0 0
\(211\) 12.2877 0.845921 0.422960 0.906148i \(-0.360991\pi\)
0.422960 + 0.906148i \(0.360991\pi\)
\(212\) 0 0
\(213\) −5.19472 −0.355937
\(214\) 0 0
\(215\) 6.30071 0.429705
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 29.9240 2.02208
\(220\) 0 0
\(221\) −7.23121 −0.486424
\(222\) 0 0
\(223\) −9.41919 −0.630755 −0.315378 0.948966i \(-0.602131\pi\)
−0.315378 + 0.948966i \(0.602131\pi\)
\(224\) 0 0
\(225\) 15.1219 1.00813
\(226\) 0 0
\(227\) 7.22445 0.479504 0.239752 0.970834i \(-0.422934\pi\)
0.239752 + 0.970834i \(0.422934\pi\)
\(228\) 0 0
\(229\) 5.55832 0.367304 0.183652 0.982991i \(-0.441208\pi\)
0.183652 + 0.982991i \(0.441208\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 11.5357 0.755728 0.377864 0.925861i \(-0.376659\pi\)
0.377864 + 0.925861i \(0.376659\pi\)
\(234\) 0 0
\(235\) 41.1299 2.68302
\(236\) 0 0
\(237\) −10.5173 −0.683173
\(238\) 0 0
\(239\) 28.9484 1.87252 0.936259 0.351309i \(-0.114263\pi\)
0.936259 + 0.351309i \(0.114263\pi\)
\(240\) 0 0
\(241\) 22.2792 1.43513 0.717566 0.696491i \(-0.245256\pi\)
0.717566 + 0.696491i \(0.245256\pi\)
\(242\) 0 0
\(243\) −21.3144 −1.36732
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −1.63029 −0.103733
\(248\) 0 0
\(249\) −4.47883 −0.283834
\(250\) 0 0
\(251\) −6.67790 −0.421505 −0.210753 0.977539i \(-0.567591\pi\)
−0.210753 + 0.977539i \(0.567591\pi\)
\(252\) 0 0
\(253\) −0.337314 −0.0212067
\(254\) 0 0
\(255\) 34.4745 2.15887
\(256\) 0 0
\(257\) −27.8378 −1.73647 −0.868236 0.496151i \(-0.834746\pi\)
−0.868236 + 0.496151i \(0.834746\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −14.4655 −0.895393
\(262\) 0 0
\(263\) −2.85226 −0.175878 −0.0879388 0.996126i \(-0.528028\pi\)
−0.0879388 + 0.996126i \(0.528028\pi\)
\(264\) 0 0
\(265\) −37.4164 −2.29847
\(266\) 0 0
\(267\) 34.8611 2.13347
\(268\) 0 0
\(269\) 8.38500 0.511242 0.255621 0.966777i \(-0.417720\pi\)
0.255621 + 0.966777i \(0.417720\pi\)
\(270\) 0 0
\(271\) −14.2567 −0.866035 −0.433017 0.901386i \(-0.642551\pi\)
−0.433017 + 0.901386i \(0.642551\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.24578 −0.135425
\(276\) 0 0
\(277\) −25.3389 −1.52247 −0.761233 0.648479i \(-0.775406\pi\)
−0.761233 + 0.648479i \(0.775406\pi\)
\(278\) 0 0
\(279\) 8.57381 0.513301
\(280\) 0 0
\(281\) 19.0107 1.13408 0.567041 0.823689i \(-0.308088\pi\)
0.567041 + 0.823689i \(0.308088\pi\)
\(282\) 0 0
\(283\) −23.5330 −1.39889 −0.699447 0.714684i \(-0.746570\pi\)
−0.699447 + 0.714684i \(0.746570\pi\)
\(284\) 0 0
\(285\) 7.77230 0.460392
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 2.67412 0.157301
\(290\) 0 0
\(291\) −17.9428 −1.05183
\(292\) 0 0
\(293\) −11.1260 −0.649989 −0.324995 0.945716i \(-0.605362\pi\)
−0.324995 + 0.945716i \(0.605362\pi\)
\(294\) 0 0
\(295\) 16.8105 0.978746
\(296\) 0 0
\(297\) 0.276487 0.0160434
\(298\) 0 0
\(299\) −1.36492 −0.0789354
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −7.65951 −0.440028
\(304\) 0 0
\(305\) 0.411049 0.0235366
\(306\) 0 0
\(307\) 26.8920 1.53481 0.767404 0.641164i \(-0.221548\pi\)
0.767404 + 0.641164i \(0.221548\pi\)
\(308\) 0 0
\(309\) 13.9513 0.793660
\(310\) 0 0
\(311\) −25.0433 −1.42007 −0.710036 0.704165i \(-0.751322\pi\)
−0.710036 + 0.704165i \(0.751322\pi\)
\(312\) 0 0
\(313\) −12.8379 −0.725642 −0.362821 0.931859i \(-0.618186\pi\)
−0.362821 + 0.931859i \(0.618186\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −12.4850 −0.701226 −0.350613 0.936520i \(-0.614027\pi\)
−0.350613 + 0.936520i \(0.614027\pi\)
\(318\) 0 0
\(319\) 2.14829 0.120281
\(320\) 0 0
\(321\) 36.6952 2.04813
\(322\) 0 0
\(323\) 4.43555 0.246801
\(324\) 0 0
\(325\) −9.08741 −0.504079
\(326\) 0 0
\(327\) 28.4998 1.57604
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 6.22963 0.342412 0.171206 0.985235i \(-0.445234\pi\)
0.171206 + 0.985235i \(0.445234\pi\)
\(332\) 0 0
\(333\) 30.9980 1.69868
\(334\) 0 0
\(335\) −8.04090 −0.439321
\(336\) 0 0
\(337\) −26.0259 −1.41772 −0.708860 0.705349i \(-0.750790\pi\)
−0.708860 + 0.705349i \(0.750790\pi\)
\(338\) 0 0
\(339\) −45.4398 −2.46795
\(340\) 0 0
\(341\) −1.27331 −0.0689534
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 6.50719 0.350335
\(346\) 0 0
\(347\) 9.20710 0.494263 0.247132 0.968982i \(-0.420512\pi\)
0.247132 + 0.968982i \(0.420512\pi\)
\(348\) 0 0
\(349\) −26.8773 −1.43871 −0.719354 0.694643i \(-0.755562\pi\)
−0.719354 + 0.694643i \(0.755562\pi\)
\(350\) 0 0
\(351\) 1.11879 0.0597166
\(352\) 0 0
\(353\) −20.7203 −1.10283 −0.551416 0.834231i \(-0.685912\pi\)
−0.551416 + 0.834231i \(0.685912\pi\)
\(354\) 0 0
\(355\) −7.06735 −0.375096
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −20.6693 −1.09088 −0.545442 0.838149i \(-0.683638\pi\)
−0.545442 + 0.838149i \(0.683638\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −25.9038 −1.35960
\(364\) 0 0
\(365\) 40.7112 2.13092
\(366\) 0 0
\(367\) −33.8926 −1.76918 −0.884590 0.466369i \(-0.845562\pi\)
−0.884590 + 0.466369i \(0.845562\pi\)
\(368\) 0 0
\(369\) −5.42577 −0.282454
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 27.0170 1.39889 0.699444 0.714687i \(-0.253431\pi\)
0.699444 + 0.714687i \(0.253431\pi\)
\(374\) 0 0
\(375\) 4.46224 0.230429
\(376\) 0 0
\(377\) 8.69293 0.447709
\(378\) 0 0
\(379\) −16.8406 −0.865041 −0.432521 0.901624i \(-0.642376\pi\)
−0.432521 + 0.901624i \(0.642376\pi\)
\(380\) 0 0
\(381\) 17.1156 0.876860
\(382\) 0 0
\(383\) −33.9718 −1.73588 −0.867940 0.496670i \(-0.834556\pi\)
−0.867940 + 0.496670i \(0.834556\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 5.25652 0.267204
\(388\) 0 0
\(389\) −11.6846 −0.592433 −0.296217 0.955121i \(-0.595725\pi\)
−0.296217 + 0.955121i \(0.595725\pi\)
\(390\) 0 0
\(391\) 3.71357 0.187803
\(392\) 0 0
\(393\) −4.68549 −0.236351
\(394\) 0 0
\(395\) −14.3087 −0.719948
\(396\) 0 0
\(397\) −10.0177 −0.502776 −0.251388 0.967886i \(-0.580887\pi\)
−0.251388 + 0.967886i \(0.580887\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 10.4698 0.522835 0.261417 0.965226i \(-0.415810\pi\)
0.261417 + 0.965226i \(0.415810\pi\)
\(402\) 0 0
\(403\) −5.15236 −0.256657
\(404\) 0 0
\(405\) −31.7989 −1.58010
\(406\) 0 0
\(407\) −4.60355 −0.228190
\(408\) 0 0
\(409\) −24.0093 −1.18719 −0.593593 0.804766i \(-0.702291\pi\)
−0.593593 + 0.804766i \(0.702291\pi\)
\(410\) 0 0
\(411\) −38.5001 −1.89907
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −6.09339 −0.299113
\(416\) 0 0
\(417\) −6.17766 −0.302521
\(418\) 0 0
\(419\) −15.1723 −0.741216 −0.370608 0.928789i \(-0.620851\pi\)
−0.370608 + 0.928789i \(0.620851\pi\)
\(420\) 0 0
\(421\) 1.77965 0.0867348 0.0433674 0.999059i \(-0.486191\pi\)
0.0433674 + 0.999059i \(0.486191\pi\)
\(422\) 0 0
\(423\) 34.3136 1.66838
\(424\) 0 0
\(425\) 24.7243 1.19930
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 1.56993 0.0757971
\(430\) 0 0
\(431\) 32.7349 1.57678 0.788392 0.615173i \(-0.210914\pi\)
0.788392 + 0.615173i \(0.210914\pi\)
\(432\) 0 0
\(433\) −4.83058 −0.232143 −0.116071 0.993241i \(-0.537030\pi\)
−0.116071 + 0.993241i \(0.537030\pi\)
\(434\) 0 0
\(435\) −41.4431 −1.98705
\(436\) 0 0
\(437\) 0.837228 0.0400500
\(438\) 0 0
\(439\) 28.3595 1.35352 0.676762 0.736202i \(-0.263383\pi\)
0.676762 + 0.736202i \(0.263383\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 19.2801 0.916026 0.458013 0.888945i \(-0.348561\pi\)
0.458013 + 0.888945i \(0.348561\pi\)
\(444\) 0 0
\(445\) 47.4281 2.24831
\(446\) 0 0
\(447\) −23.1386 −1.09442
\(448\) 0 0
\(449\) −16.0035 −0.755254 −0.377627 0.925958i \(-0.623260\pi\)
−0.377627 + 0.925958i \(0.623260\pi\)
\(450\) 0 0
\(451\) 0.805787 0.0379430
\(452\) 0 0
\(453\) 9.33215 0.438463
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 24.0347 1.12430 0.562148 0.827037i \(-0.309975\pi\)
0.562148 + 0.827037i \(0.309975\pi\)
\(458\) 0 0
\(459\) −3.04392 −0.142078
\(460\) 0 0
\(461\) 27.2907 1.27106 0.635528 0.772078i \(-0.280782\pi\)
0.635528 + 0.772078i \(0.280782\pi\)
\(462\) 0 0
\(463\) −25.5689 −1.18829 −0.594143 0.804359i \(-0.702509\pi\)
−0.594143 + 0.804359i \(0.702509\pi\)
\(464\) 0 0
\(465\) 24.5636 1.13911
\(466\) 0 0
\(467\) −9.70285 −0.448994 −0.224497 0.974475i \(-0.572074\pi\)
−0.224497 + 0.974475i \(0.572074\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 35.9358 1.65583
\(472\) 0 0
\(473\) −0.780652 −0.0358944
\(474\) 0 0
\(475\) 5.57412 0.255758
\(476\) 0 0
\(477\) −31.2155 −1.42926
\(478\) 0 0
\(479\) 27.5030 1.25665 0.628323 0.777953i \(-0.283742\pi\)
0.628323 + 0.777953i \(0.283742\pi\)
\(480\) 0 0
\(481\) −18.6280 −0.849364
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −24.4110 −1.10845
\(486\) 0 0
\(487\) 6.77476 0.306993 0.153497 0.988149i \(-0.450947\pi\)
0.153497 + 0.988149i \(0.450947\pi\)
\(488\) 0 0
\(489\) −40.8887 −1.84905
\(490\) 0 0
\(491\) −41.5603 −1.87559 −0.937796 0.347188i \(-0.887137\pi\)
−0.937796 + 0.347188i \(0.887137\pi\)
\(492\) 0 0
\(493\) −23.6510 −1.06519
\(494\) 0 0
\(495\) −3.55421 −0.159750
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −15.7228 −0.703849 −0.351924 0.936028i \(-0.614473\pi\)
−0.351924 + 0.936028i \(0.614473\pi\)
\(500\) 0 0
\(501\) 21.6702 0.968154
\(502\) 0 0
\(503\) 14.0804 0.627813 0.313906 0.949454i \(-0.398362\pi\)
0.313906 + 0.949454i \(0.398362\pi\)
\(504\) 0 0
\(505\) −10.4207 −0.463714
\(506\) 0 0
\(507\) −24.7195 −1.09783
\(508\) 0 0
\(509\) 33.4327 1.48188 0.740939 0.671572i \(-0.234381\pi\)
0.740939 + 0.671572i \(0.234381\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −0.686255 −0.0302989
\(514\) 0 0
\(515\) 18.9805 0.836382
\(516\) 0 0
\(517\) −5.09595 −0.224120
\(518\) 0 0
\(519\) 26.9743 1.18404
\(520\) 0 0
\(521\) −24.8389 −1.08821 −0.544106 0.839017i \(-0.683131\pi\)
−0.544106 + 0.839017i \(0.683131\pi\)
\(522\) 0 0
\(523\) −18.6377 −0.814971 −0.407486 0.913212i \(-0.633594\pi\)
−0.407486 + 0.913212i \(0.633594\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 14.0181 0.610640
\(528\) 0 0
\(529\) −22.2990 −0.969524
\(530\) 0 0
\(531\) 14.0246 0.608615
\(532\) 0 0
\(533\) 3.26057 0.141231
\(534\) 0 0
\(535\) 49.9234 2.15838
\(536\) 0 0
\(537\) 56.0711 2.41965
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −25.3612 −1.09036 −0.545181 0.838318i \(-0.683539\pi\)
−0.545181 + 0.838318i \(0.683539\pi\)
\(542\) 0 0
\(543\) −12.5459 −0.538396
\(544\) 0 0
\(545\) 38.7736 1.66088
\(546\) 0 0
\(547\) 30.1315 1.28833 0.644165 0.764886i \(-0.277205\pi\)
0.644165 + 0.764886i \(0.277205\pi\)
\(548\) 0 0
\(549\) 0.342928 0.0146358
\(550\) 0 0
\(551\) −5.33215 −0.227157
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 88.8081 3.76969
\(556\) 0 0
\(557\) 34.5323 1.46318 0.731589 0.681745i \(-0.238779\pi\)
0.731589 + 0.681745i \(0.238779\pi\)
\(558\) 0 0
\(559\) −3.15886 −0.133606
\(560\) 0 0
\(561\) −4.27135 −0.180337
\(562\) 0 0
\(563\) −7.92050 −0.333809 −0.166905 0.985973i \(-0.553377\pi\)
−0.166905 + 0.985973i \(0.553377\pi\)
\(564\) 0 0
\(565\) −61.8203 −2.60080
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 7.33344 0.307434 0.153717 0.988115i \(-0.450876\pi\)
0.153717 + 0.988115i \(0.450876\pi\)
\(570\) 0 0
\(571\) −23.7844 −0.995346 −0.497673 0.867365i \(-0.665812\pi\)
−0.497673 + 0.867365i \(0.665812\pi\)
\(572\) 0 0
\(573\) −46.4202 −1.93923
\(574\) 0 0
\(575\) 4.66681 0.194619
\(576\) 0 0
\(577\) 1.79722 0.0748194 0.0374097 0.999300i \(-0.488089\pi\)
0.0374097 + 0.999300i \(0.488089\pi\)
\(578\) 0 0
\(579\) −14.0794 −0.585120
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 4.63585 0.191997
\(584\) 0 0
\(585\) −14.3819 −0.594619
\(586\) 0 0
\(587\) −40.2209 −1.66009 −0.830046 0.557695i \(-0.811686\pi\)
−0.830046 + 0.557695i \(0.811686\pi\)
\(588\) 0 0
\(589\) 3.16041 0.130222
\(590\) 0 0
\(591\) 2.37725 0.0977869
\(592\) 0 0
\(593\) 9.89240 0.406232 0.203116 0.979155i \(-0.434893\pi\)
0.203116 + 0.979155i \(0.434893\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1.42538 0.0583368
\(598\) 0 0
\(599\) 25.6303 1.04723 0.523613 0.851956i \(-0.324584\pi\)
0.523613 + 0.851956i \(0.324584\pi\)
\(600\) 0 0
\(601\) 31.9887 1.30485 0.652423 0.757855i \(-0.273753\pi\)
0.652423 + 0.757855i \(0.273753\pi\)
\(602\) 0 0
\(603\) −6.70832 −0.273184
\(604\) 0 0
\(605\) −35.2418 −1.43278
\(606\) 0 0
\(607\) −41.4771 −1.68350 −0.841752 0.539864i \(-0.818476\pi\)
−0.841752 + 0.539864i \(0.818476\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −20.6205 −0.834215
\(612\) 0 0
\(613\) 3.33602 0.134741 0.0673703 0.997728i \(-0.478539\pi\)
0.0673703 + 0.997728i \(0.478539\pi\)
\(614\) 0 0
\(615\) −15.5446 −0.626819
\(616\) 0 0
\(617\) 1.45553 0.0585976 0.0292988 0.999571i \(-0.490673\pi\)
0.0292988 + 0.999571i \(0.490673\pi\)
\(618\) 0 0
\(619\) 40.0031 1.60786 0.803931 0.594722i \(-0.202738\pi\)
0.803931 + 0.594722i \(0.202738\pi\)
\(620\) 0 0
\(621\) −0.574552 −0.0230560
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −21.7998 −0.871991
\(626\) 0 0
\(627\) −0.962981 −0.0384578
\(628\) 0 0
\(629\) 50.6816 2.02081
\(630\) 0 0
\(631\) 29.6609 1.18078 0.590390 0.807118i \(-0.298974\pi\)
0.590390 + 0.807118i \(0.298974\pi\)
\(632\) 0 0
\(633\) 29.3696 1.16734
\(634\) 0 0
\(635\) 23.2856 0.924061
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −5.89611 −0.233247
\(640\) 0 0
\(641\) −31.9823 −1.26322 −0.631612 0.775285i \(-0.717606\pi\)
−0.631612 + 0.775285i \(0.717606\pi\)
\(642\) 0 0
\(643\) −19.8251 −0.781825 −0.390912 0.920428i \(-0.627840\pi\)
−0.390912 + 0.920428i \(0.627840\pi\)
\(644\) 0 0
\(645\) 15.0597 0.592976
\(646\) 0 0
\(647\) −18.8753 −0.742064 −0.371032 0.928620i \(-0.620996\pi\)
−0.371032 + 0.928620i \(0.620996\pi\)
\(648\) 0 0
\(649\) −2.08281 −0.0817573
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −2.09633 −0.0820356 −0.0410178 0.999158i \(-0.513060\pi\)
−0.0410178 + 0.999158i \(0.513060\pi\)
\(654\) 0 0
\(655\) −6.37454 −0.249074
\(656\) 0 0
\(657\) 33.9643 1.32507
\(658\) 0 0
\(659\) −37.1279 −1.44630 −0.723148 0.690693i \(-0.757306\pi\)
−0.723148 + 0.690693i \(0.757306\pi\)
\(660\) 0 0
\(661\) −26.8649 −1.04492 −0.522461 0.852663i \(-0.674986\pi\)
−0.522461 + 0.852663i \(0.674986\pi\)
\(662\) 0 0
\(663\) −17.2838 −0.671247
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −4.46423 −0.172856
\(668\) 0 0
\(669\) −22.5134 −0.870418
\(670\) 0 0
\(671\) −0.0509286 −0.00196608
\(672\) 0 0
\(673\) 4.79647 0.184890 0.0924452 0.995718i \(-0.470532\pi\)
0.0924452 + 0.995718i \(0.470532\pi\)
\(674\) 0 0
\(675\) −3.82527 −0.147235
\(676\) 0 0
\(677\) −45.3193 −1.74176 −0.870882 0.491493i \(-0.836451\pi\)
−0.870882 + 0.491493i \(0.836451\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 17.2676 0.661697
\(682\) 0 0
\(683\) 13.6586 0.522631 0.261316 0.965253i \(-0.415844\pi\)
0.261316 + 0.965253i \(0.415844\pi\)
\(684\) 0 0
\(685\) −52.3789 −2.00129
\(686\) 0 0
\(687\) 13.2853 0.506866
\(688\) 0 0
\(689\) 18.7587 0.714650
\(690\) 0 0
\(691\) −9.36288 −0.356181 −0.178090 0.984014i \(-0.556992\pi\)
−0.178090 + 0.984014i \(0.556992\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −8.40463 −0.318806
\(696\) 0 0
\(697\) −8.87110 −0.336017
\(698\) 0 0
\(699\) 27.5722 1.04288
\(700\) 0 0
\(701\) −16.3095 −0.616003 −0.308001 0.951386i \(-0.599660\pi\)
−0.308001 + 0.951386i \(0.599660\pi\)
\(702\) 0 0
\(703\) 11.4262 0.430948
\(704\) 0 0
\(705\) 98.3071 3.70246
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 35.3417 1.32728 0.663642 0.748050i \(-0.269010\pi\)
0.663642 + 0.748050i \(0.269010\pi\)
\(710\) 0 0
\(711\) −11.9374 −0.447686
\(712\) 0 0
\(713\) 2.64598 0.0990927
\(714\) 0 0
\(715\) 2.13587 0.0798772
\(716\) 0 0
\(717\) 69.1915 2.58400
\(718\) 0 0
\(719\) 32.5495 1.21389 0.606946 0.794743i \(-0.292394\pi\)
0.606946 + 0.794743i \(0.292394\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 53.2510 1.98043
\(724\) 0 0
\(725\) −29.7221 −1.10385
\(726\) 0 0
\(727\) −12.5070 −0.463859 −0.231929 0.972733i \(-0.574504\pi\)
−0.231929 + 0.972733i \(0.574504\pi\)
\(728\) 0 0
\(729\) −21.6083 −0.800306
\(730\) 0 0
\(731\) 8.59439 0.317875
\(732\) 0 0
\(733\) 16.8325 0.621721 0.310861 0.950455i \(-0.399383\pi\)
0.310861 + 0.950455i \(0.399383\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.996260 0.0366977
\(738\) 0 0
\(739\) 47.2770 1.73911 0.869556 0.493835i \(-0.164405\pi\)
0.869556 + 0.493835i \(0.164405\pi\)
\(740\) 0 0
\(741\) −3.89665 −0.143147
\(742\) 0 0
\(743\) 29.4769 1.08140 0.540701 0.841215i \(-0.318159\pi\)
0.540701 + 0.841215i \(0.318159\pi\)
\(744\) 0 0
\(745\) −31.4798 −1.15333
\(746\) 0 0
\(747\) −5.08356 −0.185998
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 32.0159 1.16828 0.584138 0.811654i \(-0.301433\pi\)
0.584138 + 0.811654i \(0.301433\pi\)
\(752\) 0 0
\(753\) −15.9613 −0.581661
\(754\) 0 0
\(755\) 12.6963 0.462065
\(756\) 0 0
\(757\) −44.8062 −1.62851 −0.814254 0.580509i \(-0.802854\pi\)
−0.814254 + 0.580509i \(0.802854\pi\)
\(758\) 0 0
\(759\) −0.806235 −0.0292645
\(760\) 0 0
\(761\) −17.4695 −0.633268 −0.316634 0.948548i \(-0.602553\pi\)
−0.316634 + 0.948548i \(0.602553\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 39.1292 1.41472
\(766\) 0 0
\(767\) −8.42796 −0.304316
\(768\) 0 0
\(769\) 18.1746 0.655392 0.327696 0.944783i \(-0.393728\pi\)
0.327696 + 0.944783i \(0.393728\pi\)
\(770\) 0 0
\(771\) −66.5368 −2.39627
\(772\) 0 0
\(773\) 26.7881 0.963500 0.481750 0.876309i \(-0.340001\pi\)
0.481750 + 0.876309i \(0.340001\pi\)
\(774\) 0 0
\(775\) 17.6165 0.632803
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2.00000 −0.0716574
\(780\) 0 0
\(781\) 0.875638 0.0313328
\(782\) 0 0
\(783\) 3.65921 0.130770
\(784\) 0 0
\(785\) 48.8902 1.74496
\(786\) 0 0
\(787\) 32.0878 1.14381 0.571904 0.820320i \(-0.306205\pi\)
0.571904 + 0.820320i \(0.306205\pi\)
\(788\) 0 0
\(789\) −6.81736 −0.242704
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −0.206080 −0.00731811
\(794\) 0 0
\(795\) −89.4312 −3.17180
\(796\) 0 0
\(797\) −15.2145 −0.538925 −0.269462 0.963011i \(-0.586846\pi\)
−0.269462 + 0.963011i \(0.586846\pi\)
\(798\) 0 0
\(799\) 56.1026 1.98477
\(800\) 0 0
\(801\) 39.5681 1.39807
\(802\) 0 0
\(803\) −5.04408 −0.178002
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 20.0415 0.705495
\(808\) 0 0
\(809\) −25.7421 −0.905043 −0.452521 0.891754i \(-0.649475\pi\)
−0.452521 + 0.891754i \(0.649475\pi\)
\(810\) 0 0
\(811\) 31.6453 1.11122 0.555608 0.831444i \(-0.312486\pi\)
0.555608 + 0.831444i \(0.312486\pi\)
\(812\) 0 0
\(813\) −34.0759 −1.19509
\(814\) 0 0
\(815\) −55.6285 −1.94858
\(816\) 0 0
\(817\) 1.93761 0.0677885
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −47.0294 −1.64134 −0.820669 0.571404i \(-0.806399\pi\)
−0.820669 + 0.571404i \(0.806399\pi\)
\(822\) 0 0
\(823\) 6.31892 0.220264 0.110132 0.993917i \(-0.464873\pi\)
0.110132 + 0.993917i \(0.464873\pi\)
\(824\) 0 0
\(825\) −5.36777 −0.186882
\(826\) 0 0
\(827\) −46.8959 −1.63073 −0.815364 0.578948i \(-0.803463\pi\)
−0.815364 + 0.578948i \(0.803463\pi\)
\(828\) 0 0
\(829\) −14.3751 −0.499269 −0.249635 0.968340i \(-0.580311\pi\)
−0.249635 + 0.968340i \(0.580311\pi\)
\(830\) 0 0
\(831\) −60.5641 −2.10094
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 29.4821 1.02027
\(836\) 0 0
\(837\) −2.16884 −0.0749662
\(838\) 0 0
\(839\) 33.5325 1.15767 0.578835 0.815445i \(-0.303507\pi\)
0.578835 + 0.815445i \(0.303507\pi\)
\(840\) 0 0
\(841\) −0.568151 −0.0195914
\(842\) 0 0
\(843\) 45.4387 1.56499
\(844\) 0 0
\(845\) −33.6305 −1.15693
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −56.2478 −1.93042
\(850\) 0 0
\(851\) 9.56635 0.327930
\(852\) 0 0
\(853\) 3.37139 0.115434 0.0577171 0.998333i \(-0.481618\pi\)
0.0577171 + 0.998333i \(0.481618\pi\)
\(854\) 0 0
\(855\) 8.82172 0.301696
\(856\) 0 0
\(857\) −38.0628 −1.30020 −0.650101 0.759848i \(-0.725273\pi\)
−0.650101 + 0.759848i \(0.725273\pi\)
\(858\) 0 0
\(859\) −28.6778 −0.978475 −0.489237 0.872151i \(-0.662725\pi\)
−0.489237 + 0.872151i \(0.662725\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 45.8689 1.56139 0.780697 0.624910i \(-0.214864\pi\)
0.780697 + 0.624910i \(0.214864\pi\)
\(864\) 0 0
\(865\) 36.6982 1.24778
\(866\) 0 0
\(867\) 6.39159 0.217070
\(868\) 0 0
\(869\) 1.77283 0.0601392
\(870\) 0 0
\(871\) 4.03131 0.136596
\(872\) 0 0
\(873\) −20.3655 −0.689267
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −12.0141 −0.405687 −0.202844 0.979211i \(-0.565018\pi\)
−0.202844 + 0.979211i \(0.565018\pi\)
\(878\) 0 0
\(879\) −26.5930 −0.896960
\(880\) 0 0
\(881\) 3.35650 0.113083 0.0565417 0.998400i \(-0.481993\pi\)
0.0565417 + 0.998400i \(0.481993\pi\)
\(882\) 0 0
\(883\) 6.45095 0.217092 0.108546 0.994091i \(-0.465381\pi\)
0.108546 + 0.994091i \(0.465381\pi\)
\(884\) 0 0
\(885\) 40.1799 1.35063
\(886\) 0 0
\(887\) 34.3674 1.15394 0.576971 0.816764i \(-0.304234\pi\)
0.576971 + 0.816764i \(0.304234\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 3.93986 0.131990
\(892\) 0 0
\(893\) 12.6484 0.423262
\(894\) 0 0
\(895\) 76.2841 2.54990
\(896\) 0 0
\(897\) −3.26238 −0.108928
\(898\) 0 0
\(899\) −16.8518 −0.562038
\(900\) 0 0
\(901\) −51.0372 −1.70030
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −17.0685 −0.567377
\(906\) 0 0
\(907\) 0.322852 0.0107201 0.00536005 0.999986i \(-0.498294\pi\)
0.00536005 + 0.999986i \(0.498294\pi\)
\(908\) 0 0
\(909\) −8.69370 −0.288352
\(910\) 0 0
\(911\) 19.3296 0.640419 0.320209 0.947347i \(-0.396247\pi\)
0.320209 + 0.947347i \(0.396247\pi\)
\(912\) 0 0
\(913\) 0.754966 0.0249857
\(914\) 0 0
\(915\) 0.982475 0.0324796
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 11.6440 0.384101 0.192050 0.981385i \(-0.438486\pi\)
0.192050 + 0.981385i \(0.438486\pi\)
\(920\) 0 0
\(921\) 64.2763 2.11798
\(922\) 0 0
\(923\) 3.54322 0.116627
\(924\) 0 0
\(925\) 63.6912 2.09415
\(926\) 0 0
\(927\) 15.8350 0.520089
\(928\) 0 0
\(929\) −10.8240 −0.355123 −0.177562 0.984110i \(-0.556821\pi\)
−0.177562 + 0.984110i \(0.556821\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −59.8575 −1.95965
\(934\) 0 0
\(935\) −5.81112 −0.190044
\(936\) 0 0
\(937\) −18.0113 −0.588402 −0.294201 0.955744i \(-0.595054\pi\)
−0.294201 + 0.955744i \(0.595054\pi\)
\(938\) 0 0
\(939\) −30.6847 −1.00136
\(940\) 0 0
\(941\) −7.35256 −0.239687 −0.119843 0.992793i \(-0.538239\pi\)
−0.119843 + 0.992793i \(0.538239\pi\)
\(942\) 0 0
\(943\) −1.67446 −0.0545278
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 5.30073 0.172251 0.0861253 0.996284i \(-0.472551\pi\)
0.0861253 + 0.996284i \(0.472551\pi\)
\(948\) 0 0
\(949\) −20.4106 −0.662556
\(950\) 0 0
\(951\) −29.8411 −0.967666
\(952\) 0 0
\(953\) −46.1846 −1.49607 −0.748033 0.663661i \(-0.769002\pi\)
−0.748033 + 0.663661i \(0.769002\pi\)
\(954\) 0 0
\(955\) −63.1541 −2.04362
\(956\) 0 0
\(957\) 5.13476 0.165983
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −21.0118 −0.677801
\(962\) 0 0
\(963\) 41.6498 1.34215
\(964\) 0 0
\(965\) −19.1548 −0.616616
\(966\) 0 0
\(967\) 9.76088 0.313889 0.156944 0.987607i \(-0.449836\pi\)
0.156944 + 0.987607i \(0.449836\pi\)
\(968\) 0 0
\(969\) 10.6017 0.340576
\(970\) 0 0
\(971\) 21.2625 0.682347 0.341174 0.940000i \(-0.389176\pi\)
0.341174 + 0.940000i \(0.389176\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −21.7204 −0.695609
\(976\) 0 0
\(977\) −1.88855 −0.0604200 −0.0302100 0.999544i \(-0.509618\pi\)
−0.0302100 + 0.999544i \(0.509618\pi\)
\(978\) 0 0
\(979\) −5.87630 −0.187807
\(980\) 0 0
\(981\) 32.3479 1.03279
\(982\) 0 0
\(983\) 25.8489 0.824453 0.412226 0.911081i \(-0.364751\pi\)
0.412226 + 0.911081i \(0.364751\pi\)
\(984\) 0 0
\(985\) 3.23421 0.103051
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 1.62222 0.0515837
\(990\) 0 0
\(991\) −16.9852 −0.539554 −0.269777 0.962923i \(-0.586950\pi\)
−0.269777 + 0.962923i \(0.586950\pi\)
\(992\) 0 0
\(993\) 14.8898 0.472515
\(994\) 0 0
\(995\) 1.93921 0.0614770
\(996\) 0 0
\(997\) −11.8086 −0.373984 −0.186992 0.982361i \(-0.559874\pi\)
−0.186992 + 0.982361i \(0.559874\pi\)
\(998\) 0 0
\(999\) −7.84130 −0.248088
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.bq.1.7 8
7.2 even 3 1064.2.q.n.305.2 16
7.4 even 3 1064.2.q.n.457.2 yes 16
7.6 odd 2 7448.2.a.br.1.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1064.2.q.n.305.2 16 7.2 even 3
1064.2.q.n.457.2 yes 16 7.4 even 3
7448.2.a.bq.1.7 8 1.1 even 1 trivial
7448.2.a.br.1.2 8 7.6 odd 2