Properties

Label 7448.2.a.bn.1.3
Level $7448$
Weight $2$
Character 7448.1
Self dual yes
Analytic conductor $59.473$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7448 = 2^{3} \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7448.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(59.4725794254\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.98211824.1
Defining polynomial: \(x^{6} - 3 x^{5} - 6 x^{4} + 15 x^{3} + 8 x^{2} - 9 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(0.511631\) of defining polynomial
Character \(\chi\) \(=\) 7448.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.488369 q^{3} -3.51566 q^{5} -2.76150 q^{9} +O(q^{10})\) \(q+0.488369 q^{3} -3.51566 q^{5} -2.76150 q^{9} -2.25811 q^{11} -2.21264 q^{13} -1.71694 q^{15} -0.716938 q^{17} -1.00000 q^{19} -7.53470 q^{23} +7.35984 q^{25} -2.81374 q^{27} -7.66391 q^{29} +0.473849 q^{31} -1.10279 q^{33} -0.268043 q^{37} -1.08059 q^{39} -11.9093 q^{41} -6.26213 q^{43} +9.70847 q^{45} +7.10998 q^{47} -0.350131 q^{51} -2.16643 q^{53} +7.93873 q^{55} -0.488369 q^{57} -0.0795286 q^{59} +15.1946 q^{61} +7.77889 q^{65} +7.97595 q^{67} -3.67972 q^{69} +0.764655 q^{71} -10.2795 q^{73} +3.59432 q^{75} -14.9272 q^{79} +6.91034 q^{81} -3.68887 q^{83} +2.52051 q^{85} -3.74282 q^{87} +2.22816 q^{89} +0.231413 q^{93} +3.51566 q^{95} +7.09236 q^{97} +6.23575 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{3} + q^{5} + 3 q^{9} + O(q^{10}) \) \( 6 q + 3 q^{3} + q^{5} + 3 q^{9} + 3 q^{11} + 6 q^{13} - 8 q^{15} - 2 q^{17} - 6 q^{19} + 2 q^{23} + 5 q^{25} + 6 q^{27} - q^{29} + 14 q^{31} + 19 q^{33} - 7 q^{37} + 22 q^{39} - 21 q^{41} + q^{43} - 4 q^{45} + 23 q^{47} + 2 q^{51} - 15 q^{53} + 2 q^{55} - 3 q^{57} + 25 q^{59} + 21 q^{61} + 6 q^{65} + 2 q^{67} - 20 q^{69} + 13 q^{71} - 2 q^{73} + 24 q^{75} - 17 q^{79} - 2 q^{81} + 4 q^{83} + 40 q^{85} + 30 q^{87} - q^{89} + 6 q^{93} - q^{95} - 13 q^{97} + 41 q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.488369 0.281960 0.140980 0.990012i \(-0.454975\pi\)
0.140980 + 0.990012i \(0.454975\pi\)
\(4\) 0 0
\(5\) −3.51566 −1.57225 −0.786125 0.618068i \(-0.787916\pi\)
−0.786125 + 0.618068i \(0.787916\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −2.76150 −0.920499
\(10\) 0 0
\(11\) −2.25811 −0.680845 −0.340423 0.940273i \(-0.610570\pi\)
−0.340423 + 0.940273i \(0.610570\pi\)
\(12\) 0 0
\(13\) −2.21264 −0.613676 −0.306838 0.951762i \(-0.599271\pi\)
−0.306838 + 0.951762i \(0.599271\pi\)
\(14\) 0 0
\(15\) −1.71694 −0.443312
\(16\) 0 0
\(17\) −0.716938 −0.173883 −0.0869415 0.996213i \(-0.527709\pi\)
−0.0869415 + 0.996213i \(0.527709\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −7.53470 −1.57109 −0.785547 0.618802i \(-0.787618\pi\)
−0.785547 + 0.618802i \(0.787618\pi\)
\(24\) 0 0
\(25\) 7.35984 1.47197
\(26\) 0 0
\(27\) −2.81374 −0.541504
\(28\) 0 0
\(29\) −7.66391 −1.42315 −0.711576 0.702609i \(-0.752018\pi\)
−0.711576 + 0.702609i \(0.752018\pi\)
\(30\) 0 0
\(31\) 0.473849 0.0851058 0.0425529 0.999094i \(-0.486451\pi\)
0.0425529 + 0.999094i \(0.486451\pi\)
\(32\) 0 0
\(33\) −1.10279 −0.191971
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −0.268043 −0.0440660 −0.0220330 0.999757i \(-0.507014\pi\)
−0.0220330 + 0.999757i \(0.507014\pi\)
\(38\) 0 0
\(39\) −1.08059 −0.173032
\(40\) 0 0
\(41\) −11.9093 −1.85991 −0.929956 0.367670i \(-0.880156\pi\)
−0.929956 + 0.367670i \(0.880156\pi\)
\(42\) 0 0
\(43\) −6.26213 −0.954966 −0.477483 0.878641i \(-0.658451\pi\)
−0.477483 + 0.878641i \(0.658451\pi\)
\(44\) 0 0
\(45\) 9.70847 1.44725
\(46\) 0 0
\(47\) 7.10998 1.03710 0.518548 0.855048i \(-0.326473\pi\)
0.518548 + 0.855048i \(0.326473\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −0.350131 −0.0490281
\(52\) 0 0
\(53\) −2.16643 −0.297583 −0.148791 0.988869i \(-0.547538\pi\)
−0.148791 + 0.988869i \(0.547538\pi\)
\(54\) 0 0
\(55\) 7.93873 1.07046
\(56\) 0 0
\(57\) −0.488369 −0.0646861
\(58\) 0 0
\(59\) −0.0795286 −0.0103537 −0.00517687 0.999987i \(-0.501648\pi\)
−0.00517687 + 0.999987i \(0.501648\pi\)
\(60\) 0 0
\(61\) 15.1946 1.94547 0.972734 0.231925i \(-0.0745022\pi\)
0.972734 + 0.231925i \(0.0745022\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 7.77889 0.964852
\(66\) 0 0
\(67\) 7.97595 0.974418 0.487209 0.873285i \(-0.338015\pi\)
0.487209 + 0.873285i \(0.338015\pi\)
\(68\) 0 0
\(69\) −3.67972 −0.442986
\(70\) 0 0
\(71\) 0.764655 0.0907479 0.0453739 0.998970i \(-0.485552\pi\)
0.0453739 + 0.998970i \(0.485552\pi\)
\(72\) 0 0
\(73\) −10.2795 −1.20313 −0.601564 0.798825i \(-0.705455\pi\)
−0.601564 + 0.798825i \(0.705455\pi\)
\(74\) 0 0
\(75\) 3.59432 0.415036
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −14.9272 −1.67945 −0.839723 0.543015i \(-0.817283\pi\)
−0.839723 + 0.543015i \(0.817283\pi\)
\(80\) 0 0
\(81\) 6.91034 0.767816
\(82\) 0 0
\(83\) −3.68887 −0.404906 −0.202453 0.979292i \(-0.564891\pi\)
−0.202453 + 0.979292i \(0.564891\pi\)
\(84\) 0 0
\(85\) 2.52051 0.273388
\(86\) 0 0
\(87\) −3.74282 −0.401272
\(88\) 0 0
\(89\) 2.22816 0.236184 0.118092 0.993003i \(-0.462322\pi\)
0.118092 + 0.993003i \(0.462322\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0.231413 0.0239964
\(94\) 0 0
\(95\) 3.51566 0.360699
\(96\) 0 0
\(97\) 7.09236 0.720120 0.360060 0.932929i \(-0.382756\pi\)
0.360060 + 0.932929i \(0.382756\pi\)
\(98\) 0 0
\(99\) 6.23575 0.626717
\(100\) 0 0
\(101\) 5.61873 0.559085 0.279542 0.960133i \(-0.409817\pi\)
0.279542 + 0.960133i \(0.409817\pi\)
\(102\) 0 0
\(103\) −0.529025 −0.0521263 −0.0260632 0.999660i \(-0.508297\pi\)
−0.0260632 + 0.999660i \(0.508297\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −16.1976 −1.56588 −0.782938 0.622099i \(-0.786280\pi\)
−0.782938 + 0.622099i \(0.786280\pi\)
\(108\) 0 0
\(109\) 9.24340 0.885357 0.442678 0.896680i \(-0.354028\pi\)
0.442678 + 0.896680i \(0.354028\pi\)
\(110\) 0 0
\(111\) −0.130904 −0.0124249
\(112\) 0 0
\(113\) −10.3591 −0.974498 −0.487249 0.873263i \(-0.662000\pi\)
−0.487249 + 0.873263i \(0.662000\pi\)
\(114\) 0 0
\(115\) 26.4894 2.47015
\(116\) 0 0
\(117\) 6.11020 0.564888
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −5.90095 −0.536450
\(122\) 0 0
\(123\) −5.81611 −0.524421
\(124\) 0 0
\(125\) −8.29639 −0.742052
\(126\) 0 0
\(127\) −12.9388 −1.14813 −0.574066 0.818809i \(-0.694635\pi\)
−0.574066 + 0.818809i \(0.694635\pi\)
\(128\) 0 0
\(129\) −3.05823 −0.269262
\(130\) 0 0
\(131\) −17.5212 −1.53084 −0.765419 0.643533i \(-0.777468\pi\)
−0.765419 + 0.643533i \(0.777468\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 9.89213 0.851379
\(136\) 0 0
\(137\) 7.30076 0.623746 0.311873 0.950124i \(-0.399044\pi\)
0.311873 + 0.950124i \(0.399044\pi\)
\(138\) 0 0
\(139\) 8.40692 0.713066 0.356533 0.934283i \(-0.383959\pi\)
0.356533 + 0.934283i \(0.383959\pi\)
\(140\) 0 0
\(141\) 3.47229 0.292420
\(142\) 0 0
\(143\) 4.99638 0.417819
\(144\) 0 0
\(145\) 26.9437 2.23755
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 5.99634 0.491239 0.245620 0.969366i \(-0.421009\pi\)
0.245620 + 0.969366i \(0.421009\pi\)
\(150\) 0 0
\(151\) −22.0572 −1.79499 −0.897494 0.441027i \(-0.854614\pi\)
−0.897494 + 0.441027i \(0.854614\pi\)
\(152\) 0 0
\(153\) 1.97982 0.160059
\(154\) 0 0
\(155\) −1.66589 −0.133808
\(156\) 0 0
\(157\) 20.7625 1.65703 0.828513 0.559969i \(-0.189187\pi\)
0.828513 + 0.559969i \(0.189187\pi\)
\(158\) 0 0
\(159\) −1.05802 −0.0839064
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 10.0347 0.785982 0.392991 0.919542i \(-0.371440\pi\)
0.392991 + 0.919542i \(0.371440\pi\)
\(164\) 0 0
\(165\) 3.87703 0.301826
\(166\) 0 0
\(167\) 11.4994 0.889854 0.444927 0.895567i \(-0.353230\pi\)
0.444927 + 0.895567i \(0.353230\pi\)
\(168\) 0 0
\(169\) −8.10422 −0.623401
\(170\) 0 0
\(171\) 2.76150 0.211177
\(172\) 0 0
\(173\) 0.407066 0.0309487 0.0154743 0.999880i \(-0.495074\pi\)
0.0154743 + 0.999880i \(0.495074\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −0.0388393 −0.00291934
\(178\) 0 0
\(179\) 0.0666375 0.00498072 0.00249036 0.999997i \(-0.499207\pi\)
0.00249036 + 0.999997i \(0.499207\pi\)
\(180\) 0 0
\(181\) −7.64418 −0.568188 −0.284094 0.958796i \(-0.591693\pi\)
−0.284094 + 0.958796i \(0.591693\pi\)
\(182\) 0 0
\(183\) 7.42057 0.548544
\(184\) 0 0
\(185\) 0.942348 0.0692828
\(186\) 0 0
\(187\) 1.61892 0.118387
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −11.8535 −0.857687 −0.428844 0.903379i \(-0.641079\pi\)
−0.428844 + 0.903379i \(0.641079\pi\)
\(192\) 0 0
\(193\) 7.34976 0.529047 0.264523 0.964379i \(-0.414785\pi\)
0.264523 + 0.964379i \(0.414785\pi\)
\(194\) 0 0
\(195\) 3.79897 0.272050
\(196\) 0 0
\(197\) 20.2535 1.44300 0.721500 0.692414i \(-0.243453\pi\)
0.721500 + 0.692414i \(0.243453\pi\)
\(198\) 0 0
\(199\) 16.8733 1.19611 0.598057 0.801453i \(-0.295940\pi\)
0.598057 + 0.801453i \(0.295940\pi\)
\(200\) 0 0
\(201\) 3.89521 0.274747
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 41.8688 2.92425
\(206\) 0 0
\(207\) 20.8070 1.44619
\(208\) 0 0
\(209\) 2.25811 0.156197
\(210\) 0 0
\(211\) 11.9286 0.821197 0.410598 0.911816i \(-0.365320\pi\)
0.410598 + 0.911816i \(0.365320\pi\)
\(212\) 0 0
\(213\) 0.373434 0.0255873
\(214\) 0 0
\(215\) 22.0155 1.50145
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −5.02020 −0.339234
\(220\) 0 0
\(221\) 1.58633 0.106708
\(222\) 0 0
\(223\) −23.2754 −1.55863 −0.779317 0.626630i \(-0.784434\pi\)
−0.779317 + 0.626630i \(0.784434\pi\)
\(224\) 0 0
\(225\) −20.3242 −1.35494
\(226\) 0 0
\(227\) −1.56606 −0.103943 −0.0519714 0.998649i \(-0.516550\pi\)
−0.0519714 + 0.998649i \(0.516550\pi\)
\(228\) 0 0
\(229\) 13.8669 0.916350 0.458175 0.888862i \(-0.348503\pi\)
0.458175 + 0.888862i \(0.348503\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −14.3117 −0.937590 −0.468795 0.883307i \(-0.655312\pi\)
−0.468795 + 0.883307i \(0.655312\pi\)
\(234\) 0 0
\(235\) −24.9962 −1.63057
\(236\) 0 0
\(237\) −7.29000 −0.473537
\(238\) 0 0
\(239\) 27.4532 1.77580 0.887899 0.460037i \(-0.152164\pi\)
0.887899 + 0.460037i \(0.152164\pi\)
\(240\) 0 0
\(241\) −8.58000 −0.552686 −0.276343 0.961059i \(-0.589123\pi\)
−0.276343 + 0.961059i \(0.589123\pi\)
\(242\) 0 0
\(243\) 11.8160 0.757997
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.21264 0.140787
\(248\) 0 0
\(249\) −1.80153 −0.114167
\(250\) 0 0
\(251\) −3.23766 −0.204359 −0.102180 0.994766i \(-0.532582\pi\)
−0.102180 + 0.994766i \(0.532582\pi\)
\(252\) 0 0
\(253\) 17.0142 1.06967
\(254\) 0 0
\(255\) 1.23094 0.0770844
\(256\) 0 0
\(257\) 1.41758 0.0884263 0.0442132 0.999022i \(-0.485922\pi\)
0.0442132 + 0.999022i \(0.485922\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 21.1639 1.31001
\(262\) 0 0
\(263\) −2.57536 −0.158803 −0.0794017 0.996843i \(-0.525301\pi\)
−0.0794017 + 0.996843i \(0.525301\pi\)
\(264\) 0 0
\(265\) 7.61644 0.467874
\(266\) 0 0
\(267\) 1.08816 0.0665946
\(268\) 0 0
\(269\) −10.9509 −0.667685 −0.333843 0.942629i \(-0.608345\pi\)
−0.333843 + 0.942629i \(0.608345\pi\)
\(270\) 0 0
\(271\) 23.1518 1.40637 0.703186 0.711006i \(-0.251760\pi\)
0.703186 + 0.711006i \(0.251760\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −16.6193 −1.00218
\(276\) 0 0
\(277\) −14.0972 −0.847017 −0.423508 0.905892i \(-0.639202\pi\)
−0.423508 + 0.905892i \(0.639202\pi\)
\(278\) 0 0
\(279\) −1.30853 −0.0783398
\(280\) 0 0
\(281\) 0.341082 0.0203473 0.0101736 0.999948i \(-0.496762\pi\)
0.0101736 + 0.999948i \(0.496762\pi\)
\(282\) 0 0
\(283\) 9.97496 0.592950 0.296475 0.955041i \(-0.404189\pi\)
0.296475 + 0.955041i \(0.404189\pi\)
\(284\) 0 0
\(285\) 1.71694 0.101703
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −16.4860 −0.969765
\(290\) 0 0
\(291\) 3.46369 0.203045
\(292\) 0 0
\(293\) −21.6737 −1.26619 −0.633097 0.774073i \(-0.718216\pi\)
−0.633097 + 0.774073i \(0.718216\pi\)
\(294\) 0 0
\(295\) 0.279595 0.0162787
\(296\) 0 0
\(297\) 6.35372 0.368680
\(298\) 0 0
\(299\) 16.6716 0.964143
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 2.74402 0.157640
\(304\) 0 0
\(305\) −53.4189 −3.05876
\(306\) 0 0
\(307\) 20.6231 1.17702 0.588510 0.808490i \(-0.299715\pi\)
0.588510 + 0.808490i \(0.299715\pi\)
\(308\) 0 0
\(309\) −0.258359 −0.0146975
\(310\) 0 0
\(311\) 7.92634 0.449461 0.224731 0.974421i \(-0.427850\pi\)
0.224731 + 0.974421i \(0.427850\pi\)
\(312\) 0 0
\(313\) −10.7662 −0.608542 −0.304271 0.952586i \(-0.598413\pi\)
−0.304271 + 0.952586i \(0.598413\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −8.02183 −0.450551 −0.225275 0.974295i \(-0.572328\pi\)
−0.225275 + 0.974295i \(0.572328\pi\)
\(318\) 0 0
\(319\) 17.3059 0.968947
\(320\) 0 0
\(321\) −7.91039 −0.441515
\(322\) 0 0
\(323\) 0.716938 0.0398915
\(324\) 0 0
\(325\) −16.2847 −0.903312
\(326\) 0 0
\(327\) 4.51419 0.249635
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 12.5703 0.690928 0.345464 0.938432i \(-0.387722\pi\)
0.345464 + 0.938432i \(0.387722\pi\)
\(332\) 0 0
\(333\) 0.740200 0.0405627
\(334\) 0 0
\(335\) −28.0407 −1.53203
\(336\) 0 0
\(337\) 25.7552 1.40297 0.701487 0.712683i \(-0.252520\pi\)
0.701487 + 0.712683i \(0.252520\pi\)
\(338\) 0 0
\(339\) −5.05904 −0.274770
\(340\) 0 0
\(341\) −1.07000 −0.0579439
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 12.9366 0.696484
\(346\) 0 0
\(347\) 6.18123 0.331826 0.165913 0.986140i \(-0.446943\pi\)
0.165913 + 0.986140i \(0.446943\pi\)
\(348\) 0 0
\(349\) 8.99215 0.481339 0.240669 0.970607i \(-0.422633\pi\)
0.240669 + 0.970607i \(0.422633\pi\)
\(350\) 0 0
\(351\) 6.22579 0.332308
\(352\) 0 0
\(353\) −17.0593 −0.907977 −0.453989 0.891007i \(-0.649999\pi\)
−0.453989 + 0.891007i \(0.649999\pi\)
\(354\) 0 0
\(355\) −2.68827 −0.142678
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 16.6501 0.878757 0.439379 0.898302i \(-0.355199\pi\)
0.439379 + 0.898302i \(0.355199\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −2.88184 −0.151257
\(364\) 0 0
\(365\) 36.1393 1.89162
\(366\) 0 0
\(367\) 33.1117 1.72842 0.864209 0.503134i \(-0.167820\pi\)
0.864209 + 0.503134i \(0.167820\pi\)
\(368\) 0 0
\(369\) 32.8873 1.71205
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 33.2511 1.72167 0.860837 0.508880i \(-0.169940\pi\)
0.860837 + 0.508880i \(0.169940\pi\)
\(374\) 0 0
\(375\) −4.05170 −0.209229
\(376\) 0 0
\(377\) 16.9575 0.873355
\(378\) 0 0
\(379\) −28.1510 −1.44602 −0.723011 0.690837i \(-0.757242\pi\)
−0.723011 + 0.690837i \(0.757242\pi\)
\(380\) 0 0
\(381\) −6.31891 −0.323727
\(382\) 0 0
\(383\) 22.7648 1.16323 0.581614 0.813465i \(-0.302421\pi\)
0.581614 + 0.813465i \(0.302421\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 17.2929 0.879045
\(388\) 0 0
\(389\) −3.90959 −0.198224 −0.0991121 0.995076i \(-0.531600\pi\)
−0.0991121 + 0.995076i \(0.531600\pi\)
\(390\) 0 0
\(391\) 5.40192 0.273187
\(392\) 0 0
\(393\) −8.55683 −0.431635
\(394\) 0 0
\(395\) 52.4790 2.64051
\(396\) 0 0
\(397\) −6.80489 −0.341527 −0.170764 0.985312i \(-0.554623\pi\)
−0.170764 + 0.985312i \(0.554623\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9.05449 −0.452160 −0.226080 0.974109i \(-0.572591\pi\)
−0.226080 + 0.974109i \(0.572591\pi\)
\(402\) 0 0
\(403\) −1.04846 −0.0522274
\(404\) 0 0
\(405\) −24.2944 −1.20720
\(406\) 0 0
\(407\) 0.605270 0.0300021
\(408\) 0 0
\(409\) 0.697334 0.0344810 0.0172405 0.999851i \(-0.494512\pi\)
0.0172405 + 0.999851i \(0.494512\pi\)
\(410\) 0 0
\(411\) 3.56547 0.175872
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 12.9688 0.636613
\(416\) 0 0
\(417\) 4.10568 0.201056
\(418\) 0 0
\(419\) −9.91019 −0.484145 −0.242072 0.970258i \(-0.577827\pi\)
−0.242072 + 0.970258i \(0.577827\pi\)
\(420\) 0 0
\(421\) −23.5825 −1.14934 −0.574670 0.818385i \(-0.694870\pi\)
−0.574670 + 0.818385i \(0.694870\pi\)
\(422\) 0 0
\(423\) −19.6342 −0.954646
\(424\) 0 0
\(425\) −5.27655 −0.255950
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 2.44008 0.117808
\(430\) 0 0
\(431\) 1.43559 0.0691498 0.0345749 0.999402i \(-0.488992\pi\)
0.0345749 + 0.999402i \(0.488992\pi\)
\(432\) 0 0
\(433\) −37.4216 −1.79837 −0.899185 0.437569i \(-0.855839\pi\)
−0.899185 + 0.437569i \(0.855839\pi\)
\(434\) 0 0
\(435\) 13.1585 0.630900
\(436\) 0 0
\(437\) 7.53470 0.360434
\(438\) 0 0
\(439\) −29.2865 −1.39777 −0.698885 0.715234i \(-0.746320\pi\)
−0.698885 + 0.715234i \(0.746320\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.27913 0.108285 0.0541424 0.998533i \(-0.482757\pi\)
0.0541424 + 0.998533i \(0.482757\pi\)
\(444\) 0 0
\(445\) −7.83344 −0.371341
\(446\) 0 0
\(447\) 2.92843 0.138510
\(448\) 0 0
\(449\) 5.22719 0.246686 0.123343 0.992364i \(-0.460638\pi\)
0.123343 + 0.992364i \(0.460638\pi\)
\(450\) 0 0
\(451\) 26.8924 1.26631
\(452\) 0 0
\(453\) −10.7720 −0.506115
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −32.2735 −1.50969 −0.754845 0.655903i \(-0.772288\pi\)
−0.754845 + 0.655903i \(0.772288\pi\)
\(458\) 0 0
\(459\) 2.01728 0.0941584
\(460\) 0 0
\(461\) −26.1333 −1.21715 −0.608576 0.793496i \(-0.708259\pi\)
−0.608576 + 0.793496i \(0.708259\pi\)
\(462\) 0 0
\(463\) 6.42014 0.298369 0.149185 0.988809i \(-0.452335\pi\)
0.149185 + 0.988809i \(0.452335\pi\)
\(464\) 0 0
\(465\) −0.813570 −0.0377284
\(466\) 0 0
\(467\) −21.8516 −1.01117 −0.505586 0.862776i \(-0.668724\pi\)
−0.505586 + 0.862776i \(0.668724\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 10.1398 0.467215
\(472\) 0 0
\(473\) 14.1406 0.650184
\(474\) 0 0
\(475\) −7.35984 −0.337693
\(476\) 0 0
\(477\) 5.98260 0.273924
\(478\) 0 0
\(479\) 28.9775 1.32402 0.662008 0.749497i \(-0.269704\pi\)
0.662008 + 0.749497i \(0.269704\pi\)
\(480\) 0 0
\(481\) 0.593083 0.0270423
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −24.9343 −1.13221
\(486\) 0 0
\(487\) −23.8101 −1.07894 −0.539469 0.842006i \(-0.681375\pi\)
−0.539469 + 0.842006i \(0.681375\pi\)
\(488\) 0 0
\(489\) 4.90066 0.221616
\(490\) 0 0
\(491\) 23.5199 1.06144 0.530718 0.847548i \(-0.321922\pi\)
0.530718 + 0.847548i \(0.321922\pi\)
\(492\) 0 0
\(493\) 5.49455 0.247462
\(494\) 0 0
\(495\) −21.9228 −0.985355
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 12.4365 0.556734 0.278367 0.960475i \(-0.410207\pi\)
0.278367 + 0.960475i \(0.410207\pi\)
\(500\) 0 0
\(501\) 5.61597 0.250903
\(502\) 0 0
\(503\) 21.3309 0.951099 0.475549 0.879689i \(-0.342249\pi\)
0.475549 + 0.879689i \(0.342249\pi\)
\(504\) 0 0
\(505\) −19.7535 −0.879021
\(506\) 0 0
\(507\) −3.95785 −0.175774
\(508\) 0 0
\(509\) 42.7523 1.89496 0.947481 0.319814i \(-0.103620\pi\)
0.947481 + 0.319814i \(0.103620\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 2.81374 0.124230
\(514\) 0 0
\(515\) 1.85987 0.0819556
\(516\) 0 0
\(517\) −16.0551 −0.706102
\(518\) 0 0
\(519\) 0.198799 0.00872629
\(520\) 0 0
\(521\) 24.9707 1.09398 0.546992 0.837138i \(-0.315773\pi\)
0.546992 + 0.837138i \(0.315773\pi\)
\(522\) 0 0
\(523\) 15.9078 0.695599 0.347800 0.937569i \(-0.386929\pi\)
0.347800 + 0.937569i \(0.386929\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −0.339721 −0.0147985
\(528\) 0 0
\(529\) 33.7717 1.46834
\(530\) 0 0
\(531\) 0.219618 0.00953060
\(532\) 0 0
\(533\) 26.3509 1.14138
\(534\) 0 0
\(535\) 56.9450 2.46195
\(536\) 0 0
\(537\) 0.0325437 0.00140437
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −8.68783 −0.373519 −0.186759 0.982406i \(-0.559798\pi\)
−0.186759 + 0.982406i \(0.559798\pi\)
\(542\) 0 0
\(543\) −3.73318 −0.160206
\(544\) 0 0
\(545\) −32.4966 −1.39200
\(546\) 0 0
\(547\) −26.9468 −1.15216 −0.576081 0.817393i \(-0.695419\pi\)
−0.576081 + 0.817393i \(0.695419\pi\)
\(548\) 0 0
\(549\) −41.9598 −1.79080
\(550\) 0 0
\(551\) 7.66391 0.326494
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0.460213 0.0195350
\(556\) 0 0
\(557\) −42.0535 −1.78187 −0.890933 0.454135i \(-0.849948\pi\)
−0.890933 + 0.454135i \(0.849948\pi\)
\(558\) 0 0
\(559\) 13.8559 0.586040
\(560\) 0 0
\(561\) 0.790632 0.0333805
\(562\) 0 0
\(563\) 25.9858 1.09517 0.547586 0.836749i \(-0.315547\pi\)
0.547586 + 0.836749i \(0.315547\pi\)
\(564\) 0 0
\(565\) 36.4189 1.53215
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −10.8816 −0.456182 −0.228091 0.973640i \(-0.573248\pi\)
−0.228091 + 0.973640i \(0.573248\pi\)
\(570\) 0 0
\(571\) 11.6649 0.488163 0.244081 0.969755i \(-0.421514\pi\)
0.244081 + 0.969755i \(0.421514\pi\)
\(572\) 0 0
\(573\) −5.78887 −0.241834
\(574\) 0 0
\(575\) −55.4542 −2.31260
\(576\) 0 0
\(577\) −35.1757 −1.46439 −0.732193 0.681097i \(-0.761503\pi\)
−0.732193 + 0.681097i \(0.761503\pi\)
\(578\) 0 0
\(579\) 3.58939 0.149170
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 4.89204 0.202608
\(584\) 0 0
\(585\) −21.4814 −0.888145
\(586\) 0 0
\(587\) 17.9581 0.741212 0.370606 0.928790i \(-0.379150\pi\)
0.370606 + 0.928790i \(0.379150\pi\)
\(588\) 0 0
\(589\) −0.473849 −0.0195246
\(590\) 0 0
\(591\) 9.89117 0.406868
\(592\) 0 0
\(593\) 7.85554 0.322588 0.161294 0.986906i \(-0.448433\pi\)
0.161294 + 0.986906i \(0.448433\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 8.24039 0.337257
\(598\) 0 0
\(599\) −14.7639 −0.603236 −0.301618 0.953429i \(-0.597527\pi\)
−0.301618 + 0.953429i \(0.597527\pi\)
\(600\) 0 0
\(601\) 6.67351 0.272218 0.136109 0.990694i \(-0.456540\pi\)
0.136109 + 0.990694i \(0.456540\pi\)
\(602\) 0 0
\(603\) −22.0256 −0.896950
\(604\) 0 0
\(605\) 20.7457 0.843433
\(606\) 0 0
\(607\) −37.8693 −1.53707 −0.768534 0.639809i \(-0.779014\pi\)
−0.768534 + 0.639809i \(0.779014\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −15.7318 −0.636442
\(612\) 0 0
\(613\) 17.6730 0.713805 0.356902 0.934142i \(-0.383833\pi\)
0.356902 + 0.934142i \(0.383833\pi\)
\(614\) 0 0
\(615\) 20.4475 0.824521
\(616\) 0 0
\(617\) −15.9720 −0.643009 −0.321505 0.946908i \(-0.604189\pi\)
−0.321505 + 0.946908i \(0.604189\pi\)
\(618\) 0 0
\(619\) −34.8682 −1.40147 −0.700735 0.713422i \(-0.747144\pi\)
−0.700735 + 0.713422i \(0.747144\pi\)
\(620\) 0 0
\(621\) 21.2007 0.850753
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −7.63195 −0.305278
\(626\) 0 0
\(627\) 1.10279 0.0440412
\(628\) 0 0
\(629\) 0.192170 0.00766233
\(630\) 0 0
\(631\) −14.4788 −0.576393 −0.288197 0.957571i \(-0.593056\pi\)
−0.288197 + 0.957571i \(0.593056\pi\)
\(632\) 0 0
\(633\) 5.82555 0.231545
\(634\) 0 0
\(635\) 45.4883 1.80515
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −2.11159 −0.0835333
\(640\) 0 0
\(641\) 28.5138 1.12623 0.563113 0.826380i \(-0.309604\pi\)
0.563113 + 0.826380i \(0.309604\pi\)
\(642\) 0 0
\(643\) 23.7793 0.937763 0.468882 0.883261i \(-0.344657\pi\)
0.468882 + 0.883261i \(0.344657\pi\)
\(644\) 0 0
\(645\) 10.7517 0.423348
\(646\) 0 0
\(647\) −35.5860 −1.39903 −0.699514 0.714619i \(-0.746600\pi\)
−0.699514 + 0.714619i \(0.746600\pi\)
\(648\) 0 0
\(649\) 0.179584 0.00704929
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −9.24174 −0.361657 −0.180829 0.983515i \(-0.557878\pi\)
−0.180829 + 0.983515i \(0.557878\pi\)
\(654\) 0 0
\(655\) 61.5986 2.40686
\(656\) 0 0
\(657\) 28.3869 1.10748
\(658\) 0 0
\(659\) −23.4715 −0.914320 −0.457160 0.889384i \(-0.651133\pi\)
−0.457160 + 0.889384i \(0.651133\pi\)
\(660\) 0 0
\(661\) 10.1636 0.395317 0.197658 0.980271i \(-0.436666\pi\)
0.197658 + 0.980271i \(0.436666\pi\)
\(662\) 0 0
\(663\) 0.774714 0.0300874
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 57.7453 2.23591
\(668\) 0 0
\(669\) −11.3670 −0.439472
\(670\) 0 0
\(671\) −34.3110 −1.32456
\(672\) 0 0
\(673\) −11.0320 −0.425251 −0.212626 0.977134i \(-0.568201\pi\)
−0.212626 + 0.977134i \(0.568201\pi\)
\(674\) 0 0
\(675\) −20.7087 −0.797076
\(676\) 0 0
\(677\) 34.5867 1.32928 0.664638 0.747165i \(-0.268586\pi\)
0.664638 + 0.747165i \(0.268586\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −0.764814 −0.0293077
\(682\) 0 0
\(683\) −26.0946 −0.998480 −0.499240 0.866464i \(-0.666387\pi\)
−0.499240 + 0.866464i \(0.666387\pi\)
\(684\) 0 0
\(685\) −25.6670 −0.980685
\(686\) 0 0
\(687\) 6.77216 0.258374
\(688\) 0 0
\(689\) 4.79354 0.182619
\(690\) 0 0
\(691\) −8.51398 −0.323887 −0.161944 0.986800i \(-0.551776\pi\)
−0.161944 + 0.986800i \(0.551776\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −29.5559 −1.12112
\(696\) 0 0
\(697\) 8.53820 0.323407
\(698\) 0 0
\(699\) −6.98939 −0.264363
\(700\) 0 0
\(701\) −7.20119 −0.271985 −0.135993 0.990710i \(-0.543422\pi\)
−0.135993 + 0.990710i \(0.543422\pi\)
\(702\) 0 0
\(703\) 0.268043 0.0101094
\(704\) 0 0
\(705\) −12.2074 −0.459757
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −20.9748 −0.787726 −0.393863 0.919169i \(-0.628861\pi\)
−0.393863 + 0.919169i \(0.628861\pi\)
\(710\) 0 0
\(711\) 41.2215 1.54593
\(712\) 0 0
\(713\) −3.57031 −0.133709
\(714\) 0 0
\(715\) −17.5656 −0.656915
\(716\) 0 0
\(717\) 13.4073 0.500704
\(718\) 0 0
\(719\) −29.7635 −1.10999 −0.554996 0.831853i \(-0.687280\pi\)
−0.554996 + 0.831853i \(0.687280\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −4.19021 −0.155835
\(724\) 0 0
\(725\) −56.4052 −2.09484
\(726\) 0 0
\(727\) −21.9856 −0.815401 −0.407700 0.913116i \(-0.633669\pi\)
−0.407700 + 0.913116i \(0.633669\pi\)
\(728\) 0 0
\(729\) −14.9605 −0.554091
\(730\) 0 0
\(731\) 4.48956 0.166052
\(732\) 0 0
\(733\) −41.0702 −1.51696 −0.758482 0.651694i \(-0.774058\pi\)
−0.758482 + 0.651694i \(0.774058\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −18.0106 −0.663428
\(738\) 0 0
\(739\) 21.2697 0.782417 0.391209 0.920302i \(-0.372057\pi\)
0.391209 + 0.920302i \(0.372057\pi\)
\(740\) 0 0
\(741\) 1.08059 0.0396963
\(742\) 0 0
\(743\) −6.24375 −0.229061 −0.114531 0.993420i \(-0.536536\pi\)
−0.114531 + 0.993420i \(0.536536\pi\)
\(744\) 0 0
\(745\) −21.0811 −0.772351
\(746\) 0 0
\(747\) 10.1868 0.372715
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 18.3670 0.670222 0.335111 0.942179i \(-0.391226\pi\)
0.335111 + 0.942179i \(0.391226\pi\)
\(752\) 0 0
\(753\) −1.58117 −0.0576211
\(754\) 0 0
\(755\) 77.5455 2.82217
\(756\) 0 0
\(757\) −3.63834 −0.132238 −0.0661188 0.997812i \(-0.521062\pi\)
−0.0661188 + 0.997812i \(0.521062\pi\)
\(758\) 0 0
\(759\) 8.30919 0.301605
\(760\) 0 0
\(761\) 5.98449 0.216938 0.108469 0.994100i \(-0.465405\pi\)
0.108469 + 0.994100i \(0.465405\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −6.96037 −0.251653
\(766\) 0 0
\(767\) 0.175968 0.00635385
\(768\) 0 0
\(769\) 45.7519 1.64986 0.824928 0.565238i \(-0.191216\pi\)
0.824928 + 0.565238i \(0.191216\pi\)
\(770\) 0 0
\(771\) 0.692303 0.0249327
\(772\) 0 0
\(773\) −33.5347 −1.20616 −0.603080 0.797681i \(-0.706060\pi\)
−0.603080 + 0.797681i \(0.706060\pi\)
\(774\) 0 0
\(775\) 3.48745 0.125273
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 11.9093 0.426693
\(780\) 0 0
\(781\) −1.72667 −0.0617853
\(782\) 0 0
\(783\) 21.5642 0.770643
\(784\) 0 0
\(785\) −72.9938 −2.60526
\(786\) 0 0
\(787\) 3.51073 0.125144 0.0625719 0.998040i \(-0.480070\pi\)
0.0625719 + 0.998040i \(0.480070\pi\)
\(788\) 0 0
\(789\) −1.25772 −0.0447762
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −33.6202 −1.19389
\(794\) 0 0
\(795\) 3.71963 0.131922
\(796\) 0 0
\(797\) 15.1264 0.535806 0.267903 0.963446i \(-0.413669\pi\)
0.267903 + 0.963446i \(0.413669\pi\)
\(798\) 0 0
\(799\) −5.09741 −0.180334
\(800\) 0 0
\(801\) −6.15305 −0.217407
\(802\) 0 0
\(803\) 23.2123 0.819144
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −5.34806 −0.188261
\(808\) 0 0
\(809\) −2.38201 −0.0837470 −0.0418735 0.999123i \(-0.513333\pi\)
−0.0418735 + 0.999123i \(0.513333\pi\)
\(810\) 0 0
\(811\) 25.9215 0.910228 0.455114 0.890433i \(-0.349599\pi\)
0.455114 + 0.890433i \(0.349599\pi\)
\(812\) 0 0
\(813\) 11.3066 0.396541
\(814\) 0 0
\(815\) −35.2787 −1.23576
\(816\) 0 0
\(817\) 6.26213 0.219084
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −53.8970 −1.88102 −0.940509 0.339769i \(-0.889651\pi\)
−0.940509 + 0.339769i \(0.889651\pi\)
\(822\) 0 0
\(823\) 12.9577 0.451677 0.225838 0.974165i \(-0.427488\pi\)
0.225838 + 0.974165i \(0.427488\pi\)
\(824\) 0 0
\(825\) −8.11636 −0.282575
\(826\) 0 0
\(827\) 29.8634 1.03845 0.519226 0.854637i \(-0.326220\pi\)
0.519226 + 0.854637i \(0.326220\pi\)
\(828\) 0 0
\(829\) 39.7956 1.38216 0.691079 0.722780i \(-0.257136\pi\)
0.691079 + 0.722780i \(0.257136\pi\)
\(830\) 0 0
\(831\) −6.88462 −0.238825
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −40.4281 −1.39907
\(836\) 0 0
\(837\) −1.33329 −0.0460851
\(838\) 0 0
\(839\) 41.5209 1.43346 0.716731 0.697350i \(-0.245638\pi\)
0.716731 + 0.697350i \(0.245638\pi\)
\(840\) 0 0
\(841\) 29.7356 1.02536
\(842\) 0 0
\(843\) 0.166574 0.00573711
\(844\) 0 0
\(845\) 28.4916 0.980142
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 4.87147 0.167188
\(850\) 0 0
\(851\) 2.01962 0.0692318
\(852\) 0 0
\(853\) −15.0014 −0.513637 −0.256818 0.966460i \(-0.582674\pi\)
−0.256818 + 0.966460i \(0.582674\pi\)
\(854\) 0 0
\(855\) −9.70847 −0.332023
\(856\) 0 0
\(857\) −21.3427 −0.729053 −0.364527 0.931193i \(-0.618769\pi\)
−0.364527 + 0.931193i \(0.618769\pi\)
\(858\) 0 0
\(859\) −23.7738 −0.811151 −0.405576 0.914062i \(-0.632929\pi\)
−0.405576 + 0.914062i \(0.632929\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −25.5643 −0.870217 −0.435109 0.900378i \(-0.643290\pi\)
−0.435109 + 0.900378i \(0.643290\pi\)
\(864\) 0 0
\(865\) −1.43111 −0.0486590
\(866\) 0 0
\(867\) −8.05125 −0.273435
\(868\) 0 0
\(869\) 33.7073 1.14344
\(870\) 0 0
\(871\) −17.6479 −0.597977
\(872\) 0 0
\(873\) −19.5855 −0.662869
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −10.1296 −0.342053 −0.171026 0.985266i \(-0.554708\pi\)
−0.171026 + 0.985266i \(0.554708\pi\)
\(878\) 0 0
\(879\) −10.5848 −0.357016
\(880\) 0 0
\(881\) −33.6185 −1.13264 −0.566319 0.824186i \(-0.691633\pi\)
−0.566319 + 0.824186i \(0.691633\pi\)
\(882\) 0 0
\(883\) 32.8755 1.10635 0.553174 0.833066i \(-0.313416\pi\)
0.553174 + 0.833066i \(0.313416\pi\)
\(884\) 0 0
\(885\) 0.136546 0.00458993
\(886\) 0 0
\(887\) −44.6026 −1.49761 −0.748804 0.662792i \(-0.769371\pi\)
−0.748804 + 0.662792i \(0.769371\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −15.6043 −0.522764
\(892\) 0 0
\(893\) −7.10998 −0.237926
\(894\) 0 0
\(895\) −0.234275 −0.00783094
\(896\) 0 0
\(897\) 8.14189 0.271850
\(898\) 0 0
\(899\) −3.63154 −0.121119
\(900\) 0 0
\(901\) 1.55320 0.0517446
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 26.8743 0.893333
\(906\) 0 0
\(907\) −51.6897 −1.71633 −0.858164 0.513376i \(-0.828395\pi\)
−0.858164 + 0.513376i \(0.828395\pi\)
\(908\) 0 0
\(909\) −15.5161 −0.514637
\(910\) 0 0
\(911\) 28.0623 0.929745 0.464872 0.885378i \(-0.346100\pi\)
0.464872 + 0.885378i \(0.346100\pi\)
\(912\) 0 0
\(913\) 8.32986 0.275678
\(914\) 0 0
\(915\) −26.0882 −0.862448
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 21.7561 0.717669 0.358834 0.933401i \(-0.383174\pi\)
0.358834 + 0.933401i \(0.383174\pi\)
\(920\) 0 0
\(921\) 10.0717 0.331873
\(922\) 0 0
\(923\) −1.69191 −0.0556898
\(924\) 0 0
\(925\) −1.97275 −0.0648638
\(926\) 0 0
\(927\) 1.46090 0.0479822
\(928\) 0 0
\(929\) −52.4361 −1.72037 −0.860186 0.509980i \(-0.829653\pi\)
−0.860186 + 0.509980i \(0.829653\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 3.87098 0.126730
\(934\) 0 0
\(935\) −5.69158 −0.186135
\(936\) 0 0
\(937\) 6.48443 0.211837 0.105919 0.994375i \(-0.466222\pi\)
0.105919 + 0.994375i \(0.466222\pi\)
\(938\) 0 0
\(939\) −5.25788 −0.171585
\(940\) 0 0
\(941\) −5.12436 −0.167049 −0.0835247 0.996506i \(-0.526618\pi\)
−0.0835247 + 0.996506i \(0.526618\pi\)
\(942\) 0 0
\(943\) 89.7327 2.92210
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −17.3046 −0.562325 −0.281163 0.959660i \(-0.590720\pi\)
−0.281163 + 0.959660i \(0.590720\pi\)
\(948\) 0 0
\(949\) 22.7449 0.738331
\(950\) 0 0
\(951\) −3.91761 −0.127037
\(952\) 0 0
\(953\) −52.4552 −1.69919 −0.849595 0.527436i \(-0.823153\pi\)
−0.849595 + 0.527436i \(0.823153\pi\)
\(954\) 0 0
\(955\) 41.6727 1.34850
\(956\) 0 0
\(957\) 8.45169 0.273204
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −30.7755 −0.992757
\(962\) 0 0
\(963\) 44.7295 1.44139
\(964\) 0 0
\(965\) −25.8392 −0.831794
\(966\) 0 0
\(967\) 39.0111 1.25451 0.627256 0.778813i \(-0.284178\pi\)
0.627256 + 0.778813i \(0.284178\pi\)
\(968\) 0 0
\(969\) 0.350131 0.0112478
\(970\) 0 0
\(971\) −25.7693 −0.826975 −0.413488 0.910510i \(-0.635689\pi\)
−0.413488 + 0.910510i \(0.635689\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −7.95294 −0.254698
\(976\) 0 0
\(977\) −3.35129 −0.107217 −0.0536087 0.998562i \(-0.517072\pi\)
−0.0536087 + 0.998562i \(0.517072\pi\)
\(978\) 0 0
\(979\) −5.03142 −0.160805
\(980\) 0 0
\(981\) −25.5256 −0.814970
\(982\) 0 0
\(983\) 25.3969 0.810037 0.405018 0.914309i \(-0.367265\pi\)
0.405018 + 0.914309i \(0.367265\pi\)
\(984\) 0 0
\(985\) −71.2043 −2.26876
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 47.1833 1.50034
\(990\) 0 0
\(991\) −35.6136 −1.13130 −0.565651 0.824645i \(-0.691375\pi\)
−0.565651 + 0.824645i \(0.691375\pi\)
\(992\) 0 0
\(993\) 6.13896 0.194814
\(994\) 0 0
\(995\) −59.3206 −1.88059
\(996\) 0 0
\(997\) 29.0273 0.919303 0.459651 0.888099i \(-0.347974\pi\)
0.459651 + 0.888099i \(0.347974\pi\)
\(998\) 0 0
\(999\) 0.754203 0.0238619
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 7448.2.a.bn.1.3 yes 6
7.6 odd 2 7448.2.a.bm.1.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7448.2.a.bm.1.4 6 7.6 odd 2
7448.2.a.bn.1.3 yes 6 1.1 even 1 trivial