Properties

Label 5445.2.a.by.1.4
Level $5445$
Weight $2$
Character 5445.1
Self dual yes
Analytic conductor $43.479$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 5445 = 3^{2} \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5445.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(43.4785439006\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.74043072.1
Defining polynomial: \(x^{6} - 9 x^{4} + 21 x^{2} - 12\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(0.924607\) of defining polynomial
Character \(\chi\) \(=\) 5445.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.924607 q^{2} -1.14510 q^{4} +1.00000 q^{5} -4.64003 q^{7} -2.90798 q^{8} +O(q^{10})\) \(q+0.924607 q^{2} -1.14510 q^{4} +1.00000 q^{5} -4.64003 q^{7} -2.90798 q^{8} +0.924607 q^{10} -4.29021 q^{14} -0.398534 q^{16} -6.37208 q^{17} -4.64003 q^{19} -1.14510 q^{20} +6.74657 q^{23} +1.00000 q^{25} +5.31331 q^{28} -3.46410 q^{29} -2.20293 q^{31} +5.44748 q^{32} -5.89167 q^{34} -4.64003 q^{35} +3.45636 q^{37} -4.29021 q^{38} -2.90798 q^{40} -5.81597 q^{41} +0.234325 q^{43} +6.23792 q^{46} -9.32698 q^{47} +14.5299 q^{49} +0.924607 q^{50} +3.54364 q^{53} +13.4931 q^{56} -3.20293 q^{58} +14.5804 q^{59} +1.96638 q^{61} -2.03684 q^{62} +5.83384 q^{64} -1.45636 q^{67} +7.29669 q^{68} -4.29021 q^{70} -2.58041 q^{71} +13.6858 q^{73} +3.19578 q^{74} +5.31331 q^{76} +3.58126 q^{79} -0.398534 q^{80} -5.37748 q^{82} -7.16253 q^{83} -6.37208 q^{85} +0.216658 q^{86} -8.98627 q^{89} -7.72551 q^{92} -8.62379 q^{94} -4.64003 q^{95} -12.4426 q^{97} +13.4345 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 6q^{4} + 6q^{5} + O(q^{10}) \) \( 6q + 6q^{4} + 6q^{5} - 6q^{16} + 6q^{20} + 24q^{23} + 6q^{25} - 6q^{31} - 6q^{34} + 30q^{37} + 12q^{47} + 12q^{49} + 12q^{53} + 48q^{56} - 12q^{58} + 36q^{59} - 18q^{67} + 36q^{71} - 6q^{80} + 12q^{82} + 60q^{86} + 12q^{89} + 18q^{92} - 18q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.924607 0.653796 0.326898 0.945060i \(-0.393997\pi\)
0.326898 + 0.945060i \(0.393997\pi\)
\(3\) 0 0
\(4\) −1.14510 −0.572551
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −4.64003 −1.75377 −0.876884 0.480702i \(-0.840382\pi\)
−0.876884 + 0.480702i \(0.840382\pi\)
\(8\) −2.90798 −1.02813
\(9\) 0 0
\(10\) 0.924607 0.292386
\(11\) 0 0
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) −4.29021 −1.14661
\(15\) 0 0
\(16\) −0.398534 −0.0996336
\(17\) −6.37208 −1.54546 −0.772729 0.634736i \(-0.781109\pi\)
−0.772729 + 0.634736i \(0.781109\pi\)
\(18\) 0 0
\(19\) −4.64003 −1.06450 −0.532248 0.846588i \(-0.678653\pi\)
−0.532248 + 0.846588i \(0.678653\pi\)
\(20\) −1.14510 −0.256053
\(21\) 0 0
\(22\) 0 0
\(23\) 6.74657 1.40676 0.703378 0.710816i \(-0.251674\pi\)
0.703378 + 0.710816i \(0.251674\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 5.31331 1.00412
\(29\) −3.46410 −0.643268 −0.321634 0.946864i \(-0.604232\pi\)
−0.321634 + 0.946864i \(0.604232\pi\)
\(30\) 0 0
\(31\) −2.20293 −0.395658 −0.197829 0.980237i \(-0.563389\pi\)
−0.197829 + 0.980237i \(0.563389\pi\)
\(32\) 5.44748 0.962987
\(33\) 0 0
\(34\) −5.89167 −1.01041
\(35\) −4.64003 −0.784309
\(36\) 0 0
\(37\) 3.45636 0.568223 0.284111 0.958791i \(-0.408301\pi\)
0.284111 + 0.958791i \(0.408301\pi\)
\(38\) −4.29021 −0.695963
\(39\) 0 0
\(40\) −2.90798 −0.459792
\(41\) −5.81597 −0.908301 −0.454151 0.890925i \(-0.650057\pi\)
−0.454151 + 0.890925i \(0.650057\pi\)
\(42\) 0 0
\(43\) 0.234325 0.0357342 0.0178671 0.999840i \(-0.494312\pi\)
0.0178671 + 0.999840i \(0.494312\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 6.23792 0.919731
\(47\) −9.32698 −1.36048 −0.680240 0.732990i \(-0.738124\pi\)
−0.680240 + 0.732990i \(0.738124\pi\)
\(48\) 0 0
\(49\) 14.5299 2.07570
\(50\) 0.924607 0.130759
\(51\) 0 0
\(52\) 0 0
\(53\) 3.54364 0.486756 0.243378 0.969932i \(-0.421744\pi\)
0.243378 + 0.969932i \(0.421744\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 13.4931 1.80310
\(57\) 0 0
\(58\) −3.20293 −0.420565
\(59\) 14.5804 1.89821 0.949104 0.314963i \(-0.101992\pi\)
0.949104 + 0.314963i \(0.101992\pi\)
\(60\) 0 0
\(61\) 1.96638 0.251769 0.125884 0.992045i \(-0.459823\pi\)
0.125884 + 0.992045i \(0.459823\pi\)
\(62\) −2.03684 −0.258680
\(63\) 0 0
\(64\) 5.83384 0.729230
\(65\) 0 0
\(66\) 0 0
\(67\) −1.45636 −0.177923 −0.0889615 0.996035i \(-0.528355\pi\)
−0.0889615 + 0.996035i \(0.528355\pi\)
\(68\) 7.29669 0.884854
\(69\) 0 0
\(70\) −4.29021 −0.512778
\(71\) −2.58041 −0.306238 −0.153119 0.988208i \(-0.548932\pi\)
−0.153119 + 0.988208i \(0.548932\pi\)
\(72\) 0 0
\(73\) 13.6858 1.60180 0.800899 0.598799i \(-0.204355\pi\)
0.800899 + 0.598799i \(0.204355\pi\)
\(74\) 3.19578 0.371501
\(75\) 0 0
\(76\) 5.31331 0.609479
\(77\) 0 0
\(78\) 0 0
\(79\) 3.58126 0.402924 0.201462 0.979496i \(-0.435431\pi\)
0.201462 + 0.979496i \(0.435431\pi\)
\(80\) −0.398534 −0.0445575
\(81\) 0 0
\(82\) −5.37748 −0.593843
\(83\) −7.16253 −0.786190 −0.393095 0.919498i \(-0.628596\pi\)
−0.393095 + 0.919498i \(0.628596\pi\)
\(84\) 0 0
\(85\) −6.37208 −0.691150
\(86\) 0.216658 0.0233628
\(87\) 0 0
\(88\) 0 0
\(89\) −8.98627 −0.952543 −0.476272 0.879298i \(-0.658012\pi\)
−0.476272 + 0.879298i \(0.658012\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −7.72551 −0.805440
\(93\) 0 0
\(94\) −8.62379 −0.889476
\(95\) −4.64003 −0.476057
\(96\) 0 0
\(97\) −12.4426 −1.26336 −0.631679 0.775230i \(-0.717634\pi\)
−0.631679 + 0.775230i \(0.717634\pi\)
\(98\) 13.4345 1.35708
\(99\) 0 0
\(100\) −1.14510 −0.114510
\(101\) −15.0960 −1.50211 −0.751056 0.660239i \(-0.770455\pi\)
−0.751056 + 0.660239i \(0.770455\pi\)
\(102\) 0 0
\(103\) 19.0230 1.87440 0.937198 0.348797i \(-0.113410\pi\)
0.937198 + 0.348797i \(0.113410\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 3.27647 0.318239
\(107\) 17.2670 1.66927 0.834634 0.550805i \(-0.185679\pi\)
0.834634 + 0.550805i \(0.185679\pi\)
\(108\) 0 0
\(109\) 14.1544 1.35575 0.677874 0.735178i \(-0.262901\pi\)
0.677874 + 0.735178i \(0.262901\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.84921 0.174734
\(113\) −3.94950 −0.371538 −0.185769 0.982593i \(-0.559478\pi\)
−0.185769 + 0.982593i \(0.559478\pi\)
\(114\) 0 0
\(115\) 6.74657 0.629121
\(116\) 3.96675 0.368304
\(117\) 0 0
\(118\) 13.4811 1.24104
\(119\) 29.5667 2.71037
\(120\) 0 0
\(121\) 0 0
\(122\) 1.81812 0.164605
\(123\) 0 0
\(124\) 2.52258 0.226535
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 16.5063 1.46470 0.732348 0.680930i \(-0.238424\pi\)
0.732348 + 0.680930i \(0.238424\pi\)
\(128\) −5.50095 −0.486220
\(129\) 0 0
\(130\) 0 0
\(131\) 15.9739 1.39565 0.697825 0.716268i \(-0.254151\pi\)
0.697825 + 0.716268i \(0.254151\pi\)
\(132\) 0 0
\(133\) 21.5299 1.86688
\(134\) −1.34656 −0.116325
\(135\) 0 0
\(136\) 18.5299 1.58893
\(137\) 5.03677 0.430321 0.215160 0.976579i \(-0.430973\pi\)
0.215160 + 0.976579i \(0.430973\pi\)
\(138\) 0 0
\(139\) −18.8479 −1.59866 −0.799330 0.600892i \(-0.794812\pi\)
−0.799330 + 0.600892i \(0.794812\pi\)
\(140\) 5.31331 0.449057
\(141\) 0 0
\(142\) −2.38586 −0.200217
\(143\) 0 0
\(144\) 0 0
\(145\) −3.46410 −0.287678
\(146\) 12.6540 1.04725
\(147\) 0 0
\(148\) −3.95789 −0.325337
\(149\) 9.74872 0.798646 0.399323 0.916810i \(-0.369245\pi\)
0.399323 + 0.916810i \(0.369245\pi\)
\(150\) 0 0
\(151\) 17.2670 1.40517 0.702586 0.711599i \(-0.252029\pi\)
0.702586 + 0.711599i \(0.252029\pi\)
\(152\) 13.4931 1.09444
\(153\) 0 0
\(154\) 0 0
\(155\) −2.20293 −0.176944
\(156\) 0 0
\(157\) −6.61718 −0.528109 −0.264054 0.964508i \(-0.585060\pi\)
−0.264054 + 0.964508i \(0.585060\pi\)
\(158\) 3.31126 0.263430
\(159\) 0 0
\(160\) 5.44748 0.430661
\(161\) −31.3043 −2.46712
\(162\) 0 0
\(163\) −12.4426 −0.974582 −0.487291 0.873240i \(-0.662015\pi\)
−0.487291 + 0.873240i \(0.662015\pi\)
\(164\) 6.65988 0.520049
\(165\) 0 0
\(166\) −6.62252 −0.514007
\(167\) −2.17101 −0.167998 −0.0839988 0.996466i \(-0.526769\pi\)
−0.0839988 + 0.996466i \(0.526769\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) −5.89167 −0.451871
\(171\) 0 0
\(172\) −0.268326 −0.0204597
\(173\) 8.81142 0.669920 0.334960 0.942232i \(-0.391277\pi\)
0.334960 + 0.942232i \(0.391277\pi\)
\(174\) 0 0
\(175\) −4.64003 −0.350754
\(176\) 0 0
\(177\) 0 0
\(178\) −8.30877 −0.622768
\(179\) 13.8990 1.03886 0.519430 0.854513i \(-0.326144\pi\)
0.519430 + 0.854513i \(0.326144\pi\)
\(180\) 0 0
\(181\) −20.6172 −1.53246 −0.766232 0.642564i \(-0.777870\pi\)
−0.766232 + 0.642564i \(0.777870\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −19.6189 −1.44632
\(185\) 3.45636 0.254117
\(186\) 0 0
\(187\) 0 0
\(188\) 10.6803 0.778944
\(189\) 0 0
\(190\) −4.29021 −0.311244
\(191\) 13.4931 0.976329 0.488165 0.872752i \(-0.337667\pi\)
0.488165 + 0.872752i \(0.337667\pi\)
\(192\) 0 0
\(193\) 18.7308 1.34827 0.674135 0.738608i \(-0.264517\pi\)
0.674135 + 0.738608i \(0.264517\pi\)
\(194\) −11.5045 −0.825978
\(195\) 0 0
\(196\) −16.6382 −1.18845
\(197\) 13.8564 0.987228 0.493614 0.869681i \(-0.335676\pi\)
0.493614 + 0.869681i \(0.335676\pi\)
\(198\) 0 0
\(199\) −19.3638 −1.37266 −0.686330 0.727290i \(-0.740779\pi\)
−0.686330 + 0.727290i \(0.740779\pi\)
\(200\) −2.90798 −0.205625
\(201\) 0 0
\(202\) −13.9579 −0.982074
\(203\) 16.0735 1.12814
\(204\) 0 0
\(205\) −5.81597 −0.406205
\(206\) 17.5888 1.22547
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −0.351487 −0.0241974 −0.0120987 0.999927i \(-0.503851\pi\)
−0.0120987 + 0.999927i \(0.503851\pi\)
\(212\) −4.05783 −0.278693
\(213\) 0 0
\(214\) 15.9652 1.09136
\(215\) 0.234325 0.0159808
\(216\) 0 0
\(217\) 10.2217 0.693892
\(218\) 13.0873 0.886382
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 2.94950 0.197513 0.0987565 0.995112i \(-0.468513\pi\)
0.0987565 + 0.995112i \(0.468513\pi\)
\(224\) −25.2765 −1.68886
\(225\) 0 0
\(226\) −3.65173 −0.242910
\(227\) 10.5732 0.701765 0.350883 0.936419i \(-0.385882\pi\)
0.350883 + 0.936419i \(0.385882\pi\)
\(228\) 0 0
\(229\) −11.9495 −0.789645 −0.394823 0.918757i \(-0.629194\pi\)
−0.394823 + 0.918757i \(0.629194\pi\)
\(230\) 6.23792 0.411316
\(231\) 0 0
\(232\) 10.0735 0.661361
\(233\) −7.48432 −0.490314 −0.245157 0.969483i \(-0.578840\pi\)
−0.245157 + 0.969483i \(0.578840\pi\)
\(234\) 0 0
\(235\) −9.32698 −0.608425
\(236\) −16.6961 −1.08682
\(237\) 0 0
\(238\) 27.3376 1.77203
\(239\) 28.3088 1.83115 0.915574 0.402150i \(-0.131737\pi\)
0.915574 + 0.402150i \(0.131737\pi\)
\(240\) 0 0
\(241\) −6.13776 −0.395368 −0.197684 0.980266i \(-0.563342\pi\)
−0.197684 + 0.980266i \(0.563342\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) −2.25170 −0.144150
\(245\) 14.5299 0.928282
\(246\) 0 0
\(247\) 0 0
\(248\) 6.40609 0.406787
\(249\) 0 0
\(250\) 0.924607 0.0584773
\(251\) −2.98627 −0.188492 −0.0942459 0.995549i \(-0.530044\pi\)
−0.0942459 + 0.995549i \(0.530044\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 15.2618 0.957612
\(255\) 0 0
\(256\) −16.7539 −1.04712
\(257\) 24.1240 1.50482 0.752408 0.658697i \(-0.228892\pi\)
0.752408 + 0.658697i \(0.228892\pi\)
\(258\) 0 0
\(259\) −16.0376 −0.996530
\(260\) 0 0
\(261\) 0 0
\(262\) 14.7696 0.912470
\(263\) −9.46092 −0.583386 −0.291693 0.956512i \(-0.594218\pi\)
−0.291693 + 0.956512i \(0.594218\pi\)
\(264\) 0 0
\(265\) 3.54364 0.217684
\(266\) 19.9067 1.22056
\(267\) 0 0
\(268\) 1.66769 0.101870
\(269\) 1.08727 0.0662923 0.0331461 0.999451i \(-0.489447\pi\)
0.0331461 + 0.999451i \(0.489447\pi\)
\(270\) 0 0
\(271\) −6.10376 −0.370777 −0.185388 0.982665i \(-0.559354\pi\)
−0.185388 + 0.982665i \(0.559354\pi\)
\(272\) 2.53950 0.153980
\(273\) 0 0
\(274\) 4.65703 0.281342
\(275\) 0 0
\(276\) 0 0
\(277\) 26.4299 1.58802 0.794011 0.607904i \(-0.207989\pi\)
0.794011 + 0.607904i \(0.207989\pi\)
\(278\) −17.4269 −1.04520
\(279\) 0 0
\(280\) 13.4931 0.806369
\(281\) −30.5333 −1.82147 −0.910733 0.412996i \(-0.864482\pi\)
−0.910733 + 0.412996i \(0.864482\pi\)
\(282\) 0 0
\(283\) 2.28817 0.136018 0.0680088 0.997685i \(-0.478335\pi\)
0.0680088 + 0.997685i \(0.478335\pi\)
\(284\) 2.95484 0.175337
\(285\) 0 0
\(286\) 0 0
\(287\) 26.9863 1.59295
\(288\) 0 0
\(289\) 23.6035 1.38844
\(290\) −3.20293 −0.188083
\(291\) 0 0
\(292\) −15.6716 −0.917112
\(293\) −21.2338 −1.24049 −0.620246 0.784408i \(-0.712967\pi\)
−0.620246 + 0.784408i \(0.712967\pi\)
\(294\) 0 0
\(295\) 14.5804 0.848904
\(296\) −10.0510 −0.584205
\(297\) 0 0
\(298\) 9.01373 0.522151
\(299\) 0 0
\(300\) 0 0
\(301\) −1.08727 −0.0626694
\(302\) 15.9652 0.918695
\(303\) 0 0
\(304\) 1.84921 0.106060
\(305\) 1.96638 0.112594
\(306\) 0 0
\(307\) 11.5682 0.660234 0.330117 0.943940i \(-0.392912\pi\)
0.330117 + 0.943940i \(0.392912\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −2.03684 −0.115685
\(311\) −13.8990 −0.788140 −0.394070 0.919080i \(-0.628933\pi\)
−0.394070 + 0.919080i \(0.628933\pi\)
\(312\) 0 0
\(313\) 12.1745 0.688146 0.344073 0.938943i \(-0.388193\pi\)
0.344073 + 0.938943i \(0.388193\pi\)
\(314\) −6.11829 −0.345275
\(315\) 0 0
\(316\) −4.10091 −0.230694
\(317\) 26.7045 1.49987 0.749936 0.661510i \(-0.230084\pi\)
0.749936 + 0.661510i \(0.230084\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 5.83384 0.326122
\(321\) 0 0
\(322\) −28.9442 −1.61300
\(323\) 29.5667 1.64513
\(324\) 0 0
\(325\) 0 0
\(326\) −11.5045 −0.637178
\(327\) 0 0
\(328\) 16.9127 0.933849
\(329\) 43.2775 2.38597
\(330\) 0 0
\(331\) −19.4648 −1.06988 −0.534940 0.844890i \(-0.679666\pi\)
−0.534940 + 0.844890i \(0.679666\pi\)
\(332\) 8.20183 0.450134
\(333\) 0 0
\(334\) −2.00733 −0.109836
\(335\) −1.45636 −0.0795696
\(336\) 0 0
\(337\) −16.5063 −0.899155 −0.449577 0.893241i \(-0.648425\pi\)
−0.449577 + 0.893241i \(0.648425\pi\)
\(338\) −12.0199 −0.653796
\(339\) 0 0
\(340\) 7.29669 0.395719
\(341\) 0 0
\(342\) 0 0
\(343\) −34.9390 −1.88653
\(344\) −0.681412 −0.0367393
\(345\) 0 0
\(346\) 8.14709 0.437991
\(347\) 1.05877 0.0568377 0.0284189 0.999596i \(-0.490953\pi\)
0.0284189 + 0.999596i \(0.490953\pi\)
\(348\) 0 0
\(349\) −13.5983 −0.727901 −0.363950 0.931418i \(-0.618572\pi\)
−0.363950 + 0.931418i \(0.618572\pi\)
\(350\) −4.29021 −0.229321
\(351\) 0 0
\(352\) 0 0
\(353\) 29.0093 1.54401 0.772005 0.635616i \(-0.219254\pi\)
0.772005 + 0.635616i \(0.219254\pi\)
\(354\) 0 0
\(355\) −2.58041 −0.136954
\(356\) 10.2902 0.545380
\(357\) 0 0
\(358\) 12.8511 0.679202
\(359\) 14.0907 0.743680 0.371840 0.928297i \(-0.378727\pi\)
0.371840 + 0.928297i \(0.378727\pi\)
\(360\) 0 0
\(361\) 2.52991 0.133153
\(362\) −19.0628 −1.00192
\(363\) 0 0
\(364\) 0 0
\(365\) 13.6858 0.716346
\(366\) 0 0
\(367\) 5.01373 0.261714 0.130857 0.991401i \(-0.458227\pi\)
0.130857 + 0.991401i \(0.458227\pi\)
\(368\) −2.68874 −0.140160
\(369\) 0 0
\(370\) 3.19578 0.166140
\(371\) −16.4426 −0.853657
\(372\) 0 0
\(373\) −9.91935 −0.513604 −0.256802 0.966464i \(-0.582669\pi\)
−0.256802 + 0.966464i \(0.582669\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 27.1227 1.39875
\(377\) 0 0
\(378\) 0 0
\(379\) 4.92112 0.252781 0.126390 0.991981i \(-0.459661\pi\)
0.126390 + 0.991981i \(0.459661\pi\)
\(380\) 5.31331 0.272567
\(381\) 0 0
\(382\) 12.4758 0.638320
\(383\) −17.9725 −0.918354 −0.459177 0.888345i \(-0.651856\pi\)
−0.459177 + 0.888345i \(0.651856\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 17.3186 0.881493
\(387\) 0 0
\(388\) 14.2481 0.723337
\(389\) −13.0598 −0.662159 −0.331080 0.943603i \(-0.607413\pi\)
−0.331080 + 0.943603i \(0.607413\pi\)
\(390\) 0 0
\(391\) −42.9897 −2.17408
\(392\) −42.2527 −2.13408
\(393\) 0 0
\(394\) 12.8117 0.645445
\(395\) 3.58126 0.180193
\(396\) 0 0
\(397\) −27.7045 −1.39045 −0.695223 0.718794i \(-0.744695\pi\)
−0.695223 + 0.718794i \(0.744695\pi\)
\(398\) −17.9039 −0.897439
\(399\) 0 0
\(400\) −0.398534 −0.0199267
\(401\) 31.0598 1.55105 0.775527 0.631315i \(-0.217484\pi\)
0.775527 + 0.631315i \(0.217484\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 17.2865 0.860036
\(405\) 0 0
\(406\) 14.8617 0.737574
\(407\) 0 0
\(408\) 0 0
\(409\) −25.8058 −1.27602 −0.638008 0.770030i \(-0.720241\pi\)
−0.638008 + 0.770030i \(0.720241\pi\)
\(410\) −5.37748 −0.265575
\(411\) 0 0
\(412\) −21.7833 −1.07319
\(413\) −67.6536 −3.32902
\(414\) 0 0
\(415\) −7.16253 −0.351595
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 15.2618 0.745589 0.372794 0.927914i \(-0.378400\pi\)
0.372794 + 0.927914i \(0.378400\pi\)
\(420\) 0 0
\(421\) 37.9220 1.84821 0.924104 0.382142i \(-0.124813\pi\)
0.924104 + 0.382142i \(0.124813\pi\)
\(422\) −0.324987 −0.0158201
\(423\) 0 0
\(424\) −10.3048 −0.500447
\(425\) −6.37208 −0.309091
\(426\) 0 0
\(427\) −9.12405 −0.441544
\(428\) −19.7725 −0.955741
\(429\) 0 0
\(430\) 0.216658 0.0104482
\(431\) −18.6671 −0.899161 −0.449581 0.893240i \(-0.648427\pi\)
−0.449581 + 0.893240i \(0.648427\pi\)
\(432\) 0 0
\(433\) −18.4426 −0.886297 −0.443148 0.896448i \(-0.646138\pi\)
−0.443148 + 0.896448i \(0.646138\pi\)
\(434\) 9.45103 0.453664
\(435\) 0 0
\(436\) −16.2083 −0.776235
\(437\) −31.3043 −1.49749
\(438\) 0 0
\(439\) −1.46373 −0.0698598 −0.0349299 0.999390i \(-0.511121\pi\)
−0.0349299 + 0.999390i \(0.511121\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −16.8853 −0.802243 −0.401122 0.916025i \(-0.631380\pi\)
−0.401122 + 0.916025i \(0.631380\pi\)
\(444\) 0 0
\(445\) −8.98627 −0.425990
\(446\) 2.72713 0.129133
\(447\) 0 0
\(448\) −27.0692 −1.27890
\(449\) −15.2618 −0.720250 −0.360125 0.932904i \(-0.617266\pi\)
−0.360125 + 0.932904i \(0.617266\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 4.52258 0.212724
\(453\) 0 0
\(454\) 9.77601 0.458811
\(455\) 0 0
\(456\) 0 0
\(457\) −1.58089 −0.0739508 −0.0369754 0.999316i \(-0.511772\pi\)
−0.0369754 + 0.999316i \(0.511772\pi\)
\(458\) −11.0486 −0.516267
\(459\) 0 0
\(460\) −7.72551 −0.360204
\(461\) −7.86550 −0.366333 −0.183166 0.983082i \(-0.558635\pi\)
−0.183166 + 0.983082i \(0.558635\pi\)
\(462\) 0 0
\(463\) 35.6677 1.65762 0.828809 0.559532i \(-0.189019\pi\)
0.828809 + 0.559532i \(0.189019\pi\)
\(464\) 1.38056 0.0640911
\(465\) 0 0
\(466\) −6.92005 −0.320565
\(467\) −20.8937 −0.966843 −0.483422 0.875388i \(-0.660606\pi\)
−0.483422 + 0.875388i \(0.660606\pi\)
\(468\) 0 0
\(469\) 6.75757 0.312036
\(470\) −8.62379 −0.397786
\(471\) 0 0
\(472\) −42.3996 −1.95160
\(473\) 0 0
\(474\) 0 0
\(475\) −4.64003 −0.212899
\(476\) −33.8569 −1.55183
\(477\) 0 0
\(478\) 26.1745 1.19720
\(479\) 10.2174 0.466843 0.233422 0.972376i \(-0.425008\pi\)
0.233422 + 0.972376i \(0.425008\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −5.67501 −0.258490
\(483\) 0 0
\(484\) 0 0
\(485\) −12.4426 −0.564991
\(486\) 0 0
\(487\) 15.3186 0.694151 0.347076 0.937837i \(-0.387175\pi\)
0.347076 + 0.937837i \(0.387175\pi\)
\(488\) −5.71819 −0.258850
\(489\) 0 0
\(490\) 13.4345 0.606907
\(491\) 34.5341 1.55850 0.779251 0.626712i \(-0.215600\pi\)
0.779251 + 0.626712i \(0.215600\pi\)
\(492\) 0 0
\(493\) 22.0735 0.994143
\(494\) 0 0
\(495\) 0 0
\(496\) 0.877944 0.0394208
\(497\) 11.9732 0.537071
\(498\) 0 0
\(499\) 29.6035 1.32523 0.662616 0.748959i \(-0.269446\pi\)
0.662616 + 0.748959i \(0.269446\pi\)
\(500\) −1.14510 −0.0512105
\(501\) 0 0
\(502\) −2.76113 −0.123235
\(503\) 3.81990 0.170321 0.0851604 0.996367i \(-0.472860\pi\)
0.0851604 + 0.996367i \(0.472860\pi\)
\(504\) 0 0
\(505\) −15.0960 −0.671765
\(506\) 0 0
\(507\) 0 0
\(508\) −18.9014 −0.838614
\(509\) 33.7980 1.49807 0.749035 0.662530i \(-0.230517\pi\)
0.749035 + 0.662530i \(0.230517\pi\)
\(510\) 0 0
\(511\) −63.5025 −2.80918
\(512\) −4.48887 −0.198382
\(513\) 0 0
\(514\) 22.3053 0.983843
\(515\) 19.0230 0.838256
\(516\) 0 0
\(517\) 0 0
\(518\) −14.8285 −0.651527
\(519\) 0 0
\(520\) 0 0
\(521\) −3.26182 −0.142903 −0.0714515 0.997444i \(-0.522763\pi\)
−0.0714515 + 0.997444i \(0.522763\pi\)
\(522\) 0 0
\(523\) 10.8653 0.475105 0.237552 0.971375i \(-0.423655\pi\)
0.237552 + 0.971375i \(0.423655\pi\)
\(524\) −18.2918 −0.799081
\(525\) 0 0
\(526\) −8.74763 −0.381415
\(527\) 14.0373 0.611473
\(528\) 0 0
\(529\) 22.5162 0.978964
\(530\) 3.27647 0.142321
\(531\) 0 0
\(532\) −24.6540 −1.06888
\(533\) 0 0
\(534\) 0 0
\(535\) 17.2670 0.746519
\(536\) 4.23508 0.182928
\(537\) 0 0
\(538\) 1.00530 0.0433416
\(539\) 0 0
\(540\) 0 0
\(541\) 20.3160 0.873451 0.436726 0.899595i \(-0.356138\pi\)
0.436726 + 0.899595i \(0.356138\pi\)
\(542\) −5.64358 −0.242412
\(543\) 0 0
\(544\) −34.7118 −1.48826
\(545\) 14.1544 0.606309
\(546\) 0 0
\(547\) −23.1365 −0.989244 −0.494622 0.869108i \(-0.664694\pi\)
−0.494622 + 0.869108i \(0.664694\pi\)
\(548\) −5.76762 −0.246381
\(549\) 0 0
\(550\) 0 0
\(551\) 16.0735 0.684756
\(552\) 0 0
\(553\) −16.6172 −0.706635
\(554\) 24.4373 1.03824
\(555\) 0 0
\(556\) 21.5828 0.915315
\(557\) −0.449182 −0.0190324 −0.00951622 0.999955i \(-0.503029\pi\)
−0.00951622 + 0.999955i \(0.503029\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 1.84921 0.0781435
\(561\) 0 0
\(562\) −28.2313 −1.19087
\(563\) 16.4426 0.692973 0.346486 0.938055i \(-0.387375\pi\)
0.346486 + 0.938055i \(0.387375\pi\)
\(564\) 0 0
\(565\) −3.94950 −0.166157
\(566\) 2.11566 0.0889277
\(567\) 0 0
\(568\) 7.50379 0.314852
\(569\) 8.97774 0.376366 0.188183 0.982134i \(-0.439740\pi\)
0.188183 + 0.982134i \(0.439740\pi\)
\(570\) 0 0
\(571\) −21.7321 −0.909461 −0.454731 0.890629i \(-0.650265\pi\)
−0.454731 + 0.890629i \(0.650265\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 24.9517 1.04146
\(575\) 6.74657 0.281351
\(576\) 0 0
\(577\) −16.4426 −0.684516 −0.342258 0.939606i \(-0.611192\pi\)
−0.342258 + 0.939606i \(0.611192\pi\)
\(578\) 21.8239 0.907755
\(579\) 0 0
\(580\) 3.96675 0.164710
\(581\) 33.2344 1.37879
\(582\) 0 0
\(583\) 0 0
\(584\) −39.7980 −1.64685
\(585\) 0 0
\(586\) −19.6329 −0.811028
\(587\) 13.8338 0.570984 0.285492 0.958381i \(-0.407843\pi\)
0.285492 + 0.958381i \(0.407843\pi\)
\(588\) 0 0
\(589\) 10.2217 0.421177
\(590\) 13.4811 0.555010
\(591\) 0 0
\(592\) −1.37748 −0.0566141
\(593\) 18.0915 0.742928 0.371464 0.928447i \(-0.378856\pi\)
0.371464 + 0.928447i \(0.378856\pi\)
\(594\) 0 0
\(595\) 29.5667 1.21212
\(596\) −11.1633 −0.457266
\(597\) 0 0
\(598\) 0 0
\(599\) −37.7138 −1.54094 −0.770472 0.637474i \(-0.779979\pi\)
−0.770472 + 0.637474i \(0.779979\pi\)
\(600\) 0 0
\(601\) −8.98205 −0.366385 −0.183193 0.983077i \(-0.558643\pi\)
−0.183193 + 0.983077i \(0.558643\pi\)
\(602\) −1.00530 −0.0409730
\(603\) 0 0
\(604\) −19.7725 −0.804533
\(605\) 0 0
\(606\) 0 0
\(607\) 8.34277 0.338623 0.169311 0.985563i \(-0.445846\pi\)
0.169311 + 0.985563i \(0.445846\pi\)
\(608\) −25.2765 −1.02510
\(609\) 0 0
\(610\) 1.81812 0.0736137
\(611\) 0 0
\(612\) 0 0
\(613\) −32.5872 −1.31618 −0.658092 0.752938i \(-0.728636\pi\)
−0.658092 + 0.752938i \(0.728636\pi\)
\(614\) 10.6961 0.431658
\(615\) 0 0
\(616\) 0 0
\(617\) −20.1745 −0.812197 −0.406098 0.913829i \(-0.633111\pi\)
−0.406098 + 0.913829i \(0.633111\pi\)
\(618\) 0 0
\(619\) −35.3354 −1.42025 −0.710124 0.704076i \(-0.751361\pi\)
−0.710124 + 0.704076i \(0.751361\pi\)
\(620\) 2.52258 0.101309
\(621\) 0 0
\(622\) −12.8511 −0.515282
\(623\) 41.6966 1.67054
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 11.2567 0.449907
\(627\) 0 0
\(628\) 7.57736 0.302369
\(629\) −22.0242 −0.878164
\(630\) 0 0
\(631\) −10.6456 −0.423793 −0.211897 0.977292i \(-0.567964\pi\)
−0.211897 + 0.977292i \(0.567964\pi\)
\(632\) −10.4143 −0.414257
\(633\) 0 0
\(634\) 24.6911 0.980610
\(635\) 16.5063 0.655032
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −5.50095 −0.217444
\(641\) 4.94018 0.195125 0.0975627 0.995229i \(-0.468895\pi\)
0.0975627 + 0.995229i \(0.468895\pi\)
\(642\) 0 0
\(643\) 41.1240 1.62177 0.810887 0.585203i \(-0.198985\pi\)
0.810887 + 0.585203i \(0.198985\pi\)
\(644\) 35.8466 1.41256
\(645\) 0 0
\(646\) 27.3376 1.07558
\(647\) −37.4005 −1.47037 −0.735183 0.677868i \(-0.762904\pi\)
−0.735183 + 0.677868i \(0.762904\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 14.2481 0.557998
\(653\) −15.2344 −0.596167 −0.298083 0.954540i \(-0.596347\pi\)
−0.298083 + 0.954540i \(0.596347\pi\)
\(654\) 0 0
\(655\) 15.9739 0.624154
\(656\) 2.31786 0.0904973
\(657\) 0 0
\(658\) 40.0147 1.55993
\(659\) 3.05484 0.119000 0.0594998 0.998228i \(-0.481049\pi\)
0.0594998 + 0.998228i \(0.481049\pi\)
\(660\) 0 0
\(661\) −34.4426 −1.33966 −0.669832 0.742513i \(-0.733634\pi\)
−0.669832 + 0.742513i \(0.733634\pi\)
\(662\) −17.9972 −0.699483
\(663\) 0 0
\(664\) 20.8285 0.808303
\(665\) 21.5299 0.834894
\(666\) 0 0
\(667\) −23.3708 −0.904921
\(668\) 2.48603 0.0961873
\(669\) 0 0
\(670\) −1.34656 −0.0520223
\(671\) 0 0
\(672\) 0 0
\(673\) −37.9345 −1.46227 −0.731134 0.682234i \(-0.761008\pi\)
−0.731134 + 0.682234i \(0.761008\pi\)
\(674\) −15.2618 −0.587863
\(675\) 0 0
\(676\) 14.8863 0.572551
\(677\) −9.15268 −0.351766 −0.175883 0.984411i \(-0.556278\pi\)
−0.175883 + 0.984411i \(0.556278\pi\)
\(678\) 0 0
\(679\) 57.7342 2.21564
\(680\) 18.5299 0.710590
\(681\) 0 0
\(682\) 0 0
\(683\) 27.7980 1.06366 0.531830 0.846851i \(-0.321504\pi\)
0.531830 + 0.846851i \(0.321504\pi\)
\(684\) 0 0
\(685\) 5.03677 0.192445
\(686\) −32.3049 −1.23341
\(687\) 0 0
\(688\) −0.0933864 −0.00356033
\(689\) 0 0
\(690\) 0 0
\(691\) 29.4373 1.11985 0.559924 0.828544i \(-0.310830\pi\)
0.559924 + 0.828544i \(0.310830\pi\)
\(692\) −10.0900 −0.383563
\(693\) 0 0
\(694\) 0.978945 0.0371603
\(695\) −18.8479 −0.714943
\(696\) 0 0
\(697\) 37.0598 1.40374
\(698\) −12.5731 −0.475898
\(699\) 0 0
\(700\) 5.31331 0.200824
\(701\) 6.92820 0.261675 0.130837 0.991404i \(-0.458233\pi\)
0.130837 + 0.991404i \(0.458233\pi\)
\(702\) 0 0
\(703\) −16.0376 −0.604871
\(704\) 0 0
\(705\) 0 0
\(706\) 26.8222 1.00947
\(707\) 70.0461 2.63435
\(708\) 0 0
\(709\) −51.9956 −1.95274 −0.976368 0.216116i \(-0.930661\pi\)
−0.976368 + 0.216116i \(0.930661\pi\)
\(710\) −2.38586 −0.0895399
\(711\) 0 0
\(712\) 26.1319 0.979335
\(713\) −14.8622 −0.556595
\(714\) 0 0
\(715\) 0 0
\(716\) −15.9158 −0.594801
\(717\) 0 0
\(718\) 13.0284 0.486215
\(719\) −27.3921 −1.02155 −0.510777 0.859713i \(-0.670642\pi\)
−0.510777 + 0.859713i \(0.670642\pi\)
\(720\) 0 0
\(721\) −88.2676 −3.28726
\(722\) 2.33917 0.0870549
\(723\) 0 0
\(724\) 23.6088 0.877414
\(725\) −3.46410 −0.128654
\(726\) 0 0
\(727\) 48.9588 1.81578 0.907891 0.419206i \(-0.137692\pi\)
0.907891 + 0.419206i \(0.137692\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 12.6540 0.468344
\(731\) −1.49314 −0.0552256
\(732\) 0 0
\(733\) 24.5510 0.906813 0.453407 0.891304i \(-0.350209\pi\)
0.453407 + 0.891304i \(0.350209\pi\)
\(734\) 4.63572 0.171108
\(735\) 0 0
\(736\) 36.7518 1.35469
\(737\) 0 0
\(738\) 0 0
\(739\) 20.5605 0.756331 0.378165 0.925738i \(-0.376555\pi\)
0.378165 + 0.925738i \(0.376555\pi\)
\(740\) −3.95789 −0.145495
\(741\) 0 0
\(742\) −15.2029 −0.558117
\(743\) 29.3082 1.07521 0.537607 0.843195i \(-0.319328\pi\)
0.537607 + 0.843195i \(0.319328\pi\)
\(744\) 0 0
\(745\) 9.74872 0.357165
\(746\) −9.17149 −0.335792
\(747\) 0 0
\(748\) 0 0
\(749\) −80.1196 −2.92751
\(750\) 0 0
\(751\) 2.95789 0.107935 0.0539675 0.998543i \(-0.482813\pi\)
0.0539675 + 0.998543i \(0.482813\pi\)
\(752\) 3.71712 0.135550
\(753\) 0 0
\(754\) 0 0
\(755\) 17.2670 0.628412
\(756\) 0 0
\(757\) 2.36909 0.0861060 0.0430530 0.999073i \(-0.486292\pi\)
0.0430530 + 0.999073i \(0.486292\pi\)
\(758\) 4.55010 0.165267
\(759\) 0 0
\(760\) 13.4931 0.489448
\(761\) 52.8599 1.91617 0.958085 0.286485i \(-0.0924869\pi\)
0.958085 + 0.286485i \(0.0924869\pi\)
\(762\) 0 0
\(763\) −65.6770 −2.37767
\(764\) −15.4510 −0.558999
\(765\) 0 0
\(766\) −16.6175 −0.600416
\(767\) 0 0
\(768\) 0 0
\(769\) −8.48531 −0.305988 −0.152994 0.988227i \(-0.548892\pi\)
−0.152994 + 0.988227i \(0.548892\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −21.4486 −0.771954
\(773\) 39.7917 1.43121 0.715605 0.698506i \(-0.246151\pi\)
0.715605 + 0.698506i \(0.246151\pi\)
\(774\) 0 0
\(775\) −2.20293 −0.0791316
\(776\) 36.1830 1.29889
\(777\) 0 0
\(778\) −12.0752 −0.432917
\(779\) 26.9863 0.966884
\(780\) 0 0
\(781\) 0 0
\(782\) −39.7486 −1.42141
\(783\) 0 0
\(784\) −5.79067 −0.206810
\(785\) −6.61718 −0.236177
\(786\) 0 0
\(787\) 14.0907 0.502280 0.251140 0.967951i \(-0.419194\pi\)
0.251140 + 0.967951i \(0.419194\pi\)
\(788\) −15.8670 −0.565239
\(789\) 0 0
\(790\) 3.31126 0.117809
\(791\) 18.3258 0.651591
\(792\) 0 0
\(793\) 0 0
\(794\) −25.6157 −0.909068
\(795\) 0 0
\(796\) 22.1735 0.785918
\(797\) −37.0598 −1.31273 −0.656363 0.754445i \(-0.727906\pi\)
−0.656363 + 0.754445i \(0.727906\pi\)
\(798\) 0 0
\(799\) 59.4323 2.10256
\(800\) 5.44748 0.192597
\(801\) 0 0
\(802\) 28.7181 1.01407
\(803\) 0 0
\(804\) 0 0
\(805\) −31.3043 −1.10333
\(806\) 0 0
\(807\) 0 0
\(808\) 43.8990 1.54436
\(809\) 7.52424 0.264538 0.132269 0.991214i \(-0.457774\pi\)
0.132269 + 0.991214i \(0.457774\pi\)
\(810\) 0 0
\(811\) −40.0579 −1.40662 −0.703312 0.710881i \(-0.748296\pi\)
−0.703312 + 0.710881i \(0.748296\pi\)
\(812\) −18.4059 −0.645919
\(813\) 0 0
\(814\) 0 0
\(815\) −12.4426 −0.435847
\(816\) 0 0
\(817\) −1.08727 −0.0380389
\(818\) −23.8602 −0.834253
\(819\) 0 0
\(820\) 6.65988 0.232573
\(821\) 42.4676 1.48213 0.741064 0.671434i \(-0.234321\pi\)
0.741064 + 0.671434i \(0.234321\pi\)
\(822\) 0 0
\(823\) 17.5299 0.611054 0.305527 0.952183i \(-0.401167\pi\)
0.305527 + 0.952183i \(0.401167\pi\)
\(824\) −55.3187 −1.92712
\(825\) 0 0
\(826\) −62.5530 −2.17650
\(827\) −24.7854 −0.861872 −0.430936 0.902383i \(-0.641816\pi\)
−0.430936 + 0.902383i \(0.641816\pi\)
\(828\) 0 0
\(829\) 8.66769 0.301041 0.150521 0.988607i \(-0.451905\pi\)
0.150521 + 0.988607i \(0.451905\pi\)
\(830\) −6.62252 −0.229871
\(831\) 0 0
\(832\) 0 0
\(833\) −92.5858 −3.20791
\(834\) 0 0
\(835\) −2.17101 −0.0751308
\(836\) 0 0
\(837\) 0 0
\(838\) 14.1112 0.487463
\(839\) 43.4657 1.50060 0.750301 0.661096i \(-0.229909\pi\)
0.750301 + 0.661096i \(0.229909\pi\)
\(840\) 0 0
\(841\) −17.0000 −0.586207
\(842\) 35.0630 1.20835
\(843\) 0 0
\(844\) 0.402489 0.0138542
\(845\) −13.0000 −0.447214
\(846\) 0 0
\(847\) 0 0
\(848\) −1.41226 −0.0484973
\(849\) 0 0
\(850\) −5.89167 −0.202083
\(851\) 23.3186 0.799351
\(852\) 0 0
\(853\) 21.7262 0.743891 0.371946 0.928254i \(-0.378691\pi\)
0.371946 + 0.928254i \(0.378691\pi\)
\(854\) −8.43615 −0.288679
\(855\) 0 0
\(856\) −50.2123 −1.71622
\(857\) 32.7977 1.12035 0.560174 0.828375i \(-0.310734\pi\)
0.560174 + 0.828375i \(0.310734\pi\)
\(858\) 0 0
\(859\) −0.442636 −0.0151025 −0.00755127 0.999971i \(-0.502404\pi\)
−0.00755127 + 0.999971i \(0.502404\pi\)
\(860\) −0.268326 −0.00914983
\(861\) 0 0
\(862\) −17.2597 −0.587868
\(863\) 19.9265 0.678304 0.339152 0.940732i \(-0.389860\pi\)
0.339152 + 0.940732i \(0.389860\pi\)
\(864\) 0 0
\(865\) 8.81142 0.299597
\(866\) −17.0522 −0.579457
\(867\) 0 0
\(868\) −11.7049 −0.397289
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) −41.1608 −1.39388
\(873\) 0 0
\(874\) −28.9442 −0.979051
\(875\) −4.64003 −0.156862
\(876\) 0 0
\(877\) −25.6590 −0.866442 −0.433221 0.901288i \(-0.642623\pi\)
−0.433221 + 0.901288i \(0.642623\pi\)
\(878\) −1.35337 −0.0456740
\(879\) 0 0
\(880\) 0 0
\(881\) −32.9863 −1.11134 −0.555668 0.831404i \(-0.687537\pi\)
−0.555668 + 0.831404i \(0.687537\pi\)
\(882\) 0 0
\(883\) 44.5897 1.50056 0.750282 0.661118i \(-0.229918\pi\)
0.750282 + 0.661118i \(0.229918\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −15.6122 −0.524503
\(887\) 25.5953 0.859405 0.429703 0.902970i \(-0.358618\pi\)
0.429703 + 0.902970i \(0.358618\pi\)
\(888\) 0 0
\(889\) −76.5897 −2.56874
\(890\) −8.30877 −0.278511
\(891\) 0 0
\(892\) −3.37748 −0.113086
\(893\) 43.2775 1.44823
\(894\) 0 0
\(895\) 13.8990 0.464592
\(896\) 25.5246 0.852716
\(897\) 0 0
\(898\) −14.1112 −0.470896
\(899\) 7.63118 0.254514
\(900\) 0 0
\(901\) −22.5804 −0.752261
\(902\) 0 0
\(903\) 0 0
\(904\) 11.4851 0.381988
\(905\) −20.6172 −0.685338
\(906\) 0 0
\(907\) −4.29554 −0.142631 −0.0713156 0.997454i \(-0.522720\pi\)
−0.0713156 + 0.997454i \(0.522720\pi\)
\(908\) −12.1074 −0.401797
\(909\) 0 0
\(910\) 0 0
\(911\) −12.6814 −0.420154 −0.210077 0.977685i \(-0.567371\pi\)
−0.210077 + 0.977685i \(0.567371\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −1.46170 −0.0483487
\(915\) 0 0
\(916\) 13.6834 0.452112
\(917\) −74.1196 −2.44765
\(918\) 0 0
\(919\) 18.6238 0.614343 0.307172 0.951654i \(-0.400617\pi\)
0.307172 + 0.951654i \(0.400617\pi\)
\(920\) −19.6189 −0.646816
\(921\) 0 0
\(922\) −7.27249 −0.239507
\(923\) 0 0
\(924\) 0 0
\(925\) 3.45636 0.113645
\(926\) 32.9786 1.08374
\(927\) 0 0
\(928\) −18.8706 −0.619458
\(929\) 42.2206 1.38521 0.692607 0.721315i \(-0.256462\pi\)
0.692607 + 0.721315i \(0.256462\pi\)
\(930\) 0 0
\(931\) −67.4193 −2.20958
\(932\) 8.57032 0.280730
\(933\) 0 0
\(934\) −19.3184 −0.632118
\(935\) 0 0
\(936\) 0 0
\(937\) 14.0270 0.458243 0.229122 0.973398i \(-0.426415\pi\)
0.229122 + 0.973398i \(0.426415\pi\)
\(938\) 6.24810 0.204008
\(939\) 0 0
\(940\) 10.6803 0.348355
\(941\) −44.0485 −1.43594 −0.717970 0.696075i \(-0.754928\pi\)
−0.717970 + 0.696075i \(0.754928\pi\)
\(942\) 0 0
\(943\) −39.2378 −1.27776
\(944\) −5.81080 −0.189125
\(945\) 0 0
\(946\) 0 0
\(947\) 30.7191 0.998237 0.499119 0.866534i \(-0.333657\pi\)
0.499119 + 0.866534i \(0.333657\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) −4.29021 −0.139193
\(951\) 0 0
\(952\) −85.9794 −2.78661
\(953\) 31.9479 1.03489 0.517447 0.855715i \(-0.326883\pi\)
0.517447 + 0.855715i \(0.326883\pi\)
\(954\) 0 0
\(955\) 13.4931 0.436628
\(956\) −32.4165 −1.04843
\(957\) 0 0
\(958\) 9.44704 0.305220
\(959\) −23.3708 −0.754682
\(960\) 0 0
\(961\) −26.1471 −0.843455
\(962\) 0 0
\(963\) 0 0
\(964\) 7.02836 0.226368
\(965\) 18.7308 0.602965
\(966\) 0 0
\(967\) 34.5978 1.11259 0.556295 0.830985i \(-0.312223\pi\)
0.556295 + 0.830985i \(0.312223\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) −11.5045 −0.369389
\(971\) −32.9588 −1.05770 −0.528849 0.848716i \(-0.677376\pi\)
−0.528849 + 0.848716i \(0.677376\pi\)
\(972\) 0 0
\(973\) 87.4550 2.80368
\(974\) 14.1637 0.453833
\(975\) 0 0
\(976\) −0.783668 −0.0250846
\(977\) −39.3584 −1.25919 −0.629594 0.776925i \(-0.716779\pi\)
−0.629594 + 0.776925i \(0.716779\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −16.6382 −0.531489
\(981\) 0 0
\(982\) 31.9304 1.01894
\(983\) 40.3868 1.28814 0.644069 0.764967i \(-0.277245\pi\)
0.644069 + 0.764967i \(0.277245\pi\)
\(984\) 0 0
\(985\) 13.8564 0.441502
\(986\) 20.4093 0.649966
\(987\) 0 0
\(988\) 0 0
\(989\) 1.58089 0.0502693
\(990\) 0 0
\(991\) −4.67302 −0.148443 −0.0742217 0.997242i \(-0.523647\pi\)
−0.0742217 + 0.997242i \(0.523647\pi\)
\(992\) −12.0004 −0.381014
\(993\) 0 0
\(994\) 11.0705 0.351135
\(995\) −19.3638 −0.613872
\(996\) 0 0
\(997\) −28.6544 −0.907495 −0.453747 0.891130i \(-0.649913\pi\)
−0.453747 + 0.891130i \(0.649913\pi\)
\(998\) 27.3716 0.866431
\(999\) 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 5445.2.a.by.1.4 yes 6
3.2 odd 2 5445.2.a.bw.1.3 6
11.10 odd 2 inner 5445.2.a.by.1.3 yes 6
33.32 even 2 5445.2.a.bw.1.4 yes 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5445.2.a.bw.1.3 6 3.2 odd 2
5445.2.a.bw.1.4 yes 6 33.32 even 2
5445.2.a.by.1.3 yes 6 11.10 odd 2 inner
5445.2.a.by.1.4 yes 6 1.1 even 1 trivial