Properties

Label 3640.2.a.p.1.2
Level $3640$
Weight $2$
Character 3640.1
Self dual yes
Analytic conductor $29.066$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3640.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(29.0655463357\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.1101.1
Defining polynomial: \( x^{3} - x^{2} - 9x + 12 \) 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 1.2
Root \(1.43163\) of defining polynomial
Character \(\chi\) \(=\) 3640.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.43163 q^{3} -1.00000 q^{5} +1.00000 q^{7} -0.950444 q^{9} +O(q^{10})\) \(q-1.43163 q^{3} -1.00000 q^{5} +1.00000 q^{7} -0.950444 q^{9} -1.00000 q^{13} +1.43163 q^{15} -3.95044 q^{17} -5.95044 q^{19} -1.43163 q^{21} -5.03763 q^{23} +1.00000 q^{25} +5.65556 q^{27} +4.46926 q^{29} +2.56837 q^{31} -1.00000 q^{35} +5.60601 q^{37} +1.43163 q^{39} -3.95044 q^{41} -1.13675 q^{43} +0.950444 q^{45} +9.03763 q^{47} +1.00000 q^{49} +5.65556 q^{51} +2.00000 q^{53} +8.51882 q^{57} -0.294881 q^{59} -10.0000 q^{61} -0.950444 q^{63} +1.00000 q^{65} -8.12482 q^{67} +7.21201 q^{69} +2.86325 q^{71} -8.76414 q^{73} -1.43163 q^{75} +5.95044 q^{79} -5.24533 q^{81} +5.03763 q^{83} +3.95044 q^{85} -6.39831 q^{87} +2.74275 q^{89} -1.00000 q^{91} -3.67695 q^{93} +5.95044 q^{95} -9.21201 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - q^{3} - 3 q^{5} + 3 q^{7} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - q^{3} - 3 q^{5} + 3 q^{7} + 10 q^{9} - 3 q^{13} + q^{15} + q^{17} - 5 q^{19} - q^{21} + 4 q^{23} + 3 q^{25} + 14 q^{27} - 9 q^{29} + 11 q^{31} - 3 q^{35} + q^{37} + q^{39} + q^{41} - 10 q^{43} - 10 q^{45} + 8 q^{47} + 3 q^{49} + 14 q^{51} + 6 q^{53} + 16 q^{57} + 9 q^{59} - 30 q^{61} + 10 q^{63} + 3 q^{65} + q^{67} - 10 q^{69} + 2 q^{71} + 6 q^{73} - q^{75} + 5 q^{79} + 7 q^{81} - 4 q^{83} - q^{85} - 7 q^{87} - q^{89} - 3 q^{91} + 15 q^{93} + 5 q^{95} + 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.43163 −0.826550 −0.413275 0.910606i \(-0.635615\pi\)
−0.413275 + 0.910606i \(0.635615\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) −0.950444 −0.316815
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 1.43163 0.369645
\(16\) 0 0
\(17\) −3.95044 −0.958123 −0.479062 0.877781i \(-0.659023\pi\)
−0.479062 + 0.877781i \(0.659023\pi\)
\(18\) 0 0
\(19\) −5.95044 −1.36513 −0.682563 0.730827i \(-0.739135\pi\)
−0.682563 + 0.730827i \(0.739135\pi\)
\(20\) 0 0
\(21\) −1.43163 −0.312407
\(22\) 0 0
\(23\) −5.03763 −1.05042 −0.525210 0.850973i \(-0.676013\pi\)
−0.525210 + 0.850973i \(0.676013\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 5.65556 1.08841
\(28\) 0 0
\(29\) 4.46926 0.829921 0.414960 0.909839i \(-0.363795\pi\)
0.414960 + 0.909839i \(0.363795\pi\)
\(30\) 0 0
\(31\) 2.56837 0.461293 0.230647 0.973038i \(-0.425916\pi\)
0.230647 + 0.973038i \(0.425916\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.00000 −0.169031
\(36\) 0 0
\(37\) 5.60601 0.921622 0.460811 0.887498i \(-0.347559\pi\)
0.460811 + 0.887498i \(0.347559\pi\)
\(38\) 0 0
\(39\) 1.43163 0.229244
\(40\) 0 0
\(41\) −3.95044 −0.616956 −0.308478 0.951232i \(-0.599820\pi\)
−0.308478 + 0.951232i \(0.599820\pi\)
\(42\) 0 0
\(43\) −1.13675 −0.173352 −0.0866761 0.996237i \(-0.527625\pi\)
−0.0866761 + 0.996237i \(0.527625\pi\)
\(44\) 0 0
\(45\) 0.950444 0.141684
\(46\) 0 0
\(47\) 9.03763 1.31827 0.659137 0.752023i \(-0.270922\pi\)
0.659137 + 0.752023i \(0.270922\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 5.65556 0.791937
\(52\) 0 0
\(53\) 2.00000 0.274721 0.137361 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 8.51882 1.12834
\(58\) 0 0
\(59\) −0.294881 −0.0383903 −0.0191951 0.999816i \(-0.506110\pi\)
−0.0191951 + 0.999816i \(0.506110\pi\)
\(60\) 0 0
\(61\) −10.0000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 0 0
\(63\) −0.950444 −0.119745
\(64\) 0 0
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) −8.12482 −0.992605 −0.496303 0.868150i \(-0.665309\pi\)
−0.496303 + 0.868150i \(0.665309\pi\)
\(68\) 0 0
\(69\) 7.21201 0.868224
\(70\) 0 0
\(71\) 2.86325 0.339806 0.169903 0.985461i \(-0.445655\pi\)
0.169903 + 0.985461i \(0.445655\pi\)
\(72\) 0 0
\(73\) −8.76414 −1.02577 −0.512883 0.858459i \(-0.671422\pi\)
−0.512883 + 0.858459i \(0.671422\pi\)
\(74\) 0 0
\(75\) −1.43163 −0.165310
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 5.95044 0.669477 0.334739 0.942311i \(-0.391352\pi\)
0.334739 + 0.942311i \(0.391352\pi\)
\(80\) 0 0
\(81\) −5.24533 −0.582814
\(82\) 0 0
\(83\) 5.03763 0.552952 0.276476 0.961021i \(-0.410833\pi\)
0.276476 + 0.961021i \(0.410833\pi\)
\(84\) 0 0
\(85\) 3.95044 0.428486
\(86\) 0 0
\(87\) −6.39831 −0.685971
\(88\) 0 0
\(89\) 2.74275 0.290731 0.145366 0.989378i \(-0.453564\pi\)
0.145366 + 0.989378i \(0.453564\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −3.67695 −0.381282
\(94\) 0 0
\(95\) 5.95044 0.610503
\(96\) 0 0
\(97\) −9.21201 −0.935338 −0.467669 0.883904i \(-0.654906\pi\)
−0.467669 + 0.883904i \(0.654906\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −3.03763 −0.302256 −0.151128 0.988514i \(-0.548291\pi\)
−0.151128 + 0.988514i \(0.548291\pi\)
\(102\) 0 0
\(103\) 8.12482 0.800563 0.400281 0.916392i \(-0.368912\pi\)
0.400281 + 0.916392i \(0.368912\pi\)
\(104\) 0 0
\(105\) 1.43163 0.139713
\(106\) 0 0
\(107\) −2.17438 −0.210205 −0.105103 0.994461i \(-0.533517\pi\)
−0.105103 + 0.994461i \(0.533517\pi\)
\(108\) 0 0
\(109\) −16.0753 −1.53973 −0.769866 0.638206i \(-0.779677\pi\)
−0.769866 + 0.638206i \(0.779677\pi\)
\(110\) 0 0
\(111\) −8.02571 −0.761767
\(112\) 0 0
\(113\) 17.2120 1.61917 0.809585 0.587003i \(-0.199692\pi\)
0.809585 + 0.587003i \(0.199692\pi\)
\(114\) 0 0
\(115\) 5.03763 0.469762
\(116\) 0 0
\(117\) 0.950444 0.0878686
\(118\) 0 0
\(119\) −3.95044 −0.362137
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 0 0
\(123\) 5.65556 0.509945
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 18.7641 1.66505 0.832524 0.553989i \(-0.186895\pi\)
0.832524 + 0.553989i \(0.186895\pi\)
\(128\) 0 0
\(129\) 1.62740 0.143284
\(130\) 0 0
\(131\) 10.7641 0.940467 0.470234 0.882542i \(-0.344170\pi\)
0.470234 + 0.882542i \(0.344170\pi\)
\(132\) 0 0
\(133\) −5.95044 −0.515969
\(134\) 0 0
\(135\) −5.65556 −0.486753
\(136\) 0 0
\(137\) 20.4693 1.74881 0.874403 0.485200i \(-0.161253\pi\)
0.874403 + 0.485200i \(0.161253\pi\)
\(138\) 0 0
\(139\) 7.90089 0.670145 0.335072 0.942192i \(-0.391239\pi\)
0.335072 + 0.942192i \(0.391239\pi\)
\(140\) 0 0
\(141\) −12.9385 −1.08962
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −4.46926 −0.371152
\(146\) 0 0
\(147\) −1.43163 −0.118079
\(148\) 0 0
\(149\) 2.00000 0.163846 0.0819232 0.996639i \(-0.473894\pi\)
0.0819232 + 0.996639i \(0.473894\pi\)
\(150\) 0 0
\(151\) 20.9385 1.70395 0.851976 0.523580i \(-0.175404\pi\)
0.851976 + 0.523580i \(0.175404\pi\)
\(152\) 0 0
\(153\) 3.75467 0.303547
\(154\) 0 0
\(155\) −2.56837 −0.206297
\(156\) 0 0
\(157\) 3.33251 0.265964 0.132982 0.991118i \(-0.457545\pi\)
0.132982 + 0.991118i \(0.457545\pi\)
\(158\) 0 0
\(159\) −2.86325 −0.227071
\(160\) 0 0
\(161\) −5.03763 −0.397021
\(162\) 0 0
\(163\) 9.43163 0.738742 0.369371 0.929282i \(-0.379573\pi\)
0.369371 + 0.929282i \(0.379573\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 18.6650 1.44434 0.722172 0.691714i \(-0.243144\pi\)
0.722172 + 0.691714i \(0.243144\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 5.65556 0.432492
\(172\) 0 0
\(173\) −25.4078 −1.93172 −0.965859 0.259069i \(-0.916584\pi\)
−0.965859 + 0.259069i \(0.916584\pi\)
\(174\) 0 0
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) 0.422160 0.0317315
\(178\) 0 0
\(179\) 6.04956 0.452165 0.226083 0.974108i \(-0.427408\pi\)
0.226083 + 0.974108i \(0.427408\pi\)
\(180\) 0 0
\(181\) 13.2120 0.982041 0.491021 0.871148i \(-0.336624\pi\)
0.491021 + 0.871148i \(0.336624\pi\)
\(182\) 0 0
\(183\) 14.3163 1.05829
\(184\) 0 0
\(185\) −5.60601 −0.412162
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 5.65556 0.411382
\(190\) 0 0
\(191\) 13.4316 0.971878 0.485939 0.873993i \(-0.338478\pi\)
0.485939 + 0.873993i \(0.338478\pi\)
\(192\) 0 0
\(193\) 4.14867 0.298628 0.149314 0.988790i \(-0.452294\pi\)
0.149314 + 0.988790i \(0.452294\pi\)
\(194\) 0 0
\(195\) −1.43163 −0.102521
\(196\) 0 0
\(197\) 27.9223 1.98938 0.994690 0.102917i \(-0.0328176\pi\)
0.994690 + 0.102917i \(0.0328176\pi\)
\(198\) 0 0
\(199\) 15.2120 1.07835 0.539175 0.842193i \(-0.318736\pi\)
0.539175 + 0.842193i \(0.318736\pi\)
\(200\) 0 0
\(201\) 11.6317 0.820438
\(202\) 0 0
\(203\) 4.46926 0.313681
\(204\) 0 0
\(205\) 3.95044 0.275911
\(206\) 0 0
\(207\) 4.78799 0.332788
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −2.39831 −0.165107 −0.0825534 0.996587i \(-0.526307\pi\)
−0.0825534 + 0.996587i \(0.526307\pi\)
\(212\) 0 0
\(213\) −4.09911 −0.280867
\(214\) 0 0
\(215\) 1.13675 0.0775254
\(216\) 0 0
\(217\) 2.56837 0.174353
\(218\) 0 0
\(219\) 12.5470 0.847847
\(220\) 0 0
\(221\) 3.95044 0.265736
\(222\) 0 0
\(223\) 1.82562 0.122253 0.0611263 0.998130i \(-0.480531\pi\)
0.0611263 + 0.998130i \(0.480531\pi\)
\(224\) 0 0
\(225\) −0.950444 −0.0633629
\(226\) 0 0
\(227\) 2.96237 0.196619 0.0983096 0.995156i \(-0.468656\pi\)
0.0983096 + 0.995156i \(0.468656\pi\)
\(228\) 0 0
\(229\) −11.9504 −0.789708 −0.394854 0.918744i \(-0.629205\pi\)
−0.394854 + 0.918744i \(0.629205\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −15.0376 −0.985148 −0.492574 0.870271i \(-0.663944\pi\)
−0.492574 + 0.870271i \(0.663944\pi\)
\(234\) 0 0
\(235\) −9.03763 −0.589550
\(236\) 0 0
\(237\) −8.51882 −0.553357
\(238\) 0 0
\(239\) 9.03763 0.584596 0.292298 0.956327i \(-0.405580\pi\)
0.292298 + 0.956327i \(0.405580\pi\)
\(240\) 0 0
\(241\) 23.7522 1.53001 0.765007 0.644021i \(-0.222735\pi\)
0.765007 + 0.644021i \(0.222735\pi\)
\(242\) 0 0
\(243\) −9.45734 −0.606688
\(244\) 0 0
\(245\) −1.00000 −0.0638877
\(246\) 0 0
\(247\) 5.95044 0.378618
\(248\) 0 0
\(249\) −7.21201 −0.457043
\(250\) 0 0
\(251\) −14.6650 −0.925648 −0.462824 0.886450i \(-0.653164\pi\)
−0.462824 + 0.886450i \(0.653164\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −5.65556 −0.354165
\(256\) 0 0
\(257\) 21.4530 1.33820 0.669101 0.743171i \(-0.266679\pi\)
0.669101 + 0.743171i \(0.266679\pi\)
\(258\) 0 0
\(259\) 5.60601 0.348340
\(260\) 0 0
\(261\) −4.24778 −0.262931
\(262\) 0 0
\(263\) 21.0376 1.29724 0.648618 0.761114i \(-0.275347\pi\)
0.648618 + 0.761114i \(0.275347\pi\)
\(264\) 0 0
\(265\) −2.00000 −0.122859
\(266\) 0 0
\(267\) −3.92660 −0.240304
\(268\) 0 0
\(269\) −5.31112 −0.323825 −0.161913 0.986805i \(-0.551766\pi\)
−0.161913 + 0.986805i \(0.551766\pi\)
\(270\) 0 0
\(271\) −18.0753 −1.09799 −0.548997 0.835824i \(-0.684990\pi\)
−0.548997 + 0.835824i \(0.684990\pi\)
\(272\) 0 0
\(273\) 1.43163 0.0866460
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −9.31112 −0.559451 −0.279726 0.960080i \(-0.590244\pi\)
−0.279726 + 0.960080i \(0.590244\pi\)
\(278\) 0 0
\(279\) −2.44109 −0.146144
\(280\) 0 0
\(281\) −30.0514 −1.79272 −0.896359 0.443329i \(-0.853797\pi\)
−0.896359 + 0.443329i \(0.853797\pi\)
\(282\) 0 0
\(283\) −18.3983 −1.09367 −0.546833 0.837242i \(-0.684167\pi\)
−0.546833 + 0.837242i \(0.684167\pi\)
\(284\) 0 0
\(285\) −8.51882 −0.504611
\(286\) 0 0
\(287\) −3.95044 −0.233187
\(288\) 0 0
\(289\) −1.39399 −0.0819996
\(290\) 0 0
\(291\) 13.1882 0.773104
\(292\) 0 0
\(293\) −12.1744 −0.711235 −0.355617 0.934632i \(-0.615729\pi\)
−0.355617 + 0.934632i \(0.615729\pi\)
\(294\) 0 0
\(295\) 0.294881 0.0171687
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 5.03763 0.291334
\(300\) 0 0
\(301\) −1.13675 −0.0655209
\(302\) 0 0
\(303\) 4.34876 0.249830
\(304\) 0 0
\(305\) 10.0000 0.572598
\(306\) 0 0
\(307\) 2.96237 0.169071 0.0845356 0.996420i \(-0.473059\pi\)
0.0845356 + 0.996420i \(0.473059\pi\)
\(308\) 0 0
\(309\) −11.6317 −0.661705
\(310\) 0 0
\(311\) −0.447871 −0.0253964 −0.0126982 0.999919i \(-0.504042\pi\)
−0.0126982 + 0.999919i \(0.504042\pi\)
\(312\) 0 0
\(313\) 29.4078 1.66223 0.831113 0.556104i \(-0.187704\pi\)
0.831113 + 0.556104i \(0.187704\pi\)
\(314\) 0 0
\(315\) 0.950444 0.0535514
\(316\) 0 0
\(317\) 9.80178 0.550523 0.275261 0.961369i \(-0.411236\pi\)
0.275261 + 0.961369i \(0.411236\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 3.11290 0.173745
\(322\) 0 0
\(323\) 23.5069 1.30796
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) 0 0
\(327\) 23.0138 1.27267
\(328\) 0 0
\(329\) 9.03763 0.498261
\(330\) 0 0
\(331\) −18.0753 −0.993507 −0.496753 0.867892i \(-0.665475\pi\)
−0.496753 + 0.867892i \(0.665475\pi\)
\(332\) 0 0
\(333\) −5.32819 −0.291983
\(334\) 0 0
\(335\) 8.12482 0.443906
\(336\) 0 0
\(337\) 7.72651 0.420890 0.210445 0.977606i \(-0.432509\pi\)
0.210445 + 0.977606i \(0.432509\pi\)
\(338\) 0 0
\(339\) −24.6412 −1.33833
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) −7.21201 −0.388282
\(346\) 0 0
\(347\) 30.9147 1.65959 0.829793 0.558071i \(-0.188458\pi\)
0.829793 + 0.558071i \(0.188458\pi\)
\(348\) 0 0
\(349\) −23.1343 −1.23835 −0.619175 0.785253i \(-0.712533\pi\)
−0.619175 + 0.785253i \(0.712533\pi\)
\(350\) 0 0
\(351\) −5.65556 −0.301872
\(352\) 0 0
\(353\) 11.5283 0.613589 0.306794 0.951776i \(-0.400744\pi\)
0.306794 + 0.951776i \(0.400744\pi\)
\(354\) 0 0
\(355\) −2.86325 −0.151966
\(356\) 0 0
\(357\) 5.65556 0.299324
\(358\) 0 0
\(359\) −32.0514 −1.69161 −0.845805 0.533493i \(-0.820879\pi\)
−0.845805 + 0.533493i \(0.820879\pi\)
\(360\) 0 0
\(361\) 16.4078 0.863567
\(362\) 0 0
\(363\) 15.7479 0.826550
\(364\) 0 0
\(365\) 8.76414 0.458736
\(366\) 0 0
\(367\) 30.0753 1.56992 0.784958 0.619549i \(-0.212684\pi\)
0.784958 + 0.619549i \(0.212684\pi\)
\(368\) 0 0
\(369\) 3.75467 0.195461
\(370\) 0 0
\(371\) 2.00000 0.103835
\(372\) 0 0
\(373\) −12.3163 −0.637712 −0.318856 0.947803i \(-0.603299\pi\)
−0.318856 + 0.947803i \(0.603299\pi\)
\(374\) 0 0
\(375\) 1.43163 0.0739289
\(376\) 0 0
\(377\) −4.46926 −0.230179
\(378\) 0 0
\(379\) 19.1129 0.981764 0.490882 0.871226i \(-0.336675\pi\)
0.490882 + 0.871226i \(0.336675\pi\)
\(380\) 0 0
\(381\) −26.8633 −1.37625
\(382\) 0 0
\(383\) 1.62740 0.0831561 0.0415780 0.999135i \(-0.486761\pi\)
0.0415780 + 0.999135i \(0.486761\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 1.08041 0.0549205
\(388\) 0 0
\(389\) 33.4787 1.69744 0.848719 0.528843i \(-0.177374\pi\)
0.848719 + 0.528843i \(0.177374\pi\)
\(390\) 0 0
\(391\) 19.9009 1.00643
\(392\) 0 0
\(393\) −15.4102 −0.777344
\(394\) 0 0
\(395\) −5.95044 −0.299399
\(396\) 0 0
\(397\) 3.62740 0.182054 0.0910269 0.995848i \(-0.470985\pi\)
0.0910269 + 0.995848i \(0.470985\pi\)
\(398\) 0 0
\(399\) 8.51882 0.426474
\(400\) 0 0
\(401\) 12.5231 0.625376 0.312688 0.949856i \(-0.398771\pi\)
0.312688 + 0.949856i \(0.398771\pi\)
\(402\) 0 0
\(403\) −2.56837 −0.127940
\(404\) 0 0
\(405\) 5.24533 0.260642
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −6.19822 −0.306482 −0.153241 0.988189i \(-0.548971\pi\)
−0.153241 + 0.988189i \(0.548971\pi\)
\(410\) 0 0
\(411\) −29.3043 −1.44548
\(412\) 0 0
\(413\) −0.294881 −0.0145102
\(414\) 0 0
\(415\) −5.03763 −0.247288
\(416\) 0 0
\(417\) −11.3111 −0.553908
\(418\) 0 0
\(419\) 15.9009 0.776809 0.388405 0.921489i \(-0.373026\pi\)
0.388405 + 0.921489i \(0.373026\pi\)
\(420\) 0 0
\(421\) −0.273492 −0.0133292 −0.00666458 0.999978i \(-0.502121\pi\)
−0.00666458 + 0.999978i \(0.502121\pi\)
\(422\) 0 0
\(423\) −8.58976 −0.417649
\(424\) 0 0
\(425\) −3.95044 −0.191625
\(426\) 0 0
\(427\) −10.0000 −0.483934
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −24.2496 −1.16806 −0.584032 0.811731i \(-0.698526\pi\)
−0.584032 + 0.811731i \(0.698526\pi\)
\(432\) 0 0
\(433\) −9.87518 −0.474571 −0.237285 0.971440i \(-0.576258\pi\)
−0.237285 + 0.971440i \(0.576258\pi\)
\(434\) 0 0
\(435\) 6.39831 0.306776
\(436\) 0 0
\(437\) 29.9762 1.43395
\(438\) 0 0
\(439\) −23.8018 −1.13600 −0.567998 0.823030i \(-0.692282\pi\)
−0.567998 + 0.823030i \(0.692282\pi\)
\(440\) 0 0
\(441\) −0.950444 −0.0452592
\(442\) 0 0
\(443\) 5.03763 0.239345 0.119673 0.992813i \(-0.461816\pi\)
0.119673 + 0.992813i \(0.461816\pi\)
\(444\) 0 0
\(445\) −2.74275 −0.130019
\(446\) 0 0
\(447\) −2.86325 −0.135427
\(448\) 0 0
\(449\) 2.78799 0.131573 0.0657866 0.997834i \(-0.479044\pi\)
0.0657866 + 0.997834i \(0.479044\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −29.9762 −1.40840
\(454\) 0 0
\(455\) 1.00000 0.0468807
\(456\) 0 0
\(457\) 12.4693 0.583287 0.291644 0.956527i \(-0.405798\pi\)
0.291644 + 0.956527i \(0.405798\pi\)
\(458\) 0 0
\(459\) −22.3420 −1.04283
\(460\) 0 0
\(461\) −15.9223 −0.741574 −0.370787 0.928718i \(-0.620912\pi\)
−0.370787 + 0.928718i \(0.620912\pi\)
\(462\) 0 0
\(463\) 21.7522 1.01091 0.505456 0.862853i \(-0.331324\pi\)
0.505456 + 0.862853i \(0.331324\pi\)
\(464\) 0 0
\(465\) 3.67695 0.170515
\(466\) 0 0
\(467\) −21.6531 −1.00199 −0.500993 0.865451i \(-0.667032\pi\)
−0.500993 + 0.865451i \(0.667032\pi\)
\(468\) 0 0
\(469\) −8.12482 −0.375169
\(470\) 0 0
\(471\) −4.77092 −0.219832
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −5.95044 −0.273025
\(476\) 0 0
\(477\) −1.90089 −0.0870357
\(478\) 0 0
\(479\) 0.493106 0.0225306 0.0112653 0.999937i \(-0.496414\pi\)
0.0112653 + 0.999937i \(0.496414\pi\)
\(480\) 0 0
\(481\) −5.60601 −0.255612
\(482\) 0 0
\(483\) 7.21201 0.328158
\(484\) 0 0
\(485\) 9.21201 0.418296
\(486\) 0 0
\(487\) −40.0967 −1.81695 −0.908476 0.417936i \(-0.862754\pi\)
−0.908476 + 0.417936i \(0.862754\pi\)
\(488\) 0 0
\(489\) −13.5026 −0.610607
\(490\) 0 0
\(491\) 8.34876 0.376774 0.188387 0.982095i \(-0.439674\pi\)
0.188387 + 0.982095i \(0.439674\pi\)
\(492\) 0 0
\(493\) −17.6556 −0.795167
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2.86325 0.128435
\(498\) 0 0
\(499\) 9.87704 0.442157 0.221079 0.975256i \(-0.429042\pi\)
0.221079 + 0.975256i \(0.429042\pi\)
\(500\) 0 0
\(501\) −26.7214 −1.19382
\(502\) 0 0
\(503\) 30.0753 1.34099 0.670495 0.741914i \(-0.266082\pi\)
0.670495 + 0.741914i \(0.266082\pi\)
\(504\) 0 0
\(505\) 3.03763 0.135173
\(506\) 0 0
\(507\) −1.43163 −0.0635808
\(508\) 0 0
\(509\) 30.1248 1.33526 0.667630 0.744494i \(-0.267309\pi\)
0.667630 + 0.744494i \(0.267309\pi\)
\(510\) 0 0
\(511\) −8.76414 −0.387703
\(512\) 0 0
\(513\) −33.6531 −1.48582
\(514\) 0 0
\(515\) −8.12482 −0.358022
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 36.3745 1.59666
\(520\) 0 0
\(521\) −43.1882 −1.89211 −0.946054 0.324009i \(-0.894969\pi\)
−0.946054 + 0.324009i \(0.894969\pi\)
\(522\) 0 0
\(523\) −9.52828 −0.416643 −0.208321 0.978060i \(-0.566800\pi\)
−0.208321 + 0.978060i \(0.566800\pi\)
\(524\) 0 0
\(525\) −1.43163 −0.0624813
\(526\) 0 0
\(527\) −10.1462 −0.441976
\(528\) 0 0
\(529\) 2.37775 0.103380
\(530\) 0 0
\(531\) 0.280268 0.0121626
\(532\) 0 0
\(533\) 3.95044 0.171113
\(534\) 0 0
\(535\) 2.17438 0.0940066
\(536\) 0 0
\(537\) −8.66071 −0.373737
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −15.8256 −0.680397 −0.340198 0.940354i \(-0.610494\pi\)
−0.340198 + 0.940354i \(0.610494\pi\)
\(542\) 0 0
\(543\) −18.9147 −0.811706
\(544\) 0 0
\(545\) 16.0753 0.688589
\(546\) 0 0
\(547\) −2.76414 −0.118186 −0.0590931 0.998252i \(-0.518821\pi\)
−0.0590931 + 0.998252i \(0.518821\pi\)
\(548\) 0 0
\(549\) 9.50444 0.405640
\(550\) 0 0
\(551\) −26.5941 −1.13295
\(552\) 0 0
\(553\) 5.95044 0.253039
\(554\) 0 0
\(555\) 8.02571 0.340672
\(556\) 0 0
\(557\) 23.7522 1.00641 0.503207 0.864166i \(-0.332153\pi\)
0.503207 + 0.864166i \(0.332153\pi\)
\(558\) 0 0
\(559\) 1.13675 0.0480792
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −31.4787 −1.32667 −0.663335 0.748322i \(-0.730860\pi\)
−0.663335 + 0.748322i \(0.730860\pi\)
\(564\) 0 0
\(565\) −17.2120 −0.724115
\(566\) 0 0
\(567\) −5.24533 −0.220283
\(568\) 0 0
\(569\) −20.2710 −0.849806 −0.424903 0.905239i \(-0.639692\pi\)
−0.424903 + 0.905239i \(0.639692\pi\)
\(570\) 0 0
\(571\) −17.4316 −0.729491 −0.364745 0.931107i \(-0.618844\pi\)
−0.364745 + 0.931107i \(0.618844\pi\)
\(572\) 0 0
\(573\) −19.2291 −0.803306
\(574\) 0 0
\(575\) −5.03763 −0.210084
\(576\) 0 0
\(577\) −25.4617 −1.05998 −0.529991 0.848003i \(-0.677805\pi\)
−0.529991 + 0.848003i \(0.677805\pi\)
\(578\) 0 0
\(579\) −5.93935 −0.246831
\(580\) 0 0
\(581\) 5.03763 0.208996
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −0.950444 −0.0392960
\(586\) 0 0
\(587\) 23.7027 0.978314 0.489157 0.872196i \(-0.337305\pi\)
0.489157 + 0.872196i \(0.337305\pi\)
\(588\) 0 0
\(589\) −15.2830 −0.629723
\(590\) 0 0
\(591\) −39.9743 −1.64432
\(592\) 0 0
\(593\) 33.1129 1.35978 0.679892 0.733312i \(-0.262027\pi\)
0.679892 + 0.733312i \(0.262027\pi\)
\(594\) 0 0
\(595\) 3.95044 0.161952
\(596\) 0 0
\(597\) −21.7779 −0.891311
\(598\) 0 0
\(599\) 26.0753 1.06541 0.532703 0.846302i \(-0.321176\pi\)
0.532703 + 0.846302i \(0.321176\pi\)
\(600\) 0 0
\(601\) 0.316271 0.0129010 0.00645048 0.999979i \(-0.497947\pi\)
0.00645048 + 0.999979i \(0.497947\pi\)
\(602\) 0 0
\(603\) 7.72219 0.314472
\(604\) 0 0
\(605\) 11.0000 0.447214
\(606\) 0 0
\(607\) −17.4316 −0.707528 −0.353764 0.935335i \(-0.615098\pi\)
−0.353764 + 0.935335i \(0.615098\pi\)
\(608\) 0 0
\(609\) −6.39831 −0.259273
\(610\) 0 0
\(611\) −9.03763 −0.365624
\(612\) 0 0
\(613\) −2.34876 −0.0948655 −0.0474327 0.998874i \(-0.515104\pi\)
−0.0474327 + 0.998874i \(0.515104\pi\)
\(614\) 0 0
\(615\) −5.65556 −0.228054
\(616\) 0 0
\(617\) 47.8513 1.92642 0.963211 0.268746i \(-0.0866093\pi\)
0.963211 + 0.268746i \(0.0866093\pi\)
\(618\) 0 0
\(619\) −14.2196 −0.571535 −0.285767 0.958299i \(-0.592248\pi\)
−0.285767 + 0.958299i \(0.592248\pi\)
\(620\) 0 0
\(621\) −28.4907 −1.14329
\(622\) 0 0
\(623\) 2.74275 0.109886
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −22.1462 −0.883027
\(630\) 0 0
\(631\) 27.7027 1.10283 0.551413 0.834233i \(-0.314089\pi\)
0.551413 + 0.834233i \(0.314089\pi\)
\(632\) 0 0
\(633\) 3.43349 0.136469
\(634\) 0 0
\(635\) −18.7641 −0.744632
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −2.72136 −0.107655
\(640\) 0 0
\(641\) 9.05902 0.357810 0.178905 0.983866i \(-0.442745\pi\)
0.178905 + 0.983866i \(0.442745\pi\)
\(642\) 0 0
\(643\) 41.3864 1.63212 0.816060 0.577967i \(-0.196154\pi\)
0.816060 + 0.577967i \(0.196154\pi\)
\(644\) 0 0
\(645\) −1.62740 −0.0640787
\(646\) 0 0
\(647\) 6.56837 0.258229 0.129115 0.991630i \(-0.458786\pi\)
0.129115 + 0.991630i \(0.458786\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −3.67695 −0.144111
\(652\) 0 0
\(653\) −3.27864 −0.128303 −0.0641515 0.997940i \(-0.520434\pi\)
−0.0641515 + 0.997940i \(0.520434\pi\)
\(654\) 0 0
\(655\) −10.7641 −0.420590
\(656\) 0 0
\(657\) 8.32982 0.324977
\(658\) 0 0
\(659\) −26.0019 −1.01289 −0.506444 0.862273i \(-0.669040\pi\)
−0.506444 + 0.862273i \(0.669040\pi\)
\(660\) 0 0
\(661\) −44.0019 −1.71147 −0.855737 0.517411i \(-0.826896\pi\)
−0.855737 + 0.517411i \(0.826896\pi\)
\(662\) 0 0
\(663\) −5.65556 −0.219644
\(664\) 0 0
\(665\) 5.95044 0.230748
\(666\) 0 0
\(667\) −22.5145 −0.871765
\(668\) 0 0
\(669\) −2.61361 −0.101048
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 6.49065 0.250196 0.125098 0.992144i \(-0.460075\pi\)
0.125098 + 0.992144i \(0.460075\pi\)
\(674\) 0 0
\(675\) 5.65556 0.217683
\(676\) 0 0
\(677\) −2.34876 −0.0902701 −0.0451351 0.998981i \(-0.514372\pi\)
−0.0451351 + 0.998981i \(0.514372\pi\)
\(678\) 0 0
\(679\) −9.21201 −0.353525
\(680\) 0 0
\(681\) −4.24100 −0.162516
\(682\) 0 0
\(683\) 22.2992 0.853255 0.426628 0.904427i \(-0.359701\pi\)
0.426628 + 0.904427i \(0.359701\pi\)
\(684\) 0 0
\(685\) −20.4693 −0.782090
\(686\) 0 0
\(687\) 17.1086 0.652733
\(688\) 0 0
\(689\) −2.00000 −0.0761939
\(690\) 0 0
\(691\) −3.15814 −0.120141 −0.0600706 0.998194i \(-0.519133\pi\)
−0.0600706 + 0.998194i \(0.519133\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −7.90089 −0.299698
\(696\) 0 0
\(697\) 15.6060 0.591120
\(698\) 0 0
\(699\) 21.5283 0.814274
\(700\) 0 0
\(701\) 18.3230 0.692052 0.346026 0.938225i \(-0.387531\pi\)
0.346026 + 0.938225i \(0.387531\pi\)
\(702\) 0 0
\(703\) −33.3582 −1.25813
\(704\) 0 0
\(705\) 12.9385 0.487293
\(706\) 0 0
\(707\) −3.03763 −0.114242
\(708\) 0 0
\(709\) 30.4907 1.14510 0.572550 0.819870i \(-0.305954\pi\)
0.572550 + 0.819870i \(0.305954\pi\)
\(710\) 0 0
\(711\) −5.65556 −0.212100
\(712\) 0 0
\(713\) −12.9385 −0.484551
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −12.9385 −0.483198
\(718\) 0 0
\(719\) −37.0804 −1.38287 −0.691433 0.722441i \(-0.743020\pi\)
−0.691433 + 0.722441i \(0.743020\pi\)
\(720\) 0 0
\(721\) 8.12482 0.302584
\(722\) 0 0
\(723\) −34.0043 −1.26463
\(724\) 0 0
\(725\) 4.46926 0.165984
\(726\) 0 0
\(727\) 1.62985 0.0604479 0.0302239 0.999543i \(-0.490378\pi\)
0.0302239 + 0.999543i \(0.490378\pi\)
\(728\) 0 0
\(729\) 29.2754 1.08427
\(730\) 0 0
\(731\) 4.49065 0.166093
\(732\) 0 0
\(733\) 43.8770 1.62064 0.810318 0.585991i \(-0.199295\pi\)
0.810318 + 0.585991i \(0.199295\pi\)
\(734\) 0 0
\(735\) 1.43163 0.0528064
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 22.1744 0.815698 0.407849 0.913049i \(-0.366279\pi\)
0.407849 + 0.913049i \(0.366279\pi\)
\(740\) 0 0
\(741\) −8.51882 −0.312947
\(742\) 0 0
\(743\) −26.5488 −0.973983 −0.486991 0.873407i \(-0.661906\pi\)
−0.486991 + 0.873407i \(0.661906\pi\)
\(744\) 0 0
\(745\) −2.00000 −0.0732743
\(746\) 0 0
\(747\) −4.78799 −0.175183
\(748\) 0 0
\(749\) −2.17438 −0.0794501
\(750\) 0 0
\(751\) 10.1719 0.371179 0.185589 0.982627i \(-0.440581\pi\)
0.185589 + 0.982627i \(0.440581\pi\)
\(752\) 0 0
\(753\) 20.9949 0.765095
\(754\) 0 0
\(755\) −20.9385 −0.762031
\(756\) 0 0
\(757\) 20.0753 0.729648 0.364824 0.931077i \(-0.381129\pi\)
0.364824 + 0.931077i \(0.381129\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 7.57352 0.274540 0.137270 0.990534i \(-0.456167\pi\)
0.137270 + 0.990534i \(0.456167\pi\)
\(762\) 0 0
\(763\) −16.0753 −0.581964
\(764\) 0 0
\(765\) −3.75467 −0.135751
\(766\) 0 0
\(767\) 0.294881 0.0106475
\(768\) 0 0
\(769\) 19.1795 0.691631 0.345816 0.938302i \(-0.387602\pi\)
0.345816 + 0.938302i \(0.387602\pi\)
\(770\) 0 0
\(771\) −30.7127 −1.10609
\(772\) 0 0
\(773\) −6.89574 −0.248023 −0.124011 0.992281i \(-0.539576\pi\)
−0.124011 + 0.992281i \(0.539576\pi\)
\(774\) 0 0
\(775\) 2.56837 0.0922587
\(776\) 0 0
\(777\) −8.02571 −0.287921
\(778\) 0 0
\(779\) 23.5069 0.842222
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 25.2762 0.903297
\(784\) 0 0
\(785\) −3.33251 −0.118943
\(786\) 0 0
\(787\) −16.5470 −0.589836 −0.294918 0.955523i \(-0.595292\pi\)
−0.294918 + 0.955523i \(0.595292\pi\)
\(788\) 0 0
\(789\) −30.1180 −1.07223
\(790\) 0 0
\(791\) 17.2120 0.611989
\(792\) 0 0
\(793\) 10.0000 0.355110
\(794\) 0 0
\(795\) 2.86325 0.101549
\(796\) 0 0
\(797\) −30.5445 −1.08194 −0.540971 0.841041i \(-0.681943\pi\)
−0.540971 + 0.841041i \(0.681943\pi\)
\(798\) 0 0
\(799\) −35.7027 −1.26307
\(800\) 0 0
\(801\) −2.60683 −0.0921079
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 5.03763 0.177553
\(806\) 0 0
\(807\) 7.60355 0.267658
\(808\) 0 0
\(809\) −8.49743 −0.298754 −0.149377 0.988780i \(-0.547727\pi\)
−0.149377 + 0.988780i \(0.547727\pi\)
\(810\) 0 0
\(811\) −46.2258 −1.62321 −0.811604 0.584208i \(-0.801405\pi\)
−0.811604 + 0.584208i \(0.801405\pi\)
\(812\) 0 0
\(813\) 25.8770 0.907547
\(814\) 0 0
\(815\) −9.43163 −0.330375
\(816\) 0 0
\(817\) 6.76414 0.236647
\(818\) 0 0
\(819\) 0.950444 0.0332112
\(820\) 0 0
\(821\) −41.7027 −1.45543 −0.727716 0.685878i \(-0.759418\pi\)
−0.727716 + 0.685878i \(0.759418\pi\)
\(822\) 0 0
\(823\) 16.5470 0.576792 0.288396 0.957511i \(-0.406878\pi\)
0.288396 + 0.957511i \(0.406878\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −2.62225 −0.0911846 −0.0455923 0.998960i \(-0.514518\pi\)
−0.0455923 + 0.998960i \(0.514518\pi\)
\(828\) 0 0
\(829\) −17.6599 −0.613353 −0.306677 0.951814i \(-0.599217\pi\)
−0.306677 + 0.951814i \(0.599217\pi\)
\(830\) 0 0
\(831\) 13.3301 0.462415
\(832\) 0 0
\(833\) −3.95044 −0.136875
\(834\) 0 0
\(835\) −18.6650 −0.645930
\(836\) 0 0
\(837\) 14.5256 0.502078
\(838\) 0 0
\(839\) −5.92473 −0.204545 −0.102272 0.994756i \(-0.532611\pi\)
−0.102272 + 0.994756i \(0.532611\pi\)
\(840\) 0 0
\(841\) −9.02571 −0.311231
\(842\) 0 0
\(843\) 43.0224 1.48177
\(844\) 0 0
\(845\) −1.00000 −0.0344010
\(846\) 0 0
\(847\) −11.0000 −0.377964
\(848\) 0 0
\(849\) 26.3395 0.903970
\(850\) 0 0
\(851\) −28.2410 −0.968089
\(852\) 0 0
\(853\) −44.7641 −1.53270 −0.766348 0.642426i \(-0.777928\pi\)
−0.766348 + 0.642426i \(0.777928\pi\)
\(854\) 0 0
\(855\) −5.65556 −0.193416
\(856\) 0 0
\(857\) 28.2283 0.964259 0.482129 0.876100i \(-0.339863\pi\)
0.482129 + 0.876100i \(0.339863\pi\)
\(858\) 0 0
\(859\) −9.97615 −0.340382 −0.170191 0.985411i \(-0.554438\pi\)
−0.170191 + 0.985411i \(0.554438\pi\)
\(860\) 0 0
\(861\) 5.65556 0.192741
\(862\) 0 0
\(863\) 8.47358 0.288444 0.144222 0.989545i \(-0.453932\pi\)
0.144222 + 0.989545i \(0.453932\pi\)
\(864\) 0 0
\(865\) 25.4078 0.863890
\(866\) 0 0
\(867\) 1.99568 0.0677768
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 8.12482 0.275299
\(872\) 0 0
\(873\) 8.75550 0.296329
\(874\) 0 0
\(875\) −1.00000 −0.0338062
\(876\) 0 0
\(877\) −43.5540 −1.47071 −0.735357 0.677680i \(-0.762985\pi\)
−0.735357 + 0.677680i \(0.762985\pi\)
\(878\) 0 0
\(879\) 17.4292 0.587871
\(880\) 0 0
\(881\) −51.6360 −1.73966 −0.869831 0.493350i \(-0.835772\pi\)
−0.869831 + 0.493350i \(0.835772\pi\)
\(882\) 0 0
\(883\) −13.8770 −0.467000 −0.233500 0.972357i \(-0.575018\pi\)
−0.233500 + 0.972357i \(0.575018\pi\)
\(884\) 0 0
\(885\) −0.422160 −0.0141908
\(886\) 0 0
\(887\) −43.5069 −1.46082 −0.730409 0.683010i \(-0.760671\pi\)
−0.730409 + 0.683010i \(0.760671\pi\)
\(888\) 0 0
\(889\) 18.7641 0.629329
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −53.7779 −1.79961
\(894\) 0 0
\(895\) −6.04956 −0.202214
\(896\) 0 0
\(897\) −7.21201 −0.240802
\(898\) 0 0
\(899\) 11.4787 0.382837
\(900\) 0 0
\(901\) −7.90089 −0.263217
\(902\) 0 0
\(903\) 1.62740 0.0541564
\(904\) 0 0
\(905\) −13.2120 −0.439182
\(906\) 0 0
\(907\) 49.5283 1.64456 0.822280 0.569083i \(-0.192702\pi\)
0.822280 + 0.569083i \(0.192702\pi\)
\(908\) 0 0
\(909\) 2.88710 0.0957591
\(910\) 0 0
\(911\) 59.7284 1.97889 0.989445 0.144911i \(-0.0462897\pi\)
0.989445 + 0.144911i \(0.0462897\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) −14.3163 −0.473281
\(916\) 0 0
\(917\) 10.7641 0.355463
\(918\) 0 0
\(919\) −0.493106 −0.0162661 −0.00813303 0.999967i \(-0.502589\pi\)
−0.00813303 + 0.999967i \(0.502589\pi\)
\(920\) 0 0
\(921\) −4.24100 −0.139746
\(922\) 0 0
\(923\) −2.86325 −0.0942452
\(924\) 0 0
\(925\) 5.60601 0.184324
\(926\) 0 0
\(927\) −7.72219 −0.253630
\(928\) 0 0
\(929\) 8.27104 0.271364 0.135682 0.990752i \(-0.456677\pi\)
0.135682 + 0.990752i \(0.456677\pi\)
\(930\) 0 0
\(931\) −5.95044 −0.195018
\(932\) 0 0
\(933\) 0.641184 0.0209914
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −12.1487 −0.396880 −0.198440 0.980113i \(-0.563587\pi\)
−0.198440 + 0.980113i \(0.563587\pi\)
\(938\) 0 0
\(939\) −42.1010 −1.37391
\(940\) 0 0
\(941\) 26.4736 0.863014 0.431507 0.902110i \(-0.357982\pi\)
0.431507 + 0.902110i \(0.357982\pi\)
\(942\) 0 0
\(943\) 19.9009 0.648062
\(944\) 0 0
\(945\) −5.65556 −0.183975
\(946\) 0 0
\(947\) 18.2001 0.591423 0.295712 0.955277i \(-0.404443\pi\)
0.295712 + 0.955277i \(0.404443\pi\)
\(948\) 0 0
\(949\) 8.76414 0.284496
\(950\) 0 0
\(951\) −14.0325 −0.455035
\(952\) 0 0
\(953\) 6.20687 0.201060 0.100530 0.994934i \(-0.467946\pi\)
0.100530 + 0.994934i \(0.467946\pi\)
\(954\) 0 0
\(955\) −13.4316 −0.434637
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 20.4693 0.660987
\(960\) 0 0
\(961\) −24.4035 −0.787208
\(962\) 0 0
\(963\) 2.06663 0.0665961
\(964\) 0 0
\(965\) −4.14867 −0.133550
\(966\) 0 0
\(967\) 10.7666 0.346230 0.173115 0.984902i \(-0.444617\pi\)
0.173115 + 0.984902i \(0.444617\pi\)
\(968\) 0 0
\(969\) −33.6531 −1.08109
\(970\) 0 0
\(971\) 33.5283 1.07597 0.537987 0.842953i \(-0.319185\pi\)
0.537987 + 0.842953i \(0.319185\pi\)
\(972\) 0 0
\(973\) 7.90089 0.253291
\(974\) 0 0
\(975\) 1.43163 0.0458488
\(976\) 0 0
\(977\) 57.2805 1.83257 0.916283 0.400532i \(-0.131175\pi\)
0.916283 + 0.400532i \(0.131175\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 15.2786 0.487809
\(982\) 0 0
\(983\) −46.7641 −1.49154 −0.745772 0.666201i \(-0.767919\pi\)
−0.745772 + 0.666201i \(0.767919\pi\)
\(984\) 0 0
\(985\) −27.9223 −0.889678
\(986\) 0 0
\(987\) −12.9385 −0.411838
\(988\) 0 0
\(989\) 5.72651 0.182092
\(990\) 0 0
\(991\) 23.3282 0.741045 0.370522 0.928824i \(-0.379179\pi\)
0.370522 + 0.928824i \(0.379179\pi\)
\(992\) 0 0
\(993\) 25.8770 0.821183
\(994\) 0 0
\(995\) −15.2120 −0.482253
\(996\) 0 0
\(997\) −15.7999 −0.500388 −0.250194 0.968196i \(-0.580494\pi\)
−0.250194 + 0.968196i \(0.580494\pi\)
\(998\) 0 0
\(999\) 31.7051 1.00311
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 3640.2.a.p.1.2 3
4.3 odd 2 7280.2.a.bn.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3640.2.a.p.1.2 3 1.1 even 1 trivial
7280.2.a.bn.1.2 3 4.3 odd 2