Properties

Label 644.2.a.d.1.5
Level $644$
Weight $2$
Character 644.1
Self dual yes
Analytic conductor $5.142$
Analytic rank $0$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 644.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(5.14236589017\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-2.25688\) of defining polynomial
Character \(\chi\) \(=\) 644.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.25688 q^{3} -3.04771 q^{5} -1.00000 q^{7} +7.60729 q^{9} +O(q^{10})\) \(q+3.25688 q^{3} -3.04771 q^{5} -1.00000 q^{7} +7.60729 q^{9} +5.22523 q^{11} +3.38206 q^{13} -9.92604 q^{15} -2.63895 q^{17} +3.39461 q^{19} -3.25688 q^{21} -1.00000 q^{23} +4.28854 q^{25} +15.0054 q^{27} -4.00190 q^{29} +6.97185 q^{31} +17.0180 q^{33} +3.04771 q^{35} -5.11916 q^{37} +11.0150 q^{39} -5.89583 q^{41} -7.90838 q^{43} -23.1848 q^{45} +9.54893 q^{47} +1.00000 q^{49} -8.59475 q^{51} -11.8200 q^{53} -15.9250 q^{55} +11.0558 q^{57} +1.51979 q^{59} +1.13934 q^{61} -7.60729 q^{63} -10.3076 q^{65} -8.80688 q^{67} -3.25688 q^{69} -14.5333 q^{71} -13.2271 q^{73} +13.9673 q^{75} -5.22523 q^{77} +14.4398 q^{79} +26.0490 q^{81} -0.693795 q^{83} +8.04275 q^{85} -13.0337 q^{87} +10.8511 q^{89} -3.38206 q^{91} +22.7065 q^{93} -10.3458 q^{95} -3.23476 q^{97} +39.7498 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q + 3 q^{3} + 2 q^{5} - 5 q^{7} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q + 3 q^{3} + 2 q^{5} - 5 q^{7} + 10 q^{9} + 2 q^{11} + 13 q^{13} + 4 q^{15} + 4 q^{17} + 12 q^{19} - 3 q^{21} - 5 q^{23} + 19 q^{25} + 15 q^{27} + 13 q^{29} - 3 q^{31} + 24 q^{33} - 2 q^{35} - 4 q^{37} + 3 q^{39} + q^{41} - 8 q^{43} - 16 q^{45} + 5 q^{47} + 5 q^{49} - 16 q^{51} - 8 q^{53} - 2 q^{55} + 12 q^{57} + 12 q^{59} + 20 q^{61} - 10 q^{63} - 12 q^{65} - 12 q^{67} - 3 q^{69} + 9 q^{71} - 9 q^{73} + 35 q^{75} - 2 q^{77} - 8 q^{79} - 11 q^{81} - 28 q^{83} + 16 q^{85} - 15 q^{87} + 32 q^{89} - 13 q^{91} - 15 q^{93} - 36 q^{95} + 4 q^{97} + 28 q^{99}+O(q^{100}) \) 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
\(3\) 3.25688 1.88036 0.940181 0.340675i \(-0.110655\pi\)
0.940181 + 0.340675i \(0.110655\pi\)
\(4\) 0 0
\(5\) −3.04771 −1.36298 −0.681489 0.731828i \(-0.738667\pi\)
−0.681489 + 0.731828i \(0.738667\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 7.60729 2.53576
\(10\) 0 0
\(11\) 5.22523 1.57546 0.787732 0.616018i \(-0.211255\pi\)
0.787732 + 0.616018i \(0.211255\pi\)
\(12\) 0 0
\(13\) 3.38206 0.938016 0.469008 0.883194i \(-0.344612\pi\)
0.469008 + 0.883194i \(0.344612\pi\)
\(14\) 0 0
\(15\) −9.92604 −2.56289
\(16\) 0 0
\(17\) −2.63895 −0.640039 −0.320019 0.947411i \(-0.603689\pi\)
−0.320019 + 0.947411i \(0.603689\pi\)
\(18\) 0 0
\(19\) 3.39461 0.778777 0.389388 0.921074i \(-0.372686\pi\)
0.389388 + 0.921074i \(0.372686\pi\)
\(20\) 0 0
\(21\) −3.25688 −0.710710
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 4.28854 0.857708
\(26\) 0 0
\(27\) 15.0054 2.88779
\(28\) 0 0
\(29\) −4.00190 −0.743134 −0.371567 0.928406i \(-0.621179\pi\)
−0.371567 + 0.928406i \(0.621179\pi\)
\(30\) 0 0
\(31\) 6.97185 1.25218 0.626091 0.779750i \(-0.284654\pi\)
0.626091 + 0.779750i \(0.284654\pi\)
\(32\) 0 0
\(33\) 17.0180 2.96245
\(34\) 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
\(39\) 11.0150 1.76381
\(40\) 0 0
\(41\) −5.89583 −0.920774 −0.460387 0.887718i \(-0.652289\pi\)
−0.460387 + 0.887718i \(0.652289\pi\)
\(42\) 0 0
\(43\) −7.90838 −1.20602 −0.603008 0.797735i \(-0.706031\pi\)
−0.603008 + 0.797735i \(0.706031\pi\)
\(44\) 0 0
\(45\) −23.1848 −3.45619
\(46\) 0 0
\(47\) 9.54893 1.39286 0.696428 0.717627i \(-0.254772\pi\)
0.696428 + 0.717627i \(0.254772\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −8.59475 −1.20351
\(52\) 0 0
\(53\) −11.8200 −1.62360 −0.811799 0.583937i \(-0.801512\pi\)
−0.811799 + 0.583937i \(0.801512\pi\)
\(54\) 0 0
\(55\) −15.9250 −2.14732
\(56\) 0 0
\(57\) 11.0558 1.46438
\(58\) 0 0
\(59\) 1.51979 0.197860 0.0989299 0.995094i \(-0.468458\pi\)
0.0989299 + 0.995094i \(0.468458\pi\)
\(60\) 0 0
\(61\) 1.13934 0.145877 0.0729385 0.997336i \(-0.476762\pi\)
0.0729385 + 0.997336i \(0.476762\pi\)
\(62\) 0 0
\(63\) −7.60729 −0.958428
\(64\) 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
\(69\) −3.25688 −0.392083
\(70\) 0 0
\(71\) −14.5333 −1.72479 −0.862394 0.506237i \(-0.831036\pi\)
−0.862394 + 0.506237i \(0.831036\pi\)
\(72\) 0 0
\(73\) −13.2271 −1.54812 −0.774059 0.633114i \(-0.781777\pi\)
−0.774059 + 0.633114i \(0.781777\pi\)
\(74\) 0 0
\(75\) 13.9673 1.61280
\(76\) 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
\(81\) 26.0490 2.89433
\(82\) 0 0
\(83\) −0.693795 −0.0761538 −0.0380769 0.999275i \(-0.512123\pi\)
−0.0380769 + 0.999275i \(0.512123\pi\)
\(84\) 0 0
\(85\) 8.04275 0.872359
\(86\) 0 0
\(87\) −13.0337 −1.39736
\(88\) 0 0
\(89\) 10.8511 1.15021 0.575106 0.818079i \(-0.304961\pi\)
0.575106 + 0.818079i \(0.304961\pi\)
\(90\) 0 0
\(91\) −3.38206 −0.354537
\(92\) 0 0
\(93\) 22.7065 2.35456
\(94\) 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
\(99\) 39.7498 3.99501
\(100\) 0 0
\(101\) −8.32672 −0.828540 −0.414270 0.910154i \(-0.635963\pi\)
−0.414270 + 0.910154i \(0.635963\pi\)
\(102\) 0 0
\(103\) 0.418345 0.0412208 0.0206104 0.999788i \(-0.493439\pi\)
0.0206104 + 0.999788i \(0.493439\pi\)
\(104\) 0 0
\(105\) 9.92604 0.968682
\(106\) 0 0
\(107\) −11.9084 −1.15123 −0.575613 0.817722i \(-0.695237\pi\)
−0.575613 + 0.817722i \(0.695237\pi\)
\(108\) 0 0
\(109\) 17.9154 1.71598 0.857992 0.513663i \(-0.171712\pi\)
0.857992 + 0.513663i \(0.171712\pi\)
\(110\) 0 0
\(111\) −16.6725 −1.58248
\(112\) 0 0
\(113\) −12.6375 −1.18884 −0.594418 0.804156i \(-0.702617\pi\)
−0.594418 + 0.804156i \(0.702617\pi\)
\(114\) 0 0
\(115\) 3.04771 0.284201
\(116\) 0 0
\(117\) 25.7283 2.37859
\(118\) 0 0
\(119\) 2.63895 0.241912
\(120\) 0 0
\(121\) 16.3030 1.48209
\(122\) 0 0
\(123\) −19.2020 −1.73139
\(124\) 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
\(129\) −25.7567 −2.26775
\(130\) 0 0
\(131\) −14.0910 −1.23114 −0.615569 0.788083i \(-0.711074\pi\)
−0.615569 + 0.788083i \(0.711074\pi\)
\(132\) 0 0
\(133\) −3.39461 −0.294350
\(134\) 0 0
\(135\) −45.7321 −3.93600
\(136\) 0 0
\(137\) 2.67250 0.228327 0.114164 0.993462i \(-0.463581\pi\)
0.114164 + 0.993462i \(0.463581\pi\)
\(138\) 0 0
\(139\) 6.23315 0.528689 0.264344 0.964428i \(-0.414844\pi\)
0.264344 + 0.964428i \(0.414844\pi\)
\(140\) 0 0
\(141\) 31.0998 2.61907
\(142\) 0 0
\(143\) 17.6721 1.47781
\(144\) 0 0
\(145\) 12.1966 1.01287
\(146\) 0 0
\(147\) 3.25688 0.268623
\(148\) 0 0
\(149\) −5.58165 −0.457267 −0.228633 0.973513i \(-0.573426\pi\)
−0.228633 + 0.973513i \(0.573426\pi\)
\(150\) 0 0
\(151\) −11.8325 −0.962916 −0.481458 0.876469i \(-0.659893\pi\)
−0.481458 + 0.876469i \(0.659893\pi\)
\(152\) 0 0
\(153\) −20.0752 −1.62299
\(154\) 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
\(159\) −38.4963 −3.05295
\(160\) 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
\(165\) −51.8658 −4.03775
\(166\) 0 0
\(167\) 6.28358 0.486238 0.243119 0.969996i \(-0.421829\pi\)
0.243119 + 0.969996i \(0.421829\pi\)
\(168\) 0 0
\(169\) −1.56164 −0.120126
\(170\) 0 0
\(171\) 25.8238 1.97479
\(172\) 0 0
\(173\) −2.60539 −0.198084 −0.0990421 0.995083i \(-0.531578\pi\)
−0.0990421 + 0.995083i \(0.531578\pi\)
\(174\) 0 0
\(175\) −4.28854 −0.324183
\(176\) 0 0
\(177\) 4.94978 0.372048
\(178\) 0 0
\(179\) 25.2341 1.88609 0.943044 0.332667i \(-0.107949\pi\)
0.943044 + 0.332667i \(0.107949\pi\)
\(180\) 0 0
\(181\) −1.36485 −0.101448 −0.0507242 0.998713i \(-0.516153\pi\)
−0.0507242 + 0.998713i \(0.516153\pi\)
\(182\) 0 0
\(183\) 3.71068 0.274302
\(184\) 0 0
\(185\) 15.6017 1.14706
\(186\) 0 0
\(187\) −13.7891 −1.00836
\(188\) 0 0
\(189\) −15.0054 −1.09148
\(190\) 0 0
\(191\) −22.1467 −1.60248 −0.801239 0.598344i \(-0.795826\pi\)
−0.801239 + 0.598344i \(0.795826\pi\)
\(192\) 0 0
\(193\) 18.3653 1.32197 0.660983 0.750401i \(-0.270139\pi\)
0.660983 + 0.750401i \(0.270139\pi\)
\(194\) 0 0
\(195\) −33.5705 −2.40403
\(196\) 0 0
\(197\) −1.07831 −0.0768261 −0.0384131 0.999262i \(-0.512230\pi\)
−0.0384131 + 0.999262i \(0.512230\pi\)
\(198\) 0 0
\(199\) −5.55335 −0.393666 −0.196833 0.980437i \(-0.563066\pi\)
−0.196833 + 0.980437i \(0.563066\pi\)
\(200\) 0 0
\(201\) −28.6830 −2.02314
\(202\) 0 0
\(203\) 4.00190 0.280878
\(204\) 0 0
\(205\) 17.9688 1.25499
\(206\) 0 0
\(207\) −7.60729 −0.528743
\(208\) 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
\(213\) −47.3334 −3.24323
\(214\) 0 0
\(215\) 24.1024 1.64377
\(216\) 0 0
\(217\) −6.97185 −0.473280
\(218\) 0 0
\(219\) −43.0792 −2.91102
\(220\) 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
\(225\) 32.6242 2.17495
\(226\) 0 0
\(227\) −8.26663 −0.548675 −0.274338 0.961633i \(-0.588459\pi\)
−0.274338 + 0.961633i \(0.588459\pi\)
\(228\) 0 0
\(229\) 26.2369 1.73378 0.866891 0.498499i \(-0.166115\pi\)
0.866891 + 0.498499i \(0.166115\pi\)
\(230\) 0 0
\(231\) −17.0180 −1.11970
\(232\) 0 0
\(233\) 1.17735 0.0771310 0.0385655 0.999256i \(-0.487721\pi\)
0.0385655 + 0.999256i \(0.487721\pi\)
\(234\) 0 0
\(235\) −29.1024 −1.89843
\(236\) 0 0
\(237\) 47.0288 3.05485
\(238\) 0 0
\(239\) 5.56911 0.360236 0.180118 0.983645i \(-0.442352\pi\)
0.180118 + 0.983645i \(0.442352\pi\)
\(240\) 0 0
\(241\) 8.12518 0.523389 0.261694 0.965151i \(-0.415719\pi\)
0.261694 + 0.965151i \(0.415719\pi\)
\(242\) 0 0
\(243\) 39.8223 2.55460
\(244\) 0 0
\(245\) −3.04771 −0.194711
\(246\) 0 0
\(247\) 11.4808 0.730505
\(248\) 0 0
\(249\) −2.25961 −0.143197
\(250\) 0 0
\(251\) 2.78542 0.175814 0.0879071 0.996129i \(-0.471982\pi\)
0.0879071 + 0.996129i \(0.471982\pi\)
\(252\) 0 0
\(253\) −5.22523 −0.328507
\(254\) 0 0
\(255\) 26.1943 1.64035
\(256\) 0 0
\(257\) −24.1150 −1.50425 −0.752126 0.659020i \(-0.770971\pi\)
−0.752126 + 0.659020i \(0.770971\pi\)
\(258\) 0 0
\(259\) 5.11916 0.318089
\(260\) 0 0
\(261\) −30.4436 −1.88441
\(262\) 0 0
\(263\) 3.40905 0.210211 0.105106 0.994461i \(-0.466482\pi\)
0.105106 + 0.994461i \(0.466482\pi\)
\(264\) 0 0
\(265\) 36.0239 2.21293
\(266\) 0 0
\(267\) 35.3407 2.16282
\(268\) 0 0
\(269\) 5.29044 0.322564 0.161282 0.986908i \(-0.448437\pi\)
0.161282 + 0.986908i \(0.448437\pi\)
\(270\) 0 0
\(271\) 16.2206 0.985331 0.492666 0.870219i \(-0.336023\pi\)
0.492666 + 0.870219i \(0.336023\pi\)
\(272\) 0 0
\(273\) −11.0150 −0.666658
\(274\) 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
\(279\) 53.0369 3.17524
\(280\) 0 0
\(281\) −5.74964 −0.342995 −0.171497 0.985185i \(-0.554860\pi\)
−0.171497 + 0.985185i \(0.554860\pi\)
\(282\) 0 0
\(283\) −14.0108 −0.832857 −0.416428 0.909169i \(-0.636718\pi\)
−0.416428 + 0.909169i \(0.636718\pi\)
\(284\) 0 0
\(285\) −33.6950 −1.99592
\(286\) 0 0
\(287\) 5.89583 0.348020
\(288\) 0 0
\(289\) −10.0360 −0.590350
\(290\) 0 0
\(291\) −10.5352 −0.617586
\(292\) 0 0
\(293\) 15.7616 0.920801 0.460400 0.887711i \(-0.347706\pi\)
0.460400 + 0.887711i \(0.347706\pi\)
\(294\) 0 0
\(295\) −4.63188 −0.269678
\(296\) 0 0
\(297\) 78.4066 4.54961
\(298\) 0 0
\(299\) −3.38206 −0.195590
\(300\) 0 0
\(301\) 7.90838 0.455831
\(302\) 0 0
\(303\) −27.1192 −1.55795
\(304\) 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
\(309\) 1.36250 0.0775100
\(310\) 0 0
\(311\) 4.41105 0.250128 0.125064 0.992149i \(-0.460086\pi\)
0.125064 + 0.992149i \(0.460086\pi\)
\(312\) 0 0
\(313\) −6.20154 −0.350532 −0.175266 0.984521i \(-0.556079\pi\)
−0.175266 + 0.984521i \(0.556079\pi\)
\(314\) 0 0
\(315\) 23.1848 1.30632
\(316\) 0 0
\(317\) −9.50769 −0.534005 −0.267003 0.963696i \(-0.586033\pi\)
−0.267003 + 0.963696i \(0.586033\pi\)
\(318\) 0 0
\(319\) −20.9108 −1.17078
\(320\) 0 0
\(321\) −38.7842 −2.16472
\(322\) 0 0
\(323\) −8.95819 −0.498447
\(324\) 0 0
\(325\) 14.5041 0.804544
\(326\) 0 0
\(327\) 58.3484 3.22667
\(328\) 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
\(333\) −38.9429 −2.13406
\(334\) 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
\(339\) −41.1589 −2.23544
\(340\) 0 0
\(341\) 36.4295 1.97277
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 9.92604 0.534400
\(346\) 0 0
\(347\) 34.8917 1.87308 0.936541 0.350558i \(-0.114008\pi\)
0.936541 + 0.350558i \(0.114008\pi\)
\(348\) 0 0
\(349\) 6.92337 0.370599 0.185300 0.982682i \(-0.440674\pi\)
0.185300 + 0.982682i \(0.440674\pi\)
\(350\) 0 0
\(351\) 50.7493 2.70880
\(352\) 0 0
\(353\) 21.6050 1.14992 0.574959 0.818182i \(-0.305018\pi\)
0.574959 + 0.818182i \(0.305018\pi\)
\(354\) 0 0
\(355\) 44.2934 2.35085
\(356\) 0 0
\(357\) 8.59475 0.454882
\(358\) 0 0
\(359\) −26.2085 −1.38323 −0.691616 0.722265i \(-0.743101\pi\)
−0.691616 + 0.722265i \(0.743101\pi\)
\(360\) 0 0
\(361\) −7.47664 −0.393507
\(362\) 0 0
\(363\) 53.0969 2.78687
\(364\) 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
\(369\) −44.8513 −2.33487
\(370\) 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
\(375\) 7.06197 0.364678
\(376\) 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
\(381\) −10.4980 −0.537829
\(382\) 0 0
\(383\) −18.4925 −0.944921 −0.472461 0.881352i \(-0.656634\pi\)
−0.472461 + 0.881352i \(0.656634\pi\)
\(384\) 0 0
\(385\) 15.9250 0.811612
\(386\) 0 0
\(387\) −60.1613 −3.05817
\(388\) 0 0
\(389\) 11.3030 0.573084 0.286542 0.958068i \(-0.407494\pi\)
0.286542 + 0.958068i \(0.407494\pi\)
\(390\) 0 0
\(391\) 2.63895 0.133457
\(392\) 0 0
\(393\) −45.8928 −2.31498
\(394\) 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
\(399\) −11.0558 −0.553484
\(400\) 0 0
\(401\) −3.01127 −0.150376 −0.0751878 0.997169i \(-0.523956\pi\)
−0.0751878 + 0.997169i \(0.523956\pi\)
\(402\) 0 0
\(403\) 23.5793 1.17457
\(404\) 0 0
\(405\) −79.3898 −3.94491
\(406\) 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
\(411\) 8.70404 0.429338
\(412\) 0 0
\(413\) −1.51979 −0.0747839
\(414\) 0 0
\(415\) 2.11449 0.103796
\(416\) 0 0
\(417\) 20.3006 0.994126
\(418\) 0 0
\(419\) −6.40028 −0.312674 −0.156337 0.987704i \(-0.549969\pi\)
−0.156337 + 0.987704i \(0.549969\pi\)
\(420\) 0 0
\(421\) −8.01082 −0.390423 −0.195212 0.980761i \(-0.562539\pi\)
−0.195212 + 0.980761i \(0.562539\pi\)
\(422\) 0 0
\(423\) 72.6415 3.53195
\(424\) 0 0
\(425\) −11.3172 −0.548967
\(426\) 0 0
\(427\) −1.13934 −0.0551363
\(428\) 0 0
\(429\) 57.5558 2.77882
\(430\) 0 0
\(431\) −27.6084 −1.32985 −0.664925 0.746910i \(-0.731537\pi\)
−0.664925 + 0.746910i \(0.731537\pi\)
\(432\) 0 0
\(433\) −14.8797 −0.715074 −0.357537 0.933899i \(-0.616383\pi\)
−0.357537 + 0.933899i \(0.616383\pi\)
\(434\) 0 0
\(435\) 39.7230 1.90457
\(436\) 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
\(441\) 7.60729 0.362252
\(442\) 0 0
\(443\) −10.5546 −0.501465 −0.250733 0.968056i \(-0.580671\pi\)
−0.250733 + 0.968056i \(0.580671\pi\)
\(444\) 0 0
\(445\) −33.0710 −1.56771
\(446\) 0 0
\(447\) −18.1788 −0.859828
\(448\) 0 0
\(449\) 39.9560 1.88564 0.942821 0.333301i \(-0.108162\pi\)
0.942821 + 0.333301i \(0.108162\pi\)
\(450\) 0 0
\(451\) −30.8071 −1.45065
\(452\) 0 0
\(453\) −38.5371 −1.81063
\(454\) 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
\(459\) −39.5985 −1.84830
\(460\) 0 0
\(461\) −6.70956 −0.312495 −0.156248 0.987718i \(-0.549940\pi\)
−0.156248 + 0.987718i \(0.549940\pi\)
\(462\) 0 0
\(463\) 16.6512 0.773848 0.386924 0.922112i \(-0.373538\pi\)
0.386924 + 0.922112i \(0.373538\pi\)
\(464\) 0 0
\(465\) −69.2029 −3.20921
\(466\) 0 0
\(467\) 39.1863 1.81332 0.906662 0.421857i \(-0.138622\pi\)
0.906662 + 0.421857i \(0.138622\pi\)
\(468\) 0 0
\(469\) 8.80688 0.406664
\(470\) 0 0
\(471\) 56.3491 2.59643
\(472\) 0 0
\(473\) −41.3230 −1.90004
\(474\) 0 0
\(475\) 14.5579 0.667963
\(476\) 0 0
\(477\) −89.9180 −4.11706
\(478\) 0 0
\(479\) −36.2704 −1.65724 −0.828619 0.559813i \(-0.810873\pi\)
−0.828619 + 0.559813i \(0.810873\pi\)
\(480\) 0 0
\(481\) −17.3133 −0.789420
\(482\) 0 0
\(483\) 3.25688 0.148193
\(484\) 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
\(489\) 46.6425 2.10925
\(490\) 0 0
\(491\) −22.3752 −1.00978 −0.504889 0.863185i \(-0.668466\pi\)
−0.504889 + 0.863185i \(0.668466\pi\)
\(492\) 0 0
\(493\) 10.5608 0.475635
\(494\) 0 0
\(495\) −121.146 −5.44510
\(496\) 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
\(501\) 20.4649 0.914304
\(502\) 0 0
\(503\) −2.57708 −0.114906 −0.0574532 0.998348i \(-0.518298\pi\)
−0.0574532 + 0.998348i \(0.518298\pi\)
\(504\) 0 0
\(505\) 25.3774 1.12928
\(506\) 0 0
\(507\) −5.08608 −0.225881
\(508\) 0 0
\(509\) 33.4091 1.48083 0.740417 0.672148i \(-0.234628\pi\)
0.740417 + 0.672148i \(0.234628\pi\)
\(510\) 0 0
\(511\) 13.2271 0.585134
\(512\) 0 0
\(513\) 50.9375 2.24894
\(514\) 0 0
\(515\) −1.27500 −0.0561830
\(516\) 0 0
\(517\) 49.8953 2.19439
\(518\) 0 0
\(519\) −8.48546 −0.372470
\(520\) 0 0
\(521\) 12.4303 0.544580 0.272290 0.962215i \(-0.412219\pi\)
0.272290 + 0.962215i \(0.412219\pi\)
\(522\) 0 0
\(523\) 1.05262 0.0460279 0.0230140 0.999735i \(-0.492674\pi\)
0.0230140 + 0.999735i \(0.492674\pi\)
\(524\) 0 0
\(525\) −13.9673 −0.609582
\(526\) 0 0
\(527\) −18.3984 −0.801445
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 11.5615 0.501725
\(532\) 0 0
\(533\) −19.9401 −0.863701
\(534\) 0 0
\(535\) 36.2933 1.56910
\(536\) 0 0
\(537\) 82.1847 3.54653
\(538\) 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
\(543\) −4.44515 −0.190760
\(544\) 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
\(549\) 8.66726 0.369910
\(550\) 0 0
\(551\) −13.5849 −0.578735
\(552\) 0 0
\(553\) −14.4398 −0.614043
\(554\) 0 0
\(555\) 50.8130 2.15689
\(556\) 0 0
\(557\) −22.2666 −0.943467 −0.471734 0.881741i \(-0.656372\pi\)
−0.471734 + 0.881741i \(0.656372\pi\)
\(558\) 0 0
\(559\) −26.7466 −1.13126
\(560\) 0 0
\(561\) −44.9095 −1.89608
\(562\) 0 0
\(563\) 22.0300 0.928453 0.464227 0.885717i \(-0.346332\pi\)
0.464227 + 0.885717i \(0.346332\pi\)
\(564\) 0 0
\(565\) 38.5154 1.62036
\(566\) 0 0
\(567\) −26.0490 −1.09395
\(568\) 0 0
\(569\) 27.9918 1.17348 0.586738 0.809777i \(-0.300412\pi\)
0.586738 + 0.809777i \(0.300412\pi\)
\(570\) 0 0
\(571\) 19.7000 0.824421 0.412210 0.911089i \(-0.364757\pi\)
0.412210 + 0.911089i \(0.364757\pi\)
\(572\) 0 0
\(573\) −72.1292 −3.01324
\(574\) 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
\(579\) 59.8138 2.48578
\(580\) 0 0
\(581\) 0.693795 0.0287834
\(582\) 0 0
\(583\) −61.7620 −2.55792
\(584\) 0 0
\(585\) −78.4126 −3.24196
\(586\) 0 0
\(587\) −19.3278 −0.797743 −0.398872 0.917007i \(-0.630598\pi\)
−0.398872 + 0.917007i \(0.630598\pi\)
\(588\) 0 0
\(589\) 23.6667 0.975170
\(590\) 0 0
\(591\) −3.51192 −0.144461
\(592\) 0 0
\(593\) 8.45045 0.347018 0.173509 0.984832i \(-0.444489\pi\)
0.173509 + 0.984832i \(0.444489\pi\)
\(594\) 0 0
\(595\) −8.04275 −0.329721
\(596\) 0 0
\(597\) −18.0866 −0.740235
\(598\) 0 0
\(599\) 5.56581 0.227413 0.113706 0.993514i \(-0.463728\pi\)
0.113706 + 0.993514i \(0.463728\pi\)
\(600\) 0 0
\(601\) −18.2258 −0.743445 −0.371722 0.928344i \(-0.621233\pi\)
−0.371722 + 0.928344i \(0.621233\pi\)
\(602\) 0 0
\(603\) −66.9965 −2.72831
\(604\) 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
\(609\) 13.0337 0.528153
\(610\) 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
\(615\) 58.5223 2.35985
\(616\) 0 0
\(617\) −14.9140 −0.600417 −0.300208 0.953874i \(-0.597056\pi\)
−0.300208 + 0.953874i \(0.597056\pi\)
\(618\) 0 0
\(619\) 32.3397 1.29984 0.649920 0.760002i \(-0.274802\pi\)
0.649920 + 0.760002i \(0.274802\pi\)
\(620\) 0 0
\(621\) −15.0054 −0.602146
\(622\) 0 0
\(623\) −10.8511 −0.434739
\(624\) 0 0
\(625\) −28.0511 −1.12204
\(626\) 0 0
\(627\) 57.7693 2.30708
\(628\) 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
\(633\) −63.0346 −2.50540
\(634\) 0 0
\(635\) 9.82377 0.389844
\(636\) 0 0
\(637\) 3.38206 0.134002
\(638\) 0 0
\(639\) −110.559 −4.37366
\(640\) 0 0
\(641\) 37.0193 1.46217 0.731087 0.682284i \(-0.239013\pi\)
0.731087 + 0.682284i \(0.239013\pi\)
\(642\) 0 0
\(643\) 24.7183 0.974796 0.487398 0.873180i \(-0.337946\pi\)
0.487398 + 0.873180i \(0.337946\pi\)
\(644\) 0 0
\(645\) 78.4988 3.09089
\(646\) 0 0
\(647\) −20.3207 −0.798887 −0.399444 0.916758i \(-0.630797\pi\)
−0.399444 + 0.916758i \(0.630797\pi\)
\(648\) 0 0
\(649\) 7.94124 0.311721
\(650\) 0 0
\(651\) −22.7065 −0.889938
\(652\) 0 0
\(653\) −13.7950 −0.539839 −0.269919 0.962883i \(-0.586997\pi\)
−0.269919 + 0.962883i \(0.586997\pi\)
\(654\) 0 0
\(655\) 42.9453 1.67801
\(656\) 0 0
\(657\) −100.623 −3.92566
\(658\) 0 0
\(659\) 39.4316 1.53604 0.768019 0.640427i \(-0.221243\pi\)
0.768019 + 0.640427i \(0.221243\pi\)
\(660\) 0 0
\(661\) 38.9211 1.51385 0.756927 0.653499i \(-0.226700\pi\)
0.756927 + 0.653499i \(0.226700\pi\)
\(662\) 0 0
\(663\) −29.0680 −1.12891
\(664\) 0 0
\(665\) 10.3458 0.401192
\(666\) 0 0
\(667\) 4.00190 0.154954
\(668\) 0 0
\(669\) −8.76865 −0.339016
\(670\) 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
\(675\) 64.3513 2.47688
\(676\) 0 0
\(677\) 16.6777 0.640977 0.320489 0.947252i \(-0.396153\pi\)
0.320489 + 0.947252i \(0.396153\pi\)
\(678\) 0 0
\(679\) 3.23476 0.124139
\(680\) 0 0
\(681\) −26.9234 −1.03171
\(682\) 0 0
\(683\) 48.7312 1.86465 0.932324 0.361625i \(-0.117778\pi\)
0.932324 + 0.361625i \(0.117778\pi\)
\(684\) 0 0
\(685\) −8.14502 −0.311205
\(686\) 0 0
\(687\) 85.4504 3.26014
\(688\) 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
\(693\) −39.7498 −1.50997
\(694\) 0 0
\(695\) −18.9968 −0.720591
\(696\) 0 0
\(697\) 15.5588 0.589331
\(698\) 0 0
\(699\) 3.83450 0.145034
\(700\) 0 0
\(701\) −28.1499 −1.06321 −0.531604 0.846993i \(-0.678410\pi\)
−0.531604 + 0.846993i \(0.678410\pi\)
\(702\) 0 0
\(703\) −17.3775 −0.655406
\(704\) 0 0
\(705\) −94.7831 −3.56974
\(706\) 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
\(711\) 109.848 4.11961
\(712\) 0 0
\(713\) −6.97185 −0.261098
\(714\) 0 0
\(715\) −53.8593 −2.01422
\(716\) 0 0
\(717\) 18.1379 0.677374
\(718\) 0 0
\(719\) −22.2623 −0.830243 −0.415122 0.909766i \(-0.636261\pi\)
−0.415122 + 0.909766i \(0.636261\pi\)
\(720\) 0 0
\(721\) −0.418345 −0.0155800
\(722\) 0 0
\(723\) 26.4628 0.984161
\(724\) 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
\(729\) 51.5497 1.90925
\(730\) 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
\(735\) −9.92604 −0.366127
\(736\) 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
\(741\) 37.3916 1.37361
\(742\) 0 0
\(743\) 30.8619 1.13222 0.566108 0.824331i \(-0.308449\pi\)
0.566108 + 0.824331i \(0.308449\pi\)
\(744\) 0 0
\(745\) 17.0113 0.623245
\(746\) 0 0
\(747\) −5.27790 −0.193108
\(748\) 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
\(753\) 9.07179 0.330594
\(754\) 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
\(759\) −17.0180 −0.617713
\(760\) 0 0
\(761\) 41.8363 1.51657 0.758283 0.651926i \(-0.226039\pi\)
0.758283 + 0.651926i \(0.226039\pi\)
\(762\) 0 0
\(763\) −17.9154 −0.648581
\(764\) 0 0
\(765\) 61.1835 2.21210
\(766\) 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
\(771\) −78.5397 −2.82854
\(772\) 0 0
\(773\) 37.1956 1.33783 0.668917 0.743337i \(-0.266758\pi\)
0.668917 + 0.743337i \(0.266758\pi\)
\(774\) 0 0
\(775\) 29.8991 1.07401
\(776\) 0 0
\(777\) 16.6725 0.598123
\(778\) 0 0
\(779\) −20.0140 −0.717077
\(780\) 0 0
\(781\) −75.9399 −2.71734
\(782\) 0 0
\(783\) −60.0501 −2.14602
\(784\) 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
\(789\) 11.1029 0.395273
\(790\) 0 0
\(791\) 12.6375 0.449338
\(792\) 0 0
\(793\) 3.85331 0.136835
\(794\) 0 0
\(795\) 117.326 4.16111
\(796\) 0 0
\(797\) 25.8311 0.914986 0.457493 0.889213i \(-0.348747\pi\)
0.457493 + 0.889213i \(0.348747\pi\)
\(798\) 0 0
\(799\) −25.1991 −0.891482
\(800\) 0 0
\(801\) 82.5473 2.91667
\(802\) 0 0
\(803\) −69.1147 −2.43901
\(804\) 0 0
\(805\) −3.04771 −0.107418
\(806\) 0 0
\(807\) 17.2303 0.606537
\(808\) 0 0
\(809\) 26.7612 0.940875 0.470437 0.882433i \(-0.344096\pi\)
0.470437 + 0.882433i \(0.344096\pi\)
\(810\) 0 0
\(811\) 30.3856 1.06698 0.533492 0.845805i \(-0.320880\pi\)
0.533492 + 0.845805i \(0.320880\pi\)
\(812\) 0 0
\(813\) 52.8286 1.85278
\(814\) 0 0
\(815\) −43.6469 −1.52888
\(816\) 0 0
\(817\) −26.8458 −0.939217
\(818\) 0 0
\(819\) −25.7283 −0.899021
\(820\) 0 0
\(821\) −16.5069 −0.576095 −0.288048 0.957616i \(-0.593006\pi\)
−0.288048 + 0.957616i \(0.593006\pi\)
\(822\) 0 0
\(823\) −19.9562 −0.695631 −0.347816 0.937563i \(-0.613076\pi\)
−0.347816 + 0.937563i \(0.613076\pi\)
\(824\) 0 0
\(825\) 72.9822 2.54091
\(826\) 0 0
\(827\) −36.8443 −1.28120 −0.640601 0.767874i \(-0.721315\pi\)
−0.640601 + 0.767874i \(0.721315\pi\)
\(828\) 0 0
\(829\) 5.80916 0.201760 0.100880 0.994899i \(-0.467834\pi\)
0.100880 + 0.994899i \(0.467834\pi\)
\(830\) 0 0
\(831\) −72.3714 −2.51054
\(832\) 0 0
\(833\) −2.63895 −0.0914341
\(834\) 0 0
\(835\) −19.1505 −0.662732
\(836\) 0 0
\(837\) 104.615 3.61604
\(838\) 0 0
\(839\) −12.2733 −0.423722 −0.211861 0.977300i \(-0.567952\pi\)
−0.211861 + 0.977300i \(0.567952\pi\)
\(840\) 0 0
\(841\) −12.9848 −0.447752
\(842\) 0 0
\(843\) −18.7259 −0.644954
\(844\) 0 0
\(845\) 4.75942 0.163729
\(846\) 0 0
\(847\) −16.3030 −0.560177
\(848\) 0 0
\(849\) −45.6316 −1.56607
\(850\) 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
\(855\) −78.7034 −2.69160
\(856\) 0 0
\(857\) −19.1066 −0.652670 −0.326335 0.945254i \(-0.605814\pi\)
−0.326335 + 0.945254i \(0.605814\pi\)
\(858\) 0 0
\(859\) −46.1878 −1.57591 −0.787953 0.615735i \(-0.788859\pi\)
−0.787953 + 0.615735i \(0.788859\pi\)
\(860\) 0 0
\(861\) 19.2020 0.654404
\(862\) 0 0
\(863\) 11.5341 0.392625 0.196313 0.980541i \(-0.437103\pi\)
0.196313 + 0.980541i \(0.437103\pi\)
\(864\) 0 0
\(865\) 7.94048 0.269984
\(866\) 0 0
\(867\) −32.6859 −1.11007
\(868\) 0 0
\(869\) 75.4512 2.55951
\(870\) 0 0
\(871\) −29.7854 −1.00924
\(872\) 0 0
\(873\) −24.6077 −0.832846
\(874\) 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
\(879\) 51.3336 1.73144
\(880\) 0 0
\(881\) 11.4505 0.385775 0.192888 0.981221i \(-0.438215\pi\)
0.192888 + 0.981221i \(0.438215\pi\)
\(882\) 0 0
\(883\) 17.3634 0.584325 0.292162 0.956369i \(-0.405625\pi\)
0.292162 + 0.956369i \(0.405625\pi\)
\(884\) 0 0
\(885\) −15.0855 −0.507093
\(886\) 0 0
\(887\) 22.7378 0.763460 0.381730 0.924274i \(-0.375328\pi\)
0.381730 + 0.924274i \(0.375328\pi\)
\(888\) 0 0
\(889\) 3.22333 0.108107
\(890\) 0 0
\(891\) 136.112 4.55992
\(892\) 0 0
\(893\) 32.4149 1.08472
\(894\) 0 0
\(895\) −76.9064 −2.57070
\(896\) 0 0
\(897\) −11.0150 −0.367780
\(898\) 0 0
\(899\) −27.9006 −0.930539
\(900\) 0 0
\(901\) 31.1923 1.03917
\(902\) 0 0
\(903\) 25.7567 0.857128
\(904\) 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
\(909\) −63.3438 −2.10098
\(910\) 0 0
\(911\) 2.92749 0.0969921 0.0484961 0.998823i \(-0.484557\pi\)
0.0484961 + 0.998823i \(0.484557\pi\)
\(912\) 0 0
\(913\) −3.62523 −0.119978
\(914\) 0 0
\(915\) −11.3091 −0.373867
\(916\) 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
\(921\) 37.4358 1.23355
\(922\) 0 0
\(923\) −49.1527 −1.61788
\(924\) 0 0
\(925\) −21.9537 −0.721834
\(926\) 0 0
\(927\) 3.18247 0.104526
\(928\) 0 0
\(929\) −23.3541 −0.766222 −0.383111 0.923702i \(-0.625147\pi\)
−0.383111 + 0.923702i \(0.625147\pi\)
\(930\) 0 0
\(931\) 3.39461 0.111254
\(932\) 0 0
\(933\) 14.3663 0.470331
\(934\) 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
\(939\) −20.1977 −0.659127
\(940\) 0 0
\(941\) 5.13868 0.167516 0.0837580 0.996486i \(-0.473308\pi\)
0.0837580 + 0.996486i \(0.473308\pi\)
\(942\) 0 0
\(943\) 5.89583 0.191995
\(944\) 0 0
\(945\) 45.7321 1.48767
\(946\) 0 0
\(947\) 29.4147 0.955851 0.477925 0.878400i \(-0.341389\pi\)
0.477925 + 0.878400i \(0.341389\pi\)
\(948\) 0 0
\(949\) −44.7350 −1.45216
\(950\) 0 0
\(951\) −30.9655 −1.00412
\(952\) 0 0
\(953\) −5.67396 −0.183797 −0.0918987 0.995768i \(-0.529294\pi\)
−0.0918987 + 0.995768i \(0.529294\pi\)
\(954\) 0 0
\(955\) 67.4967 2.18414
\(956\) 0 0
\(957\) −68.1041 −2.20149
\(958\) 0 0
\(959\) −2.67250 −0.0862997
\(960\) 0 0
\(961\) 17.6067 0.567959
\(962\) 0 0
\(963\) −90.5905 −2.91924
\(964\) 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
\(969\) −29.1758 −0.937262
\(970\) 0 0
\(971\) 34.2084 1.09780 0.548899 0.835889i \(-0.315047\pi\)
0.548899 + 0.835889i \(0.315047\pi\)
\(972\) 0 0
\(973\) −6.23315 −0.199825
\(974\) 0 0
\(975\) 47.2382 1.51283
\(976\) 0 0
\(977\) 8.19697 0.262244 0.131122 0.991366i \(-0.458142\pi\)
0.131122 + 0.991366i \(0.458142\pi\)
\(978\) 0 0
\(979\) 56.6994 1.81212
\(980\) 0 0
\(981\) 136.288 4.35133
\(982\) 0 0
\(983\) −1.12997 −0.0360406 −0.0180203 0.999838i \(-0.505736\pi\)
−0.0180203 + 0.999838i \(0.505736\pi\)
\(984\) 0 0
\(985\) 3.28637 0.104712
\(986\) 0 0
\(987\) −31.0998 −0.989917
\(988\) 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
\(993\) 32.5973 1.03444
\(994\) 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
\(999\) −76.8151 −2.43032
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 644.2.a.d.1.5 5
3.2 odd 2 5796.2.a.t.1.4 5
4.3 odd 2 2576.2.a.bb.1.1 5
7.6 odd 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 1.1 even 1 trivial
2576.2.a.bb.1.1 5 4.3 odd 2
4508.2.a.f.1.1 5 7.6 odd 2
5796.2.a.t.1.4 5 3.2 odd 2