Properties

Label 5796.2.a.t.1.4
Level $5796$
Weight $2$
Character 5796.1
Self dual yes
Analytic conductor $46.281$
Analytic rank $0$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5796 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5796.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(46.2812930115\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.6963152.1
Defining polynomial: \( x^{5} - 2x^{4} - 10x^{3} + 10x^{2} + 29x + 10 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 644)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-2.25688\) of defining polynomial
Character \(\chi\) \(=\) 5796.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.04771 q^{5} -1.00000 q^{7} +O(q^{10})\) \(q+3.04771 q^{5} -1.00000 q^{7} -5.22523 q^{11} +3.38206 q^{13} +2.63895 q^{17} +3.39461 q^{19} +1.00000 q^{23} +4.28854 q^{25} +4.00190 q^{29} +6.97185 q^{31} -3.04771 q^{35} -5.11916 q^{37} +5.89583 q^{41} -7.90838 q^{43} -9.54893 q^{47} +1.00000 q^{49} +11.8200 q^{53} -15.9250 q^{55} -1.51979 q^{59} +1.13934 q^{61} +10.3076 q^{65} -8.80688 q^{67} +14.5333 q^{71} -13.2271 q^{73} +5.22523 q^{77} +14.4398 q^{79} +0.693795 q^{83} +8.04275 q^{85} -10.8511 q^{89} -3.38206 q^{91} +10.3458 q^{95} -3.23476 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 2 q^{5} - 5 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 2 q^{5} - 5 q^{7} - 2 q^{11} + 13 q^{13} - 4 q^{17} + 12 q^{19} + 5 q^{23} + 19 q^{25} - 13 q^{29} - 3 q^{31} + 2 q^{35} - 4 q^{37} - q^{41} - 8 q^{43} - 5 q^{47} + 5 q^{49} + 8 q^{53} - 2 q^{55} - 12 q^{59} + 20 q^{61} + 12 q^{65} - 12 q^{67} - 9 q^{71} - 9 q^{73} + 2 q^{77} - 8 q^{79} + 28 q^{83} + 16 q^{85} - 32 q^{89} - 13 q^{91} + 36 q^{95} + 4 q^{97}+O(q^{100}) \) 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
\(3\) 0 0
\(4\) 0 0
\(5\) 3.04771 1.36298 0.681489 0.731828i \(-0.261333\pi\)
0.681489 + 0.731828i \(0.261333\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −5.22523 −1.57546 −0.787732 0.616018i \(-0.788745\pi\)
−0.787732 + 0.616018i \(0.788745\pi\)
\(12\) 0 0
\(13\) 3.38206 0.938016 0.469008 0.883194i \(-0.344612\pi\)
0.469008 + 0.883194i \(0.344612\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.63895 0.640039 0.320019 0.947411i \(-0.396311\pi\)
0.320019 + 0.947411i \(0.396311\pi\)
\(18\) 0 0
\(19\) 3.39461 0.778777 0.389388 0.921074i \(-0.372686\pi\)
0.389388 + 0.921074i \(0.372686\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 4.28854 0.857708
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4.00190 0.743134 0.371567 0.928406i \(-0.378821\pi\)
0.371567 + 0.928406i \(0.378821\pi\)
\(30\) 0 0
\(31\) 6.97185 1.25218 0.626091 0.779750i \(-0.284654\pi\)
0.626091 + 0.779750i \(0.284654\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3.04771 −0.515157
\(36\) 0 0
\(37\) −5.11916 −0.841585 −0.420792 0.907157i \(-0.638248\pi\)
−0.420792 + 0.907157i \(0.638248\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5.89583 0.920774 0.460387 0.887718i \(-0.347711\pi\)
0.460387 + 0.887718i \(0.347711\pi\)
\(42\) 0 0
\(43\) −7.90838 −1.20602 −0.603008 0.797735i \(-0.706031\pi\)
−0.603008 + 0.797735i \(0.706031\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −9.54893 −1.39286 −0.696428 0.717627i \(-0.745228\pi\)
−0.696428 + 0.717627i \(0.745228\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 11.8200 1.62360 0.811799 0.583937i \(-0.198488\pi\)
0.811799 + 0.583937i \(0.198488\pi\)
\(54\) 0 0
\(55\) −15.9250 −2.14732
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.51979 −0.197860 −0.0989299 0.995094i \(-0.531542\pi\)
−0.0989299 + 0.995094i \(0.531542\pi\)
\(60\) 0 0
\(61\) 1.13934 0.145877 0.0729385 0.997336i \(-0.476762\pi\)
0.0729385 + 0.997336i \(0.476762\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 10.3076 1.27849
\(66\) 0 0
\(67\) −8.80688 −1.07593 −0.537966 0.842967i \(-0.680807\pi\)
−0.537966 + 0.842967i \(0.680807\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 14.5333 1.72479 0.862394 0.506237i \(-0.168964\pi\)
0.862394 + 0.506237i \(0.168964\pi\)
\(72\) 0 0
\(73\) −13.2271 −1.54812 −0.774059 0.633114i \(-0.781777\pi\)
−0.774059 + 0.633114i \(0.781777\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 5.22523 0.595470
\(78\) 0 0
\(79\) 14.4398 1.62461 0.812303 0.583236i \(-0.198214\pi\)
0.812303 + 0.583236i \(0.198214\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 0.693795 0.0761538 0.0380769 0.999275i \(-0.487877\pi\)
0.0380769 + 0.999275i \(0.487877\pi\)
\(84\) 0 0
\(85\) 8.04275 0.872359
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −10.8511 −1.15021 −0.575106 0.818079i \(-0.695039\pi\)
−0.575106 + 0.818079i \(0.695039\pi\)
\(90\) 0 0
\(91\) −3.38206 −0.354537
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 10.3458 1.06146
\(96\) 0 0
\(97\) −3.23476 −0.328440 −0.164220 0.986424i \(-0.552511\pi\)
−0.164220 + 0.986424i \(0.552511\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 8.32672 0.828540 0.414270 0.910154i \(-0.364037\pi\)
0.414270 + 0.910154i \(0.364037\pi\)
\(102\) 0 0
\(103\) 0.418345 0.0412208 0.0206104 0.999788i \(-0.493439\pi\)
0.0206104 + 0.999788i \(0.493439\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 11.9084 1.15123 0.575613 0.817722i \(-0.304763\pi\)
0.575613 + 0.817722i \(0.304763\pi\)
\(108\) 0 0
\(109\) 17.9154 1.71598 0.857992 0.513663i \(-0.171712\pi\)
0.857992 + 0.513663i \(0.171712\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 12.6375 1.18884 0.594418 0.804156i \(-0.297383\pi\)
0.594418 + 0.804156i \(0.297383\pi\)
\(114\) 0 0
\(115\) 3.04771 0.284201
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2.63895 −0.241912
\(120\) 0 0
\(121\) 16.3030 1.48209
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −2.16832 −0.193940
\(126\) 0 0
\(127\) −3.22333 −0.286024 −0.143012 0.989721i \(-0.545679\pi\)
−0.143012 + 0.989721i \(0.545679\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 14.0910 1.23114 0.615569 0.788083i \(-0.288926\pi\)
0.615569 + 0.788083i \(0.288926\pi\)
\(132\) 0 0
\(133\) −3.39461 −0.294350
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2.67250 −0.228327 −0.114164 0.993462i \(-0.536419\pi\)
−0.114164 + 0.993462i \(0.536419\pi\)
\(138\) 0 0
\(139\) 6.23315 0.528689 0.264344 0.964428i \(-0.414844\pi\)
0.264344 + 0.964428i \(0.414844\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −17.6721 −1.47781
\(144\) 0 0
\(145\) 12.1966 1.01287
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 5.58165 0.457267 0.228633 0.973513i \(-0.426574\pi\)
0.228633 + 0.973513i \(0.426574\pi\)
\(150\) 0 0
\(151\) −11.8325 −0.962916 −0.481458 0.876469i \(-0.659893\pi\)
−0.481458 + 0.876469i \(0.659893\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 21.2482 1.70670
\(156\) 0 0
\(157\) 17.3015 1.38081 0.690406 0.723422i \(-0.257432\pi\)
0.690406 + 0.723422i \(0.257432\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1.00000 −0.0788110
\(162\) 0 0
\(163\) 14.3212 1.12172 0.560861 0.827910i \(-0.310470\pi\)
0.560861 + 0.827910i \(0.310470\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.28358 −0.486238 −0.243119 0.969996i \(-0.578171\pi\)
−0.243119 + 0.969996i \(0.578171\pi\)
\(168\) 0 0
\(169\) −1.56164 −0.120126
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 2.60539 0.198084 0.0990421 0.995083i \(-0.468422\pi\)
0.0990421 + 0.995083i \(0.468422\pi\)
\(174\) 0 0
\(175\) −4.28854 −0.324183
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −25.2341 −1.88609 −0.943044 0.332667i \(-0.892051\pi\)
−0.943044 + 0.332667i \(0.892051\pi\)
\(180\) 0 0
\(181\) −1.36485 −0.101448 −0.0507242 0.998713i \(-0.516153\pi\)
−0.0507242 + 0.998713i \(0.516153\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −15.6017 −1.14706
\(186\) 0 0
\(187\) −13.7891 −1.00836
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 22.1467 1.60248 0.801239 0.598344i \(-0.204174\pi\)
0.801239 + 0.598344i \(0.204174\pi\)
\(192\) 0 0
\(193\) 18.3653 1.32197 0.660983 0.750401i \(-0.270139\pi\)
0.660983 + 0.750401i \(0.270139\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1.07831 0.0768261 0.0384131 0.999262i \(-0.487770\pi\)
0.0384131 + 0.999262i \(0.487770\pi\)
\(198\) 0 0
\(199\) −5.55335 −0.393666 −0.196833 0.980437i \(-0.563066\pi\)
−0.196833 + 0.980437i \(0.563066\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −4.00190 −0.280878
\(204\) 0 0
\(205\) 17.9688 1.25499
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −17.7376 −1.22693
\(210\) 0 0
\(211\) −19.3543 −1.33240 −0.666201 0.745772i \(-0.732081\pi\)
−0.666201 + 0.745772i \(0.732081\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −24.1024 −1.64377
\(216\) 0 0
\(217\) −6.97185 −0.473280
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 8.92509 0.600367
\(222\) 0 0
\(223\) −2.69234 −0.180293 −0.0901464 0.995929i \(-0.528733\pi\)
−0.0901464 + 0.995929i \(0.528733\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 8.26663 0.548675 0.274338 0.961633i \(-0.411541\pi\)
0.274338 + 0.961633i \(0.411541\pi\)
\(228\) 0 0
\(229\) 26.2369 1.73378 0.866891 0.498499i \(-0.166115\pi\)
0.866891 + 0.498499i \(0.166115\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.17735 −0.0771310 −0.0385655 0.999256i \(-0.512279\pi\)
−0.0385655 + 0.999256i \(0.512279\pi\)
\(234\) 0 0
\(235\) −29.1024 −1.89843
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −5.56911 −0.360236 −0.180118 0.983645i \(-0.557648\pi\)
−0.180118 + 0.983645i \(0.557648\pi\)
\(240\) 0 0
\(241\) 8.12518 0.523389 0.261694 0.965151i \(-0.415719\pi\)
0.261694 + 0.965151i \(0.415719\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3.04771 0.194711
\(246\) 0 0
\(247\) 11.4808 0.730505
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −2.78542 −0.175814 −0.0879071 0.996129i \(-0.528018\pi\)
−0.0879071 + 0.996129i \(0.528018\pi\)
\(252\) 0 0
\(253\) −5.22523 −0.328507
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 24.1150 1.50425 0.752126 0.659020i \(-0.229029\pi\)
0.752126 + 0.659020i \(0.229029\pi\)
\(258\) 0 0
\(259\) 5.11916 0.318089
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −3.40905 −0.210211 −0.105106 0.994461i \(-0.533518\pi\)
−0.105106 + 0.994461i \(0.533518\pi\)
\(264\) 0 0
\(265\) 36.0239 2.21293
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −5.29044 −0.322564 −0.161282 0.986908i \(-0.551563\pi\)
−0.161282 + 0.986908i \(0.551563\pi\)
\(270\) 0 0
\(271\) 16.2206 0.985331 0.492666 0.870219i \(-0.336023\pi\)
0.492666 + 0.870219i \(0.336023\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −22.4086 −1.35129
\(276\) 0 0
\(277\) −22.2211 −1.33513 −0.667567 0.744550i \(-0.732664\pi\)
−0.667567 + 0.744550i \(0.732664\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 5.74964 0.342995 0.171497 0.985185i \(-0.445140\pi\)
0.171497 + 0.985185i \(0.445140\pi\)
\(282\) 0 0
\(283\) −14.0108 −0.832857 −0.416428 0.909169i \(-0.636718\pi\)
−0.416428 + 0.909169i \(0.636718\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −5.89583 −0.348020
\(288\) 0 0
\(289\) −10.0360 −0.590350
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −15.7616 −0.920801 −0.460400 0.887711i \(-0.652294\pi\)
−0.460400 + 0.887711i \(0.652294\pi\)
\(294\) 0 0
\(295\) −4.63188 −0.269678
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3.38206 0.195590
\(300\) 0 0
\(301\) 7.90838 0.455831
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 3.47237 0.198827
\(306\) 0 0
\(307\) 11.4944 0.656018 0.328009 0.944675i \(-0.393622\pi\)
0.328009 + 0.944675i \(0.393622\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −4.41105 −0.250128 −0.125064 0.992149i \(-0.539914\pi\)
−0.125064 + 0.992149i \(0.539914\pi\)
\(312\) 0 0
\(313\) −6.20154 −0.350532 −0.175266 0.984521i \(-0.556079\pi\)
−0.175266 + 0.984521i \(0.556079\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 9.50769 0.534005 0.267003 0.963696i \(-0.413967\pi\)
0.267003 + 0.963696i \(0.413967\pi\)
\(318\) 0 0
\(319\) −20.9108 −1.17078
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 8.95819 0.498447
\(324\) 0 0
\(325\) 14.5041 0.804544
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 9.54893 0.526450
\(330\) 0 0
\(331\) 10.0087 0.550130 0.275065 0.961426i \(-0.411301\pi\)
0.275065 + 0.961426i \(0.411301\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −26.8408 −1.46647
\(336\) 0 0
\(337\) 16.5389 0.900929 0.450464 0.892794i \(-0.351258\pi\)
0.450464 + 0.892794i \(0.351258\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −36.4295 −1.97277
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −34.8917 −1.87308 −0.936541 0.350558i \(-0.885992\pi\)
−0.936541 + 0.350558i \(0.885992\pi\)
\(348\) 0 0
\(349\) 6.92337 0.370599 0.185300 0.982682i \(-0.440674\pi\)
0.185300 + 0.982682i \(0.440674\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −21.6050 −1.14992 −0.574959 0.818182i \(-0.694982\pi\)
−0.574959 + 0.818182i \(0.694982\pi\)
\(354\) 0 0
\(355\) 44.2934 2.35085
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 26.2085 1.38323 0.691616 0.722265i \(-0.256899\pi\)
0.691616 + 0.722265i \(0.256899\pi\)
\(360\) 0 0
\(361\) −7.47664 −0.393507
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −40.3124 −2.11005
\(366\) 0 0
\(367\) 16.5650 0.864688 0.432344 0.901709i \(-0.357687\pi\)
0.432344 + 0.901709i \(0.357687\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −11.8200 −0.613662
\(372\) 0 0
\(373\) 15.6116 0.808340 0.404170 0.914684i \(-0.367560\pi\)
0.404170 + 0.914684i \(0.367560\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 13.5347 0.697071
\(378\) 0 0
\(379\) −9.80933 −0.503871 −0.251936 0.967744i \(-0.581067\pi\)
−0.251936 + 0.967744i \(0.581067\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 18.4925 0.944921 0.472461 0.881352i \(-0.343366\pi\)
0.472461 + 0.881352i \(0.343366\pi\)
\(384\) 0 0
\(385\) 15.9250 0.811612
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −11.3030 −0.573084 −0.286542 0.958068i \(-0.592506\pi\)
−0.286542 + 0.958068i \(0.592506\pi\)
\(390\) 0 0
\(391\) 2.63895 0.133457
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 44.0084 2.21430
\(396\) 0 0
\(397\) −1.20204 −0.0603285 −0.0301643 0.999545i \(-0.509603\pi\)
−0.0301643 + 0.999545i \(0.509603\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3.01127 0.150376 0.0751878 0.997169i \(-0.476044\pi\)
0.0751878 + 0.997169i \(0.476044\pi\)
\(402\) 0 0
\(403\) 23.5793 1.17457
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 26.7488 1.32589
\(408\) 0 0
\(409\) −33.4725 −1.65511 −0.827553 0.561387i \(-0.810268\pi\)
−0.827553 + 0.561387i \(0.810268\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1.51979 0.0747839
\(414\) 0 0
\(415\) 2.11449 0.103796
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 6.40028 0.312674 0.156337 0.987704i \(-0.450031\pi\)
0.156337 + 0.987704i \(0.450031\pi\)
\(420\) 0 0
\(421\) −8.01082 −0.390423 −0.195212 0.980761i \(-0.562539\pi\)
−0.195212 + 0.980761i \(0.562539\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 11.3172 0.548967
\(426\) 0 0
\(427\) −1.13934 −0.0551363
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 27.6084 1.32985 0.664925 0.746910i \(-0.268463\pi\)
0.664925 + 0.746910i \(0.268463\pi\)
\(432\) 0 0
\(433\) −14.8797 −0.715074 −0.357537 0.933899i \(-0.616383\pi\)
−0.357537 + 0.933899i \(0.616383\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3.39461 0.162386
\(438\) 0 0
\(439\) −36.1931 −1.72740 −0.863702 0.504004i \(-0.831860\pi\)
−0.863702 + 0.504004i \(0.831860\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 10.5546 0.501465 0.250733 0.968056i \(-0.419329\pi\)
0.250733 + 0.968056i \(0.419329\pi\)
\(444\) 0 0
\(445\) −33.0710 −1.56771
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −39.9560 −1.88564 −0.942821 0.333301i \(-0.891838\pi\)
−0.942821 + 0.333301i \(0.891838\pi\)
\(450\) 0 0
\(451\) −30.8071 −1.45065
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −10.3076 −0.483226
\(456\) 0 0
\(457\) 10.1870 0.476530 0.238265 0.971200i \(-0.423421\pi\)
0.238265 + 0.971200i \(0.423421\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 6.70956 0.312495 0.156248 0.987718i \(-0.450060\pi\)
0.156248 + 0.987718i \(0.450060\pi\)
\(462\) 0 0
\(463\) 16.6512 0.773848 0.386924 0.922112i \(-0.373538\pi\)
0.386924 + 0.922112i \(0.373538\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −39.1863 −1.81332 −0.906662 0.421857i \(-0.861378\pi\)
−0.906662 + 0.421857i \(0.861378\pi\)
\(468\) 0 0
\(469\) 8.80688 0.406664
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 41.3230 1.90004
\(474\) 0 0
\(475\) 14.5579 0.667963
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 36.2704 1.65724 0.828619 0.559813i \(-0.189127\pi\)
0.828619 + 0.559813i \(0.189127\pi\)
\(480\) 0 0
\(481\) −17.3133 −0.789420
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −9.85861 −0.447656
\(486\) 0 0
\(487\) 23.7517 1.07629 0.538146 0.842851i \(-0.319125\pi\)
0.538146 + 0.842851i \(0.319125\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 22.3752 1.00978 0.504889 0.863185i \(-0.331534\pi\)
0.504889 + 0.863185i \(0.331534\pi\)
\(492\) 0 0
\(493\) 10.5608 0.475635
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −14.5333 −0.651909
\(498\) 0 0
\(499\) 16.2296 0.726535 0.363268 0.931685i \(-0.381661\pi\)
0.363268 + 0.931685i \(0.381661\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 2.57708 0.114906 0.0574532 0.998348i \(-0.481702\pi\)
0.0574532 + 0.998348i \(0.481702\pi\)
\(504\) 0 0
\(505\) 25.3774 1.12928
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −33.4091 −1.48083 −0.740417 0.672148i \(-0.765372\pi\)
−0.740417 + 0.672148i \(0.765372\pi\)
\(510\) 0 0
\(511\) 13.2271 0.585134
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.27500 0.0561830
\(516\) 0 0
\(517\) 49.8953 2.19439
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −12.4303 −0.544580 −0.272290 0.962215i \(-0.587781\pi\)
−0.272290 + 0.962215i \(0.587781\pi\)
\(522\) 0 0
\(523\) 1.05262 0.0460279 0.0230140 0.999735i \(-0.492674\pi\)
0.0230140 + 0.999735i \(0.492674\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 18.3984 0.801445
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 19.9401 0.863701
\(534\) 0 0
\(535\) 36.2933 1.56910
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −5.22523 −0.225066
\(540\) 0 0
\(541\) 29.4265 1.26514 0.632572 0.774502i \(-0.281999\pi\)
0.632572 + 0.774502i \(0.281999\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 54.6009 2.33885
\(546\) 0 0
\(547\) −36.3851 −1.55571 −0.777857 0.628441i \(-0.783693\pi\)
−0.777857 + 0.628441i \(0.783693\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 13.5849 0.578735
\(552\) 0 0
\(553\) −14.4398 −0.614043
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 22.2666 0.943467 0.471734 0.881741i \(-0.343628\pi\)
0.471734 + 0.881741i \(0.343628\pi\)
\(558\) 0 0
\(559\) −26.7466 −1.13126
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −22.0300 −0.928453 −0.464227 0.885717i \(-0.653668\pi\)
−0.464227 + 0.885717i \(0.653668\pi\)
\(564\) 0 0
\(565\) 38.5154 1.62036
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −27.9918 −1.17348 −0.586738 0.809777i \(-0.699588\pi\)
−0.586738 + 0.809777i \(0.699588\pi\)
\(570\) 0 0
\(571\) 19.7000 0.824421 0.412210 0.911089i \(-0.364757\pi\)
0.412210 + 0.911089i \(0.364757\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 4.28854 0.178845
\(576\) 0 0
\(577\) 11.9624 0.498000 0.249000 0.968503i \(-0.419898\pi\)
0.249000 + 0.968503i \(0.419898\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −0.693795 −0.0287834
\(582\) 0 0
\(583\) −61.7620 −2.55792
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 19.3278 0.797743 0.398872 0.917007i \(-0.369402\pi\)
0.398872 + 0.917007i \(0.369402\pi\)
\(588\) 0 0
\(589\) 23.6667 0.975170
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −8.45045 −0.347018 −0.173509 0.984832i \(-0.555511\pi\)
−0.173509 + 0.984832i \(0.555511\pi\)
\(594\) 0 0
\(595\) −8.04275 −0.329721
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −5.56581 −0.227413 −0.113706 0.993514i \(-0.536272\pi\)
−0.113706 + 0.993514i \(0.536272\pi\)
\(600\) 0 0
\(601\) −18.2258 −0.743445 −0.371722 0.928344i \(-0.621233\pi\)
−0.371722 + 0.928344i \(0.621233\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 49.6868 2.02005
\(606\) 0 0
\(607\) 28.3740 1.15166 0.575832 0.817568i \(-0.304678\pi\)
0.575832 + 0.817568i \(0.304678\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −32.2951 −1.30652
\(612\) 0 0
\(613\) 15.8620 0.640660 0.320330 0.947306i \(-0.396206\pi\)
0.320330 + 0.947306i \(0.396206\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 14.9140 0.600417 0.300208 0.953874i \(-0.402944\pi\)
0.300208 + 0.953874i \(0.402944\pi\)
\(618\) 0 0
\(619\) 32.3397 1.29984 0.649920 0.760002i \(-0.274802\pi\)
0.649920 + 0.760002i \(0.274802\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 10.8511 0.434739
\(624\) 0 0
\(625\) −28.0511 −1.12204
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −13.5092 −0.538647
\(630\) 0 0
\(631\) −15.3840 −0.612426 −0.306213 0.951963i \(-0.599062\pi\)
−0.306213 + 0.951963i \(0.599062\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −9.82377 −0.389844
\(636\) 0 0
\(637\) 3.38206 0.134002
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −37.0193 −1.46217 −0.731087 0.682284i \(-0.760987\pi\)
−0.731087 + 0.682284i \(0.760987\pi\)
\(642\) 0 0
\(643\) 24.7183 0.974796 0.487398 0.873180i \(-0.337946\pi\)
0.487398 + 0.873180i \(0.337946\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 20.3207 0.798887 0.399444 0.916758i \(-0.369203\pi\)
0.399444 + 0.916758i \(0.369203\pi\)
\(648\) 0 0
\(649\) 7.94124 0.311721
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 13.7950 0.539839 0.269919 0.962883i \(-0.413003\pi\)
0.269919 + 0.962883i \(0.413003\pi\)
\(654\) 0 0
\(655\) 42.9453 1.67801
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −39.4316 −1.53604 −0.768019 0.640427i \(-0.778757\pi\)
−0.768019 + 0.640427i \(0.778757\pi\)
\(660\) 0 0
\(661\) 38.9211 1.51385 0.756927 0.653499i \(-0.226700\pi\)
0.756927 + 0.653499i \(0.226700\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −10.3458 −0.401192
\(666\) 0 0
\(667\) 4.00190 0.154954
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −5.95329 −0.229824
\(672\) 0 0
\(673\) −43.7150 −1.68509 −0.842544 0.538627i \(-0.818943\pi\)
−0.842544 + 0.538627i \(0.818943\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −16.6777 −0.640977 −0.320489 0.947252i \(-0.603847\pi\)
−0.320489 + 0.947252i \(0.603847\pi\)
\(678\) 0 0
\(679\) 3.23476 0.124139
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −48.7312 −1.86465 −0.932324 0.361625i \(-0.882222\pi\)
−0.932324 + 0.361625i \(0.882222\pi\)
\(684\) 0 0
\(685\) −8.14502 −0.311205
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 39.9759 1.52296
\(690\) 0 0
\(691\) −41.7882 −1.58970 −0.794849 0.606807i \(-0.792450\pi\)
−0.794849 + 0.606807i \(0.792450\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 18.9968 0.720591
\(696\) 0 0
\(697\) 15.5588 0.589331
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 28.1499 1.06321 0.531604 0.846993i \(-0.321590\pi\)
0.531604 + 0.846993i \(0.321590\pi\)
\(702\) 0 0
\(703\) −17.3775 −0.655406
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −8.32672 −0.313159
\(708\) 0 0
\(709\) 22.1680 0.832536 0.416268 0.909242i \(-0.363338\pi\)
0.416268 + 0.909242i \(0.363338\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 6.97185 0.261098
\(714\) 0 0
\(715\) −53.8593 −2.01422
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 22.2623 0.830243 0.415122 0.909766i \(-0.363739\pi\)
0.415122 + 0.909766i \(0.363739\pi\)
\(720\) 0 0
\(721\) −0.418345 −0.0155800
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 17.1623 0.637392
\(726\) 0 0
\(727\) −21.6618 −0.803392 −0.401696 0.915773i \(-0.631579\pi\)
−0.401696 + 0.915773i \(0.631579\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −20.8698 −0.771897
\(732\) 0 0
\(733\) −4.50596 −0.166431 −0.0832156 0.996532i \(-0.526519\pi\)
−0.0832156 + 0.996532i \(0.526519\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 46.0179 1.69509
\(738\) 0 0
\(739\) −15.7692 −0.580079 −0.290040 0.957015i \(-0.593669\pi\)
−0.290040 + 0.957015i \(0.593669\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −30.8619 −1.13222 −0.566108 0.824331i \(-0.691551\pi\)
−0.566108 + 0.824331i \(0.691551\pi\)
\(744\) 0 0
\(745\) 17.0113 0.623245
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −11.9084 −0.435123
\(750\) 0 0
\(751\) 38.1808 1.39324 0.696618 0.717442i \(-0.254687\pi\)
0.696618 + 0.717442i \(0.254687\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −36.0621 −1.31243
\(756\) 0 0
\(757\) −15.6733 −0.569655 −0.284828 0.958579i \(-0.591936\pi\)
−0.284828 + 0.958579i \(0.591936\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −41.8363 −1.51657 −0.758283 0.651926i \(-0.773961\pi\)
−0.758283 + 0.651926i \(0.773961\pi\)
\(762\) 0 0
\(763\) −17.9154 −0.648581
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −5.14003 −0.185596
\(768\) 0 0
\(769\) 5.39928 0.194703 0.0973515 0.995250i \(-0.468963\pi\)
0.0973515 + 0.995250i \(0.468963\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −37.1956 −1.33783 −0.668917 0.743337i \(-0.733242\pi\)
−0.668917 + 0.743337i \(0.733242\pi\)
\(774\) 0 0
\(775\) 29.8991 1.07401
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 20.0140 0.717077
\(780\) 0 0
\(781\) −75.9399 −2.71734
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 52.7301 1.88202
\(786\) 0 0
\(787\) −38.9942 −1.38999 −0.694997 0.719013i \(-0.744594\pi\)
−0.694997 + 0.719013i \(0.744594\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −12.6375 −0.449338
\(792\) 0 0
\(793\) 3.85331 0.136835
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −25.8311 −0.914986 −0.457493 0.889213i \(-0.651253\pi\)
−0.457493 + 0.889213i \(0.651253\pi\)
\(798\) 0 0
\(799\) −25.1991 −0.891482
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 69.1147 2.43901
\(804\) 0 0
\(805\) −3.04771 −0.107418
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −26.7612 −0.940875 −0.470437 0.882433i \(-0.655904\pi\)
−0.470437 + 0.882433i \(0.655904\pi\)
\(810\) 0 0
\(811\) 30.3856 1.06698 0.533492 0.845805i \(-0.320880\pi\)
0.533492 + 0.845805i \(0.320880\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 43.6469 1.52888
\(816\) 0 0
\(817\) −26.8458 −0.939217
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 16.5069 0.576095 0.288048 0.957616i \(-0.406994\pi\)
0.288048 + 0.957616i \(0.406994\pi\)
\(822\) 0 0
\(823\) −19.9562 −0.695631 −0.347816 0.937563i \(-0.613076\pi\)
−0.347816 + 0.937563i \(0.613076\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 36.8443 1.28120 0.640601 0.767874i \(-0.278685\pi\)
0.640601 + 0.767874i \(0.278685\pi\)
\(828\) 0 0
\(829\) 5.80916 0.201760 0.100880 0.994899i \(-0.467834\pi\)
0.100880 + 0.994899i \(0.467834\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2.63895 0.0914341
\(834\) 0 0
\(835\) −19.1505 −0.662732
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 12.2733 0.423722 0.211861 0.977300i \(-0.432048\pi\)
0.211861 + 0.977300i \(0.432048\pi\)
\(840\) 0 0
\(841\) −12.9848 −0.447752
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −4.75942 −0.163729
\(846\) 0 0
\(847\) −16.3030 −0.560177
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −5.11916 −0.175483
\(852\) 0 0
\(853\) −13.2560 −0.453878 −0.226939 0.973909i \(-0.572872\pi\)
−0.226939 + 0.973909i \(0.572872\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 19.1066 0.652670 0.326335 0.945254i \(-0.394186\pi\)
0.326335 + 0.945254i \(0.394186\pi\)
\(858\) 0 0
\(859\) −46.1878 −1.57591 −0.787953 0.615735i \(-0.788859\pi\)
−0.787953 + 0.615735i \(0.788859\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −11.5341 −0.392625 −0.196313 0.980541i \(-0.562897\pi\)
−0.196313 + 0.980541i \(0.562897\pi\)
\(864\) 0 0
\(865\) 7.94048 0.269984
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −75.4512 −2.55951
\(870\) 0 0
\(871\) −29.7854 −1.00924
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 2.16832 0.0733026
\(876\) 0 0
\(877\) −16.9695 −0.573020 −0.286510 0.958077i \(-0.592495\pi\)
−0.286510 + 0.958077i \(0.592495\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −11.4505 −0.385775 −0.192888 0.981221i \(-0.561785\pi\)
−0.192888 + 0.981221i \(0.561785\pi\)
\(882\) 0 0
\(883\) 17.3634 0.584325 0.292162 0.956369i \(-0.405625\pi\)
0.292162 + 0.956369i \(0.405625\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −22.7378 −0.763460 −0.381730 0.924274i \(-0.624672\pi\)
−0.381730 + 0.924274i \(0.624672\pi\)
\(888\) 0 0
\(889\) 3.22333 0.108107
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −32.4149 −1.08472
\(894\) 0 0
\(895\) −76.9064 −2.57070
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 27.9006 0.930539
\(900\) 0 0
\(901\) 31.1923 1.03917
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −4.15966 −0.138272
\(906\) 0 0
\(907\) −41.5359 −1.37918 −0.689588 0.724202i \(-0.742208\pi\)
−0.689588 + 0.724202i \(0.742208\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −2.92749 −0.0969921 −0.0484961 0.998823i \(-0.515443\pi\)
−0.0484961 + 0.998823i \(0.515443\pi\)
\(912\) 0 0
\(913\) −3.62523 −0.119978
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −14.0910 −0.465326
\(918\) 0 0
\(919\) 13.9648 0.460658 0.230329 0.973113i \(-0.426020\pi\)
0.230329 + 0.973113i \(0.426020\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 49.1527 1.61788
\(924\) 0 0
\(925\) −21.9537 −0.721834
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 23.3541 0.766222 0.383111 0.923702i \(-0.374853\pi\)
0.383111 + 0.923702i \(0.374853\pi\)
\(930\) 0 0
\(931\) 3.39461 0.111254
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −42.0252 −1.37437
\(936\) 0 0
\(937\) 11.1156 0.363130 0.181565 0.983379i \(-0.441884\pi\)
0.181565 + 0.983379i \(0.441884\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −5.13868 −0.167516 −0.0837580 0.996486i \(-0.526692\pi\)
−0.0837580 + 0.996486i \(0.526692\pi\)
\(942\) 0 0
\(943\) 5.89583 0.191995
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −29.4147 −0.955851 −0.477925 0.878400i \(-0.658611\pi\)
−0.477925 + 0.878400i \(0.658611\pi\)
\(948\) 0 0
\(949\) −44.7350 −1.45216
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 5.67396 0.183797 0.0918987 0.995768i \(-0.470706\pi\)
0.0918987 + 0.995768i \(0.470706\pi\)
\(954\) 0 0
\(955\) 67.4967 2.18414
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 2.67250 0.0862997
\(960\) 0 0
\(961\) 17.6067 0.567959
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 55.9723 1.80181
\(966\) 0 0
\(967\) −0.898731 −0.0289013 −0.0144506 0.999896i \(-0.504600\pi\)
−0.0144506 + 0.999896i \(0.504600\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −34.2084 −1.09780 −0.548899 0.835889i \(-0.684953\pi\)
−0.548899 + 0.835889i \(0.684953\pi\)
\(972\) 0 0
\(973\) −6.23315 −0.199825
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −8.19697 −0.262244 −0.131122 0.991366i \(-0.541858\pi\)
−0.131122 + 0.991366i \(0.541858\pi\)
\(978\) 0 0
\(979\) 56.6994 1.81212
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 1.12997 0.0360406 0.0180203 0.999838i \(-0.494264\pi\)
0.0180203 + 0.999838i \(0.494264\pi\)
\(984\) 0 0
\(985\) 3.28637 0.104712
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −7.90838 −0.251472
\(990\) 0 0
\(991\) 14.6766 0.466218 0.233109 0.972451i \(-0.425110\pi\)
0.233109 + 0.972451i \(0.425110\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −16.9250 −0.536558
\(996\) 0 0
\(997\) −1.64207 −0.0520049 −0.0260024 0.999662i \(-0.508278\pi\)
−0.0260024 + 0.999662i \(0.508278\pi\)
\(998\) 0 0
\(999\) 0 0
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 5796.2.a.t.1.4 5
3.2 odd 2 644.2.a.d.1.5 5
12.11 even 2 2576.2.a.bb.1.1 5
21.20 even 2 4508.2.a.f.1.1 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
644.2.a.d.1.5 5 3.2 odd 2
2576.2.a.bb.1.1 5 12.11 even 2
4508.2.a.f.1.1 5 21.20 even 2
5796.2.a.t.1.4 5 1.1 even 1 trivial