Properties

Label 7800.2.a.bs.1.1
Level $7800$
Weight $2$
Character 7800.1
Self dual yes
Analytic conductor $62.283$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7800.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(62.2833135766\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.3732.1
Defining polynomial: \(x^{3} - x^{2} - 13 x + 19\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(1.56943\) of defining polynomial
Character \(\chi\) \(=\) 7800.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} -4.96747 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -4.96747 q^{7} +1.00000 q^{9} +0.430572 q^{11} -1.00000 q^{13} +3.00000 q^{17} +3.39804 q^{19} -4.96747 q^{21} -5.39804 q^{23} +1.00000 q^{27} -4.13886 q^{29} +0.430572 q^{31} +0.430572 q^{33} -8.53690 q^{37} -1.00000 q^{39} -6.53690 q^{41} -6.53690 q^{43} +12.1063 q^{47} +17.6758 q^{49} +3.00000 q^{51} -4.39804 q^{53} +3.39804 q^{57} +12.1063 q^{59} +6.13886 q^{61} -4.96747 q^{63} +9.56943 q^{67} -5.39804 q^{69} +9.67575 q^{71} +9.67575 q^{73} -2.13886 q^{77} +10.5369 q^{79} +1.00000 q^{81} -7.82861 q^{83} -4.13886 q^{87} +2.86114 q^{89} +4.96747 q^{91} +0.430572 q^{93} -5.93494 q^{97} +0.430572 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 3q^{3} + q^{7} + 3q^{9} + O(q^{10}) \) \( 3q + 3q^{3} + q^{7} + 3q^{9} + 5q^{11} - 3q^{13} + 9q^{17} - 2q^{19} + q^{21} - 4q^{23} + 3q^{27} - 5q^{29} + 5q^{31} + 5q^{33} - 6q^{37} - 3q^{39} + 13q^{47} + 26q^{49} + 9q^{51} - q^{53} - 2q^{57} + 13q^{59} + 11q^{61} + q^{63} + 25q^{67} - 4q^{69} + 2q^{71} + 2q^{73} + q^{77} + 12q^{79} + 3q^{81} - 15q^{83} - 5q^{87} + 16q^{89} - q^{91} + 5q^{93} + 14q^{97} + 5q^{99} + O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −4.96747 −1.87753 −0.938763 0.344562i \(-0.888027\pi\)
−0.938763 + 0.344562i \(0.888027\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0.430572 0.129822 0.0649112 0.997891i \(-0.479324\pi\)
0.0649112 + 0.997891i \(0.479324\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 0 0
\(19\) 3.39804 0.779564 0.389782 0.920907i \(-0.372550\pi\)
0.389782 + 0.920907i \(0.372550\pi\)
\(20\) 0 0
\(21\) −4.96747 −1.08399
\(22\) 0 0
\(23\) −5.39804 −1.12557 −0.562785 0.826603i \(-0.690270\pi\)
−0.562785 + 0.826603i \(0.690270\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −4.13886 −0.768566 −0.384283 0.923215i \(-0.625551\pi\)
−0.384283 + 0.923215i \(0.625551\pi\)
\(30\) 0 0
\(31\) 0.430572 0.0773331 0.0386665 0.999252i \(-0.487689\pi\)
0.0386665 + 0.999252i \(0.487689\pi\)
\(32\) 0 0
\(33\) 0.430572 0.0749530
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −8.53690 −1.40346 −0.701729 0.712444i \(-0.747588\pi\)
−0.701729 + 0.712444i \(0.747588\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) −6.53690 −1.02089 −0.510446 0.859910i \(-0.670520\pi\)
−0.510446 + 0.859910i \(0.670520\pi\)
\(42\) 0 0
\(43\) −6.53690 −0.996867 −0.498434 0.866928i \(-0.666091\pi\)
−0.498434 + 0.866928i \(0.666091\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 12.1063 1.76589 0.882944 0.469477i \(-0.155558\pi\)
0.882944 + 0.469477i \(0.155558\pi\)
\(48\) 0 0
\(49\) 17.6758 2.52511
\(50\) 0 0
\(51\) 3.00000 0.420084
\(52\) 0 0
\(53\) −4.39804 −0.604118 −0.302059 0.953289i \(-0.597674\pi\)
−0.302059 + 0.953289i \(0.597674\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 3.39804 0.450082
\(58\) 0 0
\(59\) 12.1063 1.57611 0.788055 0.615605i \(-0.211088\pi\)
0.788055 + 0.615605i \(0.211088\pi\)
\(60\) 0 0
\(61\) 6.13886 0.786000 0.393000 0.919538i \(-0.371437\pi\)
0.393000 + 0.919538i \(0.371437\pi\)
\(62\) 0 0
\(63\) −4.96747 −0.625842
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 9.56943 1.16909 0.584546 0.811361i \(-0.301273\pi\)
0.584546 + 0.811361i \(0.301273\pi\)
\(68\) 0 0
\(69\) −5.39804 −0.649848
\(70\) 0 0
\(71\) 9.67575 1.14830 0.574150 0.818750i \(-0.305333\pi\)
0.574150 + 0.818750i \(0.305333\pi\)
\(72\) 0 0
\(73\) 9.67575 1.13246 0.566231 0.824247i \(-0.308401\pi\)
0.566231 + 0.824247i \(0.308401\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.13886 −0.243745
\(78\) 0 0
\(79\) 10.5369 1.18549 0.592747 0.805389i \(-0.298043\pi\)
0.592747 + 0.805389i \(0.298043\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −7.82861 −0.859302 −0.429651 0.902995i \(-0.641363\pi\)
−0.429651 + 0.902995i \(0.641363\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −4.13886 −0.443732
\(88\) 0 0
\(89\) 2.86114 0.303281 0.151640 0.988436i \(-0.451544\pi\)
0.151640 + 0.988436i \(0.451544\pi\)
\(90\) 0 0
\(91\) 4.96747 0.520732
\(92\) 0 0
\(93\) 0.430572 0.0446483
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −5.93494 −0.602602 −0.301301 0.953529i \(-0.597421\pi\)
−0.301301 + 0.953529i \(0.597421\pi\)
\(98\) 0 0
\(99\) 0.430572 0.0432742
\(100\) 0 0
\(101\) −16.3330 −1.62519 −0.812596 0.582827i \(-0.801946\pi\)
−0.812596 + 0.582827i \(0.801946\pi\)
\(102\) 0 0
\(103\) −8.53690 −0.841165 −0.420583 0.907254i \(-0.638174\pi\)
−0.420583 + 0.907254i \(0.638174\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 11.6572 1.12695 0.563473 0.826134i \(-0.309465\pi\)
0.563473 + 0.826134i \(0.309465\pi\)
\(108\) 0 0
\(109\) −3.67575 −0.352073 −0.176037 0.984384i \(-0.556328\pi\)
−0.176037 + 0.984384i \(0.556328\pi\)
\(110\) 0 0
\(111\) −8.53690 −0.810286
\(112\) 0 0
\(113\) −3.13886 −0.295279 −0.147639 0.989041i \(-0.547167\pi\)
−0.147639 + 0.989041i \(0.547167\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.00000 −0.0924500
\(118\) 0 0
\(119\) −14.9024 −1.36610
\(120\) 0 0
\(121\) −10.8146 −0.983146
\(122\) 0 0
\(123\) −6.53690 −0.589412
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 19.6758 1.74594 0.872970 0.487773i \(-0.162191\pi\)
0.872970 + 0.487773i \(0.162191\pi\)
\(128\) 0 0
\(129\) −6.53690 −0.575542
\(130\) 0 0
\(131\) 3.39804 0.296888 0.148444 0.988921i \(-0.452573\pi\)
0.148444 + 0.988921i \(0.452573\pi\)
\(132\) 0 0
\(133\) −16.8797 −1.46365
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −5.65723 −0.483330 −0.241665 0.970360i \(-0.577693\pi\)
−0.241665 + 0.970360i \(0.577693\pi\)
\(138\) 0 0
\(139\) 17.8699 1.51570 0.757852 0.652427i \(-0.226249\pi\)
0.757852 + 0.652427i \(0.226249\pi\)
\(140\) 0 0
\(141\) 12.1063 1.01954
\(142\) 0 0
\(143\) −0.430572 −0.0360063
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 17.6758 1.45787
\(148\) 0 0
\(149\) 16.2126 1.32819 0.664096 0.747647i \(-0.268817\pi\)
0.664096 + 0.747647i \(0.268817\pi\)
\(150\) 0 0
\(151\) −5.89368 −0.479621 −0.239810 0.970820i \(-0.577085\pi\)
−0.239810 + 0.970820i \(0.577085\pi\)
\(152\) 0 0
\(153\) 3.00000 0.242536
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −4.39804 −0.351002 −0.175501 0.984479i \(-0.556155\pi\)
−0.175501 + 0.984479i \(0.556155\pi\)
\(158\) 0 0
\(159\) −4.39804 −0.348787
\(160\) 0 0
\(161\) 26.8146 2.11329
\(162\) 0 0
\(163\) 16.4718 1.29017 0.645087 0.764109i \(-0.276821\pi\)
0.645087 + 0.764109i \(0.276821\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 12.5369 0.970134 0.485067 0.874477i \(-0.338795\pi\)
0.485067 + 0.874477i \(0.338795\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 3.39804 0.259855
\(172\) 0 0
\(173\) −7.53690 −0.573020 −0.286510 0.958077i \(-0.592495\pi\)
−0.286510 + 0.958077i \(0.592495\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 12.1063 0.909967
\(178\) 0 0
\(179\) −25.6107 −1.91423 −0.957116 0.289703i \(-0.906443\pi\)
−0.957116 + 0.289703i \(0.906443\pi\)
\(180\) 0 0
\(181\) 9.25919 0.688230 0.344115 0.938928i \(-0.388179\pi\)
0.344115 + 0.938928i \(0.388179\pi\)
\(182\) 0 0
\(183\) 6.13886 0.453797
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 1.29172 0.0944597
\(188\) 0 0
\(189\) −4.96747 −0.361330
\(190\) 0 0
\(191\) 6.00000 0.434145 0.217072 0.976156i \(-0.430349\pi\)
0.217072 + 0.976156i \(0.430349\pi\)
\(192\) 0 0
\(193\) 6.47184 0.465853 0.232926 0.972494i \(-0.425170\pi\)
0.232926 + 0.972494i \(0.425170\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −0.259187 −0.0184663 −0.00923314 0.999957i \(-0.502939\pi\)
−0.00923314 + 0.999957i \(0.502939\pi\)
\(198\) 0 0
\(199\) −8.79608 −0.623538 −0.311769 0.950158i \(-0.600921\pi\)
−0.311769 + 0.950158i \(0.600921\pi\)
\(200\) 0 0
\(201\) 9.56943 0.674975
\(202\) 0 0
\(203\) 20.5596 1.44300
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −5.39804 −0.375190
\(208\) 0 0
\(209\) 1.46310 0.101205
\(210\) 0 0
\(211\) 19.6758 1.35453 0.677267 0.735737i \(-0.263164\pi\)
0.677267 + 0.735737i \(0.263164\pi\)
\(212\) 0 0
\(213\) 9.67575 0.662972
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −2.13886 −0.145195
\(218\) 0 0
\(219\) 9.67575 0.653827
\(220\) 0 0
\(221\) −3.00000 −0.201802
\(222\) 0 0
\(223\) 14.1941 0.950509 0.475254 0.879848i \(-0.342356\pi\)
0.475254 + 0.879848i \(0.342356\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0.495634 0.0328964 0.0164482 0.999865i \(-0.494764\pi\)
0.0164482 + 0.999865i \(0.494764\pi\)
\(228\) 0 0
\(229\) 2.00000 0.132164 0.0660819 0.997814i \(-0.478950\pi\)
0.0660819 + 0.997814i \(0.478950\pi\)
\(230\) 0 0
\(231\) −2.13886 −0.140726
\(232\) 0 0
\(233\) 11.1389 0.729731 0.364865 0.931060i \(-0.381115\pi\)
0.364865 + 0.931060i \(0.381115\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 10.5369 0.684445
\(238\) 0 0
\(239\) −17.9762 −1.16278 −0.581392 0.813624i \(-0.697492\pi\)
−0.581392 + 0.813624i \(0.697492\pi\)
\(240\) 0 0
\(241\) 30.4718 1.96286 0.981432 0.191812i \(-0.0614363\pi\)
0.981432 + 0.191812i \(0.0614363\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −3.39804 −0.216212
\(248\) 0 0
\(249\) −7.82861 −0.496118
\(250\) 0 0
\(251\) 23.3330 1.47276 0.736382 0.676566i \(-0.236532\pi\)
0.736382 + 0.676566i \(0.236532\pi\)
\(252\) 0 0
\(253\) −2.32425 −0.146124
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −22.6758 −1.41447 −0.707237 0.706976i \(-0.750059\pi\)
−0.707237 + 0.706976i \(0.750059\pi\)
\(258\) 0 0
\(259\) 42.4068 2.63503
\(260\) 0 0
\(261\) −4.13886 −0.256189
\(262\) 0 0
\(263\) 4.53690 0.279757 0.139879 0.990169i \(-0.455329\pi\)
0.139879 + 0.990169i \(0.455329\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 2.86114 0.175099
\(268\) 0 0
\(269\) 12.8699 0.784690 0.392345 0.919818i \(-0.371664\pi\)
0.392345 + 0.919818i \(0.371664\pi\)
\(270\) 0 0
\(271\) −8.68976 −0.527865 −0.263933 0.964541i \(-0.585020\pi\)
−0.263933 + 0.964541i \(0.585020\pi\)
\(272\) 0 0
\(273\) 4.96747 0.300645
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 5.93494 0.356596 0.178298 0.983977i \(-0.442941\pi\)
0.178298 + 0.983977i \(0.442941\pi\)
\(278\) 0 0
\(279\) 0.430572 0.0257777
\(280\) 0 0
\(281\) 11.2039 0.668370 0.334185 0.942508i \(-0.391539\pi\)
0.334185 + 0.942508i \(0.391539\pi\)
\(282\) 0 0
\(283\) −7.20392 −0.428228 −0.214114 0.976809i \(-0.568686\pi\)
−0.214114 + 0.976809i \(0.568686\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 32.4718 1.91675
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) −5.93494 −0.347912
\(292\) 0 0
\(293\) 4.27771 0.249907 0.124953 0.992163i \(-0.460122\pi\)
0.124953 + 0.992163i \(0.460122\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0.430572 0.0249843
\(298\) 0 0
\(299\) 5.39804 0.312177
\(300\) 0 0
\(301\) 32.4718 1.87165
\(302\) 0 0
\(303\) −16.3330 −0.938305
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −14.8146 −0.845514 −0.422757 0.906243i \(-0.638938\pi\)
−0.422757 + 0.906243i \(0.638938\pi\)
\(308\) 0 0
\(309\) −8.53690 −0.485647
\(310\) 0 0
\(311\) −17.3515 −0.983914 −0.491957 0.870620i \(-0.663718\pi\)
−0.491957 + 0.870620i \(0.663718\pi\)
\(312\) 0 0
\(313\) −22.3980 −1.26601 −0.633006 0.774147i \(-0.718179\pi\)
−0.633006 + 0.774147i \(0.718179\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 27.2679 1.53152 0.765759 0.643127i \(-0.222363\pi\)
0.765759 + 0.643127i \(0.222363\pi\)
\(318\) 0 0
\(319\) −1.78208 −0.0997771
\(320\) 0 0
\(321\) 11.6572 0.650643
\(322\) 0 0
\(323\) 10.1941 0.567216
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −3.67575 −0.203270
\(328\) 0 0
\(329\) −60.1378 −3.31550
\(330\) 0 0
\(331\) −10.8797 −0.598001 −0.299000 0.954253i \(-0.596653\pi\)
−0.299000 + 0.954253i \(0.596653\pi\)
\(332\) 0 0
\(333\) −8.53690 −0.467819
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 34.2029 1.86315 0.931574 0.363551i \(-0.118436\pi\)
0.931574 + 0.363551i \(0.118436\pi\)
\(338\) 0 0
\(339\) −3.13886 −0.170479
\(340\) 0 0
\(341\) 0.185393 0.0100396
\(342\) 0 0
\(343\) −53.0315 −2.86343
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 28.2777 1.51803 0.759014 0.651075i \(-0.225682\pi\)
0.759014 + 0.651075i \(0.225682\pi\)
\(348\) 0 0
\(349\) 27.3330 1.46310 0.731550 0.681787i \(-0.238797\pi\)
0.731550 + 0.681787i \(0.238797\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) 0 0
\(353\) 3.18539 0.169541 0.0847707 0.996400i \(-0.472984\pi\)
0.0847707 + 0.996400i \(0.472984\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −14.9024 −0.788719
\(358\) 0 0
\(359\) 14.1063 0.744503 0.372252 0.928132i \(-0.378586\pi\)
0.372252 + 0.928132i \(0.378586\pi\)
\(360\) 0 0
\(361\) −7.45331 −0.392280
\(362\) 0 0
\(363\) −10.8146 −0.567620
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 25.5922 1.33590 0.667950 0.744206i \(-0.267172\pi\)
0.667950 + 0.744206i \(0.267172\pi\)
\(368\) 0 0
\(369\) −6.53690 −0.340297
\(370\) 0 0
\(371\) 21.8471 1.13425
\(372\) 0 0
\(373\) 15.4068 0.797733 0.398866 0.917009i \(-0.369404\pi\)
0.398866 + 0.917009i \(0.369404\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.13886 0.213162
\(378\) 0 0
\(379\) 21.7821 1.11887 0.559435 0.828874i \(-0.311018\pi\)
0.559435 + 0.828874i \(0.311018\pi\)
\(380\) 0 0
\(381\) 19.6758 1.00802
\(382\) 0 0
\(383\) 4.47184 0.228500 0.114250 0.993452i \(-0.463553\pi\)
0.114250 + 0.993452i \(0.463553\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −6.53690 −0.332289
\(388\) 0 0
\(389\) 13.4166 0.680247 0.340123 0.940381i \(-0.389531\pi\)
0.340123 + 0.940381i \(0.389531\pi\)
\(390\) 0 0
\(391\) −16.1941 −0.818972
\(392\) 0 0
\(393\) 3.39804 0.171409
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −36.7310 −1.84348 −0.921739 0.387812i \(-0.873231\pi\)
−0.921739 + 0.387812i \(0.873231\pi\)
\(398\) 0 0
\(399\) −16.8797 −0.845040
\(400\) 0 0
\(401\) 27.8514 1.39083 0.695415 0.718608i \(-0.255221\pi\)
0.695415 + 0.718608i \(0.255221\pi\)
\(402\) 0 0
\(403\) −0.430572 −0.0214483
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −3.67575 −0.182200
\(408\) 0 0
\(409\) 25.8514 1.27827 0.639134 0.769096i \(-0.279293\pi\)
0.639134 + 0.769096i \(0.279293\pi\)
\(410\) 0 0
\(411\) −5.65723 −0.279050
\(412\) 0 0
\(413\) −60.1378 −2.95919
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 17.8699 0.875092
\(418\) 0 0
\(419\) 28.5369 1.39412 0.697059 0.717013i \(-0.254491\pi\)
0.697059 + 0.717013i \(0.254491\pi\)
\(420\) 0 0
\(421\) 4.51837 0.220212 0.110106 0.993920i \(-0.464881\pi\)
0.110106 + 0.993920i \(0.464881\pi\)
\(422\) 0 0
\(423\) 12.1063 0.588630
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −30.4946 −1.47574
\(428\) 0 0
\(429\) −0.430572 −0.0207882
\(430\) 0 0
\(431\) 34.1941 1.64707 0.823537 0.567263i \(-0.191998\pi\)
0.823537 + 0.567263i \(0.191998\pi\)
\(432\) 0 0
\(433\) −11.6572 −0.560211 −0.280105 0.959969i \(-0.590369\pi\)
−0.280105 + 0.959969i \(0.590369\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −18.3428 −0.877454
\(438\) 0 0
\(439\) −36.6194 −1.74775 −0.873875 0.486151i \(-0.838401\pi\)
−0.873875 + 0.486151i \(0.838401\pi\)
\(440\) 0 0
\(441\) 17.6758 0.841702
\(442\) 0 0
\(443\) −4.25919 −0.202360 −0.101180 0.994868i \(-0.532262\pi\)
−0.101180 + 0.994868i \(0.532262\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 16.2126 0.766832
\(448\) 0 0
\(449\) 24.9437 1.17716 0.588582 0.808437i \(-0.299686\pi\)
0.588582 + 0.808437i \(0.299686\pi\)
\(450\) 0 0
\(451\) −2.81461 −0.132535
\(452\) 0 0
\(453\) −5.89368 −0.276909
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 7.05527 0.330032 0.165016 0.986291i \(-0.447232\pi\)
0.165016 + 0.986291i \(0.447232\pi\)
\(458\) 0 0
\(459\) 3.00000 0.140028
\(460\) 0 0
\(461\) −5.35150 −0.249244 −0.124622 0.992204i \(-0.539772\pi\)
−0.124622 + 0.992204i \(0.539772\pi\)
\(462\) 0 0
\(463\) −20.0878 −0.933559 −0.466780 0.884374i \(-0.654586\pi\)
−0.466780 + 0.884374i \(0.654586\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −9.00873 −0.416874 −0.208437 0.978036i \(-0.566838\pi\)
−0.208437 + 0.978036i \(0.566838\pi\)
\(468\) 0 0
\(469\) −47.5358 −2.19500
\(470\) 0 0
\(471\) −4.39804 −0.202651
\(472\) 0 0
\(473\) −2.81461 −0.129416
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −4.39804 −0.201373
\(478\) 0 0
\(479\) 19.5044 0.891177 0.445589 0.895238i \(-0.352994\pi\)
0.445589 + 0.895238i \(0.352994\pi\)
\(480\) 0 0
\(481\) 8.53690 0.389249
\(482\) 0 0
\(483\) 26.8146 1.22011
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 14.9860 0.679080 0.339540 0.940592i \(-0.389729\pi\)
0.339540 + 0.940592i \(0.389729\pi\)
\(488\) 0 0
\(489\) 16.4718 0.744882
\(490\) 0 0
\(491\) 22.0000 0.992846 0.496423 0.868081i \(-0.334646\pi\)
0.496423 + 0.868081i \(0.334646\pi\)
\(492\) 0 0
\(493\) −12.4166 −0.559214
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −48.0640 −2.15597
\(498\) 0 0
\(499\) −12.5596 −0.562247 −0.281123 0.959672i \(-0.590707\pi\)
−0.281123 + 0.959672i \(0.590707\pi\)
\(500\) 0 0
\(501\) 12.5369 0.560107
\(502\) 0 0
\(503\) 29.6758 1.32318 0.661588 0.749867i \(-0.269883\pi\)
0.661588 + 0.749867i \(0.269883\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.00000 0.0444116
\(508\) 0 0
\(509\) 30.3417 1.34487 0.672436 0.740155i \(-0.265248\pi\)
0.672436 + 0.740155i \(0.265248\pi\)
\(510\) 0 0
\(511\) −48.0640 −2.12623
\(512\) 0 0
\(513\) 3.39804 0.150027
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 5.21265 0.229252
\(518\) 0 0
\(519\) −7.53690 −0.330833
\(520\) 0 0
\(521\) −7.72229 −0.338320 −0.169160 0.985589i \(-0.554105\pi\)
−0.169160 + 0.985589i \(0.554105\pi\)
\(522\) 0 0
\(523\) −27.6572 −1.20937 −0.604683 0.796466i \(-0.706700\pi\)
−0.604683 + 0.796466i \(0.706700\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.29172 0.0562681
\(528\) 0 0
\(529\) 6.13886 0.266907
\(530\) 0 0
\(531\) 12.1063 0.525370
\(532\) 0 0
\(533\) 6.53690 0.283144
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −25.6107 −1.10518
\(538\) 0 0
\(539\) 7.61069 0.327816
\(540\) 0 0
\(541\) −13.6758 −0.587967 −0.293983 0.955811i \(-0.594981\pi\)
−0.293983 + 0.955811i \(0.594981\pi\)
\(542\) 0 0
\(543\) 9.25919 0.397350
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −14.1291 −0.604115 −0.302058 0.953290i \(-0.597673\pi\)
−0.302058 + 0.953290i \(0.597673\pi\)
\(548\) 0 0
\(549\) 6.13886 0.262000
\(550\) 0 0
\(551\) −14.0640 −0.599147
\(552\) 0 0
\(553\) −52.3417 −2.22580
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 10.4718 0.443706 0.221853 0.975080i \(-0.428790\pi\)
0.221853 + 0.975080i \(0.428790\pi\)
\(558\) 0 0
\(559\) 6.53690 0.276481
\(560\) 0 0
\(561\) 1.29172 0.0545363
\(562\) 0 0
\(563\) −5.95346 −0.250909 −0.125454 0.992099i \(-0.540039\pi\)
−0.125454 + 0.992099i \(0.540039\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −4.96747 −0.208614
\(568\) 0 0
\(569\) −22.4631 −0.941702 −0.470851 0.882213i \(-0.656053\pi\)
−0.470851 + 0.882213i \(0.656053\pi\)
\(570\) 0 0
\(571\) −33.2679 −1.39222 −0.696110 0.717936i \(-0.745087\pi\)
−0.696110 + 0.717936i \(0.745087\pi\)
\(572\) 0 0
\(573\) 6.00000 0.250654
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 14.4904 0.603242 0.301621 0.953428i \(-0.402472\pi\)
0.301621 + 0.953428i \(0.402472\pi\)
\(578\) 0 0
\(579\) 6.47184 0.268960
\(580\) 0 0
\(581\) 38.8884 1.61336
\(582\) 0 0
\(583\) −1.89368 −0.0784280
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −19.3742 −0.799661 −0.399830 0.916589i \(-0.630931\pi\)
−0.399830 + 0.916589i \(0.630931\pi\)
\(588\) 0 0
\(589\) 1.46310 0.0602861
\(590\) 0 0
\(591\) −0.259187 −0.0106615
\(592\) 0 0
\(593\) −26.9437 −1.10644 −0.553222 0.833034i \(-0.686602\pi\)
−0.553222 + 0.833034i \(0.686602\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −8.79608 −0.360000
\(598\) 0 0
\(599\) 3.91641 0.160020 0.0800102 0.996794i \(-0.474505\pi\)
0.0800102 + 0.996794i \(0.474505\pi\)
\(600\) 0 0
\(601\) 9.87967 0.403000 0.201500 0.979489i \(-0.435418\pi\)
0.201500 + 0.979489i \(0.435418\pi\)
\(602\) 0 0
\(603\) 9.56943 0.389697
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −27.0087 −1.09625 −0.548125 0.836396i \(-0.684658\pi\)
−0.548125 + 0.836396i \(0.684658\pi\)
\(608\) 0 0
\(609\) 20.5596 0.833119
\(610\) 0 0
\(611\) −12.1063 −0.489769
\(612\) 0 0
\(613\) −16.2777 −0.657451 −0.328725 0.944426i \(-0.606619\pi\)
−0.328725 + 0.944426i \(0.606619\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 4.99127 0.200941 0.100470 0.994940i \(-0.467965\pi\)
0.100470 + 0.994940i \(0.467965\pi\)
\(618\) 0 0
\(619\) −27.8884 −1.12093 −0.560465 0.828178i \(-0.689377\pi\)
−0.560465 + 0.828178i \(0.689377\pi\)
\(620\) 0 0
\(621\) −5.39804 −0.216616
\(622\) 0 0
\(623\) −14.2126 −0.569418
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 1.46310 0.0584307
\(628\) 0 0
\(629\) −25.6107 −1.02117
\(630\) 0 0
\(631\) −4.66702 −0.185791 −0.0928956 0.995676i \(-0.529612\pi\)
−0.0928956 + 0.995676i \(0.529612\pi\)
\(632\) 0 0
\(633\) 19.6758 0.782041
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −17.6758 −0.700339
\(638\) 0 0
\(639\) 9.67575 0.382767
\(640\) 0 0
\(641\) −21.1476 −0.835280 −0.417640 0.908613i \(-0.637143\pi\)
−0.417640 + 0.908613i \(0.637143\pi\)
\(642\) 0 0
\(643\) −34.7495 −1.37039 −0.685194 0.728360i \(-0.740283\pi\)
−0.685194 + 0.728360i \(0.740283\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 4.45331 0.175078 0.0875389 0.996161i \(-0.472100\pi\)
0.0875389 + 0.996161i \(0.472100\pi\)
\(648\) 0 0
\(649\) 5.21265 0.204614
\(650\) 0 0
\(651\) −2.13886 −0.0838283
\(652\) 0 0
\(653\) −9.00000 −0.352197 −0.176099 0.984373i \(-0.556348\pi\)
−0.176099 + 0.984373i \(0.556348\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 9.67575 0.377487
\(658\) 0 0
\(659\) 35.4806 1.38213 0.691063 0.722794i \(-0.257143\pi\)
0.691063 + 0.722794i \(0.257143\pi\)
\(660\) 0 0
\(661\) −1.33298 −0.0518469 −0.0259235 0.999664i \(-0.508253\pi\)
−0.0259235 + 0.999664i \(0.508253\pi\)
\(662\) 0 0
\(663\) −3.00000 −0.116510
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 22.3417 0.865075
\(668\) 0 0
\(669\) 14.1941 0.548777
\(670\) 0 0
\(671\) 2.64322 0.102040
\(672\) 0 0
\(673\) −31.6845 −1.22135 −0.610674 0.791882i \(-0.709101\pi\)
−0.610674 + 0.791882i \(0.709101\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −23.2039 −0.891799 −0.445899 0.895083i \(-0.647116\pi\)
−0.445899 + 0.895083i \(0.647116\pi\)
\(678\) 0 0
\(679\) 29.4816 1.13140
\(680\) 0 0
\(681\) 0.495634 0.0189927
\(682\) 0 0
\(683\) 13.0965 0.501125 0.250562 0.968100i \(-0.419384\pi\)
0.250562 + 0.968100i \(0.419384\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 2.00000 0.0763048
\(688\) 0 0
\(689\) 4.39804 0.167552
\(690\) 0 0
\(691\) −38.2539 −1.45525 −0.727624 0.685976i \(-0.759375\pi\)
−0.727624 + 0.685976i \(0.759375\pi\)
\(692\) 0 0
\(693\) −2.13886 −0.0812484
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −19.6107 −0.742808
\(698\) 0 0
\(699\) 11.1389 0.421310
\(700\) 0 0
\(701\) 34.1563 1.29007 0.645033 0.764155i \(-0.276844\pi\)
0.645033 + 0.764155i \(0.276844\pi\)
\(702\) 0 0
\(703\) −29.0087 −1.09409
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 81.1336 3.05134
\(708\) 0 0
\(709\) 21.3330 0.801177 0.400588 0.916258i \(-0.368806\pi\)
0.400588 + 0.916258i \(0.368806\pi\)
\(710\) 0 0
\(711\) 10.5369 0.395165
\(712\) 0 0
\(713\) −2.32425 −0.0870438
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −17.9762 −0.671334
\(718\) 0 0
\(719\) 0.0185238 0.000690822 0 0.000345411 1.00000i \(-0.499890\pi\)
0.000345411 1.00000i \(0.499890\pi\)
\(720\) 0 0
\(721\) 42.4068 1.57931
\(722\) 0 0
\(723\) 30.4718 1.13326
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −12.6670 −0.469794 −0.234897 0.972020i \(-0.575475\pi\)
−0.234897 + 0.972020i \(0.575475\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −19.6107 −0.725328
\(732\) 0 0
\(733\) −8.51837 −0.314633 −0.157317 0.987548i \(-0.550284\pi\)
−0.157317 + 0.987548i \(0.550284\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.12033 0.151774
\(738\) 0 0
\(739\) 11.9122 0.438197 0.219099 0.975703i \(-0.429688\pi\)
0.219099 + 0.975703i \(0.429688\pi\)
\(740\) 0 0
\(741\) −3.39804 −0.124830
\(742\) 0 0
\(743\) 21.3568 0.783504 0.391752 0.920071i \(-0.371869\pi\)
0.391752 + 0.920071i \(0.371869\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −7.82861 −0.286434
\(748\) 0 0
\(749\) −57.9069 −2.11587
\(750\) 0 0
\(751\) 18.9902 0.692963 0.346481 0.938057i \(-0.387376\pi\)
0.346481 + 0.938057i \(0.387376\pi\)
\(752\) 0 0
\(753\) 23.3330 0.850301
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −2.72229 −0.0989433 −0.0494716 0.998776i \(-0.515754\pi\)
−0.0494716 + 0.998776i \(0.515754\pi\)
\(758\) 0 0
\(759\) −2.32425 −0.0843649
\(760\) 0 0
\(761\) 3.52816 0.127896 0.0639479 0.997953i \(-0.479631\pi\)
0.0639479 + 0.997953i \(0.479631\pi\)
\(762\) 0 0
\(763\) 18.2592 0.661027
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −12.1063 −0.437134
\(768\) 0 0
\(769\) −20.0651 −0.723565 −0.361782 0.932263i \(-0.617832\pi\)
−0.361782 + 0.932263i \(0.617832\pi\)
\(770\) 0 0
\(771\) −22.6758 −0.816647
\(772\) 0 0
\(773\) 29.8048 1.07200 0.536002 0.844216i \(-0.319934\pi\)
0.536002 + 0.844216i \(0.319934\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 42.4068 1.52133
\(778\) 0 0
\(779\) −22.2126 −0.795851
\(780\) 0 0
\(781\) 4.16611 0.149075
\(782\) 0 0
\(783\) −4.13886 −0.147911
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 13.8471 0.493597 0.246799 0.969067i \(-0.420621\pi\)
0.246799 + 0.969067i \(0.420621\pi\)
\(788\) 0 0
\(789\) 4.53690 0.161518
\(790\) 0 0
\(791\) 15.5922 0.554394
\(792\) 0 0
\(793\) −6.13886 −0.217997
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 14.5271 0.514576 0.257288 0.966335i \(-0.417171\pi\)
0.257288 + 0.966335i \(0.417171\pi\)
\(798\) 0 0
\(799\) 36.3190 1.28487
\(800\) 0 0
\(801\) 2.86114 0.101094
\(802\) 0 0
\(803\) 4.16611 0.147019
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 12.8699 0.453041
\(808\) 0 0
\(809\) −0.342772 −0.0120512 −0.00602560 0.999982i \(-0.501918\pi\)
−0.00602560 + 0.999982i \(0.501918\pi\)
\(810\) 0 0
\(811\) 17.5880 0.617597 0.308798 0.951128i \(-0.400073\pi\)
0.308798 + 0.951128i \(0.400073\pi\)
\(812\) 0 0
\(813\) −8.68976 −0.304763
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −22.2126 −0.777122
\(818\) 0 0
\(819\) 4.96747 0.173577
\(820\) 0 0
\(821\) 5.22244 0.182264 0.0911322 0.995839i \(-0.470951\pi\)
0.0911322 + 0.995839i \(0.470951\pi\)
\(822\) 0 0
\(823\) −1.69428 −0.0590587 −0.0295294 0.999564i \(-0.509401\pi\)
−0.0295294 + 0.999564i \(0.509401\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 21.2637 0.739411 0.369706 0.929149i \(-0.379459\pi\)
0.369706 + 0.929149i \(0.379459\pi\)
\(828\) 0 0
\(829\) −0.804816 −0.0279524 −0.0139762 0.999902i \(-0.504449\pi\)
−0.0139762 + 0.999902i \(0.504449\pi\)
\(830\) 0 0
\(831\) 5.93494 0.205881
\(832\) 0 0
\(833\) 53.0273 1.83729
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0.430572 0.0148828
\(838\) 0 0
\(839\) −43.9535 −1.51744 −0.758721 0.651416i \(-0.774175\pi\)
−0.758721 + 0.651416i \(0.774175\pi\)
\(840\) 0 0
\(841\) −11.8699 −0.409306
\(842\) 0 0
\(843\) 11.2039 0.385883
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 53.7212 1.84588
\(848\) 0 0
\(849\) −7.20392 −0.247238
\(850\) 0 0
\(851\) 46.0825 1.57969
\(852\) 0 0
\(853\) −49.4620 −1.69355 −0.846774 0.531953i \(-0.821458\pi\)
−0.846774 + 0.531953i \(0.821458\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −49.7398 −1.69908 −0.849539 0.527526i \(-0.823120\pi\)
−0.849539 + 0.527526i \(0.823120\pi\)
\(858\) 0 0
\(859\) −30.9622 −1.05642 −0.528208 0.849115i \(-0.677136\pi\)
−0.528208 + 0.849115i \(0.677136\pi\)
\(860\) 0 0
\(861\) 32.4718 1.10664
\(862\) 0 0
\(863\) −38.4480 −1.30879 −0.654393 0.756154i \(-0.727076\pi\)
−0.654393 + 0.756154i \(0.727076\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −8.00000 −0.271694
\(868\) 0 0
\(869\) 4.53690 0.153904
\(870\) 0 0
\(871\) −9.56943 −0.324248
\(872\) 0 0
\(873\) −5.93494 −0.200867
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 13.6572 0.461172 0.230586 0.973052i \(-0.425936\pi\)
0.230586 + 0.973052i \(0.425936\pi\)
\(878\) 0 0
\(879\) 4.27771 0.144284
\(880\) 0 0
\(881\) −12.8059 −0.431441 −0.215720 0.976455i \(-0.569210\pi\)
−0.215720 + 0.976455i \(0.569210\pi\)
\(882\) 0 0
\(883\) −3.50964 −0.118109 −0.0590544 0.998255i \(-0.518809\pi\)
−0.0590544 + 0.998255i \(0.518809\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 41.3700 1.38907 0.694535 0.719459i \(-0.255610\pi\)
0.694535 + 0.719459i \(0.255610\pi\)
\(888\) 0 0
\(889\) −97.7387 −3.27805
\(890\) 0 0
\(891\) 0.430572 0.0144247
\(892\) 0 0
\(893\) 41.1378 1.37662
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 5.39804 0.180235
\(898\) 0 0
\(899\) −1.78208 −0.0594356
\(900\) 0 0
\(901\) −13.1941 −0.439560
\(902\) 0 0
\(903\) 32.4718 1.08060
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 25.4620 0.845453 0.422727 0.906257i \(-0.361073\pi\)
0.422727 + 0.906257i \(0.361073\pi\)
\(908\) 0 0
\(909\) −16.3330 −0.541731
\(910\) 0 0
\(911\) −53.1378 −1.76053 −0.880267 0.474479i \(-0.842637\pi\)
−0.880267 + 0.474479i \(0.842637\pi\)
\(912\) 0 0
\(913\) −3.37079 −0.111557
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −16.8797 −0.557416
\(918\) 0 0
\(919\) −8.86114 −0.292302 −0.146151 0.989262i \(-0.546689\pi\)
−0.146151 + 0.989262i \(0.546689\pi\)
\(920\) 0 0
\(921\) −14.8146 −0.488158
\(922\) 0 0
\(923\) −9.67575 −0.318481
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −8.53690 −0.280388
\(928\) 0 0
\(929\) −6.51837 −0.213861 −0.106930 0.994267i \(-0.534102\pi\)
−0.106930 + 0.994267i \(0.534102\pi\)
\(930\) 0 0
\(931\) 60.0629 1.96848
\(932\) 0 0
\(933\) −17.3515 −0.568063
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −3.58343 −0.117066 −0.0585328 0.998285i \(-0.518642\pi\)
−0.0585328 + 0.998285i \(0.518642\pi\)
\(938\) 0 0
\(939\) −22.3980 −0.730932
\(940\) 0 0
\(941\) −53.5456 −1.74554 −0.872769 0.488134i \(-0.837678\pi\)
−0.872769 + 0.488134i \(0.837678\pi\)
\(942\) 0 0
\(943\) 35.2864 1.14908
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −33.9947 −1.10468 −0.552340 0.833619i \(-0.686265\pi\)
−0.552340 + 0.833619i \(0.686265\pi\)
\(948\) 0 0
\(949\) −9.67575 −0.314088
\(950\) 0 0
\(951\) 27.2679 0.884223
\(952\) 0 0
\(953\) 18.4631 0.598079 0.299039 0.954241i \(-0.403334\pi\)
0.299039 + 0.954241i \(0.403334\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −1.78208 −0.0576064
\(958\) 0 0
\(959\) 28.1021 0.907464
\(960\) 0 0
\(961\) −30.8146 −0.994020
\(962\) 0 0
\(963\) 11.6572 0.375649
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −20.9209 −0.672772 −0.336386 0.941724i \(-0.609205\pi\)
−0.336386 + 0.941724i \(0.609205\pi\)
\(968\) 0 0
\(969\) 10.1941 0.327482
\(970\) 0 0
\(971\) 23.0087 0.738385 0.369193 0.929353i \(-0.379634\pi\)
0.369193 + 0.929353i \(0.379634\pi\)
\(972\) 0 0
\(973\) −88.7681 −2.84577
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −12.5184 −0.400498 −0.200249 0.979745i \(-0.564175\pi\)
−0.200249 + 0.979745i \(0.564175\pi\)
\(978\) 0 0
\(979\) 1.23193 0.0393727
\(980\) 0 0
\(981\) −3.67575 −0.117358
\(982\) 0 0
\(983\) 60.1703 1.91914 0.959568 0.281478i \(-0.0908246\pi\)
0.959568 + 0.281478i \(0.0908246\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −60.1378 −1.91421
\(988\) 0 0
\(989\) 35.2864 1.12204
\(990\) 0 0
\(991\) −59.5827 −1.89271 −0.946353 0.323134i \(-0.895263\pi\)
−0.946353 + 0.323134i \(0.895263\pi\)
\(992\) 0 0
\(993\) −10.8797 −0.345256
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −60.1193 −1.90400 −0.951998 0.306103i \(-0.900975\pi\)
−0.951998 + 0.306103i \(0.900975\pi\)
\(998\) 0 0
\(999\) −8.53690 −0.270095
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 7800.2.a.bs.1.1 yes 3
5.4 even 2 7800.2.a.bh.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7800.2.a.bh.1.3 3 5.4 even 2
7800.2.a.bs.1.1 yes 3 1.1 even 1 trivial