Properties

Label 7800.2.a.bl.1.3
Level $7800$
Weight $2$
Character 7800.1
Self dual yes
Analytic conductor $62.283$
Analytic rank $1$
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: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.148.1
Defining polynomial: \( x^{3} - x^{2} - 3x + 1 \) Copy content Toggle raw display
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 1.3
Root \(2.17009\) of defining polynomial
Character \(\chi\) \(=\) 7800.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +3.24846 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +3.24846 q^{7} +1.00000 q^{9} -0.460811 q^{11} -1.00000 q^{13} +4.26180 q^{17} +1.70928 q^{19} -3.24846 q^{21} -8.38962 q^{23} -1.00000 q^{27} +3.34017 q^{29} -7.87936 q^{31} +0.460811 q^{33} -7.46800 q^{37} +1.00000 q^{39} -8.78765 q^{41} +3.89269 q^{43} -0.751536 q^{47} +3.55252 q^{49} -4.26180 q^{51} +8.70928 q^{53} -1.70928 q^{57} -3.27513 q^{59} -8.07838 q^{61} +3.24846 q^{63} -4.95774 q^{67} +8.38962 q^{69} +8.23287 q^{71} -13.8082 q^{73} -1.49693 q^{77} -12.2062 q^{79} +1.00000 q^{81} -7.40522 q^{83} -3.34017 q^{87} -9.44521 q^{89} -3.24846 q^{91} +7.87936 q^{93} +2.49693 q^{97} -0.460811 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{3} + q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{3} + q^{7} + 3 q^{9} - 3 q^{11} - 3 q^{13} + 5 q^{17} - 2 q^{19} - q^{21} + 4 q^{23} - 3 q^{27} - q^{29} - 11 q^{31} + 3 q^{33} + 10 q^{37} + 3 q^{39} - 16 q^{41} - 11 q^{47} + 10 q^{49} - 5 q^{51} + 19 q^{53} + 2 q^{57} - 3 q^{59} - 21 q^{61} + q^{63} + q^{67} - 4 q^{69} + 2 q^{71} + 2 q^{73} + 13 q^{77} - 12 q^{79} + 3 q^{81} - 7 q^{83} + q^{87} - 16 q^{89} - q^{91} + 11 q^{93} - 10 q^{97} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 3.24846 1.22780 0.613902 0.789382i \(-0.289599\pi\)
0.613902 + 0.789382i \(0.289599\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −0.460811 −0.138940 −0.0694699 0.997584i \(-0.522131\pi\)
−0.0694699 + 0.997584i \(0.522131\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.26180 1.03364 0.516819 0.856095i \(-0.327116\pi\)
0.516819 + 0.856095i \(0.327116\pi\)
\(18\) 0 0
\(19\) 1.70928 0.392135 0.196067 0.980590i \(-0.437183\pi\)
0.196067 + 0.980590i \(0.437183\pi\)
\(20\) 0 0
\(21\) −3.24846 −0.708873
\(22\) 0 0
\(23\) −8.38962 −1.74936 −0.874678 0.484704i \(-0.838927\pi\)
−0.874678 + 0.484704i \(0.838927\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 3.34017 0.620255 0.310127 0.950695i \(-0.399628\pi\)
0.310127 + 0.950695i \(0.399628\pi\)
\(30\) 0 0
\(31\) −7.87936 −1.41518 −0.707588 0.706626i \(-0.750217\pi\)
−0.707588 + 0.706626i \(0.750217\pi\)
\(32\) 0 0
\(33\) 0.460811 0.0802169
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −7.46800 −1.22773 −0.613866 0.789410i \(-0.710386\pi\)
−0.613866 + 0.789410i \(0.710386\pi\)
\(38\) 0 0
\(39\) 1.00000 0.160128
\(40\) 0 0
\(41\) −8.78765 −1.37240 −0.686200 0.727413i \(-0.740723\pi\)
−0.686200 + 0.727413i \(0.740723\pi\)
\(42\) 0 0
\(43\) 3.89269 0.593630 0.296815 0.954935i \(-0.404076\pi\)
0.296815 + 0.954935i \(0.404076\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −0.751536 −0.109623 −0.0548114 0.998497i \(-0.517456\pi\)
−0.0548114 + 0.998497i \(0.517456\pi\)
\(48\) 0 0
\(49\) 3.55252 0.507503
\(50\) 0 0
\(51\) −4.26180 −0.596771
\(52\) 0 0
\(53\) 8.70928 1.19631 0.598155 0.801380i \(-0.295901\pi\)
0.598155 + 0.801380i \(0.295901\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −1.70928 −0.226399
\(58\) 0 0
\(59\) −3.27513 −0.426385 −0.213193 0.977010i \(-0.568386\pi\)
−0.213193 + 0.977010i \(0.568386\pi\)
\(60\) 0 0
\(61\) −8.07838 −1.03433 −0.517165 0.855886i \(-0.673013\pi\)
−0.517165 + 0.855886i \(0.673013\pi\)
\(62\) 0 0
\(63\) 3.24846 0.409268
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −4.95774 −0.605684 −0.302842 0.953041i \(-0.597935\pi\)
−0.302842 + 0.953041i \(0.597935\pi\)
\(68\) 0 0
\(69\) 8.38962 1.00999
\(70\) 0 0
\(71\) 8.23287 0.977061 0.488531 0.872547i \(-0.337533\pi\)
0.488531 + 0.872547i \(0.337533\pi\)
\(72\) 0 0
\(73\) −13.8082 −1.61612 −0.808062 0.589097i \(-0.799483\pi\)
−0.808062 + 0.589097i \(0.799483\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1.49693 −0.170591
\(78\) 0 0
\(79\) −12.2062 −1.37331 −0.686653 0.726986i \(-0.740921\pi\)
−0.686653 + 0.726986i \(0.740921\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −7.40522 −0.812828 −0.406414 0.913689i \(-0.633221\pi\)
−0.406414 + 0.913689i \(0.633221\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −3.34017 −0.358104
\(88\) 0 0
\(89\) −9.44521 −1.00119 −0.500595 0.865681i \(-0.666886\pi\)
−0.500595 + 0.865681i \(0.666886\pi\)
\(90\) 0 0
\(91\) −3.24846 −0.340532
\(92\) 0 0
\(93\) 7.87936 0.817052
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 2.49693 0.253525 0.126762 0.991933i \(-0.459541\pi\)
0.126762 + 0.991933i \(0.459541\pi\)
\(98\) 0 0
\(99\) −0.460811 −0.0463133
\(100\) 0 0
\(101\) 7.72979 0.769143 0.384572 0.923095i \(-0.374349\pi\)
0.384572 + 0.923095i \(0.374349\pi\)
\(102\) 0 0
\(103\) 1.89269 0.186493 0.0932463 0.995643i \(-0.470276\pi\)
0.0932463 + 0.995643i \(0.470276\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −7.17727 −0.693853 −0.346927 0.937892i \(-0.612775\pi\)
−0.346927 + 0.937892i \(0.612775\pi\)
\(108\) 0 0
\(109\) −11.2267 −1.07533 −0.537663 0.843160i \(-0.680693\pi\)
−0.537663 + 0.843160i \(0.680693\pi\)
\(110\) 0 0
\(111\) 7.46800 0.708831
\(112\) 0 0
\(113\) 17.9155 1.68535 0.842673 0.538425i \(-0.180981\pi\)
0.842673 + 0.538425i \(0.180981\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.00000 −0.0924500
\(118\) 0 0
\(119\) 13.8443 1.26910
\(120\) 0 0
\(121\) −10.7877 −0.980696
\(122\) 0 0
\(123\) 8.78765 0.792356
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 11.2267 0.996211 0.498105 0.867117i \(-0.334029\pi\)
0.498105 + 0.867117i \(0.334029\pi\)
\(128\) 0 0
\(129\) −3.89269 −0.342732
\(130\) 0 0
\(131\) −13.4947 −1.17903 −0.589517 0.807756i \(-0.700682\pi\)
−0.589517 + 0.807756i \(0.700682\pi\)
\(132\) 0 0
\(133\) 5.55252 0.481465
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1.65983 −0.141809 −0.0709043 0.997483i \(-0.522588\pi\)
−0.0709043 + 0.997483i \(0.522588\pi\)
\(138\) 0 0
\(139\) 14.6803 1.24517 0.622585 0.782552i \(-0.286082\pi\)
0.622585 + 0.782552i \(0.286082\pi\)
\(140\) 0 0
\(141\) 0.751536 0.0632907
\(142\) 0 0
\(143\) 0.460811 0.0385350
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −3.55252 −0.293007
\(148\) 0 0
\(149\) 10.1834 0.834258 0.417129 0.908847i \(-0.363036\pi\)
0.417129 + 0.908847i \(0.363036\pi\)
\(150\) 0 0
\(151\) 1.34736 0.109647 0.0548233 0.998496i \(-0.482540\pi\)
0.0548233 + 0.998496i \(0.482540\pi\)
\(152\) 0 0
\(153\) 4.26180 0.344546
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 18.9649 1.51357 0.756783 0.653666i \(-0.226770\pi\)
0.756783 + 0.653666i \(0.226770\pi\)
\(158\) 0 0
\(159\) −8.70928 −0.690690
\(160\) 0 0
\(161\) −27.2534 −2.14787
\(162\) 0 0
\(163\) −6.07611 −0.475918 −0.237959 0.971275i \(-0.576478\pi\)
−0.237959 + 0.971275i \(0.576478\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 16.1483 1.24960 0.624798 0.780786i \(-0.285181\pi\)
0.624798 + 0.780786i \(0.285181\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 1.70928 0.130712
\(172\) 0 0
\(173\) 22.3112 1.69629 0.848146 0.529762i \(-0.177719\pi\)
0.848146 + 0.529762i \(0.177719\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 3.27513 0.246174
\(178\) 0 0
\(179\) −9.52586 −0.711996 −0.355998 0.934487i \(-0.615859\pi\)
−0.355998 + 0.934487i \(0.615859\pi\)
\(180\) 0 0
\(181\) −19.5730 −1.45485 −0.727426 0.686186i \(-0.759284\pi\)
−0.727426 + 0.686186i \(0.759284\pi\)
\(182\) 0 0
\(183\) 8.07838 0.597171
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −1.96388 −0.143613
\(188\) 0 0
\(189\) −3.24846 −0.236291
\(190\) 0 0
\(191\) −4.52359 −0.327316 −0.163658 0.986517i \(-0.552329\pi\)
−0.163658 + 0.986517i \(0.552329\pi\)
\(192\) 0 0
\(193\) −4.38962 −0.315972 −0.157986 0.987441i \(-0.550500\pi\)
−0.157986 + 0.987441i \(0.550500\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −10.6309 −0.757420 −0.378710 0.925515i \(-0.623632\pi\)
−0.378710 + 0.925515i \(0.623632\pi\)
\(198\) 0 0
\(199\) −17.7321 −1.25699 −0.628496 0.777813i \(-0.716329\pi\)
−0.628496 + 0.777813i \(0.716329\pi\)
\(200\) 0 0
\(201\) 4.95774 0.349692
\(202\) 0 0
\(203\) 10.8504 0.761551
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −8.38962 −0.583119
\(208\) 0 0
\(209\) −0.787653 −0.0544831
\(210\) 0 0
\(211\) 14.9132 1.02667 0.513334 0.858189i \(-0.328410\pi\)
0.513334 + 0.858189i \(0.328410\pi\)
\(212\) 0 0
\(213\) −8.23287 −0.564107
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −25.5958 −1.73756
\(218\) 0 0
\(219\) 13.8082 0.933070
\(220\) 0 0
\(221\) −4.26180 −0.286679
\(222\) 0 0
\(223\) −20.5464 −1.37589 −0.687944 0.725764i \(-0.741486\pi\)
−0.687944 + 0.725764i \(0.741486\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −21.6381 −1.43617 −0.718085 0.695955i \(-0.754981\pi\)
−0.718085 + 0.695955i \(0.754981\pi\)
\(228\) 0 0
\(229\) 19.3607 1.27939 0.639695 0.768629i \(-0.279061\pi\)
0.639695 + 0.768629i \(0.279061\pi\)
\(230\) 0 0
\(231\) 1.49693 0.0984907
\(232\) 0 0
\(233\) 24.0722 1.57702 0.788512 0.615019i \(-0.210852\pi\)
0.788512 + 0.615019i \(0.210852\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 12.2062 0.792878
\(238\) 0 0
\(239\) −14.2423 −0.921259 −0.460630 0.887592i \(-0.652376\pi\)
−0.460630 + 0.887592i \(0.652376\pi\)
\(240\) 0 0
\(241\) −28.3896 −1.82874 −0.914368 0.404884i \(-0.867312\pi\)
−0.914368 + 0.404884i \(0.867312\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −1.70928 −0.108759
\(248\) 0 0
\(249\) 7.40522 0.469287
\(250\) 0 0
\(251\) 4.41628 0.278753 0.139377 0.990239i \(-0.455490\pi\)
0.139377 + 0.990239i \(0.455490\pi\)
\(252\) 0 0
\(253\) 3.86603 0.243055
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 8.34244 0.520387 0.260194 0.965556i \(-0.416214\pi\)
0.260194 + 0.965556i \(0.416214\pi\)
\(258\) 0 0
\(259\) −24.2595 −1.50741
\(260\) 0 0
\(261\) 3.34017 0.206752
\(262\) 0 0
\(263\) 7.95055 0.490252 0.245126 0.969491i \(-0.421171\pi\)
0.245126 + 0.969491i \(0.421171\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 9.44521 0.578038
\(268\) 0 0
\(269\) −6.41855 −0.391346 −0.195673 0.980669i \(-0.562689\pi\)
−0.195673 + 0.980669i \(0.562689\pi\)
\(270\) 0 0
\(271\) −17.9555 −1.09072 −0.545359 0.838203i \(-0.683607\pi\)
−0.545359 + 0.838203i \(0.683607\pi\)
\(272\) 0 0
\(273\) 3.24846 0.196606
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −1.86991 −0.112352 −0.0561759 0.998421i \(-0.517891\pi\)
−0.0561759 + 0.998421i \(0.517891\pi\)
\(278\) 0 0
\(279\) −7.87936 −0.471725
\(280\) 0 0
\(281\) 6.77924 0.404416 0.202208 0.979343i \(-0.435188\pi\)
0.202208 + 0.979343i \(0.435188\pi\)
\(282\) 0 0
\(283\) 9.73206 0.578511 0.289256 0.957252i \(-0.406592\pi\)
0.289256 + 0.957252i \(0.406592\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −28.5464 −1.68504
\(288\) 0 0
\(289\) 1.16290 0.0684058
\(290\) 0 0
\(291\) −2.49693 −0.146373
\(292\) 0 0
\(293\) 26.9939 1.57700 0.788499 0.615036i \(-0.210859\pi\)
0.788499 + 0.615036i \(0.210859\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0.460811 0.0267390
\(298\) 0 0
\(299\) 8.38962 0.485184
\(300\) 0 0
\(301\) 12.6453 0.728861
\(302\) 0 0
\(303\) −7.72979 −0.444065
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −7.95055 −0.453762 −0.226881 0.973922i \(-0.572853\pi\)
−0.226881 + 0.973922i \(0.572853\pi\)
\(308\) 0 0
\(309\) −1.89269 −0.107672
\(310\) 0 0
\(311\) −16.2557 −0.921773 −0.460887 0.887459i \(-0.652469\pi\)
−0.460887 + 0.887459i \(0.652469\pi\)
\(312\) 0 0
\(313\) 11.4885 0.649369 0.324685 0.945822i \(-0.394742\pi\)
0.324685 + 0.945822i \(0.394742\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7.18568 0.403588 0.201794 0.979428i \(-0.435323\pi\)
0.201794 + 0.979428i \(0.435323\pi\)
\(318\) 0 0
\(319\) −1.53919 −0.0861780
\(320\) 0 0
\(321\) 7.17727 0.400596
\(322\) 0 0
\(323\) 7.28458 0.405325
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 11.2267 0.620839
\(328\) 0 0
\(329\) −2.44134 −0.134595
\(330\) 0 0
\(331\) −9.49466 −0.521874 −0.260937 0.965356i \(-0.584031\pi\)
−0.260937 + 0.965356i \(0.584031\pi\)
\(332\) 0 0
\(333\) −7.46800 −0.409244
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −3.10731 −0.169266 −0.0846329 0.996412i \(-0.526972\pi\)
−0.0846329 + 0.996412i \(0.526972\pi\)
\(338\) 0 0
\(339\) −17.9155 −0.973035
\(340\) 0 0
\(341\) 3.63090 0.196624
\(342\) 0 0
\(343\) −11.1990 −0.604690
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6.99386 −0.375450 −0.187725 0.982222i \(-0.560111\pi\)
−0.187725 + 0.982222i \(0.560111\pi\)
\(348\) 0 0
\(349\) 5.52586 0.295792 0.147896 0.989003i \(-0.452750\pi\)
0.147896 + 0.989003i \(0.452750\pi\)
\(350\) 0 0
\(351\) 1.00000 0.0533761
\(352\) 0 0
\(353\) −24.3051 −1.29363 −0.646815 0.762647i \(-0.723899\pi\)
−0.646815 + 0.762647i \(0.723899\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −13.8443 −0.732717
\(358\) 0 0
\(359\) −30.9493 −1.63344 −0.816722 0.577032i \(-0.804211\pi\)
−0.816722 + 0.577032i \(0.804211\pi\)
\(360\) 0 0
\(361\) −16.0784 −0.846230
\(362\) 0 0
\(363\) 10.7877 0.566205
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −28.1978 −1.47191 −0.735956 0.677029i \(-0.763267\pi\)
−0.735956 + 0.677029i \(0.763267\pi\)
\(368\) 0 0
\(369\) −8.78765 −0.457467
\(370\) 0 0
\(371\) 28.2918 1.46884
\(372\) 0 0
\(373\) 21.6719 1.12213 0.561065 0.827772i \(-0.310392\pi\)
0.561065 + 0.827772i \(0.310392\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −3.34017 −0.172028
\(378\) 0 0
\(379\) −16.1350 −0.828800 −0.414400 0.910095i \(-0.636009\pi\)
−0.414400 + 0.910095i \(0.636009\pi\)
\(380\) 0 0
\(381\) −11.2267 −0.575162
\(382\) 0 0
\(383\) 29.3256 1.49847 0.749235 0.662305i \(-0.230422\pi\)
0.749235 + 0.662305i \(0.230422\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 3.89269 0.197877
\(388\) 0 0
\(389\) −6.39803 −0.324393 −0.162197 0.986758i \(-0.551858\pi\)
−0.162197 + 0.986758i \(0.551858\pi\)
\(390\) 0 0
\(391\) −35.7548 −1.80820
\(392\) 0 0
\(393\) 13.4947 0.680716
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 29.4863 1.47987 0.739936 0.672677i \(-0.234856\pi\)
0.739936 + 0.672677i \(0.234856\pi\)
\(398\) 0 0
\(399\) −5.55252 −0.277974
\(400\) 0 0
\(401\) 9.99159 0.498956 0.249478 0.968380i \(-0.419741\pi\)
0.249478 + 0.968380i \(0.419741\pi\)
\(402\) 0 0
\(403\) 7.87936 0.392499
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3.44134 0.170581
\(408\) 0 0
\(409\) 31.8225 1.57352 0.786762 0.617257i \(-0.211756\pi\)
0.786762 + 0.617257i \(0.211756\pi\)
\(410\) 0 0
\(411\) 1.65983 0.0818732
\(412\) 0 0
\(413\) −10.6391 −0.523517
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −14.6803 −0.718900
\(418\) 0 0
\(419\) −2.37525 −0.116038 −0.0580192 0.998315i \(-0.518478\pi\)
−0.0580192 + 0.998315i \(0.518478\pi\)
\(420\) 0 0
\(421\) 14.3090 0.697377 0.348688 0.937239i \(-0.386627\pi\)
0.348688 + 0.937239i \(0.386627\pi\)
\(422\) 0 0
\(423\) −0.751536 −0.0365409
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −26.2423 −1.26995
\(428\) 0 0
\(429\) −0.460811 −0.0222482
\(430\) 0 0
\(431\) −17.5402 −0.844883 −0.422442 0.906390i \(-0.638827\pi\)
−0.422442 + 0.906390i \(0.638827\pi\)
\(432\) 0 0
\(433\) −35.0082 −1.68239 −0.841194 0.540733i \(-0.818147\pi\)
−0.841194 + 0.540733i \(0.818147\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −14.3402 −0.685984
\(438\) 0 0
\(439\) −10.7610 −0.513594 −0.256797 0.966465i \(-0.582667\pi\)
−0.256797 + 0.966465i \(0.582667\pi\)
\(440\) 0 0
\(441\) 3.55252 0.169168
\(442\) 0 0
\(443\) −37.6658 −1.78956 −0.894778 0.446511i \(-0.852666\pi\)
−0.894778 + 0.446511i \(0.852666\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −10.1834 −0.481659
\(448\) 0 0
\(449\) 31.9299 1.50686 0.753432 0.657526i \(-0.228397\pi\)
0.753432 + 0.657526i \(0.228397\pi\)
\(450\) 0 0
\(451\) 4.04945 0.190681
\(452\) 0 0
\(453\) −1.34736 −0.0633045
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −15.2579 −0.713735 −0.356868 0.934155i \(-0.616155\pi\)
−0.356868 + 0.934155i \(0.616155\pi\)
\(458\) 0 0
\(459\) −4.26180 −0.198924
\(460\) 0 0
\(461\) 5.73206 0.266969 0.133484 0.991051i \(-0.457383\pi\)
0.133484 + 0.991051i \(0.457383\pi\)
\(462\) 0 0
\(463\) 13.6959 0.636505 0.318252 0.948006i \(-0.396904\pi\)
0.318252 + 0.948006i \(0.396904\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 21.6430 1.00152 0.500759 0.865586i \(-0.333054\pi\)
0.500759 + 0.865586i \(0.333054\pi\)
\(468\) 0 0
\(469\) −16.1050 −0.743662
\(470\) 0 0
\(471\) −18.9649 −0.873858
\(472\) 0 0
\(473\) −1.79380 −0.0824788
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 8.70928 0.398770
\(478\) 0 0
\(479\) −13.1990 −0.603078 −0.301539 0.953454i \(-0.597500\pi\)
−0.301539 + 0.953454i \(0.597500\pi\)
\(480\) 0 0
\(481\) 7.46800 0.340511
\(482\) 0 0
\(483\) 27.2534 1.24007
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −4.51867 −0.204760 −0.102380 0.994745i \(-0.532646\pi\)
−0.102380 + 0.994745i \(0.532646\pi\)
\(488\) 0 0
\(489\) 6.07611 0.274771
\(490\) 0 0
\(491\) −5.15061 −0.232444 −0.116222 0.993223i \(-0.537078\pi\)
−0.116222 + 0.993223i \(0.537078\pi\)
\(492\) 0 0
\(493\) 14.2351 0.641118
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 26.7442 1.19964
\(498\) 0 0
\(499\) 12.3991 0.555059 0.277529 0.960717i \(-0.410484\pi\)
0.277529 + 0.960717i \(0.410484\pi\)
\(500\) 0 0
\(501\) −16.1483 −0.721455
\(502\) 0 0
\(503\) −18.6042 −0.829522 −0.414761 0.909930i \(-0.636135\pi\)
−0.414761 + 0.909930i \(0.636135\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.00000 −0.0444116
\(508\) 0 0
\(509\) −0.0761103 −0.00337353 −0.00168677 0.999999i \(-0.500537\pi\)
−0.00168677 + 0.999999i \(0.500537\pi\)
\(510\) 0 0
\(511\) −44.8554 −1.98428
\(512\) 0 0
\(513\) −1.70928 −0.0754664
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0.346316 0.0152310
\(518\) 0 0
\(519\) −22.3112 −0.979355
\(520\) 0 0
\(521\) −15.8432 −0.694105 −0.347053 0.937846i \(-0.612817\pi\)
−0.347053 + 0.937846i \(0.612817\pi\)
\(522\) 0 0
\(523\) −3.97334 −0.173742 −0.0868710 0.996220i \(-0.527687\pi\)
−0.0868710 + 0.996220i \(0.527687\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −33.5802 −1.46278
\(528\) 0 0
\(529\) 47.3857 2.06025
\(530\) 0 0
\(531\) −3.27513 −0.142128
\(532\) 0 0
\(533\) 8.78765 0.380636
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 9.52586 0.411071
\(538\) 0 0
\(539\) −1.63704 −0.0705123
\(540\) 0 0
\(541\) −42.2739 −1.81750 −0.908749 0.417344i \(-0.862961\pi\)
−0.908749 + 0.417344i \(0.862961\pi\)
\(542\) 0 0
\(543\) 19.5730 0.839959
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −37.6781 −1.61100 −0.805499 0.592597i \(-0.798103\pi\)
−0.805499 + 0.592597i \(0.798103\pi\)
\(548\) 0 0
\(549\) −8.07838 −0.344777
\(550\) 0 0
\(551\) 5.70928 0.243223
\(552\) 0 0
\(553\) −39.6514 −1.68615
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −4.33630 −0.183735 −0.0918674 0.995771i \(-0.529284\pi\)
−0.0918674 + 0.995771i \(0.529284\pi\)
\(558\) 0 0
\(559\) −3.89269 −0.164643
\(560\) 0 0
\(561\) 1.96388 0.0829152
\(562\) 0 0
\(563\) 18.0183 0.759379 0.379689 0.925114i \(-0.376031\pi\)
0.379689 + 0.925114i \(0.376031\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 3.24846 0.136423
\(568\) 0 0
\(569\) −41.9854 −1.76012 −0.880061 0.474861i \(-0.842498\pi\)
−0.880061 + 0.474861i \(0.842498\pi\)
\(570\) 0 0
\(571\) 39.6925 1.66108 0.830539 0.556961i \(-0.188033\pi\)
0.830539 + 0.556961i \(0.188033\pi\)
\(572\) 0 0
\(573\) 4.52359 0.188976
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 23.8043 0.990986 0.495493 0.868612i \(-0.334987\pi\)
0.495493 + 0.868612i \(0.334987\pi\)
\(578\) 0 0
\(579\) 4.38962 0.182426
\(580\) 0 0
\(581\) −24.0556 −0.997994
\(582\) 0 0
\(583\) −4.01333 −0.166215
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.87936 0.0775696 0.0387848 0.999248i \(-0.487651\pi\)
0.0387848 + 0.999248i \(0.487651\pi\)
\(588\) 0 0
\(589\) −13.4680 −0.554939
\(590\) 0 0
\(591\) 10.6309 0.437297
\(592\) 0 0
\(593\) −1.10504 −0.0453785 −0.0226893 0.999743i \(-0.507223\pi\)
−0.0226893 + 0.999743i \(0.507223\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 17.7321 0.725725
\(598\) 0 0
\(599\) 26.4885 1.08229 0.541146 0.840929i \(-0.317991\pi\)
0.541146 + 0.840929i \(0.317991\pi\)
\(600\) 0 0
\(601\) −8.43680 −0.344144 −0.172072 0.985084i \(-0.555046\pi\)
−0.172072 + 0.985084i \(0.555046\pi\)
\(602\) 0 0
\(603\) −4.95774 −0.201895
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −31.0784 −1.26143 −0.630716 0.776014i \(-0.717239\pi\)
−0.630716 + 0.776014i \(0.717239\pi\)
\(608\) 0 0
\(609\) −10.8504 −0.439682
\(610\) 0 0
\(611\) 0.751536 0.0304039
\(612\) 0 0
\(613\) −4.47027 −0.180552 −0.0902762 0.995917i \(-0.528775\pi\)
−0.0902762 + 0.995917i \(0.528775\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −9.60197 −0.386561 −0.193280 0.981144i \(-0.561913\pi\)
−0.193280 + 0.981144i \(0.561913\pi\)
\(618\) 0 0
\(619\) 15.8348 0.636456 0.318228 0.948014i \(-0.396912\pi\)
0.318228 + 0.948014i \(0.396912\pi\)
\(620\) 0 0
\(621\) 8.38962 0.336664
\(622\) 0 0
\(623\) −30.6824 −1.22927
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0.787653 0.0314558
\(628\) 0 0
\(629\) −31.8271 −1.26903
\(630\) 0 0
\(631\) 6.88655 0.274149 0.137075 0.990561i \(-0.456230\pi\)
0.137075 + 0.990561i \(0.456230\pi\)
\(632\) 0 0
\(633\) −14.9132 −0.592747
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −3.55252 −0.140756
\(638\) 0 0
\(639\) 8.23287 0.325687
\(640\) 0 0
\(641\) −1.73820 −0.0686550 −0.0343275 0.999411i \(-0.510929\pi\)
−0.0343275 + 0.999411i \(0.510929\pi\)
\(642\) 0 0
\(643\) −11.4536 −0.451687 −0.225843 0.974164i \(-0.572514\pi\)
−0.225843 + 0.974164i \(0.572514\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −23.9688 −0.942311 −0.471155 0.882050i \(-0.656163\pi\)
−0.471155 + 0.882050i \(0.656163\pi\)
\(648\) 0 0
\(649\) 1.50921 0.0592419
\(650\) 0 0
\(651\) 25.5958 1.00318
\(652\) 0 0
\(653\) −25.2967 −0.989936 −0.494968 0.868911i \(-0.664820\pi\)
−0.494968 + 0.868911i \(0.664820\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −13.8082 −0.538708
\(658\) 0 0
\(659\) 40.4040 1.57392 0.786958 0.617006i \(-0.211655\pi\)
0.786958 + 0.617006i \(0.211655\pi\)
\(660\) 0 0
\(661\) 0.160631 0.00624783 0.00312391 0.999995i \(-0.499006\pi\)
0.00312391 + 0.999995i \(0.499006\pi\)
\(662\) 0 0
\(663\) 4.26180 0.165514
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −28.0228 −1.08505
\(668\) 0 0
\(669\) 20.5464 0.794369
\(670\) 0 0
\(671\) 3.72261 0.143710
\(672\) 0 0
\(673\) −4.89723 −0.188774 −0.0943871 0.995536i \(-0.530089\pi\)
−0.0943871 + 0.995536i \(0.530089\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 14.7792 0.568012 0.284006 0.958822i \(-0.408336\pi\)
0.284006 + 0.958822i \(0.408336\pi\)
\(678\) 0 0
\(679\) 8.11118 0.311279
\(680\) 0 0
\(681\) 21.6381 0.829173
\(682\) 0 0
\(683\) −22.2462 −0.851227 −0.425614 0.904905i \(-0.639942\pi\)
−0.425614 + 0.904905i \(0.639942\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −19.3607 −0.738656
\(688\) 0 0
\(689\) −8.70928 −0.331797
\(690\) 0 0
\(691\) −13.6732 −0.520151 −0.260076 0.965588i \(-0.583748\pi\)
−0.260076 + 0.965588i \(0.583748\pi\)
\(692\) 0 0
\(693\) −1.49693 −0.0568636
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −37.4512 −1.41856
\(698\) 0 0
\(699\) −24.0722 −0.910496
\(700\) 0 0
\(701\) −6.34632 −0.239697 −0.119849 0.992792i \(-0.538241\pi\)
−0.119849 + 0.992792i \(0.538241\pi\)
\(702\) 0 0
\(703\) −12.7649 −0.481436
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 25.1100 0.944357
\(708\) 0 0
\(709\) 41.5136 1.55907 0.779537 0.626356i \(-0.215454\pi\)
0.779537 + 0.626356i \(0.215454\pi\)
\(710\) 0 0
\(711\) −12.2062 −0.457768
\(712\) 0 0
\(713\) 66.1049 2.47565
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 14.2423 0.531889
\(718\) 0 0
\(719\) −46.9854 −1.75226 −0.876131 0.482074i \(-0.839884\pi\)
−0.876131 + 0.482074i \(0.839884\pi\)
\(720\) 0 0
\(721\) 6.14834 0.228976
\(722\) 0 0
\(723\) 28.3896 1.05582
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −48.7754 −1.80898 −0.904489 0.426497i \(-0.859748\pi\)
−0.904489 + 0.426497i \(0.859748\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 16.5899 0.613598
\(732\) 0 0
\(733\) −46.6225 −1.72204 −0.861020 0.508570i \(-0.830174\pi\)
−0.861020 + 0.508570i \(0.830174\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.28458 0.0841536
\(738\) 0 0
\(739\) 23.6837 0.871217 0.435609 0.900136i \(-0.356533\pi\)
0.435609 + 0.900136i \(0.356533\pi\)
\(740\) 0 0
\(741\) 1.70928 0.0627918
\(742\) 0 0
\(743\) 12.9044 0.473417 0.236709 0.971581i \(-0.423931\pi\)
0.236709 + 0.971581i \(0.423931\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −7.40522 −0.270943
\(748\) 0 0
\(749\) −23.3151 −0.851916
\(750\) 0 0
\(751\) −8.17501 −0.298310 −0.149155 0.988814i \(-0.547655\pi\)
−0.149155 + 0.988814i \(0.547655\pi\)
\(752\) 0 0
\(753\) −4.41628 −0.160938
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −4.83096 −0.175584 −0.0877921 0.996139i \(-0.527981\pi\)
−0.0877921 + 0.996139i \(0.527981\pi\)
\(758\) 0 0
\(759\) −3.86603 −0.140328
\(760\) 0 0
\(761\) −41.4413 −1.50225 −0.751124 0.660162i \(-0.770488\pi\)
−0.751124 + 0.660162i \(0.770488\pi\)
\(762\) 0 0
\(763\) −36.4696 −1.32029
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 3.27513 0.118258
\(768\) 0 0
\(769\) −18.1711 −0.655268 −0.327634 0.944805i \(-0.606251\pi\)
−0.327634 + 0.944805i \(0.606251\pi\)
\(770\) 0 0
\(771\) −8.34244 −0.300446
\(772\) 0 0
\(773\) 23.6598 0.850985 0.425492 0.904962i \(-0.360101\pi\)
0.425492 + 0.904962i \(0.360101\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 24.2595 0.870306
\(778\) 0 0
\(779\) −15.0205 −0.538166
\(780\) 0 0
\(781\) −3.79380 −0.135753
\(782\) 0 0
\(783\) −3.34017 −0.119368
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −39.2089 −1.39764 −0.698822 0.715295i \(-0.746292\pi\)
−0.698822 + 0.715295i \(0.746292\pi\)
\(788\) 0 0
\(789\) −7.95055 −0.283047
\(790\) 0 0
\(791\) 58.1978 2.06928
\(792\) 0 0
\(793\) 8.07838 0.286872
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 40.7998 1.44520 0.722601 0.691266i \(-0.242946\pi\)
0.722601 + 0.691266i \(0.242946\pi\)
\(798\) 0 0
\(799\) −3.20289 −0.113310
\(800\) 0 0
\(801\) −9.44521 −0.333730
\(802\) 0 0
\(803\) 6.36296 0.224544
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 6.41855 0.225944
\(808\) 0 0
\(809\) 13.0205 0.457777 0.228889 0.973453i \(-0.426491\pi\)
0.228889 + 0.973453i \(0.426491\pi\)
\(810\) 0 0
\(811\) −47.2628 −1.65962 −0.829811 0.558044i \(-0.811552\pi\)
−0.829811 + 0.558044i \(0.811552\pi\)
\(812\) 0 0
\(813\) 17.9555 0.629726
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 6.65368 0.232783
\(818\) 0 0
\(819\) −3.24846 −0.113511
\(820\) 0 0
\(821\) −43.4512 −1.51646 −0.758228 0.651989i \(-0.773935\pi\)
−0.758228 + 0.651989i \(0.773935\pi\)
\(822\) 0 0
\(823\) −36.7936 −1.28254 −0.641272 0.767313i \(-0.721593\pi\)
−0.641272 + 0.767313i \(0.721593\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −24.5018 −0.852013 −0.426006 0.904720i \(-0.640080\pi\)
−0.426006 + 0.904720i \(0.640080\pi\)
\(828\) 0 0
\(829\) 40.4908 1.40630 0.703152 0.711040i \(-0.251776\pi\)
0.703152 + 0.711040i \(0.251776\pi\)
\(830\) 0 0
\(831\) 1.86991 0.0648663
\(832\) 0 0
\(833\) 15.1401 0.524574
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 7.87936 0.272351
\(838\) 0 0
\(839\) −25.4245 −0.877752 −0.438876 0.898548i \(-0.644623\pi\)
−0.438876 + 0.898548i \(0.644623\pi\)
\(840\) 0 0
\(841\) −17.8432 −0.615284
\(842\) 0 0
\(843\) −6.77924 −0.233490
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −35.0433 −1.20410
\(848\) 0 0
\(849\) −9.73206 −0.334003
\(850\) 0 0
\(851\) 62.6537 2.14774
\(852\) 0 0
\(853\) 21.1917 0.725588 0.362794 0.931869i \(-0.381823\pi\)
0.362794 + 0.931869i \(0.381823\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 18.3135 0.625578 0.312789 0.949823i \(-0.398737\pi\)
0.312789 + 0.949823i \(0.398737\pi\)
\(858\) 0 0
\(859\) 16.8865 0.576162 0.288081 0.957606i \(-0.406983\pi\)
0.288081 + 0.957606i \(0.406983\pi\)
\(860\) 0 0
\(861\) 28.5464 0.972858
\(862\) 0 0
\(863\) −10.0095 −0.340726 −0.170363 0.985381i \(-0.554494\pi\)
−0.170363 + 0.985381i \(0.554494\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −1.16290 −0.0394941
\(868\) 0 0
\(869\) 5.62475 0.190807
\(870\) 0 0
\(871\) 4.95774 0.167987
\(872\) 0 0
\(873\) 2.49693 0.0845082
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 38.7070 1.30704 0.653521 0.756908i \(-0.273291\pi\)
0.653521 + 0.756908i \(0.273291\pi\)
\(878\) 0 0
\(879\) −26.9939 −0.910480
\(880\) 0 0
\(881\) −41.9998 −1.41501 −0.707505 0.706708i \(-0.750179\pi\)
−0.707505 + 0.706708i \(0.750179\pi\)
\(882\) 0 0
\(883\) −26.4846 −0.891279 −0.445640 0.895212i \(-0.647024\pi\)
−0.445640 + 0.895212i \(0.647024\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 43.9916 1.47709 0.738547 0.674203i \(-0.235513\pi\)
0.738547 + 0.674203i \(0.235513\pi\)
\(888\) 0 0
\(889\) 36.4696 1.22315
\(890\) 0 0
\(891\) −0.460811 −0.0154378
\(892\) 0 0
\(893\) −1.28458 −0.0429869
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −8.38962 −0.280121
\(898\) 0 0
\(899\) −26.3184 −0.877769
\(900\) 0 0
\(901\) 37.1171 1.23655
\(902\) 0 0
\(903\) −12.6453 −0.420808
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 29.1917 0.969293 0.484646 0.874710i \(-0.338948\pi\)
0.484646 + 0.874710i \(0.338948\pi\)
\(908\) 0 0
\(909\) 7.72979 0.256381
\(910\) 0 0
\(911\) 38.6453 1.28038 0.640188 0.768219i \(-0.278857\pi\)
0.640188 + 0.768219i \(0.278857\pi\)
\(912\) 0 0
\(913\) 3.41241 0.112934
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −43.8369 −1.44762
\(918\) 0 0
\(919\) 24.3857 0.804412 0.402206 0.915549i \(-0.368244\pi\)
0.402206 + 0.915549i \(0.368244\pi\)
\(920\) 0 0
\(921\) 7.95055 0.261980
\(922\) 0 0
\(923\) −8.23287 −0.270988
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 1.89269 0.0621642
\(928\) 0 0
\(929\) −7.14608 −0.234455 −0.117228 0.993105i \(-0.537401\pi\)
−0.117228 + 0.993105i \(0.537401\pi\)
\(930\) 0 0
\(931\) 6.07223 0.199009
\(932\) 0 0
\(933\) 16.2557 0.532186
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 9.76487 0.319004 0.159502 0.987198i \(-0.449011\pi\)
0.159502 + 0.987198i \(0.449011\pi\)
\(938\) 0 0
\(939\) −11.4885 −0.374914
\(940\) 0 0
\(941\) 32.6453 1.06421 0.532103 0.846680i \(-0.321402\pi\)
0.532103 + 0.846680i \(0.321402\pi\)
\(942\) 0 0
\(943\) 73.7251 2.40082
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 30.8466 1.00238 0.501189 0.865338i \(-0.332896\pi\)
0.501189 + 0.865338i \(0.332896\pi\)
\(948\) 0 0
\(949\) 13.8082 0.448232
\(950\) 0 0
\(951\) −7.18568 −0.233012
\(952\) 0 0
\(953\) 35.6596 1.15513 0.577565 0.816345i \(-0.304003\pi\)
0.577565 + 0.816345i \(0.304003\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 1.53919 0.0497549
\(958\) 0 0
\(959\) −5.39189 −0.174113
\(960\) 0 0
\(961\) 31.0843 1.00272
\(962\) 0 0
\(963\) −7.17727 −0.231284
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 31.4112 1.01012 0.505058 0.863086i \(-0.331471\pi\)
0.505058 + 0.863086i \(0.331471\pi\)
\(968\) 0 0
\(969\) −7.28458 −0.234014
\(970\) 0 0
\(971\) −24.0722 −0.772515 −0.386257 0.922391i \(-0.626232\pi\)
−0.386257 + 0.922391i \(0.626232\pi\)
\(972\) 0 0
\(973\) 47.6886 1.52883
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −9.99547 −0.319783 −0.159892 0.987135i \(-0.551114\pi\)
−0.159892 + 0.987135i \(0.551114\pi\)
\(978\) 0 0
\(979\) 4.35246 0.139105
\(980\) 0 0
\(981\) −11.2267 −0.358442
\(982\) 0 0
\(983\) 25.4112 0.810491 0.405245 0.914208i \(-0.367186\pi\)
0.405245 + 0.914208i \(0.367186\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 2.44134 0.0777086
\(988\) 0 0
\(989\) −32.6582 −1.03847
\(990\) 0 0
\(991\) 38.0638 1.20914 0.604569 0.796553i \(-0.293346\pi\)
0.604569 + 0.796553i \(0.293346\pi\)
\(992\) 0 0
\(993\) 9.49466 0.301304
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 28.5441 0.904001 0.452001 0.892018i \(-0.350711\pi\)
0.452001 + 0.892018i \(0.350711\pi\)
\(998\) 0 0
\(999\) 7.46800 0.236277
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.bl.1.3 3
5.4 even 2 7800.2.a.bo.1.1 yes 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7800.2.a.bl.1.3 3 1.1 even 1 trivial
7800.2.a.bo.1.1 yes 3 5.4 even 2