Properties

Label 7600.2.a.cd.1.3
Level $7600$
Weight $2$
Character 7600.1
Self dual yes
Analytic conductor $60.686$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7600.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(60.6863055362\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.568.1
Defining polynomial: \(x^{3} - x^{2} - 6 x - 2\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 190)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.76156\) of defining polynomial
Character \(\chi\) \(=\) 7600.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.76156 q^{3} -0.761557 q^{7} +4.62620 q^{9} +O(q^{10})\) \(q+2.76156 q^{3} -0.761557 q^{7} +4.62620 q^{9} +0.864641 q^{11} -5.62620 q^{13} +3.62620 q^{17} -1.00000 q^{19} -2.10308 q^{21} -8.01395 q^{23} +4.49084 q^{27} -7.35548 q^{29} -8.11704 q^{31} +2.38776 q^{33} -0.476886 q^{37} -15.5371 q^{39} -2.65847 q^{41} +6.86464 q^{43} +1.25240 q^{47} -6.42003 q^{49} +10.0140 q^{51} -2.37380 q^{53} -2.76156 q^{57} -4.49084 q^{59} -10.8646 q^{61} -3.52311 q^{63} +1.03228 q^{67} -22.1310 q^{69} +10.1816 q^{71} -16.4017 q^{73} -0.658473 q^{77} +12.5693 q^{79} -1.47689 q^{81} -0.270718 q^{83} -20.3126 q^{87} +0.387755 q^{89} +4.28467 q^{91} -22.4157 q^{93} +8.50479 q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 2q^{3} + 4q^{7} + 5q^{9} + O(q^{10}) \) \( 3q + 2q^{3} + 4q^{7} + 5q^{9} - 8q^{13} + 2q^{17} - 3q^{19} - 10q^{21} + 2q^{27} - 8q^{29} - 4q^{31} - 8q^{33} - 14q^{37} - 10q^{39} + 2q^{41} + 18q^{43} - 14q^{47} - 3q^{49} + 6q^{51} - 16q^{53} - 2q^{57} - 2q^{59} - 30q^{61} + 2q^{63} + 2q^{67} - 22q^{69} + 8q^{71} - 10q^{73} + 8q^{77} - 17q^{81} - 6q^{83} + 6q^{87} - 14q^{89} - 6q^{91} - 4q^{93} - 10q^{97} + 12q^{99} + O(q^{100}) \)

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
\(3\) 2.76156 1.59439 0.797193 0.603725i \(-0.206317\pi\)
0.797193 + 0.603725i \(0.206317\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −0.761557 −0.287842 −0.143921 0.989589i \(-0.545971\pi\)
−0.143921 + 0.989589i \(0.545971\pi\)
\(8\) 0 0
\(9\) 4.62620 1.54207
\(10\) 0 0
\(11\) 0.864641 0.260699 0.130350 0.991468i \(-0.458390\pi\)
0.130350 + 0.991468i \(0.458390\pi\)
\(12\) 0 0
\(13\) −5.62620 −1.56043 −0.780213 0.625514i \(-0.784889\pi\)
−0.780213 + 0.625514i \(0.784889\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.62620 0.879482 0.439741 0.898125i \(-0.355070\pi\)
0.439741 + 0.898125i \(0.355070\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) −2.10308 −0.458930
\(22\) 0 0
\(23\) −8.01395 −1.67102 −0.835512 0.549472i \(-0.814829\pi\)
−0.835512 + 0.549472i \(0.814829\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 4.49084 0.864262
\(28\) 0 0
\(29\) −7.35548 −1.36588 −0.682939 0.730475i \(-0.739299\pi\)
−0.682939 + 0.730475i \(0.739299\pi\)
\(30\) 0 0
\(31\) −8.11704 −1.45786 −0.728931 0.684587i \(-0.759983\pi\)
−0.728931 + 0.684587i \(0.759983\pi\)
\(32\) 0 0
\(33\) 2.38776 0.415655
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −0.476886 −0.0783995 −0.0391998 0.999231i \(-0.512481\pi\)
−0.0391998 + 0.999231i \(0.512481\pi\)
\(38\) 0 0
\(39\) −15.5371 −2.48792
\(40\) 0 0
\(41\) −2.65847 −0.415184 −0.207592 0.978216i \(-0.566563\pi\)
−0.207592 + 0.978216i \(0.566563\pi\)
\(42\) 0 0
\(43\) 6.86464 1.04685 0.523424 0.852072i \(-0.324654\pi\)
0.523424 + 0.852072i \(0.324654\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.25240 0.182681 0.0913404 0.995820i \(-0.470885\pi\)
0.0913404 + 0.995820i \(0.470885\pi\)
\(48\) 0 0
\(49\) −6.42003 −0.917147
\(50\) 0 0
\(51\) 10.0140 1.40223
\(52\) 0 0
\(53\) −2.37380 −0.326067 −0.163033 0.986621i \(-0.552128\pi\)
−0.163033 + 0.986621i \(0.552128\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −2.76156 −0.365777
\(58\) 0 0
\(59\) −4.49084 −0.584657 −0.292329 0.956318i \(-0.594430\pi\)
−0.292329 + 0.956318i \(0.594430\pi\)
\(60\) 0 0
\(61\) −10.8646 −1.39107 −0.695537 0.718490i \(-0.744834\pi\)
−0.695537 + 0.718490i \(0.744834\pi\)
\(62\) 0 0
\(63\) −3.52311 −0.443871
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 1.03228 0.126113 0.0630563 0.998010i \(-0.479915\pi\)
0.0630563 + 0.998010i \(0.479915\pi\)
\(68\) 0 0
\(69\) −22.1310 −2.66426
\(70\) 0 0
\(71\) 10.1816 1.20833 0.604166 0.796858i \(-0.293506\pi\)
0.604166 + 0.796858i \(0.293506\pi\)
\(72\) 0 0
\(73\) −16.4017 −1.91967 −0.959837 0.280557i \(-0.909481\pi\)
−0.959837 + 0.280557i \(0.909481\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.658473 −0.0750400
\(78\) 0 0
\(79\) 12.5693 1.41416 0.707081 0.707133i \(-0.250012\pi\)
0.707081 + 0.707133i \(0.250012\pi\)
\(80\) 0 0
\(81\) −1.47689 −0.164098
\(82\) 0 0
\(83\) −0.270718 −0.0297152 −0.0148576 0.999890i \(-0.504729\pi\)
−0.0148576 + 0.999890i \(0.504729\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −20.3126 −2.17774
\(88\) 0 0
\(89\) 0.387755 0.0411020 0.0205510 0.999789i \(-0.493458\pi\)
0.0205510 + 0.999789i \(0.493458\pi\)
\(90\) 0 0
\(91\) 4.28467 0.449156
\(92\) 0 0
\(93\) −22.4157 −2.32440
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 8.50479 0.863531 0.431765 0.901986i \(-0.357891\pi\)
0.431765 + 0.901986i \(0.357891\pi\)
\(98\) 0 0
\(99\) 4.00000 0.402015
\(100\) 0 0
\(101\) 16.4157 1.63342 0.816710 0.577049i \(-0.195796\pi\)
0.816710 + 0.577049i \(0.195796\pi\)
\(102\) 0 0
\(103\) −9.64015 −0.949872 −0.474936 0.880020i \(-0.657529\pi\)
−0.474936 + 0.880020i \(0.657529\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.28467 0.414215 0.207107 0.978318i \(-0.433595\pi\)
0.207107 + 0.978318i \(0.433595\pi\)
\(108\) 0 0
\(109\) −13.4200 −1.28541 −0.642703 0.766116i \(-0.722187\pi\)
−0.642703 + 0.766116i \(0.722187\pi\)
\(110\) 0 0
\(111\) −1.31695 −0.124999
\(112\) 0 0
\(113\) 10.3232 0.971125 0.485563 0.874202i \(-0.338615\pi\)
0.485563 + 0.874202i \(0.338615\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −26.0279 −2.40628
\(118\) 0 0
\(119\) −2.76156 −0.253152
\(120\) 0 0
\(121\) −10.2524 −0.932036
\(122\) 0 0
\(123\) −7.34153 −0.661963
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 16.9817 1.50688 0.753440 0.657517i \(-0.228393\pi\)
0.753440 + 0.657517i \(0.228393\pi\)
\(128\) 0 0
\(129\) 18.9571 1.66908
\(130\) 0 0
\(131\) −0.541436 −0.0473055 −0.0236528 0.999720i \(-0.507530\pi\)
−0.0236528 + 0.999720i \(0.507530\pi\)
\(132\) 0 0
\(133\) 0.761557 0.0660354
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2.87859 −0.245935 −0.122967 0.992411i \(-0.539241\pi\)
−0.122967 + 0.992411i \(0.539241\pi\)
\(138\) 0 0
\(139\) −3.58767 −0.304302 −0.152151 0.988357i \(-0.548620\pi\)
−0.152151 + 0.988357i \(0.548620\pi\)
\(140\) 0 0
\(141\) 3.45856 0.291264
\(142\) 0 0
\(143\) −4.86464 −0.406802
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −17.7293 −1.46229
\(148\) 0 0
\(149\) −16.8401 −1.37959 −0.689796 0.724004i \(-0.742300\pi\)
−0.689796 + 0.724004i \(0.742300\pi\)
\(150\) 0 0
\(151\) 16.9817 1.38195 0.690975 0.722879i \(-0.257182\pi\)
0.690975 + 0.722879i \(0.257182\pi\)
\(152\) 0 0
\(153\) 16.7755 1.35622
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −14.8401 −1.18437 −0.592183 0.805804i \(-0.701734\pi\)
−0.592183 + 0.805804i \(0.701734\pi\)
\(158\) 0 0
\(159\) −6.55539 −0.519876
\(160\) 0 0
\(161\) 6.10308 0.480990
\(162\) 0 0
\(163\) 13.3694 1.04717 0.523587 0.851972i \(-0.324593\pi\)
0.523587 + 0.851972i \(0.324593\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 9.84632 0.761931 0.380966 0.924589i \(-0.375592\pi\)
0.380966 + 0.924589i \(0.375592\pi\)
\(168\) 0 0
\(169\) 18.6541 1.43493
\(170\) 0 0
\(171\) −4.62620 −0.353774
\(172\) 0 0
\(173\) −2.98168 −0.226693 −0.113346 0.993556i \(-0.536157\pi\)
−0.113346 + 0.993556i \(0.536157\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −12.4017 −0.932169
\(178\) 0 0
\(179\) −11.7938 −0.881512 −0.440756 0.897627i \(-0.645290\pi\)
−0.440756 + 0.897627i \(0.645290\pi\)
\(180\) 0 0
\(181\) 14.5693 1.08293 0.541465 0.840723i \(-0.317870\pi\)
0.541465 + 0.840723i \(0.317870\pi\)
\(182\) 0 0
\(183\) −30.0033 −2.21791
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 3.13536 0.229280
\(188\) 0 0
\(189\) −3.42003 −0.248771
\(190\) 0 0
\(191\) −13.2384 −0.957900 −0.478950 0.877842i \(-0.658983\pi\)
−0.478950 + 0.877842i \(0.658983\pi\)
\(192\) 0 0
\(193\) −2.54144 −0.182937 −0.0914683 0.995808i \(-0.529156\pi\)
−0.0914683 + 0.995808i \(0.529156\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 19.9109 1.41859 0.709295 0.704911i \(-0.249013\pi\)
0.709295 + 0.704911i \(0.249013\pi\)
\(198\) 0 0
\(199\) 20.3126 1.43992 0.719960 0.694015i \(-0.244160\pi\)
0.719960 + 0.694015i \(0.244160\pi\)
\(200\) 0 0
\(201\) 2.85069 0.201072
\(202\) 0 0
\(203\) 5.60162 0.393157
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −37.0741 −2.57683
\(208\) 0 0
\(209\) −0.864641 −0.0598085
\(210\) 0 0
\(211\) −18.0419 −1.24205 −0.621026 0.783790i \(-0.713284\pi\)
−0.621026 + 0.783790i \(0.713284\pi\)
\(212\) 0 0
\(213\) 28.1170 1.92655
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 6.18159 0.419634
\(218\) 0 0
\(219\) −45.2943 −3.06070
\(220\) 0 0
\(221\) −20.4017 −1.37237
\(222\) 0 0
\(223\) −13.5231 −0.905575 −0.452787 0.891619i \(-0.649570\pi\)
−0.452787 + 0.891619i \(0.649570\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 13.6016 0.902771 0.451386 0.892329i \(-0.350930\pi\)
0.451386 + 0.892329i \(0.350930\pi\)
\(228\) 0 0
\(229\) 13.5877 0.897898 0.448949 0.893557i \(-0.351798\pi\)
0.448949 + 0.893557i \(0.351798\pi\)
\(230\) 0 0
\(231\) −1.81841 −0.119643
\(232\) 0 0
\(233\) −25.5510 −1.67390 −0.836952 0.547277i \(-0.815664\pi\)
−0.836952 + 0.547277i \(0.815664\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 34.7110 2.25472
\(238\) 0 0
\(239\) 11.3309 0.732935 0.366468 0.930431i \(-0.380567\pi\)
0.366468 + 0.930431i \(0.380567\pi\)
\(240\) 0 0
\(241\) −1.25240 −0.0806739 −0.0403370 0.999186i \(-0.512843\pi\)
−0.0403370 + 0.999186i \(0.512843\pi\)
\(242\) 0 0
\(243\) −17.5510 −1.12590
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 5.62620 0.357986
\(248\) 0 0
\(249\) −0.747604 −0.0473775
\(250\) 0 0
\(251\) −10.5939 −0.668682 −0.334341 0.942452i \(-0.608514\pi\)
−0.334341 + 0.942452i \(0.608514\pi\)
\(252\) 0 0
\(253\) −6.92919 −0.435635
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0.153681 0.00958637 0.00479319 0.999989i \(-0.498474\pi\)
0.00479319 + 0.999989i \(0.498474\pi\)
\(258\) 0 0
\(259\) 0.363176 0.0225666
\(260\) 0 0
\(261\) −34.0279 −2.10627
\(262\) 0 0
\(263\) 0.504792 0.0311268 0.0155634 0.999879i \(-0.495046\pi\)
0.0155634 + 0.999879i \(0.495046\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 1.07081 0.0655324
\(268\) 0 0
\(269\) −3.49521 −0.213107 −0.106553 0.994307i \(-0.533981\pi\)
−0.106553 + 0.994307i \(0.533981\pi\)
\(270\) 0 0
\(271\) −5.47252 −0.332432 −0.166216 0.986089i \(-0.553155\pi\)
−0.166216 + 0.986089i \(0.553155\pi\)
\(272\) 0 0
\(273\) 11.8324 0.716127
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −12.9538 −0.778317 −0.389158 0.921171i \(-0.627234\pi\)
−0.389158 + 0.921171i \(0.627234\pi\)
\(278\) 0 0
\(279\) −37.5510 −2.24812
\(280\) 0 0
\(281\) 0.153681 0.00916785 0.00458393 0.999989i \(-0.498541\pi\)
0.00458393 + 0.999989i \(0.498541\pi\)
\(282\) 0 0
\(283\) −18.2341 −1.08390 −0.541952 0.840410i \(-0.682314\pi\)
−0.541952 + 0.840410i \(0.682314\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.02458 0.119507
\(288\) 0 0
\(289\) −3.85069 −0.226511
\(290\) 0 0
\(291\) 23.4865 1.37680
\(292\) 0 0
\(293\) −2.03853 −0.119092 −0.0595462 0.998226i \(-0.518965\pi\)
−0.0595462 + 0.998226i \(0.518965\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 3.88296 0.225312
\(298\) 0 0
\(299\) 45.0881 2.60751
\(300\) 0 0
\(301\) −5.22782 −0.301326
\(302\) 0 0
\(303\) 45.3328 2.60430
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 16.5414 0.944070 0.472035 0.881580i \(-0.343520\pi\)
0.472035 + 0.881580i \(0.343520\pi\)
\(308\) 0 0
\(309\) −26.6218 −1.51446
\(310\) 0 0
\(311\) 21.4725 1.21759 0.608797 0.793326i \(-0.291652\pi\)
0.608797 + 0.793326i \(0.291652\pi\)
\(312\) 0 0
\(313\) 1.12141 0.0633856 0.0316928 0.999498i \(-0.489910\pi\)
0.0316928 + 0.999498i \(0.489910\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 29.8882 1.67869 0.839344 0.543601i \(-0.182940\pi\)
0.839344 + 0.543601i \(0.182940\pi\)
\(318\) 0 0
\(319\) −6.35985 −0.356083
\(320\) 0 0
\(321\) 11.8324 0.660418
\(322\) 0 0
\(323\) −3.62620 −0.201767
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −37.0602 −2.04943
\(328\) 0 0
\(329\) −0.953771 −0.0525831
\(330\) 0 0
\(331\) −32.3126 −1.77606 −0.888030 0.459786i \(-0.847926\pi\)
−0.888030 + 0.459786i \(0.847926\pi\)
\(332\) 0 0
\(333\) −2.20617 −0.120897
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −26.3511 −1.43544 −0.717718 0.696334i \(-0.754813\pi\)
−0.717718 + 0.696334i \(0.754813\pi\)
\(338\) 0 0
\(339\) 28.5081 1.54835
\(340\) 0 0
\(341\) −7.01832 −0.380063
\(342\) 0 0
\(343\) 10.2201 0.551835
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2.77551 −0.148997 −0.0744986 0.997221i \(-0.523736\pi\)
−0.0744986 + 0.997221i \(0.523736\pi\)
\(348\) 0 0
\(349\) 11.5510 0.618312 0.309156 0.951011i \(-0.399953\pi\)
0.309156 + 0.951011i \(0.399953\pi\)
\(350\) 0 0
\(351\) −25.2663 −1.34862
\(352\) 0 0
\(353\) 8.40171 0.447178 0.223589 0.974684i \(-0.428223\pi\)
0.223589 + 0.974684i \(0.428223\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −7.62620 −0.403621
\(358\) 0 0
\(359\) −22.7895 −1.20278 −0.601391 0.798955i \(-0.705387\pi\)
−0.601391 + 0.798955i \(0.705387\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −28.3126 −1.48602
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 4.06455 0.212168 0.106084 0.994357i \(-0.466169\pi\)
0.106084 + 0.994357i \(0.466169\pi\)
\(368\) 0 0
\(369\) −12.2986 −0.640241
\(370\) 0 0
\(371\) 1.80779 0.0938556
\(372\) 0 0
\(373\) 18.4017 0.952804 0.476402 0.879227i \(-0.341941\pi\)
0.476402 + 0.879227i \(0.341941\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 41.3834 2.13135
\(378\) 0 0
\(379\) −1.23844 −0.0636145 −0.0318073 0.999494i \(-0.510126\pi\)
−0.0318073 + 0.999494i \(0.510126\pi\)
\(380\) 0 0
\(381\) 46.8959 2.40255
\(382\) 0 0
\(383\) 16.8646 0.861743 0.430871 0.902413i \(-0.358206\pi\)
0.430871 + 0.902413i \(0.358206\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 31.7572 1.61431
\(388\) 0 0
\(389\) 8.59392 0.435729 0.217865 0.975979i \(-0.430091\pi\)
0.217865 + 0.975979i \(0.430091\pi\)
\(390\) 0 0
\(391\) −29.0602 −1.46964
\(392\) 0 0
\(393\) −1.49521 −0.0754233
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −16.0558 −0.805818 −0.402909 0.915240i \(-0.632001\pi\)
−0.402909 + 0.915240i \(0.632001\pi\)
\(398\) 0 0
\(399\) 2.10308 0.105286
\(400\) 0 0
\(401\) −14.8925 −0.743698 −0.371849 0.928293i \(-0.621276\pi\)
−0.371849 + 0.928293i \(0.621276\pi\)
\(402\) 0 0
\(403\) 45.6681 2.27489
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −0.412335 −0.0204387
\(408\) 0 0
\(409\) −18.3511 −0.907404 −0.453702 0.891153i \(-0.649897\pi\)
−0.453702 + 0.891153i \(0.649897\pi\)
\(410\) 0 0
\(411\) −7.94940 −0.392115
\(412\) 0 0
\(413\) 3.42003 0.168289
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −9.90754 −0.485174
\(418\) 0 0
\(419\) −34.7509 −1.69769 −0.848847 0.528639i \(-0.822703\pi\)
−0.848847 + 0.528639i \(0.822703\pi\)
\(420\) 0 0
\(421\) −40.1589 −1.95722 −0.978612 0.205713i \(-0.934049\pi\)
−0.978612 + 0.205713i \(0.934049\pi\)
\(422\) 0 0
\(423\) 5.79383 0.281706
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 8.27405 0.400409
\(428\) 0 0
\(429\) −13.4340 −0.648599
\(430\) 0 0
\(431\) −34.9571 −1.68382 −0.841912 0.539615i \(-0.818570\pi\)
−0.841912 + 0.539615i \(0.818570\pi\)
\(432\) 0 0
\(433\) −1.13536 −0.0545619 −0.0272809 0.999628i \(-0.508685\pi\)
−0.0272809 + 0.999628i \(0.508685\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 8.01395 0.383359
\(438\) 0 0
\(439\) 6.80009 0.324551 0.162275 0.986746i \(-0.448117\pi\)
0.162275 + 0.986746i \(0.448117\pi\)
\(440\) 0 0
\(441\) −29.7003 −1.41430
\(442\) 0 0
\(443\) 38.0679 1.80866 0.904330 0.426835i \(-0.140371\pi\)
0.904330 + 0.426835i \(0.140371\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −46.5048 −2.19960
\(448\) 0 0
\(449\) −18.5414 −0.875024 −0.437512 0.899212i \(-0.644140\pi\)
−0.437512 + 0.899212i \(0.644140\pi\)
\(450\) 0 0
\(451\) −2.29862 −0.108238
\(452\) 0 0
\(453\) 46.8959 2.20336
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −16.3738 −0.765934 −0.382967 0.923762i \(-0.625098\pi\)
−0.382967 + 0.923762i \(0.625098\pi\)
\(458\) 0 0
\(459\) 16.2847 0.760103
\(460\) 0 0
\(461\) 1.70470 0.0793959 0.0396979 0.999212i \(-0.487360\pi\)
0.0396979 + 0.999212i \(0.487360\pi\)
\(462\) 0 0
\(463\) −10.0279 −0.466036 −0.233018 0.972472i \(-0.574860\pi\)
−0.233018 + 0.972472i \(0.574860\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 32.7509 1.51553 0.757766 0.652526i \(-0.226291\pi\)
0.757766 + 0.652526i \(0.226291\pi\)
\(468\) 0 0
\(469\) −0.786137 −0.0363004
\(470\) 0 0
\(471\) −40.9817 −1.88834
\(472\) 0 0
\(473\) 5.93545 0.272912
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −10.9817 −0.502816
\(478\) 0 0
\(479\) −27.2803 −1.24647 −0.623234 0.782035i \(-0.714182\pi\)
−0.623234 + 0.782035i \(0.714182\pi\)
\(480\) 0 0
\(481\) 2.68305 0.122337
\(482\) 0 0
\(483\) 16.8540 0.766884
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −11.0741 −0.501817 −0.250908 0.968011i \(-0.580729\pi\)
−0.250908 + 0.968011i \(0.580729\pi\)
\(488\) 0 0
\(489\) 36.9205 1.66960
\(490\) 0 0
\(491\) −8.11704 −0.366317 −0.183158 0.983083i \(-0.558632\pi\)
−0.183158 + 0.983083i \(0.558632\pi\)
\(492\) 0 0
\(493\) −26.6724 −1.20127
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −7.75386 −0.347808
\(498\) 0 0
\(499\) −0.295298 −0.0132193 −0.00660967 0.999978i \(-0.502104\pi\)
−0.00660967 + 0.999978i \(0.502104\pi\)
\(500\) 0 0
\(501\) 27.1912 1.21481
\(502\) 0 0
\(503\) 19.6016 0.873993 0.436996 0.899463i \(-0.356042\pi\)
0.436996 + 0.899463i \(0.356042\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 51.5144 2.28783
\(508\) 0 0
\(509\) −1.79383 −0.0795102 −0.0397551 0.999209i \(-0.512658\pi\)
−0.0397551 + 0.999209i \(0.512658\pi\)
\(510\) 0 0
\(511\) 12.4908 0.552562
\(512\) 0 0
\(513\) −4.49084 −0.198275
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 1.08287 0.0476247
\(518\) 0 0
\(519\) −8.23407 −0.361436
\(520\) 0 0
\(521\) −2.61850 −0.114719 −0.0573593 0.998354i \(-0.518268\pi\)
−0.0573593 + 0.998354i \(0.518268\pi\)
\(522\) 0 0
\(523\) 14.9956 0.655713 0.327857 0.944728i \(-0.393674\pi\)
0.327857 + 0.944728i \(0.393674\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −29.4340 −1.28216
\(528\) 0 0
\(529\) 41.2234 1.79232
\(530\) 0 0
\(531\) −20.7755 −0.901580
\(532\) 0 0
\(533\) 14.9571 0.647864
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −32.5693 −1.40547
\(538\) 0 0
\(539\) −5.55102 −0.239099
\(540\) 0 0
\(541\) 3.40608 0.146439 0.0732194 0.997316i \(-0.476673\pi\)
0.0732194 + 0.997316i \(0.476673\pi\)
\(542\) 0 0
\(543\) 40.2341 1.72661
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 4.74760 0.202993 0.101496 0.994836i \(-0.467637\pi\)
0.101496 + 0.994836i \(0.467637\pi\)
\(548\) 0 0
\(549\) −50.2620 −2.14513
\(550\) 0 0
\(551\) 7.35548 0.313354
\(552\) 0 0
\(553\) −9.57227 −0.407054
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −43.0462 −1.82393 −0.911964 0.410271i \(-0.865434\pi\)
−0.911964 + 0.410271i \(0.865434\pi\)
\(558\) 0 0
\(559\) −38.6218 −1.63353
\(560\) 0 0
\(561\) 8.65847 0.365561
\(562\) 0 0
\(563\) 17.0096 0.716869 0.358434 0.933555i \(-0.383311\pi\)
0.358434 + 0.933555i \(0.383311\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 1.12473 0.0472343
\(568\) 0 0
\(569\) −19.7572 −0.828264 −0.414132 0.910217i \(-0.635915\pi\)
−0.414132 + 0.910217i \(0.635915\pi\)
\(570\) 0 0
\(571\) 11.3973 0.476964 0.238482 0.971147i \(-0.423350\pi\)
0.238482 + 0.971147i \(0.423350\pi\)
\(572\) 0 0
\(573\) −36.5587 −1.52726
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 18.3372 0.763386 0.381693 0.924289i \(-0.375341\pi\)
0.381693 + 0.924289i \(0.375341\pi\)
\(578\) 0 0
\(579\) −7.01832 −0.291672
\(580\) 0 0
\(581\) 0.206167 0.00855327
\(582\) 0 0
\(583\) −2.05249 −0.0850053
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −11.9475 −0.493127 −0.246563 0.969127i \(-0.579301\pi\)
−0.246563 + 0.969127i \(0.579301\pi\)
\(588\) 0 0
\(589\) 8.11704 0.334457
\(590\) 0 0
\(591\) 54.9850 2.26178
\(592\) 0 0
\(593\) 24.3911 1.00162 0.500811 0.865557i \(-0.333035\pi\)
0.500811 + 0.865557i \(0.333035\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 56.0943 2.29579
\(598\) 0 0
\(599\) 21.0708 0.860930 0.430465 0.902607i \(-0.358350\pi\)
0.430465 + 0.902607i \(0.358350\pi\)
\(600\) 0 0
\(601\) 32.3878 1.32112 0.660562 0.750771i \(-0.270318\pi\)
0.660562 + 0.750771i \(0.270318\pi\)
\(602\) 0 0
\(603\) 4.77551 0.194474
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 19.0183 0.771930 0.385965 0.922513i \(-0.373869\pi\)
0.385965 + 0.922513i \(0.373869\pi\)
\(608\) 0 0
\(609\) 15.4692 0.626843
\(610\) 0 0
\(611\) −7.04623 −0.285060
\(612\) 0 0
\(613\) 23.5756 0.952210 0.476105 0.879389i \(-0.342048\pi\)
0.476105 + 0.879389i \(0.342048\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 26.2707 1.05762 0.528810 0.848740i \(-0.322639\pi\)
0.528810 + 0.848740i \(0.322639\pi\)
\(618\) 0 0
\(619\) −11.4985 −0.462165 −0.231083 0.972934i \(-0.574227\pi\)
−0.231083 + 0.972934i \(0.574227\pi\)
\(620\) 0 0
\(621\) −35.9894 −1.44420
\(622\) 0 0
\(623\) −0.295298 −0.0118309
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −2.38776 −0.0953578
\(628\) 0 0
\(629\) −1.72928 −0.0689510
\(630\) 0 0
\(631\) 45.8130 1.82379 0.911893 0.410427i \(-0.134620\pi\)
0.911893 + 0.410427i \(0.134620\pi\)
\(632\) 0 0
\(633\) −49.8236 −1.98031
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 36.1204 1.43114
\(638\) 0 0
\(639\) 47.1020 1.86333
\(640\) 0 0
\(641\) 1.36943 0.0540894 0.0270447 0.999634i \(-0.491390\pi\)
0.0270447 + 0.999634i \(0.491390\pi\)
\(642\) 0 0
\(643\) −24.7389 −0.975606 −0.487803 0.872954i \(-0.662201\pi\)
−0.487803 + 0.872954i \(0.662201\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −6.82611 −0.268362 −0.134181 0.990957i \(-0.542840\pi\)
−0.134181 + 0.990957i \(0.542840\pi\)
\(648\) 0 0
\(649\) −3.88296 −0.152420
\(650\) 0 0
\(651\) 17.0708 0.669058
\(652\) 0 0
\(653\) −6.91713 −0.270688 −0.135344 0.990799i \(-0.543214\pi\)
−0.135344 + 0.990799i \(0.543214\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −75.8776 −2.96027
\(658\) 0 0
\(659\) −9.44461 −0.367910 −0.183955 0.982935i \(-0.558890\pi\)
−0.183955 + 0.982935i \(0.558890\pi\)
\(660\) 0 0
\(661\) −22.1955 −0.863306 −0.431653 0.902040i \(-0.642070\pi\)
−0.431653 + 0.902040i \(0.642070\pi\)
\(662\) 0 0
\(663\) −56.3405 −2.18808
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 58.9465 2.28242
\(668\) 0 0
\(669\) −37.3449 −1.44384
\(670\) 0 0
\(671\) −9.39401 −0.362652
\(672\) 0 0
\(673\) −12.2986 −0.474077 −0.237039 0.971500i \(-0.576177\pi\)
−0.237039 + 0.971500i \(0.576177\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 35.9527 1.38178 0.690888 0.722962i \(-0.257220\pi\)
0.690888 + 0.722962i \(0.257220\pi\)
\(678\) 0 0
\(679\) −6.47689 −0.248560
\(680\) 0 0
\(681\) 37.5616 1.43937
\(682\) 0 0
\(683\) −9.00958 −0.344742 −0.172371 0.985032i \(-0.555143\pi\)
−0.172371 + 0.985032i \(0.555143\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 37.5231 1.43160
\(688\) 0 0
\(689\) 13.3555 0.508803
\(690\) 0 0
\(691\) 9.11078 0.346590 0.173295 0.984870i \(-0.444559\pi\)
0.173295 + 0.984870i \(0.444559\pi\)
\(692\) 0 0
\(693\) −3.04623 −0.115717
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −9.64015 −0.365147
\(698\) 0 0
\(699\) −70.5606 −2.66885
\(700\) 0 0
\(701\) −14.7476 −0.557009 −0.278505 0.960435i \(-0.589839\pi\)
−0.278505 + 0.960435i \(0.589839\pi\)
\(702\) 0 0
\(703\) 0.476886 0.0179861
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −12.5015 −0.470166
\(708\) 0 0
\(709\) −8.63389 −0.324253 −0.162126 0.986770i \(-0.551835\pi\)
−0.162126 + 0.986770i \(0.551835\pi\)
\(710\) 0 0
\(711\) 58.1483 2.18073
\(712\) 0 0
\(713\) 65.0496 2.43613
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 31.2909 1.16858
\(718\) 0 0
\(719\) 38.2759 1.42745 0.713726 0.700425i \(-0.247006\pi\)
0.713726 + 0.700425i \(0.247006\pi\)
\(720\) 0 0
\(721\) 7.34153 0.273413
\(722\) 0 0
\(723\) −3.45856 −0.128625
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −31.1893 −1.15675 −0.578373 0.815772i \(-0.696312\pi\)
−0.578373 + 0.815772i \(0.696312\pi\)
\(728\) 0 0
\(729\) −44.0375 −1.63102
\(730\) 0 0
\(731\) 24.8925 0.920684
\(732\) 0 0
\(733\) 13.9634 0.515748 0.257874 0.966179i \(-0.416978\pi\)
0.257874 + 0.966179i \(0.416978\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.892548 0.0328774
\(738\) 0 0
\(739\) −9.02165 −0.331867 −0.165933 0.986137i \(-0.553064\pi\)
−0.165933 + 0.986137i \(0.553064\pi\)
\(740\) 0 0
\(741\) 15.5371 0.570768
\(742\) 0 0
\(743\) −15.0342 −0.551550 −0.275775 0.961222i \(-0.588934\pi\)
−0.275775 + 0.961222i \(0.588934\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1.25240 −0.0458228
\(748\) 0 0
\(749\) −3.26302 −0.119228
\(750\) 0 0
\(751\) −29.6681 −1.08260 −0.541301 0.840829i \(-0.682068\pi\)
−0.541301 + 0.840829i \(0.682068\pi\)
\(752\) 0 0
\(753\) −29.2557 −1.06614
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −10.5819 −0.384604 −0.192302 0.981336i \(-0.561595\pi\)
−0.192302 + 0.981336i \(0.561595\pi\)
\(758\) 0 0
\(759\) −19.1354 −0.694570
\(760\) 0 0
\(761\) −0.979789 −0.0355173 −0.0177587 0.999842i \(-0.505653\pi\)
−0.0177587 + 0.999842i \(0.505653\pi\)
\(762\) 0 0
\(763\) 10.2201 0.369993
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 25.2663 0.912315
\(768\) 0 0
\(769\) 43.1772 1.55701 0.778505 0.627638i \(-0.215978\pi\)
0.778505 + 0.627638i \(0.215978\pi\)
\(770\) 0 0
\(771\) 0.424399 0.0152844
\(772\) 0 0
\(773\) −37.5250 −1.34968 −0.674840 0.737964i \(-0.735787\pi\)
−0.674840 + 0.737964i \(0.735787\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 1.00293 0.0359799
\(778\) 0 0
\(779\) 2.65847 0.0952497
\(780\) 0 0
\(781\) 8.80342 0.315011
\(782\) 0 0
\(783\) −33.0323 −1.18048
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 22.5833 0.805008 0.402504 0.915418i \(-0.368140\pi\)
0.402504 + 0.915418i \(0.368140\pi\)
\(788\) 0 0
\(789\) 1.39401 0.0496282
\(790\) 0 0
\(791\) −7.86171 −0.279530
\(792\) 0 0
\(793\) 61.1266 2.17067
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −35.9806 −1.27450 −0.637250 0.770657i \(-0.719928\pi\)
−0.637250 + 0.770657i \(0.719928\pi\)
\(798\) 0 0
\(799\) 4.54144 0.160664
\(800\) 0 0
\(801\) 1.79383 0.0633820
\(802\) 0 0
\(803\) −14.1816 −0.500457
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −9.65222 −0.339774
\(808\) 0 0
\(809\) −0.955660 −0.0335992 −0.0167996 0.999859i \(-0.505348\pi\)
−0.0167996 + 0.999859i \(0.505348\pi\)
\(810\) 0 0
\(811\) 7.53707 0.264662 0.132331 0.991206i \(-0.457754\pi\)
0.132331 + 0.991206i \(0.457754\pi\)
\(812\) 0 0
\(813\) −15.1127 −0.530024
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −6.86464 −0.240163
\(818\) 0 0
\(819\) 19.8217 0.692628
\(820\) 0 0
\(821\) 13.3082 0.464460 0.232230 0.972661i \(-0.425398\pi\)
0.232230 + 0.972661i \(0.425398\pi\)
\(822\) 0 0
\(823\) 24.4050 0.850706 0.425353 0.905028i \(-0.360150\pi\)
0.425353 + 0.905028i \(0.360150\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −11.6874 −0.406411 −0.203206 0.979136i \(-0.565136\pi\)
−0.203206 + 0.979136i \(0.565136\pi\)
\(828\) 0 0
\(829\) 25.6541 0.891004 0.445502 0.895281i \(-0.353025\pi\)
0.445502 + 0.895281i \(0.353025\pi\)
\(830\) 0 0
\(831\) −35.7726 −1.24094
\(832\) 0 0
\(833\) −23.2803 −0.806615
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −36.4523 −1.25998
\(838\) 0 0
\(839\) 2.91713 0.100710 0.0503552 0.998731i \(-0.483965\pi\)
0.0503552 + 0.998731i \(0.483965\pi\)
\(840\) 0 0
\(841\) 25.1031 0.865624
\(842\) 0 0
\(843\) 0.424399 0.0146171
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 7.80779 0.268279
\(848\) 0 0
\(849\) −50.3544 −1.72816
\(850\) 0 0
\(851\) 3.82174 0.131008
\(852\) 0 0
\(853\) 6.24281 0.213750 0.106875 0.994272i \(-0.465916\pi\)
0.106875 + 0.994272i \(0.465916\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 23.2158 0.793035 0.396517 0.918027i \(-0.370219\pi\)
0.396517 + 0.918027i \(0.370219\pi\)
\(858\) 0 0
\(859\) 7.13536 0.243455 0.121728 0.992564i \(-0.461157\pi\)
0.121728 + 0.992564i \(0.461157\pi\)
\(860\) 0 0
\(861\) 5.59099 0.190541
\(862\) 0 0
\(863\) −7.31362 −0.248959 −0.124479 0.992222i \(-0.539726\pi\)
−0.124479 + 0.992222i \(0.539726\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −10.6339 −0.361146
\(868\) 0 0
\(869\) 10.8680 0.368671
\(870\) 0 0
\(871\) −5.80779 −0.196789
\(872\) 0 0
\(873\) 39.3449 1.33162
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 22.0173 0.743471 0.371735 0.928339i \(-0.378763\pi\)
0.371735 + 0.928339i \(0.378763\pi\)
\(878\) 0 0
\(879\) −5.62953 −0.189879
\(880\) 0 0
\(881\) 11.7572 0.396110 0.198055 0.980191i \(-0.436538\pi\)
0.198055 + 0.980191i \(0.436538\pi\)
\(882\) 0 0
\(883\) 55.6560 1.87297 0.936487 0.350703i \(-0.114057\pi\)
0.936487 + 0.350703i \(0.114057\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −6.41566 −0.215417 −0.107708 0.994183i \(-0.534351\pi\)
−0.107708 + 0.994183i \(0.534351\pi\)
\(888\) 0 0
\(889\) −12.9325 −0.433743
\(890\) 0 0
\(891\) −1.27698 −0.0427803
\(892\) 0 0
\(893\) −1.25240 −0.0419098
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 124.513 4.15738
\(898\) 0 0
\(899\) 59.7047 1.99126
\(900\) 0 0
\(901\) −8.60788 −0.286770
\(902\) 0 0
\(903\) −14.4369 −0.480430
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −57.1160 −1.89651 −0.948253 0.317516i \(-0.897151\pi\)
−0.948253 + 0.317516i \(0.897151\pi\)
\(908\) 0 0
\(909\) 75.9421 2.51884
\(910\) 0 0
\(911\) 26.6339 0.882420 0.441210 0.897404i \(-0.354549\pi\)
0.441210 + 0.897404i \(0.354549\pi\)
\(912\) 0 0
\(913\) −0.234074 −0.00774672
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0.412335 0.0136165
\(918\) 0 0
\(919\) −6.63246 −0.218785 −0.109392 0.993999i \(-0.534890\pi\)
−0.109392 + 0.993999i \(0.534890\pi\)
\(920\) 0 0
\(921\) 45.6801 1.50521
\(922\) 0 0
\(923\) −57.2836 −1.88551
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −44.5972 −1.46477
\(928\) 0 0
\(929\) −50.0173 −1.64101 −0.820507 0.571637i \(-0.806309\pi\)
−0.820507 + 0.571637i \(0.806309\pi\)
\(930\) 0 0
\(931\) 6.42003 0.210408
\(932\) 0 0
\(933\) 59.2976 1.94132
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 39.8882 1.30309 0.651545 0.758610i \(-0.274121\pi\)
0.651545 + 0.758610i \(0.274121\pi\)
\(938\) 0 0
\(939\) 3.09683 0.101061
\(940\) 0 0
\(941\) −5.59829 −0.182499 −0.0912495 0.995828i \(-0.529086\pi\)
−0.0912495 + 0.995828i \(0.529086\pi\)
\(942\) 0 0
\(943\) 21.3049 0.693782
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 12.7110 0.413051 0.206525 0.978441i \(-0.433784\pi\)
0.206525 + 0.978441i \(0.433784\pi\)
\(948\) 0 0
\(949\) 92.2793 2.99551
\(950\) 0 0
\(951\) 82.5379 2.67648
\(952\) 0 0
\(953\) 57.0129 1.84683 0.923415 0.383804i \(-0.125386\pi\)
0.923415 + 0.383804i \(0.125386\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −17.5631 −0.567734
\(958\) 0 0
\(959\) 2.19221 0.0707903
\(960\) 0 0
\(961\) 34.8863 1.12536
\(962\) 0 0
\(963\) 19.8217 0.638747
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −33.0183 −1.06180 −0.530899 0.847435i \(-0.678146\pi\)
−0.530899 + 0.847435i \(0.678146\pi\)
\(968\) 0 0
\(969\) −10.0140 −0.321695
\(970\) 0 0
\(971\) 3.04623 0.0977581 0.0488791 0.998805i \(-0.484435\pi\)
0.0488791 + 0.998805i \(0.484435\pi\)
\(972\) 0 0
\(973\) 2.73221 0.0875907
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −13.4465 −0.430192 −0.215096 0.976593i \(-0.569006\pi\)
−0.215096 + 0.976593i \(0.569006\pi\)
\(978\) 0 0
\(979\) 0.335269 0.0107152
\(980\) 0 0
\(981\) −62.0837 −1.98218
\(982\) 0 0
\(983\) −22.0646 −0.703750 −0.351875 0.936047i \(-0.614456\pi\)
−0.351875 + 0.936047i \(0.614456\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −2.63389 −0.0838378
\(988\) 0 0
\(989\) −55.0129 −1.74931
\(990\) 0 0
\(991\) −51.9946 −1.65166 −0.825831 0.563917i \(-0.809294\pi\)
−0.825831 + 0.563917i \(0.809294\pi\)
\(992\) 0 0
\(993\) −89.2330 −2.83172
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 37.7693 1.19616 0.598082 0.801435i \(-0.295930\pi\)
0.598082 + 0.801435i \(0.295930\pi\)
\(998\) 0 0
\(999\) −2.14162 −0.0677578
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 7600.2.a.cd.1.3 3
4.3 odd 2 950.2.a.i.1.1 3
5.2 odd 4 1520.2.d.j.609.1 6
5.3 odd 4 1520.2.d.j.609.6 6
5.4 even 2 7600.2.a.bi.1.1 3
12.11 even 2 8550.2.a.cl.1.3 3
20.3 even 4 190.2.b.b.39.4 yes 6
20.7 even 4 190.2.b.b.39.3 6
20.19 odd 2 950.2.a.n.1.3 3
60.23 odd 4 1710.2.d.d.1369.3 6
60.47 odd 4 1710.2.d.d.1369.6 6
60.59 even 2 8550.2.a.ck.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.b.b.39.3 6 20.7 even 4
190.2.b.b.39.4 yes 6 20.3 even 4
950.2.a.i.1.1 3 4.3 odd 2
950.2.a.n.1.3 3 20.19 odd 2
1520.2.d.j.609.1 6 5.2 odd 4
1520.2.d.j.609.6 6 5.3 odd 4
1710.2.d.d.1369.3 6 60.23 odd 4
1710.2.d.d.1369.6 6 60.47 odd 4
7600.2.a.bi.1.1 3 5.4 even 2
7600.2.a.cd.1.3 3 1.1 even 1 trivial
8550.2.a.ck.1.1 3 60.59 even 2
8550.2.a.cl.1.3 3 12.11 even 2